LMFDB - Embedded newform 4017.2.a.h.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4017,2,Mod(1,4017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4017, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4017 = 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4017.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:	$32.0759064919$
Analytic rank:	$1$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	4017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.0180837 q^{2} -1.00000 q^{3} -1.99967 q^{4} -4.11271 q^{5} +0.0180837 q^{6} -4.60383 q^{7} +0.0723287 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.0180837 q^{2} -1.00000 q^{3} -1.99967 q^{4} -4.11271 q^{5} +0.0180837 q^{6} -4.60383 q^{7} +0.0723287 q^{8} +1.00000 q^{9} +0.0743729 q^{10} -6.46484 q^{11} +1.99967 q^{12} +1.00000 q^{13} +0.0832542 q^{14} +4.11271 q^{15} +3.99804 q^{16} +5.67891 q^{17} -0.0180837 q^{18} +2.33925 q^{19} +8.22408 q^{20} +4.60383 q^{21} +0.116908 q^{22} -5.59276 q^{23} -0.0723287 q^{24} +11.9144 q^{25} -0.0180837 q^{26} -1.00000 q^{27} +9.20616 q^{28} -0.110638 q^{29} -0.0743729 q^{30} +6.58585 q^{31} -0.216957 q^{32} +6.46484 q^{33} -0.102695 q^{34} +18.9342 q^{35} -1.99967 q^{36} -5.18825 q^{37} -0.0423022 q^{38} -1.00000 q^{39} -0.297467 q^{40} -3.43118 q^{41} -0.0832542 q^{42} +1.33623 q^{43} +12.9276 q^{44} -4.11271 q^{45} +0.101138 q^{46} -10.3320 q^{47} -3.99804 q^{48} +14.1953 q^{49} -0.215456 q^{50} -5.67891 q^{51} -1.99967 q^{52} +12.4612 q^{53} +0.0180837 q^{54} +26.5880 q^{55} -0.332990 q^{56} -2.33925 q^{57} +0.00200074 q^{58} -3.35293 q^{59} -8.22408 q^{60} -2.71504 q^{61} -0.119096 q^{62} -4.60383 q^{63} -7.99215 q^{64} -4.11271 q^{65} -0.116908 q^{66} +0.0762221 q^{67} -11.3560 q^{68} +5.59276 q^{69} -0.342400 q^{70} +0.187658 q^{71} +0.0723287 q^{72} +3.31775 q^{73} +0.0938226 q^{74} -11.9144 q^{75} -4.67774 q^{76} +29.7630 q^{77} +0.0180837 q^{78} -7.30494 q^{79} -16.4428 q^{80} +1.00000 q^{81} +0.0620482 q^{82} +12.0914 q^{83} -9.20616 q^{84} -23.3557 q^{85} -0.0241639 q^{86} +0.110638 q^{87} -0.467593 q^{88} +0.149607 q^{89} +0.0743729 q^{90} -4.60383 q^{91} +11.1837 q^{92} -6.58585 q^{93} +0.186840 q^{94} -9.62066 q^{95} +0.216957 q^{96} +3.80773 q^{97} -0.256703 q^{98} -6.46484 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - 4 q^{2} - 25 q^{3} + 28 q^{4} - 5 q^{5} + 4 q^{6} - 7 q^{7} - 9 q^{8} + 25 q^{9}+O(q^{10}) $ 25 * q - 4 * q^2 - 25 * q^3 + 28 * q^4 - 5 * q^5 + 4 * q^6 - 7 * q^7 - 9 * q^8 + 25 * q^9	\( 25 q - 4 q^{2} - 25 q^{3} + 28 q^{4} - 5 q^{5} + 4 q^{6} - 7 q^{7} - 9 q^{8} + 25 q^{9} - 12 q^{10} - 23 q^{11} - 28 q^{12} + 25 q^{13} + 5 q^{15} + 26 q^{16} - 14 q^{17} - 4 q^{18} - 4 q^{19} - 12 q^{20} + 7 q^{21} - 7 q^{22} - 47 q^{23} + 9 q^{24} + 26 q^{25} - 4 q^{26} - 25 q^{27} - 38 q^{28} + 6 q^{29} + 12 q^{30} - 8 q^{31} - 62 q^{32} + 23 q^{33} + 25 q^{34} + 28 q^{36} - 20 q^{37} - 2 q^{38} - 25 q^{39} - 8 q^{40} - 33 q^{41} - 13 q^{43} - 13 q^{44} - 5 q^{45} - 21 q^{46} - 48 q^{47} - 26 q^{48} + 40 q^{49} - 9 q^{50} + 14 q^{51} + 28 q^{52} - 24 q^{53} + 4 q^{54} - 2 q^{55} - 14 q^{56} + 4 q^{57} - 31 q^{58} - 36 q^{59} + 12 q^{60} + 25 q^{61} - 7 q^{62} - 7 q^{63} + 45 q^{64} - 5 q^{65} + 7 q^{66} - 2 q^{67} - 32 q^{68} + 47 q^{69} - 13 q^{70} - 60 q^{71} - 9 q^{72} + 28 q^{73} - 16 q^{74} - 26 q^{75} - 12 q^{76} - 17 q^{77} + 4 q^{78} - 29 q^{79} - 88 q^{80} + 25 q^{81} - 22 q^{82} - 71 q^{83} + 38 q^{84} + 3 q^{85} - 3 q^{86} - 6 q^{87} + 23 q^{88} - 46 q^{89} - 12 q^{90} - 7 q^{91} - 69 q^{92} + 8 q^{93} + 4 q^{94} - 47 q^{95} + 62 q^{96} - 14 q^{97} - 71 q^{98} - 23 q^{99}+O(q^{100}) \) 25 * q - 4 * q^2 - 25 * q^3 + 28 * q^4 - 5 * q^5 + 4 * q^6 - 7 * q^7 - 9 * q^8 + 25 * q^9 - 12 * q^10 - 23 * q^11 - 28 * q^12 + 25 * q^13 + 5 * q^15 + 26 * q^16 - 14 * q^17 - 4 * q^18 - 4 * q^19 - 12 * q^20 + 7 * q^21 - 7 * q^22 - 47 * q^23 + 9 * q^24 + 26 * q^25 - 4 * q^26 - 25 * q^27 - 38 * q^28 + 6 * q^29 + 12 * q^30 - 8 * q^31 - 62 * q^32 + 23 * q^33 + 25 * q^34 + 28 * q^36 - 20 * q^37 - 2 * q^38 - 25 * q^39 - 8 * q^40 - 33 * q^41 - 13 * q^43 - 13 * q^44 - 5 * q^45 - 21 * q^46 - 48 * q^47 - 26 * q^48 + 40 * q^49 - 9 * q^50 + 14 * q^51 + 28 * q^52 - 24 * q^53 + 4 * q^54 - 2 * q^55 - 14 * q^56 + 4 * q^57 - 31 * q^58 - 36 * q^59 + 12 * q^60 + 25 * q^61 - 7 * q^62 - 7 * q^63 + 45 * q^64 - 5 * q^65 + 7 * q^66 - 2 * q^67 - 32 * q^68 + 47 * q^69 - 13 * q^70 - 60 * q^71 - 9 * q^72 + 28 * q^73 - 16 * q^74 - 26 * q^75 - 12 * q^76 - 17 * q^77 + 4 * q^78 - 29 * q^79 - 88 * q^80 + 25 * q^81 - 22 * q^82 - 71 * q^83 + 38 * q^84 + 3 * q^85 - 3 * q^86 - 6 * q^87 + 23 * q^88 - 46 * q^89 - 12 * q^90 - 7 * q^91 - 69 * q^92 + 8 * q^93 + 4 * q^94 - 47 * q^95 + 62 * q^96 - 14 * q^97 - 71 * q^98 - 23 * 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 $

$2$	−0.0180837	−0.0127871	−0.00639354	−	0.999980i	$-0.502035\pi$
$2$	−0.0180837	−0.0127871	−0.00639354	+	0.999980i	$0.502035\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.99967	−0.999836
$5$	−4.11271	−1.83926	−0.919630	−	0.392785i	$-0.871511\pi$
$5$	−4.11271	−1.83926	−0.919630	+	0.392785i	$0.871511\pi$
$6$	0.0180837	0.00738262
$7$	−4.60383	−1.74009	−0.870043	−	0.492976i	$-0.835909\pi$
$7$	−4.60383	−1.74009	−0.870043	+	0.492976i	$0.835909\pi$
$8$	0.0723287	0.0255721
$9$	1.00000	0.333333
$10$	0.0743729	0.0235188
$11$	−6.46484	−1.94922	−0.974611	−	0.223907i	$-0.928119\pi$
$11$	−6.46484	−1.94922	−0.974611	+	0.223907i	$0.928119\pi$
$12$	1.99967	0.577256
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	0.0832542	0.0222506
$15$	4.11271	1.06190
$16$	3.99804	0.999509
$17$	5.67891	1.37734	0.688669	−	0.725076i	$-0.258195\pi$
$17$	5.67891	1.37734	0.688669	+	0.725076i	$0.258195\pi$
$18$	−0.0180837	−0.00426236
$19$	2.33925	0.536661	0.268330	−	0.963327i	$-0.413528\pi$
$19$	2.33925	0.536661	0.268330	+	0.963327i	$0.413528\pi$
$20$	8.22408	1.83896
$21$	4.60383	1.00464
$22$	0.116908	0.0249248
$23$	−5.59276	−1.16617	−0.583085	−	0.812411i	$-0.698155\pi$
$23$	−5.59276	−1.16617	−0.583085	+	0.812411i	$0.698155\pi$
$24$	−0.0723287	−0.0147640
$25$	11.9144	2.38288
$26$	−0.0180837	−0.00354650
$27$	−1.00000	−0.192450
$28$	9.20616	1.73980
$29$	−0.110638	−0.0205450	−0.0102725	−	0.999947i	$-0.503270\pi$
$29$	−0.110638	−0.0205450	−0.0102725	+	0.999947i	$0.503270\pi$
$30$	−0.0743729	−0.0135786
