LMFDB - Embedded newform 4031.2.a.e.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4031,2,Mod(1,4031)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4031, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("4031.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4031 = 29 \cdot 139 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4031.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:	$32.1876970548$
Analytic rank:	$0$
Dimension:	$103$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	4031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.50341 q^{2} -3.31200 q^{3} +4.26704 q^{4} -1.06782 q^{5} +8.29127 q^{6} +3.43750 q^{7} -5.67533 q^{8} +7.96931 q^{9} +O(q^{10})$	\(q-2.50341 q^{2} -3.31200 q^{3} +4.26704 q^{4} -1.06782 q^{5} +8.29127 q^{6} +3.43750 q^{7} -5.67533 q^{8} +7.96931 q^{9} +2.67318 q^{10} -4.02727 q^{11} -14.1324 q^{12} +1.94835 q^{13} -8.60547 q^{14} +3.53660 q^{15} +5.67357 q^{16} -7.82274 q^{17} -19.9504 q^{18} -1.80355 q^{19} -4.55641 q^{20} -11.3850 q^{21} +10.0819 q^{22} -6.48003 q^{23} +18.7967 q^{24} -3.85977 q^{25} -4.87751 q^{26} -16.4583 q^{27} +14.6680 q^{28} -1.00000 q^{29} -8.85354 q^{30} -1.07601 q^{31} -2.85258 q^{32} +13.3383 q^{33} +19.5835 q^{34} -3.67062 q^{35} +34.0054 q^{36} +0.737505 q^{37} +4.51503 q^{38} -6.45292 q^{39} +6.06020 q^{40} +9.08843 q^{41} +28.5013 q^{42} -2.58118 q^{43} -17.1845 q^{44} -8.50975 q^{45} +16.2221 q^{46} -2.81340 q^{47} -18.7908 q^{48} +4.81643 q^{49} +9.66257 q^{50} +25.9089 q^{51} +8.31368 q^{52} -7.69253 q^{53} +41.2019 q^{54} +4.30038 q^{55} -19.5090 q^{56} +5.97336 q^{57} +2.50341 q^{58} -9.38433 q^{59} +15.0908 q^{60} +9.11854 q^{61} +2.69368 q^{62} +27.3945 q^{63} -4.20596 q^{64} -2.08048 q^{65} -33.3911 q^{66} -7.61382 q^{67} -33.3799 q^{68} +21.4618 q^{69} +9.18905 q^{70} -1.62968 q^{71} -45.2285 q^{72} -2.79556 q^{73} -1.84627 q^{74} +12.7835 q^{75} -7.69584 q^{76} -13.8437 q^{77} +16.1543 q^{78} -11.8766 q^{79} -6.05832 q^{80} +30.6020 q^{81} -22.7520 q^{82} +3.33356 q^{83} -48.5803 q^{84} +8.35324 q^{85} +6.46175 q^{86} +3.31200 q^{87} +22.8561 q^{88} +16.4294 q^{89} +21.3034 q^{90} +6.69745 q^{91} -27.6506 q^{92} +3.56373 q^{93} +7.04309 q^{94} +1.92586 q^{95} +9.44774 q^{96} -11.5118 q^{97} -12.0575 q^{98} -32.0945 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 103 q + q^{2} + 2 q^{3} + 127 q^{4} + 9 q^{5} + 19 q^{6} + 18 q^{7} + 149 q^{9}+O(q^{10}) $ 103 * q + q^2 + 2 * q^3 + 127 * q^4 + 9 * q^5 + 19 * q^6 + 18 * q^7 + 149 * q^9	\( 103 q + q^{2} + 2 q^{3} + 127 q^{4} + 9 q^{5} + 19 q^{6} + 18 q^{7} + 149 q^{9} + 20 q^{10} + 9 q^{11} + 36 q^{13} - 10 q^{14} + 16 q^{15} + 179 q^{16} + 21 q^{17} + 7 q^{18} + 42 q^{19} + 24 q^{20} + 28 q^{21} + 32 q^{22} + 25 q^{23} + 68 q^{24} + 194 q^{25} - 5 q^{26} + 14 q^{27} + 59 q^{28} - 103 q^{29} + 84 q^{30} + 34 q^{31} + 11 q^{32} + 42 q^{33} + 54 q^{34} + 35 q^{35} + 214 q^{36} + 34 q^{37} + 9 q^{38} + 23 q^{39} + 46 q^{40} + 16 q^{41} + 13 q^{42} + 68 q^{43} - 6 q^{44} + 25 q^{45} + 60 q^{46} + 6 q^{47} + 5 q^{48} + 257 q^{49} - 51 q^{50} + 68 q^{51} + 37 q^{52} + 35 q^{53} + 30 q^{54} + 66 q^{55} - 54 q^{56} + 78 q^{57} - q^{58} + 10 q^{59} - 24 q^{60} + 70 q^{61} + 29 q^{62} + 26 q^{63} + 276 q^{64} + 95 q^{65} + 77 q^{66} + 71 q^{67} - 21 q^{68} - 20 q^{69} + 48 q^{70} + 32 q^{71} + 32 q^{72} + 94 q^{73} + 35 q^{74} + 7 q^{75} + 134 q^{76} + 17 q^{77} + 58 q^{78} + 110 q^{79} + 78 q^{80} + 267 q^{81} - 71 q^{82} + 35 q^{83} + 96 q^{84} + 71 q^{85} + 33 q^{86} - 2 q^{87} + 100 q^{88} + 22 q^{89} - 134 q^{90} + 108 q^{91} - 11 q^{92} + 78 q^{93} + 90 q^{94} + 12 q^{95} + 177 q^{96} + 44 q^{97} - 18 q^{98} + 83 q^{99}+O(q^{100}) \) 103 * q + q^2 + 2 * q^3 + 127 * q^4 + 9 * q^5 + 19 * q^6 + 18 * q^7 + 149 * q^9 + 20 * q^10 + 9 * q^11 + 36 * q^13 - 10 * q^14 + 16 * q^15 + 179 * q^16 + 21 * q^17 + 7 * q^18 + 42 * q^19 + 24 * q^20 + 28 * q^21 + 32 * q^22 + 25 * q^23 + 68 * q^24 + 194 * q^25 - 5 * q^26 + 14 * q^27 + 59 * q^28 - 103 * q^29 + 84 * q^30 + 34 * q^31 + 11 * q^32 + 42 * q^33 + 54 * q^34 + 35 * q^35 + 214 * q^36 + 34 * q^37 + 9 * q^38 + 23 * q^39 + 46 * q^40 + 16 * q^41 + 13 * q^42 + 68 * q^43 - 6 * q^44 + 25 * q^45 + 60 * q^46 + 6 * q^47 + 5 * q^48 + 257 * q^49 - 51 * q^50 + 68 * q^51 + 37 * q^52 + 35 * q^53 + 30 * q^54 + 66 * q^55 - 54 * q^56 + 78 * q^57 - q^58 + 10 * q^59 - 24 * q^60 + 70 * q^61 + 29 * q^62 + 26 * q^63 + 276 * q^64 + 95 * q^65 + 77 * q^66 + 71 * q^67 - 21 * q^68 - 20 * q^69 + 48 * q^70 + 32 * q^71 + 32 * q^72 + 94 * q^73 + 35 * q^74 + 7 * q^75 + 134 * q^76 + 17 * q^77 + 58 * q^78 + 110 * q^79 + 78 * q^80 + 267 * q^81 - 71 * q^82 + 35 * q^83 + 96 * q^84 + 71 * q^85 + 33 * q^86 - 2 * q^87 + 100 * q^88 + 22 * q^89 - 134 * q^90 + 108 * q^91 - 11 * q^92 + 78 * q^93 + 90 * q^94 + 12 * q^95 + 177 * q^96 + 44 * q^97 - 18 * q^98 + 83 * 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 $

$2$	−2.50341	−1.77018	−0.885088	−	0.465424i	$-0.845902\pi$
$2$	−2.50341	−1.77018	−0.885088	+	0.465424i	$0.845902\pi$
$3$	−3.31200	−1.91218	−0.956091	−	0.293071i	$-0.905323\pi$
$3$	−3.31200	−1.91218	−0.956091	+	0.293071i	$0.905323\pi$
$4$	4.26704	2.13352
$5$	−1.06782	−0.477542	−0.238771	−	0.971076i	$-0.576744\pi$
$5$	−1.06782	−0.477542	−0.238771	+	0.971076i	$0.576744\pi$
$6$	8.29127	3.38490
$7$	3.43750	1.29925	0.649627	−	0.760253i	$-0.274925\pi$
$7$	3.43750	1.29925	0.649627	+	0.760253i	$0.274925\pi$
$8$	−5.67533	−2.00653
$9$	7.96931	2.65644
$10$	2.67318	0.845332
$11$	−4.02727	−1.21427	−0.607133	−	0.794600i	$-0.707681\pi$
$11$	−4.02727	−1.21427	−0.607133	+	0.794600i	$0.707681\pi$
$12$	−14.1324	−4.07968
$13$	1.94835	0.540375	0.270187	−	0.962808i	$-0.412914\pi$
$13$	1.94835	0.540375	0.270187	+	0.962808i	$0.412914\pi$
$14$	−8.60547	−2.29991
$15$	3.53660	0.913146
$16$	5.67357	1.41839
$17$	−7.82274	−1.89729	−0.948646	−	0.316339i	$-0.897546\pi$
$17$	−7.82274	−1.89729	−0.948646	+	0.316339i	$0.897546\pi$
$18$	−19.9504	−4.70236
$19$	−1.80355	−0.413764	−0.206882	−	0.978366i	$-0.566332\pi$
$19$	−1.80355	−0.413764	−0.206882	+	0.978366i	$0.566332\pi$
$20$	−4.55641	−1.01885
$21$	−11.3850	−2.48441
$22$	10.0819	2.14946
