LMFDB - Embedded newform 418.2.a.d.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [418,2,Mod(1,418)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("418.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(418, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.a (trivial)

Newform invariants

comment:select newform

sage:traces = [2,-2,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	yes
Analytic conductor:	$3.33774680449$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{13}) $
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 3 $ x^2 - x - 3
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.30278$ of defining polynomial
Character	$\chi$	$=$	418.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} -3.30278 q^{3} +1.00000 q^{4} +1.30278 q^{5} +3.30278 q^{6} -2.30278 q^{7} -1.00000 q^{8} +7.90833 q^{9} -1.30278 q^{10} +1.00000 q^{11} -3.30278 q^{12} +0.302776 q^{13} +2.30278 q^{14} -4.30278 q^{15} +1.00000 q^{16} +2.60555 q^{17} -7.90833 q^{18} +1.00000 q^{19} +1.30278 q^{20} +7.60555 q^{21} -1.00000 q^{22} -8.60555 q^{23} +3.30278 q^{24} -3.30278 q^{25} -0.302776 q^{26} -16.2111 q^{27} -2.30278 q^{28} -4.69722 q^{29} +4.30278 q^{30} +0.302776 q^{31} -1.00000 q^{32} -3.30278 q^{33} -2.60555 q^{34} -3.00000 q^{35} +7.90833 q^{36} -9.21110 q^{37} -1.00000 q^{38} -1.00000 q^{39} -1.30278 q^{40} -6.90833 q^{41} -7.60555 q^{42} +11.9083 q^{43} +1.00000 q^{44} +10.3028 q^{45} +8.60555 q^{46} -6.00000 q^{47} -3.30278 q^{48} -1.69722 q^{49} +3.30278 q^{50} -8.60555 q^{51} +0.302776 q^{52} -3.39445 q^{53} +16.2111 q^{54} +1.30278 q^{55} +2.30278 q^{56} -3.30278 q^{57} +4.69722 q^{58} -4.30278 q^{60} -3.21110 q^{61} -0.302776 q^{62} -18.2111 q^{63} +1.00000 q^{64} +0.394449 q^{65} +3.30278 q^{66} +11.5139 q^{67} +2.60555 q^{68} +28.4222 q^{69} +3.00000 q^{70} -13.3028 q^{71} -7.90833 q^{72} +4.60555 q^{73} +9.21110 q^{74} +10.9083 q^{75} +1.00000 q^{76} -2.30278 q^{77} +1.00000 q^{78} -5.81665 q^{79} +1.30278 q^{80} +29.8167 q^{81} +6.90833 q^{82} +10.6972 q^{83} +7.60555 q^{84} +3.39445 q^{85} -11.9083 q^{86} +15.5139 q^{87} -1.00000 q^{88} -2.60555 q^{89} -10.3028 q^{90} -0.697224 q^{91} -8.60555 q^{92} -1.00000 q^{93} +6.00000 q^{94} +1.30278 q^{95} +3.30278 q^{96} +8.00000 q^{97} +1.69722 q^{98} +7.90833 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 3 q^{3} + 2 q^{4} - q^{5} + 3 q^{6} - q^{7} - 2 q^{8} + 5 q^{9} + q^{10} + 2 q^{11} - 3 q^{12} - 3 q^{13} + q^{14} - 5 q^{15} + 2 q^{16} - 2 q^{17} - 5 q^{18} + 2 q^{19} - q^{20} + 8 q^{21}+ \cdots + 5 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 - 3 * q^3 + 2 * q^4 - q^5 + 3 * q^6 - q^7 - 2 * q^8 + 5 * q^9 + q^10 + 2 * q^11 - 3 * q^12 - 3 * q^13 + q^14 - 5 * q^15 + 2 * q^16 - 2 * q^17 - 5 * q^18 + 2 * q^19 - q^20 + 8 * q^21 - 2 * q^22 - 10 * q^23 + 3 * q^24 - 3 * q^25 + 3 * q^26 - 18 * q^27 - q^28 - 13 * q^29 + 5 * q^30 - 3 * q^31 - 2 * q^32 - 3 * q^33 + 2 * q^34 - 6 * q^35 + 5 * q^36 - 4 * q^37 - 2 * q^38 - 2 * q^39 + q^40 - 3 * q^41 - 8 * q^42 + 13 * q^43 + 2 * q^44 + 17 * q^45 + 10 * q^46 - 12 * q^47 - 3 * q^48 - 7 * q^49 + 3 * q^50 - 10 * q^51 - 3 * q^52 - 14 * q^53 + 18 * q^54 - q^55 + q^56 - 3 * q^57 + 13 * q^58 - 5 * q^60 + 8 * q^61 + 3 * q^62 - 22 * q^63 + 2 * q^64 + 8 * q^65 + 3 * q^66 + 5 * q^67 - 2 * q^68 + 28 * q^69 + 6 * q^70 - 23 * q^71 - 5 * q^72 + 2 * q^73 + 4 * q^74 + 11 * q^75 + 2 * q^76 - q^77 + 2 * q^78 + 10 * q^79 - q^80 + 38 * q^81 + 3 * q^82 + 25 * q^83 + 8 * q^84 + 14 * q^85 - 13 * q^86 + 13 * q^87 - 2 * q^88 + 2 * q^89 - 17 * q^90 - 5 * q^91 - 10 * q^92 - 2 * q^93 + 12 * q^94 - q^95 + 3 * q^96 + 16 * q^97 + 7 * q^98 + 5 * q^99

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−3.30278	−1.90686	−0.953429	−	0.301617i	$-0.902474\pi$
$3$	−3.30278	−1.90686	−0.953429	+	0.301617i	$0.902474\pi$
$4$	1.00000	0.500000
$5$	1.30278	0.582619	0.291309	−	0.956629i	$-0.405909\pi$
$5$	1.30278	0.582619	0.291309	+	0.956629i	$0.405909\pi$
$6$	3.30278	1.34835
$7$	−2.30278	−0.870367	−0.435184	−	0.900342i	$-0.643317\pi$
$7$	−2.30278	−0.870367	−0.435184	+	0.900342i	$0.643317\pi$
$8$	−1.00000	−0.353553
$9$	7.90833	2.63611
$10$	−1.30278	−0.411974
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−3.30278	−0.953429
$13$	0.302776	0.0839749	0.0419874	−	0.999118i	$-0.486631\pi$
$13$	0.302776	0.0839749	0.0419874	+	0.999118i	$0.486631\pi$
$14$	2.30278	0.615443
$15$	−4.30278	−1.11097
$16$	1.00000	0.250000
$17$	2.60555	0.631939	0.315970	−	0.948769i	$-0.397670\pi$
$17$	2.60555	0.631939	0.315970	+	0.948769i	$0.397670\pi$
$18$	−7.90833	−1.86401
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	1.30278	0.291309
$21$	7.60555	1.65967
$22$	−1.00000	−0.213201
$23$	−8.60555	−1.79438	−0.897191	−	0.441643i	$-0.854396\pi$
$23$	−8.60555	−1.79438	−0.897191	+	0.441643i	$0.854396\pi$
$24$	3.30278	0.674176
$25$	−3.30278	−0.660555
$26$	−0.302776	−0.0593792
$27$	−16.2111	−3.11983
$28$	−2.30278	−0.435184
$29$	−4.69722	−0.872253	−0.436126	−	0.899885i	$-0.643650\pi$
$29$	−4.69722	−0.872253	−0.436126	+	0.899885i	$0.643650\pi$
$30$	4.30278	0.785576
$31$	0.302776	0.0543801	0.0271901	−	0.999630i	$-0.491344\pi$
$31$	0.302776	0.0543801	0.0271901	+	0.999630i	$0.491344\pi$
$32$	−1.00000	−0.176777
$33$	−3.30278	−0.574939
$34$	−2.60555	−0.446848
$35$	−3.00000	−0.507093
$36$	7.90833	1.31805
$37$	−9.21110	−1.51430	−0.757148	−	0.653243i	$-0.773408\pi$
$37$	−9.21110	−1.51430	−0.757148	+	0.653243i	$0.773408\pi$
$38$	−1.00000	−0.162221
$39$	−1.00000	−0.160128
$40$	−1.30278	−0.205987
$41$	−6.90833	−1.07890	−0.539450	−	0.842018i	$-0.681368\pi$
$41$	−6.90833	−1.07890	−0.539450	+	0.842018i	$0.681368\pi$
$42$	−7.60555	−1.17356
$43$	11.9083	1.81600	0.908001	−	0.418967i	$-0.137608\pi$
$43$	11.9083	1.81600	0.908001	+	0.418967i	$0.137608\pi$
$44$	1.00000	0.150756
$45$	10.3028	1.53585
$46$	8.60555	1.26882
