LMFDB - Embedded newform 1805.2.a.s.1.6

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:	$1$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 3x^{8} - 6x^{7} + 16x^{6} + 12x^{5} - 27x^{4} - 8x^{3} + 15x^{2} - 1 $ x^9 - 3x^8 - 6x^7 + 16x^6 + 12x^5 - 27x^4 - 8x^3 + 15*x^2 - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$0.789016$ 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)

$f(q)$	$=$	$q-0.210984 q^{2} -0.0798955 q^{3} -1.95549 q^{4} +1.00000 q^{5} +0.0168566 q^{6} -1.68723 q^{7} +0.834543 q^{8} -2.99362 q^{9} +O(q^{10})$	\(q-0.210984 q^{2} -0.0798955 q^{3} -1.95549 q^{4} +1.00000 q^{5} +0.0168566 q^{6} -1.68723 q^{7} +0.834543 q^{8} -2.99362 q^{9} -0.210984 q^{10} -2.88678 q^{11} +0.156235 q^{12} +6.46601 q^{13} +0.355977 q^{14} -0.0798955 q^{15} +3.73490 q^{16} +2.98649 q^{17} +0.631604 q^{18} -1.95549 q^{20} +0.134802 q^{21} +0.609064 q^{22} +8.25754 q^{23} -0.0666762 q^{24} +1.00000 q^{25} -1.36422 q^{26} +0.478863 q^{27} +3.29935 q^{28} -7.25727 q^{29} +0.0168566 q^{30} -4.05600 q^{31} -2.45709 q^{32} +0.230641 q^{33} -0.630100 q^{34} -1.68723 q^{35} +5.85398 q^{36} -7.96989 q^{37} -0.516605 q^{39} +0.834543 q^{40} -5.45595 q^{41} -0.0284410 q^{42} -5.33164 q^{43} +5.64506 q^{44} -2.99362 q^{45} -1.74221 q^{46} +1.64961 q^{47} -0.298402 q^{48} -4.15326 q^{49} -0.210984 q^{50} -0.238607 q^{51} -12.6442 q^{52} -1.91194 q^{53} -0.101032 q^{54} -2.88678 q^{55} -1.40806 q^{56} +1.53116 q^{58} -3.55276 q^{59} +0.156235 q^{60} -7.90014 q^{61} +0.855750 q^{62} +5.05091 q^{63} -6.95139 q^{64} +6.46601 q^{65} -0.0486615 q^{66} -2.26533 q^{67} -5.84003 q^{68} -0.659740 q^{69} +0.355977 q^{70} -10.4224 q^{71} -2.49830 q^{72} +1.41186 q^{73} +1.68152 q^{74} -0.0798955 q^{75} +4.87066 q^{77} +0.108995 q^{78} +2.41076 q^{79} +3.73490 q^{80} +8.94259 q^{81} +1.15112 q^{82} -11.4006 q^{83} -0.263603 q^{84} +2.98649 q^{85} +1.12489 q^{86} +0.579823 q^{87} -2.40914 q^{88} +10.1161 q^{89} +0.631604 q^{90} -10.9096 q^{91} -16.1475 q^{92} +0.324057 q^{93} -0.348041 q^{94} +0.196310 q^{96} +9.86820 q^{97} +0.876270 q^{98} +8.64192 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 6 q^{2} - 9 q^{3} + 6 q^{4} + 9 q^{5} + 12 q^{6} - 6 q^{8} + 6 q^{9}+O(q^{10}) $ 9 * q - 6 * q^2 - 9 * q^3 + 6 * q^4 + 9 * q^5 + 12 * q^6 - 6 * q^8 + 6 * q^9	$ 9 q - 6 q^{2} - 9 q^{3} + 6 q^{4} + 9 q^{5} + 12 q^{6} - 6 q^{8} + 6 q^{9} - 6 q^{10} - 18 q^{12} - 9 q^{13} - 9 q^{15} + 12 q^{16} - 9 q^{17} - 24 q^{18} + 6 q^{20} - 12 q^{21} - 24 q^{22} - 12 q^{23} + 3 q^{24} + 9 q^{25} - 3 q^{26} - 24 q^{27} - 15 q^{28} - 9 q^{29} + 12 q^{30} - 18 q^{31} - 3 q^{32} + 9 q^{33} + 24 q^{34} + 18 q^{36} - 18 q^{37} + 18 q^{39} - 6 q^{40} - 6 q^{41} - 12 q^{43} + 48 q^{44} + 6 q^{45} + 9 q^{46} + 15 q^{47} + 21 q^{48} - 9 q^{49} - 6 q^{50} + 6 q^{51} - 33 q^{52} - 15 q^{53} + 63 q^{54} + 6 q^{58} - 21 q^{59} - 18 q^{60} - 12 q^{61} - 36 q^{62} + 21 q^{63} - 36 q^{64} - 9 q^{65} + 3 q^{66} - 60 q^{67} - 51 q^{68} + 15 q^{69} + 18 q^{71} + 27 q^{73} + 27 q^{74} - 9 q^{75} - 30 q^{77} + 6 q^{78} - 15 q^{79} + 12 q^{80} + 33 q^{81} + 24 q^{82} + 48 q^{84} - 9 q^{85} + 39 q^{86} + 15 q^{87} - 27 q^{88} + 39 q^{89} - 24 q^{90} - 21 q^{91} - 6 q^{92} + 15 q^{93} - 15 q^{94} - 33 q^{96} - 15 q^{97} + 15 q^{98} - 36 q^{99}+O(q^{100}) $ 9 * q - 6 * q^2 - 9 * q^3 + 6 * q^4 + 9 * q^5 + 12 * q^6 - 6 * q^8 + 6 * q^9 - 6 * q^10 - 18 * q^12 - 9 * q^13 - 9 * q^15 + 12 * q^16 - 9 * q^17 - 24 * q^18 + 6 * q^20 - 12 * q^21 - 24 * q^22 - 12 * q^23 + 3 * q^24 + 9 * q^25 - 3 * q^26 - 24 * q^27 - 15 * q^28 - 9 * q^29 + 12 * q^30 - 18 * q^31 - 3 * q^32 + 9 * q^33 + 24 * q^34 + 18 * q^36 - 18 * q^37 + 18 * q^39 - 6 * q^40 - 6 * q^41 - 12 * q^43 + 48 * q^44 + 6 * q^45 + 9 * q^46 + 15 * q^47 + 21 * q^48 - 9 * q^49 - 6 * q^50 + 6 * q^51 - 33 * q^52 - 15 * q^53 + 63 * q^54 + 6 * q^58 - 21 * q^59 - 18 * q^60 - 12 * q^61 - 36 * q^62 + 21 * q^63 - 36 * q^64 - 9 * q^65 + 3 * q^66 - 60 * q^67 - 51 * q^68 + 15 * q^69 + 18 * q^71 + 27 * q^73 + 27 * q^74 - 9 * q^75 - 30 * q^77 + 6 * q^78 - 15 * q^79 + 12 * q^80 + 33 * q^81 + 24 * q^82 + 48 * q^84 - 9 * q^85 + 39 * q^86 + 15 * q^87 - 27 * q^88 + 39 * q^89 - 24 * q^90 - 21 * q^91 - 6 * q^92 + 15 * q^93 - 15 * q^94 - 33 * q^96 - 15 * q^97 + 15 * q^98 - 36 * 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 $

$2$	−0.210984	−0.149188	−0.0745940	−	0.997214i	$-0.523766\pi$
$2$	−0.210984	−0.149188	−0.0745940	+	0.997214i	$0.523766\pi$
$3$	−0.0798955	−0.0461277	−0.0230639	−	0.999734i	$-0.507342\pi$
$3$	−0.0798955	−0.0461277	−0.0230639	+	0.999734i	$0.507342\pi$
$4$	−1.95549	−0.977743
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.0168566	0.00688170
$7$	−1.68723	−0.637712	−0.318856	−	0.947803i	$-0.603299\pi$
$7$	−1.68723	−0.637712	−0.318856	+	0.947803i	$0.603299\pi$
$8$	0.834543	0.295055
$9$	−2.99362	−0.997872
$10$	−0.210984	−0.0667189
$11$	−2.88678	−0.870398	−0.435199	−	0.900334i	$-0.643322\pi$
$11$	−2.88678	−0.870398	−0.435199	+	0.900334i	$0.643322\pi$
$12$	0.156235	0.0451010
$13$	6.46601	1.79335	0.896674	−	0.442691i	$-0.145976\pi$
$13$	6.46601	1.79335	0.896674	+	0.442691i	$0.145976\pi$
$14$	0.355977	0.0951390
$15$	−0.0798955	−0.0206289
$16$	3.73490	0.933724
$17$	2.98649	0.724329	0.362165	−	0.932114i	$-0.382038\pi$
$17$	2.98649	0.724329	0.362165	+	0.932114i	$0.382038\pi$
$18$	0.631604	0.148871
$19$	0	0
$19$	0	0
$20$	−1.95549	−0.437260
$21$	0.134802	0.0294162
$22$	0.609064	0.129853
$23$	8.25754	1.72182	0.860908	−	0.508761i	$-0.169896\pi$
$23$	8.25754	1.72182	0.860908	+	0.508761i	$0.169896\pi$
$24$	−0.0666762	−0.0136102
$25$	1.00000	0.200000
$26$	−1.36422	−0.267546
$27$	0.478863	0.0921573
$28$	3.29935	0.623519
$29$	−7.25727	−1.34764	−0.673820	−	0.738895i	$-0.735348\pi$
$29$	−7.25727	−1.34764	−0.673820	+	0.738895i	$0.735348\pi$
$30$	0.0168566	0.00307759
$31$	−4.05600	−0.728480	−0.364240	−	0.931305i	$-0.618671\pi$
$31$	−4.05600	−0.728480	−0.364240	+	0.931305i	$0.618671\pi$
$32$	−2.45709	−0.434356
$33$	0.230641	0.0401495
$34$	−0.630100	−0.108061
$35$	−1.68723	−0.285194
$36$	5.85398	0.975663
$37$	−7.96989	−1.31024	−0.655121	−	0.755524i	$-0.727382\pi$
$37$	−7.96989	−1.31024	−0.655121	+	0.755524i	$0.727382\pi$
$38$	0	0
$39$	−0.516605	−0.0827230
