LMFDB - Embedded newform 6018.2.a.o.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6018,2,Mod(1,6018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6018, 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("6018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6018 = 2 \cdot 3 \cdot 17 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6018.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:	$48.0539719364$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.725.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 3x^{2} + x + 1 $ x^4 - x^3 - 3*x^2 + x + 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			1.2
Root			$0.737640$ of defining polynomial
Character	$\chi$	$=$	6018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.880394 q^{5} +1.00000 q^{6} -1.31313 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.880394 q^{5} +1.00000 q^{6} -1.31313 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.880394 q^{10} -0.806473 q^{11} +1.00000 q^{12} +0.854102 q^{13} -1.31313 q^{14} -0.880394 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} -3.32429 q^{19} -0.880394 q^{20} -1.31313 q^{21} -0.806473 q^{22} -8.04763 q^{23} +1.00000 q^{24} -4.22491 q^{25} +0.854102 q^{26} +1.00000 q^{27} -1.31313 q^{28} +4.13668 q^{29} -0.880394 q^{30} -3.08082 q^{31} +1.00000 q^{32} -0.806473 q^{33} +1.00000 q^{34} +1.15607 q^{35} +1.00000 q^{36} -10.6356 q^{37} -3.32429 q^{38} +0.854102 q^{39} -0.880394 q^{40} +2.28684 q^{41} -1.31313 q^{42} +1.19862 q^{43} -0.806473 q^{44} -0.880394 q^{45} -8.04763 q^{46} +1.81156 q^{47} +1.00000 q^{48} -5.27568 q^{49} -4.22491 q^{50} +1.00000 q^{51} +0.854102 q^{52} +5.11780 q^{53} +1.00000 q^{54} +0.710014 q^{55} -1.31313 q^{56} -3.32429 q^{57} +4.13668 q^{58} +1.00000 q^{59} -0.880394 q^{60} -4.72333 q^{61} -3.08082 q^{62} -1.31313 q^{63} +1.00000 q^{64} -0.751946 q^{65} -0.806473 q^{66} -5.94315 q^{67} +1.00000 q^{68} -8.04763 q^{69} +1.15607 q^{70} -2.49235 q^{71} +1.00000 q^{72} -3.28175 q^{73} -10.6356 q^{74} -4.22491 q^{75} -3.32429 q^{76} +1.05901 q^{77} +0.854102 q^{78} +10.9474 q^{79} -0.880394 q^{80} +1.00000 q^{81} +2.28684 q^{82} -17.5576 q^{83} -1.31313 q^{84} -0.880394 q^{85} +1.19862 q^{86} +4.13668 q^{87} -0.806473 q^{88} -13.3627 q^{89} -0.880394 q^{90} -1.12155 q^{91} -8.04763 q^{92} -3.08082 q^{93} +1.81156 q^{94} +2.92669 q^{95} +1.00000 q^{96} +14.6113 q^{97} -5.27568 q^{98} -0.806473 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} - q^{5} + 4 q^{6} - q^{7} + 4 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 - q^5 + 4 * q^6 - q^7 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} - q^{5} + 4 q^{6} - q^{7} + 4 q^{8} + 4 q^{9} - q^{10} - 10 q^{11} + 4 q^{12} - 10 q^{13} - q^{14} - q^{15} + 4 q^{16} + 4 q^{17} + 4 q^{18} - 14 q^{19} - q^{20} - q^{21} - 10 q^{22} - 12 q^{23} + 4 q^{24} - 3 q^{25} - 10 q^{26} + 4 q^{27} - q^{28} - 7 q^{29} - q^{30} - 13 q^{31} + 4 q^{32} - 10 q^{33} + 4 q^{34} - 18 q^{35} + 4 q^{36} - 11 q^{37} - 14 q^{38} - 10 q^{39} - q^{40} - 6 q^{41} - q^{42} - 20 q^{43} - 10 q^{44} - q^{45} - 12 q^{46} - 4 q^{47} + 4 q^{48} - q^{49} - 3 q^{50} + 4 q^{51} - 10 q^{52} - 5 q^{53} + 4 q^{54} + 4 q^{55} - q^{56} - 14 q^{57} - 7 q^{58} + 4 q^{59} - q^{60} + 2 q^{61} - 13 q^{62} - q^{63} + 4 q^{64} - 20 q^{65} - 10 q^{66} - 7 q^{67} + 4 q^{68} - 12 q^{69} - 18 q^{70} + 20 q^{71} + 4 q^{72} - 16 q^{73} - 11 q^{74} - 3 q^{75} - 14 q^{76} - 6 q^{77} - 10 q^{78} + 22 q^{79} - q^{80} + 4 q^{81} - 6 q^{82} + 7 q^{83} - q^{84} - q^{85} - 20 q^{86} - 7 q^{87} - 10 q^{88} + 3 q^{89} - q^{90} + 25 q^{91} - 12 q^{92} - 13 q^{93} - 4 q^{94} + 3 q^{95} + 4 q^{96} - 16 q^{97} - q^{98} - 10 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 - q^5 + 4 * q^6 - q^7 + 4 * q^8 + 4 * q^9 - q^10 - 10 * q^11 + 4 * q^12 - 10 * q^13 - q^14 - q^15 + 4 * q^16 + 4 * q^17 + 4 * q^18 - 14 * q^19 - q^20 - q^21 - 10 * q^22 - 12 * q^23 + 4 * q^24 - 3 * q^25 - 10 * q^26 + 4 * q^27 - q^28 - 7 * q^29 - q^30 - 13 * q^31 + 4 * q^32 - 10 * q^33 + 4 * q^34 - 18 * q^35 + 4 * q^36 - 11 * q^37 - 14 * q^38 - 10 * q^39 - q^40 - 6 * q^41 - q^42 - 20 * q^43 - 10 * q^44 - q^45 - 12 * q^46 - 4 * q^47 + 4 * q^48 - q^49 - 3 * q^50 + 4 * q^51 - 10 * q^52 - 5 * q^53 + 4 * q^54 + 4 * q^55 - q^56 - 14 * q^57 - 7 * q^58 + 4 * q^59 - q^60 + 2 * q^61 - 13 * q^62 - q^63 + 4 * q^64 - 20 * q^65 - 10 * q^66 - 7 * q^67 + 4 * q^68 - 12 * q^69 - 18 * q^70 + 20 * q^71 + 4 * q^72 - 16 * q^73 - 11 * q^74 - 3 * q^75 - 14 * q^76 - 6 * q^77 - 10 * q^78 + 22 * q^79 - q^80 + 4 * q^81 - 6 * q^82 + 7 * q^83 - q^84 - q^85 - 20 * q^86 - 7 * q^87 - 10 * q^88 + 3 * q^89 - q^90 + 25 * q^91 - 12 * q^92 - 13 * q^93 - 4 * q^94 + 3 * q^95 + 4 * q^96 - 16 * q^97 - q^98 - 10 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−0.880394	−0.393724	−0.196862	−	0.980431i	$-0.563075\pi$
$5$	−0.880394	−0.393724	−0.196862	+	0.980431i	$0.563075\pi$
$6$	1.00000	0.408248
$7$	−1.31313	−0.496318	−0.248159	−	0.968719i	$-0.579826\pi$
$7$	−1.31313	−0.496318	−0.248159	+	0.968719i	$0.579826\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−0.880394	−0.278405
$11$	−0.806473	−0.243161	−0.121580	−	0.992582i	$-0.538796\pi$
$11$	−0.806473	−0.243161	−0.121580	+	0.992582i	$0.538796\pi$
$12$	1.00000	0.288675
$13$	0.854102	0.236885	0.118443	−	0.992961i	$-0.462210\pi$
$13$	0.854102	0.236885	0.118443	+	0.992961i	$0.462210\pi$
$14$	−1.31313	−0.350950
$15$	−0.880394	−0.227317
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	1.00000	0.235702
$19$	−3.32429	−0.762645	−0.381323	−	0.924442i	$-0.624531\pi$
$19$	−3.32429	−0.762645	−0.381323	+	0.924442i	$0.624531\pi$
$20$	−0.880394	−0.196862
$21$	−1.31313	−0.286549
$22$	−0.806473	−0.171941
$23$	−8.04763	−1.67805	−0.839023	−	0.544095i	$-0.816873\pi$
$23$	−8.04763	−1.67805	−0.839023	+	0.544095i	$0.816873\pi$
$24$	1.00000	0.204124
$25$	−4.22491	−0.844981
$26$	0.854102	0.167503
$27$	1.00000	0.192450
$28$	−1.31313	−0.248159
$29$	4.13668	0.768162	0.384081	−	0.923299i	$-0.374518\pi$
$29$	4.13668	0.768162	0.384081	+	0.923299i	$0.374518\pi$
$30$	−0.880394	−0.160737
$31$	−3.08082	−0.553331	−0.276666	−	0.960966i	$-0.589229\pi$
$31$	−3.08082	−0.553331	−0.276666	+	0.960966i	$0.589229\pi$
