LMFDB - Embedded newform 6010.2.a.i.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6010,2,Mod(1,6010)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6010, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6010.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6010 = 2 \cdot 5 \cdot 601 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6010.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:	$47.9900916148$
Analytic rank:	$1$
Dimension:	$29$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	6010.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -3.28561 q^{3} +1.00000 q^{4} -1.00000 q^{5} +3.28561 q^{6} -1.57080 q^{7} -1.00000 q^{8} +7.79525 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -3.28561 q^{3} +1.00000 q^{4} -1.00000 q^{5} +3.28561 q^{6} -1.57080 q^{7} -1.00000 q^{8} +7.79525 q^{9} +1.00000 q^{10} -6.34656 q^{11} -3.28561 q^{12} -2.49400 q^{13} +1.57080 q^{14} +3.28561 q^{15} +1.00000 q^{16} -3.00378 q^{17} -7.79525 q^{18} +0.666149 q^{19} -1.00000 q^{20} +5.16104 q^{21} +6.34656 q^{22} -3.32007 q^{23} +3.28561 q^{24} +1.00000 q^{25} +2.49400 q^{26} -15.7553 q^{27} -1.57080 q^{28} +4.22508 q^{29} -3.28561 q^{30} +4.85597 q^{31} -1.00000 q^{32} +20.8523 q^{33} +3.00378 q^{34} +1.57080 q^{35} +7.79525 q^{36} -0.820980 q^{37} -0.666149 q^{38} +8.19431 q^{39} +1.00000 q^{40} +9.97481 q^{41} -5.16104 q^{42} +7.41577 q^{43} -6.34656 q^{44} -7.79525 q^{45} +3.32007 q^{46} -3.51273 q^{47} -3.28561 q^{48} -4.53259 q^{49} -1.00000 q^{50} +9.86926 q^{51} -2.49400 q^{52} -9.12884 q^{53} +15.7553 q^{54} +6.34656 q^{55} +1.57080 q^{56} -2.18871 q^{57} -4.22508 q^{58} -10.0975 q^{59} +3.28561 q^{60} -2.63619 q^{61} -4.85597 q^{62} -12.2448 q^{63} +1.00000 q^{64} +2.49400 q^{65} -20.8523 q^{66} +2.68406 q^{67} -3.00378 q^{68} +10.9085 q^{69} -1.57080 q^{70} -4.57709 q^{71} -7.79525 q^{72} +13.5002 q^{73} +0.820980 q^{74} -3.28561 q^{75} +0.666149 q^{76} +9.96917 q^{77} -8.19431 q^{78} -6.47182 q^{79} -1.00000 q^{80} +28.3802 q^{81} -9.97481 q^{82} +5.28536 q^{83} +5.16104 q^{84} +3.00378 q^{85} -7.41577 q^{86} -13.8820 q^{87} +6.34656 q^{88} +4.70553 q^{89} +7.79525 q^{90} +3.91757 q^{91} -3.32007 q^{92} -15.9548 q^{93} +3.51273 q^{94} -0.666149 q^{95} +3.28561 q^{96} -2.69367 q^{97} +4.53259 q^{98} -49.4730 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 29 q - 29 q^{2} - 10 q^{3} + 29 q^{4} - 29 q^{5} + 10 q^{6} - 29 q^{8} + 29 q^{9}+O(q^{10}) $ 29 * q - 29 * q^2 - 10 * q^3 + 29 * q^4 - 29 * q^5 + 10 * q^6 - 29 * q^8 + 29 * q^9	\( 29 q - 29 q^{2} - 10 q^{3} + 29 q^{4} - 29 q^{5} + 10 q^{6} - 29 q^{8} + 29 q^{9} + 29 q^{10} - 10 q^{12} - 4 q^{13} + 10 q^{15} + 29 q^{16} - 23 q^{17} - 29 q^{18} + q^{19} - 29 q^{20} + 2 q^{21} - 9 q^{23} + 10 q^{24} + 29 q^{25} + 4 q^{26} - 43 q^{27} - 5 q^{29} - 10 q^{30} + 21 q^{31} - 29 q^{32} - 19 q^{33} + 23 q^{34} + 29 q^{36} - 6 q^{37} - q^{38} + 18 q^{39} + 29 q^{40} - 17 q^{41} - 2 q^{42} - 19 q^{43} - 29 q^{45} + 9 q^{46} - 21 q^{47} - 10 q^{48} + 45 q^{49} - 29 q^{50} + 11 q^{51} - 4 q^{52} - 53 q^{53} + 43 q^{54} - 16 q^{57} + 5 q^{58} - 30 q^{59} + 10 q^{60} + 16 q^{61} - 21 q^{62} - 17 q^{63} + 29 q^{64} + 4 q^{65} + 19 q^{66} - 35 q^{67} - 23 q^{68} + 13 q^{69} + 2 q^{71} - 29 q^{72} - q^{73} + 6 q^{74} - 10 q^{75} + q^{76} - 50 q^{77} - 18 q^{78} + 26 q^{79} - 29 q^{80} + 33 q^{81} + 17 q^{82} - 54 q^{83} + 2 q^{84} + 23 q^{85} + 19 q^{86} - 56 q^{87} - 2 q^{89} + 29 q^{90} + 27 q^{91} - 9 q^{92} - 26 q^{93} + 21 q^{94} - q^{95} + 10 q^{96} + 15 q^{97} - 45 q^{98} + 27 q^{99}+O(q^{100}) \) 29 * q - 29 * q^2 - 10 * q^3 + 29 * q^4 - 29 * q^5 + 10 * q^6 - 29 * q^8 + 29 * q^9 + 29 * q^10 - 10 * q^12 - 4 * q^13 + 10 * q^15 + 29 * q^16 - 23 * q^17 - 29 * q^18 + q^19 - 29 * q^20 + 2 * q^21 - 9 * q^23 + 10 * q^24 + 29 * q^25 + 4 * q^26 - 43 * q^27 - 5 * q^29 - 10 * q^30 + 21 * q^31 - 29 * q^32 - 19 * q^33 + 23 * q^34 + 29 * q^36 - 6 * q^37 - q^38 + 18 * q^39 + 29 * q^40 - 17 * q^41 - 2 * q^42 - 19 * q^43 - 29 * q^45 + 9 * q^46 - 21 * q^47 - 10 * q^48 + 45 * q^49 - 29 * q^50 + 11 * q^51 - 4 * q^52 - 53 * q^53 + 43 * q^54 - 16 * q^57 + 5 * q^58 - 30 * q^59 + 10 * q^60 + 16 * q^61 - 21 * q^62 - 17 * q^63 + 29 * q^64 + 4 * q^65 + 19 * q^66 - 35 * q^67 - 23 * q^68 + 13 * q^69 + 2 * q^71 - 29 * q^72 - q^73 + 6 * q^74 - 10 * q^75 + q^76 - 50 * q^77 - 18 * q^78 + 26 * q^79 - 29 * q^80 + 33 * q^81 + 17 * q^82 - 54 * q^83 + 2 * q^84 + 23 * q^85 + 19 * q^86 - 56 * q^87 - 2 * q^89 + 29 * q^90 + 27 * q^91 - 9 * q^92 - 26 * q^93 + 21 * q^94 - q^95 + 10 * q^96 + 15 * q^97 - 45 * q^98 + 27 * 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
$3$	−3.28561	−1.89695	−0.948475	−	0.316853i	$-0.897374\pi$
$3$	−3.28561	−1.89695	−0.948475	+	0.316853i	$0.897374\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	3.28561	1.34135
$7$	−1.57080	−0.593706	−0.296853	−	0.954923i	$-0.595937\pi$
$7$	−1.57080	−0.593706	−0.296853	+	0.954923i	$0.595937\pi$
$8$	−1.00000	−0.353553
$9$	7.79525	2.59842
$10$	1.00000	0.316228
$11$	−6.34656	−1.91356	−0.956780	−	0.290812i	$-0.906075\pi$
$11$	−6.34656	−1.91356	−0.956780	+	0.290812i	$0.906075\pi$
$12$	−3.28561	−0.948475
$13$	−2.49400	−0.691711	−0.345855	−	0.938288i	$-0.612411\pi$
$13$	−2.49400	−0.691711	−0.345855	+	0.938288i	$0.612411\pi$
$14$	1.57080	0.419814
$15$	3.28561	0.848342
$16$	1.00000	0.250000
$17$	−3.00378	−0.728524	−0.364262	−	0.931297i	$-0.618679\pi$
$17$	−3.00378	−0.728524	−0.364262	+	0.931297i	$0.618679\pi$
$18$	−7.79525	−1.83736
$19$	0.666149	0.152825	0.0764125	−	0.997076i	$-0.475653\pi$
$19$	0.666149	0.152825	0.0764125	+	0.997076i	$0.475653\pi$
$20$	−1.00000	−0.223607
$21$	5.16104	1.12623
$22$	6.34656	1.35309
$23$	−3.32007	−0.692283	−0.346141	−	0.938182i	$-0.612508\pi$
$23$	−3.32007	−0.692283	−0.346141	+	0.938182i	$0.612508\pi$
$24$	3.28561	0.670673
$25$	1.00000	0.200000
$26$	2.49400	0.489113
$27$	−15.7553	−3.03212
$28$	−1.57080	−0.296853
$29$	4.22508	0.784578	0.392289	−	0.919842i	$-0.371683\pi$
$29$	4.22508	0.784578	0.392289	+	0.919842i	$0.371683\pi$
$30$	−3.28561	−0.599868
$31$	4.85597	0.872158	0.436079	−	0.899908i	$-0.356367\pi$
