LMFDB - Embedded newform 605.2.a.g.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(1,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, 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("605.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.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:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.404.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 5x - 1 $ x^3 - x^2 - 5*x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-0.210756$ of defining polynomial
Character	$\chi$	$=$	605.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.74483 q^{2} -0.210756 q^{3} +5.53407 q^{4} -1.00000 q^{5} -0.578488 q^{6} +2.32331 q^{7} +9.70041 q^{8} -2.95558 q^{9} +O(q^{10})$	\(q+2.74483 q^{2} -0.210756 q^{3} +5.53407 q^{4} -1.00000 q^{5} -0.578488 q^{6} +2.32331 q^{7} +9.70041 q^{8} -2.95558 q^{9} -2.74483 q^{10} -1.16634 q^{12} +0.534070 q^{13} +6.37709 q^{14} +0.210756 q^{15} +15.5578 q^{16} -2.42151 q^{17} -8.11256 q^{18} -4.95558 q^{19} -5.53407 q^{20} -0.489652 q^{21} -4.53407 q^{23} -2.04442 q^{24} +1.00000 q^{25} +1.46593 q^{26} +1.25517 q^{27} +12.8574 q^{28} +5.48965 q^{29} +0.578488 q^{30} +1.04442 q^{31} +23.3026 q^{32} -6.64663 q^{34} -2.32331 q^{35} -16.3564 q^{36} +7.48965 q^{37} -13.6022 q^{38} -0.112558 q^{39} -9.70041 q^{40} -10.6022 q^{41} -1.34401 q^{42} -4.32331 q^{43} +2.95558 q^{45} -12.4452 q^{46} +6.76855 q^{47} -3.27890 q^{48} -1.60221 q^{49} +2.74483 q^{50} +0.510348 q^{51} +2.95558 q^{52} -4.53407 q^{53} +3.44523 q^{54} +22.5371 q^{56} +1.04442 q^{57} +15.0681 q^{58} -6.44523 q^{59} +1.16634 q^{60} -6.79861 q^{61} +2.86675 q^{62} -6.86675 q^{63} +32.8461 q^{64} -0.534070 q^{65} +0.721104 q^{67} -13.4008 q^{68} +0.955582 q^{69} -6.37709 q^{70} +4.53407 q^{71} -28.6704 q^{72} -1.06814 q^{73} +20.5578 q^{74} -0.210756 q^{75} -27.4245 q^{76} -0.308953 q^{78} -4.64663 q^{79} -15.5578 q^{80} +8.60221 q^{81} -29.1012 q^{82} -13.6022 q^{83} -2.70977 q^{84} +2.42151 q^{85} -11.8667 q^{86} -1.15698 q^{87} +12.7148 q^{89} +8.11256 q^{90} +1.24081 q^{91} -25.0919 q^{92} -0.220117 q^{93} +18.5785 q^{94} +4.95558 q^{95} -4.91116 q^{96} +4.75919 q^{97} -4.39779 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - q^{2} + q^{3} + 9 q^{4} - 3 q^{5} - 5 q^{6} + q^{7} + 9 q^{8} + 2 q^{9}+O(q^{10}) $ 3 * q - q^2 + q^3 + 9 * q^4 - 3 * q^5 - 5 * q^6 + q^7 + 9 * q^8 + 2 * q^9	$ 3 q - q^{2} + q^{3} + 9 q^{4} - 3 q^{5} - 5 q^{6} + q^{7} + 9 q^{8} + 2 q^{9} + q^{10} + 9 q^{12} - 6 q^{13} + 5 q^{14} - q^{15} + 13 q^{16} - 4 q^{17} - 20 q^{18} - 4 q^{19} - 9 q^{20} + 17 q^{21} - 6 q^{23} - 17 q^{24} + 3 q^{25} + 12 q^{26} + 13 q^{27} + 25 q^{28} - 2 q^{29} + 5 q^{30} + 14 q^{31} + 27 q^{32} - 8 q^{34} - q^{35} + 2 q^{36} + 4 q^{37} - 18 q^{38} + 4 q^{39} - 9 q^{40} - 9 q^{41} - 35 q^{42} - 7 q^{43} - 2 q^{45} - 8 q^{46} - 15 q^{47} + 7 q^{48} + 18 q^{49} - q^{50} + 20 q^{51} - 2 q^{52} - 6 q^{53} - 19 q^{54} - 3 q^{56} + 14 q^{57} + 30 q^{58} + 10 q^{59} - 9 q^{60} - 3 q^{61} - 24 q^{62} + 12 q^{63} + 29 q^{64} + 6 q^{65} + 19 q^{67} - 8 q^{69} - 5 q^{70} + 6 q^{71} - 48 q^{72} + 12 q^{73} + 28 q^{74} + q^{75} - 16 q^{76} - 2 q^{78} - 2 q^{79} - 13 q^{80} + 3 q^{81} - 27 q^{82} - 18 q^{83} + 31 q^{84} + 4 q^{85} - 3 q^{86} - 10 q^{87} + 11 q^{89} + 20 q^{90} + 20 q^{91} - 34 q^{92} + 20 q^{93} + 59 q^{94} + 4 q^{95} + 7 q^{96} - 2 q^{97} - 36 q^{98}+O(q^{100}) $ 3 * q - q^2 + q^3 + 9 * q^4 - 3 * q^5 - 5 * q^6 + q^7 + 9 * q^8 + 2 * q^9 + q^10 + 9 * q^12 - 6 * q^13 + 5 * q^14 - q^15 + 13 * q^16 - 4 * q^17 - 20 * q^18 - 4 * q^19 - 9 * q^20 + 17 * q^21 - 6 * q^23 - 17 * q^24 + 3 * q^25 + 12 * q^26 + 13 * q^27 + 25 * q^28 - 2 * q^29 + 5 * q^30 + 14 * q^31 + 27 * q^32 - 8 * q^34 - q^35 + 2 * q^36 + 4 * q^37 - 18 * q^38 + 4 * q^39 - 9 * q^40 - 9 * q^41 - 35 * q^42 - 7 * q^43 - 2 * q^45 - 8 * q^46 - 15 * q^47 + 7 * q^48 + 18 * q^49 - q^50 + 20 * q^51 - 2 * q^52 - 6 * q^53 - 19 * q^54 - 3 * q^56 + 14 * q^57 + 30 * q^58 + 10 * q^59 - 9 * q^60 - 3 * q^61 - 24 * q^62 + 12 * q^63 + 29 * q^64 + 6 * q^65 + 19 * q^67 - 8 * q^69 - 5 * q^70 + 6 * q^71 - 48 * q^72 + 12 * q^73 + 28 * q^74 + q^75 - 16 * q^76 - 2 * q^78 - 2 * q^79 - 13 * q^80 + 3 * q^81 - 27 * q^82 - 18 * q^83 + 31 * q^84 + 4 * q^85 - 3 * q^86 - 10 * q^87 + 11 * q^89 + 20 * q^90 + 20 * q^91 - 34 * q^92 + 20 * q^93 + 59 * q^94 + 4 * q^95 + 7 * q^96 - 2 * q^97 - 36 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.74483	1.94089	0.970443	−	0.241332i	$-0.0775843\pi$
$2$	2.74483	1.94089	0.970443	+	0.241332i	$0.0775843\pi$
$3$	−0.210756	−0.121680	−0.0608400	−	0.998148i	$-0.519378\pi$
$3$	−0.210756	−0.121680	−0.0608400	+	0.998148i	$0.519378\pi$
$4$	5.53407	2.76704
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.578488	−0.236167
$7$	2.32331	0.878130	0.439065	−	0.898455i	$-0.355310\pi$
$7$	2.32331	0.878130	0.439065	+	0.898455i	$0.355310\pi$
$8$	9.70041	3.42961
$9$	−2.95558	−0.985194
$10$	−2.74483	−0.867990
$11$	0	0
$11$	0	0
$12$	−1.16634	−0.336693
$13$	0.534070	0.148124	0.0740622	−	0.997254i	$-0.476404\pi$
$13$	0.534070	0.148124	0.0740622	+	0.997254i	$0.476404\pi$
$14$	6.37709	1.70435
$15$	0.210756	0.0544169
$16$	15.5578	3.88945
$17$	−2.42151	−0.587303	−0.293651	−	0.955913i	$-0.594870\pi$
$17$	−2.42151	−0.587303	−0.293651	+	0.955913i	$0.594870\pi$
$18$	−8.11256	−1.91215
$19$	−4.95558	−1.13689	−0.568444	−	0.822722i	$-0.692454\pi$
$19$	−4.95558	−1.13689	−0.568444	+	0.822722i	$0.692454\pi$
$20$	−5.53407	−1.23746
$21$	−0.489652	−0.106851
$22$	0	0
$23$	−4.53407	−0.945419	−0.472709	−	0.881218i	$-0.656724\pi$
$23$	−4.53407	−0.945419	−0.472709	+	0.881218i	$0.656724\pi$
$24$	−2.04442	−0.417315
$25$	1.00000	0.200000
$26$	1.46593	0.287492
$27$	1.25517	0.241558
$28$	12.8574	2.42982
$29$	5.48965	1.01940	0.509701	−	0.860351i	$-0.329756\pi$
$29$	5.48965	1.01940	0.509701	+	0.860351i	$0.329756\pi$
$30$	0.578488	0.105617
$31$	1.04442	0.187583	0.0937915	−	0.995592i	$-0.470101\pi$
$31$	1.04442	0.187583	0.0937915	+	0.995592i	$0.470101\pi$
$32$	23.3026	4.11936
$33$	0	0
$34$	−6.64663	−1.13989
