LMFDB - Embedded newform 4029.2.a.f.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:	$1$
Dimension:	$22$
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)

$f(q)$	$=$	$q-2.30059 q^{2} -1.00000 q^{3} +3.29272 q^{4} -0.193972 q^{5} +2.30059 q^{6} +1.10356 q^{7} -2.97403 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.30059 q^{2} -1.00000 q^{3} +3.29272 q^{4} -0.193972 q^{5} +2.30059 q^{6} +1.10356 q^{7} -2.97403 q^{8} +1.00000 q^{9} +0.446250 q^{10} +0.301019 q^{11} -3.29272 q^{12} -5.80060 q^{13} -2.53883 q^{14} +0.193972 q^{15} +0.256574 q^{16} +1.00000 q^{17} -2.30059 q^{18} +4.49165 q^{19} -0.638695 q^{20} -1.10356 q^{21} -0.692522 q^{22} +7.40780 q^{23} +2.97403 q^{24} -4.96237 q^{25} +13.3448 q^{26} -1.00000 q^{27} +3.63370 q^{28} -7.01042 q^{29} -0.446250 q^{30} +2.39973 q^{31} +5.35778 q^{32} -0.301019 q^{33} -2.30059 q^{34} -0.214059 q^{35} +3.29272 q^{36} -6.13303 q^{37} -10.3334 q^{38} +5.80060 q^{39} +0.576877 q^{40} +5.15725 q^{41} +2.53883 q^{42} +5.84456 q^{43} +0.991171 q^{44} -0.193972 q^{45} -17.0423 q^{46} +9.29028 q^{47} -0.256574 q^{48} -5.78217 q^{49} +11.4164 q^{50} -1.00000 q^{51} -19.0998 q^{52} -1.70631 q^{53} +2.30059 q^{54} -0.0583892 q^{55} -3.28200 q^{56} -4.49165 q^{57} +16.1281 q^{58} -10.8188 q^{59} +0.638695 q^{60} -0.447400 q^{61} -5.52081 q^{62} +1.10356 q^{63} -12.8392 q^{64} +1.12515 q^{65} +0.692522 q^{66} -10.4194 q^{67} +3.29272 q^{68} -7.40780 q^{69} +0.492461 q^{70} -5.44758 q^{71} -2.97403 q^{72} -2.85090 q^{73} +14.1096 q^{74} +4.96237 q^{75} +14.7897 q^{76} +0.332191 q^{77} -13.3448 q^{78} +1.00000 q^{79} -0.0497682 q^{80} +1.00000 q^{81} -11.8647 q^{82} +14.9560 q^{83} -3.63370 q^{84} -0.193972 q^{85} -13.4460 q^{86} +7.01042 q^{87} -0.895238 q^{88} -12.9775 q^{89} +0.446250 q^{90} -6.40128 q^{91} +24.3918 q^{92} -2.39973 q^{93} -21.3731 q^{94} -0.871253 q^{95} -5.35778 q^{96} +3.51484 q^{97} +13.3024 q^{98} +0.301019 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + q^{2} - 22 q^{3} + 19 q^{4} + q^{5} - q^{6} - 15 q^{7} + 15 q^{8} + 22 q^{9}+O(q^{10}) $ 22 * q + q^2 - 22 * q^3 + 19 * q^4 + q^5 - q^6 - 15 * q^7 + 15 * q^8 + 22 * q^9	\( 22 q + q^{2} - 22 q^{3} + 19 q^{4} + q^{5} - q^{6} - 15 q^{7} + 15 q^{8} + 22 q^{9} - 13 q^{10} - 23 q^{11} - 19 q^{12} - 18 q^{13} - 9 q^{14} - q^{15} + 21 q^{16} + 22 q^{17} + q^{18} - 30 q^{19} - 7 q^{20} + 15 q^{21} + 4 q^{22} - 3 q^{23} - 15 q^{24} + 19 q^{25} - 7 q^{26} - 22 q^{27} - 25 q^{28} - 7 q^{29} + 13 q^{30} - 10 q^{31} + 31 q^{32} + 23 q^{33} + q^{34} - 11 q^{35} + 19 q^{36} - q^{37} - 29 q^{38} + 18 q^{39} - 59 q^{40} + 9 q^{42} - 43 q^{43} - 80 q^{44} + q^{45} - 43 q^{46} + 2 q^{47} - 21 q^{48} + 43 q^{49} + 25 q^{50} - 22 q^{51} - 5 q^{52} - q^{53} - q^{54} - 19 q^{55} - 8 q^{56} + 30 q^{57} - 43 q^{58} - 28 q^{59} + 7 q^{60} - 29 q^{61} - 3 q^{62} - 15 q^{63} + 23 q^{64} + 19 q^{65} - 4 q^{66} - 16 q^{67} + 19 q^{68} + 3 q^{69} - 5 q^{70} - q^{71} + 15 q^{72} - 19 q^{73} - 24 q^{74} - 19 q^{75} - 72 q^{76} + 24 q^{77} + 7 q^{78} + 22 q^{79} - 82 q^{80} + 22 q^{81} - 81 q^{82} - 29 q^{83} + 25 q^{84} + q^{85} - 42 q^{86} + 7 q^{87} - 43 q^{88} - 28 q^{89} - 13 q^{90} - 96 q^{91} - 11 q^{92} + 10 q^{93} - 63 q^{94} - 23 q^{95} - 31 q^{96} - 51 q^{97} + 12 q^{98} - 23 q^{99}+O(q^{100}) \) 22 * q + q^2 - 22 * q^3 + 19 * q^4 + q^5 - q^6 - 15 * q^7 + 15 * q^8 + 22 * q^9 - 13 * q^10 - 23 * q^11 - 19 * q^12 - 18 * q^13 - 9 * q^14 - q^15 + 21 * q^16 + 22 * q^17 + q^18 - 30 * q^19 - 7 * q^20 + 15 * q^21 + 4 * q^22 - 3 * q^23 - 15 * q^24 + 19 * q^25 - 7 * q^26 - 22 * q^27 - 25 * q^28 - 7 * q^29 + 13 * q^30 - 10 * q^31 + 31 * q^32 + 23 * q^33 + q^34 - 11 * q^35 + 19 * q^36 - q^37 - 29 * q^38 + 18 * q^39 - 59 * q^40 + 9 * q^42 - 43 * q^43 - 80 * q^44 + q^45 - 43 * q^46 + 2 * q^47 - 21 * q^48 + 43 * q^49 + 25 * q^50 - 22 * q^51 - 5 * q^52 - q^53 - q^54 - 19 * q^55 - 8 * q^56 + 30 * q^57 - 43 * q^58 - 28 * q^59 + 7 * q^60 - 29 * q^61 - 3 * q^62 - 15 * q^63 + 23 * q^64 + 19 * q^65 - 4 * q^66 - 16 * q^67 + 19 * q^68 + 3 * q^69 - 5 * q^70 - q^71 + 15 * q^72 - 19 * q^73 - 24 * q^74 - 19 * q^75 - 72 * q^76 + 24 * q^77 + 7 * q^78 + 22 * q^79 - 82 * q^80 + 22 * q^81 - 81 * q^82 - 29 * q^83 + 25 * q^84 + q^85 - 42 * q^86 + 7 * q^87 - 43 * q^88 - 28 * q^89 - 13 * q^90 - 96 * q^91 - 11 * q^92 + 10 * q^93 - 63 * q^94 - 23 * q^95 - 31 * q^96 - 51 * q^97 + 12 * q^98 - 23 * 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 $

$2$	−2.30059	−1.62676	−0.813382	−	0.581730i	$-0.802376\pi$
$2$	−2.30059	−1.62676	−0.813382	+	0.581730i	$0.802376\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	3.29272	1.64636
$5$	−0.193972	−0.0867468	−0.0433734	−	0.999059i	$-0.513811\pi$
$5$	−0.193972	−0.0867468	−0.0433734	+	0.999059i	$0.513811\pi$
$6$	2.30059	0.939213
$7$	1.10356	0.417105	0.208552	−	0.978011i	$-0.433125\pi$
$7$	1.10356	0.417105	0.208552	+	0.978011i	$0.433125\pi$
$8$	−2.97403	−1.05148
$9$	1.00000	0.333333
$10$	0.446250	0.141117
$11$	0.301019	0.0907606	0.0453803	−	0.998970i	$-0.485550\pi$
$11$	0.301019	0.0907606	0.0453803	+	0.998970i	$0.485550\pi$
$12$	−3.29272	−0.950527
$13$	−5.80060	−1.60880	−0.804398	−	0.594091i	$-0.797512\pi$
$13$	−5.80060	−1.60880	−0.804398	+	0.594091i	$0.797512\pi$
$14$	−2.53883	−0.678531
$15$	0.193972	0.0500833
$16$	0.256574	0.0641436
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−2.30059	−0.542255
$19$	4.49165	1.03045	0.515227	−	0.857054i	$-0.327708\pi$
$19$	4.49165	1.03045	0.515227	+	0.857054i	$0.327708\pi$
$20$	−0.638695	−0.142817
$21$	−1.10356	−0.240815
$22$	−0.692522	−0.147646
$23$	7.40780	1.54463	0.772317	−	0.635237i	$-0.219098\pi$
$23$	7.40780	1.54463	0.772317	+	0.635237i	$0.219098\pi$
$24$	2.97403	0.607070
$25$	−4.96237	−0.992475
$26$	13.3448	2.61713
$27$	−1.00000	−0.192450
$28$	3.63370	0.686705
$29$	−7.01042	−1.30180	−0.650901	−	0.759163i	$-0.725609\pi$
$29$	−7.01042	−1.30180	−0.650901	+	0.759163i	$0.725609\pi$
$30$	−0.446250	−0.0814737
$31$	2.39973	0.431005	0.215503	−	0.976503i	$-0.430861\pi$
$31$	2.39973	0.431005	0.215503	+	0.976503i	$0.430861\pi$
$32$	5.35778	0.947130
$33$	−0.301019	−0.0524007
$34$	−2.30059	−0.394548
$35$	−0.214059	−0.0361825
$36$	3.29272	0.548787
