LMFDB - Embedded newform 4025.2.a.ba.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4025,2,Mod(1,4025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4025, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4025 = 5^{2} \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4025.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$32.1397868136$
Analytic rank:	$1$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - x^{13} - 22 x^{12} + 18 x^{11} + 187 x^{10} - 118 x^{9} - 772 x^{8} + 346 x^{7} + 1581 x^{6} + \cdots - 5 $ x^14 - x^13 - 22x^12 + 18x^11 + 187x^10 - 118x^9 - 772x^8 + 346x^7 + 1581x^6 - 443x^5 - 1429x^4 + 193x^3 + 386x^2 - 3x - 5
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$-0.116065$ 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)

$f(q)$	$=$	$q+0.116065 q^{2} -1.59146 q^{3} -1.98653 q^{4} -0.184713 q^{6} -1.00000 q^{7} -0.462695 q^{8} -0.467244 q^{9} +O(q^{10})$	\(q+0.116065 q^{2} -1.59146 q^{3} -1.98653 q^{4} -0.184713 q^{6} -1.00000 q^{7} -0.462695 q^{8} -0.467244 q^{9} -1.22412 q^{11} +3.16149 q^{12} +1.70360 q^{13} -0.116065 q^{14} +3.91936 q^{16} -4.88967 q^{17} -0.0542305 q^{18} +5.51171 q^{19} +1.59146 q^{21} -0.142077 q^{22} +1.00000 q^{23} +0.736362 q^{24} +0.197728 q^{26} +5.51799 q^{27} +1.98653 q^{28} -7.24729 q^{29} +3.84864 q^{31} +1.38029 q^{32} +1.94815 q^{33} -0.567518 q^{34} +0.928194 q^{36} -3.73599 q^{37} +0.639715 q^{38} -2.71122 q^{39} +4.64219 q^{41} +0.184713 q^{42} -4.98862 q^{43} +2.43175 q^{44} +0.116065 q^{46} +8.46013 q^{47} -6.23751 q^{48} +1.00000 q^{49} +7.78173 q^{51} -3.38426 q^{52} +12.2042 q^{53} +0.640444 q^{54} +0.462695 q^{56} -8.77168 q^{57} -0.841155 q^{58} -3.85329 q^{59} +12.6015 q^{61} +0.446692 q^{62} +0.467244 q^{63} -7.67851 q^{64} +0.226111 q^{66} +0.573683 q^{67} +9.71346 q^{68} -1.59146 q^{69} +11.8752 q^{71} +0.216191 q^{72} -1.42358 q^{73} -0.433616 q^{74} -10.9492 q^{76} +1.22412 q^{77} -0.314677 q^{78} -1.12465 q^{79} -7.37995 q^{81} +0.538794 q^{82} -13.2626 q^{83} -3.16149 q^{84} -0.579003 q^{86} +11.5338 q^{87} +0.566395 q^{88} +2.34206 q^{89} -1.70360 q^{91} -1.98653 q^{92} -6.12498 q^{93} +0.981922 q^{94} -2.19668 q^{96} -18.8773 q^{97} +0.116065 q^{98} +0.571963 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - q^{2} - 6 q^{3} + 17 q^{4} - 4 q^{6} - 14 q^{7} - 9 q^{8} + 18 q^{9}+O(q^{10}) $ 14 * q - q^2 - 6 * q^3 + 17 * q^4 - 4 * q^6 - 14 * q^7 - 9 * q^8 + 18 * q^9	$ 14 q - q^{2} - 6 q^{3} + 17 q^{4} - 4 q^{6} - 14 q^{7} - 9 q^{8} + 18 q^{9} - 3 q^{11} - 11 q^{12} - 15 q^{13} + q^{14} + 23 q^{16} - 9 q^{17} - 17 q^{18} - 4 q^{19} + 6 q^{21} - 9 q^{22} + 14 q^{23} + 10 q^{24} - 5 q^{26} - 33 q^{27} - 17 q^{28} + 11 q^{29} - q^{31} - 24 q^{32} - 26 q^{33} - 6 q^{34} + 13 q^{36} - 18 q^{37} + 6 q^{38} + 6 q^{39} - 7 q^{41} + 4 q^{42} - 18 q^{43} - 16 q^{44} - q^{46} - 10 q^{47} - 40 q^{48} + 14 q^{49} + 28 q^{51} - 46 q^{52} - 5 q^{53} - 24 q^{54} + 9 q^{56} + 26 q^{57} - 2 q^{58} - 24 q^{59} - 6 q^{61} + 16 q^{62} - 18 q^{63} + 29 q^{64} + 27 q^{66} - 61 q^{67} - 35 q^{68} - 6 q^{69} + 11 q^{71} - 12 q^{72} - 28 q^{73} - 49 q^{74} - 27 q^{76} + 3 q^{77} - 38 q^{78} + 6 q^{79} + 26 q^{81} + 14 q^{82} - 16 q^{83} + 11 q^{84} + 46 q^{86} - 61 q^{87} - 58 q^{88} - 39 q^{89} + 15 q^{91} + 17 q^{92} - 21 q^{93} - 74 q^{94} + 41 q^{96} - 19 q^{97} - q^{98} - 9 q^{99}+O(q^{100}) $ 14 * q - q^2 - 6 * q^3 + 17 * q^4 - 4 * q^6 - 14 * q^7 - 9 * q^8 + 18 * q^9 - 3 * q^11 - 11 * q^12 - 15 * q^13 + q^14 + 23 * q^16 - 9 * q^17 - 17 * q^18 - 4 * q^19 + 6 * q^21 - 9 * q^22 + 14 * q^23 + 10 * q^24 - 5 * q^26 - 33 * q^27 - 17 * q^28 + 11 * q^29 - q^31 - 24 * q^32 - 26 * q^33 - 6 * q^34 + 13 * q^36 - 18 * q^37 + 6 * q^38 + 6 * q^39 - 7 * q^41 + 4 * q^42 - 18 * q^43 - 16 * q^44 - q^46 - 10 * q^47 - 40 * q^48 + 14 * q^49 + 28 * q^51 - 46 * q^52 - 5 * q^53 - 24 * q^54 + 9 * q^56 + 26 * q^57 - 2 * q^58 - 24 * q^59 - 6 * q^61 + 16 * q^62 - 18 * q^63 + 29 * q^64 + 27 * q^66 - 61 * q^67 - 35 * q^68 - 6 * q^69 + 11 * q^71 - 12 * q^72 - 28 * q^73 - 49 * q^74 - 27 * q^76 + 3 * q^77 - 38 * q^78 + 6 * q^79 + 26 * q^81 + 14 * q^82 - 16 * q^83 + 11 * q^84 + 46 * q^86 - 61 * q^87 - 58 * q^88 - 39 * q^89 + 15 * q^91 + 17 * q^92 - 21 * q^93 - 74 * q^94 + 41 * q^96 - 19 * q^97 - q^98 - 9 * 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 $

$2$	0.116065	0.0820701	0.0410351	−	0.999158i	$-0.486934\pi$
$2$	0.116065	0.0820701	0.0410351	+	0.999158i	$0.486934\pi$
$3$	−1.59146	−0.918832	−0.459416	−	0.888221i	$-0.651941\pi$
$3$	−1.59146	−0.918832	−0.459416	+	0.888221i	$0.651941\pi$
$4$	−1.98653	−0.993264
$5$	0	0
$5$	0	0
$6$	−0.184713	−0.0754086
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−0.462695	−0.163587
$9$	−0.467244	−0.155748
$10$	0	0
$11$	−1.22412	−0.369087	−0.184543	−	0.982824i	$-0.559081\pi$
$11$	−1.22412	−0.369087	−0.184543	+	0.982824i	$0.559081\pi$
$12$	3.16149	0.912643
$13$	1.70360	0.472495	0.236247	−	0.971693i	$-0.424082\pi$
$13$	1.70360	0.472495	0.236247	+	0.971693i	$0.424082\pi$
$14$	−0.116065	−0.0310196
$15$	0	0
$16$	3.91936	0.979839
$17$	−4.88967	−1.18592	−0.592959	−	0.805233i	$-0.702040\pi$
$17$	−4.88967	−1.18592	−0.592959	+	0.805233i	$0.702040\pi$
$18$	−0.0542305	−0.0127823
$19$	5.51171	1.26447	0.632236	−	0.774776i	$-0.282137\pi$
$19$	5.51171	1.26447	0.632236	+	0.774776i	$0.282137\pi$
$20$	0	0
$21$	1.59146	0.347286
$22$	−0.142077	−0.0302910
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	0.736362	0.150309
$25$	0	0
$26$	0.197728	0.0387777
$27$	5.51799	1.06194
$28$	1.98653	0.375419
$29$	−7.24729	−1.34579	−0.672894	−	0.739739i	$-0.734949\pi$
$29$	−7.24729	−1.34579	−0.672894	+	0.739739i	$0.734949\pi$
$30$	0	0
$31$	3.84864	0.691237	0.345618	−	0.938375i	$-0.387669\pi$
