LMFDB - Embedded newform 4029.2.a.e.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4029,2,Mod(1,4029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4029, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4029 = 3 \cdot 17 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4029.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:	$32.1717269744$
Analytic rank:	$1$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 6 x^{17} - 10 x^{16} + 120 x^{15} - 56 x^{14} - 921 x^{13} + 1181 x^{12} + 3316 x^{11} + \cdots + 138 $ x^18 - 6x^17 - 10x^16 + 120x^15 - 56x^14 - 921x^13 + 1181x^12 + 3316x^11 - 6280x^10 - 5249x^9 + 15005x^8 + 1809x^7 - 16711x^6 + 2434x^5 + 8758x^4 - 1858x^3 - 1942x^2 + 318*x + 138
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			1.4
Root			$1.99378$ of defining polynomial
Character	$\chi$	$=$	4029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.99378 q^{2} +1.00000 q^{3} +1.97517 q^{4} +1.24008 q^{5} -1.99378 q^{6} -4.06333 q^{7} +0.0495043 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.99378 q^{2} +1.00000 q^{3} +1.97517 q^{4} +1.24008 q^{5} -1.99378 q^{6} -4.06333 q^{7} +0.0495043 q^{8} +1.00000 q^{9} -2.47246 q^{10} +3.04052 q^{11} +1.97517 q^{12} +2.14510 q^{13} +8.10139 q^{14} +1.24008 q^{15} -4.04904 q^{16} +1.00000 q^{17} -1.99378 q^{18} +2.62993 q^{19} +2.44937 q^{20} -4.06333 q^{21} -6.06215 q^{22} +0.657524 q^{23} +0.0495043 q^{24} -3.46220 q^{25} -4.27686 q^{26} +1.00000 q^{27} -8.02576 q^{28} -6.92925 q^{29} -2.47246 q^{30} -9.42663 q^{31} +7.97390 q^{32} +3.04052 q^{33} -1.99378 q^{34} -5.03886 q^{35} +1.97517 q^{36} +0.281380 q^{37} -5.24351 q^{38} +2.14510 q^{39} +0.0613894 q^{40} -5.67704 q^{41} +8.10139 q^{42} -12.4879 q^{43} +6.00555 q^{44} +1.24008 q^{45} -1.31096 q^{46} -0.718400 q^{47} -4.04904 q^{48} +9.51062 q^{49} +6.90287 q^{50} +1.00000 q^{51} +4.23693 q^{52} +3.71252 q^{53} -1.99378 q^{54} +3.77050 q^{55} -0.201152 q^{56} +2.62993 q^{57} +13.8154 q^{58} -7.57028 q^{59} +2.44937 q^{60} +11.2339 q^{61} +18.7947 q^{62} -4.06333 q^{63} -7.80015 q^{64} +2.66010 q^{65} -6.06215 q^{66} -7.51513 q^{67} +1.97517 q^{68} +0.657524 q^{69} +10.0464 q^{70} +4.69340 q^{71} +0.0495043 q^{72} +10.8467 q^{73} -0.561011 q^{74} -3.46220 q^{75} +5.19456 q^{76} -12.3546 q^{77} -4.27686 q^{78} -1.00000 q^{79} -5.02115 q^{80} +1.00000 q^{81} +11.3188 q^{82} -2.47158 q^{83} -8.02576 q^{84} +1.24008 q^{85} +24.8982 q^{86} -6.92925 q^{87} +0.150519 q^{88} +5.34703 q^{89} -2.47246 q^{90} -8.71623 q^{91} +1.29872 q^{92} -9.42663 q^{93} +1.43233 q^{94} +3.26133 q^{95} +7.97390 q^{96} +14.6992 q^{97} -18.9621 q^{98} +3.04052 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 6 q^{2} + 18 q^{3} + 20 q^{4} - 5 q^{5} - 6 q^{6} - 13 q^{7} - 12 q^{8} + 18 q^{9}+O(q^{10}) $ 18 * q - 6 * q^2 + 18 * q^3 + 20 * q^4 - 5 * q^5 - 6 * q^6 - 13 * q^7 - 12 * q^8 + 18 * q^9	\( 18 q - 6 q^{2} + 18 q^{3} + 20 q^{4} - 5 q^{5} - 6 q^{6} - 13 q^{7} - 12 q^{8} + 18 q^{9} - 15 q^{10} - 27 q^{11} + 20 q^{12} - 4 q^{13} - 5 q^{14} - 5 q^{15} + 16 q^{16} + 18 q^{17} - 6 q^{18} - 30 q^{19} - 16 q^{20} - 13 q^{21} + 13 q^{22} - 21 q^{23} - 12 q^{24} + 13 q^{25} - 20 q^{26} + 18 q^{27} - 33 q^{28} - 47 q^{29} - 15 q^{30} - 18 q^{31} - 45 q^{32} - 27 q^{33} - 6 q^{34} - 17 q^{35} + 20 q^{36} + q^{37} + 5 q^{38} - 4 q^{39} - 12 q^{40} - 18 q^{41} - 5 q^{42} - 39 q^{43} - 34 q^{44} - 5 q^{45} - 7 q^{46} + 16 q^{48} + 15 q^{49} - 23 q^{50} + 18 q^{51} + 5 q^{52} - 9 q^{53} - 6 q^{54} + q^{55} - 24 q^{56} - 30 q^{57} + 41 q^{58} - 42 q^{59} - 16 q^{60} - 43 q^{61} - 54 q^{62} - 13 q^{63} + 22 q^{64} - 25 q^{65} + 13 q^{66} + 20 q^{68} - 21 q^{69} + 17 q^{70} + 9 q^{71} - 12 q^{72} + 19 q^{73} - 30 q^{74} + 13 q^{75} - 17 q^{76} - 14 q^{77} - 20 q^{78} - 18 q^{79} + 36 q^{80} + 18 q^{81} - 3 q^{82} - 61 q^{83} - 33 q^{84} - 5 q^{85} - 24 q^{86} - 47 q^{87} - 25 q^{88} + 10 q^{89} - 15 q^{90} - 52 q^{91} - 74 q^{92} - 18 q^{93} + 31 q^{94} - 37 q^{95} - 45 q^{96} - 9 q^{97} + 27 q^{98} - 27 q^{99}+O(q^{100}) \) 18 * q - 6 * q^2 + 18 * q^3 + 20 * q^4 - 5 * q^5 - 6 * q^6 - 13 * q^7 - 12 * q^8 + 18 * q^9 - 15 * q^10 - 27 * q^11 + 20 * q^12 - 4 * q^13 - 5 * q^14 - 5 * q^15 + 16 * q^16 + 18 * q^17 - 6 * q^18 - 30 * q^19 - 16 * q^20 - 13 * q^21 + 13 * q^22 - 21 * q^23 - 12 * q^24 + 13 * q^25 - 20 * q^26 + 18 * q^27 - 33 * q^28 - 47 * q^29 - 15 * q^30 - 18 * q^31 - 45 * q^32 - 27 * q^33 - 6 * q^34 - 17 * q^35 + 20 * q^36 + q^37 + 5 * q^38 - 4 * q^39 - 12 * q^40 - 18 * q^41 - 5 * q^42 - 39 * q^43 - 34 * q^44 - 5 * q^45 - 7 * q^46 + 16 * q^48 + 15 * q^49 - 23 * q^50 + 18 * q^51 + 5 * q^52 - 9 * q^53 - 6 * q^54 + q^55 - 24 * q^56 - 30 * q^57 + 41 * q^58 - 42 * q^59 - 16 * q^60 - 43 * q^61 - 54 * q^62 - 13 * q^63 + 22 * q^64 - 25 * q^65 + 13 * q^66 + 20 * q^68 - 21 * q^69 + 17 * q^70 + 9 * q^71 - 12 * q^72 + 19 * q^73 - 30 * q^74 + 13 * q^75 - 17 * q^76 - 14 * q^77 - 20 * q^78 - 18 * q^79 + 36 * q^80 + 18 * q^81 - 3 * q^82 - 61 * q^83 - 33 * q^84 - 5 * q^85 - 24 * q^86 - 47 * q^87 - 25 * q^88 + 10 * q^89 - 15 * q^90 - 52 * q^91 - 74 * q^92 - 18 * q^93 + 31 * q^94 - 37 * q^95 - 45 * q^96 - 9 * q^97 + 27 * q^98 - 27 * 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 $

$2$	−1.99378	−1.40982	−0.704909	−	0.709298i	$-0.749012\pi$
$2$	−1.99378	−1.40982	−0.704909	+	0.709298i	$0.749012\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.97517	0.987585
$5$	1.24008	0.554582	0.277291	−	0.960786i	$-0.410563\pi$
$5$	1.24008	0.554582	0.277291	+	0.960786i	$0.410563\pi$
$6$	−1.99378	−0.813959
$7$	−4.06333	−1.53579	−0.767896	−	0.640574i	$-0.778696\pi$
$7$	−4.06333	−1.53579	−0.767896	+	0.640574i	$0.778696\pi$
$8$	0.0495043	0.0175024
$9$	1.00000	0.333333
$10$	−2.47246	−0.781859
$11$	3.04052	0.916753	0.458376	−	0.888758i	$-0.348431\pi$
$11$	3.04052	0.916753	0.458376	+	0.888758i	$0.348431\pi$
$12$	1.97517	0.570183
$13$	2.14510	0.594943	0.297471	−	0.954731i	$-0.403857\pi$
$13$	2.14510	0.594943	0.297471	+	0.954731i	$0.403857\pi$
$14$	8.10139	2.16519
$15$	1.24008	0.320188
$16$	−4.04904	−1.01226
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.99378	−0.469939
$19$	2.62993	0.603348	0.301674	−	0.953411i	$-0.402455\pi$
$19$	2.62993	0.603348	0.301674	+	0.953411i	$0.402455\pi$
$20$	2.44937	0.547697
