LMFDB - Embedded newform 8023.2.a.b.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8023,2,Mod(1,8023)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8023, 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("8023.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8023 = 71 \cdot 113 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8023.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:	$64.0639775417$
Analytic rank:	$1$
Dimension:	$155$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	8023.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.78061 q^{2} -3.43962 q^{3} +5.73182 q^{4} -0.171450 q^{5} +9.56425 q^{6} -3.12589 q^{7} -10.3767 q^{8} +8.83098 q^{9} +O(q^{10})$	\(q-2.78061 q^{2} -3.43962 q^{3} +5.73182 q^{4} -0.171450 q^{5} +9.56425 q^{6} -3.12589 q^{7} -10.3767 q^{8} +8.83098 q^{9} +0.476736 q^{10} -3.15975 q^{11} -19.7153 q^{12} -5.26956 q^{13} +8.69188 q^{14} +0.589723 q^{15} +17.3901 q^{16} -6.22324 q^{17} -24.5555 q^{18} -5.89812 q^{19} -0.982720 q^{20} +10.7519 q^{21} +8.78605 q^{22} -0.179756 q^{23} +35.6920 q^{24} -4.97060 q^{25} +14.6526 q^{26} -20.0563 q^{27} -17.9170 q^{28} -2.52338 q^{29} -1.63979 q^{30} +3.52678 q^{31} -27.6016 q^{32} +10.8683 q^{33} +17.3044 q^{34} +0.535933 q^{35} +50.6175 q^{36} -3.98421 q^{37} +16.4004 q^{38} +18.1253 q^{39} +1.77909 q^{40} -9.52938 q^{41} -29.8968 q^{42} +10.0307 q^{43} -18.1111 q^{44} -1.51407 q^{45} +0.499831 q^{46} -1.11234 q^{47} -59.8152 q^{48} +2.77116 q^{49} +13.8213 q^{50} +21.4056 q^{51} -30.2041 q^{52} +8.41924 q^{53} +55.7690 q^{54} +0.541740 q^{55} +32.4365 q^{56} +20.2873 q^{57} +7.01654 q^{58} -5.49947 q^{59} +3.38018 q^{60} +6.48555 q^{61} -9.80662 q^{62} -27.6046 q^{63} +41.9693 q^{64} +0.903466 q^{65} -30.2207 q^{66} +15.9543 q^{67} -35.6705 q^{68} +0.618291 q^{69} -1.49022 q^{70} +1.00000 q^{71} -91.6368 q^{72} -11.8778 q^{73} +11.0786 q^{74} +17.0970 q^{75} -33.8069 q^{76} +9.87703 q^{77} -50.3994 q^{78} +10.6835 q^{79} -2.98153 q^{80} +42.4933 q^{81} +26.4975 q^{82} -0.972012 q^{83} +61.6277 q^{84} +1.06697 q^{85} -27.8914 q^{86} +8.67945 q^{87} +32.7879 q^{88} -2.57727 q^{89} +4.21005 q^{90} +16.4720 q^{91} -1.03033 q^{92} -12.1308 q^{93} +3.09299 q^{94} +1.01123 q^{95} +94.9390 q^{96} -6.93598 q^{97} -7.70553 q^{98} -27.9037 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 155 q - 21 q^{2} - 16 q^{3} + 151 q^{4} - 26 q^{5} - 10 q^{6} - 40 q^{7} - 57 q^{8} + 135 q^{9}+O(q^{10}) $ 155 * q - 21 * q^2 - 16 * q^3 + 151 * q^4 - 26 * q^5 - 10 * q^6 - 40 * q^7 - 57 * q^8 + 135 * q^9	\( 155 q - 21 q^{2} - 16 q^{3} + 151 q^{4} - 26 q^{5} - 10 q^{6} - 40 q^{7} - 57 q^{8} + 135 q^{9} - 2 q^{10} - 24 q^{11} - 32 q^{12} - 62 q^{13} - 18 q^{14} - 12 q^{15} + 155 q^{16} - 129 q^{17} - 42 q^{18} - 18 q^{19} - 59 q^{20} - 45 q^{21} - 17 q^{22} - 38 q^{23} - 27 q^{24} + 129 q^{25} - 44 q^{26} - 43 q^{27} - 100 q^{28} - 52 q^{29} - 39 q^{30} - 56 q^{31} - 145 q^{32} - 126 q^{33} - q^{34} - 49 q^{35} + 131 q^{36} - 30 q^{37} - 91 q^{38} - 29 q^{39} - 5 q^{40} - 163 q^{41} - 80 q^{42} - 15 q^{43} - 118 q^{44} - 66 q^{45} + 2 q^{46} - 111 q^{47} - 89 q^{48} + 101 q^{49} - 121 q^{50} + 5 q^{51} - 111 q^{52} - 93 q^{53} - 68 q^{54} - 60 q^{55} - 27 q^{56} - 106 q^{57} + 16 q^{58} - 79 q^{59} - 103 q^{60} - 74 q^{61} - 102 q^{62} - 118 q^{63} + 175 q^{64} - 109 q^{65} + 65 q^{66} - 18 q^{67} - 346 q^{68} - 39 q^{69} + 32 q^{70} + 155 q^{71} - 203 q^{72} - 108 q^{73} - 87 q^{74} - 22 q^{75} - 16 q^{76} - 121 q^{77} - 75 q^{78} - 6 q^{79} - 136 q^{80} + 107 q^{81} - 30 q^{82} - 116 q^{83} - 5 q^{84} - 53 q^{85} + 8 q^{86} - 100 q^{87} - 43 q^{88} - 189 q^{89} - 76 q^{90} + 14 q^{91} - 99 q^{92} - 72 q^{93} + 17 q^{94} - 18 q^{95} - 50 q^{96} - 184 q^{97} - 249 q^{98} - 114 q^{99}+O(q^{100}) \) 155 * q - 21 * q^2 - 16 * q^3 + 151 * q^4 - 26 * q^5 - 10 * q^6 - 40 * q^7 - 57 * q^8 + 135 * q^9 - 2 * q^10 - 24 * q^11 - 32 * q^12 - 62 * q^13 - 18 * q^14 - 12 * q^15 + 155 * q^16 - 129 * q^17 - 42 * q^18 - 18 * q^19 - 59 * q^20 - 45 * q^21 - 17 * q^22 - 38 * q^23 - 27 * q^24 + 129 * q^25 - 44 * q^26 - 43 * q^27 - 100 * q^28 - 52 * q^29 - 39 * q^30 - 56 * q^31 - 145 * q^32 - 126 * q^33 - q^34 - 49 * q^35 + 131 * q^36 - 30 * q^37 - 91 * q^38 - 29 * q^39 - 5 * q^40 - 163 * q^41 - 80 * q^42 - 15 * q^43 - 118 * q^44 - 66 * q^45 + 2 * q^46 - 111 * q^47 - 89 * q^48 + 101 * q^49 - 121 * q^50 + 5 * q^51 - 111 * q^52 - 93 * q^53 - 68 * q^54 - 60 * q^55 - 27 * q^56 - 106 * q^57 + 16 * q^58 - 79 * q^59 - 103 * q^60 - 74 * q^61 - 102 * q^62 - 118 * q^63 + 175 * q^64 - 109 * q^65 + 65 * q^66 - 18 * q^67 - 346 * q^68 - 39 * q^69 + 32 * q^70 + 155 * q^71 - 203 * q^72 - 108 * q^73 - 87 * q^74 - 22 * q^75 - 16 * q^76 - 121 * q^77 - 75 * q^78 - 6 * q^79 - 136 * q^80 + 107 * q^81 - 30 * q^82 - 116 * q^83 - 5 * q^84 - 53 * q^85 + 8 * q^86 - 100 * q^87 - 43 * q^88 - 189 * q^89 - 76 * q^90 + 14 * q^91 - 99 * q^92 - 72 * q^93 + 17 * q^94 - 18 * q^95 - 50 * q^96 - 184 * q^97 - 249 * q^98 - 114 * 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 $

$2$	−2.78061	−1.96619	−0.983096	−	0.183093i	$-0.941389\pi$
$2$	−2.78061	−1.96619	−0.983096	+	0.183093i	$0.941389\pi$
$3$	−3.43962	−1.98586	−0.992932	−	0.118681i	$-0.962134\pi$
$3$	−3.43962	−1.98586	−0.992932	+	0.118681i	$0.962134\pi$
$4$	5.73182	2.86591
$5$	−0.171450	−0.0766748	−0.0383374	−	0.999265i	$-0.512206\pi$
$5$	−0.171450	−0.0766748	−0.0383374	+	0.999265i	$0.512206\pi$
$6$	9.56425	3.90459
$7$	−3.12589	−1.18147	−0.590737	−	0.806864i	$-0.701163\pi$
$7$	−3.12589	−1.18147	−0.590737	+	0.806864i	$0.701163\pi$
$8$	−10.3767	−3.66873
$9$	8.83098	2.94366
$10$	0.476736	0.150757
$11$	−3.15975	−0.952701	−0.476351	−	0.879255i	$-0.658041\pi$
$11$	−3.15975	−0.952701	−0.476351	+	0.879255i	$0.658041\pi$
$12$	−19.7153	−5.69131
$13$	−5.26956	−1.46151	−0.730756	−	0.682638i	$-0.760832\pi$
$13$	−5.26956	−1.46151	−0.730756	+	0.682638i	$0.760832\pi$
$14$	8.69188	2.32300
$15$	0.589723	0.152266
$16$	17.3901	4.34752
$17$	−6.22324	−1.50936	−0.754679	−	0.656094i	$-0.772207\pi$
$17$	−6.22324	−1.50936	−0.754679	+	0.656094i	$0.772207\pi$
$18$	−24.5555	−5.78780
$19$	−5.89812	−1.35312	−0.676560	−	0.736387i	$-0.736530\pi$
$19$	−5.89812	−1.35312	−0.676560	+	0.736387i	$0.736530\pi$
