LMFDB - Embedded newform 4025.2.a.o.1.4

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:	$0$
Dimension:	$4$
Coefficient field:	4.4.2777.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 4x^{2} + x + 2 $ x^4 - x^3 - 4*x^2 + x + 2
Coefficient ring:	$\Z[a_1, a_2]$
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			1.4
Root			$0.825785$ 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)

$f(q)$	$=$	$q+2.59615 q^{2} +1.82578 q^{3} +4.74002 q^{4} +4.74002 q^{6} -1.00000 q^{7} +7.11351 q^{8} +0.333489 q^{9} +O(q^{10})$	\(q+2.59615 q^{2} +1.82578 q^{3} +4.74002 q^{4} +4.74002 q^{6} -1.00000 q^{7} +7.11351 q^{8} +0.333489 q^{9} +1.24772 q^{11} +8.65425 q^{12} -0.0484449 q^{13} -2.59615 q^{14} +8.98774 q^{16} +7.88388 q^{17} +0.865790 q^{18} +0.643129 q^{19} -1.82578 q^{21} +3.23928 q^{22} +1.00000 q^{23} +12.9877 q^{24} -0.125771 q^{26} -4.86847 q^{27} -4.74002 q^{28} +2.42194 q^{29} -2.85085 q^{31} +9.10654 q^{32} +2.27807 q^{33} +20.4678 q^{34} +1.58075 q^{36} -3.11351 q^{37} +1.66966 q^{38} -0.0884500 q^{39} +0.326520 q^{41} -4.74002 q^{42} -4.32773 q^{43} +5.91423 q^{44} +2.59615 q^{46} +3.68192 q^{47} +16.4097 q^{48} +1.00000 q^{49} +14.3943 q^{51} -0.229630 q^{52} +2.14265 q^{53} -12.6393 q^{54} -7.11351 q^{56} +1.17422 q^{57} +6.28773 q^{58} -13.0097 q^{59} +2.96965 q^{61} -7.40124 q^{62} -0.333489 q^{63} +5.66651 q^{64} +5.91423 q^{66} +10.2627 q^{67} +37.3698 q^{68} +1.82578 q^{69} -0.800721 q^{71} +2.37228 q^{72} -8.77881 q^{73} -8.08316 q^{74} +3.04844 q^{76} -1.24772 q^{77} -0.229630 q^{78} -15.6473 q^{79} -9.88925 q^{81} +0.847696 q^{82} +10.7581 q^{83} -8.65425 q^{84} -11.2355 q^{86} +4.42194 q^{87} +8.87570 q^{88} -11.4981 q^{89} +0.0484449 q^{91} +4.74002 q^{92} -5.20503 q^{93} +9.55883 q^{94} +16.6266 q^{96} -4.62075 q^{97} +2.59615 q^{98} +0.416102 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} + 5 q^{3} + 2 q^{4} + 2 q^{6} - 4 q^{7} + 9 q^{8} + 3 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 + 5 * q^3 + 2 * q^4 + 2 * q^6 - 4 * q^7 + 9 * q^8 + 3 * q^9	$ 4 q + 2 q^{2} + 5 q^{3} + 2 q^{4} + 2 q^{6} - 4 q^{7} + 9 q^{8} + 3 q^{9} - 8 q^{11} + 3 q^{12} + 8 q^{13} - 2 q^{14} + 6 q^{16} + 6 q^{17} - 3 q^{18} + 2 q^{19} - 5 q^{21} + 4 q^{22} + 4 q^{23} + 22 q^{24} - 11 q^{26} + 14 q^{27} - 2 q^{28} - q^{29} - 2 q^{31} + 5 q^{32} + 7 q^{33} + 18 q^{34} - 10 q^{36} + 7 q^{37} - 17 q^{38} + 12 q^{39} - 9 q^{41} - 2 q^{42} + 4 q^{43} + 9 q^{44} + 2 q^{46} + 21 q^{47} + 25 q^{48} + 4 q^{49} + 9 q^{51} - 7 q^{52} + 11 q^{53} - 16 q^{54} - 9 q^{56} + 7 q^{57} + 8 q^{58} - 37 q^{59} + q^{61} + 7 q^{62} - 3 q^{63} + 21 q^{64} + 9 q^{66} + 31 q^{67} + 41 q^{68} + 5 q^{69} - 8 q^{71} + 18 q^{72} - 25 q^{73} - 2 q^{74} + 4 q^{76} + 8 q^{77} - 7 q^{78} - 19 q^{79} + 40 q^{81} + 16 q^{82} + 7 q^{83} - 3 q^{84} - 2 q^{86} + 7 q^{87} + 9 q^{88} + 7 q^{89} - 8 q^{91} + 2 q^{92} - 39 q^{93} + 7 q^{94} - 3 q^{96} + 2 q^{97} + 2 q^{98} + 40 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 + 5 * q^3 + 2 * q^4 + 2 * q^6 - 4 * q^7 + 9 * q^8 + 3 * q^9 - 8 * q^11 + 3 * q^12 + 8 * q^13 - 2 * q^14 + 6 * q^16 + 6 * q^17 - 3 * q^18 + 2 * q^19 - 5 * q^21 + 4 * q^22 + 4 * q^23 + 22 * q^24 - 11 * q^26 + 14 * q^27 - 2 * q^28 - q^29 - 2 * q^31 + 5 * q^32 + 7 * q^33 + 18 * q^34 - 10 * q^36 + 7 * q^37 - 17 * q^38 + 12 * q^39 - 9 * q^41 - 2 * q^42 + 4 * q^43 + 9 * q^44 + 2 * q^46 + 21 * q^47 + 25 * q^48 + 4 * q^49 + 9 * q^51 - 7 * q^52 + 11 * q^53 - 16 * q^54 - 9 * q^56 + 7 * q^57 + 8 * q^58 - 37 * q^59 + q^61 + 7 * q^62 - 3 * q^63 + 21 * q^64 + 9 * q^66 + 31 * q^67 + 41 * q^68 + 5 * q^69 - 8 * q^71 + 18 * q^72 - 25 * q^73 - 2 * q^74 + 4 * q^76 + 8 * q^77 - 7 * q^78 - 19 * q^79 + 40 * q^81 + 16 * q^82 + 7 * q^83 - 3 * q^84 - 2 * q^86 + 7 * q^87 + 9 * q^88 + 7 * q^89 - 8 * q^91 + 2 * q^92 - 39 * q^93 + 7 * q^94 - 3 * q^96 + 2 * q^97 + 2 * q^98 + 40 * 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 $

$2$	2.59615	1.83576	0.917879	−	0.396860i	$-0.129900\pi$
$2$	2.59615	1.83576	0.917879	+	0.396860i	$0.129900\pi$
$3$	1.82578	1.05412	0.527059	−	0.849829i	$-0.323295\pi$
$3$	1.82578	1.05412	0.527059	+	0.849829i	$0.323295\pi$
$4$	4.74002	2.37001
$5$	0	0
$5$	0	0
$6$	4.74002	1.93510
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	7.11351	2.51501
$9$	0.333489	0.111163
$10$	0	0
$11$	1.24772	0.376203	0.188101	−	0.982150i	$-0.439767\pi$
$11$	1.24772	0.376203	0.188101	+	0.982150i	$0.439767\pi$
$12$	8.65425	2.49827
$13$	−0.0484449	−0.0134362	−0.00671810	−	0.999977i	$-0.502138\pi$
$13$	−0.0484449	−0.0134362	−0.00671810	+	0.999977i	$0.502138\pi$
$14$	−2.59615	−0.693852
$15$	0	0
$16$	8.98774	2.24694
$17$	7.88388	1.91212	0.956061	−	0.293167i	$-0.0947091\pi$
$17$	7.88388	1.91212	0.956061	+	0.293167i	$0.0947091\pi$
$18$	0.865790	0.204069
$19$	0.643129	0.147544	0.0737720	−	0.997275i	$-0.476496\pi$
$19$	0.643129	0.147544	0.0737720	+	0.997275i	$0.476496\pi$
$20$	0	0
$21$	−1.82578	−0.398419
$22$	3.23928	0.690618
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	12.9877	2.65111
$25$	0	0
$26$	−0.125771	−0.0246656
$27$	−4.86847	−0.936938
$28$	−4.74002	−0.895779
$29$	2.42194	0.449743	0.224871	−	0.974388i	$-0.427804\pi$
$29$	2.42194	0.449743	0.224871	+	0.974388i	$0.427804\pi$
$30$	0	0
$31$	−2.85085	−0.512027	−0.256014	−	0.966673i	$-0.582409\pi$
$31$	−2.85085	−0.512027	−0.256014	+	0.966673i	$0.582409\pi$
$32$	9.10654	1.60982
$33$	2.27807	0.396562
$34$	20.4678	3.51020
$35$	0	0
$36$	1.58075	0.263458
$37$	−3.11351	−0.511858	−0.255929	−	0.966696i	$-0.582381\pi$
$37$	−3.11351	−0.511858	−0.255929	+	0.966696i	$0.582381\pi$
$38$	1.66966	0.270855
$39$	−0.0884500	−0.0141633
$40$	0	0
