LMFDB - Embedded newform 4033.2.a.d.1.46

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4033,2,Mod(1,4033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4033, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4033 = 37 \cdot 109 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4033.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$32.2036671352$
Analytic rank:	$1$
Dimension:	$79$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.46
Character	$\chi$	$=$	4033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.349116 q^{2} +1.27272 q^{3} -1.87812 q^{4} -1.11462 q^{5} +0.444328 q^{6} -0.249605 q^{7} -1.35391 q^{8} -1.38018 q^{9} +O(q^{10})$	\(q+0.349116 q^{2} +1.27272 q^{3} -1.87812 q^{4} -1.11462 q^{5} +0.444328 q^{6} -0.249605 q^{7} -1.35391 q^{8} -1.38018 q^{9} -0.389134 q^{10} +3.01523 q^{11} -2.39032 q^{12} +3.37064 q^{13} -0.0871413 q^{14} -1.41861 q^{15} +3.28356 q^{16} +2.58204 q^{17} -0.481843 q^{18} -8.04863 q^{19} +2.09340 q^{20} -0.317678 q^{21} +1.05267 q^{22} +3.45558 q^{23} -1.72316 q^{24} -3.75761 q^{25} +1.17675 q^{26} -5.57475 q^{27} +0.468788 q^{28} +2.16612 q^{29} -0.495259 q^{30} -2.72320 q^{31} +3.85417 q^{32} +3.83755 q^{33} +0.901433 q^{34} +0.278216 q^{35} +2.59214 q^{36} -1.00000 q^{37} -2.80991 q^{38} +4.28989 q^{39} +1.50911 q^{40} +9.05995 q^{41} -0.110907 q^{42} -9.75852 q^{43} -5.66296 q^{44} +1.53838 q^{45} +1.20640 q^{46} +2.31418 q^{47} +4.17906 q^{48} -6.93770 q^{49} -1.31184 q^{50} +3.28622 q^{51} -6.33047 q^{52} -2.67954 q^{53} -1.94624 q^{54} -3.36085 q^{55} +0.337944 q^{56} -10.2437 q^{57} +0.756229 q^{58} +1.02880 q^{59} +2.66431 q^{60} +14.4043 q^{61} -0.950714 q^{62} +0.344500 q^{63} -5.22157 q^{64} -3.75700 q^{65} +1.33975 q^{66} -15.2214 q^{67} -4.84938 q^{68} +4.39799 q^{69} +0.0971299 q^{70} +4.92479 q^{71} +1.86864 q^{72} -14.1816 q^{73} -0.349116 q^{74} -4.78240 q^{75} +15.1163 q^{76} -0.752618 q^{77} +1.49767 q^{78} -3.27815 q^{79} -3.65994 q^{80} -2.95457 q^{81} +3.16298 q^{82} -5.04712 q^{83} +0.596637 q^{84} -2.87801 q^{85} -3.40686 q^{86} +2.75687 q^{87} -4.08236 q^{88} +17.9292 q^{89} +0.537074 q^{90} -0.841331 q^{91} -6.48999 q^{92} -3.46588 q^{93} +0.807920 q^{94} +8.97120 q^{95} +4.90529 q^{96} -2.22635 q^{97} -2.42206 q^{98} -4.16156 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9}+O(q^{10}) $ 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9} - 13 q^{10} - 5 q^{11} - 40 q^{12} - 18 q^{13} - 42 q^{14} - 49 q^{15} + 83 q^{16} - 62 q^{17} - 33 q^{18} - 25 q^{19} - 39 q^{20} - 15 q^{21} - 31 q^{22} - 94 q^{23} - 39 q^{24} + 71 q^{25} - 35 q^{26} - 47 q^{27} - 13 q^{28} - 17 q^{29} + 15 q^{30} - 37 q^{31} - 105 q^{32} - 60 q^{33} + 9 q^{34} - 60 q^{35} + 43 q^{36} - 79 q^{37} - 80 q^{38} - 41 q^{39} - 64 q^{40} - 37 q^{41} - 30 q^{42} - 20 q^{43} - 14 q^{44} - 8 q^{45} + 61 q^{46} - 148 q^{47} - 39 q^{48} + 82 q^{49} - 90 q^{50} - 45 q^{51} - 27 q^{52} - 70 q^{53} - 41 q^{54} - 105 q^{55} - 68 q^{56} - 31 q^{57} - 14 q^{58} - 96 q^{59} - 74 q^{60} - 21 q^{61} + 4 q^{62} - 60 q^{63} + 132 q^{64} - 15 q^{65} + 71 q^{66} - 44 q^{67} - 166 q^{68} - 72 q^{69} - 9 q^{70} - 55 q^{71} - 126 q^{72} - 27 q^{73} + 11 q^{74} - 39 q^{75} - 4 q^{76} - 104 q^{77} - 47 q^{78} - 49 q^{79} - 82 q^{80} + 55 q^{81} + 20 q^{82} - 52 q^{83} - 29 q^{84} + 3 q^{85} - 32 q^{86} - 113 q^{87} + 14 q^{88} - 68 q^{89} - 39 q^{90} - 30 q^{91} - 179 q^{92} - 53 q^{93} - 33 q^{94} - 86 q^{95} + 33 q^{96} - 57 q^{97} - 116 q^{98} + q^{99}+O(q^{100}) \) 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9 - 13 * q^10 - 5 * q^11 - 40 * q^12 - 18 * q^13 - 42 * q^14 - 49 * q^15 + 83 * q^16 - 62 * q^17 - 33 * q^18 - 25 * q^19 - 39 * q^20 - 15 * q^21 - 31 * q^22 - 94 * q^23 - 39 * q^24 + 71 * q^25 - 35 * q^26 - 47 * q^27 - 13 * q^28 - 17 * q^29 + 15 * q^30 - 37 * q^31 - 105 * q^32 - 60 * q^33 + 9 * q^34 - 60 * q^35 + 43 * q^36 - 79 * q^37 - 80 * q^38 - 41 * q^39 - 64 * q^40 - 37 * q^41 - 30 * q^42 - 20 * q^43 - 14 * q^44 - 8 * q^45 + 61 * q^46 - 148 * q^47 - 39 * q^48 + 82 * q^49 - 90 * q^50 - 45 * q^51 - 27 * q^52 - 70 * q^53 - 41 * q^54 - 105 * q^55 - 68 * q^56 - 31 * q^57 - 14 * q^58 - 96 * q^59 - 74 * q^60 - 21 * q^61 + 4 * q^62 - 60 * q^63 + 132 * q^64 - 15 * q^65 + 71 * q^66 - 44 * q^67 - 166 * q^68 - 72 * q^69 - 9 * q^70 - 55 * q^71 - 126 * q^72 - 27 * q^73 + 11 * q^74 - 39 * q^75 - 4 * q^76 - 104 * q^77 - 47 * q^78 - 49 * q^79 - 82 * q^80 + 55 * q^81 + 20 * q^82 - 52 * q^83 - 29 * q^84 + 3 * q^85 - 32 * q^86 - 113 * q^87 + 14 * q^88 - 68 * q^89 - 39 * q^90 - 30 * q^91 - 179 * q^92 - 53 * q^93 - 33 * q^94 - 86 * q^95 + 33 * q^96 - 57 * q^97 - 116 * q^98 + 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 $

$2$	0.349116	0.246863	0.123431	−	0.992353i	$-0.460610\pi$
$2$	0.349116	0.246863	0.123431	+	0.992353i	$0.460610\pi$
$3$	1.27272	0.734806	0.367403	−	0.930062i	$-0.380247\pi$
$3$	1.27272	0.734806	0.367403	+	0.930062i	$0.380247\pi$
$4$	−1.87812	−0.939059
$5$	−1.11462	−0.498475	−0.249238	−	0.968442i	$-0.580180\pi$
$5$	−1.11462	−0.498475	−0.249238	+	0.968442i	$0.580180\pi$
$6$	0.444328	0.181396
$7$	−0.249605	−0.0943420	−0.0471710	−	0.998887i	$-0.515021\pi$
$7$	−0.249605	−0.0943420	−0.0471710	+	0.998887i	$0.515021\pi$
$8$	−1.35391	−0.478681
$9$	−1.38018	−0.460060
$10$	−0.389134	−0.123055
$11$	3.01523	0.909126	0.454563	−	0.890714i	$-0.349795\pi$
$11$	3.01523	0.909126	0.454563	+	0.890714i	$0.349795\pi$
$12$	−2.39032	−0.690026
$13$	3.37064	0.934848	0.467424	−	0.884033i	$-0.345182\pi$
$13$	3.37064	0.934848	0.467424	+	0.884033i	$0.345182\pi$
$14$	−0.0871413	−0.0232895
$15$	−1.41861	−0.366283
$16$	3.28356	0.820890
$17$	2.58204	0.626237	0.313119	−	0.949714i	$-0.398626\pi$
$17$	2.58204	0.626237	0.313119	+	0.949714i	$0.398626\pi$
$18$	−0.481843	−0.113571
$19$	−8.04863	−1.84648	−0.923241	−	0.384222i	$-0.874470\pi$
$19$	−8.04863	−1.84648	−0.923241	+	0.384222i	$0.874470\pi$
$20$	2.09340	0.468098
$21$	−0.317678	−0.0693231
$22$	1.05267	0.224429
$23$	3.45558	0.720538	0.360269	−	0.932848i	$-0.382685\pi$
$23$	3.45558	0.720538	0.360269	+	0.932848i	$0.382685\pi$
$24$	−1.72316	−0.351738
$25$	−3.75761	−0.751522
$26$	1.17675	0.230779
$27$	−5.57475	−1.07286
$28$	0.468788	0.0885927