$21$	−4.06333	−0.886690
$22$	−6.06215	−1.29245
$23$	0.657524	0.137103	0.0685516	−	0.997648i	$-0.478162\pi$
$23$	0.657524	0.137103	0.0685516	+	0.997648i	$0.478162\pi$
$24$	0.0495043	0.0101050
$25$	−3.46220	−0.692439
$26$	−4.27686	−0.838761
$27$	1.00000	0.192450
$28$	−8.02576	−1.51673
$29$	−6.92925	−1.28673	−0.643364	−	0.765560i	$-0.722462\pi$
$29$	−6.92925	−1.28673	−0.643364	+	0.765560i	$0.722462\pi$
$30$	−2.47246	−0.451406
$31$	−9.42663	−1.69307	−0.846536	−	0.532331i	$-0.821316\pi$
$31$	−9.42663	−1.69307	−0.846536	+	0.532331i	$0.821316\pi$
$32$	7.97390	1.40960
$33$	3.04052	0.529287
$34$	−1.99378	−0.341931
$35$	−5.03886	−0.851723
$36$	1.97517	0.329195
$37$	0.281380	0.0462586	0.0231293	−	0.999732i	$-0.492637\pi$
$37$	0.281380	0.0462586	0.0231293	+	0.999732i	$0.492637\pi$
$38$	−5.24351	−0.850610
$39$	2.14510	0.343490
$40$	0.0613894	0.00970651
$41$	−5.67704	−0.886605	−0.443303	−	0.896372i	$-0.646193\pi$
$41$	−5.67704	−0.886605	−0.443303	+	0.896372i	$0.646193\pi$
$42$	8.10139	1.25007
$43$	−12.4879	−1.90439	−0.952193	−	0.305497i	$-0.901178\pi$
$43$	−12.4879	−1.90439	−0.952193	+	0.305497i	$0.901178\pi$
$44$	6.00555	0.905371
$45$	1.24008	0.184861
$46$	−1.31096	−0.193291
$47$	−0.718400	−0.104789	−0.0523947	−	0.998626i	$-0.516685\pi$
$47$	−0.718400	−0.104789	−0.0523947	+	0.998626i	$0.516685\pi$
$48$	−4.04904	−0.584429
$49$	9.51062	1.35866
$50$	6.90287	0.976213
$51$	1.00000	0.140028
$52$	4.23693	0.587557
$53$	3.71252	0.509953	0.254977	−	0.966947i	$-0.417932\pi$
$53$	3.71252	0.509953	0.254977	+	0.966947i	$0.417932\pi$
$54$	−1.99378	−0.271320
$55$	3.77050	0.508414
$56$	−0.201152	−0.0268801
$57$	2.62993	0.348343
$58$	13.8154	1.81405
$59$	−7.57028	−0.985566	−0.492783	−	0.870152i	$-0.664020\pi$
$59$	−7.57028	−0.985566	−0.492783	+	0.870152i	$0.664020\pi$
$60$	2.44937	0.316213
$61$	11.2339	1.43835	0.719177	−	0.694827i	$-0.244519\pi$
$61$	11.2339	1.43835	0.719177	+	0.694827i	$0.244519\pi$
$62$	18.7947	2.38692
$63$	−4.06333	−0.511931
$64$	−7.80015	−0.975018
$65$	2.66010	0.329944
$66$	−6.06215	−0.746199
$67$	−7.51513	−0.918120	−0.459060	−	0.888405i	$-0.651814\pi$
$67$	−7.51513	−0.918120	−0.459060	+	0.888405i	$0.651814\pi$
$68$	1.97517	0.239525
$69$	0.657524	0.0791566
$70$	10.0464	1.20077
$71$	4.69340	0.557004	0.278502	−	0.960436i	$-0.410162\pi$
$71$	4.69340	0.557004	0.278502	+	0.960436i	$0.410162\pi$
$72$	0.0495043	0.00583413
$73$	10.8467	1.26951	0.634755	−	0.772714i	$-0.281101\pi$
$73$	10.8467	1.26951	0.634755	+	0.772714i	$0.281101\pi$
$74$	−0.561011	−0.0652162
$75$	−3.46220	−0.399780
$76$	5.19456	0.595857
$77$	−12.3546	−1.40794
$78$	−4.27686	−0.484259
$79$	−1.00000	−0.112509
$79$	−1.00000	−0.112509
$80$	−5.02115	−0.561381
$81$	1.00000	0.111111
$82$	11.3188	1.24995
$83$	−2.47158	−0.271292	−0.135646	−	0.990757i	$-0.543311\pi$
$83$	−2.47158	−0.271292	−0.135646	+	0.990757i	$0.543311\pi$
$84$	−8.02576	−0.875682
$85$	1.24008	0.134506
$86$	24.8982	2.68484
$87$	−6.92925	−0.742893
$88$	0.150519	0.0160454
$89$	5.34703	0.566784	0.283392	−	0.959004i	$-0.408540\pi$
$89$	5.34703	0.566784	0.283392	+	0.959004i	$0.408540\pi$
$90$	−2.47246	−0.260620
$91$	−8.71623	−0.913709
$92$	1.29872	0.135401
$93$	−9.42663	−0.977496
$94$	1.43233	0.147734
$95$	3.26133	0.334606
$96$	7.97390	0.813833
$97$	14.6992	1.49247	0.746237	−	0.665681i	$-0.231859\pi$
$97$	14.6992	1.49247	0.746237	+	0.665681i	$0.231859\pi$
$98$	−18.9621	−1.91546
$99$	3.04052	0.305584
$100$	−6.83843	−0.683843
$101$	7.81357	0.777479	0.388740	−	0.921348i	$-0.372911\pi$
$101$	7.81357	0.777479	0.388740	+	0.921348i	$0.372911\pi$
$102$	−1.99378	−0.197414
$103$	−6.11213	−0.602246	−0.301123	−	0.953585i	$-0.597361\pi$
$103$	−6.11213	−0.602246	−0.301123	+	0.953585i	$0.597361\pi$
$104$	0.106191	0.0104129
$105$	−5.03886	−0.491742
$106$	−7.40195	−0.718941
$107$	−7.11929	−0.688248	−0.344124	−	0.938924i	$-0.611824\pi$
$107$	−7.11929	−0.688248	−0.344124	+	0.938924i	$0.611824\pi$
$108$	1.97517	0.190061
$109$	−4.96541	−0.475600	−0.237800	−	0.971314i	$-0.576426\pi$
$109$	−4.96541	−0.475600	−0.237800	+	0.971314i	$0.576426\pi$
$110$	−7.51756	−0.716771
$111$	0.281380	0.0267074
$112$	16.4526	1.55462
$113$	−14.4632	−1.36058	−0.680290	−	0.732943i	$-0.738146\pi$
$113$	−14.4632	−1.36058	−0.680290	+	0.732943i	$0.738146\pi$
$114$	−5.24351	−0.491100
$115$	0.815384	0.0760349
$116$	−13.6864	−1.27075
$117$	2.14510	0.198314
$118$	15.0935	1.38947
$119$	−4.06333	−0.372484
$120$	0.0613894	0.00560406
$121$	−1.75521	−0.159565
$122$	−22.3980	−2.02782
$123$	−5.67704	−0.511882
$124$	−18.6192	−1.67205
$125$	−10.4938	−0.938596
$126$	8.10139	0.721729
$127$	11.9602	1.06129	0.530647	−	0.847593i	$-0.321949\pi$
$127$	11.9602	1.06129	0.530647	+	0.847593i	$0.321949\pi$
$128$	−0.396004	−0.0350021
$129$	−12.4879	−1.09950
$130$	−5.30366	−0.465161
$131$	−14.9889	−1.30959	−0.654794	−	0.755807i	$-0.727245\pi$
$131$	−14.9889	−1.30959	−0.654794	+	0.755807i	$0.727245\pi$
$132$	6.00555	0.522716
$133$	−10.6863	−0.926617
$134$	14.9835	1.29438
$135$	1.24008	0.106729
$136$	0.0495043	0.00424496
$137$	−8.56469	−0.731730	−0.365865	−	0.930668i	$-0.619227\pi$
$137$	−8.56469	−0.731730	−0.365865	+	0.930668i	$0.619227\pi$
$138$	−1.31096	−0.111596
$139$	14.4997	1.22985	0.614925	−	0.788586i	$-0.289186\pi$
$139$	14.4997	1.22985	0.614925	+	0.788586i	$0.289186\pi$
$140$	−9.95261	−0.841149
$141$	−0.718400	−0.0605002
$142$	−9.35762	−0.785274
$143$	6.52222	0.545415
$144$	−4.04904	−0.337420
$145$	−8.59284	−0.713596
$146$	−21.6259	−1.78978
$147$	9.51062	0.784422
$148$	0.555774	0.0456843
$149$	−5.15873	−0.422620	−0.211310	−	0.977419i	$-0.567773\pi$
$149$	−5.15873	−0.422620	−0.211310	+	0.977419i	$0.567773\pi$
$150$	6.90287	0.563617
$151$	−20.3190	−1.65354	−0.826768	−	0.562543i	$-0.809823\pi$
$151$	−20.3190	−1.65354	−0.826768	+	0.562543i	$0.809823\pi$
$152$	0.130193	0.0105600
$153$	1.00000	0.0808452
$154$	24.6325	1.98494
$155$	−11.6898	−0.938947
$156$	4.23693	0.339226
$157$	13.9313	1.11184	0.555918	−	0.831237i	$-0.312367\pi$
$157$	13.9313	1.11184	0.555918	+	0.831237i	$0.312367\pi$
$158$	1.99378	0.158617
$159$	3.71252	0.294422
$160$	9.88830	0.781738
$161$	−2.67173	−0.210562
$162$	−1.99378	−0.156646
$163$	−0.911527	−0.0713963	−0.0356981	−	0.999363i	$-0.511365\pi$
$163$	−0.911527	−0.0713963	−0.0356981	+	0.999363i	$0.511365\pi$
