LMFDB - Embedded newform 6041.2.a.f.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6041,2,Mod(1,6041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6041, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6041 = 7 \cdot 863 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6041.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$48.2376278611$
Analytic rank:	$0$
Dimension:	$132$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	6041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.25429 q^{2} -3.03067 q^{3} +3.08183 q^{4} +3.72305 q^{5} +6.83200 q^{6} +1.00000 q^{7} -2.43875 q^{8} +6.18494 q^{9} +O(q^{10})$	\(q-2.25429 q^{2} -3.03067 q^{3} +3.08183 q^{4} +3.72305 q^{5} +6.83200 q^{6} +1.00000 q^{7} -2.43875 q^{8} +6.18494 q^{9} -8.39284 q^{10} +4.60514 q^{11} -9.33999 q^{12} +6.90097 q^{13} -2.25429 q^{14} -11.2833 q^{15} -0.665999 q^{16} -2.74488 q^{17} -13.9427 q^{18} +4.67145 q^{19} +11.4738 q^{20} -3.03067 q^{21} -10.3813 q^{22} -1.63794 q^{23} +7.39104 q^{24} +8.86112 q^{25} -15.5568 q^{26} -9.65250 q^{27} +3.08183 q^{28} -8.57376 q^{29} +25.4359 q^{30} +7.04253 q^{31} +6.37886 q^{32} -13.9567 q^{33} +6.18776 q^{34} +3.72305 q^{35} +19.0609 q^{36} -9.34078 q^{37} -10.5308 q^{38} -20.9145 q^{39} -9.07960 q^{40} -0.689890 q^{41} +6.83200 q^{42} +3.66860 q^{43} +14.1923 q^{44} +23.0269 q^{45} +3.69239 q^{46} -4.36195 q^{47} +2.01842 q^{48} +1.00000 q^{49} -19.9755 q^{50} +8.31882 q^{51} +21.2676 q^{52} -4.46864 q^{53} +21.7596 q^{54} +17.1452 q^{55} -2.43875 q^{56} -14.1576 q^{57} +19.3278 q^{58} +2.35520 q^{59} -34.7733 q^{60} +5.59282 q^{61} -15.8759 q^{62} +6.18494 q^{63} -13.0478 q^{64} +25.6927 q^{65} +31.4624 q^{66} -5.53840 q^{67} -8.45924 q^{68} +4.96405 q^{69} -8.39284 q^{70} +13.6336 q^{71} -15.0835 q^{72} +3.36845 q^{73} +21.0568 q^{74} -26.8551 q^{75} +14.3966 q^{76} +4.60514 q^{77} +47.1475 q^{78} -7.88014 q^{79} -2.47955 q^{80} +10.6987 q^{81} +1.55521 q^{82} +13.3384 q^{83} -9.33999 q^{84} -10.2193 q^{85} -8.27009 q^{86} +25.9842 q^{87} -11.2308 q^{88} -9.52845 q^{89} -51.9093 q^{90} +6.90097 q^{91} -5.04784 q^{92} -21.3436 q^{93} +9.83311 q^{94} +17.3921 q^{95} -19.3322 q^{96} +10.6575 q^{97} -2.25429 q^{98} +28.4826 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q + 8 q^{2} + 10 q^{3} + 174 q^{4} + 11 q^{5} + 16 q^{6} + 132 q^{7} + 30 q^{8} + 178 q^{9}+O(q^{10}) $ 132 * q + 8 * q^2 + 10 * q^3 + 174 * q^4 + 11 * q^5 + 16 * q^6 + 132 * q^7 + 30 * q^8 + 178 * q^9	\( 132 q + 8 q^{2} + 10 q^{3} + 174 q^{4} + 11 q^{5} + 16 q^{6} + 132 q^{7} + 30 q^{8} + 178 q^{9} + 22 q^{10} + 32 q^{11} + 30 q^{12} + 16 q^{13} + 8 q^{14} + 59 q^{15} + 254 q^{16} + 11 q^{17} + 33 q^{18} + 40 q^{19} + 4 q^{20} + 10 q^{21} + 66 q^{22} + 62 q^{23} + 36 q^{24} + 235 q^{25} + 25 q^{26} + 37 q^{27} + 174 q^{28} + 28 q^{29} + 45 q^{30} + 121 q^{31} + 53 q^{32} - 13 q^{33} + 44 q^{34} + 11 q^{35} + 274 q^{36} + 61 q^{37} - 28 q^{38} + 114 q^{39} + 32 q^{40} - q^{41} + 16 q^{42} + 105 q^{43} + 54 q^{44} + 29 q^{45} + 104 q^{46} + 33 q^{47} + 16 q^{48} + 132 q^{49} - 14 q^{50} + 53 q^{51} - 11 q^{52} + 48 q^{53} + 11 q^{54} + 118 q^{55} + 30 q^{56} + 93 q^{57} + 87 q^{58} + 12 q^{59} + 41 q^{60} + 54 q^{61} - 28 q^{62} + 178 q^{63} + 376 q^{64} + 22 q^{65} + 6 q^{66} + 123 q^{67} - 47 q^{68} + 58 q^{69} + 22 q^{70} + 108 q^{71} + 97 q^{72} + q^{73} - 10 q^{74} + 23 q^{75} + 71 q^{76} + 32 q^{77} + 5 q^{78} + 204 q^{79} - 10 q^{80} + 296 q^{81} + 80 q^{82} - 10 q^{83} + 30 q^{84} + 94 q^{85} + 48 q^{86} + 4 q^{87} + 155 q^{88} + q^{89} - 66 q^{90} + 16 q^{91} + 49 q^{92} + 90 q^{93} + 79 q^{94} + 100 q^{95} + q^{96} + 18 q^{97} + 8 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q + 8 * q^2 + 10 * q^3 + 174 * q^4 + 11 * q^5 + 16 * q^6 + 132 * q^7 + 30 * q^8 + 178 * q^9 + 22 * q^10 + 32 * q^11 + 30 * q^12 + 16 * q^13 + 8 * q^14 + 59 * q^15 + 254 * q^16 + 11 * q^17 + 33 * q^18 + 40 * q^19 + 4 * q^20 + 10 * q^21 + 66 * q^22 + 62 * q^23 + 36 * q^24 + 235 * q^25 + 25 * q^26 + 37 * q^27 + 174 * q^28 + 28 * q^29 + 45 * q^30 + 121 * q^31 + 53 * q^32 - 13 * q^33 + 44 * q^34 + 11 * q^35 + 274 * q^36 + 61 * q^37 - 28 * q^38 + 114 * q^39 + 32 * q^40 - q^41 + 16 * q^42 + 105 * q^43 + 54 * q^44 + 29 * q^45 + 104 * q^46 + 33 * q^47 + 16 * q^48 + 132 * q^49 - 14 * q^50 + 53 * q^51 - 11 * q^52 + 48 * q^53 + 11 * q^54 + 118 * q^55 + 30 * q^56 + 93 * q^57 + 87 * q^58 + 12 * q^59 + 41 * q^60 + 54 * q^61 - 28 * q^62 + 178 * q^63 + 376 * q^64 + 22 * q^65 + 6 * q^66 + 123 * q^67 - 47 * q^68 + 58 * q^69 + 22 * q^70 + 108 * q^71 + 97 * q^72 + q^73 - 10 * q^74 + 23 * q^75 + 71 * q^76 + 32 * q^77 + 5 * q^78 + 204 * q^79 - 10 * q^80 + 296 * q^81 + 80 * q^82 - 10 * q^83 + 30 * q^84 + 94 * q^85 + 48 * q^86 + 4 * q^87 + 155 * q^88 + q^89 - 66 * q^90 + 16 * q^91 + 49 * q^92 + 90 * q^93 + 79 * q^94 + 100 * q^95 + q^96 + 18 * q^97 + 8 * q^98 + 96 * 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 $

$2$	−2.25429	−1.59402	−0.797012	−	0.603963i	$-0.793587\pi$
$2$	−2.25429	−1.59402	−0.797012	+	0.603963i	$0.793587\pi$
$3$	−3.03067	−1.74976	−0.874878	−	0.484343i	$-0.839059\pi$
$3$	−3.03067	−1.74976	−0.874878	+	0.484343i	$0.839059\pi$
$4$	3.08183	1.54091
$5$	3.72305	1.66500	0.832500	−	0.554025i	$-0.186909\pi$
$5$	3.72305	1.66500	0.832500	+	0.554025i	$0.186909\pi$
$6$	6.83200	2.78915
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−2.43875	−0.862229
$9$	6.18494	2.06165
$10$	−8.39284	−2.65405
$11$	4.60514	1.38850	0.694251	−	0.719733i	$-0.255736\pi$
$11$	4.60514	1.38850	0.694251	+	0.719733i	$0.255736\pi$
$12$	−9.33999	−2.69622
$13$	6.90097	1.91399	0.956993	−	0.290112i	$-0.0936927\pi$
$13$	6.90097	1.91399	0.956993	+	0.290112i	$0.0936927\pi$
$14$	−2.25429	−0.602485
$15$	−11.2833	−2.91334
$16$	−0.665999	−0.166500
$17$	−2.74488	−0.665731	−0.332866	−	0.942974i	$-0.608016\pi$
$17$	−2.74488	−0.665731	−0.332866	+	0.942974i	$0.608016\pi$
$18$	−13.9427	−3.28632
$19$	4.67145	1.07170	0.535852	−	0.844312i	$-0.319990\pi$
$19$	4.67145	1.07170	0.535852	+	0.844312i	$0.319990\pi$
$20$	11.4738	2.56562
$21$	−3.03067	−0.661346
$22$	−10.3813	−2.21331
$23$	−1.63794	−0.341534	−0.170767	−	0.985311i	$-0.554625\pi$