$35$	−2.32331	−0.392712
$36$	−16.3564	−2.72607
$37$	7.48965	1.23129	0.615646	−	0.788023i	$-0.288895\pi$
$37$	7.48965	1.23129	0.615646	+	0.788023i	$0.288895\pi$
$38$	−13.6022	−2.20657
$39$	−0.112558	−0.0180238
$40$	−9.70041	−1.53377
$41$	−10.6022	−1.65579	−0.827894	−	0.560885i	$-0.810461\pi$
$41$	−10.6022	−1.65579	−0.827894	+	0.560885i	$0.810461\pi$
$42$	−1.34401	−0.207385
$43$	−4.32331	−0.659299	−0.329650	−	0.944103i	$-0.606931\pi$
$43$	−4.32331	−0.659299	−0.329650	+	0.944103i	$0.606931\pi$
$44$	0	0
$45$	2.95558	0.440592
$46$	−12.4452	−1.83495
$47$	6.76855	0.987294	0.493647	−	0.869662i	$-0.335663\pi$
$47$	6.76855	0.987294	0.493647	+	0.869662i	$0.335663\pi$
$48$	−3.27890	−0.473268
$49$	−1.60221	−0.228887
$50$	2.74483	0.388177
$51$	0.510348	0.0714630
$52$	2.95558	0.409865
$53$	−4.53407	−0.622802	−0.311401	−	0.950279i	$-0.600798\pi$
$53$	−4.53407	−0.622802	−0.311401	+	0.950279i	$0.600798\pi$
$54$	3.44523	0.468837
$55$	0	0
$56$	22.5371	3.01165
$57$	1.04442	0.138337
$58$	15.0681	1.97854
$59$	−6.44523	−0.839098	−0.419549	−	0.907733i	$-0.637812\pi$
$59$	−6.44523	−0.839098	−0.419549	+	0.907733i	$0.637812\pi$
$60$	1.16634	0.150574
$61$	−6.79861	−0.870472	−0.435236	−	0.900316i	$-0.643335\pi$
$61$	−6.79861	−0.870472	−0.435236	+	0.900316i	$0.643335\pi$
$62$	2.86675	0.364077
$63$	−6.86675	−0.865129
$64$	32.8461	4.10576
$65$	−0.534070	−0.0662433
$66$	0	0
$67$	0.721104	0.0880968	0.0440484	−	0.999029i	$-0.485974\pi$
$67$	0.721104	0.0880968	0.0440484	+	0.999029i	$0.485974\pi$
$68$	−13.4008	−1.62509
$69$	0.955582	0.115039
$70$	−6.37709	−0.762208
$71$	4.53407	0.538095	0.269048	−	0.963127i	$-0.413291\pi$
$71$	4.53407	0.538095	0.269048	+	0.963127i	$0.413291\pi$
$72$	−28.6704	−3.37883
$73$	−1.06814	−0.125016	−0.0625082	−	0.998044i	$-0.519910\pi$
$73$	−1.06814	−0.125016	−0.0625082	+	0.998044i	$0.519910\pi$
$74$	20.5578	2.38979
$75$	−0.210756	−0.0243360
$76$	−27.4245	−3.14581
$77$	0	0
$78$	−0.308953	−0.0349821
$79$	−4.64663	−0.522787	−0.261393	−	0.965232i	$-0.584182\pi$
$79$	−4.64663	−0.522787	−0.261393	+	0.965232i	$0.584182\pi$
$80$	−15.5578	−1.73941
$81$	8.60221	0.955801
$82$	−29.1012	−3.21369
$83$	−13.6022	−1.49304	−0.746518	−	0.665365i	$-0.768276\pi$
$83$	−13.6022	−1.49304	−0.746518	+	0.665365i	$0.768276\pi$
$84$	−2.70977	−0.295660
$85$	2.42151	0.262650
$86$	−11.8667	−1.27962
$87$	−1.15698	−0.124041
$88$	0	0
$89$	12.7148	1.34776	0.673881	−	0.738840i	$-0.264626\pi$
$89$	12.7148	1.34776	0.673881	+	0.738840i	$0.264626\pi$
$90$	8.11256	0.855139
$91$	1.24081	0.130073
$92$	−25.0919	−2.61601
$93$	−0.220117	−0.0228251
$94$	18.5785	1.91622
$95$	4.95558	0.508432
$96$	−4.91116	−0.501244
$97$	4.75919	0.483222	0.241611	−	0.970373i	$-0.422324\pi$
$97$	4.75919	0.483222	0.241611	+	0.970373i	$0.422324\pi$
$98$	−4.39779	−0.444244
$99$	0	0
$100$	5.53407	0.553407
$101$	6.57849	0.654584	0.327292	−	0.944923i	$-0.393864\pi$
$101$	6.57849	0.654584	0.327292	+	0.944923i	$0.393864\pi$
$102$	1.40082	0.138701
$103$	16.3564	1.61164	0.805822	−	0.592158i	$-0.201724\pi$
$103$	16.3564	1.61164	0.805822	+	0.592158i	$0.201724\pi$
$104$	5.18070	0.508009
$105$	0.489652	0.0477852
$106$	−12.4452	−1.20879
$107$	−10.2108	−0.987111	−0.493556	−	0.869714i	$-0.664303\pi$
$107$	−10.2108	−0.987111	−0.493556	+	0.869714i	$0.664303\pi$
$108$	6.94622	0.668400
$109$	12.0919	1.15819	0.579095	−	0.815260i	$-0.303406\pi$
$109$	12.0919	1.15819	0.579095	+	0.815260i	$0.303406\pi$
$110$	0	0
$111$	−1.57849	−0.149823
$112$	36.1456	3.41544
$113$	−10.8430	−1.02003	−0.510013	−	0.860167i	$-0.670359\pi$
$113$	−10.8430	−1.02003	−0.510013	+	0.860167i	$0.670359\pi$
$114$	2.86675	0.268495
$115$	4.53407	0.422804
$116$	30.3801	2.82072
$117$	−1.57849	−0.145931
$118$	−17.6910	−1.62859
$119$	−5.62593	−0.515728
$120$	2.04442	0.186629
$121$	0	0
$122$	−18.6610	−1.68949
$123$	2.23448	0.201476
$124$	5.77988	0.519049
$125$	−1.00000	−0.0894427
$126$	−18.8480	−1.67912
$127$	8.12192	0.720704	0.360352	−	0.932816i	$-0.382657\pi$
$127$	8.12192	0.720704	0.360352	+	0.932816i	$0.382657\pi$
$128$	43.5515	3.84944
$129$	0.911164	0.0802235
$130$	−1.46593	−0.128571
$131$	−5.79861	−0.506627	−0.253313	−	0.967384i	$-0.581520\pi$
$131$	−5.79861	−0.506627	−0.253313	+	0.967384i	$0.581520\pi$
$132$	0	0
$133$	−11.5134	−0.998336
$134$	1.97930	0.170986
$135$	−1.25517	−0.108028
$136$	−23.4897	−2.01422
$137$	8.86675	0.757537	0.378769	−	0.925491i	$-0.376348\pi$
$137$	8.86675	0.757537	0.378769	+	0.925491i	$0.376348\pi$
$138$	2.62291	0.223277
$139$	16.8667	1.43062	0.715309	−	0.698808i	$-0.246286\pi$
$139$	16.8667	1.43062	0.715309	+	0.698808i	$0.246286\pi$
$140$	−12.8574	−1.08665
$141$	−1.42651	−0.120134
$142$	12.4452	1.04438
$143$	0	0
$144$	−45.9823	−3.83186
$145$	−5.48965	−0.455891
$146$	−2.93186	−0.242642
$147$	0.337675	0.0278510
$148$	41.4483	3.40703
$149$	−4.46593	−0.365863	−0.182932	−	0.983126i	$-0.558559\pi$
$149$	−4.46593	−0.365863	−0.182932	+	0.983126i	$0.558559\pi$
$150$	−0.578488	−0.0472334
$151$	11.5134	0.936945	0.468473	−	0.883478i	$-0.344804\pi$
$151$	11.5134	0.936945	0.468473	+	0.883478i	$0.344804\pi$
$152$	−48.0712	−3.89909
$153$	7.15698	0.578607
$154$	0	0
$155$	−1.04442	−0.0838897
$156$	−0.622906	−0.0498724
$157$	−5.91116	−0.471762	−0.235881	−	0.971782i	$-0.575798\pi$
$157$	−5.91116	−0.471762	−0.235881	+	0.971782i	$0.575798\pi$
$158$	−12.7542	−1.01467
$159$	0.955582	0.0757826
$160$	−23.3026	−1.84223
$161$	−10.5341	−0.830201
$162$	23.6116	1.85510
$163$	23.4990	1.84058	0.920292	−	0.391231i	$-0.127951\pi$
$163$	23.4990	1.84058	0.920292	+	0.391231i	$0.127951\pi$
$164$	−58.6734	−4.58162
$165$	0	0
$166$	−37.3357	−2.89781
$167$	−14.2345	−1.10150	−0.550748	−	0.834671i	$-0.685658\pi$
$167$	−14.2345	−1.10150	−0.550748	+	0.834671i	$0.685658\pi$
$168$	−4.74983	−0.366457
$169$	−12.7148	−0.978059
$170$	6.64663	0.509773
$171$	14.6466	1.12006
$172$	−23.9255	−1.82430
$173$	6.44523	0.490022	0.245011	−	0.969520i	$-0.421208\pi$
$173$	6.44523	0.490022	0.245011	+	0.969520i	$0.421208\pi$
$174$	−3.17570	−0.240749
$175$	2.32331	0.175626
$176$	0	0
$177$	1.35837	0.102101
$178$	34.8998	2.61585
