LMFDB - Embedded newform 6025.2.a.n.1.19

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:	$0$
Dimension:	$40$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
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)

$f(q)$	$=$	$q-0.0794983 q^{2} +0.864949 q^{3} -1.99368 q^{4} -0.0687619 q^{6} -0.264036 q^{7} +0.317491 q^{8} -2.25186 q^{9} +O(q^{10})$	\(q-0.0794983 q^{2} +0.864949 q^{3} -1.99368 q^{4} -0.0687619 q^{6} -0.264036 q^{7} +0.317491 q^{8} -2.25186 q^{9} +3.42497 q^{11} -1.72443 q^{12} -2.24294 q^{13} +0.0209904 q^{14} +3.96212 q^{16} +1.58679 q^{17} +0.179019 q^{18} -7.48022 q^{19} -0.228378 q^{21} -0.272279 q^{22} +0.593160 q^{23} +0.274613 q^{24} +0.178310 q^{26} -4.54259 q^{27} +0.526404 q^{28} +6.21365 q^{29} -5.73227 q^{31} -0.949963 q^{32} +2.96243 q^{33} -0.126147 q^{34} +4.48949 q^{36} +1.92397 q^{37} +0.594664 q^{38} -1.94003 q^{39} +7.69347 q^{41} +0.0181556 q^{42} +8.90178 q^{43} -6.82830 q^{44} -0.0471552 q^{46} -5.44201 q^{47} +3.42703 q^{48} -6.93028 q^{49} +1.37249 q^{51} +4.47171 q^{52} -10.2672 q^{53} +0.361128 q^{54} -0.0838290 q^{56} -6.47000 q^{57} -0.493974 q^{58} +1.06310 q^{59} +2.12360 q^{61} +0.455705 q^{62} +0.594573 q^{63} -7.84872 q^{64} -0.235508 q^{66} +5.04001 q^{67} -3.16355 q^{68} +0.513053 q^{69} -0.380613 q^{71} -0.714945 q^{72} -3.66842 q^{73} -0.152953 q^{74} +14.9132 q^{76} -0.904317 q^{77} +0.154229 q^{78} +17.1182 q^{79} +2.82648 q^{81} -0.611617 q^{82} -8.55128 q^{83} +0.455312 q^{84} -0.707676 q^{86} +5.37449 q^{87} +1.08740 q^{88} +6.78930 q^{89} +0.592218 q^{91} -1.18257 q^{92} -4.95812 q^{93} +0.432630 q^{94} -0.821669 q^{96} +12.3262 q^{97} +0.550946 q^{98} -7.71257 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 9 q^{2} + 8 q^{3} + 41 q^{4} + 3 q^{6} + 20 q^{7} + 27 q^{8} + 38 q^{9}+O(q^{10}) $ 40 * q + 9 * q^2 + 8 * q^3 + 41 * q^4 + 3 * q^6 + 20 * q^7 + 27 * q^8 + 38 * q^9	$ 40 q + 9 q^{2} + 8 q^{3} + 41 q^{4} + 3 q^{6} + 20 q^{7} + 27 q^{8} + 38 q^{9} + q^{11} + 26 q^{12} + 11 q^{13} - q^{14} + 43 q^{16} + 20 q^{17} + 18 q^{18} + 2 q^{21} + 23 q^{22} + 79 q^{23} - 2 q^{24} + 2 q^{26} + 26 q^{27} + 30 q^{28} + 2 q^{29} + q^{31} + 68 q^{32} + 20 q^{33} + 5 q^{34} + 32 q^{36} + 16 q^{37} + 45 q^{38} - 2 q^{39} - 2 q^{41} + 19 q^{42} + 25 q^{43} + 3 q^{44} + 14 q^{46} + 88 q^{47} + 75 q^{48} + 40 q^{49} - 10 q^{51} + 18 q^{52} + 34 q^{53} + 4 q^{54} - 15 q^{56} + 51 q^{57} + 53 q^{58} + q^{59} + 9 q^{61} + 39 q^{62} + 110 q^{63} + 17 q^{64} + 26 q^{66} + 30 q^{67} + 44 q^{68} - 7 q^{69} + 5 q^{71} + 18 q^{72} + 23 q^{73} - 18 q^{74} + 43 q^{76} + 30 q^{77} + 46 q^{78} + 5 q^{79} + 44 q^{81} + 5 q^{82} + 65 q^{83} - 65 q^{84} + 40 q^{86} + 33 q^{87} + 71 q^{88} - 9 q^{89} + q^{91} + 117 q^{92} + 68 q^{93} - 72 q^{94} + 83 q^{96} - 8 q^{97} + 76 q^{98} - 40 q^{99}+O(q^{100}) $ 40 * q + 9 * q^2 + 8 * q^3 + 41 * q^4 + 3 * q^6 + 20 * q^7 + 27 * q^8 + 38 * q^9 + q^11 + 26 * q^12 + 11 * q^13 - q^14 + 43 * q^16 + 20 * q^17 + 18 * q^18 + 2 * q^21 + 23 * q^22 + 79 * q^23 - 2 * q^24 + 2 * q^26 + 26 * q^27 + 30 * q^28 + 2 * q^29 + q^31 + 68 * q^32 + 20 * q^33 + 5 * q^34 + 32 * q^36 + 16 * q^37 + 45 * q^38 - 2 * q^39 - 2 * q^41 + 19 * q^42 + 25 * q^43 + 3 * q^44 + 14 * q^46 + 88 * q^47 + 75 * q^48 + 40 * q^49 - 10 * q^51 + 18 * q^52 + 34 * q^53 + 4 * q^54 - 15 * q^56 + 51 * q^57 + 53 * q^58 + q^59 + 9 * q^61 + 39 * q^62 + 110 * q^63 + 17 * q^64 + 26 * q^66 + 30 * q^67 + 44 * q^68 - 7 * q^69 + 5 * q^71 + 18 * q^72 + 23 * q^73 - 18 * q^74 + 43 * q^76 + 30 * q^77 + 46 * q^78 + 5 * q^79 + 44 * q^81 + 5 * q^82 + 65 * q^83 - 65 * q^84 + 40 * q^86 + 33 * q^87 + 71 * q^88 - 9 * q^89 + q^91 + 117 * q^92 + 68 * q^93 - 72 * q^94 + 83 * q^96 - 8 * q^97 + 76 * q^98 - 40 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.0794983	−0.0562138	−0.0281069	−	0.999605i	$-0.508948\pi$
$2$	−0.0794983	−0.0562138	−0.0281069	+	0.999605i	$0.508948\pi$
$3$	0.864949	0.499379	0.249689	−	0.968326i	$-0.419672\pi$
$3$	0.864949	0.499379	0.249689	+	0.968326i	$0.419672\pi$
$4$	−1.99368	−0.996840
$5$	0	0
$5$	0	0
$6$	−0.0687619	−0.0280719
$7$	−0.264036	−0.0997963	−0.0498981	−	0.998754i	$-0.515890\pi$
$7$	−0.264036	−0.0997963	−0.0498981	+	0.998754i	$0.515890\pi$
$8$	0.317491	0.112250
$9$	−2.25186	−0.750621
$10$	0	0
$11$	3.42497	1.03267	0.516334	−	0.856387i	$-0.327296\pi$
$11$	3.42497	1.03267	0.516334	+	0.856387i	$0.327296\pi$
$12$	−1.72443	−0.497800
$13$	−2.24294	−0.622081	−0.311040	−	0.950397i	$-0.600677\pi$
$13$	−2.24294	−0.622081	−0.311040	+	0.950397i	$0.600677\pi$
$14$	0.0209904	0.00560992
$15$	0	0
$16$	3.96212	0.990530
$17$	1.58679	0.384853	0.192426	−	0.981311i	$-0.438364\pi$
$17$	1.58679	0.384853	0.192426	+	0.981311i	$0.438364\pi$
$18$	0.179019	0.0421952
$19$	−7.48022	−1.71608	−0.858040	−	0.513583i	$-0.828318\pi$
$19$	−7.48022	−1.71608	−0.858040	+	0.513583i	$0.828318\pi$
$20$	0	0
$21$	−0.228378	−0.0498361
$22$	−0.272279	−0.0580502
$23$	0.593160	0.123682	0.0618412	−	0.998086i	$-0.480303\pi$
$23$	0.593160	0.123682	0.0618412	+	0.998086i	$0.480303\pi$
$24$	0.274613	0.0560552
$25$	0	0
$26$	0.178310	0.0349695
$27$	−4.54259	−0.874223
$28$	0.526404	0.0994809
$29$	6.21365	1.15385	0.576923	−	0.816799i	$-0.304253\pi$
$29$	6.21365	1.15385	0.576923	+	0.816799i	$0.304253\pi$
$30$	0	0
$31$	−5.73227	−1.02955	−0.514773	−	0.857327i	$-0.672124\pi$
$31$	−5.73227	−1.02955	−0.514773	+	0.857327i	$0.672124\pi$
$32$	−0.949963	−0.167931
$33$	2.96243	0.515692
$34$	−0.126147	−0.0216340
$35$	0	0
$36$	4.48949	0.748249
$37$	1.92397	0.316299	0.158150	−	0.987415i	$-0.449447\pi$
$37$	1.92397	0.316299	0.158150	+	0.987415i	$0.449447\pi$
$38$	0.594664	0.0964673
$39$	−1.94003	−0.310654
$40$	0	0
$41$	7.69347	1.20152	0.600759	−	0.799430i	$-0.294865\pi$
