LMFDB - Embedded newform 1805.2.a.r.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1805,2,Mod(1,1805)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1805, 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("1805.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1805 = 5 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1805.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:	$14.4129975648$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.5822000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 8x^{4} + 5x^{3} + 14x^{2} + x - 1 $ x^6 - x^5 - 8x^4 + 5x^3 + 14*x^2 + x - 1
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			1.3
Root			$-0.343361$ of defining polynomial
Character	$\chi$	$=$	1805.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.274673 q^{2} +3.09431 q^{3} -1.92455 q^{4} -1.00000 q^{5} -0.849925 q^{6} +3.63772 q^{7} +1.07797 q^{8} +6.57477 q^{9} +O(q^{10})$	\(q-0.274673 q^{2} +3.09431 q^{3} -1.92455 q^{4} -1.00000 q^{5} -0.849925 q^{6} +3.63772 q^{7} +1.07797 q^{8} +6.57477 q^{9} +0.274673 q^{10} +2.45483 q^{11} -5.95517 q^{12} +3.81342 q^{13} -0.999184 q^{14} -3.09431 q^{15} +3.55302 q^{16} -3.62089 q^{17} -1.80591 q^{18} +1.92455 q^{20} +11.2562 q^{21} -0.674276 q^{22} -9.19377 q^{23} +3.33558 q^{24} +1.00000 q^{25} -1.04744 q^{26} +11.0614 q^{27} -7.00098 q^{28} -1.81600 q^{29} +0.849925 q^{30} +7.04948 q^{31} -3.13186 q^{32} +7.59601 q^{33} +0.994562 q^{34} -3.63772 q^{35} -12.6535 q^{36} -0.500137 q^{37} +11.7999 q^{39} -1.07797 q^{40} -1.42551 q^{41} -3.09179 q^{42} +6.78124 q^{43} -4.72445 q^{44} -6.57477 q^{45} +2.52528 q^{46} +0.193490 q^{47} +10.9942 q^{48} +6.23298 q^{49} -0.274673 q^{50} -11.2042 q^{51} -7.33913 q^{52} -4.54544 q^{53} -3.03828 q^{54} -2.45483 q^{55} +3.92135 q^{56} +0.498806 q^{58} -1.29597 q^{59} +5.95517 q^{60} +8.12536 q^{61} -1.93631 q^{62} +23.9171 q^{63} -6.24580 q^{64} -3.81342 q^{65} -2.08642 q^{66} -8.17102 q^{67} +6.96860 q^{68} -28.4484 q^{69} +0.999184 q^{70} +5.69618 q^{71} +7.08741 q^{72} +2.63792 q^{73} +0.137374 q^{74} +3.09431 q^{75} +8.92998 q^{77} -3.24112 q^{78} -5.11318 q^{79} -3.55302 q^{80} +14.5033 q^{81} +0.391549 q^{82} -0.287184 q^{83} -21.6632 q^{84} +3.62089 q^{85} -1.86263 q^{86} -5.61926 q^{87} +2.64623 q^{88} +4.91011 q^{89} +1.80591 q^{90} +13.8721 q^{91} +17.6939 q^{92} +21.8133 q^{93} -0.0531467 q^{94} -9.69096 q^{96} +8.24002 q^{97} -1.71203 q^{98} +16.1399 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{2} + 4 q^{3} + 8 q^{4} - 6 q^{5} + 8 q^{6} + 7 q^{7} + 10 q^{9}+O(q^{10}) $ 6 * q + 2 * q^2 + 4 * q^3 + 8 * q^4 - 6 * q^5 + 8 * q^6 + 7 * q^7 + 10 * q^9	\( 6 q + 2 q^{2} + 4 q^{3} + 8 q^{4} - 6 q^{5} + 8 q^{6} + 7 q^{7} + 10 q^{9} - 2 q^{10} + 15 q^{11} - 20 q^{12} + 6 q^{13} + 20 q^{14} - 4 q^{15} + 20 q^{16} + 5 q^{17} - 8 q^{18} - 8 q^{20} + 7 q^{21} + 14 q^{22} + 18 q^{24} + 6 q^{25} - 22 q^{26} + 28 q^{27} + 10 q^{28} - 20 q^{29} - 8 q^{30} + 12 q^{31} - 8 q^{32} + q^{33} - 7 q^{35} - 14 q^{36} + 20 q^{37} + 16 q^{39} + 8 q^{41} - 30 q^{42} + 27 q^{43} + 46 q^{44} - 10 q^{45} + 16 q^{46} - 8 q^{47} - 24 q^{48} + 11 q^{49} + 2 q^{50} - 11 q^{51} + 4 q^{52} + 19 q^{53} + 30 q^{54} - 15 q^{55} + 62 q^{56} + 20 q^{58} - 41 q^{59} + 20 q^{60} + 6 q^{61} - 30 q^{62} - 18 q^{63} + 48 q^{64} - 6 q^{65} + 46 q^{66} - 15 q^{67} - 14 q^{68} - 10 q^{69} - 20 q^{70} + 2 q^{71} - 68 q^{72} + 8 q^{73} + 2 q^{74} + 4 q^{75} + 21 q^{77} + 46 q^{78} + 18 q^{79} - 20 q^{80} + 50 q^{81} - 18 q^{82} - 10 q^{83} + 4 q^{84} - 5 q^{85} - 10 q^{86} - 14 q^{87} - 52 q^{88} + 17 q^{89} + 8 q^{90} - 23 q^{91} + 28 q^{92} + 10 q^{93} - 28 q^{94} + 26 q^{96} - 4 q^{97} + 50 q^{98} + 58 q^{99}+O(q^{100}) \) 6 * q + 2 * q^2 + 4 * q^3 + 8 * q^4 - 6 * q^5 + 8 * q^6 + 7 * q^7 + 10 * q^9 - 2 * q^10 + 15 * q^11 - 20 * q^12 + 6 * q^13 + 20 * q^14 - 4 * q^15 + 20 * q^16 + 5 * q^17 - 8 * q^18 - 8 * q^20 + 7 * q^21 + 14 * q^22 + 18 * q^24 + 6 * q^25 - 22 * q^26 + 28 * q^27 + 10 * q^28 - 20 * q^29 - 8 * q^30 + 12 * q^31 - 8 * q^32 + q^33 - 7 * q^35 - 14 * q^36 + 20 * q^37 + 16 * q^39 + 8 * q^41 - 30 * q^42 + 27 * q^43 + 46 * q^44 - 10 * q^45 + 16 * q^46 - 8 * q^47 - 24 * q^48 + 11 * q^49 + 2 * q^50 - 11 * q^51 + 4 * q^52 + 19 * q^53 + 30 * q^54 - 15 * q^55 + 62 * q^56 + 20 * q^58 - 41 * q^59 + 20 * q^60 + 6 * q^61 - 30 * q^62 - 18 * q^63 + 48 * q^64 - 6 * q^65 + 46 * q^66 - 15 * q^67 - 14 * q^68 - 10 * q^69 - 20 * q^70 + 2 * q^71 - 68 * q^72 + 8 * q^73 + 2 * q^74 + 4 * q^75 + 21 * q^77 + 46 * q^78 + 18 * q^79 - 20 * q^80 + 50 * q^81 - 18 * q^82 - 10 * q^83 + 4 * q^84 - 5 * q^85 - 10 * q^86 - 14 * q^87 - 52 * q^88 + 17 * q^89 + 8 * q^90 - 23 * q^91 + 28 * q^92 + 10 * q^93 - 28 * q^94 + 26 * q^96 - 4 * q^97 + 50 * q^98 + 58 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.274673	−0.194223	−0.0971117	−	0.995273i	$-0.530960\pi$
$2$	−0.274673	−0.194223	−0.0971117	+	0.995273i	$0.530960\pi$
$3$	3.09431	1.78650	0.893251	−	0.449558i	$-0.148419\pi$
$3$	3.09431	1.78650	0.893251	+	0.449558i	$0.148419\pi$
$4$	−1.92455	−0.962277
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.849925	−0.346980
$7$	3.63772	1.37493	0.687464	−	0.726219i	$-0.258724\pi$
$7$	3.63772	1.37493	0.687464	+	0.726219i	$0.258724\pi$
$8$	1.07797	0.381120
$9$	6.57477	2.19159
$10$	0.274673	0.0868593
$11$	2.45483	0.740159	0.370080	−	0.929000i	$-0.379330\pi$
$11$	2.45483	0.740159	0.370080	+	0.929000i	$0.379330\pi$
$12$	−5.95517	−1.71911
$13$	3.81342	1.05765	0.528826	−	0.848730i	$-0.322633\pi$
$13$	3.81342	1.05765	0.528826	+	0.848730i	$0.322633\pi$
$14$	−0.999184	−0.267043
$15$	−3.09431	−0.798948
$16$	3.55302	0.888255
$17$	−3.62089	−0.878195	−0.439097	−	0.898439i	$-0.644702\pi$
$17$	−3.62089	−0.878195	−0.439097	+	0.898439i	$0.644702\pi$
$18$	−1.80591	−0.425658
$19$	0	0
$19$	0	0
$20$	1.92455	0.430343
$21$	11.2562	2.45631
$22$	−0.674276	−0.143756
$23$	−9.19377	−1.91703	−0.958516	−	0.285038i	$-0.907994\pi$
$23$	−9.19377	−1.91703	−0.958516	+	0.285038i	$0.907994\pi$
$24$	3.33558	0.680872
$25$	1.00000	0.200000
$26$	−1.04744	−0.205421
$27$	11.0614	2.12878
$28$	−7.00098	−1.32306
