LMFDB - Embedded newform 979.2.a.d.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [979,2,Mod(1,979)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(979, 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("979.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 979 = 11 \cdot 89 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	979.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:	$7.81735435788$
Analytic rank:	$1$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 4 x^{16} - 16 x^{15} + 74 x^{14} + 95 x^{13} - 547 x^{12} - 241 x^{11} + 2054 x^{10} + 141 x^{9} + \cdots + 1 $ x^17 - 4x^16 - 16x^15 + 74x^14 + 95x^13 - 547x^12 - 241x^11 + 2054x^10 + 141x^9 - 4103x^8 + 489x^7 + 4118x^6 - 966x^5 - 1663x^4 + 596x^3 + 94x^2 - 43x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Root			$-1.52412$ of defining polynomial
Character	$\chi$	$=$	979.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.52412 q^{2} -0.434072 q^{3} +0.322938 q^{4} -1.32648 q^{5} -0.661577 q^{6} +2.15464 q^{7} -2.55604 q^{8} -2.81158 q^{9} +O(q^{10})$	\(q+1.52412 q^{2} -0.434072 q^{3} +0.322938 q^{4} -1.32648 q^{5} -0.661577 q^{6} +2.15464 q^{7} -2.55604 q^{8} -2.81158 q^{9} -2.02172 q^{10} -1.00000 q^{11} -0.140178 q^{12} +1.40309 q^{13} +3.28393 q^{14} +0.575789 q^{15} -4.54159 q^{16} -4.46287 q^{17} -4.28518 q^{18} -2.06674 q^{19} -0.428373 q^{20} -0.935270 q^{21} -1.52412 q^{22} -0.114565 q^{23} +1.10951 q^{24} -3.24044 q^{25} +2.13848 q^{26} +2.52264 q^{27} +0.695817 q^{28} -1.31541 q^{29} +0.877571 q^{30} -9.66382 q^{31} -1.80984 q^{32} +0.434072 q^{33} -6.80194 q^{34} -2.85810 q^{35} -0.907968 q^{36} +9.35712 q^{37} -3.14996 q^{38} -0.609041 q^{39} +3.39055 q^{40} -3.47011 q^{41} -1.42546 q^{42} -7.28145 q^{43} -0.322938 q^{44} +3.72952 q^{45} -0.174611 q^{46} +0.330493 q^{47} +1.97137 q^{48} -2.35751 q^{49} -4.93882 q^{50} +1.93720 q^{51} +0.453112 q^{52} -4.74360 q^{53} +3.84481 q^{54} +1.32648 q^{55} -5.50736 q^{56} +0.897115 q^{57} -2.00484 q^{58} +3.76320 q^{59} +0.185944 q^{60} +14.4100 q^{61} -14.7288 q^{62} -6.05796 q^{63} +6.32477 q^{64} -1.86118 q^{65} +0.661577 q^{66} -10.0913 q^{67} -1.44123 q^{68} +0.0497296 q^{69} -4.35609 q^{70} +4.72131 q^{71} +7.18652 q^{72} +6.11736 q^{73} +14.2614 q^{74} +1.40658 q^{75} -0.667431 q^{76} -2.15464 q^{77} -0.928252 q^{78} +13.6947 q^{79} +6.02434 q^{80} +7.33974 q^{81} -5.28886 q^{82} -15.0276 q^{83} -0.302035 q^{84} +5.91992 q^{85} -11.0978 q^{86} +0.570981 q^{87} +2.55604 q^{88} -1.00000 q^{89} +5.68423 q^{90} +3.02316 q^{91} -0.0369976 q^{92} +4.19479 q^{93} +0.503711 q^{94} +2.74150 q^{95} +0.785599 q^{96} -0.947541 q^{97} -3.59312 q^{98} +2.81158 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q - 4 q^{2} - q^{3} + 14 q^{4} - 14 q^{5} - 6 q^{6} - 5 q^{7} - 18 q^{8} + 6 q^{9}+O(q^{10}) $ 17 * q - 4 * q^2 - q^3 + 14 * q^4 - 14 * q^5 - 6 * q^6 - 5 * q^7 - 18 * q^8 + 6 * q^9	\( 17 q - 4 q^{2} - q^{3} + 14 q^{4} - 14 q^{5} - 6 q^{6} - 5 q^{7} - 18 q^{8} + 6 q^{9} - 6 q^{10} - 17 q^{11} + q^{12} - 6 q^{13} - 17 q^{14} - 3 q^{15} + 8 q^{16} - 19 q^{17} - 9 q^{19} - 29 q^{20} - 35 q^{21} + 4 q^{22} - 13 q^{23} - 20 q^{24} + 19 q^{25} - 19 q^{27} + q^{28} - 54 q^{29} + q^{30} + 8 q^{31} - 35 q^{32} + q^{33} + 14 q^{34} - 22 q^{35} - 20 q^{36} - 3 q^{38} - 18 q^{39} + 16 q^{40} - 16 q^{41} - 37 q^{42} - 21 q^{43} - 14 q^{44} - 31 q^{45} - 31 q^{46} - 3 q^{47} + 34 q^{48} + 2 q^{49} - 5 q^{50} - 13 q^{51} + 14 q^{52} - 43 q^{53} - 19 q^{54} + 14 q^{55} + 14 q^{56} - 29 q^{57} + 22 q^{58} - q^{59} - 11 q^{60} - 29 q^{61} + 32 q^{62} + 17 q^{63} - 22 q^{64} - 44 q^{65} + 6 q^{66} + 17 q^{67} - 43 q^{68} - 21 q^{69} + 76 q^{70} + 6 q^{71} + 17 q^{72} + 3 q^{73} - 10 q^{74} - 11 q^{75} - 17 q^{76} + 5 q^{77} + 35 q^{78} - 43 q^{79} - 32 q^{80} + 13 q^{81} - 10 q^{82} - 14 q^{83} + 44 q^{84} + 5 q^{85} - 37 q^{86} - 3 q^{87} + 18 q^{88} - 17 q^{89} - 2 q^{90} - 12 q^{91} + 23 q^{92} - 26 q^{93} - 4 q^{94} - 35 q^{95} - 20 q^{96} - 6 q^{97} + q^{98} - 6 q^{99}+O(q^{100}) \) 17 * q - 4 * q^2 - q^3 + 14 * q^4 - 14 * q^5 - 6 * q^6 - 5 * q^7 - 18 * q^8 + 6 * q^9 - 6 * q^10 - 17 * q^11 + q^12 - 6 * q^13 - 17 * q^14 - 3 * q^15 + 8 * q^16 - 19 * q^17 - 9 * q^19 - 29 * q^20 - 35 * q^21 + 4 * q^22 - 13 * q^23 - 20 * q^24 + 19 * q^25 - 19 * q^27 + q^28 - 54 * q^29 + q^30 + 8 * q^31 - 35 * q^32 + q^33 + 14 * q^34 - 22 * q^35 - 20 * q^36 - 3 * q^38 - 18 * q^39 + 16 * q^40 - 16 * q^41 - 37 * q^42 - 21 * q^43 - 14 * q^44 - 31 * q^45 - 31 * q^46 - 3 * q^47 + 34 * q^48 + 2 * q^49 - 5 * q^50 - 13 * q^51 + 14 * q^52 - 43 * q^53 - 19 * q^54 + 14 * q^55 + 14 * q^56 - 29 * q^57 + 22 * q^58 - q^59 - 11 * q^60 - 29 * q^61 + 32 * q^62 + 17 * q^63 - 22 * q^64 - 44 * q^65 + 6 * q^66 + 17 * q^67 - 43 * q^68 - 21 * q^69 + 76 * q^70 + 6 * q^71 + 17 * q^72 + 3 * q^73 - 10 * q^74 - 11 * q^75 - 17 * q^76 + 5 * q^77 + 35 * q^78 - 43 * q^79 - 32 * q^80 + 13 * q^81 - 10 * q^82 - 14 * q^83 + 44 * q^84 + 5 * q^85 - 37 * q^86 - 3 * q^87 + 18 * q^88 - 17 * q^89 - 2 * q^90 - 12 * q^91 + 23 * q^92 - 26 * q^93 - 4 * q^94 - 35 * q^95 - 20 * q^96 - 6 * q^97 + q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.52412	1.07771	0.538857	−	0.842397i	$-0.318856\pi$
$2$	1.52412	1.07771	0.538857	+	0.842397i	$0.318856\pi$
$3$	−0.434072	−0.250611	−0.125306	−	0.992118i	$-0.539991\pi$
$3$	−0.434072	−0.250611	−0.125306	+	0.992118i	$0.539991\pi$
$4$	0.322938	0.161469
$5$	−1.32648	−0.593222	−0.296611	−	0.954998i	$-0.595856\pi$
$5$	−1.32648	−0.593222	−0.296611	+	0.954998i	$0.595856\pi$
$6$	−0.661577	−0.270088
$7$	2.15464	0.814379	0.407189	−	0.913344i	$-0.366509\pi$
$7$	2.15464	0.814379	0.407189	+	0.913344i	$0.366509\pi$
$8$	−2.55604	−0.903697
$9$	−2.81158	−0.937194
$10$	−2.02172	−0.639324
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−0.140178	−0.0404660
$13$	1.40309	0.389147	0.194574	−	0.980888i	$-0.437668\pi$
$13$	1.40309	0.389147	0.194574	+	0.980888i	$0.437668\pi$
$14$	3.28393	0.877668
$15$	0.575789	0.148668
$16$	−4.54159	−1.13540
$17$	−4.46287	−1.08240	−0.541202	−	0.840893i	$-0.682031\pi$
$17$	−4.46287	−1.08240	−0.541202	+	0.840893i	$0.682031\pi$
$18$	−4.28518	−1.01003
$19$	−2.06674	−0.474144	−0.237072	−	0.971492i	$-0.576188\pi$
$19$	−2.06674	−0.474144	−0.237072	+	0.971492i	$0.576188\pi$
$20$	−0.428373	−0.0957871