$41$	7.69347	1.20152	0.600759	+	0.799430i	$0.294865\pi$
$42$	0.0181556	0.00280148
$43$	8.90178	1.35751	0.678754	−	0.734366i	$-0.262520\pi$
$43$	8.90178	1.35751	0.678754	+	0.734366i	$0.262520\pi$
$44$	−6.82830	−1.02941
$45$	0	0
$46$	−0.0471552	−0.00695266
$47$	−5.44201	−0.793798	−0.396899	−	0.917862i	$-0.629914\pi$
$47$	−5.44201	−0.793798	−0.396899	+	0.917862i	$0.629914\pi$
$48$	3.42703	0.494649
$49$	−6.93028	−0.990041
$50$	0	0
$51$	1.37249	0.192187
$52$	4.47171	0.620115
$53$	−10.2672	−1.41031	−0.705155	−	0.709053i	$-0.749123\pi$
$53$	−10.2672	−1.41031	−0.705155	+	0.709053i	$0.749123\pi$
$54$	0.361128	0.0491433
$55$	0	0
$56$	−0.0838290	−0.0112021
$57$	−6.47000	−0.856973
$58$	−0.493974	−0.0648620
$59$	1.06310	0.138404	0.0692021	−	0.997603i	$-0.477955\pi$
$59$	1.06310	0.138404	0.0692021	+	0.997603i	$0.477955\pi$
$60$	0	0
$61$	2.12360	0.271899	0.135950	−	0.990716i	$-0.456591\pi$
$61$	2.12360	0.271899	0.135950	+	0.990716i	$0.456591\pi$
$62$	0.455705	0.0578747
$63$	0.594573	0.0749092
$64$	−7.84872	−0.981090
$65$	0	0
$66$	−0.235508	−0.0289890
$67$	5.04001	0.615735	0.307867	−	0.951429i	$-0.400385\pi$
$67$	5.04001	0.615735	0.307867	+	0.951429i	$0.400385\pi$
$68$	−3.16355	−0.383637
$69$	0.513053	0.0617644
$70$	0	0
$71$	−0.380613	−0.0451704	−0.0225852	−	0.999745i	$-0.507190\pi$
$71$	−0.380613	−0.0451704	−0.0225852	+	0.999745i	$0.507190\pi$
$72$	−0.714945	−0.0842571
$73$	−3.66842	−0.429356	−0.214678	−	0.976685i	$-0.568870\pi$
$73$	−3.66842	−0.429356	−0.214678	+	0.976685i	$0.568870\pi$
$74$	−0.152953	−0.0177804
$75$	0	0
$76$	14.9132	1.71066
$77$	−0.904317	−0.103056
$78$	0.154229	0.0174630
$79$	17.1182	1.92594	0.962972	−	0.269600i	$-0.0868915\pi$
$79$	17.1182	1.92594	0.962972	+	0.269600i	$0.0868915\pi$
$80$	0	0
$81$	2.82648	0.314053
$82$	−0.611617	−0.0675418
$83$	−8.55128	−0.938624	−0.469312	−	0.883032i	$-0.655498\pi$
$83$	−8.55128	−0.938624	−0.469312	+	0.883032i	$0.655498\pi$
$84$	0.455312	0.0496786
$85$	0	0
$86$	−0.707676	−0.0763106
$87$	5.37449	0.576205
$88$	1.08740	0.115917
$89$	6.78930	0.719665	0.359832	−	0.933017i	$-0.382834\pi$
$89$	6.78930	0.719665	0.359832	+	0.933017i	$0.382834\pi$
$90$	0	0
$91$	0.592218	0.0620813
$92$	−1.18257	−0.123292
$93$	−4.95812	−0.514133
$94$	0.432630	0.0446224
$95$	0	0
$96$	−0.821669	−0.0838613
$97$	12.3262	1.25153	0.625765	−	0.780011i	$-0.284787\pi$
$97$	12.3262	1.25153	0.625765	+	0.780011i	$0.284787\pi$
$98$	0.550946	0.0556539
$99$	−7.71257	−0.775143
$100$	0	0
$101$	5.20173	0.517592	0.258796	−	0.965932i	$-0.416674\pi$
$101$	5.20173	0.517592	0.258796	+	0.965932i	$0.416674\pi$
$102$	−0.109111	−0.0108036
$103$	15.4319	1.52055	0.760277	−	0.649599i	$-0.225063\pi$
$103$	15.4319	1.52055	0.760277	+	0.649599i	$0.225063\pi$
$104$	−0.712113	−0.0698285
$105$	0	0
$106$	0.816225	0.0792788
$107$	8.00664	0.774031	0.387016	−	0.922073i	$-0.373506\pi$
$107$	8.00664	0.774031	0.387016	+	0.922073i	$0.373506\pi$
$108$	9.05648	0.871460
$109$	−6.55111	−0.627483	−0.313741	−	0.949508i	$-0.601582\pi$
$109$	−6.55111	−0.627483	−0.313741	+	0.949508i	$0.601582\pi$
$110$	0	0
$111$	1.66414	0.157953
$112$	−1.04614	−0.0988512
$113$	−13.0597	−1.22855	−0.614274	−	0.789093i	$-0.710551\pi$
$113$	−13.0597	−1.22855	−0.614274	+	0.789093i	$0.710551\pi$
$114$	0.514354	0.0481737
$115$	0	0
$116$	−12.3880	−1.15020
$117$	5.05080	0.466947
$118$	−0.0845149	−0.00778023
$119$	−0.418970	−0.0384069
$120$	0	0
$121$	0.730445	0.0664041
$122$	−0.168823	−0.0152845
$123$	6.65446	0.600012
$124$	11.4283	1.02629
$125$	0	0
$126$	−0.0472675	−0.00421093
$127$	0.455378	0.0404082	0.0202041	−	0.999796i	$-0.493568\pi$
$127$	0.455378	0.0404082	0.0202041	+	0.999796i	$0.493568\pi$
$128$	2.52389	0.223082
$129$	7.69958	0.677910
$130$	0	0
$131$	−9.27784	−0.810608	−0.405304	−	0.914182i	$-0.632834\pi$
$131$	−9.27784	−0.810608	−0.405304	+	0.914182i	$0.632834\pi$
$132$	−5.90613	−0.514063
$133$	1.97505	0.171258
$134$	−0.400672	−0.0346128
$135$	0	0
$136$	0.503791	0.0431997
$137$	−2.47844	−0.211747	−0.105874	−	0.994380i	$-0.533764\pi$
$137$	−2.47844	−0.211747	−0.105874	+	0.994380i	$0.533764\pi$
$138$	−0.0407868	−0.00347201
$139$	3.74505	0.317651	0.158825	−	0.987307i	$-0.449229\pi$
$139$	3.74505	0.317651	0.158825	+	0.987307i	$0.449229\pi$
$140$	0	0
$141$	−4.70706	−0.396406
$142$	0.0302581	0.00253920
$143$	−7.68202	−0.642403
$144$	−8.92215	−0.743513
$145$	0	0
$146$	0.291633	0.0241357
$147$	−5.99434	−0.494405
$148$	−3.83579	−0.315300
$149$	−5.64664	−0.462590	−0.231295	−	0.972884i	$-0.574296\pi$
$149$	−5.64664	−0.462590	−0.231295	+	0.972884i	$0.574296\pi$
$150$	0	0
$151$	5.25578	0.427709	0.213855	−	0.976866i	$-0.431398\pi$
$151$	5.25578	0.427709	0.213855	+	0.976866i	$0.431398\pi$
$152$	−2.37490	−0.192630
$153$	−3.57323	−0.288879
$154$	0.0718916	0.00579319
$155$	0	0
$156$	3.86780	0.309672
$157$	10.3889	0.829128	0.414564	−	0.910020i	$-0.363934\pi$
$157$	10.3889	0.829128	0.414564	+	0.910020i	$0.363934\pi$
$158$	−1.36086	−0.108265
$159$	−8.88061	−0.704278
$160$	0	0
$161$	−0.156616	−0.0123430
$162$	−0.224700	−0.0176541
$163$	14.2774	1.11829	0.559147	−	0.829068i	$-0.311129\pi$
$163$	14.2774	1.11829	0.559147	+	0.829068i	$0.311129\pi$
$164$	−15.3383	−1.19772
$165$	0	0
$166$	0.679811	0.0527636
$167$	1.97609	0.152914	0.0764572	−	0.997073i	$-0.475639\pi$
$167$	1.97609	0.152914	0.0764572	+	0.997073i	$0.475639\pi$
$168$	−0.0725078	−0.00559410
$169$	−7.96920	−0.613016
$170$	0	0
$171$	16.8444	1.28813
$172$	−17.7473	−1.35322
$173$	13.7615	1.04627	0.523133	−	0.852251i	$-0.324763\pi$
$173$	13.7615	1.04627	0.523133	+	0.852251i	$0.324763\pi$
$174$	−0.427262	−0.0323907
$175$	0	0
$176$	13.5702	1.02289
$177$	0.919530	0.0691161
$178$	−0.539738	−0.0404550
$179$	15.2715	1.14145	0.570723	−	0.821143i	$-0.306663\pi$