$23$	−6.48003	−1.35118	−0.675590	−	0.737278i	$-0.736111\pi$
$23$	−6.48003	−1.35118	−0.675590	+	0.737278i	$0.736111\pi$
$24$	18.7967	3.83685
$25$	−3.85977	−0.771954
$26$	−4.87751	−0.956558
$27$	−16.4583	−3.16741
$28$	14.6680	2.77199
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	−8.85354	−1.61643
$31$	−1.07601	−0.193256	−0.0966282	−	0.995321i	$-0.530806\pi$
$31$	−1.07601	−0.193256	−0.0966282	+	0.995321i	$0.530806\pi$
$32$	−2.85258	−0.504270
$33$	13.3383	2.32190
$34$	19.5835	3.35854
$35$	−3.67062	−0.620448
$36$	34.0054	5.66756
$37$	0.737505	0.121245	0.0606225	−	0.998161i	$-0.480691\pi$
$37$	0.737505	0.121245	0.0606225	+	0.998161i	$0.480691\pi$
$38$	4.51503	0.732434
$39$	−6.45292	−1.03329
$40$	6.06020	0.958202
$41$	9.08843	1.41938	0.709688	−	0.704517i	$-0.248836\pi$
$41$	9.08843	1.41938	0.709688	+	0.704517i	$0.248836\pi$
$42$	28.5013	4.39784
$43$	−2.58118	−0.393626	−0.196813	−	0.980441i	$-0.563059\pi$
$43$	−2.58118	−0.393626	−0.196813	+	0.980441i	$0.563059\pi$
$44$	−17.1845	−2.59066
$45$	−8.50975	−1.26856
$46$	16.2221	2.39183
$47$	−2.81340	−0.410377	−0.205189	−	0.978722i	$-0.565781\pi$
$47$	−2.81340	−0.410377	−0.205189	+	0.978722i	$0.565781\pi$
$48$	−18.7908	−2.71222
$49$	4.81643	0.688062
$50$	9.66257	1.36649
$51$	25.9089	3.62797
$52$	8.31368	1.15290
$53$	−7.69253	−1.05665	−0.528325	−	0.849042i	$-0.677180\pi$
$53$	−7.69253	−1.05665	−0.528325	+	0.849042i	$0.677180\pi$
$54$	41.2019	5.60687
$55$	4.30038	0.579863
$56$	−19.5090	−2.60699
$57$	5.97336	0.791191
$58$	2.50341	0.328713
$59$	−9.38433	−1.22174	−0.610868	−	0.791733i	$-0.709179\pi$
$59$	−9.38433	−1.22174	−0.610868	+	0.791733i	$0.709179\pi$
$60$	15.0908	1.94822
$61$	9.11854	1.16751	0.583755	−	0.811930i	$-0.301583\pi$
$61$	9.11854	1.16751	0.583755	+	0.811930i	$0.301583\pi$
$62$	2.69368	0.342098
$63$	27.3945	3.45139
$64$	−4.20596	−0.525744
$65$	−2.08048	−0.258051
$66$	−33.3911	−4.11017
$67$	−7.61382	−0.930176	−0.465088	−	0.885265i	$-0.653977\pi$
$67$	−7.61382	−0.930176	−0.465088	+	0.885265i	$0.653977\pi$
$68$	−33.3799	−4.04791
$69$	21.4618	2.58370
$70$	9.18905	1.09830
$71$	−1.62968	−0.193407	−0.0967036	−	0.995313i	$-0.530830\pi$
$71$	−1.62968	−0.193407	−0.0967036	+	0.995313i	$0.530830\pi$
$72$	−45.2285	−5.33022
$73$	−2.79556	−0.327196	−0.163598	−	0.986527i	$-0.552310\pi$
$73$	−2.79556	−0.327196	−0.163598	+	0.986527i	$0.552310\pi$
$74$	−1.84627	−0.214625
$75$	12.7835	1.47612
$76$	−7.69584	−0.882773
$77$	−13.8437	−1.57764
$78$	16.1543	1.82911
$79$	−11.8766	−1.33622	−0.668109	−	0.744064i	$-0.732896\pi$
$79$	−11.8766	−1.33622	−0.668109	+	0.744064i	$0.732896\pi$
$80$	−6.05832	−0.677341
$81$	30.6020	3.40022
$82$	−22.7520	−2.51254
$83$	3.33356	0.365906	0.182953	−	0.983122i	$-0.441434\pi$
$83$	3.33356	0.365906	0.182953	+	0.983122i	$0.441434\pi$
$84$	−48.5803	−5.30054
$85$	8.35324	0.906036
$86$	6.46175	0.696788
$87$	3.31200	0.355083
$88$	22.8561	2.43646
$89$	16.4294	1.74151	0.870757	−	0.491713i	$-0.163629\pi$
$89$	16.4294	1.74151	0.870757	+	0.491713i	$0.163629\pi$
$90$	21.3034	2.24557
$91$	6.69745	0.702084
$92$	−27.6506	−2.88277
$93$	3.56373	0.369541
$94$	7.04309	0.726440
$95$	1.92586	0.197589
$96$	9.44774	0.964256
$97$	−11.5118	−1.16884	−0.584421	−	0.811450i	$-0.698678\pi$
$97$	−11.5118	−1.16884	−0.584421	+	0.811450i	$0.698678\pi$
$98$	−12.0575	−1.21799
$99$	−32.0945	−3.22562
$100$	−16.4698	−1.64698
$101$	−3.73727	−0.371872	−0.185936	−	0.982562i	$-0.559532\pi$
$101$	−3.73727	−0.371872	−0.185936	+	0.982562i	$0.559532\pi$
$102$	−64.8604	−6.42214
$103$	10.6148	1.04590	0.522952	−	0.852362i	$-0.324831\pi$
$103$	10.6148	1.04590	0.522952	+	0.852362i	$0.324831\pi$
$104$	−11.0575	−1.08428
$105$	12.1571	1.18641
$106$	19.2575	1.87046
$107$	4.98138	0.481568	0.240784	−	0.970579i	$-0.422595\pi$
$107$	4.98138	0.481568	0.240784	+	0.970579i	$0.422595\pi$
$108$	−70.2284	−6.75773
$109$	−14.7426	−1.41208	−0.706040	−	0.708172i	$-0.749520\pi$
$109$	−14.7426	−1.41208	−0.706040	+	0.708172i	$0.749520\pi$
$110$	−10.7656	−1.02646
$111$	−2.44261	−0.231843
$112$	19.5029	1.84285
$113$	−6.66725	−0.627202	−0.313601	−	0.949555i	$-0.601535\pi$
$113$	−6.66725	−0.627202	−0.313601	+	0.949555i	$0.601535\pi$
$114$	−14.9537	−1.40055
$115$	6.91948	0.645245
$116$	−4.26704	−0.396185
$117$	15.5270	1.43547
$118$	23.4928	2.16269
$119$	−26.8907	−2.46507
$120$	−20.0714	−1.83226
$121$	5.21887	0.474443
$122$	−22.8274	−2.06670
$123$	−30.1009	−2.71410
$124$	−4.59136	−0.412316
$125$	9.46060	0.846182
$126$	−68.5797	−6.10956
$127$	0.832405	0.0738640	0.0369320	−	0.999318i	$-0.488242\pi$
$127$	0.832405	0.0738640	0.0369320	+	0.999318i	$0.488242\pi$
$128$	16.2344	1.43493
$129$	8.54886	0.752685
$130$	5.20828	0.456796
$131$	−7.20661	−0.629645	−0.314822	−	0.949151i	$-0.601945\pi$
$131$	−7.20661	−0.629645	−0.314822	+	0.949151i	$0.601945\pi$
$132$	56.9150	4.95382
$133$	−6.19972	−0.537584
$134$	19.0605	1.64657
$135$	17.5745	1.51257
$136$	44.3966	3.80698
$137$	22.0435	1.88330	0.941650	−	0.336594i	$-0.109275\pi$
$137$	22.0435	1.88330	0.941650	+	0.336594i	$0.109275\pi$
$138$	−53.7277	−4.57360
$139$	1.00000	0.0848189
$139$	1.00000	0.0848189
$140$	−15.6627	−1.32374
$141$	9.31798	0.784716
$142$	4.07975	0.342365
$143$	−7.84652	−0.656159
$144$	45.2144	3.76787
$145$	1.06782	0.0886772
$146$	6.99843	0.579195
$147$	−15.9520	−1.31570
$148$	3.14696	0.258679
$149$	12.0126	0.984113	0.492056	−	0.870563i	$-0.336245\pi$
$149$	12.0126	0.984113	0.492056	+	0.870563i	$0.336245\pi$
$150$	−32.0024	−2.61298
$151$	−5.79556	−0.471636	−0.235818	−	0.971797i	$-0.575777\pi$
$151$	−5.79556	−0.471636	−0.235818	+	0.971797i	$0.575777\pi$
$152$	10.2358	0.830230
$153$	−62.3418	−5.04004
$154$	34.6565	2.79270
$155$	1.14898	0.0922879
$156$	−27.5349	−2.20455
$157$	−16.4109	−1.30973	−0.654865	−	0.755746i	$-0.727275\pi$
$157$	−16.4109	−1.30973	−0.654865	+	0.755746i	$0.727275\pi$
$158$	29.7319	2.36534
$159$	25.4776	2.02051
$160$	3.04603	0.240810
$161$	−22.2751	−1.75553
$162$	−76.6092	−6.01899
$163$	8.68064	0.679920	0.339960	−	0.940440i	$-0.389586\pi$
$163$	8.68064	0.679920	0.339960	+	0.940440i	$0.389586\pi$
$164$	38.7807	3.02827
$165$	−14.2428	−1.10880
$166$	−8.34526	−0.647718
$167$	17.7702	1.37510	0.687548	−	0.726139i	$-0.258687\pi$