$23$	−1.63794	−0.341534	−0.170767	+	0.985311i	$0.554625\pi$
$24$	7.39104	1.50869
$25$	8.86112	1.77222
$26$	−15.5568	−3.05094
$27$	−9.65250	−1.85763
$28$	3.08183	0.582410
$29$	−8.57376	−1.59211	−0.796054	−	0.605226i	$-0.793083\pi$
$29$	−8.57376	−1.59211	−0.796054	+	0.605226i	$0.793083\pi$
$30$	25.4359	4.64394
$31$	7.04253	1.26488	0.632438	−	0.774611i	$-0.282054\pi$
$31$	7.04253	1.26488	0.632438	+	0.774611i	$0.282054\pi$
$32$	6.37886	1.12763
$33$	−13.9567	−2.42954
$34$	6.18776	1.06119
$35$	3.72305	0.629311
$36$	19.0609	3.17682
$37$	−9.34078	−1.53562	−0.767808	−	0.640680i	$-0.778652\pi$
$37$	−9.34078	−1.53562	−0.767808	+	0.640680i	$0.778652\pi$
$38$	−10.5308	−1.70832
$39$	−20.9145	−3.34901
$40$	−9.07960	−1.43561
$41$	−0.689890	−0.107743	−0.0538714	−	0.998548i	$-0.517156\pi$
$41$	−0.689890	−0.107743	−0.0538714	+	0.998548i	$0.517156\pi$
$42$	6.83200	1.05420
$43$	3.66860	0.559457	0.279728	−	0.960079i	$-0.409756\pi$
$43$	3.66860	0.559457	0.279728	+	0.960079i	$0.409756\pi$
$44$	14.1923	2.13956
$45$	23.0269	3.43264
$46$	3.69239	0.544413
$47$	−4.36195	−0.636256	−0.318128	−	0.948048i	$-0.603054\pi$
$47$	−4.36195	−0.636256	−0.318128	+	0.948048i	$0.603054\pi$
$48$	2.01842	0.291334
$49$	1.00000	0.142857
$50$	−19.9755	−2.82497
$51$	8.31882	1.16487
$52$	21.2676	2.94929
$53$	−4.46864	−0.613815	−0.306907	−	0.951739i	$-0.599294\pi$
$53$	−4.46864	−0.613815	−0.306907	+	0.951739i	$0.599294\pi$
$54$	21.7596	2.96110
$55$	17.1452	2.31186
$56$	−2.43875	−0.325892
$57$	−14.1576	−1.87522
$58$	19.3278	2.53786
$59$	2.35520	0.306621	0.153310	−	0.988178i	$-0.451007\pi$
$59$	2.35520	0.306621	0.153310	+	0.988178i	$0.451007\pi$
$60$	−34.7733	−4.48921
$61$	5.59282	0.716088	0.358044	−	0.933705i	$-0.383444\pi$
$61$	5.59282	0.716088	0.358044	+	0.933705i	$0.383444\pi$
$62$	−15.8759	−2.01624
$63$	6.18494	0.779230
$64$	−13.0478	−1.63098
$65$	25.6927	3.18678
$66$	31.4624	3.87275
$67$	−5.53840	−0.676623	−0.338312	−	0.941034i	$-0.609856\pi$
$67$	−5.53840	−0.676623	−0.338312	+	0.941034i	$0.609856\pi$
$68$	−8.45924	−1.02583
$69$	4.96405	0.597601
$70$	−8.39284	−1.00314
$71$	13.6336	1.61801	0.809005	−	0.587801i	$-0.200006\pi$
$71$	13.6336	1.61801	0.809005	+	0.587801i	$0.200006\pi$
$72$	−15.0835	−1.77761
$73$	3.36845	0.394248	0.197124	−	0.980379i	$-0.436840\pi$
$73$	3.36845	0.394248	0.197124	+	0.980379i	$0.436840\pi$
$74$	21.0568	2.44781
$75$	−26.8551	−3.10096
$76$	14.3966	1.65140
$77$	4.60514	0.524805
$78$	47.1475	5.33840
$79$	−7.88014	−0.886585	−0.443293	−	0.896377i	$-0.646190\pi$
$79$	−7.88014	−0.886585	−0.443293	+	0.896377i	$0.646190\pi$
$80$	−2.47955	−0.277222
$81$	10.6987	1.18874
$82$	1.55521	0.171745
$83$	13.3384	1.46408	0.732039	−	0.681263i	$-0.238569\pi$
$83$	13.3384	1.46408	0.732039	+	0.681263i	$0.238569\pi$
$84$	−9.33999	−1.01908
$85$	−10.2193	−1.10844
$86$	−8.27009	−0.891787
$87$	25.9842	2.78580
$88$	−11.2308	−1.19721
$89$	−9.52845	−1.01001	−0.505007	−	0.863115i	$-0.668510\pi$
$89$	−9.52845	−1.01001	−0.505007	+	0.863115i	$0.668510\pi$
$90$	−51.9093	−5.47172
$91$	6.90097	0.723418
$92$	−5.04784	−0.526274
$93$	−21.3436	−2.21322
$94$	9.83311	1.01421
$95$	17.3921	1.78439
$96$	−19.3322	−1.97308
$97$	10.6575	1.08211	0.541054	−	0.840988i	$-0.318026\pi$
$97$	10.6575	1.08211	0.541054	+	0.840988i	$0.318026\pi$
$98$	−2.25429	−0.227718
$99$	28.4826	2.86260
$100$	27.3084	2.73084
$101$	12.4116	1.23500	0.617500	−	0.786571i	$-0.288146\pi$
$101$	12.4116	1.23500	0.617500	+	0.786571i	$0.288146\pi$
$102$	−18.7530	−1.85683
$103$	10.5713	1.04162	0.520809	−	0.853673i	$-0.325630\pi$
$103$	10.5713	1.04162	0.520809	+	0.853673i	$0.325630\pi$
$104$	−16.8298	−1.65029
$105$	−11.2833	−1.10114
$106$	10.0736	0.978436
$107$	−1.99044	−0.192423	−0.0962115	−	0.995361i	$-0.530673\pi$
$107$	−1.99044	−0.192423	−0.0962115	+	0.995361i	$0.530673\pi$
$108$	−29.7473	−2.86244
$109$	−12.2011	−1.16866	−0.584328	−	0.811517i	$-0.698642\pi$
$109$	−12.2011	−1.16866	−0.584328	+	0.811517i	$0.698642\pi$
$110$	−38.6502	−3.68516
$111$	28.3088	2.68695
$112$	−0.665999	−0.0629310
$113$	−1.01925	−0.0958833	−0.0479416	−	0.998850i	$-0.515266\pi$
$113$	−1.01925	−0.0958833	−0.0479416	+	0.998850i	$0.515266\pi$
$114$	31.9154	2.98915
$115$	−6.09813	−0.568654
$116$	−26.4228	−2.45330
$117$	42.6821	3.94596
$118$	−5.30930	−0.488761
$119$	−2.74488	−0.251623
$120$	27.5172	2.51197
$121$	10.2073	0.927940
$122$	−12.6078	−1.14146
$123$	2.09083	0.188524
$124$	21.7039	1.94906
$125$	14.3751	1.28575
$126$	−13.9427	−1.24211
$127$	4.26430	0.378395	0.189198	−	0.981939i	$-0.439411\pi$
$127$	4.26430	0.378395	0.189198	+	0.981939i	$0.439411\pi$
$128$	16.6558	1.47218
$129$	−11.1183	−0.978913
$130$	−57.9188	−5.07981
$131$	10.0596	0.878913	0.439457	−	0.898264i	$-0.355171\pi$
$131$	10.0596	0.878913	0.439457	+	0.898264i	$0.355171\pi$
$132$	−43.0120	−3.74371
$133$	4.67145	0.405066
$134$	12.4852	1.07855
$135$	−35.9368	−3.09295
$136$	6.69408	0.574013
$137$	−0.638694	−0.0545673	−0.0272836	−	0.999628i	$-0.508686\pi$
$137$	−0.638694	−0.0545673	−0.0272836	+	0.999628i	$0.508686\pi$
$138$	−11.1904	−0.952591
$139$	8.55547	0.725666	0.362833	−	0.931854i	$-0.381810\pi$
$139$	8.55547	0.725666	0.362833	+	0.931854i	$0.381810\pi$
$140$	11.4738	0.969713
$141$	13.2196	1.11329
$142$	−30.7341	−2.57915
$143$	31.7800	2.65757
$144$	−4.11916	−0.343264
$145$	−31.9206	−2.65086
$146$	−7.59347	−0.628440
$147$	−3.03067	−0.249965
$148$	−28.7867	−2.36625
$149$	14.6962	1.20396	0.601979	−	0.798512i	$-0.294379\pi$
$149$	14.6962	1.20396	0.601979	+	0.798512i	$0.294379\pi$
$150$	60.5392	4.94300
$151$	16.0298	1.30449	0.652244	−	0.758009i	$-0.273828\pi$
$151$	16.0298	1.30449	0.652244	+	0.758009i	$0.273828\pi$
$152$	−11.3925	−0.924055
$153$	−16.9769	−1.37250
$154$	−10.3813	−0.836552
$155$	26.2197	2.10602
$156$	−64.4550	−5.16053
$157$	−21.9839	−1.75451	−0.877254	−	0.480027i	$-0.840627\pi$
$157$	−21.9839	−1.75451	−0.877254	+	0.480027i	$0.840627\pi$
$158$	17.7641	1.41324
$159$	13.5430	1.07403
$160$	23.7488	1.87751
$161$	−1.63794	−0.129088
$162$	−24.1180	−1.89489
$163$	6.65472	0.521238	0.260619	−	0.965442i	$-0.416073\pi$
$163$	6.65472	0.521238	0.260619	+	0.965442i	$0.416073\pi$
$164$	−2.12612	−0.166022
$165$	−51.9614	−4.04519
$166$	−30.0686	−2.33378
