LMFDB - Embedded newform 6001.2.a.b.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6001,2,Mod(1,6001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6001, 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("6001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6001 = 17 \cdot 353 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6001.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:	$47.9182262530$
Analytic rank:	$1$
Dimension:	$114$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	6001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.38632 q^{2} -0.731332 q^{3} +3.69453 q^{4} +1.80073 q^{5} +1.74519 q^{6} -2.93364 q^{7} -4.04370 q^{8} -2.46515 q^{9} +O(q^{10})$	\(q-2.38632 q^{2} -0.731332 q^{3} +3.69453 q^{4} +1.80073 q^{5} +1.74519 q^{6} -2.93364 q^{7} -4.04370 q^{8} -2.46515 q^{9} -4.29713 q^{10} +0.347932 q^{11} -2.70193 q^{12} -1.80377 q^{13} +7.00060 q^{14} -1.31694 q^{15} +2.26050 q^{16} +1.00000 q^{17} +5.88265 q^{18} -1.44867 q^{19} +6.65287 q^{20} +2.14546 q^{21} -0.830278 q^{22} -1.89471 q^{23} +2.95729 q^{24} -1.75735 q^{25} +4.30438 q^{26} +3.99684 q^{27} -10.8384 q^{28} +1.23132 q^{29} +3.14263 q^{30} -3.19162 q^{31} +2.69312 q^{32} -0.254454 q^{33} -2.38632 q^{34} -5.28271 q^{35} -9.10758 q^{36} +7.85544 q^{37} +3.45699 q^{38} +1.31916 q^{39} -7.28162 q^{40} +10.4853 q^{41} -5.11977 q^{42} -5.61665 q^{43} +1.28545 q^{44} -4.43909 q^{45} +4.52138 q^{46} +6.76065 q^{47} -1.65317 q^{48} +1.60623 q^{49} +4.19361 q^{50} -0.731332 q^{51} -6.66410 q^{52} +4.45378 q^{53} -9.53775 q^{54} +0.626534 q^{55} +11.8627 q^{56} +1.05946 q^{57} -2.93834 q^{58} +9.13356 q^{59} -4.86546 q^{60} -4.99819 q^{61} +7.61622 q^{62} +7.23187 q^{63} -10.9476 q^{64} -3.24812 q^{65} +0.607209 q^{66} +3.64704 q^{67} +3.69453 q^{68} +1.38566 q^{69} +12.6062 q^{70} -1.83384 q^{71} +9.96833 q^{72} +11.1597 q^{73} -18.7456 q^{74} +1.28521 q^{75} -5.35216 q^{76} -1.02071 q^{77} -3.14794 q^{78} +8.20187 q^{79} +4.07056 q^{80} +4.47244 q^{81} -25.0212 q^{82} -1.21802 q^{83} +7.92648 q^{84} +1.80073 q^{85} +13.4031 q^{86} -0.900507 q^{87} -1.40693 q^{88} -2.60146 q^{89} +10.5931 q^{90} +5.29162 q^{91} -7.00005 q^{92} +2.33413 q^{93} -16.1331 q^{94} -2.60867 q^{95} -1.96957 q^{96} +15.2585 q^{97} -3.83299 q^{98} -0.857706 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 114 q - 8 q^{2} - 23 q^{3} + 110 q^{4} - 27 q^{5} - 23 q^{6} - 53 q^{7} - 21 q^{8} + 107 q^{9}+O(q^{10}) $ 114 * q - 8 * q^2 - 23 * q^3 + 110 * q^4 - 27 * q^5 - 23 * q^6 - 53 * q^7 - 21 * q^8 + 107 * q^9	\( 114 q - 8 q^{2} - 23 q^{3} + 110 q^{4} - 27 q^{5} - 23 q^{6} - 53 q^{7} - 21 q^{8} + 107 q^{9} - 19 q^{10} - 52 q^{11} - 49 q^{12} - 12 q^{13} - 40 q^{14} - 39 q^{15} + 110 q^{16} + 114 q^{17} - 21 q^{18} - 30 q^{19} - 88 q^{20} - 30 q^{21} - 36 q^{22} - 77 q^{23} - 72 q^{24} + 119 q^{25} - 79 q^{26} - 77 q^{27} - 92 q^{28} - 65 q^{29} - 10 q^{30} - 131 q^{31} - 30 q^{32} - 12 q^{33} - 8 q^{34} - 33 q^{35} + 109 q^{36} - 54 q^{37} - 14 q^{38} - 83 q^{39} - 42 q^{40} - 99 q^{41} + 29 q^{42} + 4 q^{43} - 98 q^{44} - 73 q^{45} - 35 q^{46} - 113 q^{47} - 86 q^{48} + 101 q^{49} - 44 q^{50} - 23 q^{51} - 3 q^{52} - 18 q^{53} - 78 q^{54} - 63 q^{55} - 117 q^{56} - 64 q^{57} - 31 q^{58} - 134 q^{59} - 6 q^{60} - 30 q^{61} - 30 q^{62} - 154 q^{63} + 117 q^{64} - 66 q^{65} - 12 q^{66} - 34 q^{67} + 110 q^{68} - 35 q^{69} + 18 q^{70} - 233 q^{71} + 16 q^{72} - 56 q^{73} - 64 q^{74} - 100 q^{75} - 64 q^{76} - 6 q^{77} + 50 q^{78} - 154 q^{79} - 128 q^{80} + 118 q^{81} + 2 q^{82} - 53 q^{83} - 6 q^{84} - 27 q^{85} - 52 q^{86} - 22 q^{87} - 52 q^{88} - 118 q^{89} - 5 q^{90} - 95 q^{91} - 102 q^{92} + 47 q^{93} - 3 q^{94} - 158 q^{95} - 144 q^{96} - 57 q^{97} + 3 q^{98} - 131 q^{99}+O(q^{100}) \) 114 * q - 8 * q^2 - 23 * q^3 + 110 * q^4 - 27 * q^5 - 23 * q^6 - 53 * q^7 - 21 * q^8 + 107 * q^9 - 19 * q^10 - 52 * q^11 - 49 * q^12 - 12 * q^13 - 40 * q^14 - 39 * q^15 + 110 * q^16 + 114 * q^17 - 21 * q^18 - 30 * q^19 - 88 * q^20 - 30 * q^21 - 36 * q^22 - 77 * q^23 - 72 * q^24 + 119 * q^25 - 79 * q^26 - 77 * q^27 - 92 * q^28 - 65 * q^29 - 10 * q^30 - 131 * q^31 - 30 * q^32 - 12 * q^33 - 8 * q^34 - 33 * q^35 + 109 * q^36 - 54 * q^37 - 14 * q^38 - 83 * q^39 - 42 * q^40 - 99 * q^41 + 29 * q^42 + 4 * q^43 - 98 * q^44 - 73 * q^45 - 35 * q^46 - 113 * q^47 - 86 * q^48 + 101 * q^49 - 44 * q^50 - 23 * q^51 - 3 * q^52 - 18 * q^53 - 78 * q^54 - 63 * q^55 - 117 * q^56 - 64 * q^57 - 31 * q^58 - 134 * q^59 - 6 * q^60 - 30 * q^61 - 30 * q^62 - 154 * q^63 + 117 * q^64 - 66 * q^65 - 12 * q^66 - 34 * q^67 + 110 * q^68 - 35 * q^69 + 18 * q^70 - 233 * q^71 + 16 * q^72 - 56 * q^73 - 64 * q^74 - 100 * q^75 - 64 * q^76 - 6 * q^77 + 50 * q^78 - 154 * q^79 - 128 * q^80 + 118 * q^81 + 2 * q^82 - 53 * q^83 - 6 * q^84 - 27 * q^85 - 52 * q^86 - 22 * q^87 - 52 * q^88 - 118 * q^89 - 5 * q^90 - 95 * q^91 - 102 * q^92 + 47 * q^93 - 3 * q^94 - 158 * q^95 - 144 * q^96 - 57 * q^97 + 3 * q^98 - 131 * 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 $

$2$	−2.38632	−1.68738	−0.843692	−	0.536827i	$-0.819623\pi$
$2$	−2.38632	−1.68738	−0.843692	+	0.536827i	$0.819623\pi$
$3$	−0.731332	−0.422235	−0.211117	−	0.977461i	$-0.567710\pi$
$3$	−0.731332	−0.422235	−0.211117	+	0.977461i	$0.567710\pi$
$4$	3.69453	1.84727
$5$	1.80073	0.805313	0.402657	−	0.915351i	$-0.368087\pi$
$5$	1.80073	0.805313	0.402657	+	0.915351i	$0.368087\pi$
$6$	1.74519	0.712473
$7$	−2.93364	−1.10881	−0.554406	−	0.832247i	$-0.687054\pi$
$7$	−2.93364	−1.10881	−0.554406	+	0.832247i	$0.687054\pi$
$8$	−4.04370	−1.42966
$9$	−2.46515	−0.821718
$10$	−4.29713	−1.35887
$11$	0.347932	0.104906	0.0524528	−	0.998623i	$-0.483296\pi$
$11$	0.347932	0.104906	0.0524528	+	0.998623i	$0.483296\pi$
$12$	−2.70193	−0.779980
$13$	−1.80377	−0.500277	−0.250138	−	0.968210i	$-0.580476\pi$
$13$	−1.80377	−0.500277	−0.250138	+	0.968210i	$0.580476\pi$
$14$	7.00060	1.87099
$15$	−1.31694	−0.340031
$16$	2.26050	0.565124
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	5.88265	1.38655
$19$	−1.44867	−0.332348	−0.166174	−	0.986096i	$-0.553141\pi$
$19$	−1.44867	−0.332348	−0.166174	+	0.986096i	$0.553141\pi$
$20$	6.65287	1.48763
$21$	2.14546	0.468179
$22$	−0.830278	−0.177016
$23$	−1.89471	−0.395073	−0.197537	−	0.980295i	$-0.563294\pi$