$29$	−1.81600	−0.337222	−0.168611	−	0.985683i	$-0.553928\pi$
$29$	−1.81600	−0.337222	−0.168611	+	0.985683i	$0.553928\pi$
$30$	0.849925	0.155174
$31$	7.04948	1.26612	0.633062	−	0.774101i	$-0.281798\pi$
$31$	7.04948	1.26612	0.633062	+	0.774101i	$0.281798\pi$
$32$	−3.13186	−0.553640
$33$	7.59601	1.32230
$34$	0.994562	0.170566
$35$	−3.63772	−0.614886
$36$	−12.6535	−2.10892
$37$	−0.500137	−0.0822221	−0.0411110	−	0.999155i	$-0.513090\pi$
$37$	−0.500137	−0.0822221	−0.0411110	+	0.999155i	$0.513090\pi$
$38$	0	0
$39$	11.7999	1.88950
$40$	−1.07797	−0.170442
$41$	−1.42551	−0.222627	−0.111313	−	0.993785i	$-0.535506\pi$
$41$	−1.42551	−0.222627	−0.111313	+	0.993785i	$0.535506\pi$
$42$	−3.09179	−0.477073
$43$	6.78124	1.03413	0.517065	−	0.855946i	$-0.327025\pi$
$43$	6.78124	1.03413	0.517065	+	0.855946i	$0.327025\pi$
$44$	−4.72445	−0.712238
$45$	−6.57477	−0.980108
$46$	2.52528	0.372333
$47$	0.193490	0.0282235	0.0141117	−	0.999900i	$-0.495508\pi$
$47$	0.193490	0.0282235	0.0141117	+	0.999900i	$0.495508\pi$
$48$	10.9942	1.58687
$49$	6.23298	0.890426
$50$	−0.274673	−0.0388447
$51$	−11.2042	−1.56890
$52$	−7.33913	−1.01775
$53$	−4.54544	−0.624365	−0.312182	−	0.950022i	$-0.601060\pi$
$53$	−4.54544	−0.624365	−0.312182	+	0.950022i	$0.601060\pi$
$54$	−3.03828	−0.413458
$55$	−2.45483	−0.331009
$56$	3.92135	0.524013
$57$	0	0
$58$	0.498806	0.0654965
$59$	−1.29597	−0.168721	−0.0843606	−	0.996435i	$-0.526885\pi$
$59$	−1.29597	−0.168721	−0.0843606	+	0.996435i	$0.526885\pi$
$60$	5.95517	0.768809
$61$	8.12536	1.04035	0.520173	−	0.854061i	$-0.325868\pi$
$61$	8.12536	1.04035	0.520173	+	0.854061i	$0.325868\pi$
$62$	−1.93631	−0.245911
$63$	23.9171	3.01328
$64$	−6.24580	−0.780725
$65$	−3.81342	−0.472996
$66$	−2.08642	−0.256821
$67$	−8.17102	−0.998249	−0.499125	−	0.866530i	$-0.666345\pi$
$67$	−8.17102	−0.998249	−0.499125	+	0.866530i	$0.666345\pi$
$68$	6.96860	0.845067
$69$	−28.4484	−3.42478
$70$	0.999184	0.119425
$71$	5.69618	0.676012	0.338006	−	0.941144i	$-0.390248\pi$
$71$	5.69618	0.676012	0.338006	+	0.941144i	$0.390248\pi$
$72$	7.08741	0.835259
$73$	2.63792	0.308745	0.154373	−	0.988013i	$-0.450664\pi$
$73$	2.63792	0.308745	0.154373	+	0.988013i	$0.450664\pi$
$74$	0.137374	0.0159695
$75$	3.09431	0.357300
$76$	0	0
$77$	8.92998	1.01767
$78$	−3.24112	−0.366984
$79$	−5.11318	−0.575278	−0.287639	−	0.957739i	$-0.592870\pi$
$79$	−5.11318	−0.575278	−0.287639	+	0.957739i	$0.592870\pi$
$80$	−3.55302	−0.397240
$81$	14.5033	1.61147
$82$	0.391549	0.0432394
$83$	−0.287184	−0.0315226	−0.0157613	−	0.999876i	$-0.505017\pi$
$83$	−0.287184	−0.0315226	−0.0157613	+	0.999876i	$0.505017\pi$
$84$	−21.6632	−2.36365
$85$	3.62089	0.392741
$86$	−1.86263	−0.200852
$87$	−5.61926	−0.602448
$88$	2.64623	0.282090
$89$	4.91011	0.520470	0.260235	−	0.965545i	$-0.416200\pi$
$89$	4.91011	0.520470	0.260235	+	0.965545i	$0.416200\pi$
$90$	1.80591	0.190360
$91$	13.8721	1.45419
$92$	17.6939	1.84472
$93$	21.8133	2.26193
$94$	−0.0531467	−0.00548166
$95$	0	0
$96$	−9.69096	−0.989079
$97$	8.24002	0.836647	0.418323	−	0.908298i	$-0.362618\pi$
$97$	8.24002	0.836647	0.418323	+	0.908298i	$0.362618\pi$
$98$	−1.71203	−0.172942
$99$	16.1399	1.62212
$100$	−1.92455	−0.192455
$101$	1.92411	0.191456	0.0957280	−	0.995408i	$-0.469482\pi$
$101$	1.92411	0.191456	0.0957280	+	0.995408i	$0.469482\pi$
$102$	3.07749	0.304716
$103$	17.9037	1.76411	0.882054	−	0.471149i	$-0.156161\pi$
$103$	17.9037	1.76411	0.882054	+	0.471149i	$0.156161\pi$
$104$	4.11075	0.403092
$105$	−11.2562	−1.09850
$106$	1.24851	0.121266
$107$	5.07641	0.490755	0.245378	−	0.969428i	$-0.421088\pi$
$107$	5.07641	0.490755	0.245378	+	0.969428i	$0.421088\pi$
$108$	−21.2884	−2.04847
$109$	−13.3118	−1.27504	−0.637519	−	0.770435i	$-0.720039\pi$
$109$	−13.3118	−1.27504	−0.637519	+	0.770435i	$0.720039\pi$
$110$	0.674276	0.0642897
$111$	−1.54758	−0.146890
$112$	12.9249	1.22129
$113$	−6.27192	−0.590012	−0.295006	−	0.955495i	$-0.595322\pi$
$113$	−6.27192	−0.590012	−0.295006	+	0.955495i	$0.595322\pi$
$114$	0	0
$115$	9.19377	0.857323
$116$	3.49499	0.324501
$117$	25.0723	2.31794
$118$	0.355969	0.0327696
$119$	−13.1718	−1.20745
$120$	−3.33558	−0.304495
$121$	−4.97381	−0.452164
$122$	−2.23182	−0.202059
$123$	−4.41097	−0.397723
$124$	−13.5671	−1.21836
$125$	−1.00000	−0.0894427
$126$	−6.56940	−0.585249
$127$	−8.47737	−0.752245	−0.376122	−	0.926570i	$-0.622743\pi$
$127$	−8.47737	−0.752245	−0.376122	+	0.926570i	$0.622743\pi$
$128$	7.97928	0.705275
$129$	20.9833	1.84747
$130$	1.04744	0.0918669
$131$	21.9423	1.91711	0.958554	−	0.284909i	$-0.0919635\pi$
$131$	21.9423	1.91711	0.958554	+	0.284909i	$0.0919635\pi$
$132$	−14.6189	−1.27242
$133$	0	0
$134$	2.24436	0.193883
$135$	−11.0614	−0.952018
$136$	−3.90321	−0.334698
$137$	10.2496	0.875685	0.437842	−	0.899052i	$-0.355743\pi$
$137$	10.2496	0.875685	0.437842	+	0.899052i	$0.355743\pi$
$138$	7.81401	0.665173
$139$	13.0518	1.10704	0.553518	−	0.832837i	$-0.313285\pi$
$139$	13.0518	1.10704	0.553518	+	0.832837i	$0.313285\pi$
$140$	7.00098	0.591691
$141$	0.598720	0.0504213
$142$	−1.56459	−0.131297
$143$	9.36129	0.782830
$144$	23.3603	1.94669
$145$	1.81600	0.150810
$146$	−0.724567	−0.0599656
$147$	19.2868	1.59075
$148$	0.962542	0.0791205
$149$	−14.3563	−1.17611	−0.588055	−	0.808821i	$-0.700106\pi$
$149$	−14.3563	−1.17611	−0.588055	+	0.808821i	$0.700106\pi$
$150$	−0.849925	−0.0693961
$151$	−20.1550	−1.64019	−0.820094	−	0.572228i	$-0.806079\pi$
$151$	−20.1550	−1.64019	−0.820094	+	0.572228i	$0.806079\pi$
$152$	0	0
$153$	−23.8065	−1.92464
$154$	−2.45283	−0.197654
$155$	−7.04948	−0.566228
$156$	−22.7096	−1.81822
$157$	−4.64044	−0.370348	−0.185174	−	0.982706i	$-0.559285\pi$
$157$	−4.64044	−0.370348	−0.185174	+	0.982706i	$0.559285\pi$
$158$	1.40445	0.111732
$159$	−14.0650	−1.11543
$160$	3.13186	0.247595
$161$	−33.4443	−2.63578
$162$	−3.98366	−0.312986
$163$	0.964446	0.0755412	0.0377706	−	0.999286i	$-0.487974\pi$
$163$	0.964446	0.0755412	0.0377706	+	0.999286i	$0.487974\pi$
$164$	2.74347	0.214229
$165$	−7.59601	−0.591349
$166$	0.0788819	0.00612242
$167$	−20.1148	−1.55653	−0.778266	−	0.627935i	$-0.783900\pi$
$167$	−20.1148	−1.55653	−0.778266	+	0.627935i	$0.783900\pi$