$167$	−24.4448	−1.89160	−0.945799	−	0.324753i	$-0.894719\pi$
$167$	−24.4448	−1.89160	−0.945799	+	0.324753i	$0.894719\pi$
$168$	7.39104	0.570231
$169$	34.6234	2.66334
$170$	23.0373	1.76688
$171$	28.8927	2.20948
$172$	11.3060	0.862074
$173$	−24.0224	−1.82639	−0.913193	−	0.407527i	$-0.866391\pi$
$173$	−24.0224	−1.82639	−0.913193	+	0.407527i	$0.866391\pi$
$174$	−58.5760	−4.44063
$175$	8.86112	0.669837
$176$	−3.06702	−0.231185
$177$	−7.13783	−0.536512
$178$	21.4799	1.60999
$179$	7.27705	0.543912	0.271956	−	0.962310i	$-0.412329\pi$
$179$	7.27705	0.543912	0.271956	+	0.962310i	$0.412329\pi$
$180$	70.9648	5.28940
$181$	17.6274	1.31024	0.655119	−	0.755526i	$-0.272619\pi$
$181$	17.6274	1.31024	0.655119	+	0.755526i	$0.272619\pi$
$182$	−15.5568	−1.15315
$183$	−16.9500	−1.25298
$184$	3.99453	0.294480
$185$	−34.7762	−2.55680
$186$	48.1146	3.52793
$187$	−12.6406	−0.924370
$188$	−13.4428	−0.980416
$189$	−9.65250	−0.702116
$190$	−39.2068	−2.84436
$191$	−15.5032	−1.12177	−0.560885	−	0.827894i	$-0.689539\pi$
$191$	−15.5032	−1.12177	−0.560885	+	0.827894i	$0.689539\pi$
$192$	39.5435	2.85381
$193$	3.94362	0.283868	0.141934	−	0.989876i	$-0.454668\pi$
$193$	3.94362	0.283868	0.141934	+	0.989876i	$0.454668\pi$
$194$	−24.0252	−1.72491
$195$	−77.8659	−5.57610
$196$	3.08183	0.220130
$197$	−12.2876	−0.875458	−0.437729	−	0.899107i	$-0.644217\pi$
$197$	−12.2876	−0.875458	−0.437729	+	0.899107i	$0.644217\pi$
$198$	−64.2079	−4.56306
$199$	−10.6334	−0.753781	−0.376891	−	0.926258i	$-0.623007\pi$
$199$	−10.6334	−0.753781	−0.376891	+	0.926258i	$0.623007\pi$
$200$	−21.6101	−1.52806
$201$	16.7850	1.18393
$202$	−27.9793	−1.96862
$203$	−8.57376	−0.601760
$204$	25.6372	1.79496
$205$	−2.56850	−0.179392
$206$	−23.8307	−1.66036
$207$	−10.1306	−0.704123
$208$	−4.59604	−0.318678
$209$	21.5127	1.48807
$210$	25.4359	1.75524
$211$	22.9316	1.57867	0.789337	−	0.613960i	$-0.210424\pi$
$211$	22.9316	1.57867	0.789337	+	0.613960i	$0.210424\pi$
$212$	−13.7716	−0.945836
$213$	−41.3189	−2.83112
$214$	4.48703	0.306727
$215$	13.6584	0.931495
$216$	23.5401	1.60170
$217$	7.04253	0.478078
$218$	27.5049	1.86287
$219$	−10.2087	−0.689837
$220$	52.8385	3.56237
$221$	−18.9423	−1.27420
$222$	−63.8163	−4.28307
$223$	5.08809	0.340723	0.170362	−	0.985382i	$-0.445506\pi$
$223$	5.08809	0.340723	0.170362	+	0.985382i	$0.445506\pi$
$224$	6.37886	0.426205
$225$	54.8055	3.65370
$226$	2.29769	0.152840
$227$	8.36899	0.555470	0.277735	−	0.960658i	$-0.410416\pi$
$227$	8.36899	0.555470	0.277735	+	0.960658i	$0.410416\pi$
$228$	−43.6313	−2.88956
$229$	−25.7656	−1.70264	−0.851320	−	0.524646i	$-0.824198\pi$
$229$	−25.7656	−1.70264	−0.851320	+	0.524646i	$0.824198\pi$
$230$	13.7470	0.906448
$231$	−13.9567	−0.918281
$232$	20.9093	1.37276
$233$	−3.54921	−0.232517	−0.116258	−	0.993219i	$-0.537090\pi$
$233$	−3.54921	−0.232517	−0.116258	+	0.993219i	$0.537090\pi$
$234$	−96.2179	−6.28996
$235$	−16.2398	−1.05937
$236$	7.25832	0.472476
$237$	23.8821	1.55131
$238$	6.18776	0.401093
$239$	3.40779	0.220431	0.110216	−	0.993908i	$-0.464846\pi$
$239$	3.40779	0.220431	0.110216	+	0.993908i	$0.464846\pi$
$240$	7.51468	0.485071
$241$	−13.7734	−0.887223	−0.443611	−	0.896219i	$-0.646303\pi$
$241$	−13.7734	−0.887223	−0.443611	+	0.896219i	$0.646303\pi$
$242$	−23.0103	−1.47916
$243$	−3.46668	−0.222387
$244$	17.2361	1.10343
$245$	3.72305	0.237857
$246$	−4.71333	−0.300511
$247$	32.2376	2.05123
$248$	−17.1750	−1.09061
$249$	−40.4242	−2.56178
$250$	−32.4057	−2.04952
$251$	9.39040	0.592717	0.296358	−	0.955077i	$-0.404228\pi$
$251$	9.39040	0.592717	0.296358	+	0.955077i	$0.404228\pi$
$252$	19.0609	1.20073
$253$	−7.54294	−0.474221
$254$	−9.61297	−0.603171
$255$	30.9714	1.93950
$256$	−11.4515	−0.715716
$257$	−11.2074	−0.699100	−0.349550	−	0.936918i	$-0.613666\pi$
$257$	−11.2074	−0.699100	−0.349550	+	0.936918i	$0.613666\pi$
$258$	25.0639	1.56041
$259$	−9.34078	−0.580408
$260$	79.1804	4.91056
$261$	−53.0282	−3.28237
$262$	−22.6773	−1.40101
$263$	−16.5851	−1.02268	−0.511340	−	0.859379i	$-0.670851\pi$
$263$	−16.5851	−1.02268	−0.511340	+	0.859379i	$0.670851\pi$
$264$	34.0368	2.09482
$265$	−16.6370	−1.02200
$266$	−10.5308	−0.645686
$267$	28.8776	1.76728
$268$	−17.0684	−1.04262
$269$	−7.57053	−0.461584	−0.230792	−	0.973003i	$-0.574132\pi$
$269$	−7.57053	−0.461584	−0.230792	+	0.973003i	$0.574132\pi$
$270$	81.0119	4.93023
$271$	−9.05037	−0.549771	−0.274885	−	0.961477i	$-0.588640\pi$
$271$	−9.05037	−0.549771	−0.274885	+	0.961477i	$0.588640\pi$
$272$	1.82809	0.110844
$273$	−20.9145	−1.26581
$274$	1.43980	0.0869815
$275$	40.8067	2.46074
$276$	15.2983	0.920851
$277$	−11.9485	−0.717916	−0.358958	−	0.933354i	$-0.616868\pi$
$277$	−11.9485	−0.717916	−0.358958	+	0.933354i	$0.616868\pi$
$278$	−19.2865	−1.15673
$279$	43.5576	2.60773
$280$	−9.07960	−0.542610
$281$	17.3429	1.03459	0.517295	−	0.855807i	$-0.326939\pi$
$281$	17.3429	1.03459	0.517295	+	0.855807i	$0.326939\pi$
$282$	−29.8009	−1.77462
$283$	7.10486	0.422340	0.211170	−	0.977449i	$-0.432273\pi$
$283$	7.10486	0.422340	0.211170	+	0.977449i	$0.432273\pi$
$284$	42.0164	2.49321
$285$	−52.7096	−3.12224
$286$	−71.6413	−4.23624
$287$	−0.689890	−0.0407229
$288$	39.4529	2.32478
$289$	−9.46563	−0.556802
$290$	71.9582	4.22553
$291$	−32.2994	−1.89343
$292$	10.3810	0.607501
$293$	15.2871	0.893080	0.446540	−	0.894764i	$-0.352656\pi$
$293$	15.2871	0.893080	0.446540	+	0.894764i	$0.352656\pi$
$294$	6.83200	0.398451
$295$	8.76853	0.510524
$296$	22.7798	1.32405
$297$	−44.4512	−2.57932
$298$	−33.1294	−1.91914
$299$	−11.3034	−0.653691
$300$	−82.7627	−4.77831
$301$	3.66860	0.211455
$302$	−36.1359	−2.07939
$303$	−37.6154	−2.16095
$304$	−3.11118	−0.178439
$305$	20.8224	1.19229
$306$	38.2709	2.18780
$307$	−28.3238	−1.61652	−0.808262	−	0.588823i	$-0.799591\pi$
$307$	−28.3238	−1.61652	−0.808262	+	0.588823i	$0.799591\pi$
$308$	14.1923	0.808679
$309$	−32.0380	−1.82258
$310$	−59.1068	−3.35704
$311$	21.5050	1.21944	0.609718	−	0.792618i	$-0.291283\pi$
$311$	21.5050	1.21944	0.609718	+	0.792618i	$0.291283\pi$
$312$	51.0054	2.88761
$313$	20.3159	1.14833	0.574163	−	0.818741i	$-0.305328\pi$
$313$	20.3159	1.14833	0.574163	+	0.818741i	$0.305328\pi$
$314$	49.5581	2.79673
$315$	23.0269	1.29742
$316$	−24.2852	−1.36615
