LMFDB - Embedded newform 4017.2.a.g.1.1

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:	$0$
Dimension:	$24$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
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)

$f(q)$	$=$	$q-2.64656 q^{2} -1.00000 q^{3} +5.00429 q^{4} +2.13528 q^{5} +2.64656 q^{6} +3.46294 q^{7} -7.95105 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.64656 q^{2} -1.00000 q^{3} +5.00429 q^{4} +2.13528 q^{5} +2.64656 q^{6} +3.46294 q^{7} -7.95105 q^{8} +1.00000 q^{9} -5.65115 q^{10} +3.03428 q^{11} -5.00429 q^{12} -1.00000 q^{13} -9.16489 q^{14} -2.13528 q^{15} +11.0344 q^{16} +5.83429 q^{17} -2.64656 q^{18} -4.49008 q^{19} +10.6856 q^{20} -3.46294 q^{21} -8.03041 q^{22} +3.00321 q^{23} +7.95105 q^{24} -0.440586 q^{25} +2.64656 q^{26} -1.00000 q^{27} +17.3296 q^{28} -1.98960 q^{29} +5.65115 q^{30} -4.26903 q^{31} -13.3011 q^{32} -3.03428 q^{33} -15.4408 q^{34} +7.39435 q^{35} +5.00429 q^{36} -9.10327 q^{37} +11.8833 q^{38} +1.00000 q^{39} -16.9777 q^{40} +9.24661 q^{41} +9.16489 q^{42} -4.21764 q^{43} +15.1844 q^{44} +2.13528 q^{45} -7.94818 q^{46} +1.62467 q^{47} -11.0344 q^{48} +4.99197 q^{49} +1.16604 q^{50} -5.83429 q^{51} -5.00429 q^{52} -2.06453 q^{53} +2.64656 q^{54} +6.47903 q^{55} -27.5340 q^{56} +4.49008 q^{57} +5.26561 q^{58} +4.74778 q^{59} -10.6856 q^{60} +6.40089 q^{61} +11.2983 q^{62} +3.46294 q^{63} +13.1333 q^{64} -2.13528 q^{65} +8.03041 q^{66} +13.0435 q^{67} +29.1965 q^{68} -3.00321 q^{69} -19.5696 q^{70} -3.28896 q^{71} -7.95105 q^{72} +8.31883 q^{73} +24.0924 q^{74} +0.440586 q^{75} -22.4697 q^{76} +10.5075 q^{77} -2.64656 q^{78} +5.66529 q^{79} +23.5615 q^{80} +1.00000 q^{81} -24.4717 q^{82} +9.21371 q^{83} -17.3296 q^{84} +12.4578 q^{85} +11.1622 q^{86} +1.98960 q^{87} -24.1257 q^{88} -6.21498 q^{89} -5.65115 q^{90} -3.46294 q^{91} +15.0289 q^{92} +4.26903 q^{93} -4.29978 q^{94} -9.58757 q^{95} +13.3011 q^{96} +7.11871 q^{97} -13.2116 q^{98} +3.03428 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 3 q^{2} - 24 q^{3} + 25 q^{4} + 3 q^{5} - 3 q^{6} + 11 q^{7} + 6 q^{8} + 24 q^{9}+O(q^{10}) $ 24 * q + 3 * q^2 - 24 * q^3 + 25 * q^4 + 3 * q^5 - 3 * q^6 + 11 * q^7 + 6 * q^8 + 24 * q^9	\( 24 q + 3 q^{2} - 24 q^{3} + 25 q^{4} + 3 q^{5} - 3 q^{6} + 11 q^{7} + 6 q^{8} + 24 q^{9} - 2 q^{10} + 7 q^{11} - 25 q^{12} - 24 q^{13} + 8 q^{14} - 3 q^{15} + 23 q^{16} + 4 q^{17} + 3 q^{18} - 20 q^{19} + 8 q^{20} - 11 q^{21} + 5 q^{22} + 41 q^{23} - 6 q^{24} + 23 q^{25} - 3 q^{26} - 24 q^{27} + 16 q^{28} + 12 q^{29} + 2 q^{30} + 2 q^{31} + 25 q^{32} - 7 q^{33} - 11 q^{34} + 36 q^{35} + 25 q^{36} + 18 q^{37} + 10 q^{38} + 24 q^{39} + 14 q^{40} - 9 q^{41} - 8 q^{42} + 23 q^{43} + 41 q^{44} + 3 q^{45} + 7 q^{46} + 32 q^{47} - 23 q^{48} + 11 q^{49} + 26 q^{50} - 4 q^{51} - 25 q^{52} + 46 q^{53} - 3 q^{54} + 18 q^{55} + 26 q^{56} + 20 q^{57} + 37 q^{58} - 12 q^{59} - 8 q^{60} - q^{61} + 53 q^{62} + 11 q^{63} + 26 q^{64} - 3 q^{65} - 5 q^{66} + 8 q^{67} + 6 q^{68} - 41 q^{69} + 19 q^{70} + 20 q^{71} + 6 q^{72} + 12 q^{73} + 86 q^{74} - 23 q^{75} - 28 q^{76} + 23 q^{77} + 3 q^{78} + 27 q^{79} + 6 q^{80} + 24 q^{81} - 28 q^{82} + 33 q^{83} - 16 q^{84} - 13 q^{85} + 63 q^{86} - 12 q^{87} + 11 q^{88} - 2 q^{90} - 11 q^{91} + 79 q^{92} - 2 q^{93} - 12 q^{94} + 37 q^{95} - 25 q^{96} - 14 q^{97} + 20 q^{98} + 7 q^{99}+O(q^{100}) \) 24 * q + 3 * q^2 - 24 * q^3 + 25 * q^4 + 3 * q^5 - 3 * q^6 + 11 * q^7 + 6 * q^8 + 24 * q^9 - 2 * q^10 + 7 * q^11 - 25 * q^12 - 24 * q^13 + 8 * q^14 - 3 * q^15 + 23 * q^16 + 4 * q^17 + 3 * q^18 - 20 * q^19 + 8 * q^20 - 11 * q^21 + 5 * q^22 + 41 * q^23 - 6 * q^24 + 23 * q^25 - 3 * q^26 - 24 * q^27 + 16 * q^28 + 12 * q^29 + 2 * q^30 + 2 * q^31 + 25 * q^32 - 7 * q^33 - 11 * q^34 + 36 * q^35 + 25 * q^36 + 18 * q^37 + 10 * q^38 + 24 * q^39 + 14 * q^40 - 9 * q^41 - 8 * q^42 + 23 * q^43 + 41 * q^44 + 3 * q^45 + 7 * q^46 + 32 * q^47 - 23 * q^48 + 11 * q^49 + 26 * q^50 - 4 * q^51 - 25 * q^52 + 46 * q^53 - 3 * q^54 + 18 * q^55 + 26 * q^56 + 20 * q^57 + 37 * q^58 - 12 * q^59 - 8 * q^60 - q^61 + 53 * q^62 + 11 * q^63 + 26 * q^64 - 3 * q^65 - 5 * q^66 + 8 * q^67 + 6 * q^68 - 41 * q^69 + 19 * q^70 + 20 * q^71 + 6 * q^72 + 12 * q^73 + 86 * q^74 - 23 * q^75 - 28 * q^76 + 23 * q^77 + 3 * q^78 + 27 * q^79 + 6 * q^80 + 24 * q^81 - 28 * q^82 + 33 * q^83 - 16 * q^84 - 13 * q^85 + 63 * q^86 - 12 * q^87 + 11 * q^88 - 2 * q^90 - 11 * q^91 + 79 * q^92 - 2 * q^93 - 12 * q^94 + 37 * q^95 - 25 * q^96 - 14 * q^97 + 20 * q^98 + 7 * 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 $

$2$	−2.64656	−1.87140	−0.935701	−	0.352793i	$-0.885232\pi$
$2$	−2.64656	−1.87140	−0.935701	+	0.352793i	$0.885232\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	5.00429	2.50215
$5$	2.13528	0.954926	0.477463	−	0.878652i	$-0.341557\pi$
$5$	2.13528	0.954926	0.477463	+	0.878652i	$0.341557\pi$
$6$	2.64656	1.08045
$7$	3.46294	1.30887	0.654435	−	0.756119i	$-0.272907\pi$
$7$	3.46294	1.30887	0.654435	+	0.756119i	$0.272907\pi$
$8$	−7.95105	−2.81112
$9$	1.00000	0.333333
$10$	−5.65115	−1.78705
$11$	3.03428	0.914870	0.457435	−	0.889243i	$-0.348768\pi$
$11$	3.03428	0.914870	0.457435	+	0.889243i	$0.348768\pi$
$12$	−5.00429	−1.44462
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−9.16489	−2.44942
$15$	−2.13528	−0.551327
$16$	11.0344	2.75859
$17$	5.83429	1.41502	0.707512	−	0.706702i	$-0.249818\pi$
$17$	5.83429	1.41502	0.707512	+	0.706702i	$0.249818\pi$
$18$	−2.64656	−0.623801
$19$	−4.49008	−1.03009	−0.515047	−	0.857162i	$-0.672226\pi$
$19$	−4.49008	−1.03009	−0.515047	+	0.857162i	$0.672226\pi$
$20$	10.6856	2.38936
$21$	−3.46294	−0.755676
$22$	−8.03041	−1.71209
$23$	3.00321	0.626212	0.313106	−	0.949718i	$-0.398630\pi$
$23$	3.00321	0.626212	0.313106	+	0.949718i	$0.398630\pi$
$24$	7.95105	1.62300
$25$	−0.440586	−0.0881171
$26$	2.64656	0.519034
$27$	−1.00000	−0.192450
$28$	17.3296	3.27498
$29$	−1.98960	−0.369460	−0.184730	−	0.982789i	$-0.559141\pi$
$29$	−1.98960	−0.369460	−0.184730	+	0.982789i	$0.559141\pi$
$30$	5.65115	1.03175
$31$	−4.26903	−0.766741	−0.383370	−	0.923595i	$-0.625237\pi$
$31$	−4.26903	−0.766741	−0.383370	+	0.923595i	$0.625237\pi$