$31$	6.58585	1.18285	0.591427	−	0.806359i	$-0.298565\pi$
$31$	6.58585	1.18285	0.591427	+	0.806359i	$0.298565\pi$
$32$	−0.216957	−0.0383529
$33$	6.46484	1.12538
$34$	−0.102695	−0.0176121
$35$	18.9342	3.20047
$36$	−1.99967	−0.333279
$37$	−5.18825	−0.852944	−0.426472	−	0.904501i	$-0.640244\pi$
$37$	−5.18825	−0.852944	−0.426472	+	0.904501i	$0.640244\pi$
$38$	−0.0423022	−0.00686232
$39$	−1.00000	−0.160128
$40$	−0.297467	−0.0470337
$41$	−3.43118	−0.535860	−0.267930	−	0.963438i	$-0.586340\pi$
$41$	−3.43118	−0.535860	−0.267930	+	0.963438i	$0.586340\pi$
$42$	−0.0832542	−0.0128464
$43$	1.33623	0.203773	0.101887	−	0.994796i	$-0.467512\pi$
$43$	1.33623	0.203773	0.101887	+	0.994796i	$0.467512\pi$
$44$	12.9276	1.94890
$45$	−4.11271	−0.613087
$46$	0.101138	0.0149119
$47$	−10.3320	−1.50708	−0.753538	−	0.657405i	$-0.771654\pi$
$47$	−10.3320	−1.50708	−0.753538	+	0.657405i	$0.771654\pi$
$48$	−3.99804	−0.577067
$49$	14.1953	2.02790
$50$	−0.215456	−0.0304701
$51$	−5.67891	−0.795206
$52$	−1.99967	−0.277305
$53$	12.4612	1.71168	0.855839	−	0.517242i	$-0.173041\pi$
$53$	12.4612	1.71168	0.855839	+	0.517242i	$0.173041\pi$
$54$	0.0180837	0.00246087
$55$	26.5880	3.58512
$56$	−0.332990	−0.0444976
$57$	−2.33925	−0.309841
$58$	0.00200074	0.000262711 0
$59$	−3.35293	−0.436514	−0.218257	−	0.975891i	$-0.570037\pi$
$59$	−3.35293	−0.436514	−0.218257	+	0.975891i	$0.570037\pi$
$60$	−8.22408	−1.06172
$61$	−2.71504	−0.347626	−0.173813	−	0.984779i	$-0.555609\pi$
$61$	−2.71504	−0.347626	−0.173813	+	0.984779i	$0.555609\pi$
$62$	−0.119096	−0.0151252
$63$	−4.60383	−0.580029
$64$	−7.99215	−0.999019
$65$	−4.11271	−0.510119
$66$	−0.116908	−0.0143904
$67$	0.0762221	0.00931201	0.00465600	−	0.999989i	$-0.498518\pi$
$67$	0.0762221	0.00931201	0.00465600	+	0.999989i	$0.498518\pi$
$68$	−11.3560	−1.37711
$69$	5.59276	0.673289
$70$	−0.342400	−0.0409247
$71$	0.187658	0.0222710	0.0111355	−	0.999938i	$-0.496455\pi$
$71$	0.187658	0.0222710	0.0111355	+	0.999938i	$0.496455\pi$
$72$	0.0723287	0.00852402
$73$	3.31775	0.388313	0.194156	−	0.980971i	$-0.437803\pi$
$73$	3.31775	0.388313	0.194156	+	0.980971i	$0.437803\pi$
$74$	0.0938226	0.0109067
$75$	−11.9144	−1.37576
$76$	−4.67774	−0.536573
$77$	29.7630	3.39181
$78$	0.0180837	0.00204757
$79$	−7.30494	−0.821870	−0.410935	−	0.911665i	$-0.634798\pi$
$79$	−7.30494	−0.821870	−0.410935	+	0.911665i	$0.634798\pi$
$80$	−16.4428	−1.83836
$81$	1.00000	0.111111
$82$	0.0620482	0.00685208
$83$	12.0914	1.32720	0.663601	−	0.748086i	$-0.269027\pi$
$83$	12.0914	1.32720	0.663601	+	0.748086i	$0.269027\pi$
$84$	−9.20616	−1.00447
$85$	−23.3557	−2.53328
$86$	−0.0241639	−0.00260566
$87$	0.110638	0.0118617
$88$	−0.467593	−0.0498456
$89$	0.149607	0.0158584	0.00792918	−	0.999969i	$-0.497476\pi$
$89$	0.149607	0.0158584	0.00792918	+	0.999969i	$0.497476\pi$
$90$	0.0743729	0.00783959
$91$	−4.60383	−0.482613
$92$	11.1837	1.16598
$93$	−6.58585	−0.682921
$94$	0.186840	0.0192711
$95$	−9.62066	−0.987059
$96$	0.216957	0.0221430
$97$	3.80773	0.386617	0.193308	−	0.981138i	$-0.438078\pi$
$97$	3.80773	0.386617	0.193308	+	0.981138i	$0.438078\pi$
$98$	−0.256703	−0.0259309
$99$	−6.46484	−0.649740
$100$	−23.8249	−2.38249
$101$	−12.3523	−1.22910	−0.614550	−	0.788878i	$-0.710662\pi$
$101$	−12.3523	−1.22910	−0.614550	+	0.788878i	$0.710662\pi$
$102$	0.102695	0.0101684
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	0.0723287	0.00709242
$105$	−18.9342	−1.84779
$106$	−0.225344	−0.0218874
$107$	13.1139	1.26777	0.633886	−	0.773426i	$-0.281459\pi$
$107$	13.1139	1.26777	0.633886	+	0.773426i	$0.281459\pi$
$108$	1.99967	0.192419
$109$	−0.714511	−0.0684377	−0.0342189	−	0.999414i	$-0.510894\pi$
$109$	−0.714511	−0.0684377	−0.0342189	+	0.999414i	$0.510894\pi$
$110$	−0.480808	−0.0458433
$111$	5.18825	0.492447
$112$	−18.4063	−1.73923
$113$	−14.2109	−1.33685	−0.668423	−	0.743782i	$-0.733030\pi$
$113$	−14.2109	−1.33685	−0.668423	+	0.743782i	$0.733030\pi$
$114$	0.0423022	0.00396196
$115$	23.0014	2.14489
$116$	0.221240	0.0205416
$117$	1.00000	0.0924500
$118$	0.0606332	0.00558174
$119$	−26.1447	−2.39669
$120$	0.297467	0.0271549
$121$	30.7941	2.79946
$122$	0.0490979	0.00444512
$123$	3.43118	0.309379
$124$	−13.1695	−1.18266
$125$	−28.4369	−2.54347
$126$	0.0832542	0.00741687
$127$	−9.81753	−0.871165	−0.435583	−	0.900149i	$-0.643458\pi$
$127$	−9.81753	−0.871165	−0.435583	+	0.900149i	$0.643458\pi$
$128$	0.578441	0.0511274
$129$	−1.33623	−0.117649
$130$	0.0743729	0.00652293
$131$	−5.31904	−0.464727	−0.232363	−	0.972629i	$-0.574646\pi$
$131$	−5.31904	−0.464727	−0.232363	+	0.972629i	$0.574646\pi$
$132$	−12.9276	−1.12520
$133$	−10.7695	−0.933836
$134$	−0.00137837	−0.000119073 0
$135$	4.11271	0.353966
$136$	0.410748	0.0352214
$137$	8.54057	0.729670	0.364835	−	0.931072i	$-0.381125\pi$
$137$	8.54057	0.729670	0.364835	+	0.931072i	$0.381125\pi$
$138$	−0.101138	−0.00860940
$139$	−0.965255	−0.0818719	−0.0409359	−	0.999162i	$-0.513034\pi$
$139$	−0.965255	−0.0818719	−0.0409359	+	0.999162i	$0.513034\pi$
$140$	−37.8623	−3.19995
$141$	10.3320	0.870110
$142$	−0.00339355	−0.000284781 0
$143$	−6.46484	−0.540617
$144$	3.99804	0.333170
$145$	0.455023	0.0377876
$146$	−0.0599970	−0.00496539
$147$	−14.1953	−1.17081
$148$	10.3748	0.852804
$149$	23.7529	1.94591	0.972956	−	0.230992i	$-0.0741972\pi$
$149$	23.7529	1.94591	0.972956	+	0.230992i	$0.0741972\pi$
$150$	0.215456	0.0175919
$151$	4.45428	0.362484	0.181242	−	0.983438i	$-0.441988\pi$
$151$	4.45428	0.362484	0.181242	+	0.983438i	$0.441988\pi$
$152$	0.169195	0.0137235
$153$	5.67891	0.459112
$154$	−0.538225	−0.0433714
$155$	−27.0857	−2.17558
$156$	1.99967	0.160102
$157$	1.04612	0.0834894	0.0417447	−	0.999128i	$-0.486708\pi$
$157$	1.04612	0.0834894	0.0417447	+	0.999128i	$0.486708\pi$
$158$	0.132100	0.0105093
$159$	−12.4612	−0.988238
$160$	0.892280	0.0705409
$161$	25.7481	2.02924
$162$	−0.0180837	−0.00142079
$163$	10.2761	0.804886	0.402443	−	0.915445i	$-0.368161\pi$
$163$	10.2761	0.804886	0.402443	+	0.915445i	$0.368161\pi$
$164$	6.86123	0.535772
$165$	−26.5880	−2.06987
$166$	−0.218657	−0.0169710
$167$	−18.4662	−1.42896	−0.714479	−	0.699657i	$-0.753336\pi$
$167$	−18.4662	−1.42896	−0.714479	+	0.699657i	$0.753336\pi$
$168$	0.332990	0.0256907
$169$	1.00000	0.0769231
$170$	0.422357	0.0323933
$171$	2.33925	0.178887
$172$	−2.67202	−0.203740
$173$	−9.57157	−0.727713	−0.363857	−	0.931455i	$-0.618540\pi$
