LMFDB - Embedded newform 4029.2.a.j.1.14

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			1.14
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)

$f(q)$	$=$	$q+0.777638 q^{2} +1.00000 q^{3} -1.39528 q^{4} +1.77745 q^{5} +0.777638 q^{6} +0.717944 q^{7} -2.64030 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.777638 q^{2} +1.00000 q^{3} -1.39528 q^{4} +1.77745 q^{5} +0.777638 q^{6} +0.717944 q^{7} -2.64030 q^{8} +1.00000 q^{9} +1.38222 q^{10} +1.42869 q^{11} -1.39528 q^{12} +6.60719 q^{13} +0.558301 q^{14} +1.77745 q^{15} +0.737363 q^{16} -1.00000 q^{17} +0.777638 q^{18} -1.06797 q^{19} -2.48005 q^{20} +0.717944 q^{21} +1.11101 q^{22} -2.45501 q^{23} -2.64030 q^{24} -1.84066 q^{25} +5.13800 q^{26} +1.00000 q^{27} -1.00173 q^{28} +4.79816 q^{29} +1.38222 q^{30} +5.49934 q^{31} +5.85400 q^{32} +1.42869 q^{33} -0.777638 q^{34} +1.27611 q^{35} -1.39528 q^{36} -2.95003 q^{37} -0.830492 q^{38} +6.60719 q^{39} -4.69301 q^{40} +4.17267 q^{41} +0.558301 q^{42} -3.22100 q^{43} -1.99343 q^{44} +1.77745 q^{45} -1.90911 q^{46} +0.511414 q^{47} +0.737363 q^{48} -6.48456 q^{49} -1.43136 q^{50} -1.00000 q^{51} -9.21887 q^{52} -2.54108 q^{53} +0.777638 q^{54} +2.53944 q^{55} -1.89559 q^{56} -1.06797 q^{57} +3.73123 q^{58} +2.89042 q^{59} -2.48005 q^{60} +9.69639 q^{61} +4.27649 q^{62} +0.717944 q^{63} +3.07756 q^{64} +11.7440 q^{65} +1.11101 q^{66} +7.90690 q^{67} +1.39528 q^{68} -2.45501 q^{69} +0.992354 q^{70} +8.49050 q^{71} -2.64030 q^{72} -11.1460 q^{73} -2.29406 q^{74} -1.84066 q^{75} +1.49011 q^{76} +1.02572 q^{77} +5.13800 q^{78} -1.00000 q^{79} +1.31063 q^{80} +1.00000 q^{81} +3.24483 q^{82} -1.13754 q^{83} -1.00173 q^{84} -1.77745 q^{85} -2.50477 q^{86} +4.79816 q^{87} -3.77218 q^{88} -0.0228972 q^{89} +1.38222 q^{90} +4.74359 q^{91} +3.42542 q^{92} +5.49934 q^{93} +0.397695 q^{94} -1.89826 q^{95} +5.85400 q^{96} +9.55752 q^{97} -5.04264 q^{98} +1.42869 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q + 6 q^{2} + 25 q^{3} + 26 q^{4} + 6 q^{5} + 6 q^{6} + 4 q^{7} + 18 q^{8} + 25 q^{9}+O(q^{10}) $ 25 * q + 6 * q^2 + 25 * q^3 + 26 * q^4 + 6 * q^5 + 6 * q^6 + 4 * q^7 + 18 * q^8 + 25 * q^9	\( 25 q + 6 q^{2} + 25 q^{3} + 26 q^{4} + 6 q^{5} + 6 q^{6} + 4 q^{7} + 18 q^{8} + 25 q^{9} + 13 q^{10} + 19 q^{11} + 26 q^{12} + 17 q^{14} + 6 q^{15} + 16 q^{16} - 25 q^{17} + 6 q^{18} + 25 q^{19} + 32 q^{20} + 4 q^{21} - 7 q^{22} + 8 q^{23} + 18 q^{24} + 15 q^{25} + 20 q^{26} + 25 q^{27} + 9 q^{28} + 21 q^{29} + 13 q^{30} + 4 q^{31} + 27 q^{32} + 19 q^{33} - 6 q^{34} + 50 q^{35} + 26 q^{36} - 8 q^{37} + 31 q^{38} + 52 q^{40} + 40 q^{41} + 17 q^{42} + 21 q^{43} + 34 q^{44} + 6 q^{45} + 29 q^{46} + 43 q^{47} + 16 q^{48} + 21 q^{49} + 13 q^{50} - 25 q^{51} + 3 q^{52} + 44 q^{53} + 6 q^{54} + 13 q^{55} + 38 q^{56} + 25 q^{57} - 5 q^{58} + 45 q^{59} + 32 q^{60} + 22 q^{61} + 4 q^{62} + 4 q^{63} + 26 q^{64} + 43 q^{65} - 7 q^{66} + 8 q^{67} - 26 q^{68} + 8 q^{69} + 29 q^{70} + 9 q^{71} + 18 q^{72} - 7 q^{73} + 18 q^{74} + 15 q^{75} + 33 q^{76} + 20 q^{77} + 20 q^{78} - 25 q^{79} + 42 q^{80} + 25 q^{81} - 43 q^{82} + 41 q^{83} + 9 q^{84} - 6 q^{85} - 12 q^{86} + 21 q^{87} - 43 q^{88} + 68 q^{89} + 13 q^{90} + 10 q^{91} + 2 q^{92} + 4 q^{93} - 17 q^{94} + 8 q^{95} + 27 q^{96} + 15 q^{97} + 11 q^{98} + 19 q^{99}+O(q^{100}) \) 25 * q + 6 * q^2 + 25 * q^3 + 26 * q^4 + 6 * q^5 + 6 * q^6 + 4 * q^7 + 18 * q^8 + 25 * q^9 + 13 * q^10 + 19 * q^11 + 26 * q^12 + 17 * q^14 + 6 * q^15 + 16 * q^16 - 25 * q^17 + 6 * q^18 + 25 * q^19 + 32 * q^20 + 4 * q^21 - 7 * q^22 + 8 * q^23 + 18 * q^24 + 15 * q^25 + 20 * q^26 + 25 * q^27 + 9 * q^28 + 21 * q^29 + 13 * q^30 + 4 * q^31 + 27 * q^32 + 19 * q^33 - 6 * q^34 + 50 * q^35 + 26 * q^36 - 8 * q^37 + 31 * q^38 + 52 * q^40 + 40 * q^41 + 17 * q^42 + 21 * q^43 + 34 * q^44 + 6 * q^45 + 29 * q^46 + 43 * q^47 + 16 * q^48 + 21 * q^49 + 13 * q^50 - 25 * q^51 + 3 * q^52 + 44 * q^53 + 6 * q^54 + 13 * q^55 + 38 * q^56 + 25 * q^57 - 5 * q^58 + 45 * q^59 + 32 * q^60 + 22 * q^61 + 4 * q^62 + 4 * q^63 + 26 * q^64 + 43 * q^65 - 7 * q^66 + 8 * q^67 - 26 * q^68 + 8 * q^69 + 29 * q^70 + 9 * q^71 + 18 * q^72 - 7 * q^73 + 18 * q^74 + 15 * q^75 + 33 * q^76 + 20 * q^77 + 20 * q^78 - 25 * q^79 + 42 * q^80 + 25 * q^81 - 43 * q^82 + 41 * q^83 + 9 * q^84 - 6 * q^85 - 12 * q^86 + 21 * q^87 - 43 * q^88 + 68 * q^89 + 13 * q^90 + 10 * q^91 + 2 * q^92 + 4 * q^93 - 17 * q^94 + 8 * q^95 + 27 * q^96 + 15 * q^97 + 11 * 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 $

$2$	0.777638	0.549873	0.274936	−	0.961462i	$-0.411343\pi$
$2$	0.777638	0.549873	0.274936	+	0.961462i	$0.411343\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.39528	−0.697640
$5$	1.77745	0.794902	0.397451	−	0.917623i	$-0.369895\pi$
$5$	1.77745	0.794902	0.397451	+	0.917623i	$0.369895\pi$
$6$	0.777638	0.317469
$7$	0.717944	0.271357	0.135679	−	0.990753i	$-0.456679\pi$
$7$	0.717944	0.271357	0.135679	+	0.990753i	$0.456679\pi$
$8$	−2.64030	−0.933486
$9$	1.00000	0.333333
$10$	1.38222	0.437095
$11$	1.42869	0.430768	0.215384	−	0.976529i	$-0.430900\pi$
$11$	1.42869	0.430768	0.215384	+	0.976529i	$0.430900\pi$
$12$	−1.39528	−0.402782
$13$	6.60719	1.83250	0.916252	−	0.400603i	$-0.131199\pi$
$13$	6.60719	1.83250	0.916252	+	0.400603i	$0.131199\pi$
$14$	0.558301	0.149212
$15$	1.77745	0.458937
$16$	0.737363	0.184341
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	0.777638	0.183291
$19$	−1.06797	−0.245009	−0.122504	−	0.992468i	$-0.539093\pi$
$19$	−1.06797	−0.245009	−0.122504	+	0.992468i	$0.539093\pi$
$20$	−2.48005	−0.554555
$21$	0.717944	0.156668
$22$	1.11101	0.236867
$23$	−2.45501	−0.511905	−0.255952	−	0.966689i	$-0.582389\pi$
$23$	−2.45501	−0.511905	−0.255952	+	0.966689i	$0.582389\pi$
$24$	−2.64030	−0.538949
$25$	−1.84066	−0.368131
$26$	5.13800	1.00764
$27$	1.00000	0.192450
$28$	−1.00173	−0.189310
$29$	4.79816	0.890996	0.445498	−	0.895283i	$-0.353027\pi$
$29$	4.79816	0.890996	0.445498	+	0.895283i	$0.353027\pi$
$30$	1.38222	0.252357
$31$	5.49934	0.987710	0.493855	−	0.869544i	$-0.335587\pi$
$31$	5.49934	0.987710	0.493855	+	0.869544i	$0.335587\pi$
$32$	5.85400	1.03485
$33$	1.42869	0.248704
$34$	−0.777638	−0.133364
$35$	1.27611	0.215702
$36$	−1.39528	−0.232547
