LMFDB - Embedded newform 6010.2.a.c.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6010,2,Mod(1,6010)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6010, 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("6010.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6010 = 2 \cdot 5 \cdot 601 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6010.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:	$47.9900916148$
Analytic rank:	$1$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 9 x^{14} + 75 x^{13} - 178 x^{12} - 232 x^{11} + 872 x^{10} + 228 x^{9} - 1986 x^{8} + \cdots - 10 $ x^16 - 8x^15 + 9x^14 + 75x^13 - 178x^12 - 232x^11 + 872x^10 + 228x^9 - 1986x^8 + 164x^7 + 2332x^6 - 440x^5 - 1344x^4 + 244x^3 + 295x^2 - 41*x - 10
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Root			$2.41044$ of defining polynomial
Character	$\chi$	$=$	6010.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.41044 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.41044 q^{6} -3.15104 q^{7} +1.00000 q^{8} -1.01066 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.41044 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.41044 q^{6} -3.15104 q^{7} +1.00000 q^{8} -1.01066 q^{9} +1.00000 q^{10} -1.04069 q^{11} +1.41044 q^{12} -3.01659 q^{13} -3.15104 q^{14} +1.41044 q^{15} +1.00000 q^{16} +2.09209 q^{17} -1.01066 q^{18} +3.54717 q^{19} +1.00000 q^{20} -4.44435 q^{21} -1.04069 q^{22} -1.80458 q^{23} +1.41044 q^{24} +1.00000 q^{25} -3.01659 q^{26} -5.65679 q^{27} -3.15104 q^{28} -0.429786 q^{29} +1.41044 q^{30} -9.55437 q^{31} +1.00000 q^{32} -1.46783 q^{33} +2.09209 q^{34} -3.15104 q^{35} -1.01066 q^{36} +7.40717 q^{37} +3.54717 q^{38} -4.25473 q^{39} +1.00000 q^{40} -9.28453 q^{41} -4.44435 q^{42} -7.43486 q^{43} -1.04069 q^{44} -1.01066 q^{45} -1.80458 q^{46} -10.5989 q^{47} +1.41044 q^{48} +2.92903 q^{49} +1.00000 q^{50} +2.95077 q^{51} -3.01659 q^{52} -7.88673 q^{53} -5.65679 q^{54} -1.04069 q^{55} -3.15104 q^{56} +5.00308 q^{57} -0.429786 q^{58} +3.06070 q^{59} +1.41044 q^{60} -4.36339 q^{61} -9.55437 q^{62} +3.18461 q^{63} +1.00000 q^{64} -3.01659 q^{65} -1.46783 q^{66} +11.1448 q^{67} +2.09209 q^{68} -2.54525 q^{69} -3.15104 q^{70} +8.28515 q^{71} -1.01066 q^{72} -5.43760 q^{73} +7.40717 q^{74} +1.41044 q^{75} +3.54717 q^{76} +3.27926 q^{77} -4.25473 q^{78} +9.01031 q^{79} +1.00000 q^{80} -4.94661 q^{81} -9.28453 q^{82} +8.94926 q^{83} -4.44435 q^{84} +2.09209 q^{85} -7.43486 q^{86} -0.606188 q^{87} -1.04069 q^{88} -8.34070 q^{89} -1.01066 q^{90} +9.50540 q^{91} -1.80458 q^{92} -13.4759 q^{93} -10.5989 q^{94} +3.54717 q^{95} +1.41044 q^{96} +6.35468 q^{97} +2.92903 q^{98} +1.05178 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{2} - 8 q^{3} + 16 q^{4} + 16 q^{5} - 8 q^{6} - 10 q^{7} + 16 q^{8} - 2 q^{9}+O(q^{10}) $ 16 * q + 16 * q^2 - 8 * q^3 + 16 * q^4 + 16 * q^5 - 8 * q^6 - 10 * q^7 + 16 * q^8 - 2 * q^9	\( 16 q + 16 q^{2} - 8 q^{3} + 16 q^{4} + 16 q^{5} - 8 q^{6} - 10 q^{7} + 16 q^{8} - 2 q^{9} + 16 q^{10} - 14 q^{11} - 8 q^{12} - 20 q^{13} - 10 q^{14} - 8 q^{15} + 16 q^{16} - 27 q^{17} - 2 q^{18} - 17 q^{19} + 16 q^{20} - 12 q^{21} - 14 q^{22} - 9 q^{23} - 8 q^{24} + 16 q^{25} - 20 q^{26} - 11 q^{27} - 10 q^{28} - 23 q^{29} - 8 q^{30} - 21 q^{31} + 16 q^{32} - 9 q^{33} - 27 q^{34} - 10 q^{35} - 2 q^{36} - 16 q^{37} - 17 q^{38} - 6 q^{39} + 16 q^{40} - 35 q^{41} - 12 q^{42} + 3 q^{43} - 14 q^{44} - 2 q^{45} - 9 q^{46} - 25 q^{47} - 8 q^{48} - 24 q^{49} + 16 q^{50} - q^{51} - 20 q^{52} - 39 q^{53} - 11 q^{54} - 14 q^{55} - 10 q^{56} - 6 q^{57} - 23 q^{58} - 32 q^{59} - 8 q^{60} - 38 q^{61} - 21 q^{62} + q^{63} + 16 q^{64} - 20 q^{65} - 9 q^{66} + 5 q^{67} - 27 q^{68} - 25 q^{69} - 10 q^{70} - 16 q^{71} - 2 q^{72} - 17 q^{73} - 16 q^{74} - 8 q^{75} - 17 q^{76} - 34 q^{77} - 6 q^{78} - 40 q^{79} + 16 q^{80} - 28 q^{81} - 35 q^{82} - 22 q^{83} - 12 q^{84} - 27 q^{85} + 3 q^{86} + 10 q^{87} - 14 q^{88} - 46 q^{89} - 2 q^{90} - q^{91} - 9 q^{92} + 14 q^{93} - 25 q^{94} - 17 q^{95} - 8 q^{96} - 21 q^{97} - 24 q^{98} + 15 q^{99}+O(q^{100}) \) 16 * q + 16 * q^2 - 8 * q^3 + 16 * q^4 + 16 * q^5 - 8 * q^6 - 10 * q^7 + 16 * q^8 - 2 * q^9 + 16 * q^10 - 14 * q^11 - 8 * q^12 - 20 * q^13 - 10 * q^14 - 8 * q^15 + 16 * q^16 - 27 * q^17 - 2 * q^18 - 17 * q^19 + 16 * q^20 - 12 * q^21 - 14 * q^22 - 9 * q^23 - 8 * q^24 + 16 * q^25 - 20 * q^26 - 11 * q^27 - 10 * q^28 - 23 * q^29 - 8 * q^30 - 21 * q^31 + 16 * q^32 - 9 * q^33 - 27 * q^34 - 10 * q^35 - 2 * q^36 - 16 * q^37 - 17 * q^38 - 6 * q^39 + 16 * q^40 - 35 * q^41 - 12 * q^42 + 3 * q^43 - 14 * q^44 - 2 * q^45 - 9 * q^46 - 25 * q^47 - 8 * q^48 - 24 * q^49 + 16 * q^50 - q^51 - 20 * q^52 - 39 * q^53 - 11 * q^54 - 14 * q^55 - 10 * q^56 - 6 * q^57 - 23 * q^58 - 32 * q^59 - 8 * q^60 - 38 * q^61 - 21 * q^62 + q^63 + 16 * q^64 - 20 * q^65 - 9 * q^66 + 5 * q^67 - 27 * q^68 - 25 * q^69 - 10 * q^70 - 16 * q^71 - 2 * q^72 - 17 * q^73 - 16 * q^74 - 8 * q^75 - 17 * q^76 - 34 * q^77 - 6 * q^78 - 40 * q^79 + 16 * q^80 - 28 * q^81 - 35 * q^82 - 22 * q^83 - 12 * q^84 - 27 * q^85 + 3 * q^86 + 10 * q^87 - 14 * q^88 - 46 * q^89 - 2 * q^90 - q^91 - 9 * q^92 + 14 * q^93 - 25 * q^94 - 17 * q^95 - 8 * q^96 - 21 * q^97 - 24 * q^98 + 15 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.41044	0.814318	0.407159	−	0.913357i	$-0.366519\pi$
$3$	1.41044	0.814318	0.407159	+	0.913357i	$0.366519\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.41044	0.575810
$7$	−3.15104	−1.19098	−0.595490	−	0.803363i	$-0.703042\pi$
$7$	−3.15104	−1.19098	−0.595490	+	0.803363i	$0.703042\pi$
$8$	1.00000	0.353553
$9$	−1.01066	−0.336885
$10$	1.00000	0.316228
$11$	−1.04069	−0.313780	−0.156890	−	0.987616i	$-0.550147\pi$
$11$	−1.04069	−0.313780	−0.156890	+	0.987616i	$0.550147\pi$
$12$	1.41044	0.407159
$13$	−3.01659	−0.836653	−0.418326	−	0.908297i	$-0.637383\pi$
$13$	−3.01659	−0.836653	−0.418326	+	0.908297i	$0.637383\pi$
$14$	−3.15104	−0.842150
$15$	1.41044	0.364174
$16$	1.00000	0.250000
$17$	2.09209	0.507406	0.253703	−	0.967282i	$-0.418351\pi$
$17$	2.09209	0.507406	0.253703	+	0.967282i	$0.418351\pi$
$18$	−1.01066	−0.238214
$19$	3.54717	0.813778	0.406889	−	0.913478i	$-0.366614\pi$
$19$	3.54717	0.813778	0.406889	+	0.913478i	$0.366614\pi$
$20$	1.00000	0.223607
$21$	−4.44435	−0.969837
