LMFDB - Embedded newform 4017.2.a.j.1.11

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:	$0$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
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)

$f(q)$	$=$	$q-0.254687 q^{2} -1.00000 q^{3} -1.93513 q^{4} -0.644426 q^{5} +0.254687 q^{6} +3.73934 q^{7} +1.00223 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.254687 q^{2} -1.00000 q^{3} -1.93513 q^{4} -0.644426 q^{5} +0.254687 q^{6} +3.73934 q^{7} +1.00223 q^{8} +1.00000 q^{9} +0.164127 q^{10} -2.16169 q^{11} +1.93513 q^{12} +1.00000 q^{13} -0.952363 q^{14} +0.644426 q^{15} +3.61501 q^{16} +6.60210 q^{17} -0.254687 q^{18} +5.07149 q^{19} +1.24705 q^{20} -3.73934 q^{21} +0.550555 q^{22} -1.31455 q^{23} -1.00223 q^{24} -4.58471 q^{25} -0.254687 q^{26} -1.00000 q^{27} -7.23613 q^{28} +6.79091 q^{29} -0.164127 q^{30} -2.74661 q^{31} -2.92515 q^{32} +2.16169 q^{33} -1.68147 q^{34} -2.40973 q^{35} -1.93513 q^{36} -2.15149 q^{37} -1.29164 q^{38} -1.00000 q^{39} -0.645862 q^{40} +1.71235 q^{41} +0.952363 q^{42} +6.80465 q^{43} +4.18316 q^{44} -0.644426 q^{45} +0.334800 q^{46} +4.86401 q^{47} -3.61501 q^{48} +6.98268 q^{49} +1.16767 q^{50} -6.60210 q^{51} -1.93513 q^{52} +1.28229 q^{53} +0.254687 q^{54} +1.39305 q^{55} +3.74767 q^{56} -5.07149 q^{57} -1.72956 q^{58} +4.33667 q^{59} -1.24705 q^{60} -9.11013 q^{61} +0.699527 q^{62} +3.73934 q^{63} -6.48503 q^{64} -0.644426 q^{65} -0.550555 q^{66} -10.0994 q^{67} -12.7759 q^{68} +1.31455 q^{69} +0.613727 q^{70} +1.97915 q^{71} +1.00223 q^{72} -10.0930 q^{73} +0.547956 q^{74} +4.58471 q^{75} -9.81401 q^{76} -8.08331 q^{77} +0.254687 q^{78} -11.7940 q^{79} -2.32961 q^{80} +1.00000 q^{81} -0.436113 q^{82} +11.9265 q^{83} +7.23613 q^{84} -4.25456 q^{85} -1.73306 q^{86} -6.79091 q^{87} -2.16651 q^{88} -7.92637 q^{89} +0.164127 q^{90} +3.73934 q^{91} +2.54384 q^{92} +2.74661 q^{93} -1.23880 q^{94} -3.26820 q^{95} +2.92515 q^{96} +13.9493 q^{97} -1.77840 q^{98} -2.16169 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q + 6 q^{2} - 25 q^{3} + 28 q^{4} + 7 q^{5} - 6 q^{6} + 17 q^{7} + 21 q^{8} + 25 q^{9}+O(q^{10}) $ 25 * q + 6 * q^2 - 25 * q^3 + 28 * q^4 + 7 * q^5 - 6 * q^6 + 17 * q^7 + 21 * q^8 + 25 * q^9	\( 25 q + 6 q^{2} - 25 q^{3} + 28 q^{4} + 7 q^{5} - 6 q^{6} + 17 q^{7} + 21 q^{8} + 25 q^{9} - 6 q^{10} + 21 q^{11} - 28 q^{12} + 25 q^{13} + 10 q^{14} - 7 q^{15} + 30 q^{16} + 14 q^{17} + 6 q^{18} + 12 q^{19} + 24 q^{20} - 17 q^{21} + 3 q^{22} + 41 q^{23} - 21 q^{24} + 30 q^{25} + 6 q^{26} - 25 q^{27} + 14 q^{28} + 22 q^{29} + 6 q^{30} + 14 q^{31} + 28 q^{32} - 21 q^{33} - 11 q^{34} + 14 q^{35} + 28 q^{36} - 6 q^{37} + 16 q^{38} - 25 q^{39} - 34 q^{40} + 33 q^{41} - 10 q^{42} + 35 q^{43} + 45 q^{44} + 7 q^{45} + 3 q^{46} + 48 q^{47} - 30 q^{48} - 4 q^{49} + 7 q^{50} - 14 q^{51} + 28 q^{52} + 18 q^{53} - 6 q^{54} + 10 q^{55} + 32 q^{56} - 12 q^{57} + 33 q^{58} + 46 q^{59} - 24 q^{60} - 19 q^{61} + 5 q^{62} + 17 q^{63} + 29 q^{64} + 7 q^{65} - 3 q^{66} + 16 q^{67} + 20 q^{68} - 41 q^{69} - 43 q^{70} + 60 q^{71} + 21 q^{72} - 14 q^{73} - 50 q^{74} - 30 q^{75} + 59 q^{77} - 6 q^{78} + 7 q^{79} + 32 q^{80} + 25 q^{81} + 18 q^{82} + 23 q^{83} - 14 q^{84} - 9 q^{85} - 9 q^{86} - 22 q^{87} + 23 q^{88} + 10 q^{89} - 6 q^{90} + 17 q^{91} + 69 q^{92} - 14 q^{93} - 30 q^{94} + 81 q^{95} - 28 q^{96} - 10 q^{97} + 55 q^{98} + 21 q^{99}+O(q^{100}) \) 25 * q + 6 * q^2 - 25 * q^3 + 28 * q^4 + 7 * q^5 - 6 * q^6 + 17 * q^7 + 21 * q^8 + 25 * q^9 - 6 * q^10 + 21 * q^11 - 28 * q^12 + 25 * q^13 + 10 * q^14 - 7 * q^15 + 30 * q^16 + 14 * q^17 + 6 * q^18 + 12 * q^19 + 24 * q^20 - 17 * q^21 + 3 * q^22 + 41 * q^23 - 21 * q^24 + 30 * q^25 + 6 * q^26 - 25 * q^27 + 14 * q^28 + 22 * q^29 + 6 * q^30 + 14 * q^31 + 28 * q^32 - 21 * q^33 - 11 * q^34 + 14 * q^35 + 28 * q^36 - 6 * q^37 + 16 * q^38 - 25 * q^39 - 34 * q^40 + 33 * q^41 - 10 * q^42 + 35 * q^43 + 45 * q^44 + 7 * q^45 + 3 * q^46 + 48 * q^47 - 30 * q^48 - 4 * q^49 + 7 * q^50 - 14 * q^51 + 28 * q^52 + 18 * q^53 - 6 * q^54 + 10 * q^55 + 32 * q^56 - 12 * q^57 + 33 * q^58 + 46 * q^59 - 24 * q^60 - 19 * q^61 + 5 * q^62 + 17 * q^63 + 29 * q^64 + 7 * q^65 - 3 * q^66 + 16 * q^67 + 20 * q^68 - 41 * q^69 - 43 * q^70 + 60 * q^71 + 21 * q^72 - 14 * q^73 - 50 * q^74 - 30 * q^75 + 59 * q^77 - 6 * q^78 + 7 * q^79 + 32 * q^80 + 25 * q^81 + 18 * q^82 + 23 * q^83 - 14 * q^84 - 9 * q^85 - 9 * q^86 - 22 * q^87 + 23 * q^88 + 10 * q^89 - 6 * q^90 + 17 * q^91 + 69 * q^92 - 14 * q^93 - 30 * q^94 + 81 * q^95 - 28 * q^96 - 10 * q^97 + 55 * q^98 + 21 * 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 $

$2$	−0.254687	−0.180091	−0.0900455	−	0.995938i	$-0.528701\pi$
$2$	−0.254687	−0.180091	−0.0900455	+	0.995938i	$0.528701\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.93513	−0.967567
$5$	−0.644426	−0.288196	−0.144098	−	0.989563i	$-0.546028\pi$
$5$	−0.644426	−0.288196	−0.144098	+	0.989563i	$0.546028\pi$
$6$	0.254687	0.103976
$7$	3.73934	1.41334	0.706669	−	0.707544i	$-0.250197\pi$
$7$	3.73934	1.41334	0.706669	+	0.707544i	$0.250197\pi$
$8$	1.00223	0.354341
$9$	1.00000	0.333333
$10$	0.164127	0.0519015
$11$	−2.16169	−0.651775	−0.325887	−	0.945409i	$-0.605663\pi$
$11$	−2.16169	−0.651775	−0.325887	+	0.945409i	$0.605663\pi$
$12$	1.93513	0.558625
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−0.952363	−0.254530
$15$	0.644426	0.166390
$16$	3.61501	0.903754
$17$	6.60210	1.60124	0.800622	−	0.599170i	$-0.204503\pi$
$17$	6.60210	1.60124	0.800622	+	0.599170i	$0.204503\pi$
$18$	−0.254687	−0.0600303
$19$	5.07149	1.16348	0.581740	−	0.813375i	$-0.302372\pi$
$19$	5.07149	1.16348	0.581740	+	0.813375i	$0.302372\pi$
$20$	1.24705	0.278849
$21$	−3.73934	−0.815991
$22$	0.550555	0.117379
$23$	−1.31455	−0.274103	−0.137052	−	0.990564i	$-0.543763\pi$
$23$	−1.31455	−0.274103	−0.137052	+	0.990564i	$0.543763\pi$
$24$	−1.00223	−0.204579
$25$	−4.58471	−0.916943
$26$	−0.254687	−0.0499483
$27$	−1.00000	−0.192450
$28$	−7.23613	−1.36750
$29$	6.79091	1.26104	0.630520	−	0.776173i	$-0.282842\pi$
$29$	6.79091	1.26104	0.630520	+	0.776173i	$0.282842\pi$
$30$	−0.164127	−0.0299654
$31$	−2.74661	−0.493306	−0.246653	−	0.969104i	$-0.579331\pi$
$31$	−2.74661	−0.493306	−0.246653	+	0.969104i	$0.579331\pi$