$37$	−6.13303	−1.00826	−0.504132	−	0.863627i	$-0.668187\pi$
$37$	−6.13303	−1.00826	−0.504132	+	0.863627i	$0.668187\pi$
$38$	−10.3334	−1.67631
$39$	5.80060	0.928839
$40$	0.576877	0.0912123
$41$	5.15725	0.805428	0.402714	−	0.915326i	$-0.368067\pi$
$41$	5.15725	0.805428	0.402714	+	0.915326i	$0.368067\pi$
$42$	2.53883	0.391750
$43$	5.84456	0.891287	0.445644	−	0.895210i	$-0.352975\pi$
$43$	5.84456	0.891287	0.445644	+	0.895210i	$0.352975\pi$
$44$	0.991171	0.149425
$45$	−0.193972	−0.0289156
$46$	−17.0423	−2.51275
$47$	9.29028	1.35513	0.677563	−	0.735465i	$-0.263036\pi$
$47$	9.29028	1.35513	0.677563	+	0.735465i	$0.263036\pi$
$48$	−0.256574	−0.0370333
$49$	−5.78217	−0.826024
$50$	11.4164	1.61452
$51$	−1.00000	−0.140028
$52$	−19.0998	−2.64866
$53$	−1.70631	−0.234380	−0.117190	−	0.993110i	$-0.537389\pi$
$53$	−1.70631	−0.234380	−0.117190	+	0.993110i	$0.537389\pi$
$54$	2.30059	0.313071
$55$	−0.0583892	−0.00787320
$56$	−3.28200	−0.438576
$57$	−4.49165	−0.594933
$58$	16.1281	2.11772
$59$	−10.8188	−1.40849	−0.704245	−	0.709957i	$-0.748714\pi$
$59$	−10.8188	−1.40849	−0.704245	+	0.709957i	$0.748714\pi$
$60$	0.638695	0.0824552
$61$	−0.447400	−0.0572837	−0.0286418	−	0.999590i	$-0.509118\pi$
$61$	−0.447400	−0.0572837	−0.0286418	+	0.999590i	$0.509118\pi$
$62$	−5.52081	−0.701144
$63$	1.10356	0.139035
$64$	−12.8392	−1.60490
$65$	1.12515	0.139558
$66$	0.692522	0.0852435
$67$	−10.4194	−1.27293	−0.636464	−	0.771306i	$-0.719604\pi$
$67$	−10.4194	−1.27293	−0.636464	+	0.771306i	$0.719604\pi$
$68$	3.29272	0.399301
$69$	−7.40780	−0.891795
$70$	0.492461	0.0588604
$71$	−5.44758	−0.646509	−0.323255	−	0.946312i	$-0.604777\pi$
$71$	−5.44758	−0.646509	−0.323255	+	0.946312i	$0.604777\pi$
$72$	−2.97403	−0.350492
$73$	−2.85090	−0.333672	−0.166836	−	0.985985i	$-0.553355\pi$
$73$	−2.85090	−0.333672	−0.166836	+	0.985985i	$0.553355\pi$
$74$	14.1096	1.64021
$75$	4.96237	0.573006
$76$	14.7897	1.69650
$77$	0.332191	0.0378567
$78$	−13.3448	−1.51100
$79$	1.00000	0.112509
$79$	1.00000	0.112509
$80$	−0.0497682	−0.00556425
$81$	1.00000	0.111111
$82$	−11.8647	−1.31024
$83$	14.9560	1.64164	0.820818	−	0.571190i	$-0.193518\pi$
$83$	14.9560	1.64164	0.820818	+	0.571190i	$0.193518\pi$
$84$	−3.63370	−0.396469
$85$	−0.193972	−0.0210392
$86$	−13.4460	−1.44991
$87$	7.01042	0.751596
$88$	−0.895238	−0.0954327
$89$	−12.9775	−1.37561	−0.687805	−	0.725896i	$-0.741426\pi$
$89$	−12.9775	−1.37561	−0.687805	+	0.725896i	$0.741426\pi$
$90$	0.446250	0.0470389
$91$	−6.40128	−0.671036
$92$	24.3918	2.54303
$93$	−2.39973	−0.248841
$94$	−21.3731	−2.20447
$95$	−0.871253	−0.0893886
$96$	−5.35778	−0.546826
$97$	3.51484	0.356878	0.178439	−	0.983951i	$-0.442895\pi$
$97$	3.51484	0.356878	0.178439	+	0.983951i	$0.442895\pi$
$98$	13.3024	1.34375
$99$	0.301019	0.0302535
$100$	−16.3397	−1.63397
$101$	4.80426	0.478041	0.239021	−	0.971014i	$-0.423174\pi$
$101$	4.80426	0.478041	0.239021	+	0.971014i	$0.423174\pi$
$102$	2.30059	0.227793
$103$	−7.94855	−0.783194	−0.391597	−	0.920137i	$-0.628077\pi$
$103$	−7.94855	−0.783194	−0.391597	+	0.920137i	$0.628077\pi$
$104$	17.2511	1.69161
$105$	0.214059	0.0208900
$106$	3.92552	0.381280
$107$	15.7347	1.52113	0.760567	−	0.649260i	$-0.224921\pi$
$107$	15.7347	1.52113	0.760567	+	0.649260i	$0.224921\pi$
$108$	−3.29272	−0.316842
$109$	−5.02251	−0.481069	−0.240534	−	0.970641i	$-0.577323\pi$
$109$	−5.02251	−0.481069	−0.240534	+	0.970641i	$0.577323\pi$
$110$	0.134330	0.0128078
$111$	6.13303	0.582121
$112$	0.283144	0.0267546
$113$	0.827572	0.0778515	0.0389257	−	0.999242i	$-0.487606\pi$
$113$	0.827572	0.0778515	0.0389257	+	0.999242i	$0.487606\pi$
$114$	10.3334	0.967816
$115$	−1.43691	−0.133992
$116$	−23.0834	−2.14324
$117$	−5.80060	−0.536265
$118$	24.8897	2.29128
$119$	1.10356	0.101163
$120$	−0.576877	−0.0526614
$121$	−10.9094	−0.991763
$122$	1.02928	0.0931870
$123$	−5.15725	−0.465014
$124$	7.90166	0.709590
$125$	1.93242	0.172841
$126$	−2.53883	−0.226177
$127$	7.54627	0.669623	0.334811	−	0.942285i	$-0.391327\pi$
$127$	7.54627	0.669623	0.334811	+	0.942285i	$0.391327\pi$
$128$	18.8222	1.66366
$129$	−5.84456	−0.514585
$130$	−2.58852	−0.227028
$131$	14.1282	1.23439	0.617193	−	0.786812i	$-0.288270\pi$
$131$	14.1282	1.23439	0.617193	+	0.786812i	$0.288270\pi$
$132$	−0.991171	−0.0862704
$133$	4.95678	0.429807
$134$	23.9707	2.07075
$135$	0.193972	0.0166944
$136$	−2.97403	−0.255021
$137$	−4.56763	−0.390239	−0.195120	−	0.980779i	$-0.562510\pi$
$137$	−4.56763	−0.390239	−0.195120	+	0.980779i	$0.562510\pi$
$138$	17.0423	1.45074
$139$	−1.62635	−0.137945	−0.0689726	−	0.997619i	$-0.521972\pi$
$139$	−1.62635	−0.137945	−0.0689726	+	0.997619i	$0.521972\pi$
$140$	−0.704835	−0.0595695
$141$	−9.29028	−0.782382
$142$	12.5327	1.05172
$143$	−1.74609	−0.146015
$144$	0.256574	0.0213812
$145$	1.35982	0.112927
$146$	6.55875	0.542806
$147$	5.78217	0.476905
$148$	−20.1943	−1.65997
$149$	12.5002	1.02406	0.512028	−	0.858969i	$-0.328894\pi$
$149$	12.5002	1.02406	0.512028	+	0.858969i	$0.328894\pi$
$150$	−11.4164	−0.932145
$151$	−4.09697	−0.333407	−0.166703	−	0.986007i	$-0.553312\pi$
$151$	−4.09697	−0.333407	−0.166703	+	0.986007i	$0.553312\pi$
$152$	−13.3583	−1.08350
$153$	1.00000	0.0808452
$154$	−0.764236	−0.0615839
$155$	−0.465481	−0.0373883
$156$	19.0998	1.52920
$157$	−3.05489	−0.243807	−0.121904	−	0.992542i	$-0.538900\pi$
$157$	−3.05489	−0.243807	−0.121904	+	0.992542i	$0.538900\pi$
$158$	−2.30059	−0.183025
$159$	1.70631	0.135319
$160$	−1.03926	−0.0821606
$161$	8.17492	0.644274
$162$	−2.30059	−0.180752
$163$	5.15182	0.403522	0.201761	−	0.979435i	$-0.435334\pi$
$163$	5.15182	0.403522	0.201761	+	0.979435i	$0.435334\pi$
$164$	16.9814	1.32602
$165$	0.0583892	0.00454559
$166$	−34.4077	−2.67055
$167$	3.90236	0.301973	0.150987	−	0.988536i	$-0.451755\pi$
$167$	3.90236	0.301973	0.150987	+	0.988536i	$0.451755\pi$
$168$	3.28200	0.253212
$169$	20.6469	1.58823
$170$	0.446250	0.0342258
$171$	4.49165	0.343485
$172$	19.2445	1.46738
$173$	−0.947346	−0.0720254	−0.0360127	−	0.999351i	$-0.511466\pi$
$173$	−0.947346	−0.0720254	−0.0360127	+	0.999351i	$0.511466\pi$
$174$	−16.1281	−1.22267
$175$	−5.47625	−0.413966
$176$	0.0772337	0.00582171
$177$	10.8188	0.813192
$178$	29.8559	2.23779
