LMFDB - Embedded newform 3525.2.a.y.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3525,2,Mod(1,3525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3525, 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("3525.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3525 = 3 \cdot 5^{2} \cdot 47 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3525.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:	$28.1472667125$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 9x^{5} + 6x^{4} + 20x^{3} - 9x^{2} - 12x + 3 $ x^7 - x^6 - 9x^5 + 6x^4 + 20x^3 - 9x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$1.10030$ of defining polynomial
Character	$\chi$	$=$	3525.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.10030 q^{2} +1.00000 q^{3} -0.789350 q^{4} -1.10030 q^{6} -1.25231 q^{7} +3.06911 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.10030 q^{2} +1.00000 q^{3} -0.789350 q^{4} -1.10030 q^{6} -1.25231 q^{7} +3.06911 q^{8} +1.00000 q^{9} +0.174573 q^{11} -0.789350 q^{12} +3.76854 q^{13} +1.37792 q^{14} -1.79823 q^{16} -6.46143 q^{17} -1.10030 q^{18} +1.34046 q^{19} -1.25231 q^{21} -0.192081 q^{22} +0.0864240 q^{23} +3.06911 q^{24} -4.14650 q^{26} +1.00000 q^{27} +0.988515 q^{28} -4.18167 q^{29} -10.3672 q^{31} -4.15964 q^{32} +0.174573 q^{33} +7.10948 q^{34} -0.789350 q^{36} +4.32175 q^{37} -1.47491 q^{38} +3.76854 q^{39} +10.6360 q^{41} +1.37792 q^{42} -7.32992 q^{43} -0.137799 q^{44} -0.0950919 q^{46} +1.00000 q^{47} -1.79823 q^{48} -5.43171 q^{49} -6.46143 q^{51} -2.97469 q^{52} -5.35712 q^{53} -1.10030 q^{54} -3.84349 q^{56} +1.34046 q^{57} +4.60108 q^{58} +7.55214 q^{59} +10.4983 q^{61} +11.4070 q^{62} -1.25231 q^{63} +8.17328 q^{64} -0.192081 q^{66} -11.8871 q^{67} +5.10033 q^{68} +0.0864240 q^{69} -7.80910 q^{71} +3.06911 q^{72} +14.0348 q^{73} -4.75521 q^{74} -1.05809 q^{76} -0.218620 q^{77} -4.14650 q^{78} +9.06544 q^{79} +1.00000 q^{81} -11.7028 q^{82} -8.99673 q^{83} +0.988515 q^{84} +8.06507 q^{86} -4.18167 q^{87} +0.535782 q^{88} -1.76521 q^{89} -4.71939 q^{91} -0.0682188 q^{92} -10.3672 q^{93} -1.10030 q^{94} -4.15964 q^{96} -2.86013 q^{97} +5.97648 q^{98} +0.174573 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - q^{2} + 7 q^{3} + 5 q^{4} - q^{6} - 11 q^{7} - 6 q^{8} + 7 q^{9}+O(q^{10}) $ 7 * q - q^2 + 7 * q^3 + 5 * q^4 - q^6 - 11 * q^7 - 6 * q^8 + 7 * q^9	$ 7 q - q^{2} + 7 q^{3} + 5 q^{4} - q^{6} - 11 q^{7} - 6 q^{8} + 7 q^{9} - 8 q^{11} + 5 q^{12} - 5 q^{13} - 3 q^{14} + 9 q^{16} - 10 q^{17} - q^{18} + 7 q^{19} - 11 q^{21} - 20 q^{22} - 4 q^{23} - 6 q^{24} + 7 q^{27} - 2 q^{28} - 11 q^{29} + 3 q^{31} - 28 q^{32} - 8 q^{33} + 8 q^{34} + 5 q^{36} - 11 q^{37} + 2 q^{38} - 5 q^{39} - 20 q^{41} - 3 q^{42} - 18 q^{43} + q^{44} - 19 q^{46} + 7 q^{47} + 9 q^{48} + 14 q^{49} - 10 q^{51} - 29 q^{52} - 12 q^{53} - q^{54} - 47 q^{56} + 7 q^{57} + 19 q^{58} + 18 q^{59} - 4 q^{61} - 12 q^{62} - 11 q^{63} + 42 q^{64} - 20 q^{66} - 22 q^{67} - 44 q^{68} - 4 q^{69} - 14 q^{71} - 6 q^{72} - 30 q^{73} + 31 q^{74} - 2 q^{76} + 8 q^{77} - q^{79} + 7 q^{81} - 29 q^{82} - 54 q^{83} - 2 q^{84} - 29 q^{86} - 11 q^{87} + 22 q^{88} - 14 q^{89} + 20 q^{91} + 5 q^{92} + 3 q^{93} - q^{94} - 28 q^{96} - 24 q^{97} + 26 q^{98} - 8 q^{99}+O(q^{100}) $ 7 * q - q^2 + 7 * q^3 + 5 * q^4 - q^6 - 11 * q^7 - 6 * q^8 + 7 * q^9 - 8 * q^11 + 5 * q^12 - 5 * q^13 - 3 * q^14 + 9 * q^16 - 10 * q^17 - q^18 + 7 * q^19 - 11 * q^21 - 20 * q^22 - 4 * q^23 - 6 * q^24 + 7 * q^27 - 2 * q^28 - 11 * q^29 + 3 * q^31 - 28 * q^32 - 8 * q^33 + 8 * q^34 + 5 * q^36 - 11 * q^37 + 2 * q^38 - 5 * q^39 - 20 * q^41 - 3 * q^42 - 18 * q^43 + q^44 - 19 * q^46 + 7 * q^47 + 9 * q^48 + 14 * q^49 - 10 * q^51 - 29 * q^52 - 12 * q^53 - q^54 - 47 * q^56 + 7 * q^57 + 19 * q^58 + 18 * q^59 - 4 * q^61 - 12 * q^62 - 11 * q^63 + 42 * q^64 - 20 * q^66 - 22 * q^67 - 44 * q^68 - 4 * q^69 - 14 * q^71 - 6 * q^72 - 30 * q^73 + 31 * q^74 - 2 * q^76 + 8 * q^77 - q^79 + 7 * q^81 - 29 * q^82 - 54 * q^83 - 2 * q^84 - 29 * q^86 - 11 * q^87 + 22 * q^88 - 14 * q^89 + 20 * q^91 + 5 * q^92 + 3 * q^93 - q^94 - 28 * q^96 - 24 * q^97 + 26 * q^98 - 8 * 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 $

$2$	−1.10030	−0.778026	−0.389013	−	0.921232i	$-0.627184\pi$
$2$	−1.10030	−0.778026	−0.389013	+	0.921232i	$0.627184\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.789350	−0.394675
$5$	0	0
$5$	0	0
$6$	−1.10030	−0.449194
$7$	−1.25231	−0.473330	−0.236665	−	0.971591i	$-0.576054\pi$
$7$	−1.25231	−0.473330	−0.236665	+	0.971591i	$0.576054\pi$
$8$	3.06911	1.08509
$9$	1.00000	0.333333
$10$	0	0
$11$	0.174573	0.0526356	0.0263178	−	0.999654i	$-0.491622\pi$
$11$	0.174573	0.0526356	0.0263178	+	0.999654i	$0.491622\pi$
$12$	−0.789350	−0.227866
$13$	3.76854	1.04520	0.522602	−	0.852577i	$-0.324961\pi$
$13$	3.76854	1.04520	0.522602	+	0.852577i	$0.324961\pi$
$14$	1.37792	0.368263
$15$	0	0
$16$	−1.79823	−0.449557
$17$	−6.46143	−1.56713	−0.783564	−	0.621311i	$-0.786600\pi$
$17$	−6.46143	−1.56713	−0.783564	+	0.621311i	$0.786600\pi$
$18$	−1.10030	−0.259342
$19$	1.34046	0.307523	0.153762	−	0.988108i	$-0.450861\pi$
$19$	1.34046	0.307523	0.153762	+	0.988108i	$0.450861\pi$
$20$	0	0
$21$	−1.25231	−0.273277
$22$	−0.192081	−0.0409519
$23$	0.0864240	0.0180206	0.00901032	−	0.999959i	$-0.497132\pi$
$23$	0.0864240	0.0180206	0.00901032	+	0.999959i	$0.497132\pi$
$24$	3.06911	0.626479
$25$	0	0
$26$	−4.14650	−0.813196
$27$	1.00000	0.192450
$28$	0.988515	0.186812
$29$	−4.18167	−0.776517	−0.388259	−	0.921550i	$-0.626923\pi$
$29$	−4.18167	−0.776517	−0.388259	+	0.921550i	$0.626923\pi$
$30$	0	0
$31$	−10.3672	−1.86201	−0.931005	−	0.365007i	$-0.881067\pi$
$31$	−10.3672	−1.86201	−0.931005	+	0.365007i	$0.881067\pi$
$32$	−4.15964	−0.735327
