LMFDB - Embedded newform 4029.2.a.h.1.18

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:	$1$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
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)

$f(q)$	$=$	$q+1.22160 q^{2} +1.00000 q^{3} -0.507691 q^{4} -3.76998 q^{5} +1.22160 q^{6} +4.22641 q^{7} -3.06340 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.22160 q^{2} +1.00000 q^{3} -0.507691 q^{4} -3.76998 q^{5} +1.22160 q^{6} +4.22641 q^{7} -3.06340 q^{8} +1.00000 q^{9} -4.60542 q^{10} -0.926807 q^{11} -0.507691 q^{12} -0.973822 q^{13} +5.16298 q^{14} -3.76998 q^{15} -2.72687 q^{16} -1.00000 q^{17} +1.22160 q^{18} +5.44996 q^{19} +1.91398 q^{20} +4.22641 q^{21} -1.13219 q^{22} -3.87975 q^{23} -3.06340 q^{24} +9.21277 q^{25} -1.18962 q^{26} +1.00000 q^{27} -2.14571 q^{28} -7.00406 q^{29} -4.60542 q^{30} +7.86292 q^{31} +2.79565 q^{32} -0.926807 q^{33} -1.22160 q^{34} -15.9335 q^{35} -0.507691 q^{36} -4.19584 q^{37} +6.65768 q^{38} -0.973822 q^{39} +11.5490 q^{40} -2.25934 q^{41} +5.16298 q^{42} -11.6237 q^{43} +0.470531 q^{44} -3.76998 q^{45} -4.73951 q^{46} -9.80670 q^{47} -2.72687 q^{48} +10.8625 q^{49} +11.2543 q^{50} -1.00000 q^{51} +0.494400 q^{52} -2.26151 q^{53} +1.22160 q^{54} +3.49405 q^{55} -12.9472 q^{56} +5.44996 q^{57} -8.55617 q^{58} +2.43661 q^{59} +1.91398 q^{60} -5.97462 q^{61} +9.60535 q^{62} +4.22641 q^{63} +8.86891 q^{64} +3.67129 q^{65} -1.13219 q^{66} -9.34093 q^{67} +0.507691 q^{68} -3.87975 q^{69} -19.4644 q^{70} +5.68137 q^{71} -3.06340 q^{72} +0.0654276 q^{73} -5.12564 q^{74} +9.21277 q^{75} -2.76689 q^{76} -3.91706 q^{77} -1.18962 q^{78} +1.00000 q^{79} +10.2802 q^{80} +1.00000 q^{81} -2.76001 q^{82} -13.8310 q^{83} -2.14571 q^{84} +3.76998 q^{85} -14.1996 q^{86} -7.00406 q^{87} +2.83918 q^{88} -6.48358 q^{89} -4.60542 q^{90} -4.11576 q^{91} +1.96971 q^{92} +7.86292 q^{93} -11.9799 q^{94} -20.5463 q^{95} +2.79565 q^{96} -0.189600 q^{97} +13.2696 q^{98} -0.926807 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - 7 q^{2} + 25 q^{3} + 21 q^{4} - 12 q^{5} - 7 q^{6} - 4 q^{7} - 21 q^{8} + 25 q^{9}+O(q^{10}) $ 25 * q - 7 * q^2 + 25 * q^3 + 21 * q^4 - 12 * q^5 - 7 * q^6 - 4 * q^7 - 21 * q^8 + 25 * q^9	\( 25 q - 7 q^{2} + 25 q^{3} + 21 q^{4} - 12 q^{5} - 7 q^{6} - 4 q^{7} - 21 q^{8} + 25 q^{9} - 9 q^{10} - 19 q^{11} + 21 q^{12} - 12 q^{13} - 15 q^{14} - 12 q^{15} + q^{16} - 25 q^{17} - 7 q^{18} - 35 q^{19} - 11 q^{20} - 4 q^{21} - 2 q^{22} - 16 q^{23} - 21 q^{24} + 19 q^{25} - 5 q^{26} + 25 q^{27} + 3 q^{28} - 37 q^{29} - 9 q^{30} - 28 q^{31} - 19 q^{32} - 19 q^{33} + 7 q^{34} - 42 q^{35} + 21 q^{36} + 8 q^{37} - 35 q^{38} - 12 q^{39} - 9 q^{40} - 34 q^{41} - 15 q^{42} - 19 q^{43} - 56 q^{44} - 12 q^{45} + q^{46} - 25 q^{47} + q^{48} + 25 q^{49} - 7 q^{50} - 25 q^{51} - 37 q^{52} - 44 q^{53} - 7 q^{54} - 11 q^{55} - 18 q^{56} - 35 q^{57} - 3 q^{58} - 47 q^{59} - 11 q^{60} - 28 q^{61} + 11 q^{62} - 4 q^{63} - 9 q^{64} - 63 q^{65} - 2 q^{66} - 28 q^{67} - 21 q^{68} - 16 q^{69} + 5 q^{70} - 27 q^{71} - 21 q^{72} - 21 q^{73} - 18 q^{74} + 19 q^{75} - 50 q^{76} - 58 q^{77} - 5 q^{78} + 25 q^{79} - 56 q^{80} + 25 q^{81} - 5 q^{82} - 61 q^{83} + 3 q^{84} + 12 q^{85} - 28 q^{86} - 37 q^{87} + 15 q^{88} - 34 q^{89} - 9 q^{90} - 30 q^{91} - 31 q^{92} - 28 q^{93} + q^{94} - 32 q^{95} - 19 q^{96} - 11 q^{97} - 66 q^{98} - 19 q^{99}+O(q^{100}) \) 25 * q - 7 * q^2 + 25 * q^3 + 21 * q^4 - 12 * q^5 - 7 * q^6 - 4 * q^7 - 21 * q^8 + 25 * q^9 - 9 * q^10 - 19 * q^11 + 21 * q^12 - 12 * q^13 - 15 * q^14 - 12 * q^15 + q^16 - 25 * q^17 - 7 * q^18 - 35 * q^19 - 11 * q^20 - 4 * q^21 - 2 * q^22 - 16 * q^23 - 21 * q^24 + 19 * q^25 - 5 * q^26 + 25 * q^27 + 3 * q^28 - 37 * q^29 - 9 * q^30 - 28 * q^31 - 19 * q^32 - 19 * q^33 + 7 * q^34 - 42 * q^35 + 21 * q^36 + 8 * q^37 - 35 * q^38 - 12 * q^39 - 9 * q^40 - 34 * q^41 - 15 * q^42 - 19 * q^43 - 56 * q^44 - 12 * q^45 + q^46 - 25 * q^47 + q^48 + 25 * q^49 - 7 * q^50 - 25 * q^51 - 37 * q^52 - 44 * q^53 - 7 * q^54 - 11 * q^55 - 18 * q^56 - 35 * q^57 - 3 * q^58 - 47 * q^59 - 11 * q^60 - 28 * q^61 + 11 * q^62 - 4 * q^63 - 9 * q^64 - 63 * q^65 - 2 * q^66 - 28 * q^67 - 21 * q^68 - 16 * q^69 + 5 * q^70 - 27 * q^71 - 21 * q^72 - 21 * q^73 - 18 * q^74 + 19 * q^75 - 50 * q^76 - 58 * q^77 - 5 * q^78 + 25 * q^79 - 56 * q^80 + 25 * q^81 - 5 * q^82 - 61 * q^83 + 3 * q^84 + 12 * q^85 - 28 * q^86 - 37 * q^87 + 15 * q^88 - 34 * q^89 - 9 * q^90 - 30 * q^91 - 31 * q^92 - 28 * q^93 + q^94 - 32 * q^95 - 19 * q^96 - 11 * q^97 - 66 * 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 $

$2$	1.22160	0.863802	0.431901	−	0.901921i	$-0.357843\pi$
$2$	1.22160	0.863802	0.431901	+	0.901921i	$0.357843\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.507691	−0.253845
$5$	−3.76998	−1.68599	−0.842994	−	0.537923i	$-0.819209\pi$
$5$	−3.76998	−1.68599	−0.842994	+	0.537923i	$0.819209\pi$
$6$	1.22160	0.498717
$7$	4.22641	1.59743	0.798716	−	0.601709i	$-0.205513\pi$
$7$	4.22641	1.59743	0.798716	+	0.601709i	$0.205513\pi$
$8$	−3.06340	−1.08307
$9$	1.00000	0.333333
$10$	−4.60542	−1.45636
$11$	−0.926807	−0.279443	−0.139721	−	0.990191i	$-0.544621\pi$
$11$	−0.926807	−0.279443	−0.139721	+	0.990191i	$0.544621\pi$
$12$	−0.507691	−0.146558
$13$	−0.973822	−0.270090	−0.135045	−	0.990839i	$-0.543118\pi$
$13$	−0.973822	−0.270090	−0.135045	+	0.990839i	$0.543118\pi$
$14$	5.16298	1.37986
$15$	−3.76998	−0.973405
$16$	−2.72687	−0.681717
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	1.22160	0.287934
$19$	5.44996	1.25031	0.625154	−	0.780502i	$-0.285036\pi$
$19$	5.44996	1.25031	0.625154	+	0.780502i	$0.285036\pi$
$20$	1.91398	0.427980
$21$	4.22641	0.922277
$22$	−1.13219	−0.241383
$23$	−3.87975	−0.808984	−0.404492	−	0.914542i	$-0.632552\pi$
$23$	−3.87975	−0.808984	−0.404492	+	0.914542i	$0.632552\pi$
$24$	−3.06340	−0.625313
$25$	9.21277	1.84255
$26$	−1.18962	−0.233304
$27$	1.00000	0.192450
$28$	−2.14571	−0.405500
$29$	−7.00406	−1.30062	−0.650311	−	0.759668i	$-0.725361\pi$
$29$	−7.00406	−1.30062	−0.650311	+	0.759668i	$0.725361\pi$
$30$	−4.60542	−0.840830
$31$	7.86292	1.41222	0.706111	−	0.708101i	$-0.250448\pi$
$31$	7.86292	1.41222	0.706111	+	0.708101i	$0.250448\pi$