$23$	−1.89471	−0.395073	−0.197537	+	0.980295i	$0.563294\pi$
$24$	2.95729	0.603653
$25$	−1.75735	−0.351471
$26$	4.30438	0.844159
$27$	3.99684	0.769193
$28$	−10.8384	−2.04827
$29$	1.23132	0.228651	0.114326	−	0.993443i	$-0.463529\pi$
$29$	1.23132	0.228651	0.114326	+	0.993443i	$0.463529\pi$
$30$	3.14263	0.573763
$31$	−3.19162	−0.573231	−0.286616	−	0.958046i	$-0.592530\pi$
$31$	−3.19162	−0.573231	−0.286616	+	0.958046i	$0.592530\pi$
$32$	2.69312	0.476081
$33$	−0.254454	−0.0442948
$34$	−2.38632	−0.409251
$35$	−5.28271	−0.892940
$36$	−9.10758	−1.51793
$37$	7.85544	1.29143	0.645713	−	0.763580i	$-0.276560\pi$
$37$	7.85544	1.29143	0.645713	+	0.763580i	$0.276560\pi$
$38$	3.45699	0.560798
$39$	1.31916	0.211234
$40$	−7.28162	−1.15133
$41$	10.4853	1.63752	0.818761	−	0.574134i	$-0.194661\pi$
$41$	10.4853	1.63752	0.818761	+	0.574134i	$0.194661\pi$
$42$	−5.11977	−0.789997
$43$	−5.61665	−0.856531	−0.428265	−	0.903653i	$-0.640875\pi$
$43$	−5.61665	−0.856531	−0.428265	+	0.903653i	$0.640875\pi$
$44$	1.28545	0.193788
$45$	−4.43909	−0.661740
$46$	4.52138	0.666641
$47$	6.76065	0.986143	0.493071	−	0.869989i	$-0.335874\pi$
$47$	6.76065	0.986143	0.493071	+	0.869989i	$0.335874\pi$
$48$	−1.65317	−0.238615
$49$	1.60623	0.229462
$50$	4.19361	0.593066
$51$	−0.731332	−0.102407
$52$	−6.66410	−0.924144
$53$	4.45378	0.611774	0.305887	−	0.952068i	$-0.401047\pi$
$53$	4.45378	0.611774	0.305887	+	0.952068i	$0.401047\pi$
$54$	−9.53775	−1.29792
$55$	0.626534	0.0844818
$56$	11.8627	1.58523
$57$	1.05946	0.140329
$58$	−2.93834	−0.385822
$59$	9.13356	1.18909	0.594544	−	0.804063i	$-0.297333\pi$
$59$	9.13356	1.18909	0.594544	+	0.804063i	$0.297333\pi$
$60$	−4.86546	−0.628128
$61$	−4.99819	−0.639953	−0.319977	−	0.947425i	$-0.603675\pi$
$61$	−4.99819	−0.639953	−0.319977	+	0.947425i	$0.603675\pi$
$62$	7.61622	0.967261
$63$	7.23187	0.911130
$64$	−10.9476	−1.36846
$65$	−3.24812	−0.402879
$66$	0.607209	0.0747423
$67$	3.64704	0.445557	0.222779	−	0.974869i	$-0.428487\pi$
$67$	3.64704	0.445557	0.222779	+	0.974869i	$0.428487\pi$
$68$	3.69453	0.448028
$69$	1.38566	0.166814
$70$	12.6062	1.50673
$71$	−1.83384	−0.217637	−0.108818	−	0.994062i	$-0.534707\pi$
$71$	−1.83384	−0.217637	−0.108818	+	0.994062i	$0.534707\pi$
$72$	9.96833	1.17478
$73$	11.1597	1.30615	0.653073	−	0.757295i	$-0.273479\pi$
$73$	11.1597	1.30615	0.653073	+	0.757295i	$0.273479\pi$
$74$	−18.7456	−2.17913
$75$	1.28521	0.148403
$76$	−5.35216	−0.613935
$77$	−1.02071	−0.116320
$78$	−3.14794	−0.356433
$79$	8.20187	0.922783	0.461391	−	0.887197i	$-0.347350\pi$
$79$	8.20187	0.922783	0.461391	+	0.887197i	$0.347350\pi$
$80$	4.07056	0.455102
$81$	4.47244	0.496938
$82$	−25.0212	−2.76313
$83$	−1.21802	−0.133695	−0.0668475	−	0.997763i	$-0.521294\pi$
$83$	−1.21802	−0.133695	−0.0668475	+	0.997763i	$0.521294\pi$
$84$	7.92648	0.864850
$85$	1.80073	0.195317
$86$	13.4031	1.44530
$87$	−0.900507	−0.0965445
$88$	−1.40693	−0.149979
$89$	−2.60146	−0.275754	−0.137877	−	0.990449i	$-0.544028\pi$
$89$	−2.60146	−0.275754	−0.137877	+	0.990449i	$0.544028\pi$
$90$	10.5931	1.11661
$91$	5.29162	0.554712
$92$	−7.00005	−0.729805
$93$	2.33413	0.242038
$94$	−16.1331	−1.66400
$95$	−2.60867	−0.267644
$96$	−1.96957	−0.201018
$97$	15.2585	1.54927	0.774635	−	0.632409i	$-0.217934\pi$
$97$	15.2585	1.54927	0.774635	+	0.632409i	$0.217934\pi$
$98$	−3.83299	−0.387191
$99$	−0.857706	−0.0862027
$100$	−6.49260	−0.649260
$101$	−7.31205	−0.727576	−0.363788	−	0.931482i	$-0.618517\pi$
$101$	−7.31205	−0.727576	−0.363788	+	0.931482i	$0.618517\pi$
$102$	1.74519	0.172800
$103$	2.60750	0.256924	0.128462	−	0.991714i	$-0.458996\pi$
$103$	2.60750	0.256924	0.128462	+	0.991714i	$0.458996\pi$
$104$	7.29391	0.715227
$105$	3.86341	0.377030
$106$	−10.6282	−1.03230
$107$	2.00243	0.193582	0.0967911	−	0.995305i	$-0.469142\pi$
$107$	2.00243	0.193582	0.0967911	+	0.995305i	$0.469142\pi$
$108$	14.7665	1.42090
$109$	−1.94507	−0.186304	−0.0931518	−	0.995652i	$-0.529694\pi$
$109$	−1.94507	−0.186304	−0.0931518	+	0.995652i	$0.529694\pi$
$110$	−1.49511	−0.142553
$111$	−5.74494	−0.545285
$112$	−6.63148	−0.626616
$113$	−14.2743	−1.34281	−0.671406	−	0.741090i	$-0.734309\pi$
$113$	−14.2743	−1.34281	−0.671406	+	0.741090i	$0.734309\pi$
$114$	−2.52821	−0.236789
$115$	−3.41186	−0.318158
$116$	4.54917	0.422379
$117$	4.44658	0.411086
$118$	−21.7956	−2.00645
$119$	−2.93364	−0.268926
$120$	5.32529	0.486130
$121$	−10.8789	−0.988995
$122$	11.9273	1.07985
$123$	−7.66821	−0.691419
$124$	−11.7915	−1.05891
$125$	−12.1682	−1.08836
$126$	−17.2576	−1.53743
$127$	−2.58523	−0.229402	−0.114701	−	0.993400i	$-0.536591\pi$
$127$	−2.58523	−0.229402	−0.114701	+	0.993400i	$0.536591\pi$
$128$	20.7384	1.83303
$129$	4.10764	0.361657
$130$	7.75105	0.679812
$131$	7.25358	0.633748	0.316874	−	0.948468i	$-0.397367\pi$
$131$	7.25358	0.633748	0.316874	+	0.948468i	$0.397367\pi$
$132$	−0.940088	−0.0818242
$133$	4.24988	0.368511
$134$	−8.70302	−0.751826
$135$	7.19725	0.619441
$136$	−4.04370	−0.346744
$137$	−16.2933	−1.39203	−0.696017	−	0.718025i	$-0.745046\pi$
$137$	−16.2933	−1.39203	−0.696017	+	0.718025i	$0.745046\pi$
$138$	−3.30663	−0.281479
$139$	0.813084	0.0689649	0.0344824	−	0.999405i	$-0.489022\pi$
$139$	0.813084	0.0689649	0.0344824	+	0.999405i	$0.489022\pi$
$140$	−19.5171	−1.64950
$141$	−4.94428	−0.416384
$142$	4.37613	0.367237
$143$	−0.627591	−0.0524818
$144$	−5.57247	−0.464373
$145$	2.21729	0.184136
$146$	−26.6307	−2.20397
$147$	−1.17469	−0.0968869
$148$	29.0222	2.38561
$149$	−5.41745	−0.443815	−0.221907	−	0.975068i	$-0.571228\pi$
$149$	−5.41745	−0.443815	−0.221907	+	0.975068i	$0.571228\pi$
$150$	−3.06692	−0.250413
$151$	−15.9860	−1.30093	−0.650463	−	0.759538i	$-0.725425\pi$
$151$	−15.9860	−1.30093	−0.650463	+	0.759538i	$0.725425\pi$
$152$	5.85798	0.475145
$153$	−2.46515	−0.199296
$154$	2.43574	0.196277
$155$	−5.74725	−0.461630
$156$	4.87367	0.390206
$157$	15.9674	1.27434	0.637170	−	0.770723i	$-0.280105\pi$
$157$	15.9674	1.27434	0.637170	+	0.770723i	$0.280105\pi$
$158$	−19.5723	−1.55709
$159$	−3.25720	−0.258312
$160$	4.84959	0.383394
$161$	5.55838	0.438062
$162$	−10.6727	−0.838525
$163$	−17.2121	−1.34815	−0.674077	−	0.738661i	$-0.735458\pi$
$163$	−17.2121	−1.34815	−0.674077	+	0.738661i	$0.735458\pi$
$164$	38.7381	3.02494
$165$	−0.458204	−0.0356712
