LMFDB - Embedded newform 6025.2.a.n.1.17

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			1.17
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)

$f(q)$	$=$	$q-0.337207 q^{2} -2.44634 q^{3} -1.88629 q^{4} +0.824921 q^{6} -2.26789 q^{7} +1.31048 q^{8} +2.98457 q^{9} +O(q^{10})$	\(q-0.337207 q^{2} -2.44634 q^{3} -1.88629 q^{4} +0.824921 q^{6} -2.26789 q^{7} +1.31048 q^{8} +2.98457 q^{9} -4.20253 q^{11} +4.61451 q^{12} -1.32648 q^{13} +0.764748 q^{14} +3.33068 q^{16} +1.12061 q^{17} -1.00642 q^{18} -1.53357 q^{19} +5.54802 q^{21} +1.41712 q^{22} +5.10896 q^{23} -3.20588 q^{24} +0.447297 q^{26} +0.0377566 q^{27} +4.27790 q^{28} -5.78602 q^{29} -4.45734 q^{31} -3.74409 q^{32} +10.2808 q^{33} -0.377877 q^{34} -5.62976 q^{36} -10.8886 q^{37} +0.517130 q^{38} +3.24501 q^{39} -3.09800 q^{41} -1.87083 q^{42} +8.63274 q^{43} +7.92719 q^{44} -1.72278 q^{46} -11.2775 q^{47} -8.14797 q^{48} -1.85667 q^{49} -2.74139 q^{51} +2.50212 q^{52} -0.172838 q^{53} -0.0127318 q^{54} -2.97203 q^{56} +3.75163 q^{57} +1.95108 q^{58} -11.7570 q^{59} -12.6485 q^{61} +1.50305 q^{62} -6.76867 q^{63} -5.39883 q^{64} -3.46675 q^{66} +7.54693 q^{67} -2.11380 q^{68} -12.4982 q^{69} +11.2779 q^{71} +3.91122 q^{72} -1.82183 q^{73} +3.67171 q^{74} +2.89276 q^{76} +9.53087 q^{77} -1.09424 q^{78} -4.65709 q^{79} -9.04606 q^{81} +1.04467 q^{82} -6.24991 q^{83} -10.4652 q^{84} -2.91102 q^{86} +14.1546 q^{87} -5.50734 q^{88} -3.91665 q^{89} +3.00831 q^{91} -9.63699 q^{92} +10.9042 q^{93} +3.80285 q^{94} +9.15932 q^{96} -10.7148 q^{97} +0.626083 q^{98} -12.5427 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.337207	−0.238441	−0.119221	−	0.992868i	$-0.538040\pi$
$2$	−0.337207	−0.238441	−0.119221	+	0.992868i	$0.538040\pi$
$3$	−2.44634	−1.41239	−0.706197	−	0.708016i	$-0.749591\pi$
$3$	−2.44634	−1.41239	−0.706197	+	0.708016i	$0.749591\pi$
$4$	−1.88629	−0.943146
$5$	0	0
$5$	0	0
$6$	0.824921	0.336773
$7$	−2.26789	−0.857182	−0.428591	−	0.903499i	$-0.640990\pi$
$7$	−2.26789	−0.857182	−0.428591	+	0.903499i	$0.640990\pi$
$8$	1.31048	0.463326
$9$	2.98457	0.994855
$10$	0	0
$11$	−4.20253	−1.26711	−0.633555	−	0.773698i	$-0.718405\pi$
$11$	−4.20253	−1.26711	−0.633555	+	0.773698i	$0.718405\pi$
$12$	4.61451	1.33209
$13$	−1.32648	−0.367899	−0.183949	−	0.982936i	$-0.558888\pi$
$13$	−1.32648	−0.367899	−0.183949	+	0.982936i	$0.558888\pi$
$14$	0.764748	0.204387
$15$	0	0
$16$	3.33068	0.832670
$17$	1.12061	0.271788	0.135894	−	0.990723i	$-0.456609\pi$
$17$	1.12061	0.271788	0.135894	+	0.990723i	$0.456609\pi$
$18$	−1.00642	−0.237214
$19$	−1.53357	−0.351825	−0.175913	−	0.984406i	$-0.556288\pi$
$19$	−1.53357	−0.351825	−0.175913	+	0.984406i	$0.556288\pi$
$20$	0	0
$21$	5.54802	1.21068
$22$	1.41712	0.302131
$23$	5.10896	1.06529	0.532646	−	0.846338i	$-0.321198\pi$
$23$	5.10896	1.06529	0.532646	+	0.846338i	$0.321198\pi$
$24$	−3.20588	−0.654398
$25$	0	0
$26$	0.447297	0.0877222
$27$	0.0377566	0.00726627
$28$	4.27790	0.808448
$29$	−5.78602	−1.07444	−0.537218	−	0.843443i	$-0.680525\pi$
$29$	−5.78602	−1.07444	−0.537218	+	0.843443i	$0.680525\pi$
$30$	0	0
$31$	−4.45734	−0.800563	−0.400281	−	0.916392i	$-0.631088\pi$
$31$	−4.45734	−0.800563	−0.400281	+	0.916392i	$0.631088\pi$
$32$	−3.74409	−0.661869
$33$	10.2808	1.78966
$34$	−0.377877	−0.0648054
$35$	0	0
$36$	−5.62976	−0.938294
$37$	−10.8886	−1.79007	−0.895037	−	0.445992i	$-0.852851\pi$
$37$	−10.8886	−1.79007	−0.895037	+	0.445992i	$0.852851\pi$
$38$	0.517130	0.0838896
$39$	3.24501	0.519618
$40$	0	0
$41$	−3.09800	−0.483827	−0.241913	−	0.970298i	$-0.577775\pi$
$41$	−3.09800	−0.483827	−0.241913	+	0.970298i	$0.577775\pi$
$42$	−1.87083	−0.288675
$43$	8.63274	1.31648	0.658240	−	0.752808i	$-0.271301\pi$
$43$	8.63274	1.31648	0.658240	+	0.752808i	$0.271301\pi$
$44$	7.92719	1.19507
$45$	0	0
$46$	−1.72278	−0.254009
$47$	−11.2775	−1.64499	−0.822496	−	0.568771i	$-0.807419\pi$
$47$	−11.2775	−1.64499	−0.822496	+	0.568771i	$0.807419\pi$
$48$	−8.14797	−1.17606
$49$	−1.85667	−0.265239
$50$	0	0
$51$	−2.74139	−0.383871
$52$	2.50212	0.346982
$53$	−0.172838	−0.0237411	−0.0118705	−	0.999930i	$-0.503779\pi$
$53$	−0.172838	−0.0237411	−0.0118705	+	0.999930i	$0.503779\pi$
$54$	−0.0127318	−0.00173258
$55$	0	0
$56$	−2.97203	−0.397155
$57$	3.75163	0.496916
$58$	1.95108	0.256190
$59$	−11.7570	−1.53064	−0.765319	−	0.643652i	$-0.777419\pi$
$59$	−11.7570	−1.53064	−0.765319	+	0.643652i	$0.777419\pi$
$60$	0	0
$61$	−12.6485	−1.61947	−0.809736	−	0.586795i	$-0.800390\pi$
$61$	−12.6485	−1.61947	−0.809736	+	0.586795i	$0.800390\pi$
$62$	1.50305	0.190887
$63$	−6.76867	−0.852772
$64$	−5.39883	−0.674853
$65$	0	0
$66$	−3.46675	−0.426728
$67$	7.54693	0.922004	0.461002	−	0.887399i	$-0.347490\pi$
$67$	7.54693	0.922004	0.461002	+	0.887399i	$0.347490\pi$
$68$	−2.11380	−0.256335
$69$	−12.4982	−1.50461
$70$	0	0
$71$	11.2779	1.33844	0.669220	−	0.743064i	$-0.266628\pi$
$71$	11.2779	1.33844	0.669220	+	0.743064i	$0.266628\pi$
$72$	3.91122	0.460942
$73$	−1.82183	−0.213230	−0.106615	−	0.994300i	$-0.534001\pi$
$73$	−1.82183	−0.213230	−0.106615	+	0.994300i	$0.534001\pi$
$74$	3.67171	0.426827
$75$	0	0
$76$	2.89276	0.331822
$77$	9.53087	1.08614
