LMFDB - Embedded newform 8033.2.a.c.1.18

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:	$154$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
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)

$f(q)$	$=$	$q-2.33650 q^{2} -1.34355 q^{3} +3.45924 q^{4} -2.97087 q^{5} +3.13920 q^{6} +1.58277 q^{7} -3.40951 q^{8} -1.19488 q^{9} +O(q^{10})$	\(q-2.33650 q^{2} -1.34355 q^{3} +3.45924 q^{4} -2.97087 q^{5} +3.13920 q^{6} +1.58277 q^{7} -3.40951 q^{8} -1.19488 q^{9} +6.94144 q^{10} +2.50527 q^{11} -4.64765 q^{12} +6.58035 q^{13} -3.69815 q^{14} +3.99150 q^{15} +1.04784 q^{16} +2.65118 q^{17} +2.79184 q^{18} -2.86001 q^{19} -10.2769 q^{20} -2.12653 q^{21} -5.85358 q^{22} +8.89786 q^{23} +4.58083 q^{24} +3.82607 q^{25} -15.3750 q^{26} +5.63602 q^{27} +5.47518 q^{28} +1.00000 q^{29} -9.32615 q^{30} -5.31724 q^{31} +4.37073 q^{32} -3.36595 q^{33} -6.19449 q^{34} -4.70221 q^{35} -4.13338 q^{36} -6.33551 q^{37} +6.68242 q^{38} -8.84102 q^{39} +10.1292 q^{40} -6.27673 q^{41} +4.96863 q^{42} -1.10472 q^{43} +8.66634 q^{44} +3.54984 q^{45} -20.7899 q^{46} +0.737109 q^{47} -1.40783 q^{48} -4.49483 q^{49} -8.93961 q^{50} -3.56199 q^{51} +22.7630 q^{52} +6.51598 q^{53} -13.1686 q^{54} -7.44284 q^{55} -5.39647 q^{56} +3.84256 q^{57} -2.33650 q^{58} -2.37244 q^{59} +13.8076 q^{60} -9.80125 q^{61} +12.4237 q^{62} -1.89122 q^{63} -12.3079 q^{64} -19.5494 q^{65} +7.86455 q^{66} +0.744514 q^{67} +9.17106 q^{68} -11.9547 q^{69} +10.9867 q^{70} +5.95688 q^{71} +4.07396 q^{72} -13.8133 q^{73} +14.8029 q^{74} -5.14050 q^{75} -9.89346 q^{76} +3.96528 q^{77} +20.6570 q^{78} +5.98764 q^{79} -3.11301 q^{80} -3.98761 q^{81} +14.6656 q^{82} -1.38215 q^{83} -7.35616 q^{84} -7.87632 q^{85} +2.58119 q^{86} -1.34355 q^{87} -8.54175 q^{88} -6.69829 q^{89} -8.29420 q^{90} +10.4152 q^{91} +30.7798 q^{92} +7.14396 q^{93} -1.72226 q^{94} +8.49673 q^{95} -5.87228 q^{96} -4.80332 q^{97} +10.5022 q^{98} -2.99351 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 154 q - 12 q^{2} - 36 q^{3} + 142 q^{4} - 9 q^{5} - 11 q^{6} - 68 q^{7} - 33 q^{8} + 146 q^{9}+O(q^{10}) $ 154 * q - 12 * q^2 - 36 * q^3 + 142 * q^4 - 9 * q^5 - 11 * q^6 - 68 * q^7 - 33 * q^8 + 146 * q^9	\( 154 q - 12 q^{2} - 36 q^{3} + 142 q^{4} - 9 q^{5} - 11 q^{6} - 68 q^{7} - 33 