$31$	4.85597	0.872158	0.436079	+	0.899908i	$0.356367\pi$
$32$	−1.00000	−0.176777
$33$	20.8523	3.62993
$34$	3.00378	0.515144
$35$	1.57080	0.265513
$36$	7.79525	1.29921
$37$	−0.820980	−0.134968	−0.0674842	−	0.997720i	$-0.521497\pi$
$37$	−0.820980	−0.134968	−0.0674842	+	0.997720i	$0.521497\pi$
$38$	−0.666149	−0.108064
$39$	8.19431	1.31214
$40$	1.00000	0.158114
$41$	9.97481	1.55780	0.778902	−	0.627146i	$-0.215777\pi$
$41$	9.97481	1.55780	0.778902	+	0.627146i	$0.215777\pi$
$42$	−5.16104	−0.796365
$43$	7.41577	1.13089	0.565447	−	0.824785i	$-0.308704\pi$
$43$	7.41577	1.13089	0.565447	+	0.824785i	$0.308704\pi$
$44$	−6.34656	−0.956780
$45$	−7.79525	−1.16205
$46$	3.32007	0.489518
$47$	−3.51273	−0.512385	−0.256192	−	0.966626i	$-0.582468\pi$
$47$	−3.51273	−0.512385	−0.256192	+	0.966626i	$0.582468\pi$
$48$	−3.28561	−0.474237
$49$	−4.53259	−0.647513
$50$	−1.00000	−0.141421
$51$	9.86926	1.38197
$52$	−2.49400	−0.345855
$53$	−9.12884	−1.25394	−0.626971	−	0.779043i	$-0.715706\pi$
$53$	−9.12884	−1.25394	−0.626971	+	0.779043i	$0.715706\pi$
$54$	15.7553	2.14403
$55$	6.34656	0.855770
$56$	1.57080	0.209907
$57$	−2.18871	−0.289901
$58$	−4.22508	−0.554781
$59$	−10.0975	−1.31459	−0.657294	−	0.753634i	$-0.728299\pi$
$59$	−10.0975	−1.31459	−0.657294	+	0.753634i	$0.728299\pi$
$60$	3.28561	0.424171
$61$	−2.63619	−0.337529	−0.168765	−	0.985656i	$-0.553978\pi$
$61$	−2.63619	−0.337529	−0.168765	+	0.985656i	$0.553978\pi$
$62$	−4.85597	−0.616709
$63$	−12.2448	−1.54270
$64$	1.00000	0.125000
$65$	2.49400	0.309342
$66$	−20.8523	−2.56675
$67$	2.68406	0.327911	0.163955	−	0.986468i	$-0.447575\pi$
$67$	2.68406	0.327911	0.163955	+	0.986468i	$0.447575\pi$
$68$	−3.00378	−0.364262
$69$	10.9085	1.31323
$70$	−1.57080	−0.187746
$71$	−4.57709	−0.543201	−0.271600	−	0.962410i	$-0.587553\pi$
$71$	−4.57709	−0.543201	−0.271600	+	0.962410i	$0.587553\pi$
$72$	−7.79525	−0.918679
$73$	13.5002	1.58008	0.790039	−	0.613057i	$-0.210060\pi$
$73$	13.5002	1.58008	0.790039	+	0.613057i	$0.210060\pi$
$74$	0.820980	0.0954370
$75$	−3.28561	−0.379390
$76$	0.666149	0.0764125
$77$	9.96917	1.13609
$78$	−8.19431	−0.927823
$79$	−6.47182	−0.728136	−0.364068	−	0.931372i	$-0.618612\pi$
$79$	−6.47182	−0.728136	−0.364068	+	0.931372i	$0.618612\pi$
$80$	−1.00000	−0.111803
$81$	28.3802	3.15335
$82$	−9.97481	−1.10153
$83$	5.28536	0.580143	0.290072	−	0.957005i	$-0.406321\pi$
$83$	5.28536	0.580143	0.290072	+	0.957005i	$0.406321\pi$
$84$	5.16104	0.563115
$85$	3.00378	0.325806
$86$	−7.41577	−0.799663
$87$	−13.8820	−1.48831
$88$	6.34656	0.676546
$89$	4.70553	0.498785	0.249392	−	0.968402i	$-0.419769\pi$
$89$	4.70553	0.498785	0.249392	+	0.968402i	$0.419769\pi$
$90$	7.79525	0.821691
$91$	3.91757	0.410673
$92$	−3.32007	−0.346141
$93$	−15.9548	−1.65444
$94$	3.51273	0.362311
$95$	−0.666149	−0.0683454
$96$	3.28561	0.335336
$97$	−2.69367	−0.273501	−0.136750	−	0.990606i	$-0.543666\pi$
$97$	−2.69367	−0.273501	−0.136750	+	0.990606i	$0.543666\pi$
$98$	4.53259	0.457861
$99$	−49.4730	−4.97223
$100$	1.00000	0.100000
$101$	6.00293	0.597314	0.298657	−	0.954360i	$-0.403461\pi$
$101$	6.00293	0.597314	0.298657	+	0.954360i	$0.403461\pi$
$102$	−9.86926	−0.977202
$103$	−10.0235	−0.987643	−0.493822	−	0.869563i	$-0.664400\pi$
$103$	−10.0235	−0.987643	−0.493822	+	0.869563i	$0.664400\pi$
$104$	2.49400	0.244557
$105$	−5.16104	−0.503666
$106$	9.12884	0.886671
$107$	11.4132	1.10335	0.551676	−	0.834058i	$-0.313988\pi$
$107$	11.4132	1.10335	0.551676	+	0.834058i	$0.313988\pi$
$108$	−15.7553	−1.51606
$109$	18.7068	1.79179	0.895894	−	0.444268i	$-0.146536\pi$
$109$	18.7068	1.79179	0.895894	+	0.444268i	$0.146536\pi$
$110$	−6.34656	−0.605121
$111$	2.69742	0.256028
$112$	−1.57080	−0.148427
$113$	−0.0255036	−0.00239917	−0.00119959	−	0.999999i	$-0.500382\pi$
$113$	−0.0255036	−0.00239917	−0.00119959	+	0.999999i	$0.500382\pi$
$114$	2.18871	0.204991
$115$	3.32007	0.309598
$116$	4.22508	0.392289
$117$	−19.4413	−1.79735
$118$	10.0975	0.929554
$119$	4.71833	0.432529
$120$	−3.28561	−0.299934
$121$	29.2788	2.66171
$122$	2.63619	0.238669
$123$	−32.7734	−2.95508
$124$	4.85597	0.436079
$125$	−1.00000	−0.0894427
$126$	12.2448	1.09085
$127$	18.2211	1.61686	0.808432	−	0.588590i	$-0.200317\pi$
$127$	18.2211	1.61686	0.808432	+	0.588590i	$0.200317\pi$
$128$	−1.00000	−0.0883883
$129$	−24.3653	−2.14525
$130$	−2.49400	−0.218738
$131$	−5.69448	−0.497529	−0.248764	−	0.968564i	$-0.580024\pi$
$131$	−5.69448	−0.497529	−0.248764	+	0.968564i	$0.580024\pi$
$132$	20.8523	1.81496
$133$	−1.04639	−0.0907332
$134$	−2.68406	−0.231868
$135$	15.7553	1.35600
$136$	3.00378	0.257572
$137$	9.84074	0.840751	0.420375	−	0.907350i	$-0.361898\pi$
$137$	9.84074	0.840751	0.420375	+	0.907350i	$0.361898\pi$
$138$	−10.9085	−0.928591
$139$	12.2418	1.03834	0.519168	−	0.854672i	$-0.326242\pi$
$139$	12.2418	1.03834	0.519168	+	0.854672i	$0.326242\pi$
$140$	1.57080	0.132757
$141$	11.5415	0.971968
$142$	4.57709	0.384101
$143$	15.8283	1.32363
$144$	7.79525	0.649604
$145$	−4.22508	−0.350874
$146$	−13.5002	−1.11728
$147$	14.8923	1.22830
$148$	−0.820980	−0.0674842
$149$	7.67756	0.628970	0.314485	−	0.949262i	$-0.398168\pi$
$149$	7.67756	0.628970	0.314485	+	0.949262i	$0.398168\pi$
$150$	3.28561	0.268269
$151$	10.9943	0.894703	0.447352	−	0.894358i	$-0.352367\pi$
$151$	10.9943	0.894703	0.447352	+	0.894358i	$0.352367\pi$
$152$	−0.666149	−0.0540318
$153$	−23.4152	−1.89301
$154$	−9.96917	−0.803339
$155$	−4.85597	−0.390041
$156$	8.19431	0.656070
$157$	−14.2720	−1.13903	−0.569516	−	0.821980i	$-0.692869\pi$
$157$	−14.2720	−1.13903	−0.569516	+	0.821980i	$0.692869\pi$
$158$	6.47182	0.514870
$159$	29.9938	2.37866
$160$	1.00000	0.0790569
$161$	5.21517	0.411013
$162$	−28.3802	−2.22976
$163$	6.63795	0.519924	0.259962	−	0.965619i	$-0.416290\pi$
$163$	6.63795	0.519924	0.259962	+	0.965619i	$0.416290\pi$
$164$	9.97481	0.778902
$165$	−20.8523	−1.62335
$166$	−5.28536	−0.410223
$167$	18.8958	1.46220	0.731102	−	0.682268i	$-0.239006\pi$
$167$	18.8958	1.46220	0.731102	+	0.682268i	$0.239006\pi$
$168$	−5.16104	−0.398183
$169$	−6.77997	−0.521536
$170$	−3.00378	−0.230379
$171$	5.19280	0.397103
$172$	7.41577	0.565447
$173$	12.4028	0.942969	0.471485	−	0.881874i	$-0.343718\pi$