$164$	−11.2131	−0.875598
$165$	3.77050	0.293533
$166$	4.92780	0.382472
$167$	15.5163	1.20068	0.600342	−	0.799743i	$-0.295031\pi$
$167$	15.5163	1.20068	0.600342	+	0.799743i	$0.295031\pi$
$168$	−0.201152	−0.0155192
$169$	−8.39856	−0.646043
$170$	−2.47246	−0.189629
$171$	2.62993	0.201116
$172$	−24.6657	−1.88074
$173$	−21.3038	−1.61970	−0.809849	−	0.586638i	$-0.800451\pi$
$173$	−21.3038	−1.61970	−0.809849	+	0.586638i	$0.800451\pi$
$174$	13.8154	1.04734
$175$	14.0680	1.06344
$176$	−12.3112	−0.927992
$177$	−7.57028	−0.569017
$178$	−10.6608	−0.799062
$179$	−10.8071	−0.807763	−0.403881	−	0.914811i	$-0.632339\pi$
$179$	−10.8071	−0.807763	−0.403881	+	0.914811i	$0.632339\pi$
$180$	2.44937	0.182566
$181$	20.2540	1.50546	0.752732	−	0.658327i	$-0.228735\pi$
$181$	20.2540	1.50546	0.752732	+	0.658327i	$0.228735\pi$
$182$	17.3783	1.28816
$183$	11.2339	0.830434
$184$	0.0325502	0.00239964
$185$	0.348935	0.0256542
$186$	18.7947	1.37809
$187$	3.04052	0.222345
$188$	−1.41896	−0.103489
$189$	−4.06333	−0.295563
$190$	−6.50239	−0.471733
$191$	−9.92121	−0.717874	−0.358937	−	0.933362i	$-0.616861\pi$
$191$	−9.92121	−0.717874	−0.358937	+	0.933362i	$0.616861\pi$
$192$	−7.80015	−0.562927
$193$	−16.9995	−1.22365	−0.611824	−	0.790994i	$-0.709564\pi$
$193$	−16.9995	−1.22365	−0.611824	+	0.790994i	$0.709564\pi$
$194$	−29.3069	−2.10411
$195$	2.66010	0.190494
$196$	18.7851	1.34179
$197$	−9.31267	−0.663500	−0.331750	−	0.943367i	$-0.607639\pi$
$197$	−9.31267	−0.663500	−0.331750	+	0.943367i	$0.607639\pi$
$198$	−6.06215	−0.430818
$199$	6.87632	0.487449	0.243725	−	0.969844i	$-0.421631\pi$
$199$	6.87632	0.487449	0.243725	+	0.969844i	$0.421631\pi$
$200$	−0.171393	−0.0121194
$201$	−7.51513	−0.530077
$202$	−15.5786	−1.09610
$203$	28.1558	1.97615
$204$	1.97517	0.138290
$205$	−7.04000	−0.491695
$206$	12.1863	0.849056
$207$	0.657524	0.0457011
$208$	−8.68559	−0.602237
$209$	7.99637	0.553120
$210$	10.0464	0.693267
$211$	−10.9511	−0.753907	−0.376954	−	0.926232i	$-0.623028\pi$
$211$	−10.9511	−0.753907	−0.376954	+	0.926232i	$0.623028\pi$
$212$	7.33285	0.503623
$213$	4.69340	0.321587
$214$	14.1943	0.970303
$215$	−15.4860	−1.05614
$216$	0.0495043	0.00336834
$217$	38.3035	2.60021
$218$	9.89995	0.670509
$219$	10.8467	0.732951
$220$	7.44738	0.502102
$221$	2.14510	0.144295
$222$	−0.561011	−0.0376526
$223$	−12.7687	−0.855056	−0.427528	−	0.904002i	$-0.640615\pi$
$223$	−12.7687	−0.855056	−0.427528	+	0.904002i	$0.640615\pi$
$224$	−32.4006	−2.16485
$225$	−3.46220	−0.230813
$226$	28.8364	1.91817
$227$	−9.26071	−0.614655	−0.307327	−	0.951604i	$-0.599435\pi$
$227$	−9.26071	−0.614655	−0.307327	+	0.951604i	$0.599435\pi$
$228$	5.19456	0.344018
$229$	−19.0851	−1.26118	−0.630588	−	0.776118i	$-0.717186\pi$
$229$	−19.0851	−1.26118	−0.630588	+	0.776118i	$0.717186\pi$
$230$	−1.62570	−0.107195
$231$	−12.3546	−0.812876
$232$	−0.343027	−0.0225209
$233$	2.01311	0.131883	0.0659417	−	0.997823i	$-0.478995\pi$
$233$	2.01311	0.131883	0.0659417	+	0.997823i	$0.478995\pi$
$234$	−4.27686	−0.279587
$235$	−0.890876	−0.0581143
$236$	−14.9526	−0.973331
$237$	−1.00000	−0.0649570
$238$	8.10139	0.525135
$239$	10.8053	0.698939	0.349470	−	0.936948i	$-0.386362\pi$
$239$	10.8053	0.698939	0.349470	+	0.936948i	$0.386362\pi$
$240$	−5.02115	−0.324114
$241$	1.74544	0.112434	0.0562168	−	0.998419i	$-0.482096\pi$
$241$	1.74544	0.112434	0.0562168	+	0.998419i	$0.482096\pi$
$242$	3.49951	0.224957
$243$	1.00000	0.0641500
$244$	22.1889	1.42050
$245$	11.7939	0.753488
$246$	11.3188	0.721660
$247$	5.64146	0.358957
$248$	−0.466658	−0.0296328
$249$	−2.47158	−0.156630
$250$	20.9224	1.32325
$251$	16.9378	1.06911	0.534554	−	0.845135i	$-0.320480\pi$
$251$	16.9378	1.06911	0.534554	+	0.845135i	$0.320480\pi$
$252$	−8.02576	−0.505575
$253$	1.99922	0.125690
$254$	−23.8460	−1.49623
$255$	1.24008	0.0776570
$256$	16.3898	1.02437
$257$	5.02392	0.313383	0.156692	−	0.987648i	$-0.449917\pi$
$257$	5.02392	0.313383	0.156692	+	0.987648i	$0.449917\pi$
$258$	24.8982	1.55009
$259$	−1.14334	−0.0710436
$260$	5.25415	0.325848
$261$	−6.92925	−0.428910
$262$	29.8846	1.84628
$263$	18.7756	1.15775	0.578876	−	0.815415i	$-0.303491\pi$
$263$	18.7756	1.15775	0.578876	+	0.815415i	$0.303491\pi$
$264$	0.150519	0.00926380
$265$	4.60383	0.282811
$266$	21.3061	1.30636
$267$	5.34703	0.327233
$268$	−14.8437	−0.906722
$269$	−20.0905	−1.22494	−0.612470	−	0.790494i	$-0.709824\pi$
$269$	−20.0905	−1.22494	−0.612470	+	0.790494i	$0.709824\pi$
$270$	−2.47246	−0.150469
$271$	9.96446	0.605298	0.302649	−	0.953102i	$-0.402129\pi$
$271$	9.96446	0.605298	0.302649	+	0.953102i	$0.402129\pi$
$272$	−4.04904	−0.245509
$273$	−8.71623	−0.527530
$274$	17.0761	1.03161
$275$	−10.5269	−0.634795
$276$	1.29872	0.0781739
$277$	12.2547	0.736313	0.368156	−	0.929764i	$-0.379989\pi$
$277$	12.2547	0.736313	0.368156	+	0.929764i	$0.379989\pi$
$278$	−28.9093	−1.73386
$279$	−9.42663	−0.564358
$280$	−0.249445	−0.0149072
$281$	−31.7099	−1.89166	−0.945828	−	0.324669i	$-0.894747\pi$
$281$	−31.7099	−1.89166	−0.945828	+	0.324669i	$0.894747\pi$
$282$	1.43233	0.0852943
$283$	−25.4031	−1.51006	−0.755030	−	0.655690i	$-0.772378\pi$
$283$	−25.4031	−1.51006	−0.755030	+	0.655690i	$0.772378\pi$
$284$	9.27027	0.550089
$285$	3.26133	0.193185
$286$	−13.0039	−0.768936
$287$	23.0677	1.36164
$288$	7.97390	0.469867
$289$	1.00000	0.0588235
$290$	17.1323	1.00604
$291$	14.6992	0.861680
$292$	21.4241	1.25375
$293$	−29.1465	−1.70276	−0.851379	−	0.524550i	$-0.824233\pi$
$293$	−29.1465	−1.70276	−0.851379	+	0.524550i	$0.824233\pi$
$294$	−18.9621	−1.10589
$295$	−9.38777	−0.546577
$296$	0.0139295	0.000809637 0
$297$	3.04052	0.176429
$298$	10.2854	0.595817
$299$	1.41045	0.0815686
$300$	−6.83843	−0.394817
$301$	50.7424	2.92474
$302$	40.5116	2.33118
$303$	7.81357	0.448878
$304$	−10.6487	−0.610745
$305$	13.9310	0.797684
$306$	−1.99378	−0.113977
$307$	20.5368	1.17210	0.586048	−	0.810276i	$-0.300683\pi$
$307$	20.5368	1.17210	0.586048	+	0.810276i	$0.300683\pi$
$308$	−24.4025	−1.39046
$309$	−6.11213	−0.347707
$310$	23.3069	1.32374
$311$	11.2977	0.640634	0.320317	−	0.947310i	$-0.396211\pi$
$311$	11.2977	0.640634	0.320317	+	0.947310i	$0.396211\pi$
$312$	0.106191	0.00601191
$313$	0.573574	0.0324203	0.0162102	−	0.999869i	$-0.494840\pi$
$313$	0.573574	0.0324203	0.0162102	+	0.999869i	$0.494840\pi$
$314$	−27.7759	−1.56749
