LMFDB - Embedded newform 4029.2.a.i.1.3

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			1.3
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)

$f(q)$	$=$	$q-2.33071 q^{2} -1.00000 q^{3} +3.43222 q^{4} -2.50795 q^{5} +2.33071 q^{6} -3.36649 q^{7} -3.33810 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.33071 q^{2} -1.00000 q^{3} +3.43222 q^{4} -2.50795 q^{5} +2.33071 q^{6} -3.36649 q^{7} -3.33810 q^{8} +1.00000 q^{9} +5.84531 q^{10} +0.826313 q^{11} -3.43222 q^{12} -3.54617 q^{13} +7.84633 q^{14} +2.50795 q^{15} +0.915716 q^{16} +1.00000 q^{17} -2.33071 q^{18} +7.67391 q^{19} -8.60784 q^{20} +3.36649 q^{21} -1.92590 q^{22} -5.59795 q^{23} +3.33810 q^{24} +1.28980 q^{25} +8.26510 q^{26} -1.00000 q^{27} -11.5546 q^{28} -2.40232 q^{29} -5.84531 q^{30} +2.51238 q^{31} +4.54194 q^{32} -0.826313 q^{33} -2.33071 q^{34} +8.44299 q^{35} +3.43222 q^{36} +5.33541 q^{37} -17.8857 q^{38} +3.54617 q^{39} +8.37179 q^{40} -3.88300 q^{41} -7.84633 q^{42} -8.76249 q^{43} +2.83609 q^{44} -2.50795 q^{45} +13.0472 q^{46} -11.3014 q^{47} -0.915716 q^{48} +4.33326 q^{49} -3.00616 q^{50} -1.00000 q^{51} -12.1712 q^{52} -12.2303 q^{53} +2.33071 q^{54} -2.07235 q^{55} +11.2377 q^{56} -7.67391 q^{57} +5.59912 q^{58} +3.58135 q^{59} +8.60784 q^{60} +6.37152 q^{61} -5.85564 q^{62} -3.36649 q^{63} -12.4174 q^{64} +8.89360 q^{65} +1.92590 q^{66} +0.844427 q^{67} +3.43222 q^{68} +5.59795 q^{69} -19.6782 q^{70} -5.65221 q^{71} -3.33810 q^{72} +5.12836 q^{73} -12.4353 q^{74} -1.28980 q^{75} +26.3386 q^{76} -2.78177 q^{77} -8.26510 q^{78} -1.00000 q^{79} -2.29657 q^{80} +1.00000 q^{81} +9.05017 q^{82} -16.3115 q^{83} +11.5546 q^{84} -2.50795 q^{85} +20.4229 q^{86} +2.40232 q^{87} -2.75832 q^{88} -12.4342 q^{89} +5.84531 q^{90} +11.9381 q^{91} -19.2134 q^{92} -2.51238 q^{93} +26.3403 q^{94} -19.2458 q^{95} -4.54194 q^{96} -15.4596 q^{97} -10.0996 q^{98} +0.826313 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - 2 q^{2} - 25 q^{3} + 26 q^{4} - 2 q^{5} + 2 q^{6} + 12 q^{7} + 25 q^{9}+O(q^{10}) $ 25 * q - 2 * q^2 - 25 * q^3 + 26 * q^4 - 2 * q^5 + 2 * q^6 + 12 * q^7 + 25 * q^9	\( 25 q - 2 q^{2} - 25 q^{3} + 26 q^{4} - 2 q^{5} + 2 q^{6} + 12 q^{7} + 25 q^{9} + 19 q^{10} + 19 q^{11} - 26 q^{12} + 4 q^{13} + 15 q^{14} + 2 q^{15} + 32 q^{16} + 25 q^{17} - 2 q^{18} + 29 q^{19} - 8 q^{20} - 12 q^{21} + 23 q^{22} + 6 q^{23} + 15 q^{25} - 8 q^{26} - 25 q^{27} + 23 q^{28} + 11 q^{29} - 19 q^{30} + 38 q^{31} - 27 q^{32} - 19 q^{33} - 2 q^{34} + 20 q^{35} + 26 q^{36} + 8 q^{37} - 25 q^{38} - 4 q^{39} + 48 q^{40} + 24 q^{41} - 15 q^{42} + 11 q^{43} + 6 q^{44} - 2 q^{45} + 25 q^{46} + 23 q^{47} - 32 q^{48} + 21 q^{49} - 21 q^{50} - 25 q^{51} + 31 q^{52} - 16 q^{53} + 2 q^{54} - 11 q^{55} + 18 q^{56} - 29 q^{57} - 5 q^{58} + 27 q^{59} + 8 q^{60} + 40 q^{61} - 34 q^{62} + 12 q^{63} + 46 q^{64} - 19 q^{65} - 23 q^{66} + 24 q^{67} + 26 q^{68} - 6 q^{69} + 17 q^{70} + 19 q^{71} + 13 q^{73} - 56 q^{74} - 15 q^{75} + 21 q^{76} - 30 q^{77} + 8 q^{78} - 25 q^{79} - 40 q^{80} + 25 q^{81} + 61 q^{82} + q^{83} - 23 q^{84} - 2 q^{85} + 62 q^{86} - 11 q^{87} - q^{88} - 10 q^{89} + 19 q^{90} + 50 q^{91} + 18 q^{92} - 38 q^{93} + 15 q^{94} + 14 q^{95} + 27 q^{96} + 19 q^{97} - 23 q^{98} + 19 q^{99}+O(q^{100}) \) 25 * q - 2 * q^2 - 25 * q^3 + 26 * q^4 - 2 * q^5 + 2 * q^6 + 12 * q^7 + 25 * q^9 + 19 * q^10 + 19 * q^11 - 26 * q^12 + 4 * q^13 + 15 * q^14 + 2 * q^15 + 32 * q^16 + 25 * q^17 - 2 * q^18 + 29 * q^19 - 8 * q^20 - 12 * q^21 + 23 * q^22 + 6 * q^23 + 15 * q^25 - 8 * q^26 - 25 * q^27 + 23 * q^28 + 11 * q^29 - 19 * q^30 + 38 * q^31 - 27 * q^32 - 19 * q^33 - 2 * q^34 + 20 * q^35 + 26 * q^36 + 8 * q^37 - 25 * q^38 - 4 * q^39 + 48 * q^40 + 24 * q^41 - 15 * q^42 + 11 * q^43 + 6 * q^44 - 2 * q^45 + 25 * q^46 + 23 * q^47 - 32 * q^48 + 21 * q^49 - 21 * q^50 - 25 * q^51 + 31 * q^52 - 16 * q^53 + 2 * q^54 - 11 * q^55 + 18 * q^56 - 29 * q^57 - 5 * q^58 + 27 * q^59 + 8 * q^60 + 40 * q^61 - 34 * q^62 + 12 * q^63 + 46 * q^64 - 19 * q^65 - 23 * q^66 + 24 * q^67 + 26 * q^68 - 6 * q^69 + 17 * q^70 + 19 * q^71 + 13 * q^73 - 56 * q^74 - 15 * q^75 + 21 * q^76 - 30 * q^77 + 8 * q^78 - 25 * q^79 - 40 * q^80 + 25 * q^81 + 61 * q^82 + q^83 - 23 * q^84 - 2 * q^85 + 62 * q^86 - 11 * q^87 - q^88 - 10 * q^89 + 19 * q^90 + 50 * q^91 + 18 * q^92 - 38 * q^93 + 15 * q^94 + 14 * q^95 + 27 * q^96 + 19 * q^97 - 23 * q^98 + 19 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.33071	−1.64806	−0.824032	−	0.566544i	$-0.808280\pi$
$2$	−2.33071	−1.64806	−0.824032	+	0.566544i	$0.808280\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	3.43222	1.71611
$5$	−2.50795	−1.12159	−0.560794	−	0.827955i	$-0.689504\pi$
$5$	−2.50795	−1.12159	−0.560794	+	0.827955i	$0.689504\pi$
$6$	2.33071	0.951510
$7$	−3.36649	−1.27241	−0.636207	−	0.771518i	$-0.719498\pi$
$7$	−3.36649	−1.27241	−0.636207	+	0.771518i	$0.719498\pi$
$8$	−3.33810	−1.18020
$9$	1.00000	0.333333
$10$	5.84531	1.84845
$11$	0.826313	0.249143	0.124571	−	0.992211i	$-0.460244\pi$
$11$	0.826313	0.249143	0.124571	+	0.992211i	$0.460244\pi$
$12$	−3.43222	−0.990798
$13$	−3.54617	−0.983530	−0.491765	−	0.870728i	$-0.663648\pi$
$13$	−3.54617	−0.983530	−0.491765	+	0.870728i	$0.663648\pi$
$14$	7.84633	2.09702
$15$	2.50795	0.647549
$16$	0.915716	0.228929
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−2.33071	−0.549354
$19$	7.67391	1.76052	0.880258	−	0.474496i	$-0.157370\pi$
$19$	7.67391	1.76052	0.880258	+	0.474496i	$0.157370\pi$
$20$	−8.60784	−1.92477
$21$	3.36649	0.734629
$22$	−1.92590	−0.410603
$23$	−5.59795	−1.16725	−0.583626	−	0.812022i	$-0.698367\pi$
$23$	−5.59795	−1.16725	−0.583626	+	0.812022i	$0.698367\pi$
$24$	3.33810	0.681388
$25$	1.28980	0.257961
$26$	8.26510	1.62092
$27$	−1.00000	−0.192450
$28$	−11.5546	−2.18361
$29$	−2.40232	−0.446100	−0.223050	−	0.974807i	$-0.571601\pi$
$29$	−2.40232	−0.446100	−0.223050	+	0.974807i	$0.571601\pi$
$30$	−5.84531	−1.06720
$31$	2.51238	0.451237	0.225618	−	0.974216i	$-0.427560\pi$
$31$	2.51238	0.451237	0.225618	+	0.974216i	$0.427560\pi$
$32$	4.54194	0.802909
$33$	−0.826313	−0.143843
$34$	−2.33071	−0.399714