$173$	12.4028	0.942969	0.471485	+	0.881874i	$0.343718\pi$
$174$	13.8820	1.05239
$175$	−1.57080	−0.118741
$176$	−6.34656	−0.478390
$177$	33.1766	2.49371
$178$	−4.70553	−0.352694
$179$	−21.9297	−1.63910	−0.819550	−	0.573008i	$-0.805776\pi$
$179$	−21.9297	−1.63910	−0.819550	+	0.573008i	$0.805776\pi$
$180$	−7.79525	−0.581024
$181$	26.6613	1.98172	0.990861	−	0.134887i	$-0.0430672\pi$
$181$	26.6613	1.98172	0.990861	+	0.134887i	$0.0430672\pi$
$182$	−3.91757	−0.290390
$183$	8.66149	0.640276
$184$	3.32007	0.244759
$185$	0.820980	0.0603597
$186$	15.9548	1.16987
$187$	19.0637	1.39407
$188$	−3.51273	−0.256192
$189$	24.7485	1.80019
$190$	0.666149	0.0483275
$191$	2.85798	0.206796	0.103398	−	0.994640i	$-0.467028\pi$
$191$	2.85798	0.206796	0.103398	+	0.994640i	$0.467028\pi$
$192$	−3.28561	−0.237119
$193$	−20.0259	−1.44149	−0.720747	−	0.693199i	$-0.756201\pi$
$193$	−20.0259	−1.44149	−0.720747	+	0.693199i	$0.756201\pi$
$194$	2.69367	0.193394
$195$	−8.19431	−0.586807
$196$	−4.53259	−0.323757
$197$	−10.8407	−0.772371	−0.386186	−	0.922421i	$-0.626208\pi$
$197$	−10.8407	−0.772371	−0.386186	+	0.922421i	$0.626208\pi$
$198$	49.4730	3.51590
$199$	13.3525	0.946531	0.473266	−	0.880920i	$-0.343075\pi$
$199$	13.3525	0.946531	0.473266	+	0.880920i	$0.343075\pi$
$200$	−1.00000	−0.0707107
$201$	−8.81880	−0.622030
$202$	−6.00293	−0.422365
$203$	−6.63676	−0.465809
$204$	9.86926	0.690986
$205$	−9.97481	−0.696671
$206$	10.0235	0.698369
$207$	−25.8808	−1.79884
$208$	−2.49400	−0.172928
$209$	−4.22776	−0.292440
$210$	5.16104	0.356145
$211$	−15.2780	−1.05178	−0.525890	−	0.850553i	$-0.676267\pi$
$211$	−15.2780	−1.05178	−0.525890	+	0.850553i	$0.676267\pi$
$212$	−9.12884	−0.626971
$213$	15.0385	1.03042
$214$	−11.4132	−0.780188
$215$	−7.41577	−0.505751
$216$	15.7553	1.07201
$217$	−7.62775	−0.517806
$218$	−18.7068	−1.26699
$219$	−44.3564	−2.99733
$220$	6.34656	0.427885
$221$	7.49143	0.503928
$222$	−2.69742	−0.181039
$223$	−12.2214	−0.818403	−0.409202	−	0.912444i	$-0.634193\pi$
$223$	−12.2214	−0.818403	−0.409202	+	0.912444i	$0.634193\pi$
$224$	1.57080	0.104953
$225$	7.79525	0.519683
$226$	0.0255036	0.00169647
$227$	−21.9484	−1.45677	−0.728384	−	0.685169i	$-0.759728\pi$
$227$	−21.9484	−1.45677	−0.728384	+	0.685169i	$0.759728\pi$
$228$	−2.18871	−0.144951
$229$	−17.5376	−1.15891	−0.579457	−	0.815003i	$-0.696735\pi$
$229$	−17.5376	−1.15891	−0.579457	+	0.815003i	$0.696735\pi$
$230$	−3.32007	−0.218919
$231$	−32.7548	−2.15511
$232$	−4.22508	−0.277390
$233$	4.51566	0.295831	0.147915	−	0.989000i	$-0.452744\pi$
$233$	4.51566	0.295831	0.147915	+	0.989000i	$0.452744\pi$
$234$	19.4413	1.27092
$235$	3.51273	0.229145
$236$	−10.0975	−0.657294
$237$	21.2639	1.38124
$238$	−4.71833	−0.305844
$239$	−3.53455	−0.228631	−0.114316	−	0.993444i	$-0.536467\pi$
$239$	−3.53455	−0.228631	−0.114316	+	0.993444i	$0.536467\pi$
$240$	3.28561	0.212085
$241$	9.15256	0.589568	0.294784	−	0.955564i	$-0.404752\pi$
$241$	9.15256	0.589568	0.294784	+	0.955564i	$0.404752\pi$
$242$	−29.2788	−1.88212
$243$	−45.9802	−2.94963
$244$	−2.63619	−0.168765
$245$	4.53259	0.289577
$246$	32.7734	2.08955
$247$	−1.66137	−0.105711
$248$	−4.85597	−0.308354
$249$	−17.3656	−1.10050
$250$	1.00000	0.0632456
$251$	−11.8200	−0.746070	−0.373035	−	0.927817i	$-0.621683\pi$
$251$	−11.8200	−0.746070	−0.373035	+	0.927817i	$0.621683\pi$
$252$	−12.2448	−0.771348
$253$	21.0710	1.32473
$254$	−18.2211	−1.14330
$255$	−9.86926	−0.618037
$256$	1.00000	0.0625000
$257$	18.6745	1.16489	0.582443	−	0.812872i	$-0.302097\pi$
$257$	18.6745	1.16489	0.582443	+	0.812872i	$0.302097\pi$
$258$	24.3653	1.51692
$259$	1.28959	0.0801315
$260$	2.49400	0.154671
$261$	32.9356	2.03866
$262$	5.69448	0.351806
$263$	18.4485	1.13758	0.568791	−	0.822482i	$-0.307411\pi$
$263$	18.4485	1.13758	0.568791	+	0.822482i	$0.307411\pi$
$264$	−20.8523	−1.28337
$265$	9.12884	0.560780
$266$	1.04639	0.0641580
$267$	−15.4605	−0.946170
$268$	2.68406	0.163955
$269$	−11.7922	−0.718982	−0.359491	−	0.933149i	$-0.617050\pi$
$269$	−11.7922	−0.718982	−0.359491	+	0.933149i	$0.617050\pi$
$270$	−15.7553	−0.958839
$271$	13.4743	0.818505	0.409253	−	0.912421i	$-0.365790\pi$
$271$	13.4743	0.818505	0.409253	+	0.912421i	$0.365790\pi$
$272$	−3.00378	−0.182131
$273$	−12.8716	−0.779026
$274$	−9.84074	−0.594501
$275$	−6.34656	−0.382712
$276$	10.9085	0.656613
$277$	4.20298	0.252533	0.126266	−	0.991996i	$-0.459701\pi$
$277$	4.20298	0.252533	0.126266	+	0.991996i	$0.459701\pi$
$278$	−12.2418	−0.734215
$279$	37.8535	2.26623
$280$	−1.57080	−0.0938732
$281$	24.9253	1.48692	0.743459	−	0.668781i	$-0.233184\pi$
$281$	24.9253	1.48692	0.743459	+	0.668781i	$0.233184\pi$
$282$	−11.5415	−0.687285
$283$	−3.66625	−0.217936	−0.108968	−	0.994045i	$-0.534755\pi$
$283$	−3.66625	−0.217936	−0.108968	+	0.994045i	$0.534755\pi$
$284$	−4.57709	−0.271600
$285$	2.18871	0.129648
$286$	−15.8283	−0.935948
$287$	−15.6684	−0.924878
$288$	−7.79525	−0.459339
$289$	−7.97730	−0.469253
$290$	4.22508	0.248105
$291$	8.85036	0.518817
$292$	13.5002	0.790039
$293$	−24.3330	−1.42155	−0.710775	−	0.703420i	$-0.751655\pi$
$293$	−24.3330	−1.42155	−0.710775	+	0.703420i	$0.751655\pi$
$294$	−14.8923	−0.868539
$295$	10.0975	0.587902
$296$	0.820980	0.0477185
$297$	99.9922	5.80214
$298$	−7.67756	−0.444749
$299$	8.28026	0.478860
$300$	−3.28561	−0.189695
$301$	−11.6487	−0.671419
$302$	−10.9943	−0.632651
$303$	−19.7233	−1.13307
$304$	0.666149	0.0382063
$305$	2.63619	0.150948
$306$	23.4152	1.33856
$307$	−11.3501	−0.647784	−0.323892	−	0.946094i	$-0.604991\pi$
$307$	−11.3501	−0.647784	−0.323892	+	0.946094i	$0.604991\pi$
$308$	9.96917	0.568046
$309$	32.9333	1.87351
$310$	4.85597	0.275801
$311$	−20.5373	−1.16456	−0.582281	−	0.812988i	$-0.697840\pi$
$311$	−20.5373	−1.16456	−0.582281	+	0.812988i	$0.697840\pi$
$312$	−8.19431	−0.463912
$313$	3.33351	0.188421	0.0942107	−	0.995552i	$-0.469967\pi$
$313$	3.33351	0.188421	0.0942107	+	0.995552i	$0.469967\pi$
$314$	14.2720	0.805417
$315$	12.2448	0.689915
$316$	−6.47182	−0.364068
$317$	6.86918	0.385812	0.192906	−	0.981217i	$-0.438209\pi$
$317$	6.86918	0.385812	0.192906	+	0.981217i	$0.438209\pi$
$318$	−29.9938	−1.68197
$319$	−26.8148	−1.50134
$320$	−1.00000	−0.0559017
