LMFDB - Embedded newform 8033.2.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8033,2,Mod(1,8033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8033, 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("8033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8033 = 29 \cdot 277 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8033.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:	$64.1438279437$
Analytic rank:	$1$
Dimension:	$153$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	8033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.80428 q^{2} -1.04470 q^{3} +5.86401 q^{4} +3.49231 q^{5} +2.92963 q^{6} -4.86354 q^{7} -10.8358 q^{8} -1.90861 q^{9} +O(q^{10})$	\(q-2.80428 q^{2} -1.04470 q^{3} +5.86401 q^{4} +3.49231 q^{5} +2.92963 q^{6} -4.86354 q^{7} -10.8358 q^{8} -1.90861 q^{9} -9.79343 q^{10} -0.472682 q^{11} -6.12612 q^{12} -3.11678 q^{13} +13.6388 q^{14} -3.64840 q^{15} +18.6586 q^{16} +0.0323478 q^{17} +5.35228 q^{18} -2.89519 q^{19} +20.4789 q^{20} +5.08093 q^{21} +1.32554 q^{22} +0.0138361 q^{23} +11.3201 q^{24} +7.19622 q^{25} +8.74033 q^{26} +5.12801 q^{27} -28.5199 q^{28} -1.00000 q^{29} +10.2312 q^{30} +9.83705 q^{31} -30.6525 q^{32} +0.493810 q^{33} -0.0907126 q^{34} -16.9850 q^{35} -11.1921 q^{36} -8.40548 q^{37} +8.11892 q^{38} +3.25609 q^{39} -37.8419 q^{40} +2.19931 q^{41} -14.2484 q^{42} +2.81229 q^{43} -2.77181 q^{44} -6.66545 q^{45} -0.0388003 q^{46} +4.29006 q^{47} -19.4926 q^{48} +16.6540 q^{49} -20.1803 q^{50} -0.0337937 q^{51} -18.2768 q^{52} -7.39483 q^{53} -14.3804 q^{54} -1.65075 q^{55} +52.7003 q^{56} +3.02459 q^{57} +2.80428 q^{58} +3.46033 q^{59} -21.3943 q^{60} -5.78126 q^{61} -27.5859 q^{62} +9.28260 q^{63} +48.6410 q^{64} -10.8847 q^{65} -1.38478 q^{66} +12.7753 q^{67} +0.189688 q^{68} -0.0144545 q^{69} +47.6307 q^{70} -7.24831 q^{71} +20.6813 q^{72} +11.6659 q^{73} +23.5714 q^{74} -7.51787 q^{75} -16.9774 q^{76} +2.29891 q^{77} -9.13100 q^{78} -2.22228 q^{79} +65.1616 q^{80} +0.368608 q^{81} -6.16749 q^{82} -9.01613 q^{83} +29.7946 q^{84} +0.112969 q^{85} -7.88647 q^{86} +1.04470 q^{87} +5.12189 q^{88} +15.8628 q^{89} +18.6918 q^{90} +15.1586 q^{91} +0.0811348 q^{92} -10.2767 q^{93} -12.0305 q^{94} -10.1109 q^{95} +32.0225 q^{96} +8.45746 q^{97} -46.7027 q^{98} +0.902165 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 153 q - 3 q^{2} - 12 q^{3} + 135 q^{4} - 11 q^{5} - 17 q^{6} - 76 q^{7} - 12 q^{8} + 133 q^{9}+O(q^{10}) $ 153 * q - 3 * q^2 - 12 * q^3 + 135 * q^4 - 11 * q^5 - 17 * q^6 - 76 * q^7 - 12 * q^8 + 133 * q^9	\( 153 q - 3 q^{2} - 12 q^{3} + 135 q^{4} - 11 q^{5} - 17 q^{6} - 76 q^{7} - 12 q^{8} + 133 q^{9} - 30 q^{10} + 4 q^{11} - 39 q^{12} - 65 q^{13} + q^{14} - 26 q^{15} + 107 q^{16} - 20 q^{17} - 21 q^{18} - 65 q^{19} - 23 q^{20} - 24 q^{21} - 59 q^{22} - 62 q^{23} - 59 q^{24} + 102 q^{25} - 18 q^{26} - 57 q^{27} - 155 q^{28} - 153 q^{29} - 82 q^{30} - 49 q^{31} - 17 q^{32} - 59 q^{33} - 68 q^{34} - 36 q^{35} + 74 q^{36} - 30 q^{37} - 67 q^{38} - 47 q^{39} - 108 q^{40} - 9 q^{41} - 62 q^{42} - 90 q^{43} - 14 q^{44} - 56 q^{45} - 52 q^{46} - 54 q^{47} - 76 q^{48} + 101 q^{49} - 36 q^{50} - 60 q^{51} - 191 q^{52} - 38 q^{53} - 82 q^{54} - 215 q^{55} + 24 q^{56} - 52 q^{57} + 3 q^{58} - 55 q^{59} - 60 q^{60} - 90 q^{61} - 66 q^{62} - 229 q^{63} + 52 q^{64} - 67 q^{65} - 29 q^{66} - 114 q^{67} - 78 q^{68} - 68 q^{69} - 61 q^{70} - 52 q^{71} - 47 q^{72} - 83 q^{73} - 21 q^{74} - 47 q^{75} - 100 q^{76} - 32 q^{77} - 17 q^{78} - 151 q^{79} - 24 q^{80} + 81 q^{81} - 151 q^{82} - 94 q^{83} - 84 q^{84} - 77 q^{85} - 43 q^{86} + 12 q^{87} - 121 q^{88} + 11 q^{89} - 14 q^{90} - 66 q^{91} - 156 q^{92} - 66 q^{93} - 22 q^{94} - 67 q^{95} - 131 q^{96} - 78 q^{97} - 67 q^{98} - 41 q^{99}+O(q^{100}) \) 153 * q - 3 * q^2 - 12 * q^3 + 135 * q^4 - 11 * q^5 - 17 * q^6 - 76 * q^7 - 12 * q^8 + 133 * q^9 - 30 * q^10 + 4 * q^11 - 39 * q^12 - 65 * q^13 + q^14 - 26 * q^15 + 107 * q^16 - 20 * q^17 - 21 * q^18 - 65 * q^19 - 23 * q^20 - 24 * q^21 - 59 * q^22 - 62 * q^23 - 59 * q^24 + 102 * q^25 - 18 * q^26 - 57 * q^27 - 155 * q^28 - 153 * q^29 - 82 * q^30 - 49 * q^31 - 17 * q^32 - 59 * q^33 - 68 * q^34 - 36 * q^35 + 74 * q^36 - 30 * q^37 - 67 * q^38 - 47 * q^39 - 108 * q^40 - 9 * q^41 - 62 * q^42 - 90 * q^43 - 14 * q^44 - 56 * q^45 - 52 * q^46 - 54 * q^47 - 76 * q^48 + 101 * q^49 - 36 * q^50 - 60 * q^51 - 191 * q^52 - 38 * q^53 - 82 * q^54 - 215 * q^55 + 24 * q^56 - 52 * q^57 + 3 * q^58 - 55 * q^59 - 60 * q^60 - 90 * q^61 - 66 * q^62 - 229 * q^63 + 52 * q^64 - 67 * q^65 - 29 * q^66 - 114 * q^67 - 78 * q^68 - 68 * q^69 - 61 * q^70 - 52 * q^71 - 47 * q^72 - 83 * q^73 - 21 * q^74 - 47 * q^75 - 100 * q^76 - 32 * q^77 - 17 * q^78 - 151 * q^79 - 24 * q^80 + 81 * q^81 - 151 * q^82 - 94 * q^83 - 84 * q^84 - 77 * q^85 - 43 * q^86 + 12 * q^87 - 121 * q^88 + 11 * q^89 - 14 * q^90 - 66 * q^91 - 156 * q^92 - 66 * q^93 - 22 * q^94 - 67 * q^95 - 131 * q^96 - 78 * q^97 - 67 * q^98 - 41 * 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 $

$2$	−2.80428	−1.98293	−0.991464	−	0.130378i	$-0.958381\pi$
$2$	−2.80428	−1.98293	−0.991464	+	0.130378i	$0.958381\pi$
$3$	−1.04470	−0.603156	−0.301578	−	0.953441i	$-0.597513\pi$
$3$	−1.04470	−0.603156	−0.301578	+	0.953441i	$0.597513\pi$
$4$	5.86401	2.93201
$5$	3.49231	1.56181	0.780904	−	0.624651i	$-0.214759\pi$
$5$	3.49231	1.56181	0.780904	+	0.624651i	$0.214759\pi$
$6$	2.92963	1.19602
$7$	−4.86354	−1.83825	−0.919123	−	0.393970i	$-0.871101\pi$
$7$	−4.86354	−1.83825	−0.919123	+	0.393970i	$0.871101\pi$
$8$	−10.8358	−3.83103
$9$	−1.90861	−0.636203
$10$	−9.79343	−3.09695
$11$	−0.472682	−0.142519	−0.0712595	−	0.997458i	$-0.522702\pi$
$11$	−0.472682	−0.142519	−0.0712595	+	0.997458i	$0.522702\pi$
$12$	−6.12612	−1.76846
$13$	−3.11678	−0.864438	−0.432219	−	0.901769i	$-0.642269\pi$
$13$	−3.11678	−0.864438	−0.432219	+	0.901769i	$0.642269\pi$
$14$	13.6388	3.64511
$15$	−3.64840	−0.942014
$16$	18.6586	4.66465
$17$	0.0323478	0.00784550	0.00392275	−	0.999992i	$-0.498751\pi$
$17$	0.0323478	0.00784550	0.00392275	+	0.999992i	$0.498751\pi$
$18$	5.35228	1.26154
$19$	−2.89519	−0.664201	−0.332101	−	0.943244i	$-0.607757\pi$
$19$	−2.89519	−0.664201	−0.332101	+	0.943244i	$0.607757\pi$
$20$	20.4789	4.57923
$21$	5.08093	1.10875