$33$	0.174573	0.0303892
$34$	7.10948	1.21927
$35$	0	0
$36$	−0.789350	−0.131558
$37$	4.32175	0.710492	0.355246	−	0.934773i	$-0.384397\pi$
$37$	4.32175	0.710492	0.355246	+	0.934773i	$0.384397\pi$
$38$	−1.47491	−0.239261
$39$	3.76854	0.603449
$40$	0	0
$41$	10.6360	1.66107	0.830535	−	0.556966i	$-0.188035\pi$
$41$	10.6360	1.66107	0.830535	+	0.556966i	$0.188035\pi$
$42$	1.37792	0.212617
$43$	−7.32992	−1.11780	−0.558901	−	0.829235i	$-0.688777\pi$
$43$	−7.32992	−1.11780	−0.558901	+	0.829235i	$0.688777\pi$
$44$	−0.137799	−0.0207740
$45$	0	0
$46$	−0.0950919	−0.0140205
$47$	1.00000	0.145865
$47$	1.00000	0.145865
$48$	−1.79823	−0.259552
$49$	−5.43171	−0.775958
$50$	0	0
$51$	−6.46143	−0.904781
$52$	−2.97469	−0.412516
$53$	−5.35712	−0.735857	−0.367928	−	0.929854i	$-0.619933\pi$
$53$	−5.35712	−0.735857	−0.367928	+	0.929854i	$0.619933\pi$
$54$	−1.10030	−0.149731
$55$	0	0
$56$	−3.84349	−0.513608
$57$	1.34046	0.177549
$58$	4.60108	0.604151
$59$	7.55214	0.983205	0.491602	−	0.870820i	$-0.336411\pi$
$59$	7.55214	0.983205	0.491602	+	0.870820i	$0.336411\pi$
$60$	0	0
$61$	10.4983	1.34417	0.672084	−	0.740475i	$-0.265399\pi$
$61$	10.4983	1.34417	0.672084	+	0.740475i	$0.265399\pi$
$62$	11.4070	1.44869
$63$	−1.25231	−0.157777
$64$	8.17328	1.02166
$65$	0	0
$66$	−0.192081	−0.0236436
$67$	−11.8871	−1.45224	−0.726120	−	0.687568i	$-0.758678\pi$
$67$	−11.8871	−1.45224	−0.726120	+	0.687568i	$0.758678\pi$
$68$	5.10033	0.618506
$69$	0.0864240	0.0104042
$70$	0	0
$71$	−7.80910	−0.926770	−0.463385	−	0.886157i	$-0.653365\pi$
$71$	−7.80910	−0.926770	−0.463385	+	0.886157i	$0.653365\pi$
$72$	3.06911	0.361698
$73$	14.0348	1.64265	0.821326	−	0.570459i	$-0.193235\pi$
$73$	14.0348	1.64265	0.821326	+	0.570459i	$0.193235\pi$
$74$	−4.75521	−0.552781
$75$	0	0
$76$	−1.05809	−0.121372
$77$	−0.218620	−0.0249140
$78$	−4.14650	−0.469499
$79$	9.06544	1.01994	0.509971	−	0.860192i	$-0.329656\pi$
$79$	9.06544	1.01994	0.509971	+	0.860192i	$0.329656\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−11.7028	−1.29236
$83$	−8.99673	−0.987519	−0.493760	−	0.869598i	$-0.664378\pi$
$83$	−8.99673	−0.987519	−0.493760	+	0.869598i	$0.664378\pi$
$84$	0.988515	0.107856
$85$	0	0
$86$	8.06507	0.869679
$87$	−4.18167	−0.448322
$88$	0.535782	0.0571146
$89$	−1.76521	−0.187112	−0.0935560	−	0.995614i	$-0.529823\pi$
$89$	−1.76521	−0.187112	−0.0935560	+	0.995614i	$0.529823\pi$
$90$	0	0
$91$	−4.71939	−0.494727
$92$	−0.0682188	−0.00711230
$93$	−10.3672	−1.07503
$94$	−1.10030	−0.113487
$95$	0	0
$96$	−4.15964	−0.424541
$97$	−2.86013	−0.290402	−0.145201	−	0.989402i	$-0.546383\pi$
$97$	−2.86013	−0.290402	−0.145201	+	0.989402i	$0.546383\pi$
$98$	5.97648	0.603716
$99$	0.174573	0.0175452
$100$	0	0
$101$	−3.78169	−0.376292	−0.188146	−	0.982141i	$-0.560248\pi$
$101$	−3.78169	−0.376292	−0.188146	+	0.982141i	$0.560248\pi$
$102$	7.10948	0.703944
$103$	−13.8986	−1.36947	−0.684733	−	0.728794i	$-0.740081\pi$
$103$	−13.8986	−1.36947	−0.684733	+	0.728794i	$0.740081\pi$
$104$	11.5660	1.13414
$105$	0	0
$106$	5.89441	0.572516
$107$	9.36552	0.905399	0.452700	−	0.891663i	$-0.350461\pi$
$107$	9.36552	0.905399	0.452700	+	0.891663i	$0.350461\pi$
$108$	−0.789350	−0.0759553
$109$	18.2990	1.75273	0.876364	−	0.481649i	$-0.159962\pi$
$109$	18.2990	1.75273	0.876364	+	0.481649i	$0.159962\pi$
$110$	0	0
$111$	4.32175	0.410203
$112$	2.25194	0.212789
$113$	−16.3129	−1.53459	−0.767296	−	0.641293i	$-0.778398\pi$
$113$	−16.3129	−1.53459	−0.767296	+	0.641293i	$0.778398\pi$
$114$	−1.47491	−0.138138
$115$	0	0
$116$	3.30080	0.306472
$117$	3.76854	0.348401
$118$	−8.30958	−0.764959
$119$	8.09174	0.741769
$120$	0	0
$121$	−10.9695	−0.997229
$122$	−11.5512	−1.04580
$123$	10.6360	0.959019
$124$	8.18337	0.734889
$125$	0	0
$126$	1.37792	0.122754
$127$	−17.4979	−1.55269	−0.776344	−	0.630310i	$-0.782928\pi$
$127$	−17.4979	−1.55269	−0.776344	+	0.630310i	$0.782928\pi$
$128$	−0.673748	−0.0595515
$129$	−7.32992	−0.645363
$130$	0	0
$131$	13.7290	1.19951	0.599754	−	0.800185i	$-0.295265\pi$
$131$	13.7290	1.19951	0.599754	+	0.800185i	$0.295265\pi$
$132$	−0.137799	−0.0119939
$133$	−1.67868	−0.145560
$134$	13.0793	1.12988
$135$	0	0
$136$	−19.8308	−1.70048
$137$	−21.4776	−1.83495	−0.917477	−	0.397789i	$-0.869778\pi$
$137$	−21.4776	−1.83495	−0.917477	+	0.397789i	$0.869778\pi$
$138$	−0.0950919	−0.00809476
$139$	3.11695	0.264376	0.132188	−	0.991225i	$-0.457800\pi$
$139$	3.11695	0.264376	0.132188	+	0.991225i	$0.457800\pi$
$140$	0	0
$141$	1.00000	0.0842152
$142$	8.59232	0.721052
$143$	0.657883	0.0550149
$144$	−1.79823	−0.149852
$145$	0	0
$146$	−15.4425	−1.27803
$147$	−5.43171	−0.448000
$148$	−3.41138	−0.280413
$149$	−12.7354	−1.04332	−0.521661	−	0.853153i	$-0.674688\pi$
$149$	−12.7354	−1.04332	−0.521661	+	0.853153i	$0.674688\pi$
$150$	0	0
$151$	−0.316182	−0.0257305	−0.0128653	−	0.999917i	$-0.504095\pi$
$151$	−0.316182	−0.0257305	−0.0128653	+	0.999917i	$0.504095\pi$
$152$	4.11403	0.333692
$153$	−6.46143	−0.522376
$154$	0.240546	0.0193838
$155$	0	0
$156$	−2.97469	−0.238166
$157$	−7.06633	−0.563954	−0.281977	−	0.959421i	$-0.590990\pi$
$157$	−7.06633	−0.563954	−0.281977	+	0.959421i	$0.590990\pi$
$158$	−9.97466	−0.793541
$159$	−5.35712	−0.424847
$160$	0	0
$161$	−0.108230	−0.00852972
$162$	−1.10030	−0.0864474
$163$	−14.7407	−1.15458	−0.577289	−	0.816540i	$-0.695890\pi$
$163$	−14.7407	−1.15458	−0.577289	+	0.816540i	$0.695890\pi$
$164$	−8.39556	−0.655583
$165$	0	0
$166$	9.89906	0.768316
$167$	−15.6390	−1.21018	−0.605090	−	0.796157i	$-0.706863\pi$
$167$	−15.6390	−1.21018	−0.605090	+	0.796157i	$0.706863\pi$
$168$	−3.84349	−0.296532
$169$	1.20186	0.0924507
$170$	0	0
$171$	1.34046	0.102508
$172$	5.78587	0.441168
$173$	10.8566	0.825410	0.412705	−	0.910865i	$-0.364584\pi$