$179$	16.9793	1.26909	0.634546	−	0.772885i	$-0.281187\pi$
$179$	16.9793	1.26909	0.634546	+	0.772885i	$0.281187\pi$
$180$	16.3564	1.21913
$181$	4.48965	0.333713	0.166857	−	0.985981i	$-0.446638\pi$
$181$	4.48965	0.333713	0.166857	+	0.985981i	$0.446638\pi$
$182$	3.40582	0.252456
$183$	1.43285	0.105919
$184$	−43.9823	−3.24242
$185$	−7.48965	−0.550650
$186$	−0.604184	−0.0443009
$187$	0	0
$188$	37.4576	2.73188
$189$	2.91616	0.212120
$190$	13.6022	0.986808
$191$	−2.75919	−0.199648	−0.0998239	−	0.995005i	$-0.531828\pi$
$191$	−2.75919	−0.199648	−0.0998239	+	0.995005i	$0.531828\pi$
$192$	−6.92250	−0.499588
$193$	−11.8036	−0.849642	−0.424821	−	0.905277i	$-0.639663\pi$
$193$	−11.8036	−0.849642	−0.424821	+	0.905277i	$0.639663\pi$
$194$	13.0631	0.937879
$195$	0.112558	0.00806048
$196$	−8.86675	−0.633339
$197$	6.51035	0.463843	0.231922	−	0.972734i	$-0.425499\pi$
$197$	6.51035	0.463843	0.231922	+	0.972734i	$0.425499\pi$
$198$	0	0
$199$	23.9586	1.69838	0.849190	−	0.528087i	$-0.177090\pi$
$199$	23.9586	1.69838	0.849190	+	0.528087i	$0.177090\pi$
$200$	9.70041	0.685922
$201$	−0.151977	−0.0107196
$202$	18.0568	1.27047
$203$	12.7542	0.895168
$204$	2.82430	0.197741
$205$	10.6022	0.740491
$206$	44.8955	3.12802
$207$	13.4008	0.931421
$208$	8.30895	0.576122
$209$	0	0
$210$	1.34401	0.0927455
$211$	16.8667	1.16115	0.580577	−	0.814205i	$-0.302827\pi$
$211$	16.8667	1.16115	0.580577	+	0.814205i	$0.302827\pi$
$212$	−25.0919	−1.72332
$213$	−0.955582	−0.0654754
$214$	−28.0267	−1.91587
$215$	4.32331	0.294848
$216$	12.1757	0.828451
$217$	2.42651	0.164722
$218$	33.1901	2.24791
$219$	0.225117	0.0152120
$220$	0	0
$221$	−1.29326	−0.0869939
$222$	−4.33268	−0.290790
$223$	−25.0174	−1.67529	−0.837644	−	0.546216i	$-0.816068\pi$
$223$	−25.0174	−1.67529	−0.837644	+	0.546216i	$0.816068\pi$
$224$	54.1393	3.61733
$225$	−2.95558	−0.197039
$226$	−29.7622	−1.97975
$227$	−4.00936	−0.266111	−0.133055	−	0.991109i	$-0.542479\pi$
$227$	−4.00936	−0.266111	−0.133055	+	0.991109i	$0.542479\pi$
$228$	5.77988	0.382782
$229$	−17.3327	−1.14538	−0.572688	−	0.819774i	$-0.694099\pi$
$229$	−17.3327	−1.14538	−0.572688	+	0.819774i	$0.694099\pi$
$230$	12.4452	0.820614
$231$	0	0
$232$	53.2519	3.49616
$233$	−2.11256	−0.138398	−0.0691992	−	0.997603i	$-0.522044\pi$
$233$	−2.11256	−0.138398	−0.0691992	+	0.997603i	$0.522044\pi$
$234$	−4.33268	−0.283236
$235$	−6.76855	−0.441531
$236$	−35.6684	−2.32181
$237$	0.979304	0.0636127
$238$	−15.4422	−1.00097
$239$	23.9349	1.54822	0.774110	−	0.633052i	$-0.218198\pi$
$239$	23.9349	1.54822	0.774110	+	0.633052i	$0.218198\pi$
$240$	3.27890	0.211652
$241$	14.5134	0.934889	0.467444	−	0.884023i	$-0.345175\pi$
$241$	14.5134	0.934889	0.467444	+	0.884023i	$0.345175\pi$
$242$	0	0
$243$	−5.57849	−0.357860
$244$	−37.6240	−2.40863
$245$	1.60221	0.102361
$246$	6.13325	0.391042
$247$	−2.64663	−0.168401
$248$	10.1313	0.643337
$249$	2.86675	0.181673
$250$	−2.74483	−0.173598
$251$	28.8066	1.81826	0.909129	−	0.416514i	$-0.136748\pi$
$251$	28.8066	1.81826	0.909129	+	0.416514i	$0.136748\pi$
$252$	−38.0011	−2.39384
$253$	0	0
$254$	22.2933	1.39880
$255$	−0.510348	−0.0319592
$256$	53.8491	3.36557
$257$	−27.6497	−1.72474	−0.862369	−	0.506280i	$-0.831020\pi$
$257$	−27.6497	−1.72474	−0.862369	+	0.506280i	$0.831020\pi$
$258$	2.50099	0.155705
$259$	17.4008	1.08123
$260$	−2.95558	−0.183297
$261$	−16.2251	−1.00431
$262$	−15.9162	−0.983304
$263$	−3.13325	−0.193205	−0.0966024	−	0.995323i	$-0.530798\pi$
$263$	−3.13325	−0.193205	−0.0966024	+	0.995323i	$0.530798\pi$
$264$	0	0
$265$	4.53407	0.278526
$266$	−31.6022	−1.93766
$267$	−2.67971	−0.163996
$268$	3.99064	0.243767
$269$	18.0030	1.09766	0.548832	−	0.835933i	$-0.315073\pi$
$269$	18.0030	1.09766	0.548832	+	0.835933i	$0.315073\pi$
$270$	−3.44523	−0.209670
$271$	−20.3327	−1.23512	−0.617561	−	0.786523i	$-0.711879\pi$
$271$	−20.3327	−1.23512	−0.617561	+	0.786523i	$0.711879\pi$
$272$	−37.6734	−2.28428
$273$	−0.261509	−0.0158272
$274$	24.3377	1.47029
$275$	0	0
$276$	5.28826	0.318316
$277$	25.4897	1.53152	0.765762	−	0.643124i	$-0.222362\pi$
$277$	25.4897	1.53152	0.765762	+	0.643124i	$0.222362\pi$
$278$	46.2963	2.77667
$279$	−3.08686	−0.184806
$280$	−22.5371	−1.34685
$281$	−18.2726	−1.09005	−0.545025	−	0.838420i	$-0.683480\pi$
$281$	−18.2726	−1.09005	−0.545025	+	0.838420i	$0.683480\pi$
$282$	−3.91553	−0.233166
$283$	11.0538	0.657079	0.328539	−	0.944490i	$-0.393444\pi$
$283$	11.0538	0.657079	0.328539	+	0.944490i	$0.393444\pi$
$284$	25.0919	1.48893
$285$	−1.04442	−0.0618660
$286$	0	0
$287$	−24.6323	−1.45400
$288$	−68.8728	−4.05837
$289$	−11.1363	−0.655075
$290$	−15.0681	−0.884832
$291$	−1.00303	−0.0587985
$292$	−5.91116	−0.345925
$293$	−27.1393	−1.58550	−0.792748	−	0.609550i	$-0.791350\pi$
$293$	−27.1393	−1.58550	−0.792748	+	0.609550i	$0.791350\pi$
$294$	0.926860	0.0540556
$295$	6.44523	0.375256
$296$	72.6527	4.22285
$297$	0	0
$298$	−12.2582	−0.710098
$299$	−2.42151	−0.140040
$300$	−1.16634	−0.0673385
$301$	−10.0444	−0.578951
$302$	31.6022	1.81850
$303$	−1.38646	−0.0796498
$304$	−77.0979	−4.42187
$305$	6.79861	0.389287
$306$	19.6447	1.12301
$307$	−11.7385	−0.669951	−0.334976	−	0.942227i	$-0.608728\pi$
$307$	−11.7385	−0.669951	−0.334976	+	0.942227i	$0.608728\pi$
$308$	0	0
$309$	−3.44721	−0.196105
$310$	−2.86675	−0.162820
$311$	10.6416	0.603431	0.301716	−	0.953398i	$-0.402441\pi$
$311$	10.6416	0.603431	0.301716	+	0.953398i	$0.402441\pi$
$312$	−1.09186	−0.0618146
$313$	−27.1807	−1.53634	−0.768172	−	0.640244i	$-0.778833\pi$
$313$	−27.1807	−1.53634	−0.768172	+	0.640244i	$0.778833\pi$
$314$	−16.2251	−0.915636
$315$	6.86675	0.386897
$316$	−25.7148	−1.44657
$317$	4.97930	0.279666	0.139833	−	0.990175i	$-0.455343\pi$
$317$	4.97930	0.279666	0.139833	+	0.990175i	$0.455343\pi$
$318$	2.62291	0.147085
$319$	0	0
$320$	−32.8461	−1.83615
$321$	2.15198	0.120112
$322$	−28.9142	−1.61132
$323$	12.0000	0.667698
$324$	47.6052	2.64474
$325$	0.534070	0.0296249
$326$	64.5007	3.57236
$327$	−2.54843	−0.140929
$328$	−102.846	−5.67871
$329$	15.7255	0.866973
$330$	0	0
$331$	7.55477	0.415247	0.207624	−	0.978209i	$-0.433427\pi$