$166$	2.90659	0.225595
$167$	−6.95504	−0.538197	−0.269099	−	0.963113i	$-0.586726\pi$
$167$	−6.95504	−0.538197	−0.269099	+	0.963113i	$0.586726\pi$
$168$	−8.67561	−0.669338
$169$	−9.74640	−0.749723
$170$	−4.29713	−0.329575
$171$	3.57119	0.273096
$172$	−20.7509	−1.58224
$173$	15.5483	1.18212	0.591059	−	0.806629i	$-0.298710\pi$
$173$	15.5483	1.18212	0.591059	+	0.806629i	$0.298710\pi$
$174$	2.14890	0.162908
$175$	5.15544	0.389715
$176$	0.786500	0.0592846
$177$	−6.67967	−0.502075
$178$	6.20792	0.465303
$179$	−16.8613	−1.26028	−0.630138	−	0.776483i	$-0.717002\pi$
$179$	−16.8613	−1.26028	−0.630138	+	0.776483i	$0.717002\pi$
$180$	−16.4003	−1.22241
$181$	−8.87793	−0.659892	−0.329946	−	0.944000i	$-0.607030\pi$
$181$	−8.87793	−0.659892	−0.329946	+	0.944000i	$0.607030\pi$
$182$	−12.6275	−0.936013
$183$	3.65534	0.270211
$184$	7.66161	0.564822
$185$	14.1456	1.04000
$186$	−5.56999	−0.408411
$187$	0.347932	0.0254433
$188$	24.9774	1.82167
$189$	−11.7253	−0.852889
$190$	6.22513	0.451618
$191$	−10.2305	−0.740250	−0.370125	−	0.928982i	$-0.620685\pi$
$191$	−10.2305	−0.740250	−0.370125	+	0.928982i	$0.620685\pi$
$192$	8.00636	0.577810
$193$	−7.55672	−0.543945	−0.271972	−	0.962305i	$-0.587676\pi$
$193$	−7.55672	−0.543945	−0.271972	+	0.962305i	$0.587676\pi$
$194$	−36.4118	−2.61421
$195$	2.37545	0.170110
$196$	5.93428	0.423877
$197$	8.75809	0.623988	0.311994	−	0.950084i	$-0.399003\pi$
$197$	8.75809	0.623988	0.311994	+	0.950084i	$0.399003\pi$
$198$	2.04676	0.145457
$199$	−27.7511	−1.96722	−0.983611	−	0.180303i	$-0.942292\pi$
$199$	−27.7511	−1.96722	−0.983611	+	0.180303i	$0.942292\pi$
$200$	7.10620	0.502484
$201$	−2.66720	−0.188130
$202$	17.4489	1.22770
$203$	−3.61226	−0.253531
$204$	−2.70193	−0.189173
$205$	18.8812	1.31872
$206$	−6.22233	−0.433530
$207$	4.67074	0.324639
$208$	−4.07742	−0.282718
$209$	−0.504039	−0.0348651
$210$	−9.21935	−0.636195
$211$	−21.8646	−1.50522	−0.752610	−	0.658467i	$-0.771205\pi$
$211$	−21.8646	−1.50522	−0.752610	+	0.658467i	$0.771205\pi$
$212$	16.4546	1.13011
$213$	1.34115	0.0918938
$214$	−4.77844	−0.326647
$215$	−10.1141	−0.689775
$216$	−16.1620	−1.09969
$217$	9.36305	0.635605
$218$	4.64155	0.314366
$219$	−8.16146	−0.551500
$220$	2.31475	0.156060
$221$	−1.80377	−0.121335
$222$	13.7093	0.920106
$223$	14.0179	0.938709	0.469354	−	0.883010i	$-0.344487\pi$
$223$	14.0179	0.938709	0.469354	+	0.883010i	$0.344487\pi$
$224$	−7.90064	−0.527884
$225$	4.33215	0.288810
$226$	34.0630	2.26584
$227$	2.91981	0.193795	0.0968973	−	0.995294i	$-0.469108\pi$
$227$	2.91981	0.193795	0.0968973	+	0.995294i	$0.469108\pi$
$228$	3.91421	0.259225
$229$	14.8579	0.981835	0.490917	−	0.871206i	$-0.336662\pi$
$229$	14.8579	0.981835	0.490917	+	0.871206i	$0.336662\pi$
$230$	8.14180	0.536854
$231$	0.746476	0.0491145
$232$	−4.97910	−0.326894
$233$	9.89756	0.648411	0.324205	−	0.945987i	$-0.394903\pi$
$233$	9.89756	0.648411	0.324205	+	0.945987i	$0.394903\pi$
$234$	−10.6110	−0.693661
$235$	12.1741	0.794154
$236$	33.7442	2.19656
$237$	−5.99829	−0.389631
$238$	7.00060	0.453782
$239$	−9.07454	−0.586983	−0.293492	−	0.955962i	$-0.594817\pi$
$239$	−9.07454	−0.586983	−0.293492	+	0.955962i	$0.594817\pi$
$240$	−2.97693	−0.192160
$241$	22.4628	1.44695	0.723477	−	0.690348i	$-0.242543\pi$
$241$	22.4628	1.44695	0.723477	+	0.690348i	$0.242543\pi$
$242$	25.9607	1.66881
$243$	−15.2614	−0.979017
$244$	−18.4660	−1.18216
$245$	2.89240	0.184789
$246$	18.2988	1.16669
$247$	2.61307	0.166266
$248$	12.9059	0.819527
$249$	0.890777	0.0564507
$250$	29.0372	1.83648
$251$	2.12835	0.134340	0.0671702	−	0.997742i	$-0.478603\pi$
$251$	2.12835	0.134340	0.0671702	+	0.997742i	$0.478603\pi$
$252$	26.7184	1.68310
$253$	−0.659229	−0.0414454
$254$	6.16919	0.387090
$255$	−1.31694	−0.0824697
$256$	−27.5931	−1.72457
$257$	−28.0764	−1.75136	−0.875679	−	0.482894i	$-0.839586\pi$
$257$	−28.0764	−1.75136	−0.875679	+	0.482894i	$0.839586\pi$
$258$	−9.80214	−0.610255
$259$	−23.0450	−1.43195
$260$	−12.0003	−0.744225
$261$	−3.03540	−0.187887
$262$	−17.3094	−1.06938
$263$	−16.3530	−1.00837	−0.504185	−	0.863596i	$-0.668207\pi$
$263$	−16.3530	−1.00837	−0.504185	+	0.863596i	$0.668207\pi$
$264$	1.02893	0.0633266
$265$	8.02008	0.492670
$266$	−10.1416	−0.621820
$267$	1.90253	0.116433
$268$	13.4741	0.823063
$269$	24.8267	1.51371	0.756855	−	0.653583i	$-0.226735\pi$
$269$	24.8267	1.51371	0.756855	+	0.653583i	$0.226735\pi$
$270$	−17.1750	−1.04524
$271$	21.5124	1.30678	0.653392	−	0.757020i	$-0.273345\pi$
$271$	21.5124	1.30678	0.653392	+	0.757020i	$0.273345\pi$
$272$	2.26050	0.137063
$273$	−3.86993	−0.234219
$274$	38.8812	2.34890
$275$	−0.611440	−0.0368712
$276$	5.11936	0.308149
$277$	−18.1491	−1.09048	−0.545238	−	0.838281i	$-0.683561\pi$
$277$	−18.1491	−1.09048	−0.545238	+	0.838281i	$0.683561\pi$
$278$	−1.94028	−0.116370
$279$	7.86782	0.471034
$280$	21.3617	1.27660
$281$	9.52494	0.568210	0.284105	−	0.958793i	$-0.408304\pi$
$281$	9.52494	0.568210	0.284105	+	0.958793i	$0.408304\pi$
$282$	11.7987	0.702600
$283$	28.4718	1.69247	0.846237	−	0.532806i	$-0.178863\pi$
$283$	28.4718	1.69247	0.846237	+	0.532806i	$0.178863\pi$
$284$	−6.77517	−0.402033
$285$	1.90781	0.113009
$286$	1.49763	0.0885570
$287$	−30.7600	−1.81570
$288$	−6.63895	−0.391204
$289$	1.00000	0.0588235
$290$	−5.29116	−0.310708
$291$	−11.1591	−0.654155
$292$	41.2299	2.41280
$293$	6.76742	0.395357	0.197678	−	0.980267i	$-0.436660\pi$
$293$	6.76742	0.395357	0.197678	+	0.980267i	$0.436660\pi$
$294$	2.80319	0.163485
$295$	16.4471	0.957588
$296$	−31.7650	−1.84630
$297$	1.39063	0.0806926
$298$	12.9278	0.748886
$299$	3.41762	0.197646
$300$	4.74825	0.274140
$301$	16.4772	0.949731
$302$	38.1478	2.19516
$303$	5.34754	0.307208
$304$	−3.27471	−0.187818
$305$	−9.00042	−0.515363
$306$	5.88265	0.336289
$307$	13.3185	0.760130	0.380065	−	0.924960i	$-0.375902\pi$
$307$	13.3185	0.760130	0.380065	+	0.924960i	$0.375902\pi$
$308$	−3.77103	−0.214875
$309$	−1.90695	−0.108482
$310$	13.7148	0.778948
$311$	−14.9468	−0.847553	−0.423777	−	0.905767i	$-0.639296\pi$
$311$	−14.9468	−0.847553	−0.423777	+	0.905767i	$0.639296\pi$
$312$	−5.33427	−0.301994
$313$	10.8435	0.612911	0.306455	−	0.951885i	$-0.400857\pi$
$313$	10.8435	0.612911	0.306455	+	0.951885i	$0.400857\pi$
$314$	−38.1034	−2.15030
$315$	13.0227	0.733745
$316$	30.3021	1.70462