$317$	19.3504	1.08683	0.543413	−	0.839465i	$-0.317132\pi$
$317$	19.3504	1.08683	0.543413	+	0.839465i	$0.317132\pi$
$318$	−30.5298	−1.71202
$319$	−39.4834	−2.21065
$320$	−48.5776	−2.71557
$321$	6.03236	0.336693
$322$	3.69239	0.205769
$323$	−12.8226	−0.713467
$324$	32.9715	1.83175
$325$	61.1503	3.39201
$326$	−15.0017	−0.830865
$327$	36.9776	2.04486
$328$	1.68247	0.0928989
$329$	−4.36195	−0.240482
$330$	117.136	6.44812
$331$	−11.3451	−0.623584	−0.311792	−	0.950150i	$-0.600929\pi$
$331$	−11.3451	−0.623584	−0.311792	+	0.950150i	$0.600929\pi$
$332$	41.1066	2.25602
$333$	−57.7722	−3.16590
$334$	55.1058	3.01525
$335$	−20.6197	−1.12658
$336$	2.01842	0.110114
$337$	2.99034	0.162894	0.0814472	−	0.996678i	$-0.474046\pi$
$337$	2.99034	0.162894	0.0814472	+	0.996678i	$0.474046\pi$
$338$	−78.0512	−4.24543
$339$	3.08902	0.167772
$340$	−31.4942	−1.70801
$341$	32.4319	1.75628
$342$	−65.1325	−3.52196
$343$	1.00000	0.0539949
$344$	−8.94681	−0.482379
$345$	18.4814	0.995006
$346$	54.1534	2.91130
$347$	29.7605	1.59763	0.798814	−	0.601578i	$-0.205461\pi$
$347$	29.7605	1.59763	0.798814	+	0.601578i	$0.205461\pi$
$348$	80.0789	4.29268
$349$	21.0109	1.12469	0.562344	−	0.826903i	$-0.309900\pi$
$349$	21.0109	1.12469	0.562344	+	0.826903i	$0.309900\pi$
$350$	−19.9755	−1.06774
$351$	−66.6117	−3.55547
$352$	29.3756	1.56572
$353$	9.94228	0.529174	0.264587	−	0.964362i	$-0.414764\pi$
$353$	9.94228	0.529174	0.264587	+	0.964362i	$0.414764\pi$
$354$	16.0907	0.855213
$355$	50.7586	2.69399
$356$	−29.3650	−1.55634
$357$	8.31882	0.440279
$358$	−16.4046	−0.867009
$359$	26.2079	1.38320	0.691600	−	0.722281i	$-0.256906\pi$
$359$	26.2079	1.38320	0.691600	+	0.722281i	$0.256906\pi$
$360$	−56.1568	−2.95972
$361$	2.82248	0.148551
$362$	−39.7374	−2.08855
$363$	−30.9351	−1.62367
$364$	21.2676	1.11472
$365$	12.5409	0.656422
$366$	38.2102	1.99728
$367$	14.9036	0.777964	0.388982	−	0.921245i	$-0.372827\pi$
$367$	14.9036	0.777964	0.388982	+	0.921245i	$0.372827\pi$
$368$	1.09087	0.0568653
$369$	−4.26693	−0.222128
$370$	78.3957	4.07560
$371$	−4.46864	−0.232000
$372$	−65.7771	−3.41039
$373$	23.8075	1.23271	0.616353	−	0.787470i	$-0.288609\pi$
$373$	23.8075	1.23271	0.616353	+	0.787470i	$0.288609\pi$
$374$	28.4955	1.47347
$375$	−43.5662	−2.24975
$376$	10.6377	0.548598
$377$	−59.1673	−3.04727
$378$	21.7596	1.11919
$379$	−12.3314	−0.633421	−0.316711	−	0.948522i	$-0.602578\pi$
$379$	−12.3314	−0.633421	−0.316711	+	0.948522i	$0.602578\pi$
$380$	53.5993	2.74959
$381$	−12.9237	−0.662100
$382$	34.9487	1.78813
$383$	−27.5813	−1.40934	−0.704670	−	0.709535i	$-0.748905\pi$
$383$	−27.5813	−1.40934	−0.704670	+	0.709535i	$0.748905\pi$
$384$	−50.4783	−2.57596
$385$	17.1452	0.873800
$386$	−8.89007	−0.452493
$387$	22.6901	1.15340
$388$	32.8446	1.66743
$389$	26.7330	1.35541	0.677707	−	0.735332i	$-0.262974\pi$
$389$	26.7330	1.35541	0.677707	+	0.735332i	$0.262974\pi$
$390$	175.532	8.88843
$391$	4.49595	0.227370
$392$	−2.43875	−0.123176
$393$	−30.4874	−1.53788
$394$	27.6999	1.39550
$395$	−29.3382	−1.47616
$396$	87.7783	4.41102
$397$	28.1100	1.41080	0.705400	−	0.708809i	$-0.250767\pi$
$397$	28.1100	1.41080	0.705400	+	0.708809i	$0.250767\pi$
$398$	23.9708	1.20155
$399$	−14.1576	−0.708768
$400$	−5.90149	−0.295075
$401$	−17.1713	−0.857493	−0.428747	−	0.903425i	$-0.641045\pi$
$401$	−17.1713	−0.857493	−0.428747	+	0.903425i	$0.641045\pi$
$402$	−37.8384	−1.88721
$403$	48.6003	2.42095
$404$	38.2504	1.90303
$405$	39.8318	1.97926
$406$	19.3278	0.959220
$407$	−43.0156	−2.13221
$408$	−20.2875	−1.00438
$409$	−7.38916	−0.365371	−0.182685	−	0.983171i	$-0.558479\pi$
$409$	−7.38916	−0.365371	−0.182685	+	0.983171i	$0.558479\pi$
$410$	5.79014	0.285955
$411$	1.93567	0.0954794
$412$	32.5788	1.60504
$413$	2.35520	0.115892
$414$	22.8372	1.12239
$415$	49.6595	2.43769
$416$	44.0203	2.15827
$417$	−25.9288	−1.26974
$418$	−48.4959	−2.37201
$419$	36.9104	1.80319	0.901595	−	0.432582i	$-0.142397\pi$
$419$	36.9104	1.80319	0.901595	+	0.432582i	$0.142397\pi$
$420$	−34.7733	−1.69676
$421$	−5.91626	−0.288341	−0.144170	−	0.989553i	$-0.546051\pi$
$421$	−5.91626	−0.288341	−0.144170	+	0.989553i	$0.546051\pi$
$422$	−51.6944	−2.51645
$423$	−26.9784	−1.31174
$424$	10.8979	0.529249
$425$	−24.3227	−1.17982
$426$	93.1448	4.51288
$427$	5.59282	0.270656
$428$	−6.13418	−0.296507
$429$	−96.3145	−4.65011
$430$	−30.7900	−1.48483
$431$	−35.5724	−1.71346	−0.856731	−	0.515763i	$-0.827508\pi$
$431$	−35.5724	−1.71346	−0.856731	+	0.515763i	$0.827508\pi$
$432$	6.42856	0.309294
$433$	−27.3652	−1.31509	−0.657543	−	0.753417i	$-0.728404\pi$
$433$	−27.3652	−1.31509	−0.657543	+	0.753417i	$0.728404\pi$
$434$	−15.8759	−0.762068
$435$	96.7406	4.63836
$436$	−37.6018	−1.80080
$437$	−7.65156	−0.366024
$438$	23.0133	1.09962
$439$	−12.5989	−0.601313	−0.300657	−	0.953732i	$-0.597206\pi$
$439$	−12.5989	−0.601313	−0.300657	+	0.953732i	$0.597206\pi$
$440$	−41.8128	−1.99335
$441$	6.18494	0.294521
$442$	42.7015	2.03111
$443$	−31.5810	−1.50046	−0.750229	−	0.661178i	$-0.770057\pi$
$443$	−31.5810	−1.50046	−0.750229	+	0.661178i	$0.770057\pi$
$444$	87.2428	4.14036
$445$	−35.4749	−1.68167
$446$	−11.4700	−0.543121
$447$	−44.5392	−2.10663
$448$	−13.0478	−0.616451
$449$	−20.8281	−0.982940	−0.491470	−	0.870895i	$-0.663540\pi$
$449$	−20.8281	−0.982940	−0.491470	+	0.870895i	$0.663540\pi$
$450$	−123.548	−5.82409
$451$	−3.17704	−0.149601
$452$	−3.14116	−0.147748
$453$	−48.5811	−2.28254
$454$	−18.8661	−0.885432
$455$	25.6927	1.20449
$456$	34.5269	1.61687
$457$	18.3454	0.858159	0.429080	−	0.903267i	$-0.358838\pi$
$457$	18.3454	0.858159	0.429080	+	0.903267i	$0.358838\pi$
$458$	58.0832	2.71405
$459$	26.4950	1.23668
$460$	−18.7934	−0.876246
$461$	26.3289	1.22626	0.613129	−	0.789983i	$-0.289911\pi$
$461$	26.3289	1.22626	0.613129	+	0.789983i	$0.289911\pi$
$462$	31.4624	1.46376
$463$	−24.1152	−1.12073	−0.560363	−	0.828247i	$-0.689338\pi$
$463$	−24.1152	−1.12073	−0.560363	+	0.828247i	$0.689338\pi$
$464$	5.71012	0.265085
$465$	−79.4632	−3.68502
$466$	8.00095	0.370637
$467$	−8.90721	−0.412177	−0.206088	−	0.978533i	$-0.566073\pi$
$467$	−8.90721	−0.412177	−0.206088	+	0.978533i	$0.566073\pi$
$468$	131.539	6.08039
$469$	−5.53840	−0.255739
$470$	36.6092	1.68866
$471$	66.6259	3.06996
$472$	−5.74375	−0.264377