$315$	−5.03886	−0.283908
$316$	−1.97517	−0.111112
$317$	6.55227	0.368012	0.184006	−	0.982925i	$-0.441093\pi$
$317$	6.55227	0.368012	0.184006	+	0.982925i	$0.441093\pi$
$318$	−7.40195	−0.415081
$319$	−21.0685	−1.17961
$320$	−9.67283	−0.540727
$321$	−7.11929	−0.397360
$322$	5.32686	0.296854
$323$	2.62993	0.146333
$324$	1.97517	0.109732
$325$	−7.42675	−0.411962
$326$	1.81739	0.100656
$327$	−4.96541	−0.274588
$328$	−0.281038	−0.0155177
$329$	2.91910	0.160935
$330$	−7.51756	−0.413828
$331$	9.15822	0.503381	0.251691	−	0.967808i	$-0.419013\pi$
$331$	9.15822	0.503381	0.251691	+	0.967808i	$0.419013\pi$
$332$	−4.88180	−0.267924
$333$	0.281380	0.0154195
$334$	−30.9361	−1.69275
$335$	−9.31939	−0.509172
$336$	16.4526	0.897562
$337$	−5.26917	−0.287030	−0.143515	−	0.989648i	$-0.545841\pi$
$337$	−5.26917	−0.287030	−0.143515	+	0.989648i	$0.545841\pi$
$338$	16.7449	0.910803
$339$	−14.4632	−0.785532
$340$	2.44937	0.132836
$341$	−28.6619	−1.55213
$342$	−5.24351	−0.283537
$343$	−10.2015	−0.550827
$344$	−0.618204	−0.0333313
$345$	0.815384	0.0438988
$346$	42.4752	2.28348
$347$	−20.6766	−1.10998	−0.554988	−	0.831858i	$-0.687277\pi$
$347$	−20.6766	−1.10998	−0.554988	+	0.831858i	$0.687277\pi$
$348$	−13.6864	−0.733671
$349$	−23.9883	−1.28406	−0.642032	−	0.766678i	$-0.721908\pi$
$349$	−23.9883	−1.28406	−0.642032	+	0.766678i	$0.721908\pi$
$350$	−28.0486	−1.49926
$351$	2.14510	0.114497
$352$	24.2448	1.29225
$353$	25.9708	1.38228	0.691142	−	0.722719i	$-0.257108\pi$
$353$	25.9708	1.38228	0.691142	+	0.722719i	$0.257108\pi$
$354$	15.0935	0.802210
$355$	5.82020	0.308904
$356$	10.5613	0.559748
$357$	−4.06333	−0.215054
$358$	21.5471	1.13880
$359$	−14.2402	−0.751571	−0.375786	−	0.926707i	$-0.622627\pi$
$359$	−14.2402	−0.751571	−0.375786	+	0.926707i	$0.622627\pi$
$360$	0.0613894	0.00323550
$361$	−12.0835	−0.635972
$362$	−40.3820	−2.12243
$363$	−1.75521	−0.0921247
$364$	−17.2160	−0.902366
$365$	13.4508	0.704046
$366$	−22.3980	−1.17076
$367$	15.8510	0.827416	0.413708	−	0.910410i	$-0.364233\pi$
$367$	15.8510	0.827416	0.413708	+	0.910410i	$0.364233\pi$
$368$	−2.66234	−0.138784
$369$	−5.67704	−0.295535
$370$	−0.695700	−0.0361677
$371$	−15.0852	−0.783183
$372$	−18.6192	−0.965361
$373$	−16.6117	−0.860121	−0.430060	−	0.902800i	$-0.641508\pi$
$373$	−16.6117	−0.860121	−0.430060	+	0.902800i	$0.641508\pi$
$374$	−6.06215	−0.313466
$375$	−10.4938	−0.541899
$376$	−0.0355639	−0.00183407
$377$	−14.8639	−0.765530
$378$	8.10139	0.416691
$379$	−9.20017	−0.472581	−0.236290	−	0.971682i	$-0.575932\pi$
$379$	−9.20017	−0.472581	−0.236290	+	0.971682i	$0.575932\pi$
$380$	6.44169	0.330452
$381$	11.9602	0.612738
$382$	19.7807	1.01207
$383$	−1.26556	−0.0646671	−0.0323335	−	0.999477i	$-0.510294\pi$
$383$	−1.26556	−0.0646671	−0.0323335	+	0.999477i	$0.510294\pi$
$384$	−0.396004	−0.0202085
$385$	−15.3208	−0.780819
$386$	33.8933	1.72512
$387$	−12.4879	−0.634795
$388$	29.0333	1.47394
$389$	−3.22900	−0.163717	−0.0818583	−	0.996644i	$-0.526086\pi$
$389$	−3.22900	−0.163717	−0.0818583	+	0.996644i	$0.526086\pi$
$390$	−5.30366	−0.268561
$391$	0.657524	0.0332524
$392$	0.470816	0.0237798
$393$	−14.9889	−0.756091
$394$	18.5674	0.935414
$395$	−1.24008	−0.0623953
$396$	6.00555	0.301790
$397$	19.6348	0.985441	0.492720	−	0.870188i	$-0.336003\pi$
$397$	19.6348	0.985441	0.492720	+	0.870188i	$0.336003\pi$
$398$	−13.7099	−0.687214
$399$	−10.6863	−0.534983
$400$	14.0186	0.700929
$401$	13.7824	0.688261	0.344130	−	0.938922i	$-0.388174\pi$
$401$	13.7824	0.688261	0.344130	+	0.938922i	$0.388174\pi$
$402$	14.9835	0.747311
$403$	−20.2210	−1.00728
$404$	15.4331	0.767827
$405$	1.24008	0.0616202
$406$	−56.1365	−2.78601
$407$	0.855543	0.0424077
$408$	0.0495043	0.00245083
$409$	−19.1457	−0.946694	−0.473347	−	0.880876i	$-0.656954\pi$
$409$	−19.1457	−0.946694	−0.473347	+	0.880876i	$0.656954\pi$
$410$	14.0362	0.693200
$411$	−8.56469	−0.422465
$412$	−12.0725	−0.594769
$413$	30.7605	1.51363
$414$	−1.31096	−0.0644302
$415$	−3.06497	−0.150453
$416$	17.1048	0.838632
$417$	14.4997	0.710054
$418$	−15.9430	−0.779799
$419$	−20.6484	−1.00874	−0.504369	−	0.863488i	$-0.668275\pi$
$419$	−20.6484	−1.00874	−0.504369	+	0.863488i	$0.668275\pi$
$420$	−9.95261	−0.485637
$421$	5.18901	0.252897	0.126448	−	0.991973i	$-0.459642\pi$
$421$	5.18901	0.252897	0.126448	+	0.991973i	$0.459642\pi$
$422$	21.8342	1.06287
$423$	−0.718400	−0.0349298
$424$	0.183785	0.00892541
$425$	−3.46220	−0.167941
$426$	−9.35762	−0.453378
$427$	−45.6470	−2.20901
$428$	−14.0618	−0.679703
$429$	6.52222	0.314896
$430$	30.8758	1.48896
$431$	−28.6255	−1.37884	−0.689422	−	0.724360i	$-0.742135\pi$
$431$	−28.6255	−1.37884	−0.689422	+	0.724360i	$0.742135\pi$
$432$	−4.04904	−0.194810
$433$	33.0337	1.58750	0.793750	−	0.608244i	$-0.208126\pi$
$433$	33.0337	1.58750	0.793750	+	0.608244i	$0.208126\pi$
$434$	−76.3688	−3.66582
$435$	−8.59284	−0.411995
$436$	−9.80753	−0.469695
$437$	1.72924	0.0827209
$438$	−21.6259	−1.03333
$439$	−27.9529	−1.33412	−0.667059	−	0.745005i	$-0.732447\pi$
$439$	−27.9529	−1.33412	−0.667059	+	0.745005i	$0.732447\pi$
$440$	0.186656	0.00889847
$441$	9.51062	0.452887
$442$	−4.27686	−0.203429
$443$	−11.4399	−0.543526	−0.271763	−	0.962364i	$-0.587607\pi$
$443$	−11.4399	−0.543526	−0.271763	+	0.962364i	$0.587607\pi$
$444$	0.555774	0.0263759
$445$	6.63076	0.314328
$446$	25.4580	1.20547
$447$	−5.15873	−0.244000
$448$	31.6945	1.49743
$449$	−25.5511	−1.20583	−0.602915	−	0.797806i	$-0.705994\pi$
$449$	−25.5511	−1.20583	−0.602915	+	0.797806i	$0.705994\pi$
$450$	6.90287	0.325404
$451$	−17.2612	−0.812798
$452$	−28.5672	−1.34369
$453$	−20.3190	−0.954669
$454$	18.4638	0.866551
$455$	−10.8088	−0.506726
$456$	0.130193	0.00609684
$457$	−4.14167	−0.193739	−0.0968696	−	0.995297i	$-0.530883\pi$
$457$	−4.14167	−0.193739	−0.0968696	+	0.995297i	$0.530883\pi$
$458$	38.0515	1.77803
$459$	1.00000	0.0466760
$460$	1.61052	0.0750910
$461$	−10.2147	−0.475747	−0.237873	−	0.971296i	$-0.576450\pi$
$461$	−10.2147	−0.475747	−0.237873	+	0.971296i	$0.576450\pi$
$462$	24.6325	1.14601
$463$	−21.4327	−0.996063	−0.498032	−	0.867159i	$-0.665944\pi$
$463$	−21.4327	−0.996063	−0.498032	+	0.867159i	$0.665944\pi$
$464$	28.0568	1.30250
$465$	−11.6898	−0.542101
$466$	−4.01371	−0.185931
$467$	2.93777	0.135944	0.0679718	−	0.997687i	$-0.478347\pi$
$467$	2.93777	0.135944	0.0679718	+	0.997687i	$0.478347\pi$