$32$	2.79565	0.494206
$33$	−0.926807	−0.161336
$34$	−1.22160	−0.209503
$35$	−15.9335	−2.69325
$36$	−0.507691	−0.0846151
$37$	−4.19584	−0.689792	−0.344896	−	0.938641i	$-0.612086\pi$
$37$	−4.19584	−0.689792	−0.344896	+	0.938641i	$0.612086\pi$
$38$	6.65768	1.08002
$39$	−0.973822	−0.155936
$40$	11.5490	1.82605
$41$	−2.25934	−0.352850	−0.176425	−	0.984314i	$-0.556453\pi$
$41$	−2.25934	−0.352850	−0.176425	+	0.984314i	$0.556453\pi$
$42$	5.16298	0.796665
$43$	−11.6237	−1.77260	−0.886302	−	0.463107i	$-0.846735\pi$
$43$	−11.6237	−1.77260	−0.886302	+	0.463107i	$0.846735\pi$
$44$	0.470531	0.0709352
$45$	−3.76998	−0.561996
$46$	−4.73951	−0.698802
$47$	−9.80670	−1.43045	−0.715227	−	0.698892i	$-0.753677\pi$
$47$	−9.80670	−1.43045	−0.715227	+	0.698892i	$0.753677\pi$
$48$	−2.72687	−0.393590
$49$	10.8625	1.55179
$50$	11.2543	1.59160
$51$	−1.00000	−0.140028
$52$	0.494400	0.0685609
$53$	−2.26151	−0.310643	−0.155321	−	0.987864i	$-0.549641\pi$
$53$	−2.26151	−0.310643	−0.155321	+	0.987864i	$0.549641\pi$
$54$	1.22160	0.166239
$55$	3.49405	0.471137
$56$	−12.9472	−1.73014
$57$	5.44996	0.721865
$58$	−8.55617	−1.12348
$59$	2.43661	0.317219	0.158610	−	0.987341i	$-0.449299\pi$
$59$	2.43661	0.317219	0.158610	+	0.987341i	$0.449299\pi$
$60$	1.91398	0.247094
$61$	−5.97462	−0.764972	−0.382486	−	0.923961i	$-0.624932\pi$
$61$	−5.97462	−0.764972	−0.382486	+	0.923961i	$0.624932\pi$
$62$	9.60535	1.21988
$63$	4.22641	0.532477
$64$	8.86891	1.10861
$65$	3.67129	0.455368
$66$	−1.13219	−0.139363
$67$	−9.34093	−1.14118	−0.570588	−	0.821236i	$-0.693285\pi$
$67$	−9.34093	−1.14118	−0.570588	+	0.821236i	$0.693285\pi$
$68$	0.507691	0.0615665
$69$	−3.87975	−0.467067
$70$	−19.4644	−2.32643
$71$	5.68137	0.674254	0.337127	−	0.941459i	$-0.390545\pi$
$71$	5.68137	0.674254	0.337127	+	0.941459i	$0.390545\pi$
$72$	−3.06340	−0.361025
$73$	0.0654276	0.00765772	0.00382886	−	0.999993i	$-0.498781\pi$
$73$	0.0654276	0.00765772	0.00382886	+	0.999993i	$0.498781\pi$
$74$	−5.12564	−0.595844
$75$	9.21277	1.06380
$76$	−2.76689	−0.317385
$77$	−3.91706	−0.446391
$78$	−1.18962	−0.134698
$79$	1.00000	0.112509
$79$	1.00000	0.112509
$80$	10.2802	1.14937
$81$	1.00000	0.111111
$82$	−2.76001	−0.304793
$83$	−13.8310	−1.51815	−0.759076	−	0.651002i	$-0.774349\pi$
$83$	−13.8310	−1.51815	−0.759076	+	0.651002i	$0.774349\pi$
$84$	−2.14571	−0.234116
$85$	3.76998	0.408912
$86$	−14.1996	−1.53118
$87$	−7.00406	−0.750914
$88$	2.83918	0.302657
$89$	−6.48358	−0.687258	−0.343629	−	0.939105i	$-0.611656\pi$
$89$	−6.48358	−0.687258	−0.343629	+	0.939105i	$0.611656\pi$
$90$	−4.60542	−0.485453
$91$	−4.11576	−0.431449
$92$	1.96971	0.205357
$93$	7.86292	0.815347
$94$	−11.9799	−1.23563
$95$	−20.5463	−2.10800
$96$	2.79565	0.285330
$97$	−0.189600	−0.0192509	−0.00962547	−	0.999954i	$-0.503064\pi$
$97$	−0.189600	−0.0192509	−0.00962547	+	0.999954i	$0.503064\pi$
$98$	13.2696	1.34044
$99$	−0.926807	−0.0931476
$100$	−4.67724	−0.467724
$101$	7.58361	0.754598	0.377299	−	0.926092i	$-0.376853\pi$
$101$	7.58361	0.754598	0.377299	+	0.926092i	$0.376853\pi$
$102$	−1.22160	−0.120957
$103$	−12.7484	−1.25613	−0.628067	−	0.778159i	$-0.716154\pi$
$103$	−12.7484	−1.25613	−0.628067	+	0.778159i	$0.716154\pi$
$104$	2.98320	0.292527
$105$	−15.9335	−1.55495
$106$	−2.76267	−0.268334
$107$	3.47455	0.335897	0.167949	−	0.985796i	$-0.446286\pi$
$107$	3.47455	0.335897	0.167949	+	0.985796i	$0.446286\pi$
$108$	−0.507691	−0.0488525
$109$	−16.5775	−1.58783	−0.793916	−	0.608027i	$-0.791961\pi$
$109$	−16.5775	−1.58783	−0.793916	+	0.608027i	$0.791961\pi$
$110$	4.26833	0.406969
$111$	−4.19584	−0.398252
$112$	−11.5249	−1.08900
$113$	−16.0299	−1.50797	−0.753985	−	0.656891i	$-0.771871\pi$
$113$	−16.0299	−1.50797	−0.753985	+	0.656891i	$0.771871\pi$
$114$	6.65768	0.623549
$115$	14.6266	1.36394
$116$	3.55590	0.330157
$117$	−0.973822	−0.0900298
$118$	2.97656	0.274015
$119$	−4.22641	−0.387434
$120$	11.5490	1.05427
$121$	−10.1410	−0.921912
$122$	−7.29860	−0.660784
$123$	−2.25934	−0.203718
$124$	−3.99193	−0.358486
$125$	−15.8821	−1.42054
$126$	5.16298	0.459955
$127$	15.5489	1.37975	0.689873	−	0.723930i	$-0.257666\pi$
$127$	15.5489	1.37975	0.689873	+	0.723930i	$0.257666\pi$
$128$	5.24297	0.463417
$129$	−11.6237	−1.02341
$130$	4.48485	0.393348
$131$	−7.72590	−0.675015	−0.337507	−	0.941323i	$-0.609584\pi$
$131$	−7.72590	−0.675015	−0.337507	+	0.941323i	$0.609584\pi$
$132$	0.470531	0.0409545
$133$	23.0337	1.99728
$134$	−11.4109	−0.985751
$135$	−3.76998	−0.324468
$136$	3.06340	0.262684
$137$	4.84982	0.414348	0.207174	−	0.978304i	$-0.433573\pi$
$137$	4.84982	0.414348	0.207174	+	0.978304i	$0.433573\pi$
$138$	−4.73951	−0.403454
$139$	−4.53289	−0.384474	−0.192237	−	0.981348i	$-0.561574\pi$
$139$	−4.53289	−0.384474	−0.192237	+	0.981348i	$0.561574\pi$
$140$	8.08927	0.683668
$141$	−9.80670	−0.825873
$142$	6.94037	0.582423
$143$	0.902545	0.0754746
$144$	−2.72687	−0.227239
$145$	26.4052	2.19283
$146$	0.0799264	0.00661476
$147$	10.8625	0.895924
$148$	2.13019	0.175100
$149$	−16.1679	−1.32452	−0.662262	−	0.749272i	$-0.730403\pi$
$149$	−16.1679	−1.32452	−0.662262	+	0.749272i	$0.730403\pi$
$150$	11.2543	0.918912
$151$	−7.03262	−0.572307	−0.286153	−	0.958184i	$-0.592377\pi$
$151$	−7.03262	−0.572307	−0.286153	+	0.958184i	$0.592377\pi$
$152$	−16.6954	−1.35418
$153$	−1.00000	−0.0808452
$154$	−4.78509	−0.385593
$155$	−29.6431	−2.38099
$156$	0.494400	0.0395837
$157$	4.76162	0.380018	0.190009	−	0.981782i	$-0.439148\pi$
$157$	4.76162	0.380018	0.190009	+	0.981782i	$0.439148\pi$
$158$	1.22160	0.0971854
$159$	−2.26151	−0.179350
$160$	−10.5395	−0.833224
$161$	−16.3974	−1.29230
$162$	1.22160	0.0959781
$163$	15.8906	1.24465	0.622324	−	0.782760i	$-0.286189\pi$
$163$	15.8906	1.24465	0.622324	+	0.782760i	$0.286189\pi$
$164$	1.14705	0.0895692
$165$	3.49405	0.272011
$166$	−16.8960	−1.31138
$167$	12.5382	0.970233	0.485117	−	0.874450i	$-0.338777\pi$
$167$	12.5382	0.970233	0.485117	+	0.874450i	$0.338777\pi$
$168$	−12.9472	−0.998895
$169$	−12.0517	−0.927052
$170$	4.60542	0.353219
$171$	5.44996	0.416769
$172$	5.90127	0.449967
$173$	18.7020	1.42189	0.710945	−	0.703248i	$-0.248268\pi$
$173$	18.7020	1.42189	0.710945	+	0.703248i	$0.248268\pi$
$174$	−8.55617	−0.648642