$173$	−9.57157	−0.727713	−0.363857	+	0.931455i	$0.618540\pi$
$174$	−0.00200074	−0.000151676 0
$175$	−54.8519	−4.14641
$176$	−25.8467	−1.94827
$177$	3.35293	0.252022
$178$	−0.00270545	−0.000202782 0
$179$	21.9052	1.63727	0.818634	−	0.574316i	$-0.194732\pi$
$179$	21.9052	1.63727	0.818634	+	0.574316i	$0.194732\pi$
$180$	8.22408	0.612987
$181$	18.5264	1.37706	0.688529	−	0.725209i	$-0.258257\pi$
$181$	18.5264	1.37706	0.688529	+	0.725209i	$0.258257\pi$
$182$	0.0832542	0.00617121
$183$	2.71504	0.200702
$184$	−0.404517	−0.0298214
$185$	21.3378	1.56879
$186$	0.119096	0.00873256
$187$	−36.7132	−2.68473
$188$	20.6606	1.50683
$189$	4.60383	0.334880
$190$	0.173977	0.0126216
$191$	3.80410	0.275255	0.137628	−	0.990484i	$-0.456052\pi$
$191$	3.80410	0.275255	0.137628	+	0.990484i	$0.456052\pi$
$192$	7.99215	0.576784
$193$	7.42418	0.534404	0.267202	−	0.963641i	$-0.413901\pi$
$193$	7.42418	0.534404	0.267202	+	0.963641i	$0.413901\pi$
$194$	−0.0688578	−0.00494370
$195$	4.11271	0.294517
$196$	−28.3859	−2.02757
$197$	12.8576	0.916065	0.458032	−	0.888935i	$-0.348554\pi$
$197$	12.8576	0.916065	0.458032	+	0.888935i	$0.348554\pi$
$198$	0.116908	0.00830828
$199$	−18.5957	−1.31821	−0.659107	−	0.752049i	$-0.729065\pi$
$199$	−18.5957	−1.31821	−0.659107	+	0.752049i	$0.729065\pi$
$200$	0.861753	0.0609351
$201$	−0.0762221	−0.00537629
$202$	0.223375	0.0157166
$203$	0.509360	0.0357501
$204$	11.3560	0.795076
$205$	14.1114	0.985585
$206$	−0.0180837	−0.00125995
$207$	−5.59276	−0.388724
$208$	3.99804	0.277214
$209$	−15.1229	−1.04607
$210$	0.342400	0.0236279
$211$	26.6073	1.83172	0.915860	−	0.401498i	$-0.131510\pi$
$211$	26.6073	1.83172	0.915860	+	0.401498i	$0.131510\pi$
$212$	−24.9183	−1.71140
$213$	−0.187658	−0.0128581
$214$	−0.237148	−0.0162111
$215$	−5.49553	−0.374792
$216$	−0.0723287	−0.00492135
$217$	−30.3202	−2.05827
$218$	0.0129210	0.000875119 0
$219$	−3.31775	−0.224193
$220$	−53.1673	−3.58454
$221$	5.67891	0.382005
$222$	−0.0938226	−0.00629696
$223$	−20.8862	−1.39864	−0.699320	−	0.714808i	$-0.746514\pi$
$223$	−20.8862	−1.39864	−0.699320	+	0.714808i	$0.746514\pi$
$224$	0.998832	0.0667373
$225$	11.9144	0.794293
$226$	0.256984	0.0170943
$227$	19.9754	1.32581	0.662907	−	0.748702i	$-0.269323\pi$
$227$	19.9754	1.32581	0.662907	+	0.748702i	$0.269323\pi$
$228$	4.67774	0.309791
$229$	26.8245	1.77261	0.886307	−	0.463098i	$-0.153262\pi$
$229$	26.8245	1.77261	0.886307	+	0.463098i	$0.153262\pi$
$230$	−0.415949	−0.0274269
$231$	−29.7630	−1.95826
$232$	−0.00800232	−0.000525378 0
$233$	14.0349	0.919454	0.459727	−	0.888060i	$-0.347947\pi$
$233$	14.0349	0.919454	0.459727	+	0.888060i	$0.347947\pi$
$234$	−0.0180837	−0.00118217
$235$	42.4925	2.77190
$236$	6.70476	0.436443
$237$	7.30494	0.474507
$238$	0.472793	0.0306466
$239$	−23.1512	−1.49753	−0.748763	−	0.662838i	$-0.769352\pi$
$239$	−23.1512	−1.49753	−0.748763	+	0.662838i	$0.769352\pi$
$240$	16.4428	1.06138
$241$	−4.69638	−0.302521	−0.151260	−	0.988494i	$-0.548333\pi$
$241$	−4.69638	−0.302521	−0.151260	+	0.988494i	$0.548333\pi$
$242$	−0.556870	−0.0357970
$243$	−1.00000	−0.0641500
$244$	5.42920	0.347569
$245$	−58.3811	−3.72983
$246$	−0.0620482	−0.00395605
$247$	2.33925	0.148843
$248$	0.476346	0.0302480
$249$	−12.0914	−0.766261
$250$	0.514243	0.0325236
$251$	−8.26959	−0.521972	−0.260986	−	0.965343i	$-0.584048\pi$
$251$	−8.26959	−0.521972	−0.260986	+	0.965343i	$0.584048\pi$
$252$	9.20616	0.579934
$253$	36.1563	2.27312
$254$	0.177537	0.0111397
$255$	23.3557	1.46259
$256$	15.9738	0.998365
$257$	−28.6065	−1.78442	−0.892212	−	0.451616i	$-0.850848\pi$
$257$	−28.6065	−1.78442	−0.892212	+	0.451616i	$0.850848\pi$
$258$	0.0241639	0.00150438
$259$	23.8859	1.48420
$260$	8.22408	0.510036
$261$	−0.110638	−0.00684833
$262$	0.0961878	0.00594250
$263$	−2.99713	−0.184811	−0.0924056	−	0.995721i	$-0.529456\pi$
$263$	−2.99713	−0.184811	−0.0924056	+	0.995721i	$0.529456\pi$
$264$	0.467593	0.0287784
$265$	−51.2493	−3.14822
$266$	0.194752	0.0119410
$267$	−0.149607	−0.00915582
$268$	−0.152419	−0.00931049
$269$	19.6292	1.19681	0.598406	−	0.801193i	$-0.295801\pi$
$269$	19.6292	1.19681	0.598406	+	0.801193i	$0.295801\pi$
$270$	−0.0743729	−0.00452619
$271$	3.01582	0.183198	0.0915989	−	0.995796i	$-0.470802\pi$
$271$	3.01582	0.183198	0.0915989	+	0.995796i	$0.470802\pi$
$272$	22.7045	1.37666
$273$	4.60383	0.278637
$274$	−0.154445	−0.00933035
$275$	−77.0246	−4.64476
$276$	−11.1837	−0.673179
$277$	15.5530	0.934488	0.467244	−	0.884128i	$-0.345247\pi$
$277$	15.5530	0.934488	0.467244	+	0.884128i	$0.345247\pi$
$278$	0.0174554	0.00104690
$279$	6.58585	0.394285
$280$	1.36949	0.0818427
$281$	−8.71038	−0.519618	−0.259809	−	0.965660i	$-0.583660\pi$
$281$	−8.71038	−0.519618	−0.259809	+	0.965660i	$0.583660\pi$
$282$	−0.186840	−0.0111262
$283$	5.72331	0.340216	0.170108	−	0.985425i	$-0.445588\pi$
$283$	5.72331	0.340216	0.170108	+	0.985425i	$0.445588\pi$
$284$	−0.375256	−0.0222673
$285$	9.62066	0.569879
$286$	0.116908	0.00691291
$287$	15.7966	0.932442
$288$	−0.216957	−0.0127843
$289$	15.2500	0.897058
$290$	−0.00822848	−0.000483193 0
$291$	−3.80773	−0.223213
$292$	−6.63441	−0.388249
$293$	10.6570	0.622588	0.311294	−	0.950314i	$-0.399238\pi$
$293$	10.6570	0.622588	0.311294	+	0.950314i	$0.399238\pi$
$294$	0.256703	0.0149712
$295$	13.7896	0.802863
$296$	−0.375260	−0.0218115
$297$	6.46484	0.375128
$298$	−0.429539	−0.0248825
$299$	−5.59276	−0.323438
$300$	23.8249	1.37553
$301$	−6.15178	−0.354583
$302$	−0.0805497	−0.00463512
$303$	12.3523	0.709622
$304$	9.35241	0.536398
$305$	11.1662	0.639374
$306$	−0.102695	−0.00587071
$307$	−19.6606	−1.12209	−0.561045	−	0.827785i	$-0.689601\pi$
$307$	−19.6606	−1.12209	−0.561045	+	0.827785i	$0.689601\pi$
$308$	−59.5163	−3.39126
$309$	−1.00000	−0.0568880
$310$	0.489809	0.0278193
$311$	22.4980	1.27575	0.637873	−	0.770141i	$-0.279814\pi$
$311$	22.4980	1.27575	0.637873	+	0.770141i	$0.279814\pi$
$312$	−0.0723287	−0.00409481
$313$	−3.33342	−0.188416	−0.0942080	−	0.995553i	$-0.530032\pi$
$313$	−3.33342	−0.188416	−0.0942080	+	0.995553i	$0.530032\pi$
$314$	−0.0189177	−0.00106759
$315$	18.9342	1.06682
$316$	14.6075	0.821735
$317$	−29.6320	−1.66430	−0.832148	−	0.554553i	$-0.812889\pi$
$317$	−29.6320	−1.66430	−0.832148	+	0.554553i	$0.812889\pi$
$318$	0.225344	0.0126367
$319$	0.715258	0.0400467
$320$	32.8694	1.83746
$321$	−13.1139	−0.731949
$322$	−0.465621	−0.0259480
