LMFDB - Embedded newform 8042.2.a.d.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8042,2,Mod(1,8042)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8042, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8042.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8042 = 2 \cdot 4021 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8042.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:	$64.2156933055$
Analytic rank:	$0$
Dimension:	$101$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	8042.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -3.33232 q^{3} +1.00000 q^{4} -1.78644 q^{5} -3.33232 q^{6} -0.0456798 q^{7} +1.00000 q^{8} +8.10435 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -3.33232 q^{3} +1.00000 q^{4} -1.78644 q^{5} -3.33232 q^{6} -0.0456798 q^{7} +1.00000 q^{8} +8.10435 q^{9} -1.78644 q^{10} -5.99217 q^{11} -3.33232 q^{12} -3.99693 q^{13} -0.0456798 q^{14} +5.95298 q^{15} +1.00000 q^{16} -5.21345 q^{17} +8.10435 q^{18} +7.52374 q^{19} -1.78644 q^{20} +0.152220 q^{21} -5.99217 q^{22} -3.44395 q^{23} -3.33232 q^{24} -1.80864 q^{25} -3.99693 q^{26} -17.0093 q^{27} -0.0456798 q^{28} -9.27212 q^{29} +5.95298 q^{30} -1.64123 q^{31} +1.00000 q^{32} +19.9678 q^{33} -5.21345 q^{34} +0.0816041 q^{35} +8.10435 q^{36} +2.25901 q^{37} +7.52374 q^{38} +13.3191 q^{39} -1.78644 q^{40} +3.31559 q^{41} +0.152220 q^{42} +1.25892 q^{43} -5.99217 q^{44} -14.4779 q^{45} -3.44395 q^{46} -7.17071 q^{47} -3.33232 q^{48} -6.99791 q^{49} -1.80864 q^{50} +17.3729 q^{51} -3.99693 q^{52} +3.90508 q^{53} -17.0093 q^{54} +10.7046 q^{55} -0.0456798 q^{56} -25.0715 q^{57} -9.27212 q^{58} -14.3500 q^{59} +5.95298 q^{60} -0.994778 q^{61} -1.64123 q^{62} -0.370205 q^{63} +1.00000 q^{64} +7.14027 q^{65} +19.9678 q^{66} +9.53428 q^{67} -5.21345 q^{68} +11.4763 q^{69} +0.0816041 q^{70} -7.73430 q^{71} +8.10435 q^{72} +11.1612 q^{73} +2.25901 q^{74} +6.02697 q^{75} +7.52374 q^{76} +0.273721 q^{77} +13.3191 q^{78} -3.45897 q^{79} -1.78644 q^{80} +32.3675 q^{81} +3.31559 q^{82} -11.2218 q^{83} +0.152220 q^{84} +9.31350 q^{85} +1.25892 q^{86} +30.8977 q^{87} -5.99217 q^{88} -11.6384 q^{89} -14.4779 q^{90} +0.182579 q^{91} -3.44395 q^{92} +5.46910 q^{93} -7.17071 q^{94} -13.4407 q^{95} -3.33232 q^{96} -7.80631 q^{97} -6.99791 q^{98} -48.5627 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 101 q + 101 q^{2} + 10 q^{3} + 101 q^{4} + 19 q^{5} + 10 q^{6} + 42 q^{7} + 101 q^{8} + 147 q^{9}+O(q^{10}) $ 101 * q + 101 * q^2 + 10 * q^3 + 101 * q^4 + 19 * q^5 + 10 * q^6 + 42 * q^7 + 101 * q^8 + 147 * q^9	\( 101 q + 101 q^{2} + 10 q^{3} + 101 q^{4} + 19 q^{5} + 10 q^{6} + 42 q^{7} + 101 q^{8} + 147 q^{9} + 19 q^{10} + 4 q^{11} + 10 q^{12} + 58 q^{13} + 42 q^{14} + 27 q^{15} + 101 q^{16} + 34 q^{17} + 147 q^{18} + 36 q^{19} + 19 q^{20} + 45 q^{21} + 4 q^{22} + 47 q^{23} + 10 q^{24} + 174 q^{25} + 58 q^{26} + 31 q^{27} + 42 q^{28} + 62 q^{29} + 27 q^{30} + 47 q^{31} + 101 q^{32} + 55 q^{33} + 34 q^{34} + 16 q^{35} + 147 q^{36} + 90 q^{37} + 36 q^{38} + 50 q^{39} + 19 q^{40} + 54 q^{41} + 45 q^{42} + 65 q^{43} + 4 q^{44} + 47 q^{45} + 47 q^{46} + 54 q^{47} + 10 q^{48} + 189 q^{49} + 174 q^{50} + 36 q^{51} + 58 q^{52} + 94 q^{53} + 31 q^{54} + 68 q^{55} + 42 q^{56} + 79 q^{57} + 62 q^{58} - 6 q^{59} + 27 q^{60} + 58 q^{61} + 47 q^{62} + 117 q^{63} + 101 q^{64} + 89 q^{65} + 55 q^{66} + 127 q^{67} + 34 q^{68} + 45 q^{69} + 16 q^{70} + 87 q^{71} + 147 q^{72} + 83 q^{73} + 90 q^{74} - 4 q^{75} + 36 q^{76} + 53 q^{77} + 50 q^{78} + 74 q^{79} + 19 q^{80} + 241 q^{81} + 54 q^{82} + 11 q^{83} + 45 q^{84} + 120 q^{85} + 65 q^{86} + 37 q^{87} + 4 q^{88} + 89 q^{89} + 47 q^{90} + 31 q^{91} + 47 q^{92} + 123 q^{93} + 54 q^{94} + 61 q^{95} + 10 q^{96} + 85 q^{97} + 189 q^{98} - 55 q^{99}+O(q^{100}) \) 101 * q + 101 * q^2 + 10 * q^3 + 101 * q^4 + 19 * q^5 + 10 * q^6 + 42 * q^7 + 101 * q^8 + 147 * q^9 + 19 * q^10 + 4 * q^11 + 10 * q^12 + 58 * q^13 + 42 * q^14 + 27 * q^15 + 101 * q^16 + 34 * q^17 + 147 * q^18 + 36 * q^19 + 19 * q^20 + 45 * q^21 + 4 * q^22 + 47 * q^23 + 10 * q^24 + 174 * q^25 + 58 * q^26 + 31 * q^27 + 42 * q^28 + 62 * q^29 + 27 * q^30 + 47 * q^31 + 101 * q^32 + 55 * q^33 + 34 * q^34 + 16 * q^35 + 147 * q^36 + 90 * q^37 + 36 * q^38 + 50 * q^39 + 19 * q^40 + 54 * q^41 + 45 * q^42 + 65 * q^43 + 4 * q^44 + 47 * q^45 + 47 * q^46 + 54 * q^47 + 10 * q^48 + 189 * q^49 + 174 * q^50 + 36 * q^51 + 58 * q^52 + 94 * q^53 + 31 * q^54 + 68 * q^55 + 42 * q^56 + 79 * q^57 + 62 * q^58 - 6 * q^59 + 27 * q^60 + 58 * q^61 + 47 * q^62 + 117 * q^63 + 101 * q^64 + 89 * q^65 + 55 * q^66 + 127 * q^67 + 34 * q^68 + 45 * q^69 + 16 * q^70 + 87 * q^71 + 147 * q^72 + 83 * q^73 + 90 * q^74 - 4 * q^75 + 36 * q^76 + 53 * q^77 + 50 * q^78 + 74 * q^79 + 19 * q^80 + 241 * q^81 + 54 * q^82 + 11 * q^83 + 45 * q^84 + 120 * q^85 + 65 * q^86 + 37 * q^87 + 4 * q^88 + 89 * q^89 + 47 * q^90 + 31 * q^91 + 47 * q^92 + 123 * q^93 + 54 * q^94 + 61 * q^95 + 10 * q^96 + 85 * q^97 + 189 * q^98 - 55 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−3.33232	−1.92392	−0.961958	−	0.273198i	$-0.911919\pi$
$3$	−3.33232	−1.92392	−0.961958	+	0.273198i	$0.911919\pi$
$4$	1.00000	0.500000
$5$	−1.78644	−0.798919	−0.399460	−	0.916751i	$-0.630802\pi$
$5$	−1.78644	−0.798919	−0.399460	+	0.916751i	$0.630802\pi$
$6$	−3.33232	−1.36041
$7$	−0.0456798	−0.0172653	−0.00863267	−	0.999963i	$-0.502748\pi$
$7$	−0.0456798	−0.0172653	−0.00863267	+	0.999963i	$0.502748\pi$
$8$	1.00000	0.353553
$9$	8.10435	2.70145
$10$	−1.78644	−0.564921
$11$	−5.99217	−1.80671	−0.903354	−	0.428895i	$-0.858903\pi$
$11$	−5.99217	−1.80671	−0.903354	+	0.428895i	$0.858903\pi$
$12$	−3.33232	−0.961958
$13$	−3.99693	−1.10855	−0.554275	−	0.832334i	$-0.687004\pi$
$13$	−3.99693	−1.10855	−0.554275	+	0.832334i	$0.687004\pi$
$14$	−0.0456798	−0.0122084
$15$	5.95298	1.53705
$16$	1.00000	0.250000
$17$	−5.21345	−1.26445	−0.632224	−	0.774786i	$-0.717858\pi$
$17$	−5.21345	−1.26445	−0.632224	+	0.774786i	$0.717858\pi$
$18$	8.10435	1.91021
$19$	7.52374	1.72606	0.863032	−	0.505149i	$-0.168563\pi$
$19$	7.52374	1.72606	0.863032	+	0.505149i	$0.168563\pi$
$20$	−1.78644	−0.399460
$21$	0.152220	0.0332171
$22$	−5.99217	−1.27754
$23$	−3.44395	−0.718113	−0.359056	−	0.933316i	$-0.616901\pi$
$23$	−3.44395	−0.718113	−0.359056	+	0.933316i	$0.616901\pi$