$179$	−20.5717	−1.53760	−0.768800	−	0.639489i	$-0.779146\pi$
$179$	−20.5717	−1.53760	−0.768800	+	0.639489i	$0.779146\pi$
$180$	−0.638695	−0.0476055
$181$	−9.11746	−0.677695	−0.338848	−	0.940841i	$-0.610037\pi$
$181$	−9.11746	−0.677695	−0.338848	+	0.940841i	$0.610037\pi$
$182$	14.7267	1.09162
$183$	0.447400	0.0330727
$184$	−22.0310	−1.62415
$185$	1.18963	0.0874636
$186$	5.52081	0.404805
$187$	0.301019	0.0220127
$188$	30.5903	2.23103
$189$	−1.10356	−0.0802718
$190$	2.00440	0.145414
$191$	1.68233	0.121729	0.0608645	−	0.998146i	$-0.480614\pi$
$191$	1.68233	0.121729	0.0608645	+	0.998146i	$0.480614\pi$
$192$	12.8392	0.926590
$193$	20.2139	1.45503	0.727515	−	0.686091i	$-0.240675\pi$
$193$	20.2139	1.45503	0.727515	+	0.686091i	$0.240675\pi$
$194$	−8.08622	−0.580557
$195$	−1.12515	−0.0805738
$196$	−19.0391	−1.35993
$197$	−19.8238	−1.41238	−0.706192	−	0.708020i	$-0.749589\pi$
$197$	−19.8238	−1.41238	−0.706192	+	0.708020i	$0.749589\pi$
$198$	−0.692522	−0.0492154
$199$	19.7253	1.39829	0.699143	−	0.714982i	$-0.253565\pi$
$199$	19.7253	1.39829	0.699143	+	0.714982i	$0.253565\pi$
$200$	14.7582	1.04356
$201$	10.4194	0.734925
$202$	−11.0526	−0.777661
$203$	−7.73638	−0.542987
$204$	−3.29272	−0.230537
$205$	−1.00036	−0.0698683
$206$	18.2864	1.27407
$207$	7.40780	0.514878
$208$	−1.48828	−0.103194
$209$	1.35207	0.0935246
$210$	−0.492461	−0.0339831
$211$	−12.9258	−0.889849	−0.444924	−	0.895568i	$-0.646769\pi$
$211$	−12.9258	−0.889849	−0.444924	+	0.895568i	$0.646769\pi$
$212$	−5.61840	−0.385873
$213$	5.44758	0.373262
$214$	−36.1992	−2.47453
$215$	−1.13368	−0.0773164
$216$	2.97403	0.202357
$217$	2.64824	0.179774
$218$	11.5547	0.782585
$219$	2.85090	0.192646
$220$	−0.192259	−0.0129621
$221$	−5.80060	−0.390190
$222$	−14.1096	−0.946974
$223$	14.8585	0.995000	0.497500	−	0.867464i	$-0.334251\pi$
$223$	14.8585	0.995000	0.497500	+	0.867464i	$0.334251\pi$
$224$	5.91260	0.395052
$225$	−4.96237	−0.330825
$226$	−1.90391	−0.126646
$227$	−5.92099	−0.392990	−0.196495	−	0.980505i	$-0.562956\pi$
$227$	−5.92099	−0.392990	−0.196495	+	0.980505i	$0.562956\pi$
$228$	−14.7897	−0.979475
$229$	−11.3579	−0.750553	−0.375276	−	0.926913i	$-0.622452\pi$
$229$	−11.3579	−0.750553	−0.375276	+	0.926913i	$0.622452\pi$
$230$	3.30573	0.217974
$231$	−0.332191	−0.0218566
$232$	20.8492	1.36881
$233$	−17.1426	−1.12305	−0.561525	−	0.827460i	$-0.689785\pi$
$233$	−17.1426	−1.12305	−0.561525	+	0.827460i	$0.689785\pi$
$234$	13.3448	0.872377
$235$	−1.80205	−0.117553
$236$	−35.6233	−2.31888
$237$	−1.00000	−0.0649570
$238$	−2.53883	−0.164568
$239$	0.195524	0.0126474	0.00632371	−	0.999980i	$-0.497987\pi$
$239$	0.195524	0.0126474	0.00632371	+	0.999980i	$0.497987\pi$
$240$	0.0497682	0.00321252
$241$	−22.0552	−1.42070	−0.710350	−	0.703849i	$-0.751463\pi$
$241$	−22.0552	−1.42070	−0.710350	+	0.703849i	$0.751463\pi$
$242$	25.0980	1.61336
$243$	−1.00000	−0.0641500
$244$	−1.47316	−0.0943096
$245$	1.12158	0.0716549
$246$	11.8647	0.756468
$247$	−26.0542	−1.65779
$248$	−7.13687	−0.453192
$249$	−14.9560	−0.947798
$250$	−4.44571	−0.281171
$251$	8.47248	0.534778	0.267389	−	0.963589i	$-0.413839\pi$
$251$	8.47248	0.534778	0.267389	+	0.963589i	$0.413839\pi$
$252$	3.63370	0.228902
$253$	2.22989	0.140192
$254$	−17.3609	−1.08932
$255$	0.193972	0.0121470
$256$	−17.6238	−1.10149
$257$	0.215587	0.0134479	0.00672397	−	0.999977i	$-0.497860\pi$
$257$	0.215587	0.0134479	0.00672397	+	0.999977i	$0.497860\pi$
$258$	13.4460	0.837108
$259$	−6.76813	−0.420551
$260$	3.70481	0.229763
$261$	−7.01042	−0.433934
$262$	−32.5032	−2.00805
$263$	26.4641	1.63185	0.815923	−	0.578161i	$-0.196230\pi$
$263$	26.4641	1.63185	0.815923	+	0.578161i	$0.196230\pi$
$264$	0.895238	0.0550981
$265$	0.330976	0.0203317
$266$	−11.4035	−0.699195
$267$	12.9775	0.794209
$268$	−34.3081	−2.09570
$269$	0.430184	0.0262288	0.0131144	−	0.999914i	$-0.495825\pi$
$269$	0.430184	0.0262288	0.0131144	+	0.999914i	$0.495825\pi$
$270$	−0.446250	−0.0271579
$271$	−21.6162	−1.31309	−0.656545	−	0.754287i	$-0.727983\pi$
$271$	−21.6162	−1.31309	−0.656545	+	0.754287i	$0.727983\pi$
$272$	0.256574	0.0155571
$273$	6.40128	0.387423
$274$	10.5083	0.634827
$275$	−1.49377	−0.0900776
$276$	−24.3918	−1.46822
$277$	5.69925	0.342435	0.171217	−	0.985233i	$-0.445230\pi$
$277$	5.69925	0.342435	0.171217	+	0.985233i	$0.445230\pi$
$278$	3.74157	0.224404
$279$	2.39973	0.143668
$280$	0.636616	0.0380451
$281$	−4.78743	−0.285594	−0.142797	−	0.989752i	$-0.545610\pi$
$281$	−4.78743	−0.285594	−0.142797	+	0.989752i	$0.545610\pi$
$282$	21.3731	1.27275
$283$	−21.7148	−1.29081	−0.645405	−	0.763841i	$-0.723311\pi$
$283$	−21.7148	−1.29081	−0.645405	+	0.763841i	$0.723311\pi$
$284$	−17.9374	−1.06439
$285$	0.871253	0.0516086
$286$	4.01704	0.237532
$287$	5.69131	0.335948
$288$	5.35778	0.315710
$289$	1.00000	0.0588235
$290$	−3.12840	−0.183706
$291$	−3.51484	−0.206044
$292$	−9.38721	−0.549345
$293$	−22.2751	−1.30133	−0.650663	−	0.759366i	$-0.725509\pi$
$293$	−22.2751	−1.30133	−0.650663	+	0.759366i	$0.725509\pi$
$294$	−13.3024	−0.775812
$295$	2.09854	0.122182
$296$	18.2398	1.06017
$297$	−0.301019	−0.0174669
$298$	−28.7579	−1.66590
$299$	−42.9697	−2.48500
$300$	16.3397	0.943374
$301$	6.44980	0.371760
$302$	9.42545	0.542374
$303$	−4.80426	−0.275997
$304$	1.15244	0.0660970
$305$	0.0867829	0.00496918
$306$	−2.30059	−0.131516
$307$	−18.3481	−1.04718	−0.523590	−	0.851970i	$-0.675408\pi$
$307$	−18.3481	−1.04718	−0.523590	+	0.851970i	$0.675408\pi$
$308$	1.09381	0.0623257
$309$	7.94855	0.452177
$310$	1.07088	0.0608220
$311$	−2.16676	−0.122866	−0.0614329	−	0.998111i	$-0.519567\pi$
$311$	−2.16676	−0.122866	−0.0614329	+	0.998111i	$0.519567\pi$
$312$	−17.2511	−0.976653
$313$	14.5931	0.824852	0.412426	−	0.910991i	$-0.364682\pi$
$313$	14.5931	0.824852	0.412426	+	0.910991i	$0.364682\pi$
$314$	7.02806	0.396616
$315$	−0.214059	−0.0120608
$316$	3.29272	0.185230
$317$	−3.57864	−0.200997	−0.100498	−	0.994937i	$-0.532044\pi$
$317$	−3.57864	−0.200997	−0.100498	+	0.994937i	$0.532044\pi$
$318$	−3.92552	−0.220132
$319$	−2.11027	−0.118152
$320$	2.49044	0.139220
$321$	−15.7347	−0.878227
$322$	−18.8072	−1.04808
$323$	4.49165	0.249922
$324$	3.29272	0.182929
$325$	28.7847	1.59669
$326$	−11.8522	−0.656435
$327$	5.02251	0.277745