$29$	2.16612	0.402239	0.201119	−	0.979567i	$-0.435542\pi$
$29$	2.16612	0.402239	0.201119	+	0.979567i	$0.435542\pi$
$30$	−0.495259	−0.0904215
$31$	−2.72320	−0.489101	−0.244551	−	0.969637i	$-0.578640\pi$
$31$	−2.72320	−0.489101	−0.244551	+	0.969637i	$0.578640\pi$
$32$	3.85417	0.681328
$33$	3.83755	0.668032
$34$	0.901433	0.154595
$35$	0.278216	0.0470271
$36$	2.59214	0.432023
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	−2.80991	−0.455827
$39$	4.28989	0.686933
$40$	1.50911	0.238611
$41$	9.05995	1.41493	0.707463	−	0.706751i	$-0.249840\pi$
$41$	9.05995	1.41493	0.707463	+	0.706751i	$0.249840\pi$
$42$	−0.110907	−0.0171133
$43$	−9.75852	−1.48816	−0.744080	−	0.668090i	$-0.767112\pi$
$43$	−9.75852	−1.48816	−0.744080	+	0.668090i	$0.767112\pi$
$44$	−5.66296	−0.853723
$45$	1.53838	0.229328
$46$	1.20640	0.177874
$47$	2.31418	0.337558	0.168779	−	0.985654i	$-0.446018\pi$
$47$	2.31418	0.337558	0.168779	+	0.985654i	$0.446018\pi$
$48$	4.17906	0.603196
$49$	−6.93770	−0.991100
$50$	−1.31184	−0.185523
$51$	3.28622	0.460163
$52$	−6.33047	−0.877878
$53$	−2.67954	−0.368063	−0.184031	−	0.982920i	$-0.558915\pi$
$53$	−2.67954	−0.368063	−0.184031	+	0.982920i	$0.558915\pi$
$54$	−1.94624	−0.264849
$55$	−3.36085	−0.453177
$56$	0.337944	0.0451597
$57$	−10.2437	−1.35681
$58$	0.756229	0.0992977
$59$	1.02880	0.133938	0.0669690	−	0.997755i	$-0.478667\pi$
$59$	1.02880	0.133938	0.0669690	+	0.997755i	$0.478667\pi$
$60$	2.66431	0.343961
$61$	14.4043	1.84428	0.922141	−	0.386855i	$-0.126439\pi$
$61$	14.4043	1.84428	0.922141	+	0.386855i	$0.126439\pi$
$62$	−0.950714	−0.120741
$63$	0.344500	0.0434029
$64$	−5.22157	−0.652696
$65$	−3.75700	−0.465999
$66$	1.33975	0.164912
$67$	−15.2214	−1.85959	−0.929795	−	0.368079i	$-0.880016\pi$
$67$	−15.2214	−1.85959	−0.929795	+	0.368079i	$0.880016\pi$
$68$	−4.84938	−0.588074
$69$	4.39799	0.529456
$70$	0.0971299	0.0116092
$71$	4.92479	0.584465	0.292233	−	0.956347i	$-0.405602\pi$
$71$	4.92479	0.584465	0.292233	+	0.956347i	$0.405602\pi$
$72$	1.86864	0.220222
$73$	−14.1816	−1.65983	−0.829916	−	0.557888i	$-0.811612\pi$
$73$	−14.1816	−1.65983	−0.829916	+	0.557888i	$0.811612\pi$
$74$	−0.349116	−0.0405840
$75$	−4.78240	−0.552223
$76$	15.1163	1.73395
$77$	−0.752618	−0.0857688
$78$	1.49767	0.169578
$79$	−3.27815	−0.368821	−0.184410	−	0.982849i	$-0.559038\pi$
$79$	−3.27815	−0.368821	−0.184410	+	0.982849i	$0.559038\pi$
$80$	−3.65994	−0.409194
$81$	−2.95457	−0.328286
$82$	3.16298	0.349292
$83$	−5.04712	−0.553993	−0.276997	−	0.960871i	$-0.589339\pi$
$83$	−5.04712	−0.553993	−0.276997	+	0.960871i	$0.589339\pi$
$84$	0.596637	0.0650985
$85$	−2.87801	−0.312164
$86$	−3.40686	−0.367371
$87$	2.75687	0.295568
$88$	−4.08236	−0.435182
$89$	17.9292	1.90049	0.950245	−	0.311503i	$-0.100833\pi$
$89$	17.9292	1.90049	0.950245	+	0.311503i	$0.100833\pi$
$90$	0.537074	0.0566126
$91$	−0.841331	−0.0881954
$92$	−6.48999	−0.676628
$93$	−3.46588	−0.359395
$94$	0.807920	0.0833305
$95$	8.97120	0.920425
$96$	4.90529	0.500644
$97$	−2.22635	−0.226052	−0.113026	−	0.993592i	$-0.536054\pi$
$97$	−2.22635	−0.226052	−0.113026	+	0.993592i	$0.536054\pi$
$98$	−2.42206	−0.244665
$99$	−4.16156	−0.418252
$100$	7.05724	0.705724
$101$	13.6766	1.36087	0.680437	−	0.732807i	$-0.261790\pi$
$101$	13.6766	1.36087	0.680437	+	0.732807i	$0.261790\pi$
$102$	1.14727	0.113597
$103$	−8.34814	−0.822567	−0.411283	−	0.911508i	$-0.634919\pi$
$103$	−8.34814	−0.822567	−0.411283	+	0.911508i	$0.634919\pi$
$104$	−4.56356	−0.447494
$105$	0.354092	0.0345558
$106$	−0.935471	−0.0908609
$107$	−19.9396	−1.92763	−0.963817	−	0.266566i	$-0.914111\pi$
$107$	−19.9396	−1.92763	−0.963817	+	0.266566i	$0.914111\pi$
$108$	10.4700	1.00748
$109$	−1.00000	−0.0957826
$109$	−1.00000	−0.0957826
$110$	−1.17333	−0.111872
$111$	−1.27272	−0.120801
$112$	−0.819595	−0.0774444
$113$	−16.7915	−1.57961	−0.789805	−	0.613358i	$-0.789818\pi$
$113$	−16.7915	−1.57961	−0.789805	+	0.613358i	$0.789818\pi$
$114$	−3.57623	−0.334945
$115$	−3.85168	−0.359171
$116$	−4.06823	−0.377726
$117$	−4.65209	−0.430086
$118$	0.359170	0.0330643
$119$	−0.644492	−0.0590804
$120$	1.92067	0.175333
$121$	−1.90838	−0.173489
$122$	5.02878	0.455284
$123$	11.5308	1.03970
$124$	5.11449	0.459295
$125$	9.76145	0.873091
$126$	0.120271	0.0107146
$127$	−0.231464	−0.0205391	−0.0102695	−	0.999947i	$-0.503269\pi$
$127$	−0.231464	−0.0205391	−0.0102695	+	0.999947i	$0.503269\pi$
$128$	−9.53128	−0.842454
$129$	−12.4199	−1.09351
$130$	−1.31163	−0.115038
$131$	−10.3468	−0.904003	−0.452001	−	0.892017i	$-0.649290\pi$
$131$	−10.3468	−0.904003	−0.452001	+	0.892017i	$0.649290\pi$
$132$	−7.20737	−0.627321
$133$	2.00898	0.174201
$134$	−5.31404	−0.459063
$135$	6.21375	0.534795
$136$	−3.49586	−0.299768
$137$	−7.29443	−0.623205	−0.311603	−	0.950213i	$-0.600866\pi$
$137$	−7.29443	−0.623205	−0.311603	+	0.950213i	$0.600866\pi$
$138$	1.53541	0.130703
$139$	−12.7594	−1.08224	−0.541119	−	0.840946i	$-0.681999\pi$
$139$	−12.7594	−1.08224	−0.541119	+	0.840946i	$0.681999\pi$
$140$	−0.522523	−0.0441612
$141$	2.94531	0.248040
$142$	1.71933	0.144283
$143$	10.1633	0.849895
$144$	−4.53190	−0.377659
$145$	−2.41441	−0.200506
$146$	−4.95103	−0.409751
$147$	−8.82976	−0.728266
$148$	1.87812	0.154380
$149$	−7.34713	−0.601901	−0.300950	−	0.953640i	$-0.597304\pi$
$149$	−7.34713	−0.601901	−0.300950	+	0.953640i	$0.597304\pi$
$150$	−1.66961	−0.136323
$151$	−10.6130	−0.863676	−0.431838	−	0.901951i	$-0.642135\pi$
$151$	−10.6130	−0.863676	−0.431838	+	0.901951i	$0.642135\pi$
$152$	10.8971	0.883876
$153$	−3.56368	−0.288106
$154$	−0.262751	−0.0211731
$155$	3.03535	0.243805
$156$	−8.05692	−0.645070
$157$	−5.63196	−0.449479	−0.224740	−	0.974419i	$-0.572153\pi$
$157$	−5.63196	−0.449479	−0.224740	+	0.974419i	$0.572153\pi$
$158$	−1.14446	−0.0910480
$159$	−3.41031	−0.270455
$160$	−4.29596	−0.339625
$161$	−0.862532	−0.0679770
$162$	−1.03149	−0.0810414
$163$	−9.82220	−0.769334	−0.384667	−	0.923055i	$-0.625684\pi$
$163$	−9.82220	−0.769334	−0.384667	+	0.923055i	$0.625684\pi$
$164$	−17.0156	−1.32870
$165$	−4.27743	−0.332997
$166$	−1.76203	−0.136760
$167$	−21.4164	−1.65725	−0.828625	−	0.559803i	$-0.810877\pi$
$167$	−21.4164	−1.65725	−0.828625	+	0.559803i	$0.810877\pi$
$168$	0.430109	0.0331836
$169$	−1.63876	−0.126058
$170$	−1.00476	−0.0770615
$171$	11.1085	0.849491