$32$	−13.3011	−2.35132
$33$	−3.03428	−0.528200
$34$	−15.4408	−2.64808
$35$	7.39435	1.24987
$36$	5.00429	0.834049
$37$	−9.10327	−1.49657	−0.748284	−	0.663379i	$-0.769122\pi$
$37$	−9.10327	−1.49657	−0.748284	+	0.663379i	$0.769122\pi$
$38$	11.8833	1.92772
$39$	1.00000	0.160128
$40$	−16.9777	−2.68441
$41$	9.24661	1.44408	0.722039	−	0.691853i	$-0.243205\pi$
$41$	9.24661	1.44408	0.722039	+	0.691853i	$0.243205\pi$
$42$	9.16489	1.41417
$43$	−4.21764	−0.643184	−0.321592	−	0.946878i	$-0.604218\pi$
$43$	−4.21764	−0.643184	−0.321592	+	0.946878i	$0.604218\pi$
$44$	15.1844	2.28914
$45$	2.13528	0.318309
$46$	−7.94818	−1.17190
$47$	1.62467	0.236982	0.118491	−	0.992955i	$-0.462194\pi$
$47$	1.62467	0.236982	0.118491	+	0.992955i	$0.462194\pi$
$48$	−11.0344	−1.59267
$49$	4.99197	0.713139
$50$	1.16604	0.164903
$51$	−5.83429	−0.816964
$52$	−5.00429	−0.693971
$53$	−2.06453	−0.283585	−0.141793	−	0.989896i	$-0.545287\pi$
$53$	−2.06453	−0.283585	−0.141793	+	0.989896i	$0.545287\pi$
$54$	2.64656	0.360152
$55$	6.47903	0.873633
$56$	−27.5340	−3.67939
$57$	4.49008	0.594726
$58$	5.26561	0.691408
$59$	4.74778	0.618108	0.309054	−	0.951045i	$-0.399988\pi$
$59$	4.74778	0.618108	0.309054	+	0.951045i	$0.399988\pi$
$60$	−10.6856	−1.37950
$61$	6.40089	0.819550	0.409775	−	0.912187i	$-0.365607\pi$
$61$	6.40089	0.819550	0.409775	+	0.912187i	$0.365607\pi$
$62$	11.2983	1.43488
$63$	3.46294	0.436290
$64$	13.1333	1.64167
$65$	−2.13528	−0.264849
$66$	8.03041	0.988475
$67$	13.0435	1.59351	0.796757	−	0.604300i	$-0.206547\pi$
$67$	13.0435	1.59351	0.796757	+	0.604300i	$0.206547\pi$
$68$	29.1965	3.54060
$69$	−3.00321	−0.361544
$70$	−19.5696	−2.33901
$71$	−3.28896	−0.390327	−0.195164	−	0.980771i	$-0.562524\pi$
$71$	−3.28896	−0.390327	−0.195164	+	0.980771i	$0.562524\pi$
$72$	−7.95105	−0.937041
$73$	8.31883	0.973645	0.486823	−	0.873501i	$-0.338156\pi$
$73$	8.31883	0.973645	0.486823	+	0.873501i	$0.338156\pi$
$74$	24.0924	2.80068
$75$	0.440586	0.0508745
$76$	−22.4697	−2.57745
$77$	10.5075	1.19744
$78$	−2.64656	−0.299664
$79$	5.66529	0.637395	0.318698	−	0.947856i	$-0.396755\pi$
$79$	5.66529	0.637395	0.318698	+	0.947856i	$0.396755\pi$
$80$	23.5615	2.63425
$81$	1.00000	0.111111
$82$	−24.4717	−2.70245
$83$	9.21371	1.01134	0.505668	−	0.862728i	$-0.331246\pi$
$83$	9.21371	1.01134	0.505668	+	0.862728i	$0.331246\pi$
$84$	−17.3296	−1.89081
$85$	12.4578	1.35124
$86$	11.1622	1.20366
$87$	1.98960	0.213308
$88$	−24.1257	−2.57181
$89$	−6.21498	−0.658787	−0.329393	−	0.944193i	$-0.606844\pi$
$89$	−6.21498	−0.658787	−0.329393	+	0.944193i	$0.606844\pi$
$90$	−5.65115	−0.595683
$91$	−3.46294	−0.363015
$92$	15.0289	1.56688
$93$	4.26903	0.442678
$94$	−4.29978	−0.443489
$95$	−9.58757	−0.983664
$96$	13.3011	1.35753
$97$	7.11871	0.722795	0.361398	−	0.932412i	$-0.382300\pi$
$97$	7.11871	0.722795	0.361398	+	0.932412i	$0.382300\pi$
$98$	−13.2116	−1.33457
$99$	3.03428	0.304957
$100$	−2.20482	−0.220482
$101$	14.2990	1.42280	0.711400	−	0.702787i	$-0.248062\pi$
$101$	14.2990	1.42280	0.711400	+	0.702787i	$0.248062\pi$
$102$	15.4408	1.52887
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	7.95105	0.779665
$105$	−7.39435	−0.721614
$106$	5.46391	0.530702
$107$	14.7664	1.42752	0.713761	−	0.700390i	$-0.246990\pi$
$107$	14.7664	1.42752	0.713761	+	0.700390i	$0.246990\pi$
$108$	−5.00429	−0.481538
$109$	−9.04142	−0.866011	−0.433006	−	0.901391i	$-0.642547\pi$
$109$	−9.04142	−0.866011	−0.433006	+	0.901391i	$0.642547\pi$
$110$	−17.1472	−1.63492
$111$	9.10327	0.864044
$112$	38.2114	3.61064
$113$	4.13060	0.388574	0.194287	−	0.980945i	$-0.437761\pi$
$113$	4.13060	0.388574	0.194287	+	0.980945i	$0.437761\pi$
$114$	−11.8833	−1.11297
$115$	6.41269	0.597986
$116$	−9.95655	−0.924443
$117$	−1.00000	−0.0924500
$118$	−12.5653	−1.15673
$119$	20.2038	1.85208
$120$	16.9777	1.54985
$121$	−1.79314	−0.163013
$122$	−16.9403	−1.53371
$123$	−9.24661	−0.833739
$124$	−21.3635	−1.91850
$125$	−11.6172	−1.03907
$126$	−9.16489	−0.816474
$127$	17.3404	1.53871	0.769357	−	0.638820i	$-0.220577\pi$
$127$	17.3404	1.53871	0.769357	+	0.638820i	$0.220577\pi$
$128$	−8.15607	−0.720901
$129$	4.21764	0.371342
$130$	5.65115	0.495639
$131$	−2.57904	−0.225332	−0.112666	−	0.993633i	$-0.535939\pi$
$131$	−2.57904	−0.225332	−0.112666	+	0.993633i	$0.535939\pi$
$132$	−15.1844	−1.32164
$133$	−15.5489	−1.34826
$134$	−34.5204	−2.98211
$135$	−2.13528	−0.183776
$136$	−46.3887	−3.97780
$137$	5.48875	0.468936	0.234468	−	0.972124i	$-0.424665\pi$
$137$	5.48875	0.468936	0.234468	+	0.972124i	$0.424665\pi$
$138$	7.94818	0.676594
$139$	−19.9672	−1.69360	−0.846798	−	0.531915i	$-0.821473\pi$
$139$	−19.9672	−1.69360	−0.846798	+	0.531915i	$0.821473\pi$
$140$	37.0035	3.12737
$141$	−1.62467	−0.136822
$142$	8.70443	0.730459
$143$	−3.03428	−0.253739
$144$	11.0344	0.919531
$145$	−4.24835	−0.352807
$146$	−22.0163	−1.82208
$147$	−4.99197	−0.411731
$148$	−45.5554	−3.74463
$149$	−6.44082	−0.527653	−0.263826	−	0.964570i	$-0.584985\pi$
$149$	−6.44082	−0.527653	−0.263826	+	0.964570i	$0.584985\pi$
$150$	−1.16604	−0.0952066
$151$	13.3197	1.08395	0.541973	−	0.840396i	$-0.317678\pi$
$151$	13.3197	1.08395	0.541973	+	0.840396i	$0.317678\pi$
$152$	35.7009	2.89572
$153$	5.83429	0.471674
$154$	−27.8089	−2.24090
$155$	−9.11557	−0.732181
$156$	5.00429	0.400664
$157$	0.774240	0.0617911	0.0308955	−	0.999523i	$-0.490164\pi$
$157$	0.774240	0.0617911	0.0308955	+	0.999523i	$0.490164\pi$
$158$	−14.9936	−1.19282
$159$	2.06453	0.163728
$160$	−28.4015	−2.24533
$161$	10.3999	0.819630
$162$	−2.64656	−0.207934
$163$	2.58245	0.202273	0.101137	−	0.994873i	$-0.467752\pi$
$163$	2.58245	0.202273	0.101137	+	0.994873i	$0.467752\pi$
$164$	46.2728	3.61329
$165$	−6.47903	−0.504392
$166$	−24.3847	−1.89262
$167$	−2.42584	−0.187717	−0.0938587	−	0.995586i	$-0.529920\pi$
$167$	−2.42584	−0.187717	−0.0938587	+	0.995586i	$0.529920\pi$
$168$	27.5340	2.12430
$169$	1.00000	0.0769231
$170$	−32.9704	−2.52872
$171$	−4.49008	−0.343365
$172$	−21.1063	−1.60934
$173$	−8.91703	−0.677950	−0.338975	−	0.940795i	$-0.610080\pi$
$173$	−8.91703	−0.677950	−0.338975	+	0.940795i	$0.610080\pi$
$174$	−5.26561	−0.399185
$175$	−1.52572	−0.115334