$167$	17.7702	1.37510	0.687548	+	0.726139i	$0.258687\pi$
$168$	64.6136	4.98505
$169$	−9.20394	−0.707995
$170$	−20.9115	−1.60384
$171$	−14.3731	−1.09914
$172$	−11.0140	−0.839810
$173$	−21.9136	−1.66606	−0.833028	−	0.553230i	$-0.813395\pi$
$173$	−21.9136	−1.66606	−0.833028	+	0.553230i	$0.813395\pi$
$174$	−8.29127	−0.628559
$175$	−13.2680	−1.00296
$176$	−22.8490	−1.72230
$177$	31.0808	2.33618
$178$	−41.1295	−3.08279
$179$	14.9730	1.11914	0.559568	−	0.828784i	$-0.310967\pi$
$179$	14.9730	1.11914	0.559568	+	0.828784i	$0.310967\pi$
$180$	−36.3115	−2.70650
$181$	−3.36076	−0.249803	−0.124902	−	0.992169i	$-0.539862\pi$
$181$	−3.36076	−0.249803	−0.124902	+	0.992169i	$0.539862\pi$
$182$	−16.7664	−1.24281
$183$	−30.2006	−2.23249
$184$	36.7763	2.71118
$185$	−0.787519	−0.0578996
$186$	−8.92145	−0.654153
$187$	31.5042	2.30382
$188$	−12.0049	−0.875549
$189$	−56.5756	−4.11527
$190$	−4.82122	−0.349768
$191$	−1.19207	−0.0862551	−0.0431276	−	0.999070i	$-0.513732\pi$
$191$	−1.19207	−0.0862551	−0.0431276	+	0.999070i	$0.513732\pi$
$192$	13.9301	1.00532
$193$	−17.3209	−1.24678	−0.623391	−	0.781910i	$-0.714246\pi$
$193$	−17.3209	−1.24678	−0.623391	+	0.781910i	$0.714246\pi$
$194$	28.8186	2.06906
$195$	6.89053	0.493441
$196$	20.5519	1.46799
$197$	−12.8907	−0.918427	−0.459214	−	0.888326i	$-0.651869\pi$
$197$	−12.8907	−0.918427	−0.459214	+	0.888326i	$0.651869\pi$
$198$	80.3457	5.70992
$199$	23.0718	1.63551	0.817757	−	0.575564i	$-0.195217\pi$
$199$	23.0718	1.63551	0.817757	+	0.575564i	$0.195217\pi$
$200$	21.9055	1.54895
$201$	25.2169	1.77866
$202$	9.35591	0.658279
$203$	−3.43750	−0.241265
$204$	110.554	7.74034
$205$	−9.70477	−0.677811
$206$	−26.5731	−1.85143
$207$	−51.6414	−3.58932
$208$	11.0541	0.766463
$209$	7.26339	0.502419
$210$	−30.4341	−2.10015
$211$	11.6495	0.801982	0.400991	−	0.916082i	$-0.368666\pi$
$211$	11.6495	0.801982	0.400991	+	0.916082i	$0.368666\pi$
$212$	−32.8244	−2.25439
$213$	5.39749	0.369830
$214$	−12.4704	−0.852461
$215$	2.75623	0.187973
$216$	93.4064	6.35550
$217$	−3.69877	−0.251089
$218$	36.9066	2.49963
$219$	9.25890	0.625658
$220$	18.3499	1.23715
$221$	−15.2414	−1.02525
$222$	6.11485	0.410402
$223$	−20.0741	−1.34426	−0.672132	−	0.740431i	$-0.734621\pi$
$223$	−20.0741	−1.34426	−0.672132	+	0.740431i	$0.734621\pi$
$224$	−9.80577	−0.655175
$225$	−30.7597	−2.05065
$226$	16.6908	1.11026
$227$	−21.2025	−1.40726	−0.703630	−	0.710567i	$-0.748439\pi$
$227$	−21.2025	−1.40726	−0.703630	+	0.710567i	$0.748439\pi$
$228$	25.4886	1.68802
$229$	−1.19290	−0.0788287	−0.0394144	−	0.999223i	$-0.512549\pi$
$229$	−1.19290	−0.0788287	−0.0394144	+	0.999223i	$0.512549\pi$
$230$	−17.3223	−1.14220
$231$	45.8504	3.01674
$232$	5.67533	0.372604
$233$	8.37135	0.548425	0.274213	−	0.961669i	$-0.411583\pi$
$233$	8.37135	0.548425	0.274213	+	0.961669i	$0.411583\pi$
$234$	−38.8704	−2.54104
$235$	3.00420	0.195972
$236$	−40.0433	−2.60660
$237$	39.3351	2.55509
$238$	67.3183	4.36360
$239$	−0.493509	−0.0319224	−0.0159612	−	0.999873i	$-0.505081\pi$
$239$	−0.493509	−0.0319224	−0.0159612	+	0.999873i	$0.505081\pi$
$240$	20.0651	1.29520
$241$	3.94900	0.254378	0.127189	−	0.991879i	$-0.459405\pi$
$241$	3.94900	0.254378	0.127189	+	0.991879i	$0.459405\pi$
$242$	−13.0650	−0.839847
$243$	−51.9786	−3.33443
$244$	38.9092	2.49091
$245$	−5.14306	−0.328578
$246$	75.3547	4.80444
$247$	−3.51395	−0.223587
$248$	6.10668	0.387775
$249$	−11.0407	−0.699678
$250$	−23.6837	−1.49789
$251$	−30.3711	−1.91701	−0.958504	−	0.285080i	$-0.907980\pi$
$251$	−30.3711	−1.91701	−0.958504	+	0.285080i	$0.907980\pi$
$252$	116.894	7.36361
$253$	26.0968	1.64069
$254$	−2.08385	−0.130752
$255$	−27.6659	−1.73250
$256$	−32.2293	−2.01433
$257$	4.21507	0.262929	0.131465	−	0.991321i	$-0.458032\pi$
$257$	4.21507	0.262929	0.131465	+	0.991321i	$0.458032\pi$
$258$	−21.4013	−1.33238
$259$	2.53518	0.157528
$260$	−8.87748	−0.550558
$261$	−7.96931	−0.493288
$262$	18.0411	1.11458
$263$	−10.2048	−0.629256	−0.314628	−	0.949215i	$-0.601880\pi$
$263$	−10.2048	−0.629256	−0.314628	+	0.949215i	$0.601880\pi$
$264$	−75.6991	−4.65896
$265$	8.21420	0.504595
$266$	15.5204	0.951618
$267$	−54.4141	−3.33009
$268$	−32.4885	−1.98455
$269$	16.8961	1.03017	0.515085	−	0.857139i	$-0.327760\pi$
$269$	16.8961	1.03017	0.515085	+	0.857139i	$0.327760\pi$
$270$	−43.9960	−2.67751
$271$	−11.6513	−0.707764	−0.353882	−	0.935290i	$-0.615139\pi$
$271$	−11.6513	−0.707764	−0.353882	+	0.935290i	$0.615139\pi$
$272$	−44.3828	−2.69110
$273$	−22.1819	−1.34251
$274$	−55.1837	−3.33377
$275$	15.5443	0.937358
$276$	91.5785	5.51238
$277$	10.1488	0.609782	0.304891	−	0.952387i	$-0.401380\pi$
$277$	10.1488	0.609782	0.304891	+	0.952387i	$0.401380\pi$
$278$	−2.50341	−0.150144
$279$	−8.57502	−0.513373
$280$	20.8320	1.24495
$281$	29.8771	1.78232	0.891160	−	0.453690i	$-0.149893\pi$
$281$	29.8771	1.78232	0.891160	+	0.453690i	$0.149893\pi$
$282$	−23.3267	−1.38908
$283$	−15.9748	−0.949602	−0.474801	−	0.880093i	$-0.657480\pi$
$283$	−15.9748	−0.949602	−0.474801	+	0.880093i	$0.657480\pi$
$284$	−6.95390	−0.412638
$285$	−6.37845	−0.377827
$286$	19.6430	1.16152
$287$	31.2415	1.84413
$288$	−22.7331	−1.33956
$289$	44.1952	2.59972
$290$	−2.67318	−0.156974
$291$	38.1269	2.23504
$292$	−11.9288	−0.698080
$293$	7.28927	0.425844	0.212922	−	0.977069i	$-0.431702\pi$
$293$	7.28927	0.425844	0.212922	+	0.977069i	$0.431702\pi$
$294$	39.9343	2.32902
$295$	10.0207	0.583429
$296$	−4.18558	−0.243282
$297$	66.2821	3.84608
$298$	−30.0725	−1.74205
$299$	−12.6254	−0.730143
$300$	54.5479	3.14932
$301$	−8.87282	−0.511421
$302$	14.5086	0.834879
$303$	12.3778	0.711087
$304$	−10.2326	−0.586879
$305$	−9.73692	−0.557534
$306$	156.067	8.92175
$307$	−29.9709	−1.71053	−0.855263	−	0.518193i	$-0.826605\pi$
$307$	−29.9709	−1.71053	−0.855263	+	0.518193i	$0.826605\pi$
$308$	−59.0718	−3.36593
$309$	−35.1560	−1.99996
$310$	−2.87635	−0.163366
$311$	30.2710	1.71651	0.858256	−	0.513223i	$-0.171548\pi$
$311$	30.2710	1.71651	0.858256	+	0.513223i	$0.171548\pi$
$312$	36.6224	2.07334
$313$	−8.21841	−0.464532	−0.232266	−	0.972652i	$-0.574614\pi$
$313$	−8.21841	−0.464532	−0.232266	+	0.972652i	$0.574614\pi$
$314$	41.0831	2.31845
$315$	−29.2523	−1.64818
$316$	−50.6778	−2.85085
$317$	−17.7669	−0.997891	−0.498945	−	0.866633i	$-0.666279\pi$
