LMFDB - Embedded newform 4003.2.a.c.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4003,2,Mod(1,4003)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4003, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4003.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4003 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4003.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:	$31.9641159291$
Analytic rank:	$0$
Dimension:	$179$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	4003.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.32611 q^{2} +2.50152 q^{3} +3.41079 q^{4} +0.271197 q^{5} -5.81882 q^{6} +2.22103 q^{7} -3.28166 q^{8} +3.25762 q^{9} +O(q^{10})$	\(q-2.32611 q^{2} +2.50152 q^{3} +3.41079 q^{4} +0.271197 q^{5} -5.81882 q^{6} +2.22103 q^{7} -3.28166 q^{8} +3.25762 q^{9} -0.630834 q^{10} +4.90915 q^{11} +8.53218 q^{12} +4.75288 q^{13} -5.16637 q^{14} +0.678405 q^{15} +0.811925 q^{16} -3.39026 q^{17} -7.57760 q^{18} -0.868020 q^{19} +0.924996 q^{20} +5.55597 q^{21} -11.4192 q^{22} -7.92420 q^{23} -8.20916 q^{24} -4.92645 q^{25} -11.0557 q^{26} +0.644453 q^{27} +7.57549 q^{28} +6.56045 q^{29} -1.57805 q^{30} -0.772720 q^{31} +4.67470 q^{32} +12.2804 q^{33} +7.88612 q^{34} +0.602337 q^{35} +11.1111 q^{36} -3.69055 q^{37} +2.01911 q^{38} +11.8894 q^{39} -0.889977 q^{40} +9.67528 q^{41} -12.9238 q^{42} -4.85912 q^{43} +16.7441 q^{44} +0.883457 q^{45} +18.4326 q^{46} +13.0957 q^{47} +2.03105 q^{48} -2.06701 q^{49} +11.4595 q^{50} -8.48082 q^{51} +16.2111 q^{52} +12.3523 q^{53} -1.49907 q^{54} +1.33135 q^{55} -7.28868 q^{56} -2.17137 q^{57} -15.2603 q^{58} +6.25615 q^{59} +2.31390 q^{60} +9.50978 q^{61} +1.79743 q^{62} +7.23529 q^{63} -12.4977 q^{64} +1.28896 q^{65} -28.5655 q^{66} +10.5996 q^{67} -11.5635 q^{68} -19.8226 q^{69} -1.40110 q^{70} -10.1120 q^{71} -10.6904 q^{72} +13.3187 q^{73} +8.58464 q^{74} -12.3236 q^{75} -2.96064 q^{76} +10.9034 q^{77} -27.6561 q^{78} -10.5815 q^{79} +0.220192 q^{80} -8.16076 q^{81} -22.5058 q^{82} +1.26181 q^{83} +18.9503 q^{84} -0.919428 q^{85} +11.3028 q^{86} +16.4111 q^{87} -16.1102 q^{88} +0.0481094 q^{89} -2.05502 q^{90} +10.5563 q^{91} -27.0278 q^{92} -1.93298 q^{93} -30.4621 q^{94} -0.235404 q^{95} +11.6939 q^{96} -4.91163 q^{97} +4.80810 q^{98} +15.9922 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 179 q + 22 q^{2} + 16 q^{3} + 196 q^{4} + 61 q^{5} + 7 q^{6} + 21 q^{7} + 60 q^{8} + 221 q^{9}+O(q^{10}) $ 179 * q + 22 * q^2 + 16 * q^3 + 196 * q^4 + 61 * q^5 + 7 * q^6 + 21 * q^7 + 60 * q^8 + 221 * q^9	\( 179 q + 22 q^{2} + 16 q^{3} + 196 q^{4} + 61 q^{5} + 7 q^{6} + 21 q^{7} + 60 q^{8} + 221 q^{9} + 9 q^{10} + 46 q^{11} + 33 q^{12} + 47 q^{13} + 22 q^{14} + 36 q^{15} + 222 q^{16} + 103 q^{17} + 43 q^{18} + 12 q^{19} + 102 q^{20} + 50 q^{21} + 39 q^{22} + 121 q^{23} - 3 q^{24} + 246 q^{25} + 52 q^{26} + 49 q^{27} + 41 q^{28} + 138 q^{29} + 28 q^{30} + 5 q^{31} + 137 q^{32} + 63 q^{33} + 2 q^{34} + 72 q^{35} + 279 q^{36} + 118 q^{37} + 123 q^{38} + q^{39} + 9 q^{40} + 50 q^{41} + 48 q^{42} + 48 q^{43} + 108 q^{44} + 158 q^{45} + 13 q^{46} + 85 q^{47} + 50 q^{48} + 230 q^{49} + 78 q^{50} + 15 q^{51} + 41 q^{52} + 399 q^{53} - 5 q^{54} + 24 q^{55} + 53 q^{56} + 45 q^{57} + 27 q^{58} + 48 q^{59} + 66 q^{60} + 46 q^{61} + 81 q^{62} + 78 q^{63} + 252 q^{64} + 153 q^{65} + 6 q^{66} + 70 q^{67} + 240 q^{68} + 120 q^{69} - 31 q^{70} + 86 q^{71} + 89 q^{72} + 45 q^{73} + 68 q^{74} + 17 q^{75} - 13 q^{76} + 362 q^{77} + 69 q^{78} + 31 q^{79} + 169 q^{80} + 303 q^{81} + 25 q^{82} + 106 q^{83} + 13 q^{84} + 115 q^{85} + 95 q^{86} + 32 q^{87} + 83 q^{88} + 105 q^{89} - 38 q^{90} + 3 q^{91} + 310 q^{92} + 298 q^{93} - 17 q^{94} + 102 q^{95} - 82 q^{96} + 34 q^{97} + 81 q^{98} + 58 q^{99}+O(q^{100}) \) 179 * q + 22 * q^2 + 16 * q^3 + 196 * q^4 + 61 * q^5 + 7 * q^6 + 21 * q^7 + 60 * q^8 + 221 * q^9 + 9 * q^10 + 46 * q^11 + 33 * q^12 + 47 * q^13 + 22 * q^14 + 36 * q^15 + 222 * q^16 + 103 * q^17 + 43 * q^18 + 12 * q^19 + 102 * q^20 + 50 * q^21 + 39 * q^22 + 121 * q^23 - 3 * q^24 + 246 * q^25 + 52 * q^26 + 49 * q^27 + 41 * q^28 + 138 * q^29 + 28 * q^30 + 5 * q^31 + 137 * q^32 + 63 * q^33 + 2 * q^34 + 72 * q^35 + 279 * q^36 + 118 * q^37 + 123 * q^38 + q^39 + 9 * q^40 + 50 * q^41 + 48 * q^42 + 48 * q^43 + 108 * q^44 + 158 * q^45 + 13 * q^46 + 85 * q^47 + 50 * q^48 + 230 * q^49 + 78 * q^50 + 15 * q^51 + 41 * q^52 + 399 * q^53 - 5 * q^54 + 24 * q^55 + 53 * q^56 + 45 * q^57 + 27 * q^58 + 48 * q^59 + 66 * q^60 + 46 * q^61 + 81 * q^62 + 78 * q^63 + 252 * q^64 + 153 * q^65 + 6 * q^66 + 70 * q^67 + 240 * q^68 + 120 * q^69 - 31 * q^70 + 86 * q^71 + 89 * q^72 + 45 * q^73 + 68 * q^74 + 17 * q^75 - 13 * q^76 + 362 * q^77 + 69 * q^78 + 31 * q^79 + 169 * q^80 + 303 * q^81 + 25 * q^82 + 106 * q^83 + 13 * q^84 + 115 * q^85 + 95 * q^86 + 32 * q^87 + 83 * q^88 + 105 * q^89 - 38 * q^90 + 3 * q^91 + 310 * q^92 + 298 * q^93 - 17 * q^94 + 102 * q^95 - 82 * q^96 + 34 * q^97 + 81 * q^98 + 58 * 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 $

$2$	−2.32611	−1.64481	−0.822405	−	0.568903i	$-0.807368\pi$
$2$	−2.32611	−1.64481	−0.822405	+	0.568903i	$0.807368\pi$
$3$	2.50152	1.44426	0.722128	−	0.691760i	$-0.243164\pi$
$3$	2.50152	1.44426	0.722128	+	0.691760i	$0.243164\pi$
$4$	3.41079	1.70540
$5$	0.271197	0.121283	0.0606415	−	0.998160i	$-0.480685\pi$
$5$	0.271197	0.121283	0.0606415	+	0.998160i	$0.480685\pi$
$6$	−5.81882	−2.37552
$7$	2.22103	0.839472	0.419736	−	0.907646i	$-0.362123\pi$
$7$	2.22103	0.839472	0.419736	+	0.907646i	$0.362123\pi$
$8$	−3.28166	−1.16024
$9$	3.25762	1.08587
$10$	−0.630834	−0.199487
$11$	4.90915	1.48016	0.740082	−	0.672516i	$-0.234786\pi$
$11$	4.90915	1.48016	0.740082	+	0.672516i	$0.234786\pi$
$12$	8.53218	2.46303
$13$	4.75288	1.31821	0.659105	−	0.752051i	$-0.270935\pi$
$13$	4.75288	1.31821	0.659105	+	0.752051i	$0.270935\pi$
$14$	−5.16637	−1.38077
$15$	0.678405	0.175164
$16$	0.811925	0.202981
$17$	−3.39026	−0.822259	−0.411130	−	0.911577i	$-0.634866\pi$
$17$	−3.39026	−0.822259	−0.411130	+	0.911577i	$0.634866\pi$
$18$	−7.57760	−1.78606
$19$	−0.868020	−0.199137	−0.0995687	−	0.995031i	$-0.531746\pi$
$19$	−0.868020	−0.199137	−0.0995687	+	0.995031i	$0.531746\pi$
$20$	0.924996	0.206835
$21$	5.55597	1.21241