$22$	1.32554	0.282605
$23$	0.0138361	0.00288502	0.00144251	−	0.999999i	$-0.499541\pi$
$23$	0.0138361	0.00288502	0.00144251	+	0.999999i	$0.499541\pi$
$24$	11.3201	2.31071
$25$	7.19622	1.43924
$26$	8.74033	1.71412
$27$	5.12801	0.986886
$28$	−28.5199	−5.38975
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	10.2312	1.86795
$31$	9.83705	1.76679	0.883393	−	0.468633i	$-0.155253\pi$
$31$	9.83705	1.76679	0.883393	+	0.468633i	$0.155253\pi$
$32$	−30.6525	−5.41864
$33$	0.493810	0.0859613
$34$	−0.0907126	−0.0155571
$35$	−16.9850	−2.87099
$36$	−11.1921	−1.86535
$37$	−8.40548	−1.38185	−0.690926	−	0.722925i	$-0.742797\pi$
$37$	−8.40548	−1.38185	−0.690926	+	0.722925i	$0.742797\pi$
$38$	8.11892	1.31706
$39$	3.25609	0.521391
$40$	−37.8419	−5.98333
$41$	2.19931	0.343474	0.171737	−	0.985143i	$-0.445062\pi$
$41$	2.19931	0.343474	0.171737	+	0.985143i	$0.445062\pi$
$42$	−14.2484	−2.19857
$43$	2.81229	0.428870	0.214435	−	0.976738i	$-0.431209\pi$
$43$	2.81229	0.428870	0.214435	+	0.976738i	$0.431209\pi$
$44$	−2.77181	−0.417867
$45$	−6.66545	−0.993626
$46$	−0.0388003	−0.00572079
$47$	4.29006	0.625769	0.312884	−	0.949791i	$-0.398705\pi$
$47$	4.29006	0.625769	0.312884	+	0.949791i	$0.398705\pi$
$48$	−19.4926	−2.81351
$49$	16.6540	2.37915
$50$	−20.1803	−2.85392
$51$	−0.0337937	−0.00473206
$52$	−18.2768	−2.53454
$53$	−7.39483	−1.01576	−0.507879	−	0.861428i	$-0.669570\pi$
$53$	−7.39483	−1.01576	−0.507879	+	0.861428i	$0.669570\pi$
$54$	−14.3804	−1.95692
$55$	−1.65075	−0.222587
$56$	52.7003	7.04238
$57$	3.02459	0.400617
$58$	2.80428	0.368221
$59$	3.46033	0.450496	0.225248	−	0.974301i	$-0.427681\pi$
$59$	3.46033	0.450496	0.225248	+	0.974301i	$0.427681\pi$
$60$	−21.3943	−2.76199
$61$	−5.78126	−0.740215	−0.370108	−	0.928989i	$-0.620679\pi$
$61$	−5.78126	−0.740215	−0.370108	+	0.928989i	$0.620679\pi$
$62$	−27.5859	−3.50341
$63$	9.28260	1.16950
$64$	48.6410	6.08013
$65$	−10.8847	−1.35009
$66$	−1.38478	−0.170455
$67$	12.7753	1.56075	0.780375	−	0.625312i	$-0.215028\pi$
$67$	12.7753	1.56075	0.780375	+	0.625312i	$0.215028\pi$
$68$	0.189688	0.0230031
$69$	−0.0144545	−0.00174012
$70$	47.6307	5.69296
$71$	−7.24831	−0.860216	−0.430108	−	0.902778i	$-0.641524\pi$
$71$	−7.24831	−0.860216	−0.430108	+	0.902778i	$0.641524\pi$
$72$	20.6813	2.43731
$73$	11.6659	1.36539	0.682695	−	0.730703i	$-0.260808\pi$
$73$	11.6659	1.36539	0.682695	+	0.730703i	$0.260808\pi$
$74$	23.5714	2.74012
$75$	−7.51787	−0.868089
$76$	−16.9774	−1.94744
$77$	2.29891	0.261985
$78$	−9.13100	−1.03388
$79$	−2.22228	−0.250026	−0.125013	−	0.992155i	$-0.539897\pi$
$79$	−2.22228	−0.250026	−0.125013	+	0.992155i	$0.539897\pi$
$80$	65.1616	7.28529
$81$	0.368608	0.0409565
$82$	−6.16749	−0.681085
$83$	−9.01613	−0.989649	−0.494825	−	0.868993i	$-0.664768\pi$
$83$	−9.01613	−0.989649	−0.494825	+	0.868993i	$0.664768\pi$
$84$	29.7946	3.25086
$85$	0.112969	0.0122532
$86$	−7.88647	−0.850419
$87$	1.04470	0.112003
$88$	5.12189	0.545995
$89$	15.8628	1.68145	0.840726	−	0.541462i	$-0.182129\pi$
$89$	15.8628	1.68145	0.840726	+	0.541462i	$0.182129\pi$
$90$	18.6918	1.97029
$91$	15.1586	1.58905
$92$	0.0811348	0.00845889
$93$	−10.2767	−1.06565
$94$	−12.0305	−1.24086
$95$	−10.1109	−1.03735
$96$	32.0225	3.26829
$97$	8.45746	0.858725	0.429362	−	0.903132i	$-0.358738\pi$
$97$	8.45746	0.858725	0.429362	+	0.903132i	$0.358738\pi$
$98$	−46.7027	−4.71768
$99$	0.902165	0.0906710
$100$	42.1987	4.21987
$101$	17.8069	1.77185	0.885926	−	0.463827i	$-0.153524\pi$
$101$	17.8069	1.77185	0.885926	+	0.463827i	$0.153524\pi$
$102$	0.0947671	0.00938335
$103$	−8.88813	−0.875774	−0.437887	−	0.899030i	$-0.644273\pi$
$103$	−8.88813	−0.875774	−0.437887	+	0.899030i	$0.644273\pi$
$104$	33.7727	3.31169
$105$	17.7442	1.73165
$106$	20.7372	2.01418
$107$	−18.2242	−1.76180	−0.880899	−	0.473305i	$-0.843061\pi$
$107$	−18.2242	−1.76180	−0.880899	+	0.473305i	$0.843061\pi$
$108$	30.0707	2.89355
$109$	18.4618	1.76832	0.884158	−	0.467187i	$-0.154733\pi$
$109$	18.4618	1.76832	0.884158	+	0.467187i	$0.154733\pi$
$110$	4.62918	0.441375
$111$	8.78118	0.833473
$112$	−90.7469	−8.57478
$113$	19.5680	1.84080	0.920401	−	0.390975i	$-0.127862\pi$
$113$	19.5680	1.84080	0.920401	+	0.390975i	$0.127862\pi$
$114$	−8.48182	−0.794395
$115$	0.0483198	0.00450585
$116$	−5.86401	−0.544460
$117$	5.94871	0.549958
$118$	−9.70374	−0.893302
$119$	−0.157325	−0.0144220
$120$	39.5333	3.60888
$121$	−10.7766	−0.979688
$122$	16.2123	1.46779
$123$	−2.29761	−0.207169
$124$	57.6846	5.18023
$125$	7.66988	0.686015
$126$	−26.0310	−2.31903
$127$	8.10175	0.718914	0.359457	−	0.933162i	$-0.382962\pi$
$127$	8.10175	0.718914	0.359457	+	0.933162i	$0.382962\pi$
$128$	−75.0984	−6.63782
$129$	−2.93799	−0.258676
$130$	30.5239	2.67713
$131$	−14.4529	−1.26275	−0.631377	−	0.775476i	$-0.717510\pi$
$131$	−14.4529	−1.26275	−0.631377	+	0.775476i	$0.717510\pi$
$132$	2.89571	0.252039
$133$	14.0809	1.22097
$134$	−35.8255	−3.09485
$135$	17.9086	1.54133
$136$	−0.350514	−0.0300564
$137$	8.27968	0.707381	0.353690	−	0.935363i	$-0.384927\pi$
$137$	8.27968	0.707381	0.353690	+	0.935363i	$0.384927\pi$
$138$	0.0405345	0.00345053
$139$	12.7128	1.07828	0.539142	−	0.842215i	$-0.318749\pi$
$139$	12.7128	1.07828	0.539142	+	0.842215i	$0.318749\pi$
$140$	−99.6002	−8.41775
$141$	−4.48181	−0.377436
$142$	20.3263	1.70575
$143$	1.47325	0.123199
$144$	−35.6120	−2.96766
$145$	−3.49231	−0.290020
$146$	−32.7145	−2.70747
$147$	−17.3984	−1.43500
$148$	−49.2898	−4.05160
$149$	1.13084	0.0926418	0.0463209	−	0.998927i	$-0.485250\pi$
$149$	1.13084	0.0926418	0.0463209	+	0.998927i	$0.485250\pi$
$150$	21.0822	1.72136
$151$	−18.6258	−1.51575	−0.757874	−	0.652401i	$-0.773762\pi$
$151$	−18.6258	−1.51575	−0.757874	+	0.652401i	$0.773762\pi$
$152$	31.3716	2.54457
$153$	−0.0617393	−0.00499133
$154$	−6.44680	−0.519498
$155$	34.3540	2.75938
$156$	19.0937	1.52872
$157$	−7.23565	−0.577467	−0.288734	−	0.957409i	$-0.593234\pi$
$157$	−7.23565	−0.577467	−0.288734	+	0.957409i	$0.593234\pi$
$158$	6.23190	0.495784
$159$	7.72536	0.612661
$160$	−107.048	−8.46288
$161$	−0.0672923	−0.00530338
$162$	−1.03368	−0.0812137
$163$	−22.1055	−1.73144	−0.865718	−	0.500532i	$-0.833138\pi$
$163$	−22.1055	−1.73144	−0.865718	+	0.500532i	$0.833138\pi$
$164$	12.8968	1.00707
$165$	1.72454	0.134255
$166$	25.2838	1.96240