$168$	12.1339	0.936150
$169$	1.54214	0.118626
$170$	−0.994562	−0.0762794
$171$	0	0
$172$	−13.0509	−0.995119
$173$	18.0664	1.37356	0.686782	−	0.726864i	$-0.259023\pi$
$173$	18.0664	1.37356	0.686782	+	0.726864i	$0.259023\pi$
$174$	1.54346	0.117010
$175$	3.63772	0.274986
$176$	8.72206	0.657450
$177$	−4.01014	−0.301421
$178$	−1.34868	−0.101087
$179$	−26.2990	−1.96568	−0.982838	−	0.184470i	$-0.940943\pi$
$179$	−26.2990	−1.96568	−0.982838	+	0.184470i	$0.940943\pi$
$180$	12.6535	0.943136
$181$	−14.0156	−1.04177	−0.520885	−	0.853627i	$-0.674398\pi$
$181$	−14.0156	−1.04177	−0.520885	+	0.853627i	$0.674398\pi$
$182$	−3.81030	−0.282439
$183$	25.1424	1.85858
$184$	−9.91061	−0.730620
$185$	0.500137	0.0367708
$186$	−5.99153	−0.439321
$187$	−8.88867	−0.650004
$188$	−0.372383	−0.0271588
$189$	40.2384	2.92691
$190$	0	0
$191$	10.2065	0.738515	0.369258	−	0.929327i	$-0.379612\pi$
$191$	10.2065	0.738515	0.369258	+	0.929327i	$0.379612\pi$
$192$	−19.3265	−1.39477
$193$	−21.2698	−1.53103	−0.765516	−	0.643416i	$-0.777516\pi$
$193$	−21.2698	−1.53103	−0.765516	+	0.643416i	$0.777516\pi$
$194$	−2.26331	−0.162496
$195$	−11.7999	−0.845008
$196$	−11.9957	−0.856837
$197$	−20.3725	−1.45148	−0.725740	−	0.687969i	$-0.758502\pi$
$197$	−20.3725	−1.45148	−0.725740	+	0.687969i	$0.758502\pi$
$198$	−4.43321	−0.315055
$199$	21.0153	1.48974	0.744869	−	0.667210i	$-0.232512\pi$
$199$	21.0153	1.48974	0.744869	+	0.667210i	$0.232512\pi$
$200$	1.07797	0.0762240
$201$	−25.2837	−1.78337
$202$	−0.528502	−0.0371852
$203$	−6.60608	−0.463656
$204$	21.5630	1.50971
$205$	1.42551	0.0995618
$206$	−4.91768	−0.342631
$207$	−60.4469	−4.20135
$208$	13.5491	0.939464
$209$	0	0
$210$	3.09179	0.213354
$211$	−11.0709	−0.762151	−0.381075	−	0.924544i	$-0.624446\pi$
$211$	−11.0709	−0.762151	−0.381075	+	0.924544i	$0.624446\pi$
$212$	8.74796	0.600812
$213$	17.6258	1.20770
$214$	−1.39435	−0.0953161
$215$	−6.78124	−0.462477
$216$	11.9239	0.811319
$217$	25.6440	1.74083
$218$	3.65639	0.247642
$219$	8.16255	0.551574
$220$	4.72445	0.318523
$221$	−13.8080	−0.928824
$222$	0.425079	0.0285295
$223$	−22.8433	−1.52970	−0.764849	−	0.644210i	$-0.777186\pi$
$223$	−22.8433	−1.52970	−0.764849	+	0.644210i	$0.777186\pi$
$224$	−11.3928	−0.761215
$225$	6.57477	0.438318
$226$	1.72273	0.114594
$227$	−22.4210	−1.48814	−0.744068	−	0.668104i	$-0.767106\pi$
$227$	−22.4210	−1.48814	−0.744068	+	0.668104i	$0.767106\pi$
$228$	0	0
$229$	15.9279	1.05255	0.526273	−	0.850316i	$-0.323589\pi$
$229$	15.9279	1.05255	0.526273	+	0.850316i	$0.323589\pi$
$230$	−2.52528	−0.166512
$231$	27.6321	1.81806
$232$	−1.95759	−0.128522
$233$	9.19629	0.602469	0.301235	−	0.953550i	$-0.402601\pi$
$233$	9.19629	0.602469	0.301235	+	0.953550i	$0.402601\pi$
$234$	−6.88670	−0.450198
$235$	−0.193490	−0.0126219
$236$	2.49417	0.162357
$237$	−15.8218	−1.02773
$238$	3.61794	0.234516
$239$	−10.3057	−0.666620	−0.333310	−	0.942817i	$-0.608165\pi$
$239$	−10.3057	−0.666620	−0.333310	+	0.942817i	$0.608165\pi$
$240$	−10.9942	−0.709669
$241$	16.4125	1.05722	0.528612	−	0.848864i	$-0.322713\pi$
$241$	16.4125	1.05722	0.528612	+	0.848864i	$0.322713\pi$
$242$	1.36617	0.0878209
$243$	11.6933	0.750124
$244$	−15.6377	−1.00110
$245$	−6.23298	−0.398211
$246$	1.21158	0.0772472
$247$	0	0
$248$	7.59914	0.482546
$249$	−0.888638	−0.0563151
$250$	0.274673	0.0173719
$251$	−2.66094	−0.167957	−0.0839785	−	0.996468i	$-0.526763\pi$
$251$	−2.66094	−0.167957	−0.0839785	+	0.996468i	$0.526763\pi$
$252$	−46.0298	−2.89961
$253$	−22.5691	−1.41891
$254$	2.32851	0.146104
$255$	11.2042	0.701632
$256$	10.2999	0.643744
$257$	8.21974	0.512734	0.256367	−	0.966580i	$-0.417475\pi$
$257$	8.21974	0.512734	0.256367	+	0.966580i	$0.417475\pi$
$258$	−5.76354	−0.358823
$259$	−1.81936	−0.113049
$260$	7.33913	0.455153
$261$	−11.9398	−0.739053
$262$	−6.02697	−0.372347
$263$	0.310912	0.0191717	0.00958583	−	0.999954i	$-0.496949\pi$
$263$	0.310912	0.0191717	0.00958583	+	0.999954i	$0.496949\pi$
$264$	8.18828	0.503954
$265$	4.54544	0.279224
$266$	0	0
$267$	15.1934	0.929821
$268$	15.7256	0.960592
$269$	−6.83610	−0.416804	−0.208402	−	0.978043i	$-0.566826\pi$
$269$	−6.83610	−0.416804	−0.208402	+	0.978043i	$0.566826\pi$
$270$	3.03828	0.184904
$271$	−14.8797	−0.903879	−0.451939	−	0.892049i	$-0.649268\pi$
$271$	−14.8797	−0.903879	−0.451939	+	0.892049i	$0.649268\pi$
$272$	−12.8651	−0.780061
$273$	42.9247	2.59792
$274$	−2.81530	−0.170079
$275$	2.45483	0.148032
$276$	54.7505	3.29559
$277$	−1.75388	−0.105381	−0.0526903	−	0.998611i	$-0.516780\pi$
$277$	−1.75388	−0.105381	−0.0526903	+	0.998611i	$0.516780\pi$
$278$	−3.58497	−0.215012
$279$	46.3487	2.77483
$280$	−3.92135	−0.234346
$281$	−1.61410	−0.0962889	−0.0481445	−	0.998840i	$-0.515331\pi$
$281$	−1.61410	−0.0962889	−0.0481445	+	0.998840i	$0.515331\pi$
$282$	−0.164452	−0.00979300
$283$	−6.86254	−0.407936	−0.203968	−	0.978978i	$-0.565384\pi$
$283$	−6.86254	−0.407936	−0.203968	+	0.978978i	$0.565384\pi$
$284$	−10.9626	−0.650511
$285$	0	0
$286$	−2.57130	−0.152044
$287$	−5.18559	−0.306096
$288$	−20.5913	−1.21335
$289$	−3.88915	−0.228774
$290$	−0.498806	−0.0292909
$291$	25.4972	1.49467
$292$	−5.07682	−0.297099
$293$	14.1064	0.824106	0.412053	−	0.911160i	$-0.364812\pi$
$293$	14.1064	0.824106	0.412053	+	0.911160i	$0.364812\pi$
$294$	−5.29757	−0.308960
$295$	1.29597	0.0754545
$296$	−0.539134	−0.0313365
$297$	27.1540	1.57563
$298$	3.94328	0.228428
$299$	−35.0597	−2.02755
$300$	−5.95517	−0.343822
$301$	24.6682	1.42185
$302$	5.53604	0.318563
$303$	5.95380	0.342037
$304$	0	0
$305$	−8.12536	−0.465257
$306$	6.53901	0.373811
$307$	−18.4079	−1.05059	−0.525297	−	0.850919i	$-0.676046\pi$
$307$	−18.4079	−1.05059	−0.525297	+	0.850919i	$0.676046\pi$
$308$	−17.1862	−0.979276
$309$	55.3997	3.15158
$310$	1.93631	0.109975
$311$	16.5997	0.941283	0.470641	−	0.882325i	$-0.344023\pi$
$311$	16.5997	0.941283	0.470641	+	0.882325i	$0.344023\pi$
$312$	12.7199	0.720125
$313$	4.54809	0.257073	0.128537	−	0.991705i	$-0.458972\pi$
$313$	4.54809	0.257073	0.128537	+	0.991705i	$0.458972\pi$
$314$	1.27461	0.0719302
$315$	−23.9171	−1.34758
$316$	9.84059	0.553576
$317$	13.0464	0.732761	0.366380	−	0.930465i	$-0.380597\pi$
