LMFDB - Embedded newform 4029.2.a.i.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4029,2,Mod(1,4029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4029, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4029 = 3 \cdot 17 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4029.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$32.1717269744$
Analytic rank:	$0$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	4029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.65426 q^{2} -1.00000 q^{3} +0.736566 q^{4} +1.27876 q^{5} +1.65426 q^{6} +3.55385 q^{7} +2.09004 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.65426 q^{2} -1.00000 q^{3} +0.736566 q^{4} +1.27876 q^{5} +1.65426 q^{6} +3.55385 q^{7} +2.09004 q^{8} +1.00000 q^{9} -2.11539 q^{10} +5.37114 q^{11} -0.736566 q^{12} -4.08480 q^{13} -5.87897 q^{14} -1.27876 q^{15} -4.93060 q^{16} +1.00000 q^{17} -1.65426 q^{18} +1.24045 q^{19} +0.941888 q^{20} -3.55385 q^{21} -8.88525 q^{22} +1.93158 q^{23} -2.09004 q^{24} -3.36478 q^{25} +6.75731 q^{26} -1.00000 q^{27} +2.61764 q^{28} +5.87620 q^{29} +2.11539 q^{30} +7.37055 q^{31} +3.97640 q^{32} -5.37114 q^{33} -1.65426 q^{34} +4.54450 q^{35} +0.736566 q^{36} +10.2075 q^{37} -2.05203 q^{38} +4.08480 q^{39} +2.67266 q^{40} +3.52942 q^{41} +5.87897 q^{42} -5.04670 q^{43} +3.95620 q^{44} +1.27876 q^{45} -3.19534 q^{46} -2.98680 q^{47} +4.93060 q^{48} +5.62982 q^{49} +5.56622 q^{50} -1.00000 q^{51} -3.00873 q^{52} +3.75522 q^{53} +1.65426 q^{54} +6.86837 q^{55} +7.42769 q^{56} -1.24045 q^{57} -9.72075 q^{58} -8.54847 q^{59} -0.941888 q^{60} +12.8880 q^{61} -12.1928 q^{62} +3.55385 q^{63} +3.28322 q^{64} -5.22346 q^{65} +8.88525 q^{66} +14.8088 q^{67} +0.736566 q^{68} -1.93158 q^{69} -7.51777 q^{70} -5.31521 q^{71} +2.09004 q^{72} +2.95962 q^{73} -16.8859 q^{74} +3.36478 q^{75} +0.913677 q^{76} +19.0882 q^{77} -6.75731 q^{78} -1.00000 q^{79} -6.30504 q^{80} +1.00000 q^{81} -5.83857 q^{82} -14.9857 q^{83} -2.61764 q^{84} +1.27876 q^{85} +8.34854 q^{86} -5.87620 q^{87} +11.2259 q^{88} +8.66018 q^{89} -2.11539 q^{90} -14.5168 q^{91} +1.42274 q^{92} -7.37055 q^{93} +4.94094 q^{94} +1.58624 q^{95} -3.97640 q^{96} -13.4131 q^{97} -9.31316 q^{98} +5.37114 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - 2 q^{2} - 25 q^{3} + 26 q^{4} - 2 q^{5} + 2 q^{6} + 12 q^{7} + 25 q^{9}+O(q^{10}) $ 25 * q - 2 * q^2 - 25 * q^3 + 26 * q^4 - 2 * q^5 + 2 * q^6 + 12 * q^7 + 25 * q^9	\( 25 q - 2 q^{2} - 25 q^{3} + 26 q^{4} - 2 q^{5} + 2 q^{6} + 12 q^{7} + 25 q^{9} + 19 q^{10} + 19 q^{11} - 26 q^{12} + 4 q^{13} + 15 q^{14} + 2 q^{15} + 32 q^{16} + 25 q^{17} - 2 q^{18} + 29 q^{19} - 8 q^{20} - 12 q^{21} + 23 q^{22} + 6 q^{23} + 15 q^{25} - 8 q^{26} - 25 q^{27} + 23 q^{28} + 11 q^{29} - 19 q^{30} + 38 q^{31} - 27 q^{32} - 19 q^{33} - 2 q^{34} + 20 q^{35} + 26 q^{36} + 8 q^{37} - 25 q^{38} - 4 q^{39} + 48 q^{40} + 24 q^{41} - 15 q^{42} + 11 q^{43} + 6 q^{44} - 2 q^{45} + 25 q^{46} + 23 q^{47} - 32 q^{48} + 21 q^{49} - 21 q^{50} - 25 q^{51} + 31 q^{52} - 16 q^{53} + 2 q^{54} - 11 q^{55} + 18 q^{56} - 29 q^{57} - 5 q^{58} + 27 q^{59} + 8 q^{60} + 40 q^{61} - 34 q^{62} + 12 q^{63} + 46 q^{64} - 19 q^{65} - 23 q^{66} + 24 q^{67} + 26 q^{68} - 6 q^{69} + 17 q^{70} + 19 q^{71} + 13 q^{73} - 56 q^{74} - 15 q^{75} + 21 q^{76} - 30 q^{77} + 8 q^{78} - 25 q^{79} - 40 q^{80} + 25 q^{81} + 61 q^{82} + q^{83} - 23 q^{84} - 2 q^{85} + 62 q^{86} - 11 q^{87} - q^{88} - 10 q^{89} + 19 q^{90} + 50 q^{91} + 18 q^{92} - 38 q^{93} + 15 q^{94} + 14 q^{95} + 27 q^{96} + 19 q^{97} - 23 q^{98} + 19 q^{99}+O(q^{100}) \) 25 * q - 2 * q^2 - 25 * q^3 + 26 * q^4 - 2 * q^5 + 2 * q^6 + 12 * q^7 + 25 * q^9 + 19 * q^10 + 19 * q^11 - 26 * q^12 + 4 * q^13 + 15 * q^14 + 2 * q^15 + 32 * q^16 + 25 * q^17 - 2 * q^18 + 29 * q^19 - 8 * q^20 - 12 * q^21 + 23 * q^22 + 6 * q^23 + 15 * q^25 - 8 * q^26 - 25 * q^27 + 23 * q^28 + 11 * q^29 - 19 * q^30 + 38 * q^31 - 27 * q^32 - 19 * q^33 - 2 * q^34 + 20 * q^35 + 26 * q^36 + 8 * q^37 - 25 * q^38 - 4 * q^39 + 48 * q^40 + 24 * q^41 - 15 * q^42 + 11 * q^43 + 6 * q^44 - 2 * q^45 + 25 * q^46 + 23 * q^47 - 32 * q^48 + 21 * q^49 - 21 * q^50 - 25 * q^51 + 31 * q^52 - 16 * q^53 + 2 * q^54 - 11 * q^55 + 18 * q^56 - 29 * q^57 - 5 * q^58 + 27 * q^59 + 8 * q^60 + 40 * q^61 - 34 * q^62 + 12 * q^63 + 46 * q^64 - 19 * q^65 - 23 * q^66 + 24 * q^67 + 26 * q^68 - 6 * q^69 + 17 * q^70 + 19 * q^71 + 13 * q^73 - 56 * q^74 - 15 * q^75 + 21 * q^76 - 30 * q^77 + 8 * q^78 - 25 * q^79 - 40 * q^80 + 25 * q^81 + 61 * q^82 + q^83 - 23 * q^84 - 2 * q^85 + 62 * q^86 - 11 * q^87 - q^88 - 10 * q^89 + 19 * q^90 + 50 * q^91 + 18 * q^92 - 38 * q^93 + 15 * q^94 + 14 * q^95 + 27 * q^96 + 19 * q^97 - 23 * q^98 + 19 * 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 $

$2$	−1.65426	−1.16974	−0.584868	−	0.811128i	$-0.698854\pi$
$2$	−1.65426	−1.16974	−0.584868	+	0.811128i	$0.698854\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.736566	0.368283
$5$	1.27876	0.571877	0.285938	−	0.958248i	$-0.407695\pi$
$5$	1.27876	0.571877	0.285938	+	0.958248i	$0.407695\pi$
$6$	1.65426	0.675348
$7$	3.55385	1.34323	0.671614	−	0.740902i	$-0.265602\pi$
$7$	3.55385	1.34323	0.671614	+	0.740902i	$0.265602\pi$
$8$	2.09004	0.738942
$9$	1.00000	0.333333
$10$	−2.11539	−0.668945
$11$	5.37114	1.61946	0.809730	−	0.586803i	$-0.199614\pi$
$11$	5.37114	1.61946	0.809730	+	0.586803i	$0.199614\pi$
$12$	−0.736566	−0.212628
$13$	−4.08480	−1.13292	−0.566460	−	0.824089i	$-0.691688\pi$
$13$	−4.08480	−1.13292	−0.566460	+	0.824089i	$0.691688\pi$
$14$	−5.87897	−1.57122
$15$	−1.27876	−0.330173
$16$	−4.93060	−1.23265
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.65426	−0.389912
$19$	1.24045	0.284580	0.142290	−	0.989825i	$-0.454553\pi$
$19$	1.24045	0.284580	0.142290	+	0.989825i	$0.454553\pi$
$20$	0.941888	0.210613
$21$	−3.55385	−0.775513
$22$	−8.88525	−1.89434
$23$	1.93158	0.402763	0.201381	−	0.979513i	$-0.435457\pi$
$23$	1.93158	0.402763	0.201381	+	0.979513i	$0.435457\pi$
$24$	−2.09004	−0.426628
$25$	−3.36478	−0.672957
$26$	6.75731	1.32522
$27$	−1.00000	−0.192450
$28$	2.61764	0.494688
$29$	5.87620	1.09118	0.545592	−	0.838051i	$-0.316305\pi$