$47$	−6.00000	−0.875190	−0.437595	−	0.899172i	$-0.644170\pi$
$47$	−6.00000	−0.875190	−0.437595	+	0.899172i	$0.644170\pi$
$48$	−3.30278	−0.476715
$49$	−1.69722	−0.242461
$50$	3.30278	0.467083
$51$	−8.60555	−1.20502
$52$	0.302776	0.0419874
$53$	−3.39445	−0.466263	−0.233132	−	0.972445i	$-0.574897\pi$
$53$	−3.39445	−0.466263	−0.233132	+	0.972445i	$0.574897\pi$
$54$	16.2111	2.20605
$55$	1.30278	0.175666
$56$	2.30278	0.307721
$57$	−3.30278	−0.437463
$58$	4.69722	0.616776
$59$	0	0		−	1.00000i	$-0.5\pi$
$59$	0	0			1.00000i	$0.5\pi$
$60$	−4.30278	−0.555486
$61$	−3.21110	−0.411140	−0.205570	−	0.978642i	$-0.565905\pi$
$61$	−3.21110	−0.411140	−0.205570	+	0.978642i	$0.565905\pi$
$62$	−0.302776	−0.0384525
$63$	−18.2111	−2.29438
$64$	1.00000	0.125000
$65$	0.394449	0.0489253
$66$	3.30278	0.406544
$67$	11.5139	1.40664	0.703322	−	0.710871i	$-0.251699\pi$
$67$	11.5139	1.40664	0.703322	+	0.710871i	$0.251699\pi$
$68$	2.60555	0.315970
$69$	28.4222	3.42163
$70$	3.00000	0.358569
$71$	−13.3028	−1.57875	−0.789375	−	0.613912i	$-0.789595\pi$
$71$	−13.3028	−1.57875	−0.789375	+	0.613912i	$0.789595\pi$
$72$	−7.90833	−0.932005
$73$	4.60555	0.539039	0.269520	−	0.962995i	$-0.413135\pi$
$73$	4.60555	0.539039	0.269520	+	0.962995i	$0.413135\pi$
$74$	9.21110	1.07077
$75$	10.9083	1.25959
$76$	1.00000	0.114708
$77$	−2.30278	−0.262426
$78$	1.00000	0.113228
$79$	−5.81665	−0.654425	−0.327212	−	0.944951i	$-0.606109\pi$
$79$	−5.81665	−0.654425	−0.327212	+	0.944951i	$0.606109\pi$
$80$	1.30278	0.145655
$81$	29.8167	3.31296
$82$	6.90833	0.762897
$83$	10.6972	1.17417	0.587086	−	0.809524i	$-0.300275\pi$
$83$	10.6972	1.17417	0.587086	+	0.809524i	$0.300275\pi$
$84$	7.60555	0.829834
$85$	3.39445	0.368180
$86$	−11.9083	−1.28411
$87$	15.5139	1.66326
$88$	−1.00000	−0.106600
$89$	−2.60555	−0.276188	−0.138094	−	0.990419i	$-0.544098\pi$
$89$	−2.60555	−0.276188	−0.138094	+	0.990419i	$0.544098\pi$
$90$	−10.3028	−1.08601
$91$	−0.697224	−0.0730890
$92$	−8.60555	−0.897191
$93$	−1.00000	−0.103695
$94$	6.00000	0.618853
$95$	1.30278	0.133662
$96$	3.30278	0.337088
$97$	8.00000	0.812277	0.406138	−	0.913812i	$-0.366875\pi$
$97$	8.00000	0.812277	0.406138	+	0.913812i	$0.366875\pi$
$98$	1.69722	0.171446
$99$	7.90833	0.794817
$100$	−3.30278	−0.330278
$101$	−13.8167	−1.37481	−0.687404	−	0.726275i	$-0.741250\pi$
$101$	−13.8167	−1.37481	−0.687404	+	0.726275i	$0.741250\pi$
$102$	8.60555	0.852077
$103$	−5.30278	−0.522498	−0.261249	−	0.965271i	$-0.584134\pi$
$103$	−5.30278	−0.522498	−0.261249	+	0.965271i	$0.584134\pi$
$104$	−0.302776	−0.0296896
$105$	9.90833	0.966954
$106$	3.39445	0.329698
$107$	−11.2111	−1.08382	−0.541909	−	0.840437i	$-0.682298\pi$
$107$	−11.2111	−1.08382	−0.541909	+	0.840437i	$0.682298\pi$
$108$	−16.2111	−1.55991
$109$	2.00000	0.191565	0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000	0.191565	0.0957826	+	0.995402i	$0.469465\pi$
$110$	−1.30278	−0.124215
$111$	30.4222	2.88755
$112$	−2.30278	−0.217592
$113$	0	0		−	1.00000i	$-0.5\pi$
$113$	0	0			1.00000i	$0.5\pi$
$114$	3.30278	0.309333
$115$	−11.2111	−1.04544
$116$	−4.69722	−0.436126
$117$	2.39445	0.221367
$118$	0	0
$119$	−6.00000	−0.550019
$120$	4.30278	0.392788
$121$	1.00000	0.0909091
$122$	3.21110	0.290720
$123$	22.8167	2.05731
$124$	0.302776	0.0271901
$125$	−10.8167	−0.967471
$126$	18.2111	1.62237
$127$	−12.6056	−1.11856	−0.559281	−	0.828978i	$-0.688923\pi$
$127$	−12.6056	−1.11856	−0.559281	+	0.828978i	$0.688923\pi$
$128$	−1.00000	−0.0883883
$129$	−39.3305	−3.46286
$130$	−0.394449	−0.0345954
$131$	−6.11943	−0.534657	−0.267329	−	0.963605i	$-0.586141\pi$
$131$	−6.11943	−0.534657	−0.267329	+	0.963605i	$0.586141\pi$
$132$	−3.30278	−0.287470
$133$	−2.30278	−0.199676
$134$	−11.5139	−0.994648
$135$	−21.1194	−1.81767
$136$	−2.60555	−0.223424
$137$	−21.5139	−1.83805	−0.919027	−	0.394194i	$-0.871024\pi$
$137$	−21.5139	−1.83805	−0.919027	+	0.394194i	$0.871024\pi$
$138$	−28.4222	−2.41946
$139$	−2.69722	−0.228776	−0.114388	−	0.993436i	$-0.536491\pi$
$139$	−2.69722	−0.228776	−0.114388	+	0.993436i	$0.536491\pi$
$140$	−3.00000	−0.253546
$141$	19.8167	1.66886
$142$	13.3028	1.11634
$143$	0.302776	0.0253194
$144$	7.90833	0.659027
$145$	−6.11943	−0.508191
$146$	−4.60555	−0.381158
$147$	5.60555	0.462338
$148$	−9.21110	−0.757148
$149$	0	0		−	1.00000i	$-0.5\pi$
$149$	0	0			1.00000i	$0.5\pi$
$150$	−10.9083	−0.890661
$151$	12.4222	1.01090	0.505452	−	0.862855i	$-0.331326\pi$
$151$	12.4222	1.01090	0.505452	+	0.862855i	$0.331326\pi$
$152$	−1.00000	−0.0811107
$153$	20.6056	1.66586
$154$	2.30278	0.185563
$155$	0.394449	0.0316829
$156$	−1.00000	−0.0800641
$157$	11.9083	0.950388	0.475194	−	0.879881i	$-0.342378\pi$
$157$	11.9083	0.950388	0.475194	+	0.879881i	$0.342378\pi$
$158$	5.81665	0.462748
$159$	11.2111	0.889098
$160$	−1.30278	−0.102993
$161$	19.8167	1.56177
$162$	−29.8167	−2.34262
$163$	−18.6056	−1.45730	−0.728650	−	0.684887i	$-0.759852\pi$
$163$	−18.6056	−1.45730	−0.728650	+	0.684887i	$0.759852\pi$
$164$	−6.90833	−0.539450
$165$	−4.30278	−0.334971
$166$	−10.6972	−0.830266
$167$	16.4222	1.27079	0.635394	−	0.772188i	$-0.280838\pi$
$167$	16.4222	1.27079	0.635394	+	0.772188i	$0.280838\pi$
$168$	−7.60555	−0.586781
$169$	−12.9083	−0.992948
$170$	−3.39445	−0.260342
$171$	7.90833	0.604765
$172$	11.9083	0.908001
$173$	20.3305	1.54570	0.772851	−	0.634588i	$-0.218830\pi$
$173$	20.3305	1.54570	0.772851	+	0.634588i	$0.218830\pi$
$174$	−15.5139	−1.17610
$175$	7.60555	0.574926
$176$	1.00000	0.0753778
$177$	0	0
$178$	2.60555	0.195294
$179$	12.1194	0.905849	0.452924	−	0.891549i	$-0.350381\pi$
$179$	12.1194	0.905849	0.452924	+	0.891549i	$0.350381\pi$
$180$	10.3028	0.767924
$181$	21.0278	1.56298	0.781490	−	0.623917i	$-0.214460\pi$
$181$	21.0278	1.56298	0.781490	+	0.623917i	$0.214460\pi$
$182$	0.697224	0.0516817
$183$	10.6056	0.783985
$184$	8.60555	0.634410
$185$	−12.0000	−0.882258
$186$	1.00000	0.0733236
$187$	2.60555	0.190537