$37$	−2.95003	−0.484982	−0.242491	−	0.970154i	$-0.577965\pi$
$37$	−2.95003	−0.484982	−0.242491	+	0.970154i	$0.577965\pi$
$38$	−0.830492	−0.134724
$39$	6.60719	1.05800
$40$	−4.69301	−0.742030
$41$	4.17267	0.651662	0.325831	−	0.945428i	$-0.394356\pi$
$41$	4.17267	0.651662	0.325831	+	0.945428i	$0.394356\pi$
$42$	0.558301	0.0861476
$43$	−3.22100	−0.491198	−0.245599	−	0.969371i	$-0.578985\pi$
$43$	−3.22100	−0.491198	−0.245599	+	0.969371i	$0.578985\pi$
$44$	−1.99343	−0.300521
$45$	1.77745	0.264967
$46$	−1.90911	−0.281483
$47$	0.511414	0.0745974	0.0372987	−	0.999304i	$-0.488125\pi$
$47$	0.511414	0.0745974	0.0372987	+	0.999304i	$0.488125\pi$
$48$	0.737363	0.106429
$49$	−6.48456	−0.926365
$50$	−1.43136	−0.202425
$51$	−1.00000	−0.140028
$52$	−9.21887	−1.27843
$53$	−2.54108	−0.349044	−0.174522	−	0.984653i	$-0.555838\pi$
$53$	−2.54108	−0.349044	−0.174522	+	0.984653i	$0.555838\pi$
$54$	0.777638	0.105823
$55$	2.53944	0.342418
$56$	−1.89559	−0.253308
$57$	−1.06797	−0.141456
$58$	3.73123	0.489935
$59$	2.89042	0.376301	0.188150	−	0.982140i	$-0.439751\pi$
$59$	2.89042	0.376301	0.188150	+	0.982140i	$0.439751\pi$
$60$	−2.48005	−0.320172
$61$	9.69639	1.24150	0.620748	−	0.784010i	$-0.286829\pi$
$61$	9.69639	1.24150	0.620748	+	0.784010i	$0.286829\pi$
$62$	4.27649	0.543115
$63$	0.717944	0.0904525
$64$	3.07756	0.384695
$65$	11.7440	1.45666
$66$	1.11101	0.136756
$67$	7.90690	0.965982	0.482991	−	0.875625i	$-0.339550\pi$
$67$	7.90690	0.965982	0.482991	+	0.875625i	$0.339550\pi$
$68$	1.39528	0.169202
$69$	−2.45501	−0.295548
$70$	0.992354	0.118609
$71$	8.49050	1.00764	0.503818	−	0.863810i	$-0.331928\pi$
$71$	8.49050	1.00764	0.503818	+	0.863810i	$0.331928\pi$
$72$	−2.64030	−0.311162
$73$	−11.1460	−1.30454	−0.652272	−	0.757985i	$-0.726184\pi$
$73$	−11.1460	−1.30454	−0.652272	+	0.757985i	$0.726184\pi$
$74$	−2.29406	−0.266679
$75$	−1.84066	−0.212541
$76$	1.49011	0.170928
$77$	1.02572	0.116892
$78$	5.13800	0.581764
$79$	−1.00000	−0.112509
$79$	−1.00000	−0.112509
$80$	1.31063	0.146533
$81$	1.00000	0.111111
$82$	3.24483	0.358332
$83$	−1.13754	−0.124861	−0.0624307	−	0.998049i	$-0.519885\pi$
$83$	−1.13754	−0.124861	−0.0624307	+	0.998049i	$0.519885\pi$
$84$	−1.00173	−0.109298
$85$	−1.77745	−0.192792
$86$	−2.50477	−0.270097
$87$	4.79816	0.514417
$88$	−3.77218	−0.402116
$89$	−0.0228972	−0.00242709	−0.00121355	−	0.999999i	$-0.500386\pi$
$89$	−0.0228972	−0.00242709	−0.00121355	+	0.999999i	$0.500386\pi$
$90$	1.38222	0.145698
$91$	4.74359	0.497263
$92$	3.42542	0.357125
$93$	5.49934	0.570255
$94$	0.397695	0.0410191
$95$	−1.89826	−0.194758
$96$	5.85400	0.597471
$97$	9.55752	0.970419	0.485210	−	0.874398i	$-0.338743\pi$
$97$	9.55752	0.970419	0.485210	+	0.874398i	$0.338743\pi$
$98$	−5.04264	−0.509383
$99$	1.42869	0.143589
$100$	2.56823	0.256823
$101$	14.7486	1.46754	0.733772	−	0.679396i	$-0.237758\pi$
$101$	14.7486	1.46754	0.733772	+	0.679396i	$0.237758\pi$
$102$	−0.777638	−0.0769976
$103$	−7.69302	−0.758016	−0.379008	−	0.925393i	$-0.623735\pi$
$103$	−7.69302	−0.758016	−0.379008	+	0.925393i	$0.623735\pi$
$104$	−17.4449	−1.71062
$105$	1.27611	0.124536
$106$	−1.97604	−0.191930
$107$	2.32410	0.224680	0.112340	−	0.993670i	$-0.464165\pi$
$107$	2.32410	0.224680	0.112340	+	0.993670i	$0.464165\pi$
$108$	−1.39528	−0.134261
$109$	1.77556	0.170068	0.0850339	−	0.996378i	$-0.472900\pi$
$109$	1.77556	0.170068	0.0850339	+	0.996378i	$0.472900\pi$
$110$	1.97476	0.188286
$111$	−2.95003	−0.280005
$112$	0.529386	0.0500223
$113$	−8.90062	−0.837300	−0.418650	−	0.908148i	$-0.637497\pi$
$113$	−8.90062	−0.837300	−0.418650	+	0.908148i	$0.637497\pi$
$114$	−0.830492	−0.0777827
$115$	−4.36366	−0.406914
$116$	−6.69478	−0.621594
$117$	6.60719	0.610834
$118$	2.24770	0.206918
$119$	−0.717944	−0.0658138
$120$	−4.69301	−0.428411
$121$	−8.95883	−0.814439
$122$	7.54028	0.682665
$123$	4.17267	0.376237
$124$	−7.67311	−0.689066
$125$	−12.1590	−1.08753
$126$	0.558301	0.0497374
$127$	5.11319	0.453723	0.226861	−	0.973927i	$-0.427154\pi$
$127$	5.11319	0.453723	0.226861	+	0.973927i	$0.427154\pi$
$128$	−9.31477	−0.823317
$129$	−3.22100	−0.283594
$130$	9.13255	0.800978
$131$	4.24056	0.370499	0.185250	−	0.982691i	$-0.440691\pi$
$131$	4.24056	0.370499	0.185250	+	0.982691i	$0.440691\pi$
$132$	−1.99343	−0.173506
$133$	−0.766741	−0.0664849
$134$	6.14871	0.531167
$135$	1.77745	0.152979
$136$	2.64030	0.226404
$137$	7.82353	0.668409	0.334204	−	0.942501i	$-0.391532\pi$
$137$	7.82353	0.668409	0.334204	+	0.942501i	$0.391532\pi$
$138$	−1.90911	−0.162514
$139$	14.6032	1.23863	0.619313	−	0.785144i	$-0.287411\pi$
$139$	14.6032	1.23863	0.619313	+	0.785144i	$0.287411\pi$
$140$	−1.78053	−0.150483
$141$	0.511414	0.0430689
$142$	6.60253	0.554072
$143$	9.43965	0.789383
$144$	0.737363	0.0614470
$145$	8.52851	0.708254
$146$	−8.66757	−0.717333
$147$	−6.48456	−0.534837
$148$	4.11612	0.338343
$149$	0.312771	0.0256232	0.0128116	−	0.999918i	$-0.495922\pi$
$149$	0.312771	0.0256232	0.0128116	+	0.999918i	$0.495922\pi$
$150$	−1.43136	−0.116870
$151$	19.3273	1.57284	0.786418	−	0.617694i	$-0.211933\pi$
$151$	19.3273	1.57284	0.786418	+	0.617694i	$0.211933\pi$
$152$	2.81975	0.228712
$153$	−1.00000	−0.0808452
$154$	0.797641	0.0642757
$155$	9.77482	0.785132
$156$	−9.21887	−0.738100
$157$	−2.53080	−0.201980	−0.100990	−	0.994887i	$-0.532201\pi$
$157$	−2.53080	−0.201980	−0.100990	+	0.994887i	$0.532201\pi$
$158$	−0.777638	−0.0618655
$159$	−2.54108	−0.201520
$160$	10.4052	0.822604
$161$	−1.76256	−0.138909
$162$	0.777638	0.0610970
$163$	−19.1483	−1.49981	−0.749905	−	0.661546i	$-0.769901\pi$
$163$	−19.1483	−1.49981	−0.749905	+	0.661546i	$0.769901\pi$
$164$	−5.82205	−0.454626
$165$	2.53944	0.197695
$166$	−0.884596	−0.0686580
$167$	0.175164	0.0135546	0.00677729	−	0.999977i	$-0.497843\pi$
$167$	0.175164	0.0135546	0.00677729	+	0.999977i	$0.497843\pi$
$168$	−1.89559	−0.146248
$169$	30.6549	2.35807
$170$	−1.38222	−0.106011
$171$	−1.06797	−0.0816695
$172$	4.49420	0.342679
$173$	3.00002	0.228087	0.114044	−	0.993476i	$-0.463620\pi$
$173$	3.00002	0.228087	0.114044	+	0.993476i	$0.463620\pi$
$174$	3.73123	0.282864
$175$	−1.32149	−0.0998952
$176$	1.05347	0.0794081
$177$	2.89042	0.217257
$178$	−0.0178057	−0.00133459