$179$	15.2715	1.14145	0.570723	+	0.821143i	$0.306663\pi$
$180$	0	0
$181$	17.5733	1.30621	0.653106	−	0.757266i	$-0.273465\pi$
$181$	17.5733	1.30621	0.653106	+	0.757266i	$0.273465\pi$
$182$	−0.0470803	−0.00348982
$183$	1.83681	0.135781
$184$	0.188323	0.0138833
$185$	0	0
$186$	0.394162	0.0289014
$187$	5.43471	0.397425
$188$	10.8496	0.791290
$189$	1.19941	0.0872442
$190$	0	0
$191$	−10.3226	−0.746919	−0.373459	−	0.927647i	$-0.621828\pi$
$191$	−10.3226	−0.746919	−0.373459	+	0.927647i	$0.621828\pi$
$192$	−6.78874	−0.489935
$193$	17.8227	1.28290	0.641452	−	0.767163i	$-0.278332\pi$
$193$	17.8227	1.28290	0.641452	+	0.767163i	$0.278332\pi$
$194$	−0.979907	−0.0703533
$195$	0	0
$196$	13.8168	0.986912
$197$	−14.6399	−1.04305	−0.521523	−	0.853237i	$-0.674636\pi$
$197$	−14.6399	−1.04305	−0.521523	+	0.853237i	$0.674636\pi$
$198$	0.613136	0.0435737
$199$	−7.81518	−0.554004	−0.277002	−	0.960869i	$-0.589341\pi$
$199$	−7.81518	−0.554004	−0.277002	+	0.960869i	$0.589341\pi$
$200$	0	0
$201$	4.35935	0.307485
$202$	−0.413529	−0.0290958
$203$	−1.64063	−0.115149
$204$	−2.73631	−0.191580
$205$	0	0
$206$	−1.22681	−0.0854761
$207$	−1.33572	−0.0928387
$208$	−8.88681	−0.616189
$209$	−25.6195	−1.77214
$210$	0	0
$211$	−5.93918	−0.408870	−0.204435	−	0.978880i	$-0.565536\pi$
$211$	−5.93918	−0.408870	−0.204435	+	0.978880i	$0.565536\pi$
$212$	20.4695	1.40585
$213$	−0.329211	−0.0225571
$214$	−0.636514	−0.0435112
$215$	0	0
$216$	−1.44223	−0.0981314
$217$	1.51353	0.102745
$218$	0.520802	0.0352732
$219$	−3.17300	−0.214411
$220$	0	0
$221$	−3.55908	−0.239410
$222$	−0.132296	−0.00887914
$223$	22.8308	1.52886	0.764430	−	0.644706i	$-0.223020\pi$
$223$	22.8308	1.52886	0.764430	+	0.644706i	$0.223020\pi$
$224$	0.250825	0.0167589
$225$	0	0
$226$	1.03822	0.0690613
$227$	24.6559	1.63647	0.818235	−	0.574884i	$-0.194953\pi$
$227$	24.6559	1.63647	0.818235	+	0.574884i	$0.194953\pi$
$228$	12.8991	0.854265
$229$	8.19904	0.541808	0.270904	−	0.962606i	$-0.412677\pi$
$229$	8.19904	0.541808	0.270904	+	0.962606i	$0.412677\pi$
$230$	0	0
$231$	−0.782188	−0.0514642
$232$	1.97277	0.129519
$233$	27.4309	1.79706	0.898529	−	0.438914i	$-0.144637\pi$
$233$	27.4309	1.79706	0.898529	+	0.438914i	$0.144637\pi$
$234$	−0.401530	−0.0262488
$235$	0	0
$236$	−2.11949	−0.137967
$237$	14.8063	0.961775
$238$	0.0333074	0.00215900
$239$	7.00866	0.453353	0.226676	−	0.973970i	$-0.427214\pi$
$239$	7.00866	0.453353	0.226676	+	0.973970i	$0.427214\pi$
$240$	0	0
$241$	1.00000	0.0644157
$241$	1.00000	0.0644157
$242$	−0.0580691	−0.00373282
$243$	16.0725	1.03105
$244$	−4.23378	−0.271040
$245$	0	0
$246$	−0.529018	−0.0337289
$247$	16.7777	1.06754
$248$	−1.81994	−0.115566
$249$	−7.39642	−0.468729
$250$	0	0
$251$	1.88565	0.119021	0.0595105	−	0.998228i	$-0.481046\pi$
$251$	1.88565	0.119021	0.0595105	+	0.998228i	$0.481046\pi$
$252$	−1.18539	−0.0746725
$253$	2.03156	0.127723
$254$	−0.0362017	−0.00227150
$255$	0	0
$256$	15.4968	0.968550
$257$	−5.17769	−0.322975	−0.161488	−	0.986875i	$-0.551629\pi$
$257$	−5.17769	−0.322975	−0.161488	+	0.986875i	$0.551629\pi$
$258$	−0.612103	−0.0381079
$259$	−0.507999	−0.0315655
$260$	0	0
$261$	−13.9923	−0.866100
$262$	0.737572	0.0455673
$263$	0.310497	0.0191461	0.00957304	−	0.999954i	$-0.496953\pi$
$263$	0.310497	0.0191461	0.00957304	+	0.999954i	$0.496953\pi$
$264$	0.940543	0.0578864
$265$	0	0
$266$	−0.157013	−0.00962707
$267$	5.87240	0.359385
$268$	−10.0482	−0.613789
$269$	5.07665	0.309529	0.154764	−	0.987951i	$-0.450538\pi$
$269$	5.07665	0.309529	0.154764	+	0.987951i	$0.450538\pi$
$270$	0	0
$271$	10.4932	0.637417	0.318708	−	0.947853i	$-0.396751\pi$
$271$	10.4932	0.637417	0.318708	+	0.947853i	$0.396751\pi$
$272$	6.28705	0.381208
$273$	0.512238	0.0310021
$274$	0.197032	0.0119031
$275$	0	0
$276$	−1.02286	−0.0615692
$277$	7.62931	0.458401	0.229200	−	0.973379i	$-0.426389\pi$
$277$	7.62931	0.458401	0.229200	+	0.973379i	$0.426389\pi$
$278$	−0.297725	−0.0178563
$279$	12.9083	0.772799
$280$	0	0
$281$	−9.86831	−0.588694	−0.294347	−	0.955699i	$-0.595102\pi$
$281$	−9.86831	−0.588694	−0.294347	+	0.955699i	$0.595102\pi$
$282$	0.374203	0.0222835
$283$	12.3435	0.733747	0.366874	−	0.930271i	$-0.380428\pi$
$283$	12.3435	0.733747	0.366874	+	0.930271i	$0.380428\pi$
$284$	0.758820	0.0450277
$285$	0	0
$286$	0.610707	0.0361119
$287$	−2.03135	−0.119907
$288$	2.13919	0.126053
$289$	−14.4821	−0.851888
$290$	0	0
$291$	10.6615	0.624988
$292$	7.31366	0.428000
$293$	4.88507	0.285389	0.142695	−	0.989767i	$-0.454423\pi$
$293$	4.88507	0.285389	0.142695	+	0.989767i	$0.454423\pi$
$294$	0.476540	0.0277924
$295$	0	0
$296$	0.610844	0.0355046
$297$	−15.5583	−0.902782
$298$	0.448898	0.0260039
$299$	−1.33042	−0.0769405
$300$	0	0
$301$	−2.35039	−0.135474
$302$	−0.417825	−0.0240431
$303$	4.49924	0.258474
$304$	−29.6375	−1.69983
$305$	0	0
$306$	0.284066	0.0162390
$307$	−25.4108	−1.45027	−0.725136	−	0.688606i	$-0.758223\pi$
$307$	−25.4108	−1.45027	−0.725136	+	0.688606i	$0.758223\pi$
$308$	1.80292	0.102731
$309$	13.3478	0.759332
$310$	0	0
$311$	−26.4548	−1.50011	−0.750056	−	0.661374i	$-0.769974\pi$
$311$	−26.4548	−1.50011	−0.750056	+	0.661374i	$0.769974\pi$
$312$	−0.615942	−0.0348708
$313$	7.23448	0.408917	0.204458	−	0.978875i	$-0.434457\pi$
$313$	7.23448	0.408917	0.204458	+	0.978875i	$0.434457\pi$
$314$	−0.825903	−0.0466084
$315$	0	0
$316$	−34.1282	−1.91986
$317$	25.8214	1.45028	0.725138	−	0.688603i	$-0.241776\pi$
$317$	25.8214	1.45028	0.725138	+	0.688603i	$0.241776\pi$
$318$	0.705993	0.0395901
$319$	21.2816	1.19154
$320$	0	0
$321$	6.92534	0.386535
$322$	0.0124507	0.000693849 0
$323$	−11.8695	−0.660438
$324$	−5.63509	−0.313061
$325$	0	0
$326$	−1.13503	−0.0628635
$327$	−5.66638	−0.313351
$328$	2.44260	0.134870
$329$	1.43689	0.0792181
$330$	0	0