$328$	−15.3378	−0.846888
$329$	10.2523	0.565229
$330$	−0.134330	−0.00739460
$331$	10.5832	0.581703	0.290851	−	0.956768i	$-0.406062\pi$
$331$	10.5832	0.581703	0.290851	+	0.956768i	$0.406062\pi$
$332$	49.2460	2.70272
$333$	−6.13303	−0.336088
$334$	−8.97773	−0.491239
$335$	2.02106	0.110422
$336$	−0.283144	−0.0154468
$337$	−6.71202	−0.365627	−0.182814	−	0.983148i	$-0.558520\pi$
$337$	−6.71202	−0.365627	−0.182814	+	0.983148i	$0.558520\pi$
$338$	−47.5002	−2.58367
$339$	−0.827572	−0.0449476
$340$	−0.638695	−0.0346381
$341$	0.722366	0.0391183
$342$	−10.3334	−0.558769
$343$	−14.1058	−0.761643
$344$	−17.3819	−0.937168
$345$	1.43691	0.0773604
$346$	2.17946	0.117168
$347$	4.00587	0.215046	0.107523	−	0.994203i	$-0.465708\pi$
$347$	4.00587	0.215046	0.107523	+	0.994203i	$0.465708\pi$
$348$	23.0834	1.23740
$349$	20.3249	1.08797	0.543983	−	0.839096i	$-0.316915\pi$
$349$	20.3249	1.08797	0.543983	+	0.839096i	$0.316915\pi$
$350$	12.5986	0.673425
$351$	5.80060	0.309613
$352$	1.61279	0.0859621
$353$	−5.88771	−0.313371	−0.156685	−	0.987649i	$-0.550081\pi$
$353$	−5.88771	−0.313371	−0.156685	+	0.987649i	$0.550081\pi$
$354$	−24.8897	−1.32287
$355$	1.05668	0.0560826
$356$	−42.7312	−2.26475
$357$	−1.10356	−0.0584063
$358$	47.3271	2.50131
$359$	−20.2137	−1.06684	−0.533420	−	0.845851i	$-0.679093\pi$
$359$	−20.2137	−1.06684	−0.533420	+	0.845851i	$0.679093\pi$
$360$	0.576877	0.0304041
$361$	1.17488	0.0618359
$362$	20.9756	1.10245
$363$	10.9094	0.572594
$364$	−21.0776	−1.10477
$365$	0.552993	0.0289450
$366$	−1.02928	−0.0538015
$367$	13.4004	0.699495	0.349747	−	0.936844i	$-0.386267\pi$
$367$	13.4004	0.699495	0.349747	+	0.936844i	$0.386267\pi$
$368$	1.90065	0.0990784
$369$	5.15725	0.268476
$370$	−2.73686	−0.142283
$371$	−1.88301	−0.0977608
$372$	−7.90166	−0.409682
$373$	−2.69730	−0.139661	−0.0698304	−	0.997559i	$-0.522246\pi$
$373$	−2.69730	−0.139661	−0.0698304	+	0.997559i	$0.522246\pi$
$374$	−0.692522	−0.0358094
$375$	−1.93242	−0.0997897
$376$	−27.6295	−1.42488
$377$	40.6646	2.09433
$378$	2.53883	0.130583
$379$	5.47377	0.281169	0.140584	−	0.990069i	$-0.455102\pi$
$379$	5.47377	0.281169	0.140584	+	0.990069i	$0.455102\pi$
$380$	−2.86879	−0.147166
$381$	−7.54627	−0.386607
$382$	−3.87035	−0.198024
$383$	−5.99665	−0.306414	−0.153207	−	0.988194i	$-0.548960\pi$
$383$	−5.99665	−0.306414	−0.153207	+	0.988194i	$0.548960\pi$
$384$	−18.8222	−0.960517
$385$	−0.0644357	−0.00328395
$386$	−46.5040	−2.36699
$387$	5.84456	0.297096
$388$	11.5734	0.587551
$389$	−25.3265	−1.28410	−0.642051	−	0.766662i	$-0.721916\pi$
$389$	−25.3265	−1.28410	−0.642051	+	0.766662i	$0.721916\pi$
$390$	2.58852	0.131075
$391$	7.40780	0.374629
$392$	17.1963	0.868545
$393$	−14.1282	−0.712673
$394$	45.6064	2.29762
$395$	−0.193972	−0.00975978
$396$	0.991171	0.0498082
$397$	−21.0140	−1.05466	−0.527331	−	0.849660i	$-0.676807\pi$
$397$	−21.0140	−1.05466	−0.527331	+	0.849660i	$0.676807\pi$
$398$	−45.3798	−2.27468
$399$	−4.95678	−0.248149
$400$	−1.27322	−0.0636609
$401$	13.3464	0.666489	0.333244	−	0.942840i	$-0.391857\pi$
$401$	13.3464	0.666489	0.333244	+	0.942840i	$0.391857\pi$
$402$	−23.9707	−1.19555
$403$	−13.9199	−0.693399
$404$	15.8191	0.787029
$405$	−0.193972	−0.00963854
$406$	17.7983	0.883312
$407$	−1.84616	−0.0915106
$408$	2.97403	0.147236
$409$	−0.0943363	−0.00466463	−0.00233231	−	0.999997i	$-0.500742\pi$
$409$	−0.0943363	−0.00466463	−0.00233231	+	0.999997i	$0.500742\pi$
$410$	2.30142	0.113659
$411$	4.56763	0.225305
$412$	−26.1724	−1.28942
$413$	−11.9392	−0.587487
$414$	−17.0423	−0.837585
$415$	−2.90104	−0.142407
$416$	−31.0783	−1.52374
$417$	1.62635	0.0796427
$418$	−3.11056	−0.152143
$419$	−21.1798	−1.03470	−0.517351	−	0.855774i	$-0.673082\pi$
$419$	−21.1798	−1.03470	−0.517351	+	0.855774i	$0.673082\pi$
$420$	0.704835	0.0343924
$421$	−11.0570	−0.538887	−0.269444	−	0.963016i	$-0.586840\pi$
$421$	−11.0570	−0.538887	−0.269444	+	0.963016i	$0.586840\pi$
$422$	29.7370	1.44757
$423$	9.29028	0.451709
$424$	5.07461	0.246445
$425$	−4.96237	−0.240711
$426$	−12.5327	−0.607209
$427$	−0.493730	−0.0238933
$428$	51.8101	2.50433
$429$	1.74609	0.0843020
$430$	2.60814	0.125775
$431$	−22.3216	−1.07519	−0.537597	−	0.843202i	$-0.680668\pi$
$431$	−22.3216	−1.07519	−0.537597	+	0.843202i	$0.680668\pi$
$432$	−0.256574	−0.0123444
$433$	−7.77702	−0.373740	−0.186870	−	0.982385i	$-0.559834\pi$
$433$	−7.77702	−0.373740	−0.186870	+	0.982385i	$0.559834\pi$
$434$	−6.09252	−0.292450
$435$	−1.35982	−0.0651985
$436$	−16.5377	−0.792013
$437$	33.2732	1.59167
$438$	−6.55875	−0.313389
$439$	−19.1951	−0.916132	−0.458066	−	0.888918i	$-0.651458\pi$
$439$	−19.1951	−0.916132	−0.458066	+	0.888918i	$0.651458\pi$
$440$	0.173651	0.00827848
$441$	−5.78217	−0.275341
$442$	13.3448	0.634748
$443$	1.62260	0.0770921	0.0385461	−	0.999257i	$-0.487727\pi$
$443$	1.62260	0.0770921	0.0385461	+	0.999257i	$0.487727\pi$
$444$	20.1943	0.958381
$445$	2.51727	0.119330
$446$	−34.1834	−1.61863
$447$	−12.5002	−0.591239
$448$	−14.1688	−0.669412
$449$	8.24543	0.389126	0.194563	−	0.980890i	$-0.437671\pi$
$449$	8.24543	0.389126	0.194563	+	0.980890i	$0.437671\pi$
$450$	11.4164	0.538174
$451$	1.55243	0.0731011
$452$	2.72497	0.128172
$453$	4.09697	0.192492
$454$	13.6218	0.639302
$455$	1.24167	0.0582103
$456$	13.3583	0.625558
$457$	−28.9296	−1.35327	−0.676636	−	0.736318i	$-0.736563\pi$
$457$	−28.9296	−1.35327	−0.676636	+	0.736318i	$0.736563\pi$
$458$	26.1299	1.22097
$459$	−1.00000	−0.0466760
$460$	−4.73133	−0.220599
$461$	−21.6937	−1.01038	−0.505188	−	0.863009i	$-0.668577\pi$
$461$	−21.6937	−1.01038	−0.505188	+	0.863009i	$0.668577\pi$
$462$	0.764236	0.0355555
$463$	−22.4249	−1.04217	−0.521087	−	0.853504i	$-0.674473\pi$
$463$	−22.4249	−1.04217	−0.521087	+	0.853504i	$0.674473\pi$
$464$	−1.79869	−0.0835022
$465$	0.465481	0.0215862
$466$	39.4382	1.82694
$467$	8.95297	0.414294	0.207147	−	0.978310i	$-0.433582\pi$
$467$	8.95297	0.414294	0.207147	+	0.978310i	$0.433582\pi$
$468$	−19.0998	−0.882887
$469$	−11.4983	−0.530944
$470$	4.14579	0.191231
$471$	3.05489	0.140762
$472$	32.1754	1.48099
$473$	1.75932	0.0808938
$474$	2.30059	0.105670
$475$	−22.2892	−1.02270
$476$	3.63370	0.166550
$477$	−1.70631	−0.0781265
$478$	−0.449822	−0.0205744