$172$	18.3277	1.39747
$173$	−0.479149	−0.0364290	−0.0182145	−	0.999834i	$-0.505798\pi$
$173$	−0.479149	−0.0364290	−0.0182145	+	0.999834i	$0.505798\pi$
$174$	0.962469	0.0729646
$175$	0.937920	0.0709001
$176$	9.90070	0.746293
$177$	1.30937	0.0984185
$178$	6.25937	0.469160
$179$	−4.66477	−0.348661	−0.174331	−	0.984687i	$-0.555776\pi$
$179$	−4.66477	−0.348661	−0.174331	+	0.984687i	$0.555776\pi$
$180$	−2.88926	−0.215353
$181$	−6.42238	−0.477372	−0.238686	−	0.971097i	$-0.576717\pi$
$181$	−6.42238	−0.477372	−0.238686	+	0.971097i	$0.576717\pi$
$182$	−0.293722	−0.0217721
$183$	18.3327	1.35519
$184$	−4.67856	−0.344908
$185$	1.11462	0.0819488
$186$	−1.20999	−0.0887211
$187$	7.78545	0.569329
$188$	−4.34631	−0.316987
$189$	1.39149	0.101216
$190$	3.13199	0.227219
$191$	−21.8716	−1.58257	−0.791286	−	0.611446i	$-0.790588\pi$
$191$	−21.8716	−1.58257	−0.791286	+	0.611446i	$0.790588\pi$
$192$	−6.64561	−0.479605
$193$	−17.8379	−1.28400	−0.642001	−	0.766704i	$-0.721896\pi$
$193$	−17.8379	−1.28400	−0.642001	+	0.766704i	$0.721896\pi$
$194$	−0.777255	−0.0558037
$195$	−4.78162	−0.342419
$196$	13.0298	0.930701
$197$	−2.28754	−0.162981	−0.0814903	−	0.996674i	$-0.525968\pi$
$197$	−2.28754	−0.162981	−0.0814903	+	0.996674i	$0.525968\pi$
$198$	−1.45287	−0.103251
$199$	−0.682240	−0.0483627	−0.0241814	−	0.999708i	$-0.507698\pi$
$199$	−0.682240	−0.0483627	−0.0241814	+	0.999708i	$0.507698\pi$
$200$	5.08748	0.359740
$201$	−19.3726	−1.36644
$202$	4.77473	0.335949
$203$	−0.540676	−0.0379480
$204$	−6.17191	−0.432120
$205$	−10.0984	−0.705305
$206$	−2.91447	−0.203061
$207$	−4.76932	−0.331491
$208$	11.0677	0.767408
$209$	−24.2685	−1.67868
$210$	0.123619	0.00853054
$211$	24.6398	1.69627	0.848137	−	0.529776i	$-0.177724\pi$
$211$	24.6398	1.69627	0.848137	+	0.529776i	$0.177724\pi$
$212$	5.03249	0.345633
$213$	6.26789	0.429469
$214$	−6.96124	−0.475861
$215$	10.8771	0.741811
$216$	7.54773	0.513558
$217$	0.679725	0.0461428
$218$	−0.349116	−0.0236451
$219$	−18.0493	−1.21966
$220$	6.31207	0.425560
$221$	8.70314	0.585437
$222$	−0.444328	−0.0298213
$223$	2.70095	0.180869	0.0904344	−	0.995902i	$-0.471174\pi$
$223$	2.70095	0.180869	0.0904344	+	0.995902i	$0.471174\pi$
$224$	−0.962023	−0.0642778
$225$	5.18618	0.345745
$226$	−5.86218	−0.389946
$227$	15.7020	1.04218	0.521088	−	0.853503i	$-0.325526\pi$
$227$	15.7020	1.04218	0.521088	+	0.853503i	$0.325526\pi$
$228$	19.2388	1.27412
$229$	−0.709163	−0.0468628	−0.0234314	−	0.999725i	$-0.507459\pi$
$229$	−0.709163	−0.0468628	−0.0234314	+	0.999725i	$0.507459\pi$
$230$	−1.34468	−0.0886658
$231$	−0.957873	−0.0630234
$232$	−2.93275	−0.192544
$233$	5.92900	0.388421	0.194211	−	0.980960i	$-0.437785\pi$
$233$	5.92900	0.388421	0.194211	+	0.980960i	$0.437785\pi$
$234$	−1.62412	−0.106172
$235$	−2.57945	−0.168265
$236$	−1.93220	−0.125776
$237$	−4.17217	−0.271012
$238$	−0.225003	−0.0145847
$239$	1.28803	0.0833160	0.0416580	−	0.999132i	$-0.486736\pi$
$239$	1.28803	0.0833160	0.0416580	+	0.999132i	$0.486736\pi$
$240$	−4.65808	−0.300678
$241$	5.97088	0.384618	0.192309	−	0.981334i	$-0.438402\pi$
$241$	5.97088	0.384618	0.192309	+	0.981334i	$0.438402\pi$
$242$	−0.666247	−0.0428280
$243$	12.9639	0.831635
$244$	−27.0530	−1.73189
$245$	7.73293	0.494039
$246$	4.02559	0.256662
$247$	−27.1290	−1.72618
$248$	3.68698	0.234123
$249$	−6.42358	−0.407078
$250$	3.40788	0.215533
$251$	−15.2171	−0.960498	−0.480249	−	0.877132i	$-0.659454\pi$
$251$	−15.2171	−0.960498	−0.480249	+	0.877132i	$0.659454\pi$
$252$	−0.647012	−0.0407579
$253$	10.4194	0.655061
$254$	−0.0808077	−0.00507033
$255$	−3.66290	−0.229380
$256$	7.11561	0.444726
$257$	25.7373	1.60545	0.802724	−	0.596351i	$-0.203383\pi$
$257$	25.7373	1.60545	0.802724	+	0.596351i	$0.203383\pi$
$258$	−4.33598	−0.269947
$259$	0.249605	0.0155097
$260$	7.05609	0.437600
$261$	−2.98964	−0.185054
$262$	−3.61223	−0.223164
$263$	−21.0307	−1.29681	−0.648406	−	0.761295i	$-0.724564\pi$
$263$	−21.0307	−1.29681	−0.648406	+	0.761295i	$0.724564\pi$
$264$	−5.19572	−0.319774
$265$	2.98668	0.183470
$266$	0.701368	0.0430036
$267$	22.8189	1.39649
$268$	28.5876	1.74626
$269$	6.36255	0.387931	0.193966	−	0.981008i	$-0.437865\pi$
$269$	6.36255	0.387931	0.193966	+	0.981008i	$0.437865\pi$
$270$	2.16932	0.132021
$271$	28.2830	1.71807	0.859034	−	0.511919i	$-0.171065\pi$
$271$	28.2830	1.71807	0.859034	+	0.511919i	$0.171065\pi$
$272$	8.47829	0.514072
$273$	−1.07078	−0.0648066
$274$	−2.54660	−0.153846
$275$	−11.3301	−0.683229
$276$	−8.25995	−0.497191
$277$	26.6445	1.60091	0.800456	−	0.599392i	$-0.204591\pi$
$277$	26.6445	1.60091	0.800456	+	0.599392i	$0.204591\pi$
$278$	−4.45452	−0.267164
$279$	3.75850	0.225016
$280$	−0.376681	−0.0225110
$281$	1.95172	0.116430	0.0582149	−	0.998304i	$-0.481459\pi$
$281$	1.95172	0.116430	0.0582149	+	0.998304i	$0.481459\pi$
$282$	1.02826	0.0612318
$283$	6.65335	0.395501	0.197750	−	0.980252i	$-0.436636\pi$
$283$	6.65335	0.395501	0.197750	+	0.980252i	$0.436636\pi$
$284$	−9.24934	−0.548847
$285$	11.4178	0.676334
$286$	3.54816	0.209807
$287$	−2.26141	−0.133487
$288$	−5.31945	−0.313452
$289$	−10.3331	−0.607827
$290$	−0.842911	−0.0494975
$291$	−2.83352	−0.166104
$292$	26.6347	1.55868
$293$	−12.3417	−0.721009	−0.360504	−	0.932757i	$-0.617395\pi$
$293$	−12.3417	−0.721009	−0.360504	+	0.932757i	$0.617395\pi$
$294$	−3.08261	−0.179782
$295$	−1.14672	−0.0667648
$296$	1.35391	0.0786947
$297$	−16.8092	−0.975366
$298$	−2.56500	−0.148587
$299$	11.6475	0.673594
$300$	8.98190	0.518570
$301$	2.43578	0.140396
$302$	−3.70518	−0.213209
$303$	17.4065	0.999979
$304$	−26.4282	−1.51576
$305$	−16.0554	−0.919328
$306$	−1.24414	−0.0711227
$307$	−8.00487	−0.456862	−0.228431	−	0.973560i	$-0.573360\pi$
$307$	−8.00487	−0.456862	−0.228431	+	0.973560i	$0.573360\pi$
$308$	1.41351	0.0805419
$309$	−10.6249	−0.604427
$310$	1.05969	0.0601863
$311$	−5.93464	−0.336522	−0.168261	−	0.985742i	$-0.553815\pi$
$311$	−5.93464	−0.336522	−0.168261	+	0.985742i	$0.553815\pi$
$312$	−5.80815	−0.328822
$313$	1.77647	0.100412	0.0502060	−	0.998739i	$-0.484012\pi$
$313$	1.77647	0.100412	0.0502060	+	0.998739i	$0.484012\pi$
$314$	−1.96621	−0.110960
$315$	−0.383988	−0.0216353
$316$	6.15675	0.346344
$317$	14.2173	0.798525	0.399263	−	0.916837i	$-0.369266\pi$
$317$	14.2173	0.798525	0.399263	+	0.916837i	$0.369266\pi$