$188$	−6.00000	−0.437595
$189$	37.3305	2.71540
$190$	−1.30278	−0.0945133
$191$	−6.00000	−0.434145	−0.217072	−	0.976156i	$-0.569651\pi$
$191$	−6.00000	−0.434145	−0.217072	+	0.976156i	$0.569651\pi$
$192$	−3.30278	−0.238357
$193$	7.72498	0.556056	0.278028	−	0.960573i	$-0.410319\pi$
$193$	7.72498	0.556056	0.278028	+	0.960573i	$0.410319\pi$
$194$	−8.00000	−0.574367
$195$	−1.30278	−0.0932937
$196$	−1.69722	−0.121230
$197$	−21.6333	−1.54131	−0.770655	−	0.637253i	$-0.780071\pi$
$197$	−21.6333	−1.54131	−0.770655	+	0.637253i	$0.780071\pi$
$198$	−7.90833	−0.562020
$199$	−23.8167	−1.68832	−0.844159	−	0.536093i	$-0.819900\pi$
$199$	−23.8167	−1.68832	−0.844159	+	0.536093i	$0.819900\pi$
$200$	3.30278	0.233542
$201$	−38.0278	−2.68227
$202$	13.8167	0.972136
$203$	10.8167	0.759180
$204$	−8.60555	−0.602509
$205$	−9.00000	−0.628587
$206$	5.30278	0.369462
$207$	−68.0555	−4.73019
$208$	0.302776	0.0209937
$209$	1.00000	0.0691714
$210$	−9.90833	−0.683740
$211$	17.3944	1.19748	0.598742	−	0.800942i	$-0.295668\pi$
$211$	17.3944	1.19748	0.598742	+	0.800942i	$0.295668\pi$
$212$	−3.39445	−0.233132
$213$	43.9361	3.01045
$214$	11.2111	0.766375
$215$	15.5139	1.05804
$216$	16.2111	1.10303
$217$	−0.697224	−0.0473307
$218$	−2.00000	−0.135457
$219$	−15.2111	−1.02787
$220$	1.30278	0.0878331
$221$	0.788897	0.0530670
$222$	−30.4222	−2.04180
$223$	−10.7889	−0.722478	−0.361239	−	0.932473i	$-0.617646\pi$
$223$	−10.7889	−0.722478	−0.361239	+	0.932473i	$0.617646\pi$
$224$	2.30278	0.153861
$225$	−26.1194	−1.74130
$226$	0	0
$227$	−19.8167	−1.31528	−0.657639	−	0.753333i	$-0.728445\pi$
$227$	−19.8167	−1.31528	−0.657639	+	0.753333i	$0.728445\pi$
$228$	−3.30278	−0.218732
$229$	1.09167	0.0721398	0.0360699	−	0.999349i	$-0.488516\pi$
$229$	1.09167	0.0721398	0.0360699	+	0.999349i	$0.488516\pi$
$230$	11.2111	0.739238
$231$	7.60555	0.500409
$232$	4.69722	0.308388
$233$	−5.21110	−0.341391	−0.170695	−	0.985324i	$-0.554601\pi$
$233$	−5.21110	−0.341391	−0.170695	+	0.985324i	$0.554601\pi$
$234$	−2.39445	−0.156530
$235$	−7.81665	−0.509902
$236$	0	0
$237$	19.2111	1.24790
$238$	6.00000	0.388922
$239$	22.9361	1.48361	0.741806	−	0.670615i	$-0.233970\pi$
$239$	22.9361	1.48361	0.741806	+	0.670615i	$0.233970\pi$
$240$	−4.30278	−0.277743
$241$	23.9083	1.54007	0.770035	−	0.638001i	$-0.220239\pi$
$241$	23.9083	1.54007	0.770035	+	0.638001i	$0.220239\pi$
$242$	−1.00000	−0.0642824
$243$	−49.8444	−3.19752
$244$	−3.21110	−0.205570
$245$	−2.21110	−0.141262
$246$	−22.8167	−1.45474
$247$	0.302776	0.0192652
$248$	−0.302776	−0.0192263
$249$	−35.3305	−2.23898
$250$	10.8167	0.684105
$251$	24.0000	1.51487	0.757433	−	0.652913i	$-0.226453\pi$
$251$	24.0000	1.51487	0.757433	+	0.652913i	$0.226453\pi$
$252$	−18.2111	−1.14719
$253$	−8.60555	−0.541026
$254$	12.6056	0.790943
$255$	−11.2111	−0.702066
$256$	1.00000	0.0625000
$257$	2.60555	0.162530	0.0812649	−	0.996693i	$-0.474104\pi$
$257$	2.60555	0.162530	0.0812649	+	0.996693i	$0.474104\pi$
$258$	39.3305	2.44861
$259$	21.2111	1.31799
$260$	0.394449	0.0244627
$261$	−37.1472	−2.29935
$262$	6.11943	0.378060
$263$	−16.6972	−1.02959	−0.514797	−	0.857312i	$-0.672133\pi$
$263$	−16.6972	−1.02959	−0.514797	+	0.857312i	$0.672133\pi$
$264$	3.30278	0.203272
$265$	−4.42221	−0.271654
$266$	2.30278	0.141192
$267$	8.60555	0.526651
$268$	11.5139	0.703322
$269$	1.81665	0.110763	0.0553817	−	0.998465i	$-0.482362\pi$
$269$	1.81665	0.110763	0.0553817	+	0.998465i	$0.482362\pi$
$270$	21.1194	1.28529
$271$	11.5139	0.699418	0.349709	−	0.936858i	$-0.386280\pi$
$271$	11.5139	0.699418	0.349709	+	0.936858i	$0.386280\pi$
$272$	2.60555	0.157985
$273$	2.30278	0.139370
$274$	21.5139	1.29970
$275$	−3.30278	−0.199165
$276$	28.4222	1.71082
$277$	−10.0000	−0.600842	−0.300421	−	0.953807i	$-0.597127\pi$
$277$	−10.0000	−0.600842	−0.300421	+	0.953807i	$0.597127\pi$
$278$	2.69722	0.161769
$279$	2.39445	0.143352
$280$	3.00000	0.179284
$281$	−18.5139	−1.10445	−0.552223	−	0.833697i	$-0.686220\pi$
$281$	−18.5139	−1.10445	−0.552223	+	0.833697i	$0.686220\pi$
$282$	−19.8167	−1.18006
$283$	27.9361	1.66063	0.830314	−	0.557296i	$-0.188161\pi$
$283$	27.9361	1.66063	0.830314	+	0.557296i	$0.188161\pi$
$284$	−13.3028	−0.789375
$285$	−4.30278	−0.254874
$286$	−0.302776	−0.0179035
$287$	15.9083	0.939039
$288$	−7.90833	−0.466003
$289$	−10.2111	−0.600653
$290$	6.11943	0.359345
$291$	−26.4222	−1.54890
$292$	4.60555	0.269520
$293$	28.5416	1.66742	0.833710	−	0.552202i	$-0.186212\pi$
$293$	28.5416	1.66742	0.833710	+	0.552202i	$0.186212\pi$
$294$	−5.60555	−0.326922
$295$	0	0
$296$	9.21110	0.535384
$297$	−16.2111	−0.940664
$298$	0	0
$299$	−2.60555	−0.150683
$300$	10.9083	0.629793
$301$	−27.4222	−1.58059
$302$	−12.4222	−0.714818
$303$	45.6333	2.62157
$304$	1.00000	0.0573539
$305$	−4.18335	−0.239538
$306$	−20.6056	−1.17794
$307$	−23.8167	−1.35929	−0.679644	−	0.733542i	$-0.737866\pi$
$307$	−23.8167	−1.35929	−0.679644	+	0.733542i	$0.737866\pi$
$308$	−2.30278	−0.131213
$309$	17.5139	0.996330
$310$	−0.394449	−0.0224032
$311$	4.18335	0.237216	0.118608	−	0.992941i	$-0.462157\pi$
$311$	4.18335	0.237216	0.118608	+	0.992941i	$0.462157\pi$
$312$	1.00000	0.0566139
$313$	−7.11943	−0.402414	−0.201207	−	0.979549i	$-0.564486\pi$
$313$	−7.11943	−0.402414	−0.201207	+	0.979549i	$0.564486\pi$
$314$	−11.9083	−0.672026
$315$	−23.7250	−1.33675
$316$	−5.81665	−0.327212
$317$	7.81665	0.439027	0.219514	−	0.975609i	$-0.429553\pi$
$317$	7.81665	0.439027	0.219514	+	0.975609i	$0.429553\pi$
$318$	−11.2111	−0.628687
$319$	−4.69722	−0.262994
$320$	1.30278	0.0728274
$321$	37.0278	2.06669
$322$	−19.8167	−1.10434
$323$	2.60555	0.144977
$324$	29.8167	1.65648
$325$	−1.00000	−0.0554700
$326$	18.6056	1.03047
$327$	−6.60555	−0.365288
$328$	6.90833	0.381449
$329$	13.8167	0.761737
$330$	4.30278	0.236860
$331$	−9.72498	−0.534533	−0.267267	−	0.963623i	$-0.586120\pi$
$331$	−9.72498	−0.534533	−0.267267	+	0.963623i	$0.586120\pi$