$175$	38.9369	2.94335
$176$	2.52728	0.190501
$177$	2.43661	0.183147
$178$	−7.92035	−0.593655
$179$	14.6450	1.09462	0.547309	−	0.836930i	$-0.315652\pi$
$179$	14.6450	1.09462	0.547309	+	0.836930i	$0.315652\pi$
$180$	1.91398	0.142660
$181$	−10.2028	−0.758367	−0.379184	−	0.925321i	$-0.623795\pi$
$181$	−10.2028	−0.758367	−0.379184	+	0.925321i	$0.623795\pi$
$182$	−5.02782	−0.372687
$183$	−5.97462	−0.441657
$184$	11.8852	0.876190
$185$	15.8182	1.16298
$186$	9.60535	0.704299
$187$	0.926807	0.0677749
$188$	4.97877	0.363114
$189$	4.22641	0.307426
$190$	−25.0993	−1.82090
$191$	−0.166071	−0.0120165	−0.00600825	−	0.999982i	$-0.501912\pi$
$191$	−0.166071	−0.0120165	−0.00600825	+	0.999982i	$0.501912\pi$
$192$	8.86891	0.640058
$193$	−7.01744	−0.505126	−0.252563	−	0.967580i	$-0.581274\pi$
$193$	−7.01744	−0.505126	−0.252563	+	0.967580i	$0.581274\pi$
$194$	−0.231615	−0.0166290
$195$	3.67129	0.262907
$196$	−5.51479	−0.393913
$197$	11.0238	0.785414	0.392707	−	0.919664i	$-0.371539\pi$
$197$	11.0238	0.785414	0.392707	+	0.919664i	$0.371539\pi$
$198$	−1.13219	−0.0804612
$199$	7.95657	0.564026	0.282013	−	0.959411i	$-0.408998\pi$
$199$	7.95657	0.564026	0.282013	+	0.959411i	$0.408998\pi$
$200$	−28.2224	−1.99562
$201$	−9.34093	−0.658859
$202$	9.26415	0.651823
$203$	−29.6020	−2.07765
$204$	0.507691	0.0355454
$205$	8.51768	0.594900
$206$	−15.5734	−1.08505
$207$	−3.87975	−0.269661
$208$	2.65548	0.184125
$209$	−5.05106	−0.349389
$210$	−19.4644	−1.34317
$211$	−7.85899	−0.541035	−0.270518	−	0.962715i	$-0.587195\pi$
$211$	−7.85899	−0.541035	−0.270518	+	0.962715i	$0.587195\pi$
$212$	1.14815	0.0788551
$213$	5.68137	0.389281
$214$	4.24451	0.290149
$215$	43.8213	2.98859
$216$	−3.06340	−0.208438
$217$	33.2319	2.25593
$218$	−20.2510	−1.37157
$219$	0.0654276	0.00442119
$220$	−1.77389	−0.119596
$221$	0.973822	0.0655063
$222$	−5.12564	−0.344011
$223$	−4.35903	−0.291902	−0.145951	−	0.989292i	$-0.546624\pi$
$223$	−4.35903	−0.291902	−0.145951	+	0.989292i	$0.546624\pi$
$224$	11.8155	0.789459
$225$	9.21277	0.614185
$226$	−19.5822	−1.30259
$227$	−18.0285	−1.19659	−0.598297	−	0.801274i	$-0.704156\pi$
$227$	−18.0285	−1.19659	−0.598297	+	0.801274i	$0.704156\pi$
$228$	−2.76689	−0.183242
$229$	9.91739	0.655359	0.327680	−	0.944789i	$-0.393733\pi$
$229$	9.91739	0.655359	0.327680	+	0.944789i	$0.393733\pi$
$230$	17.8679	1.17817
$231$	−3.91706	−0.257724
$232$	21.4562	1.40867
$233$	−26.7704	−1.75379	−0.876893	−	0.480685i	$-0.840388\pi$
$233$	−26.7704	−1.75379	−0.876893	+	0.480685i	$0.840388\pi$
$234$	−1.18962	−0.0777680
$235$	36.9711	2.41173
$236$	−1.23704	−0.0805246
$237$	1.00000	0.0649570
$238$	−5.16298	−0.334666
$239$	14.4305	0.933432	0.466716	−	0.884407i	$-0.345437\pi$
$239$	14.4305	0.933432	0.466716	+	0.884407i	$0.345437\pi$
$240$	10.2802	0.663587
$241$	−22.4439	−1.44574	−0.722870	−	0.690984i	$-0.757178\pi$
$241$	−22.4439	−1.44574	−0.722870	+	0.690984i	$0.757178\pi$
$242$	−12.3883	−0.796350
$243$	1.00000	0.0641500
$244$	3.03326	0.194184
$245$	−40.9514	−2.61629
$246$	−2.76001	−0.175972
$247$	−5.30729	−0.337695
$248$	−24.0872	−1.52954
$249$	−13.8310	−0.876505
$250$	−19.4016	−1.22706
$251$	−4.57663	−0.288874	−0.144437	−	0.989514i	$-0.546137\pi$
$251$	−4.57663	−0.288874	−0.144437	+	0.989514i	$0.546137\pi$
$252$	−2.14571	−0.135167
$253$	3.59578	0.226065
$254$	18.9946	1.19183
$255$	3.76998	0.236085
$256$	−11.3330	−0.708312
$257$	11.6528	0.726883	0.363441	−	0.931617i	$-0.381602\pi$
$257$	11.6528	0.726883	0.363441	+	0.931617i	$0.381602\pi$
$258$	−14.1996	−0.884027
$259$	−17.7333	−1.10190
$260$	−1.86388	−0.115593
$261$	−7.00406	−0.433541
$262$	−9.43797	−0.583080
$263$	8.01900	0.494473	0.247236	−	0.968955i	$-0.420478\pi$
$263$	8.01900	0.494473	0.247236	+	0.968955i	$0.420478\pi$
$264$	2.83918	0.174739
$265$	8.52586	0.523739
$266$	28.1381	1.72525
$267$	−6.48358	−0.396789
$268$	4.74230	0.289682
$269$	6.18454	0.377078	0.188539	−	0.982066i	$-0.439625\pi$
$269$	6.18454	0.377078	0.188539	+	0.982066i	$0.439625\pi$
$270$	−4.60542	−0.280277
$271$	24.0576	1.46139	0.730697	−	0.682702i	$-0.239195\pi$
$271$	24.0576	1.46139	0.730697	+	0.682702i	$0.239195\pi$
$272$	2.72687	0.165341
$273$	−4.11576	−0.249097
$274$	5.92455	0.357915
$275$	−8.53846	−0.514889
$276$	1.96971	0.118563
$277$	14.2515	0.856290	0.428145	−	0.903710i	$-0.359167\pi$
$277$	14.2515	0.856290	0.428145	+	0.903710i	$0.359167\pi$
$278$	−5.53738	−0.332110
$279$	7.86292	0.470741
$280$	48.8106	2.91699
$281$	−24.0167	−1.43272	−0.716359	−	0.697732i	$-0.754193\pi$
$281$	−24.0167	−1.43272	−0.716359	+	0.697732i	$0.754193\pi$
$282$	−11.9799	−0.713391
$283$	20.3539	1.20992	0.604958	−	0.796258i	$-0.293190\pi$
$283$	20.3539	1.20992	0.604958	+	0.796258i	$0.293190\pi$
$284$	−2.88438	−0.171156
$285$	−20.5463	−1.21706
$286$	1.10255	0.0651951
$287$	−9.54889	−0.563653
$288$	2.79565	0.164735
$289$	1.00000	0.0588235
$290$	32.2566	1.89417
$291$	−0.189600	−0.0111145
$292$	−0.0332170	−0.00194388
$293$	−0.279313	−0.0163177	−0.00815883	−	0.999967i	$-0.502597\pi$
$293$	−0.279313	−0.0163177	−0.00815883	+	0.999967i	$0.502597\pi$
$294$	13.2696	0.773901
$295$	−9.18597	−0.534828
$296$	12.8535	0.747096
$297$	−0.926807	−0.0537788
$298$	−19.7507	−1.14413
$299$	3.77818	0.218498
$300$	−4.67724	−0.270040
$301$	−49.1267	−2.83161
$302$	−8.59106	−0.494360
$303$	7.58361	0.435667
$304$	−14.8613	−0.852356
$305$	22.5242	1.28973
$306$	−1.22160	−0.0698343
$307$	−22.9294	−1.30865	−0.654325	−	0.756213i	$-0.727047\pi$
$307$	−22.9294	−1.30865	−0.654325	+	0.756213i	$0.727047\pi$
$308$	1.98866	0.113314
$309$	−12.7484	−0.725229
$310$	−36.2120	−2.05670
$311$	10.2435	0.580857	0.290429	−	0.956897i	$-0.406202\pi$
$311$	10.2435	0.580857	0.290429	+	0.956897i	$0.406202\pi$
$312$	2.98320	0.168891
$313$	−13.3393	−0.753983	−0.376992	−	0.926217i	$-0.623041\pi$
$313$	−13.3393	−0.753983	−0.376992	+	0.926217i	$0.623041\pi$
$314$	5.81680	0.328261
$315$	−15.9335	−0.897750
$316$	−0.507691	−0.0285598
$317$	26.6198	1.49512	0.747558	−	0.664197i	$-0.231226\pi$
$317$	26.6198	1.49512	0.747558	+	0.664197i	$0.231226\pi$
$318$	−2.76267	−0.154923
$319$	6.49142	0.363450
$320$	−33.4356	−1.86911
$321$	3.47455	0.193930
$322$	−20.0311	−1.11629
$323$	−5.44996	−0.303244
$324$	−0.507691	−0.0282050
