LMFDB - Embedded newform 4017.2.a.h.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4017,2,Mod(1,4017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4017, 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("4017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4017 = 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4017.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:	$32.0759064919$
Analytic rank:	$1$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	4017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.62615 q^{2} -1.00000 q^{3} +0.644365 q^{4} +0.607200 q^{5} -1.62615 q^{6} +4.96474 q^{7} -2.20447 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.62615 q^{2} -1.00000 q^{3} +0.644365 q^{4} +0.607200 q^{5} -1.62615 q^{6} +4.96474 q^{7} -2.20447 q^{8} +1.00000 q^{9} +0.987398 q^{10} -4.30429 q^{11} -0.644365 q^{12} +1.00000 q^{13} +8.07341 q^{14} -0.607200 q^{15} -4.87352 q^{16} -6.09228 q^{17} +1.62615 q^{18} +0.864761 q^{19} +0.391258 q^{20} -4.96474 q^{21} -6.99943 q^{22} -2.54794 q^{23} +2.20447 q^{24} -4.63131 q^{25} +1.62615 q^{26} -1.00000 q^{27} +3.19910 q^{28} -5.65205 q^{29} -0.987398 q^{30} -1.06818 q^{31} -3.51615 q^{32} +4.30429 q^{33} -9.90697 q^{34} +3.01459 q^{35} +0.644365 q^{36} +2.17670 q^{37} +1.40623 q^{38} -1.00000 q^{39} -1.33855 q^{40} -9.71007 q^{41} -8.07341 q^{42} -1.85589 q^{43} -2.77354 q^{44} +0.607200 q^{45} -4.14333 q^{46} -2.41399 q^{47} +4.87352 q^{48} +17.6486 q^{49} -7.53120 q^{50} +6.09228 q^{51} +0.644365 q^{52} +4.52421 q^{53} -1.62615 q^{54} -2.61357 q^{55} -10.9446 q^{56} -0.864761 q^{57} -9.19108 q^{58} -1.32918 q^{59} -0.391258 q^{60} -6.32133 q^{61} -1.73702 q^{62} +4.96474 q^{63} +4.02926 q^{64} +0.607200 q^{65} +6.99943 q^{66} -7.27122 q^{67} -3.92565 q^{68} +2.54794 q^{69} +4.90217 q^{70} +10.2952 q^{71} -2.20447 q^{72} +7.80297 q^{73} +3.53965 q^{74} +4.63131 q^{75} +0.557222 q^{76} -21.3697 q^{77} -1.62615 q^{78} -3.27991 q^{79} -2.95920 q^{80} +1.00000 q^{81} -15.7900 q^{82} +8.15429 q^{83} -3.19910 q^{84} -3.69923 q^{85} -3.01796 q^{86} +5.65205 q^{87} +9.48867 q^{88} -12.5851 q^{89} +0.987398 q^{90} +4.96474 q^{91} -1.64180 q^{92} +1.06818 q^{93} -3.92551 q^{94} +0.525083 q^{95} +3.51615 q^{96} +6.58016 q^{97} +28.6993 q^{98} -4.30429 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - 4 q^{2} - 25 q^{3} + 28 q^{4} - 5 q^{5} + 4 q^{6} - 7 q^{7} - 9 q^{8} + 25 q^{9}+O(q^{10}) $ 25 * q - 4 * q^2 - 25 * q^3 + 28 * q^4 - 5 * q^5 + 4 * q^6 - 7 * q^7 - 9 * q^8 + 25 * q^9	\( 25 q - 4 q^{2} - 25 q^{3} + 28 q^{4} - 5 q^{5} + 4 q^{6} - 7 q^{7} - 9 q^{8} + 25 q^{9} - 12 q^{10} - 23 q^{11} - 28 q^{12} + 25 q^{13} + 5 q^{15} + 26 q^{16} - 14 q^{17} - 4 q^{18} - 4 q^{19} - 12 q^{20} + 7 q^{21} - 7 q^{22} - 47 q^{23} + 9 q^{24} + 26 q^{25} - 4 q^{26} - 25 q^{27} - 38 q^{28} + 6 q^{29} + 12 q^{30} - 8 q^{31} - 62 q^{32} + 23 q^{33} + 25 q^{34} + 28 q^{36} - 20 q^{37} - 2 q^{38} - 25 q^{39} - 8 q^{40} - 33 q^{41} - 13 q^{43} - 13 q^{44} - 5 q^{45} - 21 q^{46} - 48 q^{47} - 26 q^{48} + 40 q^{49} - 9 q^{50} + 14 q^{51} + 28 q^{52} - 24 q^{53} + 4 q^{54} - 2 q^{55} - 14 q^{56} + 4 q^{57} - 31 q^{58} - 36 q^{59} + 12 q^{60} + 25 q^{61} - 7 q^{62} - 7 q^{63} + 45 q^{64} - 5 q^{65} + 7 q^{66} - 2 q^{67} - 32 q^{68} + 47 q^{69} - 13 q^{70} - 60 q^{71} - 9 q^{72} + 28 q^{73} - 16 q^{74} - 26 q^{75} - 12 q^{76} - 17 q^{77} + 4 q^{78} - 29 q^{79} - 88 q^{80} + 25 q^{81} - 22 q^{82} - 71 q^{83} + 38 q^{84} + 3 q^{85} - 3 q^{86} - 6 q^{87} + 23 q^{88} - 46 q^{89} - 12 q^{90} - 7 q^{91} - 69 q^{92} + 8 q^{93} + 4 q^{94} - 47 q^{95} + 62 q^{96} - 14 q^{97} - 71 q^{98} - 23 q^{99}+O(q^{100}) \) 25 * q - 4 * q^2 - 25 * q^3 + 28 * q^4 - 5 * q^5 + 4 * q^6 - 7 * q^7 - 9 * q^8 + 25 * q^9 - 12 * q^10 - 23 * q^11 - 28 * q^12 + 25 * q^13 + 5 * q^15 + 26 * q^16 - 14 * q^17 - 4 * q^18 - 4 * q^19 - 12 * q^20 + 7 * q^21 - 7 * q^22 - 47 * q^23 + 9 * q^24 + 26 * q^25 - 4 * q^26 - 25 * q^27 - 38 * q^28 + 6 * q^29 + 12 * q^30 - 8 * q^31 - 62 * q^32 + 23 * q^33 + 25 * q^34 + 28 * q^36 - 20 * q^37 - 2 * q^38 - 25 * q^39 - 8 * q^40 - 33 * q^41 - 13 * q^43 - 13 * q^44 - 5 * q^45 - 21 * q^46 - 48 * q^47 - 26 * q^48 + 40 * q^49 - 9 * q^50 + 14 * q^51 + 28 * q^52 - 24 * q^53 + 4 * q^54 - 2 * q^55 - 14 * q^56 + 4 * q^57 - 31 * q^58 - 36 * q^59 + 12 * q^60 + 25 * q^61 - 7 * q^62 - 7 * q^63 + 45 * q^64 - 5 * q^65 + 7 * q^66 - 2 * q^67 - 32 * q^68 + 47 * q^69 - 13 * q^70 - 60 * q^71 - 9 * q^72 + 28 * q^73 - 16 * q^74 - 26 * q^75 - 12 * q^76 - 17 * q^77 + 4 * q^78 - 29 * q^79 - 88 * q^80 + 25 * q^81 - 22 * q^82 - 71 * q^83 + 38 * q^84 + 3 * q^85 - 3 * q^86 - 6 * q^87 + 23 * q^88 - 46 * q^89 - 12 * q^90 - 7 * q^91 - 69 * q^92 + 8 * q^93 + 4 * q^94 - 47 * q^95 + 62 * q^96 - 14 * q^97 - 71 * 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 $

$2$	1.62615	1.14986	0.574931	−	0.818202i	$-0.305029\pi$
$2$	1.62615	1.14986	0.574931	+	0.818202i	$0.305029\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.644365	0.322183
$5$	0.607200	0.271548	0.135774	−	0.990740i	$-0.456648\pi$
$5$	0.607200	0.271548	0.135774	+	0.990740i	$0.456648\pi$
$6$	−1.62615	−0.663873
$7$	4.96474	1.87649	0.938247	−	0.345965i	$-0.112449\pi$
$7$	4.96474	1.87649	0.938247	+	0.345965i	$0.112449\pi$
$8$	−2.20447	−0.779397
$9$	1.00000	0.333333
$10$	0.987398	0.312243
$11$	−4.30429	−1.29779	−0.648897	−	0.760877i	$-0.724769\pi$
$11$	−4.30429	−1.29779	−0.648897	+	0.760877i	$0.724769\pi$
$12$	−0.644365	−0.186012
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	8.07341	2.15771
$15$	−0.607200	−0.156778
$16$	−4.87352	−1.21838
$17$	−6.09228	−1.47760	−0.738798	−	0.673927i	$-0.764606\pi$
$17$	−6.09228	−1.47760	−0.738798	+	0.673927i	$0.764606\pi$
$18$	1.62615	0.383287
$19$	0.864761	0.198390	0.0991949	−	0.995068i	$-0.468373\pi$
$19$	0.864761	0.198390	0.0991949	+	0.995068i	$0.468373\pi$
$20$	0.391258	0.0874880
$21$	−4.96474	−1.08339
$22$	−6.99943	−1.49228
$23$	−2.54794	−0.531281	−0.265641	−	0.964072i	$-0.585583\pi$
$23$	−2.54794	−0.531281	−0.265641	+	0.964072i	$0.585583\pi$
$24$	2.20447	0.449985
$25$	−4.63131	−0.926262
$26$	1.62615	0.318914
$27$	−1.00000	−0.192450
$28$	3.19910	0.604574
$29$	−5.65205	−1.04956	−0.524780	−	0.851238i	$-0.675852\pi$