$35$	8.44299	1.42713
$36$	3.43222	0.572037
$37$	5.33541	0.877136	0.438568	−	0.898698i	$-0.355486\pi$
$37$	5.33541	0.877136	0.438568	+	0.898698i	$0.355486\pi$
$38$	−17.8857	−2.90144
$39$	3.54617	0.567841
$40$	8.37179	1.32370
$41$	−3.88300	−0.606423	−0.303212	−	0.952923i	$-0.598059\pi$
$41$	−3.88300	−0.606423	−0.303212	+	0.952923i	$0.598059\pi$
$42$	−7.84633	−1.21071
$43$	−8.76249	−1.33627	−0.668134	−	0.744041i	$-0.732907\pi$
$43$	−8.76249	−1.33627	−0.668134	+	0.744041i	$0.732907\pi$
$44$	2.83609	0.427557
$45$	−2.50795	−0.373863
$46$	13.0472	1.92371
$47$	−11.3014	−1.64848	−0.824238	−	0.566243i	$-0.808396\pi$
$47$	−11.3014	−1.64848	−0.824238	+	0.566243i	$0.808396\pi$
$48$	−0.915716	−0.132172
$49$	4.33326	0.619038
$50$	−3.00616	−0.425136
$51$	−1.00000	−0.140028
$52$	−12.1712	−1.68785
$53$	−12.2303	−1.67996	−0.839979	−	0.542619i	$-0.817433\pi$
$53$	−12.2303	−1.67996	−0.839979	+	0.542619i	$0.817433\pi$
$54$	2.33071	0.317170
$55$	−2.07235	−0.279436
$56$	11.2377	1.50170
$57$	−7.67391	−1.01643
$58$	5.59912	0.735200
$59$	3.58135	0.466253	0.233126	−	0.972446i	$-0.425104\pi$
$59$	3.58135	0.466253	0.233126	+	0.972446i	$0.425104\pi$
$60$	8.60784	1.11127
$61$	6.37152	0.815790	0.407895	−	0.913029i	$-0.366263\pi$
$61$	6.37152	0.815790	0.407895	+	0.913029i	$0.366263\pi$
$62$	−5.85564	−0.743667
$63$	−3.36649	−0.424138
$64$	−12.4174	−1.55217
$65$	8.89360	1.10312
$66$	1.92590	0.237062
$67$	0.844427	0.103163	0.0515816	−	0.998669i	$-0.483574\pi$
$67$	0.844427	0.103163	0.0515816	+	0.998669i	$0.483574\pi$
$68$	3.43222	0.416218
$69$	5.59795	0.673914
$70$	−19.6782	−2.35199
$71$	−5.65221	−0.670794	−0.335397	−	0.942077i	$-0.608870\pi$
$71$	−5.65221	−0.670794	−0.335397	+	0.942077i	$0.608870\pi$
$72$	−3.33810	−0.393399
$73$	5.12836	0.600229	0.300115	−	0.953903i	$-0.402975\pi$
$73$	5.12836	0.600229	0.300115	+	0.953903i	$0.402975\pi$
$74$	−12.4353	−1.44557
$75$	−1.28980	−0.148934
$76$	26.3386	3.02124
$77$	−2.78177	−0.317013
$78$	−8.26510	−0.935838
$79$	−1.00000	−0.112509
$79$	−1.00000	−0.112509
$80$	−2.29657	−0.256764
$81$	1.00000	0.111111
$82$	9.05017	0.999424
$83$	−16.3115	−1.79042	−0.895210	−	0.445644i	$-0.852975\pi$
$83$	−16.3115	−1.79042	−0.895210	+	0.445644i	$0.852975\pi$
$84$	11.5546	1.26071
$85$	−2.50795	−0.272025
$86$	20.4229	2.20225
$87$	2.40232	0.257556
$88$	−2.75832	−0.294038
$89$	−12.4342	−1.31802	−0.659009	−	0.752135i	$-0.729024\pi$
$89$	−12.4342	−1.31802	−0.659009	+	0.752135i	$0.729024\pi$
$90$	5.84531	0.616150
$91$	11.9381	1.25146
$92$	−19.2134	−2.00314
$93$	−2.51238	−0.260522
$94$	26.3403	2.71679
$95$	−19.2458	−1.97457
$96$	−4.54194	−0.463560
$97$	−15.4596	−1.56968	−0.784841	−	0.619697i	$-0.787255\pi$
$97$	−15.4596	−1.56968	−0.784841	+	0.619697i	$0.787255\pi$
$98$	−10.0996	−1.02021
$99$	0.826313	0.0830476
$100$	4.42690	0.442690
$101$	−13.4804	−1.34135	−0.670676	−	0.741750i	$-0.733996\pi$
$101$	−13.4804	−1.34135	−0.670676	+	0.741750i	$0.733996\pi$
$102$	2.33071	0.230775
$103$	10.8548	1.06955	0.534776	−	0.844994i	$-0.320396\pi$
$103$	10.8548	1.06955	0.534776	+	0.844994i	$0.320396\pi$
$104$	11.8375	1.16076
$105$	−8.44299	−0.823951
$106$	28.5053	2.76868
$107$	−4.02694	−0.389299	−0.194649	−	0.980873i	$-0.562357\pi$
$107$	−4.02694	−0.389299	−0.194649	+	0.980873i	$0.562357\pi$
$108$	−3.43222	−0.330266
$109$	−3.29966	−0.316050	−0.158025	−	0.987435i	$-0.550513\pi$
$109$	−3.29966	−0.316050	−0.158025	+	0.987435i	$0.550513\pi$
$110$	4.83005	0.460528
$111$	−5.33541	−0.506414
$112$	−3.08275	−0.291292
$113$	18.8370	1.77204	0.886019	−	0.463648i	$-0.153460\pi$
$113$	18.8370	1.77204	0.886019	+	0.463648i	$0.153460\pi$
$114$	17.8857	1.67515
$115$	14.0394	1.30918
$116$	−8.24530	−0.765557
$117$	−3.54617	−0.327843
$118$	−8.34711	−0.768414
$119$	−3.36649	−0.308606
$120$	−8.37179	−0.764237
$121$	−10.3172	−0.937928
$122$	−14.8502	−1.34447
$123$	3.88300	0.350119
$124$	8.62305	0.774373
$125$	9.30498	0.832263
$126$	7.84633	0.699006
$127$	−13.9329	−1.23635	−0.618174	−	0.786041i	$-0.712127\pi$
$127$	−13.9329	−1.23635	−0.618174	+	0.786041i	$0.712127\pi$
$128$	19.8575	1.75517
$129$	8.76249	0.771494
$130$	−20.7284	−1.81800
$131$	3.06986	0.268215	0.134107	−	0.990967i	$-0.457183\pi$
$131$	3.06986	0.268215	0.134107	+	0.990967i	$0.457183\pi$
$132$	−2.83609	−0.246850
$133$	−25.8341	−2.24010
$134$	−1.96812	−0.170020
$135$	2.50795	0.215850
$136$	−3.33810	−0.286240
$137$	14.9494	1.27721	0.638605	−	0.769534i	$-0.279512\pi$
$137$	14.9494	1.27721	0.638605	+	0.769534i	$0.279512\pi$
$138$	−13.0472	−1.11065
$139$	−5.38899	−0.457088	−0.228544	−	0.973534i	$-0.573396\pi$
$139$	−5.38899	−0.457088	−0.228544	+	0.973534i	$0.573396\pi$
$140$	28.9782	2.44911
$141$	11.3014	0.951748
$142$	13.1737	1.10551
$143$	−2.93024	−0.245039
$144$	0.915716	0.0763097
$145$	6.02489	0.500340
$146$	−11.9527	−0.989215
$147$	−4.33326	−0.357401
$148$	18.3123	1.50526
$149$	−13.7340	−1.12513	−0.562565	−	0.826753i	$-0.690186\pi$
$149$	−13.7340	−1.12513	−0.562565	+	0.826753i	$0.690186\pi$
$150$	3.00616	0.245452
$151$	10.9701	0.892730	0.446365	−	0.894851i	$-0.352718\pi$
$151$	10.9701	0.892730	0.446365	+	0.894851i	$0.352718\pi$
$152$	−25.6163	−2.07776
$153$	1.00000	0.0808452
$154$	6.48352	0.522457
$155$	−6.30092	−0.506102
$156$	12.1712	0.974479
$157$	9.56311	0.763220	0.381610	−	0.924324i	$-0.375370\pi$
$157$	9.56311	0.763220	0.381610	+	0.924324i	$0.375370\pi$
$158$	2.33071	0.185422
$159$	12.2303	0.969924
$160$	−11.3909	−0.900533
$161$	18.8454	1.48523
$162$	−2.33071	−0.183118
$163$	6.78988	0.531824	0.265912	−	0.963997i	$-0.414327\pi$
$163$	6.78988	0.531824	0.265912	+	0.963997i	$0.414327\pi$
$164$	−13.3273	−1.04069
$165$	2.07235	0.161332
$166$	38.0174	2.95073
$167$	10.3994	0.804729	0.402364	−	0.915480i	$-0.368189\pi$
$167$	10.3994	0.804729	0.402364	+	0.915480i	$0.368189\pi$
$168$	−11.2377	−0.867007
$169$	−0.424705	−0.0326696
$170$	5.84531	0.448315
$171$	7.67391	0.586838
$172$	−30.0748	−2.29318
$173$	−13.6042	−1.03431	−0.517154	−	0.855892i	$-0.673009\pi$
$173$	−13.6042	−1.03431	−0.517154	+	0.855892i	$0.673009\pi$
$174$	−5.59912	−0.424468
$175$	−4.34212	−0.328233
$176$	0.756668	0.0570360
$177$	−3.58135	−0.269191