$331$	7.55477	0.415247	0.207624	+	0.978209i	$0.433427\pi$
$332$	−75.2756	−4.13128
$333$	−22.1363	−1.21306
$334$	−39.0712	−2.13788
$335$	−0.721104	−0.0393981
$336$	−7.61791	−0.415591
$337$	−3.69105	−0.201064	−0.100532	−	0.994934i	$-0.532054\pi$
$337$	−3.69105	−0.201064	−0.100532	+	0.994934i	$0.532054\pi$
$338$	−34.8998	−1.89830
$339$	2.28523	0.124117
$340$	13.4008	0.726761
$341$	0	0
$342$	40.2024	2.17390
$343$	−19.9856	−1.07912
$344$	−41.9379	−2.26114
$345$	−0.955582	−0.0514468
$346$	17.6910	0.951077
$347$	15.7655	0.846338	0.423169	−	0.906051i	$-0.360918\pi$
$347$	15.7655	0.846338	0.423169	+	0.906051i	$0.360918\pi$
$348$	−6.40279	−0.343226
$349$	10.5578	0.565146	0.282573	−	0.959246i	$-0.408812\pi$
$349$	10.5578	0.565146	0.282573	+	0.959246i	$0.408812\pi$
$350$	6.37709	0.340870
$351$	0.670351	0.0357807
$352$	0	0
$353$	−24.5528	−1.30681	−0.653407	−	0.757007i	$-0.726661\pi$
$353$	−24.5528	−1.30681	−0.653407	+	0.757007i	$0.726661\pi$
$354$	3.72849	0.198167
$355$	−4.53407	−0.240643
$356$	70.3644	3.72931
$357$	1.18570	0.0627538
$358$	46.6052	2.46316
$359$	16.6704	0.879827	0.439914	−	0.898040i	$-0.355009\pi$
$359$	16.6704	0.879827	0.439914	+	0.898040i	$0.355009\pi$
$360$	28.6704	1.51106
$361$	5.55779	0.292515
$362$	12.3233	0.647699
$363$	0	0
$364$	6.86675	0.359915
$365$	1.06814	0.0559090
$366$	3.93291	0.205577
$367$	15.2789	0.797552	0.398776	−	0.917048i	$-0.369435\pi$
$367$	15.2789	0.797552	0.398776	+	0.917048i	$0.369435\pi$
$368$	−70.5401	−3.67716
$369$	31.3357	1.63127
$370$	−20.5578	−1.06875
$371$	−10.5341	−0.546902
$372$	−1.21814	−0.0631578
$373$	−17.8461	−0.924033	−0.462017	−	0.886871i	$-0.652874\pi$
$373$	−17.8461	−0.924033	−0.462017	+	0.886871i	$0.652874\pi$
$374$	0	0
$375$	0.210756	0.0108834
$376$	65.6577	3.38604
$377$	2.93186	0.150998
$378$	8.00436	0.411700
$379$	1.89244	0.0972082	0.0486041	−	0.998818i	$-0.484523\pi$
$379$	1.89244	0.0972082	0.0486041	+	0.998818i	$0.484523\pi$
$380$	27.4245	1.40685
$381$	−1.71174	−0.0876952
$382$	−7.57349	−0.387493
$383$	5.31698	0.271685	0.135842	−	0.990730i	$-0.456626\pi$
$383$	5.31698	0.271685	0.135842	+	0.990730i	$0.456626\pi$
$384$	−9.17873	−0.468400
$385$	0	0
$386$	−32.3988	−1.64906
$387$	12.7779	0.649538
$388$	26.3377	1.33709
$389$	−26.8273	−1.36020	−0.680100	−	0.733120i	$-0.738064\pi$
$389$	−26.8273	−1.36020	−0.680100	+	0.733120i	$0.738064\pi$
$390$	0.308953	0.0156445
$391$	10.9793	0.555247
$392$	−15.5421	−0.784994
$393$	1.22209	0.0616463
$394$	17.8698	0.900266
$395$	4.64663	0.233797
$396$	0	0
$397$	31.5972	1.58582	0.792909	−	0.609340i	$-0.208565\pi$
$397$	31.5972	1.58582	0.792909	+	0.609340i	$0.208565\pi$
$398$	65.7622	3.29636
$399$	2.42651	0.121478
$400$	15.5578	0.777890
$401$	−3.13628	−0.156618	−0.0783092	−	0.996929i	$-0.524952\pi$
$401$	−3.13628	−0.156618	−0.0783092	+	0.996929i	$0.524952\pi$
$402$	−0.417150	−0.0208056
$403$	0.557793	0.0277856
$404$	36.4058	1.81126
$405$	−8.60221	−0.427447
$406$	35.0080	1.73742
$407$	0	0
$408$	4.95058	0.245090
$409$	−0.424538	−0.0209921	−0.0104960	−	0.999945i	$-0.503341\pi$
$409$	−0.424538	−0.0209921	−0.0104960	+	0.999945i	$0.503341\pi$
$410$	29.1012	1.43721
$411$	−1.86872	−0.0921771
$412$	90.5175	4.45947
$413$	−14.9743	−0.736837
$414$	36.7829	1.80778
$415$	13.6022	0.667706
$416$	12.4452	0.610178
$417$	−3.55477	−0.174078
$418$	0	0
$419$	6.71174	0.327890	0.163945	−	0.986469i	$-0.447578\pi$
$419$	6.71174	0.327890	0.163945	+	0.986469i	$0.447578\pi$
$420$	2.70977	0.132223
$421$	2.77988	0.135483	0.0677416	−	0.997703i	$-0.478421\pi$
$421$	2.77988	0.135483	0.0677416	+	0.997703i	$0.478421\pi$
$422$	46.2963	2.25367
$423$	−20.0050	−0.972676
$424$	−43.9823	−2.13597
$425$	−2.42151	−0.117461
$426$	−2.62291	−0.127080
$427$	−15.7953	−0.764388
$428$	−56.5070	−2.73137
$429$	0	0
$430$	11.8667	0.572265
$431$	−16.1964	−0.780153	−0.390076	−	0.920782i	$-0.627551\pi$
$431$	−16.1964	−0.780153	−0.390076	+	0.920782i	$0.627551\pi$
$432$	19.5277	0.939529
$433$	7.82733	0.376157	0.188079	−	0.982154i	$-0.439774\pi$
$433$	7.82733	0.376157	0.188079	+	0.982154i	$0.439774\pi$
$434$	6.66035	0.319707
$435$	1.15698	0.0554728
$436$	66.9172	3.20475
$437$	22.4690	1.07484
$438$	0.617907	0.0295247
$439$	−20.7355	−0.989650	−0.494825	−	0.868993i	$-0.664768\pi$
$439$	−20.7355	−0.989650	−0.494825	+	0.868993i	$0.664768\pi$
$440$	0	0
$441$	4.73546	0.225498
$442$	−3.54977	−0.168845
$443$	5.30262	0.251935	0.125968	−	0.992034i	$-0.459796\pi$
$443$	5.30262	0.251935	0.125968	+	0.992034i	$0.459796\pi$
$444$	−8.73546	−0.414567
$445$	−12.7148	−0.602738
$446$	−68.6684	−3.25154
$447$	0.941221	0.0445182
$448$	76.3117	3.60539
$449$	−30.0030	−1.41593	−0.707965	−	0.706247i	$-0.750387\pi$
$449$	−30.0030	−1.41593	−0.707965	+	0.706247i	$0.750387\pi$
$450$	−8.11256	−0.382430
$451$	0	0
$452$	−60.0061	−2.82245
$453$	−2.42651	−0.114007
$454$	−11.0050	−0.516490
$455$	−1.24081	−0.0581702
$456$	10.1313	0.474441
$457$	−37.5134	−1.75480	−0.877401	−	0.479758i	$-0.840724\pi$
$457$	−37.5134	−1.75480	−0.877401	+	0.479758i	$0.840724\pi$
$458$	−47.5752	−2.22304
$459$	−3.03942	−0.141868
$460$	25.0919	1.16991
$461$	−15.7829	−0.735083	−0.367542	−	0.930007i	$-0.619800\pi$
$461$	−15.7829	−0.735083	−0.367542	+	0.930007i	$0.619800\pi$
$462$	0	0
$463$	−16.5672	−0.769941	−0.384970	−	0.922929i	$-0.625788\pi$
$463$	−16.5672	−0.769941	−0.384970	+	0.922929i	$0.625788\pi$
$464$	85.4069	3.96491
$465$	0.220117	0.0102077
$466$	−5.79861	−0.268615
$467$	3.70041	0.171234	0.0856172	−	0.996328i	$-0.472714\pi$
$467$	3.70041	0.171234	0.0856172	+	0.996328i	$0.472714\pi$
$468$	−8.73546	−0.403797
$469$	1.67535	0.0773605
$470$	−18.5785	−0.856962
$471$	1.24581	0.0574040
$472$	−62.5214	−2.87778
$473$	0	0
$474$	2.68802	0.123465
$475$	−4.95558	−0.227378
$476$	−31.1343	−1.42704
$477$	13.4008	0.613581
$478$	65.6971	3.00492
$479$	−1.26454	−0.0577781	−0.0288890	−	0.999583i	$-0.509197\pi$
$479$	−1.26454	−0.0577781	−0.0288890	+	0.999583i	$0.509197\pi$
$480$	4.91116	0.224163
$481$	4.00000	0.182384
$482$	39.8367	1.81451
$483$	2.22012	0.101019
$484$	0	0
$485$	−4.75919	−0.216104
$486$	−15.3120	−0.694566