$179$	6.69084	0.500097	0.250049	−	0.968233i	$-0.419553\pi$
$179$	6.69084	0.500097	0.250049	+	0.968233i	$0.419553\pi$
$180$	−2.48005	−0.184852
$181$	3.95296	0.293821	0.146911	−	0.989150i	$-0.453067\pi$
$181$	3.95296	0.293821	0.146911	+	0.989150i	$0.453067\pi$
$182$	3.68879	0.273432
$183$	9.69639	0.716778
$184$	6.48195	0.477856
$185$	−5.24355	−0.385513
$186$	4.27649	0.313568
$187$	−1.42869	−0.104476
$188$	−0.713566	−0.0520421
$189$	0.717944	0.0522228
$190$	−1.47616	−0.107092
$191$	19.8735	1.43800	0.718998	−	0.695012i	$-0.244601\pi$
$191$	19.8735	1.43800	0.718998	+	0.695012i	$0.244601\pi$
$192$	3.07756	0.222104
$193$	7.47523	0.538079	0.269039	−	0.963129i	$-0.413294\pi$
$193$	7.47523	0.538079	0.269039	+	0.963129i	$0.413294\pi$
$194$	7.43229	0.533607
$195$	11.7440	0.841003
$196$	9.04777	0.646269
$197$	−24.2012	−1.72427	−0.862133	−	0.506683i	$-0.830872\pi$
$197$	−24.2012	−1.72427	−0.862133	+	0.506683i	$0.830872\pi$
$198$	1.11101	0.0789558
$199$	11.2825	0.799796	0.399898	−	0.916560i	$-0.369046\pi$
$199$	11.2825	0.799796	0.399898	+	0.916560i	$0.369046\pi$
$200$	4.85988	0.343646
$201$	7.90690	0.557710
$202$	11.4691	0.806962
$203$	3.44481	0.241778
$204$	1.39528	0.0976891
$205$	7.41674	0.518007
$206$	−5.98239	−0.416813
$207$	−2.45501	−0.170635
$208$	4.87190	0.337805
$209$	−1.52580	−0.105542
$210$	0.992354	0.0684789
$211$	−11.4065	−0.785259	−0.392629	−	0.919697i	$-0.628434\pi$
$211$	−11.4065	−0.785259	−0.392629	+	0.919697i	$0.628434\pi$
$212$	3.54551	0.243507
$213$	8.49050	0.581759
$214$	1.80731	0.123545
$215$	−5.72519	−0.390454
$216$	−2.64030	−0.179650
$217$	3.94822	0.268022
$218$	1.38074	0.0935157
$219$	−11.1460	−0.753178
$220$	−3.54323	−0.238884
$221$	−6.60719	−0.444447
$222$	−2.29406	−0.153967
$223$	11.5921	0.776265	0.388133	−	0.921604i	$-0.373120\pi$
$223$	11.5921	0.776265	0.388133	+	0.921604i	$0.373120\pi$
$224$	4.20284	0.280814
$225$	−1.84066	−0.122710
$226$	−6.92146	−0.460409
$227$	17.7137	1.17570	0.587848	−	0.808971i	$-0.299975\pi$
$227$	17.7137	1.17570	0.587848	+	0.808971i	$0.299975\pi$
$228$	1.49011	0.0986852
$229$	8.76721	0.579354	0.289677	−	0.957124i	$-0.406452\pi$
$229$	8.76721	0.579354	0.289677	+	0.957124i	$0.406452\pi$
$230$	−3.39335	−0.223751
$231$	1.02572	0.0674876
$232$	−12.6686	−0.831733
$233$	−21.8989	−1.43464	−0.717321	−	0.696743i	$-0.754632\pi$
$233$	−21.8989	−1.43464	−0.717321	+	0.696743i	$0.754632\pi$
$234$	5.13800	0.335881
$235$	0.909015	0.0592976
$236$	−4.03295	−0.262522
$237$	−1.00000	−0.0649570
$238$	−0.558301	−0.0361892
$239$	19.3738	1.25319	0.626593	−	0.779346i	$-0.284449\pi$
$239$	19.3738	1.25319	0.626593	+	0.779346i	$0.284449\pi$
$240$	1.31063	0.0846008
$241$	−11.4892	−0.740082	−0.370041	−	0.929015i	$-0.620656\pi$
$241$	−11.4892	−0.740082	−0.370041	+	0.929015i	$0.620656\pi$
$242$	−6.96673	−0.447838
$243$	1.00000	0.0641500
$244$	−13.5292	−0.866117
$245$	−11.5260	−0.736369
$246$	3.24483	0.206883
$247$	−7.05626	−0.448979
$248$	−14.5199	−0.922014
$249$	−1.13754	−0.0720888
$250$	−9.45526	−0.598003
$251$	−22.2967	−1.40735	−0.703677	−	0.710520i	$-0.748460\pi$
$251$	−22.2967	−1.40735	−0.703677	+	0.710520i	$0.748460\pi$
$252$	−1.00173	−0.0631032
$253$	−3.50746	−0.220512
$254$	3.97621	0.249490
$255$	−1.77745	−0.111308
$256$	−13.3986	−0.837415
$257$	−21.2961	−1.32841	−0.664207	−	0.747549i	$-0.731231\pi$
$257$	−21.2961	−1.32841	−0.664207	+	0.747549i	$0.731231\pi$
$258$	−2.50477	−0.155940
$259$	−2.11796	−0.131603
$260$	−16.3861	−1.01622
$261$	4.79816	0.296999
$262$	3.29762	0.203728
$263$	−6.21125	−0.383002	−0.191501	−	0.981492i	$-0.561336\pi$
$263$	−6.21125	−0.383002	−0.191501	+	0.981492i	$0.561336\pi$
$264$	−3.77218	−0.232162
$265$	−4.51664	−0.277455
$266$	−0.596247	−0.0365582
$267$	−0.0228972	−0.00140128
$268$	−11.0323	−0.673907
$269$	27.1328	1.65432	0.827158	−	0.561969i	$-0.189956\pi$
$269$	27.1328	1.65432	0.827158	+	0.561969i	$0.189956\pi$
$270$	1.38222	0.0841190
$271$	−30.8285	−1.87270	−0.936348	−	0.351072i	$-0.885817\pi$
$271$	−30.8285	−1.87270	−0.936348	+	0.351072i	$0.885817\pi$
$272$	−0.737363	−0.0447092
$273$	4.74359	0.287095
$274$	6.08387	0.367540
$275$	−2.62974	−0.158579
$276$	3.42542	0.206186
$277$	−10.4087	−0.625397	−0.312698	−	0.949852i	$-0.601233\pi$
$277$	−10.4087	−0.625397	−0.312698	+	0.949852i	$0.601233\pi$
$278$	11.3560	0.681087
$279$	5.49934	0.329237
$280$	−3.36932	−0.201355
$281$	−24.9349	−1.48749	−0.743745	−	0.668463i	$-0.766952\pi$
$281$	−24.9349	−1.48749	−0.743745	+	0.668463i	$0.766952\pi$
$282$	0.397695	0.0236824
$283$	6.58505	0.391440	0.195720	−	0.980660i	$-0.437296\pi$
$283$	6.58505	0.391440	0.195720	+	0.980660i	$0.437296\pi$
$284$	−11.8466	−0.702967
$285$	−1.89826	−0.112443
$286$	7.34063	0.434060
$287$	2.99575	0.176833
$288$	5.85400	0.344950
$289$	1.00000	0.0588235
$290$	6.63209	0.389450
$291$	9.55752	0.560272
$292$	15.5518	0.910101
$293$	−17.6041	−1.02844	−0.514221	−	0.857658i	$-0.671919\pi$
$293$	−17.6041	−1.02844	−0.514221	+	0.857658i	$0.671919\pi$
$294$	−5.04264	−0.294093
$295$	5.13759	0.299122
$296$	7.78896	0.452724
$297$	1.42869	0.0829013
$298$	0.243222	0.0140895
$299$	−16.2207	−0.938067
$300$	2.56823	0.148277
$301$	−2.31250	−0.133290
$302$	15.0297	0.864860
$303$	14.7486	0.847286
$304$	−0.787480	−0.0451651
$305$	17.2349	0.986867
$306$	−0.777638	−0.0444546
$307$	−26.1781	−1.49406	−0.747031	−	0.664789i	$-0.768521\pi$
$307$	−26.1781	−1.49406	−0.747031	+	0.664789i	$0.768521\pi$
$308$	−1.43117	−0.0815485
$309$	−7.69302	−0.437641
$310$	7.60127	0.431723
$311$	29.8843	1.69459	0.847293	−	0.531127i	$-0.178231\pi$
$311$	29.8843	1.69459	0.847293	+	0.531127i	$0.178231\pi$
$312$	−17.4449	−0.987625
$313$	16.4718	0.931039	0.465520	−	0.885038i	$-0.345867\pi$
$313$	16.4718	0.931039	0.465520	+	0.885038i	$0.345867\pi$
$314$	−1.96804	−0.111063
$315$	1.27611	0.0719008
$316$	1.39528	0.0784906
$317$	16.9146	0.950020	0.475010	−	0.879980i	$-0.342445\pi$
$317$	16.9146	0.950020	0.475010	+	0.879980i	$0.342445\pi$
$318$	−1.97604	−0.110811
$319$	6.85511	0.383812
$320$	5.47023	0.305795
$321$	2.32410	0.129719
$322$	−1.37063	−0.0763824
$323$	1.06797	0.0594233
$324$	−1.39528	−0.0775155
$325$	−12.1616	−0.674602
$326$	−14.8904	−0.824705
$327$	1.77556	0.0981887
$328$	−11.0171	−0.608318
$329$	0.367167	0.0202426