$31$	3.84864	0.691237	0.345618	+	0.938375i	$0.387669\pi$
$32$	1.38029	0.244003
$33$	1.94815	0.339129
$34$	−0.567518	−0.0973285
$35$	0	0
$36$	0.928194	0.154699
$37$	−3.73599	−0.614193	−0.307096	−	0.951678i	$-0.599357\pi$
$37$	−3.73599	−0.614193	−0.307096	+	0.951678i	$0.599357\pi$
$38$	0.639715	0.103775
$39$	−2.71122	−0.434143
$40$	0	0
$41$	4.64219	0.724988	0.362494	−	0.931986i	$-0.381925\pi$
$41$	4.64219	0.724988	0.362494	+	0.931986i	$0.381925\pi$
$42$	0.184713	0.0285018
$43$	−4.98862	−0.760758	−0.380379	−	0.924831i	$-0.624206\pi$
$43$	−4.98862	−0.760758	−0.380379	+	0.924831i	$0.624206\pi$
$44$	2.43175	0.366601
$45$	0	0
$46$	0.116065	0.0171128
$47$	8.46013	1.23404	0.617018	−	0.786949i	$-0.288340\pi$
$47$	8.46013	1.23404	0.617018	+	0.786949i	$0.288340\pi$
$48$	−6.23751	−0.900307
$49$	1.00000	0.142857
$50$	0	0
$51$	7.78173	1.08966
$52$	−3.38426	−0.469312
$53$	12.2042	1.67637	0.838185	−	0.545386i	$-0.183617\pi$
$53$	12.2042	1.67637	0.838185	+	0.545386i	$0.183617\pi$
$54$	0.640444	0.0871534
$55$	0	0
$56$	0.462695	0.0618302
$57$	−8.77168	−1.16184
$58$	−0.841155	−0.110449
$59$	−3.85329	−0.501655	−0.250828	−	0.968032i	$-0.580703\pi$
$59$	−3.85329	−0.501655	−0.250828	+	0.968032i	$0.580703\pi$
$60$	0	0
$61$	12.6015	1.61346	0.806731	−	0.590919i	$-0.201235\pi$
$61$	12.6015	1.61346	0.806731	+	0.590919i	$0.201235\pi$
$62$	0.446692	0.0567299
$63$	0.467244	0.0588672
$64$	−7.67851	−0.959814
$65$	0	0
$66$	0.226111	0.0278323
$67$	0.573683	0.0700865	0.0350433	−	0.999386i	$-0.488843\pi$
$67$	0.573683	0.0700865	0.0350433	+	0.999386i	$0.488843\pi$
$68$	9.71346	1.17793
$69$	−1.59146	−0.191590
$70$	0	0
$71$	11.8752	1.40933	0.704665	−	0.709540i	$-0.251097\pi$
$71$	11.8752	1.40933	0.704665	+	0.709540i	$0.251097\pi$
$72$	0.216191	0.0254784
$73$	−1.42358	−0.166618	−0.0833089	−	0.996524i	$-0.526549\pi$
$73$	−1.42358	−0.166618	−0.0833089	+	0.996524i	$0.526549\pi$
$74$	−0.433616	−0.0504069
$75$	0	0
$76$	−10.9492	−1.25596
$77$	1.22412	0.139502
$78$	−0.314677	−0.0356302
$79$	−1.12465	−0.126533	−0.0632666	−	0.997997i	$-0.520152\pi$
$79$	−1.12465	−0.126533	−0.0632666	+	0.997997i	$0.520152\pi$
$80$	0	0
$81$	−7.37995	−0.819995
$82$	0.538794	0.0594998
$83$	−13.2626	−1.45576	−0.727882	−	0.685702i	$-0.759495\pi$
$83$	−13.2626	−1.45576	−0.727882	+	0.685702i	$0.759495\pi$
$84$	−3.16149	−0.344947
$85$	0	0
$86$	−0.579003	−0.0624355
$87$	11.5338	1.23655
$88$	0.566395	0.0603779
$89$	2.34206	0.248257	0.124129	−	0.992266i	$-0.460386\pi$
$89$	2.34206	0.248257	0.124129	+	0.992266i	$0.460386\pi$
$90$	0	0
$91$	−1.70360	−0.178586
$92$	−1.98653	−0.207110
$93$	−6.12498	−0.635131
$94$	0.981922	0.101278
$95$	0	0
$96$	−2.19668	−0.224198
$97$	−18.8773	−1.91670	−0.958349	−	0.285600i	$-0.907807\pi$
$97$	−18.8773	−1.91670	−0.958349	+	0.285600i	$0.907807\pi$
$98$	0.116065	0.0117243
$99$	0.571963	0.0574845
$100$	0	0
$101$	18.9592	1.88651	0.943257	−	0.332064i	$-0.107745\pi$
$101$	18.9592	1.88651	0.943257	+	0.332064i	$0.107745\pi$
$102$	0.903183	0.0894285
$103$	−15.3786	−1.51530	−0.757649	−	0.652662i	$-0.773652\pi$
$103$	−15.3786	−1.51530	−0.757649	+	0.652662i	$0.773652\pi$
$104$	−0.788249	−0.0772942
$105$	0	0
$106$	1.41647	0.137580
$107$	−3.47012	−0.335469	−0.167735	−	0.985832i	$-0.553645\pi$
$107$	−3.47012	−0.335469	−0.167735	+	0.985832i	$0.553645\pi$
$108$	−10.9617	−1.05479
$109$	−5.32802	−0.510332	−0.255166	−	0.966897i	$-0.582130\pi$
$109$	−5.32802	−0.510332	−0.255166	+	0.966897i	$0.582130\pi$
$110$	0	0
$111$	5.94569	0.564340
$112$	−3.91936	−0.370344
$113$	−0.597747	−0.0562313	−0.0281157	−	0.999605i	$-0.508951\pi$
$113$	−0.597747	−0.0562313	−0.0281157	+	0.999605i	$0.508951\pi$
$114$	−1.01808	−0.0953522
$115$	0	0
$116$	14.3970	1.33672
$117$	−0.795998	−0.0735901
$118$	−0.447230	−0.0411709
$119$	4.88967	0.448235
$120$	0	0
$121$	−9.50153	−0.863775
$122$	1.46259	0.132417
$123$	−7.38787	−0.666142
$124$	−7.64544	−0.686581
$125$	0	0
$126$	0.0542305	0.00483124
$127$	−17.9809	−1.59555	−0.797776	−	0.602955i	$-0.793990\pi$
$127$	−17.9809	−1.59555	−0.797776	+	0.602955i	$0.793990\pi$
$128$	−3.65178	−0.322775
$129$	7.93921	0.699008
$130$	0	0
$131$	−12.5386	−1.09550	−0.547751	−	0.836641i	$-0.684516\pi$
$131$	−12.5386	−1.09550	−0.547751	+	0.836641i	$0.684516\pi$
$132$	−3.87005	−0.336844
$133$	−5.51171	−0.477926
$134$	0.0665843	0.00575201
$135$	0	0
$136$	2.26243	0.194001
$137$	−2.65763	−0.227056	−0.113528	−	0.993535i	$-0.536215\pi$
$137$	−2.65763	−0.227056	−0.113528	+	0.993535i	$0.536215\pi$
$138$	−0.184713	−0.0157238
$139$	7.57463	0.642472	0.321236	−	0.946999i	$-0.395902\pi$
$139$	7.57463	0.642472	0.321236	+	0.946999i	$0.395902\pi$
$140$	0	0
$141$	−13.4640	−1.13387
$142$	1.37829	0.115664
$143$	−2.08542	−0.174391
$144$	−1.83129	−0.152608
$145$	0	0
$146$	−0.165228	−0.0136743
$147$	−1.59146	−0.131262
$148$	7.42165	0.610056
$149$	16.1528	1.32329	0.661645	−	0.749818i	$-0.269859\pi$
$149$	16.1528	1.32329	0.661645	+	0.749818i	$0.269859\pi$
$150$	0	0
$151$	14.0544	1.14373	0.571865	−	0.820348i	$-0.306220\pi$
$151$	14.0544	1.14373	0.571865	+	0.820348i	$0.306220\pi$
$152$	−2.55024	−0.206852
$153$	2.28467	0.184704
$154$	0.142077	0.0114489
$155$	0	0
$156$	5.38592	0.431219
$157$	−15.4122	−1.23003	−0.615013	−	0.788517i	$-0.710849\pi$
$157$	−15.4122	−1.23003	−0.615013	+	0.788517i	$0.710849\pi$
$158$	−0.130532	−0.0103846
$159$	−19.4225	−1.54030
$160$	0	0
$161$	−1.00000	−0.0788110
$162$	−0.856552	−0.0672970
$163$	17.3362	1.35788	0.678938	−	0.734196i	$-0.262441\pi$
$163$	17.3362	1.35788	0.678938	+	0.734196i	$0.262441\pi$
$164$	−9.22184	−0.720104
$165$	0	0
$166$	−1.53932	−0.119475
$167$	3.20860	0.248289	0.124144	−	0.992264i	$-0.460381\pi$
$167$	3.20860	0.248289	0.124144	+	0.992264i	$0.460381\pi$
$168$	−0.736362	−0.0568116
$169$	−10.0977	−0.776749
$170$	0	0
$171$	−2.57531	−0.196939