$167$	−6.01652	−0.465572	−0.232786	−	0.972528i	$-0.574784\pi$
$167$	−6.01652	−0.465572	−0.232786	+	0.972528i	$0.574784\pi$
$168$	−55.0559	−4.24765
$169$	−3.28570	−0.252746
$170$	−0.316796	−0.0242972
$171$	5.52577	0.422567
$172$	16.4913	1.25745
$173$	−0.324311	−0.0246569	−0.0123285	−	0.999924i	$-0.503924\pi$
$173$	−0.324311	−0.0246569	−0.0123285	+	0.999924i	$0.503924\pi$
$174$	−2.92963	−0.222095
$175$	−34.9991	−2.64569
$176$	−8.81959	−0.664802
$177$	−3.61499	−0.271720
$178$	−44.4837	−3.33420
$179$	6.90352	0.515993	0.257997	−	0.966146i	$-0.416938\pi$
$179$	6.90352	0.515993	0.257997	+	0.966146i	$0.416938\pi$
$180$	−39.0863	−2.91332
$181$	−2.82335	−0.209858	−0.104929	−	0.994480i	$-0.533462\pi$
$181$	−2.82335	−0.209858	−0.104929	+	0.994480i	$0.533462\pi$
$182$	−42.5090	−3.15097
$183$	6.03967	0.446465
$184$	−0.149925	−0.0110526
$185$	−29.3545	−2.15819
$186$	28.8189	2.11310
$187$	−0.0152903	−0.00111813
$188$	25.1569	1.83476
$189$	−24.9403	−1.81414
$190$	28.3538	2.05700
$191$	−3.21320	−0.232499	−0.116250	−	0.993220i	$-0.537087\pi$
$191$	−3.21320	−0.232499	−0.116250	+	0.993220i	$0.537087\pi$
$192$	−50.8151	−3.66727
$193$	−7.08525	−0.510007	−0.255004	−	0.966940i	$-0.582077\pi$
$193$	−7.08525	−0.510007	−0.255004	+	0.966940i	$0.582077\pi$
$194$	−23.7171	−1.70279
$195$	11.3713	0.814313
$196$	97.6595	6.97568
$197$	7.90357	0.563106	0.281553	−	0.959546i	$-0.409150\pi$
$197$	7.90357	0.563106	0.281553	+	0.959546i	$0.409150\pi$
$198$	−2.52993	−0.179794
$199$	−23.5288	−1.66791	−0.833956	−	0.551831i	$-0.813929\pi$
$199$	−23.5288	−1.66791	−0.833956	+	0.551831i	$0.813929\pi$
$200$	−77.9767	−5.51379
$201$	−13.3463	−0.941376
$202$	−49.9356	−3.51346
$203$	4.86354	0.341354
$204$	−0.198167	−0.0138744
$205$	7.68067	0.536441
$206$	24.9249	1.73660
$207$	−0.0264076	−0.00183546
$208$	−58.1547	−4.03230
$209$	1.36850	0.0946613
$210$	−49.7597	−3.43375
$211$	14.5034	0.998458	0.499229	−	0.866470i	$-0.333617\pi$
$211$	14.5034	0.998458	0.499229	+	0.866470i	$0.333617\pi$
$212$	−43.3634	−2.97821
$213$	7.57228	0.518844
$214$	51.1058	3.49352
$215$	9.82139	0.669813
$216$	−55.5660	−3.78079
$217$	−47.8429	−3.24779
$218$	−51.7721	−3.50645
$219$	−12.1873	−0.823544
$220$	−9.68003	−0.652628
$221$	−0.100821	−0.00678196
$222$	−24.6249	−1.65272
$223$	6.62059	0.443347	0.221674	−	0.975121i	$-0.428848\pi$
$223$	6.62059	0.443347	0.221674	+	0.975121i	$0.428848\pi$
$224$	149.080	9.96080
$225$	−13.7348	−0.915651
$226$	−54.8742	−3.65018
$227$	5.81105	0.385693	0.192847	−	0.981229i	$-0.438228\pi$
$227$	5.81105	0.385693	0.192847	+	0.981229i	$0.438228\pi$
$228$	17.7362	1.17461
$229$	−27.2208	−1.79880	−0.899399	−	0.437129i	$-0.855995\pi$
$229$	−27.2208	−1.79880	−0.899399	+	0.437129i	$0.855995\pi$
$230$	−0.135502	−0.00893477
$231$	−2.40167	−0.158018
$232$	10.8358	0.711404
$233$	20.5249	1.34463	0.672315	−	0.740265i	$-0.265300\pi$
$233$	20.5249	1.34463	0.672315	+	0.740265i	$0.265300\pi$
$234$	−16.6819	−1.09053
$235$	14.9822	0.977331
$236$	20.2914	1.32086
$237$	2.32161	0.150805
$238$	0.441184	0.0285977
$239$	−24.3288	−1.57370	−0.786848	−	0.617147i	$-0.788289\pi$
$239$	−24.3288	−1.57370	−0.786848	+	0.617147i	$0.788289\pi$
$240$	−68.0742	−4.39417
$241$	−3.05373	−0.196708	−0.0983540	−	0.995151i	$-0.531358\pi$
$241$	−3.05373	−0.196708	−0.0983540	+	0.995151i	$0.531358\pi$
$242$	30.2206	1.94265
$243$	−15.7691	−1.01159
$244$	−33.9014	−2.17031
$245$	58.1611	3.71577
$246$	6.44316	0.410801
$247$	9.02365	0.574161
$248$	−106.592	−6.76861
$249$	9.41913	0.596913
$250$	−21.5085	−1.36032
$251$	4.00416	0.252740	0.126370	−	0.991983i	$-0.459667\pi$
$251$	4.00416	0.252740	0.126370	+	0.991983i	$0.459667\pi$
$252$	54.4332	3.42897
$253$	−0.00654006	−0.000411170 0
$254$	−22.7196	−1.42555
$255$	−0.118018	−0.00739058
$256$	113.315	7.08219
$257$	16.2683	1.01479	0.507394	−	0.861714i	$-0.330609\pi$
$257$	16.2683	1.01479	0.507394	+	0.861714i	$0.330609\pi$
$258$	8.23897	0.512936
$259$	40.8804	2.54019
$260$	−63.8283	−3.95846
$261$	1.90861	0.118140
$262$	40.5300	2.50395
$263$	6.48867	0.400109	0.200054	−	0.979785i	$-0.435888\pi$
$263$	6.48867	0.400109	0.200054	+	0.979785i	$0.435888\pi$
$264$	−5.35082	−0.329320
$265$	−25.8250	−1.58642
$266$	−39.4867	−2.42109
$267$	−16.5718	−1.01418
$268$	74.9144	4.57613
$269$	19.3458	1.17953	0.589766	−	0.807574i	$-0.299220\pi$
$269$	19.3458	1.17953	0.589766	+	0.807574i	$0.299220\pi$
$270$	−50.2208	−3.05634
$271$	12.7089	0.772009	0.386005	−	0.922497i	$-0.373855\pi$
$271$	12.7089	0.772009	0.386005	+	0.922497i	$0.373855\pi$
$272$	0.603566	0.0365965
$273$	−15.8361	−0.958446
$274$	−23.2186	−1.40269
$275$	−3.40153	−0.205120
$276$	−0.0847613	−0.00510203
$277$	−1.00000	−0.0600842
$277$	−1.00000	−0.0600842
$278$	−35.6502	−2.13816
$279$	−18.7751	−1.12403
$280$	184.046	10.9988
$281$	0.301431	0.0179819	0.00899094	−	0.999960i	$-0.497138\pi$
$281$	0.301431	0.0179819	0.00899094	+	0.999960i	$0.497138\pi$
$282$	12.5683	0.748429
$283$	−3.51510	−0.208951	−0.104476	−	0.994527i	$-0.533316\pi$
$283$	−3.51510	−0.208951	−0.104476	+	0.994527i	$0.533316\pi$
$284$	−42.5042	−2.52216
$285$	10.5628	0.625687
$286$	−4.13140	−0.244295
$287$	−10.6964	−0.631391
$288$	58.5036	3.44735
$289$	−16.9990	−0.999938
$290$	9.79343	0.575090
$291$	−8.83548	−0.517945
$292$	68.4090	4.00333
$293$	2.01017	0.117435	0.0587176	−	0.998275i	$-0.481299\pi$
$293$	2.01017	0.117435	0.0587176	+	0.998275i	$0.481299\pi$
$294$	48.7902	2.84550
$295$	12.0845	0.703589
$296$	91.0800	5.29392
$297$	−2.42392	−0.140650
$298$	−3.17119	−0.183702
$299$	−0.0431239	−0.00249392
$300$	−44.0849	−2.54524
$301$	−13.6777	−0.788370
$302$	52.2321	3.00562
$303$	−18.6028	−1.06870
$304$	−54.0201	−3.09827
$305$	−20.1900	−1.15607
$306$	0.173135	0.00989745
$307$	23.8110	1.35896	0.679482	−	0.733692i	$-0.262204\pi$
$307$	23.8110	1.35896	0.679482	+	0.733692i	$0.262204\pi$
$308$	13.4808	0.768142
$309$	9.28541	0.528228
$310$	−96.3384	−5.47165
$311$	−30.2352	−1.71448	−0.857240	−	0.514917i	$-0.827823\pi$
$311$	−30.2352	−1.71448	−0.857240	+	0.514917i	$0.827823\pi$
$312$	−35.2823	−1.99747
$313$	3.61838	0.204523	0.102261	−	0.994758i	$-0.467392\pi$
$313$	3.61838	0.204523	0.102261	+	0.994758i	$0.467392\pi$
$314$	20.2908	1.14508
$315$	32.4177	1.82653
$316$	−13.0315	−0.733077
$317$	−24.7506	−1.39013	−0.695065	−	0.718946i	$-0.744625\pi$