$173$	10.8566	0.825410	0.412705	+	0.910865i	$0.364584\pi$
$174$	4.60108	0.348807
$175$	0	0
$176$	−0.313921	−0.0236627
$177$	7.55214	0.567654
$178$	1.94225	0.145578
$179$	−20.5397	−1.53521	−0.767606	−	0.640922i	$-0.778552\pi$
$179$	−20.5397	−1.53521	−0.767606	+	0.640922i	$0.778552\pi$
$180$	0	0
$181$	−12.1810	−0.905407	−0.452704	−	0.891661i	$-0.649540\pi$
$181$	−12.1810	−0.905407	−0.452704	+	0.891661i	$0.649540\pi$
$182$	5.19272	0.384910
$183$	10.4983	0.776056
$184$	0.265245	0.0195541
$185$	0	0
$186$	11.4070	0.836403
$187$	−1.12799	−0.0824867
$188$	−0.789350	−0.0575693
$189$	−1.25231	−0.0910925
$190$	0	0
$191$	−21.2456	−1.53728	−0.768639	−	0.639682i	$-0.779066\pi$
$191$	−21.2456	−1.53728	−0.768639	+	0.639682i	$0.779066\pi$
$192$	8.17328	0.589856
$193$	6.83508	0.492000	0.246000	−	0.969270i	$-0.420884\pi$
$193$	6.83508	0.492000	0.246000	+	0.969270i	$0.420884\pi$
$194$	3.14699	0.225941
$195$	0	0
$196$	4.28752	0.306251
$197$	−10.1915	−0.726114	−0.363057	−	0.931767i	$-0.618267\pi$
$197$	−10.1915	−0.726114	−0.363057	+	0.931767i	$0.618267\pi$
$198$	−0.192081	−0.0136506
$199$	14.3519	1.01738	0.508690	−	0.860950i	$-0.330130\pi$
$199$	14.3519	1.01738	0.508690	+	0.860950i	$0.330130\pi$
$200$	0	0
$201$	−11.8871	−0.838451
$202$	4.16098	0.292765
$203$	5.23677	0.367549
$204$	5.10033	0.357095
$205$	0	0
$206$	15.2925	1.06548
$207$	0.0864240	0.00600688
$208$	−6.77668	−0.469878
$209$	0.234008	0.0161867
$210$	0	0
$211$	7.82619	0.538777	0.269389	−	0.963032i	$-0.413178\pi$
$211$	7.82619	0.538777	0.269389	+	0.963032i	$0.413178\pi$
$212$	4.22864	0.290424
$213$	−7.80910	−0.535071
$214$	−10.3048	−0.704424
$215$	0	0
$216$	3.06911	0.208826
$217$	12.9830	0.881346
$218$	−20.1343	−1.36367
$219$	14.0348	0.948385
$220$	0	0
$221$	−24.3501	−1.63797
$222$	−4.75521	−0.319148
$223$	21.5132	1.44063	0.720317	−	0.693646i	$-0.243997\pi$
$223$	21.5132	1.44063	0.720317	+	0.693646i	$0.243997\pi$
$224$	5.20918	0.348053
$225$	0	0
$226$	17.9490	1.19395
$227$	−5.95004	−0.394918	−0.197459	−	0.980311i	$-0.563269\pi$
$227$	−5.95004	−0.394918	−0.197459	+	0.980311i	$0.563269\pi$
$228$	−1.05809	−0.0700740
$229$	24.9395	1.64805	0.824025	−	0.566553i	$-0.191723\pi$
$229$	24.9395	1.64805	0.824025	+	0.566553i	$0.191723\pi$
$230$	0	0
$231$	−0.218620	−0.0143841
$232$	−12.8340	−0.842594
$233$	−28.1385	−1.84342	−0.921709	−	0.387883i	$-0.873207\pi$
$233$	−28.1385	−1.84342	−0.921709	+	0.387883i	$0.873207\pi$
$234$	−4.14650	−0.271065
$235$	0	0
$236$	−5.96128	−0.388046
$237$	9.06544	0.588864
$238$	−8.90331	−0.577116
$239$	−28.3447	−1.83347	−0.916734	−	0.399498i	$-0.869184\pi$
$239$	−28.3447	−1.83347	−0.916734	+	0.399498i	$0.869184\pi$
$240$	0	0
$241$	2.67150	0.172086	0.0860432	−	0.996291i	$-0.472578\pi$
$241$	2.67150	0.172086	0.0860432	+	0.996291i	$0.472578\pi$
$242$	12.0697	0.775871
$243$	1.00000	0.0641500
$244$	−8.28683	−0.530510
$245$	0	0
$246$	−11.7028	−0.746142
$247$	5.05158	0.321424
$248$	−31.8182	−2.02046
$249$	−8.99673	−0.570145
$250$	0	0
$251$	19.3629	1.22217	0.611087	−	0.791564i	$-0.290733\pi$
$251$	19.3629	1.22217	0.611087	+	0.791564i	$0.290733\pi$
$252$	0.988515	0.0622706
$253$	0.0150873	0.000948528 0
$254$	19.2529	1.20803
$255$	0	0
$256$	−15.6052	−0.975328
$257$	−8.60778	−0.536939	−0.268469	−	0.963288i	$-0.586518\pi$
$257$	−8.60778	−0.536939	−0.268469	+	0.963288i	$0.586518\pi$
$258$	8.06507	0.502109
$259$	−5.41219	−0.336297
$260$	0	0
$261$	−4.18167	−0.258839
$262$	−15.1059	−0.933249
$263$	−3.17385	−0.195708	−0.0978540	−	0.995201i	$-0.531198\pi$
$263$	−3.17385	−0.195708	−0.0978540	+	0.995201i	$0.531198\pi$
$264$	0.535782	0.0329751
$265$	0	0
$266$	1.84705	0.113250
$267$	−1.76521	−0.108029
$268$	9.38308	0.573163
$269$	−28.1994	−1.71935	−0.859673	−	0.510845i	$-0.829333\pi$
$269$	−28.1994	−1.71935	−0.859673	+	0.510845i	$0.829333\pi$
$270$	0	0
$271$	7.70341	0.467949	0.233975	−	0.972243i	$-0.424827\pi$
$271$	7.70341	0.467949	0.233975	+	0.972243i	$0.424827\pi$
$272$	11.6191	0.704512
$273$	−4.71939	−0.285631
$274$	23.6317	1.42764
$275$	0	0
$276$	−0.0682188	−0.00410629
$277$	−12.9310	−0.776947	−0.388474	−	0.921460i	$-0.626998\pi$
$277$	−12.9310	−0.776947	−0.388474	+	0.921460i	$0.626998\pi$
$278$	−3.42956	−0.205692
$279$	−10.3672	−0.620670
$280$	0	0
$281$	−2.55220	−0.152251	−0.0761256	−	0.997098i	$-0.524255\pi$
$281$	−2.55220	−0.152251	−0.0761256	+	0.997098i	$0.524255\pi$
$282$	−1.10030	−0.0655216
$283$	−12.7312	−0.756794	−0.378397	−	0.925643i	$-0.623524\pi$
$283$	−12.7312	−0.756794	−0.378397	+	0.925643i	$0.623524\pi$
$284$	6.16412	0.365773
$285$	0	0
$286$	−0.723865	−0.0428031
$287$	−13.3197	−0.786235
$288$	−4.15964	−0.245109
$289$	24.7501	1.45589
$290$	0	0
$291$	−2.86013	−0.167664
$292$	−11.0784	−0.648314
$293$	−9.76378	−0.570406	−0.285203	−	0.958467i	$-0.592061\pi$
$293$	−9.76378	−0.570406	−0.285203	+	0.958467i	$0.592061\pi$
$294$	5.97648	0.348556
$295$	0	0
$296$	13.2639	0.770950
$297$	0.174573	0.0101297
$298$	14.0127	0.811733
$299$	0.325692	0.0188352
$300$	0	0
$301$	9.17936	0.529089
$302$	0.347893	0.0200190
$303$	−3.78169	−0.217252
$304$	−2.41046	−0.138249
$305$	0	0
$306$	7.10948	0.406422
$307$	8.45675	0.482652	0.241326	−	0.970444i	$-0.422418\pi$
$307$	8.45675	0.482652	0.241326	+	0.970444i	$0.422418\pi$
$308$	0.172568	0.00983295
$309$	−13.8986	−0.790661
$310$	0	0
$311$	4.86620	0.275937	0.137968	−	0.990437i	$-0.455943\pi$
$311$	4.86620	0.275937	0.137968	+	0.990437i	$0.455943\pi$
$312$	11.5660	0.654798
$313$	−0.995054	−0.0562438	−0.0281219	−	0.999605i	$-0.508953\pi$
$313$	−0.995054	−0.0562438	−0.0281219	+	0.999605i	$0.508953\pi$
$314$	7.77505	0.438771
$315$	0	0
$316$	−7.15581	−0.402545
$317$	6.65938	0.374028	0.187014	−	0.982357i	$-0.440119\pi$
$317$	6.65938	0.374028	0.187014	+	0.982357i	$0.440119\pi$
$318$	5.89441	0.330542
