LMFDB - Embedded newform 4033.2.a.d.1.65

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			1.65
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)

$f(q)$	$=$	$q+1.91390 q^{2} +1.04700 q^{3} +1.66300 q^{4} -1.25893 q^{5} +2.00386 q^{6} +1.67126 q^{7} -0.644974 q^{8} -1.90378 q^{9} +O(q^{10})$	\(q+1.91390 q^{2} +1.04700 q^{3} +1.66300 q^{4} -1.25893 q^{5} +2.00386 q^{6} +1.67126 q^{7} -0.644974 q^{8} -1.90378 q^{9} -2.40946 q^{10} -2.90825 q^{11} +1.74117 q^{12} -1.01664 q^{13} +3.19861 q^{14} -1.31810 q^{15} -4.56042 q^{16} +0.885418 q^{17} -3.64364 q^{18} -0.121148 q^{19} -2.09361 q^{20} +1.74981 q^{21} -5.56610 q^{22} +3.85968 q^{23} -0.675291 q^{24} -3.41510 q^{25} -1.94574 q^{26} -5.13428 q^{27} +2.77931 q^{28} -1.76425 q^{29} -2.52272 q^{30} +3.44028 q^{31} -7.43824 q^{32} -3.04495 q^{33} +1.69460 q^{34} -2.10399 q^{35} -3.16600 q^{36} -1.00000 q^{37} -0.231864 q^{38} -1.06442 q^{39} +0.811978 q^{40} -4.02342 q^{41} +3.34896 q^{42} -7.42314 q^{43} -4.83644 q^{44} +2.39673 q^{45} +7.38703 q^{46} -4.03137 q^{47} -4.77478 q^{48} -4.20690 q^{49} -6.53614 q^{50} +0.927036 q^{51} -1.69067 q^{52} +1.23055 q^{53} -9.82649 q^{54} +3.66128 q^{55} -1.07792 q^{56} -0.126842 q^{57} -3.37660 q^{58} -9.30739 q^{59} -2.19201 q^{60} +7.62374 q^{61} +6.58434 q^{62} -3.18171 q^{63} -5.11518 q^{64} +1.27988 q^{65} -5.82773 q^{66} -5.51351 q^{67} +1.47245 q^{68} +4.04110 q^{69} -4.02683 q^{70} -2.88685 q^{71} +1.22789 q^{72} -10.7648 q^{73} -1.91390 q^{74} -3.57562 q^{75} -0.201469 q^{76} -4.86043 q^{77} -2.03720 q^{78} -0.889282 q^{79} +5.74125 q^{80} +0.335731 q^{81} -7.70041 q^{82} +5.41964 q^{83} +2.90995 q^{84} -1.11468 q^{85} -14.2071 q^{86} -1.84718 q^{87} +1.87575 q^{88} +1.24752 q^{89} +4.58709 q^{90} -1.69906 q^{91} +6.41866 q^{92} +3.60199 q^{93} -7.71563 q^{94} +0.152516 q^{95} -7.78787 q^{96} +4.96204 q^{97} -8.05158 q^{98} +5.53668 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.91390	1.35333	0.676665	−	0.736291i	$-0.263425\pi$
$2$	1.91390	1.35333	0.676665	+	0.736291i	$0.263425\pi$
$3$	1.04700	0.604488	0.302244	−	0.953231i	$-0.402264\pi$
$3$	1.04700	0.604488	0.302244	+	0.953231i	$0.402264\pi$
$4$	1.66300	0.831502
$5$	−1.25893	−0.563010	−0.281505	−	0.959560i	$-0.590834\pi$
$5$	−1.25893	−0.563010	−0.281505	+	0.959560i	$0.590834\pi$
$6$	2.00386	0.818072
$7$	1.67126	0.631675	0.315838	−	0.948813i	$-0.397714\pi$
$7$	1.67126	0.631675	0.315838	+	0.948813i	$0.397714\pi$
$8$	−0.644974	−0.228033
$9$	−1.90378	−0.634594
$10$	−2.40946	−0.761939
$11$	−2.90825	−0.876871	−0.438435	−	0.898763i	$-0.644467\pi$
$11$	−2.90825	−0.876871	−0.438435	+	0.898763i	$0.644467\pi$
$12$	1.74117	0.502633
$13$	−1.01664	−0.281965	−0.140982	−	0.990012i	$-0.545026\pi$
$13$	−1.01664	−0.281965	−0.140982	+	0.990012i	$0.545026\pi$
$14$	3.19861	0.854865
$15$	−1.31810	−0.340333
$16$	−4.56042	−1.14011
$17$	0.885418	0.214745	0.107373	−	0.994219i	$-0.465756\pi$
$17$	0.885418	0.214745	0.107373	+	0.994219i	$0.465756\pi$
$18$	−3.64364	−0.858815
$19$	−0.121148	−0.0277932	−0.0138966	−	0.999903i	$-0.504424\pi$
$19$	−0.121148	−0.0277932	−0.0138966	+	0.999903i	$0.504424\pi$
$20$	−2.09361	−0.468145
$21$	1.74981	0.381840
$22$	−5.56610	−1.18670
$23$	3.85968	0.804798	0.402399	−	0.915464i	$-0.368176\pi$
$23$	3.85968	0.804798	0.402399	+	0.915464i	$0.368176\pi$
$24$	−0.675291	−0.137843
$25$	−3.41510	−0.683019
$26$	−1.94574	−0.381591
$27$	−5.13428	−0.988093
$28$	2.77931	0.525240
$29$	−1.76425	−0.327614	−0.163807	−	0.986492i	$-0.552377\pi$
$29$	−1.76425	−0.327614	−0.163807	+	0.986492i	$0.552377\pi$
$30$	−2.52272	−0.460583
$31$	3.44028	0.617892	0.308946	−	0.951080i	$-0.400024\pi$
$31$	3.44028	0.617892	0.308946	+	0.951080i	$0.400024\pi$
$32$	−7.43824	−1.31491
$33$	−3.04495	−0.530058
$34$	1.69460	0.290621
$35$	−2.10399	−0.355640
$36$	−3.16600	−0.527666
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	−0.231864	−0.0376133
$39$	−1.06442	−0.170444
$40$	0.811978	0.128385
$41$	−4.02342	−0.628352	−0.314176	−	0.949365i	$-0.601728\pi$
$41$	−4.02342	−0.628352	−0.314176	+	0.949365i	$0.601728\pi$
$42$	3.34896	0.516756
$43$	−7.42314	−1.13202	−0.566009	−	0.824399i	$-0.691513\pi$
$43$	−7.42314	−1.13202	−0.566009	+	0.824399i	$0.691513\pi$
$44$	−4.83644	−0.729120
$45$	2.39673	0.357283
$46$	7.38703	1.08916
$47$	−4.03137	−0.588036	−0.294018	−	0.955800i	$-0.594993\pi$
$47$	−4.03137	−0.588036	−0.294018	+	0.955800i	$0.594993\pi$
$48$	−4.77478	−0.689181
$49$	−4.20690	−0.600986
$50$	−6.53614	−0.924350
$51$	0.927036	0.129811
$52$	−1.69067	−0.234454
$53$	1.23055	0.169029	0.0845145	−	0.996422i	$-0.473066\pi$
$53$	1.23055	0.169029	0.0845145	+	0.996422i	$0.473066\pi$
$54$	−9.82649	−1.33722
$55$	3.66128	0.493688
$56$	−1.07792	−0.144043
$57$	−0.126842	−0.0168006
$58$	−3.37660	−0.443370
$59$	−9.30739	−1.21172	−0.605859	−	0.795572i	$-0.707171\pi$
$59$	−9.30739	−1.21172	−0.605859	+	0.795572i	$0.707171\pi$
$60$	−2.19201	−0.282988
$61$	7.62374	0.976120	0.488060	−	0.872810i	$-0.337705\pi$
$61$	7.62374	0.976120	0.488060	+	0.872810i	$0.337705\pi$
$62$	6.58434	0.836212
$63$	−3.18171	−0.400857
$64$	−5.11518	−0.639397
$65$	1.27988	0.158749
$66$	−5.82773	−0.717344
$67$	−5.51351	−0.673583	−0.336792	−	0.941579i	$-0.609342\pi$
$67$	−5.51351	−0.673583	−0.336792	+	0.941579i	$0.609342\pi$
$68$	1.47245	0.178561
$69$	4.04110	0.486491
$70$	−4.02683	−0.481298
$71$	−2.88685	−0.342606	−0.171303	−	0.985218i	$-0.554798\pi$
$71$	−2.88685	−0.342606	−0.171303	+	0.985218i	$0.554798\pi$
$72$	1.22789	0.144708
$73$	−10.7648	−1.25992	−0.629960	−	0.776628i	$-0.716929\pi$
$73$	−10.7648	−1.25992	−0.629960	+	0.776628i	$0.716929\pi$
