LMFDB - Embedded newform 6035.2.a.b.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6035,2,Mod(1,6035)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6035, 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("6035.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6035 = 5 \cdot 17 \cdot 71 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6035.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:	$48.1897176198$
Analytic rank:	$1$
Dimension:	$36$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	6035.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.31945 q^{2} -2.05009 q^{3} +3.37984 q^{4} +1.00000 q^{5} +4.75509 q^{6} +0.529758 q^{7} -3.20047 q^{8} +1.20289 q^{9} +O(q^{10})$	\(q-2.31945 q^{2} -2.05009 q^{3} +3.37984 q^{4} +1.00000 q^{5} +4.75509 q^{6} +0.529758 q^{7} -3.20047 q^{8} +1.20289 q^{9} -2.31945 q^{10} -1.91606 q^{11} -6.92899 q^{12} -3.07870 q^{13} -1.22875 q^{14} -2.05009 q^{15} +0.663649 q^{16} -1.00000 q^{17} -2.79003 q^{18} -3.37753 q^{19} +3.37984 q^{20} -1.08605 q^{21} +4.44420 q^{22} +0.777479 q^{23} +6.56127 q^{24} +1.00000 q^{25} +7.14089 q^{26} +3.68425 q^{27} +1.79050 q^{28} -9.08420 q^{29} +4.75509 q^{30} -0.124006 q^{31} +4.86165 q^{32} +3.92810 q^{33} +2.31945 q^{34} +0.529758 q^{35} +4.06556 q^{36} +8.52192 q^{37} +7.83402 q^{38} +6.31163 q^{39} -3.20047 q^{40} +9.07671 q^{41} +2.51905 q^{42} +7.55443 q^{43} -6.47598 q^{44} +1.20289 q^{45} -1.80332 q^{46} +2.06752 q^{47} -1.36054 q^{48} -6.71936 q^{49} -2.31945 q^{50} +2.05009 q^{51} -10.4055 q^{52} +3.24840 q^{53} -8.54544 q^{54} -1.91606 q^{55} -1.69548 q^{56} +6.92426 q^{57} +21.0703 q^{58} +2.82255 q^{59} -6.92899 q^{60} -0.275068 q^{61} +0.287626 q^{62} +0.637238 q^{63} -12.6036 q^{64} -3.07870 q^{65} -9.11104 q^{66} -7.61608 q^{67} -3.37984 q^{68} -1.59391 q^{69} -1.22875 q^{70} +1.00000 q^{71} -3.84980 q^{72} +10.1976 q^{73} -19.7662 q^{74} -2.05009 q^{75} -11.4155 q^{76} -1.01505 q^{77} -14.6395 q^{78} -1.22881 q^{79} +0.663649 q^{80} -11.1617 q^{81} -21.0530 q^{82} +2.37009 q^{83} -3.67069 q^{84} -1.00000 q^{85} -17.5221 q^{86} +18.6235 q^{87} +6.13230 q^{88} +5.54934 q^{89} -2.79003 q^{90} -1.63097 q^{91} +2.62776 q^{92} +0.254225 q^{93} -4.79551 q^{94} -3.37753 q^{95} -9.96683 q^{96} -0.175786 q^{97} +15.5852 q^{98} -2.30480 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - q^{2} - 4 q^{3} + 23 q^{4} + 36 q^{5} - 2 q^{6} - 7 q^{7} - 3 q^{8} + 10 q^{9}+O(q^{10}) $ 36 * q - q^2 - 4 * q^3 + 23 * q^4 + 36 * q^5 - 2 * q^6 - 7 * q^7 - 3 * q^8 + 10 * q^9	\( 36 q - q^{2} - 4 q^{3} + 23 q^{4} + 36 q^{5} - 2 q^{6} - 7 q^{7} - 3 q^{8} + 10 q^{9} - q^{10} - 22 q^{11} - 14 q^{12} - 15 q^{13} - 28 q^{14} - 4 q^{15} + q^{16} - 36 q^{17} - 12 q^{18} - 23 q^{19} + 23 q^{20} - 21 q^{21} + 2 q^{23} - 13 q^{24} + 36 q^{25} - 18 q^{26} - 13 q^{27} - 20 q^{28} - 4 q^{29} - 2 q^{30} - 43 q^{31} - 2 q^{32} - 19 q^{33} + q^{34} - 7 q^{35} - 35 q^{36} - 30 q^{37} - 11 q^{38} - 20 q^{39} - 3 q^{40} - 39 q^{41} + 2 q^{42} - 7 q^{43} - 45 q^{44} + 10 q^{45} - 52 q^{46} - 12 q^{47} - 12 q^{48} - 15 q^{49} - q^{50} + 4 q^{51} - 19 q^{52} - 31 q^{53} + 48 q^{54} - 22 q^{55} - 30 q^{56} + 18 q^{57} - 12 q^{58} - 66 q^{59} - 14 q^{60} - 93 q^{61} - 7 q^{62} - 22 q^{63} - 41 q^{64} - 15 q^{65} - 21 q^{66} - 19 q^{67} - 23 q^{68} - 73 q^{69} - 28 q^{70} + 36 q^{71} - q^{72} - 47 q^{73} - 27 q^{74} - 4 q^{75} - 56 q^{76} - 9 q^{77} - 78 q^{78} - 21 q^{79} + q^{80} - 40 q^{81} - 15 q^{82} - 8 q^{83} - 54 q^{84} - 36 q^{85} - 17 q^{86} - 32 q^{87} - 13 q^{88} - 62 q^{89} - 12 q^{90} - 33 q^{91} + 42 q^{92} - 24 q^{93} - 40 q^{94} - 23 q^{95} + 21 q^{96} - 60 q^{97} + 11 q^{98} - 65 q^{99}+O(q^{100}) \) 36 * q - q^2 - 4 * q^3 + 23 * q^4 + 36 * q^5 - 2 * q^6 - 7 * q^7 - 3 * q^8 + 10 * q^9 - q^10 - 22 * q^11 - 14 * q^12 - 15 * q^13 - 28 * q^14 - 4 * q^15 + q^16 - 36 * q^17 - 12 * q^18 - 23 * q^19 + 23 * q^20 - 21 * q^21 + 2 * q^23 - 13 * q^24 + 36 * q^25 - 18 * q^26 - 13 * q^27 - 20 * q^28 - 4 * q^29 - 2 * q^30 - 43 * q^31 - 2 * q^32 - 19 * q^33 + q^34 - 7 * q^35 - 35 * q^36 - 30 * q^37 - 11 * q^38 - 20 * q^39 - 3 * q^40 - 39 * q^41 + 2 * q^42 - 7 * q^43 - 45 * q^44 + 10 * q^45 - 52 * q^46 - 12 * q^47 - 12 * q^48 - 15 * q^49 - q^50 + 4 * q^51 - 19 * q^52 - 31 * q^53 + 48 * q^54 - 22 * q^55 - 30 * q^56 + 18 * q^57 - 12 * q^58 - 66 * q^59 - 14 * q^60 - 93 * q^61 - 7 * q^62 - 22 * q^63 - 41 * q^64 - 15 * q^65 - 21 * q^66 - 19 * q^67 - 23 * q^68 - 73 * q^69 - 28 * q^70 + 36 * q^71 - q^72 - 47 * q^73 - 27 * q^74 - 4 * q^75 - 56 * q^76 - 9 * q^77 - 78 * q^78 - 21 * q^79 + q^80 - 40 * q^81 - 15 * q^82 - 8 * q^83 - 54 * q^84 - 36 * q^85 - 17 * q^86 - 32 * q^87 - 13 * q^88 - 62 * q^89 - 12 * q^90 - 33 * q^91 + 42 * q^92 - 24 * q^93 - 40 * q^94 - 23 * q^95 + 21 * q^96 - 60 * q^97 + 11 * q^98 - 65 * 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 $

$2$	−2.31945	−1.64010	−0.820049	−	0.572293i	$-0.806054\pi$
$2$	−2.31945	−1.64010	−0.820049	+	0.572293i	$0.806054\pi$
$3$	−2.05009	−1.18362	−0.591811	−	0.806077i	$-0.701587\pi$
$3$	−2.05009	−1.18362	−0.591811	+	0.806077i	$0.701587\pi$
$4$	3.37984	1.68992
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	4.75509	1.94126
$7$	0.529758	0.200230	0.100115	−	0.994976i	$-0.468079\pi$
$7$	0.529758	0.200230	0.100115	+	0.994976i	$0.468079\pi$
$8$	−3.20047	−1.13154
$9$	1.20289	0.400962
$10$	−2.31945	−0.733474
$11$	−1.91606	−0.577714	−0.288857	−	0.957372i	$-0.593275\pi$
$11$	−1.91606	−0.577714	−0.288857	+	0.957372i	$0.593275\pi$
$12$	−6.92899	−2.00023
$13$	−3.07870	−0.853878	−0.426939	−	0.904280i	$-0.640408\pi$
$13$	−3.07870	−0.853878	−0.426939	+	0.904280i	$0.640408\pi$
$14$	−1.22875	−0.328396
$15$	−2.05009	−0.529332
$16$	0.663649	0.165912
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−2.79003	−0.657617
$19$	−3.37753	−0.774860	−0.387430	−	0.921899i	$-0.626637\pi$
$19$	−3.37753	−0.774860	−0.387430	+	0.921899i	$0.626637\pi$
$20$	3.37984	0.755756
$21$	−1.08605	−0.236996
$22$	4.44420	0.947508
$23$	0.777479	0.162116	0.0810578	−	0.996709i	$-0.474170\pi$
$23$	0.777479	0.162116	0.0810578	+	0.996709i	$0.474170\pi$
$24$	6.56127	1.33931
$25$	1.00000	0.200000
$26$	7.14089	1.40044
$27$	3.68425	0.709035
$28$	1.79050	0.338372
