LMFDB - Embedded newform 6011.2.a.f.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6011,2,Mod(1,6011)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6011, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6011.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6011.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$47.9980766550$
Analytic rank:	$0$
Dimension:	$275$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	6011.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.53734 q^{2} +2.44850 q^{3} +4.43808 q^{4} +2.44812 q^{5} -6.21267 q^{6} +1.86592 q^{7} -6.18624 q^{8} +2.99515 q^{9} +O(q^{10})$	\(q-2.53734 q^{2} +2.44850 q^{3} +4.43808 q^{4} +2.44812 q^{5} -6.21267 q^{6} +1.86592 q^{7} -6.18624 q^{8} +2.99515 q^{9} -6.21172 q^{10} -1.64340 q^{11} +10.8666 q^{12} +5.14189 q^{13} -4.73447 q^{14} +5.99423 q^{15} +6.82041 q^{16} -5.01069 q^{17} -7.59970 q^{18} +2.38124 q^{19} +10.8650 q^{20} +4.56871 q^{21} +4.16987 q^{22} +8.88276 q^{23} -15.1470 q^{24} +0.993312 q^{25} -13.0467 q^{26} -0.0118782 q^{27} +8.28111 q^{28} -3.39208 q^{29} -15.2094 q^{30} -3.49817 q^{31} -4.93321 q^{32} -4.02387 q^{33} +12.7138 q^{34} +4.56801 q^{35} +13.2927 q^{36} +9.38299 q^{37} -6.04202 q^{38} +12.5899 q^{39} -15.1447 q^{40} -1.07845 q^{41} -11.5923 q^{42} +12.4180 q^{43} -7.29355 q^{44} +7.33250 q^{45} -22.5386 q^{46} -0.175653 q^{47} +16.6998 q^{48} -3.51834 q^{49} -2.52037 q^{50} -12.2687 q^{51} +22.8201 q^{52} +6.26106 q^{53} +0.0301391 q^{54} -4.02325 q^{55} -11.5430 q^{56} +5.83047 q^{57} +8.60685 q^{58} -2.94664 q^{59} +26.6029 q^{60} +7.69816 q^{61} +8.87603 q^{62} +5.58871 q^{63} -1.12360 q^{64} +12.5880 q^{65} +10.2099 q^{66} +0.641793 q^{67} -22.2379 q^{68} +21.7494 q^{69} -11.5906 q^{70} -13.9373 q^{71} -18.5287 q^{72} +8.67821 q^{73} -23.8078 q^{74} +2.43212 q^{75} +10.5682 q^{76} -3.06646 q^{77} -31.9449 q^{78} -12.8356 q^{79} +16.6972 q^{80} -9.01453 q^{81} +2.73639 q^{82} -3.81393 q^{83} +20.2763 q^{84} -12.2668 q^{85} -31.5086 q^{86} -8.30550 q^{87} +10.1665 q^{88} -0.743886 q^{89} -18.6050 q^{90} +9.59436 q^{91} +39.4224 q^{92} -8.56526 q^{93} +0.445690 q^{94} +5.82958 q^{95} -12.0790 q^{96} -3.79350 q^{97} +8.92722 q^{98} -4.92223 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 275 q + 16 q^{2} + 9 q^{3} + 316 q^{4} + 36 q^{5} + 30 q^{6} + 41 q^{7} + 36 q^{8} + 322 q^{9}+O(q^{10}) $ 275 * q + 16 * q^2 + 9 * q^3 + 316 * q^4 + 36 * q^5 + 30 * q^6 + 41 * q^7 + 36 * q^8 + 322 * q^9	\( 275 q + 16 q^{2} + 9 q^{3} + 316 q^{4} + 36 q^{5} + 30 q^{6} + 41 q^{7} + 36 q^{8} + 322 q^{9} + 44 q^{10} + 42 q^{11} + 26 q^{12} + 97 q^{13} + 24 q^{14} + 46 q^{15} + 386 q^{16} + 35 q^{17} + 47 q^{18} + 101 q^{19} + 60 q^{20} + 187 q^{21} + 72 q^{22} + 35 q^{23} + 73 q^{24} + 373 q^{25} + 21 q^{26} + 27 q^{27} + 97 q^{28} + 162 q^{29} + 13 q^{30} + 113 q^{31} + 58 q^{32} + 16 q^{33} + 52 q^{34} + 23 q^{35} + 426 q^{36} + 257 q^{37} + 8 q^{38} + 87 q^{39} + 126 q^{40} + 77 q^{41} - 7 q^{42} + 107 q^{43} + 133 q^{44} + 140 q^{45} + 207 q^{46} + 24 q^{47} + 4 q^{48} + 418 q^{49} + 65 q^{50} + 94 q^{51} + 142 q^{52} + 81 q^{53} + 79 q^{54} + 26 q^{55} + 62 q^{56} + 112 q^{57} + 44 q^{58} + 30 q^{59} + 83 q^{60} + 347 q^{61} + 5 q^{62} + 97 q^{63} + 508 q^{64} + 94 q^{65} + 4 q^{66} + 98 q^{67} + 28 q^{68} + 91 q^{69} + 17 q^{70} + 58 q^{71} + 99 q^{72} + 157 q^{73} + 80 q^{74} + 83 q^{75} + 264 q^{76} + 61 q^{77} + 5 q^{78} + 282 q^{79} + 49 q^{80} + 403 q^{81} + 46 q^{82} + 43 q^{83} + 318 q^{84} + 396 q^{85} + 57 q^{86} + 31 q^{87} + 180 q^{88} + 98 q^{89} + 67 q^{90} + 195 q^{91} + 97 q^{92} + 83 q^{93} + 96 q^{94} + 28 q^{95} + 127 q^{96} + 167 q^{97} + 24 q^{98} + 133 q^{99}+O(q^{100}) \) 275 * q + 16 * q^2 + 9 * q^3 + 316 * q^4 + 36 * q^5 + 30 * q^6 + 41 * q^7 + 36 * q^8 + 322 * q^9 + 44 * q^10 + 42 * q^11 + 26 * q^12 + 97 * q^13 + 24 * q^14 + 46 * q^15 + 386 * q^16 + 35 * q^17 + 47 * q^18 + 101 * q^19 + 60 * q^20 + 187 * q^21 + 72 * q^22 + 35 * q^23 + 73 * q^24 + 373 * q^25 + 21 * q^26 + 27 * q^27 + 97 * q^28 + 162 * q^29 + 13 * q^30 + 113 * q^31 + 58 * q^32 + 16 * q^33 + 52 * q^34 + 23 * q^35 + 426 * q^36 + 257 * q^37 + 8 * q^38 + 87 * q^39 + 126 * q^40 + 77 * q^41 - 7 * q^42 + 107 * q^43 + 133 * q^44 + 140 * q^45 + 207 * q^46 + 24 * q^47 + 4 * q^48 + 418 * q^49 + 65 * q^50 + 94 * q^51 + 142 * q^52 + 81 * q^53 + 79 * q^54 + 26 * q^55 + 62 * q^56 + 112 * q^57 + 44 * q^58 + 30 * q^59 + 83 * q^60 + 347 * q^61 + 5 * q^62 + 97 * q^63 + 508 * q^64 + 94 * q^65 + 4 * q^66 + 98 * q^67 + 28 * q^68 + 91 * q^69 + 17 * q^70 + 58 * q^71 + 99 * q^72 + 157 * q^73 + 80 * q^74 + 83 * q^75 + 264 * q^76 + 61 * q^77 + 5 * q^78 + 282 * q^79 + 49 * q^80 + 403 * q^81 + 46 * q^82 + 43 * q^83 + 318 * q^84 + 396 * q^85 + 57 * q^86 + 31 * q^87 + 180 * q^88 + 98 * q^89 + 67 * q^90 + 195 * q^91 + 97 * q^92 + 83 * q^93 + 96 * q^94 + 28 * q^95 + 127 * q^96 + 167 * q^97 + 24 * q^98 + 133 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.53734	−1.79417	−0.897084	−	0.441859i	$-0.854319\pi$
$2$	−2.53734	−1.79417	−0.897084	+	0.441859i	$0.854319\pi$
$3$	2.44850	1.41364	0.706821	−	0.707393i	$-0.250129\pi$
$3$	2.44850	1.41364	0.706821	+	0.707393i	$0.250129\pi$
$4$	4.43808	2.21904
$5$	2.44812	1.09483	0.547417	−	0.836860i	$-0.315611\pi$
$5$	2.44812	1.09483	0.547417	+	0.836860i	$0.315611\pi$
$6$	−6.21267	−2.53631
$7$	1.86592	0.705252	0.352626	−	0.935764i	$-0.385289\pi$
$7$	1.86592	0.705252	0.352626	+	0.935764i	$0.385289\pi$
$8$	−6.18624	−2.18717
$9$	2.99515	0.998383
$10$	−6.21172	−1.96432
$11$	−1.64340	−0.495504	−0.247752	−	0.968823i	$-0.579692\pi$
$11$	−1.64340	−0.495504	−0.247752	+	0.968823i	$0.579692\pi$
$12$	10.8666	3.13693
$13$	5.14189	1.42610	0.713052	−	0.701111i	$-0.247312\pi$
$13$	5.14189	1.42610	0.713052	+	0.701111i	$0.247312\pi$
$14$	−4.73447	−1.26534
$15$	5.99423	1.54770
$16$	6.82041	1.70510
$17$	−5.01069	−1.21527	−0.607636	−	0.794216i	$-0.707882\pi$
$17$	−5.01069	−1.21527	−0.607636	+	0.794216i	$0.707882\pi$
$18$	−7.59970	−1.79127
$19$	2.38124	0.546295	0.273147	−	0.961972i	$-0.411935\pi$
$19$	2.38124	0.546295	0.273147	+	0.961972i	$0.411935\pi$
$20$	10.8650	2.42948
$21$	4.56871	0.996973
$22$	4.16987	0.889018
$23$	8.88276	1.85218	0.926091	−	0.377299i	$-0.123147\pi$