$330$	1.97476	0.108707
$331$	−3.46151	−0.190262	−0.0951308	−	0.995465i	$-0.530327\pi$
$331$	−3.46151	−0.190262	−0.0951308	+	0.995465i	$0.530327\pi$
$332$	1.58719	0.0871083
$333$	−2.95003	−0.161661
$334$	0.136214	0.00745330
$335$	14.0542	0.767861
$336$	0.529386	0.0288804
$337$	−0.628125	−0.0342162	−0.0171081	−	0.999854i	$-0.505446\pi$
$337$	−0.628125	−0.0342162	−0.0171081	+	0.999854i	$0.505446\pi$
$338$	23.8384	1.29664
$339$	−8.90062	−0.483415
$340$	2.48005	0.134499
$341$	7.85687	0.425474
$342$	−0.830492	−0.0449079
$343$	−9.68116	−0.522733
$344$	8.50441	0.458527
$345$	−4.36366	−0.234932
$346$	2.33293	0.125419
$347$	−5.16003	−0.277005	−0.138502	−	0.990362i	$-0.544229\pi$
$347$	−5.16003	−0.277005	−0.138502	+	0.990362i	$0.544229\pi$
$348$	−6.69478	−0.358878
$349$	−22.6403	−1.21191	−0.605954	−	0.795499i	$-0.707209\pi$
$349$	−22.6403	−1.21191	−0.605954	+	0.795499i	$0.707209\pi$
$350$	−1.02764	−0.0549297
$351$	6.60719	0.352665
$352$	8.36357	0.445780
$353$	−29.5990	−1.57540	−0.787699	−	0.616060i	$-0.788728\pi$
$353$	−29.5990	−1.57540	−0.787699	+	0.616060i	$0.788728\pi$
$354$	2.24770	0.119464
$355$	15.0915	0.800972
$356$	0.0319479	0.00169324
$357$	−0.717944	−0.0379976
$358$	5.20305	0.274990
$359$	4.16726	0.219940	0.109970	−	0.993935i	$-0.464925\pi$
$359$	4.16726	0.219940	0.109970	+	0.993935i	$0.464925\pi$
$360$	−4.69301	−0.247343
$361$	−17.8594	−0.939971
$362$	3.07397	0.161564
$363$	−8.95883	−0.470217
$364$	−6.61863	−0.346911
$365$	−19.8115	−1.03698
$366$	7.54028	0.394137
$367$	0.636468	0.0332234	0.0166117	−	0.999862i	$-0.494712\pi$
$367$	0.636468	0.0332234	0.0166117	+	0.999862i	$0.494712\pi$
$368$	−1.81023	−0.0943649
$369$	4.17267	0.217221
$370$	−4.07758	−0.211983
$371$	−1.82435	−0.0947155
$372$	−7.67311	−0.397832
$373$	−12.3186	−0.637835	−0.318917	−	0.947783i	$-0.603319\pi$
$373$	−12.3186	−0.637835	−0.318917	+	0.947783i	$0.603319\pi$
$374$	−1.11101	−0.0574488
$375$	−12.1590	−0.627886
$376$	−1.35029	−0.0696357
$377$	31.7023	1.63275
$378$	0.558301	0.0287159
$379$	18.6940	0.960248	0.480124	−	0.877201i	$-0.340592\pi$
$379$	18.6940	0.960248	0.480124	+	0.877201i	$0.340592\pi$
$380$	2.64861	0.135871
$381$	5.11319	0.261957
$382$	15.4544	0.790715
$383$	−11.8676	−0.606408	−0.303204	−	0.952926i	$-0.598056\pi$
$383$	−11.8676	−0.606408	−0.303204	+	0.952926i	$0.598056\pi$
$384$	−9.31477	−0.475342
$385$	1.82318	0.0929176
$386$	5.81302	0.295875
$387$	−3.22100	−0.163733
$388$	−13.3354	−0.677003
$389$	1.02530	0.0519848	0.0259924	−	0.999662i	$-0.491725\pi$
$389$	1.02530	0.0519848	0.0259924	+	0.999662i	$0.491725\pi$
$390$	9.13255	0.462445
$391$	2.45501	0.124155
$392$	17.1212	0.864749
$393$	4.24056	0.213908
$394$	−18.8198	−0.948127
$395$	−1.77745	−0.0894334
$396$	−1.99343	−0.100174
$397$	1.64174	0.0823966	0.0411983	−	0.999151i	$-0.486882\pi$
$397$	1.64174	0.0823966	0.0411983	+	0.999151i	$0.486882\pi$
$398$	8.77370	0.439786
$399$	−0.766741	−0.0383851
$400$	−1.35723	−0.0678617
$401$	22.0668	1.10196	0.550982	−	0.834517i	$-0.314253\pi$
$401$	22.0668	1.10196	0.550982	+	0.834517i	$0.314253\pi$
$402$	6.14871	0.306670
$403$	36.3351	1.80998
$404$	−20.5785	−1.02382
$405$	1.77745	0.0883224
$406$	2.67882	0.132947
$407$	−4.21469	−0.208915
$408$	2.64030	0.130714
$409$	−32.4608	−1.60508	−0.802541	−	0.596597i	$-0.796519\pi$
$409$	−32.4608	−1.60508	−0.802541	+	0.596597i	$0.796519\pi$
$410$	5.76754	0.284838
$411$	7.82353	0.385906
$412$	10.7339	0.528822
$413$	2.07516	0.102112
$414$	−1.90911	−0.0938275
$415$	−2.02193	−0.0992526
$416$	38.6784	1.89637
$417$	14.6032	0.715121
$418$	−1.18652	−0.0580346
$419$	−22.5056	−1.09947	−0.549735	−	0.835339i	$-0.685271\pi$
$419$	−22.5056	−1.09947	−0.549735	+	0.835339i	$0.685271\pi$
$420$	−1.78053	−0.0868812
$421$	−28.8510	−1.40611	−0.703056	−	0.711135i	$-0.748182\pi$
$421$	−28.8510	−1.40611	−0.703056	+	0.711135i	$0.748182\pi$
$422$	−8.87016	−0.431793
$423$	0.511414	0.0248658
$424$	6.70919	0.325827
$425$	1.84066	0.0892850
$426$	6.60253	0.319894
$427$	6.96147	0.336889
$428$	−3.24277	−0.156745
$429$	9.43965	0.455751
$430$	−4.45212	−0.214700
$431$	9.03475	0.435189	0.217594	−	0.976039i	$-0.430179\pi$
$431$	9.03475	0.435189	0.217594	+	0.976039i	$0.430179\pi$
$432$	0.737363	0.0354764
$433$	−33.3384	−1.60214	−0.801071	−	0.598569i	$-0.795736\pi$
$433$	−33.3384	−1.60214	−0.801071	+	0.598569i	$0.795736\pi$
$434$	3.07028	0.147378
$435$	8.52851	0.408911
$436$	−2.47740	−0.118646
$437$	2.62187	0.125421
$438$	−8.66757	−0.414152
$439$	−14.2492	−0.680075	−0.340037	−	0.940412i	$-0.610440\pi$
$439$	−14.2492	−0.680075	−0.340037	+	0.940412i	$0.610440\pi$
$440$	−6.70488	−0.319642
$441$	−6.48456	−0.308788
$442$	−5.13800	−0.244390
$443$	−9.16688	−0.435532	−0.217766	−	0.976001i	$-0.569877\pi$
$443$	−9.16688	−0.435532	−0.217766	+	0.976001i	$0.569877\pi$
$444$	4.11612	0.195342
$445$	−0.0406987	−0.00192930
$446$	9.01446	0.426847
$447$	0.312771	0.0147935
$448$	2.20952	0.104390
$449$	9.42042	0.444577	0.222289	−	0.974981i	$-0.428647\pi$
$449$	9.42042	0.444577	0.222289	+	0.974981i	$0.428647\pi$
$450$	−1.43136	−0.0674752
$451$	5.96148	0.280715
$452$	12.4189	0.584134
$453$	19.3273	0.908078
$454$	13.7748	0.646484
$455$	8.43151	0.395275
$456$	2.81975	0.132047
$457$	6.82274	0.319154	0.159577	−	0.987185i	$-0.448987\pi$
$457$	6.82274	0.319154	0.159577	+	0.987185i	$0.448987\pi$
$458$	6.81772	0.318571
$459$	−1.00000	−0.0466760
$460$	6.08853	0.283879
$461$	31.4397	1.46429	0.732145	−	0.681148i	$-0.238519\pi$
$461$	31.4397	1.46429	0.732145	+	0.681148i	$0.238519\pi$
$462$	0.797641	0.0371096
$463$	35.6803	1.65820	0.829102	−	0.559098i	$-0.188852\pi$
$463$	35.6803	1.65820	0.829102	+	0.559098i	$0.188852\pi$
$464$	3.53799	0.164247
$465$	9.77482	0.453296
$466$	−17.0294	−0.788871
$467$	−19.1932	−0.888156	−0.444078	−	0.895988i	$-0.646469\pi$
$467$	−19.1932	−0.888156	−0.444078	+	0.895988i	$0.646469\pi$
$468$	−9.21887	−0.426142
$469$	5.67671	0.262126
$470$	0.706885	0.0326062
$471$	−2.53080	−0.116613
$472$	−7.63157	−0.351272
$473$	−4.60183	−0.211592
$474$	−0.777638	−0.0357181
$475$	1.96576	0.0901953
$476$	1.00173	0.0459143
$477$	−2.54108	−0.116348
$478$	15.0658	0.689094
$479$	−8.33558	−0.380862	−0.190431	−	0.981701i	$-0.560989\pi$
$479$	−8.33558	−0.380862	−0.190431	+	0.981701i	$0.560989\pi$