$41$	0.326520	0.0509938	0.0254969	−	0.999675i	$-0.491883\pi$
$41$	0.326520	0.0509938	0.0254969	+	0.999675i	$0.491883\pi$
$42$	−4.74002	−0.731401
$43$	−4.32773	−0.659973	−0.329987	−	0.943986i	$-0.607044\pi$
$43$	−4.32773	−0.659973	−0.329987	+	0.943986i	$0.607044\pi$
$44$	5.91423	0.891604
$45$	0	0
$46$	2.59615	0.382782
$47$	3.68192	0.537063	0.268532	−	0.963271i	$-0.413462\pi$
$47$	3.68192	0.537063	0.268532	+	0.963271i	$0.413462\pi$
$48$	16.4097	2.36853
$49$	1.00000	0.142857
$50$	0	0
$51$	14.3943	2.01560
$52$	−0.229630	−0.0318439
$53$	2.14265	0.294316	0.147158	−	0.989113i	$-0.452987\pi$
$53$	2.14265	0.294316	0.147158	+	0.989113i	$0.452987\pi$
$54$	−12.6393	−1.71999
$55$	0	0
$56$	−7.11351	−0.950583
$57$	1.17422	0.155529
$58$	6.28773	0.825619
$59$	−13.0097	−1.69371	−0.846856	−	0.531822i	$-0.821508\pi$
$59$	−13.0097	−1.69371	−0.846856	+	0.531822i	$0.821508\pi$
$60$	0	0
$61$	2.96965	0.380225	0.190112	−	0.981762i	$-0.439115\pi$
$61$	2.96965	0.380225	0.190112	+	0.981762i	$0.439115\pi$
$62$	−7.40124	−0.939959
$63$	−0.333489	−0.0420157
$64$	5.66651	0.708314
$65$	0	0
$66$	5.91423	0.727992
$67$	10.2627	1.25378	0.626892	−	0.779106i	$-0.284327\pi$
$67$	10.2627	1.25378	0.626892	+	0.779106i	$0.284327\pi$
$68$	37.3698	4.53175
$69$	1.82578	0.219799
$70$	0	0
$71$	−0.800721	−0.0950281	−0.0475141	−	0.998871i	$-0.515130\pi$
$71$	−0.800721	−0.0950281	−0.0475141	+	0.998871i	$0.515130\pi$
$72$	2.37228	0.279576
$73$	−8.77881	−1.02748	−0.513741	−	0.857945i	$-0.671741\pi$
$73$	−8.77881	−1.02748	−0.513741	+	0.857945i	$0.671741\pi$
$74$	−8.08316	−0.939649
$75$	0	0
$76$	3.04844	0.349681
$77$	−1.24772	−0.142191
$78$	−0.229630	−0.0260005
$79$	−15.6473	−1.76046	−0.880229	−	0.474550i	$-0.842611\pi$
$79$	−15.6473	−1.76046	−0.880229	+	0.474550i	$0.842611\pi$
$80$	0	0
$81$	−9.88925	−1.09881
$82$	0.847696	0.0936123
$83$	10.7581	1.18086	0.590428	−	0.807090i	$-0.298959\pi$
$83$	10.7581	1.18086	0.590428	+	0.807090i	$0.298959\pi$
$84$	−8.65425	−0.944256
$85$	0	0
$86$	−11.2355	−1.21155
$87$	4.42194	0.474082
$88$	8.87570	0.946153
$89$	−11.4981	−1.21880	−0.609400	−	0.792863i	$-0.708590\pi$
$89$	−11.4981	−1.21880	−0.609400	+	0.792863i	$0.708590\pi$
$90$	0	0
$91$	0.0484449	0.00507841
$92$	4.74002	0.494181
$93$	−5.20503	−0.539737
$94$	9.55883	0.985918
$95$	0	0
$96$	16.6266	1.69694
$97$	−4.62075	−0.469166	−0.234583	−	0.972096i	$-0.575372\pi$
$97$	−4.62075	−0.469166	−0.234583	+	0.972096i	$0.575372\pi$
$98$	2.59615	0.262251
$99$	0.416102	0.0418199
$100$	0	0
$101$	5.77474	0.574608	0.287304	−	0.957839i	$-0.407241\pi$
$101$	5.77474	0.574608	0.287304	+	0.957839i	$0.407241\pi$
$102$	37.3698	3.70016
$103$	11.3986	1.12313	0.561567	−	0.827432i	$-0.310199\pi$
$103$	11.3986	1.12313	0.561567	+	0.827432i	$0.310199\pi$
$104$	−0.344614	−0.0337921
$105$	0	0
$106$	5.56265	0.540292
$107$	17.3304	1.67539	0.837697	−	0.546135i	$-0.183901\pi$
$107$	17.3304	1.67539	0.837697	+	0.546135i	$0.183901\pi$
$108$	−23.0767	−2.22055
$109$	0.627720	0.0601247	0.0300623	−	0.999548i	$-0.490429\pi$
$109$	0.627720	0.0601247	0.0300623	+	0.999548i	$0.490429\pi$
$110$	0	0
$111$	−5.68460	−0.539559
$112$	−8.98774	−0.849262
$113$	−15.8304	−1.48920	−0.744600	−	0.667511i	$-0.767360\pi$
$113$	−15.8304	−1.48920	−0.744600	+	0.667511i	$0.767360\pi$
$114$	3.04844	0.285513
$115$	0	0
$116$	11.4800	1.06589
$117$	−0.0161559	−0.00149361
$118$	−33.7751	−3.10925
$119$	−7.88388	−0.722714
$120$	0	0
$121$	−9.44319	−0.858471
$122$	7.70967	0.698001
$123$	0.596155	0.0537535
$124$	−13.5131	−1.21351
$125$	0	0
$126$	−0.865790	−0.0771307
$127$	−6.66001	−0.590980	−0.295490	−	0.955346i	$-0.595483\pi$
$127$	−6.66001	−0.590980	−0.295490	+	0.955346i	$0.595483\pi$
$128$	−3.50195	−0.309532
$129$	−7.90151	−0.695689
$130$	0	0
$131$	3.62075	0.316346	0.158173	−	0.987411i	$-0.449440\pi$
$131$	3.62075	0.316346	0.158173	+	0.987411i	$0.449440\pi$
$132$	10.7981	0.939856
$133$	−0.643129	−0.0557664
$134$	26.6435	2.30164
$135$	0	0
$136$	56.0821	4.80900
$137$	4.18581	0.357618	0.178809	−	0.983884i	$-0.442776\pi$
$137$	4.18581	0.357618	0.178809	+	0.983884i	$0.442776\pi$
$138$	4.74002	0.403497
$139$	7.30414	0.619529	0.309765	−	0.950813i	$-0.399750\pi$
$139$	7.30414	0.619529	0.309765	+	0.950813i	$0.399750\pi$
$140$	0	0
$141$	6.72239	0.566128
$142$	−2.07880	−0.174449
$143$	−0.0604459	−0.00505474
$144$	2.99732	0.249776
$145$	0	0
$146$	−22.7911	−1.88621
$147$	1.82578	0.150588
$148$	−14.7581	−1.21311
$149$	8.95592	0.733698	0.366849	−	0.930281i	$-0.380437\pi$
$149$	8.95592	0.733698	0.366849	+	0.930281i	$0.380437\pi$
$150$	0	0
$151$	−8.21162	−0.668252	−0.334126	−	0.942528i	$-0.608441\pi$
$151$	−8.21162	−0.668252	−0.334126	+	0.942528i	$0.608441\pi$
$152$	4.57491	0.371074
$153$	2.62919	0.212557
$154$	−3.23928	−0.261029
$155$	0	0
$156$	−0.419255	−0.0335672
$157$	20.9131	1.66905	0.834524	−	0.550972i	$-0.185743\pi$
$157$	20.9131	1.66905	0.834524	+	0.550972i	$0.185743\pi$
$158$	−40.6228	−3.23177
$159$	3.91202	0.310243
$160$	0	0
$161$	−1.00000	−0.0788110
$162$	−25.6740	−2.01714
$163$	−6.54221	−0.512425	−0.256213	−	0.966620i	$-0.582475\pi$
$163$	−6.54221	−0.512425	−0.256213	+	0.966620i	$0.582475\pi$
$164$	1.54771	0.120856
$165$	0	0
$166$	27.9297	2.16777
$167$	24.4000	1.88813	0.944065	−	0.329758i	$-0.106967\pi$
$167$	24.4000	1.88813	0.944065	+	0.329758i	$0.106967\pi$
$168$	−12.9877	−1.00203
$169$	−12.9977	−0.999819
$170$	0	0
$171$	0.214477	0.0164014
$172$	−20.5135	−1.56414
$173$	10.8824	0.827375	0.413687	−	0.910419i	$-0.364241\pi$
$173$	10.8824	0.827375	0.413687	+	0.910419i	$0.364241\pi$
$174$	11.4800	0.870299
$175$	0	0
$176$	11.2142	0.845304
$177$	−23.7528	−1.78537
$178$	−29.8509	−2.23742
$179$	−22.6104	−1.68998	−0.844991	−	0.534780i	$-0.820395\pi$