$21$	−0.935270	−0.204093
$22$	−1.52412	−0.324943
$23$	−0.114565	−0.0238885	−0.0119443	−	0.999929i	$-0.503802\pi$
$23$	−0.114565	−0.0238885	−0.0119443	+	0.999929i	$0.503802\pi$
$24$	1.10951	0.226477
$25$	−3.24044	−0.648088
$26$	2.13848	0.419390
$27$	2.52264	0.485483
$28$	0.695817	0.131497
$29$	−1.31541	−0.244265	−0.122132	−	0.992514i	$-0.538973\pi$
$29$	−1.31541	−0.244265	−0.122132	+	0.992514i	$0.538973\pi$
$30$	0.877571	0.160222
$31$	−9.66382	−1.73567	−0.867836	−	0.496850i	$-0.834490\pi$
$31$	−9.66382	−1.73567	−0.867836	+	0.496850i	$0.834490\pi$
$32$	−1.80984	−0.319937
$33$	0.434072	0.0755622
$34$	−6.80194	−1.16652
$35$	−2.85810	−0.483107
$36$	−0.907968	−0.151328
$37$	9.35712	1.53830	0.769151	−	0.639068i	$-0.220680\pi$
$37$	9.35712	1.53830	0.769151	+	0.639068i	$0.220680\pi$
$38$	−3.14996	−0.510992
$39$	−0.609041	−0.0975247
$40$	3.39055	0.536093
$41$	−3.47011	−0.541940	−0.270970	−	0.962588i	$-0.587344\pi$
$41$	−3.47011	−0.541940	−0.270970	+	0.962588i	$0.587344\pi$
$42$	−1.42546	−0.219954
$43$	−7.28145	−1.11041	−0.555206	−	0.831713i	$-0.687360\pi$
$43$	−7.28145	−1.11041	−0.555206	+	0.831713i	$0.687360\pi$
$44$	−0.322938	−0.0486848
$45$	3.72952	0.555964
$46$	−0.174611	−0.0257450
$47$	0.330493	0.0482074	0.0241037	−	0.999709i	$-0.492327\pi$
$47$	0.330493	0.0482074	0.0241037	+	0.999709i	$0.492327\pi$
$48$	1.97137	0.284543
$49$	−2.35751	−0.336787
$50$	−4.93882	−0.698454
$51$	1.93720	0.271263
$52$	0.453112	0.0628353
$53$	−4.74360	−0.651584	−0.325792	−	0.945441i	$-0.605631\pi$
$53$	−4.74360	−0.651584	−0.325792	+	0.945441i	$0.605631\pi$
$54$	3.84481	0.523212
$55$	1.32648	0.178863
$56$	−5.50736	−0.735952
$57$	0.897115	0.118826
$58$	−2.00484	−0.263248
$59$	3.76320	0.489926	0.244963	−	0.969532i	$-0.421224\pi$
$59$	3.76320	0.489926	0.244963	+	0.969532i	$0.421224\pi$
$60$	0.185944	0.0240053
$61$	14.4100	1.84501	0.922507	−	0.385981i	$-0.126137\pi$
$61$	14.4100	1.84501	0.922507	+	0.385981i	$0.126137\pi$
$62$	−14.7288	−1.87056
$63$	−6.05796	−0.763231
$64$	6.32477	0.790596
$65$	−1.86118	−0.230851
$66$	0.661577	0.0814345
$67$	−10.0913	−1.23285	−0.616426	−	0.787413i	$-0.711420\pi$
$67$	−10.0913	−1.23285	−0.616426	+	0.787413i	$0.711420\pi$
$68$	−1.44123	−0.174775
$69$	0.0497296	0.00598674
$70$	−4.35609	−0.520652
$71$	4.72131	0.560316	0.280158	−	0.959954i	$-0.409613\pi$
$71$	4.72131	0.560316	0.280158	+	0.959954i	$0.409613\pi$
$72$	7.18652	0.846939
$73$	6.11736	0.715983	0.357992	−	0.933725i	$-0.383462\pi$
$73$	6.11736	0.715983	0.357992	+	0.933725i	$0.383462\pi$
$74$	14.2614	1.65785
$75$	1.40658	0.162418
$76$	−0.667431	−0.0765596
$77$	−2.15464	−0.245545
$78$	−0.928252	−0.105104
$79$	13.6947	1.54077	0.770386	−	0.637578i	$-0.220064\pi$
$79$	13.6947	1.54077	0.770386	+	0.637578i	$0.220064\pi$
$80$	6.02434	0.673542
$81$	7.33974	0.815526
$82$	−5.28886	−0.584057
$83$	−15.0276	−1.64949	−0.824744	−	0.565506i	$-0.808681\pi$
$83$	−15.0276	−1.64949	−0.824744	+	0.565506i	$0.808681\pi$
$84$	−0.302035	−0.0329547
$85$	5.91992	0.642106
$86$	−11.0978	−1.19671
$87$	0.570981	0.0612156
$88$	2.55604	0.272475
$89$	−1.00000	−0.106000
$89$	−1.00000	−0.106000
$90$	5.68423	0.599170
$91$	3.02316	0.316913
$92$	−0.0369976	−0.00385726
$93$	4.19479	0.434979
$94$	0.503711	0.0519538
$95$	2.74150	0.281272
$96$	0.785599	0.0801799
$97$	−0.947541	−0.0962082	−0.0481041	−	0.998842i	$-0.515318\pi$
$97$	−0.947541	−0.0962082	−0.0481041	+	0.998842i	$0.515318\pi$
$98$	−3.59312	−0.362960
$99$	2.81158	0.282575
$100$	−1.04646	−0.104646
$101$	−4.08724	−0.406695	−0.203348	−	0.979107i	$-0.565182\pi$
$101$	−4.08724	−0.406695	−0.203348	+	0.979107i	$0.565182\pi$
$102$	2.95253	0.292344
$103$	−1.32436	−0.130493	−0.0652466	−	0.997869i	$-0.520783\pi$
$103$	−1.32436	−0.130493	−0.0652466	+	0.997869i	$0.520783\pi$
$104$	−3.58636	−0.351671
$105$	1.24062	0.121072
$106$	−7.22981	−0.702222
$107$	1.61781	0.156400	0.0781998	−	0.996938i	$-0.475083\pi$
$107$	1.61781	0.156400	0.0781998	+	0.996938i	$0.475083\pi$
$108$	0.814658	0.0783905
$109$	0.397584	0.0380816	0.0190408	−	0.999819i	$-0.493939\pi$
$109$	0.397584	0.0380816	0.0190408	+	0.999819i	$0.493939\pi$
$110$	2.02172	0.192763
$111$	−4.06166	−0.385516
$112$	−9.78551	−0.924643
$113$	−9.08412	−0.854562	−0.427281	−	0.904119i	$-0.640528\pi$
$113$	−9.08412	−0.854562	−0.427281	+	0.904119i	$0.640528\pi$
$114$	1.36731	0.128060
$115$	0.151969	0.0141712
$116$	−0.424796	−0.0394413
$117$	−3.94490	−0.364706
$118$	5.73556	0.528001
$119$	−9.61589	−0.881487
$120$	−1.47174	−0.134351
$121$	1.00000	0.0909091
$122$	21.9626	1.98840
$123$	1.50628	0.135816
$124$	−3.12082	−0.280258
$125$	10.9308	0.977682
$126$	−9.23305	−0.822545
$127$	6.06257	0.537966	0.268983	−	0.963145i	$-0.413312\pi$
$127$	6.06257	0.537966	0.268983	+	0.963145i	$0.413312\pi$
$128$	13.2594	1.17197
$129$	3.16067	0.278282
$130$	−2.83665	−0.248791
$131$	1.15737	0.101120	0.0505601	−	0.998721i	$-0.483899\pi$
$131$	1.15737	0.101120	0.0505601	+	0.998721i	$0.483899\pi$
$132$	0.140178	0.0122010
$133$	−4.45310	−0.386133
$134$	−15.3804	−1.32866
$135$	−3.34625	−0.287999
$136$	11.4073	0.978165
$137$	−15.2344	−1.30156	−0.650782	−	0.759265i	$-0.725559\pi$
$137$	−15.2344	−1.30156	−0.650782	+	0.759265i	$0.725559\pi$
$138$	0.0757938	0.00645200
$139$	6.04771	0.512960	0.256480	−	0.966550i	$-0.417437\pi$
$139$	6.04771	0.512960	0.256480	+	0.966550i	$0.417437\pi$
$140$	−0.922991	−0.0780070
$141$	−0.143458	−0.0120813
$142$	7.19584	0.603861
$143$	−1.40309	−0.117332
$144$	12.7690	1.06409
$145$	1.74487	0.144903
$146$	9.32359	0.771626
$147$	1.02333	0.0844026
$148$	3.02177	0.248388
$149$	9.98734	0.818195	0.409097	−	0.912491i	$-0.365844\pi$
$149$	9.98734	0.818195	0.409097	+	0.912491i	$0.365844\pi$
$150$	2.14380	0.175041
$151$	6.15960	0.501261	0.250631	−	0.968083i	$-0.419362\pi$
$151$	6.15960	0.501261	0.250631	+	0.968083i	$0.419362\pi$
$152$	5.28268	0.428482
$153$	12.5477	1.01442
$154$	−3.28393	−0.264627
$155$	12.8189	1.02964
$156$	−0.196683	−0.0157472
$157$	24.2025	1.93157	0.965785	−	0.259343i	$-0.0835058\pi$
$157$	24.2025	1.93157	0.965785	+	0.259343i	$0.0835058\pi$
$158$	20.8723	1.66051
$159$	2.05906	0.163294
$160$	2.40072	0.189794
$161$	−0.246848	−0.0194543
$162$	11.1866	0.878905
$163$	2.76989	0.216954	0.108477	−	0.994099i	$-0.465403\pi$
$163$	2.76989	0.216954	0.108477	+	0.994099i	$0.465403\pi$
$164$	−1.12063	−0.0875066