$78$	−1.09424	−0.123898
$79$	−4.65709	−0.523964	−0.261982	−	0.965073i	$-0.584376\pi$
$79$	−4.65709	−0.523964	−0.261982	+	0.965073i	$0.584376\pi$
$80$	0	0
$81$	−9.04606	−1.00512
$82$	1.04467	0.115364
$83$	−6.24991	−0.686017	−0.343009	−	0.939332i	$-0.611446\pi$
$83$	−6.24991	−0.686017	−0.343009	+	0.939332i	$0.611446\pi$
$84$	−10.4652	−1.14185
$85$	0	0
$86$	−2.91102	−0.313903
$87$	14.1546	1.51753
$88$	−5.50734	−0.587085
$89$	−3.91665	−0.415164	−0.207582	−	0.978218i	$-0.566559\pi$
$89$	−3.91665	−0.415164	−0.207582	+	0.978218i	$0.566559\pi$
$90$	0	0
$91$	3.00831	0.315356
$92$	−9.63699	−1.00473
$93$	10.9042	1.13071
$94$	3.80285	0.392234
$95$	0	0
$96$	9.15932	0.934819
$97$	−10.7148	−1.08793	−0.543964	−	0.839109i	$-0.683077\pi$
$97$	−10.7148	−1.08793	−0.543964	+	0.839109i	$0.683077\pi$
$98$	0.626083	0.0632439
$99$	−12.5427	−1.26059
$100$	0	0
$101$	−12.2105	−1.21499	−0.607495	−	0.794323i	$-0.707826\pi$
$101$	−12.2105	−1.21499	−0.607495	+	0.794323i	$0.707826\pi$
$102$	0.924415	0.0915307
$103$	−5.49779	−0.541714	−0.270857	−	0.962620i	$-0.587307\pi$
$103$	−5.49779	−0.541714	−0.270857	+	0.962620i	$0.587307\pi$
$104$	−1.73833	−0.170457
$105$	0	0
$106$	0.0582820	0.00566085
$107$	0.911232	0.0880922	0.0440461	−	0.999030i	$-0.485975\pi$
$107$	0.911232	0.0880922	0.0440461	+	0.999030i	$0.485975\pi$
$108$	−0.0712200	−0.00685315
$109$	−1.71399	−0.164170	−0.0820852	−	0.996625i	$-0.526158\pi$
$109$	−1.71399	−0.164170	−0.0820852	+	0.996625i	$0.526158\pi$
$110$	0	0
$111$	26.6372	2.52829
$112$	−7.55362	−0.713750
$113$	6.55408	0.616556	0.308278	−	0.951296i	$-0.400247\pi$
$113$	6.55408	0.616556	0.308278	+	0.951296i	$0.400247\pi$
$114$	−1.26507	−0.118485
$115$	0	0
$116$	10.9141	1.01335
$117$	−3.95896	−0.366006
$118$	3.96455	0.364967
$119$	−2.54142	−0.232972
$120$	0	0
$121$	6.66124	0.605567
$122$	4.26515	0.386149
$123$	7.57876	0.683354
$124$	8.40785	0.755047
$125$	0	0
$126$	2.28244	0.203336
$127$	−8.08835	−0.717725	−0.358863	−	0.933390i	$-0.616835\pi$
$127$	−8.08835	−0.717725	−0.358863	+	0.933390i	$0.616835\pi$
$128$	9.30871	0.822781
$129$	−21.1186	−1.85939
$130$	0	0
$131$	−19.4247	−1.69714	−0.848572	−	0.529080i	$-0.822537\pi$
$131$	−19.4247	−1.69714	−0.848572	+	0.529080i	$0.822537\pi$
$132$	−19.3926	−1.68791
$133$	3.47797	0.301578
$134$	−2.54487	−0.219844
$135$	0	0
$136$	1.46854	0.125926
$137$	−3.78274	−0.323181	−0.161591	−	0.986858i	$-0.551662\pi$
$137$	−3.78274	−0.323181	−0.161591	+	0.986858i	$0.551662\pi$
$138$	4.21449	0.358761
$139$	−17.9316	−1.52094	−0.760468	−	0.649375i	$-0.775030\pi$
$139$	−17.9316	−1.52094	−0.760468	+	0.649375i	$0.775030\pi$
$140$	0	0
$141$	27.5885	2.32337
$142$	−3.80298	−0.319139
$143$	5.57456	0.466168
$144$	9.94063	0.828386
$145$	0	0
$146$	0.614334	0.0508427
$147$	4.54205	0.374622
$148$	20.5391	1.68830
$149$	−2.55276	−0.209130	−0.104565	−	0.994518i	$-0.533345\pi$
$149$	−2.55276	−0.209130	−0.104565	+	0.994518i	$0.533345\pi$
$150$	0	0
$151$	17.0014	1.38355	0.691776	−	0.722113i	$-0.256829\pi$
$151$	17.0014	1.38355	0.691776	+	0.722113i	$0.256829\pi$
$152$	−2.00972	−0.163010
$153$	3.34453	0.270390
$154$	−3.21387	−0.258981
$155$	0	0
$156$	−6.12104	−0.490075
$157$	−18.6221	−1.48621	−0.743103	−	0.669177i	$-0.766647\pi$
$157$	−18.6221	−1.48621	−0.743103	+	0.669177i	$0.766647\pi$
$158$	1.57040	0.124934
$159$	0.422819	0.0335317
$160$	0	0
$161$	−11.5866	−0.913149
$162$	3.05039	0.239661
$163$	15.4103	1.20703	0.603514	−	0.797352i	$-0.293767\pi$
$163$	15.4103	1.20703	0.603514	+	0.797352i	$0.293767\pi$
$164$	5.84374	0.456319
$165$	0	0
$166$	2.10751	0.163575
$167$	4.57629	0.354124	0.177062	−	0.984200i	$-0.443341\pi$
$167$	4.57629	0.354124	0.177062	+	0.984200i	$0.443341\pi$
$168$	7.27059	0.560938
$169$	−11.2405	−0.864650
$170$	0	0
$171$	−4.57704	−0.350015
$172$	−16.2839	−1.24163
$173$	−18.9865	−1.44352	−0.721758	−	0.692145i	$-0.756666\pi$
$173$	−18.9865	−1.44352	−0.721758	+	0.692145i	$0.756666\pi$
$174$	−4.77301	−0.361841
$175$	0	0
$176$	−13.9973	−1.05508
$177$	28.7617	2.16186
$178$	1.32072	0.0989921
$179$	3.53027	0.263865	0.131932	−	0.991259i	$-0.457882\pi$
$179$	3.53027	0.263865	0.131932	+	0.991259i	$0.457882\pi$
$180$	0	0
$181$	10.2750	0.763736	0.381868	−	0.924217i	$-0.375281\pi$
$181$	10.2750	0.763736	0.381868	+	0.924217i	$0.375281\pi$
$182$	−1.01442	−0.0751939
$183$	30.9424	2.28733
$184$	6.69521	0.493577
$185$	0	0
$186$	−3.67696	−0.269608
$187$	−4.70939	−0.344385
$188$	21.2726	1.55147
$189$	−0.0856279	−0.00622851
$190$	0	0
$191$	−16.3162	−1.18060	−0.590298	−	0.807185i	$-0.700990\pi$
$191$	−16.3162	−1.18060	−0.590298	+	0.807185i	$0.700990\pi$
$192$	13.2073	0.953158
$193$	−11.7744	−0.847540	−0.423770	−	0.905770i	$-0.639294\pi$
$193$	−11.7744	−0.847540	−0.423770	+	0.905770i	$0.639294\pi$
$194$	3.61312	0.259407
$195$	0	0
$196$	3.50223	0.250159
$197$	0.192368	0.0137056	0.00685282	−	0.999977i	$-0.497819\pi$
$197$	0.192368	0.0137056	0.00685282	+	0.999977i	$0.497819\pi$
$198$	4.22949	0.300577
$199$	−15.4789	−1.09727	−0.548636	−	0.836061i	$-0.684853\pi$
$199$	−15.4789	−1.09727	−0.548636	+	0.836061i	$0.684853\pi$
$200$	0	0
$201$	−18.4623	−1.30223
$202$	4.11746	0.289704
$203$	13.1221	0.920988
$204$	5.17106	0.362047