$179$	−22.6104	−1.68998	−0.844991	+	0.534780i	$0.820395\pi$
$180$	0	0
$181$	2.40410	0.178695	0.0893477	−	0.996000i	$-0.471522\pi$
$181$	2.40410	0.178695	0.0893477	+	0.996000i	$0.471522\pi$
$182$	0.125771	0.00932273
$183$	5.42194	0.400801
$184$	7.11351	0.524415
$185$	0	0
$186$	−13.5131	−0.990827
$187$	9.83691	0.719346
$188$	17.4524	1.27285
$189$	4.86847	0.354129
$190$	0	0
$191$	5.96843	0.431861	0.215930	−	0.976409i	$-0.430722\pi$
$191$	5.96843	0.431861	0.215930	+	0.976409i	$0.430722\pi$
$192$	10.3458	0.746646
$193$	−20.1273	−1.44880	−0.724398	−	0.689382i	$-0.757882\pi$
$193$	−20.1273	−1.44880	−0.724398	+	0.689382i	$0.757882\pi$
$194$	−11.9962	−0.861276
$195$	0	0
$196$	4.74002	0.338573
$197$	−24.2562	−1.72819	−0.864093	−	0.503332i	$-0.832107\pi$
$197$	−24.2562	−1.72819	−0.864093	+	0.503332i	$0.832107\pi$
$198$	1.08027	0.0767712
$199$	−22.3213	−1.58232	−0.791158	−	0.611612i	$-0.790521\pi$
$199$	−22.3213	−1.58232	−0.791158	+	0.611612i	$0.790521\pi$
$200$	0	0
$201$	18.7374	1.32164
$202$	14.9921	1.05484
$203$	−2.42194	−0.169987
$204$	68.2291	4.77699
$205$	0	0
$206$	29.5924	2.06180
$207$	0.333489	0.0231791
$208$	−0.435411	−0.0301903
$209$	0.802448	0.0555065
$210$	0	0
$211$	3.47836	0.239460	0.119730	−	0.992806i	$-0.461797\pi$
$211$	3.47836	0.239460	0.119730	+	0.992806i	$0.461797\pi$
$212$	10.1562	0.697531
$213$	−1.46194	−0.100171
$214$	44.9924	3.07562
$215$	0	0
$216$	−34.6320	−2.35641
$217$	2.85085	0.193528
$218$	1.62966	0.110374
$219$	−16.0282	−1.08309
$220$	0	0
$221$	−0.381934	−0.0256917
$222$	−14.7581	−0.990500
$223$	−2.94606	−0.197282	−0.0986412	−	0.995123i	$-0.531450\pi$
$223$	−2.94606	−0.197282	−0.0986412	+	0.995123i	$0.531450\pi$
$224$	−9.10654	−0.608457
$225$	0	0
$226$	−41.0982	−2.73381
$227$	17.6933	1.17434	0.587171	−	0.809463i	$-0.300241\pi$
$227$	17.6933	1.17434	0.587171	+	0.809463i	$0.300241\pi$
$228$	5.56580	0.368604
$229$	−28.0541	−1.85387	−0.926934	−	0.375225i	$-0.877565\pi$
$229$	−28.0541	−1.85387	−0.926934	+	0.375225i	$0.877565\pi$
$230$	0	0
$231$	−2.27807	−0.149886
$232$	17.2285	1.13111
$233$	7.06532	0.462865	0.231432	−	0.972851i	$-0.425659\pi$
$233$	7.06532	0.462865	0.231432	+	0.972851i	$0.425659\pi$
$234$	−0.0419431	−0.00274191
$235$	0	0
$236$	−61.6660	−4.01412
$237$	−28.5686	−1.85573
$238$	−20.4678	−1.32673
$239$	−18.2818	−1.18255	−0.591275	−	0.806470i	$-0.701375\pi$
$239$	−18.2818	−1.18255	−0.591275	+	0.806470i	$0.701375\pi$
$240$	0	0
$241$	−25.6575	−1.65274	−0.826372	−	0.563125i	$-0.809599\pi$
$241$	−25.6575	−1.65274	−0.826372	+	0.563125i	$0.809599\pi$
$242$	−24.5160	−1.57595
$243$	−3.45022	−0.221332
$244$	14.0762	0.901136
$245$	0	0
$246$	1.54771	0.0986784
$247$	−0.0311563	−0.00198243
$248$	−20.2795	−1.28775
$249$	19.6420	1.24476
$250$	0	0
$251$	19.2798	1.21693	0.608466	−	0.793580i	$-0.291785\pi$
$251$	19.2798	1.21693	0.608466	+	0.793580i	$0.291785\pi$
$252$	−1.58075	−0.0995776
$253$	1.24772	0.0784437
$254$	−17.2904	−1.08490
$255$	0	0
$256$	−20.4246	−1.27654
$257$	−17.5769	−1.09642	−0.548209	−	0.836341i	$-0.684690\pi$
$257$	−17.5769	−1.09642	−0.548209	+	0.836341i	$0.684690\pi$
$258$	−20.5135	−1.27712
$259$	3.11351	0.193464
$260$	0	0
$261$	0.807691	0.0499948
$262$	9.40003	0.580736
$263$	−12.5466	−0.773655	−0.386828	−	0.922152i	$-0.626429\pi$
$263$	−12.5466	−0.773655	−0.386828	+	0.922152i	$0.626429\pi$
$264$	16.2051	0.997356
$265$	0	0
$266$	−1.66966	−0.102374
$267$	−20.9931	−1.28476
$268$	48.6452	2.97148
$269$	−16.0911	−0.981094	−0.490547	−	0.871415i	$-0.663203\pi$
$269$	−16.0911	−0.981094	−0.490547	+	0.871415i	$0.663203\pi$
$270$	0	0
$271$	10.4268	0.633381	0.316691	−	0.948529i	$-0.397428\pi$
$271$	10.4268	0.633381	0.316691	+	0.948529i	$0.397428\pi$
$272$	70.8583	4.29642
$273$	0.0884500	0.00535324
$274$	10.8670	0.656500
$275$	0	0
$276$	8.65425	0.520925
$277$	−16.2465	−0.976158	−0.488079	−	0.872799i	$-0.662302\pi$
$277$	−16.2465	−0.976158	−0.488079	+	0.872799i	$0.662302\pi$
$278$	18.9627	1.13731
$279$	−0.950727	−0.0569185
$280$	0	0
$281$	5.61110	0.334730	0.167365	−	0.985895i	$-0.446474\pi$
$281$	5.61110	0.334730	0.167365	+	0.985895i	$0.446474\pi$
$282$	17.4524	1.03927
$283$	−30.4098	−1.80767	−0.903836	−	0.427878i	$-0.859261\pi$
$283$	−30.4098	−1.80767	−0.903836	+	0.427878i	$0.859261\pi$
$284$	−3.79543	−0.225218
$285$	0	0
$286$	−0.156927	−0.00927928
$287$	−0.326520	−0.0192739
$288$	3.03693	0.178953
$289$	45.1556	2.65621
$290$	0	0
$291$	−8.43649	−0.494556
$292$	−41.6117	−2.43514
$293$	7.37610	0.430916	0.215458	−	0.976513i	$-0.430876\pi$
$293$	7.37610	0.430916	0.215458	+	0.976513i	$0.430876\pi$
$294$	4.74002	0.276444
$295$	0	0
$296$	−22.1480	−1.28733
$297$	−6.07451	−0.352479
$298$	23.2510	1.34689
$299$	−0.0484449	−0.00280164
$300$	0	0
$301$	4.32773	0.249446
$302$	−21.3186	−1.22675
$303$	10.5434	0.605704
$304$	5.78028	0.331522
$305$	0	0
$306$	6.82578	0.390204
$307$	33.6457	1.92026	0.960130	−	0.279553i	$-0.0901862\pi$
$307$	33.6457	1.92026	0.960130	+	0.279553i	$0.0901862\pi$
$308$	−5.91423	−0.336995
$309$	20.8113	1.18391
$310$	0	0
$311$	3.26695	0.185252	0.0926259	−	0.995701i	$-0.470474\pi$
$311$	3.26695	0.185252	0.0926259	+	0.995701i	$0.470474\pi$
$312$	−0.629190	−0.0356209
$313$	−13.4405	−0.759702	−0.379851	−	0.925048i	$-0.624025\pi$
$313$	−13.4405	−0.759702	−0.379851	+	0.925048i	$0.624025\pi$
$314$	54.2936	3.06397
$315$	0	0
$316$	−74.1684	−4.17230
$317$	16.2175	0.910863	0.455431	−	0.890271i	$-0.349485\pi$
$317$	16.2175	0.910863	0.455431	+	0.890271i	$0.349485\pi$
$318$	10.1562	0.569532
$319$	3.02191	0.169195
$320$	0	0
$321$	31.6416	1.76606
$322$	−2.59615	−0.144678
$323$	5.07036	0.282122
$324$	−46.8752	−2.60418
$325$	0	0
$326$	−16.9846	−0.940689
$327$	1.14608	0.0633784
$328$	2.32270	0.128250
