LMFDB - Embedded newform 6025.2.a.j.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("6025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.1098672178$
Analytic rank:	$1$
Dimension:	$25$
Twist minimal:	no (minimal twist has level 1205)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
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)

$f(q)$	$=$	$q-0.300307 q^{2} -0.482693 q^{3} -1.90982 q^{4} +0.144956 q^{6} -5.09571 q^{7} +1.17415 q^{8} -2.76701 q^{9} +O(q^{10})$	\(q-0.300307 q^{2} -0.482693 q^{3} -1.90982 q^{4} +0.144956 q^{6} -5.09571 q^{7} +1.17415 q^{8} -2.76701 q^{9} +0.862510 q^{11} +0.921854 q^{12} -3.43008 q^{13} +1.53028 q^{14} +3.46703 q^{16} +0.818064 q^{17} +0.830953 q^{18} +2.57343 q^{19} +2.45966 q^{21} -0.259018 q^{22} +5.66046 q^{23} -0.566752 q^{24} +1.03008 q^{26} +2.78369 q^{27} +9.73186 q^{28} -5.53773 q^{29} +4.94707 q^{31} -3.38947 q^{32} -0.416327 q^{33} -0.245671 q^{34} +5.28447 q^{36} -4.57319 q^{37} -0.772820 q^{38} +1.65568 q^{39} +7.33536 q^{41} -0.738654 q^{42} -9.02043 q^{43} -1.64724 q^{44} -1.69988 q^{46} +2.26452 q^{47} -1.67351 q^{48} +18.9663 q^{49} -0.394873 q^{51} +6.55082 q^{52} -0.408023 q^{53} -0.835963 q^{54} -5.98311 q^{56} -1.24218 q^{57} +1.66302 q^{58} +1.97491 q^{59} +8.00721 q^{61} -1.48564 q^{62} +14.0999 q^{63} -5.91617 q^{64} +0.125026 q^{66} +6.16371 q^{67} -1.56235 q^{68} -2.73226 q^{69} +0.108795 q^{71} -3.24887 q^{72} +2.86621 q^{73} +1.37336 q^{74} -4.91478 q^{76} -4.39510 q^{77} -0.497211 q^{78} +6.71247 q^{79} +6.95736 q^{81} -2.20286 q^{82} +10.4557 q^{83} -4.69750 q^{84} +2.70890 q^{86} +2.67302 q^{87} +1.01271 q^{88} -1.79713 q^{89} +17.4787 q^{91} -10.8104 q^{92} -2.38791 q^{93} -0.680052 q^{94} +1.63607 q^{96} -7.99473 q^{97} -5.69570 q^{98} -2.38657 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - 6 q^{2} - 15 q^{3} + 32 q^{4} - q^{6} - 19 q^{7} - 15 q^{8} + 32 q^{9}+O(q^{10}) $ 25 * q - 6 * q^2 - 15 * q^3 + 32 * q^4 - q^6 - 19 * q^7 - 15 * q^8 + 32 * q^9	$ 25 q - 6 q^{2} - 15 q^{3} + 32 q^{4} - q^{6} - 19 q^{7} - 15 q^{8} + 32 q^{9} + 2 q^{11} - 20 q^{12} - 14 q^{13} - 5 q^{14} + 38 q^{16} - 7 q^{17} - 9 q^{18} + 30 q^{19} + q^{21} - q^{22} - 43 q^{23} - 6 q^{24} - 22 q^{26} - 42 q^{27} - 32 q^{28} - 4 q^{29} + 14 q^{31} - 26 q^{32} - 4 q^{33} + 7 q^{34} + 15 q^{36} - 16 q^{37} - 14 q^{38} - 21 q^{39} - q^{41} + 25 q^{42} - 35 q^{43} - 52 q^{44} - 27 q^{46} - 50 q^{47} - 26 q^{48} + 46 q^{49} - 7 q^{51} - 3 q^{52} - 4 q^{53} - 31 q^{54} - 51 q^{56} - 2 q^{58} + 6 q^{59} + 19 q^{61} - 28 q^{63} + 49 q^{64} - 27 q^{66} - 65 q^{67} + 25 q^{68} + 2 q^{69} - 34 q^{71} + 10 q^{72} - 8 q^{73} - 42 q^{74} + 71 q^{76} - q^{77} + 59 q^{78} - 12 q^{79} + 29 q^{81} - 11 q^{82} - 41 q^{83} - 10 q^{84} - 13 q^{86} - 40 q^{87} + 52 q^{88} - 24 q^{89} + 46 q^{91} - 85 q^{92} + 30 q^{93} + 14 q^{94} - 30 q^{96} - 9 q^{97} + 64 q^{98} + 2 q^{99}+O(q^{100}) $ 25 * q - 6 * q^2 - 15 * q^3 + 32 * q^4 - q^6 - 19 * q^7 - 15 * q^8 + 32 * q^9 + 2 * q^11 - 20 * q^12 - 14 * q^13 - 5 * q^14 + 38 * q^16 - 7 * q^17 - 9 * q^18 + 30 * q^19 + q^21 - q^22 - 43 * q^23 - 6 * q^24 - 22 * q^26 - 42 * q^27 - 32 * q^28 - 4 * q^29 + 14 * q^31 - 26 * q^32 - 4 * q^33 + 7 * q^34 + 15 * q^36 - 16 * q^37 - 14 * q^38 - 21 * q^39 - q^41 + 25 * q^42 - 35 * q^43 - 52 * q^44 - 27 * q^46 - 50 * q^47 - 26 * q^48 + 46 * q^49 - 7 * q^51 - 3 * q^52 - 4 * q^53 - 31 * q^54 - 51 * q^56 - 2 * q^58 + 6 * q^59 + 19 * q^61 - 28 * q^63 + 49 * q^64 - 27 * q^66 - 65 * q^67 + 25 * q^68 + 2 * q^69 - 34 * q^71 + 10 * q^72 - 8 * q^73 - 42 * q^74 + 71 * q^76 - q^77 + 59 * q^78 - 12 * q^79 + 29 * q^81 - 11 * q^82 - 41 * q^83 - 10 * q^84 - 13 * q^86 - 40 * q^87 + 52 * q^88 - 24 * q^89 + 46 * q^91 - 85 * q^92 + 30 * q^93 + 14 * q^94 - 30 * q^96 - 9 * q^97 + 64 * q^98 + 2 * 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 $

$2$	−0.300307	−0.212349	−0.106175	−	0.994347i	$-0.533860\pi$
$2$	−0.300307	−0.212349	−0.106175	+	0.994347i	$0.533860\pi$
$3$	−0.482693	−0.278683	−0.139341	−	0.990244i	$-0.544499\pi$
$3$	−0.482693	−0.278683	−0.139341	+	0.990244i	$0.544499\pi$
$4$	−1.90982	−0.954908
$5$	0	0
$5$	0	0
$6$	0.144956	0.0591781
$7$	−5.09571	−1.92600	−0.962999	−	0.269507i	$-0.913139\pi$
$7$	−5.09571	−1.92600	−0.962999	+	0.269507i	$0.913139\pi$
$8$	1.17415	0.415123
$9$	−2.76701	−0.922336
$10$	0	0
$11$	0.862510	0.260057	0.130028	−	0.991510i	$-0.458493\pi$
$11$	0.862510	0.260057	0.130028	+	0.991510i	$0.458493\pi$
$12$	0.921854	0.266116
$13$	−3.43008	−0.951334	−0.475667	−	0.879626i	$-0.657793\pi$
$13$	−3.43008	−0.951334	−0.475667	+	0.879626i	$0.657793\pi$
$14$	1.53028	0.408984
$15$	0	0
$16$	3.46703	0.866757
$17$	0.818064	0.198410	0.0992048	−	0.995067i	$-0.468370\pi$
$17$	0.818064	0.198410	0.0992048	+	0.995067i	$0.468370\pi$
$18$	0.830953	0.195857
$19$	2.57343	0.590385	0.295193	−	0.955438i	$-0.404616\pi$
$19$	2.57343	0.590385	0.295193	+	0.955438i	$0.404616\pi$
$20$	0	0
$21$	2.45966	0.536742
$22$	−0.259018	−0.0552228
$23$	5.66046	1.18029	0.590144	−	0.807298i	$-0.299071\pi$
$23$	5.66046	1.18029	0.590144	+	0.807298i	$0.299071\pi$
$24$	−0.566752	−0.115688
$25$	0	0
$26$	1.03008	0.202015
$27$	2.78369	0.535722
$28$	9.73186	1.83915
$29$	−5.53773	−1.02833	−0.514165	−	0.857691i	$-0.671898\pi$
$29$	−5.53773	−1.02833	−0.514165	+	0.857691i	$0.671898\pi$
$30$	0	0
$31$	4.94707	0.888520	0.444260	−	0.895898i	$-0.353467\pi$
$31$	4.94707	0.888520	0.444260	+	0.895898i	$0.353467\pi$
$32$	−3.38947	−0.599179
$33$	−0.416327	−0.0724733
$34$	−0.245671	−0.0421322
$35$	0	0
$36$	5.28447	0.880746
$37$	−4.57319	−0.751828	−0.375914	−	0.926655i	$-0.622671\pi$
$37$	−4.57319	−0.751828	−0.375914	+	0.926655i	$0.622671\pi$