$22$	−1.04069	−0.221876
$23$	−1.80458	−0.376281	−0.188141	−	0.982142i	$-0.560246\pi$
$23$	−1.80458	−0.376281	−0.188141	+	0.982142i	$0.560246\pi$
$24$	1.41044	0.287905
$25$	1.00000	0.200000
$26$	−3.01659	−0.591603
$27$	−5.65679	−1.08865
$28$	−3.15104	−0.595490
$29$	−0.429786	−0.0798093	−0.0399047	−	0.999203i	$-0.512705\pi$
$29$	−0.429786	−0.0798093	−0.0399047	+	0.999203i	$0.512705\pi$
$30$	1.41044	0.257510
$31$	−9.55437	−1.71602	−0.858008	−	0.513637i	$-0.828298\pi$
$31$	−9.55437	−1.71602	−0.858008	+	0.513637i	$0.828298\pi$
$32$	1.00000	0.176777
$33$	−1.46783	−0.255517
$34$	2.09209	0.358790
$35$	−3.15104	−0.532622
$36$	−1.01066	−0.168443
$37$	7.40717	1.21773	0.608866	−	0.793273i	$-0.291625\pi$
$37$	7.40717	1.21773	0.608866	+	0.793273i	$0.291625\pi$
$38$	3.54717	0.575428
$39$	−4.25473	−0.681302
$40$	1.00000	0.158114
$41$	−9.28453	−1.45000	−0.725000	−	0.688749i	$-0.758160\pi$
$41$	−9.28453	−1.45000	−0.725000	+	0.688749i	$0.758160\pi$
$42$	−4.44435	−0.685778
$43$	−7.43486	−1.13381	−0.566903	−	0.823785i	$-0.691858\pi$
$43$	−7.43486	−1.13381	−0.566903	+	0.823785i	$0.691858\pi$
$44$	−1.04069	−0.156890
$45$	−1.01066	−0.150660
$46$	−1.80458	−0.266071
$47$	−10.5989	−1.54601	−0.773006	−	0.634399i	$-0.781248\pi$
$47$	−10.5989	−1.54601	−0.773006	+	0.634399i	$0.781248\pi$
$48$	1.41044	0.203580
$49$	2.92903	0.418433
$50$	1.00000	0.141421
$51$	2.95077	0.413190
$52$	−3.01659	−0.418326
$53$	−7.88673	−1.08333	−0.541663	−	0.840596i	$-0.682205\pi$
$53$	−7.88673	−1.08333	−0.541663	+	0.840596i	$0.682205\pi$
$54$	−5.65679	−0.769792
$55$	−1.04069	−0.140327
$56$	−3.15104	−0.421075
$57$	5.00308	0.662674
$58$	−0.429786	−0.0564337
$59$	3.06070	0.398469	0.199235	−	0.979952i	$-0.436154\pi$
$59$	3.06070	0.398469	0.199235	+	0.979952i	$0.436154\pi$
$60$	1.41044	0.182087
$61$	−4.36339	−0.558675	−0.279337	−	0.960193i	$-0.590115\pi$
$61$	−4.36339	−0.558675	−0.279337	+	0.960193i	$0.590115\pi$
$62$	−9.55437	−1.21341
$63$	3.18461	0.401224
$64$	1.00000	0.125000
$65$	−3.01659	−0.374162
$66$	−1.46783	−0.180678
$67$	11.1448	1.36155	0.680774	−	0.732493i	$-0.261643\pi$
$67$	11.1448	1.36155	0.680774	+	0.732493i	$0.261643\pi$
$68$	2.09209	0.253703
$69$	−2.54525	−0.306413
$70$	−3.15104	−0.376621
$71$	8.28515	0.983266	0.491633	−	0.870802i	$-0.336400\pi$
$71$	8.28515	0.983266	0.491633	+	0.870802i	$0.336400\pi$
$72$	−1.01066	−0.119107
$73$	−5.43760	−0.636423	−0.318212	−	0.948020i	$-0.603082\pi$
$73$	−5.43760	−0.636423	−0.318212	+	0.948020i	$0.603082\pi$
$74$	7.40717	0.861066
$75$	1.41044	0.162864
$76$	3.54717	0.406889
$77$	3.27926	0.373706
$78$	−4.25473	−0.481753
$79$	9.01031	1.01374	0.506869	−	0.862023i	$-0.330803\pi$
$79$	9.01031	1.01374	0.506869	+	0.862023i	$0.330803\pi$
$80$	1.00000	0.111803
$81$	−4.94661	−0.549623
$82$	−9.28453	−1.02531
$83$	8.94926	0.982309	0.491154	−	0.871073i	$-0.336575\pi$
$83$	8.94926	0.982309	0.491154	+	0.871073i	$0.336575\pi$
$84$	−4.44435	−0.484918
$85$	2.09209	0.226919
$86$	−7.43486	−0.801721
$87$	−0.606188	−0.0649902
$88$	−1.04069	−0.110938
$89$	−8.34070	−0.884112	−0.442056	−	0.896987i	$-0.645751\pi$
$89$	−8.34070	−0.884112	−0.442056	+	0.896987i	$0.645751\pi$
$90$	−1.01066	−0.106533
$91$	9.50540	0.996436
$92$	−1.80458	−0.188141
$93$	−13.4759	−1.39738
$94$	−10.5989	−1.09320
$95$	3.54717	0.363932
$96$	1.41044	0.143953
$97$	6.35468	0.645220	0.322610	−	0.946532i	$-0.395440\pi$
$97$	6.35468	0.645220	0.322610	+	0.946532i	$0.395440\pi$
$98$	2.92903	0.295877
$99$	1.05178	0.105708
$100$	1.00000	0.100000
$101$	−4.10281	−0.408245	−0.204122	−	0.978945i	$-0.565434\pi$
$101$	−4.10281	−0.408245	−0.204122	+	0.978945i	$0.565434\pi$
$102$	2.95077	0.292170
$103$	−8.66854	−0.854136	−0.427068	−	0.904219i	$-0.640454\pi$
$103$	−8.66854	−0.854136	−0.427068	+	0.904219i	$0.640454\pi$
$104$	−3.01659	−0.295801
$105$	−4.44435	−0.433724
$106$	−7.88673	−0.766027
$107$	−15.3045	−1.47954	−0.739770	−	0.672860i	$-0.765066\pi$
$107$	−15.3045	−1.47954	−0.739770	+	0.672860i	$0.765066\pi$
$108$	−5.65679	−0.544325
$109$	−13.5541	−1.29825	−0.649126	−	0.760681i	$-0.724865\pi$
$109$	−13.5541	−1.29825	−0.649126	+	0.760681i	$0.724865\pi$
$110$	−1.04069	−0.0992261
$111$	10.4474	0.991621
$112$	−3.15104	−0.297745
$113$	16.1227	1.51670	0.758349	−	0.651849i	$-0.226006\pi$
$113$	16.1227	1.51670	0.758349	+	0.651849i	$0.226006\pi$
$114$	5.00308	0.468581
$115$	−1.80458	−0.168278
$116$	−0.429786	−0.0399047
$117$	3.04874	0.281856
$118$	3.06070	0.281760
$119$	−6.59225	−0.604311
$120$	1.41044	0.128755
$121$	−9.91696	−0.901542
$122$	−4.36339	−0.395043
$123$	−13.0953	−1.18076
$124$	−9.55437	−0.858008
$125$	1.00000	0.0894427
$126$	3.18461	0.283708
$127$	12.6071	1.11870	0.559351	−	0.828931i	$-0.311050\pi$
$127$	12.6071	1.11870	0.559351	+	0.828931i	$0.311050\pi$
$128$	1.00000	0.0883883
$129$	−10.4864	−0.923278
$130$	−3.01659	−0.264573
$131$	9.23835	0.807158	0.403579	−	0.914945i	$-0.367766\pi$
$131$	9.23835	0.807158	0.403579	+	0.914945i	$0.367766\pi$
$132$	−1.46783	−0.127759
$133$	−11.1773	−0.969193
$134$	11.1448	0.962760
$135$	−5.65679	−0.486859
$136$	2.09209	0.179395
$137$	−22.3754	−1.91166	−0.955829	−	0.293925i	$-0.905038\pi$
$137$	−22.3754	−1.91166	−0.955829	+	0.293925i	$0.905038\pi$
$138$	−2.54525	−0.216666
$139$	−14.1367	−1.19906	−0.599529	−	0.800353i	$-0.704646\pi$
$139$	−14.1367	−1.19906	−0.599529	+	0.800353i	$0.704646\pi$
$140$	−3.15104	−0.266311
$141$	−14.9492	−1.25895
$142$	8.28515	0.695274
$143$	3.13935	0.262525
$144$	−1.01066	−0.0842214
$145$	−0.429786	−0.0356918
$146$	−5.43760	−0.450019
$147$	4.13122	0.340738
$148$	7.40717	0.608866
$149$	−7.35152	−0.602260	−0.301130	−	0.953583i	$-0.597364\pi$
$149$	−7.35152	−0.602260	−0.301130	+	0.953583i	$0.597364\pi$
$150$	1.41044	0.115162
$151$	16.3564	1.33107	0.665533	−	0.746368i	$-0.268204\pi$
$151$	16.3564	1.33107	0.665533	+	0.746368i	$0.268204\pi$
$152$	3.54717	0.287714
$153$	−2.11438	−0.170938
$154$	3.27926	0.264250
$155$	−9.55437	−0.767425
$156$	−4.25473	−0.340651
$157$	−7.76589	−0.619785	−0.309893	−	0.950772i	$-0.600293\pi$
$157$	−7.76589	−0.619785	−0.309893	+	0.950772i	$0.600293\pi$
$158$	9.01031	0.716822
$159$	−11.1238	−0.882172
$160$	1.00000	0.0790569
$161$	5.68630	0.448143
$162$	−4.94661	−0.388642
$163$	15.3338	1.20104	0.600519	−	0.799610i	$-0.294961\pi$
$163$	15.3338	1.20104	0.600519	+	0.799610i	$0.294961\pi$
