LMFDB - Embedded newform 4025.2.a.r.1.2

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:	$5$
Coefficient field:	5.5.122821.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 4x^{3} + 4x^{2} + 3x - 1 $ x^5 - 2x^4 - 4x^3 + 4x^2 + 3x - 1
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			1.2
Root			$1.17316$ 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)

$f(q)$	$=$	$q-0.173158 q^{2} -1.11762 q^{3} -1.97002 q^{4} +0.193524 q^{6} +1.00000 q^{7} +0.687440 q^{8} -1.75093 q^{9} +O(q^{10})$	\(q-0.173158 q^{2} -1.11762 q^{3} -1.97002 q^{4} +0.193524 q^{6} +1.00000 q^{7} +0.687440 q^{8} -1.75093 q^{9} -5.19730 q^{11} +2.20172 q^{12} -3.30671 q^{13} -0.173158 q^{14} +3.82100 q^{16} +5.71133 q^{17} +0.303188 q^{18} -1.66707 q^{19} -1.11762 q^{21} +0.899953 q^{22} -1.00000 q^{23} -0.768294 q^{24} +0.572584 q^{26} +5.30972 q^{27} -1.97002 q^{28} -9.33549 q^{29} -9.77065 q^{31} -2.03652 q^{32} +5.80858 q^{33} -0.988963 q^{34} +3.44937 q^{36} -10.6963 q^{37} +0.288667 q^{38} +3.69564 q^{39} +3.98783 q^{41} +0.193524 q^{42} -4.54495 q^{43} +10.2388 q^{44} +0.173158 q^{46} +7.18910 q^{47} -4.27041 q^{48} +1.00000 q^{49} -6.38308 q^{51} +6.51428 q^{52} +1.81090 q^{53} -0.919421 q^{54} +0.687440 q^{56} +1.86315 q^{57} +1.61651 q^{58} +8.45809 q^{59} -5.79921 q^{61} +1.69187 q^{62} -1.75093 q^{63} -7.28935 q^{64} -1.00580 q^{66} -0.111771 q^{67} -11.2514 q^{68} +1.11762 q^{69} -14.9669 q^{71} -1.20366 q^{72} +3.29219 q^{73} +1.85215 q^{74} +3.28416 q^{76} -5.19730 q^{77} -0.639929 q^{78} +6.62115 q^{79} -0.681428 q^{81} -0.690525 q^{82} -10.1793 q^{83} +2.20172 q^{84} +0.786995 q^{86} +10.4335 q^{87} -3.57283 q^{88} -5.56837 q^{89} -3.30671 q^{91} +1.97002 q^{92} +10.9198 q^{93} -1.24485 q^{94} +2.27604 q^{96} +0.969460 q^{97} -0.173158 q^{98} +9.10012 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 3 q^{2} + 6 q^{3} + 3 q^{4} + 7 q^{6} + 5 q^{7} + 3 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q + 3 * q^2 + 6 * q^3 + 3 * q^4 + 7 * q^6 + 5 * q^7 + 3 * q^8 + 5 * q^9	$ 5 q + 3 q^{2} + 6 q^{3} + 3 q^{4} + 7 q^{6} + 5 q^{7} + 3 q^{8} + 5 q^{9} - 11 q^{11} + 14 q^{12} + 7 q^{13} + 3 q^{14} - q^{16} - q^{17} + 17 q^{18} + 2 q^{19} + 6 q^{21} - 2 q^{22} - 5 q^{23} + 12 q^{24} + 8 q^{26} + 15 q^{27} + 3 q^{28} - 14 q^{29} - 6 q^{31} + 4 q^{32} - 22 q^{33} + 4 q^{34} + 28 q^{36} + q^{37} + 31 q^{38} + 15 q^{39} + 7 q^{41} + 7 q^{42} + 12 q^{43} - 11 q^{44} - 3 q^{46} + 24 q^{47} + 4 q^{48} + 5 q^{49} - 28 q^{51} + 36 q^{52} + 21 q^{53} + 49 q^{54} + 3 q^{56} + 15 q^{57} - 9 q^{58} - q^{59} + 7 q^{61} + 26 q^{62} + 5 q^{63} - 15 q^{64} - 45 q^{66} + 35 q^{67} - 43 q^{68} - 6 q^{69} - 32 q^{71} + 36 q^{72} + 7 q^{73} - 10 q^{74} + 10 q^{76} - 11 q^{77} + 8 q^{78} + 18 q^{79} + 21 q^{81} - 33 q^{82} + q^{83} + 14 q^{84} - 26 q^{86} + 18 q^{87} - 41 q^{88} + q^{89} + 7 q^{91} - 3 q^{92} + 19 q^{93} + 14 q^{94} + 26 q^{96} + 9 q^{97} + 3 q^{98} - 54 q^{99}+O(q^{100}) $ 5 * q + 3 * q^2 + 6 * q^3 + 3 * q^4 + 7 * q^6 + 5 * q^7 + 3 * q^8 + 5 * q^9 - 11 * q^11 + 14 * q^12 + 7 * q^13 + 3 * q^14 - q^16 - q^17 + 17 * q^18 + 2 * q^19 + 6 * q^21 - 2 * q^22 - 5 * q^23 + 12 * q^24 + 8 * q^26 + 15 * q^27 + 3 * q^28 - 14 * q^29 - 6 * q^31 + 4 * q^32 - 22 * q^33 + 4 * q^34 + 28 * q^36 + q^37 + 31 * q^38 + 15 * q^39 + 7 * q^41 + 7 * q^42 + 12 * q^43 - 11 * q^44 - 3 * q^46 + 24 * q^47 + 4 * q^48 + 5 * q^49 - 28 * q^51 + 36 * q^52 + 21 * q^53 + 49 * q^54 + 3 * q^56 + 15 * q^57 - 9 * q^58 - q^59 + 7 * q^61 + 26 * q^62 + 5 * q^63 - 15 * q^64 - 45 * q^66 + 35 * q^67 - 43 * q^68 - 6 * q^69 - 32 * q^71 + 36 * q^72 + 7 * q^73 - 10 * q^74 + 10 * q^76 - 11 * q^77 + 8 * q^78 + 18 * q^79 + 21 * q^81 - 33 * q^82 + q^83 + 14 * q^84 - 26 * q^86 + 18 * q^87 - 41 * q^88 + q^89 + 7 * q^91 - 3 * q^92 + 19 * q^93 + 14 * q^94 + 26 * q^96 + 9 * q^97 + 3 * q^98 - 54 * 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 $

$2$	−0.173158	−0.122441	−0.0612206	−	0.998124i	$-0.519499\pi$
$2$	−0.173158	−0.122441	−0.0612206	+	0.998124i	$0.519499\pi$
$3$	−1.11762	−0.645256	−0.322628	−	0.946526i	$-0.604566\pi$
$3$	−1.11762	−0.645256	−0.322628	+	0.946526i	$0.604566\pi$
$4$	−1.97002	−0.985008
$5$	0	0
$5$	0	0
$6$	0.193524	0.0790059
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	0.687440	0.243047
$9$	−1.75093	−0.583645
$10$	0	0
$11$	−5.19730	−1.56704	−0.783522	−	0.621364i	$-0.786579\pi$
$11$	−5.19730	−1.56704	−0.783522	+	0.621364i	$0.786579\pi$
$12$	2.20172	0.635582
$13$	−3.30671	−0.917118	−0.458559	−	0.888664i	$-0.651634\pi$
$13$	−3.30671	−0.917118	−0.458559	+	0.888664i	$0.651634\pi$
$14$	−0.173158	−0.0462784
$15$	0	0
$16$	3.82100	0.955249
$17$	5.71133	1.38520	0.692601	−	0.721321i	$-0.256465\pi$
$17$	5.71133	1.38520	0.692601	+	0.721321i	$0.256465\pi$
$18$	0.303188	0.0714622
$19$	−1.66707	−0.382453	−0.191226	−	0.981546i	$-0.561246\pi$
$19$	−1.66707	−0.382453	−0.191226	+	0.981546i	$0.561246\pi$
$20$	0	0
$21$	−1.11762	−0.243884
$22$	0.899953	0.191871
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−0.768294	−0.156827
$25$	0	0
$26$	0.572584	0.112293
$27$	5.30972	1.02186
$28$	−1.97002	−0.372298
$29$	−9.33549	−1.73356	−0.866778	−	0.498694i	$-0.833813\pi$
$29$	−9.33549	−1.73356	−0.866778	+	0.498694i	$0.833813\pi$
$30$	0	0
$31$	−9.77065	−1.75486	−0.877430	−	0.479705i	$-0.840744\pi$
$31$	−9.77065	−1.75486	−0.877430	+	0.479705i	$0.840744\pi$
$32$	−2.03652	−0.360009
$33$	5.80858	1.01114
$34$	−0.988963	−0.169606
$35$	0	0
$36$	3.44937	0.574895
$37$	−10.6963	−1.75847	−0.879233	−	0.476393i	$-0.841944\pi$
$37$	−10.6963	−1.75847	−0.879233	+	0.476393i	$0.841944\pi$
$38$	0.288667	0.0468280
$39$	3.69564	0.591776
$40$	0	0
$41$	3.98783	0.622795	0.311397	−	0.950280i	$-0.399203\pi$