$38$	−0.772820	−0.125368
$39$	1.65568	0.265120
$40$	0	0
$41$	7.33536	1.14559	0.572795	−	0.819699i	$-0.305859\pi$
$41$	7.33536	1.14559	0.572795	+	0.819699i	$0.305859\pi$
$42$	−0.738654	−0.113977
$43$	−9.02043	−1.37560	−0.687801	−	0.725899i	$-0.741424\pi$
$43$	−9.02043	−1.37560	−0.687801	+	0.725899i	$0.741424\pi$
$44$	−1.64724	−0.248330
$45$	0	0
$46$	−1.69988	−0.250633
$47$	2.26452	0.330314	0.165157	−	0.986267i	$-0.447187\pi$
$47$	2.26452	0.330314	0.165157	+	0.986267i	$0.447187\pi$
$48$	−1.67351	−0.241550
$49$	18.9663	2.70946
$50$	0	0
$51$	−0.394873	−0.0552933
$52$	6.55082	0.908436
$53$	−0.408023	−0.0560462	−0.0280231	−	0.999607i	$-0.508921\pi$
$53$	−0.408023	−0.0560462	−0.0280231	+	0.999607i	$0.508921\pi$
$54$	−0.835963	−0.113760
$55$	0	0
$56$	−5.98311	−0.799526
$57$	−1.24218	−0.164530
$58$	1.66302	0.218365
$59$	1.97491	0.257112	0.128556	−	0.991702i	$-0.458966\pi$
$59$	1.97491	0.257112	0.128556	+	0.991702i	$0.458966\pi$
$60$	0	0
$61$	8.00721	1.02522	0.512609	−	0.858622i	$-0.328679\pi$
$61$	8.00721	1.02522	0.512609	+	0.858622i	$0.328679\pi$
$62$	−1.48564	−0.188677
$63$	14.0999	1.77642
$64$	−5.91617	−0.739521
$65$	0	0
$66$	0.125026	0.0153896
$67$	6.16371	0.753017	0.376508	−	0.926413i	$-0.377125\pi$
$67$	6.16371	0.753017	0.376508	+	0.926413i	$0.377125\pi$
$68$	−1.56235	−0.189463
$69$	−2.73226	−0.328926
$70$	0	0
$71$	0.108795	0.0129116	0.00645578	−	0.999979i	$-0.497945\pi$
$71$	0.108795	0.0129116	0.00645578	+	0.999979i	$0.497945\pi$
$72$	−3.24887	−0.382883
$73$	2.86621	0.335465	0.167732	−	0.985833i	$-0.446356\pi$
$73$	2.86621	0.335465	0.167732	+	0.985833i	$0.446356\pi$
$74$	1.37336	0.159650
$75$	0	0
$76$	−4.91478	−0.563763
$77$	−4.39510	−0.500868
$78$	−0.497211	−0.0562981
$79$	6.71247	0.755212	0.377606	−	0.925966i	$-0.376747\pi$
$79$	6.71247	0.755212	0.377606	+	0.925966i	$0.376747\pi$
$80$	0	0
$81$	6.95736	0.773040
$82$	−2.20286	−0.243265
$83$	10.4557	1.14767	0.573833	−	0.818972i	$-0.305456\pi$
$83$	10.4557	1.14767	0.573833	+	0.818972i	$0.305456\pi$
$84$	−4.69750	−0.512539
$85$	0	0
$86$	2.70890	0.292108
$87$	2.67302	0.286578
$88$	1.01271	0.107956
$89$	−1.79713	−0.190495	−0.0952477	−	0.995454i	$-0.530364\pi$
$89$	−1.79713	−0.190495	−0.0952477	+	0.995454i	$0.530364\pi$
$90$	0	0
$91$	17.4787	1.83227
$92$	−10.8104	−1.12707
$93$	−2.38791	−0.247615
$94$	−0.680052	−0.0701420
$95$	0	0
$96$	1.63607	0.166981
$97$	−7.99473	−0.811742	−0.405871	−	0.913930i	$-0.633032\pi$
$97$	−7.99473	−0.811742	−0.405871	+	0.913930i	$0.633032\pi$
$98$	−5.69570	−0.575353
$99$	−2.38657	−0.239860
$100$	0	0
$101$	3.81072	0.379181	0.189590	−	0.981863i	$-0.439284\pi$
$101$	3.81072	0.379181	0.189590	+	0.981863i	$0.439284\pi$
$102$	0.118583	0.0117415
$103$	3.29951	0.325110	0.162555	−	0.986699i	$-0.448027\pi$
$103$	3.29951	0.325110	0.162555	+	0.986699i	$0.448027\pi$
$104$	−4.02742	−0.394921
$105$	0	0
$106$	0.122532	0.0119014
$107$	−1.29614	−0.125303	−0.0626513	−	0.998035i	$-0.519956\pi$
$107$	−1.29614	−0.125303	−0.0626513	+	0.998035i	$0.519956\pi$
$108$	−5.31634	−0.511565
$109$	−10.0786	−0.965350	−0.482675	−	0.875799i	$-0.660335\pi$
$109$	−10.0786	−0.965350	−0.482675	+	0.875799i	$0.660335\pi$
$110$	0	0
$111$	2.20745	0.209521
$112$	−17.6670	−1.66937
$113$	−3.25095	−0.305824	−0.152912	−	0.988240i	$-0.548865\pi$
$113$	−3.25095	−0.305824	−0.152912	+	0.988240i	$0.548865\pi$
$114$	0.373034	0.0349379
$115$	0	0
$116$	10.5760	0.981961
$117$	9.49107	0.877449
$118$	−0.593081	−0.0545975
$119$	−4.16862	−0.382136
$120$	0	0
$121$	−10.2561	−0.932371
$122$	−2.40462	−0.217704
$123$	−3.54072	−0.319256
$124$	−9.44799	−0.848455
$125$	0	0
$126$	−4.23429	−0.377221
$127$	−12.3008	−1.09152	−0.545759	−	0.837942i	$-0.683759\pi$
$127$	−12.3008	−1.09152	−0.545759	+	0.837942i	$0.683759\pi$
$128$	8.55560	0.756215
$129$	4.35409	0.383357
$130$	0	0
$131$	−6.51876	−0.569546	−0.284773	−	0.958595i	$-0.591918\pi$
$131$	−6.51876	−0.569546	−0.284773	+	0.958595i	$0.591918\pi$
$132$	0.795108	0.0692053
$133$	−13.1134	−1.13708
$134$	−1.85101	−0.159903
$135$	0	0
$136$	0.960527	0.0823645
$137$	12.8773	1.10018	0.550091	−	0.835105i	$-0.314593\pi$
$137$	12.8773	1.10018	0.550091	+	0.835105i	$0.314593\pi$
$138$	0.820518	0.0698471
$139$	−17.9043	−1.51863	−0.759313	−	0.650725i	$-0.774465\pi$
$139$	−17.9043	−1.51863	−0.759313	+	0.650725i	$0.774465\pi$
$140$	0	0
$141$	−1.09307	−0.0920528
$142$	−0.0326719	−0.00274176
$143$	−2.95848	−0.247401
$144$	−9.59329	−0.799441
$145$	0	0
$146$	−0.860745	−0.0712358
$147$	−9.15487	−0.755081
$148$	8.73395	0.717926
$149$	20.6979	1.69564	0.847820	−	0.530284i	$-0.177915\pi$
$149$	20.6979	1.69564	0.847820	+	0.530284i	$0.177915\pi$
$150$	0	0
$151$	−12.7918	−1.04098	−0.520491	−	0.853867i	$-0.674251\pi$
$151$	−12.7918	−1.04098	−0.520491	+	0.853867i	$0.674251\pi$
$152$	3.02158	0.245083
$153$	−2.26359	−0.183000
$154$	1.31988	0.106359
$155$	0	0
$156$	−3.16203	−0.253165
$157$	−8.11295	−0.647484	−0.323742	−	0.946145i	$-0.604941\pi$
$157$	−8.11295	−0.647484	−0.323742	+	0.946145i	$0.604941\pi$
$158$	−2.01580	−0.160369
$159$	0.196949	0.0156191
$160$	0	0
$161$	−28.8441	−2.27323
$162$	−2.08935	−0.164154
$163$	4.88945	0.382971	0.191485	−	0.981495i	$-0.438670\pi$
$163$	4.88945	0.382971	0.191485	+	0.981495i	$0.438670\pi$
$164$	−14.0092	−1.09393
$165$	0	0
$166$	−3.13994	−0.243706
$167$	−11.7620	−0.910170	−0.455085	−	0.890448i	$-0.650391\pi$
$167$	−11.7620	−0.910170	−0.455085	+	0.890448i	$0.650391\pi$
$168$	2.88800	0.222814
$169$	−1.23453	−0.0949641
$170$	0	0
$171$	−7.12070	−0.544534
$172$	17.2274	1.31357
$173$	2.73650	0.208052	0.104026	−	0.994575i	$-0.466827\pi$
$173$	2.73650	0.208052	0.104026	+	0.994575i	$0.466827\pi$
$174$	−0.802728	−0.0608546
$175$	0	0
$176$	2.99035	0.225406