$317$	13.0464	0.732761	0.366380	+	0.930465i	$0.380597\pi$
$318$	3.86329	0.216642
$319$	−4.45797	−0.249598
$320$	6.24580	0.349151
$321$	15.7080	0.876735
$322$	9.18626	0.511930
$323$	0	0
$324$	−27.9123	−1.55068
$325$	3.81342	0.211530
$326$	−0.264908	−0.0146719
$327$	−41.1908	−2.27786
$328$	−1.53666	−0.0848476
$329$	0.703863	0.0388052
$330$	2.08642	0.114854
$331$	−9.51322	−0.522894	−0.261447	−	0.965218i	$-0.584200\pi$
$331$	−9.51322	−0.522894	−0.261447	+	0.965218i	$0.584200\pi$
$332$	0.552702	0.0303335
$333$	−3.28829	−0.180197
$334$	5.52501	0.302315
$335$	8.17102	0.446431
$336$	39.9936	2.18183
$337$	−5.26448	−0.286774	−0.143387	−	0.989667i	$-0.545799\pi$
$337$	−5.26448	−0.286774	−0.143387	+	0.989667i	$0.545799\pi$
$338$	−0.423586	−0.0230400
$339$	−19.4073	−1.05406
$340$	−6.96860	−0.377925
$341$	17.3053	0.937134
$342$	0	0
$343$	−2.79019	−0.150656
$344$	7.30998	0.394127
$345$	28.4484	1.53161
$346$	−4.96236	−0.266778
$347$	17.2556	0.926326	0.463163	−	0.886273i	$-0.346714\pi$
$347$	17.2556	0.926326	0.463163	+	0.886273i	$0.346714\pi$
$348$	10.8146	0.579722
$349$	18.2146	0.975005	0.487502	−	0.873122i	$-0.337908\pi$
$349$	18.2146	0.975005	0.487502	+	0.873122i	$0.337908\pi$
$350$	−0.999184	−0.0534086
$351$	42.1819	2.25150
$352$	−7.68819	−0.409782
$353$	31.7219	1.68839	0.844193	−	0.536039i	$-0.180080\pi$
$353$	31.7219	1.68839	0.844193	+	0.536039i	$0.180080\pi$
$354$	1.10148	0.0585430
$355$	−5.69618	−0.302322
$356$	−9.44976	−0.500837
$357$	−40.7576	−2.15712
$358$	7.22362	0.381780
$359$	−0.696745	−0.0367728	−0.0183864	−	0.999831i	$-0.505853\pi$
$359$	−0.696745	−0.0367728	−0.0183864	+	0.999831i	$0.505853\pi$
$360$	−7.08741	−0.373539
$361$	0	0
$362$	3.84971	0.202336
$363$	−15.3905	−0.807793
$364$	−26.6977	−1.39934
$365$	−2.63792	−0.138075
$366$	−6.90595	−0.360980
$367$	−36.6138	−1.91122	−0.955612	−	0.294629i	$-0.904804\pi$
$367$	−36.6138	−1.91122	−0.955612	+	0.294629i	$0.904804\pi$
$368$	−32.6656	−1.70281
$369$	−9.37238	−0.487907
$370$	−0.137374	−0.00714176
$371$	−16.5350	−0.858457
$372$	−41.9809	−2.17661
$373$	5.11894	0.265049	0.132524	−	0.991180i	$-0.457692\pi$
$373$	5.11894	0.265049	0.132524	+	0.991180i	$0.457692\pi$
$374$	2.44148	0.126246
$375$	−3.09431	−0.159790
$376$	0.208577	0.0107565
$377$	−6.92516	−0.356664
$378$	−11.0524	−0.568475
$379$	−22.5010	−1.15580	−0.577898	−	0.816109i	$-0.696127\pi$
$379$	−22.5010	−1.15580	−0.577898	+	0.816109i	$0.696127\pi$
$380$	0	0
$381$	−26.2316	−1.34389
$382$	−2.80345	−0.143437
$383$	10.9940	0.561769	0.280884	−	0.959742i	$-0.409372\pi$
$383$	10.9940	0.561769	0.280884	+	0.959742i	$0.409372\pi$
$384$	24.6904	1.25998
$385$	−8.92998	−0.455114
$386$	5.84224	0.297362
$387$	44.5851	2.26639
$388$	−15.8584	−0.805086
$389$	−27.6543	−1.40213	−0.701064	−	0.713098i	$-0.747291\pi$
$389$	−27.6543	−1.40213	−0.701064	+	0.713098i	$0.747291\pi$
$390$	3.24112	0.164120
$391$	33.2896	1.68353
$392$	6.71897	0.339359
$393$	67.8964	3.42492
$394$	5.59578	0.281911
$395$	5.11318	0.257272
$396$	−31.0622	−1.56093
$397$	−6.28147	−0.315258	−0.157629	−	0.987498i	$-0.550385\pi$
$397$	−6.28147	−0.315258	−0.157629	+	0.987498i	$0.550385\pi$
$398$	−5.77236	−0.289342
$399$	0	0
$400$	3.55302	0.177651
$401$	−16.1708	−0.807532	−0.403766	−	0.914862i	$-0.632299\pi$
$401$	−16.1708	−0.807532	−0.403766	+	0.914862i	$0.632299\pi$
$402$	6.94476	0.346373
$403$	26.8826	1.33912
$404$	−3.70305	−0.184234
$405$	−14.5033	−0.720673
$406$	1.81452	0.0900529
$407$	−1.22775	−0.0608574
$408$	−12.0778	−0.597938
$409$	33.7233	1.66751	0.833754	−	0.552136i	$-0.186187\pi$
$409$	33.7233	1.66751	0.833754	+	0.552136i	$0.186187\pi$
$410$	−0.391549	−0.0193372
$411$	31.7156	1.56441
$412$	−34.4567	−1.69756
$413$	−4.71438	−0.231980
$414$	16.6031	0.816000
$415$	0.287184	0.0140973
$416$	−11.9431	−0.585558
$417$	40.3862	1.97772
$418$	0	0
$419$	−35.5118	−1.73487	−0.867433	−	0.497553i	$-0.834232\pi$
$419$	−35.5118	−1.73487	−0.867433	+	0.497553i	$0.834232\pi$
$420$	21.6632	1.05706
$421$	−27.5883	−1.34457	−0.672286	−	0.740292i	$-0.734687\pi$
$421$	−27.5883	−1.34457	−0.672286	+	0.740292i	$0.734687\pi$
$422$	3.04088	0.148028
$423$	1.27215	0.0618543
$424$	−4.89986	−0.237958
$425$	−3.62089	−0.175639
$426$	−4.84132	−0.234563
$427$	29.5578	1.43040
$428$	−9.76983	−0.472242
$429$	28.9667	1.39853
$430$	1.86263	0.0898238
$431$	−17.2312	−0.830000	−0.415000	−	0.909821i	$-0.636218\pi$
$431$	−17.2312	−0.830000	−0.415000	+	0.909821i	$0.636218\pi$
$432$	39.3015	1.89090
$433$	−7.75207	−0.372541	−0.186270	−	0.982499i	$-0.559640\pi$
$433$	−7.75207	−0.372541	−0.186270	+	0.982499i	$0.559640\pi$
$434$	−7.04373	−0.338110
$435$	5.61926	0.269423
$436$	25.6193	1.22694
$437$	0	0
$438$	−2.24204	−0.107129
$439$	14.3607	0.685397	0.342699	−	0.939445i	$-0.388659\pi$
$439$	14.3607	0.685397	0.342699	+	0.939445i	$0.388659\pi$
$440$	−2.64623	−0.126154
$441$	40.9804	1.95145
$442$	3.79268	0.180399
$443$	−13.1725	−0.625844	−0.312922	−	0.949779i	$-0.601308\pi$
$443$	−13.1725	−0.625844	−0.312922	+	0.949779i	$0.601308\pi$
$444$	2.97840	0.141349
$445$	−4.91011	−0.232761
$446$	6.27443	0.297103
$447$	−44.4228	−2.10112
$448$	−22.7204	−1.07344
$449$	18.3579	0.866363	0.433181	−	0.901307i	$-0.357391\pi$
$449$	18.3579	0.866363	0.433181	+	0.901307i	$0.357391\pi$
$450$	−1.80591	−0.0851316
$451$	−3.49938	−0.164779
$452$	12.0706	0.567756
$453$	−62.3658	−2.93020
$454$	6.15846	0.289031
$455$	−13.8721	−0.650335
$456$	0	0
$457$	−6.56691	−0.307187	−0.153594	−	0.988134i	$-0.549085\pi$
$457$	−6.56691	−0.307187	−0.153594	+	0.988134i	$0.549085\pi$
$458$	−4.37497	−0.204429
$459$	−40.0523	−1.86948
$460$	−17.6939	−0.824982
$461$	−22.6799	−1.05631	−0.528155	−	0.849148i	$-0.677116\pi$
$461$	−22.6799	−1.05631	−0.528155	+	0.849148i	$0.677116\pi$
$462$	−7.58981	−0.353110
$463$	−8.95953	−0.416385	−0.208192	−	0.978088i	$-0.566758\pi$
$463$	−8.95953	−0.416385	−0.208192	+	0.978088i	$0.566758\pi$
$464$	−6.45227	−0.299539
$465$	−21.8133	−1.01157
$466$	−2.52598	−0.117014
$467$	−8.99842	−0.416397	−0.208199	−	0.978087i	$-0.566760\pi$
$467$	−8.99842	−0.416397	−0.208199	+	0.978087i	$0.566760\pi$
$468$	−48.2531	−2.23050
$469$	−29.7239	−1.37252
$470$	0.0531467	0.00245147
