LMFDB - Embedded newform 6025.2.a.i.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6025,2,Mod(1,6025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6025, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6025 = 5^{2} \cdot 241 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6025.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:	$48.1098672178$
Analytic rank:	$1$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 2 x^{14} - 16 x^{13} + 31 x^{12} + 99 x^{11} - 184 x^{10} - 296 x^{9} + 519 x^{8} + 437 x^{7} + \cdots - 1 $ x^15 - 2x^14 - 16x^13 + 31x^12 + 99x^11 - 184x^10 - 296x^9 + 519x^8 + 437x^7 - 699x^6 - 297x^5 + 394x^4 + 89x^3 - 57x^2 - 17x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1205)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.14166$ of defining polynomial
Character	$\chi$	$=$	6025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.14166 q^{2} +0.668121 q^{3} +2.58670 q^{4} -1.43089 q^{6} +3.26618 q^{7} -1.25651 q^{8} -2.55361 q^{9} +O(q^{10})$	\(q-2.14166 q^{2} +0.668121 q^{3} +2.58670 q^{4} -1.43089 q^{6} +3.26618 q^{7} -1.25651 q^{8} -2.55361 q^{9} +4.95460 q^{11} +1.72823 q^{12} +1.16266 q^{13} -6.99504 q^{14} -2.48239 q^{16} +4.82940 q^{17} +5.46897 q^{18} -5.79410 q^{19} +2.18220 q^{21} -10.6110 q^{22} -1.06284 q^{23} -0.839500 q^{24} -2.49001 q^{26} -3.71049 q^{27} +8.44862 q^{28} -0.384786 q^{29} -3.94830 q^{31} +7.82944 q^{32} +3.31027 q^{33} -10.3429 q^{34} -6.60543 q^{36} +1.60067 q^{37} +12.4090 q^{38} +0.776795 q^{39} -11.9879 q^{41} -4.67353 q^{42} -10.2206 q^{43} +12.8160 q^{44} +2.27623 q^{46} -2.62902 q^{47} -1.65854 q^{48} +3.66793 q^{49} +3.22662 q^{51} +3.00744 q^{52} -6.32499 q^{53} +7.94660 q^{54} -4.10398 q^{56} -3.87116 q^{57} +0.824080 q^{58} -8.94773 q^{59} +3.85801 q^{61} +8.45591 q^{62} -8.34056 q^{63} -11.8032 q^{64} -7.08947 q^{66} +2.79607 q^{67} +12.4922 q^{68} -0.710104 q^{69} -9.85226 q^{71} +3.20864 q^{72} -10.6976 q^{73} -3.42809 q^{74} -14.9876 q^{76} +16.1826 q^{77} -1.66363 q^{78} -3.71264 q^{79} +5.18179 q^{81} +25.6740 q^{82} -16.0296 q^{83} +5.64471 q^{84} +21.8891 q^{86} -0.257084 q^{87} -6.22549 q^{88} -14.2400 q^{89} +3.79744 q^{91} -2.74924 q^{92} -2.63794 q^{93} +5.63046 q^{94} +5.23102 q^{96} -8.83549 q^{97} -7.85545 q^{98} -12.6521 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q - 2 q^{2} + 7 q^{3} + 6 q^{4} - 5 q^{6} + 3 q^{7} - 3 q^{8} + 6 q^{9}+O(q^{10}) $ 15 * q - 2 * q^2 + 7 * q^3 + 6 * q^4 - 5 * q^6 + 3 * q^7 - 3 * q^8 + 6 * q^9	$ 15 q - 2 q^{2} + 7 q^{3} + 6 q^{4} - 5 q^{6} + 3 q^{7} - 3 q^{8} + 6 q^{9} - 10 q^{11} + 6 q^{12} + 8 q^{13} - 5 q^{14} - 16 q^{16} + q^{17} + 3 q^{18} - 30 q^{19} - 11 q^{21} + 5 q^{22} - 19 q^{23} - 14 q^{24} - 18 q^{26} + 22 q^{27} + 20 q^{28} - 12 q^{29} - 22 q^{31} + 2 q^{32} - 4 q^{33} - 29 q^{34} - 7 q^{36} + 12 q^{37} + 18 q^{38} - 17 q^{39} - 13 q^{41} + q^{42} + 25 q^{43} - 20 q^{44} - 7 q^{46} - 16 q^{47} + 22 q^{48} - 24 q^{49} - 27 q^{51} + 15 q^{52} + 4 q^{53} - 43 q^{54} - 3 q^{56} - 22 q^{57} + 20 q^{58} - 50 q^{59} - 41 q^{61} - 12 q^{62} - 6 q^{63} - 53 q^{64} + 5 q^{66} + 43 q^{67} - 5 q^{68} - 50 q^{69} - 14 q^{71} - 32 q^{72} + 10 q^{73} - 26 q^{74} - 13 q^{76} + 7 q^{77} - 3 q^{78} - 44 q^{79} + 7 q^{81} + 19 q^{82} - 7 q^{83} - 42 q^{84} + 7 q^{86} - 10 q^{87} + 28 q^{88} + 4 q^{89} - 50 q^{91} - 25 q^{92} - 22 q^{93} - 14 q^{94} + 14 q^{96} - 9 q^{97} - 2 q^{98} - 46 q^{99}+O(q^{100}) $ 15 * q - 2 * q^2 + 7 * q^3 + 6 * q^4 - 5 * q^6 + 3 * q^7 - 3 * q^8 + 6 * q^9 - 10 * q^11 + 6 * q^12 + 8 * q^13 - 5 * q^14 - 16 * q^16 + q^17 + 3 * q^18 - 30 * q^19 - 11 * q^21 + 5 * q^22 - 19 * q^23 - 14 * q^24 - 18 * q^26 + 22 * q^27 + 20 * q^28 - 12 * q^29 - 22 * q^31 + 2 * q^32 - 4 * q^33 - 29 * q^34 - 7 * q^36 + 12 * q^37 + 18 * q^38 - 17 * q^39 - 13 * q^41 + q^42 + 25 * q^43 - 20 * q^44 - 7 * q^46 - 16 * q^47 + 22 * q^48 - 24 * q^49 - 27 * q^51 + 15 * q^52 + 4 * q^53 - 43 * q^54 - 3 * q^56 - 22 * q^57 + 20 * q^58 - 50 * q^59 - 41 * q^61 - 12 * q^62 - 6 * q^63 - 53 * q^64 + 5 * q^66 + 43 * q^67 - 5 * q^68 - 50 * q^69 - 14 * q^71 - 32 * q^72 + 10 * q^73 - 26 * q^74 - 13 * q^76 + 7 * q^77 - 3 * q^78 - 44 * q^79 + 7 * q^81 + 19 * q^82 - 7 * q^83 - 42 * q^84 + 7 * q^86 - 10 * q^87 + 28 * q^88 + 4 * q^89 - 50 * q^91 - 25 * q^92 - 22 * q^93 - 14 * q^94 + 14 * q^96 - 9 * q^97 - 2 * q^98 - 46 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.14166	−1.51438	−0.757190	−	0.653194i	$-0.773429\pi$
$2$	−2.14166	−1.51438	−0.757190	+	0.653194i	$0.773429\pi$
$3$	0.668121	0.385740	0.192870	−	0.981224i	$-0.438220\pi$
$3$	0.668121	0.385740	0.192870	+	0.981224i	$0.438220\pi$
$4$	2.58670	1.29335
$5$	0	0
$5$	0	0
$6$	−1.43089	−0.584157
$7$	3.26618	1.23450	0.617250	−	0.786767i	$-0.288247\pi$
$7$	3.26618	1.23450	0.617250	+	0.786767i	$0.288247\pi$
$8$	−1.25651	−0.444243
$9$	−2.55361	−0.851205
$10$	0	0
$11$	4.95460	1.49387	0.746933	−	0.664899i	$-0.231525\pi$
$11$	4.95460	1.49387	0.746933	+	0.664899i	$0.231525\pi$
$12$	1.72823	0.498897
$13$	1.16266	0.322463	0.161231	−	0.986917i	$-0.448453\pi$
$13$	1.16266	0.322463	0.161231	+	0.986917i	$0.448453\pi$
$14$	−6.99504	−1.86950
$15$	0	0
$16$	−2.48239	−0.620597
$17$	4.82940	1.17130	0.585650	−	0.810564i	$-0.300839\pi$
$17$	4.82940	1.17130	0.585650	+	0.810564i	$0.300839\pi$
$18$	5.46897	1.28905
$19$	−5.79410	−1.32926	−0.664629	−	0.747173i	$-0.731410\pi$
$19$	−5.79410	−1.32926	−0.664629	+	0.747173i	$0.731410\pi$
$20$	0	0
$21$	2.18220	0.476196
$22$	−10.6110	−2.26228
$23$	−1.06284	−0.221617	−0.110808	−	0.993842i	$-0.535344\pi$
$23$	−1.06284	−0.221617	−0.110808	+	0.993842i	$0.535344\pi$
$24$	−0.839500	−0.171362
$25$	0	0
$26$	−2.49001	−0.488331
$27$	−3.71049	−0.714084