$40$	0.834543	0.131953
$41$	−5.45595	−0.852076	−0.426038	−	0.904705i	$-0.640091\pi$
$41$	−5.45595	−0.852076	−0.426038	+	0.904705i	$0.640091\pi$
$42$	−0.0284410	−0.00438854
$43$	−5.33164	−0.813068	−0.406534	−	0.913636i	$-0.633263\pi$
$43$	−5.33164	−0.813068	−0.406534	+	0.913636i	$0.633263\pi$
$44$	5.64506	0.851025
$45$	−2.99362	−0.446262
$46$	−1.74221	−0.256874
$47$	1.64961	0.240620	0.120310	−	0.992736i	$-0.461611\pi$
$47$	1.64961	0.240620	0.120310	+	0.992736i	$0.461611\pi$
$48$	−0.298402	−0.0430706
$49$	−4.15326	−0.593323
$50$	−0.210984	−0.0298376
$51$	−0.238607	−0.0334117
$52$	−12.6442	−1.75343
$53$	−1.91194	−0.262625	−0.131312	−	0.991341i	$-0.541919\pi$
$53$	−1.91194	−0.262625	−0.131312	+	0.991341i	$0.541919\pi$
$54$	−0.101032	−0.0137488
$55$	−2.88678	−0.389254
$56$	−1.40806	−0.188160
$57$	0	0
$58$	1.53116	0.201052
$59$	−3.55276	−0.462530	−0.231265	−	0.972891i	$-0.574286\pi$
$59$	−3.55276	−0.462530	−0.231265	+	0.972891i	$0.574286\pi$
$60$	0.156235	0.0201698
$61$	−7.90014	−1.01151	−0.505755	−	0.862677i	$-0.668786\pi$
$61$	−7.90014	−1.01151	−0.505755	+	0.862677i	$0.668786\pi$
$62$	0.855750	0.108680
$63$	5.05091	0.636355
$64$	−6.95139	−0.868924
$65$	6.46601	0.802010
$66$	−0.0486615	−0.00598982
$67$	−2.26533	−0.276754	−0.138377	−	0.990380i	$-0.544189\pi$
$67$	−2.26533	−0.276754	−0.138377	+	0.990380i	$0.544189\pi$
$68$	−5.84003	−0.708208
$69$	−0.659740	−0.0794234
$70$	0.355977	0.0425474
$71$	−10.4224	−1.23692	−0.618458	−	0.785818i	$-0.712242\pi$
$71$	−10.4224	−1.23692	−0.618458	+	0.785818i	$0.712242\pi$
$72$	−2.49830	−0.294428
$73$	1.41186	0.165246	0.0826231	−	0.996581i	$-0.473670\pi$
$73$	1.41186	0.165246	0.0826231	+	0.996581i	$0.473670\pi$
$74$	1.68152	0.195472
$75$	−0.0798955	−0.00922554
$76$	0	0
$77$	4.87066	0.555063
$78$	0.108995	0.0123413
$79$	2.41076	0.271232	0.135616	−	0.990761i	$-0.456699\pi$
$79$	2.41076	0.271232	0.135616	+	0.990761i	$0.456699\pi$
$80$	3.73490	0.417574
$81$	8.94259	0.993621
$82$	1.15112	0.127120
$83$	−11.4006	−1.25138	−0.625688	−	0.780073i	$-0.715182\pi$
$83$	−11.4006	−1.25138	−0.625688	+	0.780073i	$0.715182\pi$
$84$	−0.263603	−0.0287615
$85$	2.98649	0.323930
$86$	1.12489	0.121300
$87$	0.579823	0.0621636
$88$	−2.40914	−0.256816
$89$	10.1161	1.07230	0.536152	−	0.844121i	$-0.319877\pi$
$89$	10.1161	1.07230	0.536152	+	0.844121i	$0.319877\pi$
$90$	0.631604	0.0665769
$91$	−10.9096	−1.14364
$92$	−16.1475	−1.68349
$93$	0.324057	0.0336031
$94$	−0.348041	−0.0358977
$95$	0	0
$96$	0.196310	0.0200358
$97$	9.86820	1.00196	0.500982	−	0.865458i	$-0.332972\pi$
$97$	9.86820	1.00196	0.500982	+	0.865458i	$0.332972\pi$
$98$	0.876270	0.0885167
$99$	8.64192	0.868546
$100$	−1.95549	−0.195549
$101$	4.16975	0.414906	0.207453	−	0.978245i	$-0.433483\pi$
$101$	4.16975	0.414906	0.207453	+	0.978245i	$0.433483\pi$
$102$	0.0503422	0.00498462
$103$	12.5636	1.23793	0.618964	−	0.785419i	$-0.287552\pi$
$103$	12.5636	1.23793	0.618964	+	0.785419i	$0.287552\pi$
$104$	5.39616	0.529137
$105$	0.134802	0.0131553
$106$	0.403387	0.0391805
$107$	−14.9423	−1.44453	−0.722264	−	0.691617i	$-0.756898\pi$
$107$	−14.9423	−1.44453	−0.722264	+	0.691617i	$0.756898\pi$
$108$	−0.936410	−0.0901061
$109$	−5.20496	−0.498545	−0.249272	−	0.968433i	$-0.580191\pi$
$109$	−5.20496	−0.498545	−0.249272	+	0.968433i	$0.580191\pi$
$110$	0.609064	0.0580720
$111$	0.636759	0.0604385
$112$	−6.30162	−0.595447
$113$	−8.57064	−0.806258	−0.403129	−	0.915143i	$-0.632077\pi$
$113$	−8.57064	−0.806258	−0.403129	+	0.915143i	$0.632077\pi$
$114$	0	0
$115$	8.25754	0.770019
$116$	14.1915	1.31765
$117$	−19.3568	−1.78953
$118$	0.749575	0.0690039
$119$	−5.03888	−0.461914
$120$	−0.0666762	−0.00608668
$121$	−2.66648	−0.242407
$122$	1.66680	0.150905
$123$	0.435906	0.0393043
$124$	7.93146	0.712266
$125$	1.00000	0.0894427
$126$	−1.06566	−0.0949365
$127$	−13.0369	−1.15684	−0.578421	−	0.815738i	$-0.696331\pi$
$127$	−13.0369	−1.15684	−0.578421	+	0.815738i	$0.696331\pi$
$128$	6.38080	0.563989
$129$	0.425974	0.0375050
$130$	−1.36422	−0.119650
$131$	0.187083	0.0163456	0.00817278	−	0.999967i	$-0.497398\pi$
$131$	0.187083	0.0163456	0.00817278	+	0.999967i	$0.497398\pi$
$132$	−0.451015	−0.0392558
$133$	0	0
$134$	0.477948	0.0412884
$135$	0.478863	0.0412140
$136$	2.49235	0.213717
$137$	2.15559	0.184164	0.0920821	−	0.995751i	$-0.470648\pi$
$137$	2.15559	0.184164	0.0920821	+	0.995751i	$0.470648\pi$
$138$	0.139194	0.0118490
$139$	−7.89712	−0.669825	−0.334913	−	0.942249i	$-0.608707\pi$
$139$	−7.89712	−0.669825	−0.334913	+	0.942249i	$0.608707\pi$
$140$	3.29935	0.278846
$141$	−0.131796	−0.0110993
$142$	2.19897	0.184533
$143$	−18.6660	−1.56093
$144$	−11.1808	−0.931737
$145$	−7.25727	−0.602683
$146$	−0.297880	−0.0246527
$147$	0.331827	0.0273686
$148$	15.5850	1.28108
$149$	17.8966	1.46615	0.733074	−	0.680149i	$-0.238085\pi$
$149$	17.8966	1.46615	0.733074	+	0.680149i	$0.238085\pi$
$150$	0.0168566	0.00137634
$151$	−2.93984	−0.239241	−0.119620	−	0.992820i	$-0.538168\pi$
$151$	−2.93984	−0.239241	−0.119620	+	0.992820i	$0.538168\pi$
$152$	0	0
$153$	−8.94040	−0.722788
$154$	−1.02763	−0.0828088
$155$	−4.05600	−0.325786
$156$	1.01021	0.0808819
$157$	6.76687	0.540055	0.270028	−	0.962853i	$-0.412967\pi$
$157$	6.76687	0.540055	0.270028	+	0.962853i	$0.412967\pi$
$158$	−0.508631	−0.0404645
$159$	0.152755	0.0121143
$160$	−2.45709	−0.194250
$161$	−13.9323	−1.09802
$162$	−1.88674	−0.148236
$163$	−0.907834	−0.0711070	−0.0355535	−	0.999368i	$-0.511319\pi$
$163$	−0.907834	−0.0711070	−0.0355535	+	0.999368i	$0.511319\pi$
$164$	10.6690	0.833111
$165$	0.230641	0.0179554
$166$	2.40534	0.186690
$167$	−14.2716	−1.10437	−0.552184	−	0.833722i	$-0.686205\pi$
$167$	−14.2716	−1.10437	−0.552184	+	0.833722i	$0.686205\pi$
$168$	0.112498	0.00867941
$169$	28.8093	2.21610
$170$	−0.630100	−0.0483264
$171$	0	0
$172$	10.4260	0.794971
$173$	−14.0774	−1.07029	−0.535144	−	0.844761i	$-0.679743\pi$
$173$	−14.0774	−1.07029	−0.535144	+	0.844761i	$0.679743\pi$
$174$	−0.122333	−0.00927406
$175$	−1.68723	−0.127542
$176$	−10.7818	−0.812712
$177$	0.283850	0.0213355
$178$	−2.13433	−0.159975
$179$	−15.7498	−1.17719	−0.588596	−	0.808427i	$-0.700319\pi$
$179$	−15.7498	−1.17719	−0.588596	+	0.808427i	$0.700319\pi$
$180$	5.85398	0.436330