$29$	−5.65205	−1.04956	−0.524780	+	0.851238i	$0.675852\pi$
$30$	−0.987398	−0.180273
$31$	−1.06818	−0.191851	−0.0959254	−	0.995389i	$-0.530581\pi$
$31$	−1.06818	−0.191851	−0.0959254	+	0.995389i	$0.530581\pi$
$32$	−3.51615	−0.621573
$33$	4.30429	0.749281
$34$	−9.90697	−1.69903
$35$	3.01459	0.509558
$36$	0.644365	0.107394
$37$	2.17670	0.357848	0.178924	−	0.983863i	$-0.442738\pi$
$37$	2.17670	0.357848	0.178924	+	0.983863i	$0.442738\pi$
$38$	1.40623	0.228121
$39$	−1.00000	−0.160128
$40$	−1.33855	−0.211644
$41$	−9.71007	−1.51646	−0.758229	−	0.651988i	$-0.773935\pi$
$41$	−9.71007	−1.51646	−0.758229	+	0.651988i	$0.773935\pi$
$42$	−8.07341	−1.24575
$43$	−1.85589	−0.283021	−0.141511	−	0.989937i	$-0.545196\pi$
$43$	−1.85589	−0.283021	−0.141511	+	0.989937i	$0.545196\pi$
$44$	−2.77354	−0.418126
$45$	0.607200	0.0905160
$46$	−4.14333	−0.610900
$47$	−2.41399	−0.352116	−0.176058	−	0.984380i	$-0.556335\pi$
$47$	−2.41399	−0.352116	−0.176058	+	0.984380i	$0.556335\pi$
$48$	4.87352	0.703433
$49$	17.6486	2.52123
$50$	−7.53120	−1.06507
$51$	6.09228	0.853090
$52$	0.644365	0.0893574
$53$	4.52421	0.621448	0.310724	−	0.950500i	$-0.399428\pi$
$53$	4.52421	0.621448	0.310724	+	0.950500i	$0.399428\pi$
$54$	−1.62615	−0.221291
$55$	−2.61357	−0.352413
$56$	−10.9446	−1.46253
$57$	−0.864761	−0.114540
$58$	−9.19108	−1.20685
$59$	−1.32918	−0.173045	−0.0865225	−	0.996250i	$-0.527575\pi$
$59$	−1.32918	−0.173045	−0.0865225	+	0.996250i	$0.527575\pi$
$60$	−0.391258	−0.0505112
$61$	−6.32133	−0.809363	−0.404682	−	0.914458i	$-0.632618\pi$
$61$	−6.32133	−0.809363	−0.404682	+	0.914458i	$0.632618\pi$
$62$	−1.73702	−0.220602
$63$	4.96474	0.625498
$64$	4.02926	0.503657
$65$	0.607200	0.0753139
$66$	6.99943	0.861570
$67$	−7.27122	−0.888321	−0.444161	−	0.895947i	$-0.646498\pi$
$67$	−7.27122	−0.888321	−0.444161	+	0.895947i	$0.646498\pi$
$68$	−3.92565	−0.476055
$69$	2.54794	0.306735
$70$	4.90217	0.585922
$71$	10.2952	1.22182	0.610909	−	0.791701i	$-0.290804\pi$
$71$	10.2952	1.22182	0.610909	+	0.791701i	$0.290804\pi$
$72$	−2.20447	−0.259799
$73$	7.80297	0.913268	0.456634	−	0.889655i	$-0.349055\pi$
$73$	7.80297	0.913268	0.456634	+	0.889655i	$0.349055\pi$
$74$	3.53965	0.411476
$75$	4.63131	0.534777
$76$	0.557222	0.0639177
$77$	−21.3697	−2.43530
$78$	−1.62615	−0.184125
$79$	−3.27991	−0.369018	−0.184509	−	0.982831i	$-0.559070\pi$
$79$	−3.27991	−0.369018	−0.184509	+	0.982831i	$0.559070\pi$
$80$	−2.95920	−0.330849
$81$	1.00000	0.111111
$82$	−15.7900	−1.74372
$83$	8.15429	0.895049	0.447525	−	0.894272i	$-0.352306\pi$
$83$	8.15429	0.895049	0.447525	+	0.894272i	$0.352306\pi$
$84$	−3.19910	−0.349051
$85$	−3.69923	−0.401238
$86$	−3.01796	−0.325435
$87$	5.65205	0.605963
$88$	9.48867	1.01150
$89$	−12.5851	−1.33402	−0.667009	−	0.745049i	$-0.732426\pi$
$89$	−12.5851	−1.33402	−0.667009	+	0.745049i	$0.732426\pi$
$90$	0.987398	0.104081
$91$	4.96474	0.520446
$92$	−1.64180	−0.171170
$93$	1.06818	0.110765
$94$	−3.92551	−0.404885
$95$	0.525083	0.0538724
$96$	3.51615	0.358866
$97$	6.58016	0.668114	0.334057	−	0.942553i	$-0.391582\pi$
$97$	6.58016	0.668114	0.334057	+	0.942553i	$0.391582\pi$
$98$	28.6993	2.89907
$99$	−4.30429	−0.432598
$100$	−2.98425	−0.298425
$101$	−13.1438	−1.30786	−0.653930	−	0.756555i	$-0.726881\pi$
$101$	−13.1438	−1.30786	−0.653930	+	0.756555i	$0.726881\pi$
$102$	9.90697	0.980936
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	−2.20447	−0.216166
$105$	−3.01459	−0.294194
$106$	7.35705	0.714580
$107$	−8.05888	−0.779081	−0.389541	−	0.921009i	$-0.627366\pi$
$107$	−8.05888	−0.779081	−0.389541	+	0.921009i	$0.627366\pi$
$108$	−0.644365	−0.0620041
$109$	10.0455	0.962185	0.481093	−	0.876670i	$-0.340240\pi$
$109$	10.0455	0.962185	0.481093	+	0.876670i	$0.340240\pi$
$110$	−4.25005	−0.405227
$111$	−2.17670	−0.206604
$112$	−24.1958	−2.28629
$113$	−2.36469	−0.222452	−0.111226	−	0.993795i	$-0.535478\pi$
$113$	−2.36469	−0.222452	−0.111226	+	0.993795i	$0.535478\pi$
$114$	−1.40623	−0.131706
$115$	−1.54711	−0.144268
$116$	−3.64198	−0.338150
$117$	1.00000	0.0924500
$118$	−2.16145	−0.198978
$119$	−30.2466	−2.77270
$120$	1.33855	0.122192
$121$	7.52694	0.684267
$122$	−10.2794	−0.930656
$123$	9.71007	0.875528
$124$	−0.688298	−0.0618110
$125$	−5.84813	−0.523073
$126$	8.07341	0.719237
$127$	0.163749	0.0145304	0.00726520	−	0.999974i	$-0.497687\pi$
$127$	0.163749	0.0145304	0.00726520	+	0.999974i	$0.497687\pi$
$128$	13.5845	1.20071
$129$	1.85589	0.163402
$130$	0.987398	0.0866006
$131$	8.40055	0.733960	0.366980	−	0.930229i	$-0.380392\pi$
$131$	8.40055	0.733960	0.366980	+	0.930229i	$0.380392\pi$
$132$	2.77354	0.241405
$133$	4.29331	0.372277
$134$	−11.8241	−1.02145
$135$	−0.607200	−0.0522594
$136$	13.4302	1.15163
$137$	−5.83263	−0.498315	−0.249158	−	0.968463i	$-0.580154\pi$
$137$	−5.83263	−0.498315	−0.249158	+	0.968463i	$0.580154\pi$
$138$	4.14333	0.352703
$139$	0.616370	0.0522799	0.0261399	−	0.999658i	$-0.491678\pi$
$139$	0.616370	0.0522799	0.0261399	+	0.999658i	$0.491678\pi$
$140$	1.94250	0.164171
$141$	2.41399	0.203294
$142$	16.7416	1.40492
$143$	−4.30429	−0.359943
$144$	−4.87352	−0.406127
$145$	−3.43192	−0.285006
$146$	12.6888	1.05013
$147$	−17.6486	−1.45563
$148$	1.40259	0.115292
$149$	−4.17068	−0.341675	−0.170838	−	0.985299i	$-0.554647\pi$
$149$	−4.17068	−0.341675	−0.170838	+	0.985299i	$0.554647\pi$
$150$	7.53120	0.614920
$151$	−16.5650	−1.34804	−0.674019	−	0.738714i	$-0.735433\pi$
$151$	−16.5650	−1.34804	−0.674019	+	0.738714i	$0.735433\pi$
$152$	−1.90634	−0.154624
$153$	−6.09228	−0.492532
$154$	−34.7503	−2.80026
$155$	−0.648599	−0.0520967
$156$	−0.644365	−0.0515905
$157$	−14.1661	−1.13058	−0.565290	−	0.824892i	$-0.691236\pi$
$157$	−14.1661	−1.13058	−0.565290	+	0.824892i	$0.691236\pi$
$158$	−5.33362	−0.424320
$159$	−4.52421	−0.358793
$160$	−2.13501	−0.168787
$161$	−12.6498	−0.996947
$162$	1.62615	0.127762
$163$	16.3809	1.28305	0.641527	−	0.767101i	$-0.278301\pi$
$163$	16.3809	1.28305	0.641527	+	0.767101i	$0.278301\pi$
$164$	−6.25683	−0.488576
$165$	2.61357	0.203466
$166$	13.2601	1.02918
$167$	0.100963	0.00781274	0.00390637	−	0.999992i	$-0.498757\pi$
$167$	0.100963	0.00781274	0.00390637	+	0.999992i	$0.498757\pi$
$168$	10.9446	0.844394
$169$	1.00000	0.0769231
$170$	−6.01551	−0.461369
$171$	0.864761	0.0661299