$172$	9.91004	0.755634
$173$	−13.9724	−1.06230	−0.531150	−	0.847278i	$-0.678240\pi$
$173$	−13.9724	−1.06230	−0.531150	+	0.847278i	$0.678240\pi$
$174$	1.33867	0.101484
$175$	0	0
$176$	−4.79777	−0.361645
$177$	6.13236	0.460937
$178$	0.271830	0.0203745
$179$	−23.0884	−1.72571	−0.862855	−	0.505452i	$-0.831326\pi$
$179$	−23.0884	−1.72571	−0.862855	+	0.505452i	$0.831326\pi$
$180$	0	0
$181$	−8.57755	−0.637564	−0.318782	−	0.947828i	$-0.603274\pi$
$181$	−8.57755	−0.637564	−0.318782	+	0.947828i	$0.603274\pi$
$182$	−0.197728	−0.0146566
$183$	−20.0549	−1.48250
$184$	−0.462695	−0.0341103
$185$	0	0
$186$	−0.710893	−0.0521252
$187$	5.98555	0.437707
$188$	−16.8063	−1.22572
$189$	−5.51799	−0.401375
$190$	0	0
$191$	24.9215	1.80326	0.901629	−	0.432511i	$-0.142372\pi$
$191$	24.9215	1.80326	0.901629	+	0.432511i	$0.142372\pi$
$192$	12.2201	0.881907
$193$	−14.9464	−1.07587	−0.537933	−	0.842988i	$-0.680795\pi$
$193$	−14.9464	−1.07587	−0.537933	+	0.842988i	$0.680795\pi$
$194$	−2.19099	−0.157304
$195$	0	0
$196$	−1.98653	−0.141895
$197$	9.44487	0.672919	0.336459	−	0.941698i	$-0.390771\pi$
$197$	9.44487	0.672919	0.336459	+	0.941698i	$0.390771\pi$
$198$	0.0663847	0.00471776
$199$	16.1276	1.14326	0.571629	−	0.820512i	$-0.306312\pi$
$199$	16.1276	1.14326	0.571629	+	0.820512i	$0.306312\pi$
$200$	0	0
$201$	−0.912995	−0.0643977
$202$	2.20050	0.154826
$203$	7.24729	0.508660
$204$	−15.4586	−1.08232
$205$	0	0
$206$	−1.78491	−0.124361
$207$	−0.467244	−0.0324757
$208$	6.67703	0.462969
$209$	−6.74700	−0.466700
$210$	0	0
$211$	−21.9969	−1.51433	−0.757164	−	0.653225i	$-0.773416\pi$
$211$	−21.9969	−1.51433	−0.757164	+	0.653225i	$0.773416\pi$
$212$	−24.2439	−1.66508
$213$	−18.8990	−1.29494
$214$	−0.402758	−0.0275320
$215$	0	0
$216$	−2.55315	−0.173720
$217$	−3.84864	−0.261263
$218$	−0.618395	−0.0418830
$219$	2.26558	0.153094
$220$	0	0
$221$	−8.33005	−0.560340
$222$	0.690085	0.0463154
$223$	20.6765	1.38460	0.692301	−	0.721609i	$-0.256597\pi$
$223$	20.6765	1.38460	0.692301	+	0.721609i	$0.256597\pi$
$224$	−1.38029	−0.0922244
$225$	0	0
$226$	−0.0693773	−0.00461491
$227$	−18.8712	−1.25252	−0.626262	−	0.779613i	$-0.715416\pi$
$227$	−18.8712	−1.25252	−0.626262	+	0.779613i	$0.715416\pi$
$228$	17.4252	1.15401
$229$	0.434043	0.0286824	0.0143412	−	0.999897i	$-0.495435\pi$
$229$	0.434043	0.0286824	0.0143412	+	0.999897i	$0.495435\pi$
$230$	0	0
$231$	−1.94815	−0.128179
$232$	3.35329	0.220154
$233$	8.64575	0.566402	0.283201	−	0.959061i	$-0.408604\pi$
$233$	8.64575	0.566402	0.283201	+	0.959061i	$0.408604\pi$
$234$	−0.0923873	−0.00603955
$235$	0	0
$236$	7.65466	0.498276
$237$	1.78984	0.116263
$238$	0.567518	0.0367867
$239$	2.01228	0.130163	0.0650817	−	0.997880i	$-0.479269\pi$
$239$	2.01228	0.130163	0.0650817	+	0.997880i	$0.479269\pi$
$240$	0	0
$241$	−12.5342	−0.807397	−0.403698	−	0.914892i	$-0.632275\pi$
$241$	−12.5342	−0.807397	−0.403698	+	0.914892i	$0.632275\pi$
$242$	−1.10279	−0.0708901
$243$	−4.80905	−0.308501
$244$	−25.0333	−1.60259
$245$	0	0
$246$	−0.857471	−0.0546703
$247$	9.38977	0.597457
$248$	−1.78075	−0.113078
$249$	21.1070	1.33760
$250$	0	0
$251$	−15.6325	−0.986714	−0.493357	−	0.869827i	$-0.664230\pi$
$251$	−15.6325	−0.986714	−0.493357	+	0.869827i	$0.664230\pi$
$252$	−0.928194	−0.0584707
$253$	−1.22412	−0.0769599
$254$	−2.08695	−0.130947
$255$	0	0
$256$	14.9332	0.933323
$257$	6.50759	0.405932	0.202966	−	0.979186i	$-0.434942\pi$
$257$	6.50759	0.405932	0.202966	+	0.979186i	$0.434942\pi$
$258$	0.921462	0.0573677
$259$	3.73599	0.232143
$260$	0	0
$261$	3.38625	0.209604
$262$	−1.45529	−0.0899080
$263$	−13.9472	−0.860019	−0.430010	−	0.902824i	$-0.641490\pi$
$263$	−13.9472	−0.860019	−0.430010	+	0.902824i	$0.641490\pi$
$264$	−0.901397	−0.0554772
$265$	0	0
$266$	−0.639715	−0.0392234
$267$	−3.72730	−0.228107
$268$	−1.13964	−0.0696144
$269$	22.2583	1.35711	0.678555	−	0.734549i	$-0.262606\pi$
$269$	22.2583	1.35711	0.678555	+	0.734549i	$0.262606\pi$
$270$	0	0
$271$	−20.8704	−1.26779	−0.633894	−	0.773420i	$-0.718544\pi$
$271$	−20.8704	−1.26779	−0.633894	+	0.773420i	$0.718544\pi$
$272$	−19.1643	−1.16201
$273$	2.71122	0.164091
$274$	−0.308457	−0.0186345
$275$	0	0
$276$	3.16149	0.190299
$277$	−17.3637	−1.04328	−0.521642	−	0.853165i	$-0.674680\pi$
$277$	−17.3637	−1.04328	−0.521642	+	0.853165i	$0.674680\pi$
$278$	0.879147	0.0527277
$279$	−1.79826	−0.107659
$280$	0	0
$281$	−1.65285	−0.0986006	−0.0493003	−	0.998784i	$-0.515699\pi$
$281$	−1.65285	−0.0986006	−0.0493003	+	0.998784i	$0.515699\pi$
$282$	−1.56269	−0.0930570
$283$	−32.1515	−1.91121	−0.955604	−	0.294654i	$-0.904796\pi$
$283$	−32.1515	−1.91121	−0.955604	+	0.294654i	$0.904796\pi$
$284$	−23.5905	−1.39984
$285$	0	0
$286$	−0.242043	−0.0143123
$287$	−4.64219	−0.274020
$288$	−0.644932	−0.0380030
$289$	6.90884	0.406402
$290$	0	0
$291$	30.0425	1.76112
$292$	2.82799	0.165495
$293$	−12.6726	−0.740341	−0.370170	−	0.928964i	$-0.620701\pi$
$293$	−12.6726	−0.740341	−0.370170	+	0.928964i	$0.620701\pi$
$294$	−0.184713	−0.0107727
$295$	0	0
$296$	1.72862	0.100474
$297$	−6.75469	−0.391947
$298$	1.87477	0.108602
$299$	1.70360	0.0985219
$300$	0	0
$301$	4.98862	0.287539
$302$	1.63122	0.0938661
$303$	−30.1729	−1.73339
$304$	21.6023	1.23898
$305$	0	0
$306$	0.265169	0.0151587
$307$	−3.82773	−0.218460	−0.109230	−	0.994016i	$-0.534839\pi$
$307$	−3.82773	−0.218460	−0.109230	+	0.994016i	$0.534839\pi$
$308$	−2.43175	−0.138562
$309$	24.4745	1.39231
$310$	0	0
$311$	−1.12488	−0.0637859	−0.0318930	−	0.999491i	$-0.510154\pi$
$311$	−1.12488	−0.0637859	−0.0318930	+	0.999491i	$0.510154\pi$
$312$	1.25447	0.0710204
$313$	14.4888	0.818958	0.409479	−	0.912320i	$-0.365711\pi$
$313$	14.4888	0.818958	0.409479	+	0.912320i	$0.365711\pi$
$314$	−1.78881	−0.100948
$315$	0	0
$316$	2.23415	0.125681
$317$	21.7630	1.22233	0.611166	−	0.791503i	$-0.290701\pi$