$176$	33.4814	2.52375
$177$	−4.74778	−0.356865
$178$	16.4483	1.23286
$179$	−26.1092	−1.95149	−0.975747	−	0.218902i	$-0.929752\pi$
$179$	−26.1092	−1.95149	−0.975747	+	0.218902i	$0.929752\pi$
$180$	10.6856	0.796455
$181$	14.9521	1.11138	0.555689	−	0.831390i	$-0.312454\pi$
$181$	14.9521	1.11138	0.555689	+	0.831390i	$0.312454\pi$
$182$	9.16489	0.679347
$183$	−6.40089	−0.473167
$184$	−23.8787	−1.76036
$185$	−19.4380	−1.42911
$186$	−11.2983	−0.828429
$187$	17.7029	1.29456
$188$	8.13031	0.592964
$189$	−3.46294	−0.251892
$190$	25.3741	1.84083
$191$	−4.98629	−0.360796	−0.180398	−	0.983594i	$-0.557738\pi$
$191$	−4.98629	−0.360796	−0.180398	+	0.983594i	$0.557738\pi$
$192$	−13.1333	−0.947816
$193$	10.5679	0.760692	0.380346	−	0.924844i	$-0.375805\pi$
$193$	10.5679	0.760692	0.380346	+	0.924844i	$0.375805\pi$
$194$	−18.8401	−1.35264
$195$	2.13528	0.152910
$196$	24.9813	1.78438
$197$	−4.94175	−0.352085	−0.176043	−	0.984383i	$-0.556330\pi$
$197$	−4.94175	−0.352085	−0.176043	+	0.984383i	$0.556330\pi$
$198$	−8.03041	−0.570697
$199$	6.13713	0.435050	0.217525	−	0.976055i	$-0.430202\pi$
$199$	6.13713	0.435050	0.217525	+	0.976055i	$0.430202\pi$
$200$	3.50312	0.247708
$201$	−13.0435	−0.920016
$202$	−37.8431	−2.66263
$203$	−6.88988	−0.483575
$204$	−29.1965	−2.04416
$205$	19.7441	1.37899
$206$	−2.64656	−0.184395
$207$	3.00321	0.208737
$208$	−11.0344	−0.765096
$209$	−13.6242	−0.942403
$210$	19.5696	1.35043
$211$	23.9662	1.64990	0.824951	−	0.565204i	$-0.191202\pi$
$211$	23.9662	1.64990	0.824951	+	0.565204i	$0.191202\pi$
$212$	−10.3315	−0.709572
$213$	3.28896	0.225356
$214$	−39.0802	−2.67147
$215$	−9.00583	−0.614193
$216$	7.95105	0.541001
$217$	−14.7834	−1.00356
$218$	23.9287	1.62066
$219$	−8.31883	−0.562134
$220$	32.4230	2.18596
$221$	−5.83429	−0.392457
$222$	−24.0924	−1.61697
$223$	−7.51533	−0.503264	−0.251632	−	0.967823i	$-0.580967\pi$
$223$	−7.51533	−0.503264	−0.251632	+	0.967823i	$0.580967\pi$
$224$	−46.0608	−3.07757
$225$	−0.440586	−0.0293724
$226$	−10.9319	−0.727178
$227$	−10.3162	−0.684711	−0.342355	−	0.939571i	$-0.611225\pi$
$227$	−10.3162	−0.684711	−0.342355	+	0.939571i	$0.611225\pi$
$228$	22.4697	1.48809
$229$	5.99956	0.396462	0.198231	−	0.980155i	$-0.436480\pi$
$229$	5.99956	0.396462	0.198231	+	0.980155i	$0.436480\pi$
$230$	−16.9716	−1.11907
$231$	−10.5075	−0.691345
$232$	15.8194	1.03860
$233$	−10.5969	−0.694225	−0.347112	−	0.937824i	$-0.612838\pi$
$233$	−10.5969	−0.694225	−0.347112	+	0.937824i	$0.612838\pi$
$234$	2.64656	0.173011
$235$	3.46912	0.226300
$236$	23.7593	1.54660
$237$	−5.66529	−0.368000
$238$	−53.4706	−3.46599
$239$	−13.9296	−0.901033	−0.450517	−	0.892768i	$-0.648760\pi$
$239$	−13.9296	−0.901033	−0.450517	+	0.892768i	$0.648760\pi$
$240$	−23.5615	−1.52089
$241$	−4.23785	−0.272984	−0.136492	−	0.990641i	$-0.543583\pi$
$241$	−4.23785	−0.272984	−0.136492	+	0.990641i	$0.543583\pi$
$242$	4.74567	0.305063
$243$	−1.00000	−0.0641500
$244$	32.0319	2.05063
$245$	10.6592	0.680994
$246$	24.4717	1.56026
$247$	4.49008	0.285697
$248$	33.9433	2.15540
$249$	−9.21371	−0.583895
$250$	30.7456	1.94452
$251$	4.25676	0.268685	0.134342	−	0.990935i	$-0.457108\pi$
$251$	4.25676	0.268685	0.134342	+	0.990935i	$0.457108\pi$
$252$	17.3296	1.09166
$253$	9.11258	0.572903
$254$	−45.8925	−2.87955
$255$	−12.4578	−0.780140
$256$	−4.68111	−0.292570
$257$	−14.4553	−0.901697	−0.450848	−	0.892601i	$-0.648878\pi$
$257$	−14.4553	−0.901697	−0.450848	+	0.892601i	$0.648878\pi$
$258$	−11.1622	−0.694931
$259$	−31.5241	−1.95881
$260$	−10.6856	−0.662690
$261$	−1.98960	−0.123153
$262$	6.82560	0.421687
$263$	31.3505	1.93315	0.966576	−	0.256380i	$-0.0825298\pi$
$263$	31.3505	1.93315	0.966576	+	0.256380i	$0.0825298\pi$
$264$	24.1257	1.48484
$265$	−4.40835	−0.270803
$266$	41.1511	2.52314
$267$	6.21498	0.380351
$268$	65.2734	3.98721
$269$	21.9813	1.34022	0.670112	−	0.742260i	$-0.266246\pi$
$269$	21.9813	1.34022	0.670112	+	0.742260i	$0.266246\pi$
$270$	5.65115	0.343918
$271$	−10.5260	−0.639411	−0.319705	−	0.947517i	$-0.603584\pi$
$271$	−10.5260	−0.639411	−0.319705	+	0.947517i	$0.603584\pi$
$272$	64.3777	3.90347
$273$	3.46294	0.209587
$274$	−14.5263	−0.877567
$275$	−1.33686	−0.0806157
$276$	−15.0289	−0.904636
$277$	1.36837	0.0822175	0.0411087	−	0.999155i	$-0.486911\pi$
$277$	1.36837	0.0822175	0.0411087	+	0.999155i	$0.486911\pi$
$278$	52.8445	3.16940
$279$	−4.26903	−0.255580
$280$	−58.7928	−3.51354
$281$	−0.526720	−0.0314215	−0.0157107	−	0.999877i	$-0.505001\pi$
$281$	−0.526720	−0.0314215	−0.0157107	+	0.999877i	$0.505001\pi$
$282$	4.29978	0.256048
$283$	−7.59818	−0.451665	−0.225833	−	0.974166i	$-0.572510\pi$
$283$	−7.59818	−0.451665	−0.225833	+	0.974166i	$0.572510\pi$
$284$	−16.4589	−0.976656
$285$	9.58757	0.567919
$286$	8.03041	0.474848
$287$	32.0205	1.89011
$288$	−13.3011	−0.783772
$289$	17.0389	1.00229
$290$	11.2435	0.660243
$291$	−7.11871	−0.417306
$292$	41.6299	2.43620
$293$	1.63227	0.0953584	0.0476792	−	0.998863i	$-0.484817\pi$
$293$	1.63227	0.0953584	0.0476792	+	0.998863i	$0.484817\pi$
$294$	13.2116	0.770514
$295$	10.1378	0.590247
$296$	72.3806	4.20703
$297$	−3.03428	−0.176067
$298$	17.0460	0.987450
$299$	−3.00321	−0.173680
$300$	2.20482	0.127295
$301$	−14.6054	−0.841844
$302$	−35.2515	−2.02850
$303$	−14.2990	−0.821454
$304$	−49.5452	−2.84161
$305$	13.6677	0.782609
$306$	−15.4408	−0.882693
$307$	−13.5637	−0.774121	−0.387060	−	0.922054i	$-0.626509\pi$
$307$	−13.5637	−0.774121	−0.387060	+	0.922054i	$0.626509\pi$
$308$	52.5828	2.99618
$309$	−1.00000	−0.0568880
$310$	24.1249	1.37020
$311$	33.6162	1.90620	0.953101	−	0.302652i	$-0.0978719\pi$
$311$	33.6162	1.90620	0.953101	+	0.302652i	$0.0978719\pi$
$312$	−7.95105	−0.450140
$313$	15.4064	0.870819	0.435409	−	0.900233i	$-0.356604\pi$
$313$	15.4064	0.870819	0.435409	+	0.900233i	$0.356604\pi$
$314$	−2.04907	−0.115636
$315$	7.39435	0.416624
$316$	28.3508	1.59486
$317$	12.7187	0.714353	0.357176	−	0.934037i	$-0.383739\pi$
$317$	12.7187	0.714353	0.357176	+	0.934037i	$0.383739\pi$
$318$	−5.46391	−0.306401
$319$	−6.03701	−0.338008
$320$	28.0433	1.56767
$321$	−14.7664	−0.824180
$322$	−27.5241	−1.53386
$323$	−26.1964	−1.45761
$324$	5.00429	0.278016
$325$	0.440586	0.0244393