$471$	−14.3590	−0.661627
$472$	−1.39702	−0.0643031
$473$	16.6468	0.765420
$474$	4.34582	0.199610
$475$	0	0
$476$	25.3498	1.16191
$477$	−29.8852	−1.36835
$478$	2.83070	0.129473
$479$	10.8348	0.495054	0.247527	−	0.968881i	$-0.420382\pi$
$479$	10.8348	0.495054	0.247527	+	0.968881i	$0.420382\pi$
$480$	9.69096	0.442330
$481$	−1.90723	−0.0869623
$482$	−4.50808	−0.205337
$483$	−103.487	−4.70883
$484$	9.57237	0.435108
$485$	−8.24002	−0.374160
$486$	−3.21183	−0.145692
$487$	1.56541	0.0709356	0.0354678	−	0.999371i	$-0.488708\pi$
$487$	1.56541	0.0709356	0.0354678	+	0.999371i	$0.488708\pi$
$488$	8.75890	0.396497
$489$	2.98430	0.134955
$490$	1.71203	0.0773418
$491$	32.7267	1.47693	0.738467	−	0.674290i	$-0.235550\pi$
$491$	32.7267	1.47693	0.738467	+	0.674290i	$0.235550\pi$
$492$	8.48915	0.382720
$493$	6.57553	0.296147
$494$	0	0
$495$	−16.1399	−0.725436
$496$	25.0470	1.12464
$497$	20.7211	0.929468
$498$	0.244085	0.0109377
$499$	32.8576	1.47091	0.735454	−	0.677575i	$-0.236969\pi$
$499$	32.8576	1.47091	0.735454	+	0.677575i	$0.236969\pi$
$500$	1.92455	0.0860687
$501$	−62.2416	−2.78075
$502$	0.730889	0.0326212
$503$	−32.7872	−1.46191	−0.730955	−	0.682426i	$-0.760925\pi$
$503$	−32.7872	−1.46191	−0.730955	+	0.682426i	$0.760925\pi$
$504$	25.7820	1.14842
$505$	−1.92411	−0.0856218
$506$	6.19914	0.275585
$507$	4.77187	0.211926
$508$	16.3152	0.723868
$509$	−26.7934	−1.18760	−0.593798	−	0.804614i	$-0.702372\pi$
$509$	−26.7934	−1.18760	−0.593798	+	0.804614i	$0.702372\pi$
$510$	−3.07749	−0.136273
$511$	9.59601	0.424502
$512$	−18.7877	−0.830305
$513$	0	0
$514$	−2.25774	−0.0995848
$515$	−17.9037	−0.788933
$516$	−40.3834	−1.77778
$517$	0.474986	0.0208899
$518$	0.499729	0.0219568
$519$	55.9031	2.45387
$520$	−4.11075	−0.180268
$521$	−3.25012	−0.142390	−0.0711952	−	0.997462i	$-0.522681\pi$
$521$	−3.25012	−0.142390	−0.0711952	+	0.997462i	$0.522681\pi$
$522$	3.27953	0.143541
$523$	9.58082	0.418940	0.209470	−	0.977815i	$-0.432826\pi$
$523$	9.58082	0.418940	0.209470	+	0.977815i	$0.432826\pi$
$524$	−42.2292	−1.84479
$525$	11.2562	0.491262
$526$	−0.0853993	−0.00372359
$527$	−25.5254	−1.11190
$528$	26.9888	1.17454
$529$	61.5253	2.67501
$530$	−1.24851	−0.0542319
$531$	−8.52072	−0.369768
$532$	0	0
$533$	−5.43606	−0.235462
$534$	−4.17322	−0.180593
$535$	−5.07641	−0.219472
$536$	−8.80812	−0.380453
$537$	−81.3772	−3.51168
$538$	1.87769	0.0809531
$539$	15.3009	0.659057
$540$	21.2884	0.916105
$541$	7.64121	0.328521	0.164261	−	0.986417i	$-0.447476\pi$
$541$	7.64121	0.328521	0.164261	+	0.986417i	$0.447476\pi$
$542$	4.08706	0.175554
$543$	−43.3686	−1.86112
$544$	11.3401	0.486204
$545$	13.3118	0.570214
$546$	−11.7903	−0.504577
$547$	5.15767	0.220526	0.110263	−	0.993902i	$-0.464831\pi$
$547$	5.15767	0.220526	0.110263	+	0.993902i	$0.464831\pi$
$548$	−19.7260	−0.842652
$549$	53.4223	2.28001
$550$	−0.674276	−0.0287512
$551$	0	0
$552$	−30.6665	−1.30525
$553$	−18.6003	−0.790965
$554$	0.481745	0.0204674
$555$	1.54758	0.0656912
$556$	−25.1188	−1.06527
$557$	24.0846	1.02050	0.510248	−	0.860027i	$-0.329554\pi$
$557$	24.0846	1.02050	0.510248	+	0.860027i	$0.329554\pi$
$558$	−12.7308	−0.538936
$559$	25.8597	1.09375
$560$	−12.9249	−0.546176
$561$	−27.5043	−1.16123
$562$	0.443349	0.0187016
$563$	−36.0131	−1.51777	−0.758886	−	0.651224i	$-0.774256\pi$
$563$	−36.0131	−1.51777	−0.758886	+	0.651224i	$0.774256\pi$
$564$	−1.15227	−0.0485193
$565$	6.27192	0.263862
$566$	1.88496	0.0792306
$567$	52.7587	2.21566
$568$	6.14031	0.257642
$569$	34.5464	1.44826	0.724131	−	0.689663i	$-0.242241\pi$
$569$	34.5464	1.44826	0.724131	+	0.689663i	$0.242241\pi$
$570$	0	0
$571$	−8.33925	−0.348987	−0.174493	−	0.984658i	$-0.555829\pi$
$571$	−8.33925	−0.348987	−0.174493	+	0.984658i	$0.555829\pi$
$572$	−18.0163	−0.753300
$573$	31.5820	1.31936
$574$	1.42434	0.0594510
$575$	−9.19377	−0.383407
$576$	−41.0647	−1.71103
$577$	11.1638	0.464754	0.232377	−	0.972626i	$-0.425350\pi$
$577$	11.1638	0.464754	0.232377	+	0.972626i	$0.425350\pi$
$578$	1.06825	0.0444332
$579$	−65.8154	−2.73519
$580$	−3.49499	−0.145121
$581$	−1.04470	−0.0433413
$582$	−7.00340	−0.290300
$583$	−11.1583	−0.462129
$584$	2.84360	0.117669
$585$	−25.0723	−1.03661
$586$	−3.87466	−0.160061
$587$	−3.12443	−0.128959	−0.0644796	−	0.997919i	$-0.520539\pi$
$587$	−3.12443	−0.128959	−0.0644796	+	0.997919i	$0.520539\pi$
$588$	−37.1185	−1.53074
$589$	0	0
$590$	−0.355969	−0.0146550
$591$	−63.0389	−2.59307
$592$	−1.77700	−0.0730342
$593$	−4.11412	−0.168947	−0.0844734	−	0.996426i	$-0.526921\pi$
$593$	−4.11412	−0.168947	−0.0844734	+	0.996426i	$0.526921\pi$
$594$	−7.45847	−0.306025
$595$	13.1718	0.539990
$596$	27.6294	1.13174
$597$	65.0280	2.66142
$598$	9.62995	0.393798
$599$	20.7620	0.848314	0.424157	−	0.905589i	$-0.360570\pi$
$599$	20.7620	0.848314	0.424157	+	0.905589i	$0.360570\pi$
$600$	3.33558	0.136174
$601$	−12.2431	−0.499405	−0.249703	−	0.968323i	$-0.580333\pi$
$601$	−12.2431	−0.499405	−0.249703	+	0.968323i	$0.580333\pi$
$602$	−6.77570	−0.276157
$603$	−53.7226	−2.18775
$604$	38.7894	1.57832
$605$	4.97381	0.202214
$606$	−1.63535	−0.0664315
$607$	−39.2469	−1.59298	−0.796491	−	0.604650i	$-0.793313\pi$
$607$	−39.2469	−1.59298	−0.796491	+	0.604650i	$0.793313\pi$
$608$	0	0
$609$	−20.4413	−0.828323
$610$	2.23182	0.0903637
$611$	0.737860	0.0298506
$612$	45.8169	1.85204
$613$	−19.8681	−0.802466	−0.401233	−	0.915976i	$-0.631418\pi$
$613$	−19.8681	−0.802466	−0.401233	+	0.915976i	$0.631418\pi$
$614$	5.05616	0.204050
$615$	4.41097	0.177867
$616$	9.62625	0.387853
$617$	23.8143	0.958726	0.479363	−	0.877617i	$-0.340868\pi$
$617$	23.8143	0.958726	0.479363	+	0.877617i	$0.340868\pi$
$618$	−15.2168	−0.612111
$619$	0.628838	0.0252751	0.0126376	−	0.999920i	$-0.495977\pi$
$619$	0.628838	0.0252751	0.0126376	+	0.999920i	$0.495977\pi$
$620$	13.5671	0.544869
$621$	−101.696	−4.08093
$622$	−4.55950	−0.182819
$623$	17.8616	0.715609
$624$	41.9253	1.67835
$625$	1.00000	0.0400000
$626$	−1.24924	−0.0499296
$627$	0	0
$628$	8.93079	0.356377
$629$	1.81094	0.0722070
$630$	6.56940	0.261731
$631$	14.0216	0.558193	0.279096	−	0.960263i	$-0.409965\pi$
$631$	14.0216	0.558193	0.279096	+	0.960263i	$0.409965\pi$