$172$	−1.19587	−0.0911844
$173$	−14.7038	−1.11791	−0.558956	−	0.829197i	$-0.688798\pi$
$173$	−14.7038	−1.11791	−0.558956	+	0.829197i	$0.688798\pi$
$174$	9.19108	0.696774
$175$	−22.9932	−1.73812
$176$	20.9771	1.58121
$177$	1.32918	0.0999076
$178$	−20.4653	−1.53394
$179$	−17.0716	−1.27599	−0.637995	−	0.770041i	$-0.720236\pi$
$179$	−17.0716	−1.27599	−0.637995	+	0.770041i	$0.720236\pi$
$180$	0.391258	0.0291627
$181$	23.1630	1.72170	0.860848	−	0.508863i	$-0.169934\pi$
$181$	23.1630	1.72170	0.860848	+	0.508863i	$0.169934\pi$
$182$	8.07341	0.598441
$183$	6.32133	0.467286
$184$	5.61684	0.414079
$185$	1.32169	0.0971729
$186$	1.73702	0.127365
$187$	26.2230	1.91761
$188$	−1.55549	−0.113446
$189$	−4.96474	−0.361132
$190$	0.853864	0.0619458
$191$	−1.33733	−0.0967655	−0.0483827	−	0.998829i	$-0.515407\pi$
$191$	−1.33733	−0.0967655	−0.0483827	+	0.998829i	$0.515407\pi$
$192$	−4.02926	−0.290787
$193$	−14.1788	−1.02061	−0.510305	−	0.859993i	$-0.670468\pi$
$193$	−14.1788	−1.02061	−0.510305	+	0.859993i	$0.670468\pi$
$194$	10.7003	0.768239
$195$	−0.607200	−0.0434825
$196$	11.3722	0.812297
$197$	9.07151	0.646318	0.323159	−	0.946345i	$-0.395255\pi$
$197$	9.07151	0.646318	0.323159	+	0.946345i	$0.395255\pi$
$198$	−6.99943	−0.497428
$199$	−22.2819	−1.57952	−0.789761	−	0.613415i	$-0.789795\pi$
$199$	−22.2819	−1.57952	−0.789761	+	0.613415i	$0.789795\pi$
$200$	10.2096	0.721925
$201$	7.27122	0.512872
$202$	−21.3738	−1.50386
$203$	−28.0609	−1.96949
$204$	3.92565	0.274851
$205$	−5.89595	−0.411791
$206$	1.62615	0.113299
$207$	−2.54794	−0.177094
$208$	−4.87352	−0.337918
$209$	−3.72219	−0.257469
$210$	−4.90217	−0.338282
$211$	−7.44390	−0.512459	−0.256230	−	0.966616i	$-0.582480\pi$
$211$	−7.44390	−0.512459	−0.256230	+	0.966616i	$0.582480\pi$
$212$	2.91524	0.200220
$213$	−10.2952	−0.705417
$214$	−13.1049	−0.895836
$215$	−1.12690	−0.0768538
$216$	2.20447	0.149995
$217$	−5.30323	−0.360007
$218$	16.3355	1.10638
$219$	−7.80297	−0.527276
$220$	−1.68409	−0.113541
$221$	−6.09228	−0.409811
$222$	−3.53965	−0.237566
$223$	2.29168	0.153462	0.0767310	−	0.997052i	$-0.475552\pi$
$223$	2.29168	0.153462	0.0767310	+	0.997052i	$0.475552\pi$
$224$	−17.4568	−1.16638
$225$	−4.63131	−0.308754
$226$	−3.84535	−0.255789
$227$	6.62472	0.439698	0.219849	−	0.975534i	$-0.429443\pi$
$227$	6.62472	0.439698	0.219849	+	0.975534i	$0.429443\pi$
$228$	−0.557222	−0.0369029
$229$	12.2894	0.812109	0.406055	−	0.913849i	$-0.366904\pi$
$229$	12.2894	0.812109	0.406055	+	0.913849i	$0.366904\pi$
$230$	−2.51583	−0.165889
$231$	21.3697	1.40602
$232$	12.4598	0.818023
$233$	−15.3050	−1.00266	−0.501331	−	0.865256i	$-0.667156\pi$
$233$	−15.3050	−1.00266	−0.501331	+	0.865256i	$0.667156\pi$
$234$	1.62615	0.106305
$235$	−1.46577	−0.0956164
$236$	−0.856480	−0.0557521
$237$	3.27991	0.213053
$238$	−49.1855	−3.18822
$239$	17.5844	1.13744	0.568719	−	0.822532i	$-0.307439\pi$
$239$	17.5844	1.13744	0.568719	+	0.822532i	$0.307439\pi$
$240$	2.95920	0.191016
$241$	−20.5920	−1.32645	−0.663223	−	0.748422i	$-0.730812\pi$
$241$	−20.5920	−1.32645	−0.663223	+	0.748422i	$0.730812\pi$
$242$	12.2399	0.786813
$243$	−1.00000	−0.0641500
$244$	−4.07324	−0.260763
$245$	10.7162	0.684636
$246$	15.7900	1.00674
$247$	0.864761	0.0550234
$248$	2.35477	0.149528
$249$	−8.15429	−0.516757
$250$	−9.50994	−0.601461
$251$	24.1971	1.52731	0.763654	−	0.645626i	$-0.223403\pi$
$251$	24.1971	1.52731	0.763654	+	0.645626i	$0.223403\pi$
$252$	3.19910	0.201525
$253$	10.9671	0.689494
$254$	0.266281	0.0167079
$255$	3.69923	0.231655
$256$	14.0319	0.876993
$257$	6.69123	0.417388	0.208694	−	0.977981i	$-0.433079\pi$
$257$	6.69123	0.417388	0.208694	+	0.977981i	$0.433079\pi$
$258$	3.01796	0.187890
$259$	10.8068	0.671500
$260$	0.391258	0.0242648
$261$	−5.65205	−0.349853
$262$	13.6606	0.843952
$263$	−13.2835	−0.819094	−0.409547	−	0.912289i	$-0.634313\pi$
$263$	−13.2835	−0.819094	−0.409547	+	0.912289i	$0.634313\pi$
$264$	−9.48867	−0.583987
$265$	2.74710	0.168753
$266$	6.98157	0.428068
$267$	12.5851	0.770196
$268$	−4.68532	−0.286202
$269$	−5.93293	−0.361737	−0.180869	−	0.983507i	$-0.557891\pi$
$269$	−5.93293	−0.361737	−0.180869	+	0.983507i	$0.557891\pi$
$270$	−0.987398	−0.0600911
$271$	−13.2765	−0.806489	−0.403245	−	0.915092i	$-0.632118\pi$
$271$	−13.2765	−0.806489	−0.403245	+	0.915092i	$0.632118\pi$
$272$	29.6909	1.80027
$273$	−4.96474	−0.300480
$274$	−9.48474	−0.572994
$275$	19.9345	1.20210
$276$	1.64180	0.0988248
$277$	12.2901	0.738438	0.369219	−	0.929342i	$-0.379625\pi$
$277$	12.2901	0.738438	0.369219	+	0.929342i	$0.379625\pi$
$278$	1.00231	0.0601146
$279$	−1.06818	−0.0639503
$280$	−6.64556	−0.397148
$281$	30.5619	1.82317	0.911585	−	0.411112i	$-0.134859\pi$
$281$	30.5619	1.82317	0.911585	+	0.411112i	$0.134859\pi$
$282$	3.92551	0.233760
$283$	−8.12039	−0.482707	−0.241353	−	0.970437i	$-0.577591\pi$
$283$	−8.12039	−0.482707	−0.241353	+	0.970437i	$0.577591\pi$
$284$	6.63388	0.393648
$285$	−0.525083	−0.0311032
$286$	−6.99943	−0.413885
$287$	−48.2080	−2.84563
$288$	−3.51615	−0.207191
$289$	20.1159	1.18329
$290$	−5.58082	−0.327717
$291$	−6.58016	−0.385736
$292$	5.02796	0.294239
$293$	11.4708	0.670133	0.335067	−	0.942194i	$-0.391241\pi$
$293$	11.4708	0.670133	0.335067	+	0.942194i	$0.391241\pi$
$294$	−28.6993	−1.67378
$295$	−0.807081	−0.0469900
$296$	−4.79847	−0.278905
$297$	4.30429	0.249760
$298$	−6.78215	−0.392879
$299$	−2.54794	−0.147351
$300$	2.98425	0.172296
$301$	−9.21402	−0.531088
$302$	−26.9371	−1.55006
$303$	13.1438	0.755093
$304$	−4.21443	−0.241714
$305$	−3.83831	−0.219781
$306$	−9.90697	−0.566344
$307$	−2.38114	−0.135899	−0.0679494	−	0.997689i	$-0.521646\pi$
$307$	−2.38114	−0.135899	−0.0679494	+	0.997689i	$0.521646\pi$
$308$	−13.7699	−0.784612
$309$	−1.00000	−0.0568880
$310$	−1.05472	−0.0599040
$311$	−2.37154	−0.134478	−0.0672389	−	0.997737i	$-0.521419\pi$
$311$	−2.37154	−0.134478	−0.0672389	+	0.997737i	$0.521419\pi$
$312$	2.20447	0.124803
$313$	−9.49139	−0.536485	−0.268242	−	0.963351i	$-0.586443\pi$
$313$	−9.49139	−0.536485	−0.268242	+	0.963351i	$0.586443\pi$
$314$	−23.0363	−1.30001
$315$	3.01459	0.169853
$316$	−2.11346	−0.118891
$317$	31.8606	1.78947	0.894736	−	0.446596i	$-0.147364\pi$
$317$	31.8606	1.78947	0.894736	+	0.446596i	$0.147364\pi$
$318$	−7.35705	−0.412563