$317$	−17.7669	−0.997891	−0.498945	+	0.866633i	$0.666279\pi$
$318$	−63.7808	−3.57665
$319$	4.02727	0.225484
$320$	4.49118	0.251065
$321$	−16.4983	−0.920846
$322$	55.7637	3.10759
$323$	14.1087	0.785030
$324$	130.580	7.25444
$325$	−7.52018	−0.417144
$326$	−21.7312	−1.20358
$327$	48.8273	2.70015
$328$	−51.5798	−2.84802
$329$	−9.67109	−0.533184
$330$	35.6556	1.96278
$331$	14.9415	0.821261	0.410631	−	0.911802i	$-0.365309\pi$
$331$	14.9415	0.821261	0.410631	+	0.911802i	$0.365309\pi$
$332$	14.2244	0.780668
$333$	5.87741	0.322080
$334$	−44.4859	−2.43416
$335$	8.13015	0.444198
$336$	−64.5935	−3.52387
$337$	28.3974	1.54690	0.773451	−	0.633855i	$-0.218529\pi$
$337$	28.3974	1.54690	0.773451	+	0.633855i	$0.218529\pi$
$338$	23.0412	1.25328
$339$	22.0819	1.19932
$340$	35.6436	1.93305
$341$	4.33336	0.234665
$342$	35.9817	1.94567
$343$	−7.50602	−0.405287
$344$	14.6491	0.789824
$345$	−22.9173	−1.23382
$346$	54.8585	2.94921
$347$	−14.3876	−0.772365	−0.386183	−	0.922422i	$-0.626207\pi$
$347$	−14.3876	−0.772365	−0.386183	+	0.922422i	$0.626207\pi$
$348$	14.1324	0.757577
$349$	13.8309	0.740351	0.370176	−	0.928962i	$-0.379298\pi$
$349$	13.8309	0.740351	0.370176	+	0.928962i	$0.379298\pi$
$350$	33.2151	1.77542
$351$	−32.0666	−1.71159
$352$	11.4881	0.612318
$353$	24.1162	1.28358	0.641788	−	0.766882i	$-0.278193\pi$
$353$	24.1162	1.28358	0.641788	+	0.766882i	$0.278193\pi$
$354$	−77.8080	−4.13545
$355$	1.74020	0.0923600
$356$	70.1050	3.71556
$357$	89.0618	4.71365
$358$	−37.4836	−1.98107
$359$	4.50654	0.237846	0.118923	−	0.992903i	$-0.462056\pi$
$359$	4.50654	0.237846	0.118923	+	0.992903i	$0.462056\pi$
$360$	48.2956	2.54540
$361$	−15.7472	−0.828800
$362$	8.41335	0.442196
$363$	−17.2849	−0.907221
$364$	28.5783	1.49791
$365$	2.98515	0.156250
$366$	75.6043	3.95190
$367$	−1.06031	−0.0553478	−0.0276739	−	0.999617i	$-0.508810\pi$
$367$	−1.06031	−0.0553478	−0.0276739	+	0.999617i	$0.508810\pi$
$368$	−36.7649	−1.91650
$369$	72.4286	3.77048
$370$	1.97148	0.102492
$371$	−26.4431	−1.37286
$372$	15.2066	0.788424
$373$	−18.6163	−0.963917	−0.481958	−	0.876194i	$-0.660074\pi$
$373$	−18.6163	−0.963917	−0.481958	+	0.876194i	$0.660074\pi$
$374$	−78.8679	−4.07816
$375$	−31.3335	−1.61805
$376$	15.9670	0.823435
$377$	−1.94835	−0.100345
$378$	141.632	7.28475
$379$	20.7822	1.06751	0.533754	−	0.845640i	$-0.320781\pi$
$379$	20.7822	1.06751	0.533754	+	0.845640i	$0.320781\pi$
$380$	8.21774	0.421561
$381$	−2.75692	−0.141241
$382$	2.98423	0.152687
$383$	−2.38048	−0.121637	−0.0608183	−	0.998149i	$-0.519371\pi$
$383$	−2.38048	−0.121637	−0.0608183	+	0.998149i	$0.519371\pi$
$384$	−53.7682	−2.74385
$385$	14.7826	0.753389
$386$	43.3611	2.20702
$387$	−20.5702	−1.04564
$388$	−49.1212	−2.49375
$389$	6.83389	0.346492	0.173246	−	0.984879i	$-0.444574\pi$
$389$	6.83389	0.346492	0.173246	+	0.984879i	$0.444574\pi$
$390$	−17.2498	−0.873477
$391$	50.6916	2.56358
$392$	−27.3348	−1.38062
$393$	23.8683	1.20399
$394$	32.2708	1.62578
$395$	12.6820	0.638099
$396$	−136.949	−6.88193
$397$	−14.4925	−0.727357	−0.363678	−	0.931525i	$-0.618479\pi$
$397$	−14.4925	−0.727357	−0.363678	+	0.931525i	$0.618479\pi$
$398$	−57.7580	−2.89515
$399$	20.5335	1.02796
$400$	−21.8987	−1.09493
$401$	−6.35570	−0.317389	−0.158694	−	0.987328i	$-0.550728\pi$
$401$	−6.35570	−0.317389	−0.158694	+	0.987328i	$0.550728\pi$
$402$	−63.1282	−3.14855
$403$	−2.09643	−0.104431
$404$	−15.9471	−0.793397
$405$	−32.6773	−1.62375
$406$	8.60547	0.427082
$407$	−2.97013	−0.147224
$408$	−147.041	−7.27963
$409$	15.4977	0.766312	0.383156	−	0.923684i	$-0.374837\pi$
$409$	15.4977	0.766312	0.383156	+	0.923684i	$0.374837\pi$
$410$	24.2950	1.19984
$411$	−73.0078	−3.60121
$412$	45.2936	2.23146
$413$	−32.2587	−1.58734
$414$	129.279	6.35373
$415$	−3.55963	−0.174735
$416$	−5.55783	−0.272495
$417$	−3.31200	−0.162189
$418$	−18.1832	−0.889370
$419$	−23.6331	−1.15455	−0.577275	−	0.816550i	$-0.695884\pi$
$419$	−23.6331	−1.15455	−0.577275	+	0.816550i	$0.695884\pi$
$420$	51.8747	2.53123
$421$	−10.7418	−0.523523	−0.261761	−	0.965133i	$-0.584303\pi$
$421$	−10.7418	−0.523523	−0.261761	+	0.965133i	$0.584303\pi$
$422$	−29.1633	−1.41965
$423$	−22.4209	−1.09014
$424$	43.6576	2.12020
$425$	30.1940	1.46462
$426$	−13.5121	−0.654663
$427$	31.3450	1.51689
$428$	21.2558	1.02744
$429$	25.9876	1.25469
$430$	−6.89995	−0.332745
$431$	13.4668	0.648674	0.324337	−	0.945942i	$-0.394859\pi$
$431$	13.4668	0.648674	0.324337	+	0.945942i	$0.394859\pi$
$432$	−93.3774	−4.49262
$433$	9.62026	0.462320	0.231160	−	0.972916i	$-0.425748\pi$
$433$	9.62026	0.462320	0.231160	+	0.972916i	$0.425748\pi$
$434$	9.25953	0.444472
$435$	−3.53660	−0.169567
$436$	−62.9071	−3.01270
$437$	11.6871	0.559069
$438$	−23.1788	−1.10752
$439$	−40.8003	−1.94729	−0.973646	−	0.228066i	$-0.926760\pi$
$439$	−40.8003	−1.94729	−0.973646	+	0.228066i	$0.926760\pi$
$440$	−24.4060	−1.16351
$441$	38.3836	1.82779
$442$	38.1554	1.81487
$443$	24.3112	1.15506	0.577531	−	0.816369i	$-0.304016\pi$
$443$	24.3112	1.15506	0.577531	+	0.816369i	$0.304016\pi$
$444$	−10.4227	−0.494641
$445$	−17.5436	−0.831646
$446$	50.2537	2.37958
$447$	−39.7858	−1.88180
$448$	−14.4580	−0.683076
$449$	36.9706	1.74475	0.872375	−	0.488838i	$-0.162579\pi$
$449$	36.9706	1.74475	0.872375	+	0.488838i	$0.162579\pi$
$450$	77.0040	3.63001
$451$	−36.6015	−1.72350
$452$	−28.4494	−1.33815
$453$	19.1949	0.901854
$454$	53.0785	2.49110
$455$	−7.15164	−0.335274
$456$	−33.9008	−1.58755
$457$	24.7234	1.15651	0.578255	−	0.815856i	$-0.303734\pi$
$457$	24.7234	1.15651	0.578255	+	0.815856i	$0.303734\pi$
$458$	2.98630	0.139541
$459$	128.749	6.00950
$460$	29.5257	1.37664
$461$	−33.7341	−1.57115	−0.785577	−	0.618765i	$-0.787634\pi$
$461$	−33.7341	−1.57115	−0.785577	+	0.618765i	$0.787634\pi$
$462$	−114.782	−5.34015
$463$	42.0600	1.95469	0.977347	−	0.211644i	$-0.0678818\pi$
$463$	42.0600	1.95469	0.977347	+	0.211644i	$0.0678818\pi$
$464$	−5.67357	−0.263389
$465$	−3.80540	−0.176471
$466$	−20.9569	−0.970809
$467$	−26.2170	−1.21318	−0.606589	−	0.795015i	$-0.707463\pi$
$467$	−26.2170	−1.21318	−0.606589	+	0.795015i	$0.707463\pi$
$468$	66.2543	3.06261
$469$	−26.1725	−1.20853
$470$	−7.52073	−0.346905
$471$	54.3527	2.50444