$41$	3.98783	0.622795	0.311397	+	0.950280i	$0.399203\pi$
$42$	0.193524	0.0298614
$43$	−4.54495	−0.693099	−0.346549	−	0.938032i	$-0.612647\pi$
$43$	−4.54495	−0.693099	−0.346549	+	0.938032i	$0.612647\pi$
$44$	10.2388	1.54355
$45$	0	0
$46$	0.173158	0.0255308
$47$	7.18910	1.04864	0.524319	−	0.851522i	$-0.324320\pi$
$47$	7.18910	1.04864	0.524319	+	0.851522i	$0.324320\pi$
$48$	−4.27041	−0.616380
$49$	1.00000	0.142857
$50$	0	0
$51$	−6.38308	−0.893810
$52$	6.51428	0.903368
$53$	1.81090	0.248746	0.124373	−	0.992236i	$-0.460308\pi$
$53$	1.81090	0.248746	0.124373	+	0.992236i	$0.460308\pi$
$54$	−0.919421	−0.125117
$55$	0	0
$56$	0.687440	0.0918630
$57$	1.86315	0.246780
$58$	1.61651	0.212259
$59$	8.45809	1.10115	0.550575	−	0.834786i	$-0.314409\pi$
$59$	8.45809	1.10115	0.550575	+	0.834786i	$0.314409\pi$
$60$	0	0
$61$	−5.79921	−0.742513	−0.371256	−	0.928530i	$-0.621073\pi$
$61$	−5.79921	−0.742513	−0.371256	+	0.928530i	$0.621073\pi$
$62$	1.69187	0.214867
$63$	−1.75093	−0.220597
$64$	−7.28935	−0.911169
$65$	0	0
$66$	−1.00580	−0.123806
$67$	−0.111771	−0.0136550	−0.00682750	−	0.999977i	$-0.502173\pi$
$67$	−0.111771	−0.0136550	−0.00682750	+	0.999977i	$0.502173\pi$
$68$	−11.2514	−1.36443
$69$	1.11762	0.134545
$70$	0	0
$71$	−14.9669	−1.77625	−0.888124	−	0.459604i	$-0.847991\pi$
$71$	−14.9669	−1.77625	−0.888124	+	0.459604i	$0.847991\pi$
$72$	−1.20366	−0.141853
$73$	3.29219	0.385322	0.192661	−	0.981265i	$-0.438288\pi$
$73$	3.29219	0.385322	0.192661	+	0.981265i	$0.438288\pi$
$74$	1.85215	0.215309
$75$	0	0
$76$	3.28416	0.376719
$77$	−5.19730	−0.592287
$78$	−0.639929	−0.0724577
$79$	6.62115	0.744938	0.372469	−	0.928045i	$-0.378511\pi$
$79$	6.62115	0.744938	0.372469	+	0.928045i	$0.378511\pi$
$80$	0	0
$81$	−0.681428	−0.0757142
$82$	−0.690525	−0.0762557
$83$	−10.1793	−1.11732	−0.558661	−	0.829396i	$-0.688685\pi$
$83$	−10.1793	−1.11732	−0.558661	+	0.829396i	$0.688685\pi$
$84$	2.20172	0.240228
$85$	0	0
$86$	0.786995	0.0848639
$87$	10.4335	1.11859
$88$	−3.57283	−0.380865
$89$	−5.56837	−0.590246	−0.295123	−	0.955459i	$-0.595361\pi$
$89$	−5.56837	−0.590246	−0.295123	+	0.955459i	$0.595361\pi$
$90$	0	0
$91$	−3.30671	−0.346638
$92$	1.97002	0.205388
$93$	10.9198	1.13233
$94$	−1.24485	−0.128396
$95$	0	0
$96$	2.27604	0.232298
$97$	0.969460	0.0984337	0.0492168	−	0.998788i	$-0.484327\pi$
$97$	0.969460	0.0984337	0.0492168	+	0.998788i	$0.484327\pi$
$98$	−0.173158	−0.0174916
$99$	9.10012	0.914597
$100$	0	0
$101$	9.44491	0.939803	0.469902	−	0.882719i	$-0.344289\pi$
$101$	9.44491	0.939803	0.469902	+	0.882719i	$0.344289\pi$
$102$	1.10528	0.109439
$103$	3.69397	0.363978	0.181989	−	0.983301i	$-0.441746\pi$
$103$	3.69397	0.363978	0.181989	+	0.983301i	$0.441746\pi$
$104$	−2.27317	−0.222902
$105$	0	0
$106$	−0.313572	−0.0304568
$107$	18.1514	1.75476	0.877380	−	0.479797i	$-0.159290\pi$
$107$	18.1514	1.75476	0.877380	+	0.479797i	$0.159290\pi$
$108$	−10.4602	−1.00654
$109$	−5.98333	−0.573099	−0.286549	−	0.958065i	$-0.592508\pi$
$109$	−5.98333	−0.573099	−0.286549	+	0.958065i	$0.592508\pi$
$110$	0	0
$111$	11.9544	1.13466
$112$	3.82100	0.361050
$113$	−17.8826	−1.68226	−0.841128	−	0.540836i	$-0.818108\pi$
$113$	−17.8826	−1.68226	−0.841128	+	0.540836i	$0.818108\pi$
$114$	−0.322619	−0.0302160
$115$	0	0
$116$	18.3911	1.70757
$117$	5.78984	0.535271
$118$	−1.46459	−0.134826
$119$	5.71133	0.523557
$120$	0	0
$121$	16.0119	1.45563
$122$	1.00418	0.0909142
$123$	−4.45687	−0.401862
$124$	19.2483	1.72855
$125$	0	0
$126$	0.303188	0.0270102
$127$	0.905589	0.0803580	0.0401790	−	0.999192i	$-0.487207\pi$
$127$	0.905589	0.0803580	0.0401790	+	0.999192i	$0.487207\pi$
$128$	5.33524	0.471573
$129$	5.07951	0.447226
$130$	0	0
$131$	3.41094	0.298015	0.149008	−	0.988836i	$-0.452392\pi$
$131$	3.41094	0.298015	0.149008	+	0.988836i	$0.452392\pi$
$132$	−11.4430	−0.995986
$133$	−1.66707	−0.144554
$134$	0.0193541	0.00167194
$135$	0	0
$136$	3.92620	0.336669
$137$	−8.71652	−0.744703	−0.372351	−	0.928092i	$-0.621448\pi$
$137$	−8.71652	−0.744703	−0.372351	+	0.928092i	$0.621448\pi$
$138$	−0.193524	−0.0164739
$139$	1.76599	0.149789	0.0748946	−	0.997191i	$-0.476138\pi$
$139$	1.76599	0.149789	0.0748946	+	0.997191i	$0.476138\pi$
$140$	0	0
$141$	−8.03465	−0.676640
$142$	2.59164	0.217486
$143$	17.1860	1.43716
$144$	−6.69031	−0.557526
$145$	0	0
$146$	−0.570070	−0.0471793
$147$	−1.11762	−0.0921794
$148$	21.0719	1.73210
$149$	21.7001	1.77774	0.888869	−	0.458161i	$-0.151492\pi$
$149$	21.7001	1.77774	0.888869	+	0.458161i	$0.151492\pi$
$150$	0	0
$151$	2.78067	0.226288	0.113144	−	0.993579i	$-0.463908\pi$
$151$	2.78067	0.226288	0.113144	+	0.993579i	$0.463908\pi$
$152$	−1.14601	−0.0929540
$153$	−10.0002	−0.808466
$154$	0.899953	0.0725203
$155$	0	0
$156$	−7.28047	−0.582904
$157$	−0.190926	−0.0152375	−0.00761876	−	0.999971i	$-0.502425\pi$
$157$	−0.190926	−0.0152375	−0.00761876	+	0.999971i	$0.502425\pi$
$158$	−1.14651	−0.0912110
$159$	−2.02389	−0.160505
$160$	0	0
$161$	−1.00000	−0.0788110
$162$	0.117995	0.00927054
$163$	−6.86169	−0.537449	−0.268725	−	0.963217i	$-0.586602\pi$
$163$	−6.86169	−0.537449	−0.268725	+	0.963217i	$0.586602\pi$
$164$	−7.85609	−0.613458
$165$	0	0
$166$	1.76262	0.136806
$167$	9.22220	0.713635	0.356818	−	0.934174i	$-0.383862\pi$
$167$	9.22220	0.713635	0.356818	+	0.934174i	$0.383862\pi$
$168$	−0.768294	−0.0592752
$169$	−2.06564	−0.158895
$170$	0	0
$171$	2.91894	0.223217
$172$	8.95363	0.682708
$173$	−11.9718	−0.910200	−0.455100	−	0.890440i	$-0.650396\pi$
$173$	−11.9718	−0.910200	−0.455100	+	0.890440i	$0.650396\pi$
$174$	−1.80664	−0.136961
$175$	0	0
$176$	−19.8589	−1.49692
$177$	−9.45290	−0.710523
$178$	0.964207	0.0722704
$179$	−17.6879	−1.32206	−0.661029	−	0.750361i	$-0.729880\pi$