$319$	−0.730005	−0.0408725
$320$	0	0
$321$	9.36552	0.522733
$322$	0.119085	0.00663635
$323$	−8.66131	−0.481928
$324$	−0.789350	−0.0438528
$325$	0	0
$326$	16.2191	0.898293
$327$	18.2990	1.01194
$328$	32.6432	1.80242
$329$	−1.25231	−0.0690423
$330$	0	0
$331$	10.1026	0.555287	0.277643	−	0.960684i	$-0.410447\pi$
$331$	10.1026	0.555287	0.277643	+	0.960684i	$0.410447\pi$
$332$	7.10157	0.389749
$333$	4.32175	0.236831
$334$	17.2075	0.941553
$335$	0	0
$336$	2.25194	0.122854
$337$	18.2962	0.996656	0.498328	−	0.866989i	$-0.333948\pi$
$337$	18.2962	0.996656	0.498328	+	0.866989i	$0.333948\pi$
$338$	−1.32240	−0.0719291
$339$	−16.3129	−0.885997
$340$	0	0
$341$	−1.80983	−0.0980080
$342$	−1.47491	−0.0797537
$343$	15.5684	0.840615
$344$	−22.4963	−1.21292
$345$	0	0
$346$	−11.9454	−0.642191
$347$	−12.6954	−0.681526	−0.340763	−	0.940149i	$-0.610685\pi$
$347$	−12.6954	−0.681526	−0.340763	+	0.940149i	$0.610685\pi$
$348$	3.30080	0.176942
$349$	−12.6145	−0.675241	−0.337621	−	0.941282i	$-0.609622\pi$
$349$	−12.6145	−0.675241	−0.337621	+	0.941282i	$0.609622\pi$
$350$	0	0
$351$	3.76854	0.201150
$352$	−0.726159	−0.0387044
$353$	16.4701	0.876615	0.438307	−	0.898825i	$-0.355578\pi$
$353$	16.4701	0.876615	0.438307	+	0.898825i	$0.355578\pi$
$354$	−8.30958	−0.441649
$355$	0	0
$356$	1.39337	0.0738485
$357$	8.09174	0.428261
$358$	22.5998	1.19444
$359$	7.56020	0.399012	0.199506	−	0.979897i	$-0.436066\pi$
$359$	7.56020	0.399012	0.199506	+	0.979897i	$0.436066\pi$
$360$	0	0
$361$	−17.2032	−0.905429
$362$	13.4027	0.704431
$363$	−10.9695	−0.575751
$364$	3.72525	0.195256
$365$	0	0
$366$	−11.5512	−0.603792
$367$	16.9823	0.886466	0.443233	−	0.896406i	$-0.353831\pi$
$367$	16.9823	0.886466	0.443233	+	0.896406i	$0.353831\pi$
$368$	−0.155410	−0.00810130
$369$	10.6360	0.553690
$370$	0	0
$371$	6.70880	0.348303
$372$	8.18337	0.424288
$373$	3.93995	0.204003	0.102001	−	0.994784i	$-0.467475\pi$
$373$	3.93995	0.204003	0.102001	+	0.994784i	$0.467475\pi$
$374$	1.24112	0.0641768
$375$	0	0
$376$	3.06911	0.158277
$377$	−15.7588	−0.811619
$378$	1.37792	0.0708723
$379$	−8.35311	−0.429071	−0.214535	−	0.976716i	$-0.568824\pi$
$379$	−8.35311	−0.429071	−0.214535	+	0.976716i	$0.568824\pi$
$380$	0	0
$381$	−17.4979	−0.896444
$382$	23.3765	1.19604
$383$	13.3239	0.680818	0.340409	−	0.940278i	$-0.389435\pi$
$383$	13.3239	0.680818	0.340409	+	0.940278i	$0.389435\pi$
$384$	−0.673748	−0.0343821
$385$	0	0
$386$	−7.52061	−0.382789
$387$	−7.32992	−0.372601
$388$	2.25764	0.114615
$389$	7.62367	0.386535	0.193268	−	0.981146i	$-0.438091\pi$
$389$	7.62367	0.386535	0.193268	+	0.981146i	$0.438091\pi$
$390$	0	0
$391$	−0.558423	−0.0282406
$392$	−16.6705	−0.841988
$393$	13.7290	0.692536
$394$	11.2137	0.564936
$395$	0	0
$396$	−0.137799	−0.00692465
$397$	21.9666	1.10247	0.551237	−	0.834349i	$-0.314156\pi$
$397$	21.9666	1.10247	0.551237	+	0.834349i	$0.314156\pi$
$398$	−15.7913	−0.791548
$399$	−1.67868	−0.0840392
$400$	0	0
$401$	19.3220	0.964897	0.482449	−	0.875924i	$-0.339748\pi$
$401$	19.3220	0.964897	0.482449	+	0.875924i	$0.339748\pi$
$402$	13.0793	0.652337
$403$	−39.0693	−1.94618
$404$	2.98508	0.148513
$405$	0	0
$406$	−5.76199	−0.285963
$407$	0.754460	0.0373972
$408$	−19.8308	−0.981773
$409$	−5.81063	−0.287317	−0.143659	−	0.989627i	$-0.545887\pi$
$409$	−5.81063	−0.287317	−0.143659	+	0.989627i	$0.545887\pi$
$410$	0	0
$411$	−21.4776	−1.05941
$412$	10.9708	0.540494
$413$	−9.45765	−0.465381
$414$	−0.0950919	−0.00467351
$415$	0	0
$416$	−15.6757	−0.768567
$417$	3.11695	0.152638
$418$	−0.257478	−0.0125937
$419$	−8.58519	−0.419414	−0.209707	−	0.977764i	$-0.567251\pi$
$419$	−8.58519	−0.419414	−0.209707	+	0.977764i	$0.567251\pi$
$420$	0	0
$421$	22.4690	1.09507	0.547536	−	0.836782i	$-0.315566\pi$
$421$	22.4690	1.09507	0.547536	+	0.836782i	$0.315566\pi$
$422$	−8.61112	−0.419183
$423$	1.00000	0.0486217
$424$	−16.4416	−0.798474
$425$	0	0
$426$	8.59232	0.416299
$427$	−13.1472	−0.636236
$428$	−7.39268	−0.357339
$429$	0.657883	0.0317629
$430$	0	0
$431$	−12.6484	−0.609252	−0.304626	−	0.952472i	$-0.598532\pi$
$431$	−12.6484	−0.609252	−0.304626	+	0.952472i	$0.598532\pi$
$432$	−1.79823	−0.0865172
$433$	−11.4240	−0.549003	−0.274501	−	0.961587i	$-0.588513\pi$
$433$	−11.4240	−0.549003	−0.274501	+	0.961587i	$0.588513\pi$
$434$	−14.2852	−0.685710
$435$	0	0
$436$	−14.4443	−0.691758
$437$	0.115848	0.00554177
$438$	−15.4425	−0.737869
$439$	−30.8949	−1.47453	−0.737266	−	0.675603i	$-0.763883\pi$
$439$	−30.8949	−1.47453	−0.737266	+	0.675603i	$0.763883\pi$
$440$	0	0
$441$	−5.43171	−0.258653
$442$	26.7923	1.27438
$443$	−17.3379	−0.823750	−0.411875	−	0.911240i	$-0.635126\pi$
$443$	−17.3379	−0.823750	−0.411875	+	0.911240i	$0.635126\pi$
$444$	−3.41138	−0.161897
$445$	0	0
$446$	−23.6709	−1.12085
$447$	−12.7354	−0.602363
$448$	−10.2355	−0.483583
$449$	−9.99021	−0.471467	−0.235734	−	0.971818i	$-0.575749\pi$
$449$	−9.99021	−0.471467	−0.235734	+	0.971818i	$0.575749\pi$
$450$	0	0
$451$	1.85676	0.0874314
$452$	12.8766	0.605665
$453$	−0.316182	−0.0148555
$454$	6.54680	0.307256
$455$	0	0
$456$	4.11403	0.192657
$457$	−40.0154	−1.87184	−0.935922	−	0.352208i	$-0.885431\pi$
$457$	−40.0154	−1.87184	−0.935922	+	0.352208i	$0.885431\pi$
$458$	−27.4408	−1.28223
$459$	−6.46143	−0.301594
$460$	0	0
$461$	7.79934	0.363252	0.181626	−	0.983368i	$-0.441864\pi$
$461$	7.79934	0.363252	0.181626	+	0.983368i	$0.441864\pi$
$462$	0.240546	0.0111912
$463$	−36.2615	−1.68521	−0.842607	−	0.538528i	$-0.818980\pi$
$463$	−36.2615	−1.68521	−0.842607	+	0.538528i	$0.818980\pi$
$464$	7.51959	0.349088
$465$	0	0
$466$	30.9607	1.43423
$467$	0.977834	0.0452488	0.0226244	−	0.999744i	$-0.492798\pi$
$467$	0.977834	0.0452488	0.0226244	+	0.999744i	$0.492798\pi$
$468$	−2.97469	−0.137505
$469$	14.8864	0.687390