$317$	21.7630	1.22233	0.611166	+	0.791503i	$0.290701\pi$
$318$	−2.25426	−0.126413
$319$	8.87157	0.496712
$320$	0	0
$321$	5.52257	0.308240
$322$	−0.116065	−0.00646803
$323$	−26.9504	−1.49956
$324$	14.6605	0.814472
$325$	0	0
$326$	2.01212	0.111441
$327$	8.47935	0.468909
$328$	−2.14792	−0.118599
$329$	−8.46013	−0.466422
$330$	0	0
$331$	−21.9371	−1.20577	−0.602887	−	0.797827i	$-0.705983\pi$
$331$	−21.9371	−1.20577	−0.602887	+	0.797827i	$0.705983\pi$
$332$	26.3466	1.44596
$333$	1.74562	0.0956593
$334$	0.372405	0.0203771
$335$	0	0
$336$	6.23751	0.340284
$337$	2.15813	0.117561	0.0587803	−	0.998271i	$-0.481279\pi$
$337$	2.15813	0.117561	0.0587803	+	0.998271i	$0.481279\pi$
$338$	−1.17199	−0.0637479
$339$	0.951293	0.0516671
$340$	0	0
$341$	−4.71121	−0.255126
$342$	−0.298903	−0.0161628
$343$	−1.00000	−0.0539949
$344$	2.30821	0.124450
$345$	0	0
$346$	−1.62170	−0.0871831
$347$	23.0102	1.23525	0.617625	−	0.786473i	$-0.288095\pi$
$347$	23.0102	1.23525	0.617625	+	0.786473i	$0.288095\pi$
$348$	−22.9122	−1.22822
$349$	20.2375	1.08329	0.541644	−	0.840608i	$-0.317802\pi$
$349$	20.2375	1.08329	0.541644	+	0.840608i	$0.317802\pi$
$350$	0	0
$351$	9.40047	0.501760
$352$	−1.68964	−0.0900582
$353$	−15.5852	−0.829518	−0.414759	−	0.909931i	$-0.636134\pi$
$353$	−15.5852	−0.829518	−0.414759	+	0.909931i	$0.636134\pi$
$354$	0.711751	0.0378291
$355$	0	0
$356$	−4.65256	−0.246585
$357$	−7.78173	−0.411853
$358$	−2.67975	−0.141629
$359$	−27.7720	−1.46575	−0.732875	−	0.680363i	$-0.761822\pi$
$359$	−27.7720	−1.46575	−0.732875	+	0.680363i	$0.761822\pi$
$360$	0	0
$361$	11.3789	0.598891
$362$	−0.995550	−0.0523250
$363$	15.1213	0.793664
$364$	3.38426	0.177383
$365$	0	0
$366$	−2.32766	−0.121669
$367$	−16.7182	−0.872682	−0.436341	−	0.899781i	$-0.643726\pi$
$367$	−16.7182	−0.872682	−0.436341	+	0.899781i	$0.643726\pi$
$368$	3.91936	0.204311
$369$	−2.16903	−0.112915
$370$	0	0
$371$	−12.2042	−0.633609
$372$	12.1674	0.630853
$373$	−27.6701	−1.43270	−0.716351	−	0.697740i	$-0.754189\pi$
$373$	−27.6701	−1.43270	−0.716351	+	0.697740i	$0.754189\pi$
$374$	0.694711	0.0359226
$375$	0	0
$376$	−3.91446	−0.201873
$377$	−12.3465	−0.635878
$378$	−0.640444	−0.0329409
$379$	−14.2503	−0.731989	−0.365994	−	0.930617i	$-0.619271\pi$
$379$	−14.2503	−0.731989	−0.365994	+	0.930617i	$0.619271\pi$
$380$	0	0
$381$	28.6160	1.46604
$382$	2.89251	0.147994
$383$	−31.5662	−1.61296	−0.806479	−	0.591263i	$-0.798630\pi$
$383$	−31.5662	−1.61296	−0.806479	+	0.591263i	$0.798630\pi$
$384$	5.81168	0.296576
$385$	0	0
$386$	−1.73475	−0.0882964
$387$	2.33090	0.118486
$388$	37.5003	1.90379
$389$	−26.1801	−1.32738	−0.663692	−	0.748006i	$-0.731011\pi$
$389$	−26.1801	−1.32738	−0.663692	+	0.748006i	$0.731011\pi$
$390$	0	0
$391$	−4.88967	−0.247281
$392$	−0.462695	−0.0233696
$393$	19.9547	1.00658
$394$	1.09622	0.0552265
$395$	0	0
$396$	−1.13622	−0.0570973
$397$	7.01345	0.351995	0.175997	−	0.984391i	$-0.443685\pi$
$397$	7.01345	0.351995	0.175997	+	0.984391i	$0.443685\pi$
$398$	1.87185	0.0938273
$399$	8.77168	0.439133
$400$	0	0
$401$	−4.63041	−0.231232	−0.115616	−	0.993294i	$-0.536884\pi$
$401$	−4.63041	−0.231232	−0.115616	+	0.993294i	$0.536884\pi$
$402$	−0.105966	−0.00528513
$403$	6.55656	0.326606
$404$	−37.6631	−1.87381
$405$	0	0
$406$	0.841155	0.0417458
$407$	4.57331	0.226690
$408$	−3.60057	−0.178255
$409$	36.4066	1.80019	0.900095	−	0.435694i	$-0.143497\pi$
$409$	36.4066	1.80019	0.900095	+	0.435694i	$0.143497\pi$
$410$	0	0
$411$	4.22952	0.208627
$412$	30.5500	1.50509
$413$	3.85329	0.189608
$414$	−0.0542305	−0.00266528
$415$	0	0
$416$	2.35147	0.115290
$417$	−12.0547	−0.590324
$418$	−0.783089	−0.0383021
$419$	−4.18967	−0.204679	−0.102339	−	0.994750i	$-0.532633\pi$
$419$	−4.18967	−0.204679	−0.102339	+	0.994750i	$0.532633\pi$
$420$	0	0
$421$	−23.5185	−1.14622	−0.573112	−	0.819477i	$-0.694264\pi$
$421$	−23.5185	−1.14622	−0.573112	+	0.819477i	$0.694264\pi$
$422$	−2.55306	−0.124281
$423$	−3.95294	−0.192199
$424$	−5.64681	−0.274233
$425$	0	0
$426$	−2.19350	−0.106276
$427$	−12.6015	−0.609831
$428$	6.89349	0.333210
$429$	3.31887	0.160236
$430$	0	0
$431$	4.93507	0.237714	0.118857	−	0.992911i	$-0.462077\pi$
$431$	4.93507	0.237714	0.118857	+	0.992911i	$0.462077\pi$
$432$	21.6270	1.04053
$433$	12.1972	0.586161	0.293080	−	0.956088i	$-0.405320\pi$
$433$	12.1972	0.586161	0.293080	+	0.956088i	$0.405320\pi$
$434$	−0.446692	−0.0214419
$435$	0	0
$436$	10.5843	0.506894
$437$	5.51171	0.263661
$438$	0.262954	0.0125644
$439$	−16.0077	−0.764007	−0.382003	−	0.924161i	$-0.624766\pi$
$439$	−16.0077	−0.764007	−0.382003	+	0.924161i	$0.624766\pi$
$440$	0	0
$441$	−0.467244	−0.0222497
$442$	−0.966825	−0.0459872
$443$	25.6644	1.21935	0.609677	−	0.792650i	$-0.291299\pi$
$443$	25.6644	1.21935	0.609677	+	0.792650i	$0.291299\pi$
$444$	−11.8113	−0.560539
$445$	0	0
$446$	2.39981	0.113634
$447$	−25.7066	−1.21588
$448$	7.67851	0.362775
$449$	−23.1940	−1.09459	−0.547297	−	0.836939i	$-0.684343\pi$
$449$	−23.1940	−1.09459	−0.547297	+	0.836939i	$0.684343\pi$
$450$	0	0
$451$	−5.68260	−0.267583
$452$	1.18744	0.0558526
$453$	−22.3670	−1.05090
$454$	−2.19028	−0.102795
$455$	0	0
$456$	4.05862	0.190062
$457$	28.8935	1.35158	0.675789	−	0.737095i	$-0.263803\pi$
$457$	28.8935	1.35158	0.675789	+	0.737095i	$0.263803\pi$
$458$	0.0503771	0.00235397
$459$	−26.9811	−1.25937
$460$	0	0
$461$	−4.88652	−0.227588	−0.113794	−	0.993504i	$-0.536300\pi$
$461$	−4.88652	−0.227588	−0.113794	+	0.993504i	$0.536300\pi$
$462$	−0.226111	−0.0105196
$463$	21.4844	0.998466	0.499233	−	0.866468i	$-0.333615\pi$
$463$	21.4844	0.998466	0.499233	+	0.866468i	$0.333615\pi$
$464$	−28.4047	−1.31866
$465$	0	0
$466$	1.00347	0.0464847
$467$	4.29983	0.198972	0.0994862	−	0.995039i	$-0.468280\pi$
$467$	4.29983	0.198972	0.0994862	+	0.995039i	$0.468280\pi$