$28$	8.44862	1.59664
$29$	−0.384786	−0.0714530	−0.0357265	−	0.999362i	$-0.511375\pi$
$29$	−0.384786	−0.0714530	−0.0357265	+	0.999362i	$0.511375\pi$
$30$	0	0
$31$	−3.94830	−0.709136	−0.354568	−	0.935030i	$-0.615372\pi$
$31$	−3.94830	−0.709136	−0.354568	+	0.935030i	$0.615372\pi$
$32$	7.82944	1.38406
$33$	3.31027	0.576244
$34$	−10.3429	−1.77380
$35$	0	0
$36$	−6.60543	−1.10091
$37$	1.60067	0.263149	0.131574	−	0.991306i	$-0.457997\pi$
$37$	1.60067	0.263149	0.131574	+	0.991306i	$0.457997\pi$
$38$	12.4090	2.01300
$39$	0.776795	0.124387
$40$	0	0
$41$	−11.9879	−1.87220	−0.936098	−	0.351741i	$-0.885590\pi$
$41$	−11.9879	−1.87220	−0.936098	+	0.351741i	$0.885590\pi$
$42$	−4.67353	−0.721142
$43$	−10.2206	−1.55863	−0.779315	−	0.626632i	$-0.784433\pi$
$43$	−10.2206	−1.55863	−0.779315	+	0.626632i	$0.784433\pi$
$44$	12.8160	1.93209
$45$	0	0
$46$	2.27623	0.335612
$47$	−2.62902	−0.383482	−0.191741	−	0.981446i	$-0.561413\pi$
$47$	−2.62902	−0.383482	−0.191741	+	0.981446i	$0.561413\pi$
$48$	−1.65854	−0.239389
$49$	3.66793	0.523990
$50$	0	0
$51$	3.22662	0.451818
$52$	3.00744	0.417057
$53$	−6.32499	−0.868805	−0.434402	−	0.900719i	$-0.643040\pi$
$53$	−6.32499	−0.868805	−0.434402	+	0.900719i	$0.643040\pi$
$54$	7.94660	1.08139
$55$	0	0
$56$	−4.10398	−0.548418
$57$	−3.87116	−0.512748
$58$	0.824080	0.108207
$59$	−8.94773	−1.16490	−0.582448	−	0.812868i	$-0.697905\pi$
$59$	−8.94773	−1.16490	−0.582448	+	0.812868i	$0.697905\pi$
$60$	0	0
$61$	3.85801	0.493968	0.246984	−	0.969020i	$-0.420561\pi$
$61$	3.85801	0.493968	0.246984	+	0.969020i	$0.420561\pi$
$62$	8.45591	1.07390
$63$	−8.34056	−1.05081
$64$	−11.8032	−1.47540
$65$	0	0
$66$	−7.08947	−0.872653
$67$	2.79607	0.341594	0.170797	−	0.985306i	$-0.445366\pi$
$67$	2.79607	0.341594	0.170797	+	0.985306i	$0.445366\pi$
$68$	12.4922	1.51490
$69$	−0.710104	−0.0854865
$70$	0	0
$71$	−9.85226	−1.16925	−0.584624	−	0.811304i	$-0.698758\pi$
$71$	−9.85226	−1.16925	−0.584624	+	0.811304i	$0.698758\pi$
$72$	3.20864	0.378142
$73$	−10.6976	−1.25206	−0.626032	−	0.779797i	$-0.715322\pi$
$73$	−10.6976	−1.25206	−0.626032	+	0.779797i	$0.715322\pi$
$74$	−3.42809	−0.398508
$75$	0	0
$76$	−14.9876	−1.71920
$77$	16.1826	1.84418
$78$	−1.66363	−0.188369
$79$	−3.71264	−0.417704	−0.208852	−	0.977947i	$-0.566973\pi$
$79$	−3.71264	−0.417704	−0.208852	+	0.977947i	$0.566973\pi$
$80$	0	0
$81$	5.18179	0.575754
$82$	25.6740	2.83522
$83$	−16.0296	−1.75948	−0.879738	−	0.475459i	$-0.842282\pi$
$83$	−16.0296	−1.75948	−0.879738	+	0.475459i	$0.842282\pi$
$84$	5.64471	0.615888
$85$	0	0
$86$	21.8891	2.36036
$87$	−0.257084	−0.0275623
$88$	−6.22549	−0.663640
$89$	−14.2400	−1.50944	−0.754720	−	0.656048i	$-0.772227\pi$
$89$	−14.2400	−1.50944	−0.754720	+	0.656048i	$0.772227\pi$
$90$	0	0
$91$	3.79744	0.398080
$92$	−2.74924	−0.286628
$93$	−2.63794	−0.273542
$94$	5.63046	0.580738
$95$	0	0
$96$	5.23102	0.533888
$97$	−8.83549	−0.897108	−0.448554	−	0.893756i	$-0.648061\pi$
$97$	−8.83549	−0.897108	−0.448554	+	0.893756i	$0.648061\pi$
$98$	−7.85545	−0.793520
$99$	−12.6521	−1.27159
$100$	0	0
$101$	8.68779	0.864468	0.432234	−	0.901762i	$-0.357726\pi$
$101$	8.68779	0.864468	0.432234	+	0.901762i	$0.357726\pi$
$102$	−6.91032	−0.684224
$103$	−13.6846	−1.34839	−0.674193	−	0.738555i	$-0.735508\pi$
$103$	−13.6846	−1.34839	−0.674193	+	0.738555i	$0.735508\pi$
$104$	−1.46089	−0.143252
$105$	0	0
$106$	13.5460	1.31570
$107$	−12.0464	−1.16457	−0.582285	−	0.812985i	$-0.697841\pi$
$107$	−12.0464	−1.16457	−0.582285	+	0.812985i	$0.697841\pi$
$108$	−9.59792	−0.923560
$109$	14.2982	1.36951	0.684757	−	0.728771i	$-0.259908\pi$
$109$	14.2982	1.36951	0.684757	+	0.728771i	$0.259908\pi$
$110$	0	0
$111$	1.06944	0.101507
$112$	−8.10792	−0.766126
$113$	14.4838	1.36252	0.681260	−	0.732041i	$-0.261432\pi$
$113$	14.4838	1.36252	0.681260	+	0.732041i	$0.261432\pi$
$114$	8.29071	0.776496
$115$	0	0
$116$	−0.995326	−0.0924137
$117$	−2.96897	−0.274482
$118$	19.1630	1.76409
$119$	15.7737	1.44597
$120$	0	0
$121$	13.5480	1.23164
$122$	−8.26254	−0.748055
$123$	−8.00937	−0.722181
$124$	−10.2131	−0.917160
$125$	0	0
$126$	17.8626	1.59133
$127$	18.5680	1.64764	0.823820	−	0.566851i	$-0.191838\pi$
$127$	18.5680	1.64764	0.823820	+	0.566851i	$0.191838\pi$
$128$	9.61956	0.850257
$129$	−6.82862	−0.601226
$130$	0	0
$131$	−20.3391	−1.77704	−0.888518	−	0.458843i	$-0.848264\pi$
$131$	−20.3391	−1.77704	−0.888518	+	0.458843i	$0.848264\pi$
$132$	8.56268	0.745285
$133$	−18.9246	−1.64097
$134$	−5.98822	−0.517304
$135$	0	0
$136$	−6.06818	−0.520342
$137$	−2.42972	−0.207585	−0.103793	−	0.994599i	$-0.533098\pi$
$137$	−2.42972	−0.207585	−0.103793	+	0.994599i	$0.533098\pi$
$138$	1.52080	0.129459
$139$	−15.6435	−1.32686	−0.663431	−	0.748238i	$-0.730900\pi$
$139$	−15.6435	−1.32686	−0.663431	+	0.748238i	$0.730900\pi$
$140$	0	0
$141$	−1.75650	−0.147924
$142$	21.1002	1.77069
$143$	5.76049	0.481716
$144$	6.33906	0.528255
$145$	0	0
$146$	22.9107	1.89610
$147$	2.45062	0.202124
$148$	4.14046	0.340343
$149$	0.0291152	0.00238521	0.00119261	−	0.999999i	$-0.499620\pi$
$149$	0.0291152	0.00238521	0.00119261	+	0.999999i	$0.499620\pi$
$150$	0	0
$151$	3.09586	0.251938	0.125969	−	0.992034i	$-0.459796\pi$
$151$	3.09586	0.251938	0.125969	+	0.992034i	$0.459796\pi$
$152$	7.28034	0.590513
$153$	−12.3324	−0.997017
$154$	−34.6576	−2.79279
$155$	0	0
$156$	2.00933	0.160876
$157$	10.4666	0.835325	0.417662	−	0.908602i	$-0.362849\pi$
$157$	10.4666	0.835325	0.417662	+	0.908602i	$0.362849\pi$
$158$	7.95120	0.632563
$159$	−4.22586	−0.335133
$160$	0	0
$161$	−3.47142	−0.273586
$162$	−11.0976	−0.871911
$163$	−10.1600	−0.795792	−0.397896	−	0.917430i	$-0.630260\pi$
$163$	−10.1600	−0.795792	−0.397896	+	0.917430i	$0.630260\pi$
$164$	−31.0091	−2.42140
$165$	0	0
$166$	34.3299	2.66452