$317$	28.0955	1.57800	0.789001	−	0.614392i	$-0.210599\pi$
$317$	28.0955	1.57800	0.789001	+	0.614392i	$0.210599\pi$
$318$	7.77272	0.435872
$319$	0.428417	0.0239868
$320$	−19.7138	−1.10204
$321$	−1.46444	−0.0817371
$322$	−13.2641	−0.739179
$323$	−1.44867	−0.0806062
$324$	16.5236	0.917976
$325$	3.16987	0.175833
$326$	41.0735	2.27485
$327$	1.42249	0.0786638
$328$	−42.3992	−2.34110
$329$	−19.8333	−1.09345
$330$	1.09342	0.0601910
$331$	6.19250	0.340371	0.170185	−	0.985412i	$-0.445563\pi$
$331$	6.19250	0.340371	0.170185	+	0.985412i	$0.445563\pi$
$332$	−4.50001	−0.246970
$333$	−19.3649	−1.06119
$334$	16.5970	0.908145
$335$	6.56736	0.358813
$336$	4.84982	0.264579
$337$	27.5485	1.50066	0.750332	−	0.661061i	$-0.229894\pi$
$337$	27.5485	1.50066	0.750332	+	0.661061i	$0.229894\pi$
$338$	23.2580	1.26507
$339$	10.4392	0.566982
$340$	6.65287	0.360803
$341$	−1.11047	−0.0601351
$342$	−8.52202	−0.460818
$343$	15.8234	0.854381
$344$	22.7120	1.22455
$345$	2.49521	0.134337
$346$	−37.1033	−1.99469
$347$	−3.93699	−0.211349	−0.105674	−	0.994401i	$-0.533700\pi$
$347$	−3.93699	−0.211349	−0.105674	+	0.994401i	$0.533700\pi$
$348$	−3.32695	−0.178343
$349$	3.06845	0.164251	0.0821253	−	0.996622i	$-0.473829\pi$
$349$	3.06845	0.164251	0.0821253	+	0.996622i	$0.473829\pi$
$350$	−12.3025	−0.657598
$351$	−7.20940	−0.384809
$352$	0.937023	0.0499435
$353$	1.00000	0.0532246
$353$	1.00000	0.0532246
$354$	15.9398	0.847193
$355$	−3.30226	−0.175266
$356$	−9.61117	−0.509391
$357$	2.14546	0.113550
$358$	40.2366	2.12657
$359$	−12.8218	−0.676707	−0.338354	−	0.941019i	$-0.609870\pi$
$359$	−12.8218	−0.676707	−0.338354	+	0.941019i	$0.609870\pi$
$360$	17.9503	0.946065
$361$	−16.9014	−0.889545
$362$	21.1856	1.11349
$363$	7.95612	0.417588
$364$	19.5501	1.02470
$365$	20.0957	1.05186
$366$	−8.72282	−0.455949
$367$	−23.3278	−1.21770	−0.608849	−	0.793286i	$-0.708369\pi$
$367$	−23.3278	−1.21770	−0.608849	+	0.793286i	$0.708369\pi$
$368$	−4.28298	−0.223266
$369$	−25.8478	−1.34558
$370$	−33.7559	−1.75488
$371$	−13.0658	−0.678342
$372$	8.62352	0.447109
$373$	−28.1304	−1.45654	−0.728268	−	0.685293i	$-0.759674\pi$
$373$	−28.1304	−1.45654	−0.728268	+	0.685293i	$0.759674\pi$
$374$	−0.830278	−0.0429327
$375$	8.89900	0.459542
$376$	−27.3380	−1.40985
$377$	−2.22103	−0.114389
$378$	27.9803	1.43915
$379$	−12.4012	−0.637004	−0.318502	−	0.947922i	$-0.603180\pi$
$379$	−12.4012	−0.637004	−0.318502	+	0.947922i	$0.603180\pi$
$380$	−9.63782	−0.494410
$381$	1.89066	0.0968616
$382$	24.4132	1.24909
$383$	−19.9183	−1.01778	−0.508888	−	0.860833i	$-0.669943\pi$
$383$	−19.9183	−1.01778	−0.508888	+	0.860833i	$0.669943\pi$
$384$	−15.1666	−0.773969
$385$	−1.83802	−0.0936743
$386$	18.0328	0.917844
$387$	13.8459	0.703826
$388$	56.3731	2.86191
$389$	1.68839	0.0856048	0.0428024	−	0.999084i	$-0.486371\pi$
$389$	1.68839	0.0856048	0.0428024	+	0.999084i	$0.486371\pi$
$390$	−5.66860	−0.287041
$391$	−1.89471	−0.0958194
$392$	−6.49512	−0.328053
$393$	−5.30478	−0.267591
$394$	−20.8996	−1.05291
$395$	14.7694	0.743129
$396$	−3.16882	−0.159239
$397$	−36.3951	−1.82662	−0.913308	−	0.407269i	$-0.866481\pi$
$397$	−36.3951	−1.82662	−0.913308	+	0.407269i	$0.866481\pi$
$398$	66.2230	3.31946
$399$	−3.10807	−0.155598
$400$	−3.97249	−0.198625
$401$	21.1548	1.05642	0.528210	−	0.849114i	$-0.322863\pi$
$401$	21.1548	1.05642	0.528210	+	0.849114i	$0.322863\pi$
$402$	6.36480	0.317447
$403$	5.75695	0.286774
$404$	−27.0146	−1.34403
$405$	8.05368	0.400190
$406$	8.62001	0.427804
$407$	2.73316	0.135478
$408$	2.95729	0.146407
$409$	6.03160	0.298243	0.149122	−	0.988819i	$-0.452355\pi$
$409$	6.03160	0.298243	0.149122	+	0.988819i	$0.452355\pi$
$410$	−45.0565	−2.22518
$411$	11.9158	0.587765
$412$	9.63348	0.474607
$413$	−26.7946	−1.31847
$414$	−11.1459	−0.547790
$415$	−2.19333	−0.107666
$416$	−4.85778	−0.238172
$417$	−0.594635	−0.0291194
$418$	1.20280	0.0588308
$419$	−28.7800	−1.40599	−0.702996	−	0.711193i	$-0.748155\pi$
$419$	−28.7800	−1.40599	−0.702996	+	0.711193i	$0.748155\pi$
$420$	14.2735	0.696475
$421$	−26.4896	−1.29102	−0.645512	−	0.763750i	$-0.723356\pi$
$421$	−26.4896	−1.29102	−0.645512	+	0.763750i	$0.723356\pi$
$422$	52.1759	2.53988
$423$	−16.6660	−0.810331
$424$	−18.0097	−0.874630
$425$	−1.75735	−0.0852442
$426$	−3.20040	−0.155060
$427$	14.6629	0.709587
$428$	7.39804	0.357598
$429$	0.458978	0.0221596
$430$	24.1355	1.16392
$431$	−19.0198	−0.916154	−0.458077	−	0.888913i	$-0.651462\pi$
$431$	−19.0198	−0.916154	−0.458077	+	0.888913i	$0.651462\pi$
$432$	9.03485	0.434689
$433$	27.3321	1.31350	0.656748	−	0.754110i	$-0.271931\pi$
$433$	27.3321	1.31350	0.656748	+	0.754110i	$0.271931\pi$
$434$	−22.3432	−1.07251
$435$	−1.62157	−0.0777486
$436$	−7.18611	−0.344152
$437$	2.74480	0.131302
$438$	19.4759	0.930593
$439$	8.16086	0.389497	0.194748	−	0.980853i	$-0.437611\pi$
$439$	8.16086	0.389497	0.194748	+	0.980853i	$0.437611\pi$
$440$	−2.53351	−0.120780
$441$	−3.95961	−0.188553
$442$	4.30438	0.204739
$443$	−29.3754	−1.39567	−0.697835	−	0.716259i	$-0.745853\pi$
$443$	−29.3754	−1.39567	−0.697835	+	0.716259i	$0.745853\pi$
$444$	−21.2248	−1.00729
$445$	−4.68454	−0.222068
$446$	−33.4512	−1.58396
$447$	3.96196	0.187394
$448$	32.1164	1.51736
$449$	14.1923	0.669775	0.334888	−	0.942258i	$-0.391302\pi$
$449$	14.1923	0.669775	0.334888	+	0.942258i	$0.391302\pi$
$450$	−10.3379	−0.487333
$451$	3.64816	0.171785
$452$	−52.7368	−2.48053
$453$	11.6911	0.549296
$454$	−6.96760	−0.327006
$455$	9.52880	0.446717
$456$	−4.28413	−0.200623
$457$	−13.6666	−0.639296	−0.319648	−	0.947536i	$-0.603565\pi$
$457$	−13.6666	−0.639296	−0.319648	+	0.947536i	$0.603565\pi$
$458$	−35.4556	−1.65673
$459$	3.99684	0.186557
$460$	−12.6052	−0.587722
$461$	−22.9365	−1.06826	−0.534129	−	0.845403i	$-0.679360\pi$
$461$	−22.9365	−1.06826	−0.534129	+	0.845403i	$0.679360\pi$
$462$	−1.78133	−0.0828751
$463$	−10.9090	−0.506985	−0.253492	−	0.967337i	$-0.581579\pi$
$463$	−10.9090	−0.506985	−0.253492	+	0.967337i	$0.581579\pi$
$464$	2.78340	0.129216
$465$	4.20315	0.194916
$466$	−23.6188	−1.09412
$467$	−15.6351	−0.723507	−0.361753	−	0.932274i	$-0.617822\pi$
$467$	−15.6351	−0.723507	−0.361753	+	0.932274i	$0.617822\pi$
$468$	16.4280	0.759385
$469$	−10.6991	−0.494039
$470$	−29.0514	−1.34004
$471$	−11.6775	−0.538071
$472$	−36.9333	−1.69999
$473$	−1.95421	−0.0898548