$325$	−8.97159	−0.497654
$326$	19.4120	1.07513
$327$	−16.5775	−0.916736
$328$	6.92126	0.382163
$329$	−41.4471	−2.28505
$330$	4.26833	0.234964
$331$	4.64650	0.255395	0.127697	−	0.991813i	$-0.459241\pi$
$331$	4.64650	0.255395	0.127697	+	0.991813i	$0.459241\pi$
$332$	7.02188	0.385376
$333$	−4.19584	−0.229931
$334$	15.3166	0.838090
$335$	35.2152	1.92401
$336$	−11.5249	−0.628732
$337$	−20.7332	−1.12941	−0.564705	−	0.825293i	$-0.691010\pi$
$337$	−20.7332	−1.12941	−0.564705	+	0.825293i	$0.691010\pi$
$338$	−14.7223	−0.800790
$339$	−16.0299	−0.870627
$340$	−1.91398	−0.103800
$341$	−7.28741	−0.394635
$342$	6.65768	0.360006
$343$	16.3245	0.881440
$344$	35.6082	1.91986
$345$	14.6266	0.787469
$346$	22.8464	1.22823
$347$	16.1041	0.864513	0.432256	−	0.901751i	$-0.357718\pi$
$347$	16.1041	0.864513	0.432256	+	0.901751i	$0.357718\pi$
$348$	3.55590	0.190616
$349$	−7.36058	−0.394003	−0.197001	−	0.980403i	$-0.563120\pi$
$349$	−7.36058	−0.394003	−0.197001	+	0.980403i	$0.563120\pi$
$350$	47.5654	2.54248
$351$	−0.973822	−0.0519788
$352$	−2.59103	−0.138102
$353$	30.8360	1.64123	0.820617	−	0.571478i	$-0.193630\pi$
$353$	30.8360	1.64123	0.820617	+	0.571478i	$0.193630\pi$
$354$	2.97656	0.158203
$355$	−21.4187	−1.13678
$356$	3.29165	0.174457
$357$	−4.22641	−0.223685
$358$	17.8904	0.945535
$359$	24.5261	1.29444	0.647219	−	0.762304i	$-0.275932\pi$
$359$	24.5261	1.29444	0.647219	+	0.762304i	$0.275932\pi$
$360$	11.5490	0.608683
$361$	10.7021	0.563268
$362$	−12.4637	−0.655080
$363$	−10.1410	−0.532266
$364$	2.08953	0.109521
$365$	−0.246661	−0.0129108
$366$	−7.29860	−0.381504
$367$	7.14426	0.372927	0.186464	−	0.982462i	$-0.440297\pi$
$367$	7.14426	0.372927	0.186464	+	0.982462i	$0.440297\pi$
$368$	10.5796	0.551498
$369$	−2.25934	−0.117617
$370$	19.3236	1.00459
$371$	−9.55807	−0.496230
$372$	−3.99193	−0.206972
$373$	−23.8117	−1.23293	−0.616463	−	0.787384i	$-0.711435\pi$
$373$	−23.8117	−1.23293	−0.616463	+	0.787384i	$0.711435\pi$
$374$	1.13219	0.0585441
$375$	−15.8821	−0.820146
$376$	30.0418	1.54929
$377$	6.82071	0.351284
$378$	5.16298	0.265555
$379$	−34.3264	−1.76323	−0.881614	−	0.471971i	$-0.843543\pi$
$379$	−34.3264	−1.76323	−0.881614	+	0.471971i	$0.843543\pi$
$380$	10.4311	0.535106
$381$	15.5489	0.796597
$382$	−0.202873	−0.0103799
$383$	−17.2522	−0.881547	−0.440773	−	0.897618i	$-0.645296\pi$
$383$	−17.2522	−0.881547	−0.440773	+	0.897618i	$0.645296\pi$
$384$	5.24297	0.267554
$385$	14.7673	0.752609
$386$	−8.57251	−0.436329
$387$	−11.6237	−0.590868
$388$	0.0962580	0.00488676
$389$	−13.7826	−0.698806	−0.349403	−	0.936972i	$-0.613616\pi$
$389$	−13.7826	−0.698806	−0.349403	+	0.936972i	$0.613616\pi$
$390$	4.48485	0.227099
$391$	3.87975	0.196207
$392$	−33.2762	−1.68070
$393$	−7.72590	−0.389720
$394$	13.4667	0.678442
$395$	−3.76998	−0.189688
$396$	0.470531	0.0236451
$397$	−21.7418	−1.09119	−0.545596	−	0.838048i	$-0.683697\pi$
$397$	−21.7418	−1.09119	−0.545596	+	0.838048i	$0.683697\pi$
$398$	9.71975	0.487207
$399$	23.0337	1.15313
$400$	−25.1220	−1.25610
$401$	32.5696	1.62645	0.813223	−	0.581952i	$-0.197711\pi$
$401$	32.5696	1.62645	0.813223	+	0.581952i	$0.197711\pi$
$402$	−11.4109	−0.569124
$403$	−7.65708	−0.381426
$404$	−3.85013	−0.191551
$405$	−3.76998	−0.187332
$406$	−36.1619	−1.79468
$407$	3.88874	0.192757
$408$	3.06340	0.151661
$409$	−7.23185	−0.357592	−0.178796	−	0.983886i	$-0.557220\pi$
$409$	−7.23185	−0.357592	−0.178796	+	0.983886i	$0.557220\pi$
$410$	10.4052	0.513876
$411$	4.84982	0.239224
$412$	6.47223	0.318864
$413$	10.2981	0.506736
$414$	−4.73951	−0.232934
$415$	52.1427	2.55958
$416$	−2.72246	−0.133480
$417$	−4.53289	−0.221976
$418$	−6.17039	−0.301803
$419$	29.0425	1.41882	0.709410	−	0.704796i	$-0.248962\pi$
$419$	29.0425	1.41882	0.709410	+	0.704796i	$0.248962\pi$
$420$	8.08927	0.394716
$421$	−11.2058	−0.546138	−0.273069	−	0.961994i	$-0.588039\pi$
$421$	−11.2058	−0.546138	−0.273069	+	0.961994i	$0.588039\pi$
$422$	−9.60055	−0.467348
$423$	−9.80670	−0.476818
$424$	6.92791	0.336449
$425$	−9.21277	−0.446885
$426$	6.94037	0.336262
$427$	−25.2512	−1.22199
$428$	−1.76399	−0.0852659
$429$	0.902545	0.0435753
$430$	53.5322	2.58155
$431$	−9.43447	−0.454442	−0.227221	−	0.973843i	$-0.572964\pi$
$431$	−9.43447	−0.454442	−0.227221	+	0.973843i	$0.572964\pi$
$432$	−2.72687	−0.131197
$433$	8.99450	0.432248	0.216124	−	0.976366i	$-0.430658\pi$
$433$	8.99450	0.432248	0.216124	+	0.976366i	$0.430658\pi$
$434$	40.5961	1.94868
$435$	26.4052	1.26603
$436$	8.41622	0.403064
$437$	−21.1445	−1.01148
$438$	0.0799264	0.00381903
$439$	17.0957	0.815935	0.407967	−	0.912997i	$-0.366238\pi$
$439$	17.0957	0.815935	0.407967	+	0.912997i	$0.366238\pi$
$440$	−10.7037	−0.510277
$441$	10.8625	0.517262
$442$	1.18962	0.0565845
$443$	30.5815	1.45297	0.726487	−	0.687181i	$-0.241152\pi$
$443$	30.5815	1.45297	0.726487	+	0.687181i	$0.241152\pi$
$444$	2.13019	0.101094
$445$	24.4430	1.15871
$446$	−5.32500	−0.252146
$447$	−16.1679	−0.764714
$448$	37.4836	1.77093
$449$	−28.9664	−1.36701	−0.683504	−	0.729947i	$-0.739545\pi$
$449$	−28.9664	−1.36701	−0.683504	+	0.729947i	$0.739545\pi$
$450$	11.2543	0.530534
$451$	2.09397	0.0986014
$452$	8.13825	0.382791
$453$	−7.03262	−0.330421
$454$	−22.0237	−1.03362
$455$	15.5164	0.727418
$456$	−16.6954	−0.781834
$457$	34.0525	1.59291	0.796456	−	0.604697i	$-0.206706\pi$
$457$	34.0525	1.59291	0.796456	+	0.604697i	$0.206706\pi$
$458$	12.1151	0.566101
$459$	−1.00000	−0.0466760
$460$	−7.42578	−0.346229
$461$	−1.55379	−0.0723670	−0.0361835	−	0.999345i	$-0.511520\pi$
$461$	−1.55379	−0.0723670	−0.0361835	+	0.999345i	$0.511520\pi$
$462$	−4.78509	−0.222622
$463$	22.0567	1.02506	0.512531	−	0.858669i	$-0.328708\pi$
$463$	22.0567	1.02506	0.512531	+	0.858669i	$0.328708\pi$
$464$	19.0992	0.886657
$465$	−29.6431	−1.37466
$466$	−32.7027	−1.51493
$467$	14.2832	0.660948	0.330474	−	0.943815i	$-0.392791\pi$
$467$	14.2832	0.660948	0.330474	+	0.943815i	$0.392791\pi$
$468$	0.494400	0.0228536
$469$	−39.4786	−1.82295
$470$	45.1639	2.08326
$471$	4.76162	0.219404
$472$	−7.46430	−0.343572
$473$	10.7730	0.495342
$474$	1.22160	0.0561100
$475$	50.2092	2.30376
$476$	2.14571	0.0983483
$477$	−2.26151	−0.103548
$478$	17.6283	0.806301