$167$	15.3839	1.19044	0.595220	−	0.803563i	$-0.297065\pi$
$167$	15.3839	1.19044	0.595220	+	0.803563i	$0.297065\pi$
$168$	−2.74196	−0.211547
$169$	−11.6482	−0.896018
$170$	0	0
$171$	14.7959	1.13147
$172$	−26.4377	−2.01585
$173$	5.33498	0.405611	0.202805	−	0.979219i	$-0.434994\pi$
$173$	5.33498	0.405611	0.202805	+	0.979219i	$0.434994\pi$
$174$	0.550585	0.0417398
$175$	0	0
$176$	−12.2992	−0.927089
$177$	−5.97817	−0.449347
$178$	30.4973	2.28587
$179$	15.2028	1.13631	0.568156	−	0.822921i	$-0.307657\pi$
$179$	15.2028	1.13631	0.568156	+	0.822921i	$0.307657\pi$
$180$	0	0
$181$	−1.78208	−0.132461	−0.0662306	−	0.997804i	$-0.521097\pi$
$181$	−1.78208	−0.132461	−0.0662306	+	0.997804i	$0.521097\pi$
$182$	−8.13282	−0.602845
$183$	2.57762	0.190543
$184$	1.33546	0.0984517
$185$	0	0
$186$	5.64957	0.414247
$187$	23.9277	1.74977
$188$	−6.80048	−0.495976
$189$	−12.1191	−0.881536
$190$	0	0
$191$	−19.2734	−1.39457	−0.697287	−	0.716792i	$-0.745610\pi$
$191$	−19.2734	−1.39457	−0.697287	+	0.716792i	$0.745610\pi$
$192$	−7.88598	−0.569121
$193$	19.9908	1.43897	0.719485	−	0.694508i	$-0.244378\pi$
$193$	19.9908	1.43897	0.719485	+	0.694508i	$0.244378\pi$
$194$	18.9226	1.35856
$195$	0	0
$196$	9.48782	0.677702
$197$	−9.87059	−0.703250	−0.351625	−	0.936141i	$-0.614371\pi$
$197$	−9.87059	−0.703250	−0.351625	+	0.936141i	$0.614371\pi$
$198$	27.0965	1.92567
$199$	5.33477	0.378172	0.189086	−	0.981961i	$-0.439448\pi$
$199$	5.33477	0.378172	0.189086	+	0.981961i	$0.439448\pi$
$200$	0	0
$201$	1.86811	0.131767
$202$	−18.6063	−1.30913
$203$	−1.25678	−0.0882087
$204$	8.34630	0.584358
$205$	0	0
$206$	29.3078	2.04197
$207$	2.71408	0.188641
$208$	−2.88616	−0.200119
$209$	−28.7074	−1.98573
$210$	0	0
$211$	−11.9008	−0.819282	−0.409641	−	0.912247i	$-0.634346\pi$
$211$	−11.9008	−0.819282	−0.409641	+	0.912247i	$0.634346\pi$
$212$	−16.3609	−1.12367
$213$	−6.58250	−0.451026
$214$	25.7993	1.76360
$215$	0	0
$216$	4.66226	0.317227
$217$	−12.8959	−0.875428
$218$	−30.6218	−2.07397
$219$	−7.14732	−0.482971
$220$	0	0
$221$	5.61493	0.377701
$222$	−2.29038	−0.153720
$223$	17.7362	1.18770	0.593851	−	0.804575i	$-0.297607\pi$
$223$	17.7362	1.18770	0.593851	+	0.804575i	$0.297607\pi$
$224$	25.5724	1.70862
$225$	0	0
$226$	−31.0193	−2.06338
$227$	−7.74218	−0.513867	−0.256933	−	0.966429i	$-0.582712\pi$
$227$	−7.74218	−0.513867	−0.256933	+	0.966429i	$0.582712\pi$
$228$	−10.0135	−0.663162
$229$	9.77791	0.646143	0.323071	−	0.946375i	$-0.395285\pi$
$229$	9.77791	0.646143	0.323071	+	0.946375i	$0.395285\pi$
$230$	0	0
$231$	10.8119	0.711373
$232$	0.483487	0.0317425
$233$	−9.15354	−0.599668	−0.299834	−	0.953991i	$-0.596931\pi$
$233$	−9.15354	−0.599668	−0.299834	+	0.953991i	$0.596931\pi$
$234$	6.35852	0.415670
$235$	0	0
$236$	−23.1451	−1.50662
$237$	−2.48049	−0.161125
$238$	−33.7818	−2.18975
$239$	−23.6676	−1.53093	−0.765465	−	0.643477i	$-0.777491\pi$
$239$	−23.6676	−1.53093	−0.765465	+	0.643477i	$0.777491\pi$
$240$	0	0
$241$	−1.00000	−0.0644157
$241$	−1.00000	−0.0644157
$242$	−29.0152	−1.86517
$243$	14.5935	0.936175
$244$	9.97952	0.638873
$245$	0	0
$246$	17.1533	1.09366
$247$	−6.73654	−0.428636
$248$	4.96107	0.315028
$249$	−10.7097	−0.678700
$250$	0	0
$251$	20.3164	1.28236	0.641178	−	0.767392i	$-0.278446\pi$
$251$	20.3164	1.28236	0.641178	+	0.767392i	$0.278446\pi$
$252$	−21.5745	−1.35907
$253$	−5.26593	−0.331066
$254$	−39.7662	−2.49516
$255$	0	0
$256$	3.00461	0.187788
$257$	2.77261	0.172951	0.0864754	−	0.996254i	$-0.472440\pi$
$257$	2.77261	0.172951	0.0864754	+	0.996254i	$0.472440\pi$
$258$	14.6246	0.910486
$259$	5.22808	0.324857
$260$	0	0
$261$	0.982595	0.0608211
$262$	43.5594	2.69111
$263$	13.3085	0.820638	0.410319	−	0.911942i	$-0.365417\pi$
$263$	13.3085	0.820638	0.410319	+	0.911942i	$0.365417\pi$
$264$	−4.15938	−0.255992
$265$	0	0
$266$	40.5300	2.48505
$267$	−9.51406	−0.582251
$268$	7.23259	0.441801
$269$	12.6626	0.772054	0.386027	−	0.922487i	$-0.373847\pi$
$269$	12.6626	0.772054	0.386027	+	0.922487i	$0.373847\pi$
$270$	0	0
$271$	1.33076	0.0808382	0.0404191	−	0.999183i	$-0.487131\pi$
$271$	1.33076	0.0808382	0.0404191	+	0.999183i	$0.487131\pi$
$272$	−11.9884	−0.726905
$273$	2.53715	0.153555
$274$	5.20363	0.314363
$275$	0	0
$276$	−1.83683	−0.110564
$277$	24.0562	1.44540	0.722700	−	0.691162i	$-0.242901\pi$
$277$	24.0562	1.44540	0.722700	+	0.691162i	$0.242901\pi$
$278$	33.5030	2.00937
$279$	10.0824	0.603620
$280$	0	0
$281$	12.0823	0.720767	0.360383	−	0.932804i	$-0.382646\pi$
$281$	12.0823	0.720767	0.360383	+	0.932804i	$0.382646\pi$
$282$	3.76183	0.224014
$283$	30.4250	1.80858	0.904289	−	0.426921i	$-0.140402\pi$
$283$	30.4250	1.80858	0.904289	+	0.426921i	$0.140402\pi$
$284$	−25.4848	−1.51225
$285$	0	0
$286$	−12.3370	−0.729502
$287$	−39.1546	−2.31122
$288$	−19.9934	−1.17812
$289$	6.32308	0.371946
$290$	0	0
$291$	−5.90318	−0.346050
$292$	−27.6716	−1.61936
$293$	−14.2566	−0.832877	−0.416439	−	0.909164i	$-0.636722\pi$
$293$	−14.2566	−0.832877	−0.416439	+	0.909164i	$0.636722\pi$
$294$	−5.24839	−0.306092
$295$	0	0
$296$	−2.01126	−0.116902
$297$	−18.3840	−1.06675
$298$	−0.0623548	−0.00361212
$299$	−1.23571	−0.0714632
$300$	0	0
$301$	−33.3824	−1.92413
$302$	−6.63028	−0.381530
$303$	5.80450	0.333460
$304$	14.3832	0.824933
$305$	0	0
$306$	26.4118	1.50986
$307$	20.5271	1.17154	0.585772	−	0.810476i	$-0.300792\pi$
$307$	20.5271	1.17154	0.585772	+	0.810476i	$0.300792\pi$
$308$	41.8595	2.38517
$309$	−9.14299	−0.520126
$310$	0	0
$311$	27.6525	1.56803	0.784015	−	0.620742i	$-0.213168\pi$
$311$	27.6525	1.56803	0.784015	+	0.620742i	$0.213168\pi$
$312$	−0.976049	−0.0552579
$313$	14.9864	0.847084	0.423542	−	0.905877i	$-0.360787\pi$
$313$	14.9864	0.847084	0.423542	+	0.905877i	$0.360787\pi$
$314$	−22.4159	−1.26500
$315$	0	0
$316$	−9.60347	−0.540237