$178$	28.9804	2.17218
$179$	−26.2960	−1.96545	−0.982726	−	0.185066i	$-0.940750\pi$
$179$	−26.2960	−1.96545	−0.982726	+	0.185066i	$0.940750\pi$
$180$	−8.60784	−0.641591
$181$	4.71027	0.350112	0.175056	−	0.984559i	$-0.443989\pi$
$181$	4.71027	0.350112	0.175056	+	0.984559i	$0.443989\pi$
$182$	−27.8244	−2.06248
$183$	−6.37152	−0.470996
$184$	18.6865	1.37759
$185$	−13.3809	−0.983785
$186$	5.85564	0.429356
$187$	0.826313	0.0604260
$188$	−38.7889	−2.82897
$189$	3.36649	0.244876
$190$	44.8564	3.25422
$191$	18.4652	1.33610	0.668049	−	0.744117i	$-0.267130\pi$
$191$	18.4652	1.33610	0.668049	+	0.744117i	$0.267130\pi$
$192$	12.4174	0.896148
$193$	18.7863	1.35226	0.676132	−	0.736780i	$-0.263655\pi$
$193$	18.7863	1.35226	0.676132	+	0.736780i	$0.263655\pi$
$194$	36.0318	2.58694
$195$	−8.89360	−0.636884
$196$	14.8727	1.06234
$197$	−13.3555	−0.951539	−0.475769	−	0.879570i	$-0.657830\pi$
$197$	−13.3555	−0.951539	−0.475769	+	0.879570i	$0.657830\pi$
$198$	−1.92590	−0.136868
$199$	−23.4295	−1.66088	−0.830438	−	0.557111i	$-0.811910\pi$
$199$	−23.4295	−1.66088	−0.830438	+	0.557111i	$0.811910\pi$
$200$	−4.30550	−0.304445
$201$	−0.844427	−0.0595613
$202$	31.4190	2.21063
$203$	8.08739	0.567623
$204$	−3.43222	−0.240304
$205$	9.73837	0.680158
$206$	−25.2993	−1.76269
$207$	−5.59795	−0.389084
$208$	−3.24728	−0.225158
$209$	6.34105	0.438619
$210$	19.6782	1.35792
$211$	6.97309	0.480048	0.240024	−	0.970767i	$-0.422845\pi$
$211$	6.97309	0.480048	0.240024	+	0.970767i	$0.422845\pi$
$212$	−41.9770	−2.88300
$213$	5.65221	0.387283
$214$	9.38564	0.641589
$215$	21.9759	1.49874
$216$	3.33810	0.227129
$217$	−8.45791	−0.574160
$218$	7.69056	0.520871
$219$	−5.12836	−0.346542
$220$	−7.11277	−0.479543
$221$	−3.54617	−0.238541
$222$	12.4353	0.834603
$223$	−8.04548	−0.538765	−0.269383	−	0.963033i	$-0.586820\pi$
$223$	−8.04548	−0.538765	−0.269383	+	0.963033i	$0.586820\pi$
$224$	−15.2904	−1.02163
$225$	1.28980	0.0859870
$226$	−43.9037	−2.92043
$227$	−24.6277	−1.63460	−0.817299	−	0.576213i	$-0.804530\pi$
$227$	−24.6277	−1.63460	−0.817299	+	0.576213i	$0.804530\pi$
$228$	−26.3386	−1.74431
$229$	−6.07202	−0.401250	−0.200625	−	0.979668i	$-0.564297\pi$
$229$	−6.07202	−0.401250	−0.200625	+	0.979668i	$0.564297\pi$
$230$	−32.7217	−2.15761
$231$	2.78177	0.183027
$232$	8.01920	0.526486
$233$	10.6868	0.700113	0.350057	−	0.936729i	$-0.386162\pi$
$233$	10.6868	0.700113	0.350057	+	0.936729i	$0.386162\pi$
$234$	8.26510	0.540306
$235$	28.3433	1.84891
$236$	12.2920	0.800142
$237$	1.00000	0.0649570
$238$	7.84633	0.508602
$239$	14.8695	0.961827	0.480914	−	0.876768i	$-0.340305\pi$
$239$	14.8695	0.961827	0.480914	+	0.876768i	$0.340305\pi$
$240$	2.29657	0.148243
$241$	−23.1447	−1.49088	−0.745440	−	0.666573i	$-0.767761\pi$
$241$	−23.1447	−1.49088	−0.745440	+	0.666573i	$0.767761\pi$
$242$	24.0465	1.54576
$243$	−1.00000	−0.0641500
$244$	21.8685	1.39999
$245$	−10.8676	−0.694305
$246$	−9.05017	−0.577018
$247$	−27.2130	−1.73152
$248$	−8.38659	−0.532549
$249$	16.3115	1.03370
$250$	−21.6872	−1.37162
$251$	−5.07000	−0.320015	−0.160008	−	0.987116i	$-0.551152\pi$
$251$	−5.07000	−0.320015	−0.160008	+	0.987116i	$0.551152\pi$
$252$	−11.5546	−0.727868
$253$	−4.62565	−0.290812
$254$	32.4737	2.03758
$255$	2.50795	0.157054
$256$	−21.4473	−1.34046
$257$	−10.8792	−0.678627	−0.339314	−	0.940673i	$-0.610195\pi$
$257$	−10.8792	−0.678627	−0.339314	+	0.940673i	$0.610195\pi$
$258$	−20.4229	−1.27147
$259$	−17.9616	−1.11608
$260$	30.5248	1.89307
$261$	−2.40232	−0.148700
$262$	−7.15495	−0.442034
$263$	−15.9949	−0.986285	−0.493143	−	0.869949i	$-0.664152\pi$
$263$	−15.9949	−0.986285	−0.493143	+	0.869949i	$0.664152\pi$
$264$	2.75832	0.169763
$265$	30.6729	1.88422
$266$	60.2120	3.69183
$267$	12.4342	0.760958
$268$	2.89826	0.177040
$269$	−4.86209	−0.296447	−0.148223	−	0.988954i	$-0.547355\pi$
$269$	−4.86209	−0.296447	−0.148223	+	0.988954i	$0.547355\pi$
$270$	−5.84531	−0.355734
$271$	−10.3784	−0.630446	−0.315223	−	0.949018i	$-0.602079\pi$
$271$	−10.3784	−0.630446	−0.315223	+	0.949018i	$0.602079\pi$
$272$	0.915716	0.0555234
$273$	−11.9381	−0.722529
$274$	−34.8427	−2.10492
$275$	1.06578	0.0642691
$276$	19.2134	1.15651
$277$	9.62030	0.578028	0.289014	−	0.957325i	$-0.406673\pi$
$277$	9.62030	0.578028	0.289014	+	0.957325i	$0.406673\pi$
$278$	12.5602	0.753310
$279$	2.51238	0.150412
$280$	−28.1836	−1.68429
$281$	10.5910	0.631808	0.315904	−	0.948791i	$-0.397692\pi$
$281$	10.5910	0.631808	0.315904	+	0.948791i	$0.397692\pi$
$282$	−26.3403	−1.56854
$283$	−4.85712	−0.288726	−0.144363	−	0.989525i	$-0.546113\pi$
$283$	−4.85712	−0.288726	−0.144363	+	0.989525i	$0.546113\pi$
$284$	−19.3997	−1.15116
$285$	19.2458	1.14002
$286$	6.82956	0.403840
$287$	13.0721	0.771622
$288$	4.54194	0.267636
$289$	1.00000	0.0588235
$290$	−14.0423	−0.824592
$291$	15.4596	0.906256
$292$	17.6017	1.03006
$293$	−19.9362	−1.16469	−0.582344	−	0.812943i	$-0.697864\pi$
$293$	−19.9362	−1.16469	−0.582344	+	0.812943i	$0.697864\pi$
$294$	10.0996	0.589020
$295$	−8.98185	−0.522944
$296$	−17.8101	−1.03519
$297$	−0.826313	−0.0479475
$298$	32.0099	1.85429
$299$	19.8512	1.14803
$300$	−4.42690	−0.255587
$301$	29.4988	1.70029
$302$	−25.5681	−1.47128
$303$	13.4804	0.774430
$304$	7.02712	0.403033
$305$	−15.9794	−0.914980
$306$	−2.33071	−0.133238
$307$	15.2504	0.870386	0.435193	−	0.900337i	$-0.356680\pi$
$307$	15.2504	0.870386	0.435193	+	0.900337i	$0.356680\pi$
$308$	−9.54768	−0.544029
$309$	−10.8548	−0.617506
$310$	14.6856	0.834088
$311$	16.5341	0.937560	0.468780	−	0.883315i	$-0.344694\pi$
$311$	16.5341	0.937560	0.468780	+	0.883315i	$0.344694\pi$
$312$	−11.8375	−0.670165
$313$	20.0854	1.13529	0.567647	−	0.823272i	$-0.307854\pi$
$313$	20.0854	1.13529	0.567647	+	0.823272i	$0.307854\pi$
$314$	−22.2889	−1.25783
$315$	8.44299	0.475708
$316$	−3.43222	−0.193078
$317$	4.68544	0.263161	0.131580	−	0.991306i	$-0.457995\pi$
$317$	4.68544	0.263161	0.131580	+	0.991306i	$0.457995\pi$
$318$	−28.5053	−1.59850
$319$	−1.98507	−0.111142
$320$	31.1422	1.74090
$321$	4.02694	0.224762
$322$	−43.9233	−2.44775
$323$	7.67391	0.426988
$324$	3.43222	0.190679
$325$	−4.57386	−0.253712
$326$	−15.8253	−0.876480