$29$	5.87620	1.09118	0.545592	+	0.838051i	$0.316305\pi$
$30$	2.11539	0.386216
$31$	7.37055	1.32379	0.661895	−	0.749596i	$-0.269752\pi$
$31$	7.37055	1.32379	0.661895	+	0.749596i	$0.269752\pi$
$32$	3.97640	0.702934
$33$	−5.37114	−0.934995
$34$	−1.65426	−0.283703
$35$	4.54450	0.768161
$36$	0.736566	0.122761
$37$	10.2075	1.67811	0.839053	−	0.544049i	$-0.183110\pi$
$37$	10.2075	1.67811	0.839053	+	0.544049i	$0.183110\pi$
$38$	−2.05203	−0.332883
$39$	4.08480	0.654092
$40$	2.67266	0.422584
$41$	3.52942	0.551203	0.275601	−	0.961272i	$-0.411123\pi$
$41$	3.52942	0.551203	0.275601	+	0.961272i	$0.411123\pi$
$42$	5.87897	0.907145
$43$	−5.04670	−0.769614	−0.384807	−	0.922997i	$-0.625732\pi$
$43$	−5.04670	−0.769614	−0.384807	+	0.922997i	$0.625732\pi$
$44$	3.95620	0.596420
$45$	1.27876	0.190626
$46$	−3.19534	−0.471126
$47$	−2.98680	−0.435670	−0.217835	−	0.975986i	$-0.569899\pi$
$47$	−2.98680	−0.435670	−0.217835	+	0.975986i	$0.569899\pi$
$48$	4.93060	0.711671
$49$	5.62982	0.804259
$50$	5.56622	0.787182
$51$	−1.00000	−0.140028
$52$	−3.00873	−0.417236
$53$	3.75522	0.515819	0.257910	−	0.966169i	$-0.416966\pi$
$53$	3.75522	0.515819	0.257910	+	0.966169i	$0.416966\pi$
$54$	1.65426	0.225116
$55$	6.86837	0.926131
$56$	7.42769	0.992567
$57$	−1.24045	−0.164302
$58$	−9.72075	−1.27640
$59$	−8.54847	−1.11292	−0.556458	−	0.830876i	$-0.687840\pi$
$59$	−8.54847	−1.11292	−0.556458	+	0.830876i	$0.687840\pi$
$60$	−0.941888	−0.121597
$61$	12.8880	1.65014	0.825072	−	0.565028i	$-0.191134\pi$
$61$	12.8880	1.65014	0.825072	+	0.565028i	$0.191134\pi$
$62$	−12.1928	−1.54849
$63$	3.55385	0.447742
$64$	3.28322	0.410403
$65$	−5.22346	−0.647891
$66$	8.88525	1.09370
$67$	14.8088	1.80918	0.904592	−	0.426279i	$-0.140176\pi$
$67$	14.8088	1.80918	0.904592	+	0.426279i	$0.140176\pi$
$68$	0.736566	0.0893218
$69$	−1.93158	−0.232535
$70$	−7.51777	−0.898545
$71$	−5.31521	−0.630799	−0.315400	−	0.948959i	$-0.602139\pi$
$71$	−5.31521	−0.630799	−0.315400	+	0.948959i	$0.602139\pi$
$72$	2.09004	0.246314
$73$	2.95962	0.346397	0.173198	−	0.984887i	$-0.444590\pi$
$73$	2.95962	0.346397	0.173198	+	0.984887i	$0.444590\pi$
$74$	−16.8859	−1.96294
$75$	3.36478	0.388532
$76$	0.913677	0.104806
$77$	19.0882	2.17530
$78$	−6.75731	−0.765115
$79$	−1.00000	−0.112509
$79$	−1.00000	−0.112509
$80$	−6.30504	−0.704924
$81$	1.00000	0.111111
$82$	−5.83857	−0.644762
$83$	−14.9857	−1.64489	−0.822447	−	0.568842i	$-0.807392\pi$
$83$	−14.9857	−1.64489	−0.822447	+	0.568842i	$0.807392\pi$
$84$	−2.61764	−0.285608
$85$	1.27876	0.138701
$86$	8.34854	0.900246
$87$	−5.87620	−0.629995
$88$	11.2259	1.19669
$89$	8.66018	0.917977	0.458989	−	0.888442i	$-0.348212\pi$
$89$	8.66018	0.917977	0.458989	+	0.888442i	$0.348212\pi$
$90$	−2.11539	−0.222982
$91$	−14.5168	−1.52177
$92$	1.42274	0.148331
$93$	−7.37055	−0.764291
$94$	4.94094	0.509619
$95$	1.58624	0.162745
$96$	−3.97640	−0.405839
$97$	−13.4131	−1.36190	−0.680949	−	0.732331i	$-0.738433\pi$
$97$	−13.4131	−1.36190	−0.680949	+	0.732331i	$0.738433\pi$
$98$	−9.31316	−0.940772
$99$	5.37114	0.539820
$100$	−2.47839	−0.247839
$101$	−2.54824	−0.253559	−0.126780	−	0.991931i	$-0.540464\pi$
$101$	−2.54824	−0.253559	−0.126780	+	0.991931i	$0.540464\pi$
$102$	1.65426	0.163796
$103$	3.91036	0.385299	0.192650	−	0.981268i	$-0.438292\pi$
$103$	3.91036	0.385299	0.192650	+	0.981268i	$0.438292\pi$
$104$	−8.53742	−0.837163
$105$	−4.54450	−0.443498
$106$	−6.21210	−0.603373
$107$	−9.90279	−0.957339	−0.478670	−	0.877995i	$-0.658881\pi$
$107$	−9.90279	−0.957339	−0.478670	+	0.877995i	$0.658881\pi$
$108$	−0.736566	−0.0708761
$109$	−18.6608	−1.78738	−0.893692	−	0.448682i	$-0.851894\pi$
$109$	−18.6608	−1.78738	−0.893692	+	0.448682i	$0.851894\pi$
$110$	−11.3621	−1.08333
$111$	−10.2075	−0.968855
$112$	−17.5226	−1.65573
$113$	−7.63799	−0.718521	−0.359261	−	0.933237i	$-0.616971\pi$
$113$	−7.63799	−0.718521	−0.359261	+	0.933237i	$0.616971\pi$
$114$	2.05203	0.192190
$115$	2.47002	0.230331
$116$	4.32821	0.401864
$117$	−4.08480	−0.377640
$118$	14.1414	1.30182
$119$	3.55385	0.325780
$120$	−2.67266	−0.243979
$121$	17.8491	1.62265
$122$	−21.3201	−1.93023
$123$	−3.52942	−0.318237
$124$	5.42890	0.487530
$125$	−10.6965	−0.956725
$126$	−5.87897	−0.523741
$127$	7.82008	0.693920	0.346960	−	0.937880i	$-0.387214\pi$
$127$	7.82008	0.693920	0.346960	+	0.937880i	$0.387214\pi$
$128$	−13.3841	−1.18300
$129$	5.04670	0.444337
$130$	8.64095	0.757862
$131$	−5.46464	−0.477448	−0.238724	−	0.971087i	$-0.576729\pi$
$131$	−5.46464	−0.477448	−0.238724	+	0.971087i	$0.576729\pi$
$132$	−3.95620	−0.344343
$133$	4.40838	0.382255
$134$	−24.4976	−2.11627
$135$	−1.27876	−0.110058
$136$	2.09004	0.179220
$137$	−12.4040	−1.05974	−0.529872	−	0.848078i	$-0.677760\pi$
$137$	−12.4040	−1.05974	−0.529872	+	0.848078i	$0.677760\pi$
$138$	3.19534	0.272005
$139$	13.6008	1.15361	0.576803	−	0.816883i	$-0.304300\pi$
$139$	13.6008	1.15361	0.576803	+	0.816883i	$0.304300\pi$
$140$	3.34733	0.282901
$141$	2.98680	0.251534
$142$	8.79272	0.737869
$143$	−21.9400	−1.83472
$144$	−4.93060	−0.410884
$145$	7.51422	0.624022
$146$	−4.89596	−0.405193
$147$	−5.62982	−0.464339
$148$	7.51852	0.618018
$149$	11.0383	0.904291	0.452146	−	0.891944i	$-0.350659\pi$
$149$	11.0383	0.904291	0.452146	+	0.891944i	$0.350659\pi$
$150$	−5.56622	−0.454480
$151$	15.5106	1.26224	0.631118	−	0.775687i	$-0.282596\pi$
$151$	15.5106	1.26224	0.631118	+	0.775687i	$0.282596\pi$
$152$	2.59260	0.210288
$153$	1.00000	0.0808452
$154$	−31.5768	−2.54453
$155$	9.42514	0.757045
$156$	3.00873	0.240891
$157$	13.9603	1.11415	0.557077	−	0.830461i	$-0.311923\pi$
$157$	13.9603	1.11415	0.557077	+	0.830461i	$0.311923\pi$
$158$	1.65426	0.131606
$159$	−3.75522	−0.297808
$160$	5.08484	0.401992
$161$	6.86455	0.541002
$162$	−1.65426	−0.129971
$163$	−18.7271	−1.46682	−0.733411	−	0.679786i	$-0.762073\pi$
$163$	−18.7271	−1.46682	−0.733411	+	0.679786i	$0.762073\pi$
$164$	2.59965	0.202999
$165$	−6.86837	−0.534702
$166$	24.7902	1.92409
$167$	4.17476	0.323053	0.161526	−	0.986868i	$-0.448358\pi$
$167$	4.17476	0.323053	0.161526	+	0.986868i	$0.448358\pi$
$168$	−7.42769	−0.573059
$169$	3.68561	0.283509
$170$	−2.11539	−0.162243
$171$	1.24045	0.0948599
$172$	−3.71723	−0.283436
$173$	16.7265	1.27169	0.635844	−	0.771817i	$-0.280652\pi$