$23$	8.88276	1.85218	0.926091	+	0.377299i	$0.123147\pi$
$24$	−15.1470	−3.09187
$25$	0.993312	0.198662
$26$	−13.0467	−2.55867
$27$	−0.0118782	−0.00228597
$28$	8.28111	1.56498
$29$	−3.39208	−0.629893	−0.314947	−	0.949109i	$-0.601987\pi$
$29$	−3.39208	−0.629893	−0.314947	+	0.949109i	$0.601987\pi$
$30$	−15.2094	−2.77684
$31$	−3.49817	−0.628289	−0.314145	−	0.949375i	$-0.601718\pi$
$31$	−3.49817	−0.628289	−0.314145	+	0.949375i	$0.601718\pi$
$32$	−4.93321	−0.872077
$33$	−4.02387	−0.700466
$34$	12.7138	2.18040
$35$	4.56801	0.772134
$36$	13.2927	2.21545
$37$	9.38299	1.54255	0.771277	−	0.636499i	$-0.219618\pi$
$37$	9.38299	1.54255	0.771277	+	0.636499i	$0.219618\pi$
$38$	−6.04202	−0.980145
$39$	12.5899	2.01600
$40$	−15.1447	−2.39458
$41$	−1.07845	−0.168426	−0.0842129	−	0.996448i	$-0.526838\pi$
$41$	−1.07845	−0.168426	−0.0842129	+	0.996448i	$0.526838\pi$
$42$	−11.5923	−1.78874
$43$	12.4180	1.89372	0.946861	−	0.321644i	$-0.104235\pi$
$43$	12.4180	1.89372	0.946861	+	0.321644i	$0.104235\pi$
$44$	−7.29355	−1.09954
$45$	7.33250	1.09306
$46$	−22.5386	−3.32313
$47$	−0.175653	−0.0256216	−0.0128108	−	0.999918i	$-0.504078\pi$
$47$	−0.175653	−0.0256216	−0.0128108	+	0.999918i	$0.504078\pi$
$48$	16.6998	2.41040
$49$	−3.51834	−0.502620
$50$	−2.52037	−0.356434
$51$	−12.2687	−1.71796
$52$	22.8201	3.16458
$53$	6.26106	0.860023	0.430011	−	0.902824i	$-0.358510\pi$
$53$	6.26106	0.860023	0.430011	+	0.902824i	$0.358510\pi$
$54$	0.0301391	0.00410142
$55$	−4.02325	−0.542495
$56$	−11.5430	−1.54250
$57$	5.83047	0.772265
$58$	8.60685	1.13013
$59$	−2.94664	−0.383620	−0.191810	−	0.981432i	$-0.561436\pi$
$59$	−2.94664	−0.383620	−0.191810	+	0.981432i	$0.561436\pi$
$60$	26.6029	3.43442
$61$	7.69816	0.985648	0.492824	−	0.870129i	$-0.335965\pi$
$61$	7.69816	0.985648	0.492824	+	0.870129i	$0.335965\pi$
$62$	8.87603	1.12726
$63$	5.58871	0.704111
$64$	−1.12360	−0.140450
$65$	12.5880	1.56135
$66$	10.2099	1.25675
$67$	0.641793	0.0784075	0.0392038	−	0.999231i	$-0.487518\pi$
$67$	0.641793	0.0784075	0.0392038	+	0.999231i	$0.487518\pi$
$68$	−22.2379	−2.69674
$69$	21.7494	2.61832
$70$	−11.5906	−1.38534
$71$	−13.9373	−1.65406	−0.827028	−	0.562161i	$-0.809970\pi$
$71$	−13.9373	−1.65406	−0.827028	+	0.562161i	$0.809970\pi$
$72$	−18.5287	−2.18363
$73$	8.67821	1.01571	0.507854	−	0.861443i	$-0.330439\pi$
$73$	8.67821	1.01571	0.507854	+	0.861443i	$0.330439\pi$
$74$	−23.8078	−2.76760
$75$	2.43212	0.280838
$76$	10.5682	1.21225
$77$	−3.06646	−0.349455
$78$	−31.9449	−3.61704
$79$	−12.8356	−1.44412	−0.722058	−	0.691832i	$-0.756804\pi$
$79$	−12.8356	−1.44412	−0.722058	+	0.691832i	$0.756804\pi$
$80$	16.6972	1.86681
$81$	−9.01453	−1.00161
$82$	2.73639	0.302184
$83$	−3.81393	−0.418634	−0.209317	−	0.977848i	$-0.567124\pi$
$83$	−3.81393	−0.418634	−0.209317	+	0.977848i	$0.567124\pi$
$84$	20.2763	2.21232
$85$	−12.2668	−1.33052
$86$	−31.5086	−3.39766
$87$	−8.30550	−0.890443
$88$	10.1665	1.08375
$89$	−0.743886	−0.0788517	−0.0394259	−	0.999222i	$-0.512553\pi$
$89$	−0.743886	−0.0788517	−0.0394259	+	0.999222i	$0.512553\pi$
$90$	−18.6050	−1.96114
$91$	9.59436	1.00576
$92$	39.4224	4.11007
$93$	−8.56526	−0.888176
$94$	0.445690	0.0459694
$95$	5.82958	0.598102
$96$	−12.0790	−1.23280
$97$	−3.79350	−0.385171	−0.192586	−	0.981280i	$-0.561687\pi$
$97$	−3.79350	−0.385171	−0.192586	+	0.981280i	$0.561687\pi$
$98$	8.92722	0.901785
$99$	−4.92223	−0.494703
$100$	4.40840	0.440840
$101$	8.79046	0.874683	0.437342	−	0.899295i	$-0.355920\pi$
$101$	8.79046	0.874683	0.437342	+	0.899295i	$0.355920\pi$
$102$	31.1298	3.08231
$103$	−8.21654	−0.809600	−0.404800	−	0.914405i	$-0.632659\pi$
$103$	−8.21654	−0.809600	−0.404800	+	0.914405i	$0.632659\pi$
$104$	−31.8090	−3.11913
$105$	11.1848	1.09152
$106$	−15.8864	−1.54303
$107$	12.6624	1.22412	0.612062	−	0.790810i	$-0.290340\pi$
$107$	12.6624	1.22412	0.612062	+	0.790810i	$0.290340\pi$
$108$	−0.0527166	−0.00507266
$109$	9.19930	0.881134	0.440567	−	0.897720i	$-0.354777\pi$
$109$	9.19930	0.881134	0.440567	+	0.897720i	$0.354777\pi$
$110$	10.2083	0.973328
$111$	22.9743	2.18062
$112$	12.7263	1.20253
$113$	−1.10606	−0.104049	−0.0520246	−	0.998646i	$-0.516567\pi$
$113$	−1.10606	−0.104049	−0.0520246	+	0.998646i	$0.516567\pi$
$114$	−14.7939	−1.38557
$115$	21.7461	2.02783
$116$	−15.0543	−1.39776
$117$	15.4007	1.42380
$118$	7.47662	0.688278
$119$	−9.34956	−0.857073
$120$	−37.0817	−3.38508
$121$	−8.29923	−0.754475
$122$	−19.5328	−1.76842
$123$	−2.64059	−0.238094
$124$	−15.5252	−1.39420
$125$	−9.80887	−0.877332
$126$	−14.1804	−1.26329
$127$	6.74464	0.598490	0.299245	−	0.954176i	$-0.403265\pi$
$127$	6.74464	0.598490	0.299245	+	0.954176i	$0.403265\pi$
$128$	12.7174	1.12407
$129$	30.4054	2.67704
$130$	−31.9400	−2.80132
$131$	6.13671	0.536167	0.268083	−	0.963396i	$-0.413610\pi$
$131$	6.13671	0.536167	0.268083	+	0.963396i	$0.413610\pi$
$132$	−17.8583	−1.55436
$133$	4.44321	0.385275
$134$	−1.62845	−0.140676
$135$	−0.0290794	−0.00250276
$136$	30.9973	2.65800
$137$	−4.12846	−0.352718	−0.176359	−	0.984326i	$-0.556432\pi$
$137$	−4.12846	−0.352718	−0.176359	+	0.984326i	$0.556432\pi$
$138$	−55.1856	−4.69771
$139$	−6.21732	−0.527346	−0.263673	−	0.964612i	$-0.584934\pi$
$139$	−6.21732	−0.527346	−0.263673	+	0.964612i	$0.584934\pi$
$140$	20.2732	1.71340
$141$	−0.430086	−0.0362197
$142$	35.3637	2.96765
$143$	−8.45019	−0.706641
$144$	20.4281	1.70235
$145$	−8.30423	−0.689629
$146$	−22.0195	−1.82235
$147$	−8.61465	−0.710525
$148$	41.6425	3.42299
$149$	−1.41121	−0.115611	−0.0578055	−	0.998328i	$-0.518410\pi$
$149$	−1.41121	−0.115611	−0.0578055	+	0.998328i	$0.518410\pi$
$150$	−6.17112	−0.503870
$151$	5.14650	0.418816	0.209408	−	0.977828i	$-0.432846\pi$
$151$	5.14650	0.418816	0.209408	+	0.977828i	$0.432846\pi$
$152$	−14.7309	−1.19484
$153$	−15.0078	−1.21331
$154$	7.78064	0.626982
$155$	−8.56395	−0.687873
$156$	55.8751	4.47359
$157$	13.8879	1.10838	0.554189	−	0.832391i	$-0.313029\pi$
$157$	13.8879	1.10838	0.554189	+	0.832391i	$0.313029\pi$
$158$	32.5682	2.59099
$159$	15.3302	1.21576
$160$	−12.0771	−0.954779
$161$	16.5745	1.30626
$162$	22.8729	1.79707
$163$	0.789939	0.0618728	0.0309364	−	0.999521i	$-0.490151\pi$
$163$	0.789939	0.0618728	0.0309364	+	0.999521i	$0.490151\pi$
$164$	−4.78625	−0.373744
$165$	−9.85093	−0.766894