$318$	−1.19059	−0.0667652
$319$	6.53136	0.365686
$320$	5.82009	0.325353
$321$	−25.3776	−1.41644
$322$	−0.301124	−0.0167810
$323$	−20.7819	−1.15634
$324$	5.54903	0.308280
$325$	−12.6656	−0.702560
$326$	−3.42909	−0.189920
$327$	−1.27272	−0.0703817
$328$	−12.2664	−0.677298
$329$	−0.577633	−0.0318459
$330$	−1.49332	−0.0822046
$331$	−1.22009	−0.0670624	−0.0335312	−	0.999438i	$-0.510675\pi$
$331$	−1.22009	−0.0670624	−0.0335312	+	0.999438i	$0.510675\pi$
$332$	9.47908	0.520232
$333$	1.38018	0.0756333
$334$	−7.47682	−0.409113
$335$	16.9661	0.926959
$336$	−1.04312	−0.0569067
$337$	7.00266	0.381459	0.190730	−	0.981643i	$-0.438915\pi$
$337$	7.00266	0.381459	0.190730	+	0.981643i	$0.438915\pi$
$338$	−0.572118	−0.0311191
$339$	−21.3709	−1.16071
$340$	5.40524	0.293140
$341$	−8.21108	−0.444655
$342$	3.87817	0.209708
$343$	3.47892	0.187844
$344$	13.2122	0.712354
$345$	−4.90211	−0.263921
$346$	−0.167279	−0.00899296
$347$	1.47715	0.0792977	0.0396489	−	0.999214i	$-0.487376\pi$
$347$	1.47715	0.0792977	0.0396489	+	0.999214i	$0.487376\pi$
$348$	−5.17773	−0.277556
$349$	−8.71368	−0.466433	−0.233216	−	0.972425i	$-0.574925\pi$
$349$	−8.71368	−0.466433	−0.233216	+	0.972425i	$0.574925\pi$
$350$	0.327443	0.0175026
$351$	−18.7905	−1.00296
$352$	11.6212	0.619413
$353$	28.1251	1.49695	0.748473	−	0.663166i	$-0.230787\pi$
$353$	28.1251	1.49695	0.748473	+	0.663166i	$0.230787\pi$
$354$	0.457123	0.0242958
$355$	−5.48929	−0.291341
$356$	−33.6731	−1.78467
$357$	−0.820259	−0.0434127
$358$	−1.62855	−0.0860713
$359$	4.47502	0.236183	0.118091	−	0.993003i	$-0.462322\pi$
$359$	4.47502	0.236183	0.118091	+	0.993003i	$0.462322\pi$
$360$	−2.08284	−0.109775
$361$	45.7804	2.40949
$362$	−2.24216	−0.117845
$363$	−2.42884	−0.127481
$364$	1.58012	0.0828207
$365$	15.8072	0.827386
$366$	6.40023	0.334546
$367$	20.1739	1.05307	0.526535	−	0.850154i	$-0.323491\pi$
$367$	20.1739	1.05307	0.526535	+	0.850154i	$0.323491\pi$
$368$	11.3466	0.591483
$369$	−12.5043	−0.650950
$370$	0.389134	0.0202301
$371$	0.668827	0.0347238
$372$	6.50932	0.337493
$373$	21.2316	1.09933	0.549665	−	0.835385i	$-0.314755\pi$
$373$	21.2316	1.09933	0.549665	+	0.835385i	$0.314755\pi$
$374$	2.71803	0.140546
$375$	12.4236	0.641553
$376$	−3.13321	−0.161583
$377$	7.30123	0.376032
$378$	0.485791	0.0249864
$379$	15.0699	0.774091	0.387045	−	0.922061i	$-0.373496\pi$
$379$	15.0699	0.774091	0.387045	+	0.922061i	$0.373496\pi$
$380$	−16.8490	−0.864334
$381$	−0.294589	−0.0150922
$382$	−7.63573	−0.390678
$383$	−26.5327	−1.35576	−0.677878	−	0.735174i	$-0.737100\pi$
$383$	−26.5327	−1.35576	−0.677878	+	0.735174i	$0.737100\pi$
$384$	−12.1307	−0.619041
$385$	0.838886	0.0427536
$386$	−6.22751	−0.316972
$387$	13.4685	0.684642
$388$	4.18135	0.212276
$389$	32.1063	1.62786	0.813928	−	0.580966i	$-0.197325\pi$
$389$	32.1063	1.62786	0.813928	+	0.580966i	$0.197325\pi$
$390$	−1.66934	−0.0845304
$391$	8.92245	0.451228
$392$	9.39305	0.474421
$393$	−13.1686	−0.664267
$394$	−0.798619	−0.0402338
$395$	3.65391	0.183848
$396$	7.81590	0.392764
$397$	8.24639	0.413874	0.206937	−	0.978354i	$-0.433650\pi$
$397$	8.24639	0.413874	0.206937	+	0.978354i	$0.433650\pi$
$398$	−0.238181	−0.0119390
$399$	2.55687	0.128004
$400$	−12.3384	−0.616918
$401$	−11.3759	−0.568084	−0.284042	−	0.958812i	$-0.591676\pi$
$401$	−11.3759	−0.568084	−0.284042	+	0.958812i	$0.591676\pi$
$402$	−6.76329	−0.337322
$403$	−9.17894	−0.457235
$404$	−25.6863	−1.27794
$405$	3.29324	0.163642
$406$	−0.188759	−0.00936794
$407$	−3.01523	−0.149459
$408$	−4.44926	−0.220271
$409$	−14.1566	−0.699996	−0.349998	−	0.936750i	$-0.613818\pi$
$409$	−14.1566	−0.699996	−0.349998	+	0.936750i	$0.613818\pi$
$410$	−3.52553	−0.174114
$411$	−9.28378	−0.457935
$412$	15.6788	0.772439
$413$	−0.256793	−0.0126360
$414$	−1.66505	−0.0818326
$415$	5.62564	0.276152
$416$	12.9910	0.636939
$417$	−16.2392	−0.795236
$418$	−8.47252	−0.414404
$419$	19.3555	0.945579	0.472790	−	0.881175i	$-0.343247\pi$
$419$	19.3555	0.945579	0.472790	+	0.881175i	$0.343247\pi$
$420$	−0.665026	−0.0324500
$421$	−40.0849	−1.95362	−0.976808	−	0.214117i	$-0.931313\pi$
$421$	−40.0849	−1.95362	−0.976808	+	0.214117i	$0.931313\pi$
$422$	8.60216	0.418747
$423$	−3.19399	−0.155297
$424$	3.62787	0.176185
$425$	−9.70231	−0.470631
$426$	2.18822	0.106020
$427$	−3.59539	−0.173993
$428$	37.4489	1.81016
$429$	12.9350	0.624509
$430$	3.79737	0.183125
$431$	7.35728	0.354388	0.177194	−	0.984176i	$-0.443298\pi$
$431$	7.35728	0.354388	0.177194	+	0.984176i	$0.443298\pi$
$432$	−18.3050	−0.880701
$433$	27.2556	1.30982	0.654911	−	0.755706i	$-0.272706\pi$
$433$	27.2556	1.30982	0.654911	+	0.755706i	$0.272706\pi$
$434$	0.237303	0.0113909
$435$	−3.07288	−0.147333
$436$	1.87812	0.0899455
$437$	−27.8127	−1.33046
$438$	−6.30129	−0.301087
$439$	27.6184	1.31816	0.659078	−	0.752075i	$-0.270947\pi$
$439$	27.6184	1.31816	0.659078	+	0.752075i	$0.270947\pi$
$440$	4.55030	0.216927
$441$	9.57526	0.455965
$442$	3.03841	0.144522
$443$	33.6698	1.59970	0.799851	−	0.600199i	$-0.204912\pi$
$443$	33.6698	1.59970	0.799851	+	0.600199i	$0.204912\pi$
$444$	2.39032	0.113440
$445$	−19.9843	−0.947347
$446$	0.942944	0.0446497
$447$	−9.35086	−0.442280
$448$	1.30333	0.0615766
$449$	12.1226	0.572101	0.286050	−	0.958215i	$-0.407658\pi$
$449$	12.1226	0.572101	0.286050	+	0.958215i	$0.407658\pi$
$450$	1.81058	0.0853515
$451$	27.3178	1.28635
$452$	31.5364	1.48335
$453$	−13.5074	−0.634634
$454$	5.48182	0.257274
$455$	0.937768	0.0439632
$456$	13.8690	0.649477
$457$	−31.3384	−1.46595	−0.732974	−	0.680256i	$-0.761868\pi$
$457$	−31.3384	−1.46595	−0.732974	+	0.680256i	$0.761868\pi$
$458$	−0.247580	−0.0115687
$459$	−14.3942	−0.671865
$460$	7.23390	0.337282
$461$	1.75012	0.0815112	0.0407556	−	0.999169i	$-0.487023\pi$
$461$	1.75012	0.0815112	0.0407556	+	0.999169i	$0.487023\pi$
$462$	−0.334409	−0.0155581
$463$	−17.9646	−0.834885	−0.417442	−	0.908703i	$-0.637073\pi$
$463$	−17.9646	−0.834885	−0.417442	+	0.908703i	$0.637073\pi$
$464$	7.11260	0.330194
$465$	3.86315	0.179149
$466$	2.06991	0.0958867
$467$	−19.6192	−0.907868	−0.453934	−	0.891035i	$-0.649980\pi$
$467$	−19.6192	−0.907868	−0.453934	+	0.891035i	$0.649980\pi$
$468$	8.73717	0.403876
$469$	3.79934	0.175437
$470$	−0.900527	−0.0415382
$471$	−7.16792	−0.330280
$472$	−1.39290	−0.0641136