$173$	16.7265	1.27169	0.635844	+	0.771817i	$0.280652\pi$
$174$	9.72075	0.736928
$175$	−11.9579	−0.903934
$176$	−26.4830	−1.99623
$177$	8.54847	0.642542
$178$	−14.3262	−1.07379
$179$	−13.8829	−1.03766	−0.518830	−	0.854878i	$-0.673632\pi$
$179$	−13.8829	−1.03766	−0.518830	+	0.854878i	$0.673632\pi$
$180$	0.941888	0.0702042
$181$	1.92929	0.143403	0.0717016	−	0.997426i	$-0.477157\pi$
$181$	1.92929	0.143403	0.0717016	+	0.997426i	$0.477157\pi$
$182$	24.0144	1.78007
$183$	−12.8880	−0.952711
$184$	4.03709	0.297619
$185$	13.0529	0.959670
$186$	12.1928	0.894019
$187$	5.37114	0.392777
$188$	−2.19998	−0.160450
$189$	−3.55385	−0.258504
$190$	−2.62405	−0.190368
$191$	12.9916	0.940041	0.470020	−	0.882656i	$-0.344247\pi$
$191$	12.9916	0.940041	0.470020	+	0.882656i	$0.344247\pi$
$192$	−3.28322	−0.236946
$193$	−23.0412	−1.65854	−0.829270	−	0.558848i	$-0.811244\pi$
$193$	−23.0412	−1.65854	−0.829270	+	0.558848i	$0.811244\pi$
$194$	22.1888	1.59306
$195$	5.22346	0.374060
$196$	4.14673	0.296195
$197$	16.0224	1.14155	0.570773	−	0.821108i	$-0.306644\pi$
$197$	16.0224	1.14155	0.570773	+	0.821108i	$0.306644\pi$
$198$	−8.88525	−0.631447
$199$	−0.688268	−0.0487900	−0.0243950	−	0.999702i	$-0.507766\pi$
$199$	−0.688268	−0.0487900	−0.0243950	+	0.999702i	$0.507766\pi$
$200$	−7.03255	−0.497276
$201$	−14.8088	−1.04453
$202$	4.21544	0.296598
$203$	20.8831	1.46571
$204$	−0.736566	−0.0515700
$205$	4.51327	0.315220
$206$	−6.46874	−0.450698
$207$	1.93158	0.134254
$208$	20.1405	1.39650
$209$	6.66265	0.460865
$210$	7.51777	0.518775
$211$	−15.5379	−1.06968	−0.534838	−	0.844954i	$-0.679627\pi$
$211$	−15.5379	−1.06968	−0.534838	+	0.844954i	$0.679627\pi$
$212$	2.76597	0.189968
$213$	5.31521	0.364192
$214$	16.3818	1.11983
$215$	−6.45350	−0.440125
$216$	−2.09004	−0.142209
$217$	26.1938	1.77815
$218$	30.8698	2.09077
$219$	−2.95962	−0.199992
$220$	5.05901	0.341079
$221$	−4.08480	−0.274774
$222$	16.8859	1.13331
$223$	14.9630	1.00200	0.500998	−	0.865449i	$-0.332967\pi$
$223$	14.9630	1.00200	0.500998	+	0.865449i	$0.332967\pi$
$224$	14.1315	0.944200
$225$	−3.36478	−0.224319
$226$	12.6352	0.840481
$227$	−12.0189	−0.797723	−0.398861	−	0.917011i	$-0.630595\pi$
$227$	−12.0189	−0.797723	−0.398861	+	0.917011i	$0.630595\pi$
$228$	−0.913677	−0.0605097
$229$	−16.7887	−1.10943	−0.554716	−	0.832040i	$-0.687173\pi$
$229$	−16.7887	−1.10943	−0.554716	+	0.832040i	$0.687173\pi$
$230$	−4.08605	−0.269426
$231$	−19.0882	−1.25591
$232$	12.2815	0.806321
$233$	−26.8810	−1.76103	−0.880517	−	0.474015i	$-0.842804\pi$
$233$	−26.8810	−1.76103	−0.880517	+	0.474015i	$0.842804\pi$
$234$	6.75731	0.441739
$235$	−3.81939	−0.249149
$236$	−6.29651	−0.409868
$237$	1.00000	0.0649570
$238$	−5.87897	−0.381077
$239$	−4.80058	−0.310524	−0.155262	−	0.987873i	$-0.549622\pi$
$239$	−4.80058	−0.310524	−0.155262	+	0.987873i	$0.549622\pi$
$240$	6.30504	0.406988
$241$	20.2229	1.30267	0.651335	−	0.758790i	$-0.274209\pi$
$241$	20.2229	1.30267	0.651335	+	0.758790i	$0.274209\pi$
$242$	−29.5271	−1.89807
$243$	−1.00000	−0.0641500
$244$	9.49289	0.607720
$245$	7.19916	0.459937
$246$	5.83857	0.372253
$247$	−5.06701	−0.322406
$248$	15.4048	0.978204
$249$	14.9857	0.949680
$250$	17.6948	1.11912
$251$	−2.95799	−0.186707	−0.0933533	−	0.995633i	$-0.529759\pi$
$251$	−2.95799	−0.186707	−0.0933533	+	0.995633i	$0.529759\pi$
$252$	2.61764	0.164896
$253$	10.3748	0.652258
$254$	−12.9364	−0.811703
$255$	−1.27876	−0.0800788
$256$	15.5743	0.973392
$257$	−2.20983	−0.137846	−0.0689229	−	0.997622i	$-0.521956\pi$
$257$	−2.20983	−0.137846	−0.0689229	+	0.997622i	$0.521956\pi$
$258$	−8.34854	−0.519757
$259$	36.2760	2.25408
$260$	−3.84743	−0.238607
$261$	5.87620	0.363728
$262$	9.03992	0.558488
$263$	24.8707	1.53359	0.766796	−	0.641891i	$-0.221850\pi$
$263$	24.8707	1.53359	0.766796	+	0.641891i	$0.221850\pi$
$264$	−11.2259	−0.690907
$265$	4.80201	0.294985
$266$	−7.29260	−0.447138
$267$	−8.66018	−0.529994
$268$	10.9077	0.666292
$269$	−1.80963	−0.110335	−0.0551675	−	0.998477i	$-0.517569\pi$
$269$	−1.80963	−0.110335	−0.0551675	+	0.998477i	$0.517569\pi$
$270$	2.11539	0.128739
$271$	7.23613	0.439563	0.219782	−	0.975549i	$-0.429465\pi$
$271$	7.23613	0.439563	0.219782	+	0.975549i	$0.429465\pi$
$272$	−4.93060	−0.298962
$273$	14.5168	0.878594
$274$	20.5194	1.23962
$275$	−18.0727	−1.08983
$276$	−1.42274	−0.0856388
$277$	−20.4655	−1.22965	−0.614827	−	0.788662i	$-0.710774\pi$
$277$	−20.4655	−1.22965	−0.614827	+	0.788662i	$0.710774\pi$
$278$	−22.4992	−1.34942
$279$	7.37055	0.441263
$280$	9.49820	0.567626
$281$	−13.0150	−0.776408	−0.388204	−	0.921574i	$-0.626904\pi$
$281$	−13.0150	−0.776408	−0.388204	+	0.921574i	$0.626904\pi$
$282$	−4.94094	−0.294228
$283$	5.55729	0.330347	0.165173	−	0.986265i	$-0.447182\pi$
$283$	5.55729	0.330347	0.165173	+	0.986265i	$0.447182\pi$
$284$	−3.91500	−0.232313
$285$	−1.58624	−0.0939606
$286$	36.2945	2.14614
$287$	12.5430	0.740391
$288$	3.97640	0.234311
$289$	1.00000	0.0588235
$290$	−12.4305	−0.729942
$291$	13.4131	0.786292
$292$	2.17995	0.127572
$293$	32.2902	1.88642	0.943208	−	0.332203i	$-0.107792\pi$
$293$	32.2902	1.88642	0.943208	+	0.332203i	$0.107792\pi$
$294$	9.31316	0.543155
$295$	−10.9314	−0.636451
$296$	21.3342	1.24002
$297$	−5.37114	−0.311665
$298$	−18.2602	−1.05778
$299$	−7.89014	−0.456298
$300$	2.47839	0.143090
$301$	−17.9352	−1.03377
$302$	−25.6586	−1.47648
$303$	2.54824	0.146393
$304$	−6.11619	−0.350787
$305$	16.4806	0.943679
$306$	−1.65426	−0.0945676
$307$	−27.4789	−1.56830	−0.784150	−	0.620571i	$-0.786901\pi$
$307$	−27.4789	−1.56830	−0.784150	+	0.620571i	$0.786901\pi$
$308$	14.0597	0.801127
$309$	−3.91036	−0.222453
$310$	−15.5916	−0.885543
$311$	−3.79254	−0.215055	−0.107528	−	0.994202i	$-0.534293\pi$
$311$	−3.79254	−0.215055	−0.107528	+	0.994202i	$0.534293\pi$
$312$	8.53742	0.483336
$313$	3.88519	0.219604	0.109802	−	0.993953i	$-0.464978\pi$
$313$	3.88519	0.219604	0.109802	+	0.993953i	$0.464978\pi$
$314$	−23.0940	−1.30327
$315$	4.54450	0.256054
$316$	−0.736566	−0.0414351
$317$	11.1411	0.625748	0.312874	−	0.949795i	$-0.398708\pi$
$317$	11.1411	0.625748	0.312874	+	0.949795i	$0.398708\pi$
$318$	6.21210	0.348357
$319$	31.5619	1.76713
$320$	4.19844	0.234700
$321$	9.90279	0.552720