$179$	−17.6879	−1.32206	−0.661029	+	0.750361i	$0.729880\pi$
$180$	0	0
$181$	−8.71369	−0.647683	−0.323842	−	0.946111i	$-0.604974\pi$
$181$	−8.71369	−0.647683	−0.323842	+	0.946111i	$0.604974\pi$
$182$	0.572584	0.0424428
$183$	6.48129	0.479111
$184$	−0.687440	−0.0506788
$185$	0	0
$186$	−1.89086	−0.138644
$187$	−29.6835	−2.17067
$188$	−14.1626	−1.03292
$189$	5.30972	0.386225
$190$	0	0
$191$	10.6338	0.769438	0.384719	−	0.923034i	$-0.374298\pi$
$191$	10.6338	0.769438	0.384719	+	0.923034i	$0.374298\pi$
$192$	8.14670	0.587937
$193$	24.0260	1.72943	0.864714	−	0.502265i	$-0.167500\pi$
$193$	24.0260	1.72943	0.864714	+	0.502265i	$0.167500\pi$
$194$	−0.167870	−0.0120523
$195$	0	0
$196$	−1.97002	−0.140715
$197$	5.93082	0.422554	0.211277	−	0.977426i	$-0.432238\pi$
$197$	5.93082	0.422554	0.211277	+	0.977426i	$0.432238\pi$
$198$	−1.57576	−0.111984
$199$	20.4915	1.45261	0.726303	−	0.687375i	$-0.241237\pi$
$199$	20.4915	1.45261	0.726303	+	0.687375i	$0.241237\pi$
$200$	0	0
$201$	0.124917	0.00881098
$202$	−1.63546	−0.115071
$203$	−9.33549	−0.655223
$204$	12.5748	0.880410
$205$	0	0
$206$	−0.639641	−0.0445659
$207$	1.75093	0.121698
$208$	−12.6349	−0.876076
$209$	8.66428	0.599321
$210$	0	0
$211$	19.0551	1.31181	0.655904	−	0.754844i	$-0.272287\pi$
$211$	19.0551	1.31181	0.655904	+	0.754844i	$0.272287\pi$
$212$	−3.56751	−0.245017
$213$	16.7273	1.14613
$214$	−3.14306	−0.214855
$215$	0	0
$216$	3.65011	0.248359
$217$	−9.77065	−0.663275
$218$	1.03606	0.0701709
$219$	−3.67941	−0.248631
$220$	0	0
$221$	−18.8857	−1.27039
$222$	−2.07000	−0.138929
$223$	16.1252	1.07982	0.539910	−	0.841723i	$-0.318458\pi$
$223$	16.1252	1.07982	0.539910	+	0.841723i	$0.318458\pi$
$224$	−2.03652	−0.136070
$225$	0	0
$226$	3.09652	0.205977
$227$	15.7740	1.04695	0.523477	−	0.852040i	$-0.324634\pi$
$227$	15.7740	1.04695	0.523477	+	0.852040i	$0.324634\pi$
$228$	−3.67043	−0.243080
$229$	0.0800089	0.00528714	0.00264357	−	0.999997i	$-0.499159\pi$
$229$	0.0800089	0.00528714	0.00264357	+	0.999997i	$0.499159\pi$
$230$	0	0
$231$	5.80858	0.382177
$232$	−6.41759	−0.421335
$233$	3.16622	0.207426	0.103713	−	0.994607i	$-0.466928\pi$
$233$	3.16622	0.207426	0.103713	+	0.994607i	$0.466928\pi$
$234$	−1.00256	−0.0655392
$235$	0	0
$236$	−16.6626	−1.08464
$237$	−7.39990	−0.480675
$238$	−0.988963	−0.0641049
$239$	−18.2374	−1.17968	−0.589840	−	0.807520i	$-0.700809\pi$
$239$	−18.2374	−1.17968	−0.589840	+	0.807520i	$0.700809\pi$
$240$	0	0
$241$	22.6971	1.46205	0.731025	−	0.682351i	$-0.239042\pi$
$241$	22.6971	1.46205	0.731025	+	0.682351i	$0.239042\pi$
$242$	−2.77259	−0.178229
$243$	−15.1676	−0.973001
$244$	11.4245	0.731381
$245$	0	0
$246$	0.771742	0.0492045
$247$	5.51254	0.350754
$248$	−6.71673	−0.426513
$249$	11.3765	0.720958
$250$	0	0
$251$	−4.99947	−0.315563	−0.157782	−	0.987474i	$-0.550434\pi$
$251$	−4.99947	−0.315563	−0.157782	+	0.987474i	$0.550434\pi$
$252$	3.44937	0.217290
$253$	5.19730	0.326751
$254$	−0.156810	−0.00983913
$255$	0	0
$256$	13.6549	0.853429
$257$	20.8290	1.29928	0.649639	−	0.760243i	$-0.274920\pi$
$257$	20.8290	1.29928	0.649639	+	0.760243i	$0.274920\pi$
$258$	−0.879558	−0.0547589
$259$	−10.6963	−0.664637
$260$	0	0
$261$	16.3458	1.01178
$262$	−0.590632	−0.0364894
$263$	9.48853	0.585088	0.292544	−	0.956252i	$-0.405498\pi$
$263$	9.48853	0.585088	0.292544	+	0.956252i	$0.405498\pi$
$264$	3.99305	0.245755
$265$	0	0
$266$	0.288667	0.0176993
$267$	6.22330	0.380860
$268$	0.220191	0.0134503
$269$	−7.23368	−0.441045	−0.220523	−	0.975382i	$-0.570776\pi$
$269$	−7.23368	−0.441045	−0.220523	+	0.975382i	$0.570776\pi$
$270$	0	0
$271$	27.9466	1.69763	0.848816	−	0.528688i	$-0.177316\pi$
$271$	27.9466	1.69763	0.848816	+	0.528688i	$0.177316\pi$
$272$	21.8230	1.32321
$273$	3.69564	0.223670
$274$	1.50934	0.0911823
$275$	0	0
$276$	−2.20172	−0.132528
$277$	−0.889335	−0.0534350	−0.0267175	−	0.999643i	$-0.508505\pi$
$277$	−0.889335	−0.0534350	−0.0267175	+	0.999643i	$0.508505\pi$
$278$	−0.305795	−0.0183404
$279$	17.1078	1.02421
$280$	0	0
$281$	−14.3386	−0.855369	−0.427684	−	0.903928i	$-0.640671\pi$
$281$	−14.3386	−0.855369	−0.427684	+	0.903928i	$0.640671\pi$
$282$	1.39126	0.0828486
$283$	11.1086	0.660335	0.330168	−	0.943922i	$-0.392895\pi$
$283$	11.1086	0.660335	0.330168	+	0.943922i	$0.392895\pi$
$284$	29.4851	1.74962
$285$	0	0
$286$	−2.97589	−0.175968
$287$	3.98783	0.235394
$288$	3.56581	0.210117
$289$	15.6193	0.918784
$290$	0	0
$291$	−1.08348	−0.0635149
$292$	−6.48568	−0.379545
$293$	5.26448	0.307554	0.153777	−	0.988106i	$-0.450856\pi$
$293$	5.26448	0.307554	0.153777	+	0.988106i	$0.450856\pi$
$294$	0.193524	0.0112866
$295$	0	0
$296$	−7.35308	−0.427389
$297$	−27.5962	−1.60129
$298$	−3.75754	−0.217668
$299$	3.30671	0.191232
$300$	0	0
$301$	−4.54495	−0.261967
$302$	−0.481496	−0.0277070
$303$	−10.5558	−0.606414
$304$	−6.36988	−0.365338
$305$	0	0
$306$	1.73161	0.0989895
$307$	−8.73985	−0.498810	−0.249405	−	0.968399i	$-0.580235\pi$
$307$	−8.73985	−0.498810	−0.249405	+	0.968399i	$0.580235\pi$
$308$	10.2388	0.583407
$309$	−4.12844	−0.234859
$310$	0	0
$311$	−20.1775	−1.14416	−0.572081	−	0.820197i	$-0.693864\pi$
$311$	−20.1775	−1.14416	−0.572081	+	0.820197i	$0.693864\pi$
$312$	2.54053	0.143829
$313$	6.99651	0.395466	0.197733	−	0.980256i	$-0.436642\pi$
$313$	6.99651	0.395466	0.197733	+	0.980256i	$0.436642\pi$
$314$	0.0330603	0.00186570
$315$	0	0
$316$	−13.0438	−0.733770
$317$	26.4529	1.48574	0.742871	−	0.669435i	$-0.233464\pi$
$317$	26.4529	1.48574	0.742871	+	0.669435i	$0.233464\pi$
$318$	0.350453	0.0196524
$319$	48.5193	2.71656
$320$	0	0
$321$	−20.2863	−1.13227
$322$	0.173158	0.00964972
$323$	−9.52121	−0.529775
$324$	1.34242	0.0745791
$325$	0	0
$326$	1.18816	0.0658059
$327$	6.68706	0.369795
$328$	2.74140	0.151368