$29$	−9.08420	−1.68689	−0.843447	−	0.537213i	$-0.819477\pi$
$29$	−9.08420	−1.68689	−0.843447	+	0.537213i	$0.819477\pi$
$30$	4.75509	0.868156
$31$	−0.124006	−0.0222722	−0.0111361	−	0.999938i	$-0.503545\pi$
$31$	−0.124006	−0.0222722	−0.0111361	+	0.999938i	$0.503545\pi$
$32$	4.86165	0.859426
$33$	3.92810	0.683795
$34$	2.31945	0.397782
$35$	0.529758	0.0895454
$36$	4.06556	0.677594
$37$	8.52192	1.40100	0.700498	−	0.713655i	$-0.252961\pi$
$37$	8.52192	1.40100	0.700498	+	0.713655i	$0.252961\pi$
$38$	7.83402	1.27085
$39$	6.31163	1.01067
$40$	−3.20047	−0.506039
$41$	9.07671	1.41754	0.708772	−	0.705438i	$-0.249250\pi$
$41$	9.07671	1.41754	0.708772	+	0.705438i	$0.249250\pi$
$42$	2.51905	0.388697
$43$	7.55443	1.15204	0.576020	−	0.817436i	$-0.304605\pi$
$43$	7.55443	1.15204	0.576020	+	0.817436i	$0.304605\pi$
$44$	−6.47598	−0.976291
$45$	1.20289	0.179316
$46$	−1.80332	−0.265885
$47$	2.06752	0.301579	0.150789	−	0.988566i	$-0.451818\pi$
$47$	2.06752	0.301579	0.150789	+	0.988566i	$0.451818\pi$
$48$	−1.36054	−0.196378
$49$	−6.71936	−0.959908
$50$	−2.31945	−0.328020
$51$	2.05009	0.287071
$52$	−10.4055	−1.44299
$53$	3.24840	0.446202	0.223101	−	0.974795i	$-0.428382\pi$
$53$	3.24840	0.446202	0.223101	+	0.974795i	$0.428382\pi$
$54$	−8.54544	−1.16289
$55$	−1.91606	−0.258362
$56$	−1.69548	−0.226567
$57$	6.92426	0.917141
$58$	21.0703	2.76667
$59$	2.82255	0.367465	0.183732	−	0.982976i	$-0.441182\pi$
$59$	2.82255	0.367465	0.183732	+	0.982976i	$0.441182\pi$
$60$	−6.92899	−0.894529
$61$	−0.275068	−0.0352188	−0.0176094	−	0.999845i	$-0.505606\pi$
$61$	−0.275068	−0.0352188	−0.0176094	+	0.999845i	$0.505606\pi$
$62$	0.287626	0.0365286
$63$	0.637238	0.0802844
$64$	−12.6036	−1.57545
$65$	−3.07870	−0.381866
$66$	−9.11104	−1.12149
$67$	−7.61608	−0.930452	−0.465226	−	0.885192i	$-0.654027\pi$
$67$	−7.61608	−0.930452	−0.465226	+	0.885192i	$0.654027\pi$
$68$	−3.37984	−0.409866
$69$	−1.59391	−0.191884
$70$	−1.22875	−0.146863
$71$	1.00000	0.118678
$71$	1.00000	0.118678
$72$	−3.84980	−0.453704
$73$	10.1976	1.19354	0.596768	−	0.802414i	$-0.296451\pi$
$73$	10.1976	1.19354	0.596768	+	0.802414i	$0.296451\pi$
$74$	−19.7662	−2.29777
$75$	−2.05009	−0.236724
$76$	−11.4155	−1.30945
$77$	−1.01505	−0.115675
$78$	−14.6395	−1.65760
$79$	−1.22881	−0.138252	−0.0691260	−	0.997608i	$-0.522021\pi$
$79$	−1.22881	−0.138252	−0.0691260	+	0.997608i	$0.522021\pi$
$80$	0.663649	0.0741982
$81$	−11.1617	−1.24019
$82$	−21.0530	−2.32491
$83$	2.37009	0.260151	0.130075	−	0.991504i	$-0.458478\pi$
$83$	2.37009	0.260151	0.130075	+	0.991504i	$0.458478\pi$
$84$	−3.67069	−0.400505
$85$	−1.00000	−0.108465
$86$	−17.5221	−1.88946
$87$	18.6235	1.99664
$88$	6.13230	0.653706
$89$	5.54934	0.588229	0.294115	−	0.955770i	$-0.404975\pi$
$89$	5.54934	0.588229	0.294115	+	0.955770i	$0.404975\pi$
$90$	−2.79003	−0.294095
$91$	−1.63097	−0.170972
$92$	2.62776	0.273963
$93$	0.254225	0.0263619
$94$	−4.79551	−0.494619
$95$	−3.37753	−0.346528
$96$	−9.96683	−1.01724
$97$	−0.175786	−0.0178484	−0.00892419	−	0.999960i	$-0.502841\pi$
$97$	−0.175786	−0.0178484	−0.00892419	+	0.999960i	$0.502841\pi$
$98$	15.5852	1.57434
$99$	−2.30480	−0.231641
$100$	3.37984	0.337984
$101$	3.24155	0.322546	0.161273	−	0.986910i	$-0.448440\pi$
$101$	3.24155	0.322546	0.161273	+	0.986910i	$0.448440\pi$
$102$	−4.75509	−0.470824
$103$	−2.46877	−0.243255	−0.121628	−	0.992576i	$-0.538811\pi$
$103$	−2.46877	−0.243255	−0.121628	+	0.992576i	$0.538811\pi$
$104$	9.85330	0.966196
$105$	−1.08605	−0.105988
$106$	−7.53450	−0.731815
$107$	4.92403	0.476024	0.238012	−	0.971262i	$-0.423504\pi$
$107$	4.92403	0.476024	0.238012	+	0.971262i	$0.423504\pi$
$108$	12.4522	1.19821
$109$	−9.10141	−0.871757	−0.435878	−	0.900006i	$-0.643562\pi$
$109$	−9.10141	−0.871757	−0.435878	+	0.900006i	$0.643562\pi$
$110$	4.44420	0.423738
$111$	−17.4707	−1.65825
$112$	0.351573	0.0332206
$113$	1.89181	0.177966	0.0889832	−	0.996033i	$-0.471638\pi$
$113$	1.89181	0.177966	0.0889832	+	0.996033i	$0.471638\pi$
$114$	−16.0605	−1.50420
$115$	0.777479	0.0725003
$116$	−30.7032	−2.85072
$117$	−3.70333	−0.342373
$118$	−6.54676	−0.602678
$119$	−0.529758	−0.0485628
$120$	6.56127	0.598959
$121$	−7.32871	−0.666246
$122$	0.638006	0.0577623
$123$	−18.6081	−1.67784
$124$	−0.419122	−0.0376382
$125$	1.00000	0.0894427
$126$	−1.47804	−0.131674
$127$	4.66818	0.414234	0.207117	−	0.978316i	$-0.433592\pi$
$127$	4.66818	0.414234	0.207117	+	0.978316i	$0.433592\pi$
$128$	19.5102	1.72447
$129$	−15.4873	−1.36358
$130$	7.14089	0.626298
$131$	2.77662	0.242594	0.121297	−	0.992616i	$-0.461295\pi$
$131$	2.77662	0.242594	0.121297	+	0.992616i	$0.461295\pi$
$132$	13.2764	1.15556
$133$	−1.78928	−0.155150
$134$	17.6651	1.52603
$135$	3.68425	0.317090
$136$	3.20047	0.274438
$137$	−2.82630	−0.241467	−0.120733	−	0.992685i	$-0.538525\pi$
$137$	−2.82630	−0.241467	−0.120733	+	0.992685i	$0.538525\pi$
$138$	3.69698	0.314708
$139$	−6.51764	−0.552819	−0.276410	−	0.961040i	$-0.589145\pi$
$139$	−6.51764	−0.552819	−0.276410	+	0.961040i	$0.589145\pi$
$140$	1.79050	0.151325
$141$	−4.23861	−0.356955
$142$	−2.31945	−0.194644
$143$	5.89898	0.493297
$144$	0.798294	0.0665245
$145$	−9.08420	−0.754402
$146$	−23.6528	−1.95752
$147$	13.7753	1.13617
$148$	28.8028	2.36757
$149$	16.6673	1.36544	0.682719	−	0.730681i	$-0.260797\pi$
$149$	16.6673	1.36544	0.682719	+	0.730681i	$0.260797\pi$
$150$	4.75509	0.388251
$151$	10.9939	0.894668	0.447334	−	0.894367i	$-0.352374\pi$
$151$	10.9939	0.894668	0.447334	+	0.894367i	$0.352374\pi$
$152$	10.8097	0.876783
$153$	−1.20289	−0.0972475
$154$	2.35435	0.189719
$155$	−0.124006	−0.00996042
$156$	21.3323	1.70795
$157$	13.3399	1.06464	0.532319	−	0.846544i	$-0.321321\pi$
$157$	13.3399	1.06464	0.532319	+	0.846544i	$0.321321\pi$
$158$	2.85017	0.226747
$159$	−6.65953	−0.528135
$160$	4.86165	0.384347
$161$	0.411876	0.0324603
$162$	25.8890	2.03404
$163$	−6.95719	−0.544929	−0.272465	−	0.962166i	$-0.587839\pi$
$163$	−6.95719	−0.544929	−0.272465	+	0.962166i	$0.587839\pi$
$164$	30.6778	2.39554
$165$	3.92810	0.305803
$166$	−5.49729	−0.426673
$167$	−21.2230	−1.64228	−0.821141	−	0.570725i	$-0.806662\pi$
$167$	−21.2230	−1.64228	−0.821141	+	0.570725i	$0.806662\pi$
$168$	3.47588	0.268170
$169$	−3.52159	−0.270892
$170$	2.31945	0.177894
$171$	−4.06279	−0.310689
$172$	25.5328	1.94686