$632$	−5.51186	−0.219250
$633$	−34.2568	−1.36158
$634$	−3.58351	−0.142319
$635$	8.47737	0.336414
$636$	27.0689	1.07335
$637$	23.7690	0.941760
$638$	1.22448	0.0484778
$639$	37.4510	1.48154
$640$	−7.97928	−0.315409
$641$	45.6046	1.80127	0.900637	−	0.434573i	$-0.143101\pi$
$641$	45.6046	1.80127	0.900637	+	0.434573i	$0.143101\pi$
$642$	−4.31457	−0.170282
$643$	20.4136	0.805034	0.402517	−	0.915412i	$-0.368135\pi$
$643$	20.4136	0.805034	0.402517	+	0.915412i	$0.368135\pi$
$644$	64.3654	2.53635
$645$	−20.9833	−0.826215
$646$	0	0
$647$	33.8616	1.33124	0.665619	−	0.746292i	$-0.268168\pi$
$647$	33.8616	1.33124	0.665619	+	0.746292i	$0.268168\pi$
$648$	15.6341	0.614165
$649$	−3.18139	−0.124881
$650$	−1.04744	−0.0410841
$651$	79.3506	3.11000
$652$	−1.85613	−0.0726916
$653$	−31.1781	−1.22009	−0.610046	−	0.792366i	$-0.708849\pi$
$653$	−31.1781	−1.22009	−0.610046	+	0.792366i	$0.708849\pi$
$654$	11.3140	0.442413
$655$	−21.9423	−0.857357
$656$	−5.06486	−0.197749
$657$	17.3437	0.676643
$658$	−0.193333	−0.00753689
$659$	12.4310	0.484243	0.242121	−	0.970246i	$-0.422157\pi$
$659$	12.4310	0.484243	0.242121	+	0.970246i	$0.422157\pi$
$660$	14.6189	0.569041
$661$	37.5106	1.45899	0.729497	−	0.683984i	$-0.239754\pi$
$661$	37.5106	1.45899	0.729497	+	0.683984i	$0.239754\pi$
$662$	2.61303	0.101558
$663$	−42.7261	−1.65935
$664$	−0.309576	−0.0120139
$665$	0	0
$666$	0.903205	0.0349985
$667$	16.6959	0.646466
$668$	38.7121	1.49782
$669$	−70.6842	−2.73281
$670$	−2.24436	−0.0867073
$671$	19.9464	0.770021
$672$	−35.2529	−1.35991
$673$	−30.3081	−1.16829	−0.584145	−	0.811650i	$-0.698570\pi$
$673$	−30.3081	−1.16829	−0.584145	+	0.811650i	$0.698570\pi$
$674$	1.44601	0.0556983
$675$	11.0614	0.425755
$676$	−2.96794	−0.114152
$677$	−28.6126	−1.09967	−0.549835	−	0.835273i	$-0.685310\pi$
$677$	−28.6126	−1.09967	−0.549835	+	0.835273i	$0.685310\pi$
$678$	5.33066	0.204723
$679$	29.9748	1.15033
$680$	3.90321	0.149681
$681$	−69.3776	−2.65856
$682$	−4.75330	−0.182013
$683$	29.9256	1.14507	0.572535	−	0.819880i	$-0.305960\pi$
$683$	29.9256	1.14507	0.572535	+	0.819880i	$0.305960\pi$
$684$	0	0
$685$	−10.2496	−0.391618
$686$	0.766392	0.0292610
$687$	49.2859	1.88038
$688$	24.0939	0.918570
$689$	−17.3337	−0.660360
$690$	−7.81401	−0.297474
$691$	21.7025	0.825601	0.412801	−	0.910821i	$-0.364551\pi$
$691$	21.7025	0.825601	0.412801	+	0.910821i	$0.364551\pi$
$692$	−34.7698	−1.32175
$693$	58.7125	2.23030
$694$	−4.73964	−0.179914
$695$	−13.0518	−0.495081
$696$	−6.05740	−0.229605
$697$	5.16161	0.195510
$698$	−5.00306	−0.189369
$699$	28.4562	1.07631
$700$	−7.00098	−0.264612
$701$	−28.4817	−1.07574	−0.537870	−	0.843028i	$-0.680771\pi$
$701$	−28.4817	−1.07574	−0.537870	+	0.843028i	$0.680771\pi$
$702$	−11.5862	−0.437295
$703$	0	0
$704$	−15.3324	−0.577861
$705$	−0.598720	−0.0225491
$706$	−8.71316	−0.327924
$707$	6.99937	0.263238
$708$	7.71774	0.290050
$709$	−11.1270	−0.417882	−0.208941	−	0.977928i	$-0.567002\pi$
$709$	−11.1270	−0.417882	−0.208941	+	0.977928i	$0.567002\pi$
$710$	1.56459	0.0587180
$711$	−33.6180	−1.26077
$712$	5.29295	0.198362
$713$	−64.8113	−2.42720
$714$	11.1950	0.418963
$715$	−9.36129	−0.350092
$716$	50.6138	1.89153
$717$	−31.8890	−1.19092
$718$	0.191377	0.00714214
$719$	−44.7414	−1.66857	−0.834287	−	0.551331i	$-0.814120\pi$
$719$	−44.7414	−1.66857	−0.834287	+	0.551331i	$0.814120\pi$
$720$	−23.3603	−0.870586
$721$	65.1287	2.42552
$722$	0	0
$723$	50.7855	1.88873
$724$	26.9737	1.00247
$725$	−1.81600	−0.0674445
$726$	4.22737	0.156892
$727$	1.09629	0.0406592	0.0203296	−	0.999793i	$-0.493528\pi$
$727$	1.09629	0.0406592	0.0203296	+	0.999793i	$0.493528\pi$
$728$	14.9537	0.554223
$729$	−7.32713	−0.271375
$730$	0.724567	0.0268174
$731$	−24.5541	−0.908167
$732$	−48.3879	−1.78847
$733$	−3.10835	−0.114809	−0.0574047	−	0.998351i	$-0.518283\pi$
$733$	−3.10835	−0.114809	−0.0574047	+	0.998351i	$0.518283\pi$
$734$	10.0568	0.371204
$735$	−19.2868	−0.711404
$736$	28.7936	1.06135
$737$	−20.0585	−0.738863
$738$	2.57434	0.0947629
$739$	−29.4118	−1.08193	−0.540965	−	0.841045i	$-0.681941\pi$
$739$	−29.4118	−1.08193	−0.540965	+	0.841045i	$0.681941\pi$
$740$	−0.962542	−0.0353837
$741$	0	0
$742$	4.54174	0.166732
$743$	−21.8551	−0.801784	−0.400892	−	0.916125i	$-0.631300\pi$
$743$	−21.8551	−0.801784	−0.400892	+	0.916125i	$0.631300\pi$
$744$	23.5141	0.862069
$745$	14.3563	0.525973
$746$	−1.40604	−0.0514787
$747$	−1.88817	−0.0690845
$748$	17.1067	0.625484
$749$	18.4665	0.674753
$750$	0.849925	0.0310349
$751$	−26.6866	−0.973807	−0.486903	−	0.873456i	$-0.661874\pi$
$751$	−26.6866	−0.973807	−0.486903	+	0.873456i	$0.661874\pi$
$752$	0.687475	0.0250696
$753$	−8.23378	−0.300056
$754$	1.90216	0.0692724
$755$	20.1550	0.733515
$756$	−77.4410	−2.81650
$757$	27.5577	1.00160	0.500800	−	0.865563i	$-0.333039\pi$
$757$	27.5577	1.00160	0.500800	+	0.865563i	$0.333039\pi$
$758$	6.18041	0.224483
$759$	−69.8359	−2.53488
$760$	0	0
$761$	35.1188	1.27306	0.636528	−	0.771253i	$-0.280370\pi$
$761$	35.1188	1.27306	0.636528	+	0.771253i	$0.280370\pi$
$762$	7.20513	0.261014
$763$	−48.4245	−1.75309
$764$	−19.6429	−0.710656
$765$	23.8065	0.860726
$766$	−3.01977	−0.109109
$767$	−4.94208	−0.178448
$768$	31.8711	1.15005
$769$	−9.04997	−0.326350	−0.163175	−	0.986597i	$-0.552174\pi$
$769$	−9.04997	−0.326350	−0.163175	+	0.986597i	$0.552174\pi$
$770$	2.45283	0.0883937
$771$	25.4345	0.915999
$772$	40.9349	1.47328
$773$	−17.8731	−0.642852	−0.321426	−	0.946935i	$-0.604162\pi$
$773$	−17.8731	−0.642852	−0.321426	+	0.946935i	$0.604162\pi$
$774$	−12.2463	−0.440185
$775$	7.04948	0.253225
$776$	8.88249	0.318863
$777$	−5.62966	−0.201963
$778$	7.59590	0.272326
$779$	0	0
$780$	22.7096	0.813132
$781$	13.9831	0.500356
$782$	−9.14377	−0.326981
$783$	−20.0876	−0.717871
$784$	22.1459	0.790925
$785$	4.64044	0.165625
$786$	−18.6493	−0.665199
$787$	26.0736	0.929425	0.464713	−	0.885462i	$-0.346158\pi$
$787$	26.0736	0.929425	0.464713	+	0.885462i	$0.346158\pi$
$788$	39.2080	1.39673
$789$	0.962059	0.0342502
$790$	−1.40445	−0.0499682
$791$	−22.8155	−0.811224
$792$	17.3984	0.618224
$793$	30.9854	1.10032
$794$	1.72535	0.0612305
$795$	14.0650	0.498835
$796$	−40.4452	−1.43354