$329$	7.18910	0.396348
$330$	0	0
$331$	13.4893	0.741438	0.370719	−	0.928745i	$-0.379111\pi$
$331$	13.4893	0.741438	0.370719	+	0.928745i	$0.379111\pi$
$332$	20.0534	1.10057
$333$	18.7286	1.02632
$334$	−1.59690	−0.0873784
$335$	0	0
$336$	−4.27041	−0.232970
$337$	−6.56858	−0.357813	−0.178907	−	0.983866i	$-0.557256\pi$
$337$	−6.56858	−0.357813	−0.178907	+	0.983866i	$0.557256\pi$
$338$	0.357682	0.0194553
$339$	19.9859	1.08549
$340$	0	0
$341$	50.7809	2.74994
$342$	−0.505437	−0.0273309
$343$	1.00000	0.0539949
$344$	−3.12438	−0.168455
$345$	0	0
$346$	2.07302	0.111446
$347$	6.06204	0.325427	0.162714	−	0.986673i	$-0.447975\pi$
$347$	6.06204	0.325427	0.162714	+	0.986673i	$0.447975\pi$
$348$	−20.5542	−1.10182
$349$	10.6335	0.569196	0.284598	−	0.958647i	$-0.408140\pi$
$349$	10.6335	0.569196	0.284598	+	0.958647i	$0.408140\pi$
$350$	0	0
$351$	−17.5577	−0.937162
$352$	10.5844	0.564149
$353$	−0.489490	−0.0260529	−0.0130265	−	0.999915i	$-0.504147\pi$
$353$	−0.489490	−0.0260529	−0.0130265	+	0.999915i	$0.504147\pi$
$354$	1.63684	0.0869973
$355$	0	0
$356$	10.9698	0.581397
$357$	−6.38308	−0.337828
$358$	3.06280	0.161874
$359$	−7.85718	−0.414686	−0.207343	−	0.978268i	$-0.566482\pi$
$359$	−7.85718	−0.414686	−0.207343	+	0.978268i	$0.566482\pi$
$360$	0	0
$361$	−16.2209	−0.853730
$362$	1.50884	0.0793031
$363$	−17.8951	−0.939252
$364$	6.51428	0.341441
$365$	0	0
$366$	−1.12229	−0.0586629
$367$	30.7548	1.60539	0.802694	−	0.596390i	$-0.203399\pi$
$367$	30.7548	1.60539	0.802694	+	0.596390i	$0.203399\pi$
$368$	−3.82100	−0.199183
$369$	−6.98243	−0.363491
$370$	0	0
$371$	1.81090	0.0940173
$372$	−21.5122	−1.11536
$373$	7.18176	0.371858	0.185929	−	0.982563i	$-0.440471\pi$
$373$	7.18176	0.371858	0.185929	+	0.982563i	$0.440471\pi$
$374$	5.13993	0.265780
$375$	0	0
$376$	4.94207	0.254868
$377$	30.8698	1.58988
$378$	−0.919421	−0.0472899
$379$	−25.3260	−1.30091	−0.650454	−	0.759545i	$-0.725421\pi$
$379$	−25.3260	−1.30091	−0.650454	+	0.759545i	$0.725421\pi$
$380$	0	0
$381$	−1.01210	−0.0518515
$382$	−1.84134	−0.0942109
$383$	25.9621	1.32660	0.663302	−	0.748352i	$-0.269155\pi$
$383$	25.9621	1.32660	0.663302	+	0.748352i	$0.269155\pi$
$384$	−5.96275	−0.304285
$385$	0	0
$386$	−4.16029	−0.211753
$387$	7.95791	0.404523
$388$	−1.90985	−0.0969580
$389$	13.2676	0.672694	0.336347	−	0.941738i	$-0.390809\pi$
$389$	13.2676	0.672694	0.336347	+	0.941738i	$0.390809\pi$
$390$	0	0
$391$	−5.71133	−0.288835
$392$	0.687440	0.0347210
$393$	−3.81212	−0.192296
$394$	−1.02697	−0.0517380
$395$	0	0
$396$	−17.9274	−0.900885
$397$	−20.9647	−1.05219	−0.526093	−	0.850427i	$-0.676344\pi$
$397$	−20.9647	−1.05219	−0.526093	+	0.850427i	$0.676344\pi$
$398$	−3.54827	−0.177859
$399$	1.86315	0.0932741
$400$	0	0
$401$	−37.2401	−1.85968	−0.929842	−	0.367959i	$-0.880057\pi$
$401$	−37.2401	−1.85968	−0.929842	+	0.367959i	$0.880057\pi$
$402$	−0.0216304	−0.00107883
$403$	32.3087	1.60941
$404$	−18.6066	−0.925714
$405$	0	0
$406$	1.61651	0.0802263
$407$	55.5920	2.75559
$408$	−4.38798	−0.217238
$409$	−32.0837	−1.58644	−0.793219	−	0.608937i	$-0.791596\pi$
$409$	−32.0837	−1.58644	−0.793219	+	0.608937i	$0.791596\pi$
$410$	0	0
$411$	9.74173	0.480524
$412$	−7.27719	−0.358521
$413$	8.45809	0.416195
$414$	−0.303188	−0.0149009
$415$	0	0
$416$	6.73418	0.330170
$417$	−1.97370	−0.0966524
$418$	−1.50029	−0.0733815
$419$	−22.8981	−1.11865	−0.559323	−	0.828950i	$-0.688939\pi$
$419$	−22.8981	−1.11865	−0.559323	+	0.828950i	$0.688939\pi$
$420$	0	0
$421$	−5.44518	−0.265382	−0.132691	−	0.991157i	$-0.542362\pi$
$421$	−5.44518	−0.265382	−0.132691	+	0.991157i	$0.542362\pi$
$422$	−3.29955	−0.160619
$423$	−12.5876	−0.612032
$424$	1.24489	0.0604570
$425$	0	0
$426$	−2.89646	−0.140334
$427$	−5.79921	−0.280643
$428$	−35.7585	−1.72845
$429$	−19.2073	−0.927338
$430$	0	0
$431$	14.3414	0.690800	0.345400	−	0.938456i	$-0.387743\pi$
$431$	14.3414	0.690800	0.345400	+	0.938456i	$0.387743\pi$
$432$	20.2884	0.976127
$433$	−0.158396	−0.00761205	−0.00380602	−	0.999993i	$-0.501211\pi$
$433$	−0.158396	−0.00761205	−0.00380602	+	0.999993i	$0.501211\pi$
$434$	1.69187	0.0812122
$435$	0	0
$436$	11.7873	0.564507
$437$	1.66707	0.0797470
$438$	0.637119	0.0304427
$439$	−16.8246	−0.802992	−0.401496	−	0.915861i	$-0.631510\pi$
$439$	−16.8246	−0.802992	−0.401496	+	0.915861i	$0.631510\pi$
$440$	0	0
$441$	−1.75093	−0.0833778
$442$	3.27022	0.155548
$443$	37.6722	1.78986	0.894930	−	0.446207i	$-0.147226\pi$
$443$	37.6722	1.78986	0.894930	+	0.446207i	$0.147226\pi$
$444$	−23.5503	−1.11765
$445$	0	0
$446$	−2.79220	−0.132215
$447$	−24.2523	−1.14710
$448$	−7.28935	−0.344390
$449$	−8.51490	−0.401843	−0.200921	−	0.979607i	$-0.564394\pi$
$449$	−8.51490	−0.401843	−0.200921	+	0.979607i	$0.564394\pi$
$450$	0	0
$451$	−20.7259	−0.975947
$452$	35.2291	1.65704
$453$	−3.10772	−0.146014
$454$	−2.73139	−0.128190
$455$	0	0
$456$	1.28080	0.0599791
$457$	7.69804	0.360099	0.180049	−	0.983658i	$-0.442374\pi$
$457$	7.69804	0.360099	0.180049	+	0.983658i	$0.442374\pi$
$458$	−0.0138542	−0.000647364 0
$459$	30.3256	1.41548
$460$	0	0
$461$	16.6990	0.777750	0.388875	−	0.921291i	$-0.372864\pi$
$461$	16.6990	0.777750	0.388875	+	0.921291i	$0.372864\pi$
$462$	−1.00580	−0.0467942
$463$	8.47705	0.393962	0.196981	−	0.980407i	$-0.436886\pi$
$463$	8.47705	0.393962	0.196981	+	0.980407i	$0.436886\pi$
$464$	−35.6709	−1.65598
$465$	0	0
$466$	−0.548256	−0.0253975
$467$	−35.6016	−1.64744	−0.823722	−	0.566994i	$-0.808106\pi$
$467$	−35.6016	−1.64744	−0.823722	+	0.566994i	$0.808106\pi$
$468$	−11.4061	−0.527246
$469$	−0.111771	−0.00516111
$470$	0	0
$471$	0.213381	0.00983210
$472$	5.81443	0.267631
$473$	23.6215	1.08612
$474$	1.28135	0.0588545
$475$	0	0
$476$	−11.2514	−0.515708
$477$	−3.17077	−0.145180