$173$	−17.3555	−1.31952	−0.659759	−	0.751478i	$-0.729341\pi$
$173$	−17.3555	−1.31952	−0.659759	+	0.751478i	$0.729341\pi$
$174$	−43.1962	−3.27469
$175$	0.529758	0.0400459
$176$	−1.27159	−0.0958499
$177$	−5.78650	−0.434940
$178$	−12.8714	−0.964753
$179$	10.6210	0.793849	0.396924	−	0.917851i	$-0.370078\pi$
$179$	10.6210	0.793849	0.396924	+	0.917851i	$0.370078\pi$
$180$	4.06556	0.303029
$181$	−4.17432	−0.310275	−0.155137	−	0.987893i	$-0.549582\pi$
$181$	−4.17432	−0.310275	−0.155137	+	0.987893i	$0.549582\pi$
$182$	3.78294	0.280410
$183$	0.563915	0.0416858
$184$	−2.48830	−0.183440
$185$	8.52192	0.626544
$186$	−0.589661	−0.0432360
$187$	1.91606	0.140116
$188$	6.98789	0.509644
$189$	1.95176	0.141970
$190$	7.83402	0.568339
$191$	6.68722	0.483871	0.241935	−	0.970292i	$-0.422218\pi$
$191$	6.68722	0.483871	0.241935	+	0.970292i	$0.422218\pi$
$192$	25.8386	1.86474
$193$	−11.5857	−0.833954	−0.416977	−	0.908917i	$-0.636910\pi$
$193$	−11.5857	−0.833954	−0.416977	+	0.908917i	$0.636910\pi$
$194$	0.407727	0.0292731
$195$	6.31163	0.451985
$196$	−22.7104	−1.62217
$197$	−22.4274	−1.59789	−0.798943	−	0.601406i	$-0.794607\pi$
$197$	−22.4274	−1.59789	−0.798943	+	0.601406i	$0.794607\pi$
$198$	5.34587	0.379914
$199$	3.18466	0.225755	0.112877	−	0.993609i	$-0.463993\pi$
$199$	3.18466	0.225755	0.112877	+	0.993609i	$0.463993\pi$
$200$	−3.20047	−0.226308
$201$	15.6137	1.10130
$202$	−7.51861	−0.529007
$203$	−4.81243	−0.337766
$204$	6.92899	0.485127
$205$	9.07671	0.633945
$206$	5.72619	0.398962
$207$	0.935218	0.0650022
$208$	−2.04318	−0.141669
$209$	6.47156	0.447647
$210$	2.51905	0.173831
$211$	−2.30266	−0.158522	−0.0792608	−	0.996854i	$-0.525256\pi$
$211$	−2.30266	−0.158522	−0.0792608	+	0.996854i	$0.525256\pi$
$212$	10.9791	0.754046
$213$	−2.05009	−0.140470
$214$	−11.4210	−0.780726
$215$	7.55443	0.515208
$216$	−11.7914	−0.802300
$217$	−0.0656933	−0.00445955
$218$	21.1102	1.42977
$219$	−20.9060	−1.41270
$220$	−6.47598	−0.436611
$221$	3.07870	0.207096
$222$	40.5225	2.71969
$223$	22.5347	1.50903	0.754517	−	0.656280i	$-0.227871\pi$
$223$	22.5347	1.50903	0.754517	+	0.656280i	$0.227871\pi$
$224$	2.57550	0.172083
$225$	1.20289	0.0801924
$226$	−4.38796	−0.291882
$227$	−4.73384	−0.314196	−0.157098	−	0.987583i	$-0.550214\pi$
$227$	−4.73384	−0.314196	−0.157098	+	0.987583i	$0.550214\pi$
$228$	23.4029	1.54990
$229$	−14.1913	−0.937786	−0.468893	−	0.883255i	$-0.655347\pi$
$229$	−14.1913	−0.937786	−0.468893	+	0.883255i	$0.655347\pi$
$230$	−1.80332	−0.118908
$231$	2.08094	0.136916
$232$	29.0737	1.90878
$233$	16.3519	1.07125	0.535626	−	0.844456i	$-0.320076\pi$
$233$	16.3519	1.07125	0.535626	+	0.844456i	$0.320076\pi$
$234$	8.58967	0.561525
$235$	2.06752	0.134870
$236$	9.53978	0.620987
$237$	2.51918	0.163638
$238$	1.22875	0.0796478
$239$	5.04809	0.326534	0.163267	−	0.986582i	$-0.447797\pi$
$239$	5.04809	0.326534	0.163267	+	0.986582i	$0.447797\pi$
$240$	−1.36054	−0.0878227
$241$	10.2874	0.662669	0.331334	−	0.943513i	$-0.392501\pi$
$241$	10.2874	0.662669	0.331334	+	0.943513i	$0.392501\pi$
$242$	16.9986	1.09271
$243$	11.8298	0.758883
$244$	−0.929686	−0.0595171
$245$	−6.71936	−0.429284
$246$	43.1605	2.75182
$247$	10.3984	0.661636
$248$	0.396879	0.0252018
$249$	−4.85890	−0.307920
$250$	−2.31945	−0.146695
$251$	1.46318	0.0923551	0.0461776	−	0.998933i	$-0.485296\pi$
$251$	1.46318	0.0923551	0.0461776	+	0.998933i	$0.485296\pi$
$252$	2.15376	0.135674
$253$	−1.48970	−0.0936565
$254$	−10.8276	−0.679385
$255$	2.05009	0.128382
$256$	−20.0456	−1.25285
$257$	13.2769	0.828193	0.414097	−	0.910233i	$-0.364098\pi$
$257$	13.2769	0.828193	0.414097	+	0.910233i	$0.364098\pi$
$258$	35.9220	2.23641
$259$	4.51455	0.280521
$260$	−10.4055	−0.645323
$261$	−10.9273	−0.676380
$262$	−6.44023	−0.397878
$263$	24.6671	1.52104	0.760520	−	0.649314i	$-0.224944\pi$
$263$	24.6671	1.52104	0.760520	+	0.649314i	$0.224944\pi$
$264$	−12.5718	−0.773740
$265$	3.24840	0.199548
$266$	4.15013	0.254461
$267$	−11.3767	−0.696241
$268$	−25.7411	−1.57239
$269$	−12.9234	−0.787951	−0.393976	−	0.919121i	$-0.628901\pi$
$269$	−12.9234	−0.787951	−0.393976	+	0.919121i	$0.628901\pi$
$270$	−8.54544	−0.520059
$271$	−20.9056	−1.26993	−0.634963	−	0.772543i	$-0.718985\pi$
$271$	−20.9056	−1.26993	−0.634963	+	0.772543i	$0.718985\pi$
$272$	−0.663649	−0.0402396
$273$	3.34363	0.202366
$274$	6.55545	0.396029
$275$	−1.91606	−0.115543
$276$	−5.38715	−0.324268
$277$	16.5938	0.997024	0.498512	−	0.866883i	$-0.333880\pi$
$277$	16.5938	0.997024	0.498512	+	0.866883i	$0.333880\pi$
$278$	15.1173	0.906678
$279$	−0.149165	−0.00893030
$280$	−1.69548	−0.101324
$281$	17.4168	1.03900	0.519498	−	0.854471i	$-0.326119\pi$
$281$	17.4168	1.03900	0.519498	+	0.854471i	$0.326119\pi$
$282$	9.83124	0.585442
$283$	3.47275	0.206433	0.103217	−	0.994659i	$-0.467086\pi$
$283$	3.47275	0.206433	0.103217	+	0.994659i	$0.467086\pi$
$284$	3.37984	0.200557
$285$	6.92426	0.410158
$286$	−13.6824	−0.809056
$287$	4.80846	0.283834
$288$	5.84800	0.344597
$289$	1.00000	0.0588235
$290$	21.0703	1.23729
$291$	0.360378	0.0211257
$292$	34.4662	2.01698
$293$	10.2835	0.600767	0.300383	−	0.953819i	$-0.402885\pi$
$293$	10.2835	0.600767	0.300383	+	0.953819i	$0.402885\pi$
$294$	−31.9511	−1.86343
$295$	2.82255	0.164335
$296$	−27.2742	−1.58528
$297$	−7.05925	−0.409619
$298$	−38.6590	−2.23945
$299$	−2.39363	−0.138427
$300$	−6.92899	−0.400046
$301$	4.00202	0.230673
$302$	−25.4997	−1.46734
$303$	−6.64548	−0.381773
$304$	−2.24150	−0.128559
$305$	−0.275068	−0.0157503
$306$	2.79003	0.159495
$307$	−0.516970	−0.0295050	−0.0147525	−	0.999891i	$-0.504696\pi$
$307$	−0.516970	−0.0295050	−0.0147525	+	0.999891i	$0.504696\pi$
$308$	−3.43070	−0.195482
$309$	5.06121	0.287922
$310$	0.287626	0.0163361
$311$	5.02009	0.284663	0.142331	−	0.989819i	$-0.454540\pi$
$311$	5.02009	0.284663	0.142331	+	0.989819i	$0.454540\pi$
$312$	−20.2002	−1.14361
$313$	−13.5467	−0.765707	−0.382854	−	0.923809i	$-0.625059\pi$
$313$	−13.5467	−0.765707	−0.382854	+	0.923809i	$0.625059\pi$
$314$	−30.9411	−1.74611
$315$	0.637238	0.0359043
$316$	−4.15319	−0.233635
$317$	−22.7509	−1.27782	−0.638908	−	0.769283i	$-0.720613\pi$
$317$	−22.7509	−1.27782	−0.638908	+	0.769283i	$0.720613\pi$
$318$	15.4464	0.866193
$319$	17.4059	0.974542
$320$	−12.6036	−0.704565
$321$	−10.0947	−0.563433