$20$	−0.982720	−0.219743
$21$	10.7519	2.34625
$22$	8.78605	1.87319
$23$	−0.179756	−0.0374816	−0.0187408	−	0.999824i	$-0.505966\pi$
$23$	−0.179756	−0.0374816	−0.0187408	+	0.999824i	$0.505966\pi$
$24$	35.6920	7.28560
$25$	−4.97060	−0.994121
$26$	14.6526	2.87361
$27$	−20.0563	−3.85985
$28$	−17.9170	−3.38599
$29$	−2.52338	−0.468579	−0.234290	−	0.972167i	$-0.575276\pi$
$29$	−2.52338	−0.468579	−0.234290	+	0.972167i	$0.575276\pi$
$30$	−1.63979	−0.299383
$31$	3.52678	0.633429	0.316714	−	0.948521i	$-0.397420\pi$
$31$	3.52678	0.633429	0.316714	+	0.948521i	$0.397420\pi$
$32$	−27.6016	−4.87932
$33$	10.8683	1.89194
$34$	17.3044	2.96769
$35$	0.535933	0.0905892
$36$	50.6175	8.43626
$37$	−3.98421	−0.655001	−0.327500	−	0.944851i	$-0.606206\pi$
$37$	−3.98421	−0.655001	−0.327500	+	0.944851i	$0.606206\pi$
$38$	16.4004	2.66049
$39$	18.1253	2.90237
$40$	1.77909	0.281299
$41$	−9.52938	−1.48824	−0.744120	−	0.668046i	$-0.767131\pi$
$41$	−9.52938	−1.48824	−0.744120	+	0.668046i	$0.767131\pi$
$42$	−29.8968	−4.61317
$43$	10.0307	1.52966	0.764831	−	0.644231i	$-0.222823\pi$
$43$	10.0307	1.52966	0.764831	+	0.644231i	$0.222823\pi$
$44$	−18.1111	−2.73035
$45$	−1.51407	−0.225704
$46$	0.499831	0.0736960
$47$	−1.11234	−0.162252	−0.0811258	−	0.996704i	$-0.525852\pi$
$47$	−1.11234	−0.162252	−0.0811258	+	0.996704i	$0.525852\pi$
$48$	−59.8152	−8.63359
$49$	2.77116	0.395880
$50$	13.8213	1.95463
$51$	21.4056	2.99738
$52$	−30.2041	−4.18856
$53$	8.41924	1.15647	0.578236	−	0.815870i	$-0.303741\pi$
$53$	8.41924	1.15647	0.578236	+	0.815870i	$0.303741\pi$
$54$	55.7690	7.58919
$55$	0.541740	0.0730481
$56$	32.4365	4.33451
$57$	20.2873	2.68711
$58$	7.01654	0.921316
$59$	−5.49947	−0.715970	−0.357985	−	0.933727i	$-0.616536\pi$
$59$	−5.49947	−0.715970	−0.357985	+	0.933727i	$0.616536\pi$
$60$	3.38018	0.436379
$61$	6.48555	0.830390	0.415195	−	0.909732i	$-0.363713\pi$
$61$	6.48555	0.830390	0.415195	+	0.909732i	$0.363713\pi$
$62$	−9.80662	−1.24544
$63$	−27.6046	−3.47786
$64$	41.9693	5.24616
$65$	0.903466	0.112061
$66$	−30.2207	−3.71991
$67$	15.9543	1.94913	0.974565	−	0.224105i	$-0.0719458\pi$
$67$	15.9543	1.94913	0.974565	+	0.224105i	$0.0719458\pi$
$68$	−35.6705	−4.32568
$69$	0.618291	0.0744335
$70$	−1.49022	−0.178116
$71$	1.00000	0.118678
$71$	1.00000	0.118678
$72$	−91.6368	−10.7995
$73$	−11.8778	−1.39019	−0.695096	−	0.718917i	$-0.744638\pi$
$73$	−11.8778	−1.39019	−0.695096	+	0.718917i	$0.744638\pi$
$74$	11.0786	1.28786
$75$	17.0970	1.97419
$76$	−33.8069	−3.87792
$77$	9.87703	1.12559
$78$	−50.3994	−5.70661
$79$	10.6835	1.20198	0.600992	−	0.799255i	$-0.294772\pi$
$79$	10.6835	1.20198	0.600992	+	0.799255i	$0.294772\pi$
$80$	−2.98153	−0.333345
$81$	42.4933	4.72147
$82$	26.4975	2.92616
$83$	−0.972012	−0.106692	−0.0533461	−	0.998576i	$-0.516989\pi$
$83$	−0.972012	−0.106692	−0.0533461	+	0.998576i	$0.516989\pi$
$84$	61.6277	6.72413
$85$	1.06697	0.115730
$86$	−27.8914	−3.00761
$87$	8.67945	0.930535
$88$	32.7879	3.49521
$89$	−2.57727	−0.273190	−0.136595	−	0.990627i	$-0.543616\pi$
$89$	−2.57727	−0.273190	−0.136595	+	0.990627i	$0.543616\pi$
$90$	4.21005	0.443778
$91$	16.4720	1.72674
$92$	−1.03033	−0.107419
$93$	−12.1308	−1.25790
$94$	3.09299	0.319018
$95$	1.01123	0.103750
$96$	94.9390	9.68968
$97$	−6.93598	−0.704242	−0.352121	−	0.935955i	$-0.614539\pi$
$97$	−6.93598	−0.704242	−0.352121	+	0.935955i	$0.614539\pi$
$98$	−7.70553	−0.778376
$99$	−27.9037	−2.80443
$100$	−28.4906	−2.84906
$101$	2.60851	0.259556	0.129778	−	0.991543i	$-0.458574\pi$
$101$	2.60851	0.259556	0.129778	+	0.991543i	$0.458574\pi$
$102$	−59.5207	−5.89342
$103$	13.3570	1.31610	0.658050	−	0.752974i	$-0.271382\pi$
$103$	13.3570	1.31610	0.658050	+	0.752974i	$0.271382\pi$
$104$	54.6808	5.36190
$105$	−1.84341	−0.179898
$106$	−23.4107	−2.27384
$107$	7.65945	0.740467	0.370234	−	0.928939i	$-0.379278\pi$
$107$	7.65945	0.740467	0.370234	+	0.928939i	$0.379278\pi$
$108$	−114.959	−11.0620
$109$	−20.5905	−1.97221	−0.986104	−	0.166127i	$-0.946874\pi$
$109$	−20.5905	−1.97221	−0.986104	+	0.166127i	$0.946874\pi$
$110$	−1.50637	−0.143627
$111$	13.7042	1.30074
$112$	−54.3594	−5.13648
$113$	1.00000	0.0940721
$113$	1.00000	0.0940721
$114$	−56.4111	−5.28338
$115$	0.0308191	0.00287389
$116$	−14.4635	−1.34290
$117$	−46.5354	−4.30220
$118$	15.2919	1.40773
$119$	19.4531	1.78327
$120$	−6.11940	−0.558622
$121$	−1.01596	−0.0923600
$122$	−18.0338	−1.63271
$123$	32.7774	2.95544
$124$	20.2149	1.81535
$125$	1.70946	0.152899
$126$	76.7578	6.83813
$127$	−8.53257	−0.757143	−0.378571	−	0.925572i	$-0.623585\pi$
$127$	−8.53257	−0.757143	−0.378571	+	0.925572i	$0.623585\pi$
$128$	−61.4972	−5.43563
$129$	−34.5017	−3.03770
$130$	−2.51219	−0.220334
$131$	−0.241773	−0.0211238	−0.0105619	−	0.999944i	$-0.503362\pi$
$131$	−0.241773	−0.0211238	−0.0105619	+	0.999944i	$0.503362\pi$
$132$	62.2954	5.42212
$133$	18.4368	1.59868
$134$	−44.3628	−3.83236
$135$	3.43866	0.295953
$136$	64.5770	5.53743
$137$	14.2107	1.21410	0.607051	−	0.794663i	$-0.292352\pi$
$137$	14.2107	1.21410	0.607051	+	0.794663i	$0.292352\pi$
$138$	−1.71923	−0.146350
$139$	8.98059	0.761724	0.380862	−	0.924632i	$-0.375627\pi$
$139$	8.98059	0.761724	0.380862	+	0.924632i	$0.375627\pi$
$140$	3.07187	0.259620
$141$	3.82603	0.322210
$142$	−2.78061	−0.233344
$143$	16.6505	1.39239
$144$	153.571	12.7976
$145$	0.432633	0.0359282
$146$	33.0276	2.73338
$147$	−9.53174	−0.786165
$148$	−22.8368	−1.87717
$149$	−16.6981	−1.36796	−0.683982	−	0.729499i	$-0.739753\pi$
$149$	−16.6981	−1.36796	−0.683982	+	0.729499i	$0.739753\pi$
$150$	−47.5401	−3.88163
$151$	−15.9914	−1.30136	−0.650679	−	0.759352i	$-0.725516\pi$
$151$	−15.9914	−1.30136	−0.650679	+	0.759352i	$0.725516\pi$
$152$	61.2032	4.96424
$153$	−54.9573	−4.44304
$154$	−27.4642	−2.21313
$155$	−0.604667	−0.0485680
$156$	103.891	8.31792
$157$	17.2562	1.37720	0.688599	−	0.725143i	$-0.258226\pi$
$157$	17.2562	1.37720	0.688599	+	0.725143i	$0.258226\pi$
$158$	−29.7066	−2.36333
$159$	−28.9590	−2.29660
$160$	4.73230	0.374121
$161$	0.561895	0.0442836
$162$	−118.157	−9.28332
$163$	2.58884	0.202774	0.101387	−	0.994847i	$-0.467672\pi$
$163$	2.58884	0.202774	0.101387	+	0.994847i	$0.467672\pi$
$164$	−54.6207	−4.26516
$165$	−1.86338	−0.145064
$166$	2.70279	0.209777
$167$	−6.34830	−0.491246	−0.245623	−	0.969365i	$-0.578993\pi$