$164$	−9.28453	−0.725000
$165$	−1.46783	−0.114271
$166$	8.94926	0.694597
$167$	−20.5909	−1.59337	−0.796686	−	0.604393i	$-0.793416\pi$
$167$	−20.5909	−1.59337	−0.796686	+	0.604393i	$0.793416\pi$
$168$	−4.44435	−0.342889
$169$	−3.90016	−0.300012
$170$	2.09209	0.160456
$171$	−3.58497	−0.274150
$172$	−7.43486	−0.566903
$173$	9.79839	0.744958	0.372479	−	0.928041i	$-0.378508\pi$
$173$	9.79839	0.744958	0.372479	+	0.928041i	$0.378508\pi$
$174$	−0.606188	−0.0459550
$175$	−3.15104	−0.238196
$176$	−1.04069	−0.0784451
$177$	4.31694	0.324481
$178$	−8.34070	−0.625162
$179$	11.9994	0.896877	0.448439	−	0.893814i	$-0.351980\pi$
$179$	11.9994	0.896877	0.448439	+	0.893814i	$0.351980\pi$
$180$	−1.01066	−0.0753299
$181$	0.246164	0.0182972	0.00914860	−	0.999958i	$-0.497088\pi$
$181$	0.246164	0.0182972	0.00914860	+	0.999958i	$0.497088\pi$
$182$	9.50540	0.704587
$183$	−6.15430	−0.454939
$184$	−1.80458	−0.133035
$185$	7.40717	0.544586
$186$	−13.4759	−0.988099
$187$	−2.17722	−0.159214
$188$	−10.5989	−0.773006
$189$	17.8248	1.29656
$190$	3.54717	0.257339
$191$	20.4010	1.47617	0.738084	−	0.674709i	$-0.235731\pi$
$191$	20.4010	1.47617	0.738084	+	0.674709i	$0.235731\pi$
$192$	1.41044	0.101790
$193$	2.54753	0.183375	0.0916875	−	0.995788i	$-0.470774\pi$
$193$	2.54753	0.183375	0.0916875	+	0.995788i	$0.470774\pi$
$194$	6.35468	0.456240
$195$	−4.25473	−0.304687
$196$	2.92903	0.209216
$197$	−3.59037	−0.255803	−0.127901	−	0.991787i	$-0.540824\pi$
$197$	−3.59037	−0.255803	−0.127901	+	0.991787i	$0.540824\pi$
$198$	1.05178	0.0747469
$199$	−22.6077	−1.60262	−0.801308	−	0.598251i	$-0.795862\pi$
$199$	−22.6077	−1.60262	−0.801308	+	0.598251i	$0.795862\pi$
$200$	1.00000	0.0707107
$201$	15.7190	1.10873
$202$	−4.10281	−0.288673
$203$	1.35427	0.0950513
$204$	2.95077	0.206595
$205$	−9.28453	−0.648460
$206$	−8.66854	−0.603966
$207$	1.82381	0.126764
$208$	−3.01659	−0.209163
$209$	−3.69152	−0.255348
$210$	−4.44435	−0.306689
$211$	−0.563633	−0.0388021	−0.0194011	−	0.999812i	$-0.506176\pi$
$211$	−0.563633	−0.0388021	−0.0194011	+	0.999812i	$0.506176\pi$
$212$	−7.88673	−0.541663
$213$	11.6857	0.800692
$214$	−15.3045	−1.04619
$215$	−7.43486	−0.507053
$216$	−5.65679	−0.384896
$217$	30.1062	2.04374
$218$	−13.5541	−0.918002
$219$	−7.66942	−0.518251
$220$	−1.04069	−0.0701634
$221$	−6.31099	−0.424523
$222$	10.4474	0.701182
$223$	−9.19193	−0.615537	−0.307769	−	0.951461i	$-0.599582\pi$
$223$	−9.19193	−0.615537	−0.307769	+	0.951461i	$0.599582\pi$
$224$	−3.15104	−0.210537
$225$	−1.01066	−0.0673771
$226$	16.1227	1.07247
$227$	−4.76633	−0.316353	−0.158176	−	0.987411i	$-0.550561\pi$
$227$	−4.76633	−0.316353	−0.158176	+	0.987411i	$0.550561\pi$
$228$	5.00308	0.331337
$229$	−11.9104	−0.787060	−0.393530	−	0.919312i	$-0.628746\pi$
$229$	−11.9104	−0.787060	−0.393530	+	0.919312i	$0.628746\pi$
$230$	−1.80458	−0.118991
$231$	4.62520	0.304316
$232$	−0.429786	−0.0282169
$233$	15.3681	1.00680	0.503398	−	0.864055i	$-0.332083\pi$
$233$	15.3681	1.00680	0.503398	+	0.864055i	$0.332083\pi$
$234$	3.04874	0.199302
$235$	−10.5989	−0.691398
$236$	3.06070	0.199235
$237$	12.7085	0.825506
$238$	−6.59225	−0.427312
$239$	−8.67620	−0.561217	−0.280608	−	0.959822i	$-0.590536\pi$
$239$	−8.67620	−0.561217	−0.280608	+	0.959822i	$0.590536\pi$
$240$	1.41044	0.0910436
$241$	−11.9235	−0.768063	−0.384031	−	0.923320i	$-0.625465\pi$
$241$	−11.9235	−0.768063	−0.384031	+	0.923320i	$0.625465\pi$
$242$	−9.91696	−0.637486
$243$	9.99349	0.641082
$244$	−4.36339	−0.279337
$245$	2.92903	0.187129
$246$	−13.0953	−0.834925
$247$	−10.7004	−0.680849
$248$	−9.55437	−0.606703
$249$	12.6224	0.799912
$250$	1.00000	0.0632456
$251$	−11.7240	−0.740015	−0.370008	−	0.929029i	$-0.620645\pi$
$251$	−11.7240	−0.740015	−0.370008	+	0.929029i	$0.620645\pi$
$252$	3.18461	0.200612
$253$	1.87801	0.118070
$254$	12.6071	0.791042
$255$	2.95077	0.184784
$256$	1.00000	0.0625000
$257$	16.6262	1.03712	0.518558	−	0.855042i	$-0.326469\pi$
$257$	16.6262	1.03712	0.518558	+	0.855042i	$0.326469\pi$
$258$	−10.4864	−0.652856
$259$	−23.3403	−1.45029
$260$	−3.01659	−0.187081
$261$	0.434366	0.0268866
$262$	9.23835	0.570747
$263$	17.0636	1.05219	0.526094	−	0.850426i	$-0.323656\pi$
$263$	17.0636	1.05219	0.526094	+	0.850426i	$0.323656\pi$
$264$	−1.46783	−0.0903390
$265$	−7.88673	−0.484478
$266$	−11.1773	−0.685323
$267$	−11.7641	−0.719949
$268$	11.1448	0.680774
$269$	−7.54805	−0.460213	−0.230106	−	0.973165i	$-0.573907\pi$
$269$	−7.54805	−0.460213	−0.230106	+	0.973165i	$0.573907\pi$
$270$	−5.65679	−0.344262
$271$	2.98704	0.181450	0.0907249	−	0.995876i	$-0.471082\pi$
$271$	2.98704	0.181450	0.0907249	+	0.995876i	$0.471082\pi$
$272$	2.09209	0.126852
$273$	13.4068	0.811417
$274$	−22.3754	−1.35175
$275$	−1.04069	−0.0627561
$276$	−2.54525	−0.153206
$277$	−0.626895	−0.0376665	−0.0188332	−	0.999823i	$-0.505995\pi$
$277$	−0.626895	−0.0376665	−0.0188332	+	0.999823i	$0.505995\pi$
$278$	−14.1367	−0.847862
$279$	9.65618	0.578101
$280$	−3.15104	−0.188310
$281$	23.0483	1.37495	0.687473	−	0.726210i	$-0.258720\pi$
$281$	23.0483	1.37495	0.687473	+	0.726210i	$0.258720\pi$
$282$	−14.9492	−0.890209
$283$	1.83831	0.109276	0.0546381	−	0.998506i	$-0.482599\pi$
$283$	1.83831	0.109276	0.0546381	+	0.998506i	$0.482599\pi$
$284$	8.28515	0.491633
$285$	5.00308	0.296357
$286$	3.13935	0.185633
$287$	29.2559	1.72692
$288$	−1.01066	−0.0595535
$289$	−12.6232	−0.742539
$290$	−0.429786	−0.0252379
$291$	8.96291	0.525415
$292$	−5.43760	−0.318212
$293$	−11.1006	−0.648504	−0.324252	−	0.945971i	$-0.605113\pi$
$293$	−11.1006	−0.648504	−0.324252	+	0.945971i	$0.605113\pi$
$294$	4.13122	0.240938
$295$	3.06070	0.178201
$296$	7.40717	0.430533
$297$	5.88698	0.341597
$298$	−7.35152	−0.425862
$299$	5.44369	0.314817
$300$	1.41044	0.0814318
$301$	23.4275	1.35034
$302$	16.3564	0.941206
$303$	−5.78677	−0.332441
$304$	3.54717	0.203444
$305$	−4.36339	−0.249847
$306$	−2.11438	−0.120871
$307$	10.5173	0.600255	0.300128	−	0.953899i	$-0.402971\pi$
$307$	10.5173	0.600255	0.300128	+	0.953899i	$0.402971\pi$
$308$	3.27926	0.186853
$309$	−12.2265	−0.695539
$310$	−9.55437	−0.542652
$311$	9.81794	0.556725	0.278362	−	0.960476i	$-0.410208\pi$
$311$	9.81794	0.556725	0.278362	+	0.960476i	$0.410208\pi$
$312$	−4.25473	−0.240877
$313$	26.9734	1.52463	0.762314	−	0.647208i	$-0.224063\pi$
$313$	26.9734	1.52463	0.762314	+	0.647208i	$0.224063\pi$