$205$	0	0
$206$	1.85389	0.129167
$207$	15.2480	1.05981
$208$	−4.41807	−0.306338
$209$	6.44487	0.445801
$210$	0	0
$211$	15.9282	1.09654	0.548271	−	0.836301i	$-0.315286\pi$
$211$	15.9282	1.09654	0.548271	+	0.836301i	$0.315286\pi$
$212$	0.326022	0.0223913
$213$	−27.5895	−1.89040
$214$	−0.307274	−0.0210048
$215$	0	0
$216$	0.0494794	0.00336665
$217$	10.1088	0.686228
$218$	0.577969	0.0391450
$219$	4.45682	0.301164
$220$	0	0
$221$	−1.48646	−0.0999904
$222$	−8.98223	−0.602848
$223$	19.1070	1.27950	0.639748	−	0.768584i	$-0.279039\pi$
$223$	19.1070	1.27950	0.639748	+	0.768584i	$0.279039\pi$
$224$	8.49119	0.567342
$225$	0	0
$226$	−2.21008	−0.147012
$227$	−7.91832	−0.525557	−0.262779	−	0.964856i	$-0.584639\pi$
$227$	−7.91832	−0.525557	−0.262779	+	0.964856i	$0.584639\pi$
$228$	−7.07667	−0.468664
$229$	−3.42996	−0.226658	−0.113329	−	0.993558i	$-0.536151\pi$
$229$	−3.42996	−0.226658	−0.113329	+	0.993558i	$0.536151\pi$
$230$	0	0
$231$	−23.3157	−1.53406
$232$	−7.58248	−0.497814
$233$	15.4048	1.00920	0.504601	−	0.863353i	$-0.331640\pi$
$233$	15.4048	1.00920	0.504601	+	0.863353i	$0.331640\pi$
$234$	1.33499	0.0872709
$235$	0	0
$236$	22.1772	1.44361
$237$	11.3928	0.740043
$238$	0.856984	0.0555500
$239$	−18.4647	−1.19438	−0.597192	−	0.802098i	$-0.703717\pi$
$239$	−18.4647	−1.19438	−0.597192	+	0.802098i	$0.703717\pi$
$240$	0	0
$241$	1.00000	0.0644157
$241$	1.00000	0.0644157
$242$	−2.24621	−0.144392
$243$	22.0165	1.41236
$244$	23.8587	1.52740
$245$	0	0
$246$	−2.55561	−0.162940
$247$	2.03425	0.129436
$248$	−5.84127	−0.370921
$249$	15.2894	0.968926
$250$	0	0
$251$	−18.4339	−1.16353	−0.581767	−	0.813355i	$-0.697639\pi$
$251$	−18.4339	−1.16353	−0.581767	+	0.813355i	$0.697639\pi$
$252$	12.7677	0.804288
$253$	−21.4706	−1.34984
$254$	2.72745	0.171135
$255$	0	0
$256$	7.65869	0.478668
$257$	22.0397	1.37480	0.687400	−	0.726279i	$-0.258752\pi$
$257$	22.0397	1.37480	0.687400	+	0.726279i	$0.258752\pi$
$258$	7.12133	0.443355
$259$	24.6941	1.53442
$260$	0	0
$261$	−17.2688	−1.06891
$262$	6.55014	0.404669
$263$	6.07521	0.374614	0.187307	−	0.982301i	$-0.440024\pi$
$263$	6.07521	0.374614	0.187307	+	0.982301i	$0.440024\pi$
$264$	13.4728	0.829195
$265$	0	0
$266$	−1.17279	−0.0719086
$267$	9.58144	0.586375
$268$	−14.2357	−0.869584
$269$	18.1483	1.10652	0.553261	−	0.833008i	$-0.313383\pi$
$269$	18.1483	1.10652	0.553261	+	0.833008i	$0.313383\pi$
$270$	0	0
$271$	26.6621	1.61961	0.809804	−	0.586701i	$-0.199573\pi$
$271$	26.6621	1.61961	0.809804	+	0.586701i	$0.199573\pi$
$272$	3.73239	0.226309
$273$	−7.35933	−0.445407
$274$	1.27557	0.0770597
$275$	0	0
$276$	23.5753	1.41907
$277$	−31.4739	−1.89108	−0.945542	−	0.325500i	$-0.894467\pi$
$277$	−31.4739	−1.89108	−0.945542	+	0.325500i	$0.894467\pi$
$278$	6.04664	0.362654
$279$	−13.3032	−0.796444
$280$	0	0
$281$	−0.160185	−0.00955583	−0.00477791	−	0.999989i	$-0.501521\pi$
$281$	−0.160185	−0.00955583	−0.00477791	+	0.999989i	$0.501521\pi$
$282$	−9.30304	−0.553988
$283$	−14.3042	−0.850294	−0.425147	−	0.905124i	$-0.639778\pi$
$283$	−14.3042	−0.850294	−0.425147	+	0.905124i	$0.639778\pi$
$284$	−21.2734	−1.26234
$285$	0	0
$286$	−1.87978	−0.111154
$287$	7.02593	0.414727
$288$	−11.1745	−0.658463
$289$	−15.7442	−0.926131
$290$	0	0
$291$	26.2121	1.53658
$292$	3.43651	0.201107
$293$	−26.4136	−1.54310	−0.771550	−	0.636169i	$-0.780518\pi$
$293$	−26.4136	−1.54310	−0.771550	+	0.636169i	$0.780518\pi$
$294$	−1.53161	−0.0893253
$295$	0	0
$296$	−14.2693	−0.829387
$297$	−0.158673	−0.00920716
$298$	0.860808	0.0498653
$299$	−6.77693	−0.391920
$300$	0	0
$301$	−19.5781	−1.12846
$302$	−5.73297	−0.329895
$303$	29.8710	1.71605
$304$	−5.10783	−0.292954
$305$	0	0
$306$	−1.12780	−0.0644720
$307$	−1.75621	−0.100232	−0.0501161	−	0.998743i	$-0.515959\pi$
$307$	−1.75621	−0.100232	−0.0501161	+	0.998743i	$0.515959\pi$
$308$	−17.9780	−1.02439
$309$	13.4495	0.765113
$310$	0	0
$311$	−10.5598	−0.598792	−0.299396	−	0.954129i	$-0.596785\pi$
$311$	−10.5598	−0.598792	−0.299396	+	0.954129i	$0.596785\pi$
$312$	4.25254	0.240752
$313$	24.9424	1.40983	0.704913	−	0.709293i	$-0.250986\pi$
$313$	24.9424	1.40983	0.704913	+	0.709293i	$0.250986\pi$
$314$	6.27950	0.354372
$315$	0	0
$316$	8.78463	0.494174
$317$	14.8376	0.833363	0.416681	−	0.909053i	$-0.363193\pi$
$317$	14.8376	0.833363	0.416681	+	0.909053i	$0.363193\pi$
$318$	−0.142577	−0.00799534
$319$	24.3159	1.36143
$320$	0	0
$321$	−2.22918	−0.124421
$322$	3.90707	0.217732
$323$	−1.71853	−0.0956218
$324$	17.0635	0.947973
$325$	0	0
$326$	−5.19646	−0.287805
$327$	4.19300	0.231873
$328$	−4.05988	−0.224169
$329$	25.5761	1.41006
$330$	0	0
$331$	26.2102	1.44064	0.720321	−	0.693640i	$-0.243994\pi$
$331$	26.2102	1.44064	0.720321	+	0.693640i	$0.243994\pi$
$332$	11.7892	0.647014
$333$	−32.4977	−1.78086
$334$	−1.54316	−0.0844378
$335$	0	0
$336$	18.4787	1.00810
$337$	−11.3964	−0.620801	−0.310401	−	0.950606i	$-0.600463\pi$
$337$	−11.3964	−0.620801	−0.310401	+	0.950606i	$0.600463\pi$
$338$	3.79036	0.206168
$339$	−16.0335	−0.870820
$340$	0	0
$341$	18.7321	1.01440
$342$	1.54341	0.0834580
$343$	20.0860	1.08454
$344$	11.3131	0.609959
$345$	0	0
$346$	6.40237	0.344194
$347$	8.63612	0.463611	0.231806	−	0.972762i	$-0.425537\pi$