$167$	−6.34830	−0.491246	−0.245623	+	0.969365i	$0.578993\pi$
$168$	−111.569	−8.60775
$169$	14.7683	1.13602
$170$	−2.96684	−0.227547
$171$	−52.0861	−3.98313
$172$	57.4939	4.38387
$173$	−10.1494	−0.771648	−0.385824	−	0.922572i	$-0.626083\pi$
$173$	−10.1494	−0.771648	−0.385824	+	0.922572i	$0.626083\pi$
$174$	−24.1342	−1.82961
$175$	15.5375	1.17453
$176$	−54.9484	−4.14189
$177$	18.9161	1.42182
$178$	7.16638	0.537143
$179$	−6.58182	−0.491948	−0.245974	−	0.969276i	$-0.579108\pi$
$179$	−6.58182	−0.491948	−0.245974	+	0.969276i	$0.579108\pi$
$180$	−8.67838	−0.646848
$181$	3.61424	0.268645	0.134322	−	0.990938i	$-0.457114\pi$
$181$	3.61424	0.268645	0.134322	+	0.990938i	$0.457114\pi$
$182$	−45.8024	−3.39510
$183$	−22.3078	−1.64904
$184$	1.86528	0.137510
$185$	0.683093	0.0502220
$186$	33.7310	2.47328
$187$	19.6639	1.43797
$188$	−6.37573	−0.464998
$189$	62.6938	4.56031
$190$	−2.81185	−0.203993
$191$	−14.2142	−1.02851	−0.514253	−	0.857639i	$-0.671931\pi$
$191$	−14.2142	−1.02851	−0.514253	+	0.857639i	$0.671931\pi$
$192$	−144.358	−10.4182
$193$	−0.748658	−0.0538896	−0.0269448	−	0.999637i	$-0.508578\pi$
$193$	−0.748658	−0.0538896	−0.0269448	+	0.999637i	$0.508578\pi$
$194$	19.2863	1.38467
$195$	−3.10758	−0.222538
$196$	15.8838	1.13456
$197$	13.4701	0.959705	0.479853	−	0.877349i	$-0.340690\pi$
$197$	13.4701	0.959705	0.479853	+	0.877349i	$0.340690\pi$
$198$	77.5895	5.51404
$199$	7.05861	0.500371	0.250186	−	0.968198i	$-0.419508\pi$
$199$	7.05861	0.500371	0.250186	+	0.968198i	$0.419508\pi$
$200$	51.5787	3.64716
$201$	−54.8768	−3.87071
$202$	−7.25325	−0.510337
$203$	7.88779	0.553614
$204$	122.693	8.59022
$205$	1.63381	0.114110
$206$	−37.1405	−2.58770
$207$	−1.58742	−0.110333
$208$	−91.6380	−6.35395
$209$	18.6366	1.28912
$210$	5.12580	0.353714
$211$	7.14699	0.492019	0.246010	−	0.969267i	$-0.420881\pi$
$211$	7.14699	0.492019	0.246010	+	0.969267i	$0.420881\pi$
$212$	48.2575	3.31434
$213$	−3.43962	−0.235679
$214$	−21.2980	−1.45590
$215$	−1.71976	−0.117286
$216$	208.119	14.1607
$217$	−11.0243	−0.748380
$218$	57.2541	3.87774
$219$	40.8551	2.76074
$220$	3.10515	0.209349
$221$	32.7937	2.20595
$222$	−38.1060	−2.55751
$223$	−7.48659	−0.501339	−0.250669	−	0.968073i	$-0.580651\pi$
$223$	−7.48659	−0.501339	−0.250669	+	0.968073i	$0.580651\pi$
$224$	86.2795	5.76479
$225$	−43.8953	−2.92635
$226$	−2.78061	−0.184964
$227$	17.7279	1.17664	0.588321	−	0.808628i	$-0.299789\pi$
$227$	17.7279	1.17664	0.588321	+	0.808628i	$0.299789\pi$
$228$	116.283	7.70102
$229$	−0.708547	−0.0468221	−0.0234111	−	0.999726i	$-0.507453\pi$
$229$	−0.708547	−0.0468221	−0.0234111	+	0.999726i	$0.507453\pi$
$230$	−0.0856960	−0.00565063
$231$	−33.9732	−2.23527
$232$	26.1844	1.71909
$233$	10.1450	0.664622	0.332311	−	0.943170i	$-0.392172\pi$
$233$	10.1450	0.664622	0.332311	+	0.943170i	$0.392172\pi$
$234$	129.397	8.45894
$235$	0.190711	0.0124406
$236$	−31.5219	−2.05190
$237$	−36.7470	−2.38698
$238$	−54.0917	−3.50624
$239$	−2.57255	−0.166404	−0.0832021	−	0.996533i	$-0.526515\pi$
$239$	−2.57255	−0.166404	−0.0832021	+	0.996533i	$0.526515\pi$
$240$	10.2553	0.661978
$241$	−14.3610	−0.925074	−0.462537	−	0.886600i	$-0.653061\pi$
$241$	−14.3610	−0.925074	−0.462537	+	0.886600i	$0.653061\pi$
$242$	2.82499	0.181597
$243$	−85.9916	−5.51636
$244$	37.1740	2.37982
$245$	−0.475116	−0.0303540
$246$	−91.1414	−5.81097
$247$	31.0805	1.97760
$248$	−36.5965	−2.32388
$249$	3.34335	0.211876
$250$	−4.75335	−0.300628
$251$	−2.05933	−0.129984	−0.0649919	−	0.997886i	$-0.520702\pi$
$251$	−2.05933	−0.129984	−0.0649919	+	0.997886i	$0.520702\pi$
$252$	−158.225	−9.96722
$253$	0.567983	0.0357088
$254$	23.7258	1.48869
$255$	−3.66999	−0.229823
$256$	87.0613	5.44133
$257$	2.45428	0.153094	0.0765468	−	0.997066i	$-0.475611\pi$
$257$	2.45428	0.153094	0.0765468	+	0.997066i	$0.475611\pi$
$258$	95.9358	5.97270
$259$	12.4542	0.773866
$260$	5.17850	0.321157
$261$	−22.2839	−1.37934
$262$	0.672278	0.0415334
$263$	−13.4371	−0.828569	−0.414284	−	0.910148i	$-0.635968\pi$
$263$	−13.4371	−0.828569	−0.414284	+	0.910148i	$0.635968\pi$
$264$	−112.778	−6.94101
$265$	−1.44348	−0.0886722
$266$	−51.2657	−3.14330
$267$	8.86481	0.542518
$268$	91.4472	5.58603
$269$	−0.0589899	−0.00359668	−0.00179834	−	0.999998i	$-0.500572\pi$
$269$	−0.0589899	−0.00359668	−0.00179834	+	0.999998i	$0.500572\pi$
$270$	−9.56159	−0.581900
$271$	0.195300	0.0118637	0.00593183	−	0.999982i	$-0.498112\pi$
$271$	0.195300	0.0118637	0.00593183	+	0.999982i	$0.498112\pi$
$272$	−108.223	−6.56196
$273$	−56.6575	−3.42907
$274$	−39.5145	−2.38716
$275$	15.7059	0.947100
$276$	3.54393	0.213319
$277$	27.7006	1.66437	0.832183	−	0.554501i	$-0.187091\pi$
$277$	27.7006	1.66437	0.832183	+	0.554501i	$0.187091\pi$
$278$	−24.9716	−1.49769
$279$	31.1449	1.86460
$280$	−5.56124	−0.332347
$281$	−6.02831	−0.359619	−0.179809	−	0.983701i	$-0.557548\pi$
$281$	−6.02831	−0.359619	−0.179809	+	0.983701i	$0.557548\pi$
$282$	−10.6387	−0.633526
$283$	25.5315	1.51769	0.758846	−	0.651270i	$-0.225763\pi$
$283$	25.5315	1.51769	0.758846	+	0.651270i	$0.225763\pi$
$284$	5.73182	0.340121
$285$	−3.47825	−0.206034
$286$	−46.2986	−2.73770
$287$	29.7878	1.75832
$288$	−243.749	−14.3631
$289$	21.7287	1.27816
$290$	−1.20299	−0.0706417
$291$	23.8571	1.39853
$292$	−68.0814	−3.98416
$293$	−29.8893	−1.74615	−0.873075	−	0.487587i	$-0.837877\pi$
$293$	−29.8893	−1.74615	−0.873075	+	0.487587i	$0.837877\pi$
$294$	26.5041	1.54575
$295$	0.942883	0.0548968
$296$	41.3431	2.40302
$297$	63.3731	3.67728
$298$	46.4310	2.68968
$299$	0.947233	0.0547799
$300$	97.9968	5.65785
$301$	−31.3547	−1.80725
$302$	44.4658	2.55872
$303$	−8.97227	−0.515443
$304$	−102.569	−5.88272
$305$	−1.11195	−0.0636699
$306$	152.815	8.73586
$307$	14.3033	0.816335	0.408168	−	0.912907i	$-0.366168\pi$
$307$	14.3033	0.816335	0.408168	+	0.912907i	$0.366168\pi$
$308$	56.6133	3.22584
$309$	−45.9428	−2.61360
$310$	1.68134	0.0954940
$311$	5.91035	0.335145	0.167572	−	0.985860i	$-0.446407\pi$
$311$	5.91035	0.335145	0.167572	+	0.985860i	$0.446407\pi$
$312$	−188.081	−10.6480
$313$	34.0133	1.92255	0.961273	−	0.275597i	$-0.0888756\pi$
$313$	34.0133	1.92255	0.961273	+	0.275597i	$0.0888756\pi$
$314$	−47.9829	−2.70783
$315$	4.73281	0.266664
$316$	61.2356	3.44477
$317$	2.13347	0.119828	0.0599138	−	0.998204i	$-0.480917\pi$