$473$	−29.4242	−1.35293
$474$	−1.45657	−0.0669026
$475$	30.2436	1.38767
$476$	1.21043	0.0554800
$477$	3.69824	0.169331
$478$	0.449674	0.0205676
$479$	−0.909262	−0.0415453	−0.0207726	−	0.999784i	$-0.506613\pi$
$479$	−0.909262	−0.0415453	−0.0207726	+	0.999784i	$0.506613\pi$
$480$	−5.46756	−0.249559
$481$	−3.37064	−0.153688
$482$	2.08453	0.0949479
$483$	−1.09776	−0.0499499
$484$	3.58416	0.162917
$485$	2.48154	0.112681
$486$	4.52591	0.205299
$487$	20.5607	0.931695	0.465848	−	0.884865i	$-0.345749\pi$
$487$	20.5607	0.931695	0.465848	+	0.884865i	$0.345749\pi$
$488$	−19.5022	−0.882822
$489$	−12.5009	−0.565312
$490$	2.69969	0.121960
$491$	−3.28616	−0.148302	−0.0741511	−	0.997247i	$-0.523625\pi$
$491$	−3.28616	−0.148302	−0.0741511	+	0.997247i	$0.523625\pi$
$492$	−21.6562	−0.976336
$493$	5.59302	0.251897
$494$	−9.47120	−0.426129
$495$	4.63857	0.208488
$496$	−8.94180	−0.401498
$497$	−1.22925	−0.0551396
$498$	−2.24258	−0.100492
$499$	2.08985	0.0935545	0.0467772	−	0.998905i	$-0.485105\pi$
$499$	2.08985	0.0935545	0.0467772	+	0.998905i	$0.485105\pi$
$500$	−18.3332	−0.819883
$501$	−27.2571	−1.21776
$502$	−5.31256	−0.237111
$503$	7.63592	0.340469	0.170235	−	0.985404i	$-0.445547\pi$
$503$	7.63592	0.340469	0.170235	+	0.985404i	$0.445547\pi$
$504$	−0.466424	−0.0207762
$505$	−15.2443	−0.678362
$506$	3.63757	0.161710
$507$	−2.08569	−0.0926286
$508$	0.434716	0.0192874
$509$	−27.8826	−1.23587	−0.617937	−	0.786227i	$-0.712031\pi$
$509$	−27.8826	−1.23587	−0.617937	+	0.786227i	$0.712031\pi$
$510$	−1.27878	−0.0566253
$511$	3.53981	0.156592
$512$	21.5467	0.952240
$513$	44.8691	1.98102
$514$	8.98530	0.396325
$515$	9.30504	0.410029
$516$	23.3260	1.02687
$517$	6.97780	0.306883
$518$	0.0871413	0.00382877
$519$	−0.609823	−0.0267683
$520$	5.08666	0.223065
$521$	10.4429	0.457513	0.228757	−	0.973484i	$-0.426534\pi$
$521$	10.4429	0.457513	0.228757	+	0.973484i	$0.426534\pi$
$522$	−1.04373	−0.0456829
$523$	−26.9887	−1.18013	−0.590066	−	0.807355i	$-0.700898\pi$
$523$	−26.9887	−1.18013	−0.590066	+	0.807355i	$0.700898\pi$
$524$	19.4325	0.848912
$525$	1.19371	0.0520978
$526$	−7.34218	−0.320134
$527$	−7.03142	−0.306293
$528$	12.6008	0.548381
$529$	−11.0590	−0.480824
$530$	1.04270	0.0452919
$531$	−1.41992	−0.0616195
$532$	−3.77310	−0.163585
$533$	30.5378	1.32274
$534$	7.96644	0.344742
$535$	22.2252	0.960878
$536$	20.6085	0.890150
$537$	−5.93695	−0.256198
$538$	2.22127	0.0957657
$539$	−20.9188	−0.901035
$540$	−11.6702	−0.502204
$541$	−19.3275	−0.830953	−0.415476	−	0.909604i	$-0.636385\pi$
$541$	−19.3275	−0.830953	−0.415476	+	0.909604i	$0.636385\pi$
$542$	9.87405	0.424127
$543$	−8.17391	−0.350776
$544$	9.95164	0.426673
$545$	1.11462	0.0477453
$546$	−0.373827	−0.0159983
$547$	26.6753	1.14055	0.570277	−	0.821452i	$-0.306836\pi$
$547$	26.6753	1.14055	0.570277	+	0.821452i	$0.306836\pi$
$548$	13.6998	0.585226
$549$	−19.8805	−0.848479
$550$	−3.95551	−0.168664
$551$	−17.4343	−0.742727
$552$	−5.95451	−0.253441
$553$	0.818244	0.0347953
$554$	9.30202	0.395205
$555$	1.41861	0.0602165
$556$	23.9637	1.01629
$557$	20.3964	0.864224	0.432112	−	0.901820i	$-0.357768\pi$
$557$	20.3964	0.864224	0.432112	+	0.901820i	$0.357768\pi$
$558$	1.31215	0.0555479
$559$	−32.8925	−1.39120
$560$	0.913540	0.0386041
$561$	9.90872	0.418346
$562$	0.681377	0.0287421
$563$	32.9328	1.38795	0.693976	−	0.719998i	$-0.255857\pi$
$563$	32.9328	1.38795	0.693976	+	0.719998i	$0.255857\pi$
$564$	−5.53164	−0.232924
$565$	18.7162	0.787396
$566$	2.32279	0.0976343
$567$	0.737477	0.0309711
$568$	−6.66775	−0.279772
$569$	−19.3964	−0.813141	−0.406570	−	0.913620i	$-0.633275\pi$
$569$	−19.3964	−0.813141	−0.406570	+	0.913620i	$0.633275\pi$
$570$	3.98615	0.166962
$571$	27.6090	1.15540	0.577700	−	0.816249i	$-0.303950\pi$
$571$	27.6090	1.15540	0.577700	+	0.816249i	$0.303950\pi$
$572$	−19.0878	−0.798102
$573$	−27.8364	−1.16288
$574$	−0.789496	−0.0329529
$575$	−12.9847	−0.541501
$576$	7.20670	0.300279
$577$	−15.5041	−0.645443	−0.322722	−	0.946494i	$-0.604598\pi$
$577$	−15.5041	−0.645443	−0.322722	+	0.946494i	$0.604598\pi$
$578$	−3.60744	−0.150050
$579$	−22.7027	−0.943493
$580$	4.53455	0.188287
$581$	1.25979	0.0522648
$582$	−0.989229	−0.0410049
$583$	−8.07943	−0.334616
$584$	19.2007	0.794530
$585$	5.18533	0.214387
$586$	−4.30868	−0.177990
$587$	−13.3071	−0.549241	−0.274621	−	0.961553i	$-0.588552\pi$
$587$	−13.3071	−0.549241	−0.274621	+	0.961553i	$0.588552\pi$
$588$	16.5833	0.683885
$589$	21.9180	0.903116
$590$	−0.400340	−0.0164817
$591$	−2.91141	−0.119759
$592$	−3.28356	−0.134954
$593$	−26.6131	−1.09287	−0.546435	−	0.837502i	$-0.684015\pi$
$593$	−26.6131	−1.09287	−0.546435	+	0.837502i	$0.684015\pi$
$594$	−5.86835	−0.240781
$595$	0.718366	0.0294501
$596$	13.7988	0.565220
$597$	−0.868302	−0.0355373
$598$	4.06634	0.166285
$599$	−16.2397	−0.663535	−0.331767	−	0.943361i	$-0.607645\pi$
$599$	−16.2397	−0.663535	−0.331767	+	0.943361i	$0.607645\pi$
$600$	6.47495	0.264339
$601$	−8.18227	−0.333762	−0.166881	−	0.985977i	$-0.553370\pi$
$601$	−8.18227	−0.333762	−0.166881	+	0.985977i	$0.553370\pi$
$602$	0.850370	0.0346585
$603$	21.0082	0.855522
$604$	19.9325	0.811042
$605$	2.12713	0.0864800
$606$	6.07690	0.246857
$607$	−12.4790	−0.506505	−0.253252	−	0.967400i	$-0.581500\pi$
$607$	−12.4790	−0.506505	−0.253252	+	0.967400i	$0.581500\pi$
$608$	−31.0208	−1.25806
$609$	−0.688130	−0.0278844
$610$	−5.60520	−0.226948
$611$	7.80029	0.315566
$612$	6.69301	0.270549
$613$	−32.9333	−1.33016	−0.665082	−	0.746770i	$-0.731603\pi$
$613$	−32.9333	−1.33016	−0.665082	+	0.746770i	$0.731603\pi$
$614$	−2.79463	−0.112782
$615$	−12.8525	−0.518263
$616$	1.01898	0.0410559
$617$	27.1683	1.09375	0.546877	−	0.837213i	$-0.315817\pi$
$617$	27.1683	1.09375	0.546877	+	0.837213i	$0.315817\pi$
$618$	−3.70931	−0.149210
$619$	36.6871	1.47458	0.737289	−	0.675578i	$-0.236106\pi$
$619$	36.6871	1.47458	0.737289	+	0.675578i	$0.236106\pi$
$620$	−5.70074	−0.228947
$621$	−19.2640	−0.773038
$622$	−2.07188	−0.0830748
$623$	−4.47522	−0.179296
$624$	14.0861	0.563896
$625$	7.90771	0.316308
$626$	0.620195	0.0247880
$627$	−30.8870	−1.23351
$628$	10.5775	0.422088
$629$	−2.58204	−0.102953
$630$	−0.134057	−0.00534094
$631$	28.7951	1.14632	0.573158	−	0.819445i	$-0.305718\pi$
$631$	28.7951	1.14632	0.573158	+	0.819445i	$0.305718\pi$