$347$	8.63612	0.463611	0.231806	+	0.972762i	$0.425537\pi$
$348$	−26.6996	−1.43125
$349$	24.9456	1.33531	0.667654	−	0.744471i	$-0.267298\pi$
$349$	24.9456	1.33531	0.667654	+	0.744471i	$0.267298\pi$
$350$	0	0
$351$	−0.0500834	−0.00267325
$352$	15.7347	0.838660
$353$	−31.2640	−1.66401	−0.832006	−	0.554766i	$-0.812808\pi$
$353$	−31.2640	−1.66401	−0.832006	+	0.554766i	$0.812808\pi$
$354$	−9.69864	−0.515477
$355$	0	0
$356$	7.38794	0.391560
$357$	6.21717	0.329048
$358$	−1.19043	−0.0629162
$359$	−24.8826	−1.31325	−0.656625	−	0.754217i	$-0.728017\pi$
$359$	−24.8826	−1.31325	−0.656625	+	0.754217i	$0.728017\pi$
$360$	0	0
$361$	−16.6482	−0.876219
$362$	−3.46480	−0.182106
$363$	−16.2956	−0.855299
$364$	−5.67454	−0.297427
$365$	0	0
$366$	−10.4340	−0.545394
$367$	25.2590	1.31851	0.659254	−	0.751921i	$-0.270872\pi$
$367$	25.2590	1.31851	0.659254	+	0.751921i	$0.270872\pi$
$368$	17.0163	0.887037
$369$	−9.24619	−0.481337
$370$	0	0
$371$	0.391977	0.0203504
$372$	−20.5684	−1.06642
$373$	23.2045	1.20148	0.600741	−	0.799444i	$-0.294872\pi$
$373$	23.2045	1.20148	0.600741	+	0.799444i	$0.294872\pi$
$374$	1.58804	0.0821155
$375$	0	0
$376$	−14.7790	−0.762167
$377$	7.67503	0.395284
$378$	0.0288743	0.00148513
$379$	8.50533	0.436890	0.218445	−	0.975849i	$-0.429902\pi$
$379$	8.50533	0.436890	0.218445	+	0.975849i	$0.429902\pi$
$380$	0	0
$381$	19.7868	1.01371
$382$	5.50192	0.281503
$383$	24.2694	1.24011	0.620054	−	0.784559i	$-0.287111\pi$
$383$	24.2694	1.24011	0.620054	+	0.784559i	$0.287111\pi$
$384$	−22.7722	−1.16209
$385$	0	0
$386$	3.97041	0.202088
$387$	25.7650	1.30971
$388$	20.2113	1.02607
$389$	−6.60657	−0.334967	−0.167483	−	0.985875i	$-0.553564\pi$
$389$	−6.60657	−0.334967	−0.167483	+	0.985875i	$0.553564\pi$
$390$	0	0
$391$	5.72515	0.289533
$392$	−2.43314	−0.122892
$393$	47.5194	2.39703
$394$	−0.0648677	−0.00326799
$395$	0	0
$396$	23.6592	1.18892
$397$	−1.67129	−0.0838794	−0.0419397	−	0.999120i	$-0.513354\pi$
$397$	−1.67129	−0.0838794	−0.0419397	+	0.999120i	$0.513354\pi$
$398$	5.21960	0.261635
$399$	−8.50829	−0.425947
$400$	0	0
$401$	−10.3255	−0.515632	−0.257816	−	0.966194i	$-0.583003\pi$
$401$	−10.3255	−0.515632	−0.257816	+	0.966194i	$0.583003\pi$
$402$	6.22562	0.310506
$403$	5.91257	0.294526
$404$	23.0326	1.14591
$405$	0	0
$406$	−4.42485	−0.219601
$407$	45.7596	2.26822
$408$	−3.59254	−0.177857
$409$	−20.3547	−1.00647	−0.503237	−	0.864148i	$-0.667858\pi$
$409$	−20.3547	−1.00647	−0.503237	+	0.864148i	$0.667858\pi$
$410$	0	0
$411$	9.25386	0.456459
$412$	10.3704	0.510915
$413$	26.6637	1.31203
$414$	−5.14174	−0.252703
$415$	0	0
$416$	4.96646	0.243501
$417$	43.8667	2.14816
$418$	−2.17325	−0.106297
$419$	31.9110	1.55895	0.779477	−	0.626431i	$-0.215485\pi$
$419$	31.9110	1.55895	0.779477	+	0.626431i	$0.215485\pi$
$420$	0	0
$421$	11.1981	0.545763	0.272881	−	0.962048i	$-0.412023\pi$
$421$	11.1981	0.545763	0.272881	+	0.962048i	$0.412023\pi$
$422$	−5.37109	−0.261461
$423$	−33.6584	−1.63653
$424$	−0.226501	−0.0109999
$425$	0	0
$426$	9.30337	0.450750
$427$	28.6854	1.38818
$428$	−1.71885	−0.0830837
$429$	−13.6373	−0.658413
$430$	0	0
$431$	19.3928	0.934119	0.467060	−	0.884226i	$-0.345313\pi$
$431$	19.3928	0.934119	0.467060	+	0.884226i	$0.345313\pi$
$432$	0.125755	0.00605040
$433$	17.0714	0.820401	0.410200	−	0.911995i	$-0.365459\pi$
$433$	17.0714	0.820401	0.410200	+	0.911995i	$0.365459\pi$
$434$	−3.40874	−0.163625
$435$	0	0
$436$	3.23308	0.154837
$437$	−7.83495	−0.374797
$438$	−1.50287	−0.0718099
$439$	13.8034	0.658798	0.329399	−	0.944191i	$-0.393154\pi$
$439$	13.8034	0.658798	0.329399	+	0.944191i	$0.393154\pi$
$440$	0	0
$441$	−5.54136	−0.263875
$442$	0.501246	0.0238418
$443$	−10.0355	−0.476803	−0.238401	−	0.971167i	$-0.576623\pi$
$443$	−10.0355	−0.476803	−0.238401	+	0.971167i	$0.576623\pi$
$444$	−50.2455	−2.38454
$445$	0	0
$446$	−6.44299	−0.305085
$447$	6.24491	0.295374
$448$	12.2439	0.578472
$449$	11.2359	0.530257	0.265128	−	0.964213i	$-0.414586\pi$
$449$	11.2359	0.530257	0.265128	+	0.964213i	$0.414586\pi$
$450$	0	0
$451$	13.0194	0.613061
$452$	−12.3629	−0.581503
$453$	−41.5911	−1.95412
$454$	2.67011	0.125314
$455$	0	0
$456$	4.91645	0.230234
$457$	−7.99075	−0.373792	−0.186896	−	0.982380i	$-0.559843\pi$
$457$	−7.99075	−0.373792	−0.186896	+	0.982380i	$0.559843\pi$
$458$	1.15660	0.0540446
$459$	0.0423104	0.00197488
$460$	0	0
$461$	−9.62469	−0.448267	−0.224133	−	0.974559i	$-0.571955\pi$
$461$	−9.62469	−0.448267	−0.224133	+	0.974559i	$0.571955\pi$
$462$	7.86222	0.365783
$463$	−18.9524	−0.880793	−0.440397	−	0.897803i	$-0.645162\pi$
$463$	−18.9524	−0.880793	−0.440397	+	0.897803i	$0.645162\pi$
$464$	−19.2714	−0.894651
$465$	0	0
$466$	−5.19460	−0.240635
$467$	28.6276	1.32473	0.662365	−	0.749182i	$-0.269553\pi$
$467$	28.6276	1.32473	0.662365	+	0.749182i	$0.269553\pi$
$468$	7.46776	0.345197
$469$	−17.1156	−0.790325
$470$	0	0
$471$	45.5559	2.09911
$472$	−15.4074	−0.709184
$473$	−36.2793	−1.66813
$474$	−3.84173	−0.176457
$475$	0	0
$476$	4.79386	0.219726
$477$	−0.515845	−0.0236189
$478$	6.22643	0.284790
$479$	11.2258	0.512919	0.256459	−	0.966555i	$-0.417444\pi$
$479$	11.2258	0.512919	0.256459	+	0.966555i	$0.417444\pi$