$317$	−27.0688	−1.52034	−0.760168	−	0.649726i	$-0.774883\pi$
$317$	−27.0688	−1.52034	−0.760168	+	0.649726i	$0.774883\pi$
$318$	9.05036	0.507519
$319$	−1.90646	−0.106741
$320$	0	0
$321$	−8.04846	−0.449221
$322$	7.43459	0.414313
$323$	−27.9820	−1.55696
$324$	13.4037	0.744651
$325$	0	0
$326$	21.7592	1.20513
$327$	9.55290	0.528277
$328$	15.0629	0.831709
$329$	−8.58685	−0.473408
$330$	0	0
$331$	7.19907	0.395697	0.197848	−	0.980233i	$-0.436605\pi$
$331$	7.19907	0.395697	0.197848	+	0.980233i	$0.436605\pi$
$332$	−41.4637	−2.27562
$333$	−4.08750	−0.223994
$334$	−32.9470	−1.80278
$335$	0	0
$336$	−5.41707	−0.295526
$337$	−16.0864	−0.876282	−0.438141	−	0.898906i	$-0.644363\pi$
$337$	−16.0864	−0.876282	−0.438141	+	0.898906i	$0.644363\pi$
$338$	24.9465	1.35691
$339$	9.67693	0.525579
$340$	0	0
$341$	−19.5622	−1.05935
$342$	−31.6878	−1.71348
$343$	−10.8831	−0.587635
$344$	12.8423	0.692411
$345$	0	0
$346$	−11.4257	−0.614249
$347$	−21.6786	−1.16377	−0.581883	−	0.813272i	$-0.697684\pi$
$347$	−21.6786	−1.16377	−0.581883	+	0.813272i	$0.697684\pi$
$348$	−0.664998	−0.0356476
$349$	35.9326	1.92343	0.961713	−	0.274059i	$-0.0883663\pi$
$349$	35.9326	1.92343	0.961713	+	0.274059i	$0.0883663\pi$
$350$	0	0
$351$	−4.31402	−0.230265
$352$	38.7917	2.06761
$353$	6.78947	0.361367	0.180683	−	0.983541i	$-0.442169\pi$
$353$	6.78947	0.361367	0.180683	+	0.983541i	$0.442169\pi$
$354$	12.8032	0.680482
$355$	0	0
$356$	−36.8346	−1.95223
$357$	10.5387	0.557769
$358$	−32.5592	−1.72081
$359$	−16.7916	−0.886227	−0.443114	−	0.896465i	$-0.646126\pi$
$359$	−16.7916	−0.886227	−0.443114	+	0.896465i	$0.646126\pi$
$360$	0	0
$361$	14.5716	0.766927
$362$	3.81661	0.200597
$363$	9.05172	0.475092
$364$	9.82284	0.514857
$365$	0	0
$366$	−5.52038	−0.288555
$367$	26.5050	1.38355	0.691775	−	0.722113i	$-0.256829\pi$
$367$	26.5050	1.38355	0.691775	+	0.722113i	$0.256829\pi$
$368$	2.63837	0.137535
$369$	30.6125	1.59362
$370$	0	0
$371$	−20.6586	−1.07254
$372$	−6.82357	−0.353785
$373$	15.6507	0.810363	0.405182	−	0.914236i	$-0.367208\pi$
$373$	15.6507	0.810363	0.405182	+	0.914236i	$0.367208\pi$
$374$	−51.2450	−2.64981
$375$	0	0
$376$	3.30339	0.170359
$377$	−0.447374	−0.0230409
$378$	25.9550	1.33498
$379$	−27.1299	−1.39357	−0.696784	−	0.717281i	$-0.745386\pi$
$379$	−27.1299	−1.39357	−0.696784	+	0.717281i	$0.745386\pi$
$380$	0	0
$381$	12.4057	0.635561
$382$	41.2770	2.11192
$383$	32.7943	1.67571	0.837855	−	0.545893i	$-0.183810\pi$
$383$	32.7943	1.67571	0.837855	+	0.545893i	$0.183810\pi$
$384$	6.42703	0.327978
$385$	0	0
$386$	−42.8135	−2.17915
$387$	26.0995	1.32671
$388$	−22.8548	−1.16027
$389$	−19.6781	−0.997719	−0.498859	−	0.866683i	$-0.666248\pi$
$389$	−19.6781	−0.997719	−0.498859	+	0.866683i	$0.666248\pi$
$390$	0	0
$391$	−5.13286	−0.259580
$392$	−4.60878	−0.232779
$393$	−13.5890	−0.685474
$394$	21.1394	1.06499
$395$	0	0
$396$	−32.7272	−1.64461
$397$	−12.9733	−0.651112	−0.325556	−	0.945523i	$-0.605551\pi$
$397$	−12.9733	−0.651112	−0.325556	+	0.945523i	$0.605551\pi$
$398$	−11.4252	−0.572696
$399$	−12.6439	−0.632987
$400$	0	0
$401$	1.70161	0.0849741	0.0424871	−	0.999097i	$-0.486472\pi$
$401$	1.70161	0.0849741	0.0424871	+	0.999097i	$0.486472\pi$
$402$	−4.00086	−0.199545
$403$	−4.59051	−0.228670
$404$	22.4727	1.11806
$405$	0	0
$406$	2.69159	0.133582
$407$	7.93068	0.393109
$408$	−4.05428	−0.200717
$409$	−8.83196	−0.436712	−0.218356	−	0.975869i	$-0.570069\pi$
$409$	−8.83196	−0.436712	−0.218356	+	0.975869i	$0.570069\pi$
$410$	0	0
$411$	−1.62335	−0.0800739
$412$	−35.3980	−1.74393
$413$	−29.2249	−1.43806
$414$	−5.81262	−0.285675
$415$	0	0
$416$	9.10294	0.446308
$417$	−10.4517	−0.511824
$418$	61.4815	3.00716
$419$	−29.8230	−1.45695	−0.728473	−	0.685074i	$-0.759770\pi$
$419$	−29.8230	−1.45695	−0.728473	+	0.685074i	$0.759770\pi$
$420$	0	0
$421$	12.5669	0.612471	0.306236	−	0.951956i	$-0.400930\pi$
$421$	12.5669	0.612471	0.306236	+	0.951956i	$0.400930\pi$
$422$	25.4874	1.24070
$423$	6.71350	0.326422
$424$	7.94741	0.385960
$425$	0	0
$426$	14.0975	0.683025
$427$	12.6010	0.609803
$428$	−31.1604	−1.50619
$429$	3.84870	0.185817
$430$	0	0
$431$	17.3929	0.837786	0.418893	−	0.908036i	$-0.362418\pi$
$431$	17.3929	0.837786	0.418893	+	0.908036i	$0.362418\pi$
$432$	9.21086	0.443158
$433$	22.6040	1.08628	0.543140	−	0.839642i	$-0.317235\pi$
$433$	22.6040	1.08628	0.543140	+	0.839642i	$0.317235\pi$
$434$	27.6185	1.32573
$435$	0	0
$436$	36.9850	1.77126
$437$	6.15819	0.294586
$438$	15.3071	0.731403
$439$	30.9701	1.47812	0.739061	−	0.673638i	$-0.235269\pi$
$439$	30.9701	1.47812	0.739061	+	0.673638i	$0.235269\pi$
$440$	0	0
$441$	−9.36647	−0.446022
$442$	−12.0252	−0.571983
$443$	15.6463	0.743381	0.371690	−	0.928357i	$-0.378778\pi$
$443$	15.6463	0.743381	0.371690	+	0.928357i	$0.378778\pi$
$444$	2.76633	0.131284
$445$	0	0
$446$	−37.9848	−1.79863
$447$	0.0194525	0.000920071 0
$448$	−38.5514	−1.82138
$449$	21.9087	1.03394	0.516968	−	0.856005i	$-0.327061\pi$
$449$	21.9087	1.03394	0.516968	+	0.856005i	$0.327061\pi$
$450$	0	0
$451$	−59.3952	−2.79681
$452$	37.4652	1.76222
$453$	2.06841	0.0971825
$454$	16.5811	0.778190
$455$	0	0
$456$	4.86415	0.227785
$457$	2.24888	0.105198	0.0525990	−	0.998616i	$-0.483249\pi$
$457$	2.24888	0.105198	0.0525990	+	0.998616i	$0.483249\pi$
$458$	−20.9409	−0.978506
$459$	−17.9194	−0.836407
$460$	0	0
$461$	15.4913	0.721503	0.360751	−	0.932662i	$-0.382520\pi$
$461$	15.4913	0.721503	0.360751	+	0.932662i	$0.382520\pi$
$462$	−23.1555	−1.07729
$463$	24.0845	1.11930	0.559652	−	0.828728i	$-0.310935\pi$
$463$	24.0845	1.11930	0.559652	+	0.828728i	$0.310935\pi$
$464$	0.955188	0.0443435
$465$	0	0
$466$	19.6038	0.908126
$467$	16.6747	0.771611	0.385806	−	0.922580i	$-0.373924\pi$
$467$	16.6747	0.771611	0.385806	+	0.922580i	$0.373924\pi$
$468$	−7.67984	−0.355001