$473$	16.8944	0.776807
$474$	−53.8372	−2.47282
$475$	41.3943	1.89930
$476$	−8.45924	−0.387729
$477$	−27.6383	−1.26547
$478$	−7.68214	−0.351373
$479$	−37.8103	−1.72760	−0.863799	−	0.503837i	$-0.831921\pi$
$479$	−37.8103	−1.72760	−0.863799	+	0.503837i	$0.831921\pi$
$480$	−71.9748	−3.28518
$481$	−64.4605	−2.93914
$482$	31.0493	1.41425
$483$	4.96405	0.225872
$484$	31.4573	1.42988
$485$	39.6785	1.80171
$486$	7.81490	0.354491
$487$	14.1828	0.642682	0.321341	−	0.946964i	$-0.395866\pi$
$487$	14.1828	0.642682	0.321341	+	0.946964i	$0.395866\pi$
$488$	−13.6395	−0.617431
$489$	−20.1682	−0.912039
$490$	−8.39284	−0.379150
$491$	4.26214	0.192348	0.0961739	−	0.995365i	$-0.469339\pi$
$491$	4.26214	0.192348	0.0961739	+	0.995365i	$0.469339\pi$
$492$	6.44357	0.290498
$493$	23.5340	1.05992
$494$	−72.6728	−3.26971
$495$	106.042	4.76623
$496$	−4.69032	−0.210601
$497$	13.6336	0.611551
$498$	91.1279	4.08354
$499$	38.3623	1.71733	0.858667	−	0.512535i	$-0.171293\pi$
$499$	38.3623	1.71733	0.858667	+	0.512535i	$0.171293\pi$
$500$	44.3017	1.98123
$501$	74.0841	3.30984
$502$	−21.1687	−0.944805
$503$	−19.9391	−0.889040	−0.444520	−	0.895769i	$-0.646626\pi$
$503$	−19.9391	−0.889040	−0.444520	+	0.895769i	$0.646626\pi$
$504$	−15.0835	−0.671874
$505$	46.2090	2.05627
$506$	17.0040	0.755919
$507$	−104.932	−4.66020
$508$	13.1418	0.583074
$509$	11.7075	0.518928	0.259464	−	0.965753i	$-0.416454\pi$
$509$	11.7075	0.518928	0.259464	+	0.965753i	$0.416454\pi$
$510$	−69.8185	−3.09162
$511$	3.36845	0.149012
$512$	−7.49672	−0.331311
$513$	−45.0912	−1.99083
$514$	25.2648	1.11438
$515$	39.3574	1.73429
$516$	−34.2647	−1.50842
$517$	−20.0874	−0.883444
$518$	21.0568	0.925184
$519$	72.8038	3.19573
$520$	−62.6580	−2.74774
$521$	21.9536	0.961805	0.480903	−	0.876774i	$-0.340309\pi$
$521$	21.9536	0.961805	0.480903	+	0.876774i	$0.340309\pi$
$522$	119.541	5.23217
$523$	21.2931	0.931081	0.465540	−	0.885027i	$-0.345860\pi$
$523$	21.2931	0.931081	0.465540	+	0.885027i	$0.345860\pi$
$524$	31.0020	1.35433
$525$	−26.8551	−1.17205
$526$	37.3876	1.63018
$527$	−19.3309	−0.842067
$528$	9.29512	0.404518
$529$	−20.3172	−0.883355
$530$	37.5046	1.62910
$531$	14.5668	0.632144
$532$	14.3966	0.624172
$533$	−4.76091	−0.206218
$534$	−65.0984	−2.81708
$535$	−7.41050	−0.320384
$536$	13.5068	0.583404
$537$	−22.0543	−0.951714
$538$	17.0662	0.735775
$539$	4.60514	0.198358
$540$	−110.751	−4.76596
$541$	37.4091	1.60834	0.804171	−	0.594398i	$-0.202609\pi$
$541$	37.4091	1.60834	0.804171	+	0.594398i	$0.202609\pi$
$542$	20.4022	0.876348
$543$	−53.4229	−2.29260
$544$	−17.5092	−0.750701
$545$	−45.4254	−1.94581
$546$	47.1475	2.01773
$547$	24.5552	1.04990	0.524952	−	0.851132i	$-0.324083\pi$
$547$	24.5552	1.04990	0.524952	+	0.851132i	$0.324083\pi$
$548$	−1.96834	−0.0840834
$549$	34.5913	1.47632
$550$	−91.9902	−3.92247
$551$	−40.0519	−1.70627
$552$	−12.1061	−0.515269
$553$	−7.88014	−0.335098
$554$	26.9354	1.14438
$555$	105.395	4.47378
$556$	26.3665	1.11819
$557$	21.0497	0.891904	0.445952	−	0.895057i	$-0.352865\pi$
$557$	21.0497	0.891904	0.445952	+	0.895057i	$0.352865\pi$
$558$	−98.1916	−4.15678
$559$	25.3169	1.07079
$560$	−2.47955	−0.104780
$561$	38.3093	1.61742
$562$	−39.0959	−1.64916
$563$	−36.1074	−1.52175	−0.760873	−	0.648901i	$-0.775229\pi$
$563$	−36.1074	−1.52175	−0.760873	+	0.648901i	$0.775229\pi$
$564$	40.7406	1.71549
$565$	−3.79473	−0.159646
$566$	−16.0164	−0.673221
$567$	10.6987	0.449303
$568$	−33.2490	−1.39510
$569$	−20.8710	−0.874956	−0.437478	−	0.899229i	$-0.644128\pi$
$569$	−20.8710	−0.874956	−0.437478	+	0.899229i	$0.644128\pi$
$570$	118.823	4.97693
$571$	21.0708	0.881786	0.440893	−	0.897560i	$-0.354662\pi$
$571$	21.0708	0.881786	0.440893	+	0.897560i	$0.354662\pi$
$572$	97.9403	4.09509
$573$	46.9850	1.96283
$574$	1.55521	0.0649133
$575$	−14.5140	−0.605274
$576$	−80.6999	−3.36250
$577$	−9.03741	−0.376232	−0.188116	−	0.982147i	$-0.560238\pi$
$577$	−9.03741	−0.376232	−0.188116	+	0.982147i	$0.560238\pi$
$578$	21.3383	0.887556
$579$	−11.9518	−0.496700
$580$	−98.3736	−4.08474
$581$	13.3384	0.553369
$582$	72.8123	3.01817
$583$	−20.5787	−0.852284
$584$	−8.21482	−0.339932
$585$	158.908	6.57003
$586$	−34.4615	−1.42359
$587$	11.2515	0.464397	0.232199	−	0.972668i	$-0.425408\pi$
$587$	11.2515	0.464397	0.232199	+	0.972668i	$0.425408\pi$
$588$	−9.33999	−0.385175
$589$	32.8988	1.35557
$590$	−19.7668	−0.813787
$591$	37.2397	1.53184
$592$	6.22095	0.255679
$593$	−2.67163	−0.109711	−0.0548554	−	0.998494i	$-0.517470\pi$
$593$	−2.67163	−0.109711	−0.0548554	+	0.998494i	$0.517470\pi$
$594$	100.206	4.11150
$595$	−10.2193	−0.418952
$596$	45.2911	1.85519
$597$	32.2263	1.31893
$598$	25.4811	1.04200
$599$	4.78630	0.195563	0.0977815	−	0.995208i	$-0.468825\pi$
$599$	4.78630	0.195563	0.0977815	+	0.995208i	$0.468825\pi$
$600$	65.4929	2.67374
$601$	35.2968	1.43978	0.719892	−	0.694086i	$-0.244191\pi$
$601$	35.2968	1.43978	0.719892	+	0.694086i	$0.244191\pi$
$602$	−8.27009	−0.337064
$603$	−34.2547	−1.39496
$604$	49.4011	2.01010
$605$	38.0025	1.54502
$606$	84.7961	3.44460
$607$	26.6218	1.08054	0.540272	−	0.841490i	$-0.318321\pi$
$607$	26.6218	1.08054	0.540272	+	0.841490i	$0.318321\pi$
$608$	29.7985	1.20849
$609$	25.9842	1.05293
$610$	−46.9397	−1.90053
$611$	−30.1017	−1.21779
$612$	−52.3199	−2.11491
$613$	39.2277	1.58439	0.792195	−	0.610268i	$-0.208938\pi$
$613$	39.2277	1.58439	0.792195	+	0.610268i	$0.208938\pi$
$614$	63.8500	2.57678
$615$	7.78426	0.313892
$616$	−11.2308	−0.452502
$617$	−28.0508	−1.12928	−0.564641	−	0.825337i	$-0.690985\pi$
$617$	−28.0508	−1.12928	−0.564641	+	0.825337i	$0.690985\pi$
$618$	72.2230	2.90523
$619$	−27.9342	−1.12277	−0.561386	−	0.827554i	$-0.689732\pi$
$619$	−27.9342	−1.12277	−0.561386	+	0.827554i	$0.689732\pi$
$620$	80.8046	3.24519
$621$	15.8102	0.634442
$622$	−48.4785	−1.94381
$623$	−9.52845	−0.381749
$624$	13.9291	0.557609
$625$	9.21379	0.368552
$626$	−45.7980	−1.83046
$627$	−65.1979	−2.60375
$628$	−67.7506	−2.70354
$629$	25.6393	1.02231
$630$	−51.9093	−2.06811
$631$	38.9245	1.54956	0.774779	−	0.632232i	$-0.217861\pi$
$631$	38.9245	1.54956	0.774779	+	0.632232i	$0.217861\pi$
$632$	19.2177	0.764439
$633$	−69.4980	−2.76230
$634$	−43.6214	−1.73243
$635$	15.8762	0.630028