$480$	10.4052	0.474931
$481$	−19.4914	−0.888731
$482$	−8.93440	−0.406951
$483$	−1.76256	−0.0801992
$484$	12.5001	0.568185
$485$	16.9881	0.771388
$486$	0.777638	0.0352744
$487$	−2.75489	−0.124836	−0.0624180	−	0.998050i	$-0.519881\pi$
$487$	−2.75489	−0.124836	−0.0624180	+	0.998050i	$0.519881\pi$
$488$	−25.6014	−1.15892
$489$	−19.1483	−0.865915
$490$	−8.96305	−0.404910
$491$	8.80815	0.397506	0.198753	−	0.980050i	$-0.436311\pi$
$491$	8.80815	0.397506	0.198753	+	0.980050i	$0.436311\pi$
$492$	−5.82205	−0.262478
$493$	−4.79816	−0.216098
$494$	−5.48721	−0.246881
$495$	2.53944	0.114139
$496$	4.05501	0.182075
$497$	6.09570	0.273430
$498$	−0.884596	−0.0396397
$499$	−10.6419	−0.476398	−0.238199	−	0.971216i	$-0.576557\pi$
$499$	−10.6419	−0.476398	−0.238199	+	0.971216i	$0.576557\pi$
$500$	16.9651	0.758704
$501$	0.175164	0.00782574
$502$	−17.3387	−0.773866
$503$	10.3411	0.461085	0.230543	−	0.973062i	$-0.425950\pi$
$503$	10.3411	0.461085	0.230543	+	0.973062i	$0.425950\pi$
$504$	−1.89559	−0.0844361
$505$	26.2150	1.16655
$506$	−2.72753	−0.121254
$507$	30.6549	1.36143
$508$	−7.13433	−0.316535
$509$	−3.27972	−0.145371	−0.0726856	−	0.997355i	$-0.523157\pi$
$509$	−3.27972	−0.145371	−0.0726856	+	0.997355i	$0.523157\pi$
$510$	−1.38222	−0.0612055
$511$	−8.00222	−0.353997
$512$	8.21024	0.362845
$513$	−1.06797	−0.0471519
$514$	−16.5606	−0.730459
$515$	−13.6740	−0.602548
$516$	4.49420	0.197846
$517$	0.730655	0.0321342
$518$	−1.64700	−0.0723652
$519$	3.00002	0.131686
$520$	−31.0076	−1.35977
$521$	−30.5061	−1.33650	−0.668248	−	0.743938i	$-0.732956\pi$
$521$	−30.5061	−1.33650	−0.668248	+	0.743938i	$0.732956\pi$
$522$	3.73123	0.163312
$523$	−12.3381	−0.539506	−0.269753	−	0.962929i	$-0.586942\pi$
$523$	−12.3381	−0.539506	−0.269753	+	0.962929i	$0.586942\pi$
$524$	−5.91677	−0.258475
$525$	−1.32149	−0.0576745
$526$	−4.83010	−0.210602
$527$	−5.49934	−0.239555
$528$	1.05347	0.0458463
$529$	−16.9729	−0.737954
$530$	−3.51231	−0.152565
$531$	2.89042	0.125434
$532$	1.06982	0.0463825
$533$	27.5696	1.19417
$534$	−0.0178057	−0.000770528 0
$535$	4.13099	0.178598
$536$	−20.8766	−0.901731
$537$	6.69084	0.288731
$538$	21.0995	0.909664
$539$	−9.26445	−0.399048
$540$	−2.48005	−0.106724
$541$	−12.5082	−0.537770	−0.268885	−	0.963172i	$-0.586655\pi$
$541$	−12.5082	−0.537770	−0.268885	+	0.963172i	$0.586655\pi$
$542$	−23.9734	−1.02975
$543$	3.95296	0.169638
$544$	−5.85400	−0.250988
$545$	3.15598	0.135187
$546$	3.68879	0.157866
$547$	10.0502	0.429714	0.214857	−	0.976645i	$-0.431071\pi$
$547$	10.0502	0.429714	0.214857	+	0.976645i	$0.431071\pi$
$548$	−10.9160	−0.466309
$549$	9.69639	0.413832
$550$	−2.04498	−0.0871984
$551$	−5.12428	−0.218302
$552$	6.48195	0.275890
$553$	−0.717944	−0.0305301
$554$	−8.09418	−0.343889
$555$	−5.24355	−0.222576
$556$	−20.3755	−0.864115
$557$	19.1448	0.811192	0.405596	−	0.914052i	$-0.367064\pi$
$557$	19.1448	0.811192	0.405596	+	0.914052i	$0.367064\pi$
$558$	4.27649	0.181038
$559$	−21.2818	−0.900123
$560$	0.940959	0.0397628
$561$	−1.42869	−0.0603195
$562$	−19.3903	−0.817931
$563$	−39.0785	−1.64696	−0.823481	−	0.567344i	$-0.807971\pi$
$563$	−39.0785	−1.64696	−0.823481	+	0.567344i	$0.807971\pi$
$564$	−0.713566	−0.0300465
$565$	−15.8204	−0.665571
$566$	5.12078	0.215243
$567$	0.717944	0.0301508
$568$	−22.4174	−0.940615
$569$	−40.4307	−1.69494	−0.847472	−	0.530840i	$-0.821876\pi$
$569$	−40.4307	−1.69494	−0.847472	+	0.530840i	$0.821876\pi$
$570$	−1.47616	−0.0618296
$571$	−32.4360	−1.35740	−0.678702	−	0.734413i	$-0.737457\pi$
$571$	−32.4360	−1.35740	−0.678702	+	0.734413i	$0.737457\pi$
$572$	−13.1709	−0.550705
$573$	19.8735	0.830227
$574$	2.32961	0.0972359
$575$	4.51883	0.188448
$576$	3.07756	0.128232
$577$	5.75708	0.239670	0.119835	−	0.992794i	$-0.461763\pi$
$577$	5.75708	0.239670	0.119835	+	0.992794i	$0.461763\pi$
$578$	0.777638	0.0323455
$579$	7.47523	0.310660
$580$	−11.8997	−0.494106
$581$	−0.816692	−0.0338821
$582$	7.43229	0.308078
$583$	−3.63042	−0.150357
$584$	29.4288	1.21777
$585$	11.7440	0.485553
$586$	−13.6896	−0.565513
$587$	30.2538	1.24871	0.624355	−	0.781141i	$-0.285362\pi$
$587$	30.2538	1.24871	0.624355	+	0.781141i	$0.285362\pi$
$588$	9.04777	0.373124
$589$	−5.87311	−0.241997
$590$	3.99519	0.164479
$591$	−24.2012	−0.995505
$592$	−2.17525	−0.0894020
$593$	26.4234	1.08508	0.542539	−	0.840031i	$-0.317463\pi$
$593$	26.4234	1.08508	0.542539	+	0.840031i	$0.317463\pi$
$594$	1.11101	0.0455852
$595$	−1.27611	−0.0523155
$596$	−0.436403	−0.0178757
$597$	11.2825	0.461762
$598$	−12.6138	−0.515818
$599$	25.8108	1.05460	0.527301	−	0.849679i	$-0.323204\pi$
$599$	25.8108	1.05460	0.527301	+	0.849679i	$0.323204\pi$
$600$	4.85988	0.198404
$601$	−29.6882	−1.21101	−0.605504	−	0.795842i	$-0.707029\pi$
$601$	−29.6882	−1.21101	−0.605504	+	0.795842i	$0.707029\pi$
$602$	−1.79829	−0.0732927
$603$	7.90690	0.321994
$604$	−26.9670	−1.09727
$605$	−15.9239	−0.647399
$606$	11.4691	0.465900
$607$	−36.8527	−1.49581	−0.747903	−	0.663808i	$-0.768939\pi$
$607$	−36.8527	−1.49581	−0.747903	+	0.663808i	$0.768939\pi$
$608$	−6.25188	−0.253547
$609$	3.44481	0.139591
$610$	13.4025	0.542651
$611$	3.37901	0.136700
$612$	1.39528	0.0564008
$613$	−29.2953	−1.18323	−0.591614	−	0.806222i	$-0.701509\pi$
$613$	−29.2953	−1.18323	−0.591614	+	0.806222i	$0.701509\pi$
$614$	−20.3571	−0.821544
$615$	7.41674	0.299072
$616$	−2.70821	−0.109117
$617$	−14.2308	−0.572911	−0.286455	−	0.958094i	$-0.592477\pi$
$617$	−14.2308	−0.572911	−0.286455	+	0.958094i	$0.592477\pi$
$618$	−5.98239	−0.240647
$619$	6.48680	0.260727	0.130363	−	0.991466i	$-0.458386\pi$
$619$	6.48680	0.260727	0.130363	+	0.991466i	$0.458386\pi$
$620$	−13.6386	−0.547739
$621$	−2.45501	−0.0985161
$622$	23.2392	0.931807
$623$	−0.0164389	−0.000658610 0
$624$	4.87190	0.195032
$625$	−12.4087	−0.496348
$626$	12.8091	0.511953
$627$	−1.52580	−0.0609346
$628$	3.53117	0.140909
$629$	2.95003	0.117625
$630$	0.992354	0.0395363
$631$	11.0576	0.440197	0.220099	−	0.975478i	$-0.429362\pi$
$631$	11.0576	0.440197	0.220099	+	0.975478i	$0.429362\pi$
$632$	2.64030	0.105025
$633$	−11.4065	−0.453369
$634$	13.1534	0.522390
$635$	9.08847	0.360665
$636$	3.54551	0.140589
$637$	−42.8447	−1.69757
$638$	5.33079	0.211048
$639$	8.49050	0.335879