$165$	−0.575789	−0.0448251
$166$	−22.9038	−1.77768
$167$	19.3650	1.49851	0.749255	−	0.662281i	$-0.230412\pi$
$167$	19.3650	1.49851	0.749255	+	0.662281i	$0.230412\pi$
$168$	2.39059	0.184438
$169$	−11.0313	−0.848565
$170$	9.02267	0.692007
$171$	5.81082	0.444365
$172$	−2.35146	−0.179297
$173$	−13.9932	−1.06389	−0.531943	−	0.846780i	$-0.678538\pi$
$173$	−13.9932	−1.06389	−0.531943	+	0.846780i	$0.678538\pi$
$174$	0.870243	0.0659729
$175$	−6.98199	−0.527789
$176$	4.54159	0.342335
$177$	−1.63350	−0.122781
$178$	−1.52412	−0.114238
$179$	−7.48423	−0.559398	−0.279699	−	0.960088i	$-0.590235\pi$
$179$	−7.48423	−0.559398	−0.279699	+	0.960088i	$0.590235\pi$
$180$	1.20441	0.0897711
$181$	−24.9787	−1.85665	−0.928324	−	0.371771i	$-0.878751\pi$
$181$	−24.9787	−1.85665	−0.928324	+	0.371771i	$0.878751\pi$
$182$	4.60765	0.341542
$183$	−6.25498	−0.462381
$184$	0.292834	0.0215880
$185$	−12.4121	−0.912554
$186$	6.39336	0.468784
$187$	4.46287	0.326357
$188$	0.106729	0.00778401
$189$	5.43540	0.395367
$190$	4.17838	0.303131
$191$	−14.1413	−1.02323	−0.511615	−	0.859215i	$-0.670953\pi$
$191$	−14.1413	−1.02323	−0.511615	+	0.859215i	$0.670953\pi$
$192$	−2.74540	−0.198132
$193$	19.7291	1.42013	0.710066	−	0.704135i	$-0.248665\pi$
$193$	19.7291	1.42013	0.710066	+	0.704135i	$0.248665\pi$
$194$	−1.44417	−0.103685
$195$	0.807884	0.0578538
$196$	−0.761330	−0.0543807
$197$	−22.0246	−1.56919	−0.784595	−	0.620009i	$-0.787129\pi$
$197$	−22.0246	−1.56919	−0.784595	+	0.620009i	$0.787129\pi$
$198$	4.28518	0.304535
$199$	−4.85027	−0.343826	−0.171913	−	0.985112i	$-0.554995\pi$
$199$	−4.85027	−0.343826	−0.171913	+	0.985112i	$0.554995\pi$
$200$	8.28270	0.585675
$201$	4.38036	0.308967
$202$	−6.22944	−0.438302
$203$	−2.83423	−0.198924
$204$	0.625598	0.0438006
$205$	4.60304	0.321491
$206$	−2.01848	−0.140634
$207$	0.322110	0.0223882
$208$	−6.37226	−0.441836
$209$	2.06674	0.142960
$210$	1.89085	0.130481
$211$	−12.3370	−0.849313	−0.424657	−	0.905354i	$-0.639605\pi$
$211$	−12.3370	−0.849313	−0.424657	+	0.905354i	$0.639605\pi$
$212$	−1.53189	−0.105211
$213$	−2.04939	−0.140422
$214$	2.46574	0.168554
$215$	9.65873	0.658720
$216$	−6.44798	−0.438729
$217$	−20.8221	−1.41350
$218$	0.605965	0.0410412
$219$	−2.65537	−0.179434
$220$	0.428373	0.0288809
$221$	−6.26180	−0.421214
$222$	−6.19045	−0.415476
$223$	3.54078	0.237108	0.118554	−	0.992948i	$-0.462174\pi$
$223$	3.54078	0.237108	0.118554	+	0.992948i	$0.462174\pi$
$224$	−3.89956	−0.260550
$225$	9.11076	0.607384
$226$	−13.8453	−0.920974
$227$	16.7392	1.11102	0.555511	−	0.831509i	$-0.312523\pi$
$227$	16.7392	1.11102	0.555511	+	0.831509i	$0.312523\pi$
$228$	0.289713	0.0191867
$229$	1.52487	0.100766	0.0503830	−	0.998730i	$-0.483956\pi$
$229$	1.52487	0.100766	0.0503830	+	0.998730i	$0.483956\pi$
$230$	0.231619	0.0152725
$231$	0.935270	0.0615362
$232$	3.36223	0.220742
$233$	−21.2451	−1.39181	−0.695905	−	0.718133i	$-0.744997\pi$
$233$	−21.2451	−1.39181	−0.695905	+	0.718133i	$0.744997\pi$
$234$	−6.01250	−0.393049
$235$	−0.438394	−0.0285977
$236$	1.21528	0.0791081
$237$	−5.94447	−0.386135
$238$	−14.6558	−0.949992
$239$	15.7684	1.01997	0.509986	−	0.860182i	$-0.329650\pi$
$239$	15.7684	1.01997	0.509986	+	0.860182i	$0.329650\pi$
$240$	−2.61500	−0.168797
$241$	−10.3948	−0.669585	−0.334793	−	0.942292i	$-0.608666\pi$
$241$	−10.3948	−0.669585	−0.334793	+	0.942292i	$0.608666\pi$
$242$	1.52412	0.0979741
$243$	−10.7539	−0.689863
$244$	4.65355	0.297913
$245$	3.12720	0.199789
$246$	2.29574	0.146371
$247$	−2.89983	−0.184512
$248$	24.7011	1.56852
$249$	6.52303	0.413381
$250$	16.6599	1.05366
$251$	−14.2283	−0.898084	−0.449042	−	0.893511i	$-0.648235\pi$
$251$	−14.2283	−0.898084	−0.449042	+	0.893511i	$0.648235\pi$
$252$	−1.95635	−0.123238
$253$	0.114565	0.00720267
$254$	9.24008	0.579774
$255$	−2.56967	−0.160919
$256$	7.55932	0.472458
$257$	−27.6424	−1.72429	−0.862143	−	0.506666i	$-0.830878\pi$
$257$	−27.6424	−1.72429	−0.862143	+	0.506666i	$0.830878\pi$
$258$	4.81724	0.299908
$259$	20.1613	1.25276
$260$	−0.601045	−0.0372753
$261$	3.69837	0.228924
$262$	1.76398	0.108979
$263$	−6.49409	−0.400443	−0.200221	−	0.979751i	$-0.564166\pi$
$263$	−6.49409	−0.400443	−0.200221	+	0.979751i	$0.564166\pi$
$264$	−1.10951	−0.0682853
$265$	6.29231	0.386534
$266$	−6.78705	−0.416141
$267$	0.434072	0.0265648
$268$	−3.25888	−0.199068
$269$	11.8594	0.723081	0.361541	−	0.932356i	$-0.382251\pi$
$269$	11.8594	0.723081	0.361541	+	0.932356i	$0.382251\pi$
$270$	−5.10008	−0.310381
$271$	−11.5663	−0.702601	−0.351300	−	0.936263i	$-0.614260\pi$
$271$	−11.5663	−0.702601	−0.351300	+	0.936263i	$0.614260\pi$
$272$	20.2685	1.22896
$273$	−1.31227	−0.0794221
$274$	−23.2191	−1.40271
$275$	3.24044	0.195406
$276$	0.0160596	0.000966675 0
$277$	−3.78928	−0.227676	−0.113838	−	0.993499i	$-0.536314\pi$
$277$	−3.78928	−0.227676	−0.113838	+	0.993499i	$0.536314\pi$
$278$	9.21743	0.552825
$279$	27.1706	1.62666
$280$	7.30543	0.436583
$281$	16.4065	0.978730	0.489365	−	0.872079i	$-0.337229\pi$
$281$	16.4065	0.978730	0.489365	+	0.872079i	$0.337229\pi$
$282$	−0.218647	−0.0130202
$283$	1.04199	0.0619399	0.0309700	−	0.999520i	$-0.490140\pi$
$283$	1.04199	0.0619399	0.0309700	+	0.999520i	$0.490140\pi$
$284$	1.52469	0.0904738
$285$	−1.19001	−0.0704901
$286$	−2.13848	−0.126451
$287$	−7.47685	−0.441344
$288$	5.08851	0.299843
$289$	2.91718	0.171599
$290$	2.65938	0.156164
$291$	0.411301	0.0241109
$292$	1.97553	0.115609
$293$	−24.0600	−1.40560	−0.702800	−	0.711387i	$-0.748067\pi$
$293$	−24.0600	−1.40560	−0.702800	+	0.711387i	$0.748067\pi$
$294$	1.55967	0.0909620
$295$	−4.99182	−0.290635
$296$	−23.9172	−1.39016
$297$	−2.52264	−0.146379
$298$	15.2219	0.881780
$299$	−0.160746	−0.00929616
$300$	0.454240	0.0262255
$301$	−15.6889	−0.904296
$302$	9.38797	0.540217
$303$	1.77415	0.101922
$304$	9.38630	0.538341
$305$	−19.1147	−1.09450
$306$	19.1242	1.09326
$307$	−14.4382	−0.824031	−0.412015	−	0.911177i	$-0.635175\pi$
$307$	−14.4382	−0.824031	−0.412015	+	0.911177i	$0.635175\pi$
$308$	−0.695817	−0.0396479
$309$	0.574867	0.0327031
$310$	19.5375	1.10966
$311$	24.3888	1.38296	0.691482	−	0.722393i	$-0.256958\pi$
$311$	24.3888	1.38296	0.691482	+	0.722393i	$0.256958\pi$
$312$	1.55674	0.0881328
$313$	24.0312	1.35833	0.679163	−	0.733988i	$-0.262343\pi$
$313$	24.0312	1.35833	0.679163	+	0.733988i	$0.262343\pi$