$329$	−3.68192	−0.202991
$330$	0	0
$331$	−6.88267	−0.378306	−0.189153	−	0.981948i	$-0.560574\pi$
$331$	−6.88267	−0.378306	−0.189153	+	0.981948i	$0.560574\pi$
$332$	50.9937	2.79864
$333$	−1.03832	−0.0568998
$334$	63.3462	3.46615
$335$	0	0
$336$	−16.4097	−0.895222
$337$	2.66538	0.145192	0.0725962	−	0.997361i	$-0.476872\pi$
$337$	2.66538	0.145192	0.0725962	+	0.997361i	$0.476872\pi$
$338$	−33.7439	−1.83543
$339$	−28.9029	−1.56979
$340$	0	0
$341$	−3.55707	−0.192626
$342$	0.556815	0.0301091
$343$	−1.00000	−0.0539949
$344$	−30.7854	−1.65984
$345$	0	0
$346$	28.2524	1.51886
$347$	−27.8445	−1.49477	−0.747386	−	0.664390i	$-0.768691\pi$
$347$	−27.8445	−1.49477	−0.747386	+	0.664390i	$0.768691\pi$
$348$	20.9601	1.12358
$349$	−17.4213	−0.932539	−0.466270	−	0.884643i	$-0.654402\pi$
$349$	−17.4213	−0.932539	−0.466270	+	0.884643i	$0.654402\pi$
$350$	0	0
$351$	0.235853	0.0125889
$352$	11.3625	0.605621
$353$	9.84870	0.524193	0.262097	−	0.965042i	$-0.415586\pi$
$353$	9.84870	0.524193	0.262097	+	0.965042i	$0.415586\pi$
$354$	−61.6660	−3.27751
$355$	0	0
$356$	−54.5014	−2.88857
$357$	−14.3943	−0.761826
$358$	−58.7002	−3.10240
$359$	29.9249	1.57938	0.789688	−	0.613509i	$-0.210242\pi$
$359$	29.9249	1.57938	0.789688	+	0.613509i	$0.210242\pi$
$360$	0	0
$361$	−18.5864	−0.978231
$362$	6.24142	0.328042
$363$	−17.2412	−0.904929
$364$	0.229630	0.0120359
$365$	0	0
$366$	14.0762	0.735774
$367$	4.83523	0.252397	0.126198	−	0.992005i	$-0.459722\pi$
$367$	4.83523	0.252397	0.126198	+	0.992005i	$0.459722\pi$
$368$	8.98774	0.468518
$369$	0.108891	0.00566863
$370$	0	0
$371$	−2.14265	−0.111241
$372$	−24.6720	−1.27918
$373$	15.2656	0.790421	0.395210	−	0.918591i	$-0.370672\pi$
$373$	15.2656	0.790421	0.395210	+	0.918591i	$0.370672\pi$
$374$	25.5381	1.32055
$375$	0	0
$376$	26.1914	1.35072
$377$	−0.117331	−0.00604284
$378$	12.6393	0.650096
$379$	−25.5606	−1.31296	−0.656480	−	0.754344i	$-0.727955\pi$
$379$	−25.5606	−1.31296	−0.656480	+	0.754344i	$0.727955\pi$
$380$	0	0
$381$	−12.1597	−0.622962
$382$	15.4950	0.792792
$383$	−9.73373	−0.497370	−0.248685	−	0.968584i	$-0.579998\pi$
$383$	−9.73373	−0.497370	−0.248685	+	0.968584i	$0.579998\pi$
$384$	−6.39381	−0.326282
$385$	0	0
$386$	−52.2536	−2.65964
$387$	−1.44325	−0.0733647
$388$	−21.9024	−1.11193
$389$	3.88804	0.197131	0.0985657	−	0.995131i	$-0.468575\pi$
$389$	3.88804	0.197131	0.0985657	+	0.995131i	$0.468575\pi$
$390$	0	0
$391$	7.88388	0.398705
$392$	7.11351	0.359287
$393$	6.61071	0.333466
$394$	−62.9730	−3.17253
$395$	0	0
$396$	1.97233	0.0991135
$397$	30.7544	1.54352	0.771759	−	0.635915i	$-0.219377\pi$
$397$	30.7544	1.54352	0.771759	+	0.635915i	$0.219377\pi$
$398$	−57.9496	−2.90475
$399$	−1.17422	−0.0587843
$400$	0	0
$401$	31.6948	1.58276	0.791382	−	0.611322i	$-0.209362\pi$
$401$	31.6948	1.58276	0.791382	+	0.611322i	$0.209362\pi$
$402$	48.6452	2.42620
$403$	0.138109	0.00687971
$404$	27.3724	1.36183
$405$	0	0
$406$	−6.28773	−0.312055
$407$	−3.88480	−0.192563
$408$	102.394	5.06925
$409$	26.9490	1.33254	0.666270	−	0.745711i	$-0.267890\pi$
$409$	26.9490	1.33254	0.666270	+	0.745711i	$0.267890\pi$
$410$	0	0
$411$	7.64238	0.376971
$412$	54.0294	2.66184
$413$	13.0097	0.640163
$414$	0.865790	0.0425512
$415$	0	0
$416$	−0.441166	−0.0216299
$417$	13.3358	0.653056
$418$	2.08328	0.101896
$419$	4.26942	0.208575	0.104287	−	0.994547i	$-0.466744\pi$
$419$	4.26942	0.208575	0.104287	+	0.994547i	$0.466744\pi$
$420$	0	0
$421$	−20.7664	−1.01209	−0.506046	−	0.862507i	$-0.668893\pi$
$421$	−20.7664	−1.01209	−0.506046	+	0.862507i	$0.668893\pi$
$422$	9.03035	0.439591
$423$	1.22788	0.0597016
$424$	15.2418	0.740206
$425$	0	0
$426$	−3.79543	−0.183889
$427$	−2.96965	−0.143711
$428$	82.1465	3.97070
$429$	−0.110361	−0.00532829
$430$	0	0
$431$	35.5688	1.71329	0.856645	−	0.515906i	$-0.172545\pi$
$431$	35.5688	1.71329	0.856645	+	0.515906i	$0.172545\pi$
$432$	−43.7566	−2.10524
$433$	−10.5249	−0.505793	−0.252897	−	0.967493i	$-0.581383\pi$
$433$	−10.5249	−0.505793	−0.252897	+	0.967493i	$0.581383\pi$
$434$	7.40124	0.355271
$435$	0	0
$436$	2.97540	0.142496
$437$	0.643129	0.0307650
$438$	−41.6117	−1.98829
$439$	14.5335	0.693647	0.346823	−	0.937930i	$-0.387260\pi$
$439$	14.5335	0.693647	0.346823	+	0.937930i	$0.387260\pi$
$440$	0	0
$441$	0.333489	0.0158804
$442$	−0.991560	−0.0471637
$443$	−15.1798	−0.721214	−0.360607	−	0.932718i	$-0.617430\pi$
$443$	−15.1798	−0.721214	−0.360607	+	0.932718i	$0.617430\pi$
$444$	−26.9451	−1.27876
$445$	0	0
$446$	−7.64842	−0.362163
$447$	16.3516	0.773403
$448$	−5.66651	−0.267717
$449$	18.2339	0.860509	0.430255	−	0.902708i	$-0.358424\pi$
$449$	18.2339	0.860509	0.430255	+	0.902708i	$0.358424\pi$
$450$	0	0
$451$	0.407406	0.0191840
$452$	−75.0364	−3.52942
$453$	−14.9926	−0.704416
$454$	45.9344	2.15581
$455$	0	0
$456$	8.35280	0.391156
$457$	2.91210	0.136222	0.0681111	−	0.997678i	$-0.478303\pi$
$457$	2.91210	0.136222	0.0681111	+	0.997678i	$0.478303\pi$
$458$	−72.8328	−3.40325
$459$	−38.3825	−1.79154
$460$	0	0
$461$	26.4693	1.23280	0.616400	−	0.787433i	$-0.288591\pi$
$461$	26.4693	1.23280	0.616400	+	0.787433i	$0.288591\pi$
$462$	−5.91423	−0.275155
$463$	33.9514	1.57786	0.788928	−	0.614485i	$-0.210636\pi$
$463$	33.9514	1.57786	0.788928	+	0.614485i	$0.210636\pi$
$464$	21.7678	1.01054
$465$	0	0
$466$	18.3427	0.849708
$467$	−24.7878	−1.14704	−0.573521	−	0.819191i	$-0.694423\pi$
$467$	−24.7878	−1.14704	−0.573521	+	0.819191i	$0.694423\pi$
$468$	−0.0765791	−0.00353987
$469$	−10.2627	−0.473886
$470$	0	0
$471$	38.1828	1.75937
$472$	−92.5443	−4.25970
$473$	−5.39982	−0.248284
$474$	−74.1684	−3.40667
$475$	0	0
$476$	−37.3698	−1.71284
$477$	0.714551	0.0327170
$478$	−47.4623	−2.17088