$74$	−1.91390	−0.222486
$75$	−3.57562	−0.412877
$76$	−0.201469	−0.0231101
$77$	−4.86043	−0.553898
$78$	−2.03720	−0.230667
$79$	−0.889282	−0.100052	−0.0500260	−	0.998748i	$-0.515930\pi$
$79$	−0.889282	−0.100052	−0.0500260	+	0.998748i	$0.515930\pi$
$80$	5.74125	0.641892
$81$	0.335731	0.0373034
$82$	−7.70041	−0.850368
$83$	5.41964	0.594882	0.297441	−	0.954740i	$-0.403867\pi$
$83$	5.41964	0.594882	0.297441	+	0.954740i	$0.403867\pi$
$84$	2.90995	0.317501
$85$	−1.11468	−0.120904
$86$	−14.2071	−1.53199
$87$	−1.84718	−0.198039
$88$	1.87575	0.199955
$89$	1.24752	0.132237	0.0661185	−	0.997812i	$-0.478938\pi$
$89$	1.24752	0.132237	0.0661185	+	0.997812i	$0.478938\pi$
$90$	4.58709	0.483522
$91$	−1.69906	−0.178110
$92$	6.41866	0.669192
$93$	3.60199	0.373509
$94$	−7.71563	−0.795807
$95$	0.152516	0.0156478
$96$	−7.78787	−0.794846
$97$	4.96204	0.503818	0.251909	−	0.967751i	$-0.418942\pi$
$97$	4.96204	0.503818	0.251909	+	0.967751i	$0.418942\pi$
$98$	−8.05158	−0.813333
$99$	5.53668	0.556457
$100$	−5.67932	−0.567932
$101$	−14.0922	−1.40222	−0.701111	−	0.713052i	$-0.747312\pi$
$101$	−14.0922	−1.40222	−0.701111	+	0.713052i	$0.747312\pi$
$102$	1.77425	0.175677
$103$	16.7697	1.65237	0.826183	−	0.563401i	$-0.190508\pi$
$103$	16.7697	1.65237	0.826183	+	0.563401i	$0.190508\pi$
$104$	0.655705	0.0642972
$105$	−2.20289	−0.214980
$106$	2.35515	0.228752
$107$	−11.6412	−1.12540	−0.562698	−	0.826663i	$-0.690237\pi$
$107$	−11.6412	−1.12540	−0.562698	+	0.826663i	$0.690237\pi$
$108$	−8.53833	−0.821602
$109$	−1.00000	−0.0957826
$109$	−1.00000	−0.0957826
$110$	7.00732	0.668122
$111$	−1.04700	−0.0993773
$112$	−7.62164	−0.720177
$113$	1.39533	0.131261	0.0656307	−	0.997844i	$-0.479094\pi$
$113$	1.39533	0.131261	0.0656307	+	0.997844i	$0.479094\pi$
$114$	−0.242763	−0.0227368
$115$	−4.85906	−0.453110
$116$	−2.93396	−0.272412
$117$	1.93546	0.178933
$118$	−17.8134	−1.63986
$119$	1.47976	0.135649
$120$	0.850144	0.0776072
$121$	−2.54207	−0.231097
$122$	14.5911	1.32101
$123$	−4.21254	−0.379832
$124$	5.72120	0.513779
$125$	10.5940	0.947557
$126$	−6.08946	−0.542492
$127$	2.54167	0.225536	0.112768	−	0.993621i	$-0.464028\pi$
$127$	2.54167	0.225536	0.112768	+	0.993621i	$0.464028\pi$
$128$	5.08655	0.449592
$129$	−7.77206	−0.684292
$130$	2.44955	0.214840
$131$	12.1076	1.05784	0.528921	−	0.848671i	$-0.322597\pi$
$131$	12.1076	1.05784	0.528921	+	0.848671i	$0.322597\pi$
$132$	−5.06377	−0.440745
$133$	−0.202469	−0.0175563
$134$	−10.5523	−0.911580
$135$	6.46370	0.556307
$136$	−0.571072	−0.0489690
$137$	−14.4989	−1.23873	−0.619364	−	0.785104i	$-0.712610\pi$
$137$	−14.4989	−1.23873	−0.619364	+	0.785104i	$0.712610\pi$
$138$	7.73425	0.658383
$139$	−5.30187	−0.449699	−0.224849	−	0.974394i	$-0.572189\pi$
$139$	−5.30187	−0.449699	−0.224849	+	0.974394i	$0.572189\pi$
$140$	−3.49895	−0.295715
$141$	−4.22086	−0.355461
$142$	−5.52513	−0.463659
$143$	2.95664	0.247247
$144$	8.68205	0.723504
$145$	2.22107	0.184450
$146$	−20.6026	−1.70509
$147$	−4.40465	−0.363289
$148$	−1.66300	−0.136698
$149$	19.4013	1.58942	0.794709	−	0.606991i	$-0.207624\pi$
$149$	19.4013	1.58942	0.794709	+	0.606991i	$0.207624\pi$
$150$	−6.84337	−0.558759
$151$	−2.70313	−0.219978	−0.109989	−	0.993933i	$-0.535082\pi$
$151$	−2.70313	−0.219978	−0.109989	+	0.993933i	$0.535082\pi$
$152$	0.0781371	0.00633776
$153$	−1.68564	−0.136276
$154$	−9.30237	−0.749607
$155$	−4.33107	−0.347880
$156$	−1.77014	−0.141725
$157$	16.9139	1.34988	0.674938	−	0.737874i	$-0.264170\pi$
$157$	16.9139	1.34988	0.674938	+	0.737874i	$0.264170\pi$
$158$	−1.70200	−0.135404
$159$	1.28839	0.102176
$160$	9.36422	0.740306
$161$	6.45051	0.508371
$162$	0.642554	0.0504838
$163$	3.27193	0.256277	0.128139	−	0.991756i	$-0.459100\pi$
$163$	3.27193	0.256277	0.128139	+	0.991756i	$0.459100\pi$
$164$	−6.69096	−0.522476
$165$	3.83338	0.298428
$166$	10.3726	0.805072
$167$	4.91984	0.380709	0.190354	−	0.981715i	$-0.439036\pi$
$167$	4.91984	0.380709	0.190354	+	0.981715i	$0.439036\pi$
$168$	−1.12858	−0.0870722
$169$	−11.9664	−0.920496
$170$	−2.13338	−0.163623
$171$	0.230639	0.0176374
$172$	−12.3447	−0.941276
$173$	−2.92126	−0.222099	−0.111050	−	0.993815i	$-0.535421\pi$
$173$	−2.92126	−0.222099	−0.111050	+	0.993815i	$0.535421\pi$
$174$	−3.53532	−0.268012
$175$	−5.70750	−0.431446
$176$	13.2629	0.999726
$177$	−9.74488	−0.732470
$178$	2.38763	0.178960
$179$	12.5327	0.936737	0.468369	−	0.883533i	$-0.344842\pi$
$179$	12.5327	0.936737	0.468369	+	0.883533i	$0.344842\pi$
$180$	3.98577	0.297082
$181$	3.67880	0.273443	0.136721	−	0.990610i	$-0.456344\pi$
$181$	3.67880	0.273443	0.136721	+	0.990610i	$0.456344\pi$
$182$	−3.25183	−0.241042
$183$	7.98209	0.590053
$184$	−2.48939	−0.183520
$185$	1.25893	0.0925584
$186$	6.89384	0.505481
$187$	−2.57502	−0.188304
$188$	−6.70419	−0.488953
$189$	−8.58070	−0.624154
$190$	0.291901	0.0211767
$191$	−0.918538	−0.0664631	−0.0332315	−	0.999448i	$-0.510580\pi$
$191$	−0.918538	−0.0664631	−0.0332315	+	0.999448i	$0.510580\pi$
$192$	−5.35561	−0.386508
$193$	0.310264	0.0223333	0.0111666	−	0.999938i	$-0.496445\pi$
$193$	0.310264	0.0223333	0.0111666	+	0.999938i	$0.496445\pi$
$194$	9.49683	0.681833
$195$	1.34004	0.0959619
$196$	−6.99610	−0.499721
$197$	−10.8439	−0.772596	−0.386298	−	0.922374i	$-0.626246\pi$
$197$	−10.8439	−0.772596	−0.386298	+	0.922374i	$0.626246\pi$
$198$	10.5966	0.753070
$199$	19.6908	1.39584	0.697920	−	0.716176i	$-0.254109\pi$
$199$	19.6908	1.39584	0.697920	+	0.716176i	$0.254109\pi$
$200$	2.20265	0.155751
$201$	−5.77267	−0.407173
$202$	−26.9710	−1.89767
$203$	−2.94852	−0.206946
$204$	1.54167	0.107938