$479$	40.5530	1.85291	0.926457	−	0.376400i	$-0.122838\pi$
$479$	40.5530	1.85291	0.926457	+	0.376400i	$0.122838\pi$
$480$	−10.5395	−0.481062
$481$	4.08600	0.186306
$482$	−27.4175	−1.24883
$483$	−16.3974	−0.746107
$484$	5.14850	0.234023
$485$	0.714788	0.0324568
$486$	1.22160	0.0554130
$487$	−0.406291	−0.0184108	−0.00920540	−	0.999958i	$-0.502930\pi$
$487$	−0.406291	−0.0184108	−0.00920540	+	0.999958i	$0.502930\pi$
$488$	18.3026	0.828521
$489$	15.8906	0.718598
$490$	−50.0263	−2.25996
$491$	−38.4922	−1.73713	−0.868563	−	0.495578i	$-0.834956\pi$
$491$	−38.4922	−1.73713	−0.868563	+	0.495578i	$0.834956\pi$
$492$	1.14705	0.0517128
$493$	7.00406	0.315447
$494$	−6.48339	−0.291702
$495$	3.49405	0.157046
$496$	−21.4412	−0.962736
$497$	24.0118	1.07707
$498$	−16.8960	−0.757128
$499$	−35.0288	−1.56810	−0.784052	−	0.620695i	$-0.786851\pi$
$499$	−35.0288	−1.56810	−0.784052	+	0.620695i	$0.786851\pi$
$500$	8.06317	0.360596
$501$	12.5382	0.560164
$502$	−5.59082	−0.249530
$503$	22.0130	0.981512	0.490756	−	0.871297i	$-0.336721\pi$
$503$	22.0130	0.981512	0.490756	+	0.871297i	$0.336721\pi$
$504$	−12.9472	−0.576712
$505$	−28.5901	−1.27224
$506$	4.39261	0.195275
$507$	−12.0517	−0.535234
$508$	−7.89405	−0.350242
$509$	−6.39233	−0.283335	−0.141667	−	0.989914i	$-0.545246\pi$
$509$	−6.39233	−0.283335	−0.141667	+	0.989914i	$0.545246\pi$
$510$	4.60542	0.203931
$511$	0.276523	0.0122327
$512$	−24.3303	−1.07526
$513$	5.44996	0.240622
$514$	14.2351	0.627883
$515$	48.0611	2.11783
$516$	5.90127	0.259789
$517$	9.08892	0.399730
$518$	−21.6631	−0.951820
$519$	18.7020	0.820928
$520$	−11.2466	−0.493197
$521$	15.1587	0.664114	0.332057	−	0.943259i	$-0.392257\pi$
$521$	15.1587	0.664114	0.332057	+	0.943259i	$0.392257\pi$
$522$	−8.55617	−0.374494
$523$	−6.76351	−0.295748	−0.147874	−	0.989006i	$-0.547243\pi$
$523$	−6.76351	−0.295748	−0.147874	+	0.989006i	$0.547243\pi$
$524$	3.92237	0.171349
$525$	38.9369	1.69935
$526$	9.79603	0.427127
$527$	−7.86292	−0.342514
$528$	2.52728	0.109986
$529$	−7.94755	−0.345546
$530$	10.4152	0.452407
$531$	2.43661	0.105740
$532$	−11.6940	−0.507000
$533$	2.20020	0.0953010
$534$	−7.92035	−0.342747
$535$	−13.0990	−0.566318
$536$	28.6150	1.23598
$537$	14.6450	0.631979
$538$	7.55504	0.325721
$539$	−10.0674	−0.433636
$540$	1.91398	0.0823648
$541$	−45.1834	−1.94258	−0.971292	−	0.237889i	$-0.923545\pi$
$541$	−45.1834	−1.94258	−0.971292	+	0.237889i	$0.923545\pi$
$542$	29.3888	1.26236
$543$	−10.2028	−0.437844
$544$	−2.79565	−0.119862
$545$	62.4967	2.67707
$546$	−5.02782	−0.215171
$547$	13.6400	0.583202	0.291601	−	0.956540i	$-0.405812\pi$
$547$	13.6400	0.583202	0.291601	+	0.956540i	$0.405812\pi$
$548$	−2.46221	−0.105180
$549$	−5.97462	−0.254991
$550$	−10.4306	−0.444762
$551$	−38.1719	−1.62618
$552$	11.8852	0.505868
$553$	4.22641	0.179725
$554$	17.4096	0.739665
$555$	15.8182	0.671447
$556$	2.30130	0.0975970
$557$	26.7074	1.13163	0.565815	−	0.824532i	$-0.308562\pi$
$557$	26.7074	1.13163	0.565815	+	0.824532i	$0.308562\pi$
$558$	9.60535	0.406627
$559$	11.3195	0.478762
$560$	43.4485	1.83603
$561$	0.926807	0.0391298
$562$	−29.3389	−1.23758
$563$	−23.0479	−0.971355	−0.485678	−	0.874138i	$-0.661427\pi$
$563$	−23.0479	−0.971355	−0.485678	+	0.874138i	$0.661427\pi$
$564$	4.97877	0.209644
$565$	60.4326	2.54242
$566$	24.8644	1.04513
$567$	4.22641	0.177492
$568$	−17.4043	−0.730268
$569$	−23.8873	−1.00141	−0.500703	−	0.865619i	$-0.666925\pi$
$569$	−23.8873	−1.00141	−0.500703	+	0.865619i	$0.666925\pi$
$570$	−25.0993	−1.05130
$571$	−10.9716	−0.459149	−0.229574	−	0.973291i	$-0.573733\pi$
$571$	−10.9716	−0.459149	−0.229574	+	0.973291i	$0.573733\pi$
$572$	−0.458213	−0.0191589
$573$	−0.166071	−0.00693773
$574$	−11.6649	−0.486885
$575$	−35.7432	−1.49060
$576$	8.86891	0.369538
$577$	31.4097	1.30760	0.653800	−	0.756667i	$-0.273174\pi$
$577$	31.4097	1.30760	0.653800	+	0.756667i	$0.273174\pi$
$578$	1.22160	0.0508119
$579$	−7.01744	−0.291635
$580$	−13.4057	−0.556640
$581$	−58.4555	−2.42514
$582$	−0.231615	−0.00960076
$583$	2.09599	0.0868069
$584$	−0.200431	−0.00829388
$585$	3.67129	0.151789
$586$	−0.341209	−0.0140952
$587$	37.0130	1.52769	0.763844	−	0.645401i	$-0.223310\pi$
$587$	37.0130	1.52769	0.763844	+	0.645401i	$0.223310\pi$
$588$	−5.51479	−0.227426
$589$	42.8526	1.76571
$590$	−11.2216	−0.461986
$591$	11.0238	0.453459
$592$	11.4415	0.470243
$593$	−20.2935	−0.833356	−0.416678	−	0.909054i	$-0.636806\pi$
$593$	−20.2935	−0.833356	−0.416678	+	0.909054i	$0.636806\pi$
$594$	−1.13219	−0.0464543
$595$	15.9335	0.653209
$596$	8.20828	0.336224
$597$	7.95657	0.325641
$598$	4.61543	0.188739
$599$	34.7643	1.42043	0.710215	−	0.703985i	$-0.248598\pi$
$599$	34.7643	1.42043	0.710215	+	0.703985i	$0.248598\pi$
$600$	−28.2224	−1.15217
$601$	15.5260	0.633318	0.316659	−	0.948539i	$-0.397439\pi$
$601$	15.5260	0.633318	0.316659	+	0.948539i	$0.397439\pi$
$602$	−60.0132	−2.44596
$603$	−9.34093	−0.380392
$604$	3.57040	0.145277
$605$	38.2315	1.55433
$606$	9.26415	0.376330
$607$	9.47219	0.384464	0.192232	−	0.981349i	$-0.438427\pi$
$607$	9.47219	0.384464	0.192232	+	0.981349i	$0.438427\pi$
$608$	15.2362	0.617909
$609$	−29.6020	−1.19953
$610$	27.5156	1.11407
$611$	9.54997	0.386351
$612$	0.507691	0.0205222
$613$	−33.0931	−1.33662	−0.668309	−	0.743884i	$-0.732982\pi$
$613$	−33.0931	−1.33662	−0.668309	+	0.743884i	$0.732982\pi$
$614$	−28.0106	−1.13042
$615$	8.51768	0.343466
$616$	11.9995	0.483474
$617$	5.97527	0.240555	0.120278	−	0.992740i	$-0.461622\pi$
$617$	5.97527	0.240555	0.120278	+	0.992740i	$0.461622\pi$
$618$	−15.5734	−0.626455
$619$	11.1028	0.446257	0.223129	−	0.974789i	$-0.428373\pi$
$619$	11.1028	0.446257	0.223129	+	0.974789i	$0.428373\pi$
$620$	15.0495	0.604403
$621$	−3.87975	−0.155689
$622$	12.5135	0.501746
$623$	−27.4022	−1.09785
$624$	2.65548	0.106304
$625$	13.8113	0.552451
$626$	−16.2953	−0.651292
$627$	−5.05106	−0.201720
$628$	−2.41743	−0.0964659
$629$	4.19584	0.167299
$630$	−19.4644	−0.775478
$631$	31.0651	1.23668	0.618341	−	0.785910i	$-0.287805\pi$
$631$	31.0651	1.23668	0.618341	+	0.785910i	$0.287805\pi$
$632$	−3.06340	−0.121855
$633$	−7.85899	−0.312367
$634$	32.5188	1.29148
$635$	−58.6193	−2.32623
$636$	1.14815	0.0455270
$637$	−10.5781	−0.419121
$638$	7.92992	0.313949