$468$	4.23693	0.195852
$469$	30.5364	1.41004
$470$	1.77621	0.0819306
$471$	13.9313	0.641919
$472$	−0.374761	−0.0172498
$473$	−37.9698	−1.74585
$474$	1.99378	0.0915775
$475$	−9.10534	−0.417781
$476$	−8.02576	−0.367860
$477$	3.71252	0.169984
$478$	−21.5435	−0.985377
$479$	6.88273	0.314480	0.157240	−	0.987560i	$-0.449740\pi$
$479$	6.88273	0.314480	0.157240	+	0.987560i	$0.449740\pi$
$480$	9.88830	0.451337
$481$	0.603588	0.0275212
$482$	−3.48003	−0.158511
$483$	−2.67173	−0.121568
$484$	−3.46684	−0.157584
$485$	18.2282	0.827698
$486$	−1.99378	−0.0904398
$487$	23.8594	1.08117	0.540587	−	0.841288i	$-0.318202\pi$
$487$	23.8594	1.08117	0.540587	+	0.841288i	$0.318202\pi$
$488$	0.556126	0.0251746
$489$	−0.911527	−0.0412207
$490$	−23.5146	−1.06228
$491$	−34.8463	−1.57259	−0.786297	−	0.617849i	$-0.788004\pi$
$491$	−34.8463	−1.57259	−0.786297	+	0.617849i	$0.788004\pi$
$492$	−11.2131	−0.505527
$493$	−6.92925	−0.312078
$494$	−11.2478	−0.506064
$495$	3.77050	0.169471
$496$	38.1688	1.71383
$497$	−19.0708	−0.855443
$498$	4.92780	0.220820
$499$	−16.6662	−0.746082	−0.373041	−	0.927815i	$-0.621685\pi$
$499$	−16.6662	−0.746082	−0.373041	+	0.927815i	$0.621685\pi$
$500$	−20.7271	−0.926943
$501$	15.5163	0.693216
$502$	−33.7704	−1.50725
$503$	12.1983	0.543894	0.271947	−	0.962312i	$-0.412332\pi$
$503$	12.1983	0.543894	0.271947	+	0.962312i	$0.412332\pi$
$504$	−0.201152	−0.00896002
$505$	9.68947	0.431176
$506$	−3.98601	−0.177200
$507$	−8.39856	−0.372993
$508$	23.6234	1.04812
$509$	36.3424	1.61085	0.805425	−	0.592697i	$-0.201937\pi$
$509$	36.3424	1.61085	0.805425	+	0.592697i	$0.201937\pi$
$510$	−2.47246	−0.109482
$511$	−44.0736	−1.94970
$512$	−31.8858	−1.40917
$513$	2.62993	0.116114
$514$	−10.0166	−0.441813
$515$	−7.57954	−0.333994
$516$	−24.6657	−1.08585
$517$	−2.18431	−0.0960660
$518$	2.27957	0.100159
$519$	−21.3038	−0.935133
$520$	0.131686	0.00577482
$521$	−40.1634	−1.75959	−0.879795	−	0.475353i	$-0.842320\pi$
$521$	−40.1634	−1.75959	−0.879795	+	0.475353i	$0.842320\pi$
$522$	13.8154	0.604684
$523$	22.1168	0.967102	0.483551	−	0.875316i	$-0.339347\pi$
$523$	22.1168	0.967102	0.483551	+	0.875316i	$0.339347\pi$
$524$	−29.6057	−1.29333
$525$	14.0680	0.613979
$526$	−37.4345	−1.63222
$527$	−9.42663	−0.410630
$528$	−12.3112	−0.535777
$529$	−22.5677	−0.981203
$530$	−9.17903	−0.398712
$531$	−7.57028	−0.328522
$532$	−21.1072	−0.915113
$533$	−12.1778	−0.527480
$534$	−10.6608	−0.461339
$535$	−8.82850	−0.381690
$536$	−0.372031	−0.0160693
$537$	−10.8071	−0.466362
$538$	40.0561	1.72694
$539$	28.9173	1.24555
$540$	2.44937	0.105404
$541$	−19.2111	−0.825948	−0.412974	−	0.910743i	$-0.635510\pi$
$541$	−19.2111	−0.825948	−0.412974	+	0.910743i	$0.635510\pi$
$542$	−19.8670	−0.853360
$543$	20.2540	0.869181
$544$	7.97390	0.341878
$545$	−6.15752	−0.263759
$546$	17.3783	0.743721
$547$	2.36893	0.101288	0.0506440	−	0.998717i	$-0.483873\pi$
$547$	2.36893	0.101288	0.0506440	+	0.998717i	$0.483873\pi$
$548$	−16.9167	−0.722646
$549$	11.2339	0.479451
$550$	20.9883	0.894946
$551$	−18.2234	−0.776345
$552$	0.0325502	0.00138543
$553$	4.06333	0.172790
$554$	−24.4332	−1.03807
$555$	0.348935	0.0148114
$556$	28.6394	1.21458
$557$	30.6295	1.29781	0.648906	−	0.760868i	$-0.275227\pi$
$557$	30.6295	1.29781	0.648906	+	0.760868i	$0.275227\pi$
$558$	18.7947	0.795641
$559$	−26.7878	−1.13300
$560$	20.4026	0.862165
$561$	3.04052	0.128371
$562$	63.2227	2.66689
$563$	−22.1016	−0.931470	−0.465735	−	0.884924i	$-0.654210\pi$
$563$	−22.1016	−0.931470	−0.465735	+	0.884924i	$0.654210\pi$
$564$	−1.41896	−0.0597491
$565$	−17.9355	−0.754553
$566$	50.6484	2.12891
$567$	−4.06333	−0.170644
$568$	0.232343	0.00974891
$569$	10.5189	0.440975	0.220488	−	0.975390i	$-0.429235\pi$
$569$	10.5189	0.440975	0.220488	+	0.975390i	$0.429235\pi$
$570$	−6.50239	−0.272355
$571$	−46.3361	−1.93911	−0.969553	−	0.244882i	$-0.921251\pi$
$571$	−46.3361	−1.93911	−0.969553	+	0.244882i	$0.921251\pi$
$572$	12.8825	0.538644
$573$	−9.92121	−0.414465
$574$	−45.9919	−1.91967
$575$	−2.27648	−0.0949356
$576$	−7.80015	−0.325006
$577$	6.77766	0.282158	0.141079	−	0.989998i	$-0.454943\pi$
$577$	6.77766	0.282158	0.141079	+	0.989998i	$0.454943\pi$
$578$	−1.99378	−0.0829304
$579$	−16.9995	−0.706474
$580$	−16.9723	−0.704737
$581$	10.0429	0.416648
$582$	−29.3069	−1.21481
$583$	11.2880	0.467501
$584$	0.536958	0.0222195
$585$	2.66010	0.109981
$586$	58.1119	2.40058
$587$	14.1594	0.584423	0.292211	−	0.956354i	$-0.405609\pi$
$587$	14.1594	0.584423	0.292211	+	0.956354i	$0.405609\pi$
$588$	18.7851	0.774684
$589$	−24.7914	−1.02151
$590$	18.7172	0.770574
$591$	−9.31267	−0.383072
$592$	−1.13932	−0.0468258
$593$	9.10754	0.374002	0.187001	−	0.982360i	$-0.440123\pi$
$593$	9.10754	0.374002	0.187001	+	0.982360i	$0.440123\pi$
$594$	−6.06215	−0.248733
$595$	−5.03886	−0.206573
$596$	−10.1894	−0.417373
$597$	6.87632	0.281429
$598$	−2.81214	−0.114997
$599$	15.8601	0.648025	0.324013	−	0.946053i	$-0.394968\pi$
$599$	15.8601	0.648025	0.324013	+	0.946053i	$0.394968\pi$
$600$	−0.171393	−0.00699711
$601$	−23.0922	−0.941952	−0.470976	−	0.882146i	$-0.656098\pi$
$601$	−23.0922	−0.941952	−0.470976	+	0.882146i	$0.656098\pi$
$602$	−101.169	−4.12335
$603$	−7.51513	−0.306040
$604$	−40.1335	−1.63301
$605$	−2.17661	−0.0884917
$606$	−15.5786	−0.632836
$607$	−18.7954	−0.762882	−0.381441	−	0.924393i	$-0.624572\pi$
$607$	−18.7954	−0.762882	−0.381441	+	0.924393i	$0.624572\pi$
$608$	20.9708	0.850479
$609$	28.1558	1.14093
$610$	−27.7753	−1.12459
$611$	−1.54104	−0.0623438
$612$	1.97517	0.0798415
$613$	−3.13593	−0.126659	−0.0633295	−	0.997993i	$-0.520172\pi$
$613$	−3.13593	−0.126659	−0.0633295	+	0.997993i	$0.520172\pi$
$614$	−40.9459	−1.65244
$615$	−7.04000	−0.283880
$616$	−0.611608	−0.0246424
$617$	32.9366	1.32598	0.662990	−	0.748628i	$-0.269287\pi$
$617$	32.9366	1.32598	0.662990	+	0.748628i	$0.269287\pi$
$618$	12.1863	0.490203
$619$	30.0183	1.20654	0.603270	−	0.797537i	$-0.293864\pi$
$619$	30.0183	1.20654	0.603270	+	0.797537i	$0.293864\pi$
$620$	−23.0893	−0.927290
$621$	0.657524	0.0263855
$622$	−22.5252	−0.903177
$623$	−21.7267	−0.870463
$624$	−8.68559	−0.347702
$625$	4.29778	0.171911
$626$	−1.14358	−0.0457067
$627$	7.99637	0.319344
$628$	27.5166	1.09803
$629$	0.281380	0.0112194
$630$	10.0464	0.400258