$177$	−0.953276	−0.0716526
$178$	0.539691	0.0404516
$179$	24.1893	1.80799	0.903996	−	0.427541i	$-0.140620\pi$
$179$	24.1893	1.80799	0.903996	+	0.427541i	$0.140620\pi$
$180$	0	0
$181$	−19.5913	−1.45621	−0.728106	−	0.685465i	$-0.759599\pi$
$181$	−19.5913	−1.45621	−0.728106	+	0.685465i	$0.759599\pi$
$182$	−5.24898	−0.389080
$183$	−3.86502	−0.285710
$184$	6.64621	0.489965
$185$	0	0
$186$	0.717108	0.0525809
$187$	0.705589	0.0515977
$188$	−4.32481	−0.315420
$189$	−14.1849	−1.03180
$190$	0	0
$191$	−12.7823	−0.924892	−0.462446	−	0.886647i	$-0.653028\pi$
$191$	−12.7823	−0.924892	−0.462446	+	0.886647i	$0.653028\pi$
$192$	2.85569	0.206092
$193$	0.484555	0.0348790	0.0174395	−	0.999848i	$-0.494449\pi$
$193$	0.484555	0.0348790	0.0174395	+	0.999848i	$0.494449\pi$
$194$	2.40088	0.172373
$195$	0	0
$196$	−36.2220	−2.58729
$197$	21.7304	1.54823	0.774113	−	0.633047i	$-0.218196\pi$
$197$	21.7304	1.54823	0.774113	+	0.633047i	$0.218196\pi$
$198$	0.716705	0.0509340
$199$	−28.0339	−1.98727	−0.993634	−	0.112657i	$-0.964064\pi$
$199$	−28.0339	−1.98727	−0.993634	+	0.112657i	$0.964064\pi$
$200$	0	0
$201$	−2.97517	−0.209853
$202$	−1.14439	−0.0805188
$203$	28.2187	1.98056
$204$	0.754135	0.0528000
$205$	0	0
$206$	−0.990865	−0.0690369
$207$	−15.6625	−1.08862
$208$	−11.8922	−0.824575
$209$	2.21961	0.153534
$210$	0	0
$211$	−9.33644	−0.642747	−0.321374	−	0.946953i	$-0.604145\pi$
$211$	−9.33644	−0.642747	−0.321374	+	0.946953i	$0.604145\pi$
$212$	0.779248	0.0535190
$213$	−0.0525144	−0.00359823
$214$	0.389240	0.0266079
$215$	0	0
$216$	3.26846	0.222391
$217$	−25.2088	−1.71129
$218$	3.02666	0.204991
$219$	−1.38350	−0.0934883
$220$	0	0
$221$	−2.80603	−0.188754
$222$	−0.662912	−0.0444917
$223$	19.3203	1.29379	0.646893	−	0.762581i	$-0.276068\pi$
$223$	19.3203	1.29379	0.646893	+	0.762581i	$0.276068\pi$
$224$	17.2717	1.15402
$225$	0	0
$226$	0.976285	0.0649415
$227$	16.8197	1.11636	0.558180	−	0.829720i	$-0.311500\pi$
$227$	16.8197	1.11636	0.558180	+	0.829720i	$0.311500\pi$
$228$	2.37233	0.157111
$229$	−3.11496	−0.205843	−0.102921	−	0.994690i	$-0.532819\pi$
$229$	−3.11496	−0.205843	−0.102921	+	0.994690i	$0.532819\pi$
$230$	0	0
$231$	2.12148	0.139583
$232$	−6.50210	−0.426884
$233$	10.0304	0.657115	0.328558	−	0.944484i	$-0.393437\pi$
$233$	10.0304	0.657115	0.328558	+	0.944484i	$0.393437\pi$
$234$	−2.85024	−0.186326
$235$	0	0
$236$	−3.77172	−0.245518
$237$	−3.24006	−0.210464
$238$	1.25187	0.0811464
$239$	24.0374	1.55485	0.777424	−	0.628977i	$-0.216526\pi$
$239$	24.0374	1.55485	0.777424	+	0.628977i	$0.216526\pi$
$240$	0	0
$241$	−1.00000	−0.0644157
$241$	−1.00000	−0.0644157
$242$	3.07997	0.197988
$243$	−11.7093	−0.751154
$244$	−15.2923	−0.978988
$245$	0	0
$246$	1.06330	0.0677938
$247$	−8.82708	−0.561653
$248$	5.80858	0.368845
$249$	−5.04691	−0.319835
$250$	0	0
$251$	−13.3896	−0.845143	−0.422572	−	0.906329i	$-0.638873\pi$
$251$	−13.3896	−0.845143	−0.422572	+	0.906329i	$0.638873\pi$
$252$	−26.9281	−1.69631
$253$	4.88220	0.306942
$254$	3.69401	0.231783
$255$	0	0
$256$	9.26303	0.578940
$257$	2.77993	0.173407	0.0867037	−	0.996234i	$-0.472367\pi$
$257$	2.77993	0.173407	0.0867037	+	0.996234i	$0.472367\pi$
$258$	−1.30757	−0.0814055
$259$	23.3037	1.44802
$260$	0	0
$261$	15.3229	0.948466
$262$	1.95763	0.120943
$263$	−11.7223	−0.722830	−0.361415	−	0.932405i	$-0.617706\pi$
$263$	−11.7223	−0.722830	−0.361415	+	0.932405i	$0.617706\pi$
$264$	−0.488829	−0.0300853
$265$	0	0
$266$	3.93806	0.241458
$267$	0.867461	0.0530878
$268$	−11.7715	−0.719061
$269$	−15.3329	−0.934864	−0.467432	−	0.884029i	$-0.654821\pi$
$269$	−15.3329	−0.934864	−0.467432	+	0.884029i	$0.654821\pi$
$270$	0	0
$271$	20.8363	1.26572	0.632858	−	0.774268i	$-0.281882\pi$
$271$	20.8363	1.26572	0.632858	+	0.774268i	$0.281882\pi$
$272$	2.83625	0.171973
$273$	−8.43684	−0.510621
$274$	−3.86715	−0.233623
$275$	0	0
$276$	5.21812	0.314094
$277$	−3.77390	−0.226751	−0.113376	−	0.993552i	$-0.536166\pi$
$277$	−3.77390	−0.226751	−0.113376	+	0.993552i	$0.536166\pi$
$278$	5.37680	0.322479
$279$	−13.6886	−0.819514
$280$	0	0
$281$	3.20443	0.191160	0.0955802	−	0.995422i	$-0.469529\pi$
$281$	3.20443	0.191160	0.0955802	+	0.995422i	$0.469529\pi$
$282$	0.328256	0.0195474
$283$	26.1978	1.55730	0.778650	−	0.627459i	$-0.215905\pi$
$283$	26.1978	1.55730	0.778650	+	0.627459i	$0.215905\pi$
$284$	−0.207778	−0.0123294
$285$	0	0
$286$	0.888453	0.0525354
$287$	−37.3788	−2.20640
$288$	9.37868	0.552644
$289$	−16.3308	−0.960634
$290$	0	0
$291$	3.85900	0.226218
$292$	−5.47394	−0.320338
$293$	−28.3980	−1.65903	−0.829515	−	0.558485i	$-0.811383\pi$
$293$	−28.3980	−1.65903	−0.829515	+	0.558485i	$0.811383\pi$
$294$	2.74927	0.160341
$295$	0	0
$296$	−5.36960	−0.312101
$297$	2.40096	0.139318
$298$	−6.21574	−0.360068
$299$	−19.4158	−1.12285
$300$	0	0
$301$	45.9655	2.64941
$302$	3.84147	0.221052
$303$	−1.83941	−0.105671
$304$	8.92215	0.511720
$305$	0	0
$306$	0.679773	0.0388600
$307$	−9.33407	−0.532724	−0.266362	−	0.963873i	$-0.585822\pi$
$307$	−9.33407	−0.532724	−0.266362	+	0.963873i	$0.585822\pi$
$308$	8.39383	0.478283
$309$	−1.59265	−0.0906025
$310$	0	0
$311$	−20.9699	−1.18909	−0.594546	−	0.804062i	$-0.702668\pi$
$311$	−20.9699	−1.18909	−0.594546	+	0.804062i	$0.702668\pi$
$312$	1.94400	0.110058
$313$	23.2381	1.31350	0.656748	−	0.754110i	$-0.271931\pi$
$313$	23.2381	1.31350	0.656748	+	0.754110i	$0.271931\pi$
$314$	2.43638	0.137493
$315$	0	0
$316$	−12.8196	−0.721158
$317$	31.7764	1.78474	0.892369	−	0.451307i	$-0.149042\pi$
$317$	31.7764	1.78474	0.892369	+	0.451307i	$0.149042\pi$
$318$	−0.0591454	−0.00331671
$319$	−4.77635	−0.267424
$320$	0	0
$321$	0.625637	0.0349197
$322$	8.66208	0.482719
$323$	2.10523	0.117138
$324$	−13.2873	−0.738182
