LMFDB - Embedded newform 8042.2.a.a.1.11

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:	$1$
Dimension:	$67$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
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)

$f(q)$	$=$	$q+1.00000 q^{2} -2.32940 q^{3} +1.00000 q^{4} -2.43485 q^{5} -2.32940 q^{6} +0.839554 q^{7} +1.00000 q^{8} +2.42611 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.32940 q^{3} +1.00000 q^{4} -2.43485 q^{5} -2.32940 q^{6} +0.839554 q^{7} +1.00000 q^{8} +2.42611 q^{9} -2.43485 q^{10} -5.28397 q^{11} -2.32940 q^{12} -0.826967 q^{13} +0.839554 q^{14} +5.67174 q^{15} +1.00000 q^{16} +1.19444 q^{17} +2.42611 q^{18} +3.71172 q^{19} -2.43485 q^{20} -1.95566 q^{21} -5.28397 q^{22} -1.07783 q^{23} -2.32940 q^{24} +0.928478 q^{25} -0.826967 q^{26} +1.33681 q^{27} +0.839554 q^{28} +8.71254 q^{29} +5.67174 q^{30} -1.57356 q^{31} +1.00000 q^{32} +12.3085 q^{33} +1.19444 q^{34} -2.04418 q^{35} +2.42611 q^{36} -1.49810 q^{37} +3.71172 q^{38} +1.92634 q^{39} -2.43485 q^{40} -0.609475 q^{41} -1.95566 q^{42} -2.45587 q^{43} -5.28397 q^{44} -5.90722 q^{45} -1.07783 q^{46} +4.85052 q^{47} -2.32940 q^{48} -6.29515 q^{49} +0.928478 q^{50} -2.78234 q^{51} -0.826967 q^{52} +3.68255 q^{53} +1.33681 q^{54} +12.8657 q^{55} +0.839554 q^{56} -8.64608 q^{57} +8.71254 q^{58} +2.81044 q^{59} +5.67174 q^{60} +14.9799 q^{61} -1.57356 q^{62} +2.03685 q^{63} +1.00000 q^{64} +2.01354 q^{65} +12.3085 q^{66} -6.07332 q^{67} +1.19444 q^{68} +2.51070 q^{69} -2.04418 q^{70} +10.5814 q^{71} +2.42611 q^{72} -12.0486 q^{73} -1.49810 q^{74} -2.16280 q^{75} +3.71172 q^{76} -4.43618 q^{77} +1.92634 q^{78} +11.2960 q^{79} -2.43485 q^{80} -10.3923 q^{81} -0.609475 q^{82} -1.64570 q^{83} -1.95566 q^{84} -2.90828 q^{85} -2.45587 q^{86} -20.2950 q^{87} -5.28397 q^{88} +3.88182 q^{89} -5.90722 q^{90} -0.694283 q^{91} -1.07783 q^{92} +3.66546 q^{93} +4.85052 q^{94} -9.03746 q^{95} -2.32940 q^{96} -8.04003 q^{97} -6.29515 q^{98} -12.8195 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 67 q + 67 q^{2} - 11 q^{3} + 67 q^{4} - 20 q^{5} - 11 q^{6} - 40 q^{7} + 67 q^{8} + 24 q^{9}+O(q^{10}) $ 67 * q + 67 * q^2 - 11 * q^3 + 67 * q^4 - 20 * q^5 - 11 * q^6 - 40 * q^7 + 67 * q^8 + 24 * q^9	\( 67 q + 67 q^{2} - 11 q^{3} + 67 q^{4} - 20 q^{5} - 11 q^{6} - 40 q^{7} + 67 q^{8} + 24 q^{9} - 20 q^{10} - 13 q^{11} - 11 q^{12} - 51 q^{13} - 40 q^{14} - 31 q^{15} + 67 q^{16} - 34 q^{17} + 24 q^{18} - 33 q^{19} - 20 q^{20} - 39 q^{21} - 13 q^{22} - 43 q^{23} - 11 q^{24} - 9 q^{25} - 51 q^{26} - 29 q^{27} - 40 q^{28} - 63 q^{29} - 31 q^{30} - 43 q^{31} + 67 q^{32} - 49 q^{33} - 34 q^{34} - 20 q^{35} + 24 q^{36} - 77 q^{37} - 33 q^{38} - 40 q^{39} - 20 q^{40} - 50 q^{41} - 39 q^{42} - 56 q^{43} - 13 q^{44} - 48 q^{45} - 43 q^{46} - 48 q^{47} - 11 q^{48} + q^{49} - 9 q^{50} - 18 q^{51} - 51 q^{52} - 91 q^{53} - 29 q^{54} - 58 q^{55} - 40 q^{56} - 65 q^{57} - 63 q^{58} - 17 q^{59} - 31 q^{60} - 45 q^{61} - 43 q^{62} - 67 q^{63} + 67 q^{64} - 65 q^{65} - 49 q^{66} - 112 q^{67} - 34 q^{68} - 57 q^{69} - 20 q^{70} - 75 q^{71} + 24 q^{72} - 79 q^{73} - 77 q^{74} - 5 q^{75} - 33 q^{76} - 85 q^{77} - 40 q^{78} - 80 q^{79} - 20 q^{80} - 77 q^{81} - 50 q^{82} - 22 q^{83} - 39 q^{84} - 134 q^{85} - 56 q^{86} - 49 q^{87} - 13 q^{88} - 77 q^{89} - 48 q^{90} - 17 q^{91} - 43 q^{92} - 97 q^{93} - 48 q^{94} - 73 q^{95} - 11 q^{96} - 87 q^{97} + q^{98} - 44 q^{99}+O(q^{100}) \) 67 * q + 67 * q^2 - 11 * q^3 + 67 * q^4 - 20 * q^5 - 11 * q^6 - 40 * q^7 + 67 * q^8 + 24 * q^9 - 20 * q^10 - 13 * q^11 - 11 * q^12 - 51 * q^13 - 40 * q^14 - 31 * q^15 + 67 * q^16 - 34 * q^17 + 24 * q^18 - 33 * q^19 - 20 * q^20 - 39 * q^21 - 13 * q^22 - 43 * q^23 - 11 * q^24 - 9 * q^25 - 51 * q^26 - 29 * q^27 - 40 * q^28 - 63 * q^29 - 31 * q^30 - 43 * q^31 + 67 * q^32 - 49 * q^33 - 34 * q^34 - 20 * q^35 + 24 * q^36 - 77 * q^37 - 33 * q^38 - 40 * q^39 - 20 * q^40 - 50 * q^41 - 39 * q^42 - 56 * q^43 - 13 * q^44 - 48 * q^45 - 43 * q^46 - 48 * q^47 - 11 * q^48 + q^49 - 9 * q^50 - 18 * q^51 - 51 * q^52 - 91 * q^53 - 29 * q^54 - 58 * q^55 - 40 * q^56 - 65 * q^57 - 63 * q^58 - 17 * q^59 - 31 * q^60 - 45 * q^61 - 43 * q^62 - 67 * q^63 + 67 * q^64 - 65 * q^65 - 49 * q^66 - 112 * q^67 - 34 * q^68 - 57 * q^69 - 20 * q^70 - 75 * q^71 + 24 * q^72 - 79 * q^73 - 77 * q^74 - 5 * q^75 - 33 * q^76 - 85 * q^77 - 40 * q^78 - 80 * q^79 - 20 * q^80 - 77 * q^81 - 50 * q^82 - 22 * q^83 - 39 * q^84 - 134 * q^85 - 56 * q^86 - 49 * q^87 - 13 * q^88 - 77 * q^89 - 48 * q^90 - 17 * q^91 - 43 * q^92 - 97 * q^93 - 48 * q^94 - 73 * q^95 - 11 * q^96 - 87 * q^97 + q^98 - 44 * 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
$3$	−2.32940	−1.34488	−0.672440	−	0.740151i	$-0.734754\pi$
$3$	−2.32940	−1.34488	−0.672440	+	0.740151i	$0.734754\pi$
$4$	1.00000	0.500000
$5$	−2.43485	−1.08890	−0.544448	−	0.838794i	$-0.683261\pi$
$5$	−2.43485	−1.08890	−0.544448	+	0.838794i	$0.683261\pi$
$6$	−2.32940	−0.950974
$7$	0.839554	0.317322	0.158661	−	0.987333i	$-0.449282\pi$
$7$	0.839554	0.317322	0.158661	+	0.987333i	$0.449282\pi$
$8$	1.00000	0.353553
$9$	2.42611	0.808705
$10$	−2.43485	−0.769966
$11$	−5.28397	−1.59318	−0.796588	−	0.604522i	$-0.793364\pi$
$11$	−5.28397	−1.59318	−0.796588	+	0.604522i	$0.793364\pi$
$12$	−2.32940	−0.672440
$13$	−0.826967	−0.229359	−0.114680	−	0.993403i	$-0.536584\pi$
$13$	−0.826967	−0.229359	−0.114680	+	0.993403i	$0.536584\pi$
$14$	0.839554	0.224380
$15$	5.67174	1.46444
$16$	1.00000	0.250000
$17$	1.19444	0.289695	0.144847	−	0.989454i	$-0.453731\pi$
$17$	1.19444	0.289695	0.144847	+	0.989454i	$0.453731\pi$
$18$	2.42611	0.571841
$19$	3.71172	0.851526	0.425763	−	0.904835i	$-0.360006\pi$
$19$	3.71172	0.851526	0.425763	+	0.904835i	$0.360006\pi$
$20$	−2.43485	−0.544448
$21$	−1.95566	−0.426760
$22$	−5.28397	−1.12655
$23$	−1.07783	−0.224743	−0.112371	−	0.993666i	$-0.535845\pi$
$23$	−1.07783	−0.224743	−0.112371	+	0.993666i	$0.535845\pi$
$24$	−2.32940	−0.475487
$25$	0.928478	0.185696
$26$	−0.826967	−0.162182
$27$	1.33681	0.257269
$28$	0.839554	0.158661
$29$	8.71254	1.61788	0.808939	−	0.587893i	$-0.200042\pi$
$29$	8.71254	1.61788	0.808939	+	0.587893i	$0.200042\pi$
$30$	5.67174	1.03551
$31$	−1.57356	−0.282620	−0.141310	−	0.989965i	$-0.545131\pi$