$314$	36.8875	2.08168
$315$	8.03579	0.452765
$316$	4.42254	0.248787
$317$	−18.1060	−1.01693	−0.508466	−	0.861082i	$-0.669787\pi$
$317$	−18.1060	−1.01693	−0.508466	+	0.861082i	$0.669787\pi$
$318$	3.13826	0.175985
$319$	1.31541	0.0736487
$320$	−8.38971	−0.468999
$321$	−0.702246	−0.0391955
$322$	−0.376225	−0.0209662
$323$	9.22360	0.513215
$324$	2.37028	0.131682
$325$	−4.54663	−0.252202
$326$	4.22164	0.233815
$327$	−0.172580	−0.00954369
$328$	8.86974	0.489749
$329$	0.712095	0.0392591
$330$	−0.877571	−0.0483087
$331$	−25.2065	−1.38547	−0.692737	−	0.721191i	$-0.743595\pi$
$331$	−25.2065	−1.38547	−0.692737	+	0.721191i	$0.743595\pi$
$332$	−4.85297	−0.266342
$333$	−26.3083	−1.44169
$334$	29.5146	1.61497
$335$	13.3860	0.731354
$336$	4.24761	0.231726
$337$	6.14256	0.334607	0.167303	−	0.985905i	$-0.446494\pi$
$337$	6.14256	0.334607	0.167303	+	0.985905i	$0.446494\pi$
$338$	−16.8131	−0.914511
$339$	3.94316	0.214163
$340$	1.91177	0.103680
$341$	9.66382	0.523325
$342$	8.85638	0.478898
$343$	−20.1621	−1.08865
$344$	18.6117	1.00348
$345$	−0.0659655	−0.00355147
$346$	−21.3274	−1.14657
$347$	−22.0060	−1.18134	−0.590672	−	0.806912i	$-0.701137\pi$
$347$	−22.0060	−1.18134	−0.590672	+	0.806912i	$0.701137\pi$
$348$	0.184392	0.00988443
$349$	−8.56583	−0.458518	−0.229259	−	0.973365i	$-0.573630\pi$
$349$	−8.56583	−0.458518	−0.229259	+	0.973365i	$0.573630\pi$
$350$	−10.6414	−0.568806
$351$	3.53949	0.188924
$352$	1.80984	0.0964646
$353$	−36.4869	−1.94200	−0.971000	−	0.239079i	$-0.923155\pi$
$353$	−36.4869	−1.94200	−0.971000	+	0.239079i	$0.923155\pi$
$354$	−2.48964	−0.132323
$355$	−6.26274	−0.332392
$356$	−0.322938	−0.0171157
$357$	4.17399	0.220911
$358$	−11.4069	−0.602871
$359$	−11.1348	−0.587671	−0.293835	−	0.955856i	$-0.594932\pi$
$359$	−11.1348	−0.587671	−0.293835	+	0.955856i	$0.594932\pi$
$360$	−9.53280	−0.502423
$361$	−14.7286	−0.775188
$362$	−38.0704	−2.00094
$363$	−0.434072	−0.0227829
$364$	0.976294	0.0511717
$365$	−8.11459	−0.424737
$366$	−9.53333	−0.498315
$367$	26.5350	1.38512	0.692559	−	0.721361i	$-0.256483\pi$
$367$	26.5350	1.38512	0.692559	+	0.721361i	$0.256483\pi$
$368$	0.520309	0.0271230
$369$	9.75649	0.507903
$370$	−18.9175	−0.983473
$371$	−10.2208	−0.530636
$372$	1.35466	0.0702358
$373$	−2.39847	−0.124188	−0.0620941	−	0.998070i	$-0.519778\pi$
$373$	−2.39847	−0.124188	−0.0620941	+	0.998070i	$0.519778\pi$
$374$	6.80194	0.351720
$375$	−4.74476	−0.245018
$376$	−0.844754	−0.0435649
$377$	−1.84563	−0.0950550
$378$	8.28419	0.426093
$379$	−23.4896	−1.20658	−0.603291	−	0.797521i	$-0.706144\pi$
$379$	−23.4896	−1.20658	−0.603291	+	0.797521i	$0.706144\pi$
$380$	0.885337	0.0454168
$381$	−2.63159	−0.134820
$382$	−21.5531	−1.10275
$383$	24.5171	1.25277	0.626384	−	0.779515i	$-0.284534\pi$
$383$	24.5171	1.25277	0.626384	+	0.779515i	$0.284534\pi$
$384$	−5.75552	−0.293710
$385$	2.85810	0.145662
$386$	30.0695	1.53050
$387$	20.4724	1.04067
$388$	−0.305998	−0.0155347
$389$	37.0144	1.87671	0.938353	−	0.345678i	$-0.112351\pi$
$389$	37.0144	1.87671	0.938353	+	0.345678i	$0.112351\pi$
$390$	1.23131	0.0623499
$391$	0.511290	0.0258571
$392$	6.02589	0.304353
$393$	−0.502383	−0.0253419
$394$	−33.5681	−1.69114
$395$	−18.1658	−0.914019
$396$	0.907968	0.0456271
$397$	−15.0254	−0.754105	−0.377053	−	0.926192i	$-0.623062\pi$
$397$	−15.0254	−0.754105	−0.377053	+	0.926192i	$0.623062\pi$
$398$	−7.39238	−0.370547
$399$	1.93296	0.0967692
$400$	14.7167	0.735837
$401$	9.97096	0.497926	0.248963	−	0.968513i	$-0.419910\pi$
$401$	9.97096	0.497926	0.248963	+	0.968513i	$0.419910\pi$
$402$	6.67619	0.332978
$403$	−13.5592	−0.675432
$404$	−1.31993	−0.0656688
$405$	−9.73605	−0.483788
$406$	−4.31971	−0.214384
$407$	−9.35712	−0.463815
$408$	−4.95157	−0.245139
$409$	19.4084	0.959684	0.479842	−	0.877355i	$-0.340694\pi$
$409$	19.4084	0.959684	0.479842	+	0.877355i	$0.340694\pi$
$410$	7.01559	0.346475
$411$	6.61283	0.326187
$412$	−0.427687	−0.0210706
$413$	8.10835	0.398986
$414$	0.490934	0.0241281
$415$	19.9338	0.978512
$416$	−2.53936	−0.124503
$417$	−2.62514	−0.128554
$418$	3.14996	0.154070
$419$	14.1580	0.691665	0.345832	−	0.938296i	$-0.387597\pi$
$419$	14.1580	0.691665	0.345832	+	0.938296i	$0.387597\pi$
$420$	0.400644	0.0195494
$421$	−28.8889	−1.40796	−0.703979	−	0.710221i	$-0.748595\pi$
$421$	−28.8889	−1.40796	−0.703979	+	0.710221i	$0.748595\pi$
$422$	−18.8030	−0.915318
$423$	−0.929208	−0.0451797
$424$	12.1248	0.588834
$425$	14.4616	0.701493
$426$	−3.12351	−0.151334
$427$	31.0485	1.50254
$428$	0.522453	0.0252537
$429$	0.609041	0.0294048
$430$	14.7211	0.709913
$431$	9.40776	0.453156	0.226578	−	0.973993i	$-0.427246\pi$
$431$	9.40776	0.453156	0.226578	+	0.973993i	$0.427246\pi$
$432$	−11.4568	−0.551216
$433$	−1.75314	−0.0842505	−0.0421253	−	0.999112i	$-0.513413\pi$
$433$	−1.75314	−0.0842505	−0.0421253	+	0.999112i	$0.513413\pi$
$434$	−31.7353	−1.52335
$435$	−0.757397	−0.0363144
$436$	0.128395	0.00614901
$437$	0.236777	0.0113266
$438$	−4.04711	−0.193378
$439$	30.3476	1.44841	0.724206	−	0.689584i	$-0.242207\pi$
$439$	30.3476	1.44841	0.724206	+	0.689584i	$0.242207\pi$
$440$	−3.39055	−0.161638
$441$	6.62833	0.315635
$442$	−9.54373	−0.453949
$443$	−18.2044	−0.864918	−0.432459	−	0.901654i	$-0.642354\pi$
$443$	−18.2044	−0.864918	−0.432459	+	0.901654i	$0.642354\pi$
$444$	−1.31167	−0.0622489
$445$	1.32648	0.0628814
$446$	5.39657	0.255535
$447$	−4.33522	−0.205049
$448$	13.6276	0.643845
$449$	−7.55153	−0.356379	−0.178189	−	0.983996i	$-0.557024\pi$
$449$	−7.55153	−0.356379	−0.178189	+	0.983996i	$0.557024\pi$
$450$	13.8859	0.654587
$451$	3.47011	0.163401
$452$	−2.93361	−0.137985
$453$	−2.67371	−0.125622
$454$	25.5126	1.19736
$455$	−4.01017	−0.188000
$456$	−2.29306	−0.107383
$457$	8.11930	0.379805	0.189902	−	0.981803i	$-0.439183\pi$
$457$	8.11930	0.379805	0.189902	+	0.981803i	$0.439183\pi$
$458$	2.32408	0.108597
$459$	−11.2582	−0.525489
$460$	0.0490767	0.00228821
$461$	−9.48433	−0.441729	−0.220865	−	0.975304i	$-0.570888\pi$
$461$	−9.48433	−0.441729	−0.220865	+	0.975304i	$0.570888\pi$
$462$	1.42546	0.0663185
$463$	−6.33931	−0.294613	−0.147306	−	0.989091i	$-0.547060\pi$
$463$	−6.33931	−0.294613	−0.147306	+	0.989091i	$0.547060\pi$
$464$	5.97404	0.277338
$465$	−5.56432	−0.258039
$466$	−32.3800	−1.49998
$467$	−4.80719	−0.222450	−0.111225	−	0.993795i	$-0.535477\pi$
$467$	−4.80719	−0.222450	−0.111225	+	0.993795i	$0.535477\pi$