$326$	−6.83462	−0.378534
$327$	9.04142	0.499992
$328$	−73.5203	−4.05948
$329$	5.62613	0.310178
$330$	17.1472	0.943920
$331$	−24.8178	−1.36411	−0.682054	−	0.731302i	$-0.738913\pi$
$331$	−24.8178	−1.36411	−0.682054	+	0.731302i	$0.738913\pi$
$332$	46.1081	2.53051
$333$	−9.10327	−0.498856
$334$	6.42015	0.351295
$335$	27.8514	1.52169
$336$	−38.2114	−2.08460
$337$	−27.5458	−1.50051	−0.750257	−	0.661147i	$-0.770070\pi$
$337$	−27.5458	−1.50051	−0.750257	+	0.661147i	$0.770070\pi$
$338$	−2.64656	−0.143954
$339$	−4.13060	−0.224343
$340$	62.3427	3.38101
$341$	−12.9534	−0.701468
$342$	11.8833	0.642574
$343$	−6.95369	−0.375464
$344$	33.5347	1.80807
$345$	−6.41269	−0.345247
$346$	23.5995	1.26872
$347$	15.1717	0.814458	0.407229	−	0.913326i	$-0.366495\pi$
$347$	15.1717	0.814458	0.407229	+	0.913326i	$0.366495\pi$
$348$	9.95655	0.533727
$349$	−32.1866	−1.72291	−0.861456	−	0.507832i	$-0.830447\pi$
$349$	−32.1866	−1.72291	−0.861456	+	0.507832i	$0.830447\pi$
$350$	4.03792	0.215836
$351$	1.00000	0.0533761
$352$	−40.3591	−2.15115
$353$	36.4633	1.94074	0.970372	−	0.241617i	$-0.0776778\pi$
$353$	36.4633	1.94074	0.970372	+	0.241617i	$0.0776778\pi$
$354$	12.5653	0.667838
$355$	−7.02284	−0.372733
$356$	−31.1016	−1.64838
$357$	−20.2038	−1.06930
$358$	69.0996	3.65203
$359$	−18.2230	−0.961774	−0.480887	−	0.876782i	$-0.659685\pi$
$359$	−18.2230	−0.961774	−0.480887	+	0.876782i	$0.659685\pi$
$360$	−16.9777	−0.894804
$361$	1.16082	0.0610956
$362$	−39.5716	−2.07984
$363$	1.79314	0.0941157
$364$	−17.3296	−0.908317
$365$	17.7630	0.929759
$366$	16.9403	0.885486
$367$	35.2053	1.83770	0.918851	−	0.394604i	$-0.129118\pi$
$367$	35.2053	1.83770	0.918851	+	0.394604i	$0.129118\pi$
$368$	33.1385	1.72747
$369$	9.24661	0.481359
$370$	51.4439	2.67444
$371$	−7.14936	−0.371176
$372$	21.3635	1.10765
$373$	−31.0352	−1.60694	−0.803471	−	0.595344i	$-0.797016\pi$
$373$	−31.0352	−1.60694	−0.803471	+	0.595344i	$0.797016\pi$
$374$	−46.8518	−2.42265
$375$	11.6172	0.599908
$376$	−12.9178	−0.666185
$377$	1.98960	0.102470
$378$	9.16489	0.471391
$379$	21.4436	1.10148	0.550741	−	0.834676i	$-0.314345\pi$
$379$	21.4436	1.10148	0.550741	+	0.834676i	$0.314345\pi$
$380$	−47.9790	−2.46127
$381$	−17.3404	−0.888376
$382$	13.1965	0.675194
$383$	28.1708	1.43946	0.719730	−	0.694254i	$-0.244266\pi$
$383$	28.1708	1.43946	0.719730	+	0.694254i	$0.244266\pi$
$384$	8.15607	0.416212
$385$	22.4365	1.14347
$386$	−27.9685	−1.42356
$387$	−4.21764	−0.214395
$388$	35.6241	1.80854
$389$	−3.53386	−0.179174	−0.0895868	−	0.995979i	$-0.528555\pi$
$389$	−3.53386	−0.179174	−0.0895868	+	0.995979i	$0.528555\pi$
$390$	−5.65115	−0.286157
$391$	17.5216	0.886105
$392$	−39.6914	−2.00472
$393$	2.57904	0.130095
$394$	13.0786	0.658893
$395$	12.0970	0.608665
$396$	15.1844	0.763046
$397$	25.9769	1.30375	0.651873	−	0.758328i	$-0.273984\pi$
$397$	25.9769	1.30375	0.651873	+	0.758328i	$0.273984\pi$
$398$	−16.2423	−0.814153
$399$	15.5489	0.778418
$400$	−4.86159	−0.243079
$401$	−10.3724	−0.517973	−0.258986	−	0.965881i	$-0.583388\pi$
$401$	−10.3724	−0.517973	−0.258986	+	0.965881i	$0.583388\pi$
$402$	34.5204	1.72172
$403$	4.26903	0.212656
$404$	71.5562	3.56005
$405$	2.13528	0.106103
$406$	18.2345	0.904963
$407$	−27.6219	−1.36916
$408$	46.3887	2.29659
$409$	−7.42182	−0.366985	−0.183493	−	0.983021i	$-0.558740\pi$
$409$	−7.42182	−0.366985	−0.183493	+	0.983021i	$0.558740\pi$
$410$	−52.2540	−2.58064
$411$	−5.48875	−0.270740
$412$	5.00429	0.246544
$413$	16.4413	0.809022
$414$	−7.94818	−0.390632
$415$	19.6738	0.965750
$416$	13.3011	0.652138
$417$	19.9672	0.977798
$418$	36.0572	1.76361
$419$	−3.48670	−0.170336	−0.0851682	−	0.996367i	$-0.527143\pi$
$419$	−3.48670	−0.170336	−0.0851682	+	0.996367i	$0.527143\pi$
$420$	−37.0035	−1.80559
$421$	4.54735	0.221624	0.110812	−	0.993841i	$-0.464655\pi$
$421$	4.54735	0.221624	0.110812	+	0.993841i	$0.464655\pi$
$422$	−63.4281	−3.08763
$423$	1.62467	0.0789940
$424$	16.4152	0.797193
$425$	−2.57050	−0.124688
$426$	−8.70443	−0.421731
$427$	22.1659	1.07268
$428$	73.8954	3.57187
$429$	3.03428	0.146496
$430$	23.8345	1.14940
$431$	−19.5030	−0.939427	−0.469714	−	0.882819i	$-0.655643\pi$
$431$	−19.5030	−0.939427	−0.469714	+	0.882819i	$0.655643\pi$
$432$	−11.0344	−0.530892
$433$	8.07957	0.388279	0.194140	−	0.980974i	$-0.437809\pi$
$433$	8.07957	0.388279	0.194140	+	0.980974i	$0.437809\pi$
$434$	39.1252	1.87807
$435$	4.24835	0.203693
$436$	−45.2459	−2.16689
$437$	−13.4846	−0.645058
$438$	22.0163	1.05198
$439$	−16.5821	−0.791421	−0.395710	−	0.918375i	$-0.629502\pi$
$439$	−16.5821	−0.791421	−0.395710	+	0.918375i	$0.629502\pi$
$440$	−51.5151	−2.45589
$441$	4.99197	0.237713
$442$	15.4408	0.734445
$443$	40.1439	1.90729	0.953646	−	0.300930i	$-0.0972971\pi$
$443$	40.1439	1.90729	0.953646	+	0.300930i	$0.0972971\pi$
$444$	45.5554	2.16196
$445$	−13.2707	−0.629092
$446$	19.8898	0.941809
$447$	6.44082	0.304640
$448$	45.4800	2.14873
$449$	2.27516	0.107371	0.0536857	−	0.998558i	$-0.482903\pi$
$449$	2.27516	0.107371	0.0536857	+	0.998558i	$0.482903\pi$
$450$	1.16604	0.0549675
$451$	28.0568	1.32114
$452$	20.6707	0.972269
$453$	−13.3197	−0.625816
$454$	27.3025	1.28137
$455$	−7.39435	−0.346652
$456$	−35.7009	−1.67185
$457$	−27.5506	−1.28876	−0.644380	−	0.764705i	$-0.722885\pi$
$457$	−27.5506	−1.28876	−0.644380	+	0.764705i	$0.722885\pi$
$458$	−15.8782	−0.741940
$459$	−5.83429	−0.272321
$460$	32.0910	1.49625
$461$	15.8536	0.738377	0.369189	−	0.929354i	$-0.379636\pi$
$461$	15.8536	0.738377	0.369189	+	0.929354i	$0.379636\pi$
$462$	27.8089	1.29379
$463$	28.5167	1.32528	0.662641	−	0.748937i	$-0.269435\pi$
$463$	28.5167	1.32528	0.662641	+	0.748937i	$0.269435\pi$
$464$	−21.9540	−1.01919
$465$	9.11557	0.422725
$466$	28.0453	1.29917
$467$	1.26991	0.0587643	0.0293821	−	0.999568i	$-0.490646\pi$
$467$	1.26991	0.0587643	0.0293821	+	0.999568i	$0.490646\pi$
$468$	−5.00429	−0.231324
$469$	45.1688	2.08570
$470$	−9.18123	−0.423499
$471$	−0.774240	−0.0356751
$472$	−37.7498	−1.73758
$473$	−12.7975	−0.588430
$474$	14.9936	0.688677
$475$	1.97826	0.0907690
$476$	101.106	4.63418
$477$	−2.06453	−0.0945284
$478$	36.8657	1.68620
$479$	−10.0565	−0.459493	−0.229746	−	0.973251i	$-0.573790\pi$