$317$	2.13347	0.119828	0.0599138	+	0.998204i	$0.480917\pi$
$318$	80.5238	4.51555
$319$	7.97325	0.446416
$320$	−7.19563	−0.402248
$321$	−26.3456	−1.47047
$322$	−1.56241	−0.0870699
$323$	36.7054	2.04234
$324$	243.563	13.5313
$325$	26.1929	1.45292
$326$	−7.19857	−0.398692
$327$	70.8234	3.91654
$328$	98.8839	5.45995
$329$	3.47705	0.191696
$330$	5.18133	0.285223
$331$	17.1832	0.944472	0.472236	−	0.881472i	$-0.343447\pi$
$331$	17.1832	0.944472	0.472236	+	0.881472i	$0.343447\pi$
$332$	−5.57139	−0.305770
$333$	−35.1845	−1.92810
$334$	17.6522	0.965884
$335$	−2.73537	−0.149449
$336$	186.976	10.2004
$337$	−17.9036	−0.975269	−0.487635	−	0.873048i	$-0.662140\pi$
$337$	−17.9036	−0.975269	−0.487635	+	0.873048i	$0.662140\pi$
$338$	−41.0648	−2.23363
$339$	−3.43962	−0.186814
$340$	6.11570	0.331670
$341$	−11.1438	−0.603469
$342$	144.831	7.83159
$343$	13.2189	0.713752
$344$	−104.086	−5.61192
$345$	−0.106006	−0.00570717
$346$	28.2217	1.51721
$347$	−17.0502	−0.915303	−0.457651	−	0.889132i	$-0.651309\pi$
$347$	−17.0502	−0.915303	−0.457651	+	0.889132i	$0.651309\pi$
$348$	49.7490	2.66683
$349$	−3.66349	−0.196102	−0.0980510	−	0.995181i	$-0.531261\pi$
$349$	−3.66349	−0.196102	−0.0980510	+	0.995181i	$0.531261\pi$
$350$	−43.2039	−2.30935
$351$	105.688	5.64121
$352$	87.2143	4.64854
$353$	−23.1961	−1.23461	−0.617303	−	0.786726i	$-0.711775\pi$
$353$	−23.1961	−1.23461	−0.617303	+	0.786726i	$0.711775\pi$
$354$	−52.5983	−2.79557
$355$	−0.171450	−0.00909962
$356$	−14.7724	−0.782936
$357$	−66.9114	−3.54133
$358$	18.3015	0.967264
$359$	23.5473	1.24278	0.621388	−	0.783503i	$-0.286569\pi$
$359$	23.5473	1.24278	0.621388	+	0.783503i	$0.286569\pi$
$360$	15.7111	0.828049
$361$	15.7878	0.830935
$362$	−10.0498	−0.528207
$363$	3.49451	0.183414
$364$	94.4147	4.94867
$365$	2.03645	0.106593
$366$	62.0295	3.24233
$367$	16.5582	0.864333	0.432167	−	0.901794i	$-0.357749\pi$
$367$	16.5582	0.864333	0.432167	+	0.901794i	$0.357749\pi$
$368$	−3.12596	−0.162952
$369$	−84.1538	−4.38087
$370$	−1.89942	−0.0987461
$371$	−26.3176	−1.36634
$372$	−69.5314	−3.60504
$373$	−11.9909	−0.620867	−0.310433	−	0.950595i	$-0.600474\pi$
$373$	−11.9909	−0.620867	−0.310433	+	0.950595i	$0.600474\pi$
$374$	−54.6777	−2.82732
$375$	−5.87989	−0.303636
$376$	11.5425	0.595258
$377$	13.2971	0.684835
$378$	−174.327	−8.96643
$379$	24.4320	1.25499	0.627494	−	0.778621i	$-0.284081\pi$
$379$	24.4320	1.25499	0.627494	+	0.778621i	$0.284081\pi$
$380$	5.79619	0.297338
$381$	29.3488	1.50358
$382$	39.5243	2.02224
$383$	8.24670	0.421387	0.210693	−	0.977552i	$-0.432428\pi$
$383$	8.24670	0.421387	0.210693	+	0.977552i	$0.432428\pi$
$384$	211.527	10.7944
$385$	−1.69342	−0.0863045
$386$	2.08173	0.105957
$387$	88.5806	4.50280
$388$	−39.7557	−2.01829
$389$	29.1228	1.47659	0.738293	−	0.674480i	$-0.235632\pi$
$389$	29.1228	1.47659	0.738293	+	0.674480i	$0.235632\pi$
$390$	8.64098	0.437553
$391$	1.11866	0.0565732
$392$	−28.7556	−1.45238
$393$	0.831607	0.0419490
$394$	−37.4552	−1.88696
$395$	−1.83168	−0.0921618
$396$	−159.939	−8.03723
$397$	22.2570	1.11705	0.558523	−	0.829489i	$-0.311368\pi$
$397$	22.2570	1.11705	0.558523	+	0.829489i	$0.311368\pi$
$398$	−19.6273	−0.983826
$399$	−63.4157	−3.17476
$400$	−86.4392	−4.32196
$401$	26.2654	1.31163	0.655815	−	0.754922i	$-0.272325\pi$
$401$	26.2654	1.31163	0.655815	+	0.754922i	$0.272325\pi$
$402$	152.591	7.61055
$403$	−18.5846	−0.925764
$404$	14.9515	0.743864
$405$	−7.28547	−0.362018
$406$	−21.9329	−1.08851
$407$	12.5891	0.624020
$408$	−222.120	−10.9966
$409$	−1.85716	−0.0918305	−0.0459153	−	0.998945i	$-0.514620\pi$
$409$	−1.85716	−0.0918305	−0.0459153	+	0.998945i	$0.514620\pi$
$410$	−4.54300	−0.224363
$411$	−48.8794	−2.41104
$412$	76.5596	3.77182
$413$	17.1907	0.845899
$414$	4.41400	0.216936
$415$	0.166651	0.00818059
$416$	145.448	7.13119
$417$	−30.8898	−1.51268
$418$	−51.8212	−2.53466
$419$	−30.0672	−1.46888	−0.734439	−	0.678675i	$-0.762555\pi$
$419$	−30.0672	−1.46888	−0.734439	+	0.678675i	$0.762555\pi$
$420$	−10.5661	−0.515571
$421$	0.587294	0.0286229	0.0143115	−	0.999898i	$-0.495444\pi$
$421$	0.587294	0.0286229	0.0143115	+	0.999898i	$0.495444\pi$
$422$	−19.8730	−0.967404
$423$	−9.82306	−0.477614
$424$	−87.3643	−4.24278
$425$	30.9333	1.50048
$426$	9.56425	0.463390
$427$	−20.2731	−0.981084
$428$	43.9026	2.12211
$429$	−57.2714	−2.76509
$430$	4.78198	0.230608
$431$	18.3339	0.883113	0.441557	−	0.897233i	$-0.354426\pi$
$431$	18.3339	0.883113	0.441557	+	0.897233i	$0.354426\pi$
$432$	−348.781	−16.7808
$433$	1.16909	0.0561829	0.0280914	−	0.999605i	$-0.491057\pi$
$433$	1.16909	0.0561829	0.0280914	+	0.999605i	$0.491057\pi$
$434$	30.6544	1.47146
$435$	−1.48809	−0.0713486
$436$	−118.021	−5.65217
$437$	1.06022	0.0507172
$438$	−113.602	−5.42813
$439$	9.81717	0.468548	0.234274	−	0.972171i	$-0.424729\pi$
$439$	9.81717	0.468548	0.234274	+	0.972171i	$0.424729\pi$
$440$	−5.62149	−0.267994
$441$	24.4721	1.16534
$442$	−91.1867	−4.33731
$443$	−17.2539	−0.819756	−0.409878	−	0.912140i	$-0.634429\pi$
$443$	−17.2539	−0.819756	−0.409878	+	0.912140i	$0.634429\pi$
$444$	78.5498	3.72781
$445$	0.441872	0.0209467
$446$	20.8173	0.985728
$447$	57.4352	2.71659
$448$	−131.191	−6.19820
$449$	−0.0846730	−0.00399596	−0.00199798	−	0.999998i	$-0.500636\pi$
$449$	−0.0846730	−0.00399596	−0.00199798	+	0.999998i	$0.500636\pi$
$450$	122.056	5.75377
$451$	30.1105	1.41785
$452$	5.73182	0.269602
$453$	55.0042	2.58432
$454$	−49.2944	−2.31350
$455$	−2.82413	−0.132397
$456$	−210.516	−9.85830
$457$	−11.4048	−0.533494	−0.266747	−	0.963767i	$-0.585949\pi$
$457$	−11.4048	−0.533494	−0.266747	+	0.963767i	$0.585949\pi$
$458$	1.97020	0.0920612
$459$	124.815	5.82589
$460$	0.176649	0.00823632
$461$	−25.2998	−1.17833	−0.589164	−	0.808014i	$-0.700543\pi$
$461$	−25.2998	−1.17833	−0.589164	+	0.808014i	$0.700543\pi$
$462$	94.4664	4.39497
$463$	1.26029	0.0585708	0.0292854	−	0.999571i	$-0.490677\pi$
$463$	1.26029	0.0585708	0.0292854	+	0.999571i	$0.490677\pi$
$464$	−43.8817	−2.03716
$465$	2.07982	0.0964495
$466$	−28.2094	−1.30677
$467$	−14.0796	−0.651524	−0.325762	−	0.945452i	$-0.605621\pi$
$467$	−14.0796	−0.651524	−0.325762	+	0.945452i	$0.605621\pi$
$468$	−266.732	−12.3297
$469$	−49.8714	−2.30285
$470$	−0.530293	−0.0244606
$471$	−59.3549	−2.73493
$472$	57.0665	2.62670
$473$	−31.6944	−1.45731