$331$	−27.8687	−1.53180	−0.765902	−	0.642957i	$-0.777707\pi$
$331$	−27.8687	−1.53180	−0.765902	+	0.642957i	$0.777707\pi$
$332$	17.0485	0.935658
$333$	−4.33253	−0.237421
$334$	−0.157096	−0.00859589
$335$	0	0
$336$	−0.904860	−0.0493642
$337$	30.0511	1.63699	0.818493	−	0.574517i	$-0.194810\pi$
$337$	30.0511	1.63699	0.818493	+	0.574517i	$0.194810\pi$
$338$	0.633538	0.0344599
$339$	−11.2959	−0.613511
$340$	0	0
$341$	−19.6329	−1.06318
$342$	−1.33910	−0.0724104
$343$	3.67810	0.198599
$344$	2.82623	0.152380
$345$	0	0
$346$	−1.09401	−0.0588145
$347$	32.7902	1.76027	0.880135	−	0.474723i	$-0.157452\pi$
$347$	32.7902	1.76027	0.880135	+	0.474723i	$0.157452\pi$
$348$	−10.7150	−0.574385
$349$	0.922150	0.0493615	0.0246808	−	0.999695i	$-0.492143\pi$
$349$	0.922150	0.0493615	0.0246808	+	0.999695i	$0.492143\pi$
$350$	0	0
$351$	10.1888	0.543837
$352$	−3.25360	−0.173417
$353$	11.0507	0.588167	0.294083	−	0.955780i	$-0.404986\pi$
$353$	11.0507	0.588167	0.294083	+	0.955780i	$0.404986\pi$
$354$	−0.0731011	−0.00388528
$355$	0	0
$356$	−13.5357	−0.717390
$357$	−0.362387	−0.0191796
$358$	−1.21406	−0.0641650
$359$	9.50873	0.501851	0.250926	−	0.968006i	$-0.419265\pi$
$359$	9.50873	0.501851	0.250926	+	0.968006i	$0.419265\pi$
$360$	0	0
$361$	36.9536	1.94493
$362$	−1.39705	−0.0734271
$363$	0.631798	0.0331608
$364$	−1.18069	−0.0618851
$365$	0	0
$366$	−0.146023	−0.00763275
$367$	14.4391	0.753716	0.376858	−	0.926271i	$-0.377004\pi$
$367$	14.4391	0.753716	0.376858	+	0.926271i	$0.377004\pi$
$368$	2.35017	0.122511
$369$	−17.3246	−0.901885
$370$	0	0
$371$	2.71091	0.140744
$372$	9.88491	0.512509
$373$	15.4281	0.798836	0.399418	−	0.916769i	$-0.369212\pi$
$373$	15.4281	0.798836	0.399418	+	0.916769i	$0.369212\pi$
$374$	−0.432050	−0.0223408
$375$	0	0
$376$	−1.72779	−0.0891037
$377$	−13.9369	−0.717785
$378$	−0.0953509	−0.00490432
$379$	0.809224	0.0415671	0.0207835	−	0.999784i	$-0.493384\pi$
$379$	0.809224	0.0415671	0.0207835	+	0.999784i	$0.493384\pi$
$380$	0	0
$381$	0.393879	0.0201790
$382$	0.820631	0.0419871
$383$	24.4826	1.25100	0.625501	−	0.780224i	$-0.284895\pi$
$383$	24.4826	1.25100	0.625501	+	0.780224i	$0.284895\pi$
$384$	2.18303	0.111402
$385$	0	0
$386$	−1.41687	−0.0721169
$387$	−20.0456	−1.01897
$388$	−24.5744	−1.24758
$389$	0.145356	0.00736986	0.00368493	−	0.999993i	$-0.498827\pi$
$389$	0.145356	0.00736986	0.00368493	+	0.999993i	$0.498827\pi$
$390$	0	0
$391$	0.941220	0.0475996
$392$	−2.20030	−0.111132
$393$	−8.02485	−0.404800
$394$	1.16384	0.0586336
$395$	0	0
$396$	15.3764	0.772693
$397$	−24.2902	−1.21909	−0.609544	−	0.792752i	$-0.708648\pi$
$397$	−24.2902	−1.21909	−0.609544	+	0.792752i	$0.708648\pi$
$398$	0.621293	0.0311426
$399$	1.70832	0.0855227
$400$	0	0
$401$	11.2739	0.562992	0.281496	−	0.959562i	$-0.409169\pi$
$401$	11.2739	0.562992	0.281496	+	0.959562i	$0.409169\pi$
$402$	−0.346561	−0.0172849
$403$	12.8572	0.640461
$404$	−10.3706	−0.515956
$405$	0	0
$406$	0.130427	0.00647298
$407$	6.58956	0.326632
$408$	0.435753	0.0215730
$409$	−5.87004	−0.290255	−0.145127	−	0.989413i	$-0.546359\pi$
$409$	−5.87004	−0.290255	−0.145127	+	0.989413i	$0.546359\pi$
$410$	0	0
$411$	−2.14372	−0.105742
$412$	−30.7664	−1.51575
$413$	−0.280698	−0.0138122
$414$	0.106187	0.00521881
$415$	0	0
$416$	2.13071	0.104467
$417$	3.23928	0.158628
$418$	2.03671	0.0996187
$419$	−21.2802	−1.03961	−0.519803	−	0.854286i	$-0.673995\pi$
$419$	−21.2802	−1.03961	−0.519803	+	0.854286i	$0.673995\pi$
$420$	0	0
$421$	0.359157	0.0175042	0.00875212	−	0.999962i	$-0.497214\pi$
$421$	0.359157	0.0175042	0.00875212	+	0.999962i	$0.497214\pi$
$422$	0.472154	0.0229841
$423$	12.2547	0.595842
$424$	−3.25974	−0.158307
$425$	0	0
$426$	0.0261717	0.00126802
$427$	−0.560708	−0.0271346
$428$	−15.9627	−0.771585
$429$	−6.64456	−0.320802
$430$	0	0
$431$	25.1776	1.21276	0.606382	−	0.795174i	$-0.292620\pi$
$431$	25.1776	1.21276	0.606382	+	0.795174i	$0.292620\pi$
$432$	−17.9983	−0.865944
$433$	−19.8640	−0.954603	−0.477301	−	0.878740i	$-0.658385\pi$
$433$	−19.8640	−0.954603	−0.477301	+	0.878740i	$0.658385\pi$
$434$	−0.120323	−0.00577567
$435$	0	0
$436$	13.0608	0.625500
$437$	−4.43697	−0.212249
$438$	0.252248	0.0120529
$439$	12.1176	0.578340	0.289170	−	0.957278i	$-0.406621\pi$
$439$	12.1176	0.578340	0.289170	+	0.957278i	$0.406621\pi$
$440$	0	0
$441$	15.6061	0.743145
$442$	0.282941	0.0134581
$443$	4.05069	0.192454	0.0962270	−	0.995359i	$-0.469323\pi$
$443$	4.05069	0.192454	0.0962270	+	0.995359i	$0.469323\pi$
$444$	−3.31776	−0.157454
$445$	0	0
$446$	−1.81501	−0.0859430
$447$	−4.88405	−0.231008
$448$	2.07235	0.0979091
$449$	−2.33560	−0.110224	−0.0551120	−	0.998480i	$-0.517552\pi$
$449$	−2.33560	−0.110224	−0.0551120	+	0.998480i	$0.517552\pi$
$450$	0	0
$451$	26.3499	1.24077
$452$	26.0368	1.22467
$453$	4.54598	0.213589
$454$	−1.96010	−0.0919921
$455$	0	0
$456$	−2.05417	−0.0961951
$457$	13.5966	0.636021	0.318010	−	0.948087i	$-0.396985\pi$
$457$	13.5966	0.636021	0.318010	+	0.948087i	$0.396985\pi$
$458$	−0.651809	−0.0304571
$459$	−7.20814	−0.336447
$460$	0	0
$461$	31.4549	1.46500	0.732500	−	0.680767i	$-0.238354\pi$
$461$	31.4549	1.46500	0.732500	+	0.680767i	$0.238354\pi$
$462$	0.0621826	0.00289300
$463$	5.02592	0.233574	0.116787	−	0.993157i	$-0.462741\pi$
$463$	5.02592	0.233574	0.116787	+	0.993157i	$0.462741\pi$
$464$	24.6192	1.14292
$465$	0	0
$466$	−2.18071	−0.101019
$467$	−34.9311	−1.61642	−0.808210	−	0.588894i	$-0.799563\pi$
$467$	−34.9311	−1.61642	−0.808210	+	0.588894i	$0.799563\pi$
$468$	−10.0697	−0.465471
$469$	−1.33074	−0.0614480
$470$	0	0
$471$	8.98591	0.414049
$472$	0.337525	0.0155359
$473$	30.4884	1.40186
$474$	−1.17708	−0.0540650
$475$	0	0
$476$	0.835291	0.0382855
$477$	23.1204	1.05861
$478$	−0.557177	−0.0254847