$32$	−2.92515	−0.517099
$33$	2.16169	0.376302
$34$	−1.68147	−0.288370
$35$	−2.40973	−0.407319
$36$	−1.93513	−0.322522
$37$	−2.15149	−0.353702	−0.176851	−	0.984238i	$-0.556591\pi$
$37$	−2.15149	−0.353702	−0.176851	+	0.984238i	$0.556591\pi$
$38$	−1.29164	−0.209532
$39$	−1.00000	−0.160128
$40$	−0.645862	−0.102120
$41$	1.71235	0.267424	0.133712	−	0.991020i	$-0.457310\pi$
$41$	1.71235	0.267424	0.133712	+	0.991020i	$0.457310\pi$
$42$	0.952363	0.146953
$43$	6.80465	1.03770	0.518850	−	0.854866i	$-0.326360\pi$
$43$	6.80465	1.03770	0.518850	+	0.854866i	$0.326360\pi$
$44$	4.18316	0.630636
$45$	−0.644426	−0.0960654
$46$	0.334800	0.0493635
$47$	4.86401	0.709488	0.354744	−	0.934963i	$-0.384568\pi$
$47$	4.86401	0.709488	0.354744	+	0.934963i	$0.384568\pi$
$48$	−3.61501	−0.521782
$49$	6.98268	0.997526
$50$	1.16767	0.165133
$51$	−6.60210	−0.924478
$52$	−1.93513	−0.268355
$53$	1.28229	0.176136	0.0880681	−	0.996114i	$-0.471931\pi$
$53$	1.28229	0.176136	0.0880681	+	0.996114i	$0.471931\pi$
$54$	0.254687	0.0346585
$55$	1.39305	0.187839
$56$	3.74767	0.500804
$57$	−5.07149	−0.671735
$58$	−1.72956	−0.227102
$59$	4.33667	0.564587	0.282293	−	0.959328i	$-0.408905\pi$
$59$	4.33667	0.564587	0.282293	+	0.959328i	$0.408905\pi$
$60$	−1.24705	−0.160994
$61$	−9.11013	−1.16643	−0.583217	−	0.812317i	$-0.698206\pi$
$61$	−9.11013	−1.16643	−0.583217	+	0.812317i	$0.698206\pi$
$62$	0.699527	0.0888400
$63$	3.73934	0.471113
$64$	−6.48503	−0.810629
$65$	−0.644426	−0.0799312
$66$	−0.550555	−0.0677687
$67$	−10.0994	−1.23384	−0.616920	−	0.787026i	$-0.711620\pi$
$67$	−10.0994	−1.23384	−0.616920	+	0.787026i	$0.711620\pi$
$68$	−12.7759	−1.54931
$69$	1.31455	0.158254
$70$	0.613727	0.0733544
$71$	1.97915	0.234882	0.117441	−	0.993080i	$-0.462531\pi$
$71$	1.97915	0.234882	0.117441	+	0.993080i	$0.462531\pi$
$72$	1.00223	0.118114
$73$	−10.0930	−1.18129	−0.590647	−	0.806930i	$-0.701127\pi$
$73$	−10.0930	−1.18129	−0.590647	+	0.806930i	$0.701127\pi$
$74$	0.547956	0.0636986
$75$	4.58471	0.529397
$76$	−9.81401	−1.12574
$77$	−8.08331	−0.921178
$78$	0.254687	0.0288376
$79$	−11.7940	−1.32693	−0.663463	−	0.748209i	$-0.730914\pi$
$79$	−11.7940	−1.32693	−0.663463	+	0.748209i	$0.730914\pi$
$80$	−2.32961	−0.260458
$81$	1.00000	0.111111
$82$	−0.436113	−0.0481606
$83$	11.9265	1.30910	0.654552	−	0.756017i	$-0.272857\pi$
$83$	11.9265	1.30910	0.654552	+	0.756017i	$0.272857\pi$
$84$	7.23613	0.789527
$85$	−4.25456	−0.461472
$86$	−1.73306	−0.186880
$87$	−6.79091	−0.728062
$88$	−2.16651	−0.230951
$89$	−7.92637	−0.840193	−0.420097	−	0.907479i	$-0.638004\pi$
$89$	−7.92637	−0.840193	−0.420097	+	0.907479i	$0.638004\pi$
$90$	0.164127	0.0173005
$91$	3.73934	0.391990
$92$	2.54384	0.265213
$93$	2.74661	0.284811
$94$	−1.23880	−0.127772
$95$	−3.26820	−0.335310
$96$	2.92515	0.298547
$97$	13.9493	1.41634	0.708170	−	0.706042i	$-0.249521\pi$
$97$	13.9493	1.41634	0.708170	+	0.706042i	$0.249521\pi$
$98$	−1.77840	−0.179645
$99$	−2.16169	−0.217258
$100$	8.87204	0.887204
$101$	−4.53003	−0.450754	−0.225377	−	0.974272i	$-0.572361\pi$
$101$	−4.53003	−0.450754	−0.225377	+	0.974272i	$0.572361\pi$
$102$	1.68147	0.166490
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	1.00223	0.0982766
$105$	2.40973	0.235166
$106$	−0.326583	−0.0317205
$107$	−9.63958	−0.931893	−0.465946	−	0.884813i	$-0.654286\pi$
$107$	−9.63958	−0.931893	−0.465946	+	0.884813i	$0.654286\pi$
$108$	1.93513	0.186208
$109$	6.50575	0.623138	0.311569	−	0.950223i	$-0.399145\pi$
$109$	6.50575	0.623138	0.311569	+	0.950223i	$0.399145\pi$
$110$	−0.354792	−0.0338281
$111$	2.15149	0.204210
$112$	13.5178	1.27731
$113$	14.2418	1.33976	0.669878	−	0.742472i	$-0.266347\pi$
$113$	14.2418	1.33976	0.669878	+	0.742472i	$0.266347\pi$
$114$	1.29164	0.120973
$115$	0.847132	0.0789955
$116$	−13.1413	−1.22014
$117$	1.00000	0.0924500
$118$	−1.10450	−0.101677
$119$	24.6875	2.26310
$120$	0.645862	0.0589589
$121$	−6.32709	−0.575190
$122$	2.32023	0.210064
$123$	−1.71235	−0.154397
$124$	5.31507	0.477307
$125$	6.17664	0.552456
$126$	−0.952363	−0.0848432
$127$	−5.59992	−0.496913	−0.248456	−	0.968643i	$-0.579923\pi$
$127$	−5.59992	−0.496913	−0.248456	+	0.968643i	$0.579923\pi$
$128$	7.50196	0.663086
$129$	−6.80465	−0.599116
$130$	0.164127	0.0143949
$131$	10.0378	0.877003	0.438501	−	0.898731i	$-0.355509\pi$
$131$	10.0378	0.877003	0.438501	+	0.898731i	$0.355509\pi$
$132$	−4.18316	−0.364098
$133$	18.9640	1.64439
$134$	2.57219	0.222204
$135$	0.644426	0.0554634
$136$	6.61681	0.567387
$137$	5.55075	0.474233	0.237116	−	0.971481i	$-0.423798\pi$
$137$	5.55075	0.474233	0.237116	+	0.971481i	$0.423798\pi$
$138$	−0.334800	−0.0285001
$139$	8.74256	0.741534	0.370767	−	0.928726i	$-0.379095\pi$
$139$	8.74256	0.741534	0.370767	+	0.928726i	$0.379095\pi$
$140$	4.66315	0.394108
$141$	−4.86401	−0.409623
$142$	−0.504064	−0.0423001
$143$	−2.16169	−0.180770
$144$	3.61501	0.301251
$145$	−4.37624	−0.363427
$146$	2.57055	0.212740
$147$	−6.98268	−0.575922
$148$	4.16342	0.342231
$149$	10.0949	0.827003	0.413501	−	0.910504i	$-0.364306\pi$
$149$	10.0949	0.827003	0.413501	+	0.910504i	$0.364306\pi$
$150$	−1.16767	−0.0953397
$151$	0.629840	0.0512557	0.0256278	−	0.999672i	$-0.491842\pi$
$151$	0.629840	0.0512557	0.0256278	+	0.999672i	$0.491842\pi$
$152$	5.08279	0.412269
$153$	6.60210	0.533748
$154$	2.05871	0.165896
$155$	1.76999	0.142169
$156$	1.93513	0.154935
$157$	2.57454	0.205471	0.102735	−	0.994709i	$-0.467241\pi$
$157$	2.57454	0.205471	0.102735	+	0.994709i	$0.467241\pi$
$158$	3.00377	0.238967
$159$	−1.28229	−0.101692
$160$	1.88505	0.149026
$161$	−4.91556	−0.387401
$162$	−0.254687	−0.0200101
$163$	−8.11253	−0.635422	−0.317711	−	0.948188i	$-0.602914\pi$
$163$	−8.11253	−0.635422	−0.317711	+	0.948188i	$0.602914\pi$
$164$	−3.31362	−0.258751
$165$	−1.39305	−0.108449
$166$	−3.03753	−0.235758
$167$	14.8223	1.14698	0.573490	−	0.819212i	$-0.305589\pi$
$167$	14.8223	1.14698	0.573490	+	0.819212i	$0.305589\pi$
$168$	−3.74767	−0.289139
$169$	1.00000	0.0769231
$170$	1.08358	0.0831070
$171$	5.07149	0.387827
$172$	−13.1679	−1.00404
$173$	−5.58518	−0.424634	−0.212317	−	0.977201i	$-0.568101\pi$
$173$	−5.58518	−0.424634	−0.212317	+	0.977201i	$0.568101\pi$
$174$	1.72956	0.131117
$175$	−17.1438	−1.29595
$176$	−7.81455	−0.589044