$322$	−11.3557	−0.632830
$323$	1.24045	0.0690207
$324$	0.736566	0.0409204
$325$	13.7445	0.762407
$326$	30.9795	1.71579
$327$	18.6608	1.03195
$328$	7.37664	0.407307
$329$	−10.6146	−0.585203
$330$	11.3621	0.625461
$331$	−20.7708	−1.14167	−0.570833	−	0.821066i	$-0.693380\pi$
$331$	−20.7708	−1.14167	−0.570833	+	0.821066i	$0.693380\pi$
$332$	−11.0380	−0.605787
$333$	10.2075	0.559369
$334$	−6.90613	−0.377887
$335$	18.9368	1.03463
$336$	17.5226	0.955936
$337$	24.6697	1.34384	0.671922	−	0.740622i	$-0.265469\pi$
$337$	24.6697	1.34384	0.671922	+	0.740622i	$0.265469\pi$
$338$	−6.09695	−0.331630
$339$	7.63799	0.414838
$340$	0.941888	0.0510811
$341$	39.5883	2.14382
$342$	−2.05203	−0.110961
$343$	−4.86942	−0.262924
$344$	−10.5478	−0.568701
$345$	−2.47002	−0.132982
$346$	−27.6699	−1.48754
$347$	3.23194	0.173499	0.0867497	−	0.996230i	$-0.472352\pi$
$347$	3.23194	0.173499	0.0867497	+	0.996230i	$0.472352\pi$
$348$	−4.32821	−0.232017
$349$	35.2711	1.88802	0.944008	−	0.329922i	$-0.107022\pi$
$349$	35.2711	1.88802	0.944008	+	0.329922i	$0.107022\pi$
$350$	19.7815	1.05736
$351$	4.08480	0.218031
$352$	21.3578	1.13837
$353$	−5.38424	−0.286574	−0.143287	−	0.989681i	$-0.545767\pi$
$353$	−5.38424	−0.286574	−0.143287	+	0.989681i	$0.545767\pi$
$354$	−14.1414	−0.751605
$355$	−6.79685	−0.360739
$356$	6.37880	0.338076
$357$	−3.55385	−0.188089
$358$	22.9659	1.21379
$359$	−28.3219	−1.49477	−0.747386	−	0.664390i	$-0.768691\pi$
$359$	−28.3219	−1.49477	−0.747386	+	0.664390i	$0.768691\pi$
$360$	2.67266	0.140861
$361$	−17.4613	−0.919014
$362$	−3.19155	−0.167744
$363$	−17.8491	−0.936837
$364$	−10.6926	−0.560442
$365$	3.78462	0.198096
$366$	21.3201	1.11442
$367$	21.4622	1.12032	0.560160	−	0.828385i	$-0.310740\pi$
$367$	21.4622	1.12032	0.560160	+	0.828385i	$0.310740\pi$
$368$	−9.52387	−0.496466
$369$	3.52942	0.183734
$370$	−21.5929	−1.12256
$371$	13.3455	0.692863
$372$	−5.42890	−0.281475
$373$	−4.65958	−0.241264	−0.120632	−	0.992697i	$-0.538492\pi$
$373$	−4.65958	−0.241264	−0.120632	+	0.992697i	$0.538492\pi$
$374$	−8.88525	−0.459445
$375$	10.6965	0.552366
$376$	−6.24254	−0.321935
$377$	−24.0031	−1.23622
$378$	5.87897	0.302382
$379$	12.3564	0.634707	0.317354	−	0.948307i	$-0.397206\pi$
$379$	12.3564	0.634707	0.317354	+	0.948307i	$0.397206\pi$
$380$	1.16837	0.0599361
$381$	−7.82008	−0.400635
$382$	−21.4915	−1.09960
$383$	−26.8033	−1.36958	−0.684792	−	0.728738i	$-0.740107\pi$
$383$	−26.8033	−1.36958	−0.684792	+	0.728738i	$0.740107\pi$
$384$	13.3841	0.683004
$385$	24.4091	1.24401
$386$	38.1160	1.94005
$387$	−5.04670	−0.256538
$388$	−9.87967	−0.501564
$389$	−18.2738	−0.926521	−0.463260	−	0.886222i	$-0.653320\pi$
$389$	−18.2738	−0.926521	−0.463260	+	0.886222i	$0.653320\pi$
$390$	−8.64095	−0.437552
$391$	1.93158	0.0976844
$392$	11.7666	0.594301
$393$	5.46464	0.275655
$394$	−26.5051	−1.33531
$395$	−1.27876	−0.0643412
$396$	3.95620	0.198807
$397$	17.7768	0.892193	0.446096	−	0.894985i	$-0.352814\pi$
$397$	17.7768	0.892193	0.446096	+	0.894985i	$0.352814\pi$
$398$	1.13857	0.0570714
$399$	−4.40838	−0.220695
$400$	16.5904	0.829521
$401$	30.6269	1.52944	0.764718	−	0.644366i	$-0.222879\pi$
$401$	30.6269	1.52944	0.764718	+	0.644366i	$0.222879\pi$
$402$	24.4976	1.22183
$403$	−30.1073	−1.49975
$404$	−1.87695	−0.0933816
$405$	1.27876	0.0635419
$406$	−34.5460	−1.71449
$407$	54.8260	2.71763
$408$	−2.09004	−0.103473
$409$	3.64897	0.180430	0.0902149	−	0.995922i	$-0.471245\pi$
$409$	3.64897	0.180430	0.0902149	+	0.995922i	$0.471245\pi$
$410$	−7.46610	−0.368724
$411$	12.4040	0.611843
$412$	2.88024	0.141899
$413$	−30.3799	−1.49490
$414$	−3.19534	−0.157042
$415$	−19.1630	−0.940677
$416$	−16.2428	−0.796368
$417$	−13.6008	−0.666035
$418$	−11.0217	−0.539091
$419$	−4.55121	−0.222341	−0.111171	−	0.993801i	$-0.535460\pi$
$419$	−4.55121	−0.222341	−0.111171	+	0.993801i	$0.535460\pi$
$420$	−3.34733	−0.163333
$421$	−14.7938	−0.721005	−0.360503	−	0.932758i	$-0.617395\pi$
$421$	−14.7938	−0.721005	−0.360503	+	0.932758i	$0.617395\pi$
$422$	25.7038	1.25124
$423$	−2.98680	−0.145223
$424$	7.84858	0.381161
$425$	−3.36478	−0.163216
$426$	−8.79272	−0.426009
$427$	45.8021	2.21652
$428$	−7.29406	−0.352572
$429$	21.9400	1.05928
$430$	10.6757	0.514830
$431$	27.3408	1.31696	0.658480	−	0.752598i	$-0.271200\pi$
$431$	27.3408	1.31696	0.658480	+	0.752598i	$0.271200\pi$
$432$	4.93060	0.237224
$433$	−17.2731	−0.830091	−0.415045	−	0.909801i	$-0.636234\pi$
$433$	−17.2731	−0.830091	−0.415045	+	0.909801i	$0.636234\pi$
$434$	−43.3313	−2.07997
$435$	−7.51422	−0.360279
$436$	−13.7449	−0.658263
$437$	2.39604	0.114618
$438$	4.89596	0.233938
$439$	27.7835	1.32603	0.663016	−	0.748605i	$-0.269276\pi$
$439$	27.7835	1.32603	0.663016	+	0.748605i	$0.269276\pi$
$440$	14.3552	0.684358
$441$	5.62982	0.268086
$442$	6.75731	0.321413
$443$	4.80162	0.228132	0.114066	−	0.993473i	$-0.463612\pi$
$443$	4.80162	0.228132	0.114066	+	0.993473i	$0.463612\pi$
$444$	−7.51852	−0.356813
$445$	11.0743	0.524970
$446$	−24.7526	−1.17207
$447$	−11.0383	−0.522093
$448$	11.6681	0.551264
$449$	0.536679	0.0253274	0.0126637	−	0.999920i	$-0.495969\pi$
$449$	0.536679	0.0253274	0.0126637	+	0.999920i	$0.495969\pi$
$450$	5.56622	0.262394
$451$	18.9570	0.892651
$452$	−5.62588	−0.264619
$453$	−15.5106	−0.728753
$454$	19.8824	0.933125
$455$	−18.5634	−0.870265
$456$	−2.59260	−0.121410
$457$	−14.0396	−0.656744	−0.328372	−	0.944549i	$-0.606500\pi$
$457$	−14.0396	−0.656744	−0.328372	+	0.944549i	$0.606500\pi$
$458$	27.7729	1.29774
$459$	−1.00000	−0.0466760
$460$	1.81934	0.0848270
$461$	−31.5319	−1.46859	−0.734293	−	0.678833i	$-0.762486\pi$
$461$	−31.5319	−1.46859	−0.734293	+	0.678833i	$0.762486\pi$
$462$	31.5768	1.46909
$463$	9.15515	0.425476	0.212738	−	0.977109i	$-0.431762\pi$
$463$	9.15515	0.425476	0.212738	+	0.977109i	$0.431762\pi$
$464$	−28.9732	−1.34505
$465$	−9.42514	−0.437080
$466$	44.4681	2.05994
$467$	−1.93504	−0.0895432	−0.0447716	−	0.998997i	$-0.514256\pi$
$467$	−1.93504	−0.0895432	−0.0447716	+	0.998997i	$0.514256\pi$
$468$	−3.00873	−0.139079
$469$	52.6282	2.43014
$470$	6.31825	0.291439
$471$	−13.9603	−0.643258
$472$	−17.8667	−0.822380
$473$	−27.1065	−1.24636
$474$	−1.65426	−0.0759825
$475$	−4.17386	−0.191510
$476$	2.61764	0.119979