$479$	−10.0565	−0.459493	−0.229746	+	0.973251i	$0.573790\pi$
$480$	28.4015	1.29634
$481$	9.10327	0.415073
$482$	11.2157	0.510863
$483$	−10.3999	−0.473214
$484$	−8.97342	−0.407883
$485$	15.2004	0.690216
$486$	2.64656	0.120051
$487$	4.43120	0.200797	0.100398	−	0.994947i	$-0.467988\pi$
$487$	4.43120	0.200797	0.100398	+	0.994947i	$0.467988\pi$
$488$	−50.8938	−2.30385
$489$	−2.58245	−0.116782
$490$	−28.2104	−1.27441
$491$	13.1660	0.594172	0.297086	−	0.954851i	$-0.403985\pi$
$491$	13.1660	0.594172	0.297086	+	0.954851i	$0.403985\pi$
$492$	−46.2728	−2.08614
$493$	−11.6079	−0.522794
$494$	−11.8833	−0.534654
$495$	6.47903	0.291211
$496$	−47.1061	−2.11513
$497$	−11.3895	−0.510887
$498$	24.3847	1.09270
$499$	−37.5268	−1.67993	−0.839965	−	0.542641i	$-0.817424\pi$
$499$	−37.5268	−1.67993	−0.839965	+	0.542641i	$0.817424\pi$
$500$	−58.1357	−2.59991
$501$	2.42584	0.108379
$502$	−11.2658	−0.502817
$503$	3.28684	0.146553	0.0732766	−	0.997312i	$-0.476654\pi$
$503$	3.28684	0.146553	0.0732766	+	0.997312i	$0.476654\pi$
$504$	−27.5340	−1.22646
$505$	30.5323	1.35867
$506$	−24.1170	−1.07213
$507$	−1.00000	−0.0444116
$508$	86.7765	3.85009
$509$	−3.58187	−0.158764	−0.0793819	−	0.996844i	$-0.525295\pi$
$509$	−3.58187	−0.158764	−0.0793819	+	0.996844i	$0.525295\pi$
$510$	32.9704	1.45996
$511$	28.8076	1.27437
$512$	28.7010	1.26842
$513$	4.49008	0.198242
$514$	38.2569	1.68744
$515$	2.13528	0.0940916
$516$	21.1063	0.929153
$517$	4.92969	0.216808
$518$	83.4305	3.66572
$519$	8.91703	0.391414
$520$	16.9777	0.744522
$521$	43.7000	1.91453	0.957266	−	0.289208i	$-0.0933919\pi$
$521$	43.7000	1.91453	0.957266	+	0.289208i	$0.0933919\pi$
$522$	5.26561	0.230469
$523$	2.00048	0.0874751	0.0437375	−	0.999043i	$-0.486073\pi$
$523$	2.00048	0.0874751	0.0437375	+	0.999043i	$0.486073\pi$
$524$	−12.9063	−0.563814
$525$	1.52572	0.0665880
$526$	−82.9710	−3.61771
$527$	−24.9068	−1.08496
$528$	−33.4814	−1.45709
$529$	−13.9807	−0.607858
$530$	11.6670	0.506781
$531$	4.74778	0.206036
$532$	−77.8112	−3.37354
$533$	−9.24661	−0.400515
$534$	−16.4483	−0.711789
$535$	31.5304	1.36318
$536$	−103.709	−4.47956
$537$	26.1092	1.12670
$538$	−58.1749	−2.50810
$539$	15.1470	0.652429
$540$	−10.6856	−0.459833
$541$	−39.9659	−1.71827	−0.859135	−	0.511749i	$-0.828998\pi$
$541$	−39.9659	−1.71827	−0.859135	+	0.511749i	$0.828998\pi$
$542$	27.8578	1.19660
$543$	−14.9521	−0.641655
$544$	−77.6022	−3.32717
$545$	−19.3060	−0.826976
$546$	−9.16489	−0.392221
$547$	−10.3433	−0.442247	−0.221123	−	0.975246i	$-0.570972\pi$
$547$	−10.3433	−0.442247	−0.221123	+	0.975246i	$0.570972\pi$
$548$	27.4673	1.17335
$549$	6.40089	0.273183
$550$	3.53808	0.150864
$551$	8.93347	0.380579
$552$	23.8787	1.01634
$553$	19.6186	0.834267
$554$	−3.62148	−0.153862
$555$	19.4380	0.825098
$556$	−99.9218	−4.23763
$557$	−35.9799	−1.52452	−0.762259	−	0.647272i	$-0.775910\pi$
$557$	−35.9799	−1.52452	−0.762259	+	0.647272i	$0.775910\pi$
$558$	11.2983	0.478294
$559$	4.21764	0.178387
$560$	81.5920	3.44789
$561$	−17.7029	−0.747416
$562$	1.39400	0.0588022
$563$	0.454795	0.0191673	0.00958366	−	0.999954i	$-0.496949\pi$
$563$	0.454795	0.0191673	0.00958366	+	0.999954i	$0.496949\pi$
$564$	−8.13031	−0.342348
$565$	8.81997	0.371059
$566$	20.1091	0.845247
$567$	3.46294	0.145430
$568$	26.1507	1.09726
$569$	−15.9384	−0.668170	−0.334085	−	0.942543i	$-0.608427\pi$
$569$	−15.9384	−0.668170	−0.334085	+	0.942543i	$0.608427\pi$
$570$	−25.3741	−1.06280
$571$	−12.9042	−0.540024	−0.270012	−	0.962857i	$-0.587028\pi$
$571$	−12.9042	−0.540024	−0.270012	+	0.962857i	$0.587028\pi$
$572$	−15.1844	−0.634893
$573$	4.98629	0.208305
$574$	−84.7442	−3.53715
$575$	−1.32317	−0.0551800
$576$	13.1333	0.547222
$577$	−8.64318	−0.359820	−0.179910	−	0.983683i	$-0.557581\pi$
$577$	−8.64318	−0.359820	−0.179910	+	0.983683i	$0.557581\pi$
$578$	−45.0946	−1.87569
$579$	−10.5679	−0.439186
$580$	−21.2600	−0.882774
$581$	31.9065	1.32371
$582$	18.8401	0.780948
$583$	−6.26437	−0.259444
$584$	−66.1435	−2.73704
$585$	−2.13528	−0.0882829
$586$	−4.31991	−0.178454
$587$	29.2866	1.20879	0.604394	−	0.796686i	$-0.293415\pi$
$587$	29.2866	1.20879	0.604394	+	0.796686i	$0.293415\pi$
$588$	−24.9813	−1.03021
$589$	19.1683	0.789816
$590$	−26.8304	−1.10459
$591$	4.94175	0.203276
$592$	−100.449	−4.12842
$593$	10.3867	0.426532	0.213266	−	0.976994i	$-0.431590\pi$
$593$	10.3867	0.426532	0.213266	+	0.976994i	$0.431590\pi$
$594$	8.03041	0.329492
$595$	43.1408	1.76860
$596$	−32.2318	−1.32026
$597$	−6.13713	−0.251176
$598$	7.94818	0.325025
$599$	24.1133	0.985243	0.492621	−	0.870244i	$-0.336039\pi$
$599$	24.1133	0.985243	0.492621	+	0.870244i	$0.336039\pi$
$600$	−3.50312	−0.143014
$601$	17.3668	0.708408	0.354204	−	0.935168i	$-0.384752\pi$
$601$	17.3668	0.708408	0.354204	+	0.935168i	$0.384752\pi$
$602$	38.6542	1.57543
$603$	13.0435	0.531171
$604$	66.6559	2.71219
$605$	−3.82886	−0.155665
$606$	37.8431	1.53727
$607$	−3.98356	−0.161688	−0.0808439	−	0.996727i	$-0.525762\pi$
$607$	−3.98356	−0.161688	−0.0808439	+	0.996727i	$0.525762\pi$
$608$	59.7228	2.42208
$609$	6.88988	0.279192
$610$	−36.1724	−1.46458
$611$	−1.62467	−0.0657270
$612$	29.1965	1.18020
$613$	49.4935	1.99903	0.999513	−	0.0312165i	$-0.00993813\pi$
$613$	49.4935	1.99903	0.999513	+	0.0312165i	$0.00993813\pi$
$614$	35.8972	1.44869
$615$	−19.7441	−0.796158
$616$	−83.5460	−3.36616
$617$	−9.54218	−0.384154	−0.192077	−	0.981380i	$-0.561522\pi$
$617$	−9.54218	−0.384154	−0.192077	+	0.981380i	$0.561522\pi$
$618$	2.64656	0.106460
$619$	−24.2096	−0.973066	−0.486533	−	0.873662i	$-0.661739\pi$
$619$	−24.2096	−0.973066	−0.486533	+	0.873662i	$0.661739\pi$
$620$	−45.6170	−1.83202
$621$	−3.00321	−0.120515
$622$	−88.9675	−3.56727
$623$	−21.5221	−0.862266
$624$	11.0344	0.441728
$625$	−22.6030	−0.904118
$626$	−40.7739	−1.62965
$627$	13.6242	0.544097
$628$	3.87452	0.154610
$629$	−53.1111	−2.11768
$630$	−19.5696	−0.779672
$631$	10.5774	0.421081	0.210541	−	0.977585i	$-0.432478\pi$
$631$	10.5774	0.421081	0.210541	+	0.977585i	$0.432478\pi$
$632$	−45.0451	−1.79180
$633$	−23.9662	−0.952572
$634$	−33.6608	−1.33684
$635$	37.0266	1.46936
$636$	10.3315	0.409672
$637$	−4.99197	−0.197789