$474$	102.179	4.69325
$475$	29.3172	1.34517
$476$	111.502	5.11068
$477$	74.3501	3.40426
$478$	7.15326	0.327183
$479$	11.2462	0.513850	0.256925	−	0.966431i	$-0.417291\pi$
$479$	11.2462	0.513850	0.256925	+	0.966431i	$0.417291\pi$
$480$	−16.2773	−0.742953
$481$	20.9951	0.957292
$482$	39.9324	1.81887
$483$	−1.93271	−0.0879412
$484$	−5.82329	−0.264695
$485$	1.18917	0.0539976
$486$	239.109	10.8462
$487$	7.76015	0.351646	0.175823	−	0.984422i	$-0.443741\pi$
$487$	7.76015	0.351646	0.175823	+	0.984422i	$0.443741\pi$
$488$	−67.2989	−3.04648
$489$	−8.90463	−0.402682
$490$	1.32111	0.0596818
$491$	−24.4648	−1.10408	−0.552040	−	0.833818i	$-0.686150\pi$
$491$	−24.4648	−1.10408	−0.552040	+	0.833818i	$0.686150\pi$
$492$	187.874	8.47003
$493$	15.7036	0.707254
$494$	−86.4228	−3.88835
$495$	4.78409	0.215029
$496$	61.3310	2.75384
$497$	−3.12589	−0.140215
$498$	−9.29657	−0.416589
$499$	17.9989	0.805743	0.402871	−	0.915257i	$-0.368012\pi$
$499$	17.9989	0.805743	0.402871	+	0.915257i	$0.368012\pi$
$500$	9.79831	0.438194
$501$	21.8357	0.975549
$502$	5.72621	0.255573
$503$	0.349311	0.0155750	0.00778751	−	0.999970i	$-0.497521\pi$
$503$	0.349311	0.0155750	0.00778751	+	0.999970i	$0.497521\pi$
$504$	286.446	12.7593
$505$	−0.447228	−0.0199014
$506$	−1.57934	−0.0702103
$507$	−50.7972	−2.25598
$508$	−48.9071	−2.16990
$509$	−24.7969	−1.09910	−0.549552	−	0.835459i	$-0.685202\pi$
$509$	−24.7969	−1.09910	−0.549552	+	0.835459i	$0.685202\pi$
$510$	10.2048	0.451877
$511$	37.1287	1.64248
$512$	−119.090	−5.26307
$513$	118.295	5.22284
$514$	−6.82439	−0.301011
$515$	−2.29005	−0.100912
$516$	−197.757	−8.70577
$517$	3.51472	0.154577
$518$	−34.6303	−1.52157
$519$	34.9102	1.53239
$520$	−9.37503	−0.411122
$521$	−3.01169	−0.131945	−0.0659723	−	0.997821i	$-0.521015\pi$
$521$	−3.01169	−0.131945	−0.0659723	+	0.997821i	$0.521015\pi$
$522$	61.9629	2.71204
$523$	5.87176	0.256754	0.128377	−	0.991725i	$-0.459023\pi$
$523$	5.87176	0.256754	0.128377	+	0.991725i	$0.459023\pi$
$524$	−1.38580	−0.0605389
$525$	−53.4432	−2.33245
$526$	37.3635	1.62912
$527$	−21.9480	−0.956071
$528$	189.001	8.22523
$529$	−22.9677	−0.998595
$530$	4.01376	0.174346
$531$	−48.5657	−2.10757
$532$	105.677	4.58166
$533$	50.2156	2.17508
$534$	−24.6496	−1.06669
$535$	−1.31321	−0.0567751
$536$	−165.554	−7.15083
$537$	22.6389	0.976942
$538$	0.164028	0.00707175
$539$	−8.75619	−0.377156
$540$	19.7098	0.848173
$541$	24.9744	1.07373	0.536867	−	0.843667i	$-0.319608\pi$
$541$	24.9744	1.07373	0.536867	+	0.843667i	$0.319608\pi$
$542$	−0.543055	−0.0233262
$543$	−12.4316	−0.533492
$544$	171.772	7.36464
$545$	3.53023	0.151219
$546$	157.543	6.74221
$547$	8.04788	0.344103	0.172051	−	0.985088i	$-0.444961\pi$
$547$	8.04788	0.344103	0.172051	+	0.985088i	$0.444961\pi$
$548$	81.4532	3.47951
$549$	57.2738	2.44439
$550$	−43.6720	−1.86218
$551$	14.8832	0.634044
$552$	−6.41584	−0.273076
$553$	−33.3953	−1.42011
$554$	−77.0246	−3.27246
$555$	−2.34958	−0.0997342
$556$	51.4751	2.18303
$557$	−11.4103	−0.483469	−0.241735	−	0.970342i	$-0.577716\pi$
$557$	−11.4103	−0.483469	−0.241735	+	0.970342i	$0.577716\pi$
$558$	−86.6021	−3.66616
$559$	−52.8572	−2.23562
$560$	9.31992	0.393838
$561$	−67.6364	−2.85561
$562$	16.7624	0.707080
$563$	4.61699	0.194583	0.0972914	−	0.995256i	$-0.468982\pi$
$563$	4.61699	0.194583	0.0972914	+	0.995256i	$0.468982\pi$
$564$	21.9301	0.923424
$565$	−0.171450	−0.00721295
$566$	−70.9934	−2.98407
$567$	−132.829	−5.57830
$568$	−10.3767	−0.435398
$569$	−15.5837	−0.653301	−0.326651	−	0.945145i	$-0.605920\pi$
$569$	−15.5837	−0.653301	−0.326651	+	0.945145i	$0.605920\pi$
$570$	9.67168	0.405102
$571$	−3.21612	−0.134590	−0.0672951	−	0.997733i	$-0.521437\pi$
$571$	−3.21612	−0.134590	−0.0672951	+	0.997733i	$0.521437\pi$
$572$	95.4376	3.99045
$573$	48.8915	2.04247
$574$	−82.8283	−3.45719
$575$	0.893494	0.0372613
$576$	370.630	15.4429
$577$	−24.3484	−1.01364	−0.506818	−	0.862053i	$-0.669178\pi$
$577$	−24.3484	−1.01364	−0.506818	+	0.862053i	$0.669178\pi$
$578$	−60.4192	−2.51311
$579$	2.57510	0.107017
$580$	2.47977	0.102967
$581$	3.03840	0.126054
$582$	−66.3374	−2.74977
$583$	−26.6027	−1.10177
$584$	123.253	5.10024
$585$	7.97849	0.329870
$586$	83.1105	3.43326
$587$	−18.9230	−0.781034	−0.390517	−	0.920596i	$-0.627704\pi$
$587$	−18.9230	−0.781034	−0.390517	+	0.920596i	$0.627704\pi$
$588$	−54.6342	−2.25308
$589$	−20.8014	−0.857106
$590$	−2.62179	−0.107938
$591$	−46.3320	−1.90584
$592$	−69.2858	−2.84763
$593$	−26.9551	−1.10691	−0.553456	−	0.832878i	$-0.686691\pi$
$593$	−26.9551	−1.10691	−0.553456	+	0.832878i	$0.686691\pi$
$594$	−176.216	−7.23024
$595$	−3.33524	−0.136732
$596$	−95.7105	−3.92046
$597$	−24.2789	−0.993670
$598$	−2.63389	−0.107708
$599$	−6.65183	−0.271787	−0.135893	−	0.990723i	$-0.543390\pi$
$599$	−6.65183	−0.271787	−0.135893	+	0.990723i	$0.543390\pi$
$600$	−177.411	−7.24277
$601$	37.1461	1.51522	0.757610	−	0.652707i	$-0.226367\pi$
$601$	37.1461	1.51522	0.757610	+	0.652707i	$0.226367\pi$
$602$	87.1853	3.55341
$603$	140.892	5.73758
$604$	−91.6596	−3.72957
$605$	0.174186	0.00708168
$606$	24.9484	1.01346
$607$	−9.03537	−0.366734	−0.183367	−	0.983044i	$-0.558700\pi$
$607$	−9.03537	−0.366734	−0.183367	+	0.983044i	$0.558700\pi$
$608$	162.798	6.60231
$609$	−27.1310	−1.09940
$610$	3.09190	0.125187
$611$	5.86155	0.237133
$612$	−315.005	−12.7333
$613$	9.11387	0.368106	0.184053	−	0.982916i	$-0.441078\pi$
$613$	9.11387	0.368106	0.184053	+	0.982916i	$0.441078\pi$
$614$	−39.7721	−1.60507
$615$	−5.61969	−0.226608
$616$	−102.491	−4.12949
$617$	−37.4913	−1.50934	−0.754672	−	0.656103i	$-0.772204\pi$
$617$	−37.4913	−1.50934	−0.754672	+	0.656103i	$0.772204\pi$
$618$	127.749	5.13883
$619$	−10.2135	−0.410515	−0.205257	−	0.978708i	$-0.565803\pi$
$619$	−10.2135	−0.410515	−0.205257	+	0.978708i	$0.565803\pi$
$620$	−3.46584	−0.139191
$621$	3.60524	0.144673
$622$	−16.4344	−0.658959
$623$	8.05624	0.322766
$624$	315.200	12.6181
$625$	24.5599	0.982398
$626$	−94.5779	−3.78009
$627$	−64.1028	−2.56002
$628$	98.9095	3.94692
$629$	24.7947	0.988631
$630$	−13.1601	−0.524312
$631$	−14.8643	−0.591740	−0.295870	−	0.955228i	$-0.595610\pi$
$631$	−14.8643	−0.591740	−0.295870	+	0.955228i	$0.595610\pi$
$632$	−110.860	−4.40975
$633$	−24.5829	−0.977084
$634$	−5.93235	−0.235604
$635$	1.46291	0.0580537