$468$	−1.27396	−0.0588888
$469$	−21.7432	−1.00401
$470$	−0.668164	−0.0308201
$471$	−10.5056	−0.484074
$472$	−9.61889	−0.442745
$473$	7.28145	0.334802
$474$	−9.06008	−0.416143
$475$	6.69716	0.307287
$476$	−3.10534	−0.142333
$477$	13.3370	0.610661
$478$	24.0329	1.09924
$479$	−16.7859	−0.766970	−0.383485	−	0.923547i	$-0.625276\pi$
$479$	−16.7859	−0.766970	−0.383485	+	0.923547i	$0.625276\pi$
$480$	−1.04208	−0.0475644
$481$	13.1289	0.598625
$482$	−15.8428	−0.721622
$483$	0.107150	0.00487548
$484$	0.322938	0.0146790
$485$	1.25690	0.0570728
$486$	−16.3902	−0.743476
$487$	29.2120	1.32372	0.661862	−	0.749626i	$-0.269767\pi$
$487$	29.2120	1.32372	0.661862	+	0.749626i	$0.269767\pi$
$488$	−36.8326	−1.66733
$489$	−1.20233	−0.0543712
$490$	4.76622	0.215316
$491$	−37.8108	−1.70638	−0.853188	−	0.521604i	$-0.825334\pi$
$491$	−37.8108	−1.70638	−0.853188	+	0.521604i	$0.825334\pi$
$492$	0.486434	0.0219302
$493$	5.87049	0.264393
$494$	−4.41968	−0.198851
$495$	−3.72952	−0.167629
$496$	43.8891	1.97068
$497$	10.1727	0.456310
$498$	9.94188	0.445506
$499$	2.78451	0.124652	0.0623259	−	0.998056i	$-0.480148\pi$
$499$	2.78451	0.124652	0.0623259	+	0.998056i	$0.480148\pi$
$500$	3.52998	0.157865
$501$	−8.40581	−0.375544
$502$	−21.6857	−0.967878
$503$	4.17734	0.186258	0.0931291	−	0.995654i	$-0.470313\pi$
$503$	4.17734	0.186258	0.0931291	+	0.995654i	$0.470313\pi$
$504$	15.4844	0.689730
$505$	5.42166	0.241261
$506$	0.174611	0.00776242
$507$	4.78839	0.212660
$508$	1.95784	0.0868650
$509$	0.539977	0.0239341	0.0119670	−	0.999928i	$-0.496191\pi$
$509$	0.539977	0.0239341	0.0119670	+	0.999928i	$0.496191\pi$
$510$	−3.91648	−0.173425
$511$	13.1807	0.583082
$512$	−14.9974	−0.662799
$513$	−5.21366	−0.230189
$514$	−42.1303	−1.85829
$515$	1.75674	0.0774114
$516$	1.02070	0.0449339
$517$	−0.330493	−0.0145351
$518$	30.7282	1.35012
$519$	6.07407	0.266622
$520$	4.75724	0.208619
$521$	−10.8579	−0.475693	−0.237846	−	0.971303i	$-0.576441\pi$
$521$	−10.8579	−0.475693	−0.237846	+	0.971303i	$0.576441\pi$
$522$	5.63676	0.246714
$523$	6.75396	0.295330	0.147665	−	0.989037i	$-0.452824\pi$
$523$	6.75396	0.295330	0.147665	+	0.989037i	$0.452824\pi$
$524$	0.373761	0.0163278
$525$	3.03069	0.132270
$526$	−9.89776	−0.431563
$527$	43.1283	1.87870
$528$	−1.97137	−0.0857931
$529$	−22.9869	−0.999429
$530$	9.59023	0.416573
$531$	−10.5805	−0.459156
$532$	−1.43808	−0.0623485
$533$	−4.86887	−0.210894
$534$	0.661577	0.0286292
$535$	−2.14600	−0.0927797
$536$	25.7938	1.11412
$537$	3.24869	0.140191
$538$	18.0752	0.779276
$539$	2.35751	0.101545
$540$	−1.08063	−0.0465030
$541$	−36.9246	−1.58751	−0.793756	−	0.608236i	$-0.791878\pi$
$541$	−36.9246	−1.58751	−0.793756	+	0.608236i	$0.791878\pi$
$542$	−17.6284	−0.757203
$543$	10.8425	0.465297
$544$	8.07706	0.346301
$545$	−0.527389	−0.0225909
$546$	−2.00005	−0.0855943
$547$	−27.9986	−1.19713	−0.598566	−	0.801074i	$-0.704263\pi$
$547$	−27.9986	−1.19713	−0.598566	+	0.801074i	$0.704263\pi$
$548$	−4.91978	−0.210162
$549$	−40.5149	−1.72914
$550$	4.93882	0.210592
$551$	2.71861	0.115817
$552$	−0.127111	−0.00541020
$553$	29.5072	1.25477
$554$	−5.77531	−0.245369
$555$	5.38773	0.228696
$556$	1.95304	0.0828273
$557$	11.5074	0.487586	0.243793	−	0.969827i	$-0.421608\pi$
$557$	11.5074	0.487586	0.243793	+	0.969827i	$0.421608\pi$
$558$	41.4112	1.75308
$559$	−10.2165	−0.432113
$560$	12.9803	0.548519
$561$	−1.93720	−0.0817888
$562$	25.0055	1.05479
$563$	−2.23378	−0.0941425	−0.0470712	−	0.998892i	$-0.514989\pi$
$563$	−2.23378	−0.0941425	−0.0470712	+	0.998892i	$0.514989\pi$
$564$	−0.0463280	−0.00195076
$565$	12.0499	0.506945
$566$	1.58812	0.0667536
$567$	15.8145	0.664148
$568$	−12.0679	−0.506356
$569$	1.81543	0.0761069	0.0380534	−	0.999276i	$-0.487884\pi$
$569$	1.81543	0.0761069	0.0380534	+	0.999276i	$0.487884\pi$
$570$	−1.81372	−0.0759682
$571$	40.6126	1.69959	0.849793	−	0.527117i	$-0.176727\pi$
$571$	40.6126	1.69959	0.849793	+	0.527117i	$0.176727\pi$
$572$	−0.453112	−0.0189455
$573$	6.13835	0.256433
$574$	−11.3956	−0.475643
$575$	0.371242	0.0154819
$576$	−17.7826	−0.740942
$577$	−16.0741	−0.669174	−0.334587	−	0.942365i	$-0.608597\pi$
$577$	−16.0741	−0.669174	−0.334587	+	0.942365i	$0.608597\pi$
$578$	4.44613	0.184934
$579$	−8.56385	−0.355901
$580$	0.563485	0.0233974
$581$	−32.3790	−1.34331
$582$	0.626871	0.0259847
$583$	4.74360	0.196460
$584$	−15.6362	−0.647032
$585$	5.23285	0.216352
$586$	−36.6703	−1.51484
$587$	35.9749	1.48484	0.742422	−	0.669932i	$-0.233677\pi$
$587$	35.9749	1.48484	0.742422	+	0.669932i	$0.233677\pi$
$588$	0.330472	0.0136284
$589$	19.9726	0.822958
$590$	−7.60813	−0.313222
$591$	9.56027	0.393257
$592$	−42.4962	−1.74658
$593$	8.99211	0.369262	0.184631	−	0.982808i	$-0.440891\pi$
$593$	8.99211	0.369262	0.184631	+	0.982808i	$0.440891\pi$
$594$	−3.84481	−0.157754
$595$	12.7553	0.522917
$596$	3.22530	0.132113
$597$	2.10536	0.0861668
$598$	−0.244995	−0.0100186
$599$	−4.47373	−0.182792	−0.0913958	−	0.995815i	$-0.529133\pi$
$599$	−4.47373	−0.182792	−0.0913958	+	0.995815i	$0.529133\pi$
$600$	−3.59528	−0.146777
$601$	−7.04456	−0.287354	−0.143677	−	0.989625i	$-0.545893\pi$
$601$	−7.04456	−0.287354	−0.143677	+	0.989625i	$0.545893\pi$
$602$	−23.9118	−0.974573
$603$	28.3726	1.15542
$604$	1.98917	0.0809383
$605$	−1.32648	−0.0539293
$606$	2.70402	0.109843
$607$	31.4458	1.27635	0.638173	−	0.769893i	$-0.279690\pi$
$607$	31.4458	1.27635	0.638173	+	0.769893i	$0.279690\pi$
$608$	3.74047	0.151696
$609$	1.23026	0.0498527
$610$	−29.1330	−1.17956
$611$	0.463711	0.0187598
$612$	4.05214	0.163798
$613$	−18.6693	−0.754047	−0.377024	−	0.926204i	$-0.623052\pi$
$613$	−18.6693	−0.754047	−0.377024	+	0.926204i	$0.623052\pi$
$614$	−22.0055	−0.888070
$615$	−1.99805	−0.0805692
$616$	5.50736	0.221898
$617$	−17.2983	−0.696404	−0.348202	−	0.937419i	$-0.613208\pi$
$617$	−17.2983	−0.696404	−0.348202	+	0.937419i	$0.613208\pi$
$618$	0.876166	0.0352446
$619$	31.6637	1.27267	0.636336	−	0.771412i	$-0.280449\pi$
$619$	31.6637	1.27267	0.636336	+	0.771412i	$0.280449\pi$
$620$	4.13972	0.166255
$621$	−0.289008	−0.0115975
$622$	37.1715	1.49044
$623$	−2.15464	−0.0863240
$624$	2.76602	0.110729
$625$	1.70265	0.0681059
$626$	36.6265	1.46389
$627$	−0.897115	−0.0358273
$628$	7.81592	0.311889
$629$	−41.7596	−1.66506
$630$	12.2475	0.487952
$631$	37.3706	1.48770	0.743850	−	0.668347i	$-0.232998\pi$