$31$	−1.57356	−0.282620	−0.141310	+	0.989965i	$0.545131\pi$
$32$	1.00000	0.176777
$33$	12.3085	2.14263
$34$	1.19444	0.204845
$35$	−2.04418	−0.345530
$36$	2.42611	0.404352
$37$	−1.49810	−0.246286	−0.123143	−	0.992389i	$-0.539297\pi$
$37$	−1.49810	−0.246286	−0.123143	+	0.992389i	$0.539297\pi$
$38$	3.71172	0.602120
$39$	1.92634	0.308461
$40$	−2.43485	−0.384983
$41$	−0.609475	−0.0951839	−0.0475920	−	0.998867i	$-0.515155\pi$
$41$	−0.609475	−0.0951839	−0.0475920	+	0.998867i	$0.515155\pi$
$42$	−1.95566	−0.301765
$43$	−2.45587	−0.374516	−0.187258	−	0.982311i	$-0.559960\pi$
$43$	−2.45587	−0.374516	−0.187258	+	0.982311i	$0.559960\pi$
$44$	−5.28397	−0.796588
$45$	−5.90722	−0.880596
$46$	−1.07783	−0.158917
$47$	4.85052	0.707520	0.353760	−	0.935336i	$-0.384903\pi$
$47$	4.85052	0.707520	0.353760	+	0.935336i	$0.384903\pi$
$48$	−2.32940	−0.336220
$49$	−6.29515	−0.899307
$50$	0.928478	0.131307
$51$	−2.78234	−0.389605
$52$	−0.826967	−0.114680
$53$	3.68255	0.505838	0.252919	−	0.967488i	$-0.418609\pi$
$53$	3.68255	0.505838	0.252919	+	0.967488i	$0.418609\pi$
$54$	1.33681	0.181917
$55$	12.8657	1.73480
$56$	0.839554	0.112190
$57$	−8.64608	−1.14520
$58$	8.71254	1.14401
$59$	2.81044	0.365888	0.182944	−	0.983123i	$-0.441437\pi$
$59$	2.81044	0.365888	0.182944	+	0.983123i	$0.441437\pi$
$60$	5.67174	0.732218
$61$	14.9799	1.91798	0.958992	−	0.283432i	$-0.0914730\pi$
$61$	14.9799	1.91798	0.958992	+	0.283432i	$0.0914730\pi$
$62$	−1.57356	−0.199843
$63$	2.03685	0.256619
$64$	1.00000	0.125000
$65$	2.01354	0.249749
$66$	12.3085	1.51507
$67$	−6.07332	−0.741974	−0.370987	−	0.928638i	$-0.620981\pi$
$67$	−6.07332	−0.741974	−0.370987	+	0.928638i	$0.620981\pi$
$68$	1.19444	0.144847
$69$	2.51070	0.302252
$70$	−2.04418	−0.244327
$71$	10.5814	1.25578	0.627891	−	0.778301i	$-0.283918\pi$
$71$	10.5814	1.25578	0.627891	+	0.778301i	$0.283918\pi$
$72$	2.42611	0.285920
$73$	−12.0486	−1.41018	−0.705090	−	0.709118i	$-0.749093\pi$
$73$	−12.0486	−1.41018	−0.705090	+	0.709118i	$0.749093\pi$
$74$	−1.49810	−0.174151
$75$	−2.16280	−0.249739
$76$	3.71172	0.425763
$77$	−4.43618	−0.505549
$78$	1.92634	0.218115
$79$	11.2960	1.27089	0.635447	−	0.772145i	$-0.280816\pi$
$79$	11.2960	1.27089	0.635447	+	0.772145i	$0.280816\pi$
$80$	−2.43485	−0.272224
$81$	−10.3923	−1.15470
$82$	−0.609475	−0.0673052
$83$	−1.64570	−0.180639	−0.0903195	−	0.995913i	$-0.528789\pi$
$83$	−1.64570	−0.180639	−0.0903195	+	0.995913i	$0.528789\pi$
$84$	−1.95566	−0.213380
$85$	−2.90828	−0.315448
$86$	−2.45587	−0.264823
$87$	−20.2950	−2.17585
$88$	−5.28397	−0.563273
$89$	3.88182	0.411472	0.205736	−	0.978608i	$-0.434041\pi$
$89$	3.88182	0.411472	0.205736	+	0.978608i	$0.434041\pi$
$90$	−5.90722	−0.622675
$91$	−0.694283	−0.0727806
$92$	−1.07783	−0.112371
$93$	3.66546	0.380090
$94$	4.85052	0.500292
$95$	−9.03746	−0.927224
$96$	−2.32940	−0.237744
$97$	−8.04003	−0.816342	−0.408171	−	0.912906i	$-0.633833\pi$
$97$	−8.04003	−0.816342	−0.408171	+	0.912906i	$0.633833\pi$
$98$	−6.29515	−0.635906
$99$	−12.8195	−1.28841
$100$	0.928478	0.0928478
$101$	−12.2146	−1.21540	−0.607699	−	0.794167i	$-0.707907\pi$
$101$	−12.2146	−1.21540	−0.607699	+	0.794167i	$0.707907\pi$
$102$	−2.78234	−0.275492
$103$	−1.71547	−0.169030	−0.0845150	−	0.996422i	$-0.526934\pi$
$103$	−1.71547	−0.169030	−0.0845150	+	0.996422i	$0.526934\pi$
$104$	−0.826967	−0.0810908
$105$	4.76173	0.464697
$106$	3.68255	0.357681
$107$	17.9762	1.73782	0.868911	−	0.494968i	$-0.164820\pi$
$107$	17.9762	1.73782	0.868911	+	0.494968i	$0.164820\pi$
$108$	1.33681	0.128635
$109$	−1.80745	−0.173122	−0.0865610	−	0.996247i	$-0.527588\pi$
$109$	−1.80745	−0.173122	−0.0865610	+	0.996247i	$0.527588\pi$
$110$	12.8657	1.22669
$111$	3.48968	0.331226
$112$	0.839554	0.0793304
$113$	−10.3727	−0.975785	−0.487892	−	0.872904i	$-0.662234\pi$
$113$	−10.3727	−0.975785	−0.487892	+	0.872904i	$0.662234\pi$
$114$	−8.64608	−0.809779
$115$	2.62435	0.244722
$116$	8.71254	0.808939
$117$	−2.00632	−0.185484
$118$	2.81044	0.258722
$119$	1.00280	0.0919264
$120$	5.67174	0.517756
$121$	16.9203	1.53821
$122$	14.9799	1.35622
$123$	1.41971	0.128011
$124$	−1.57356	−0.141310
$125$	9.91353	0.886693
$126$	2.03685	0.181457
$127$	−0.603915	−0.0535888	−0.0267944	−	0.999641i	$-0.508530\pi$
$127$	−0.603915	−0.0535888	−0.0267944	+	0.999641i	$0.508530\pi$
$128$	1.00000	0.0883883
$129$	5.72070	0.503680
$130$	2.01354	0.176599
$131$	−13.6610	−1.19357	−0.596784	−	0.802402i	$-0.703555\pi$
$131$	−13.6610	−1.19357	−0.596784	+	0.802402i	$0.703555\pi$
$132$	12.3085	1.07132
$133$	3.11618	0.270208
$134$	−6.07332	−0.524655
$135$	−3.25493	−0.280140
$136$	1.19444	0.102423
$137$	−5.93477	−0.507042	−0.253521	−	0.967330i	$-0.581589\pi$
$137$	−5.93477	−0.507042	−0.253521	+	0.967330i	$0.581589\pi$
$138$	2.51070	0.213725
$139$	−1.81978	−0.154352	−0.0771759	−	0.997017i	$-0.524590\pi$
$139$	−1.81978	−0.154352	−0.0771759	+	0.997017i	$0.524590\pi$
$140$	−2.04418	−0.172765
$141$	−11.2988	−0.951531
$142$	10.5814	0.887972
$143$	4.36967	0.365410
$144$	2.42611	0.202176
$145$	−21.2137	−1.76170
$146$	−12.0486	−0.997148
$147$	14.6639	1.20946
$148$	−1.49810	−0.123143
$149$	13.0036	1.06529	0.532646	−	0.846338i	$-0.321198\pi$
$149$	13.0036	1.06529	0.532646	+	0.846338i	$0.321198\pi$
$150$	−2.16280	−0.176592
$151$	−9.41130	−0.765881	−0.382940	−	0.923773i	$-0.625089\pi$
$151$	−9.41130	−0.765881	−0.382940	+	0.923773i	$0.625089\pi$
$152$	3.71172	0.301060
$153$	2.89785	0.234278
$154$	−4.43618	−0.357477
$155$	3.83138	0.307744
$156$	1.92634	0.154230
$157$	−7.04207	−0.562018	−0.281009	−	0.959705i	$-0.590669\pi$
$157$	−7.04207	−0.562018	−0.281009	+	0.959705i	$0.590669\pi$
$158$	11.2960	0.898658
$159$	−8.57815	−0.680291
$160$	−2.43485	−0.192492
$161$	−0.904895	−0.0713157
$162$	−10.3923	−0.816497
$163$	6.87365	0.538386	0.269193	−	0.963086i	$-0.413243\pi$
$163$	6.87365	0.538386	0.269193	+	0.963086i	$0.413243\pi$
$164$	−0.609475	−0.0475920
$165$	−29.9693	−2.33310
$166$	−1.64570	−0.127731
$167$	−5.22780	−0.404539	−0.202270	−	0.979330i	$-0.564832\pi$
$167$	−5.22780	−0.404539	−0.202270	+	0.979330i	$0.564832\pi$
$168$	−1.95566	−0.150882
$169$	−12.3161	−0.947394
$170$	−2.90828	−0.223055
$171$	9.00504	0.688633
$172$	−2.45587	−0.187258
$173$	11.4441	0.870077	0.435038	−	0.900412i	$-0.356735\pi$