$636$	−165.988	−6.58183
$637$	−14.6028	−0.578584
$638$	−22.1705	−0.877740
$639$	8.83098	0.349348
$640$	10.5437	0.416776
$641$	1.48132	0.0585085	0.0292542	−	0.999572i	$-0.490687\pi$
$641$	1.48132	0.0585085	0.0292542	+	0.999572i	$0.490687\pi$
$642$	73.2569	2.89122
$643$	−28.7633	−1.13431	−0.567156	−	0.823610i	$-0.691956\pi$
$643$	−28.7633	−1.13431	−0.567156	+	0.823610i	$0.691956\pi$
$644$	3.22068	0.126913
$645$	5.91531	0.232915
$646$	−102.064	−4.01564
$647$	0.322935	0.0126959	0.00634795	−	0.999980i	$-0.497979\pi$
$647$	0.322935	0.0126959	0.00634795	+	0.999980i	$0.497979\pi$
$648$	−440.941	−17.3218
$649$	17.3770	0.682105
$650$	−72.8323	−2.85672
$651$	37.9195	1.48618
$652$	14.8388	0.581131
$653$	−10.7443	−0.420455	−0.210228	−	0.977652i	$-0.567421\pi$
$653$	−10.7443	−0.420455	−0.210228	+	0.977652i	$0.567421\pi$
$654$	−196.932	−7.70067
$655$	0.0414520	0.00161966
$656$	−165.717	−6.47015
$657$	−104.893	−4.09225
$658$	−9.66834	−0.376911
$659$	6.48241	0.252519	0.126259	−	0.991997i	$-0.459703\pi$
$659$	6.48241	0.252519	0.126259	+	0.991997i	$0.459703\pi$
$660$	−10.6805	−0.415739
$661$	3.47675	0.135230	0.0676149	−	0.997711i	$-0.478461\pi$
$661$	3.47675	0.135230	0.0676149	+	0.997711i	$0.478461\pi$
$662$	−47.7798	−1.85701
$663$	−112.798	−4.38071
$664$	10.0863	0.391425
$665$	−3.16099	−0.122578
$666$	97.8346	3.79101
$667$	0.453591	0.0175631
$668$	−36.3873	−1.40787
$669$	25.7510	0.995592
$670$	7.60600	0.293845
$671$	−20.4927	−0.791114
$672$	−296.769	−11.4481
$673$	2.17661	0.0839022	0.0419511	−	0.999120i	$-0.486643\pi$
$673$	2.17661	0.0839022	0.0419511	+	0.999120i	$0.486643\pi$
$674$	49.7829	1.91757
$675$	99.6922	3.83715
$676$	84.6489	3.25573
$677$	21.6167	0.830799	0.415399	−	0.909639i	$-0.363642\pi$
$677$	21.6167	0.830799	0.415399	+	0.909639i	$0.363642\pi$
$678$	9.56425	0.367313
$679$	21.6811	0.832043
$680$	−11.0717	−0.424581
$681$	−60.9772	−2.33665
$682$	30.9865	1.18653
$683$	−0.580124	−0.0221978	−0.0110989	−	0.999938i	$-0.503533\pi$
$683$	−0.580124	−0.0221978	−0.0110989	+	0.999938i	$0.503533\pi$
$684$	−298.548	−11.4153
$685$	−2.43643	−0.0930910
$686$	−36.7566	−1.40337
$687$	2.43713	0.0929824
$688$	174.434	6.65023
$689$	−44.3657	−1.69020
$690$	0.294762	0.0112214
$691$	−10.8649	−0.413320	−0.206660	−	0.978413i	$-0.566259\pi$
$691$	−10.8649	−0.413320	−0.206660	+	0.978413i	$0.566259\pi$
$692$	−58.1748	−2.21147
$693$	87.2238	3.31336
$694$	47.4100	1.79966
$695$	−1.53972	−0.0584050
$696$	−90.0644	−3.41388
$697$	59.3036	2.24629
$698$	10.1867	0.385574
$699$	−34.8950	−1.31985
$700$	89.0583	3.36609
$701$	48.4116	1.82848	0.914240	−	0.405173i	$-0.132789\pi$
$701$	48.4116	1.82848	0.914240	+	0.405173i	$0.132789\pi$
$702$	−293.878	−11.0917
$703$	23.4994	0.886295
$704$	−132.613	−4.99803
$705$	−0.655973	−0.0247054
$706$	64.4995	2.42747
$707$	−8.15389	−0.306659
$708$	108.423	4.07480
$709$	−0.482102	−0.0181057	−0.00905287	−	0.999959i	$-0.502882\pi$
$709$	−0.482102	−0.0181057	−0.00905287	+	0.999959i	$0.502882\pi$
$710$	0.476736	0.0178916
$711$	94.3454	3.53823
$712$	26.7436	1.00226
$713$	−0.633959	−0.0237419
$714$	186.055	6.96293
$715$	−2.85473	−0.106761
$716$	−37.7258	−1.40988
$717$	8.84858	0.330456
$718$	−65.4759	−2.44354
$719$	31.4190	1.17173	0.585865	−	0.810408i	$-0.300755\pi$
$719$	31.4190	1.17173	0.585865	+	0.810408i	$0.300755\pi$
$720$	−26.3298	−0.981254
$721$	−41.7523	−1.55494
$722$	−43.8997	−1.63378
$723$	49.3964	1.83707
$724$	20.7162	0.769911
$725$	12.5427	0.465825
$726$	−9.71689	−0.360628
$727$	−50.2114	−1.86224	−0.931119	−	0.364716i	$-0.881166\pi$
$727$	−50.2114	−1.86224	−0.931119	+	0.364716i	$0.881166\pi$
$728$	−170.926	−6.33494
$729$	168.298	6.23328
$730$	−5.66258	−0.209582
$731$	−62.4232	−2.30881
$732$	−127.864	−4.72600
$733$	14.5127	0.536040	0.268020	−	0.963413i	$-0.413631\pi$
$733$	14.5127	0.536040	0.268020	+	0.963413i	$0.413631\pi$
$734$	−46.0421	−1.69944
$735$	1.63422	0.0602790
$736$	4.96154	0.182885
$737$	−50.4117	−1.85694
$738$	233.999	8.61363
$739$	41.0266	1.50919	0.754594	−	0.656192i	$-0.227834\pi$
$739$	41.0266	1.50919	0.754594	+	0.656192i	$0.227834\pi$
$740$	3.91537	0.143932
$741$	−106.905	−3.92725
$742$	73.1790	2.68649
$743$	−41.5999	−1.52615	−0.763076	−	0.646308i	$-0.776312\pi$
$743$	−41.5999	−1.52615	−0.763076	+	0.646308i	$0.776312\pi$
$744$	125.878	4.61491
$745$	2.86289	0.104888
$746$	33.3422	1.22074
$747$	−8.58381	−0.314065
$748$	112.710	4.12108
$749$	−23.9426	−0.874842
$750$	16.3497	0.597007
$751$	−22.2673	−0.812546	−0.406273	−	0.913752i	$-0.633172\pi$
$751$	−22.2673	−0.812546	−0.406273	+	0.913752i	$0.633172\pi$
$752$	−19.3437	−0.705392
$753$	7.08332	0.258130
$754$	−36.9741	−1.34652
$755$	2.74172	0.0997814
$756$	359.350	13.0694
$757$	−23.8403	−0.866492	−0.433246	−	0.901276i	$-0.642632\pi$
$757$	−23.8403	−0.866492	−0.433246	+	0.901276i	$0.642632\pi$
$758$	−67.9360	−2.46755
$759$	−1.95365	−0.0709129
$760$	−10.4933	−0.380632
$761$	−25.3954	−0.920581	−0.460290	−	0.887768i	$-0.652255\pi$
$761$	−25.3954	−0.920581	−0.460290	+	0.887768i	$0.652255\pi$
$762$	−81.6076	−2.95633
$763$	64.3634	2.33011
$764$	−81.4733	−2.94760
$765$	9.42243	0.340669
$766$	−22.9309	−0.828527
$767$	28.9798	1.04640
$768$	−299.458	−10.8058
$769$	2.25368	0.0812696	0.0406348	−	0.999174i	$-0.487062\pi$
$769$	2.25368	0.0812696	0.0406348	+	0.999174i	$0.487062\pi$
$770$	4.70874	0.169691
$771$	−8.44177	−0.304023
$772$	−4.29117	−0.154443
$773$	2.02366	0.0727860	0.0363930	−	0.999338i	$-0.488413\pi$
$773$	2.02366	0.0727860	0.0363930	+	0.999338i	$0.488413\pi$
$774$	−246.308	−8.85337
$775$	−17.5302	−0.629705
$776$	71.9728	2.58367
$777$	−42.8377	−1.53679
$778$	−80.9794	−2.90325
$779$	56.2054	2.01377
$780$	−17.8121	−0.637774
$781$	−3.15975	−0.113065
$782$	−3.11057	−0.111234
$783$	50.6097	1.80864
$784$	48.1907	1.72110
$785$	−2.95858	−0.105596
$786$	−2.31238	−0.0824798
$787$	43.8802	1.56416	0.782080	−	0.623178i	$-0.214159\pi$
$787$	43.8802	1.56416	0.782080	+	0.623178i	$0.214159\pi$
$788$	77.2081	2.75043
$789$	46.2186	1.64543
$790$	5.09319	0.181208
$791$	−3.12589	−0.111144
$792$	289.550	10.2887
$793$	−34.1760	−1.21363
$794$	−61.8881	−2.19633
$795$	4.96502	0.176091
$796$	40.4586	1.43402
$797$	−26.7631	−0.947997	−0.473998	−	0.880526i	$-0.657190\pi$
$797$	−26.7631	−0.947997	−0.473998	+	0.880526i	$0.657190\pi$
$798$	176.335	6.24218