$205$	5.06520	0.353769
$206$	32.0955	2.23620
$207$	−7.34798	−0.510720
$208$	4.63630	0.321470
$209$	0.352328	0.0243710
$210$	−4.21611	−0.290939
$211$	21.7219	1.49540	0.747699	−	0.664038i	$-0.231159\pi$
$211$	21.7219	1.49540	0.747699	+	0.664038i	$0.231159\pi$
$212$	2.04641	0.140548
$213$	−3.02254	−0.207101
$214$	−22.2800	−1.52303
$215$	9.34521	0.637338
$216$	3.31148	0.225318
$217$	5.74959	0.390307
$218$	−1.91390	−0.129626
$219$	−11.2707	−0.761607
$220$	6.08873	0.410502
$221$	−0.900149	−0.0605506
$222$	−2.00386	−0.134490
$223$	−3.67693	−0.246225	−0.123113	−	0.992393i	$-0.539288\pi$
$223$	−3.67693	−0.246225	−0.123113	+	0.992393i	$0.539288\pi$
$224$	−12.4312	−0.830594
$225$	6.50160	0.433440
$226$	2.67051	0.177640
$227$	28.5655	1.89596	0.947980	−	0.318330i	$-0.103122\pi$
$227$	28.5655	1.89596	0.947980	+	0.318330i	$0.103122\pi$
$228$	−0.210939	−0.0139698
$229$	3.08057	0.203570	0.101785	−	0.994806i	$-0.467545\pi$
$229$	3.08057	0.203570	0.101785	+	0.994806i	$0.467545\pi$
$230$	−9.29975	−0.613207
$231$	−5.08890	−0.334825
$232$	1.13790	0.0747067
$233$	−26.5147	−1.73703	−0.868516	−	0.495661i	$-0.834926\pi$
$233$	−26.5147	−1.73703	−0.868516	+	0.495661i	$0.834926\pi$
$234$	3.70427	0.242155
$235$	5.07521	0.331070
$236$	−15.4782	−1.00755
$237$	−0.931083	−0.0604803
$238$	2.83211	0.183578
$239$	3.85143	0.249128	0.124564	−	0.992212i	$-0.460247\pi$
$239$	3.85143	0.249128	0.124564	+	0.992212i	$0.460247\pi$
$240$	6.01112	0.388016
$241$	−12.1207	−0.780764	−0.390382	−	0.920653i	$-0.627657\pi$
$241$	−12.1207	−0.780764	−0.390382	+	0.920653i	$0.627657\pi$
$242$	−4.86526	−0.312751
$243$	15.7544	1.01064
$244$	12.6783	0.811646
$245$	5.29620	0.338362
$246$	−8.06236	−0.514037
$247$	0.123163	0.00783669
$248$	−2.21889	−0.140900
$249$	5.67438	0.359599
$250$	20.2759	1.28236
$251$	−14.3857	−0.908018	−0.454009	−	0.890997i	$-0.650007\pi$
$251$	−14.3857	−0.908018	−0.454009	+	0.890997i	$0.650007\pi$
$252$	−5.29119	−0.333314
$253$	−11.2249	−0.705704
$254$	4.86449	0.305225
$255$	−1.16707	−0.0730850
$256$	19.9655	1.24784
$257$	−2.30833	−0.143989	−0.0719947	−	0.997405i	$-0.522936\pi$
$257$	−2.30833	−0.143989	−0.0719947	+	0.997405i	$0.522936\pi$
$258$	−14.8749	−0.926073
$259$	−1.67126	−0.103847
$260$	2.12844	0.132000
$261$	3.35875	0.207902
$262$	23.1726	1.43161
$263$	12.5767	0.775511	0.387755	−	0.921762i	$-0.373251\pi$
$263$	12.5767	0.775511	0.387755	+	0.921762i	$0.373251\pi$
$264$	1.96392	0.120871
$265$	−1.54918	−0.0951651
$266$	−0.387504	−0.0237594
$267$	1.30616	0.0799357
$268$	−9.16900	−0.560086
$269$	21.4482	1.30772	0.653858	−	0.756617i	$-0.273149\pi$
$269$	21.4482	1.30772	0.653858	+	0.756617i	$0.273149\pi$
$270$	12.3709	0.752866
$271$	−13.8093	−0.838857	−0.419429	−	0.907788i	$-0.637770\pi$
$271$	−13.8093	−0.838857	−0.419429	+	0.907788i	$0.637770\pi$
$272$	−4.03788	−0.244833
$273$	−1.77893	−0.107665
$274$	−27.7495	−1.67641
$275$	9.93196	0.598920
$276$	6.72037	0.404519
$277$	14.3773	0.863850	0.431925	−	0.901909i	$-0.357834\pi$
$277$	14.3773	0.863850	0.431925	+	0.901909i	$0.357834\pi$
$278$	−10.1472	−0.608591
$279$	−6.54954	−0.392111
$280$	1.35702	0.0810976
$281$	28.5674	1.70419	0.852096	−	0.523386i	$-0.175332\pi$
$281$	28.5674	1.70419	0.852096	+	0.523386i	$0.175332\pi$
$282$	−8.07830	−0.481056
$283$	−24.4290	−1.45215	−0.726076	−	0.687615i	$-0.758658\pi$
$283$	−24.4290	−1.45215	−0.726076	+	0.687615i	$0.758658\pi$
$284$	−4.80084	−0.284878
$285$	0.159685	0.00945894
$286$	5.65870	0.334606
$287$	−6.72416	−0.396915
$288$	14.1608	0.834432
$289$	−16.2160	−0.953884
$290$	4.25090	0.249622
$291$	5.19527	0.304552
$292$	−17.9018	−1.04763
$293$	−3.72444	−0.217584	−0.108792	−	0.994065i	$-0.534698\pi$
$293$	−3.72444	−0.217584	−0.108792	+	0.994065i	$0.534698\pi$
$294$	−8.43004	−0.491650
$295$	11.7173	0.682210
$296$	0.644974	0.0374884
$297$	14.9318	0.866430
$298$	37.1321	2.15101
$299$	−3.92389	−0.226925
$300$	−5.94627	−0.343308
$301$	−12.4060	−0.715068
$302$	−5.17352	−0.297703
$303$	−14.7546	−0.847627
$304$	0.552484	0.0316872
$305$	−9.59775	−0.549566
$306$	−3.22615	−0.184427
$307$	21.4210	1.22256	0.611280	−	0.791414i	$-0.290655\pi$
$307$	21.4210	1.22256	0.611280	+	0.791414i	$0.290655\pi$
$308$	−8.08292	−0.460567
$309$	17.5579	0.998836
$310$	−8.28923	−0.470796
$311$	−19.7693	−1.12102	−0.560508	−	0.828149i	$-0.689394\pi$
$311$	−19.7693	−1.12102	−0.560508	+	0.828149i	$0.689394\pi$
$312$	0.686526	0.0388669
$313$	17.3207	0.979021	0.489511	−	0.871997i	$-0.337175\pi$
$313$	17.3207	0.979021	0.489511	+	0.871997i	$0.337175\pi$
$314$	32.3715	1.82683
$315$	4.00555	0.225687
$316$	−1.47888	−0.0831935
$317$	−20.8589	−1.17155	−0.585777	−	0.810473i	$-0.699210\pi$
$317$	−20.8589	−1.17155	−0.585777	+	0.810473i	$0.699210\pi$
$318$	2.46585	0.138278
$319$	5.13089	0.287275
$320$	6.43965	0.359987
$321$	−12.1884	−0.680289
$322$	12.3456	0.687994
$323$	−0.107266	−0.00596845
$324$	0.558322	0.0310179
$325$	3.47192	0.192587
$326$	6.26214	0.346828
$327$	−1.04700	−0.0578995
$328$	2.59500	0.143285
$329$	−6.73745	−0.371448
$330$	7.33670	0.403872
$331$	−14.7816	−0.812471	−0.406236	−	0.913768i	$-0.633159\pi$
$331$	−14.7816	−0.812471	−0.406236	+	0.913768i	$0.633159\pi$
$332$	9.01288	0.494646
$333$	1.90378	0.104327
$334$	9.41607	0.515224
$335$	6.94113	0.379234
$336$	−7.97989	−0.435339
$337$	−26.7133	−1.45516	−0.727582	−	0.686021i	$-0.759356\pi$
$337$	−26.7133	−1.45516	−0.727582	+	0.686021i	$0.759356\pi$
$338$	−22.9026	−1.24573
$339$	1.46091	0.0793459
$340$	−1.85372	−0.100532
$341$	−10.0052	−0.541812
$342$	0.441419	0.0238692
$343$	−18.7296	−1.01130
$344$	4.78774	0.258137