$173$	11.4441	0.870077	0.435038	+	0.900412i	$0.356735\pi$
$174$	−20.2950	−1.53856
$175$	0.779508	0.0589252
$176$	−5.28397	−0.398294
$177$	−6.54664	−0.492075
$178$	3.88182	0.290955
$179$	−1.65368	−0.123602	−0.0618009	−	0.998088i	$-0.519684\pi$
$179$	−1.65368	−0.123602	−0.0618009	+	0.998088i	$0.519684\pi$
$180$	−5.90722	−0.440298
$181$	−8.36335	−0.621643	−0.310821	−	0.950468i	$-0.600604\pi$
$181$	−8.36335	−0.621643	−0.310821	+	0.950468i	$0.600604\pi$
$182$	−0.694283	−0.0514637
$183$	−34.8943	−2.57946
$184$	−1.07783	−0.0794585
$185$	3.64765	0.268180
$186$	3.66546	0.268764
$187$	−6.31139	−0.461535
$188$	4.85052	0.353760
$189$	1.12232	0.0816371
$190$	−9.03746	−0.655646
$191$	−9.06744	−0.656097	−0.328048	−	0.944661i	$-0.606391\pi$
$191$	−9.06744	−0.656097	−0.328048	+	0.944661i	$0.606391\pi$
$192$	−2.32940	−0.168110
$193$	−4.66340	−0.335679	−0.167839	−	0.985814i	$-0.553679\pi$
$193$	−4.66340	−0.335679	−0.167839	+	0.985814i	$0.553679\pi$
$194$	−8.04003	−0.577241
$195$	−4.69034	−0.335882
$196$	−6.29515	−0.449654
$197$	−13.6852	−0.975033	−0.487516	−	0.873114i	$-0.662097\pi$
$197$	−13.6852	−0.975033	−0.487516	+	0.873114i	$0.662097\pi$
$198$	−12.8195	−0.911043
$199$	−12.0896	−0.857007	−0.428504	−	0.903540i	$-0.640959\pi$
$199$	−12.0896	−0.857007	−0.428504	+	0.903540i	$0.640959\pi$
$200$	0.928478	0.0656533
$201$	14.1472	0.997866
$202$	−12.2146	−0.859416
$203$	7.31465	0.513388
$204$	−2.78234	−0.194803
$205$	1.48398	0.103645
$206$	−1.71547	−0.119522
$207$	−2.61493	−0.181750
$208$	−0.826967	−0.0573398
$209$	−19.6126	−1.35663
$210$	4.76173	0.328590
$211$	−6.42797	−0.442520	−0.221260	−	0.975215i	$-0.571017\pi$
$211$	−6.42797	−0.442520	−0.221260	+	0.975215i	$0.571017\pi$
$212$	3.68255	0.252919
$213$	−24.6484	−1.68888
$214$	17.9762	1.22883
$215$	5.97966	0.407809
$216$	1.33681	0.0909585
$217$	−1.32109	−0.0896814
$218$	−1.80745	−0.122416
$219$	28.0660	1.89652
$220$	12.8657	0.867402
$221$	−0.987764	−0.0664442
$222$	3.48968	0.234212
$223$	24.1728	1.61873	0.809364	−	0.587308i	$-0.199812\pi$
$223$	24.1728	1.61873	0.809364	+	0.587308i	$0.199812\pi$
$224$	0.839554	0.0560950
$225$	2.25259	0.150173
$226$	−10.3727	−0.689984
$227$	−17.2841	−1.14719	−0.573593	−	0.819140i	$-0.694451\pi$
$227$	−17.2841	−1.14719	−0.573593	+	0.819140i	$0.694451\pi$
$228$	−8.64608	−0.572600
$229$	29.0334	1.91858	0.959291	−	0.282419i	$-0.0911369\pi$
$229$	29.0334	1.91858	0.959291	+	0.282419i	$0.0911369\pi$
$230$	2.62435	0.173044
$231$	10.3336	0.679903
$232$	8.71254	0.572006
$233$	9.67858	0.634065	0.317032	−	0.948415i	$-0.397314\pi$
$233$	9.67858	0.634065	0.317032	+	0.948415i	$0.397314\pi$
$234$	−2.00632	−0.131157
$235$	−11.8103	−0.770417
$236$	2.81044	0.182944
$237$	−26.3128	−1.70920
$238$	1.00280	0.0650018
$239$	−22.7208	−1.46968	−0.734842	−	0.678239i	$-0.762744\pi$
$239$	−22.7208	−1.46968	−0.734842	+	0.678239i	$0.762744\pi$
$240$	5.67174	0.366109
$241$	−28.6211	−1.84365	−0.921824	−	0.387610i	$-0.873301\pi$
$241$	−28.6211	−1.84365	−0.921824	+	0.387610i	$0.873301\pi$
$242$	16.9203	1.08768
$243$	20.1974	1.29567
$244$	14.9799	0.958992
$245$	15.3277	0.979252
$246$	1.41971	0.0905175
$247$	−3.06947	−0.195305
$248$	−1.57356	−0.0999213
$249$	3.83350	0.242938
$250$	9.91353	0.626987
$251$	9.58402	0.604938	0.302469	−	0.953159i	$-0.402189\pi$
$251$	9.58402	0.604938	0.302469	+	0.953159i	$0.402189\pi$
$252$	2.03685	0.128310
$253$	5.69521	0.358055
$254$	−0.603915	−0.0378930
$255$	6.77456	0.424240
$256$	1.00000	0.0625000
$257$	−29.3218	−1.82905	−0.914523	−	0.404533i	$-0.867434\pi$
$257$	−29.3218	−1.82905	−0.914523	+	0.404533i	$0.867434\pi$
$258$	5.72070	0.356155
$259$	−1.25774	−0.0781519
$260$	2.01354	0.124874
$261$	21.1376	1.30839
$262$	−13.6610	−0.843980
$263$	−6.18250	−0.381229	−0.190615	−	0.981665i	$-0.561048\pi$
$263$	−6.18250	−0.381229	−0.190615	+	0.981665i	$0.561048\pi$
$264$	12.3085	0.757535
$265$	−8.96645	−0.550805
$266$	3.11618	0.191066
$267$	−9.04232	−0.553381
$268$	−6.07332	−0.370987
$269$	5.97166	0.364099	0.182049	−	0.983289i	$-0.441727\pi$
$269$	5.97166	0.364099	0.182049	+	0.983289i	$0.441727\pi$
$270$	−3.25493	−0.198089
$271$	15.4945	0.941222	0.470611	−	0.882341i	$-0.344034\pi$
$271$	15.4945	0.941222	0.470611	+	0.882341i	$0.344034\pi$
$272$	1.19444	0.0724237
$273$	1.61726	0.0978813
$274$	−5.93477	−0.358533
$275$	−4.90605	−0.295846
$276$	2.51070	0.151126
$277$	17.7529	1.06667	0.533334	−	0.845905i	$-0.320939\pi$
$277$	17.7529	1.06667	0.533334	+	0.845905i	$0.320939\pi$
$278$	−1.81978	−0.109143
$279$	−3.81764	−0.228556
$280$	−2.04418	−0.122163
$281$	−10.3974	−0.620258	−0.310129	−	0.950694i	$-0.600372\pi$
$281$	−10.3974	−0.620258	−0.310129	+	0.950694i	$0.600372\pi$
$282$	−11.2988	−0.672834
$283$	6.89539	0.409889	0.204944	−	0.978774i	$-0.434299\pi$
$283$	6.89539	0.409889	0.204944	+	0.978774i	$0.434299\pi$
$284$	10.5814	0.627891
$285$	21.0519	1.24701
$286$	4.36967	0.258384
$287$	−0.511687	−0.0302039
$288$	2.42611	0.142960
$289$	−15.5733	−0.916077
$290$	−21.2137	−1.24571
$291$	18.7285	1.09788
$292$	−12.0486	−0.705090
$293$	8.75954	0.511738	0.255869	−	0.966711i	$-0.417638\pi$
$293$	8.75954	0.511738	0.255869	+	0.966711i	$0.417638\pi$
$294$	14.6639	0.855218
$295$	−6.84298	−0.398414
$296$	−1.49810	−0.0870753
$297$	−7.06367	−0.409876
$298$	13.0036	0.753276
$299$	0.891328	0.0515468
$300$	−2.16280	−0.124869
$301$	−2.06183	−0.118842
$302$	−9.41130	−0.541560
$303$	28.4527	1.63457
$304$	3.71172	0.212881
$305$	−36.4739	−2.08849
$306$	2.89785	0.165659
$307$	−2.88547	−0.164683	−0.0823413	−	0.996604i	$-0.526240\pi$
$307$	−2.88547	−0.164683	−0.0823413	+	0.996604i	$0.526240\pi$
$308$	−4.43618	−0.252775
$309$	3.99601	0.227325
$310$	3.83138	0.217608
$311$	31.2564	1.77239	0.886195	−	0.463313i	$-0.153339\pi$
$311$	31.2564	1.77239	0.886195	+	0.463313i	$0.153339\pi$
$312$	1.92634	0.109057
$313$	−29.2113	−1.65112	−0.825559	−	0.564316i	$-0.809140\pi$
$313$	−29.2113	−1.65112	−0.825559	+	0.564316i	$0.809140\pi$
$314$	−7.04207	−0.397407
$315$	−4.95943	−0.279432
$316$	11.2960	0.635447
$317$	19.4126	1.09032	0.545159	−	0.838333i	$-0.316469\pi$
$317$	19.4126	1.09032	0.545159	+	0.838333i	$0.316469\pi$
$318$	−8.57815	−0.481039
$319$	−46.0368	−2.57756
$320$	−2.43485	−0.136112
$321$	−41.8737	−2.33716