$477$	3.75522	0.171940
$478$	7.94140	0.363231
$479$	−35.3226	−1.61393	−0.806966	−	0.590598i	$-0.798892\pi$
$479$	−35.3226	−1.61393	−0.806966	+	0.590598i	$0.798892\pi$
$480$	−5.08484	−0.232090
$481$	−41.6957	−1.90116
$482$	−33.4538	−1.52378
$483$	−6.86455	−0.312348
$484$	13.1471	0.597594
$485$	−17.1521	−0.778838
$486$	1.65426	0.0750386
$487$	3.86123	0.174969	0.0874846	−	0.996166i	$-0.472117\pi$
$487$	3.86123	0.174969	0.0874846	+	0.996166i	$0.472117\pi$
$488$	26.9366	1.21936
$489$	18.7271	0.846870
$490$	−11.9093	−0.538005
$491$	31.0339	1.40054	0.700271	−	0.713877i	$-0.253062\pi$
$491$	31.0339	1.40054	0.700271	+	0.713877i	$0.253062\pi$
$492$	−2.59965	−0.117201
$493$	5.87620	0.264651
$494$	8.38214	0.377130
$495$	6.86837	0.308710
$496$	−36.3413	−1.63177
$497$	−18.8894	−0.847307
$498$	−24.7902	−1.11088
$499$	44.5082	1.99246	0.996231	−	0.0867347i	$-0.0276432\pi$
$499$	44.5082	1.99246	0.996231	+	0.0867347i	$0.0276432\pi$
$500$	−7.87869	−0.352346
$501$	−4.17476	−0.186515
$502$	4.89327	0.218397
$503$	−29.4173	−1.31165	−0.655826	−	0.754912i	$-0.727679\pi$
$503$	−29.4173	−1.31165	−0.655826	+	0.754912i	$0.727679\pi$
$504$	7.42769	0.330856
$505$	−3.25858	−0.145005
$506$	−17.1626	−0.762970
$507$	−3.68561	−0.163684
$508$	5.76001	0.255559
$509$	35.6630	1.58074	0.790368	−	0.612633i	$-0.209889\pi$
$509$	35.6630	1.58074	0.790368	+	0.612633i	$0.209889\pi$
$510$	2.11539	0.0936711
$511$	10.5180	0.465290
$512$	1.00432	0.0443852
$513$	−1.24045	−0.0547674
$514$	3.65563	0.161243
$515$	5.00039	0.220344
$516$	3.71723	0.163642
$517$	−16.0425	−0.705549
$518$	−60.0098	−2.63668
$519$	−16.7265	−0.734210
$520$	−10.9173	−0.478754
$521$	7.10414	0.311238	0.155619	−	0.987817i	$-0.450263\pi$
$521$	7.10414	0.311238	0.155619	+	0.987817i	$0.450263\pi$
$522$	−9.72075	−0.425466
$523$	−28.0363	−1.22594	−0.612971	−	0.790105i	$-0.710026\pi$
$523$	−28.0363	−1.22594	−0.612971	+	0.790105i	$0.710026\pi$
$524$	−4.02507	−0.175836
$525$	11.9579	0.521887
$526$	−41.1425	−1.79390
$527$	7.37055	0.321066
$528$	26.4830	1.15252
$529$	−19.2690	−0.837782
$530$	−7.94376	−0.345055
$531$	−8.54847	−0.370972
$532$	3.24707	0.140778
$533$	−14.4170	−0.624469
$534$	14.3262	0.619954
$535$	−12.6633	−0.547480
$536$	30.9511	1.33688
$537$	13.8829	0.599093
$538$	2.99359	0.129063
$539$	30.2385	1.30247
$540$	−0.941888	−0.0405324
$541$	−35.1510	−1.51126	−0.755630	−	0.654999i	$-0.772669\pi$
$541$	−35.1510	−1.51126	−0.755630	+	0.654999i	$0.772669\pi$
$542$	−11.9704	−0.514173
$543$	−1.92929	−0.0827939
$544$	3.97640	0.170487
$545$	−23.8626	−1.02216
$546$	−24.0144	−1.02772
$547$	18.1102	0.774337	0.387168	−	0.922009i	$-0.373453\pi$
$547$	18.1102	0.774337	0.387168	+	0.922009i	$0.373453\pi$
$548$	−9.13635	−0.390286
$549$	12.8880	0.550048
$550$	29.8969	1.27481
$551$	7.28916	0.310529
$552$	−4.03709	−0.171830
$553$	−3.55385	−0.151125
$554$	33.8552	1.43837
$555$	−13.0529	−0.554066
$556$	10.0179	0.424854
$557$	−27.9293	−1.18340	−0.591702	−	0.806157i	$-0.701544\pi$
$557$	−27.9293	−1.18340	−0.591702	+	0.806157i	$0.701544\pi$
$558$	−12.1928	−0.516162
$559$	20.6148	0.871912
$560$	−22.4071	−0.946874
$561$	−5.37114	−0.226770
$562$	21.5301	0.908192
$563$	3.48795	0.147000	0.0734999	−	0.997295i	$-0.476583\pi$
$563$	3.48795	0.147000	0.0734999	+	0.997295i	$0.476583\pi$
$564$	2.19998	0.0926357
$565$	−9.76712	−0.410906
$566$	−9.19319	−0.386418
$567$	3.55385	0.149247
$568$	−11.1090	−0.466124
$569$	11.1930	0.469234	0.234617	−	0.972088i	$-0.424616\pi$
$569$	11.1930	0.469234	0.234617	+	0.972088i	$0.424616\pi$
$570$	2.62405	0.109909
$571$	15.4355	0.645956	0.322978	−	0.946407i	$-0.395316\pi$
$571$	15.4355	0.645956	0.322978	+	0.946407i	$0.395316\pi$
$572$	−16.1603	−0.675696
$573$	−12.9916	−0.542733
$574$	−20.7494	−0.866062
$575$	−6.49936	−0.271042
$576$	3.28322	0.136801
$577$	22.5555	0.938998	0.469499	−	0.882933i	$-0.344435\pi$
$577$	22.5555	0.938998	0.469499	+	0.882933i	$0.344435\pi$
$578$	−1.65426	−0.0688080
$579$	23.0412	0.957559
$580$	5.53473	0.229817
$581$	−53.2568	−2.20947
$582$	−22.1888	−0.919755
$583$	20.1698	0.835349
$584$	6.18573	0.255967
$585$	−5.22346	−0.215964
$586$	−53.4164	−2.20661
$587$	12.2299	0.504781	0.252391	−	0.967625i	$-0.418783\pi$
$587$	12.2299	0.504781	0.252391	+	0.967625i	$0.418783\pi$
$588$	−4.14673	−0.171008
$589$	9.14283	0.376724
$590$	18.0833	0.744480
$591$	−16.0224	−0.659072
$592$	−50.3292	−2.06852
$593$	18.5331	0.761063	0.380531	−	0.924768i	$-0.375741\pi$
$593$	18.5331	0.761063	0.380531	+	0.924768i	$0.375741\pi$
$594$	8.88525	0.364566
$595$	4.54450	0.186306
$596$	8.13043	0.333035
$597$	0.688268	0.0281689
$598$	13.0523	0.533749
$599$	8.58091	0.350607	0.175303	−	0.984514i	$-0.443909\pi$
$599$	8.58091	0.350607	0.175303	+	0.984514i	$0.443909\pi$
$600$	7.03255	0.287103
$601$	16.4879	0.672554	0.336277	−	0.941763i	$-0.390832\pi$
$601$	16.4879	0.672554	0.336277	+	0.941763i	$0.390832\pi$
$602$	29.6694	1.20924
$603$	14.8088	0.603061
$604$	11.4246	0.464861
$605$	22.8247	0.927956
$606$	−4.21544	−0.171241
$607$	37.2617	1.51241	0.756204	−	0.654336i	$-0.227052\pi$
$607$	37.2617	1.51241	0.756204	+	0.654336i	$0.227052\pi$
$608$	4.93254	0.200041
$609$	−20.8831	−0.846226
$610$	−27.2632	−1.10386
$611$	12.2005	0.493579
$612$	0.736566	0.0297739
$613$	35.7081	1.44224	0.721118	−	0.692812i	$-0.243628\pi$
$613$	35.7081	1.44224	0.721118	+	0.692812i	$0.243628\pi$
$614$	45.4571	1.83450
$615$	−4.51327	−0.181992
$616$	39.8952	1.60742
$617$	−25.7171	−1.03533	−0.517666	−	0.855583i	$-0.673199\pi$
$617$	−25.7171	−1.03533	−0.517666	+	0.855583i	$0.673199\pi$
$618$	6.46874	0.260211
$619$	−21.4138	−0.860692	−0.430346	−	0.902664i	$-0.641608\pi$
$619$	−21.4138	−0.860692	−0.430346	+	0.902664i	$0.641608\pi$
$620$	6.94224	0.278807
$621$	−1.93158	−0.0775118
$622$	6.27383	0.251558
$623$	30.7769	1.23305
$624$	−20.1405	−0.806267
$625$	3.14569	0.125828
$626$	−6.42710	−0.256879
$627$	−6.66265	−0.266081
$628$	10.2827	0.410324
$629$	10.2075	0.407001
$630$	−7.51777	−0.299515
$631$	47.7411	1.90054	0.950272	−	0.311421i	$-0.100805\pi$
$631$	47.7411	1.90054	0.950272	+	0.311421i	$0.100805\pi$
$632$	−2.09004	−0.0831375
$633$	15.5379	0.617578
$634$	−18.4303	−0.731960
$635$	9.99997	0.396837
$636$	−2.76597	−0.109678