$479$	20.3607	0.930303	0.465151	−	0.885231i	$-0.346000\pi$
$479$	20.3607	0.930303	0.465151	+	0.885231i	$0.346000\pi$
$480$	0	0
$481$	−4.31536	−0.196764
$482$	−0.0794983	−0.00362105
$483$	−0.135465	−0.00616385
$484$	−1.45627	−0.0661943
$485$	0	0
$486$	−1.27774	−0.0579594
$487$	−17.4138	−0.789093	−0.394547	−	0.918876i	$-0.629098\pi$
$487$	−17.4138	−0.789093	−0.394547	+	0.918876i	$0.629098\pi$
$488$	0.674224	0.0305207
$489$	12.3492	0.558452
$490$	0	0
$491$	−27.4939	−1.24078	−0.620391	−	0.784293i	$-0.713026\pi$
$491$	−27.4939	−1.24078	−0.620391	+	0.784293i	$0.713026\pi$
$492$	−13.2669	−0.598116
$493$	9.85975	0.444061
$494$	−1.33380	−0.0600104
$495$	0	0
$496$	−22.7119	−1.01980
$497$	0.100496	0.00450784
$498$	0.588002	0.0263490
$499$	−3.16971	−0.141896	−0.0709478	−	0.997480i	$-0.522602\pi$
$499$	−3.16971	−0.141896	−0.0709478	+	0.997480i	$0.522602\pi$
$500$	0	0
$501$	1.70922	0.0763621
$502$	−0.149906	−0.00669062
$503$	−42.5423	−1.89687	−0.948434	−	0.316974i	$-0.897333\pi$
$503$	−42.5423	−1.89687	−0.948434	+	0.316974i	$0.897333\pi$
$504$	0.188771	0.00840855
$505$	0	0
$506$	−0.161505	−0.00717979
$507$	−6.89296	−0.306127
$508$	−0.907878	−0.0402806
$509$	3.17054	0.140532	0.0702659	−	0.997528i	$-0.477615\pi$
$509$	3.17054	0.140532	0.0702659	+	0.997528i	$0.477615\pi$
$510$	0	0
$511$	0.968596	0.0428482
$512$	−6.27974	−0.277528
$513$	33.9796	1.50024
$514$	0.411617	0.0181557
$515$	0	0
$516$	−15.3505	−0.675768
$517$	−18.6387	−0.819730
$518$	0.0403850	0.00177442
$519$	11.9030	0.522482
$520$	0	0
$521$	6.69525	0.293324	0.146662	−	0.989187i	$-0.453147\pi$
$521$	6.69525	0.293324	0.146662	+	0.989187i	$0.453147\pi$
$522$	1.11236	0.0486868
$523$	10.8377	0.473900	0.236950	−	0.971522i	$-0.423852\pi$
$523$	10.8377	0.473900	0.236950	+	0.971522i	$0.423852\pi$
$524$	18.4970	0.808047
$525$	0	0
$526$	−0.0246840	−0.00107627
$527$	−9.09590	−0.396224
$528$	11.7375	0.510809
$529$	−22.6482	−0.984703
$530$	0	0
$531$	−2.39396	−0.103889
$532$	−3.93761	−0.170717
$533$	−17.2560	−0.747441
$534$	−0.466845	−0.0202024
$535$	0	0
$536$	1.60015	0.0691162
$537$	13.2091	0.570014
$538$	−0.403585	−0.0173998
$539$	−23.7360	−1.02238
$540$	0	0
$541$	−31.2181	−1.34217	−0.671086	−	0.741379i	$-0.734172\pi$
$541$	−31.2181	−1.34217	−0.671086	+	0.741379i	$0.734172\pi$
$542$	−0.834191	−0.0358316
$543$	15.2000	0.652295
$544$	−1.50739	−0.0646288
$545$	0	0
$546$	−0.0407221	−0.00174274
$547$	21.5026	0.919384	0.459692	−	0.888078i	$-0.347960\pi$
$547$	21.5026	0.919384	0.459692	+	0.888078i	$0.347960\pi$
$548$	4.94122	0.211078
$549$	−4.78206	−0.204093
$550$	0	0
$551$	−46.4794	−1.98009
$552$	0.162890	0.00693304
$553$	−4.51982	−0.192202
$554$	−0.606517	−0.0257684
$555$	0	0
$556$	−7.46643	−0.316647
$557$	−16.9197	−0.716910	−0.358455	−	0.933547i	$-0.616696\pi$
$557$	−16.9197	−0.716910	−0.358455	+	0.933547i	$0.616696\pi$
$558$	−1.02619	−0.0434419
$559$	−19.9662	−0.844480
$560$	0	0
$561$	4.70075	0.198466
$562$	0.784514	0.0330927
$563$	15.1482	0.638419	0.319209	−	0.947684i	$-0.396583\pi$
$563$	15.1482	0.638419	0.319209	+	0.947684i	$0.396583\pi$
$564$	9.38437	0.395153
$565$	0	0
$566$	−0.981290	−0.0412467
$567$	−0.746292	−0.0313413
$568$	−0.120841	−0.00507037
$569$	19.4901	0.817068	0.408534	−	0.912743i	$-0.366040\pi$
$569$	19.4901	0.817068	0.408534	+	0.912743i	$0.366040\pi$
$570$	0	0
$571$	16.6575	0.697096	0.348548	−	0.937291i	$-0.386675\pi$
$571$	16.6575	0.697096	0.348548	+	0.937291i	$0.386675\pi$
$572$	15.3155	0.640373
$573$	−8.92854	−0.372995
$574$	0.161489	0.00674042
$575$	0	0
$576$	17.6742	0.736427
$577$	−8.41230	−0.350209	−0.175104	−	0.984550i	$-0.556026\pi$
$577$	−8.41230	−0.350209	−0.175104	+	0.984550i	$0.556026\pi$
$578$	1.15130	0.0478878
$579$	15.4157	0.640655
$580$	0	0
$581$	2.25785	0.0936712
$582$	−0.847570	−0.0351329
$583$	−35.1649	−1.45638
$584$	−1.16469	−0.0481952
$585$	0	0
$586$	−0.388355	−0.0160428
$587$	19.6667	0.811733	0.405866	−	0.913932i	$-0.366970\pi$
$587$	19.6667	0.811733	0.405866	+	0.913932i	$0.366970\pi$
$588$	11.9508	0.492843
$589$	42.8786	1.76678
$590$	0	0
$591$	−12.6627	−0.520875
$592$	7.62302	0.313304
$593$	18.5767	0.762855	0.381427	−	0.924399i	$-0.375433\pi$
$593$	18.5767	0.762855	0.381427	+	0.924399i	$0.375433\pi$
$594$	1.23685	0.0507488
$595$	0	0
$596$	11.2576	0.461129
$597$	−6.75973	−0.276657
$598$	0.105766	0.00432511
$599$	0.166741	0.00681284	0.00340642	−	0.999994i	$-0.498916\pi$
$599$	0.166741	0.00681284	0.00340642	+	0.999994i	$0.498916\pi$
$600$	0	0
$601$	−31.0804	−1.26780	−0.633898	−	0.773416i	$-0.718546\pi$
$601$	−31.0804	−1.26780	−0.633898	+	0.773416i	$0.718546\pi$
$602$	0.186852	0.00761552
$603$	−11.3494	−0.462184
$604$	−10.4783	−0.426358
$605$	0	0
$606$	−0.357681	−0.0145298
$607$	19.5445	0.793288	0.396644	−	0.917972i	$-0.370175\pi$
$607$	19.5445	0.793288	0.396644	+	0.917972i	$0.370175\pi$
$608$	7.10593	0.288183
$609$	−1.41906	−0.0575032
$610$	0	0
$611$	12.2061	0.493806
$612$	7.12388	0.287966
$613$	43.0109	1.73719	0.868597	−	0.495519i	$-0.165022\pi$
$613$	43.0109	1.73719	0.868597	+	0.495519i	$0.165022\pi$
$614$	2.02012	0.0815253
$615$	0	0
$616$	−0.287112	−0.0115681
$617$	21.3116	0.857971	0.428986	−	0.903311i	$-0.358871\pi$
$617$	21.3116	0.857971	0.428986	+	0.903311i	$0.358871\pi$
$618$	−1.06113	−0.0426849
$619$	−32.8596	−1.32074	−0.660370	−	0.750940i	$-0.729601\pi$
$619$	−32.8596	−1.32074	−0.660370	+	0.750940i	$0.729601\pi$
$620$	0	0
$621$	−2.69449	−0.108126
$622$	2.10311	0.0843270
$623$	−1.79262	−0.0718198
$624$	−7.68664	−0.307712
$625$	0	0
$626$	−0.575128	−0.0229868
$627$	−22.1596	−0.884969
$628$	−20.7122	−0.826508
$629$	3.05294	0.121729
$630$	0	0
$631$	−42.5355	−1.69331	−0.846655	−	0.532142i	$-0.821387\pi$
$631$	−42.5355	−1.69331	−0.846655	+	0.532142i	$0.821387\pi$
$632$	5.43486	0.216187