$181$	−4.55831	−0.338816	−0.169408	−	0.985546i	$-0.554186\pi$
$181$	−4.55831	−0.338816	−0.169408	+	0.985546i	$0.554186\pi$
$182$	2.30175	0.170617
$183$	0.631186	0.0466586
$184$	6.89127	0.508031
$185$	−7.96989	−0.585958
$186$	−0.0683706	−0.00501318
$187$	−8.62134	−0.630455
$188$	−3.22579	−0.235265
$189$	−0.807951	−0.0587698
$190$	0	0
$191$	−9.95887	−0.720599	−0.360299	−	0.932837i	$-0.617325\pi$
$191$	−9.95887	−0.720599	−0.360299	+	0.932837i	$0.617325\pi$
$192$	0.555385	0.0400814
$193$	21.4012	1.54049	0.770247	−	0.637746i	$-0.220133\pi$
$193$	21.4012	1.54049	0.770247	+	0.637746i	$0.220133\pi$
$194$	−2.08203	−0.149481
$195$	−0.516605	−0.0369949
$196$	8.12165	0.580118
$197$	1.36674	0.0973765	0.0486883	−	0.998814i	$-0.484496\pi$
$197$	1.36674	0.0973765	0.0486883	+	0.998814i	$0.484496\pi$
$198$	−1.82330	−0.129577
$199$	−17.9359	−1.27144	−0.635722	−	0.771918i	$-0.719298\pi$
$199$	−17.9359	−1.27144	−0.635722	+	0.771918i	$0.719298\pi$
$200$	0.834543	0.0590111
$201$	0.180990	0.0127660
$202$	−0.879749	−0.0618989
$203$	12.2447	0.859407
$204$	0.466592	0.0326680
$205$	−5.45595	−0.381060
$206$	−2.65072	−0.184684
$207$	−24.7199	−1.71815
$208$	24.1499	1.67449
$209$	0	0
$210$	−0.0284410	−0.00196262
$211$	−20.7678	−1.42971	−0.714857	−	0.699270i	$-0.753508\pi$
$211$	−20.7678	−1.42971	−0.714857	+	0.699270i	$0.753508\pi$
$212$	3.73877	0.256779
$213$	0.832707	0.0570561
$214$	3.15258	0.215506
$215$	−5.33164	−0.363615
$216$	0.399632	0.0271915
$217$	6.84340	0.464560
$218$	1.09816	0.0743769
$219$	−0.112802	−0.00762243
$220$	5.64506	0.380590
$221$	19.3107	1.29898
$222$	−0.134346	−0.00901669
$223$	−1.94996	−0.130579	−0.0652894	−	0.997866i	$-0.520797\pi$
$223$	−1.94996	−0.130579	−0.0652894	+	0.997866i	$0.520797\pi$
$224$	4.14567	0.276994
$225$	−2.99362	−0.199574
$226$	1.80827	0.120284
$227$	−12.6099	−0.836950	−0.418475	−	0.908228i	$-0.637435\pi$
$227$	−12.6099	−0.836950	−0.418475	+	0.908228i	$0.637435\pi$
$228$	0	0
$229$	−6.12765	−0.404926	−0.202463	−	0.979290i	$-0.564895\pi$
$229$	−6.12765	−0.404926	−0.202463	+	0.979290i	$0.564895\pi$
$230$	−1.74221	−0.114878
$231$	−0.389144	−0.0256038
$232$	−6.05650	−0.397629
$233$	6.60713	0.432848	0.216424	−	0.976299i	$-0.430561\pi$
$233$	6.60713	0.432848	0.216424	+	0.976299i	$0.430561\pi$
$234$	4.08396	0.266977
$235$	1.64961	0.107609
$236$	6.94738	0.452236
$237$	−0.192609	−0.0125113
$238$	1.06312	0.0689120
$239$	−2.20382	−0.142553	−0.0712766	−	0.997457i	$-0.522707\pi$
$239$	−2.20382	−0.142553	−0.0712766	+	0.997457i	$0.522707\pi$
$240$	−0.298402	−0.0192617
$241$	0.124850	0.00804232	0.00402116	−	0.999992i	$-0.498720\pi$
$241$	0.124850	0.00804232	0.00402116	+	0.999992i	$0.498720\pi$
$242$	0.562584	0.0361643
$243$	−2.15106	−0.137991
$244$	15.4486	0.988996
$245$	−4.15326	−0.265342
$246$	−0.0919690	−0.00586373
$247$	0	0
$248$	−3.38491	−0.214942
$249$	0.910855	0.0577231
$250$	−0.210984	−0.0133438
$251$	3.71679	0.234602	0.117301	−	0.993096i	$-0.462576\pi$
$251$	3.71679	0.234602	0.117301	+	0.993096i	$0.462576\pi$
$252$	−9.87699	−0.622192
$253$	−23.8377	−1.49866
$254$	2.75058	0.172587
$255$	−0.238607	−0.0149421
$256$	12.5565	0.784783
$257$	26.9757	1.68270	0.841349	−	0.540492i	$-0.181762\pi$
$257$	26.9757	1.68270	0.841349	+	0.540492i	$0.181762\pi$
$258$	−0.0898736	−0.00559529
$259$	13.4470	0.835557
$260$	−12.6442	−0.784159
$261$	21.7255	1.34477
$262$	−0.0394715	−0.00243856
$263$	20.6759	1.27493	0.637464	−	0.770480i	$-0.279983\pi$
$263$	20.6759	1.27493	0.637464	+	0.770480i	$0.279983\pi$
$264$	0.192480	0.0118463
$265$	−1.91194	−0.117449
$266$	0	0
$267$	−0.808231	−0.0494629
$268$	4.42982	0.270594
$269$	13.7249	0.836820	0.418410	−	0.908258i	$-0.362587\pi$
$269$	13.7249	0.836820	0.418410	+	0.908258i	$0.362587\pi$
$270$	−0.101032	−0.00614863
$271$	−5.38346	−0.327022	−0.163511	−	0.986542i	$-0.552282\pi$
$271$	−5.38346	−0.327022	−0.163511	+	0.986542i	$0.552282\pi$
$272$	11.1542	0.676324
$273$	0.871631	0.0527535
$274$	−0.454794	−0.0274751
$275$	−2.88678	−0.174080
$276$	1.29011	0.0776557
$277$	22.7985	1.36983	0.684916	−	0.728622i	$-0.259839\pi$
$277$	22.7985	1.36983	0.684916	+	0.728622i	$0.259839\pi$
$278$	1.66616	0.0999299
$279$	12.1421	0.726930
$280$	−1.40806	−0.0841479
$281$	17.2290	1.02780	0.513899	−	0.857851i	$-0.328201\pi$
$281$	17.2290	1.02780	0.513899	+	0.857851i	$0.328201\pi$
$282$	0.0278069	0.00165588
$283$	16.2988	0.968866	0.484433	−	0.874828i	$-0.339026\pi$
$283$	16.2988	0.968866	0.484433	+	0.874828i	$0.339026\pi$
$284$	20.3809	1.20939
$285$	0	0
$286$	3.93821	0.232871
$287$	9.20543	0.543379
$288$	7.35558	0.433432
$289$	−8.08090	−0.475347
$290$	1.53116	0.0899131
$291$	−0.788425	−0.0462183
$292$	−2.76088	−0.161568
$293$	−25.2882	−1.47735	−0.738675	−	0.674061i	$-0.764548\pi$
$293$	−25.2882	−1.47735	−0.738675	+	0.674061i	$0.764548\pi$
$294$	−0.0700101	−0.00408307
$295$	−3.55276	−0.206850
$296$	−6.65122	−0.386594
$297$	−1.38237	−0.0802135
$298$	−3.77589	−0.218731
$299$	53.3933	3.08781
$300$	0.156235	0.00902021
$301$	8.99570	0.518503
$302$	0.620258	0.0356918
$303$	−0.333144	−0.0191386
$304$	0	0
$305$	−7.90014	−0.452361
$306$	1.88628	0.107831
$307$	−17.2290	−0.983309	−0.491655	−	0.870790i	$-0.663608\pi$
$307$	−17.2290	−0.983309	−0.491655	+	0.870790i	$0.663608\pi$
$308$	−9.52451	−0.542709
$309$	−1.00378	−0.0571028
$310$	0.855750	0.0486034
$311$	24.9724	1.41606	0.708028	−	0.706184i	$-0.249585\pi$
$311$	24.9724	1.41606	0.708028	+	0.706184i	$0.249585\pi$
$312$	−0.431129	−0.0244079
$313$	−16.8633	−0.953167	−0.476584	−	0.879129i	$-0.658125\pi$
$313$	−16.8633	−0.953167	−0.476584	+	0.879129i	$0.658125\pi$
$314$	−1.42770	−0.0805697
$315$	5.05091	0.284587
$316$	−4.71421	−0.265195
$317$	−24.1211	−1.35478	−0.677389	−	0.735625i	$-0.736889\pi$
$317$	−24.1211	−1.35478	−0.677389	+	0.735625i	$0.736889\pi$
$318$	−0.0322288	−0.00180730
$319$	20.9502	1.17298
$320$	−6.95139	−0.388594
$321$	1.19382	0.0666328
$322$	2.93950	0.163812
$323$	0	0
$324$	−17.4871	−0.971506
$325$	6.46601	0.358670
$326$	0.191538	0.0106083
$327$	0.415853	0.0229967
$328$	−4.55322	−0.251410
$329$	−2.78327	−0.153447
$330$	−0.0486615	−0.00267873
$331$	−15.5403	−0.854174	−0.427087	−	0.904211i	$-0.640460\pi$
$331$	−15.5403	−0.854174	−0.427087	+	0.904211i	$0.640460\pi$
$332$	22.2937	1.22352