$636$	41.7371	1.65498
$637$	6.90097	0.273426
$638$	89.0071	3.52382
$639$	84.3230	3.33577
$640$	62.0105	2.45118
$641$	24.6770	0.974682	0.487341	−	0.873212i	$-0.337967\pi$
$641$	24.6770	0.974682	0.487341	+	0.873212i	$0.337967\pi$
$642$	−13.5987	−0.536697
$643$	−32.9601	−1.29982	−0.649911	−	0.760011i	$-0.725194\pi$
$643$	−32.9601	−1.29982	−0.649911	+	0.760011i	$0.725194\pi$
$644$	−5.04784	−0.198913
$645$	−41.3940	−1.62989
$646$	28.9058	1.13728
$647$	−40.9674	−1.61060	−0.805298	−	0.592870i	$-0.797995\pi$
$647$	−40.9674	−1.61060	−0.805298	+	0.592870i	$0.797995\pi$
$648$	−26.0915	−1.02497
$649$	10.8460	0.425744
$650$	−137.851	−5.40694
$651$	−21.3436	−0.836520
$652$	20.5087	0.803182
$653$	−44.7385	−1.75075	−0.875376	−	0.483442i	$-0.839386\pi$
$653$	−44.7385	−1.75075	−0.875376	+	0.483442i	$0.839386\pi$
$654$	−83.3582	−3.25956
$655$	37.4525	1.46339
$656$	0.459466	0.0179391
$657$	20.8337	0.812800
$658$	9.83311	0.383335
$659$	−43.8139	−1.70675	−0.853373	−	0.521300i	$-0.825447\pi$
$659$	−43.8139	−1.70675	−0.853373	+	0.521300i	$0.825447\pi$
$660$	−160.136	−6.23328
$661$	−6.02501	−0.234346	−0.117173	−	0.993112i	$-0.537383\pi$
$661$	−6.02501	−0.234346	−0.117173	+	0.993112i	$0.537383\pi$
$662$	25.5752	0.994009
$663$	57.4079	2.22954
$664$	−32.5290	−1.26237
$665$	17.3921	0.674435
$666$	130.235	5.04652
$667$	14.0433	0.543759
$668$	−75.3347	−2.91479
$669$	−15.4203	−0.596183
$670$	46.4829	1.79579
$671$	25.7557	0.994290
$672$	−19.3322	−0.745756
$673$	6.44598	0.248474	0.124237	−	0.992253i	$-0.460352\pi$
$673$	6.44598	0.248474	0.124237	+	0.992253i	$0.460352\pi$
$674$	−6.74111	−0.259658
$675$	−85.5320	−3.29213
$676$	106.703	4.10397
$677$	−7.30889	−0.280903	−0.140452	−	0.990088i	$-0.544855\pi$
$677$	−7.30889	−0.280903	−0.140452	+	0.990088i	$0.544855\pi$
$678$	−6.96354	−0.267433
$679$	10.6575	0.408998
$680$	24.9224	0.955731
$681$	−25.3636	−0.971936
$682$	−73.1108	−2.79956
$683$	−11.5913	−0.443530	−0.221765	−	0.975100i	$-0.571182\pi$
$683$	−11.5913	−0.443530	−0.221765	+	0.975100i	$0.571182\pi$
$684$	89.0422	3.40461
$685$	−2.37789	−0.0908545
$686$	−2.25429	−0.0860692
$687$	78.0871	2.97921
$688$	−2.44328	−0.0931493
$689$	−30.8380	−1.17483
$690$	−41.6625	−1.58606
$691$	10.1183	0.384919	0.192459	−	0.981305i	$-0.438354\pi$
$691$	10.1183	0.384919	0.192459	+	0.981305i	$0.438354\pi$
$692$	−74.0328	−2.81430
$693$	28.4826	1.08196
$694$	−67.0888	−2.54666
$695$	31.8525	1.20823
$696$	−63.3691	−2.40200
$697$	1.89367	0.0717277
$698$	−47.3647	−1.79278
$699$	10.7565	0.406847
$700$	27.3084	1.03216
$701$	0.686891	0.0259435	0.0129718	−	0.999916i	$-0.495871\pi$
$701$	0.686891	0.0259435	0.0129718	+	0.999916i	$0.495871\pi$
$702$	150.162	5.66750
$703$	−43.6350	−1.64573
$704$	−60.0870	−2.26461
$705$	49.2174	1.85363
$706$	−22.4128	−0.843516
$707$	12.4116	0.466786
$708$	−21.9975	−0.826718
$709$	20.6481	0.775454	0.387727	−	0.921774i	$-0.373260\pi$
$709$	20.6481	0.775454	0.387727	+	0.921774i	$0.373260\pi$
$710$	−114.425	−4.29428
$711$	−48.7382	−1.82783
$712$	23.2375	0.870863
$713$	−11.5352	−0.431998
$714$	−18.7530	−0.701815
$715$	118.318	4.42486
$716$	22.4266	0.838121
$717$	−10.3279	−0.385701
$718$	−59.0802	−2.20485
$719$	17.0181	0.634669	0.317334	−	0.948314i	$-0.397212\pi$
$719$	17.0181	0.634669	0.317334	+	0.948314i	$0.397212\pi$
$720$	−15.3359	−0.571534
$721$	10.5713	0.393695
$722$	−6.36268	−0.236795
$723$	41.7426	1.55242
$724$	54.3247	2.01896
$725$	−75.9731	−2.82157
$726$	69.7366	2.58817
$727$	37.6283	1.39556	0.697779	−	0.716313i	$-0.254172\pi$
$727$	37.6283	1.39556	0.697779	+	0.716313i	$0.254172\pi$
$728$	−16.8298	−0.623752
$729$	−21.5897	−0.799620
$730$	−28.2709	−1.04635
$731$	−10.0699	−0.372448
$732$	−52.2369	−1.93073
$733$	−9.87426	−0.364714	−0.182357	−	0.983232i	$-0.558373\pi$
$733$	−9.87426	−0.364714	−0.182357	+	0.983232i	$0.558373\pi$
$734$	−33.5971	−1.24009
$735$	−11.2833	−0.416192
$736$	−10.4482	−0.385125
$737$	−25.5051	−0.939493
$738$	9.61890	0.354077
$739$	23.6321	0.869323	0.434661	−	0.900594i	$-0.356868\pi$
$739$	23.6321	0.869323	0.434661	+	0.900594i	$0.356868\pi$
$740$	−107.174	−3.93980
$741$	−97.7013	−3.58915
$742$	10.0736	0.369814
$743$	29.0739	1.06662	0.533308	−	0.845921i	$-0.320949\pi$
$743$	29.0739	1.06662	0.533308	+	0.845921i	$0.320949\pi$
$744$	52.0516	1.90831
$745$	54.7146	2.00459
$746$	−53.6691	−1.96496
$747$	82.4971	3.01841
$748$	−38.9560	−1.42437
$749$	−1.99044	−0.0727290
$750$	98.2110	3.58616
$751$	−21.1003	−0.769960	−0.384980	−	0.922925i	$-0.625792\pi$
$751$	−21.1003	−0.769960	−0.384980	+	0.922925i	$0.625792\pi$
$752$	2.90506	0.105936
$753$	−28.4592	−1.03711
$754$	133.380	4.85742
$755$	59.6799	2.17197
$756$	−29.7473	−1.08190
$757$	29.3371	1.06628	0.533138	−	0.846028i	$-0.321013\pi$
$757$	29.3371	1.06628	0.533138	+	0.846028i	$0.321013\pi$
$758$	27.7986	1.00969
$759$	22.8602	0.829771
$760$	−42.4149	−1.53855
$761$	−52.5553	−1.90513	−0.952563	−	0.304340i	$-0.901564\pi$
$761$	−52.5553	−1.90513	−0.952563	+	0.304340i	$0.901564\pi$
$762$	29.1337	1.05540
$763$	−12.2011	−0.441711
$764$	−47.7781	−1.72855
$765$	−63.2060	−2.28522
$766$	62.1763	2.24652
$767$	16.2532	0.586868
$768$	34.7056	1.25233
$769$	−29.7038	−1.07115	−0.535573	−	0.844489i	$-0.679904\pi$
$769$	−29.7038	−1.07115	−0.535573	+	0.844489i	$0.679904\pi$
$770$	−38.6502	−1.39286
$771$	33.9660	1.22326
$772$	12.1536	0.437416
$773$	−21.9188	−0.788366	−0.394183	−	0.919032i	$-0.628972\pi$
$773$	−21.9188	−0.788366	−0.394183	+	0.919032i	$0.628972\pi$
$774$	−51.1501	−1.83855
$775$	62.4047	2.24164
$776$	−25.9911	−0.933024
$777$	28.3088	1.01557
$778$	−60.2639	−2.16056
$779$	−3.22279	−0.115468
$780$	−239.969	−8.59228
$781$	62.7847	2.24661
$782$	−10.1352	−0.362433
$783$	82.7583	2.95754
$784$	−0.665999	−0.0237857
$785$	−81.8473	−2.92125
$786$	68.7274	2.45143
$787$	44.5772	1.58901	0.794503	−	0.607261i	$-0.207732\pi$
$787$	44.5772	1.58901	0.794503	+	0.607261i	$0.207732\pi$
$788$	−37.8684	−1.34900
$789$	50.2638	1.78944
$790$	66.1368	2.35304
$791$	−1.01925	−0.0362405
$792$	−69.4619	−2.46822
$793$	38.5959	1.37058
$794$	−63.3681	−2.24885
$795$	50.4211	1.78825
$796$	−32.7703	−1.16151
$797$	0.0778664	0.00275817	0.00137909	−	0.999999i	$-0.499561\pi$
$797$	0.0778664	0.00275817	0.00137909	+	0.999999i	$0.499561\pi$