$487$	21.6022	0.978890	0.489445	−	0.872034i	$-0.337199\pi$
$487$	21.6022	0.978890	0.489445	+	0.872034i	$0.337199\pi$
$488$	−65.9492	−2.98538
$489$	−4.95256	−0.223962
$490$	4.39779	0.198672
$491$	−25.5371	−1.15247	−0.576237	−	0.817283i	$-0.695479\pi$
$491$	−25.5371	−1.15247	−0.576237	+	0.817283i	$0.695479\pi$
$492$	12.3658	0.557491
$493$	−13.2933	−0.598698
$494$	−7.26454	−0.326847
$495$	0	0
$496$	16.2488	0.729594
$497$	10.5341	0.472518
$498$	7.86872	0.352606
$499$	24.3614	1.09057	0.545283	−	0.838252i	$-0.316422\pi$
$499$	24.3614	1.09057	0.545283	+	0.838252i	$0.316422\pi$
$500$	−5.53407	−0.247491
$501$	3.00000	0.134030
$502$	79.0692	3.52903
$503$	12.4960	0.557169	0.278584	−	0.960412i	$-0.410135\pi$
$503$	12.4960	0.557169	0.278584	+	0.960412i	$0.410135\pi$
$504$	−66.6102	−2.96706
$505$	−6.57849	−0.292739
$506$	0	0
$507$	2.67971	0.119010
$508$	44.9473	1.99421
$509$	24.4483	1.08365	0.541825	−	0.840491i	$-0.317734\pi$
$509$	24.4483	1.08365	0.541825	+	0.840491i	$0.317734\pi$
$510$	−1.40082	−0.0620292
$511$	−2.48163	−0.109781
$512$	60.7034	2.68274
$513$	−6.22012	−0.274625
$514$	−75.8935	−3.34752
$515$	−16.3564	−0.720749
$516$	5.04245	0.221981
$517$	0	0
$518$	47.7622	2.09855
$519$	−1.35837	−0.0596259
$520$	−5.18070	−0.227189
$521$	−0.0394184	−0.00172695	−0.000863476	−	1.00000i	$-0.500275\pi$
$521$	−0.0394184	−0.00172695	−0.000863476		1.00000i	$0.500275\pi$
$522$	−44.5351	−1.94925
$523$	21.0919	0.922283	0.461141	−	0.887327i	$-0.347440\pi$
$523$	21.0919	0.922283	0.461141	+	0.887327i	$0.347440\pi$
$524$	−32.0899	−1.40185
$525$	−0.489652	−0.0213702
$526$	−8.60024	−0.374988
$527$	−2.52907	−0.110168
$528$	0	0
$529$	−2.44221	−0.106183
$530$	12.4452	0.540586
$531$	19.0494	0.826674
$532$	−63.7158	−2.76243
$533$	−5.66232	−0.245263
$534$	−7.35534	−0.318297
$535$	10.2108	0.441449
$536$	6.99500	0.302138
$537$	−3.57849	−0.154423
$538$	49.4152	2.13044
$539$	0	0
$540$	−6.94622	−0.298918
$541$	33.4402	1.43771	0.718854	−	0.695161i	$-0.244667\pi$
$541$	33.4402	1.43771	0.718854	+	0.695161i	$0.244667\pi$
$542$	−55.8097	−2.39723
$543$	−0.946221	−0.0406062
$544$	−56.4276	−2.41931
$545$	−12.0919	−0.517958
$546$	−0.717796	−0.0307188
$547$	−32.8066	−1.40271	−0.701355	−	0.712812i	$-0.747421\pi$
$547$	−32.8066	−1.40271	−0.701355	+	0.712812i	$0.747421\pi$
$548$	49.0692	2.09613
$549$	20.0938	0.857584
$550$	0	0
$551$	−27.2044	−1.15895
$552$	9.26953	0.394538
$553$	−10.7956	−0.459075
$554$	69.9647	2.97251
$555$	1.57849	0.0670031
$556$	93.3418	3.95857
$557$	−28.3327	−1.20049	−0.600247	−	0.799815i	$-0.704931\pi$
$557$	−28.3327	−1.20049	−0.600247	+	0.799815i	$0.704931\pi$
$558$	−8.47290	−0.358687
$559$	−2.30895	−0.0976583
$560$	−36.1456	−1.52743
$561$	0	0
$562$	−50.1550	−2.11566
$563$	−29.0361	−1.22373	−0.611863	−	0.790964i	$-0.709580\pi$
$563$	−29.0361	−1.22373	−0.611863	+	0.790964i	$0.709580\pi$
$564$	−7.89441	−0.332415
$565$	10.8430	0.456169
$566$	30.3407	1.27531
$567$	19.9856	0.839318
$568$	43.9823	1.84546
$569$	−28.7098	−1.20358	−0.601788	−	0.798656i	$-0.705545\pi$
$569$	−28.7098	−1.20358	−0.601788	+	0.798656i	$0.705545\pi$
$570$	−2.86675	−0.120075
$571$	−0.824301	−0.0344959	−0.0172480	−	0.999851i	$-0.505490\pi$
$571$	−0.824301	−0.0344959	−0.0172480	+	0.999851i	$0.505490\pi$
$572$	0	0
$573$	0.581515	0.0242931
$574$	−67.6113	−2.82204
$575$	−4.53407	−0.189084
$576$	−97.0792	−4.04497
$577$	−31.5421	−1.31311	−0.656557	−	0.754276i	$-0.727988\pi$
$577$	−31.5421	−1.31311	−0.656557	+	0.754276i	$0.727988\pi$
$578$	−30.5672	−1.27143
$579$	2.48768	0.103384
$580$	−30.3801	−1.26147
$581$	−31.6022	−1.31108
$582$	−2.75313	−0.114121
$583$	0	0
$584$	−10.3614	−0.428758
$585$	1.57849	0.0652625
$586$	−74.4927	−3.07726
$587$	−26.7735	−1.10506	−0.552531	−	0.833492i	$-0.686338\pi$
$587$	−26.7735	−1.10506	−0.552531	+	0.833492i	$0.686338\pi$
$588$	1.86872	0.0770647
$589$	−5.17570	−0.213261
$590$	17.6910	0.728329
$591$	−1.37209	−0.0564404
$592$	116.522	4.78904
$593$	11.0731	0.454719	0.227360	−	0.973811i	$-0.426991\pi$
$593$	11.0731	0.454719	0.227360	+	0.973811i	$0.426991\pi$
$594$	0	0
$595$	5.62593	0.230641
$596$	−24.7148	−1.01236
$597$	−5.04942	−0.206659
$598$	−6.64663	−0.271801
$599$	−11.9349	−0.487646	−0.243823	−	0.969820i	$-0.578402\pi$
$599$	−11.9349	−0.487646	−0.243823	+	0.969820i	$0.578402\pi$
$600$	−2.04442	−0.0834630
$601$	−5.26454	−0.214745	−0.107372	−	0.994219i	$-0.534244\pi$
$601$	−5.26454	−0.214745	−0.107372	+	0.994219i	$0.534244\pi$
$602$	−27.5702	−1.12368
$603$	−2.13128	−0.0867925
$604$	63.7158	2.59256
$605$	0	0
$606$	−3.80558	−0.154591
$607$	−35.8461	−1.45495	−0.727473	−	0.686136i	$-0.759305\pi$
$607$	−35.8461	−1.45495	−0.727473	+	0.686136i	$0.759305\pi$
$608$	−115.478	−4.68325
$609$	−2.68802	−0.108924
$610$	18.6610	0.755561
$611$	3.61488	0.146242
$612$	39.6072	1.60103
$613$	−6.55779	−0.264867	−0.132433	−	0.991192i	$-0.542279\pi$
$613$	−6.55779	−0.264867	−0.132433	+	0.991192i	$0.542279\pi$
$614$	−32.2201	−1.30030
$615$	−2.23448	−0.0901029
$616$	0	0
$617$	17.7986	0.716545	0.358272	−	0.933617i	$-0.383366\pi$
$617$	17.7986	0.716545	0.358272	+	0.933617i	$0.383366\pi$
$618$	−9.46198	−0.380617
$619$	44.8905	1.80430	0.902150	−	0.431422i	$-0.141988\pi$
$619$	44.8905	1.80430	0.902150	+	0.431422i	$0.141988\pi$
$620$	−5.77988	−0.232126
$621$	−5.69105	−0.228374
$622$	29.2094	1.17119
$623$	29.5404	1.18351
$624$	−1.75116	−0.0701025
$625$	1.00000	0.0400000
$626$	−74.6063	−2.98187
$627$	0	0
$628$	−32.7128	−1.30538
$629$	−18.1363	−0.723141
$630$	18.8480	0.750923
$631$	21.9112	0.872270	0.436135	−	0.899881i	$-0.356347\pi$
$631$	21.9112	0.872270	0.436135	+	0.899881i	$0.356347\pi$
$632$	−45.0742	−1.79296
$633$	−3.55477	−0.141289
$634$	13.6673	0.542799
$635$	−8.12192	−0.322309
$636$	5.28826	0.209693
$637$	−0.855693	−0.0339038
$638$	0	0
$639$	−13.4008	−0.530128
$640$	−43.5515	−1.72152
$641$	35.7335	1.41139	0.705694	−	0.708517i	$-0.250635\pi$
$641$	35.7335	1.41139	0.705694	+	0.708517i	$0.250635\pi$
$642$	5.90680	0.233123
$643$	0.412150	0.0162536	0.00812681	−	0.999967i	$-0.497413\pi$
$643$	0.412150	0.0162536	0.00812681	+	0.999967i	$0.497413\pi$
$644$	−58.2963	−2.29720