$468$	1.58127	0.0730944
$469$	−0.573683	−0.0264902
$470$	0	0
$471$	24.5279	1.13019
$472$	1.78290	0.0820645
$473$	6.10668	0.280785
$474$	0.207737	0.00954169
$475$	0	0
$476$	−9.71346	−0.445216
$477$	−5.70232	−0.261091
$478$	0.233554	0.0106825
$479$	20.9765	0.958442	0.479221	−	0.877694i	$-0.340919\pi$
$479$	20.9765	0.958442	0.479221	+	0.877694i	$0.340919\pi$
$480$	0	0
$481$	−6.36465	−0.290203
$482$	−1.45477	−0.0662631
$483$	1.59146	0.0724141
$484$	18.8751	0.857957
$485$	0	0
$486$	−0.558161	−0.0253187
$487$	−19.5847	−0.887468	−0.443734	−	0.896159i	$-0.646347\pi$
$487$	−19.5847	−0.887468	−0.443734	+	0.896159i	$0.646347\pi$
$488$	−5.83067	−0.263942
$489$	−27.5899	−1.24766
$490$	0	0
$491$	−18.2324	−0.822817	−0.411408	−	0.911451i	$-0.634963\pi$
$491$	−18.2324	−0.822817	−0.411408	+	0.911451i	$0.634963\pi$
$492$	14.6762	0.661655
$493$	35.4368	1.59600
$494$	1.08982	0.0490333
$495$	0	0
$496$	15.0842	0.677301
$497$	−11.8752	−0.532677
$498$	2.44978	0.109777
$499$	−3.46815	−0.155256	−0.0776278	−	0.996982i	$-0.524735\pi$
$499$	−3.46815	−0.155256	−0.0776278	+	0.996982i	$0.524735\pi$
$500$	0	0
$501$	−5.10637	−0.228136
$502$	−1.81438	−0.0809797
$503$	2.69552	0.120187	0.0600936	−	0.998193i	$-0.480860\pi$
$503$	2.69552	0.120187	0.0600936	+	0.998193i	$0.480860\pi$
$504$	−0.216191	−0.00962993
$505$	0	0
$506$	−0.142077	−0.00631611
$507$	16.0702	0.713702
$508$	35.7197	1.58480
$509$	2.57456	0.114116	0.0570578	−	0.998371i	$-0.481828\pi$
$509$	2.57456	0.114116	0.0570578	+	0.998371i	$0.481828\pi$
$510$	0	0
$511$	1.42358	0.0629756
$512$	9.03678	0.399373
$513$	30.4136	1.34279
$514$	0.755301	0.0333149
$515$	0	0
$516$	−15.7715	−0.694300
$517$	−10.3562	−0.455466
$518$	0.433616	0.0190520
$519$	22.2365	0.976075
$520$	0	0
$521$	6.99973	0.306664	0.153332	−	0.988175i	$-0.451000\pi$
$521$	6.99973	0.306664	0.153332	+	0.988175i	$0.451000\pi$
$522$	0.393024	0.0172022
$523$	−22.7375	−0.994239	−0.497120	−	0.867682i	$-0.665609\pi$
$523$	−22.7375	−0.994239	−0.497120	+	0.867682i	$0.665609\pi$
$524$	24.9083	1.08812
$525$	0	0
$526$	−1.61877	−0.0705819
$527$	−18.8186	−0.819751
$528$	7.63547	0.332291
$529$	1.00000	0.0434783
$530$	0	0
$531$	1.80042	0.0781318
$532$	10.9492	0.474707
$533$	7.90844	0.342553
$534$	−0.432607	−0.0187208
$535$	0	0
$536$	−0.265440	−0.0114653
$537$	36.7444	1.58564
$538$	2.58340	0.111378
$539$	−1.22412	−0.0527267
$540$	0	0
$541$	38.1283	1.63926	0.819632	−	0.572891i	$-0.194178\pi$
$541$	38.1283	1.63926	0.819632	+	0.572891i	$0.194178\pi$
$542$	−2.42232	−0.104047
$543$	13.6509	0.585814
$544$	−6.74915	−0.289368
$545$	0	0
$546$	0.314677	0.0134669
$547$	3.23768	0.138433	0.0692165	−	0.997602i	$-0.477950\pi$
$547$	3.23768	0.138433	0.0692165	+	0.997602i	$0.477950\pi$
$548$	5.27945	0.225527
$549$	−5.88799	−0.251293
$550$	0	0
$551$	−39.9450	−1.70171
$552$	0.736362	0.0313417
$553$	1.12465	0.0478250
$554$	−2.01531	−0.0856224
$555$	0	0
$556$	−15.0472	−0.638145
$557$	24.5896	1.04189	0.520947	−	0.853589i	$-0.325579\pi$
$557$	24.5896	1.04189	0.520947	+	0.853589i	$0.325579\pi$
$558$	−0.208714	−0.00883557
$559$	−8.49863	−0.359454
$560$	0	0
$561$	−9.52578	−0.402179
$562$	−0.191837	−0.00809216
$563$	6.75613	0.284737	0.142369	−	0.989814i	$-0.454528\pi$
$563$	6.75613	0.284737	0.142369	+	0.989814i	$0.454528\pi$
$564$	26.7466	1.12624
$565$	0	0
$566$	−3.73165	−0.156853
$567$	7.37995	0.309929
$568$	−5.49461	−0.230549
$569$	25.1251	1.05330	0.526648	−	0.850083i	$-0.323448\pi$
$569$	25.1251	1.05330	0.526648	+	0.850083i	$0.323448\pi$
$570$	0	0
$571$	18.5131	0.774748	0.387374	−	0.921923i	$-0.373382\pi$
$571$	18.5131	0.774748	0.387374	+	0.921923i	$0.373382\pi$
$572$	4.14274	0.173217
$573$	−39.6617	−1.65689
$574$	−0.538794	−0.0224888
$575$	0	0
$576$	3.58774	0.149489
$577$	−6.88693	−0.286707	−0.143353	−	0.989672i	$-0.545789\pi$
$577$	−6.88693	−0.286707	−0.143353	+	0.989672i	$0.545789\pi$
$578$	0.801872	0.0333535
$579$	23.7867	0.988540
$580$	0	0
$581$	13.2626	0.550227
$582$	3.48687	0.144536
$583$	−14.9394	−0.618726
$584$	0.658685	0.0272566
$585$	0	0
$586$	−1.47084	−0.0607599
$587$	−23.9192	−0.987252	−0.493626	−	0.869674i	$-0.664329\pi$
$587$	−23.9192	−0.987252	−0.493626	+	0.869674i	$0.664329\pi$
$588$	3.16149	0.130378
$589$	21.2126	0.874050
$590$	0	0
$591$	−15.0312	−0.618299
$592$	−14.6427	−0.601810
$593$	−8.24873	−0.338735	−0.169367	−	0.985553i	$-0.554172\pi$
$593$	−8.24873	−0.338735	−0.169367	+	0.985553i	$0.554172\pi$
$594$	−0.783981	−0.0321671
$595$	0	0
$596$	−32.0880	−1.31438
$597$	−25.6665	−1.05046
$598$	0.197728	0.00808571
$599$	9.51380	0.388723	0.194362	−	0.980930i	$-0.437736\pi$
$599$	9.51380	0.388723	0.194362	+	0.980930i	$0.437736\pi$
$600$	0	0
$601$	8.90914	0.363411	0.181706	−	0.983353i	$-0.441838\pi$
$601$	8.90914	0.363411	0.181706	+	0.983353i	$0.441838\pi$
$602$	0.579003	0.0235984
$603$	−0.268050	−0.0109158
$604$	−27.9195	−1.13603
$605$	0	0
$606$	−3.50201	−0.142259
$607$	11.7624	0.477422	0.238711	−	0.971091i	$-0.423275\pi$
$607$	11.7624	0.477422	0.238711	+	0.971091i	$0.423275\pi$
$608$	7.60775	0.308535
$609$	−11.5338	−0.467373
$610$	0	0
$611$	14.4127	0.583076
$612$	−4.53856	−0.183460
$613$	36.3891	1.46974	0.734871	−	0.678207i	$-0.237243\pi$
$613$	36.3891	1.46974	0.734871	+	0.678207i	$0.237243\pi$
$614$	−0.444264	−0.0179291
$615$	0	0
$616$	−0.566395	−0.0228207
$617$	4.28166	0.172373	0.0861867	−	0.996279i	$-0.472532\pi$
$617$	4.28166	0.172373	0.0861867	+	0.996279i	$0.472532\pi$
$618$	2.84062	0.114267
$619$	−16.4315	−0.660438	−0.330219	−	0.943904i	$-0.607123\pi$
$619$	−16.4315	−0.660438	−0.330219	+	0.943904i	$0.607123\pi$
$620$	0	0
$621$	5.51799	0.221429
$622$	−0.130558	−0.00523492
$623$	−2.34206	−0.0938325
$624$	−10.6262	−0.425390
$625$	0	0
$626$	1.68164	0.0672120
$627$	10.7376	0.428819
$628$	30.6168	1.22174