$32$	1.00000	0.176777
$33$	−0.806473	−0.140389
$34$	1.00000	0.171499
$35$	1.15607	0.195412
$36$	1.00000	0.166667
$37$	−10.6356	−1.74848	−0.874242	−	0.485490i	$-0.838641\pi$
$37$	−10.6356	−1.74848	−0.874242	+	0.485490i	$0.838641\pi$
$38$	−3.32429	−0.539272
$39$	0.854102	0.136766
$40$	−0.880394	−0.139202
$41$	2.28684	0.357145	0.178572	−	0.983927i	$-0.442852\pi$
$41$	2.28684	0.357145	0.178572	+	0.983927i	$0.442852\pi$
$42$	−1.31313	−0.202621
$43$	1.19862	0.182787	0.0913936	−	0.995815i	$-0.470868\pi$
$43$	1.19862	0.182787	0.0913936	+	0.995815i	$0.470868\pi$
$44$	−0.806473	−0.121580
$45$	−0.880394	−0.131241
$46$	−8.04763	−1.18656
$47$	1.81156	0.264243	0.132122	−	0.991234i	$-0.457821\pi$
$47$	1.81156	0.264243	0.132122	+	0.991234i	$0.457821\pi$
$48$	1.00000	0.144338
$49$	−5.27568	−0.753669
$50$	−4.22491	−0.597492
$51$	1.00000	0.140028
$52$	0.854102	0.118443
$53$	5.11780	0.702983	0.351492	−	0.936191i	$-0.385675\pi$
$53$	5.11780	0.702983	0.351492	+	0.936191i	$0.385675\pi$
$54$	1.00000	0.136083
$55$	0.710014	0.0957382
$56$	−1.31313	−0.175475
$57$	−3.32429	−0.440314
$58$	4.13668	0.543173
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	−0.880394	−0.113658
$61$	−4.72333	−0.604761	−0.302381	−	0.953187i	$-0.597781\pi$
$61$	−4.72333	−0.604761	−0.302381	+	0.953187i	$0.597781\pi$
$62$	−3.08082	−0.391264
$63$	−1.31313	−0.165439
$64$	1.00000	0.125000
$65$	−0.751946	−0.0932674
$66$	−0.806473	−0.0992700
$67$	−5.94315	−0.726072	−0.363036	−	0.931775i	$-0.618260\pi$
$67$	−5.94315	−0.726072	−0.363036	+	0.931775i	$0.618260\pi$
$68$	1.00000	0.121268
$69$	−8.04763	−0.968821
$70$	1.15607	0.138177
$71$	−2.49235	−0.295788	−0.147894	−	0.989003i	$-0.547249\pi$
$71$	−2.49235	−0.295788	−0.147894	+	0.989003i	$0.547249\pi$
$72$	1.00000	0.117851
$73$	−3.28175	−0.384100	−0.192050	−	0.981385i	$-0.561514\pi$
$73$	−3.28175	−0.384100	−0.192050	+	0.981385i	$0.561514\pi$
$74$	−10.6356	−1.23637
$75$	−4.22491	−0.487850
$76$	−3.32429	−0.381323
$77$	1.05901	0.120685
$78$	0.854102	0.0967080
$79$	10.9474	1.23168	0.615840	−	0.787871i	$-0.288817\pi$
$79$	10.9474	1.23168	0.615840	+	0.787871i	$0.288817\pi$
$80$	−0.880394	−0.0984310
$81$	1.00000	0.111111
$82$	2.28684	0.252539
$83$	−17.5576	−1.92719	−0.963597	−	0.267360i	$-0.913849\pi$
$83$	−17.5576	−1.92719	−0.963597	+	0.267360i	$0.913849\pi$
$84$	−1.31313	−0.143275
$85$	−0.880394	−0.0954921
$86$	1.19862	0.129250
$87$	4.13668	0.443499
$88$	−0.806473	−0.0859703
$89$	−13.3627	−1.41644	−0.708222	−	0.705990i	$-0.750502\pi$
$89$	−13.3627	−1.41644	−0.708222	+	0.705990i	$0.750502\pi$
$90$	−0.880394	−0.0928016
$91$	−1.12155	−0.117570
$92$	−8.04763	−0.839023
$93$	−3.08082	−0.319466
$94$	1.81156	0.186848
$95$	2.92669	0.300272
$96$	1.00000	0.102062
$97$	14.6113	1.48355	0.741775	−	0.670649i	$-0.233984\pi$
$97$	14.6113	1.48355	0.741775	+	0.670649i	$0.233984\pi$
$98$	−5.27568	−0.532924
$99$	−0.806473	−0.0810536
$100$	−4.22491	−0.422491
$101$	−16.4578	−1.63762	−0.818808	−	0.574068i	$-0.805365\pi$
$101$	−16.4578	−1.63762	−0.818808	+	0.574068i	$0.805365\pi$
$102$	1.00000	0.0990148
$103$	11.3727	1.12059	0.560295	−	0.828293i	$-0.310688\pi$
$103$	11.3727	1.12059	0.560295	+	0.828293i	$0.310688\pi$
$104$	0.854102	0.0837516
$105$	1.15607	0.112821
$106$	5.11780	0.497084
$107$	10.0131	0.968003	0.484002	−	0.875067i	$-0.339183\pi$
$107$	10.0131	0.968003	0.484002	+	0.875067i	$0.339183\pi$
$108$	1.00000	0.0962250
$109$	6.08703	0.583031	0.291516	−	0.956566i	$-0.405840\pi$
$109$	6.08703	0.583031	0.291516	+	0.956566i	$0.405840\pi$
$110$	0.710014	0.0676971
$111$	−10.6356	−1.00949
$112$	−1.31313	−0.124079
$113$	−1.28948	−0.121304	−0.0606519	−	0.998159i	$-0.519318\pi$
$113$	−1.28948	−0.121304	−0.0606519	+	0.998159i	$0.519318\pi$
$114$	−3.32429	−0.311349
$115$	7.08508	0.660687
$116$	4.13668	0.384081
$117$	0.854102	0.0789618
$118$	1.00000	0.0920575
$119$	−1.31313	−0.120375
$120$	−0.880394	−0.0803686
$121$	−10.3496	−0.940873
$122$	−4.72333	−0.427631
$123$	2.28684	0.206198
$124$	−3.08082	−0.276666
$125$	8.12155	0.726413
$126$	−1.31313	−0.116983
$127$	9.44374	0.837997	0.418998	−	0.907987i	$-0.362381\pi$
$127$	9.44374	0.837997	0.418998	+	0.907987i	$0.362381\pi$
$128$	1.00000	0.0883883
$129$	1.19862	0.105532
$130$	−0.751946	−0.0659500
$131$	0.750136	0.0655397	0.0327699	−	0.999463i	$-0.489567\pi$
$131$	0.750136	0.0655397	0.0327699	+	0.999463i	$0.489567\pi$
$132$	−0.806473	−0.0701945
$133$	4.36524	0.378514
$134$	−5.94315	−0.513410
$135$	−0.880394	−0.0757722
$136$	1.00000	0.0857493
$137$	−9.06995	−0.774898	−0.387449	−	0.921891i	$-0.626644\pi$
$137$	−9.06995	−0.774898	−0.387449	+	0.921891i	$0.626644\pi$
$138$	−8.04763	−0.685060
$139$	−0.267958	−0.0227279	−0.0113639	−	0.999935i	$-0.503617\pi$
$139$	−0.267958	−0.0227279	−0.0113639	+	0.999935i	$0.503617\pi$
$140$	1.15607	0.0977061
$141$	1.81156	0.152561
$142$	−2.49235	−0.209154
$143$	−0.688810	−0.0576012
$144$	1.00000	0.0833333
$145$	−3.64191	−0.302444
$146$	−3.28175	−0.271600
$147$	−5.27568	−0.435131
$148$	−10.6356	−0.874242
$149$	−9.92488	−0.813078	−0.406539	−	0.913633i	$-0.633264\pi$
$149$	−9.92488	−0.813078	−0.406539	+	0.913633i	$0.633264\pi$
$150$	−4.22491	−0.344962
$151$	1.64036	0.133490	0.0667451	−	0.997770i	$-0.478739\pi$
$151$	1.64036	0.133490	0.0667451	+	0.997770i	$0.478739\pi$
$152$	−3.32429	−0.269636
$153$	1.00000	0.0808452
$154$	1.05901	0.0853372
$155$	2.71233	0.217860
$156$	0.854102	0.0683829
$157$	−18.9964	−1.51608	−0.758038	−	0.652210i	$-0.773842\pi$
$157$	−18.9964	−1.51608	−0.758038	+	0.652210i	$0.773842\pi$
$158$	10.9474	0.870930
$159$	5.11780	0.405868
$160$	−0.880394	−0.0696012
$161$	10.5676	0.832844
$162$	1.00000	0.0785674
$163$	8.85048	0.693223	0.346612	−	0.938009i	$-0.387332\pi$
$163$	8.85048	0.693223	0.346612	+	0.938009i	$0.387332\pi$
$164$	2.28684	0.178572
$165$	0.710014	0.0552745
$166$	−17.5576	−1.36273
$167$	8.96268	0.693553	0.346777	−	0.937948i	$-0.387276\pi$
$167$	8.96268	0.693553	0.346777	+	0.937948i	$0.387276\pi$
$168$	−1.31313	−0.101310
$169$	−12.2705	−0.943885
$170$	−0.880394	−0.0675231
$171$	−3.32429	−0.254215
$172$	1.19862	0.0913936
$173$	−2.15900	−0.164146	−0.0820730	−	0.996626i	$-0.526154\pi$
$173$	−2.15900	−0.164146	−0.0820730	+	0.996626i	$0.526154\pi$