$631$	31.2226	1.24295	0.621476	−	0.783433i	$-0.286533\pi$
$631$	31.2226	1.24295	0.621476	+	0.783433i	$0.286533\pi$
$632$	−0.0495043	−0.00196917
$633$	−10.9511	−0.435269
$634$	−13.0638	−0.518830
$635$	14.8316	0.588574
$636$	7.33285	0.290767
$637$	20.4012	0.808325
$638$	42.0061	1.66304
$639$	4.69340	0.185668
$640$	−0.491077	−0.0194115
$641$	13.5050	0.533416	0.266708	−	0.963777i	$-0.414064\pi$
$641$	13.5050	0.533416	0.266708	+	0.963777i	$0.414064\pi$
$642$	14.1943	0.560205
$643$	27.7769	1.09541	0.547707	−	0.836670i	$-0.315501\pi$
$643$	27.7769	1.09541	0.547707	+	0.836670i	$0.315501\pi$
$644$	−5.27713	−0.207948
$645$	−15.4860	−0.609761
$646$	−5.24351	−0.206303
$647$	11.6109	0.456471	0.228235	−	0.973606i	$-0.426704\pi$
$647$	11.6109	0.456471	0.228235	+	0.973606i	$0.426704\pi$
$648$	0.0495043	0.00194471
$649$	−23.0176	−0.903520
$650$	14.8073	0.580791
$651$	38.3035	1.50123
$652$	−1.80042	−0.0705099
$653$	28.5532	1.11737	0.558687	−	0.829379i	$-0.311305\pi$
$653$	28.5532	1.11737	0.558687	+	0.829379i	$0.311305\pi$
$654$	9.89995	0.387119
$655$	−18.5875	−0.726273
$656$	22.9866	0.897476
$657$	10.8467	0.423170
$658$	−5.82004	−0.226889
$659$	23.9503	0.932972	0.466486	−	0.884529i	$-0.345520\pi$
$659$	23.9503	0.932972	0.466486	+	0.884529i	$0.345520\pi$
$660$	7.44738	0.289889
$661$	21.4766	0.835342	0.417671	−	0.908598i	$-0.362846\pi$
$661$	21.4766	0.835342	0.417671	+	0.908598i	$0.362846\pi$
$662$	−18.2595	−0.709676
$663$	2.14510	0.0833087
$664$	−0.122354	−0.00474826
$665$	−13.2519	−0.513885
$666$	−0.561011	−0.0217387
$667$	−4.55615	−0.176415
$668$	30.6473	1.18578
$669$	−12.7687	−0.493667
$670$	18.5808	0.717840
$671$	34.1569	1.31861
$672$	−32.4006	−1.24988
$673$	−23.1492	−0.892335	−0.446167	−	0.894950i	$-0.647211\pi$
$673$	−23.1492	−0.892335	−0.446167	+	0.894950i	$0.647211\pi$
$674$	10.5056	0.404660
$675$	−3.46220	−0.133260
$676$	−16.5886	−0.638023
$677$	43.9370	1.68864	0.844319	−	0.535842i	$-0.180006\pi$
$677$	43.9370	1.68864	0.844319	+	0.535842i	$0.180006\pi$
$678$	28.8364	1.10746
$679$	−59.7275	−2.29213
$680$	0.0613894	0.00235418
$681$	−9.26071	−0.354871
$682$	57.1456	2.18822
$683$	−1.86892	−0.0715122	−0.0357561	−	0.999361i	$-0.511384\pi$
$683$	−1.86892	−0.0715122	−0.0357561	+	0.999361i	$0.511384\pi$
$684$	5.19456	0.198619
$685$	−10.6209	−0.405804
$686$	20.3395	0.776565
$687$	−19.0851	−0.728140
$688$	50.5640	1.92774
$689$	7.96371	0.303393
$690$	−1.62570	−0.0618893
$691$	−33.0494	−1.25726	−0.628628	−	0.777706i	$-0.716383\pi$
$691$	−33.0494	−1.25726	−0.628628	+	0.777706i	$0.716383\pi$
$692$	−42.0786	−1.59959
$693$	−12.3546	−0.469314
$694$	41.2246	1.56486
$695$	17.9808	0.682052
$696$	−0.343027	−0.0130024
$697$	−5.67704	−0.215033
$698$	47.8274	1.81030
$699$	2.01311	0.0761429
$700$	27.7868	1.05024
$701$	22.4441	0.847703	0.423852	−	0.905732i	$-0.360678\pi$
$701$	22.4441	0.847703	0.423852	+	0.905732i	$0.360678\pi$
$702$	−4.27686	−0.161420
$703$	0.740010	0.0279100
$704$	−23.7165	−0.893851
$705$	−0.890876	−0.0335523
$706$	−51.7801	−1.94877
$707$	−31.7491	−1.19405
$708$	−14.9526	−0.561953
$709$	−33.0857	−1.24256	−0.621279	−	0.783589i	$-0.713387\pi$
$709$	−33.0857	−1.24256	−0.621279	+	0.783589i	$0.713387\pi$
$710$	−11.6042	−0.435499
$711$	−1.00000	−0.0375029
$712$	0.264701	0.00992009
$713$	−6.19824	−0.232126
$714$	8.10139	0.303187
$715$	8.08809	0.302477
$716$	−21.3459	−0.797735
$717$	10.8053	0.403533
$718$	28.3920	1.05958
$719$	1.18162	0.0440669	0.0220335	−	0.999757i	$-0.492986\pi$
$719$	1.18162	0.0440669	0.0220335	+	0.999757i	$0.492986\pi$
$720$	−5.02115	−0.187127
$721$	24.8356	0.924924
$722$	24.0918	0.896604
$723$	1.74544	0.0649136
$724$	40.0050	1.48677
$725$	23.9904	0.890981
$726$	3.49951	0.129879
$727$	41.1273	1.52533	0.762663	−	0.646796i	$-0.223891\pi$
$727$	41.1273	1.52533	0.762663	+	0.646796i	$0.223891\pi$
$728$	−0.431491	−0.0159921
$729$	1.00000	0.0370370
$730$	−26.8180	−0.992577
$731$	−12.4879	−0.461882
$732$	22.1889	0.820124
$733$	41.1779	1.52094	0.760470	−	0.649373i	$-0.224969\pi$
$733$	41.1779	1.52094	0.760470	+	0.649373i	$0.224969\pi$
$734$	−31.6035	−1.16651
$735$	11.7939	0.435026
$736$	5.24303	0.193261
$737$	−22.8500	−0.841689
$738$	11.3188	0.416651
$739$	7.66144	0.281831	0.140915	−	0.990022i	$-0.454995\pi$
$739$	7.66144	0.281831	0.140915	+	0.990022i	$0.454995\pi$
$740$	0.689205	0.0253357
$741$	5.64146	0.207244
$742$	30.0765	1.10414
$743$	−53.7536	−1.97203	−0.986013	−	0.166666i	$-0.946700\pi$
$743$	−53.7536	−1.97203	−0.986013	+	0.166666i	$0.946700\pi$
$744$	−0.466658	−0.0171085
$745$	−6.39725	−0.234377
$746$	33.1201	1.21261
$747$	−2.47158	−0.0904305
$748$	6.00555	0.219585
$749$	28.9280	1.05701
$750$	20.9224	0.763978
$751$	4.41187	0.160991	0.0804957	−	0.996755i	$-0.474350\pi$
$751$	4.41187	0.160991	0.0804957	+	0.996755i	$0.474350\pi$
$752$	2.90883	0.106074
$753$	16.9378	0.617249
$754$	29.6354	1.07926
$755$	−25.1972	−0.917020
$756$	−8.02576	−0.291894
$757$	34.6286	1.25860	0.629298	−	0.777164i	$-0.283342\pi$
$757$	34.6286	1.25860	0.629298	+	0.777164i	$0.283342\pi$
$758$	18.3431	0.666253
$759$	1.99922	0.0725670
$760$	0.161450	0.00585640
$761$	−18.6879	−0.677438	−0.338719	−	0.940888i	$-0.609994\pi$
$761$	−18.6879	−0.677438	−0.338719	+	0.940888i	$0.609994\pi$
$762$	−23.8460	−0.863849
$763$	20.1761	0.730423
$764$	−19.5961	−0.708962
$765$	1.24008	0.0448353
$766$	2.52325	0.0911688
$767$	−16.2390	−0.586356
$768$	16.3898	0.591417
$769$	−26.6215	−0.959995	−0.479997	−	0.877270i	$-0.659362\pi$
$769$	−26.6215	−0.959995	−0.479997	+	0.877270i	$0.659362\pi$
$770$	30.5463	1.10081
$771$	5.02392	0.180932
$772$	−33.5769	−1.20846
$773$	42.3211	1.52218	0.761091	−	0.648645i	$-0.224664\pi$
$773$	42.3211	1.52218	0.761091	+	0.648645i	$0.224664\pi$
$774$	24.8982	0.894946
$775$	32.6368	1.17235
$776$	0.727671	0.0261219
$777$	−1.14334	−0.0410171
$778$	6.43792	0.230811
$779$	−14.9302	−0.534931
$780$	5.25415	0.188129
$781$	14.2704	0.510635
$782$	−1.31096	−0.0468798
$783$	−6.92925	−0.247631
$784$	−38.5089	−1.37532
$785$	17.2759	0.616604
$786$	29.8846	1.06595
$787$	11.1702	0.398175	0.199088	−	0.979982i	$-0.436202\pi$
$787$	11.1702	0.398175	0.199088	+	0.979982i	$0.436202\pi$
$788$	−18.3941	−0.655263
$789$	18.7756	0.668429
$790$	2.47246	0.0879660
$791$	58.7686	2.08957
$792$	0.150519	0.00534846
$793$	24.0978	0.855738
$794$	−39.1475	−1.38929