$319$	24.3281	1.36211
$320$	2.44657	0.136767
$321$	8.05888	0.449803
$322$	−20.5705	−1.14635
$323$	−5.26837	−0.293140
$324$	0.644365	0.0357981
$325$	−4.63131	−0.256899
$326$	26.6379	1.47533
$327$	−10.0455	−0.555518
$328$	21.4055	1.18192
$329$	−11.9848	−0.660744
$330$	4.25005	0.233958
$331$	−24.0148	−1.31997	−0.659986	−	0.751278i	$-0.729438\pi$
$331$	−24.0148	−1.31997	−0.659986	+	0.751278i	$0.729438\pi$
$332$	5.25434	0.288369
$333$	2.17670	0.119283
$334$	0.164181	0.00898357
$335$	−4.41509	−0.241222
$336$	24.1958	1.31999
$337$	−2.21858	−0.120854	−0.0604270	−	0.998173i	$-0.519246\pi$
$337$	−2.21858	−0.120854	−0.0604270	+	0.998173i	$0.519246\pi$
$338$	1.62615	0.0884509
$339$	2.36469	0.128432
$340$	−2.38366	−0.129272
$341$	4.59776	0.248983
$342$	1.40623	0.0760403
$343$	52.8676	2.85458
$344$	4.09125	0.220586
$345$	1.54711	0.0832934
$346$	−23.9106	−1.28544
$347$	26.0345	1.39761	0.698803	−	0.715314i	$-0.253716\pi$
$347$	26.0345	1.39761	0.698803	+	0.715314i	$0.253716\pi$
$348$	3.64198	0.195231
$349$	−2.22991	−0.119365	−0.0596823	−	0.998217i	$-0.519009\pi$
$349$	−2.22991	−0.119365	−0.0596823	+	0.998217i	$0.519009\pi$
$350$	−37.3905	−1.99860
$351$	−1.00000	−0.0533761
$352$	15.1345	0.806674
$353$	8.00675	0.426156	0.213078	−	0.977035i	$-0.431651\pi$
$353$	8.00675	0.426156	0.213078	+	0.977035i	$0.431651\pi$
$354$	2.16145	0.114880
$355$	6.25126	0.331782
$356$	−8.10940	−0.429797
$357$	30.2466	1.60082
$358$	−27.7610	−1.46721
$359$	0.305642	0.0161312	0.00806560	−	0.999967i	$-0.497433\pi$
$359$	0.305642	0.0161312	0.00806560	+	0.999967i	$0.497433\pi$
$360$	−1.33855	−0.0705479
$361$	−18.2522	−0.960641
$362$	37.6666	1.97971
$363$	−7.52694	−0.395062
$364$	3.19910	0.167679
$365$	4.73796	0.247996
$366$	10.2794	0.537314
$367$	−20.0474	−1.04647	−0.523233	−	0.852190i	$-0.675274\pi$
$367$	−20.0474	−1.04647	−0.523233	+	0.852190i	$0.675274\pi$
$368$	12.4174	0.647303
$369$	−9.71007	−0.505486
$370$	2.14927	0.111735
$371$	22.4615	1.16614
$372$	0.688298	0.0356866
$373$	26.9698	1.39644	0.698221	−	0.715883i	$-0.253975\pi$
$373$	26.9698	1.39644	0.698221	+	0.715883i	$0.253975\pi$
$374$	42.6425	2.20499
$375$	5.84813	0.301996
$376$	5.32155	0.274438
$377$	−5.65205	−0.291095
$378$	−8.07341	−0.415251
$379$	−20.8909	−1.07309	−0.536547	−	0.843871i	$-0.680272\pi$
$379$	−20.8909	−1.07309	−0.536547	+	0.843871i	$0.680272\pi$
$380$	0.338345	0.0173567
$381$	−0.163749	−0.00838912
$382$	−2.17469	−0.111267
$383$	31.4615	1.60761	0.803803	−	0.594896i	$-0.202807\pi$
$383$	31.4615	1.60761	0.803803	+	0.594896i	$0.202807\pi$
$384$	−13.5845	−0.693230
$385$	−12.9757	−0.661301
$386$	−23.0568	−1.17356
$387$	−1.85589	−0.0943404
$388$	4.24003	0.215255
$389$	−5.08830	−0.257987	−0.128994	−	0.991645i	$-0.541175\pi$
$389$	−5.08830	−0.257987	−0.128994	+	0.991645i	$0.541175\pi$
$390$	−0.987398	−0.0499989
$391$	15.5227	0.785019
$392$	−38.9058	−1.96504
$393$	−8.40055	−0.423752
$394$	14.7516	0.743177
$395$	−1.99156	−0.100206
$396$	−2.77354	−0.139375
$397$	−23.9082	−1.19992	−0.599959	−	0.800031i	$-0.704816\pi$
$397$	−23.9082	−1.19992	−0.599959	+	0.800031i	$0.704816\pi$
$398$	−36.2337	−1.81623
$399$	−4.29331	−0.214934
$400$	22.5708	1.12854
$401$	−33.1524	−1.65555	−0.827775	−	0.561060i	$-0.810394\pi$
$401$	−33.1524	−1.65555	−0.827775	+	0.561060i	$0.810394\pi$
$402$	11.8241	0.589733
$403$	−1.06818	−0.0532098
$404$	−8.46942	−0.421369
$405$	0.607200	0.0301720
$406$	−45.6313	−2.26464
$407$	−9.36917	−0.464413
$408$	−13.4302	−0.664896
$409$	−26.3445	−1.30265	−0.651327	−	0.758797i	$-0.725787\pi$
$409$	−26.3445	−1.30265	−0.651327	+	0.758797i	$0.725787\pi$
$410$	−9.58771	−0.473503
$411$	5.83263	0.287702
$412$	0.644365	0.0317456
$413$	−6.59905	−0.324718
$414$	−4.14333	−0.203633
$415$	4.95128	0.243049
$416$	−3.51615	−0.172393
$417$	−0.616370	−0.0301838
$418$	−6.05283	−0.296054
$419$	−13.5575	−0.662327	−0.331164	−	0.943573i	$-0.607441\pi$
$419$	−13.5575	−0.662327	−0.331164	+	0.943573i	$0.607441\pi$
$420$	−1.94250	−0.0947841
$421$	33.1640	1.61631	0.808156	−	0.588968i	$-0.200466\pi$
$421$	33.1640	1.61631	0.808156	+	0.588968i	$0.200466\pi$
$422$	−12.1049	−0.589257
$423$	−2.41399	−0.117372
$424$	−9.97348	−0.484355
$425$	28.2152	1.36864
$426$	−16.7416	−0.811132
$427$	−31.3837	−1.51877
$428$	−5.19286	−0.251006
$429$	4.30429	0.207813
$430$	−1.83251	−0.0883713
$431$	−2.26990	−0.109337	−0.0546687	−	0.998505i	$-0.517410\pi$
$431$	−2.26990	−0.109337	−0.0546687	+	0.998505i	$0.517410\pi$
$432$	4.87352	0.234478
$433$	2.75856	0.132568	0.0662840	−	0.997801i	$-0.478886\pi$
$433$	2.75856	0.132568	0.0662840	+	0.997801i	$0.478886\pi$
$434$	−8.62386	−0.413958
$435$	3.43192	0.164548
$436$	6.47298	0.309999
$437$	−2.20336	−0.105401
$438$	−12.6888	−0.606294
$439$	−23.9911	−1.14503	−0.572517	−	0.819893i	$-0.694033\pi$
$439$	−23.9911	−1.14503	−0.572517	+	0.819893i	$0.694033\pi$
$440$	5.76152	0.274670
$441$	17.6486	0.840411
$442$	−9.90697	−0.471226
$443$	10.0032	0.475268	0.237634	−	0.971355i	$-0.423628\pi$
$443$	10.0032	0.475268	0.237634	+	0.971355i	$0.423628\pi$
$444$	−1.40259	−0.0665641
$445$	−7.64167	−0.362250
$446$	3.72661	0.176460
$447$	4.17068	0.197266
$448$	20.0042	0.945110
$449$	25.1971	1.18912	0.594562	−	0.804049i	$-0.297325\pi$
$449$	25.1971	1.18912	0.594562	+	0.804049i	$0.297325\pi$
$450$	−7.53120	−0.355024
$451$	41.7950	1.96805
$452$	−1.52373	−0.0716700
$453$	16.5650	0.778290
$454$	10.7728	0.505592
$455$	3.01459	0.141326
$456$	1.90634	0.0892724
$457$	−17.7050	−0.828205	−0.414103	−	0.910230i	$-0.635905\pi$
$457$	−17.7050	−0.828205	−0.414103	+	0.910230i	$0.635905\pi$
$458$	19.9845	0.933814
$459$	6.09228	0.284363
$460$	−0.996901	−0.0464808
$461$	−30.0398	−1.39909	−0.699547	−	0.714587i	$-0.746615\pi$
$461$	−30.0398	−1.39909	−0.699547	+	0.714587i	$0.746615\pi$
$462$	34.7503	1.61673
$463$	14.4694	0.672448	0.336224	−	0.941782i	$-0.390850\pi$
$463$	14.4694	0.672448	0.336224	+	0.941782i	$0.390850\pi$
$464$	27.5454	1.27876
$465$	0.648599	0.0300781
$466$	−24.8882	−1.15292
$467$	−9.23661	−0.427419	−0.213710	−	0.976897i	$-0.568555\pi$
$467$	−9.23661	−0.427419	−0.213710	+	0.976897i	$0.568555\pi$
$468$	0.644365	0.0297858
$469$	−36.0997	−1.66693
$470$	−2.38357	−0.109946
$471$	14.1661	0.652741
$472$	2.93014	0.134871
$473$	7.98831	0.367303
