LMFDB - Embedded newform 6025.2.a.e.1.1

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:	$5$
Coefficient field:	5.5.38569.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 5x^{3} + 4x - 1 $ x^5 - 5x^3 + 4x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1205)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$0.275834$ of defining polynomial
Character	$\chi$	$=$	6025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.34953 q^{2} +1.80652 q^{3} +3.52030 q^{4} -4.24447 q^{6} +4.19975 q^{7} -3.57200 q^{8} +0.263500 q^{9} +O(q^{10})$	\(q-2.34953 q^{2} +1.80652 q^{3} +3.52030 q^{4} -4.24447 q^{6} +4.19975 q^{7} -3.57200 q^{8} +0.263500 q^{9} -2.93358 q^{11} +6.35948 q^{12} -1.23213 q^{13} -9.86745 q^{14} +1.35192 q^{16} +4.88288 q^{17} -0.619101 q^{18} -4.31817 q^{19} +7.58691 q^{21} +6.89255 q^{22} +1.20315 q^{23} -6.45287 q^{24} +2.89493 q^{26} -4.94353 q^{27} +14.7844 q^{28} +4.59032 q^{29} -2.00865 q^{31} +3.96762 q^{32} -5.29956 q^{33} -11.4725 q^{34} +0.927598 q^{36} -3.72076 q^{37} +10.1457 q^{38} -2.22587 q^{39} +2.70145 q^{41} -17.8257 q^{42} +5.82225 q^{43} -10.3271 q^{44} -2.82684 q^{46} +2.60336 q^{47} +2.44226 q^{48} +10.6379 q^{49} +8.82100 q^{51} -4.33748 q^{52} +3.47970 q^{53} +11.6150 q^{54} -15.0015 q^{56} -7.80083 q^{57} -10.7851 q^{58} -2.88628 q^{59} -5.40831 q^{61} +4.71939 q^{62} +1.10663 q^{63} -12.0259 q^{64} +12.4515 q^{66} -11.8387 q^{67} +17.1892 q^{68} +2.17351 q^{69} +6.50487 q^{71} -0.941220 q^{72} +8.66042 q^{73} +8.74205 q^{74} -15.2012 q^{76} -12.3203 q^{77} +5.22975 q^{78} -0.141985 q^{79} -9.72107 q^{81} -6.34715 q^{82} +14.4788 q^{83} +26.7082 q^{84} -13.6796 q^{86} +8.29248 q^{87} +10.4788 q^{88} +16.1576 q^{89} -5.17465 q^{91} +4.23546 q^{92} -3.62866 q^{93} -6.11669 q^{94} +7.16756 q^{96} +0.378748 q^{97} -24.9941 q^{98} -0.772998 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + q^{2} + 5 q^{3} + 3 q^{4} - 8 q^{6} + 10 q^{7} + 6 q^{9}+O(q^{10}) $ 5 * q + q^2 + 5 * q^3 + 3 * q^4 - 8 * q^6 + 10 * q^7 + 6 * q^9	$ 5 q + q^{2} + 5 q^{3} + 3 q^{4} - 8 q^{6} + 10 q^{7} + 6 q^{9} - 3 q^{11} - 8 q^{12} + q^{13} - q^{14} + 15 q^{16} + 5 q^{17} - 4 q^{18} + 3 q^{19} + 11 q^{21} + 13 q^{22} + 8 q^{23} - 14 q^{24} + 14 q^{26} + 14 q^{27} + 17 q^{28} + 9 q^{29} - 16 q^{31} + 16 q^{32} - 23 q^{33} - 10 q^{34} - 17 q^{36} - 7 q^{37} + 22 q^{38} - 19 q^{39} + 9 q^{41} - 17 q^{42} + 32 q^{43} - 8 q^{44} + 5 q^{46} + 7 q^{47} + 6 q^{48} + 9 q^{49} - 8 q^{51} + 10 q^{52} + 32 q^{53} + 32 q^{54} - 18 q^{56} - 3 q^{57} - 11 q^{58} - 8 q^{59} - 12 q^{61} - 17 q^{62} + 11 q^{63} - 16 q^{64} + 15 q^{66} + 5 q^{67} + 2 q^{68} + 7 q^{69} - 11 q^{71} - 7 q^{72} + 29 q^{73} + 10 q^{74} - 8 q^{76} + 5 q^{77} - 2 q^{78} + 16 q^{79} - 15 q^{81} + 2 q^{82} + 10 q^{83} + 5 q^{84} + 14 q^{86} + 37 q^{87} - 10 q^{88} + 9 q^{89} + 12 q^{91} + 25 q^{92} - 15 q^{93} - 11 q^{94} - 3 q^{96} + 43 q^{97} - 30 q^{98} - 30 q^{99}+O(q^{100}) $ 5 * q + q^2 + 5 * q^3 + 3 * q^4 - 8 * q^6 + 10 * q^7 + 6 * q^9 - 3 * q^11 - 8 * q^12 + q^13 - q^14 + 15 * q^16 + 5 * q^17 - 4 * q^18 + 3 * q^19 + 11 * q^21 + 13 * q^22 + 8 * q^23 - 14 * q^24 + 14 * q^26 + 14 * q^27 + 17 * q^28 + 9 * q^29 - 16 * q^31 + 16 * q^32 - 23 * q^33 - 10 * q^34 - 17 * q^36 - 7 * q^37 + 22 * q^38 - 19 * q^39 + 9 * q^41 - 17 * q^42 + 32 * q^43 - 8 * q^44 + 5 * q^46 + 7 * q^47 + 6 * q^48 + 9 * q^49 - 8 * q^51 + 10 * q^52 + 32 * q^53 + 32 * q^54 - 18 * q^56 - 3 * q^57 - 11 * q^58 - 8 * q^59 - 12 * q^61 - 17 * q^62 + 11 * q^63 - 16 * q^64 + 15 * q^66 + 5 * q^67 + 2 * q^68 + 7 * q^69 - 11 * q^71 - 7 * q^72 + 29 * q^73 + 10 * q^74 - 8 * q^76 + 5 * q^77 - 2 * q^78 + 16 * q^79 - 15 * q^81 + 2 * q^82 + 10 * q^83 + 5 * q^84 + 14 * q^86 + 37 * q^87 - 10 * q^88 + 9 * q^89 + 12 * q^91 + 25 * q^92 - 15 * q^93 - 11 * q^94 - 3 * q^96 + 43 * q^97 - 30 * q^98 - 30 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.34953	−1.66137	−0.830685	−	0.556743i	$-0.812051\pi$
$2$	−2.34953	−1.66137	−0.830685	+	0.556743i	$0.812051\pi$
$3$	1.80652	1.04299	0.521496	−	0.853254i	$-0.325374\pi$
$3$	1.80652	1.04299	0.521496	+	0.853254i	$0.325374\pi$
$4$	3.52030	1.76015
$5$	0	0
$5$	0	0
$6$	−4.24447	−1.73280
$7$	4.19975	1.58736	0.793678	−	0.608338i	$-0.208163\pi$
$7$	4.19975	1.58736	0.793678	+	0.608338i	$0.208163\pi$
$8$	−3.57200	−1.26289
$9$	0.263500	0.0878332
$10$	0	0
$11$	−2.93358	−0.884509	−0.442254	−	0.896890i	$-0.645821\pi$
$11$	−2.93358	−0.884509	−0.442254	+	0.896890i	$0.645821\pi$
$12$	6.35948	1.83582
$13$	−1.23213	−0.341732	−0.170866	−	0.985294i	$-0.554657\pi$
$13$	−1.23213	−0.341732	−0.170866	+	0.985294i	$0.554657\pi$
$14$	−9.86745	−2.63719
$15$	0	0
$16$	1.35192	0.337980
$17$	4.88288	1.18427	0.592136	−	0.805838i	$-0.298285\pi$
$17$	4.88288	1.18427	0.592136	+	0.805838i	$0.298285\pi$
$18$	−0.619101	−0.145923
$19$	−4.31817	−0.990655	−0.495328	−	0.868706i	$-0.664952\pi$
$19$	−4.31817	−0.990655	−0.495328	+	0.868706i	$0.664952\pi$
$20$	0	0
$21$	7.58691	1.65560
$22$	6.89255	1.46950
$23$	1.20315	0.250875	0.125437	−	0.992102i	$-0.459967\pi$
$23$	1.20315	0.250875	0.125437	+	0.992102i	$0.459967\pi$
$24$	−6.45287	−1.31719
$25$	0	0
$26$	2.89493	0.567743
$27$	−4.94353	−0.951383
$28$	14.7844	2.79399
$29$	4.59032	0.852400	0.426200	−	0.904629i	$-0.359852\pi$
$29$	4.59032	0.852400	0.426200	+	0.904629i	$0.359852\pi$
$30$	0	0
$31$	−2.00865	−0.360765	−0.180382	−	0.983597i	$-0.557733\pi$
$31$	−2.00865	−0.360765	−0.180382	+	0.983597i	$0.557733\pi$
$32$	3.96762	0.701382
$33$	−5.29956	−0.922536
$34$	−11.4725	−1.96751
$35$	0	0
$36$	0.927598	0.154600
$37$	−3.72076	−0.611690	−0.305845	−	0.952081i	$-0.598939\pi$