$645$	−0.911164	−0.0358770
$646$	32.9379	1.29592
$647$	−16.5484	−0.650586	−0.325293	−	0.945613i	$-0.605463\pi$
$647$	−16.5484	−0.650586	−0.325293	+	0.945613i	$0.605463\pi$
$648$	83.4450	3.27803
$649$	0	0
$650$	1.46593	0.0574985
$651$	−0.511402	−0.0200434
$652$	130.045	5.09296
$653$	11.0080	0.430777	0.215389	−	0.976528i	$-0.430898\pi$
$653$	11.0080	0.430777	0.215389	+	0.976528i	$0.430898\pi$
$654$	−6.99500	−0.273526
$655$	5.79861	0.226570
$656$	−164.947	−6.44010
$657$	3.15698	0.123165
$658$	43.1637	1.68269
$659$	−42.9980	−1.67497	−0.837483	−	0.546464i	$-0.815974\pi$
$659$	−42.9980	−1.67497	−0.837483	+	0.546464i	$0.815974\pi$
$660$	0	0
$661$	19.4927	0.758177	0.379089	−	0.925360i	$-0.376238\pi$
$661$	19.4927	0.758177	0.379089	+	0.925360i	$0.376238\pi$
$662$	20.7365	0.805948
$663$	0.272562	0.0105854
$664$	−131.947	−5.12054
$665$	11.5134	0.446470
$666$	−60.7602	−2.35441
$667$	−24.8905	−0.963763
$668$	−78.7746	−3.04788
$669$	5.27256	0.203849
$670$	−1.97930	−0.0764672
$671$	0	0
$672$	−11.4102	−0.440157
$673$	6.80663	0.262376	0.131188	−	0.991357i	$-0.458121\pi$
$673$	6.80663	0.262376	0.131188	+	0.991357i	$0.458121\pi$
$674$	−10.1313	−0.390242
$675$	1.25517	0.0483117
$676$	−70.3644	−2.70632
$677$	1.02070	0.0392285	0.0196143	−	0.999808i	$-0.493756\pi$
$677$	1.02070	0.0392285	0.0196143	+	0.999808i	$0.493756\pi$
$678$	6.27256	0.240896
$679$	11.0571	0.424332
$680$	23.4897	0.900787
$681$	0.844996	0.0323803
$682$	0	0
$683$	2.09820	0.0802853	0.0401426	−	0.999194i	$-0.487219\pi$
$683$	2.09820	0.0802853	0.0401426	+	0.999194i	$0.487219\pi$
$684$	81.0555	3.09923
$685$	−8.86675	−0.338781
$686$	−54.8571	−2.09445
$687$	3.65296	0.139369
$688$	−67.2612	−2.56431
$689$	−2.42151	−0.0922523
$690$	−2.62291	−0.0998523
$691$	11.9950	0.456311	0.228156	−	0.973625i	$-0.426730\pi$
$691$	11.9950	0.456311	0.228156	+	0.973625i	$0.426730\pi$
$692$	35.6684	1.35591
$693$	0	0
$694$	43.2736	1.64264
$695$	−16.8667	−0.639792
$696$	−11.2231	−0.425412
$697$	25.6734	0.972449
$698$	28.9793	1.09688
$699$	0.445234	0.0168403
$700$	12.8574	0.485963
$701$	−29.3594	−1.10889	−0.554445	−	0.832220i	$-0.687069\pi$
$701$	−29.3594	−1.10889	−0.554445	+	0.832220i	$0.687069\pi$
$702$	1.84000	0.0694462
$703$	−37.1156	−1.39984
$704$	0	0
$705$	1.42651	0.0537255
$706$	−67.3931	−2.53637
$707$	15.2839	0.574810
$708$	7.51732	0.282518
$709$	−37.5451	−1.41004	−0.705018	−	0.709189i	$-0.749061\pi$
$709$	−37.5451	−1.41004	−0.705018	+	0.709189i	$0.749061\pi$
$710$	−12.4452	−0.467061
$711$	13.7335	0.515046
$712$	123.338	4.62230
$713$	−4.73546	−0.177345
$714$	3.25454	0.121798
$715$	0	0
$716$	93.9647	3.51162
$717$	−5.04442	−0.188387
$718$	45.7572	1.70764
$719$	−3.99500	−0.148988	−0.0744942	−	0.997221i	$-0.523734\pi$
$719$	−3.99500	−0.148988	−0.0744942	+	0.997221i	$0.523734\pi$
$720$	45.9823	1.71366
$721$	38.0011	1.41523
$722$	15.2552	0.567739
$723$	−3.05878	−0.113757
$724$	24.8461	0.923396
$725$	5.48965	0.203881
$726$	0	0
$727$	−25.4990	−0.945706	−0.472853	−	0.881141i	$-0.656776\pi$
$727$	−25.4990	−0.945706	−0.472853	+	0.881141i	$0.656776\pi$
$728$	12.0364	0.446098
$729$	−24.6309	−0.912257
$730$	2.93186	0.108513
$731$	10.4690	0.387208
$732$	7.92947	0.293082
$733$	36.2024	1.33717	0.668584	−	0.743637i	$-0.266901\pi$
$733$	36.2024	1.33717	0.668584	+	0.743637i	$0.266901\pi$
$734$	41.9379	1.54796
$735$	−0.337675	−0.0124553
$736$	−105.656	−3.89452
$737$	0	0
$738$	86.0111	3.16611
$739$	6.06011	0.222925	0.111462	−	0.993769i	$-0.464447\pi$
$739$	6.06011	0.222925	0.111462	+	0.993769i	$0.464447\pi$
$740$	−41.4483	−1.52367
$741$	0.557793	0.0204910
$742$	−28.9142	−1.06147
$743$	−36.2869	−1.33124	−0.665619	−	0.746292i	$-0.731832\pi$
$743$	−36.2869	−1.33124	−0.665619	+	0.746292i	$0.731832\pi$
$744$	−2.13523	−0.0782812
$745$	4.46593	0.163619
$746$	−48.9843	−1.79344
$747$	40.2024	1.47093
$748$	0	0
$749$	−23.7228	−0.866812
$750$	0.578488	0.0211234
$751$	−15.7335	−0.574123	−0.287062	−	0.957912i	$-0.592678\pi$
$751$	−15.7335	−0.574123	−0.287062	+	0.957912i	$0.592678\pi$
$752$	105.304	3.84003
$753$	−6.07117	−0.221246
$754$	8.04744	0.293071
$755$	−11.5134	−0.419015
$756$	16.1383	0.586943
$757$	−25.1393	−0.913704	−0.456852	−	0.889543i	$-0.651023\pi$
$757$	−25.1393	−0.913704	−0.456852	+	0.889543i	$0.651023\pi$
$758$	5.19442	0.188670
$759$	0	0
$760$	48.0712	1.74372
$761$	15.4709	0.560821	0.280410	−	0.959880i	$-0.409529\pi$
$761$	15.4709	0.560821	0.280410	+	0.959880i	$0.409529\pi$
$762$	−4.69844	−0.170206
$763$	28.0932	1.01704
$764$	−15.2695	−0.552432
$765$	−7.15698	−0.258761
$766$	14.5942	0.527309
$767$	−3.44221	−0.124291
$768$	−11.3490	−0.409522
$769$	−17.3220	−0.624647	−0.312323	−	0.949976i	$-0.601107\pi$
$769$	−17.3220	−0.624647	−0.312323	+	0.949976i	$0.601107\pi$
$770$	0	0
$771$	5.82733	0.209866
$772$	−65.3220	−2.35099
$773$	−22.6991	−0.816429	−0.408214	−	0.912886i	$-0.633848\pi$
$773$	−22.6991	−0.816429	−0.408214	+	0.912886i	$0.633848\pi$
$774$	35.0731	1.26068
$775$	1.04442	0.0375166
$776$	46.1661	1.65726
$777$	−3.66732	−0.131565
$778$	−73.6363	−2.63999
$779$	52.5401	1.88245
$780$	0.622906	0.0223036
$781$	0	0
$782$	30.1363	1.07767
$783$	6.89047	0.246245
$784$	−24.9269	−0.890245
$785$	5.91116	0.210978
$786$	3.35443	0.119648
$787$	−3.10122	−0.110547	−0.0552734	−	0.998471i	$-0.517603\pi$
$787$	−3.10122	−0.110547	−0.0552734	+	0.998471i	$0.517603\pi$
$788$	36.0287	1.28347
$789$	0.660352	0.0235091
$790$	12.7542	0.453774
$791$	−25.1918	−0.895716
$792$	0	0
$793$	−3.63093	−0.128938
$794$	86.7288	3.07789
$795$	−0.955582	−0.0338910
$796$	132.589	4.69948
$797$	−19.0919	−0.676268	−0.338134	−	0.941098i	$-0.609796\pi$
$797$	−19.0919	−0.676268	−0.338134	+	0.941098i	$0.609796\pi$
$798$	6.66035	0.235774
$799$	−16.3901	−0.579841
$800$	23.3026	0.823872
$801$	−37.5795	−1.32781
$802$	−8.60855	−0.303978
$803$	0	0
$804$	−0.841051	−0.0296616
$805$	10.5341	0.371277
$806$	1.53104	0.0539287
$807$	−3.79424	−0.133564
$808$	63.8140	2.24497
$809$	−4.46896	−0.157120	−0.0785601	−	0.996909i	$-0.525032\pi$
$809$	−4.46896	−0.157120	−0.0785601	+	0.996909i	$0.525032\pi$
$810$	−23.6116	−0.829626