$333$	23.8588	1.30745
$334$	3.01107	0.164758
$335$	−2.26533	−0.123768
$336$	0.503471	0.0274666
$337$	−11.0057	−0.599516	−0.299758	−	0.954015i	$-0.596906\pi$
$337$	−11.0057	−0.599516	−0.299758	+	0.954015i	$0.596906\pi$
$338$	−6.07829	−0.330615
$339$	0.684756	0.0371908
$340$	−5.84003	−0.316720
$341$	11.7088	0.634067
$342$	0	0
$343$	18.8181	1.01608
$344$	−4.44948	−0.239900
$345$	−0.659740	−0.0355192
$346$	2.97011	0.159674
$347$	30.4697	1.63570	0.817849	−	0.575433i	$-0.195167\pi$
$347$	30.4697	1.63570	0.817849	+	0.575433i	$0.195167\pi$
$348$	−1.13384	−0.0607800
$349$	5.61744	0.300695	0.150347	−	0.988633i	$-0.451961\pi$
$349$	5.61744	0.300695	0.150347	+	0.988633i	$0.451961\pi$
$350$	0.355977	0.0190278
$351$	3.09633	0.165270
$352$	7.09308	0.378062
$353$	−7.48617	−0.398449	−0.199224	−	0.979954i	$-0.563842\pi$
$353$	−7.48617	−0.398449	−0.199224	+	0.979954i	$0.563842\pi$
$354$	−0.0598877	−0.00318299
$355$	−10.4224	−0.553166
$356$	−19.7819	−1.04844
$357$	0.402584	0.0213070
$358$	3.32294	0.175623
$359$	−25.4854	−1.34507	−0.672534	−	0.740066i	$-0.734794\pi$
$359$	−25.4854	−1.34507	−0.672534	+	0.740066i	$0.734794\pi$
$360$	−2.49830	−0.131672
$361$	0	0
$362$	0.961728	0.0505473
$363$	0.213040	0.0111817
$364$	21.3336	1.11819
$365$	1.41186	0.0739003
$366$	−0.133170	−0.00696090
$367$	−33.4662	−1.74692	−0.873461	−	0.486894i	$-0.838130\pi$
$367$	−33.4662	−1.74692	−0.873461	+	0.486894i	$0.838130\pi$
$368$	30.8410	1.60770
$369$	16.3330	0.850263
$370$	1.68152	0.0874179
$371$	3.22587	0.167479
$372$	−0.633688	−0.0328552
$373$	10.4787	0.542566	0.271283	−	0.962500i	$-0.412552\pi$
$373$	10.4787	0.542566	0.271283	+	0.962500i	$0.412552\pi$
$374$	1.81896	0.0940563
$375$	−0.0798955	−0.00412579
$376$	1.37667	0.0709964
$377$	−46.9256	−2.41679
$378$	0.170464	0.00876775
$379$	14.2962	0.734344	0.367172	−	0.930153i	$-0.380326\pi$
$379$	14.2962	0.734344	0.367172	+	0.930153i	$0.380326\pi$
$380$	0	0
$381$	1.04159	0.0533625
$382$	2.10116	0.107505
$383$	−36.9815	−1.88967	−0.944833	−	0.327552i	$-0.893776\pi$
$383$	−36.9815	−1.88967	−0.944833	+	0.327552i	$0.893776\pi$
$384$	−0.509798	−0.0260155
$385$	4.87066	0.248232
$386$	−4.51531	−0.229823
$387$	15.9609	0.811338
$388$	−19.2971	−0.979663
$389$	−16.6074	−0.842029	−0.421015	−	0.907054i	$-0.638326\pi$
$389$	−16.6074	−0.842029	−0.421015	+	0.907054i	$0.638326\pi$
$390$	0.108995	0.00551919
$391$	24.6610	1.24716
$392$	−3.46608	−0.175063
$393$	−0.0149471	−0.000753983 0
$394$	−0.288361	−0.0145274
$395$	2.41076	0.121299
$396$	−16.8992	−0.849215
$397$	−26.6383	−1.33694	−0.668470	−	0.743739i	$-0.733051\pi$
$397$	−26.6383	−1.33694	−0.668470	+	0.743739i	$0.733051\pi$
$398$	3.78419	0.189684
$399$	0	0
$400$	3.73490	0.186745
$401$	−1.29475	−0.0646570	−0.0323285	−	0.999477i	$-0.510292\pi$
$401$	−1.29475	−0.0646570	−0.0323285	+	0.999477i	$0.510292\pi$
$402$	−0.0381859	−0.00190454
$403$	−26.2262	−1.30642
$404$	−8.15389	−0.405671
$405$	8.94259	0.444361
$406$	−2.58342	−0.128213
$407$	23.0074	1.14043
$408$	−0.199128	−0.00985829
$409$	−27.0318	−1.33664	−0.668318	−	0.743876i	$-0.732985\pi$
$409$	−27.0318	−1.33664	−0.668318	+	0.743876i	$0.732985\pi$
$410$	1.15112	0.0568496
$411$	−0.172222	−0.00849507
$412$	−24.5680	−1.21038
$413$	5.99432	0.294961
$414$	5.21549	0.256328
$415$	−11.4006	−0.559632
$416$	−15.8876	−0.778951
$417$	0.630945	0.0308975
$418$	0	0
$419$	−4.15498	−0.202984	−0.101492	−	0.994836i	$-0.532362\pi$
$419$	−4.15498	−0.202984	−0.101492	+	0.994836i	$0.532362\pi$
$420$	−0.263603	−0.0128625
$421$	26.4050	1.28690	0.643449	−	0.765489i	$-0.277503\pi$
$421$	26.4050	1.28690	0.643449	+	0.765489i	$0.277503\pi$
$422$	4.38167	0.213296
$423$	−4.93830	−0.240108
$424$	−1.59559	−0.0774889
$425$	2.98649	0.144866
$426$	−0.175687	−0.00851209
$427$	13.3293	0.645052
$428$	29.2195	1.41238
$429$	1.49133	0.0720020
$430$	1.12489	0.0542470
$431$	9.72137	0.468262	0.234131	−	0.972205i	$-0.424776\pi$
$431$	9.72137	0.468262	0.234131	+	0.972205i	$0.424776\pi$
$432$	1.78850	0.0860495
$433$	0.659842	0.0317100	0.0158550	−	0.999874i	$-0.494953\pi$
$433$	0.659842	0.0317100	0.0158550	+	0.999874i	$0.494953\pi$
$434$	−1.44385	−0.0693068
$435$	0.579823	0.0278004
$436$	10.1782	0.487449
$437$	0	0
$438$	0.0237993	0.00113717
$439$	−27.1898	−1.29770	−0.648849	−	0.760917i	$-0.724749\pi$
$439$	−27.1898	−1.29770	−0.648849	+	0.760917i	$0.724749\pi$
$440$	−2.40914	−0.114851
$441$	12.4333	0.592061
$442$	−4.07423	−0.193791
$443$	37.7880	1.79536	0.897682	−	0.440644i	$-0.145250\pi$
$443$	37.7880	1.79536	0.897682	+	0.440644i	$0.145250\pi$
$444$	−1.24517	−0.0590933
$445$	10.1161	0.479549
$446$	0.411409	0.0194808
$447$	−1.42986	−0.0676300
$448$	11.7286	0.554123
$449$	16.5499	0.781039	0.390520	−	0.920595i	$-0.372295\pi$
$449$	16.5499	0.781039	0.390520	+	0.920595i	$0.372295\pi$
$450$	0.631604	0.0297741
$451$	15.7501	0.741645
$452$	16.7598	0.788313
$453$	0.234880	0.0110356
$454$	2.66049	0.124863
$455$	−10.9096	−0.511451
$456$	0	0
$457$	11.4492	0.535571	0.267785	−	0.963479i	$-0.413708\pi$
$457$	11.4492	0.535571	0.267785	+	0.963479i	$0.413708\pi$
$458$	1.29283	0.0604101
$459$	1.43012	0.0667522
$460$	−16.1475	−0.752881
$461$	−10.7597	−0.501127	−0.250563	−	0.968100i	$-0.580616\pi$
$461$	−10.7597	−0.501127	−0.250563	+	0.968100i	$0.580616\pi$
$462$	0.0821030	0.00381978
$463$	17.0882	0.794155	0.397078	−	0.917785i	$-0.370024\pi$
$463$	17.0882	0.794155	0.397078	+	0.917785i	$0.370024\pi$
$464$	−27.1051	−1.25832
$465$	0.324057	0.0150278
$466$	−1.39400	−0.0645757
$467$	31.8559	1.47412	0.737058	−	0.675829i	$-0.236214\pi$
$467$	31.8559	1.47412	0.737058	+	0.675829i	$0.236214\pi$
$468$	37.8519	1.74970
$469$	3.82213	0.176489
$470$	−0.348041	−0.0160539
$471$	−0.540643	−0.0249115
$472$	−2.96493	−0.136472
$473$	15.3913	0.707693
$474$	0.0406374	0.00186654
$475$	0	0
$476$	9.85346	0.451633
$477$	5.72361	0.262066
$478$	0.464970	0.0212672
$479$	−3.85027	−0.175923	−0.0879616	−	0.996124i	$-0.528035\pi$
$479$	−3.85027	−0.175923	−0.0879616	+	0.996124i	$0.528035\pi$
$480$	0.196310	0.00896030
$481$	−51.5334	−2.34972
$482$	−0.0263414	−0.00119982
$483$	1.11313	0.0506493
$484$	5.21427	0.237012
$485$	9.86820	0.448092
$486$	0.453839	0.0205866
$487$	−35.4075	−1.60447	−0.802233	−	0.597011i	$-0.796355\pi$