$24$	−3.33232	−0.680207
$25$	−1.80864	−0.361728
$26$	−3.99693	−0.783863
$27$	−17.0093	−3.27345
$28$	−0.0456798	−0.00863267
$29$	−9.27212	−1.72179	−0.860895	−	0.508783i	$-0.830096\pi$
$29$	−9.27212	−1.72179	−0.860895	+	0.508783i	$0.830096\pi$
$30$	5.95298	1.08686
$31$	−1.64123	−0.294774	−0.147387	−	0.989079i	$-0.547086\pi$
$31$	−1.64123	−0.294774	−0.147387	+	0.989079i	$0.547086\pi$
$32$	1.00000	0.176777
$33$	19.9678	3.47595
$34$	−5.21345	−0.894099
$35$	0.0816041	0.0137936
$36$	8.10435	1.35073
$37$	2.25901	0.371379	0.185690	−	0.982608i	$-0.440548\pi$
$37$	2.25901	0.371379	0.185690	+	0.982608i	$0.440548\pi$
$38$	7.52374	1.22051
$39$	13.3191	2.13276
$40$	−1.78644	−0.282461
$41$	3.31559	0.517808	0.258904	−	0.965903i	$-0.416639\pi$
$41$	3.31559	0.517808	0.258904	+	0.965903i	$0.416639\pi$
$42$	0.152220	0.0234880
$43$	1.25892	0.191983	0.0959915	−	0.995382i	$-0.469398\pi$
$43$	1.25892	0.191983	0.0959915	+	0.995382i	$0.469398\pi$
$44$	−5.99217	−0.903354
$45$	−14.4779	−2.15824
$46$	−3.44395	−0.507783
$47$	−7.17071	−1.04596	−0.522978	−	0.852346i	$-0.675179\pi$
$47$	−7.17071	−1.04596	−0.522978	+	0.852346i	$0.675179\pi$
$48$	−3.33232	−0.480979
$49$	−6.99791	−0.999702
$50$	−1.80864	−0.255780
$51$	17.3729	2.43269
$52$	−3.99693	−0.554275
$53$	3.90508	0.536404	0.268202	−	0.963363i	$-0.413571\pi$
$53$	3.90508	0.536404	0.268202	+	0.963363i	$0.413571\pi$
$54$	−17.0093	−2.31468
$55$	10.7046	1.44341
$56$	−0.0456798	−0.00610422
$57$	−25.0715	−3.32080
$58$	−9.27212	−1.21749
$59$	−14.3500	−1.86821	−0.934103	−	0.357004i	$-0.883798\pi$
$59$	−14.3500	−1.86821	−0.934103	+	0.357004i	$0.883798\pi$
$60$	5.95298	0.768527
$61$	−0.994778	−0.127368	−0.0636842	−	0.997970i	$-0.520285\pi$
$61$	−0.994778	−0.127368	−0.0636842	+	0.997970i	$0.520285\pi$
$62$	−1.64123	−0.208436
$63$	−0.370205	−0.0466415
$64$	1.00000	0.125000
$65$	7.14027	0.885642
$66$	19.9678	2.45787
$67$	9.53428	1.16480	0.582399	−	0.812903i	$-0.302114\pi$
$67$	9.53428	1.16480	0.582399	+	0.812903i	$0.302114\pi$
$68$	−5.21345	−0.632224
$69$	11.4763	1.38159
$70$	0.0816041	0.00975356
$71$	−7.73430	−0.917892	−0.458946	−	0.888464i	$-0.651773\pi$
$71$	−7.73430	−0.917892	−0.458946	+	0.888464i	$0.651773\pi$
$72$	8.10435	0.955107
$73$	11.1612	1.30633	0.653163	−	0.757218i	$-0.273442\pi$
$73$	11.1612	1.30633	0.653163	+	0.757218i	$0.273442\pi$
$74$	2.25901	0.262605
$75$	6.02697	0.695935
$76$	7.52374	0.863032
$77$	0.273721	0.0311934
$78$	13.3191	1.50809
$79$	−3.45897	−0.389165	−0.194582	−	0.980886i	$-0.562335\pi$
$79$	−3.45897	−0.389165	−0.194582	+	0.980886i	$0.562335\pi$
$80$	−1.78644	−0.199730
$81$	32.3675	3.59639
$82$	3.31559	0.366145
$83$	−11.2218	−1.23176	−0.615878	−	0.787841i	$-0.711199\pi$
$83$	−11.2218	−1.23176	−0.615878	+	0.787841i	$0.711199\pi$
$84$	0.152220	0.0166085
$85$	9.31350	1.01019
$86$	1.25892	0.135752
$87$	30.8977	3.31258
$88$	−5.99217	−0.638768
$89$	−11.6384	−1.23367	−0.616835	−	0.787093i	$-0.711585\pi$
$89$	−11.6384	−1.23367	−0.616835	+	0.787093i	$0.711585\pi$
$90$	−14.4779	−1.52611
$91$	0.182579	0.0191395
$92$	−3.44395	−0.359056
$93$	5.46910	0.567119
$94$	−7.17071	−0.739602
$95$	−13.4407	−1.37899
$96$	−3.33232	−0.340103
$97$	−7.80631	−0.792611	−0.396305	−	0.918119i	$-0.629708\pi$
$97$	−7.80631	−0.792611	−0.396305	+	0.918119i	$0.629708\pi$
$98$	−6.99791	−0.706896
$99$	−48.5627	−4.88073
$100$	−1.80864	−0.180864
$101$	−19.1410	−1.90460	−0.952302	−	0.305156i	$-0.901291\pi$
$101$	−19.1410	−1.90460	−0.952302	+	0.305156i	$0.901291\pi$
$102$	17.3729	1.72017
$103$	9.60007	0.945923	0.472962	−	0.881083i	$-0.343185\pi$
$103$	9.60007	0.945923	0.472962	+	0.881083i	$0.343185\pi$
$104$	−3.99693	−0.391931
$105$	−0.271931	−0.0265378
$106$	3.90508	0.379295
$107$	−19.4405	−1.87938	−0.939691	−	0.342024i	$-0.888888\pi$
$107$	−19.4405	−1.87938	−0.939691	+	0.342024i	$0.888888\pi$
$108$	−17.0093	−1.63672
$109$	1.19210	0.114183	0.0570914	−	0.998369i	$-0.481817\pi$
$109$	1.19210	0.114183	0.0570914	+	0.998369i	$0.481817\pi$
$110$	10.7046	1.02065
$111$	−7.52775	−0.714502
$112$	−0.0456798	−0.00431634
$113$	7.80682	0.734404	0.367202	−	0.930141i	$-0.380316\pi$
$113$	7.80682	0.734404	0.367202	+	0.930141i	$0.380316\pi$
$114$	−25.0715	−2.34816
$115$	6.15240	0.573714
$116$	−9.27212	−0.860895
$117$	−32.3926	−2.99469
$118$	−14.3500	−1.32102
$119$	0.238149	0.0218311
$120$	5.95298	0.543430
$121$	24.9061	2.26419
$122$	−0.994778	−0.0900630
$123$	−11.0486	−0.996218
$124$	−1.64123	−0.147387
$125$	12.1632	1.08791
$126$	−0.370205	−0.0329805
$127$	−4.90074	−0.434870	−0.217435	−	0.976075i	$-0.569769\pi$
$127$	−4.90074	−0.434870	−0.217435	+	0.976075i	$0.569769\pi$
$128$	1.00000	0.0883883
$129$	−4.19511	−0.369359
$130$	7.14027	0.626243
$131$	0.0423374	0.00369903	0.00184952	−	0.999998i	$-0.499411\pi$
$131$	0.0423374	0.00369903	0.00184952	+	0.999998i	$0.499411\pi$
$132$	19.9678	1.73798
$133$	−0.343683	−0.0298011
$134$	9.53428	0.823636
$135$	30.3861	2.61522
$136$	−5.21345	−0.447050
$137$	13.3736	1.14258	0.571291	−	0.820747i	$-0.306443\pi$
$137$	13.3736	1.14258	0.571291	+	0.820747i	$0.306443\pi$
$138$	11.4763	0.976931
$139$	−17.4041	−1.47620	−0.738100	−	0.674691i	$-0.764277\pi$
$139$	−17.4041	−1.47620	−0.738100	+	0.674691i	$0.764277\pi$
$140$	0.0816041	0.00689681
$141$	23.8951	2.01233
$142$	−7.73430	−0.649048
$143$	23.9503	2.00283
$144$	8.10435	0.675363
$145$	16.5641	1.37557
$146$	11.1612	0.923711
$147$	23.3193	1.92334
$148$	2.25901	0.185690
$149$	−12.1563	−0.995881	−0.497941	−	0.867211i	$-0.665910\pi$
$149$	−12.1563	−0.995881	−0.497941	+	0.867211i	$0.665910\pi$
$150$	6.02697	0.492100
$151$	−12.8654	−1.04697	−0.523484	−	0.852036i	$-0.675368\pi$
$151$	−12.8654	−1.04697	−0.523484	+	0.852036i	$0.675368\pi$
$152$	7.52374	0.610256
$153$	−42.2516	−3.41584
$154$	0.273721	0.0220571
$155$	2.93195	0.235500
$156$	13.3191	1.06638
$157$	10.9317	0.872442	0.436221	−	0.899839i	$-0.356317\pi$
$157$	10.9317	0.872442	0.436221	+	0.899839i	$0.356317\pi$
$158$	−3.45897	−0.275181
$159$	−13.0130	−1.03200
$160$	−1.78644	−0.141230
$161$	0.157319	0.0123985
$162$	32.3675	2.54303
$163$	−15.1361	−1.18555	−0.592775	−	0.805368i	$-0.701968\pi$
$163$	−15.1361	−1.18555	−0.592775	+	0.805368i	$0.701968\pi$
$164$	3.31559	0.258904
$165$	−35.6713	−2.77701
$166$	−11.2218	−0.870984
$167$	4.80684	0.371964	0.185982	−	0.982553i	$-0.440453\pi$