$470$	0	0
$471$	−7.06633	−0.325599
$472$	23.1783	1.06687
$473$	−1.27960	−0.0588362
$474$	−9.97466	−0.458151
$475$	0	0
$476$	−6.38722	−0.292758
$477$	−5.35712	−0.245286
$478$	31.1876	1.42649
$479$	−37.4010	−1.70890	−0.854448	−	0.519538i	$-0.826104\pi$
$479$	−37.4010	−1.70890	−0.854448	+	0.519538i	$0.826104\pi$
$480$	0	0
$481$	16.2867	0.742609
$482$	−2.93944	−0.133888
$483$	−0.108230	−0.00492464
$484$	8.65880	0.393582
$485$	0	0
$486$	−1.10030	−0.0499104
$487$	4.45527	0.201888	0.100944	−	0.994892i	$-0.467814\pi$
$487$	4.45527	0.201888	0.100944	+	0.994892i	$0.467814\pi$
$488$	32.2204	1.45855
$489$	−14.7407	−0.666596
$490$	0	0
$491$	−30.5663	−1.37944	−0.689718	−	0.724078i	$-0.742266\pi$
$491$	−30.5663	−1.37944	−0.689718	+	0.724078i	$0.742266\pi$
$492$	−8.39556	−0.378501
$493$	27.0196	1.21690
$494$	−5.55823	−0.250077
$495$	0	0
$496$	18.6426	0.837079
$497$	9.77945	0.438668
$498$	9.89906	0.443587
$499$	27.4124	1.22715	0.613574	−	0.789637i	$-0.289731\pi$
$499$	27.4124	1.22715	0.613574	+	0.789637i	$0.289731\pi$
$500$	0	0
$501$	−15.6390	−0.698698
$502$	−21.3049	−0.950883
$503$	1.95586	0.0872075	0.0436037	−	0.999049i	$-0.486116\pi$
$503$	1.95586	0.0872075	0.0436037	+	0.999049i	$0.486116\pi$
$504$	−3.84349	−0.171203
$505$	0	0
$506$	−0.0166004	−0.000737979 0
$507$	1.20186	0.0533765
$508$	13.8120	0.612807
$509$	−26.3930	−1.16985	−0.584925	−	0.811088i	$-0.698876\pi$
$509$	−26.3930	−1.16985	−0.584925	+	0.811088i	$0.698876\pi$
$510$	0	0
$511$	−17.5760	−0.777517
$512$	18.5179	0.818382
$513$	1.34046	0.0591829
$514$	9.47110	0.417752
$515$	0	0
$516$	5.78587	0.254709
$517$	0.174573	0.00767769
$518$	5.95501	0.261648
$519$	10.8566	0.476551
$520$	0	0
$521$	42.0665	1.84297	0.921484	−	0.388417i	$-0.126978\pi$
$521$	42.0665	1.84297	0.921484	+	0.388417i	$0.126978\pi$
$522$	4.60108	0.201384
$523$	27.0602	1.18326	0.591631	−	0.806209i	$-0.298484\pi$
$523$	27.0602	1.18326	0.591631	+	0.806209i	$0.298484\pi$
$524$	−10.8370	−0.473416
$525$	0	0
$526$	3.49217	0.152266
$527$	66.9872	2.91801
$528$	−0.313921	−0.0136617
$529$	−22.9925	−0.999675
$530$	0	0
$531$	7.55214	0.327735
$532$	1.32507	0.0574490
$533$	40.0823	1.73616
$534$	1.94225	0.0840496
$535$	0	0
$536$	−36.4828	−1.57582
$537$	−20.5397	−0.886355
$538$	31.0276	1.33770
$539$	−0.948227	−0.0408430
$540$	0	0
$541$	−0.426786	−0.0183490	−0.00917448	−	0.999958i	$-0.502920\pi$
$541$	−0.426786	−0.0183490	−0.00917448	+	0.999958i	$0.502920\pi$
$542$	−8.47603	−0.364077
$543$	−12.1810	−0.522737
$544$	26.8772	1.15235
$545$	0	0
$546$	5.19272	0.222228
$547$	−15.3255	−0.655271	−0.327636	−	0.944804i	$-0.606252\pi$
$547$	−15.3255	−0.655271	−0.327636	+	0.944804i	$0.606252\pi$
$548$	16.9533	0.724210
$549$	10.4983	0.448056
$550$	0	0
$551$	−5.60538	−0.238797
$552$	0.265245	0.0112896
$553$	−11.3528	−0.482769
$554$	14.2279	0.604485
$555$	0	0
$556$	−2.46036	−0.104343
$557$	16.6591	0.705868	0.352934	−	0.935648i	$-0.385184\pi$
$557$	16.6591	0.705868	0.352934	+	0.935648i	$0.385184\pi$
$558$	11.4070	0.482897
$559$	−27.6230	−1.16833
$560$	0	0
$561$	−1.12799	−0.0476237
$562$	2.80817	0.118455
$563$	−8.79675	−0.370739	−0.185370	−	0.982669i	$-0.559348\pi$
$563$	−8.79675	−0.370739	−0.185370	+	0.982669i	$0.559348\pi$
$564$	−0.789350	−0.0332376
$565$	0	0
$566$	14.0081	0.588805
$567$	−1.25231	−0.0525923
$568$	−23.9670	−1.00563
$569$	−13.4134	−0.562320	−0.281160	−	0.959661i	$-0.590719\pi$
$569$	−13.4134	−0.562320	−0.281160	+	0.959661i	$0.590719\pi$
$570$	0	0
$571$	25.1537	1.05265	0.526325	−	0.850284i	$-0.323570\pi$
$571$	25.1537	1.05265	0.526325	+	0.850284i	$0.323570\pi$
$572$	−0.519300	−0.0217130
$573$	−21.2456	−0.887548
$574$	14.6556	0.611712
$575$	0	0
$576$	8.17328	0.340553
$577$	2.85506	0.118858	0.0594289	−	0.998233i	$-0.481072\pi$
$577$	2.85506	0.118858	0.0594289	+	0.998233i	$0.481072\pi$
$578$	−27.2324	−1.13272
$579$	6.83508	0.284056
$580$	0	0
$581$	11.2667	0.467423
$582$	3.14699	0.130447
$583$	−0.935206	−0.0387323
$584$	43.0744	1.78243
$585$	0	0
$586$	10.7430	0.443791
$587$	−29.5703	−1.22050	−0.610249	−	0.792210i	$-0.708930\pi$
$587$	−29.5703	−1.22050	−0.610249	+	0.792210i	$0.708930\pi$
$588$	4.28752	0.176814
$589$	−13.8969	−0.572611
$590$	0	0
$591$	−10.1915	−0.419222
$592$	−7.77149	−0.319406
$593$	26.9745	1.10771	0.553856	−	0.832613i	$-0.313156\pi$
$593$	26.9745	1.10771	0.553856	+	0.832613i	$0.313156\pi$
$594$	−0.192081	−0.00788119
$595$	0	0
$596$	10.0527	0.411773
$597$	14.3519	0.587384
$598$	−0.358357	−0.0146543
$599$	0.608925	0.0248800	0.0124400	−	0.999923i	$-0.496040\pi$
$599$	0.608925	0.0248800	0.0124400	+	0.999923i	$0.496040\pi$
$600$	0	0
$601$	−26.4043	−1.07705	−0.538527	−	0.842608i	$-0.681019\pi$
$601$	−26.4043	−1.07705	−0.538527	+	0.842608i	$0.681019\pi$
$602$	−10.1000	−0.411646
$603$	−11.8871	−0.484080
$604$	0.249578	0.0101552
$605$	0	0
$606$	4.16098	0.169028
$607$	−37.5136	−1.52263	−0.761315	−	0.648382i	$-0.775446\pi$
$607$	−37.5136	−1.52263	−0.761315	+	0.648382i	$0.775446\pi$
$608$	−5.57584	−0.226130
$609$	5.23677	0.212205
$610$	0	0
$611$	3.76854	0.152459
$612$	5.10033	0.206169
$613$	34.6585	1.39984	0.699922	−	0.714219i	$-0.253218\pi$
$613$	34.6585	1.39984	0.699922	+	0.714219i	$0.253218\pi$
$614$	−9.30492	−0.375516
$615$	0	0
$616$	−0.670968	−0.0270341
$617$	−6.06163	−0.244032	−0.122016	−	0.992528i	$-0.538936\pi$
$617$	−6.06163	−0.244032	−0.122016	+	0.992528i	$0.538936\pi$
$618$	15.2925	0.615155
$619$	24.0998	0.968652	0.484326	−	0.874888i	$-0.339065\pi$
$619$	24.0998	0.968652	0.484326	+	0.874888i	$0.339065\pi$
$620$	0	0
$621$	0.0864240	0.00346807
$622$	−5.35426	−0.214686
$623$	2.21060	0.0885658
$624$	−6.77668	−0.271284
$625$	0	0
$626$	1.09485	0.0437591
$627$	0.234008	0.00934538
$628$	5.57781	0.222579
$629$	−27.9247	−1.11343
$630$	0	0