$478$	3.15795	0.144441
$479$	1.98146	0.0905353	0.0452676	−	0.998975i	$-0.485586\pi$
$479$	1.98146	0.0905353	0.0452676	+	0.998975i	$0.485586\pi$
$480$	0	0
$481$	35.3697	1.61272
$482$	−3.93019	−0.179015
$483$	1.11762	0.0508533
$484$	−31.5437	−1.43380
$485$	0	0
$486$	2.62639	0.119135
$487$	30.5434	1.38406	0.692028	−	0.721871i	$-0.256718\pi$
$487$	30.5434	1.38406	0.692028	+	0.721871i	$0.256718\pi$
$488$	−3.98661	−0.180465
$489$	7.66874	0.346792
$490$	0	0
$491$	−2.93215	−0.132326	−0.0661629	−	0.997809i	$-0.521076\pi$
$491$	−2.93215	−0.132326	−0.0661629	+	0.997809i	$0.521076\pi$
$492$	8.78010	0.395837
$493$	−53.3181	−2.40133
$494$	−0.954540	−0.0429468
$495$	0	0
$496$	−37.3336	−1.67633
$497$	−14.9669	−0.671359
$498$	−1.96994	−0.0882750
$499$	−4.84192	−0.216754	−0.108377	−	0.994110i	$-0.534565\pi$
$499$	−4.84192	−0.216754	−0.108377	+	0.994110i	$0.534565\pi$
$500$	0	0
$501$	−10.3069	−0.460478
$502$	0.865697	0.0386380
$503$	10.6144	0.473272	0.236636	−	0.971598i	$-0.423955\pi$
$503$	10.6144	0.473272	0.236636	+	0.971598i	$0.423955\pi$
$504$	−1.20366	−0.0536154
$505$	0	0
$506$	−0.899953	−0.0400078
$507$	2.30859	0.102528
$508$	−1.78403	−0.0791533
$509$	7.51019	0.332883	0.166442	−	0.986051i	$-0.446772\pi$
$509$	7.51019	0.332883	0.166442	+	0.986051i	$0.446772\pi$
$510$	0	0
$511$	3.29219	0.145638
$512$	−13.0349	−0.576068
$513$	−8.85170	−0.390812
$514$	−3.60671	−0.159085
$515$	0	0
$516$	−10.0067	−0.440521
$517$	−37.3639	−1.64326
$518$	1.85215	0.0813790
$519$	13.3799	0.587312
$520$	0	0
$521$	21.8889	0.958970	0.479485	−	0.877550i	$-0.340824\pi$
$521$	21.8889	0.958970	0.479485	+	0.877550i	$0.340824\pi$
$522$	−2.83041	−0.123884
$523$	−33.3066	−1.45639	−0.728197	−	0.685367i	$-0.759642\pi$
$523$	−33.3066	−1.45639	−0.728197	+	0.685367i	$0.759642\pi$
$524$	−6.71961	−0.293548
$525$	0	0
$526$	−1.64301	−0.0716388
$527$	−55.8034	−2.43084
$528$	22.1946	0.965895
$529$	1.00000	0.0434783
$530$	0	0
$531$	−14.8096	−0.642680
$532$	3.28416	0.142387
$533$	−13.1866	−0.571176
$534$	−1.07761	−0.0466329
$535$	0	0
$536$	−0.0768359	−0.00331881
$537$	19.7683	0.853065
$538$	1.25257	0.0540021
$539$	−5.19730	−0.223863
$540$	0	0
$541$	−31.8086	−1.36756	−0.683780	−	0.729689i	$-0.739665\pi$
$541$	−31.8086	−1.36756	−0.683780	+	0.729689i	$0.739665\pi$
$542$	−4.83917	−0.207860
$543$	9.73856	0.417921
$544$	−11.6312	−0.498685
$545$	0	0
$546$	−0.639929	−0.0273864
$547$	−10.3782	−0.443739	−0.221870	−	0.975076i	$-0.571216\pi$
$547$	−10.3782	−0.443739	−0.221870	+	0.975076i	$0.571216\pi$
$548$	17.1717	0.733538
$549$	10.1540	0.433364
$550$	0	0
$551$	15.5629	0.663004
$552$	0.768294	0.0327008
$553$	6.62115	0.281560
$554$	0.153996	0.00654264
$555$	0	0
$556$	−3.47903	−0.147544
$557$	−37.3980	−1.58460	−0.792302	−	0.610129i	$-0.791118\pi$
$557$	−37.3980	−1.58460	−0.792302	+	0.610129i	$0.791118\pi$
$558$	−2.96235	−0.125406
$559$	15.0289	0.635653
$560$	0	0
$561$	33.1747	1.40064
$562$	2.48284	0.104732
$563$	36.8338	1.55236	0.776179	−	0.630512i	$-0.217155\pi$
$563$	36.8338	1.55236	0.776179	+	0.630512i	$0.217155\pi$
$564$	15.8284	0.666496
$565$	0	0
$566$	−1.92354	−0.0808522
$567$	−0.681428	−0.0286173
$568$	−10.2889	−0.431711
$569$	3.13176	0.131290	0.0656451	−	0.997843i	$-0.479089\pi$
$569$	3.13176	0.131290	0.0656451	+	0.997843i	$0.479089\pi$
$570$	0	0
$571$	−29.8893	−1.25083	−0.625414	−	0.780293i	$-0.715070\pi$
$571$	−29.8893	−1.25083	−0.625414	+	0.780293i	$0.715070\pi$
$572$	−33.8567	−1.41562
$573$	−11.8846	−0.496484
$574$	−0.690525	−0.0288220
$575$	0	0
$576$	12.7632	0.531799
$577$	−25.7738	−1.07298	−0.536489	−	0.843908i	$-0.680250\pi$
$577$	−25.7738	−1.07298	−0.536489	+	0.843908i	$0.680250\pi$
$578$	−2.70461	−0.112497
$579$	−26.8518	−1.11592
$580$	0	0
$581$	−10.1793	−0.422308
$582$	0.187614	0.00777684
$583$	−9.41179	−0.389797
$584$	2.26319	0.0936513
$585$	0	0
$586$	−0.911588	−0.0376573
$587$	−0.300763	−0.0124138	−0.00620691	−	0.999981i	$-0.501976\pi$
$587$	−0.300763	−0.0124138	−0.00620691	+	0.999981i	$0.501976\pi$
$588$	2.20172	0.0907975
$589$	16.2884	0.671151
$590$	0	0
$591$	−6.62838	−0.272655
$592$	−40.8706	−1.67977
$593$	−19.6355	−0.806331	−0.403166	−	0.915127i	$-0.632090\pi$
$593$	−19.6355	−0.806331	−0.403166	+	0.915127i	$0.632090\pi$
$594$	4.77850	0.196064
$595$	0	0
$596$	−42.7495	−1.75109
$597$	−22.9017	−0.937302
$598$	−0.572584	−0.0234147
$599$	−11.6440	−0.475759	−0.237880	−	0.971295i	$-0.576452\pi$
$599$	−11.6440	−0.475759	−0.237880	+	0.971295i	$0.576452\pi$
$600$	0	0
$601$	4.24923	0.173330	0.0866648	−	0.996238i	$-0.472379\pi$
$601$	4.24923	0.173330	0.0866648	+	0.996238i	$0.472379\pi$
$602$	0.786995	0.0320755
$603$	0.195704	0.00796967
$604$	−5.47797	−0.222895
$605$	0	0
$606$	1.82782	0.0742500
$607$	38.9045	1.57909	0.789543	−	0.613695i	$-0.210318\pi$
$607$	38.9045	1.57909	0.789543	+	0.613695i	$0.210318\pi$
$608$	3.39502	0.137686
$609$	10.4335	0.422786
$610$	0	0
$611$	−23.7723	−0.961724
$612$	19.7005	0.796345
$613$	24.6510	0.995644	0.497822	−	0.867279i	$-0.334133\pi$
$613$	24.6510	0.995644	0.497822	+	0.867279i	$0.334133\pi$
$614$	1.51337	0.0610748
$615$	0	0
$616$	−3.57283	−0.143953
$617$	−25.8002	−1.03868	−0.519338	−	0.854569i	$-0.673821\pi$
$617$	−25.8002	−1.03868	−0.519338	+	0.854569i	$0.673821\pi$
$618$	0.714873	0.0287564
$619$	−44.3106	−1.78100	−0.890498	−	0.454988i	$-0.849644\pi$
$619$	−44.3106	−1.78100	−0.890498	+	0.454988i	$0.849644\pi$
$620$	0	0
$621$	−5.30972	−0.213072
$622$	3.49390	0.140093
$623$	−5.56837	−0.223092
$624$	14.1210	0.565293
$625$	0	0
$626$	−1.21150	−0.0484213
$627$	−9.68334	−0.386715
$628$	0.376126	0.0150091
$629$	−61.0903	−2.43583
$630$	0	0
$631$	44.9503	1.78944	0.894722	−	0.446624i	$-0.147374\pi$
$631$	44.9503	1.78944	0.894722	+	0.446624i	$0.147374\pi$