$22$	−11.4192	−2.43459
$23$	−7.92420	−1.65231	−0.826155	−	0.563443i	$-0.809476\pi$
$23$	−7.92420	−1.65231	−0.826155	+	0.563443i	$0.809476\pi$
$24$	−8.20916	−1.67569
$25$	−4.92645	−0.985290
$26$	−11.0557	−2.16820
$27$	0.644453	0.124025
$28$	7.57549	1.43163
$29$	6.56045	1.21825	0.609123	−	0.793076i	$-0.291522\pi$
$29$	6.56045	1.21825	0.609123	+	0.793076i	$0.291522\pi$
$30$	−1.57805	−0.288111
$31$	−0.772720	−0.138785	−0.0693923	−	0.997589i	$-0.522106\pi$
$31$	−0.772720	−0.138785	−0.0693923	+	0.997589i	$0.522106\pi$
$32$	4.67470	0.826377
$33$	12.2804	2.13774
$34$	7.88612	1.35246
$35$	0.602337	0.101814
$36$	11.1111	1.85185
$37$	−3.69055	−0.606723	−0.303362	−	0.952876i	$-0.598109\pi$
$37$	−3.69055	−0.606723	−0.303362	+	0.952876i	$0.598109\pi$
$38$	2.01911	0.327543
$39$	11.8894	1.90383
$40$	−0.889977	−0.140718
$41$	9.67528	1.51102	0.755512	−	0.655134i	$-0.227388\pi$
$41$	9.67528	1.51102	0.755512	+	0.655134i	$0.227388\pi$
$42$	−12.9238	−1.99419
$43$	−4.85912	−0.741009	−0.370504	−	0.928831i	$-0.620815\pi$
$43$	−4.85912	−0.741009	−0.370504	+	0.928831i	$0.620815\pi$
$44$	16.7441	2.52427
$45$	0.883457	0.131698
$46$	18.4326	2.71773
$47$	13.0957	1.91021	0.955104	−	0.296269i	$-0.0957425\pi$
$47$	13.0957	1.91021	0.955104	+	0.296269i	$0.0957425\pi$
$48$	2.03105	0.293157
$49$	−2.06701	−0.295287
$50$	11.4595	1.62061
$51$	−8.48082	−1.18755
$52$	16.2111	2.24807
$53$	12.3523	1.69672	0.848361	−	0.529419i	$-0.177590\pi$
$53$	12.3523	1.69672	0.848361	+	0.529419i	$0.177590\pi$
$54$	−1.49907	−0.203997
$55$	1.33135	0.179519
$56$	−7.28868	−0.973991
$57$	−2.17137	−0.287605
$58$	−15.2603	−2.00378
$59$	6.25615	0.814481	0.407241	−	0.913321i	$-0.366491\pi$
$59$	6.25615	0.814481	0.407241	+	0.913321i	$0.366491\pi$
$60$	2.31390	0.298723
$61$	9.50978	1.21760	0.608801	−	0.793323i	$-0.291651\pi$
$61$	9.50978	1.21760	0.608801	+	0.793323i	$0.291651\pi$
$62$	1.79743	0.228274
$63$	7.23529	0.911561
$64$	−12.4977	−1.56221
$65$	1.28896	0.159876
$66$	−28.5655	−3.51617
$67$	10.5996	1.29494	0.647471	−	0.762090i	$-0.275827\pi$
$67$	10.5996	1.29494	0.647471	+	0.762090i	$0.275827\pi$
$68$	−11.5635	−1.40228
$69$	−19.8226	−2.38636
$70$	−1.40110	−0.167464
$71$	−10.1120	−1.20007	−0.600036	−	0.799973i	$-0.704847\pi$
$71$	−10.1120	−1.20007	−0.600036	+	0.799973i	$0.704847\pi$
$72$	−10.6904	−1.25988
$73$	13.3187	1.55884	0.779418	−	0.626504i	$-0.215515\pi$
$73$	13.3187	1.55884	0.779418	+	0.626504i	$0.215515\pi$
$74$	8.58464	0.997944
$75$	−12.3236	−1.42301
$76$	−2.96064	−0.339608
$77$	10.9034	1.24256
$78$	−27.6561	−3.13144
$79$	−10.5815	−1.19052	−0.595258	−	0.803534i	$-0.702950\pi$
$79$	−10.5815	−1.19052	−0.595258	+	0.803534i	$0.702950\pi$
$80$	0.220192	0.0246182
$81$	−8.16076	−0.906751
$82$	−22.5058	−2.48535
$83$	1.26181	0.138502	0.0692509	−	0.997599i	$-0.477939\pi$
$83$	1.26181	0.138502	0.0692509	+	0.997599i	$0.477939\pi$
$84$	18.9503	2.06764
$85$	−0.919428	−0.0997260
$86$	11.3028	1.21882
$87$	16.4111	1.75946
$88$	−16.1102	−1.71735
$89$	0.0481094	0.00509958	0.00254979	−	0.999997i	$-0.499188\pi$
$89$	0.0481094	0.00509958	0.00254979	+	0.999997i	$0.499188\pi$
$90$	−2.05502	−0.216618
$91$	10.5563	1.10660
$92$	−27.0278	−2.81784
$93$	−1.93298	−0.200440
$94$	−30.4621	−3.14193
$95$	−0.235404	−0.0241520
$96$	11.6939	1.19350
$97$	−4.91163	−0.498700	−0.249350	−	0.968413i	$-0.580217\pi$
$97$	−4.91163	−0.498700	−0.249350	+	0.968413i	$0.580217\pi$
$98$	4.80810	0.485691
$99$	15.9922	1.60727
$100$	−16.8031	−1.68031
$101$	−0.0247299	−0.00246071	−0.00123036	−	0.999999i	$-0.500392\pi$
$101$	−0.0247299	−0.00246071	−0.00123036	+	0.999999i	$0.500392\pi$
$102$	19.7273	1.95330
$103$	−10.5795	−1.04243	−0.521213	−	0.853427i	$-0.674520\pi$
$103$	−10.5795	−1.04243	−0.521213	+	0.853427i	$0.674520\pi$
$104$	−15.5973	−1.52944
$105$	1.50676	0.147045
$106$	−28.7329	−2.79078
$107$	−10.0790	−0.974370	−0.487185	−	0.873299i	$-0.661976\pi$
$107$	−10.0790	−0.974370	−0.487185	+	0.873299i	$0.661976\pi$
$108$	2.19810	0.211512
$109$	−3.04268	−0.291435	−0.145718	−	0.989326i	$-0.546549\pi$
$109$	−3.04268	−0.291435	−0.145718	+	0.989326i	$0.546549\pi$
$110$	−3.09686	−0.295274
$111$	−9.23201	−0.876263
$112$	1.80331	0.170397
$113$	20.1706	1.89749	0.948743	−	0.316047i	$-0.102356\pi$
$113$	20.1706	1.89749	0.948743	+	0.316047i	$0.102356\pi$
$114$	5.05085	0.473056
$115$	−2.14902	−0.200397
$116$	22.3763	2.07759
$117$	15.4831	1.43141
$118$	−14.5525	−1.33967
$119$	−7.52988	−0.690263
$120$	−2.22630	−0.203232
$121$	13.0998	1.19089
$122$	−22.1208	−2.00272
$123$	24.2029	2.18231
$124$	−2.63559	−0.236683
$125$	−2.69202	−0.240782
$126$	−16.8301	−1.49934
$127$	5.48670	0.486866	0.243433	−	0.969918i	$-0.421726\pi$
$127$	5.48670	0.486866	0.243433	+	0.969918i	$0.421726\pi$
$128$	19.7217	1.74317
$129$	−12.1552	−1.07021
$130$	−2.99828	−0.262966
$131$	6.37401	0.556900	0.278450	−	0.960451i	$-0.410179\pi$
$131$	6.37401	0.556900	0.278450	+	0.960451i	$0.410179\pi$
$132$	41.8858	3.64569
$133$	−1.92790	−0.167170
$134$	−24.6557	−2.12993
$135$	0.174774	0.0150421
$136$	11.1257	0.954020
$137$	14.3030	1.22199	0.610994	−	0.791635i	$-0.290770\pi$
$137$	14.3030	1.22199	0.610994	+	0.791635i	$0.290770\pi$
$138$	46.1095	3.92510
$139$	−0.576912	−0.0489331	−0.0244665	−	0.999701i	$-0.507789\pi$
$139$	−0.576912	−0.0489331	−0.0244665	+	0.999701i	$0.507789\pi$
$140$	2.05445	0.173633
$141$	32.7593	2.75883
$142$	23.5216	1.97389
$143$	23.3326	1.95117
$144$	2.64495	0.220412
$145$	1.77917	0.147752
$146$	−30.9808	−2.56399
$147$	−5.17068	−0.426470
$148$	−12.5877	−1.03470
$149$	−15.9403	−1.30588	−0.652940	−	0.757410i	$-0.726464\pi$
$149$	−15.9403	−1.30588	−0.652940	+	0.757410i	$0.726464\pi$
$150$	28.6662	2.34058
$151$	−7.37360	−0.600055	−0.300028	−	0.953931i	$-0.596996\pi$
$151$	−7.37360	−0.600055	−0.300028	+	0.953931i	$0.596996\pi$
$152$	2.84855	0.231048
$153$	−11.0442	−0.892870
$154$	−25.3625	−2.04377
$155$	−0.209559	−0.0168322
$156$	40.5524	3.24679
$157$	−8.69718	−0.694111	−0.347055	−	0.937845i	$-0.612818\pi$
$157$	−8.69718	−0.694111	−0.347055	+	0.937845i	$0.612818\pi$
$158$	24.6138	1.95817
$159$	30.8996	2.45050
$160$	1.26776	0.100225
$161$	−17.5999	−1.38707
$162$	18.9828	1.49143
$163$	−15.8668	−1.24278	−0.621391	−	0.783500i	$-0.713432\pi$
$163$	−15.8668	−1.24278	−0.621391	+	0.783500i	$0.713432\pi$
$164$	33.0004	2.57690