$323$	13.2844	0.739163
$324$	−1.99967	−0.111093
$325$	11.9144	0.660892
$326$	−0.185829	−0.0102921
$327$	0.714511	0.0395125
$328$	−0.248173	−0.0137030
$329$	47.5668	2.62244
$330$	0.480808	0.0264676
$331$	1.86555	0.102540	0.0512699	−	0.998685i	$-0.483673\pi$
$331$	1.86555	0.102540	0.0512699	+	0.998685i	$0.483673\pi$
$332$	−24.1788	−1.32699
$333$	−5.18825	−0.284315
$334$	0.333937	0.0182722
$335$	−0.313479	−0.0171272
$336$	18.4063	1.00415
$337$	−12.6741	−0.690405	−0.345202	−	0.938528i	$-0.612190\pi$
$337$	−12.6741	−0.690405	−0.345202	+	0.938528i	$0.612190\pi$
$338$	−0.0180837	−0.000983621 0
$339$	14.2109	0.771828
$340$	46.7038	2.53287
$341$	−42.5764	−2.30564
$342$	−0.0423022	−0.00228744
$343$	−33.1259	−1.78863
$344$	0.0966478	0.00521090
$345$	−23.0014	−1.23835
$346$	0.173089	0.00930533
$347$	−19.8281	−1.06443	−0.532215	−	0.846609i	$-0.678640\pi$
$347$	−19.8281	−1.06443	−0.532215	+	0.846609i	$0.678640\pi$
$348$	−0.221240	−0.0118597
$349$	−1.16725	−0.0624815	−0.0312408	−	0.999512i	$-0.509946\pi$
$349$	−1.16725	−0.0624815	−0.0312408	+	0.999512i	$0.509946\pi$
$350$	0.991923	0.0530205
$351$	−1.00000	−0.0533761
$352$	1.40259	0.0747582
$353$	−24.6155	−1.31015	−0.655076	−	0.755563i	$-0.727364\pi$
$353$	−24.6155	−1.31015	−0.655076	+	0.755563i	$0.727364\pi$
$354$	−0.0606332	−0.00322262
$355$	−0.771785	−0.0409621
$356$	−0.299166	−0.0158558
$357$	26.1447	1.38373
$358$	−0.396125	−0.0209359
$359$	−30.2121	−1.59453	−0.797266	−	0.603628i	$-0.793721\pi$
$359$	−30.2121	−1.59453	−0.797266	+	0.603628i	$0.793721\pi$
$360$	−0.297467	−0.0156779
$361$	−13.5279	−0.711995
$362$	−0.335026	−0.0176086
$363$	−30.7941	−1.61627
$364$	9.20616	0.482534
$365$	−13.6449	−0.714209
$366$	−0.0490979	−0.00256639
$367$	−2.87504	−0.150076	−0.0750379	−	0.997181i	$-0.523908\pi$
$367$	−2.87504	−0.150076	−0.0750379	+	0.997181i	$0.523908\pi$
$368$	−22.3601	−1.16560
$369$	−3.43118	−0.178620
$370$	−0.385865	−0.0200602
$371$	−57.3693	−2.97847
$372$	13.1695	0.682809
$373$	15.8829	0.822385	0.411193	−	0.911548i	$-0.365112\pi$
$373$	15.8829	0.822385	0.411193	+	0.911548i	$0.365112\pi$
$374$	0.663909	0.0343299
$375$	28.4369	1.46847
$376$	−0.747300	−0.0385390
$377$	−0.110638	−0.00569816
$378$	−0.0832542	−0.00428213
$379$	−23.3715	−1.20051	−0.600256	−	0.799808i	$-0.704935\pi$
$379$	−23.3715	−1.20051	−0.600256	+	0.799808i	$0.704935\pi$
$380$	19.2382	0.986897
$381$	9.81753	0.502968
$382$	−0.0687921	−0.00351971
$383$	−9.99003	−0.510467	−0.255233	−	0.966880i	$-0.582152\pi$
$383$	−9.99003	−0.510467	−0.255233	+	0.966880i	$0.582152\pi$
$384$	−0.578441	−0.0295184
$385$	−122.407	−6.23843
$386$	−0.134256	−0.00683347
$387$	1.33623	0.0679244
$388$	−7.61422	−0.386554
$389$	−19.6215	−0.994847	−0.497424	−	0.867508i	$-0.665721\pi$
$389$	−19.6215	−0.994847	−0.497424	+	0.867508i	$0.665721\pi$
$390$	−0.0743729	−0.00376602
$391$	−31.7608	−1.60621
$392$	1.02673	0.0518576
$393$	5.31904	0.268310
$394$	−0.232512	−0.0117138
$395$	30.0431	1.51163
$396$	12.9276	0.649634
$397$	18.5380	0.930398	0.465199	−	0.885206i	$-0.345983\pi$
$397$	18.5380	0.930398	0.465199	+	0.885206i	$0.345983\pi$
$398$	0.336278	0.0168561
$399$	10.7695	0.539150
$400$	47.6342	2.38171
$401$	9.39463	0.469145	0.234573	−	0.972099i	$-0.424631\pi$
$401$	9.39463	0.469145	0.234573	+	0.972099i	$0.424631\pi$
$402$	0.00137837	6.87470e−5 0
$403$	6.58585	0.328065
$404$	24.7006	1.22890
$405$	−4.11271	−0.204362
$406$	−0.00921109	−0.000457139 0
$407$	33.5412	1.66258
$408$	−0.410748	−0.0203351
$409$	3.76851	0.186341	0.0931704	−	0.995650i	$-0.470300\pi$
$409$	3.76851	0.186341	0.0931704	+	0.995650i	$0.470300\pi$
$410$	−0.255186	−0.0126028
$411$	−8.54057	−0.421275
$412$	−1.99967	−0.0985168
$413$	15.4363	0.759572
$414$	0.101138	0.00497064
$415$	−49.7284	−2.44107
$416$	−0.216957	−0.0106372
$417$	0.965255	0.0472688
$418$	0.273477	0.0133762
$419$	36.6245	1.78922	0.894612	−	0.446843i	$-0.147452\pi$
$419$	36.6245	1.78922	0.894612	+	0.446843i	$0.147452\pi$
$420$	37.8623	1.84749
$421$	5.79629	0.282494	0.141247	−	0.989974i	$-0.454889\pi$
$421$	5.79629	0.282494	0.141247	+	0.989974i	$0.454889\pi$
$422$	−0.481157	−0.0234223
$423$	−10.3320	−0.502358
$424$	0.901303	0.0437712
$425$	67.6607	3.28203
$426$	0.00339355	0.000164418 0
$427$	12.4996	0.604898
$428$	−26.2236	−1.26756
$429$	6.46484	0.312125
$430$	0.0993793	0.00479249
$431$	8.08982	0.389673	0.194836	−	0.980836i	$-0.437582\pi$
$431$	8.08982	0.389673	0.194836	+	0.980836i	$0.437582\pi$
$432$	−3.99804	−0.192356
$433$	10.8198	0.519966	0.259983	−	0.965613i	$-0.416283\pi$
$433$	10.8198	0.519966	0.259983	+	0.965613i	$0.416283\pi$
$434$	0.548300	0.0263192
$435$	−0.455023	−0.0218167
$436$	1.42879	0.0684266
$437$	−13.0829	−0.625838
$438$	0.0599970	0.00286677
$439$	36.1755	1.72656	0.863281	−	0.504724i	$-0.168406\pi$
$439$	36.1755	1.72656	0.863281	+	0.504724i	$0.168406\pi$
$440$	1.92308	0.0916791
$441$	14.1953	0.675966
$442$	−0.102695	−0.00488472
$443$	3.09231	0.146920	0.0734601	−	0.997298i	$-0.476596\pi$
$443$	3.09231	0.146920	0.0734601	+	0.997298i	$0.476596\pi$
$444$	−10.3748	−0.492367
$445$	−0.615292	−0.0291676
$446$	0.377698	0.0178845
$447$	−23.7529	−1.12347
$448$	36.7945	1.73838
$449$	−34.8841	−1.64628	−0.823140	−	0.567838i	$-0.807780\pi$
$449$	−34.8841	−1.64628	−0.823140	+	0.567838i	$0.807780\pi$
$450$	−0.215456	−0.0101567
$451$	22.1820	1.04451
$452$	28.4171	1.33663
$453$	−4.45428	−0.209280
$454$	−0.361228	−0.0169533
$455$	18.9342	0.887651
$456$	−0.169195	−0.00792328
$457$	22.1373	1.03554	0.517769	−	0.855520i	$-0.326763\pi$
$457$	22.1373	1.03554	0.517769	+	0.855520i	$0.326763\pi$
$458$	−0.485085	−0.0226666
$459$	−5.67891	−0.265069
$460$	−45.9953	−2.14454
$461$	2.54802	0.118673	0.0593366	−	0.998238i	$-0.481101\pi$
$461$	2.54802	0.118673	0.0593366	+	0.998238i	$0.481101\pi$
$462$	0.538225	0.0250405
$463$	−18.9935	−0.882702	−0.441351	−	0.897334i	$-0.645501\pi$
$463$	−18.9935	−0.882702	−0.441351	+	0.897334i	$0.645501\pi$
$464$	−0.442336	−0.0205349
$465$	27.0857	1.25607
$466$	−0.253802	−0.0117571
$467$	30.9221	1.43091	0.715453	−	0.698661i	$-0.246220\pi$
$467$	30.9221	1.43091	0.715453	+	0.698661i	$0.246220\pi$
$468$	−1.99967	−0.0924349
$469$	−0.350914	−0.0162037
$470$	−0.768420	−0.0354446
$471$	−1.04612	−0.0482026
$472$	−0.242513	−0.0111626
$473$	−8.63851	−0.397199
$474$	−0.132100	−0.00606755
$475$	27.8707	1.27880
$476$	52.2809	2.39629
$477$	12.4612	0.570559