$37$	−3.72076	−0.611690	−0.305845	+	0.952081i	$0.598939\pi$
$38$	10.1457	1.64584
$39$	−2.22587	−0.356424
$40$	0	0
$41$	2.70145	0.421896	0.210948	−	0.977497i	$-0.432345\pi$
$41$	2.70145	0.421896	0.210948	+	0.977497i	$0.432345\pi$
$42$	−17.8257	−2.75057
$43$	5.82225	0.887885	0.443943	−	0.896055i	$-0.353579\pi$
$43$	5.82225	0.887885	0.443943	+	0.896055i	$0.353579\pi$
$44$	−10.3271	−1.55687
$45$	0	0
$46$	−2.82684	−0.416795
$47$	2.60336	0.379740	0.189870	−	0.981809i	$-0.439193\pi$
$47$	2.60336	0.379740	0.189870	+	0.981809i	$0.439193\pi$
$48$	2.44226	0.352510
$49$	10.6379	1.51970
$50$	0	0
$51$	8.82100	1.23519
$52$	−4.33748	−0.601500
$53$	3.47970	0.477973	0.238987	−	0.971023i	$-0.423185\pi$
$53$	3.47970	0.477973	0.238987	+	0.971023i	$0.423185\pi$
$54$	11.6150	1.58060
$55$	0	0
$56$	−15.0015	−2.00466
$57$	−7.80083	−1.03325
$58$	−10.7851	−1.41615
$59$	−2.88628	−0.375762	−0.187881	−	0.982192i	$-0.560162\pi$
$59$	−2.88628	−0.375762	−0.187881	+	0.982192i	$0.560162\pi$
$60$	0	0
$61$	−5.40831	−0.692463	−0.346232	−	0.938149i	$-0.612539\pi$
$61$	−5.40831	−0.692463	−0.346232	+	0.938149i	$0.612539\pi$
$62$	4.71939	0.599363
$63$	1.10663	0.139423
$64$	−12.0259	−1.50324
$65$	0	0
$66$	12.4515	1.53267
$67$	−11.8387	−1.44633	−0.723167	−	0.690674i	$-0.757314\pi$
$67$	−11.8387	−1.44633	−0.723167	+	0.690674i	$0.757314\pi$
$68$	17.1892	2.08450
$69$	2.17351	0.261660
$70$	0	0
$71$	6.50487	0.771986	0.385993	−	0.922502i	$-0.373859\pi$
$71$	6.50487	0.771986	0.385993	+	0.922502i	$0.373859\pi$
$72$	−0.941220	−0.110924
$73$	8.66042	1.01363	0.506813	−	0.862056i	$-0.330824\pi$
$73$	8.66042	1.01363	0.506813	+	0.862056i	$0.330824\pi$
$74$	8.74205	1.01624
$75$	0	0
$76$	−15.2012	−1.74370
$77$	−12.3203	−1.40403
$78$	5.22975	0.592152
$79$	−0.141985	−0.0159746	−0.00798729	−	0.999968i	$-0.502542\pi$
$79$	−0.141985	−0.0159746	−0.00798729	+	0.999968i	$0.502542\pi$
$80$	0	0
$81$	−9.72107	−1.08012
$82$	−6.34715	−0.700925
$83$	14.4788	1.58925	0.794625	−	0.607101i	$-0.207668\pi$
$83$	14.4788	1.58925	0.794625	+	0.607101i	$0.207668\pi$
$84$	26.7082	2.91411
$85$	0	0
$86$	−13.6796	−1.47511
$87$	8.29248	0.889047
$88$	10.4788	1.11704
$89$	16.1576	1.71271	0.856354	−	0.516390i	$-0.172724\pi$
$89$	16.1576	1.71271	0.856354	+	0.516390i	$0.172724\pi$
$90$	0	0
$91$	−5.17465	−0.542451
$92$	4.23546	0.441577
$93$	−3.62866	−0.376275
$94$	−6.11669	−0.630888
$95$	0	0
$96$	7.16756	0.731536
$97$	0.378748	0.0384561	0.0192280	−	0.999815i	$-0.493879\pi$
$97$	0.378748	0.0384561	0.0192280	+	0.999815i	$0.493879\pi$
$98$	−24.9941	−2.52478
$99$	−0.772998	−0.0776892
$100$	0	0
$101$	0.713589	0.0710047	0.0355024	−	0.999370i	$-0.488697\pi$
$101$	0.713589	0.0710047	0.0355024	+	0.999370i	$0.488697\pi$
$102$	−20.7252	−2.05210
$103$	16.4695	1.62279	0.811395	−	0.584498i	$-0.198708\pi$
$103$	16.4695	1.62279	0.811395	+	0.584498i	$0.198708\pi$
$104$	4.40117	0.431571
$105$	0	0
$106$	−8.17566	−0.794091
$107$	−3.40945	−0.329604	−0.164802	−	0.986327i	$-0.552698\pi$
$107$	−3.40945	−0.329604	−0.164802	+	0.986327i	$0.552698\pi$
$108$	−17.4027	−1.67458
$109$	12.0251	1.15179	0.575896	−	0.817523i	$-0.304653\pi$
$109$	12.0251	1.15179	0.575896	+	0.817523i	$0.304653\pi$
$110$	0	0
$111$	−6.72162	−0.637988
$112$	5.67772	0.536494
$113$	7.92062	0.745109	0.372555	−	0.928010i	$-0.378482\pi$
$113$	7.92062	0.745109	0.372555	+	0.928010i	$0.378482\pi$
$114$	18.3283	1.71660
$115$	0	0
$116$	16.1593	1.50035
$117$	−0.324666	−0.0300154
$118$	6.78141	0.624280
$119$	20.5069	1.87986
$120$	0	0
$121$	−2.39409	−0.217644
$122$	12.7070	1.15044
$123$	4.88021	0.440034
$124$	−7.07106	−0.635000
$125$	0	0
$126$	−2.60007	−0.231632
$127$	0.929901	0.0825154	0.0412577	−	0.999149i	$-0.486864\pi$
$127$	0.929901	0.0825154	0.0412577	+	0.999149i	$0.486864\pi$
$128$	20.3200	1.79605
$129$	10.5180	0.926058
$130$	0	0
$131$	13.1197	1.14627	0.573137	−	0.819459i	$-0.305726\pi$
$131$	13.1197	1.14627	0.573137	+	0.819459i	$0.305726\pi$
$132$	−18.6561	−1.62380
$133$	−18.1352	−1.57252
$134$	27.8155	2.40289
$135$	0	0
$136$	−17.4416	−1.49561
$137$	2.18197	0.186418	0.0932091	−	0.995647i	$-0.470287\pi$
$137$	2.18197	0.186418	0.0932091	+	0.995647i	$0.470287\pi$
$138$	−5.10674	−0.434714
$139$	15.8938	1.34809	0.674046	−	0.738690i	$-0.264555\pi$
$139$	15.8938	1.34809	0.674046	+	0.738690i	$0.264555\pi$
$140$	0	0
$141$	4.70302	0.396066
$142$	−15.2834	−1.28255
$143$	3.61456	0.302265
$144$	0.356230	0.0296858
$145$	0	0
$146$	−20.3479	−1.68401
$147$	19.2175	1.58504
$148$	−13.0982	−1.07667
$149$	−9.32400	−0.763852	−0.381926	−	0.924193i	$-0.624739\pi$
$149$	−9.32400	−0.763852	−0.381926	+	0.924193i	$0.624739\pi$
$150$	0	0
$151$	12.5373	1.02027	0.510137	−	0.860093i	$-0.329595\pi$
$151$	12.5373	1.02027	0.510137	+	0.860093i	$0.329595\pi$
$152$	15.4245	1.25109
$153$	1.28664	0.104018
$154$	28.9470	2.33261
$155$	0	0
$156$	−7.83572	−0.627360
$157$	−2.03555	−0.162455	−0.0812273	−	0.996696i	$-0.525884\pi$
$157$	−2.03555	−0.162455	−0.0812273	+	0.996696i	$0.525884\pi$
$158$	0.333599	0.0265397
$159$	6.28613	0.498523
$160$	0	0
$161$	5.05294	0.398227
$162$	22.8400	1.79448
$163$	−9.83753	−0.770535	−0.385267	−	0.922805i	$-0.625891\pi$
$163$	−9.83753	−0.770535	−0.385267	+	0.922805i	$0.625891\pi$
$164$	9.50992	0.742600
$165$	0	0
$166$	−34.0183	−2.64033
$167$	17.5153	1.35537	0.677687	−	0.735350i	$-0.262982\pi$
$167$	17.5153	1.35537	0.677687	+	0.735350i	$0.262982\pi$
$168$	−27.1004	−2.09084
$169$	−11.4818	−0.883219
$170$	0	0
$171$	−1.13783	−0.0870124
$172$	20.4961	1.56281
$173$	8.77938	0.667484	0.333742	−	0.942664i	$-0.391689\pi$
$173$	8.77938	0.667484	0.333742	+	0.942664i	$0.391689\pi$
$174$	−19.4834	−1.47704
$175$	0	0
$176$	−3.96597	−0.298946