$640$	−16.5566	−0.654456
$641$	29.1665	1.15201	0.576003	−	0.817448i	$-0.304612\pi$
$641$	29.1665	1.15201	0.576003	+	0.817448i	$0.304612\pi$
$642$	1.80731	0.0713289
$643$	−0.106763	−0.00421034	−0.00210517	−	0.999998i	$-0.500670\pi$
$643$	−0.106763	−0.00421034	−0.00210517	+	0.999998i	$0.500670\pi$
$644$	2.45926	0.0969085
$645$	−5.72519	−0.225429
$646$	0.830492	0.0326753
$647$	7.83758	0.308127	0.154064	−	0.988061i	$-0.450764\pi$
$647$	7.83758	0.308127	0.154064	+	0.988061i	$0.450764\pi$
$648$	−2.64030	−0.103721
$649$	4.12953	0.162098
$650$	−9.45729	−0.370945
$651$	3.94822	0.154743
$652$	26.7172	1.04633
$653$	−18.6015	−0.727934	−0.363967	−	0.931412i	$-0.618578\pi$
$653$	−18.6015	−0.727934	−0.363967	+	0.931412i	$0.618578\pi$
$654$	1.38074	0.0539913
$655$	7.53740	0.294511
$656$	3.07678	0.120128
$657$	−11.1460	−0.434848
$658$	0.285523	0.0111308
$659$	−11.6381	−0.453355	−0.226678	−	0.973970i	$-0.572786\pi$
$659$	−11.6381	−0.453355	−0.226678	+	0.973970i	$0.572786\pi$
$660$	−3.54323	−0.137920
$661$	49.7194	1.93386	0.966930	−	0.255042i	$-0.0820892\pi$
$661$	49.7194	1.93386	0.966930	+	0.255042i	$0.0820892\pi$
$662$	−2.69180	−0.104620
$663$	−6.60719	−0.256602
$664$	3.00345	0.116556
$665$	−1.36285	−0.0528489
$666$	−2.29406	−0.0888929
$667$	−11.7795	−0.456105
$668$	−0.244402	−0.00945621
$669$	11.5921	0.448177
$670$	10.9290	0.422226
$671$	13.8532	0.534796
$672$	4.20284	0.162128
$673$	0.465734	0.0179527	0.00897637	−	0.999960i	$-0.497143\pi$
$673$	0.465734	0.0179527	0.00897637	+	0.999960i	$0.497143\pi$
$674$	−0.488454	−0.0188145
$675$	−1.84066	−0.0708469
$676$	−42.7721	−1.64508
$677$	20.5556	0.790016	0.395008	−	0.918678i	$-0.370742\pi$
$677$	20.5556	0.790016	0.395008	+	0.918678i	$0.370742\pi$
$678$	−6.92146	−0.265817
$679$	6.86177	0.263330
$680$	4.69301	0.179969
$681$	17.7137	0.678789
$682$	6.10980	0.233956
$683$	−7.91486	−0.302854	−0.151427	−	0.988468i	$-0.548387\pi$
$683$	−7.91486	−0.302854	−0.151427	+	0.988468i	$0.548387\pi$
$684$	1.49011	0.0569759
$685$	13.9060	0.531319
$686$	−7.52843	−0.287437
$687$	8.76721	0.334490
$688$	−2.37505	−0.0905479
$689$	−16.7894	−0.639623
$690$	−3.39335	−0.129183
$691$	−30.7463	−1.16964	−0.584822	−	0.811162i	$-0.698836\pi$
$691$	−30.7463	−1.16964	−0.584822	+	0.811162i	$0.698836\pi$
$692$	−4.18587	−0.159123
$693$	1.02572	0.0389640
$694$	−4.01263	−0.152317
$695$	25.9565	0.984586
$696$	−12.6686	−0.480201
$697$	−4.17267	−0.158051
$698$	−17.6060	−0.666396
$699$	−21.8989	−0.828291
$700$	1.84385	0.0696908
$701$	36.4781	1.37776	0.688879	−	0.724876i	$-0.258103\pi$
$701$	36.4781	1.37776	0.688879	+	0.724876i	$0.258103\pi$
$702$	5.13800	0.193921
$703$	3.15054	0.118825
$704$	4.39690	0.165714
$705$	0.909015	0.0342355
$706$	−23.0173	−0.866269
$707$	10.5887	0.398229
$708$	−4.03295	−0.151567
$709$	−27.6477	−1.03833	−0.519166	−	0.854673i	$-0.673757\pi$
$709$	−27.6477	−1.03833	−0.519166	+	0.854673i	$0.673757\pi$
$710$	11.7357	0.440433
$711$	−1.00000	−0.0375029
$712$	0.0604553	0.00226566
$713$	−13.5009	−0.505613
$714$	−0.558301	−0.0208939
$715$	16.7785	0.627482
$716$	−9.33560	−0.348888
$717$	19.3738	0.723528
$718$	3.24062	0.120939
$719$	11.1309	0.415113	0.207556	−	0.978223i	$-0.433449\pi$
$719$	11.1309	0.415113	0.207556	+	0.978223i	$0.433449\pi$
$720$	1.31063	0.0488443
$721$	−5.52316	−0.205693
$722$	−13.8882	−0.516865
$723$	−11.4892	−0.427286
$724$	−5.51548	−0.204981
$725$	−8.83177	−0.328004
$726$	−6.96673	−0.258559
$727$	−27.1493	−1.00691	−0.503456	−	0.864021i	$-0.667938\pi$
$727$	−27.1493	−1.00691	−0.503456	+	0.864021i	$0.667938\pi$
$728$	−12.5245	−0.464188
$729$	1.00000	0.0370370
$730$	−15.4062	−0.570209
$731$	3.22100	0.119133
$732$	−13.5292	−0.500053
$733$	38.0028	1.40366	0.701832	−	0.712343i	$-0.252366\pi$
$733$	38.0028	1.40366	0.701832	+	0.712343i	$0.252366\pi$
$734$	0.494942	0.0182686
$735$	−11.5260	−0.425143
$736$	−14.3716	−0.529745
$737$	11.2965	0.416114
$738$	3.24483	0.119444
$739$	−17.2689	−0.635245	−0.317623	−	0.948217i	$-0.602884\pi$
$739$	−17.2689	−0.635245	−0.317623	+	0.948217i	$0.602884\pi$
$740$	7.31621	0.268949
$741$	−7.05626	−0.259218
$742$	−1.41868	−0.0520815
$743$	−41.2197	−1.51220	−0.756102	−	0.654454i	$-0.772898\pi$
$743$	−41.2197	−1.51220	−0.756102	+	0.654454i	$0.772898\pi$
$744$	−14.5199	−0.532325
$745$	0.555936	0.0203679
$746$	−9.57944	−0.350728
$747$	−1.13754	−0.0416205
$748$	1.99343	0.0728870
$749$	1.66858	0.0609685
$750$	−9.45526	−0.345257
$751$	47.3324	1.72718	0.863591	−	0.504193i	$-0.168210\pi$
$751$	47.3324	1.72718	0.863591	+	0.504193i	$0.168210\pi$
$752$	0.377098	0.0137514
$753$	−22.2967	−0.812537
$754$	24.6529	0.897807
$755$	34.3535	1.25025
$756$	−1.00173	−0.0364327
$757$	−49.4339	−1.79671	−0.898353	−	0.439274i	$-0.855236\pi$
$757$	−49.4339	−1.79671	−0.898353	+	0.439274i	$0.855236\pi$
$758$	14.5372	0.528014
$759$	−3.50746	−0.127313
$760$	5.01198	0.181804
$761$	45.8946	1.66368	0.831838	−	0.555018i	$-0.187289\pi$
$761$	45.8946	1.66368	0.831838	+	0.555018i	$0.187289\pi$
$762$	3.97621	0.144043
$763$	1.27475	0.0461491
$764$	−27.7291	−1.00320
$765$	−1.77745	−0.0642640
$766$	−9.22872	−0.333447
$767$	19.0976	0.689573
$768$	−13.3986	−0.483482
$769$	25.3882	0.915523	0.457761	−	0.889075i	$-0.348651\pi$
$769$	25.3882	0.915523	0.457761	+	0.889075i	$0.348651\pi$
$770$	1.41777	0.0510929
$771$	−21.2961	−0.766960
$772$	−10.4300	−0.375385
$773$	−18.2443	−0.656203	−0.328102	−	0.944642i	$-0.606409\pi$
$773$	−18.2443	−0.656203	−0.328102	+	0.944642i	$0.606409\pi$
$774$	−2.50477	−0.0900322
$775$	−10.1224	−0.363607
$776$	−25.2347	−0.905873
$777$	−2.11796	−0.0759813
$778$	0.797313	0.0285850
$779$	−4.45628	−0.159663
$780$	−16.3861	−0.586717
$781$	12.1303	0.434057
$782$	1.90911	0.0682695
$783$	4.79816	0.171472
$784$	−4.78147	−0.170767
$785$	−4.49838	−0.160554
$786$	3.29762	0.117622
$787$	27.1143	0.966522	0.483261	−	0.875476i	$-0.339452\pi$
$787$	27.1143	0.966522	0.483261	+	0.875476i	$0.339452\pi$
$788$	33.7675	1.20292
$789$	−6.21125	−0.221126
$790$	−1.38222	−0.0491770
$791$	−6.39015	−0.227208
$792$	−3.77218	−0.134039
$793$	64.0658	2.27504
$794$	1.27668	0.0453077
$795$	−4.51664	−0.160189
$796$	−15.7422	−0.557969
$797$	−31.5392	−1.11718	−0.558588	−	0.829445i	$-0.688657\pi$