$317$	−24.7506	−1.39013	−0.695065	+	0.718946i	$0.744625\pi$
$318$	−21.6641	−1.21486
$319$	0.472682	0.0264651
$320$	169.870	9.49599
$321$	19.0387	1.06264
$322$	0.188707	0.0105162
$323$	−0.0936530	−0.00521099
$324$	2.16152	0.120085
$325$	−22.4290	−1.24414
$326$	61.9901	3.43331
$327$	−19.2870	−1.06657
$328$	−23.8313	−1.31586
$329$	−20.8649	−1.15032
$330$	−4.83609	−0.266218
$331$	−1.08011	−0.0593681	−0.0296840	−	0.999559i	$-0.509450\pi$
$331$	−1.08011	−0.0593681	−0.0296840	+	0.999559i	$0.509450\pi$
$332$	−52.8707	−2.90166
$333$	16.0428	0.879138
$334$	16.8720	0.923196
$335$	44.6152	2.43759
$336$	94.8031	5.17193
$337$	−5.22496	−0.284622	−0.142311	−	0.989822i	$-0.545453\pi$
$337$	−5.22496	−0.284622	−0.142311	+	0.989822i	$0.545453\pi$
$338$	9.21404	0.501178
$339$	−20.4426	−1.11029
$340$	0.662449	0.0359264
$341$	−4.64980	−0.251801
$342$	−15.4958	−0.837919
$343$	−46.9529	−2.53522
$344$	−30.4734	−1.64302
$345$	−0.0504796	−0.00271773
$346$	0.909460	0.0488929
$347$	−14.8056	−0.794806	−0.397403	−	0.917644i	$-0.630089\pi$
$347$	−14.8056	−0.794806	−0.397403	+	0.917644i	$0.630089\pi$
$348$	6.12612	0.328394
$349$	−18.2931	−0.979206	−0.489603	−	0.871946i	$-0.662858\pi$
$349$	−18.2931	−0.979206	−0.489603	+	0.871946i	$0.662858\pi$
$350$	98.1475	5.24620
$351$	−15.9829	−0.853102
$352$	14.4889	0.772260
$353$	27.0270	1.43850	0.719251	−	0.694750i	$-0.244485\pi$
$353$	27.0270	1.43850	0.719251	+	0.694750i	$0.244485\pi$
$354$	10.1375	0.538800
$355$	−25.3133	−1.34349
$356$	93.0195	4.93002
$357$	0.164357	0.00869870
$358$	−19.3594	−1.02318
$359$	−27.1834	−1.43469	−0.717344	−	0.696720i	$-0.754642\pi$
$359$	−27.1834	−1.43469	−0.717344	+	0.696720i	$0.754642\pi$
$360$	72.2254	3.80661
$361$	−10.6179	−0.558837
$362$	7.91748	0.416134
$363$	11.2583	0.590905
$364$	88.8901	4.65911
$365$	40.7409	2.13248
$366$	−16.9370	−0.885309
$367$	−14.3739	−0.750309	−0.375155	−	0.926962i	$-0.622410\pi$
$367$	−14.3739	−0.750309	−0.375155	+	0.926962i	$0.622410\pi$
$368$	0.258162	0.0134576
$369$	−4.19762	−0.218519
$370$	82.3185	4.27953
$371$	35.9651	1.86721
$372$	−60.2629	−3.12449
$373$	−11.6809	−0.604814	−0.302407	−	0.953179i	$-0.597790\pi$
$373$	−11.6809	−0.604814	−0.302407	+	0.953179i	$0.597790\pi$
$374$	0.0428782	0.00221718
$375$	−8.01270	−0.413774
$376$	−46.4861	−2.39734
$377$	3.11678	0.160522
$378$	69.9397	3.59731
$379$	4.72394	0.242653	0.121326	−	0.992613i	$-0.461285\pi$
$379$	4.72394	0.242653	0.121326	+	0.992613i	$0.461285\pi$
$380$	−59.2903	−3.04153
$381$	−8.46387	−0.433617
$382$	9.01074	0.461030
$383$	1.90503	0.0973426	0.0486713	−	0.998815i	$-0.484501\pi$
$383$	1.90503	0.0973426	0.0486713	+	0.998815i	$0.484501\pi$
$384$	78.4550	4.00364
$385$	8.02851	0.409171
$386$	19.8691	1.01131
$387$	−5.36756	−0.272849
$388$	49.5946	2.51779
$389$	8.92384	0.452457	0.226228	−	0.974074i	$-0.427360\pi$
$389$	8.92384	0.452457	0.226228	+	0.974074i	$0.427360\pi$
$390$	−31.8883	−1.61472
$391$	0.000447567 0	2.26344e−5 0
$392$	−180.460	−9.11459
$393$	15.0989	0.761638
$394$	−22.1639	−1.11660
$395$	−7.76089	−0.390493
$396$	5.29031	0.265848
$397$	−14.3183	−0.718617	−0.359308	−	0.933219i	$-0.616987\pi$
$397$	−14.3183	−0.718617	−0.359308	+	0.933219i	$0.616987\pi$
$398$	65.9814	3.30735
$399$	−14.7102	−0.736433
$400$	134.271	6.71357
$401$	−1.70469	−0.0851282	−0.0425641	−	0.999094i	$-0.513553\pi$
$401$	−1.70469	−0.0851282	−0.0425641	+	0.999094i	$0.513553\pi$
$402$	37.4268	1.86668
$403$	−30.6599	−1.52728
$404$	104.420	5.19508
$405$	1.28729	0.0639661
$406$	−13.6388	−0.676880
$407$	3.97312	0.196940
$408$	0.366181	0.0181287
$409$	20.0413	0.990980	0.495490	−	0.868614i	$-0.334989\pi$
$409$	20.0413	0.990980	0.495490	+	0.868614i	$0.334989\pi$
$410$	−21.5388	−1.06372
$411$	−8.64976	−0.426661
$412$	−52.1201	−2.56777
$413$	−16.8294	−0.828123
$414$	0.0740545	0.00363958
$415$	−31.4871	−1.54564
$416$	95.5369	4.68408
$417$	−13.2810	−0.650373
$418$	−3.83767	−0.187707
$419$	5.74360	0.280593	0.140297	−	0.990110i	$-0.455194\pi$
$419$	5.74360	0.280593	0.140297	+	0.990110i	$0.455194\pi$
$420$	104.052	5.07722
$421$	−28.6916	−1.39835	−0.699173	−	0.714953i	$-0.746448\pi$
$421$	−28.6916	−1.39835	−0.699173	+	0.714953i	$0.746448\pi$
$422$	−40.6718	−1.97987
$423$	−8.18803	−0.398116
$424$	80.1289	3.89140
$425$	0.232782	0.0112916
$426$	−21.2348	−1.02883
$427$	28.1174	1.36070
$428$	−106.867	−5.16560
$429$	−1.53910	−0.0743082
$430$	−27.5420	−1.32819
$431$	16.6979	0.804309	0.402154	−	0.915572i	$-0.368261\pi$
$431$	16.6979	0.804309	0.402154	+	0.915572i	$0.368261\pi$
$432$	95.6815	4.60348
$433$	−21.2545	−1.02142	−0.510712	−	0.859752i	$-0.670618\pi$
$433$	−21.2545	−1.02142	−0.510712	+	0.859752i	$0.670618\pi$
$434$	134.165	6.44013
$435$	3.64840	0.174928
$436$	108.260	5.18472
$437$	−0.0400580	−0.00191623
$438$	34.1767	1.63303
$439$	−11.6032	−0.553790	−0.276895	−	0.960900i	$-0.589305\pi$
$439$	−11.6032	−0.553790	−0.276895	+	0.960900i	$0.589305\pi$
$440$	17.8872	0.852739
$441$	−31.7860	−1.51362
$442$	0.282731	0.0134481
$443$	−16.3013	−0.774499	−0.387249	−	0.921975i	$-0.626575\pi$
$443$	−16.3013	−0.774499	−0.387249	+	0.921975i	$0.626575\pi$
$444$	51.4930	2.44375
$445$	55.3977	2.62610
$446$	−18.5660	−0.879126
$447$	−1.18138	−0.0558774
$448$	−236.568	−11.1768
$449$	11.4332	0.539566	0.269783	−	0.962921i	$-0.413048\pi$
$449$	11.4332	0.539566	0.269783	+	0.962921i	$0.413048\pi$
$450$	38.5162	1.81567
$451$	−1.03957	−0.0489517
$452$	114.747	5.39724
$453$	19.4583	0.914232
$454$	−16.2958	−0.764802
$455$	52.9384	2.48179
$456$	−32.7738	−1.53478
$457$	−18.4089	−0.861131	−0.430565	−	0.902559i	$-0.641686\pi$
$457$	−18.4089	−0.861131	−0.430565	+	0.902559i	$0.641686\pi$
$458$	76.3347	3.56689
$459$	0.165880	0.00774262
$460$	0.283348	0.0132112
$461$	20.9542	0.975936	0.487968	−	0.872861i	$-0.337738\pi$
$461$	20.9542	0.975936	0.487968	+	0.872861i	$0.337738\pi$
$462$	6.73495	0.313338
$463$	−18.0918	−0.840798	−0.420399	−	0.907339i	$-0.638110\pi$
$463$	−18.0918	−0.840798	−0.420399	+	0.907339i	$0.638110\pi$
$464$	−18.6586	−0.866204
$465$	−35.8895	−1.66434
$466$	−57.5576	−2.66630
$467$	26.5738	1.22969	0.614845	−	0.788648i	$-0.289218\pi$
$467$	26.5738	1.22969	0.614845	+	0.788648i	$0.289218\pi$
$468$	34.8833	1.61248
$469$	−62.1331	−2.86904
$470$	−42.0143	−1.93798
$471$	7.55906	0.348303
$472$	−37.4954	−1.72586
$473$	−1.32932	−0.0611222