$631$	−19.3868	−0.771776	−0.385888	−	0.922546i	$-0.626105\pi$
$631$	−19.3868	−0.771776	−0.385888	+	0.922546i	$0.626105\pi$
$632$	27.8228	1.10673
$633$	7.82619	0.311063
$634$	−7.32729	−0.291004
$635$	0	0
$636$	4.22864	0.167677
$637$	−20.4696	−0.811035
$638$	0.803222	0.0317998
$639$	−7.80910	−0.308923
$640$	0	0
$641$	−42.2000	−1.66680	−0.833401	−	0.552669i	$-0.813609\pi$
$641$	−42.2000	−1.66680	−0.833401	+	0.552669i	$0.813609\pi$
$642$	−10.3048	−0.406700
$643$	−22.8996	−0.903071	−0.451536	−	0.892253i	$-0.649124\pi$
$643$	−22.8996	−0.903071	−0.451536	+	0.892253i	$0.649124\pi$
$644$	0.0854314	0.00336647
$645$	0	0
$646$	9.53000	0.374953
$647$	38.1317	1.49911	0.749555	−	0.661942i	$-0.230267\pi$
$647$	38.1317	1.49911	0.749555	+	0.661942i	$0.230267\pi$
$648$	3.06911	0.120566
$649$	1.31840	0.0517516
$650$	0	0
$651$	12.9830	0.508845
$652$	11.6356	0.455683
$653$	33.3341	1.30447	0.652233	−	0.758019i	$-0.273833\pi$
$653$	33.3341	1.30447	0.652233	+	0.758019i	$0.273833\pi$
$654$	−20.1343	−0.787315
$655$	0	0
$656$	−19.1260	−0.746745
$657$	14.0348	0.547551
$658$	1.37792	0.0537167
$659$	20.4698	0.797391	0.398696	−	0.917083i	$-0.369463\pi$
$659$	20.4698	0.797391	0.398696	+	0.917083i	$0.369463\pi$
$660$	0	0
$661$	30.3980	1.18234	0.591172	−	0.806545i	$-0.298665\pi$
$661$	30.3980	1.18234	0.591172	+	0.806545i	$0.298665\pi$
$662$	−11.1158	−0.432028
$663$	−24.3501	−0.945681
$664$	−27.6119	−1.07155
$665$	0	0
$666$	−4.75521	−0.184260
$667$	−0.361397	−0.0139933
$668$	12.3446	0.477628
$669$	21.5132	0.831750
$670$	0	0
$671$	1.83271	0.0707511
$672$	5.20918	0.200948
$673$	42.6859	1.64542	0.822710	−	0.568462i	$-0.192461\pi$
$673$	42.6859	1.64542	0.822710	+	0.568462i	$0.192461\pi$
$674$	−20.1312	−0.775425
$675$	0	0
$676$	−0.948688	−0.0364880
$677$	−11.2278	−0.431521	−0.215761	−	0.976446i	$-0.569223\pi$
$677$	−11.2278	−0.431521	−0.215761	+	0.976446i	$0.569223\pi$
$678$	17.9490	0.689329
$679$	3.58178	0.137456
$680$	0	0
$681$	−5.95004	−0.228006
$682$	1.99135	0.0762528
$683$	47.7136	1.82571	0.912854	−	0.408285i	$-0.133873\pi$
$683$	47.7136	1.82571	0.912854	+	0.408285i	$0.133873\pi$
$684$	−1.05809	−0.0404573
$685$	0	0
$686$	−17.1298	−0.654021
$687$	24.9395	0.951502
$688$	13.1808	0.502515
$689$	−20.1885	−0.769120
$690$	0	0
$691$	19.9865	0.760322	0.380161	−	0.924920i	$-0.375869\pi$
$691$	19.9865	0.760322	0.380161	+	0.924920i	$0.375869\pi$
$692$	−8.56964	−0.325769
$693$	−0.218620	−0.00830468
$694$	13.9687	0.530245
$695$	0	0
$696$	−12.8340	−0.486472
$697$	−68.7241	−2.60311
$698$	13.8797	0.525355
$699$	−28.1385	−1.06430
$700$	0	0
$701$	1.98648	0.0750284	0.0375142	−	0.999296i	$-0.488056\pi$
$701$	1.98648	0.0750284	0.0375142	+	0.999296i	$0.488056\pi$
$702$	−4.14650	−0.156500
$703$	5.79315	0.218493
$704$	1.42683	0.0537757
$705$	0	0
$706$	−18.1220	−0.682029
$707$	4.73586	0.178111
$708$	−5.96128	−0.224039
$709$	48.5275	1.82249	0.911245	−	0.411865i	$-0.135123\pi$
$709$	48.5275	1.82249	0.911245	+	0.411865i	$0.135123\pi$
$710$	0	0
$711$	9.06544	0.339981
$712$	−5.41763	−0.203034
$713$	−0.895977	−0.0335546
$714$	−8.90331	−0.333198
$715$	0	0
$716$	16.2130	0.605910
$717$	−28.3447	−1.05855
$718$	−8.31845	−0.310442
$719$	−15.6138	−0.582295	−0.291148	−	0.956678i	$-0.594037\pi$
$719$	−15.6138	−0.582295	−0.291148	+	0.956678i	$0.594037\pi$
$720$	0	0
$721$	17.4054	0.648210
$722$	18.9286	0.704448
$723$	2.67150	0.0993541
$724$	9.61508	0.357342
$725$	0	0
$726$	12.0697	0.447949
$727$	−22.8028	−0.845708	−0.422854	−	0.906198i	$-0.638972\pi$
$727$	−22.8028	−0.845708	−0.422854	+	0.906198i	$0.638972\pi$
$728$	−14.4843	−0.536825
$729$	1.00000	0.0370370
$730$	0	0
$731$	47.3618	1.75174
$732$	−8.28683	−0.306290
$733$	2.58687	0.0955483	0.0477742	−	0.998858i	$-0.484787\pi$
$733$	2.58687	0.0955483	0.0477742	+	0.998858i	$0.484787\pi$
$734$	−18.6855	−0.689694
$735$	0	0
$736$	−0.359492	−0.0132511
$737$	−2.07516	−0.0764396
$738$	−11.7028	−0.430785
$739$	0.0313619	0.00115367	0.000576834	−	1.00000i	$-0.499816\pi$
$739$	0.0313619	0.00115367	0.000576834		1.00000i	$0.499816\pi$
$740$	0	0
$741$	5.05158	0.185575
$742$	−7.38166	−0.270989
$743$	35.5918	1.30574	0.652869	−	0.757471i	$-0.273565\pi$
$743$	35.5918	1.30574	0.652869	+	0.757471i	$0.273565\pi$
$744$	−31.8182	−1.16651
$745$	0	0
$746$	−4.33511	−0.158720
$747$	−8.99673	−0.329173
$748$	0.890378	0.0325554
$749$	−11.7286	−0.428553
$750$	0	0
$751$	7.75046	0.282818	0.141409	−	0.989951i	$-0.454837\pi$
$751$	7.75046	0.282818	0.141409	+	0.989951i	$0.454837\pi$
$752$	−1.79823	−0.0655746
$753$	19.3629	0.705622
$754$	17.3393	0.631461
$755$	0	0
$756$	0.988515	0.0359519
$757$	15.4794	0.562607	0.281303	−	0.959619i	$-0.409233\pi$
$757$	15.4794	0.562607	0.281303	+	0.959619i	$0.409233\pi$
$758$	9.19089	0.333828
$759$	0.0150873	0.000547633 0
$760$	0	0
$761$	−21.1961	−0.768359	−0.384179	−	0.923258i	$-0.625516\pi$
$761$	−21.1961	−0.768359	−0.384179	+	0.923258i	$0.625516\pi$
$762$	19.2529	0.697457
$763$	−22.9161	−0.829620
$764$	16.7702	0.606726
$765$	0	0
$766$	−14.6602	−0.529694
$767$	28.4605	1.02765
$768$	−15.6052	−0.563106
$769$	−34.6832	−1.25071	−0.625353	−	0.780342i	$-0.715045\pi$
$769$	−34.6832	−1.25071	−0.625353	+	0.780342i	$0.715045\pi$
$770$	0	0
$771$	−8.60778	−0.310002
$772$	−5.39527	−0.194180
$773$	37.0101	1.33116	0.665580	−	0.746327i	$-0.268184\pi$
$773$	37.0101	1.33116	0.665580	+	0.746327i	$0.268184\pi$
$774$	8.06507	0.289893
$775$	0	0
$776$	−8.77805	−0.315114
$777$	−5.41219	−0.194161
$778$	−8.38828	−0.300735
$779$	14.2572	0.510818
$780$	0	0
$781$	−1.36326	−0.0487811
$782$	0.614430	0.0219720
$783$	−4.18167	−0.149441
$784$	9.76744	0.348837
$785$	0	0
$786$	−15.1059	−0.538811
$787$	−32.9195	−1.17345	−0.586727	−	0.809785i	$-0.699584\pi$
$787$	−32.9195	−1.17345	−0.586727	+	0.809785i	$0.699584\pi$