$797$	−31.5392	−1.11718	−0.558588	+	0.829445i	$0.688657\pi$
$798$	−0.596247	−0.0211069
$799$	−0.511414	−0.0180925
$800$	−10.7752	−0.380961
$801$	−0.0228972	−0.000809031 0
$802$	17.1600	0.605940
$803$	−15.9243	−0.561955
$804$	−11.0323	−0.389081
$805$	−3.13287	−0.110419
$806$	28.2556	0.995260
$807$	27.1328	0.955120
$808$	−38.9408	−1.36993
$809$	−3.71532	−0.130624	−0.0653119	−	0.997865i	$-0.520804\pi$
$809$	−3.71532	−0.130624	−0.0653119	+	0.997865i	$0.520804\pi$
$810$	1.38222	0.0485661
$811$	−45.6594	−1.60332	−0.801658	−	0.597782i	$-0.796049\pi$
$811$	−45.6594	−1.60332	−0.801658	+	0.597782i	$0.796049\pi$
$812$	−4.80648	−0.168674
$813$	−30.8285	−1.08120
$814$	−3.27751	−0.114877
$815$	−34.0352	−1.19220
$816$	−0.737363	−0.0258129
$817$	3.43993	0.120348
$818$	−25.2427	−0.882591
$819$	4.74359	0.165754
$820$	−10.3484	−0.361383
$821$	−4.67428	−0.163133	−0.0815667	−	0.996668i	$-0.525992\pi$
$821$	−4.67428	−0.163133	−0.0815667	+	0.996668i	$0.525992\pi$
$822$	6.08387	0.212199
$823$	−12.9711	−0.452143	−0.226071	−	0.974111i	$-0.572588\pi$
$823$	−12.9711	−0.452143	−0.226071	+	0.974111i	$0.572588\pi$
$824$	20.3119	0.707598
$825$	−2.62974	−0.0915557
$826$	1.61372	0.0561486
$827$	23.3918	0.813414	0.406707	−	0.913559i	$-0.366677\pi$
$827$	23.3918	0.813414	0.406707	+	0.913559i	$0.366677\pi$
$828$	3.42542	0.119042
$829$	−18.0786	−0.627894	−0.313947	−	0.949440i	$-0.601651\pi$
$829$	−18.0786	−0.627894	−0.313947	+	0.949440i	$0.601651\pi$
$830$	−1.57233	−0.0545763
$831$	−10.4087	−0.361073
$832$	20.3340	0.704956
$833$	6.48456	0.224677
$834$	11.3560	0.393226
$835$	0.311346	0.0107746
$836$	2.12892	0.0736301
$837$	5.49934	0.190085
$838$	−17.5012	−0.604569
$839$	−4.71461	−0.162766	−0.0813831	−	0.996683i	$-0.525934\pi$
$839$	−4.71461	−0.162766	−0.0813831	+	0.996683i	$0.525934\pi$
$840$	−3.36932	−0.116252
$841$	−5.97764	−0.206125
$842$	−22.4356	−0.773183
$843$	−24.9349	−0.858803
$844$	15.9153	0.547828
$845$	54.4877	1.87443
$846$	0.397695	0.0136730
$847$	−6.43194	−0.221004
$848$	−1.87370	−0.0643430
$849$	6.58505	0.225998
$850$	1.43136	0.0490954
$851$	7.24235	0.248265
$852$	−11.8466	−0.405858
$853$	−36.9736	−1.26595	−0.632977	−	0.774171i	$-0.718167\pi$
$853$	−36.9736	−1.26595	−0.632977	+	0.774171i	$0.718167\pi$
$854$	5.41350	0.185246
$855$	−1.89826	−0.0649192
$856$	−6.13632	−0.209735
$857$	−33.2689	−1.13644	−0.568222	−	0.822875i	$-0.692369\pi$
$857$	−33.2689	−1.13644	−0.568222	+	0.822875i	$0.692369\pi$
$858$	7.34063	0.250605
$859$	−15.6953	−0.535515	−0.267758	−	0.963486i	$-0.586283\pi$
$859$	−15.6953	−0.535515	−0.267758	+	0.963486i	$0.586283\pi$
$860$	7.98823	0.272396
$861$	2.99575	0.102095
$862$	7.02576	0.239298
$863$	18.1770	0.618752	0.309376	−	0.950940i	$-0.399880\pi$
$863$	18.1770	0.618752	0.309376	+	0.950940i	$0.399880\pi$
$864$	5.85400	0.199157
$865$	5.33240	0.181307
$866$	−25.9252	−0.880975
$867$	1.00000	0.0339618
$868$	−5.50887	−0.186983
$869$	−1.42869	−0.0484651
$870$	6.63209	0.224849
$871$	52.2424	1.77017
$872$	−4.68801	−0.158756
$873$	9.55752	0.323473
$874$	2.03886	0.0689656
$875$	−8.72945	−0.295109
$876$	15.5518	0.525447
$877$	−18.3066	−0.618171	−0.309086	−	0.951034i	$-0.600023\pi$
$877$	−18.3066	−0.618171	−0.309086	+	0.951034i	$0.600023\pi$
$878$	−11.0807	−0.373955
$879$	−17.6041	−0.593772
$880$	1.87249	0.0631216
$881$	47.2992	1.59355	0.796776	−	0.604275i	$-0.206537\pi$
$881$	47.2992	1.59355	0.796776	+	0.604275i	$0.206537\pi$
$882$	−5.04264	−0.169794
$883$	−41.3351	−1.39104	−0.695518	−	0.718509i	$-0.744825\pi$
$883$	−41.3351	−1.39104	−0.695518	+	0.718509i	$0.744825\pi$
$884$	9.21887	0.310064
$885$	5.13759	0.172698
$886$	−7.12851	−0.239487
$887$	17.7000	0.594306	0.297153	−	0.954830i	$-0.403963\pi$
$887$	17.7000	0.594306	0.297153	+	0.954830i	$0.403963\pi$
$888$	7.78896	0.261380
$889$	3.67099	0.123121
$890$	−0.0316488	−0.00106087
$891$	1.42869	0.0478631
$892$	−16.1742	−0.541553
$893$	−0.546174	−0.0182770
$894$	0.243222	0.00813457
$895$	11.8927	0.397528
$896$	−6.68748	−0.223413
$897$	−16.2207	−0.541593
$898$	7.32568	0.244461
$899$	26.3867	0.880046
$900$	2.56823	0.0856077
$901$	2.54108	0.0846555
$902$	4.63587	0.154358
$903$	−2.31250	−0.0769552
$904$	23.5003	0.781608
$905$	7.02620	0.233559
$906$	15.0297	0.499327
$907$	50.7479	1.68506	0.842529	−	0.538651i	$-0.181066\pi$
$907$	50.7479	1.68506	0.842529	+	0.538651i	$0.181066\pi$
$908$	−24.7155	−0.820213
$909$	14.7486	0.489181
$910$	6.55666	0.217351
$911$	−30.4599	−1.00918	−0.504591	−	0.863359i	$-0.668357\pi$
$911$	−30.4599	−1.00918	−0.504591	+	0.863359i	$0.668357\pi$
$912$	−0.787480	−0.0260761
$913$	−1.62520	−0.0537863
$914$	5.30562	0.175494
$915$	17.2349	0.569768
$916$	−12.2327	−0.404180
$917$	3.04449	0.100538
$918$	−0.777638	−0.0256659
$919$	8.04135	0.265260	0.132630	−	0.991166i	$-0.457658\pi$
$919$	8.04135	0.265260	0.132630	+	0.991166i	$0.457658\pi$
$920$	11.5214	0.379848
$921$	−26.1781	−0.862597
$922$	24.4487	0.805174
$923$	56.0983	1.84650
$924$	−1.43117	−0.0470820
$925$	5.43000	0.178537
$926$	27.7463	0.911801
$927$	−7.69302	−0.252672
$928$	28.0884	0.922048
$929$	−22.9711	−0.753658	−0.376829	−	0.926283i	$-0.622986\pi$
$929$	−22.9711	−0.753658	−0.376829	+	0.926283i	$0.622986\pi$
$930$	7.60127	0.249255
$931$	6.92530	0.226967
$932$	30.5550	1.00086
$933$	29.8843	0.978369
$934$	−14.9254	−0.488373
$935$	−2.53944	−0.0830485
$936$	−17.4449	−0.570206
$937$	−6.68651	−0.218439	−0.109219	−	0.994018i	$-0.534835\pi$
$937$	−6.68651	−0.218439	−0.109219	+	0.994018i	$0.534835\pi$
$938$	4.41443	0.144136
$939$	16.4718	0.537536
$940$	−1.26833	−0.0413684
$941$	41.3948	1.34943	0.674715	−	0.738078i	$-0.264266\pi$
$941$	41.3948	1.34943	0.674715	+	0.738078i	$0.264266\pi$
$942$	−1.96804	−0.0641223
$943$	−10.2440	−0.333589
$944$	2.13129	0.0693676
$945$	1.27611	0.0415120
$946$	−3.57856	−0.116349
$947$	−28.5954	−0.929227	−0.464613	−	0.885514i	$-0.653807\pi$
$947$	−28.5954	−0.929227	−0.464613	+	0.885514i	$0.653807\pi$
$948$	1.39528	0.0453166
$949$	−73.6438	−2.39058
$950$	1.52865	0.0495960
$951$	16.9146	0.548494
$952$	1.89559	0.0614363
$953$	34.3056	1.11127	0.555634	−	0.831427i	$-0.312476\pi$
$953$	34.3056	1.11127	0.555634	+	0.831427i	$0.312476\pi$
$954$	−1.97604	−0.0639765
$955$	35.3242	1.14307
$956$	−27.0319	−0.874273