$322$	−0.955324	−0.0532381
$323$	3.37753	0.187931
$324$	−37.7249	−2.09583
$325$	−3.07870	−0.170776
$326$	16.1368	0.893737
$327$	18.6587	1.03183
$328$	−29.0498	−1.60400
$329$	1.09528	0.0603850
$330$	−9.11104	−0.501546
$331$	−8.95563	−0.492246	−0.246123	−	0.969239i	$-0.579157\pi$
$331$	−8.95563	−0.492246	−0.246123	+	0.969239i	$0.579157\pi$
$332$	8.01052	0.439634
$333$	10.2509	0.561746
$334$	49.2256	2.69350
$335$	−7.61608	−0.416111
$336$	−0.720759	−0.0393206
$337$	0.866061	0.0471773	0.0235887	−	0.999722i	$-0.492491\pi$
$337$	0.866061	0.0471773	0.0235887	+	0.999722i	$0.492491\pi$
$338$	8.16816	0.444289
$339$	−3.87839	−0.210645
$340$	−3.37984	−0.183298
$341$	0.237604	0.0128670
$342$	9.42343	0.509561
$343$	−7.26794	−0.392432
$344$	−24.1778	−1.30358
$345$	−1.59391	−0.0858130
$346$	40.2553	2.16414
$347$	27.2036	1.46037	0.730184	−	0.683251i	$-0.239434\pi$
$347$	27.2036	1.46037	0.730184	+	0.683251i	$0.239434\pi$
$348$	62.9444	3.37417
$349$	1.65773	0.0887365	0.0443682	−	0.999015i	$-0.485873\pi$
$349$	1.65773	0.0887365	0.0443682	+	0.999015i	$0.485873\pi$
$350$	−1.22875	−0.0656792
$351$	−11.3427	−0.605430
$352$	−9.31521	−0.496502
$353$	−12.1453	−0.646428	−0.323214	−	0.946326i	$-0.604763\pi$
$353$	−12.1453	−0.646428	−0.323214	+	0.946326i	$0.604763\pi$
$354$	13.4215	0.713344
$355$	1.00000	0.0530745
$356$	18.7559	0.994061
$357$	1.08605	0.0574800
$358$	−24.6348	−1.30199
$359$	−4.49981	−0.237491	−0.118745	−	0.992925i	$-0.537887\pi$
$359$	−4.49981	−0.237491	−0.118745	+	0.992925i	$0.537887\pi$
$360$	−3.84980	−0.202902
$361$	−7.59226	−0.399593
$362$	9.68213	0.508881
$363$	15.0245	0.788584
$364$	−5.51241	−0.288929
$365$	10.1976	0.533766
$366$	−1.30797	−0.0683688
$367$	−17.3313	−0.904684	−0.452342	−	0.891845i	$-0.649411\pi$
$367$	−17.3313	−0.904684	−0.452342	+	0.891845i	$0.649411\pi$
$368$	0.515973	0.0268970
$369$	10.9182	0.568381
$370$	−19.7662	−1.02759
$371$	1.72087	0.0893429
$372$	0.859239	0.0445495
$373$	−15.5203	−0.803609	−0.401804	−	0.915726i	$-0.631617\pi$
$373$	−15.5203	−0.803609	−0.401804	+	0.915726i	$0.631617\pi$
$374$	−4.44420	−0.229804
$375$	−2.05009	−0.105866
$376$	−6.61704	−0.341248
$377$	27.9675	1.44040
$378$	−4.52701	−0.232844
$379$	−6.39427	−0.328451	−0.164226	−	0.986423i	$-0.552513\pi$
$379$	−6.39427	−0.328451	−0.164226	+	0.986423i	$0.552513\pi$
$380$	−11.4155	−0.585605
$381$	−9.57021	−0.490297
$382$	−15.5107	−0.793595
$383$	9.69587	0.495436	0.247718	−	0.968832i	$-0.420319\pi$
$383$	9.69587	0.495436	0.247718	+	0.968832i	$0.420319\pi$
$384$	−39.9977	−2.04113
$385$	−1.01505	−0.0517316
$386$	26.8724	1.36777
$387$	9.08712	0.461924
$388$	−0.594129	−0.0301623
$389$	−34.3993	−1.74412	−0.872058	−	0.489403i	$-0.837215\pi$
$389$	−34.3993	−1.74412	−0.872058	+	0.489403i	$0.837215\pi$
$390$	−14.6395	−0.741300
$391$	−0.777479	−0.0393188
$392$	21.5051	1.08617
$393$	−5.69233	−0.287140
$394$	52.0192	2.62069
$395$	−1.22881	−0.0618282
$396$	−7.78987	−0.391456
$397$	0.459896	0.0230815	0.0115408	−	0.999933i	$-0.496326\pi$
$397$	0.459896	0.0230815	0.0115408	+	0.999933i	$0.496326\pi$
$398$	−7.38666	−0.370260
$399$	3.66818	0.183639
$400$	0.663649	0.0331825
$401$	−0.107245	−0.00535558	−0.00267779	−	0.999996i	$-0.500852\pi$
$401$	−0.107245	−0.00535558	−0.00267779	+	0.999996i	$0.500852\pi$
$402$	−36.2151	−1.80625
$403$	0.381778	0.0190177
$404$	10.9559	0.545078
$405$	−11.1617	−0.554630
$406$	11.1622	0.553969
$407$	−16.3285	−0.809375
$408$	−6.56127	−0.324831
$409$	−11.0834	−0.548039	−0.274020	−	0.961724i	$-0.588353\pi$
$409$	−11.0834	−0.548039	−0.274020	+	0.961724i	$0.588353\pi$
$410$	−21.0530	−1.03973
$411$	5.79417	0.285805
$412$	−8.34406	−0.411082
$413$	1.49527	0.0735774
$414$	−2.16919	−0.106610
$415$	2.37009	0.116343
$416$	−14.9676	−0.733845
$417$	13.3618	0.654329
$418$	−15.0105	−0.734185
$419$	18.3269	0.895326	0.447663	−	0.894202i	$-0.352256\pi$
$419$	18.3269	0.895326	0.447663	+	0.894202i	$0.352256\pi$
$420$	−3.67069	−0.179111
$421$	−11.2572	−0.548644	−0.274322	−	0.961638i	$-0.588453\pi$
$421$	−11.2572	−0.548644	−0.274322	+	0.961638i	$0.588453\pi$
$422$	5.34090	0.259991
$423$	2.48699	0.120922
$424$	−10.3964	−0.504895
$425$	−1.00000	−0.0485071
$426$	4.75509	0.230385
$427$	−0.145719	−0.00705186
$428$	16.6425	0.804444
$429$	−12.0935	−0.583878
$430$	−17.5221	−0.844992
$431$	7.15102	0.344453	0.172226	−	0.985057i	$-0.444904\pi$
$431$	7.15102	0.344453	0.172226	+	0.985057i	$0.444904\pi$
$432$	2.44505	0.117638
$433$	−6.93032	−0.333050	−0.166525	−	0.986037i	$-0.553255\pi$
$433$	−6.93032	−0.333050	−0.166525	+	0.986037i	$0.553255\pi$
$434$	0.152372	0.00731410
$435$	18.6235	0.892927
$436$	−30.7613	−1.47320
$437$	−2.62596	−0.125617
$438$	48.4904	2.31696
$439$	−25.8624	−1.23435	−0.617173	−	0.786827i	$-0.711722\pi$
$439$	−25.8624	−1.23435	−0.617173	+	0.786827i	$0.711722\pi$
$440$	6.13230	0.292346
$441$	−8.08262	−0.384887
$442$	−7.14089	−0.339658
$443$	−39.6117	−1.88201	−0.941005	−	0.338393i	$-0.890117\pi$
$443$	−39.6117	−1.88201	−0.941005	+	0.338393i	$0.890117\pi$
$444$	−59.0483	−2.80231
$445$	5.54934	0.263064
$446$	−52.2681	−2.47496
$447$	−34.1695	−1.61616
$448$	−6.67688	−0.315453
$449$	−15.0530	−0.710396	−0.355198	−	0.934791i	$-0.615587\pi$
$449$	−15.0530	−0.710396	−0.355198	+	0.934791i	$0.615587\pi$
$450$	−2.79003	−0.131523
$451$	−17.3915	−0.818935
$452$	6.39402	0.300749
$453$	−22.5384	−1.05895
$454$	10.9799	0.515312
$455$	−1.63097	−0.0764609
$456$	−22.1609	−1.03778
$457$	−40.5642	−1.89751	−0.948756	−	0.316008i	$-0.897657\pi$
$457$	−40.5642	−1.89751	−0.948756	+	0.316008i	$0.897657\pi$
$458$	32.9160	1.53806
$459$	−3.68425	−0.171966
$460$	2.62776	0.122520
$461$	25.2270	1.17494	0.587468	−	0.809247i	$-0.300125\pi$
$461$	25.2270	1.17494	0.587468	+	0.809247i	$0.300125\pi$
$462$	−4.82664	−0.224556
$463$	−28.6720	−1.33250	−0.666250	−	0.745729i	$-0.732102\pi$
$463$	−28.6720	−1.33250	−0.666250	+	0.745729i	$0.732102\pi$
$464$	−6.02872	−0.279876
$465$	0.254225	0.0117894
$466$	−37.9275	−1.75696
$467$	34.9679	1.61812	0.809060	−	0.587726i	$-0.199976\pi$
$467$	34.9679	1.61812	0.809060	+	0.587726i	$0.199976\pi$
$468$	−12.5167	−0.578583
$469$	−4.03468	−0.186304
$470$	−4.79551	−0.221200
$471$	−27.3480	−1.26013
$472$	−9.03350	−0.415801
$473$	−14.4748	−0.665550
$474$	−5.84311	−0.268383