$325$	0	0
$326$	−1.46834	−0.0813236
$327$	4.86484	0.269026
$328$	8.61278	0.475561
$329$	−11.5393	−0.636184
$330$	0	0
$331$	−17.9508	−0.986666	−0.493333	−	0.869841i	$-0.664222\pi$
$331$	−17.9508	−0.986666	−0.493333	+	0.869841i	$0.664222\pi$
$332$	−19.9685	−1.09592
$333$	12.6541	0.693438
$334$	3.53221	0.193274
$335$	0	0
$336$	8.52771	0.465225
$337$	−25.3922	−1.38320	−0.691601	−	0.722280i	$-0.743094\pi$
$337$	−25.3922	−1.38320	−0.691601	+	0.722280i	$0.743094\pi$
$338$	0.370739	0.0201656
$339$	1.56921	0.0852278
$340$	0	0
$341$	4.26690	0.231066
$342$	2.13840	0.115631
$343$	−60.9765	−3.29242
$344$	−10.5913	−0.571045
$345$	0	0
$346$	−0.821790	−0.0441797
$347$	22.3685	1.20080	0.600401	−	0.799699i	$-0.295008\pi$
$347$	22.3685	1.20080	0.600401	+	0.799699i	$0.295008\pi$
$348$	−5.10498	−0.273655
$349$	−3.16596	−0.169470	−0.0847349	−	0.996404i	$-0.527004\pi$
$349$	−3.16596	−0.169470	−0.0847349	+	0.996404i	$0.527004\pi$
$350$	0	0
$351$	−9.54829	−0.509650
$352$	−2.92345	−0.155820
$353$	−23.9007	−1.27210	−0.636052	−	0.771646i	$-0.719434\pi$
$353$	−23.9007	−1.27210	−0.636052	+	0.771646i	$0.719434\pi$
$354$	0.286276	0.0152154
$355$	0	0
$356$	3.43219	0.181906
$357$	2.01216	0.106495
$358$	−7.26422	−0.383926
$359$	11.5177	0.607881	0.303941	−	0.952691i	$-0.401698\pi$
$359$	11.5177	0.607881	0.303941	+	0.952691i	$0.401698\pi$
$360$	0	0
$361$	−12.3775	−0.651445
$362$	5.88342	0.309226
$363$	4.95053	0.259835
$364$	−33.3811	−1.74965
$365$	0	0
$366$	1.16069	0.0606704
$367$	−15.5708	−0.812790	−0.406395	−	0.913698i	$-0.633214\pi$
$367$	−15.5708	−0.812790	−0.406395	+	0.913698i	$0.633214\pi$
$368$	19.6250	1.02302
$369$	−20.2970	−1.05662
$370$	0	0
$371$	2.07916	0.107945
$372$	4.56047	0.236450
$373$	−11.3849	−0.589486	−0.294743	−	0.955577i	$-0.595234\pi$
$373$	−11.3849	−0.589486	−0.294743	+	0.955577i	$0.595234\pi$
$374$	−0.211893	−0.0109567
$375$	0	0
$376$	2.65888	0.137121
$377$	18.9949	0.978286
$378$	4.25982	0.219102
$379$	17.8705	0.917946	0.458973	−	0.888450i	$-0.348218\pi$
$379$	17.8705	0.917946	0.458973	+	0.888450i	$0.348218\pi$
$380$	0	0
$381$	5.93750	0.304187
$382$	3.83861	0.196400
$383$	10.1696	0.519640	0.259820	−	0.965657i	$-0.416337\pi$
$383$	10.1696	0.519640	0.259820	+	0.965657i	$0.416337\pi$
$384$	−4.12972	−0.210744
$385$	0	0
$386$	−0.145515	−0.00740654
$387$	24.9596	1.26877
$388$	15.2685	0.775139
$389$	−3.64108	−0.184610	−0.0923049	−	0.995731i	$-0.529423\pi$
$389$	−3.64108	−0.184610	−0.0923049	+	0.995731i	$0.529423\pi$
$390$	0	0
$391$	4.63062	0.234180
$392$	22.2692	1.12476
$393$	3.14655	0.158723
$394$	−6.52580	−0.328765
$395$	0	0
$396$	4.55791	0.229044
$397$	7.37319	0.370050	0.185025	−	0.982734i	$-0.440763\pi$
$397$	7.37319	0.370050	0.185025	+	0.982734i	$0.440763\pi$
$398$	8.41877	0.421995
$399$	6.32976	0.316885
$400$	0	0
$401$	−11.4154	−0.570060	−0.285030	−	0.958519i	$-0.592004\pi$
$401$	−11.4154	−0.570060	−0.285030	+	0.958519i	$0.592004\pi$
$402$	0.893467	0.0445621
$403$	−16.9689	−0.845279
$404$	−7.27777	−0.362083
$405$	0	0
$406$	−8.47427	−0.420571
$407$	−3.94442	−0.195518
$408$	−0.463639	−0.0229536
$409$	−29.8373	−1.47536	−0.737680	−	0.675150i	$-0.764079\pi$
$409$	−29.8373	−1.47536	−0.737680	+	0.675150i	$0.764079\pi$
$410$	0	0
$411$	−6.21578	−0.306602
$412$	−6.30145	−0.310450
$413$	−10.0636	−0.495197
$414$	4.70357	0.231168
$415$	0	0
$416$	11.6261	0.570019
$417$	8.64229	0.423215
$418$	−0.666565	−0.0326028
$419$	−0.987145	−0.0482252	−0.0241126	−	0.999709i	$-0.507676\pi$
$419$	−0.987145	−0.0482252	−0.0241126	+	0.999709i	$0.507676\pi$
$420$	0	0
$421$	12.2761	0.598299	0.299149	−	0.954206i	$-0.403297\pi$
$421$	12.2761	0.598299	0.299149	+	0.954206i	$0.403297\pi$
$422$	2.80380	0.136487
$423$	−6.26594	−0.304661
$424$	−0.479078	−0.0232661
$425$	0	0
$426$	0.0157705	0.000764081 0
$427$	−40.8024	−1.97457
$428$	2.47539	0.119652
$429$	1.42804	0.0689463
$430$	0	0
$431$	31.2173	1.50368	0.751842	−	0.659344i	$-0.229166\pi$
$431$	31.2173	1.50368	0.751842	+	0.659344i	$0.229166\pi$
$432$	9.65113	0.464340
$433$	16.1840	0.777755	0.388878	−	0.921289i	$-0.372863\pi$
$433$	16.1840	0.777755	0.388878	+	0.921289i	$0.372863\pi$
$434$	7.57040	0.363391
$435$	0	0
$436$	19.2482	0.921821
$437$	14.5668	0.696824
$438$	0.415475	0.0198522
$439$	−2.82115	−0.134646	−0.0673232	−	0.997731i	$-0.521446\pi$
$439$	−2.82115	−0.134646	−0.0673232	+	0.997731i	$0.521446\pi$
$440$	0	0
$441$	−52.4798	−2.49904
$442$	0.842670	0.0400817
$443$	−8.37664	−0.397986	−0.198993	−	0.980001i	$-0.563767\pi$
$443$	−8.37664	−0.397986	−0.198993	+	0.980001i	$0.563767\pi$
$444$	−4.21581	−0.200074
$445$	0	0
$446$	−5.80204	−0.274734
$447$	−9.99074	−0.472546
$448$	30.1471	1.42432
$449$	6.88850	0.325088	0.162544	−	0.986701i	$-0.448030\pi$
$449$	6.88850	0.325088	0.162544	+	0.986701i	$0.448030\pi$
$450$	0	0
$451$	6.32682	0.297918
$452$	6.20872	0.292034
$453$	6.17450	0.290103
$454$	−5.05107	−0.237058
$455$	0	0
$456$	−1.45850	−0.0683003
$457$	26.3409	1.23217	0.616087	−	0.787678i	$-0.288717\pi$
$457$	26.3409	1.23217	0.616087	+	0.787678i	$0.288717\pi$
$458$	0.935446	0.0437105
$459$	2.27724	0.106292
$460$	0	0
$461$	17.3822	0.809570	0.404785	−	0.914412i	$-0.367346\pi$
$461$	17.3822	0.809570	0.404785	+	0.914412i	$0.367346\pi$
$462$	−0.637097	−0.0296404
$463$	13.0339	0.605738	0.302869	−	0.953032i	$-0.402055\pi$
$463$	13.0339	0.605738	0.302869	+	0.953032i	$0.402055\pi$
$464$	−19.1995	−0.891312
$465$	0	0
$466$	−3.01221	−0.139538
$467$	−31.0600	−1.43729	−0.718643	−	0.695379i	$-0.755237\pi$
$467$	−31.0600	−1.43729	−0.718643	+	0.695379i	$0.755237\pi$
$468$	−18.1262	−0.837883
$469$	−31.4085	−1.45031
$470$	0	0
$471$	3.91606	0.180443
$472$	2.31884	0.106733
$473$	−7.78021	−0.357735
$474$	0.973013	0.0446920