$166$	9.67724	0.751100
$167$	4.94132	0.382371	0.191185	−	0.981554i	$-0.438767\pi$
$167$	4.94132	0.382371	0.191185	+	0.981554i	$0.438767\pi$
$168$	−28.2631	−2.18055
$169$	13.4391	1.03377
$170$	31.1250	2.38718
$171$	7.13218	0.545411
$172$	55.1119	4.20225
$173$	−13.1538	−1.00007	−0.500033	−	0.866006i	$-0.666679\pi$
$173$	−13.1538	−1.00007	−0.500033	+	0.866006i	$0.666679\pi$
$174$	21.0739	1.59761
$175$	1.85344	0.140107
$176$	−11.2087	−0.844886
$177$	−7.21484	−0.542301
$178$	1.88749	0.141473
$179$	5.17650	0.386910	0.193455	−	0.981109i	$-0.438031\pi$
$179$	5.17650	0.386910	0.193455	+	0.981109i	$0.438031\pi$
$180$	32.5422	2.42555
$181$	12.2794	0.912723	0.456362	−	0.889794i	$-0.349152\pi$
$181$	12.2794	0.912723	0.456362	+	0.889794i	$0.349152\pi$
$182$	−24.3441	−1.80451
$183$	18.8489	1.39335
$184$	−54.9509	−4.05103
$185$	22.9707	1.68884
$186$	21.7330	1.59354
$187$	8.23458	0.602172
$188$	−0.779561	−0.0568554
$189$	−0.0221639	−0.00161218
$190$	−14.7916	−1.07310
$191$	−17.8910	−1.29455	−0.647274	−	0.762258i	$-0.724091\pi$
$191$	−17.8910	−1.29455	−0.647274	+	0.762258i	$0.724091\pi$
$192$	−2.75114	−0.198547
$193$	19.4600	1.40076	0.700381	−	0.713769i	$-0.253013\pi$
$193$	19.4600	1.40076	0.700381	+	0.713769i	$0.253013\pi$
$194$	9.62538	0.691062
$195$	30.8217	2.20719
$196$	−15.6147	−1.11533
$197$	1.60515	0.114362	0.0571812	−	0.998364i	$-0.481789\pi$
$197$	1.60515	0.114362	0.0571812	+	0.998364i	$0.481789\pi$
$198$	12.4894	0.887581
$199$	9.73676	0.690220	0.345110	−	0.938562i	$-0.387842\pi$
$199$	9.73676	0.690220	0.345110	+	0.938562i	$0.387842\pi$
$200$	−6.14487	−0.434508
$201$	1.57143	0.110840
$202$	−22.3044	−1.56933
$203$	−6.32935	−0.444233
$204$	−54.4494	−3.81222
$205$	−2.64018	−0.184398
$206$	20.8481	1.45256
$207$	26.6052	1.84919
$208$	35.0698	2.43165
$209$	−3.91334	−0.270691
$210$	−28.3795	−1.95837
$211$	−8.21926	−0.565837	−0.282918	−	0.959144i	$-0.591303\pi$
$211$	−8.21926	−0.565837	−0.282918	+	0.959144i	$0.591303\pi$
$212$	27.7871	1.90843
$213$	−34.1255	−2.33824
$214$	−32.1289	−2.19629
$215$	30.4007	2.07331
$216$	0.0734817	0.00499980
$217$	−6.52730	−0.443102
$218$	−23.3417	−1.58090
$219$	21.2486	1.43585
$220$	−17.8555	−1.20382
$221$	−25.7644	−1.73310
$222$	−58.2934	−3.91240
$223$	13.2652	0.888306	0.444153	−	0.895951i	$-0.353505\pi$
$223$	13.2652	0.888306	0.444153	+	0.895951i	$0.353505\pi$
$224$	−9.20498	−0.615034
$225$	2.97512	0.198341
$226$	2.80645	0.186682
$227$	21.3225	1.41522	0.707612	−	0.706601i	$-0.249772\pi$
$227$	21.3225	1.41522	0.707612	+	0.706601i	$0.249772\pi$
$228$	25.8761	1.71369
$229$	−18.7150	−1.23672	−0.618361	−	0.785894i	$-0.712203\pi$
$229$	−18.7150	−1.23672	−0.618361	+	0.785894i	$0.712203\pi$
$230$	−55.1772	−3.63828
$231$	−7.50822	−0.494005
$232$	20.9842	1.37768
$233$	12.7215	0.833415	0.416707	−	0.909041i	$-0.363184\pi$
$233$	12.7215	0.833415	0.416707	+	0.909041i	$0.363184\pi$
$234$	−39.0769	−2.55453
$235$	−0.430020	−0.0280514
$236$	−13.0774	−0.851268
$237$	−31.4279	−2.04146
$238$	23.7230	1.53773
$239$	−10.9805	−0.710267	−0.355134	−	0.934816i	$-0.615565\pi$
$239$	−10.9805	−0.710267	−0.355134	+	0.934816i	$0.615565\pi$
$240$	40.8831	2.63899
$241$	8.33659	0.537007	0.268504	−	0.963279i	$-0.413471\pi$
$241$	8.33659	0.537007	0.268504	+	0.963279i	$0.413471\pi$
$242$	21.0579	1.35366
$243$	−22.0364	−1.41364
$244$	34.1651	2.18719
$245$	−8.61333	−0.550286
$246$	6.70006	0.427180
$247$	12.2441	0.779073
$248$	21.6405	1.37417
$249$	−9.33842	−0.591798
$250$	24.8884	1.57408
$251$	−22.3952	−1.41358	−0.706788	−	0.707426i	$-0.749856\pi$
$251$	−22.3952	−1.41358	−0.706788	+	0.707426i	$0.749856\pi$
$252$	24.8032	1.56245
$253$	−14.5979	−0.917765
$254$	−17.1134	−1.07379
$255$	−30.0353	−1.88088
$256$	−30.0211	−1.87632
$257$	6.30167	0.393087	0.196544	−	0.980495i	$-0.437028\pi$
$257$	6.30167	0.393087	0.196544	+	0.980495i	$0.437028\pi$
$258$	−77.1487	−4.80307
$259$	17.5079	1.08789
$260$	55.8665	3.46470
$261$	−10.1598	−0.628875
$262$	−15.5709	−0.961973
$263$	22.2561	1.37237	0.686184	−	0.727428i	$-0.259285\pi$
$263$	22.2561	1.37237	0.686184	+	0.727428i	$0.259285\pi$
$264$	24.8926	1.53203
$265$	15.3278	0.941582
$266$	−11.2739	−0.691249
$267$	−1.82140	−0.111468
$268$	2.84833	0.173989
$269$	8.96859	0.546824	0.273412	−	0.961897i	$-0.411848\pi$
$269$	8.96859	0.546824	0.273412	+	0.961897i	$0.411848\pi$
$270$	0.0737843	0.00449037
$271$	16.7015	1.01454	0.507270	−	0.861787i	$-0.330655\pi$
$271$	16.7015	1.01454	0.507270	+	0.861787i	$0.330655\pi$
$272$	−34.1750	−2.07216
$273$	23.4918	1.42179
$274$	10.4753	0.632836
$275$	−1.63241	−0.0984381
$276$	96.5257	5.81017
$277$	−31.4400	−1.88905	−0.944524	−	0.328442i	$-0.893476\pi$
$277$	−31.4400	−1.88905	−0.944524	+	0.328442i	$0.893476\pi$
$278$	15.7754	0.946148
$279$	−10.4775	−0.627273
$280$	−28.2588	−1.68878
$281$	−11.7491	−0.700890	−0.350445	−	0.936583i	$-0.613970\pi$
$281$	−11.7491	−0.700890	−0.350445	+	0.936583i	$0.613970\pi$
$282$	1.09127	0.0649843
$283$	−0.147897	−0.00879158	−0.00439579	−	0.999990i	$-0.501399\pi$
$283$	−0.147897	−0.00879158	−0.00439579	+	0.999990i	$0.501399\pi$
$284$	−61.8550	−3.67042
$285$	14.2737	0.845503
$286$	21.4410	1.26783
$287$	−2.01230	−0.118783
$288$	−14.7757	−0.870666
$289$	8.10705	0.476886
$290$	21.0706	1.23731
$291$	−9.28837	−0.544494
$292$	38.5146	2.25390
$293$	15.4383	0.901913	0.450957	−	0.892546i	$-0.351083\pi$
$293$	15.4383	0.901913	0.450957	+	0.892546i	$0.351083\pi$
$294$	21.8583	1.27480
$295$	−7.21374	−0.420000
$296$	−58.0454	−3.37382
$297$	0.0195207	0.00113271
$298$	3.58072	0.207426
$299$	45.6742	2.64141
$300$	10.7940	0.623190
$301$	23.1709	1.33555
$302$	−13.0584	−0.751427
$303$	21.5234	1.23649
$304$	16.2411	0.931489
$305$	18.8460	1.07912
$306$	38.0798	2.17688
$307$	12.3023	0.702130	0.351065	−	0.936351i	$-0.385820\pi$
$307$	12.3023	0.702130	0.351065	+	0.936351i	$0.385820\pi$
$308$	−13.6092	−0.775456
$309$	−20.1182	−1.14448
$310$	21.7296	1.23416
$311$	20.1936	1.14508	0.572538	−	0.819878i	$-0.305959\pi$
$311$	20.1936	1.14508	0.572538	+	0.819878i	$0.305959\pi$
$312$	−77.8842	−4.40933
$313$	−18.9864	−1.07318	−0.536588	−	0.843845i	$-0.680287\pi$
$313$	−18.9864	−1.07318	−0.536588	+	0.843845i	$0.680287\pi$
$314$	−35.2384	−1.98862
$315$	13.6819	0.770885
$316$	−56.9654	−3.20455
$317$	−25.7875	−1.44837	−0.724186	−	0.689605i	$-0.757784\pi$