$632$	4.55164	0.181055
$633$	−21.2963	−0.846452
$634$	−4.58053	−0.181916
$635$	0	0
$636$	3.98710	0.158099
$637$	−3.30671	−0.131017
$638$	−8.40151	−0.332619
$639$	26.2061	1.03670
$640$	0	0
$641$	−7.82703	−0.309149	−0.154575	−	0.987981i	$-0.549401\pi$
$641$	−7.82703	−0.309149	−0.154575	+	0.987981i	$0.549401\pi$
$642$	3.51273	0.138636
$643$	−41.1356	−1.62223	−0.811115	−	0.584887i	$-0.801139\pi$
$643$	−41.1356	−1.62223	−0.811115	+	0.584887i	$0.801139\pi$
$644$	1.97002	0.0776295
$645$	0	0
$646$	1.64867	0.0648662
$647$	−11.0704	−0.435221	−0.217611	−	0.976036i	$-0.569826\pi$
$647$	−11.0704	−0.435221	−0.217611	+	0.976036i	$0.569826\pi$
$648$	−0.468441	−0.0184021
$649$	−43.9592	−1.72555
$650$	0	0
$651$	10.9198	0.427982
$652$	13.5176	0.529392
$653$	−46.1799	−1.80716	−0.903580	−	0.428419i	$-0.859071\pi$
$653$	−46.1799	−1.80716	−0.903580	+	0.428419i	$0.859071\pi$
$654$	−1.15792	−0.0452782
$655$	0	0
$656$	15.2375	0.594924
$657$	−5.76441	−0.224891
$658$	−1.24485	−0.0485293
$659$	12.4878	0.486456	0.243228	−	0.969969i	$-0.421794\pi$
$659$	12.4878	0.486456	0.243228	+	0.969969i	$0.421794\pi$
$660$	0	0
$661$	34.4125	1.33849	0.669246	−	0.743041i	$-0.266617\pi$
$661$	34.4125	1.33849	0.669246	+	0.743041i	$0.266617\pi$
$662$	−2.33578	−0.0907825
$663$	21.1070	0.819729
$664$	−6.99765	−0.271561
$665$	0	0
$666$	−3.24300	−0.125664
$667$	9.33549	0.361472
$668$	−18.1679	−0.702937
$669$	−18.0217	−0.696761
$670$	0	0
$671$	30.1402	1.16355
$672$	2.27604	0.0878003
$673$	6.46382	0.249162	0.124581	−	0.992209i	$-0.460241\pi$
$673$	6.46382	0.249162	0.124581	+	0.992209i	$0.460241\pi$
$674$	1.13740	0.0438111
$675$	0	0
$676$	4.06934	0.156513
$677$	−30.9761	−1.19051	−0.595255	−	0.803537i	$-0.702949\pi$
$677$	−30.9761	−1.19051	−0.595255	+	0.803537i	$0.702949\pi$
$678$	−3.46072	−0.132908
$679$	0.969460	0.0372044
$680$	0	0
$681$	−17.6292	−0.675554
$682$	−8.79313	−0.336706
$683$	3.17288	0.121407	0.0607034	−	0.998156i	$-0.480666\pi$
$683$	3.17288	0.121407	0.0607034	+	0.998156i	$0.480666\pi$
$684$	−5.75035	−0.219870
$685$	0	0
$686$	−0.173158	−0.00661120
$687$	−0.0894193	−0.00341156
$688$	−17.3663	−0.662082
$689$	−5.98813	−0.228130
$690$	0	0
$691$	−34.8750	−1.32671	−0.663353	−	0.748307i	$-0.730867\pi$
$691$	−34.8750	−1.32671	−0.663353	+	0.748307i	$0.730867\pi$
$692$	23.5847	0.896554
$693$	9.10012	0.345685
$694$	−1.04969	−0.0398457
$695$	0	0
$696$	7.17240	0.271869
$697$	22.7758	0.862696
$698$	−1.84127	−0.0696931
$699$	−3.53862	−0.133843
$700$	0	0
$701$	−2.22105	−0.0838880	−0.0419440	−	0.999120i	$-0.513355\pi$
$701$	−2.22105	−0.0838880	−0.0419440	+	0.999120i	$0.513355\pi$
$702$	3.04026	0.114747
$703$	17.8316	0.672530
$704$	37.8849	1.42784
$705$	0	0
$706$	0.0847592	0.00318995
$707$	9.44491	0.355212
$708$	18.6224	0.699871
$709$	46.1903	1.73471	0.867357	−	0.497686i	$-0.165817\pi$
$709$	46.1903	1.73471	0.867357	+	0.497686i	$0.165817\pi$
$710$	0	0
$711$	−11.5932	−0.434779
$712$	−3.82792	−0.143457
$713$	9.77065	0.365914
$714$	1.10528	0.0413641
$715$	0	0
$716$	34.8455	1.30224
$717$	20.3824	0.761196
$718$	1.36053	0.0507747
$719$	−39.7000	−1.48056	−0.740280	−	0.672298i	$-0.765307\pi$
$719$	−39.7000	−1.48056	−0.740280	+	0.672298i	$0.765307\pi$
$720$	0	0
$721$	3.69397	0.137571
$722$	2.80877	0.104532
$723$	−25.3667	−0.943396
$724$	17.1661	0.637973
$725$	0	0
$726$	3.09869	0.115003
$727$	−43.6075	−1.61731	−0.808655	−	0.588283i	$-0.799804\pi$
$727$	−43.6075	−1.61731	−0.808655	+	0.588283i	$0.799804\pi$
$728$	−2.27317	−0.0842492
$729$	18.9958	0.703549
$730$	0	0
$731$	−25.9577	−0.960082
$732$	−12.7683	−0.471928
$733$	27.3492	1.01017	0.505083	−	0.863071i	$-0.331462\pi$
$733$	27.3492	1.01017	0.505083	+	0.863071i	$0.331462\pi$
$734$	−5.32544	−0.196566
$735$	0	0
$736$	2.03652	0.0750670
$737$	0.580907	0.0213980
$738$	1.20906	0.0445062
$739$	16.5135	0.607460	0.303730	−	0.952758i	$-0.401768\pi$
$739$	16.5135	0.607460	0.303730	+	0.952758i	$0.401768\pi$
$740$	0	0
$741$	−6.16090	−0.226326
$742$	−0.313572	−0.0115116
$743$	19.6088	0.719378	0.359689	−	0.933072i	$-0.382883\pi$
$743$	19.6088	0.719378	0.359689	+	0.933072i	$0.382883\pi$
$744$	7.50673	0.275210
$745$	0	0
$746$	−1.24358	−0.0455307
$747$	17.8233	0.652119
$748$	58.4770	2.13813
$749$	18.1514	0.663237
$750$	0	0
$751$	38.1360	1.39160	0.695800	−	0.718235i	$-0.255050\pi$
$751$	38.1360	1.39160	0.695800	+	0.718235i	$0.255050\pi$
$752$	27.4695	1.00171
$753$	5.58748	0.203619
$754$	−5.34535	−0.194666
$755$	0	0
$756$	−10.4602	−0.380435
$757$	17.9450	0.652221	0.326111	−	0.945332i	$-0.394262\pi$
$757$	17.9450	0.652221	0.326111	+	0.945332i	$0.394262\pi$
$758$	4.38540	0.159285
$759$	−5.80858	−0.210838
$760$	0	0
$761$	35.3384	1.28102	0.640508	−	0.767951i	$-0.278724\pi$
$761$	35.3384	1.28102	0.640508	+	0.767951i	$0.278724\pi$
$762$	0.175253	0.00634876
$763$	−5.98333	−0.216611
$764$	−20.9488	−0.757903
$765$	0	0
$766$	−4.49555	−0.162431
$767$	−27.9685	−1.00988
$768$	−15.2609	−0.550680
$769$	29.7565	1.07305	0.536523	−	0.843886i	$-0.319737\pi$
$769$	29.7565	1.07305	0.536523	+	0.843886i	$0.319737\pi$
$770$	0	0
$771$	−23.2788	−0.838366
$772$	−47.3316	−1.70350
$773$	−40.9790	−1.47391	−0.736957	−	0.675940i	$-0.763738\pi$
$773$	−40.9790	−1.47391	−0.736957	+	0.675940i	$0.763738\pi$
$774$	−1.37798	−0.0495303
$775$	0	0
$776$	0.666445	0.0239240
$777$	11.9544	0.428861
$778$	−2.29739	−0.0823654
$779$	−6.64801	−0.238190
$780$	0	0
$781$	77.7876	2.78346
$782$	0.988963	0.0353652
$783$	−49.5688	−1.77145
$784$	3.82100	0.136464
$785$	0	0
$786$	0.660100	0.0235450
$787$	23.2840	0.829985	0.414992	−	0.909825i	$-0.363784\pi$
$787$	23.2840	0.829985	0.414992	+	0.909825i	$0.363784\pi$
$788$	−11.6838	−0.416219
$789$	−10.6045	−0.377531
$790$	0	0
$791$	−17.8826	−0.635833