$631$	37.3706	1.48770	0.743850	+	0.668347i	$0.232998\pi$
$632$	−35.0042	−1.39239
$633$	5.35514	0.212848
$634$	−27.5957	−1.09596
$635$	−8.04191	−0.319133
$636$	0.664951	0.0263670
$637$	−3.30780	−0.131060
$638$	2.00484	0.0793723
$639$	−13.2743	−0.525125
$640$	−17.5883	−0.695241
$641$	−31.6734	−1.25102	−0.625512	−	0.780215i	$-0.715110\pi$
$641$	−31.6734	−1.25102	−0.625512	+	0.780215i	$0.715110\pi$
$642$	−1.07031	−0.0422416
$643$	−12.5439	−0.494683	−0.247342	−	0.968928i	$-0.579557\pi$
$643$	−12.5439	−0.494683	−0.247342	+	0.968928i	$0.579557\pi$
$644$	−0.0797166	−0.00314128
$645$	−4.19258	−0.165083
$646$	14.0579	0.553099
$647$	−16.2911	−0.640470	−0.320235	−	0.947338i	$-0.603762\pi$
$647$	−16.2911	−0.640470	−0.320235	+	0.947338i	$0.603762\pi$
$648$	−18.7607	−0.736989
$649$	−3.76320	−0.147718
$650$	−6.92960	−0.271801
$651$	9.03828	0.354238
$652$	0.894503	0.0350315
$653$	23.1438	0.905686	0.452843	−	0.891590i	$-0.350410\pi$
$653$	23.1438	0.905686	0.452843	+	0.891590i	$0.350410\pi$
$654$	−0.263032	−0.0102854
$655$	−1.53524	−0.0599867
$656$	15.7598	0.615317
$657$	−17.1995	−0.671015
$658$	1.08532	0.0423101
$659$	−15.5358	−0.605188	−0.302594	−	0.953120i	$-0.597853\pi$
$659$	−15.5358	−0.605188	−0.302594	+	0.953120i	$0.597853\pi$
$660$	−0.185944	−0.00723788
$661$	15.0365	0.584852	0.292426	−	0.956288i	$-0.405537\pi$
$661$	15.0365	0.584852	0.292426	+	0.956288i	$0.405537\pi$
$662$	−38.4177	−1.49315
$663$	2.71807	0.105561
$664$	38.4110	1.49064
$665$	5.90697	0.229062
$666$	−40.0970	−1.55373
$667$	0.150700	0.00583514
$668$	6.25371	0.241963
$669$	−1.53695	−0.0594220
$670$	20.4018	0.788191
$671$	−14.4100	−0.556292
$672$	1.69269	0.0652968
$673$	−10.2714	−0.395932	−0.197966	−	0.980209i	$-0.563434\pi$
$673$	−10.2714	−0.395932	−0.197966	+	0.980209i	$0.563434\pi$
$674$	9.36199	0.360611
$675$	−8.17447	−0.314636
$676$	−3.56244	−0.137017
$677$	−16.3046	−0.626638	−0.313319	−	0.949648i	$-0.601441\pi$
$677$	−16.3046	−0.626638	−0.313319	+	0.949648i	$0.601441\pi$
$678$	6.00984	0.230807
$679$	−2.04161	−0.0783500
$680$	−15.1316	−0.580269
$681$	−7.26602	−0.278435
$682$	14.7288	0.563995
$683$	−21.3045	−0.815195	−0.407597	−	0.913162i	$-0.633633\pi$
$683$	−21.3045	−0.815195	−0.407597	+	0.913162i	$0.633633\pi$
$684$	1.87654	0.0717512
$685$	20.2082	0.772116
$686$	−30.7294	−1.17326
$687$	−0.661901	−0.0252531
$688$	33.0694	1.26076
$689$	−6.65570	−0.253562
$690$	−0.100539	−0.00382747
$691$	27.1939	1.03450	0.517252	−	0.855833i	$-0.326955\pi$
$691$	27.1939	1.03450	0.517252	+	0.855833i	$0.326955\pi$
$692$	−4.51896	−0.171785
$693$	6.05796	0.230123
$694$	−33.5397	−1.27315
$695$	−8.02219	−0.304299
$696$	−1.45945	−0.0553203
$697$	15.4866	0.586598
$698$	−13.0553	−0.494152
$699$	9.22188	0.348804
$700$	−2.25475	−0.0852217
$701$	−47.7406	−1.80314	−0.901570	−	0.432634i	$-0.857584\pi$
$701$	−47.7406	−1.80314	−0.901570	+	0.432634i	$0.857584\pi$
$702$	5.39461	0.203606
$703$	−19.3388	−0.729376
$704$	−6.32477	−0.238374
$705$	0.190294	0.00716690
$706$	−55.6103	−2.09292
$707$	−8.80654	−0.331204
$708$	−0.527519	−0.0198254
$709$	−7.40983	−0.278282	−0.139141	−	0.990273i	$-0.544434\pi$
$709$	−7.40983	−0.278282	−0.139141	+	0.990273i	$0.544434\pi$
$710$	−9.54516	−0.358224
$711$	−38.5037	−1.44400
$712$	2.55604	0.0957917
$713$	1.10714	0.0414627
$714$	6.36165	0.238079
$715$	1.86118	0.0696041
$716$	−2.41695	−0.0903255
$717$	−6.84461	−0.255617
$718$	−16.9707	−0.633342
$719$	25.8872	0.965429	0.482714	−	0.875778i	$-0.339651\pi$
$719$	25.8872	0.965429	0.482714	+	0.875778i	$0.339651\pi$
$720$	−16.9379	−0.631240
$721$	−2.85353	−0.106271
$722$	−22.4481	−0.835431
$723$	4.51207	0.167806
$724$	−8.06657	−0.299792
$725$	4.26250	0.158305
$726$	−0.661577	−0.0245534
$727$	15.1179	0.560692	0.280346	−	0.959899i	$-0.409551\pi$
$727$	15.1179	0.560692	0.280346	+	0.959899i	$0.409551\pi$
$728$	−7.72732	−0.286394
$729$	−17.3512	−0.642639
$730$	−12.3676	−0.457745
$731$	32.4962	1.20191
$732$	−2.01997	−0.0746604
$733$	−29.4134	−1.08641	−0.543204	−	0.839601i	$-0.682789\pi$
$733$	−29.4134	−1.08641	−0.543204	+	0.839601i	$0.682789\pi$
$734$	40.4426	1.49276
$735$	−1.35743	−0.0500695
$736$	0.207345	0.00764283
$737$	10.0913	0.371719
$738$	14.8701	0.547374
$739$	4.00091	0.147176	0.0735879	−	0.997289i	$-0.476555\pi$
$739$	4.00091	0.147176	0.0735879	+	0.997289i	$0.476555\pi$
$740$	−4.00834	−0.147349
$741$	1.25873	0.0462407
$742$	−15.5777	−0.571875
$743$	−15.6865	−0.575480	−0.287740	−	0.957709i	$-0.592904\pi$
$743$	−15.6865	−0.575480	−0.287740	+	0.957709i	$0.592904\pi$
$744$	−10.7221	−0.393090
$745$	−13.2480	−0.485371
$746$	−3.65556	−0.133840
$747$	42.2512	1.54589
$748$	1.44123	0.0526966
$749$	3.48581	0.127369
$750$	−7.23157	−0.264060
$751$	−1.32229	−0.0482511	−0.0241255	−	0.999709i	$-0.507680\pi$
$751$	−1.32229	−0.0482511	−0.0241255	+	0.999709i	$0.507680\pi$
$752$	−1.50096	−0.0547345
$753$	6.17611	0.225070
$754$	−2.81297	−0.102442
$755$	−8.17062	−0.297359
$756$	1.75530	0.0638396
$757$	38.4901	1.39895	0.699474	−	0.714658i	$-0.253418\pi$
$757$	38.4901	1.39895	0.699474	+	0.714658i	$0.253418\pi$
$758$	−35.8010	−1.30035
$759$	−0.0497296	−0.00180507
$760$	−7.00740	−0.254185
$761$	5.29948	0.192106	0.0960531	−	0.995376i	$-0.469378\pi$
$761$	5.29948	0.192106	0.0960531	+	0.995376i	$0.469378\pi$
$762$	−4.01086	−0.145298
$763$	0.856652	0.0310129
$764$	−4.56678	−0.165220
$765$	−16.6443	−0.601778
$766$	37.3670	1.35013
$767$	5.28010	0.190653
$768$	−3.28129	−0.118403
$769$	−3.65801	−0.131911	−0.0659556	−	0.997823i	$-0.521010\pi$
$769$	−3.65801	−0.131911	−0.0659556	+	0.997823i	$0.521010\pi$
$770$	4.35609	0.156982
$771$	11.9988	0.432126
$772$	6.37129	0.229308
$773$	−32.9441	−1.18492	−0.592459	−	0.805600i	$-0.701843\pi$
$773$	−32.9441	−1.18492	−0.592459	+	0.805600i	$0.701843\pi$
$774$	31.2024	1.12155
$775$	31.3150	1.12487
$776$	2.42195	0.0869431
$777$	−8.75143	−0.313956
$778$	56.4144	2.02255
$779$	7.17183	0.256957
$780$	0.260897	0.00934160
$781$	−4.72131	−0.168942
$782$	0.779267	0.0278665
$783$	−3.31830	−0.118586
$784$	10.7068	0.382387
$785$	−32.1043	−1.14585
$786$	−0.765692	−0.0273113
$787$	6.86883	0.244847	0.122424	−	0.992478i	$-0.460933\pi$
$787$	6.86883	0.244847	0.122424	+	0.992478i	$0.460933\pi$
$788$	−7.11260	−0.253376
$789$	2.81890	0.100355
$790$	−27.6868	−0.985052
$791$	−19.5730	−0.695937
$792$	−7.18652	−0.255362