$472$	53.2591	2.45145
$473$	10.3951	0.477967
$474$	−98.4717	−4.52296
$475$	6.96130	0.319406
$476$	−114.744	−5.25927
$477$	−61.3042	−2.80693
$478$	1.23545	0.0565083
$479$	6.04752	0.276318	0.138159	−	0.990410i	$-0.455881\pi$
$479$	6.04752	0.276318	0.138159	+	0.990410i	$0.455881\pi$
$480$	−10.0884	−0.460472
$481$	1.43692	0.0655177
$482$	−9.88596	−0.450293
$483$	73.7751	3.35688
$484$	22.2691	1.01223
$485$	12.2924	0.558171
$486$	130.124	5.90253
$487$	−8.30352	−0.376269	−0.188134	−	0.982143i	$-0.560244\pi$
$487$	−8.30352	−0.376269	−0.188134	+	0.982143i	$0.560244\pi$
$488$	−51.7507	−2.34265
$489$	−28.7502	−1.30013
$490$	12.8752	0.581641
$491$	15.5076	0.699847	0.349924	−	0.936778i	$-0.386208\pi$
$491$	15.5076	0.699847	0.349924	+	0.936778i	$0.386208\pi$
$492$	−128.442	−5.79059
$493$	7.82274	0.352318
$494$	8.79685	0.395789
$495$	34.2710	1.54037
$496$	−6.10479	−0.274113
$497$	−5.60202	−0.251285
$498$	27.6395	1.23855
$499$	23.1392	1.03585	0.517925	−	0.855426i	$-0.326704\pi$
$499$	23.1392	1.03585	0.517925	+	0.855426i	$0.326704\pi$
$500$	40.3688	1.80535
$501$	−58.8547	−2.62943
$502$	76.0312	3.39344
$503$	−23.1743	−1.03329	−0.516645	−	0.856199i	$-0.672819\pi$
$503$	−23.1743	−1.03329	−0.516645	+	0.856199i	$0.672819\pi$
$504$	−155.473	−6.92532
$505$	3.99072	0.177584
$506$	−65.3309	−2.90431
$507$	30.4834	1.35382
$508$	3.55191	0.157590
$509$	6.05541	0.268401	0.134201	−	0.990954i	$-0.457153\pi$
$509$	6.05541	0.268401	0.134201	+	0.990954i	$0.457153\pi$
$510$	69.2589	3.06684
$511$	−9.60976	−0.425111
$512$	48.2144	2.13079
$513$	29.6835	1.31056
$514$	−10.5520	−0.465430
$515$	−11.3346	−0.499462
$516$	36.4783	1.60587
$517$	11.3303	0.498307
$518$	−6.34657	−0.278852
$519$	72.5776	3.18580
$520$	11.8074	0.517788
$521$	−30.0139	−1.31493	−0.657466	−	0.753485i	$-0.728371\pi$
$521$	−30.0139	−1.31493	−0.657466	+	0.753485i	$0.728371\pi$
$522$	19.9504	0.873206
$523$	−29.8866	−1.30685	−0.653425	−	0.756991i	$-0.726668\pi$
$523$	−29.8866	−1.30685	−0.653425	+	0.756991i	$0.726668\pi$
$524$	−30.7509	−1.34336
$525$	43.9435	1.91785
$526$	25.5468	1.11389
$527$	8.41731	0.366664
$528$	75.6756	3.29336
$529$	18.9908	0.825687
$530$	−20.5635	−0.893221
$531$	−74.7866	−3.24546
$532$	−26.4545	−1.14695
$533$	17.7074	0.766994
$534$	136.221	5.89485
$535$	−5.31920	−0.229969
$536$	43.2109	1.86643
$537$	−49.5906	−2.13999
$538$	−42.2977	−1.82358
$539$	−19.3971	−0.835490
$540$	74.9910	3.22710
$541$	1.42716	0.0613586	0.0306793	−	0.999529i	$-0.490233\pi$
$541$	1.42716	0.0613586	0.0306793	+	0.999529i	$0.490233\pi$
$542$	29.1678	1.25287
$543$	11.1308	0.477669
$544$	22.3150	0.956748
$545$	15.7423	0.674327
$546$	55.5304	2.37648
$547$	−35.0814	−1.49997	−0.749986	−	0.661454i	$-0.769940\pi$
$547$	−35.0814	−1.49997	−0.749986	+	0.661454i	$0.769940\pi$
$548$	94.0604	4.01806
$549$	72.6685	3.10142
$550$	−38.9137	−1.65929
$551$	1.80355	0.0768340
$552$	−121.803	−5.18428
$553$	−40.8257	−1.73609
$554$	−25.4066	−1.07942
$555$	2.60826	0.110714
$556$	4.26704	0.180963
$557$	14.8543	0.629395	0.314698	−	0.949192i	$-0.398097\pi$
$557$	14.8543	0.629395	0.314698	+	0.949192i	$0.398097\pi$
$558$	21.4668	0.908761
$559$	−5.02904	−0.212706
$560$	−20.8255	−0.880038
$561$	−104.342	−4.40532
$562$	−74.7946	−3.15502
$563$	1.95265	0.0822943	0.0411472	−	0.999153i	$-0.486899\pi$
$563$	1.95265	0.0822943	0.0411472	+	0.999153i	$0.486899\pi$
$564$	39.7602	1.67421
$565$	7.11940	0.299515
$566$	39.9914	1.68096
$567$	105.194	4.41775
$568$	9.24896	0.388078
$569$	3.07172	0.128773	0.0643865	−	0.997925i	$-0.479491\pi$
$569$	3.07172	0.128773	0.0643865	+	0.997925i	$0.479491\pi$
$570$	15.9678	0.668819
$571$	−8.21590	−0.343825	−0.171912	−	0.985112i	$-0.554995\pi$
$571$	−8.21590	−0.343825	−0.171912	+	0.985112i	$0.554995\pi$
$572$	−33.4814	−1.39993
$573$	3.94813	0.164935
$574$	−78.2102	−3.26443
$575$	25.0114	1.04305
$576$	−33.5186	−1.39661
$577$	36.9695	1.53906	0.769531	−	0.638610i	$-0.220490\pi$
$577$	36.9695	1.53906	0.769531	+	0.638610i	$0.220490\pi$
$578$	−110.639	−4.60196
$579$	57.3666	2.38407
$580$	4.55641	0.189195
$581$	11.4591	0.475405
$582$	−95.4472	−3.95641
$583$	30.9799	1.28306
$584$	15.8657	0.656529
$585$	−16.5800	−0.685497
$586$	−18.2480	−0.753818
$587$	−23.7770	−0.981381	−0.490691	−	0.871334i	$-0.663255\pi$
$587$	−23.7770	−0.981381	−0.490691	+	0.871334i	$0.663255\pi$
$588$	−68.0678	−2.80707
$589$	1.94063	0.0799624
$590$	−25.0860	−1.03277
$591$	42.6941	1.75620
$592$	4.18428	0.171973
$593$	24.6052	1.01042	0.505208	−	0.862998i	$-0.331416\pi$
$593$	24.6052	1.01042	0.505208	+	0.862998i	$0.331416\pi$
$594$	−165.931	−6.80823
$595$	28.7143	1.17717
$596$	51.2584	2.09963
$597$	−76.4136	−3.12740
$598$	31.6064	1.29248
$599$	−44.3070	−1.81033	−0.905167	−	0.425056i	$-0.860254\pi$
$599$	−44.3070	−1.81033	−0.905167	+	0.425056i	$0.860254\pi$
$600$	−72.5508	−2.96187
$601$	−20.8422	−0.850172	−0.425086	−	0.905153i	$-0.639756\pi$
$601$	−20.8422	−0.850172	−0.425086	+	0.905153i	$0.639756\pi$
$602$	22.2123	0.905305
$603$	−60.6769	−2.47095
$604$	−24.7299	−1.00625
$605$	−5.57279	−0.226566
$606$	−30.9867	−1.25875
$607$	−44.6128	−1.81078	−0.905388	−	0.424585i	$-0.860420\pi$
$607$	−44.6128	−1.81078	−0.905388	+	0.424585i	$0.860420\pi$
$608$	5.14479	0.208649
$609$	11.3850	0.461343
$610$	24.3755	0.986934
$611$	−5.48149	−0.221757
$612$	−266.015	−10.7530
$613$	40.9334	1.65329	0.826643	−	0.562727i	$-0.190248\pi$
$613$	40.9334	1.65329	0.826643	+	0.562727i	$0.190248\pi$
$614$	75.0292	3.02793
$615$	32.1422	1.29610
$616$	78.5678	3.16559
$617$	12.6098	0.507653	0.253826	−	0.967250i	$-0.418311\pi$
$617$	12.6098	0.507653	0.253826	+	0.967250i	$0.418311\pi$
$618$	88.0098	3.54027
$619$	0.116911	0.00469907	0.00234953	−	0.999997i	$-0.499252\pi$
$619$	0.116911	0.00469907	0.00234953	+	0.999997i	$0.499252\pi$
$620$	4.90273	0.196898
$621$	106.651	4.27974
$622$	−75.7806	−3.03853
$623$	56.4762	2.26267
$624$	−36.6111	−1.46562
$625$	9.19668	0.367867
$626$	20.5740	0.822304
$627$	−24.0563	−0.960717
$628$	−70.0259	−2.79434
$629$	−5.76931	−0.230037
$630$	73.2304	2.91757
$631$	−32.4791	−1.29297	−0.646486	−	0.762926i	$-0.723762\pi$
$631$	−32.4791	−1.29297	−0.646486	+	0.762926i	$0.723762\pi$
$632$	67.4034	2.68116
$633$	−38.5830	−1.53354
$634$	44.4779	1.76644