$788$	8.04466	0.286579
$789$	−3.17385	−0.112992
$790$	0	0
$791$	20.4289	0.726369
$792$	0.535782	0.0190382
$793$	39.5632	1.40493
$794$	−24.1698	−0.857754
$795$	0	0
$796$	−11.3287	−0.401534
$797$	−17.8085	−0.630809	−0.315404	−	0.948957i	$-0.602140\pi$
$797$	−17.8085	−0.630809	−0.315404	+	0.948957i	$0.602140\pi$
$798$	1.84705	0.0653847
$799$	−6.46143	−0.228589
$800$	0	0
$801$	−1.76521	−0.0623707
$802$	−21.2600	−0.750715
$803$	2.45009	0.0864620
$804$	9.38308	0.330916
$805$	0	0
$806$	42.9877	1.51418
$807$	−28.1994	−0.992665
$808$	−11.6064	−0.408312
$809$	−17.3800	−0.611049	−0.305525	−	0.952184i	$-0.598832\pi$
$809$	−17.3800	−0.611049	−0.305525	+	0.952184i	$0.598832\pi$
$810$	0	0
$811$	45.4460	1.59582	0.797912	−	0.602774i	$-0.205938\pi$
$811$	45.4460	1.59582	0.797912	+	0.602774i	$0.205938\pi$
$812$	−4.13365	−0.145063
$813$	7.70341	0.270171
$814$	−0.830128	−0.0290960
$815$	0	0
$816$	11.6191	0.406750
$817$	−9.82548	−0.343750
$818$	6.39341	0.223540
$819$	−4.71939	−0.164909
$820$	0	0
$821$	1.72990	0.0603740	0.0301870	−	0.999544i	$-0.490390\pi$
$821$	1.72990	0.0603740	0.0301870	+	0.999544i	$0.490390\pi$
$822$	23.6317	0.824250
$823$	3.91286	0.136394	0.0681968	−	0.997672i	$-0.478275\pi$
$823$	3.91286	0.136394	0.0681968	+	0.997672i	$0.478275\pi$
$824$	−42.6562	−1.48600
$825$	0	0
$826$	10.4062	0.362078
$827$	9.13600	0.317690	0.158845	−	0.987304i	$-0.449223\pi$
$827$	9.13600	0.317690	0.158845	+	0.987304i	$0.449223\pi$
$828$	−0.0682188	−0.00237077
$829$	−0.816040	−0.0283423	−0.0141711	−	0.999900i	$-0.504511\pi$
$829$	−0.816040	−0.0283423	−0.0141711	+	0.999900i	$0.504511\pi$
$830$	0	0
$831$	−12.9310	−0.448571
$832$	30.8013	1.06784
$833$	35.0966	1.21603
$834$	−3.42956	−0.118756
$835$	0	0
$836$	−0.184714	−0.00638848
$837$	−10.3672	−0.358344
$838$	9.44624	0.326315
$839$	17.0299	0.587937	0.293969	−	0.955815i	$-0.405024\pi$
$839$	17.0299	0.587937	0.293969	+	0.955815i	$0.405024\pi$
$840$	0	0
$841$	−11.5136	−0.397021
$842$	−24.7225	−0.851995
$843$	−2.55220	−0.0879023
$844$	−6.17760	−0.212642
$845$	0	0
$846$	−1.10030	−0.0378289
$847$	13.7373	0.472019
$848$	9.63331	0.330809
$849$	−12.7312	−0.436935
$850$	0	0
$851$	0.373503	0.0128035
$852$	6.16412	0.211179
$853$	−13.2789	−0.454662	−0.227331	−	0.973818i	$-0.573000\pi$
$853$	−13.2789	−0.454662	−0.227331	+	0.973818i	$0.573000\pi$
$854$	14.4658	0.495008
$855$	0	0
$856$	28.7438	0.982443
$857$	25.1876	0.860392	0.430196	−	0.902736i	$-0.358444\pi$
$857$	25.1876	0.860392	0.430196	+	0.902736i	$0.358444\pi$
$858$	−0.723865	−0.0247124
$859$	54.7126	1.86677	0.933384	−	0.358878i	$-0.116841\pi$
$859$	54.7126	1.86677	0.933384	+	0.358878i	$0.116841\pi$
$860$	0	0
$861$	−13.3197	−0.453933
$862$	13.9170	0.474014
$863$	−27.4839	−0.935563	−0.467782	−	0.883844i	$-0.654947\pi$
$863$	−27.4839	−0.935563	−0.467782	+	0.883844i	$0.654947\pi$
$864$	−4.15964	−0.141514
$865$	0	0
$866$	12.5698	0.427138
$867$	24.7501	0.840558
$868$	−10.2482	−0.347845
$869$	1.58258	0.0536852
$870$	0	0
$871$	−44.7970	−1.51789
$872$	56.1617	1.90188
$873$	−2.86013	−0.0968008
$874$	−0.127467	−0.00431164
$875$	0	0
$876$	−11.0784	−0.374304
$877$	36.7138	1.23974	0.619869	−	0.784706i	$-0.287186\pi$
$877$	36.7138	1.23974	0.619869	+	0.784706i	$0.287186\pi$
$878$	33.9935	1.14722
$879$	−9.76378	−0.329324
$880$	0	0
$881$	7.48022	0.252015	0.126007	−	0.992029i	$-0.459784\pi$
$881$	7.48022	0.252015	0.126007	+	0.992029i	$0.459784\pi$
$882$	5.97648	0.201239
$883$	11.1573	0.375472	0.187736	−	0.982219i	$-0.439885\pi$
$883$	11.1573	0.375472	0.187736	+	0.982219i	$0.439885\pi$
$884$	19.2208	0.646465
$885$	0	0
$886$	19.0768	0.640899
$887$	−50.5868	−1.69854	−0.849269	−	0.527961i	$-0.822957\pi$
$887$	−50.5868	−1.69854	−0.849269	+	0.527961i	$0.822957\pi$
$888$	13.2639	0.445108
$889$	21.9129	0.734934
$890$	0	0
$891$	0.174573	0.00584840
$892$	−16.9815	−0.568582
$893$	1.34046	0.0448569
$894$	14.0127	0.468654
$895$	0	0
$896$	0.843745	0.0281875
$897$	0.325692	0.0108745
$898$	10.9922	0.366814
$899$	43.3524	1.44588
$900$	0	0
$901$	34.6147	1.15318
$902$	−2.04299	−0.0680240
$903$	9.17936	0.305470
$904$	−50.0662	−1.66518
$905$	0	0
$906$	0.347893	0.0115580
$907$	6.43162	0.213558	0.106779	−	0.994283i	$-0.465946\pi$
$907$	6.43162	0.213558	0.106779	+	0.994283i	$0.465946\pi$
$908$	4.69666	0.155864
$909$	−3.78169	−0.125431
$910$	0	0
$911$	−27.5974	−0.914342	−0.457171	−	0.889379i	$-0.651137\pi$
$911$	−27.5974	−0.914342	−0.457171	+	0.889379i	$0.651137\pi$
$912$	−2.41046	−0.0798182
$913$	−1.57058	−0.0519787
$914$	44.0288	1.45634
$915$	0	0
$916$	−19.6860	−0.650444
$917$	−17.1930	−0.567763
$918$	7.10948	0.234648
$919$	−29.4189	−0.970439	−0.485220	−	0.874392i	$-0.661260\pi$
$919$	−29.4189	−0.970439	−0.485220	+	0.874392i	$0.661260\pi$
$920$	0	0
$921$	8.45675	0.278659
$922$	−8.58158	−0.282619
$923$	−29.4289	−0.968664
$924$	0.172568	0.00567705
$925$	0	0
$926$	39.8984	1.31114
$927$	−13.8986	−0.456488
$928$	17.3942	0.570994
$929$	9.24967	0.303472	0.151736	−	0.988421i	$-0.451514\pi$
$929$	9.24967	0.303472	0.151736	+	0.988421i	$0.451514\pi$
$930$	0	0
$931$	−7.28100	−0.238625
$932$	22.2112	0.727551
$933$	4.86620	0.159312
$934$	−1.07591	−0.0352047
$935$	0	0
$936$	11.5660	0.378048
$937$	−2.15588	−0.0704294	−0.0352147	−	0.999380i	$-0.511212\pi$
$937$	−2.15588	−0.0704294	−0.0352147	+	0.999380i	$0.511212\pi$
$938$	−16.3794	−0.534807
$939$	−0.995054	−0.0324724
$940$	0	0
$941$	39.6778	1.29346	0.646730	−	0.762719i	$-0.276136\pi$
$941$	39.6778	1.29346	0.646730	+	0.762719i	$0.276136\pi$
$942$	7.77505	0.253325
$943$	0.919209	0.0299336
$944$	−13.5805	−0.442006
$945$	0	0
$946$	1.40794	0.0457761
$947$	−35.2291	−1.14479	−0.572396	−	0.819977i	$-0.693986\pi$
$947$	−35.2291	−1.14479	−0.572396	+	0.819977i	$0.693986\pi$
$948$	−7.15581	−0.232410