$479$	29.3630	1.34163	0.670815	−	0.741625i	$-0.265945\pi$
$479$	29.3630	1.34163	0.670815	+	0.741625i	$0.265945\pi$
$480$	0	0
$481$	0.150834	0.00687744
$482$	−66.6108	−3.03404
$483$	−1.82578	−0.0830761
$484$	−44.7609	−2.03459
$485$	0	0
$486$	−8.95731	−0.406312
$487$	−22.7541	−1.03109	−0.515544	−	0.856863i	$-0.672410\pi$
$487$	−22.7541	−1.03109	−0.515544	+	0.856863i	$0.672410\pi$
$488$	21.1246	0.956267
$489$	−11.9447	−0.540157
$490$	0	0
$491$	−24.4623	−1.10397	−0.551984	−	0.833855i	$-0.686129\pi$
$491$	−24.4623	−1.10397	−0.551984	+	0.833855i	$0.686129\pi$
$492$	2.82578	0.127396
$493$	19.0943	0.859963
$494$	−0.0808867	−0.00363926
$495$	0	0
$496$	−25.6227	−1.15049
$497$	0.800721	0.0359173
$498$	50.9937	2.28508
$499$	−1.56849	−0.0702152	−0.0351076	−	0.999384i	$-0.511177\pi$
$499$	−1.56849	−0.0702152	−0.0351076	+	0.999384i	$0.511177\pi$
$500$	0	0
$501$	44.5492	1.99031
$502$	50.0534	2.23399
$503$	31.6182	1.40979	0.704894	−	0.709313i	$-0.250995\pi$
$503$	31.6182	1.40979	0.704894	+	0.709313i	$0.250995\pi$
$504$	−2.37228	−0.105670
$505$	0	0
$506$	3.23928	0.144004
$507$	−23.7309	−1.05393
$508$	−31.5686	−1.40063
$509$	15.7138	0.696503	0.348251	−	0.937401i	$-0.386776\pi$
$509$	15.7138	0.696503	0.348251	+	0.937401i	$0.386776\pi$
$510$	0	0
$511$	8.77881	0.388352
$512$	−46.0216	−2.03389
$513$	−3.13106	−0.138240
$514$	−45.6324	−2.01276
$515$	0	0
$516$	−37.4533	−1.64879
$517$	4.59402	0.202045
$518$	8.08316	0.355154
$519$	19.8689	0.872150
$520$	0	0
$521$	24.2543	1.06260	0.531300	−	0.847184i	$-0.321704\pi$
$521$	24.2543	1.06260	0.531300	+	0.847184i	$0.321704\pi$
$522$	2.09689	0.0917784
$523$	−10.1444	−0.443584	−0.221792	−	0.975094i	$-0.571191\pi$
$523$	−10.1444	−0.443584	−0.221792	+	0.975094i	$0.571191\pi$
$524$	17.1624	0.749744
$525$	0	0
$526$	−32.5729	−1.42024
$527$	−22.4758	−0.979059
$528$	20.4748	0.891049
$529$	1.00000	0.0434783
$530$	0	0
$531$	−4.33858	−0.188278
$532$	−3.04844	−0.132167
$533$	−0.0158182	−0.000685163 0
$534$	−54.5014	−2.35850
$535$	0	0
$536$	73.0036	3.15328
$537$	−41.2818	−1.78144
$538$	−41.7751	−1.80105
$539$	1.24772	0.0537433
$540$	0	0
$541$	29.9380	1.28713	0.643567	−	0.765390i	$-0.277454\pi$
$541$	29.9380	1.28713	0.643567	+	0.765390i	$0.277454\pi$
$542$	27.0695	1.16274
$543$	4.38937	0.188366
$544$	71.7949	3.07818
$545$	0	0
$546$	0.229630	0.00982725
$547$	−12.4373	−0.531783	−0.265891	−	0.964003i	$-0.585666\pi$
$547$	−12.4373	−0.531783	−0.265891	+	0.964003i	$0.585666\pi$
$548$	19.8408	0.847557
$549$	0.990346	0.0422669
$550$	0	0
$551$	1.55762	0.0663568
$552$	12.9877	0.552795
$553$	15.6473	0.665390
$554$	−42.1785	−1.79199
$555$	0	0
$556$	34.6218	1.46829
$557$	1.18101	0.0500410	0.0250205	−	0.999687i	$-0.492035\pi$
$557$	1.18101	0.0500410	0.0250205	+	0.999687i	$0.492035\pi$
$558$	−2.46823	−0.104489
$559$	0.209657	0.00886754
$560$	0	0
$561$	17.9601	0.758275
$562$	14.5673	0.614483
$563$	37.4675	1.57907	0.789534	−	0.613707i	$-0.210322\pi$
$563$	37.4675	1.57907	0.789534	+	0.613707i	$0.210322\pi$
$564$	31.8643	1.34173
$565$	0	0
$566$	−78.9484	−3.31845
$567$	9.88925	0.415310
$568$	−5.69594	−0.238996
$569$	1.87905	0.0787738	0.0393869	−	0.999224i	$-0.487460\pi$
$569$	1.87905	0.0787738	0.0393869	+	0.999224i	$0.487460\pi$
$570$	0	0
$571$	17.5063	0.732617	0.366308	−	0.930494i	$-0.380622\pi$
$571$	17.5063	0.732617	0.366308	+	0.930494i	$0.380622\pi$
$572$	−0.286515	−0.0119798
$573$	10.8971	0.455232
$574$	−0.847696	−0.0353821
$575$	0	0
$576$	1.88972	0.0787383
$577$	−6.39227	−0.266114	−0.133057	−	0.991108i	$-0.542479\pi$
$577$	−6.39227	−0.266114	−0.133057	+	0.991108i	$0.542479\pi$
$578$	117.231	4.87617
$579$	−36.7482	−1.52720
$580$	0	0
$581$	−10.7581	−0.446322
$582$	−21.9024	−0.907886
$583$	2.67344	0.110722
$584$	−62.4482	−2.58412
$585$	0	0
$586$	19.1495	0.791058
$587$	25.0940	1.03574	0.517871	−	0.855459i	$-0.326725\pi$
$587$	25.0940	1.03574	0.517871	+	0.855459i	$0.326725\pi$
$588$	8.65425	0.356895
$589$	−1.83346	−0.0755466
$590$	0	0
$591$	−44.2867	−1.82171
$592$	−27.9835	−1.15011
$593$	−8.40540	−0.345168	−0.172584	−	0.984995i	$-0.555212\pi$
$593$	−8.40540	−0.345168	−0.172584	+	0.984995i	$0.555212\pi$
$594$	−15.7704	−0.647066
$595$	0	0
$596$	42.4512	1.73887
$597$	−40.7539	−1.66795
$598$	−0.125771	−0.00514314
$599$	24.9086	1.01774	0.508869	−	0.860844i	$-0.330064\pi$
$599$	24.9086	1.01774	0.508869	+	0.860844i	$0.330064\pi$
$600$	0	0
$601$	−30.3003	−1.23597	−0.617987	−	0.786188i	$-0.712052\pi$
$601$	−30.3003	−1.23597	−0.617987	+	0.786188i	$0.712052\pi$
$602$	11.2355	0.457923
$603$	3.42249	0.139375
$604$	−38.9232	−1.58376
$605$	0	0
$606$	27.3724	1.11193
$607$	29.6204	1.20225	0.601127	−	0.799153i	$-0.294719\pi$
$607$	29.6204	1.20225	0.601127	+	0.799153i	$0.294719\pi$
$608$	5.85668	0.237520
$609$	−4.42194	−0.179186
$610$	0	0
$611$	−0.178370	−0.00721609
$612$	12.4624	0.503763
$613$	23.3823	0.944401	0.472201	−	0.881491i	$-0.343460\pi$
$613$	23.3823	0.944401	0.472201	+	0.881491i	$0.343460\pi$
$614$	87.3494	3.52513
$615$	0	0
$616$	−8.87570	−0.357612
$617$	−33.7043	−1.35688	−0.678441	−	0.734655i	$-0.737344\pi$
$617$	−33.7043	−1.35688	−0.678441	+	0.734655i	$0.737344\pi$
$618$	54.0294	2.17338
$619$	−6.65807	−0.267610	−0.133805	−	0.991008i	$-0.542720\pi$
$619$	−6.65807	−0.267610	−0.133805	+	0.991008i	$0.542720\pi$
$620$	0	0
$621$	−4.86847	−0.195365
$622$	8.48151	0.340078
$623$	11.4981	0.460663
$624$	−0.794966	−0.0318241
$625$	0	0
$626$	−34.8936	−1.39463
$627$	1.46510	0.0585103
$628$	99.1285	3.95566
$629$	−24.5466	−0.978736
$630$	0	0
$631$	25.5442	1.01690	0.508449	−	0.861092i	$-0.330219\pi$
$631$	25.5442	1.01690	0.508449	+	0.861092i	$0.330219\pi$
$632$	−111.307	−4.42756
$633$	6.35073	0.252419
$634$	42.1030	1.67212
$635$	0	0