$637$	−22.9967	−0.911162
$638$	−52.2115	−2.06707
$639$	−5.31521	−0.210266
$640$	−17.1150	−0.676529
$641$	18.9609	0.748912	0.374456	−	0.927245i	$-0.377830\pi$
$641$	18.9609	0.748912	0.374456	+	0.927245i	$0.377830\pi$
$642$	−16.3818	−0.646537
$643$	49.8352	1.96531	0.982655	−	0.185443i	$-0.0593719\pi$
$643$	49.8352	1.96531	0.982655	+	0.185443i	$0.0593719\pi$
$644$	5.05620	0.199242
$645$	6.45350	0.254106
$646$	−2.05203	−0.0807361
$647$	−34.1793	−1.34373	−0.671863	−	0.740675i	$-0.734506\pi$
$647$	−34.1793	−1.34373	−0.671863	+	0.740675i	$0.734506\pi$
$648$	2.09004	0.0821047
$649$	−45.9150	−1.80232
$650$	−22.7369	−0.891815
$651$	−26.1938	−1.02662
$652$	−13.7938	−0.540206
$653$	−35.1400	−1.37514	−0.687568	−	0.726120i	$-0.741322\pi$
$653$	−35.1400	−1.37514	−0.687568	+	0.726120i	$0.741322\pi$
$654$	−30.8698	−1.20710
$655$	−6.98794	−0.273041
$656$	−17.4022	−0.679440
$657$	2.95962	0.115466
$658$	17.5593	0.684534
$659$	12.7268	0.495766	0.247883	−	0.968790i	$-0.420265\pi$
$659$	12.7268	0.495766	0.247883	+	0.968790i	$0.420265\pi$
$660$	−5.05901	−0.196922
$661$	19.6462	0.764150	0.382075	−	0.924131i	$-0.375210\pi$
$661$	19.6462	0.764150	0.382075	+	0.924131i	$0.375210\pi$
$662$	34.3602	1.33545
$663$	4.08480	0.158641
$664$	−31.3208	−1.21548
$665$	5.63724	0.218603
$666$	−16.8859	−0.654314
$667$	11.3504	0.439488
$668$	3.07499	0.118975
$669$	−14.9630	−0.578502
$670$	−31.3264	−1.21024
$671$	69.2234	2.67234
$672$	−14.1315	−0.545134
$673$	−24.6561	−0.950421	−0.475211	−	0.879872i	$-0.657628\pi$
$673$	−24.6561	−0.950421	−0.475211	+	0.879872i	$0.657628\pi$
$674$	−40.8100	−1.57194
$675$	3.36478	0.129511
$676$	2.71470	0.104411
$677$	47.1091	1.81055	0.905276	−	0.424825i	$-0.139664\pi$
$677$	47.1091	1.81055	0.905276	+	0.424825i	$0.139664\pi$
$678$	−12.6352	−0.485252
$679$	−47.6682	−1.82934
$680$	2.67266	0.102492
$681$	12.0189	0.460565
$682$	−65.4892	−2.50771
$683$	35.0014	1.33929	0.669646	−	0.742681i	$-0.266446\pi$
$683$	35.0014	1.33929	0.669646	+	0.742681i	$0.266446\pi$
$684$	0.913677	0.0349353
$685$	−15.8617	−0.606043
$686$	8.05527	0.307552
$687$	16.7887	0.640531
$688$	24.8833	0.948666
$689$	−15.3393	−0.584382
$690$	4.08605	0.155553
$691$	1.01178	0.0384899	0.0192449	−	0.999815i	$-0.493874\pi$
$691$	1.01178	0.0384899	0.0192449	+	0.999815i	$0.493874\pi$
$692$	12.3201	0.468342
$693$	19.0882	0.725101
$694$	−5.34646	−0.202949
$695$	17.3921	0.659721
$696$	−12.2815	−0.465530
$697$	3.52942	0.133686
$698$	−58.3474	−2.20848
$699$	26.8810	1.01673
$700$	−8.80780	−0.332904
$701$	−32.7998	−1.23883	−0.619415	−	0.785063i	$-0.712630\pi$
$701$	−32.7998	−1.23883	−0.619415	+	0.785063i	$0.712630\pi$
$702$	−6.75731	−0.255038
$703$	12.6620	0.477555
$704$	17.6347	0.664631
$705$	3.81939	0.143846
$706$	8.90691	0.335216
$707$	−9.05605	−0.340588
$708$	6.29651	0.236637
$709$	9.76231	0.366631	0.183316	−	0.983054i	$-0.441317\pi$
$709$	9.76231	0.366631	0.183316	+	0.983054i	$0.441317\pi$
$710$	11.2437	0.421970
$711$	−1.00000	−0.0375029
$712$	18.1002	0.678332
$713$	14.2368	0.533174
$714$	5.87897	0.220015
$715$	−28.0560	−1.04923
$716$	−10.2257	−0.382152
$717$	4.80058	0.179281
$718$	46.8517	1.74849
$719$	−9.72457	−0.362665	−0.181333	−	0.983422i	$-0.558041\pi$
$719$	−9.72457	−0.362665	−0.181333	+	0.983422i	$0.558041\pi$
$720$	−6.30504	−0.234975
$721$	13.8968	0.517544
$722$	28.8854	1.07500
$723$	−20.2229	−0.752097
$724$	1.42105	0.0528130
$725$	−19.7721	−0.734319
$726$	29.5271	1.09585
$727$	22.2639	0.825721	0.412860	−	0.910794i	$-0.364530\pi$
$727$	22.2639	0.825721	0.412860	+	0.910794i	$0.364530\pi$
$728$	−30.3407	−1.12450
$729$	1.00000	0.0370370
$730$	−6.26074	−0.231720
$731$	−5.04670	−0.186659
$732$	−9.49289	−0.350867
$733$	17.6428	0.651652	0.325826	−	0.945430i	$-0.394358\pi$
$733$	17.6428	0.651652	0.325826	+	0.945430i	$0.394358\pi$
$734$	−35.5040	−1.31048
$735$	−7.19916	−0.265545
$736$	7.68074	0.283116
$737$	79.5402	2.92990
$738$	−5.83857	−0.214921
$739$	−28.1613	−1.03593	−0.517964	−	0.855402i	$-0.673310\pi$
$739$	−28.1613	−1.03593	−0.517964	+	0.855402i	$0.673310\pi$
$740$	9.61435	0.353430
$741$	5.06701	0.186141
$742$	−22.0769	−0.810467
$743$	−21.1793	−0.776992	−0.388496	−	0.921451i	$-0.627005\pi$
$743$	−21.1793	−0.776992	−0.388496	+	0.921451i	$0.627005\pi$
$744$	−15.4048	−0.564767
$745$	14.1153	0.517143
$746$	7.70814	0.282215
$747$	−14.9857	−0.548298
$748$	3.95620	0.144653
$749$	−35.1930	−1.28592
$750$	−17.6948	−0.646122
$751$	−41.5757	−1.51712	−0.758559	−	0.651604i	$-0.774096\pi$
$751$	−41.5757	−1.51712	−0.758559	+	0.651604i	$0.774096\pi$
$752$	14.7267	0.537028
$753$	2.95799	0.107795
$754$	39.7073	1.44606
$755$	19.8343	0.721844
$756$	−2.61764	−0.0952028
$757$	−22.0458	−0.801268	−0.400634	−	0.916238i	$-0.631210\pi$
$757$	−22.0458	−0.801268	−0.400634	+	0.916238i	$0.631210\pi$
$758$	−20.4407	−0.742440
$759$	−10.3748	−0.376581
$760$	3.31531	0.120259
$761$	24.1253	0.874543	0.437271	−	0.899330i	$-0.355945\pi$
$761$	24.1253	0.874543	0.437271	+	0.899330i	$0.355945\pi$
$762$	12.9364	0.468637
$763$	−66.3177	−2.40086
$764$	9.56919	0.346201
$765$	1.27876	0.0462335
$766$	44.3395	1.60205
$767$	34.9188	1.26084
$768$	−15.5743	−0.561988
$769$	8.77684	0.316501	0.158250	−	0.987399i	$-0.449415\pi$
$769$	8.77684	0.316501	0.158250	+	0.987399i	$0.449415\pi$
$770$	−40.3790	−1.45516
$771$	2.20983	0.0795853
$772$	−16.9714	−0.610813
$773$	44.4435	1.59852	0.799261	−	0.600984i	$-0.205224\pi$
$773$	44.4435	1.59852	0.799261	+	0.600984i	$0.205224\pi$
$774$	8.34854	0.300082
$775$	−24.8003	−0.890854
$776$	−28.0341	−1.00636
$777$	−36.2760	−1.30139
$778$	30.2296	1.08378
$779$	4.37808	0.156861
$780$	3.84743	0.137760
$781$	−28.5487	−1.02155
$782$	−3.19534	−0.114265
$783$	−5.87620	−0.209998
$784$	−27.7584	−0.991371
$785$	17.8518	0.637159
$786$	−9.03992	−0.322443
$787$	13.3430	0.475627	0.237814	−	0.971311i	$-0.423569\pi$
$787$	13.3430	0.475627	0.237814	+	0.971311i	$0.423569\pi$
$788$	11.8015	0.420412
$789$	−24.8707	−0.885420
$790$	2.11539	0.0752622
$791$	−27.1442	−0.965137
$792$	11.2259	0.398896
$793$	−52.6451	−1.86948
$794$	−29.4074	−1.04363
$795$	−4.80201	−0.170310
$796$	−0.506955	−0.0179685
$797$	−17.2626	−0.611472	−0.305736	−	0.952116i	$-0.598902\pi$
$797$	−17.2626	−0.611472	−0.305736	+	0.952116i	$0.598902\pi$