$474$	14.3139	0.657457
$475$	2.54583	0.116811
$476$	−10.8384	−0.496778
$477$	−10.9793	−0.502706
$478$	21.6548	0.990466
$479$	26.1414	1.19443	0.597216	−	0.802080i	$-0.296273\pi$
$479$	26.1414	1.19443	0.597216	+	0.802080i	$0.296273\pi$
$480$	−3.54666	−0.161882
$481$	−14.1694	−0.646071
$482$	−53.6034	−2.44157
$483$	−4.06502	−0.184965
$484$	−40.1926	−1.82694
$485$	27.4766	1.24765
$486$	36.4185	1.65198
$487$	28.9095	1.31002	0.655008	−	0.755622i	$-0.272665\pi$
$487$	28.9095	1.31002	0.655008	+	0.755622i	$0.272665\pi$
$488$	20.2112	0.914917
$489$	12.5877	0.569237
$490$	−6.90220	−0.311810
$491$	6.07604	0.274208	0.137104	−	0.990557i	$-0.456221\pi$
$491$	6.07604	0.274208	0.137104	+	0.990557i	$0.456221\pi$
$492$	−28.3304	−1.27723
$493$	1.23132	0.0554561
$494$	−6.23563	−0.280554
$495$	−1.54450	−0.0694202
$496$	−7.21464	−0.323947
$497$	5.37982	0.241318
$498$	−2.12568	−0.0952541
$499$	38.8961	1.74123	0.870614	−	0.491966i	$-0.163722\pi$
$499$	38.8961	1.74123	0.870614	+	0.491966i	$0.163722\pi$
$500$	−44.9558	−2.01048
$501$	5.08645	0.227246
$502$	−5.07893	−0.226684
$503$	−32.4758	−1.44802	−0.724012	−	0.689787i	$-0.757704\pi$
$503$	−32.4758	−1.44802	−0.724012	+	0.689787i	$0.757704\pi$
$504$	−29.2435	−1.30261
$505$	−13.1671	−0.585926
$506$	1.57313	0.0699343
$507$	7.12786	0.316559
$508$	−9.55122	−0.423767
$509$	−24.7597	−1.09746	−0.548728	−	0.836001i	$-0.684888\pi$
$509$	−24.7597	−1.09746	−0.548728	+	0.836001i	$0.684888\pi$
$510$	3.14263	0.139158
$511$	−32.7386	−1.44827
$512$	24.3693	1.07698
$513$	−5.79011	−0.255640
$514$	66.9993	2.95521
$515$	4.69541	0.206905
$516$	15.1758	0.668077
$517$	2.35225	0.103452
$518$	54.9928	2.41625
$519$	−11.3710	−0.499131
$520$	13.1344	0.575982
$521$	−41.3687	−1.81240	−0.906198	−	0.422853i	$-0.861029\pi$
$521$	−41.3687	−1.81240	−0.906198	+	0.422853i	$0.861029\pi$
$522$	7.24345	0.317037
$523$	9.02974	0.394843	0.197422	−	0.980319i	$-0.436743\pi$
$523$	9.02974	0.394843	0.197422	+	0.980319i	$0.436743\pi$
$524$	26.7986	1.17070
$525$	−3.77034	−0.164551
$526$	39.0236	1.70151
$527$	−3.19162	−0.139029
$528$	−0.575193	−0.0250320
$529$	−19.4101	−0.843917
$530$	−19.1385	−0.831323
$531$	−22.5156	−0.977095
$532$	15.7013	0.680738
$533$	−18.9130	−0.819214
$534$	−4.54005	−0.196467
$535$	3.60584	0.155894
$536$	−14.7475	−0.636996
$537$	12.3312	0.532132
$538$	−59.2445	−2.55421
$539$	0.558861	0.0240718
$540$	26.5905	1.14427
$541$	−39.1174	−1.68179	−0.840895	−	0.541198i	$-0.817971\pi$
$541$	−39.1174	−1.68179	−0.840895	+	0.541198i	$0.817971\pi$
$542$	−51.3354	−2.20505
$543$	6.49272	0.278629
$544$	2.69312	0.115467
$545$	−3.50255	−0.150033
$546$	9.23490	0.395217
$547$	−33.1264	−1.41638	−0.708192	−	0.706020i	$-0.750489\pi$
$547$	−33.1264	−1.41638	−0.708192	+	0.706020i	$0.750489\pi$
$548$	−60.1963	−2.57146
$549$	12.3213	0.525861
$550$	1.45909	0.0622159
$551$	−1.78378	−0.0759917
$552$	−5.60318	−0.238487
$553$	−24.0613	−1.02319
$554$	43.3097	1.84005
$555$	−10.3451	−0.439125
$556$	3.00396	0.127396
$557$	11.8344	0.501439	0.250719	−	0.968060i	$-0.419333\pi$
$557$	11.8344	0.501439	0.250719	+	0.968060i	$0.419333\pi$
$558$	−18.7751	−0.794815
$559$	10.1312	0.428502
$560$	−11.9415	−0.504622
$561$	−0.254454	−0.0107431
$562$	−22.7296	−0.958789
$563$	1.38282	0.0582788	0.0291394	−	0.999575i	$-0.490723\pi$
$563$	1.38282	0.0582788	0.0291394	+	0.999575i	$0.490723\pi$
$564$	−18.2668	−0.769172
$565$	−25.7042	−1.08138
$566$	−67.9429	−2.85585
$567$	−13.1205	−0.551010
$568$	7.41548	0.311147
$569$	14.2588	0.597760	0.298880	−	0.954291i	$-0.403387\pi$
$569$	14.2588	0.597760	0.298880	+	0.954291i	$0.403387\pi$
$570$	−4.55264	−0.190689
$571$	−12.7902	−0.535254	−0.267627	−	0.963523i	$-0.586239\pi$
$571$	−12.7902	−0.535254	−0.267627	+	0.963523i	$0.586239\pi$
$572$	−2.31865	−0.0969478
$573$	7.48187	0.312560
$574$	73.4032	3.06379
$575$	3.32967	0.138857
$576$	26.9876	1.12448
$577$	−15.9144	−0.662525	−0.331262	−	0.943539i	$-0.607475\pi$
$577$	−15.9144	−0.662525	−0.331262	+	0.943539i	$0.607475\pi$
$578$	−2.38632	−0.0992579
$579$	5.52648	0.229673
$580$	8.19184	0.340148
$581$	3.57323	0.148243
$582$	26.6291	1.10381
$583$	1.54961	0.0641785
$584$	−45.1265	−1.86735
$585$	8.00711	0.331053
$586$	−16.1492	−0.667119
$587$	−23.6222	−0.974992	−0.487496	−	0.873125i	$-0.662090\pi$
$587$	−23.6222	−0.974992	−0.487496	+	0.873125i	$0.662090\pi$
$588$	−4.33993	−0.178976
$589$	4.62360	0.190512
$590$	−39.2481	−1.61582
$591$	−6.40507	−0.263469
$592$	17.7572	0.729816
$593$	25.4016	1.04312	0.521560	−	0.853215i	$-0.325350\pi$
$593$	25.4016	1.04312	0.521560	+	0.853215i	$0.325350\pi$
$594$	−3.31849	−0.136159
$595$	−5.28271	−0.216570
$596$	−20.0149	−0.819844
$597$	20.2953	0.830630
$598$	−8.15554	−0.333505
$599$	−19.8692	−0.811833	−0.405916	−	0.913910i	$-0.633048\pi$
$599$	−19.8692	−0.811833	−0.405916	+	0.913910i	$0.633048\pi$
$600$	−5.19700	−0.212166
$601$	−2.68442	−0.109500	−0.0547500	−	0.998500i	$-0.517436\pi$
$601$	−2.68442	−0.109500	−0.0547500	+	0.998500i	$0.517436\pi$
$602$	−39.3199	−1.60256
$603$	−8.99052	−0.366122
$604$	−59.0609	−2.40315
$605$	−19.5901	−0.796451
$606$	−12.7609	−0.518378
$607$	48.1090	1.95268	0.976342	−	0.216233i	$-0.0693770\pi$
$607$	48.1090	1.95268	0.976342	+	0.216233i	$0.0693770\pi$
$608$	−3.90144	−0.158224
$609$	2.64176	0.107050
$610$	21.4779	0.869615
$611$	−12.1947	−0.493344
$612$	−9.10758	−0.368152
$613$	−8.90899	−0.359831	−0.179915	−	0.983682i	$-0.557582\pi$
$613$	−8.90899	−0.359831	−0.179915	+	0.983682i	$0.557582\pi$
$614$	−31.7823	−1.28263
$615$	−13.8084	−0.556809
$616$	4.12743	0.166299
$617$	16.7211	0.673165	0.336582	−	0.941654i	$-0.390729\pi$
$617$	16.7211	0.673165	0.336582	+	0.941654i	$0.390729\pi$
$618$	4.55059	0.183052
$619$	−1.04364	−0.0419474	−0.0209737	−	0.999780i	$-0.506677\pi$
$619$	−1.04364	−0.0419474	−0.0209737	+	0.999780i	$0.506677\pi$
$620$	−21.2334	−0.852754
$621$	−7.57284	−0.303888
$622$	35.6678	1.43015
$623$	7.63174	0.305759
$624$	2.98195	0.119374
$625$	−13.1249	−0.524998
$626$	−25.8761	−1.03422
$627$	0.368620	0.0147213
$628$	58.9922	2.35404
$629$	7.85544	0.313217
$630$	−31.0763	−1.23811
$631$	−23.6152	−0.940108	−0.470054	−	0.882638i	$-0.655766\pi$
$631$	−23.6152	−0.940108	−0.470054	+	0.882638i	$0.655766\pi$
$632$	−33.1659	−1.31927
$633$	15.9903	0.635556
$634$	−67.0450	−2.66270
$635$	−4.65532	−0.184741