$475$	0	0
$476$	7.96129	0.364905
$477$	1.12900	0.0516934
$478$	−7.21860	−0.330171
$479$	−28.2560	−1.29105	−0.645525	−	0.763739i	$-0.723361\pi$
$479$	−28.2560	−1.29105	−0.645525	+	0.763739i	$0.723361\pi$
$480$	0	0
$481$	15.6864	0.715239
$482$	0.300307	0.0136786
$483$	13.9228	0.633510
$484$	19.5872	0.890328
$485$	0	0
$486$	3.51640	0.159507
$487$	−38.7529	−1.75606	−0.878031	−	0.478604i	$-0.841143\pi$
$487$	−38.7529	−1.75606	−0.878031	+	0.478604i	$0.841143\pi$
$488$	9.40163	0.425592
$489$	−2.36010	−0.106727
$490$	0	0
$491$	32.7195	1.47661	0.738305	−	0.674467i	$-0.235627\pi$
$491$	32.7195	1.47661	0.738305	+	0.674467i	$0.235627\pi$
$492$	6.76213	0.304860
$493$	−4.53022	−0.204031
$494$	2.65084	0.119267
$495$	0	0
$496$	17.1516	0.770131
$497$	−0.554387	−0.0248676
$498$	1.51562	0.0679167
$499$	9.83279	0.440176	0.220088	−	0.975480i	$-0.429366\pi$
$499$	9.83279	0.440176	0.220088	+	0.975480i	$0.429366\pi$
$500$	0	0
$501$	5.67743	0.253649
$502$	4.02099	0.179466
$503$	−28.4625	−1.26908	−0.634540	−	0.772890i	$-0.718810\pi$
$503$	−28.4625	−1.26908	−0.634540	+	0.772890i	$0.718810\pi$
$504$	16.5553	0.737432
$505$	0	0
$506$	−1.46616	−0.0651788
$507$	0.595900	0.0264649
$508$	23.4922	1.04230
$509$	−40.2201	−1.78272	−0.891362	−	0.453293i	$-0.850249\pi$
$509$	−40.2201	−1.78272	−0.891362	+	0.453293i	$0.850249\pi$
$510$	0	0
$511$	−14.6054	−0.646105
$512$	−19.8930	−0.879153
$513$	7.16363	0.316282
$514$	−0.834834	−0.0368229
$515$	0	0
$516$	−8.31552	−0.366070
$517$	1.95317	0.0859004
$518$	−6.99826	−0.307486
$519$	−1.32089	−0.0579805
$520$	0	0
$521$	14.1325	0.619154	0.309577	−	0.950874i	$-0.399813\pi$
$521$	14.1325	0.619154	0.309577	+	0.950874i	$0.399813\pi$
$522$	−4.60159	−0.201406
$523$	−42.9594	−1.87848	−0.939241	−	0.343258i	$-0.888470\pi$
$523$	−42.9594	−1.87848	−0.939241	+	0.343258i	$0.888470\pi$
$524$	12.4496	0.543864
$525$	0	0
$526$	3.52030	0.153492
$527$	4.04702	0.176291
$528$	−1.44342	−0.0628167
$529$	9.04080	0.393078
$530$	0	0
$531$	−5.46460	−0.237144
$532$	25.0443	1.08581
$533$	−25.1609	−1.08984
$534$	−0.260505	−0.0112732
$535$	0	0
$536$	7.23709	0.312595
$537$	−11.6760	−0.503856
$538$	4.60458	0.198518
$539$	16.3586	0.704614
$540$	0	0
$541$	15.4888	0.665918	0.332959	−	0.942941i	$-0.391953\pi$
$541$	15.4888	0.665918	0.332959	+	0.942941i	$0.391953\pi$
$542$	−6.25730	−0.268774
$543$	9.45658	0.405821
$544$	−2.77280	−0.118883
$545$	0	0
$546$	2.53364	0.108430
$547$	8.22553	0.351698	0.175849	−	0.984417i	$-0.443733\pi$
$547$	8.22553	0.351698	0.175849	+	0.984417i	$0.443733\pi$
$548$	−24.5933	−1.05057
$549$	−22.1560	−0.945595
$550$	0	0
$551$	−14.2510	−0.607111
$552$	−3.20807	−0.136545
$553$	−34.2048	−1.45454
$554$	1.13333	0.0481505
$555$	0	0
$556$	34.1940	1.45015
$557$	11.7446	0.497635	0.248818	−	0.968550i	$-0.419958\pi$
$557$	11.7446	0.497635	0.248818	+	0.968550i	$0.419958\pi$
$558$	4.11078	0.174023
$559$	30.9408	1.30866
$560$	0	0
$561$	−0.340582	−0.0143794
$562$	−0.962315	−0.0405928
$563$	39.2326	1.65346	0.826729	−	0.562600i	$-0.190199\pi$
$563$	39.2326	1.65346	0.826729	+	0.562600i	$0.190199\pi$
$564$	2.08756	0.0879019
$565$	0	0
$566$	−7.86740	−0.330691
$567$	−35.4527	−1.48887
$568$	0.127741	0.00535989
$569$	13.8526	0.580731	0.290365	−	0.956916i	$-0.406223\pi$
$569$	13.8526	0.580731	0.290365	+	0.956916i	$0.406223\pi$
$570$	0	0
$571$	3.28000	0.137264	0.0686318	−	0.997642i	$-0.478137\pi$
$571$	3.28000	0.137264	0.0686318	+	0.997642i	$0.478137\pi$
$572$	5.65015	0.236245
$573$	6.16990	0.257751
$574$	11.2251	0.468528
$575$	0	0
$576$	16.3701	0.682087
$577$	26.4335	1.10044	0.550220	−	0.835020i	$-0.314544\pi$
$577$	26.4335	1.10044	0.550220	+	0.835020i	$0.314544\pi$
$578$	4.90425	0.203990
$579$	−0.233891	−0.00972018
$580$	0	0
$581$	−53.2794	−2.21040
$582$	−1.15889	−0.0480373
$583$	−0.351924	−0.0145752
$584$	3.36535	0.139259
$585$	0	0
$586$	8.52813	0.352294
$587$	−9.48021	−0.391290	−0.195645	−	0.980675i	$-0.562680\pi$
$587$	−9.48021	−0.391290	−0.195645	+	0.980675i	$0.562680\pi$
$588$	17.4841	0.721032
$589$	12.7309	0.524569
$590$	0	0
$591$	−10.4891	−0.431464
$592$	−15.8554	−0.651652
$593$	−25.5976	−1.05117	−0.525585	−	0.850741i	$-0.676153\pi$
$593$	−25.5976	−1.05117	−0.525585	+	0.850741i	$0.676153\pi$
$594$	−0.721026	−0.0295841
$595$	0	0
$596$	−39.5292	−1.61918
$597$	13.5317	0.553817
$598$	5.83072	0.238436
$599$	8.42810	0.344363	0.172181	−	0.985065i	$-0.444918\pi$
$599$	8.42810	0.344363	0.172181	+	0.985065i	$0.444918\pi$
$600$	0	0
$601$	−20.5135	−0.836764	−0.418382	−	0.908271i	$-0.637403\pi$
$601$	−20.5135	−0.836764	−0.418382	+	0.908271i	$0.637403\pi$
$602$	−13.8038	−0.562600
$603$	−17.0550	−0.694534
$604$	24.4300	0.994041
$605$	0	0
$606$	0.552387	0.0224392
$607$	−15.6858	−0.636666	−0.318333	−	0.947979i	$-0.603123\pi$
$607$	−15.6858	−0.636666	−0.318333	+	0.947979i	$0.603123\pi$
$608$	−8.72255	−0.353746
$609$	−13.6209	−0.551948
$610$	0	0
$611$	−7.76749	−0.314239
$612$	4.32304	0.174748
$613$	−37.5979	−1.51856	−0.759282	−	0.650762i	$-0.774450\pi$
$613$	−37.5979	−1.51856	−0.759282	+	0.650762i	$0.774450\pi$
$614$	2.80309	0.113124
$615$	0	0
$616$	−5.16049	−0.207922
$617$	22.7836	0.917234	0.458617	−	0.888634i	$-0.348345\pi$
$617$	22.7836	0.917234	0.458617	+	0.888634i	$0.348345\pi$
$618$	0.478283	0.0192394
$619$	−22.2322	−0.893587	−0.446793	−	0.894637i	$-0.647434\pi$
$619$	−22.2322	−0.893587	−0.446793	+	0.894637i	$0.647434\pi$
$620$	0	0
$621$	15.7570	0.632306
$622$	6.29740	0.252503
$623$	9.15765	0.366894
$624$	5.74027	0.229795
$625$	0	0
$626$	−6.97858	−0.278920
$627$	−1.07139	−0.0427871
$628$	15.4942	0.618288
$629$	−3.74116	−0.149170
$630$	0	0
$631$	31.5060	1.25423	0.627116	−	0.778926i	$-0.284235\pi$
$631$	31.5060	1.25423	0.627116	+	0.778926i	$0.284235\pi$