$480$	0	0
$481$	14.4435	0.658566
$482$	−0.337207	−0.0153593
$483$	28.3447	1.28973
$484$	−12.5650	−0.571138
$485$	0	0
$486$	−7.42409	−0.336764
$487$	12.8286	0.581321	0.290660	−	0.956826i	$-0.406125\pi$
$487$	12.8286	0.581321	0.290660	+	0.956826i	$0.406125\pi$
$488$	−16.5756	−0.750343
$489$	−37.6988	−1.70480
$490$	0	0
$491$	−28.1872	−1.27207	−0.636036	−	0.771659i	$-0.719427\pi$
$491$	−28.1872	−1.27207	−0.636036	+	0.771659i	$0.719427\pi$
$492$	−14.2957	−0.644502
$493$	−6.48387	−0.292019
$494$	−0.685962	−0.0308629
$495$	0	0
$496$	−14.8460	−0.666604
$497$	−25.5770	−1.14729
$498$	−5.15569	−0.231032
$499$	−30.6615	−1.37260	−0.686298	−	0.727320i	$-0.740765\pi$
$499$	−30.6615	−1.37260	−0.686298	+	0.727320i	$0.740765\pi$
$500$	0	0
$501$	−11.1952	−0.500163
$502$	6.21602	0.277434
$503$	19.8349	0.884393	0.442196	−	0.896918i	$-0.354199\pi$
$503$	19.8349	0.884393	0.442196	+	0.896918i	$0.354199\pi$
$504$	−8.87023	−0.395111
$505$	0	0
$506$	7.24001	0.321858
$507$	27.4979	1.22123
$508$	15.2570	0.676919
$509$	34.2400	1.51766	0.758832	−	0.651287i	$-0.225770\pi$
$509$	34.2400	1.51766	0.758832	+	0.651287i	$0.225770\pi$
$510$	0	0
$511$	4.13172	0.182776
$512$	−21.2000	−0.936916
$513$	−0.0579025	−0.00255646
$514$	−7.43193	−0.327809
$515$	0	0
$516$	39.8358	1.75367
$517$	47.3940	2.08438
$518$	−8.32702	−0.365868
$519$	46.4474	2.03881
$520$	0	0
$521$	3.58996	0.157279	0.0786395	−	0.996903i	$-0.474942\pi$
$521$	3.58996	0.157279	0.0786395	+	0.996903i	$0.474942\pi$
$522$	5.82314	0.254872
$523$	−45.5580	−1.99211	−0.996056	−	0.0887278i	$-0.971720\pi$
$523$	−45.5580	−1.99211	−0.996056	+	0.0887278i	$0.971720\pi$
$524$	36.6406	1.60065
$525$	0	0
$526$	−2.04860	−0.0893233
$527$	−4.99494	−0.217583
$528$	34.2421	1.49019
$529$	3.10150	0.134848
$530$	0	0
$531$	−35.0897	−1.52276
$532$	−6.56046	−0.284432
$533$	4.10943	0.177999
$534$	−3.23093	−0.139816
$535$	0	0
$536$	9.89012	0.427188
$537$	−8.63623	−0.372681
$538$	−6.11973	−0.263840
$539$	7.80272	0.336087
$540$	0	0
$541$	6.34504	0.272795	0.136397	−	0.990654i	$-0.456448\pi$
$541$	6.34504	0.272795	0.136397	+	0.990654i	$0.456448\pi$
$542$	−8.99064	−0.386181
$543$	−25.1362	−1.07870
$544$	−4.19567	−0.179888
$545$	0	0
$546$	2.48162	0.106203
$547$	−26.2434	−1.12209	−0.561044	−	0.827786i	$-0.689600\pi$
$547$	−26.2434	−1.12209	−0.561044	+	0.827786i	$0.689600\pi$
$548$	7.13535	0.304807
$549$	−37.7502	−1.61114
$550$	0	0
$551$	8.87327	0.378014
$552$	−16.3787	−0.697126
$553$	10.5618	0.449132
$554$	10.6132	0.450912
$555$	0	0
$556$	33.8242	1.43446
$557$	6.32484	0.267992	0.133996	−	0.990982i	$-0.457219\pi$
$557$	6.32484	0.267992	0.133996	+	0.990982i	$0.457219\pi$
$558$	4.48594	0.189905
$559$	−11.4511	−0.484332
$560$	0	0
$561$	11.5208	0.486407
$562$	0.0540154	0.00227850
$563$	−13.6479	−0.575189	−0.287595	−	0.957752i	$-0.592856\pi$
$563$	−13.6479	−0.575189	−0.287595	+	0.957752i	$0.592856\pi$
$564$	−52.0401	−2.19128
$565$	0	0
$566$	4.82346	0.202745
$567$	20.5155	0.861569
$568$	14.7795	0.620134
$569$	−1.11611	−0.0467896	−0.0233948	−	0.999726i	$-0.507447\pi$
$569$	−1.11611	−0.0467896	−0.0233948	+	0.999726i	$0.507447\pi$
$570$	0	0
$571$	10.7554	0.450099	0.225050	−	0.974347i	$-0.427746\pi$
$571$	10.7554	0.450099	0.225050	+	0.974347i	$0.427746\pi$
$572$	−10.5152	−0.439665
$573$	39.9149	1.66747
$574$	−2.36919	−0.0988881
$575$	0	0
$576$	−16.1132	−0.671381
$577$	−18.4662	−0.768760	−0.384380	−	0.923175i	$-0.625585\pi$
$577$	−18.4662	−0.768760	−0.384380	+	0.923175i	$0.625585\pi$
$578$	5.30906	0.220828
$579$	28.8042	1.19706
$580$	0	0
$581$	14.1741	0.588042
$582$	−8.83890	−0.366384
$583$	0.726355	0.0300825
$584$	−2.38748	−0.0987947
$585$	0	0
$586$	8.90684	0.367938
$587$	11.6199	0.479605	0.239803	−	0.970822i	$-0.422917\pi$
$587$	11.6199	0.479605	0.239803	+	0.970822i	$0.422917\pi$
$588$	−8.56763	−0.353323
$589$	6.83565	0.281658
$590$	0	0
$591$	−0.470597	−0.0193578
$592$	−36.2664	−1.49054
$593$	25.4913	1.04680	0.523400	−	0.852087i	$-0.324663\pi$
$593$	25.4913	1.04680	0.523400	+	0.852087i	$0.324663\pi$
$594$	0.0535057	0.00219537
$595$	0	0
$596$	4.81525	0.197240
$597$	37.8667	1.54978
$598$	2.28523	0.0934498
$599$	−17.6882	−0.722719	−0.361360	−	0.932426i	$-0.617687\pi$
$599$	−17.6882	−0.722719	−0.361360	+	0.932426i	$0.617687\pi$
$600$	0	0
$601$	−0.765446	−0.0312232	−0.0156116	−	0.999878i	$-0.504970\pi$
$601$	−0.765446	−0.0312232	−0.0156116	+	0.999878i	$0.504970\pi$
$602$	6.60187	0.269072
$603$	22.5243	0.917260
$604$	−32.0695	−1.30489
$605$	0	0
$606$	−10.0727	−0.409176
$607$	27.4107	1.11256	0.556282	−	0.830993i	$-0.312227\pi$
$607$	27.4107	1.11256	0.556282	+	0.830993i	$0.312227\pi$
$608$	5.74183	0.232862
$609$	−32.1010	−1.30080
$610$	0	0
$611$	14.9593	0.605190
$612$	−6.30877	−0.255017
$613$	−41.2331	−1.66539	−0.832694	−	0.553733i	$-0.813203\pi$
$613$	−41.2331	−1.66539	−0.832694	+	0.553733i	$0.813203\pi$
$614$	0.592205	0.0238995
$615$	0	0
$616$	12.4900	0.503238
$617$	−37.7067	−1.51801	−0.759007	−	0.651082i	$-0.774315\pi$
$617$	−37.7067	−1.51801	−0.759007	+	0.651082i	$0.774315\pi$
$618$	−4.53524	−0.182434
$619$	29.6231	1.19065	0.595326	−	0.803484i	$-0.297023\pi$
$619$	29.6231	1.19065	0.595326	+	0.803484i	$0.297023\pi$