$167$	4.80684	0.371964	0.185982	+	0.982553i	$0.440453\pi$
$168$	0.152220	0.0117440
$169$	2.97547	0.228882
$170$	9.31350	0.714313
$171$	60.9750	4.66288
$172$	1.25892	0.0959915
$173$	−20.7456	−1.57726	−0.788630	−	0.614868i	$-0.789209\pi$
$173$	−20.7456	−1.57726	−0.788630	+	0.614868i	$0.789209\pi$
$174$	30.8977	2.34235
$175$	0.0826184	0.00624536
$176$	−5.99217	−0.451677
$177$	47.8186	3.59427
$178$	−11.6384	−0.872336
$179$	18.5653	1.38763	0.693816	−	0.720152i	$-0.255928\pi$
$179$	18.5653	1.38763	0.693816	+	0.720152i	$0.255928\pi$
$180$	−14.4779	−1.07912
$181$	−5.54249	−0.411970	−0.205985	−	0.978555i	$-0.566040\pi$
$181$	−5.54249	−0.411970	−0.205985	+	0.978555i	$0.566040\pi$
$182$	0.182579	0.0135337
$183$	3.31492	0.245046
$184$	−3.44395	−0.253891
$185$	−4.03558	−0.296702
$186$	5.46910	0.401014
$187$	31.2399	2.28449
$188$	−7.17071	−0.522978
$189$	0.776983	0.0565172
$190$	−13.4407	−0.975090
$191$	19.4819	1.40966	0.704831	−	0.709375i	$-0.251023\pi$
$191$	19.4819	1.40966	0.704831	+	0.709375i	$0.251023\pi$
$192$	−3.33232	−0.240489
$193$	7.04618	0.507195	0.253598	−	0.967310i	$-0.418386\pi$
$193$	7.04618	0.507195	0.253598	+	0.967310i	$0.418386\pi$
$194$	−7.80631	−0.560461
$195$	−23.7937	−1.70390
$196$	−6.99791	−0.499851
$197$	−10.1771	−0.725091	−0.362545	−	0.931966i	$-0.618092\pi$
$197$	−10.1771	−0.725091	−0.362545	+	0.931966i	$0.618092\pi$
$198$	−48.5627	−3.45120
$199$	−22.0979	−1.56648	−0.783238	−	0.621722i	$-0.786433\pi$
$199$	−22.0979	−1.56648	−0.783238	+	0.621722i	$0.786433\pi$
$200$	−1.80864	−0.127890
$201$	−31.7713	−2.24097
$202$	−19.1410	−1.34676
$203$	0.423549	0.0297273
$204$	17.3729	1.21635
$205$	−5.92309	−0.413686
$206$	9.60007	0.668869
$207$	−27.9110	−1.93995
$208$	−3.99693	−0.277137
$209$	−45.0835	−3.11849
$210$	−0.271931	−0.0187650
$211$	−3.61114	−0.248601	−0.124301	−	0.992245i	$-0.539669\pi$
$211$	−3.61114	−0.248601	−0.124301	+	0.992245i	$0.539669\pi$
$212$	3.90508	0.268202
$213$	25.7732	1.76595
$214$	−19.4405	−1.32892
$215$	−2.24898	−0.153379
$216$	−17.0093	−1.15734
$217$	0.0749710	0.00508937
$218$	1.19210	0.0807394
$219$	−37.1928	−2.51326
$220$	10.7046	0.721707
$221$	20.8378	1.40170
$222$	−7.52775	−0.505229
$223$	27.5961	1.84797	0.923985	−	0.382429i	$-0.124912\pi$
$223$	27.5961	1.84797	0.923985	+	0.382429i	$0.124912\pi$
$224$	−0.0456798	−0.00305211
$225$	−14.6579	−0.977191
$226$	7.80682	0.519302
$227$	−0.943344	−0.0626119	−0.0313060	−	0.999510i	$-0.509967\pi$
$227$	−0.943344	−0.0626119	−0.0313060	+	0.999510i	$0.509967\pi$
$228$	−25.0715	−1.66040
$229$	24.0474	1.58910	0.794549	−	0.607200i	$-0.207707\pi$
$229$	24.0474	1.58910	0.794549	+	0.607200i	$0.207707\pi$
$230$	6.15240	0.405677
$231$	−0.912127	−0.0600135
$232$	−9.27212	−0.608745
$233$	22.9761	1.50521	0.752607	−	0.658470i	$-0.228796\pi$
$233$	22.9761	1.50521	0.752607	+	0.658470i	$0.228796\pi$
$234$	−32.3926	−2.11757
$235$	12.8100	0.835634
$236$	−14.3500	−0.934103
$237$	11.5264	0.748720
$238$	0.238149	0.0154369
$239$	24.8270	1.60592	0.802962	−	0.596030i	$-0.203256\pi$
$239$	24.8270	1.60592	0.802962	+	0.596030i	$0.203256\pi$
$240$	5.95298	0.384263
$241$	−7.80312	−0.502643	−0.251321	−	0.967904i	$-0.580865\pi$
$241$	−7.80312	−0.502643	−0.251321	+	0.967904i	$0.580865\pi$
$242$	24.9061	1.60103
$243$	−56.8308	−3.64570
$244$	−0.994778	−0.0636842
$245$	12.5013	0.798681
$246$	−11.0486	−0.704433
$247$	−30.0719	−1.91343
$248$	−1.64123	−0.104218
$249$	37.3948	2.36980
$250$	12.1632	0.769269
$251$	−16.1182	−1.01737	−0.508686	−	0.860952i	$-0.669868\pi$
$251$	−16.1182	−1.01737	−0.508686	+	0.860952i	$0.669868\pi$
$252$	−0.370205	−0.0233207
$253$	20.6367	1.29742
$254$	−4.90074	−0.307500
$255$	−31.0356	−1.94352
$256$	1.00000	0.0625000
$257$	9.83165	0.613282	0.306641	−	0.951825i	$-0.400795\pi$
$257$	9.83165	0.613282	0.306641	+	0.951825i	$0.400795\pi$
$258$	−4.19511	−0.261176
$259$	−0.103191	−0.00641199
$260$	7.14027	0.442821
$261$	−75.1446	−4.65133
$262$	0.0423374	0.00261561
$263$	11.5127	0.709902	0.354951	−	0.934885i	$-0.384498\pi$
$263$	11.5127	0.709902	0.354951	+	0.934885i	$0.384498\pi$
$264$	19.9678	1.22894
$265$	−6.97618	−0.428543
$266$	−0.343683	−0.0210726
$267$	38.7829	2.37348
$268$	9.53428	0.582399
$269$	3.56835	0.217566	0.108783	−	0.994066i	$-0.465305\pi$
$269$	3.56835	0.217566	0.108783	+	0.994066i	$0.465305\pi$
$270$	30.3861	1.84924
$271$	−17.3637	−1.05477	−0.527384	−	0.849627i	$-0.676827\pi$
$271$	−17.3637	−1.05477	−0.527384	+	0.849627i	$0.676827\pi$
$272$	−5.21345	−0.316112
$273$	−0.608412	−0.0368228
$274$	13.3736	0.807928
$275$	10.8377	0.653537
$276$	11.4763	0.690794
$277$	10.8762	0.653487	0.326744	−	0.945113i	$-0.394049\pi$
$277$	10.8762	0.653487	0.326744	+	0.945113i	$0.394049\pi$
$278$	−17.4041	−1.04383
$279$	−13.3011	−0.796316
$280$	0.0816041	0.00487678
$281$	14.9283	0.890545	0.445273	−	0.895395i	$-0.353107\pi$
$281$	14.9283	0.890545	0.445273	+	0.895395i	$0.353107\pi$
$282$	23.8951	1.42293
$283$	4.18073	0.248519	0.124259	−	0.992250i	$-0.460345\pi$
$283$	4.18073	0.248519	0.124259	+	0.992250i	$0.460345\pi$
$284$	−7.73430	−0.458946
$285$	44.7887	2.65305
$286$	23.9503	1.41621
$287$	−0.151455	−0.00894013
$288$	8.10435	0.477554
$289$	10.1801	0.598827
$290$	16.5641	0.972676
$291$	26.0131	1.52492
$292$	11.1612	0.653163
$293$	8.37668	0.489371	0.244685	−	0.969603i	$-0.421315\pi$
$293$	8.37668	0.489371	0.244685	+	0.969603i	$0.421315\pi$
$294$	23.3193	1.36001
$295$	25.6353	1.49255
$296$	2.25901	0.131302
$297$	101.923	5.91417
$298$	−12.1563	−0.704195
$299$	13.7652	0.796064
$300$	6.02697	0.347967
$301$	−0.0575071	−0.00331465
$302$	−12.8654	−0.740318
$303$	63.7841	3.66430
$304$	7.52374	0.431516
$305$	1.77711	0.101757
$306$	−42.2516	−2.41537
$307$	−8.69430	−0.496210	−0.248105	−	0.968733i	$-0.579808\pi$
$307$	−8.69430	−0.496210	−0.248105	+	0.968733i	$0.579808\pi$
$308$	0.273721	0.0155967
$309$	−31.9905	−1.81988
$310$	2.93195	0.166524
$311$	−19.4626	−1.10362	−0.551810	−	0.833970i	$-0.686063\pi$
$311$	−19.4626	−1.10362	−0.551810	+	0.833970i	$0.686063\pi$
$312$	13.3191	0.754043
$313$	26.6362	1.50557	0.752783	−	0.658269i	$-0.228711\pi$
$313$	26.6362	1.50557	0.752783	+	0.658269i	$0.228711\pi$
$314$	10.9317	0.616910
$315$	0.661349	0.0372628
$316$	−3.45897	−0.194582
$317$	32.0635	1.80086	0.900432	−	0.434997i	$-0.143251\pi$