$165$	3.33040	0.259271
$166$	−2.93511	−0.227809
$167$	−0.228934	−0.0177155	−0.00885773	−	0.999961i	$-0.502820\pi$
$167$	−0.228934	−0.0177155	−0.00885773	+	0.999961i	$0.502820\pi$
$168$	−18.2328	−1.40669
$169$	9.58982	0.737679
$170$	2.13869	0.164030
$171$	−2.82768	−0.216238
$172$	−16.5734	−1.26371
$173$	1.11355	0.0846620	0.0423310	−	0.999104i	$-0.486522\pi$
$173$	1.11355	0.0846620	0.0423310	+	0.999104i	$0.486522\pi$
$174$	−38.1741	−2.89397
$175$	−10.9418	−0.827123
$176$	3.98587	0.300446
$177$	15.6499	1.17632
$178$	−0.111908	−0.00838784
$179$	−3.83925	−0.286959	−0.143480	−	0.989653i	$-0.545829\pi$
$179$	−3.83925	−0.286959	−0.143480	+	0.989653i	$0.545829\pi$
$180$	3.01329	0.224597
$181$	8.09138	0.601428	0.300714	−	0.953714i	$-0.402775\pi$
$181$	8.09138	0.601428	0.300714	+	0.953714i	$0.402775\pi$
$182$	−24.5551	−1.82015
$183$	23.7890	1.75853
$184$	26.0046	1.91708
$185$	−1.00087	−0.0735851
$186$	4.49632	0.329686
$187$	−16.6433	−1.21708
$188$	44.6668	3.25766
$189$	1.43135	0.104116
$190$	0.547576	0.0397254
$191$	−13.0090	−0.941296	−0.470648	−	0.882321i	$-0.655980\pi$
$191$	−13.0090	−0.941296	−0.470648	+	0.882321i	$0.655980\pi$
$192$	−31.2633	−2.25624
$193$	5.25224	0.378065	0.189032	−	0.981971i	$-0.439465\pi$
$193$	5.25224	0.378065	0.189032	+	0.981971i	$0.439465\pi$
$194$	11.4250	0.820266
$195$	3.22438	0.230902
$196$	−7.05015	−0.503582
$197$	24.1401	1.71991	0.859955	−	0.510370i	$-0.170492\pi$
$197$	24.1401	1.71991	0.859955	+	0.510370i	$0.170492\pi$
$198$	−37.1996	−2.64366
$199$	−20.4144	−1.44714	−0.723569	−	0.690253i	$-0.757499\pi$
$199$	−20.4144	−1.44714	−0.723569	+	0.690253i	$0.757499\pi$
$200$	16.1670	1.14318
$201$	26.5150	1.87023
$202$	0.0575244	0.00404741
$203$	14.5710	1.02268
$204$	−28.9263	−2.02525
$205$	2.62390	0.183261
$206$	24.6090	1.71459
$207$	−25.8141	−1.79420
$208$	3.85898	0.267572
$209$	−4.26124	−0.294756
$210$	−3.50489	−0.241861
$211$	9.24353	0.636351	0.318175	−	0.948032i	$-0.396930\pi$
$211$	9.24353	0.636351	0.318175	+	0.948032i	$0.396930\pi$
$212$	42.1312	2.89358
$213$	−25.2954	−1.73321
$214$	23.4448	1.60265
$215$	−1.31778	−0.0898717
$216$	−2.11488	−0.143899
$217$	−1.71624	−0.116506
$218$	7.07760	0.479356
$219$	33.3171	2.25136
$220$	4.54095	0.306151
$221$	−16.1135	−1.08391
$222$	21.4747	1.44129
$223$	11.2975	0.756537	0.378269	−	0.925696i	$-0.376520\pi$
$223$	11.2975	0.756537	0.378269	+	0.925696i	$0.376520\pi$
$224$	10.3827	0.693720
$225$	−16.0485	−1.06990
$226$	−46.9190	−3.12100
$227$	2.02413	0.134346	0.0671732	−	0.997741i	$-0.478602\pi$
$227$	2.02413	0.134346	0.0671732	+	0.997741i	$0.478602\pi$
$228$	−7.40610	−0.490481
$229$	11.9549	0.789999	0.395000	−	0.918681i	$-0.370745\pi$
$229$	11.9549	0.789999	0.395000	+	0.918681i	$0.370745\pi$
$230$	4.99886	0.329615
$231$	27.2751	1.79457
$232$	−21.5292	−1.41346
$233$	−28.1718	−1.84560	−0.922799	−	0.385282i	$-0.874104\pi$
$233$	−28.1718	−1.84560	−0.922799	+	0.385282i	$0.874104\pi$
$234$	−36.0154	−2.35440
$235$	3.55152	0.231676
$236$	21.3384	1.38901
$237$	−26.4700	−1.71941
$238$	17.5153	1.13535
$239$	−4.49543	−0.290785	−0.145393	−	0.989374i	$-0.546444\pi$
$239$	−4.49543	−0.290785	−0.145393	+	0.989374i	$0.546444\pi$
$240$	0.550815	0.0355549
$241$	15.3477	0.988631	0.494315	−	0.869283i	$-0.335419\pi$
$241$	15.3477	0.988631	0.494315	+	0.869283i	$0.335419\pi$
$242$	−30.4715	−1.95878
$243$	−22.3477	−1.43361
$244$	32.4359	2.07650
$245$	−0.560567	−0.0358133
$246$	−56.2987	−3.58948
$247$	−4.12559	−0.262505
$248$	2.53581	0.161024
$249$	3.15645	0.200032
$250$	6.26194	0.396040
$251$	14.2360	0.898570	0.449285	−	0.893388i	$-0.351679\pi$
$251$	14.2360	0.898570	0.449285	+	0.893388i	$0.351679\pi$
$252$	24.6781	1.55457
$253$	−38.9011	−2.44569
$254$	−12.7627	−0.800801
$255$	−2.29997	−0.144030
$256$	−20.8794	−1.30496
$257$	−19.4820	−1.21525	−0.607627	−	0.794223i	$-0.707878\pi$
$257$	−19.4820	−1.21525	−0.607627	+	0.794223i	$0.707878\pi$
$258$	28.2744	1.76028
$259$	−8.19684	−0.509327
$260$	4.39639	0.272653
$261$	21.3715	1.32286
$262$	−14.8267	−0.915994
$263$	−13.5147	−0.833353	−0.416676	−	0.909055i	$-0.636805\pi$
$263$	−13.5147	−0.833353	−0.416676	+	0.909055i	$0.636805\pi$
$264$	−40.3000	−2.48029
$265$	3.34991	0.205783
$266$	4.48451	0.274963
$267$	0.120347	0.00736510
$268$	36.1529	2.20839
$269$	20.2994	1.23767	0.618837	−	0.785519i	$-0.287604\pi$
$269$	20.2994	1.23767	0.618837	+	0.785519i	$0.287604\pi$
$270$	−0.406543	−0.0247414
$271$	−2.42275	−0.147171	−0.0735857	−	0.997289i	$-0.523444\pi$
$271$	−2.42275	−0.147171	−0.0735857	+	0.997289i	$0.523444\pi$
$272$	−2.75264	−0.166903
$273$	26.4068	1.59821
$274$	−33.2704	−2.00994
$275$	−24.1847	−1.45839
$276$	−67.6107	−4.06969
$277$	8.18806	0.491973	0.245986	−	0.969273i	$-0.420888\pi$
$277$	8.18806	0.491973	0.245986	+	0.969273i	$0.420888\pi$
$278$	1.34196	0.0804855
$279$	−2.51723	−0.150703
$280$	−1.97667	−0.118128
$281$	20.4467	1.21975	0.609875	−	0.792498i	$-0.291220\pi$
$281$	20.4467	1.21975	0.609875	+	0.792498i	$0.291220\pi$
$282$	−76.2018	−4.53775
$283$	−22.1221	−1.31503	−0.657513	−	0.753444i	$-0.728391\pi$
$283$	−22.1221	−1.31503	−0.657513	+	0.753444i	$0.728391\pi$
$284$	−34.4899	−2.04660
$285$	−0.588869	−0.0348816
$286$	−54.2742	−3.20930
$287$	21.4891	1.26846
$288$	15.2284	0.897342
$289$	−5.50613	−0.323890
$290$	−4.13856	−0.243024
$291$	−12.2866	−0.720250
$292$	45.4273	2.65843
$293$	−22.8363	−1.33411	−0.667054	−	0.745009i	$-0.732445\pi$
$293$	−22.8363	−1.33411	−0.667054	+	0.745009i	$0.732445\pi$
$294$	12.0276	0.701462
$295$	1.69665	0.0987827
$296$	12.1111	0.703946
$297$	3.16372	0.183577
$298$	37.0789	2.14792
$299$	−37.6627	−2.17809
$300$	−42.0334	−2.42680
$301$	−10.7923	−0.622056
$302$	17.1518	0.986976
$303$	−0.0618624	−0.00355390
$304$	−0.704767	−0.0404212
$305$	2.57902	0.147674
$306$	25.6900	1.46860
$307$	12.3684	0.705901	0.352951	−	0.935642i	$-0.385178\pi$
$307$	12.3684	0.705901	0.352951	+	0.935642i	$0.385178\pi$
$308$	37.1892	2.11905
$309$	−26.4648	−1.50553
$310$	0.487458	0.0276857
$311$	−11.1417	−0.631788	−0.315894	−	0.948794i	$-0.602304\pi$
$311$	−11.1417	−0.631788	−0.315894	+	0.948794i	$0.602304\pi$
$312$	−39.0171	−2.20891
$313$	−5.13903	−0.290475	−0.145238	−	0.989397i	$-0.546395\pi$
$313$	−5.13903	−0.290475	−0.145238	+	0.989397i	$0.546395\pi$
$314$	20.2306	1.14168
$315$	1.96219	0.110557