$949$	52.8907	1.71691
$950$	0	0
$951$	6.65938	0.215945
$952$	24.8344	0.804889
$953$	49.8635	1.61524	0.807619	−	0.589705i	$-0.200756\pi$
$953$	49.8635	1.61524	0.807619	+	0.589705i	$0.200756\pi$
$954$	5.89441	0.190839
$955$	0	0
$956$	22.3739	0.723624
$957$	−0.730005	−0.0235977
$958$	41.1521	1.32957
$959$	26.8967	0.868539
$960$	0	0
$961$	76.4795	2.46708
$962$	−17.9202	−0.577769
$963$	9.36552	0.301800
$964$	−2.10875	−0.0679182
$965$	0	0
$966$	0.119085	0.00383150
$967$	6.77852	0.217983	0.108991	−	0.994043i	$-0.465238\pi$
$967$	6.77852	0.217983	0.108991	+	0.994043i	$0.465238\pi$
$968$	−33.6667	−1.08209
$969$	−8.66131	−0.278241
$970$	0	0
$971$	−16.4191	−0.526913	−0.263457	−	0.964671i	$-0.584863\pi$
$971$	−16.4191	−0.526913	−0.263457	+	0.964671i	$0.584863\pi$
$972$	−0.789350	−0.0253184
$973$	−3.90340	−0.125137
$974$	−4.90212	−0.157074
$975$	0	0
$976$	−18.8783	−0.604280
$977$	30.1807	0.965566	0.482783	−	0.875740i	$-0.339626\pi$
$977$	30.1807	0.965566	0.482783	+	0.875740i	$0.339626\pi$
$978$	16.2191	0.518629
$979$	−0.308158	−0.00984876
$980$	0	0
$981$	18.2990	0.584243
$982$	33.6319	1.07324
$983$	−28.2921	−0.902378	−0.451189	−	0.892428i	$-0.649000\pi$
$983$	−28.2921	−0.902378	−0.451189	+	0.892428i	$0.649000\pi$
$984$	32.6432	1.04063
$985$	0	0
$986$	−29.7295	−0.946781
$987$	−1.25231	−0.0398616
$988$	−3.98747	−0.126858
$989$	−0.633480	−0.0201435
$990$	0	0
$991$	53.5090	1.69977	0.849885	−	0.526969i	$-0.176671\pi$
$991$	53.5090	1.69977	0.849885	+	0.526969i	$0.176671\pi$
$992$	43.1239	1.36919
$993$	10.1026	0.320595
$994$	−10.7603	−0.341296
$995$	0	0
$996$	7.10157	0.225022
$997$	22.0315	0.697744	0.348872	−	0.937170i	$-0.386565\pi$
$997$	22.0315	0.697744	0.348872	+	0.937170i	$0.386565\pi$
$998$	−30.1618	−0.954754
$999$	4.32175	0.136734

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3525.2.a.y.1.3	✓	7
5.4	even	2		3525.2.a.bb.1.5	yes	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3525.2.a.y.1.3	✓	7	1.1	even	1	trivial
3525.2.a.bb.1.5	yes	7	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:	\( N \)	\(=\)	\( 3525 = 3 \cdot 5^{2} \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3525.a (trivial)

\(f(q)\)	\(=\)	\(q-1.10030 q^{2} +1.00000 q^{3} -0.789350 q^{4} -1.10030 q^{6} -1.25231 q^{7} +3.06911 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.10030 q^{2} +1.00000 q^{3} -0.789350 q^{4} -1.10030 q^{6} -1.25231 q^{7} +3.06911 q^{8} +1.00000 q^{9} +0.174573 q^{11} -0.789350 q^{12} +3.76854 q^{13} +1.37792 q^{14} -1.79823 q^{16} -6.46143 q^{17} -1.10030 q^{18} +1.34046 q^{19} -1.25231 q^{21} -0.192081 q^{22} +0.0864240 q^{23} +3.06911 q^{24} -4.14650 q^{26} +1.00000 q^{27} +0.988515 q^{28} -4.18167 q^{29} -10.3672 q^{31} -4.15964 q^{32} +0.174573 q^{33} +7.10948 q^{34} -0.789350 q^{36} +4.32175 q^{37} -1.47491 q^{38} +3.76854 q^{39} +10.6360 q^{41} +1.37792 q^{42} -7.32992 q^{43} -0.137799 q^{44} -0.0950919 q^{46} +1.00000 q^{47} -1.79823 q^{48} -5.43171 q^{49} -6.46143 q^{51} -2.97469 q^{52} -5.35712 q^{53} -1.10030 q^{54} -3.84349 q^{56} +1.34046 q^{57} +4.60108 q^{58} +7.55214 q^{59} +10.4983 q^{61} +11.4070 q^{62} -1.25231 q^{63} +8.17328 q^{64} -0.192081 q^{66} -11.8871 q^{67} +5.10033 q^{68} +0.0864240 q^{69} -7.80910 q^{71} +3.06911 q^{72} +14.0348 q^{73} -4.75521 q^{74} -1.05809 q^{76} -0.218620 q^{77} -4.14650 q^{78} +9.06544 q^{79} +1.00000 q^{81} -11.7028 q^{82} -8.99673 q^{83} +0.988515 q^{84} +8.06507 q^{86} -4.18167 q^{87} +0.535782 q^{88} -1.76521 q^{89} -4.71939 q^{91} -0.0682188 q^{92} -10.3672 q^{93} -1.10030 q^{94} -4.15964 q^{96} -2.86013 q^{97} +5.97648 q^{98} +0.174573 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - q^{2} + 7 q^{3} + 5 q^{4} - q^{6} - 11 q^{7} - 6 q^{8} + 7 q^{9}+O(q^{10}) \) 7 * q - q^2 + 7 * q^3 + 5 * q^4 - q^6 - 11 * q^7 - 6 * q^8 + 7 * q^9	\( 7 q - q^{2} + 7 q^{3} + 5 q^{4} - q^{6} - 11 q^{7} - 6 q^{8} + 7 q^{9} - 8 q^{11} + 5 q^{12} - 5 q^{13} - 3 q^{14} + 9 q^{16} - 10 q^{17} - q^{18} + 7 q^{19} - 11 q^{21} - 20 q^{22} - 4 q^{23} - 6 q^{24} + 7 q^{27} - 2 q^{28} - 11 q^{29} + 3 q^{31} - 28 q^{32} - 8 q^{33} + 8 q^{34} + 5 q^{36} - 11 q^{37} + 2 q^{38} - 5 q^{39} - 20 q^{41} - 3 q^{42} - 18 q^{43} + q^{44} - 19 q^{46} + 7 q^{47} + 9 q^{48} + 14 q^{49} - 10 q^{51} - 29 q^{52} - 12 q^{53} - q^{54} - 47 q^{56} + 7 q^{57} + 19 q^{58} + 18 q^{59} - 4 q^{61} - 12 q^{62} - 11 q^{63} + 42 q^{64} - 20 q^{66} - 22 q^{67} - 44 q^{68} - 4 q^{69} - 14 q^{71} - 6 q^{72} - 30 q^{73} + 31 q^{74} - 2 q^{76} + 8 q^{77} - q^{79} + 7 q^{81} - 29 q^{82} - 54 q^{83} - 2 q^{84} - 29 q^{86} - 11 q^{87} + 22 q^{88} - 14 q^{89} + 20 q^{91} + 5 q^{92} + 3 q^{93} - q^{94} - 28 q^{96} - 24 q^{97} + 26 q^{98} - 8 q^{99}+O(q^{100}) \) 7 * q - q^2 + 7 * q^3 + 5 * q^4 - q^6 - 11 * q^7 - 6 * q^8 + 7 * q^9 - 8 * q^11 + 5 * q^12 - 5 * q^13 - 3 * q^14 + 9 * q^16 - 10 * q^17 - q^18 + 7 * q^19 - 11 * q^21 - 20 * q^22 - 4 * q^23 - 6 * q^24 + 7 * q^27 - 2 * q^28 - 11 * q^29 + 3 * q^31 - 28 * q^32 - 8 * q^33 + 8 * q^34 + 5 * q^36 - 11 * q^37 + 2 * q^38 - 5 * q^39 - 20 * q^41 - 3 * q^42 - 18 * q^43 + q^44 - 19 * q^46 + 7 * q^47 + 9 * q^48 + 14 * q^49 - 10 * q^51 - 29 * q^52 - 12 * q^53 - q^54 - 47 * q^56 + 7 * q^57 + 19 * q^58 + 18 * q^59 - 4 * q^61 - 12 * q^62 - 11 * q^63 + 42 * q^64 - 20 * q^66 - 22 * q^67 - 44 * q^68 - 4 * q^69 - 14 * q^71 - 6 * q^72 - 30 * q^73 + 31 * q^74 - 2 * q^76 + 8 * q^77 - q^79 + 7 * q^81 - 29 * q^82 - 54 * q^83 - 2 * q^84 - 29 * q^86 - 11 * q^87 + 22 * q^88 - 14 * q^89 + 20 * q^91 + 5 * q^92 + 3 * q^93 - q^94 - 28 * q^96 - 24 * q^97 + 26 * q^98 - 8 * q^99

Introduction

L-functions

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Database

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