$478$	0.418658	0.0191490
$479$	22.6511	1.03495	0.517477	−	0.855697i	$-0.326871\pi$
$479$	22.6511	1.03495	0.517477	+	0.855697i	$0.326871\pi$
$480$	−0.892280	−0.0407268
$481$	−5.18825	−0.236564
$482$	0.0849278	0.00386836
$483$	−25.7481	−1.17158
$484$	−61.5781	−2.79901
$485$	−15.6601	−0.711089
$486$	0.0180837	0.000820292 0
$487$	13.8976	0.629759	0.314880	−	0.949132i	$-0.398036\pi$
$487$	13.8976	0.629759	0.314880	+	0.949132i	$0.398036\pi$
$488$	−0.196376	−0.00888951
$489$	−10.2761	−0.464701
$490$	1.05574	0.0476937
$491$	−29.4504	−1.32908	−0.664539	−	0.747253i	$-0.731372\pi$
$491$	−29.4504	−1.32908	−0.664539	+	0.747253i	$0.731372\pi$
$492$	−6.86123	−0.309328
$493$	−0.628304	−0.0282974
$494$	−0.0423022	−0.00190327
$495$	26.5880	1.19504
$496$	26.3305	1.18227
$497$	−0.863949	−0.0387534
$498$	0.218657	0.00979824
$499$	38.7688	1.73553	0.867766	−	0.496973i	$-0.165555\pi$
$499$	38.7688	1.73553	0.867766	+	0.496973i	$0.165555\pi$
$500$	56.8645	2.54306
$501$	18.4662	0.825010
$502$	0.149545	0.00667450
$503$	−30.9755	−1.38113	−0.690565	−	0.723271i	$-0.742638\pi$
$503$	−30.9755	−1.38113	−0.690565	+	0.723271i	$0.742638\pi$
$504$	−0.332990	−0.0148325
$505$	50.8015	2.26064
$506$	−0.653838	−0.0290666
$507$	−1.00000	−0.0444116
$508$	19.6319	0.871023
$509$	−0.370611	−0.0164270	−0.00821352	−	0.999966i	$-0.502614\pi$
$509$	−0.370611	−0.0164270	−0.00821352	+	0.999966i	$0.502614\pi$
$510$	−0.422357	−0.0187023
$511$	−15.2744	−0.675698
$512$	−1.44575	−0.0638936
$513$	−2.33925	−0.103280
$514$	0.517310	0.0228176
$515$	−4.11271	−0.181228
$516$	2.67202	0.117629
$517$	66.7946	2.93762
$518$	−0.431944	−0.0189785
$519$	9.57157	0.420145
$520$	−0.297467	−0.0130448
$521$	−33.2218	−1.45547	−0.727737	−	0.685857i	$-0.759428\pi$
$521$	−33.2218	−1.45547	−0.727737	+	0.685857i	$0.759428\pi$
$522$	0.00200074	8.75702e−5 0
$523$	−10.9966	−0.480849	−0.240425	−	0.970668i	$-0.577287\pi$
$523$	−10.9966	−0.480849	−0.240425	+	0.970668i	$0.577287\pi$
$524$	10.6363	0.464651
$525$	54.8519	2.39393
$526$	0.0541992	0.00236320
$527$	37.4004	1.62919
$528$	25.8467	1.12483
$529$	8.27895	0.359954
$530$	0.926776	0.0402566
$531$	−3.35293	−0.145505
$532$	21.5355	0.933683
$533$	−3.43118	−0.148621
$534$	0.00270545	0.000117076 0
$535$	−53.9338	−2.33176
$536$	0.00551305	0.000238127 0
$537$	−21.9052	−0.945277
$538$	−0.354967	−0.0153037
$539$	−91.7702	−3.95282
$540$	−8.22408	−0.353908
$541$	−27.1260	−1.16624	−0.583119	−	0.812387i	$-0.698168\pi$
$541$	−27.1260	−1.16624	−0.583119	+	0.812387i	$0.698168\pi$
$542$	−0.0545370	−0.00234256
$543$	−18.5264	−0.795045
$544$	−1.23208	−0.0528248
$545$	2.93858	0.125875
$546$	−0.0832542	−0.00356295
$547$	−4.86272	−0.207915	−0.103957	−	0.994582i	$-0.533151\pi$
$547$	−4.86272	−0.207915	−0.103957	+	0.994582i	$0.533151\pi$
$548$	−17.0783	−0.729551
$549$	−2.71504	−0.115875
$550$	1.39289	0.0593929
$551$	−0.258810	−0.0110257
$552$	0.404517	0.0172174
$553$	33.6307	1.43012
$554$	−0.281255	−0.0119494
$555$	−21.3378	−0.905739
$556$	1.93020	0.0818585
$557$	7.65752	0.324460	0.162230	−	0.986753i	$-0.448131\pi$
$557$	7.65752	0.324460	0.162230	+	0.986753i	$0.448131\pi$
$558$	−0.119096	−0.00504175
$559$	1.33623	0.0565165
$560$	75.6998	3.19890
$561$	36.7132	1.55003
$562$	0.157516	0.00664439
$563$	34.9025	1.47096	0.735482	−	0.677544i	$-0.236956\pi$
$563$	34.9025	1.47096	0.735482	+	0.677544i	$0.236956\pi$
$564$	−20.6606	−0.869968
$565$	58.4452	2.45881
$566$	−0.103498	−0.00435036
$567$	−4.60383	−0.193343
$568$	0.0135731	0.000569515 0
$569$	10.9753	0.460111	0.230055	−	0.973178i	$-0.426109\pi$
$569$	10.9753	0.460111	0.230055	+	0.973178i	$0.426109\pi$
$570$	−0.173977	−0.00728708
$571$	−35.7842	−1.49752	−0.748762	−	0.662839i	$-0.769351\pi$
$571$	−35.7842	−1.49752	−0.748762	+	0.662839i	$0.769351\pi$
$572$	12.9276	0.540528
$573$	−3.80410	−0.158919
$574$	−0.285660	−0.0119232
$575$	−66.6343	−2.77884
$576$	−7.99215	−0.333006
$577$	−12.3242	−0.513063	−0.256531	−	0.966536i	$-0.582580\pi$
$577$	−12.3242	−0.513063	−0.256531	+	0.966536i	$0.582580\pi$
$578$	−0.275776	−0.0114708
$579$	−7.42418	−0.308538
$580$	−0.909897	−0.0377814
$581$	−55.6668	−2.30945
$582$	0.0688578	0.00285425
$583$	−80.5597	−3.33644
$584$	0.239968	0.00992996
$585$	−4.11271	−0.170040
$586$	−0.192718	−0.00796109
$587$	−0.361465	−0.0149193	−0.00745963	−	0.999972i	$-0.502374\pi$
$587$	−0.361465	−0.0149193	−0.00745963	+	0.999972i	$0.502374\pi$
$588$	28.3859	1.17062
$589$	15.4060	0.634791
$590$	−0.249367	−0.0102663
$591$	−12.8576	−0.528890
$592$	−20.7428	−0.852525
$593$	7.66165	0.314626	0.157313	−	0.987549i	$-0.449717\pi$
$593$	7.66165	0.314626	0.157313	+	0.987549i	$0.449717\pi$
$594$	−0.116908	−0.00479679
$595$	107.526	4.40813
$596$	−47.4980	−1.94559
$597$	18.5957	0.761071
$598$	0.101138	0.00413582
$599$	7.16632	0.292808	0.146404	−	0.989225i	$-0.453230\pi$
$599$	7.16632	0.292808	0.146404	+	0.989225i	$0.453230\pi$
$600$	−0.861753	−0.0351809
$601$	−18.2846	−0.745843	−0.372922	−	0.927863i	$-0.621644\pi$
$601$	−18.2846	−0.745843	−0.372922	+	0.927863i	$0.621644\pi$
$602$	0.111247	0.00453408
$603$	0.0762221	0.00310400
$604$	−8.90711	−0.362425
$605$	−126.647	−5.14894
$606$	−0.223375	−0.00907399
$607$	24.6854	1.00195	0.500974	−	0.865462i	$-0.332975\pi$
$607$	24.6854	1.00195	0.500974	+	0.865462i	$0.332975\pi$
$608$	−0.507516	−0.0205825
$609$	−0.509360	−0.0206403
$610$	−0.201926	−0.00817573
$611$	−10.3320	−0.417987
$612$	−11.3560	−0.459037
$613$	42.1395	1.70200	0.850999	−	0.525168i	$-0.175997\pi$
$613$	42.1395	1.70200	0.850999	+	0.525168i	$0.175997\pi$
$614$	0.355536	0.0143483
$615$	−14.1114	−0.569028
$616$	2.15272	0.0867357
$617$	32.6952	1.31626	0.658129	−	0.752905i	$-0.271348\pi$
$617$	32.6952	1.31626	0.658129	+	0.752905i	$0.271348\pi$
$618$	0.0180837	0.000727432 0
$619$	−19.7610	−0.794261	−0.397131	−	0.917762i	$-0.629994\pi$
$619$	−19.7610	−0.794261	−0.397131	+	0.917762i	$0.629994\pi$
$620$	54.1625	2.17522
$621$	5.59276	0.224430
$622$	−0.406847	−0.0163131
$623$	−0.688768	−0.0275949
$624$	−3.99804	−0.160050
$625$	57.3808	2.29523
$626$	0.0602804	0.00240929
$627$	15.1229	0.603949
$628$	−2.09190	−0.0834757
$629$	−29.4636	−1.17479
$630$	−0.342400	−0.0136416
$631$	36.0256	1.43416	0.717078	−	0.696993i	$-0.245479\pi$
$631$	36.0256	1.43416	0.717078	+	0.696993i	$0.245479\pi$
$632$	−0.528357	−0.0210169
$633$	−26.6073	−1.05754
$634$	0.535854	0.0212815
$635$	40.3767	1.60230