$177$	−4.33667	−0.325964
$178$	2.01874	0.151311
$179$	−6.51826	−0.487197	−0.243599	−	0.969876i	$-0.578328\pi$
$179$	−6.51826	−0.487197	−0.243599	+	0.969876i	$0.578328\pi$
$180$	1.24705	0.0929497
$181$	5.43008	0.403615	0.201807	−	0.979425i	$-0.435319\pi$
$181$	5.43008	0.403615	0.201807	+	0.979425i	$0.435319\pi$
$182$	−0.952363	−0.0705938
$183$	9.11013	0.673440
$184$	−1.31748	−0.0971261
$185$	1.38647	0.101936
$186$	−0.699527	−0.0512918
$187$	−14.2717	−1.04365
$188$	−9.41251	−0.686478
$189$	−3.73934	−0.271997
$190$	0.832369	0.0603864
$191$	18.9436	1.37071	0.685354	−	0.728210i	$-0.259647\pi$
$191$	18.9436	1.37071	0.685354	+	0.728210i	$0.259647\pi$
$192$	6.48503	0.468017
$193$	3.56540	0.256643	0.128322	−	0.991733i	$-0.459041\pi$
$193$	3.56540	0.256643	0.128322	+	0.991733i	$0.459041\pi$
$194$	−3.55271	−0.255070
$195$	0.644426	0.0461483
$196$	−13.5124	−0.965173
$197$	−10.2323	−0.729024	−0.364512	−	0.931199i	$-0.618764\pi$
$197$	−10.2323	−0.729024	−0.364512	+	0.931199i	$0.618764\pi$
$198$	0.550555	0.0391263
$199$	24.0522	1.70502	0.852509	−	0.522713i	$-0.175080\pi$
$199$	24.0522	1.70502	0.852509	+	0.522713i	$0.175080\pi$
$200$	−4.59493	−0.324911
$201$	10.0994	0.712358
$202$	1.15374	0.0811768
$203$	25.3935	1.78228
$204$	12.7759	0.894495
$205$	−1.10348	−0.0770705
$206$	0.254687	0.0177449
$207$	−1.31455	−0.0913678
$208$	3.61501	0.250656
$209$	−10.9630	−0.758326
$210$	−0.613727	−0.0423512
$211$	11.5341	0.794041	0.397020	−	0.917810i	$-0.370044\pi$
$211$	11.5341	0.794041	0.397020	+	0.917810i	$0.370044\pi$
$212$	−2.48140	−0.170424
$213$	−1.97915	−0.135609
$214$	2.45508	0.167826
$215$	−4.38509	−0.299061
$216$	−1.00223	−0.0681930
$217$	−10.2705	−0.697209
$218$	−1.65693	−0.112222
$219$	10.0930	0.682020
$220$	−2.69574	−0.181747
$221$	6.60210	0.444105
$222$	−0.547956	−0.0367764
$223$	24.6702	1.65204	0.826018	−	0.563644i	$-0.190601\pi$
$223$	24.6702	1.65204	0.826018	+	0.563644i	$0.190601\pi$
$224$	−10.9382	−0.730836
$225$	−4.58471	−0.305648
$226$	−3.62720	−0.241278
$227$	−20.4670	−1.35845	−0.679223	−	0.733932i	$-0.737683\pi$
$227$	−20.4670	−1.35845	−0.679223	+	0.733932i	$0.737683\pi$
$228$	9.81401	0.649949
$229$	2.02798	0.134013	0.0670063	−	0.997753i	$-0.478655\pi$
$229$	2.02798	0.134013	0.0670063	+	0.997753i	$0.478655\pi$
$230$	−0.215754	−0.0142264
$231$	8.08331	0.531842
$232$	6.80604	0.446839
$233$	−4.31964	−0.282989	−0.141494	−	0.989939i	$-0.545191\pi$
$233$	−4.31964	−0.282989	−0.141494	+	0.989939i	$0.545191\pi$
$234$	−0.254687	−0.0166494
$235$	−3.13449	−0.204472
$236$	−8.39205	−0.546276
$237$	11.7940	0.766101
$238$	−6.28759	−0.407564
$239$	−4.38877	−0.283886	−0.141943	−	0.989875i	$-0.545335\pi$
$239$	−4.38877	−0.283886	−0.141943	+	0.989875i	$0.545335\pi$
$240$	2.32961	0.150376
$241$	18.4681	1.18963	0.594817	−	0.803861i	$-0.297225\pi$
$241$	18.4681	1.18963	0.594817	+	0.803861i	$0.297225\pi$
$242$	1.61143	0.103587
$243$	−1.00000	−0.0641500
$244$	17.6293	1.12860
$245$	−4.49982	−0.287483
$246$	0.436113	0.0278056
$247$	5.07149	0.322691
$248$	−2.75273	−0.174799
$249$	−11.9265	−0.755811
$250$	−1.57311	−0.0994923
$251$	−11.2714	−0.711446	−0.355723	−	0.934592i	$-0.615765\pi$
$251$	−11.2714	−0.711446	−0.355723	+	0.934592i	$0.615765\pi$
$252$	−7.23613	−0.455833
$253$	2.84166	0.178654
$254$	1.42623	0.0894896
$255$	4.25456	0.266431
$256$	11.0594	0.691213
$257$	14.3567	0.895547	0.447774	−	0.894147i	$-0.352217\pi$
$257$	14.3567	0.895547	0.447774	+	0.894147i	$0.352217\pi$
$258$	1.73306	0.107895
$259$	−8.04515	−0.499901
$260$	1.24705	0.0773388
$261$	6.79091	0.420347
$262$	−2.55649	−0.157940
$263$	18.9401	1.16789	0.583947	−	0.811792i	$-0.301508\pi$
$263$	18.9401	1.16789	0.583947	+	0.811792i	$0.301508\pi$
$264$	2.16651	0.133339
$265$	−0.826342	−0.0507618
$266$	−4.82990	−0.296140
$267$	7.92637	0.485086
$268$	19.5437	1.19382
$269$	26.4369	1.61189	0.805945	−	0.591991i	$-0.201658\pi$
$269$	26.4369	1.61189	0.805945	+	0.591991i	$0.201658\pi$
$270$	−0.164127	−0.00998846
$271$	−15.6578	−0.951142	−0.475571	−	0.879677i	$-0.657759\pi$
$271$	−15.6578	−0.951142	−0.475571	+	0.879677i	$0.657759\pi$
$272$	23.8667	1.44713
$273$	−3.73934	−0.226315
$274$	−1.41370	−0.0854050
$275$	9.91074	0.597640
$276$	−2.54384	−0.153121
$277$	0.0438679	0.00263577	0.00131788	−	0.999999i	$-0.499581\pi$
$277$	0.0438679	0.00263577	0.00131788	+	0.999999i	$0.499581\pi$
$278$	−2.22662	−0.133544
$279$	−2.74661	−0.164435
$280$	−2.41510	−0.144330
$281$	−8.85075	−0.527991	−0.263996	−	0.964524i	$-0.585040\pi$
$281$	−8.85075	−0.527991	−0.263996	+	0.964524i	$0.585040\pi$
$282$	1.23880	0.0737695
$283$	−0.731884	−0.0435060	−0.0217530	−	0.999763i	$-0.506925\pi$
$283$	−0.731884	−0.0435060	−0.0217530	+	0.999763i	$0.506925\pi$
$284$	−3.82992	−0.227264
$285$	3.26820	0.193592
$286$	0.550555	0.0325550
$287$	6.40306	0.377961
$288$	−2.92515	−0.172366
$289$	26.5877	1.56398
$290$	1.11457	0.0654499
$291$	−13.9493	−0.817724
$292$	19.5313	1.14298
$293$	−17.4078	−1.01698	−0.508488	−	0.861069i	$-0.669795\pi$
$293$	−17.4078	−1.01698	−0.508488	+	0.861069i	$0.669795\pi$
$294$	1.77840	0.103718
$295$	−2.79467	−0.162712
$296$	−2.15628	−0.125331
$297$	2.16169	0.125434
$298$	−2.57103	−0.148936
$299$	−1.31455	−0.0760226
$300$	−8.87204	−0.512227
$301$	25.4449	1.46662
$302$	−0.160412	−0.00923069
$303$	4.53003	0.260243
$304$	18.3335	1.05150
$305$	5.87081	0.336161
$306$	−1.68147	−0.0961232
$307$	6.42085	0.366457	0.183229	−	0.983070i	$-0.441345\pi$
$307$	6.42085	0.366457	0.183229	+	0.983070i	$0.441345\pi$
$308$	15.6423	0.891302
$309$	1.00000	0.0568880
$310$	−0.450794	−0.0256034
$311$	21.8263	1.23766	0.618828	−	0.785527i	$-0.287608\pi$
$311$	21.8263	1.23766	0.618828	+	0.785527i	$0.287608\pi$
$312$	−1.00223	−0.0567400
$313$	−26.9981	−1.52602	−0.763012	−	0.646384i	$-0.776280\pi$
$313$	−26.9981	−1.52602	−0.763012	+	0.646384i	$0.776280\pi$
$314$	−0.655702	−0.0370034
$315$	−2.40973	−0.135773
$316$	22.8229	1.28389
$317$	−29.5618	−1.66036	−0.830178	−	0.557498i	$-0.811761\pi$
$317$	−29.5618	−1.66036	−0.830178	+	0.557498i	$0.811761\pi$
$318$	0.326583	0.0183139
$319$	−14.6799	−0.821914
$320$	4.17912	0.233620
$321$	9.63958	0.538029
$322$	1.25193	0.0697674
$323$	33.4825	1.86301
$324$	−1.93513	−0.107507
$325$	−4.58471	−0.254314