$314$	−7.76589	−0.438254
$315$	3.18461	0.179433
$316$	9.01031	0.506869
$317$	9.77743	0.549155	0.274578	−	0.961565i	$-0.411462\pi$
$317$	9.77743	0.549155	0.274578	+	0.961565i	$0.411462\pi$
$318$	−11.1238	−0.623790
$319$	0.447275	0.0250426
$320$	1.00000	0.0559017
$321$	−21.5861	−1.20482
$322$	5.68630	0.316885
$323$	7.42101	0.412916
$324$	−4.94661	−0.274811
$325$	−3.01659	−0.167331
$326$	15.3338	0.849262
$327$	−19.1173	−1.05719
$328$	−9.28453	−0.512653
$329$	33.3976	1.84127
$330$	−1.46783	−0.0808016
$331$	9.21802	0.506668	0.253334	−	0.967379i	$-0.418473\pi$
$331$	9.21802	0.506668	0.253334	+	0.967379i	$0.418473\pi$
$332$	8.94926	0.491154
$333$	−7.48610	−0.410236
$334$	−20.5909	−1.12668
$335$	11.1448	0.608903
$336$	−4.44435	−0.242459
$337$	−3.83268	−0.208779	−0.104390	−	0.994536i	$-0.533289\pi$
$337$	−3.83268	−0.208779	−0.104390	+	0.994536i	$0.533289\pi$
$338$	−3.90016	−0.212141
$339$	22.7401	1.23508
$340$	2.09209	0.113460
$341$	9.94316	0.538452
$342$	−3.58497	−0.193853
$343$	12.8278	0.692635
$344$	−7.43486	−0.400861
$345$	−2.54525	−0.137032
$346$	9.79839	0.526765
$347$	28.8686	1.54975	0.774875	−	0.632115i	$-0.217813\pi$
$347$	28.8686	1.54975	0.774875	+	0.632115i	$0.217813\pi$
$348$	−0.606188	−0.0324951
$349$	26.4828	1.41759	0.708795	−	0.705414i	$-0.249239\pi$
$349$	26.4828	1.41759	0.708795	+	0.705414i	$0.249239\pi$
$350$	−3.15104	−0.168430
$351$	17.0643	0.910822
$352$	−1.04069	−0.0554691
$353$	−17.6764	−0.940818	−0.470409	−	0.882449i	$-0.655894\pi$
$353$	−17.6764	−0.940818	−0.470409	+	0.882449i	$0.655894\pi$
$354$	4.31694	0.229443
$355$	8.28515	0.439730
$356$	−8.34070	−0.442056
$357$	−9.29798	−0.492101
$358$	11.9994	0.634188
$359$	−17.0247	−0.898528	−0.449264	−	0.893399i	$-0.648314\pi$
$359$	−17.0247	−0.898528	−0.449264	+	0.893399i	$0.648314\pi$
$360$	−1.01066	−0.0532663
$361$	−6.41755	−0.337766
$362$	0.246164	0.0129381
$363$	−13.9873	−0.734142
$364$	9.50540	0.498218
$365$	−5.43760	−0.284617
$366$	−6.15430	−0.321691
$367$	−36.4460	−1.90247	−0.951233	−	0.308474i	$-0.900182\pi$
$367$	−36.4460	−1.90247	−0.951233	+	0.308474i	$0.900182\pi$
$368$	−1.80458	−0.0940703
$369$	9.38347	0.488484
$370$	7.40717	0.385080
$371$	24.8514	1.29022
$372$	−13.4759	−0.698692
$373$	−15.9187	−0.824239	−0.412119	−	0.911130i	$-0.635211\pi$
$373$	−15.9187	−0.824239	−0.412119	+	0.911130i	$0.635211\pi$
$374$	−2.17722	−0.112581
$375$	1.41044	0.0728349
$376$	−10.5989	−0.546598
$377$	1.29649	0.0667727
$378$	17.8248	0.916807
$379$	−9.80431	−0.503614	−0.251807	−	0.967778i	$-0.581025\pi$
$379$	−9.80431	−0.503614	−0.251807	+	0.967778i	$0.581025\pi$
$380$	3.54717	0.181966
$381$	17.7816	0.910980
$382$	20.4010	1.04381
$383$	−9.63675	−0.492415	−0.246207	−	0.969217i	$-0.579184\pi$
$383$	−9.63675	−0.492415	−0.246207	+	0.969217i	$0.579184\pi$
$384$	1.41044	0.0719763
$385$	3.27926	0.167126
$386$	2.54753	0.129666
$387$	7.51408	0.381962
$388$	6.35468	0.322610
$389$	10.6926	0.542137	0.271069	−	0.962560i	$-0.412623\pi$
$389$	10.6926	0.542137	0.271069	+	0.962560i	$0.412623\pi$
$390$	−4.25473	−0.215447
$391$	−3.77534	−0.190927
$392$	2.92903	0.147938
$393$	13.0301	0.657284
$394$	−3.59037	−0.180880
$395$	9.01031	0.453358
$396$	1.05178	0.0528540
$397$	3.69620	0.185507	0.0927534	−	0.995689i	$-0.470433\pi$
$397$	3.69620	0.185507	0.0927534	+	0.995689i	$0.470433\pi$
$398$	−22.6077	−1.13322
$399$	−15.7649	−0.789232
$400$	1.00000	0.0500000
$401$	2.95099	0.147366	0.0736828	−	0.997282i	$-0.476525\pi$
$401$	2.95099	0.147366	0.0736828	+	0.997282i	$0.476525\pi$
$402$	15.7190	0.783994
$403$	28.8217	1.43571
$404$	−4.10281	−0.204122
$405$	−4.94661	−0.245799
$406$	1.35427	0.0672114
$407$	−7.70858	−0.382100
$408$	2.95077	0.146085
$409$	34.2197	1.69205	0.846027	−	0.533141i	$-0.178988\pi$
$409$	34.2197	1.69205	0.846027	+	0.533141i	$0.178988\pi$
$410$	−9.28453	−0.458530
$411$	−31.5591	−1.55670
$412$	−8.66854	−0.427068
$413$	−9.64438	−0.474569
$414$	1.82381	0.0896354
$415$	8.94926	0.439302
$416$	−3.01659	−0.147901
$417$	−19.9390	−0.976416
$418$	−3.69152	−0.180558
$419$	−29.3149	−1.43213	−0.716064	−	0.698035i	$-0.754058\pi$
$419$	−29.3149	−1.43213	−0.716064	+	0.698035i	$0.754058\pi$
$420$	−4.44435	−0.216862
$421$	−11.7698	−0.573623	−0.286812	−	0.957987i	$-0.592595\pi$
$421$	−11.7698	−0.573623	−0.286812	+	0.957987i	$0.592595\pi$
$422$	−0.563633	−0.0274372
$423$	10.7119	0.520829
$424$	−7.88673	−0.383013
$425$	2.09209	0.101481
$426$	11.6857	0.566175
$427$	13.7492	0.665370
$428$	−15.3045	−0.739770
$429$	4.42786	0.213779
$430$	−7.43486	−0.358541
$431$	17.6035	0.847932	0.423966	−	0.905678i	$-0.360638\pi$
$431$	17.6035	0.847932	0.423966	+	0.905678i	$0.360638\pi$
$432$	−5.65679	−0.272163
$433$	19.7338	0.948348	0.474174	−	0.880431i	$-0.342747\pi$
$433$	19.7338	0.948348	0.474174	+	0.880431i	$0.342747\pi$
$434$	30.1062	1.44514
$435$	−0.606188	−0.0290645
$436$	−13.5541	−0.649126
$437$	−6.40116	−0.306209
$438$	−7.66942	−0.366459
$439$	−20.8591	−0.995553	−0.497776	−	0.867305i	$-0.665850\pi$
$439$	−20.8591	−0.995553	−0.497776	+	0.867305i	$0.665850\pi$
$440$	−1.04069	−0.0496130
$441$	−2.96024	−0.140964
$442$	−6.31099	−0.300183
$443$	−21.5858	−1.02557	−0.512785	−	0.858517i	$-0.671386\pi$
$443$	−21.5858	−1.02557	−0.512785	+	0.858517i	$0.671386\pi$
$444$	10.4474	0.495810
$445$	−8.34070	−0.395387
$446$	−9.19193	−0.435251
$447$	−10.3689	−0.490432
$448$	−3.15104	−0.148872
$449$	15.1846	0.716608	0.358304	−	0.933605i	$-0.383355\pi$
$449$	15.1846	0.716608	0.358304	+	0.933605i	$0.383355\pi$
$450$	−1.01066	−0.0476428
$451$	9.66234	0.454982
$452$	16.1227	0.758349
$453$	23.0698	1.08391
$454$	−4.76633	−0.223695
$455$	9.50540	0.445620
$456$	5.00308	0.234291
$457$	10.6088	0.496257	0.248129	−	0.968727i	$-0.420184\pi$
$457$	10.6088	0.496257	0.248129	+	0.968727i	$0.420184\pi$
$458$	−11.9104	−0.556536
$459$	−11.8345	−0.552388
$460$	−1.80458	−0.0841390
$461$	−3.89885	−0.181588	−0.0907938	−	0.995870i	$-0.528940\pi$
$461$	−3.89885	−0.181588	−0.0907938	+	0.995870i	$0.528940\pi$
$462$	4.62520	0.215184
$463$	3.98126	0.185025	0.0925125	−	0.995712i	$-0.470510\pi$
$463$	3.98126	0.185025	0.0925125	+	0.995712i	$0.470510\pi$
$464$	−0.429786	−0.0199523
$465$	−13.4759	−0.624929
$466$	15.3681	0.711912
$467$	12.8211	0.593291	0.296646	−	0.954988i	$-0.404132\pi$