$638$	15.9773	0.632548
$639$	−3.28896	−0.130109
$640$	−17.4155	−0.688407
$641$	−2.46081	−0.0971961	−0.0485980	−	0.998818i	$-0.515475\pi$
$641$	−2.46081	−0.0971961	−0.0485980	+	0.998818i	$0.515475\pi$
$642$	39.0802	1.54237
$643$	−32.0247	−1.26293	−0.631465	−	0.775405i	$-0.717546\pi$
$643$	−32.0247	−1.26293	−0.631465	+	0.775405i	$0.717546\pi$
$644$	52.0444	2.05084
$645$	9.00583	0.354604
$646$	69.3305	2.72777
$647$	9.15235	0.359816	0.179908	−	0.983683i	$-0.442420\pi$
$647$	9.15235	0.359816	0.179908	+	0.983683i	$0.442420\pi$
$648$	−7.95105	−0.312347
$649$	14.4061	0.565488
$650$	−1.16604	−0.0457358
$651$	14.7834	0.579408
$652$	12.9233	0.506117
$653$	−17.8329	−0.697854	−0.348927	−	0.937150i	$-0.613454\pi$
$653$	−17.8329	−0.697854	−0.348927	+	0.937150i	$0.613454\pi$
$654$	−23.9287	−0.935686
$655$	−5.50697	−0.215175
$656$	102.031	3.98362
$657$	8.31883	0.324548
$658$	−14.8899	−0.580469
$659$	28.5048	1.11039	0.555194	−	0.831721i	$-0.312644\pi$
$659$	28.5048	1.11039	0.555194	+	0.831721i	$0.312644\pi$
$660$	−32.4230	−1.26206
$661$	28.3548	1.10287	0.551437	−	0.834217i	$-0.314080\pi$
$661$	28.3548	1.10287	0.551437	+	0.834217i	$0.314080\pi$
$662$	65.6818	2.55280
$663$	5.83429	0.226585
$664$	−73.2587	−2.84299
$665$	−33.2012	−1.28749
$666$	24.0924	0.933560
$667$	−5.97519	−0.231360
$668$	−12.1396	−0.469697
$669$	7.51533	0.290559
$670$	−73.7106	−2.84769
$671$	19.4221	0.749781
$672$	46.0608	1.77683
$673$	−23.1195	−0.891191	−0.445595	−	0.895234i	$-0.647008\pi$
$673$	−23.1195	−0.891191	−0.445595	+	0.895234i	$0.647008\pi$
$674$	72.9016	2.80806
$675$	0.440586	0.0169582
$676$	5.00429	0.192473
$677$	−22.2873	−0.856569	−0.428285	−	0.903644i	$-0.640882\pi$
$677$	−22.2873	−0.856569	−0.428285	+	0.903644i	$0.640882\pi$
$678$	10.9319	0.419836
$679$	24.6517	0.946045
$680$	−99.0529	−3.79851
$681$	10.3162	0.395318
$682$	34.2821	1.31273
$683$	26.3795	1.00939	0.504693	−	0.863299i	$-0.331606\pi$
$683$	26.3795	1.00939	0.504693	+	0.863299i	$0.331606\pi$
$684$	−22.4697	−0.859150
$685$	11.7200	0.447799
$686$	18.4034	0.702644
$687$	−5.99956	−0.228897
$688$	−46.5390	−1.77428
$689$	2.06453	0.0786524
$690$	16.9716	0.646097
$691$	−35.4002	−1.34669	−0.673343	−	0.739330i	$-0.735142\pi$
$691$	−35.4002	−1.34669	−0.673343	+	0.739330i	$0.735142\pi$
$692$	−44.6235	−1.69633
$693$	10.5075	0.399148
$694$	−40.1528	−1.52418
$695$	−42.6355	−1.61726
$696$	−15.8194	−0.599634
$697$	53.9474	2.04340
$698$	85.1840	3.22426
$699$	10.5969	0.400811
$700$	−7.63517	−0.288582
$701$	0.283351	0.0107020	0.00535102	−	0.999986i	$-0.498297\pi$
$701$	0.283351	0.0107020	0.00535102	+	0.999986i	$0.498297\pi$
$702$	−2.64656	−0.0998881
$703$	40.8744	1.54161
$704$	39.8502	1.50191
$705$	−3.46912	−0.130654
$706$	−96.5023	−3.63191
$707$	49.5165	1.86226
$708$	−23.7593	−0.892928
$709$	21.9772	0.825373	0.412686	−	0.910873i	$-0.364591\pi$
$709$	21.9772	0.825373	0.412686	+	0.910873i	$0.364591\pi$
$710$	18.5864	0.697534
$711$	5.66529	0.212465
$712$	49.4157	1.85193
$713$	−12.8208	−0.480143
$714$	53.4706	2.00109
$715$	−6.47903	−0.242302
$716$	−130.658	−4.88292
$717$	13.9296	0.520212
$718$	48.2284	1.79987
$719$	−11.9879	−0.447072	−0.223536	−	0.974696i	$-0.571760\pi$
$719$	−11.9879	−0.447072	−0.223536	+	0.974696i	$0.571760\pi$
$720$	23.5615	0.878084
$721$	3.46294	0.128967
$722$	−3.07217	−0.114334
$723$	4.23785	0.157607
$724$	74.8246	2.78083
$725$	0.876590	0.0325557
$726$	−4.74567	−0.176128
$727$	−7.42996	−0.275562	−0.137781	−	0.990463i	$-0.543997\pi$
$727$	−7.42996	−0.275562	−0.137781	+	0.990463i	$0.543997\pi$
$728$	27.5340	1.02048
$729$	1.00000	0.0370370
$730$	−47.0109	−1.73995
$731$	−24.6069	−0.910120
$732$	−32.0319	−1.18393
$733$	−5.35318	−0.197724	−0.0988620	−	0.995101i	$-0.531520\pi$
$733$	−5.35318	−0.197724	−0.0988620	+	0.995101i	$0.531520\pi$
$734$	−93.1731	−3.43908
$735$	−10.6592	−0.393172
$736$	−39.9458	−1.47242
$737$	39.5775	1.45786
$738$	−24.4717	−0.900817
$739$	−44.4674	−1.63576	−0.817879	−	0.575390i	$-0.804850\pi$
$739$	−44.4674	−1.63576	−0.817879	+	0.575390i	$0.804850\pi$
$740$	−97.2735	−3.57585
$741$	−4.49008	−0.164947
$742$	18.9212	0.694620
$743$	22.1478	0.812525	0.406262	−	0.913756i	$-0.366832\pi$
$743$	22.1478	0.812525	0.406262	+	0.913756i	$0.366832\pi$
$744$	−33.9433	−1.24442
$745$	−13.7529	−0.503869
$746$	82.1366	3.00723
$747$	9.21371	0.337112
$748$	88.5904	3.23918
$749$	51.1352	1.86844
$750$	−30.7456	−1.12267
$751$	50.8618	1.85597	0.927986	−	0.372615i	$-0.121539\pi$
$751$	50.8618	1.85597	0.927986	+	0.372615i	$0.121539\pi$
$752$	17.9272	0.653737
$753$	−4.25676	−0.155125
$754$	−5.26561	−0.191762
$755$	28.4414	1.03509
$756$	−17.3296	−0.630271
$757$	22.0236	0.800462	0.400231	−	0.916414i	$-0.368930\pi$
$757$	22.0236	0.800462	0.400231	+	0.916414i	$0.368930\pi$
$758$	−56.7518	−2.06132
$759$	−9.11258	−0.330766
$760$	76.2313	2.76520
$761$	−20.7469	−0.752073	−0.376037	−	0.926605i	$-0.622713\pi$
$761$	−20.7469	−0.752073	−0.376037	+	0.926605i	$0.622713\pi$
$762$	45.8925	1.66251
$763$	−31.3099	−1.13350
$764$	−24.9529	−0.902764
$765$	12.4578	0.450414
$766$	−74.5557	−2.69381
$767$	−4.74778	−0.171432
$768$	4.68111	0.168915
$769$	−6.72815	−0.242623	−0.121312	−	0.992614i	$-0.538710\pi$
$769$	−6.72815	−0.242623	−0.121312	+	0.992614i	$0.538710\pi$
$770$	−59.3797	−2.13989
$771$	14.4553	0.520595
$772$	52.8847	1.90336
$773$	−48.5601	−1.74659	−0.873294	−	0.487194i	$-0.838020\pi$
$773$	−48.5601	−1.74659	−0.873294	+	0.487194i	$0.838020\pi$
$774$	11.1622	0.401219
$775$	1.88087	0.0675630
$776$	−56.6012	−2.03187
$777$	31.5241	1.13092
$778$	9.35257	0.335306
$779$	−41.5180	−1.48754
$780$	10.6856	0.382604
$781$	−9.97961	−0.357099
$782$	−46.3720	−1.65826
$783$	1.98960	0.0711026
$784$	55.0833	1.96726
$785$	1.65322	0.0590059
$786$	−6.82560	−0.243461
$787$	−23.4577	−0.836178	−0.418089	−	0.908406i	$-0.637300\pi$
$787$	−23.4577	−0.836178	−0.418089	+	0.908406i	$0.637300\pi$
$788$	−24.7300	−0.880969
$789$	−31.3505	−1.11611
$790$	−32.0154	−1.13906
$791$	14.3040	0.508592
$792$	−24.1257	−0.857270
$793$	−6.40089	−0.227302
$794$	−68.7496	−2.43983
$795$	4.40835	0.156348
$796$	30.7120	1.08856
$797$	13.8923	0.492090	0.246045	−	0.969258i	$-0.420869\pi$