$174$	4.13668	0.313601
$175$	5.54787	0.419379
$176$	−0.806473	−0.0607902
$177$	1.00000	0.0751646
$178$	−13.3627	−1.00158
$179$	−12.8127	−0.957665	−0.478832	−	0.877906i	$-0.658940\pi$
$179$	−12.8127	−0.957665	−0.478832	+	0.877906i	$0.658940\pi$
$180$	−0.880394	−0.0656207
$181$	−1.96862	−0.146326	−0.0731632	−	0.997320i	$-0.523309\pi$
$181$	−1.96862	−0.146326	−0.0731632	+	0.997320i	$0.523309\pi$
$182$	−1.12155	−0.0831348
$183$	−4.72333	−0.349159
$184$	−8.04763	−0.593279
$185$	9.36353	0.688420
$186$	−3.08082	−0.225897
$187$	−0.806473	−0.0589751
$188$	1.81156	0.132122
$189$	−1.31313	−0.0955164
$190$	2.92669	0.212324
$191$	−4.28500	−0.310051	−0.155026	−	0.987910i	$-0.549546\pi$
$191$	−4.28500	−0.310051	−0.155026	+	0.987910i	$0.549546\pi$
$192$	1.00000	0.0721688
$193$	6.00607	0.432327	0.216163	−	0.976357i	$-0.430646\pi$
$193$	6.00607	0.432327	0.216163	+	0.976357i	$0.430646\pi$
$194$	14.6113	1.04903
$195$	−0.751946	−0.0538480
$196$	−5.27568	−0.376834
$197$	−9.64678	−0.687305	−0.343652	−	0.939097i	$-0.611664\pi$
$197$	−9.64678	−0.687305	−0.343652	+	0.939097i	$0.611664\pi$
$198$	−0.806473	−0.0573135
$199$	9.95056	0.705377	0.352688	−	0.935741i	$-0.385268\pi$
$199$	9.95056	0.705377	0.352688	+	0.935741i	$0.385268\pi$
$200$	−4.22491	−0.298746
$201$	−5.94315	−0.419198
$202$	−16.4578	−1.15797
$203$	−5.43201	−0.381253
$204$	1.00000	0.0700140
$205$	−2.01332	−0.140616
$206$	11.3727	0.792377
$207$	−8.04763	−0.559349
$208$	0.854102	0.0592213
$209$	2.68095	0.185445
$210$	1.15607	0.0797767
$211$	3.34766	0.230462	0.115231	−	0.993339i	$-0.463239\pi$
$211$	3.34766	0.230462	0.115231	+	0.993339i	$0.463239\pi$
$212$	5.11780	0.351492
$213$	−2.49235	−0.170773
$214$	10.0131	0.684482
$215$	−1.05525	−0.0719677
$216$	1.00000	0.0680414
$217$	4.04553	0.274628
$218$	6.08703	0.412265
$219$	−3.28175	−0.221760
$220$	0.710014	0.0478691
$221$	0.854102	0.0574531
$222$	−10.6356	−0.713816
$223$	−21.7814	−1.45859	−0.729294	−	0.684201i	$-0.760151\pi$
$223$	−21.7814	−1.45859	−0.729294	+	0.684201i	$0.760151\pi$
$224$	−1.31313	−0.0877374
$225$	−4.22491	−0.281660
$226$	−1.28948	−0.0857747
$227$	9.58881	0.636432	0.318216	−	0.948018i	$-0.396916\pi$
$227$	9.58881	0.636432	0.318216	+	0.948018i	$0.396916\pi$
$228$	−3.32429	−0.220157
$229$	18.5177	1.22368	0.611841	−	0.790981i	$-0.290429\pi$
$229$	18.5177	1.22368	0.611841	+	0.790981i	$0.290429\pi$
$230$	7.08508	0.467176
$231$	1.05901	0.0696775
$232$	4.13668	0.271586
$233$	−9.25957	−0.606614	−0.303307	−	0.952893i	$-0.598091\pi$
$233$	−9.25957	−0.606614	−0.303307	+	0.952893i	$0.598091\pi$
$234$	0.854102	0.0558344
$235$	−1.59489	−0.104039
$236$	1.00000	0.0650945
$237$	10.9474	0.711111
$238$	−1.31313	−0.0851178
$239$	−7.92592	−0.512685	−0.256343	−	0.966586i	$-0.582518\pi$
$239$	−7.92592	−0.512685	−0.256343	+	0.966586i	$0.582518\pi$
$240$	−0.880394	−0.0568292
$241$	1.38295	0.0890837	0.0445418	−	0.999008i	$-0.485817\pi$
$241$	1.38295	0.0890837	0.0445418	+	0.999008i	$0.485817\pi$
$242$	−10.3496	−0.665298
$243$	1.00000	0.0641500
$244$	−4.72333	−0.302381
$245$	4.64468	0.296737
$246$	2.28684	0.145804
$247$	−2.83929	−0.180659
$248$	−3.08082	−0.195632
$249$	−17.5576	−1.11267
$250$	8.12155	0.513652
$251$	−2.68604	−0.169541	−0.0847707	−	0.996400i	$-0.527016\pi$
$251$	−2.68604	−0.169541	−0.0847707	+	0.996400i	$0.527016\pi$
$252$	−1.31313	−0.0827196
$253$	6.49019	0.408035
$254$	9.44374	0.592553
$255$	−0.880394	−0.0551324
$256$	1.00000	0.0625000
$257$	−13.7337	−0.856686	−0.428343	−	0.903616i	$-0.640903\pi$
$257$	−13.7337	−0.856686	−0.428343	+	0.903616i	$0.640903\pi$
$258$	1.19862	0.0746225
$259$	13.9660	0.867804
$260$	−0.751946	−0.0466337
$261$	4.13668	0.256054
$262$	0.750136	0.0463436
$263$	−18.0752	−1.11456	−0.557281	−	0.830324i	$-0.688156\pi$
$263$	−18.0752	−1.11456	−0.557281	+	0.830324i	$0.688156\pi$
$264$	−0.806473	−0.0496350
$265$	−4.50568	−0.276781
$266$	4.36524	0.267650
$267$	−13.3627	−0.817784
$268$	−5.94315	−0.363036
$269$	−23.2846	−1.41968	−0.709842	−	0.704361i	$-0.751234\pi$
$269$	−23.2846	−1.41968	−0.709842	+	0.704361i	$0.751234\pi$
$270$	−0.880394	−0.0535791
$271$	−6.71428	−0.407863	−0.203932	−	0.978985i	$-0.565372\pi$
$271$	−6.71428	−0.407863	−0.203932	+	0.978985i	$0.565372\pi$
$272$	1.00000	0.0606339
$273$	−1.12155	−0.0678793
$274$	−9.06995	−0.547936
$275$	3.40727	0.205466
$276$	−8.04763	−0.484410
$277$	−24.3896	−1.46543	−0.732716	−	0.680535i	$-0.761748\pi$
$277$	−24.3896	−1.46543	−0.732716	+	0.680535i	$0.761748\pi$
$278$	−0.267958	−0.0160710
$279$	−3.08082	−0.184444
$280$	1.15607	0.0690887
$281$	11.7140	0.698800	0.349400	−	0.936974i	$-0.386385\pi$
$281$	11.7140	0.698800	0.349400	+	0.936974i	$0.386385\pi$
$282$	1.81156	0.107877
$283$	14.7340	0.875847	0.437923	−	0.899012i	$-0.355714\pi$
$283$	14.7340	0.875847	0.437923	+	0.899012i	$0.355714\pi$
$284$	−2.49235	−0.147894
$285$	2.92669	0.173362
$286$	−0.688810	−0.0407302
$287$	−3.00293	−0.177257
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	−3.64191	−0.213860
$291$	14.6113	0.856528
$292$	−3.28175	−0.192050
$293$	12.4874	0.729522	0.364761	−	0.931101i	$-0.381151\pi$
$293$	12.4874	0.729522	0.364761	+	0.931101i	$0.381151\pi$
$294$	−5.27568	−0.307684
$295$	−0.880394	−0.0512585
$296$	−10.6356	−0.618183
$297$	−0.806473	−0.0467963
$298$	−9.92488	−0.574933
$299$	−6.87350	−0.397505
$300$	−4.22491	−0.243925
$301$	−1.57394	−0.0907205
$302$	1.64036	0.0943919
$303$	−16.4578	−0.945478
$304$	−3.32429	−0.190661
$305$	4.15839	0.238109
$306$	1.00000	0.0571662
$307$	20.1040	1.14739	0.573697	−	0.819068i	$-0.305509\pi$
$307$	20.1040	1.14739	0.573697	+	0.819068i	$0.305509\pi$
$308$	1.05901	0.0603425
$309$	11.3727	0.646973
$310$	2.71233	0.154050
$311$	34.3174	1.94596	0.972980	−	0.230890i	$-0.0741639\pi$
$311$	34.3174	1.94596	0.972980	+	0.230890i	$0.0741639\pi$
$312$	0.854102	0.0483540
$313$	−29.1995	−1.65045	−0.825226	−	0.564803i	$-0.808952\pi$
$313$	−29.1995	−1.65045	−0.825226	+	0.564803i	$0.808952\pi$
$314$	−18.9964	−1.07203
$315$	1.15607	0.0651374
$316$	10.9474	0.615840
$317$	−12.5378	−0.704194	−0.352097	−	0.935963i	$-0.614531\pi$
$317$	−12.5378	−0.704194	−0.352097	+	0.935963i	$0.614531\pi$
$318$	5.11780	0.286992
$319$	−3.33612	−0.186787
$320$	−0.880394	−0.0492155
$321$	10.0131	0.558877