$316$	−36.0915	−2.03030
$317$	15.8677	0.891217	0.445609	−	0.895228i	$-0.352987\pi$
$317$	15.8677	0.891217	0.445609	+	0.895228i	$0.352987\pi$
$318$	−71.8760	−4.03060
$319$	32.2062	1.80320
$320$	−3.38934	−0.189470
$321$	−25.2128	−1.40724
$322$	40.9394	2.28146
$323$	2.94281	0.163743
$324$	−27.8347	−1.54637
$325$	−23.4148	−1.29882
$326$	36.9079	2.04414
$327$	−7.61133	−0.420907
$328$	−31.7510	−1.75316
$329$	29.0861	1.60357
$330$	−7.74687	−0.426451
$331$	35.3509	1.94306	0.971530	−	0.236918i	$-0.0761374\pi$
$331$	35.3509	1.94306	0.971530	+	0.236918i	$0.0761374\pi$
$332$	4.30378	0.236200
$333$	−12.0224	−0.658825
$334$	0.532526	0.0291386
$335$	2.87457	0.157054
$336$	4.51103	0.246097
$337$	0.272100	0.0148222	0.00741111	−	0.999973i	$-0.497641\pi$
$337$	0.272100	0.0148222	0.00741111	+	0.999973i	$0.497641\pi$
$338$	−22.3070	−1.21334
$339$	50.4572	2.74046
$340$	−3.13598	−0.170072
$341$	−3.79340	−0.205424
$342$	6.57750	0.355671
$343$	−20.1381	−1.08736
$344$	15.9460	0.859750
$345$	−5.37582	−0.289424
$346$	−2.59025	−0.139253
$347$	−21.4339	−1.15063	−0.575316	−	0.817931i	$-0.695121\pi$
$347$	−21.4339	−1.15063	−0.575316	+	0.817931i	$0.695121\pi$
$348$	55.9750	3.00057
$349$	15.8190	0.846771	0.423386	−	0.905950i	$-0.360842\pi$
$349$	15.8190	0.846771	0.423386	+	0.905950i	$0.360842\pi$
$350$	25.4519	1.36046
$351$	3.06300	0.163491
$352$	22.9488	1.22317
$353$	6.05735	0.322400	0.161200	−	0.986922i	$-0.448464\pi$
$353$	6.05735	0.322400	0.161200	+	0.986922i	$0.448464\pi$
$354$	−36.4034	−1.93482
$355$	−2.74234	−0.145548
$356$	0.164091	0.00869681
$357$	−18.8362	−0.996917
$358$	8.93052	0.471993
$359$	−10.3774	−0.547697	−0.273848	−	0.961773i	$-0.588297\pi$
$359$	−10.3774	−0.547697	−0.273848	+	0.961773i	$0.588297\pi$
$360$	−2.89921	−0.152802
$361$	−18.2465	−0.960344
$362$	−18.8215	−0.989234
$363$	32.7694	1.71995
$364$	36.0053	1.88719
$365$	3.61199	0.189060
$366$	−55.3357	−2.89245
$367$	30.7027	1.60267	0.801335	−	0.598216i	$-0.204124\pi$
$367$	30.7027	1.60267	0.801335	+	0.598216i	$0.204124\pi$
$368$	−6.43386	−0.335388
$369$	31.5184	1.64078
$370$	2.32813	0.121034
$371$	27.4349	1.42435
$372$	−6.59299	−0.341830
$373$	−29.1844	−1.51111	−0.755557	−	0.655083i	$-0.772634\pi$
$373$	−29.1844	−1.51111	−0.755557	+	0.655083i	$0.772634\pi$
$374$	38.7142	2.00186
$375$	−6.73416	−0.347751
$376$	−42.9758	−2.21631
$377$	31.1810	1.60590
$378$	−3.32948	−0.171250
$379$	−22.3543	−1.14827	−0.574133	−	0.818762i	$-0.694661\pi$
$379$	−22.3543	−1.14827	−0.574133	+	0.818762i	$0.694661\pi$
$380$	−0.802915	−0.0411887
$381$	13.7251	0.703158
$382$	30.2603	1.54825
$383$	35.6178	1.81998	0.909991	−	0.414627i	$-0.136088\pi$
$383$	35.6178	1.81998	0.909991	+	0.414627i	$0.136088\pi$
$384$	49.3343	2.51758
$385$	2.95696	0.150701
$386$	−12.2173	−0.621844
$387$	−15.8292	−0.804642
$388$	−16.7525	−0.850481
$389$	−0.784297	−0.0397654	−0.0198827	−	0.999802i	$-0.506329\pi$
$389$	−0.784297	−0.0397654	−0.0198827	+	0.999802i	$0.506329\pi$
$390$	−7.50026	−0.379790
$391$	26.8651	1.35863
$392$	6.78323	0.342605
$393$	15.9447	0.804306
$394$	−56.1525	−2.82892
$395$	−2.86968	−0.144389
$396$	54.5460	2.74104
$397$	−21.4992	−1.07902	−0.539508	−	0.841981i	$-0.681390\pi$
$397$	−21.4992	−1.07902	−0.539508	+	0.841981i	$0.681390\pi$
$398$	47.4861	2.38026
$399$	−4.82269	−0.241436
$400$	−3.99991	−0.199996
$401$	−27.2862	−1.36261	−0.681303	−	0.732002i	$-0.738586\pi$
$401$	−27.2862	−1.36261	−0.681303	+	0.732002i	$0.738586\pi$
$402$	−61.6770	−3.07617
$403$	−3.67264	−0.182947
$404$	−0.0843485	−0.00419649
$405$	−2.21317	−0.109973
$406$	−33.8937	−1.68212
$407$	−18.1175	−0.898050
$408$	27.8312	1.37785
$409$	−17.6447	−0.872473	−0.436237	−	0.899832i	$-0.643689\pi$
$409$	−17.6447	−0.872473	−0.436237	+	0.899832i	$0.643689\pi$
$410$	−6.10349	−0.301430
$411$	35.7793	1.76486
$412$	−36.0844	−1.77775
$413$	13.8951	0.683734
$414$	60.0464	2.95112
$415$	0.342199	0.0167979
$416$	22.2182	1.08934
$417$	−1.44316	−0.0706719
$418$	9.91212	0.484818
$419$	12.5452	0.612876	0.306438	−	0.951891i	$-0.400863\pi$
$419$	12.5452	0.612876	0.306438	+	0.951891i	$0.400863\pi$
$420$	5.13925	0.250770
$421$	40.4126	1.96959	0.984794	−	0.173725i	$-0.0555803\pi$
$421$	40.4126	1.96959	0.984794	+	0.173725i	$0.0555803\pi$
$422$	−21.5015	−1.04668
$423$	42.6610	2.07425
$424$	−40.5361	−1.96861
$425$	16.7020	0.810164
$426$	58.8399	2.85080
$427$	21.1215	1.02214
$428$	−34.3773	−1.66169
$429$	58.3670	2.81799
$430$	3.06530	0.147822
$431$	28.2987	1.36310	0.681551	−	0.731771i	$-0.261306\pi$
$431$	28.2987	1.36310	0.681551	+	0.731771i	$0.261306\pi$
$432$	0.523248	0.0251748
$433$	14.1155	0.678346	0.339173	−	0.940724i	$-0.389853\pi$
$433$	14.1155	0.678346	0.339173	+	0.940724i	$0.389853\pi$
$434$	3.99216	0.191630
$435$	4.45065	0.213392
$436$	−10.3779	−0.497013
$437$	6.87836	0.329037
$438$	−77.4992	−3.70305
$439$	−34.1947	−1.63202	−0.816012	−	0.578035i	$-0.803820\pi$
$439$	−34.1947	−1.63202	−0.816012	+	0.578035i	$0.803820\pi$
$440$	−4.36903	−0.208285
$441$	−6.73354	−0.320645
$442$	37.4818	1.78283
$443$	−29.5320	−1.40311	−0.701553	−	0.712617i	$-0.747510\pi$
$443$	−29.5320	−1.40311	−0.701553	+	0.712617i	$0.747510\pi$
$444$	−31.4885	−1.49438
$445$	0.0130471	0.000618492 0
$446$	−26.2793	−1.24436
$447$	−39.8750	−1.88602
$448$	−27.7578	−1.31143
$449$	−7.90501	−0.373060	−0.186530	−	0.982449i	$-0.559724\pi$
$449$	−7.90501	−0.373060	−0.186530	+	0.982449i	$0.559724\pi$
$450$	37.3307	1.75978
$451$	47.4974	2.23657
$452$	68.7976	3.23597
$453$	−18.4452	−0.866633
$454$	−4.70836	−0.220974
$455$	2.86283	0.134212
$456$	7.12571	0.333692
$457$	9.83855	0.460228	0.230114	−	0.973164i	$-0.426090\pi$
$457$	9.83855	0.460228	0.230114	+	0.973164i	$0.426090\pi$
$458$	−27.8083	−1.29940
$459$	−2.18486	−0.101981
$460$	−7.32986	−0.341756
$461$	−29.8511	−1.39030	−0.695152	−	0.718862i	$-0.744663\pi$
$461$	−29.8511	−1.39030	−0.695152	+	0.718862i	$0.744663\pi$
$462$	−63.4449	−2.95172
$463$	−38.9046	−1.80805	−0.904025	−	0.427480i	$-0.859402\pi$
$463$	−38.9046	−1.80805	−0.904025	+	0.427480i	$0.859402\pi$
$464$	5.32660	0.247281
$465$	−0.524217	−0.0243100
$466$	65.5308	3.03566
$467$	10.3800	0.480330	0.240165	−	0.970732i	$-0.422798\pi$
$467$	10.3800	0.480330	0.240165	+	0.970732i	$0.422798\pi$
$468$	52.8096	2.44112
$469$	23.5420	1.08707
$470$	−8.26123	−0.381062