$792$	6.25579	0.222290
$793$	19.1763	0.680972
$794$	3.63020	0.128831
$795$	0	0
$796$	−40.3686	−1.43083
$797$	14.2114	0.503394	0.251697	−	0.967806i	$-0.419011\pi$
$797$	14.2114	0.503394	0.251697	+	0.967806i	$0.419011\pi$
$798$	−0.322619	−0.0114206
$799$	41.0593	1.45257
$800$	0	0
$801$	9.74985	0.344494
$802$	6.44843	0.227702
$803$	−17.1105	−0.603817
$804$	−0.246089	−0.00867888
$805$	0	0
$806$	−5.59452	−0.197058
$807$	8.08448	0.284587
$808$	6.49281	0.228416
$809$	−43.0468	−1.51344	−0.756722	−	0.653737i	$-0.773200\pi$
$809$	−43.0468	−1.51344	−0.756722	+	0.653737i	$0.773200\pi$
$810$	0	0
$811$	−32.6389	−1.14611	−0.573054	−	0.819518i	$-0.694241\pi$
$811$	−32.6389	−1.14611	−0.573054	+	0.819518i	$0.694241\pi$
$812$	18.3911	0.645400
$813$	−31.2335	−1.09541
$814$	−9.62620	−0.337398
$815$	0	0
$816$	−24.3897	−0.853811
$817$	7.57677	0.265078
$818$	5.55555	0.194245
$819$	5.78984	0.202313
$820$	0	0
$821$	0.619425	0.0216181	0.0108090	−	0.999942i	$-0.496559\pi$
$821$	0.619425	0.0216181	0.0108090	+	0.999942i	$0.496559\pi$
$822$	−1.68686	−0.0588359
$823$	28.7047	1.00058	0.500292	−	0.865857i	$-0.333226\pi$
$823$	28.7047	1.00058	0.500292	+	0.865857i	$0.333226\pi$
$824$	2.53938	0.0884637
$825$	0	0
$826$	−1.46459	−0.0509594
$827$	−20.5684	−0.715232	−0.357616	−	0.933869i	$-0.616410\pi$
$827$	−20.5684	−0.715232	−0.357616	+	0.933869i	$0.616410\pi$
$828$	−3.44937	−0.119874
$829$	−27.9294	−0.970027	−0.485014	−	0.874507i	$-0.661185\pi$
$829$	−27.9294	−0.970027	−0.485014	+	0.874507i	$0.661185\pi$
$830$	0	0
$831$	0.993936	0.0344792
$832$	24.1038	0.835649
$833$	5.71133	0.197886
$834$	0.341762	0.0118342
$835$	0	0
$836$	−17.0688	−0.590336
$837$	−51.8794	−1.79321
$838$	3.96499	0.136968
$839$	16.2144	0.559783	0.279891	−	0.960032i	$-0.409702\pi$
$839$	16.2144	0.559783	0.279891	+	0.960032i	$0.409702\pi$
$840$	0	0
$841$	58.1513	2.00522
$842$	0.942876	0.0324936
$843$	16.0250	0.551932
$844$	−37.5389	−1.29214
$845$	0	0
$846$	2.17965	0.0749379
$847$	16.0119	0.550175
$848$	6.91945	0.237615
$849$	−12.4151	−0.426085
$850$	0	0
$851$	10.6963	0.366665
$852$	−32.9530	−1.12895
$853$	−25.1517	−0.861177	−0.430588	−	0.902548i	$-0.641694\pi$
$853$	−25.1517	−0.861177	−0.430588	+	0.902548i	$0.641694\pi$
$854$	1.00418	0.0343623
$855$	0	0
$856$	12.4780	0.426489
$857$	−35.3759	−1.20842	−0.604208	−	0.796826i	$-0.706511\pi$
$857$	−35.3759	−1.20842	−0.604208	+	0.796826i	$0.706511\pi$
$858$	3.32590	0.113544
$859$	−38.1478	−1.30159	−0.650793	−	0.759255i	$-0.725564\pi$
$859$	−38.1478	−1.30159	−0.650793	+	0.759255i	$0.725564\pi$
$860$	0	0
$861$	−4.45687	−0.151890
$862$	−2.48332	−0.0845824
$863$	46.6973	1.58960	0.794798	−	0.606874i	$-0.207577\pi$
$863$	46.6973	1.58960	0.794798	+	0.606874i	$0.207577\pi$
$864$	−10.8133	−0.367877
$865$	0	0
$866$	0.0274276	0.000932028 0
$867$	−17.4564	−0.592851
$868$	19.2483	0.653331
$869$	−34.4121	−1.16735
$870$	0	0
$871$	0.369595	0.0125233
$872$	−4.11318	−0.139290
$873$	−1.69746	−0.0574503
$874$	−0.288667	−0.00976431
$875$	0	0
$876$	7.24850	0.244904
$877$	14.2620	0.481593	0.240796	−	0.970576i	$-0.422591\pi$
$877$	14.2620	0.481593	0.240796	+	0.970576i	$0.422591\pi$
$878$	2.91331	0.0983194
$879$	−5.88367	−0.198451
$880$	0	0
$881$	−20.2023	−0.680634	−0.340317	−	0.940311i	$-0.610534\pi$
$881$	−20.2023	−0.680634	−0.340317	+	0.940311i	$0.610534\pi$
$882$	0.303188	0.0102089
$883$	0.993471	0.0334330	0.0167165	−	0.999860i	$-0.494679\pi$
$883$	0.993471	0.0334330	0.0167165	+	0.999860i	$0.494679\pi$
$884$	37.2052	1.25135
$885$	0	0
$886$	−6.52324	−0.219153
$887$	−28.1256	−0.944364	−0.472182	−	0.881501i	$-0.656533\pi$
$887$	−28.1256	−0.944364	−0.472182	+	0.881501i	$0.656533\pi$
$888$	8.21792	0.275775
$889$	0.905589	0.0303725
$890$	0	0
$891$	3.54158	0.118648
$892$	−31.7668	−1.06363
$893$	−11.9848	−0.401055
$894$	4.19949	0.140452
$895$	0	0
$896$	5.33524	0.178238
$897$	−3.69564	−0.123394
$898$	1.47442	0.0492021
$899$	91.2138	3.04215
$900$	0	0
$901$	10.3427	0.344564
$902$	3.58886	0.119496
$903$	5.07951	0.169036
$904$	−12.2932	−0.408867
$905$	0	0
$906$	0.538127	0.0178781
$907$	15.3414	0.509402	0.254701	−	0.967020i	$-0.418023\pi$
$907$	15.3414	0.509402	0.254701	+	0.967020i	$0.418023\pi$
$908$	−31.0750	−1.03126
$909$	−16.5374	−0.548511
$910$	0	0
$911$	45.0912	1.49394	0.746968	−	0.664860i	$-0.231509\pi$
$911$	45.0912	1.49394	0.746968	+	0.664860i	$0.231509\pi$
$912$	7.11909	0.235736
$913$	52.9048	1.75089
$914$	−1.33298	−0.0440910
$915$	0	0
$916$	−0.157619	−0.00520787
$917$	3.41094	0.112639
$918$	−5.25112	−0.173313
$919$	6.69907	0.220982	0.110491	−	0.993877i	$-0.464758\pi$
$919$	6.69907	0.220982	0.110491	+	0.993877i	$0.464758\pi$
$920$	0	0
$921$	9.76780	0.321860
$922$	−2.89157	−0.0952287
$923$	49.4914	1.62903
$924$	−11.4430	−0.376447
$925$	0	0
$926$	−1.46787	−0.0482371
$927$	−6.46790	−0.212434
$928$	19.0119	0.624095
$929$	−27.5616	−0.904267	−0.452133	−	0.891950i	$-0.649337\pi$
$929$	−27.5616	−0.904267	−0.452133	+	0.891950i	$0.649337\pi$
$930$	0	0
$931$	−1.66707	−0.0546361
$932$	−6.23750	−0.204316
$933$	22.5507	0.738277
$934$	6.16469	0.201715
$935$	0	0
$936$	3.98017	0.130096
$937$	−55.9032	−1.82628	−0.913140	−	0.407647i	$-0.866349\pi$
$937$	−55.9032	−1.82628	−0.913140	+	0.407647i	$0.866349\pi$
$938$	0.0193541	0.000631932 0
$939$	−7.81941	−0.255177
$940$	0	0
$941$	−2.36394	−0.0770624	−0.0385312	−	0.999257i	$-0.512268\pi$
$941$	−2.36394	−0.0770624	−0.0385312	+	0.999257i	$0.512268\pi$
$942$	−0.0369487	−0.00120385
$943$	−3.98783	−0.129862
$944$	32.3183	1.05187
$945$	0	0
$946$	−4.09025	−0.132985
$947$	−14.1236	−0.458954	−0.229477	−	0.973314i	$-0.573702\pi$
$947$	−14.1236	−0.458954	−0.229477	+	0.973314i	$0.573702\pi$
$948$	14.5779	0.473469
$949$	−10.8863	−0.353386
$950$	0	0