$632$	7.88142	0.313506
$633$	4.50663	0.179122
$634$	−9.54267	−0.378988
$635$	0	0
$636$	−0.376137	−0.0149148
$637$	−65.0558	−2.57761
$638$	1.43437	0.0567873
$639$	−0.301036	−0.0119088
$640$	0	0
$641$	−37.7209	−1.48989	−0.744943	−	0.667128i	$-0.767524\pi$
$641$	−37.7209	−1.48989	−0.744943	+	0.667128i	$0.767524\pi$
$642$	−0.187883	−0.00741517
$643$	−34.4038	−1.35675	−0.678377	−	0.734714i	$-0.737316\pi$
$643$	−34.4038	−1.35675	−0.678377	+	0.734714i	$0.737316\pi$
$644$	55.0868	2.17073
$645$	0	0
$646$	−0.632216	−0.0248742
$647$	23.3066	0.916277	0.458138	−	0.888881i	$-0.348516\pi$
$647$	23.3066	0.916277	0.458138	+	0.888881i	$0.348516\pi$
$648$	8.16895	0.320907
$649$	1.70338	0.0668637
$650$	0	0
$651$	12.1681	0.476906
$652$	−9.33794	−0.365702
$653$	39.5660	1.54834	0.774169	−	0.632978i	$-0.218168\pi$
$653$	39.5660	1.54834	0.774169	+	0.632978i	$0.218168\pi$
$654$	−1.46095	−0.0571276
$655$	0	0
$656$	25.4319	0.992948
$657$	−7.93084	−0.309411
$658$	3.46535	0.135093
$659$	38.8879	1.51486	0.757428	−	0.652918i	$-0.226456\pi$
$659$	38.8879	1.51486	0.757428	+	0.652918i	$0.226456\pi$
$660$	0	0
$661$	4.09860	0.159417	0.0797086	−	0.996818i	$-0.474601\pi$
$661$	4.09860	0.159417	0.0797086	+	0.996818i	$0.474601\pi$
$662$	5.39076	0.209518
$663$	1.35445	0.0526024
$664$	12.2766	0.476423
$665$	0	0
$666$	−3.80011	−0.147251
$667$	−31.3461	−1.21373
$668$	22.4632	0.869129
$669$	−9.32578	−0.360556
$670$	0	0
$671$	6.90630	0.266615
$672$	−8.33694	−0.321604
$673$	22.5859	0.870624	0.435312	−	0.900280i	$-0.356638\pi$
$673$	22.5859	0.870624	0.435312	+	0.900280i	$0.356638\pi$
$674$	7.62547	0.293722
$675$	0	0
$676$	2.35773	0.0906820
$677$	17.3209	0.665698	0.332849	−	0.942980i	$-0.391990\pi$
$677$	17.3209	0.665698	0.332849	+	0.942980i	$0.391990\pi$
$678$	−0.471245	−0.0180981
$679$	40.7388	1.56341
$680$	0	0
$681$	−8.11872	−0.311110
$682$	−1.28138	−0.0490666
$683$	−22.6416	−0.866358	−0.433179	−	0.901308i	$-0.642608\pi$
$683$	−22.6416	−0.866358	−0.433179	+	0.901308i	$0.642608\pi$
$684$	13.5992	0.519979
$685$	0	0
$686$	18.3117	0.699144
$687$	1.50357	0.0573648
$688$	−31.2741	−1.19231
$689$	1.39955	0.0533187
$690$	0	0
$691$	10.6940	0.406819	0.203409	−	0.979094i	$-0.434798\pi$
$691$	10.6940	0.406819	0.203409	+	0.979094i	$0.434798\pi$
$692$	−5.22620	−0.198670
$693$	12.1613	0.461969
$694$	−6.71742	−0.254990
$695$	0	0
$696$	3.13852	0.118965
$697$	6.00079	0.227296
$698$	0.950761	0.0359868
$699$	−4.84161	−0.183127
$700$	0	0
$701$	6.51784	0.246175	0.123088	−	0.992396i	$-0.460720\pi$
$701$	6.51784	0.246175	0.123088	+	0.992396i	$0.460720\pi$
$702$	2.86742	0.108224
$703$	−11.7688	−0.443868
$704$	−5.10276	−0.192317
$705$	0	0
$706$	7.17755	0.270130
$707$	−19.4183	−0.730301
$708$	1.82058	0.0684217
$709$	−24.1127	−0.905572	−0.452786	−	0.891619i	$-0.649570\pi$
$709$	−24.1127	−0.905572	−0.452786	+	0.891619i	$0.649570\pi$
$710$	0	0
$711$	−18.5735	−0.696559
$712$	−2.11009	−0.0790791
$713$	28.0027	1.04871
$714$	−0.604266	−0.0226141
$715$	0	0
$716$	−46.1971	−1.72647
$717$	−11.6027	−0.433309
$718$	−3.45885	−0.129083
$719$	−49.4626	−1.84464	−0.922322	−	0.386422i	$-0.873711\pi$
$719$	−49.4626	−1.84464	−0.922322	+	0.386422i	$0.873711\pi$
$720$	0	0
$721$	−16.8133	−0.626161
$722$	3.71704	0.138334
$723$	0.482693	0.0179515
$724$	37.4158	1.39055
$725$	0	0
$726$	−1.48668	−0.0551759
$727$	−17.4062	−0.645560	−0.322780	−	0.946474i	$-0.604617\pi$
$727$	−17.4062	−0.645560	−0.322780	+	0.946474i	$0.604617\pi$
$728$	20.5226	0.760616
$729$	−15.2201	−0.563706
$730$	0	0
$731$	−7.37929	−0.272933
$732$	7.38147	0.272827
$733$	−39.0769	−1.44334	−0.721669	−	0.692238i	$-0.756625\pi$
$733$	−39.0769	−1.44334	−0.721669	+	0.692238i	$0.756625\pi$
$734$	4.67603	0.172595
$735$	0	0
$736$	−19.1859	−0.707203
$737$	5.31626	0.195827
$738$	6.09533	0.224372
$739$	−47.3807	−1.74293	−0.871463	−	0.490461i	$-0.836829\pi$
$739$	−47.3807	−1.74293	−0.871463	+	0.490461i	$0.836829\pi$
$740$	0	0
$741$	4.26076	0.156523
$742$	−0.624388	−0.0229220
$743$	38.4091	1.40909	0.704546	−	0.709658i	$-0.251151\pi$
$743$	38.4091	1.40909	0.704546	+	0.709658i	$0.251151\pi$
$744$	−2.80376	−0.102791
$745$	0	0
$746$	3.41896	0.125177
$747$	−28.9311	−1.05853
$748$	−1.34754	−0.0492711
$749$	6.60476	0.241333
$750$	0	0
$751$	−38.3776	−1.40042	−0.700209	−	0.713938i	$-0.746910\pi$
$751$	−38.3776	−1.40042	−0.700209	+	0.713938i	$0.746910\pi$
$752$	7.85115	0.286302
$753$	6.46305	0.235527
$754$	−5.70430	−0.207738
$755$	0	0
$756$	27.0905	0.985272
$757$	−23.6061	−0.857979	−0.428989	−	0.903310i	$-0.641130\pi$
$757$	−23.6061	−0.857979	−0.428989	+	0.903310i	$0.641130\pi$
$758$	−5.36664	−0.194925
$759$	−2.35660	−0.0855393
$760$	0	0
$761$	10.9029	0.395231	0.197616	−	0.980280i	$-0.436680\pi$
$761$	10.9029	0.395231	0.197616	+	0.980280i	$0.436680\pi$
$762$	−1.78307	−0.0645939
$763$	51.3574	1.85926
$764$	24.4118	0.883187
$765$	0	0
$766$	−3.05399	−0.110345
$767$	−6.77412	−0.244599
$768$	−4.47120	−0.161340
$769$	19.8977	0.717528	0.358764	−	0.933428i	$-0.383198\pi$
$769$	19.8977	0.717528	0.358764	+	0.933428i	$0.383198\pi$
$770$	0	0
$771$	−1.34185	−0.0483256
$772$	−0.925411	−0.0333063
$773$	29.0277	1.04405	0.522027	−	0.852929i	$-0.325176\pi$
$773$	29.0277	1.04405	0.522027	+	0.852929i	$0.325176\pi$
$774$	−7.49555	−0.269422
$775$	0	0
$776$	−9.38699	−0.336973
$777$	−11.2485	−0.403538
$778$	1.09344	0.0392018
$779$	18.8770	0.676340
$780$	0	0
$781$	0.0938366	0.00335774
$782$	−1.39061	−0.0497281
$783$	−15.4153	−0.550899
$784$	65.7565	2.34845
$785$	0	0
$786$	−0.944933	−0.0337047
$787$	41.6603	1.48503	0.742515	−	0.669829i	$-0.233633\pi$
$787$	41.6603	1.48503	0.742515	+	0.669829i	$0.233633\pi$
$788$	−41.5010	−1.47841
$789$	5.65828	0.201440