$322$	−0.904895	−0.0504278
$323$	4.43343	0.246683
$324$	−10.3923	−0.577351
$325$	−0.767821	−0.0425910
$326$	6.87365	0.380696
$327$	4.21027	0.232828
$328$	−0.609475	−0.0336526
$329$	4.07227	0.224511
$330$	−29.9693	−1.64975
$331$	−8.75448	−0.481190	−0.240595	−	0.970626i	$-0.577342\pi$
$331$	−8.75448	−0.481190	−0.240595	+	0.970626i	$0.577342\pi$
$332$	−1.64570	−0.0903195
$333$	−3.63456	−0.199173
$334$	−5.22780	−0.286053
$335$	14.7876	0.807933
$336$	−1.95566	−0.106690
$337$	−24.9438	−1.35878	−0.679388	−	0.733779i	$-0.737755\pi$
$337$	−24.9438	−1.35878	−0.679388	+	0.733779i	$0.737755\pi$
$338$	−12.3161	−0.669909
$339$	24.1623	1.31231
$340$	−2.90828	−0.157724
$341$	8.31465	0.450264
$342$	9.00504	0.486937
$343$	−11.1620	−0.602691
$344$	−2.45587	−0.132411
$345$	−6.11316	−0.329121
$346$	11.4441	0.615237
$347$	−29.1632	−1.56556	−0.782782	−	0.622296i	$-0.786200\pi$
$347$	−29.1632	−1.56556	−0.782782	+	0.622296i	$0.786200\pi$
$348$	−20.2950	−1.08793
$349$	0.661633	0.0354164	0.0177082	−	0.999843i	$-0.494363\pi$
$349$	0.661633	0.0354164	0.0177082	+	0.999843i	$0.494363\pi$
$350$	0.779508	0.0416664
$351$	−1.10550	−0.0590071
$352$	−5.28397	−0.281636
$353$	21.1964	1.12817	0.564086	−	0.825716i	$-0.309229\pi$
$353$	21.1964	1.12817	0.564086	+	0.825716i	$0.309229\pi$
$354$	−6.54664	−0.347950
$355$	−25.7641	−1.36742
$356$	3.88182	0.205736
$357$	−2.33592	−0.123630
$358$	−1.65368	−0.0873996
$359$	−31.5311	−1.66415	−0.832073	−	0.554666i	$-0.812846\pi$
$359$	−31.5311	−1.66415	−0.832073	+	0.554666i	$0.812846\pi$
$360$	−5.90722	−0.311338
$361$	−5.22317	−0.274904
$362$	−8.36335	−0.439568
$363$	−39.4142	−2.06871
$364$	−0.694283	−0.0363903
$365$	29.3364	1.53554
$366$	−34.8943	−1.82395
$367$	−17.7182	−0.924884	−0.462442	−	0.886650i	$-0.653027\pi$
$367$	−17.7182	−0.924884	−0.462442	+	0.886650i	$0.653027\pi$
$368$	−1.07783	−0.0561857
$369$	−1.47865	−0.0769757
$370$	3.64765	0.189632
$371$	3.09170	0.160513
$372$	3.66546	0.190045
$373$	−26.0262	−1.34759	−0.673794	−	0.738920i	$-0.735336\pi$
$373$	−26.0262	−1.34759	−0.673794	+	0.738920i	$0.735336\pi$
$374$	−6.31139	−0.326354
$375$	−23.0926	−1.19250
$376$	4.85052	0.250146
$377$	−7.20498	−0.371075
$378$	1.12232	0.0577262
$379$	−0.634769	−0.0326059	−0.0163029	−	0.999867i	$-0.505190\pi$
$379$	−0.634769	−0.0326059	−0.0163029	+	0.999867i	$0.505190\pi$
$380$	−9.03746	−0.463612
$381$	1.40676	0.0720706
$382$	−9.06744	−0.463931
$383$	8.55509	0.437145	0.218572	−	0.975821i	$-0.429860\pi$
$383$	8.55509	0.437145	0.218572	+	0.975821i	$0.429860\pi$
$384$	−2.32940	−0.118872
$385$	10.8014	0.550491
$386$	−4.66340	−0.237361
$387$	−5.95821	−0.302873
$388$	−8.04003	−0.408171
$389$	7.48402	0.379455	0.189728	−	0.981837i	$-0.439240\pi$
$389$	7.48402	0.379455	0.189728	+	0.981837i	$0.439240\pi$
$390$	−4.69034	−0.237504
$391$	−1.28740	−0.0651068
$392$	−6.29515	−0.317953
$393$	31.8220	1.60521
$394$	−13.6852	−0.689452
$395$	−27.5039	−1.38387
$396$	−12.8195	−0.644205
$397$	−0.224964	−0.0112906	−0.00564532	−	0.999984i	$-0.501797\pi$
$397$	−0.224964	−0.0112906	−0.00564532	+	0.999984i	$0.501797\pi$
$398$	−12.0896	−0.605996
$399$	−7.25885	−0.363397
$400$	0.928478	0.0464239
$401$	11.8662	0.592569	0.296284	−	0.955100i	$-0.404252\pi$
$401$	11.8662	0.592569	0.296284	+	0.955100i	$0.404252\pi$
$402$	14.1472	0.705598
$403$	1.30128	0.0648215
$404$	−12.2146	−0.607699
$405$	25.3037	1.25735
$406$	7.31465	0.363020
$407$	7.91592	0.392377
$408$	−2.78234	−0.137746
$409$	−1.66699	−0.0824275	−0.0412137	−	0.999150i	$-0.513122\pi$
$409$	−1.66699	−0.0824275	−0.0412137	+	0.999150i	$0.513122\pi$
$410$	1.48398	0.0732884
$411$	13.8245	0.681911
$412$	−1.71547	−0.0845150
$413$	2.35951	0.116104
$414$	−2.61493	−0.128517
$415$	4.00703	0.196697
$416$	−0.826967	−0.0405454
$417$	4.23900	0.207585
$418$	−19.6126	−0.959283
$419$	−12.6731	−0.619122	−0.309561	−	0.950880i	$-0.600182\pi$
$419$	−12.6731	−0.619122	−0.309561	+	0.950880i	$0.600182\pi$
$420$	4.76173	0.232349
$421$	−25.5422	−1.24485	−0.622426	−	0.782679i	$-0.713853\pi$
$421$	−25.5422	−1.24485	−0.622426	+	0.782679i	$0.713853\pi$
$422$	−6.42797	−0.312909
$423$	11.7679	0.572175
$424$	3.68255	0.178841
$425$	1.10901	0.0537951
$426$	−24.6484	−1.19422
$427$	12.5765	0.608618
$428$	17.9762	0.868911
$429$	−10.1787	−0.491433
$430$	5.97966	0.288365
$431$	30.7220	1.47982	0.739912	−	0.672703i	$-0.234867\pi$
$431$	30.7220	1.47982	0.739912	+	0.672703i	$0.234867\pi$
$432$	1.33681	0.0643174
$433$	2.16933	0.104252	0.0521258	−	0.998641i	$-0.483400\pi$
$433$	2.16933	0.104252	0.0521258	+	0.998641i	$0.483400\pi$
$434$	−1.32109	−0.0634143
$435$	49.4152	2.36928
$436$	−1.80745	−0.0865610
$437$	−4.00059	−0.191374
$438$	28.0660	1.34104
$439$	11.2301	0.535984	0.267992	−	0.963421i	$-0.413640\pi$
$439$	11.2301	0.535984	0.267992	+	0.963421i	$0.413640\pi$
$440$	12.8657	0.613346
$441$	−15.2728	−0.727274
$442$	−0.987764	−0.0469831
$443$	−15.0579	−0.715423	−0.357711	−	0.933832i	$-0.616443\pi$
$443$	−15.0579	−0.715423	−0.357711	+	0.933832i	$0.616443\pi$
$444$	3.48968	0.165613
$445$	−9.45164	−0.448051
$446$	24.1728	1.14461
$447$	−30.2905	−1.43269
$448$	0.839554	0.0396652
$449$	−4.70643	−0.222110	−0.111055	−	0.993814i	$-0.535423\pi$
$449$	−4.70643	−0.222110	−0.111055	+	0.993814i	$0.535423\pi$
$450$	2.25259	0.106188
$451$	3.22044	0.151645
$452$	−10.3727	−0.487892
$453$	21.9227	1.03002
$454$	−17.2841	−0.811183
$455$	1.69047	0.0792506
$456$	−8.64608	−0.404890
$457$	−33.9258	−1.58698	−0.793491	−	0.608582i	$-0.791739\pi$
$457$	−33.9258	−1.58698	−0.793491	+	0.608582i	$0.791739\pi$
$458$	29.0334	1.35664
$459$	1.59674	0.0745296
$460$	2.62435	0.122361
$461$	−14.5339	−0.676909	−0.338455	−	0.940983i	$-0.609904\pi$
$461$	−14.5339	−0.676909	−0.338455	+	0.940983i	$0.609904\pi$
$462$	10.3336	0.480764
$463$	17.3313	0.805453	0.402726	−	0.915320i	$-0.368063\pi$
$463$	17.3313	0.805453	0.402726	+	0.915320i	$0.368063\pi$
$464$	8.71254	0.404470
$465$	−8.92483	−0.413879
$466$	9.67858	0.448351
$467$	6.04447	0.279705	0.139852	−	0.990172i	$-0.455337\pi$
$467$	6.04447	0.279705	0.139852	+	0.990172i	$0.455337\pi$
$468$	−2.00632	−0.0927420
$469$	−5.09888	−0.235444
$470$	−11.8103	−0.544767
$471$	16.4038	0.755847
$472$	2.81044	0.129361
$473$	12.9767	0.596670
$474$	−26.3128	−1.20859
$475$	3.44625	0.158125