$321$	−37.4992	−2.09300
$322$	−5.21517	−0.290630
$323$	−2.00097	−0.111337
$324$	28.3802	1.57668
$325$	−2.49400	−0.138342
$326$	−6.63795	−0.367642
$327$	−61.4633	−3.39893
$328$	−9.97481	−0.550767
$329$	5.51780	0.304206
$330$	20.8523	1.14788
$331$	−27.4110	−1.50665	−0.753323	−	0.657651i	$-0.771550\pi$
$331$	−27.4110	−1.50665	−0.753323	+	0.657651i	$0.771550\pi$
$332$	5.28536	0.290072
$333$	−6.39975	−0.350704
$334$	−18.8958	−1.03393
$335$	−2.68406	−0.146646
$336$	5.16104	0.281558
$337$	30.4966	1.66126	0.830629	−	0.556827i	$-0.187981\pi$
$337$	30.4966	1.66126	0.830629	+	0.556827i	$0.187981\pi$
$338$	6.77997	0.368782
$339$	0.0837949	0.00455111
$340$	3.00378	0.162903
$341$	−30.8187	−1.66893
$342$	−5.19280	−0.280794
$343$	18.1154	0.978139
$344$	−7.41577	−0.399831
$345$	−10.9085	−0.587292
$346$	−12.4028	−0.666780
$347$	−19.7396	−1.05968	−0.529838	−	0.848099i	$-0.677747\pi$
$347$	−19.7396	−1.05968	−0.529838	+	0.848099i	$0.677747\pi$
$348$	−13.8820	−0.744153
$349$	13.9551	0.746999	0.373499	−	0.927630i	$-0.378158\pi$
$349$	13.9551	0.746999	0.373499	+	0.927630i	$0.378158\pi$
$350$	1.57080	0.0839627
$351$	39.2938	2.09735
$352$	6.34656	0.338273
$353$	−12.3519	−0.657423	−0.328711	−	0.944430i	$-0.606614\pi$
$353$	−12.3519	−0.657423	−0.328711	+	0.944430i	$0.606614\pi$
$354$	−33.1766	−1.76332
$355$	4.57709	0.242927
$356$	4.70553	0.249392
$357$	−15.5026	−0.820486
$358$	21.9297	1.15902
$359$	5.52318	0.291502	0.145751	−	0.989321i	$-0.453440\pi$
$359$	5.52318	0.291502	0.145751	+	0.989321i	$0.453440\pi$
$360$	7.79525	0.410846
$361$	−18.5562	−0.976645
$362$	−26.6613	−1.40129
$363$	−96.1989	−5.04914
$364$	3.91757	0.205336
$365$	−13.5002	−0.706632
$366$	−8.66149	−0.452744
$367$	1.76259	0.0920064	0.0460032	−	0.998941i	$-0.485352\pi$
$367$	1.76259	0.0920064	0.0460032	+	0.998941i	$0.485352\pi$
$368$	−3.32007	−0.173071
$369$	77.7562	4.04782
$370$	−0.820980	−0.0426807
$371$	14.3396	0.744473
$372$	−15.9548	−0.827220
$373$	25.9933	1.34588	0.672941	−	0.739696i	$-0.265031\pi$
$373$	25.9933	1.34588	0.672941	+	0.739696i	$0.265031\pi$
$374$	−19.0637	−0.985759
$375$	3.28561	0.169668
$376$	3.51273	0.181155
$377$	−10.5374	−0.542701
$378$	−24.7485	−1.27292
$379$	26.6470	1.36876	0.684381	−	0.729124i	$-0.260072\pi$
$379$	26.6470	1.36876	0.684381	+	0.729124i	$0.260072\pi$
$380$	−0.666149	−0.0341727
$381$	−59.8676	−3.06711
$382$	−2.85798	−0.146227
$383$	−0.371021	−0.0189583	−0.00947915	−	0.999955i	$-0.503017\pi$
$383$	−0.371021	−0.0189583	−0.00947915	+	0.999955i	$0.503017\pi$
$384$	3.28561	0.167668
$385$	−9.96917	−0.508076
$386$	20.0259	1.01929
$387$	57.8078	2.93853
$388$	−2.69367	−0.136750
$389$	28.6957	1.45493	0.727466	−	0.686144i	$-0.240698\pi$
$389$	28.6957	1.45493	0.727466	+	0.686144i	$0.240698\pi$
$390$	8.19431	0.414935
$391$	9.97277	0.504345
$392$	4.53259	0.228930
$393$	18.7098	0.943787
$394$	10.8407	0.546149
$395$	6.47182	0.325632
$396$	−49.4730	−2.48611
$397$	−28.4030	−1.42551	−0.712753	−	0.701415i	$-0.752552\pi$
$397$	−28.4030	−1.42551	−0.712753	+	0.701415i	$0.752552\pi$
$398$	−13.3525	−0.669299
$399$	3.43802	0.172116
$400$	1.00000	0.0500000
$401$	6.16612	0.307922	0.153961	−	0.988077i	$-0.450797\pi$
$401$	6.16612	0.307922	0.153961	+	0.988077i	$0.450797\pi$
$402$	8.81880	0.439842
$403$	−12.1108	−0.603281
$404$	6.00293	0.298657
$405$	−28.3802	−1.41022
$406$	6.63676	0.329377
$407$	5.21040	0.258270
$408$	−9.86926	−0.488601
$409$	−13.6226	−0.673596	−0.336798	−	0.941577i	$-0.609344\pi$
$409$	−13.6226	−0.673596	−0.336798	+	0.941577i	$0.609344\pi$
$410$	9.97481	0.492621
$411$	−32.3329	−1.59486
$412$	−10.0235	−0.493822
$413$	15.8612	0.780479
$414$	25.8808	1.27197
$415$	−5.28536	−0.259448
$416$	2.49400	0.122278
$417$	−40.2218	−1.96967
$418$	4.22776	0.206786
$419$	−16.4536	−0.803811	−0.401906	−	0.915681i	$-0.631652\pi$
$419$	−16.4536	−0.803811	−0.401906	+	0.915681i	$0.631652\pi$
$420$	−5.16104	−0.251833
$421$	−0.419813	−0.0204605	−0.0102302	−	0.999948i	$-0.503256\pi$
$421$	−0.419813	−0.0204605	−0.0102302	+	0.999948i	$0.503256\pi$
$422$	15.2780	0.743720
$423$	−27.3826	−1.33139
$424$	9.12884	0.443335
$425$	−3.00378	−0.145705
$426$	−15.0385	−0.728620
$427$	4.14092	0.200393
$428$	11.4132	0.551676
$429$	−52.0057	−2.51086
$430$	7.41577	0.357620
$431$	−30.5677	−1.47239	−0.736197	−	0.676768i	$-0.763380\pi$
$431$	−30.5677	−1.47239	−0.736197	+	0.676768i	$0.763380\pi$
$432$	−15.7553	−0.758029
$433$	−10.4326	−0.501356	−0.250678	−	0.968070i	$-0.580654\pi$
$433$	−10.4326	−0.501356	−0.250678	+	0.968070i	$0.580654\pi$
$434$	7.62775	0.366144
$435$	13.8820	0.665590
$436$	18.7068	0.895894
$437$	−2.21166	−0.105798
$438$	44.3564	2.11943
$439$	18.9749	0.905621	0.452811	−	0.891607i	$-0.350421\pi$
$439$	18.9749	0.905621	0.452811	+	0.891607i	$0.350421\pi$
$440$	−6.34656	−0.302560
$441$	−35.3327	−1.68251
$442$	−7.49143	−0.356331
$443$	−0.950893	−0.0451783	−0.0225891	−	0.999745i	$-0.507191\pi$
$443$	−0.950893	−0.0451783	−0.0225891	+	0.999745i	$0.507191\pi$
$444$	2.69742	0.128014
$445$	−4.70553	−0.223063
$446$	12.2214	0.578698
$447$	−25.2255	−1.19312
$448$	−1.57080	−0.0742133
$449$	11.7451	0.554284	0.277142	−	0.960829i	$-0.410613\pi$
$449$	11.7451	0.554284	0.277142	+	0.960829i	$0.410613\pi$
$450$	−7.79525	−0.367472
$451$	−63.3058	−2.98095
$452$	−0.0255036	−0.00119959
$453$	−36.1230	−1.69721
$454$	21.9484	1.03009
$455$	−3.91757	−0.183659
$456$	2.18871	0.102496
$457$	−30.8048	−1.44099	−0.720495	−	0.693460i	$-0.756085\pi$
$457$	−30.8048	−1.44099	−0.720495	+	0.693460i	$0.756085\pi$
$458$	17.5376	0.819476
$459$	47.3256	2.20897
$460$	3.32007	0.154799
$461$	−24.6621	−1.14863	−0.574315	−	0.818634i	$-0.694732\pi$
$461$	−24.6621	−1.14863	−0.574315	+	0.818634i	$0.694732\pi$
$462$	32.7548	1.52389
$463$	19.5120	0.906801	0.453401	−	0.891307i	$-0.350211\pi$
$463$	19.5120	0.906801	0.453401	+	0.891307i	$0.350211\pi$
$464$	4.22508	0.196145
$465$	15.9548	0.739888
$466$	−4.51566	−0.209184
$467$	−35.3491	−1.63576	−0.817881	−	0.575388i	$-0.804851\pi$
$467$	−35.3491	−1.63576	−0.817881	+	0.575388i	$0.804851\pi$
$468$	−19.4413	−0.898676
$469$	−4.21612	−0.194683
$470$	−3.51273	−0.162030
$471$	46.8923	2.16068
$472$	10.0975	0.464777
$473$	−47.0646	−2.16403