$332$	10.6972	0.587086
$333$	−72.8444	−3.99185
$334$	−16.4222	−0.898583
$335$	15.0000	0.819538
$336$	7.60555	0.414917
$337$	−5.69722	−0.310348	−0.155174	−	0.987887i	$-0.549594\pi$
$337$	−5.69722	−0.310348	−0.155174	+	0.987887i	$0.549594\pi$
$338$	12.9083	0.702120
$339$	0	0
$340$	3.39445	0.184090
$341$	0.302776	0.0163962
$342$	−7.90833	−0.427633
$343$	20.0278	1.08140
$344$	−11.9083	−0.642054
$345$	37.0278	1.99351
$346$	−20.3305	−1.09298
$347$	17.2111	0.923940	0.461970	−	0.886895i	$-0.347143\pi$
$347$	17.2111	0.923940	0.461970	+	0.886895i	$0.347143\pi$
$348$	15.5139	0.831631
$349$	3.57779	0.191515	0.0957575	−	0.995405i	$-0.469473\pi$
$349$	3.57779	0.191515	0.0957575	+	0.995405i	$0.469473\pi$
$350$	−7.60555	−0.406534
$351$	−4.90833	−0.261987
$352$	−1.00000	−0.0533002
$353$	−0.788897	−0.0419888	−0.0209944	−	0.999780i	$-0.506683\pi$
$353$	−0.788897	−0.0419888	−0.0209944	+	0.999780i	$0.506683\pi$
$354$	0	0
$355$	−17.3305	−0.919809
$356$	−2.60555	−0.138094
$357$	19.8167	1.04881
$358$	−12.1194	−0.640532
$359$	−27.5139	−1.45213	−0.726063	−	0.687628i	$-0.758652\pi$
$359$	−27.5139	−1.45213	−0.726063	+	0.687628i	$0.758652\pi$
$360$	−10.3028	−0.543004
$361$	1.00000	0.0526316
$362$	−21.0278	−1.10519
$363$	−3.30278	−0.173351
$364$	−0.697224	−0.0365445
$365$	6.00000	0.314054
$366$	−10.6056	−0.554361
$367$	7.21110	0.376416	0.188208	−	0.982129i	$-0.439732\pi$
$367$	7.21110	0.376416	0.188208	+	0.982129i	$0.439732\pi$
$368$	−8.60555	−0.448595
$369$	−54.6333	−2.84410
$370$	12.0000	0.623850
$371$	7.81665	0.405820
$372$	−1.00000	−0.0518476
$373$	17.9083	0.927258	0.463629	−	0.886029i	$-0.346547\pi$
$373$	17.9083	0.927258	0.463629	+	0.886029i	$0.346547\pi$
$374$	−2.60555	−0.134730
$375$	35.7250	1.84483
$376$	6.00000	0.309426
$377$	−1.42221	−0.0732473
$378$	−37.3305	−1.92008
$379$	−31.5139	−1.61876	−0.809380	−	0.587286i	$-0.800196\pi$
$379$	−31.5139	−1.61876	−0.809380	+	0.587286i	$0.800196\pi$
$380$	1.30278	0.0668310
$381$	41.6333	2.13294
$382$	6.00000	0.306987
$383$	21.5139	1.09931	0.549654	−	0.835392i	$-0.314760\pi$
$383$	21.5139	1.09931	0.549654	+	0.835392i	$0.314760\pi$
$384$	3.30278	0.168544
$385$	−3.00000	−0.152894
$386$	−7.72498	−0.393191
$387$	94.1749	4.78718
$388$	8.00000	0.406138
$389$	−19.5416	−0.990800	−0.495400	−	0.868665i	$-0.664979\pi$
$389$	−19.5416	−0.990800	−0.495400	+	0.868665i	$0.664979\pi$
$390$	1.30278	0.0659686
$391$	−22.4222	−1.13394
$392$	1.69722	0.0857228
$393$	20.2111	1.01952
$394$	21.6333	1.08987
$395$	−7.57779	−0.381280
$396$	7.90833	0.397408
$397$	35.7527	1.79438	0.897189	−	0.441646i	$-0.145605\pi$
$397$	35.7527	1.79438	0.897189	+	0.441646i	$0.145605\pi$
$398$	23.8167	1.19382
$399$	7.60555	0.380754
$400$	−3.30278	−0.165139
$401$	15.3944	0.768762	0.384381	−	0.923175i	$-0.374415\pi$
$401$	15.3944	0.768762	0.384381	+	0.923175i	$0.374415\pi$
$402$	38.0278	1.89665
$403$	0.0916731	0.00456656
$404$	−13.8167	−0.687404
$405$	38.8444	1.93019
$406$	−10.8167	−0.536822
$407$	−9.21110	−0.456577
$408$	8.60555	0.426038
$409$	−38.1472	−1.88626	−0.943128	−	0.332428i	$-0.892132\pi$
$409$	−38.1472	−1.88626	−0.943128	+	0.332428i	$0.892132\pi$
$410$	9.00000	0.444478
$411$	71.0555	3.50491
$412$	−5.30278	−0.261249
$413$	0	0
$414$	68.0555	3.34475
$415$	13.9361	0.684095
$416$	−0.302776	−0.0148448
$417$	8.90833	0.436243
$418$	−1.00000	−0.0489116
$419$	23.2111	1.13394	0.566968	−	0.823740i	$-0.308116\pi$
$419$	23.2111	1.13394	0.566968	+	0.823740i	$0.308116\pi$
$420$	9.90833	0.483477
$421$	20.2389	0.986382	0.493191	−	0.869921i	$-0.335830\pi$
$421$	20.2389	0.986382	0.493191	+	0.869921i	$0.335830\pi$
$422$	−17.3944	−0.846749
$423$	−47.4500	−2.30710
$424$	3.39445	0.164849
$425$	−8.60555	−0.417431
$426$	−43.9361	−2.12871
$427$	7.39445	0.357842
$428$	−11.2111	−0.541909
$429$	−1.00000	−0.0482805
$430$	−15.5139	−0.748146
$431$	17.2111	0.829030	0.414515	−	0.910043i	$-0.363951\pi$
$431$	17.2111	0.829030	0.414515	+	0.910043i	$0.363951\pi$
$432$	−16.2111	−0.779957
$433$	26.2389	1.26096	0.630480	−	0.776206i	$-0.282858\pi$
$433$	26.2389	1.26096	0.630480	+	0.776206i	$0.282858\pi$
$434$	0.697224	0.0334678
$435$	20.2111	0.969048
$436$	2.00000	0.0957826
$437$	−8.60555	−0.411659
$438$	15.2111	0.726815
$439$	−10.7889	−0.514926	−0.257463	−	0.966288i	$-0.582887\pi$
$439$	−10.7889	−0.514926	−0.257463	+	0.966288i	$0.582887\pi$
$440$	−1.30278	−0.0621074
$441$	−13.4222	−0.639153
$442$	−0.788897	−0.0375240
$443$	−3.63331	−0.172624	−0.0863118	−	0.996268i	$-0.527508\pi$
$443$	−3.63331	−0.172624	−0.0863118	+	0.996268i	$0.527508\pi$
$444$	30.4222	1.44377
$445$	−3.39445	−0.160912
$446$	10.7889	0.510869
$447$	0	0
$448$	−2.30278	−0.108796
$449$	−10.1833	−0.480582	−0.240291	−	0.970701i	$-0.577243\pi$
$449$	−10.1833	−0.480582	−0.240291	+	0.970701i	$0.577243\pi$
$450$	26.1194	1.23128
$451$	−6.90833	−0.325300
$452$	0	0
$453$	−41.0278	−1.92765
$454$	19.8167	0.930042
$455$	−0.908327	−0.0425830
$456$	3.30278	0.154667
$457$	0.183346	0.00857657	0.00428829	−	0.999991i	$-0.498635\pi$
$457$	0.183346	0.00857657	0.00428829	+	0.999991i	$0.498635\pi$
$458$	−1.09167	−0.0510105
$459$	−42.2389	−1.97154
$460$	−11.2111	−0.522720
$461$	−22.4222	−1.04431	−0.522153	−	0.852852i	$-0.674871\pi$
$461$	−22.4222	−1.04431	−0.522153	+	0.852852i	$0.674871\pi$
$462$	−7.60555	−0.353842
$463$	13.2111	0.613972	0.306986	−	0.951714i	$-0.400680\pi$
$463$	13.2111	0.613972	0.306986	+	0.951714i	$0.400680\pi$
$464$	−4.69722	−0.218063
$465$	−1.30278	−0.0604148
$466$	5.21110	0.241400
$467$	−15.3944	−0.712370	−0.356185	−	0.934415i	$-0.615923\pi$
$467$	−15.3944	−0.712370	−0.356185	+	0.934415i	$0.615923\pi$
$468$	2.39445	0.110683
$469$	−26.5139	−1.22430
$470$	7.81665	0.360555
$471$	−39.3305	−1.81226
$472$	0	0
$473$	11.9083	0.547545
$474$	−19.2111	−0.882395
$475$	−3.30278	−0.151542
$476$	−6.00000	−0.275010
$477$	−26.8444	−1.22912
$478$	−22.9361	−1.04907