$317$	32.0635	1.80086	0.900432	+	0.434997i	$0.143251\pi$
$318$	−13.0130	−0.729731
$319$	55.5602	3.11077
$320$	−1.78644	−0.0998649
$321$	64.7819	3.61577
$322$	0.157319	0.00876704
$323$	−39.2246	−2.18252
$324$	32.3675	1.79819
$325$	7.22902	0.400994
$326$	−15.1361	−0.838311
$327$	−3.97247	−0.219678
$328$	3.31559	0.183073
$329$	0.327557	0.0180588
$330$	−35.6713	−1.96364
$331$	−5.72045	−0.314424	−0.157212	−	0.987565i	$-0.550251\pi$
$331$	−5.72045	−0.314424	−0.157212	+	0.987565i	$0.550251\pi$
$332$	−11.2218	−0.615878
$333$	18.3078	1.00326
$334$	4.80684	0.263018
$335$	−17.0324	−0.930579
$336$	0.152220	0.00830427
$337$	19.8182	1.07957	0.539783	−	0.841804i	$-0.318506\pi$
$337$	19.8182	1.07957	0.539783	+	0.841804i	$0.318506\pi$
$338$	2.97547	0.161844
$339$	−26.0148	−1.41293
$340$	9.31350	0.505096
$341$	9.83453	0.532570
$342$	60.9750	3.29715
$343$	0.639422	0.0345255
$344$	1.25892	0.0678762
$345$	−20.5018	−1.10378
$346$	−20.7456	−1.11529
$347$	10.0129	0.537521	0.268760	−	0.963207i	$-0.413386\pi$
$347$	10.0129	0.537521	0.268760	+	0.963207i	$0.413386\pi$
$348$	30.8977	1.65629
$349$	−17.7000	−0.947457	−0.473728	−	0.880671i	$-0.657092\pi$
$349$	−17.7000	−0.947457	−0.473728	+	0.880671i	$0.657092\pi$
$350$	0.0826184	0.00441614
$351$	67.9852	3.62878
$352$	−5.99217	−0.319384
$353$	−8.83685	−0.470338	−0.235169	−	0.971954i	$-0.575564\pi$
$353$	−8.83685	−0.470338	−0.235169	+	0.971954i	$0.575564\pi$
$354$	47.8186	2.54153
$355$	13.8168	0.733322
$356$	−11.6384	−0.616835
$357$	−0.793590	−0.0420012
$358$	18.5653	0.981205
$359$	−5.41121	−0.285593	−0.142796	−	0.989752i	$-0.545609\pi$
$359$	−5.41121	−0.285593	−0.142796	+	0.989752i	$0.545609\pi$
$360$	−14.4779	−0.763054
$361$	37.6066	1.97930
$362$	−5.54249	−0.291307
$363$	−82.9952	−4.35612
$364$	0.182579	0.00956975
$365$	−19.9389	−1.04365
$366$	3.31492	0.173274
$367$	−6.31701	−0.329745	−0.164873	−	0.986315i	$-0.552721\pi$
$367$	−6.31701	−0.329745	−0.164873	+	0.986315i	$0.552721\pi$
$368$	−3.44395	−0.179528
$369$	26.8707	1.39883
$370$	−4.03558	−0.209800
$371$	−0.178383	−0.00926120
$372$	5.46910	0.283560
$373$	−30.3325	−1.57056	−0.785278	−	0.619144i	$-0.787480\pi$
$373$	−30.3325	−1.57056	−0.785278	+	0.619144i	$0.787480\pi$
$374$	31.2399	1.61538
$375$	−40.5317	−2.09305
$376$	−7.17071	−0.369801
$377$	37.0600	1.90869
$378$	0.776983	0.0399637
$379$	−23.1780	−1.19058	−0.595288	−	0.803513i	$-0.702962\pi$
$379$	−23.1780	−1.19058	−0.595288	+	0.803513i	$0.702962\pi$
$380$	−13.4407	−0.689493
$381$	16.3308	0.836654
$382$	19.4819	0.996781
$383$	−17.8105	−0.910075	−0.455037	−	0.890472i	$-0.650374\pi$
$383$	−17.8105	−0.910075	−0.455037	+	0.890472i	$0.650374\pi$
$384$	−3.33232	−0.170052
$385$	−0.488986	−0.0249210
$386$	7.04618	0.358641
$387$	10.2027	0.518633
$388$	−7.80631	−0.396305
$389$	11.7610	0.596308	0.298154	−	0.954518i	$-0.403629\pi$
$389$	11.7610	0.596308	0.298154	+	0.954518i	$0.403629\pi$
$390$	−23.7937	−1.20484
$391$	17.9549	0.908016
$392$	−6.99791	−0.353448
$393$	−0.141082	−0.00711663
$394$	−10.1771	−0.512717
$395$	6.17924	0.310911
$396$	−48.5627	−2.44037
$397$	29.1986	1.46544	0.732718	−	0.680533i	$-0.238252\pi$
$397$	29.1986	1.46544	0.732718	+	0.680533i	$0.238252\pi$
$398$	−22.0979	−1.10767
$399$	1.14526	0.0573348
$400$	−1.80864	−0.0904321
$401$	−24.2048	−1.20873	−0.604364	−	0.796708i	$-0.706573\pi$
$401$	−24.2048	−1.20873	−0.604364	+	0.796708i	$0.706573\pi$
$402$	−31.7713	−1.58461
$403$	6.55988	0.326771
$404$	−19.1410	−0.952302
$405$	−57.8225	−2.87322
$406$	0.423549	0.0210204
$407$	−13.5364	−0.670974
$408$	17.3729	0.860086
$409$	0.457063	0.0226003	0.0113002	−	0.999936i	$-0.496403\pi$
$409$	0.457063	0.0226003	0.0113002	+	0.999936i	$0.496403\pi$
$410$	−5.92309	−0.292520
$411$	−44.5651	−2.19823
$412$	9.60007	0.472962
$413$	0.655503	0.0322552
$414$	−27.9110	−1.37175
$415$	20.0471	0.984074
$416$	−3.99693	−0.195966
$417$	57.9962	2.84008
$418$	−45.0835	−2.20511
$419$	5.91917	0.289170	0.144585	−	0.989492i	$-0.453815\pi$
$419$	5.91917	0.289170	0.144585	+	0.989492i	$0.453815\pi$
$420$	−0.271931	−0.0132689
$421$	32.7175	1.59455	0.797277	−	0.603613i	$-0.206273\pi$
$421$	32.7175	1.59455	0.797277	+	0.603613i	$0.206273\pi$
$422$	−3.61114	−0.175788
$423$	−58.1140	−2.82560
$424$	3.90508	0.189647
$425$	9.42926	0.457386
$426$	25.7732	1.24871
$427$	0.0454413	0.00219906
$428$	−19.4405	−0.939691
$429$	−79.8101	−3.85327
$430$	−2.24898	−0.108455
$431$	11.4489	0.551472	0.275736	−	0.961233i	$-0.411078\pi$
$431$	11.4489	0.551472	0.275736	+	0.961233i	$0.411078\pi$
$432$	−17.0093	−0.818362
$433$	24.8040	1.19201	0.596003	−	0.802983i	$-0.296755\pi$
$433$	24.8040	1.19201	0.596003	+	0.802983i	$0.296755\pi$
$434$	0.0749710	0.00359873
$435$	−55.1968	−2.64648
$436$	1.19210	0.0570914
$437$	−25.9114	−1.23951
$438$	−37.1928	−1.77714
$439$	−1.23427	−0.0589086	−0.0294543	−	0.999566i	$-0.509377\pi$
$439$	−1.23427	−0.0589086	−0.0294543	+	0.999566i	$0.509377\pi$
$440$	10.7046	0.510324
$441$	−56.7136	−2.70065
$442$	20.8378	0.991153
$443$	−18.7445	−0.890577	−0.445289	−	0.895387i	$-0.646899\pi$
$443$	−18.7445	−0.890577	−0.445289	+	0.895387i	$0.646899\pi$
$444$	−7.52775	−0.357251
$445$	20.7913	0.985602
$446$	27.5961	1.30671
$447$	40.5086	1.91599
$448$	−0.0456798	−0.00215817
$449$	−12.1335	−0.572615	−0.286307	−	0.958138i	$-0.592428\pi$
$449$	−12.1335	−0.572615	−0.286307	+	0.958138i	$0.592428\pi$
$450$	−14.6579	−0.690979
$451$	−19.8676	−0.935527
$452$	7.80682	0.367202
$453$	42.8715	2.01428
$454$	−0.943344	−0.0442733
$455$	−0.326166	−0.0152909
$456$	−25.0715	−1.17408
$457$	12.6490	0.591695	0.295848	−	0.955235i	$-0.404398\pi$
$457$	12.6490	0.591695	0.295848	+	0.955235i	$0.404398\pi$
$458$	24.0474	1.12366
$459$	88.6773	4.13910
$460$	6.15240	0.286857
$461$	5.47232	0.254871	0.127436	−	0.991847i	$-0.459325\pi$
$461$	5.47232	0.254871	0.127436	+	0.991847i	$0.459325\pi$
$462$	−0.912127	−0.0424360
$463$	−14.8364	−0.689507	−0.344754	−	0.938693i	$-0.612037\pi$
$463$	−14.8364	−0.689507	−0.344754	+	0.938693i	$0.612037\pi$
$464$	−9.27212	−0.430447
$465$	−9.77021	−0.453083
$466$	22.9761	1.06435
$467$	21.6849	1.00346	0.501729	−	0.865025i	$-0.332698\pi$
$467$	21.6849	1.00346	0.501729	+	0.865025i	$0.332698\pi$
$468$	−32.3926	−1.49735
$469$	−0.435524	−0.0201106
$470$	12.8100	0.590882
$471$	−36.4278	−1.67851
$472$	−14.3500	−0.660510
$473$	−7.54365	−0.346857