$326$	2.06616	0.114434
$327$	−6.50575	−0.359769
$328$	1.71616	0.0947593
$329$	18.1882	1.00275
$330$	0.354792	0.0195307
$331$	3.54256	0.194716	0.0973582	−	0.995249i	$-0.468961\pi$
$331$	3.54256	0.194716	0.0973582	+	0.995249i	$0.468961\pi$
$332$	−23.0794	−1.26665
$333$	−2.15149	−0.117901
$334$	−3.77504	−0.206561
$335$	6.50833	0.355588
$336$	−13.5178	−0.737455
$337$	−17.6455	−0.961214	−0.480607	−	0.876936i	$-0.659584\pi$
$337$	−17.6455	−0.961214	−0.480607	+	0.876936i	$0.659584\pi$
$338$	−0.254687	−0.0138532
$339$	−14.2418	−0.773508
$340$	8.23315	0.446505
$341$	5.93733	0.321525
$342$	−1.29164	−0.0698441
$343$	−0.0647594	−0.00349668
$344$	6.81981	0.367700
$345$	−0.847132	−0.0456081
$346$	1.42247	0.0764727
$347$	21.9422	1.17792	0.588959	−	0.808163i	$-0.299538\pi$
$347$	21.9422	1.17792	0.588959	+	0.808163i	$0.299538\pi$
$348$	13.1413	0.704449
$349$	15.6683	0.838703	0.419351	−	0.907824i	$-0.362258\pi$
$349$	15.6683	0.838703	0.419351	+	0.907824i	$0.362258\pi$
$350$	4.36631	0.233389
$351$	−1.00000	−0.0533761
$352$	6.32328	0.337032
$353$	23.1715	1.23330	0.616648	−	0.787239i	$-0.288490\pi$
$353$	23.1715	1.23330	0.616648	+	0.787239i	$0.288490\pi$
$354$	1.10450	0.0587033
$355$	−1.27542	−0.0676920
$356$	15.3386	0.812943
$357$	−24.6875	−1.30660
$358$	1.66012	0.0877399
$359$	26.0955	1.37727	0.688635	−	0.725109i	$-0.258210\pi$
$359$	26.0955	1.37727	0.688635	+	0.725109i	$0.258210\pi$
$360$	−0.645862	−0.0340399
$361$	6.72001	0.353685
$362$	−1.38297	−0.0726874
$363$	6.32709	0.332086
$364$	−7.23613	−0.379276
$365$	6.50418	0.340444
$366$	−2.32023	−0.121281
$367$	15.3892	0.803310	0.401655	−	0.915791i	$-0.368435\pi$
$367$	15.3892	0.803310	0.401655	+	0.915791i	$0.368435\pi$
$368$	−4.75213	−0.247722
$369$	1.71235	0.0891413
$370$	−0.353117	−0.0183577
$371$	4.79492	0.248940
$372$	−5.31507	−0.275573
$373$	−15.1942	−0.786724	−0.393362	−	0.919384i	$-0.628688\pi$
$373$	−15.1942	−0.786724	−0.393362	+	0.919384i	$0.628688\pi$
$374$	3.63482	0.187952
$375$	−6.17664	−0.318960
$376$	4.87485	0.251401
$377$	6.79091	0.349750
$378$	0.952363	0.0489842
$379$	−10.8656	−0.558126	−0.279063	−	0.960273i	$-0.590024\pi$
$379$	−10.8656	−0.558126	−0.279063	+	0.960273i	$0.590024\pi$
$380$	6.32441	0.324435
$381$	5.59992	0.286893
$382$	−4.82468	−0.246852
$383$	7.53663	0.385104	0.192552	−	0.981287i	$-0.438324\pi$
$383$	7.53663	0.385104	0.192552	+	0.981287i	$0.438324\pi$
$384$	−7.50196	−0.382833
$385$	5.20909	0.265480
$386$	−0.908062	−0.0462192
$387$	6.80465	0.345900
$388$	−26.9938	−1.37040
$389$	4.82746	0.244762	0.122381	−	0.992483i	$-0.460947\pi$
$389$	4.82746	0.244762	0.122381	+	0.992483i	$0.460947\pi$
$390$	−0.164127	−0.00831090
$391$	−8.67881	−0.438906
$392$	6.99824	0.353465
$393$	−10.0378	−0.506338
$394$	2.60604	0.131291
$395$	7.60035	0.382415
$396$	4.18316	0.210212
$397$	−13.3155	−0.668285	−0.334142	−	0.942523i	$-0.608447\pi$
$397$	−13.3155	−0.668285	−0.334142	+	0.942523i	$0.608447\pi$
$398$	−6.12580	−0.307058
$399$	−18.9640	−0.949389
$400$	−16.5738	−0.828690
$401$	−16.9664	−0.847261	−0.423630	−	0.905835i	$-0.639244\pi$
$401$	−16.9664	−0.847261	−0.423630	+	0.905835i	$0.639244\pi$
$402$	−2.57219	−0.128289
$403$	−2.74661	−0.136819
$404$	8.76621	0.436135
$405$	−0.644426	−0.0320218
$406$	−6.46741	−0.320972
$407$	4.65085	0.230534
$408$	−6.61681	−0.327581
$409$	7.28698	0.360318	0.180159	−	0.983638i	$-0.442339\pi$
$409$	7.28698	0.360318	0.180159	+	0.983638i	$0.442339\pi$
$410$	0.281043	0.0138797
$411$	−5.55075	−0.273798
$412$	1.93513	0.0953372
$413$	16.2163	0.797953
$414$	0.334800	0.0164545
$415$	−7.68575	−0.377279
$416$	−2.92515	−0.143417
$417$	−8.74256	−0.428125
$418$	2.79214	0.136568
$419$	31.9297	1.55987	0.779935	−	0.625861i	$-0.215252\pi$
$419$	31.9297	1.55987	0.779935	+	0.625861i	$0.215252\pi$
$420$	−4.66315	−0.227538
$421$	25.2163	1.22897	0.614484	−	0.788929i	$-0.289364\pi$
$421$	25.2163	1.22897	0.614484	+	0.788929i	$0.289364\pi$
$422$	−2.93759	−0.143000
$423$	4.86401	0.236496
$424$	1.28515	0.0624123
$425$	−30.2687	−1.46825
$426$	0.504064	0.0244220
$427$	−34.0659	−1.64856
$428$	18.6539	0.901669
$429$	2.16169	0.104367
$430$	1.11683	0.0538582
$431$	28.1693	1.35687	0.678434	−	0.734661i	$-0.262659\pi$
$431$	28.1693	1.35687	0.678434	+	0.734661i	$0.262659\pi$
$432$	−3.61501	−0.173927
$433$	14.6452	0.703805	0.351903	−	0.936037i	$-0.385535\pi$
$433$	14.6452	0.703805	0.351903	+	0.936037i	$0.385535\pi$
$434$	2.61577	0.125561
$435$	4.37624	0.209825
$436$	−12.5895	−0.602928
$437$	−6.66674	−0.318914
$438$	−2.57055	−0.122826
$439$	−27.9316	−1.33310	−0.666550	−	0.745460i	$-0.732230\pi$
$439$	−27.9316	−1.33310	−0.666550	+	0.745460i	$0.732230\pi$
$440$	1.39615	0.0665591
$441$	6.98268	0.332509
$442$	−1.68147	−0.0799793
$443$	−8.49135	−0.403436	−0.201718	−	0.979444i	$-0.564653\pi$
$443$	−8.49135	−0.403436	−0.201718	+	0.979444i	$0.564653\pi$
$444$	−4.16342	−0.197587
$445$	5.10796	0.242140
$446$	−6.28317	−0.297517
$447$	−10.0949	−0.477470
$448$	−24.2497	−1.14569
$449$	−7.50853	−0.354350	−0.177175	−	0.984179i	$-0.556696\pi$
$449$	−7.50853	−0.354350	−0.177175	+	0.984179i	$0.556696\pi$
$450$	1.16767	0.0550444
$451$	−3.70157	−0.174300
$452$	−27.5598	−1.29630
$453$	−0.629840	−0.0295925
$454$	5.21269	0.244644
$455$	−2.40973	−0.112970
$456$	−5.08279	−0.238023
$457$	38.7505	1.81267	0.906335	−	0.422560i	$-0.138868\pi$
$457$	38.7505	1.81267	0.906335	+	0.422560i	$0.138868\pi$
$458$	−0.516500	−0.0241345
$459$	−6.60210	−0.308159
$460$	−1.63932	−0.0764335
$461$	13.1493	0.612425	0.306213	−	0.951963i	$-0.400938\pi$
$461$	13.1493	0.612425	0.306213	+	0.951963i	$0.400938\pi$
$462$	−2.05871	−0.0957801
$463$	8.91855	0.414480	0.207240	−	0.978290i	$-0.433552\pi$
$463$	8.91855	0.414480	0.207240	+	0.978290i	$0.433552\pi$
$464$	24.5492	1.13967
$465$	−1.76999	−0.0820813
$466$	1.10016	0.0509637
$467$	−29.5599	−1.36787	−0.683935	−	0.729543i	$-0.739733\pi$
$467$	−29.5599	−1.36787	−0.683935	+	0.729543i	$0.739733\pi$
$468$	−1.93513	−0.0894516
$469$	−37.7652	−1.74383
$470$	0.798315	0.0368235
$471$	−2.57454	−0.118628
$472$	4.34634	0.200056
$473$	−14.7096	−0.676346
$474$	−3.00377	−0.137968
$475$	−23.2513	−1.06684
$476$	−47.7736	−2.18970
$477$	1.28229	0.0587120
$478$	1.11776	0.0511254
$479$	20.6892	0.945316	0.472658	−	0.881246i	$-0.343295\pi$