$479$	−6.05552	−0.276684	−0.138342	−	0.990385i	$-0.544177\pi$
$479$	−6.05552	−0.276684	−0.138342	+	0.990385i	$0.544177\pi$
$480$	1.03926	0.0474354
$481$	35.5752	1.62209
$482$	50.7400	2.31114
$483$	−8.17492	−0.371972
$484$	−35.9216	−1.63280
$485$	−0.681781	−0.0309581
$486$	2.30059	0.104357
$487$	−10.7341	−0.486407	−0.243203	−	0.969975i	$-0.578198\pi$
$487$	−10.7341	−0.486407	−0.243203	+	0.969975i	$0.578198\pi$
$488$	1.33058	0.0602324
$489$	−5.15182	−0.232973
$490$	−2.58029	−0.116566
$491$	−32.3666	−1.46068	−0.730342	−	0.683082i	$-0.760639\pi$
$491$	−32.3666	−1.46068	−0.730342	+	0.683082i	$0.760639\pi$
$492$	−16.9814	−0.765581
$493$	−7.01042	−0.315733
$494$	59.9401	2.69683
$495$	−0.0583892	−0.00262440
$496$	0.615711	0.0276462
$497$	−6.01171	−0.269662
$498$	34.4077	1.54184
$499$	−32.7192	−1.46471	−0.732357	−	0.680921i	$-0.761580\pi$
$499$	−32.7192	−1.46471	−0.732357	+	0.680921i	$0.761580\pi$
$500$	6.36292	0.284559
$501$	−3.90236	−0.174344
$502$	−19.4917	−0.869958
$503$	−10.9159	−0.486715	−0.243357	−	0.969937i	$-0.578249\pi$
$503$	−10.9159	−0.486715	−0.243357	+	0.969937i	$0.578249\pi$
$504$	−3.28200	−0.146192
$505$	−0.931890	−0.0414686
$506$	−5.13006	−0.228059
$507$	−20.6469	−0.916963
$508$	24.8478	1.10244
$509$	−30.2578	−1.34116	−0.670578	−	0.741839i	$-0.733954\pi$
$509$	−30.2578	−1.34116	−0.670578	+	0.741839i	$0.733954\pi$
$510$	−0.446250	−0.0197603
$511$	−3.14612	−0.139176
$512$	2.90079	0.128198
$513$	−4.49165	−0.198311
$514$	−0.495977	−0.0218766
$515$	1.54179	0.0679396
$516$	−19.2445	−0.847193
$517$	2.79655	0.122992
$518$	15.5707	0.684138
$519$	0.947346	0.0415839
$520$	−3.34623	−0.146742
$521$	−21.2917	−0.932807	−0.466404	−	0.884572i	$-0.654451\pi$
$521$	−21.2917	−0.932807	−0.466404	+	0.884572i	$0.654451\pi$
$522$	16.1281	0.705908
$523$	−38.3763	−1.67808	−0.839038	−	0.544072i	$-0.816882\pi$
$523$	−38.3763	−1.67808	−0.839038	+	0.544072i	$0.816882\pi$
$524$	46.5202	2.03224
$525$	5.47625	0.239003
$526$	−60.8830	−2.65463
$527$	2.39973	0.104534
$528$	−0.0772337	−0.00336117
$529$	31.8756	1.38589
$530$	−0.761440	−0.0330748
$531$	−10.8188	−0.469496
$532$	16.3213	0.707618
$533$	−29.9151	−1.29577
$534$	−29.8559	−1.29199
$535$	−3.05209	−0.131954
$536$	30.9875	1.33845
$537$	20.5717	0.887734
$538$	−0.989677	−0.0426680
$539$	−1.74054	−0.0749704
$540$	0.638695	0.0274851
$541$	−8.19573	−0.352362	−0.176181	−	0.984358i	$-0.556374\pi$
$541$	−8.19573	−0.352362	−0.176181	+	0.984358i	$0.556374\pi$
$542$	49.7300	2.13609
$543$	9.11746	0.391268
$544$	5.35778	0.229713
$545$	0.974224	0.0417312
$546$	−14.7267	−0.630246
$547$	−29.7675	−1.27277	−0.636384	−	0.771373i	$-0.719570\pi$
$547$	−29.7675	−1.27277	−0.636384	+	0.771373i	$0.719570\pi$
$548$	−15.0400	−0.642475
$549$	−0.447400	−0.0190946
$550$	3.43655	0.146535
$551$	−31.4883	−1.34145
$552$	22.0310	0.937702
$553$	1.10356	0.0469279
$554$	−13.1117	−0.557061
$555$	−1.18963	−0.0504972
$556$	−5.35512	−0.227108
$557$	−0.996749	−0.0422336	−0.0211168	−	0.999777i	$-0.506722\pi$
$557$	−0.996749	−0.0422336	−0.0211168	+	0.999777i	$0.506722\pi$
$558$	−5.52081	−0.233715
$559$	−33.9020	−1.43390
$560$	−0.0549220	−0.00232088
$561$	−0.301019	−0.0127090
$562$	11.0139	0.464594
$563$	−12.9841	−0.547214	−0.273607	−	0.961842i	$-0.588217\pi$
$563$	−12.9841	−0.547214	−0.273607	+	0.961842i	$0.588217\pi$
$564$	−30.5903	−1.28808
$565$	−0.160526	−0.00675337
$566$	49.9568	2.09984
$567$	1.10356	0.0463450
$568$	16.2012	0.679789
$569$	24.7756	1.03865	0.519323	−	0.854578i	$-0.326184\pi$
$569$	24.7756	1.03865	0.519323	+	0.854578i	$0.326184\pi$
$570$	−2.00440	−0.0839549
$571$	−44.8591	−1.87729	−0.938647	−	0.344880i	$-0.887920\pi$
$571$	−44.8591	−1.87729	−0.938647	+	0.344880i	$0.887920\pi$
$572$	−5.74939	−0.240394
$573$	−1.68233	−0.0702802
$574$	−13.0934	−0.546507
$575$	−36.7603	−1.53301
$576$	−12.8392	−0.534967
$577$	10.6916	0.445098	0.222549	−	0.974922i	$-0.428562\pi$
$577$	10.6916	0.445098	0.222549	+	0.974922i	$0.428562\pi$
$578$	−2.30059	−0.0956920
$579$	−20.2139	−0.840062
$580$	4.47752	0.185919
$581$	16.5048	0.684734
$582$	8.08622	0.335185
$583$	−0.513631	−0.0212724
$584$	8.47864	0.350848
$585$	1.12515	0.0465193
$586$	51.2460	2.11695
$587$	0.717363	0.0296087	0.0148044	−	0.999890i	$-0.495287\pi$
$587$	0.717363	0.0296087	0.0148044	+	0.999890i	$0.495287\pi$
$588$	19.0391	0.785158
$589$	10.7788	0.444131
$590$	−4.82789	−0.198761
$591$	19.8238	0.815441
$592$	−1.57358	−0.0646736
$593$	−18.5227	−0.760636	−0.380318	−	0.924856i	$-0.624185\pi$
$593$	−18.5227	−0.760636	−0.380318	+	0.924856i	$0.624185\pi$
$594$	0.692522	0.0284145
$595$	−0.214059	−0.00877555
$596$	41.1597	1.68597
$597$	−19.7253	−0.807301
$598$	98.8557	4.04251
$599$	41.2463	1.68528	0.842639	−	0.538479i	$-0.181001\pi$
$599$	41.2463	1.68528	0.842639	+	0.538479i	$0.181001\pi$
$600$	−14.7582	−0.602502
$601$	−1.91800	−0.0782367	−0.0391184	−	0.999235i	$-0.512455\pi$
$601$	−1.91800	−0.0782367	−0.0391184	+	0.999235i	$0.512455\pi$
$602$	−14.8383	−0.604766
$603$	−10.4194	−0.424309
$604$	−13.4902	−0.548908
$605$	2.11611	0.0860323
$606$	11.0526	0.448983
$607$	40.5292	1.64503	0.822515	−	0.568744i	$-0.192570\pi$
$607$	40.5292	1.64503	0.822515	+	0.568744i	$0.192570\pi$
$608$	24.0652	0.975974
$609$	7.73638	0.313494
$610$	−0.199652	−0.00808368
$611$	−53.8892	−2.18012
$612$	3.29272	0.133100
$613$	5.09626	0.205836	0.102918	−	0.994690i	$-0.467182\pi$
$613$	5.09626	0.205836	0.102918	+	0.994690i	$0.467182\pi$
$614$	42.2115	1.70352
$615$	1.00036	0.0403385
$616$	−0.987944	−0.0398054
$617$	−11.8289	−0.476214	−0.238107	−	0.971239i	$-0.576527\pi$
$617$	−11.8289	−0.476214	−0.238107	+	0.971239i	$0.576527\pi$
$618$	−18.2864	−0.735586
$619$	20.5486	0.825920	0.412960	−	0.910749i	$-0.364495\pi$
$619$	20.5486	0.825920	0.412960	+	0.910749i	$0.364495\pi$
$620$	−1.53270	−0.0615547
$621$	−7.40780	−0.297265
$622$	4.98484	0.199874
$623$	−14.3214	−0.573773
$624$	1.48828	0.0595791
$625$	24.4370	0.977482
$626$	−33.5728	−1.34184
$627$	−1.35207	−0.0539965
$628$	−10.0589	−0.401394
$629$	−6.13303	−0.244540
$630$	0.492461	0.0196201
$631$	29.7250	1.18333	0.591666	−	0.806183i	$-0.298470\pi$
$631$	29.7250	1.18333	0.591666	+	0.806183i	$0.298470\pi$
$632$	−2.97403	−0.118300
$633$	12.9258	0.513755
$634$	8.23300	0.326974