$636$	−12.0338	−0.477172
$637$	−2.89728	−0.114795
$638$	−1.02234	−0.0404749
$639$	4.52069	0.178836
$640$	37.3443	1.47616
$641$	22.5720	0.891541	0.445770	−	0.895147i	$-0.352930\pi$
$641$	22.5720	0.891541	0.445770	+	0.895147i	$0.352930\pi$
$642$	3.49463	0.137922
$643$	−37.5789	−1.48197	−0.740984	−	0.671522i	$-0.765641\pi$
$643$	−37.5789	−1.48197	−0.740984	+	0.671522i	$0.765641\pi$
$644$	20.5356	0.809216
$645$	7.39676	0.291247
$646$	3.45699	0.136014
$647$	−7.42682	−0.291978	−0.145989	−	0.989286i	$-0.546636\pi$
$647$	−7.42682	−0.291978	−0.145989	+	0.989286i	$0.546636\pi$
$648$	−18.0852	−0.710453
$649$	3.17786	0.124742
$650$	−7.56433	−0.296697
$651$	−6.84750	−0.268375
$652$	−63.5905	−2.49040
$653$	32.5806	1.27498	0.637488	−	0.770460i	$-0.279973\pi$
$653$	32.5806	1.27498	0.637488	+	0.770460i	$0.279973\pi$
$654$	−3.39452	−0.132736
$655$	13.0618	0.510366
$656$	23.7019	0.925403
$657$	−27.5104	−1.07328
$658$	47.3287	1.84506
$659$	33.3575	1.29942	0.649712	−	0.760181i	$-0.274890\pi$
$659$	33.3575	1.29942	0.649712	+	0.760181i	$0.274890\pi$
$660$	−1.69285	−0.0658941
$661$	13.0929	0.509256	0.254628	−	0.967039i	$-0.418047\pi$
$661$	13.0929	0.509256	0.254628	+	0.967039i	$0.418047\pi$
$662$	−14.7773	−0.574336
$663$	1.31916	0.0512318
$664$	4.92530	0.191139
$665$	7.65290	0.296767
$666$	46.2108	1.79063
$667$	−2.33300	−0.0903340
$668$	−25.6956	−0.994193
$669$	−10.2517	−0.396356
$670$	−15.6718	−0.605456
$671$	−1.73903	−0.0671346
$672$	5.77799	0.222891
$673$	−13.4103	−0.516931	−0.258465	−	0.966020i	$-0.583217\pi$
$673$	−13.4103	−0.516931	−0.258465	+	0.966020i	$0.583217\pi$
$674$	−65.7397	−2.53220
$675$	−7.02387	−0.270349
$676$	−36.0084	−1.38494
$677$	−27.3196	−1.04998	−0.524989	−	0.851109i	$-0.675931\pi$
$677$	−27.3196	−1.04998	−0.524989	+	0.851109i	$0.675931\pi$
$678$	−24.9114	−0.956717
$679$	−44.7630	−1.71785
$680$	−7.28162	−0.279238
$681$	−2.13535	−0.0818268
$682$	2.64993	0.101471
$683$	−3.80562	−0.145618	−0.0728089	−	0.997346i	$-0.523196\pi$
$683$	−3.80562	−0.145618	−0.0728089	+	0.997346i	$0.523196\pi$
$684$	13.1939	0.504481
$685$	−29.3400	−1.12102
$686$	−37.7596	−1.44167
$687$	−10.8660	−0.414565
$688$	−12.6964	−0.484046
$689$	−8.03362	−0.306056
$690$	−5.95436	−0.226679
$691$	−19.2715	−0.733123	−0.366562	−	0.930394i	$-0.619465\pi$
$691$	−19.2715	−0.733123	−0.366562	+	0.930394i	$0.619465\pi$
$692$	57.4438	2.18368
$693$	2.51620	0.0955825
$694$	9.39493	0.356627
$695$	1.46415	0.0555383
$696$	3.64138	0.138026
$697$	10.4853	0.397158
$698$	−7.32232	−0.277154
$699$	−7.23841	−0.273782
$700$	19.0469	0.719906
$701$	−45.4262	−1.71572	−0.857862	−	0.513880i	$-0.828208\pi$
$701$	−45.4262	−1.71572	−0.857862	+	0.513880i	$0.828208\pi$
$702$	17.2039	0.649321
$703$	−11.3799	−0.429203
$704$	−3.80904	−0.143559
$705$	−8.90335	−0.335319
$706$	−2.38632	−0.0898104
$707$	21.4509	0.806744
$708$	−24.6782	−0.927465
$709$	−5.02016	−0.188536	−0.0942680	−	0.995547i	$-0.530051\pi$
$709$	−5.02016	−0.188536	−0.0942680	+	0.995547i	$0.530051\pi$
$710$	7.88025	0.295740
$711$	−20.2189	−0.758267
$712$	10.5195	0.394235
$713$	6.04717	0.226468
$714$	−5.11977	−0.191603
$715$	−1.13013	−0.0422643
$716$	−62.2947	−2.32806
$717$	6.63651	0.247845
$718$	30.5969	1.14186
$719$	0.626950	0.0233813	0.0116907	−	0.999932i	$-0.496279\pi$
$719$	0.626950	0.0233813	0.0116907	+	0.999932i	$0.496279\pi$
$720$	−10.0345	−0.373965
$721$	−7.64945	−0.284881
$722$	40.3321	1.50100
$723$	−16.4277	−0.610955
$724$	−32.7998	−1.21899
$725$	−2.16387	−0.0803642
$726$	−18.9859	−0.704632
$727$	8.82628	0.327349	0.163674	−	0.986514i	$-0.447665\pi$
$727$	8.82628	0.327349	0.163674	+	0.986514i	$0.447665\pi$
$728$	−21.3977	−0.793051
$729$	−2.25619	−0.0835624
$730$	−47.9548	−1.77489
$731$	−5.61665	−0.207739
$732$	13.5048	0.499151
$733$	41.5035	1.53297	0.766484	−	0.642263i	$-0.222004\pi$
$733$	41.5035	1.53297	0.766484	+	0.642263i	$0.222004\pi$
$734$	55.6675	2.05473
$735$	−2.11531	−0.0780243
$736$	−5.10267	−0.188087
$737$	1.26892	0.0467414
$738$	61.6811	2.27051
$739$	−20.0707	−0.738312	−0.369156	−	0.929367i	$-0.620353\pi$
$739$	−20.0707	−0.738312	−0.369156	+	0.929367i	$0.620353\pi$
$740$	52.2612	1.92116
$741$	−1.91103	−0.0702033
$742$	31.1792	1.14462
$743$	24.6198	0.903211	0.451606	−	0.892218i	$-0.350851\pi$
$743$	24.6198	0.903211	0.451606	+	0.892218i	$0.350851\pi$
$744$	−9.43852	−0.346033
$745$	−9.75539	−0.357410
$746$	67.1281	2.45774
$747$	3.00261	0.109860
$748$	1.28545	0.0470006
$749$	−5.87440	−0.214646
$750$	−21.2359	−0.775425
$751$	20.2311	0.738242	0.369121	−	0.929381i	$-0.379659\pi$
$751$	20.2311	0.738242	0.369121	+	0.929381i	$0.379659\pi$
$752$	15.2824	0.557293
$753$	−1.55653	−0.0567232
$754$	5.30009	0.193018
$755$	−28.7866	−1.04765
$756$	−43.3195	−1.57551
$757$	1.00053	0.0363648	0.0181824	−	0.999835i	$-0.494212\pi$
$757$	1.00053	0.0363648	0.0181824	+	0.999835i	$0.494212\pi$
$758$	29.5931	1.07487
$759$	0.482116	0.0174997
$760$	10.5487	0.382641
$761$	−10.7841	−0.390925	−0.195462	−	0.980711i	$-0.562621\pi$
$761$	−10.7841	−0.390925	−0.195462	+	0.980711i	$0.562621\pi$
$762$	−4.51173	−0.163443
$763$	5.70612	0.206575
$764$	−37.7968	−1.36744
$765$	−4.43909	−0.160496
$766$	47.5314	1.71738
$767$	−16.4749	−0.594873
$768$	20.1797	0.728173
$769$	9.46018	0.341143	0.170571	−	0.985345i	$-0.445439\pi$
$769$	9.46018	0.341143	0.170571	+	0.985345i	$0.445439\pi$
$770$	4.38611	0.158065
$771$	20.5332	0.739484
$772$	−27.9185	−1.00481
$773$	−26.8074	−0.964196	−0.482098	−	0.876117i	$-0.660125\pi$
$773$	−26.8074	−0.964196	−0.482098	+	0.876117i	$0.660125\pi$
$774$	−33.0408	−1.18763
$775$	5.60880	0.201474
$776$	−61.7009	−2.21493
$777$	16.8536	0.604618
$778$	−4.02904	−0.144448
$779$	−15.1897	−0.544227
$780$	8.77619	0.314238
$781$	−0.638051	−0.0228313
$782$	4.52138	0.161684
$783$	4.92141	0.175877
$784$	3.63089	0.129675
$785$	28.7531	1.02624
$786$	12.6589	0.451528
$787$	−32.6755	−1.16476	−0.582378	−	0.812918i	$-0.697878\pi$
$787$	−32.6755	−1.16476	−0.582378	+	0.812918i	$0.697878\pi$
$788$	32.3570	1.15267
$789$	11.9595	0.425769
$790$	−35.2445	−1.25394
$791$	41.8756	1.48892
$792$	3.46830	0.123241
$793$	9.01561	0.320154
$794$	86.8504	3.08220
$795$	−5.86535	−0.208022
$796$	−102.527	−3.63398
$797$	25.4005	0.899730	0.449865	−	0.893096i	$-0.351472\pi$
$797$	25.4005	0.899730	0.449865	+	0.893096i	$0.351472\pi$