$467$	12.8211	0.593291	0.296646	+	0.954988i	$0.404132\pi$
$468$	3.04874	0.140928
$469$	−35.1175	−1.62158
$470$	−10.5989	−0.488892
$471$	−10.9533	−0.504703
$472$	3.06070	0.140880
$473$	7.73740	0.355766
$474$	12.7085	0.583721
$475$	3.54717	0.162756
$476$	−6.59225	−0.302155
$477$	7.97077	0.364956
$478$	−8.67620	−0.396840
$479$	−21.5439	−0.984367	−0.492184	−	0.870491i	$-0.663801\pi$
$479$	−21.5439	−0.984367	−0.492184	+	0.870491i	$0.663801\pi$
$480$	1.41044	0.0643775
$481$	−22.3444	−1.01882
$482$	−11.9235	−0.543103
$483$	8.02019	0.364931
$484$	−9.91696	−0.450771
$485$	6.35468	0.288551
$486$	9.99349	0.453314
$487$	31.2923	1.41799	0.708994	−	0.705215i	$-0.249149\pi$
$487$	31.2923	1.41799	0.708994	+	0.705215i	$0.249149\pi$
$488$	−4.36339	−0.197521
$489$	21.6275	0.978028
$490$	2.92903	0.132320
$491$	16.7735	0.756978	0.378489	−	0.925606i	$-0.376444\pi$
$491$	16.7735	0.756978	0.378489	+	0.925606i	$0.376444\pi$
$492$	−13.0953	−0.590381
$493$	−0.899152	−0.0404958
$494$	−10.7004	−0.481433
$495$	1.05178	0.0472741
$496$	−9.55437	−0.429004
$497$	−26.1068	−1.17105
$498$	12.6224	0.565623
$499$	10.5285	0.471320	0.235660	−	0.971836i	$-0.424275\pi$
$499$	10.5285	0.471320	0.235660	+	0.971836i	$0.424275\pi$
$500$	1.00000	0.0447214
$501$	−29.0423	−1.29751
$502$	−11.7240	−0.523270
$503$	6.54465	0.291811	0.145906	−	0.989299i	$-0.453390\pi$
$503$	6.54465	0.291811	0.145906	+	0.989299i	$0.453390\pi$
$504$	3.18461	0.141854
$505$	−4.10281	−0.182573
$506$	1.87801	0.0834878
$507$	−5.50094	−0.244305
$508$	12.6071	0.559351
$509$	16.4367	0.728545	0.364272	−	0.931292i	$-0.381318\pi$
$509$	16.4367	0.728545	0.364272	+	0.931292i	$0.381318\pi$
$510$	2.95077	0.130662
$511$	17.1341	0.757967
$512$	1.00000	0.0441942
$513$	−20.0656	−0.885920
$514$	16.6262	0.733352
$515$	−8.66854	−0.381981
$516$	−10.4864	−0.461639
$517$	11.0302	0.485108
$518$	−23.3403	−1.02551
$519$	13.8201	0.606633
$520$	−3.01659	−0.132286
$521$	31.6137	1.38502	0.692510	−	0.721408i	$-0.256505\pi$
$521$	31.6137	1.38502	0.692510	+	0.721408i	$0.256505\pi$
$522$	0.434366	0.0190117
$523$	−11.3152	−0.494781	−0.247390	−	0.968916i	$-0.579573\pi$
$523$	−11.3152	−0.494781	−0.247390	+	0.968916i	$0.579573\pi$
$524$	9.23835	0.403579
$525$	−4.44435	−0.193967
$526$	17.0636	0.744009
$527$	−19.9886	−0.870717
$528$	−1.46783	−0.0638793
$529$	−19.7435	−0.858413
$530$	−7.88673	−0.342578
$531$	−3.09332	−0.134239
$532$	−11.1773	−0.484596
$533$	28.0077	1.21315
$534$	−11.7641	−0.509081
$535$	−15.3045	−0.661671
$536$	11.1448	0.481380
$537$	16.9244	0.730344
$538$	−7.54805	−0.325420
$539$	−3.04822	−0.131296
$540$	−5.65679	−0.243430
$541$	−35.4631	−1.52468	−0.762338	−	0.647179i	$-0.775949\pi$
$541$	−35.4631	−1.52468	−0.762338	+	0.647179i	$0.775949\pi$
$542$	2.98704	0.128304
$543$	0.347199	0.0148998
$544$	2.09209	0.0896976
$545$	−13.5541	−0.580596
$546$	13.4068	0.573758
$547$	11.7442	0.502147	0.251073	−	0.967968i	$-0.419216\pi$
$547$	11.7442	0.502147	0.251073	+	0.967968i	$0.419216\pi$
$548$	−22.3754	−0.955829
$549$	4.40989	0.188209
$550$	−1.04069	−0.0443753
$551$	−1.52453	−0.0649471
$552$	−2.54525	−0.108333
$553$	−28.3918	−1.20734
$554$	−0.626895	−0.0266342
$555$	10.4474	0.443466
$556$	−14.1367	−0.599529
$557$	6.71231	0.284410	0.142205	−	0.989837i	$-0.454581\pi$
$557$	6.71231	0.284410	0.142205	+	0.989837i	$0.454581\pi$
$558$	9.65618	0.408779
$559$	22.4279	0.948601
$560$	−3.15104	−0.133156
$561$	−3.07084	−0.129651
$562$	23.0483	0.972233
$563$	−3.19238	−0.134543	−0.0672713	−	0.997735i	$-0.521429\pi$
$563$	−3.19238	−0.134543	−0.0672713	+	0.997735i	$0.521429\pi$
$564$	−14.9492	−0.629473
$565$	16.1227	0.678288
$566$	1.83831	0.0772699
$567$	15.5869	0.654590
$568$	8.28515	0.347637
$569$	−40.2457	−1.68719	−0.843593	−	0.536983i	$-0.819564\pi$
$569$	−40.2457	−1.68719	−0.843593	+	0.536983i	$0.819564\pi$
$570$	5.00308	0.209556
$571$	−9.96583	−0.417057	−0.208529	−	0.978016i	$-0.566867\pi$
$571$	−9.96583	−0.417057	−0.208529	+	0.978016i	$0.566867\pi$
$572$	3.13935	0.131263
$573$	28.7745	1.20207
$574$	29.2559	1.22112
$575$	−1.80458	−0.0752562
$576$	−1.01066	−0.0421107
$577$	−29.0788	−1.21057	−0.605284	−	0.796010i	$-0.706940\pi$
$577$	−29.0788	−1.21057	−0.605284	+	0.796010i	$0.706940\pi$
$578$	−12.6232	−0.525054
$579$	3.59314	0.149326
$580$	−0.429786	−0.0178459
$581$	−28.1994	−1.16991
$582$	8.96291	0.371524
$583$	8.20765	0.339926
$584$	−5.43760	−0.225010
$585$	3.04874	0.126050
$586$	−11.1006	−0.458562
$587$	6.93147	0.286092	0.143046	−	0.989716i	$-0.454310\pi$
$587$	6.93147	0.286092	0.143046	+	0.989716i	$0.454310\pi$
$588$	4.13122	0.170369
$589$	−33.8910	−1.39646
$590$	3.06070	0.126007
$591$	−5.06400	−0.208305
$592$	7.40717	0.304433
$593$	−40.2143	−1.65140	−0.825701	−	0.564108i	$-0.809220\pi$
$593$	−40.2143	−1.65140	−0.825701	+	0.564108i	$0.809220\pi$
$594$	5.88698	0.241546
$595$	−6.59225	−0.270256
$596$	−7.35152	−0.301130
$597$	−31.8868	−1.30504
$598$	5.44369	0.222609
$599$	39.7203	1.62293	0.811464	−	0.584402i	$-0.198671\pi$
$599$	39.7203	1.62293	0.811464	+	0.584402i	$0.198671\pi$
$600$	1.41044	0.0575810
$601$	−1.00000	−0.0407909
$601$	−1.00000	−0.0407909
$602$	23.4275	0.954834
$603$	−11.2635	−0.458686
$604$	16.3564	0.665533
$605$	−9.91696	−0.403182
$606$	−5.78677	−0.235071
$607$	−1.07765	−0.0437405	−0.0218702	−	0.999761i	$-0.506962\pi$
$607$	−1.07765	−0.0437405	−0.0218702	+	0.999761i	$0.506962\pi$
$608$	3.54717	0.143857
$609$	1.91012	0.0774020
$610$	−4.36339	−0.176668
$611$	31.9727	1.29348
$612$	−2.11438	−0.0854689
$613$	16.2193	0.655091	0.327546	−	0.944835i	$-0.393778\pi$
$613$	16.2193	0.655091	0.327546	+	0.944835i	$0.393778\pi$
$614$	10.5173	0.424444
$615$	−13.0953	−0.528053
$616$	3.27926	0.132125
$617$	35.2021	1.41718	0.708591	−	0.705619i	$-0.249331\pi$
$617$	35.2021	1.41718	0.708591	+	0.705619i	$0.249331\pi$
$618$	−12.2265	−0.491820
$619$	39.2335	1.57693	0.788463	−	0.615082i	$-0.210877\pi$
$619$	39.2335	1.57693	0.788463	+	0.615082i	$0.210877\pi$
$620$	−9.55437	−0.383713
$621$	10.2081	0.409638
$622$	9.81794	0.393664
$623$	26.2818	1.05296
$624$	−4.25473	−0.170325
$625$	1.00000	0.0400000
$626$	26.9734	1.07807
$627$	−5.20667	−0.207934
$628$	−7.76589	−0.309893
$629$	15.4965	0.617884
$630$	3.18461	0.126878
$631$	35.7483	1.42312	0.711558	−	0.702628i	$-0.247990\pi$
$631$	35.7483	1.42312	0.711558	+	0.702628i	$0.247990\pi$
$632$	9.01031	0.358411