$471$	−21.7562	−1.00247
$472$	−20.5306	−0.944996
$473$	−23.8541	−1.09681
$474$	61.5721	2.82810
$475$	4.27626	0.196208
$476$	−25.6829	−1.17717
$477$	40.2392	1.84243
$478$	10.4569	0.478286
$479$	11.3549	0.518817	0.259408	−	0.965768i	$-0.416472\pi$
$479$	11.3549	0.518817	0.259408	+	0.965768i	$0.416472\pi$
$480$	3.17134	0.144751
$481$	−17.5407	−0.799789
$482$	−35.7004	−1.62611
$483$	−44.0266	−2.00328
$484$	44.6806	2.03094
$485$	−1.33202	−0.0604838
$486$	51.9832	2.35801
$487$	10.6873	0.484287	0.242143	−	0.970240i	$-0.422150\pi$
$487$	10.6873	0.484287	0.242143	+	0.970240i	$0.422150\pi$
$488$	−31.2079	−1.41272
$489$	−39.6912	−1.79490
$490$	1.30394	0.0589060
$491$	16.0231	0.723112	0.361556	−	0.932350i	$-0.382246\pi$
$491$	16.0231	0.723112	0.361556	+	0.932350i	$0.382246\pi$
$492$	82.5512	3.72170
$493$	−22.2416	−1.00171
$494$	9.59658	0.431770
$495$	4.33703	0.194935
$496$	−0.627391	−0.0281707
$497$	−22.4591	−1.00743
$498$	−7.34226	−0.329014
$499$	−14.3257	−0.641306	−0.320653	−	0.947197i	$-0.603902\pi$
$499$	−14.3257	−0.641306	−0.320653	+	0.947197i	$0.603902\pi$
$500$	−9.18193	−0.410629
$501$	−0.572685	−0.0255857
$502$	−33.1146	−1.47798
$503$	31.9707	1.42550	0.712751	−	0.701417i	$-0.247449\pi$
$503$	31.9707	1.42550	0.712751	+	0.701417i	$0.247449\pi$
$504$	−23.7438	−1.05763
$505$	−0.00670666	−0.000298443 0
$506$	90.4883	4.02270
$507$	23.9892	1.06540
$508$	18.7140	0.830299
$509$	−0.711031	−0.0315159	−0.0157579	−	0.999876i	$-0.505016\pi$
$509$	−0.711031	−0.0315159	−0.0157579	+	0.999876i	$0.505016\pi$
$510$	5.34999	0.236902
$511$	29.5813	1.30860
$512$	9.12444	0.403247
$513$	−0.559398	−0.0246980
$514$	45.3173	1.99886
$515$	−2.86912	−0.126428
$516$	−41.4589	−1.82513
$517$	64.2889	2.82742
$518$	19.0668	0.837745
$519$	2.78558	0.122274
$520$	−4.22995	−0.185495
$521$	−28.8712	−1.26487	−0.632435	−	0.774613i	$-0.717945\pi$
$521$	−28.8712	−1.26487	−0.632435	+	0.774613i	$0.717945\pi$
$522$	−49.7124	−2.17585
$523$	−27.9348	−1.22150	−0.610751	−	0.791823i	$-0.709132\pi$
$523$	−27.9348	−1.22150	−0.610751	+	0.791823i	$0.709132\pi$
$524$	21.7404	0.949735
$525$	−27.3712	−1.19458
$526$	31.4367	1.37071
$527$	2.61972	0.114117
$528$	9.97074	0.433921
$529$	39.7930	1.73013
$530$	−7.79226	−0.338474
$531$	20.3802	0.884425
$532$	−6.57567	−0.285091
$533$	45.9854	1.99185
$534$	−0.279940	−0.0121142
$535$	−2.73338	−0.118174
$536$	−34.7842	−1.50245
$537$	−9.60398	−0.414442
$538$	−47.2186	−2.03574
$539$	−10.1473	−0.437074
$540$	0.596117	0.0256528
$541$	−23.0677	−0.991757	−0.495879	−	0.868392i	$-0.665154\pi$
$541$	−23.0677	−0.991757	−0.495879	+	0.868392i	$0.665154\pi$
$542$	5.63558	0.242069
$543$	20.2408	0.868615
$544$	−15.8484	−0.679496
$545$	−0.825164	−0.0353461
$546$	−61.4252	−2.62876
$547$	10.4165	0.445377	0.222688	−	0.974890i	$-0.428517\pi$
$547$	10.4165	0.445377	0.222688	+	0.974890i	$0.428517\pi$
$548$	48.7846	2.08397
$549$	30.9793	1.32216
$550$	56.2563	2.39878
$551$	−5.69460	−0.242598
$552$	65.0510	2.76876
$553$	−23.5020	−0.999405
$554$	−19.0463	−0.809201
$555$	−2.50369	−0.106276
$556$	−1.96773	−0.0834503
$557$	−17.6256	−0.746819	−0.373410	−	0.927667i	$-0.621811\pi$
$557$	−17.6256	−0.746819	−0.373410	+	0.927667i	$0.621811\pi$
$558$	5.85536	0.247877
$559$	−23.0948	−0.976805
$560$	0.489053	0.0206663
$561$	−41.6336	−1.75777
$562$	−47.5614	−2.00626
$563$	15.4735	0.652128	0.326064	−	0.945348i	$-0.394277\pi$
$563$	15.4735	0.652128	0.326064	+	0.945348i	$0.394277\pi$
$564$	111.735	4.70490
$565$	5.47019	0.230133
$566$	51.4586	2.16297
$567$	−18.1253	−0.761192
$568$	33.1841	1.39238
$569$	−19.2204	−0.805763	−0.402881	−	0.915252i	$-0.631991\pi$
$569$	−19.2204	−0.805763	−0.402881	+	0.915252i	$0.631991\pi$
$570$	1.36978	0.0573736
$571$	−5.21232	−0.218129	−0.109064	−	0.994035i	$-0.534785\pi$
$571$	−5.21232	−0.218129	−0.109064	+	0.994035i	$0.534785\pi$
$572$	79.5826	3.32752
$573$	−32.5423	−1.35947
$574$	−49.9861	−2.08638
$575$	39.0382	1.62801
$576$	−40.7129	−1.69637
$577$	−38.7555	−1.61341	−0.806707	−	0.590952i	$-0.798752\pi$
$577$	−38.7555	−1.61341	−0.806707	+	0.590952i	$0.798752\pi$
$578$	12.8079	0.532737
$579$	13.1386	0.546022
$580$	6.06839	0.251976
$581$	2.80252	0.116268
$582$	28.5799	1.18467
$583$	60.6394	2.51143
$584$	−43.7075	−1.80863
$585$	4.19896	0.173606
$586$	53.1197	2.19435
$587$	3.06646	0.126566	0.0632832	−	0.997996i	$-0.479843\pi$
$587$	3.06646	0.126566	0.0632832	+	0.997996i	$0.479843\pi$
$588$	−17.6361	−0.727301
$589$	0.670736	0.0276372
$590$	−3.94659	−0.162479
$591$	60.3870	2.48399
$592$	−2.99645	−0.123153
$593$	−6.84348	−0.281028	−0.140514	−	0.990079i	$-0.544876\pi$
$593$	−6.84348	−0.281028	−0.140514	+	0.990079i	$0.544876\pi$
$594$	−7.35916	−0.301950
$595$	−2.04208	−0.0837171
$596$	−54.3690	−2.22704
$597$	−51.0671	−2.09004
$598$	87.6077	3.58255
$599$	−37.0353	−1.51322	−0.756610	−	0.653866i	$-0.773146\pi$
$599$	−37.0353	−1.51322	−0.756610	+	0.653866i	$0.773146\pi$
$600$	40.4420	1.65104
$601$	38.9440	1.58856	0.794280	−	0.607552i	$-0.207848\pi$
$601$	38.9440	1.58856	0.794280	+	0.607552i	$0.207848\pi$
$602$	25.1040	1.02316
$603$	34.5294	1.40614
$604$	−25.1498	−1.02333
$605$	3.55262	0.144434
$606$	0.143899	0.00584549
$607$	1.58674	0.0644040	0.0322020	−	0.999481i	$-0.489748\pi$
$607$	1.58674	0.0644040	0.0322020	+	0.999481i	$0.489748\pi$
$608$	−4.05773	−0.164563
$609$	36.4497	1.47701
$610$	−5.99909	−0.242896
$611$	62.2424	2.51806
$612$	−37.6695	−1.52270
$613$	−3.52832	−0.142507	−0.0712537	−	0.997458i	$-0.522700\pi$
$613$	−3.52832	−0.142507	−0.0712537	+	0.997458i	$0.522700\pi$
$614$	−28.7703	−1.16107
$615$	6.56376	0.264676
$616$	−35.7812	−1.44167
$617$	35.4685	1.42791	0.713955	−	0.700192i	$-0.246902\pi$
$617$	35.4685	1.42791	0.713955	+	0.700192i	$0.246902\pi$
$618$	61.5600	2.47631
$619$	39.6901	1.59528	0.797640	−	0.603133i	$-0.206081\pi$
$619$	39.6901	1.59528	0.797640	+	0.603133i	$0.206081\pi$
$620$	−0.714763	−0.0287056
$621$	−5.10677	−0.204928
$622$	25.9169	1.03917
$623$	0.106852	0.00428095
$624$	9.65333	0.386443
$625$	23.9022	0.956088
$626$	11.9540	0.477776
$627$	−10.6596	−0.425703
$628$	−29.6643	−1.18373
$629$	12.5119	0.498884
$630$	−4.56427	−0.181845
$631$	12.0235	0.478646	0.239323	−	0.970940i	$-0.423074\pi$
$631$	12.0235	0.478646	0.239323	+	0.970940i	$0.423074\pi$
$632$	34.7251	1.38129
$633$	23.1229	0.919053