$469$	9.13247	0.421698
$470$	0	0
$471$	6.99295	0.322218
$472$	11.2429	0.517496
$473$	−50.6391	−2.32839
$474$	5.31236	0.244005
$475$	0	0
$476$	40.8018	1.87015
$477$	16.1516	0.739531
$478$	50.6879	2.31841
$479$	−34.4901	−1.57589	−0.787946	−	0.615745i	$-0.788855\pi$
$479$	−34.4901	−1.57589	−0.787946	+	0.615745i	$0.788855\pi$
$480$	0	0
$481$	1.86103	0.0848557
$482$	2.14166	0.0975498
$483$	−2.31933	−0.105533
$484$	35.0447	1.59294
$485$	0	0
$486$	−31.2543	−1.41773
$487$	−15.0896	−0.683775	−0.341887	−	0.939741i	$-0.611066\pi$
$487$	−15.0896	−0.683775	−0.341887	+	0.939741i	$0.611066\pi$
$488$	−4.84763	−0.219442
$489$	−6.78811	−0.306969
$490$	0	0
$491$	−13.8338	−0.624311	−0.312156	−	0.950031i	$-0.601051\pi$
$491$	−13.8338	−0.624311	−0.312156	+	0.950031i	$0.601051\pi$
$492$	−20.7178	−0.934032
$493$	−1.85828	−0.0836929
$494$	14.4274	0.649118
$495$	0	0
$496$	9.80121	0.440087
$497$	−32.1792	−1.44344
$498$	22.9365	1.02781
$499$	16.2493	0.727421	0.363710	−	0.931512i	$-0.381510\pi$
$499$	16.2493	0.727421	0.363710	+	0.931512i	$0.381510\pi$
$500$	0	0
$501$	10.2783	0.459200
$502$	−43.5107	−1.94198
$503$	3.41926	0.152457	0.0762287	−	0.997090i	$-0.475712\pi$
$503$	3.41926	0.152457	0.0762287	+	0.997090i	$0.475712\pi$
$504$	10.4800	0.466816
$505$	0	0
$506$	11.2778	0.501360
$507$	−7.78243	−0.345630
$508$	48.0297	2.13098
$509$	−2.20760	−0.0978501	−0.0489250	−	0.998802i	$-0.515580\pi$
$509$	−2.20760	−0.0978501	−0.0489250	+	0.998802i	$0.515580\pi$
$510$	0	0
$511$	−34.9404	−1.54567
$512$	−25.6740	−1.13464
$513$	21.4989	0.949202
$514$	−5.93799	−0.261913
$515$	0	0
$516$	−17.6636	−0.777596
$517$	−13.0257	−0.572871
$518$	−11.1968	−0.491958
$519$	3.56441	0.156460
$520$	0	0
$521$	−20.7390	−0.908594	−0.454297	−	0.890850i	$-0.650109\pi$
$521$	−20.7390	−0.908594	−0.454297	+	0.890850i	$0.650109\pi$
$522$	−2.10438	−0.0921063
$523$	−19.1525	−0.837481	−0.418741	−	0.908106i	$-0.637528\pi$
$523$	−19.1525	−0.837481	−0.418741	+	0.908106i	$0.637528\pi$
$524$	−52.6111	−2.29833
$525$	0	0
$526$	−28.5023	−1.24276
$527$	−19.0679	−0.830611
$528$	−8.21737	−0.357615
$529$	−21.8704	−0.950886
$530$	0	0
$531$	22.8490	0.991564
$532$	−48.9522	−2.12235
$533$	−13.9378	−0.603713
$534$	20.3759	0.881750
$535$	0	0
$536$	−3.51329	−0.151751
$537$	10.1573	0.438321
$538$	−27.1190	−1.16918
$539$	18.1731	0.782771
$540$	0	0
$541$	−9.23177	−0.396905	−0.198452	−	0.980111i	$-0.563592\pi$
$541$	−9.23177	−0.396905	−0.198452	+	0.980111i	$0.563592\pi$
$542$	−2.85004	−0.122420
$543$	−1.19065	−0.0510956
$544$	37.8115	1.62115
$545$	0	0
$546$	−5.43371	−0.232541
$547$	10.2430	0.437958	0.218979	−	0.975730i	$-0.429727\pi$
$547$	10.2430	0.437958	0.218979	+	0.975730i	$0.429727\pi$
$548$	−6.28496	−0.268480
$549$	−9.85187	−0.420468
$550$	0	0
$551$	2.22949	0.0949794
$552$	0.892252	0.0379768
$553$	−12.1261	−0.515656
$554$	−51.5202	−2.18889
$555$	0	0
$556$	−40.4649	−1.71610
$557$	8.93719	0.378681	0.189340	−	0.981912i	$-0.439365\pi$
$557$	8.93719	0.378681	0.189340	+	0.981912i	$0.439365\pi$
$558$	−21.5931	−0.914110
$559$	−11.8831	−0.502600
$560$	0	0
$561$	15.9866	0.674955
$562$	−25.8761	−1.09152
$563$	13.1364	0.553632	0.276816	−	0.960923i	$-0.410721\pi$
$563$	13.1364	0.553632	0.276816	+	0.960923i	$0.410721\pi$
$564$	−4.54355	−0.191318
$565$	0	0
$566$	−65.1599	−2.73888
$567$	16.9246	0.710768
$568$	12.3794	0.519430
$569$	−0.827279	−0.0346813	−0.0173407	−	0.999850i	$-0.505520\pi$
$569$	−0.827279	−0.0346813	−0.0173407	+	0.999850i	$0.505520\pi$
$570$	0	0
$571$	−31.3194	−1.31068	−0.655338	−	0.755335i	$-0.727474\pi$
$571$	−31.3194	−1.31068	−0.655338	+	0.755335i	$0.727474\pi$
$572$	14.9006	0.623027
$573$	−12.8770	−0.537943
$574$	83.8558	3.50007
$575$	0	0
$576$	30.1408	1.25587
$577$	6.14406	0.255781	0.127890	−	0.991788i	$-0.459179\pi$
$577$	6.14406	0.255781	0.127890	+	0.991788i	$0.459179\pi$
$578$	−13.5419	−0.563268
$579$	13.3563	0.555068
$580$	0	0
$581$	−52.3555	−2.17207
$582$	12.6426	0.524052
$583$	−31.3378	−1.29788
$584$	13.4417	0.556221
$585$	0	0
$586$	30.5327	1.26129
$587$	10.8307	0.447029	0.223515	−	0.974701i	$-0.428247\pi$
$587$	10.8307	0.447029	0.223515	+	0.974701i	$0.428247\pi$
$588$	6.33902	0.261417
$589$	22.8769	0.942624
$590$	0	0
$591$	−6.59475	−0.271272
$592$	−3.97349	−0.163309
$593$	−1.35332	−0.0555742	−0.0277871	−	0.999614i	$-0.508846\pi$
$593$	−1.35332	−0.0555742	−0.0277871	+	0.999614i	$0.508846\pi$
$594$	39.3722	1.61546
$595$	0	0
$596$	0.0753123	0.00308491
$597$	3.56427	0.145876
$598$	2.64648	0.108222
$599$	0.439903	0.0179739	0.00898697	−	0.999960i	$-0.497139\pi$
$599$	0.439903	0.0179739	0.00898697	+	0.999960i	$0.497139\pi$
$600$	0	0
$601$	−20.3825	−0.831418	−0.415709	−	0.909498i	$-0.636467\pi$
$601$	−20.3825	−0.831418	−0.415709	+	0.909498i	$0.636467\pi$
$602$	71.4937	2.91386
$603$	−7.14008	−0.290767
$604$	8.00807	0.325844
$605$	0	0
$606$	−12.4313	−0.504985
$607$	−21.5327	−0.873987	−0.436993	−	0.899465i	$-0.643957\pi$
$607$	−21.5327	−0.873987	−0.436993	+	0.899465i	$0.643957\pi$
$608$	−45.3646	−1.83978
$609$	−0.839682	−0.0340256
$610$	0	0
$611$	−3.05664	−0.123659
$612$	−31.9003	−1.28949
$613$	−31.5481	−1.27421	−0.637107	−	0.770775i	$-0.719869\pi$
$613$	−31.5481	−1.27421	−0.637107	+	0.770775i	$0.719869\pi$
$614$	−43.9620	−1.77416
$615$	0	0
$616$	−20.3336	−0.819263
$617$	17.5057	0.704755	0.352377	−	0.935858i	$-0.385373\pi$
$617$	17.5057	0.704755	0.352377	+	0.935858i	$0.385373\pi$
$618$	19.5812	0.787669
$619$	−17.9898	−0.723070	−0.361535	−	0.932359i	$-0.617747\pi$
$619$	−17.9898	−0.723070	−0.361535	+	0.932359i	$0.617747\pi$
$620$	0	0
$621$	3.94365	0.158253
$622$	−59.2222	−2.37460
$623$	−46.5105	−1.86340
$624$	−1.92830	−0.0771940
$625$	0	0
$626$	−32.0958	−1.28281
$627$	−19.1800	−0.765977
$628$	27.0739	1.08037