$322$	10.5676	0.588910
$323$	−3.32429	−0.184969
$324$	1.00000	0.0555556
$325$	−3.60850	−0.200164
$326$	8.85048	0.490183
$327$	6.08703	0.336613
$328$	2.28684	0.126270
$329$	−2.37882	−0.131149
$330$	0.710014	0.0390850
$331$	3.30684	0.181761	0.0908803	−	0.995862i	$-0.471032\pi$
$331$	3.30684	0.181761	0.0908803	+	0.995862i	$0.471032\pi$
$332$	−17.5576	−0.963597
$333$	−10.6356	−0.582828
$334$	8.96268	0.490416
$335$	5.23231	0.285872
$336$	−1.31313	−0.0716373
$337$	−1.00120	−0.0545389	−0.0272695	−	0.999628i	$-0.508681\pi$
$337$	−1.00120	−0.0545389	−0.0272695	+	0.999628i	$0.508681\pi$
$338$	−12.2705	−0.667428
$339$	−1.28948	−0.0700347
$340$	−0.880394	−0.0477461
$341$	2.48460	0.134548
$342$	−3.32429	−0.179757
$343$	16.1196	0.870377
$344$	1.19862	0.0646250
$345$	7.08508	0.381448
$346$	−2.15900	−0.116069
$347$	−1.79449	−0.0963331	−0.0481666	−	0.998839i	$-0.515338\pi$
$347$	−1.79449	−0.0963331	−0.0481666	+	0.998839i	$0.515338\pi$
$348$	4.13668	0.221749
$349$	16.4028	0.878023	0.439012	−	0.898481i	$-0.355329\pi$
$349$	16.4028	0.878023	0.439012	+	0.898481i	$0.355329\pi$
$350$	5.54787	0.296546
$351$	0.854102	0.0455886
$352$	−0.806473	−0.0429852
$353$	−31.3537	−1.66879	−0.834394	−	0.551168i	$-0.814182\pi$
$353$	−31.3537	−1.66879	−0.834394	+	0.551168i	$0.814182\pi$
$354$	1.00000	0.0531494
$355$	2.19425	0.116459
$356$	−13.3627	−0.708222
$357$	−1.31313	−0.0694984
$358$	−12.8127	−0.677171
$359$	24.0213	1.26780	0.633899	−	0.773416i	$-0.281454\pi$
$359$	24.0213	1.26780	0.633899	+	0.773416i	$0.281454\pi$
$360$	−0.880394	−0.0464008
$361$	−7.94907	−0.418372
$362$	−1.96862	−0.103468
$363$	−10.3496	−0.543213
$364$	−1.12155	−0.0587852
$365$	2.88924	0.151229
$366$	−4.72333	−0.246893
$367$	−17.0572	−0.890378	−0.445189	−	0.895437i	$-0.646864\pi$
$367$	−17.0572	−0.890378	−0.445189	+	0.895437i	$0.646864\pi$
$368$	−8.04763	−0.419512
$369$	2.28684	0.119048
$370$	9.36353	0.486787
$371$	−6.72035	−0.348903
$372$	−3.08082	−0.159733
$373$	14.1389	0.732085	0.366043	−	0.930598i	$-0.380712\pi$
$373$	14.1389	0.732085	0.366043	+	0.930598i	$0.380712\pi$
$374$	−0.806473	−0.0417017
$375$	8.12155	0.419395
$376$	1.81156	0.0934241
$377$	3.53315	0.181966
$378$	−1.31313	−0.0675403
$379$	10.6967	0.549455	0.274728	−	0.961522i	$-0.411412\pi$
$379$	10.6967	0.549455	0.274728	+	0.961522i	$0.411412\pi$
$380$	2.92669	0.150136
$381$	9.44374	0.483818
$382$	−4.28500	−0.219240
$383$	21.9782	1.12303	0.561516	−	0.827466i	$-0.310218\pi$
$383$	21.9782	1.12303	0.561516	+	0.827466i	$0.310218\pi$
$384$	1.00000	0.0510310
$385$	−0.932343	−0.0475166
$386$	6.00607	0.305701
$387$	1.19862	0.0609290
$388$	14.6113	0.741775
$389$	33.1693	1.68175	0.840875	−	0.541229i	$-0.182041\pi$
$389$	33.1693	1.68175	0.840875	+	0.541229i	$0.182041\pi$
$390$	−0.751946	−0.0380763
$391$	−8.04763	−0.406986
$392$	−5.27568	−0.266462
$393$	0.750136	0.0378394
$394$	−9.64678	−0.485998
$395$	−9.63804	−0.484942
$396$	−0.806473	−0.0405268
$397$	31.3458	1.57320	0.786602	−	0.617461i	$-0.211839\pi$
$397$	31.3458	1.57320	0.786602	+	0.617461i	$0.211839\pi$
$398$	9.95056	0.498777
$399$	4.36524	0.218535
$400$	−4.22491	−0.211245
$401$	−1.06479	−0.0531729	−0.0265864	−	0.999647i	$-0.508464\pi$
$401$	−1.06479	−0.0531729	−0.0265864	+	0.999647i	$0.508464\pi$
$402$	−5.94315	−0.296418
$403$	−2.63133	−0.131076
$404$	−16.4578	−0.818808
$405$	−0.880394	−0.0437471
$406$	−5.43201	−0.269586
$407$	8.57734	0.425163
$408$	1.00000	0.0495074
$409$	−17.8012	−0.880213	−0.440106	−	0.897946i	$-0.645059\pi$
$409$	−17.8012	−0.880213	−0.440106	+	0.897946i	$0.645059\pi$
$410$	−2.01332	−0.0994308
$411$	−9.06995	−0.447388
$412$	11.3727	0.560295
$413$	−1.31313	−0.0646151
$414$	−8.04763	−0.395519
$415$	15.4576	0.758782
$416$	0.854102	0.0418758
$417$	−0.267958	−0.0131219
$418$	2.68095	0.131130
$419$	−27.8247	−1.35933	−0.679663	−	0.733525i	$-0.737874\pi$
$419$	−27.8247	−1.35933	−0.679663	+	0.733525i	$0.737874\pi$
$420$	1.15607	0.0564107
$421$	27.2478	1.32798	0.663989	−	0.747742i	$-0.268862\pi$
$421$	27.2478	1.32798	0.663989	+	0.747742i	$0.268862\pi$
$422$	3.34766	0.162961
$423$	1.81156	0.0880811
$424$	5.11780	0.248542
$425$	−4.22491	−0.204938
$426$	−2.49235	−0.120755
$427$	6.20237	0.300154
$428$	10.0131	0.484002
$429$	−0.688810	−0.0332561
$430$	−1.05525	−0.0508888
$431$	3.75967	0.181097	0.0905484	−	0.995892i	$-0.471138\pi$
$431$	3.75967	0.181097	0.0905484	+	0.995892i	$0.471138\pi$
$432$	1.00000	0.0481125
$433$	27.9332	1.34239	0.671193	−	0.741283i	$-0.265782\pi$
$433$	27.9332	1.34239	0.671193	+	0.741283i	$0.265782\pi$
$434$	4.04553	0.194191
$435$	−3.64191	−0.174616
$436$	6.08703	0.291516
$437$	26.7527	1.27975
$438$	−3.28175	−0.156808
$439$	−2.91484	−0.139118	−0.0695588	−	0.997578i	$-0.522159\pi$
$439$	−2.91484	−0.139118	−0.0695588	+	0.997578i	$0.522159\pi$
$440$	0.710014	0.0338486
$441$	−5.27568	−0.251223
$442$	0.854102	0.0406255
$443$	7.62100	0.362085	0.181042	−	0.983475i	$-0.442053\pi$
$443$	7.62100	0.362085	0.181042	+	0.983475i	$0.442053\pi$
$444$	−10.6356	−0.504744
$445$	11.7644	0.557688
$446$	−21.7814	−1.03138
$447$	−9.92488	−0.469431
$448$	−1.31313	−0.0620397
$449$	23.7416	1.12043	0.560217	−	0.828346i	$-0.310718\pi$
$449$	23.7416	1.12043	0.560217	+	0.828346i	$0.310718\pi$
$450$	−4.22491	−0.199164
$451$	−1.84428	−0.0868436
$452$	−1.28948	−0.0606519
$453$	1.64036	0.0770706
$454$	9.58881	0.450025
$455$	0.987405	0.0462903
$456$	−3.32429	−0.155674
$457$	−16.1234	−0.754219	−0.377109	−	0.926169i	$-0.623082\pi$
$457$	−16.1234	−0.754219	−0.377109	+	0.926169i	$0.623082\pi$
$458$	18.5177	0.865274
$459$	1.00000	0.0466760
$460$	7.08508	0.330344
$461$	24.0954	1.12223	0.561117	−	0.827736i	$-0.310372\pi$
$461$	24.0954	1.12223	0.561117	+	0.827736i	$0.310372\pi$
$462$	1.05901	0.0492694
$463$	−8.23296	−0.382618	−0.191309	−	0.981530i	$-0.561273\pi$
$463$	−8.23296	−0.382618	−0.191309	+	0.981530i	$0.561273\pi$
$464$	4.13668	0.192041
$465$	2.71233	0.125781
$466$	−9.25957	−0.428941
$467$	−17.6501	−0.816748	−0.408374	−	0.912815i	$-0.633904\pi$
$467$	−17.6501	−0.816748	−0.408374	+	0.912815i	$0.633904\pi$
$468$	0.854102	0.0394809
$469$	7.80415	0.360362
$470$	−1.59489	−0.0735666
$471$	−18.9964	−0.875307
$472$	1.00000	0.0460287
$473$	−0.966651	−0.0444466
$474$	10.9474	0.502831