$345$	−5.08746	−0.273900
$346$	−5.59099	−0.300574
$347$	−35.8760	−1.92592	−0.962962	−	0.269636i	$-0.913097\pi$
$347$	−35.8760	−1.92592	−0.962962	+	0.269636i	$0.913097\pi$
$348$	−3.07187	−0.164670
$349$	28.3550	1.51781	0.758905	−	0.651202i	$-0.225735\pi$
$349$	28.3550	1.51781	0.758905	+	0.651202i	$0.225735\pi$
$350$	−10.9236	−0.583889
$351$	5.21970	0.278607
$352$	21.6323	1.15300
$353$	−33.5836	−1.78747	−0.893737	−	0.448591i	$-0.851926\pi$
$353$	−33.5836	−1.78747	−0.893737	+	0.448591i	$0.851926\pi$
$354$	−18.6507	−0.991273
$355$	3.63434	0.192891
$356$	2.07463	0.109955
$357$	1.54932	0.0819985
$358$	23.9863	1.26772
$359$	17.6818	0.933210	0.466605	−	0.884466i	$-0.345477\pi$
$359$	17.6818	0.933210	0.466605	+	0.884466i	$0.345477\pi$
$360$	−1.54583	−0.0814723
$361$	−18.9853	−0.999228
$362$	7.04084	0.370058
$363$	−2.66156	−0.139696
$364$	−2.82555	−0.148099
$365$	13.5521	0.709348
$366$	15.2769	0.798536
$367$	−10.1030	−0.527373	−0.263686	−	0.964608i	$-0.584938\pi$
$367$	−10.1030	−0.527373	−0.263686	+	0.964608i	$0.584938\pi$
$368$	−17.6018	−0.917555
$369$	7.65971	0.398749
$370$	2.40946	0.125262
$371$	2.05656	0.106771
$372$	5.99012	0.310573
$373$	34.1356	1.76747	0.883736	−	0.467985i	$-0.155020\pi$
$373$	34.1356	1.76747	0.883736	+	0.467985i	$0.155020\pi$
$374$	−4.92832	−0.254837
$375$	11.0920	0.572787
$376$	2.60013	0.134092
$377$	1.79361	0.0923755
$378$	−16.4226	−0.844686
$379$	21.0196	1.07970	0.539852	−	0.841760i	$-0.318480\pi$
$379$	21.0196	1.07970	0.539852	+	0.841760i	$0.318480\pi$
$380$	0.253635	0.0130112
$381$	2.66114	0.136334
$382$	−1.75799	−0.0899465
$383$	33.5456	1.71410	0.857050	−	0.515234i	$-0.172295\pi$
$383$	33.5456	1.71410	0.857050	+	0.515234i	$0.172295\pi$
$384$	5.32564	0.271773
$385$	6.11894	0.311850
$386$	0.593813	0.0302243
$387$	14.1320	0.718372
$388$	8.25189	0.418926
$389$	−15.0203	−0.761557	−0.380779	−	0.924666i	$-0.624344\pi$
$389$	−15.0203	−0.761557	−0.380779	+	0.924666i	$0.624344\pi$
$390$	2.56469	0.129868
$391$	3.41743	0.172827
$392$	2.71335	0.137045
$393$	12.6767	0.639453
$394$	−20.7541	−1.04558
$395$	1.11954	0.0563304
$396$	9.20752	0.462695
$397$	−15.8759	−0.796790	−0.398395	−	0.917214i	$-0.630433\pi$
$397$	−15.8759	−0.796790	−0.398395	+	0.917214i	$0.630433\pi$
$398$	37.6861	1.88903
$399$	−0.211986	−0.0106126
$400$	15.5743	0.778714
$401$	−6.72323	−0.335742	−0.167871	−	0.985809i	$-0.553689\pi$
$401$	−6.72323	−0.335742	−0.167871	+	0.985809i	$0.553689\pi$
$402$	−11.0483	−0.551040
$403$	−3.49752	−0.174224
$404$	−23.4353	−1.16595
$405$	−0.422661	−0.0210022
$406$	−5.64317	−0.280066
$407$	2.90825	0.144157
$408$	−0.597915	−0.0296012
$409$	−14.1275	−0.698561	−0.349281	−	0.937018i	$-0.613574\pi$
$409$	−14.1275	−0.698561	−0.349281	+	0.937018i	$0.613574\pi$
$410$	9.69427	0.478766
$411$	−15.1805	−0.748797
$412$	27.8881	1.37395
$413$	−15.5550	−0.765413
$414$	−14.0633	−0.691173
$415$	−6.82294	−0.334925
$416$	7.56199	0.370757
$417$	−5.55108	−0.271838
$418$	0.674319	0.0329820
$419$	−12.3823	−0.604914	−0.302457	−	0.953163i	$-0.597807\pi$
$419$	−12.3823	−0.604914	−0.302457	+	0.953163i	$0.597807\pi$
$420$	−3.66342	−0.178756
$421$	−17.1049	−0.833642	−0.416821	−	0.908989i	$-0.636856\pi$
$421$	−17.1049	−0.833642	−0.416821	+	0.908989i	$0.636856\pi$
$422$	41.5735	2.02377
$423$	7.67485	0.373164
$424$	−0.793673	−0.0385442
$425$	−3.02379	−0.146675
$426$	−5.78484	−0.280276
$427$	12.7412	0.616591
$428$	−19.3593	−0.935769
$429$	3.09561	0.149458
$430$	17.8858	0.862529
$431$	−40.2057	−1.93664	−0.968320	−	0.249714i	$-0.919664\pi$
$431$	−40.2057	−1.93664	−0.968320	+	0.249714i	$0.919664\pi$
$432$	23.4145	1.12653
$433$	11.5579	0.555436	0.277718	−	0.960663i	$-0.410422\pi$
$433$	11.5579	0.555436	0.277718	+	0.960663i	$0.410422\pi$
$434$	11.0041	0.528215
$435$	2.32547	0.111498
$436$	−1.66300	−0.0796435
$437$	−0.467591	−0.0223679
$438$	−21.5711	−1.03071
$439$	−10.3906	−0.495917	−0.247959	−	0.968771i	$-0.579760\pi$
$439$	−10.3906	−0.495917	−0.247959	+	0.968771i	$0.579760\pi$
$440$	−2.36144	−0.112577
$441$	8.00903	0.381382
$442$	−1.72279	−0.0819449
$443$	−40.8701	−1.94179	−0.970897	−	0.239495i	$-0.923018\pi$
$443$	−40.8701	−1.94179	−0.970897	+	0.239495i	$0.923018\pi$
$444$	−1.74117	−0.0826324
$445$	−1.57054	−0.0744508
$446$	−7.03726	−0.333224
$447$	20.3133	0.960784
$448$	−8.54877	−0.403891
$449$	−34.4878	−1.62758	−0.813791	−	0.581158i	$-0.802600\pi$
$449$	−34.4878	−1.62758	−0.813791	+	0.581158i	$0.802600\pi$
$450$	12.4434	0.586587
$451$	11.7011	0.550984
$452$	2.32044	0.109144
$453$	−2.83019	−0.132974
$454$	54.6715	2.56586
$455$	2.13900	0.100278
$456$	0.0818099	0.00383110
$457$	27.8602	1.30325	0.651623	−	0.758543i	$-0.274089\pi$
$457$	27.8602	1.30325	0.651623	+	0.758543i	$0.274089\pi$
$458$	5.89590	0.275497
$459$	−4.54598	−0.212188
$460$	−8.08064	−0.376762
$461$	−34.8237	−1.62190	−0.810951	−	0.585114i	$-0.801050\pi$
$461$	−34.8237	−1.62190	−0.810951	+	0.585114i	$0.801050\pi$
$462$	−9.73963	−0.453128
$463$	32.7623	1.52259	0.761297	−	0.648403i	$-0.224563\pi$
$463$	32.7623	1.52259	0.761297	+	0.648403i	$0.224563\pi$
$464$	8.04575	0.373514
$465$	−4.53465	−0.210289
$466$	−50.7463	−2.35078
$467$	−31.2536	−1.44624	−0.723122	−	0.690721i	$-0.757293\pi$
$467$	−31.2536	−1.44624	−0.723122	+	0.690721i	$0.757293\pi$
$468$	3.21867	0.148783
$469$	−9.21449	−0.425486
$470$	9.71344	0.448047
$471$	17.7089	0.815985
$472$	6.00303	0.276312
$473$	21.5884	0.992634
$474$	−1.78200	−0.0818498
$475$	0.413731	0.0189833
$476$	2.46085	0.112793
$477$	−2.34270	−0.107265
$478$	7.37124	0.337153
$479$	19.0737	0.871498	0.435749	−	0.900068i	$-0.356484\pi$