$479$	20.6892	0.945316	0.472658	+	0.881246i	$0.343295\pi$
$480$	−1.88505	−0.0860402
$481$	−2.15149	−0.0980994
$482$	−4.70358	−0.214242
$483$	4.91556	0.223666
$484$	12.2438	0.556535
$485$	−8.98931	−0.408184
$486$	0.254687	0.0115528
$487$	−30.5248	−1.38321	−0.691605	−	0.722276i	$-0.743096\pi$
$487$	−30.5248	−1.38321	−0.691605	+	0.722276i	$0.743096\pi$
$488$	−9.13043	−0.413315
$489$	8.11253	0.366861
$490$	1.14605	0.0517731
$491$	−40.7131	−1.83735	−0.918677	−	0.395009i	$-0.870742\pi$
$491$	−40.7131	−1.83735	−0.918677	+	0.395009i	$0.870742\pi$
$492$	3.31362	0.149390
$493$	44.8343	2.01923
$494$	−1.29164	−0.0581138
$495$	1.39305	0.0626130
$496$	−9.92905	−0.445827
$497$	7.40072	0.331968
$498$	3.03753	0.136115
$499$	−17.9990	−0.805746	−0.402873	−	0.915256i	$-0.631988\pi$
$499$	−17.9990	−0.805746	−0.402873	+	0.915256i	$0.631988\pi$
$500$	−11.9526	−0.534538
$501$	−14.8223	−0.662209
$502$	2.87069	0.128125
$503$	−8.49851	−0.378930	−0.189465	−	0.981887i	$-0.560675\pi$
$503$	−8.49851	−0.378930	−0.189465	+	0.981887i	$0.560675\pi$
$504$	3.74767	0.166935
$505$	2.91927	0.129906
$506$	−0.723734	−0.0321739
$507$	−1.00000	−0.0444116
$508$	10.8366	0.480797
$509$	−19.6135	−0.869351	−0.434676	−	0.900587i	$-0.643137\pi$
$509$	−19.6135	−0.869351	−0.434676	+	0.900587i	$0.643137\pi$
$510$	−1.08358	−0.0479819
$511$	−37.7411	−1.66957
$512$	−17.8206	−0.787567
$513$	−5.07149	−0.223912
$514$	−3.65647	−0.161280
$515$	0.644426	0.0283968
$516$	13.1679	0.579685
$517$	−10.5145	−0.462427
$518$	2.04900	0.0900277
$519$	5.58518	0.245162
$520$	−0.645862	−0.0283229
$521$	39.6357	1.73647	0.868237	−	0.496150i	$-0.165253\pi$
$521$	39.6357	1.73647	0.868237	+	0.496150i	$0.165253\pi$
$522$	−1.72956	−0.0757007
$523$	−26.5714	−1.16189	−0.580943	−	0.813945i	$-0.697316\pi$
$523$	−26.5714	−1.16189	−0.580943	+	0.813945i	$0.697316\pi$
$524$	−19.4244	−0.848559
$525$	17.1438	0.748218
$526$	−4.82379	−0.210327
$527$	−18.1334	−0.789904
$528$	7.81455	0.340084
$529$	−21.2719	−0.924867
$530$	0.210459	0.00914174
$531$	4.33667	0.188196
$532$	−36.6980	−1.59106
$533$	1.71235	0.0741700
$534$	−2.01874	−0.0873596
$535$	6.21199	0.268568
$536$	−10.1219	−0.437200
$537$	6.51826	0.281284
$538$	−6.73315	−0.290287
$539$	−15.0944	−0.650162
$540$	−1.24705	−0.0536645
$541$	0.912594	0.0392355	0.0196177	−	0.999808i	$-0.493755\pi$
$541$	0.912594	0.0392355	0.0196177	+	0.999808i	$0.493755\pi$
$542$	3.98783	0.171292
$543$	−5.43008	−0.233027
$544$	−19.3122	−0.828002
$545$	−4.19248	−0.179586
$546$	0.952363	0.0407574
$547$	−12.8909	−0.551173	−0.275586	−	0.961276i	$-0.588872\pi$
$547$	−12.8909	−0.551173	−0.275586	+	0.961276i	$0.588872\pi$
$548$	−10.7414	−0.458852
$549$	−9.11013	−0.388811
$550$	−2.52414	−0.107630
$551$	34.4400	1.46719
$552$	1.31748	0.0560758
$553$	−44.1017	−1.87540
$554$	−0.0111726	−0.000474678 0
$555$	−1.38647	−0.0588526
$556$	−16.9180	−0.717484
$557$	−34.7494	−1.47238	−0.736189	−	0.676776i	$-0.763377\pi$
$557$	−34.7494	−1.47238	−0.736189	+	0.676776i	$0.763377\pi$
$558$	0.699527	0.0296133
$559$	6.80465	0.287806
$560$	−8.71121	−0.368116
$561$	14.2717	0.602552
$562$	2.25417	0.0950865
$563$	1.06371	0.0448300	0.0224150	−	0.999749i	$-0.492864\pi$
$563$	1.06371	0.0448300	0.0224150	+	0.999749i	$0.492864\pi$
$564$	9.41251	0.396338
$565$	−9.17778	−0.386112
$566$	0.186402	0.00783504
$567$	3.73934	0.157038
$568$	1.98356	0.0832283
$569$	−2.43593	−0.102119	−0.0510597	−	0.998696i	$-0.516260\pi$
$569$	−2.43593	−0.102119	−0.0510597	+	0.998696i	$0.516260\pi$
$570$	−0.832369	−0.0348641
$571$	−6.01254	−0.251617	−0.125809	−	0.992055i	$-0.540152\pi$
$571$	−6.01254	−0.251617	−0.125809	+	0.992055i	$0.540152\pi$
$572$	4.18316	0.174907
$573$	−18.9436	−0.791379
$574$	−1.63078	−0.0680673
$575$	6.02685	0.251337
$576$	−6.48503	−0.270210
$577$	−9.32838	−0.388345	−0.194173	−	0.980967i	$-0.562202\pi$
$577$	−9.32838	−0.388345	−0.194173	+	0.980967i	$0.562202\pi$
$578$	−6.77154	−0.281659
$579$	−3.56540	−0.148173
$580$	8.46861	0.351640
$581$	44.5973	1.85021
$582$	3.55271	0.147265
$583$	−2.77192	−0.114801
$584$	−10.1155	−0.418581
$585$	−0.644426	−0.0266437
$586$	4.43355	0.183148
$587$	8.00992	0.330605	0.165302	−	0.986243i	$-0.447140\pi$
$587$	8.00992	0.330605	0.165302	+	0.986243i	$0.447140\pi$
$588$	13.5124	0.557243
$589$	−13.9294	−0.573952
$590$	0.711766	0.0293029
$591$	10.2323	0.420902
$592$	−7.77766	−0.319660
$593$	30.2498	1.24221	0.621106	−	0.783727i	$-0.286684\pi$
$593$	30.2498	1.24221	0.621106	+	0.783727i	$0.286684\pi$
$594$	−0.550555	−0.0225896
$595$	−15.9093	−0.652217
$596$	−19.5349	−0.800181
$597$	−24.0522	−0.984392
$598$	0.334800	0.0136910
$599$	19.8497	0.811037	0.405519	−	0.914087i	$-0.367091\pi$
$599$	19.8497	0.811037	0.405519	+	0.914087i	$0.367091\pi$
$600$	4.59493	0.187587
$601$	41.7106	1.70141	0.850705	−	0.525643i	$-0.176175\pi$
$601$	41.7106	1.70141	0.850705	+	0.525643i	$0.176175\pi$
$602$	−6.48049	−0.264125
$603$	−10.0994	−0.411280
$604$	−1.21883	−0.0495933
$605$	4.07734	0.165767
$606$	−1.15374	−0.0468675
$607$	−43.3222	−1.75839	−0.879196	−	0.476460i	$-0.841920\pi$
$607$	−43.3222	−1.75839	−0.879196	+	0.476460i	$0.841920\pi$
$608$	−14.8349	−0.601634
$609$	−25.3935	−1.02900
$610$	−1.49522	−0.0605397
$611$	4.86401	0.196777
$612$	−12.7759	−0.516437
$613$	0.808238	0.0326444	0.0163222	−	0.999867i	$-0.494804\pi$
$613$	0.808238	0.0326444	0.0163222	+	0.999867i	$0.494804\pi$
$614$	−1.63531	−0.0659957
$615$	1.10348	0.0444967
$616$	−8.10132	−0.326411
$617$	−41.6766	−1.67784	−0.838918	−	0.544257i	$-0.816812\pi$
$617$	−41.6766	−1.67784	−0.838918	+	0.544257i	$0.816812\pi$
$618$	−0.254687	−0.0102450
$619$	43.6835	1.75579	0.877894	−	0.478855i	$-0.158948\pi$
$619$	43.6835	1.75579	0.877894	+	0.478855i	$0.158948\pi$
$620$	−3.42517	−0.137558
$621$	1.31455	0.0527512
$622$	−5.55888	−0.222891
$623$	−29.6394	−1.18748
$624$	−3.61501	−0.144716
$625$	18.9432	0.757727
$626$	6.87607	0.274823
$627$	10.9630	0.437820
$628$	−4.98208	−0.198807
$629$	−14.2043	−0.566364
$630$	0.613727	0.0244515
$631$	4.26254	0.169689	0.0848446	−	0.996394i	$-0.472961\pi$
$631$	4.26254	0.169689	0.0848446	+	0.996394i	$0.472961\pi$
$632$	−11.8203	−0.470185
$633$	−11.5341	−0.458440
$634$	7.52901	0.299015
$635$	3.60874	0.143208
$636$	2.48140	0.0983941