$474$	−21.2639	−0.976682
$475$	0.666149	0.0305650
$476$	4.71833	0.216265
$477$	−71.1616	−3.25826
$478$	3.53455	0.161667
$479$	12.6405	0.577561	0.288780	−	0.957395i	$-0.406750\pi$
$479$	12.6405	0.577561	0.288780	+	0.957395i	$0.406750\pi$
$480$	−3.28561	−0.149967
$481$	2.04752	0.0933590
$482$	−9.15256	−0.416888
$483$	−17.1350	−0.779670
$484$	29.2788	1.33086
$485$	2.69367	0.122313
$486$	45.9802	2.08571
$487$	−20.0759	−0.909726	−0.454863	−	0.890561i	$-0.650312\pi$
$487$	−20.0759	−0.909726	−0.454863	+	0.890561i	$0.650312\pi$
$488$	2.63619	0.119335
$489$	−21.8097	−0.986270
$490$	−4.53259	−0.204762
$491$	26.6923	1.20460	0.602302	−	0.798268i	$-0.294250\pi$
$491$	26.6923	1.20460	0.602302	+	0.798268i	$0.294250\pi$
$492$	−32.7734	−1.47754
$493$	−12.6912	−0.571584
$494$	1.66137	0.0747488
$495$	49.4730	2.22365
$496$	4.85597	0.218040
$497$	7.18969	0.322502
$498$	17.3656	0.778173
$499$	−22.2931	−0.997978	−0.498989	−	0.866608i	$-0.666295\pi$
$499$	−22.2931	−0.997978	−0.498989	+	0.866608i	$0.666295\pi$
$500$	−1.00000	−0.0447214
$501$	−62.0844	−2.77373
$502$	11.8200	0.527551
$503$	−27.5880	−1.23009	−0.615043	−	0.788493i	$-0.710861\pi$
$503$	−27.5880	−1.23009	−0.615043	+	0.788493i	$0.710861\pi$
$504$	12.2448	0.545425
$505$	−6.00293	−0.267127
$506$	−21.0710	−0.936722
$507$	22.2764	0.989328
$508$	18.2211	0.808432
$509$	27.1373	1.20284	0.601420	−	0.798933i	$-0.294602\pi$
$509$	27.1373	1.20284	0.601420	+	0.798933i	$0.294602\pi$
$510$	9.86926	0.437018
$511$	−21.2061	−0.938102
$512$	−1.00000	−0.0441942
$513$	−10.4954	−0.463383
$514$	−18.6745	−0.823699
$515$	10.0235	0.441688
$516$	−24.3653	−1.07262
$517$	22.2938	0.980479
$518$	−1.28959	−0.0566615
$519$	−40.7509	−1.78876
$520$	−2.49400	−0.109369
$521$	−28.5280	−1.24983	−0.624916	−	0.780692i	$-0.714867\pi$
$521$	−28.5280	−1.24983	−0.624916	+	0.780692i	$0.714867\pi$
$522$	−32.9356	−1.44155
$523$	26.7059	1.16777	0.583884	−	0.811837i	$-0.301532\pi$
$523$	26.7059	1.16777	0.583884	+	0.811837i	$0.301532\pi$
$524$	−5.69448	−0.248764
$525$	5.16104	0.225246
$526$	−18.4485	−0.804392
$527$	−14.5863	−0.635388
$528$	20.8523	0.907482
$529$	−11.9771	−0.520744
$530$	−9.12884	−0.396531
$531$	−78.7129	−3.41585
$532$	−1.04639	−0.0453666
$533$	−24.8772	−1.07755
$534$	15.4605	0.669043
$535$	−11.4132	−0.493434
$536$	−2.68406	−0.115934
$537$	72.0524	3.10929
$538$	11.7922	0.508397
$539$	28.7664	1.23906
$540$	15.7553	0.678002
$541$	3.91130	0.168160	0.0840800	−	0.996459i	$-0.473205\pi$
$541$	3.91130	0.168160	0.0840800	+	0.996459i	$0.473205\pi$
$542$	−13.4743	−0.578770
$543$	−87.5988	−3.75923
$544$	3.00378	0.128786
$545$	−18.7068	−0.801312
$546$	12.8716	0.550854
$547$	26.5813	1.13654	0.568268	−	0.822844i	$-0.307614\pi$
$547$	26.5813	1.13654	0.568268	+	0.822844i	$0.307614\pi$
$548$	9.84074	0.420375
$549$	−20.5497	−0.877042
$550$	6.34656	0.270618
$551$	2.81454	0.119903
$552$	−10.9085	−0.464295
$553$	10.1659	0.432299
$554$	−4.20298	−0.178568
$555$	−2.69742	−0.114499
$556$	12.2418	0.519168
$557$	−0.312054	−0.0132221	−0.00661107	−	0.999978i	$-0.502104\pi$
$557$	−0.312054	−0.0132221	−0.00661107	+	0.999978i	$0.502104\pi$
$558$	−37.8535	−1.60247
$559$	−18.4949	−0.782252
$560$	1.57080	0.0663784
$561$	−62.6359	−2.64449
$562$	−24.9253	−1.05141
$563$	−35.6091	−1.50075	−0.750373	−	0.661015i	$-0.770126\pi$
$563$	−35.6091	−1.50075	−0.750373	+	0.661015i	$0.770126\pi$
$564$	11.5415	0.485984
$565$	0.0255036	0.00107294
$566$	3.66625	0.154104
$567$	−44.5795	−1.87216
$568$	4.57709	0.192050
$569$	−1.23676	−0.0518478	−0.0259239	−	0.999664i	$-0.508253\pi$
$569$	−1.23676	−0.0518478	−0.0259239	+	0.999664i	$0.508253\pi$
$570$	−2.18871	−0.0916749
$571$	13.3694	0.559493	0.279746	−	0.960074i	$-0.409750\pi$
$571$	13.3694	0.559493	0.279746	+	0.960074i	$0.409750\pi$
$572$	15.8283	0.661815
$573$	−9.39022	−0.392282
$574$	15.6684	0.653987
$575$	−3.32007	−0.138457
$576$	7.79525	0.324802
$577$	−25.5055	−1.06181	−0.530904	−	0.847432i	$-0.678148\pi$
$577$	−25.5055	−1.06181	−0.530904	+	0.847432i	$0.678148\pi$
$578$	7.97730	0.331812
$579$	65.7972	2.73444
$580$	−4.22508	−0.175437
$581$	−8.30223	−0.344435
$582$	−8.85036	−0.366859
$583$	57.9367	2.39949
$584$	−13.5002	−0.558642
$585$	19.4413	0.803801
$586$	24.3330	1.00519
$587$	11.4381	0.472102	0.236051	−	0.971741i	$-0.424147\pi$
$587$	11.4381	0.472102	0.236051	+	0.971741i	$0.424147\pi$
$588$	14.8923	0.614150
$589$	3.23480	0.133288
$590$	−10.0975	−0.415709
$591$	35.6185	1.46515
$592$	−0.820980	−0.0337421
$593$	25.0767	1.02978	0.514889	−	0.857257i	$-0.327833\pi$
$593$	25.0767	1.02978	0.514889	+	0.857257i	$0.327833\pi$
$594$	−99.9922	−4.10273
$595$	−4.71833	−0.193433
$596$	7.67756	0.314485
$597$	−43.8710	−1.79552
$598$	−8.28026	−0.338605
$599$	1.87927	0.0767848	0.0383924	−	0.999263i	$-0.487776\pi$
$599$	1.87927	0.0767848	0.0383924	+	0.999263i	$0.487776\pi$
$600$	3.28561	0.134135
$601$	−1.00000	−0.0407909
$601$	−1.00000	−0.0407909
$602$	11.6487	0.474765
$603$	20.9230	0.852048
$604$	10.9943	0.447352
$605$	−29.2788	−1.19035
$606$	19.7233	0.801205
$607$	9.89199	0.401503	0.200752	−	0.979642i	$-0.435662\pi$
$607$	9.89199	0.401503	0.200752	+	0.979642i	$0.435662\pi$
$608$	−0.666149	−0.0270159
$609$	21.8058	0.883616
$610$	−2.63619	−0.106736
$611$	8.76075	0.354422
$612$	−23.4152	−0.946504
$613$	−27.1473	−1.09647	−0.548235	−	0.836324i	$-0.684700\pi$
$613$	−27.1473	−1.09647	−0.548235	+	0.836324i	$0.684700\pi$
$614$	11.3501	0.458053
$615$	32.7734	1.32155
$616$	−9.96917	−0.401669
$617$	43.0504	1.73314	0.866571	−	0.499053i	$-0.166319\pi$
$617$	43.0504	1.73314	0.866571	+	0.499053i	$0.166319\pi$
$618$	−32.9333	−1.32477
$619$	12.9059	0.518730	0.259365	−	0.965779i	$-0.416487\pi$
$619$	12.9059	0.518730	0.259365	+	0.965779i	$0.416487\pi$
$620$	−4.85597	−0.195020
$621$	52.3088	2.09908
$622$	20.5373	0.823469
$623$	−7.39144	−0.296132
$624$	8.19431	0.328035
$625$	1.00000	0.0400000
$626$	−3.33351	−0.133234
$627$	13.8908	0.554744
$628$	−14.2720	−0.569516
$629$	2.46604	0.0983276
$630$	−12.2448	−0.487843
$631$	−38.8415	−1.54626	−0.773128	−	0.634250i	$-0.781309\pi$
$631$	−38.8415	−1.54626	−0.773128	+	0.634250i	$0.781309\pi$
$632$	6.47182	0.257435
$633$	50.1975	1.99517
$634$	−6.86918	−0.272810