$811$	4.86675	0.170895	0.0854473	−	0.996343i	$-0.472768\pi$
$811$	4.86675	0.170895	0.0854473	+	0.996343i	$0.472768\pi$
$812$	70.5826	2.47696
$813$	4.28523	0.150290
$814$	0	0
$815$	−23.4990	−0.823135
$816$	7.93989	0.277952
$817$	21.4245	0.749550
$818$	−1.16528	−0.0407432
$819$	−3.66732	−0.128147
$820$	58.6734	2.04896
$821$	−17.0050	−0.593479	−0.296739	−	0.954959i	$-0.595899\pi$
$821$	−17.0050	−0.593479	−0.296739	+	0.954959i	$0.595899\pi$
$822$	−5.12931	−0.178905
$823$	−21.7479	−0.758082	−0.379041	−	0.925380i	$-0.623746\pi$
$823$	−21.7479	−0.758082	−0.379041	+	0.925380i	$0.623746\pi$
$824$	158.664	5.52731
$825$	0	0
$826$	−41.1019	−1.43012
$827$	20.7084	0.720103	0.360051	−	0.932932i	$-0.382759\pi$
$827$	20.7084	0.720103	0.360051	+	0.932932i	$0.382759\pi$
$828$	74.1611	2.57727
$829$	11.3090	0.392776	0.196388	−	0.980526i	$-0.437079\pi$
$829$	11.3090	0.392776	0.196388	+	0.980526i	$0.437079\pi$
$830$	37.3357	1.29594
$831$	−5.37209	−0.186356
$832$	17.5421	0.608163
$833$	3.87977	0.134426
$834$	−9.75721	−0.337865
$835$	14.2345	0.492604
$836$	0	0
$837$	1.31093	0.0453122
$838$	18.4226	0.636397
$839$	−43.5084	−1.50208	−0.751038	−	0.660259i	$-0.770446\pi$
$839$	−43.5084	−1.50208	−0.751038	+	0.660259i	$0.770446\pi$
$840$	4.74983	0.163885
$841$	1.13628	0.0391821
$842$	7.63029	0.262957
$843$	3.85105	0.132637
$844$	93.3418	3.21296
$845$	12.7148	0.437401
$846$	−54.9102	−1.88785
$847$	0	0
$848$	−70.5401	−2.42236
$849$	−2.32965	−0.0799533
$850$	−6.64663	−0.227977
$851$	−33.9586	−1.16409
$852$	−5.28826	−0.181173
$853$	1.11559	0.0381969	0.0190985	−	0.999818i	$-0.493920\pi$
$853$	1.11559	0.0381969	0.0190985	+	0.999818i	$0.493920\pi$
$854$	−43.3553	−1.48359
$855$	−14.6466	−0.500904
$856$	−99.0485	−3.38541
$857$	−7.80361	−0.266566	−0.133283	−	0.991078i	$-0.542552\pi$
$857$	−7.80361	−0.266566	−0.133283	+	0.991078i	$0.542552\pi$
$858$	0	0
$859$	30.5341	1.04181	0.520905	−	0.853615i	$-0.325595\pi$
$859$	30.5341	1.04181	0.520905	+	0.853615i	$0.325595\pi$
$860$	23.9255	0.815854
$861$	5.19140	0.176922
$862$	−44.4563	−1.51419
$863$	−4.28959	−0.146019	−0.0730097	−	0.997331i	$-0.523260\pi$
$863$	−4.28959	−0.146019	−0.0730097	+	0.997331i	$0.523260\pi$
$864$	29.2488	0.995066
$865$	−6.44523	−0.219145
$866$	21.4847	0.730078
$867$	2.34704	0.0797095
$868$	13.4285	0.455792
$869$	0	0
$870$	3.17570	0.107666
$871$	0.385120	0.0130493
$872$	117.296	3.97214
$873$	−14.0662	−0.476068
$874$	61.6734	2.08613
$875$	−2.32331	−0.0785424
$876$	1.24581	0.0420921
$877$	−11.3644	−0.383749	−0.191875	−	0.981419i	$-0.561457\pi$
$877$	−11.3644	−0.383749	−0.191875	+	0.981419i	$0.561457\pi$
$878$	−56.9152	−1.92080
$879$	5.71977	0.192923
$880$	0	0
$881$	−11.3277	−0.381639	−0.190820	−	0.981625i	$-0.561115\pi$
$881$	−11.3277	−0.381639	−0.190820	+	0.981625i	$0.561115\pi$
$882$	12.9980	0.437666
$883$	31.2883	1.05293	0.526467	−	0.850196i	$-0.323516\pi$
$883$	31.2883	1.05293	0.526467	+	0.850196i	$0.323516\pi$
$884$	−7.15698	−0.240715
$885$	−1.35837	−0.0456611
$886$	14.5548	0.488977
$887$	28.2819	0.949614	0.474807	−	0.880090i	$-0.342518\pi$
$887$	28.2819	0.949614	0.474807	+	0.880090i	$0.342518\pi$
$888$	−15.3120	−0.513836
$889$	18.8698	0.632872
$890$	−34.8998	−1.16984
$891$	0	0
$892$	−138.448	−4.63558
$893$	−33.5421	−1.12244
$894$	2.58349	0.0864048
$895$	−16.9793	−0.567556
$896$	101.184	3.38031
$897$	0.510348	0.0170400
$898$	−82.3531	−2.74816
$899$	5.73349	0.191223
$900$	−16.3564	−0.545213
$901$	10.9793	0.365774
$902$	0	0
$903$	2.11692	0.0704467
$904$	−105.182	−3.49829
$905$	−4.48965	−0.149241
$906$	−6.66035	−0.221275
$907$	33.6166	1.11622	0.558110	−	0.829767i	$-0.311527\pi$
$907$	33.6166	1.11622	0.558110	+	0.829767i	$0.311527\pi$
$908$	−22.1881	−0.736338
$909$	−19.4433	−0.644892
$910$	−3.40582	−0.112902
$911$	7.53104	0.249515	0.124757	−	0.992187i	$-0.460185\pi$
$911$	7.53104	0.249515	0.124757	+	0.992187i	$0.460185\pi$
$912$	16.2488	0.538053
$913$	0	0
$914$	−102.968	−3.40587
$915$	−1.43285	−0.0473684
$916$	−95.9202	−3.16929
$917$	−13.4720	−0.444884
$918$	−8.34267	−0.275349
$919$	−40.0424	−1.32088	−0.660439	−	0.750880i	$-0.729630\pi$
$919$	−40.0424	−1.32088	−0.660439	+	0.750880i	$0.729630\pi$
$920$	43.9823	1.45005
$921$	2.47396	0.0815196
$922$	−43.3213	−1.42671
$923$	2.42151	0.0797050
$924$	0	0
$925$	7.48965	0.246258
$926$	−45.4740	−1.49437
$927$	−48.3427	−1.58778
$928$	127.923	4.19929
$929$	51.3407	1.68443	0.842217	−	0.539139i	$-0.181250\pi$
$929$	51.3407	1.68443	0.842217	+	0.539139i	$0.181250\pi$
$930$	0.604184	0.0198120
$931$	7.93989	0.260219
$932$	−11.6910	−0.382953
$933$	−2.24279	−0.0734255
$934$	10.1570	0.332346
$935$	0	0
$936$	−15.3120	−0.500488
$937$	35.8510	1.17120	0.585601	−	0.810599i	$-0.300858\pi$
$937$	35.8510	1.17120	0.585601	+	0.810599i	$0.300858\pi$
$938$	4.59855	0.150148
$939$	5.72849	0.186942
$940$	−37.4576	−1.22173
$941$	0.607210	0.0197945	0.00989724	−	0.999951i	$-0.496850\pi$
$941$	0.607210	0.0197945	0.00989724	+	0.999951i	$0.496850\pi$
$942$	3.41954	0.111415
$943$	48.0712	1.56541
$944$	−100.274	−3.26363
$945$	−2.91616	−0.0948628
$946$	0	0
$947$	−26.3851	−0.857401	−0.428701	−	0.903447i	$-0.641028\pi$
$947$	−26.3851	−0.857401	−0.428701	+	0.903447i	$0.641028\pi$
$948$	5.41954	0.176018
$949$	−0.570462	−0.0185180
$950$	−13.6022	−0.441314
$951$	−1.04942	−0.0340297
$952$	−54.5738	−1.76875
$953$	35.3594	1.14540	0.572702	−	0.819764i	$-0.305895\pi$
$953$	35.3594	1.14540	0.572702	+	0.819764i	$0.305895\pi$
$954$	36.7829	1.19089
$955$	2.75919	0.0892852
$956$	132.457	4.28398
$957$	0	0
$958$	−3.47093	−0.112141
$959$	20.6002	0.665216
$960$	6.92250	0.223423
$961$	−29.9092	−0.964813
$962$	10.9793	0.353987
$963$	30.1787	0.972496
$964$	80.3180	2.58687
$965$	11.8036	0.379971
$966$	6.09384	0.196066
$967$	3.86872	0.124410	0.0622048	−	0.998063i	$-0.480187\pi$
$967$	3.86872	0.124410	0.0622048	+	0.998063i	$0.480187\pi$
$968$	0	0
$969$	−2.52907	−0.0812455
$970$	−13.0631	−0.419432
$971$	24.1076	0.773648	0.386824	−	0.922153i	$-0.373572\pi$
$971$	24.1076	0.773648	0.386824	+	0.922153i	$0.373572\pi$
$972$	−30.8717	−0.990212
$973$	39.1868	1.25627
$974$	59.2943	1.89991