$633$	−5.13709	−0.204181
$634$	−2.05276	−0.0815255
$635$	0	0
$636$	17.7051	0.702053
$637$	15.5442	0.615885
$638$	−1.69185	−0.0669809
$639$	0.857088	0.0339059
$640$	0	0
$641$	9.79869	0.387025	0.193512	−	0.981098i	$-0.438012\pi$
$641$	9.79869	0.387025	0.193512	+	0.981098i	$0.438012\pi$
$642$	−0.550552	−0.0217286
$643$	−30.2709	−1.19377	−0.596884	−	0.802328i	$-0.703595\pi$
$643$	−30.2709	−1.19377	−0.596884	+	0.802328i	$0.703595\pi$
$644$	0.312242	0.0123040
$645$	0	0
$646$	0.943607	0.0371257
$647$	−47.4116	−1.86394	−0.931971	−	0.362534i	$-0.881912\pi$
$647$	−47.4116	−1.86394	−0.931971	+	0.362534i	$0.881912\pi$
$648$	0.897380	0.0352524
$649$	3.64110	0.142926
$650$	0	0
$651$	1.30912	0.0513086
$652$	−28.4646	−1.11476
$653$	−40.8392	−1.59816	−0.799081	−	0.601223i	$-0.794680\pi$
$653$	−40.8392	−1.59816	−0.799081	+	0.601223i	$0.794680\pi$
$654$	0.450467	0.0176147
$655$	0	0
$656$	30.4824	1.19014
$657$	8.26078	0.322284
$658$	−0.114230	−0.00445315
$659$	−23.1842	−0.903129	−0.451564	−	0.892239i	$-0.649134\pi$
$659$	−23.1842	−0.903129	−0.451564	+	0.892239i	$0.649134\pi$
$660$	0	0
$661$	−26.4632	−1.02930	−0.514650	−	0.857400i	$-0.672078\pi$
$661$	−26.4632	−1.02930	−0.514650	+	0.857400i	$0.672078\pi$
$662$	2.21552	0.0861085
$663$	−3.07842	−0.119556
$664$	−2.71495	−0.105360
$665$	0	0
$666$	0.344428	0.0133463
$667$	3.68569	0.142710
$668$	−3.93969	−0.152431
$669$	19.7474	0.763480
$670$	0	0
$671$	7.27328	0.280782
$672$	0.216950	0.00836904
$673$	2.96782	0.114401	0.0572004	−	0.998363i	$-0.481783\pi$
$673$	2.96782	0.114401	0.0572004	+	0.998363i	$0.481783\pi$
$674$	−2.38901	−0.0920211
$675$	0	0
$676$	15.8880	0.611079
$677$	34.8071	1.33775	0.668874	−	0.743376i	$-0.266777\pi$
$677$	34.8071	1.33775	0.668874	+	0.743376i	$0.266777\pi$
$678$	0.898007	0.0344877
$679$	−3.25455	−0.124898
$680$	0	0
$681$	21.3261	0.817218
$682$	1.56078	0.0597653
$683$	0.205918	0.00787922	0.00393961	−	0.999992i	$-0.498746\pi$
$683$	0.205918	0.00787922	0.00393961	+	0.999992i	$0.498746\pi$
$684$	−33.5824	−1.28405
$685$	0	0
$686$	−0.292402	−0.0111640
$687$	7.09175	0.270567
$688$	35.2699	1.34465
$689$	23.0288	0.877326
$690$	0	0
$691$	32.7038	1.24411	0.622055	−	0.782973i	$-0.286298\pi$
$691$	32.7038	1.24411	0.622055	+	0.782973i	$0.286298\pi$
$692$	−27.4360	−1.04296
$693$	2.03640	0.0773564
$694$	−2.60676	−0.0989514
$695$	0	0
$696$	1.70635	0.0646790
$697$	12.2079	0.462408
$698$	−0.0733093	−0.00277480
$699$	23.7263	0.897412
$700$	0	0
$701$	−43.0600	−1.62636	−0.813178	−	0.582015i	$-0.802264\pi$
$701$	−43.0600	−1.62636	−0.813178	+	0.582015i	$0.802264\pi$
$702$	−0.809990	−0.0305711
$703$	−14.3917	−0.542795
$704$	−26.8817	−1.01314
$705$	0	0
$706$	−0.878507	−0.0330631
$707$	−1.37345	−0.0516538
$708$	−1.83325	−0.0688977
$709$	50.4037	1.89295	0.946476	−	0.322773i	$-0.104615\pi$
$709$	50.4037	1.89295	0.946476	+	0.322773i	$0.104615\pi$
$710$	0	0
$711$	−38.5478	−1.44565
$712$	2.15554	0.0807823
$713$	−3.40015	−0.127337
$714$	0.0288092	0.00107816
$715$	0	0
$716$	−30.4465	−1.13784
$717$	6.06214	0.226395
$718$	−0.755927	−0.0282109
$719$	20.4860	0.764000	0.382000	−	0.924162i	$-0.375235\pi$
$719$	20.4860	0.764000	0.382000	+	0.924162i	$0.375235\pi$
$720$	0	0
$721$	−4.07459	−0.151746
$722$	−2.93775	−0.109332
$723$	0.864949	0.0321678
$724$	−35.0355	−1.30209
$725$	0	0
$726$	−0.0502268	−0.00186409
$727$	−3.03039	−0.112391	−0.0561955	−	0.998420i	$-0.517897\pi$
$727$	−3.03039	−0.112391	−0.0561955	+	0.998420i	$0.517897\pi$
$728$	0.188024	0.00696862
$729$	5.42249	0.200833
$730$	0	0
$731$	14.1252	0.522441
$732$	−3.66201	−0.135352
$733$	−17.6217	−0.650871	−0.325436	−	0.945564i	$-0.605511\pi$
$733$	−17.6217	−0.650871	−0.325436	+	0.945564i	$0.605511\pi$
$734$	−1.14789	−0.0423692
$735$	0	0
$736$	−0.563480	−0.0207702
$737$	17.2619	0.635850
$738$	1.37728	0.0506983
$739$	−24.1436	−0.888136	−0.444068	−	0.895993i	$-0.646465\pi$
$739$	−24.1436	−0.888136	−0.444068	+	0.895993i	$0.646465\pi$
$740$	0	0
$741$	14.5119	0.533106
$742$	−0.215513	−0.00791173
$743$	24.7683	0.908659	0.454330	−	0.890834i	$-0.349879\pi$
$743$	24.7683	0.908659	0.454330	+	0.890834i	$0.349879\pi$
$744$	−1.57416	−0.0577114
$745$	0	0
$746$	−1.22651	−0.0449056
$747$	19.2563	0.704551
$748$	−10.8351	−0.396170
$749$	−2.11404	−0.0772454
$750$	0	0
$751$	−0.599032	−0.0218590	−0.0109295	−	0.999940i	$-0.503479\pi$
$751$	−0.599032	−0.0218590	−0.0109295	+	0.999940i	$0.503479\pi$
$752$	−21.5619	−0.786281
$753$	1.63099	0.0594366
$754$	1.10796	0.0403494
$755$	0	0
$756$	−2.39124	−0.0869685
$757$	3.78406	0.137534	0.0687670	−	0.997633i	$-0.478093\pi$
$757$	3.78406	0.137534	0.0687670	+	0.997633i	$0.478093\pi$
$758$	−0.0643319	−0.00233664
$759$	1.75719	0.0637821
$760$	0	0
$761$	18.7487	0.679639	0.339819	−	0.940491i	$-0.389634\pi$
$761$	18.7487	0.679639	0.339819	+	0.940491i	$0.389634\pi$
$762$	−0.0313127	−0.00113434
$763$	1.72973	0.0626204
$764$	20.5800	0.744559
$765$	0	0
$766$	−1.94632	−0.0703235
$767$	−2.38448	−0.0860986
$768$	13.4039	0.483673
$769$	−18.7178	−0.674980	−0.337490	−	0.941329i	$-0.609578\pi$
$769$	−18.7178	−0.674980	−0.337490	+	0.941329i	$0.609578\pi$
$770$	0	0
$771$	−4.47844	−0.161287
$772$	−35.5327	−1.27885
$773$	20.8387	0.749516	0.374758	−	0.927123i	$-0.377726\pi$
$773$	20.8387	0.749516	0.374758	+	0.927123i	$0.377726\pi$
$774$	1.59359	0.0572804
$775$	0	0
$776$	3.91344	0.140484
$777$	−0.439393	−0.0157631
$778$	−0.0115556	−0.000414287 0
$779$	−57.5488	−2.06190
$780$	0	0
$781$	−1.30359	−0.0466461
$782$	−0.0748254	−0.00267575
$783$	−28.2261	−1.00872
$784$	−27.4586	−0.980665
$785$	0	0
$786$	0.637962	0.0227553
$787$	36.5242	1.30195	0.650973	−	0.759101i	$-0.274361\pi$
$787$	36.5242	1.30195	0.650973	+	0.759101i	$0.274361\pi$
$788$	29.1872	1.03975
$789$	0.268564	0.00956114
$790$	0	0