$475$	14.0448	0.644421
$476$	−1.31313	−0.0601874
$477$	5.11780	0.234328
$478$	−7.92592	−0.362523
$479$	28.9556	1.32302	0.661508	−	0.749938i	$-0.269917\pi$
$479$	28.9556	1.32302	0.661508	+	0.749938i	$0.269917\pi$
$480$	−0.880394	−0.0401843
$481$	−9.08390	−0.414190
$482$	1.38295	0.0629917
$483$	10.5676	0.480843
$484$	−10.3496	−0.470436
$485$	−12.8637	−0.584109
$486$	1.00000	0.0453609
$487$	12.0378	0.545483	0.272742	−	0.962087i	$-0.412070\pi$
$487$	12.0378	0.545483	0.272742	+	0.962087i	$0.412070\pi$
$488$	−4.72333	−0.213815
$489$	8.85048	0.400233
$490$	4.64468	0.209825
$491$	−1.57084	−0.0708909	−0.0354455	−	0.999372i	$-0.511285\pi$
$491$	−1.57084	−0.0708909	−0.0354455	+	0.999372i	$0.511285\pi$
$492$	2.28684	0.103099
$493$	4.13668	0.186307
$494$	−2.83929	−0.127746
$495$	0.710014	0.0319127
$496$	−3.08082	−0.138333
$497$	3.27279	0.146805
$498$	−17.5576	−0.786773
$499$	10.5078	0.470393	0.235196	−	0.971948i	$-0.424427\pi$
$499$	10.5078	0.470393	0.235196	+	0.971948i	$0.424427\pi$
$500$	8.12155	0.363207
$501$	8.96268	0.400423
$502$	−2.68604	−0.119884
$503$	−15.8471	−0.706588	−0.353294	−	0.935512i	$-0.614939\pi$
$503$	−15.8471	−0.706588	−0.353294	+	0.935512i	$0.614939\pi$
$504$	−1.31313	−0.0584916
$505$	14.4894	0.644768
$506$	6.49019	0.288524
$507$	−12.2705	−0.544952
$508$	9.44374	0.418998
$509$	−36.0403	−1.59746	−0.798730	−	0.601690i	$-0.794494\pi$
$509$	−36.0403	−1.59746	−0.798730	+	0.601690i	$0.794494\pi$
$510$	−0.880394	−0.0389845
$511$	4.30938	0.190636
$512$	1.00000	0.0441942
$513$	−3.32429	−0.146771
$514$	−13.7337	−0.605769
$515$	−10.0125	−0.441203
$516$	1.19862	0.0527661
$517$	−1.46097	−0.0642536
$518$	13.9660	0.613630
$519$	−2.15900	−0.0947697
$520$	−0.751946	−0.0329750
$521$	−11.4615	−0.502137	−0.251068	−	0.967969i	$-0.580782\pi$
$521$	−11.4615	−0.502137	−0.251068	+	0.967969i	$0.580782\pi$
$522$	4.13668	0.181058
$523$	−29.3343	−1.28270	−0.641350	−	0.767249i	$-0.721625\pi$
$523$	−29.3343	−1.28270	−0.641350	+	0.767249i	$0.721625\pi$
$524$	0.750136	0.0327699
$525$	5.54787	0.242129
$526$	−18.0752	−0.788115
$527$	−3.08082	−0.134203
$528$	−0.806473	−0.0350972
$529$	41.7643	1.81584
$530$	−4.50568	−0.195714
$531$	1.00000	0.0433963
$532$	4.36524	0.189257
$533$	1.95320	0.0846023
$534$	−13.3627	−0.578261
$535$	−8.81547	−0.381126
$536$	−5.94315	−0.256705
$537$	−12.8127	−0.552908
$538$	−23.2846	−1.00387
$539$	4.25469	0.183263
$540$	−0.880394	−0.0378861
$541$	37.7165	1.62156	0.810780	−	0.585350i	$-0.199043\pi$
$541$	37.7165	1.62156	0.810780	+	0.585350i	$0.199043\pi$
$542$	−6.71428	−0.288403
$543$	−1.96862	−0.0844816
$544$	1.00000	0.0428746
$545$	−5.35898	−0.229553
$546$	−1.12155	−0.0479979
$547$	43.8934	1.87675	0.938373	−	0.345625i	$-0.112333\pi$
$547$	43.8934	1.87675	0.938373	+	0.345625i	$0.112333\pi$
$548$	−9.06995	−0.387449
$549$	−4.72333	−0.201587
$550$	3.40727	0.145287
$551$	−13.7515	−0.585835
$552$	−8.04763	−0.342530
$553$	−14.3754	−0.611305
$554$	−24.3896	−1.03622
$555$	9.36353	0.397460
$556$	−0.267958	−0.0113639
$557$	−6.77350	−0.287002	−0.143501	−	0.989650i	$-0.545836\pi$
$557$	−6.77350	−0.287002	−0.143501	+	0.989650i	$0.545836\pi$
$558$	−3.08082	−0.130421
$559$	1.02374	0.0432996
$560$	1.15607	0.0488531
$561$	−0.806473	−0.0340493
$562$	11.7140	0.494126
$563$	21.6865	0.913978	0.456989	−	0.889472i	$-0.348928\pi$
$563$	21.6865	0.913978	0.456989	+	0.889472i	$0.348928\pi$
$564$	1.81156	0.0762805
$565$	1.13525	0.0477602
$566$	14.7340	0.619317
$567$	−1.31313	−0.0551464
$568$	−2.49235	−0.104577
$569$	−16.8081	−0.704633	−0.352317	−	0.935881i	$-0.614606\pi$
$569$	−16.8081	−0.704633	−0.352317	+	0.935881i	$0.614606\pi$
$570$	2.92669	0.122585
$571$	−31.5062	−1.31849	−0.659246	−	0.751927i	$-0.729125\pi$
$571$	−31.5062	−1.31849	−0.659246	+	0.751927i	$0.729125\pi$
$572$	−0.688810	−0.0288006
$573$	−4.28500	−0.179008
$574$	−3.00293	−0.125340
$575$	34.0005	1.41792
$576$	1.00000	0.0416667
$577$	−14.7803	−0.615313	−0.307656	−	0.951498i	$-0.599545\pi$
$577$	−14.7803	−0.615313	−0.307656	+	0.951498i	$0.599545\pi$
$578$	1.00000	0.0415945
$579$	6.00607	0.249604
$580$	−3.64191	−0.151222
$581$	23.0554	0.956500
$582$	14.6113	0.605657
$583$	−4.12736	−0.170938
$584$	−3.28175	−0.135800
$585$	−0.751946	−0.0310891
$586$	12.4874	0.515850
$587$	−18.6535	−0.769913	−0.384957	−	0.922935i	$-0.625784\pi$
$587$	−18.6535	−0.769913	−0.384957	+	0.922935i	$0.625784\pi$
$588$	−5.27568	−0.217565
$589$	10.2415	0.421996
$590$	−0.880394	−0.0362452
$591$	−9.64678	−0.396815
$592$	−10.6356	−0.437121
$593$	0.602001	0.0247212	0.0123606	−	0.999924i	$-0.496065\pi$
$593$	0.602001	0.0247212	0.0123606	+	0.999924i	$0.496065\pi$
$594$	−0.806473	−0.0330900
$595$	1.15607	0.0473944
$596$	−9.92488	−0.406539
$597$	9.95056	0.407249
$598$	−6.87350	−0.281078
$599$	−40.4299	−1.65192	−0.825961	−	0.563727i	$-0.809367\pi$
$599$	−40.4299	−1.65192	−0.825961	+	0.563727i	$0.809367\pi$
$600$	−4.22491	−0.172481
$601$	11.4505	0.467076	0.233538	−	0.972348i	$-0.424970\pi$
$601$	11.4505	0.467076	0.233538	+	0.972348i	$0.424970\pi$
$602$	−1.57394	−0.0641491
$603$	−5.94315	−0.242024
$604$	1.64036	0.0667451
$605$	9.11172	0.370444
$606$	−16.4578	−0.668554
$607$	10.6778	0.433400	0.216700	−	0.976238i	$-0.430471\pi$
$607$	10.6778	0.433400	0.216700	+	0.976238i	$0.430471\pi$
$608$	−3.32429	−0.134818
$609$	−5.43201	−0.220116
$610$	4.15839	0.168368
$611$	1.54726	0.0625954
$612$	1.00000	0.0404226
$613$	15.3644	0.620560	0.310280	−	0.950645i	$-0.399577\pi$
$613$	15.3644	0.620560	0.310280	+	0.950645i	$0.399577\pi$
$614$	20.1040	0.811330
$615$	−2.01332	−0.0811849
$616$	1.05901	0.0426686
$617$	−25.7269	−1.03573	−0.517863	−	0.855464i	$-0.673272\pi$
$617$	−25.7269	−1.03573	−0.517863	+	0.855464i	$0.673272\pi$
$618$	11.3727	0.457479
$619$	−2.94720	−0.118458	−0.0592290	−	0.998244i	$-0.518864\pi$
$619$	−2.94720	−0.118458	−0.0592290	+	0.998244i	$0.518864\pi$
$620$	2.71233	0.108930
$621$	−8.04763	−0.322940
$622$	34.3174	1.37600
$623$	17.5470	0.703006
$624$	0.854102	0.0341914
$625$	13.9744	0.558975
$626$	−29.1995	−1.16705
$627$	2.68095	0.107067
$628$	−18.9964	−0.758038
$629$	−10.6356	−0.424070
$630$	1.15607	0.0460591
$631$	24.5502	0.977330	0.488665	−	0.872472i	$-0.337484\pi$
$631$	24.5502	0.977330	0.488665	+	0.872472i	$0.337484\pi$