$487$	−35.4075	−1.60447	−0.802233	+	0.597011i	$0.796355\pi$
$488$	−6.59300	−0.298451
$489$	0.0725319	0.00328000
$490$	0.876270	0.0395859
$491$	20.2571	0.914192	0.457096	−	0.889417i	$-0.348890\pi$
$491$	20.2571	0.914192	0.457096	+	0.889417i	$0.348890\pi$
$492$	−0.852408	−0.0384295
$493$	−21.6737	−0.976136
$494$	0	0
$495$	8.64192	0.388426
$496$	−15.1488	−0.680199
$497$	17.5850	0.788797
$498$	−0.192176	−0.00861159
$499$	0.589427	0.0263864	0.0131932	−	0.999913i	$-0.495800\pi$
$499$	0.589427	0.0263864	0.0131932	+	0.999913i	$0.495800\pi$
$500$	−1.95549	−0.0874520
$501$	1.14024	0.0509420
$502$	−0.784181	−0.0349997
$503$	−11.3500	−0.506073	−0.253037	−	0.967457i	$-0.581429\pi$
$503$	−11.3500	−0.506073	−0.253037	+	0.967457i	$0.581429\pi$
$504$	4.21520	0.187760
$505$	4.16975	0.185551
$506$	5.02937	0.223583
$507$	−2.30173	−0.102224
$508$	25.4936	1.13109
$509$	−11.8654	−0.525926	−0.262963	−	0.964806i	$-0.584700\pi$
$509$	−11.8654	−0.525926	−0.262963	+	0.964806i	$0.584700\pi$
$510$	0.0503422	0.00222919
$511$	−2.38214	−0.105379
$512$	−15.4108	−0.681069
$513$	0	0
$514$	−5.69143	−0.251038
$515$	12.5636	0.553619
$516$	−0.832987	−0.0366702
$517$	−4.76207	−0.209436
$518$	−2.83710	−0.124655
$519$	1.12472	0.0493699
$520$	5.39616	0.236637
$521$	24.5221	1.07433	0.537166	−	0.843476i	$-0.319495\pi$
$521$	24.5221	1.07433	0.537166	+	0.843476i	$0.319495\pi$
$522$	−4.58372	−0.200624
$523$	−21.2338	−0.928488	−0.464244	−	0.885707i	$-0.653674\pi$
$523$	−21.2338	−0.928488	−0.464244	+	0.885707i	$0.653674\pi$
$524$	−0.365839	−0.0159817
$525$	0.134802	0.00588324
$526$	−4.36227	−0.190204
$527$	−12.1132	−0.527659
$528$	0.861421	0.0374885
$529$	45.1869	1.96465
$530$	0.403387	0.0175220
$531$	10.6356	0.461546
$532$	0	0
$533$	−35.2782	−1.52807
$534$	0.170524	0.00737928
$535$	−14.9423	−0.646013
$536$	−1.89051	−0.0816578
$537$	1.25833	0.0543012
$538$	−2.89572	−0.124844
$539$	11.9896	0.516427
$540$	−0.936410	−0.0402967
$541$	14.8259	0.637414	0.318707	−	0.947853i	$-0.396751\pi$
$541$	14.8259	0.637414	0.318707	+	0.947853i	$0.396751\pi$
$542$	1.13582	0.0487877
$543$	0.364188	0.0156288
$544$	−7.33806	−0.314617
$545$	−5.20496	−0.222956
$546$	−0.183900	−0.00787019
$547$	−7.96145	−0.340407	−0.170203	−	0.985409i	$-0.554442\pi$
$547$	−7.96145	−0.340407	−0.170203	+	0.985409i	$0.554442\pi$
$548$	−4.21522	−0.180065
$549$	23.6500	1.00936
$550$	0.609064	0.0259706
$551$	0	0
$552$	−0.550581	−0.0234343
$553$	−4.06750	−0.172968
$554$	−4.81012	−0.204362
$555$	0.636759	0.0270289
$556$	15.4427	0.654917
$557$	−8.10522	−0.343429	−0.171715	−	0.985147i	$-0.554931\pi$
$557$	−8.10522	−0.343429	−0.171715	+	0.985147i	$0.554931\pi$
$558$	−2.56179	−0.108449
$559$	−34.4745	−1.45811
$560$	−6.30162	−0.266292
$561$	0.688806	0.0290814
$562$	−3.63504	−0.153335
$563$	−8.29823	−0.349729	−0.174864	−	0.984593i	$-0.555949\pi$
$563$	−8.29823	−0.349729	−0.174864	+	0.984593i	$0.555949\pi$
$564$	0.257726	0.0108522
$565$	−8.57064	−0.360570
$566$	−3.43879	−0.144543
$567$	−15.0882	−0.633644
$568$	−8.69798	−0.364959
$569$	7.28643	0.305463	0.152732	−	0.988268i	$-0.451193\pi$
$569$	7.28643	0.305463	0.152732	+	0.988268i	$0.451193\pi$
$570$	0	0
$571$	−20.6974	−0.866159	−0.433080	−	0.901356i	$-0.642573\pi$
$571$	−20.6974	−0.866159	−0.433080	+	0.901356i	$0.642573\pi$
$572$	36.5010	1.52619
$573$	0.795669	0.0332396
$574$	−1.94219	−0.0810657
$575$	8.25754	0.344363
$576$	20.8098	0.867075
$577$	14.5909	0.607429	0.303715	−	0.952763i	$-0.401773\pi$
$577$	14.5909	0.607429	0.303715	+	0.952763i	$0.401773\pi$
$578$	1.70494	0.0709160
$579$	−1.70986	−0.0710594
$580$	14.1915	0.589269
$581$	19.2354	0.798018
$582$	0.166345	0.00689521
$583$	5.51935	0.228588
$584$	1.17826	0.0487568
$585$	−19.3568	−0.800303
$586$	5.33539	0.220403
$587$	−10.5077	−0.433699	−0.216849	−	0.976205i	$-0.569578\pi$
$587$	−10.5077	−0.433699	−0.216849	+	0.976205i	$0.569578\pi$
$588$	−0.648883	−0.0267595
$589$	0	0
$590$	0.749575	0.0308595
$591$	−0.109197	−0.00449175
$592$	−29.7667	−1.22340
$593$	24.3159	0.998535	0.499267	−	0.866448i	$-0.333603\pi$
$593$	24.3159	0.998535	0.499267	+	0.866448i	$0.333603\pi$
$594$	0.291658	0.0119669
$595$	−5.03888	−0.206574
$596$	−34.9966	−1.43351
$597$	1.43300	0.0586488
$598$	−11.2651	−0.460665
$599$	37.9095	1.54894	0.774471	−	0.632609i	$-0.218016\pi$
$599$	37.9095	1.54894	0.774471	+	0.632609i	$0.218016\pi$
$600$	−0.0666762	−0.00272205
$601$	−25.9476	−1.05843	−0.529213	−	0.848489i	$-0.677513\pi$
$601$	−25.9476	−1.05843	−0.529213	+	0.848489i	$0.677513\pi$
$602$	−1.89794	−0.0773544
$603$	6.78153	0.276165
$604$	5.74881	0.233916
$605$	−2.66648	−0.108408
$606$	0.0702880	0.00285525
$607$	11.5300	0.467988	0.233994	−	0.972238i	$-0.424820\pi$
$607$	11.5300	0.467988	0.233994	+	0.972238i	$0.424820\pi$
$608$	0	0
$609$	−0.978294	−0.0396425
$610$	1.66680	0.0674868
$611$	10.6664	0.431516
$612$	17.4828	0.706701
$613$	22.6581	0.915154	0.457577	−	0.889170i	$-0.348717\pi$
$613$	22.6581	0.915154	0.457577	+	0.889170i	$0.348717\pi$
$614$	3.63503	0.146698
$615$	0.435906	0.0175774
$616$	4.06477	0.163774
$617$	5.97675	0.240615	0.120307	−	0.992737i	$-0.461612\pi$
$617$	5.97675	0.240615	0.120307	+	0.992737i	$0.461612\pi$
$618$	0.211780	0.00851905
$619$	−34.2062	−1.37486	−0.687431	−	0.726249i	$-0.741262\pi$
$619$	−34.2062	−1.37486	−0.687431	+	0.726249i	$0.741262\pi$
$620$	7.93146	0.318535
$621$	3.95423	0.158678
$622$	−5.26877	−0.211259
$623$	−17.0682	−0.683822
$624$	−1.92947	−0.0772405
$625$	1.00000	0.0400000
$626$	3.55787	0.142201
$627$	0	0
$628$	−13.2325	−0.528035
$629$	−23.8020	−0.949047
$630$	−1.06566	−0.0424569
$631$	−14.2510	−0.567325	−0.283662	−	0.958924i	$-0.591549\pi$
$631$	−14.2510	−0.567325	−0.283662	+	0.958924i	$0.591549\pi$
$632$	2.01188	0.0800284
$633$	1.65925	0.0659494
$634$	5.08916	0.202117
$635$	−13.0369	−0.517355
$636$	−0.298711	−0.0118446
$637$	−26.8550	−1.06404
$638$	−4.42014	−0.174995
$639$	31.2008	1.23428
$640$	6.38080	0.252223
$641$	39.7444	1.56981	0.784904	−	0.619617i	$-0.212712\pi$
$641$	39.7444	1.56981	0.784904	+	0.619617i	$0.212712\pi$
$642$	−0.251877	−0.00994081
$643$	15.9065	0.627290	0.313645	−	0.949540i	$-0.398450\pi$
$643$	15.9065	0.627290	0.313645	+	0.949540i	$0.398450\pi$
$644$	27.2445	1.07358
$645$	0.425974	0.0167727
$646$	0	0