$474$	−6.51045	−0.299035
$475$	−20.8344	−0.955948
$476$	−0.922556	−0.0422853
$477$	14.1138	0.646228
$478$	68.2248	3.12053
$479$	−19.4932	−0.890669	−0.445334	−	0.895364i	$-0.646915\pi$
$479$	−19.4932	−0.890669	−0.445334	+	0.895364i	$0.646915\pi$
$480$	111.833	5.10444
$481$	26.1980	1.19453
$482$	8.56353	0.390058
$483$	0.0703001	0.00319876
$484$	−63.1939	−2.87245
$485$	29.5360	1.34116
$486$	44.2211	2.00591
$487$	−32.7270	−1.48300	−0.741502	−	0.670951i	$-0.765886\pi$
$487$	−32.7270	−1.48300	−0.741502	+	0.670951i	$0.765886\pi$
$488$	62.6446	2.83579
$489$	23.0936	1.04433
$490$	−163.100	−7.36811
$491$	−5.03755	−0.227341	−0.113671	−	0.993518i	$-0.536261\pi$
$491$	−5.03755	−0.227341	−0.113671	+	0.993518i	$0.536261\pi$
$492$	−13.4732	−0.607420
$493$	−0.0323478	−0.00145687
$494$	−25.3049	−1.13852
$495$	3.15064	0.141611
$496$	183.546	8.24144
$497$	35.2524	1.58129
$498$	−26.4139	−1.18364
$499$	−35.1980	−1.57568	−0.787840	−	0.615879i	$-0.788801\pi$
$499$	−35.1980	−1.57568	−0.787840	+	0.615879i	$0.788801\pi$
$500$	44.9763	2.01140
$501$	6.28544	0.280813
$502$	−11.2288	−0.501166
$503$	−3.07934	−0.137301	−0.0686506	−	0.997641i	$-0.521869\pi$
$503$	−3.07934	−0.137301	−0.0686506	+	0.997641i	$0.521869\pi$
$504$	−100.584	−4.48038
$505$	62.1872	2.76729
$506$	0.0183402	0.000815321 0
$507$	3.43256	0.152445
$508$	47.5087	2.10786
$509$	30.8069	1.36549	0.682746	−	0.730656i	$-0.260786\pi$
$509$	30.8069	1.36549	0.682746	+	0.730656i	$0.260786\pi$
$510$	0.330956	0.0146550
$511$	−56.7376	−2.50992
$512$	−167.571	−7.40566
$513$	−14.8465	−0.655491
$514$	−45.6209	−2.01225
$515$	−31.0401	−1.36779
$516$	−17.2284	−0.758439
$517$	−2.02783	−0.0891840
$518$	−114.640	−5.03701
$519$	0.338807	0.0148720
$520$	117.945	5.17222
$521$	−16.2799	−0.713234	−0.356617	−	0.934251i	$-0.616070\pi$
$521$	−16.2799	−0.713234	−0.356617	+	0.934251i	$0.616070\pi$
$522$	−5.35228	−0.234263
$523$	21.4250	0.936852	0.468426	−	0.883503i	$-0.344821\pi$
$523$	21.4250	0.936852	0.468426	+	0.883503i	$0.344821\pi$
$524$	−84.7518	−3.70240
$525$	36.5635	1.59576
$526$	−18.1961	−0.793387
$527$	0.318207	0.0138613
$528$	9.21380	0.400979
$529$	−22.9998	−0.999992
$530$	72.4208	3.14576
$531$	−6.60441	−0.286607
$532$	82.5703	3.57988
$533$	−6.85476	−0.296913
$534$	46.4720	2.01104
$535$	−63.6444	−2.75159
$536$	−138.430	−5.97928
$537$	−7.21208	−0.311224
$538$	−54.2510	−2.33893
$539$	−7.87207	−0.339074
$540$	105.016	4.51918
$541$	34.0155	1.46244	0.731221	−	0.682141i	$-0.238951\pi$
$541$	34.0155	1.46244	0.731221	+	0.682141i	$0.238951\pi$
$542$	−35.6393	−1.53084
$543$	2.94955	0.126577
$544$	−0.991541	−0.0425120
$545$	64.4742	2.76177
$546$	44.4090	1.90053
$547$	38.9684	1.66617	0.833084	−	0.553147i	$-0.186573\pi$
$547$	38.9684	1.66617	0.833084	+	0.553147i	$0.186573\pi$
$548$	48.5522	2.07405
$549$	11.0342	0.470927
$550$	9.53885	0.406738
$551$	2.89519	0.123339
$552$	0.156626	0.00666644
$553$	10.8081	0.459609
$554$	2.80428	0.119143
$555$	30.6666	1.30172
$556$	74.5479	3.16153
$557$	−13.0757	−0.554033	−0.277017	−	0.960865i	$-0.589346\pi$
$557$	−13.0757	−0.554033	−0.277017	+	0.960865i	$0.589346\pi$
$558$	52.6506	2.22888
$559$	−8.76529	−0.370732
$560$	−316.916	−13.3922
$561$	0.0159737	0.000674409 0
$562$	−0.845299	−0.0356568
$563$	−15.9122	−0.670618	−0.335309	−	0.942108i	$-0.608841\pi$
$563$	−15.9122	−0.670618	−0.335309	+	0.942108i	$0.608841\pi$
$564$	−26.2814	−1.10665
$565$	68.3375	2.87498
$566$	9.85734	0.414335
$567$	−1.79274	−0.0752881
$568$	78.5411	3.29551
$569$	−19.7462	−0.827803	−0.413901	−	0.910322i	$-0.635834\pi$
$569$	−19.7462	−0.827803	−0.413901	+	0.910322i	$0.635834\pi$
$570$	−29.6211	−1.24069
$571$	8.83912	0.369906	0.184953	−	0.982747i	$-0.440787\pi$
$571$	8.83912	0.369906	0.184953	+	0.982747i	$0.440787\pi$
$572$	8.63913	0.361220
$573$	3.35683	0.140233
$574$	29.9959	1.25200
$575$	0.0995674	0.00415225
$576$	−92.8367	−3.86819
$577$	5.48645	0.228404	0.114202	−	0.993458i	$-0.463569\pi$
$577$	5.48645	0.228404	0.114202	+	0.993458i	$0.463569\pi$
$578$	47.6699	1.98281
$579$	7.40194	0.307614
$580$	−20.4789	−0.850342
$581$	43.8503	1.81922
$582$	24.7772	1.02705
$583$	3.49541	0.144765
$584$	−126.409	−5.23085
$585$	20.7747	0.858929
$586$	−5.63708	−0.232866
$587$	18.6030	0.767827	0.383914	−	0.923369i	$-0.374576\pi$
$587$	18.6030	0.767827	0.383914	+	0.923369i	$0.374576\pi$
$588$	−102.025	−4.20742
$589$	−28.4801	−1.17350
$590$	−33.8885	−1.39517
$591$	−8.25684	−0.339641
$592$	−156.835	−6.44586
$593$	11.2457	0.461804	0.230902	−	0.972977i	$-0.425832\pi$
$593$	11.2457	0.461804	0.230902	+	0.972977i	$0.425832\pi$
$594$	6.79736	0.278899
$595$	−0.549428	−0.0225243
$596$	6.63124	0.271626
$597$	24.5805	1.00601
$598$	0.120932	0.00494527
$599$	−21.1595	−0.864553	−0.432276	−	0.901741i	$-0.642290\pi$
$599$	−21.1595	−0.864553	−0.432276	+	0.901741i	$0.642290\pi$
$600$	81.4621	3.32567
$601$	20.1150	0.820509	0.410255	−	0.911971i	$-0.365440\pi$
$601$	20.1150	0.820509	0.410255	+	0.911971i	$0.365440\pi$
$602$	38.3562	1.56328
$603$	−24.3830	−0.992953
$604$	−109.222	−4.44418
$605$	−37.6351	−1.53009
$606$	52.1676	2.11916
$607$	−36.7185	−1.49036	−0.745180	−	0.666864i	$-0.767636\pi$
$607$	−36.7185	−1.49036	−0.745180	+	0.666864i	$0.767636\pi$
$608$	88.7446	3.59907
$609$	−5.08093	−0.205890
$610$	56.6184	2.29241
$611$	−13.3711	−0.540939
$612$	−0.362040	−0.0146346
$613$	−0.697028	−0.0281527	−0.0140763	−	0.999901i	$-0.504481\pi$
$613$	−0.697028	−0.0281527	−0.0140763	+	0.999901i	$0.504481\pi$
$614$	−66.7728	−2.69473
$615$	−8.02397	−0.323558
$616$	−24.9105	−1.00367
$617$	−25.1063	−1.01074	−0.505370	−	0.862903i	$-0.668644\pi$
$617$	−25.1063	−1.01074	−0.505370	+	0.862903i	$0.668644\pi$
$618$	−26.0389	−1.04744
$619$	14.1249	0.567729	0.283864	−	0.958864i	$-0.408383\pi$
$619$	14.1249	0.567729	0.283864	+	0.958864i	$0.408383\pi$
$620$	201.452	8.09052
$621$	0.0709515	0.00284718
$622$	84.7881	3.39969
$623$	−77.1493	−3.09092
$624$	60.7541	2.43211
$625$	−9.19551	−0.367820
$626$	−10.1470	−0.405554
$627$	−1.42967	−0.0570956
$628$	−42.4299	−1.69314
$629$	−0.271899	−0.0108413
$630$	−90.9084	−3.62188
$631$	−37.7752	−1.50381	−0.751903	−	0.659274i	$-0.770864\pi$
$631$	−37.7752	−1.50381	−0.751903	+	0.659274i	$0.770864\pi$
$632$	24.0801	0.957857
$633$	−15.1517	−0.602226
$634$	69.4077	2.75653
$635$	28.2938	1.12281