$475$	−3.37753	−0.154972
$476$	−1.79050	−0.0820673
$477$	3.90745	0.178910
$478$	−11.7088	−0.535547
$479$	−6.32959	−0.289206	−0.144603	−	0.989490i	$-0.546191\pi$
$479$	−6.32959	−0.289206	−0.144603	+	0.989490i	$0.546191\pi$
$480$	−9.96683	−0.454922
$481$	−26.2365	−1.19628
$482$	−23.8611	−1.08684
$483$	−0.844384	−0.0384208
$484$	−24.7699	−1.12590
$485$	−0.175786	−0.00798203
$486$	−27.4387	−1.24464
$487$	−2.05933	−0.0933169	−0.0466585	−	0.998911i	$-0.514857\pi$
$487$	−2.05933	−0.0933169	−0.0466585	+	0.998911i	$0.514857\pi$
$488$	0.880348	0.0398515
$489$	14.2629	0.644990
$490$	15.5852	0.704068
$491$	−10.9592	−0.494580	−0.247290	−	0.968942i	$-0.579540\pi$
$491$	−10.9592	−0.494580	−0.247290	+	0.968942i	$0.579540\pi$
$492$	−62.8925	−2.83541
$493$	9.08420	0.409132
$494$	−24.1186	−1.08515
$495$	−2.30480	−0.103593
$496$	−0.0822967	−0.00369523
$497$	0.529758	0.0237629
$498$	11.2700	0.505019
$499$	9.16996	0.410504	0.205252	−	0.978709i	$-0.434199\pi$
$499$	9.16996	0.410504	0.205252	+	0.978709i	$0.434199\pi$
$500$	3.37984	0.151151
$501$	43.5091	1.94384
$502$	−3.39377	−0.151471
$503$	6.04957	0.269737	0.134869	−	0.990863i	$-0.456939\pi$
$503$	6.04957	0.269737	0.134869	+	0.990863i	$0.456939\pi$
$504$	−2.03946	−0.0908449
$505$	3.24155	0.144247
$506$	3.45528	0.153606
$507$	7.21960	0.320634
$508$	15.7777	0.700023
$509$	−5.61822	−0.249023	−0.124512	−	0.992218i	$-0.539736\pi$
$509$	−5.61822	−0.249023	−0.124512	+	0.992218i	$0.539736\pi$
$510$	−4.75509	−0.210559
$511$	5.40225	0.238981
$512$	7.47441	0.330325
$513$	−12.4437	−0.549403
$514$	−30.7952	−1.35832
$515$	−2.46877	−0.108787
$516$	−52.3446	−2.30434
$517$	−3.96149	−0.174226
$518$	−10.4713	−0.460082
$519$	35.5805	1.56181
$520$	9.85330	0.432096
$521$	22.5374	0.987382	0.493691	−	0.869638i	$-0.335647\pi$
$521$	22.5374	0.987382	0.493691	+	0.869638i	$0.335647\pi$
$522$	25.3452	1.10933
$523$	−14.7737	−0.646007	−0.323003	−	0.946398i	$-0.604693\pi$
$523$	−14.7737	−0.646007	−0.323003	+	0.946398i	$0.604693\pi$
$524$	9.38453	0.409965
$525$	−1.08605	−0.0473993
$526$	−57.2142	−2.49466
$527$	0.124006	0.00540180
$528$	2.60688	0.113450
$529$	−22.3955	−0.973719
$530$	−7.53450	−0.327278
$531$	3.39521	0.147339
$532$	−6.04747	−0.262191
$533$	−27.9445	−1.21041
$534$	26.3876	1.14190
$535$	4.92403	0.212885
$536$	24.3751	1.05284
$537$	−21.7740	−0.939617
$538$	29.9751	1.29232
$539$	12.8747	0.554552
$540$	12.4522	0.535857
$541$	−6.93685	−0.298238	−0.149119	−	0.988819i	$-0.547644\pi$
$541$	−6.93685	−0.298238	−0.149119	+	0.988819i	$0.547644\pi$
$542$	48.4895	2.08280
$543$	8.55775	0.367248
$544$	−4.86165	−0.208441
$545$	−9.10141	−0.389861
$546$	−7.75539	−0.331900
$547$	37.1140	1.58688	0.793440	−	0.608649i	$-0.208288\pi$
$547$	37.1140	1.58688	0.793440	+	0.608649i	$0.208288\pi$
$548$	−9.55243	−0.408060
$549$	−0.330875	−0.0141214
$550$	4.44420	0.189502
$551$	30.6822	1.30711
$552$	5.10125	0.217124
$553$	−0.650973	−0.0276822
$554$	−38.4884	−1.63522
$555$	−17.4707	−0.741592
$556$	−22.0286	−0.934221
$557$	−23.4102	−0.991923	−0.495962	−	0.868344i	$-0.665184\pi$
$557$	−23.4102	−0.991923	−0.495962	+	0.868344i	$0.665184\pi$
$558$	0.345981	0.0146466
$559$	−23.2578	−0.983702
$560$	0.351573	0.0148567
$561$	−3.92810	−0.165845
$562$	−40.3973	−1.70406
$563$	18.8356	0.793825	0.396913	−	0.917856i	$-0.370082\pi$
$563$	18.8356	0.793825	0.396913	+	0.917856i	$0.370082\pi$
$564$	−14.3258	−0.603226
$565$	1.89181	0.0795890
$566$	−8.05486	−0.338571
$567$	−5.91301	−0.248323
$568$	−3.20047	−0.134289
$569$	7.31563	0.306687	0.153344	−	0.988173i	$-0.450996\pi$
$569$	7.31563	0.306687	0.153344	+	0.988173i	$0.450996\pi$
$570$	−16.0605	−0.672699
$571$	−9.56534	−0.400297	−0.200149	−	0.979766i	$-0.564142\pi$
$571$	−9.56534	−0.400297	−0.200149	+	0.979766i	$0.564142\pi$
$572$	19.9376	0.833634
$573$	−13.7094	−0.572720
$574$	−11.1530	−0.465516
$575$	0.777479	0.0324231
$576$	−15.1607	−0.631697
$577$	−28.2699	−1.17689	−0.588445	−	0.808537i	$-0.700260\pi$
$577$	−28.2699	−1.17689	−0.588445	+	0.808537i	$0.700260\pi$
$578$	−2.31945	−0.0964763
$579$	23.7517	0.987087
$580$	−30.7032	−1.27488
$581$	1.25557	0.0520899
$582$	−0.835878	−0.0346483
$583$	−6.22413	−0.257777
$584$	−32.6371	−1.35053
$585$	−3.70333	−0.153114
$586$	−23.8520	−0.985317
$587$	−7.05860	−0.291340	−0.145670	−	0.989333i	$-0.546534\pi$
$587$	−7.05860	−0.291340	−0.145670	+	0.989333i	$0.546534\pi$
$588$	46.5584	1.92004
$589$	0.418836	0.0172578
$590$	−6.54676	−0.269526
$591$	45.9783	1.89129
$592$	5.65557	0.232442
$593$	44.5463	1.82930	0.914649	−	0.404250i	$-0.132467\pi$
$593$	44.5463	1.82930	0.914649	+	0.404250i	$0.132467\pi$
$594$	16.3736	0.671816
$595$	−0.529758	−0.0217180
$596$	56.3329	2.30748
$597$	−6.52885	−0.267208
$598$	5.55189	0.227034
$599$	−9.15441	−0.374039	−0.187019	−	0.982356i	$-0.559883\pi$
$599$	−9.15441	−0.374039	−0.187019	+	0.982356i	$0.559883\pi$
$600$	6.56127	0.267863
$601$	−15.7086	−0.640766	−0.320383	−	0.947288i	$-0.603812\pi$
$601$	−15.7086	−0.640766	−0.320383	+	0.947288i	$0.603812\pi$
$602$	−9.28248	−0.378326
$603$	−9.16127	−0.373076
$604$	37.1575	1.51192
$605$	−7.32871	−0.297954
$606$	15.4139	0.626145
$607$	30.8867	1.25365	0.626826	−	0.779160i	$-0.284354\pi$
$607$	30.8867	1.25365	0.626826	+	0.779160i	$0.284354\pi$
$608$	−16.4204	−0.665934
$609$	9.86593	0.399788
$610$	0.638006	0.0258321
$611$	−6.36528	−0.257512
$612$	−4.06556	−0.164341
$613$	−8.30408	−0.335399	−0.167699	−	0.985838i	$-0.553634\pi$
$613$	−8.30408	−0.335399	−0.167699	+	0.985838i	$0.553634\pi$
$614$	1.19908	0.0483911
$615$	−18.6081	−0.750351
$616$	3.24863	0.130891
$617$	10.6299	0.427945	0.213973	−	0.976840i	$-0.431360\pi$
$617$	10.6299	0.427945	0.213973	+	0.976840i	$0.431360\pi$
$618$	−11.7392	−0.472221
$619$	−28.8788	−1.16074	−0.580368	−	0.814354i	$-0.697091\pi$
$619$	−28.8788	−1.16074	−0.580368	+	0.814354i	$0.697091\pi$
$620$	−0.419122	−0.0168323
$621$	2.86443	0.114946
$622$	−11.6438	−0.466875
$623$	2.93981	0.117781
$624$	4.18871	0.167683
$625$	1.00000	0.0400000
$626$	31.4210	1.25584
$627$	−13.2673	−0.529845
$628$	45.0866	1.79915
$629$	−8.52192	−0.339791
$630$	−1.47804	−0.0588866
$631$	−18.3944	−0.732268	−0.366134	−	0.930562i	$-0.619319\pi$
$631$	−18.3944	−0.732268	−0.366134	+	0.930562i	$0.619319\pi$
$632$	3.93278	0.156438
$633$	4.72067	0.187630