$620$	0	0
$621$	0.192897	0.00774070
$622$	3.56084	0.142777
$623$	8.88253	0.355871
$624$	10.8081	0.432670
$625$	0	0
$626$	−8.41074	−0.336161
$627$	−15.7663	−0.629647
$628$	35.1267	1.40171
$629$	−12.2019	−0.486520
$630$	0	0
$631$	−10.9817	−0.437175	−0.218588	−	0.975817i	$-0.570145\pi$
$631$	−10.9817	−0.437175	−0.218588	+	0.975817i	$0.570145\pi$
$632$	−6.10304	−0.242766
$633$	−38.9657	−1.54875
$634$	−5.00334	−0.198708
$635$	0	0
$636$	−0.797560	−0.0316253
$637$	2.46284	0.0975812
$638$	−8.19949	−0.324621
$639$	33.6596	1.33155
$640$	0	0
$641$	−37.7945	−1.49279	−0.746397	−	0.665501i	$-0.768218\pi$
$641$	−37.7945	−1.49279	−0.746397	+	0.665501i	$0.768218\pi$
$642$	0.751695	0.0296670
$643$	−25.0321	−0.987171	−0.493585	−	0.869697i	$-0.664314\pi$
$643$	−25.0321	−0.987171	−0.493585	+	0.869697i	$0.664314\pi$
$644$	21.8556	0.861233
$645$	0	0
$646$	0.579501	0.0228002
$647$	−23.2272	−0.913156	−0.456578	−	0.889683i	$-0.650925\pi$
$647$	−23.2272	−0.913156	−0.456578	+	0.889683i	$0.650925\pi$
$648$	−11.8547	−0.465697
$649$	49.4093	1.93949
$650$	0	0
$651$	−24.7295	−0.969224
$652$	−29.0683	−1.13840
$653$	26.7287	1.04598	0.522988	−	0.852340i	$-0.324817\pi$
$653$	26.7287	1.04598	0.522988	+	0.852340i	$0.324817\pi$
$654$	−1.41391	−0.0552881
$655$	0	0
$656$	−10.3185	−0.402868
$657$	−5.43738	−0.212133
$658$	−8.62444	−0.336216
$659$	−30.2579	−1.17868	−0.589340	−	0.807885i	$-0.700612\pi$
$659$	−30.2579	−1.17868	−0.589340	+	0.807885i	$0.700612\pi$
$660$	0	0
$661$	−36.4366	−1.41722	−0.708610	−	0.705600i	$-0.750677\pi$
$661$	−36.4366	−1.41722	−0.708610	+	0.705600i	$0.750677\pi$
$662$	−8.83825	−0.343508
$663$	3.63639	0.141226
$664$	−8.19041	−0.317849
$665$	0	0
$666$	10.9584	0.424631
$667$	−29.5606	−1.14459
$668$	−8.63222	−0.333991
$669$	−46.7421	−1.80715
$670$	0	0
$671$	53.1556	2.05205
$672$	−20.7723	−0.801310
$673$	−0.0655090	−0.00252519	−0.00126259	−	0.999999i	$-0.500402\pi$
$673$	−0.0655090	−0.00252519	−0.00126259	+	0.999999i	$0.500402\pi$
$674$	3.84294	0.148025
$675$	0	0
$676$	21.2028	0.815491
$677$	−22.8483	−0.878130	−0.439065	−	0.898455i	$-0.644690\pi$
$677$	−22.8483	−0.878130	−0.439065	+	0.898455i	$0.644690\pi$
$678$	5.40660	0.207639
$679$	24.3001	0.932552
$680$	0	0
$681$	19.3709	0.742294
$682$	−6.31659	−0.241875
$683$	−30.0047	−1.14810	−0.574050	−	0.818821i	$-0.694628\pi$
$683$	−30.0047	−1.14810	−0.574050	+	0.818821i	$0.694628\pi$
$684$	8.63364	0.330115
$685$	0	0
$686$	−6.77312	−0.258599
$687$	8.39083	0.320130
$688$	28.7529	1.09619
$689$	0.229265	0.00873431
$690$	0	0
$691$	−13.9664	−0.531307	−0.265653	−	0.964069i	$-0.585588\pi$
$691$	−13.9664	−0.531307	−0.265653	+	0.964069i	$0.585588\pi$
$692$	35.8141	1.36145
$693$	28.4455	1.08056
$694$	−2.91216	−0.110544
$695$	0	0
$696$	18.5493	0.703110
$697$	−3.47165	−0.131498
$698$	−8.41183	−0.318392
$699$	−37.6853	−1.42539
$700$	0	0
$701$	5.68340	0.214659	0.107329	−	0.994224i	$-0.465770\pi$
$701$	5.68340	0.214659	0.107329	+	0.994224i	$0.465770\pi$
$702$	0.0168884	0.000637413 0
$703$	16.6984	0.629793
$704$	22.6887	0.855113
$705$	0	0
$706$	10.5424	0.396769
$707$	27.6921	1.04147
$708$	−54.2530	−2.03895
$709$	35.2798	1.32496	0.662480	−	0.749079i	$-0.269504\pi$
$709$	35.2798	1.32496	0.662480	+	0.749079i	$0.269504\pi$
$710$	0	0
$711$	−13.8994	−0.521268
$712$	−5.13270	−0.192356
$713$	−22.7724	−0.852833
$714$	−2.09647	−0.0784585
$715$	0	0
$716$	−6.65912	−0.248863
$717$	45.1710	1.68694
$718$	8.39056	0.313133
$719$	43.6410	1.62753	0.813767	−	0.581191i	$-0.197413\pi$
$719$	43.6410	1.62753	0.813767	+	0.581191i	$0.197413\pi$
$720$	0	0
$721$	12.4684	0.464347
$722$	5.61387	0.208927
$723$	−2.44634	−0.0909803
$724$	−19.3817	−0.720315
$725$	0	0
$726$	5.49500	0.203938
$727$	−28.0938	−1.04194	−0.520972	−	0.853574i	$-0.674430\pi$
$727$	−28.0938	−1.04194	−0.520972	+	0.853574i	$0.674430\pi$
$728$	3.94234	0.146113
$729$	−26.7215	−0.989684
$730$	0	0
$731$	9.67393	0.357803
$732$	−58.3665	−2.15729
$733$	−5.94556	−0.219604	−0.109802	−	0.993953i	$-0.535022\pi$
$733$	−5.94556	−0.219604	−0.109802	+	0.993953i	$0.535022\pi$
$734$	−8.51749	−0.314386
$735$	0	0
$736$	−19.1284	−0.705084
$737$	−31.7162	−1.16828
$738$	3.11788	0.114771
$739$	46.1688	1.69835	0.849173	−	0.528114i	$-0.177101\pi$
$739$	46.1688	1.69835	0.849173	+	0.528114i	$0.177101\pi$
$740$	0	0
$741$	−4.97646	−0.182815
$742$	−0.132177	−0.00485238
$743$	29.0731	1.06659	0.533294	−	0.845930i	$-0.320954\pi$
$743$	29.0731	1.06659	0.533294	+	0.845930i	$0.320954\pi$
$744$	14.2897	0.523887
$745$	0	0
$746$	−7.82470	−0.286483
$747$	−18.6533	−0.682488
$748$	8.88329	0.324805
$749$	−2.06657	−0.0755110
$750$	0	0
$751$	21.2592	0.775759	0.387879	−	0.921710i	$-0.373208\pi$
$751$	21.2592	0.775759	0.387879	+	0.921710i	$0.373208\pi$
$752$	−37.5617	−1.36973
$753$	45.0954	1.64337
$754$	−2.58807	−0.0942520
$755$	0	0
$756$	0.161519	0.00587440
$757$	17.1586	0.623642	0.311821	−	0.950141i	$-0.399061\pi$
$757$	17.1586	0.623642	0.311821	+	0.950141i	$0.399061\pi$
$758$	−2.86805	−0.104172
$759$	52.5242	1.90651
$760$	0	0
$761$	33.1779	1.20270	0.601349	−	0.798987i	$-0.294630\pi$
$761$	33.1779	1.20270	0.601349	+	0.798987i	$0.294630\pi$
$762$	−6.67225	−0.241710