$799$	6.92237	0.244896
$800$	137.197	4.85064
$801$	−22.7598	−0.804177
$802$	−73.0339	−2.57892
$803$	37.5310	1.32444
$804$	−314.544	−11.0931
$805$	−0.0963369	−0.00339543
$806$	51.6766	1.82023
$807$	0.202903	0.00714251
$808$	−27.0678	−0.952242
$809$	22.9918	0.808348	0.404174	−	0.914682i	$-0.367559\pi$
$809$	22.9918	0.808348	0.404174	+	0.914682i	$0.367559\pi$
$810$	20.2581	0.711796
$811$	27.1599	0.953711	0.476856	−	0.878982i	$-0.341776\pi$
$811$	27.1599	0.953711	0.476856	+	0.878982i	$0.341776\pi$
$812$	45.2113	1.58661
$813$	−0.671759	−0.0235596
$814$	−35.0055	−1.22694
$815$	−0.443857	−0.0155476
$816$	372.245	13.0312
$817$	−59.1620	−2.06982
$818$	5.16404	0.180556
$819$	145.464	5.08293
$820$	9.36471	0.327030
$821$	39.7436	1.38706	0.693531	−	0.720427i	$-0.256054\pi$
$821$	39.7436	1.38706	0.693531	+	0.720427i	$0.256054\pi$
$822$	135.915	4.74057
$823$	21.7319	0.757525	0.378762	−	0.925494i	$-0.376350\pi$
$823$	21.7319	0.757525	0.378762	+	0.925494i	$0.376350\pi$
$824$	−138.602	−4.82842
$825$	−54.0223	−1.88081
$826$	−47.8007	−1.66320
$827$	28.1222	0.977904	0.488952	−	0.872311i	$-0.337379\pi$
$827$	28.1222	0.977904	0.488952	+	0.872311i	$0.337379\pi$
$828$	−9.09879	−0.316205
$829$	−31.1628	−1.08233	−0.541164	−	0.840917i	$-0.682016\pi$
$829$	−31.1628	−1.08233	−0.541164	+	0.840917i	$0.682016\pi$
$830$	−0.463393	−0.0160846
$831$	−95.2794	−3.30521
$832$	−221.160	−7.66733
$833$	−17.2456	−0.597525
$834$	85.8926	2.97422
$835$	1.08842	0.0376662
$836$	106.821	3.69450
$837$	−70.7344	−2.44494
$838$	83.6052	2.88809
$839$	−21.5342	−0.743442	−0.371721	−	0.928345i	$-0.621232\pi$
$839$	−21.5342	−0.743442	−0.371721	+	0.928345i	$0.621232\pi$
$840$	19.1285	0.659997
$841$	−22.6326	−0.780433
$842$	−1.63304	−0.0562782
$843$	20.7351	0.714155
$844$	40.9652	1.41008
$845$	−2.53202	−0.0871040
$846$	27.3141	0.939080
$847$	3.17577	0.109121
$848$	146.411	5.02778
$849$	−87.8188	−3.01393
$850$	−86.0135	−2.95024
$851$	0.716185	0.0245505
$852$	−19.7153	−0.675434
$853$	29.3706	1.00563	0.502815	−	0.864394i	$-0.332298\pi$
$853$	29.3706	1.00563	0.502815	+	0.864394i	$0.332298\pi$
$854$	56.3717	1.92900
$855$	8.93017	0.305405
$856$	−79.4801	−2.71657
$857$	51.3402	1.75375	0.876875	−	0.480719i	$-0.159624\pi$
$857$	51.3402	1.75375	0.876875	+	0.480719i	$0.159624\pi$
$858$	159.250	5.43669
$859$	−11.5517	−0.394139	−0.197069	−	0.980390i	$-0.563142\pi$
$859$	−11.5517	−0.394139	−0.197069	+	0.980390i	$0.563142\pi$
$860$	−9.85733	−0.336132
$861$	−102.459	−3.49178
$862$	−50.9795	−1.73637
$863$	−8.25075	−0.280859	−0.140429	−	0.990091i	$-0.544848\pi$
$863$	−8.25075	−0.280859	−0.140429	+	0.990091i	$0.544848\pi$
$864$	553.588	18.8334
$865$	1.74012	0.0591659
$866$	−3.25079	−0.110466
$867$	−74.7386	−2.53826
$868$	−63.1894	−2.14479
$869$	−33.7571	−1.14513
$870$	4.13781	0.140285
$871$	−84.0722	−2.84868
$872$	213.662	7.23550
$873$	−61.2515	−2.07305
$874$	−2.94806	−0.0997196
$875$	−5.34358	−0.180646
$876$	234.174	7.91201
$877$	8.35461	0.282115	0.141058	−	0.990001i	$-0.454950\pi$
$877$	8.35461	0.282115	0.141058	+	0.990001i	$0.454950\pi$
$878$	−27.2978	−0.921255
$879$	102.808	3.46762
$880$	9.42089	0.317578
$881$	56.8775	1.91625	0.958126	−	0.286348i	$-0.0924413\pi$
$881$	56.8775	1.91625	0.958126	+	0.286348i	$0.0924413\pi$
$882$	−68.0474	−2.29127
$883$	36.4967	1.22821	0.614106	−	0.789223i	$-0.289517\pi$
$883$	36.4967	1.22821	0.614106	+	0.789223i	$0.289517\pi$
$884$	187.968	6.32204
$885$	−3.24316	−0.109018
$886$	47.9764	1.61180
$887$	−52.3892	−1.75906	−0.879528	−	0.475847i	$-0.842141\pi$
$887$	−52.3892	−1.75906	−0.879528	+	0.475847i	$0.842141\pi$
$888$	−142.205	−4.77208
$889$	26.6718	0.894544
$890$	−1.22868	−0.0411853
$891$	−134.268	−4.49815
$892$	−42.9117	−1.43679
$893$	6.56072	0.219546
$894$	−159.705	−5.34134
$895$	1.12845	0.0377200
$896$	192.233	6.42206
$897$	−3.25812	−0.108785
$898$	0.235443	0.00785683
$899$	−8.89940	−0.296812
$900$	−251.600	−8.38666
$901$	−52.3950	−1.74553
$902$	−83.7257	−2.78776
$903$	107.848	3.58896
$904$	−10.3767	−0.345125
$905$	−0.619662	−0.0205983
$906$	−152.945	−5.08127
$907$	12.9387	0.429622	0.214811	−	0.976656i	$-0.431086\pi$
$907$	12.9387	0.429622	0.214811	+	0.976656i	$0.431086\pi$
$908$	101.613	3.37215
$909$	23.0357	0.764045
$910$	7.85282	0.260318
$911$	−52.8289	−1.75030	−0.875150	−	0.483852i	$-0.839237\pi$
$911$	−52.8289	−1.75030	−0.875150	+	0.483852i	$0.839237\pi$
$912$	352.797	11.6823
$913$	3.07132	0.101646
$914$	31.7123	1.04895
$915$	3.82468	0.126440
$916$	−4.06126	−0.134188
$917$	0.755755	0.0249572
$918$	−347.064	−11.4548
$919$	−55.3696	−1.82647	−0.913236	−	0.407430i	$-0.866425\pi$
$919$	−55.3696	−1.82647	−0.913236	+	0.407430i	$0.866425\pi$
$920$	−0.319802	−0.0105435
$921$	−49.1981	−1.62113
$922$	70.3489	2.31682
$923$	−5.26956	−0.173450
$924$	−194.728	−6.40609
$925$	19.8040	0.651150
$926$	−3.50439	−0.115161
$927$	117.955	3.87415
$928$	69.6493	2.28635
$929$	3.57544	0.117307	0.0586533	−	0.998278i	$-0.481319\pi$
$929$	3.57544	0.117307	0.0586533	+	0.998278i	$0.481319\pi$
$930$	−5.78319	−0.189638
$931$	−16.3446	−0.535674
$932$	58.1494	1.90475
$933$	−20.3293	−0.665553
$934$	39.1498	1.28102
$935$	−3.37138	−0.110256
$936$	482.885	15.7836
$937$	−7.33224	−0.239534	−0.119767	−	0.992802i	$-0.538215\pi$
$937$	−7.33224	−0.239534	−0.119767	+	0.992802i	$0.538215\pi$
$938$	138.673	4.52784
$939$	−116.993	−3.81792
$940$	1.09312	0.0356536
$941$	−8.05743	−0.262665	−0.131332	−	0.991338i	$-0.541926\pi$
$941$	−8.05743	−0.262665	−0.131332	+	0.991338i	$0.541926\pi$
$942$	165.043	5.37739
$943$	1.71296	0.0557816
$944$	−95.6361	−3.11269
$945$	−10.7489	−0.349660
$946$	88.1299	2.86535
$947$	39.1497	1.27220	0.636098	−	0.771609i	$-0.280548\pi$
$947$	39.1497	1.27220	0.636098	+	0.771609i	$0.280548\pi$
$948$	−210.627	−6.84086
$949$	62.5908	2.03178
$950$	−81.5198	−2.64485
$951$	−7.33832	−0.237961
$952$	−201.860	−6.54233
$953$	24.6353	0.798017	0.399009	−	0.916947i	$-0.369354\pi$
$953$	24.6353	0.798017	0.399009	+	0.916947i	$0.369354\pi$
$954$	−206.739	−6.69342
$955$	2.43703	0.0788604
$956$	−14.7454	−0.476899
$957$	−27.4249	−0.886522
$958$	−31.2712	−1.01033
$959$	−44.4210	−1.43443
$960$	24.7502	0.798811
$961$	−18.5618	−0.598768
$962$	−58.3791	−1.88222
$963$	67.6405	2.17968
$964$	−82.3147	−2.65118
$965$	0.128357	0.00413197