$795$	4.60383	0.163281
$796$	13.5819	0.481398
$797$	−42.8549	−1.51800	−0.759000	−	0.651091i	$-0.774312\pi$
$797$	−42.8549	−1.51800	−0.759000	+	0.651091i	$0.774312\pi$
$798$	21.3061	0.754228
$799$	−0.718400	−0.0254152
$800$	−27.6072	−0.976062
$801$	5.34703	0.188928
$802$	−27.4791	−0.970322
$803$	32.9796	1.16383
$804$	−14.8437	−0.523496
$805$	−3.31317	−0.116774
$806$	40.3164	1.42008
$807$	−20.0905	−0.707220
$808$	0.386805	0.0136078
$809$	−12.9265	−0.454473	−0.227236	−	0.973840i	$-0.572969\pi$
$809$	−12.9265	−0.454473	−0.227236	+	0.973840i	$0.572969\pi$
$810$	−2.47246	−0.0868732
$811$	−35.8183	−1.25775	−0.628876	−	0.777506i	$-0.716485\pi$
$811$	−35.8183	−1.25775	−0.628876	+	0.777506i	$0.716485\pi$
$812$	55.6125	1.95162
$813$	9.96446	0.349469
$814$	−1.70577	−0.0597871
$815$	−1.13037	−0.0395951
$816$	−4.04904	−0.141745
$817$	−32.8423	−1.14901
$818$	38.1724	1.33467
$819$	−8.71623	−0.304570
$820$	−13.9052	−0.485591
$821$	20.6643	0.721188	0.360594	−	0.932723i	$-0.382574\pi$
$821$	20.6643	0.721188	0.360594	+	0.932723i	$0.382574\pi$
$822$	17.0761	0.595598
$823$	−7.09059	−0.247162	−0.123581	−	0.992334i	$-0.539438\pi$
$823$	−7.09059	−0.247162	−0.123581	+	0.992334i	$0.539438\pi$
$824$	−0.302576	−0.0105407
$825$	−10.5269	−0.366499
$826$	−61.3298	−2.13394
$827$	−11.5687	−0.402284	−0.201142	−	0.979562i	$-0.564465\pi$
$827$	−11.5687	−0.402284	−0.201142	+	0.979562i	$0.564465\pi$
$828$	1.29872	0.0451337
$829$	13.7255	0.476707	0.238353	−	0.971178i	$-0.423392\pi$
$829$	13.7255	0.476707	0.238353	+	0.971178i	$0.423392\pi$
$830$	6.11088	0.212112
$831$	12.2547	0.425110
$832$	−16.7321	−0.580080
$833$	9.51062	0.329523
$834$	−28.9093	−1.00105
$835$	19.2414	0.665878
$836$	15.7942	0.546254
$837$	−9.42663	−0.325832
$838$	41.1684	1.42214
$839$	−35.8273	−1.23690	−0.618448	−	0.785826i	$-0.712238\pi$
$839$	−35.8273	−1.23690	−0.618448	+	0.785826i	$0.712238\pi$
$840$	−0.249445	−0.00860667
$841$	19.0145	0.655671
$842$	−10.3458	−0.356538
$843$	−31.7099	−1.09215
$844$	−21.6304	−0.744548
$845$	−10.4149	−0.358284
$846$	1.43233	0.0492447
$847$	7.13200	0.245058
$848$	−15.0321	−0.516206
$849$	−25.4031	−0.871834
$850$	6.90287	0.236766
$851$	0.185014	0.00634220
$852$	9.27027	0.317594
$853$	18.4170	0.630587	0.315293	−	0.948994i	$-0.397897\pi$
$853$	18.4170	0.630587	0.315293	+	0.948994i	$0.397897\pi$
$854$	91.0102	3.11430
$855$	3.26133	0.111535
$856$	−0.352435	−0.0120460
$857$	27.8908	0.952730	0.476365	−	0.879247i	$-0.341954\pi$
$857$	27.8908	0.952730	0.476365	+	0.879247i	$0.341954\pi$
$858$	−13.0039	−0.443946
$859$	−3.80154	−0.129707	−0.0648534	−	0.997895i	$-0.520658\pi$
$859$	−3.80154	−0.129707	−0.0648534	+	0.997895i	$0.520658\pi$
$860$	−30.5875	−1.04303
$861$	23.0677	0.786144
$862$	57.0731	1.94392
$863$	−32.9757	−1.12251	−0.561253	−	0.827644i	$-0.689681\pi$
$863$	−32.9757	−1.12251	−0.561253	+	0.827644i	$0.689681\pi$
$864$	7.97390	0.271278
$865$	−26.4185	−0.898255
$866$	−65.8621	−2.23809
$867$	1.00000	0.0339618
$868$	75.6559	2.56793
$869$	−3.04052	−0.103143
$870$	17.1323	0.580838
$871$	−16.1207	−0.546229
$872$	−0.245809	−0.00832414
$873$	14.6992	0.497491
$874$	−3.44774	−0.116621
$875$	42.6398	1.44149
$876$	21.4241	0.723852
$877$	14.4737	0.488742	0.244371	−	0.969682i	$-0.421419\pi$
$877$	14.4737	0.488742	0.244371	+	0.969682i	$0.421419\pi$
$878$	55.7320	1.88086
$879$	−29.1465	−0.983088
$880$	−15.2669	−0.514648
$881$	−32.7529	−1.10347	−0.551736	−	0.834019i	$-0.686034\pi$
$881$	−32.7529	−1.10347	−0.551736	+	0.834019i	$0.686034\pi$
$882$	−18.9621	−0.638487
$883$	12.1652	0.409393	0.204696	−	0.978826i	$-0.434379\pi$
$883$	12.1652	0.409393	0.204696	+	0.978826i	$0.434379\pi$
$884$	4.23693	0.142503
$885$	−9.38777	−0.315566
$886$	22.8087	0.766272
$887$	−43.5098	−1.46092	−0.730459	−	0.682957i	$-0.760694\pi$
$887$	−43.5098	−1.46092	−0.730459	+	0.682957i	$0.760694\pi$
$888$	0.0139295	0.000467444 0
$889$	−48.5981	−1.62993
$890$	−13.2203	−0.443145
$891$	3.04052	0.101861
$892$	−25.2204	−0.844440
$893$	−1.88934	−0.0632245
$894$	10.2854	0.343995
$895$	−13.4017	−0.447970
$896$	1.60909	0.0537560
$897$	1.41045	0.0470936
$898$	50.9433	1.70000
$899$	65.3194	2.17853
$900$	−6.83843	−0.227948
$901$	3.71252	0.123682
$902$	34.4151	1.14590
$903$	50.7424	1.68860
$904$	−0.715989	−0.0238134
$905$	25.1166	0.834903
$906$	40.5116	1.34591
$907$	−10.7402	−0.356623	−0.178311	−	0.983974i	$-0.557063\pi$
$907$	−10.7402	−0.356623	−0.178311	+	0.983974i	$0.557063\pi$
$908$	−18.2915	−0.607024
$909$	7.81357	0.259160
$910$	21.5505	0.714392
$911$	−1.98958	−0.0659177	−0.0329589	−	0.999457i	$-0.510493\pi$
$911$	−1.98958	−0.0659177	−0.0329589	+	0.999457i	$0.510493\pi$
$912$	−10.6487	−0.352614
$913$	−7.51491	−0.248707
$914$	8.25759	0.273137
$915$	13.9310	0.460543
$916$	−37.6962	−1.24552
$917$	60.9049	2.01126
$918$	−1.99378	−0.0658046
$919$	−33.9113	−1.11863	−0.559315	−	0.828955i	$-0.688936\pi$
$919$	−33.9113	−1.11863	−0.559315	+	0.828955i	$0.688936\pi$
$920$	0.0403650	0.00133079
$921$	20.5368	0.676710
$922$	20.3659	0.670716
$923$	10.0678	0.331386
$924$	−24.4025	−0.802784
$925$	−0.974193	−0.0320313
$926$	42.7322	1.40427
$927$	−6.11213	−0.200749
$928$	−55.2531	−1.81377
$929$	51.9637	1.70487	0.852436	−	0.522831i	$-0.175124\pi$
$929$	51.9637	1.70487	0.852436	+	0.522831i	$0.175124\pi$
$930$	23.3069	0.764264
$931$	25.0123	0.819744
$932$	3.97624	0.130246
$933$	11.2977	0.369870
$934$	−5.85727	−0.191656
$935$	3.77050	0.123309
$936$	0.106191	0.00347098
$937$	2.70731	0.0884439	0.0442219	−	0.999022i	$-0.485919\pi$
$937$	2.70731	0.0884439	0.0442219	+	0.999022i	$0.485919\pi$
$938$	−60.8830	−1.98790
$939$	0.573574	0.0187179
$940$	−1.75963	−0.0573929
$941$	−6.07303	−0.197975	−0.0989876	−	0.995089i	$-0.531560\pi$
$941$	−6.07303	−0.197975	−0.0989876	+	0.995089i	$0.531560\pi$
$942$	−27.7759	−0.904989
$943$	−3.73279	−0.121556
$944$	30.6524	0.997650
$945$	−5.03886	−0.163914
$946$	75.7034	2.46133
$947$	−51.5344	−1.67464	−0.837321	−	0.546711i	$-0.815879\pi$
$947$	−51.5344	−1.67464	−0.837321	+	0.546711i	$0.815879\pi$
$948$	−1.97517	−0.0641506
$949$	23.2672	0.755285
$950$	18.1541	0.588996
$951$	6.55227	0.212472
$952$	−0.201152	−0.00651937
$953$	−28.7496	−0.931292	−0.465646	−	0.884971i	$-0.654178\pi$
$953$	−28.7496	−0.931292	−0.465646	+	0.884971i	$0.654178\pi$
$954$	−7.40195	−0.239647
$955$	−12.3031	−0.398120