$317$	−25.7875	−1.44837	−0.724186	+	0.689605i	$0.757784\pi$
$318$	−38.8979	−2.18129
$319$	5.57455	0.312115
$320$	−2.75072	−0.153770
$321$	31.0040	1.73047
$322$	−42.0552	−2.34364
$323$	−11.9317	−0.663897
$324$	−40.0072	−2.22262
$325$	5.10750	0.283313
$326$	−2.00434	−0.111010
$327$	22.5245	1.24561
$328$	6.67155	0.368375
$329$	−0.327754	−0.0180697
$330$	24.9951	1.37594
$331$	−0.101026	−0.00555288	−0.00277644	−	0.999996i	$-0.500884\pi$
$331$	−0.101026	−0.00555288	−0.00277644	+	0.999996i	$0.500884\pi$
$332$	−16.9266	−0.928966
$333$	28.1035	1.54006
$334$	−12.5378	−0.686037
$335$	1.57119	0.0858432
$336$	31.1605	1.69994
$337$	−18.3656	−1.00044	−0.500220	−	0.865898i	$-0.666748\pi$
$337$	−18.3656	−1.00044	−0.500220	+	0.865898i	$0.666748\pi$
$338$	−34.0994	−1.85476
$339$	−2.70818	−0.147088
$340$	−54.4411	−2.95248
$341$	5.74889	0.311320
$342$	−18.0968	−0.978560
$343$	−19.6264	−1.05973
$344$	−76.8205	−4.14188
$345$	53.2453	2.86663
$346$	33.3757	1.79429
$347$	−8.21930	−0.441235	−0.220618	−	0.975360i	$-0.570807\pi$
$347$	−8.21930	−0.441235	−0.220618	+	0.975360i	$0.570807\pi$
$348$	−36.8605	−1.97593
$349$	−14.7129	−0.787566	−0.393783	−	0.919203i	$-0.628834\pi$
$349$	−14.7129	−0.787566	−0.393783	+	0.919203i	$0.628834\pi$
$350$	−4.70281	−0.251376
$351$	−0.0610767	−0.00326003
$352$	8.10725	0.432118
$353$	−10.8763	−0.578887	−0.289444	−	0.957195i	$-0.593470\pi$
$353$	−10.8763	−0.578887	−0.289444	+	0.957195i	$0.593470\pi$
$354$	18.3065	0.972979
$355$	−34.1203	−1.81092
$356$	−3.30143	−0.174975
$357$	−22.8924	−1.21159
$358$	−13.1345	−0.694181
$359$	22.4231	1.18344	0.591722	−	0.806142i	$-0.298448\pi$
$359$	22.4231	1.18344	0.591722	+	0.806142i	$0.298448\pi$
$360$	−45.3606	−2.39071
$361$	−13.3297	−0.701562
$362$	−31.1571	−1.63758
$363$	−20.3207	−1.06656
$364$	42.5806	2.23183
$365$	21.2453	1.11203
$366$	−47.8261	−2.49991
$367$	15.2887	0.798065	0.399032	−	0.916937i	$-0.369346\pi$
$367$	15.2887	0.798065	0.399032	+	0.916937i	$0.369346\pi$
$368$	60.5841	3.15816
$369$	−3.23012	−0.168153
$370$	−58.2845	−3.03007
$371$	11.6826	0.606532
$372$	−38.0133	−1.97090
$373$	−34.0254	−1.76177	−0.880883	−	0.473334i	$-0.843050\pi$
$373$	−34.0254	−1.76177	−0.880883	+	0.473334i	$0.843050\pi$
$374$	−20.8939	−1.08040
$375$	−24.0170	−1.24023
$376$	1.08663	0.0560387
$377$	−17.4417	−0.898293
$378$	0.0562372	0.00289253
$379$	8.24815	0.423679	0.211839	−	0.977304i	$-0.432055\pi$
$379$	8.24815	0.423679	0.211839	+	0.977304i	$0.432055\pi$
$380$	25.8722	1.32721
$381$	16.5142	0.846050
$382$	45.3955	2.32264
$383$	−27.0753	−1.38348	−0.691741	−	0.722145i	$-0.743156\pi$
$383$	−27.0753	−1.38348	−0.691741	+	0.722145i	$0.743156\pi$
$384$	31.1385	1.58903
$385$	−7.50707	−0.382596
$386$	−49.3766	−2.51320
$387$	37.1936	1.89066
$388$	−16.8359	−0.854711
$389$	−17.9263	−0.908898	−0.454449	−	0.890773i	$-0.650164\pi$
$389$	−17.9263	−0.908898	−0.454449	+	0.890773i	$0.650164\pi$
$390$	−78.2050	−3.96007
$391$	−44.5088	−2.25091
$392$	21.7653	1.09931
$393$	15.0257	0.757947
$394$	−4.07281	−0.205185
$395$	−31.4231	−1.58107
$396$	−21.8453	−1.09777
$397$	7.77633	0.390283	0.195141	−	0.980775i	$-0.437483\pi$
$397$	7.77633	0.390283	0.195141	+	0.980775i	$0.437483\pi$
$398$	−24.7054	−1.23837
$399$	10.8792	0.544641
$400$	6.77480	0.338740
$401$	5.75722	0.287502	0.143751	−	0.989614i	$-0.454084\pi$
$401$	5.75722	0.287502	0.143751	+	0.989614i	$0.454084\pi$
$402$	−3.98725	−0.198866
$403$	−17.9872	−0.896006
$404$	39.0128	1.94096
$405$	−22.0687	−1.09660
$406$	16.0597	0.797029
$407$	−15.4200	−0.764343
$408$	75.8970	3.75746
$409$	37.2785	1.84330	0.921651	−	0.388021i	$-0.126841\pi$
$409$	37.2785	1.84330	0.921651	+	0.388021i	$0.126841\pi$
$410$	6.69903	0.330842
$411$	−10.1085	−0.498617
$412$	−36.4657	−1.79654
$413$	−5.49819	−0.270548
$414$	−67.5063	−3.31775
$415$	−9.33699	−0.458335
$416$	−25.3660	−1.24367
$417$	−15.2231	−0.745478
$418$	9.92947	0.485666
$419$	18.8139	0.919121	0.459560	−	0.888147i	$-0.348007\pi$
$419$	18.8139	0.919121	0.459560	+	0.888147i	$0.348007\pi$
$420$	49.6389	2.42213
$421$	−23.4481	−1.14279	−0.571396	−	0.820675i	$-0.693598\pi$
$421$	−23.4481	−1.14279	−0.571396	+	0.820675i	$0.693598\pi$
$422$	20.8550	1.01521
$423$	−0.526106	−0.0255802
$424$	−38.7324	−1.88101
$425$	−4.97718	−0.241429
$426$	86.5879	4.19520
$427$	14.3641	0.695130
$428$	56.1969	2.71638
$429$	−20.6903	−0.998937
$430$	−77.1369	−3.71987
$431$	−32.7893	−1.57940	−0.789702	−	0.613491i	$-0.789765\pi$
$431$	−32.7893	−1.57940	−0.789702	+	0.613491i	$0.789765\pi$
$432$	−0.0810145	−0.00389781
$433$	7.60935	0.365682	0.182841	−	0.983143i	$-0.441471\pi$
$433$	7.60935	0.365682	0.182841	+	0.983143i	$0.441471\pi$
$434$	16.5620	0.795000
$435$	−20.3329	−0.974888
$436$	40.8273	1.95527
$437$	21.1520	1.01184
$438$	−53.9148	−2.57615
$439$	−10.6896	−0.510186	−0.255093	−	0.966916i	$-0.582106\pi$
$439$	−10.6896	−0.510186	−0.255093	+	0.966916i	$0.582106\pi$
$440$	24.8888	1.18653
$441$	−10.5380	−0.501807
$442$	65.3731	3.10948
$443$	1.29663	0.0616048	0.0308024	−	0.999525i	$-0.490194\pi$
$443$	1.29663	0.0616048	0.0308024	+	0.999525i	$0.490194\pi$
$444$	101.962	4.83889
$445$	−1.82112	−0.0863296
$446$	−33.6584	−1.59377
$447$	−3.45535	−0.163433
$448$	−2.09655	−0.0990529
$449$	10.6214	0.501256	0.250628	−	0.968083i	$-0.419363\pi$
$449$	10.6214	0.501256	0.250628	+	0.968083i	$0.419363\pi$
$450$	−7.54888	−0.355858
$451$	1.77233	0.0834557
$452$	−4.90878	−0.230890
$453$	12.6012	0.592056
$454$	−54.1024	−2.53915
$455$	23.4882	1.10114
$456$	−36.0687	−1.68907
$457$	−5.60328	−0.262110	−0.131055	−	0.991375i	$-0.541836\pi$
$457$	−5.60328	−0.262110	−0.131055	+	0.991375i	$0.541836\pi$
$458$	47.4863	2.21889
$459$	0.0595183	0.00277807
$460$	96.5110	4.49985
$461$	−32.1906	−1.49927	−0.749634	−	0.661853i	$-0.769770\pi$
$461$	−32.1906	−1.49927	−0.749634	+	0.661853i	$0.769770\pi$
$462$	19.0509	0.886328
$463$	−1.19542	−0.0555557	−0.0277779	−	0.999614i	$-0.508843\pi$
$463$	−1.19542	−0.0555557	−0.0277779	+	0.999614i	$0.508843\pi$
$464$	−23.1354	−1.07403
$465$	−20.9688	−0.972406
$466$	−32.2788	−1.49529
$467$	9.58607	0.443590	0.221795	−	0.975093i	$-0.428808\pi$
$467$	9.58607	0.443590	0.221795	+	0.975093i	$0.428808\pi$
$468$	68.3497	3.15947
$469$	1.19753	0.0552970
$470$	1.09111	0.0503289