$177$	−5.21412	−0.391917
$178$	−37.9629	−2.84544
$179$	−0.586741	−0.0438551	−0.0219275	−	0.999760i	$-0.506980\pi$
$179$	−0.586741	−0.0438551	−0.0219275	+	0.999760i	$0.506980\pi$
$180$	0	0
$181$	9.18965	0.683061	0.341531	−	0.939871i	$-0.389055\pi$
$181$	9.18965	0.683061	0.341531	+	0.939871i	$0.389055\pi$
$182$	12.1580	0.901211
$183$	−9.77020	−0.722234
$184$	−4.29766	−0.316827
$185$	0	0
$186$	8.52566	0.625132
$187$	−14.3243	−1.04750
$188$	9.16463	0.668399
$189$	−20.7616	−1.51018
$190$	0	0
$191$	−14.2321	−1.02980	−0.514901	−	0.857250i	$-0.672171\pi$
$191$	−14.2321	−1.02980	−0.514901	+	0.857250i	$0.672171\pi$
$192$	−21.7249	−1.56786
$193$	6.76782	0.487158	0.243579	−	0.969881i	$-0.421678\pi$
$193$	6.76782	0.487158	0.243579	+	0.969881i	$0.421678\pi$
$194$	−0.889882	−0.0638898
$195$	0	0
$196$	37.4486	2.67490
$197$	6.24098	0.444651	0.222326	−	0.974972i	$-0.428635\pi$
$197$	6.24098	0.444651	0.222326	+	0.974972i	$0.428635\pi$
$198$	1.81618	0.129071
$199$	−20.2085	−1.43254	−0.716270	−	0.697823i	$-0.754152\pi$
$199$	−20.2085	−1.43254	−0.716270	+	0.697823i	$0.754152\pi$
$200$	0	0
$201$	−21.3869	−1.50851
$202$	−1.67660	−0.117965
$203$	19.2782	1.35306
$204$	31.0526	2.17412
$205$	0	0
$206$	−38.6957	−2.69606
$207$	0.317030	0.0220351
$208$	−1.66574	−0.115498
$209$	12.6677	0.876243
$210$	0	0
$211$	0.534644	0.0368064	0.0184032	−	0.999831i	$-0.494142\pi$
$211$	0.534644	0.0368064	0.0184032	+	0.999831i	$0.494142\pi$
$212$	12.2496	0.841305
$213$	11.7511	0.805175
$214$	8.01061	0.547594
$215$	0	0
$216$	17.6583	1.20149
$217$	−8.43584	−0.572662
$218$	−28.2533	−1.91355
$219$	15.6452	1.05720
$220$	0	0
$221$	−6.01636	−0.404704
$222$	15.7927	1.05993
$223$	25.7574	1.72484	0.862422	−	0.506190i	$-0.168947\pi$
$223$	25.7574	1.72484	0.862422	+	0.506190i	$0.168947\pi$
$224$	16.6630	1.11334
$225$	0	0
$226$	−18.6098	−1.23790
$227$	11.3202	0.751349	0.375674	−	0.926752i	$-0.377411\pi$
$227$	11.3202	0.751349	0.375674	+	0.926752i	$0.377411\pi$
$228$	−27.4613	−1.81867
$229$	18.1213	1.19749	0.598744	−	0.800941i	$-0.295667\pi$
$229$	18.1213	1.19749	0.598744	+	0.800941i	$0.295667\pi$
$230$	0	0
$231$	−22.2568	−1.46439
$232$	−16.3966	−1.07649
$233$	−9.07824	−0.594735	−0.297367	−	0.954763i	$-0.596109\pi$
$233$	−9.07824	−0.594735	−0.297367	+	0.954763i	$0.596109\pi$
$234$	0.762814	0.0498667
$235$	0	0
$236$	−10.1606	−0.661398
$237$	−0.256498	−0.0166614
$238$	−48.1816	−3.12315
$239$	19.3957	1.25460	0.627301	−	0.778777i	$-0.284160\pi$
$239$	19.3957	1.25460	0.627301	+	0.778777i	$0.284160\pi$
$240$	0	0
$241$	1.00000	0.0644157
$241$	1.00000	0.0644157
$242$	5.62499	0.361588
$243$	−2.73067	−0.175172
$244$	−19.0389	−1.21884
$245$	0	0
$246$	−11.4662	−0.731059
$247$	5.32055	0.338539
$248$	7.17490	0.455607
$249$	26.1561	1.65758
$250$	0	0
$251$	11.7123	0.739271	0.369635	−	0.929177i	$-0.379483\pi$
$251$	11.7123	0.739271	0.369635	+	0.929177i	$0.379483\pi$
$252$	3.89568	0.245405
$253$	−3.52955	−0.221901
$254$	−2.18483	−0.137089
$255$	0	0
$256$	−23.6906	−1.48066
$257$	−9.31679	−0.581165	−0.290583	−	0.956850i	$-0.593849\pi$
$257$	−9.31679	−0.581165	−0.290583	+	0.956850i	$0.593849\pi$
$258$	−24.7124	−1.53852
$259$	−15.6263	−0.970970
$260$	0	0
$261$	1.20955	0.0748691
$262$	−30.8252	−1.90439
$263$	3.66604	0.226058	0.113029	−	0.993592i	$-0.463945\pi$
$263$	3.66604	0.226058	0.113029	+	0.993592i	$0.463945\pi$
$264$	18.9300	1.16506
$265$	0	0
$266$	42.6093	2.61254
$267$	29.1890	1.78634
$268$	−41.6760	−2.54576
$269$	−20.6904	−1.26151	−0.630757	−	0.775980i	$-0.717256\pi$
$269$	−20.6904	−1.26151	−0.630757	+	0.775980i	$0.717256\pi$
$270$	0	0
$271$	15.3436	0.932060	0.466030	−	0.884769i	$-0.345684\pi$
$271$	15.3436	0.932060	0.466030	+	0.884769i	$0.345684\pi$
$272$	6.60126	0.400260
$273$	−9.34808	−0.565772
$274$	−5.12661	−0.309710
$275$	0	0
$276$	7.65142	0.460561
$277$	−30.7507	−1.84763	−0.923816	−	0.382838i	$-0.874947\pi$
$277$	−30.7507	−1.84763	−0.923816	+	0.382838i	$0.874947\pi$
$278$	−37.3429	−2.23968
$279$	−0.529279	−0.0316871
$280$	0	0
$281$	8.62443	0.514491	0.257245	−	0.966346i	$-0.417185\pi$
$281$	8.62443	0.514491	0.257245	+	0.966346i	$0.417185\pi$
$282$	−11.0499	−0.658012
$283$	−18.1767	−1.08049	−0.540247	−	0.841506i	$-0.681669\pi$
$283$	−18.1767	−1.08049	−0.540247	+	0.841506i	$0.681669\pi$
$284$	22.8991	1.35881
$285$	0	0
$286$	−8.49253	−0.502174
$287$	11.3454	0.669699
$288$	1.04547	0.0616046
$289$	6.84252	0.402501
$290$	0	0
$291$	0.684215	0.0401094
$292$	30.4873	1.78413
$293$	30.9216	1.80646	0.903230	−	0.429156i	$-0.141189\pi$
$293$	30.9216	1.80646	0.903230	+	0.429156i	$0.141189\pi$
$294$	−45.1522	−2.63333
$295$	0	0
$296$	13.2906	0.772498
$297$	14.5023	0.841507
$298$	21.9070	1.26904
$299$	−1.48244	−0.0857319
$300$	0	0
$301$	24.4520	1.40939
$302$	−29.4569	−1.69505
$303$	1.28911	0.0740574
$304$	−5.83781	−0.334821
$305$	0	0
$306$	−3.02300	−0.172813
$307$	4.69074	0.267715	0.133857	−	0.991001i	$-0.457264\pi$
$307$	4.69074	0.267715	0.133857	+	0.991001i	$0.457264\pi$
$308$	−43.3712	−2.47130
$309$	29.7525	1.69256
$310$	0	0
$311$	−24.9749	−1.41620	−0.708099	−	0.706114i	$-0.750447\pi$
$311$	−24.9749	−1.41620	−0.708099	+	0.706114i	$0.750447\pi$
$312$	7.95079	0.450125
$313$	28.9363	1.63558	0.817788	−	0.575520i	$-0.195200\pi$
$313$	28.9363	1.63558	0.817788	+	0.575520i	$0.195200\pi$
$314$	4.78259	0.269897
$315$	0	0
$316$	−0.499831	−0.0281177
$317$	−25.7549	−1.44654	−0.723269	−	0.690567i	$-0.757361\pi$
$317$	−25.7549	−1.44654	−0.723269	+	0.690567i	$0.757361\pi$
$318$	−14.7695	−0.828231
$319$	−13.4661	−0.753956
$320$	0	0
$321$	−6.15922	−0.343774
$322$	−11.8720	−0.661603
$323$	−21.0851	−1.17321
$324$	−34.2211	−1.90117
$325$	0	0