$797$	13.8923	0.492090	0.246045	+	0.969258i	$0.420869\pi$
$798$	−41.1511	−1.45673
$799$	9.47877	0.335335
$800$	5.86025	0.207191
$801$	−6.21498	−0.219596
$802$	27.4512	0.969335
$803$	25.2417	0.890759
$804$	−65.2734	−2.30201
$805$	22.2068	0.782686
$806$	−11.2983	−0.397964
$807$	−21.9813	−0.773778
$808$	−113.692	−3.99966
$809$	−37.5975	−1.32186	−0.660929	−	0.750449i	$-0.729837\pi$
$809$	−37.5975	−1.32186	−0.660929	+	0.750449i	$0.729837\pi$
$810$	−5.65115	−0.198561
$811$	29.3234	1.02969	0.514843	−	0.857285i	$-0.327850\pi$
$811$	29.3234	1.02969	0.514843	+	0.857285i	$0.327850\pi$
$812$	−34.4790	−1.20997
$813$	10.5260	0.369164
$814$	73.1030	2.56226
$815$	5.51425	0.193156
$816$	−64.3777	−2.25367
$817$	18.9375	0.662541
$818$	19.6423	0.686777
$819$	−3.46294	−0.121005
$820$	98.8052	3.45043
$821$	−23.3910	−0.816351	−0.408176	−	0.912903i	$-0.633835\pi$
$821$	−23.3910	−0.816351	−0.408176	+	0.912903i	$0.633835\pi$
$822$	14.5263	0.506664
$823$	46.7211	1.62859	0.814297	−	0.580448i	$-0.197123\pi$
$823$	46.7211	1.62859	0.814297	+	0.580448i	$0.197123\pi$
$824$	−7.95105	−0.276988
$825$	1.33686	0.0465435
$826$	−43.5129	−1.51401
$827$	−42.3624	−1.47309	−0.736543	−	0.676391i	$-0.763543\pi$
$827$	−42.3624	−1.47309	−0.736543	+	0.676391i	$0.763543\pi$
$828$	15.0289	0.522292
$829$	−42.5229	−1.47688	−0.738441	−	0.674318i	$-0.764438\pi$
$829$	−42.5229	−1.47688	−0.738441	+	0.674318i	$0.764438\pi$
$830$	−52.0680	−1.80731
$831$	−1.36837	−0.0474683
$832$	−13.1333	−0.455316
$833$	29.1246	1.00911
$834$	−52.8445	−1.82985
$835$	−5.17985	−0.179256
$836$	−68.1793	−2.35803
$837$	4.26903	0.147559
$838$	9.22777	0.318768
$839$	−53.7132	−1.85439	−0.927193	−	0.374584i	$-0.877785\pi$
$839$	−53.7132	−1.85439	−0.927193	+	0.374584i	$0.877785\pi$
$840$	58.7928	2.02855
$841$	−25.0415	−0.863499
$842$	−12.0349	−0.414749
$843$	0.526720	0.0181412
$844$	119.934	4.12830
$845$	2.13528	0.0734558
$846$	−4.29978	−0.147830
$847$	−6.20956	−0.213363
$848$	−22.7808	−0.782297
$849$	7.59818	0.260769
$850$	6.80300	0.233341
$851$	−27.3390	−0.937169
$852$	16.4589	0.563873
$853$	−4.52952	−0.155088	−0.0775439	−	0.996989i	$-0.524708\pi$
$853$	−4.52952	−0.155088	−0.0775439	+	0.996989i	$0.524708\pi$
$854$	−58.6635	−2.00742
$855$	−9.58757	−0.327888
$856$	−117.408	−4.01294
$857$	13.7182	0.468606	0.234303	−	0.972164i	$-0.424719\pi$
$857$	13.7182	0.468606	0.234303	+	0.972164i	$0.424719\pi$
$858$	−8.03041	−0.274154
$859$	13.6322	0.465126	0.232563	−	0.972581i	$-0.425289\pi$
$859$	13.6322	0.465126	0.232563	+	0.972581i	$0.425289\pi$
$860$	−45.0678	−1.53680
$861$	−32.0205	−1.09125
$862$	51.6160	1.75805
$863$	−33.5268	−1.14127	−0.570633	−	0.821205i	$-0.693302\pi$
$863$	−33.5268	−1.14127	−0.570633	+	0.821205i	$0.693302\pi$
$864$	13.3011	0.452511
$865$	−19.0404	−0.647391
$866$	−21.3831	−0.726627
$867$	−17.0389	−0.578673
$868$	−73.9806	−2.51106
$869$	17.1901	0.583134
$870$	−11.2435	−0.381192
$871$	−13.0435	−0.441961
$872$	71.8888	2.43446
$873$	7.11871	0.240932
$874$	35.6880	1.20716
$875$	−40.2296	−1.36001
$876$	−41.6299	−1.40654
$877$	−8.24244	−0.278328	−0.139164	−	0.990269i	$-0.544441\pi$
$877$	−8.24244	−0.278328	−0.139164	+	0.990269i	$0.544441\pi$
$878$	43.8856	1.48107
$879$	−1.63227	−0.0550552
$880$	71.4921	2.41000
$881$	47.5315	1.60138	0.800688	−	0.599082i	$-0.204468\pi$
$881$	47.5315	1.60138	0.800688	+	0.599082i	$0.204468\pi$
$882$	−13.2116	−0.444856
$883$	−32.7753	−1.10298	−0.551488	−	0.834183i	$-0.685940\pi$
$883$	−32.7753	−1.10298	−0.551488	+	0.834183i	$0.685940\pi$
$884$	−29.1965	−0.981985
$885$	−10.1378	−0.340779
$886$	−106.243	−3.56931
$887$	33.0000	1.10803	0.554016	−	0.832506i	$-0.313095\pi$
$887$	33.0000	1.10803	0.554016	+	0.832506i	$0.313095\pi$
$888$	−72.3806	−2.42893
$889$	60.0489	2.01397
$890$	35.1218	1.17729
$891$	3.03428	0.101652
$892$	−37.6089	−1.25924
$893$	−7.29488	−0.244114
$894$	−17.0460	−0.570105
$895$	−55.7504	−1.86353
$896$	−28.2440	−0.943565
$897$	3.00321	0.100274
$898$	−6.02135	−0.200935
$899$	8.49368	0.283280
$900$	−2.20482	−0.0734940
$901$	−12.0451	−0.401280
$902$	−74.2541	−2.47239
$903$	14.6054	0.486039
$904$	−32.8426	−1.09233
$905$	31.9268	1.06128
$906$	35.2515	1.17115
$907$	25.9093	0.860305	0.430153	−	0.902756i	$-0.358460\pi$
$907$	25.9093	0.860305	0.430153	+	0.902756i	$0.358460\pi$
$908$	−51.6253	−1.71325
$909$	14.2990	0.474267
$910$	19.5696	0.648726
$911$	38.9295	1.28979	0.644896	−	0.764271i	$-0.276901\pi$
$911$	38.9295	1.28979	0.644896	+	0.764271i	$0.276901\pi$
$912$	49.5452	1.64061
$913$	27.9570	0.925240
$914$	72.9143	2.41179
$915$	−13.6677	−0.451839
$916$	30.0236	0.992006
$917$	−8.93107	−0.294930
$918$	15.4408	0.509623
$919$	56.9672	1.87917	0.939587	−	0.342309i	$-0.111209\pi$
$919$	56.9672	1.87917	0.939587	+	0.342309i	$0.111209\pi$
$920$	−50.9876	−1.68101
$921$	13.5637	0.446939
$922$	−41.9576	−1.38180
$923$	3.28896	0.108257
$924$	−52.5828	−1.72985
$925$	4.01077	0.131873
$926$	−75.4712	−2.48014
$927$	1.00000	0.0328443
$928$	26.4638	0.868717
$929$	−38.4728	−1.26225	−0.631126	−	0.775680i	$-0.717407\pi$
$929$	−38.4728	−1.26225	−0.631126	+	0.775680i	$0.717407\pi$
$930$	−24.1249	−0.791088
$931$	−22.4143	−0.734600
$932$	−53.0299	−1.73705
$933$	−33.6162	−1.10055
$934$	−3.36089	−0.109972
$935$	37.8006	1.23621
$936$	7.95105	0.259888
$937$	−18.2869	−0.597407	−0.298703	−	0.954346i	$-0.596554\pi$
$937$	−18.2869	−0.597407	−0.298703	+	0.954346i	$0.596554\pi$
$938$	−119.542	−3.90319
$939$	−15.4064	−0.502767
$940$	17.3605	0.566236
$941$	−12.8052	−0.417436	−0.208718	−	0.977976i	$-0.566929\pi$
$941$	−12.8052	−0.417436	−0.208718	+	0.977976i	$0.566929\pi$
$942$	2.04907	0.0667625
$943$	27.7695	0.904299
$944$	52.3887	1.70511
$945$	−7.39435	−0.240538
$946$	33.8694	1.10119
$947$	−42.9016	−1.39411	−0.697057	−	0.717015i	$-0.745508\pi$
$947$	−42.9016	−1.39411	−0.697057	+	0.717015i	$0.745508\pi$
$948$	−28.3508	−0.920791
$949$	−8.31883	−0.270041
$950$	−5.23560	−0.169865
$951$	−12.7187	−0.412432
$952$	−160.642	−5.20642
$953$	9.32856	0.302182	0.151091	−	0.988520i	$-0.451721\pi$
$953$	9.32856	0.302182	0.151091	+	0.988520i	$0.451721\pi$
$954$	5.46391	0.176901
$955$	−10.6471	−0.344533
$956$	−69.7080	−2.25452