$474$	11.5264	0.529425
$475$	−13.6077	−0.624366
$476$	0.238149	0.0109156
$477$	31.6481	1.44907
$478$	24.8270	1.13556
$479$	4.68033	0.213850	0.106925	−	0.994267i	$-0.465900\pi$
$479$	4.68033	0.213850	0.106925	+	0.994267i	$0.465900\pi$
$480$	5.95298	0.271715
$481$	−9.02912	−0.411692
$482$	−7.80312	−0.355422
$483$	−0.524237	−0.0238536
$484$	24.9061	1.13210
$485$	13.9455	0.633232
$486$	−56.8308	−2.57790
$487$	−5.84601	−0.264908	−0.132454	−	0.991189i	$-0.542286\pi$
$487$	−5.84601	−0.264908	−0.132454	+	0.991189i	$0.542286\pi$
$488$	−0.994778	−0.0450315
$489$	50.4383	2.28090
$490$	12.5013	0.564753
$491$	−20.6216	−0.930641	−0.465320	−	0.885142i	$-0.654061\pi$
$491$	−20.6216	−0.930641	−0.465320	+	0.885142i	$0.654061\pi$
$492$	−11.0486	−0.498109
$493$	48.3397	2.17711
$494$	−30.0719	−1.35300
$495$	86.7542	3.89931
$496$	−1.64123	−0.0736934
$497$	0.353301	0.0158477
$498$	37.3948	1.67570
$499$	−37.5242	−1.67981	−0.839906	−	0.542732i	$-0.817390\pi$
$499$	−37.5242	−1.67981	−0.839906	+	0.542732i	$0.817390\pi$
$500$	12.1632	0.543955
$501$	−16.0179	−0.715628
$502$	−16.1182	−0.719390
$503$	42.2041	1.88179	0.940894	−	0.338702i	$-0.109988\pi$
$503$	42.2041	1.88179	0.940894	+	0.338702i	$0.109988\pi$
$504$	−0.370205	−0.0164903
$505$	34.1943	1.52162
$506$	20.6367	0.917415
$507$	−9.91522	−0.440350
$508$	−4.90074	−0.217435
$509$	2.68260	0.118904	0.0594520	−	0.998231i	$-0.481065\pi$
$509$	2.68260	0.118904	0.0594520	+	0.998231i	$0.481065\pi$
$510$	−31.0356	−1.37428
$511$	−0.509844	−0.0225542
$512$	1.00000	0.0441942
$513$	−127.974	−5.65018
$514$	9.83165	0.433656
$515$	−17.1499	−0.755716
$516$	−4.19511	−0.184680
$517$	42.9681	1.88974
$518$	−0.103191	−0.00453396
$519$	69.1310	3.03452
$520$	7.14027	0.313122
$521$	7.91356	0.346699	0.173350	−	0.984860i	$-0.444541\pi$
$521$	7.91356	0.346699	0.173350	+	0.984860i	$0.444541\pi$
$522$	−75.1446	−3.28899
$523$	−11.6184	−0.508036	−0.254018	−	0.967200i	$-0.581752\pi$
$523$	−11.6184	−0.508036	−0.254018	+	0.967200i	$0.581752\pi$
$524$	0.0423374	0.00184952
$525$	−0.275311	−0.0120156
$526$	11.5127	0.501977
$527$	8.55647	0.372726
$528$	19.9678	0.868989
$529$	−11.1392	−0.484314
$530$	−6.97618	−0.303026
$531$	−116.297	−5.04687
$532$	−0.343683	−0.0149005
$533$	−13.2522	−0.574015
$534$	38.7829	1.67830
$535$	34.7292	1.50147
$536$	9.53428	0.411818
$537$	−61.8654	−2.66969
$538$	3.56835	0.153843
$539$	41.9327	1.80617
$540$	30.3861	1.30761
$541$	3.03516	0.130492	0.0652460	−	0.997869i	$-0.479217\pi$
$541$	3.03516	0.130492	0.0652460	+	0.997869i	$0.479217\pi$
$542$	−17.3637	−0.745834
$543$	18.4693	0.792595
$544$	−5.21345	−0.223525
$545$	−2.12962	−0.0912228
$546$	−0.608412	−0.0260376
$547$	9.14473	0.391000	0.195500	−	0.980704i	$-0.437367\pi$
$547$	9.14473	0.391000	0.195500	+	0.980704i	$0.437367\pi$
$548$	13.3736	0.571291
$549$	−8.06204	−0.344079
$550$	10.8377	0.462121
$551$	−69.7610	−2.97192
$552$	11.4763	0.488465
$553$	0.158005	0.00671907
$554$	10.8762	0.462085
$555$	13.4479	0.570829
$556$	−17.4041	−0.738100
$557$	34.1064	1.44514	0.722568	−	0.691300i	$-0.242962\pi$
$557$	34.1064	1.44514	0.722568	+	0.691300i	$0.242962\pi$
$558$	−13.3011	−0.563081
$559$	−5.03181	−0.212823
$560$	0.0816041	0.00344840
$561$	−104.101	−4.39516
$562$	14.9283	0.629711
$563$	18.1694	0.765751	0.382875	−	0.923800i	$-0.374934\pi$
$563$	18.1694	0.765751	0.382875	+	0.923800i	$0.374934\pi$
$564$	23.8951	1.00617
$565$	−13.9464	−0.586729
$566$	4.18073	0.175729
$567$	−1.47854	−0.0620929
$568$	−7.73430	−0.324524
$569$	−9.28177	−0.389112	−0.194556	−	0.980891i	$-0.562327\pi$
$569$	−9.28177	−0.389112	−0.194556	+	0.980891i	$0.562327\pi$
$570$	44.7887	1.87599
$571$	−17.9764	−0.752288	−0.376144	−	0.926561i	$-0.622750\pi$
$571$	−17.9764	−0.752288	−0.376144	+	0.926561i	$0.622750\pi$
$572$	23.9503	1.00141
$573$	−64.9200	−2.71207
$574$	−0.151455	−0.00632162
$575$	6.22887	0.259762
$576$	8.10435	0.337681
$577$	5.11062	0.212758	0.106379	−	0.994326i	$-0.466074\pi$
$577$	5.11062	0.212758	0.106379	+	0.994326i	$0.466074\pi$
$578$	10.1801	0.423435
$579$	−23.4801	−0.975800
$580$	16.5641	0.687785
$581$	0.512611	0.0212667
$582$	26.0131	1.07828
$583$	−23.3999	−0.969125
$584$	11.1612	0.461856
$585$	57.8673	2.39252
$586$	8.37668	0.346037
$587$	−16.6668	−0.687914	−0.343957	−	0.938985i	$-0.611767\pi$
$587$	−16.6668	−0.687914	−0.343957	+	0.938985i	$0.611767\pi$
$588$	23.3193	0.961671
$589$	−12.3482	−0.508798
$590$	25.6353	1.05539
$591$	33.9135	1.39501
$592$	2.25901	0.0928448
$593$	−16.2944	−0.669131	−0.334566	−	0.942372i	$-0.608590\pi$
$593$	−16.2944	−0.669131	−0.334566	+	0.942372i	$0.608590\pi$
$594$	101.923	4.18195
$595$	−0.425439	−0.0174413
$596$	−12.1563	−0.497941
$597$	73.6371	3.01377
$598$	13.7652	0.562902
$599$	24.1569	0.987023	0.493511	−	0.869739i	$-0.335713\pi$
$599$	24.1569	0.987023	0.493511	+	0.869739i	$0.335713\pi$
$600$	6.02697	0.246050
$601$	−34.4737	−1.40621	−0.703106	−	0.711085i	$-0.748204\pi$
$601$	−34.4737	−1.40621	−0.703106	+	0.711085i	$0.748204\pi$
$602$	−0.0575071	−0.00234381
$603$	77.2692	3.14664
$604$	−12.8654	−0.523484
$605$	−44.4933	−1.80891
$606$	63.7841	2.59105
$607$	30.2446	1.22759	0.613795	−	0.789466i	$-0.289642\pi$
$607$	30.2446	1.22759	0.613795	+	0.789466i	$0.289642\pi$
$608$	7.52374	0.305128
$609$	−1.41140	−0.0571928
$610$	1.77711	0.0719530
$611$	28.6608	1.15949
$612$	−42.2516	−1.70792
$613$	21.7807	0.879715	0.439858	−	0.898068i	$-0.355029\pi$
$613$	21.7807	0.879715	0.439858	+	0.898068i	$0.355029\pi$
$614$	−8.69430	−0.350873
$615$	19.7376	0.795898
$616$	0.273721	0.0110285
$617$	−15.1926	−0.611632	−0.305816	−	0.952091i	$-0.598929\pi$
$617$	−15.1926	−0.611632	−0.305816	+	0.952091i	$0.598929\pi$
$618$	−31.9905	−1.28685
$619$	26.6242	1.07012	0.535058	−	0.844816i	$-0.320290\pi$
$619$	26.6242	1.07012	0.535058	+	0.844816i	$0.320290\pi$
$620$	2.93195	0.117750
$621$	58.5793	2.35071
$622$	−19.4626	−0.780377
$623$	0.531641	0.0212997
$624$	13.3191	0.533189
$625$	−12.6856	−0.507424
$626$	26.6362	1.06460
$627$	150.233	5.99972
$628$	10.9317	0.436221
$629$	−11.7772	−0.469589
$630$	0.661349	0.0263488
$631$	−38.7055	−1.54084	−0.770421	−	0.637535i	$-0.779954\pi$
$631$	−38.7055	−1.54084	−0.770421	+	0.637535i	$0.779954\pi$
$632$	−3.45897	−0.137591
$633$	12.0335	0.478288
$634$	32.0635	1.27340
$635$	8.75487	0.347426
$636$	−13.0130	−0.515998