$790$	0	0
$791$	16.5659	0.589016
$792$	−2.80218	−0.0995713
$793$	−27.4654	−0.975324
$794$	−2.21422	−0.0785798
$795$	0	0
$796$	53.5395	1.89766
$797$	33.6446	1.19175	0.595876	−	0.803077i	$-0.296805\pi$
$797$	33.6446	1.19175	0.595876	+	0.803077i	$0.296805\pi$
$798$	−1.90087	−0.0672902
$799$	1.85252	0.0655375
$800$	0	0
$801$	4.97267	0.175701
$802$	3.42814	0.121052
$803$	2.47214	0.0872399
$804$	5.68204	0.200390
$805$	0	0
$806$	5.09587	0.179494
$807$	7.40108	0.260530
$808$	4.47434	0.157407
$809$	49.5984	1.74379	0.871893	−	0.489696i	$-0.162892\pi$
$809$	49.5984	1.74379	0.871893	+	0.489696i	$0.162892\pi$
$810$	0	0
$811$	−8.80246	−0.309096	−0.154548	−	0.987985i	$-0.549392\pi$
$811$	−8.80246	−0.309096	−0.154548	+	0.987985i	$0.549392\pi$
$812$	−53.8924	−1.89125
$813$	−10.0575	−0.352733
$814$	1.18454	0.0415181
$815$	0	0
$816$	−1.36904	−0.0479259
$817$	−23.2134	−0.812136
$818$	8.96037	0.313292
$819$	−48.3637	−1.68996
$820$	0	0
$821$	−0.693079	−0.0241886	−0.0120943	−	0.999927i	$-0.503850\pi$
$821$	−0.693079	−0.0241886	−0.0120943	+	0.999927i	$0.503850\pi$
$822$	1.86664	0.0651067
$823$	−30.4005	−1.05969	−0.529847	−	0.848093i	$-0.677751\pi$
$823$	−30.4005	−1.05969	−0.529847	+	0.848093i	$0.677751\pi$
$824$	3.87410	0.134961
$825$	0	0
$826$	3.02217	0.105155
$827$	−21.2895	−0.740309	−0.370154	−	0.928970i	$-0.620695\pi$
$827$	−21.2895	−0.740309	−0.370154	+	0.928970i	$0.620695\pi$
$828$	29.9126	1.03953
$829$	20.9294	0.726908	0.363454	−	0.931612i	$-0.381597\pi$
$829$	20.9294	0.726908	0.363454	+	0.931612i	$0.381597\pi$
$830$	0	0
$831$	1.82163	0.0631917
$832$	20.2930	0.703532
$833$	15.5156	0.537584
$834$	−2.59534	−0.0898694
$835$	0	0
$836$	−4.23904	−0.146610
$837$	13.7711	0.475999
$838$	0.296447	0.0102406
$839$	18.8970	0.652397	0.326198	−	0.945301i	$-0.394232\pi$
$839$	18.8970	0.652397	0.326198	+	0.945301i	$0.394232\pi$
$840$	0	0
$841$	1.66646	0.0574641
$842$	−3.68659	−0.127048
$843$	−1.54676	−0.0532731
$844$	17.8309	0.613764
$845$	0	0
$846$	1.88171	0.0646945
$847$	52.2620	1.79574
$848$	−1.41463	−0.0485784
$849$	−12.6455	−0.433992
$850$	0	0
$851$	−25.8864	−0.887373
$852$	0.100293	0.00343598
$853$	−40.7552	−1.39543	−0.697716	−	0.716374i	$-0.745800\pi$
$853$	−40.7552	−1.39543	−0.697716	+	0.716374i	$0.745800\pi$
$854$	12.2533	0.419298
$855$	0	0
$856$	−1.52186	−0.0520161
$857$	48.6456	1.66170	0.830850	−	0.556496i	$-0.187855\pi$
$857$	48.6456	1.66170	0.830850	+	0.556496i	$0.187855\pi$
$858$	−0.428850	−0.0146407
$859$	38.2329	1.30449	0.652244	−	0.758009i	$-0.273828\pi$
$859$	38.2329	1.30449	0.652244	+	0.758009i	$0.273828\pi$
$860$	0	0
$861$	18.0425	0.614886
$862$	−9.37478	−0.319306
$863$	−48.5192	−1.65161	−0.825806	−	0.563954i	$-0.809280\pi$
$863$	−48.5192	−1.65161	−0.825806	+	0.563954i	$0.809280\pi$
$864$	−9.43523	−0.320993
$865$	0	0
$866$	−4.86018	−0.165156
$867$	7.88274	0.267712
$868$	48.1442	1.63412
$869$	5.78957	0.196398
$870$	0	0
$871$	−21.1420	−0.716370
$872$	−11.8337	−0.400739
$873$	22.1215	0.748699
$874$	−4.37451	−0.147970
$875$	0	0
$876$	2.64223	0.0892727
$877$	−3.32745	−0.112360	−0.0561799	−	0.998421i	$-0.517892\pi$
$877$	−3.32745	−0.112360	−0.0561799	+	0.998421i	$0.517892\pi$
$878$	0.847213	0.0285921
$879$	13.7075	0.462343
$880$	0	0
$881$	−19.9449	−0.671962	−0.335981	−	0.941869i	$-0.609068\pi$
$881$	−19.9449	−0.671962	−0.335981	+	0.941869i	$0.609068\pi$
$882$	15.7601	0.530669
$883$	−11.7047	−0.393893	−0.196947	−	0.980414i	$-0.563103\pi$
$883$	−11.7047	−0.393893	−0.196947	+	0.980414i	$0.563103\pi$
$884$	5.35899	0.180242
$885$	0	0
$886$	2.51557	0.0845121
$887$	−20.4508	−0.686671	−0.343336	−	0.939213i	$-0.611557\pi$
$887$	−20.4508	−0.686671	−0.343336	+	0.939213i	$0.611557\pi$
$888$	2.59186	0.0869772
$889$	62.6812	2.10226
$890$	0	0
$891$	6.00079	0.201034
$892$	−36.8983	−1.23545
$893$	5.82758	0.195013
$894$	3.00029	0.100345
$895$	0	0
$896$	−43.5969	−1.45647
$897$	9.37188	0.312918
$898$	−2.06867	−0.0690323
$899$	−27.3955	−0.913692
$900$	0	0
$901$	−0.333789	−0.0111201
$902$	−1.89999	−0.0632628
$903$	−22.1872	−0.738344
$904$	−3.81709	−0.126955
$905$	0	0
$906$	−1.85425	−0.0616033
$907$	13.2375	0.439545	0.219772	−	0.975551i	$-0.429469\pi$
$907$	13.2375	0.439545	0.219772	+	0.975551i	$0.429469\pi$
$908$	−32.1224	−1.06602
$909$	−10.5443	−0.349732
$910$	0	0
$911$	−55.5735	−1.84123	−0.920616	−	0.390469i	$-0.872313\pi$
$911$	−55.5735	−1.84123	−0.920616	+	0.390469i	$0.872313\pi$
$912$	−4.30665	−0.142608
$913$	9.01818	0.298458
$914$	−7.91036	−0.261651
$915$	0	0
$916$	5.94901	0.196561
$917$	33.2177	1.09694
$918$	−0.683871	−0.0225711
$919$	−9.38220	−0.309490	−0.154745	−	0.987954i	$-0.549456\pi$
$919$	−9.38220	−0.309490	−0.154745	+	0.987954i	$0.549456\pi$
$920$	0	0
$921$	4.50549	0.148461
$922$	−5.22000	−0.171912
$923$	−0.373175	−0.0122832
$924$	−4.05164	−0.133289
$925$	0	0
$926$	−3.91419	−0.128628
$927$	−9.12976	−0.299861
$928$	18.7699	0.616154
$929$	−29.5456	−0.969359	−0.484680	−	0.874692i	$-0.661064\pi$
$929$	−29.5456	−0.969359	−0.484680	+	0.874692i	$0.661064\pi$
$930$	0	0
$931$	48.8083	1.59963
$932$	−19.1563	−0.627485
$933$	10.1220	0.331379
$934$	9.32755	0.305207
$935$	0	0
$936$	11.1439	0.364250
$937$	43.0335	1.40584	0.702921	−	0.711268i	$-0.251879\pi$
$937$	43.0335	1.40584	0.702921	+	0.711268i	$0.251879\pi$
$938$	9.43219	0.307972
$939$	−11.2169	−0.366049
$940$	0	0
$941$	40.9374	1.33452	0.667260	−	0.744824i	$-0.267467\pi$
$941$	40.9374	1.33452	0.667260	+	0.744824i	$0.267467\pi$
$942$	−1.17602	−0.0383169
$943$	41.5215	1.35213
$944$	6.84708	0.222853
$945$	0	0
$946$	2.33646	0.0759647
$947$	−27.3029	−0.887225	−0.443613	−	0.896219i	$-0.646303\pi$
$947$	−27.3029	−0.887225	−0.443613	+	0.896219i	$0.646303\pi$
$948$	6.18791	0.200974