$636$	18.5430	0.735279
$637$	−0.0484449	−0.00191946
$638$	7.84535	0.310600
$639$	−0.267032	−0.0105636
$640$	0	0
$641$	−26.9765	−1.06551	−0.532754	−	0.846270i	$-0.678843\pi$
$641$	−26.9765	−1.06551	−0.532754	+	0.846270i	$0.678843\pi$
$642$	82.1465	3.24206
$643$	3.62642	0.143012	0.0715061	−	0.997440i	$-0.477219\pi$
$643$	3.62642	0.143012	0.0715061	+	0.997440i	$0.477219\pi$
$644$	−4.74002	−0.186783
$645$	0	0
$646$	13.1634	0.517908
$647$	12.3456	0.485356	0.242678	−	0.970107i	$-0.421974\pi$
$647$	12.3456	0.485356	0.242678	+	0.970107i	$0.421974\pi$
$648$	−70.3473	−2.76350
$649$	−16.2325	−0.637180
$650$	0	0
$651$	5.20503	0.204001
$652$	−31.0102	−1.21445
$653$	−28.8699	−1.12977	−0.564884	−	0.825170i	$-0.691079\pi$
$653$	−28.8699	−1.12977	−0.564884	+	0.825170i	$0.691079\pi$
$654$	2.97540	0.116348
$655$	0	0
$656$	2.93468	0.114580
$657$	−2.92764	−0.114218
$658$	−9.55883	−0.372642
$659$	26.0451	1.01457	0.507287	−	0.861777i	$-0.330648\pi$
$659$	26.0451	1.01457	0.507287	+	0.861777i	$0.330648\pi$
$660$	0	0
$661$	34.5864	1.34526	0.672628	−	0.739981i	$-0.265166\pi$
$661$	34.5864	1.34526	0.672628	+	0.739981i	$0.265166\pi$
$662$	−17.8685	−0.694478
$663$	−0.697329	−0.0270820
$664$	76.5280	2.96986
$665$	0	0
$666$	−2.69565	−0.104454
$667$	2.42194	0.0937779
$668$	115.657	4.47489
$669$	−5.37886	−0.207959
$670$	0	0
$671$	3.70530	0.143042
$672$	−16.6266	−0.641385
$673$	−0.640526	−0.0246905	−0.0123452	−	0.999924i	$-0.503930\pi$
$673$	−0.640526	−0.0246905	−0.0123452	+	0.999924i	$0.503930\pi$
$674$	6.91973	0.266538
$675$	0	0
$676$	−61.6091	−2.36958
$677$	31.3521	1.20496	0.602480	−	0.798134i	$-0.294179\pi$
$677$	31.3521	1.20496	0.602480	+	0.798134i	$0.294179\pi$
$678$	−75.0364	−2.88176
$679$	4.62075	0.177328
$680$	0	0
$681$	32.3041	1.23789
$682$	−9.23471	−0.353615
$683$	24.7326	0.946366	0.473183	−	0.880964i	$-0.343105\pi$
$683$	24.7326	0.946366	0.473183	+	0.880964i	$0.343105\pi$
$684$	1.01662	0.0388716
$685$	0	0
$686$	−2.59615	−0.0991216
$687$	−51.2208	−1.95419
$688$	−38.8966	−1.48292
$689$	−0.103801	−0.00395449
$690$	0	0
$691$	15.1723	0.577183	0.288591	−	0.957452i	$-0.406813\pi$
$691$	15.1723	0.577183	0.288591	+	0.957452i	$0.406813\pi$
$692$	51.5828	1.96089
$693$	−0.416102	−0.0158064
$694$	−72.2887	−2.74404
$695$	0	0
$696$	31.4555	1.19232
$697$	2.57424	0.0975064
$698$	−45.2283	−1.71192
$699$	12.8998	0.487914
$700$	0	0
$701$	−45.0365	−1.70101	−0.850503	−	0.525970i	$-0.823702\pi$
$701$	−45.0365	−1.70101	−0.850503	+	0.525970i	$0.823702\pi$
$702$	0.612311	0.0231102
$703$	−2.00239	−0.0755216
$704$	7.07024	0.266470
$705$	0	0
$706$	25.5687	0.962292
$707$	−5.77474	−0.217181
$708$	−112.589	−4.23135
$709$	32.5039	1.22071	0.610355	−	0.792128i	$-0.291027\pi$
$709$	32.5039	1.22071	0.610355	+	0.792128i	$0.291027\pi$
$710$	0	0
$711$	−5.21820	−0.195698
$712$	−81.7921	−3.06529
$713$	−2.85085	−0.106765
$714$	−37.3698	−1.39853
$715$	0	0
$716$	−107.174	−4.00528
$717$	−33.3786	−1.24655
$718$	77.6897	2.89935
$719$	−28.9938	−1.08129	−0.540644	−	0.841252i	$-0.681819\pi$
$719$	−28.9938	−1.08129	−0.540644	+	0.841252i	$0.681819\pi$
$720$	0	0
$721$	−11.3986	−0.424504
$722$	−48.2531	−1.79580
$723$	−46.8450	−1.74219
$724$	11.3955	0.423510
$725$	0	0
$726$	−44.7609	−1.66123
$727$	−13.5415	−0.502226	−0.251113	−	0.967958i	$-0.580797\pi$
$727$	−13.5415	−0.502226	−0.251113	+	0.967958i	$0.580797\pi$
$728$	0.344614	0.0127722
$729$	23.3684	0.865496
$730$	0	0
$731$	−34.1194	−1.26195
$732$	25.7001	0.949903
$733$	−0.785312	−0.0290062	−0.0145031	−	0.999895i	$-0.504617\pi$
$733$	−0.785312	−0.0290062	−0.0145031	+	0.999895i	$0.504617\pi$
$734$	12.5530	0.463340
$735$	0	0
$736$	9.10654	0.335672
$737$	12.8050	0.471677
$738$	0.282697	0.0104062
$739$	32.1503	1.18267	0.591333	−	0.806427i	$-0.298602\pi$
$739$	32.1503	1.18267	0.591333	+	0.806427i	$0.298602\pi$
$740$	0	0
$741$	−0.0568848	−0.00208971
$742$	−5.56265	−0.204211
$743$	−0.392524	−0.0144003	−0.00720015	−	0.999974i	$-0.502292\pi$
$743$	−0.392524	−0.0144003	−0.00720015	+	0.999974i	$0.502292\pi$
$744$	−37.0261	−1.35744
$745$	0	0
$746$	39.6318	1.45102
$747$	3.58771	0.131268
$748$	46.6271	1.70486
$749$	−17.3304	−0.633240
$750$	0	0
$751$	12.5057	0.456338	0.228169	−	0.973622i	$-0.426726\pi$
$751$	12.5057	0.456338	0.228169	+	0.973622i	$0.426726\pi$
$752$	33.0922	1.20675
$753$	35.2008	1.28279
$754$	−0.304609	−0.0110932
$755$	0	0
$756$	23.0767	0.839290
$757$	31.9343	1.16067	0.580336	−	0.814377i	$-0.302921\pi$
$757$	31.9343	1.16067	0.580336	+	0.814377i	$0.302921\pi$
$758$	−66.3593	−2.41028
$759$	2.27807	0.0826889
$760$	0	0
$761$	32.1468	1.16532	0.582660	−	0.812716i	$-0.302012\pi$
$761$	32.1468	1.16532	0.582660	+	0.812716i	$0.302012\pi$
$762$	−31.5686	−1.14361
$763$	−0.627720	−0.0227250
$764$	28.2905	1.02351
$765$	0	0
$766$	−25.2703	−0.913052
$767$	0.630252	0.0227571
$768$	−37.2910	−1.34562
$769$	44.5341	1.60594	0.802970	−	0.596020i	$-0.203252\pi$
$769$	44.5341	1.60594	0.802970	+	0.596020i	$0.203252\pi$
$770$	0	0
$771$	−32.0917	−1.15575
$772$	−95.4039	−3.43366
$773$	−8.92796	−0.321116	−0.160558	−	0.987026i	$-0.551329\pi$
$773$	−8.92796	−0.321116	−0.160558	+	0.987026i	$0.551329\pi$
$774$	−3.74691	−0.134680
$775$	0	0
$776$	−32.8698	−1.17996
$777$	5.68460	0.203934
$778$	10.0939	0.361886
$779$	0.209994	0.00752383
$780$	0	0
$781$	−0.999079	−0.0357499
$782$	20.4678	0.731926
$783$	−11.7911	−0.421381
$784$	8.98774	0.320991
$785$	0	0
$786$	17.1624	0.612163
$787$	2.03169	0.0724220	0.0362110	−	0.999344i	$-0.488471\pi$
$787$	2.03169	0.0724220	0.0362110	+	0.999344i	$0.488471\pi$
$788$	−114.975	−4.09582
$789$	−22.9073	−0.815523
$790$	0	0
$791$	15.8304	0.562864
$792$	2.95995	0.105177
$793$	−0.143864	−0.00510878
$794$	79.8431	2.83353
$795$	0	0