$637$	6.98268	0.276664
$638$	3.73877	0.148019
$639$	1.97915	0.0782939
$640$	−4.83446	−0.191099
$641$	30.2657	1.19542	0.597712	−	0.801711i	$-0.296077\pi$
$641$	30.2657	1.19542	0.597712	+	0.801711i	$0.296077\pi$
$642$	−2.45508	−0.0968941
$643$	19.5187	0.769741	0.384871	−	0.922970i	$-0.374246\pi$
$643$	19.5187	0.769741	0.384871	+	0.922970i	$0.374246\pi$
$644$	9.51228	0.374836
$645$	4.38509	0.172663
$646$	−8.52755	−0.335512
$647$	13.9595	0.548803	0.274402	−	0.961615i	$-0.411520\pi$
$647$	13.9595	0.548803	0.274402	+	0.961615i	$0.411520\pi$
$648$	1.00223	0.0393712
$649$	−9.37455	−0.367983
$650$	1.16767	0.0457997
$651$	10.2705	0.402534
$652$	15.6988	0.614814
$653$	28.5723	1.11812	0.559060	−	0.829127i	$-0.311162\pi$
$653$	28.5723	1.11812	0.559060	+	0.829127i	$0.311162\pi$
$654$	1.65693	0.0647912
$655$	−6.46859	−0.252749
$656$	6.19016	0.241685
$657$	−10.0930	−0.393764
$658$	−4.63230	−0.180586
$659$	37.5112	1.46123	0.730615	−	0.682790i	$-0.239234\pi$
$659$	37.5112	1.46123	0.730615	+	0.682790i	$0.239234\pi$
$660$	2.69574	0.104932
$661$	−33.2455	−1.29310	−0.646549	−	0.762872i	$-0.723789\pi$
$661$	−33.2455	−1.29310	−0.646549	+	0.762872i	$0.723789\pi$
$662$	−0.902244	−0.0350667
$663$	−6.60210	−0.256404
$664$	11.9531	0.463869
$665$	−12.2209	−0.473907
$666$	0.547956	0.0212329
$667$	−8.92701	−0.345655
$668$	−28.6831	−1.10978
$669$	−24.6702	−0.953803
$670$	−1.65759	−0.0640382
$671$	19.6933	0.760251
$672$	10.9382	0.421948
$673$	28.0118	1.07978	0.539888	−	0.841737i	$-0.318467\pi$
$673$	28.0118	1.07978	0.539888	+	0.841737i	$0.318467\pi$
$674$	4.49409	0.173106
$675$	4.58471	0.176466
$676$	−1.93513	−0.0744282
$677$	35.7561	1.37422	0.687109	−	0.726555i	$-0.258880\pi$
$677$	35.7561	1.37422	0.687109	+	0.726555i	$0.258880\pi$
$678$	3.62720	0.139302
$679$	52.1613	2.00177
$680$	−4.26404	−0.163519
$681$	20.4670	0.784299
$682$	−1.51216	−0.0579037
$683$	−7.99852	−0.306055	−0.153027	−	0.988222i	$-0.548902\pi$
$683$	−7.99852	−0.306055	−0.153027	+	0.988222i	$0.548902\pi$
$684$	−9.81401	−0.375248
$685$	−3.57705	−0.136672
$686$	0.0164934	0.000629720 0
$687$	−2.02798	−0.0773722
$688$	24.5989	0.937824
$689$	1.28229	0.0488514
$690$	0.215754	0.00821361
$691$	−9.17935	−0.349199	−0.174599	−	0.984640i	$-0.555863\pi$
$691$	−9.17935	−0.349199	−0.174599	+	0.984640i	$0.555863\pi$
$692$	10.8081	0.410862
$693$	−8.08331	−0.307059
$694$	−5.58839	−0.212132
$695$	−5.63393	−0.213707
$696$	−6.80604	−0.257982
$697$	11.3051	0.428211
$698$	−3.99051	−0.151043
$699$	4.31964	0.163384
$700$	33.1756	1.25392
$701$	6.22959	0.235288	0.117644	−	0.993056i	$-0.462466\pi$
$701$	6.22959	0.235288	0.117644	+	0.993056i	$0.462466\pi$
$702$	0.254687	0.00961255
$703$	−10.9112	−0.411525
$704$	14.0186	0.528347
$705$	3.13449	0.118052
$706$	−5.90149	−0.222105
$707$	−16.9393	−0.637069
$708$	8.39205	0.315392
$709$	−46.8130	−1.75810	−0.879049	−	0.476731i	$-0.841822\pi$
$709$	−46.8130	−1.75810	−0.879049	+	0.476731i	$0.841822\pi$
$710$	0.324832	0.0121907
$711$	−11.7940	−0.442309
$712$	−7.94403	−0.297715
$713$	3.61057	0.135217
$714$	6.28759	0.235307
$715$	1.39305	0.0520971
$716$	12.6137	0.471396
$717$	4.38877	0.163902
$718$	−6.64620	−0.248034
$719$	−22.9077	−0.854314	−0.427157	−	0.904177i	$-0.640485\pi$
$719$	−22.9077	−0.854314	−0.427157	+	0.904177i	$0.640485\pi$
$720$	−2.32961	−0.0868194
$721$	−3.73934	−0.139260
$722$	−1.71150	−0.0636954
$723$	−18.4681	−0.686835
$724$	−10.5079	−0.390524
$725$	−31.1344	−1.15630
$726$	−1.61143	−0.0598057
$727$	32.6195	1.20979	0.604895	−	0.796305i	$-0.293215\pi$
$727$	32.6195	1.20979	0.604895	+	0.796305i	$0.293215\pi$
$728$	3.74767	0.138898
$729$	1.00000	0.0370370
$730$	−1.65653	−0.0613109
$731$	44.9249	1.66161
$732$	−17.6293	−0.651599
$733$	3.46368	0.127934	0.0639670	−	0.997952i	$-0.479625\pi$
$733$	3.46368	0.127934	0.0639670	+	0.997952i	$0.479625\pi$
$734$	−3.91943	−0.144669
$735$	4.49982	0.165978
$736$	3.84527	0.141739
$737$	21.8318	0.804186
$738$	−0.436113	−0.0160535
$739$	−23.0306	−0.847194	−0.423597	−	0.905851i	$-0.639233\pi$
$739$	−23.0306	−0.847194	−0.423597	+	0.905851i	$0.639233\pi$
$740$	−2.68301	−0.0986296
$741$	−5.07149	−0.186306
$742$	−1.22121	−0.0448319
$743$	41.3720	1.51779	0.758896	−	0.651211i	$-0.225739\pi$
$743$	41.3720	1.51779	0.758896	+	0.651211i	$0.225739\pi$
$744$	2.75273	0.100920
$745$	−6.50539	−0.238339
$746$	3.86976	0.141682
$747$	11.9265	0.436368
$748$	27.6177	1.00980
$749$	−36.0457	−1.31708
$750$	1.57311	0.0574419
$751$	−2.76373	−0.100850	−0.0504250	−	0.998728i	$-0.516058\pi$
$751$	−2.76373	−0.100850	−0.0504250	+	0.998728i	$0.516058\pi$
$752$	17.5835	0.641203
$753$	11.2714	0.410753
$754$	−1.72956	−0.0629868
$755$	−0.405886	−0.0147717
$756$	7.23613	0.263176
$757$	−25.7833	−0.937111	−0.468556	−	0.883434i	$-0.655225\pi$
$757$	−25.7833	−0.937111	−0.468556	+	0.883434i	$0.655225\pi$
$758$	2.76732	0.100514
$759$	−2.84166	−0.103146
$760$	−3.27548	−0.118814
$761$	−22.3274	−0.809367	−0.404683	−	0.914457i	$-0.632618\pi$
$761$	−22.3274	−0.809367	−0.404683	+	0.914457i	$0.632618\pi$
$762$	−1.42623	−0.0516668
$763$	24.3272	0.880705
$764$	−36.6584	−1.32625
$765$	−4.25456	−0.153824
$766$	−1.91948	−0.0693538
$767$	4.33667	0.156588
$768$	−11.0594	−0.399072
$769$	−11.3354	−0.408764	−0.204382	−	0.978891i	$-0.565518\pi$
$769$	−11.3354	−0.408764	−0.204382	+	0.978891i	$0.565518\pi$
$770$	−1.32669	−0.0478106
$771$	−14.3567	−0.517044
$772$	−6.89953	−0.248320
$773$	−31.8718	−1.14635	−0.573174	−	0.819433i	$-0.694288\pi$
$773$	−31.8718	−1.14635	−0.573174	+	0.819433i	$0.694288\pi$
$774$	−1.73306	−0.0622934
$775$	12.5924	0.452334
$776$	13.9804	0.501867
$777$	8.04515	0.288618
$778$	−1.22949	−0.0440794
$779$	8.68416	0.311142
$780$	−1.24705	−0.0446516
$781$	−4.27831	−0.153090
$782$	2.21038	0.0790431
$783$	−6.79091	−0.242687
$784$	25.2425	0.901518
$785$	−1.65910	−0.0592158
$786$	2.55649	0.0911869
$787$	18.3423	0.653833	0.326917	−	0.945053i	$-0.393990\pi$
$787$	18.3423	0.653833	0.326917	+	0.945053i	$0.393990\pi$
$788$	19.8009	0.705379
$789$	−18.9401	−0.674284
$790$	−1.93571	−0.0688695
$791$	53.2549	1.89353
$792$	−2.16651	−0.0769835
$793$	−9.11013	−0.323510
$794$	3.39128	0.120352
$795$	0.826342	0.0293073
$796$	−46.5443	−1.64972
$797$	0.714027	0.0252921	0.0126461	−	0.999920i	$-0.495975\pi$