$632$	4.43833	0.176547
$633$	31.3596	1.24643
$634$	4.96350	0.197126
$635$	0.257995	0.0102382
$636$	6.40496	0.253973
$637$	−23.3845	−0.926528
$638$	2.28021	0.0902742
$639$	−6.79709	−0.268889
$640$	10.6238	0.419943
$641$	48.6287	1.92072	0.960360	−	0.278763i	$-0.0899245\pi$
$641$	48.6287	1.92072	0.960360	+	0.278763i	$0.0899245\pi$
$642$	−8.85972	−0.349665
$643$	6.28047	0.247678	0.123839	−	0.992302i	$-0.460479\pi$
$643$	6.28047	0.247678	0.123839	+	0.992302i	$0.460479\pi$
$644$	1.61994	0.0638344
$645$	13.8435	0.545088
$646$	−7.25530	−0.285456
$647$	−4.47809	−0.176052	−0.0880260	−	0.996118i	$-0.528056\pi$
$647$	−4.47809	−0.176052	−0.0880260	+	0.996118i	$0.528056\pi$
$648$	4.00024	0.157144
$649$	3.10206	0.121767
$650$	−4.42176	−0.173436
$651$	0.865101	0.0339060
$652$	18.4473	0.722450
$653$	−42.4879	−1.66268	−0.831339	−	0.555765i	$-0.812425\pi$
$653$	−42.4879	−1.66268	−0.831339	+	0.555765i	$0.812425\pi$
$654$	−0.444328	−0.0173746
$655$	11.5328	0.450623
$656$	29.7489	1.16150
$657$	19.5732	0.763622
$658$	−0.201661	−0.00786157
$659$	−17.3255	−0.674907	−0.337453	−	0.941342i	$-0.609565\pi$
$659$	−17.3255	−0.674907	−0.337453	+	0.941342i	$0.609565\pi$
$660$	8.03352	0.312704
$661$	−30.0347	−1.16821	−0.584107	−	0.811676i	$-0.698555\pi$
$661$	−30.0347	−1.16821	−0.584107	+	0.811676i	$0.698555\pi$
$662$	−0.425955	−0.0165552
$663$	11.0767	0.430183
$664$	6.83336	0.265186
$665$	−2.23926	−0.0868347
$666$	0.481843	0.0186710
$667$	7.48521	0.289829
$668$	40.2225	1.55626
$669$	3.43755	0.132903
$670$	5.92316	0.228832
$671$	43.4323	1.67668
$672$	−1.22439	−0.0472318
$673$	−34.9905	−1.34879	−0.674393	−	0.738373i	$-0.735595\pi$
$673$	−34.9905	−1.34879	−0.674393	+	0.738373i	$0.735595\pi$
$674$	2.44474	0.0941679
$675$	20.9477	0.806279
$676$	3.07778	0.118376
$677$	−34.6900	−1.33324	−0.666622	−	0.745396i	$-0.732260\pi$
$677$	−34.6900	−1.33324	−0.666622	+	0.745396i	$0.732260\pi$
$678$	−7.46093	−0.286535
$679$	0.555709	0.0213261
$680$	3.89658	0.149427
$681$	19.9842	0.765798
$682$	−2.86662	−0.109769
$683$	34.8000	1.33159	0.665793	−	0.746137i	$-0.268093\pi$
$683$	34.8000	1.33159	0.665793	+	0.746137i	$0.268093\pi$
$684$	−20.8631	−0.797722
$685$	8.13055	0.310652
$686$	1.21455	0.0463717
$687$	−0.902567	−0.0344351
$688$	−32.0427	−1.22162
$689$	−9.03177	−0.344083
$690$	−1.71141	−0.0651522
$691$	10.1964	0.387889	0.193944	−	0.981013i	$-0.437872\pi$
$691$	10.1964	0.387889	0.193944	+	0.981013i	$0.437872\pi$
$692$	0.899898	0.0342090
$693$	1.03875	0.0394587
$694$	0.515698	0.0195756
$695$	14.2219	0.539469
$696$	−3.73257	−0.141483
$697$	23.3932	0.886079
$698$	−3.04209	−0.115145
$699$	7.54596	0.285415
$700$	−1.76152	−0.0665794
$701$	12.2112	0.461212	0.230606	−	0.973047i	$-0.425929\pi$
$701$	12.2112	0.461212	0.230606	+	0.973047i	$0.425929\pi$
$702$	−6.56007	−0.247594
$703$	8.04863	0.303560
$704$	−15.7442	−0.593383
$705$	−3.28292	−0.123642
$706$	9.81892	0.369540
$707$	−3.41376	−0.128388
$708$	−2.45916	−0.0924208
$709$	−16.9787	−0.637650	−0.318825	−	0.947814i	$-0.603288\pi$
$709$	−16.9787	−0.637650	−0.318825	+	0.947814i	$0.603288\pi$
$710$	−1.91640	−0.0719213
$711$	4.52443	0.169679
$712$	−24.2746	−0.909728
$713$	−9.41024	−0.352416
$714$	−0.286366	−0.0107170
$715$	−11.3282	−0.423652
$716$	8.76098	0.327413
$717$	1.63931	0.0612211
$718$	1.56230	0.0583046
$719$	−3.24590	−0.121052	−0.0605258	−	0.998167i	$-0.519278\pi$
$719$	−3.24590	−0.121052	−0.0605258	+	0.998167i	$0.519278\pi$
$720$	5.05137	0.188253
$721$	2.08374	0.0776026
$722$	15.9827	0.594814
$723$	7.59927	0.282620
$724$	12.0620	0.448280
$725$	−8.13945	−0.302292
$726$	−0.847947	−0.0314703
$727$	−51.6870	−1.91696	−0.958482	−	0.285151i	$-0.907956\pi$
$727$	−51.6870	−1.91696	−0.958482	+	0.285151i	$0.907956\pi$
$728$	1.13909	0.0422175
$729$	25.3632	0.939376
$730$	5.51854	0.204251
$731$	−25.1969	−0.931941
$732$	−34.4309	−1.27260
$733$	−29.1335	−1.07607	−0.538035	−	0.842922i	$-0.680833\pi$
$733$	−29.1335	−1.07607	−0.538035	+	0.842922i	$0.680833\pi$
$734$	7.04304	0.259963
$735$	9.84187	0.363023
$736$	13.3184	0.490923
$737$	−45.8960	−1.69060
$738$	−4.36547	−0.160695
$739$	40.9057	1.50474	0.752371	−	0.658740i	$-0.228910\pi$
$739$	40.9057	1.50474	0.752371	+	0.658740i	$0.228910\pi$
$740$	−2.09340	−0.0769548
$741$	−34.5277	−1.26841
$742$	0.233498	0.00857200
$743$	11.7594	0.431409	0.215704	−	0.976459i	$-0.430795\pi$
$743$	11.7594	0.431409	0.215704	+	0.976459i	$0.430795\pi$
$744$	4.69250	0.172035
$745$	8.18929	0.300033
$746$	7.41230	0.271383
$747$	6.96592	0.254870
$748$	−14.6220	−0.534633
$749$	4.97703	0.181857
$750$	4.33729	0.158375
$751$	−53.8623	−1.96546	−0.982731	−	0.185037i	$-0.940759\pi$
$751$	−53.8623	−1.96546	−0.982731	+	0.185037i	$0.940759\pi$
$752$	7.59877	0.277099
$753$	−19.3672	−0.705780
$754$	2.54898	0.0928283
$755$	11.8295	0.430521
$756$	−2.61338	−0.0950476
$757$	−8.39355	−0.305069	−0.152534	−	0.988298i	$-0.548743\pi$
$757$	−8.39355	−0.305069	−0.152534	+	0.988298i	$0.548743\pi$
$758$	5.26116	0.191094
$759$	13.2610	0.481343
$760$	−12.1462	−0.440590
$761$	35.7742	1.29681	0.648407	−	0.761293i	$-0.275435\pi$
$761$	35.7742	1.29681	0.648407	+	0.761293i	$0.275435\pi$
$762$	−0.102846	−0.00372571
$763$	0.249605	0.00903632
$764$	41.0774	1.48613
$765$	3.97216	0.143614
$766$	−9.26299	−0.334685
$767$	3.46771	0.125212
$768$	9.05619	0.326787
$769$	−28.7618	−1.03718	−0.518589	−	0.855024i	$-0.673542\pi$
$769$	−28.7618	−1.03718	−0.518589	+	0.855024i	$0.673542\pi$
$770$	0.292869	0.0105543
$771$	32.7564	1.17969
$772$	33.5017	1.20575
$773$	−13.4349	−0.483221	−0.241611	−	0.970373i	$-0.577676\pi$
$773$	−13.4349	−0.483221	−0.241611	+	0.970373i	$0.577676\pi$
$774$	4.70207	0.169013
$775$	10.2327	0.367570
$776$	3.01429	0.108207
$777$	0.317678	0.0113966
$778$	11.2088	0.401857
$779$	−72.9201	−2.61263
$780$	8.98044	0.321552
$781$	14.8494	0.531353
$782$	3.11497	0.111391
$783$	−12.0756	−0.431547
$784$	−22.7804	−0.813584
$785$	6.27752	0.224054
$786$	−4.59737	−0.163983
$787$	−13.2832	−0.473496	−0.236748	−	0.971571i	$-0.576082\pi$
$787$	−13.2832	−0.473496	−0.236748	+	0.971571i	$0.576082\pi$
$788$	4.29627	0.153048
$789$	−26.7663	−0.952905
$790$	1.27564	0.0453852
$791$	4.19124	0.149023
$792$	5.63439	0.200209
$793$	48.5517	1.72412
$794$	2.87895	0.102170
$795$	3.80121	0.134815