$476$	1.00280	0.0459632
$477$	8.93429	0.409073
$478$	−22.7208	−1.03922
$479$	32.2044	1.47146	0.735728	−	0.677277i	$-0.236840\pi$
$479$	32.2044	1.47146	0.735728	+	0.677277i	$0.236840\pi$
$480$	5.67174	0.258878
$481$	1.23888	0.0564880
$482$	−28.6211	−1.30366
$483$	2.10786	0.0959111
$484$	16.9203	0.769105
$485$	19.5762	0.888912
$486$	20.1974	0.916175
$487$	−31.7527	−1.43885	−0.719426	−	0.694569i	$-0.755595\pi$
$487$	−31.7527	−1.43885	−0.719426	+	0.694569i	$0.755595\pi$
$488$	14.9799	0.678110
$489$	−16.0115	−0.724065
$490$	15.3277	0.692436
$491$	−23.6489	−1.06726	−0.533629	−	0.845718i	$-0.679172\pi$
$491$	−23.6489	−1.06726	−0.533629	+	0.845718i	$0.679172\pi$
$492$	1.41971	0.0640055
$493$	10.4066	0.468691
$494$	−3.06947	−0.138102
$495$	31.2135	1.40294
$496$	−1.57356	−0.0706550
$497$	8.88367	0.398487
$498$	3.83350	0.171783
$499$	−24.6965	−1.10557	−0.552783	−	0.833325i	$-0.686434\pi$
$499$	−24.6965	−1.10557	−0.552783	+	0.833325i	$0.686434\pi$
$500$	9.91353	0.443347
$501$	12.1777	0.544057
$502$	9.58402	0.427756
$503$	−6.93249	−0.309105	−0.154552	−	0.987985i	$-0.549393\pi$
$503$	−6.93249	−0.309105	−0.154552	+	0.987985i	$0.549393\pi$
$504$	2.03685	0.0907287
$505$	29.7407	1.32344
$506$	5.69521	0.253183
$507$	28.6892	1.27413
$508$	−0.603915	−0.0267944
$509$	−15.2412	−0.675556	−0.337778	−	0.941226i	$-0.609675\pi$
$509$	−15.2412	−0.675556	−0.337778	+	0.941226i	$0.609675\pi$
$510$	6.77456	0.299983
$511$	−10.1154	−0.447480
$512$	1.00000	0.0441942
$513$	4.96186	0.219072
$514$	−29.3218	−1.29333
$515$	4.17690	0.184056
$516$	5.72070	0.251840
$517$	−25.6300	−1.12720
$518$	−1.25774	−0.0552618
$519$	−26.6578	−1.17015
$520$	2.01354	0.0882994
$521$	20.9887	0.919532	0.459766	−	0.888040i	$-0.347933\pi$
$521$	20.9887	0.919532	0.459766	+	0.888040i	$0.347933\pi$
$522$	21.1376	0.925168
$523$	−11.2784	−0.493170	−0.246585	−	0.969121i	$-0.579308\pi$
$523$	−11.2784	−0.493170	−0.246585	+	0.969121i	$0.579308\pi$
$524$	−13.6610	−0.596784
$525$	−1.81579	−0.0792474
$526$	−6.18250	−0.269570
$527$	−1.87953	−0.0818736
$528$	12.3085	0.535658
$529$	−21.8383	−0.949491
$530$	−8.96645	−0.389478
$531$	6.81844	0.295895
$532$	3.11618	0.135104
$533$	0.504015	0.0218313
$534$	−9.04232	−0.391300
$535$	−43.7692	−1.89231
$536$	−6.07332	−0.262327
$537$	3.85208	0.166230
$538$	5.97166	0.257457
$539$	33.2634	1.43275
$540$	−3.25493	−0.140070
$541$	−40.0672	−1.72263	−0.861313	−	0.508075i	$-0.830357\pi$
$541$	−40.0672	−1.72263	−0.861313	+	0.508075i	$0.830357\pi$
$542$	15.4945	0.665545
$543$	19.4816	0.836036
$544$	1.19444	0.0512113
$545$	4.40085	0.188512
$546$	1.61726	0.0692125
$547$	19.0009	0.812420	0.406210	−	0.913780i	$-0.366850\pi$
$547$	19.0009	0.812420	0.406210	+	0.913780i	$0.366850\pi$
$548$	−5.93477	−0.253521
$549$	36.3430	1.55108
$550$	−4.90605	−0.209195
$551$	32.3385	1.37767
$552$	2.51070	0.106862
$553$	9.48356	0.403282
$554$	17.7529	0.754248
$555$	−8.49683	−0.360671
$556$	−1.81978	−0.0771759
$557$	−8.37592	−0.354899	−0.177450	−	0.984130i	$-0.556785\pi$
$557$	−8.37592	−0.354899	−0.177450	+	0.984130i	$0.556785\pi$
$558$	−3.81764	−0.161614
$559$	2.03092	0.0858988
$560$	−2.04418	−0.0863826
$561$	14.7018	0.620709
$562$	−10.3974	−0.438589
$563$	−29.2806	−1.23403	−0.617015	−	0.786952i	$-0.711658\pi$
$563$	−29.2806	−1.23403	−0.617015	+	0.786952i	$0.711658\pi$
$564$	−11.2988	−0.475765
$565$	25.2560	1.06253
$566$	6.89539	0.289835
$567$	−8.72491	−0.366412
$568$	10.5814	0.443986
$569$	−35.7409	−1.49834	−0.749168	−	0.662380i	$-0.769546\pi$
$569$	−35.7409	−1.49834	−0.749168	+	0.662380i	$0.769546\pi$
$570$	21.0519	0.881766
$571$	39.1562	1.63864	0.819319	−	0.573338i	$-0.194352\pi$
$571$	39.1562	1.63864	0.819319	+	0.573338i	$0.194352\pi$
$572$	4.36967	0.182705
$573$	21.1217	0.882372
$574$	−0.511687	−0.0213574
$575$	−1.00074	−0.0417337
$576$	2.42611	0.101088
$577$	19.5386	0.813402	0.406701	−	0.913561i	$-0.366679\pi$
$577$	19.5386	0.813402	0.406701	+	0.913561i	$0.366679\pi$
$578$	−15.5733	−0.647764
$579$	10.8629	0.451448
$580$	−21.2137	−0.880851
$581$	−1.38165	−0.0573206
$582$	18.7285	0.776320
$583$	−19.4585	−0.805889
$584$	−12.0486	−0.498574
$585$	4.88507	0.201973
$586$	8.75954	0.361853
$587$	6.93614	0.286285	0.143143	−	0.989702i	$-0.454279\pi$
$587$	6.93614	0.286285	0.143143	+	0.989702i	$0.454279\pi$
$588$	14.6639	0.604730
$589$	−5.84061	−0.240658
$590$	−6.84298	−0.281721
$591$	31.8784	1.31130
$592$	−1.49810	−0.0615716
$593$	34.9109	1.43362	0.716810	−	0.697268i	$-0.245601\pi$
$593$	34.9109	1.43362	0.716810	+	0.697268i	$0.245601\pi$
$594$	−7.06367	−0.289826
$595$	−2.44166	−0.100098
$596$	13.0036	0.532646
$597$	28.1615	1.15257
$598$	0.891328	0.0364491
$599$	−6.07663	−0.248284	−0.124142	−	0.992264i	$-0.539618\pi$
$599$	−6.07663	−0.248284	−0.124142	+	0.992264i	$0.539618\pi$
$600$	−2.16280	−0.0882959
$601$	−10.3947	−0.424010	−0.212005	−	0.977269i	$-0.567999\pi$
$601$	−10.3947	−0.424010	−0.212005	+	0.977269i	$0.567999\pi$
$602$	−2.06183	−0.0840340
$603$	−14.7346	−0.600038
$604$	−9.41130	−0.382940
$605$	−41.1984	−1.67495
$606$	28.4527	1.15581
$607$	−33.3950	−1.35546	−0.677731	−	0.735310i	$-0.737037\pi$
$607$	−33.3950	−1.35546	−0.677731	+	0.735310i	$0.737037\pi$
$608$	3.71172	0.150530
$609$	−17.0388	−0.690445
$610$	−36.4739	−1.47678
$611$	−4.01121	−0.162276
$612$	2.89785	0.117139
$613$	8.51003	0.343717	0.171859	−	0.985122i	$-0.445023\pi$
$613$	8.51003	0.343717	0.171859	+	0.985122i	$0.445023\pi$
$614$	−2.88547	−0.116448
$615$	−3.45678	−0.139391
$616$	−4.43618	−0.178739
$617$	5.27523	0.212373	0.106186	−	0.994346i	$-0.466136\pi$
$617$	5.27523	0.212373	0.106186	+	0.994346i	$0.466136\pi$
$618$	3.99601	0.160743
$619$	−18.7411	−0.753267	−0.376634	−	0.926362i	$-0.622918\pi$
$619$	−18.7411	−0.753267	−0.376634	+	0.926362i	$0.622918\pi$
$620$	3.83138	0.153872
$621$	−1.44085	−0.0578194
$622$	31.2564	1.25327
$623$	3.25900	0.130569
$624$	1.92634	0.0771152
$625$	−28.7803	−1.15121
$626$	−29.2113	−1.16752
$627$	45.6856	1.82451
$628$	−7.04207	−0.281009
$629$	−1.78940	−0.0713479
$630$	−4.95943	−0.197588
$631$	−9.07510	−0.361274	−0.180637	−	0.983550i	$-0.557816\pi$
$631$	−9.07510	−0.361274	−0.180637	+	0.983550i	$0.557816\pi$
$632$	11.2960	0.449329
$633$	14.9733	0.595137
$634$	19.4126	0.770972
$635$	1.47044	0.0583527