$632$	10.9474	0.435465
$633$	3.34766	0.133057
$634$	−12.5378	−0.497941
$635$	−8.31421	−0.329939
$636$	5.11780	0.202934
$637$	−4.50597	−0.178533
$638$	−3.33612	−0.132078
$639$	−2.49235	−0.0985960
$640$	−0.880394	−0.0348006
$641$	−7.98353	−0.315331	−0.157665	−	0.987493i	$-0.550397\pi$
$641$	−7.98353	−0.315331	−0.157665	+	0.987493i	$0.550397\pi$
$642$	10.0131	0.395186
$643$	5.46145	0.215379	0.107689	−	0.994185i	$-0.465655\pi$
$643$	5.46145	0.215379	0.107689	+	0.994185i	$0.465655\pi$
$644$	10.5676	0.416422
$645$	−1.05525	−0.0415506
$646$	−3.32429	−0.130793
$647$	−10.1019	−0.397147	−0.198573	−	0.980086i	$-0.563631\pi$
$647$	−10.1019	−0.397147	−0.198573	+	0.980086i	$0.563631\pi$
$648$	1.00000	0.0392837
$649$	−0.806473	−0.0316568
$650$	−3.60850	−0.141537
$651$	4.04553	0.158557
$652$	8.85048	0.346612
$653$	5.12597	0.200595	0.100297	−	0.994958i	$-0.468021\pi$
$653$	5.12597	0.200595	0.100297	+	0.994958i	$0.468021\pi$
$654$	6.08703	0.238022
$655$	−0.660415	−0.0258046
$656$	2.28684	0.0892862
$657$	−3.28175	−0.128033
$658$	−2.37882	−0.0927361
$659$	30.9922	1.20729	0.603643	−	0.797255i	$-0.293715\pi$
$659$	30.9922	1.20729	0.603643	+	0.797255i	$0.293715\pi$
$660$	0.710014	0.0276372
$661$	2.39792	0.0932683	0.0466342	−	0.998912i	$-0.485150\pi$
$661$	2.39792	0.0932683	0.0466342	+	0.998912i	$0.485150\pi$
$662$	3.30684	0.128524
$663$	0.854102	0.0331706
$664$	−17.5576	−0.681366
$665$	−3.84313	−0.149030
$666$	−10.6356	−0.412122
$667$	−33.2905	−1.28901
$668$	8.96268	0.346777
$669$	−21.7814	−0.842116
$670$	5.23231	0.202142
$671$	3.80924	0.147054
$672$	−1.31313	−0.0506552
$673$	37.5403	1.44707	0.723535	−	0.690288i	$-0.242516\pi$
$673$	37.5403	1.44707	0.723535	+	0.690288i	$0.242516\pi$
$674$	−1.00120	−0.0385648
$675$	−4.22491	−0.162617
$676$	−12.2705	−0.471943
$677$	−22.4298	−0.862047	−0.431024	−	0.902341i	$-0.641847\pi$
$677$	−22.4298	−0.862047	−0.431024	+	0.902341i	$0.641847\pi$
$678$	−1.28948	−0.0495220
$679$	−19.1865	−0.736312
$680$	−0.880394	−0.0337616
$681$	9.58881	0.367444
$682$	2.48460	0.0951401
$683$	6.80437	0.260362	0.130181	−	0.991490i	$-0.458444\pi$
$683$	6.80437	0.260362	0.130181	+	0.991490i	$0.458444\pi$
$684$	−3.32429	−0.127108
$685$	7.98513	0.305096
$686$	16.1196	0.615449
$687$	18.5177	0.706493
$688$	1.19862	0.0456968
$689$	4.37112	0.166526
$690$	7.08508	0.269724
$691$	9.95991	0.378893	0.189446	−	0.981891i	$-0.439331\pi$
$691$	9.95991	0.378893	0.189446	+	0.981891i	$0.439331\pi$
$692$	−2.15900	−0.0820730
$693$	1.05901	0.0402283
$694$	−1.79449	−0.0681178
$695$	0.235908	0.00894851
$696$	4.13668	0.156800
$697$	2.28684	0.0866203
$698$	16.4028	0.620856
$699$	−9.25957	−0.350229
$700$	5.54787	0.209690
$701$	19.1599	0.723659	0.361829	−	0.932244i	$-0.382152\pi$
$701$	19.1599	0.723659	0.361829	+	0.932244i	$0.382152\pi$
$702$	0.854102	0.0322360
$703$	35.3559	1.33347
$704$	−0.806473	−0.0303951
$705$	−1.59489	−0.0600669
$706$	−31.3537	−1.18001
$707$	21.6113	0.812778
$708$	1.00000	0.0375823
$709$	34.7234	1.30406	0.652032	−	0.758192i	$-0.273917\pi$
$709$	34.7234	1.30406	0.652032	+	0.758192i	$0.273917\pi$
$710$	2.19425	0.0823489
$711$	10.9474	0.410560
$712$	−13.3627	−0.500789
$713$	24.7933	0.928516
$714$	−1.31313	−0.0491428
$715$	0.606424	0.0226790
$716$	−12.8127	−0.478832
$717$	−7.92592	−0.295999
$718$	24.0213	0.896468
$719$	−1.24564	−0.0464544	−0.0232272	−	0.999730i	$-0.507394\pi$
$719$	−1.24564	−0.0464544	−0.0232272	+	0.999730i	$0.507394\pi$
$720$	−0.880394	−0.0328103
$721$	−14.9339	−0.556169
$722$	−7.94907	−0.295834
$723$	1.38295	0.0514325
$724$	−1.96862	−0.0731632
$725$	−17.4771	−0.649083
$726$	−10.3496	−0.384110
$727$	0.00913483	0.000338792 0	0.000169396	−	1.00000i	$-0.499946\pi$
$727$	0.00913483	0.000338792 0	0.000169396		1.00000i	$0.499946\pi$
$728$	−1.12155	−0.0415674
$729$	1.00000	0.0370370
$730$	2.88924	0.106935
$731$	1.19862	0.0443324
$732$	−4.72333	−0.174579
$733$	20.3541	0.751797	0.375899	−	0.926661i	$-0.377334\pi$
$733$	20.3541	0.751797	0.375899	+	0.926661i	$0.377334\pi$
$734$	−17.0572	−0.629593
$735$	4.64468	0.171321
$736$	−8.04763	−0.296640
$737$	4.79299	0.176552
$738$	2.28684	0.0841798
$739$	−10.7639	−0.395956	−0.197978	−	0.980206i	$-0.563438\pi$
$739$	−10.7639	−0.395956	−0.197978	+	0.980206i	$0.563438\pi$
$740$	9.36353	0.344210
$741$	−2.83929	−0.104304
$742$	−6.72035	−0.246712
$743$	1.17610	0.0431470	0.0215735	−	0.999767i	$-0.493132\pi$
$743$	1.17610	0.0431470	0.0215735	+	0.999767i	$0.493132\pi$
$744$	−3.08082	−0.112948
$745$	8.73780	0.320128
$746$	14.1389	0.517663
$747$	−17.5576	−0.642398
$748$	−0.806473	−0.0294876
$749$	−13.1485	−0.480437
$750$	8.12155	0.296557
$751$	−4.00320	−0.146079	−0.0730393	−	0.997329i	$-0.523270\pi$
$751$	−4.00320	−0.146079	−0.0730393	+	0.997329i	$0.523270\pi$
$752$	1.81156	0.0660608
$753$	−2.68604	−0.0978848
$754$	3.53315	0.128670
$755$	−1.44416	−0.0525583
$756$	−1.31313	−0.0477582
$757$	17.2749	0.627868	0.313934	−	0.949445i	$-0.398353\pi$
$757$	17.2749	0.627868	0.313934	+	0.949445i	$0.398353\pi$
$758$	10.6967	0.388523
$759$	6.49019	0.235579
$760$	2.92669	0.106162
$761$	45.7027	1.65672	0.828361	−	0.560195i	$-0.189274\pi$
$761$	45.7027	1.65672	0.828361	+	0.560195i	$0.189274\pi$
$762$	9.44374	0.342111
$763$	−7.99308	−0.289369
$764$	−4.28500	−0.155026
$765$	−0.880394	−0.0318307
$766$	21.9782	0.794104
$767$	0.854102	0.0308398
$768$	1.00000	0.0360844
$769$	37.0407	1.33572	0.667861	−	0.744286i	$-0.267210\pi$
$769$	37.0407	1.33572	0.667861	+	0.744286i	$0.267210\pi$
$770$	−0.932343	−0.0335993
$771$	−13.7337	−0.494608
$772$	6.00607	0.216163
$773$	−2.82968	−0.101776	−0.0508882	−	0.998704i	$-0.516205\pi$
$773$	−2.82968	−0.101776	−0.0508882	+	0.998704i	$0.516205\pi$
$774$	1.19862	0.0430833
$775$	13.0162	0.467555
$776$	14.6113	0.524514
$777$	13.9660	0.501027
$778$	33.1693	1.18918
$779$	−7.60214	−0.272375
$780$	−0.751946	−0.0269240
$781$	2.01002	0.0719241
$782$	−8.04763	−0.287783
$783$	4.13668	0.147833
$784$	−5.27568	−0.188417
$785$	16.7243	0.596916
$786$	0.750136	0.0267565
$787$	−20.5531	−0.732637	−0.366319	−	0.930489i	$-0.619382\pi$
$787$	−20.5531	−0.732637	−0.366319	+	0.930489i	$0.619382\pi$
$788$	−9.64678	−0.343652
$789$	−18.0752	−0.643493
$790$	−9.63804	−0.342906