$474$	5.33362	0.244981
$475$	−4.00497	−0.183761
$476$	−19.4898	−0.893316
$477$	4.52421	0.207149
$478$	28.5948	1.30790
$479$	41.3051	1.88728	0.943638	−	0.330978i	$-0.107379\pi$
$479$	41.3051	1.88728	0.943638	+	0.330978i	$0.107379\pi$
$480$	2.13501	0.0974492
$481$	2.17670	0.0992492
$482$	−33.4856	−1.52523
$483$	12.6498	0.575587
$484$	4.85010	0.220459
$485$	3.99547	0.181425
$486$	−1.62615	−0.0737637
$487$	28.3884	1.28640	0.643200	−	0.765698i	$-0.277606\pi$
$487$	28.3884	1.28640	0.643200	+	0.765698i	$0.277606\pi$
$488$	13.9352	0.630815
$489$	−16.3809	−0.740771
$490$	17.4262	0.787236
$491$	6.70919	0.302781	0.151391	−	0.988474i	$-0.451625\pi$
$491$	6.70919	0.302781	0.151391	+	0.988474i	$0.451625\pi$
$492$	6.25683	0.282080
$493$	34.4339	1.55082
$494$	1.40623	0.0632693
$495$	−2.61357	−0.117471
$496$	5.20580	0.233747
$497$	51.1131	2.29274
$498$	−13.2601	−0.594199
$499$	−26.0768	−1.16736	−0.583680	−	0.811984i	$-0.698388\pi$
$499$	−26.0768	−1.16736	−0.583680	+	0.811984i	$0.698388\pi$
$500$	−3.76833	−0.168525
$501$	−0.100963	−0.00451069
$502$	39.3481	1.75619
$503$	−42.4098	−1.89096	−0.945480	−	0.325680i	$-0.894407\pi$
$503$	−42.4098	−1.89096	−0.945480	+	0.325680i	$0.894407\pi$
$504$	−10.9446	−0.487511
$505$	−7.98093	−0.355147
$506$	17.8341	0.792822
$507$	−1.00000	−0.0444116
$508$	0.105514	0.00468144
$509$	30.1461	1.33620	0.668102	−	0.744069i	$-0.267107\pi$
$509$	30.1461	1.33620	0.668102	+	0.744069i	$0.267107\pi$
$510$	6.01551	0.266371
$511$	38.7397	1.71374
$512$	−4.35100	−0.192289
$513$	−0.864761	−0.0381801
$514$	10.8810	0.479938
$515$	0.607200	0.0267564
$516$	1.19587	0.0526454
$517$	10.3905	0.456974
$518$	17.5734	0.772132
$519$	14.7038	0.645427
$520$	−1.33855	−0.0586994
$521$	43.7760	1.91786	0.958931	−	0.283640i	$-0.0915422\pi$
$521$	43.7760	1.91786	0.958931	+	0.283640i	$0.0915422\pi$
$522$	−9.19108	−0.402283
$523$	23.4553	1.02563	0.512814	−	0.858499i	$-0.328603\pi$
$523$	23.4553	1.02563	0.512814	+	0.858499i	$0.328603\pi$
$524$	5.41302	0.236469
$525$	22.9932	1.00351
$526$	−21.6009	−0.941845
$527$	6.50766	0.283478
$528$	−20.9771	−0.912910
$529$	−16.5080	−0.717740
$530$	4.46720	0.194043
$531$	−1.32918	−0.0576817
$532$	2.76646	0.119941
$533$	−9.71007	−0.420590
$534$	20.4653	0.885619
$535$	−4.89335	−0.211558
$536$	16.0292	0.692354
$537$	17.0716	0.736693
$538$	−9.64784	−0.415948
$539$	−75.9648	−3.27204
$540$	−0.391258	−0.0168371
$541$	6.34913	0.272971	0.136485	−	0.990642i	$-0.456419\pi$
$541$	6.34913	0.272971	0.136485	+	0.990642i	$0.456419\pi$
$542$	−21.5896	−0.927351
$543$	−23.1630	−0.994021
$544$	21.4214	0.918434
$545$	6.09963	0.261280
$546$	−8.07341	−0.345510
$547$	37.6148	1.60829	0.804147	−	0.594431i	$-0.202623\pi$
$547$	37.6148	1.60829	0.804147	+	0.594431i	$0.202623\pi$
$548$	−3.75834	−0.160548
$549$	−6.32133	−0.269788
$550$	32.4165	1.38224
$551$	−4.88767	−0.208222
$552$	−5.61684	−0.239069
$553$	−16.2839	−0.692461
$554$	19.9855	0.849101
$555$	−1.32169	−0.0561028
$556$	0.397168	0.0168437
$557$	−5.02791	−0.213039	−0.106520	−	0.994311i	$-0.533971\pi$
$557$	−5.02791	−0.213039	−0.106520	+	0.994311i	$0.533971\pi$
$558$	−1.73702	−0.0735340
$559$	−1.85589	−0.0784959
$560$	−14.6917	−0.620836
$561$	−26.2230	−1.10713
$562$	49.6982	2.09639
$563$	−20.6516	−0.870363	−0.435181	−	0.900343i	$-0.643316\pi$
$563$	−20.6516	−0.870363	−0.435181	+	0.900343i	$0.643316\pi$
$564$	1.55549	0.0654979
$565$	−1.43584	−0.0604063
$566$	−13.2050	−0.555046
$567$	4.96474	0.208499
$568$	−22.6955	−0.952281
$569$	16.5957	0.695729	0.347865	−	0.937545i	$-0.386907\pi$
$569$	16.5957	0.695729	0.347865	+	0.937545i	$0.386907\pi$
$570$	−0.853864	−0.0357644
$571$	6.24855	0.261494	0.130747	−	0.991416i	$-0.458262\pi$
$571$	6.24855	0.261494	0.130747	+	0.991416i	$0.458262\pi$
$572$	−2.77354	−0.115967
$573$	1.33733	0.0558676
$574$	−78.3934	−3.27208
$575$	11.8003	0.492106
$576$	4.02926	0.167886
$577$	−15.6425	−0.651207	−0.325603	−	0.945506i	$-0.605567\pi$
$577$	−15.6425	−0.651207	−0.325603	+	0.945506i	$0.605567\pi$
$578$	32.7115	1.36062
$579$	14.1788	0.589250
$580$	−2.21141	−0.0918239
$581$	40.4839	1.67955
$582$	−10.7003	−0.443543
$583$	−19.4735	−0.806512
$584$	−17.2014	−0.711798
$585$	0.607200	0.0251046
$586$	18.6533	0.770561
$587$	45.5496	1.88004	0.940018	−	0.341126i	$-0.110808\pi$
$587$	45.5496	1.88004	0.940018	+	0.341126i	$0.110808\pi$
$588$	−11.3722	−0.468980
$589$	−0.923721	−0.0380612
$590$	−1.31243	−0.0540321
$591$	−9.07151	−0.373152
$592$	−10.6082	−0.435995
$593$	9.45031	0.388078	0.194039	−	0.980994i	$-0.437841\pi$
$593$	9.45031	0.388078	0.194039	+	0.980994i	$0.437841\pi$
$594$	6.99943	0.287190
$595$	−18.3657	−0.752921
$596$	−2.68744	−0.110082
$597$	22.2819	0.911937
$598$	−4.14333	−0.169433
$599$	4.54953	0.185889	0.0929443	−	0.995671i	$-0.470372\pi$
$599$	4.54953	0.185889	0.0929443	+	0.995671i	$0.470372\pi$
$600$	−10.2096	−0.416804
$601$	−5.94269	−0.242407	−0.121204	−	0.992628i	$-0.538675\pi$
$601$	−5.94269	−0.242407	−0.121204	+	0.992628i	$0.538675\pi$
$602$	−14.9834	−0.610677
$603$	−7.27122	−0.296107
$604$	−10.6739	−0.434314
$605$	4.57036	0.185811
$606$	21.3738	0.868253
$607$	−0.594456	−0.0241282	−0.0120641	−	0.999927i	$-0.503840\pi$
$607$	−0.594456	−0.0241282	−0.0120641	+	0.999927i	$0.503840\pi$
$608$	−3.04063	−0.123314
$609$	28.0609	1.13709
$610$	−6.24167	−0.252718
$611$	−2.41399	−0.0976594
$612$	−3.92565	−0.158685
$613$	28.3589	1.14540	0.572702	−	0.819764i	$-0.305895\pi$
$613$	28.3589	1.14540	0.572702	+	0.819764i	$0.305895\pi$
$614$	−3.87209	−0.156265
$615$	5.89595	0.237748
$616$	47.1088	1.89807
$617$	−3.51161	−0.141372	−0.0706860	−	0.997499i	$-0.522519\pi$
$617$	−3.51161	−0.141372	−0.0706860	+	0.997499i	$0.522519\pi$
$618$	−1.62615	−0.0654134
$619$	−32.7196	−1.31511	−0.657557	−	0.753405i	$-0.728410\pi$
$619$	−32.7196	−1.31511	−0.657557	+	0.753405i	$0.728410\pi$
$620$	−0.417934	−0.0167847
$621$	2.54794	0.102245
$622$	−3.85648	−0.154631
$623$	−62.4817	−2.50328
$624$	4.87352	0.195097
$625$	19.6056	0.784222
$626$	−15.4344	−0.616884
$627$	3.72219	0.148650
$628$	−9.12816	−0.364253
$629$	−13.2611	−0.528755
$630$	4.90217	0.195307
$631$	33.7120	1.34205	0.671026	−	0.741434i	$-0.265854\pi$
$631$	33.7120	1.34205	0.671026	+	0.741434i	$0.265854\pi$
$632$	7.23045	0.287612
$633$	7.44390	0.295868