$798$	7.29260	0.258155
$799$	−2.98680	−0.105665
$800$	−13.3797	−0.473044
$801$	8.66018	0.305992
$802$	−50.6648	−1.78904
$803$	15.8965	0.560976
$804$	−10.9077	−0.384684
$805$	8.77808	0.309387
$806$	49.8051	1.75431
$807$	1.80963	0.0637019
$808$	−5.32593	−0.187366
$809$	−6.55272	−0.230381	−0.115191	−	0.993343i	$-0.536748\pi$
$809$	−6.55272	−0.230381	−0.115191	+	0.993343i	$0.536748\pi$
$810$	−2.11539	−0.0743272
$811$	26.4742	0.929635	0.464818	−	0.885406i	$-0.346120\pi$
$811$	26.4742	0.929635	0.464818	+	0.885406i	$0.346120\pi$
$812$	15.3818	0.539795
$813$	−7.23613	−0.253782
$814$	−90.6963	−3.17891
$815$	−23.9474	−0.838841
$816$	4.93060	0.172606
$817$	−6.26020	−0.219017
$818$	−6.03633	−0.211055
$819$	−14.5168	−0.507257
$820$	3.32432	0.116090
$821$	−31.3791	−1.09514	−0.547569	−	0.836761i	$-0.684447\pi$
$821$	−31.3791	−1.09514	−0.547569	+	0.836761i	$0.684447\pi$
$822$	−20.5194	−0.715695
$823$	15.7893	0.550380	0.275190	−	0.961390i	$-0.411259\pi$
$823$	15.7893	0.550380	0.275190	+	0.961390i	$0.411259\pi$
$824$	8.17282	0.284714
$825$	18.0727	0.629212
$826$	50.2562	1.74864
$827$	−3.45492	−0.120139	−0.0600697	−	0.998194i	$-0.519132\pi$
$827$	−3.45492	−0.120139	−0.0600697	+	0.998194i	$0.519132\pi$
$828$	1.42274	0.0494436
$829$	−7.16822	−0.248962	−0.124481	−	0.992222i	$-0.539727\pi$
$829$	−7.16822	−0.248962	−0.124481	+	0.992222i	$0.539727\pi$
$830$	31.7006	1.10034
$831$	20.4655	0.709941
$832$	−13.4113	−0.464954
$833$	5.62982	0.195062
$834$	22.4992	0.779085
$835$	5.33850	0.184746
$836$	4.90749	0.169729
$837$	−7.37055	−0.254764
$838$	7.52887	0.260080
$839$	−18.3742	−0.634347	−0.317174	−	0.948367i	$-0.602734\pi$
$839$	−18.3742	−0.634347	−0.317174	+	0.948367i	$0.602734\pi$
$840$	−9.49820	−0.327719
$841$	5.52974	0.190681
$842$	24.4727	0.843386
$843$	13.0150	0.448259
$844$	−11.4447	−0.393944
$845$	4.71300	0.162132
$846$	4.94094	0.169873
$847$	63.4331	2.17959
$848$	−18.5155	−0.635825
$849$	−5.55729	−0.190726
$850$	5.56622	0.190920
$851$	19.7167	0.675879
$852$	3.91500	0.134126
$853$	−55.7551	−1.90902	−0.954509	−	0.298182i	$-0.903620\pi$
$853$	−55.7551	−1.90902	−0.954509	+	0.298182i	$0.903620\pi$
$854$	−75.7684	−2.59274
$855$	1.58624	0.0542482
$856$	−20.6973	−0.707418
$857$	19.6964	0.672816	0.336408	−	0.941716i	$-0.390788\pi$
$857$	19.6964	0.672816	0.336408	+	0.941716i	$0.390788\pi$
$858$	−36.2945	−1.23907
$859$	29.4171	1.00370	0.501850	−	0.864955i	$-0.332653\pi$
$859$	29.4171	1.00370	0.501850	+	0.864955i	$0.332653\pi$
$860$	−4.75343	−0.162091
$861$	−12.5430	−0.427465
$862$	−45.2287	−1.54050
$863$	−24.7687	−0.843135	−0.421568	−	0.906797i	$-0.638520\pi$
$863$	−24.7687	−0.843135	−0.421568	+	0.906797i	$0.638520\pi$
$864$	−3.97640	−0.135280
$865$	21.3891	0.727250
$866$	28.5741	0.970987
$867$	−1.00000	−0.0339618
$868$	19.2935	0.654863
$869$	−5.37114	−0.182203
$870$	12.4305	0.421432
$871$	−60.4910	−2.04966
$872$	−39.0020	−1.32077
$873$	−13.4131	−0.453966
$874$	−3.96367	−0.134073
$875$	−38.0138	−1.28510
$876$	−2.17995	−0.0736538
$877$	−28.2575	−0.954187	−0.477093	−	0.878853i	$-0.658310\pi$
$877$	−28.2575	−0.954187	−0.477093	+	0.878853i	$0.658310\pi$
$878$	−45.9610	−1.55111
$879$	−32.2902	−1.08912
$880$	−33.8652	−1.14160
$881$	−13.9273	−0.469223	−0.234611	−	0.972089i	$-0.575382\pi$
$881$	−13.9273	−0.469223	−0.234611	+	0.972089i	$0.575382\pi$
$882$	−9.31316	−0.313591
$883$	31.4182	1.05731	0.528653	−	0.848838i	$-0.322697\pi$
$883$	31.4182	1.05731	0.528653	+	0.848838i	$0.322697\pi$
$884$	−3.00873	−0.101194
$885$	10.9314	0.367455
$886$	−7.94312	−0.266854
$887$	−48.6591	−1.63381	−0.816907	−	0.576770i	$-0.804313\pi$
$887$	−48.6591	−1.63381	−0.816907	+	0.576770i	$0.804313\pi$
$888$	−21.3342	−0.715928
$889$	27.7913	0.932092
$890$	−18.3197	−0.614076
$891$	5.37114	0.179940
$892$	11.0212	0.369018
$893$	−3.70499	−0.123983
$894$	18.2602	0.610711
$895$	−17.7529	−0.593413
$896$	−47.5650	−1.58903
$897$	7.89014	0.263444
$898$	−0.887805	−0.0296264
$899$	43.3108	1.44450
$900$	−2.47839	−0.0826129
$901$	3.75522	0.125105
$902$	−31.3598	−1.04417
$903$	17.9352	0.596846
$904$	−15.9637	−0.530946
$905$	2.46709	0.0820090
$906$	25.6586	0.852449
$907$	−25.4663	−0.845596	−0.422798	−	0.906224i	$-0.638952\pi$
$907$	−25.4663	−0.845596	−0.422798	+	0.906224i	$0.638952\pi$
$908$	−8.85272	−0.293788
$909$	−2.54824	−0.0845198
$910$	30.7086	1.01798
$911$	38.1610	1.26433	0.632165	−	0.774834i	$-0.282166\pi$
$911$	38.1610	1.26433	0.632165	+	0.774834i	$0.282166\pi$
$912$	6.11619	0.202527
$913$	−80.4903	−2.66384
$914$	23.2251	0.768217
$915$	−16.4806	−0.544833
$916$	−12.3660	−0.408585
$917$	−19.4205	−0.641321
$918$	1.65426	0.0545986
$919$	0.639215	0.0210858	0.0105429	−	0.999944i	$-0.496644\pi$
$919$	0.639215	0.0210858	0.0105429	+	0.999944i	$0.496644\pi$
$920$	5.16246	0.170201
$921$	27.4789	0.905459
$922$	52.1618	1.71786
$923$	21.7116	0.714645
$924$	−14.0597	−0.462531
$925$	−34.3461	−1.12929
$926$	−15.1450	−0.497695
$927$	3.91036	0.128433
$928$	23.3661	0.767030
$929$	−44.8003	−1.46985	−0.734925	−	0.678148i	$-0.762783\pi$
$929$	−44.8003	−1.46985	−0.734925	+	0.678148i	$0.762783\pi$
$930$	15.5916	0.511269
$931$	6.98353	0.228876
$932$	−19.7996	−0.648559
$933$	3.79254	0.124162
$934$	3.20106	0.104742
$935$	6.86837	0.224620
$936$	−8.53742	−0.279054
$937$	−21.1198	−0.689954	−0.344977	−	0.938611i	$-0.612113\pi$
$937$	−21.1198	−0.689954	−0.344977	+	0.938611i	$0.612113\pi$
$938$	−87.0606	−2.84263
$939$	−3.88519	−0.126788
$940$	−2.81323	−0.0917575
$941$	9.02961	0.294357	0.147178	−	0.989110i	$-0.452981\pi$
$941$	9.02961	0.294357	0.147178	+	0.989110i	$0.452981\pi$
$942$	23.0940	0.752442
$943$	6.81737	0.222004
$944$	42.1491	1.37184
$945$	−4.54450	−0.147833
$946$	44.8412	1.45791
$947$	−27.9622	−0.908649	−0.454325	−	0.890836i	$-0.650119\pi$
$947$	−27.9622	−0.908649	−0.454325	+	0.890836i	$0.650119\pi$
$948$	0.736566	0.0239226
$949$	−12.0894	−0.392440
$950$	6.90464	0.224016
$951$	−11.1411	−0.361275
$952$	7.42769	0.240733
$953$	−18.8077	−0.609243	−0.304621	−	0.952474i	$-0.598530\pi$
$953$	−18.8077	−0.609243	−0.304621	+	0.952474i	$0.598530\pi$
$954$	−6.21210	−0.201124
$955$	16.6131	0.537587
$956$	−3.53595	−0.114361
$957$	−31.5619	−1.02025
$958$	58.4327	1.88787