$647$	18.8549	0.741262	0.370631	−	0.928780i	$-0.379142\pi$
$647$	18.8549	0.741262	0.370631	+	0.928780i	$0.379142\pi$
$648$	7.46297	0.293173
$649$	10.2561	0.402585
$650$	−1.36422	−0.0535092
$651$	−0.546757	−0.0214291
$652$	1.77526	0.0695244
$653$	−42.5252	−1.66414	−0.832070	−	0.554670i	$-0.812844\pi$
$653$	−42.5252	−1.66414	−0.832070	+	0.554670i	$0.812844\pi$
$654$	−0.0877382	−0.00343083
$655$	0.187083	0.00730995
$656$	−20.3774	−0.795604
$657$	−4.22658	−0.164895
$658$	0.587224	0.0228924
$659$	45.8272	1.78517	0.892587	−	0.450874i	$-0.148888\pi$
$659$	45.8272	1.78517	0.892587	+	0.450874i	$0.148888\pi$
$660$	−0.451015	−0.0175557
$661$	46.1676	1.79571	0.897856	−	0.440289i	$-0.145124\pi$
$661$	46.1676	1.79571	0.897856	+	0.440289i	$0.145124\pi$
$662$	3.27876	0.127432
$663$	−1.54283	−0.0599187
$664$	−9.51427	−0.369225
$665$	0	0
$666$	−5.03382	−0.195056
$667$	−59.9271	−2.32039
$668$	27.9079	1.07979
$669$	0.155793	0.00602330
$670$	0.477948	0.0184647
$671$	22.8060	0.880415
$672$	−0.331220	−0.0127771
$673$	−5.48820	−0.211555	−0.105777	−	0.994390i	$-0.533733\pi$
$673$	−5.48820	−0.211555	−0.105777	+	0.994390i	$0.533733\pi$
$674$	2.32201	0.0894406
$675$	0.478863	0.0184315
$676$	−56.3362	−2.16678
$677$	29.4307	1.13111	0.565557	−	0.824709i	$-0.308661\pi$
$677$	29.4307	1.13111	0.565557	+	0.824709i	$0.308661\pi$
$678$	−0.144472	−0.00554843
$679$	−16.6499	−0.638965
$680$	2.49235	0.0955773
$681$	1.00748	0.0386066
$682$	−2.47037	−0.0945952
$683$	27.4543	1.05051	0.525254	−	0.850945i	$-0.323970\pi$
$683$	27.4543	1.05051	0.525254	+	0.850945i	$0.323970\pi$
$684$	0	0
$685$	2.15559	0.0823608
$686$	−3.97031	−0.151587
$687$	0.489571	0.0186783
$688$	−19.9131	−0.759181
$689$	−12.3626	−0.470978
$690$	0.139194	0.00529904
$691$	3.42779	0.130399	0.0651997	−	0.997872i	$-0.479232\pi$
$691$	3.42779	0.130399	0.0651997	+	0.997872i	$0.479232\pi$
$692$	27.5282	1.04647
$693$	−14.5809	−0.553882
$694$	−6.42860	−0.244026
$695$	−7.89712	−0.299555
$696$	0.483887	0.0183417
$697$	−16.2941	−0.617184
$698$	−1.18519	−0.0448600
$699$	−0.527880	−0.0199663
$700$	3.29935	0.124704
$701$	−3.26100	−0.123166	−0.0615832	−	0.998102i	$-0.519615\pi$
$701$	−3.26100	−0.123166	−0.0615832	+	0.998102i	$0.519615\pi$
$702$	−0.653276	−0.0246563
$703$	0	0
$704$	20.0672	0.756309
$705$	−0.131796	−0.00496374
$706$	1.57946	0.0594437
$707$	−7.03532	−0.264590
$708$	−0.555064	−0.0208606
$709$	−17.1381	−0.643633	−0.321817	−	0.946802i	$-0.604293\pi$
$709$	−17.1381	−0.643633	−0.321817	+	0.946802i	$0.604293\pi$
$710$	2.19897	0.0825257
$711$	−7.21690	−0.270655
$712$	8.44232	0.316389
$713$	−33.4926	−1.25431
$714$	−0.0849387	−0.00317875
$715$	−18.6660	−0.698068
$716$	30.7984	1.15099
$717$	0.176075	0.00657565
$718$	5.37701	0.200668
$719$	6.22549	0.232172	0.116086	−	0.993239i	$-0.462965\pi$
$719$	6.22549	0.232172	0.116086	+	0.993239i	$0.462965\pi$
$720$	−11.1808	−0.416686
$721$	−21.1977	−0.789442
$722$	0	0
$723$	−0.00997498	−0.000370974 0
$724$	8.91371	0.331275
$725$	−7.25727	−0.269528
$726$	−0.0449480	−0.00166817
$727$	−42.3189	−1.56952	−0.784760	−	0.619800i	$-0.787214\pi$
$727$	−42.3189	−1.56952	−0.784760	+	0.619800i	$0.787214\pi$
$728$	−9.10455	−0.337437
$729$	−26.6559	−0.987256
$730$	−0.297880	−0.0110250
$731$	−15.9229	−0.588929
$732$	−1.23427	−0.0456201
$733$	−22.7630	−0.840771	−0.420386	−	0.907346i	$-0.638105\pi$
$733$	−22.7630	−0.840771	−0.420386	+	0.907346i	$0.638105\pi$
$734$	7.06082	0.260620
$735$	0.331827	0.0122396
$736$	−20.2895	−0.747881
$737$	6.53952	0.240886
$738$	−3.44600	−0.126849
$739$	17.9424	0.660023	0.330012	−	0.943977i	$-0.392947\pi$
$739$	17.9424	0.660023	0.330012	+	0.943977i	$0.392947\pi$
$740$	15.5850	0.572916
$741$	0	0
$742$	−0.680606	−0.0249858
$743$	17.3309	0.635810	0.317905	−	0.948123i	$-0.397021\pi$
$743$	17.3309	0.635810	0.317905	+	0.948123i	$0.397021\pi$
$744$	0.270439	0.00991478
$745$	17.8966	0.655681
$746$	−2.21083	−0.0809443
$747$	34.1290	1.24871
$748$	16.8589	0.616423
$749$	25.2111	0.921193
$750$	0.0168566	0.000615518 0
$751$	2.18627	0.0797781	0.0398890	−	0.999204i	$-0.487300\pi$
$751$	2.18627	0.0797781	0.0398890	+	0.999204i	$0.487300\pi$
$752$	6.16113	0.224673
$753$	−0.296955	−0.0108216
$754$	9.90053	0.360556
$755$	−2.93984	−0.106992
$756$	1.57994	0.0574618
$757$	−15.6387	−0.568397	−0.284198	−	0.958766i	$-0.591727\pi$
$757$	−15.6387	−0.568397	−0.284198	+	0.958766i	$0.591727\pi$
$758$	−3.01625	−0.109555
$759$	1.90453	0.0691299
$760$	0	0
$761$	26.2993	0.953349	0.476675	−	0.879080i	$-0.341842\pi$
$761$	26.2993	0.953349	0.476675	+	0.879080i	$0.341842\pi$
$762$	−0.219759	−0.00796104
$763$	8.78195	0.317928
$764$	19.4744	0.704560
$765$	−8.94040	−0.323241
$766$	7.80249	0.281915
$767$	−22.9722	−0.829478
$768$	−1.00321	−0.0362002
$769$	0.0847497	0.00305615	0.00152808	−	0.999999i	$-0.499514\pi$
$769$	0.0847497	0.00305615	0.00152808	+	0.999999i	$0.499514\pi$
$770$	−1.02763	−0.0370332
$771$	−2.15524	−0.0776190
$772$	−41.8498	−1.50621
$773$	0.0114752	0.000412734 0	0.000206367	−	1.00000i	$-0.499934\pi$
$773$	0.0114752	0.000412734 0	0.000206367		1.00000i	$0.499934\pi$
$774$	−3.36749	−0.121042
$775$	−4.05600	−0.145696
$776$	8.23544	0.295635
$777$	−1.07436	−0.0385423
$778$	3.50389	0.125621
$779$	0	0
$780$	1.01021	0.0361715
$781$	30.0873	1.07661
$782$	−5.20307	−0.186061
$783$	−3.47524	−0.124195
$784$	−15.5120	−0.554000
$785$	6.76687	0.241520
$786$	0.00315360	0.000112485 0
$787$	−30.1068	−1.07319	−0.536596	−	0.843839i	$-0.680290\pi$
$787$	−30.1068	−1.07319	−0.536596	+	0.843839i	$0.680290\pi$
$788$	−2.67265	−0.0952092
$789$	−1.65191	−0.0588095
$790$	−0.508631	−0.0180963
$791$	14.4606	0.514161
$792$	7.21205	0.256269
$793$	−51.0824	−1.81399
$794$	5.62026	0.199455
$795$	0.152755	0.00541767
$796$	35.0735	1.24315
$797$	−38.2339	−1.35432	−0.677158	−	0.735838i	$-0.736789\pi$
$797$	−38.2339	−1.35432	−0.677158	+	0.735838i	$0.736789\pi$
$798$	0	0
$799$	4.92654	0.174288
$800$	−2.45709	−0.0868712
$801$	−30.2837	−1.07002
$802$	0.273172	0.00964604
$803$	−4.07574	−0.143830
$804$	−0.353923	−0.0124819
$805$	−13.9323	−0.491051
$806$	5.53329	0.194902
$807$	−1.09656	−0.0386006
$808$	3.47983	0.122420
$809$	3.70003	0.130086	0.0650431	−	0.997882i	$-0.479282\pi$
$809$	3.70003	0.130086	0.0650431	+	0.997882i	$0.479282\pi$
$810$	−1.88674	−0.0662933