$634$	−36.9100	−1.46588
$635$	1.48797	0.0590485
$636$	105.392	4.17907
$637$	−9.82424	−0.389251
$638$	−74.9153	−2.96593
$639$	−32.9411	−1.30313
$640$	5.34846	0.211416
$641$	−19.0504	−0.752445	−0.376223	−	0.926529i	$-0.622777\pi$
$641$	−19.0504	−0.752445	−0.376223	+	0.926529i	$0.622777\pi$
$642$	58.6477	2.31464
$643$	−30.9846	−1.22191	−0.610956	−	0.791665i	$-0.709215\pi$
$643$	−30.9846	−1.22191	−0.610956	+	0.791665i	$0.709215\pi$
$644$	−60.0297	−2.36550
$645$	−3.29645	−0.129798
$646$	−6.84531	−0.269325
$647$	19.0168	0.747627	0.373814	−	0.927504i	$-0.378050\pi$
$647$	19.0168	0.747627	0.373814	+	0.927504i	$0.378050\pi$
$648$	26.7809	1.05205
$649$	30.7124	1.20557
$650$	54.4655	2.13631
$651$	−4.29321	−0.168264
$652$	−54.1183	−2.11944
$653$	28.3896	1.11097	0.555486	−	0.831526i	$-0.312532\pi$
$653$	28.3896	1.11097	0.555486	+	0.831526i	$0.312532\pi$
$654$	17.7048	0.692312
$655$	1.72861	0.0675424
$656$	7.85560	0.306710
$657$	43.3873	1.69270
$658$	−67.6574	−2.63756
$659$	−34.2699	−1.33497	−0.667483	−	0.744625i	$-0.732628\pi$
$659$	−34.2699	−1.33497	−0.667483	+	0.744625i	$0.732628\pi$
$660$	11.3593	0.442160
$661$	3.09710	0.120463	0.0602316	−	0.998184i	$-0.480816\pi$
$661$	3.09710	0.120463	0.0602316	+	0.998184i	$0.480816\pi$
$662$	−82.2300	−3.19596
$663$	−40.3083	−1.56544
$664$	−4.14084	−0.160696
$665$	−0.522841	−0.0202749
$666$	27.9655	1.08364
$667$	−51.9863	−2.01292
$668$	−0.780847	−0.0302119
$669$	28.2610	1.09263
$670$	−6.68656	−0.258324
$671$	46.6850	1.80225
$672$	25.9725	1.00191
$673$	26.6957	1.02904	0.514522	−	0.857477i	$-0.327969\pi$
$673$	26.6957	1.02904	0.514522	+	0.857477i	$0.327969\pi$
$674$	−0.632935	−0.0243797
$675$	−3.17487	−0.122201
$676$	32.7089	1.25803
$677$	2.19321	0.0842917	0.0421459	−	0.999111i	$-0.486581\pi$
$677$	2.19321	0.0842917	0.0421459	+	0.999111i	$0.486581\pi$
$678$	−117.369	−4.50753
$679$	−10.9089	−0.418645
$680$	3.01725	0.115706
$681$	5.06342	0.194031
$682$	8.82387	0.337883
$683$	20.0502	0.767200	0.383600	−	0.923499i	$-0.374684\pi$
$683$	20.0502	0.767200	0.383600	+	0.923499i	$0.374684\pi$
$684$	−9.64464	−0.368772
$685$	3.87893	0.148206
$686$	46.8435	1.78849
$687$	29.9054	1.14096
$688$	−3.94524	−0.150411
$689$	58.7090	2.23664
$690$	12.5048	0.476048
$691$	16.5811	0.630774	0.315387	−	0.948963i	$-0.397866\pi$
$691$	16.5811	0.630774	0.315387	+	0.948963i	$0.397866\pi$
$692$	3.79811	0.144382
$693$	35.5191	1.34926
$694$	49.8576	1.89257
$695$	−0.156457	−0.00593474
$696$	−53.8558	−2.04140
$697$	−32.8017	−1.24245
$698$	−36.7967	−1.39278
$699$	−70.4725	−2.66552
$700$	−37.3203	−1.41057
$701$	−30.3337	−1.14569	−0.572844	−	0.819664i	$-0.694160\pi$
$701$	−30.3337	−1.14569	−0.572844	+	0.819664i	$0.694160\pi$
$702$	−7.12489	−0.268912
$703$	3.20347	0.120821
$704$	−61.3532	−2.31233
$705$	8.88422	0.334599
$706$	−14.0901	−0.530287
$707$	−0.0549259	−0.00206570
$708$	53.3786	2.00609
$709$	−48.3777	−1.81686	−0.908431	−	0.418035i	$-0.862719\pi$
$709$	−48.3777	−1.81686	−0.908431	+	0.418035i	$0.862719\pi$
$710$	6.37899	0.239399
$711$	−34.4707	−1.29275
$712$	−0.157879	−0.00591675
$713$	6.12319	0.229315
$714$	43.8151	1.63974
$715$	6.32772	0.236643
$716$	−13.0949	−0.489379
$717$	−11.2454	−0.419968
$718$	24.1389	0.900856
$719$	−24.6084	−0.917738	−0.458869	−	0.888504i	$-0.651745\pi$
$719$	−24.6084	−0.917738	−0.458869	+	0.888504i	$0.651745\pi$
$720$	0.717302	0.0267322
$721$	−23.4973	−0.875087
$722$	42.4435	1.57958
$723$	38.3926	1.42784
$724$	27.5980	1.02567
$725$	−32.3197	−1.20033
$726$	−76.2252	−2.82898
$727$	−11.0507	−0.409847	−0.204924	−	0.978778i	$-0.565695\pi$
$727$	−11.0507	−0.409847	−0.204924	+	0.978778i	$0.565695\pi$
$728$	−34.6422	−1.28393
$729$	−31.4210	−1.16374
$730$	−8.40189	−0.310968
$731$	16.4737	0.609301
$732$	81.1392	2.99899
$733$	−11.4154	−0.421639	−0.210819	−	0.977525i	$-0.567613\pi$
$733$	−11.4154	−0.421639	−0.210819	+	0.977525i	$0.567613\pi$
$734$	−71.4180	−2.63609
$735$	−1.40227	−0.0517236
$736$	−37.0432	−1.36543
$737$	52.0348	1.91673
$738$	−73.3154	−2.69878
$739$	−42.8950	−1.57792	−0.788959	−	0.614446i	$-0.789379\pi$
$739$	−42.8950	−1.57792	−0.788959	+	0.614446i	$0.789379\pi$
$740$	−3.41375	−0.125492
$741$	−10.3203	−0.379124
$742$	−63.8167	−2.34278
$743$	−21.8038	−0.799905	−0.399953	−	0.916536i	$-0.630973\pi$
$743$	−21.8038	−0.799905	−0.399953	+	0.916536i	$0.630973\pi$
$744$	6.34338	0.232560
$745$	−4.32296	−0.158381
$746$	67.8863	2.48549
$747$	4.11051	0.150396
$748$	−56.7669	−2.07560
$749$	−22.3857	−0.817956
$750$	15.6644	0.571983
$751$	−6.10080	−0.222621	−0.111311	−	0.993786i	$-0.535505\pi$
$751$	−6.10080	−0.222621	−0.111311	+	0.993786i	$0.535505\pi$
$752$	10.6328	0.387737
$753$	35.6118	1.29777
$754$	−72.5305	−2.64140
$755$	−1.99970	−0.0727764
$756$	4.88204	0.177558
$757$	−34.2410	−1.24451	−0.622255	−	0.782815i	$-0.713783\pi$
$757$	−34.2410	−1.24451	−0.622255	+	0.782815i	$0.713783\pi$
$758$	51.9987	1.88868
$759$	−97.3120	−3.53220
$760$	0.772517	0.0280221
$761$	−18.5644	−0.672957	−0.336479	−	0.941691i	$-0.609236\pi$
$761$	−18.5644	−0.672957	−0.336479	+	0.941691i	$0.609236\pi$
$762$	−31.9261	−1.15656
$763$	−6.75788	−0.244652
$764$	−44.3709	−1.60528
$765$	−2.99515	−0.108290
$766$	−82.8509	−2.99352
$767$	29.7347	1.07366
$768$	−52.2303	−1.88470
$769$	24.7904	0.893966	0.446983	−	0.894542i	$-0.352498\pi$
$769$	24.7904	0.893966	0.446983	+	0.894542i	$0.352498\pi$
$770$	−6.87823	−0.247874
$771$	−48.7347	−1.75514
$772$	17.9143	0.644750
$773$	−38.7959	−1.39539	−0.697696	−	0.716394i	$-0.745791\pi$
$773$	−38.7959	−1.39539	−0.697696	+	0.716394i	$0.745791\pi$
$774$	36.8204	1.32348
$775$	3.80677	0.136743
$776$	16.1183	0.578613
$777$	−20.5046	−0.735598
$778$	1.82436	0.0654065
$779$	−8.39833	−0.300901
$780$	10.9977	0.393780
$781$	−49.6413	−1.77631
$782$	−62.4912	−2.23468
$783$	4.22790	0.151093
$784$	−1.67826	−0.0599378
$785$	−2.35865	−0.0841838
$786$	−37.0892	−1.32293
$787$	0.957677	0.0341375	0.0170687	−	0.999854i	$-0.494567\pi$
$787$	0.957677	0.0341375	0.0170687	+	0.999854i	$0.494567\pi$
$788$	82.3368	2.93313
$789$	−33.8074	−1.20357
$790$	6.67520	0.237493
$791$	44.7995	1.59289
$792$	−52.4809	−1.86483
$793$	45.1988	1.60506
$794$	50.0096	1.77477
$795$	8.37988	0.297204
$796$	−69.6292	−2.46794
$797$	46.0174	1.63002	0.815009	−	0.579448i	$-0.196732\pi$