$326$	23.1136	1.28014
$327$	21.7235	1.20131
$328$	−9.64957	−0.532809
$329$	10.9335	0.602782
$330$	0	0
$331$	−28.7767	−1.58171	−0.790855	−	0.612003i	$-0.790364\pi$
$331$	−28.7767	−1.58171	−0.790855	+	0.612003i	$0.790364\pi$
$332$	50.9696	2.79732
$333$	−0.980420	−0.0537267
$334$	−41.1527	−2.25178
$335$	0	0
$336$	10.2569	0.559559
$337$	−34.6144	−1.88556	−0.942782	−	0.333409i	$-0.891801\pi$
$337$	−34.6144	−1.88556	−0.942782	+	0.333409i	$0.891801\pi$
$338$	26.9770	1.46735
$339$	14.3087	0.777143
$340$	0	0
$341$	5.89255	0.319099
$342$	2.67338	0.144560
$343$	15.2783	0.824948
$344$	−20.7971	−1.12130
$345$	0	0
$346$	−20.6274	−1.10894
$347$	−9.14212	−0.490775	−0.245387	−	0.969425i	$-0.578915\pi$
$347$	−9.14212	−0.490775	−0.245387	+	0.969425i	$0.578915\pi$
$348$	29.1920	1.56486
$349$	−26.2739	−1.40641	−0.703204	−	0.710988i	$-0.748248\pi$
$349$	−26.2739	−1.40641	−0.703204	+	0.710988i	$0.748248\pi$
$350$	0	0
$351$	6.09109	0.325118
$352$	−11.6393	−0.620379
$353$	15.8005	0.840976	0.420488	−	0.907298i	$-0.361859\pi$
$353$	15.8005	0.840976	0.420488	+	0.907298i	$0.361859\pi$
$354$	12.2507	0.651119
$355$	0	0
$356$	56.8798	3.01462
$357$	37.0460	1.96068
$358$	1.37857	0.0728595
$359$	22.8609	1.20655	0.603275	−	0.797533i	$-0.293862\pi$
$359$	22.8609	1.20655	0.603275	+	0.797533i	$0.293862\pi$
$360$	0	0
$361$	−0.353450	−0.0186027
$362$	−21.5914	−1.13482
$363$	−4.32496	−0.227001
$364$	−18.2163	−0.954795
$365$	0	0
$366$	22.9554	1.19990
$367$	35.9260	1.87532	0.937661	−	0.347551i	$-0.112987\pi$
$367$	35.9260	1.87532	0.937661	+	0.347551i	$0.112987\pi$
$368$	1.62656	0.0847905
$369$	0.711831	0.0370565
$370$	0	0
$371$	14.6139	0.758714
$372$	−12.7740	−0.662300
$373$	−16.8651	−0.873240	−0.436620	−	0.899646i	$-0.643825\pi$
$373$	−16.8651	−0.873240	−0.436620	+	0.899646i	$0.643825\pi$
$374$	33.6555	1.74028
$375$	0	0
$376$	−9.29921	−0.479570
$377$	−5.65588	−0.291293
$378$	48.7800	2.50897
$379$	−22.3345	−1.14724	−0.573622	−	0.819120i	$-0.694462\pi$
$379$	−22.3345	−1.14724	−0.573622	+	0.819120i	$0.694462\pi$
$380$	0	0
$381$	1.67988	0.0860629
$382$	33.4389	1.71088
$383$	11.2673	0.575734	0.287867	−	0.957670i	$-0.407054\pi$
$383$	11.2673	0.575734	0.287867	+	0.957670i	$0.407054\pi$
$384$	36.7083	1.87326
$385$	0	0
$386$	−15.9012	−0.809350
$387$	1.53416	0.0779858
$388$	1.33331	0.0676885
$389$	−34.0760	−1.72772	−0.863860	−	0.503733i	$-0.831960\pi$
$389$	−34.0760	−1.72772	−0.863860	+	0.503733i	$0.831960\pi$
$390$	0	0
$391$	5.87485	0.297104
$392$	−37.9985	−1.91922
$393$	23.7010	1.19556
$394$	−14.6634	−0.738731
$395$	0	0
$396$	−2.72119	−0.136745
$397$	24.5107	1.23016	0.615079	−	0.788466i	$-0.289124\pi$
$397$	24.5107	1.23016	0.615079	+	0.788466i	$0.289124\pi$
$398$	47.4804	2.37998
$399$	−32.7615	−1.64013
$400$	0	0
$401$	6.17812	0.308520	0.154260	−	0.988030i	$-0.450701\pi$
$401$	6.17812	0.308520	0.154260	+	0.988030i	$0.450701\pi$
$402$	50.2492	2.50620
$403$	2.47493	0.123285
$404$	2.51205	0.124979
$405$	0	0
$406$	−45.2947	−2.24794
$407$	10.9152	0.541045
$408$	−31.5086	−1.55991
$409$	−22.5214	−1.11361	−0.556807	−	0.830642i	$-0.687974\pi$
$409$	−22.5214	−1.11361	−0.556807	+	0.830642i	$0.687974\pi$
$410$	0	0
$411$	3.94176	0.194433
$412$	57.9777	2.85636
$413$	−12.1217	−0.596468
$414$	−0.744872	−0.0366085
$415$	0	0
$416$	−4.88863	−0.239685
$417$	28.7123	1.40605
$418$	−29.7632	−1.45576
$419$	20.2464	0.989100	0.494550	−	0.869149i	$-0.335333\pi$
$419$	20.2464	0.989100	0.494550	+	0.869149i	$0.335333\pi$
$420$	0	0
$421$	−18.8517	−0.918778	−0.459389	−	0.888235i	$-0.651932\pi$
$421$	−18.8517	−0.918778	−0.459389	+	0.888235i	$0.651932\pi$
$422$	−1.25616	−0.0611491
$423$	0.685985	0.0333537
$424$	−12.4295	−0.603629
$425$	0	0
$426$	−27.6097	−1.33769
$427$	−22.7136	−1.09919
$428$	−12.0023	−0.580152
$429$	6.52977	0.315260
$430$	0	0
$431$	−29.1744	−1.40528	−0.702640	−	0.711546i	$-0.747995\pi$
$431$	−29.1744	−1.40528	−0.702640	+	0.711546i	$0.747995\pi$
$432$	−6.68325	−0.321548
$433$	29.6333	1.42408	0.712042	−	0.702137i	$-0.247770\pi$
$433$	29.6333	1.42408	0.712042	+	0.702137i	$0.247770\pi$
$434$	19.8203	0.951403
$435$	0	0
$436$	42.3318	2.02733
$437$	−5.19541	−0.248530
$438$	−36.7589	−1.75641
$439$	1.34182	0.0640415	0.0320208	−	0.999487i	$-0.489806\pi$
$439$	1.34182	0.0640415	0.0320208	+	0.999487i	$0.489806\pi$
$440$	0	0
$441$	2.80308	0.133480
$442$	14.1356	0.672363
$443$	1.84538	0.0876767	0.0438384	−	0.999039i	$-0.486041\pi$
$443$	1.84538	0.0876767	0.0438384	+	0.999039i	$0.486041\pi$
$444$	−23.6621	−1.12295
$445$	0	0
$446$	−60.5179	−2.86560
$447$	−16.8440	−0.796692
$448$	−50.5057	−2.38617
$449$	28.4462	1.34246	0.671230	−	0.741249i	$-0.265766\pi$
$449$	28.4462	1.34246	0.671230	+	0.741249i	$0.265766\pi$
$450$	0	0
$451$	−7.92493	−0.373170
$452$	27.8830	1.31150
$453$	22.6489	1.06414
$454$	−26.5972	−1.24827
$455$	0	0
$456$	27.8646	1.30488
$457$	−38.5520	−1.80339	−0.901694	−	0.432374i	$-0.857676\pi$
$457$	−38.5520	−1.80339	−0.901694	+	0.432374i	$0.857676\pi$
$458$	−42.5765	−1.98947
$459$	−24.1387	−1.12670
$460$	0	0
$461$	−34.8914	−1.62505	−0.812527	−	0.582924i	$-0.801908\pi$
$461$	−34.8914	−1.62505	−0.812527	+	0.582924i	$0.801908\pi$
$462$	52.2932	2.43290
$463$	−16.8688	−0.783959	−0.391979	−	0.919974i	$-0.628210\pi$
$463$	−16.8688	−0.783959	−0.391979	+	0.919974i	$0.628210\pi$
$464$	6.20574	0.288094
$465$	0	0
$466$	21.3296	0.988075
$467$	15.6603	0.724672	0.362336	−	0.932048i	$-0.381979\pi$
$467$	15.6603	0.724672	0.362336	+	0.932048i	$0.381979\pi$
$468$	−1.14292	−0.0528317
$469$	−49.7198	−2.29585
$470$	0	0
$471$	−3.67725	−0.169439
$472$	10.3098	0.474547
$473$	−17.0801	−0.785342
$474$	0.602651	0.0276807
$475$	0	0