$635$	−0.888855	−0.0352731
$636$	108.714	4.31079
$637$	9.38409	0.371811
$638$	−10.0819	−0.399146
$639$	−12.9874	−0.513774
$640$	−17.3353	−0.685239
$641$	7.81240	0.308571	0.154286	−	0.988026i	$-0.450692\pi$
$641$	7.81240	0.308571	0.154286	+	0.988026i	$0.450692\pi$
$642$	41.3020	1.63006
$643$	38.9972	1.53790	0.768949	−	0.639310i	$-0.220780\pi$
$643$	38.9972	1.53790	0.768949	+	0.639310i	$0.220780\pi$
$644$	−95.0489	−3.74545
$645$	−9.12861	−0.359438
$646$	−35.3199	−1.38964
$647$	28.9564	1.13839	0.569197	−	0.822201i	$-0.307254\pi$
$647$	28.9564	1.13839	0.569197	+	0.822201i	$0.307254\pi$
$648$	−173.676	−6.82265
$649$	37.7932	1.48351
$650$	18.8261	0.738419
$651$	12.2503	0.480128
$652$	37.0407	1.45062
$653$	−31.1465	−1.21886	−0.609428	−	0.792842i	$-0.708601\pi$
$653$	−31.1465	−1.21886	−0.609428	+	0.792842i	$0.708601\pi$
$654$	−122.234	−4.77975
$655$	7.69533	0.300682
$656$	51.5638	2.01323
$657$	−22.2787	−0.869176
$658$	24.2107	0.943830
$659$	−5.87956	−0.229035	−0.114518	−	0.993421i	$-0.536532\pi$
$659$	−5.87956	−0.229035	−0.114518	+	0.993421i	$0.536532\pi$
$660$	−60.7747	−2.36565
$661$	−4.34483	−0.168994	−0.0844971	−	0.996424i	$-0.526928\pi$
$661$	−4.34483	−0.168994	−0.0844971	+	0.996424i	$0.526928\pi$
$662$	−37.4047	−1.45378
$663$	50.4795	1.96046
$664$	−18.9191	−0.734202
$665$	6.62016	0.256719
$666$	−14.7135	−0.570138
$667$	6.48003	0.250908
$668$	75.8260	2.93380
$669$	66.4855	2.57048
$670$	−20.3531	−0.786308
$671$	−36.7228	−1.41767
$672$	32.4767	1.25281
$673$	−5.62501	−0.216828	−0.108414	−	0.994106i	$-0.534577\pi$
$673$	−5.62501	−0.216828	−0.108414	+	0.994106i	$0.534577\pi$
$674$	−71.0901	−2.73829
$675$	63.5254	2.44509
$676$	−39.2736	−1.51052
$677$	7.42476	0.285357	0.142678	−	0.989769i	$-0.454429\pi$
$677$	7.42476	0.285357	0.142678	+	0.989769i	$0.454429\pi$
$678$	−55.2800	−2.12301
$679$	−39.5717	−1.51862
$680$	−47.4074	−1.81799
$681$	70.2226	2.69094
$682$	−10.8482	−0.415398
$683$	37.2262	1.42442	0.712210	−	0.701966i	$-0.247694\pi$
$683$	37.2262	1.42442	0.712210	+	0.701966i	$0.247694\pi$
$684$	−61.3305	−2.34503
$685$	−23.5383	−0.899354
$686$	18.7906	0.717430
$687$	3.95086	0.150735
$688$	−14.6445	−0.558316
$689$	−14.9877	−0.570987
$690$	57.3712	2.18409
$691$	−9.70907	−0.369351	−0.184675	−	0.982800i	$-0.559123\pi$
$691$	−9.70907	−0.369351	−0.184675	+	0.982800i	$0.559123\pi$
$692$	−93.5061	−3.55457
$693$	−110.325	−4.19090
$694$	36.0179	1.36722
$695$	−1.06782	−0.0405045
$696$	−18.7967	−0.712485
$697$	−71.0964	−2.69297
$698$	−34.6244	−1.31055
$699$	−27.7259	−1.04869
$700$	−56.6150	−2.13985
$701$	−25.3845	−0.958759	−0.479379	−	0.877608i	$-0.659138\pi$
$701$	−25.3845	−0.958759	−0.479379	+	0.877608i	$0.659138\pi$
$702$	80.2756	3.02981
$703$	−1.33013	−0.0501668
$704$	16.9385	0.638394
$705$	−9.94989	−0.374734
$706$	−60.3726	−2.27215
$707$	−12.8469	−0.483157
$708$	132.623	4.98429
$709$	4.67864	0.175710	0.0878550	−	0.996133i	$-0.471999\pi$
$709$	4.67864	0.175710	0.0878550	+	0.996133i	$0.471999\pi$
$710$	−4.35642	−0.163493
$711$	−94.6480	−3.54958
$712$	−93.2423	−3.49440
$713$	6.97255	0.261124
$714$	−222.958	−8.34399
$715$	8.37863	0.313343
$716$	63.8905	2.38770
$717$	1.63450	0.0610415
$718$	−11.2817	−0.421029
$719$	25.4444	0.948915	0.474458	−	0.880278i	$-0.342644\pi$
$719$	25.4444	0.948915	0.474458	+	0.880278i	$0.342644\pi$
$720$	−48.2806	−1.79931
$721$	36.4883	1.35889
$722$	39.4216	1.46712
$723$	−13.0791	−0.486416
$724$	−14.3405	−0.532961
$725$	3.85977	0.143348
$726$	43.2711	1.60594
$727$	24.1624	0.896134	0.448067	−	0.894000i	$-0.352113\pi$
$727$	24.1624	0.896134	0.448067	+	0.894000i	$0.352113\pi$
$728$	−38.0102	−1.40875
$729$	80.3470	2.97581
$730$	−7.47304	−0.276589
$731$	20.1919	0.746824
$732$	−128.867	−4.76307
$733$	40.4989	1.49586	0.747931	−	0.663776i	$-0.231047\pi$
$733$	40.4989	1.49586	0.747931	+	0.663776i	$0.231047\pi$
$734$	2.65439	0.0979754
$735$	17.0338	0.628301
$736$	18.4848	0.681360
$737$	30.6629	1.12948
$738$	−181.318	−6.67441
$739$	20.9632	0.771145	0.385572	−	0.922678i	$-0.374004\pi$
$739$	20.9632	0.771145	0.385572	+	0.922678i	$0.374004\pi$
$740$	−3.36038	−0.123530
$741$	11.6382	0.427539
$742$	66.1978	2.43020
$743$	9.46239	0.347142	0.173571	−	0.984821i	$-0.444469\pi$
$743$	9.46239	0.347142	0.173571	+	0.984821i	$0.444469\pi$
$744$	−20.2253	−0.741496
$745$	−12.8273	−0.469955
$746$	46.6042	1.70630
$747$	26.5662	0.972006
$748$	134.430	4.91524
$749$	17.1235	0.625680
$750$	78.4404	2.86424
$751$	16.2061	0.591371	0.295685	−	0.955285i	$-0.404452\pi$
$751$	16.2061	0.591371	0.295685	+	0.955285i	$0.404452\pi$
$752$	−15.9620	−0.582076
$753$	100.589	3.66567
$754$	4.87751	0.177628
$755$	6.18859	0.225226
$756$	−241.410	−8.78001
$757$	49.2146	1.78873	0.894367	−	0.447334i	$-0.147627\pi$
$757$	49.2146	1.78873	0.894367	+	0.447334i	$0.147627\pi$
$758$	−52.0262	−1.88968
$759$	−86.4325	−3.13730
$760$	−10.9299	−0.396469
$761$	31.2484	1.13275	0.566376	−	0.824147i	$-0.308345\pi$
$761$	31.2484	1.13275	0.566376	+	0.824147i	$0.308345\pi$
$762$	6.90169	0.250022
$763$	−50.6776	−1.83465
$764$	−5.08661	−0.184027
$765$	66.5696	2.40683
$766$	5.95930	0.215318
$767$	−18.2839	−0.660195
$768$	106.743	3.85177
$769$	25.2707	0.911286	0.455643	−	0.890163i	$-0.349409\pi$
$769$	25.2707	0.911286	0.455643	+	0.890163i	$0.349409\pi$
$770$	−37.0068	−1.33363
$771$	−13.9603	−0.502768
$772$	−73.9088	−2.66004
$773$	−3.24407	−0.116681	−0.0583406	−	0.998297i	$-0.518581\pi$
$773$	−3.24407	−0.116681	−0.0583406	+	0.998297i	$0.518581\pi$
$774$	51.4957	1.85097
$775$	4.15313	0.149185
$776$	65.3331	2.34532
$777$	−8.39649	−0.301222
$778$	−17.1080	−0.613351
$779$	−16.3915	−0.587286
$780$	29.4022	1.05277
$781$	6.56315	0.234848
$782$	−126.902	−4.53799
$783$	16.4583	0.588173
$784$	27.3263	0.975941
$785$	17.5238	0.625451
$786$	−59.7520	−2.13128
$787$	−17.4852	−0.623281	−0.311640	−	0.950200i	$-0.600878\pi$
$787$	−17.4852	−0.623281	−0.311640	+	0.950200i	$0.600878\pi$
$788$	−55.0053	−1.95948
$789$	33.7983	1.20325
$790$	−31.7481	−1.12955
$791$	−22.9187	−0.814895
$792$	182.147	6.47231
$793$	17.7661	0.630893
$794$	36.2806	1.28755
$795$	−27.2054	−0.964876
$796$	98.4482	3.48940
$797$	3.18247	0.112729	0.0563644	−	0.998410i	$-0.482049\pi$