$479$	19.0737	0.871498	0.435749	+	0.900068i	$0.356484\pi$
$480$	9.80438	0.447507
$481$	1.01664	0.0463547
$482$	−23.1978	−1.05663
$483$	6.75371	0.307304
$484$	−4.22748	−0.192158
$485$	−6.24685	−0.283655
$486$	30.1522	1.36773
$487$	−25.9482	−1.17582	−0.587912	−	0.808925i	$-0.700050\pi$
$487$	−25.9482	−1.17582	−0.587912	+	0.808925i	$0.700050\pi$
$488$	−4.91712	−0.222587
$489$	3.42573	0.154917
$490$	10.1364	0.457915
$491$	−10.8877	−0.491354	−0.245677	−	0.969352i	$-0.579010\pi$
$491$	−10.8877	−0.491354	−0.245677	+	0.969352i	$0.579010\pi$
$492$	−7.00547	−0.315831
$493$	−1.56210	−0.0703535
$494$	0.235722	0.0106056
$495$	−6.97029	−0.313291
$496$	−15.6891	−0.704463
$497$	−4.82466	−0.216416
$498$	10.8602	0.486657
$499$	43.8838	1.96451	0.982254	−	0.187556i	$-0.0600566\pi$
$499$	43.8838	1.96451	0.982254	+	0.187556i	$0.0600566\pi$
$500$	17.6179	0.787896
$501$	5.15109	0.230134
$502$	−27.5328	−1.22885
$503$	−26.3356	−1.17425	−0.587124	−	0.809497i	$-0.699740\pi$
$503$	−26.3356	−1.17425	−0.587124	+	0.809497i	$0.699740\pi$
$504$	2.05212	0.0914087
$505$	17.7410	0.789466
$506$	−21.4833	−0.955051
$507$	−12.5289	−0.556429
$508$	4.22680	0.187534
$509$	38.0863	1.68814	0.844072	−	0.536230i	$-0.180152\pi$
$509$	38.0863	1.68814	0.844072	+	0.536230i	$0.180152\pi$
$510$	−2.23366	−0.0989081
$511$	−17.9907	−0.795860
$512$	28.0388	1.23915
$513$	0.622006	0.0274622
$514$	−4.41790	−0.194865
$515$	−21.1119	−0.930300
$516$	−12.9250	−0.568990
$517$	11.7242	0.515631
$518$	−3.19861	−0.140539
$519$	−3.05857	−0.134256
$520$	−0.825487	−0.0362000
$521$	−13.0036	−0.569698	−0.284849	−	0.958572i	$-0.591943\pi$
$521$	−13.0036	−0.569698	−0.284849	+	0.958572i	$0.591943\pi$
$522$	6.42831	0.281360
$523$	9.66415	0.422584	0.211292	−	0.977423i	$-0.432233\pi$
$523$	9.66415	0.422584	0.211292	+	0.977423i	$0.432233\pi$
$524$	20.1349	0.879598
$525$	−5.97578	−0.260804
$526$	24.0705	1.04952
$527$	3.04609	0.132690
$528$	13.8863	0.604323
$529$	−8.10289	−0.352300
$530$	−2.96496	−0.128790
$531$	17.7192	0.768949
$532$	−0.336706	−0.0145981
$533$	4.09036	0.177173
$534$	2.49986	0.108179
$535$	14.6554	0.633610
$536$	3.55608	0.153599
$537$	13.1218	0.566247
$538$	41.0496	1.76977
$539$	12.2347	0.526987
$540$	10.7492	0.462570
$541$	−20.3793	−0.876174	−0.438087	−	0.898932i	$-0.644344\pi$
$541$	−20.3793	−0.876174	−0.438087	+	0.898932i	$0.644344\pi$
$542$	−26.4297	−1.13525
$543$	3.85172	0.165293
$544$	−6.58595	−0.282370
$545$	1.25893	0.0539266
$546$	−3.40468	−0.145707
$547$	−13.6100	−0.581923	−0.290962	−	0.956735i	$-0.593975\pi$
$547$	−13.6100	−0.581923	−0.290962	+	0.956735i	$0.593975\pi$
$548$	−24.1118	−1.03001
$549$	−14.5139	−0.619440
$550$	19.0088	0.810536
$551$	0.213735	0.00910542
$552$	−2.60641	−0.110936
$553$	−1.48622	−0.0632004
$554$	27.5168	1.16907
$555$	1.31810	0.0559504
$556$	−8.81703	−0.373925
$557$	2.30490	0.0976617	0.0488309	−	0.998807i	$-0.484450\pi$
$557$	2.30490	0.0976617	0.0488309	+	0.998807i	$0.484450\pi$
$558$	−12.5352	−0.530655
$559$	7.54664	0.319189
$560$	9.59511	0.405467
$561$	−2.69606	−0.113828
$562$	54.6752	2.30633
$563$	5.65654	0.238395	0.119197	−	0.992871i	$-0.461968\pi$
$563$	5.65654	0.238395	0.119197	+	0.992871i	$0.461968\pi$
$564$	−7.01931	−0.295566
$565$	−1.75662	−0.0739015
$566$	−46.7545	−1.96524
$567$	0.561092	0.0235636
$568$	1.86194	0.0781254
$569$	15.5749	0.652933	0.326467	−	0.945209i	$-0.394142\pi$
$569$	15.5749	0.652933	0.326467	+	0.945209i	$0.394142\pi$
$570$	0.305621	0.0128011
$571$	6.21838	0.260231	0.130115	−	0.991499i	$-0.458465\pi$
$571$	6.21838	0.260231	0.130115	+	0.991499i	$0.458465\pi$
$572$	4.91690	0.205586
$573$	−0.961713	−0.0401762
$574$	−12.8694	−0.537157
$575$	−13.1812	−0.549693
$576$	9.73818	0.405758
$577$	−5.62906	−0.234341	−0.117170	−	0.993112i	$-0.537382\pi$
$577$	−5.62906	−0.234341	−0.117170	+	0.993112i	$0.537382\pi$
$578$	−31.0358	−1.29092
$579$	0.324848	0.0135002
$580$	3.69365	0.153371
$581$	9.05760	0.375772
$582$	9.94322	0.412160
$583$	−3.57875	−0.148217
$584$	6.94299	0.287303
$585$	−2.43660	−0.100741
$586$	−7.12820	−0.294463
$587$	12.5846	0.519422	0.259711	−	0.965686i	$-0.416373\pi$
$587$	12.5846	0.519422	0.259711	+	0.965686i	$0.416373\pi$
$588$	−7.32495	−0.302076
$589$	−0.416782	−0.0171732
$590$	22.4258	0.923256
$591$	−11.3536	−0.467025
$592$	4.56042	0.187432
$593$	−10.5224	−0.432102	−0.216051	−	0.976382i	$-0.569318\pi$
$593$	−10.5224	−0.432102	−0.216051	+	0.976382i	$0.569318\pi$
$594$	28.5779	1.17257
$595$	−1.86291	−0.0763720
$596$	32.2645	1.32160
$597$	20.6163	0.843769
$598$	−7.50993	−0.307104
$599$	13.4894	0.551160	0.275580	−	0.961278i	$-0.411130\pi$
$599$	13.4894	0.551160	0.275580	+	0.961278i	$0.411130\pi$
$600$	2.30618	0.0941496
$601$	29.7364	1.21297	0.606486	−	0.795094i	$-0.292579\pi$
$601$	29.7364	1.21297	0.606486	+	0.795094i	$0.292579\pi$
$602$	−23.7438	−0.967723
$603$	10.4965	0.427452
$604$	−4.49532	−0.182912
$605$	3.20029	0.130110
$606$	−28.2387	−1.14712
$607$	12.6037	0.511568	0.255784	−	0.966734i	$-0.417666\pi$
$607$	12.6037	0.511568	0.255784	+	0.966734i	$0.417666\pi$
$608$	0.901125	0.0365454
$609$	−3.08711	−0.125096
$610$	−18.3691	−0.743744
$611$	4.09844	0.165805
$612$	−2.80323	−0.113314
$613$	46.8662	1.89291	0.946454	−	0.322838i	$-0.104637\pi$
$613$	46.8662	1.89291	0.946454	+	0.322838i	$0.104637\pi$
$614$	40.9976	1.65453
$615$	5.30329	0.213849
$616$	3.13486	0.126307
$617$	−23.1700	−0.932788	−0.466394	−	0.884577i	$-0.654447\pi$
$617$	−23.1700	−0.932788	−0.466394	+	0.884577i	$0.654447\pi$
$618$	33.6041	1.35176
$619$	18.7140	0.752180	0.376090	−	0.926583i	$-0.377268\pi$
$619$	18.7140	0.752180	0.376090	+	0.926583i	$0.377268\pi$