$791$	1.69325	0.0602052
$792$	−0.806473	−0.0286568
$793$	−4.03421	−0.143259
$794$	31.3458	1.11242
$795$	−4.50568	−0.159800
$796$	9.95056	0.352688
$797$	−10.2033	−0.361420	−0.180710	−	0.983536i	$-0.557840\pi$
$797$	−10.2033	−0.361420	−0.180710	+	0.983536i	$0.557840\pi$
$798$	4.36524	0.154528
$799$	1.81156	0.0640884
$800$	−4.22491	−0.149373
$801$	−13.3627	−0.472148
$802$	−1.06479	−0.0375989
$803$	2.64665	0.0933981
$804$	−5.94315	−0.209599
$805$	−9.30366	−0.327911
$806$	−2.63133	−0.0926848
$807$	−23.2846	−0.819655
$808$	−16.4578	−0.578984
$809$	−27.4509	−0.965122	−0.482561	−	0.875862i	$-0.660293\pi$
$809$	−27.4509	−0.965122	−0.482561	+	0.875862i	$0.660293\pi$
$810$	−0.880394	−0.0309339
$811$	−22.0488	−0.774237	−0.387119	−	0.922030i	$-0.626530\pi$
$811$	−22.0488	−0.774237	−0.387119	+	0.922030i	$0.626530\pi$
$812$	−5.43201	−0.190626
$813$	−6.71428	−0.235480
$814$	8.57734	0.300636
$815$	−7.79191	−0.272939
$816$	1.00000	0.0350070
$817$	−3.98455	−0.139402
$818$	−17.8012	−0.622404
$819$	−1.12155	−0.0391901
$820$	−2.01332	−0.0703082
$821$	−15.1607	−0.529110	−0.264555	−	0.964371i	$-0.585225\pi$
$821$	−15.1607	−0.529110	−0.264555	+	0.964371i	$0.585225\pi$
$822$	−9.06995	−0.316351
$823$	−39.2010	−1.36646	−0.683231	−	0.730203i	$-0.739426\pi$
$823$	−39.2010	−1.36646	−0.683231	+	0.730203i	$0.739426\pi$
$824$	11.3727	0.396188
$825$	3.40727	0.118626
$826$	−1.31313	−0.0456898
$827$	22.0141	0.765504	0.382752	−	0.923851i	$-0.374976\pi$
$827$	22.0141	0.765504	0.382752	+	0.923851i	$0.374976\pi$
$828$	−8.04763	−0.279674
$829$	−34.8762	−1.21130	−0.605651	−	0.795731i	$-0.707087\pi$
$829$	−34.8762	−1.21130	−0.605651	+	0.795731i	$0.707087\pi$
$830$	15.4576	0.536540
$831$	−24.3896	−0.846067
$832$	0.854102	0.0296107
$833$	−5.27568	−0.182792
$834$	−0.267958	−0.00927862
$835$	−7.89069	−0.273069
$836$	2.68095	0.0927227
$837$	−3.08082	−0.106489
$838$	−27.8247	−0.961188
$839$	25.3696	0.875855	0.437928	−	0.899010i	$-0.355713\pi$
$839$	25.3696	0.875855	0.437928	+	0.899010i	$0.355713\pi$
$840$	1.15607	0.0398884
$841$	−11.8879	−0.409927
$842$	27.2478	0.939023
$843$	11.7140	0.403452
$844$	3.34766	0.115231
$845$	10.8029	0.371630
$846$	1.81156	0.0622828
$847$	13.5904	0.466972
$848$	5.11780	0.175746
$849$	14.7340	0.505670
$850$	−4.22491	−0.144913
$851$	85.5915	2.93404
$852$	−2.49235	−0.0853867
$853$	54.2940	1.85899	0.929496	−	0.368833i	$-0.120243\pi$
$853$	54.2940	1.85899	0.929496	+	0.368833i	$0.120243\pi$
$854$	6.20237	0.212241
$855$	2.92669	0.100091
$856$	10.0131	0.342241
$857$	−48.2525	−1.64827	−0.824137	−	0.566391i	$-0.808339\pi$
$857$	−48.2525	−1.64827	−0.824137	+	0.566391i	$0.808339\pi$
$858$	−0.688810	−0.0235156
$859$	20.1892	0.688846	0.344423	−	0.938815i	$-0.388075\pi$
$859$	20.1892	0.688846	0.344423	+	0.938815i	$0.388075\pi$
$860$	−1.05525	−0.0359838
$861$	−3.00293	−0.102340
$862$	3.75967	0.128055
$863$	18.2720	0.621987	0.310994	−	0.950412i	$-0.399338\pi$
$863$	18.2720	0.621987	0.310994	+	0.950412i	$0.399338\pi$
$864$	1.00000	0.0340207
$865$	1.90077	0.0646282
$866$	27.9332	0.949210
$867$	1.00000	0.0339618
$868$	4.04553	0.137314
$869$	−8.82879	−0.299496
$870$	−3.64191	−0.123472
$871$	−5.07606	−0.171996
$872$	6.08703	0.206133
$873$	14.6113	0.494517
$874$	26.7527	0.904923
$875$	−10.6647	−0.360532
$876$	−3.28175	−0.110880
$877$	−46.7999	−1.58032	−0.790160	−	0.612900i	$-0.790003\pi$
$877$	−46.7999	−1.58032	−0.790160	+	0.612900i	$0.790003\pi$
$878$	−2.91484	−0.0983709
$879$	12.4874	0.421190
$880$	0.710014	0.0239346
$881$	31.0324	1.04551	0.522754	−	0.852484i	$-0.324905\pi$
$881$	31.0324	1.04551	0.522754	+	0.852484i	$0.324905\pi$
$882$	−5.27568	−0.177641
$883$	−44.9979	−1.51430	−0.757150	−	0.653241i	$-0.773409\pi$
$883$	−44.9979	−1.51430	−0.757150	+	0.653241i	$0.773409\pi$
$884$	0.854102	0.0287266
$885$	−0.880394	−0.0295941
$886$	7.62100	0.256032
$887$	35.3204	1.18594	0.592971	−	0.805224i	$-0.297955\pi$
$887$	35.3204	1.18594	0.592971	+	0.805224i	$0.297955\pi$
$888$	−10.6356	−0.356908
$889$	−12.4009	−0.415913
$890$	11.7644	0.394345
$891$	−0.806473	−0.0270179
$892$	−21.7814	−0.729294
$893$	−6.02216	−0.201524
$894$	−9.92488	−0.331938
$895$	11.2802	0.377056
$896$	−1.31313	−0.0438687
$897$	−6.87350	−0.229499
$898$	23.7416	0.792266
$899$	−12.7444	−0.425048
$900$	−4.22491	−0.140830
$901$	5.11780	0.170499
$902$	−1.84428	−0.0614077
$903$	−1.57394	−0.0523775
$904$	−1.28948	−0.0428873
$905$	1.73316	0.0576122
$906$	1.64036	0.0544972
$907$	25.4875	0.846299	0.423149	−	0.906060i	$-0.360925\pi$
$907$	25.4875	0.846299	0.423149	+	0.906060i	$0.360925\pi$
$908$	9.58881	0.318216
$909$	−16.4578	−0.545872
$910$	0.987405	0.0327322
$911$	−53.4244	−1.77003	−0.885015	−	0.465562i	$-0.845852\pi$
$911$	−53.4244	−1.77003	−0.885015	+	0.465562i	$0.845852\pi$
$912$	−3.32429	−0.110078
$913$	14.1597	0.468618
$914$	−16.1234	−0.533313
$915$	4.15839	0.137472
$916$	18.5177	0.611841
$917$	−0.985029	−0.0325285
$918$	1.00000	0.0330049
$919$	41.4575	1.36756	0.683778	−	0.729690i	$-0.260336\pi$
$919$	41.4575	1.36756	0.683778	+	0.729690i	$0.260336\pi$
$920$	7.08508	0.233588
$921$	20.1040	0.662448
$922$	24.0954	0.793539
$923$	−2.12873	−0.0700678
$924$	1.05901	0.0348388
$925$	44.9345	1.47744
$926$	−8.23296	−0.270552
$927$	11.3727	0.373530
$928$	4.13668	0.135793
$929$	−15.1093	−0.495720	−0.247860	−	0.968796i	$-0.579727\pi$
$929$	−15.1093	−0.495720	−0.247860	+	0.968796i	$0.579727\pi$
$930$	2.71233	0.0889409
$931$	17.5379	0.574782
$932$	−9.25957	−0.303307
$933$	34.3174	1.12350
$934$	−17.6501	−0.577528
$935$	0.710014	0.0232199
$936$	0.854102	0.0279172
$937$	12.2498	0.400183	0.200091	−	0.979777i	$-0.435876\pi$
$937$	12.2498	0.400183	0.200091	+	0.979777i	$0.435876\pi$
$938$	7.80415	0.254815
$939$	−29.1995	−0.952889
$940$	−1.59489	−0.0520195
$941$	−13.0741	−0.426205	−0.213102	−	0.977030i	$-0.568357\pi$
$941$	−13.0741	−0.426205	−0.213102	+	0.977030i	$0.568357\pi$
$942$	−18.9964	−0.618936
$943$	−18.4037	−0.599305
$944$	1.00000	0.0325472
$945$	1.15607	0.0376071
$946$	−0.966651	−0.0314285
$947$	1.10440	0.0358881	0.0179441	−	0.999839i	$-0.494288\pi$
$947$	1.10440	0.0358881	0.0179441	+	0.999839i	$0.494288\pi$
$948$	10.9474	0.355556
$949$	−2.80295	−0.0909877
$950$	14.0448	0.455675
$951$	−12.5378	−0.406567