$635$	−18.2211	−0.723083
$636$	29.9938	1.18933
$637$	11.3043	0.447892
$638$	26.8148	1.06161
$639$	−35.6796	−1.41146
$640$	1.00000	0.0395285
$641$	17.0652	0.674033	0.337017	−	0.941499i	$-0.390582\pi$
$641$	17.0652	0.674033	0.337017	+	0.941499i	$0.390582\pi$
$642$	37.4992	1.47998
$643$	13.0495	0.514623	0.257311	−	0.966329i	$-0.417163\pi$
$643$	13.0495	0.514623	0.257311	+	0.966329i	$0.417163\pi$
$644$	5.21517	0.205506
$645$	24.3653	0.959384
$646$	2.00097	0.0787269
$647$	0.919336	0.0361428	0.0180714	−	0.999837i	$-0.494247\pi$
$647$	0.919336	0.0361428	0.0180714	+	0.999837i	$0.494247\pi$
$648$	−28.3802	−1.11488
$649$	64.0847	2.51554
$650$	2.49400	0.0978227
$651$	25.0618	0.982251
$652$	6.63795	0.259962
$653$	−20.0089	−0.783008	−0.391504	−	0.920176i	$-0.628045\pi$
$653$	−20.0089	−0.783008	−0.391504	+	0.920176i	$0.628045\pi$
$654$	61.4633	2.40341
$655$	5.69448	0.222502
$656$	9.97481	0.389451
$657$	105.237	4.10570
$658$	−5.51780	−0.215106
$659$	−33.9107	−1.32097	−0.660487	−	0.750837i	$-0.729650\pi$
$659$	−33.9107	−1.32097	−0.660487	+	0.750837i	$0.729650\pi$
$660$	−20.8523	−0.811676
$661$	−23.3840	−0.909531	−0.454766	−	0.890611i	$-0.650277\pi$
$661$	−23.3840	−0.909531	−0.454766	+	0.890611i	$0.650277\pi$
$662$	27.4110	1.06536
$663$	−24.6139	−0.955925
$664$	−5.28536	−0.205112
$665$	1.04639	0.0405771
$666$	6.39975	0.247985
$667$	−14.0276	−0.543150
$668$	18.8958	0.731102
$669$	40.1547	1.55247
$670$	2.68406	0.103694
$671$	16.7307	0.645883
$672$	−5.16104	−0.199091
$673$	−8.99613	−0.346775	−0.173388	−	0.984854i	$-0.555471\pi$
$673$	−8.99613	−0.346775	−0.173388	+	0.984854i	$0.555471\pi$
$674$	−30.4966	−1.17469
$675$	−15.7553	−0.606423
$676$	−6.77997	−0.260768
$677$	−33.3503	−1.28175	−0.640877	−	0.767643i	$-0.721429\pi$
$677$	−33.3503	−1.28175	−0.640877	+	0.767643i	$0.721429\pi$
$678$	−0.0837949	−0.00321812
$679$	4.23121	0.162379
$680$	−3.00378	−0.115190
$681$	72.1141	2.76342
$682$	30.8187	1.18011
$683$	−34.9261	−1.33641	−0.668205	−	0.743978i	$-0.732937\pi$
$683$	−34.9261	−1.33641	−0.668205	+	0.743978i	$0.732937\pi$
$684$	5.19280	0.198552
$685$	−9.84074	−0.375995
$686$	−18.1154	−0.691648
$687$	57.6216	2.19840
$688$	7.41577	0.282724
$689$	22.7673	0.867365
$690$	10.9085	0.415278
$691$	13.7401	0.522700	0.261350	−	0.965244i	$-0.415832\pi$
$691$	13.7401	0.522700	0.261350	+	0.965244i	$0.415832\pi$
$692$	12.4028	0.471485
$693$	77.7122	2.95204
$694$	19.7396	0.749304
$695$	−12.2418	−0.464358
$696$	13.8820	0.526195
$697$	−29.9621	−1.13490
$698$	−13.9551	−0.528208
$699$	−14.8367	−0.561176
$700$	−1.57080	−0.0593706
$701$	7.57430	0.286077	0.143039	−	0.989717i	$-0.454313\pi$
$701$	7.57430	0.286077	0.143039	+	0.989717i	$0.454313\pi$
$702$	−39.2938	−1.48305
$703$	−0.546895	−0.0206265
$704$	−6.34656	−0.239195
$705$	−11.5415	−0.434677
$706$	12.3519	0.464868
$707$	−9.42940	−0.354629
$708$	33.1766	1.24685
$709$	4.73464	0.177813	0.0889067	−	0.996040i	$-0.471663\pi$
$709$	4.73464	0.177813	0.0889067	+	0.996040i	$0.471663\pi$
$710$	−4.57709	−0.171775
$711$	−50.4494	−1.89200
$712$	−4.70553	−0.176347
$713$	−16.1222	−0.603780
$714$	15.5026	0.580171
$715$	−15.8283	−0.591946
$716$	−21.9297	−0.819550
$717$	11.6132	0.433701
$718$	−5.52318	−0.206123
$719$	−40.5762	−1.51324	−0.756618	−	0.653857i	$-0.773150\pi$
$719$	−40.5762	−1.51324	−0.756618	+	0.653857i	$0.773150\pi$
$720$	−7.79525	−0.290512
$721$	15.7449	0.586370
$722$	18.5562	0.690592
$723$	−30.0718	−1.11838
$724$	26.6613	0.990861
$725$	4.22508	0.156916
$726$	96.1989	3.57028
$727$	1.22062	0.0452703	0.0226351	−	0.999744i	$-0.492794\pi$
$727$	1.22062	0.0452703	0.0226351	+	0.999744i	$0.492794\pi$
$728$	−3.91757	−0.145195
$729$	65.9327	2.44195
$730$	13.5002	0.499665
$731$	−22.2753	−0.823883
$732$	8.66149	0.320138
$733$	−15.8615	−0.585858	−0.292929	−	0.956134i	$-0.594630\pi$
$733$	−15.8615	−0.585858	−0.292929	+	0.956134i	$0.594630\pi$
$734$	−1.76259	−0.0650583
$735$	−14.8923	−0.549312
$736$	3.32007	0.122379
$737$	−17.0346	−0.627477
$738$	−77.7562	−2.86224
$739$	−41.8873	−1.54085	−0.770425	−	0.637531i	$-0.779956\pi$
$739$	−41.8873	−1.54085	−0.770425	+	0.637531i	$0.779956\pi$
$740$	0.820980	0.0301798
$741$	5.45863	0.200528
$742$	−14.3396	−0.526422
$743$	48.0232	1.76180	0.880900	−	0.473303i	$-0.156938\pi$
$743$	48.0232	1.76180	0.880900	+	0.473303i	$0.156938\pi$
$744$	15.9548	0.584933
$745$	−7.67756	−0.281284
$746$	−25.9933	−0.951683
$747$	41.2007	1.50745
$748$	19.0637	0.697037
$749$	−17.9278	−0.655067
$750$	−3.28561	−0.119974
$751$	38.5091	1.40522	0.702609	−	0.711577i	$-0.252019\pi$
$751$	38.5091	1.40522	0.702609	+	0.711577i	$0.252019\pi$
$752$	−3.51273	−0.128096
$753$	38.8359	1.41526
$754$	10.5374	0.383748
$755$	−10.9943	−0.400123
$756$	24.7485	0.900093
$757$	−23.7837	−0.864434	−0.432217	−	0.901770i	$-0.642269\pi$
$757$	−23.7837	−0.864434	−0.432217	+	0.901770i	$0.642269\pi$
$758$	−26.6470	−0.967861
$759$	−69.2313	−2.51294
$760$	0.666149	0.0241638
$761$	−40.1279	−1.45463	−0.727317	−	0.686302i	$-0.759233\pi$
$761$	−40.1279	−1.45463	−0.727317	+	0.686302i	$0.759233\pi$
$762$	59.8676	2.16877
$763$	−29.3846	−1.06380
$764$	2.85798	0.103398
$765$	23.4152	0.846579
$766$	0.371021	0.0134055
$767$	25.1833	0.909315
$768$	−3.28561	−0.118559
$769$	−1.48724	−0.0536311	−0.0268156	−	0.999640i	$-0.508537\pi$
$769$	−1.48724	−0.0536311	−0.0268156	+	0.999640i	$0.508537\pi$
$770$	9.96917	0.359264
$771$	−61.3573	−2.20973
$772$	−20.0259	−0.720747
$773$	−32.4239	−1.16621	−0.583103	−	0.812398i	$-0.698162\pi$
$773$	−32.4239	−1.16621	−0.583103	+	0.812398i	$0.698162\pi$
$774$	−57.8078	−2.07786
$775$	4.85597	0.174432
$776$	2.69367	0.0966971
$777$	−4.23711	−0.152005
$778$	−28.6957	−1.02879
$779$	6.64471	0.238071
$780$	−8.19431	−0.293404
$781$	29.0488	1.03945
$782$	−9.97277	−0.356625
$783$	−66.5676	−2.37893
$784$	−4.53259	−0.161878
$785$	14.2720	0.509390
$786$	−18.7098	−0.667358
$787$	30.0068	1.06963	0.534814	−	0.844970i	$-0.320382\pi$
$787$	30.0068	1.06963	0.534814	+	0.844970i	$0.320382\pi$
$788$	−10.8407	−0.386186
$789$	−60.6146	−2.15794
$790$	−6.47182	−0.230257
$791$	0.0400610	0.00142440
$792$	49.4730	1.75795
$793$	6.57465	0.233473
$794$	28.4030	1.00799
$795$	−29.9938	−1.06377