$796$	−105.803	−3.75010
$797$	−8.79703	−0.311607	−0.155803	−	0.987788i	$-0.549797\pi$
$797$	−8.79703	−0.311607	−0.155803	+	0.987788i	$0.549797\pi$
$798$	−3.04844	−0.107914
$799$	29.0278	1.02693
$800$	0	0
$801$	−3.83450	−0.135486
$802$	82.2846	2.90557
$803$	−10.9535	−0.386542
$804$	88.8157	3.13229
$805$	0	0
$806$	0.358553	0.0126295
$807$	−29.3789	−1.03419
$808$	41.0787	1.44514
$809$	1.86894	0.0657085	0.0328542	−	0.999460i	$-0.489540\pi$
$809$	1.86894	0.0657085	0.0328542	+	0.999460i	$0.489540\pi$
$810$	0	0
$811$	21.9612	0.771162	0.385581	−	0.922674i	$-0.374001\pi$
$811$	21.9612	0.771162	0.385581	+	0.922674i	$0.374001\pi$
$812$	−11.4800	−0.402870
$813$	19.0370	0.667658
$814$	−10.0856	−0.353498
$815$	0	0
$816$	129.372	4.52893
$817$	−2.78329	−0.0973751
$818$	69.9636	2.44622
$819$	0.0161559	0.000564531 0
$820$	0	0
$821$	26.5692	0.927273	0.463636	−	0.886026i	$-0.346544\pi$
$821$	26.5692	0.927273	0.463636	+	0.886026i	$0.346544\pi$
$822$	19.8408	0.692028
$823$	−1.42715	−0.0497472	−0.0248736	−	0.999691i	$-0.507918\pi$
$823$	−1.42715	−0.0497472	−0.0248736	+	0.999691i	$0.507918\pi$
$824$	81.0838	2.82469
$825$	0	0
$826$	33.7751	1.17519
$827$	−33.1216	−1.15175	−0.575875	−	0.817538i	$-0.695339\pi$
$827$	−33.1216	−1.15175	−0.575875	+	0.817538i	$0.695339\pi$
$828$	1.58075	0.0549347
$829$	−14.9587	−0.519535	−0.259768	−	0.965671i	$-0.583646\pi$
$829$	−14.9587	−0.519535	−0.259768	+	0.965671i	$0.583646\pi$
$830$	0	0
$831$	−29.6626	−1.02899
$832$	−0.274514	−0.00951705
$833$	7.88388	0.273160
$834$	34.6218	1.19885
$835$	0	0
$836$	3.80362	0.131551
$837$	13.8793	0.479738
$838$	11.0841	0.382893
$839$	−7.51949	−0.259602	−0.129801	−	0.991540i	$-0.541434\pi$
$839$	−7.51949	−0.259602	−0.129801	+	0.991540i	$0.541434\pi$
$840$	0	0
$841$	−23.1342	−0.797731
$842$	−53.9127	−1.85796
$843$	10.2447	0.352845
$844$	16.4875	0.567522
$845$	0	0
$846$	3.18777	0.109598
$847$	9.44319	0.324472
$848$	19.2576	0.661308
$849$	−55.5217	−1.90550
$850$	0	0
$851$	−3.11351	−0.106730
$852$	−6.92964	−0.237406
$853$	25.8589	0.885392	0.442696	−	0.896672i	$-0.354022\pi$
$853$	25.8589	0.885392	0.442696	+	0.896672i	$0.354022\pi$
$854$	−7.70967	−0.263819
$855$	0	0
$856$	123.280	4.21363
$857$	15.7166	0.536870	0.268435	−	0.963298i	$-0.413494\pi$
$857$	15.7166	0.536870	0.268435	+	0.963298i	$0.413494\pi$
$858$	−0.286515	−0.00978145
$859$	−30.6108	−1.04443	−0.522214	−	0.852815i	$-0.674894\pi$
$859$	−30.6108	−1.04443	−0.522214	+	0.852815i	$0.674894\pi$
$860$	0	0
$861$	−0.596155	−0.0203169
$862$	92.3422	3.14519
$863$	17.3833	0.591734	0.295867	−	0.955229i	$-0.404392\pi$
$863$	17.3833	0.591734	0.295867	+	0.955229i	$0.404392\pi$
$864$	−44.3350	−1.50831
$865$	0	0
$866$	−27.3242	−0.928514
$867$	82.4444	2.79996
$868$	13.5131	0.458664
$869$	−19.5235	−0.662289
$870$	0	0
$871$	−0.497174	−0.0168461
$872$	4.46529	0.151214
$873$	−1.54097	−0.0521539
$874$	1.66966	0.0564772
$875$	0	0
$876$	−75.9740	−2.56693
$877$	−44.0377	−1.48705	−0.743524	−	0.668709i	$-0.766847\pi$
$877$	−44.0377	−1.48705	−0.743524	+	0.668709i	$0.766847\pi$
$878$	37.7313	1.27337
$879$	13.4672	0.454236
$880$	0	0
$881$	25.1295	0.846633	0.423316	−	0.905982i	$-0.360866\pi$
$881$	25.1295	0.846633	0.423316	+	0.905982i	$0.360866\pi$
$882$	0.865790	0.0291527
$883$	3.49482	0.117610	0.0588050	−	0.998269i	$-0.481271\pi$
$883$	3.49482	0.117610	0.0588050	+	0.998269i	$0.481271\pi$
$884$	−1.81038	−0.0608895
$885$	0	0
$886$	−39.4091	−1.32397
$887$	−10.2347	−0.343646	−0.171823	−	0.985128i	$-0.554966\pi$
$887$	−10.2347	−0.343646	−0.171823	+	0.985128i	$0.554966\pi$
$888$	−40.4375	−1.35699
$889$	6.66001	0.223370
$890$	0	0
$891$	−12.3391	−0.413374
$892$	−13.9644	−0.467561
$893$	2.36795	0.0792404
$894$	42.4512	1.41978
$895$	0	0
$896$	3.50195	0.116992
$897$	−0.0884500	−0.00295326
$898$	47.3379	1.57969
$899$	−6.90458	−0.230281
$900$	0	0
$901$	16.8924	0.562768
$902$	1.05769	0.0352172
$903$	7.90151	0.262946
$904$	−112.610	−3.74535
$905$	0	0
$906$	−38.9232	−1.29314
$907$	15.6526	0.519736	0.259868	−	0.965644i	$-0.416321\pi$
$907$	15.6526	0.519736	0.259868	+	0.965644i	$0.416321\pi$
$908$	83.8664	2.78320
$909$	1.92581	0.0638752
$910$	0	0
$911$	21.9471	0.727138	0.363569	−	0.931567i	$-0.381558\pi$
$911$	21.9471	0.727138	0.363569	+	0.931567i	$0.381558\pi$
$912$	10.5535	0.349463
$913$	13.4232	0.444242
$914$	7.56026	0.250071
$915$	0	0
$916$	−132.977	−4.39368
$917$	−3.62075	−0.119568
$918$	−99.6469	−3.28884
$919$	−20.0736	−0.662168	−0.331084	−	0.943601i	$-0.607414\pi$
$919$	−20.0736	−0.662168	−0.331084	+	0.943601i	$0.607414\pi$
$920$	0	0
$921$	61.4298	2.02418
$922$	68.7185	2.26312
$923$	0.0387909	0.00127682
$924$	−10.7981	−0.355232
$925$	0	0
$926$	88.1432	2.89656
$927$	3.80130	0.124851
$928$	22.0555	0.724007
$929$	4.39668	0.144250	0.0721252	−	0.997396i	$-0.477022\pi$
$929$	4.39668	0.144250	0.0721252	+	0.997396i	$0.477022\pi$
$930$	0	0
$931$	0.643129	0.0210777
$932$	33.4898	1.09699
$933$	5.96475	0.195277
$934$	−64.3530	−2.10569
$935$	0	0
$936$	−0.114925	−0.00375644
$937$	25.0355	0.817875	0.408937	−	0.912562i	$-0.365899\pi$
$937$	25.0355	0.817875	0.408937	+	0.912562i	$0.365899\pi$
$938$	−26.6435	−0.869940
$939$	−24.5395	−0.800815
$940$	0	0
$941$	−37.7528	−1.23071	−0.615353	−	0.788251i	$-0.710987\pi$
$941$	−37.7528	−1.23071	−0.615353	+	0.788251i	$0.710987\pi$
$942$	99.1285	3.22978
$943$	0.326520	0.0106329
$944$	−116.927	−3.80566
$945$	0	0
$946$	−14.0188	−0.455789
$947$	53.7878	1.74787	0.873934	−	0.486044i	$-0.161561\pi$
$947$	53.7878	1.74787	0.873934	+	0.486044i	$0.161561\pi$
$948$	−135.416	−4.39809
$949$	0.425289	0.0138055
$950$	0	0
$951$	29.6096	0.960156
$952$	−56.0821	−1.81763
$953$	31.8425	1.03148	0.515739	−	0.856745i	$-0.327517\pi$