$975$	−0.112558	−0.00360475
$976$	−105.771	−3.38566
$977$	10.8143	0.345980	0.172990	−	0.984924i	$-0.444657\pi$
$977$	10.8143	0.345980	0.172990	+	0.984924i	$0.444657\pi$
$978$	−13.5939	−0.434685
$979$	0	0
$980$	8.86675	0.283238
$981$	−35.7385	−1.14104
$982$	−70.0949	−2.23682
$983$	−38.7084	−1.23461	−0.617304	−	0.786725i	$-0.711775\pi$
$983$	−38.7084	−1.23461	−0.617304	+	0.786725i	$0.711775\pi$
$984$	21.6754	0.690985
$985$	−6.51035	−0.207437
$986$	−36.4877	−1.16200
$987$	−3.31423	−0.105493
$988$	−14.6466	−0.465971
$989$	19.6022	0.623314
$990$	0	0
$991$	61.4533	1.95213	0.976064	−	0.217485i	$-0.0697854\pi$
$991$	61.4533	1.95213	0.976064	+	0.217485i	$0.0697854\pi$
$992$	24.3377	0.772722
$993$	−1.59221	−0.0505273
$994$	28.9142	0.917102
$995$	−23.9586	−0.759539
$996$	15.8648	0.502695
$997$	38.3377	1.21417	0.607083	−	0.794638i	$-0.292339\pi$
$997$	38.3377	1.21417	0.607083	+	0.794638i	$0.292339\pi$
$998$	66.8678	2.11666
$999$	9.40082	0.297429

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.a.g.1.3	✓	3
3.2	odd	2		5445.2.a.bd.1.1		3
4.3	odd	2		9680.2.a.bz.1.2		3
5.4	even	2		3025.2.a.u.1.1		3
11.2	odd	10		605.2.g.o.81.3		12
11.3	even	5		605.2.g.p.251.3		12
11.4	even	5		605.2.g.p.511.3		12
11.5	even	5		605.2.g.p.366.1		12
11.6	odd	10		605.2.g.o.366.3		12
11.7	odd	10		605.2.g.o.511.1		12
11.8	odd	10		605.2.g.o.251.1		12
11.9	even	5		605.2.g.p.81.1		12
11.10	odd	2		605.2.a.h.1.1	yes	3
33.32	even	2		5445.2.a.bb.1.3		3
44.43	even	2		9680.2.a.cb.1.2		3
55.54	odd	2		3025.2.a.p.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
605.2.a.g.1.3	✓	3	1.1	even	1	trivial
605.2.a.h.1.1	yes	3	11.10	odd	2
605.2.g.o.81.3		12	11.2	odd	10
605.2.g.o.251.1		12	11.8	odd	10
605.2.g.o.366.3		12	11.6	odd	10
605.2.g.o.511.1		12	11.7	odd	10
605.2.g.p.81.1		12	11.9	even	5
605.2.g.p.251.3		12	11.3	even	5
605.2.g.p.366.1		12	11.5	even	5
605.2.g.p.511.3		12	11.4	even	5
3025.2.a.p.1.3		3	55.54	odd	2
3025.2.a.u.1.1		3	5.4	even	2
5445.2.a.bb.1.3		3	33.32	even	2
5445.2.a.bd.1.1		3	3.2	odd	2
9680.2.a.bz.1.2		3	4.3	odd	2
9680.2.a.cb.1.2		3	44.43	even	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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.a (trivial)

\(f(q)\)	\(=\)	\(q+2.74483 q^{2} -0.210756 q^{3} +5.53407 q^{4} -1.00000 q^{5} -0.578488 q^{6} +2.32331 q^{7} +9.70041 q^{8} -2.95558 q^{9} +O(q^{10})\)	\(q+2.74483 q^{2} -0.210756 q^{3} +5.53407 q^{4} -1.00000 q^{5} -0.578488 q^{6} +2.32331 q^{7} +9.70041 q^{8} -2.95558 q^{9} -2.74483 q^{10} -1.16634 q^{12} +0.534070 q^{13} +6.37709 q^{14} +0.210756 q^{15} +15.5578 q^{16} -2.42151 q^{17} -8.11256 q^{18} -4.95558 q^{19} -5.53407 q^{20} -0.489652 q^{21} -4.53407 q^{23} -2.04442 q^{24} +1.00000 q^{25} +1.46593 q^{26} +1.25517 q^{27} +12.8574 q^{28} +5.48965 q^{29} +0.578488 q^{30} +1.04442 q^{31} +23.3026 q^{32} -6.64663 q^{34} -2.32331 q^{35} -16.3564 q^{36} +7.48965 q^{37} -13.6022 q^{38} -0.112558 q^{39} -9.70041 q^{40} -10.6022 q^{41} -1.34401 q^{42} -4.32331 q^{43} +2.95558 q^{45} -12.4452 q^{46} +6.76855 q^{47} -3.27890 q^{48} -1.60221 q^{49} +2.74483 q^{50} +0.510348 q^{51} +2.95558 q^{52} -4.53407 q^{53} +3.44523 q^{54} +22.5371 q^{56} +1.04442 q^{57} +15.0681 q^{58} -6.44523 q^{59} +1.16634 q^{60} -6.79861 q^{61} +2.86675 q^{62} -6.86675 q^{63} +32.8461 q^{64} -0.534070 q^{65} +0.721104 q^{67} -13.4008 q^{68} +0.955582 q^{69} -6.37709 q^{70} +4.53407 q^{71} -28.6704 q^{72} -1.06814 q^{73} +20.5578 q^{74} -0.210756 q^{75} -27.4245 q^{76} -0.308953 q^{78} -4.64663 q^{79} -15.5578 q^{80} +8.60221 q^{81} -29.1012 q^{82} -13.6022 q^{83} -2.70977 q^{84} +2.42151 q^{85} -11.8667 q^{86} -1.15698 q^{87} +12.7148 q^{89} +8.11256 q^{90} +1.24081 q^{91} -25.0919 q^{92} -0.220117 q^{93} +18.5785 q^{94} +4.95558 q^{95} -4.91116 q^{96} +4.75919 q^{97} -4.39779 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - q^{2} + q^{3} + 9 q^{4} - 3 q^{5} - 5 q^{6} + q^{7} + 9 q^{8} + 2 q^{9}+O(q^{10}) \) 3 * q - q^2 + q^3 + 9 * q^4 - 3 * q^5 - 5 * q^6 + q^7 + 9 * q^8 + 2 * q^9	\( 3 q - q^{2} + q^{3} + 9 q^{4} - 3 q^{5} - 5 q^{6} + q^{7} + 9 q^{8} + 2 q^{9} + q^{10} + 9 q^{12} - 6 q^{13} + 5 q^{14} - q^{15} + 13 q^{16} - 4 q^{17} - 20 q^{18} - 4 q^{19} - 9 q^{20} + 17 q^{21} - 6 q^{23} - 17 q^{24} + 3 q^{25} + 12 q^{26} + 13 q^{27} + 25 q^{28} - 2 q^{29} + 5 q^{30} + 14 q^{31} + 27 q^{32} - 8 q^{34} - q^{35} + 2 q^{36} + 4 q^{37} - 18 q^{38} + 4 q^{39} - 9 q^{40} - 9 q^{41} - 35 q^{42} - 7 q^{43} - 2 q^{45} - 8 q^{46} - 15 q^{47} + 7 q^{48} + 18 q^{49} - q^{50} + 20 q^{51} - 2 q^{52} - 6 q^{53} - 19 q^{54} - 3 q^{56} + 14 q^{57} + 30 q^{58} + 10 q^{59} - 9 q^{60} - 3 q^{61} - 24 q^{62} + 12 q^{63} + 29 q^{64} + 6 q^{65} + 19 q^{67} - 8 q^{69} - 5 q^{70} + 6 q^{71} - 48 q^{72} + 12 q^{73} + 28 q^{74} + q^{75} - 16 q^{76} - 2 q^{78} - 2 q^{79} - 13 q^{80} + 3 q^{81} - 27 q^{82} - 18 q^{83} + 31 q^{84} + 4 q^{85} - 3 q^{86} - 10 q^{87} + 11 q^{89} + 20 q^{90} + 20 q^{91} - 34 q^{92} + 20 q^{93} + 59 q^{94} + 4 q^{95} + 7 q^{96} - 2 q^{97} - 36 q^{98}+O(q^{100}) \) 3 * q - q^2 + q^3 + 9 * q^4 - 3 * q^5 - 5 * q^6 + q^7 + 9 * q^8 + 2 * q^9 + q^10 + 9 * q^12 - 6 * q^13 + 5 * q^14 - q^15 + 13 * q^16 - 4 * q^17 - 20 * q^18 - 4 * q^19 - 9 * q^20 + 17 * q^21 - 6 * q^23 - 17 * q^24 + 3 * q^25 + 12 * q^26 + 13 * q^27 + 25 * q^28 - 2 * q^29 + 5 * q^30 + 14 * q^31 + 27 * q^32 - 8 * q^34 - q^35 + 2 * q^36 + 4 * q^37 - 18 * q^38 + 4 * q^39 - 9 * q^40 - 9 * q^41 - 35 * q^42 - 7 * q^43 - 2 * q^45 - 8 * q^46 - 15 * q^47 + 7 * q^48 + 18 * q^49 - q^50 + 20 * q^51 - 2 * q^52 - 6 * q^53 - 19 * q^54 - 3 * q^56 + 14 * q^57 + 30 * q^58 + 10 * q^59 - 9 * q^60 - 3 * q^61 - 24 * q^62 + 12 * q^63 + 29 * q^64 + 6 * q^65 + 19 * q^67 - 8 * q^69 - 5 * q^70 + 6 * q^71 - 48 * q^72 + 12 * q^73 + 28 * q^74 + q^75 - 16 * q^76 - 2 * q^78 - 2 * q^79 - 13 * q^80 + 3 * q^81 - 27 * q^82 - 18 * q^83 + 31 * q^84 + 4 * q^85 - 3 * q^86 - 10 * q^87 + 11 * q^89 + 20 * q^90 + 20 * q^91 - 34 * q^92 + 20 * q^93 + 59 * q^94 + 4 * q^95 + 7 * q^96 - 2 * q^97 - 36 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more