$639$	5.68137	0.224751
$640$	−19.7659	−0.781316
$641$	38.6746	1.52756	0.763778	−	0.645479i	$-0.223342\pi$
$641$	38.6746	1.52756	0.763778	+	0.645479i	$0.223342\pi$
$642$	4.24451	0.167517
$643$	49.0085	1.93271	0.966353	−	0.257219i	$-0.0828062\pi$
$643$	49.0085	1.93271	0.966353	+	0.257219i	$0.0828062\pi$
$644$	8.32480	0.328043
$645$	43.8213	1.72546
$646$	−6.65768	−0.261943
$647$	23.6445	0.929560	0.464780	−	0.885426i	$-0.346133\pi$
$647$	23.6445	0.929560	0.464780	+	0.885426i	$0.346133\pi$
$648$	−3.06340	−0.120342
$649$	−2.25827	−0.0886447
$650$	−10.9597	−0.429875
$651$	33.2319	1.30246
$652$	−8.06751	−0.315948
$653$	22.9876	0.899574	0.449787	−	0.893136i	$-0.351500\pi$
$653$	22.9876	0.899574	0.449787	+	0.893136i	$0.351500\pi$
$654$	−20.2510	−0.791879
$655$	29.1265	1.13807
$656$	6.16093	0.240544
$657$	0.0654276	0.00255257
$658$	−50.6318	−1.97383
$659$	−19.1916	−0.747597	−0.373799	−	0.927510i	$-0.621945\pi$
$659$	−19.1916	−0.747597	−0.373799	+	0.927510i	$0.621945\pi$
$660$	−1.77389	−0.0690487
$661$	−40.9984	−1.59465	−0.797327	−	0.603548i	$-0.793753\pi$
$661$	−40.9984	−1.59465	−0.797327	+	0.603548i	$0.793753\pi$
$662$	5.67617	0.220611
$663$	0.973822	0.0378201
$664$	42.3699	1.64427
$665$	−86.8368	−3.36739
$666$	−5.12564	−0.198615
$667$	27.1740	1.05218
$668$	−6.36551	−0.246289
$669$	−4.35903	−0.168530
$670$	43.0189	1.66196
$671$	5.53732	0.213766
$672$	11.8155	0.455795
$673$	−13.3253	−0.513652	−0.256826	−	0.966458i	$-0.582677\pi$
$673$	−13.3253	−0.513652	−0.256826	+	0.966458i	$0.582677\pi$
$674$	−25.3277	−0.975588
$675$	9.21277	0.354600
$676$	6.11852	0.235328
$677$	−19.0775	−0.733207	−0.366603	−	0.930377i	$-0.619479\pi$
$677$	−19.0775	−0.733207	−0.366603	+	0.930377i	$0.619479\pi$
$678$	−19.5822	−0.752050
$679$	−0.801325	−0.0307520
$680$	−11.5490	−0.442882
$681$	−18.0285	−0.690854
$682$	−8.90231	−0.340887
$683$	39.5479	1.51326	0.756628	−	0.653845i	$-0.226845\pi$
$683$	39.5479	1.51326	0.756628	+	0.653845i	$0.226845\pi$
$684$	−2.76689	−0.105795
$685$	−18.2838	−0.698586
$686$	19.9420	0.761390
$687$	9.91739	0.378372
$688$	31.6964	1.20842
$689$	2.20231	0.0839013
$690$	17.8679	0.680218
$691$	5.16863	0.196624	0.0983120	−	0.995156i	$-0.468656\pi$
$691$	5.16863	0.196624	0.0983120	+	0.995156i	$0.468656\pi$
$692$	−9.49485	−0.360940
$693$	−3.91706	−0.148797
$694$	19.6728	0.746768
$695$	17.0889	0.648219
$696$	21.4562	0.813296
$697$	2.25934	0.0855786
$698$	−8.99169	−0.340341
$699$	−26.7704	−1.01255
$700$	−19.7679	−0.747156
$701$	−35.7327	−1.34961	−0.674803	−	0.737998i	$-0.735771\pi$
$701$	−35.7327	−1.34961	−0.674803	+	0.737998i	$0.735771\pi$
$702$	−1.18962	−0.0448994
$703$	−22.8672	−0.862452
$704$	−8.21977	−0.309794
$705$	36.9711	1.39241
$706$	37.6693	1.41770
$707$	32.0514	1.20542
$708$	−1.23704	−0.0464909
$709$	−5.58464	−0.209736	−0.104868	−	0.994486i	$-0.533442\pi$
$709$	−5.58464	−0.209736	−0.104868	+	0.994486i	$0.533442\pi$
$710$	−26.1651	−0.981957
$711$	1.00000	0.0375029
$712$	19.8618	0.744352
$713$	−30.5061	−1.14246
$714$	−5.16298	−0.193220
$715$	−3.40258	−0.127249
$716$	−7.43513	−0.277864
$717$	14.4305	0.538917
$718$	29.9611	1.11814
$719$	−42.3077	−1.57781	−0.788906	−	0.614513i	$-0.789352\pi$
$719$	−42.3077	−1.57781	−0.788906	+	0.614513i	$0.789352\pi$
$720$	10.2802	0.383122
$721$	−53.8798	−2.00659
$722$	13.0737	0.486552
$723$	−22.4439	−0.834699
$724$	5.17986	0.192508
$725$	−64.5268	−2.39647
$726$	−12.3883	−0.459773
$727$	37.0251	1.37318	0.686592	−	0.727043i	$-0.259106\pi$
$727$	37.0251	1.37318	0.686592	+	0.727043i	$0.259106\pi$
$728$	12.6082	0.467292
$729$	1.00000	0.0370370
$730$	−0.301321	−0.0111524
$731$	11.6237	0.429920
$732$	3.03326	0.112112
$733$	−6.38454	−0.235818	−0.117909	−	0.993024i	$-0.537619\pi$
$733$	−6.38454	−0.235818	−0.117909	+	0.993024i	$0.537619\pi$
$734$	8.72743	0.322135
$735$	−40.9514	−1.51052
$736$	−10.8464	−0.399804
$737$	8.65724	0.318894
$738$	−2.76001	−0.101598
$739$	12.8544	0.472856	0.236428	−	0.971649i	$-0.424023\pi$
$739$	12.8544	0.472856	0.236428	+	0.971649i	$0.424023\pi$
$740$	−8.03077	−0.295217
$741$	−5.30729	−0.194968
$742$	−11.6761	−0.428645
$743$	8.00371	0.293628	0.146814	−	0.989164i	$-0.453098\pi$
$743$	8.00371	0.293628	0.146814	+	0.989164i	$0.453098\pi$
$744$	−24.0872	−0.883081
$745$	60.9526	2.23313
$746$	−29.0885	−1.06500
$747$	−13.8310	−0.506051
$748$	−0.470531	−0.0172043
$749$	14.6848	0.536572
$750$	−19.4016	−0.708444
$751$	1.33971	0.0488866	0.0244433	−	0.999701i	$-0.492219\pi$
$751$	1.33971	0.0488866	0.0244433	+	0.999701i	$0.492219\pi$
$752$	26.7416	0.975165
$753$	−4.57663	−0.166782
$754$	8.33219	0.303440
$755$	26.5129	0.964902
$756$	−2.14571	−0.0780386
$757$	9.96620	0.362228	0.181114	−	0.983462i	$-0.442030\pi$
$757$	9.96620	0.362228	0.181114	+	0.983462i	$0.442030\pi$
$758$	−41.9331	−1.52308
$759$	3.59578	0.130519
$760$	62.9414	2.28312
$761$	−51.2309	−1.85712	−0.928559	−	0.371186i	$-0.878951\pi$
$761$	−51.2309	−1.85712	−0.928559	+	0.371186i	$0.878951\pi$
$762$	18.9946	0.688102
$763$	−70.0631	−2.53645
$764$	0.0843129	0.00305033
$765$	3.76998	0.136304
$766$	−21.0753	−0.761482
$767$	−2.37282	−0.0856776
$768$	−11.3330	−0.408944
$769$	30.8536	1.11261	0.556305	−	0.830978i	$-0.312219\pi$
$769$	30.8536	1.11261	0.556305	+	0.830978i	$0.312219\pi$
$770$	18.0397	0.650106
$771$	11.6528	0.419666
$772$	3.56269	0.128224
$773$	−30.4465	−1.09508	−0.547542	−	0.836778i	$-0.684436\pi$
$773$	−30.4465	−1.09508	−0.547542	+	0.836778i	$0.684436\pi$
$774$	−14.1996	−0.510394
$775$	72.4393	2.60209
$776$	0.580820	0.0208502
$777$	−17.7333	−0.636180
$778$	−16.8369	−0.603631
$779$	−12.3133	−0.441171
$780$	−1.86388	−0.0667376
$781$	−5.26553	−0.188416
$782$	4.73951	0.169484
$783$	−7.00406	−0.250305
$784$	−29.6206	−1.05788
$785$	−17.9512	−0.640706
$786$	−9.43797	−0.336641
$787$	−35.8667	−1.27851	−0.639255	−	0.768995i	$-0.720757\pi$
$787$	−35.8667	−1.27851	−0.639255	+	0.768995i	$0.720757\pi$
$788$	−5.59668	−0.199374
$789$	8.01900	0.285484
$790$	−4.60542	−0.163853
$791$	−67.7490	−2.40888
$792$	2.83918	0.100886
$793$	5.81821	0.206611
$794$	−26.5599	−0.942574
$795$	8.52586	0.302381
$796$	−4.03947	−0.143175
$797$	−26.2376	−0.929385	−0.464692	−	0.885472i	$-0.653835\pi$
$797$	−26.2376	−0.929385	−0.464692	+	0.885472i	$0.653835\pi$