$633$	−0.794972	−0.0315973
$634$	9.77743	0.388311
$635$	12.6071	0.500299
$636$	−11.1238	−0.441086
$637$	−8.83569	−0.350083
$638$	0.447275	0.0177078
$639$	−8.37344	−0.331248
$640$	1.00000	0.0395285
$641$	−12.6490	−0.499604	−0.249802	−	0.968297i	$-0.580366\pi$
$641$	−12.6490	−0.499604	−0.249802	+	0.968297i	$0.580366\pi$
$642$	−21.5861	−0.851934
$643$	17.2681	0.680987	0.340494	−	0.940247i	$-0.389406\pi$
$643$	17.2681	0.680987	0.340494	+	0.940247i	$0.389406\pi$
$644$	5.68630	0.224072
$645$	−10.4864	−0.412903
$646$	7.42101	0.291976
$647$	−10.9293	−0.429677	−0.214838	−	0.976650i	$-0.568922\pi$
$647$	−10.9293	−0.429677	−0.214838	+	0.976650i	$0.568922\pi$
$648$	−4.94661	−0.194321
$649$	−3.18525	−0.125032
$650$	−3.01659	−0.118321
$651$	42.4630	1.66426
$652$	15.3338	0.600519
$653$	−10.2745	−0.402071	−0.201036	−	0.979584i	$-0.564431\pi$
$653$	−10.2745	−0.402071	−0.201036	+	0.979584i	$0.564431\pi$
$654$	−19.1173	−0.747546
$655$	9.23835	0.360972
$656$	−9.28453	−0.362500
$657$	5.49555	0.214402
$658$	33.3976	1.30197
$659$	−1.44077	−0.0561245	−0.0280623	−	0.999606i	$-0.508934\pi$
$659$	−1.44077	−0.0561245	−0.0280623	+	0.999606i	$0.508934\pi$
$660$	−1.46783	−0.0571354
$661$	−15.7992	−0.614518	−0.307259	−	0.951626i	$-0.599412\pi$
$661$	−15.7992	−0.614518	−0.307259	+	0.951626i	$0.599412\pi$
$662$	9.21802	0.358268
$663$	−8.90127	−0.345697
$664$	8.94926	0.347299
$665$	−11.1773	−0.433436
$666$	−7.48610	−0.290081
$667$	0.775584	0.0300307
$668$	−20.5909	−0.796686
$669$	−12.9647	−0.501244
$670$	11.1448	0.430559
$671$	4.54094	0.175301
$672$	−4.44435	−0.171445
$673$	38.0739	1.46764	0.733821	−	0.679343i	$-0.237735\pi$
$673$	38.0739	1.46764	0.733821	+	0.679343i	$0.237735\pi$
$674$	−3.83268	−0.147629
$675$	−5.65679	−0.217730
$676$	−3.90016	−0.150006
$677$	−34.5726	−1.32873	−0.664366	−	0.747407i	$-0.731298\pi$
$677$	−34.5726	−1.32873	−0.664366	+	0.747407i	$0.731298\pi$
$678$	22.7401	0.873330
$679$	−20.0238	−0.768444
$680$	2.09209	0.0802280
$681$	−6.72263	−0.257612
$682$	9.94316	0.380743
$683$	30.5658	1.16957	0.584784	−	0.811189i	$-0.301179\pi$
$683$	30.5658	1.16957	0.584784	+	0.811189i	$0.301179\pi$
$684$	−3.58497	−0.137075
$685$	−22.3754	−0.854919
$686$	12.8278	0.489767
$687$	−16.7989	−0.640918
$688$	−7.43486	−0.283451
$689$	23.7911	0.906367
$690$	−2.54525	−0.0968962
$691$	−20.9029	−0.795184	−0.397592	−	0.917562i	$-0.630154\pi$
$691$	−20.9029	−0.795184	−0.397592	+	0.917562i	$0.630154\pi$
$692$	9.79839	0.372479
$693$	−3.31420	−0.125896
$694$	28.8686	1.09584
$695$	−14.1367	−0.536235
$696$	−0.606188	−0.0229775
$697$	−19.4241	−0.735739
$698$	26.4828	1.00239
$699$	21.6758	0.819852
$700$	−3.15104	−0.119098
$701$	−23.0749	−0.871526	−0.435763	−	0.900061i	$-0.643521\pi$
$701$	−23.0749	−0.871526	−0.435763	+	0.900061i	$0.643521\pi$
$702$	17.0643	0.644049
$703$	26.2745	0.990962
$704$	−1.04069	−0.0392226
$705$	−14.9492	−0.563018
$706$	−17.6764	−0.665259
$707$	12.9281	0.486211
$708$	4.31694	0.162241
$709$	−38.6734	−1.45241	−0.726204	−	0.687479i	$-0.758717\pi$
$709$	−38.6734	−1.45241	−0.726204	+	0.687479i	$0.758717\pi$
$710$	8.28515	0.310936
$711$	−9.10632	−0.341514
$712$	−8.34070	−0.312581
$713$	17.2416	0.645704
$714$	−9.29798	−0.347968
$715$	3.13935	0.117405
$716$	11.9994	0.448439
$717$	−12.2373	−0.457009
$718$	−17.0247	−0.635356
$719$	25.4717	0.949935	0.474968	−	0.880003i	$-0.342460\pi$
$719$	25.4717	0.949935	0.474968	+	0.880003i	$0.342460\pi$
$720$	−1.01066	−0.0376649
$721$	27.3149	1.01726
$722$	−6.41755	−0.238837
$723$	−16.8175	−0.625448
$724$	0.246164	0.00914860
$725$	−0.429786	−0.0159619
$726$	−13.9873	−0.519117
$727$	23.5111	0.871977	0.435989	−	0.899952i	$-0.356399\pi$
$727$	23.5111	0.871977	0.435989	+	0.899952i	$0.356399\pi$
$728$	9.50540	0.352293
$729$	28.9350	1.07167
$730$	−5.43760	−0.201255
$731$	−15.5544	−0.575300
$732$	−6.15430	−0.227470
$733$	−5.37759	−0.198626	−0.0993129	−	0.995056i	$-0.531664\pi$
$733$	−5.37759	−0.198626	−0.0993129	+	0.995056i	$0.531664\pi$
$734$	−36.4460	−1.34525
$735$	4.13122	0.152382
$736$	−1.80458	−0.0665177
$737$	−11.5983	−0.427227
$738$	9.38347	0.345410
$739$	−15.8932	−0.584642	−0.292321	−	0.956320i	$-0.594427\pi$
$739$	−15.8932	−0.584642	−0.292321	+	0.956320i	$0.594427\pi$
$740$	7.40717	0.272293
$741$	−15.0923	−0.554428
$742$	24.8514	0.912322
$743$	12.1988	0.447530	0.223765	−	0.974643i	$-0.428165\pi$
$743$	12.1988	0.447530	0.223765	+	0.974643i	$0.428165\pi$
$744$	−13.4759	−0.494050
$745$	−7.35152	−0.269339
$746$	−15.9187	−0.582825
$747$	−9.04462	−0.330926
$748$	−2.17722	−0.0796071
$749$	48.2250	1.76210
$750$	1.41044	0.0515020
$751$	38.6497	1.41035	0.705173	−	0.709035i	$-0.250869\pi$
$751$	38.6497	1.41035	0.705173	+	0.709035i	$0.250869\pi$
$752$	−10.5989	−0.386503
$753$	−16.5361	−0.602608
$754$	1.29649	0.0472154
$755$	16.3564	0.595271
$756$	17.8248	0.648280
$757$	−1.02975	−0.0374268	−0.0187134	−	0.999825i	$-0.505957\pi$
$757$	−1.02975	−0.0374268	−0.0187134	+	0.999825i	$0.505957\pi$
$758$	−9.80431	−0.356109
$759$	2.64883	0.0961463
$760$	3.54717	0.128670
$761$	22.6429	0.820806	0.410403	−	0.911904i	$-0.365388\pi$
$761$	22.6429	0.820806	0.410403	+	0.911904i	$0.365388\pi$
$762$	17.7816	0.644160
$763$	42.7096	1.54619
$764$	20.4010	0.738084
$765$	−2.11438	−0.0764457
$766$	−9.63675	−0.348190
$767$	−9.23290	−0.333381
$768$	1.41044	0.0508949
$769$	0.211541	0.00762835	0.00381417	−	0.999993i	$-0.498786\pi$
$769$	0.211541	0.00762835	0.00381417	+	0.999993i	$0.498786\pi$
$770$	3.27926	0.118176
$771$	23.4503	0.844543
$772$	2.54753	0.0916875
$773$	6.41109	0.230591	0.115295	−	0.993331i	$-0.463219\pi$
$773$	6.41109	0.230591	0.115295	+	0.993331i	$0.463219\pi$
$774$	7.51408	0.270088
$775$	−9.55437	−0.343203
$776$	6.35468	0.228120
$777$	−32.9201	−1.18100
$778$	10.6926	0.383349
$779$	−32.9339	−1.17998
$780$	−4.25473	−0.152344
$781$	−8.62229	−0.308530
$782$	−3.77534	−0.135006
$783$	2.43121	0.0868845
$784$	2.92903	0.104608
$785$	−7.76589	−0.277176
$786$	13.0301	0.464770
$787$	15.8847	0.566227	0.283114	−	0.959086i	$-0.408633\pi$
$787$	15.8847	0.566227	0.283114	+	0.959086i	$0.408633\pi$
$788$	−3.59037	−0.127901
$789$	24.0672	0.856816
$790$	9.01031	0.320572
$791$	−50.8033	−1.80636
$792$	1.05178	0.0373734
$793$	13.1626	0.467417
$794$	3.69620	0.131173
$795$	−11.1238	−0.394519
$796$	−22.6077	−0.801308