$796$	1.28133	0.0454155
$797$	39.4511	1.39743	0.698716	−	0.715400i	$-0.253755\pi$
$797$	39.4511	1.39743	0.698716	+	0.715400i	$0.253755\pi$
$798$	0.892646	0.0315993
$799$	5.97532	0.211392
$800$	−14.4825	−0.512033
$801$	−24.7455	−0.874339
$802$	−3.97151	−0.140239
$803$	−42.7609	−1.50900
$804$	36.3840	1.28317
$805$	0.961399	0.0338849
$806$	−3.20452	−0.112874
$807$	8.09776	0.285055
$808$	−18.5170	−0.651424
$809$	3.14334	0.110514	0.0552569	−	0.998472i	$-0.482402\pi$
$809$	3.14334	0.110514	0.0552569	+	0.998472i	$0.482402\pi$
$810$	1.14972	0.0403971
$811$	−19.8104	−0.695636	−0.347818	−	0.937562i	$-0.613077\pi$
$811$	−19.8104	−0.695636	−0.347818	+	0.937562i	$0.613077\pi$
$812$	1.01545	0.0356354
$813$	35.9964	1.26245
$814$	−1.05267	−0.0368959
$815$	10.9481	0.383494
$816$	10.7905	0.377743
$817$	78.5427	2.74786
$818$	−4.94228	−0.172803
$819$	1.16119	0.0405752
$820$	18.9661	0.662323
$821$	19.1742	0.669183	0.334591	−	0.942363i	$-0.391402\pi$
$821$	19.1742	0.669183	0.334591	+	0.942363i	$0.391402\pi$
$822$	−3.24112	−0.113047
$823$	−46.9975	−1.63823	−0.819115	−	0.573630i	$-0.805535\pi$
$823$	−46.9975	−1.63823	−0.819115	+	0.573630i	$0.805535\pi$
$824$	11.3027	0.393747
$825$	−14.4200	−0.502041
$826$	−0.0896507	−0.00311935
$827$	−23.9807	−0.833890	−0.416945	−	0.908932i	$-0.636899\pi$
$827$	−23.9807	−0.833890	−0.416945	+	0.908932i	$0.636899\pi$
$828$	8.95734	0.311289
$829$	23.4031	0.812824	0.406412	−	0.913690i	$-0.366780\pi$
$829$	23.4031	0.812824	0.406412	+	0.913690i	$0.366780\pi$
$830$	1.96400	0.0681715
$831$	33.9110	1.17636
$832$	−17.6000	−0.610172
$833$	−17.9134	−0.620663
$834$	−5.66936	−0.196314
$835$	23.8712	0.826099
$836$	45.5790	1.57638
$837$	15.1812	0.524738
$838$	6.75733	0.233428
$839$	10.8026	0.372946	0.186473	−	0.982460i	$-0.440294\pi$
$839$	10.8026	0.372946	0.186473	+	0.982460i	$0.440294\pi$
$840$	−0.479410	−0.0165412
$841$	−24.3079	−0.838204
$842$	−13.9943	−0.482275
$843$	2.48399	0.0855533
$844$	−46.2765	−1.59290
$845$	1.82660	0.0628370
$846$	−1.11507	−0.0383370
$847$	0.476342	0.0163673
$848$	−8.79843	−0.302139
$849$	8.46787	0.290617
$850$	−3.38724	−0.116181
$851$	−3.45558	−0.118456
$852$	−11.7718	−0.403297
$853$	18.0035	0.616428	0.308214	−	0.951317i	$-0.400269\pi$
$853$	18.0035	0.616428	0.308214	+	0.951317i	$0.400269\pi$
$854$	−1.25521	−0.0429524
$855$	−12.3819	−0.423450
$856$	26.9965	0.922722
$857$	−27.4661	−0.938226	−0.469113	−	0.883138i	$-0.655426\pi$
$857$	−27.4661	−0.938226	−0.469113	+	0.883138i	$0.655426\pi$
$858$	4.51583	0.154168
$859$	−30.0794	−1.02630	−0.513148	−	0.858300i	$-0.671521\pi$
$859$	−30.0794	−1.02630	−0.513148	+	0.858300i	$0.671521\pi$
$860$	−20.4285	−0.696604
$861$	−2.87815	−0.0980870
$862$	2.56855	0.0874850
$863$	42.0746	1.43224	0.716118	−	0.697979i	$-0.245917\pi$
$863$	42.0746	1.43224	0.716118	+	0.697979i	$0.245917\pi$
$864$	−21.4861	−0.730970
$865$	0.534071	0.0181590
$866$	9.51538	0.323346
$867$	−13.1511	−0.446635
$868$	−1.27660	−0.0433308
$869$	−9.88438	−0.335305
$870$	−1.07279	−0.0363711
$871$	−51.3059	−1.73843
$872$	1.35391	0.0458493
$873$	3.07276	0.103997
$874$	−9.70986	−0.328441
$875$	−2.43651	−0.0823691
$876$	33.8986	1.14533
$877$	−39.4937	−1.33361	−0.666803	−	0.745234i	$-0.732338\pi$
$877$	−39.4937	−1.33361	−0.666803	+	0.745234i	$0.732338\pi$
$878$	9.64204	0.325403
$879$	−15.7075	−0.529802
$880$	−11.0356	−0.372009
$881$	−2.81187	−0.0947342	−0.0473671	−	0.998878i	$-0.515083\pi$
$881$	−2.81187	−0.0947342	−0.0473671	+	0.998878i	$0.515083\pi$
$882$	3.34288	0.112561
$883$	20.0560	0.674937	0.337469	−	0.941337i	$-0.390429\pi$
$883$	20.0560	0.674937	0.337469	+	0.941337i	$0.390429\pi$
$884$	−16.3455	−0.549760
$885$	−1.45946	−0.0490592
$886$	11.7547	0.394906
$887$	−52.6810	−1.76885	−0.884427	−	0.466678i	$-0.845451\pi$
$887$	−52.6810	−1.76885	−0.884427	+	0.466678i	$0.845451\pi$
$888$	1.72316	0.0578253
$889$	0.0577746	0.00193770
$890$	−6.97685	−0.233865
$891$	−8.90871	−0.298453
$892$	−5.07269	−0.169846
$893$	−18.6260	−0.623295
$894$	−3.26454	−0.109182
$895$	5.19946	0.173799
$896$	2.37906	0.0794788
$897$	14.8241	0.494961
$898$	4.23220	0.141230
$899$	−5.89879	−0.196736
$900$	−9.74025	−0.324675
$901$	−6.91868	−0.230495
$902$	9.53710	0.317551
$903$	3.10007	0.103164
$904$	22.7342	0.756129
$905$	7.15854	0.237958
$906$	−4.71567	−0.156667
$907$	−30.8663	−1.02490	−0.512449	−	0.858718i	$-0.671262\pi$
$907$	−30.8663	−1.02490	−0.512449	+	0.858718i	$0.671262\pi$
$908$	−29.4902	−0.978665
$909$	−18.8762	−0.626083
$910$	0.327390	0.0108529
$911$	−40.8482	−1.35336	−0.676681	−	0.736277i	$-0.736582\pi$
$911$	−40.8482	−1.35336	−0.676681	+	0.736277i	$0.736582\pi$
$912$	−33.6357	−1.11379
$913$	−15.2182	−0.503650
$914$	−10.9407	−0.361888
$915$	−20.4340	−0.675528
$916$	1.33189	0.0440069
$917$	2.58261	0.0852854
$918$	−5.02526	−0.165858
$919$	13.0077	0.429084	0.214542	−	0.976715i	$-0.431174\pi$
$919$	13.0077	0.429084	0.214542	+	0.976715i	$0.431174\pi$
$920$	5.21484	0.171928
$921$	−10.1880	−0.335705
$922$	0.610996	0.0201221
$923$	16.5997	0.546386
$924$	1.79900	0.0591827
$925$	3.75761	0.123550
$926$	−6.27173	−0.206102
$927$	11.5219	0.378430
$928$	8.34862	0.274057
$929$	0.555433	0.0182232	0.00911159	−	0.999958i	$-0.497100\pi$
$929$	0.555433	0.0182232	0.00911159	+	0.999958i	$0.497100\pi$
$930$	1.34869	0.0442253
$931$	55.8389	1.83005
$932$	−11.1354	−0.364751
$933$	−7.55314	−0.247279
$934$	−6.84938	−0.224119
$935$	−8.67786	−0.283796
$936$	6.29853	0.205874
$937$	−7.96990	−0.260365	−0.130183	−	0.991490i	$-0.541556\pi$
$937$	−7.96990	−0.260365	−0.130183	+	0.991490i	$0.541556\pi$
$938$	1.32641	0.0433089
$939$	2.26095	0.0737834
$940$	4.84450	0.158010
$941$	−20.4811	−0.667664	−0.333832	−	0.942633i	$-0.608342\pi$
$941$	−20.4811	−0.667664	−0.333832	+	0.942633i	$0.608342\pi$
$942$	−2.50244	−0.0815339
$943$	31.3074	1.01951
$944$	3.37812	0.109948
$945$	−1.55099	−0.0504536
$946$	−10.2725	−0.333987
$947$	0.0221888	0.000721040 0	0.000360520	−	1.00000i	$-0.499885\pi$
$947$	0.0221888	0.000721040 0	0.000360520		1.00000i	$0.499885\pi$
$948$	7.83583	0.254496
$949$	−47.8012	−1.55169
$950$	10.5585	0.342564
$951$	18.0947	0.586761
$952$	0.872586	0.0282807
$953$	1.35690	0.0439544	0.0219772	−	0.999758i	$-0.493004\pi$
$953$	1.35690	0.0439544	0.0219772	+	0.999758i	$0.493004\pi$