$479$	3.27502	0.149639	0.0748197	−	0.997197i	$-0.476162\pi$
$479$	3.27502	0.149639	0.0748197	+	0.997197i	$0.476162\pi$
$480$	4.30278	0.196394
$481$	−2.78890	−0.127163
$482$	−23.9083	−1.08899
$483$	−65.4500	−2.97808
$484$	1.00000	0.0454545
$485$	10.4222	0.473248
$486$	49.8444	2.26099
$487$	10.3305	0.468121	0.234061	−	0.972222i	$-0.424799\pi$
$487$	10.3305	0.468121	0.234061	+	0.972222i	$0.424799\pi$
$488$	3.21110	0.145360
$489$	61.4500	2.77886
$490$	2.21110	0.0998874
$491$	31.9361	1.44126	0.720628	−	0.693322i	$-0.243854\pi$
$491$	31.9361	1.44126	0.720628	+	0.693322i	$0.243854\pi$
$492$	22.8167	1.02865
$493$	−12.2389	−0.551210
$494$	−0.302776	−0.0136225
$495$	10.3028	0.463075
$496$	0.302776	0.0135950
$497$	30.6333	1.37409
$498$	35.3305	1.58320
$499$	−34.0000	−1.52205	−0.761025	−	0.648723i	$-0.775303\pi$
$499$	−34.0000	−1.52205	−0.761025	+	0.648723i	$0.775303\pi$
$500$	−10.8167	−0.483735
$501$	−54.2389	−2.42321
$502$	−24.0000	−1.07117
$503$	−3.11943	−0.139088	−0.0695442	−	0.997579i	$-0.522155\pi$
$503$	−3.11943	−0.139088	−0.0695442	+	0.997579i	$0.522155\pi$
$504$	18.2111	0.811187
$505$	−18.0000	−0.800989
$506$	8.60555	0.382563
$507$	42.6333	1.89341
$508$	−12.6056	−0.559281
$509$	10.4222	0.461956	0.230978	−	0.972959i	$-0.425807\pi$
$509$	10.4222	0.461956	0.230978	+	0.972959i	$0.425807\pi$
$510$	11.2111	0.496436
$511$	−10.6056	−0.469162
$512$	−1.00000	−0.0441942
$513$	−16.2111	−0.715738
$514$	−2.60555	−0.114926
$515$	−6.90833	−0.304417
$516$	−39.3305	−1.73143
$517$	−6.00000	−0.263880
$518$	−21.2111	−0.931962
$519$	−67.1472	−2.94743
$520$	−0.394449	−0.0172977
$521$	7.57779	0.331989	0.165995	−	0.986127i	$-0.446917\pi$
$521$	7.57779	0.331989	0.165995	+	0.986127i	$0.446917\pi$
$522$	37.1472	1.62589
$523$	−17.0278	−0.744572	−0.372286	−	0.928118i	$-0.621426\pi$
$523$	−17.0278	−0.744572	−0.372286	+	0.928118i	$0.621426\pi$
$524$	−6.11943	−0.267329
$525$	−25.1194	−1.09630
$526$	16.6972	0.728034
$527$	0.788897	0.0343649
$528$	−3.30278	−0.143735
$529$	51.0555	2.21980
$530$	4.42221	0.192088
$531$	0	0
$532$	−2.30278	−0.0998380
$533$	−2.09167	−0.0906004
$534$	−8.60555	−0.372399
$535$	−14.6056	−0.631453
$536$	−11.5139	−0.497324
$537$	−40.0278	−1.72733
$538$	−1.81665	−0.0783215
$539$	−1.69722	−0.0731046
$540$	−21.1194	−0.908836
$541$	−17.8167	−0.765998	−0.382999	−	0.923749i	$-0.625109\pi$
$541$	−17.8167	−0.765998	−0.382999	+	0.923749i	$0.625109\pi$
$542$	−11.5139	−0.494563
$543$	−69.4500	−2.98038
$544$	−2.60555	−0.111712
$545$	2.60555	0.111610
$546$	−2.30278	−0.0985497
$547$	−4.00000	−0.171028	−0.0855138	−	0.996337i	$-0.527253\pi$
$547$	−4.00000	−0.171028	−0.0855138	+	0.996337i	$0.527253\pi$
$548$	−21.5139	−0.919027
$549$	−25.3944	−1.08381
$550$	3.30278	0.140831
$551$	−4.69722	−0.200108
$552$	−28.4222	−1.20973
$553$	13.3944	0.569590
$554$	10.0000	0.424859
$555$	39.6333	1.68234
$556$	−2.69722	−0.114388
$557$	15.6333	0.662405	0.331202	−	0.943560i	$-0.392546\pi$
$557$	15.6333	0.662405	0.331202	+	0.943560i	$0.392546\pi$
$558$	−2.39445	−0.101365
$559$	3.60555	0.152499
$560$	−3.00000	−0.126773
$561$	−8.60555	−0.363327
$562$	18.5139	0.780961
$563$	−21.6333	−0.911735	−0.455868	−	0.890048i	$-0.650671\pi$
$563$	−21.6333	−0.911735	−0.455868	+	0.890048i	$0.650671\pi$
$564$	19.8167	0.834432
$565$	0	0
$566$	−27.9361	−1.17424
$567$	−68.6611	−2.88349
$568$	13.3028	0.558172
$569$	44.7250	1.87497	0.937484	−	0.348027i	$-0.113148\pi$
$569$	44.7250	1.87497	0.937484	+	0.348027i	$0.113148\pi$
$570$	4.30278	0.180223
$571$	39.9361	1.67127	0.835637	−	0.549283i	$-0.185099\pi$
$571$	39.9361	1.67127	0.835637	+	0.549283i	$0.185099\pi$
$572$	0.302776	0.0126597
$573$	19.8167	0.827853
$574$	−15.9083	−0.664001
$575$	28.4222	1.18529
$576$	7.90833	0.329514
$577$	−28.9083	−1.20347	−0.601735	−	0.798696i	$-0.705524\pi$
$577$	−28.9083	−1.20347	−0.601735	+	0.798696i	$0.705524\pi$
$578$	10.2111	0.424726
$579$	−25.5139	−1.06032
$580$	−6.11943	−0.254095
$581$	−24.6333	−1.02196
$582$	26.4222	1.09524
$583$	−3.39445	−0.140584
$584$	−4.60555	−0.190579
$585$	3.11943	0.128973
$586$	−28.5416	−1.17904
$587$	12.0000	0.495293	0.247647	−	0.968850i	$-0.420343\pi$
$587$	12.0000	0.495293	0.247647	+	0.968850i	$0.420343\pi$
$588$	5.60555	0.231169
$589$	0.302776	0.0124757
$590$	0	0
$591$	71.4500	2.93906
$592$	−9.21110	−0.378574
$593$	−42.0000	−1.72473	−0.862367	−	0.506284i	$-0.831019\pi$
$593$	−42.0000	−1.72473	−0.862367	+	0.506284i	$0.831019\pi$
$594$	16.2111	0.665150
$595$	−7.81665	−0.320452
$596$	0	0
$597$	78.6611	3.21938
$598$	2.60555	0.106549
$599$	−45.1194	−1.84353	−0.921765	−	0.387749i	$-0.873253\pi$
$599$	−45.1194	−1.84353	−0.921765	+	0.387749i	$0.873253\pi$
$600$	−10.9083	−0.445331
$601$	14.9083	0.608123	0.304062	−	0.952652i	$-0.401657\pi$
$601$	14.9083	0.608123	0.304062	+	0.952652i	$0.401657\pi$
$602$	27.4222	1.11765
$603$	91.0555	3.70807
$604$	12.4222	0.505452
$605$	1.30278	0.0529654
$606$	−45.6333	−1.85373
$607$	−17.8167	−0.723156	−0.361578	−	0.932342i	$-0.617762\pi$
$607$	−17.8167	−0.723156	−0.361578	+	0.932342i	$0.617762\pi$
$608$	−1.00000	−0.0405554
$609$	−35.7250	−1.44765
$610$	4.18335	0.169379
$611$	−1.81665	−0.0734939
$612$	20.6056	0.832930
$613$	2.00000	0.0807792	0.0403896	−	0.999184i	$-0.487140\pi$
$613$	2.00000	0.0807792	0.0403896	+	0.999184i	$0.487140\pi$
$614$	23.8167	0.961162
$615$	29.7250	1.19863
$616$	2.30278	0.0927815
$617$	12.9083	0.519670	0.259835	−	0.965653i	$-0.416332\pi$
$617$	12.9083	0.519670	0.259835	+	0.965653i	$0.416332\pi$
$618$	−17.5139	−0.704512
$619$	22.8444	0.918194	0.459097	−	0.888386i	$-0.348173\pi$
$619$	22.8444	0.918194	0.459097	+	0.888386i	$0.348173\pi$
$620$	0.394449	0.0158414
$621$	139.505	5.59816
$622$	−4.18335	−0.167737
$623$	6.00000	0.240385
$624$	−1.00000	−0.0400320
$625$	2.42221	0.0968882
$626$	7.11943	0.284550
$627$	−3.30278	−0.131900
$628$	11.9083	0.475194
$629$	−24.0000	−0.956943