$634$	51.8102	2.05764
$635$	0.0994285	0.00394570
$636$	−2.91524	−0.115597
$637$	17.6486	0.699264
$638$	39.5611	1.56624
$639$	10.2952	0.407273
$640$	8.24849	0.326050
$641$	−28.1831	−1.11317	−0.556583	−	0.830792i	$-0.687888\pi$
$641$	−28.1831	−1.11317	−0.556583	+	0.830792i	$0.687888\pi$
$642$	13.1049	0.517211
$643$	−11.8953	−0.469105	−0.234553	−	0.972103i	$-0.575363\pi$
$643$	−11.8953	−0.469105	−0.234553	+	0.972103i	$0.575363\pi$
$644$	−8.15111	−0.321199
$645$	1.12690	0.0443716
$646$	−8.56716	−0.337070
$647$	−12.6984	−0.499224	−0.249612	−	0.968346i	$-0.580303\pi$
$647$	−12.6984	−0.499224	−0.249612	+	0.968346i	$0.580303\pi$
$648$	−2.20447	−0.0865996
$649$	5.72120	0.224577
$650$	−7.53120	−0.295398
$651$	5.30323	0.207850
$652$	10.5553	0.413378
$653$	31.7653	1.24307	0.621537	−	0.783385i	$-0.286509\pi$
$653$	31.7653	1.24307	0.621537	+	0.783385i	$0.286509\pi$
$654$	−16.3355	−0.638769
$655$	5.10081	0.199305
$656$	47.3223	1.84762
$657$	7.80297	0.304423
$658$	−19.4891	−0.759764
$659$	−44.1820	−1.72109	−0.860543	−	0.509378i	$-0.829875\pi$
$659$	−44.1820	−1.72109	−0.860543	+	0.509378i	$0.829875\pi$
$660$	1.68409	0.0655531
$661$	20.6959	0.804976	0.402488	−	0.915425i	$-0.368146\pi$
$661$	20.6959	0.804976	0.402488	+	0.915425i	$0.368146\pi$
$662$	−39.0516	−1.51779
$663$	6.09228	0.236605
$664$	−17.9758	−0.697598
$665$	2.60690	0.101091
$666$	3.53965	0.137159
$667$	14.4011	0.557611
$668$	0.0650569	0.00251713
$669$	−2.29168	−0.0886013
$670$	−7.17959	−0.277372
$671$	27.2088	1.05039
$672$	17.4568	0.673409
$673$	18.9871	0.731900	0.365950	−	0.930635i	$-0.380744\pi$
$673$	18.9871	0.731900	0.365950	+	0.930635i	$0.380744\pi$
$674$	−3.60775	−0.138965
$675$	4.63131	0.178259
$676$	0.644365	0.0247833
$677$	−8.23916	−0.316656	−0.158328	−	0.987387i	$-0.550610\pi$
$677$	−8.23916	−0.316656	−0.158328	+	0.987387i	$0.550610\pi$
$678$	3.84535	0.147680
$679$	32.6688	1.25371
$680$	8.15484	0.312724
$681$	−6.62472	−0.253860
$682$	7.47665	0.286296
$683$	−30.7076	−1.17499	−0.587497	−	0.809226i	$-0.699887\pi$
$683$	−30.7076	−1.17499	−0.587497	+	0.809226i	$0.699887\pi$
$684$	0.557222	0.0213059
$685$	−3.54157	−0.135317
$686$	85.9707	3.28238
$687$	−12.2894	−0.468872
$688$	9.04474	0.344828
$689$	4.52421	0.172359
$690$	2.51583	0.0957759
$691$	−3.10274	−0.118034	−0.0590169	−	0.998257i	$-0.518797\pi$
$691$	−3.10274	−0.118034	−0.0590169	+	0.998257i	$0.518797\pi$
$692$	−9.47464	−0.360172
$693$	−21.3697	−0.811767
$694$	42.3361	1.60705
$695$	0.374260	0.0141965
$696$	−12.4598	−0.472286
$697$	59.1565	2.24071
$698$	−3.62617	−0.137253
$699$	15.3050	0.578887
$700$	−14.8160	−0.559993
$701$	−5.60170	−0.211573	−0.105787	−	0.994389i	$-0.533736\pi$
$701$	−5.60170	−0.211573	−0.105787	+	0.994389i	$0.533736\pi$
$702$	−1.62615	−0.0613751
$703$	1.88233	0.0709934
$704$	−17.3431	−0.653643
$705$	1.46577	0.0552042
$706$	13.0202	0.490021
$707$	−65.2556	−2.45419
$708$	0.856480	0.0321885
$709$	46.7305	1.75500	0.877500	−	0.479577i	$-0.159210\pi$
$709$	46.7305	1.75500	0.877500	+	0.479577i	$0.159210\pi$
$710$	10.1655	0.381504
$711$	−3.27991	−0.123006
$712$	27.7434	1.03973
$713$	2.72166	0.101927
$714$	49.1855	1.84072
$715$	−2.61357	−0.0977418
$716$	−11.0003	−0.411102
$717$	−17.5844	−0.656700
$718$	0.497021	0.0185486
$719$	−5.33189	−0.198846	−0.0994230	−	0.995045i	$-0.531700\pi$
$719$	−5.33189	−0.198846	−0.0994230	+	0.995045i	$0.531700\pi$
$720$	−2.95920	−0.110283
$721$	4.96474	0.184896
$722$	−29.6808	−1.10461
$723$	20.5920	0.765823
$724$	14.9255	0.554700
$725$	26.1764	0.972167
$726$	−12.2399	−0.454267
$727$	−35.6930	−1.32378	−0.661889	−	0.749602i	$-0.730245\pi$
$727$	−35.6930	−1.32378	−0.661889	+	0.749602i	$0.730245\pi$
$728$	−10.9446	−0.405634
$729$	1.00000	0.0370370
$730$	7.70464	0.285161
$731$	11.3066	0.418191
$732$	4.07324	0.150551
$733$	25.8475	0.954697	0.477349	−	0.878714i	$-0.341598\pi$
$733$	25.8475	0.954697	0.477349	+	0.878714i	$0.341598\pi$
$734$	−32.6001	−1.20329
$735$	−10.7162	−0.395274
$736$	8.95893	0.330230
$737$	31.2975	1.15286
$738$	−15.7900	−0.581239
$739$	−11.0265	−0.405618	−0.202809	−	0.979218i	$-0.565007\pi$
$739$	−11.0265	−0.405618	−0.202809	+	0.979218i	$0.565007\pi$
$740$	0.851654	0.0313074
$741$	−0.864761	−0.0317678
$742$	36.5258	1.34091
$743$	−39.9337	−1.46502	−0.732512	−	0.680754i	$-0.761652\pi$
$743$	−39.9337	−1.46502	−0.732512	+	0.680754i	$0.761652\pi$
$744$	−2.35477	−0.0863300
$745$	−2.53243	−0.0927812
$746$	43.8569	1.60571
$747$	8.15429	0.298350
$748$	16.8972	0.617822
$749$	−40.0102	−1.46194
$750$	9.50994	0.347254
$751$	8.80844	0.321425	0.160712	−	0.987001i	$-0.448621\pi$
$751$	8.80844	0.321425	0.160712	+	0.987001i	$0.448621\pi$
$752$	11.7646	0.429012
$753$	−24.1971	−0.881791
$754$	−9.19108	−0.334720
$755$	−10.0582	−0.366057
$756$	−3.19910	−0.116350
$757$	13.6864	0.497440	0.248720	−	0.968575i	$-0.419990\pi$
$757$	13.6864	0.497440	0.248720	+	0.968575i	$0.419990\pi$
$758$	−33.9718	−1.23391
$759$	−10.9671	−0.398079
$760$	−1.15753	−0.0419879
$761$	17.7217	0.642411	0.321205	−	0.947010i	$-0.395912\pi$
$761$	17.7217	0.642411	0.321205	+	0.947010i	$0.395912\pi$
$762$	−0.266281	−0.00964634
$763$	49.8733	1.80554
$764$	−0.861726	−0.0311761
$765$	−3.69923	−0.133746
$766$	51.1611	1.84852
$767$	−1.32918	−0.0479941
$768$	−14.0319	−0.506332
$769$	40.1359	1.44734	0.723669	−	0.690148i	$-0.242454\pi$
$769$	40.1359	1.44734	0.723669	+	0.690148i	$0.242454\pi$
$770$	−21.1004	−0.760405
$771$	−6.69123	−0.240979
$772$	−9.13631	−0.328823
$773$	−0.195438	−0.00702943	−0.00351471	−	0.999994i	$-0.501119\pi$
$773$	−0.195438	−0.00702943	−0.00351471	+	0.999994i	$0.501119\pi$
$774$	−3.01796	−0.108478
$775$	4.94707	0.177704
$776$	−14.5057	−0.520726
$777$	−10.8068	−0.387691
$778$	−8.27434	−0.296649
$779$	−8.39689	−0.300850
$780$	−0.391258	−0.0140093
$781$	−44.3137	−1.58567
$782$	25.2423	0.902664
$783$	5.65205	0.201988
$784$	−86.0110	−3.07182
$785$	−8.60168	−0.307007
$786$	−13.6606	−0.487256
$787$	10.6116	0.378264	0.189132	−	0.981952i	$-0.439433\pi$
$787$	10.6116	0.378264	0.189132	+	0.981952i	$0.439433\pi$
$788$	5.84536	0.208232
$789$	13.2835	0.472904
$790$	−3.23857	−0.115223
$791$	−11.7401	−0.417429
$792$	9.48867	0.337165
$793$	−6.32133	−0.224477
$794$	−38.8783	−1.37974
$795$	−2.74710	−0.0974297
$796$	−14.3577	−0.508894