$636$	45.3016	1.79633
$637$	−51.9069	−2.05663
$638$	−1.32554	−0.0524785
$639$	13.8342	0.547272
$640$	−262.267	−10.3670
$641$	17.9447	0.708772	0.354386	−	0.935099i	$-0.384690\pi$
$641$	17.9447	0.708772	0.354386	+	0.935099i	$0.384690\pi$
$642$	−53.3900	−2.10714
$643$	5.74790	0.226675	0.113337	−	0.993557i	$-0.463846\pi$
$643$	5.74790	0.226675	0.113337	+	0.993557i	$0.463846\pi$
$644$	−0.394603	−0.0155495
$645$	−10.2604	−0.404002
$646$	0.262630	0.0103330
$647$	−20.4131	−0.802520	−0.401260	−	0.915964i	$-0.631428\pi$
$647$	−20.4131	−0.802520	−0.401260	+	0.915964i	$0.631428\pi$
$648$	−3.99416	−0.156905
$649$	−1.63564	−0.0642043
$650$	62.8973	2.46704
$651$	49.9813	1.95892
$652$	−129.627	−5.07658
$653$	−23.7123	−0.927935	−0.463967	−	0.885852i	$-0.653574\pi$
$653$	−23.7123	−0.927935	−0.463967	+	0.885852i	$0.653574\pi$
$654$	54.0861	2.11493
$655$	−50.4739	−1.97218
$656$	41.0361	1.60219
$657$	−22.2656	−0.868665
$658$	58.5110	2.28100
$659$	13.1525	0.512350	0.256175	−	0.966630i	$-0.417538\pi$
$659$	13.1525	0.512350	0.256175	+	0.966630i	$0.417538\pi$
$660$	10.1127	0.393636
$661$	−22.8153	−0.887413	−0.443707	−	0.896172i	$-0.646337\pi$
$661$	−22.8153	−0.887413	−0.443707	+	0.896172i	$0.646337\pi$
$662$	3.02893	0.117723
$663$	0.105327	0.00409058
$664$	97.6969	3.79137
$665$	49.1747	1.90691
$666$	−44.9885	−1.74327
$667$	−0.0138361	−0.000535735 0
$668$	−35.2809	−1.36506
$669$	−6.91651	−0.267408
$670$	−125.114	−4.83357
$671$	2.73270	0.105495
$672$	−155.743	−6.00792
$673$	21.7501	0.838404	0.419202	−	0.907893i	$-0.362310\pi$
$673$	21.7501	0.838404	0.419202	+	0.907893i	$0.362310\pi$
$674$	14.6523	0.564384
$675$	36.9023	1.42037
$676$	−19.2674	−0.741053
$677$	−5.77674	−0.222018	−0.111009	−	0.993819i	$-0.535408\pi$
$677$	−5.77674	−0.222018	−0.111009	+	0.993819i	$0.535408\pi$
$678$	57.3269	2.20163
$679$	−41.1332	−1.57855
$680$	−1.22410	−0.0469423
$681$	−6.07079	−0.232633
$682$	13.0394	0.499303
$683$	−6.54616	−0.250482	−0.125241	−	0.992126i	$-0.539970\pi$
$683$	−6.54616	−0.250482	−0.125241	+	0.992126i	$0.539970\pi$
$684$	32.4032	1.23897
$685$	28.9152	1.10479
$686$	131.669	5.02715
$687$	28.4374	1.08496
$688$	52.4734	2.00053
$689$	23.0481	0.878061
$690$	0.141559	0.00538906
$691$	−39.1401	−1.48896	−0.744480	−	0.667645i	$-0.767303\pi$
$691$	−39.1401	−1.48896	−0.744480	+	0.667645i	$0.767303\pi$
$692$	−1.90176	−0.0722942
$693$	−4.38772	−0.166676
$694$	41.5191	1.57604
$695$	44.3969	1.68407
$696$	−11.3201	−0.429088
$697$	0.0711429	0.00269473
$698$	51.2990	1.94169
$699$	−21.4423	−0.811022
$700$	−205.235	−7.75716
$701$	12.9468	0.488995	0.244497	−	0.969650i	$-0.421377\pi$
$701$	12.9468	0.488995	0.244497	+	0.969650i	$0.421377\pi$
$702$	44.8205	1.69164
$703$	24.3354	0.917828
$704$	−22.9918	−0.866534
$705$	−15.6519	−0.589483
$706$	−75.7914	−2.85245
$707$	−86.6046	−3.25710
$708$	−21.1984	−0.796683
$709$	41.1024	1.54363	0.771816	−	0.635846i	$-0.219349\pi$
$709$	41.1024	1.54363	0.771816	+	0.635846i	$0.219349\pi$
$710$	70.9858	2.66405
$711$	4.24146	0.159067
$712$	−171.886	−6.44169
$713$	0.136106	0.00509721
$714$	−0.460904	−0.0172489
$715$	5.14503	0.192413
$716$	40.4823	1.51289
$717$	25.4162	0.949185
$718$	76.2301	2.84488
$719$	34.8904	1.30119	0.650596	−	0.759424i	$-0.274519\pi$
$719$	34.8904	1.30119	0.650596	+	0.759424i	$0.274519\pi$
$720$	−124.368	−4.63492
$721$	43.2278	1.60989
$722$	29.7756	1.10813
$723$	3.19022	0.118646
$724$	−16.5562	−0.615305
$725$	−7.19622	−0.267261
$726$	−31.5713	−1.17172
$727$	23.0651	0.855437	0.427719	−	0.903912i	$-0.359317\pi$
$727$	23.0651	0.855437	0.427719	+	0.903912i	$0.359317\pi$
$728$	−164.255	−6.08770
$729$	15.3681	0.569190
$730$	−114.249	−4.22855
$731$	0.0909716	0.00336470
$732$	35.4167	1.30904
$733$	−10.8974	−0.402503	−0.201251	−	0.979540i	$-0.564501\pi$
$733$	−10.8974	−0.402503	−0.201251	+	0.979540i	$0.564501\pi$
$734$	40.3084	1.48781
$735$	−60.7607	−2.24119
$736$	−0.424110	−0.0156329
$737$	−6.03865	−0.222437
$738$	11.7713	0.433308
$739$	−0.645956	−0.0237619	−0.0118809	−	0.999929i	$-0.503782\pi$
$739$	−0.645956	−0.0237619	−0.0118809	+	0.999929i	$0.503782\pi$
$740$	−172.135	−6.32782
$741$	−9.42698	−0.346309
$742$	−100.856	−3.70255
$743$	−29.3328	−1.07612	−0.538058	−	0.842908i	$-0.680842\pi$
$743$	−29.3328	−1.07612	−0.538058	+	0.842908i	$0.680842\pi$
$744$	111.357	4.08253
$745$	3.94923	0.144689
$746$	32.7565	1.19930
$747$	17.2083	0.629617
$748$	−0.0896622	−0.00327838
$749$	88.6340	3.23862
$750$	22.4699	0.820485
$751$	2.44995	0.0893999	0.0447000	−	0.999000i	$-0.485767\pi$
$751$	2.44995	0.0893999	0.0447000	+	0.999000i	$0.485767\pi$
$752$	80.0465	2.91899
$753$	−4.18313	−0.152442
$754$	−8.74033	−0.318304
$755$	−65.0471	−2.36731
$756$	−146.250	−5.31907
$757$	−29.7309	−1.08059	−0.540294	−	0.841476i	$-0.681687\pi$
$757$	−29.7309	−1.08059	−0.540294	+	0.841476i	$0.681687\pi$
$758$	−13.2473	−0.481163
$759$	0.00683238	0.000248000 0
$760$	109.559	3.97414
$761$	−17.5166	−0.634977	−0.317489	−	0.948262i	$-0.602840\pi$
$761$	−17.5166	−0.634977	−0.317489	+	0.948262i	$0.602840\pi$
$762$	23.7351	0.859832
$763$	−89.7896	−3.25060
$764$	−18.8423	−0.681689
$765$	−0.215613	−0.00779550
$766$	−5.34225	−0.193023
$767$	−10.7851	−0.389426
$768$	−118.380	−4.27167
$769$	50.1717	1.80924	0.904618	−	0.426222i	$-0.140156\pi$
$769$	50.1717	1.80924	0.904618	+	0.426222i	$0.140156\pi$
$770$	−22.5142	−0.811356
$771$	−16.9954	−0.612076
$772$	−41.5480	−1.49534
$773$	5.61537	0.201971	0.100985	−	0.994888i	$-0.467800\pi$
$773$	5.61537	0.201971	0.100985	+	0.994888i	$0.467800\pi$
$774$	15.0522	0.541039
$775$	70.7896	2.54284
$776$	−91.6432	−3.28980
$777$	−42.7077	−1.53213
$778$	−25.0250	−0.897189
$779$	−6.36741	−0.228136
$780$	66.6812	2.38757
$781$	3.42615	0.122597
$782$	−0.00125510	−4.48825e−5 0
$783$	−5.12801	−0.183260
$784$	310.741	11.0979
$785$	−25.2691	−0.901893
$786$	−42.3416	−1.51027
$787$	−22.6902	−0.808820	−0.404410	−	0.914578i	$-0.632523\pi$
$787$	−22.6902	−0.808820	−0.404410	+	0.914578i	$0.632523\pi$
$788$	46.3466	1.65103
$789$	−6.77870	−0.241328
$790$	21.7637	0.774319
$791$	−95.1698	−3.38385
$792$	−9.77567	−0.347363
$793$	18.0189	0.639870
$794$	40.1527	1.42497
$795$	26.9794	0.956859
$796$	−137.973	−4.89033
$797$	38.0522	1.34788	0.673940	−	0.738786i	$-0.264601\pi$
$797$	38.0522	1.34788	0.673940	+	0.738786i	$0.264601\pi$