$635$	−1.46376	−0.0580877
$636$	5.61840	0.222784
$637$	33.5400	1.32890
$638$	4.85486	0.192206
$639$	−5.44758	−0.215503
$640$	−3.65098	−0.144318
$641$	28.0833	1.10922	0.554612	−	0.832109i	$-0.312867\pi$
$641$	28.0833	1.10922	0.554612	+	0.832109i	$0.312867\pi$
$642$	36.1992	1.42867
$643$	1.48586	0.0585965	0.0292982	−	0.999571i	$-0.490673\pi$
$643$	1.48586	0.0585965	0.0292982	+	0.999571i	$0.490673\pi$
$644$	26.9177	1.06071
$645$	1.13368	0.0446386
$646$	−10.3334	−0.406564
$647$	−45.9640	−1.80703	−0.903515	−	0.428557i	$-0.859022\pi$
$647$	−45.9640	−1.80703	−0.903515	+	0.428557i	$0.859022\pi$
$648$	−2.97403	−0.116831
$649$	−3.25667	−0.127835
$650$	−66.2219	−2.59744
$651$	−2.64824	−0.103793
$652$	16.9635	0.664342
$653$	19.8817	0.778031	0.389016	−	0.921231i	$-0.372815\pi$
$653$	19.8817	0.778031	0.389016	+	0.921231i	$0.372815\pi$
$654$	−11.5547	−0.451826
$655$	−2.74047	−0.107079
$656$	1.32322	0.0516630
$657$	−2.85090	−0.111224
$658$	−23.5864	−0.919495
$659$	−19.6529	−0.765570	−0.382785	−	0.923838i	$-0.625035\pi$
$659$	−19.6529	−0.765570	−0.382785	+	0.923838i	$0.625035\pi$
$660$	0.192259	0.00748368
$661$	11.5779	0.450329	0.225164	−	0.974321i	$-0.427708\pi$
$661$	11.5779	0.450329	0.225164	+	0.974321i	$0.427708\pi$
$662$	−24.3475	−0.946293
$663$	5.80060	0.225277
$664$	−44.4796	−1.72614
$665$	−0.961475	−0.0372844
$666$	14.1096	0.546735
$667$	−51.9318	−2.01081
$668$	12.8494	0.497157
$669$	−14.8585	−0.574464
$670$	−4.64964	−0.179631
$671$	−0.134676	−0.00519910
$672$	−5.91260	−0.228084
$673$	16.3395	0.629842	0.314921	−	0.949118i	$-0.398022\pi$
$673$	16.3395	0.629842	0.314921	+	0.949118i	$0.398022\pi$
$674$	15.4416	0.594789
$675$	4.96237	0.191002
$676$	67.9846	2.61479
$677$	−10.5171	−0.404204	−0.202102	−	0.979364i	$-0.564777\pi$
$677$	−10.5171	−0.404204	−0.202102	+	0.979364i	$0.564777\pi$
$678$	1.90391	0.0731191
$679$	3.87882	0.148856
$680$	0.576877	0.0221222
$681$	5.92099	0.226893
$682$	−1.66187	−0.0636362
$683$	3.45425	0.132173	0.0660866	−	0.997814i	$-0.478949\pi$
$683$	3.45425	0.132173	0.0660866	+	0.997814i	$0.478949\pi$
$684$	14.7897	0.565500
$685$	0.885992	0.0338520
$686$	32.4517	1.23901
$687$	11.3579	0.433332
$688$	1.49956	0.0571704
$689$	9.89761	0.377069
$690$	−3.30573	−0.125847
$691$	−19.3766	−0.737121	−0.368560	−	0.929604i	$-0.620149\pi$
$691$	−19.3766	−0.737121	−0.368560	+	0.929604i	$0.620149\pi$
$692$	−3.11935	−0.118580
$693$	0.332191	0.0126189
$694$	−9.21588	−0.349830
$695$	0.315466	0.0119663
$696$	−20.8492	−0.790285
$697$	5.15725	0.195345
$698$	−46.7593	−1.76987
$699$	17.1426	0.648393
$700$	−18.0318	−0.681537
$701$	−49.4559	−1.86793	−0.933963	−	0.357371i	$-0.883673\pi$
$701$	−49.4559	−1.86793	−0.933963	+	0.357371i	$0.883673\pi$
$702$	−13.3448	−0.503667
$703$	−27.5474	−1.03897
$704$	−3.86484	−0.145662
$705$	1.80205	0.0678692
$706$	13.5452	0.509781
$707$	5.30176	0.199393
$708$	35.6233	1.33881
$709$	−33.7886	−1.26896	−0.634478	−	0.772941i	$-0.718785\pi$
$709$	−33.7886	−1.26896	−0.634478	+	0.772941i	$0.718785\pi$
$710$	−2.43098	−0.0912332
$711$	1.00000	0.0375029
$712$	38.5954	1.44642
$713$	17.7768	0.665745
$714$	2.53883	0.0950133
$715$	0.338692	0.0126664
$716$	−67.7369	−2.53145
$717$	−0.195524	−0.00730199
$718$	46.5035	1.73550
$719$	42.2214	1.57459	0.787296	−	0.616575i	$-0.211480\pi$
$719$	42.2214	1.57459	0.787296	+	0.616575i	$0.211480\pi$
$720$	−0.0497682	−0.00185475
$721$	−8.77166	−0.326674
$722$	−2.70292	−0.100592
$723$	22.0552	0.820241
$724$	−30.0213	−1.11573
$725$	34.7883	1.29201
$726$	−25.0980	−0.931476
$727$	−19.3715	−0.718448	−0.359224	−	0.933251i	$-0.616959\pi$
$727$	−19.3715	−0.718448	−0.359224	+	0.933251i	$0.616959\pi$
$728$	19.0376	0.705579
$729$	1.00000	0.0370370
$730$	−1.27221	−0.0470867
$731$	5.84456	0.216169
$732$	1.47316	0.0544497
$733$	0.507526	0.0187459	0.00937296	−	0.999956i	$-0.497016\pi$
$733$	0.507526	0.0187459	0.00937296	+	0.999956i	$0.497016\pi$
$734$	−30.8288	−1.13791
$735$	−1.12158	−0.0413700
$736$	39.6894	1.46297
$737$	−3.13643	−0.115532
$738$	−11.8647	−0.436747
$739$	32.2336	1.18573	0.592866	−	0.805301i	$-0.297997\pi$
$739$	32.2336	1.18573	0.592866	+	0.805301i	$0.297997\pi$
$740$	3.91713	0.143997
$741$	26.0542	0.957126
$742$	4.33203	0.159034
$743$	16.1500	0.592485	0.296242	−	0.955113i	$-0.404266\pi$
$743$	16.1500	0.592485	0.296242	+	0.955113i	$0.404266\pi$
$744$	7.13687	0.261650
$745$	−2.42469	−0.0888336
$746$	6.20538	0.227195
$747$	14.9560	0.547212
$748$	0.991171	0.0362408
$749$	17.3641	0.634472
$750$	4.44571	0.162334
$751$	8.74592	0.319143	0.159572	−	0.987186i	$-0.448989\pi$
$751$	8.74592	0.319143	0.159572	+	0.987186i	$0.448989\pi$
$752$	2.38365	0.0869227
$753$	−8.47248	−0.308754
$754$	−93.5527	−3.40699
$755$	0.794696	0.0289220
$756$	−3.63370	−0.132156
$757$	−9.29329	−0.337770	−0.168885	−	0.985636i	$-0.554017\pi$
$757$	−9.29329	−0.337770	−0.168885	+	0.985636i	$0.554017\pi$
$758$	−12.5929	−0.457395
$759$	−2.22989	−0.0809398
$760$	2.59113	0.0939901
$761$	−12.2600	−0.444426	−0.222213	−	0.974998i	$-0.571328\pi$
$761$	−12.2600	−0.444426	−0.222213	+	0.974998i	$0.571328\pi$
$762$	17.3609	0.628918
$763$	−5.54261	−0.200656
$764$	5.53944	0.200410
$765$	−0.193972	−0.00701307
$766$	13.7958	0.498464
$767$	62.7556	2.26597
$768$	17.6238	0.635945
$769$	0.825760	0.0297777	0.0148888	−	0.999889i	$-0.495261\pi$
$769$	0.825760	0.0297777	0.0148888	+	0.999889i	$0.495261\pi$
$770$	0.148240	0.00534221
$771$	−0.215587	−0.00776417
$772$	66.5589	2.39551
$773$	22.3773	0.804855	0.402428	−	0.915452i	$-0.368166\pi$
$773$	22.3773	0.804855	0.402428	+	0.915452i	$0.368166\pi$
$774$	−13.4460	−0.483305
$775$	−11.9084	−0.427762
$776$	−10.4532	−0.375249
$777$	6.76813	0.242805
$778$	58.2658	2.08893
$779$	23.1646	0.829956
$780$	−3.70481	−0.132654
$781$	−1.63982	−0.0586776
$782$	−17.0423	−0.609433
$783$	7.01042	0.250532
$784$	−1.48356	−0.0529841
$785$	0.592563	0.0211495
$786$	32.5032	1.15935
$787$	−31.4580	−1.12136	−0.560678	−	0.828034i	$-0.689459\pi$
$787$	−31.4580	−1.12136	−0.560678	+	0.828034i	$0.689459\pi$
$788$	−65.2741	−2.32529
$789$	−26.4641	−0.942146
$790$	0.446250	0.0158769
$791$	0.913272	0.0324722
$792$	−0.895238	−0.0318109
$793$	2.59519	0.0921577
$794$	48.3446	1.71569
$795$	−0.330976	−0.0117385