$620$	−7.20259	−0.289263
$621$	−19.8167	−0.795215
$622$	−37.8365	−1.51710
$623$	2.08493	0.0835309
$624$	4.85423	0.194325
$625$	3.73836	0.149534
$626$	33.1500	1.32494
$627$	0.368889	0.0147320
$628$	28.1279	1.12243
$629$	−0.885418	−0.0353039
$630$	7.66620	0.305429
$631$	−37.6619	−1.49930	−0.749649	−	0.661836i	$-0.769777\pi$
$631$	−37.6619	−1.49930	−0.749649	+	0.661836i	$0.769777\pi$
$632$	0.573564	0.0228152
$633$	22.7429	0.903950
$634$	−39.9218	−1.58550
$635$	−3.19978	−0.126979
$636$	2.14260	0.0849597
$637$	4.27690	0.169457
$638$	9.82001	0.388778
$639$	5.49593	0.217416
$640$	−6.40361	−0.253125
$641$	−19.2286	−0.759482	−0.379741	−	0.925093i	$-0.623987\pi$
$641$	−19.2286	−0.759482	−0.379741	+	0.925093i	$0.623987\pi$
$642$	−23.3273	−0.920655
$643$	7.35922	0.290219	0.145110	−	0.989416i	$-0.453646\pi$
$643$	7.35922	0.290219	0.145110	+	0.989416i	$0.453646\pi$
$644$	10.7272	0.422712
$645$	9.78448	0.385263
$646$	−0.205297	−0.00807729
$647$	10.4082	0.409188	0.204594	−	0.978847i	$-0.434413\pi$
$647$	10.4082	0.409188	0.204594	+	0.978847i	$0.434413\pi$
$648$	−0.216538	−0.00850640
$649$	27.0682	1.06252
$650$	6.64489	0.260634
$651$	6.01984	0.235936
$652$	5.44124	0.213095
$653$	−29.1993	−1.14266	−0.571328	−	0.820722i	$-0.693571\pi$
$653$	−29.1993	−1.14266	−0.571328	+	0.820722i	$0.693571\pi$
$654$	−2.00386	−0.0783571
$655$	−15.2426	−0.595576
$656$	18.3485	0.716388
$657$	20.4937	0.799537
$658$	−12.8948	−0.502691
$659$	2.03535	0.0792861	0.0396430	−	0.999214i	$-0.487378\pi$
$659$	2.03535	0.0792861	0.0396430	+	0.999214i	$0.487378\pi$
$660$	6.37493	0.248144
$661$	47.5072	1.84782	0.923908	−	0.382614i	$-0.124976\pi$
$661$	47.5072	1.84782	0.923908	+	0.382614i	$0.124976\pi$
$662$	−28.2905	−1.09954
$663$	−0.942460	−0.0366021
$664$	−3.49553	−0.135653
$665$	0.254894	0.00988436
$666$	3.64364	0.141188
$667$	−6.80945	−0.263663
$668$	8.18172	0.316560
$669$	−3.84976	−0.148840
$670$	13.2846	0.513229
$671$	−22.1718	−0.855931
$672$	−13.0155	−0.502085
$673$	44.7810	1.72618	0.863090	−	0.505050i	$-0.168526\pi$
$673$	44.7810	1.72618	0.863090	+	0.505050i	$0.168526\pi$
$674$	−51.1265	−1.96932
$675$	17.5341	0.674886
$676$	−19.9003	−0.765395
$677$	14.1379	0.543362	0.271681	−	0.962387i	$-0.412420\pi$
$677$	14.1379	0.543362	0.271681	+	0.962387i	$0.412420\pi$
$678$	2.79604	0.107381
$679$	8.29283	0.318250
$680$	0.718939	0.0275701
$681$	29.9082	1.14609
$682$	−19.1489	−0.733250
$683$	42.2188	1.61546	0.807729	−	0.589554i	$-0.200697\pi$
$683$	42.2188	1.61546	0.807729	+	0.589554i	$0.200697\pi$
$684$	0.383553	0.0146655
$685$	18.2531	0.697417
$686$	−35.8465	−1.36863
$687$	3.22537	0.123056
$688$	33.8527	1.29062
$689$	−1.25102	−0.0476602
$690$	−9.73688	−0.370677
$691$	−24.1178	−0.917485	−0.458743	−	0.888569i	$-0.651700\pi$
$691$	−24.1178	−0.917485	−0.458743	+	0.888569i	$0.651700\pi$
$692$	−4.85807	−0.184676
$693$	9.25321	0.351500
$694$	−68.6630	−2.60641
$695$	6.67468	0.253185
$696$	1.19138	0.0451593
$697$	−3.56241	−0.134936
$698$	54.2686	2.05410
$699$	−27.7610	−1.05002
$700$	−9.49160	−0.358749
$701$	29.5654	1.11667	0.558335	−	0.829615i	$-0.311440\pi$
$701$	29.5654	1.11667	0.558335	+	0.829615i	$0.311440\pi$
$702$	9.98998	0.377047
$703$	0.121148	0.00456917
$704$	14.8762	0.560669
$705$	5.31377	0.200128
$706$	−64.2756	−2.41904
$707$	−23.5516	−0.885749
$708$	−16.2058	−0.609050
$709$	−41.3896	−1.55442	−0.777209	−	0.629243i	$-0.783365\pi$
$709$	−41.3896	−1.55442	−0.777209	+	0.629243i	$0.783365\pi$
$710$	6.95576	0.261045
$711$	1.69300	0.0634924
$712$	−0.804619	−0.0301544
$713$	13.2784	0.497279
$714$	2.96523	0.110971
$715$	−3.72220	−0.139202
$716$	20.8419	0.778899
$717$	4.03246	0.150595
$718$	33.8412	1.26294
$719$	8.61398	0.321247	0.160624	−	0.987016i	$-0.448649\pi$
$719$	8.61398	0.321247	0.160624	+	0.987016i	$0.448649\pi$
$720$	−10.9301	−0.407341
$721$	28.0264	1.04376
$722$	−36.3360	−1.35228
$723$	−12.6904	−0.471963
$724$	6.11785	0.227368
$725$	6.02510	0.223766
$726$	−5.09395	−0.189054
$727$	−5.32082	−0.197338	−0.0986691	−	0.995120i	$-0.531459\pi$
$727$	−5.32082	−0.197338	−0.0986691	+	0.995120i	$0.531459\pi$
$728$	1.09585	0.0406150
$729$	15.4877	0.573618
$730$	25.9373	0.959982
$731$	−6.57258	−0.243096
$732$	13.2743	0.490630
$733$	−9.21010	−0.340183	−0.170091	−	0.985428i	$-0.554406\pi$
$733$	−9.21010	−0.340183	−0.170091	+	0.985428i	$0.554406\pi$
$734$	−19.3361	−0.713710
$735$	5.54514	0.204536
$736$	−28.7092	−1.05823
$737$	16.0347	0.590645
$738$	14.6599	0.539638
$739$	−36.6892	−1.34963	−0.674817	−	0.737985i	$-0.735778\pi$
$739$	−36.6892	−1.34963	−0.674817	+	0.737985i	$0.735778\pi$
$740$	2.09361	0.0769625
$741$	0.128952	0.00473718
$742$	3.93605	0.144497
$743$	−39.8147	−1.46066	−0.730330	−	0.683095i	$-0.760634\pi$
$743$	−39.8147	−1.46066	−0.730330	+	0.683095i	$0.760634\pi$
$744$	−2.32319	−0.0851723
$745$	−24.4249	−0.894859
$746$	65.3320	2.39197
$747$	−10.3178	−0.377509
$748$	−4.28227	−0.156575
$749$	−19.4554	−0.710885
$750$	21.2289	0.775170
$751$	17.9016	0.653238	0.326619	−	0.945156i	$-0.394091\pi$
$751$	17.9016	0.653238	0.326619	+	0.945156i	$0.394091\pi$
$752$	18.3848	0.670423
$753$	−15.0619	−0.548886
$754$	3.43278	0.125014
$755$	3.40305	0.123850
$756$	−14.2697	−0.518985
$757$	19.1176	0.694840	0.347420	−	0.937710i	$-0.387058\pi$
$757$	19.1176	0.694840	0.347420	+	0.937710i	$0.387058\pi$
$758$	40.2294	1.46120
$759$	−11.7525	−0.426590
$760$	−0.0983691	−0.00356822
$761$	−34.0875	−1.23567	−0.617835	−	0.786308i	$-0.711990\pi$
$761$	−34.0875	−1.23567	−0.617835	+	0.786308i	$0.711990\pi$
$762$	5.09314	0.184505
$763$	−1.67126	−0.0605035
$764$	−1.52753	−0.0552642