$471$	34.0046	1.56685
$472$	18.2286	0.839040
$473$	−20.4077	−0.938347
$474$	79.7433	3.66273
$475$	2.36532	0.108528
$476$	−41.4941	−1.90188
$477$	18.7528	0.858632
$478$	27.8612	1.27434
$479$	−42.4138	−1.93794	−0.968968	−	0.247187i	$-0.920494\pi$
$479$	−42.4138	−1.93794	−0.968968	+	0.247187i	$0.920494\pi$
$480$	−29.5708	−1.34972
$481$	48.2463	2.19984
$482$	−21.1528	−0.963482
$483$	40.5827	1.84658
$484$	−36.8327	−1.67421
$485$	−9.28695	−0.421699
$486$	55.9139	2.53631
$487$	−18.7913	−0.851515	−0.425758	−	0.904837i	$-0.639992\pi$
$487$	−18.7913	−0.851515	−0.425758	+	0.904837i	$0.639992\pi$
$488$	−47.6226	−2.15578
$489$	1.93417	0.0874660
$490$	21.8549	0.987305
$491$	−39.9948	−1.80494	−0.902470	−	0.430753i	$-0.858248\pi$
$491$	−39.9948	−1.80494	−0.902470	+	0.430753i	$0.858248\pi$
$492$	−11.7191	−0.528340
$493$	16.9967	0.765491
$494$	−31.0674	−1.39779
$495$	−12.0502	−0.541618
$496$	−23.8589	−1.07130
$497$	−26.0059	−1.16653
$498$	23.6947	1.06179
$499$	−24.2264	−1.08452	−0.542261	−	0.840210i	$-0.682431\pi$
$499$	−24.2264	−1.08452	−0.542261	+	0.840210i	$0.682431\pi$
$500$	−43.5326	−1.94684
$501$	12.0988	0.540535
$502$	56.8243	2.53619
$503$	6.09346	0.271694	0.135847	−	0.990730i	$-0.456624\pi$
$503$	6.09346	0.271694	0.135847	+	0.990730i	$0.456624\pi$
$504$	−34.5731	−1.54001
$505$	21.5201	0.957633
$506$	37.0399	1.64662
$507$	32.9055	1.46138
$508$	29.9333	1.32807
$509$	30.4620	1.35020	0.675102	−	0.737725i	$-0.264100\pi$
$509$	30.4620	1.35020	0.675102	+	0.737725i	$0.264100\pi$
$510$	76.2096	3.37462
$511$	16.1928	0.716329
$512$	50.7389	2.24236
$513$	−0.0282850	−0.00124881
$514$	−15.9895	−0.705265
$515$	−20.1151	−0.886378
$516$	134.942	5.94047
$517$	0.288668	0.0126956
$518$	−44.4235	−1.95186
$519$	−32.2071	−1.41373
$520$	−77.8723	−3.41493
$521$	−2.66243	−0.116643	−0.0583215	−	0.998298i	$-0.518575\pi$
$521$	−2.66243	−0.116643	−0.0583215	+	0.998298i	$0.518575\pi$
$522$	25.7788	1.12831
$523$	−36.0944	−1.57830	−0.789149	−	0.614202i	$-0.789478\pi$
$523$	−36.0944	−1.57830	−0.789149	+	0.614202i	$0.789478\pi$
$524$	27.2352	1.18978
$525$	4.53815	0.198061
$526$	−56.4711	−2.46226
$527$	17.5282	0.763542
$528$	−27.4444	−1.19437
$529$	55.9034	2.43058
$530$	−38.8919	−1.68936
$531$	−8.82562	−0.382999
$532$	19.7193	0.854942
$533$	−5.54528	−0.240193
$534$	4.62152	0.199993
$535$	30.9992	1.34021
$536$	−3.97029	−0.171490
$537$	12.6747	0.546952
$538$	−22.7563	−0.981095
$539$	5.78205	0.249050
$540$	−0.129057	−0.00555372
$541$	−6.89146	−0.296287	−0.148144	−	0.988966i	$-0.547330\pi$
$541$	−6.89146	−0.296287	−0.148144	+	0.988966i	$0.547330\pi$
$542$	−42.3772	−1.82026
$543$	30.0662	1.29026
$544$	24.7188	1.05981
$545$	22.5210	0.964695
$546$	−59.6066	−2.55093
$547$	45.8794	1.96166	0.980831	−	0.194863i	$-0.0624261\pi$
$547$	45.8794	1.96166	0.980831	+	0.194863i	$0.0624261\pi$
$548$	−18.3224	−0.782696
$549$	23.0571	0.984054
$550$	4.14198	0.176615
$551$	−8.07737	−0.344107
$552$	−134.547	−5.72671
$553$	−23.9502	−1.01847
$554$	79.7740	3.38927
$555$	56.2438	2.38742
$556$	−27.5930	−1.17020
$557$	−16.0122	−0.678458	−0.339229	−	0.940704i	$-0.610166\pi$
$557$	−16.0122	−0.678458	−0.339229	+	0.940704i	$0.610166\pi$
$558$	26.5850	1.12543
$559$	63.8518	2.70064
$560$	31.1557	1.31657
$561$	20.1624	0.851256
$562$	29.8113	1.25751
$563$	−29.5662	−1.24607	−0.623034	−	0.782195i	$-0.714100\pi$
$563$	−29.5662	−1.24607	−0.623034	+	0.782195i	$0.714100\pi$
$564$	−1.90876	−0.0803731
$565$	−2.70777	−0.113917
$566$	0.375265	0.0157736
$567$	−16.8204	−0.706390
$568$	86.2196	3.61769
$569$	8.95071	0.375233	0.187617	−	0.982242i	$-0.439924\pi$
$569$	8.95071	0.375233	0.187617	+	0.982242i	$0.439924\pi$
$570$	−36.2173	−1.51697
$571$	22.1853	0.928427	0.464214	−	0.885723i	$-0.346337\pi$
$571$	22.1853	0.928427	0.464214	+	0.885723i	$0.346337\pi$
$572$	−37.5027	−1.56807
$573$	−43.8061	−1.83003
$574$	5.10589	0.213116
$575$	8.82335	0.367959
$576$	−3.36536	−0.140223
$577$	18.1062	0.753773	0.376886	−	0.926260i	$-0.376995\pi$
$577$	18.1062	0.753773	0.376886	+	0.926260i	$0.376995\pi$
$578$	−20.5703	−0.855613
$579$	47.6478	1.98018
$580$	−36.8549	−1.53031
$581$	−7.11650	−0.295242
$582$	23.5677	0.976914
$583$	−10.2894	−0.426145
$584$	−53.6855	−2.22152
$585$	37.7029	1.55882
$586$	−39.1721	−1.61818
$587$	28.1451	1.16167	0.580837	−	0.814020i	$-0.302725\pi$
$587$	28.1451	1.16167	0.580837	+	0.814020i	$0.302725\pi$
$588$	−38.2325	−1.57668
$589$	−8.32999	−0.343231
$590$	18.3037	0.753551
$591$	3.93022	0.161667
$592$	63.9959	2.63021
$593$	2.76386	0.113498	0.0567491	−	0.998388i	$-0.481926\pi$
$593$	2.76386	0.113498	0.0567491	+	0.998388i	$0.481926\pi$
$594$	−0.0495307	−0.00203227
$595$	−22.8889	−0.938353
$596$	−6.26308	−0.256546
$597$	23.8404	0.975724
$598$	−115.891	−4.73913
$599$	−7.87599	−0.321804	−0.160902	−	0.986970i	$-0.551440\pi$
$599$	−7.87599	−0.321804	−0.160902	+	0.986970i	$0.551440\pi$
$600$	−15.0457	−0.614238
$601$	42.0697	1.71606	0.858030	−	0.513599i	$-0.171688\pi$
$601$	42.0697	1.71606	0.858030	+	0.513599i	$0.171688\pi$
$602$	−58.7925	−2.39620
$603$	1.92227	0.0782807
$604$	22.8406	0.929371
$605$	−20.3175	−0.826026
$606$	−54.6122	−2.21847
$607$	20.2840	0.823301	0.411651	−	0.911342i	$-0.364952\pi$
$607$	20.2840	0.823301	0.411651	+	0.911342i	$0.364952\pi$
$608$	−11.7472	−0.476411
$609$	−15.4974	−0.627987
$610$	−47.8188	−1.93613
$611$	−0.903187	−0.0365391
$612$	−66.6057	−2.69238
$613$	11.4588	0.462816	0.231408	−	0.972857i	$-0.425667\pi$
$613$	11.4588	0.462816	0.231408	+	0.972857i	$0.425667\pi$
$614$	−31.2151	−1.25974
$615$	−6.46448	−0.260673
$616$	18.9698	0.764317
$617$	27.2066	1.09529	0.547647	−	0.836709i	$-0.315524\pi$
$617$	27.2066	1.09529	0.547647	+	0.836709i	$0.315524\pi$
$618$	51.0466	2.05340
$619$	−19.6888	−0.791360	−0.395680	−	0.918389i	$-0.629491\pi$
$619$	−19.6888	−0.791360	−0.395680	+	0.918389i	$0.629491\pi$
$620$	−38.0075	−1.52642
$621$	−0.105512	−0.00423403
$622$	−51.2380	−2.05446
$623$	−1.38803	−0.0556103
$624$	85.8684	3.43749
$625$	−28.9799	−1.15920
$626$	48.1749	1.92546
$627$	−9.58181	−0.382661
$628$	61.6358	2.45954
$629$	−47.0153	−1.87462
$630$	−34.7155	−1.38310
$631$	−15.6539	−0.623173	−0.311587	−	0.950218i	$-0.600860\pi$
$631$	−15.6539	−0.623173	−0.311587	+	0.950218i	$0.600860\pi$
$632$	79.4040	3.15852
$633$	−20.1248	−0.799891