$798$	31.9154	1.12979
$799$	11.9730	0.423576
$800$	56.5238	1.99842
$801$	−58.9329	−2.08229
$802$	38.7091	1.36686
$803$	15.5122	0.547414
$804$	51.7286	1.82433
$805$	−6.09813	−0.214931
$806$	−109.559	−3.85906
$807$	22.9438	0.807659
$808$	−30.2688	−1.06485
$809$	−26.2864	−0.924182	−0.462091	−	0.886833i	$-0.652901\pi$
$809$	−26.2864	−0.924182	−0.462091	+	0.886833i	$0.652901\pi$
$810$	−89.7925	−3.15499
$811$	−11.0002	−0.386270	−0.193135	−	0.981172i	$-0.561865\pi$
$811$	−11.0002	−0.386270	−0.193135	+	0.981172i	$0.561865\pi$
$812$	−26.4228	−0.927260
$813$	27.4286	0.961965
$814$	96.9698	3.39879
$815$	24.7759	0.867860
$816$	−5.54032	−0.193950
$817$	17.1377	0.599572
$818$	16.6573	0.582410
$819$	42.6821	1.49143
$820$	−7.91566	−0.276427
$821$	−36.9123	−1.28825	−0.644124	−	0.764921i	$-0.722778\pi$
$821$	−36.9123	−1.28825	−0.644124	+	0.764921i	$0.722778\pi$
$822$	−4.36356	−0.152197
$823$	−18.6814	−0.651194	−0.325597	−	0.945509i	$-0.605565\pi$
$823$	−18.6814	−0.651194	−0.325597	+	0.945509i	$0.605565\pi$
$824$	−25.7807	−0.898113
$825$	−123.672	−4.30569
$826$	−5.30930	−0.184734
$827$	−8.30608	−0.288831	−0.144415	−	0.989517i	$-0.546130\pi$
$827$	−8.30608	−0.288831	−0.144415	+	0.989517i	$0.546130\pi$
$828$	−31.2206	−1.08499
$829$	−43.6011	−1.51433	−0.757165	−	0.653224i	$-0.773416\pi$
$829$	−43.6011	−1.51433	−0.757165	+	0.653224i	$0.773416\pi$
$830$	−111.947	−3.88573
$831$	36.2119	1.25618
$832$	−90.0425	−3.12166
$833$	−2.74488	−0.0951045
$834$	58.4510	2.02399
$835$	−91.0094	−3.14951
$836$	66.2984	2.29298
$837$	−67.9780	−2.34966
$838$	−83.2067	−2.87433
$839$	24.2757	0.838089	0.419044	−	0.907966i	$-0.362365\pi$
$839$	24.2757	0.838089	0.419044	+	0.907966i	$0.362365\pi$
$840$	27.5172	0.949435
$841$	44.5094	1.53481
$842$	13.3370	0.459622
$843$	−52.5605	−1.81028
$844$	70.6711	2.43260
$845$	128.905	4.43446
$846$	60.8172	2.09094
$847$	10.2073	0.350728
$848$	2.97611	0.102200
$849$	−21.5325	−0.738993
$850$	54.8304	1.88067
$851$	15.2996	0.524465
$852$	−127.338	−4.36252
$853$	15.3152	0.524383	0.262192	−	0.965016i	$-0.415555\pi$
$853$	15.3152	0.524383	0.262192	+	0.965016i	$0.415555\pi$
$854$	−12.6078	−0.431432
$855$	107.569	3.67878
$856$	4.85418	0.165913
$857$	−14.4846	−0.494786	−0.247393	−	0.968915i	$-0.579574\pi$
$857$	−14.4846	−0.494786	−0.247393	+	0.968915i	$0.579574\pi$
$858$	217.121	7.41238
$859$	−25.8375	−0.881564	−0.440782	−	0.897614i	$-0.645299\pi$
$859$	−25.8375	−0.881564	−0.440782	+	0.897614i	$0.645299\pi$
$860$	42.0928	1.43535
$861$	2.09083	0.0712552
$862$	80.1905	2.73130
$863$	−1.00000	−0.0340404
$863$	−1.00000	−0.0340404
$864$	−61.5719	−2.09472
$865$	−89.4365	−3.04093
$866$	61.6890	2.09628
$867$	28.6872	0.974268
$868$	21.7039	0.736677
$869$	−36.2892	−1.23103
$870$	−218.081	−7.39365
$871$	−38.2203	−1.29505
$872$	29.7555	1.00765
$873$	65.9162	2.23093
$874$	17.2488	0.583450
$875$	14.3751	0.485968
$876$	−31.4613	−1.06298
$877$	−32.6768	−1.10342	−0.551709	−	0.834037i	$-0.686024\pi$
$877$	−32.6768	−1.10342	−0.551709	+	0.834037i	$0.686024\pi$
$878$	28.4016	0.958508
$879$	−46.3300	−1.56267
$880$	−11.4187	−0.384923
$881$	−56.9219	−1.91775	−0.958873	−	0.283835i	$-0.908393\pi$
$881$	−56.9219	−1.91775	−0.958873	+	0.283835i	$0.908393\pi$
$882$	−13.9427	−0.469474
$883$	−21.1937	−0.713226	−0.356613	−	0.934252i	$-0.616068\pi$
$883$	−21.1937	−0.713226	−0.356613	+	0.934252i	$0.616068\pi$
$884$	−58.3770	−1.96343
$885$	−26.5745	−0.893292
$886$	71.1927	2.39177
$887$	3.67028	0.123236	0.0616180	−	0.998100i	$-0.480374\pi$
$887$	3.67028	0.123236	0.0616180	+	0.998100i	$0.480374\pi$
$888$	−69.0381	−2.31677
$889$	4.26430	0.143020
$890$	79.9708	2.68063
$891$	49.2690	1.65057
$892$	15.6806	0.525025
$893$	−20.3767	−0.681879
$894$	100.404	3.35802
$895$	27.0928	0.905613
$896$	16.6558	0.556432
$897$	34.2568	1.14380
$898$	46.9526	1.56683
$899$	−60.3810	−2.01382
$900$	168.901	5.63003
$901$	12.2659	0.408636
$902$	7.16198	0.238468
$903$	−11.1183	−0.369994
$904$	2.48571	0.0826733
$905$	65.6279	2.18154
$906$	109.516	3.63842
$907$	10.0018	0.332105	0.166053	−	0.986117i	$-0.446898\pi$
$907$	10.0018	0.332105	0.166053	+	0.986117i	$0.446898\pi$
$908$	25.7918	0.855930
$909$	76.7650	2.54613
$910$	−57.9188	−1.91999
$911$	23.6799	0.784550	0.392275	−	0.919848i	$-0.371688\pi$
$911$	23.6799	0.784550	0.392275	+	0.919848i	$0.371688\pi$
$912$	9.42896	0.312224
$913$	61.4252	2.03288
$914$	−41.3558	−1.36793
$915$	−63.1057	−2.08621
$916$	−79.4052	−2.62362
$917$	10.0596	0.332198
$918$	−59.7274	−1.97130
$919$	22.0085	0.725995	0.362998	−	0.931790i	$-0.381753\pi$
$919$	22.0085	0.725995	0.362998	+	0.931790i	$0.381753\pi$
$920$	14.8718	0.490310
$921$	85.8399	2.82852
$922$	−59.3529	−1.95468
$923$	94.0851	3.09685
$924$	−43.0120	−1.41499
$925$	−82.7698	−2.72145
$926$	54.3626	1.78646
$927$	65.3827	2.14745
$928$	−54.6908	−1.79531
$929$	−14.4510	−0.474121	−0.237061	−	0.971495i	$-0.576184\pi$
$929$	−14.4510	−0.474121	−0.237061	+	0.971495i	$0.576184\pi$
$930$	179.133	5.87401
$931$	4.67145	0.153101
$932$	−10.9381	−0.358288
$933$	−65.1745	−2.13372
$934$	20.0794	0.657019
$935$	−47.0615	−1.53908
$936$	−104.091	−3.40232
$937$	23.2434	0.759328	0.379664	−	0.925124i	$-0.376040\pi$
$937$	23.2434	0.759328	0.379664	+	0.925124i	$0.376040\pi$
$938$	12.4852	0.407655
$939$	−61.5709	−2.00929
$940$	−50.0482	−1.63239
$941$	−60.8281	−1.98294	−0.991470	−	0.130336i	$-0.958394\pi$
$941$	−60.8281	−1.98294	−0.991470	+	0.130336i	$0.958394\pi$
$942$	−150.194	−4.89359
$943$	1.13000	0.0367978
$944$	−1.56856	−0.0510523
$945$	−35.9368	−1.16902
$946$	−38.0850	−1.23825
$947$	−25.4286	−0.826318	−0.413159	−	0.910659i	$-0.635575\pi$
$947$	−25.4286	−0.826318	−0.413159	+	0.910659i	$0.635575\pi$
$948$	73.6005	2.39043
$949$	23.2456	0.754584
$950$	−93.3148	−3.02753
$951$	−58.6446	−1.90168
$952$	6.69408	0.216956
$953$	28.8238	0.933696	0.466848	−	0.884338i	$-0.345390\pi$
$953$	28.8238	0.933696	0.466848	+	0.884338i	$0.345390\pi$
$954$	62.3047	2.01719
$955$	−57.7191	−1.86775
$956$	10.5022	0.339666
$957$	119.661	3.86809
$958$	85.2354	2.75383
$959$	−0.638694	−0.0206245
$960$	147.223	4.75159
$961$	18.5972	0.599910
$962$	145.313	4.68507
$963$	−12.3107	−0.396708
$964$	−42.4472	−1.36713
$965$	14.6823	0.472640