$634$	52.7694	2.09574
$635$	4.66818	0.185251
$636$	−22.5081	−0.892506
$637$	20.6869	0.819645
$638$	−40.3720	−1.59834
$639$	1.20289	0.0475854
$640$	19.5102	0.771208
$641$	37.8858	1.49640	0.748200	−	0.663473i	$-0.230918\pi$
$641$	37.8858	1.49640	0.748200	+	0.663473i	$0.230918\pi$
$642$	23.4142	0.924085
$643$	−5.79901	−0.228691	−0.114345	−	0.993441i	$-0.536477\pi$
$643$	−5.79901	−0.228691	−0.114345	+	0.993441i	$0.536477\pi$
$644$	1.39207	0.0548554
$645$	−15.4873	−0.609812
$646$	−7.83402	−0.308225
$647$	−16.6117	−0.653072	−0.326536	−	0.945185i	$-0.605881\pi$
$647$	−16.6117	−0.653072	−0.326536	+	0.945185i	$0.605881\pi$
$648$	35.7228	1.40332
$649$	−5.40818	−0.212290
$650$	7.14089	0.280089
$651$	0.134677	0.00527843
$652$	−23.5142	−0.920887
$653$	−35.7520	−1.39908	−0.699542	−	0.714591i	$-0.746613\pi$
$653$	−35.7520	−1.39908	−0.699542	+	0.714591i	$0.746613\pi$
$654$	−43.2780	−1.69230
$655$	2.77662	0.108491
$656$	6.02375	0.235188
$657$	12.2665	0.478562
$658$	−2.54046	−0.0990373
$659$	5.66245	0.220578	0.110289	−	0.993900i	$-0.464822\pi$
$659$	5.66245	0.220578	0.110289	+	0.993900i	$0.464822\pi$
$660$	13.2764	0.516782
$661$	−15.6579	−0.609020	−0.304510	−	0.952509i	$-0.598493\pi$
$661$	−15.6579	−0.609020	−0.304510	+	0.952509i	$0.598493\pi$
$662$	20.7721	0.807332
$663$	−6.31163	−0.245123
$664$	−7.58540	−0.294371
$665$	−1.78928	−0.0693851
$666$	−23.7764	−0.921318
$667$	−7.06278	−0.273472
$668$	−71.7303	−2.77533
$669$	−46.1982	−1.78613
$670$	17.6651	0.682462
$671$	0.527047	0.0203464
$672$	−5.28001	−0.203681
$673$	−6.48700	−0.250055	−0.125028	−	0.992153i	$-0.539902\pi$
$673$	−6.48700	−0.250055	−0.125028	+	0.992153i	$0.539902\pi$
$674$	−2.00878	−0.0773755
$675$	3.68425	0.141807
$676$	−11.9024	−0.457786
$677$	−22.0487	−0.847400	−0.423700	−	0.905803i	$-0.639269\pi$
$677$	−22.0487	−0.847400	−0.423700	+	0.905803i	$0.639269\pi$
$678$	8.99572	0.345479
$679$	−0.0931241	−0.00357377
$680$	3.20047	0.122733
$681$	9.70481	0.371889
$682$	−0.551109	−0.0211031
$683$	2.56392	0.0981057	0.0490529	−	0.998796i	$-0.484380\pi$
$683$	2.56392	0.0981057	0.0490529	+	0.998796i	$0.484380\pi$
$684$	−13.7316	−0.525040
$685$	−2.82630	−0.107987
$686$	16.8576	0.643626
$687$	29.0935	1.10998
$688$	5.01349	0.191138
$689$	−10.0009	−0.381002
$690$	3.69698	0.140742
$691$	3.22420	0.122654	0.0613271	−	0.998118i	$-0.480467\pi$
$691$	3.22420	0.122654	0.0613271	+	0.998118i	$0.480467\pi$
$692$	−58.6590	−2.22988
$693$	−1.22099	−0.0463815
$694$	−63.0974	−2.39515
$695$	−6.51764	−0.247228
$696$	−59.6039	−2.25928
$697$	−9.07671	−0.343805
$698$	−3.84503	−0.145537
$699$	−33.5230	−1.26796
$700$	1.79050	0.0676745
$701$	−18.2292	−0.688508	−0.344254	−	0.938877i	$-0.611868\pi$
$701$	−18.2292	−0.688508	−0.344254	+	0.938877i	$0.611868\pi$
$702$	26.3089	0.992964
$703$	−28.7831	−1.08557
$704$	24.1493	0.910162
$705$	−4.23861	−0.159635
$706$	28.1704	1.06021
$707$	1.71724	0.0645833
$708$	−19.5574	−0.735014
$709$	−13.0856	−0.491441	−0.245721	−	0.969341i	$-0.579025\pi$
$709$	−13.0856	−0.491441	−0.245721	+	0.969341i	$0.579025\pi$
$710$	−2.31945	−0.0870474
$711$	−1.47812	−0.0554338
$712$	−17.7605	−0.665604
$713$	−0.0964123	−0.00361067
$714$	−2.51905	−0.0942729
$715$	5.89898	0.220609
$716$	35.8972	1.34154
$717$	−10.3491	−0.386493
$718$	10.4371	0.389508
$719$	12.8310	0.478514	0.239257	−	0.970956i	$-0.423096\pi$
$719$	12.8310	0.478514	0.239257	+	0.970956i	$0.423096\pi$
$720$	0.798294	0.0297507
$721$	−1.30785	−0.0487069
$722$	17.6099	0.655371
$723$	−21.0901	−0.784350
$724$	−14.1086	−0.524340
$725$	−9.08420	−0.337379
$726$	−34.8487	−1.29336
$727$	34.3187	1.27281	0.636405	−	0.771355i	$-0.280421\pi$
$727$	34.3187	1.27281	0.636405	+	0.771355i	$0.280421\pi$
$728$	5.21986	0.193461
$729$	9.23292	0.341960
$730$	−23.6528	−0.875428
$731$	−7.55443	−0.279411
$732$	1.90594	0.0704457
$733$	−17.1137	−0.632110	−0.316055	−	0.948741i	$-0.602358\pi$
$733$	−17.1137	−0.632110	−0.316055	+	0.948741i	$0.602358\pi$
$734$	40.1989	1.48377
$735$	13.7753	0.508110
$736$	3.77983	0.139326
$737$	14.5929	0.537535
$738$	−25.3243	−0.932200
$739$	33.7945	1.24315	0.621575	−	0.783355i	$-0.286493\pi$
$739$	33.7945	1.24315	0.621575	+	0.783355i	$0.286493\pi$
$740$	28.8028	1.05881
$741$	−21.3177	−0.783127
$742$	−3.99146	−0.146531
$743$	21.2040	0.777899	0.388950	−	0.921259i	$-0.372838\pi$
$743$	21.2040	0.777899	0.388950	+	0.921259i	$0.372838\pi$
$744$	−0.813639	−0.0298295
$745$	16.6673	0.610643
$746$	35.9985	1.31800
$747$	2.85094	0.104311
$748$	6.47598	0.236785
$749$	2.60855	0.0953142
$750$	4.75509	0.173631
$751$	36.1573	1.31940	0.659699	−	0.751530i	$-0.270684\pi$
$751$	36.1573	1.31940	0.659699	+	0.751530i	$0.270684\pi$
$752$	1.37211	0.0500356
$753$	−2.99966	−0.109314
$754$	−64.8693	−2.36240
$755$	10.9939	0.400108
$756$	6.59665	0.239918
$757$	−14.0287	−0.509880	−0.254940	−	0.966957i	$-0.582056\pi$
$757$	−14.0287	−0.509880	−0.254940	+	0.966957i	$0.582056\pi$
$758$	14.8312	0.538692
$759$	3.05402	0.110854
$760$	10.8097	0.392109
$761$	−17.3285	−0.628156	−0.314078	−	0.949397i	$-0.601695\pi$
$761$	−17.3285	−0.628156	−0.314078	+	0.949397i	$0.601695\pi$
$762$	22.1976	0.804135
$763$	−4.82154	−0.174552
$764$	22.6018	0.817703
$765$	−1.20289	−0.0434904
$766$	−22.4891	−0.812563
$767$	−8.68980	−0.313770
$768$	41.0954	1.48290
$769$	−12.9168	−0.465793	−0.232896	−	0.972502i	$-0.574820\pi$
$769$	−12.9168	−0.465793	−0.232896	+	0.972502i	$0.574820\pi$
$770$	2.35435	0.0848450
$771$	−27.2190	−0.980268
$772$	−39.1577	−1.40932
$773$	−29.1694	−1.04915	−0.524575	−	0.851364i	$-0.675776\pi$
$773$	−29.1694	−1.04915	−0.524575	+	0.851364i	$0.675776\pi$
$774$	−21.0771	−0.757601
$775$	−0.124006	−0.00445444
$776$	0.562599	0.0201961
$777$	−9.25526	−0.332031
$778$	79.7875	2.86052
$779$	−30.6569	−1.09840
$780$	21.3323	0.763819
$781$	−1.91606	−0.0685620
$782$	1.80332	0.0644867
$783$	−33.4685	−1.19607
$784$	−4.45930	−0.159261
$785$	13.3399	0.476120
$786$	13.2031	0.470938
$787$	−17.3296	−0.617734	−0.308867	−	0.951105i	$-0.599950\pi$
$787$	−17.3296	−0.617734	−0.308867	+	0.951105i	$0.599950\pi$
$788$	−75.8011	−2.70030
$789$	−50.5699	−1.80034
$790$	2.85017	0.101404
$791$	1.00220	0.0356342
$792$	7.37646	0.262111
$793$	0.846852	0.0300726
$794$	−1.06671	−0.0378559
$795$	−6.65953	−0.236189
$796$	10.7637	0.381507