$798$	41.2517	1.46029
$799$	0.138774	0.00490947
$800$	−220.582	−7.79875
$801$	−30.2758	−1.06974
$802$	4.78044	0.168803
$803$	−5.51426	−0.194594
$804$	−78.2629	−2.76012
$805$	−0.235005	−0.00828285
$806$	85.9790	3.02848
$807$	−20.2104	−0.711442
$808$	−192.952	−6.78802
$809$	0.535668	0.0188331	0.00941653	−	0.999956i	$-0.497003\pi$
$809$	0.535668	0.0188331	0.00941653	+	0.999956i	$0.497003\pi$
$810$	−3.60994	−0.126840
$811$	29.1994	1.02533	0.512665	−	0.858589i	$-0.328658\pi$
$811$	29.1994	1.02533	0.512665	+	0.858589i	$0.328658\pi$
$812$	28.5199	1.00085
$813$	−13.2769	−0.465642
$814$	−11.1418	−0.390519
$815$	−77.1992	−2.70417
$816$	−0.630543	−0.0220734
$817$	−8.14211	−0.284856
$818$	−56.2016	−1.96504
$819$	−28.9318	−1.01096
$820$	45.0395	1.57285
$821$	17.0987	0.596748	0.298374	−	0.954449i	$-0.403556\pi$
$821$	17.0987	0.596748	0.298374	+	0.954449i	$0.403556\pi$
$822$	24.2564	0.846039
$823$	40.0575	1.39632	0.698158	−	0.715944i	$-0.254003\pi$
$823$	40.0575	1.39632	0.698158	+	0.715944i	$0.254003\pi$
$824$	96.3099	3.35512
$825$	3.55356	0.123719
$826$	47.1946	1.64211
$827$	51.7204	1.79850	0.899248	−	0.437440i	$-0.144115\pi$
$827$	51.7204	1.79850	0.899248	+	0.437440i	$0.144115\pi$
$828$	−0.154855	−0.00538157
$829$	−4.09068	−0.142075	−0.0710375	−	0.997474i	$-0.522631\pi$
$829$	−4.09068	−0.142075	−0.0710375	+	0.997474i	$0.522631\pi$
$830$	88.2988	3.06490
$831$	1.04470	0.0362401
$832$	−151.603	−5.25590
$833$	0.538722	0.0186656
$834$	37.2437	1.28964
$835$	−21.0115	−0.727134
$836$	8.02492	0.277548
$837$	50.4445	1.74362
$838$	−16.1067	−0.556396
$839$	8.39242	0.289738	0.144869	−	0.989451i	$-0.453724\pi$
$839$	8.39242	0.289738	0.144869	+	0.989451i	$0.453724\pi$
$840$	−192.272	−6.63402
$841$	1.00000	0.0344828
$842$	80.4595	2.77282
$843$	−0.314904	−0.0108459
$844$	85.0483	2.92748
$845$	−11.4747	−0.394741
$846$	22.9616	0.789435
$847$	52.4123	1.80091
$848$	−137.977	−4.73816
$849$	3.67221	0.126030
$850$	−0.652788	−0.0223904
$851$	−0.116299	−0.00398667
$852$	44.4040	1.52125
$853$	6.59119	0.225678	0.112839	−	0.993613i	$-0.464006\pi$
$853$	6.59119	0.225678	0.112839	+	0.993613i	$0.464006\pi$
$854$	−78.8493	−2.69817
$855$	19.2977	0.659968
$856$	197.473	6.74950
$857$	−23.1819	−0.791879	−0.395940	−	0.918277i	$-0.629581\pi$
$857$	−23.1819	−0.791879	−0.395940	+	0.918277i	$0.629581\pi$
$858$	4.31606	0.147348
$859$	−16.7291	−0.570790	−0.285395	−	0.958410i	$-0.592125\pi$
$859$	−16.7291	−0.570790	−0.285395	+	0.958410i	$0.592125\pi$
$860$	57.5928	1.96390
$861$	11.1745	0.380827
$862$	−46.8256	−1.59489
$863$	1.61103	0.0548400	0.0274200	−	0.999624i	$-0.491271\pi$
$863$	1.61103	0.0548400	0.0274200	+	0.999624i	$0.491271\pi$
$864$	−157.186	−5.34758
$865$	−1.13259	−0.0385094
$866$	59.6036	2.02541
$867$	17.7588	0.603119
$868$	−280.551	−9.52253
$869$	1.05043	0.0356335
$870$	−10.2312	−0.346869
$871$	−39.8177	−1.34917
$872$	−200.048	−6.77447
$873$	−16.1420	−0.546323
$874$	0.112334	0.00379975
$875$	−37.3028	−1.26106
$876$	−71.4667	−2.41463
$877$	−42.2401	−1.42635	−0.713174	−	0.700988i	$-0.752743\pi$
$877$	−42.2401	−1.42635	−0.713174	+	0.700988i	$0.752743\pi$
$878$	32.5387	1.09813
$879$	−2.10002	−0.0708318
$880$	−30.8007	−1.03829
$881$	−14.8643	−0.500792	−0.250396	−	0.968144i	$-0.580561\pi$
$881$	−14.8643	−0.500792	−0.250396	+	0.968144i	$0.580561\pi$
$882$	89.1371	3.00140
$883$	−21.5386	−0.724833	−0.362416	−	0.932016i	$-0.618048\pi$
$883$	−21.5386	−0.724833	−0.362416	+	0.932016i	$0.618048\pi$
$884$	−0.591216	−0.0198847
$885$	−12.6247	−0.424374
$886$	45.7135	1.53578
$887$	20.8320	0.699471	0.349735	−	0.936849i	$-0.386272\pi$
$887$	20.8320	0.699471	0.349735	+	0.936849i	$0.386272\pi$
$888$	−95.1510	−3.19306
$889$	−39.4032	−1.32154
$890$	−155.351	−5.20738
$891$	−0.174235	−0.00583708
$892$	38.8232	1.29990
$893$	−12.4205	−0.415636
$894$	3.31293	0.110801
$895$	24.1092	0.805882
$896$	365.244	12.2019
$897$	0.0450514	0.00150422
$898$	−32.0620	−1.06992
$899$	−9.83705	−0.328084
$900$	−80.5408	−2.68469
$901$	−0.239207	−0.00796914
$902$	2.91526	0.0970677
$903$	14.2891	0.475510
$904$	−212.035	−7.05217
$905$	−9.86002	−0.327758
$906$	−54.5667	−1.81286
$907$	17.0440	0.565938	0.282969	−	0.959129i	$-0.408681\pi$
$907$	17.0440	0.565938	0.282969	+	0.959129i	$0.408681\pi$
$908$	34.0761	1.13085
$909$	−33.9864	−1.12726
$910$	−148.454	−4.92122
$911$	−45.7562	−1.51597	−0.757985	−	0.652272i	$-0.773816\pi$
$911$	−45.7562	−1.51597	−0.757985	+	0.652272i	$0.773816\pi$
$912$	56.4347	1.86874
$913$	4.26177	0.141044
$914$	51.6237	1.70756
$915$	21.0924	0.697293
$916$	−159.623	−5.27409
$917$	70.2922	2.32125
$918$	−0.465175	−0.0153531
$919$	10.0436	0.331308	0.165654	−	0.986184i	$-0.447026\pi$
$919$	10.0436	0.331308	0.165654	+	0.986184i	$0.447026\pi$
$920$	−0.523583	−0.0172620
$921$	−24.8753	−0.819668
$922$	−58.7617	−1.93521
$923$	22.5914	0.743604
$924$	−14.0834	−0.463310
$925$	−60.4877	−1.98882
$926$	50.7346	1.66724
$927$	16.9640	0.557170
$928$	30.6525	1.00622
$929$	−33.8729	−1.11133	−0.555667	−	0.831405i	$-0.687537\pi$
$929$	−33.8729	−1.11133	−0.555667	+	0.831405i	$0.687537\pi$
$930$	100.644	3.30026
$931$	−48.2165	−1.58023
$932$	120.358	3.94246
$933$	31.5866	1.03410
$934$	−74.5206	−2.43839
$935$	−0.0533983	−0.00174631
$936$	−64.4589	−2.10691
$937$	23.2515	0.759592	0.379796	−	0.925070i	$-0.375994\pi$
$937$	23.2515	0.759592	0.379796	+	0.925070i	$0.375994\pi$
$938$	174.239	5.68910
$939$	−3.78011	−0.123359
$940$	87.8558	2.86554
$941$	55.6095	1.81282	0.906409	−	0.422401i	$-0.138812\pi$
$941$	55.6095	1.81282	0.906409	+	0.422401i	$0.138812\pi$
$942$	−21.1977	−0.690660
$943$	0.0304298	0.000990930 0
$944$	64.5649	2.10141
$945$	−87.0992	−2.83334
$946$	3.72779	0.121201
$947$	57.3669	1.86417	0.932087	−	0.362235i	$-0.117986\pi$
$947$	57.3669	1.86417	0.932087	+	0.362235i	$0.117986\pi$
$948$	13.6139	0.442160
$949$	−36.3600	−1.18030
$950$	58.4256	1.89558
$951$	25.8569	0.838466
$952$	1.70474	0.0552510
$953$	−23.1515	−0.749951	−0.374975	−	0.927035i	$-0.622349\pi$
$953$	−23.1515	−0.749951	−0.374975	+	0.927035i	$0.622349\pi$
$954$	−39.5792	−1.28142
$955$	−11.2215	−0.363119
$956$	−142.664	−4.61409
$957$	−0.493810	−0.0159626
$958$	54.6646	1.76613
$959$	−40.2686	−1.30034
$960$	−177.462	−5.72757
$961$	65.7675	2.12153
$962$	−73.4667	−2.36866
$963$	34.7828	1.12086