$793$	20.2185	0.717982
$794$	−22.9006	−0.812710
$795$	−2.73132	−0.0968698
$796$	−1.56634	−0.0555174
$797$	48.6134	1.72197	0.860987	−	0.508628i	$-0.169847\pi$
$797$	48.6134	1.72197	0.860987	+	0.508628i	$0.169847\pi$
$798$	2.94607	0.104290
$799$	−1.47495	−0.0521799
$800$	5.86467	0.207347
$801$	2.81158	0.0993424
$802$	15.1969	0.536622
$803$	−6.11736	−0.215877
$804$	1.41459	0.0498886
$805$	0.327440	0.0115407
$806$	−20.6658	−0.727923
$807$	−5.14784	−0.181212
$808$	10.4471	0.367529
$809$	−35.4896	−1.24775	−0.623873	−	0.781526i	$-0.714442\pi$
$809$	−35.4896	−1.24775	−0.623873	+	0.781526i	$0.714442\pi$
$810$	−14.8389	−0.521386
$811$	41.9727	1.47386	0.736930	−	0.675969i	$-0.236275\pi$
$811$	41.9727	1.47386	0.736930	+	0.675969i	$0.236275\pi$
$812$	−0.915283	−0.0321201
$813$	5.02059	0.176080
$814$	−14.2614	−0.499861
$815$	−3.67421	−0.128702
$816$	−8.79798	−0.307991
$817$	15.0489	0.526495
$818$	29.5807	1.03427
$819$	−8.49986	−0.297009
$820$	1.48650	0.0519108
$821$	33.4223	1.16645	0.583224	−	0.812311i	$-0.301791\pi$
$821$	33.4223	1.16645	0.583224	+	0.812311i	$0.301791\pi$
$822$	10.0787	0.351536
$823$	9.88210	0.344469	0.172234	−	0.985056i	$-0.444901\pi$
$823$	9.88210	0.344469	0.172234	+	0.985056i	$0.444901\pi$
$824$	3.38512	0.117926
$825$	−1.40658	−0.0489709
$826$	12.3581	0.429993
$827$	−38.3581	−1.33384	−0.666921	−	0.745129i	$-0.732388\pi$
$827$	−38.3581	−1.33384	−0.666921	+	0.745129i	$0.732388\pi$
$828$	0.104022	0.00361501
$829$	25.5238	0.886480	0.443240	−	0.896403i	$-0.353829\pi$
$829$	25.5238	0.886480	0.443240	+	0.896403i	$0.353829\pi$
$830$	30.3815	1.05456
$831$	1.64482	0.0570581
$832$	8.87422	0.307658
$833$	10.5212	0.364539
$834$	−4.00102	−0.138544
$835$	−25.6874	−0.888949
$836$	0.667431	0.0230836
$837$	−24.3784	−0.842639
$838$	21.5785	0.745417
$839$	8.12802	0.280610	0.140305	−	0.990108i	$-0.455192\pi$
$839$	8.12802	0.280610	0.140305	+	0.990108i	$0.455192\pi$
$840$	−3.17108	−0.109413
$841$	−27.2697	−0.940335
$842$	−44.0301	−1.51738
$843$	−7.12160	−0.245281
$844$	−3.98409	−0.137138
$845$	14.6329	0.503387
$846$	−1.41622	−0.0486908
$847$	2.15464	0.0740345
$848$	21.5435	0.739806
$849$	−0.452299	−0.0155228
$850$	22.0413	0.756009
$851$	−1.07200	−0.0367478
$852$	−0.661826	−0.0226738
$853$	−1.65956	−0.0568222	−0.0284111	−	0.999596i	$-0.509045\pi$
$853$	−1.65956	−0.0568222	−0.0284111	+	0.999596i	$0.509045\pi$
$854$	47.3215	1.61931
$855$	−7.70796	−0.263607
$856$	−4.13519	−0.141338
$857$	25.3687	0.866577	0.433289	−	0.901255i	$-0.357353\pi$
$857$	25.3687	0.866577	0.433289	+	0.901255i	$0.357353\pi$
$858$	0.928252	0.0316900
$859$	21.5898	0.736635	0.368318	−	0.929700i	$-0.379934\pi$
$859$	21.5898	0.736635	0.368318	+	0.929700i	$0.379934\pi$
$860$	3.11918	0.106363
$861$	3.24549	0.110606
$862$	14.3385	0.488373
$863$	31.2070	1.06230	0.531150	−	0.847278i	$-0.321760\pi$
$863$	31.2070	1.06230	0.531150	+	0.847278i	$0.321760\pi$
$864$	−4.56557	−0.155324
$865$	18.5618	0.631121
$866$	−2.67199	−0.0907980
$867$	−1.26626	−0.0430046
$868$	−6.72425	−0.228236
$869$	−13.6947	−0.464560
$870$	−1.15436	−0.0391366
$871$	−14.1590	−0.479761
$872$	−1.01624	−0.0344143
$873$	2.66409	0.0901658
$874$	0.360877	0.0122068
$875$	23.5520	0.796203
$876$	−0.857522	−0.0289730
$877$	−51.8767	−1.75175	−0.875876	−	0.482537i	$-0.839715\pi$
$877$	−51.8767	−1.75175	−0.875876	+	0.482537i	$0.839715\pi$
$878$	46.2533	1.56097
$879$	10.4438	0.352259
$880$	−6.02434	−0.203081
$881$	53.1736	1.79147	0.895733	−	0.444593i	$-0.146652\pi$
$881$	53.1736	1.79147	0.895733	+	0.444593i	$0.146652\pi$
$882$	10.1024	0.340164
$883$	−8.99031	−0.302548	−0.151274	−	0.988492i	$-0.548338\pi$
$883$	−8.99031	−0.302548	−0.151274	+	0.988492i	$0.548338\pi$
$884$	−2.02218	−0.0680132
$885$	2.16681	0.0728365
$886$	−27.7457	−0.932135
$887$	56.0682	1.88259	0.941293	−	0.337589i	$-0.109612\pi$
$887$	56.0682	1.88259	0.941293	+	0.337589i	$0.109612\pi$
$888$	10.3818	0.348389
$889$	13.0627	0.438109
$890$	2.02172	0.0677682
$891$	−7.33974	−0.245890
$892$	1.14345	0.0382857
$893$	−0.683045	−0.0228572
$894$	−6.60739	−0.220984
$895$	9.92772	0.331847
$896$	28.5692	0.954431
$897$	0.0697751	0.00232972
$898$	−11.5094	−0.384075
$899$	12.7119	0.423964
$900$	2.94222	0.0980738
$901$	21.1701	0.705277
$902$	5.28886	0.176100
$903$	6.81013	0.226627
$904$	23.2194	0.772265
$905$	33.1338	1.10140
$906$	−4.07505	−0.135384
$907$	14.2298	0.472492	0.236246	−	0.971693i	$-0.424083\pi$
$907$	14.2298	0.472492	0.236246	+	0.971693i	$0.424083\pi$
$908$	5.40574	0.179396
$909$	11.4916	0.381152
$910$	−6.11198	−0.202610
$911$	−46.9475	−1.55544	−0.777720	−	0.628611i	$-0.783624\pi$
$911$	−46.9475	−1.55544	−0.777720	+	0.628611i	$0.783624\pi$
$912$	−4.07433	−0.134914
$913$	15.0276	0.497339
$914$	12.3748	0.409321
$915$	8.29713	0.274295
$916$	0.492438	0.0162706
$917$	2.49373	0.0823502
$918$	−17.1589	−0.566327
$919$	−42.7315	−1.40958	−0.704792	−	0.709414i	$-0.748959\pi$
$919$	−42.7315	−1.40958	−0.704792	+	0.709414i	$0.748959\pi$
$920$	−0.388440	−0.0128065
$921$	6.26721	0.206511
$922$	−14.4552	−0.476058
$923$	6.62442	0.218045
$924$	0.302035	0.00993621
$925$	−30.3212	−0.996954
$926$	−9.66186	−0.317509
$927$	3.72355	0.122297
$928$	2.38067	0.0781494
$929$	16.9953	0.557598	0.278799	−	0.960349i	$-0.410064\pi$
$929$	16.9953	0.557598	0.278799	+	0.960349i	$0.410064\pi$
$930$	−8.48069	−0.278093
$931$	4.87237	0.159685
$932$	−6.86085	−0.224735
$933$	−10.5865	−0.346587
$934$	−7.32673	−0.239738
$935$	−5.91992	−0.193602
$936$	10.0833	0.329584
$937$	45.4494	1.48477	0.742384	−	0.669975i	$-0.233695\pi$
$937$	45.4494	1.48477	0.742384	+	0.669975i	$0.233695\pi$
$938$	−33.1392	−1.08203
$939$	−10.4313	−0.340412
$940$	−0.141574	−0.00461764
$941$	35.6503	1.16217	0.581084	−	0.813844i	$-0.302629\pi$
$941$	35.6503	1.16217	0.581084	+	0.813844i	$0.302629\pi$
$942$	−16.0118	−0.521693
$943$	0.397554	0.0129462
$944$	−17.0909	−0.556261
$945$	−7.20997	−0.234540
$946$	11.0978	0.360821
$947$	−11.7373	−0.381412	−0.190706	−	0.981647i	$-0.561078\pi$
$947$	−11.7373	−0.381412	−0.190706	+	0.981647i	$0.561078\pi$
$948$	−1.91970	−0.0623489
$949$	8.58321	0.278623
$950$	10.2073	0.331168
$951$	7.85929	0.254855
$952$	24.5786	0.796597
$953$	42.8910	1.38938	0.694688	−	0.719311i	$-0.255542\pi$
$953$	42.8910	1.38938	0.694688	+	0.719311i	$0.255542\pi$
$954$	20.3272	0.658118
$955$	18.7582	0.607002