$327$	3.29966	0.182472
$328$	12.9619	0.715700
$329$	38.0460	2.09754
$330$	−4.83005	−0.265886
$331$	−27.9989	−1.53896	−0.769479	−	0.638672i	$-0.779484\pi$
$331$	−27.9989	−1.53896	−0.769479	+	0.638672i	$0.779484\pi$
$332$	−55.9848	−3.07256
$333$	5.33541	0.292379
$334$	−24.2380	−1.32624
$335$	−2.11778	−0.115707
$336$	3.08275	0.168178
$337$	25.5284	1.39062	0.695311	−	0.718709i	$-0.255267\pi$
$337$	25.5284	1.39062	0.695311	+	0.718709i	$0.255267\pi$
$338$	0.989865	0.0538415
$339$	−18.8370	−1.02309
$340$	−8.60784	−0.466826
$341$	2.07601	0.112422
$342$	−17.8857	−0.967147
$343$	8.97755	0.484742
$344$	29.2501	1.57706
$345$	−14.0394	−0.755854
$346$	31.7075	1.70461
$347$	20.1285	1.08056	0.540278	−	0.841487i	$-0.318319\pi$
$347$	20.1285	1.08056	0.540278	+	0.841487i	$0.318319\pi$
$348$	8.24530	0.441995
$349$	4.49416	0.240567	0.120283	−	0.992740i	$-0.461620\pi$
$349$	4.49416	0.240567	0.120283	+	0.992740i	$0.461620\pi$
$350$	10.1202	0.540949
$351$	3.54617	0.189280
$352$	3.75306	0.200039
$353$	22.9132	1.21954	0.609772	−	0.792577i	$-0.291261\pi$
$353$	22.9132	1.21954	0.609772	+	0.792577i	$0.291261\pi$
$354$	8.34711	0.443644
$355$	14.1755	0.752355
$356$	−42.6768	−2.26187
$357$	3.36649	0.178174
$358$	61.2883	3.23919
$359$	22.6710	1.19653	0.598264	−	0.801299i	$-0.295858\pi$
$359$	22.6710	1.19653	0.598264	+	0.801299i	$0.295858\pi$
$360$	8.37179	0.441232
$361$	39.8889	2.09941
$362$	−10.9783	−0.577006
$363$	10.3172	0.541513
$364$	40.9744	2.14764
$365$	−12.8617	−0.673210
$366$	14.8502	0.776232
$367$	20.6206	1.07639	0.538193	−	0.842822i	$-0.319107\pi$
$367$	20.6206	1.07639	0.538193	+	0.842822i	$0.319107\pi$
$368$	−5.12613	−0.267218
$369$	−3.88300	−0.202141
$370$	31.1871	1.62134
$371$	41.1731	2.13760
$372$	−8.62305	−0.447085
$373$	−12.1493	−0.629069	−0.314535	−	0.949246i	$-0.601848\pi$
$373$	−12.1493	−0.629069	−0.314535	+	0.949246i	$0.601848\pi$
$374$	−1.92590	−0.0995858
$375$	−9.30498	−0.480507
$376$	37.7252	1.94553
$377$	8.51903	0.438752
$378$	−7.84633	−0.403571
$379$	5.43845	0.279355	0.139677	−	0.990197i	$-0.455393\pi$
$379$	5.43845	0.279355	0.139677	+	0.990197i	$0.455393\pi$
$380$	−66.0558	−3.38859
$381$	13.9329	0.713806
$382$	−43.0372	−2.20197
$383$	2.60963	0.133346	0.0666730	−	0.997775i	$-0.478762\pi$
$383$	2.60963	0.133346	0.0666730	+	0.997775i	$0.478762\pi$
$384$	−19.8575	−1.01335
$385$	6.97655	0.355558
$386$	−43.7854	−2.22862
$387$	−8.76249	−0.445422
$388$	−53.0607	−2.69375
$389$	20.3176	1.03014	0.515072	−	0.857147i	$-0.327765\pi$
$389$	20.3176	1.03014	0.515072	+	0.857147i	$0.327765\pi$
$390$	20.7284	1.04963
$391$	−5.59795	−0.283100
$392$	−14.4649	−0.730587
$393$	−3.06986	−0.154854
$394$	31.1278	1.56820
$395$	2.50795	0.126189
$396$	2.83609	0.142519
$397$	21.6664	1.08740	0.543702	−	0.839278i	$-0.317022\pi$
$397$	21.6664	1.08740	0.543702	+	0.839278i	$0.317022\pi$
$398$	54.6075	2.73723
$399$	25.8341	1.29332
$400$	1.18109	0.0590547
$401$	−11.1457	−0.556592	−0.278296	−	0.960495i	$-0.589770\pi$
$401$	−11.1457	−0.556592	−0.278296	+	0.960495i	$0.589770\pi$
$402$	1.96812	0.0981608
$403$	−8.90932	−0.443805
$404$	−46.2679	−2.30191
$405$	−2.50795	−0.124621
$406$	−18.8494	−0.935479
$407$	4.40872	0.218532
$408$	3.33810	0.165261
$409$	−19.9517	−0.986548	−0.493274	−	0.869874i	$-0.664200\pi$
$409$	−19.9517	−0.986548	−0.493274	+	0.869874i	$0.664200\pi$
$410$	−22.6974	−1.12094
$411$	−14.9494	−0.737398
$412$	37.2560	1.83547
$413$	−12.0566	−0.593266
$414$	13.0472	0.641235
$415$	40.9084	2.00812
$416$	−16.1065	−0.789685
$417$	5.38899	0.263900
$418$	−14.7792	−0.722873
$419$	25.5307	1.24726	0.623629	−	0.781721i	$-0.285658\pi$
$419$	25.5307	1.24726	0.623629	+	0.781721i	$0.285658\pi$
$420$	−28.9782	−1.41399
$421$	−0.271382	−0.0132264	−0.00661318	−	0.999978i	$-0.502105\pi$
$421$	−0.271382	−0.0132264	−0.00661318	+	0.999978i	$0.502105\pi$
$422$	−16.2523	−0.791149
$423$	−11.3014	−0.549492
$424$	40.8259	1.98268
$425$	1.28980	0.0625647
$426$	−13.1737	−0.638267
$427$	−21.4497	−1.03802
$428$	−13.8214	−0.668081
$429$	2.93024	0.141473
$430$	−51.2195	−2.47002
$431$	−21.4346	−1.03247	−0.516235	−	0.856447i	$-0.672667\pi$
$431$	−21.4346	−1.03247	−0.516235	+	0.856447i	$0.672667\pi$
$432$	−0.915716	−0.0440574
$433$	−4.08319	−0.196225	−0.0981127	−	0.995175i	$-0.531281\pi$
$433$	−4.08319	−0.196225	−0.0981127	+	0.995175i	$0.531281\pi$
$434$	19.7130	0.946252
$435$	−6.02489	−0.288872
$436$	−11.3252	−0.542378
$437$	−42.9581	−2.05497
$438$	11.9527	0.571124
$439$	11.9415	0.569937	0.284969	−	0.958537i	$-0.408017\pi$
$439$	11.9415	0.569937	0.284969	+	0.958537i	$0.408017\pi$
$440$	6.91772	0.329789
$441$	4.33326	0.206346
$442$	8.26510	0.393131
$443$	36.0255	1.71162	0.855812	−	0.517287i	$-0.173058\pi$
$443$	36.0255	1.71162	0.855812	+	0.517287i	$0.173058\pi$
$444$	−18.3123	−0.869064
$445$	31.1842	1.47827
$446$	18.7517	0.887919
$447$	13.7340	0.649595
$448$	41.8030	1.97501
$449$	25.4875	1.20283	0.601414	−	0.798938i	$-0.294604\pi$
$449$	25.4875	1.20283	0.601414	+	0.798938i	$0.294604\pi$
$450$	−3.00616	−0.141712
$451$	−3.20858	−0.151086
$452$	64.6529	3.04102
$453$	−10.9701	−0.515418
$454$	57.4001	2.69392
$455$	−29.9402	−1.40362
$456$	25.6163	1.19959
$457$	−35.0032	−1.63738	−0.818690	−	0.574235i	$-0.805299\pi$
$457$	−35.0032	−1.63738	−0.818690	+	0.574235i	$0.805299\pi$
$458$	14.1521	0.661286
$459$	−1.00000	−0.0466760
$460$	48.1862	2.24669
$461$	−11.5918	−0.539885	−0.269942	−	0.962876i	$-0.587005\pi$
$461$	−11.5918	−0.539885	−0.269942	+	0.962876i	$0.587005\pi$
$462$	−6.48352	−0.301641
$463$	−37.3231	−1.73455	−0.867275	−	0.497830i	$-0.834130\pi$
$463$	−37.3231	−1.73455	−0.867275	+	0.497830i	$0.834130\pi$
$464$	−2.19984	−0.102125
$465$	6.30092	0.292198
$466$	−24.9078	−1.15383
$467$	37.6461	1.74205	0.871027	−	0.491234i	$-0.163454\pi$
$467$	37.6461	1.74205	0.871027	+	0.491234i	$0.163454\pi$
$468$	−12.1712	−0.562616
$469$	−2.84276	−0.131266
$470$	−66.0601	−3.04712
$471$	−9.56311	−0.440645
$472$	−11.9549	−0.550270
$473$	−7.24056	−0.332921
$474$	−2.33071	−0.107053
$475$	9.89784	0.454144
$476$	−11.5546	−0.529602
$477$	−12.2303	−0.559986
$478$	−34.6565	−1.58515
$479$	33.4068	1.52640	0.763198	−	0.646165i	$-0.223628\pi$