$796$	13.3525	0.473266
$797$	−0.349349	−0.0123746	−0.00618729	−	0.999981i	$-0.501969\pi$
$797$	−0.349349	−0.0123746	−0.00618729	+	0.999981i	$0.501969\pi$
$798$	−3.43802	−0.121705
$799$	10.5515	0.373284
$800$	−1.00000	−0.0353553
$801$	36.6808	1.29605
$802$	−6.16612	−0.217733
$803$	−85.6798	−3.02357
$804$	−8.81880	−0.311015
$805$	−5.21517	−0.183810
$806$	12.1108	0.426584
$807$	38.7445	1.36387
$808$	−6.00293	−0.211182
$809$	32.9682	1.15910	0.579549	−	0.814937i	$-0.303229\pi$
$809$	32.9682	1.15910	0.579549	+	0.814937i	$0.303229\pi$
$810$	28.3802	0.997177
$811$	−3.13153	−0.109963	−0.0549814	−	0.998487i	$-0.517510\pi$
$811$	−3.13153	−0.109963	−0.0549814	+	0.998487i	$0.517510\pi$
$812$	−6.63676	−0.232904
$813$	−44.2713	−1.55266
$814$	−5.21040	−0.182624
$815$	−6.63795	−0.232517
$816$	9.86926	0.345493
$817$	4.94001	0.172829
$818$	13.6226	0.476304
$819$	30.5384	1.06710
$820$	−9.97481	−0.348336
$821$	−17.5723	−0.613277	−0.306639	−	0.951826i	$-0.599204\pi$
$821$	−17.5723	−0.613277	−0.306639	+	0.951826i	$0.599204\pi$
$822$	32.3329	1.12774
$823$	23.9969	0.836478	0.418239	−	0.908337i	$-0.362647\pi$
$823$	23.9969	0.836478	0.418239	+	0.908337i	$0.362647\pi$
$824$	10.0235	0.349185
$825$	20.8523	0.725985
$826$	−15.8612	−0.551882
$827$	51.5764	1.79349	0.896743	−	0.442551i	$-0.145926\pi$
$827$	51.5764	1.79349	0.896743	+	0.442551i	$0.145926\pi$
$828$	−25.8808	−0.899420
$829$	−23.5443	−0.817727	−0.408863	−	0.912596i	$-0.634075\pi$
$829$	−23.5443	−0.817727	−0.408863	+	0.912596i	$0.634075\pi$
$830$	5.28536	0.183457
$831$	−13.8094	−0.479042
$832$	−2.49400	−0.0864639
$833$	13.6149	0.471729
$834$	40.2218	1.39277
$835$	−18.8958	−0.653917
$836$	−4.22776	−0.146220
$837$	−76.5074	−2.64448
$838$	16.4536	0.568380
$839$	12.9560	0.447291	0.223646	−	0.974671i	$-0.428204\pi$
$839$	12.9560	0.447291	0.223646	+	0.974671i	$0.428204\pi$
$840$	5.16104	0.178073
$841$	−11.1487	−0.384437
$842$	0.419813	0.0144677
$843$	−81.8949	−2.82061
$844$	−15.2780	−0.525890
$845$	6.77997	0.233238
$846$	27.3826	0.941434
$847$	−45.9912	−1.58028
$848$	−9.12884	−0.313486
$849$	12.0459	0.413413
$850$	3.00378	0.103029
$851$	2.72571	0.0934363
$852$	15.0385	0.515212
$853$	23.6830	0.810890	0.405445	−	0.914120i	$-0.367117\pi$
$853$	23.6830	0.810890	0.405445	+	0.914120i	$0.367117\pi$
$854$	−4.14092	−0.141699
$855$	−5.19280	−0.177590
$856$	−11.4132	−0.390094
$857$	46.3833	1.58442	0.792212	−	0.610247i	$-0.208930\pi$
$857$	46.3833	1.58442	0.792212	+	0.610247i	$0.208930\pi$
$858$	52.0057	1.77545
$859$	26.3640	0.899530	0.449765	−	0.893147i	$-0.351508\pi$
$859$	26.3640	0.899530	0.449765	+	0.893147i	$0.351508\pi$
$860$	−7.41577	−0.252876
$861$	51.4804	1.75445
$862$	30.5677	1.04114
$863$	−7.94989	−0.270617	−0.135309	−	0.990804i	$-0.543203\pi$
$863$	−7.94989	−0.270617	−0.135309	+	0.990804i	$0.543203\pi$
$864$	15.7553	0.536007
$865$	−12.4028	−0.421709
$866$	10.4326	0.354512
$867$	26.2103	0.890149
$868$	−7.62775	−0.258903
$869$	41.0738	1.39333
$870$	−13.8820	−0.470643
$871$	−6.69405	−0.226819
$872$	−18.7068	−0.633493
$873$	−20.9978	−0.710669
$874$	2.21166	0.0748106
$875$	1.57080	0.0531027
$876$	−44.3564	−1.49866
$877$	−49.7673	−1.68052	−0.840261	−	0.542183i	$-0.817598\pi$
$877$	−49.7673	−1.68052	−0.840261	+	0.542183i	$0.817598\pi$
$878$	−18.9749	−0.640371
$879$	79.9488	2.69661
$880$	6.34656	0.213943
$881$	8.24005	0.277614	0.138807	−	0.990319i	$-0.455673\pi$
$881$	8.24005	0.277614	0.138807	+	0.990319i	$0.455673\pi$
$882$	35.3327	1.18971
$883$	−7.68950	−0.258772	−0.129386	−	0.991594i	$-0.541301\pi$
$883$	−7.68950	−0.258772	−0.129386	+	0.991594i	$0.541301\pi$
$884$	7.49143	0.251964
$885$	−33.1766	−1.11522
$886$	0.950893	0.0319459
$887$	−27.8218	−0.934164	−0.467082	−	0.884214i	$-0.654695\pi$
$887$	−27.8218	−0.934164	−0.467082	+	0.884214i	$0.654695\pi$
$888$	−2.69742	−0.0905196
$889$	−28.6217	−0.959942
$890$	4.70553	0.157730
$891$	−180.116	−6.03413
$892$	−12.2214	−0.409202
$893$	−2.34000	−0.0783052
$894$	25.2255	0.843666
$895$	21.9297	0.733028
$896$	1.57080	0.0524767
$897$	−27.2057	−0.908372
$898$	−11.7451	−0.391938
$899$	20.5169	0.684276
$900$	7.79525	0.259842
$901$	27.4210	0.913527
$902$	63.3058	2.10785
$903$	38.2730	1.27365
$904$	0.0255036	0.000848236 0
$905$	−26.6613	−0.886253
$906$	36.1230	1.20011
$907$	−0.0331383	−0.00110034	−0.000550169	−	1.00000i	$-0.500175\pi$
$907$	−0.0331383	−0.00110034	−0.000550169		1.00000i	$0.500175\pi$
$908$	−21.9484	−0.728384
$909$	46.7944	1.55207
$910$	3.91757	0.129866
$911$	22.8217	0.756117	0.378059	−	0.925782i	$-0.376592\pi$
$911$	22.8217	0.756117	0.378059	+	0.925782i	$0.376592\pi$
$912$	−2.18871	−0.0724753
$913$	−33.5439	−1.11014
$914$	30.8048	1.01893
$915$	−8.66149	−0.286340
$916$	−17.5376	−0.579457
$917$	8.94488	0.295386
$918$	−47.3256	−1.56198
$919$	22.8801	0.754744	0.377372	−	0.926062i	$-0.376828\pi$
$919$	22.8801	0.754744	0.377372	+	0.926062i	$0.376828\pi$
$920$	−3.32007	−0.109460
$921$	37.2920	1.22881
$922$	24.6621	0.812204
$923$	11.4153	0.375738
$924$	−32.7548	−1.07755
$925$	−0.820980	−0.0269937
$926$	−19.5120	−0.641205
$927$	−78.1356	−2.56631
$928$	−4.22508	−0.138695
$929$	−40.1360	−1.31682	−0.658410	−	0.752659i	$-0.728771\pi$
$929$	−40.1360	−1.31682	−0.658410	+	0.752659i	$0.728771\pi$
$930$	−15.9548	−0.523180
$931$	−3.01938	−0.0989562
$932$	4.51566	0.147915
$933$	67.4775	2.20911
$934$	35.3491	1.15666
$935$	−19.0637	−0.623449
$936$	19.4413	0.635460
$937$	−46.5634	−1.52116	−0.760579	−	0.649245i	$-0.775085\pi$
$937$	−46.5634	−1.52116	−0.760579	+	0.649245i	$0.775085\pi$
$938$	4.21612	0.137661
$939$	−10.9526	−0.357426
$940$	3.51273	0.114573
$941$	31.1861	1.01664	0.508318	−	0.861169i	$-0.330267\pi$
$941$	31.1861	1.01664	0.508318	+	0.861169i	$0.330267\pi$
$942$	−46.8923	−1.52783
$943$	−33.1171	−1.07844
$944$	−10.0975	−0.328647
$945$	−24.7485	−0.805067
$946$	47.0646	1.53020
$947$	48.2043	1.56643	0.783214	−	0.621752i	$-0.213579\pi$
$947$	48.2043	1.56643	0.783214	+	0.621752i	$0.213579\pi$
$948$	21.2639	0.690619
$949$	−33.6695	−1.09296
$950$	−0.666149	−0.0216127
$951$	−22.5695	−0.731865
$952$	−4.71833	−0.152922
$953$	21.6310	0.700695	0.350348	−	0.936620i	$-0.386063\pi$
$953$	21.6310	0.700695	0.350348	+	0.936620i	$0.386063\pi$