$476$	72.1904	3.30884
$477$	0.916899	0.0419819
$478$	−45.5707	−2.08436
$479$	−6.05631	−0.276720	−0.138360	−	0.990382i	$-0.544183\pi$
$479$	−6.05631	−0.276720	−0.138360	+	0.990382i	$0.544183\pi$
$480$	0	0
$481$	4.58447	0.209034
$482$	−2.34953	−0.107018
$483$	9.12821	0.415348
$484$	−8.42791	−0.383087
$485$	0	0
$486$	6.41579	0.291026
$487$	−0.712845	−0.0323021	−0.0161510	−	0.999870i	$-0.505141\pi$
$487$	−0.712845	−0.0323021	−0.0161510	+	0.999870i	$0.505141\pi$
$488$	19.3185	0.874506
$489$	−17.7717	−0.803662
$490$	0	0
$491$	14.6101	0.659346	0.329673	−	0.944095i	$-0.393062\pi$
$491$	14.6101	0.659346	0.329673	+	0.944095i	$0.393062\pi$
$492$	17.1798	0.774526
$493$	22.4140	1.00947
$494$	−12.5008	−0.562438
$495$	0	0
$496$	−2.71553	−0.121931
$497$	27.3188	1.22542
$498$	−61.4546	−2.75385
$499$	−13.3383	−0.597105	−0.298553	−	0.954393i	$-0.596504\pi$
$499$	−13.3383	−0.597105	−0.298553	+	0.954393i	$0.596504\pi$
$500$	0	0
$501$	31.6417	1.41364
$502$	−27.5183	−1.22820
$503$	−42.5917	−1.89907	−0.949535	−	0.313660i	$-0.898445\pi$
$503$	−42.5917	−1.89907	−0.949535	+	0.313660i	$0.898445\pi$
$504$	−3.95289	−0.176076
$505$	0	0
$506$	8.29278	0.368659
$507$	−20.7421	−0.921191
$508$	3.27353	0.145239
$509$	−26.1139	−1.15748	−0.578738	−	0.815513i	$-0.696455\pi$
$509$	−26.1139	−1.15748	−0.578738	+	0.815513i	$0.696455\pi$
$510$	0	0
$511$	36.3716	1.60898
$512$	15.0220	0.663885
$513$	21.3470	0.942492
$514$	21.8901	0.965530
$515$	0	0
$516$	37.0265	1.63000
$517$	−7.63718	−0.335883
$518$	36.7144	1.61314
$519$	15.8601	0.696181
$520$	0	0
$521$	−12.7365	−0.557996	−0.278998	−	0.960292i	$-0.590002\pi$
$521$	−12.7365	−0.557996	−0.278998	+	0.960292i	$0.590002\pi$
$522$	−2.84187	−0.124385
$523$	43.1501	1.88682	0.943410	−	0.331628i	$-0.107598\pi$
$523$	43.1501	1.88682	0.943410	+	0.331628i	$0.107598\pi$
$524$	46.1853	2.01762
$525$	0	0
$526$	−8.61349	−0.375566
$527$	−9.80801	−0.427244
$528$	−7.16458	−0.311798
$529$	−21.5524	−0.937062
$530$	0	0
$531$	−0.760534	−0.0330044
$532$	−63.8414	−2.76788
$533$	−3.32855	−0.144175
$534$	−68.5806	−2.96777
$535$	0	0
$536$	42.2880	1.82656
$537$	−1.05996	−0.0457405
$538$	48.6127	2.09584
$539$	−31.2072	−1.34419
$540$	0	0
$541$	36.6747	1.57677	0.788385	−	0.615182i	$-0.210918\pi$
$541$	36.6747	1.57677	0.788385	+	0.615182i	$0.210918\pi$
$542$	−36.0504	−1.54850
$543$	16.6012	0.712428
$544$	19.3734	0.830628
$545$	0	0
$546$	21.9636	0.939956
$547$	46.1794	1.97449	0.987244	−	0.159213i	$-0.0508956\pi$
$547$	46.1794	1.97449	0.987244	+	0.159213i	$0.0508956\pi$
$548$	7.68119	0.328124
$549$	−1.42509	−0.0608213
$550$	0	0
$551$	−19.8217	−0.844435
$552$	−7.76378	−0.330449
$553$	−0.596302	−0.0253573
$554$	72.2498	3.06960
$555$	0	0
$556$	55.9508	2.37284
$557$	16.8538	0.714119	0.357060	−	0.934082i	$-0.383779\pi$
$557$	16.8538	0.714119	0.357060	+	0.934082i	$0.383779\pi$
$558$	1.24356	0.0526440
$559$	−7.17379	−0.303419
$560$	0	0
$561$	−25.8771	−1.09253
$562$	−20.2634	−0.854759
$563$	−28.0349	−1.18153	−0.590766	−	0.806843i	$-0.701174\pi$
$563$	−28.0349	−1.18153	−0.590766	+	0.806843i	$0.701174\pi$
$564$	16.5560	0.697135
$565$	0	0
$566$	42.7068	1.79510
$567$	−40.8260	−1.71453
$568$	−23.2354	−0.974934
$569$	17.7872	0.745678	0.372839	−	0.927896i	$-0.378384\pi$
$569$	17.7872	0.745678	0.372839	+	0.927896i	$0.378384\pi$
$570$	0	0
$571$	2.83049	0.118453	0.0592263	−	0.998245i	$-0.481137\pi$
$571$	2.83049	0.118453	0.0592263	+	0.998245i	$0.481137\pi$
$572$	12.7244	0.532032
$573$	−25.7106	−1.07408
$574$	−26.6564	−1.11262
$575$	0	0
$576$	−3.16881	−0.132034
$577$	4.96422	0.206663	0.103332	−	0.994647i	$-0.467050\pi$
$577$	4.96422	0.206663	0.103332	+	0.994647i	$0.467050\pi$
$578$	−16.0767	−0.668704
$579$	12.2262	0.508102
$580$	0	0
$581$	60.8071	2.52270
$582$	−1.60759	−0.0666366
$583$	−10.2080	−0.422772
$584$	−30.9350	−1.28010
$585$	0	0
$586$	−72.6513	−3.00120
$587$	−10.7142	−0.442222	−0.221111	−	0.975249i	$-0.570968\pi$
$587$	−10.7142	−0.442222	−0.221111	+	0.975249i	$0.570968\pi$
$588$	67.6515	2.78990
$589$	8.67369	0.357393
$590$	0	0
$591$	11.2744	0.463768
$592$	−5.03017	−0.206739
$593$	−0.120848	−0.00496264	−0.00248132	−	0.999997i	$-0.500790\pi$
$593$	−0.120848	−0.00496264	−0.00248132	+	0.999997i	$0.500790\pi$
$594$	−34.0735	−1.39805
$595$	0	0
$596$	−32.8233	−1.34449
$597$	−36.5069	−1.49413
$598$	3.48305	0.142432
$599$	−8.45587	−0.345498	−0.172749	−	0.984966i	$-0.555265\pi$
$599$	−8.45587	−0.345498	−0.172749	+	0.984966i	$0.555265\pi$
$600$	0	0
$601$	43.5195	1.77520	0.887598	−	0.460619i	$-0.152373\pi$
$601$	43.5195	1.77520	0.887598	+	0.460619i	$0.152373\pi$
$602$	−57.4508	−2.34152
$603$	−3.11950	−0.127036
$604$	44.1352	1.79584
$605$	0	0
$606$	−3.02880	−0.123037
$607$	−29.7432	−1.20724	−0.603619	−	0.797273i	$-0.706275\pi$
$607$	−29.7432	−1.20724	−0.603619	+	0.797273i	$0.706275\pi$
$608$	−17.1328	−0.694828
$609$	34.8263	1.41123
$610$	0	0
$611$	−3.20769	−0.129769
$612$	4.52935	0.183088
$613$	−25.1062	−1.01403	−0.507015	−	0.861937i	$-0.669251\pi$
$613$	−25.1062	−1.01403	−0.507015	+	0.861937i	$0.669251\pi$
$614$	−11.0210	−0.444773
$615$	0	0
$616$	44.0081	1.77314
$617$	26.7011	1.07495	0.537474	−	0.843280i	$-0.319379\pi$
$617$	26.7011	1.07495	0.537474	+	0.843280i	$0.319379\pi$
$618$	−69.9044	−2.81197
$619$	−37.4624	−1.50574	−0.752871	−	0.658168i	$-0.771332\pi$
$619$	−37.4624	−1.50574	−0.752871	+	0.658168i	$0.771332\pi$
$620$	0	0
$621$	−5.94782	−0.238678
$622$	58.6794	2.35283
$623$	67.8581	2.71868
$624$	−3.00919	−0.120464
$625$	0	0
$626$	−67.9867	−2.71730
$627$	22.8844	0.913915
$628$	−7.16575	−0.285944
$629$	−18.1680	−0.724407
$630$	0	0
$631$	4.12528	0.164225	0.0821124	−	0.996623i	$-0.473833\pi$