$629$	18.2677	0.728383
$630$	0	0
$631$	−45.3699	−1.80615	−0.903074	−	0.429486i	$-0.858695\pi$
$631$	−45.3699	−1.80615	−0.903074	+	0.429486i	$0.858695\pi$
$632$	0.520371	0.0206992
$633$	35.0072	1.39141
$634$	2.52591	0.100317
$635$	0	0
$636$	38.5833	1.52993
$637$	1.70360	0.0674992
$638$	1.02968	0.0407652
$639$	−5.54863	−0.219500
$640$	0	0
$641$	31.6396	1.24969	0.624845	−	0.780749i	$-0.285162\pi$
$641$	31.6396	1.24969	0.624845	+	0.780749i	$0.285162\pi$
$642$	0.640975	0.0252973
$643$	−8.74837	−0.345002	−0.172501	−	0.985009i	$-0.555185\pi$
$643$	−8.74837	−0.345002	−0.172501	+	0.985009i	$0.555185\pi$
$644$	1.98653	0.0782802
$645$	0	0
$646$	−3.12799	−0.123069
$647$	−18.7231	−0.736079	−0.368040	−	0.929810i	$-0.619971\pi$
$647$	−18.7231	−0.736079	−0.368040	+	0.929810i	$0.619971\pi$
$648$	3.41467	0.134141
$649$	4.71689	0.185154
$650$	0	0
$651$	6.12498	0.240057
$652$	−34.4388	−1.34873
$653$	26.3635	1.03168	0.515842	−	0.856684i	$-0.327479\pi$
$653$	26.3635	1.03168	0.515842	+	0.856684i	$0.327479\pi$
$654$	0.984153	0.0384834
$655$	0	0
$656$	18.1944	0.710371
$657$	0.665160	0.0259504
$658$	−0.981922	−0.0382793
$659$	7.96679	0.310342	0.155171	−	0.987888i	$-0.450407\pi$
$659$	7.96679	0.310342	0.155171	+	0.987888i	$0.450407\pi$
$660$	0	0
$661$	−8.53428	−0.331945	−0.165973	−	0.986130i	$-0.553076\pi$
$661$	−8.53428	−0.331945	−0.165973	+	0.986130i	$0.553076\pi$
$662$	−2.54613	−0.0989580
$663$	13.2570	0.514858
$664$	6.13656	0.238145
$665$	0	0
$666$	0.202605	0.00785077
$667$	−7.24729	−0.280616
$668$	−6.37397	−0.246616
$669$	−32.9059	−1.27222
$670$	0	0
$671$	−15.4258	−0.595507
$672$	2.19668	0.0847388
$673$	11.8396	0.456384	0.228192	−	0.973616i	$-0.426719\pi$
$673$	11.8396	0.456384	0.228192	+	0.973616i	$0.426719\pi$
$674$	0.250482	0.00964822
$675$	0	0
$676$	20.0594	0.771517
$677$	34.5129	1.32644	0.663219	−	0.748425i	$-0.269190\pi$
$677$	34.5129	1.32644	0.663219	+	0.748425i	$0.269190\pi$
$678$	0.110412	0.00424033
$679$	18.8773	0.724444
$680$	0	0
$681$	30.0328	1.15086
$682$	−0.546805	−0.0209382
$683$	32.2077	1.23239	0.616196	−	0.787593i	$-0.288673\pi$
$683$	32.2077	1.23239	0.616196	+	0.787593i	$0.288673\pi$
$684$	5.11593	0.195613
$685$	0	0
$686$	−0.116065	−0.00443137
$687$	−0.690764	−0.0263543
$688$	−19.5522	−0.745420
$689$	20.7911	0.792076
$690$	0	0
$691$	−7.13096	−0.271274	−0.135637	−	0.990759i	$-0.543308\pi$
$691$	−7.13096	−0.271274	−0.135637	+	0.990759i	$0.543308\pi$
$692$	27.7565	1.05514
$693$	−0.571963	−0.0217271
$694$	2.67067	0.101377
$695$	0	0
$696$	−5.33663	−0.202285
$697$	−22.6987	−0.859776
$698$	2.34886	0.0889056
$699$	−13.7594	−0.520428
$700$	0	0
$701$	42.8089	1.61687	0.808435	−	0.588585i	$-0.200315\pi$
$701$	42.8089	1.61687	0.808435	+	0.588585i	$0.200315\pi$
$702$	1.09106	0.0411795
$703$	−20.5917	−0.776630
$704$	9.39943	0.354254
$705$	0	0
$706$	−1.80889	−0.0680786
$707$	−18.9592	−0.713035
$708$	−12.1821	−0.457832
$709$	39.0744	1.46747	0.733735	−	0.679436i	$-0.237776\pi$
$709$	39.0744	1.46747	0.733735	+	0.679436i	$0.237776\pi$
$710$	0	0
$711$	0.525486	0.0197073
$712$	−1.08366	−0.0406118
$713$	3.84864	0.144133
$714$	−0.903183	−0.0338008
$715$	0	0
$716$	45.8658	1.71409
$717$	−3.20247	−0.119598
$718$	−3.22335	−0.120294
$719$	24.3855	0.909427	0.454713	−	0.890638i	$-0.349742\pi$
$719$	24.3855	0.909427	0.454713	+	0.890638i	$0.349742\pi$
$720$	0	0
$721$	15.3786	0.572729
$722$	1.32069	0.0491511
$723$	19.9477	0.741862
$724$	17.0395	0.633270
$725$	0	0
$726$	1.75505	0.0651361
$727$	−7.93197	−0.294180	−0.147090	−	0.989123i	$-0.546991\pi$
$727$	−7.93197	−0.294180	−0.147090	+	0.989123i	$0.546991\pi$
$728$	0.788249	0.0292145
$729$	29.7933	1.10346
$730$	0	0
$731$	24.3927	0.902196
$732$	39.8396	1.47251
$733$	13.1137	0.484365	0.242182	−	0.970231i	$-0.422137\pi$
$733$	13.1137	0.484365	0.242182	+	0.970231i	$0.422137\pi$
$734$	−1.94039	−0.0716211
$735$	0	0
$736$	1.38029	0.0508781
$737$	−0.702258	−0.0258680
$738$	−0.251748	−0.00926698
$739$	13.5898	0.499909	0.249955	−	0.968258i	$-0.419584\pi$
$739$	13.5898	0.499909	0.249955	+	0.968258i	$0.419584\pi$
$740$	0	0
$741$	−14.9435	−0.548962
$742$	−1.41647	−0.0520003
$743$	12.5098	0.458941	0.229471	−	0.973316i	$-0.426301\pi$
$743$	12.5098	0.458941	0.229471	+	0.973316i	$0.426301\pi$
$744$	2.83400	0.103899
$745$	0	0
$746$	−3.21152	−0.117582
$747$	6.19689	0.226732
$748$	−11.8905	−0.434758
$749$	3.47012	0.126795
$750$	0	0
$751$	−46.9493	−1.71320	−0.856602	−	0.515978i	$-0.827429\pi$
$751$	−46.9493	−1.71320	−0.856602	+	0.515978i	$0.827429\pi$
$752$	33.1583	1.20916
$753$	24.8785	0.906624
$754$	−1.43299	−0.0521866
$755$	0	0
$756$	10.9617	0.398671
$757$	5.40801	0.196558	0.0982788	−	0.995159i	$-0.468666\pi$
$757$	5.40801	0.196558	0.0982788	+	0.995159i	$0.468666\pi$
$758$	−1.65396	−0.0600744
$759$	1.94815	0.0707132
$760$	0	0
$761$	−40.9571	−1.48470	−0.742348	−	0.670015i	$-0.766288\pi$
$761$	−40.9571	−1.48470	−0.742348	+	0.670015i	$0.766288\pi$
$762$	3.32131	0.120318
$763$	5.32802	0.192887
$764$	−49.5073	−1.79111
$765$	0	0
$766$	−3.66372	−0.132376
$767$	−6.56447	−0.237029
$768$	−23.7656	−0.857567
$769$	38.2867	1.38066	0.690328	−	0.723497i	$-0.257466\pi$
$769$	38.2867	1.38066	0.690328	+	0.723497i	$0.257466\pi$
$770$	0	0
$771$	−10.3566	−0.372983
$772$	29.6915	1.06862
$773$	−20.2164	−0.727134	−0.363567	−	0.931568i	$-0.618441\pi$
$773$	−20.2164	−0.727134	−0.363567	+	0.931568i	$0.618441\pi$
$774$	0.270535	0.00972420
$775$	0	0
$776$	8.73443	0.313548
$777$	−5.94569	−0.213300
$778$	−3.03858	−0.108939
$779$	25.5864	0.916727
$780$	0	0
$781$	−14.5367	−0.520165
$782$	−0.567518	−0.0202944
$783$	−39.9905	−1.42914
$784$	3.91936	0.139977
$785$	0	0
$786$	2.31604	0.0826103
$787$	−17.6812	−0.630267	−0.315133	−	0.949047i	$-0.602049\pi$
$787$	−17.6812	−0.630267	−0.315133	+	0.949047i	$0.602049\pi$