$957$	6.85511	0.221594
$958$	−6.48206	−0.209426
$959$	5.61685	0.181378
$960$	5.47023	0.176551
$961$	−0.757297	−0.0244289
$962$	−15.1573	−0.488689
$963$	2.32410	0.0748932
$964$	16.0306	0.516310
$965$	13.2869	0.427720
$966$	−1.37063	−0.0440994
$967$	−41.5709	−1.33683	−0.668415	−	0.743789i	$-0.733027\pi$
$967$	−41.5709	−1.33683	−0.668415	+	0.743789i	$0.733027\pi$
$968$	23.6540	0.760268
$969$	1.06797	0.0343081
$970$	13.2106	0.424165
$971$	−60.1165	−1.92923	−0.964616	−	0.263661i	$-0.915070\pi$
$971$	−60.1165	−1.92923	−0.964616	+	0.263661i	$0.915070\pi$
$972$	−1.39528	−0.0447536
$973$	10.4843	0.336110
$974$	−2.14231	−0.0686440
$975$	−12.1616	−0.389482
$976$	7.14976	0.228858
$977$	−23.7310	−0.759222	−0.379611	−	0.925146i	$-0.623942\pi$
$977$	−23.7310	−0.759222	−0.379611	+	0.925146i	$0.623942\pi$
$978$	−14.8904	−0.476144
$979$	−0.0327131	−0.00104551
$980$	16.0820	0.513720
$981$	1.77556	0.0566893
$982$	6.84955	0.218578
$983$	−17.4742	−0.557341	−0.278671	−	0.960387i	$-0.589894\pi$
$983$	−17.4742	−0.557341	−0.278671	+	0.960387i	$0.589894\pi$
$984$	−11.0171	−0.351212
$985$	−43.0165	−1.37062
$986$	−3.73123	−0.118827
$987$	0.367167	0.0116871
$988$	9.84545	0.313226
$989$	7.90759	0.251447
$990$	1.97476	0.0627621
$991$	−11.6397	−0.369747	−0.184873	−	0.982762i	$-0.559187\pi$
$991$	−11.6397	−0.369747	−0.184873	+	0.982762i	$0.559187\pi$
$992$	32.1931	1.02213
$993$	−3.46151	−0.109848
$994$	4.74025	0.150352
$995$	20.0541	0.635759
$996$	1.58719	0.0502920
$997$	2.64129	0.0836504	0.0418252	−	0.999125i	$-0.486683\pi$
$997$	2.64129	0.0836504	0.0418252	+	0.999125i	$0.486683\pi$
$998$	−8.27556	−0.261958
$999$	−2.95003	−0.0933349

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.j.1.14	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.j.1.14	✓	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)

\(f(q)\)	\(=\)	\(q+0.777638 q^{2} +1.00000 q^{3} -1.39528 q^{4} +1.77745 q^{5} +0.777638 q^{6} +0.717944 q^{7} -2.64030 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.777638 q^{2} +1.00000 q^{3} -1.39528 q^{4} +1.77745 q^{5} +0.777638 q^{6} +0.717944 q^{7} -2.64030 q^{8} +1.00000 q^{9} +1.38222 q^{10} +1.42869 q^{11} -1.39528 q^{12} +6.60719 q^{13} +0.558301 q^{14} +1.77745 q^{15} +0.737363 q^{16} -1.00000 q^{17} +0.777638 q^{18} -1.06797 q^{19} -2.48005 q^{20} +0.717944 q^{21} +1.11101 q^{22} -2.45501 q^{23} -2.64030 q^{24} -1.84066 q^{25} +5.13800 q^{26} +1.00000 q^{27} -1.00173 q^{28} +4.79816 q^{29} +1.38222 q^{30} +5.49934 q^{31} +5.85400 q^{32} +1.42869 q^{33} -0.777638 q^{34} +1.27611 q^{35} -1.39528 q^{36} -2.95003 q^{37} -0.830492 q^{38} +6.60719 q^{39} -4.69301 q^{40} +4.17267 q^{41} +0.558301 q^{42} -3.22100 q^{43} -1.99343 q^{44} +1.77745 q^{45} -1.90911 q^{46} +0.511414 q^{47} +0.737363 q^{48} -6.48456 q^{49} -1.43136 q^{50} -1.00000 q^{51} -9.21887 q^{52} -2.54108 q^{53} +0.777638 q^{54} +2.53944 q^{55} -1.89559 q^{56} -1.06797 q^{57} +3.73123 q^{58} +2.89042 q^{59} -2.48005 q^{60} +9.69639 q^{61} +4.27649 q^{62} +0.717944 q^{63} +3.07756 q^{64} +11.7440 q^{65} +1.11101 q^{66} +7.90690 q^{67} +1.39528 q^{68} -2.45501 q^{69} +0.992354 q^{70} +8.49050 q^{71} -2.64030 q^{72} -11.1460 q^{73} -2.29406 q^{74} -1.84066 q^{75} +1.49011 q^{76} +1.02572 q^{77} +5.13800 q^{78} -1.00000 q^{79} +1.31063 q^{80} +1.00000 q^{81} +3.24483 q^{82} -1.13754 q^{83} -1.00173 q^{84} -1.77745 q^{85} -2.50477 q^{86} +4.79816 q^{87} -3.77218 q^{88} -0.0228972 q^{89} +1.38222 q^{90} +4.74359 q^{91} +3.42542 q^{92} +5.49934 q^{93} +0.397695 q^{94} -1.89826 q^{95} +5.85400 q^{96} +9.55752 q^{97} -5.04264 q^{98} +1.42869 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 6 q^{2} + 25 q^{3} + 26 q^{4} + 6 q^{5} + 6 q^{6} + 4 q^{7} + 18 q^{8} + 25 q^{9}+O(q^{10}) \) 25 * q + 6 * q^2 + 25 * q^3 + 26 * q^4 + 6 * q^5 + 6 * q^6 + 4 * q^7 + 18 * q^8 + 25 * q^9	\( 25 q + 6 q^{2} + 25 q^{3} + 26 q^{4} + 6 q^{5} + 6 q^{6} + 4 q^{7} + 18 q^{8} + 25 q^{9} + 13 q^{10} + 19 q^{11} + 26 q^{12} + 17 q^{14} + 6 q^{15} + 16 q^{16} - 25 q^{17} + 6 q^{18} + 25 q^{19} + 32 q^{20} + 4 q^{21} - 7 q^{22} + 8 q^{23} + 18 q^{24} + 15 q^{25} + 20 q^{26} + 25 q^{27} + 9 q^{28} + 21 q^{29} + 13 q^{30} + 4 q^{31} + 27 q^{32} + 19 q^{33} - 6 q^{34} + 50 q^{35} + 26 q^{36} - 8 q^{37} + 31 q^{38} + 52 q^{40} + 40 q^{41} + 17 q^{42} + 21 q^{43} + 34 q^{44} + 6 q^{45} + 29 q^{46} + 43 q^{47} + 16 q^{48} + 21 q^{49} + 13 q^{50} - 25 q^{51} + 3 q^{52} + 44 q^{53} + 6 q^{54} + 13 q^{55} + 38 q^{56} + 25 q^{57} - 5 q^{58} + 45 q^{59} + 32 q^{60} + 22 q^{61} + 4 q^{62} + 4 q^{63} + 26 q^{64} + 43 q^{65} - 7 q^{66} + 8 q^{67} - 26 q^{68} + 8 q^{69} + 29 q^{70} + 9 q^{71} + 18 q^{72} - 7 q^{73} + 18 q^{74} + 15 q^{75} + 33 q^{76} + 20 q^{77} + 20 q^{78} - 25 q^{79} + 42 q^{80} + 25 q^{81} - 43 q^{82} + 41 q^{83} + 9 q^{84} - 6 q^{85} - 12 q^{86} + 21 q^{87} - 43 q^{88} + 68 q^{89} + 13 q^{90} + 10 q^{91} + 2 q^{92} + 4 q^{93} - 17 q^{94} + 8 q^{95} + 27 q^{96} + 15 q^{97} + 11 q^{98} + 19 q^{99}+O(q^{100}) \) 25 * q + 6 * q^2 + 25 * q^3 + 26 * q^4 + 6 * q^5 + 6 * q^6 + 4 * q^7 + 18 * q^8 + 25 * q^9 + 13 * q^10 + 19 * q^11 + 26 * q^12 + 17 * q^14 + 6 * q^15 + 16 * q^16 - 25 * q^17 + 6 * q^18 + 25 * q^19 + 32 * q^20 + 4 * q^21 - 7 * q^22 + 8 * q^23 + 18 * q^24 + 15 * q^25 + 20 * q^26 + 25 * q^27 + 9 * q^28 + 21 * q^29 + 13 * q^30 + 4 * q^31 + 27 * q^32 + 19 * q^33 - 6 * q^34 + 50 * q^35 + 26 * q^36 - 8 * q^37 + 31 * q^38 + 52 * q^40 + 40 * q^41 + 17 * q^42 + 21 * q^43 + 34 * q^44 + 6 * q^45 + 29 * q^46 + 43 * q^47 + 16 * q^48 + 21 * q^49 + 13 * q^50 - 25 * q^51 + 3 * q^52 + 44 * q^53 + 6 * q^54 + 13 * q^55 + 38 * q^56 + 25 * q^57 - 5 * q^58 + 45 * q^59 + 32 * q^60 + 22 * q^61 + 4 * q^62 + 4 * q^63 + 26 * q^64 + 43 * q^65 - 7 * q^66 + 8 * q^67 - 26 * q^68 + 8 * q^69 + 29 * q^70 + 9 * q^71 + 18 * q^72 - 7 * q^73 + 18 * q^74 + 15 * q^75 + 33 * q^76 + 20 * q^77 + 20 * q^78 - 25 * q^79 + 42 * q^80 + 25 * q^81 - 43 * q^82 + 41 * q^83 + 9 * q^84 - 6 * q^85 - 12 * q^86 + 21 * q^87 - 43 * q^88 + 68 * q^89 + 13 * q^90 + 10 * q^91 + 2 * q^92 + 4 * q^93 - 17 * q^94 + 8 * q^95 + 27 * q^96 + 15 * q^97 + 11 * q^98 + 19 * q^99

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