$797$	0.714027	0.0252921	0.0126461	+	0.999920i	$0.495975\pi$
$798$	4.82990	0.170977
$799$	32.1126	1.13606
$800$	13.4110	0.474150
$801$	−7.92637	−0.280064
$802$	4.32112	0.152584
$803$	21.8179	0.769937
$804$	−19.5437	−0.689254
$805$	3.16772	0.111647
$806$	0.699527	0.0246398
$807$	−26.4369	−0.930625
$808$	−4.54012	−0.159721
$809$	−11.6088	−0.408145	−0.204072	−	0.978956i	$-0.565418\pi$
$809$	−11.6088	−0.408145	−0.204072	+	0.978956i	$0.565418\pi$
$810$	0.164127	0.00576684
$811$	36.2146	1.27167	0.635834	−	0.771826i	$-0.280656\pi$
$811$	36.2146	1.27167	0.635834	+	0.771826i	$0.280656\pi$
$812$	−49.1399	−1.72447
$813$	15.6578	0.549142
$814$	−1.18451	−0.0415171
$815$	5.22792	0.183126
$816$	−23.8667	−0.835501
$817$	34.5097	1.20734
$818$	−1.85590	−0.0648900
$819$	3.73934	0.130663
$820$	2.13539	0.0745709
$821$	−12.7163	−0.443802	−0.221901	−	0.975069i	$-0.571226\pi$
$821$	−12.7163	−0.443802	−0.221901	+	0.975069i	$0.571226\pi$
$822$	1.41370	0.0493086
$823$	−57.3548	−1.99926	−0.999632	−	0.0271267i	$-0.991364\pi$
$823$	−57.3548	−1.99926	−0.999632	+	0.0271267i	$0.991364\pi$
$824$	−1.00223	−0.0349143
$825$	−9.91074	−0.345048
$826$	−4.13009	−0.143704
$827$	−30.0051	−1.04338	−0.521690	−	0.853135i	$-0.674698\pi$
$827$	−30.0051	−1.04338	−0.521690	+	0.853135i	$0.674698\pi$
$828$	2.54384	0.0884045
$829$	−55.1564	−1.91566	−0.957831	−	0.287332i	$-0.907232\pi$
$829$	−55.1564	−1.91566	−0.957831	+	0.287332i	$0.907232\pi$
$830$	1.95746	0.0679445
$831$	−0.0438679	−0.00152176
$832$	−6.48503	−0.224828
$833$	46.1003	1.59728
$834$	2.22662	0.0771015
$835$	−9.55185	−0.330555
$836$	21.2149	0.733732
$837$	2.74661	0.0949368
$838$	−8.13210	−0.280919
$839$	−44.0453	−1.52061	−0.760307	−	0.649564i	$-0.774951\pi$
$839$	−44.0453	−1.52061	−0.760307	+	0.649564i	$0.774951\pi$
$840$	2.41510	0.0833289
$841$	17.1165	0.590223
$842$	−6.42227	−0.221326
$843$	8.85075	0.304836
$844$	−22.3201	−0.768288
$845$	−0.644426	−0.0221689
$846$	−1.23880	−0.0425908
$847$	−23.6591	−0.812938
$848$	4.63550	0.159184
$849$	0.731884	0.0251182
$850$	7.70906	0.264419
$851$	2.82824	0.0969510
$852$	3.82992	0.131211
$853$	9.63675	0.329956	0.164978	−	0.986297i	$-0.447245\pi$
$853$	9.63675	0.329956	0.164978	+	0.986297i	$0.447245\pi$
$854$	8.67615	0.296892
$855$	−3.26820	−0.111770
$856$	−9.66106	−0.330208
$857$	5.95689	0.203484	0.101742	−	0.994811i	$-0.467558\pi$
$857$	5.95689	0.203484	0.101742	+	0.994811i	$0.467558\pi$
$858$	−0.550555	−0.0187956
$859$	−52.8737	−1.80403	−0.902014	−	0.431707i	$-0.857911\pi$
$859$	−52.8737	−1.80403	−0.902014	+	0.431707i	$0.857911\pi$
$860$	8.48575	0.289362
$861$	−6.40306	−0.218216
$862$	−7.17437	−0.244360
$863$	−18.4493	−0.628022	−0.314011	−	0.949419i	$-0.601673\pi$
$863$	−18.4493	−0.628022	−0.314011	+	0.949419i	$0.601673\pi$
$864$	2.92515	0.0995158
$865$	3.59924	0.122378
$866$	−3.72995	−0.126749
$867$	−26.5877	−0.902965
$868$	19.8749	0.674596
$869$	25.4949	0.864857
$870$	−1.11457	−0.0377875
$871$	−10.0994	−0.342206
$872$	6.52025	0.220804
$873$	13.9493	0.472113
$874$	1.69793	0.0574335
$875$	23.0966	0.780807
$876$	−19.5313	−0.659900
$877$	6.40935	0.216428	0.108214	−	0.994128i	$-0.465487\pi$
$877$	6.40935	0.216428	0.108214	+	0.994128i	$0.465487\pi$
$878$	7.11381	0.240080
$879$	17.4078	0.587151
$880$	5.03590	0.169760
$881$	27.7176	0.933828	0.466914	−	0.884303i	$-0.345366\pi$
$881$	27.7176	0.933828	0.466914	+	0.884303i	$0.345366\pi$
$882$	−1.77840	−0.0598818
$883$	−21.2500	−0.715120	−0.357560	−	0.933890i	$-0.616391\pi$
$883$	−21.2500	−0.715120	−0.357560	+	0.933890i	$0.616391\pi$
$884$	−12.7759	−0.429702
$885$	2.79467	0.0939417
$886$	2.16264	0.0726553
$887$	39.7947	1.33617	0.668087	−	0.744083i	$-0.267113\pi$
$887$	39.7947	1.33617	0.668087	+	0.744083i	$0.267113\pi$
$888$	2.15628	0.0723601
$889$	−20.9400	−0.702306
$890$	−1.30093	−0.0436073
$891$	−2.16169	−0.0724194
$892$	−47.7401	−1.59846
$893$	24.6678	0.825475
$894$	2.57103	0.0859881
$895$	4.20054	0.140408
$896$	28.0524	0.937165
$897$	1.31455	0.0438917
$898$	1.91233	0.0638152
$899$	−18.6520	−0.622079
$900$	8.87204	0.295735
$901$	8.46581	0.282037
$902$	0.942742	0.0313899
$903$	−25.4449	−0.846754
$904$	14.2735	0.474730
$905$	−3.49929	−0.116320
$906$	0.160412	0.00532934
$907$	17.2661	0.573312	0.286656	−	0.958034i	$-0.407456\pi$
$907$	17.2661	0.573312	0.286656	+	0.958034i	$0.407456\pi$
$908$	39.6065	1.31439
$909$	−4.53003	−0.150251
$910$	0.613727	0.0203449
$911$	−29.8074	−0.987564	−0.493782	−	0.869586i	$-0.664386\pi$
$911$	−29.8074	−0.987564	−0.493782	+	0.869586i	$0.664386\pi$
$912$	−18.3335	−0.607083
$913$	−25.7814	−0.853240
$914$	−9.86925	−0.326446
$915$	−5.87081	−0.194083
$916$	−3.92441	−0.129666
$917$	37.5346	1.23950
$918$	1.68147	0.0554968
$919$	−46.2600	−1.52598	−0.762988	−	0.646413i	$-0.776268\pi$
$919$	−46.2600	−1.52598	−0.762988	+	0.646413i	$0.776268\pi$
$920$	0.849020	0.0279914
$921$	−6.42085	−0.211574
$922$	−3.34897	−0.110292
$923$	1.97915	0.0651445
$924$	−15.6423	−0.514593
$925$	9.86396	0.324325
$926$	−2.27144	−0.0746442
$927$	−1.00000	−0.0328443
$928$	−19.8645	−0.652083
$929$	1.34876	0.0442512	0.0221256	−	0.999755i	$-0.492957\pi$
$929$	1.34876	0.0442512	0.0221256	+	0.999755i	$0.492957\pi$
$930$	0.450794	0.0147821
$931$	35.4126	1.16060
$932$	8.35908	0.273811
$933$	−21.8263	−0.714561
$934$	7.52854	0.246341
$935$	9.19706	0.300776
$936$	1.00223	0.0327589
$937$	−13.3982	−0.437702	−0.218851	−	0.975758i	$-0.570231\pi$
$937$	−13.3982	−0.437702	−0.218851	+	0.975758i	$0.570231\pi$
$938$	9.61831	0.314049
$939$	26.9981	0.881050
$940$	6.06567	0.197840
$941$	15.0246	0.489788	0.244894	−	0.969550i	$-0.421247\pi$
$941$	15.0246	0.489788	0.244894	+	0.969550i	$0.421247\pi$
$942$	0.655702	0.0213639
$943$	−2.25097	−0.0733018
$944$	15.6771	0.510247
$945$	2.40973	0.0783885
$946$	3.74633	0.121804
$947$	32.1115	1.04348	0.521741	−	0.853104i	$-0.325283\pi$
$947$	32.1115	1.04348	0.521741	+	0.853104i	$0.325283\pi$
$948$	−22.8229	−0.741254
$949$	−10.0930	−0.327632
$950$	5.92182	0.192129
$951$	29.5618	0.958607
$952$	24.7425	0.801909
$953$	−16.7620	−0.542973	−0.271487	−	0.962442i	$-0.587515\pi$
$953$	−16.7620	−0.542973	−0.271487	+	0.962442i	$0.587515\pi$
$954$	−0.326583	−0.0105735
$955$	−12.2077	−0.395033
$956$	8.49287	0.274679