$797$	−5.26465	−0.186484	−0.0932418	−	0.995643i	$-0.529723\pi$
$797$	−5.26465	−0.186484	−0.0932418	+	0.995643i	$0.529723\pi$
$798$	−8.50816	−0.301186
$799$	−2.06752	−0.0731436
$800$	4.86165	0.171885
$801$	6.67522	0.235857
$802$	0.248750	0.00878368
$803$	−19.5392	−0.689522
$804$	52.7718	1.86112
$805$	0.411876	0.0145167
$806$	−0.885515	−0.0311910
$807$	26.4941	0.932637
$808$	−10.3745	−0.364973
$809$	−13.0550	−0.458990	−0.229495	−	0.973310i	$-0.573707\pi$
$809$	−13.0550	−0.458990	−0.229495	+	0.973310i	$0.573707\pi$
$810$	25.8890	0.909648
$811$	−41.2338	−1.44792	−0.723958	−	0.689844i	$-0.757679\pi$
$811$	−41.2338	−1.44792	−0.723958	+	0.689844i	$0.757679\pi$
$812$	−16.2652	−0.570798
$813$	42.8585	1.50311
$814$	37.8732	1.32745
$815$	−6.95719	−0.243700
$816$	1.36054	0.0476285
$817$	−25.5154	−0.892669
$818$	25.7074	0.898838
$819$	−1.96187	−0.0685531
$820$	30.6778	1.07132
$821$	−43.5047	−1.51833	−0.759163	−	0.650901i	$-0.774391\pi$
$821$	−43.5047	−1.51833	−0.759163	+	0.650901i	$0.774391\pi$
$822$	−13.4393	−0.468749
$823$	−2.55730	−0.0891418	−0.0445709	−	0.999006i	$-0.514192\pi$
$823$	−2.55730	−0.0891418	−0.0445709	+	0.999006i	$0.514192\pi$
$824$	7.90124	0.275253
$825$	3.92810	0.136759
$826$	−3.46820	−0.120674
$827$	10.5207	0.365840	0.182920	−	0.983128i	$-0.441445\pi$
$827$	10.5207	0.365840	0.182920	+	0.983128i	$0.441445\pi$
$828$	3.16089	0.109849
$829$	−24.9247	−0.865669	−0.432835	−	0.901473i	$-0.642487\pi$
$829$	−24.9247	−0.865669	−0.432835	+	0.901473i	$0.642487\pi$
$830$	−5.49729	−0.190814
$831$	−34.0188	−1.18010
$832$	38.8028	1.34525
$833$	6.71936	0.232812
$834$	−30.9920	−1.07316
$835$	−21.2230	−0.734451
$836$	21.8729	0.756489
$837$	−0.456871	−0.0157918
$838$	−42.5082	−1.46842
$839$	−19.0828	−0.658813	−0.329406	−	0.944188i	$-0.606849\pi$
$839$	−19.0828	−0.658813	−0.329406	+	0.944188i	$0.606849\pi$
$840$	3.47588	0.119929
$841$	53.5227	1.84561
$842$	26.1106	0.899830
$843$	−35.7060	−1.22978
$844$	−7.78262	−0.267889
$845$	−3.52159	−0.121147
$846$	−5.76845	−0.198323
$847$	−3.88244	−0.133402
$848$	2.15580	0.0740304
$849$	−7.11946	−0.244339
$850$	2.31945	0.0795564
$851$	6.62562	0.227123
$852$	−6.92899	−0.237383
$853$	−42.4441	−1.45326	−0.726630	−	0.687029i	$-0.758914\pi$
$853$	−42.4441	−1.45326	−0.726630	+	0.687029i	$0.758914\pi$
$854$	0.337989	0.0115657
$855$	−4.06279	−0.138944
$856$	−15.7592	−0.538640
$857$	−11.7931	−0.402845	−0.201423	−	0.979504i	$-0.564556\pi$
$857$	−11.7931	−0.402845	−0.201423	+	0.979504i	$0.564556\pi$
$858$	28.0502	0.957617
$859$	−27.9223	−0.952698	−0.476349	−	0.879256i	$-0.658040\pi$
$859$	−27.9223	−0.952698	−0.476349	+	0.879256i	$0.658040\pi$
$860$	25.5328	0.870661
$861$	−9.85779	−0.335953
$862$	−16.5864	−0.564936
$863$	−28.2634	−0.962096	−0.481048	−	0.876694i	$-0.659744\pi$
$863$	−28.2634	−0.962096	−0.481048	+	0.876694i	$0.659744\pi$
$864$	17.9115	0.609363
$865$	−17.3555	−0.590106
$866$	16.0745	0.546234
$867$	−2.05009	−0.0696248
$868$	−0.222033	−0.00753629
$869$	2.35448	0.0798702
$870$	−43.1962	−1.46449
$871$	23.4476	0.794493
$872$	29.1288	0.986426
$873$	−0.211451	−0.00715652
$874$	6.09079	0.206024
$875$	0.529758	0.0179091
$876$	−70.6589	−2.38734
$877$	−23.3600	−0.788811	−0.394405	−	0.918937i	$-0.629049\pi$
$877$	−23.3600	−0.788811	−0.394405	+	0.918937i	$0.629049\pi$
$878$	59.9866	2.02445
$879$	−21.0821	−0.711081
$880$	−1.27159	−0.0428654
$881$	10.6219	0.357860	0.178930	−	0.983862i	$-0.442736\pi$
$881$	10.6219	0.357860	0.178930	+	0.983862i	$0.442736\pi$
$882$	18.7472	0.631252
$883$	34.5113	1.16140	0.580698	−	0.814119i	$-0.302780\pi$
$883$	34.5113	1.16140	0.580698	+	0.814119i	$0.302780\pi$
$884$	10.4055	0.349976
$885$	−5.78650	−0.194511
$886$	91.8773	3.08668
$887$	54.4301	1.82758	0.913792	−	0.406182i	$-0.133140\pi$
$887$	54.4301	1.82758	0.913792	+	0.406182i	$0.133140\pi$
$888$	55.9146	1.87637
$889$	2.47301	0.0829420
$890$	−12.8714	−0.431451
$891$	21.3865	0.716476
$892$	76.1637	2.55015
$893$	−6.98312	−0.233681
$894$	79.2545	2.65067
$895$	10.6210	0.355020
$896$	10.3357	0.345291
$897$	4.90716	0.163845
$898$	34.9147	1.16512
$899$	1.12650	0.0375708
$900$	4.06556	0.135519
$901$	−3.24840	−0.108220
$902$	40.3387	1.34313
$903$	−8.20452	−0.273029
$904$	−6.05469	−0.201376
$905$	−4.17432	−0.138759
$906$	52.2768	1.73678
$907$	−33.8556	−1.12416	−0.562078	−	0.827084i	$-0.689998\pi$
$907$	−33.8556	−1.12416	−0.562078	+	0.827084i	$0.689998\pi$
$908$	−15.9996	−0.530966
$909$	3.89921	0.129329
$910$	3.78294	0.125403
$911$	−3.24125	−0.107387	−0.0536937	−	0.998557i	$-0.517099\pi$
$911$	−3.24125	−0.107387	−0.0536937	+	0.998557i	$0.517099\pi$
$912$	4.59528	0.152165
$913$	−4.54123	−0.150293
$914$	94.0866	3.11211
$915$	0.563915	0.0186425
$916$	−47.9643	−1.58478
$917$	1.47094	0.0485746
$918$	8.54544	0.282041
$919$	1.74857	0.0576799	0.0288399	−	0.999584i	$-0.490819\pi$
$919$	1.74857	0.0576799	0.0288399	+	0.999584i	$0.490819\pi$
$920$	−2.48830	−0.0820369
$921$	1.05984	0.0349228
$922$	−58.5126	−1.92701
$923$	−3.07870	−0.101337
$924$	7.03326	0.231377
$925$	8.52192	0.280199
$926$	66.5032	2.18543
$927$	−2.96965	−0.0975361
$928$	−44.1642	−1.44976
$929$	−30.8971	−1.01370	−0.506851	−	0.862034i	$-0.669191\pi$
$929$	−30.8971	−1.01370	−0.506851	+	0.862034i	$0.669191\pi$
$930$	−0.589661	−0.0193357
$931$	22.6949	0.743794
$932$	55.2670	1.81033
$933$	−10.2916	−0.336933
$934$	−81.1062	−2.65388
$935$	1.91606	0.0626619
$936$	11.8524	0.387408
$937$	−24.5416	−0.801740	−0.400870	−	0.916135i	$-0.631292\pi$
$937$	−24.5416	−0.801740	−0.400870	+	0.916135i	$0.631292\pi$
$938$	9.35823	0.305557
$939$	27.7721	0.906308
$940$	6.98789	0.227920
$941$	42.8810	1.39788	0.698940	−	0.715181i	$-0.253656\pi$
$941$	42.8810	1.39788	0.698940	+	0.715181i	$0.253656\pi$
$942$	63.4322	2.06673
$943$	7.05695	0.229806
$944$	1.87318	0.0609670
$945$	1.95176	0.0634908
$946$	33.5734	1.09157
$947$	−7.48810	−0.243331	−0.121665	−	0.992571i	$-0.538823\pi$
$947$	−7.48810	−0.243331	−0.121665	+	0.992571i	$0.538823\pi$
$948$	8.51443	0.276536
$949$	−31.3953	−1.01913
$950$	7.83402	0.254169
$951$	46.6414	1.51245
$952$	1.69548	0.0549507
$953$	9.87168	0.319775	0.159888	−	0.987135i	$-0.448887\pi$
$953$	9.87168	0.319775	0.159888	+	0.987135i	$0.448887\pi$
$954$	−9.06314	−0.293430
$955$	6.68722	0.216394
$956$	17.0617	0.551816