$798$	7.41686	0.262554
$799$	6.76065	0.239175
$800$	−4.73276	−0.167328
$801$	6.41300	0.226592
$802$	−50.4821	−1.78259
$803$	3.88283	0.137022
$804$	−9.85406	−0.347526
$805$	10.0092	0.352777
$806$	−13.7379	−0.483898
$807$	−18.1566	−0.639141
$808$	29.5677	1.04019
$809$	−50.4976	−1.77540	−0.887701	−	0.460420i	$-0.847699\pi$
$809$	−50.4976	−1.77540	−0.887701	+	0.460420i	$0.847699\pi$
$810$	−19.2187	−0.675275
$811$	−40.3610	−1.41727	−0.708633	−	0.705577i	$-0.750688\pi$
$811$	−40.3610	−1.41727	−0.708633	+	0.705577i	$0.750688\pi$
$812$	−13.3456	−0.468339
$813$	−15.7327	−0.551770
$814$	−6.52220	−0.228603
$815$	−30.9944	−1.08569
$816$	−1.65317	−0.0578727
$817$	8.13667	0.284666
$818$	−14.3933	−0.503251
$819$	−13.0447	−0.455817
$820$	69.7571	2.43602
$821$	−11.2198	−0.391575	−0.195788	−	0.980646i	$-0.562726\pi$
$821$	−11.2198	−0.391575	−0.195788	+	0.980646i	$0.562726\pi$
$822$	−28.4350	−0.991786
$823$	15.4730	0.539356	0.269678	−	0.962951i	$-0.413083\pi$
$823$	15.4730	0.539356	0.269678	+	0.962951i	$0.413083\pi$
$824$	−10.5439	−0.367315
$825$	0.447166	0.0155683
$826$	63.9404	2.22477
$827$	−54.6475	−1.90028	−0.950139	−	0.311826i	$-0.899059\pi$
$827$	−54.6475	−1.90028	−0.950139	+	0.311826i	$0.899059\pi$
$828$	17.2562	0.599694
$829$	26.8692	0.933206	0.466603	−	0.884467i	$-0.345478\pi$
$829$	26.8692	0.933206	0.466603	+	0.884467i	$0.345478\pi$
$830$	5.23399	0.181675
$831$	13.2730	0.460437
$832$	19.7471	0.684606
$833$	1.60623	0.0556527
$834$	1.41899	0.0491356
$835$	−12.5242	−0.433417
$836$	−1.86219	−0.0644051
$837$	−12.7564	−0.440925
$838$	68.6782	2.37245
$839$	−36.2163	−1.25033	−0.625163	−	0.780494i	$-0.714968\pi$
$839$	−36.2163	−1.25033	−0.625163	+	0.780494i	$0.714968\pi$
$840$	−15.6225	−0.539026
$841$	−27.4838	−0.947719
$842$	63.2127	2.17845
$843$	−6.96589	−0.239918
$844$	−80.7794	−2.78054
$845$	−17.5507	−0.603762
$846$	39.7705	1.36734
$847$	31.9149	1.09661
$848$	10.0678	0.345728
$849$	−20.8224	−0.714622
$850$	4.19361	0.143840
$851$	−14.8837	−0.510208
$852$	4.95490	0.169752
$853$	36.0100	1.23296	0.616480	−	0.787371i	$-0.288558\pi$
$853$	36.0100	1.23296	0.616480	+	0.787371i	$0.288558\pi$
$854$	−34.9904	−1.19735
$855$	6.43077	0.219928
$856$	−8.09721	−0.276757
$857$	−22.7172	−0.776005	−0.388002	−	0.921658i	$-0.626835\pi$
$857$	−22.7172	−0.776005	−0.388002	+	0.921658i	$0.626835\pi$
$858$	−1.09527	−0.0373918
$859$	37.6812	1.28567	0.642833	−	0.766006i	$-0.277759\pi$
$859$	37.6812	1.28567	0.642833	+	0.766006i	$0.277759\pi$
$860$	−37.3668	−1.27420
$861$	22.4958	0.766653
$862$	45.3875	1.54590
$863$	−0.110067	−0.00374674	−0.00187337	−	0.999998i	$-0.500596\pi$
$863$	−0.110067	−0.00374674	−0.00187337	+	0.999998i	$0.500596\pi$
$864$	10.7640	0.366198
$865$	27.9984	0.951975
$866$	−65.2232	−2.21637
$867$	−0.731332	−0.0248373
$868$	34.5921	1.17413
$869$	2.85370	0.0968050
$870$	3.86960	0.131192
$871$	−6.57844	−0.222902
$872$	7.86525	0.266351
$873$	−37.6146	−1.27306
$874$	−6.54999	−0.221557
$875$	35.6971	1.20678
$876$	−30.1528	−1.01877
$877$	20.4861	0.691766	0.345883	−	0.938278i	$-0.387579\pi$
$877$	20.4861	0.691766	0.345883	+	0.938278i	$0.387579\pi$
$878$	−19.4744	−0.657230
$879$	−4.94923	−0.166934
$880$	1.41628	0.0477427
$881$	14.5965	0.491768	0.245884	−	0.969299i	$-0.420922\pi$
$881$	14.5965	0.491768	0.245884	+	0.969299i	$0.420922\pi$
$882$	9.44891	0.318161
$883$	−13.8615	−0.466478	−0.233239	−	0.972419i	$-0.574932\pi$
$883$	−13.8615	−0.466478	−0.233239	+	0.972419i	$0.574932\pi$
$884$	−6.66410	−0.224138
$885$	−12.0283	−0.404327
$886$	70.0992	2.35503
$887$	25.1704	0.845138	0.422569	−	0.906331i	$-0.361128\pi$
$887$	25.1704	0.845138	0.422569	+	0.906331i	$0.361128\pi$
$888$	23.2308	0.779574
$889$	7.58413	0.254364
$890$	11.1788	0.374715
$891$	1.55611	0.0521315
$892$	51.7896	1.73404
$893$	−9.79396	−0.327742
$894$	−9.45450	−0.316206
$895$	−30.3628	−1.01492
$896$	−60.8388	−2.03248
$897$	−2.49942	−0.0834531
$898$	−33.8674	−1.13017
$899$	−3.92991	−0.131070
$900$	16.0052	0.533508
$901$	4.45378	0.148377
$902$	−8.70568	−0.289868
$903$	−12.0503	−0.401009
$904$	57.7209	1.91977
$905$	−15.9868	−0.531419
$906$	−27.8987	−0.926874
$907$	34.5184	1.14616	0.573082	−	0.819498i	$-0.305748\pi$
$907$	34.5184	1.14616	0.573082	+	0.819498i	$0.305748\pi$
$908$	10.7873	0.357990
$909$	18.0253	0.597862
$910$	−22.7388	−0.753784
$911$	−37.5898	−1.24541	−0.622704	−	0.782458i	$-0.713966\pi$
$911$	−37.5898	−1.24541	−0.622704	+	0.782458i	$0.713966\pi$
$912$	2.39490	0.0793032
$913$	−0.423788	−0.0140254
$914$	32.6129	1.07874
$915$	6.58230	0.217604
$916$	54.8928	1.81371
$917$	−21.2794	−0.702707
$918$	−9.53775	−0.314793
$919$	7.78236	0.256717	0.128358	−	0.991728i	$-0.459029\pi$
$919$	7.78236	0.256717	0.128358	+	0.991728i	$0.459029\pi$
$920$	13.7965	0.454858
$921$	−9.74029	−0.320953
$922$	54.7338	1.80256
$923$	3.30783	0.108879
$924$	2.75788	0.0907276
$925$	−13.8048	−0.453899
$926$	26.0324	0.855478
$927$	−6.42788	−0.211119
$928$	3.31610	0.108856
$929$	20.6721	0.678231	0.339115	−	0.940745i	$-0.389872\pi$
$929$	20.6721	0.678231	0.339115	+	0.940745i	$0.389872\pi$
$930$	−10.0301	−0.328899
$931$	−2.32690	−0.0762612
$932$	36.5668	1.19779
$933$	10.9311	0.357867
$934$	37.3104	1.22083
$935$	0.626534	0.0204898
$936$	−17.9806	−0.587715
$937$	49.1773	1.60655	0.803277	−	0.595606i	$-0.203088\pi$
$937$	49.1773	1.60655	0.803277	+	0.595606i	$0.203088\pi$
$938$	25.5315	0.833633
$939$	−7.93020	−0.258792
$940$	44.9778	1.46701
$941$	−32.3644	−1.05505	−0.527524	−	0.849540i	$-0.676880\pi$
$941$	−32.3644	−1.05505	−0.527524	+	0.849540i	$0.676880\pi$
$942$	27.8663	0.907932
$943$	−19.8665	−0.646942
$944$	20.6464	0.671983
$945$	−21.1141	−0.686843
$946$	4.66338	0.151620
$947$	36.6625	1.19137	0.595685	−	0.803218i	$-0.296881\pi$
$947$	36.6625	1.19137	0.595685	+	0.803218i	$0.296881\pi$
$948$	−22.1609	−0.719752
$949$	−20.1296	−0.653435
$950$	−6.07516	−0.197104
$951$	−20.5472	−0.666288
$952$	11.8627	0.384474
$953$	−37.0481	−1.20011	−0.600053	−	0.799960i	$-0.704854\pi$
$953$	−37.0481	−1.20011	−0.600053	+	0.799960i	$0.704854\pi$
$954$	26.2000	0.848258
$955$	−18.4224	−0.596133
$956$	−33.5262	−1.08431
$957$	−0.313315	−0.0101281
$958$	−62.3818	−2.01547
$959$	47.7988	1.54350
$960$	14.4173	0.465318
$961$	−20.8136	−0.671406
$962$	33.8128	1.09017
$963$	−4.93629	−0.159070