$951$	−29.5642	−0.958684
$952$	3.92620	0.127249
$953$	9.12290	0.295520	0.147760	−	0.989023i	$-0.452794\pi$
$953$	9.12290	0.295520	0.147760	+	0.989023i	$0.452794\pi$
$954$	0.549044	0.0177760
$955$	0	0
$956$	35.9280	1.16199
$957$	−54.2260	−1.75288
$958$	−0.343106	−0.0110852
$959$	−8.71652	−0.281471
$960$	0	0
$961$	64.4655	2.07953
$962$	−6.12455	−0.197463
$963$	−31.7819	−1.02416
$964$	−44.7137	−1.44013
$965$	0	0
$966$	−0.193524	−0.00622654
$967$	−50.9846	−1.63955	−0.819777	−	0.572683i	$-0.805902\pi$
$967$	−50.9846	−1.63955	−0.819777	+	0.572683i	$0.805902\pi$
$968$	11.0072	0.353785
$969$	10.6411	0.341840
$970$	0	0
$971$	−50.0685	−1.60678	−0.803388	−	0.595457i	$-0.796971\pi$
$971$	−50.0685	−1.60678	−0.803388	+	0.595457i	$0.796971\pi$
$972$	29.8804	0.958414
$973$	1.76599	0.0566150
$974$	−5.28884	−0.169465
$975$	0	0
$976$	−22.1588	−0.709285
$977$	−29.3837	−0.940068	−0.470034	−	0.882648i	$-0.655758\pi$
$977$	−29.3837	−0.940068	−0.470034	+	0.882648i	$0.655758\pi$
$978$	−1.32790	−0.0424617
$979$	28.9405	0.924941
$980$	0	0
$981$	10.4764	0.334486
$982$	0.507724	0.0162021
$983$	−19.6111	−0.625498	−0.312749	−	0.949836i	$-0.601250\pi$
$983$	−19.6111	−0.625498	−0.312749	+	0.949836i	$0.601250\pi$
$984$	−3.06383	−0.0976713
$985$	0	0
$986$	9.23245	0.294021
$987$	−8.03465	−0.255746
$988$	−10.8598	−0.345496
$989$	4.54495	0.144521
$990$	0	0
$991$	−28.0961	−0.892503	−0.446251	−	0.894908i	$-0.647241\pi$
$991$	−28.0961	−0.892503	−0.446251	+	0.894908i	$0.647241\pi$
$992$	19.8981	0.631765
$993$	−15.0758	−0.478417
$994$	2.59164	0.0822020
$995$	0	0
$996$	−22.4120	−0.710150
$997$	−57.6120	−1.82459	−0.912295	−	0.409534i	$-0.865691\pi$
$997$	−57.6120	−1.82459	−0.912295	+	0.409534i	$0.865691\pi$
$998$	0.838417	0.0265396
$999$	−56.7945	−1.79690

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4025.2.a.r.1.2		5
5.4	even	2		805.2.a.k.1.4	✓	5
15.14	odd	2		7245.2.a.bi.1.2		5
35.34	odd	2		5635.2.a.x.1.4		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
805.2.a.k.1.4	✓	5	5.4	even	2
4025.2.a.r.1.2		5	1.1	even	1	trivial
5635.2.a.x.1.4		5	35.34	odd	2
7245.2.a.bi.1.2		5	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)

\(f(q)\)	\(=\)	\(q-0.173158 q^{2} -1.11762 q^{3} -1.97002 q^{4} +0.193524 q^{6} +1.00000 q^{7} +0.687440 q^{8} -1.75093 q^{9} +O(q^{10})\)	\(q-0.173158 q^{2} -1.11762 q^{3} -1.97002 q^{4} +0.193524 q^{6} +1.00000 q^{7} +0.687440 q^{8} -1.75093 q^{9} -5.19730 q^{11} +2.20172 q^{12} -3.30671 q^{13} -0.173158 q^{14} +3.82100 q^{16} +5.71133 q^{17} +0.303188 q^{18} -1.66707 q^{19} -1.11762 q^{21} +0.899953 q^{22} -1.00000 q^{23} -0.768294 q^{24} +0.572584 q^{26} +5.30972 q^{27} -1.97002 q^{28} -9.33549 q^{29} -9.77065 q^{31} -2.03652 q^{32} +5.80858 q^{33} -0.988963 q^{34} +3.44937 q^{36} -10.6963 q^{37} +0.288667 q^{38} +3.69564 q^{39} +3.98783 q^{41} +0.193524 q^{42} -4.54495 q^{43} +10.2388 q^{44} +0.173158 q^{46} +7.18910 q^{47} -4.27041 q^{48} +1.00000 q^{49} -6.38308 q^{51} +6.51428 q^{52} +1.81090 q^{53} -0.919421 q^{54} +0.687440 q^{56} +1.86315 q^{57} +1.61651 q^{58} +8.45809 q^{59} -5.79921 q^{61} +1.69187 q^{62} -1.75093 q^{63} -7.28935 q^{64} -1.00580 q^{66} -0.111771 q^{67} -11.2514 q^{68} +1.11762 q^{69} -14.9669 q^{71} -1.20366 q^{72} +3.29219 q^{73} +1.85215 q^{74} +3.28416 q^{76} -5.19730 q^{77} -0.639929 q^{78} +6.62115 q^{79} -0.681428 q^{81} -0.690525 q^{82} -10.1793 q^{83} +2.20172 q^{84} +0.786995 q^{86} +10.4335 q^{87} -3.57283 q^{88} -5.56837 q^{89} -3.30671 q^{91} +1.97002 q^{92} +10.9198 q^{93} -1.24485 q^{94} +2.27604 q^{96} +0.969460 q^{97} -0.173158 q^{98} +9.10012 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 3 q^{2} + 6 q^{3} + 3 q^{4} + 7 q^{6} + 5 q^{7} + 3 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q + 3 * q^2 + 6 * q^3 + 3 * q^4 + 7 * q^6 + 5 * q^7 + 3 * q^8 + 5 * q^9	\( 5 q + 3 q^{2} + 6 q^{3} + 3 q^{4} + 7 q^{6} + 5 q^{7} + 3 q^{8} + 5 q^{9} - 11 q^{11} + 14 q^{12} + 7 q^{13} + 3 q^{14} - q^{16} - q^{17} + 17 q^{18} + 2 q^{19} + 6 q^{21} - 2 q^{22} - 5 q^{23} + 12 q^{24} + 8 q^{26} + 15 q^{27} + 3 q^{28} - 14 q^{29} - 6 q^{31} + 4 q^{32} - 22 q^{33} + 4 q^{34} + 28 q^{36} + q^{37} + 31 q^{38} + 15 q^{39} + 7 q^{41} + 7 q^{42} + 12 q^{43} - 11 q^{44} - 3 q^{46} + 24 q^{47} + 4 q^{48} + 5 q^{49} - 28 q^{51} + 36 q^{52} + 21 q^{53} + 49 q^{54} + 3 q^{56} + 15 q^{57} - 9 q^{58} - q^{59} + 7 q^{61} + 26 q^{62} + 5 q^{63} - 15 q^{64} - 45 q^{66} + 35 q^{67} - 43 q^{68} - 6 q^{69} - 32 q^{71} + 36 q^{72} + 7 q^{73} - 10 q^{74} + 10 q^{76} - 11 q^{77} + 8 q^{78} + 18 q^{79} + 21 q^{81} - 33 q^{82} + q^{83} + 14 q^{84} - 26 q^{86} + 18 q^{87} - 41 q^{88} + q^{89} + 7 q^{91} - 3 q^{92} + 19 q^{93} + 14 q^{94} + 26 q^{96} + 9 q^{97} + 3 q^{98} - 54 q^{99}+O(q^{100}) \) 5 * q + 3 * q^2 + 6 * q^3 + 3 * q^4 + 7 * q^6 + 5 * q^7 + 3 * q^8 + 5 * q^9 - 11 * q^11 + 14 * q^12 + 7 * q^13 + 3 * q^14 - q^16 - q^17 + 17 * q^18 + 2 * q^19 + 6 * q^21 - 2 * q^22 - 5 * q^23 + 12 * q^24 + 8 * q^26 + 15 * q^27 + 3 * q^28 - 14 * q^29 - 6 * q^31 + 4 * q^32 - 22 * q^33 + 4 * q^34 + 28 * q^36 + q^37 + 31 * q^38 + 15 * q^39 + 7 * q^41 + 7 * q^42 + 12 * q^43 - 11 * q^44 - 3 * q^46 + 24 * q^47 + 4 * q^48 + 5 * q^49 - 28 * q^51 + 36 * q^52 + 21 * q^53 + 49 * q^54 + 3 * q^56 + 15 * q^57 - 9 * q^58 - q^59 + 7 * q^61 + 26 * q^62 + 5 * q^63 - 15 * q^64 - 45 * q^66 + 35 * q^67 - 43 * q^68 - 6 * q^69 - 32 * q^71 + 36 * q^72 + 7 * q^73 - 10 * q^74 + 10 * q^76 - 11 * q^77 + 8 * q^78 + 18 * q^79 + 21 * q^81 - 33 * q^82 + q^83 + 14 * q^84 - 26 * q^86 + 18 * q^87 - 41 * q^88 + q^89 + 7 * q^91 - 3 * q^92 + 19 * q^93 + 14 * q^94 + 26 * q^96 + 9 * q^97 + 3 * q^98 - 54 * q^99

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