$952$	−1.31313	−0.0425589
$953$	−57.2641	−1.85497	−0.927484	−	0.373863i	$-0.878033\pi$
$953$	−57.2641	−1.85497	−0.927484	+	0.373863i	$0.878033\pi$
$954$	5.11780	0.165695
$955$	3.77248	0.122075
$956$	−7.92592	−0.256343
$957$	−3.33612	−0.107841
$958$	28.9556	0.935514
$959$	11.9101	0.384596
$960$	−0.880394	−0.0284146
$961$	−21.5086	−0.693824
$962$	−9.08390	−0.292877
$963$	10.0131	0.322668
$964$	1.38295	0.0445418
$965$	−5.28771	−0.170217
$966$	10.5676	0.340007
$967$	23.6296	0.759878	0.379939	−	0.925012i	$-0.375945\pi$
$967$	23.6296	0.759878	0.379939	+	0.925012i	$0.375945\pi$
$968$	−10.3496	−0.332649
$969$	−3.32429	−0.106792
$970$	−12.8637	−0.413028
$971$	−17.7369	−0.569203	−0.284601	−	0.958646i	$-0.591861\pi$
$971$	−17.7369	−0.569203	−0.284601	+	0.958646i	$0.591861\pi$
$972$	1.00000	0.0320750
$973$	0.351864	0.0112803
$974$	12.0378	0.385715
$975$	−3.60850	−0.115565
$976$	−4.72333	−0.151190
$977$	−41.4950	−1.32754	−0.663772	−	0.747935i	$-0.731045\pi$
$977$	−41.4950	−1.32754	−0.663772	+	0.747935i	$0.731045\pi$
$978$	8.85048	0.283007
$979$	10.7767	0.344424
$980$	4.64468	0.148369
$981$	6.08703	0.194344
$982$	−1.57084	−0.0501274
$983$	16.4299	0.524031	0.262016	−	0.965064i	$-0.415613\pi$
$983$	16.4299	0.524031	0.262016	+	0.965064i	$0.415613\pi$
$984$	2.28684	0.0729019
$985$	8.49296	0.270608
$986$	4.13668	0.131739
$987$	−2.37882	−0.0757187
$988$	−2.83929	−0.0903297
$989$	−9.64601	−0.306725
$990$	0.710014	0.0225657
$991$	−38.0071	−1.20733	−0.603667	−	0.797236i	$-0.706294\pi$
$991$	−38.0071	−1.20733	−0.603667	+	0.797236i	$0.706294\pi$
$992$	−3.08082	−0.0978161
$993$	3.30684	0.104940
$994$	3.27279	0.103807
$995$	−8.76041	−0.277724
$996$	−17.5576	−0.556333
$997$	−0.443231	−0.0140373	−0.00701864	−	0.999975i	$-0.502234\pi$
$997$	−0.443231	−0.0140373	−0.00701864	+	0.999975i	$0.502234\pi$
$998$	10.5078	0.332618
$999$	−10.6356	−0.336496

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.o.1.2	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.o.1.2	✓	4	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:	\( N \)	\(=\)	\( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6018.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.880394 q^{5} +1.00000 q^{6} -1.31313 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.880394 q^{5} +1.00000 q^{6} -1.31313 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.880394 q^{10} -0.806473 q^{11} +1.00000 q^{12} +0.854102 q^{13} -1.31313 q^{14} -0.880394 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} -3.32429 q^{19} -0.880394 q^{20} -1.31313 q^{21} -0.806473 q^{22} -8.04763 q^{23} +1.00000 q^{24} -4.22491 q^{25} +0.854102 q^{26} +1.00000 q^{27} -1.31313 q^{28} +4.13668 q^{29} -0.880394 q^{30} -3.08082 q^{31} +1.00000 q^{32} -0.806473 q^{33} +1.00000 q^{34} +1.15607 q^{35} +1.00000 q^{36} -10.6356 q^{37} -3.32429 q^{38} +0.854102 q^{39} -0.880394 q^{40} +2.28684 q^{41} -1.31313 q^{42} +1.19862 q^{43} -0.806473 q^{44} -0.880394 q^{45} -8.04763 q^{46} +1.81156 q^{47} +1.00000 q^{48} -5.27568 q^{49} -4.22491 q^{50} +1.00000 q^{51} +0.854102 q^{52} +5.11780 q^{53} +1.00000 q^{54} +0.710014 q^{55} -1.31313 q^{56} -3.32429 q^{57} +4.13668 q^{58} +1.00000 q^{59} -0.880394 q^{60} -4.72333 q^{61} -3.08082 q^{62} -1.31313 q^{63} +1.00000 q^{64} -0.751946 q^{65} -0.806473 q^{66} -5.94315 q^{67} +1.00000 q^{68} -8.04763 q^{69} +1.15607 q^{70} -2.49235 q^{71} +1.00000 q^{72} -3.28175 q^{73} -10.6356 q^{74} -4.22491 q^{75} -3.32429 q^{76} +1.05901 q^{77} +0.854102 q^{78} +10.9474 q^{79} -0.880394 q^{80} +1.00000 q^{81} +2.28684 q^{82} -17.5576 q^{83} -1.31313 q^{84} -0.880394 q^{85} +1.19862 q^{86} +4.13668 q^{87} -0.806473 q^{88} -13.3627 q^{89} -0.880394 q^{90} -1.12155 q^{91} -8.04763 q^{92} -3.08082 q^{93} +1.81156 q^{94} +2.92669 q^{95} +1.00000 q^{96} +14.6113 q^{97} -5.27568 q^{98} -0.806473 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} - q^{5} + 4 q^{6} - q^{7} + 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 - q^5 + 4 * q^6 - q^7 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} - q^{5} + 4 q^{6} - q^{7} + 4 q^{8} + 4 q^{9} - q^{10} - 10 q^{11} + 4 q^{12} - 10 q^{13} - q^{14} - q^{15} + 4 q^{16} + 4 q^{17} + 4 q^{18} - 14 q^{19} - q^{20} - q^{21} - 10 q^{22} - 12 q^{23} + 4 q^{24} - 3 q^{25} - 10 q^{26} + 4 q^{27} - q^{28} - 7 q^{29} - q^{30} - 13 q^{31} + 4 q^{32} - 10 q^{33} + 4 q^{34} - 18 q^{35} + 4 q^{36} - 11 q^{37} - 14 q^{38} - 10 q^{39} - q^{40} - 6 q^{41} - q^{42} - 20 q^{43} - 10 q^{44} - q^{45} - 12 q^{46} - 4 q^{47} + 4 q^{48} - q^{49} - 3 q^{50} + 4 q^{51} - 10 q^{52} - 5 q^{53} + 4 q^{54} + 4 q^{55} - q^{56} - 14 q^{57} - 7 q^{58} + 4 q^{59} - q^{60} + 2 q^{61} - 13 q^{62} - q^{63} + 4 q^{64} - 20 q^{65} - 10 q^{66} - 7 q^{67} + 4 q^{68} - 12 q^{69} - 18 q^{70} + 20 q^{71} + 4 q^{72} - 16 q^{73} - 11 q^{74} - 3 q^{75} - 14 q^{76} - 6 q^{77} - 10 q^{78} + 22 q^{79} - q^{80} + 4 q^{81} - 6 q^{82} + 7 q^{83} - q^{84} - q^{85} - 20 q^{86} - 7 q^{87} - 10 q^{88} + 3 q^{89} - q^{90} + 25 q^{91} - 12 q^{92} - 13 q^{93} - 4 q^{94} + 3 q^{95} + 4 q^{96} - 16 q^{97} - q^{98} - 10 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 - q^5 + 4 * q^6 - q^7 + 4 * q^8 + 4 * q^9 - q^10 - 10 * q^11 + 4 * q^12 - 10 * q^13 - q^14 - q^15 + 4 * q^16 + 4 * q^17 + 4 * q^18 - 14 * q^19 - q^20 - q^21 - 10 * q^22 - 12 * q^23 + 4 * q^24 - 3 * q^25 - 10 * q^26 + 4 * q^27 - q^28 - 7 * q^29 - q^30 - 13 * q^31 + 4 * q^32 - 10 * q^33 + 4 * q^34 - 18 * q^35 + 4 * q^36 - 11 * q^37 - 14 * q^38 - 10 * q^39 - q^40 - 6 * q^41 - q^42 - 20 * q^43 - 10 * q^44 - q^45 - 12 * q^46 - 4 * q^47 + 4 * q^48 - q^49 - 3 * q^50 + 4 * q^51 - 10 * q^52 - 5 * q^53 + 4 * q^54 + 4 * q^55 - q^56 - 14 * q^57 - 7 * q^58 + 4 * q^59 - q^60 + 2 * q^61 - 13 * q^62 - q^63 + 4 * q^64 - 20 * q^65 - 10 * q^66 - 7 * q^67 + 4 * q^68 - 12 * q^69 - 18 * q^70 + 20 * q^71 + 4 * q^72 - 16 * q^73 - 11 * q^74 - 3 * q^75 - 14 * q^76 - 6 * q^77 - 10 * q^78 + 22 * q^79 - q^80 + 4 * q^81 - 6 * q^82 + 7 * q^83 - q^84 - q^85 - 20 * q^86 - 7 * q^87 - 10 * q^88 + 3 * q^89 - q^90 + 25 * q^91 - 12 * q^92 - 13 * q^93 - 4 * q^94 + 3 * q^95 + 4 * q^96 - 16 * q^97 - q^98 - 10 * q^99

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