$954$	71.1616	2.30394
$955$	−2.85798	−0.0924821
$956$	−3.53455	−0.114316
$957$	88.1029	2.84796
$958$	−12.6405	−0.408397
$959$	−15.4578	−0.499159
$960$	3.28561	0.106043
$961$	−7.41954	−0.239340
$962$	−2.04752	−0.0660148
$963$	88.9685	2.86697
$964$	9.15256	0.294784
$965$	20.0259	0.644655
$966$	17.1350	0.551310
$967$	15.8052	0.508261	0.254130	−	0.967170i	$-0.418211\pi$
$967$	15.8052	0.508261	0.254130	+	0.967170i	$0.418211\pi$
$968$	−29.2788	−0.941058
$969$	6.57440	0.211200
$970$	−2.69367	−0.0864885
$971$	−54.6377	−1.75341	−0.876703	−	0.481031i	$-0.840262\pi$
$971$	−54.6377	−1.75341	−0.876703	+	0.481031i	$0.840262\pi$
$972$	−45.9802	−1.47482
$973$	−19.2294	−0.616467
$974$	20.0759	0.643273
$975$	8.19431	0.262428
$976$	−2.63619	−0.0843823
$977$	53.6464	1.71630	0.858150	−	0.513399i	$-0.171614\pi$
$977$	53.6464	1.71630	0.858150	+	0.513399i	$0.171614\pi$
$978$	21.8097	0.697398
$979$	−29.8639	−0.954455
$980$	4.53259	0.144788
$981$	145.824	4.65581
$982$	−26.6923	−0.851784
$983$	21.8083	0.695578	0.347789	−	0.937573i	$-0.386933\pi$
$983$	21.8083	0.695578	0.347789	+	0.937573i	$0.386933\pi$
$984$	32.7734	1.04478
$985$	10.8407	0.345415
$986$	12.6912	0.404171
$987$	−18.1293	−0.577063
$988$	−1.66137	−0.0528554
$989$	−24.6209	−0.782899
$990$	−49.4730	−1.57236
$991$	−16.4169	−0.521499	−0.260749	−	0.965407i	$-0.583970\pi$
$991$	−16.4169	−0.521499	−0.260749	+	0.965407i	$0.583970\pi$
$992$	−4.85597	−0.154177
$993$	90.0620	2.85803
$994$	−7.18969	−0.228043
$995$	−13.3525	−0.423302
$996$	−17.3656	−0.550251
$997$	57.4199	1.81851	0.909253	−	0.416245i	$-0.136654\pi$
$997$	57.4199	1.81851	0.909253	+	0.416245i	$0.136654\pi$
$998$	22.2931	0.705677
$999$	12.9348	0.409239

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6010.2.a.i.1.2	✓	29

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6010.2.a.i.1.2	✓	29	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:	\( N \)	\(=\)	\( 6010 = 2 \cdot 5 \cdot 601 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6010.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.28561 q^{3} +1.00000 q^{4} -1.00000 q^{5} +3.28561 q^{6} -1.57080 q^{7} -1.00000 q^{8} +7.79525 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -3.28561 q^{3} +1.00000 q^{4} -1.00000 q^{5} +3.28561 q^{6} -1.57080 q^{7} -1.00000 q^{8} +7.79525 q^{9} +1.00000 q^{10} -6.34656 q^{11} -3.28561 q^{12} -2.49400 q^{13} +1.57080 q^{14} +3.28561 q^{15} +1.00000 q^{16} -3.00378 q^{17} -7.79525 q^{18} +0.666149 q^{19} -1.00000 q^{20} +5.16104 q^{21} +6.34656 q^{22} -3.32007 q^{23} +3.28561 q^{24} +1.00000 q^{25} +2.49400 q^{26} -15.7553 q^{27} -1.57080 q^{28} +4.22508 q^{29} -3.28561 q^{30} +4.85597 q^{31} -1.00000 q^{32} +20.8523 q^{33} +3.00378 q^{34} +1.57080 q^{35} +7.79525 q^{36} -0.820980 q^{37} -0.666149 q^{38} +8.19431 q^{39} +1.00000 q^{40} +9.97481 q^{41} -5.16104 q^{42} +7.41577 q^{43} -6.34656 q^{44} -7.79525 q^{45} +3.32007 q^{46} -3.51273 q^{47} -3.28561 q^{48} -4.53259 q^{49} -1.00000 q^{50} +9.86926 q^{51} -2.49400 q^{52} -9.12884 q^{53} +15.7553 q^{54} +6.34656 q^{55} +1.57080 q^{56} -2.18871 q^{57} -4.22508 q^{58} -10.0975 q^{59} +3.28561 q^{60} -2.63619 q^{61} -4.85597 q^{62} -12.2448 q^{63} +1.00000 q^{64} +2.49400 q^{65} -20.8523 q^{66} +2.68406 q^{67} -3.00378 q^{68} +10.9085 q^{69} -1.57080 q^{70} -4.57709 q^{71} -7.79525 q^{72} +13.5002 q^{73} +0.820980 q^{74} -3.28561 q^{75} +0.666149 q^{76} +9.96917 q^{77} -8.19431 q^{78} -6.47182 q^{79} -1.00000 q^{80} +28.3802 q^{81} -9.97481 q^{82} +5.28536 q^{83} +5.16104 q^{84} +3.00378 q^{85} -7.41577 q^{86} -13.8820 q^{87} +6.34656 q^{88} +4.70553 q^{89} +7.79525 q^{90} +3.91757 q^{91} -3.32007 q^{92} -15.9548 q^{93} +3.51273 q^{94} -0.666149 q^{95} +3.28561 q^{96} -2.69367 q^{97} +4.53259 q^{98} -49.4730 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 29 q - 29 q^{2} - 10 q^{3} + 29 q^{4} - 29 q^{5} + 10 q^{6} - 29 q^{8} + 29 q^{9}+O(q^{10}) \) 29 * q - 29 * q^2 - 10 * q^3 + 29 * q^4 - 29 * q^5 + 10 * q^6 - 29 * q^8 + 29 * q^9	\( 29 q - 29 q^{2} - 10 q^{3} + 29 q^{4} - 29 q^{5} + 10 q^{6} - 29 q^{8} + 29 q^{9} + 29 q^{10} - 10 q^{12} - 4 q^{13} + 10 q^{15} + 29 q^{16} - 23 q^{17} - 29 q^{18} + q^{19} - 29 q^{20} + 2 q^{21} - 9 q^{23} + 10 q^{24} + 29 q^{25} + 4 q^{26} - 43 q^{27} - 5 q^{29} - 10 q^{30} + 21 q^{31} - 29 q^{32} - 19 q^{33} + 23 q^{34} + 29 q^{36} - 6 q^{37} - q^{38} + 18 q^{39} + 29 q^{40} - 17 q^{41} - 2 q^{42} - 19 q^{43} - 29 q^{45} + 9 q^{46} - 21 q^{47} - 10 q^{48} + 45 q^{49} - 29 q^{50} + 11 q^{51} - 4 q^{52} - 53 q^{53} + 43 q^{54} - 16 q^{57} + 5 q^{58} - 30 q^{59} + 10 q^{60} + 16 q^{61} - 21 q^{62} - 17 q^{63} + 29 q^{64} + 4 q^{65} + 19 q^{66} - 35 q^{67} - 23 q^{68} + 13 q^{69} + 2 q^{71} - 29 q^{72} - q^{73} + 6 q^{74} - 10 q^{75} + q^{76} - 50 q^{77} - 18 q^{78} + 26 q^{79} - 29 q^{80} + 33 q^{81} + 17 q^{82} - 54 q^{83} + 2 q^{84} + 23 q^{85} + 19 q^{86} - 56 q^{87} - 2 q^{89} + 29 q^{90} + 27 q^{91} - 9 q^{92} - 26 q^{93} + 21 q^{94} - q^{95} + 10 q^{96} + 15 q^{97} - 45 q^{98} + 27 q^{99}+O(q^{100}) \) 29 * q - 29 * q^2 - 10 * q^3 + 29 * q^4 - 29 * q^5 + 10 * q^6 - 29 * q^8 + 29 * q^9 + 29 * q^10 - 10 * q^12 - 4 * q^13 + 10 * q^15 + 29 * q^16 - 23 * q^17 - 29 * q^18 + q^19 - 29 * q^20 + 2 * q^21 - 9 * q^23 + 10 * q^24 + 29 * q^25 + 4 * q^26 - 43 * q^27 - 5 * q^29 - 10 * q^30 + 21 * q^31 - 29 * q^32 - 19 * q^33 + 23 * q^34 + 29 * q^36 - 6 * q^37 - q^38 + 18 * q^39 + 29 * q^40 - 17 * q^41 - 2 * q^42 - 19 * q^43 - 29 * q^45 + 9 * q^46 - 21 * q^47 - 10 * q^48 + 45 * q^49 - 29 * q^50 + 11 * q^51 - 4 * q^52 - 53 * q^53 + 43 * q^54 - 16 * q^57 + 5 * q^58 - 30 * q^59 + 10 * q^60 + 16 * q^61 - 21 * q^62 - 17 * q^63 + 29 * q^64 + 4 * q^65 + 19 * q^66 - 35 * q^67 - 23 * q^68 + 13 * q^69 + 2 * q^71 - 29 * q^72 - q^73 + 6 * q^74 - 10 * q^75 + q^76 - 50 * q^77 - 18 * q^78 + 26 * q^79 - 29 * q^80 + 33 * q^81 + 17 * q^82 - 54 * q^83 + 2 * q^84 + 23 * q^85 + 19 * q^86 - 56 * q^87 - 2 * q^89 + 29 * q^90 + 27 * q^91 - 9 * q^92 - 26 * q^93 + 21 * q^94 - q^95 + 10 * q^96 + 15 * q^97 - 45 * q^98 + 27 * q^99

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