$949$	−9.83135	−0.319139
$950$	0	0
$951$	−15.3382	−0.497376
$952$	−4.89456	−0.158634
$953$	−0.737786	−0.0238992	−0.0119496	−	0.999929i	$-0.503804\pi$
$953$	−0.737786	−0.0238992	−0.0119496	+	0.999929i	$0.503804\pi$
$954$	−0.339047	−0.0109771
$955$	0	0
$956$	−45.9069	−1.48474
$957$	2.30551	0.0745265
$958$	8.48548	0.274153
$959$	−65.6190	−2.11895
$960$	0	0
$961$	−6.52650	−0.210532
$962$	−4.71075	−0.151881
$963$	3.58643	0.115571
$964$	1.90982	0.0615110
$965$	0	0
$966$	−4.18112	−0.134525
$967$	−17.6392	−0.567239	−0.283620	−	0.958937i	$-0.591535\pi$
$967$	−17.6392	−0.567239	−0.283620	+	0.958937i	$0.591535\pi$
$968$	−12.0421	−0.387049
$969$	−1.01618	−0.0326444
$970$	0	0
$971$	−32.7620	−1.05138	−0.525691	−	0.850676i	$-0.676193\pi$
$971$	−32.7620	−1.05138	−0.525691	+	0.850676i	$0.676193\pi$
$972$	22.3627	0.717283
$973$	91.2353	2.92487
$974$	11.6378	0.372898
$975$	0	0
$976$	27.7612	0.888614
$977$	29.2423	0.935545	0.467772	−	0.883849i	$-0.345057\pi$
$977$	29.2423	0.935545	0.467772	+	0.883849i	$0.345057\pi$
$978$	0.708755	0.0226635
$979$	−1.55004	−0.0495396
$980$	0	0
$981$	27.8874	0.890377
$982$	−9.82590	−0.313557
$983$	−52.8054	−1.68423	−0.842116	−	0.539297i	$-0.818690\pi$
$983$	−52.8054	−1.68423	−0.842116	+	0.539297i	$0.818690\pi$
$984$	−4.15732	−0.132531
$985$	0	0
$986$	1.36046	0.0433258
$987$	5.56995	0.177293
$988$	16.8581	0.536327
$989$	−51.0598	−1.62361
$990$	0	0
$991$	−19.2875	−0.612688	−0.306344	−	0.951921i	$-0.599106\pi$
$991$	−19.2875	−0.612688	−0.306344	+	0.951921i	$0.599106\pi$
$992$	−16.7679	−0.532382
$993$	8.66472	0.274967
$994$	0.166486	0.00528063
$995$	0	0
$996$	9.63866	0.305413
$997$	28.4893	0.902265	0.451132	−	0.892457i	$-0.351020\pi$
$997$	28.4893	0.902265	0.451132	+	0.892457i	$0.351020\pi$
$998$	−2.95286	−0.0934711
$999$	−12.7304	−0.402771

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6025.2.a.j.1.14		25
5.4	even	2		1205.2.a.e.1.12	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1205.2.a.e.1.12	✓	25	5.4	even	2
6025.2.a.j.1.14		25	1.1	even	1	trivial

Overview	Random
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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)

\(f(q)\)	\(=\)	\(q-0.300307 q^{2} -0.482693 q^{3} -1.90982 q^{4} +0.144956 q^{6} -5.09571 q^{7} +1.17415 q^{8} -2.76701 q^{9} +O(q^{10})\)	\(q-0.300307 q^{2} -0.482693 q^{3} -1.90982 q^{4} +0.144956 q^{6} -5.09571 q^{7} +1.17415 q^{8} -2.76701 q^{9} +0.862510 q^{11} +0.921854 q^{12} -3.43008 q^{13} +1.53028 q^{14} +3.46703 q^{16} +0.818064 q^{17} +0.830953 q^{18} +2.57343 q^{19} +2.45966 q^{21} -0.259018 q^{22} +5.66046 q^{23} -0.566752 q^{24} +1.03008 q^{26} +2.78369 q^{27} +9.73186 q^{28} -5.53773 q^{29} +4.94707 q^{31} -3.38947 q^{32} -0.416327 q^{33} -0.245671 q^{34} +5.28447 q^{36} -4.57319 q^{37} -0.772820 q^{38} +1.65568 q^{39} +7.33536 q^{41} -0.738654 q^{42} -9.02043 q^{43} -1.64724 q^{44} -1.69988 q^{46} +2.26452 q^{47} -1.67351 q^{48} +18.9663 q^{49} -0.394873 q^{51} +6.55082 q^{52} -0.408023 q^{53} -0.835963 q^{54} -5.98311 q^{56} -1.24218 q^{57} +1.66302 q^{58} +1.97491 q^{59} +8.00721 q^{61} -1.48564 q^{62} +14.0999 q^{63} -5.91617 q^{64} +0.125026 q^{66} +6.16371 q^{67} -1.56235 q^{68} -2.73226 q^{69} +0.108795 q^{71} -3.24887 q^{72} +2.86621 q^{73} +1.37336 q^{74} -4.91478 q^{76} -4.39510 q^{77} -0.497211 q^{78} +6.71247 q^{79} +6.95736 q^{81} -2.20286 q^{82} +10.4557 q^{83} -4.69750 q^{84} +2.70890 q^{86} +2.67302 q^{87} +1.01271 q^{88} -1.79713 q^{89} +17.4787 q^{91} -10.8104 q^{92} -2.38791 q^{93} -0.680052 q^{94} +1.63607 q^{96} -7.99473 q^{97} -5.69570 q^{98} -2.38657 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 6 q^{2} - 15 q^{3} + 32 q^{4} - q^{6} - 19 q^{7} - 15 q^{8} + 32 q^{9}+O(q^{10}) \) 25 * q - 6 * q^2 - 15 * q^3 + 32 * q^4 - q^6 - 19 * q^7 - 15 * q^8 + 32 * q^9	\( 25 q - 6 q^{2} - 15 q^{3} + 32 q^{4} - q^{6} - 19 q^{7} - 15 q^{8} + 32 q^{9} + 2 q^{11} - 20 q^{12} - 14 q^{13} - 5 q^{14} + 38 q^{16} - 7 q^{17} - 9 q^{18} + 30 q^{19} + q^{21} - q^{22} - 43 q^{23} - 6 q^{24} - 22 q^{26} - 42 q^{27} - 32 q^{28} - 4 q^{29} + 14 q^{31} - 26 q^{32} - 4 q^{33} + 7 q^{34} + 15 q^{36} - 16 q^{37} - 14 q^{38} - 21 q^{39} - q^{41} + 25 q^{42} - 35 q^{43} - 52 q^{44} - 27 q^{46} - 50 q^{47} - 26 q^{48} + 46 q^{49} - 7 q^{51} - 3 q^{52} - 4 q^{53} - 31 q^{54} - 51 q^{56} - 2 q^{58} + 6 q^{59} + 19 q^{61} - 28 q^{63} + 49 q^{64} - 27 q^{66} - 65 q^{67} + 25 q^{68} + 2 q^{69} - 34 q^{71} + 10 q^{72} - 8 q^{73} - 42 q^{74} + 71 q^{76} - q^{77} + 59 q^{78} - 12 q^{79} + 29 q^{81} - 11 q^{82} - 41 q^{83} - 10 q^{84} - 13 q^{86} - 40 q^{87} + 52 q^{88} - 24 q^{89} + 46 q^{91} - 85 q^{92} + 30 q^{93} + 14 q^{94} - 30 q^{96} - 9 q^{97} + 64 q^{98} + 2 q^{99}+O(q^{100}) \) 25 * q - 6 * q^2 - 15 * q^3 + 32 * q^4 - q^6 - 19 * q^7 - 15 * q^8 + 32 * q^9 + 2 * q^11 - 20 * q^12 - 14 * q^13 - 5 * q^14 + 38 * q^16 - 7 * q^17 - 9 * q^18 + 30 * q^19 + q^21 - q^22 - 43 * q^23 - 6 * q^24 - 22 * q^26 - 42 * q^27 - 32 * q^28 - 4 * q^29 + 14 * q^31 - 26 * q^32 - 4 * q^33 + 7 * q^34 + 15 * q^36 - 16 * q^37 - 14 * q^38 - 21 * q^39 - q^41 + 25 * q^42 - 35 * q^43 - 52 * q^44 - 27 * q^46 - 50 * q^47 - 26 * q^48 + 46 * q^49 - 7 * q^51 - 3 * q^52 - 4 * q^53 - 31 * q^54 - 51 * q^56 - 2 * q^58 + 6 * q^59 + 19 * q^61 - 28 * q^63 + 49 * q^64 - 27 * q^66 - 65 * q^67 + 25 * q^68 + 2 * q^69 - 34 * q^71 + 10 * q^72 - 8 * q^73 - 42 * q^74 + 71 * q^76 - q^77 + 59 * q^78 - 12 * q^79 + 29 * q^81 - 11 * q^82 - 41 * q^83 - 10 * q^84 - 13 * q^86 - 40 * q^87 + 52 * q^88 - 24 * q^89 + 46 * q^91 - 85 * q^92 + 30 * q^93 + 14 * q^94 - 30 * q^96 - 9 * q^97 + 64 * q^98 + 2 * q^99

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