$631$	4.12528	0.164225	0.0821124	+	0.996623i	$0.473833\pi$
$632$	0.507171	0.0201742
$633$	0.965843	0.0383888
$634$	60.5119	2.40323
$635$	0	0
$636$	22.1291	0.877475
$637$	−13.1073	−0.519330
$638$	31.6390	1.25260
$639$	1.71403	0.0678060
$640$	0	0
$641$	−38.1607	−1.50726	−0.753628	−	0.657301i	$-0.771698\pi$
$641$	−38.1607	−1.50726	−0.753628	+	0.657301i	$0.771698\pi$
$642$	14.4713	0.571136
$643$	29.0507	1.14565	0.572823	−	0.819679i	$-0.305848\pi$
$643$	29.0507	1.14565	0.572823	+	0.819679i	$0.305848\pi$
$644$	17.7879	0.700940
$645$	0	0
$646$	49.5401	1.94913
$647$	−0.0989482	−0.00389005	−0.00194503	−	0.999998i	$-0.500619\pi$
$647$	−0.0989482	−0.00389005	−0.00194503	+	0.999998i	$0.500619\pi$
$648$	34.7236	1.36407
$649$	8.46715	0.332365
$650$	0	0
$651$	−15.2395	−0.597282
$652$	−34.6311	−1.35626
$653$	2.26584	0.0886693	0.0443347	−	0.999017i	$-0.485883\pi$
$653$	2.26584	0.0886693	0.0443347	+	0.999017i	$0.485883\pi$
$654$	−51.0400	−1.99582
$655$	0	0
$656$	3.65214	0.142592
$657$	2.28202	0.0890299
$658$	−25.6886	−1.00144
$659$	35.8795	1.39767	0.698833	−	0.715285i	$-0.253703\pi$
$659$	35.8795	1.39767	0.698833	+	0.715285i	$0.253703\pi$
$660$	0	0
$661$	−1.77315	−0.0689677	−0.0344839	−	0.999405i	$-0.510979\pi$
$661$	−1.77315	−0.0689677	−0.0344839	+	0.999405i	$0.510979\pi$
$662$	67.6118	2.62781
$663$	−10.8686	−0.422103
$664$	−51.7181	−2.00705
$665$	0	0
$666$	2.30353	0.0892599
$667$	5.52285	0.213846
$668$	61.6591	2.38566
$669$	46.5312	1.79900
$670$	0	0
$671$	15.8657	0.612490
$672$	30.1020	1.16121
$673$	12.3856	0.477432	0.238716	−	0.971089i	$-0.423274\pi$
$673$	12.3856	0.477432	0.238716	+	0.971089i	$0.423274\pi$
$674$	81.3276	3.13262
$675$	0	0
$676$	−40.4196	−1.55460
$677$	−3.47705	−0.133634	−0.0668169	−	0.997765i	$-0.521284\pi$
$677$	−3.47705	−0.133634	−0.0668169	+	0.997765i	$0.521284\pi$
$678$	−33.6188	−1.29112
$679$	1.59065	0.0610435
$680$	0	0
$681$	20.4501	0.783651
$682$	−13.8447	−0.530142
$683$	−7.18059	−0.274758	−0.137379	−	0.990519i	$-0.543868\pi$
$683$	−7.18059	−0.274758	−0.137379	+	0.990519i	$0.543868\pi$
$684$	−4.00552	−0.153155
$685$	0	0
$686$	−35.8968	−1.37054
$687$	32.7364	1.24897
$688$	7.87121	0.300087
$689$	−4.28745	−0.163339
$690$	0	0
$691$	23.9444	0.910888	0.455444	−	0.890264i	$-0.349481\pi$
$691$	23.9444	0.910888	0.455444	+	0.890264i	$0.349481\pi$
$692$	30.9061	1.17487
$693$	−3.24640	−0.123320
$694$	21.4797	0.815359
$695$	0	0
$696$	−29.6207	−1.12277
$697$	13.1909	0.499640
$698$	61.7313	2.33656
$699$	−16.4000	−0.620304
$700$	0	0
$701$	−26.7788	−1.01142	−0.505711	−	0.862703i	$-0.668770\pi$
$701$	−26.7788	−1.01142	−0.505711	+	0.862703i	$0.668770\pi$
$702$	−14.3112	−0.540142
$703$	16.0669	0.605974
$704$	35.2789	1.32962
$705$	0	0
$706$	−37.1238	−1.39717
$707$	2.99689	0.112710
$708$	−18.3553	−0.689833
$709$	11.6778	0.438570	0.219285	−	0.975661i	$-0.429628\pi$
$709$	11.6778	0.438570	0.219285	+	0.975661i	$0.429628\pi$
$710$	0	0
$711$	−0.0374130	−0.00140310
$712$	−57.7151	−2.16296
$713$	−2.41671	−0.0905066
$714$	−87.0408	−3.25742
$715$	0	0
$716$	−2.06551	−0.0771916
$717$	35.0386	1.30854
$718$	−53.7123	−2.00453
$719$	44.4738	1.65859	0.829296	−	0.558810i	$-0.188742\pi$
$719$	44.4738	1.65859	0.829296	+	0.558810i	$0.188742\pi$
$720$	0	0
$721$	69.1679	2.57595
$722$	0.830443	0.0309059
$723$	1.80652	0.0671850
$724$	32.3503	1.20229
$725$	0	0
$726$	10.1616	0.377133
$727$	−44.7578	−1.65998	−0.829988	−	0.557781i	$-0.811653\pi$
$727$	−44.7578	−1.65998	−0.829988	+	0.557781i	$0.811653\pi$
$728$	18.4838	0.685056
$729$	24.2302	0.897415
$730$	0	0
$731$	28.4294	1.05150
$732$	−34.3941	−1.27124
$733$	43.9820	1.62451	0.812256	−	0.583301i	$-0.198239\pi$
$733$	43.9820	1.62451	0.812256	+	0.583301i	$0.198239\pi$
$734$	−84.4093	−3.11560
$735$	0	0
$736$	4.77365	0.175959
$737$	34.7299	1.27929
$738$	−1.67247	−0.0615645
$739$	−0.709090	−0.0260843	−0.0130421	−	0.999915i	$-0.504152\pi$
$739$	−0.709090	−0.0260843	−0.0130421	+	0.999915i	$0.504152\pi$
$740$	0	0
$741$	9.61166	0.353093
$742$	−34.3357	−1.26050
$743$	−14.4204	−0.529035	−0.264517	−	0.964381i	$-0.585213\pi$
$743$	−14.4204	−0.529035	−0.264517	+	0.964381i	$0.585213\pi$
$744$	12.9616	0.475194
$745$	0	0
$746$	39.6250	1.45077
$747$	3.81514	0.139589
$748$	−50.4260	−1.84376
$749$	−14.3188	−0.523199
$750$	0	0
$751$	3.00612	0.109695	0.0548475	−	0.998495i	$-0.482533\pi$
$751$	3.00612	0.109695	0.0548475	+	0.998495i	$0.482533\pi$
$752$	3.51954	0.128344
$753$	21.1584	0.771054
$754$	13.2887	0.483945
$755$	0	0
$756$	−73.0871	−2.65815
$757$	44.5404	1.61885	0.809424	−	0.587225i	$-0.199780\pi$
$757$	44.5404	1.61885	0.809424	+	0.587225i	$0.199780\pi$
$758$	52.4756	1.90600
$759$	−6.37618	−0.231441
$760$	0	0
$761$	33.3531	1.20905	0.604525	−	0.796586i	$-0.293363\pi$
$761$	33.3531	1.20905	0.604525	+	0.796586i	$0.293363\pi$
$762$	−3.94693	−0.142982
$763$	50.5023	1.82830
$764$	−50.1014	−1.81261
$765$	0	0
$766$	−26.4730	−0.956508
$767$	3.55628	0.128410
$768$	−42.7975	−1.54432
$769$	1.26058	0.0454578	0.0227289	−	0.999742i	$-0.492765\pi$
$769$	1.26058	0.0454578	0.0227289	+	0.999742i	$0.492765\pi$
$770$	0	0
$771$	−16.8309	−0.606151
$772$	23.8248	0.857472
$773$	14.8554	0.534312	0.267156	−	0.963653i	$-0.413916\pi$
$773$	14.8554	0.534312	0.267156	+	0.963653i	$0.413916\pi$
$774$	−3.60456	−0.129563
$775$	0	0
$776$	−1.35289	−0.0485659
$777$	−28.2291	−1.01271
$778$	80.0625	2.87038
$779$	−11.6653	−0.417953
$780$	0	0
$781$	−19.0826	−0.682828
$782$	−13.8031	−0.493599
$783$	−22.6924	−0.810959
$784$	14.3816	0.513628
$785$	0	0
$786$	−55.6862	−1.98626
$787$	26.3469	0.939165	0.469583	−	0.882889i	$-0.344404\pi$
$787$	26.3469	0.939165	0.469583	+	0.882889i	$0.344404\pi$
$788$	21.9701	0.782654