$957$	6.03701	0.195149
$958$	26.6151	0.859896
$959$	19.0072	0.613775
$960$	−28.0433	−0.905094
$961$	−12.7754	−0.412108
$962$	−24.0924	−0.776769
$963$	14.7664	0.475841
$964$	−21.2075	−0.683047
$965$	22.5653	0.726404
$966$	27.5241	0.885573
$967$	34.1140	1.09703	0.548516	−	0.836140i	$-0.315193\pi$
$967$	34.1140	1.09703	0.548516	+	0.836140i	$0.315193\pi$
$968$	14.2574	0.458250
$969$	26.1964	0.841550
$970$	−40.2289	−1.29167
$971$	−10.3973	−0.333667	−0.166833	−	0.985985i	$-0.553354\pi$
$971$	−10.3973	−0.333667	−0.166833	+	0.985985i	$0.553354\pi$
$972$	−5.00429	−0.160513
$973$	−69.1453	−2.21670
$974$	−11.7275	−0.375772
$975$	−0.440586	−0.0141100
$976$	70.6298	2.26080
$977$	−42.3343	−1.35440	−0.677198	−	0.735801i	$-0.736806\pi$
$977$	−42.3343	−1.35440	−0.677198	+	0.735801i	$0.736806\pi$
$978$	6.83462	0.218547
$979$	−18.8580	−0.602704
$980$	53.3420	1.70395
$981$	−9.04142	−0.288670
$982$	−34.8446	−1.11194
$983$	−30.3668	−0.968550	−0.484275	−	0.874916i	$-0.660917\pi$
$983$	−30.3668	−0.968550	−0.484275	+	0.874916i	$0.660917\pi$
$984$	73.5203	2.34374
$985$	−10.5520	−0.336215
$986$	30.7211	0.978358
$987$	−5.62613	−0.179082
$988$	22.4697	0.714856
$989$	−12.6665	−0.402770
$990$	−17.1472	−0.544973
$991$	−34.5368	−1.09710	−0.548548	−	0.836119i	$-0.684819\pi$
$991$	−34.5368	−1.09710	−0.548548	+	0.836119i	$0.684819\pi$
$992$	56.7826	1.80285
$993$	24.8178	0.787568
$994$	30.1429	0.956076
$995$	13.1045	0.415440
$996$	−46.1081	−1.46099
$997$	14.2181	0.450292	0.225146	−	0.974325i	$-0.427714\pi$
$997$	14.2181	0.450292	0.225146	+	0.974325i	$0.427714\pi$
$998$	99.3170	3.14382
$999$	9.10327	0.288015

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.g.1.1	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.g.1.1	✓	24	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)

\(f(q)\)	\(=\)	\(q-2.64656 q^{2} -1.00000 q^{3} +5.00429 q^{4} +2.13528 q^{5} +2.64656 q^{6} +3.46294 q^{7} -7.95105 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.64656 q^{2} -1.00000 q^{3} +5.00429 q^{4} +2.13528 q^{5} +2.64656 q^{6} +3.46294 q^{7} -7.95105 q^{8} +1.00000 q^{9} -5.65115 q^{10} +3.03428 q^{11} -5.00429 q^{12} -1.00000 q^{13} -9.16489 q^{14} -2.13528 q^{15} +11.0344 q^{16} +5.83429 q^{17} -2.64656 q^{18} -4.49008 q^{19} +10.6856 q^{20} -3.46294 q^{21} -8.03041 q^{22} +3.00321 q^{23} +7.95105 q^{24} -0.440586 q^{25} +2.64656 q^{26} -1.00000 q^{27} +17.3296 q^{28} -1.98960 q^{29} +5.65115 q^{30} -4.26903 q^{31} -13.3011 q^{32} -3.03428 q^{33} -15.4408 q^{34} +7.39435 q^{35} +5.00429 q^{36} -9.10327 q^{37} +11.8833 q^{38} +1.00000 q^{39} -16.9777 q^{40} +9.24661 q^{41} +9.16489 q^{42} -4.21764 q^{43} +15.1844 q^{44} +2.13528 q^{45} -7.94818 q^{46} +1.62467 q^{47} -11.0344 q^{48} +4.99197 q^{49} +1.16604 q^{50} -5.83429 q^{51} -5.00429 q^{52} -2.06453 q^{53} +2.64656 q^{54} +6.47903 q^{55} -27.5340 q^{56} +4.49008 q^{57} +5.26561 q^{58} +4.74778 q^{59} -10.6856 q^{60} +6.40089 q^{61} +11.2983 q^{62} +3.46294 q^{63} +13.1333 q^{64} -2.13528 q^{65} +8.03041 q^{66} +13.0435 q^{67} +29.1965 q^{68} -3.00321 q^{69} -19.5696 q^{70} -3.28896 q^{71} -7.95105 q^{72} +8.31883 q^{73} +24.0924 q^{74} +0.440586 q^{75} -22.4697 q^{76} +10.5075 q^{77} -2.64656 q^{78} +5.66529 q^{79} +23.5615 q^{80} +1.00000 q^{81} -24.4717 q^{82} +9.21371 q^{83} -17.3296 q^{84} +12.4578 q^{85} +11.1622 q^{86} +1.98960 q^{87} -24.1257 q^{88} -6.21498 q^{89} -5.65115 q^{90} -3.46294 q^{91} +15.0289 q^{92} +4.26903 q^{93} -4.29978 q^{94} -9.58757 q^{95} +13.3011 q^{96} +7.11871 q^{97} -13.2116 q^{98} +3.03428 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{2} - 24 q^{3} + 25 q^{4} + 3 q^{5} - 3 q^{6} + 11 q^{7} + 6 q^{8} + 24 q^{9}+O(q^{10}) \) 24 * q + 3 * q^2 - 24 * q^3 + 25 * q^4 + 3 * q^5 - 3 * q^6 + 11 * q^7 + 6 * q^8 + 24 * q^9	\( 24 q + 3 q^{2} - 24 q^{3} + 25 q^{4} + 3 q^{5} - 3 q^{6} + 11 q^{7} + 6 q^{8} + 24 q^{9} - 2 q^{10} + 7 q^{11} - 25 q^{12} - 24 q^{13} + 8 q^{14} - 3 q^{15} + 23 q^{16} + 4 q^{17} + 3 q^{18} - 20 q^{19} + 8 q^{20} - 11 q^{21} + 5 q^{22} + 41 q^{23} - 6 q^{24} + 23 q^{25} - 3 q^{26} - 24 q^{27} + 16 q^{28} + 12 q^{29} + 2 q^{30} + 2 q^{31} + 25 q^{32} - 7 q^{33} - 11 q^{34} + 36 q^{35} + 25 q^{36} + 18 q^{37} + 10 q^{38} + 24 q^{39} + 14 q^{40} - 9 q^{41} - 8 q^{42} + 23 q^{43} + 41 q^{44} + 3 q^{45} + 7 q^{46} + 32 q^{47} - 23 q^{48} + 11 q^{49} + 26 q^{50} - 4 q^{51} - 25 q^{52} + 46 q^{53} - 3 q^{54} + 18 q^{55} + 26 q^{56} + 20 q^{57} + 37 q^{58} - 12 q^{59} - 8 q^{60} - q^{61} + 53 q^{62} + 11 q^{63} + 26 q^{64} - 3 q^{65} - 5 q^{66} + 8 q^{67} + 6 q^{68} - 41 q^{69} + 19 q^{70} + 20 q^{71} + 6 q^{72} + 12 q^{73} + 86 q^{74} - 23 q^{75} - 28 q^{76} + 23 q^{77} + 3 q^{78} + 27 q^{79} + 6 q^{80} + 24 q^{81} - 28 q^{82} + 33 q^{83} - 16 q^{84} - 13 q^{85} + 63 q^{86} - 12 q^{87} + 11 q^{88} - 2 q^{90} - 11 q^{91} + 79 q^{92} - 2 q^{93} - 12 q^{94} + 37 q^{95} - 25 q^{96} - 14 q^{97} + 20 q^{98} + 7 q^{99}+O(q^{100}) \) 24 * q + 3 * q^2 - 24 * q^3 + 25 * q^4 + 3 * q^5 - 3 * q^6 + 11 * q^7 + 6 * q^8 + 24 * q^9 - 2 * q^10 + 7 * q^11 - 25 * q^12 - 24 * q^13 + 8 * q^14 - 3 * q^15 + 23 * q^16 + 4 * q^17 + 3 * q^18 - 20 * q^19 + 8 * q^20 - 11 * q^21 + 5 * q^22 + 41 * q^23 - 6 * q^24 + 23 * q^25 - 3 * q^26 - 24 * q^27 + 16 * q^28 + 12 * q^29 + 2 * q^30 + 2 * q^31 + 25 * q^32 - 7 * q^33 - 11 * q^34 + 36 * q^35 + 25 * q^36 + 18 * q^37 + 10 * q^38 + 24 * q^39 + 14 * q^40 - 9 * q^41 - 8 * q^42 + 23 * q^43 + 41 * q^44 + 3 * q^45 + 7 * q^46 + 32 * q^47 - 23 * q^48 + 11 * q^49 + 26 * q^50 - 4 * q^51 - 25 * q^52 + 46 * q^53 - 3 * q^54 + 18 * q^55 + 26 * q^56 + 20 * q^57 + 37 * q^58 - 12 * q^59 - 8 * q^60 - q^61 + 53 * q^62 + 11 * q^63 + 26 * q^64 - 3 * q^65 - 5 * q^66 + 8 * q^67 + 6 * q^68 - 41 * q^69 + 19 * q^70 + 20 * q^71 + 6 * q^72 + 12 * q^73 + 86 * q^74 - 23 * q^75 - 28 * q^76 + 23 * q^77 + 3 * q^78 + 27 * q^79 + 6 * q^80 + 24 * q^81 - 28 * q^82 + 33 * q^83 - 16 * q^84 - 13 * q^85 + 63 * q^86 - 12 * q^87 + 11 * q^88 - 2 * q^90 - 11 * q^91 + 79 * q^92 - 2 * q^93 - 12 * q^94 + 37 * q^95 - 25 * q^96 - 14 * q^97 + 20 * q^98 + 7 * q^99

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