$797$	−4.82841	−0.171031	−0.0855156	−	0.996337i	$-0.527254\pi$
$797$	−4.82841	−0.171031	−0.0855156	+	0.996337i	$0.527254\pi$
$798$	0	0
$799$	−0.700608	−0.0247857
$800$	−3.13186	−0.110728
$801$	32.2828	1.14066
$802$	4.44169	0.156842
$803$	6.47565	0.228521
$804$	48.6598	1.71610
$805$	33.4443	1.17876
$806$	−7.38394	−0.260088
$807$	−21.1530	−0.744622
$808$	2.07413	0.0729678
$809$	39.5224	1.38953	0.694766	−	0.719236i	$-0.255508\pi$
$809$	39.5224	1.38953	0.694766	+	0.719236i	$0.255508\pi$
$810$	3.98366	0.139972
$811$	9.26116	0.325203	0.162602	−	0.986692i	$-0.448011\pi$
$811$	9.26116	0.325203	0.162602	+	0.986692i	$0.448011\pi$
$812$	12.7138	0.446166
$813$	−46.0425	−1.61478
$814$	0.337231	0.0118199
$815$	−0.964446	−0.0337831
$816$	−39.8086	−1.39358
$817$	0	0
$818$	−9.26289	−0.323869
$819$	91.2060	3.18700
$820$	−2.74347	−0.0958061
$821$	−20.7559	−0.724387	−0.362194	−	0.932103i	$-0.617972\pi$
$821$	−20.7559	−0.724387	−0.362194	+	0.932103i	$0.617972\pi$
$822$	−8.71142	−0.303846
$823$	−19.6486	−0.684907	−0.342453	−	0.939535i	$-0.611258\pi$
$823$	−19.6486	−0.684907	−0.342453	+	0.939535i	$0.611258\pi$
$824$	19.2997	0.672337
$825$	7.59601	0.264459
$826$	1.29492	0.0450559
$827$	53.4817	1.85974	0.929870	−	0.367888i	$-0.119919\pi$
$827$	53.4817	1.85974	0.929870	+	0.367888i	$0.119919\pi$
$828$	116.333	4.04286
$829$	0.0378061	0.00131306	0.000656531	−	1.00000i	$-0.499791\pi$
$829$	0.0378061	0.00131306	0.000656531		1.00000i	$0.499791\pi$
$830$	−0.0788819	−0.00273803
$831$	−5.42706	−0.188263
$832$	−23.8178	−0.825735
$833$	−22.5689	−0.781968
$834$	−11.0930	−0.384120
$835$	20.1148	0.696102
$836$	0	0
$837$	77.9775	2.69530
$838$	9.75416	0.336952
$839$	11.4861	0.396544	0.198272	−	0.980147i	$-0.436467\pi$
$839$	11.4861	0.396544	0.198272	+	0.980147i	$0.436467\pi$
$840$	−12.1339	−0.418659
$841$	−25.7022	−0.886281
$842$	7.57777	0.261147
$843$	−4.99452	−0.172020
$844$	21.3065	0.733400
$845$	−1.54214	−0.0530514
$846$	−0.349427	−0.0120135
$847$	−18.0933	−0.621693
$848$	−16.1501	−0.554595
$849$	−21.2348	−0.728778
$850$	0.994562	0.0341132
$851$	4.59815	0.157622
$852$	−33.9217	−1.16214
$853$	5.83253	0.199702	0.0998510	−	0.995002i	$-0.468163\pi$
$853$	5.83253	0.199702	0.0998510	+	0.995002i	$0.468163\pi$
$854$	−8.11873	−0.277817
$855$	0	0
$856$	5.47222	0.187037
$857$	−9.08506	−0.310340	−0.155170	−	0.987888i	$-0.549592\pi$
$857$	−9.08506	−0.310340	−0.155170	+	0.987888i	$0.549592\pi$
$858$	−7.95639	−0.271627
$859$	45.9268	1.56700	0.783500	−	0.621391i	$-0.213432\pi$
$859$	45.9268	1.56700	0.783500	+	0.621391i	$0.213432\pi$
$860$	13.0509	0.445031
$861$	−16.0458	−0.546841
$862$	4.73296	0.161205
$863$	20.4157	0.694958	0.347479	−	0.937688i	$-0.387038\pi$
$863$	20.4157	0.694958	0.347479	+	0.937688i	$0.387038\pi$
$864$	−34.6429	−1.17858
$865$	−18.0664	−0.614276
$866$	2.12929	0.0723561
$867$	−12.0343	−0.408705
$868$	−49.3533	−1.67516
$869$	−12.5520	−0.425797
$870$	−1.54346	−0.0523283
$871$	−31.1595	−1.05580
$872$	−14.3497	−0.485943
$873$	54.1762	1.83359
$874$	0	0
$875$	−3.63772	−0.122977
$876$	−15.7093	−0.530767
$877$	36.8908	1.24571	0.622857	−	0.782336i	$-0.285972\pi$
$877$	36.8908	1.24571	0.622857	+	0.782336i	$0.285972\pi$
$878$	−3.94449	−0.133120
$879$	43.6497	1.47227
$880$	−8.72206	−0.294021
$881$	−11.1110	−0.374340	−0.187170	−	0.982328i	$-0.559932\pi$
$881$	−11.1110	−0.374340	−0.187170	+	0.982328i	$0.559932\pi$
$882$	−11.2562	−0.379017
$883$	26.5136	0.892253	0.446127	−	0.894970i	$-0.352803\pi$
$883$	26.5136	0.892253	0.446127	+	0.894970i	$0.352803\pi$
$884$	26.5742	0.893786
$885$	4.01014	0.134800
$886$	3.61813	0.121553
$887$	8.31764	0.279279	0.139640	−	0.990202i	$-0.455406\pi$
$887$	8.31764	0.279279	0.139640	+	0.990202i	$0.455406\pi$
$888$	−1.66825	−0.0559827
$889$	−30.8383	−1.03428
$890$	1.34868	0.0452077
$891$	35.6030	1.19275
$892$	43.9631	1.47199
$893$	0	0
$894$	12.2017	0.408088
$895$	26.2990	0.879077
$896$	29.0263	0.969702
$897$	−108.486	−3.62223
$898$	−5.04243	−0.168268
$899$	−12.8018	−0.426966
$900$	−12.6535	−0.421783
$901$	16.4586	0.548314
$902$	0.961187	0.0320040
$903$	76.3312	2.54014
$904$	−6.76094	−0.224866
$905$	14.0156	0.465894
$906$	17.1302	0.569114
$907$	−17.0838	−0.567260	−0.283630	−	0.958934i	$-0.591539\pi$
$907$	−17.0838	−0.567260	−0.283630	+	0.958934i	$0.591539\pi$
$908$	43.1505	1.43200
$909$	12.6506	0.419593
$910$	3.81030	0.126310
$911$	−41.2327	−1.36610	−0.683050	−	0.730372i	$-0.739347\pi$
$911$	−41.2327	−1.36610	−0.683050	+	0.730372i	$0.739347\pi$
$912$	0	0
$913$	−0.704989	−0.0233317
$914$	1.80376	0.0596629
$915$	−25.1424	−0.831182
$916$	−30.6541	−1.01284
$917$	79.8199	2.63589
$918$	11.0013	0.363097
$919$	25.1985	0.831222	0.415611	−	0.909542i	$-0.363568\pi$
$919$	25.1985	0.831222	0.415611	+	0.909542i	$0.363568\pi$
$920$	9.91061	0.326743
$921$	−56.9597	−1.87689
$922$	6.22957	0.205160
$923$	21.7219	0.714985
$924$	−53.1795	−1.74948
$925$	−0.500137	−0.0164444
$926$	2.46094	0.0808716
$927$	117.713	3.86620
$928$	5.68745	0.186700
$929$	−34.7803	−1.14111	−0.570553	−	0.821261i	$-0.693271\pi$
$929$	−34.7803	−1.14111	−0.570553	+	0.821261i	$0.693271\pi$
$930$	5.99153	0.196470
$931$	0	0
$932$	−17.6988	−0.579742
$933$	51.3647	1.68160
$934$	2.47163	0.0808741
$935$	8.88867	0.290691
$936$	27.0272	0.883413
$937$	16.0407	0.524026	0.262013	−	0.965064i	$-0.415614\pi$
$937$	16.0407	0.524026	0.262013	+	0.965064i	$0.415614\pi$
$938$	8.16435	0.266576
$939$	14.0732	0.459261
$940$	0.372383	0.0121458
$941$	58.2227	1.89801	0.949003	−	0.315268i	$-0.102094\pi$
$941$	58.2227	1.89801	0.949003	+	0.315268i	$0.102094\pi$
$942$	3.94403	0.128503
$943$	13.1058	0.426783
$944$	−4.60462	−0.149868
$945$	−40.2384	−1.30896
$946$	−4.57243	−0.148662
$947$	−5.48637	−0.178283	−0.0891415	−	0.996019i	$-0.528412\pi$
$947$	−5.48637	−0.178283	−0.0891415	+	0.996019i	$0.528412\pi$
$948$	30.4499	0.988965
$949$	10.0595	0.326545
$950$	0	0
$951$	40.3697	1.30908
$952$	−14.1988	−0.460185
$953$	−43.2618	−1.40139	−0.700694	−	0.713462i	$-0.747126\pi$
$953$	−43.2618	−1.40139	−0.700694	+	0.713462i	$0.747126\pi$
$954$	8.20868	0.265766
$955$	−10.2065	−0.330274
$956$	19.8339	0.641473
$957$	−13.7943	−0.445908