$811$	−40.9256	−1.43709	−0.718545	−	0.695480i	$-0.755192\pi$
$811$	−40.9256	−1.43709	−0.718545	+	0.695480i	$0.755192\pi$
$812$	−23.9443	−0.840279
$813$	0.430114	0.0150848
$814$	−4.85417	−0.170139
$815$	−0.907834	−0.0318000
$816$	−0.891172	−0.0311973
$817$	0	0
$818$	5.70327	0.199410
$819$	32.6593	1.14121
$820$	10.6690	0.372579
$821$	17.4402	0.608666	0.304333	−	0.952566i	$-0.401566\pi$
$821$	17.4402	0.608666	0.304333	+	0.952566i	$0.401566\pi$
$822$	0.0363360	0.00126736
$823$	−6.50473	−0.226741	−0.113370	−	0.993553i	$-0.536165\pi$
$823$	−6.50473	−0.226741	−0.113370	+	0.993553i	$0.536165\pi$
$824$	10.4849	0.365258
$825$	0.230641	0.00802989
$826$	−1.26470	−0.0440046
$827$	−1.62225	−0.0564112	−0.0282056	−	0.999602i	$-0.508979\pi$
$827$	−1.62225	−0.0564112	−0.0282056	+	0.999602i	$0.508979\pi$
$828$	48.3394	1.67991
$829$	−32.6503	−1.13399	−0.566996	−	0.823721i	$-0.691895\pi$
$829$	−32.6503	−1.13399	−0.566996	+	0.823721i	$0.691895\pi$
$830$	2.40534	0.0834904
$831$	−1.82150	−0.0631872
$832$	−44.9477	−1.55828
$833$	−12.4037	−0.429761
$834$	−0.133119	−0.00460953
$835$	−14.2716	−0.493888
$836$	0	0
$837$	−1.94227	−0.0671347
$838$	0.876632	0.0302827
$839$	11.5599	0.399093	0.199547	−	0.979888i	$-0.436053\pi$
$839$	11.5599	0.399093	0.199547	+	0.979888i	$0.436053\pi$
$840$	0.112498	0.00388155
$841$	23.6679	0.816135
$842$	−5.57101	−0.191990
$843$	−1.37652	−0.0474099
$844$	40.6111	1.39789
$845$	28.8093	0.991070
$846$	1.04190	0.0358213
$847$	4.49896	0.154586
$848$	−7.14089	−0.245219
$849$	−1.30220	−0.0446915
$850$	−0.630100	−0.0216122
$851$	−65.8117	−2.25600
$852$	−1.62835	−0.0557862
$853$	47.7141	1.63370	0.816850	−	0.576850i	$-0.195718\pi$
$853$	47.7141	1.63370	0.816850	+	0.576850i	$0.195718\pi$
$854$	−2.81227	−0.0962339
$855$	0	0
$856$	−12.4700	−0.426216
$857$	38.5358	1.31636	0.658179	−	0.752862i	$-0.271327\pi$
$857$	38.5358	1.31636	0.658179	+	0.752862i	$0.271327\pi$
$858$	−0.314646	−0.0107418
$859$	19.1921	0.654826	0.327413	−	0.944881i	$-0.393823\pi$
$859$	19.1921	0.654826	0.327413	+	0.944881i	$0.393823\pi$
$860$	10.4260	0.355522
$861$	−0.735473	−0.0250648
$862$	−2.05105	−0.0698591
$863$	9.16794	0.312080	0.156040	−	0.987751i	$-0.450127\pi$
$863$	9.16794	0.312080	0.156040	+	0.987751i	$0.450127\pi$
$864$	−1.17661	−0.0400290
$865$	−14.0774	−0.478647
$866$	−0.139216	−0.00473075
$867$	0.645628	0.0219267
$868$	−13.3822	−0.454221
$869$	−6.95935	−0.236080
$870$	−0.122333	−0.00414748
$871$	−14.6476	−0.496317
$872$	−4.34376	−0.147098
$873$	−29.5416	−0.999832
$874$	0	0
$875$	−1.68723	−0.0570387
$876$	0.220582	0.00745277
$877$	3.62989	0.122573	0.0612864	−	0.998120i	$-0.480480\pi$
$877$	3.62989	0.122573	0.0612864	+	0.998120i	$0.480480\pi$
$878$	5.73660	0.193601
$879$	2.02041	0.0681468
$880$	−10.7818	−0.363456
$881$	−8.34382	−0.281111	−0.140555	−	0.990073i	$-0.544889\pi$
$881$	−8.34382	−0.281111	−0.140555	+	0.990073i	$0.544889\pi$
$882$	−2.62322	−0.0883283
$883$	28.2122	0.949415	0.474708	−	0.880144i	$-0.342554\pi$
$883$	28.2122	0.949415	0.474708	+	0.880144i	$0.342554\pi$
$884$	−37.7617	−1.27006
$885$	0.283850	0.00954151
$886$	−7.97266	−0.267847
$887$	8.84194	0.296883	0.148442	−	0.988921i	$-0.452574\pi$
$887$	8.84194	0.296883	0.148442	+	0.988921i	$0.452574\pi$
$888$	0.531402	0.0178327
$889$	21.9963	0.737732
$890$	−2.13433	−0.0715430
$891$	−25.8153	−0.864846
$892$	3.81312	0.127673
$893$	0	0
$894$	0.301677	0.0100896
$895$	−15.7498	−0.526456
$896$	−10.7659	−0.359662
$897$	−4.26589	−0.142434
$898$	−3.49176	−0.116522
$899$	29.4355	0.981729
$900$	5.85398	0.195133
$901$	−5.70997	−0.190227
$902$	−3.32302	−0.110645
$903$	−0.718716	−0.0239174
$904$	−7.15257	−0.237891
$905$	−4.55831	−0.151523
$906$	−0.0495558	−0.00164638
$907$	−4.22931	−0.140432	−0.0702159	−	0.997532i	$-0.522369\pi$
$907$	−4.22931	−0.140432	−0.0702159	+	0.997532i	$0.522369\pi$
$908$	24.6585	0.818322
$909$	−12.4826	−0.414023
$910$	2.30175	0.0763024
$911$	−10.1182	−0.335231	−0.167616	−	0.985852i	$-0.553607\pi$
$911$	−10.1182	−0.335231	−0.167616	+	0.985852i	$0.553607\pi$
$912$	0	0
$913$	32.9110	1.08920
$914$	−2.41559	−0.0799007
$915$	0.631186	0.0208664
$916$	11.9825	0.395914
$917$	−0.315652	−0.0104238
$918$	−0.301732	−0.00995863
$919$	−47.8757	−1.57927	−0.789637	−	0.613575i	$-0.789731\pi$
$919$	−47.8757	−1.57927	−0.789637	+	0.613575i	$0.789731\pi$
$920$	6.89127	0.227198
$921$	1.37652	0.0453578
$922$	2.27011	0.0747621
$923$	−67.3916	−2.21822
$924$	0.760966	0.0250339
$925$	−7.96989	−0.262048
$926$	−3.60533	−0.118478
$927$	−37.6106	−1.23529
$928$	17.8317	0.585356
$929$	−21.6302	−0.709662	−0.354831	−	0.934930i	$-0.615462\pi$
$929$	−21.6302	−0.709662	−0.354831	+	0.934930i	$0.615462\pi$
$930$	−0.0683706	−0.00224196
$931$	0	0
$932$	−12.9202	−0.423214
$933$	−1.99518	−0.0653194
$934$	−6.72108	−0.219920
$935$	−8.62134	−0.281948
$936$	−16.1540	−0.528011
$937$	36.0833	1.17879	0.589395	−	0.807845i	$-0.299366\pi$
$937$	36.0833	1.17879	0.589395	+	0.807845i	$0.299366\pi$
$938$	−0.806406	−0.0263301
$939$	1.34730	0.0439674
$940$	−3.22579	−0.105214
$941$	48.4806	1.58042	0.790212	−	0.612834i	$-0.209970\pi$
$941$	48.4806	1.58042	0.790212	+	0.612834i	$0.209970\pi$
$942$	0.114067	0.00371650
$943$	−45.0527	−1.46712
$944$	−13.2692	−0.431876
$945$	−0.807951	−0.0262827
$946$	−3.24731	−0.105579
$947$	35.2103	1.14418	0.572091	−	0.820190i	$-0.306132\pi$
$947$	35.2103	1.14418	0.572091	+	0.820190i	$0.306132\pi$
$948$	0.376644	0.0122328
$949$	9.12913	0.296344
$950$	0	0
$951$	1.92717	0.0624928
$952$	−4.20516	−0.136290
$953$	−44.5937	−1.44453	−0.722265	−	0.691616i	$-0.756899\pi$
$953$	−44.5937	−1.44453	−0.722265	+	0.691616i	$0.756899\pi$
$954$	−1.20759	−0.0390971
$955$	−9.95887	−0.322262
$956$	4.30954	0.139380
$957$	−1.67382	−0.0541070
$958$	0.812343	0.0262456
$959$	−3.63697	−0.117444
$960$	0.555385	0.0179250
$961$	−14.5488	−0.469317
$962$	10.8727	0.350550
$963$	44.7316	1.44145
$964$	−0.244143	−0.00786332
$965$	21.4012	0.688930
$966$	−0.234853	−0.00755626
$967$	2.70529	0.0869963	0.0434981	−	0.999054i	$-0.486150\pi$
$967$	2.70529	0.0869963	0.0434981	+	0.999054i	$0.486150\pi$
$968$	−2.22529	−0.0715236
$969$	0	0
$970$	−2.08203	−0.0668499
$971$	7.14238	0.229210	0.114605	−	0.993411i	$-0.463440\pi$
$971$	7.14238	0.229210	0.114605	+	0.993411i	$0.463440\pi$