$788$	−18.7625	−0.668386
$789$	22.1964	0.790213
$790$	0	0
$791$	0.597747	0.0212534
$792$	−0.264645	−0.00940374
$793$	21.4680	0.762352
$794$	0.814014	0.0288883
$795$	0	0
$796$	−32.0380	−1.13556
$797$	14.6445	0.518736	0.259368	−	0.965779i	$-0.416486\pi$
$797$	14.6445	0.518736	0.259368	+	0.965779i	$0.416486\pi$
$798$	1.01808	0.0360397
$799$	−41.3672	−1.46347
$800$	0	0
$801$	−1.09431	−0.0386656
$802$	−0.537427	−0.0189772
$803$	1.74264	0.0614964
$804$	1.81369	0.0639640
$805$	0	0
$806$	0.760985	0.0268046
$807$	−35.4232	−1.24696
$808$	−8.77234	−0.308610
$809$	0.157185	0.00552634	0.00276317	−	0.999996i	$-0.499120\pi$
$809$	0.157185	0.00552634	0.00276317	+	0.999996i	$0.499120\pi$
$810$	0	0
$811$	−39.1412	−1.37443	−0.687216	−	0.726453i	$-0.741167\pi$
$811$	−39.1412	−1.37443	−0.687216	+	0.726453i	$0.741167\pi$
$812$	−14.3970	−0.505234
$813$	33.2145	1.16488
$814$	0.530799	0.0186045
$815$	0	0
$816$	30.4994	1.06769
$817$	−27.4958	−0.961957
$818$	4.22552	0.147742
$819$	0.795998	0.0278144
$820$	0	0
$821$	−27.6342	−0.964442	−0.482221	−	0.876050i	$-0.660170\pi$
$821$	−27.6342	−0.964442	−0.482221	+	0.876050i	$0.660170\pi$
$822$	0.490897	0.0171220
$823$	−9.25318	−0.322546	−0.161273	−	0.986910i	$-0.551560\pi$
$823$	−9.25318	−0.322546	−0.161273	+	0.986910i	$0.551560\pi$
$824$	7.11561	0.247884
$825$	0	0
$826$	0.447230	0.0155611
$827$	44.6391	1.55225	0.776127	−	0.630577i	$-0.217182\pi$
$827$	44.6391	1.55225	0.776127	+	0.630577i	$0.217182\pi$
$828$	0.928194	0.0322570
$829$	−52.1937	−1.81276	−0.906382	−	0.422460i	$-0.861167\pi$
$829$	−52.1937	−1.81276	−0.906382	+	0.422460i	$0.861167\pi$
$830$	0	0
$831$	27.6337	0.958602
$832$	−13.0811	−0.453507
$833$	−4.88967	−0.169417
$834$	−1.39913	−0.0484479
$835$	0	0
$836$	13.4031	0.463556
$837$	21.2368	0.734051
$838$	−0.486272	−0.0167980
$839$	−21.6036	−0.745841	−0.372920	−	0.927863i	$-0.621644\pi$
$839$	−21.6036	−0.745841	−0.372920	+	0.927863i	$0.621644\pi$
$840$	0	0
$841$	23.5233	0.811147
$842$	−2.72967	−0.0940707
$843$	2.63045	0.0905974
$844$	43.6974	1.50413
$845$	0	0
$846$	−0.458797	−0.0157738
$847$	9.50153	0.326476
$848$	47.8324	1.64257
$849$	51.1679	1.75608
$850$	0	0
$851$	−3.73599	−0.128068
$852$	37.5434	1.28622
$853$	−0.544970	−0.0186594	−0.00932971	−	0.999956i	$-0.502970\pi$
$853$	−0.544970	−0.0186594	−0.00932971	+	0.999956i	$0.502970\pi$
$854$	−1.46259	−0.0500489
$855$	0	0
$856$	1.60561	0.0548785
$857$	−56.3880	−1.92618	−0.963088	−	0.269186i	$-0.913245\pi$
$857$	−56.3880	−1.92618	−0.963088	+	0.269186i	$0.913245\pi$
$858$	0.385203	0.0131506
$859$	−16.4925	−0.562716	−0.281358	−	0.959603i	$-0.590785\pi$
$859$	−16.4925	−0.562716	−0.281358	+	0.959603i	$0.590785\pi$
$860$	0	0
$861$	7.38787	0.251778
$862$	0.572787	0.0195092
$863$	53.3308	1.81540	0.907701	−	0.419618i	$-0.137836\pi$
$863$	53.3308	1.81540	0.907701	+	0.419618i	$0.137836\pi$
$864$	7.61642	0.259116
$865$	0	0
$866$	1.41567	0.0481063
$867$	−10.9952	−0.373415
$868$	7.64544	0.259503
$869$	1.37671	0.0467017
$870$	0	0
$871$	0.977328	0.0331155
$872$	2.46525	0.0834838
$873$	8.82030	0.298522
$874$	0.639715	0.0216387
$875$	0	0
$876$	−4.50064	−0.152063
$877$	23.3200	0.787461	0.393731	−	0.919226i	$-0.371184\pi$
$877$	23.3200	0.787461	0.393731	+	0.919226i	$0.371184\pi$
$878$	−1.85793	−0.0627021
$879$	20.1680	0.680249
$880$	0	0
$881$	−53.8013	−1.81261	−0.906306	−	0.422623i	$-0.861110\pi$
$881$	−53.8013	−1.81261	−0.906306	+	0.422623i	$0.861110\pi$
$882$	−0.0542305	−0.00182604
$883$	−55.2868	−1.86055	−0.930274	−	0.366866i	$-0.880431\pi$
$883$	−55.2868	−1.86055	−0.930274	+	0.366866i	$0.880431\pi$
$884$	16.5479	0.556566
$885$	0	0
$886$	2.97873	0.100072
$887$	−45.9081	−1.54144	−0.770721	−	0.637173i	$-0.780104\pi$
$887$	−45.9081	−1.54144	−0.770721	+	0.637173i	$0.780104\pi$
$888$	−2.75104	−0.0923189
$889$	17.9809	0.603062
$890$	0	0
$891$	9.03396	0.302649
$892$	−41.0745	−1.37528
$893$	46.6298	1.56041
$894$	−2.98363	−0.0997874
$895$	0	0
$896$	3.65178	0.121997
$897$	−2.71122	−0.0905251
$898$	−2.69201	−0.0898334
$899$	−27.8923	−0.930259
$900$	0	0
$901$	−59.6743	−1.98804
$902$	−0.659549	−0.0219606
$903$	−7.93921	−0.264200
$904$	0.276575	0.00919874
$905$	0	0
$906$	−2.59602	−0.0862471
$907$	11.5603	0.383854	0.191927	−	0.981409i	$-0.438526\pi$
$907$	11.5603	0.383854	0.191927	+	0.981409i	$0.438526\pi$
$908$	37.4881	1.24409
$909$	−8.85858	−0.293821
$910$	0	0
$911$	−3.45327	−0.114412	−0.0572060	−	0.998362i	$-0.518219\pi$
$911$	−3.45327	−0.114412	−0.0572060	+	0.998362i	$0.518219\pi$
$912$	−34.3793	−1.13841
$913$	16.2351	0.537303
$914$	3.35351	0.110924
$915$	0	0
$916$	−0.862239	−0.0284892
$917$	12.5386	0.414061
$918$	−3.13156	−0.103357
$919$	33.5535	1.10683	0.553414	−	0.832906i	$-0.313325\pi$
$919$	33.5535	1.10683	0.553414	+	0.832906i	$0.313325\pi$
$920$	0	0
$921$	6.09170	0.200728
$922$	−0.567152	−0.0186782
$923$	20.2307	0.665901
$924$	3.87005	0.127315
$925$	0	0
$926$	2.49358	0.0819442
$927$	7.18556	0.236005
$928$	−10.0034	−0.328376
$929$	−17.4381	−0.572125	−0.286063	−	0.958211i	$-0.592347\pi$
$929$	−17.4381	−0.572125	−0.286063	+	0.958211i	$0.592347\pi$
$930$	0	0
$931$	5.51171	0.180639
$932$	−17.1750	−0.562587
$933$	1.79020	0.0586085
$934$	0.499058	0.0163297
$935$	0	0
$936$	0.368305	0.0120384
$937$	2.96959	0.0970123	0.0485062	−	0.998823i	$-0.484554\pi$
$937$	2.96959	0.0970123	0.0485062	+	0.998823i	$0.484554\pi$
$938$	−0.0665843	−0.00217405
$939$	−23.0585	−0.752485
$940$	0	0
$941$	−37.0690	−1.20842	−0.604208	−	0.796827i	$-0.706510\pi$
$941$	−37.0690	−1.20842	−0.604208	+	0.796827i	$0.706510\pi$
$942$	2.84683	0.0927546
$943$	4.64219	0.151170
$944$	−15.1024	−0.491541
$945$	0	0
$946$	0.708770	0.0230441
$947$	18.1955	0.591274	0.295637	−	0.955300i	$-0.404468\pi$
$947$	18.1955	0.591274	0.295637	+	0.955300i	$0.404468\pi$
$948$	−3.55557	−0.115480