$964$	−17.9071	−0.576749
$965$	−24.7439	−0.796534
$966$	−0.197141	−0.00634292
$967$	−20.8873	−0.671691	−0.335846	−	0.941917i	$-0.609022\pi$
$967$	−20.8873	−0.671691	−0.335846	+	0.941917i	$0.609022\pi$
$968$	116.773	3.75321
$969$	0.0978390	0.00314304
$970$	−82.8275	−2.65943
$971$	−36.7956	−1.18083	−0.590413	−	0.807101i	$-0.701035\pi$
$971$	−36.7956	−1.18083	−0.590413	+	0.807101i	$0.701035\pi$
$972$	−92.4702	−2.96598
$973$	−61.8291	−1.98215
$974$	91.7759	2.94069
$975$	23.4315	0.750410
$976$	−107.870	−3.45285
$977$	−7.10691	−0.227370	−0.113685	−	0.993517i	$-0.536265\pi$
$977$	−7.10691	−0.227370	−0.113685	+	0.993517i	$0.536265\pi$
$978$	−64.7609	−2.07083
$979$	−7.49805	−0.239639
$980$	341.057	10.8947
$981$	−35.2363	−1.12501
$982$	14.1267	0.450801
$983$	13.7098	0.437276	0.218638	−	0.975806i	$-0.429839\pi$
$983$	13.7098	0.437276	0.218638	+	0.975806i	$0.429839\pi$
$984$	24.8964	0.793670
$985$	27.6017	0.879464
$986$	0.0907126	0.00288888
$987$	21.7975	0.693821
$988$	52.9148	1.68344
$989$	0.0389110	0.00123730
$990$	−8.83529	−0.280804
$991$	1.60559	0.0510034	0.0255017	−	0.999675i	$-0.491882\pi$
$991$	1.60559	0.0510034	0.0255017	+	0.999675i	$0.491882\pi$
$992$	−301.530	−9.57358
$993$	1.12838	0.0358082
$994$	−98.8579	−3.13558
$995$	−82.1698	−2.60496
$996$	55.2339	1.75015
$997$	−32.2616	−1.02173	−0.510867	−	0.859660i	$-0.670675\pi$
$997$	−32.2616	−1.02173	−0.510867	+	0.859660i	$0.670675\pi$
$998$	98.7053	3.12446
$999$	−43.1034	−1.36373

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8033.2.a.b.1.1	✓	153

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8033.2.a.b.1.1	✓	153	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:	\( N \)	\(=\)	\( 8033 = 29 \cdot 277 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8033.a (trivial)

\(f(q)\)	\(=\)	\(q-2.80428 q^{2} -1.04470 q^{3} +5.86401 q^{4} +3.49231 q^{5} +2.92963 q^{6} -4.86354 q^{7} -10.8358 q^{8} -1.90861 q^{9} +O(q^{10})\)	\(q-2.80428 q^{2} -1.04470 q^{3} +5.86401 q^{4} +3.49231 q^{5} +2.92963 q^{6} -4.86354 q^{7} -10.8358 q^{8} -1.90861 q^{9} -9.79343 q^{10} -0.472682 q^{11} -6.12612 q^{12} -3.11678 q^{13} +13.6388 q^{14} -3.64840 q^{15} +18.6586 q^{16} +0.0323478 q^{17} +5.35228 q^{18} -2.89519 q^{19} +20.4789 q^{20} +5.08093 q^{21} +1.32554 q^{22} +0.0138361 q^{23} +11.3201 q^{24} +7.19622 q^{25} +8.74033 q^{26} +5.12801 q^{27} -28.5199 q^{28} -1.00000 q^{29} +10.2312 q^{30} +9.83705 q^{31} -30.6525 q^{32} +0.493810 q^{33} -0.0907126 q^{34} -16.9850 q^{35} -11.1921 q^{36} -8.40548 q^{37} +8.11892 q^{38} +3.25609 q^{39} -37.8419 q^{40} +2.19931 q^{41} -14.2484 q^{42} +2.81229 q^{43} -2.77181 q^{44} -6.66545 q^{45} -0.0388003 q^{46} +4.29006 q^{47} -19.4926 q^{48} +16.6540 q^{49} -20.1803 q^{50} -0.0337937 q^{51} -18.2768 q^{52} -7.39483 q^{53} -14.3804 q^{54} -1.65075 q^{55} +52.7003 q^{56} +3.02459 q^{57} +2.80428 q^{58} +3.46033 q^{59} -21.3943 q^{60} -5.78126 q^{61} -27.5859 q^{62} +9.28260 q^{63} +48.6410 q^{64} -10.8847 q^{65} -1.38478 q^{66} +12.7753 q^{67} +0.189688 q^{68} -0.0144545 q^{69} +47.6307 q^{70} -7.24831 q^{71} +20.6813 q^{72} +11.6659 q^{73} +23.5714 q^{74} -7.51787 q^{75} -16.9774 q^{76} +2.29891 q^{77} -9.13100 q^{78} -2.22228 q^{79} +65.1616 q^{80} +0.368608 q^{81} -6.16749 q^{82} -9.01613 q^{83} +29.7946 q^{84} +0.112969 q^{85} -7.88647 q^{86} +1.04470 q^{87} +5.12189 q^{88} +15.8628 q^{89} +18.6918 q^{90} +15.1586 q^{91} +0.0811348 q^{92} -10.2767 q^{93} -12.0305 q^{94} -10.1109 q^{95} +32.0225 q^{96} +8.45746 q^{97} -46.7027 q^{98} +0.902165 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 153 q - 3 q^{2} - 12 q^{3} + 135 q^{4} - 11 q^{5} - 17 q^{6} - 76 q^{7} - 12 q^{8} + 133 q^{9}+O(q^{10}) \) 153 * q - 3 * q^2 - 12 * q^3 + 135 * q^4 - 11 * q^5 - 17 * q^6 - 76 * q^7 - 12 * q^8 + 133 * q^9	\( 153 q - 3 q^{2} - 12 q^{3} + 135 q^{4} - 11 q^{5} - 17 q^{6} - 76 q^{7} - 12 q^{8} + 133 q^{9} - 30 q^{10} + 4 q^{11} - 39 q^{12} - 65 q^{13} + q^{14} - 26 q^{15} + 107 q^{16} - 20 q^{17} - 21 q^{18} - 65 q^{19} - 23 q^{20} - 24 q^{21} - 59 q^{22} - 62 q^{23} - 59 q^{24} + 102 q^{25} - 18 q^{26} - 57 q^{27} - 155 q^{28} - 153 q^{29} - 82 q^{30} - 49 q^{31} - 17 q^{32} - 59 q^{33} - 68 q^{34} - 36 q^{35} + 74 q^{36} - 30 q^{37} - 67 q^{38} - 47 q^{39} - 108 q^{40} - 9 q^{41} - 62 q^{42} - 90 q^{43} - 14 q^{44} - 56 q^{45} - 52 q^{46} - 54 q^{47} - 76 q^{48} + 101 q^{49} - 36 q^{50} - 60 q^{51} - 191 q^{52} - 38 q^{53} - 82 q^{54} - 215 q^{55} + 24 q^{56} - 52 q^{57} + 3 q^{58} - 55 q^{59} - 60 q^{60} - 90 q^{61} - 66 q^{62} - 229 q^{63} + 52 q^{64} - 67 q^{65} - 29 q^{66} - 114 q^{67} - 78 q^{68} - 68 q^{69} - 61 q^{70} - 52 q^{71} - 47 q^{72} - 83 q^{73} - 21 q^{74} - 47 q^{75} - 100 q^{76} - 32 q^{77} - 17 q^{78} - 151 q^{79} - 24 q^{80} + 81 q^{81} - 151 q^{82} - 94 q^{83} - 84 q^{84} - 77 q^{85} - 43 q^{86} + 12 q^{87} - 121 q^{88} + 11 q^{89} - 14 q^{90} - 66 q^{91} - 156 q^{92} - 66 q^{93} - 22 q^{94} - 67 q^{95} - 131 q^{96} - 78 q^{97} - 67 q^{98} - 41 q^{99}+O(q^{100}) \) 153 * q - 3 * q^2 - 12 * q^3 + 135 * q^4 - 11 * q^5 - 17 * q^6 - 76 * q^7 - 12 * q^8 + 133 * q^9 - 30 * q^10 + 4 * q^11 - 39 * q^12 - 65 * q^13 + q^14 - 26 * q^15 + 107 * q^16 - 20 * q^17 - 21 * q^18 - 65 * q^19 - 23 * q^20 - 24 * q^21 - 59 * q^22 - 62 * q^23 - 59 * q^24 + 102 * q^25 - 18 * q^26 - 57 * q^27 - 155 * q^28 - 153 * q^29 - 82 * q^30 - 49 * q^31 - 17 * q^32 - 59 * q^33 - 68 * q^34 - 36 * q^35 + 74 * q^36 - 30 * q^37 - 67 * q^38 - 47 * q^39 - 108 * q^40 - 9 * q^41 - 62 * q^42 - 90 * q^43 - 14 * q^44 - 56 * q^45 - 52 * q^46 - 54 * q^47 - 76 * q^48 + 101 * q^49 - 36 * q^50 - 60 * q^51 - 191 * q^52 - 38 * q^53 - 82 * q^54 - 215 * q^55 + 24 * q^56 - 52 * q^57 + 3 * q^58 - 55 * q^59 - 60 * q^60 - 90 * q^61 - 66 * q^62 - 229 * q^63 + 52 * q^64 - 67 * q^65 - 29 * q^66 - 114 * q^67 - 78 * q^68 - 68 * q^69 - 61 * q^70 - 52 * q^71 - 47 * q^72 - 83 * q^73 - 21 * q^74 - 47 * q^75 - 100 * q^76 - 32 * q^77 - 17 * q^78 - 151 * q^79 - 24 * q^80 + 81 * q^81 - 151 * q^82 - 94 * q^83 - 84 * q^84 - 77 * q^85 - 43 * q^86 + 12 * q^87 - 121 * q^88 + 11 * q^89 - 14 * q^90 - 66 * q^91 - 156 * q^92 - 66 * q^93 - 22 * q^94 - 67 * q^95 - 131 * q^96 - 78 * q^97 - 67 * q^98 - 41 * q^99

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