$479$	33.4068	1.52640	0.763198	+	0.646165i	$0.223628\pi$
$480$	11.3909	0.519923
$481$	−18.9202	−0.862689
$482$	53.9436	2.45706
$483$	−18.8454	−0.857497
$484$	−35.4110	−1.60959
$485$	38.7718	1.76054
$486$	2.33071	0.105723
$487$	16.1459	0.731643	0.365821	−	0.930685i	$-0.380788\pi$
$487$	16.1459	0.731643	0.365821	+	0.930685i	$0.380788\pi$
$488$	−21.2688	−0.962794
$489$	−6.78988	−0.307049
$490$	25.3293	1.14426
$491$	16.4981	0.744548	0.372274	−	0.928123i	$-0.378578\pi$
$491$	16.4981	0.744548	0.372274	+	0.928123i	$0.378578\pi$
$492$	13.3273	0.600843
$493$	−2.40232	−0.108195
$494$	63.4256	2.85365
$495$	−2.07235	−0.0931452
$496$	2.30063	0.103301
$497$	19.0281	0.853528
$498$	−38.0174	−1.70360
$499$	5.32376	0.238324	0.119162	−	0.992875i	$-0.461979\pi$
$499$	5.32376	0.238324	0.119162	+	0.992875i	$0.461979\pi$
$500$	31.9368	1.42826
$501$	−10.3994	−0.464610
$502$	11.8167	0.527406
$503$	20.8293	0.928732	0.464366	−	0.885643i	$-0.346282\pi$
$503$	20.8293	0.928732	0.464366	+	0.885643i	$0.346282\pi$
$504$	11.2377	0.500567
$505$	33.8082	1.50445
$506$	10.7811	0.479277
$507$	0.424705	0.0188618
$508$	−47.8210	−2.12171
$509$	7.17725	0.318126	0.159063	−	0.987268i	$-0.449153\pi$
$509$	7.17725	0.318126	0.159063	+	0.987268i	$0.449153\pi$
$510$	−5.84531	−0.258835
$511$	−17.2646	−0.763740
$512$	10.2726	0.453991
$513$	−7.67391	−0.338811
$514$	25.3564	1.11842
$515$	−27.2232	−1.19960
$516$	30.0748	1.32397
$517$	−9.33848	−0.410706
$518$	41.8633	1.83937
$519$	13.6042	0.597158
$520$	−29.6878	−1.30189
$521$	13.2379	0.579964	0.289982	−	0.957032i	$-0.406351\pi$
$521$	13.2379	0.579964	0.289982	+	0.957032i	$0.406351\pi$
$522$	5.59912	0.245067
$523$	44.2584	1.93528	0.967642	−	0.252325i	$-0.0811953\pi$
$523$	44.2584	1.93528	0.967642	+	0.252325i	$0.0811953\pi$
$524$	10.5364	0.460286
$525$	4.34212	0.189505
$526$	37.2794	1.62546
$527$	2.51238	0.109441
$528$	−0.756668	−0.0329297
$529$	8.33700	0.362478
$530$	−71.4897	−3.10532
$531$	3.58135	0.155418
$532$	−88.6686	−3.84427
$533$	13.7698	0.596435
$534$	−28.9804	−1.25411
$535$	10.0994	0.436633
$536$	−2.81879	−0.121753
$537$	26.2960	1.13475
$538$	11.3321	0.488563
$539$	3.58063	0.154229
$540$	8.60784	0.370423
$541$	2.63975	0.113492	0.0567459	−	0.998389i	$-0.481927\pi$
$541$	2.63975	0.113492	0.0567459	+	0.998389i	$0.481927\pi$
$542$	24.1892	1.03901
$543$	−4.71027	−0.202137
$544$	4.54194	0.194734
$545$	8.27538	0.354478
$546$	27.8244	1.19077
$547$	18.9547	0.810444	0.405222	−	0.914218i	$-0.367194\pi$
$547$	18.9547	0.810444	0.405222	+	0.914218i	$0.367194\pi$
$548$	51.3096	2.19184
$549$	6.37152	0.271930
$550$	−2.48403	−0.105920
$551$	−18.4352	−0.785365
$552$	−18.6865	−0.795352
$553$	3.36649	0.143158
$554$	−22.4222	−0.952626
$555$	13.3809	0.567989
$556$	−18.4962	−0.784414
$557$	−17.8445	−0.756096	−0.378048	−	0.925786i	$-0.623405\pi$
$557$	−17.8445	−0.756096	−0.378048	+	0.925786i	$0.623405\pi$
$558$	−5.85564	−0.247889
$559$	31.0732	1.31426
$560$	7.73138	0.326710
$561$	−0.826313	−0.0348870
$562$	−24.6847	−1.04126
$563$	29.1250	1.22747	0.613736	−	0.789511i	$-0.289666\pi$
$563$	29.1250	1.22747	0.613736	+	0.789511i	$0.289666\pi$
$564$	38.7889	1.63331
$565$	−47.2423	−1.98750
$566$	11.3206	0.475838
$567$	−3.36649	−0.141379
$568$	18.8677	0.791670
$569$	−41.2954	−1.73119	−0.865596	−	0.500743i	$-0.833060\pi$
$569$	−41.2954	−1.73119	−0.865596	+	0.500743i	$0.833060\pi$
$570$	−44.8564	−1.87883
$571$	−18.4470	−0.771984	−0.385992	−	0.922502i	$-0.626141\pi$
$571$	−18.4470	−0.771984	−0.385992	+	0.922502i	$0.626141\pi$
$572$	−10.0573	−0.420515
$573$	−18.4652	−0.771396
$574$	−30.4673	−1.27168
$575$	−7.22026	−0.301106
$576$	−12.4174	−0.517391
$577$	−9.24209	−0.384753	−0.192377	−	0.981321i	$-0.561620\pi$
$577$	−9.24209	−0.384753	−0.192377	+	0.981321i	$0.561620\pi$
$578$	−2.33071	−0.0969449
$579$	−18.7863	−0.780730
$580$	20.6788	0.858640
$581$	54.9125	2.27816
$582$	−36.0318	−1.49357
$583$	−10.1060	−0.418549
$584$	−17.1190	−0.708389
$585$	8.89360	0.367705
$586$	46.4656	1.91948
$587$	34.2687	1.41442	0.707211	−	0.707003i	$-0.249953\pi$
$587$	34.2687	1.41442	0.707211	+	0.707003i	$0.249953\pi$
$588$	−14.8727	−0.613341
$589$	19.2798	0.794409
$590$	20.9341	0.861844
$591$	13.3555	0.549371
$592$	4.88572	0.200802
$593$	−23.7677	−0.976024	−0.488012	−	0.872837i	$-0.662278\pi$
$593$	−23.7677	−0.976024	−0.488012	+	0.872837i	$0.662278\pi$
$594$	1.92590	0.0790206
$595$	8.44299	0.346129
$596$	−47.1381	−1.93085
$597$	23.4295	0.958907
$598$	−46.2676	−1.89202
$599$	10.8390	0.442871	0.221435	−	0.975175i	$-0.428926\pi$
$599$	10.8390	0.442871	0.221435	+	0.975175i	$0.428926\pi$
$600$	4.30550	0.175771
$601$	−15.6104	−0.636763	−0.318381	−	0.947963i	$-0.603139\pi$
$601$	−15.6104	−0.636763	−0.318381	+	0.947963i	$0.603139\pi$
$602$	−68.7534	−2.80218
$603$	0.844427	0.0343877
$604$	37.6517	1.53203
$605$	25.8750	1.05197
$606$	−31.4190	−1.27631
$607$	−4.41745	−0.179299	−0.0896493	−	0.995973i	$-0.528575\pi$
$607$	−4.41745	−0.179299	−0.0896493	+	0.995973i	$0.528575\pi$
$608$	34.8544	1.41353
$609$	−8.08739	−0.327718
$610$	37.2435	1.50795
$611$	40.0766	1.62133
$612$	3.43222	0.138739
$613$	−42.6354	−1.72203	−0.861013	−	0.508582i	$-0.830170\pi$
$613$	−42.6354	−1.72203	−0.861013	+	0.508582i	$0.830170\pi$
$614$	−35.5443	−1.43445
$615$	−9.73837	−0.392689
$616$	9.28586	0.374138
$617$	−9.64925	−0.388464	−0.194232	−	0.980956i	$-0.562221\pi$
$617$	−9.64925	−0.388464	−0.194232	+	0.980956i	$0.562221\pi$
$618$	25.2993	1.01769
$619$	−26.8512	−1.07924	−0.539621	−	0.841908i	$-0.681433\pi$
$619$	−26.8512	−1.07924	−0.539621	+	0.841908i	$0.681433\pi$
$620$	−21.6262	−0.868528
$621$	5.59795	0.224638
$622$	−38.5361	−1.54516
$623$	41.8595	1.67706
$624$	3.24728	0.129995
$625$	−29.7854	−1.19142
$626$	−46.8133	−1.87104
$627$	−6.34105	−0.253237
$628$	32.8228	1.30977
$629$	5.33541	0.212737
$630$	−19.6782	−0.783997
$631$	14.2721	0.568163	0.284081	−	0.958800i	$-0.408311\pi$
$631$	14.2721	0.568163	0.284081	+	0.958800i	$0.408311\pi$
$632$	3.33810	0.132783
$633$	−6.97309	−0.277156
$634$	−10.9204	−0.433706
$635$	34.9431	1.38667
$636$	41.9770	1.66450
$637$	−15.3665	−0.608842
$638$	4.62662	0.183170