$953$	31.8425	1.03148	0.515739	+	0.856745i	$0.327517\pi$
$954$	1.85508	0.0600606
$955$	0	0
$956$	−86.6560	−2.80265
$957$	5.51736	0.178351
$958$	76.2309	2.46291
$959$	−4.18581	−0.135167
$960$	0	0
$961$	−22.8727	−0.737828
$962$	0.391588	0.0126253
$963$	5.77951	0.186242
$964$	−121.617	−3.91702
$965$	0	0
$966$	−4.74002	−0.152508
$967$	26.3912	0.848684	0.424342	−	0.905502i	$-0.360505\pi$
$967$	26.3912	0.848684	0.424342	+	0.905502i	$0.360505\pi$
$968$	−67.1742	−2.15906
$969$	9.25738	0.297390
$970$	0	0
$971$	−26.2260	−0.841633	−0.420817	−	0.907146i	$-0.638256\pi$
$971$	−26.2260	−0.841633	−0.420817	+	0.907146i	$0.638256\pi$
$972$	−16.3541	−0.524559
$973$	−7.30414	−0.234160
$974$	−59.0732	−1.89283
$975$	0	0
$976$	26.6904	0.854340
$977$	−54.0228	−1.72834	−0.864172	−	0.503197i	$-0.832157\pi$
$977$	−54.0228	−1.72834	−0.864172	+	0.503197i	$0.832157\pi$
$978$	−31.0102	−0.991597
$979$	−14.3465	−0.458516
$980$	0	0
$981$	0.209338	0.00668364
$982$	−63.5079	−2.02662
$983$	−51.1712	−1.63211	−0.816055	−	0.577975i	$-0.803843\pi$
$983$	−51.1712	−1.63211	−0.816055	+	0.577975i	$0.803843\pi$
$984$	4.24075	0.135190
$985$	0	0
$986$	49.5717	1.57869
$987$	−6.72239	−0.213976
$988$	−0.147682	−0.00469838
$989$	−4.32773	−0.137614
$990$	0	0
$991$	18.9674	0.602520	0.301260	−	0.953542i	$-0.402593\pi$
$991$	18.9674	0.602520	0.301260	+	0.953542i	$0.402593\pi$
$992$	−25.9614	−0.824274
$993$	−12.5663	−0.398779
$994$	2.07880	0.0659354
$995$	0	0
$996$	93.1034	2.95010
$997$	42.5912	1.34888	0.674438	−	0.738331i	$-0.264386\pi$
$997$	42.5912	1.34888	0.674438	+	0.738331i	$0.264386\pi$
$998$	−4.07204	−0.128898
$999$	15.1581	0.479580

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4025.2.a.o.1.4		4
5.4	even	2		805.2.a.g.1.1	✓	4
15.14	odd	2		7245.2.a.bf.1.4		4
35.34	odd	2		5635.2.a.s.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
805.2.a.g.1.1	✓	4	5.4	even	2
4025.2.a.o.1.4		4	1.1	even	1	trivial
5635.2.a.s.1.1		4	35.34	odd	2
7245.2.a.bf.1.4		4	15.14	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:	\( N \)	\(=\)	\( 4025 = 5^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4025.a (trivial)

\(f(q)\)	\(=\)	\(q+2.59615 q^{2} +1.82578 q^{3} +4.74002 q^{4} +4.74002 q^{6} -1.00000 q^{7} +7.11351 q^{8} +0.333489 q^{9} +O(q^{10})\)	\(q+2.59615 q^{2} +1.82578 q^{3} +4.74002 q^{4} +4.74002 q^{6} -1.00000 q^{7} +7.11351 q^{8} +0.333489 q^{9} +1.24772 q^{11} +8.65425 q^{12} -0.0484449 q^{13} -2.59615 q^{14} +8.98774 q^{16} +7.88388 q^{17} +0.865790 q^{18} +0.643129 q^{19} -1.82578 q^{21} +3.23928 q^{22} +1.00000 q^{23} +12.9877 q^{24} -0.125771 q^{26} -4.86847 q^{27} -4.74002 q^{28} +2.42194 q^{29} -2.85085 q^{31} +9.10654 q^{32} +2.27807 q^{33} +20.4678 q^{34} +1.58075 q^{36} -3.11351 q^{37} +1.66966 q^{38} -0.0884500 q^{39} +0.326520 q^{41} -4.74002 q^{42} -4.32773 q^{43} +5.91423 q^{44} +2.59615 q^{46} +3.68192 q^{47} +16.4097 q^{48} +1.00000 q^{49} +14.3943 q^{51} -0.229630 q^{52} +2.14265 q^{53} -12.6393 q^{54} -7.11351 q^{56} +1.17422 q^{57} +6.28773 q^{58} -13.0097 q^{59} +2.96965 q^{61} -7.40124 q^{62} -0.333489 q^{63} +5.66651 q^{64} +5.91423 q^{66} +10.2627 q^{67} +37.3698 q^{68} +1.82578 q^{69} -0.800721 q^{71} +2.37228 q^{72} -8.77881 q^{73} -8.08316 q^{74} +3.04844 q^{76} -1.24772 q^{77} -0.229630 q^{78} -15.6473 q^{79} -9.88925 q^{81} +0.847696 q^{82} +10.7581 q^{83} -8.65425 q^{84} -11.2355 q^{86} +4.42194 q^{87} +8.87570 q^{88} -11.4981 q^{89} +0.0484449 q^{91} +4.74002 q^{92} -5.20503 q^{93} +9.55883 q^{94} +16.6266 q^{96} -4.62075 q^{97} +2.59615 q^{98} +0.416102 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + 5 q^{3} + 2 q^{4} + 2 q^{6} - 4 q^{7} + 9 q^{8} + 3 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 + 5 * q^3 + 2 * q^4 + 2 * q^6 - 4 * q^7 + 9 * q^8 + 3 * q^9	\( 4 q + 2 q^{2} + 5 q^{3} + 2 q^{4} + 2 q^{6} - 4 q^{7} + 9 q^{8} + 3 q^{9} - 8 q^{11} + 3 q^{12} + 8 q^{13} - 2 q^{14} + 6 q^{16} + 6 q^{17} - 3 q^{18} + 2 q^{19} - 5 q^{21} + 4 q^{22} + 4 q^{23} + 22 q^{24} - 11 q^{26} + 14 q^{27} - 2 q^{28} - q^{29} - 2 q^{31} + 5 q^{32} + 7 q^{33} + 18 q^{34} - 10 q^{36} + 7 q^{37} - 17 q^{38} + 12 q^{39} - 9 q^{41} - 2 q^{42} + 4 q^{43} + 9 q^{44} + 2 q^{46} + 21 q^{47} + 25 q^{48} + 4 q^{49} + 9 q^{51} - 7 q^{52} + 11 q^{53} - 16 q^{54} - 9 q^{56} + 7 q^{57} + 8 q^{58} - 37 q^{59} + q^{61} + 7 q^{62} - 3 q^{63} + 21 q^{64} + 9 q^{66} + 31 q^{67} + 41 q^{68} + 5 q^{69} - 8 q^{71} + 18 q^{72} - 25 q^{73} - 2 q^{74} + 4 q^{76} + 8 q^{77} - 7 q^{78} - 19 q^{79} + 40 q^{81} + 16 q^{82} + 7 q^{83} - 3 q^{84} - 2 q^{86} + 7 q^{87} + 9 q^{88} + 7 q^{89} - 8 q^{91} + 2 q^{92} - 39 q^{93} + 7 q^{94} - 3 q^{96} + 2 q^{97} + 2 q^{98} + 40 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 + 5 * q^3 + 2 * q^4 + 2 * q^6 - 4 * q^7 + 9 * q^8 + 3 * q^9 - 8 * q^11 + 3 * q^12 + 8 * q^13 - 2 * q^14 + 6 * q^16 + 6 * q^17 - 3 * q^18 + 2 * q^19 - 5 * q^21 + 4 * q^22 + 4 * q^23 + 22 * q^24 - 11 * q^26 + 14 * q^27 - 2 * q^28 - q^29 - 2 * q^31 + 5 * q^32 + 7 * q^33 + 18 * q^34 - 10 * q^36 + 7 * q^37 - 17 * q^38 + 12 * q^39 - 9 * q^41 - 2 * q^42 + 4 * q^43 + 9 * q^44 + 2 * q^46 + 21 * q^47 + 25 * q^48 + 4 * q^49 + 9 * q^51 - 7 * q^52 + 11 * q^53 - 16 * q^54 - 9 * q^56 + 7 * q^57 + 8 * q^58 - 37 * q^59 + q^61 + 7 * q^62 - 3 * q^63 + 21 * q^64 + 9 * q^66 + 31 * q^67 + 41 * q^68 + 5 * q^69 - 8 * q^71 + 18 * q^72 - 25 * q^73 - 2 * q^74 + 4 * q^76 + 8 * q^77 - 7 * q^78 - 19 * q^79 + 40 * q^81 + 16 * q^82 + 7 * q^83 - 3 * q^84 - 2 * q^86 + 7 * q^87 + 9 * q^88 + 7 * q^89 - 8 * q^91 + 2 * q^92 - 39 * q^93 + 7 * q^94 - 3 * q^96 + 2 * q^97 + 2 * q^98 + 40 * q^99

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