$966$	−11.1904	−0.360045
$967$	−26.0562	−0.837911	−0.418955	−	0.908007i	$-0.637604\pi$
$967$	−26.0562	−0.837911	−0.418955	+	0.908007i	$0.637604\pi$
$968$	−24.8932	−0.800097
$969$	38.8610	1.24839
$970$	−89.4469	−2.87197
$971$	−9.74612	−0.312768	−0.156384	−	0.987696i	$-0.549984\pi$
$971$	−9.74612	−0.312768	−0.156384	+	0.987696i	$0.549984\pi$
$972$	−10.6837	−0.342680
$973$	8.55547	0.274276
$974$	−31.9720	−1.02445
$975$	−185.326	−5.93519
$976$	−3.72481	−0.119228
$977$	−41.5512	−1.32934	−0.664671	−	0.747137i	$-0.731428\pi$
$977$	−41.5512	−1.32934	−0.664671	+	0.747137i	$0.731428\pi$
$978$	45.4651	1.45381
$979$	−43.8799	−1.40241
$980$	11.4738	0.366517
$981$	−75.4633	−2.40936
$982$	−9.60811	−0.306607
$983$	27.4507	0.875542	0.437771	−	0.899087i	$-0.355768\pi$
$983$	27.4507	0.875542	0.437771	+	0.899087i	$0.355768\pi$
$984$	−5.09901	−0.162550
$985$	−45.7475	−1.45764
$986$	−53.0524	−1.68953
$987$	13.2196	0.420785
$988$	99.3506	3.16076
$989$	−6.00895	−0.191073
$990$	−239.050	−7.59749
$991$	−23.0233	−0.731358	−0.365679	−	0.930741i	$-0.619163\pi$
$991$	−23.0233	−0.731358	−0.365679	+	0.930741i	$0.619163\pi$
$992$	44.9233	1.42632
$993$	34.3833	1.09112
$994$	−30.7341	−0.974826
$995$	−39.5887	−1.25505
$996$	−124.580	−3.94748
$997$	−52.9713	−1.67762	−0.838809	−	0.544426i	$-0.816747\pi$
$997$	−52.9713	−1.67762	−0.838809	+	0.544426i	$0.816747\pi$
$998$	−86.4798	−2.73747
$999$	90.1619	2.85260

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6041.2.a.f.1.18	✓	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6041.2.a.f.1.18	✓	132	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:	\( N \)	\(=\)	\( 6041 = 7 \cdot 863 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6041.a (trivial)

\(f(q)\)	\(=\)	\(q-2.25429 q^{2} -3.03067 q^{3} +3.08183 q^{4} +3.72305 q^{5} +6.83200 q^{6} +1.00000 q^{7} -2.43875 q^{8} +6.18494 q^{9} +O(q^{10})\)	\(q-2.25429 q^{2} -3.03067 q^{3} +3.08183 q^{4} +3.72305 q^{5} +6.83200 q^{6} +1.00000 q^{7} -2.43875 q^{8} +6.18494 q^{9} -8.39284 q^{10} +4.60514 q^{11} -9.33999 q^{12} +6.90097 q^{13} -2.25429 q^{14} -11.2833 q^{15} -0.665999 q^{16} -2.74488 q^{17} -13.9427 q^{18} +4.67145 q^{19} +11.4738 q^{20} -3.03067 q^{21} -10.3813 q^{22} -1.63794 q^{23} +7.39104 q^{24} +8.86112 q^{25} -15.5568 q^{26} -9.65250 q^{27} +3.08183 q^{28} -8.57376 q^{29} +25.4359 q^{30} +7.04253 q^{31} +6.37886 q^{32} -13.9567 q^{33} +6.18776 q^{34} +3.72305 q^{35} +19.0609 q^{36} -9.34078 q^{37} -10.5308 q^{38} -20.9145 q^{39} -9.07960 q^{40} -0.689890 q^{41} +6.83200 q^{42} +3.66860 q^{43} +14.1923 q^{44} +23.0269 q^{45} +3.69239 q^{46} -4.36195 q^{47} +2.01842 q^{48} +1.00000 q^{49} -19.9755 q^{50} +8.31882 q^{51} +21.2676 q^{52} -4.46864 q^{53} +21.7596 q^{54} +17.1452 q^{55} -2.43875 q^{56} -14.1576 q^{57} +19.3278 q^{58} +2.35520 q^{59} -34.7733 q^{60} +5.59282 q^{61} -15.8759 q^{62} +6.18494 q^{63} -13.0478 q^{64} +25.6927 q^{65} +31.4624 q^{66} -5.53840 q^{67} -8.45924 q^{68} +4.96405 q^{69} -8.39284 q^{70} +13.6336 q^{71} -15.0835 q^{72} +3.36845 q^{73} +21.0568 q^{74} -26.8551 q^{75} +14.3966 q^{76} +4.60514 q^{77} +47.1475 q^{78} -7.88014 q^{79} -2.47955 q^{80} +10.6987 q^{81} +1.55521 q^{82} +13.3384 q^{83} -9.33999 q^{84} -10.2193 q^{85} -8.27009 q^{86} +25.9842 q^{87} -11.2308 q^{88} -9.52845 q^{89} -51.9093 q^{90} +6.90097 q^{91} -5.04784 q^{92} -21.3436 q^{93} +9.83311 q^{94} +17.3921 q^{95} -19.3322 q^{96} +10.6575 q^{97} -2.25429 q^{98} +28.4826 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 8 q^{2} + 10 q^{3} + 174 q^{4} + 11 q^{5} + 16 q^{6} + 132 q^{7} + 30 q^{8} + 178 q^{9}+O(q^{10}) \) 132 * q + 8 * q^2 + 10 * q^3 + 174 * q^4 + 11 * q^5 + 16 * q^6 + 132 * q^7 + 30 * q^8 + 178 * q^9	\( 132 q + 8 q^{2} + 10 q^{3} + 174 q^{4} + 11 q^{5} + 16 q^{6} + 132 q^{7} + 30 q^{8} + 178 q^{9} + 22 q^{10} + 32 q^{11} + 30 q^{12} + 16 q^{13} + 8 q^{14} + 59 q^{15} + 254 q^{16} + 11 q^{17} + 33 q^{18} + 40 q^{19} + 4 q^{20} + 10 q^{21} + 66 q^{22} + 62 q^{23} + 36 q^{24} + 235 q^{25} + 25 q^{26} + 37 q^{27} + 174 q^{28} + 28 q^{29} + 45 q^{30} + 121 q^{31} + 53 q^{32} - 13 q^{33} + 44 q^{34} + 11 q^{35} + 274 q^{36} + 61 q^{37} - 28 q^{38} + 114 q^{39} + 32 q^{40} - q^{41} + 16 q^{42} + 105 q^{43} + 54 q^{44} + 29 q^{45} + 104 q^{46} + 33 q^{47} + 16 q^{48} + 132 q^{49} - 14 q^{50} + 53 q^{51} - 11 q^{52} + 48 q^{53} + 11 q^{54} + 118 q^{55} + 30 q^{56} + 93 q^{57} + 87 q^{58} + 12 q^{59} + 41 q^{60} + 54 q^{61} - 28 q^{62} + 178 q^{63} + 376 q^{64} + 22 q^{65} + 6 q^{66} + 123 q^{67} - 47 q^{68} + 58 q^{69} + 22 q^{70} + 108 q^{71} + 97 q^{72} + q^{73} - 10 q^{74} + 23 q^{75} + 71 q^{76} + 32 q^{77} + 5 q^{78} + 204 q^{79} - 10 q^{80} + 296 q^{81} + 80 q^{82} - 10 q^{83} + 30 q^{84} + 94 q^{85} + 48 q^{86} + 4 q^{87} + 155 q^{88} + q^{89} - 66 q^{90} + 16 q^{91} + 49 q^{92} + 90 q^{93} + 79 q^{94} + 100 q^{95} + q^{96} + 18 q^{97} + 8 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q + 8 * q^2 + 10 * q^3 + 174 * q^4 + 11 * q^5 + 16 * q^6 + 132 * q^7 + 30 * q^8 + 178 * q^9 + 22 * q^10 + 32 * q^11 + 30 * q^12 + 16 * q^13 + 8 * q^14 + 59 * q^15 + 254 * q^16 + 11 * q^17 + 33 * q^18 + 40 * q^19 + 4 * q^20 + 10 * q^21 + 66 * q^22 + 62 * q^23 + 36 * q^24 + 235 * q^25 + 25 * q^26 + 37 * q^27 + 174 * q^28 + 28 * q^29 + 45 * q^30 + 121 * q^31 + 53 * q^32 - 13 * q^33 + 44 * q^34 + 11 * q^35 + 274 * q^36 + 61 * q^37 - 28 * q^38 + 114 * q^39 + 32 * q^40 - q^41 + 16 * q^42 + 105 * q^43 + 54 * q^44 + 29 * q^45 + 104 * q^46 + 33 * q^47 + 16 * q^48 + 132 * q^49 - 14 * q^50 + 53 * q^51 - 11 * q^52 + 48 * q^53 + 11 * q^54 + 118 * q^55 + 30 * q^56 + 93 * q^57 + 87 * q^58 + 12 * q^59 + 41 * q^60 + 54 * q^61 - 28 * q^62 + 178 * q^63 + 376 * q^64 + 22 * q^65 + 6 * q^66 + 123 * q^67 - 47 * q^68 + 58 * q^69 + 22 * q^70 + 108 * q^71 + 97 * q^72 + q^73 - 10 * q^74 + 23 * q^75 + 71 * q^76 + 32 * q^77 + 5 * q^78 + 204 * q^79 - 10 * q^80 + 296 * q^81 + 80 * q^82 - 10 * q^83 + 30 * q^84 + 94 * q^85 + 48 * q^86 + 4 * q^87 + 155 * q^88 + q^89 - 66 * q^90 + 16 * q^91 + 49 * q^92 + 90 * q^93 + 79 * q^94 + 100 * q^95 + q^96 + 18 * q^97 + 8 * q^98 + 96 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more