$639$	−5.65221	−0.223598
$640$	−49.8016	−1.96858
$641$	−38.5102	−1.52106	−0.760530	−	0.649303i	$-0.775061\pi$
$641$	−38.5102	−1.52106	−0.760530	+	0.649303i	$0.775061\pi$
$642$	−9.38564	−0.370422
$643$	−13.3795	−0.527636	−0.263818	−	0.964573i	$-0.584982\pi$
$643$	−13.3795	−0.527636	−0.263818	+	0.964573i	$0.584982\pi$
$644$	64.6818	2.54882
$645$	−21.9759	−0.865299
$646$	−17.8857	−0.703703
$647$	−23.1288	−0.909286	−0.454643	−	0.890674i	$-0.650233\pi$
$647$	−23.1288	−0.909286	−0.454643	+	0.890674i	$0.650233\pi$
$648$	−3.33810	−0.131133
$649$	2.95932	0.116163
$650$	10.6604	0.418134
$651$	8.45791	0.331491
$652$	23.3044	0.912670
$653$	−12.1167	−0.474161	−0.237081	−	0.971490i	$-0.576191\pi$
$653$	−12.1167	−0.474161	−0.237081	+	0.971490i	$0.576191\pi$
$654$	−7.69056	−0.300725
$655$	−7.69904	−0.300826
$656$	−3.55573	−0.138828
$657$	5.12836	0.200076
$658$	−88.6743	−3.45689
$659$	27.4891	1.07082	0.535411	−	0.844591i	$-0.320157\pi$
$659$	27.4891	1.07082	0.535411	+	0.844591i	$0.320157\pi$
$660$	7.11277	0.276864
$661$	13.6375	0.530435	0.265218	−	0.964189i	$-0.414556\pi$
$661$	13.6375	0.530435	0.265218	+	0.964189i	$0.414556\pi$
$662$	65.2574	2.53630
$663$	3.54617	0.137722
$664$	54.4495	2.11305
$665$	64.7907	2.51248
$666$	−12.4353	−0.481858
$667$	13.4481	0.520711
$668$	35.6930	1.38100
$669$	8.04548	0.311056
$670$	4.93594	0.190692
$671$	5.26487	0.203248
$672$	15.2904	0.589840
$673$	42.0670	1.62156	0.810782	−	0.585348i	$-0.199042\pi$
$673$	42.0670	1.62156	0.810782	+	0.585348i	$0.199042\pi$
$674$	−59.4994	−2.29183
$675$	−1.28980	−0.0496446
$676$	−1.45768	−0.0560647
$677$	−11.4476	−0.439969	−0.219984	−	0.975503i	$-0.570601\pi$
$677$	−11.4476	−0.439969	−0.219984	+	0.975503i	$0.570601\pi$
$678$	43.9037	1.68611
$679$	52.0445	1.99729
$680$	8.37179	0.321044
$681$	24.6277	0.943736
$682$	−4.83859	−0.185279
$683$	−11.7822	−0.450833	−0.225417	−	0.974262i	$-0.572374\pi$
$683$	−11.7822	−0.450833	−0.225417	+	0.974262i	$0.572374\pi$
$684$	26.3386	1.00708
$685$	−37.4922	−1.43250
$686$	−20.9241	−0.798885
$687$	6.07202	0.231662
$688$	−8.02395	−0.305910
$689$	43.3706	1.65229
$690$	32.7217	1.24569
$691$	−15.7181	−0.597944	−0.298972	−	0.954262i	$-0.596644\pi$
$691$	−15.7181	−0.597944	−0.298972	+	0.954262i	$0.596644\pi$
$692$	−46.6927	−1.77499
$693$	−2.78177	−0.105671
$694$	−46.9138	−1.78082
$695$	13.5153	0.512665
$696$	−8.01920	−0.303967
$697$	−3.88300	−0.147079
$698$	−10.4746	−0.396469
$699$	−10.6868	−0.404211
$700$	−14.9031	−0.563285
$701$	47.5099	1.79443	0.897213	−	0.441599i	$-0.145589\pi$
$701$	47.5099	1.79443	0.897213	+	0.441599i	$0.145589\pi$
$702$	−8.26510	−0.311946
$703$	40.9434	1.54421
$704$	−10.2606	−0.386713
$705$	−28.3433	−1.06747
$706$	−53.4040	−2.00989
$707$	45.3817	1.70676
$708$	−12.2920	−0.461962
$709$	24.9596	0.937376	0.468688	−	0.883364i	$-0.344727\pi$
$709$	24.9596	0.937376	0.468688	+	0.883364i	$0.344727\pi$
$710$	−33.0389	−1.23993
$711$	−1.00000	−0.0375029
$712$	41.5065	1.55552
$713$	−14.0642	−0.526707
$714$	−7.84633	−0.293641
$715$	7.34890	0.274833
$716$	−90.2536	−3.37294
$717$	−14.8695	−0.555311
$718$	−52.8395	−1.97195
$719$	0.539293	0.0201122	0.0100561	−	0.999949i	$-0.496799\pi$
$719$	0.539293	0.0201122	0.0100561	+	0.999949i	$0.496799\pi$
$720$	−2.29657	−0.0855880
$721$	−36.5425	−1.36091
$722$	−92.9695	−3.45997
$723$	23.1447	0.860760
$724$	16.1667	0.600831
$725$	−3.09852	−0.115076
$726$	−24.0465	−0.892448
$727$	−17.6123	−0.653205	−0.326603	−	0.945162i	$-0.605904\pi$
$727$	−17.6123	−0.653205	−0.326603	+	0.945162i	$0.605904\pi$
$728$	−39.8508	−1.47697
$729$	1.00000	0.0370370
$730$	29.9768	1.10949
$731$	−8.76249	−0.324092
$732$	−21.8685	−0.808283
$733$	−25.8453	−0.954617	−0.477308	−	0.878736i	$-0.658388\pi$
$733$	−25.8453	−0.954617	−0.477308	+	0.878736i	$0.658388\pi$
$734$	−48.0607	−1.77395
$735$	10.8676	0.400857
$736$	−25.4255	−0.937197
$737$	0.697761	0.0257024
$738$	9.05017	0.333141
$739$	4.99581	0.183774	0.0918869	−	0.995769i	$-0.470710\pi$
$739$	4.99581	0.183774	0.0918869	+	0.995769i	$0.470710\pi$
$740$	−45.9263	−1.68829
$741$	27.2130	0.999693
$742$	−95.9627	−3.52290
$743$	−32.3803	−1.18792	−0.593958	−	0.804496i	$-0.702436\pi$
$743$	−32.3803	−1.18792	−0.593958	+	0.804496i	$0.702436\pi$
$744$	8.38659	0.307467
$745$	34.4441	1.26193
$746$	28.3166	1.03675
$747$	−16.3115	−0.596807
$748$	2.83609	0.103698
$749$	13.5567	0.495349
$750$	21.6872	0.791906
$751$	13.5656	0.495016	0.247508	−	0.968886i	$-0.420388\pi$
$751$	13.5656	0.495016	0.247508	+	0.968886i	$0.420388\pi$
$752$	−10.3489	−0.377384
$753$	5.07000	0.184761
$754$	−19.8554	−0.723091
$755$	−27.5123	−1.00128
$756$	11.5546	0.420235
$757$	14.2386	0.517512	0.258756	−	0.965943i	$-0.416687\pi$
$757$	14.2386	0.517512	0.258756	+	0.965943i	$0.416687\pi$
$758$	−12.6755	−0.460394
$759$	4.62565	0.167901
$760$	64.2444	2.33039
$761$	48.7414	1.76688	0.883438	−	0.468549i	$-0.155223\pi$
$761$	48.7414	1.76688	0.883438	+	0.468549i	$0.155223\pi$
$762$	−32.4737	−1.17640
$763$	11.1083	0.402147
$764$	63.3768	2.29289
$765$	−2.50795	−0.0906751
$766$	−6.08231	−0.219763
$767$	−12.7001	−0.458573
$768$	21.4473	0.773915
$769$	13.0026	0.468886	0.234443	−	0.972130i	$-0.424673\pi$
$769$	13.0026	0.468886	0.234443	+	0.972130i	$0.424673\pi$
$770$	−16.2603	−0.585982
$771$	10.8792	0.391806
$772$	64.4787	2.32064
$773$	−48.6434	−1.74958	−0.874791	−	0.484501i	$-0.839001\pi$
$773$	−48.6434	−1.74958	−0.874791	+	0.484501i	$0.839001\pi$
$774$	20.4229	0.734084
$775$	3.24048	0.116401
$776$	51.6057	1.85254
$777$	17.9616	0.644369
$778$	−47.3545	−1.69774
$779$	−29.7978	−1.06762
$780$	−30.5248	−1.09296
$781$	−4.67049	−0.167123
$782$	13.0472	0.466567
$783$	2.40232	0.0858519
$784$	3.96804	0.141716
$785$	−23.9838	−0.856018
$786$	7.15495	0.255209
$787$	40.3518	1.43839	0.719193	−	0.694810i	$-0.244512\pi$
$787$	40.3518	1.43839	0.719193	+	0.694810i	$0.244512\pi$
$788$	−45.8390	−1.63295
$789$	15.9949	0.569432
$790$	−5.84531	−0.207967
$791$	−63.4147	−2.25477
$792$	−2.75832	−0.0980126
$793$	−22.5945	−0.802353
$794$	−50.4981	−1.79211
$795$	−30.6729	−1.08786
$796$	−80.4154	−2.85025
$797$	30.7556	1.08942	0.544710	−	0.838624i	$-0.316640\pi$