$636$	24.9183	0.988076
$637$	14.1953	0.562438
$638$	−0.0129345	−0.000512081 0
$639$	0.187658	0.00742365
$640$	−2.37896	−0.0940366
$641$	−22.0085	−0.869283	−0.434642	−	0.900603i	$-0.643125\pi$
$641$	−22.0085	−0.869283	−0.434642	+	0.900603i	$0.643125\pi$
$642$	0.237148	0.00935948
$643$	−32.5757	−1.28466	−0.642331	−	0.766427i	$-0.722032\pi$
$643$	−32.5757	−1.28466	−0.642331	+	0.766427i	$0.722032\pi$
$644$	−51.4878	−2.02891
$645$	5.49553	0.216386
$646$	−0.240230	−0.00945173
$647$	−6.65704	−0.261715	−0.130858	−	0.991401i	$-0.541773\pi$
$647$	−6.65704	−0.261715	−0.130858	+	0.991401i	$0.541773\pi$
$648$	0.0723287	0.00284134
$649$	21.6761	0.850863
$650$	−0.215456	−0.00845087
$651$	30.3202	1.18834
$652$	−20.5488	−0.804754
$653$	−25.1005	−0.982259	−0.491130	−	0.871086i	$-0.663416\pi$
$653$	−25.1005	−0.982259	−0.491130	+	0.871086i	$0.663416\pi$
$654$	−0.0129210	−0.000505250 0
$655$	21.8757	0.854754
$656$	−13.7180	−0.535597
$657$	3.31775	0.129438
$658$	−0.860181	−0.0335334
$659$	−16.1924	−0.630767	−0.315384	−	0.948964i	$-0.602133\pi$
$659$	−16.1924	−0.630767	−0.315384	+	0.948964i	$0.602133\pi$
$660$	53.1673	2.06953
$661$	−26.1228	−1.01606	−0.508030	−	0.861340i	$-0.669626\pi$
$661$	−26.1228	−1.01606	−0.508030	+	0.861340i	$0.669626\pi$
$662$	−0.0337360	−0.00131119
$663$	−5.67891	−0.220550
$664$	0.874555	0.0339393
$665$	44.2919	1.71757
$666$	0.0938226	0.00363555
$667$	0.618773	0.0239590
$668$	36.9264	1.42872
$669$	20.8862	0.807505
$670$	0.00566885	0.000219007 0
$671$	17.5523	0.677599
$672$	−0.998832	−0.0385308
$673$	26.8792	1.03612	0.518059	−	0.855345i	$-0.326655\pi$
$673$	26.8792	1.03612	0.518059	+	0.855345i	$0.326655\pi$
$674$	0.229195	0.00882826
$675$	−11.9144	−0.458585
$676$	−1.99967	−0.0769105
$677$	−23.8300	−0.915860	−0.457930	−	0.888988i	$-0.651409\pi$
$677$	−23.8300	−0.915860	−0.457930	+	0.888988i	$0.651409\pi$
$678$	−0.256984	−0.00986942
$679$	−17.5302	−0.672747
$680$	−1.68929	−0.0647813
$681$	−19.9754	−0.765459
$682$	0.769938	0.0294824
$683$	−37.1728	−1.42238	−0.711189	−	0.703001i	$-0.751843\pi$
$683$	−37.1728	−1.42238	−0.711189	+	0.703001i	$0.751843\pi$
$684$	−4.67774	−0.178858
$685$	−35.1249	−1.34205
$686$	0.599038	0.0228714
$687$	−26.8245	−1.02342
$688$	5.34230	0.203673
$689$	12.4612	0.474734
$690$	0.415949	0.0158349
$691$	7.68088	0.292194	0.146097	−	0.989270i	$-0.453329\pi$
$691$	7.68088	0.292194	0.146097	+	0.989270i	$0.453329\pi$
$692$	19.1400	0.727594
$693$	29.7630	1.13060
$694$	0.358565	0.0136109
$695$	3.96982	0.150584
$696$	0.00800232	0.000303327 0
$697$	−19.4853	−0.738059
$698$	0.0211082	0.000798956 0
$699$	−14.0349	−0.530847
$700$	109.686	4.14573
$701$	−46.1958	−1.74479	−0.872396	−	0.488799i	$-0.837435\pi$
$701$	−46.1958	−1.74479	−0.872396	+	0.488799i	$0.837435\pi$
$702$	0.0180837	0.000682524 0
$703$	−12.1366	−0.457741
$704$	51.6679	1.94731
$705$	−42.4925	−1.60036
$706$	0.445139	0.0167530
$707$	56.8680	2.13874
$708$	−6.70476	−0.251980
$709$	19.6827	0.739200	0.369600	−	0.929191i	$-0.379495\pi$
$709$	19.6827	0.739200	0.369600	+	0.929191i	$0.379495\pi$
$710$	0.0139567	0.000523786 0
$711$	−7.30494	−0.273957
$712$	0.0108209	0.000405531 0
$713$	−36.8331	−1.37941
$714$	−0.472793	−0.0176938
$715$	26.5880	0.994335
$716$	−43.8031	−1.63700
$717$	23.1512	0.864597
$718$	0.546345	0.0203894
$719$	−6.86010	−0.255839	−0.127919	−	0.991785i	$-0.540830\pi$
$719$	−6.86010	−0.255839	−0.127919	+	0.991785i	$0.540830\pi$
$720$	−16.4428	−0.612786
$721$	−4.60383	−0.171456
$722$	0.244634	0.00910434
$723$	4.69638	0.174660
$724$	−37.0468	−1.37683
$725$	−1.31819	−0.0489562
$726$	0.556870	0.0206674
$727$	16.9116	0.627216	0.313608	−	0.949553i	$-0.398462\pi$
$727$	16.9116	0.627216	0.313608	+	0.949553i	$0.398462\pi$
$728$	−0.332990	−0.0123414
$729$	1.00000	0.0370370
$730$	0.246750	0.00913264
$731$	7.58833	0.280664
$732$	−5.42920	−0.200669
$733$	−35.8712	−1.32493	−0.662467	−	0.749091i	$-0.730491\pi$
$733$	−35.8712	−1.32493	−0.662467	+	0.749091i	$0.730491\pi$
$734$	0.0519912	0.00191903
$735$	58.3811	2.15342
$736$	1.21339	0.0447260
$737$	−0.492763	−0.0181512
$738$	0.0620482	0.00228403
$739$	0.0360554	0.00132632	0.000663160	−	1.00000i	$-0.499789\pi$
$739$	0.0360554	0.00132632	0.000663160		1.00000i	$0.499789\pi$
$740$	−42.6686	−1.56853
$741$	−2.33925	−0.0859345
$742$	1.03745	0.0380859
$743$	−46.2618	−1.69718	−0.848590	−	0.529051i	$-0.822548\pi$
$743$	−46.2618	−1.69718	−0.848590	+	0.529051i	$0.822548\pi$
$744$	−0.476346	−0.0174637
$745$	−97.6887	−3.57904
$746$	−0.287221	−0.0105159
$747$	12.0914	0.442401
$748$	73.4144	2.68430
$749$	−60.3744	−2.20603
$750$	−0.514243	−0.0187775
$751$	36.5331	1.33311	0.666555	−	0.745455i	$-0.267768\pi$
$751$	36.5331	1.33311	0.666555	+	0.745455i	$0.267768\pi$
$752$	−41.3077	−1.50634
$753$	8.26959	0.301361
$754$	0.00200074	7.28628e−5 0
$755$	−18.3192	−0.666703
$756$	−9.20616	−0.334825
$757$	−27.4395	−0.997307	−0.498653	−	0.866801i	$-0.666172\pi$
$757$	−27.4395	−0.997307	−0.498653	+	0.866801i	$0.666172\pi$
$758$	0.422642	0.0153510
$759$	−36.1563	−1.31239
$760$	−0.695850	−0.0252411
$761$	49.7969	1.80513	0.902567	−	0.430549i	$-0.141680\pi$
$761$	49.7969	1.80513	0.902567	+	0.430549i	$0.141680\pi$
$762$	−0.177537	−0.00643149
$763$	3.28949	0.119088
$764$	−7.60696	−0.275210
$765$	−23.3557	−0.844427
$766$	0.180656	0.00652738
$767$	−3.35293	−0.121067
$768$	−15.9738	−0.576406
$769$	−28.1546	−1.01528	−0.507641	−	0.861569i	$-0.669482\pi$
$769$	−28.1546	−1.01528	−0.507641	+	0.861569i	$0.669482\pi$
$770$	2.21356	0.0797712
$771$	28.6065	1.03024
$772$	−14.8459	−0.534317
$773$	16.2849	0.585726	0.292863	−	0.956154i	$-0.405392\pi$
$773$	16.2849	0.585726	0.292863	+	0.956154i	$0.405392\pi$
$774$	−0.0241639	−0.000868555 0
$775$	78.4664	2.81860
$776$	0.275409	0.00988659
$777$	−23.8859	−0.856900
$778$	0.354828	0.0127212
$779$	−8.02638	−0.287575
$780$	−8.22408	−0.294469
$781$	−1.21318	−0.0434110
$782$	0.574351	0.0205387
$783$	0.110638	0.00395389
$784$	56.7533	2.02690
$785$	−4.30238	−0.153559
$786$	−0.0961878	−0.00343090
$787$	16.7401	0.596719	0.298360	−	0.954454i	$-0.403561\pi$
$787$	16.7401	0.596719	0.298360	+	0.954454i	$0.403561\pi$
$788$	−25.7110	−0.915915
$789$	2.99713	0.106701
$790$	−0.543289	−0.0193294
$791$	65.4244	2.32623
$792$	−0.467593	−0.0166152
$793$	−2.71504	−0.0964140
$794$	−0.335236	−0.0118971
$795$	51.2493	1.81763
$796$	37.1853	1.31800