$797$	3.18247	0.112729	0.0563644	+	0.998410i	$0.482049\pi$
$798$	−51.4036	−1.81967
$799$	22.0085	0.778606
$800$	11.0103	0.389274
$801$	130.931	4.62622
$802$	15.9109	0.561833
$803$	11.2585	0.397303
$804$	107.602	3.79482
$805$	23.7857	0.838337
$806$	5.24822	0.184861
$807$	−55.9597	−1.96987
$808$	21.2102	0.746173
$809$	13.7543	0.483575	0.241787	−	0.970329i	$-0.422266\pi$
$809$	13.7543	0.483575	0.241787	+	0.970329i	$0.422266\pi$
$810$	81.8045	2.87432
$811$	40.6516	1.42747	0.713736	−	0.700415i	$-0.247002\pi$
$811$	40.6516	1.42747	0.713736	+	0.700415i	$0.247002\pi$
$812$	−14.6680	−0.514745
$813$	38.5889	1.35337
$814$	7.43544	0.260612
$815$	−9.26932	−0.324690
$816$	146.996	5.14588
$817$	4.65530	0.162868
$818$	−38.7971	−1.35651
$819$	53.3741	1.86504
$820$	−41.4107	−1.44612
$821$	9.89593	0.345370	0.172685	−	0.984977i	$-0.444756\pi$
$821$	9.89593	0.345370	0.172685	+	0.984977i	$0.444756\pi$
$822$	182.768	6.37477
$823$	26.0659	0.908600	0.454300	−	0.890849i	$-0.349889\pi$
$823$	26.0659	0.908600	0.454300	+	0.890849i	$0.349889\pi$
$824$	−60.2422	−2.09864
$825$	−51.4827	−1.79240
$826$	80.7565	2.80988
$827$	−14.5893	−0.507321	−0.253660	−	0.967293i	$-0.581635\pi$
$827$	−14.5893	−0.507321	−0.253660	+	0.967293i	$0.581635\pi$
$828$	−220.356	−7.65790
$829$	20.6912	0.718634	0.359317	−	0.933216i	$-0.383010\pi$
$829$	20.6912	0.718634	0.359317	+	0.933216i	$0.383010\pi$
$830$	8.91120	0.309312
$831$	−33.6128	−1.16601
$832$	−8.19467	−0.284099
$833$	−37.6777	−1.30545
$834$	8.29127	0.287103
$835$	−18.9752	−0.656665
$836$	30.9932	1.07192
$837$	17.7093	0.612122
$838$	59.1632	2.04376
$839$	−23.6306	−0.815819	−0.407909	−	0.913022i	$-0.633742\pi$
$839$	−23.6306	−0.815819	−0.407909	+	0.913022i	$0.633742\pi$
$840$	−68.9954	−2.38057
$841$	1.00000	0.0344828
$842$	26.8911	0.926727
$843$	−98.9529	−3.40812
$844$	49.7088	1.71105
$845$	9.82811	0.338097
$846$	56.1286	1.92974
$847$	17.9399	0.616422
$848$	−43.6441	−1.49874
$849$	52.9084	1.81581
$850$	−75.5878	−2.59264
$851$	−4.77905	−0.163824
$852$	23.0313	0.789039
$853$	11.6789	0.399878	0.199939	−	0.979808i	$-0.435926\pi$
$853$	11.6789	0.399878	0.199939	+	0.979808i	$0.435926\pi$
$854$	−78.4693	−2.68517
$855$	15.3478	0.524884
$856$	−28.2710	−0.966282
$857$	−13.4442	−0.459245	−0.229623	−	0.973280i	$-0.573749\pi$
$857$	−13.4442	−0.459245	−0.229623	+	0.973280i	$0.573749\pi$
$858$	−65.0576	−2.22103
$859$	−48.0456	−1.63929	−0.819647	−	0.572869i	$-0.805830\pi$
$859$	−48.0456	−1.63929	−0.819647	+	0.572869i	$0.805830\pi$
$860$	11.7609	0.401044
$861$	−103.472	−3.52631
$862$	−33.7129	−1.14827
$863$	−8.48379	−0.288792	−0.144396	−	0.989520i	$-0.546124\pi$
$863$	−8.48379	−0.288792	−0.144396	+	0.989520i	$0.546124\pi$
$864$	46.9488	1.59723
$865$	23.3996	0.795611
$866$	−24.0834	−0.818388
$867$	−146.374	−4.97113
$868$	−15.7828	−0.535704
$869$	47.8301	1.62252
$870$	8.85354	0.300163
$871$	−14.8344	−0.502643
$872$	83.6688	2.83338
$873$	−91.7409	−3.10496
$874$	−29.2575	−0.989650
$875$	32.5208	1.09941
$876$	39.5081	1.33486
$877$	52.5717	1.77522	0.887610	−	0.460595i	$-0.152364\pi$
$877$	52.5717	1.77522	0.887610	+	0.460595i	$0.152364\pi$
$878$	102.140	3.44705
$879$	−24.1420	−0.814290
$880$	24.3985	0.822472
$881$	32.4210	1.09229	0.546145	−	0.837691i	$-0.316095\pi$
$881$	32.4210	1.09229	0.546145	+	0.837691i	$0.316095\pi$
$882$	−96.0898	−3.23551
$883$	−13.8072	−0.464648	−0.232324	−	0.972638i	$-0.574633\pi$
$883$	−13.8072	−0.464648	−0.232324	+	0.972638i	$0.574633\pi$
$884$	−65.0358	−2.18739
$885$	−33.1886	−1.11562
$886$	−60.8609	−2.04466
$887$	−32.3597	−1.08653	−0.543266	−	0.839561i	$-0.682813\pi$
$887$	−32.3597	−1.08653	−0.543266	+	0.839561i	$0.682813\pi$
$888$	13.8626	0.465199
$889$	2.86140	0.0959681
$890$	43.9187	1.47216
$891$	−123.242	−4.12877
$892$	−85.6572	−2.86802
$893$	5.07413	0.169799
$894$	99.5999	3.33112
$895$	−15.9884	−0.534434
$896$	55.8058	1.86434
$897$	41.8151	1.39617
$898$	−92.5524	−3.08851
$899$	1.07601	0.0358868
$900$	−131.253	−4.37510
$901$	60.1766	2.00477
$902$	91.6285	3.05090
$903$	29.3867	0.977929
$904$	37.8388	1.25850
$905$	3.58867	0.119291
$906$	−48.0526	−1.59644
$907$	−9.34932	−0.310439	−0.155220	−	0.987880i	$-0.549609\pi$
$907$	−9.34932	−0.310439	−0.155220	+	0.987880i	$0.549609\pi$
$908$	−90.4720	−3.00242
$909$	−29.7835	−0.987855
$910$	17.9035	0.593494
$911$	35.2811	1.16892	0.584458	−	0.811424i	$-0.301307\pi$
$911$	35.2811	1.16892	0.584458	+	0.811424i	$0.301307\pi$
$912$	33.8903	1.12222
$913$	−13.4251	−0.444307
$914$	−61.8927	−2.04723
$915$	32.2486	1.06611
$916$	−5.09013	−0.168183
$917$	−24.7728	−0.818069
$918$	−322.312	−10.6379
$919$	15.9231	0.525254	0.262627	−	0.964897i	$-0.415411\pi$
$919$	15.9231	0.525254	0.262627	+	0.964897i	$0.415411\pi$
$920$	−39.2703	−1.29470
$921$	99.2633	3.27084
$922$	84.4501	2.78122
$923$	−3.17518	−0.104512
$924$	195.646	6.43627
$925$	−2.84660	−0.0935956
$926$	−105.293	−3.46015
$927$	84.5923	2.77838
$928$	2.85258	0.0936406
$929$	−49.1647	−1.61304	−0.806520	−	0.591206i	$-0.798652\pi$
$929$	−49.1647	−1.61304	−0.806520	+	0.591206i	$0.798652\pi$
$930$	9.52646	0.312385
$931$	−8.68669	−0.284695
$932$	35.7209	1.17008
$933$	−100.257	−3.28228
$934$	65.6318	2.14754
$935$	−33.6407	−1.10017
$936$	−88.1208	−2.88032
$937$	−50.5393	−1.65105	−0.825524	−	0.564367i	$-0.809120\pi$
$937$	−50.5393	−1.65105	−0.825524	+	0.564367i	$0.809120\pi$
$938$	65.5205	2.13932
$939$	27.2193	0.888270
$940$	12.8190	0.418111
$941$	27.2219	0.887409	0.443705	−	0.896173i	$-0.353664\pi$
$941$	27.2219	0.887409	0.443705	+	0.896173i	$0.353664\pi$
$942$	−136.067	−4.43330
$943$	−58.8933	−1.91783
$944$	−53.2426	−1.73290
$945$	60.4123	1.96521
$946$	−26.0232	−0.846086
$947$	8.49315	0.275990	0.137995	−	0.990433i	$-0.455934\pi$
$947$	8.49315	0.275990	0.137995	+	0.990433i	$0.455934\pi$
$948$	167.845	5.45134
$949$	−5.44673	−0.176808
$950$	−17.4270	−0.565406
$951$	58.8440	1.90815
$952$	152.613	4.94623
$953$	−21.1970	−0.686637	−0.343318	−	0.939219i	$-0.611551\pi$
$953$	−21.1970	−0.686637	−0.343318	+	0.939219i	$0.611551\pi$
$954$	153.469	4.96875
$955$	1.27291	0.0411904
$956$	−2.10582	−0.0681072
$957$	−13.3383	−0.431166
$958$	−15.1394	−0.489132
$959$	75.7745	2.44688
$960$	−14.8748	−0.480081
$961$	−29.8422	−0.962652