$789$	6.62277	0.235777
$790$	0	0
$791$	33.2646	1.18275
$792$	2.76115	0.0981131
$793$	6.66376	0.236637
$794$	−57.5887	−2.04375
$795$	0	0
$796$	−71.1399	−2.52149
$797$	−28.3328	−1.00360	−0.501799	−	0.864984i	$-0.667328\pi$
$797$	−28.3328	−1.00360	−0.501799	+	0.864984i	$0.667328\pi$
$798$	76.9743	2.72486
$799$	12.7119	0.449715
$800$	0	0
$801$	4.25753	0.150433
$802$	−14.5157	−0.512567
$803$	−25.4061	−0.896560
$804$	−75.2883	−2.65521
$805$	0	0
$806$	−5.81492	−0.204822
$807$	−37.3775	−1.31575
$808$	−2.54894	−0.0896713
$809$	36.9035	1.29746	0.648729	−	0.761019i	$-0.275301\pi$
$809$	36.9035	1.29746	0.648729	+	0.761019i	$0.275301\pi$
$810$	0	0
$811$	−4.10494	−0.144144	−0.0720720	−	0.997399i	$-0.522961\pi$
$811$	−4.10494	−0.144144	−0.0720720	+	0.997399i	$0.522961\pi$
$812$	67.8650	2.38159
$813$	27.7185	0.972131
$814$	−25.6455	−0.898876
$815$	0	0
$816$	11.9253	0.417468
$817$	−25.1414	−0.879588
$818$	52.9148	1.85012
$819$	−1.36352	−0.0476452
$820$	0	0
$821$	50.9887	1.77952	0.889758	−	0.456432i	$-0.150873\pi$
$821$	50.9887	1.77952	0.889758	+	0.456432i	$0.150873\pi$
$822$	−9.26129	−0.323025
$823$	−22.9584	−0.800281	−0.400141	−	0.916454i	$-0.631039\pi$
$823$	−22.9584	−0.800281	−0.400141	+	0.916454i	$0.631039\pi$
$824$	−58.8291	−2.04941
$825$	0	0
$826$	28.4802	0.990954
$827$	−23.4314	−0.814790	−0.407395	−	0.913252i	$-0.633563\pi$
$827$	−23.4314	−0.814790	−0.407395	+	0.913252i	$0.633563\pi$
$828$	1.11604	0.0387851
$829$	23.6823	0.822519	0.411260	−	0.911518i	$-0.365089\pi$
$829$	23.6823	0.822519	0.411260	+	0.911518i	$0.365089\pi$
$830$	0	0
$831$	−55.5517	−1.92707
$832$	14.8175	0.513704
$833$	51.9436	1.79974
$834$	−67.4605	−2.33597
$835$	0	0
$836$	44.5941	1.54232
$837$	9.92983	0.343225
$838$	−47.5695	−1.64326
$839$	36.5159	1.26067	0.630334	−	0.776324i	$-0.282918\pi$
$839$	36.5159	1.26067	0.630334	+	0.776324i	$0.282918\pi$
$840$	0	0
$841$	−7.92899	−0.273414
$842$	44.2928	1.52643
$843$	15.5802	0.536610
$844$	1.88211	0.0647849
$845$	0	0
$846$	−1.61174	−0.0554129
$847$	−10.0546	−0.345479
$848$	4.70427	0.161545
$849$	−32.8365	−1.12695
$850$	0	0
$851$	−4.47664	−0.153457
$852$	41.3676	1.41723
$853$	−21.5309	−0.737204	−0.368602	−	0.929587i	$-0.620163\pi$
$853$	−21.5309	−0.737204	−0.368602	+	0.929587i	$0.620163\pi$
$854$	53.3662	1.82615
$855$	0	0
$856$	12.1785	0.416254
$857$	6.40870	0.218917	0.109458	−	0.993991i	$-0.465088\pi$
$857$	6.40870	0.218917	0.109458	+	0.993991i	$0.465088\pi$
$858$	−15.3419	−0.523764
$859$	35.1678	1.19991	0.599955	−	0.800034i	$-0.295185\pi$
$859$	35.1678	1.19991	0.599955	+	0.800034i	$0.295185\pi$
$860$	0	0
$861$	20.4957	0.698491
$862$	68.5461	2.33469
$863$	−15.3249	−0.521664	−0.260832	−	0.965384i	$-0.583997\pi$
$863$	−15.3249	−0.521664	−0.260832	+	0.965384i	$0.583997\pi$
$864$	−19.6140	−0.667283
$865$	0	0
$866$	−69.6243	−2.36593
$867$	12.3611	0.419806
$868$	−29.6967	−1.00797
$869$	0.416525	0.0141297
$870$	0	0
$871$	14.5869	0.494258
$872$	−42.9535	−1.45459
$873$	0.0998001	0.00337772
$874$	12.2068	0.412901
$875$	0	0
$876$	55.0757	1.86084
$877$	−13.9779	−0.472000	−0.236000	−	0.971753i	$-0.575837\pi$
$877$	−13.9779	−0.472000	−0.236000	+	0.971753i	$0.575837\pi$
$878$	−3.15265	−0.106397
$879$	55.8604	1.88412
$880$	0	0
$881$	29.6558	0.999129	0.499565	−	0.866277i	$-0.333493\pi$
$881$	29.6558	0.999129	0.499565	+	0.866277i	$0.333493\pi$
$882$	−6.58593	−0.221760
$883$	38.5686	1.29794	0.648968	−	0.760815i	$-0.275201\pi$
$883$	38.5686	1.29794	0.648968	+	0.760815i	$0.275201\pi$
$884$	−21.1794	−0.712340
$885$	0	0
$886$	−4.33578	−0.145663
$887$	−29.6803	−0.996567	−0.498283	−	0.867014i	$-0.666036\pi$
$887$	−29.6803	−0.996567	−0.498283	+	0.867014i	$0.666036\pi$
$888$	24.0096	0.805709
$889$	3.90535	0.130981
$890$	0	0
$891$	28.5176	0.955374
$892$	90.6739	3.03599
$893$	−11.2418	−0.376191
$894$	39.5754	1.32360
$895$	0	0
$896$	85.3387	2.85097
$897$	−2.67806	−0.0894177
$898$	−66.8353	−2.23032
$899$	−9.22035	−0.307516
$900$	0	0
$901$	16.9910	0.566051
$902$	18.6199	0.619974
$903$	44.1729	1.46998
$904$	−28.2924	−0.940992
$905$	0	0
$906$	−53.2143	−1.76793
$907$	−5.58274	−0.185372	−0.0926859	−	0.995695i	$-0.529545\pi$
$907$	−5.58274	−0.185372	−0.0926859	+	0.995695i	$0.529545\pi$
$908$	39.8505	1.32249
$909$	0.188030	0.00623657
$910$	0	0
$911$	−14.7056	−0.487220	−0.243610	−	0.969873i	$-0.578332\pi$
$911$	−14.7056	−0.487220	−0.243610	+	0.969873i	$0.578332\pi$
$912$	−10.5461	−0.349216
$913$	−42.4746	−1.40570
$914$	90.5793	2.99610
$915$	0	0
$916$	63.7924	2.10776
$917$	55.0995	1.81955
$918$	56.7146	1.87186
$919$	33.3834	1.10122	0.550608	−	0.834764i	$-0.314396\pi$
$919$	33.3834	1.10122	0.550608	+	0.834764i	$0.314396\pi$
$920$	0	0
$921$	8.47389	0.279224
$922$	81.9784	2.69981
$923$	−8.01486	−0.263812
$924$	−78.3508	−2.57755
$925$	0	0
$926$	39.6337	1.30245
$927$	4.33971	0.142535
$928$	18.2126	0.597859
$929$	31.5306	1.03448	0.517242	−	0.855839i	$-0.326959\pi$
$929$	31.5306	1.03448	0.517242	+	0.855839i	$0.326959\pi$
$930$	0	0
$931$	−45.9362	−1.50550
$932$	−31.9581	−1.04682
$933$	−45.1176	−1.47708
$934$	−36.7943	−1.20395
$935$	0	0
$936$	1.15971	0.0379062
$937$	−14.3752	−0.469616	−0.234808	−	0.972042i	$-0.575446\pi$
$937$	−14.3752	−0.469616	−0.234808	+	0.972042i	$0.575446\pi$
$938$	116.818	3.81425
$939$	52.2739	1.70589
$940$	0	0
$941$	0.351405	0.0114555	0.00572773	−	0.999984i	$-0.498177\pi$
$941$	0.351405	0.0114555	0.00572773	+	0.999984i	$0.498177\pi$
$942$	8.63982	0.281501
$943$	3.25026	0.105843
$944$	−3.90202	−0.127000
$945$	0	0
$946$	40.1302	1.30474
$947$	14.2767	0.463932	0.231966	−	0.972724i	$-0.425484\pi$
$947$	14.2767	0.463932	0.231966	+	0.972724i	$0.425484\pi$