$636$	−8.57815	−0.340146
$637$	5.20588	0.206264
$638$	−46.0368	−1.82261
$639$	25.6717	1.01556
$640$	−2.43485	−0.0962458
$641$	−38.7985	−1.53245	−0.766225	−	0.642573i	$-0.777867\pi$
$641$	−38.7985	−1.53245	−0.766225	+	0.642573i	$0.777867\pi$
$642$	−41.8737	−1.65262
$643$	−45.6826	−1.80154	−0.900772	−	0.434291i	$-0.856999\pi$
$643$	−45.6826	−1.80154	−0.900772	+	0.434291i	$0.856999\pi$
$644$	−0.904895	−0.0356578
$645$	−13.9290	−0.548455
$646$	4.43343	0.174431
$647$	−7.20417	−0.283225	−0.141613	−	0.989922i	$-0.545229\pi$
$647$	−7.20417	−0.283225	−0.141613	+	0.989922i	$0.545229\pi$
$648$	−10.3923	−0.408249
$649$	−14.8503	−0.582924
$650$	−0.767821	−0.0301164
$651$	3.07735	0.120611
$652$	6.87365	0.269193
$653$	−7.03589	−0.275336	−0.137668	−	0.990478i	$-0.543961\pi$
$653$	−7.03589	−0.275336	−0.137668	+	0.990478i	$0.543961\pi$
$654$	4.21027	0.164635
$655$	33.2625	1.29967
$656$	−0.609475	−0.0237960
$657$	−29.2312	−1.14042
$658$	4.07227	0.158754
$659$	21.4415	0.835243	0.417621	−	0.908621i	$-0.362864\pi$
$659$	21.4415	0.835243	0.417621	+	0.908621i	$0.362864\pi$
$660$	−29.9693	−1.16655
$661$	48.3581	1.88091	0.940456	−	0.339915i	$-0.110398\pi$
$661$	48.3581	1.88091	0.940456	+	0.339915i	$0.110398\pi$
$662$	−8.75448	−0.340252
$663$	2.30090	0.0893595
$664$	−1.64570	−0.0638655
$665$	−7.58743	−0.294228
$666$	−3.63456	−0.140836
$667$	−9.39062	−0.363606
$668$	−5.22780	−0.202270
$669$	−56.3081	−2.17700
$670$	14.7876	0.571295
$671$	−79.1535	−3.05569
$672$	−1.95566	−0.0754412
$673$	20.5451	0.791956	0.395978	−	0.918260i	$-0.370406\pi$
$673$	20.5451	0.791956	0.395978	+	0.918260i	$0.370406\pi$
$674$	−24.9438	−0.960800
$675$	1.24120	0.0477738
$676$	−12.3161	−0.473697
$677$	30.6479	1.17789	0.588947	−	0.808172i	$-0.299543\pi$
$677$	30.6479	1.17789	0.588947	+	0.808172i	$0.299543\pi$
$678$	24.1623	0.927947
$679$	−6.75004	−0.259043
$680$	−2.90828	−0.111528
$681$	40.2616	1.54283
$682$	8.31465	0.318384
$683$	20.5442	0.786102	0.393051	−	0.919517i	$-0.371420\pi$
$683$	20.5442	0.786102	0.393051	+	0.919517i	$0.371420\pi$
$684$	9.00504	0.344316
$685$	14.4503	0.552116
$686$	−11.1620	−0.426167
$687$	−67.6305	−2.58026
$688$	−2.45587	−0.0936291
$689$	−3.04535	−0.116019
$690$	−6.11316	−0.232724
$691$	9.15226	0.348168	0.174084	−	0.984731i	$-0.444304\pi$
$691$	9.15226	0.348168	0.174084	+	0.984731i	$0.444304\pi$
$692$	11.4441	0.435038
$693$	−10.7627	−0.408840
$694$	−29.1632	−1.10702
$695$	4.43089	0.168073
$696$	−20.2950	−0.769280
$697$	−0.727982	−0.0275743
$698$	0.661633	0.0250432
$699$	−22.5453	−0.852742
$700$	0.779508	0.0294626
$701$	−43.0248	−1.62502	−0.812512	−	0.582945i	$-0.801900\pi$
$701$	−43.0248	−1.62502	−0.812512	+	0.582945i	$0.801900\pi$
$702$	−1.10550	−0.0417243
$703$	−5.56052	−0.209719
$704$	−5.28397	−0.199147
$705$	27.5108	1.03612
$706$	21.1964	0.797738
$707$	−10.2548	−0.385672
$708$	−6.54664	−0.246038
$709$	−36.0122	−1.35247	−0.676233	−	0.736688i	$-0.736389\pi$
$709$	−36.0122	−1.35247	−0.676233	+	0.736688i	$0.736389\pi$
$710$	−25.7641	−0.966910
$711$	27.4053	1.02778
$712$	3.88182	0.145477
$713$	1.69603	0.0635168
$714$	−2.33592	−0.0874196
$715$	−10.6395	−0.397893
$716$	−1.65368	−0.0618009
$717$	52.9258	1.97655
$718$	−31.5311	−1.17673
$719$	−46.1319	−1.72043	−0.860214	−	0.509932i	$-0.829670\pi$
$719$	−46.1319	−1.72043	−0.860214	+	0.509932i	$0.829670\pi$
$720$	−5.90722	−0.220149
$721$	−1.44023	−0.0536369
$722$	−5.22317	−0.194386
$723$	66.6701	2.47949
$724$	−8.36335	−0.310821
$725$	8.08941	0.300433
$726$	−39.4142	−1.46280
$727$	17.3359	0.642953	0.321476	−	0.946918i	$-0.395821\pi$
$727$	17.3359	0.642953	0.321476	+	0.946918i	$0.395821\pi$
$728$	−0.694283	−0.0257318
$729$	−15.8710	−0.587816
$730$	29.3364	1.08579
$731$	−2.93339	−0.108495
$732$	−34.8943	−1.28973
$733$	−7.93149	−0.292956	−0.146478	−	0.989214i	$-0.546794\pi$
$733$	−7.93149	−0.292956	−0.146478	+	0.989214i	$0.546794\pi$
$734$	−17.7182	−0.653992
$735$	−35.7044	−1.31698
$736$	−1.07783	−0.0397293
$737$	32.0912	1.18209
$738$	−1.47865	−0.0544300
$739$	−3.96053	−0.145691	−0.0728453	−	0.997343i	$-0.523208\pi$
$739$	−3.96053	−0.145691	−0.0728453	+	0.997343i	$0.523208\pi$
$740$	3.64765	0.134090
$741$	7.15002	0.262662
$742$	3.09170	0.113500
$743$	−8.63437	−0.316764	−0.158382	−	0.987378i	$-0.550628\pi$
$743$	−8.63437	−0.316764	−0.158382	+	0.987378i	$0.550628\pi$
$744$	3.66546	0.134382
$745$	−31.6617	−1.15999
$746$	−26.0262	−0.952888
$747$	−3.99265	−0.146084
$748$	−6.31139	−0.230767
$749$	15.0920	0.551448
$750$	−23.0926	−0.843223
$751$	12.2092	0.445519	0.222759	−	0.974873i	$-0.428494\pi$
$751$	12.2092	0.445519	0.222759	+	0.974873i	$0.428494\pi$
$752$	4.85052	0.176880
$753$	−22.3250	−0.813569
$754$	−7.20498	−0.262390
$755$	22.9151	0.833965
$756$	1.12232	0.0408186
$757$	−17.9274	−0.651583	−0.325791	−	0.945442i	$-0.605631\pi$
$757$	−17.9274	−0.651583	−0.325791	+	0.945442i	$0.605631\pi$
$758$	−0.634769	−0.0230558
$759$	−13.2664	−0.481541
$760$	−9.03746	−0.327823
$761$	−27.4872	−0.996408	−0.498204	−	0.867060i	$-0.666007\pi$
$761$	−27.4872	−0.996408	−0.498204	+	0.867060i	$0.666007\pi$
$762$	1.40676	0.0509616
$763$	−1.51745	−0.0549353
$764$	−9.06744	−0.328048
$765$	−7.05583	−0.255104
$766$	8.55509	0.309108
$767$	−2.32414	−0.0839197
$768$	−2.32940	−0.0840551
$769$	−27.7383	−1.00027	−0.500134	−	0.865948i	$-0.666716\pi$
$769$	−27.7383	−1.00027	−0.500134	+	0.865948i	$0.666716\pi$
$770$	10.8014	0.389256
$771$	68.3024	2.45985
$772$	−4.66340	−0.167839
$773$	30.2622	1.08846	0.544229	−	0.838937i	$-0.316822\pi$
$773$	30.2622	1.08846	0.544229	+	0.838937i	$0.316822\pi$
$774$	−5.95821	−0.214164
$775$	−1.46102	−0.0524813
$776$	−8.04003	−0.288620
$777$	2.92977	0.105105
$778$	7.48402	0.268315
$779$	−2.26220	−0.0810516
$780$	−4.69034	−0.167941
$781$	−55.9118	−2.00068
$782$	−1.28740	−0.0460375
$783$	11.6470	0.416231
$784$	−6.29515	−0.224827
$785$	17.1464	0.611980
$786$	31.8220	1.13505
$787$	−0.118372	−0.00421949	−0.00210974	−	0.999998i	$-0.500672\pi$
$787$	−0.118372	−0.00421949	−0.00210974	+	0.999998i	$0.500672\pi$
$788$	−13.6852	−0.487516
$789$	14.4015	0.512708
$790$	−27.5039	−0.978545
$791$	−8.70847	−0.309638
$792$	−12.8195	−0.455521
$793$	−12.3879	−0.439908
$794$	−0.224964	−0.00798369
$795$	20.8865	0.740767
$796$	−12.0896	−0.428504