$629$	7.73028	0.308227
$630$	0	0
$631$	12.8394	0.511129	0.255564	−	0.966792i	$-0.417739\pi$
$631$	12.8394	0.511129	0.255564	+	0.966792i	$0.417739\pi$
$632$	4.66496	0.185562
$633$	−7.95115	−0.316030
$634$	57.9722	2.30237
$635$	0	0
$636$	−10.9310	−0.433444
$637$	4.26454	0.168967
$638$	4.08298	0.161647
$639$	25.1589	0.995269
$640$	0	0
$641$	20.7711	0.820409	0.410204	−	0.911994i	$-0.365457\pi$
$641$	20.7711	0.820409	0.410204	+	0.911994i	$0.365457\pi$
$642$	17.2370	0.680292
$643$	39.5976	1.56158	0.780788	−	0.624796i	$-0.214818\pi$
$643$	39.5976	1.56158	0.780788	+	0.624796i	$0.214818\pi$
$644$	−8.97951	−0.353842
$645$	0	0
$646$	59.9279	2.35783
$647$	−40.3929	−1.58801	−0.794004	−	0.607913i	$-0.792007\pi$
$647$	−40.3929	−1.58801	−0.794004	+	0.607913i	$0.792007\pi$
$648$	−6.51096	−0.255775
$649$	−44.3324	−1.74020
$650$	0	0
$651$	−8.61600	−0.337688
$652$	−26.2808	−1.02924
$653$	−30.0280	−1.17509	−0.587544	−	0.809192i	$-0.699905\pi$
$653$	−30.0280	−1.17509	−0.587544	+	0.809192i	$0.699905\pi$
$654$	−20.4590	−0.800012
$655$	0	0
$656$	29.7586	1.16188
$657$	27.3177	1.06576
$658$	18.3901	0.716921
$659$	10.3905	0.404757	0.202378	−	0.979307i	$-0.435133\pi$
$659$	10.3905	0.404757	0.202378	+	0.979307i	$0.435133\pi$
$660$	0	0
$661$	15.1209	0.588135	0.294068	−	0.955785i	$-0.404991\pi$
$661$	15.1209	0.588135	0.294068	+	0.955785i	$0.404991\pi$
$662$	−15.4179	−0.599236
$663$	3.75145	0.145694
$664$	20.1413	0.781635
$665$	0	0
$666$	8.75402	0.339211
$667$	0.408965	0.0158352
$668$	39.7934	1.53965
$669$	11.8499	0.458144
$670$	0	0
$671$	19.1149	0.737922
$672$	17.0854	0.659085
$673$	−21.3727	−0.823858	−0.411929	−	0.911216i	$-0.635145\pi$
$673$	−21.3727	−0.823858	−0.411929	+	0.911216i	$0.635145\pi$
$674$	34.4516	1.32702
$675$	0	0
$676$	−30.1305	−1.15886
$677$	−0.698276	−0.0268369	−0.0134185	−	0.999910i	$-0.504271\pi$
$677$	−0.698276	−0.0268369	−0.0134185	+	0.999910i	$0.504271\pi$
$678$	−20.7247	−0.795926
$679$	−28.8583	−1.10748
$680$	0	0
$681$	−5.17272	−0.198219
$682$	41.8956	1.60427
$683$	−13.5557	−0.518696	−0.259348	−	0.965784i	$-0.583508\pi$
$683$	−13.5557	−0.518696	−0.259348	+	0.965784i	$0.583508\pi$
$684$	38.2725	1.46339
$685$	0	0
$686$	23.3080	0.889903
$687$	6.53283	0.249243
$688$	25.3715	0.967281
$689$	−7.35379	−0.280157
$690$	0	0
$691$	42.0039	1.59790	0.798952	−	0.601394i	$-0.205388\pi$
$691$	42.0039	1.59790	0.798952	+	0.601394i	$0.205388\pi$
$692$	13.8000	0.524596
$693$	−41.3241	−1.56977
$694$	46.4281	1.76239
$695$	0	0
$696$	0.323028	0.0122443
$697$	−57.8943	−2.19290
$698$	−76.9553	−2.91280
$699$	−6.11568	−0.231316
$700$	0	0
$701$	−25.8338	−0.975730	−0.487865	−	0.872919i	$-0.662224\pi$
$701$	−25.8338	−0.975730	−0.487865	+	0.872919i	$0.662224\pi$
$702$	9.23915	0.348709
$703$	−9.27446	−0.349793
$704$	−58.4801	−2.20405
$705$	0	0
$706$	−14.5407	−0.547247
$707$	28.3759	1.06719
$708$	−15.4637	−0.581162
$709$	14.4431	0.542422	0.271211	−	0.962520i	$-0.412576\pi$
$709$	14.4431	0.542422	0.271211	+	0.962520i	$0.412576\pi$
$710$	0	0
$711$	9.48064	0.355552
$712$	17.8927	0.670558
$713$	4.19640	0.157156
$714$	−22.5704	−0.844674
$715$	0	0
$716$	39.3251	1.46965
$717$	−15.8128	−0.590541
$718$	35.9619	1.34209
$719$	−24.6188	−0.918127	−0.459064	−	0.888403i	$-0.651815\pi$
$719$	−24.6188	−0.918127	−0.459064	+	0.888403i	$0.651815\pi$
$720$	0	0
$721$	−44.6964	−1.66458
$722$	−31.2074	−1.16142
$723$	−0.668121	−0.0248477
$724$	−4.60971	−0.171319
$725$	0	0
$726$	−19.3857	−0.719471
$727$	−12.6489	−0.469120	−0.234560	−	0.972102i	$-0.575365\pi$
$727$	−12.6489	−0.469120	−0.234560	+	0.972102i	$0.575365\pi$
$728$	−4.77152	−0.176844
$729$	−5.79511	−0.214634
$730$	0	0
$731$	−49.3595	−1.82563
$732$	6.66753	0.246439
$733$	−9.47689	−0.350037	−0.175018	−	0.984565i	$-0.555999\pi$
$733$	−9.47689	−0.350037	−0.175018	+	0.984565i	$0.555999\pi$
$734$	−56.7646	−2.09522
$735$	0	0
$736$	−8.32142	−0.306732
$737$	13.8534	0.510296
$738$	−65.5614	−2.41335
$739$	−20.0104	−0.736094	−0.368047	−	0.929807i	$-0.619973\pi$
$739$	−20.0104	−0.736094	−0.368047	+	0.929807i	$0.619973\pi$
$740$	0	0
$741$	−4.50083	−0.165342
$742$	44.2436	1.62423
$743$	−41.0448	−1.50579	−0.752894	−	0.658142i	$-0.771343\pi$
$743$	−41.0448	−1.50579	−0.752894	+	0.658142i	$0.771343\pi$
$744$	3.31460	0.121519
$745$	0	0
$746$	−33.5185	−1.22720
$747$	40.9334	1.49767
$748$	61.8938	2.26306
$749$	−39.3457	−1.43766
$750$	0	0
$751$	−4.23259	−0.154450	−0.0772248	−	0.997014i	$-0.524606\pi$
$751$	−4.23259	−0.154450	−0.0772248	+	0.997014i	$0.524606\pi$
$752$	6.52624	0.237988
$753$	13.5738	0.494656
$754$	0.958121	0.0348927
$755$	0	0
$756$	−31.3485	−1.14013
$757$	−10.3305	−0.375468	−0.187734	−	0.982220i	$-0.560114\pi$
$757$	−10.3305	−0.375468	−0.187734	+	0.982220i	$0.560114\pi$
$758$	58.1029	2.11039
$759$	−3.51828	−0.127705
$760$	0	0
$761$	−19.0087	−0.689064	−0.344532	−	0.938775i	$-0.611962\pi$
$761$	−19.0087	−0.689064	−0.344532	+	0.938775i	$0.611962\pi$
$762$	−26.5687	−0.962481
$763$	46.7003	1.69067
$764$	−49.8545	−1.80367
$765$	0	0
$766$	−70.2341	−2.53766
$767$	−10.4031	−0.375635
$768$	2.00745	0.0724375
$769$	13.7862	0.497143	0.248571	−	0.968614i	$-0.420039\pi$
$769$	13.7862	0.497143	0.248571	+	0.968614i	$0.420039\pi$
$770$	0	0
$771$	1.85244	0.0667140
$772$	51.7102	1.86109
$773$	27.7899	0.999532	0.499766	−	0.866160i	$-0.333419\pi$
$773$	27.7899	0.999532	0.499766	+	0.866160i	$0.333419\pi$
$774$	−55.8963	−2.00915
$775$	0	0
$776$	11.1019	0.398534
$777$	3.49299	0.125310
$778$	42.1437	1.51093
$779$	69.4591	2.48863
$780$	0	0
$781$	−48.8140	−1.74670
$782$	10.9928	0.393103
$783$	1.42774	0.0510234
$784$	−9.10521	−0.325186
$785$	0	0
$786$	29.1030	1.03807
$787$	20.0211	0.713676	0.356838	−	0.934166i	$-0.383855\pi$
$787$	20.0211	0.713676	0.356838	+	0.934166i	$0.383855\pi$