$798$	28.1381	0.996076
$799$	9.80670	0.346936
$800$	25.7557	0.910600
$801$	−6.48358	−0.229086
$802$	39.7870	1.40493
$803$	−0.0606387	−0.00213989
$804$	4.74230	0.167248
$805$	61.8179	2.17879
$806$	−9.35390	−0.329477
$807$	6.18454	0.217706
$808$	−23.2316	−0.817285
$809$	25.4613	0.895171	0.447585	−	0.894241i	$-0.352284\pi$
$809$	25.4613	0.895171	0.447585	+	0.894241i	$0.352284\pi$
$810$	−4.60542	−0.161818
$811$	−3.93816	−0.138288	−0.0691438	−	0.997607i	$-0.522027\pi$
$811$	−3.93816	−0.138288	−0.0691438	+	0.997607i	$0.522027\pi$
$812$	15.0287	0.527403
$813$	24.0576	0.843736
$814$	4.75048	0.166504
$815$	−59.9073	−2.09846
$816$	2.72687	0.0954595
$817$	−63.3490	−2.21630
$818$	−8.83443	−0.308889
$819$	−4.11576	−0.143816
$820$	−4.32434	−0.151013
$821$	3.34556	0.116761	0.0583805	−	0.998294i	$-0.481406\pi$
$821$	3.34556	0.116761	0.0583805	+	0.998294i	$0.481406\pi$
$822$	5.92455	0.206642
$823$	42.0481	1.46570	0.732852	−	0.680388i	$-0.238189\pi$
$823$	42.0481	1.46570	0.732852	+	0.680388i	$0.238189\pi$
$824$	39.0533	1.36049
$825$	−8.53846	−0.297271
$826$	12.5802	0.437720
$827$	21.9638	0.763755	0.381877	−	0.924213i	$-0.375278\pi$
$827$	21.9638	0.763755	0.381877	+	0.924213i	$0.375278\pi$
$828$	1.96971	0.0684522
$829$	4.05597	0.140870	0.0704348	−	0.997516i	$-0.477561\pi$
$829$	4.05597	0.140870	0.0704348	+	0.997516i	$0.477561\pi$
$830$	63.6976	2.21098
$831$	14.2515	0.494379
$832$	−8.63673	−0.299425
$833$	−10.8625	−0.376363
$834$	−5.53738	−0.191744
$835$	−47.2687	−1.63580
$836$	2.56438	0.0886908
$837$	7.86292	0.271782
$838$	35.4784	1.22558
$839$	−24.4742	−0.844943	−0.422471	−	0.906376i	$-0.638837\pi$
$839$	−24.4742	−0.844943	−0.422471	+	0.906376i	$0.638837\pi$
$840$	48.8106	1.68412
$841$	20.0569	0.691618
$842$	−13.6890	−0.471756
$843$	−24.0167	−0.827180
$844$	3.98994	0.137339
$845$	45.4346	1.56300
$846$	−11.9799	−0.411877
$847$	−42.8601	−1.47269
$848$	6.16685	0.211770
$849$	20.3539	0.698545
$850$	−11.2543	−0.386020
$851$	16.2788	0.558030
$852$	−2.88438	−0.0988171
$853$	−7.56030	−0.258860	−0.129430	−	0.991589i	$-0.541315\pi$
$853$	−7.56030	−0.258860	−0.129430	+	0.991589i	$0.541315\pi$
$854$	−30.8469	−1.05556
$855$	−20.5463	−0.702667
$856$	−10.6439	−0.363802
$857$	−9.95858	−0.340179	−0.170089	−	0.985429i	$-0.554406\pi$
$857$	−9.95858	−0.340179	−0.170089	+	0.985429i	$0.554406\pi$
$858$	1.10255	0.0376404
$859$	−17.8504	−0.609046	−0.304523	−	0.952505i	$-0.598497\pi$
$859$	−17.8504	−0.609046	−0.304523	+	0.952505i	$0.598497\pi$
$860$	−22.2477	−0.758639
$861$	−9.54889	−0.325425
$862$	−11.5252	−0.392548
$863$	40.6409	1.38343	0.691716	−	0.722170i	$-0.256855\pi$
$863$	40.6409	1.38343	0.691716	+	0.722170i	$0.256855\pi$
$864$	2.79565	0.0951099
$865$	−70.5064	−2.39729
$866$	10.9877	0.373377
$867$	1.00000	0.0339618
$868$	−16.8715	−0.572656
$869$	−0.926807	−0.0314398
$870$	32.2566	1.09360
$871$	9.09640	0.308220
$872$	50.7834	1.71974
$873$	−0.189600	−0.00641698
$874$	−25.8301	−0.873717
$875$	−67.1240	−2.26921
$876$	−0.0332170	−0.00112230
$877$	−28.7878	−0.972096	−0.486048	−	0.873932i	$-0.661562\pi$
$877$	−28.7878	−0.972096	−0.486048	+	0.873932i	$0.661562\pi$
$878$	20.8842	0.704806
$879$	−0.279313	−0.00942100
$880$	−9.52781	−0.321182
$881$	−47.9458	−1.61533	−0.807667	−	0.589639i	$-0.799270\pi$
$881$	−47.9458	−1.61533	−0.807667	+	0.589639i	$0.799270\pi$
$882$	13.2696	0.446812
$883$	−14.5145	−0.488452	−0.244226	−	0.969718i	$-0.578534\pi$
$883$	−14.5145	−0.488452	−0.244226	+	0.969718i	$0.578534\pi$
$884$	−0.494400	−0.0166285
$885$	−9.18597	−0.308783
$886$	37.3585	1.25508
$887$	−36.5935	−1.22869	−0.614345	−	0.789037i	$-0.710580\pi$
$887$	−36.5935	−1.22869	−0.614345	+	0.789037i	$0.710580\pi$
$888$	12.8535	0.431336
$889$	65.7162	2.20405
$890$	29.8596	1.00090
$891$	−0.926807	−0.0310492
$892$	2.21304	0.0740981
$893$	−53.4461	−1.78851
$894$	−19.7507	−0.660562
$895$	−55.2114	−1.84551
$896$	22.1589	0.740277
$897$	3.77818	0.126150
$898$	−35.3853	−1.18082
$899$	−55.0724	−1.83677
$900$	−4.67724	−0.155908
$901$	2.26151	0.0753419
$902$	2.55800	0.0851721
$903$	−49.1267	−1.63483
$904$	49.1061	1.63324
$905$	38.4643	1.27860
$906$	−8.59106	−0.285419
$907$	14.4904	0.481147	0.240573	−	0.970631i	$-0.422665\pi$
$907$	14.4904	0.481147	0.240573	+	0.970631i	$0.422665\pi$
$908$	9.15290	0.303750
$909$	7.58361	0.251533
$910$	18.9548	0.628346
$911$	−39.4490	−1.30700	−0.653501	−	0.756925i	$-0.726701\pi$
$911$	−39.4490	−1.30700	−0.653501	+	0.756925i	$0.726701\pi$
$912$	−14.8613	−0.492108
$913$	12.8187	0.424237
$914$	41.5986	1.37596
$915$	22.5242	0.744628
$916$	−5.03496	−0.166360
$917$	−32.6528	−1.07829
$918$	−1.22160	−0.0403188
$919$	−30.1549	−0.994720	−0.497360	−	0.867544i	$-0.665697\pi$
$919$	−30.1549	−0.994720	−0.497360	+	0.867544i	$0.665697\pi$
$920$	−44.8070	−1.47724
$921$	−22.9294	−0.755550
$922$	−1.89811	−0.0625108
$923$	−5.53264	−0.182109
$924$	1.98866	0.0654220
$925$	−38.6553	−1.27098
$926$	26.9445	0.885451
$927$	−12.7484	−0.418711
$928$	−19.5809	−0.642775
$929$	−18.5383	−0.608222	−0.304111	−	0.952637i	$-0.598359\pi$
$929$	−18.5383	−0.608222	−0.304111	+	0.952637i	$0.598359\pi$
$930$	−36.2120	−1.18744
$931$	59.2002	1.94021
$932$	13.5911	0.445190
$933$	10.2435	0.335358
$934$	17.4484	0.570929
$935$	−3.49405	−0.114268
$936$	2.98320	0.0975090
$937$	−17.5745	−0.574135	−0.287067	−	0.957910i	$-0.592680\pi$
$937$	−17.5745	−0.574135	−0.287067	+	0.957910i	$0.592680\pi$
$938$	−48.2271	−1.57467
$939$	−13.3393	−0.435312
$940$	−18.7699	−0.612206
$941$	−10.8538	−0.353824	−0.176912	−	0.984227i	$-0.556611\pi$
$941$	−10.8538	−0.353824	−0.176912	+	0.984227i	$0.556611\pi$
$942$	5.81680	0.189522
$943$	8.76568	0.285450
$944$	−6.64431	−0.216254
$945$	−15.9335	−0.518316
$946$	13.1603	0.427877
$947$	18.0136	0.585363	0.292681	−	0.956210i	$-0.405453\pi$
$947$	18.0136	0.585363	0.292681	+	0.956210i	$0.405453\pi$
$948$	−0.507691	−0.0164890
$949$	−0.0637148	−0.00206827
$950$	61.3357	1.98999
$951$	26.6198	0.863206
$952$	12.9472	0.419620
$953$	−48.9091	−1.58432	−0.792160	−	0.610314i	$-0.791043\pi$
$953$	−48.9091	−1.58432	−0.792160	+	0.610314i	$0.791043\pi$
$954$	−2.76267	−0.0894446
$955$	0.626086	0.0202597
$956$	−7.32623	−0.236947