$797$	27.8852	0.987743	0.493872	−	0.869535i	$-0.335581\pi$
$797$	27.8852	0.987743	0.493872	+	0.869535i	$0.335581\pi$
$798$	−7.25885	−0.256960
$799$	5.79366	0.204965
$800$	0.928478	0.0328267
$801$	9.41774	0.332760
$802$	11.8662	0.419010
$803$	63.6643	2.24666
$804$	14.1472	0.498933
$805$	2.20328	0.0776554
$806$	1.30128	0.0458358
$807$	−13.9104	−0.489669
$808$	−12.2146	−0.429708
$809$	−8.48860	−0.298443	−0.149222	−	0.988804i	$-0.547677\pi$
$809$	−8.48860	−0.298443	−0.149222	+	0.988804i	$0.547677\pi$
$810$	25.3037	0.889081
$811$	37.6517	1.32213	0.661065	−	0.750328i	$-0.270105\pi$
$811$	37.6517	1.32213	0.661065	+	0.750328i	$0.270105\pi$
$812$	7.31465	0.256694
$813$	−36.0929	−1.26583
$814$	7.91592	0.277453
$815$	−16.7363	−0.586246
$816$	−2.78234	−0.0974013
$817$	−9.11548	−0.318910
$818$	−1.66699	−0.0582850
$819$	−1.68441	−0.0588580
$820$	1.48398	0.0518227
$821$	26.1360	0.912151	0.456076	−	0.889941i	$-0.349255\pi$
$821$	26.1360	0.912151	0.456076	+	0.889941i	$0.349255\pi$
$822$	13.8245	0.482184
$823$	−16.2827	−0.567579	−0.283789	−	0.958887i	$-0.591592\pi$
$823$	−16.2827	−0.567579	−0.283789	+	0.958887i	$0.591592\pi$
$824$	−1.71547	−0.0597611
$825$	11.4282	0.397878
$826$	2.35951	0.0820980
$827$	37.4397	1.30191	0.650953	−	0.759118i	$-0.274370\pi$
$827$	37.4397	1.30191	0.650953	+	0.759118i	$0.274370\pi$
$828$	−2.61493	−0.0908752
$829$	−17.3493	−0.602566	−0.301283	−	0.953535i	$-0.597415\pi$
$829$	−17.3493	−0.602566	−0.301283	+	0.953535i	$0.597415\pi$
$830$	4.00703	0.139086
$831$	−41.3536	−1.43454
$832$	−0.826967	−0.0286699
$833$	−7.51919	−0.260525
$834$	4.23900	0.146785
$835$	12.7289	0.440502
$836$	−19.6126	−0.678315
$837$	−2.10356	−0.0727095
$838$	−12.6731	−0.437785
$839$	26.6947	0.921604	0.460802	−	0.887503i	$-0.347562\pi$
$839$	26.6947	0.921604	0.460802	+	0.887503i	$0.347562\pi$
$840$	4.76173	0.164295
$841$	46.9084	1.61753
$842$	−25.5422	−0.880243
$843$	24.2198	0.834174
$844$	−6.42797	−0.221260
$845$	29.9879	1.03161
$846$	11.7679	0.404589
$847$	14.2055	0.488107
$848$	3.68255	0.126459
$849$	−16.0621	−0.551251
$850$	1.10901	0.0380389
$851$	1.61470	0.0553510
$852$	−24.6484	−0.844439
$853$	−56.4901	−1.93419	−0.967093	−	0.254424i	$-0.918114\pi$
$853$	−56.4901	−1.93419	−0.967093	+	0.254424i	$0.918114\pi$
$854$	12.5765	0.430358
$855$	−21.9259	−0.749850
$856$	17.9762	0.614413
$857$	21.1982	0.724118	0.362059	−	0.932155i	$-0.382074\pi$
$857$	21.1982	0.724118	0.362059	+	0.932155i	$0.382074\pi$
$858$	−10.1787	−0.347495
$859$	32.9341	1.12370	0.561849	−	0.827240i	$-0.310090\pi$
$859$	32.9341	1.12370	0.561849	+	0.827240i	$0.310090\pi$
$860$	5.97966	0.203905
$861$	1.19192	0.0406207
$862$	30.7220	1.04639
$863$	31.6222	1.07643	0.538217	−	0.842806i	$-0.319098\pi$
$863$	31.6222	1.07643	0.538217	+	0.842806i	$0.319098\pi$
$864$	1.33681	0.0454792
$865$	−27.8646	−0.947424
$866$	2.16933	0.0737170
$867$	36.2765	1.23201
$868$	−1.32109	−0.0448407
$869$	−59.6874	−2.02476
$870$	49.4152	1.67533
$871$	5.02243	0.170179
$872$	−1.80745	−0.0612078
$873$	−19.5060	−0.660179
$874$	−4.00059	−0.135322
$875$	8.32294	0.281367
$876$	28.0660	0.948262
$877$	−13.1255	−0.443215	−0.221608	−	0.975136i	$-0.571130\pi$
$877$	−13.1255	−0.443215	−0.221608	+	0.975136i	$0.571130\pi$
$878$	11.2301	0.378998
$879$	−20.4045	−0.688227
$880$	12.8657	0.433701
$881$	41.6652	1.40373	0.701867	−	0.712308i	$-0.252350\pi$
$881$	41.6652	1.40373	0.701867	+	0.712308i	$0.252350\pi$
$882$	−15.2728	−0.514260
$883$	−7.85921	−0.264483	−0.132242	−	0.991217i	$-0.542218\pi$
$883$	−7.85921	−0.264483	−0.132242	+	0.991217i	$0.542218\pi$
$884$	−0.987764	−0.0332221
$885$	15.9401	0.535819
$886$	−15.0579	−0.505880
$887$	26.2520	0.881456	0.440728	−	0.897641i	$-0.354720\pi$
$887$	26.2520	0.881456	0.440728	+	0.897641i	$0.354720\pi$
$888$	3.48968	0.117106
$889$	−0.507019	−0.0170049
$890$	−9.45164	−0.316820
$891$	54.9126	1.83964
$892$	24.1728	0.809364
$893$	18.0037	0.602472
$894$	−30.2905	−1.01307
$895$	4.02645	0.134590
$896$	0.839554	0.0280475
$897$	−2.07626	−0.0693243
$898$	−4.70643	−0.157055
$899$	−13.7097	−0.457245
$900$	2.25259	0.0750865
$901$	4.39860	0.146539
$902$	3.22044	0.107229
$903$	4.80284	0.159828
$904$	−10.3727	−0.344992
$905$	20.3635	0.676905
$906$	21.9227	0.728333
$907$	47.7509	1.58554	0.792772	−	0.609519i	$-0.208637\pi$
$907$	47.7509	1.58554	0.792772	+	0.609519i	$0.208637\pi$
$908$	−17.2841	−0.573593
$909$	−29.6340	−0.982898
$910$	1.69047	0.0560386
$911$	−8.59572	−0.284789	−0.142395	−	0.989810i	$-0.545480\pi$
$911$	−8.59572	−0.284789	−0.142395	+	0.989810i	$0.545480\pi$
$912$	−8.64608	−0.286300
$913$	8.69582	0.287790
$914$	−33.9258	−1.12217
$915$	84.9623	2.80877
$916$	29.0334	0.959291
$917$	−11.4692	−0.378745
$918$	1.59674	0.0527004
$919$	35.2148	1.16163	0.580815	−	0.814036i	$-0.302734\pi$
$919$	35.2148	1.16163	0.580815	+	0.814036i	$0.302734\pi$
$920$	2.62435	0.0865221
$921$	6.72142	0.221478
$922$	−14.5339	−0.478647
$923$	−8.75048	−0.288025
$924$	10.3336	0.339952
$925$	−1.39095	−0.0457343
$926$	17.3313	0.569541
$927$	−4.16192	−0.136695
$928$	8.71254	0.286003
$929$	55.6573	1.82606	0.913029	−	0.407894i	$-0.133737\pi$
$929$	55.6573	1.82606	0.913029	+	0.407894i	$0.133737\pi$
$930$	−8.92483	−0.292657
$931$	−23.3658	−0.765783
$932$	9.67858	0.317032
$933$	−72.8088	−2.38365
$934$	6.04447	0.197781
$935$	15.3673	0.502564
$936$	−2.00632	−0.0655785
$937$	−10.4278	−0.340661	−0.170331	−	0.985387i	$-0.554484\pi$
$937$	−10.4278	−0.340661	−0.170331	+	0.985387i	$0.554484\pi$
$938$	−5.09888	−0.166484
$939$	68.0447	2.22056
$940$	−11.8103	−0.385208
$941$	−0.429183	−0.0139910	−0.00699548	−	0.999976i	$-0.502227\pi$
$941$	−0.429183	−0.0139910	−0.00699548	+	0.999976i	$0.502227\pi$
$942$	16.4038	0.534465
$943$	0.656909	0.0213919
$944$	2.81044	0.0914719
$945$	−2.73269	−0.0888944
$946$	12.9767	0.421910
$947$	−24.9345	−0.810263	−0.405132	−	0.914258i	$-0.632774\pi$
$947$	−24.9345	−0.810263	−0.405132	+	0.914258i	$0.632774\pi$
$948$	−26.3128	−0.854600
$949$	9.96377	0.323438
$950$	3.44625	0.111811
$951$	−45.2197	−1.46635
$952$	1.00280	0.0325009
$953$	−9.58228	−0.310400	−0.155200	−	0.987883i	$-0.549602\pi$
$953$	−9.58228	−0.310400	−0.155200	+	0.987883i	$0.549602\pi$
$954$	8.93429	0.289258
$955$	22.0778	0.714422
$956$	−22.7208	−0.734842
$957$	107.238	3.46652