$797$	23.4966	0.832293	0.416146	−	0.909298i	$-0.363380\pi$
$797$	23.4966	0.832293	0.416146	+	0.909298i	$0.363380\pi$
$798$	−6.98157	−0.247145
$799$	14.7067	0.520285
$800$	16.2844	0.575740
$801$	−12.5851	−0.444673
$802$	−53.9107	−1.90365
$803$	−33.5863	−1.18523
$804$	4.68532	0.165239
$805$	−7.68098	−0.270719
$806$	−1.73702	−0.0611840
$807$	5.93293	0.208849
$808$	28.9751	1.01934
$809$	2.50956	0.0882314	0.0441157	−	0.999026i	$-0.485953\pi$
$809$	2.50956	0.0882314	0.0441157	+	0.999026i	$0.485953\pi$
$810$	0.987398	0.0346936
$811$	39.0116	1.36988	0.684941	−	0.728598i	$-0.259828\pi$
$811$	39.0116	1.36988	0.684941	+	0.728598i	$0.259828\pi$
$812$	−18.0815	−0.634536
$813$	13.2765	0.465627
$814$	−15.2357	−0.534010
$815$	9.94650	0.348411
$816$	−29.6909	−1.03939
$817$	−1.60490	−0.0561485
$818$	−42.8402	−1.49787
$819$	4.96474	0.173482
$820$	−3.79915	−0.132672
$821$	−13.7505	−0.479895	−0.239948	−	0.970786i	$-0.577130\pi$
$821$	−13.7505	−0.479895	−0.239948	+	0.970786i	$0.577130\pi$
$822$	9.48474	0.330818
$823$	−55.5542	−1.93650	−0.968248	−	0.249991i	$-0.919572\pi$
$823$	−55.5542	−1.93650	−0.968248	+	0.249991i	$0.919572\pi$
$824$	−2.20447	−0.0767962
$825$	−19.9345	−0.694031
$826$	−10.7311	−0.373381
$827$	−33.2267	−1.15540	−0.577702	−	0.816247i	$-0.696051\pi$
$827$	−33.2267	−1.15540	−0.577702	+	0.816247i	$0.696051\pi$
$828$	−1.64180	−0.0570565
$829$	−37.9510	−1.31809	−0.659046	−	0.752103i	$-0.729040\pi$
$829$	−37.9510	−1.31809	−0.659046	+	0.752103i	$0.729040\pi$
$830$	8.05153	0.279473
$831$	−12.2901	−0.426337
$832$	4.02926	0.139689
$833$	−107.520	−3.72536
$834$	−1.00231	−0.0347072
$835$	0.0613046	0.00212153
$836$	−2.39845	−0.0829520
$837$	1.06818	0.0369217
$838$	−22.0465	−0.761585
$839$	44.6640	1.54197	0.770986	−	0.636852i	$-0.219764\pi$
$839$	44.6640	1.54197	0.770986	+	0.636852i	$0.219764\pi$
$840$	6.64556	0.229294
$841$	2.94567	0.101575
$842$	53.9296	1.85854
$843$	−30.5619	−1.05261
$844$	−4.79659	−0.165105
$845$	0.607200	0.0208883
$846$	−3.92551	−0.134962
$847$	37.3693	1.28402
$848$	−22.0489	−0.757161
$849$	8.12039	0.278691
$850$	45.8822	1.57375
$851$	−5.54610	−0.190118
$852$	−6.63388	−0.227273
$853$	29.3751	1.00579	0.502893	−	0.864349i	$-0.332269\pi$
$853$	29.3751	1.00579	0.502893	+	0.864349i	$0.332269\pi$
$854$	−51.0347	−1.74637
$855$	0.525083	0.0179575
$856$	17.7655	0.607213
$857$	19.5220	0.666859	0.333430	−	0.942775i	$-0.391794\pi$
$857$	19.5220	0.666859	0.333430	+	0.942775i	$0.391794\pi$
$858$	6.99943	0.238957
$859$	−13.7533	−0.469256	−0.234628	−	0.972085i	$-0.575387\pi$
$859$	−13.7533	−0.469256	−0.234628	+	0.972085i	$0.575387\pi$
$860$	−0.726134	−0.0247610
$861$	48.2080	1.64292
$862$	−3.69120	−0.125723
$863$	12.5352	0.426702	0.213351	−	0.976976i	$-0.431562\pi$
$863$	12.5352	0.426702	0.213351	+	0.976976i	$0.431562\pi$
$864$	3.51615	0.119622
$865$	−8.92816	−0.303567
$866$	4.48583	0.152435
$867$	−20.1159	−0.683172
$868$	−3.41722	−0.115988
$869$	14.1177	0.478910
$870$	5.58082	0.189208
$871$	−7.27122	−0.246376
$872$	−22.1450	−0.749924
$873$	6.58016	0.222705
$874$	−3.58299	−0.121196
$875$	−29.0344	−0.981543
$876$	−5.02796	−0.169879
$877$	−1.22391	−0.0413285	−0.0206643	−	0.999786i	$-0.506578\pi$
$877$	−1.22391	−0.0413285	−0.0206643	+	0.999786i	$0.506578\pi$
$878$	−39.0132	−1.31663
$879$	−11.4708	−0.386902
$880$	12.7373	0.429374
$881$	−30.4083	−1.02448	−0.512241	−	0.858842i	$-0.671184\pi$
$881$	−30.4083	−1.02448	−0.512241	+	0.858842i	$0.671184\pi$
$882$	28.6993	0.966356
$883$	−26.5771	−0.894392	−0.447196	−	0.894436i	$-0.647577\pi$
$883$	−26.5771	−0.894392	−0.447196	+	0.894436i	$0.647577\pi$
$884$	−3.92565	−0.132034
$885$	0.807081	0.0271297
$886$	16.2668	0.546493
$887$	40.0509	1.34478	0.672388	−	0.740198i	$-0.265268\pi$
$887$	40.0509	1.34478	0.672388	+	0.740198i	$0.265268\pi$
$888$	4.79847	0.161026
$889$	0.812972	0.0272662
$890$	−12.4265	−0.416538
$891$	−4.30429	−0.144199
$892$	1.47668	0.0494428
$893$	−2.08752	−0.0698562
$894$	6.78215	0.226829
$895$	−10.3659	−0.346492
$896$	67.4434	2.25313
$897$	2.54794	0.0850731
$898$	40.9743	1.36733
$899$	6.03741	0.201359
$900$	−2.98425	−0.0994751
$901$	−27.5628	−0.918250
$902$	67.9649	2.26298
$903$	9.21402	0.306624
$904$	5.21288	0.173378
$905$	14.0646	0.467523
$906$	26.9371	0.894926
$907$	−39.4644	−1.31040	−0.655198	−	0.755458i	$-0.727415\pi$
$907$	−39.4644	−1.31040	−0.655198	+	0.755458i	$0.727415\pi$
$908$	4.26874	0.141663
$909$	−13.1438	−0.435953
$910$	4.90217	0.162505
$911$	−46.2018	−1.53073	−0.765367	−	0.643595i	$-0.777442\pi$
$911$	−46.2018	−1.53073	−0.765367	+	0.643595i	$0.777442\pi$
$912$	4.21443	0.139554
$913$	−35.0984	−1.16159
$914$	−28.7910	−0.952322
$915$	3.83831	0.126891
$916$	7.91889	0.261647
$917$	41.7065	1.37727
$918$	9.90697	0.326979
$919$	−32.2509	−1.06386	−0.531930	−	0.846789i	$-0.678533\pi$
$919$	−32.2509	−1.06386	−0.531930	+	0.846789i	$0.678533\pi$
$920$	3.41054	0.112442
$921$	2.38114	0.0784612
$922$	−48.8492	−1.60876
$923$	10.2952	0.338871
$924$	13.7699	0.452996
$925$	−10.0810	−0.331461
$926$	23.5294	0.773222
$927$	1.00000	0.0328443
$928$	19.8735	0.652378
$929$	−4.21429	−0.138266	−0.0691332	−	0.997607i	$-0.522023\pi$
$929$	−4.21429	−0.138266	−0.0691332	+	0.997607i	$0.522023\pi$
$930$	1.05472	0.0345856
$931$	15.2618	0.500187
$932$	−9.86198	−0.323040
$933$	2.37154	0.0776407
$934$	−15.0201	−0.491473
$935$	15.9226	0.520724
$936$	−2.20447	−0.0720552
$937$	−1.68837	−0.0551567	−0.0275784	−	0.999620i	$-0.508780\pi$
$937$	−1.68837	−0.0551567	−0.0275784	+	0.999620i	$0.508780\pi$
$938$	−58.7036	−1.91674
$939$	9.49139	0.309740
$940$	−0.944492	−0.0308059
$941$	42.8313	1.39626	0.698129	−	0.715972i	$-0.254016\pi$
$941$	42.8313	1.39626	0.698129	+	0.715972i	$0.254016\pi$
$942$	23.0363	0.750562
$943$	24.7406	0.805666
$944$	6.47781	0.210835
$945$	−3.01459	−0.0980646
$946$	12.9902	0.422348
$947$	−35.4303	−1.15133	−0.575665	−	0.817686i	$-0.695257\pi$
$947$	−35.4303	−1.15133	−0.575665	+	0.817686i	$0.695257\pi$
$948$	2.11346	0.0686419
$949$	7.80297	0.253295
$950$	−6.51269	−0.211300
$951$	−31.8606	−1.03315
$952$	66.6776	2.16103
$953$	−43.0177	−1.39348	−0.696740	−	0.717324i	$-0.745367\pi$
$953$	−43.0177	−1.39348	−0.696740	+	0.717324i	$0.745367\pi$
$954$	7.35705	0.238193
$955$	−0.812024	−0.0262765
$956$	11.3308	0.366463