$797$	46.0174	1.63002	0.815009	+	0.579448i	$0.196732\pi$
$798$	11.2181	0.397117
$799$	−44.3980	−1.57069
$800$	−23.0297	−0.814222
$801$	0.156722	0.00553751
$802$	63.4706	2.24123
$803$	65.3835	2.30733
$804$	90.4374	3.18948
$805$	−4.77304	−0.168228
$806$	8.54297	0.300913
$807$	50.7794	1.78752
$808$	0.0811551	0.00285503
$809$	−24.4160	−0.858420	−0.429210	−	0.903205i	$-0.641208\pi$
$809$	−24.4160	−0.858420	−0.429210	+	0.903205i	$0.641208\pi$
$810$	5.14808	0.180885
$811$	−34.1686	−1.19982	−0.599911	−	0.800066i	$-0.704798\pi$
$811$	−34.1686	−1.19982	−0.599911	+	0.800066i	$0.704798\pi$
$812$	49.6986	1.74408
$813$	−6.06056	−0.212553
$814$	42.1433	1.47712
$815$	−4.30302	−0.150728
$816$	−6.88579	−0.241051
$817$	4.21781	0.147562
$818$	41.0435	1.43505
$819$	34.3884	1.20163
$820$	8.94960	0.312534
$821$	−25.3672	−0.885320	−0.442660	−	0.896690i	$-0.645965\pi$
$821$	−25.3672	−0.885320	−0.442660	+	0.896690i	$0.645965\pi$
$822$	−83.2266	−2.90286
$823$	37.5985	1.31060	0.655301	−	0.755368i	$-0.272542\pi$
$823$	37.5985	1.31060	0.655301	+	0.755368i	$0.272542\pi$
$824$	34.7182	1.20947
$825$	−60.4986	−2.10629
$826$	−32.3216	−1.12461
$827$	−12.1826	−0.423629	−0.211815	−	0.977310i	$-0.567937\pi$
$827$	−12.1826	−0.423629	−0.211815	+	0.977310i	$0.567937\pi$
$828$	−88.0464	−3.05983
$829$	−28.0127	−0.972923	−0.486461	−	0.873702i	$-0.661713\pi$
$829$	−28.0127	−0.972923	−0.486461	+	0.873702i	$0.661713\pi$
$830$	−0.795993	−0.0276293
$831$	20.4826	0.710534
$832$	−59.4001	−2.05933
$833$	7.00771	0.242803
$834$	3.35695	0.116242
$835$	−0.0620862	−0.00214858
$836$	−14.5342	−0.502676
$837$	−0.497982	−0.0172128
$838$	−29.1816	−1.00806
$839$	10.1670	0.351002	0.175501	−	0.984479i	$-0.443845\pi$
$839$	10.1670	0.351002	0.175501	+	0.984479i	$0.443845\pi$
$840$	−4.94468	−0.170608
$841$	14.0395	0.484121
$842$	−94.0042	−3.23960
$843$	51.1480	1.76163
$844$	31.5278	1.08523
$845$	2.60073	0.0894678
$846$	−99.2342	−3.41174
$847$	29.0950	0.999717
$848$	10.0292	0.344403
$849$	−55.3391	−1.89923
$850$	−38.8506	−1.33257
$851$	29.2447	1.00249
$852$	−86.2773	−2.95581
$853$	7.02855	0.240653	0.120326	−	0.992734i	$-0.461606\pi$
$853$	7.02855	0.240653	0.120326	+	0.992734i	$0.461606\pi$
$854$	−49.1311	−1.68123
$855$	−0.766858	−0.0262260
$856$	33.0758	1.13051
$857$	17.7230	0.605407	0.302703	−	0.953085i	$-0.402111\pi$
$857$	17.7230	0.605407	0.302703	+	0.953085i	$0.402111\pi$
$858$	−135.768	−4.63505
$859$	−29.5077	−1.00679	−0.503395	−	0.864057i	$-0.667916\pi$
$859$	−29.5077	−1.00679	−0.503395	+	0.864057i	$0.667916\pi$
$860$	−4.49467	−0.153267
$861$	53.7555	1.83198
$862$	−65.8260	−2.24204
$863$	53.6261	1.82545	0.912727	−	0.408571i	$-0.133973\pi$
$863$	53.6261	1.82545	0.912727	+	0.408571i	$0.133973\pi$
$864$	3.01262	0.102491
$865$	0.301993	0.0102681
$866$	−32.8341	−1.11575
$867$	−13.7737	−0.467780
$868$	−5.85373	−0.198688
$869$	−51.9464	−1.76216
$870$	−10.3527	−0.350989
$871$	50.3784	1.70701
$872$	9.98503	0.338136
$873$	−16.0002	−0.541526
$874$	−15.9998	−0.541202
$875$	−5.97907	−0.202130
$876$	113.638	3.83946
$877$	−39.7822	−1.34335	−0.671674	−	0.740847i	$-0.734425\pi$
$877$	−39.7822	−1.34335	−0.671674	+	0.740847i	$0.734425\pi$
$878$	79.5407	2.68437
$879$	−57.1255	−1.92679
$880$	1.08095	0.0364390
$881$	41.0685	1.38363	0.691816	−	0.722074i	$-0.256811\pi$
$881$	41.0685	1.38363	0.691816	+	0.722074i	$0.256811\pi$
$882$	15.6630	0.527400
$883$	−14.0568	−0.473048	−0.236524	−	0.971626i	$-0.576008\pi$
$883$	−14.0568	−0.473048	−0.236524	+	0.971626i	$0.576008\pi$
$884$	−54.9598	−1.84850
$885$	4.24421	0.142667
$886$	68.6947	2.30784
$887$	53.7433	1.80452	0.902261	−	0.431190i	$-0.141906\pi$
$887$	53.7433	1.80452	0.902261	+	0.431190i	$0.141906\pi$
$888$	30.2963	1.01668
$889$	12.1861	0.408710
$890$	−0.0303490	−0.00101730
$891$	−40.0624	−1.34214
$892$	38.5335	1.29020
$893$	−11.3674	−0.380394
$894$	92.7537	3.10215
$895$	−1.04119	−0.0348032
$896$	43.8025	1.46334
$897$	−94.2142	−3.14572
$898$	18.3879	0.613613
$899$	−5.06939	−0.169074
$900$	−54.7382	−1.82461
$901$	−41.8776	−1.39514
$902$	−110.484	−3.67872
$903$	−26.9971	−0.898408
$904$	−66.1930	−2.20155
$905$	2.19436	0.0729429
$906$	42.9057	1.42545
$907$	−44.3918	−1.47401	−0.737003	−	0.675889i	$-0.763760\pi$
$907$	−44.3918	−1.47401	−0.737003	+	0.675889i	$0.763760\pi$
$908$	6.90390	0.229114
$909$	−0.0805606	−0.00267203
$910$	−6.65927	−0.220753
$911$	28.4411	0.942297	0.471149	−	0.882054i	$-0.343840\pi$
$911$	28.4411	0.942297	0.471149	+	0.882054i	$0.343840\pi$
$912$	−1.76299	−0.0583785
$913$	6.19442	0.205005
$914$	−22.8856	−0.756987
$915$	6.45149	0.213280
$916$	40.7755	1.34726
$917$	14.1569	0.467502
$918$	5.08224	0.167739
$919$	2.36681	0.0780738	0.0390369	−	0.999238i	$-0.487571\pi$
$919$	2.36681	0.0780738	0.0390369	+	0.999238i	$0.487571\pi$
$920$	7.05235	0.232509
$921$	30.9398	1.01950
$922$	69.4370	2.28679
$923$	−48.0610	−1.58195
$924$	93.0297	3.06045
$925$	18.1813	0.597798
$926$	90.4964	2.97390
$927$	−34.4639	−1.13194
$928$	30.6681	1.00673
$929$	−10.9903	−0.360580	−0.180290	−	0.983613i	$-0.557704\pi$
$929$	−10.9903	−0.360580	−0.180290	+	0.983613i	$0.557704\pi$
$930$	1.21939	0.0399853
$931$	1.79421	0.0588027
$932$	−96.0883	−3.14748
$933$	−27.8713	−0.912464
$934$	−24.1451	−0.790051
$935$	−4.51361	−0.147611
$936$	−50.8102	−1.66078
$937$	13.6099	0.444617	0.222308	−	0.974976i	$-0.428641\pi$
$937$	13.6099	0.444617	0.222308	+	0.974976i	$0.428641\pi$
$938$	−54.7612	−1.78802
$939$	−12.8554	−0.419521
$940$	12.1135	0.395099
$941$	36.7911	1.19935	0.599677	−	0.800242i	$-0.295296\pi$
$941$	36.7911	1.19935	0.599677	+	0.800242i	$0.295296\pi$
$942$	50.6074	1.64888
$943$	−76.6688	−2.49668
$944$	5.07953	0.165325
$945$	0.388178	0.0126274
$946$	55.4874	1.80405
$947$	−18.9667	−0.616334	−0.308167	−	0.951332i	$-0.599716\pi$
$947$	−18.9667	−0.616334	−0.308167	+	0.951332i	$0.599716\pi$
$948$	−90.2837	−2.93228
$949$	63.3021	2.05487
$950$	−9.94705	−0.322725
$951$	39.6934	1.28715
$952$	24.7105	0.800873
$953$	37.2818	1.20768	0.603838	−	0.797107i	$-0.293637\pi$
$953$	37.2818	1.20768	0.603838	+	0.797107i	$0.293637\pi$
$954$	−93.6009	−3.03044
$955$	−3.52799	−0.114163
$956$	−15.3330	−0.495904
$957$	80.5647	2.60429
$958$	−26.4127	−0.853354
$959$	31.7674	1.02582
$960$	−8.47852	−0.273643
$961$	−30.4029	−0.980739
$962$	40.8017	1.31550
$963$	−32.8335	−1.05804