$962$	−3.59719	−0.115978
$963$	39.6982	1.27926
$964$	16.8506	0.542720
$965$	18.4955	0.595390
$966$	−184.689	−5.94227
$967$	23.2548	0.747823	0.373911	−	0.927464i	$-0.378016\pi$
$967$	23.2548	0.747823	0.373911	+	0.927464i	$0.378016\pi$
$968$	−29.6188	−0.951984
$969$	−46.7280	−1.50112
$970$	−30.7730	−0.988061
$971$	−3.85840	−0.123822	−0.0619109	−	0.998082i	$-0.519719\pi$
$971$	−3.85840	−0.123822	−0.0619109	+	0.998082i	$0.519719\pi$
$972$	−221.795	−7.11408
$973$	3.43750	0.110201
$974$	20.7871	0.666061
$975$	24.9068	0.797656
$976$	51.7347	1.65599
$977$	20.2362	0.647414	0.323707	−	0.946157i	$-0.395071\pi$
$977$	20.2362	0.647414	0.323707	+	0.946157i	$0.395071\pi$
$978$	71.9735	2.30146
$979$	−66.1656	−2.11466
$980$	−21.9457	−0.701028
$981$	−117.488	−3.75110
$982$	−38.8218	−1.23885
$983$	−13.9480	−0.444873	−0.222436	−	0.974947i	$-0.571401\pi$
$983$	−13.9480	−0.444873	−0.222436	+	0.974947i	$0.571401\pi$
$984$	170.832	5.44593
$985$	13.7649	0.438587
$986$	−19.5835	−0.623665
$987$	32.0306	1.01955
$988$	−14.9942	−0.477028
$989$	16.7261	0.531860
$990$	−85.7943	−2.72672
$991$	12.2927	0.390491	0.195245	−	0.980754i	$-0.437450\pi$
$991$	12.2927	0.390491	0.195245	+	0.980754i	$0.437450\pi$
$992$	3.06940	0.0974534
$993$	−49.4863	−1.57040
$994$	14.0241	0.444819
$995$	−24.6364	−0.781026
$996$	−47.1113	−1.49278
$997$	−28.9414	−0.916582	−0.458291	−	0.888802i	$-0.651538\pi$
$997$	−28.9414	−0.916582	−0.458291	+	0.888802i	$0.651538\pi$
$998$	−57.9267	−1.83364
$999$	−12.1381	−0.384033

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4031.2.a.e.1.10	✓	103

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4031.2.a.e.1.10	✓	103	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:	\( N \)	\(=\)	\( 4031 = 29 \cdot 139 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4031.a (trivial)

\(f(q)\)	\(=\)	\(q-2.50341 q^{2} -3.31200 q^{3} +4.26704 q^{4} -1.06782 q^{5} +8.29127 q^{6} +3.43750 q^{7} -5.67533 q^{8} +7.96931 q^{9} +O(q^{10})\)	\(q-2.50341 q^{2} -3.31200 q^{3} +4.26704 q^{4} -1.06782 q^{5} +8.29127 q^{6} +3.43750 q^{7} -5.67533 q^{8} +7.96931 q^{9} +2.67318 q^{10} -4.02727 q^{11} -14.1324 q^{12} +1.94835 q^{13} -8.60547 q^{14} +3.53660 q^{15} +5.67357 q^{16} -7.82274 q^{17} -19.9504 q^{18} -1.80355 q^{19} -4.55641 q^{20} -11.3850 q^{21} +10.0819 q^{22} -6.48003 q^{23} +18.7967 q^{24} -3.85977 q^{25} -4.87751 q^{26} -16.4583 q^{27} +14.6680 q^{28} -1.00000 q^{29} -8.85354 q^{30} -1.07601 q^{31} -2.85258 q^{32} +13.3383 q^{33} +19.5835 q^{34} -3.67062 q^{35} +34.0054 q^{36} +0.737505 q^{37} +4.51503 q^{38} -6.45292 q^{39} +6.06020 q^{40} +9.08843 q^{41} +28.5013 q^{42} -2.58118 q^{43} -17.1845 q^{44} -8.50975 q^{45} +16.2221 q^{46} -2.81340 q^{47} -18.7908 q^{48} +4.81643 q^{49} +9.66257 q^{50} +25.9089 q^{51} +8.31368 q^{52} -7.69253 q^{53} +41.2019 q^{54} +4.30038 q^{55} -19.5090 q^{56} +5.97336 q^{57} +2.50341 q^{58} -9.38433 q^{59} +15.0908 q^{60} +9.11854 q^{61} +2.69368 q^{62} +27.3945 q^{63} -4.20596 q^{64} -2.08048 q^{65} -33.3911 q^{66} -7.61382 q^{67} -33.3799 q^{68} +21.4618 q^{69} +9.18905 q^{70} -1.62968 q^{71} -45.2285 q^{72} -2.79556 q^{73} -1.84627 q^{74} +12.7835 q^{75} -7.69584 q^{76} -13.8437 q^{77} +16.1543 q^{78} -11.8766 q^{79} -6.05832 q^{80} +30.6020 q^{81} -22.7520 q^{82} +3.33356 q^{83} -48.5803 q^{84} +8.35324 q^{85} +6.46175 q^{86} +3.31200 q^{87} +22.8561 q^{88} +16.4294 q^{89} +21.3034 q^{90} +6.69745 q^{91} -27.6506 q^{92} +3.56373 q^{93} +7.04309 q^{94} +1.92586 q^{95} +9.44774 q^{96} -11.5118 q^{97} -12.0575 q^{98} -32.0945 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 103 q + q^{2} + 2 q^{3} + 127 q^{4} + 9 q^{5} + 19 q^{6} + 18 q^{7} + 149 q^{9}+O(q^{10}) \) 103 * q + q^2 + 2 * q^3 + 127 * q^4 + 9 * q^5 + 19 * q^6 + 18 * q^7 + 149 * q^9	\( 103 q + q^{2} + 2 q^{3} + 127 q^{4} + 9 q^{5} + 19 q^{6} + 18 q^{7} + 149 q^{9} + 20 q^{10} + 9 q^{11} + 36 q^{13} - 10 q^{14} + 16 q^{15} + 179 q^{16} + 21 q^{17} + 7 q^{18} + 42 q^{19} + 24 q^{20} + 28 q^{21} + 32 q^{22} + 25 q^{23} + 68 q^{24} + 194 q^{25} - 5 q^{26} + 14 q^{27} + 59 q^{28} - 103 q^{29} + 84 q^{30} + 34 q^{31} + 11 q^{32} + 42 q^{33} + 54 q^{34} + 35 q^{35} + 214 q^{36} + 34 q^{37} + 9 q^{38} + 23 q^{39} + 46 q^{40} + 16 q^{41} + 13 q^{42} + 68 q^{43} - 6 q^{44} + 25 q^{45} + 60 q^{46} + 6 q^{47} + 5 q^{48} + 257 q^{49} - 51 q^{50} + 68 q^{51} + 37 q^{52} + 35 q^{53} + 30 q^{54} + 66 q^{55} - 54 q^{56} + 78 q^{57} - q^{58} + 10 q^{59} - 24 q^{60} + 70 q^{61} + 29 q^{62} + 26 q^{63} + 276 q^{64} + 95 q^{65} + 77 q^{66} + 71 q^{67} - 21 q^{68} - 20 q^{69} + 48 q^{70} + 32 q^{71} + 32 q^{72} + 94 q^{73} + 35 q^{74} + 7 q^{75} + 134 q^{76} + 17 q^{77} + 58 q^{78} + 110 q^{79} + 78 q^{80} + 267 q^{81} - 71 q^{82} + 35 q^{83} + 96 q^{84} + 71 q^{85} + 33 q^{86} - 2 q^{87} + 100 q^{88} + 22 q^{89} - 134 q^{90} + 108 q^{91} - 11 q^{92} + 78 q^{93} + 90 q^{94} + 12 q^{95} + 177 q^{96} + 44 q^{97} - 18 q^{98} + 83 q^{99}+O(q^{100}) \) 103 * q + q^2 + 2 * q^3 + 127 * q^4 + 9 * q^5 + 19 * q^6 + 18 * q^7 + 149 * q^9 + 20 * q^10 + 9 * q^11 + 36 * q^13 - 10 * q^14 + 16 * q^15 + 179 * q^16 + 21 * q^17 + 7 * q^18 + 42 * q^19 + 24 * q^20 + 28 * q^21 + 32 * q^22 + 25 * q^23 + 68 * q^24 + 194 * q^25 - 5 * q^26 + 14 * q^27 + 59 * q^28 - 103 * q^29 + 84 * q^30 + 34 * q^31 + 11 * q^32 + 42 * q^33 + 54 * q^34 + 35 * q^35 + 214 * q^36 + 34 * q^37 + 9 * q^38 + 23 * q^39 + 46 * q^40 + 16 * q^41 + 13 * q^42 + 68 * q^43 - 6 * q^44 + 25 * q^45 + 60 * q^46 + 6 * q^47 + 5 * q^48 + 257 * q^49 - 51 * q^50 + 68 * q^51 + 37 * q^52 + 35 * q^53 + 30 * q^54 + 66 * q^55 - 54 * q^56 + 78 * q^57 - q^58 + 10 * q^59 - 24 * q^60 + 70 * q^61 + 29 * q^62 + 26 * q^63 + 276 * q^64 + 95 * q^65 + 77 * q^66 + 71 * q^67 - 21 * q^68 - 20 * q^69 + 48 * q^70 + 32 * q^71 + 32 * q^72 + 94 * q^73 + 35 * q^74 + 7 * q^75 + 134 * q^76 + 17 * q^77 + 58 * q^78 + 110 * q^79 + 78 * q^80 + 267 * q^81 - 71 * q^82 + 35 * q^83 + 96 * q^84 + 71 * q^85 + 33 * q^86 - 2 * q^87 + 100 * q^88 + 22 * q^89 - 134 * q^90 + 108 * q^91 - 11 * q^92 + 78 * q^93 + 90 * q^94 + 12 * q^95 + 177 * q^96 + 44 * q^97 - 18 * q^98 + 83 * q^99

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