$637$	27.9702	1.10822
$638$	55.5602	2.19965
$639$	−62.6815	−2.47964
$640$	−1.78644	−0.0706151
$641$	−4.30263	−0.169944	−0.0849718	−	0.996383i	$-0.527080\pi$
$641$	−4.30263	−0.169944	−0.0849718	+	0.996383i	$0.527080\pi$
$642$	64.7819	2.55674
$643$	8.41134	0.331711	0.165855	−	0.986150i	$-0.446962\pi$
$643$	8.41134	0.331711	0.165855	+	0.986150i	$0.446962\pi$
$644$	0.157319	0.00619923
$645$	7.49431	0.295088
$646$	−39.2246	−1.54327
$647$	−36.0218	−1.41616	−0.708082	−	0.706130i	$-0.750439\pi$
$647$	−36.0218	−1.41616	−0.708082	+	0.706130i	$0.750439\pi$
$648$	32.3675	1.27152
$649$	85.9874	3.37530
$650$	7.22902	0.283545
$651$	−0.249828	−0.00979151
$652$	−15.1361	−0.592775
$653$	16.8394	0.658977	0.329488	−	0.944160i	$-0.393124\pi$
$653$	16.8394	0.658977	0.329488	+	0.944160i	$0.393124\pi$
$654$	−3.97247	−0.155336
$655$	−0.0756330	−0.00295523
$656$	3.31559	0.129452
$657$	90.4547	3.52897
$658$	0.327557	0.0127695
$659$	23.1572	0.902076	0.451038	−	0.892505i	$-0.351054\pi$
$659$	23.1572	0.902076	0.451038	+	0.892505i	$0.351054\pi$
$660$	−35.6713	−1.38850
$661$	7.05309	0.274333	0.137167	−	0.990548i	$-0.456200\pi$
$661$	7.05309	0.274333	0.137167	+	0.990548i	$0.456200\pi$
$662$	−5.72045	−0.222331
$663$	−69.4382	−2.69676
$664$	−11.2218	−0.435492
$665$	0.613968	0.0238087
$666$	18.3078	0.709414
$667$	31.9327	1.23644
$668$	4.80684	0.185982
$669$	−91.9589	−3.55534
$670$	−17.0324	−0.658019
$671$	5.96088	0.230117
$672$	0.152220	0.00587200
$673$	−21.9716	−0.846941	−0.423471	−	0.905910i	$-0.639188\pi$
$673$	−21.9716	−0.846941	−0.423471	+	0.905910i	$0.639188\pi$
$674$	19.8182	0.763368
$675$	30.7638	1.18410
$676$	2.97547	0.114441
$677$	−28.3767	−1.09061	−0.545303	−	0.838239i	$-0.683585\pi$
$677$	−28.3767	−1.09061	−0.545303	+	0.838239i	$0.683585\pi$
$678$	−26.0148	−0.999093
$679$	0.356591	0.0136847
$680$	9.31350	0.357157
$681$	3.14352	0.120460
$682$	9.83453	0.376584
$683$	40.3115	1.54248	0.771239	−	0.636546i	$-0.219637\pi$
$683$	40.3115	1.54248	0.771239	+	0.636546i	$0.219637\pi$
$684$	60.9750	2.33144
$685$	−23.8911	−0.912831
$686$	0.639422	0.0244132
$687$	−80.1337	−3.05729
$688$	1.25892	0.0479958
$689$	−15.6083	−0.594630
$690$	−20.5018	−0.780489
$691$	−41.4012	−1.57498	−0.787488	−	0.616330i	$-0.788619\pi$
$691$	−41.4012	−1.57498	−0.787488	+	0.616330i	$0.788619\pi$
$692$	−20.7456	−0.788630
$693$	2.21833	0.0842676
$694$	10.0129	0.380084
$695$	31.0914	1.17936
$696$	30.8977	1.17117
$697$	−17.2856	−0.654740
$698$	−17.7000	−0.669953
$699$	−76.5637	−2.89590
$700$	0.0826184	0.00312268
$701$	47.0232	1.77604	0.888021	−	0.459804i	$-0.152080\pi$
$701$	47.0232	1.77604	0.888021	+	0.459804i	$0.152080\pi$
$702$	67.9852	2.56594
$703$	16.9962	0.641024
$704$	−5.99217	−0.225839
$705$	−42.6871	−1.60769
$706$	−8.83685	−0.332579
$707$	0.874359	0.0328837
$708$	47.8186	1.79713
$709$	−18.5213	−0.695581	−0.347791	−	0.937572i	$-0.613068\pi$
$709$	−18.5213	−0.695581	−0.347791	+	0.937572i	$0.613068\pi$
$710$	13.8168	0.518537
$711$	−28.0327	−1.05131
$712$	−11.6384	−0.436168
$713$	5.65231	0.211681
$714$	−0.793590	−0.0296994
$715$	−42.7857	−1.60010
$716$	18.5653	0.693816
$717$	−82.7315	−3.08966
$718$	−5.41121	−0.201944
$719$	0.00622605	0.000232192 0	0.000116096	−	1.00000i	$-0.499963\pi$
$719$	0.00622605	0.000232192 0	0.000116096		1.00000i	$0.499963\pi$
$720$	−14.4779	−0.539560
$721$	−0.438530	−0.0163317
$722$	37.6066	1.39957
$723$	26.0025	0.967042
$724$	−5.54249	−0.205985
$725$	16.7699	0.622820
$726$	−82.9952	−3.08024
$727$	10.4015	0.385771	0.192886	−	0.981221i	$-0.438215\pi$
$727$	10.4015	0.385771	0.192886	+	0.981221i	$0.438215\pi$
$728$	0.182579	0.00676683
$729$	92.2760	3.41763
$730$	−19.9389	−0.737971
$731$	−6.56330	−0.242752
$732$	3.31492	0.122523
$733$	−1.51491	−0.0559546	−0.0279773	−	0.999609i	$-0.508907\pi$
$733$	−1.51491	−0.0559546	−0.0279773	+	0.999609i	$0.508907\pi$
$734$	−6.31701	−0.233165
$735$	−41.6584	−1.53659
$736$	−3.44395	−0.126946
$737$	−57.1311	−2.10445
$738$	26.8707	0.989124
$739$	2.87726	0.105842	0.0529208	−	0.998599i	$-0.483147\pi$
$739$	2.87726	0.105842	0.0529208	+	0.998599i	$0.483147\pi$
$740$	−4.03558	−0.148351
$741$	100.209	3.68127
$742$	−0.178383	−0.00654866
$743$	11.6400	0.427030	0.213515	−	0.976940i	$-0.431509\pi$
$743$	11.6400	0.427030	0.213515	+	0.976940i	$0.431509\pi$
$744$	5.46910	0.200507
$745$	21.7164	0.795629
$746$	−30.3325	−1.11055
$747$	−90.9458	−3.32753
$748$	31.2399	1.14224
$749$	0.888038	0.0324482
$750$	−40.5317	−1.48001
$751$	38.6642	1.41087	0.705437	−	0.708772i	$-0.250751\pi$
$751$	38.6642	1.41087	0.705437	+	0.708772i	$0.250751\pi$
$752$	−7.17071	−0.261489
$753$	53.7110	1.95734
$754$	37.0600	1.34965
$755$	22.9832	0.836443
$756$	0.776983	0.0282586
$757$	−44.1737	−1.60552	−0.802761	−	0.596301i	$-0.796637\pi$
$757$	−44.1737	−1.60552	−0.802761	+	0.596301i	$0.796637\pi$
$758$	−23.1780	−0.841864
$759$	−68.7682	−2.49613
$760$	−13.4407	−0.487545
$761$	19.7288	0.715167	0.357583	−	0.933881i	$-0.383601\pi$
$761$	19.7288	0.715167	0.357583	+	0.933881i	$0.383601\pi$
$762$	16.3308	0.591604
$763$	−0.0544550	−0.00197140
$764$	19.4819	0.704831
$765$	75.4799	2.72898
$766$	−17.8105	−0.643520
$767$	57.3558	2.07100
$768$	−3.33232	−0.120245
$769$	37.0141	1.33476	0.667381	−	0.744716i	$-0.267415\pi$
$769$	37.0141	1.33476	0.667381	+	0.744716i	$0.267415\pi$
$770$	−0.488986	−0.0176218
$771$	−32.7622	−1.17990
$772$	7.04618	0.253598
$773$	11.3622	0.408671	0.204336	−	0.978901i	$-0.434497\pi$
$773$	11.3622	0.408671	0.204336	+	0.978901i	$0.434497\pi$
$774$	10.2027	0.366729
$775$	2.96840	0.106628
$776$	−7.80631	−0.280230
$777$	0.343866	0.0123361
$778$	11.7610	0.421654
$779$	24.9456	0.893769
$780$	−23.7937	−0.851950
$781$	46.3452	1.65836
$782$	17.9549	0.642064
$783$	157.713	5.63619
$784$	−6.99791	−0.249925
$785$	−19.5287	−0.697011
$786$	−0.141082	−0.00503221
$787$	5.66513	0.201940	0.100970	−	0.994889i	$-0.467805\pi$
$787$	5.66513	0.201940	0.100970	+	0.994889i	$0.467805\pi$
$788$	−10.1771	−0.362545
$789$	−38.3639	−1.36579
$790$	6.17924	0.219847
$791$	−0.356614	−0.0126797
$792$	−48.5627	−1.72560
$793$	3.97606	0.141194
$794$	29.1986	1.03622
$795$	23.2469	0.824481
$796$	−22.0979	−0.783238
$797$	−11.2364	−0.398015	−0.199008	−	0.979998i	$-0.563772\pi$
$797$	−11.2364	−0.398015	−0.199008	+	0.979998i	$0.563772\pi$
$798$	1.14526	0.0405418
$799$	37.3841	1.32256