$957$	−24.3281	−0.786415
$958$	67.1683	2.17011
$959$	−28.9575	−0.935086
$960$	−2.44657	−0.0789626
$961$	−29.8590	−0.963193
$962$	3.53965	0.114123
$963$	−8.05888	−0.259694
$964$	−13.2687	−0.427357
$965$	−8.60935	−0.277145
$966$	20.5705	0.661846
$967$	−25.0657	−0.806057	−0.403029	−	0.915187i	$-0.632042\pi$
$967$	−25.0657	−0.806057	−0.403029	+	0.915187i	$0.632042\pi$
$968$	−16.5929	−0.533316
$969$	5.26837	0.169244
$970$	6.49724	0.208614
$971$	−48.1363	−1.54477	−0.772383	−	0.635157i	$-0.780935\pi$
$971$	−48.1363	−1.54477	−0.772383	+	0.635157i	$0.780935\pi$
$972$	−0.644365	−0.0206680
$973$	3.06012	0.0981029
$974$	46.1638	1.47918
$975$	4.63131	0.148321
$976$	30.8071	0.986113
$977$	20.7704	0.664503	0.332252	−	0.943191i	$-0.392192\pi$
$977$	20.7704	0.664503	0.332252	+	0.943191i	$0.392192\pi$
$978$	−26.6379	−0.851785
$979$	54.1700	1.73128
$980$	6.90517	0.220578
$981$	10.0455	0.320728
$982$	10.9102	0.348157
$983$	29.9478	0.955185	0.477592	−	0.878582i	$-0.341510\pi$
$983$	29.9478	0.955185	0.477592	+	0.878582i	$0.341510\pi$
$984$	−21.4055	−0.682383
$985$	5.50822	0.175506
$986$	55.9947	1.78323
$987$	11.9848	0.381481
$988$	0.557222	0.0177276
$989$	4.72870	0.150364
$990$	−4.25005	−0.135076
$991$	−10.2524	−0.325679	−0.162840	−	0.986653i	$-0.552065\pi$
$991$	−10.2524	−0.325679	−0.162840	+	0.986653i	$0.552065\pi$
$992$	3.75588	0.119249
$993$	24.0148	0.762086
$994$	83.1176	2.63633
$995$	−13.5296	−0.428916
$996$	−5.25434	−0.166490
$997$	53.8901	1.70672	0.853359	−	0.521324i	$-0.174562\pi$
$997$	53.8901	1.70672	0.853359	+	0.521324i	$0.174562\pi$
$998$	−42.4049	−1.34230
$999$	−2.17670	−0.0688679

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.h.1.19	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.h.1.19	✓	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:	\( N \)	\(=\)	\( 4017 = 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4017.a (trivial)

\(f(q)\)	\(=\)	\(q+1.62615 q^{2} -1.00000 q^{3} +0.644365 q^{4} +0.607200 q^{5} -1.62615 q^{6} +4.96474 q^{7} -2.20447 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.62615 q^{2} -1.00000 q^{3} +0.644365 q^{4} +0.607200 q^{5} -1.62615 q^{6} +4.96474 q^{7} -2.20447 q^{8} +1.00000 q^{9} +0.987398 q^{10} -4.30429 q^{11} -0.644365 q^{12} +1.00000 q^{13} +8.07341 q^{14} -0.607200 q^{15} -4.87352 q^{16} -6.09228 q^{17} +1.62615 q^{18} +0.864761 q^{19} +0.391258 q^{20} -4.96474 q^{21} -6.99943 q^{22} -2.54794 q^{23} +2.20447 q^{24} -4.63131 q^{25} +1.62615 q^{26} -1.00000 q^{27} +3.19910 q^{28} -5.65205 q^{29} -0.987398 q^{30} -1.06818 q^{31} -3.51615 q^{32} +4.30429 q^{33} -9.90697 q^{34} +3.01459 q^{35} +0.644365 q^{36} +2.17670 q^{37} +1.40623 q^{38} -1.00000 q^{39} -1.33855 q^{40} -9.71007 q^{41} -8.07341 q^{42} -1.85589 q^{43} -2.77354 q^{44} +0.607200 q^{45} -4.14333 q^{46} -2.41399 q^{47} +4.87352 q^{48} +17.6486 q^{49} -7.53120 q^{50} +6.09228 q^{51} +0.644365 q^{52} +4.52421 q^{53} -1.62615 q^{54} -2.61357 q^{55} -10.9446 q^{56} -0.864761 q^{57} -9.19108 q^{58} -1.32918 q^{59} -0.391258 q^{60} -6.32133 q^{61} -1.73702 q^{62} +4.96474 q^{63} +4.02926 q^{64} +0.607200 q^{65} +6.99943 q^{66} -7.27122 q^{67} -3.92565 q^{68} +2.54794 q^{69} +4.90217 q^{70} +10.2952 q^{71} -2.20447 q^{72} +7.80297 q^{73} +3.53965 q^{74} +4.63131 q^{75} +0.557222 q^{76} -21.3697 q^{77} -1.62615 q^{78} -3.27991 q^{79} -2.95920 q^{80} +1.00000 q^{81} -15.7900 q^{82} +8.15429 q^{83} -3.19910 q^{84} -3.69923 q^{85} -3.01796 q^{86} +5.65205 q^{87} +9.48867 q^{88} -12.5851 q^{89} +0.987398 q^{90} +4.96474 q^{91} -1.64180 q^{92} +1.06818 q^{93} -3.92551 q^{94} +0.525083 q^{95} +3.51615 q^{96} +6.58016 q^{97} +28.6993 q^{98} -4.30429 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 4 q^{2} - 25 q^{3} + 28 q^{4} - 5 q^{5} + 4 q^{6} - 7 q^{7} - 9 q^{8} + 25 q^{9}+O(q^{10}) \) 25 * q - 4 * q^2 - 25 * q^3 + 28 * q^4 - 5 * q^5 + 4 * q^6 - 7 * q^7 - 9 * q^8 + 25 * q^9	\( 25 q - 4 q^{2} - 25 q^{3} + 28 q^{4} - 5 q^{5} + 4 q^{6} - 7 q^{7} - 9 q^{8} + 25 q^{9} - 12 q^{10} - 23 q^{11} - 28 q^{12} + 25 q^{13} + 5 q^{15} + 26 q^{16} - 14 q^{17} - 4 q^{18} - 4 q^{19} - 12 q^{20} + 7 q^{21} - 7 q^{22} - 47 q^{23} + 9 q^{24} + 26 q^{25} - 4 q^{26} - 25 q^{27} - 38 q^{28} + 6 q^{29} + 12 q^{30} - 8 q^{31} - 62 q^{32} + 23 q^{33} + 25 q^{34} + 28 q^{36} - 20 q^{37} - 2 q^{38} - 25 q^{39} - 8 q^{40} - 33 q^{41} - 13 q^{43} - 13 q^{44} - 5 q^{45} - 21 q^{46} - 48 q^{47} - 26 q^{48} + 40 q^{49} - 9 q^{50} + 14 q^{51} + 28 q^{52} - 24 q^{53} + 4 q^{54} - 2 q^{55} - 14 q^{56} + 4 q^{57} - 31 q^{58} - 36 q^{59} + 12 q^{60} + 25 q^{61} - 7 q^{62} - 7 q^{63} + 45 q^{64} - 5 q^{65} + 7 q^{66} - 2 q^{67} - 32 q^{68} + 47 q^{69} - 13 q^{70} - 60 q^{71} - 9 q^{72} + 28 q^{73} - 16 q^{74} - 26 q^{75} - 12 q^{76} - 17 q^{77} + 4 q^{78} - 29 q^{79} - 88 q^{80} + 25 q^{81} - 22 q^{82} - 71 q^{83} + 38 q^{84} + 3 q^{85} - 3 q^{86} - 6 q^{87} + 23 q^{88} - 46 q^{89} - 12 q^{90} - 7 q^{91} - 69 q^{92} + 8 q^{93} + 4 q^{94} - 47 q^{95} + 62 q^{96} - 14 q^{97} - 71 q^{98} - 23 q^{99}+O(q^{100}) \) 25 * q - 4 * q^2 - 25 * q^3 + 28 * q^4 - 5 * q^5 + 4 * q^6 - 7 * q^7 - 9 * q^8 + 25 * q^9 - 12 * q^10 - 23 * q^11 - 28 * q^12 + 25 * q^13 + 5 * q^15 + 26 * q^16 - 14 * q^17 - 4 * q^18 - 4 * q^19 - 12 * q^20 + 7 * q^21 - 7 * q^22 - 47 * q^23 + 9 * q^24 + 26 * q^25 - 4 * q^26 - 25 * q^27 - 38 * q^28 + 6 * q^29 + 12 * q^30 - 8 * q^31 - 62 * q^32 + 23 * q^33 + 25 * q^34 + 28 * q^36 - 20 * q^37 - 2 * q^38 - 25 * q^39 - 8 * q^40 - 33 * q^41 - 13 * q^43 - 13 * q^44 - 5 * q^45 - 21 * q^46 - 48 * q^47 - 26 * q^48 + 40 * q^49 - 9 * q^50 + 14 * q^51 + 28 * q^52 - 24 * q^53 + 4 * q^54 - 2 * q^55 - 14 * q^56 + 4 * q^57 - 31 * q^58 - 36 * q^59 + 12 * q^60 + 25 * q^61 - 7 * q^62 - 7 * q^63 + 45 * q^64 - 5 * q^65 + 7 * q^66 - 2 * q^67 - 32 * q^68 + 47 * q^69 - 13 * q^70 - 60 * q^71 - 9 * q^72 + 28 * q^73 - 16 * q^74 - 26 * q^75 - 12 * q^76 - 17 * q^77 + 4 * q^78 - 29 * q^79 - 88 * q^80 + 25 * q^81 - 22 * q^82 - 71 * q^83 + 38 * q^84 + 3 * q^85 - 3 * q^86 - 6 * q^87 + 23 * q^88 - 46 * q^89 - 12 * q^90 - 7 * q^91 - 69 * q^92 + 8 * q^93 + 4 * q^94 - 47 * q^95 + 62 * q^96 - 14 * q^97 - 71 * q^98 - 23 * q^99

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