$797$	1.13750	0.0402923	0.0201461	−	0.999797i	$-0.493587\pi$
$797$	1.13750	0.0402923	0.0201461	+	0.999797i	$0.493587\pi$
$798$	−0.194752	−0.00689416
$799$	−58.6744	−2.07575
$800$	−2.58491	−0.0913902
$801$	0.149607	0.00528612
$802$	−0.169889	−0.00599900
$803$	−21.4487	−0.756908
$804$	0.152419	0.00537541
$805$	−105.895	−3.73230
$806$	−0.119096	−0.00419499
$807$	−19.6292	−0.690980
$808$	−0.893427	−0.0314306
$809$	−20.3244	−0.714567	−0.357284	−	0.933996i	$-0.616297\pi$
$809$	−20.3244	−0.714567	−0.357284	+	0.933996i	$0.616297\pi$
$810$	0.0743729	0.00261320
$811$	−8.89985	−0.312516	−0.156258	−	0.987716i	$-0.549943\pi$
$811$	−8.89985	−0.312516	−0.156258	+	0.987716i	$0.549943\pi$
$812$	−1.01855	−0.0357442
$813$	−3.01582	−0.105769
$814$	−0.606548	−0.0212595
$815$	−42.2626	−1.48039
$816$	−22.7045	−0.794816
$817$	3.12578	0.109357
$818$	−0.0681484	−0.00238275
$819$	−4.60383	−0.160871
$820$	−28.2183	−0.985424
$821$	−30.6721	−1.07047	−0.535233	−	0.844705i	$-0.679776\pi$
$821$	−30.6721	−1.07047	−0.535233	+	0.844705i	$0.679776\pi$
$822$	0.154445	0.00538688
$823$	−20.8100	−0.725389	−0.362695	−	0.931908i	$-0.618143\pi$
$823$	−20.8100	−0.725389	−0.362695	+	0.931908i	$0.618143\pi$
$824$	0.0723287	0.00251969
$825$	77.0246	2.68165
$826$	−0.279145	−0.00971271
$827$	−18.0461	−0.627526	−0.313763	−	0.949501i	$-0.601590\pi$
$827$	−18.0461	−0.627526	−0.313763	+	0.949501i	$0.601590\pi$
$828$	11.1837	0.388660
$829$	26.5782	0.923098	0.461549	−	0.887115i	$-0.347294\pi$
$829$	26.5782	0.923098	0.461549	+	0.887115i	$0.347294\pi$
$830$	0.899271	0.0312142
$831$	−15.5530	−0.539527
$832$	−7.99215	−0.277078
$833$	80.6137	2.79310
$834$	−0.0174554	−0.000604429 0
$835$	75.9462	2.62823
$836$	30.2408	1.04590
$837$	−6.58585	−0.227640
$838$	−0.662305	−0.0228790
$839$	55.7428	1.92445	0.962227	−	0.272248i	$-0.0877672\pi$
$839$	55.7428	1.92445	0.962227	+	0.272248i	$0.0877672\pi$
$840$	−1.36949	−0.0472519
$841$	−28.9878	−0.999578
$842$	−0.104818	−0.00361227
$843$	8.71038	0.300001
$844$	−53.2058	−1.83142
$845$	−4.11271	−0.141482
$846$	0.186840	0.00642370
$847$	−141.771	−4.87131
$848$	49.8204	1.71084
$849$	−5.72331	−0.196424
$850$	−1.22355	−0.0419675
$851$	29.0166	0.994678
$852$	0.375256	0.0128560
$853$	23.9658	0.820572	0.410286	−	0.911957i	$-0.365429\pi$
$853$	23.9658	0.820572	0.410286	+	0.911957i	$0.365429\pi$
$854$	−0.226039	−0.00773488
$855$	−9.62066	−0.329020
$856$	0.948514	0.0324196
$857$	28.1747	0.962430	0.481215	−	0.876603i	$-0.340196\pi$
$857$	28.1747	0.962430	0.481215	+	0.876603i	$0.340196\pi$
$858$	−0.116908	−0.00399117
$859$	33.6683	1.14875	0.574373	−	0.818594i	$-0.305246\pi$
$859$	33.6683	1.14875	0.574373	+	0.818594i	$0.305246\pi$
$860$	10.9893	0.374731
$861$	−15.7966	−0.538345
$862$	−0.146294	−0.00498278
$863$	28.4066	0.966971	0.483485	−	0.875352i	$-0.339371\pi$
$863$	28.4066	0.966971	0.483485	+	0.875352i	$0.339371\pi$
$864$	0.216957	0.00738101
$865$	39.3651	1.33845
$866$	−0.195661	−0.00664884
$867$	−15.2500	−0.517917
$868$	60.6304	2.05793
$869$	47.2252	1.60201
$870$	0.00822848	0.000278972 0
$871$	0.0762221	0.00258269
$872$	−0.0516797	−0.00175009
$873$	3.80773	0.128872
$874$	0.236586	0.00800264
$875$	130.919	4.42586
$876$	6.63441	0.224156
$877$	−35.5865	−1.20167	−0.600835	−	0.799373i	$-0.705165\pi$
$877$	−35.5865	−1.20167	−0.600835	+	0.799373i	$0.705165\pi$
$878$	−0.654185	−0.0220777
$879$	−10.6570	−0.359452
$880$	106.300	3.58337
$881$	−40.6830	−1.37065	−0.685323	−	0.728239i	$-0.740339\pi$
$881$	−40.6830	−1.37065	−0.685323	+	0.728239i	$0.740339\pi$
$882$	−0.256703	−0.00864363
$883$	23.4317	0.788541	0.394271	−	0.918994i	$-0.370997\pi$
$883$	23.4317	0.788541	0.394271	+	0.918994i	$0.370997\pi$
$884$	−11.3560	−0.381942
$885$	−13.7896	−0.463533
$886$	−0.0559203	−0.00187868
$887$	6.64218	0.223023	0.111511	−	0.993763i	$-0.464431\pi$
$887$	6.64218	0.223023	0.111511	+	0.993763i	$0.464431\pi$
$888$	0.375260	0.0125929
$889$	45.1983	1.51590
$890$	0.0111267	0.000372969 0
$891$	−6.46484	−0.216580
$892$	41.7655	1.39841
$893$	−24.1691	−0.808788
$894$	0.429539	0.0143659
$895$	−90.0896	−3.01136
$896$	−2.66304	−0.0889661
$897$	5.59276	0.186737
$898$	0.630831	0.0210511
$899$	−0.728647	−0.0243017
$900$	−23.8249	−0.794163
$901$	70.7660	2.35756
$902$	−0.401131	−0.0133562
$903$	6.15178	0.204719
$904$	−1.02785	−0.0341859
$905$	−76.1938	−2.53277
$906$	0.0805497	0.00267609
$907$	39.5289	1.31254	0.656268	−	0.754528i	$-0.272134\pi$
$907$	39.5289	1.31254	0.656268	+	0.754528i	$0.272134\pi$
$908$	−39.9443	−1.32560
$909$	−12.3523	−0.409700
$910$	−0.342400	−0.0113505
$911$	−0.695890	−0.0230559	−0.0115279	−	0.999934i	$-0.503670\pi$
$911$	−0.695890	−0.0230559	−0.0115279	+	0.999934i	$0.503670\pi$
$912$	−9.35241	−0.309689
$913$	−78.1688	−2.58701
$914$	−0.400323	−0.0132415
$915$	−11.1662	−0.369143
$916$	−53.6403	−1.77232
$917$	24.4880	0.808665
$918$	0.102695	0.00338945
$919$	1.70065	0.0560994	0.0280497	−	0.999607i	$-0.491070\pi$
$919$	1.70065	0.0560994	0.0280497	+	0.999607i	$0.491070\pi$
$920$	1.66366	0.0548493
$921$	19.6606	0.647839
$922$	−0.0460776	−0.00151748
$923$	0.187658	0.00617685
$924$	59.5163	1.95794
$925$	−61.8149	−2.03246
$926$	0.343472	0.0112872
$927$	1.00000	0.0328443
$928$	0.0240037	0.000787960 0
$929$	48.0024	1.57491	0.787453	−	0.616374i	$-0.211399\pi$
$929$	48.0024	1.57491	0.787453	+	0.616374i	$0.211399\pi$
$930$	−0.489809	−0.0160615
$931$	33.2063	1.08829
$932$	−28.0651	−0.919303
$933$	−22.4980	−0.736552
$934$	−0.559185	−0.0182971
$935$	150.991	4.93793
$936$	0.0723287	0.00236414
$937$	−33.6306	−1.09867	−0.549333	−	0.835604i	$-0.685118\pi$
$937$	−33.6306	−1.09867	−0.549333	+	0.835604i	$0.685118\pi$
$938$	0.00634581	0.000207198 0
$939$	3.33342	0.108782
$940$	−84.9711	−2.77145
$941$	42.0723	1.37152	0.685759	−	0.727829i	$-0.259470\pi$
$941$	42.0723	1.37152	0.685759	+	0.727829i	$0.259470\pi$
$942$	0.0189177	0.000616371 0
$943$	19.1897	0.624904
$944$	−13.4051	−0.436300
$945$	−18.9342	−0.615931
$946$	0.156216	0.00507902
$947$	53.6256	1.74260	0.871298	−	0.490754i	$-0.163279\pi$
$947$	53.6256	1.74260	0.871298	+	0.490754i	$0.163279\pi$
$948$	−14.6075	−0.474429
$949$	3.31775	0.107699
$950$	−0.504005	−0.0163521
$951$	29.6320	0.960882
$952$	−1.89102	−0.0612882
$953$	11.7854	0.381765	0.190883	−	0.981613i	$-0.438865\pi$
$953$	11.7854	0.381765	0.190883	+	0.981613i	$0.438865\pi$
$954$	−0.225344	−0.00729579
$955$	−15.6452	−0.506266