$797$	−20.6779	−0.732449	−0.366225	−	0.930526i	$-0.619350\pi$
$797$	−20.6779	−0.732449	−0.366225	+	0.930526i	$0.619350\pi$
$798$	−15.7649	−0.558071
$799$	−22.1739	−0.784456
$800$	1.00000	0.0353553
$801$	8.42958	0.297845
$802$	2.95099	0.104203
$803$	5.65887	0.199697
$804$	15.7190	0.554367
$805$	5.68630	0.200416
$806$	28.8217	1.01520
$807$	−10.6461	−0.374760
$808$	−4.10281	−0.144336
$809$	−44.6175	−1.56867	−0.784334	−	0.620339i	$-0.786995\pi$
$809$	−44.6175	−1.56867	−0.784334	+	0.620339i	$0.786995\pi$
$810$	−4.94661	−0.173806
$811$	−2.34123	−0.0822119	−0.0411059	−	0.999155i	$-0.513088\pi$
$811$	−2.34123	−0.0822119	−0.0411059	+	0.999155i	$0.513088\pi$
$812$	1.35427	0.0475257
$813$	4.21304	0.147758
$814$	−7.70858	−0.270186
$815$	15.3338	0.537121
$816$	2.95077	0.103298
$817$	−26.3727	−0.922665
$818$	34.2197	1.19646
$819$	−9.60669	−0.335685
$820$	−9.28453	−0.324230
$821$	20.3297	0.709510	0.354755	−	0.934959i	$-0.384564\pi$
$821$	20.3297	0.709510	0.354755	+	0.934959i	$0.384564\pi$
$822$	−31.5591	−1.10075
$823$	−33.4109	−1.16463	−0.582316	−	0.812963i	$-0.697853\pi$
$823$	−33.4109	−1.16463	−0.582316	+	0.812963i	$0.697853\pi$
$824$	−8.66854	−0.301983
$825$	−1.46783	−0.0511034
$826$	−9.64438	−0.335571
$827$	14.0651	0.489092	0.244546	−	0.969638i	$-0.421361\pi$
$827$	14.0651	0.489092	0.244546	+	0.969638i	$0.421361\pi$
$828$	1.82381	0.0633818
$829$	−27.2410	−0.946119	−0.473060	−	0.881030i	$-0.656850\pi$
$829$	−27.2410	−0.946119	−0.473060	+	0.881030i	$0.656850\pi$
$830$	8.94926	0.310633
$831$	−0.884198	−0.0306725
$832$	−3.01659	−0.104582
$833$	6.12779	0.212315
$834$	−19.9390	−0.690430
$835$	−20.5909	−0.712578
$836$	−3.69152	−0.127674
$837$	54.0471	1.86814
$838$	−29.3149	−1.01267
$839$	−24.1273	−0.832968	−0.416484	−	0.909143i	$-0.636738\pi$
$839$	−24.1273	−0.832968	−0.416484	+	0.909143i	$0.636738\pi$
$840$	−4.44435	−0.153345
$841$	−28.8153	−0.993630
$842$	−11.7698	−0.405613
$843$	32.5082	1.11964
$844$	−0.563633	−0.0194011
$845$	−3.90016	−0.134170
$846$	10.7119	0.368282
$847$	31.2487	1.07372
$848$	−7.88673	−0.270831
$849$	2.59283	0.0889856
$850$	2.09209	0.0717581
$851$	−13.3668	−0.458209
$852$	11.6857	0.400346
$853$	−21.3206	−0.730002	−0.365001	−	0.931007i	$-0.618931\pi$
$853$	−21.3206	−0.730002	−0.365001	+	0.931007i	$0.618931\pi$
$854$	13.7492	0.470488
$855$	−3.58497	−0.122604
$856$	−15.3045	−0.523096
$857$	37.7178	1.28842	0.644208	−	0.764850i	$-0.277187\pi$
$857$	37.7178	1.28842	0.644208	+	0.764850i	$0.277187\pi$
$858$	4.42786	0.151165
$859$	21.5115	0.733963	0.366982	−	0.930228i	$-0.380391\pi$
$859$	21.5115	0.733963	0.366982	+	0.930228i	$0.380391\pi$
$860$	−7.43486	−0.253527
$861$	41.2637	1.40626
$862$	17.6035	0.599578
$863$	3.67152	0.124980	0.0624900	−	0.998046i	$-0.480096\pi$
$863$	3.67152	0.124980	0.0624900	+	0.998046i	$0.480096\pi$
$864$	−5.65679	−0.192448
$865$	9.79839	0.333155
$866$	19.7338	0.670583
$867$	−17.8042	−0.604663
$868$	30.1062	1.02187
$869$	−9.37696	−0.318091
$870$	−0.606188	−0.0205517
$871$	−33.6192	−1.13914
$872$	−13.5541	−0.459001
$873$	−6.42240	−0.217365
$874$	−6.40116	−0.216523
$875$	−3.15104	−0.106524
$876$	−7.66942	−0.259126
$877$	−55.2201	−1.86465	−0.932325	−	0.361620i	$-0.882224\pi$
$877$	−55.2201	−1.86465	−0.932325	+	0.361620i	$0.882224\pi$
$878$	−20.8591	−0.703962
$879$	−15.6568	−0.528089
$880$	−1.04069	−0.0350817
$881$	−30.9841	−1.04388	−0.521940	−	0.852982i	$-0.674792\pi$
$881$	−30.9841	−1.04388	−0.521940	+	0.852982i	$0.674792\pi$
$882$	−2.96024	−0.0996765
$883$	−5.21387	−0.175461	−0.0877304	−	0.996144i	$-0.527961\pi$
$883$	−5.21387	−0.175461	−0.0877304	+	0.996144i	$0.527961\pi$
$884$	−6.31099	−0.212261
$885$	4.31694	0.145112
$886$	−21.5858	−0.725188
$887$	3.86782	0.129869	0.0649343	−	0.997890i	$-0.479316\pi$
$887$	3.86782	0.129869	0.0649343	+	0.997890i	$0.479316\pi$
$888$	10.4474	0.350591
$889$	−39.7255	−1.33235
$890$	−8.34070	−0.279581
$891$	5.14789	0.172461
$892$	−9.19193	−0.307769
$893$	−37.5962	−1.25811
$894$	−10.3689	−0.346787
$895$	11.9994	0.401096
$896$	−3.15104	−0.105269
$897$	7.67800	0.256361
$898$	15.1846	0.506718
$899$	4.10634	0.136954
$900$	−1.01066	−0.0336885
$901$	−16.4997	−0.549686
$902$	9.66234	0.321721
$903$	33.0431	1.09961
$904$	16.1227	0.536234
$905$	0.246164	0.00818276
$906$	23.0698	0.766441
$907$	−46.4004	−1.54070	−0.770350	−	0.637622i	$-0.779918\pi$
$907$	−46.4004	−1.54070	−0.770350	+	0.637622i	$0.779918\pi$
$908$	−4.76633	−0.158176
$909$	4.14653	0.137532
$910$	9.50540	0.315101
$911$	−31.7722	−1.05266	−0.526330	−	0.850280i	$-0.676432\pi$
$911$	−31.7722	−1.05266	−0.526330	+	0.850280i	$0.676432\pi$
$912$	5.00308	0.165669
$913$	−9.31342	−0.308229
$914$	10.6088	0.350907
$915$	−6.15430	−0.203455
$916$	−11.9104	−0.393530
$917$	−29.1104	−0.961309
$918$	−11.8345	−0.390597
$919$	−38.7173	−1.27717	−0.638584	−	0.769553i	$-0.720479\pi$
$919$	−38.7173	−1.27717	−0.638584	+	0.769553i	$0.720479\pi$
$920$	−1.80458	−0.0594953
$921$	14.8341	0.488799
$922$	−3.89885	−0.128402
$923$	−24.9929	−0.822652
$924$	4.62520	0.152158
$925$	7.40717	0.243546
$926$	3.98126	0.130832
$927$	8.76091	0.287746
$928$	−0.429786	−0.0141084
$929$	−21.4597	−0.704071	−0.352035	−	0.935987i	$-0.614510\pi$
$929$	−21.4597	−0.704071	−0.352035	+	0.935987i	$0.614510\pi$
$930$	−13.4759	−0.441891
$931$	10.3898	0.340511
$932$	15.3681	0.503398
$933$	13.8476	0.453351
$934$	12.8211	0.419520
$935$	−2.17722	−0.0712027
$936$	3.04874	0.0996512
$937$	7.45122	0.243421	0.121710	−	0.992566i	$-0.461162\pi$
$937$	7.45122	0.243421	0.121710	+	0.992566i	$0.461162\pi$
$938$	−35.1175	−1.14663
$939$	38.0444	1.24153
$940$	−10.5989	−0.345699
$941$	37.2907	1.21564	0.607822	−	0.794073i	$-0.292044\pi$
$941$	37.2907	1.21564	0.607822	+	0.794073i	$0.292044\pi$
$942$	−10.9533	−0.356879
$943$	16.7547	0.545608
$944$	3.06070	0.0996174
$945$	17.8248	0.579840
$946$	7.73740	0.251564
$947$	−47.3493	−1.53865	−0.769323	−	0.638859i	$-0.779407\pi$
$947$	−47.3493	−1.53865	−0.769323	+	0.638859i	$0.779407\pi$
$948$	12.7085	0.412753
$949$	16.4030	0.532465
$950$	3.54717	0.115086
$951$	13.7905	0.447187
$952$	−6.59225	−0.213656
$953$	29.2932	0.948899	0.474450	−	0.880283i	$-0.342647\pi$
$953$	29.2932	0.948899	0.474450	+	0.880283i	$0.342647\pi$
$954$	7.97077	0.258063
$955$	20.4010	0.660162
$956$	−8.67620	−0.280608
$957$	0.630855	0.0203927
$958$	−21.5439	−0.696053