$634$	65.4317	2.59862
$635$	16.5117	0.655247
$636$	68.0367	2.69783
$637$	−18.0909	−0.716788
$638$	−14.1445	−0.559987
$639$	−41.7443	−1.65138
$640$	31.1337	1.23067
$641$	−38.5433	−1.52237	−0.761185	−	0.648535i	$-0.775382\pi$
$641$	−38.5433	−1.52237	−0.761185	+	0.648535i	$0.775382\pi$
$642$	−78.6675	−3.10476
$643$	−8.43160	−0.332510	−0.166255	−	0.986083i	$-0.553167\pi$
$643$	−8.43160	−0.332510	−0.166255	+	0.986083i	$0.553167\pi$
$644$	73.5591	2.89863
$645$	74.4361	2.93092
$646$	30.2747	1.19114
$647$	27.1189	1.06615	0.533077	−	0.846067i	$-0.321035\pi$
$647$	27.1189	1.06615	0.533077	+	0.846067i	$0.321035\pi$
$648$	55.7660	2.19070
$649$	4.84251	0.190085
$650$	−12.9595	−0.508312
$651$	−15.9821	−0.626388
$652$	3.50582	0.137298
$653$	−27.1794	−1.06361	−0.531805	−	0.846867i	$-0.678486\pi$
$653$	−27.1794	−1.06361	−0.531805	+	0.846867i	$0.678486\pi$
$654$	−57.1522	−2.23483
$655$	15.0234	0.587014
$656$	−7.35548	−0.287183
$657$	25.9925	1.01406
$658$	0.831623	0.0324200
$659$	−16.0599	−0.625605	−0.312803	−	0.949818i	$-0.601268\pi$
$659$	−16.0599	−0.625605	−0.312803	+	0.949818i	$0.601268\pi$
$660$	−43.7192	−1.70177
$661$	−39.4785	−1.53553	−0.767767	−	0.640729i	$-0.778632\pi$
$661$	−39.4785	−1.53553	−0.767767	+	0.640729i	$0.778632\pi$
$662$	0.256336	0.00996280
$663$	−63.0842	−2.44999
$664$	23.5939	0.915621
$665$	10.8775	0.421813
$666$	−71.3080	−2.76313
$667$	−30.1310	−1.16668
$668$	21.9300	0.848496
$669$	32.4799	1.25575
$670$	−3.98664	−0.154017
$671$	−12.6512	−0.488393
$672$	−22.5384	−0.869437
$673$	19.9234	0.767992	0.383996	−	0.923335i	$-0.374548\pi$
$673$	19.9234	0.767992	0.383996	+	0.923335i	$0.374548\pi$
$674$	46.5998	1.79496
$675$	−0.0117988	−0.000454136 0
$676$	59.6436	2.29399
$677$	29.4196	1.13069	0.565343	−	0.824856i	$-0.308744\pi$
$677$	29.4196	1.13069	0.565343	+	0.824856i	$0.308744\pi$
$678$	6.87158	0.263901
$679$	−7.07836	−0.271643
$680$	75.8854	2.91007
$681$	52.2081	2.00062
$682$	−14.5869	−0.558561
$683$	−26.2544	−1.00460	−0.502298	−	0.864694i	$-0.667512\pi$
$683$	−26.2544	−1.00460	−0.502298	+	0.864694i	$0.667512\pi$
$684$	31.6532	1.21029
$685$	−10.1070	−0.386168
$686$	49.7988	1.90133
$687$	−45.8237	−1.74828
$688$	84.6956	3.22899
$689$	32.1937	1.22648
$690$	−135.101	−5.14322
$691$	−1.85422	−0.0705379	−0.0352689	−	0.999378i	$-0.511229\pi$
$691$	−1.85422	−0.0705379	−0.0352689	+	0.999378i	$0.511229\pi$
$692$	−58.3777	−2.21919
$693$	−9.18450	−0.348890
$694$	20.8551	0.791651
$695$	−15.2208	−0.577357
$696$	51.3798	1.94755
$697$	5.40379	0.204683
$698$	37.3317	1.41303
$699$	31.1486	1.17815
$700$	8.22573	0.310903
$701$	36.6544	1.38442	0.692209	−	0.721697i	$-0.256638\pi$
$701$	36.6544	1.38442	0.692209	+	0.721697i	$0.256638\pi$
$702$	0.154972	0.00584905
$703$	22.3432	0.842690
$704$	1.84653	0.0695938
$705$	−1.05290	−0.0396546
$706$	27.5969	1.03862
$707$	16.4023	0.616872
$708$	−32.0201	−1.20339
$709$	23.5830	0.885677	0.442839	−	0.896601i	$-0.353971\pi$
$709$	23.5830	0.885677	0.442839	+	0.896601i	$0.353971\pi$
$710$	86.5747	3.24909
$711$	−38.4445	−1.44178
$712$	4.60185	0.172462
$713$	−31.0734	−1.16371
$714$	58.0857	2.17380
$715$	−20.6871	−0.773655
$716$	22.9737	0.858569
$717$	−26.8857	−1.00406
$718$	−56.8949	−2.12330
$719$	33.7675	1.25932	0.629658	−	0.776872i	$-0.283195\pi$
$719$	33.7675	1.25932	0.629658	+	0.776872i	$0.283195\pi$
$720$	50.0106	1.86379
$721$	−15.3314	−0.570972
$722$	33.8219	1.25872
$723$	20.4121	0.759136
$724$	54.4972	2.02537
$725$	−3.36939	−0.125136
$726$	51.5604	1.91358
$727$	−30.9213	−1.14681	−0.573404	−	0.819273i	$-0.694378\pi$
$727$	−30.9213	−1.14681	−0.573404	+	0.819273i	$0.694378\pi$
$728$	−59.3530	−2.19977
$729$	−26.9126	−0.996763
$730$	−53.9066	−1.99517
$731$	−62.2226	−2.30139
$732$	83.6531	3.09191
$733$	20.6509	0.762758	0.381379	−	0.924419i	$-0.375449\pi$
$733$	20.6509	0.762758	0.381379	+	0.924419i	$0.375449\pi$
$734$	−38.7926	−1.43186
$735$	−21.0897	−0.777907
$736$	−43.8205	−1.61525
$737$	−1.05472	−0.0388513
$738$	8.19591	0.301695
$739$	36.5232	1.34353	0.671763	−	0.740766i	$-0.265537\pi$
$739$	36.5232	1.34353	0.671763	+	0.740766i	$0.265537\pi$
$740$	101.946	3.74761
$741$	29.9797	1.10133
$742$	−29.6428	−1.08822
$743$	−5.67529	−0.208206	−0.104103	−	0.994567i	$-0.533197\pi$
$743$	−5.67529	−0.208206	−0.104103	+	0.994567i	$0.533197\pi$
$744$	52.9867	1.94259
$745$	−3.45482	−0.126575
$746$	86.3338	3.16091
$747$	−11.4233	−0.417957
$748$	36.5458	1.33625
$749$	23.6271	0.863316
$750$	60.9393	2.22519
$751$	23.7035	0.864955	0.432477	−	0.901645i	$-0.357640\pi$
$751$	23.7035	0.864955	0.432477	+	0.901645i	$0.357640\pi$
$752$	−1.19802	−0.0436874
$753$	−54.8347	−1.99829
$754$	44.2555	1.61169
$755$	12.5993	0.458535
$756$	−0.0983651	−0.00357750
$757$	−25.2104	−0.916287	−0.458144	−	0.888878i	$-0.651485\pi$
$757$	−25.2104	−0.916287	−0.458144	+	0.888878i	$0.651485\pi$
$758$	−20.9283	−0.760151
$759$	−35.7430	−1.29739
$760$	−36.0632	−1.30815
$761$	25.6080	0.928291	0.464146	−	0.885759i	$-0.346361\pi$
$761$	25.6080	0.928291	0.464146	+	0.885759i	$0.346361\pi$
$762$	−41.9022	−1.51796
$763$	17.1652	0.621421
$764$	−79.4018	−2.87265
$765$	−36.7409	−1.32837
$766$	68.6991	2.48220
$767$	−15.1513	−0.547082
$768$	−73.5066	−2.65244
$769$	−2.61755	−0.0943914	−0.0471957	−	0.998886i	$-0.515028\pi$
$769$	−2.61755	−0.0943914	−0.0471957	+	0.998886i	$0.515028\pi$
$770$	19.0480	0.686441
$771$	15.4296	0.555684
$772$	86.3652	3.10835
$773$	−9.20592	−0.331114	−0.165557	−	0.986200i	$-0.552942\pi$
$773$	−9.20592	−0.331114	−0.165557	+	0.986200i	$0.552942\pi$
$774$	−94.3728	−3.39216
$775$	−3.47477	−0.124817
$776$	23.4675	0.842433
$777$	42.8681	1.53789
$778$	45.4850	1.63072
$779$	−2.56805	−0.0920101
$780$	136.789	4.89784
$781$	22.9046	0.819591
$782$	112.934	4.03850
$783$	0.0402919	0.00143992
$784$	−23.9965	−0.857019
$785$	33.9994	1.21349
$786$	−38.1253	−1.35989
$787$	25.6817	0.915454	0.457727	−	0.889093i	$-0.348664\pi$
$787$	25.6817	0.915454	0.457727	+	0.889093i	$0.348664\pi$
$788$	7.12380	0.253775
$789$	54.4939	1.94004
$790$	79.7310	2.83670
$791$	−2.06382	−0.0733809
$792$	30.4501	1.08200
$793$	39.5831	1.40564
$794$	−19.7312	−0.700233
$795$	37.5302	1.33106
$796$	43.2125	1.53163
$797$	29.1436	1.03232	0.516159	−	0.856493i	$-0.327361\pi$
$797$	29.1436	1.03232	0.516159	+	0.856493i	$0.327361\pi$