$964$	82.9894	2.67291
$965$	−13.6077	−0.438046
$966$	9.70045	0.312107
$967$	48.9858	1.57528	0.787639	−	0.616138i	$-0.211303\pi$
$967$	48.9858	1.57528	0.787639	+	0.616138i	$0.211303\pi$
$968$	43.9911	1.41393
$969$	1.05946	0.0340347
$970$	−65.5679	−2.10526
$971$	−28.5391	−0.915865	−0.457932	−	0.888987i	$-0.651410\pi$
$971$	−28.5391	−0.915865	−0.457932	+	0.888987i	$0.651410\pi$
$972$	−56.3836	−1.80850
$973$	−2.38529	−0.0764690
$974$	−68.9875	−2.21050
$975$	−2.31823	−0.0742427
$976$	−11.2984	−0.361653
$977$	−13.5098	−0.432216	−0.216108	−	0.976369i	$-0.569336\pi$
$977$	−13.5098	−0.432216	−0.216108	+	0.976369i	$0.569336\pi$
$978$	−30.0384	−0.960522
$979$	−0.905132	−0.0289281
$980$	10.6861	0.341354
$981$	4.79489	0.153089
$982$	−14.4994	−0.462694
$983$	39.6418	1.26438	0.632188	−	0.774815i	$-0.282157\pi$
$983$	39.6418	1.26438	0.632188	+	0.774815i	$0.282157\pi$
$984$	31.0079	0.988496
$985$	15.7710	0.502506
$986$	−2.93834	−0.0935757
$987$	14.5047	0.461691
$988$	9.65408	0.307137
$989$	10.6419	0.338393
$990$	3.68568	0.117139
$991$	1.60031	0.0508355	0.0254178	−	0.999677i	$-0.491908\pi$
$991$	1.60031	0.0508355	0.0254178	+	0.999677i	$0.491908\pi$
$992$	−8.59540	−0.272904
$993$	−4.52878	−0.143716
$994$	−12.8380	−0.407196
$995$	−49.9723	−1.58423
$996$	3.29100	0.104279
$997$	30.0064	0.950313	0.475157	−	0.879901i	$-0.342391\pi$
$997$	30.0064	0.950313	0.475157	+	0.879901i	$0.342391\pi$
$998$	−92.8186	−2.93812
$999$	31.3970	0.993356

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6001.2.a.b.1.11	✓	114

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6001.2.a.b.1.11	✓	114	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:	\( N \)	\(=\)	\( 6001 = 17 \cdot 353 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6001.a (trivial)

\(f(q)\)	\(=\)	\(q-2.38632 q^{2} -0.731332 q^{3} +3.69453 q^{4} +1.80073 q^{5} +1.74519 q^{6} -2.93364 q^{7} -4.04370 q^{8} -2.46515 q^{9} +O(q^{10})\)	\(q-2.38632 q^{2} -0.731332 q^{3} +3.69453 q^{4} +1.80073 q^{5} +1.74519 q^{6} -2.93364 q^{7} -4.04370 q^{8} -2.46515 q^{9} -4.29713 q^{10} +0.347932 q^{11} -2.70193 q^{12} -1.80377 q^{13} +7.00060 q^{14} -1.31694 q^{15} +2.26050 q^{16} +1.00000 q^{17} +5.88265 q^{18} -1.44867 q^{19} +6.65287 q^{20} +2.14546 q^{21} -0.830278 q^{22} -1.89471 q^{23} +2.95729 q^{24} -1.75735 q^{25} +4.30438 q^{26} +3.99684 q^{27} -10.8384 q^{28} +1.23132 q^{29} +3.14263 q^{30} -3.19162 q^{31} +2.69312 q^{32} -0.254454 q^{33} -2.38632 q^{34} -5.28271 q^{35} -9.10758 q^{36} +7.85544 q^{37} +3.45699 q^{38} +1.31916 q^{39} -7.28162 q^{40} +10.4853 q^{41} -5.11977 q^{42} -5.61665 q^{43} +1.28545 q^{44} -4.43909 q^{45} +4.52138 q^{46} +6.76065 q^{47} -1.65317 q^{48} +1.60623 q^{49} +4.19361 q^{50} -0.731332 q^{51} -6.66410 q^{52} +4.45378 q^{53} -9.53775 q^{54} +0.626534 q^{55} +11.8627 q^{56} +1.05946 q^{57} -2.93834 q^{58} +9.13356 q^{59} -4.86546 q^{60} -4.99819 q^{61} +7.61622 q^{62} +7.23187 q^{63} -10.9476 q^{64} -3.24812 q^{65} +0.607209 q^{66} +3.64704 q^{67} +3.69453 q^{68} +1.38566 q^{69} +12.6062 q^{70} -1.83384 q^{71} +9.96833 q^{72} +11.1597 q^{73} -18.7456 q^{74} +1.28521 q^{75} -5.35216 q^{76} -1.02071 q^{77} -3.14794 q^{78} +8.20187 q^{79} +4.07056 q^{80} +4.47244 q^{81} -25.0212 q^{82} -1.21802 q^{83} +7.92648 q^{84} +1.80073 q^{85} +13.4031 q^{86} -0.900507 q^{87} -1.40693 q^{88} -2.60146 q^{89} +10.5931 q^{90} +5.29162 q^{91} -7.00005 q^{92} +2.33413 q^{93} -16.1331 q^{94} -2.60867 q^{95} -1.96957 q^{96} +15.2585 q^{97} -3.83299 q^{98} -0.857706 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 114 q - 8 q^{2} - 23 q^{3} + 110 q^{4} - 27 q^{5} - 23 q^{6} - 53 q^{7} - 21 q^{8} + 107 q^{9}+O(q^{10}) \) 114 * q - 8 * q^2 - 23 * q^3 + 110 * q^4 - 27 * q^5 - 23 * q^6 - 53 * q^7 - 21 * q^8 + 107 * q^9	\( 114 q - 8 q^{2} - 23 q^{3} + 110 q^{4} - 27 q^{5} - 23 q^{6} - 53 q^{7} - 21 q^{8} + 107 q^{9} - 19 q^{10} - 52 q^{11} - 49 q^{12} - 12 q^{13} - 40 q^{14} - 39 q^{15} + 110 q^{16} + 114 q^{17} - 21 q^{18} - 30 q^{19} - 88 q^{20} - 30 q^{21} - 36 q^{22} - 77 q^{23} - 72 q^{24} + 119 q^{25} - 79 q^{26} - 77 q^{27} - 92 q^{28} - 65 q^{29} - 10 q^{30} - 131 q^{31} - 30 q^{32} - 12 q^{33} - 8 q^{34} - 33 q^{35} + 109 q^{36} - 54 q^{37} - 14 q^{38} - 83 q^{39} - 42 q^{40} - 99 q^{41} + 29 q^{42} + 4 q^{43} - 98 q^{44} - 73 q^{45} - 35 q^{46} - 113 q^{47} - 86 q^{48} + 101 q^{49} - 44 q^{50} - 23 q^{51} - 3 q^{52} - 18 q^{53} - 78 q^{54} - 63 q^{55} - 117 q^{56} - 64 q^{57} - 31 q^{58} - 134 q^{59} - 6 q^{60} - 30 q^{61} - 30 q^{62} - 154 q^{63} + 117 q^{64} - 66 q^{65} - 12 q^{66} - 34 q^{67} + 110 q^{68} - 35 q^{69} + 18 q^{70} - 233 q^{71} + 16 q^{72} - 56 q^{73} - 64 q^{74} - 100 q^{75} - 64 q^{76} - 6 q^{77} + 50 q^{78} - 154 q^{79} - 128 q^{80} + 118 q^{81} + 2 q^{82} - 53 q^{83} - 6 q^{84} - 27 q^{85} - 52 q^{86} - 22 q^{87} - 52 q^{88} - 118 q^{89} - 5 q^{90} - 95 q^{91} - 102 q^{92} + 47 q^{93} - 3 q^{94} - 158 q^{95} - 144 q^{96} - 57 q^{97} + 3 q^{98} - 131 q^{99}+O(q^{100}) \) 114 * q - 8 * q^2 - 23 * q^3 + 110 * q^4 - 27 * q^5 - 23 * q^6 - 53 * q^7 - 21 * q^8 + 107 * q^9 - 19 * q^10 - 52 * q^11 - 49 * q^12 - 12 * q^13 - 40 * q^14 - 39 * q^15 + 110 * q^16 + 114 * q^17 - 21 * q^18 - 30 * q^19 - 88 * q^20 - 30 * q^21 - 36 * q^22 - 77 * q^23 - 72 * q^24 + 119 * q^25 - 79 * q^26 - 77 * q^27 - 92 * q^28 - 65 * q^29 - 10 * q^30 - 131 * q^31 - 30 * q^32 - 12 * q^33 - 8 * q^34 - 33 * q^35 + 109 * q^36 - 54 * q^37 - 14 * q^38 - 83 * q^39 - 42 * q^40 - 99 * q^41 + 29 * q^42 + 4 * q^43 - 98 * q^44 - 73 * q^45 - 35 * q^46 - 113 * q^47 - 86 * q^48 + 101 * q^49 - 44 * q^50 - 23 * q^51 - 3 * q^52 - 18 * q^53 - 78 * q^54 - 63 * q^55 - 117 * q^56 - 64 * q^57 - 31 * q^58 - 134 * q^59 - 6 * q^60 - 30 * q^61 - 30 * q^62 - 154 * q^63 + 117 * q^64 - 66 * q^65 - 12 * q^66 - 34 * q^67 + 110 * q^68 - 35 * q^69 + 18 * q^70 - 233 * q^71 + 16 * q^72 - 56 * q^73 - 64 * q^74 - 100 * q^75 - 64 * q^76 - 6 * q^77 + 50 * q^78 - 154 * q^79 - 128 * q^80 + 118 * q^81 + 2 * q^82 - 53 * q^83 - 6 * q^84 - 27 * q^85 - 52 * q^86 - 22 * q^87 - 52 * q^88 - 118 * q^89 - 5 * q^90 - 95 * q^91 - 102 * q^92 + 47 * q^93 - 3 * q^94 - 158 * q^95 - 144 * q^96 - 57 * q^97 + 3 * q^98 - 131 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more