$964$	52.3478	1.68601
$965$	1.42439	0.0458528
$966$	102.411	3.29501
$967$	−13.5739	−0.436508	−0.218254	−	0.975892i	$-0.570036\pi$
$967$	−13.5739	−0.436508	−0.218254	+	0.975892i	$0.570036\pi$
$968$	−42.9890	−1.38172
$969$	7.36152	0.236486
$970$	3.09842	0.0994843
$971$	−22.7808	−0.731072	−0.365536	−	0.930797i	$-0.619114\pi$
$971$	−22.7808	−0.731072	−0.365536	+	0.930797i	$0.619114\pi$
$972$	−76.2234	−2.44487
$973$	−1.28134	−0.0410779
$974$	−24.8598	−0.796559
$975$	−58.5727	−1.87583
$976$	7.72123	0.247151
$977$	−33.0961	−1.05884	−0.529420	−	0.848360i	$-0.677590\pi$
$977$	−33.0961	−1.05884	−0.529420	+	0.848360i	$0.677590\pi$
$978$	92.3261	2.95226
$979$	0.236176	0.00754822
$980$	−1.91198	−0.0610759
$981$	−9.91189	−0.316462
$982$	−37.2715	−1.18938
$983$	32.3224	1.03092	0.515462	−	0.856913i	$-0.327620\pi$
$983$	32.3224	1.03092	0.515462	+	0.856913i	$0.327620\pi$
$984$	−79.4259	−2.53201
$985$	6.54671	0.208596
$986$	51.7365	1.64763
$987$	72.7595	2.31596
$988$	−14.0715	−0.447675
$989$	38.5046	1.22438
$990$	−10.0884	−0.320631
$991$	2.33683	0.0742318	0.0371159	−	0.999311i	$-0.488183\pi$
$991$	2.33683	0.0742318	0.0371159	+	0.999311i	$0.488183\pi$
$992$	−3.61223	−0.114688
$993$	88.4310	2.80627
$994$	52.2423	1.65702
$995$	−5.53632	−0.175513
$996$	10.7660	0.341134
$997$	13.3112	0.421568	0.210784	−	0.977533i	$-0.432398\pi$
$997$	13.3112	0.421568	0.210784	+	0.977533i	$0.432398\pi$
$998$	33.3232	1.05483
$999$	−2.37839	−0.0752489

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4003.2.a.c.1.20	✓	179

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4003.2.a.c.1.20	✓	179	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:	\( N \)	\(=\)	\( 4003 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4003.a (trivial)

\(f(q)\)	\(=\)	\(q-2.32611 q^{2} +2.50152 q^{3} +3.41079 q^{4} +0.271197 q^{5} -5.81882 q^{6} +2.22103 q^{7} -3.28166 q^{8} +3.25762 q^{9} +O(q^{10})\)	\(q-2.32611 q^{2} +2.50152 q^{3} +3.41079 q^{4} +0.271197 q^{5} -5.81882 q^{6} +2.22103 q^{7} -3.28166 q^{8} +3.25762 q^{9} -0.630834 q^{10} +4.90915 q^{11} +8.53218 q^{12} +4.75288 q^{13} -5.16637 q^{14} +0.678405 q^{15} +0.811925 q^{16} -3.39026 q^{17} -7.57760 q^{18} -0.868020 q^{19} +0.924996 q^{20} +5.55597 q^{21} -11.4192 q^{22} -7.92420 q^{23} -8.20916 q^{24} -4.92645 q^{25} -11.0557 q^{26} +0.644453 q^{27} +7.57549 q^{28} +6.56045 q^{29} -1.57805 q^{30} -0.772720 q^{31} +4.67470 q^{32} +12.2804 q^{33} +7.88612 q^{34} +0.602337 q^{35} +11.1111 q^{36} -3.69055 q^{37} +2.01911 q^{38} +11.8894 q^{39} -0.889977 q^{40} +9.67528 q^{41} -12.9238 q^{42} -4.85912 q^{43} +16.7441 q^{44} +0.883457 q^{45} +18.4326 q^{46} +13.0957 q^{47} +2.03105 q^{48} -2.06701 q^{49} +11.4595 q^{50} -8.48082 q^{51} +16.2111 q^{52} +12.3523 q^{53} -1.49907 q^{54} +1.33135 q^{55} -7.28868 q^{56} -2.17137 q^{57} -15.2603 q^{58} +6.25615 q^{59} +2.31390 q^{60} +9.50978 q^{61} +1.79743 q^{62} +7.23529 q^{63} -12.4977 q^{64} +1.28896 q^{65} -28.5655 q^{66} +10.5996 q^{67} -11.5635 q^{68} -19.8226 q^{69} -1.40110 q^{70} -10.1120 q^{71} -10.6904 q^{72} +13.3187 q^{73} +8.58464 q^{74} -12.3236 q^{75} -2.96064 q^{76} +10.9034 q^{77} -27.6561 q^{78} -10.5815 q^{79} +0.220192 q^{80} -8.16076 q^{81} -22.5058 q^{82} +1.26181 q^{83} +18.9503 q^{84} -0.919428 q^{85} +11.3028 q^{86} +16.4111 q^{87} -16.1102 q^{88} +0.0481094 q^{89} -2.05502 q^{90} +10.5563 q^{91} -27.0278 q^{92} -1.93298 q^{93} -30.4621 q^{94} -0.235404 q^{95} +11.6939 q^{96} -4.91163 q^{97} +4.80810 q^{98} +15.9922 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 179 q + 22 q^{2} + 16 q^{3} + 196 q^{4} + 61 q^{5} + 7 q^{6} + 21 q^{7} + 60 q^{8} + 221 q^{9}+O(q^{10}) \) 179 * q + 22 * q^2 + 16 * q^3 + 196 * q^4 + 61 * q^5 + 7 * q^6 + 21 * q^7 + 60 * q^8 + 221 * q^9	\( 179 q + 22 q^{2} + 16 q^{3} + 196 q^{4} + 61 q^{5} + 7 q^{6} + 21 q^{7} + 60 q^{8} + 221 q^{9} + 9 q^{10} + 46 q^{11} + 33 q^{12} + 47 q^{13} + 22 q^{14} + 36 q^{15} + 222 q^{16} + 103 q^{17} + 43 q^{18} + 12 q^{19} + 102 q^{20} + 50 q^{21} + 39 q^{22} + 121 q^{23} - 3 q^{24} + 246 q^{25} + 52 q^{26} + 49 q^{27} + 41 q^{28} + 138 q^{29} + 28 q^{30} + 5 q^{31} + 137 q^{32} + 63 q^{33} + 2 q^{34} + 72 q^{35} + 279 q^{36} + 118 q^{37} + 123 q^{38} + q^{39} + 9 q^{40} + 50 q^{41} + 48 q^{42} + 48 q^{43} + 108 q^{44} + 158 q^{45} + 13 q^{46} + 85 q^{47} + 50 q^{48} + 230 q^{49} + 78 q^{50} + 15 q^{51} + 41 q^{52} + 399 q^{53} - 5 q^{54} + 24 q^{55} + 53 q^{56} + 45 q^{57} + 27 q^{58} + 48 q^{59} + 66 q^{60} + 46 q^{61} + 81 q^{62} + 78 q^{63} + 252 q^{64} + 153 q^{65} + 6 q^{66} + 70 q^{67} + 240 q^{68} + 120 q^{69} - 31 q^{70} + 86 q^{71} + 89 q^{72} + 45 q^{73} + 68 q^{74} + 17 q^{75} - 13 q^{76} + 362 q^{77} + 69 q^{78} + 31 q^{79} + 169 q^{80} + 303 q^{81} + 25 q^{82} + 106 q^{83} + 13 q^{84} + 115 q^{85} + 95 q^{86} + 32 q^{87} + 83 q^{88} + 105 q^{89} - 38 q^{90} + 3 q^{91} + 310 q^{92} + 298 q^{93} - 17 q^{94} + 102 q^{95} - 82 q^{96} + 34 q^{97} + 81 q^{98} + 58 q^{99}+O(q^{100}) \) 179 * q + 22 * q^2 + 16 * q^3 + 196 * q^4 + 61 * q^5 + 7 * q^6 + 21 * q^7 + 60 * q^8 + 221 * q^9 + 9 * q^10 + 46 * q^11 + 33 * q^12 + 47 * q^13 + 22 * q^14 + 36 * q^15 + 222 * q^16 + 103 * q^17 + 43 * q^18 + 12 * q^19 + 102 * q^20 + 50 * q^21 + 39 * q^22 + 121 * q^23 - 3 * q^24 + 246 * q^25 + 52 * q^26 + 49 * q^27 + 41 * q^28 + 138 * q^29 + 28 * q^30 + 5 * q^31 + 137 * q^32 + 63 * q^33 + 2 * q^34 + 72 * q^35 + 279 * q^36 + 118 * q^37 + 123 * q^38 + q^39 + 9 * q^40 + 50 * q^41 + 48 * q^42 + 48 * q^43 + 108 * q^44 + 158 * q^45 + 13 * q^46 + 85 * q^47 + 50 * q^48 + 230 * q^49 + 78 * q^50 + 15 * q^51 + 41 * q^52 + 399 * q^53 - 5 * q^54 + 24 * q^55 + 53 * q^56 + 45 * q^57 + 27 * q^58 + 48 * q^59 + 66 * q^60 + 46 * q^61 + 81 * q^62 + 78 * q^63 + 252 * q^64 + 153 * q^65 + 6 * q^66 + 70 * q^67 + 240 * q^68 + 120 * q^69 - 31 * q^70 + 86 * q^71 + 89 * q^72 + 45 * q^73 + 68 * q^74 + 17 * q^75 - 13 * q^76 + 362 * q^77 + 69 * q^78 + 31 * q^79 + 169 * q^80 + 303 * q^81 + 25 * q^82 + 106 * q^83 + 13 * q^84 + 115 * q^85 + 95 * q^86 + 32 * q^87 + 83 * q^88 + 105 * q^89 - 38 * q^90 + 3 * q^91 + 310 * q^92 + 298 * q^93 - 17 * q^94 + 102 * q^95 - 82 * q^96 + 34 * q^97 + 81 * q^98 + 58 * q^99

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