$765$	2.12211	0.0767249
$766$	64.2028	2.31974
$767$	9.46224	0.341662
$768$	20.9040	0.754307
$769$	−46.8522	−1.68953	−0.844767	−	0.535134i	$-0.820261\pi$
$769$	−46.8522	−1.68953	−0.844767	+	0.535134i	$0.820261\pi$
$770$	11.7110	0.422036
$771$	−2.41683	−0.0870399
$772$	0.515970	0.0185702
$773$	−29.3844	−1.05688	−0.528441	−	0.848970i	$-0.677223\pi$
$773$	−29.3844	−1.05688	−0.528441	+	0.848970i	$0.677223\pi$
$774$	27.0473	0.972194
$775$	−11.7489	−0.422032
$776$	−3.20039	−0.114887
$777$	−1.74981	−0.0627742
$778$	−28.7472	−1.03064
$779$	0.487427	0.0174639
$780$	2.22848	0.0797926
$781$	8.39569	0.300421
$782$	6.54061	0.233892
$783$	9.05818	0.323713
$784$	19.1853	0.685188
$785$	−21.2934	−0.759995
$786$	24.2618	0.865391
$787$	0.230135	0.00820344	0.00410172	−	0.999992i	$-0.498694\pi$
$787$	0.230135	0.00820344	0.00410172	+	0.999992i	$0.498694\pi$
$788$	−18.0335	−0.642415
$789$	13.1678	0.468787
$790$	2.14269	0.0762336
$791$	2.33195	0.0829145
$792$	−3.57102	−0.126891
$793$	−7.75058	−0.275231
$794$	−30.3849	−1.07832
$795$	−1.62199	−0.0575262
$796$	32.7458	1.16064
$797$	−4.63610	−0.164219	−0.0821095	−	0.996623i	$-0.526166\pi$
$797$	−4.63610	−0.164219	−0.0821095	+	0.996623i	$0.526166\pi$
$798$	−0.405719	−0.0143623
$799$	−3.56945	−0.126278
$800$	25.4023	0.898107
$801$	−2.37501	−0.0839168
$802$	−12.8676	−0.454370
$803$	31.3066	1.10479
$804$	−9.59998	−0.338565
$805$	−8.12074	−0.286218
$806$	−6.69389	−0.235782
$807$	22.4563	0.790499
$808$	9.08908	0.319753
$809$	−15.0080	−0.527652	−0.263826	−	0.964570i	$-0.584984\pi$
$809$	−15.0080	−0.527652	−0.263826	+	0.964570i	$0.584984\pi$
$810$	−0.808930	−0.0284229
$811$	27.7982	0.976128	0.488064	−	0.872808i	$-0.337703\pi$
$811$	27.7982	0.976128	0.488064	+	0.872808i	$0.337703\pi$
$812$	−4.90340	−0.172076
$813$	−14.4584	−0.507079
$814$	5.56610	0.195092
$815$	−4.11913	−0.144287
$816$	−4.22768	−0.147998
$817$	0.899295	0.0314624
$818$	−27.0386	−0.945384
$819$	3.23464	0.113028
$820$	8.42345	0.294160
$821$	−20.5694	−0.717876	−0.358938	−	0.933361i	$-0.616861\pi$
$821$	−20.5694	−0.717876	−0.358938	+	0.933361i	$0.616861\pi$
$822$	−29.0538	−1.01337
$823$	7.97039	0.277830	0.138915	−	0.990304i	$-0.455638\pi$
$823$	7.97039	0.277830	0.138915	+	0.990304i	$0.455638\pi$
$824$	−10.8160	−0.376794
$825$	10.3988	0.362040
$826$	−29.7707	−1.03586
$827$	28.6714	0.997003	0.498501	−	0.866889i	$-0.333884\pi$
$827$	28.6714	0.997003	0.498501	+	0.866889i	$0.333884\pi$
$828$	−12.2197	−0.424665
$829$	−46.7164	−1.62253	−0.811264	−	0.584680i	$-0.801220\pi$
$829$	−46.7164	−1.62253	−0.811264	+	0.584680i	$0.801220\pi$
$830$	−13.0584	−0.453264
$831$	15.0531	0.522187
$832$	5.20028	0.180287
$833$	−3.72487	−0.129059
$834$	−10.6242	−0.367886
$835$	−6.19373	−0.214343
$836$	0.585923	0.0202646
$837$	−17.6634	−0.610535
$838$	−23.6984	−0.818649
$839$	30.0780	1.03841	0.519205	−	0.854650i	$-0.326228\pi$
$839$	30.0780	1.03841	0.519205	+	0.854650i	$0.326228\pi$
$840$	1.42081	0.0490225
$841$	−25.8874	−0.892669
$842$	−32.7370	−1.12819
$843$	29.9102	1.03016
$844$	36.1236	1.24343
$845$	15.0649	0.518249
$846$	14.6889	0.505014
$847$	−4.24845	−0.145979
$848$	−5.61183	−0.192711
$849$	−25.5772	−0.877808
$850$	−5.78722	−0.198500
$851$	−3.85968	−0.132308
$852$	−5.02651	−0.172205
$853$	−39.6377	−1.35717	−0.678585	−	0.734522i	$-0.737407\pi$
$853$	−39.6377	−1.35717	−0.678585	+	0.734522i	$0.737407\pi$
$854$	24.3854	0.834451
$855$	−0.290358	−0.00993003
$856$	7.50827	0.256627
$857$	−39.0354	−1.33342	−0.666712	−	0.745316i	$-0.732299\pi$
$857$	−39.0354	−1.33342	−0.666712	+	0.745316i	$0.732299\pi$
$858$	5.92469	0.202265
$859$	−9.89601	−0.337648	−0.168824	−	0.985646i	$-0.553997\pi$
$859$	−9.89601	−0.337648	−0.168824	+	0.985646i	$0.553997\pi$
$860$	15.5411	0.529948
$861$	−7.04023	−0.239930
$862$	−76.9496	−2.62091
$863$	0.0544156	0.00185233	0.000926165	−	1.00000i	$-0.499705\pi$
$863$	0.0544156	0.00185233	0.000926165		1.00000i	$0.499705\pi$
$864$	38.1900	1.29925
$865$	3.67766	0.125044
$866$	22.1206	0.751688
$867$	−16.9783	−0.576612
$868$	9.56159	0.324542
$869$	2.58626	0.0877328
$870$	4.45072	0.150893
$871$	5.60525	0.189927
$872$	0.644974	0.0218416
$873$	−9.44663	−0.319720
$874$	−0.894920	−0.0302711
$875$	17.7053	0.598549
$876$	−18.7433	−0.633278
$877$	3.70915	0.125249	0.0626245	−	0.998037i	$-0.480053\pi$
$877$	3.70915	0.125249	0.0626245	+	0.998037i	$0.480053\pi$
$878$	−19.8866	−0.671140
$879$	−3.89951	−0.131527
$880$	−16.6970	−0.562856
$881$	−35.9348	−1.21067	−0.605337	−	0.795969i	$-0.706962\pi$
$881$	−35.9348	−1.21067	−0.605337	+	0.795969i	$0.706962\pi$
$882$	15.3285	0.516136
$883$	35.0901	1.18088	0.590438	−	0.807083i	$-0.298955\pi$
$883$	35.0901	1.18088	0.590438	+	0.807083i	$0.298955\pi$
$884$	−1.49695	−0.0503480
$885$	12.2681	0.412388
$886$	−78.2211	−2.62789
$887$	−28.5314	−0.957991	−0.478996	−	0.877817i	$-0.658999\pi$
$887$	−28.5314	−0.957991	−0.478996	+	0.877817i	$0.658999\pi$
$888$	0.675291	0.0226613
$889$	4.24777	0.142466
$890$	−3.00586	−0.100757
$891$	−0.976389	−0.0327103
$892$	−6.11475	−0.204737
$893$	0.488391	0.0163434
$894$	38.8775	1.30026
$895$	−15.7778	−0.527393
$896$	8.50093	0.283996
$897$	−4.10833	−0.137173
$898$	−66.0062	−2.20265
$899$	−6.06953	−0.202430
$900$	10.8122	0.360406
$901$	1.08955	0.0362982
$902$	22.3947	0.745663
$903$	−12.9891	−0.432250
$904$	−0.899950	−0.0299319
$905$	−4.63134	−0.153951
$906$	−5.41670	−0.179958
$907$	−3.54186	−0.117605	−0.0588027	−	0.998270i	$-0.518728\pi$
$907$	−3.54186	−0.117605	−0.0588027	+	0.998270i	$0.518728\pi$
$908$	47.5046	1.57650
$909$	26.8284	0.889842
$910$	4.09383	0.135709