$959$	−44.0818	−1.42348
$960$	−4.19844	−0.135504
$961$	23.3251	0.752421
$962$	68.9754	2.22386
$963$	−9.90279	−0.319113
$964$	14.8955	0.479751
$965$	−29.4640	−0.948481
$966$	11.3557	0.365365
$967$	−1.52578	−0.0490659	−0.0245330	−	0.999699i	$-0.507810\pi$
$967$	−1.52578	−0.0490659	−0.0245330	+	0.999699i	$0.507810\pi$
$968$	37.3055	1.19904
$969$	−1.24045	−0.0398491
$970$	28.3740	0.911035
$971$	42.9284	1.37764	0.688819	−	0.724934i	$-0.258130\pi$
$971$	42.9284	1.37764	0.688819	+	0.724934i	$0.258130\pi$
$972$	−0.736566	−0.0236254
$973$	48.3352	1.54956
$974$	−6.38747	−0.204668
$975$	−13.7445	−0.440176
$976$	−63.5458	−2.03405
$977$	−45.0193	−1.44029	−0.720147	−	0.693822i	$-0.755926\pi$
$977$	−45.0193	−1.44029	−0.720147	+	0.693822i	$0.755926\pi$
$978$	−30.9795	−0.990614
$979$	46.5150	1.48663
$980$	5.30266	0.169387
$981$	−18.6608	−0.595794
$982$	−51.3381	−1.63827
$983$	−34.7434	−1.10814	−0.554072	−	0.832469i	$-0.686927\pi$
$983$	−34.7434	−1.10814	−0.554072	+	0.832469i	$0.686927\pi$
$984$	−7.37664	−0.235159
$985$	20.4887	0.652823
$986$	−9.72075	−0.309572
$987$	10.6146	0.337867
$988$	−3.73219	−0.118737
$989$	−9.74812	−0.309972
$990$	−11.3621	−0.361110
$991$	14.5302	0.461566	0.230783	−	0.973005i	$-0.425871\pi$
$991$	14.5302	0.461566	0.230783	+	0.973005i	$0.425871\pi$
$992$	29.3082	0.930538
$993$	20.7708	0.659141
$994$	31.2480	0.991125
$995$	−0.880126	−0.0279019
$996$	11.0380	0.349751
$997$	37.6294	1.19173	0.595867	−	0.803083i	$-0.296809\pi$
$997$	37.6294	1.19173	0.595867	+	0.803083i	$0.296809\pi$
$998$	−73.6281	−2.33066
$999$	−10.2075	−0.322952

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.i.1.7	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.i.1.7	✓	25	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:	\( N \)	\(=\)	\( 4029 = 3 \cdot 17 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4029.a (trivial)

\(f(q)\)	\(=\)	\(q-1.65426 q^{2} -1.00000 q^{3} +0.736566 q^{4} +1.27876 q^{5} +1.65426 q^{6} +3.55385 q^{7} +2.09004 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.65426 q^{2} -1.00000 q^{3} +0.736566 q^{4} +1.27876 q^{5} +1.65426 q^{6} +3.55385 q^{7} +2.09004 q^{8} +1.00000 q^{9} -2.11539 q^{10} +5.37114 q^{11} -0.736566 q^{12} -4.08480 q^{13} -5.87897 q^{14} -1.27876 q^{15} -4.93060 q^{16} +1.00000 q^{17} -1.65426 q^{18} +1.24045 q^{19} +0.941888 q^{20} -3.55385 q^{21} -8.88525 q^{22} +1.93158 q^{23} -2.09004 q^{24} -3.36478 q^{25} +6.75731 q^{26} -1.00000 q^{27} +2.61764 q^{28} +5.87620 q^{29} +2.11539 q^{30} +7.37055 q^{31} +3.97640 q^{32} -5.37114 q^{33} -1.65426 q^{34} +4.54450 q^{35} +0.736566 q^{36} +10.2075 q^{37} -2.05203 q^{38} +4.08480 q^{39} +2.67266 q^{40} +3.52942 q^{41} +5.87897 q^{42} -5.04670 q^{43} +3.95620 q^{44} +1.27876 q^{45} -3.19534 q^{46} -2.98680 q^{47} +4.93060 q^{48} +5.62982 q^{49} +5.56622 q^{50} -1.00000 q^{51} -3.00873 q^{52} +3.75522 q^{53} +1.65426 q^{54} +6.86837 q^{55} +7.42769 q^{56} -1.24045 q^{57} -9.72075 q^{58} -8.54847 q^{59} -0.941888 q^{60} +12.8880 q^{61} -12.1928 q^{62} +3.55385 q^{63} +3.28322 q^{64} -5.22346 q^{65} +8.88525 q^{66} +14.8088 q^{67} +0.736566 q^{68} -1.93158 q^{69} -7.51777 q^{70} -5.31521 q^{71} +2.09004 q^{72} +2.95962 q^{73} -16.8859 q^{74} +3.36478 q^{75} +0.913677 q^{76} +19.0882 q^{77} -6.75731 q^{78} -1.00000 q^{79} -6.30504 q^{80} +1.00000 q^{81} -5.83857 q^{82} -14.9857 q^{83} -2.61764 q^{84} +1.27876 q^{85} +8.34854 q^{86} -5.87620 q^{87} +11.2259 q^{88} +8.66018 q^{89} -2.11539 q^{90} -14.5168 q^{91} +1.42274 q^{92} -7.37055 q^{93} +4.94094 q^{94} +1.58624 q^{95} -3.97640 q^{96} -13.4131 q^{97} -9.31316 q^{98} +5.37114 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 2 q^{2} - 25 q^{3} + 26 q^{4} - 2 q^{5} + 2 q^{6} + 12 q^{7} + 25 q^{9}+O(q^{10}) \) 25 * q - 2 * q^2 - 25 * q^3 + 26 * q^4 - 2 * q^5 + 2 * q^6 + 12 * q^7 + 25 * q^9	\( 25 q - 2 q^{2} - 25 q^{3} + 26 q^{4} - 2 q^{5} + 2 q^{6} + 12 q^{7} + 25 q^{9} + 19 q^{10} + 19 q^{11} - 26 q^{12} + 4 q^{13} + 15 q^{14} + 2 q^{15} + 32 q^{16} + 25 q^{17} - 2 q^{18} + 29 q^{19} - 8 q^{20} - 12 q^{21} + 23 q^{22} + 6 q^{23} + 15 q^{25} - 8 q^{26} - 25 q^{27} + 23 q^{28} + 11 q^{29} - 19 q^{30} + 38 q^{31} - 27 q^{32} - 19 q^{33} - 2 q^{34} + 20 q^{35} + 26 q^{36} + 8 q^{37} - 25 q^{38} - 4 q^{39} + 48 q^{40} + 24 q^{41} - 15 q^{42} + 11 q^{43} + 6 q^{44} - 2 q^{45} + 25 q^{46} + 23 q^{47} - 32 q^{48} + 21 q^{49} - 21 q^{50} - 25 q^{51} + 31 q^{52} - 16 q^{53} + 2 q^{54} - 11 q^{55} + 18 q^{56} - 29 q^{57} - 5 q^{58} + 27 q^{59} + 8 q^{60} + 40 q^{61} - 34 q^{62} + 12 q^{63} + 46 q^{64} - 19 q^{65} - 23 q^{66} + 24 q^{67} + 26 q^{68} - 6 q^{69} + 17 q^{70} + 19 q^{71} + 13 q^{73} - 56 q^{74} - 15 q^{75} + 21 q^{76} - 30 q^{77} + 8 q^{78} - 25 q^{79} - 40 q^{80} + 25 q^{81} + 61 q^{82} + q^{83} - 23 q^{84} - 2 q^{85} + 62 q^{86} - 11 q^{87} - q^{88} - 10 q^{89} + 19 q^{90} + 50 q^{91} + 18 q^{92} - 38 q^{93} + 15 q^{94} + 14 q^{95} + 27 q^{96} + 19 q^{97} - 23 q^{98} + 19 q^{99}+O(q^{100}) \) 25 * q - 2 * q^2 - 25 * q^3 + 26 * q^4 - 2 * q^5 + 2 * q^6 + 12 * q^7 + 25 * q^9 + 19 * q^10 + 19 * q^11 - 26 * q^12 + 4 * q^13 + 15 * q^14 + 2 * q^15 + 32 * q^16 + 25 * q^17 - 2 * q^18 + 29 * q^19 - 8 * q^20 - 12 * q^21 + 23 * q^22 + 6 * q^23 + 15 * q^25 - 8 * q^26 - 25 * q^27 + 23 * q^28 + 11 * q^29 - 19 * q^30 + 38 * q^31 - 27 * q^32 - 19 * q^33 - 2 * q^34 + 20 * q^35 + 26 * q^36 + 8 * q^37 - 25 * q^38 - 4 * q^39 + 48 * q^40 + 24 * q^41 - 15 * q^42 + 11 * q^43 + 6 * q^44 - 2 * q^45 + 25 * q^46 + 23 * q^47 - 32 * q^48 + 21 * q^49 - 21 * q^50 - 25 * q^51 + 31 * q^52 - 16 * q^53 + 2 * q^54 - 11 * q^55 + 18 * q^56 - 29 * q^57 - 5 * q^58 + 27 * q^59 + 8 * q^60 + 40 * q^61 - 34 * q^62 + 12 * q^63 + 46 * q^64 - 19 * q^65 - 23 * q^66 + 24 * q^67 + 26 * q^68 - 6 * q^69 + 17 * q^70 + 19 * q^71 + 13 * q^73 - 56 * q^74 - 15 * q^75 + 21 * q^76 - 30 * q^77 + 8 * q^78 - 25 * q^79 - 40 * q^80 + 25 * q^81 + 61 * q^82 + q^83 - 23 * q^84 - 2 * q^85 + 62 * q^86 - 11 * q^87 - q^88 - 10 * q^89 + 19 * q^90 + 50 * q^91 + 18 * q^92 - 38 * q^93 + 15 * q^94 + 14 * q^95 + 27 * q^96 + 19 * q^97 - 23 * q^98 + 19 * q^99

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