$763$	3.88714	0.140724
$764$	30.7771	1.11347
$765$	0	0
$766$	−8.18380	−0.295693
$767$	15.5955	0.563120
$768$	−18.7357	−0.676068
$769$	18.6832	0.673733	0.336866	−	0.941552i	$-0.390633\pi$
$769$	18.6832	0.673733	0.336866	+	0.941552i	$0.390633\pi$
$770$	0	0
$771$	−53.9166	−1.94176
$772$	22.2100	0.799354
$773$	−24.4134	−0.878089	−0.439044	−	0.898465i	$-0.644683\pi$
$773$	−24.4134	−0.878089	−0.439044	+	0.898465i	$0.644683\pi$
$774$	−8.68812	−0.312288
$775$	0	0
$776$	−14.0416	−0.504065
$777$	−60.4102	−2.16720
$778$	2.22778	0.0798698
$779$	4.75100	0.170222
$780$	0	0
$781$	−47.3957	−1.69595
$782$	−1.93056	−0.0690367
$783$	−0.218461	−0.00780715
$784$	−6.18398	−0.220857
$785$	0	0
$786$	−16.0238	−0.571551
$787$	−24.1396	−0.860483	−0.430241	−	0.902714i	$-0.641572\pi$
$787$	−24.1396	−0.860483	−0.430241	+	0.902714i	$0.641572\pi$
$788$	−0.362862	−0.0129264
$789$	−14.8620	−0.529102
$790$	0	0
$791$	−14.8639	−0.528501
$792$	−16.4370	−0.584064
$793$	16.7779	0.595802
$794$	0.563569	0.0200003
$795$	0	0
$796$	29.1978	1.03489
$797$	−20.4487	−0.724331	−0.362165	−	0.932114i	$-0.617962\pi$
$797$	−20.4487	−0.724331	−0.362165	+	0.932114i	$0.617962\pi$
$798$	2.86905	0.101563
$799$	−12.6377	−0.447088
$800$	0	0
$801$	−11.6895	−0.413028
$802$	3.48184	0.122948
$803$	7.65631	0.270185
$804$	34.8253	1.22819
$805$	0	0
$806$	−1.99376	−0.0702271
$807$	−44.3969	−1.56285
$808$	−16.0017	−0.562937
$809$	23.0375	0.809956	0.404978	−	0.914326i	$-0.367279\pi$
$809$	23.0375	0.809956	0.404978	+	0.914326i	$0.367279\pi$
$810$	0	0
$811$	−31.2018	−1.09564	−0.547822	−	0.836595i	$-0.684543\pi$
$811$	−31.2018	−1.09564	−0.547822	+	0.836595i	$0.684543\pi$
$812$	−24.7520	−0.868626
$813$	−65.2245	−2.28752
$814$	−15.4304	−0.540837
$815$	0	0
$816$	−9.13069	−0.319638
$817$	−13.2389	−0.463171
$818$	6.86373	0.239985
$819$	8.97849	0.313734
$820$	0	0
$821$	19.8399	0.692416	0.346208	−	0.938158i	$-0.387469\pi$
$821$	19.8399	0.692416	0.346208	+	0.938158i	$0.387469\pi$
$822$	−3.12046	−0.108839
$823$	−12.6604	−0.441313	−0.220657	−	0.975352i	$-0.570820\pi$
$823$	−12.6604	−0.441313	−0.220657	+	0.975352i	$0.570820\pi$
$824$	−7.20476	−0.250990
$825$	0	0
$826$	−8.99117	−0.312843
$827$	17.5997	0.612003	0.306002	−	0.952031i	$-0.401009\pi$
$827$	17.5997	0.612003	0.306002	+	0.952031i	$0.401009\pi$
$828$	−28.7622	−0.999557
$829$	−28.7997	−1.00026	−0.500128	−	0.865951i	$-0.666714\pi$
$829$	−28.7997	−1.00026	−0.500128	+	0.865951i	$0.666714\pi$
$830$	0	0
$831$	76.9958	2.67095
$832$	7.16143	0.248278
$833$	−2.08061	−0.0720887
$834$	−14.7921	−0.512210
$835$	0	0
$836$	−12.1569	−0.420455
$837$	−0.168294	−0.00581710
$838$	−10.7606	−0.371719
$839$	−15.4172	−0.532261	−0.266130	−	0.963937i	$-0.585745\pi$
$839$	−15.4172	−0.532261	−0.266130	+	0.963937i	$0.585745\pi$
$840$	0	0
$841$	4.47803	0.154415
$842$	−3.77608	−0.130132
$843$	0.391866	0.0134966
$844$	−30.0452	−1.03420
$845$	0	0
$846$	11.3498	0.390216
$847$	−15.1070	−0.519081
$848$	−0.575667	−0.0197685
$849$	34.9928	1.20095
$850$	0	0
$851$	−55.6294	−1.90695
$852$	52.0419	1.78293
$853$	−8.05157	−0.275681	−0.137840	−	0.990454i	$-0.544016\pi$
$853$	−8.05157	−0.275681	−0.137840	+	0.990454i	$0.544016\pi$
$854$	−9.67289	−0.331000
$855$	0	0
$856$	1.19415	0.0408154
$857$	−3.06794	−0.104799	−0.0523995	−	0.998626i	$-0.516687\pi$
$857$	−3.06794	−0.104799	−0.0523995	+	0.998626i	$0.516687\pi$
$858$	4.59857	0.156993
$859$	2.78437	0.0950016	0.0475008	−	0.998871i	$-0.484874\pi$
$859$	2.78437	0.0950016	0.0475008	+	0.998871i	$0.484874\pi$
$860$	0	0
$861$	−17.1878	−0.585758
$862$	−6.53939	−0.222732
$863$	13.0900	0.445588	0.222794	−	0.974866i	$-0.428482\pi$
$863$	13.0900	0.445588	0.222794	+	0.974866i	$0.428482\pi$
$864$	−0.141364	−0.00480931
$865$	0	0
$866$	−5.75660	−0.195617
$867$	38.5157	1.30806
$868$	−19.0681	−0.647213
$869$	19.5716	0.663919
$870$	0	0
$871$	−10.0108	−0.339204
$872$	−2.24615	−0.0760644
$873$	−31.9792	−1.08233
$874$	2.64200	0.0893669
$875$	0	0
$876$	−8.40686	−0.284042
$877$	5.80301	0.195954	0.0979769	−	0.995189i	$-0.468763\pi$
$877$	5.80301	0.195954	0.0979769	+	0.995189i	$0.468763\pi$
$878$	−4.65458	−0.157085
$879$	64.6166	2.17946
$880$	0	0
$881$	−55.7960	−1.87981	−0.939907	−	0.341429i	$-0.889089\pi$
$881$	−55.7960	−1.87981	−0.939907	+	0.341429i	$0.889089\pi$
$882$	1.86858	0.0629185
$883$	−19.7798	−0.665643	−0.332821	−	0.942990i	$-0.608001\pi$
$883$	−19.7798	−0.665643	−0.332821	+	0.942990i	$0.608001\pi$
$884$	2.80391	0.0943055
$885$	0	0
$886$	3.38405	0.113689
$887$	4.62814	0.155398	0.0776988	−	0.996977i	$-0.475243\pi$
$887$	4.62814	0.155398	0.0776988	+	0.996977i	$0.475243\pi$
$888$	34.9076	1.17142
$889$	18.3435	0.615221
$890$	0	0
$891$	38.0163	1.27360
$892$	−36.0413	−1.20675
$893$	17.2948	0.578749
$894$	−2.10583	−0.0704294
$895$	0	0
$896$	−21.1111	−0.705273
$897$	16.5787	0.553545
$898$	−3.78883	−0.126435
$899$	25.7903	0.860154
$900$	0	0
$901$	−0.193684	−0.00645253
$902$	−4.39024	−0.146179
$903$	47.8947	1.59383
$904$	8.58902	0.285667
$905$	0	0
$906$	14.0248	0.465942
$907$	−6.20096	−0.205899	−0.102950	−	0.994687i	$-0.532828\pi$
$907$	−6.20096	−0.205899	−0.102950	+	0.994687i	$0.532828\pi$
$908$	14.9363	0.495677
$909$	−36.4431	−1.20874