$958$	32.2044	1.04048
$959$	−4.98256	−0.160895
$960$	5.67174	0.183055
$961$	−28.5239	−0.920126
$962$	1.23888	0.0399431
$963$	43.6122	1.40538
$964$	−28.6211	−0.921824
$965$	11.3547	0.365520
$966$	2.10786	0.0678194
$967$	−10.6500	−0.342482	−0.171241	−	0.985229i	$-0.554778\pi$
$967$	−10.6500	−0.342482	−0.171241	+	0.985229i	$0.554778\pi$
$968$	16.9203	0.543840
$969$	−10.3272	−0.331759
$970$	19.5762	0.628555
$971$	−26.7795	−0.859394	−0.429697	−	0.902973i	$-0.641380\pi$
$971$	−26.7795	−0.859394	−0.429697	+	0.902973i	$0.641380\pi$
$972$	20.1974	0.647833
$973$	−1.52780	−0.0489791
$974$	−31.7527	−1.01742
$975$	1.78856	0.0572799
$976$	14.9799	0.479496
$977$	−13.8623	−0.443495	−0.221748	−	0.975104i	$-0.571176\pi$
$977$	−13.8623	−0.443495	−0.221748	+	0.975104i	$0.571176\pi$
$978$	−16.0115	−0.511991
$979$	−20.5114	−0.655548
$980$	15.3277	0.489626
$981$	−4.38507	−0.140004
$982$	−23.6489	−0.754666
$983$	39.6329	1.26409	0.632046	−	0.774931i	$-0.282215\pi$
$983$	39.6329	1.26409	0.632046	+	0.774931i	$0.282215\pi$
$984$	1.41971	0.0452587
$985$	33.3214	1.06171
$986$	10.4066	0.331414
$987$	−9.48595	−0.301941
$988$	−3.06947	−0.0976527
$989$	2.64700	0.0841698
$990$	31.2135	0.992031
$991$	40.3000	1.28017	0.640086	−	0.768303i	$-0.278899\pi$
$991$	40.3000	1.28017	0.640086	+	0.768303i	$0.278899\pi$
$992$	−1.57356	−0.0499606
$993$	20.3927	0.647143
$994$	8.88367	0.281773
$995$	29.4363	0.933192
$996$	3.83350	0.121469
$997$	−14.8039	−0.468844	−0.234422	−	0.972135i	$-0.575320\pi$
$997$	−14.8039	−0.468844	−0.234422	+	0.972135i	$0.575320\pi$
$998$	−24.6965	−0.781753
$999$	−2.00268	−0.0633619

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8042.2.a.a.1.11	✓	67

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8042.2.a.a.1.11	✓	67	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.32940 q^{3} +1.00000 q^{4} -2.43485 q^{5} -2.32940 q^{6} +0.839554 q^{7} +1.00000 q^{8} +2.42611 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.32940 q^{3} +1.00000 q^{4} -2.43485 q^{5} -2.32940 q^{6} +0.839554 q^{7} +1.00000 q^{8} +2.42611 q^{9} -2.43485 q^{10} -5.28397 q^{11} -2.32940 q^{12} -0.826967 q^{13} +0.839554 q^{14} +5.67174 q^{15} +1.00000 q^{16} +1.19444 q^{17} +2.42611 q^{18} +3.71172 q^{19} -2.43485 q^{20} -1.95566 q^{21} -5.28397 q^{22} -1.07783 q^{23} -2.32940 q^{24} +0.928478 q^{25} -0.826967 q^{26} +1.33681 q^{27} +0.839554 q^{28} +8.71254 q^{29} +5.67174 q^{30} -1.57356 q^{31} +1.00000 q^{32} +12.3085 q^{33} +1.19444 q^{34} -2.04418 q^{35} +2.42611 q^{36} -1.49810 q^{37} +3.71172 q^{38} +1.92634 q^{39} -2.43485 q^{40} -0.609475 q^{41} -1.95566 q^{42} -2.45587 q^{43} -5.28397 q^{44} -5.90722 q^{45} -1.07783 q^{46} +4.85052 q^{47} -2.32940 q^{48} -6.29515 q^{49} +0.928478 q^{50} -2.78234 q^{51} -0.826967 q^{52} +3.68255 q^{53} +1.33681 q^{54} +12.8657 q^{55} +0.839554 q^{56} -8.64608 q^{57} +8.71254 q^{58} +2.81044 q^{59} +5.67174 q^{60} +14.9799 q^{61} -1.57356 q^{62} +2.03685 q^{63} +1.00000 q^{64} +2.01354 q^{65} +12.3085 q^{66} -6.07332 q^{67} +1.19444 q^{68} +2.51070 q^{69} -2.04418 q^{70} +10.5814 q^{71} +2.42611 q^{72} -12.0486 q^{73} -1.49810 q^{74} -2.16280 q^{75} +3.71172 q^{76} -4.43618 q^{77} +1.92634 q^{78} +11.2960 q^{79} -2.43485 q^{80} -10.3923 q^{81} -0.609475 q^{82} -1.64570 q^{83} -1.95566 q^{84} -2.90828 q^{85} -2.45587 q^{86} -20.2950 q^{87} -5.28397 q^{88} +3.88182 q^{89} -5.90722 q^{90} -0.694283 q^{91} -1.07783 q^{92} +3.66546 q^{93} +4.85052 q^{94} -9.03746 q^{95} -2.32940 q^{96} -8.04003 q^{97} -6.29515 q^{98} -12.8195 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 67 q + 67 q^{2} - 11 q^{3} + 67 q^{4} - 20 q^{5} - 11 q^{6} - 40 q^{7} + 67 q^{8} + 24 q^{9}+O(q^{10}) \) 67 * q + 67 * q^2 - 11 * q^3 + 67 * q^4 - 20 * q^5 - 11 * q^6 - 40 * q^7 + 67 * q^8 + 24 * q^9	\( 67 q + 67 q^{2} - 11 q^{3} + 67 q^{4} - 20 q^{5} - 11 q^{6} - 40 q^{7} + 67 q^{8} + 24 q^{9} - 20 q^{10} - 13 q^{11} - 11 q^{12} - 51 q^{13} - 40 q^{14} - 31 q^{15} + 67 q^{16} - 34 q^{17} + 24 q^{18} - 33 q^{19} - 20 q^{20} - 39 q^{21} - 13 q^{22} - 43 q^{23} - 11 q^{24} - 9 q^{25} - 51 q^{26} - 29 q^{27} - 40 q^{28} - 63 q^{29} - 31 q^{30} - 43 q^{31} + 67 q^{32} - 49 q^{33} - 34 q^{34} - 20 q^{35} + 24 q^{36} - 77 q^{37} - 33 q^{38} - 40 q^{39} - 20 q^{40} - 50 q^{41} - 39 q^{42} - 56 q^{43} - 13 q^{44} - 48 q^{45} - 43 q^{46} - 48 q^{47} - 11 q^{48} + q^{49} - 9 q^{50} - 18 q^{51} - 51 q^{52} - 91 q^{53} - 29 q^{54} - 58 q^{55} - 40 q^{56} - 65 q^{57} - 63 q^{58} - 17 q^{59} - 31 q^{60} - 45 q^{61} - 43 q^{62} - 67 q^{63} + 67 q^{64} - 65 q^{65} - 49 q^{66} - 112 q^{67} - 34 q^{68} - 57 q^{69} - 20 q^{70} - 75 q^{71} + 24 q^{72} - 79 q^{73} - 77 q^{74} - 5 q^{75} - 33 q^{76} - 85 q^{77} - 40 q^{78} - 80 q^{79} - 20 q^{80} - 77 q^{81} - 50 q^{82} - 22 q^{83} - 39 q^{84} - 134 q^{85} - 56 q^{86} - 49 q^{87} - 13 q^{88} - 77 q^{89} - 48 q^{90} - 17 q^{91} - 43 q^{92} - 97 q^{93} - 48 q^{94} - 73 q^{95} - 11 q^{96} - 87 q^{97} + q^{98} - 44 q^{99}+O(q^{100}) \) 67 * q + 67 * q^2 - 11 * q^3 + 67 * q^4 - 20 * q^5 - 11 * q^6 - 40 * q^7 + 67 * q^8 + 24 * q^9 - 20 * q^10 - 13 * q^11 - 11 * q^12 - 51 * q^13 - 40 * q^14 - 31 * q^15 + 67 * q^16 - 34 * q^17 + 24 * q^18 - 33 * q^19 - 20 * q^20 - 39 * q^21 - 13 * q^22 - 43 * q^23 - 11 * q^24 - 9 * q^25 - 51 * q^26 - 29 * q^27 - 40 * q^28 - 63 * q^29 - 31 * q^30 - 43 * q^31 + 67 * q^32 - 49 * q^33 - 34 * q^34 - 20 * q^35 + 24 * q^36 - 77 * q^37 - 33 * q^38 - 40 * q^39 - 20 * q^40 - 50 * q^41 - 39 * q^42 - 56 * q^43 - 13 * q^44 - 48 * q^45 - 43 * q^46 - 48 * q^47 - 11 * q^48 + q^49 - 9 * q^50 - 18 * q^51 - 51 * q^52 - 91 * q^53 - 29 * q^54 - 58 * q^55 - 40 * q^56 - 65 * q^57 - 63 * q^58 - 17 * q^59 - 31 * q^60 - 45 * q^61 - 43 * q^62 - 67 * q^63 + 67 * q^64 - 65 * q^65 - 49 * q^66 - 112 * q^67 - 34 * q^68 - 57 * q^69 - 20 * q^70 - 75 * q^71 + 24 * q^72 - 79 * q^73 - 77 * q^74 - 5 * q^75 - 33 * q^76 - 85 * q^77 - 40 * q^78 - 80 * q^79 - 20 * q^80 - 77 * q^81 - 50 * q^82 - 22 * q^83 - 39 * q^84 - 134 * q^85 - 56 * q^86 - 49 * q^87 - 13 * q^88 - 77 * q^89 - 48 * q^90 - 17 * q^91 - 43 * q^92 - 97 * q^93 - 48 * q^94 - 73 * q^95 - 11 * q^96 - 87 * q^97 + q^98 - 44 * q^99

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