$796$	64.9498	2.30208
$797$	−10.2778	−0.364058	−0.182029	−	0.983293i	$-0.558267\pi$
$797$	−10.2778	−0.364058	−0.182029	+	0.983293i	$0.558267\pi$
$798$	11.4035	0.403680
$799$	9.29028	0.328666
$800$	−26.5873	−0.940003
$801$	−12.9775	−0.458537
$802$	−30.7047	−1.08422
$803$	−0.858173	−0.0302843
$804$	34.3081	1.20995
$805$	−1.58570	−0.0558887
$806$	32.0240	1.12800
$807$	−0.430184	−0.0151432
$808$	−14.2880	−0.502649
$809$	−37.4884	−1.31802	−0.659011	−	0.752133i	$-0.729025\pi$
$809$	−37.4884	−1.31802	−0.659011	+	0.752133i	$0.729025\pi$
$810$	0.446250	0.0156796
$811$	38.5099	1.35227	0.676133	−	0.736779i	$-0.263654\pi$
$811$	38.5099	1.35227	0.676133	+	0.736779i	$0.263654\pi$
$812$	−25.4738	−0.893953
$813$	21.6162	0.758113
$814$	4.24725	0.148866
$815$	−0.999308	−0.0350042
$816$	−0.256574	−0.00898190
$817$	26.2517	0.918431
$818$	0.217029	0.00758825
$819$	−6.40128	−0.223679
$820$	−3.29391	−0.115028
$821$	49.2458	1.71869	0.859345	−	0.511397i	$-0.170872\pi$
$821$	49.2458	1.71869	0.859345	+	0.511397i	$0.170872\pi$
$822$	−10.5083	−0.366518
$823$	24.8869	0.867504	0.433752	−	0.901032i	$-0.357189\pi$
$823$	24.8869	0.867504	0.433752	+	0.901032i	$0.357189\pi$
$824$	23.6392	0.823510
$825$	1.49377	0.0520063
$826$	27.4671	0.955703
$827$	−40.6539	−1.41368	−0.706838	−	0.707376i	$-0.749879\pi$
$827$	−40.6539	−1.41368	−0.706838	+	0.707376i	$0.749879\pi$
$828$	24.3918	0.847675
$829$	11.8764	0.412486	0.206243	−	0.978501i	$-0.433876\pi$
$829$	11.8764	0.412486	0.206243	+	0.978501i	$0.433876\pi$
$830$	6.67412	0.231662
$831$	−5.69925	−0.197705
$832$	74.4751	2.58196
$833$	−5.78217	−0.200340
$834$	−3.74157	−0.129560
$835$	−0.756947	−0.0261952
$836$	4.45199	0.153975
$837$	−2.39973	−0.0829470
$838$	48.7261	1.68321
$839$	20.0049	0.690647	0.345323	−	0.938484i	$-0.387769\pi$
$839$	20.0049	0.690647	0.345323	+	0.938484i	$0.387769\pi$
$840$	−0.636616	−0.0219653
$841$	20.1459	0.694688
$842$	25.4377	0.876642
$843$	4.78743	0.164888
$844$	−42.5611	−1.46501
$845$	−4.00492	−0.137774
$846$	−21.3731	−0.734824
$847$	−12.0391	−0.413669
$848$	−0.437795	−0.0150339
$849$	21.7148	0.745249
$850$	11.4164	0.391579
$851$	−45.4323	−1.55740
$852$	17.9374	0.614524
$853$	0.416945	0.0142759	0.00713796	−	0.999975i	$-0.497728\pi$
$853$	0.416945	0.0142759	0.00713796	+	0.999975i	$0.497728\pi$
$854$	1.13587	0.0388687
$855$	−0.871253	−0.0297962
$856$	−46.7955	−1.59944
$857$	−39.0359	−1.33344	−0.666721	−	0.745307i	$-0.732303\pi$
$857$	−39.0359	−1.33344	−0.666721	+	0.745307i	$0.732303\pi$
$858$	−4.01704	−0.137139
$859$	9.83116	0.335435	0.167717	−	0.985835i	$-0.446360\pi$
$859$	9.83116	0.335435	0.167717	+	0.985835i	$0.446360\pi$
$860$	−3.73289	−0.127291
$861$	−5.69131	−0.193959
$862$	51.3529	1.74909
$863$	48.9147	1.66508	0.832538	−	0.553969i	$-0.186887\pi$
$863$	48.9147	1.66508	0.832538	+	0.553969i	$0.186887\pi$
$864$	−5.35778	−0.182275
$865$	0.183758	0.00624798
$866$	17.8918	0.607987
$867$	−1.00000	−0.0339618
$868$	8.71992	0.295973
$869$	0.301019	0.0102114
$870$	3.12840	0.106063
$871$	60.4386	2.04788
$872$	14.9371	0.505833
$873$	3.51484	0.118959
$874$	−76.5481	−2.58928
$875$	2.13253	0.0720927
$876$	9.38721	0.317164
$877$	−19.1227	−0.645727	−0.322863	−	0.946446i	$-0.604645\pi$
$877$	−19.1227	−0.645727	−0.322863	+	0.946446i	$0.604645\pi$
$878$	44.1601	1.49033
$879$	22.2751	0.751321
$880$	−0.0149812	−0.000505015 0
$881$	18.6306	0.627681	0.313841	−	0.949476i	$-0.398384\pi$
$881$	18.6306	0.627681	0.313841	+	0.949476i	$0.398384\pi$
$882$	13.3024	0.447915
$883$	39.5968	1.33254	0.666269	−	0.745711i	$-0.267890\pi$
$883$	39.5968	1.33254	0.666269	+	0.745711i	$0.267890\pi$
$884$	−19.0998	−0.642394
$885$	−2.09854	−0.0705418
$886$	−3.73294	−0.125411
$887$	46.1491	1.54953	0.774767	−	0.632247i	$-0.217867\pi$
$887$	46.1491	1.54953	0.774767	+	0.632247i	$0.217867\pi$
$888$	−18.2398	−0.612087
$889$	8.32772	0.279303
$890$	−5.79120	−0.194121
$891$	0.301019	0.0100845
$892$	48.9250	1.63813
$893$	41.7286	1.39640
$894$	28.7579	0.961807
$895$	3.99033	0.133382
$896$	20.7714	0.693922
$897$	42.9697	1.43472
$898$	−18.9694	−0.633016
$899$	−16.8231	−0.561083
$900$	−16.3397	−0.544657
$901$	−1.70631	−0.0568454
$902$	−3.57151	−0.118918
$903$	−6.44980	−0.214636
$904$	−2.46122	−0.0818590
$905$	1.76853	0.0587879
$906$	−9.42545	−0.313140
$907$	16.8321	0.558899	0.279450	−	0.960160i	$-0.409848\pi$
$907$	16.8321	0.558899	0.279450	+	0.960160i	$0.409848\pi$
$908$	−19.4962	−0.647003
$909$	4.80426	0.159347
$910$	−2.85657	−0.0946944
$911$	−37.8234	−1.25315	−0.626573	−	0.779363i	$-0.715543\pi$
$911$	−37.8234	−1.25315	−0.626573	+	0.779363i	$0.715543\pi$
$912$	−1.15244	−0.0381611
$913$	4.50204	0.148996
$914$	66.5553	2.20145
$915$	−0.0867829	−0.00286895
$916$	−37.3985	−1.23568
$917$	15.5912	0.514868
$918$	2.30059	0.0759308
$919$	8.30715	0.274027	0.137014	−	0.990569i	$-0.456250\pi$
$919$	8.30715	0.274027	0.137014	+	0.990569i	$0.456250\pi$
$920$	4.27339	0.140890
$921$	18.3481	0.604590
$922$	49.9083	1.64364
$923$	31.5992	1.04010
$924$	−1.09381	−0.0359838
$925$	30.4344	1.00068
$926$	51.5906	1.69537
$927$	−7.94855	−0.261065
$928$	−37.5603	−1.23298
$929$	−9.35740	−0.307006	−0.153503	−	0.988148i	$-0.549056\pi$
$929$	−9.35740	−0.307006	−0.153503	+	0.988148i	$0.549056\pi$
$930$	−1.07088	−0.0351156
$931$	−25.9714	−0.851180
$932$	−56.4459	−1.84895
$933$	2.16676	0.0709367
$934$	−20.5971	−0.673958
$935$	−0.0583892	−0.00190953
$936$	17.2511	0.563871
$937$	−36.1267	−1.18021	−0.590104	−	0.807327i	$-0.700913\pi$
$937$	−36.1267	−1.18021	−0.590104	+	0.807327i	$0.700913\pi$
$938$	26.4530	0.863721
$939$	−14.5931	−0.476228
$940$	−5.93366	−0.193535
$941$	5.37783	0.175312	0.0876561	−	0.996151i	$-0.472062\pi$
$941$	5.37783	0.175312	0.0876561	+	0.996151i	$0.472062\pi$
$942$	−7.02806	−0.228987
$943$	38.2039	1.24409
$944$	−2.77583	−0.0903456
$945$	0.214059	0.00696333
$946$	−4.04749	−0.131595
$947$	21.7132	0.705584	0.352792	−	0.935702i	$-0.385232\pi$
$947$	21.7132	0.705584	0.352792	+	0.935702i	$0.385232\pi$
$948$	−3.29272	−0.106943
$949$	16.5369	0.536810
$950$	51.2784	1.66369
$951$	3.57864	0.116045
$952$	−3.28200	−0.106370
$953$	−28.8270	−0.933799	−0.466900	−	0.884310i	$-0.654629\pi$
$953$	−28.8270	−0.933799	−0.466900	+	0.884310i	$0.654629\pi$