$958$	−2.97603	−0.0961511
$959$	37.2852	1.20400
$960$	19.3265	0.623759
$961$	18.6952	0.603072
$962$	0.523866	0.0168901
$963$	33.3762	1.07553
$964$	−31.5868	−1.01734
$965$	21.2698	0.684699
$966$	28.4252	0.914565
$967$	−0.579244	−0.0186272	−0.00931362	−	0.999957i	$-0.502965\pi$
$967$	−0.579244	−0.0186272	−0.00931362	+	0.999957i	$0.502965\pi$
$968$	−5.36162	−0.172329
$969$	0	0
$970$	2.26331	0.0726706
$971$	51.2908	1.64600	0.822999	−	0.568042i	$-0.192299\pi$
$971$	51.2908	1.64600	0.822999	+	0.568042i	$0.192299\pi$
$972$	−22.5043	−0.721827
$973$	47.4786	1.52209
$974$	−0.429977	−0.0137774
$975$	11.7999	0.377899
$976$	28.8696	0.924092
$977$	21.5880	0.690662	0.345331	−	0.938481i	$-0.387767\pi$
$977$	21.5880	0.690662	0.345331	+	0.938481i	$0.387767\pi$
$978$	−0.819707	−0.0262113
$979$	12.0535	0.385231
$980$	11.9957	0.383189
$981$	−87.5219	−2.79436
$982$	−8.98915	−0.286855
$983$	−22.9384	−0.731621	−0.365811	−	0.930689i	$-0.619208\pi$
$983$	−22.9384	−0.731621	−0.365811	+	0.930689i	$0.619208\pi$
$984$	−4.75489	−0.151580
$985$	20.3725	0.649122
$986$	−1.80612	−0.0575187
$987$	2.17797	0.0693256
$988$	0	0
$989$	−62.3451	−1.98246
$990$	4.43321	0.140897
$991$	1.82776	0.0580606	0.0290303	−	0.999579i	$-0.490758\pi$
$991$	1.82776	0.0580606	0.0290303	+	0.999579i	$0.490758\pi$
$992$	−22.0780	−0.700977
$993$	−29.4369	−0.934151
$994$	−5.69153	−0.180524
$995$	−21.0153	−0.666231
$996$	1.71023	0.0541908
$997$	33.0058	1.04531	0.522653	−	0.852546i	$-0.324942\pi$
$997$	33.0058	1.04531	0.522653	+	0.852546i	$0.324942\pi$
$998$	−9.02511	−0.285685
$999$	−5.53224	−0.175032

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1805.2.a.r.1.3	yes	6
5.4	even	2		9025.2.a.bq.1.4		6
19.18	odd	2		1805.2.a.q.1.4	✓	6
95.94	odd	2		9025.2.a.ca.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1805.2.a.q.1.4	✓	6	19.18	odd	2
1805.2.a.r.1.3	yes	6	1.1	even	1	trivial
9025.2.a.bq.1.4		6	5.4	even	2
9025.2.a.ca.1.3		6	95.94	odd	2

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:	\( N \)	\(=\)	\( 1805 = 5 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1805.a (trivial)

\(f(q)\)	\(=\)	\(q-0.274673 q^{2} +3.09431 q^{3} -1.92455 q^{4} -1.00000 q^{5} -0.849925 q^{6} +3.63772 q^{7} +1.07797 q^{8} +6.57477 q^{9} +O(q^{10})\)	\(q-0.274673 q^{2} +3.09431 q^{3} -1.92455 q^{4} -1.00000 q^{5} -0.849925 q^{6} +3.63772 q^{7} +1.07797 q^{8} +6.57477 q^{9} +0.274673 q^{10} +2.45483 q^{11} -5.95517 q^{12} +3.81342 q^{13} -0.999184 q^{14} -3.09431 q^{15} +3.55302 q^{16} -3.62089 q^{17} -1.80591 q^{18} +1.92455 q^{20} +11.2562 q^{21} -0.674276 q^{22} -9.19377 q^{23} +3.33558 q^{24} +1.00000 q^{25} -1.04744 q^{26} +11.0614 q^{27} -7.00098 q^{28} -1.81600 q^{29} +0.849925 q^{30} +7.04948 q^{31} -3.13186 q^{32} +7.59601 q^{33} +0.994562 q^{34} -3.63772 q^{35} -12.6535 q^{36} -0.500137 q^{37} +11.7999 q^{39} -1.07797 q^{40} -1.42551 q^{41} -3.09179 q^{42} +6.78124 q^{43} -4.72445 q^{44} -6.57477 q^{45} +2.52528 q^{46} +0.193490 q^{47} +10.9942 q^{48} +6.23298 q^{49} -0.274673 q^{50} -11.2042 q^{51} -7.33913 q^{52} -4.54544 q^{53} -3.03828 q^{54} -2.45483 q^{55} +3.92135 q^{56} +0.498806 q^{58} -1.29597 q^{59} +5.95517 q^{60} +8.12536 q^{61} -1.93631 q^{62} +23.9171 q^{63} -6.24580 q^{64} -3.81342 q^{65} -2.08642 q^{66} -8.17102 q^{67} +6.96860 q^{68} -28.4484 q^{69} +0.999184 q^{70} +5.69618 q^{71} +7.08741 q^{72} +2.63792 q^{73} +0.137374 q^{74} +3.09431 q^{75} +8.92998 q^{77} -3.24112 q^{78} -5.11318 q^{79} -3.55302 q^{80} +14.5033 q^{81} +0.391549 q^{82} -0.287184 q^{83} -21.6632 q^{84} +3.62089 q^{85} -1.86263 q^{86} -5.61926 q^{87} +2.64623 q^{88} +4.91011 q^{89} +1.80591 q^{90} +13.8721 q^{91} +17.6939 q^{92} +21.8133 q^{93} -0.0531467 q^{94} -9.69096 q^{96} +8.24002 q^{97} -1.71203 q^{98} +16.1399 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{2} + 4 q^{3} + 8 q^{4} - 6 q^{5} + 8 q^{6} + 7 q^{7} + 10 q^{9}+O(q^{10}) \) 6 * q + 2 * q^2 + 4 * q^3 + 8 * q^4 - 6 * q^5 + 8 * q^6 + 7 * q^7 + 10 * q^9	\( 6 q + 2 q^{2} + 4 q^{3} + 8 q^{4} - 6 q^{5} + 8 q^{6} + 7 q^{7} + 10 q^{9} - 2 q^{10} + 15 q^{11} - 20 q^{12} + 6 q^{13} + 20 q^{14} - 4 q^{15} + 20 q^{16} + 5 q^{17} - 8 q^{18} - 8 q^{20} + 7 q^{21} + 14 q^{22} + 18 q^{24} + 6 q^{25} - 22 q^{26} + 28 q^{27} + 10 q^{28} - 20 q^{29} - 8 q^{30} + 12 q^{31} - 8 q^{32} + q^{33} - 7 q^{35} - 14 q^{36} + 20 q^{37} + 16 q^{39} + 8 q^{41} - 30 q^{42} + 27 q^{43} + 46 q^{44} - 10 q^{45} + 16 q^{46} - 8 q^{47} - 24 q^{48} + 11 q^{49} + 2 q^{50} - 11 q^{51} + 4 q^{52} + 19 q^{53} + 30 q^{54} - 15 q^{55} + 62 q^{56} + 20 q^{58} - 41 q^{59} + 20 q^{60} + 6 q^{61} - 30 q^{62} - 18 q^{63} + 48 q^{64} - 6 q^{65} + 46 q^{66} - 15 q^{67} - 14 q^{68} - 10 q^{69} - 20 q^{70} + 2 q^{71} - 68 q^{72} + 8 q^{73} + 2 q^{74} + 4 q^{75} + 21 q^{77} + 46 q^{78} + 18 q^{79} - 20 q^{80} + 50 q^{81} - 18 q^{82} - 10 q^{83} + 4 q^{84} - 5 q^{85} - 10 q^{86} - 14 q^{87} - 52 q^{88} + 17 q^{89} + 8 q^{90} - 23 q^{91} + 28 q^{92} + 10 q^{93} - 28 q^{94} + 26 q^{96} - 4 q^{97} + 50 q^{98} + 58 q^{99}+O(q^{100}) \) 6 * q + 2 * q^2 + 4 * q^3 + 8 * q^4 - 6 * q^5 + 8 * q^6 + 7 * q^7 + 10 * q^9 - 2 * q^10 + 15 * q^11 - 20 * q^12 + 6 * q^13 + 20 * q^14 - 4 * q^15 + 20 * q^16 + 5 * q^17 - 8 * q^18 - 8 * q^20 + 7 * q^21 + 14 * q^22 + 18 * q^24 + 6 * q^25 - 22 * q^26 + 28 * q^27 + 10 * q^28 - 20 * q^29 - 8 * q^30 + 12 * q^31 - 8 * q^32 + q^33 - 7 * q^35 - 14 * q^36 + 20 * q^37 + 16 * q^39 + 8 * q^41 - 30 * q^42 + 27 * q^43 + 46 * q^44 - 10 * q^45 + 16 * q^46 - 8 * q^47 - 24 * q^48 + 11 * q^49 + 2 * q^50 - 11 * q^51 + 4 * q^52 + 19 * q^53 + 30 * q^54 - 15 * q^55 + 62 * q^56 + 20 * q^58 - 41 * q^59 + 20 * q^60 + 6 * q^61 - 30 * q^62 - 18 * q^63 + 48 * q^64 - 6 * q^65 + 46 * q^66 - 15 * q^67 - 14 * q^68 - 10 * q^69 - 20 * q^70 + 2 * q^71 - 68 * q^72 + 8 * q^73 + 2 * q^74 + 4 * q^75 + 21 * q^77 + 46 * q^78 + 18 * q^79 - 20 * q^80 + 50 * q^81 - 18 * q^82 - 10 * q^83 + 4 * q^84 - 5 * q^85 - 10 * q^86 - 14 * q^87 - 52 * q^88 + 17 * q^89 + 8 * q^90 - 23 * q^91 + 28 * q^92 + 10 * q^93 - 28 * q^94 + 26 * q^96 - 4 * q^97 + 50 * q^98 + 58 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more