$956$	5.09222	0.164694
$957$	−0.570981	−0.0184572
$958$	−25.5838	−0.826574
$959$	−32.8247	−1.05997
$960$	3.64173	0.117536
$961$	62.3894	2.01256
$962$	20.0100	0.645147
$963$	−4.54861	−0.146577
$964$	−3.35687	−0.108117
$965$	−26.1704	−0.842453
$966$	0.163309	0.00525437
$967$	−19.8632	−0.638756	−0.319378	−	0.947627i	$-0.603474\pi$
$967$	−19.8632	−0.638756	−0.319378	+	0.947627i	$0.603474\pi$
$968$	−2.55604	−0.0821543
$969$	−4.00370	−0.128618
$970$	1.91566	0.0615082
$971$	−18.2216	−0.584758	−0.292379	−	0.956303i	$-0.594447\pi$
$971$	−18.2216	−0.584758	−0.292379	+	0.956303i	$0.594447\pi$
$972$	−3.47285	−0.111392
$973$	13.0307	0.417744
$974$	44.5226	1.42660
$975$	1.97356	0.0632046
$976$	−65.4443	−2.09482
$977$	19.2926	0.617226	0.308613	−	0.951188i	$-0.400135\pi$
$977$	19.2926	0.617226	0.308613	+	0.951188i	$0.400135\pi$
$978$	−1.83249	−0.0585967
$979$	1.00000	0.0319601
$980$	1.00989	0.0322598
$981$	−1.11784	−0.0356899
$982$	−57.6281	−1.83899
$983$	−24.3613	−0.777006	−0.388503	−	0.921447i	$-0.627008\pi$
$983$	−24.3613	−0.777006	−0.388503	+	0.921447i	$0.627008\pi$
$984$	−3.85010	−0.122737
$985$	29.2153	0.930877
$986$	8.94732	0.284941
$987$	−0.309100	−0.00983877
$988$	−0.936466	−0.0297929
$989$	0.834203	0.0265261
$990$	−5.68423	−0.180657
$991$	53.0063	1.68380	0.841900	−	0.539634i	$-0.181437\pi$
$991$	53.0063	1.68380	0.841900	+	0.539634i	$0.181437\pi$
$992$	17.4899	0.555306
$993$	10.9414	0.347215
$994$	15.5045	0.491772
$995$	6.43380	0.203965
$996$	2.10654	0.0667482
$997$	24.0929	0.763030	0.381515	−	0.924363i	$-0.375402\pi$
$997$	24.0929	0.763030	0.381515	+	0.924363i	$0.375402\pi$
$998$	4.24393	0.134339
$999$	23.6047	0.746819

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	979.2.a.d.1.14	✓	17
3.2	odd	2		8811.2.a.p.1.4		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
979.2.a.d.1.14	✓	17	1.1	even	1	trivial
8811.2.a.p.1.4		17	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 979 = 11 \cdot 89 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	979.a (trivial)

\(f(q)\)	\(=\)	\(q+1.52412 q^{2} -0.434072 q^{3} +0.322938 q^{4} -1.32648 q^{5} -0.661577 q^{6} +2.15464 q^{7} -2.55604 q^{8} -2.81158 q^{9} +O(q^{10})\)	\(q+1.52412 q^{2} -0.434072 q^{3} +0.322938 q^{4} -1.32648 q^{5} -0.661577 q^{6} +2.15464 q^{7} -2.55604 q^{8} -2.81158 q^{9} -2.02172 q^{10} -1.00000 q^{11} -0.140178 q^{12} +1.40309 q^{13} +3.28393 q^{14} +0.575789 q^{15} -4.54159 q^{16} -4.46287 q^{17} -4.28518 q^{18} -2.06674 q^{19} -0.428373 q^{20} -0.935270 q^{21} -1.52412 q^{22} -0.114565 q^{23} +1.10951 q^{24} -3.24044 q^{25} +2.13848 q^{26} +2.52264 q^{27} +0.695817 q^{28} -1.31541 q^{29} +0.877571 q^{30} -9.66382 q^{31} -1.80984 q^{32} +0.434072 q^{33} -6.80194 q^{34} -2.85810 q^{35} -0.907968 q^{36} +9.35712 q^{37} -3.14996 q^{38} -0.609041 q^{39} +3.39055 q^{40} -3.47011 q^{41} -1.42546 q^{42} -7.28145 q^{43} -0.322938 q^{44} +3.72952 q^{45} -0.174611 q^{46} +0.330493 q^{47} +1.97137 q^{48} -2.35751 q^{49} -4.93882 q^{50} +1.93720 q^{51} +0.453112 q^{52} -4.74360 q^{53} +3.84481 q^{54} +1.32648 q^{55} -5.50736 q^{56} +0.897115 q^{57} -2.00484 q^{58} +3.76320 q^{59} +0.185944 q^{60} +14.4100 q^{61} -14.7288 q^{62} -6.05796 q^{63} +6.32477 q^{64} -1.86118 q^{65} +0.661577 q^{66} -10.0913 q^{67} -1.44123 q^{68} +0.0497296 q^{69} -4.35609 q^{70} +4.72131 q^{71} +7.18652 q^{72} +6.11736 q^{73} +14.2614 q^{74} +1.40658 q^{75} -0.667431 q^{76} -2.15464 q^{77} -0.928252 q^{78} +13.6947 q^{79} +6.02434 q^{80} +7.33974 q^{81} -5.28886 q^{82} -15.0276 q^{83} -0.302035 q^{84} +5.91992 q^{85} -11.0978 q^{86} +0.570981 q^{87} +2.55604 q^{88} -1.00000 q^{89} +5.68423 q^{90} +3.02316 q^{91} -0.0369976 q^{92} +4.19479 q^{93} +0.503711 q^{94} +2.74150 q^{95} +0.785599 q^{96} -0.947541 q^{97} -3.59312 q^{98} +2.81158 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 4 q^{2} - q^{3} + 14 q^{4} - 14 q^{5} - 6 q^{6} - 5 q^{7} - 18 q^{8} + 6 q^{9}+O(q^{10}) \) 17 * q - 4 * q^2 - q^3 + 14 * q^4 - 14 * q^5 - 6 * q^6 - 5 * q^7 - 18 * q^8 + 6 * q^9	\( 17 q - 4 q^{2} - q^{3} + 14 q^{4} - 14 q^{5} - 6 q^{6} - 5 q^{7} - 18 q^{8} + 6 q^{9} - 6 q^{10} - 17 q^{11} + q^{12} - 6 q^{13} - 17 q^{14} - 3 q^{15} + 8 q^{16} - 19 q^{17} - 9 q^{19} - 29 q^{20} - 35 q^{21} + 4 q^{22} - 13 q^{23} - 20 q^{24} + 19 q^{25} - 19 q^{27} + q^{28} - 54 q^{29} + q^{30} + 8 q^{31} - 35 q^{32} + q^{33} + 14 q^{34} - 22 q^{35} - 20 q^{36} - 3 q^{38} - 18 q^{39} + 16 q^{40} - 16 q^{41} - 37 q^{42} - 21 q^{43} - 14 q^{44} - 31 q^{45} - 31 q^{46} - 3 q^{47} + 34 q^{48} + 2 q^{49} - 5 q^{50} - 13 q^{51} + 14 q^{52} - 43 q^{53} - 19 q^{54} + 14 q^{55} + 14 q^{56} - 29 q^{57} + 22 q^{58} - q^{59} - 11 q^{60} - 29 q^{61} + 32 q^{62} + 17 q^{63} - 22 q^{64} - 44 q^{65} + 6 q^{66} + 17 q^{67} - 43 q^{68} - 21 q^{69} + 76 q^{70} + 6 q^{71} + 17 q^{72} + 3 q^{73} - 10 q^{74} - 11 q^{75} - 17 q^{76} + 5 q^{77} + 35 q^{78} - 43 q^{79} - 32 q^{80} + 13 q^{81} - 10 q^{82} - 14 q^{83} + 44 q^{84} + 5 q^{85} - 37 q^{86} - 3 q^{87} + 18 q^{88} - 17 q^{89} - 2 q^{90} - 12 q^{91} + 23 q^{92} - 26 q^{93} - 4 q^{94} - 35 q^{95} - 20 q^{96} - 6 q^{97} + q^{98} - 6 q^{99}+O(q^{100}) \) 17 * q - 4 * q^2 - q^3 + 14 * q^4 - 14 * q^5 - 6 * q^6 - 5 * q^7 - 18 * q^8 + 6 * q^9 - 6 * q^10 - 17 * q^11 + q^12 - 6 * q^13 - 17 * q^14 - 3 * q^15 + 8 * q^16 - 19 * q^17 - 9 * q^19 - 29 * q^20 - 35 * q^21 + 4 * q^22 - 13 * q^23 - 20 * q^24 + 19 * q^25 - 19 * q^27 + q^28 - 54 * q^29 + q^30 + 8 * q^31 - 35 * q^32 + q^33 + 14 * q^34 - 22 * q^35 - 20 * q^36 - 3 * q^38 - 18 * q^39 + 16 * q^40 - 16 * q^41 - 37 * q^42 - 21 * q^43 - 14 * q^44 - 31 * q^45 - 31 * q^46 - 3 * q^47 + 34 * q^48 + 2 * q^49 - 5 * q^50 - 13 * q^51 + 14 * q^52 - 43 * q^53 - 19 * q^54 + 14 * q^55 + 14 * q^56 - 29 * q^57 + 22 * q^58 - q^59 - 11 * q^60 - 29 * q^61 + 32 * q^62 + 17 * q^63 - 22 * q^64 - 44 * q^65 + 6 * q^66 + 17 * q^67 - 43 * q^68 - 21 * q^69 + 76 * q^70 + 6 * q^71 + 17 * q^72 + 3 * q^73 - 10 * q^74 - 11 * q^75 - 17 * q^76 + 5 * q^77 + 35 * q^78 - 43 * q^79 - 32 * q^80 + 13 * q^81 - 10 * q^82 - 14 * q^83 + 44 * q^84 + 5 * q^85 - 37 * q^86 - 3 * q^87 + 18 * q^88 - 17 * q^89 - 2 * q^90 - 12 * q^91 + 23 * q^92 - 26 * q^93 - 4 * q^94 - 35 * q^95 - 20 * q^96 - 6 * q^97 + q^98 - 6 * q^99

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