$798$	−27.6042	−0.977179
$799$	0.880142	0.0311372
$800$	−4.90022	−0.173249
$801$	−2.22805	−0.0787242
$802$	−14.6080	−0.515827
$803$	−14.2618	−0.503287
$804$	6.97414	0.245959
$805$	40.5765	1.43013
$806$	45.6396	1.60759
$807$	21.9596	0.773014
$808$	−54.3799	−1.91308
$809$	−27.5997	−0.970354	−0.485177	−	0.874416i	$-0.661245\pi$
$809$	−27.5997	−0.970354	−0.485177	+	0.874416i	$0.661245\pi$
$810$	55.9957	1.96749
$811$	−44.0785	−1.54780	−0.773902	−	0.633305i	$-0.781698\pi$
$811$	−44.0785	−1.54780	−0.773902	+	0.633305i	$0.781698\pi$
$812$	−28.0902	−0.985772
$813$	40.8935	1.43420
$814$	39.1258	1.37136
$815$	1.93387	0.0677405
$816$	−83.6775	−2.92930
$817$	29.5702	1.03453
$818$	−94.5880	−3.30719
$819$	28.7365	1.00414
$820$	−11.7173	−0.409187
$821$	−35.8595	−1.25151	−0.625753	−	0.780022i	$-0.715208\pi$
$821$	−35.8595	−1.25151	−0.625753	+	0.780022i	$0.715208\pi$
$822$	25.6487	0.894603
$823$	48.2102	1.68050	0.840250	−	0.542199i	$-0.182408\pi$
$823$	48.2102	1.68050	0.840250	+	0.542199i	$0.182408\pi$
$824$	50.8295	1.77073
$825$	−3.99696	−0.139156
$826$	13.9508	0.485410
$827$	43.9613	1.52868	0.764342	−	0.644811i	$-0.223064\pi$
$827$	43.9613	1.52868	0.764342	+	0.644811i	$0.223064\pi$
$828$	118.076	4.10342
$829$	33.0116	1.14654	0.573270	−	0.819367i	$-0.305675\pi$
$829$	33.0116	1.14654	0.573270	+	0.819367i	$0.305675\pi$
$830$	23.6911	0.822330
$831$	−76.9809	−2.67044
$832$	−5.77745	−0.200297
$833$	17.6293	0.610820
$834$	38.6261	1.33751
$835$	12.0970	0.418632
$836$	−17.3677	−0.600676
$837$	0.0415521	0.00143625
$838$	−47.7373	−1.64906
$839$	−50.9984	−1.76066	−0.880330	−	0.474362i	$-0.842679\pi$
$839$	−50.9984	−1.76066	−0.880330	+	0.474362i	$0.842679\pi$
$840$	−69.1916	−2.38734
$841$	−17.4938	−0.603235
$842$	59.4958	2.05036
$843$	−28.7676	−0.990807
$844$	−36.4777	−1.25562
$845$	32.9005	1.13181
$846$	1.33491	0.0458951
$847$	−15.4857	−0.532095
$848$	42.7030	1.46643
$849$	−0.362126	−0.0124281
$850$	12.6288	0.433164
$851$	83.3469	2.85709
$852$	−151.452	−5.18865
$853$	−30.2412	−1.03544	−0.517720	−	0.855550i	$-0.673219\pi$
$853$	−30.2412	−1.03544	−0.517720	+	0.855550i	$0.673219\pi$
$854$	−36.4467	−1.24718
$855$	17.4605	0.597135
$856$	−78.3329	−2.67736
$857$	−49.0317	−1.67489	−0.837445	−	0.546521i	$-0.815952\pi$
$857$	−49.0317	−1.67489	−0.837445	+	0.546521i	$0.815952\pi$
$858$	52.4983	1.79226
$859$	−26.9276	−0.918758	−0.459379	−	0.888240i	$-0.651928\pi$
$859$	−26.9276	−0.918758	−0.459379	+	0.888240i	$0.651928\pi$
$860$	134.921	4.60076
$861$	−4.92712	−0.167916
$862$	83.1975	2.83372
$863$	−8.34638	−0.284114	−0.142057	−	0.989858i	$-0.545372\pi$
$863$	−8.34638	−0.284114	−0.142057	+	0.989858i	$0.545372\pi$
$864$	0.0585979	0.00199354
$865$	−32.2022	−1.09491
$866$	−19.3075	−0.656095
$867$	19.8501	0.674145
$868$	−28.9687	−0.983262
$869$	21.0940	0.715566
$870$	51.5914	1.74911
$871$	3.30003	0.111817
$872$	−56.9091	−1.92719
$873$	−11.3621	−0.384548
$874$	−53.6698	−1.81541
$875$	−18.3026	−0.618740
$876$	94.3030	3.18620
$877$	12.4890	0.421725	0.210863	−	0.977516i	$-0.432373\pi$
$877$	12.4890	0.421725	0.210863	+	0.977516i	$0.432373\pi$
$878$	27.1231	0.915360
$879$	37.8006	1.27498
$880$	−27.4402	−0.925010
$881$	−53.1197	−1.78965	−0.894824	−	0.446418i	$-0.852699\pi$
$881$	−53.1197	−1.78965	−0.894824	+	0.446418i	$0.852699\pi$
$882$	26.7383	0.900327
$883$	−4.46852	−0.150378	−0.0751889	−	0.997169i	$-0.523956\pi$
$883$	−4.46852	−0.150378	−0.0751889	+	0.997169i	$0.523956\pi$
$884$	−114.345	−3.84583
$885$	−17.6628	−0.593730
$886$	−3.28999	−0.110529
$887$	−31.0186	−1.04150	−0.520751	−	0.853708i	$-0.674348\pi$
$887$	−31.0186	−1.04150	−0.520751	+	0.853708i	$0.674348\pi$
$888$	−142.124	−4.76938
$889$	12.5850	0.422086
$890$	4.62081	0.154890
$891$	14.8145	0.496304
$892$	58.8722	1.97119
$893$	−0.418272	−0.0139969
$894$	8.76739	0.293226
$895$	12.6727	0.423602
$896$	23.7296	0.792751
$897$	111.833	3.73400
$898$	−26.9501	−0.899338
$899$	11.8661	0.395755
$900$	13.2038	0.440127
$901$	−31.3722	−1.04516
$902$	−4.49699	−0.149734
$903$	56.7340	1.88799
$904$	6.84235	0.227573
$905$	30.0616	0.999281
$906$	−31.9735	−1.06225
$907$	8.00510	0.265805	0.132902	−	0.991129i	$-0.457570\pi$
$907$	8.00510	0.265805	0.132902	+	0.991129i	$0.457570\pi$
$908$	94.6310	3.14044
$909$	26.3287	0.873269
$910$	−59.5975	−1.97564
$911$	27.0929	0.897628	0.448814	−	0.893625i	$-0.351847\pi$
$911$	27.0929	0.897628	0.448814	+	0.893625i	$0.351847\pi$
$912$	39.7662	1.31679
$913$	6.26783	0.207435
$914$	14.2174	0.470270
$915$	46.1445	1.52549
$916$	−83.0588	−2.74434
$917$	11.4506	0.378132
$918$	−0.151018	−0.00498433
$919$	17.0292	0.561743	0.280871	−	0.959745i	$-0.409377\pi$
$919$	17.0292	0.561743	0.280871	+	0.959745i	$0.409377\pi$
$920$	−134.527	−4.43521
$921$	30.1222	0.992560
$922$	81.6785	2.68994
$923$	−71.6642	−2.35885
$924$	−33.3221	−1.09622
$925$	9.32024	0.306448
$926$	3.03318	0.0996764
$927$	−24.6098	−0.808291
$928$	16.7338	0.549315
$929$	40.4326	1.32655	0.663276	−	0.748375i	$-0.269166\pi$
$929$	40.4326	1.32655	0.663276	+	0.748375i	$0.269166\pi$
$930$	53.2050	1.74466
$931$	−8.37803	−0.274579
$932$	56.4592	1.84938
$933$	49.4441	1.61873
$934$	−24.3231	−0.795876
$935$	20.1593	0.659279
$936$	−95.2726	−3.11408
$937$	40.1838	1.31275	0.656374	−	0.754436i	$-0.272090\pi$
$937$	40.1838	1.31275	0.656374	+	0.754436i	$0.272090\pi$
$938$	−3.03855	−0.0992122
$939$	−46.4882	−1.51709
$940$	−1.90846	−0.0622472
$941$	−24.6919	−0.804932	−0.402466	−	0.915435i	$-0.631847\pi$
$941$	−24.6919	−0.804932	−0.402466	+	0.915435i	$0.631847\pi$
$942$	−86.2811	−2.81119
$943$	−9.57962	−0.311955
$944$	−20.0973	−0.654111
$945$	−0.0542599	−0.00176508
$946$	51.7812	1.68355
$947$	25.4596	0.827326	0.413663	−	0.910430i	$-0.364249\pi$
$947$	25.4596	0.827326	0.413663	+	0.910430i	$0.364249\pi$
$948$	−139.480	−4.53009
$949$	44.6224	1.44850
$950$	−6.00161	−0.194718
$951$	−63.1408	−2.04748
$952$	57.8386	1.87456
$953$	−9.52623	−0.308585	−0.154292	−	0.988025i	$-0.549310\pi$
$953$	−9.52623	−0.308585	−0.154292	+	0.988025i	$0.549310\pi$
$954$	−47.5822	−1.54053
$955$	−43.7994	−1.41732
$956$	−48.7322	−1.57611
$957$	13.6493	0.441218
$958$	107.618	3.47698
$959$	−7.70338	−0.248755
$960$	−6.73514	−0.217376
$961$	−18.7628	−0.605253
$962$	−122.417	−3.94689
$963$	37.9259	1.22214