$630$	23.7250	0.945226
$631$	−8.97224	−0.357179	−0.178590	−	0.983924i	$-0.557153\pi$
$631$	−8.97224	−0.357179	−0.178590	+	0.983924i	$0.557153\pi$
$632$	5.81665	0.231374
$633$	−57.4500	−2.28343
$634$	−7.81665	−0.310439
$635$	−16.4222	−0.651695
$636$	11.2111	0.444549
$637$	−0.513878	−0.0203606
$638$	4.69722	0.185965
$639$	−105.203	−4.16175
$640$	−1.30278	−0.0514967
$641$	−30.2389	−1.19436	−0.597182	−	0.802106i	$-0.703713\pi$
$641$	−30.2389	−1.19436	−0.597182	+	0.802106i	$0.703713\pi$
$642$	−37.0278	−1.46137
$643$	−2.42221	−0.0955224	−0.0477612	−	0.998859i	$-0.515209\pi$
$643$	−2.42221	−0.0955224	−0.0477612	+	0.998859i	$0.515209\pi$
$644$	19.8167	0.780886
$645$	−51.2389	−2.01753
$646$	−2.60555	−0.102514
$647$	4.18335	0.164464	0.0822322	−	0.996613i	$-0.473795\pi$
$647$	4.18335	0.164464	0.0822322	+	0.996613i	$0.473795\pi$
$648$	−29.8167	−1.17131
$649$	0	0
$650$	1.00000	0.0392232
$651$	2.30278	0.0902529
$652$	−18.6056	−0.728650
$653$	−17.3305	−0.678196	−0.339098	−	0.940751i	$-0.610122\pi$
$653$	−17.3305	−0.678196	−0.339098	+	0.940751i	$0.610122\pi$
$654$	6.60555	0.258297
$655$	−7.97224	−0.311501
$656$	−6.90833	−0.269725
$657$	36.4222	1.42097
$658$	−13.8167	−0.538629
$659$	−7.02776	−0.273763	−0.136881	−	0.990587i	$-0.543708\pi$
$659$	−7.02776	−0.273763	−0.136881	+	0.990587i	$0.543708\pi$
$660$	−4.30278	−0.167485
$661$	−19.6333	−0.763647	−0.381824	−	0.924235i	$-0.624704\pi$
$661$	−19.6333	−0.763647	−0.381824	+	0.924235i	$0.624704\pi$
$662$	9.72498	0.377972
$663$	−2.60555	−0.101191
$664$	−10.6972	−0.415133
$665$	−3.00000	−0.116335
$666$	72.8444	2.82266
$667$	40.4222	1.56515
$668$	16.4222	0.635394
$669$	35.6333	1.37766
$670$	−15.0000	−0.579501
$671$	−3.21110	−0.123963
$672$	−7.60555	−0.293391
$673$	−2.30278	−0.0887655	−0.0443827	−	0.999015i	$-0.514132\pi$
$673$	−2.30278	−0.0887655	−0.0443827	+	0.999015i	$0.514132\pi$
$674$	5.69722	0.219449
$675$	53.5416	2.06082
$676$	−12.9083	−0.496474
$677$	−4.69722	−0.180529	−0.0902645	−	0.995918i	$-0.528771\pi$
$677$	−4.69722	−0.180529	−0.0902645	+	0.995918i	$0.528771\pi$
$678$	0	0
$679$	−18.4222	−0.706979
$680$	−3.39445	−0.130171
$681$	65.4500	2.50805
$682$	−0.302776	−0.0115939
$683$	−46.4222	−1.77630	−0.888148	−	0.459557i	$-0.848008\pi$
$683$	−46.4222	−1.77630	−0.888148	+	0.459557i	$0.848008\pi$
$684$	7.90833	0.302382
$685$	−28.0278	−1.07089
$686$	−20.0278	−0.764663
$687$	−3.60555	−0.137560
$688$	11.9083	0.454001
$689$	−1.02776	−0.0391544
$690$	−37.0278	−1.40962
$691$	3.57779	0.136106	0.0680529	−	0.997682i	$-0.478321\pi$
$691$	3.57779	0.136106	0.0680529	+	0.997682i	$0.478321\pi$
$692$	20.3305	0.772851
$693$	−18.2111	−0.691783
$694$	−17.2111	−0.653325
$695$	−3.51388	−0.133289
$696$	−15.5139	−0.588052
$697$	−18.0000	−0.681799
$698$	−3.57779	−0.135422
$699$	17.2111	0.650984
$700$	7.60555	0.287463
$701$	15.6333	0.590462	0.295231	−	0.955426i	$-0.404603\pi$
$701$	15.6333	0.590462	0.295231	+	0.955426i	$0.404603\pi$
$702$	4.90833	0.185253
$703$	−9.21110	−0.347403
$704$	1.00000	0.0376889
$705$	25.8167	0.972311
$706$	0.788897	0.0296905
$707$	31.8167	1.19659
$708$	0	0
$709$	18.3028	0.687375	0.343688	−	0.939084i	$-0.388324\pi$
$709$	18.3028	0.687375	0.343688	+	0.939084i	$0.388324\pi$
$710$	17.3305	0.650403
$711$	−46.0000	−1.72513
$712$	2.60555	0.0976472
$713$	−2.60555	−0.0975787
$714$	−19.8167	−0.741620
$715$	0.394449	0.0147515
$716$	12.1194	0.452924
$717$	−75.7527	−2.82904
$718$	27.5139	1.02681
$719$	−4.18335	−0.156012	−0.0780062	−	0.996953i	$-0.524855\pi$
$719$	−4.18335	−0.156012	−0.0780062	+	0.996953i	$0.524855\pi$
$720$	10.3028	0.383962
$721$	12.2111	0.454765
$722$	−1.00000	−0.0372161
$723$	−78.9638	−2.93670
$724$	21.0278	0.781490
$725$	15.5139	0.576171
$726$	3.30278	0.122578
$727$	−43.6333	−1.61827	−0.809135	−	0.587623i	$-0.800064\pi$
$727$	−43.6333	−1.61827	−0.809135	+	0.587623i	$0.800064\pi$
$728$	0.697224	0.0258409
$729$	75.1749	2.78426
$730$	−6.00000	−0.222070
$731$	31.0278	1.14760
$732$	10.6056	0.391992
$733$	7.21110	0.266348	0.133174	−	0.991093i	$-0.457483\pi$
$733$	7.21110	0.266348	0.133174	+	0.991093i	$0.457483\pi$
$734$	−7.21110	−0.266167
$735$	7.30278	0.269367
$736$	8.60555	0.317205
$737$	11.5139	0.424119
$738$	54.6333	2.01108
$739$	35.3583	1.30068	0.650338	−	0.759645i	$-0.274627\pi$
$739$	35.3583	1.30068	0.650338	+	0.759645i	$0.274627\pi$
$740$	−12.0000	−0.441129
$741$	−1.00000	−0.0367359
$742$	−7.81665	−0.286958
$743$	45.6333	1.67412	0.837062	−	0.547108i	$-0.184271\pi$
$743$	45.6333	1.67412	0.837062	+	0.547108i	$0.184271\pi$
$744$	1.00000	0.0366618
$745$	0	0
$746$	−17.9083	−0.655670
$747$	84.5971	3.09525
$748$	2.60555	0.0952684
$749$	25.8167	0.943320
$750$	−35.7250	−1.30449
$751$	16.8444	0.614661	0.307331	−	0.951603i	$-0.400564\pi$
$751$	16.8444	0.614661	0.307331	+	0.951603i	$0.400564\pi$
$752$	−6.00000	−0.218797
$753$	−79.2666	−2.88864
$754$	1.42221	0.0517937
$755$	16.1833	0.588972
$756$	37.3305	1.35770
$757$	−23.5416	−0.855635	−0.427818	−	0.903865i	$-0.640717\pi$
$757$	−23.5416	−0.855635	−0.427818	+	0.903865i	$0.640717\pi$
$758$	31.5139	1.14464
$759$	28.4222	1.03166
$760$	−1.30278	−0.0472566
$761$	−30.2389	−1.09616	−0.548079	−	0.836427i	$-0.684641\pi$
$761$	−30.2389	−1.09616	−0.548079	+	0.836427i	$0.684641\pi$
$762$	−41.6333	−1.50822
$763$	−4.60555	−0.166732
$764$	−6.00000	−0.217072
$765$	26.8444	0.970562
$766$	−21.5139	−0.777328
$767$	0	0
$768$	−3.30278	−0.119179
$769$	5.63331	0.203142	0.101571	−	0.994828i	$-0.467613\pi$
$769$	5.63331	0.203142	0.101571	+	0.994828i	$0.467613\pi$
$770$	3.00000	0.108112
$771$	−8.60555	−0.309921
$772$	7.72498	0.278028
$773$	19.5778	0.704164	0.352082	−	0.935969i	$-0.385474\pi$
$773$	19.5778	0.704164	0.352082	+	0.935969i	$0.385474\pi$
$774$	−94.1749	−3.38505
$775$	−1.00000	−0.0359211
$776$	−8.00000	−0.287183
$777$	−70.0555	−2.51323
$778$	19.5416	0.700602
$779$	−6.90833	−0.247516
$780$	−1.30278	−0.0466469