$788$	−25.5322	−0.909548
$789$	8.89171	0.316553
$790$	0	0
$791$	47.3067	1.68203
$792$	15.8975	0.564893
$793$	4.48554	0.159286
$794$	27.7844	0.986031
$795$	0	0
$796$	13.7994	0.489108
$797$	17.9513	0.635866	0.317933	−	0.948113i	$-0.397011\pi$
$797$	17.9513	0.635866	0.317933	+	0.948113i	$0.397011\pi$
$798$	27.0789	0.958584
$799$	−12.6966	−0.449173
$800$	0	0
$801$	36.3635	1.28484
$802$	−3.64426	−0.128683
$803$	−53.0025	−1.87042
$804$	4.83225	0.170420
$805$	0	0
$806$	9.83131	0.346293
$807$	8.46018	0.297812
$808$	−10.9163	−0.384034
$809$	14.3886	0.505876	0.252938	−	0.967483i	$-0.418603\pi$
$809$	14.3886	0.505876	0.252938	+	0.967483i	$0.418603\pi$
$810$	0	0
$811$	38.3356	1.34615	0.673073	−	0.739576i	$-0.264974\pi$
$811$	38.3356	1.34615	0.673073	+	0.739576i	$0.264974\pi$
$812$	−3.25091	−0.114085
$813$	0.889112	0.0311825
$814$	−16.9848	−0.595317
$815$	0	0
$816$	−8.00973	−0.280397
$817$	59.2193	2.07182
$818$	18.9150	0.661349
$819$	−9.69720	−0.338848
$820$	0	0
$821$	−3.60954	−0.125974	−0.0629870	−	0.998014i	$-0.520063\pi$
$821$	−3.60954	−0.125974	−0.0629870	+	0.998014i	$0.520063\pi$
$822$	3.47666	0.121262
$823$	8.67508	0.302394	0.151197	−	0.988504i	$-0.451687\pi$
$823$	8.67508	0.302394	0.151197	+	0.988504i	$0.451687\pi$
$824$	17.1948	0.599011
$825$	0	0
$826$	62.5897	2.17777
$827$	−48.7273	−1.69441	−0.847207	−	0.531263i	$-0.821718\pi$
$827$	−48.7273	−1.69441	−0.847207	+	0.531263i	$0.821718\pi$
$828$	7.02050	0.243979
$829$	−39.4920	−1.37161	−0.685806	−	0.727784i	$-0.740550\pi$
$829$	−39.4920	−1.37161	−0.685806	+	0.727784i	$0.740550\pi$
$830$	0	0
$831$	16.0725	0.557548
$832$	−13.7231	−0.475762
$833$	17.7139	0.613750
$834$	22.3840	0.775096
$835$	0	0
$836$	−74.2575	−2.56825
$837$	14.6501	0.506382
$838$	63.8706	2.20637
$839$	46.1683	1.59391	0.796953	−	0.604042i	$-0.206444\pi$
$839$	46.1683	1.59391	0.796953	+	0.604042i	$0.206444\pi$
$840$	0	0
$841$	−28.8519	−0.994894
$842$	−26.9139	−0.927515
$843$	8.07241	0.278029
$844$	−30.7837	−1.05962
$845$	0	0
$846$	−14.3780	−0.494327
$847$	44.2503	1.52046
$848$	15.7011	0.539177
$849$	20.3276	0.697641
$850$	0	0
$851$	−1.70125	−0.0583182
$852$	−17.0270	−0.583334
$853$	−29.7086	−1.01720	−0.508601	−	0.861002i	$-0.669837\pi$
$853$	−29.7086	−1.01720	−0.508601	+	0.861002i	$0.669837\pi$
$854$	−26.9869	−0.923474
$855$	0	0
$856$	15.1364	0.517352
$857$	−37.2388	−1.27205	−0.636026	−	0.771667i	$-0.719423\pi$
$857$	−37.2388	−1.27205	−0.636026	+	0.771667i	$0.719423\pi$
$858$	−8.24261	−0.281398
$859$	−37.3956	−1.27592	−0.637960	−	0.770069i	$-0.720222\pi$
$859$	−37.3956	−1.27592	−0.637960	+	0.770069i	$0.720222\pi$
$860$	0	0
$861$	−26.1600	−0.891532
$862$	−37.2496	−1.26873
$863$	−4.68539	−0.159493	−0.0797463	−	0.996815i	$-0.525411\pi$
$863$	−4.68539	−0.159493	−0.0797463	+	0.996815i	$0.525411\pi$
$864$	−29.0510	−0.988337
$865$	0	0
$866$	−48.4101	−1.64504
$867$	4.22459	0.143474
$868$	−33.3577	−1.13223
$869$	−18.3946	−0.623994
$870$	0	0
$871$	3.25087	0.110151
$872$	−17.9657	−0.608397
$873$	22.5624	0.763622
$874$	−13.1887	−0.446116
$875$	0	0
$876$	−18.4880	−0.624651
$877$	−55.7903	−1.88390	−0.941952	−	0.335747i	$-0.891011\pi$
$877$	−55.7903	−1.88390	−0.941952	+	0.335747i	$0.891011\pi$
$878$	−66.3274	−2.23844
$879$	−9.52512	−0.321274
$880$	0	0
$881$	36.2433	1.22107	0.610533	−	0.791990i	$-0.290955\pi$
$881$	36.2433	1.22107	0.610533	+	0.791990i	$0.290955\pi$
$882$	20.0598	0.675448
$883$	43.1430	1.45188	0.725938	−	0.687760i	$-0.241406\pi$
$883$	43.1430	1.45188	0.725938	+	0.687760i	$0.241406\pi$
$884$	14.5241	0.488499
$885$	0	0
$886$	−33.5091	−1.12576
$887$	−1.82371	−0.0612343	−0.0306171	−	0.999531i	$-0.509747\pi$
$887$	−1.82371	−0.0612343	−0.0306171	+	0.999531i	$0.509747\pi$
$888$	−1.34376	−0.0450938
$889$	60.6463	2.03401
$890$	0	0
$891$	25.6737	0.860100
$892$	45.8781	1.53611
$893$	15.2328	0.509746
$894$	−0.0416606	−0.00139334
$895$	0	0
$896$	31.4192	1.04964
$897$	−0.825607	−0.0275662
$898$	−46.9210	−1.56577
$899$	1.51925	0.0506698
$900$	0	0
$901$	−30.5459	−1.01763
$902$	127.204	4.23544
$903$	−22.3035	−0.742214
$904$	−18.1990	−0.605290
$905$	0	0
$906$	−4.42983	−0.147171
$907$	0.682189	0.0226517	0.0113259	−	0.999936i	$-0.496395\pi$
$907$	0.682189	0.0226517	0.0113259	+	0.999936i	$0.496395\pi$
$908$	−20.0267	−0.664609
$909$	−22.1853	−0.735839
$910$	0	0
$911$	19.1362	0.634011	0.317005	−	0.948424i	$-0.397323\pi$
$911$	19.1362	0.634011	0.317005	+	0.948424i	$0.397323\pi$
$912$	9.60972	0.318210
$913$	−79.4201	−2.62842
$914$	−4.81633	−0.159310
$915$	0	0
$916$	25.2925	0.835688
$917$	−66.4311	−2.19375
$918$	38.3773	1.26664
$919$	−11.9392	−0.393837	−0.196919	−	0.980420i	$-0.563093\pi$
$919$	−11.9392	−0.393837	−0.196919	+	0.980420i	$0.563093\pi$
$920$	0	0
$921$	13.7146	0.451911
$922$	−33.1771	−1.09263
$923$	−11.4548	−0.377039
$924$	27.9672	0.920054
$925$	0	0
$926$	−51.5808	−1.69505
$927$	34.9452	1.14775
$928$	−3.01266	−0.0988954
$929$	−40.6930	−1.33509	−0.667546	−	0.744568i	$-0.732655\pi$
$929$	−40.6930	−1.33509	−0.667546	+	0.744568i	$0.732655\pi$
$930$	0	0
$931$	−21.2523	−0.696518
$932$	−23.6775	−0.775581
$933$	18.4752	0.604852
$934$	−35.7114	−1.16851
$935$	0	0
$936$	3.73054	0.121937
$937$	13.1431	0.429367	0.214683	−	0.976684i	$-0.431128\pi$
$937$	13.1431	0.429367	0.214683	+	0.976684i	$0.431128\pi$
$938$	−19.5586	−0.638611
$939$	10.0128	0.326754
$940$	0	0
$941$	44.5371	1.45187	0.725934	−	0.687764i	$-0.241408\pi$
$941$	44.5371	1.45187	0.725934	+	0.687764i	$0.241408\pi$
$942$	−14.9765	−0.487961
$943$	12.7412	0.414910
$944$	22.2117	0.722930
$945$	0	0
$946$	108.452	3.52606
$947$	−26.2467	−0.852902	−0.426451	−	0.904511i	$-0.640236\pi$
$947$	−26.2467	−0.852902	−0.426451	+	0.904511i	$0.640236\pi$
$948$	−6.41628	−0.208391
$949$	−12.4377	−0.403744
$950$	0	0
$951$	−18.0853	−0.586455