$949$	−2.42522	−0.0787260
$950$	0	0
$951$	−34.6350	−1.12312
$952$	−2.26243	−0.0733256
$953$	−14.5623	−0.471718	−0.235859	−	0.971787i	$-0.575790\pi$
$953$	−14.5623	−0.471718	−0.235859	+	0.971787i	$0.575790\pi$
$954$	−0.661838	−0.0214278
$955$	0	0
$956$	−3.99745	−0.129287
$957$	−14.1188	−0.456395
$958$	2.43463	0.0786595
$959$	2.65763	0.0858192
$960$	0	0
$961$	−16.1879	−0.522192
$962$	−0.738710	−0.0238170
$963$	1.62139	0.0522486
$964$	24.8995	0.801959
$965$	0	0
$966$	0.184713	0.00594303
$967$	−9.99229	−0.321330	−0.160665	−	0.987009i	$-0.551364\pi$
$967$	−9.99229	−0.321330	−0.160665	+	0.987009i	$0.551364\pi$
$968$	4.39631	0.141303
$969$	42.8906	1.37784
$970$	0	0
$971$	−3.51788	−0.112894	−0.0564470	−	0.998406i	$-0.517977\pi$
$971$	−3.51788	−0.112894	−0.0564470	+	0.998406i	$0.517977\pi$
$972$	9.55332	0.306423
$973$	−7.57463	−0.242832
$974$	−2.27309	−0.0728346
$975$	0	0
$976$	49.3899	1.58093
$977$	−27.0429	−0.865178	−0.432589	−	0.901591i	$-0.642400\pi$
$977$	−27.0429	−0.865178	−0.432589	+	0.901591i	$0.642400\pi$
$978$	−3.20221	−0.102396
$979$	−2.86696	−0.0916285
$980$	0	0
$981$	2.48948	0.0794831
$982$	−2.11614	−0.0675286
$983$	31.7747	1.01345	0.506727	−	0.862106i	$-0.330855\pi$
$983$	31.7747	1.01345	0.506727	+	0.862106i	$0.330855\pi$
$984$	3.41833	0.108972
$985$	0	0
$986$	4.11297	0.130984
$987$	13.4640	0.428563
$988$	−18.6530	−0.593432
$989$	−4.98862	−0.158629
$990$	0	0
$991$	−44.8758	−1.42553	−0.712764	−	0.701404i	$-0.752557\pi$
$991$	−44.8758	−1.42553	−0.712764	+	0.701404i	$0.752557\pi$
$992$	5.31224	0.168664
$993$	34.9121	1.10790
$994$	−1.37829	−0.0437168
$995$	0	0
$996$	−41.9297	−1.32859
$997$	3.92757	0.124387	0.0621936	−	0.998064i	$-0.480190\pi$
$997$	3.92757	0.124387	0.0621936	+	0.998064i	$0.480190\pi$
$998$	−0.402530	−0.0127419
$999$	−20.6152	−0.652235

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4025.2.a.ba.1.8	✓	14
5.4	even	2		4025.2.a.bb.1.7	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4025.2.a.ba.1.8	✓	14	1.1	even	1	trivial
4025.2.a.bb.1.7	yes	14	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4025 = 5^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4025.a (trivial)

\(f(q)\)	\(=\)	\(q+0.116065 q^{2} -1.59146 q^{3} -1.98653 q^{4} -0.184713 q^{6} -1.00000 q^{7} -0.462695 q^{8} -0.467244 q^{9} +O(q^{10})\)	\(q+0.116065 q^{2} -1.59146 q^{3} -1.98653 q^{4} -0.184713 q^{6} -1.00000 q^{7} -0.462695 q^{8} -0.467244 q^{9} -1.22412 q^{11} +3.16149 q^{12} +1.70360 q^{13} -0.116065 q^{14} +3.91936 q^{16} -4.88967 q^{17} -0.0542305 q^{18} +5.51171 q^{19} +1.59146 q^{21} -0.142077 q^{22} +1.00000 q^{23} +0.736362 q^{24} +0.197728 q^{26} +5.51799 q^{27} +1.98653 q^{28} -7.24729 q^{29} +3.84864 q^{31} +1.38029 q^{32} +1.94815 q^{33} -0.567518 q^{34} +0.928194 q^{36} -3.73599 q^{37} +0.639715 q^{38} -2.71122 q^{39} +4.64219 q^{41} +0.184713 q^{42} -4.98862 q^{43} +2.43175 q^{44} +0.116065 q^{46} +8.46013 q^{47} -6.23751 q^{48} +1.00000 q^{49} +7.78173 q^{51} -3.38426 q^{52} +12.2042 q^{53} +0.640444 q^{54} +0.462695 q^{56} -8.77168 q^{57} -0.841155 q^{58} -3.85329 q^{59} +12.6015 q^{61} +0.446692 q^{62} +0.467244 q^{63} -7.67851 q^{64} +0.226111 q^{66} +0.573683 q^{67} +9.71346 q^{68} -1.59146 q^{69} +11.8752 q^{71} +0.216191 q^{72} -1.42358 q^{73} -0.433616 q^{74} -10.9492 q^{76} +1.22412 q^{77} -0.314677 q^{78} -1.12465 q^{79} -7.37995 q^{81} +0.538794 q^{82} -13.2626 q^{83} -3.16149 q^{84} -0.579003 q^{86} +11.5338 q^{87} +0.566395 q^{88} +2.34206 q^{89} -1.70360 q^{91} -1.98653 q^{92} -6.12498 q^{93} +0.981922 q^{94} -2.19668 q^{96} -18.8773 q^{97} +0.116065 q^{98} +0.571963 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - q^{2} - 6 q^{3} + 17 q^{4} - 4 q^{6} - 14 q^{7} - 9 q^{8} + 18 q^{9}+O(q^{10}) \) 14 * q - q^2 - 6 * q^3 + 17 * q^4 - 4 * q^6 - 14 * q^7 - 9 * q^8 + 18 * q^9	\( 14 q - q^{2} - 6 q^{3} + 17 q^{4} - 4 q^{6} - 14 q^{7} - 9 q^{8} + 18 q^{9} - 3 q^{11} - 11 q^{12} - 15 q^{13} + q^{14} + 23 q^{16} - 9 q^{17} - 17 q^{18} - 4 q^{19} + 6 q^{21} - 9 q^{22} + 14 q^{23} + 10 q^{24} - 5 q^{26} - 33 q^{27} - 17 q^{28} + 11 q^{29} - q^{31} - 24 q^{32} - 26 q^{33} - 6 q^{34} + 13 q^{36} - 18 q^{37} + 6 q^{38} + 6 q^{39} - 7 q^{41} + 4 q^{42} - 18 q^{43} - 16 q^{44} - q^{46} - 10 q^{47} - 40 q^{48} + 14 q^{49} + 28 q^{51} - 46 q^{52} - 5 q^{53} - 24 q^{54} + 9 q^{56} + 26 q^{57} - 2 q^{58} - 24 q^{59} - 6 q^{61} + 16 q^{62} - 18 q^{63} + 29 q^{64} + 27 q^{66} - 61 q^{67} - 35 q^{68} - 6 q^{69} + 11 q^{71} - 12 q^{72} - 28 q^{73} - 49 q^{74} - 27 q^{76} + 3 q^{77} - 38 q^{78} + 6 q^{79} + 26 q^{81} + 14 q^{82} - 16 q^{83} + 11 q^{84} + 46 q^{86} - 61 q^{87} - 58 q^{88} - 39 q^{89} + 15 q^{91} + 17 q^{92} - 21 q^{93} - 74 q^{94} + 41 q^{96} - 19 q^{97} - q^{98} - 9 q^{99}+O(q^{100}) \) 14 * q - q^2 - 6 * q^3 + 17 * q^4 - 4 * q^6 - 14 * q^7 - 9 * q^8 + 18 * q^9 - 3 * q^11 - 11 * q^12 - 15 * q^13 + q^14 + 23 * q^16 - 9 * q^17 - 17 * q^18 - 4 * q^19 + 6 * q^21 - 9 * q^22 + 14 * q^23 + 10 * q^24 - 5 * q^26 - 33 * q^27 - 17 * q^28 + 11 * q^29 - q^31 - 24 * q^32 - 26 * q^33 - 6 * q^34 + 13 * q^36 - 18 * q^37 + 6 * q^38 + 6 * q^39 - 7 * q^41 + 4 * q^42 - 18 * q^43 - 16 * q^44 - q^46 - 10 * q^47 - 40 * q^48 + 14 * q^49 + 28 * q^51 - 46 * q^52 - 5 * q^53 - 24 * q^54 + 9 * q^56 + 26 * q^57 - 2 * q^58 - 24 * q^59 - 6 * q^61 + 16 * q^62 - 18 * q^63 + 29 * q^64 + 27 * q^66 - 61 * q^67 - 35 * q^68 - 6 * q^69 + 11 * q^71 - 12 * q^72 - 28 * q^73 - 49 * q^74 - 27 * q^76 + 3 * q^77 - 38 * q^78 + 6 * q^79 + 26 * q^81 + 14 * q^82 - 16 * q^83 + 11 * q^84 + 46 * q^86 - 61 * q^87 - 58 * q^88 - 39 * q^89 + 15 * q^91 + 17 * q^92 - 21 * q^93 - 74 * q^94 + 41 * q^96 - 19 * q^97 - q^98 - 9 * q^99

Introduction

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