$957$	14.6799	0.474532
$958$	−5.26929	−0.170243
$959$	20.7562	0.670251
$960$	−4.17912	−0.134881
$961$	−23.4561	−0.756649
$962$	0.547956	0.0176668
$963$	−9.63958	−0.310631
$964$	−35.7382	−1.15105
$965$	−2.29764	−0.0739636
$966$	−1.25193	−0.0402802
$967$	49.6640	1.59709	0.798544	−	0.601937i	$-0.205604\pi$
$967$	49.6640	1.59709	0.798544	+	0.601937i	$0.205604\pi$
$968$	−6.34119	−0.203813
$969$	−33.4825	−1.07561
$970$	2.28946	0.0735102
$971$	−49.0060	−1.57268	−0.786339	−	0.617795i	$-0.788026\pi$
$971$	−49.0060	−1.57268	−0.786339	+	0.617795i	$0.788026\pi$
$972$	1.93513	0.0620695
$973$	32.6914	1.04804
$974$	7.77427	0.249104
$975$	4.58471	0.146828
$976$	−32.9333	−1.05417
$977$	−53.9425	−1.72577	−0.862886	−	0.505398i	$-0.831346\pi$
$977$	−53.9425	−1.72577	−0.862886	+	0.505398i	$0.831346\pi$
$978$	−2.06616	−0.0660684
$979$	17.1344	0.547617
$980$	8.70776	0.278159
$981$	6.50575	0.207713
$982$	10.3691	0.330891
$983$	21.3824	0.681992	0.340996	−	0.940065i	$-0.389236\pi$
$983$	21.3824	0.681992	0.340996	+	0.940065i	$0.389236\pi$
$984$	−1.71616	−0.0547093
$985$	6.59398	0.210102
$986$	−11.4187	−0.363646
$987$	−18.1882	−0.578936
$988$	−9.81401	−0.312225
$989$	−8.94507	−0.284437
$990$	−0.354792	−0.0112760
$991$	50.0625	1.59029	0.795143	−	0.606421i	$-0.207396\pi$
$991$	50.0625	1.59029	0.795143	+	0.606421i	$0.207396\pi$
$992$	8.03427	0.255088
$993$	−3.54256	−0.112420
$994$	−1.88487	−0.0597844
$995$	−15.4999	−0.491380
$996$	23.0794	0.731298
$997$	36.5990	1.15910	0.579552	−	0.814935i	$-0.303228\pi$
$997$	36.5990	1.15910	0.579552	+	0.814935i	$0.303228\pi$
$998$	4.58411	0.145108
$999$	2.15149	0.0680700

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.j.1.11	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.j.1.11	✓	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)

\(f(q)\)	\(=\)	\(q-0.254687 q^{2} -1.00000 q^{3} -1.93513 q^{4} -0.644426 q^{5} +0.254687 q^{6} +3.73934 q^{7} +1.00223 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.254687 q^{2} -1.00000 q^{3} -1.93513 q^{4} -0.644426 q^{5} +0.254687 q^{6} +3.73934 q^{7} +1.00223 q^{8} +1.00000 q^{9} +0.164127 q^{10} -2.16169 q^{11} +1.93513 q^{12} +1.00000 q^{13} -0.952363 q^{14} +0.644426 q^{15} +3.61501 q^{16} +6.60210 q^{17} -0.254687 q^{18} +5.07149 q^{19} +1.24705 q^{20} -3.73934 q^{21} +0.550555 q^{22} -1.31455 q^{23} -1.00223 q^{24} -4.58471 q^{25} -0.254687 q^{26} -1.00000 q^{27} -7.23613 q^{28} +6.79091 q^{29} -0.164127 q^{30} -2.74661 q^{31} -2.92515 q^{32} +2.16169 q^{33} -1.68147 q^{34} -2.40973 q^{35} -1.93513 q^{36} -2.15149 q^{37} -1.29164 q^{38} -1.00000 q^{39} -0.645862 q^{40} +1.71235 q^{41} +0.952363 q^{42} +6.80465 q^{43} +4.18316 q^{44} -0.644426 q^{45} +0.334800 q^{46} +4.86401 q^{47} -3.61501 q^{48} +6.98268 q^{49} +1.16767 q^{50} -6.60210 q^{51} -1.93513 q^{52} +1.28229 q^{53} +0.254687 q^{54} +1.39305 q^{55} +3.74767 q^{56} -5.07149 q^{57} -1.72956 q^{58} +4.33667 q^{59} -1.24705 q^{60} -9.11013 q^{61} +0.699527 q^{62} +3.73934 q^{63} -6.48503 q^{64} -0.644426 q^{65} -0.550555 q^{66} -10.0994 q^{67} -12.7759 q^{68} +1.31455 q^{69} +0.613727 q^{70} +1.97915 q^{71} +1.00223 q^{72} -10.0930 q^{73} +0.547956 q^{74} +4.58471 q^{75} -9.81401 q^{76} -8.08331 q^{77} +0.254687 q^{78} -11.7940 q^{79} -2.32961 q^{80} +1.00000 q^{81} -0.436113 q^{82} +11.9265 q^{83} +7.23613 q^{84} -4.25456 q^{85} -1.73306 q^{86} -6.79091 q^{87} -2.16651 q^{88} -7.92637 q^{89} +0.164127 q^{90} +3.73934 q^{91} +2.54384 q^{92} +2.74661 q^{93} -1.23880 q^{94} -3.26820 q^{95} +2.92515 q^{96} +13.9493 q^{97} -1.77840 q^{98} -2.16169 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 6 q^{2} - 25 q^{3} + 28 q^{4} + 7 q^{5} - 6 q^{6} + 17 q^{7} + 21 q^{8} + 25 q^{9}+O(q^{10}) \) 25 * q + 6 * q^2 - 25 * q^3 + 28 * q^4 + 7 * q^5 - 6 * q^6 + 17 * q^7 + 21 * q^8 + 25 * q^9	\( 25 q + 6 q^{2} - 25 q^{3} + 28 q^{4} + 7 q^{5} - 6 q^{6} + 17 q^{7} + 21 q^{8} + 25 q^{9} - 6 q^{10} + 21 q^{11} - 28 q^{12} + 25 q^{13} + 10 q^{14} - 7 q^{15} + 30 q^{16} + 14 q^{17} + 6 q^{18} + 12 q^{19} + 24 q^{20} - 17 q^{21} + 3 q^{22} + 41 q^{23} - 21 q^{24} + 30 q^{25} + 6 q^{26} - 25 q^{27} + 14 q^{28} + 22 q^{29} + 6 q^{30} + 14 q^{31} + 28 q^{32} - 21 q^{33} - 11 q^{34} + 14 q^{35} + 28 q^{36} - 6 q^{37} + 16 q^{38} - 25 q^{39} - 34 q^{40} + 33 q^{41} - 10 q^{42} + 35 q^{43} + 45 q^{44} + 7 q^{45} + 3 q^{46} + 48 q^{47} - 30 q^{48} - 4 q^{49} + 7 q^{50} - 14 q^{51} + 28 q^{52} + 18 q^{53} - 6 q^{54} + 10 q^{55} + 32 q^{56} - 12 q^{57} + 33 q^{58} + 46 q^{59} - 24 q^{60} - 19 q^{61} + 5 q^{62} + 17 q^{63} + 29 q^{64} + 7 q^{65} - 3 q^{66} + 16 q^{67} + 20 q^{68} - 41 q^{69} - 43 q^{70} + 60 q^{71} + 21 q^{72} - 14 q^{73} - 50 q^{74} - 30 q^{75} + 59 q^{77} - 6 q^{78} + 7 q^{79} + 32 q^{80} + 25 q^{81} + 18 q^{82} + 23 q^{83} - 14 q^{84} - 9 q^{85} - 9 q^{86} - 22 q^{87} + 23 q^{88} + 10 q^{89} - 6 q^{90} + 17 q^{91} + 69 q^{92} - 14 q^{93} - 30 q^{94} + 81 q^{95} - 28 q^{96} - 10 q^{97} + 55 q^{98} + 21 q^{99}+O(q^{100}) \) 25 * q + 6 * q^2 - 25 * q^3 + 28 * q^4 + 7 * q^5 - 6 * q^6 + 17 * q^7 + 21 * q^8 + 25 * q^9 - 6 * q^10 + 21 * q^11 - 28 * q^12 + 25 * q^13 + 10 * q^14 - 7 * q^15 + 30 * q^16 + 14 * q^17 + 6 * q^18 + 12 * q^19 + 24 * q^20 - 17 * q^21 + 3 * q^22 + 41 * q^23 - 21 * q^24 + 30 * q^25 + 6 * q^26 - 25 * q^27 + 14 * q^28 + 22 * q^29 + 6 * q^30 + 14 * q^31 + 28 * q^32 - 21 * q^33 - 11 * q^34 + 14 * q^35 + 28 * q^36 - 6 * q^37 + 16 * q^38 - 25 * q^39 - 34 * q^40 + 33 * q^41 - 10 * q^42 + 35 * q^43 + 45 * q^44 + 7 * q^45 + 3 * q^46 + 48 * q^47 - 30 * q^48 - 4 * q^49 + 7 * q^50 - 14 * q^51 + 28 * q^52 + 18 * q^53 - 6 * q^54 + 10 * q^55 + 32 * q^56 - 12 * q^57 + 33 * q^58 + 46 * q^59 - 24 * q^60 - 19 * q^61 + 5 * q^62 + 17 * q^63 + 29 * q^64 + 7 * q^65 - 3 * q^66 + 16 * q^67 + 20 * q^68 - 41 * q^69 - 43 * q^70 + 60 * q^71 + 21 * q^72 - 14 * q^73 - 50 * q^74 - 30 * q^75 + 59 * q^77 - 6 * q^78 + 7 * q^79 + 32 * q^80 + 25 * q^81 + 18 * q^82 + 23 * q^83 - 14 * q^84 - 9 * q^85 - 9 * q^86 - 22 * q^87 + 23 * q^88 + 10 * q^89 - 6 * q^90 + 17 * q^91 + 69 * q^92 - 14 * q^93 - 30 * q^94 + 81 * q^95 - 28 * q^96 - 10 * q^97 + 55 * q^98 + 21 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more