$957$	−35.6837	−1.15349
$958$	14.6812	0.474327
$959$	−1.49725	−0.0483488
$960$	25.8386	0.833939
$961$	−30.9846	−0.999504
$962$	60.8541	1.96202
$963$	5.92305	0.190868
$964$	34.7698	1.11986
$965$	−11.5857	−0.372956
$966$	1.95850	0.0630139
$967$	38.9163	1.25146	0.625732	−	0.780038i	$-0.284800\pi$
$967$	38.9163	1.25146	0.625732	+	0.780038i	$0.284800\pi$
$968$	23.4553	0.753883
$969$	−6.92426	−0.222439
$970$	0.407727	0.0130913
$971$	−0.0321169	−0.00103068	−0.000515340	−	1.00000i	$-0.500164\pi$
$971$	−0.0321169	−0.00103068	−0.000515340		1.00000i	$0.500164\pi$
$972$	39.9829	1.28245
$973$	−3.45277	−0.110691
$974$	4.77650	0.153049
$975$	6.31163	0.202134
$976$	−0.182549	−0.00584324
$977$	34.0235	1.08851	0.544254	−	0.838921i	$-0.316813\pi$
$977$	34.0235	1.08851	0.544254	+	0.838921i	$0.316813\pi$
$978$	−33.0821	−1.05785
$979$	−10.6329	−0.339828
$980$	−22.7104	−0.725456
$981$	−10.9480	−0.349541
$982$	25.4192	0.811159
$983$	7.03998	0.224540	0.112270	−	0.993678i	$-0.464188\pi$
$983$	7.03998	0.224540	0.112270	+	0.993678i	$0.464188\pi$
$984$	59.5547	1.89854
$985$	−22.4274	−0.714597
$986$	−21.0703	−0.671016
$987$	−2.24544	−0.0714730
$988$	35.1450	1.11811
$989$	5.87341	0.186764
$990$	5.34587	0.169903
$991$	55.2151	1.75397	0.876983	−	0.480522i	$-0.159553\pi$
$991$	55.2151	1.75397	0.876983	+	0.480522i	$0.159553\pi$
$992$	−0.602875	−0.0191413
$993$	18.3599	0.582633
$994$	−1.22875	−0.0389735
$995$	3.18466	0.100961
$996$	−16.4223	−0.520361
$997$	43.7457	1.38544	0.692721	−	0.721206i	$-0.256412\pi$
$997$	43.7457	1.38544	0.692721	+	0.721206i	$0.256412\pi$
$998$	−21.2693	−0.673267
$999$	31.3969	0.993355

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6035.2.a.b.1.4	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6035.2.a.b.1.4	✓	36	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:	\( N \)	\(=\)	\( 6035 = 5 \cdot 17 \cdot 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6035.a (trivial)

\(f(q)\)	\(=\)	\(q-2.31945 q^{2} -2.05009 q^{3} +3.37984 q^{4} +1.00000 q^{5} +4.75509 q^{6} +0.529758 q^{7} -3.20047 q^{8} +1.20289 q^{9} +O(q^{10})\)	\(q-2.31945 q^{2} -2.05009 q^{3} +3.37984 q^{4} +1.00000 q^{5} +4.75509 q^{6} +0.529758 q^{7} -3.20047 q^{8} +1.20289 q^{9} -2.31945 q^{10} -1.91606 q^{11} -6.92899 q^{12} -3.07870 q^{13} -1.22875 q^{14} -2.05009 q^{15} +0.663649 q^{16} -1.00000 q^{17} -2.79003 q^{18} -3.37753 q^{19} +3.37984 q^{20} -1.08605 q^{21} +4.44420 q^{22} +0.777479 q^{23} +6.56127 q^{24} +1.00000 q^{25} +7.14089 q^{26} +3.68425 q^{27} +1.79050 q^{28} -9.08420 q^{29} +4.75509 q^{30} -0.124006 q^{31} +4.86165 q^{32} +3.92810 q^{33} +2.31945 q^{34} +0.529758 q^{35} +4.06556 q^{36} +8.52192 q^{37} +7.83402 q^{38} +6.31163 q^{39} -3.20047 q^{40} +9.07671 q^{41} +2.51905 q^{42} +7.55443 q^{43} -6.47598 q^{44} +1.20289 q^{45} -1.80332 q^{46} +2.06752 q^{47} -1.36054 q^{48} -6.71936 q^{49} -2.31945 q^{50} +2.05009 q^{51} -10.4055 q^{52} +3.24840 q^{53} -8.54544 q^{54} -1.91606 q^{55} -1.69548 q^{56} +6.92426 q^{57} +21.0703 q^{58} +2.82255 q^{59} -6.92899 q^{60} -0.275068 q^{61} +0.287626 q^{62} +0.637238 q^{63} -12.6036 q^{64} -3.07870 q^{65} -9.11104 q^{66} -7.61608 q^{67} -3.37984 q^{68} -1.59391 q^{69} -1.22875 q^{70} +1.00000 q^{71} -3.84980 q^{72} +10.1976 q^{73} -19.7662 q^{74} -2.05009 q^{75} -11.4155 q^{76} -1.01505 q^{77} -14.6395 q^{78} -1.22881 q^{79} +0.663649 q^{80} -11.1617 q^{81} -21.0530 q^{82} +2.37009 q^{83} -3.67069 q^{84} -1.00000 q^{85} -17.5221 q^{86} +18.6235 q^{87} +6.13230 q^{88} +5.54934 q^{89} -2.79003 q^{90} -1.63097 q^{91} +2.62776 q^{92} +0.254225 q^{93} -4.79551 q^{94} -3.37753 q^{95} -9.96683 q^{96} -0.175786 q^{97} +15.5852 q^{98} -2.30480 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - q^{2} - 4 q^{3} + 23 q^{4} + 36 q^{5} - 2 q^{6} - 7 q^{7} - 3 q^{8} + 10 q^{9}+O(q^{10}) \) 36 * q - q^2 - 4 * q^3 + 23 * q^4 + 36 * q^5 - 2 * q^6 - 7 * q^7 - 3 * q^8 + 10 * q^9	\( 36 q - q^{2} - 4 q^{3} + 23 q^{4} + 36 q^{5} - 2 q^{6} - 7 q^{7} - 3 q^{8} + 10 q^{9} - q^{10} - 22 q^{11} - 14 q^{12} - 15 q^{13} - 28 q^{14} - 4 q^{15} + q^{16} - 36 q^{17} - 12 q^{18} - 23 q^{19} + 23 q^{20} - 21 q^{21} + 2 q^{23} - 13 q^{24} + 36 q^{25} - 18 q^{26} - 13 q^{27} - 20 q^{28} - 4 q^{29} - 2 q^{30} - 43 q^{31} - 2 q^{32} - 19 q^{33} + q^{34} - 7 q^{35} - 35 q^{36} - 30 q^{37} - 11 q^{38} - 20 q^{39} - 3 q^{40} - 39 q^{41} + 2 q^{42} - 7 q^{43} - 45 q^{44} + 10 q^{45} - 52 q^{46} - 12 q^{47} - 12 q^{48} - 15 q^{49} - q^{50} + 4 q^{51} - 19 q^{52} - 31 q^{53} + 48 q^{54} - 22 q^{55} - 30 q^{56} + 18 q^{57} - 12 q^{58} - 66 q^{59} - 14 q^{60} - 93 q^{61} - 7 q^{62} - 22 q^{63} - 41 q^{64} - 15 q^{65} - 21 q^{66} - 19 q^{67} - 23 q^{68} - 73 q^{69} - 28 q^{70} + 36 q^{71} - q^{72} - 47 q^{73} - 27 q^{74} - 4 q^{75} - 56 q^{76} - 9 q^{77} - 78 q^{78} - 21 q^{79} + q^{80} - 40 q^{81} - 15 q^{82} - 8 q^{83} - 54 q^{84} - 36 q^{85} - 17 q^{86} - 32 q^{87} - 13 q^{88} - 62 q^{89} - 12 q^{90} - 33 q^{91} + 42 q^{92} - 24 q^{93} - 40 q^{94} - 23 q^{95} + 21 q^{96} - 60 q^{97} + 11 q^{98} - 65 q^{99}+O(q^{100}) \) 36 * q - q^2 - 4 * q^3 + 23 * q^4 + 36 * q^5 - 2 * q^6 - 7 * q^7 - 3 * q^8 + 10 * q^9 - q^10 - 22 * q^11 - 14 * q^12 - 15 * q^13 - 28 * q^14 - 4 * q^15 + q^16 - 36 * q^17 - 12 * q^18 - 23 * q^19 + 23 * q^20 - 21 * q^21 + 2 * q^23 - 13 * q^24 + 36 * q^25 - 18 * q^26 - 13 * q^27 - 20 * q^28 - 4 * q^29 - 2 * q^30 - 43 * q^31 - 2 * q^32 - 19 * q^33 + q^34 - 7 * q^35 - 35 * q^36 - 30 * q^37 - 11 * q^38 - 20 * q^39 - 3 * q^40 - 39 * q^41 + 2 * q^42 - 7 * q^43 - 45 * q^44 + 10 * q^45 - 52 * q^46 - 12 * q^47 - 12 * q^48 - 15 * q^49 - q^50 + 4 * q^51 - 19 * q^52 - 31 * q^53 + 48 * q^54 - 22 * q^55 - 30 * q^56 + 18 * q^57 - 12 * q^58 - 66 * q^59 - 14 * q^60 - 93 * q^61 - 7 * q^62 - 22 * q^63 - 41 * q^64 - 15 * q^65 - 21 * q^66 - 19 * q^67 - 23 * q^68 - 73 * q^69 - 28 * q^70 + 36 * q^71 - q^72 - 47 * q^73 - 27 * q^74 - 4 * q^75 - 56 * q^76 - 9 * q^77 - 78 * q^78 - 21 * q^79 + q^80 - 40 * q^81 - 15 * q^82 - 8 * q^83 - 54 * q^84 - 36 * q^85 - 17 * q^86 - 32 * q^87 - 13 * q^88 - 62 * q^89 - 12 * q^90 - 33 * q^91 + 42 * q^92 - 24 * q^93 - 40 * q^94 - 23 * q^95 + 21 * q^96 - 60 * q^97 + 11 * q^98 - 65 * q^99

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