$954$	3.92552	0.127093
$955$	−0.326324	−0.0105596
$956$	0.643807	0.0208222
$957$	2.11027	0.0682153
$958$	13.9313	0.450099
$959$	−5.04064	−0.162771
$960$	−2.49044	−0.0803788
$961$	−25.2413	−0.814235
$962$	−81.8440	−2.63876
$963$	15.7347	0.507044
$964$	−72.6216	−2.33898
$965$	−3.92093	−0.126219
$966$	18.8072	0.605110
$967$	−2.94013	−0.0945482	−0.0472741	−	0.998882i	$-0.515053\pi$
$967$	−2.94013	−0.0945482	−0.0472741	+	0.998882i	$0.515053\pi$
$968$	32.4448	1.04282
$969$	−4.49165	−0.144292
$970$	1.56850	0.0503615
$971$	−36.8915	−1.18390	−0.591952	−	0.805973i	$-0.701642\pi$
$971$	−36.8915	−1.18390	−0.591952	+	0.805973i	$0.701642\pi$
$972$	−3.29272	−0.105614
$973$	−1.79477	−0.0575376
$974$	24.6947	0.791269
$975$	−28.7847	−0.921850
$976$	−0.114791	−0.00367438
$977$	47.4791	1.51899	0.759496	−	0.650512i	$-0.225446\pi$
$977$	47.4791	1.51899	0.759496	+	0.650512i	$0.225446\pi$
$978$	11.8522	0.378993
$979$	−3.90647	−0.124851
$980$	3.69304	0.117970
$981$	−5.02251	−0.160356
$982$	74.4623	2.37619
$983$	26.9766	0.860420	0.430210	−	0.902729i	$-0.358440\pi$
$983$	26.9766	0.860420	0.430210	+	0.902729i	$0.358440\pi$
$984$	15.3378	0.488951
$985$	3.84525	0.122520
$986$	16.1281	0.513624
$987$	−10.2523	−0.326335
$988$	−85.7893	−2.72932
$989$	43.2954	1.37671
$990$	0.134330	0.00426928
$991$	−34.5769	−1.09837	−0.549185	−	0.835701i	$-0.685062\pi$
$991$	−34.5769	−1.09837	−0.549185	+	0.835701i	$0.685062\pi$
$992$	12.8572	0.408218
$993$	−10.5832	−0.335846
$994$	13.8305	0.438676
$995$	−3.82614	−0.121297
$996$	−49.2460	−1.56042
$997$	−6.80978	−0.215668	−0.107834	−	0.994169i	$-0.534392\pi$
$997$	−6.80978	−0.215668	−0.107834	+	0.994169i	$0.534392\pi$
$998$	75.2736	2.38274
$999$	6.13303	0.194040

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.f.1.3	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.f.1.3	✓	22	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)

\(f(q)\)	\(=\)	\(q-2.30059 q^{2} -1.00000 q^{3} +3.29272 q^{4} -0.193972 q^{5} +2.30059 q^{6} +1.10356 q^{7} -2.97403 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.30059 q^{2} -1.00000 q^{3} +3.29272 q^{4} -0.193972 q^{5} +2.30059 q^{6} +1.10356 q^{7} -2.97403 q^{8} +1.00000 q^{9} +0.446250 q^{10} +0.301019 q^{11} -3.29272 q^{12} -5.80060 q^{13} -2.53883 q^{14} +0.193972 q^{15} +0.256574 q^{16} +1.00000 q^{17} -2.30059 q^{18} +4.49165 q^{19} -0.638695 q^{20} -1.10356 q^{21} -0.692522 q^{22} +7.40780 q^{23} +2.97403 q^{24} -4.96237 q^{25} +13.3448 q^{26} -1.00000 q^{27} +3.63370 q^{28} -7.01042 q^{29} -0.446250 q^{30} +2.39973 q^{31} +5.35778 q^{32} -0.301019 q^{33} -2.30059 q^{34} -0.214059 q^{35} +3.29272 q^{36} -6.13303 q^{37} -10.3334 q^{38} +5.80060 q^{39} +0.576877 q^{40} +5.15725 q^{41} +2.53883 q^{42} +5.84456 q^{43} +0.991171 q^{44} -0.193972 q^{45} -17.0423 q^{46} +9.29028 q^{47} -0.256574 q^{48} -5.78217 q^{49} +11.4164 q^{50} -1.00000 q^{51} -19.0998 q^{52} -1.70631 q^{53} +2.30059 q^{54} -0.0583892 q^{55} -3.28200 q^{56} -4.49165 q^{57} +16.1281 q^{58} -10.8188 q^{59} +0.638695 q^{60} -0.447400 q^{61} -5.52081 q^{62} +1.10356 q^{63} -12.8392 q^{64} +1.12515 q^{65} +0.692522 q^{66} -10.4194 q^{67} +3.29272 q^{68} -7.40780 q^{69} +0.492461 q^{70} -5.44758 q^{71} -2.97403 q^{72} -2.85090 q^{73} +14.1096 q^{74} +4.96237 q^{75} +14.7897 q^{76} +0.332191 q^{77} -13.3448 q^{78} +1.00000 q^{79} -0.0497682 q^{80} +1.00000 q^{81} -11.8647 q^{82} +14.9560 q^{83} -3.63370 q^{84} -0.193972 q^{85} -13.4460 q^{86} +7.01042 q^{87} -0.895238 q^{88} -12.9775 q^{89} +0.446250 q^{90} -6.40128 q^{91} +24.3918 q^{92} -2.39973 q^{93} -21.3731 q^{94} -0.871253 q^{95} -5.35778 q^{96} +3.51484 q^{97} +13.3024 q^{98} +0.301019 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + q^{2} - 22 q^{3} + 19 q^{4} + q^{5} - q^{6} - 15 q^{7} + 15 q^{8} + 22 q^{9}+O(q^{10}) \) 22 * q + q^2 - 22 * q^3 + 19 * q^4 + q^5 - q^6 - 15 * q^7 + 15 * q^8 + 22 * q^9	\( 22 q + q^{2} - 22 q^{3} + 19 q^{4} + q^{5} - q^{6} - 15 q^{7} + 15 q^{8} + 22 q^{9} - 13 q^{10} - 23 q^{11} - 19 q^{12} - 18 q^{13} - 9 q^{14} - q^{15} + 21 q^{16} + 22 q^{17} + q^{18} - 30 q^{19} - 7 q^{20} + 15 q^{21} + 4 q^{22} - 3 q^{23} - 15 q^{24} + 19 q^{25} - 7 q^{26} - 22 q^{27} - 25 q^{28} - 7 q^{29} + 13 q^{30} - 10 q^{31} + 31 q^{32} + 23 q^{33} + q^{34} - 11 q^{35} + 19 q^{36} - q^{37} - 29 q^{38} + 18 q^{39} - 59 q^{40} + 9 q^{42} - 43 q^{43} - 80 q^{44} + q^{45} - 43 q^{46} + 2 q^{47} - 21 q^{48} + 43 q^{49} + 25 q^{50} - 22 q^{51} - 5 q^{52} - q^{53} - q^{54} - 19 q^{55} - 8 q^{56} + 30 q^{57} - 43 q^{58} - 28 q^{59} + 7 q^{60} - 29 q^{61} - 3 q^{62} - 15 q^{63} + 23 q^{64} + 19 q^{65} - 4 q^{66} - 16 q^{67} + 19 q^{68} + 3 q^{69} - 5 q^{70} - q^{71} + 15 q^{72} - 19 q^{73} - 24 q^{74} - 19 q^{75} - 72 q^{76} + 24 q^{77} + 7 q^{78} + 22 q^{79} - 82 q^{80} + 22 q^{81} - 81 q^{82} - 29 q^{83} + 25 q^{84} + q^{85} - 42 q^{86} + 7 q^{87} - 43 q^{88} - 28 q^{89} - 13 q^{90} - 96 q^{91} - 11 q^{92} + 10 q^{93} - 63 q^{94} - 23 q^{95} - 31 q^{96} - 51 q^{97} + 12 q^{98} - 23 q^{99}+O(q^{100}) \) 22 * q + q^2 - 22 * q^3 + 19 * q^4 + q^5 - q^6 - 15 * q^7 + 15 * q^8 + 22 * q^9 - 13 * q^10 - 23 * q^11 - 19 * q^12 - 18 * q^13 - 9 * q^14 - q^15 + 21 * q^16 + 22 * q^17 + q^18 - 30 * q^19 - 7 * q^20 + 15 * q^21 + 4 * q^22 - 3 * q^23 - 15 * q^24 + 19 * q^25 - 7 * q^26 - 22 * q^27 - 25 * q^28 - 7 * q^29 + 13 * q^30 - 10 * q^31 + 31 * q^32 + 23 * q^33 + q^34 - 11 * q^35 + 19 * q^36 - q^37 - 29 * q^38 + 18 * q^39 - 59 * q^40 + 9 * q^42 - 43 * q^43 - 80 * q^44 + q^45 - 43 * q^46 + 2 * q^47 - 21 * q^48 + 43 * q^49 + 25 * q^50 - 22 * q^51 - 5 * q^52 - q^53 - q^54 - 19 * q^55 - 8 * q^56 + 30 * q^57 - 43 * q^58 - 28 * q^59 + 7 * q^60 - 29 * q^61 - 3 * q^62 - 15 * q^63 + 23 * q^64 + 19 * q^65 - 4 * q^66 - 16 * q^67 + 19 * q^68 + 3 * q^69 - 5 * q^70 - q^71 + 15 * q^72 - 19 * q^73 - 24 * q^74 - 19 * q^75 - 72 * q^76 + 24 * q^77 + 7 * q^78 + 22 * q^79 - 82 * q^80 + 22 * q^81 - 81 * q^82 - 29 * q^83 + 25 * q^84 + q^85 - 42 * q^86 + 7 * q^87 - 43 * q^88 - 28 * q^89 - 13 * q^90 - 96 * q^91 - 11 * q^92 + 10 * q^93 - 63 * q^94 - 23 * q^95 - 31 * q^96 - 51 * q^97 + 12 * q^98 - 23 * q^99

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