$800$	−1.80864	−0.0639451
$801$	−94.3219	−3.33270
$802$	−24.2048	−0.854700
$803$	−66.8801	−2.36015
$804$	−31.7713	−1.12049
$805$	−0.281040	−0.00990537
$806$	6.55988	0.231062
$807$	−11.8909	−0.418579
$808$	−19.1410	−0.673379
$809$	48.8289	1.71673	0.858367	−	0.513036i	$-0.171479\pi$
$809$	48.8289	1.71673	0.858367	+	0.513036i	$0.171479\pi$
$810$	−57.8225	−2.03168
$811$	−53.2223	−1.86889	−0.934445	−	0.356109i	$-0.884103\pi$
$811$	−53.2223	−1.86889	−0.934445	+	0.356109i	$0.884103\pi$
$812$	0.423549	0.0148636
$813$	57.8613	2.02928
$814$	−13.5364	−0.474450
$815$	27.0397	0.947159
$816$	17.3729	0.608173
$817$	9.47176	0.331375
$818$	0.457063	0.0159808
$819$	1.47969	0.0517044
$820$	−5.92309	−0.206843
$821$	16.8490	0.588035	0.294017	−	0.955800i	$-0.405008\pi$
$821$	16.8490	0.588035	0.294017	+	0.955800i	$0.405008\pi$
$822$	−44.5651	−1.55439
$823$	−30.5468	−1.06480	−0.532398	−	0.846494i	$-0.678709\pi$
$823$	−30.5468	−1.06480	−0.532398	+	0.846494i	$0.678709\pi$
$824$	9.60007	0.334434
$825$	−36.1147	−1.25735
$826$	0.655503	0.0228079
$827$	37.2086	1.29387	0.646935	−	0.762545i	$-0.276051\pi$
$827$	37.2086	1.29387	0.646935	+	0.762545i	$0.276051\pi$
$828$	−27.9110	−0.969974
$829$	−33.4034	−1.16015	−0.580074	−	0.814564i	$-0.696976\pi$
$829$	−33.4034	−1.16015	−0.580074	+	0.814564i	$0.696976\pi$
$830$	20.0471	0.695845
$831$	−36.2429	−1.25725
$832$	−3.99693	−0.138569
$833$	36.4833	1.26407
$834$	57.9962	2.00824
$835$	−8.58712	−0.297169
$836$	−45.0835	−1.55925
$837$	27.9162	0.964926
$838$	5.91917	0.204474
$839$	16.2587	0.561314	0.280657	−	0.959808i	$-0.409448\pi$
$839$	16.2587	0.561314	0.280657	+	0.959808i	$0.409448\pi$
$840$	−0.271931	−0.00938251
$841$	56.9723	1.96456
$842$	32.7175	1.12752
$843$	−49.7457	−1.71333
$844$	−3.61114	−0.124301
$845$	−5.31549	−0.182858
$846$	−58.1140	−1.99800
$847$	−1.13771	−0.0390921
$848$	3.90508	0.134101
$849$	−13.9315	−0.478129
$850$	9.42926	0.323421
$851$	−7.77992	−0.266692
$852$	25.7732	0.882974
$853$	−55.1169	−1.88717	−0.943583	−	0.331137i	$-0.892568\pi$
$853$	−55.1169	−1.88717	−0.943583	+	0.331137i	$0.892568\pi$
$854$	0.0454413	0.00155497
$855$	−108.928	−3.72526
$856$	−19.4405	−0.664462
$857$	−57.0214	−1.94781	−0.973907	−	0.226949i	$-0.927125\pi$
$857$	−57.0214	−1.94781	−0.973907	+	0.226949i	$0.927125\pi$
$858$	−79.8101	−2.72467
$859$	−38.3661	−1.30903	−0.654517	−	0.756047i	$-0.727128\pi$
$859$	−38.3661	−1.30903	−0.654517	+	0.756047i	$0.727128\pi$
$860$	−2.24898	−0.0766894
$861$	0.504698	0.0172001
$862$	11.4489	0.389949
$863$	7.05681	0.240217	0.120108	−	0.992761i	$-0.461676\pi$
$863$	7.05681	0.240217	0.120108	+	0.992761i	$0.461676\pi$
$864$	−17.0093	−0.578670
$865$	37.0608	1.26010
$866$	24.8040	0.842875
$867$	−33.9232	−1.15209
$868$	0.0749710	0.00254468
$869$	20.7268	0.703107
$870$	−55.1968	−1.87135
$871$	−38.1079	−1.29124
$872$	1.19210	0.0403697
$873$	−63.2651	−2.14120
$874$	−25.9114	−0.876465
$875$	−0.555613	−0.0187832
$876$	−37.1928	−1.25663
$877$	31.6903	1.07011	0.535053	−	0.844818i	$-0.320292\pi$
$877$	31.6903	1.07011	0.535053	+	0.844818i	$0.320292\pi$
$878$	−1.23427	−0.0416547
$879$	−27.9138	−0.941508
$880$	10.7046	0.360853
$881$	27.5687	0.928813	0.464406	−	0.885622i	$-0.346268\pi$
$881$	27.5687	0.928813	0.464406	+	0.885622i	$0.346268\pi$
$882$	−56.7136	−1.90965
$883$	−18.4578	−0.621154	−0.310577	−	0.950548i	$-0.600522\pi$
$883$	−18.4578	−0.621154	−0.310577	+	0.950548i	$0.600522\pi$
$884$	20.8378	0.700851
$885$	−85.4250	−2.87153
$886$	−18.7445	−0.629733
$887$	4.71498	0.158313	0.0791567	−	0.996862i	$-0.474777\pi$
$887$	4.71498	0.158313	0.0791567	+	0.996862i	$0.474777\pi$
$888$	−7.52775	−0.252615
$889$	0.223865	0.00750819
$890$	20.7913	0.696926
$891$	−193.952	−6.49762
$892$	27.5961	0.923985
$893$	−53.9505	−1.80539
$894$	40.5086	1.35481
$895$	−33.1657	−1.10861
$896$	−0.0456798	−0.00152606
$897$	−45.8701	−1.53156
$898$	−12.1335	−0.404900
$899$	15.2177	0.507538
$900$	−14.6579	−0.488596
$901$	−20.3589	−0.678254
$902$	−19.8676	−0.661518
$903$	0.191632	0.00637711
$904$	7.80682	0.259651
$905$	9.90131	0.329131
$906$	42.8715	1.42431
$907$	4.73020	0.157064	0.0785319	−	0.996912i	$-0.474977\pi$
$907$	4.73020	0.157064	0.0785319	+	0.996912i	$0.474977\pi$
$908$	−0.943344	−0.0313060
$909$	−155.126	−5.14520
$910$	−0.326166	−0.0108123
$911$	−4.01569	−0.133046	−0.0665229	−	0.997785i	$-0.521191\pi$
$911$	−4.01569	−0.133046	−0.0665229	+	0.997785i	$0.521191\pi$
$912$	−25.0715	−0.830200
$913$	67.2432	2.22543
$914$	12.6490	0.418392
$915$	−5.92190	−0.195772
$916$	24.0474	0.794549
$917$	−0.00193396	−6.38651e−5 0
$918$	88.6773	2.92679
$919$	−10.6672	−0.351878	−0.175939	−	0.984401i	$-0.556296\pi$
$919$	−10.6672	−0.351878	−0.175939	+	0.984401i	$0.556296\pi$
$920$	6.15240	0.202839
$921$	28.9722	0.954666
$922$	5.47232	0.180221
$923$	30.9135	1.01753
$924$	−0.912127	−0.0300068
$925$	−4.08574	−0.134338
$926$	−14.8364	−0.487555
$927$	77.8024	2.55537
$928$	−9.27212	−0.304372
$929$	−45.0625	−1.47845	−0.739227	−	0.673456i	$-0.764809\pi$
$929$	−45.0625	−1.47845	−0.739227	+	0.673456i	$0.764809\pi$
$930$	−9.77021	−0.320378
$931$	−52.6505	−1.72555
$932$	22.9761	0.752607
$933$	64.8555	2.12327
$934$	21.6849	0.709551
$935$	−55.8081	−1.82512
$936$	−32.3926	−1.05878
$937$	17.0483	0.556942	0.278471	−	0.960445i	$-0.410172\pi$
$937$	17.0483	0.556942	0.278471	+	0.960445i	$0.410172\pi$
$938$	−0.435524	−0.0142204
$939$	−88.7603	−2.89658
$940$	12.8100	0.417817
$941$	38.3587	1.25046	0.625229	−	0.780441i	$-0.285005\pi$
$941$	38.3587	1.25046	0.625229	+	0.780441i	$0.285005\pi$
$942$	−36.4278	−1.18688
$943$	−11.4187	−0.371844
$944$	−14.3500	−0.467051
$945$	−1.38803	−0.0451527
$946$	−7.54365	−0.245265
$947$	−44.8344	−1.45692	−0.728461	−	0.685088i	$-0.759764\pi$
$947$	−44.8344	−1.45692	−0.728461	+	0.685088i	$0.759764\pi$
$948$	11.5264	0.374360
$949$	−44.6108	−1.44813
$950$	−13.6077	−0.441493
$951$	−106.846	−3.46471
$952$	0.238149	0.00771847
$953$	−33.7243	−1.09244	−0.546219	−	0.837643i	$-0.683933\pi$
$953$	−33.7243	−1.09244	−0.546219	+	0.837643i	$0.683933\pi$
$954$	31.6481	1.02465
$955$	−34.8032	−1.12621
$956$	24.8270	0.802962
$957$	−185.144	−5.98486
$958$	4.68033	0.151215
$959$	−0.610903	−0.0197271
$960$	5.95298	0.192132
$961$	−28.3064	−0.913109
$962$	−9.02912	−0.291110
$963$	−157.553	−5.07706
$964$	−7.80312	−0.251321