$952$	−19.8198	−0.642362
$953$	4.59496	0.148845	0.0744227	−	0.997227i	$-0.476289\pi$
$953$	4.59496	0.148845	0.0744227	+	0.997227i	$0.476289\pi$
$954$	−34.5912	−1.11993
$955$	0	0
$956$	−61.2210	−1.98003
$957$	−1.27375	−0.0411744
$958$	73.8659	2.38650
$959$	−7.93590	−0.256264
$960$	0	0
$961$	−15.4109	−0.497127
$962$	−3.98569	−0.128504
$963$	30.7618	0.991287
$964$	−2.58670	−0.0833120
$965$	0	0
$966$	4.96721	0.159817
$967$	−45.8291	−1.47377	−0.736883	−	0.676020i	$-0.763703\pi$
$967$	−45.8291	−1.47377	−0.736883	+	0.676020i	$0.763703\pi$
$968$	−17.0232	−0.547146
$969$	−18.6954	−0.600582
$970$	0	0
$971$	28.5431	0.915991	0.457996	−	0.888954i	$-0.348568\pi$
$971$	28.5431	0.915991	0.457996	+	0.888954i	$0.348568\pi$
$972$	37.7491	1.21080
$973$	−51.0944	−1.63801
$974$	32.3167	1.03550
$975$	0	0
$976$	−9.57708	−0.306555
$977$	−27.0869	−0.866586	−0.433293	−	0.901253i	$-0.642648\pi$
$977$	−27.0869	−0.866586	−0.433293	+	0.901253i	$0.642648\pi$
$978$	14.5378	0.464868
$979$	−70.5535	−2.25490
$980$	0	0
$981$	−36.5120	−1.16574
$982$	29.6273	0.945445
$983$	32.8360	1.04731	0.523653	−	0.851932i	$-0.324569\pi$
$983$	32.8360	1.04731	0.523653	+	0.851932i	$0.324569\pi$
$984$	10.0638	0.320824
$985$	0	0
$986$	3.97981	0.126743
$987$	−5.73706	−0.182613
$988$	−17.4254	−0.554376
$989$	10.8629	0.345419
$990$	0	0
$991$	24.5231	0.779002	0.389501	−	0.921026i	$-0.372648\pi$
$991$	24.5231	0.779002	0.389501	+	0.921026i	$0.372648\pi$
$992$	−30.9130	−0.981488
$993$	4.80985	0.152636
$994$	68.9169	2.18591
$995$	0	0
$996$	−27.7028	−0.877797
$997$	−26.7747	−0.847962	−0.423981	−	0.905671i	$-0.639368\pi$
$997$	−26.7747	−0.847962	−0.423981	+	0.905671i	$0.639368\pi$
$998$	−34.8005	−1.10159
$999$	−5.93927	−0.187910

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6025.2.a.i.1.2		15
5.4	even	2		1205.2.a.c.1.14	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1205.2.a.c.1.14	✓	15	5.4	even	2
6025.2.a.i.1.2		15	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6025 = 5^{2} \cdot 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6025.a (trivial)

\(f(q)\)	\(=\)	\(q-2.14166 q^{2} +0.668121 q^{3} +2.58670 q^{4} -1.43089 q^{6} +3.26618 q^{7} -1.25651 q^{8} -2.55361 q^{9} +O(q^{10})\)	\(q-2.14166 q^{2} +0.668121 q^{3} +2.58670 q^{4} -1.43089 q^{6} +3.26618 q^{7} -1.25651 q^{8} -2.55361 q^{9} +4.95460 q^{11} +1.72823 q^{12} +1.16266 q^{13} -6.99504 q^{14} -2.48239 q^{16} +4.82940 q^{17} +5.46897 q^{18} -5.79410 q^{19} +2.18220 q^{21} -10.6110 q^{22} -1.06284 q^{23} -0.839500 q^{24} -2.49001 q^{26} -3.71049 q^{27} +8.44862 q^{28} -0.384786 q^{29} -3.94830 q^{31} +7.82944 q^{32} +3.31027 q^{33} -10.3429 q^{34} -6.60543 q^{36} +1.60067 q^{37} +12.4090 q^{38} +0.776795 q^{39} -11.9879 q^{41} -4.67353 q^{42} -10.2206 q^{43} +12.8160 q^{44} +2.27623 q^{46} -2.62902 q^{47} -1.65854 q^{48} +3.66793 q^{49} +3.22662 q^{51} +3.00744 q^{52} -6.32499 q^{53} +7.94660 q^{54} -4.10398 q^{56} -3.87116 q^{57} +0.824080 q^{58} -8.94773 q^{59} +3.85801 q^{61} +8.45591 q^{62} -8.34056 q^{63} -11.8032 q^{64} -7.08947 q^{66} +2.79607 q^{67} +12.4922 q^{68} -0.710104 q^{69} -9.85226 q^{71} +3.20864 q^{72} -10.6976 q^{73} -3.42809 q^{74} -14.9876 q^{76} +16.1826 q^{77} -1.66363 q^{78} -3.71264 q^{79} +5.18179 q^{81} +25.6740 q^{82} -16.0296 q^{83} +5.64471 q^{84} +21.8891 q^{86} -0.257084 q^{87} -6.22549 q^{88} -14.2400 q^{89} +3.79744 q^{91} -2.74924 q^{92} -2.63794 q^{93} +5.63046 q^{94} +5.23102 q^{96} -8.83549 q^{97} -7.85545 q^{98} -12.6521 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 2 q^{2} + 7 q^{3} + 6 q^{4} - 5 q^{6} + 3 q^{7} - 3 q^{8} + 6 q^{9}+O(q^{10}) \) 15 * q - 2 * q^2 + 7 * q^3 + 6 * q^4 - 5 * q^6 + 3 * q^7 - 3 * q^8 + 6 * q^9	\( 15 q - 2 q^{2} + 7 q^{3} + 6 q^{4} - 5 q^{6} + 3 q^{7} - 3 q^{8} + 6 q^{9} - 10 q^{11} + 6 q^{12} + 8 q^{13} - 5 q^{14} - 16 q^{16} + q^{17} + 3 q^{18} - 30 q^{19} - 11 q^{21} + 5 q^{22} - 19 q^{23} - 14 q^{24} - 18 q^{26} + 22 q^{27} + 20 q^{28} - 12 q^{29} - 22 q^{31} + 2 q^{32} - 4 q^{33} - 29 q^{34} - 7 q^{36} + 12 q^{37} + 18 q^{38} - 17 q^{39} - 13 q^{41} + q^{42} + 25 q^{43} - 20 q^{44} - 7 q^{46} - 16 q^{47} + 22 q^{48} - 24 q^{49} - 27 q^{51} + 15 q^{52} + 4 q^{53} - 43 q^{54} - 3 q^{56} - 22 q^{57} + 20 q^{58} - 50 q^{59} - 41 q^{61} - 12 q^{62} - 6 q^{63} - 53 q^{64} + 5 q^{66} + 43 q^{67} - 5 q^{68} - 50 q^{69} - 14 q^{71} - 32 q^{72} + 10 q^{73} - 26 q^{74} - 13 q^{76} + 7 q^{77} - 3 q^{78} - 44 q^{79} + 7 q^{81} + 19 q^{82} - 7 q^{83} - 42 q^{84} + 7 q^{86} - 10 q^{87} + 28 q^{88} + 4 q^{89} - 50 q^{91} - 25 q^{92} - 22 q^{93} - 14 q^{94} + 14 q^{96} - 9 q^{97} - 2 q^{98} - 46 q^{99}+O(q^{100}) \) 15 * q - 2 * q^2 + 7 * q^3 + 6 * q^4 - 5 * q^6 + 3 * q^7 - 3 * q^8 + 6 * q^9 - 10 * q^11 + 6 * q^12 + 8 * q^13 - 5 * q^14 - 16 * q^16 + q^17 + 3 * q^18 - 30 * q^19 - 11 * q^21 + 5 * q^22 - 19 * q^23 - 14 * q^24 - 18 * q^26 + 22 * q^27 + 20 * q^28 - 12 * q^29 - 22 * q^31 + 2 * q^32 - 4 * q^33 - 29 * q^34 - 7 * q^36 + 12 * q^37 + 18 * q^38 - 17 * q^39 - 13 * q^41 + q^42 + 25 * q^43 - 20 * q^44 - 7 * q^46 - 16 * q^47 + 22 * q^48 - 24 * q^49 - 27 * q^51 + 15 * q^52 + 4 * q^53 - 43 * q^54 - 3 * q^56 - 22 * q^57 + 20 * q^58 - 50 * q^59 - 41 * q^61 - 12 * q^62 - 6 * q^63 - 53 * q^64 + 5 * q^66 + 43 * q^67 - 5 * q^68 - 50 * q^69 - 14 * q^71 - 32 * q^72 + 10 * q^73 - 26 * q^74 - 13 * q^76 + 7 * q^77 - 3 * q^78 - 44 * q^79 + 7 * q^81 + 19 * q^82 - 7 * q^83 - 42 * q^84 + 7 * q^86 - 10 * q^87 + 28 * q^88 + 4 * q^89 - 50 * q^91 - 25 * q^92 - 22 * q^93 - 14 * q^94 + 14 * q^96 - 9 * q^97 - 2 * q^98 - 46 * q^99

Introduction

L-functions

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Database

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