$781$	−13.3028	−0.476011
$782$	22.4222	0.801816
$783$	76.1472	2.72128
$784$	−1.69722	−0.0606152
$785$	15.5139	0.553714
$786$	−20.2111	−0.720906
$787$	21.0278	0.749559	0.374779	−	0.927114i	$-0.377718\pi$
$787$	21.0278	0.749559	0.374779	+	0.927114i	$0.377718\pi$
$788$	−21.6333	−0.770655
$789$	55.1472	1.96329
$790$	7.57779	0.269606
$791$	0	0
$792$	−7.90833	−0.281010
$793$	−0.972244	−0.0345254
$794$	−35.7527	−1.26882
$795$	14.6056	0.518006
$796$	−23.8167	−0.844159
$797$	9.39445	0.332768	0.166384	−	0.986061i	$-0.446791\pi$
$797$	9.39445	0.332768	0.166384	+	0.986061i	$0.446791\pi$
$798$	−7.60555	−0.269234
$799$	−15.6333	−0.553067
$800$	3.30278	0.116771
$801$	−20.6056	−0.728061
$802$	−15.3944	−0.543597
$803$	4.60555	0.162526
$804$	−38.0278	−1.34114
$805$	25.8167	0.909917
$806$	−0.0916731	−0.00322905
$807$	−6.00000	−0.211210
$808$	13.8167	0.486068
$809$	18.7889	0.660582	0.330291	−	0.943879i	$-0.392853\pi$
$809$	18.7889	0.660582	0.330291	+	0.943879i	$0.392853\pi$
$810$	−38.8444	−1.36485
$811$	−13.6333	−0.478730	−0.239365	−	0.970930i	$-0.576939\pi$
$811$	−13.6333	−0.478730	−0.239365	+	0.970930i	$0.576939\pi$
$812$	10.8167	0.379590
$813$	−38.0278	−1.33369
$814$	9.21110	0.322849
$815$	−24.2389	−0.849050
$816$	−8.60555	−0.301255
$817$	11.9083	0.416620
$818$	38.1472	1.33379
$819$	−5.51388	−0.192670
$820$	−9.00000	−0.314294
$821$	−27.3944	−0.956073	−0.478036	−	0.878340i	$-0.658651\pi$
$821$	−27.3944	−0.956073	−0.478036	+	0.878340i	$0.658651\pi$
$822$	−71.0555	−2.47835
$823$	32.0000	1.11545	0.557725	−	0.830026i	$-0.311674\pi$
$823$	32.0000	1.11545	0.557725	+	0.830026i	$0.311674\pi$
$824$	5.30278	0.184731
$825$	10.9083	0.379779
$826$	0	0
$827$	−50.0555	−1.74060	−0.870300	−	0.492521i	$-0.836075\pi$
$827$	−50.0555	−1.74060	−0.870300	+	0.492521i	$0.836075\pi$
$828$	−68.0555	−2.36509
$829$	−56.4222	−1.95962	−0.979812	−	0.199921i	$-0.935932\pi$
$829$	−56.4222	−1.95962	−0.979812	+	0.199921i	$0.935932\pi$
$830$	−13.9361	−0.483729
$831$	33.0278	1.14572
$832$	0.302776	0.0104969
$833$	−4.42221	−0.153220
$834$	−8.90833	−0.308470
$835$	21.3944	0.740385
$836$	1.00000	0.0345857
$837$	−4.90833	−0.169657
$838$	−23.2111	−0.801814
$839$	45.1194	1.55770	0.778848	−	0.627213i	$-0.215804\pi$
$839$	45.1194	1.55770	0.778848	+	0.627213i	$0.215804\pi$
$840$	−9.90833	−0.341870
$841$	−6.93608	−0.239175
$842$	−20.2389	−0.697477
$843$	61.1472	2.10602
$844$	17.3944	0.598742
$845$	−16.8167	−0.578510
$846$	47.4500	1.63136
$847$	−2.30278	−0.0791243
$848$	−3.39445	−0.116566
$849$	−92.2666	−3.16658
$850$	8.60555	0.295168
$851$	79.2666	2.71722
$852$	43.9361	1.50523
$853$	−17.5778	−0.601852	−0.300926	−	0.953647i	$-0.597296\pi$
$853$	−17.5778	−0.601852	−0.300926	+	0.953647i	$0.597296\pi$
$854$	−7.39445	−0.253033
$855$	10.3028	0.352347
$856$	11.2111	0.383188
$857$	10.5416	0.360095	0.180048	−	0.983658i	$-0.442375\pi$
$857$	10.5416	0.360095	0.180048	+	0.983658i	$0.442375\pi$
$858$	1.00000	0.0341394
$859$	−48.8444	−1.66655	−0.833275	−	0.552859i	$-0.813537\pi$
$859$	−48.8444	−1.66655	−0.833275	+	0.552859i	$0.813537\pi$
$860$	15.5139	0.529019
$861$	−52.5416	−1.79061
$862$	−17.2111	−0.586212
$863$	14.7250	0.501244	0.250622	−	0.968085i	$-0.419365\pi$
$863$	14.7250	0.501244	0.250622	+	0.968085i	$0.419365\pi$
$864$	16.2111	0.551513
$865$	26.4861	0.900555
$866$	−26.2389	−0.891633
$867$	33.7250	1.14536
$868$	−0.697224	−0.0236653
$869$	−5.81665	−0.197316
$870$	−20.2111	−0.685221
$871$	3.48612	0.118123
$872$	−2.00000	−0.0677285
$873$	63.2666	2.14125
$874$	8.60555	0.291087
$875$	24.9083	0.842055
$876$	−15.2111	−0.513936
$877$	−42.5694	−1.43747	−0.718733	−	0.695286i	$-0.755278\pi$
$877$	−42.5694	−1.43747	−0.718733	+	0.695286i	$0.755278\pi$
$878$	10.7889	0.364108
$879$	−94.2666	−3.17953
$880$	1.30278	0.0439166
$881$	−23.0917	−0.777978	−0.388989	−	0.921242i	$-0.627176\pi$
$881$	−23.0917	−0.777978	−0.388989	+	0.921242i	$0.627176\pi$
$882$	13.4222	0.451949
$883$	−2.97224	−0.100024	−0.0500120	−	0.998749i	$-0.515926\pi$
$883$	−2.97224	−0.100024	−0.0500120	+	0.998749i	$0.515926\pi$
$884$	0.788897	0.0265335
$885$	0	0
$886$	3.63331	0.122063
$887$	−32.8444	−1.10281	−0.551404	−	0.834239i	$-0.685908\pi$
$887$	−32.8444	−1.10281	−0.551404	+	0.834239i	$0.685908\pi$
$888$	−30.4222	−1.02090
$889$	29.0278	0.973560
$890$	3.39445	0.113782
$891$	29.8167	0.998895
$892$	−10.7889	−0.361239
$893$	−6.00000	−0.200782
$894$	0	0
$895$	15.7889	0.527765
$896$	2.30278	0.0769303
$897$	8.60555	0.287331
$898$	10.1833	0.339823
$899$	−1.42221	−0.0474332
$900$	−26.1194	−0.870648
$901$	−8.84441	−0.294650
$902$	6.90833	0.230022
$903$	90.5694	3.01396
$904$	0	0
$905$	27.3944	0.910622
$906$	41.0278	1.36306
$907$	52.8444	1.75467	0.877335	−	0.479879i	$-0.159319\pi$
$907$	52.8444	1.75467	0.877335	+	0.479879i	$0.159319\pi$
$908$	−19.8167	−0.657639
$909$	−109.267	−3.62414
$910$	0.908327	0.0301107
$911$	−15.6333	−0.517955	−0.258977	−	0.965883i	$-0.583385\pi$
$911$	−15.6333	−0.517955	−0.258977	+	0.965883i	$0.583385\pi$
$912$	−3.30278	−0.109366
$913$	10.6972	0.354026
$914$	−0.183346	−0.00606455
$915$	13.8167	0.456764
$916$	1.09167	0.0360699
$917$	14.0917	0.465348
$918$	42.2389	1.39409
$919$	−19.1194	−0.630692	−0.315346	−	0.948977i	$-0.602121\pi$
$919$	−19.1194	−0.630692	−0.315346	+	0.948977i	$0.602121\pi$
$920$	11.2111	0.369619
$921$	78.6611	2.59197
$922$	22.4222	0.738436
$923$	−4.02776	−0.132575
$924$	7.60555	0.250204
$925$	30.4222	1.00028
$926$	−13.2111	−0.434144
$927$	−41.9361	−1.37736
$928$	4.69722	0.154194
$929$	9.51388	0.312140	0.156070	−	0.987746i	$-0.450117\pi$
$929$	9.51388	0.312140	0.156070	+	0.987746i	$0.450117\pi$
$930$	1.30278	0.0427197
$931$	−1.69722	−0.0556243
$932$	−5.21110	−0.170695
$933$	−13.8167	−0.452337
$934$	15.3944	0.503722
$935$	3.39445	0.111010
$936$	−2.39445	−0.0782650
$937$	58.8444	1.92236	0.961182	−	0.275917i	$-0.0889814\pi$