$797$	30.7556	1.08942	0.544710	+	0.838624i	$0.316640\pi$
$798$	−60.2120	−2.13148
$799$	−11.3014	−0.399814
$800$	5.85821	0.207119
$801$	−12.4342	−0.439339
$802$	25.9775	0.917299
$803$	4.23763	0.149543
$804$	−2.89826	−0.102214
$805$	−47.2634	−1.66582
$806$	20.7651	0.731418
$807$	4.86209	0.171154
$808$	44.9991	1.58306
$809$	6.08443	0.213917	0.106959	−	0.994263i	$-0.465889\pi$
$809$	6.08443	0.213917	0.106959	+	0.994263i	$0.465889\pi$
$810$	5.84531	0.205383
$811$	48.0751	1.68814	0.844072	−	0.536230i	$-0.180152\pi$
$811$	48.0751	1.68814	0.844072	+	0.536230i	$0.180152\pi$
$812$	27.7577	0.974106
$813$	10.3784	0.363988
$814$	−10.2755	−0.360154
$815$	−17.0287	−0.596488
$816$	−0.915716	−0.0320565
$817$	−67.2425	−2.35252
$818$	46.5017	1.62589
$819$	11.9381	0.417152
$820$	33.4243	1.16723
$821$	−16.5538	−0.577732	−0.288866	−	0.957370i	$-0.593278\pi$
$821$	−16.5538	−0.577732	−0.288866	+	0.957370i	$0.593278\pi$
$822$	34.8427	1.21528
$823$	−52.1021	−1.81617	−0.908083	−	0.418791i	$-0.862454\pi$
$823$	−52.1021	−1.81617	−0.908083	+	0.418791i	$0.862454\pi$
$824$	−36.2343	−1.26228
$825$	−1.06578	−0.0371058
$826$	28.1005	0.977740
$827$	32.1298	1.11726	0.558631	−	0.829416i	$-0.311327\pi$
$827$	32.1298	1.11726	0.558631	+	0.829416i	$0.311327\pi$
$828$	−19.2134	−0.667712
$829$	27.6813	0.961413	0.480707	−	0.876882i	$-0.340380\pi$
$829$	27.6813	0.961413	0.480707	+	0.876882i	$0.340380\pi$
$830$	−95.3458	−3.30950
$831$	−9.62030	−0.333724
$832$	44.0341	1.52661
$833$	4.33326	0.150139
$834$	−12.5602	−0.434924
$835$	−26.0811	−0.902574
$836$	21.7639	0.752720
$837$	−2.51238	−0.0868406
$838$	−59.5048	−2.05556
$839$	−39.6029	−1.36724	−0.683622	−	0.729837i	$-0.739596\pi$
$839$	−39.6029	−1.36724	−0.683622	+	0.729837i	$0.739596\pi$
$840$	28.1836	0.972426
$841$	−23.2289	−0.800995
$842$	0.632514	0.0217979
$843$	−10.5910	−0.364774
$844$	23.9332	0.823816
$845$	1.06514	0.0366418
$846$	26.3403	0.905598
$847$	34.7328	1.19343
$848$	−11.1995	−0.384591
$849$	4.85712	0.166696
$850$	−3.00616	−0.103111
$851$	−29.8673	−1.02384
$852$	19.3997	0.664621
$853$	10.9081	0.373486	0.186743	−	0.982409i	$-0.440207\pi$
$853$	10.9081	0.373486	0.186743	+	0.982409i	$0.440207\pi$
$854$	49.9930	1.71073
$855$	−19.2458	−0.658191
$856$	13.4423	0.459450
$857$	−41.8884	−1.43088	−0.715441	−	0.698674i	$-0.753774\pi$
$857$	−41.8884	−1.43088	−0.715441	+	0.698674i	$0.753774\pi$
$858$	−6.82956	−0.233157
$859$	−28.4856	−0.971915	−0.485957	−	0.873983i	$-0.661529\pi$
$859$	−28.4856	−0.971915	−0.485957	+	0.873983i	$0.661529\pi$
$860$	75.4261	2.57201
$861$	−13.0721	−0.445496
$862$	49.9580	1.70158
$863$	−31.1091	−1.05897	−0.529484	−	0.848320i	$-0.677614\pi$
$863$	−31.1091	−1.05897	−0.529484	+	0.848320i	$0.677614\pi$
$864$	−4.54194	−0.154520
$865$	34.1186	1.16007
$866$	9.51673	0.323392
$867$	−1.00000	−0.0339618
$868$	−29.0294	−0.985323
$869$	−0.826313	−0.0280307
$870$	14.0423	0.476079
$871$	−2.99448	−0.101464
$872$	11.0146	0.373002
$873$	−15.4596	−0.523227
$874$	100.123	3.38671
$875$	−31.3251	−1.05898
$876$	−17.6017	−0.594706
$877$	−6.12776	−0.206920	−0.103460	−	0.994634i	$-0.532991\pi$
$877$	−6.12776	−0.206920	−0.103460	+	0.994634i	$0.532991\pi$
$878$	−27.8322	−0.939293
$879$	19.9362	0.672432
$880$	−1.89768	−0.0639709
$881$	−54.8915	−1.84934	−0.924670	−	0.380768i	$-0.875660\pi$
$881$	−54.8915	−1.84934	−0.924670	+	0.380768i	$0.875660\pi$
$882$	−10.0996	−0.340071
$883$	9.49024	0.319372	0.159686	−	0.987168i	$-0.448952\pi$
$883$	9.49024	0.319372	0.159686	+	0.987168i	$0.448952\pi$
$884$	−12.1712	−0.409363
$885$	8.98185	0.301922
$886$	−83.9652	−2.82086
$887$	−23.4365	−0.786921	−0.393460	−	0.919342i	$-0.628722\pi$
$887$	−23.4365	−0.786921	−0.393460	+	0.919342i	$0.628722\pi$
$888$	17.8101	0.597669
$889$	46.9051	1.57315
$890$	−72.6815	−2.43629
$891$	0.826313	0.0276825
$892$	−27.6139	−0.924582
$893$	−86.7258	−2.90217
$894$	−32.0099	−1.07057
$895$	65.9489	2.20443
$896$	−66.8501	−2.23330
$897$	−19.8512	−0.662814
$898$	−59.4039	−1.98234
$899$	−6.03554	−0.201297
$900$	4.42690	0.147563
$901$	−12.2303	−0.407450
$902$	7.47827	0.248999
$903$	−29.4988	−0.981660
$904$	−62.8800	−2.09136
$905$	−11.8131	−0.392681
$906$	25.5681	0.849442
$907$	8.74515	0.290378	0.145189	−	0.989404i	$-0.453621\pi$
$907$	8.74515	0.290378	0.145189	+	0.989404i	$0.453621\pi$
$908$	−84.5278	−2.80515
$909$	−13.4804	−0.447118
$910$	69.7821	2.31325
$911$	−43.0682	−1.42691	−0.713456	−	0.700700i	$-0.752871\pi$
$911$	−43.0682	−1.42691	−0.713456	+	0.700700i	$0.752871\pi$
$912$	−7.02712	−0.232691
$913$	−13.4784	−0.446070
$914$	81.5824	2.69851
$915$	15.9794	0.528264
$916$	−20.8405	−0.688591
$917$	−10.3346	−0.341280
$918$	2.33071	0.0769250
$919$	33.2329	1.09625	0.548126	−	0.836396i	$-0.315342\pi$
$919$	33.2329	1.09625	0.548126	+	0.836396i	$0.315342\pi$
$920$	−46.8649	−1.54509
$921$	−15.2504	−0.502518
$922$	27.0172	0.889764
$923$	20.0437	0.659746
$924$	9.54768	0.314095
$925$	6.88163	0.226267
$926$	86.9893	2.85865
$927$	10.8548	0.356517
$928$	−10.9112	−0.358177
$929$	23.2968	0.764344	0.382172	−	0.924091i	$-0.375176\pi$
$929$	23.2968	0.764344	0.382172	+	0.924091i	$0.375176\pi$
$930$	−14.6856	−0.481561
$931$	33.2531	1.08982
$932$	36.6794	1.20147
$933$	−16.5341	−0.541301
$934$	−87.7423	−2.87102
$935$	−2.07235	−0.0677731
$936$	11.8375	0.386920
$937$	6.97994	0.228025	0.114012	−	0.993479i	$-0.463630\pi$
$937$	6.97994	0.228025	0.114012	+	0.993479i	$0.463630\pi$
$938$	6.62565	0.216335
$939$	−20.0854	−0.655462
$940$	97.2805	3.17294
$941$	−16.3691	−0.533617	−0.266809	−	0.963750i	$-0.585969\pi$
$941$	−16.3691	−0.533617	−0.266809	+	0.963750i	$0.585969\pi$
$942$	22.2889	0.726211
$943$	21.7368	0.707849
$944$	3.27950	0.106739
$945$	−8.44299	−0.274650
$946$	16.8757	0.548675
$947$	−35.7201	−1.16075	−0.580373	−	0.814351i	$-0.697093\pi$
$947$	−35.7201	−1.16075	−0.580373	+	0.814351i	$0.697093\pi$
$948$	3.43222	0.111473
$949$	−18.1860	−0.590343
$950$	−23.0690	−0.748458
$951$	−4.68544	−0.151936
$952$	11.2377	0.364216
$953$	−53.5169	−1.73358	−0.866791	−	0.498671i	$-0.833822\pi$
$953$	−53.5169	−1.73358	−0.866791	+	0.498671i	$0.833822\pi$
$954$	28.5053	0.922892
$955$	−46.3099	−1.49855