$911$	0.467441	0.0154870	0.00774350	−	0.999970i	$-0.497535\pi$
$911$	0.467441	0.0154870	0.00774350	+	0.999970i	$0.497535\pi$
$912$	0.578454	0.0191545
$913$	−15.7617	−0.521635
$914$	53.3216	1.76372
$915$	−10.0489	−0.332206
$916$	5.12300	0.169269
$917$	20.2348	0.668213
$918$	−8.70055	−0.287161
$919$	−24.7138	−0.815235	−0.407617	−	0.913153i	$-0.633640\pi$
$919$	−24.7138	−0.815235	−0.407617	+	0.913153i	$0.633640\pi$
$920$	3.13397	0.103324
$921$	22.4279	0.739023
$922$	−66.6490	−2.19497
$923$	2.93488	0.0966027
$924$	−8.46286	−0.278408
$925$	3.41510	0.112288
$926$	62.7037	2.06057
$927$	−31.9258	−1.04858
$928$	13.1229	0.430782
$929$	−17.0243	−0.558550	−0.279275	−	0.960211i	$-0.590094\pi$
$929$	−17.0243	−0.558550	−0.279275	+	0.960211i	$0.590094\pi$
$930$	−8.67886	−0.284591
$931$	0.509656	0.0167033
$932$	−44.0940	−1.44435
$933$	−20.6986	−0.677641
$934$	−59.8162	−1.95724
$935$	3.24177	0.106017
$936$	−1.24832	−0.0408026
$937$	−8.21055	−0.268227	−0.134114	−	0.990966i	$-0.542819\pi$
$937$	−8.21055	−0.268227	−0.134114	+	0.990966i	$0.542819\pi$
$938$	−17.6356	−0.575823
$939$	18.1348	0.591807
$940$	8.44010	0.275286
$941$	16.3653	0.533493	0.266746	−	0.963767i	$-0.414051\pi$
$941$	16.3653	0.533493	0.266746	+	0.963767i	$0.414051\pi$
$942$	33.8931	1.10430
$943$	−15.5291	−0.505697
$944$	42.4456	1.38149
$945$	10.8025	0.351405
$946$	41.3179	1.34336
$947$	−6.47808	−0.210509	−0.105255	−	0.994445i	$-0.533566\pi$
$947$	−6.47808	−0.210509	−0.105255	+	0.994445i	$0.533566\pi$
$948$	−1.54839	−0.0502895
$949$	10.9439	0.355253
$950$	0.791838	0.0256906
$951$	−21.8394	−0.708190
$952$	−0.954407	−0.0309325
$953$	−16.5998	−0.537721	−0.268861	−	0.963179i	$-0.586647\pi$
$953$	−16.5998	−0.537721	−0.268861	+	0.963179i	$0.586647\pi$
$954$	−4.48369	−0.145165
$955$	1.15637	0.0374194
$956$	6.40495	0.207151
$957$	5.37207	0.173654
$958$	36.5050	1.17942
$959$	−24.2314	−0.782474
$960$	6.74234	0.217608
$961$	−19.1645	−0.618209
$962$	1.94574	0.0627332
$963$	22.1623	0.714169
$964$	−20.1568	−0.649207
$965$	−0.390600	−0.0125739
$966$	12.9259	0.415884
$967$	−19.2081	−0.617691	−0.308846	−	0.951112i	$-0.599943\pi$
$967$	−19.2081	−0.617691	−0.308846	+	0.951112i	$0.599943\pi$
$968$	1.63957	0.0526978
$969$	−0.112308	−0.00360786
$970$	−11.9558	−0.383879
$971$	−28.2016	−0.905033	−0.452517	−	0.891756i	$-0.649474\pi$
$971$	−28.2016	−0.905033	−0.452517	+	0.891756i	$0.649474\pi$
$972$	26.1996	0.840351
$973$	−8.86078	−0.284064
$974$	−49.6622	−1.59128
$975$	3.63511	0.116417
$976$	−34.7675	−1.11288
$977$	−2.60879	−0.0834625	−0.0417312	−	0.999129i	$-0.513287\pi$
$977$	−2.60879	−0.0834625	−0.0417312	+	0.999129i	$0.513287\pi$
$978$	6.55649	0.209653
$979$	−3.62811	−0.115955
$980$	8.80760	0.281348
$981$	1.90378	0.0607831
$982$	−20.8379	−0.664965
$983$	60.5171	1.93019	0.965097	−	0.261891i	$-0.0843462\pi$
$983$	60.5171	1.93019	0.965097	+	0.261891i	$0.0843462\pi$
$984$	2.71698	0.0866141
$985$	13.6517	0.434980
$986$	−2.98970	−0.0952116
$987$	−7.05414	−0.224536
$988$	0.204821	0.00651622
$989$	−28.6509	−0.911046
$990$	−13.3404	−0.423986
$991$	47.5677	1.51104	0.755519	−	0.655127i	$-0.227385\pi$
$991$	47.5677	1.51104	0.755519	+	0.655127i	$0.227385\pi$
$992$	−25.5896	−0.812471
$993$	−15.4764	−0.491129
$994$	−9.23391	−0.292882
$995$	−24.7893	−0.785873
$996$	9.43652	0.299008
$997$	−18.4345	−0.583827	−0.291914	−	0.956445i	$-0.594292\pi$
$997$	−18.4345	−0.583827	−0.291914	+	0.956445i	$0.594292\pi$
$998$	83.9891	2.65863
$999$	5.13428	0.162441

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4033.2.a.d.1.65	✓	79

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4033.2.a.d.1.65	✓	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)

\(f(q)\)	\(=\)	\(q+1.91390 q^{2} +1.04700 q^{3} +1.66300 q^{4} -1.25893 q^{5} +2.00386 q^{6} +1.67126 q^{7} -0.644974 q^{8} -1.90378 q^{9} +O(q^{10})\)	\(q+1.91390 q^{2} +1.04700 q^{3} +1.66300 q^{4} -1.25893 q^{5} +2.00386 q^{6} +1.67126 q^{7} -0.644974 q^{8} -1.90378 q^{9} -2.40946 q^{10} -2.90825 q^{11} +1.74117 q^{12} -1.01664 q^{13} +3.19861 q^{14} -1.31810 q^{15} -4.56042 q^{16} +0.885418 q^{17} -3.64364 q^{18} -0.121148 q^{19} -2.09361 q^{20} +1.74981 q^{21} -5.56610 q^{22} +3.85968 q^{23} -0.675291 q^{24} -3.41510 q^{25} -1.94574 q^{26} -5.13428 q^{27} +2.77931 q^{28} -1.76425 q^{29} -2.52272 q^{30} +3.44028 q^{31} -7.43824 q^{32} -3.04495 q^{33} +1.69460 q^{34} -2.10399 q^{35} -3.16600 q^{36} -1.00000 q^{37} -0.231864 q^{38} -1.06442 q^{39} +0.811978 q^{40} -4.02342 q^{41} +3.34896 q^{42} -7.42314 q^{43} -4.83644 q^{44} +2.39673 q^{45} +7.38703 q^{46} -4.03137 q^{47} -4.77478 q^{48} -4.20690 q^{49} -6.53614 q^{50} +0.927036 q^{51} -1.69067 q^{52} +1.23055 q^{53} -9.82649 q^{54} +3.66128 q^{55} -1.07792 q^{56} -0.126842 q^{57} -3.37660 q^{58} -9.30739 q^{59} -2.19201 q^{60} +7.62374 q^{61} +6.58434 q^{62} -3.18171 q^{63} -5.11518 q^{64} +1.27988 q^{65} -5.82773 q^{66} -5.51351 q^{67} +1.47245 q^{68} +4.04110 q^{69} -4.02683 q^{70} -2.88685 q^{71} +1.22789 q^{72} -10.7648 q^{73} -1.91390 q^{74} -3.57562 q^{75} -0.201469 q^{76} -4.86043 q^{77} -2.03720 q^{78} -0.889282 q^{79} +5.74125 q^{80} +0.335731 q^{81} -7.70041 q^{82} +5.41964 q^{83} +2.90995 q^{84} -1.11468 q^{85} -14.2071 q^{86} -1.84718 q^{87} +1.87575 q^{88} +1.24752 q^{89} +4.58709 q^{90} -1.69906 q^{91} +6.41866 q^{92} +3.60199 q^{93} -7.71563 q^{94} +0.152516 q^{95} -7.78787 q^{96} +4.96204 q^{97} -8.05158 q^{98} +5.53668 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9}+O(q^{10}) \) 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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