$937$	58.8444	1.92236	0.961182	+	0.275917i	$0.0889814\pi$
$938$	26.5139	0.865709
$939$	23.5139	0.767346
$940$	−7.81665	−0.254951
$941$	−14.3667	−0.468341	−0.234170	−	0.972196i	$-0.575237\pi$
$941$	−14.3667	−0.468341	−0.234170	+	0.972196i	$0.575237\pi$
$942$	39.3305	1.28146
$943$	59.4500	1.93596
$944$	0	0
$945$	48.6333	1.58204
$946$	−11.9083	−0.387173
$947$	4.18335	0.135940	0.0679702	−	0.997687i	$-0.478348\pi$
$947$	4.18335	0.135940	0.0679702	+	0.997687i	$0.478348\pi$
$948$	19.2111	0.623948
$949$	1.39445	0.0452657
$950$	3.30278	0.107156
$951$	−25.8167	−0.837162
$952$	6.00000	0.194461
$953$	21.6333	0.700772	0.350386	−	0.936605i	$-0.386050\pi$
$953$	21.6333	0.700772	0.350386	+	0.936605i	$0.386050\pi$
$954$	26.8444	0.869120
$955$	−7.81665	−0.252941
$956$	22.9361	0.741806
$957$	15.5139	0.501492
$958$	−3.27502	−0.105811
$959$	49.5416	1.59978
$960$	−4.30278	−0.138871
$961$	−30.9083	−0.997043
$962$	2.78890	0.0899177
$963$	−88.6611	−2.85706
$964$	23.9083	0.770035
$965$	10.0639	0.323969
$966$	65.4500	2.10582
$967$	−19.6333	−0.631365	−0.315682	−	0.948865i	$-0.602233\pi$
$967$	−19.6333	−0.631365	−0.315682	+	0.948865i	$0.602233\pi$
$968$	−1.00000	−0.0321412
$969$	−8.60555	−0.276450
$970$	−10.4222	−0.334637
$971$	22.9361	0.736054	0.368027	−	0.929815i	$-0.380033\pi$
$971$	22.9361	0.736054	0.368027	+	0.929815i	$0.380033\pi$
$972$	−49.8444	−1.59876
$973$	6.21110	0.199119
$974$	−10.3305	−0.331012
$975$	3.30278	0.105773
$976$	−3.21110	−0.102785
$977$	−15.6333	−0.500154	−0.250077	−	0.968226i	$-0.580456\pi$
$977$	−15.6333	−0.500154	−0.250077	+	0.968226i	$0.580456\pi$
$978$	−61.4500	−1.96495
$979$	−2.60555	−0.0832738
$980$	−2.21110	−0.0706311
$981$	15.8167	0.504987
$982$	−31.9361	−1.01912
$983$	19.6972	0.628244	0.314122	−	0.949383i	$-0.398290\pi$
$983$	19.6972	0.628244	0.314122	+	0.949383i	$0.398290\pi$
$984$	−22.8167	−0.727368
$985$	−28.1833	−0.897996
$986$	12.2389	0.389765
$987$	−45.6333	−1.45252
$988$	0.302776	0.00963258
$989$	−102.478	−3.25860
$990$	−10.3028	−0.327444
$991$	−15.0917	−0.479403	−0.239701	−	0.970847i	$-0.577050\pi$
$991$	−15.0917	−0.479403	−0.239701	+	0.970847i	$0.577050\pi$
$992$	−0.302776	−0.00961314
$993$	32.1194	1.01928
$994$	−30.6333	−0.971630
$995$	−31.0278	−0.983646
$996$	−35.3305	−1.11949
$997$	21.8167	0.690940	0.345470	−	0.938430i	$-0.387719\pi$
$997$	21.8167	0.690940	0.345470	+	0.938430i	$0.387719\pi$
$998$	34.0000	1.07625
$999$	149.322	4.72434

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.a.d.1.1	✓	2
3.2	odd	2		3762.2.a.bb.1.1		2
4.3	odd	2		3344.2.a.o.1.2		2
11.10	odd	2		4598.2.a.bc.1.1		2
19.18	odd	2		7942.2.a.bb.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.a.d.1.1	✓	2	1.1	even	1	trivial
3344.2.a.o.1.2		2	4.3	odd	2
3762.2.a.bb.1.1		2	3.2	odd	2
4598.2.a.bc.1.1		2	11.10	odd	2
7942.2.a.bb.1.2		2	19.18	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.30278 q^{3} +1.00000 q^{4} +1.30278 q^{5} +3.30278 q^{6} -2.30278 q^{7} -1.00000 q^{8} +7.90833 q^{9} -1.30278 q^{10} +1.00000 q^{11} -3.30278 q^{12} +0.302776 q^{13} +2.30278 q^{14} -4.30278 q^{15} +1.00000 q^{16} +2.60555 q^{17} -7.90833 q^{18} +1.00000 q^{19} +1.30278 q^{20} +7.60555 q^{21} -1.00000 q^{22} -8.60555 q^{23} +3.30278 q^{24} -3.30278 q^{25} -0.302776 q^{26} -16.2111 q^{27} -2.30278 q^{28} -4.69722 q^{29} +4.30278 q^{30} +0.302776 q^{31} -1.00000 q^{32} -3.30278 q^{33} -2.60555 q^{34} -3.00000 q^{35} +7.90833 q^{36} -9.21110 q^{37} -1.00000 q^{38} -1.00000 q^{39} -1.30278 q^{40} -6.90833 q^{41} -7.60555 q^{42} +11.9083 q^{43} +1.00000 q^{44} +10.3028 q^{45} +8.60555 q^{46} -6.00000 q^{47} -3.30278 q^{48} -1.69722 q^{49} +3.30278 q^{50} -8.60555 q^{51} +0.302776 q^{52} -3.39445 q^{53} +16.2111 q^{54} +1.30278 q^{55} +2.30278 q^{56} -3.30278 q^{57} +4.69722 q^{58} -4.30278 q^{60} -3.21110 q^{61} -0.302776 q^{62} -18.2111 q^{63} +1.00000 q^{64} +0.394449 q^{65} +3.30278 q^{66} +11.5139 q^{67} +2.60555 q^{68} +28.4222 q^{69} +3.00000 q^{70} -13.3028 q^{71} -7.90833 q^{72} +4.60555 q^{73} +9.21110 q^{74} +10.9083 q^{75} +1.00000 q^{76} -2.30278 q^{77} +1.00000 q^{78} -5.81665 q^{79} +1.30278 q^{80} +29.8167 q^{81} +6.90833 q^{82} +10.6972 q^{83} +7.60555 q^{84} +3.39445 q^{85} -11.9083 q^{86} +15.5139 q^{87} -1.00000 q^{88} -2.60555 q^{89} -10.3028 q^{90} -0.697224 q^{91} -8.60555 q^{92} -1.00000 q^{93} +6.00000 q^{94} +1.30278 q^{95} +3.30278 q^{96} +8.00000 q^{97} +1.69722 q^{98} +7.90833 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 3 q^{3} + 2 q^{4} - q^{5} + 3 q^{6} - q^{7} - 2 q^{8} + 5 q^{9} + q^{10} + 2 q^{11} - 3 q^{12} - 3 q^{13} + q^{14} - 5 q^{15} + 2 q^{16} - 2 q^{17} - 5 q^{18} + 2 q^{19} - q^{20} + 8 q^{21}+ \cdots + 5 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - 3 * q^3 + 2 * q^4 - q^5 + 3 * q^6 - q^7 - 2 * q^8 + 5 * q^9 + q^10 + 2 * q^11 - 3 * q^12 - 3 * q^13 + q^14 - 5 * q^15 + 2 * q^16 - 2 * q^17 - 5 * q^18 + 2 * q^19 - q^20 + 8 * q^21 - 2 * q^22 - 10 * q^23 + 3 * q^24 - 3 * q^25 + 3 * q^26 - 18 * q^27 - q^28 - 13 * q^29 + 5 * q^30 - 3 * q^31 - 2 * q^32 - 3 * q^33 + 2 * q^34 - 6 * q^35 + 5 * q^36 - 4 * q^37 - 2 * q^38 - 2 * q^39 + q^40 - 3 * q^41 - 8 * q^42 + 13 * q^43 + 2 * q^44 + 17 * q^45 + 10 * q^46 - 12 * q^47 - 3 * q^48 - 7 * q^49 + 3 * q^50 - 10 * q^51 - 3 * q^52 - 14 * q^53 + 18 * q^54 - q^55 + q^56 - 3 * q^57 + 13 * q^58 - 5 * q^60 + 8 * q^61 + 3 * q^62 - 22 * q^63 + 2 * q^64 + 8 * q^65 + 3 * q^66 + 5 * q^67 - 2 * q^68 + 28 * q^69 + 6 * q^70 - 23 * q^71 - 5 * q^72 + 2 * q^73 + 4 * q^74 + 11 * q^75 + 2 * q^76 - q^77 + 2 * q^78 + 10 * q^79 - q^80 + 38 * q^81 + 3 * q^82 + 25 * q^83 + 8 * q^84 + 14 * q^85 - 13 * q^86 + 13 * q^87 - 2 * q^88 + 2 * q^89 - 17 * q^90 - 5 * q^91 - 10 * q^92 - 2 * q^93 + 12 * q^94 - q^95 + 3 * q^96 + 16 * q^97 + 7 * q^98 + 5 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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