$956$	21.3424	0.690262
$957$	−21.0685	−0.681049
$958$	−13.7227	−0.443359
$959$	34.8011	1.12379
$960$	−9.67283	−0.312189
$961$	57.8613	1.86649
$962$	−1.20342	−0.0387999
$963$	−7.11929	−0.229416
$964$	3.44754	0.111038
$965$	−21.0807	−0.678613
$966$	5.32686	0.171389
$967$	4.53812	0.145936	0.0729681	−	0.997334i	$-0.476753\pi$
$967$	4.53812	0.145936	0.0729681	+	0.997334i	$0.476753\pi$
$968$	−0.0868905	−0.00279277
$969$	2.62993	0.0844856
$970$	−36.3430	−1.16690
$971$	40.6182	1.30350	0.651751	−	0.758433i	$-0.274035\pi$
$971$	40.6182	1.30350	0.651751	+	0.758433i	$0.274035\pi$
$972$	1.97517	0.0633536
$973$	−58.9171	−1.88879
$974$	−47.5705	−1.52426
$975$	−7.42675	−0.237846
$976$	−45.4865	−1.45599
$977$	55.0475	1.76112	0.880562	−	0.473931i	$-0.157165\pi$
$977$	55.0475	1.76112	0.880562	+	0.473931i	$0.157165\pi$
$978$	1.81739	0.0581136
$979$	16.2578	0.519601
$980$	23.2951	0.744133
$981$	−4.96541	−0.158533
$982$	69.4760	2.21707
$983$	43.8142	1.39745	0.698727	−	0.715388i	$-0.253750\pi$
$983$	43.8142	1.39745	0.698727	+	0.715388i	$0.253750\pi$
$984$	−0.281038	−0.00895916
$985$	−11.5485	−0.367965
$986$	13.8154	0.439972
$987$	2.91910	0.0929158
$988$	11.1428	0.354501
$989$	−8.21109	−0.261098
$990$	−7.51756	−0.238924
$991$	−53.0115	−1.68397	−0.841983	−	0.539505i	$-0.818612\pi$
$991$	−53.0115	−1.68397	−0.841983	+	0.539505i	$0.818612\pi$
$992$	−75.1670	−2.38656
$993$	9.15822	0.290627
$994$	38.0231	1.20602
$995$	8.52720	0.270330
$996$	−4.88180	−0.154686
$997$	−25.8839	−0.819753	−0.409876	−	0.912141i	$-0.634428\pi$
$997$	−25.8839	−0.819753	−0.409876	+	0.912141i	$0.634428\pi$
$998$	33.2288	1.05184
$999$	0.281380	0.00890247

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.e.1.4	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.e.1.4	✓	18	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 4029 = 3 \cdot 17 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4029.a (trivial)

\(f(q)\)	\(=\)	\(q-1.99378 q^{2} +1.00000 q^{3} +1.97517 q^{4} +1.24008 q^{5} -1.99378 q^{6} -4.06333 q^{7} +0.0495043 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.99378 q^{2} +1.00000 q^{3} +1.97517 q^{4} +1.24008 q^{5} -1.99378 q^{6} -4.06333 q^{7} +0.0495043 q^{8} +1.00000 q^{9} -2.47246 q^{10} +3.04052 q^{11} +1.97517 q^{12} +2.14510 q^{13} +8.10139 q^{14} +1.24008 q^{15} -4.04904 q^{16} +1.00000 q^{17} -1.99378 q^{18} +2.62993 q^{19} +2.44937 q^{20} -4.06333 q^{21} -6.06215 q^{22} +0.657524 q^{23} +0.0495043 q^{24} -3.46220 q^{25} -4.27686 q^{26} +1.00000 q^{27} -8.02576 q^{28} -6.92925 q^{29} -2.47246 q^{30} -9.42663 q^{31} +7.97390 q^{32} +3.04052 q^{33} -1.99378 q^{34} -5.03886 q^{35} +1.97517 q^{36} +0.281380 q^{37} -5.24351 q^{38} +2.14510 q^{39} +0.0613894 q^{40} -5.67704 q^{41} +8.10139 q^{42} -12.4879 q^{43} +6.00555 q^{44} +1.24008 q^{45} -1.31096 q^{46} -0.718400 q^{47} -4.04904 q^{48} +9.51062 q^{49} +6.90287 q^{50} +1.00000 q^{51} +4.23693 q^{52} +3.71252 q^{53} -1.99378 q^{54} +3.77050 q^{55} -0.201152 q^{56} +2.62993 q^{57} +13.8154 q^{58} -7.57028 q^{59} +2.44937 q^{60} +11.2339 q^{61} +18.7947 q^{62} -4.06333 q^{63} -7.80015 q^{64} +2.66010 q^{65} -6.06215 q^{66} -7.51513 q^{67} +1.97517 q^{68} +0.657524 q^{69} +10.0464 q^{70} +4.69340 q^{71} +0.0495043 q^{72} +10.8467 q^{73} -0.561011 q^{74} -3.46220 q^{75} +5.19456 q^{76} -12.3546 q^{77} -4.27686 q^{78} -1.00000 q^{79} -5.02115 q^{80} +1.00000 q^{81} +11.3188 q^{82} -2.47158 q^{83} -8.02576 q^{84} +1.24008 q^{85} +24.8982 q^{86} -6.92925 q^{87} +0.150519 q^{88} +5.34703 q^{89} -2.47246 q^{90} -8.71623 q^{91} +1.29872 q^{92} -9.42663 q^{93} +1.43233 q^{94} +3.26133 q^{95} +7.97390 q^{96} +14.6992 q^{97} -18.9621 q^{98} +3.04052 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 6 q^{2} + 18 q^{3} + 20 q^{4} - 5 q^{5} - 6 q^{6} - 13 q^{7} - 12 q^{8} + 18 q^{9}+O(q^{10}) \) 18 * q - 6 * q^2 + 18 * q^3 + 20 * q^4 - 5 * q^5 - 6 * q^6 - 13 * q^7 - 12 * q^8 + 18 * q^9	\( 18 q - 6 q^{2} + 18 q^{3} + 20 q^{4} - 5 q^{5} - 6 q^{6} - 13 q^{7} - 12 q^{8} + 18 q^{9} - 15 q^{10} - 27 q^{11} + 20 q^{12} - 4 q^{13} - 5 q^{14} - 5 q^{15} + 16 q^{16} + 18 q^{17} - 6 q^{18} - 30 q^{19} - 16 q^{20} - 13 q^{21} + 13 q^{22} - 21 q^{23} - 12 q^{24} + 13 q^{25} - 20 q^{26} + 18 q^{27} - 33 q^{28} - 47 q^{29} - 15 q^{30} - 18 q^{31} - 45 q^{32} - 27 q^{33} - 6 q^{34} - 17 q^{35} + 20 q^{36} + q^{37} + 5 q^{38} - 4 q^{39} - 12 q^{40} - 18 q^{41} - 5 q^{42} - 39 q^{43} - 34 q^{44} - 5 q^{45} - 7 q^{46} + 16 q^{48} + 15 q^{49} - 23 q^{50} + 18 q^{51} + 5 q^{52} - 9 q^{53} - 6 q^{54} + q^{55} - 24 q^{56} - 30 q^{57} + 41 q^{58} - 42 q^{59} - 16 q^{60} - 43 q^{61} - 54 q^{62} - 13 q^{63} + 22 q^{64} - 25 q^{65} + 13 q^{66} + 20 q^{68} - 21 q^{69} + 17 q^{70} + 9 q^{71} - 12 q^{72} + 19 q^{73} - 30 q^{74} + 13 q^{75} - 17 q^{76} - 14 q^{77} - 20 q^{78} - 18 q^{79} + 36 q^{80} + 18 q^{81} - 3 q^{82} - 61 q^{83} - 33 q^{84} - 5 q^{85} - 24 q^{86} - 47 q^{87} - 25 q^{88} + 10 q^{89} - 15 q^{90} - 52 q^{91} - 74 q^{92} - 18 q^{93} + 31 q^{94} - 37 q^{95} - 45 q^{96} - 9 q^{97} + 27 q^{98} - 27 q^{99}+O(q^{100}) \) 18 * q - 6 * q^2 + 18 * q^3 + 20 * q^4 - 5 * q^5 - 6 * q^6 - 13 * q^7 - 12 * q^8 + 18 * q^9 - 15 * q^10 - 27 * q^11 + 20 * q^12 - 4 * q^13 - 5 * q^14 - 5 * q^15 + 16 * q^16 + 18 * q^17 - 6 * q^18 - 30 * q^19 - 16 * q^20 - 13 * q^21 + 13 * q^22 - 21 * q^23 - 12 * q^24 + 13 * q^25 - 20 * q^26 + 18 * q^27 - 33 * q^28 - 47 * q^29 - 15 * q^30 - 18 * q^31 - 45 * q^32 - 27 * q^33 - 6 * q^34 - 17 * q^35 + 20 * q^36 + q^37 + 5 * q^38 - 4 * q^39 - 12 * q^40 - 18 * q^41 - 5 * q^42 - 39 * q^43 - 34 * q^44 - 5 * q^45 - 7 * q^46 + 16 * q^48 + 15 * q^49 - 23 * q^50 + 18 * q^51 + 5 * q^52 - 9 * q^53 - 6 * q^54 + q^55 - 24 * q^56 - 30 * q^57 + 41 * q^58 - 42 * q^59 - 16 * q^60 - 43 * q^61 - 54 * q^62 - 13 * q^63 + 22 * q^64 - 25 * q^65 + 13 * q^66 + 20 * q^68 - 21 * q^69 + 17 * q^70 + 9 * q^71 - 12 * q^72 + 19 * q^73 - 30 * q^74 + 13 * q^75 - 17 * q^76 - 14 * q^77 - 20 * q^78 - 18 * q^79 + 36 * q^80 + 18 * q^81 - 3 * q^82 - 61 * q^83 - 33 * q^84 - 5 * q^85 - 24 * q^86 - 47 * q^87 - 25 * q^88 + 10 * q^89 - 15 * q^90 - 52 * q^91 - 74 * q^92 - 18 * q^93 + 31 * q^94 - 37 * q^95 - 45 * q^96 - 9 * q^97 + 27 * q^98 - 27 * q^99

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