$966$	5.37411	0.172909
$967$	15.3634	0.494053	0.247026	−	0.969009i	$-0.420547\pi$
$967$	15.3634	0.494053	0.247026	+	0.969009i	$0.420547\pi$
$968$	10.5423	0.338844
$969$	−126.253	−4.05582
$970$	−3.30663	−0.106170
$971$	−52.0268	−1.66962	−0.834810	−	0.550538i	$-0.814423\pi$
$971$	−52.0268	−1.66962	−0.834810	+	0.550538i	$0.814423\pi$
$972$	−492.888	−15.8094
$973$	−28.0723	−0.899956
$974$	−21.5780	−0.691403
$975$	−90.0936	−2.88530
$976$	112.784	3.61014
$977$	−20.2874	−0.649052	−0.324526	−	0.945877i	$-0.605205\pi$
$977$	−20.2874	−0.649052	−0.324526	+	0.945877i	$0.605205\pi$
$978$	24.7604	0.791749
$979$	8.14352	0.260268
$980$	−2.72327	−0.0869918
$981$	−181.834	−5.80551
$982$	68.0271	2.17083
$983$	−5.22903	−0.166780	−0.0833901	−	0.996517i	$-0.526575\pi$
$983$	−5.22903	−0.166780	−0.0833901	+	0.996517i	$0.526575\pi$
$984$	−340.123	−10.8427
$985$	−2.30945	−0.0735852
$986$	−43.6656	−1.39060
$987$	−11.9597	−0.380683
$988$	178.147	5.66763
$989$	−1.80307	−0.0573342
$990$	−13.3027	−0.422788
$991$	−17.9599	−0.570514	−0.285257	−	0.958451i	$-0.592079\pi$
$991$	−17.9599	−0.570514	−0.285257	+	0.958451i	$0.592079\pi$
$992$	−97.3449	−3.09070
$993$	−59.1035	−1.87559
$994$	8.69188	0.275690
$995$	−1.21020	−0.0383659
$996$	19.1635	0.607218
$997$	0.258483	0.00818624	0.00409312	−	0.999992i	$-0.498697\pi$
$997$	0.258483	0.00818624	0.00409312	+	0.999992i	$0.498697\pi$
$998$	−50.0481	−1.58424
$999$	79.9088	2.52820

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8023.2.a.b.1.3	✓	155

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8023.2.a.b.1.3	✓	155	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:	\( N \)	\(=\)	\( 8023 = 71 \cdot 113 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8023.a (trivial)

\(f(q)\)	\(=\)	\(q-2.78061 q^{2} -3.43962 q^{3} +5.73182 q^{4} -0.171450 q^{5} +9.56425 q^{6} -3.12589 q^{7} -10.3767 q^{8} +8.83098 q^{9} +O(q^{10})\)	\(q-2.78061 q^{2} -3.43962 q^{3} +5.73182 q^{4} -0.171450 q^{5} +9.56425 q^{6} -3.12589 q^{7} -10.3767 q^{8} +8.83098 q^{9} +0.476736 q^{10} -3.15975 q^{11} -19.7153 q^{12} -5.26956 q^{13} +8.69188 q^{14} +0.589723 q^{15} +17.3901 q^{16} -6.22324 q^{17} -24.5555 q^{18} -5.89812 q^{19} -0.982720 q^{20} +10.7519 q^{21} +8.78605 q^{22} -0.179756 q^{23} +35.6920 q^{24} -4.97060 q^{25} +14.6526 q^{26} -20.0563 q^{27} -17.9170 q^{28} -2.52338 q^{29} -1.63979 q^{30} +3.52678 q^{31} -27.6016 q^{32} +10.8683 q^{33} +17.3044 q^{34} +0.535933 q^{35} +50.6175 q^{36} -3.98421 q^{37} +16.4004 q^{38} +18.1253 q^{39} +1.77909 q^{40} -9.52938 q^{41} -29.8968 q^{42} +10.0307 q^{43} -18.1111 q^{44} -1.51407 q^{45} +0.499831 q^{46} -1.11234 q^{47} -59.8152 q^{48} +2.77116 q^{49} +13.8213 q^{50} +21.4056 q^{51} -30.2041 q^{52} +8.41924 q^{53} +55.7690 q^{54} +0.541740 q^{55} +32.4365 q^{56} +20.2873 q^{57} +7.01654 q^{58} -5.49947 q^{59} +3.38018 q^{60} +6.48555 q^{61} -9.80662 q^{62} -27.6046 q^{63} +41.9693 q^{64} +0.903466 q^{65} -30.2207 q^{66} +15.9543 q^{67} -35.6705 q^{68} +0.618291 q^{69} -1.49022 q^{70} +1.00000 q^{71} -91.6368 q^{72} -11.8778 q^{73} +11.0786 q^{74} +17.0970 q^{75} -33.8069 q^{76} +9.87703 q^{77} -50.3994 q^{78} +10.6835 q^{79} -2.98153 q^{80} +42.4933 q^{81} +26.4975 q^{82} -0.972012 q^{83} +61.6277 q^{84} +1.06697 q^{85} -27.8914 q^{86} +8.67945 q^{87} +32.7879 q^{88} -2.57727 q^{89} +4.21005 q^{90} +16.4720 q^{91} -1.03033 q^{92} -12.1308 q^{93} +3.09299 q^{94} +1.01123 q^{95} +94.9390 q^{96} -6.93598 q^{97} -7.70553 q^{98} -27.9037 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 155 q - 21 q^{2} - 16 q^{3} + 151 q^{4} - 26 q^{5} - 10 q^{6} - 40 q^{7} - 57 q^{8} + 135 q^{9}+O(q^{10}) \) 155 * q - 21 * q^2 - 16 * q^3 + 151 * q^4 - 26 * q^5 - 10 * q^6 - 40 * q^7 - 57 * q^8 + 135 * q^9	\( 155 q - 21 q^{2} - 16 q^{3} + 151 q^{4} - 26 q^{5} - 10 q^{6} - 40 q^{7} - 57 q^{8} + 135 q^{9} - 2 q^{10} - 24 q^{11} - 32 q^{12} - 62 q^{13} - 18 q^{14} - 12 q^{15} + 155 q^{16} - 129 q^{17} - 42 q^{18} - 18 q^{19} - 59 q^{20} - 45 q^{21} - 17 q^{22} - 38 q^{23} - 27 q^{24} + 129 q^{25} - 44 q^{26} - 43 q^{27} - 100 q^{28} - 52 q^{29} - 39 q^{30} - 56 q^{31} - 145 q^{32} - 126 q^{33} - q^{34} - 49 q^{35} + 131 q^{36} - 30 q^{37} - 91 q^{38} - 29 q^{39} - 5 q^{40} - 163 q^{41} - 80 q^{42} - 15 q^{43} - 118 q^{44} - 66 q^{45} + 2 q^{46} - 111 q^{47} - 89 q^{48} + 101 q^{49} - 121 q^{50} + 5 q^{51} - 111 q^{52} - 93 q^{53} - 68 q^{54} - 60 q^{55} - 27 q^{56} - 106 q^{57} + 16 q^{58} - 79 q^{59} - 103 q^{60} - 74 q^{61} - 102 q^{62} - 118 q^{63} + 175 q^{64} - 109 q^{65} + 65 q^{66} - 18 q^{67} - 346 q^{68} - 39 q^{69} + 32 q^{70} + 155 q^{71} - 203 q^{72} - 108 q^{73} - 87 q^{74} - 22 q^{75} - 16 q^{76} - 121 q^{77} - 75 q^{78} - 6 q^{79} - 136 q^{80} + 107 q^{81} - 30 q^{82} - 116 q^{83} - 5 q^{84} - 53 q^{85} + 8 q^{86} - 100 q^{87} - 43 q^{88} - 189 q^{89} - 76 q^{90} + 14 q^{91} - 99 q^{92} - 72 q^{93} + 17 q^{94} - 18 q^{95} - 50 q^{96} - 184 q^{97} - 249 q^{98} - 114 q^{99}+O(q^{100}) \) 155 * q - 21 * q^2 - 16 * q^3 + 151 * q^4 - 26 * q^5 - 10 * q^6 - 40 * q^7 - 57 * q^8 + 135 * q^9 - 2 * q^10 - 24 * q^11 - 32 * q^12 - 62 * q^13 - 18 * q^14 - 12 * q^15 + 155 * q^16 - 129 * q^17 - 42 * q^18 - 18 * q^19 - 59 * q^20 - 45 * q^21 - 17 * q^22 - 38 * q^23 - 27 * q^24 + 129 * q^25 - 44 * q^26 - 43 * q^27 - 100 * q^28 - 52 * q^29 - 39 * q^30 - 56 * q^31 - 145 * q^32 - 126 * q^33 - q^34 - 49 * q^35 + 131 * q^36 - 30 * q^37 - 91 * q^38 - 29 * q^39 - 5 * q^40 - 163 * q^41 - 80 * q^42 - 15 * q^43 - 118 * q^44 - 66 * q^45 + 2 * q^46 - 111 * q^47 - 89 * q^48 + 101 * q^49 - 121 * q^50 + 5 * q^51 - 111 * q^52 - 93 * q^53 - 68 * q^54 - 60 * q^55 - 27 * q^56 - 106 * q^57 + 16 * q^58 - 79 * q^59 - 103 * q^60 - 74 * q^61 - 102 * q^62 - 118 * q^63 + 175 * q^64 - 109 * q^65 + 65 * q^66 - 18 * q^67 - 346 * q^68 - 39 * q^69 + 32 * q^70 + 155 * q^71 - 203 * q^72 - 108 * q^73 - 87 * q^74 - 22 * q^75 - 16 * q^76 - 121 * q^77 - 75 * q^78 - 6 * q^79 - 136 * q^80 + 107 * q^81 - 30 * q^82 - 116 * q^83 - 5 * q^84 - 53 * q^85 + 8 * q^86 - 100 * q^87 - 43 * q^88 - 189 * q^89 - 76 * q^90 + 14 * q^91 - 99 * q^92 - 72 * q^93 + 17 * q^94 - 18 * q^95 - 50 * q^96 - 184 * q^97 - 249 * q^98 - 114 * q^99

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