$948$	−0.902952	−0.0293265
$949$	−10.6708	−0.346388
$950$	0	0
$951$	−46.5266	−1.50873
$952$	−73.2505	−2.37406
$953$	−27.3746	−0.886752	−0.443376	−	0.896336i	$-0.646219\pi$
$953$	−27.3746	−0.886752	−0.443376	+	0.896336i	$0.646219\pi$
$954$	−2.15428	−0.0697475
$955$	0	0
$956$	68.2786	2.20829
$957$	−24.3267	−0.786370
$958$	14.2295	0.459734
$959$	9.16372	0.295912
$960$	0	0
$961$	−26.9653	−0.869849
$962$	−10.7714	−0.347283
$963$	−0.898388	−0.0289501
$964$	3.52030	0.113381
$965$	0	0
$966$	−21.4470	−0.690047
$967$	−13.0865	−0.420834	−0.210417	−	0.977612i	$-0.567482\pi$
$967$	−13.0865	−0.420834	−0.210417	+	0.977612i	$0.567482\pi$
$968$	8.55168	0.274861
$969$	−38.0905	−1.22364
$970$	0	0
$971$	23.6548	0.759118	0.379559	−	0.925167i	$-0.376076\pi$
$971$	23.6548	0.759118	0.379559	+	0.925167i	$0.376076\pi$
$972$	−9.61277	−0.308330
$973$	66.7498	2.13990
$974$	1.67485	0.0536657
$975$	0	0
$976$	−7.31160	−0.234039
$977$	41.5189	1.32831	0.664154	−	0.747596i	$-0.268792\pi$
$977$	41.5189	1.32831	0.664154	+	0.747596i	$0.268792\pi$
$978$	41.7551	1.33518
$979$	−47.3998	−1.51490
$980$	0	0
$981$	3.16860	0.101166
$982$	−34.3270	−1.09542
$983$	−60.4544	−1.92820	−0.964098	−	0.265546i	$-0.914448\pi$
$983$	−60.4544	−1.92820	−0.964098	+	0.265546i	$0.914448\pi$
$984$	−17.4321	−0.555715
$985$	0	0
$986$	−52.6623	−1.67711
$987$	19.7515	0.628697
$988$	18.7299	0.595879
$989$	7.00506	0.222748
$990$	0	0
$991$	−40.3538	−1.28188	−0.640941	−	0.767590i	$-0.721456\pi$
$991$	−40.3538	−1.28188	−0.640941	+	0.767590i	$0.721456\pi$
$992$	−7.96956	−0.253034
$993$	−51.9856	−1.64971
$994$	−64.1864	−2.03587
$995$	0	0
$996$	92.0773	2.91758
$997$	6.41705	0.203230	0.101615	−	0.994824i	$-0.467599\pi$
$997$	6.41705	0.203230	0.101615	+	0.994824i	$0.467599\pi$
$998$	31.3388	0.992013
$999$	18.3937	0.581951

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6025.2.a.e.1.1		5
5.4	even	2		1205.2.a.a.1.5	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1205.2.a.a.1.5	✓	5	5.4	even	2
6025.2.a.e.1.1		5	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-2.34953 q^{2} +1.80652 q^{3} +3.52030 q^{4} -4.24447 q^{6} +4.19975 q^{7} -3.57200 q^{8} +0.263500 q^{9} +O(q^{10})\)	\(q-2.34953 q^{2} +1.80652 q^{3} +3.52030 q^{4} -4.24447 q^{6} +4.19975 q^{7} -3.57200 q^{8} +0.263500 q^{9} -2.93358 q^{11} +6.35948 q^{12} -1.23213 q^{13} -9.86745 q^{14} +1.35192 q^{16} +4.88288 q^{17} -0.619101 q^{18} -4.31817 q^{19} +7.58691 q^{21} +6.89255 q^{22} +1.20315 q^{23} -6.45287 q^{24} +2.89493 q^{26} -4.94353 q^{27} +14.7844 q^{28} +4.59032 q^{29} -2.00865 q^{31} +3.96762 q^{32} -5.29956 q^{33} -11.4725 q^{34} +0.927598 q^{36} -3.72076 q^{37} +10.1457 q^{38} -2.22587 q^{39} +2.70145 q^{41} -17.8257 q^{42} +5.82225 q^{43} -10.3271 q^{44} -2.82684 q^{46} +2.60336 q^{47} +2.44226 q^{48} +10.6379 q^{49} +8.82100 q^{51} -4.33748 q^{52} +3.47970 q^{53} +11.6150 q^{54} -15.0015 q^{56} -7.80083 q^{57} -10.7851 q^{58} -2.88628 q^{59} -5.40831 q^{61} +4.71939 q^{62} +1.10663 q^{63} -12.0259 q^{64} +12.4515 q^{66} -11.8387 q^{67} +17.1892 q^{68} +2.17351 q^{69} +6.50487 q^{71} -0.941220 q^{72} +8.66042 q^{73} +8.74205 q^{74} -15.2012 q^{76} -12.3203 q^{77} +5.22975 q^{78} -0.141985 q^{79} -9.72107 q^{81} -6.34715 q^{82} +14.4788 q^{83} +26.7082 q^{84} -13.6796 q^{86} +8.29248 q^{87} +10.4788 q^{88} +16.1576 q^{89} -5.17465 q^{91} +4.23546 q^{92} -3.62866 q^{93} -6.11669 q^{94} +7.16756 q^{96} +0.378748 q^{97} -24.9941 q^{98} -0.772998 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + q^{2} + 5 q^{3} + 3 q^{4} - 8 q^{6} + 10 q^{7} + 6 q^{9}+O(q^{10}) \) 5 * q + q^2 + 5 * q^3 + 3 * q^4 - 8 * q^6 + 10 * q^7 + 6 * q^9	\( 5 q + q^{2} + 5 q^{3} + 3 q^{4} - 8 q^{6} + 10 q^{7} + 6 q^{9} - 3 q^{11} - 8 q^{12} + q^{13} - q^{14} + 15 q^{16} + 5 q^{17} - 4 q^{18} + 3 q^{19} + 11 q^{21} + 13 q^{22} + 8 q^{23} - 14 q^{24} + 14 q^{26} + 14 q^{27} + 17 q^{28} + 9 q^{29} - 16 q^{31} + 16 q^{32} - 23 q^{33} - 10 q^{34} - 17 q^{36} - 7 q^{37} + 22 q^{38} - 19 q^{39} + 9 q^{41} - 17 q^{42} + 32 q^{43} - 8 q^{44} + 5 q^{46} + 7 q^{47} + 6 q^{48} + 9 q^{49} - 8 q^{51} + 10 q^{52} + 32 q^{53} + 32 q^{54} - 18 q^{56} - 3 q^{57} - 11 q^{58} - 8 q^{59} - 12 q^{61} - 17 q^{62} + 11 q^{63} - 16 q^{64} + 15 q^{66} + 5 q^{67} + 2 q^{68} + 7 q^{69} - 11 q^{71} - 7 q^{72} + 29 q^{73} + 10 q^{74} - 8 q^{76} + 5 q^{77} - 2 q^{78} + 16 q^{79} - 15 q^{81} + 2 q^{82} + 10 q^{83} + 5 q^{84} + 14 q^{86} + 37 q^{87} - 10 q^{88} + 9 q^{89} + 12 q^{91} + 25 q^{92} - 15 q^{93} - 11 q^{94} - 3 q^{96} + 43 q^{97} - 30 q^{98} - 30 q^{99}+O(q^{100}) \) 5 * q + q^2 + 5 * q^3 + 3 * q^4 - 8 * q^6 + 10 * q^7 + 6 * q^9 - 3 * q^11 - 8 * q^12 + q^13 - q^14 + 15 * q^16 + 5 * q^17 - 4 * q^18 + 3 * q^19 + 11 * q^21 + 13 * q^22 + 8 * q^23 - 14 * q^24 + 14 * q^26 + 14 * q^27 + 17 * q^28 + 9 * q^29 - 16 * q^31 + 16 * q^32 - 23 * q^33 - 10 * q^34 - 17 * q^36 - 7 * q^37 + 22 * q^38 - 19 * q^39 + 9 * q^41 - 17 * q^42 + 32 * q^43 - 8 * q^44 + 5 * q^46 + 7 * q^47 + 6 * q^48 + 9 * q^49 - 8 * q^51 + 10 * q^52 + 32 * q^53 + 32 * q^54 - 18 * q^56 - 3 * q^57 - 11 * q^58 - 8 * q^59 - 12 * q^61 - 17 * q^62 + 11 * q^63 - 16 * q^64 + 15 * q^66 + 5 * q^67 + 2 * q^68 + 7 * q^69 - 11 * q^71 - 7 * q^72 + 29 * q^73 + 10 * q^74 - 8 * q^76 + 5 * q^77 - 2 * q^78 + 16 * q^79 - 15 * q^81 + 2 * q^82 + 10 * q^83 + 5 * q^84 + 14 * q^86 + 37 * q^87 - 10 * q^88 + 9 * q^89 + 12 * q^91 + 25 * q^92 - 15 * q^93 - 11 * q^94 - 3 * q^96 + 43 * q^97 - 30 * q^98 - 30 * q^99

Introduction

L-functions

Modular forms

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Database

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