$954$	1.29112	0.0418014
$955$	24.3786	0.788873
$956$	−2.41908	−0.0782386
$957$	8.31261	0.268708
$958$	−0.317438	−0.0102560
$959$	1.82073	0.0587944
$960$	7.40735	0.239071
$961$	−23.5842	−0.760780
$962$	−1.17675	−0.0379398
$963$	27.5202	0.886826
$964$	−11.2140	−0.361179
$965$	19.8826	0.640043
$966$	−0.383247	−0.0123308
$967$	20.6181	0.663035	0.331517	−	0.943449i	$-0.392439\pi$
$967$	20.6181	0.663035	0.331517	+	0.943449i	$0.392439\pi$
$968$	2.58378	0.0830459
$969$	−26.4496	−0.849683
$970$	0.866347	0.0278167
$971$	−33.5394	−1.07633	−0.538166	−	0.842839i	$-0.680882\pi$
$971$	−33.5394	−1.07633	−0.538166	+	0.842839i	$0.680882\pi$
$972$	−24.3477	−0.780954
$973$	3.18482	0.102101
$974$	7.17809	0.230001
$975$	−16.1198	−0.516245
$976$	47.2974	1.51395
$977$	26.6958	0.854074	0.427037	−	0.904234i	$-0.359557\pi$
$977$	26.6958	0.854074	0.427037	+	0.904234i	$0.359557\pi$
$978$	−4.36428	−0.139554
$979$	54.0606	1.72779
$980$	−14.5233	−0.463931
$981$	1.38018	0.0440657
$982$	−1.14725	−0.0366103
$983$	1.78208	0.0568395	0.0284197	−	0.999596i	$-0.490952\pi$
$983$	1.78208	0.0568395	0.0284197	+	0.999596i	$0.490952\pi$
$984$	−15.6117	−0.497683
$985$	2.54975	0.0812418
$986$	1.95262	0.0621839
$987$	−0.735166	−0.0234006
$988$	50.9516	1.62098
$989$	−33.7214	−1.07228
$990$	1.61940	0.0514680
$991$	−16.3652	−0.519859	−0.259929	−	0.965628i	$-0.583699\pi$
$991$	−16.3652	−0.519859	−0.259929	+	0.965628i	$0.583699\pi$
$992$	−10.4957	−0.333238
$993$	−1.55284	−0.0492779
$994$	−0.429153	−0.0136119
$995$	0.760442	0.0241076
$996$	12.0642	0.382270
$997$	39.6070	1.25437	0.627183	−	0.778872i	$-0.284208\pi$
$997$	39.6070	1.25437	0.627183	+	0.778872i	$0.284208\pi$
$998$	0.729600	0.0230951
$999$	5.57475	0.176377

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4033.2.a.d.1.46	✓	79

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4033.2.a.d.1.46	✓	79	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:	\( N \)	\(=\)	\( 4033 = 37 \cdot 109 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4033.a (trivial)

\(f(q)\)	\(=\)	\(q+0.349116 q^{2} +1.27272 q^{3} -1.87812 q^{4} -1.11462 q^{5} +0.444328 q^{6} -0.249605 q^{7} -1.35391 q^{8} -1.38018 q^{9} +O(q^{10})\)	\(q+0.349116 q^{2} +1.27272 q^{3} -1.87812 q^{4} -1.11462 q^{5} +0.444328 q^{6} -0.249605 q^{7} -1.35391 q^{8} -1.38018 q^{9} -0.389134 q^{10} +3.01523 q^{11} -2.39032 q^{12} +3.37064 q^{13} -0.0871413 q^{14} -1.41861 q^{15} +3.28356 q^{16} +2.58204 q^{17} -0.481843 q^{18} -8.04863 q^{19} +2.09340 q^{20} -0.317678 q^{21} +1.05267 q^{22} +3.45558 q^{23} -1.72316 q^{24} -3.75761 q^{25} +1.17675 q^{26} -5.57475 q^{27} +0.468788 q^{28} +2.16612 q^{29} -0.495259 q^{30} -2.72320 q^{31} +3.85417 q^{32} +3.83755 q^{33} +0.901433 q^{34} +0.278216 q^{35} +2.59214 q^{36} -1.00000 q^{37} -2.80991 q^{38} +4.28989 q^{39} +1.50911 q^{40} +9.05995 q^{41} -0.110907 q^{42} -9.75852 q^{43} -5.66296 q^{44} +1.53838 q^{45} +1.20640 q^{46} +2.31418 q^{47} +4.17906 q^{48} -6.93770 q^{49} -1.31184 q^{50} +3.28622 q^{51} -6.33047 q^{52} -2.67954 q^{53} -1.94624 q^{54} -3.36085 q^{55} +0.337944 q^{56} -10.2437 q^{57} +0.756229 q^{58} +1.02880 q^{59} +2.66431 q^{60} +14.4043 q^{61} -0.950714 q^{62} +0.344500 q^{63} -5.22157 q^{64} -3.75700 q^{65} +1.33975 q^{66} -15.2214 q^{67} -4.84938 q^{68} +4.39799 q^{69} +0.0971299 q^{70} +4.92479 q^{71} +1.86864 q^{72} -14.1816 q^{73} -0.349116 q^{74} -4.78240 q^{75} +15.1163 q^{76} -0.752618 q^{77} +1.49767 q^{78} -3.27815 q^{79} -3.65994 q^{80} -2.95457 q^{81} +3.16298 q^{82} -5.04712 q^{83} +0.596637 q^{84} -2.87801 q^{85} -3.40686 q^{86} +2.75687 q^{87} -4.08236 q^{88} +17.9292 q^{89} +0.537074 q^{90} -0.841331 q^{91} -6.48999 q^{92} -3.46588 q^{93} +0.807920 q^{94} +8.97120 q^{95} +4.90529 q^{96} -2.22635 q^{97} -2.42206 q^{98} -4.16156 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9}+O(q^{10}) \) 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9} - 13 q^{10} - 5 q^{11} - 40 q^{12} - 18 q^{13} - 42 q^{14} - 49 q^{15} + 83 q^{16} - 62 q^{17} - 33 q^{18} - 25 q^{19} - 39 q^{20} - 15 q^{21} - 31 q^{22} - 94 q^{23} - 39 q^{24} + 71 q^{25} - 35 q^{26} - 47 q^{27} - 13 q^{28} - 17 q^{29} + 15 q^{30} - 37 q^{31} - 105 q^{32} - 60 q^{33} + 9 q^{34} - 60 q^{35} + 43 q^{36} - 79 q^{37} - 80 q^{38} - 41 q^{39} - 64 q^{40} - 37 q^{41} - 30 q^{42} - 20 q^{43} - 14 q^{44} - 8 q^{45} + 61 q^{46} - 148 q^{47} - 39 q^{48} + 82 q^{49} - 90 q^{50} - 45 q^{51} - 27 q^{52} - 70 q^{53} - 41 q^{54} - 105 q^{55} - 68 q^{56} - 31 q^{57} - 14 q^{58} - 96 q^{59} - 74 q^{60} - 21 q^{61} + 4 q^{62} - 60 q^{63} + 132 q^{64} - 15 q^{65} + 71 q^{66} - 44 q^{67} - 166 q^{68} - 72 q^{69} - 9 q^{70} - 55 q^{71} - 126 q^{72} - 27 q^{73} + 11 q^{74} - 39 q^{75} - 4 q^{76} - 104 q^{77} - 47 q^{78} - 49 q^{79} - 82 q^{80} + 55 q^{81} + 20 q^{82} - 52 q^{83} - 29 q^{84} + 3 q^{85} - 32 q^{86} - 113 q^{87} + 14 q^{88} - 68 q^{89} - 39 q^{90} - 30 q^{91} - 179 q^{92} - 53 q^{93} - 33 q^{94} - 86 q^{95} + 33 q^{96} - 57 q^{97} - 116 q^{98} + q^{99}+O(q^{100}) \) 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9 - 13 * q^10 - 5 * q^11 - 40 * q^12 - 18 * q^13 - 42 * q^14 - 49 * q^15 + 83 * q^16 - 62 * q^17 - 33 * q^18 - 25 * q^19 - 39 * q^20 - 15 * q^21 - 31 * q^22 - 94 * q^23 - 39 * q^24 + 71 * q^25 - 35 * q^26 - 47 * q^27 - 13 * q^28 - 17 * q^29 + 15 * q^30 - 37 * q^31 - 105 * q^32 - 60 * q^33 + 9 * q^34 - 60 * q^35 + 43 * q^36 - 79 * q^37 - 80 * q^38 - 41 * q^39 - 64 * q^40 - 37 * q^41 - 30 * q^42 - 20 * q^43 - 14 * q^44 - 8 * q^45 + 61 * q^46 - 148 * q^47 - 39 * q^48 + 82 * q^49 - 90 * q^50 - 45 * q^51 - 27 * q^52 - 70 * q^53 - 41 * q^54 - 105 * q^55 - 68 * q^56 - 31 * q^57 - 14 * q^58 - 96 * q^59 - 74 * q^60 - 21 * q^61 + 4 * q^62 - 60 * q^63 + 132 * q^64 - 15 * q^65 + 71 * q^66 - 44 * q^67 - 166 * q^68 - 72 * q^69 - 9 * q^70 - 55 * q^71 - 126 * q^72 - 27 * q^73 + 11 * q^74 - 39 * q^75 - 4 * q^76 - 104 * q^77 - 47 * q^78 - 49 * q^79 - 82 * q^80 + 55 * q^81 + 20 * q^82 - 52 * q^83 - 29 * q^84 + 3 * q^85 - 32 * q^86 - 113 * q^87 + 14 * q^88 - 68 * q^89 - 39 * q^90 - 30 * q^91 - 179 * q^92 - 53 * q^93 - 33 * q^94 - 86 * q^95 + 33 * q^96 - 57 * q^97 - 116 * q^98 + q^99

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