$965$	−12.5876	−0.405208
$966$	−0.524237	−0.0168670
$967$	3.89921	0.125390	0.0626951	−	0.998033i	$-0.480030\pi$
$967$	3.89921	0.125390	0.0626951	+	0.998033i	$0.480030\pi$
$968$	24.9061	0.800514
$969$	130.709	4.19898
$970$	13.9455	0.447763
$971$	−11.7148	−0.375946	−0.187973	−	0.982174i	$-0.560192\pi$
$971$	−11.7148	−0.375946	−0.187973	+	0.982174i	$0.560192\pi$
$972$	−56.8308	−1.82285
$973$	0.795018	0.0254871
$974$	−5.84601	−0.187318
$975$	−24.0894	−0.771478
$976$	−0.994778	−0.0318421
$977$	−15.4739	−0.495055	−0.247527	−	0.968881i	$-0.579618\pi$
$977$	−15.4739	−0.495055	−0.247527	+	0.968881i	$0.579618\pi$
$978$	50.4383	1.61284
$979$	69.7394	2.22888
$980$	12.5013	0.399340
$981$	9.66122	0.308459
$982$	−20.6216	−0.658062
$983$	−1.40716	−0.0448815	−0.0224407	−	0.999748i	$-0.507144\pi$
$983$	−1.40716	−0.0448815	−0.0224407	+	0.999748i	$0.507144\pi$
$984$	−11.0486	−0.352216
$985$	18.1808	0.579289
$986$	48.3397	1.53945
$987$	−1.09152	−0.0347436
$988$	−30.0719	−0.956714
$989$	−4.33564	−0.137865
$990$	86.7542	2.75723
$991$	−5.55710	−0.176527	−0.0882635	−	0.996097i	$-0.528132\pi$
$991$	−5.55710	−0.176527	−0.0882635	+	0.996097i	$0.528132\pi$
$992$	−1.64123	−0.0521091
$993$	19.0624	0.604926
$994$	0.353301	0.0112060
$995$	39.4764	1.25149
$996$	37.3948	1.18490
$997$	−27.8387	−0.881661	−0.440831	−	0.897590i	$-0.645316\pi$
$997$	−27.8387	−0.881661	−0.440831	+	0.897590i	$0.645316\pi$
$998$	−37.5242	−1.18781
$999$	−38.4243	−1.21569

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8042.2.a.d.1.3	✓	101

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8042.2.a.d.1.3	✓	101	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:	\( N \)	\(=\)	\( 8042 = 2 \cdot 4021 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8042.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -3.33232 q^{3} +1.00000 q^{4} -1.78644 q^{5} -3.33232 q^{6} -0.0456798 q^{7} +1.00000 q^{8} +8.10435 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -3.33232 q^{3} +1.00000 q^{4} -1.78644 q^{5} -3.33232 q^{6} -0.0456798 q^{7} +1.00000 q^{8} +8.10435 q^{9} -1.78644 q^{10} -5.99217 q^{11} -3.33232 q^{12} -3.99693 q^{13} -0.0456798 q^{14} +5.95298 q^{15} +1.00000 q^{16} -5.21345 q^{17} +8.10435 q^{18} +7.52374 q^{19} -1.78644 q^{20} +0.152220 q^{21} -5.99217 q^{22} -3.44395 q^{23} -3.33232 q^{24} -1.80864 q^{25} -3.99693 q^{26} -17.0093 q^{27} -0.0456798 q^{28} -9.27212 q^{29} +5.95298 q^{30} -1.64123 q^{31} +1.00000 q^{32} +19.9678 q^{33} -5.21345 q^{34} +0.0816041 q^{35} +8.10435 q^{36} +2.25901 q^{37} +7.52374 q^{38} +13.3191 q^{39} -1.78644 q^{40} +3.31559 q^{41} +0.152220 q^{42} +1.25892 q^{43} -5.99217 q^{44} -14.4779 q^{45} -3.44395 q^{46} -7.17071 q^{47} -3.33232 q^{48} -6.99791 q^{49} -1.80864 q^{50} +17.3729 q^{51} -3.99693 q^{52} +3.90508 q^{53} -17.0093 q^{54} +10.7046 q^{55} -0.0456798 q^{56} -25.0715 q^{57} -9.27212 q^{58} -14.3500 q^{59} +5.95298 q^{60} -0.994778 q^{61} -1.64123 q^{62} -0.370205 q^{63} +1.00000 q^{64} +7.14027 q^{65} +19.9678 q^{66} +9.53428 q^{67} -5.21345 q^{68} +11.4763 q^{69} +0.0816041 q^{70} -7.73430 q^{71} +8.10435 q^{72} +11.1612 q^{73} +2.25901 q^{74} +6.02697 q^{75} +7.52374 q^{76} +0.273721 q^{77} +13.3191 q^{78} -3.45897 q^{79} -1.78644 q^{80} +32.3675 q^{81} +3.31559 q^{82} -11.2218 q^{83} +0.152220 q^{84} +9.31350 q^{85} +1.25892 q^{86} +30.8977 q^{87} -5.99217 q^{88} -11.6384 q^{89} -14.4779 q^{90} +0.182579 q^{91} -3.44395 q^{92} +5.46910 q^{93} -7.17071 q^{94} -13.4407 q^{95} -3.33232 q^{96} -7.80631 q^{97} -6.99791 q^{98} -48.5627 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 101 q + 101 q^{2} + 10 q^{3} + 101 q^{4} + 19 q^{5} + 10 q^{6} + 42 q^{7} + 101 q^{8} + 147 q^{9}+O(q^{10}) \) 101 * q + 101 * q^2 + 10 * q^3 + 101 * q^4 + 19 * q^5 + 10 * q^6 + 42 * q^7 + 101 * q^8 + 147 * q^9	\( 101 q + 101 q^{2} + 10 q^{3} + 101 q^{4} + 19 q^{5} + 10 q^{6} + 42 q^{7} + 101 q^{8} + 147 q^{9} + 19 q^{10} + 4 q^{11} + 10 q^{12} + 58 q^{13} + 42 q^{14} + 27 q^{15} + 101 q^{16} + 34 q^{17} + 147 q^{18} + 36 q^{19} + 19 q^{20} + 45 q^{21} + 4 q^{22} + 47 q^{23} + 10 q^{24} + 174 q^{25} + 58 q^{26} + 31 q^{27} + 42 q^{28} + 62 q^{29} + 27 q^{30} + 47 q^{31} + 101 q^{32} + 55 q^{33} + 34 q^{34} + 16 q^{35} + 147 q^{36} + 90 q^{37} + 36 q^{38} + 50 q^{39} + 19 q^{40} + 54 q^{41} + 45 q^{42} + 65 q^{43} + 4 q^{44} + 47 q^{45} + 47 q^{46} + 54 q^{47} + 10 q^{48} + 189 q^{49} + 174 q^{50} + 36 q^{51} + 58 q^{52} + 94 q^{53} + 31 q^{54} + 68 q^{55} + 42 q^{56} + 79 q^{57} + 62 q^{58} - 6 q^{59} + 27 q^{60} + 58 q^{61} + 47 q^{62} + 117 q^{63} + 101 q^{64} + 89 q^{65} + 55 q^{66} + 127 q^{67} + 34 q^{68} + 45 q^{69} + 16 q^{70} + 87 q^{71} + 147 q^{72} + 83 q^{73} + 90 q^{74} - 4 q^{75} + 36 q^{76} + 53 q^{77} + 50 q^{78} + 74 q^{79} + 19 q^{80} + 241 q^{81} + 54 q^{82} + 11 q^{83} + 45 q^{84} + 120 q^{85} + 65 q^{86} + 37 q^{87} + 4 q^{88} + 89 q^{89} + 47 q^{90} + 31 q^{91} + 47 q^{92} + 123 q^{93} + 54 q^{94} + 61 q^{95} + 10 q^{96} + 85 q^{97} + 189 q^{98} - 55 q^{99}+O(q^{100}) \) 101 * q + 101 * q^2 + 10 * q^3 + 101 * q^4 + 19 * q^5 + 10 * q^6 + 42 * q^7 + 101 * q^8 + 147 * q^9 + 19 * q^10 + 4 * q^11 + 10 * q^12 + 58 * q^13 + 42 * q^14 + 27 * q^15 + 101 * q^16 + 34 * q^17 + 147 * q^18 + 36 * q^19 + 19 * q^20 + 45 * q^21 + 4 * q^22 + 47 * q^23 + 10 * q^24 + 174 * q^25 + 58 * q^26 + 31 * q^27 + 42 * q^28 + 62 * q^29 + 27 * q^30 + 47 * q^31 + 101 * q^32 + 55 * q^33 + 34 * q^34 + 16 * q^35 + 147 * q^36 + 90 * q^37 + 36 * q^38 + 50 * q^39 + 19 * q^40 + 54 * q^41 + 45 * q^42 + 65 * q^43 + 4 * q^44 + 47 * q^45 + 47 * q^46 + 54 * q^47 + 10 * q^48 + 189 * q^49 + 174 * q^50 + 36 * q^51 + 58 * q^52 + 94 * q^53 + 31 * q^54 + 68 * q^55 + 42 * q^56 + 79 * q^57 + 62 * q^58 - 6 * q^59 + 27 * q^60 + 58 * q^61 + 47 * q^62 + 117 * q^63 + 101 * q^64 + 89 * q^65 + 55 * q^66 + 127 * q^67 + 34 * q^68 + 45 * q^69 + 16 * q^70 + 87 * q^71 + 147 * q^72 + 83 * q^73 + 90 * q^74 - 4 * q^75 + 36 * q^76 + 53 * q^77 + 50 * q^78 + 74 * q^79 + 19 * q^80 + 241 * q^81 + 54 * q^82 + 11 * q^83 + 45 * q^84 + 120 * q^85 + 65 * q^86 + 37 * q^87 + 4 * q^88 + 89 * q^89 + 47 * q^90 + 31 * q^91 + 47 * q^92 + 123 * q^93 + 54 * q^94 + 61 * q^95 + 10 * q^96 + 85 * q^97 + 189 * q^98 - 55 * q^99

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