$791$	3.44822	0.122605
$792$	−2.44867	−0.0870097
$793$	−4.76312	−0.169143
$794$	1.93103	0.0685295
$795$	0	0
$796$	15.5810	0.552253
$797$	3.25764	0.115391	0.0576957	−	0.998334i	$-0.481625\pi$
$797$	3.25764	0.115391	0.0576957	+	0.998334i	$0.481625\pi$
$798$	−0.135808	−0.00480755
$799$	−8.63532	−0.305496
$800$	0	0
$801$	−15.2886	−0.540195
$802$	−0.896256	−0.0316479
$803$	−12.5642	−0.443383
$804$	−8.69115	−0.306513
$805$	0	0
$806$	−1.02212	−0.0360027
$807$	4.39104	0.154572
$808$	1.65150	0.0580996
$809$	0.590536	0.0207622	0.0103811	−	0.999946i	$-0.496696\pi$
$809$	0.590536	0.0207622	0.0103811	+	0.999946i	$0.496696\pi$
$810$	0	0
$811$	15.9879	0.561413	0.280706	−	0.959794i	$-0.409431\pi$
$811$	15.9879	0.561413	0.280706	+	0.959794i	$0.409431\pi$
$812$	3.27089	0.114786
$813$	9.07608	0.318312
$814$	−0.523859	−0.0183612
$815$	0	0
$816$	5.43798	0.190367
$817$	−66.5872	−2.32959
$818$	0.466658	0.0163163
$819$	−1.33359	−0.0465996
$820$	0	0
$821$	−15.8363	−0.552689	−0.276345	−	0.961059i	$-0.589123\pi$
$821$	−15.8363	−0.552689	−0.276345	+	0.961059i	$0.589123\pi$
$822$	0.170422	0.00594416
$823$	−8.07178	−0.281364	−0.140682	−	0.990055i	$-0.544930\pi$
$823$	−8.07178	−0.281364	−0.140682	+	0.990055i	$0.544930\pi$
$824$	4.89950	0.170682
$825$	0	0
$826$	0.0223150	0.000776437 0
$827$	−32.2666	−1.12202	−0.561010	−	0.827809i	$-0.689587\pi$
$827$	−32.2666	−1.12202	−0.561010	+	0.827809i	$0.689587\pi$
$828$	2.66299	0.0925453
$829$	21.6295	0.751225	0.375612	−	0.926777i	$-0.377432\pi$
$829$	21.6295	0.751225	0.375612	+	0.926777i	$0.377432\pi$
$830$	0	0
$831$	6.59897	0.228916
$832$	17.6042	0.610317
$833$	−10.9969	−0.381020
$834$	−0.257517	−0.00891708
$835$	0	0
$836$	51.0772	1.76654
$837$	26.0394	0.900052
$838$	1.69174	0.0584402
$839$	45.5037	1.57096	0.785481	−	0.618886i	$-0.212416\pi$
$839$	45.5037	1.57096	0.785481	+	0.618886i	$0.212416\pi$
$840$	0	0
$841$	9.60939	0.331358
$842$	−0.0285523	−0.000983979 0
$843$	−8.53559	−0.293981
$844$	11.8408	0.407578
$845$	0	0
$846$	−0.974224	−0.0334945
$847$	−0.192864	−0.00662688
$848$	−40.6799	−1.39695
$849$	10.6765	0.366418
$850$	0	0
$851$	1.14122	0.0391207
$852$	0.656341	0.0224859
$853$	12.3672	0.423446	0.211723	−	0.977330i	$-0.432093\pi$
$853$	12.3672	0.423446	0.211723	+	0.977330i	$0.432093\pi$
$854$	0.0445753	0.00152534
$855$	0	0
$856$	2.54203	0.0868849
$857$	−24.8560	−0.849065	−0.424532	−	0.905413i	$-0.639561\pi$
$857$	−24.8560	−0.849065	−0.424532	+	0.905413i	$0.639561\pi$
$858$	0.528231	0.0180335
$859$	−53.3641	−1.82076	−0.910380	−	0.413772i	$-0.864211\pi$
$859$	−53.3641	−1.82076	−0.910380	+	0.413772i	$0.864211\pi$
$860$	0	0
$861$	−1.75702	−0.0598790
$862$	−2.00158	−0.0681740
$863$	−20.3648	−0.693225	−0.346613	−	0.938008i	$-0.612668\pi$
$863$	−20.3648	−0.693225	−0.346613	+	0.938008i	$0.612668\pi$
$864$	4.31530	0.146809
$865$	0	0
$866$	1.57915	0.0536618
$867$	−12.5263	−0.425415
$868$	−3.01749	−0.102420
$869$	58.6293	1.98886
$870$	0	0
$871$	−11.3044	−0.383037
$872$	−2.07992	−0.0704349
$873$	−27.7568	−0.939426
$874$	0.352731	0.0119313
$875$	0	0
$876$	6.32594	0.213734
$877$	40.2494	1.35913	0.679564	−	0.733617i	$-0.262169\pi$
$877$	40.2494	1.35913	0.679564	+	0.733617i	$0.262169\pi$
$878$	−0.963326	−0.0325107
$879$	4.22534	0.142517
$880$	0	0
$881$	−21.3894	−0.720627	−0.360314	−	0.932831i	$-0.617330\pi$
$881$	−21.3894	−0.720627	−0.360314	+	0.932831i	$0.617330\pi$
$882$	−1.24065	−0.0417750
$883$	23.4645	0.789642	0.394821	−	0.918758i	$-0.370807\pi$
$883$	23.4645	0.789642	0.394821	+	0.918758i	$0.370807\pi$
$884$	7.09566	0.238653
$885$	0	0
$886$	−0.322023	−0.0108186
$887$	−47.7768	−1.60419	−0.802094	−	0.597198i	$-0.796281\pi$
$887$	−47.7768	−1.60419	−0.802094	+	0.597198i	$0.796281\pi$
$888$	0.528349	0.0177302
$889$	−0.120236	−0.00403259
$890$	0	0
$891$	9.68061	0.324313
$892$	−45.5172	−1.52403
$893$	40.7074	1.36222
$894$	0.388274	0.0129858
$895$	0	0
$896$	−0.666397	−0.0222628
$897$	−1.15075	−0.0384224
$898$	0.185676	0.00619610
$899$	−35.6183	−1.18794
$900$	0	0
$901$	−16.2919	−0.542762
$902$	−2.09477	−0.0697483
$903$	−2.03297	−0.0676529
$904$	−4.14632	−0.137904
$905$	0	0
$906$	−0.361397	−0.0120066
$907$	21.9082	0.727450	0.363725	−	0.931506i	$-0.381505\pi$
$907$	21.9082	0.727450	0.363725	+	0.931506i	$0.381505\pi$
$908$	−49.1560	−1.63130
$909$	−11.7136	−0.388515
$910$	0	0
$911$	13.0419	0.432098	0.216049	−	0.976383i	$-0.430683\pi$
$911$	13.0419	0.432098	0.216049	+	0.976383i	$0.430683\pi$
$912$	−25.6349	−0.848858
$913$	−29.2879	−0.969288
$914$	−1.08090	−0.0357531
$915$	0	0
$916$	−16.3463	−0.540096
$917$	2.44968	0.0808957
$918$	0.573034	0.0189130
$919$	34.9104	1.15159	0.575794	−	0.817595i	$-0.304693\pi$
$919$	34.9104	1.15159	0.575794	+	0.817595i	$0.304693\pi$
$920$	0	0
$921$	−21.9791	−0.724235
$922$	−2.50061	−0.0823531
$923$	0.853693	0.0280996
$924$	1.55943	0.0513016
$925$	0	0
$926$	−0.399551	−0.0131301
$927$	−34.7506	−1.14136
$928$	−5.90273	−0.193767
$929$	−31.4536	−1.03196	−0.515979	−	0.856601i	$-0.672572\pi$
$929$	−31.4536	−1.03196	−0.515979	+	0.856601i	$0.672572\pi$
$930$	0	0
$931$	51.8400	1.69899
$932$	−54.6884	−1.79138
$933$	−22.8820	−0.749124
$934$	2.77696	0.0908650
$935$	0	0
$936$	1.60358	0.0524147
$937$	−40.6615	−1.32835	−0.664177	−	0.747576i	$-0.731218\pi$
$937$	−40.6615	−1.32835	−0.664177	+	0.747576i	$0.731218\pi$
$938$	0.105792	0.00345422
$939$	6.25745	0.204204
$940$	0	0
$941$	−0.497854	−0.0162296	−0.00811478	−	0.999967i	$-0.502583\pi$
$941$	−0.497854	−0.0162296	−0.00811478	+	0.999967i	$0.502583\pi$
$942$	−0.714364	−0.0232752
$943$	4.56346	0.148607
$944$	4.21214	0.137094
$945$	0	0
$946$	−2.42377	−0.0788036
$947$	−4.36164	−0.141734	−0.0708671	−	0.997486i	$-0.522577\pi$
$947$	−4.36164	−0.141734	−0.0708671	+	0.997486i	$0.522577\pi$