$957$	6.49142	0.209838
$958$	49.5396	1.60055
$959$	20.4973	0.661893
$960$	−33.4356	−1.07913
$961$	30.8255	0.994371
$962$	4.99146	0.160931
$963$	3.47455	0.111966
$964$	11.3946	0.366994
$965$	26.4556	0.851636
$966$	−20.0311	−0.644489
$967$	−18.3554	−0.590270	−0.295135	−	0.955456i	$-0.595365\pi$
$967$	−18.3554	−0.590270	−0.295135	+	0.955456i	$0.595365\pi$
$968$	31.0660	0.998499
$969$	−5.44996	−0.175078
$970$	0.873186	0.0280363
$971$	−28.0827	−0.901215	−0.450608	−	0.892722i	$-0.648793\pi$
$971$	−28.0827	−0.901215	−0.450608	+	0.892722i	$0.648793\pi$
$972$	−0.507691	−0.0162842
$973$	−19.1578	−0.614171
$974$	−0.496325	−0.0159033
$975$	−8.97159	−0.287321
$976$	16.2920	0.521494
$977$	−53.1970	−1.70192	−0.850961	−	0.525229i	$-0.823980\pi$
$977$	−53.1970	−1.70192	−0.850961	+	0.525229i	$0.823980\pi$
$978$	19.4120	0.620727
$979$	6.00903	0.192049
$980$	20.7907	0.664133
$981$	−16.5775	−0.529278
$982$	−47.0221	−1.50053
$983$	−28.4850	−0.908532	−0.454266	−	0.890866i	$-0.650098\pi$
$983$	−28.4850	−0.908532	−0.454266	+	0.890866i	$0.650098\pi$
$984$	6.92126	0.220642
$985$	−41.5596	−1.32420
$986$	8.55617	0.272484
$987$	−41.4471	−1.31927
$988$	2.69446	0.0857222
$989$	45.0972	1.43401
$990$	4.26833	0.135656
$991$	49.8326	1.58298	0.791492	−	0.611180i	$-0.209305\pi$
$991$	49.8326	1.58298	0.791492	+	0.611180i	$0.209305\pi$
$992$	21.9820	0.697928
$993$	4.64650	0.147452
$994$	29.3328	0.930380
$995$	−29.9961	−0.950941
$996$	7.02188	0.222497
$997$	29.7398	0.941868	0.470934	−	0.882168i	$-0.343917\pi$
$997$	29.7398	0.941868	0.470934	+	0.882168i	$0.343917\pi$
$998$	−42.7912	−1.35453
$999$	−4.19584	−0.132751

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.h.1.18	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.h.1.18	✓	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)

\(f(q)\)	\(=\)	\(q+1.22160 q^{2} +1.00000 q^{3} -0.507691 q^{4} -3.76998 q^{5} +1.22160 q^{6} +4.22641 q^{7} -3.06340 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.22160 q^{2} +1.00000 q^{3} -0.507691 q^{4} -3.76998 q^{5} +1.22160 q^{6} +4.22641 q^{7} -3.06340 q^{8} +1.00000 q^{9} -4.60542 q^{10} -0.926807 q^{11} -0.507691 q^{12} -0.973822 q^{13} +5.16298 q^{14} -3.76998 q^{15} -2.72687 q^{16} -1.00000 q^{17} +1.22160 q^{18} +5.44996 q^{19} +1.91398 q^{20} +4.22641 q^{21} -1.13219 q^{22} -3.87975 q^{23} -3.06340 q^{24} +9.21277 q^{25} -1.18962 q^{26} +1.00000 q^{27} -2.14571 q^{28} -7.00406 q^{29} -4.60542 q^{30} +7.86292 q^{31} +2.79565 q^{32} -0.926807 q^{33} -1.22160 q^{34} -15.9335 q^{35} -0.507691 q^{36} -4.19584 q^{37} +6.65768 q^{38} -0.973822 q^{39} +11.5490 q^{40} -2.25934 q^{41} +5.16298 q^{42} -11.6237 q^{43} +0.470531 q^{44} -3.76998 q^{45} -4.73951 q^{46} -9.80670 q^{47} -2.72687 q^{48} +10.8625 q^{49} +11.2543 q^{50} -1.00000 q^{51} +0.494400 q^{52} -2.26151 q^{53} +1.22160 q^{54} +3.49405 q^{55} -12.9472 q^{56} +5.44996 q^{57} -8.55617 q^{58} +2.43661 q^{59} +1.91398 q^{60} -5.97462 q^{61} +9.60535 q^{62} +4.22641 q^{63} +8.86891 q^{64} +3.67129 q^{65} -1.13219 q^{66} -9.34093 q^{67} +0.507691 q^{68} -3.87975 q^{69} -19.4644 q^{70} +5.68137 q^{71} -3.06340 q^{72} +0.0654276 q^{73} -5.12564 q^{74} +9.21277 q^{75} -2.76689 q^{76} -3.91706 q^{77} -1.18962 q^{78} +1.00000 q^{79} +10.2802 q^{80} +1.00000 q^{81} -2.76001 q^{82} -13.8310 q^{83} -2.14571 q^{84} +3.76998 q^{85} -14.1996 q^{86} -7.00406 q^{87} +2.83918 q^{88} -6.48358 q^{89} -4.60542 q^{90} -4.11576 q^{91} +1.96971 q^{92} +7.86292 q^{93} -11.9799 q^{94} -20.5463 q^{95} +2.79565 q^{96} -0.189600 q^{97} +13.2696 q^{98} -0.926807 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 7 q^{2} + 25 q^{3} + 21 q^{4} - 12 q^{5} - 7 q^{6} - 4 q^{7} - 21 q^{8} + 25 q^{9}+O(q^{10}) \) 25 * q - 7 * q^2 + 25 * q^3 + 21 * q^4 - 12 * q^5 - 7 * q^6 - 4 * q^7 - 21 * q^8 + 25 * q^9	\( 25 q - 7 q^{2} + 25 q^{3} + 21 q^{4} - 12 q^{5} - 7 q^{6} - 4 q^{7} - 21 q^{8} + 25 q^{9} - 9 q^{10} - 19 q^{11} + 21 q^{12} - 12 q^{13} - 15 q^{14} - 12 q^{15} + q^{16} - 25 q^{17} - 7 q^{18} - 35 q^{19} - 11 q^{20} - 4 q^{21} - 2 q^{22} - 16 q^{23} - 21 q^{24} + 19 q^{25} - 5 q^{26} + 25 q^{27} + 3 q^{28} - 37 q^{29} - 9 q^{30} - 28 q^{31} - 19 q^{32} - 19 q^{33} + 7 q^{34} - 42 q^{35} + 21 q^{36} + 8 q^{37} - 35 q^{38} - 12 q^{39} - 9 q^{40} - 34 q^{41} - 15 q^{42} - 19 q^{43} - 56 q^{44} - 12 q^{45} + q^{46} - 25 q^{47} + q^{48} + 25 q^{49} - 7 q^{50} - 25 q^{51} - 37 q^{52} - 44 q^{53} - 7 q^{54} - 11 q^{55} - 18 q^{56} - 35 q^{57} - 3 q^{58} - 47 q^{59} - 11 q^{60} - 28 q^{61} + 11 q^{62} - 4 q^{63} - 9 q^{64} - 63 q^{65} - 2 q^{66} - 28 q^{67} - 21 q^{68} - 16 q^{69} + 5 q^{70} - 27 q^{71} - 21 q^{72} - 21 q^{73} - 18 q^{74} + 19 q^{75} - 50 q^{76} - 58 q^{77} - 5 q^{78} + 25 q^{79} - 56 q^{80} + 25 q^{81} - 5 q^{82} - 61 q^{83} + 3 q^{84} + 12 q^{85} - 28 q^{86} - 37 q^{87} + 15 q^{88} - 34 q^{89} - 9 q^{90} - 30 q^{91} - 31 q^{92} - 28 q^{93} + q^{94} - 32 q^{95} - 19 q^{96} - 11 q^{97} - 66 q^{98} - 19 q^{99}+O(q^{100}) \) 25 * q - 7 * q^2 + 25 * q^3 + 21 * q^4 - 12 * q^5 - 7 * q^6 - 4 * q^7 - 21 * q^8 + 25 * q^9 - 9 * q^10 - 19 * q^11 + 21 * q^12 - 12 * q^13 - 15 * q^14 - 12 * q^15 + q^16 - 25 * q^17 - 7 * q^18 - 35 * q^19 - 11 * q^20 - 4 * q^21 - 2 * q^22 - 16 * q^23 - 21 * q^24 + 19 * q^25 - 5 * q^26 + 25 * q^27 + 3 * q^28 - 37 * q^29 - 9 * q^30 - 28 * q^31 - 19 * q^32 - 19 * q^33 + 7 * q^34 - 42 * q^35 + 21 * q^36 + 8 * q^37 - 35 * q^38 - 12 * q^39 - 9 * q^40 - 34 * q^41 - 15 * q^42 - 19 * q^43 - 56 * q^44 - 12 * q^45 + q^46 - 25 * q^47 + q^48 + 25 * q^49 - 7 * q^50 - 25 * q^51 - 37 * q^52 - 44 * q^53 - 7 * q^54 - 11 * q^55 - 18 * q^56 - 35 * q^57 - 3 * q^58 - 47 * q^59 - 11 * q^60 - 28 * q^61 + 11 * q^62 - 4 * q^63 - 9 * q^64 - 63 * q^65 - 2 * q^66 - 28 * q^67 - 21 * q^68 - 16 * q^69 + 5 * q^70 - 27 * q^71 - 21 * q^72 - 21 * q^73 - 18 * q^74 + 19 * q^75 - 50 * q^76 - 58 * q^77 - 5 * q^78 + 25 * q^79 - 56 * q^80 + 25 * q^81 - 5 * q^82 - 61 * q^83 + 3 * q^84 + 12 * q^85 - 28 * q^86 - 37 * q^87 + 15 * q^88 - 34 * q^89 - 9 * q^90 - 30 * q^91 - 31 * q^92 - 28 * q^93 + q^94 - 32 * q^95 - 19 * q^96 - 11 * q^97 - 66 * q^98 - 19 * q^99

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