$956$	46.2948	1.49728
$957$	−0.715258	−0.0231210
$958$	−0.409614	−0.0132340
$959$	−39.3194	−1.26969
$960$	−32.8694	−1.06086
$961$	12.3734	0.399143
$962$	0.0938226	0.00302496
$963$	13.1139	0.422591
$964$	9.39123	0.302471
$965$	−30.5335	−0.982908
$966$	0.465621	0.0149811
$967$	−55.3030	−1.77842	−0.889212	−	0.457496i	$-0.848746\pi$
$967$	−55.3030	−1.77842	−0.889212	+	0.457496i	$0.848746\pi$
$968$	2.22730	0.0715881
$969$	−13.2844	−0.426756
$970$	0.283192	0.00909275
$971$	−56.1804	−1.80291	−0.901457	−	0.432869i	$-0.857501\pi$
$971$	−56.1804	−1.80291	−0.901457	+	0.432869i	$0.857501\pi$
$972$	1.99967	0.0641395
$973$	4.44388	0.142464
$974$	−0.251319	−0.00805278
$975$	−11.9144	−0.381566
$976$	−10.8548	−0.347455
$977$	−51.6394	−1.65209	−0.826046	−	0.563603i	$-0.809415\pi$
$977$	−51.6394	−1.65209	−0.826046	+	0.563603i	$0.809415\pi$
$978$	0.185829	0.00594217
$979$	−0.967187	−0.0309114
$980$	116.743	3.72922
$981$	−0.714511	−0.0228126
$982$	0.532571	0.0169950
$983$	21.6648	0.690999	0.345500	−	0.938419i	$-0.387709\pi$
$983$	21.6648	0.690999	0.345500	+	0.938419i	$0.387709\pi$
$984$	0.248173	0.00791145
$985$	−52.8795	−1.68488
$986$	0.0113620	0.000361841 0
$987$	−47.5668	−1.51407
$988$	−4.67774	−0.148819
$989$	−7.47321	−0.237634
$990$	−0.480808	−0.0152811
$991$	27.5583	0.875418	0.437709	−	0.899117i	$-0.355790\pi$
$991$	27.5583	0.875418	0.437709	+	0.899117i	$0.355790\pi$
$992$	−1.42884	−0.0453658
$993$	−1.86555	−0.0592014
$994$	0.0156234	0.000495543 0
$995$	76.4787	2.42454
$996$	24.1788	0.766135
$997$	−19.9429	−0.631597	−0.315798	−	0.948826i	$-0.602272\pi$
$997$	−19.9429	−0.631597	−0.315798	+	0.948826i	$0.602272\pi$
$998$	−0.701083	−0.0221924
$999$	5.18825	0.164149

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.h.1.14	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.h.1.14	✓	25	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:	\( N \)	\(=\)	\( 4017 = 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4017.a (trivial)

\(f(q)\)	\(=\)	\(q-0.0180837 q^{2} -1.00000 q^{3} -1.99967 q^{4} -4.11271 q^{5} +0.0180837 q^{6} -4.60383 q^{7} +0.0723287 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.0180837 q^{2} -1.00000 q^{3} -1.99967 q^{4} -4.11271 q^{5} +0.0180837 q^{6} -4.60383 q^{7} +0.0723287 q^{8} +1.00000 q^{9} +0.0743729 q^{10} -6.46484 q^{11} +1.99967 q^{12} +1.00000 q^{13} +0.0832542 q^{14} +4.11271 q^{15} +3.99804 q^{16} +5.67891 q^{17} -0.0180837 q^{18} +2.33925 q^{19} +8.22408 q^{20} +4.60383 q^{21} +0.116908 q^{22} -5.59276 q^{23} -0.0723287 q^{24} +11.9144 q^{25} -0.0180837 q^{26} -1.00000 q^{27} +9.20616 q^{28} -0.110638 q^{29} -0.0743729 q^{30} +6.58585 q^{31} -0.216957 q^{32} +6.46484 q^{33} -0.102695 q^{34} +18.9342 q^{35} -1.99967 q^{36} -5.18825 q^{37} -0.0423022 q^{38} -1.00000 q^{39} -0.297467 q^{40} -3.43118 q^{41} -0.0832542 q^{42} +1.33623 q^{43} +12.9276 q^{44} -4.11271 q^{45} +0.101138 q^{46} -10.3320 q^{47} -3.99804 q^{48} +14.1953 q^{49} -0.215456 q^{50} -5.67891 q^{51} -1.99967 q^{52} +12.4612 q^{53} +0.0180837 q^{54} +26.5880 q^{55} -0.332990 q^{56} -2.33925 q^{57} +0.00200074 q^{58} -3.35293 q^{59} -8.22408 q^{60} -2.71504 q^{61} -0.119096 q^{62} -4.60383 q^{63} -7.99215 q^{64} -4.11271 q^{65} -0.116908 q^{66} +0.0762221 q^{67} -11.3560 q^{68} +5.59276 q^{69} -0.342400 q^{70} +0.187658 q^{71} +0.0723287 q^{72} +3.31775 q^{73} +0.0938226 q^{74} -11.9144 q^{75} -4.67774 q^{76} +29.7630 q^{77} +0.0180837 q^{78} -7.30494 q^{79} -16.4428 q^{80} +1.00000 q^{81} +0.0620482 q^{82} +12.0914 q^{83} -9.20616 q^{84} -23.3557 q^{85} -0.0241639 q^{86} +0.110638 q^{87} -0.467593 q^{88} +0.149607 q^{89} +0.0743729 q^{90} -4.60383 q^{91} +11.1837 q^{92} -6.58585 q^{93} +0.186840 q^{94} -9.62066 q^{95} +0.216957 q^{96} +3.80773 q^{97} -0.256703 q^{98} -6.46484 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 4 q^{2} - 25 q^{3} + 28 q^{4} - 5 q^{5} + 4 q^{6} - 7 q^{7} - 9 q^{8} + 25 q^{9}+O(q^{10}) \) 25 * q - 4 * q^2 - 25 * q^3 + 28 * q^4 - 5 * q^5 + 4 * q^6 - 7 * q^7 - 9 * q^8 + 25 * q^9	\( 25 q - 4 q^{2} - 25 q^{3} + 28 q^{4} - 5 q^{5} + 4 q^{6} - 7 q^{7} - 9 q^{8} + 25 q^{9} - 12 q^{10} - 23 q^{11} - 28 q^{12} + 25 q^{13} + 5 q^{15} + 26 q^{16} - 14 q^{17} - 4 q^{18} - 4 q^{19} - 12 q^{20} + 7 q^{21} - 7 q^{22} - 47 q^{23} + 9 q^{24} + 26 q^{25} - 4 q^{26} - 25 q^{27} - 38 q^{28} + 6 q^{29} + 12 q^{30} - 8 q^{31} - 62 q^{32} + 23 q^{33} + 25 q^{34} + 28 q^{36} - 20 q^{37} - 2 q^{38} - 25 q^{39} - 8 q^{40} - 33 q^{41} - 13 q^{43} - 13 q^{44} - 5 q^{45} - 21 q^{46} - 48 q^{47} - 26 q^{48} + 40 q^{49} - 9 q^{50} + 14 q^{51} + 28 q^{52} - 24 q^{53} + 4 q^{54} - 2 q^{55} - 14 q^{56} + 4 q^{57} - 31 q^{58} - 36 q^{59} + 12 q^{60} + 25 q^{61} - 7 q^{62} - 7 q^{63} + 45 q^{64} - 5 q^{65} + 7 q^{66} - 2 q^{67} - 32 q^{68} + 47 q^{69} - 13 q^{70} - 60 q^{71} - 9 q^{72} + 28 q^{73} - 16 q^{74} - 26 q^{75} - 12 q^{76} - 17 q^{77} + 4 q^{78} - 29 q^{79} - 88 q^{80} + 25 q^{81} - 22 q^{82} - 71 q^{83} + 38 q^{84} + 3 q^{85} - 3 q^{86} - 6 q^{87} + 23 q^{88} - 46 q^{89} - 12 q^{90} - 7 q^{91} - 69 q^{92} + 8 q^{93} + 4 q^{94} - 47 q^{95} + 62 q^{96} - 14 q^{97} - 71 q^{98} - 23 q^{99}+O(q^{100}) \) 25 * q - 4 * q^2 - 25 * q^3 + 28 * q^4 - 5 * q^5 + 4 * q^6 - 7 * q^7 - 9 * q^8 + 25 * q^9 - 12 * q^10 - 23 * q^11 - 28 * q^12 + 25 * q^13 + 5 * q^15 + 26 * q^16 - 14 * q^17 - 4 * q^18 - 4 * q^19 - 12 * q^20 + 7 * q^21 - 7 * q^22 - 47 * q^23 + 9 * q^24 + 26 * q^25 - 4 * q^26 - 25 * q^27 - 38 * q^28 + 6 * q^29 + 12 * q^30 - 8 * q^31 - 62 * q^32 + 23 * q^33 + 25 * q^34 + 28 * q^36 - 20 * q^37 - 2 * q^38 - 25 * q^39 - 8 * q^40 - 33 * q^41 - 13 * q^43 - 13 * q^44 - 5 * q^45 - 21 * q^46 - 48 * q^47 - 26 * q^48 + 40 * q^49 - 9 * q^50 + 14 * q^51 + 28 * q^52 - 24 * q^53 + 4 * q^54 - 2 * q^55 - 14 * q^56 + 4 * q^57 - 31 * q^58 - 36 * q^59 + 12 * q^60 + 25 * q^61 - 7 * q^62 - 7 * q^63 + 45 * q^64 - 5 * q^65 + 7 * q^66 - 2 * q^67 - 32 * q^68 + 47 * q^69 - 13 * q^70 - 60 * q^71 - 9 * q^72 + 28 * q^73 - 16 * q^74 - 26 * q^75 - 12 * q^76 - 17 * q^77 + 4 * q^78 - 29 * q^79 - 88 * q^80 + 25 * q^81 - 22 * q^82 - 71 * q^83 + 38 * q^84 + 3 * q^85 - 3 * q^86 - 6 * q^87 + 23 * q^88 - 46 * q^89 - 12 * q^90 - 7 * q^91 - 69 * q^92 + 8 * q^93 + 4 * q^94 - 47 * q^95 + 62 * q^96 - 14 * q^97 - 71 * q^98 - 23 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more