$948$	−29.5191	−0.958736
$949$	8.22806	0.267094
$950$	0	0
$951$	22.3342	0.724237
$952$	−0.133019	−0.00431117
$953$	−35.4460	−1.14821	−0.574104	−	0.818782i	$-0.694650\pi$
$953$	−35.4460	−1.14821	−0.574104	+	0.818782i	$0.694650\pi$
$954$	−1.83803	−0.0595083
$955$	0	0
$956$	−13.9730	−0.451920
$957$	18.4075	0.595029
$958$	−1.61864	−0.0522958
$959$	0.654398	0.0211316
$960$	0	0
$961$	1.85892	0.0599651
$962$	0.343064	0.0110608
$963$	−18.0299	−0.581004
$964$	−1.99368	−0.0642121
$965$	0	0
$966$	0.0107692	0.000346493 0
$967$	−48.4218	−1.55714	−0.778571	−	0.627557i	$-0.784055\pi$
$967$	−48.4218	−1.55714	−0.778571	+	0.627557i	$0.784055\pi$
$968$	0.231909	0.00745385
$969$	−10.2665	−0.329809
$970$	0	0
$971$	−41.8117	−1.34180	−0.670901	−	0.741547i	$-0.734093\pi$
$971$	−41.8117	−1.34180	−0.670901	+	0.741547i	$0.734093\pi$
$972$	−32.0435	−1.02780
$973$	−0.988828	−0.0317004
$974$	1.38436	0.0443579
$975$	0	0
$976$	8.41397	0.269325
$977$	61.2181	1.95854	0.979271	−	0.202555i	$-0.0649245\pi$
$977$	61.2181	1.95854	0.979271	+	0.202555i	$0.0649245\pi$
$978$	−0.981744	−0.0313927
$979$	23.2532	0.743175
$980$	0	0
$981$	14.7522	0.471002
$982$	2.18572	0.0697490
$983$	−7.90022	−0.251978	−0.125989	−	0.992032i	$-0.540210\pi$
$983$	−7.90022	−0.251978	−0.125989	+	0.992032i	$0.540210\pi$
$984$	2.11273	0.0673513
$985$	0	0
$986$	−0.783833	−0.0249623
$987$	1.24283	0.0395598
$988$	−33.4494	−1.06417
$989$	5.28018	0.167900
$990$	0	0
$991$	49.6655	1.57768	0.788838	−	0.614601i	$-0.210683\pi$
$991$	49.6655	1.57768	0.788838	+	0.614601i	$0.210683\pi$
$992$	5.44544	0.172893
$993$	−24.1050	−0.764950
$994$	−0.00798922	−0.000253403 0
$995$	0	0
$996$	14.7461	0.467248
$997$	1.31437	0.0416265	0.0208132	−	0.999783i	$-0.493374\pi$
$997$	1.31437	0.0416265	0.0208132	+	0.999783i	$0.493374\pi$
$998$	0.251986	0.00797648
$999$	−8.73983	−0.276516

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6025.2.a.n.1.19	yes	40
5.4	even	2		6025.2.a.m.1.22	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6025.2.a.m.1.22	✓	40	5.4	even	2
6025.2.a.n.1.19	yes	40	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)

\(f(q)\)	\(=\)	\(q-0.0794983 q^{2} +0.864949 q^{3} -1.99368 q^{4} -0.0687619 q^{6} -0.264036 q^{7} +0.317491 q^{8} -2.25186 q^{9} +O(q^{10})\)	\(q-0.0794983 q^{2} +0.864949 q^{3} -1.99368 q^{4} -0.0687619 q^{6} -0.264036 q^{7} +0.317491 q^{8} -2.25186 q^{9} +3.42497 q^{11} -1.72443 q^{12} -2.24294 q^{13} +0.0209904 q^{14} +3.96212 q^{16} +1.58679 q^{17} +0.179019 q^{18} -7.48022 q^{19} -0.228378 q^{21} -0.272279 q^{22} +0.593160 q^{23} +0.274613 q^{24} +0.178310 q^{26} -4.54259 q^{27} +0.526404 q^{28} +6.21365 q^{29} -5.73227 q^{31} -0.949963 q^{32} +2.96243 q^{33} -0.126147 q^{34} +4.48949 q^{36} +1.92397 q^{37} +0.594664 q^{38} -1.94003 q^{39} +7.69347 q^{41} +0.0181556 q^{42} +8.90178 q^{43} -6.82830 q^{44} -0.0471552 q^{46} -5.44201 q^{47} +3.42703 q^{48} -6.93028 q^{49} +1.37249 q^{51} +4.47171 q^{52} -10.2672 q^{53} +0.361128 q^{54} -0.0838290 q^{56} -6.47000 q^{57} -0.493974 q^{58} +1.06310 q^{59} +2.12360 q^{61} +0.455705 q^{62} +0.594573 q^{63} -7.84872 q^{64} -0.235508 q^{66} +5.04001 q^{67} -3.16355 q^{68} +0.513053 q^{69} -0.380613 q^{71} -0.714945 q^{72} -3.66842 q^{73} -0.152953 q^{74} +14.9132 q^{76} -0.904317 q^{77} +0.154229 q^{78} +17.1182 q^{79} +2.82648 q^{81} -0.611617 q^{82} -8.55128 q^{83} +0.455312 q^{84} -0.707676 q^{86} +5.37449 q^{87} +1.08740 q^{88} +6.78930 q^{89} +0.592218 q^{91} -1.18257 q^{92} -4.95812 q^{93} +0.432630 q^{94} -0.821669 q^{96} +12.3262 q^{97} +0.550946 q^{98} -7.71257 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 9 q^{2} + 8 q^{3} + 41 q^{4} + 3 q^{6} + 20 q^{7} + 27 q^{8} + 38 q^{9}+O(q^{10}) \) 40 * q + 9 * q^2 + 8 * q^3 + 41 * q^4 + 3 * q^6 + 20 * q^7 + 27 * q^8 + 38 * q^9	\( 40 q + 9 q^{2} + 8 q^{3} + 41 q^{4} + 3 q^{6} + 20 q^{7} + 27 q^{8} + 38 q^{9} + q^{11} + 26 q^{12} + 11 q^{13} - q^{14} + 43 q^{16} + 20 q^{17} + 18 q^{18} + 2 q^{21} + 23 q^{22} + 79 q^{23} - 2 q^{24} + 2 q^{26} + 26 q^{27} + 30 q^{28} + 2 q^{29} + q^{31} + 68 q^{32} + 20 q^{33} + 5 q^{34} + 32 q^{36} + 16 q^{37} + 45 q^{38} - 2 q^{39} - 2 q^{41} + 19 q^{42} + 25 q^{43} + 3 q^{44} + 14 q^{46} + 88 q^{47} + 75 q^{48} + 40 q^{49} - 10 q^{51} + 18 q^{52} + 34 q^{53} + 4 q^{54} - 15 q^{56} + 51 q^{57} + 53 q^{58} + q^{59} + 9 q^{61} + 39 q^{62} + 110 q^{63} + 17 q^{64} + 26 q^{66} + 30 q^{67} + 44 q^{68} - 7 q^{69} + 5 q^{71} + 18 q^{72} + 23 q^{73} - 18 q^{74} + 43 q^{76} + 30 q^{77} + 46 q^{78} + 5 q^{79} + 44 q^{81} + 5 q^{82} + 65 q^{83} - 65 q^{84} + 40 q^{86} + 33 q^{87} + 71 q^{88} - 9 q^{89} + q^{91} + 117 q^{92} + 68 q^{93} - 72 q^{94} + 83 q^{96} - 8 q^{97} + 76 q^{98} - 40 q^{99}+O(q^{100}) \) 40 * q + 9 * q^2 + 8 * q^3 + 41 * q^4 + 3 * q^6 + 20 * q^7 + 27 * q^8 + 38 * q^9 + q^11 + 26 * q^12 + 11 * q^13 - q^14 + 43 * q^16 + 20 * q^17 + 18 * q^18 + 2 * q^21 + 23 * q^22 + 79 * q^23 - 2 * q^24 + 2 * q^26 + 26 * q^27 + 30 * q^28 + 2 * q^29 + q^31 + 68 * q^32 + 20 * q^33 + 5 * q^34 + 32 * q^36 + 16 * q^37 + 45 * q^38 - 2 * q^39 - 2 * q^41 + 19 * q^42 + 25 * q^43 + 3 * q^44 + 14 * q^46 + 88 * q^47 + 75 * q^48 + 40 * q^49 - 10 * q^51 + 18 * q^52 + 34 * q^53 + 4 * q^54 - 15 * q^56 + 51 * q^57 + 53 * q^58 + q^59 + 9 * q^61 + 39 * q^62 + 110 * q^63 + 17 * q^64 + 26 * q^66 + 30 * q^67 + 44 * q^68 - 7 * q^69 + 5 * q^71 + 18 * q^72 + 23 * q^73 - 18 * q^74 + 43 * q^76 + 30 * q^77 + 46 * q^78 + 5 * q^79 + 44 * q^81 + 5 * q^82 + 65 * q^83 - 65 * q^84 + 40 * q^86 + 33 * q^87 + 71 * q^88 - 9 * q^89 + q^91 + 117 * q^92 + 68 * q^93 - 72 * q^94 + 83 * q^96 - 8 * q^97 + 76 * q^98 - 40 * q^99

Introduction

L-functions

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