$910$	0	0
$911$	17.7331	0.587525	0.293763	−	0.955878i	$-0.405093\pi$
$911$	17.7331	0.587525	0.293763	+	0.955878i	$0.405093\pi$
$912$	12.4955	0.413767
$913$	26.2654	0.869259
$914$	2.69454	0.0891273
$915$	0	0
$916$	6.46990	0.213772
$917$	44.0531	1.45476
$918$	−0.0142674	−0.000470893 0
$919$	−32.1588	−1.06082	−0.530410	−	0.847741i	$-0.677962\pi$
$919$	−32.1588	−1.06082	−0.530410	+	0.847741i	$0.677962\pi$
$920$	0	0
$921$	4.29628	0.141567
$922$	3.24551	0.106885
$923$	−14.9599	−0.492410
$924$	43.9803	1.44684
$925$	0	0
$926$	6.39088	0.210017
$927$	−16.4085	−0.538927
$928$	21.6634	0.711136
$929$	−39.4312	−1.29370	−0.646849	−	0.762618i	$-0.723913\pi$
$929$	−39.4312	−1.29370	−0.646849	+	0.762618i	$0.723913\pi$
$930$	0	0
$931$	2.84734	0.0933178
$932$	−29.0579	−0.951824
$933$	25.8329	0.845730
$934$	−9.65343	−0.315870
$935$	0	0
$936$	−5.18815	−0.169580
$937$	7.06368	0.230760	0.115380	−	0.993321i	$-0.463191\pi$
$937$	7.06368	0.230760	0.115380	+	0.993321i	$0.463191\pi$
$938$	5.77149	0.188446
$939$	−61.0175	−1.99123
$940$	0	0
$941$	−30.7496	−1.00241	−0.501205	−	0.865329i	$-0.667110\pi$
$941$	−30.7496	−1.00241	−0.501205	+	0.865329i	$0.667110\pi$
$942$	−15.3618	−0.500513
$943$	−15.8276	−0.515417
$944$	−39.1590	−1.27452
$945$	0	0
$946$	12.2336	0.397750
$947$	−7.60797	−0.247226	−0.123613	−	0.992331i	$-0.539448\pi$
$947$	−7.60797	−0.247226	−0.123613	+	0.992331i	$0.539448\pi$
$948$	−21.4902	−0.697968
$949$	2.41662	0.0784469
$950$	0	0
$951$	−36.2978	−1.17704
$952$	−3.33049	−0.107942
$953$	−27.4814	−0.890209	−0.445104	−	0.895479i	$-0.646833\pi$
$953$	−27.4814	−0.890209	−0.445104	+	0.895479i	$0.646833\pi$
$954$	0.173946	0.00563172
$955$	0	0
$956$	34.8299	1.12648
$957$	−59.4849	−1.92287
$958$	−3.78540	−0.122301
$959$	8.57884	0.277025
$960$	0	0
$961$	−11.1321	−0.359100
$962$	−4.87044	−0.157029
$963$	2.71963	0.0876389
$964$	−1.88629	−0.0607534
$965$	0	0
$966$	−9.55800	−0.307524
$967$	43.5237	1.39963	0.699815	−	0.714324i	$-0.253266\pi$
$967$	43.5237	1.39963	0.699815	+	0.714324i	$0.253266\pi$
$968$	8.72944	0.280575
$969$	4.20411	0.135056
$970$	0	0
$971$	−48.8467	−1.56756	−0.783782	−	0.621036i	$-0.786712\pi$
$971$	−48.8467	−1.56756	−0.783782	+	0.621036i	$0.786712\pi$
$972$	−41.5295	−1.33206
$973$	40.6668	1.30372
$974$	−4.32590	−0.138611
$975$	0	0
$976$	−42.1280	−1.34849
$977$	−3.39731	−0.108689	−0.0543447	−	0.998522i	$-0.517307\pi$
$977$	−3.39731	−0.108689	−0.0543447	+	0.998522i	$0.517307\pi$
$978$	12.7123	0.406494
$979$	16.4598	0.526058
$980$	0	0
$981$	−5.11551	−0.163326
$982$	9.50492	0.303314
$983$	38.0148	1.21248	0.606241	−	0.795281i	$-0.292677\pi$
$983$	38.0148	1.21248	0.606241	+	0.795281i	$0.292677\pi$
$984$	9.93184	0.316615
$985$	0	0
$986$	2.18640	0.0696293
$987$	−62.5678	−1.99156
$988$	−3.83718	−0.122077
$989$	44.1044	1.40244
$990$	0	0
$991$	10.4684	0.332541	0.166270	−	0.986080i	$-0.446828\pi$
$991$	10.4684	0.332541	0.166270	+	0.986080i	$0.446828\pi$
$992$	16.6887	0.529867
$993$	−64.1190	−2.03475
$994$	8.62474	0.273560
$995$	0	0
$996$	−28.8403	−0.913839
$997$	−22.4425	−0.710761	−0.355380	−	0.934722i	$-0.615649\pi$
$997$	−22.4425	−0.710761	−0.355380	+	0.934722i	$0.615649\pi$
$998$	10.3393	0.327283
$999$	−0.411117	−0.0130072

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6025.2.a.n.1.17	yes	40
5.4	even	2		6025.2.a.m.1.24	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6025.2.a.m.1.24	✓	40	5.4	even	2
6025.2.a.n.1.17	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)

\(f(q)\)	\(=\)	\(q-0.337207 q^{2} -2.44634 q^{3} -1.88629 q^{4} +0.824921 q^{6} -2.26789 q^{7} +1.31048 q^{8} +2.98457 q^{9} +O(q^{10})\)	\(q-0.337207 q^{2} -2.44634 q^{3} -1.88629 q^{4} +0.824921 q^{6} -2.26789 q^{7} +1.31048 q^{8} +2.98457 q^{9} -4.20253 q^{11} +4.61451 q^{12} -1.32648 q^{13} +0.764748 q^{14} +3.33068 q^{16} +1.12061 q^{17} -1.00642 q^{18} -1.53357 q^{19} +5.54802 q^{21} +1.41712 q^{22} +5.10896 q^{23} -3.20588 q^{24} +0.447297 q^{26} +0.0377566 q^{27} +4.27790 q^{28} -5.78602 q^{29} -4.45734 q^{31} -3.74409 q^{32} +10.2808 q^{33} -0.377877 q^{34} -5.62976 q^{36} -10.8886 q^{37} +0.517130 q^{38} +3.24501 q^{39} -3.09800 q^{41} -1.87083 q^{42} +8.63274 q^{43} +7.92719 q^{44} -1.72278 q^{46} -11.2775 q^{47} -8.14797 q^{48} -1.85667 q^{49} -2.74139 q^{51} +2.50212 q^{52} -0.172838 q^{53} -0.0127318 q^{54} -2.97203 q^{56} +3.75163 q^{57} +1.95108 q^{58} -11.7570 q^{59} -12.6485 q^{61} +1.50305 q^{62} -6.76867 q^{63} -5.39883 q^{64} -3.46675 q^{66} +7.54693 q^{67} -2.11380 q^{68} -12.4982 q^{69} +11.2779 q^{71} +3.91122 q^{72} -1.82183 q^{73} +3.67171 q^{74} +2.89276 q^{76} +9.53087 q^{77} -1.09424 q^{78} -4.65709 q^{79} -9.04606 q^{81} +1.04467 q^{82} -6.24991 q^{83} -10.4652 q^{84} -2.91102 q^{86} +14.1546 q^{87} -5.50734 q^{88} -3.91665 q^{89} +3.00831 q^{91} -9.63699 q^{92} +10.9042 q^{93} +3.80285 q^{94} +9.15932 q^{96} -10.7148 q^{97} +0.626083 q^{98} -12.5427 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 9 q^{2} + 8 q^{3} + 41 q^{4} + 3 q^{6} + 20 q^{7} + 27 q^{8} + 38 q^{9}+O(q^{10}) \) 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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