$964$	36.9985	1.19164
$965$	47.6405	1.53360
$966$	−102.972	−3.31307
$967$	−12.8064	−0.411826	−0.205913	−	0.978570i	$-0.566016\pi$
$967$	−12.8064	−0.411826	−0.205913	+	0.978570i	$0.566016\pi$
$968$	51.3410	1.65016
$969$	−29.2147	−0.938512
$970$	23.5641	0.756599
$971$	40.4284	1.29741	0.648705	−	0.761040i	$-0.275311\pi$
$971$	40.4284	1.29741	0.648705	+	0.761040i	$0.275311\pi$
$972$	−97.7995	−3.13692
$973$	−11.6010	−0.371912
$974$	47.6799	1.52776
$975$	12.5057	0.400504
$976$	52.5046	1.68063
$977$	37.2550	1.19189	0.595947	−	0.803024i	$-0.296777\pi$
$977$	37.2550	1.19189	0.595947	+	0.803024i	$0.296777\pi$
$978$	−4.90763	−0.156929
$979$	1.22250	0.0390714
$980$	−38.2267	−1.22111
$981$	27.5533	0.879709
$982$	101.480	3.23837
$983$	−24.9744	−0.796560	−0.398280	−	0.917264i	$-0.630393\pi$
$983$	−24.9744	−0.796560	−0.398280	+	0.917264i	$0.630393\pi$
$984$	16.3353	0.520750
$985$	3.92961	0.125208
$986$	−43.1263	−1.37342
$987$	−0.802506	−0.0255440
$988$	54.3403	1.72880
$989$	110.306	3.50752
$990$	30.5755	0.971754
$991$	−31.7547	−1.00872	−0.504361	−	0.863493i	$-0.668272\pi$
$991$	−31.7547	−1.00872	−0.504361	+	0.863493i	$0.668272\pi$
$992$	17.2572	0.547916
$993$	−0.247362	−0.00784978
$994$	65.9858	2.09294
$995$	23.8368	0.755677
$996$	−41.4447	−1.31322
$997$	27.9408	0.884896	0.442448	−	0.896794i	$-0.354110\pi$
$997$	27.9408	0.884896	0.442448	+	0.896794i	$0.354110\pi$
$998$	61.4705	1.94581
$999$	−0.111454	−0.00352623

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6011.2.a.f.1.19	✓	275

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6011.2.a.f.1.19	✓	275	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:	\( N \)	\(=\)	\( 6011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6011.a (trivial)

\(f(q)\)	\(=\)	\(q-2.53734 q^{2} +2.44850 q^{3} +4.43808 q^{4} +2.44812 q^{5} -6.21267 q^{6} +1.86592 q^{7} -6.18624 q^{8} +2.99515 q^{9} +O(q^{10})\)	\(q-2.53734 q^{2} +2.44850 q^{3} +4.43808 q^{4} +2.44812 q^{5} -6.21267 q^{6} +1.86592 q^{7} -6.18624 q^{8} +2.99515 q^{9} -6.21172 q^{10} -1.64340 q^{11} +10.8666 q^{12} +5.14189 q^{13} -4.73447 q^{14} +5.99423 q^{15} +6.82041 q^{16} -5.01069 q^{17} -7.59970 q^{18} +2.38124 q^{19} +10.8650 q^{20} +4.56871 q^{21} +4.16987 q^{22} +8.88276 q^{23} -15.1470 q^{24} +0.993312 q^{25} -13.0467 q^{26} -0.0118782 q^{27} +8.28111 q^{28} -3.39208 q^{29} -15.2094 q^{30} -3.49817 q^{31} -4.93321 q^{32} -4.02387 q^{33} +12.7138 q^{34} +4.56801 q^{35} +13.2927 q^{36} +9.38299 q^{37} -6.04202 q^{38} +12.5899 q^{39} -15.1447 q^{40} -1.07845 q^{41} -11.5923 q^{42} +12.4180 q^{43} -7.29355 q^{44} +7.33250 q^{45} -22.5386 q^{46} -0.175653 q^{47} +16.6998 q^{48} -3.51834 q^{49} -2.52037 q^{50} -12.2687 q^{51} +22.8201 q^{52} +6.26106 q^{53} +0.0301391 q^{54} -4.02325 q^{55} -11.5430 q^{56} +5.83047 q^{57} +8.60685 q^{58} -2.94664 q^{59} +26.6029 q^{60} +7.69816 q^{61} +8.87603 q^{62} +5.58871 q^{63} -1.12360 q^{64} +12.5880 q^{65} +10.2099 q^{66} +0.641793 q^{67} -22.2379 q^{68} +21.7494 q^{69} -11.5906 q^{70} -13.9373 q^{71} -18.5287 q^{72} +8.67821 q^{73} -23.8078 q^{74} +2.43212 q^{75} +10.5682 q^{76} -3.06646 q^{77} -31.9449 q^{78} -12.8356 q^{79} +16.6972 q^{80} -9.01453 q^{81} +2.73639 q^{82} -3.81393 q^{83} +20.2763 q^{84} -12.2668 q^{85} -31.5086 q^{86} -8.30550 q^{87} +10.1665 q^{88} -0.743886 q^{89} -18.6050 q^{90} +9.59436 q^{91} +39.4224 q^{92} -8.56526 q^{93} +0.445690 q^{94} +5.82958 q^{95} -12.0790 q^{96} -3.79350 q^{97} +8.92722 q^{98} -4.92223 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 275 q + 16 q^{2} + 9 q^{3} + 316 q^{4} + 36 q^{5} + 30 q^{6} + 41 q^{7} + 36 q^{8} + 322 q^{9}+O(q^{10}) \) 275 * q + 16 * q^2 + 9 * q^3 + 316 * q^4 + 36 * q^5 + 30 * q^6 + 41 * q^7 + 36 * q^8 + 322 * q^9	\( 275 q + 16 q^{2} + 9 q^{3} + 316 q^{4} + 36 q^{5} + 30 q^{6} + 41 q^{7} + 36 q^{8} + 322 q^{9} + 44 q^{10} + 42 q^{11} + 26 q^{12} + 97 q^{13} + 24 q^{14} + 46 q^{15} + 386 q^{16} + 35 q^{17} + 47 q^{18} + 101 q^{19} + 60 q^{20} + 187 q^{21} + 72 q^{22} + 35 q^{23} + 73 q^{24} + 373 q^{25} + 21 q^{26} + 27 q^{27} + 97 q^{28} + 162 q^{29} + 13 q^{30} + 113 q^{31} + 58 q^{32} + 16 q^{33} + 52 q^{34} + 23 q^{35} + 426 q^{36} + 257 q^{37} + 8 q^{38} + 87 q^{39} + 126 q^{40} + 77 q^{41} - 7 q^{42} + 107 q^{43} + 133 q^{44} + 140 q^{45} + 207 q^{46} + 24 q^{47} + 4 q^{48} + 418 q^{49} + 65 q^{50} + 94 q^{51} + 142 q^{52} + 81 q^{53} + 79 q^{54} + 26 q^{55} + 62 q^{56} + 112 q^{57} + 44 q^{58} + 30 q^{59} + 83 q^{60} + 347 q^{61} + 5 q^{62} + 97 q^{63} + 508 q^{64} + 94 q^{65} + 4 q^{66} + 98 q^{67} + 28 q^{68} + 91 q^{69} + 17 q^{70} + 58 q^{71} + 99 q^{72} + 157 q^{73} + 80 q^{74} + 83 q^{75} + 264 q^{76} + 61 q^{77} + 5 q^{78} + 282 q^{79} + 49 q^{80} + 403 q^{81} + 46 q^{82} + 43 q^{83} + 318 q^{84} + 396 q^{85} + 57 q^{86} + 31 q^{87} + 180 q^{88} + 98 q^{89} + 67 q^{90} + 195 q^{91} + 97 q^{92} + 83 q^{93} + 96 q^{94} + 28 q^{95} + 127 q^{96} + 167 q^{97} + 24 q^{98} + 133 q^{99}+O(q^{100}) \) 275 * q + 16 * q^2 + 9 * q^3 + 316 * q^4 + 36 * q^5 + 30 * q^6 + 41 * q^7 + 36 * q^8 + 322 * q^9 + 44 * q^10 + 42 * q^11 + 26 * q^12 + 97 * q^13 + 24 * q^14 + 46 * q^15 + 386 * q^16 + 35 * q^17 + 47 * q^18 + 101 * q^19 + 60 * q^20 + 187 * q^21 + 72 * q^22 + 35 * q^23 + 73 * q^24 + 373 * q^25 + 21 * q^26 + 27 * q^27 + 97 * q^28 + 162 * q^29 + 13 * q^30 + 113 * q^31 + 58 * q^32 + 16 * q^33 + 52 * q^34 + 23 * q^35 + 426 * q^36 + 257 * q^37 + 8 * q^38 + 87 * q^39 + 126 * q^40 + 77 * q^41 - 7 * q^42 + 107 * q^43 + 133 * q^44 + 140 * q^45 + 207 * q^46 + 24 * q^47 + 4 * q^48 + 418 * q^49 + 65 * q^50 + 94 * q^51 + 142 * q^52 + 81 * q^53 + 79 * q^54 + 26 * q^55 + 62 * q^56 + 112 * q^57 + 44 * q^58 + 30 * q^59 + 83 * q^60 + 347 * q^61 + 5 * q^62 + 97 * q^63 + 508 * q^64 + 94 * q^65 + 4 * q^66 + 98 * q^67 + 28 * q^68 + 91 * q^69 + 17 * q^70 + 58 * q^71 + 99 * q^72 + 157 * q^73 + 80 * q^74 + 83 * q^75 + 264 * q^76 + 61 * q^77 + 5 * q^78 + 282 * q^79 + 49 * q^80 + 403 * q^81 + 46 * q^82 + 43 * q^83 + 318 * q^84 + 396 * q^85 + 57 * q^86 + 31 * q^87 + 180 * q^88 + 98 * q^89 + 67 * q^90 + 195 * q^91 + 97 * q^92 + 83 * q^93 + 96 * q^94 + 28 * q^95 + 127 * q^96 + 167 * q^97 + 24 * q^98 + 133 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more