$959$	70.5056	2.27674
$960$	1.41044	0.0455218
$961$	60.2860	1.94471
$962$	−22.3444	−0.720413
$963$	15.4676	0.498436
$964$	−11.9235	−0.384031
$965$	2.54753	0.0820078
$966$	8.02019	0.258045
$967$	−40.1468	−1.29103	−0.645517	−	0.763746i	$-0.723358\pi$
$967$	−40.1468	−1.29103	−0.645517	+	0.763746i	$0.723358\pi$
$968$	−9.91696	−0.318743
$969$	10.4669	0.336245
$970$	6.35468	0.204037
$971$	16.4345	0.527410	0.263705	−	0.964603i	$-0.415056\pi$
$971$	16.4345	0.527410	0.263705	+	0.964603i	$0.415056\pi$
$972$	9.99349	0.320541
$973$	44.5452	1.42805
$974$	31.2923	1.00267
$975$	−4.25473	−0.136260
$976$	−4.36339	−0.139669
$977$	35.9031	1.14864	0.574322	−	0.818630i	$-0.305266\pi$
$977$	35.9031	1.14864	0.574322	+	0.818630i	$0.305266\pi$
$978$	21.6275	0.691570
$979$	8.68010	0.277417
$980$	2.92903	0.0935644
$981$	13.6986	0.437362
$982$	16.7735	0.535265
$983$	−23.9468	−0.763785	−0.381893	−	0.924207i	$-0.624728\pi$
$983$	−23.9468	−0.763785	−0.381893	+	0.924207i	$0.624728\pi$
$984$	−13.0953	−0.417462
$985$	−3.59037	−0.114399
$986$	−0.899152	−0.0286348
$987$	47.1053	1.49938
$988$	−10.7004	−0.340425
$989$	13.4168	0.426629
$990$	1.05178	0.0334278
$991$	37.5903	1.19410	0.597048	−	0.802205i	$-0.296340\pi$
$991$	37.5903	1.19410	0.597048	+	0.802205i	$0.296340\pi$
$992$	−9.55437	−0.303352
$993$	13.0015	0.412589
$994$	−26.1068	−0.828057
$995$	−22.6077	−0.716712
$996$	12.6224	0.399956
$997$	−0.824218	−0.0261033	−0.0130516	−	0.999915i	$-0.504155\pi$
$997$	−0.824218	−0.0261033	−0.0130516	+	0.999915i	$0.504155\pi$
$998$	10.5285	0.333273
$999$	−41.9008	−1.32568

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6010.2.a.c.1.14	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6010.2.a.c.1.14	✓	16	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:	\( N \)	\(=\)	\( 6010 = 2 \cdot 5 \cdot 601 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6010.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.41044 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.41044 q^{6} -3.15104 q^{7} +1.00000 q^{8} -1.01066 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.41044 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.41044 q^{6} -3.15104 q^{7} +1.00000 q^{8} -1.01066 q^{9} +1.00000 q^{10} -1.04069 q^{11} +1.41044 q^{12} -3.01659 q^{13} -3.15104 q^{14} +1.41044 q^{15} +1.00000 q^{16} +2.09209 q^{17} -1.01066 q^{18} +3.54717 q^{19} +1.00000 q^{20} -4.44435 q^{21} -1.04069 q^{22} -1.80458 q^{23} +1.41044 q^{24} +1.00000 q^{25} -3.01659 q^{26} -5.65679 q^{27} -3.15104 q^{28} -0.429786 q^{29} +1.41044 q^{30} -9.55437 q^{31} +1.00000 q^{32} -1.46783 q^{33} +2.09209 q^{34} -3.15104 q^{35} -1.01066 q^{36} +7.40717 q^{37} +3.54717 q^{38} -4.25473 q^{39} +1.00000 q^{40} -9.28453 q^{41} -4.44435 q^{42} -7.43486 q^{43} -1.04069 q^{44} -1.01066 q^{45} -1.80458 q^{46} -10.5989 q^{47} +1.41044 q^{48} +2.92903 q^{49} +1.00000 q^{50} +2.95077 q^{51} -3.01659 q^{52} -7.88673 q^{53} -5.65679 q^{54} -1.04069 q^{55} -3.15104 q^{56} +5.00308 q^{57} -0.429786 q^{58} +3.06070 q^{59} +1.41044 q^{60} -4.36339 q^{61} -9.55437 q^{62} +3.18461 q^{63} +1.00000 q^{64} -3.01659 q^{65} -1.46783 q^{66} +11.1448 q^{67} +2.09209 q^{68} -2.54525 q^{69} -3.15104 q^{70} +8.28515 q^{71} -1.01066 q^{72} -5.43760 q^{73} +7.40717 q^{74} +1.41044 q^{75} +3.54717 q^{76} +3.27926 q^{77} -4.25473 q^{78} +9.01031 q^{79} +1.00000 q^{80} -4.94661 q^{81} -9.28453 q^{82} +8.94926 q^{83} -4.44435 q^{84} +2.09209 q^{85} -7.43486 q^{86} -0.606188 q^{87} -1.04069 q^{88} -8.34070 q^{89} -1.01066 q^{90} +9.50540 q^{91} -1.80458 q^{92} -13.4759 q^{93} -10.5989 q^{94} +3.54717 q^{95} +1.41044 q^{96} +6.35468 q^{97} +2.92903 q^{98} +1.05178 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{2} - 8 q^{3} + 16 q^{4} + 16 q^{5} - 8 q^{6} - 10 q^{7} + 16 q^{8} - 2 q^{9}+O(q^{10}) \) 16 * q + 16 * q^2 - 8 * q^3 + 16 * q^4 + 16 * q^5 - 8 * q^6 - 10 * q^7 + 16 * q^8 - 2 * q^9	\( 16 q + 16 q^{2} - 8 q^{3} + 16 q^{4} + 16 q^{5} - 8 q^{6} - 10 q^{7} + 16 q^{8} - 2 q^{9} + 16 q^{10} - 14 q^{11} - 8 q^{12} - 20 q^{13} - 10 q^{14} - 8 q^{15} + 16 q^{16} - 27 q^{17} - 2 q^{18} - 17 q^{19} + 16 q^{20} - 12 q^{21} - 14 q^{22} - 9 q^{23} - 8 q^{24} + 16 q^{25} - 20 q^{26} - 11 q^{27} - 10 q^{28} - 23 q^{29} - 8 q^{30} - 21 q^{31} + 16 q^{32} - 9 q^{33} - 27 q^{34} - 10 q^{35} - 2 q^{36} - 16 q^{37} - 17 q^{38} - 6 q^{39} + 16 q^{40} - 35 q^{41} - 12 q^{42} + 3 q^{43} - 14 q^{44} - 2 q^{45} - 9 q^{46} - 25 q^{47} - 8 q^{48} - 24 q^{49} + 16 q^{50} - q^{51} - 20 q^{52} - 39 q^{53} - 11 q^{54} - 14 q^{55} - 10 q^{56} - 6 q^{57} - 23 q^{58} - 32 q^{59} - 8 q^{60} - 38 q^{61} - 21 q^{62} + q^{63} + 16 q^{64} - 20 q^{65} - 9 q^{66} + 5 q^{67} - 27 q^{68} - 25 q^{69} - 10 q^{70} - 16 q^{71} - 2 q^{72} - 17 q^{73} - 16 q^{74} - 8 q^{75} - 17 q^{76} - 34 q^{77} - 6 q^{78} - 40 q^{79} + 16 q^{80} - 28 q^{81} - 35 q^{82} - 22 q^{83} - 12 q^{84} - 27 q^{85} + 3 q^{86} + 10 q^{87} - 14 q^{88} - 46 q^{89} - 2 q^{90} - q^{91} - 9 q^{92} + 14 q^{93} - 25 q^{94} - 17 q^{95} - 8 q^{96} - 21 q^{97} - 24 q^{98} + 15 q^{99}+O(q^{100}) \) 16 * q + 16 * q^2 - 8 * q^3 + 16 * q^4 + 16 * q^5 - 8 * q^6 - 10 * q^7 + 16 * q^8 - 2 * q^9 + 16 * q^10 - 14 * q^11 - 8 * q^12 - 20 * q^13 - 10 * q^14 - 8 * q^15 + 16 * q^16 - 27 * q^17 - 2 * q^18 - 17 * q^19 + 16 * q^20 - 12 * q^21 - 14 * q^22 - 9 * q^23 - 8 * q^24 + 16 * q^25 - 20 * q^26 - 11 * q^27 - 10 * q^28 - 23 * q^29 - 8 * q^30 - 21 * q^31 + 16 * q^32 - 9 * q^33 - 27 * q^34 - 10 * q^35 - 2 * q^36 - 16 * q^37 - 17 * q^38 - 6 * q^39 + 16 * q^40 - 35 * q^41 - 12 * q^42 + 3 * q^43 - 14 * q^44 - 2 * q^45 - 9 * q^46 - 25 * q^47 - 8 * q^48 - 24 * q^49 + 16 * q^50 - q^51 - 20 * q^52 - 39 * q^53 - 11 * q^54 - 14 * q^55 - 10 * q^56 - 6 * q^57 - 23 * q^58 - 32 * q^59 - 8 * q^60 - 38 * q^61 - 21 * q^62 + q^63 + 16 * q^64 - 20 * q^65 - 9 * q^66 + 5 * q^67 - 27 * q^68 - 25 * q^69 - 10 * q^70 - 16 * q^71 - 2 * q^72 - 17 * q^73 - 16 * q^74 - 8 * q^75 - 17 * q^76 - 34 * q^77 - 6 * q^78 - 40 * q^79 + 16 * q^80 - 28 * q^81 - 35 * q^82 - 22 * q^83 - 12 * q^84 - 27 * q^85 + 3 * q^86 + 10 * q^87 - 14 * q^88 - 46 * q^89 - 2 * q^90 - q^91 - 9 * q^92 + 14 * q^93 - 25 * q^94 - 17 * q^95 - 8 * q^96 - 21 * q^97 - 24 * q^98 + 15 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more