$956$	51.0354	1.65060
$957$	1.98507	0.0641681
$958$	−77.8617	−2.51560
$959$	−50.3269	−1.62514
$960$	−31.1422	−1.00511
$961$	−24.6879	−0.796385
$962$	44.0977	1.42177
$963$	−4.02694	−0.129766
$964$	−79.4377	−2.55852
$965$	−47.1150	−1.51668
$966$	43.9233	1.41321
$967$	−50.4166	−1.62129	−0.810644	−	0.585540i	$-0.800883\pi$
$967$	−50.4166	−1.62129	−0.810644	+	0.585540i	$0.800883\pi$
$968$	34.4399	1.10694
$969$	−7.67391	−0.246521
$970$	−90.3660	−2.90148
$971$	30.4511	0.977223	0.488611	−	0.872502i	$-0.337504\pi$
$971$	30.4511	0.977223	0.488611	+	0.872502i	$0.337504\pi$
$972$	−3.43222	−0.110089
$973$	18.1420	0.581605
$974$	−37.6316	−1.20579
$975$	4.57386	0.146481
$976$	5.83450	0.186758
$977$	11.7425	0.375676	0.187838	−	0.982200i	$-0.439852\pi$
$977$	11.7425	0.375676	0.187838	+	0.982200i	$0.439852\pi$
$978$	15.8253	0.506036
$979$	−10.2745	−0.328374
$980$	−37.3000	−1.19151
$981$	−3.29966	−0.105350
$982$	−38.4523	−1.22706
$983$	11.1196	0.354661	0.177330	−	0.984151i	$-0.443254\pi$
$983$	11.1196	0.354661	0.177330	+	0.984151i	$0.443254\pi$
$984$	−12.9619	−0.413209
$985$	33.4949	1.06723
$986$	5.59912	0.178312
$987$	−38.0460	−1.21102
$988$	−93.4010	−2.97148
$989$	49.0519	1.55976
$990$	4.83005	0.153509
$991$	−46.7559	−1.48525	−0.742626	−	0.669707i	$-0.766420\pi$
$991$	−46.7559	−1.48525	−0.742626	+	0.669707i	$0.766420\pi$
$992$	11.4111	0.362302
$993$	27.9989	0.888518
$994$	−44.3491	−1.40667
$995$	58.7601	1.86282
$996$	55.9848	1.77394
$997$	39.6580	1.25598	0.627991	−	0.778220i	$-0.283877\pi$
$997$	39.6580	1.25598	0.627991	+	0.778220i	$0.283877\pi$
$998$	−12.4082	−0.392773
$999$	−5.33541	−0.168805

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.i.1.3	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.i.1.3	✓	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)

\(f(q)\)	\(=\)	\(q-2.33071 q^{2} -1.00000 q^{3} +3.43222 q^{4} -2.50795 q^{5} +2.33071 q^{6} -3.36649 q^{7} -3.33810 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.33071 q^{2} -1.00000 q^{3} +3.43222 q^{4} -2.50795 q^{5} +2.33071 q^{6} -3.36649 q^{7} -3.33810 q^{8} +1.00000 q^{9} +5.84531 q^{10} +0.826313 q^{11} -3.43222 q^{12} -3.54617 q^{13} +7.84633 q^{14} +2.50795 q^{15} +0.915716 q^{16} +1.00000 q^{17} -2.33071 q^{18} +7.67391 q^{19} -8.60784 q^{20} +3.36649 q^{21} -1.92590 q^{22} -5.59795 q^{23} +3.33810 q^{24} +1.28980 q^{25} +8.26510 q^{26} -1.00000 q^{27} -11.5546 q^{28} -2.40232 q^{29} -5.84531 q^{30} +2.51238 q^{31} +4.54194 q^{32} -0.826313 q^{33} -2.33071 q^{34} +8.44299 q^{35} +3.43222 q^{36} +5.33541 q^{37} -17.8857 q^{38} +3.54617 q^{39} +8.37179 q^{40} -3.88300 q^{41} -7.84633 q^{42} -8.76249 q^{43} +2.83609 q^{44} -2.50795 q^{45} +13.0472 q^{46} -11.3014 q^{47} -0.915716 q^{48} +4.33326 q^{49} -3.00616 q^{50} -1.00000 q^{51} -12.1712 q^{52} -12.2303 q^{53} +2.33071 q^{54} -2.07235 q^{55} +11.2377 q^{56} -7.67391 q^{57} +5.59912 q^{58} +3.58135 q^{59} +8.60784 q^{60} +6.37152 q^{61} -5.85564 q^{62} -3.36649 q^{63} -12.4174 q^{64} +8.89360 q^{65} +1.92590 q^{66} +0.844427 q^{67} +3.43222 q^{68} +5.59795 q^{69} -19.6782 q^{70} -5.65221 q^{71} -3.33810 q^{72} +5.12836 q^{73} -12.4353 q^{74} -1.28980 q^{75} +26.3386 q^{76} -2.78177 q^{77} -8.26510 q^{78} -1.00000 q^{79} -2.29657 q^{80} +1.00000 q^{81} +9.05017 q^{82} -16.3115 q^{83} +11.5546 q^{84} -2.50795 q^{85} +20.4229 q^{86} +2.40232 q^{87} -2.75832 q^{88} -12.4342 q^{89} +5.84531 q^{90} +11.9381 q^{91} -19.2134 q^{92} -2.51238 q^{93} +26.3403 q^{94} -19.2458 q^{95} -4.54194 q^{96} -15.4596 q^{97} -10.0996 q^{98} +0.826313 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 2 q^{2} - 25 q^{3} + 26 q^{4} - 2 q^{5} + 2 q^{6} + 12 q^{7} + 25 q^{9}+O(q^{10}) \) 25 * q - 2 * q^2 - 25 * q^3 + 26 * q^4 - 2 * q^5 + 2 * q^6 + 12 * q^7 + 25 * q^9	\( 25 q - 2 q^{2} - 25 q^{3} + 26 q^{4} - 2 q^{5} + 2 q^{6} + 12 q^{7} + 25 q^{9} + 19 q^{10} + 19 q^{11} - 26 q^{12} + 4 q^{13} + 15 q^{14} + 2 q^{15} + 32 q^{16} + 25 q^{17} - 2 q^{18} + 29 q^{19} - 8 q^{20} - 12 q^{21} + 23 q^{22} + 6 q^{23} + 15 q^{25} - 8 q^{26} - 25 q^{27} + 23 q^{28} + 11 q^{29} - 19 q^{30} + 38 q^{31} - 27 q^{32} - 19 q^{33} - 2 q^{34} + 20 q^{35} + 26 q^{36} + 8 q^{37} - 25 q^{38} - 4 q^{39} + 48 q^{40} + 24 q^{41} - 15 q^{42} + 11 q^{43} + 6 q^{44} - 2 q^{45} + 25 q^{46} + 23 q^{47} - 32 q^{48} + 21 q^{49} - 21 q^{50} - 25 q^{51} + 31 q^{52} - 16 q^{53} + 2 q^{54} - 11 q^{55} + 18 q^{56} - 29 q^{57} - 5 q^{58} + 27 q^{59} + 8 q^{60} + 40 q^{61} - 34 q^{62} + 12 q^{63} + 46 q^{64} - 19 q^{65} - 23 q^{66} + 24 q^{67} + 26 q^{68} - 6 q^{69} + 17 q^{70} + 19 q^{71} + 13 q^{73} - 56 q^{74} - 15 q^{75} + 21 q^{76} - 30 q^{77} + 8 q^{78} - 25 q^{79} - 40 q^{80} + 25 q^{81} + 61 q^{82} + q^{83} - 23 q^{84} - 2 q^{85} + 62 q^{86} - 11 q^{87} - q^{88} - 10 q^{89} + 19 q^{90} + 50 q^{91} + 18 q^{92} - 38 q^{93} + 15 q^{94} + 14 q^{95} + 27 q^{96} + 19 q^{97} - 23 q^{98} + 19 q^{99}+O(q^{100}) \) 25 * q - 2 * q^2 - 25 * q^3 + 26 * q^4 - 2 * q^5 + 2 * q^6 + 12 * q^7 + 25 * q^9 + 19 * q^10 + 19 * q^11 - 26 * q^12 + 4 * q^13 + 15 * q^14 + 2 * q^15 + 32 * q^16 + 25 * q^17 - 2 * q^18 + 29 * q^19 - 8 * q^20 - 12 * q^21 + 23 * q^22 + 6 * q^23 + 15 * q^25 - 8 * q^26 - 25 * q^27 + 23 * q^28 + 11 * q^29 - 19 * q^30 + 38 * q^31 - 27 * q^32 - 19 * q^33 - 2 * q^34 + 20 * q^35 + 26 * q^36 + 8 * q^37 - 25 * q^38 - 4 * q^39 + 48 * q^40 + 24 * q^41 - 15 * q^42 + 11 * q^43 + 6 * q^44 - 2 * q^45 + 25 * q^46 + 23 * q^47 - 32 * q^48 + 21 * q^49 - 21 * q^50 - 25 * q^51 + 31 * q^52 - 16 * q^53 + 2 * q^54 - 11 * q^55 + 18 * q^56 - 29 * q^57 - 5 * q^58 + 27 * q^59 + 8 * q^60 + 40 * q^61 - 34 * q^62 + 12 * q^63 + 46 * q^64 - 19 * q^65 - 23 * q^66 + 24 * q^67 + 26 * q^68 - 6 * q^69 + 17 * q^70 + 19 * q^71 + 13 * q^73 - 56 * q^74 - 15 * q^75 + 21 * q^76 - 30 * q^77 + 8 * q^78 - 25 * q^79 - 40 * q^80 + 25 * q^81 + 61 * q^82 + q^83 - 23 * q^84 - 2 * q^85 + 62 * q^86 - 11 * q^87 - q^88 - 10 * q^89 + 19 * q^90 + 50 * q^91 + 18 * q^92 - 38 * q^93 + 15 * q^94 + 14 * q^95 + 27 * q^96 + 19 * q^97 - 23 * q^98 + 19 * q^99

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