$972$	4.20637	0.134919
$973$	13.3242	0.427156
$974$	7.47040	0.239367
$975$	−0.516605	−0.0165446
$976$	−29.5062	−0.944471
$977$	28.8990	0.924560	0.462280	−	0.886734i	$-0.347032\pi$
$977$	28.8990	0.924560	0.462280	+	0.886734i	$0.347032\pi$
$978$	−0.0153030	−0.000489337 0
$979$	−29.2030	−0.933332
$980$	8.12165	0.259436
$981$	15.5817	0.497484
$982$	−4.27392	−0.136386
$983$	−10.3410	−0.329827	−0.164914	−	0.986308i	$-0.552735\pi$
$983$	−10.3410	−0.329827	−0.164914	+	0.986308i	$0.552735\pi$
$984$	0.363782	0.0115970
$985$	1.36674	0.0435481
$986$	4.57280	0.145628
$987$	0.222371	0.00707814
$988$	0	0
$989$	−44.0262	−1.39995
$990$	−1.82330	−0.0579484
$991$	−31.6203	−1.00445	−0.502226	−	0.864736i	$-0.667486\pi$
$991$	−31.6203	−1.00445	−0.502226	+	0.864736i	$0.667486\pi$
$992$	9.96596	0.316419
$993$	1.24160	0.0394011
$994$	−3.71015	−0.117679
$995$	−17.9359	−0.568607
$996$	−1.78116	−0.0564384
$997$	7.87725	0.249475	0.124737	−	0.992190i	$-0.460191\pi$
$997$	7.87725	0.249475	0.124737	+	0.992190i	$0.460191\pi$
$998$	−0.124359	−0.00393653
$999$	−3.81649	−0.120748

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1805.2.a.s.1.6		9
5.4	even	2		9025.2.a.cf.1.4		9
19.3	odd	18		95.2.k.a.66.2	yes	18
19.13	odd	18		95.2.k.a.36.2	✓	18
19.18	odd	2		1805.2.a.v.1.4		9
57.32	even	18		855.2.bs.c.226.2		18
57.41	even	18		855.2.bs.c.541.2		18
95.3	even	36		475.2.u.b.199.4		36
95.13	even	36		475.2.u.b.74.3		36
95.22	even	36		475.2.u.b.199.3		36
95.32	even	36		475.2.u.b.74.4		36
95.79	odd	18		475.2.l.c.351.2		18
95.89	odd	18		475.2.l.c.226.2		18
95.94	odd	2		9025.2.a.cc.1.6		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.k.a.36.2	✓	18	19.13	odd	18
95.2.k.a.66.2	yes	18	19.3	odd	18
475.2.l.c.226.2		18	95.89	odd	18
475.2.l.c.351.2		18	95.79	odd	18
475.2.u.b.74.3		36	95.13	even	36
475.2.u.b.74.4		36	95.32	even	36
475.2.u.b.199.3		36	95.22	even	36
475.2.u.b.199.4		36	95.3	even	36
855.2.bs.c.226.2		18	57.32	even	18
855.2.bs.c.541.2		18	57.41	even	18
1805.2.a.s.1.6		9	1.1	even	1	trivial
1805.2.a.v.1.4		9	19.18	odd	2
9025.2.a.cc.1.6		9	95.94	odd	2
9025.2.a.cf.1.4		9	5.4	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:	\( N \)	\(=\)	\( 1805 = 5 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1805.a (trivial)

\(f(q)\)	\(=\)	\(q-0.210984 q^{2} -0.0798955 q^{3} -1.95549 q^{4} +1.00000 q^{5} +0.0168566 q^{6} -1.68723 q^{7} +0.834543 q^{8} -2.99362 q^{9} +O(q^{10})\)	\(q-0.210984 q^{2} -0.0798955 q^{3} -1.95549 q^{4} +1.00000 q^{5} +0.0168566 q^{6} -1.68723 q^{7} +0.834543 q^{8} -2.99362 q^{9} -0.210984 q^{10} -2.88678 q^{11} +0.156235 q^{12} +6.46601 q^{13} +0.355977 q^{14} -0.0798955 q^{15} +3.73490 q^{16} +2.98649 q^{17} +0.631604 q^{18} -1.95549 q^{20} +0.134802 q^{21} +0.609064 q^{22} +8.25754 q^{23} -0.0666762 q^{24} +1.00000 q^{25} -1.36422 q^{26} +0.478863 q^{27} +3.29935 q^{28} -7.25727 q^{29} +0.0168566 q^{30} -4.05600 q^{31} -2.45709 q^{32} +0.230641 q^{33} -0.630100 q^{34} -1.68723 q^{35} +5.85398 q^{36} -7.96989 q^{37} -0.516605 q^{39} +0.834543 q^{40} -5.45595 q^{41} -0.0284410 q^{42} -5.33164 q^{43} +5.64506 q^{44} -2.99362 q^{45} -1.74221 q^{46} +1.64961 q^{47} -0.298402 q^{48} -4.15326 q^{49} -0.210984 q^{50} -0.238607 q^{51} -12.6442 q^{52} -1.91194 q^{53} -0.101032 q^{54} -2.88678 q^{55} -1.40806 q^{56} +1.53116 q^{58} -3.55276 q^{59} +0.156235 q^{60} -7.90014 q^{61} +0.855750 q^{62} +5.05091 q^{63} -6.95139 q^{64} +6.46601 q^{65} -0.0486615 q^{66} -2.26533 q^{67} -5.84003 q^{68} -0.659740 q^{69} +0.355977 q^{70} -10.4224 q^{71} -2.49830 q^{72} +1.41186 q^{73} +1.68152 q^{74} -0.0798955 q^{75} +4.87066 q^{77} +0.108995 q^{78} +2.41076 q^{79} +3.73490 q^{80} +8.94259 q^{81} +1.15112 q^{82} -11.4006 q^{83} -0.263603 q^{84} +2.98649 q^{85} +1.12489 q^{86} +0.579823 q^{87} -2.40914 q^{88} +10.1161 q^{89} +0.631604 q^{90} -10.9096 q^{91} -16.1475 q^{92} +0.324057 q^{93} -0.348041 q^{94} +0.196310 q^{96} +9.86820 q^{97} +0.876270 q^{98} +8.64192 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 6 q^{2} - 9 q^{3} + 6 q^{4} + 9 q^{5} + 12 q^{6} - 6 q^{8} + 6 q^{9}+O(q^{10}) \) 9 * q - 6 * q^2 - 9 * q^3 + 6 * q^4 + 9 * q^5 + 12 * q^6 - 6 * q^8 + 6 * q^9	\( 9 q - 6 q^{2} - 9 q^{3} + 6 q^{4} + 9 q^{5} + 12 q^{6} - 6 q^{8} + 6 q^{9} - 6 q^{10} - 18 q^{12} - 9 q^{13} - 9 q^{15} + 12 q^{16} - 9 q^{17} - 24 q^{18} + 6 q^{20} - 12 q^{21} - 24 q^{22} - 12 q^{23} + 3 q^{24} + 9 q^{25} - 3 q^{26} - 24 q^{27} - 15 q^{28} - 9 q^{29} + 12 q^{30} - 18 q^{31} - 3 q^{32} + 9 q^{33} + 24 q^{34} + 18 q^{36} - 18 q^{37} + 18 q^{39} - 6 q^{40} - 6 q^{41} - 12 q^{43} + 48 q^{44} + 6 q^{45} + 9 q^{46} + 15 q^{47} + 21 q^{48} - 9 q^{49} - 6 q^{50} + 6 q^{51} - 33 q^{52} - 15 q^{53} + 63 q^{54} + 6 q^{58} - 21 q^{59} - 18 q^{60} - 12 q^{61} - 36 q^{62} + 21 q^{63} - 36 q^{64} - 9 q^{65} + 3 q^{66} - 60 q^{67} - 51 q^{68} + 15 q^{69} + 18 q^{71} + 27 q^{73} + 27 q^{74} - 9 q^{75} - 30 q^{77} + 6 q^{78} - 15 q^{79} + 12 q^{80} + 33 q^{81} + 24 q^{82} + 48 q^{84} - 9 q^{85} + 39 q^{86} + 15 q^{87} - 27 q^{88} + 39 q^{89} - 24 q^{90} - 21 q^{91} - 6 q^{92} + 15 q^{93} - 15 q^{94} - 33 q^{96} - 15 q^{97} + 15 q^{98} - 36 q^{99}+O(q^{100}) \) 9 * q - 6 * q^2 - 9 * q^3 + 6 * q^4 + 9 * q^5 + 12 * q^6 - 6 * q^8 + 6 * q^9 - 6 * q^10 - 18 * q^12 - 9 * q^13 - 9 * q^15 + 12 * q^16 - 9 * q^17 - 24 * q^18 + 6 * q^20 - 12 * q^21 - 24 * q^22 - 12 * q^23 + 3 * q^24 + 9 * q^25 - 3 * q^26 - 24 * q^27 - 15 * q^28 - 9 * q^29 + 12 * q^30 - 18 * q^31 - 3 * q^32 + 9 * q^33 + 24 * q^34 + 18 * q^36 - 18 * q^37 + 18 * q^39 - 6 * q^40 - 6 * q^41 - 12 * q^43 + 48 * q^44 + 6 * q^45 + 9 * q^46 + 15 * q^47 + 21 * q^48 - 9 * q^49 - 6 * q^50 + 6 * q^51 - 33 * q^52 - 15 * q^53 + 63 * q^54 + 6 * q^58 - 21 * q^59 - 18 * q^60 - 12 * q^61 - 36 * q^62 + 21 * q^63 - 36 * q^64 - 9 * q^65 + 3 * q^66 - 60 * q^67 - 51 * q^68 + 15 * q^69 + 18 * q^71 + 27 * q^73 + 27 * q^74 - 9 * q^75 - 30 * q^77 + 6 * q^78 - 15 * q^79 + 12 * q^80 + 33 * q^81 + 24 * q^82 + 48 * q^84 - 9 * q^85 + 39 * q^86 + 15 * q^87 - 27 * q^88 + 39 * q^89 - 24 * q^90 - 21 * q^91 - 6 * q^92 + 15 * q^93 - 15 * q^94 - 33 * q^96 - 15 * q^97 + 15 * q^98 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more