q^{8} + 146 q^{9} - 40 q^{10} - 36 q^{11} - 67 q^{12} - 51 q^{13} - 19 q^{14} - 48 q^{15} + 122 q^{16} - 54 q^{17} - 46 q^{18} - 73 q^{19} - 21 q^{20} - 8 q^{21} - 23 q^{22} - 38 q^{23} - 17 q^{24} + 133 q^{25} - 20 q^{26} - 129 q^{27} - 99 q^{28} + 154 q^{29} - 10 q^{30} - 91 q^{31} - 88 q^{32} - 39 q^{33} - 42 q^{34} - 36 q^{35} + 101 q^{36} - 50 q^{37} - 17 q^{38} - 33 q^{39} - 92 q^{40} - 31 q^{41} - 62 q^{42} - 154 q^{43} - 42 q^{44} - 14 q^{45} - 24 q^{46} - 140 q^{47} - 118 q^{48} + 126 q^{49} - 5 q^{50} - 16 q^{51} - 133 q^{52} - 40 q^{53} + 14 q^{54} - 203 q^{55} - 44 q^{56} - 16 q^{57} - 12 q^{58} + 5 q^{59} - 28 q^{60} - 106 q^{61} - 30 q^{62} - 145 q^{63} + 111 q^{64} - 15 q^{65} - 49 q^{66} - 78 q^{67} - 118 q^{68} - 32 q^{69} - 43 q^{70} - 4 q^{71} - 152 q^{72} - 137 q^{73} + 9 q^{74} - 129 q^{75} - 204 q^{76} - 76 q^{77} + 15 q^{78} - 141 q^{79} - 44 q^{80} + 122 q^{81} - 71 q^{82} - 90 q^{83} + 92 q^{84} - 41 q^{85} + 9 q^{86} - 36 q^{87} - 109 q^{88} - 51 q^{89} - 82 q^{90} - 22 q^{91} - 8 q^{92} - 10 q^{93} - 106 q^{94} - 55 q^{95} - 49 q^{96} - 140 q^{97} - 4 q^{98} - 101 q^{99}+O(q^{100}) \) 154 * q - 12 * q^2 - 36 * q^3 + 142 * q^4 - 9 * q^5 - 11 * q^6 - 68 * q^7 - 33 * q^8 + 146 * q^9 - 40 * q^10 - 36 * q^11 - 67 * q^12 - 51 * q^13 - 19 * q^14 - 48 * q^15 + 122 * q^16 - 54 * q^17 - 46 * q^18 - 73 * q^19 - 21 * q^20 - 8 * q^21 - 23 * q^22 - 38 * q^23 - 17 * q^24 + 133 * q^25 - 20 * q^26 - 129 * q^27 - 99 * q^28 + 154 * q^29 - 10 * q^30 - 91 * q^31 - 88 * q^32 - 39 * q^33 - 42 * q^34 - 36 * q^35 + 101 * q^36 - 50 * q^37 - 17 * q^38 - 33 * q^39 - 92 * q^40 - 31 * q^41 - 62 * q^42 - 154 * q^43 - 42 * q^44 - 14 * q^45 - 24 * q^46 - 140 * q^47 - 118 * q^48 + 126 * q^49 - 5 * q^50 - 16 * q^51 - 133 * q^52 - 40 * q^53 + 14 * q^54 - 203 * q^55 - 44 * q^56 - 16 * q^57 - 12 * q^58 + 5 * q^59 - 28 * q^60 - 106 * q^61 - 30 * q^62 - 145 * q^63 + 111 * q^64 - 15 * q^65 - 49 * q^66 - 78 * q^67 - 118 * q^68 - 32 * q^69 - 43 * q^70 - 4 * q^71 - 152 * q^72 - 137 * q^73 + 9 * q^74 - 129 * q^75 - 204 * q^76 - 76 * q^77 + 15 * q^78 - 141 * q^79 - 44 * q^80 + 122 * q^81 - 71 * q^82 - 90 * q^83 + 92 * q^84 - 41 * q^85 + 9 * q^86 - 36 * q^87 - 109 * q^88 - 51 * q^89 - 82 * q^90 - 22 * q^91 - 8 * q^92 - 10 * q^93 - 106 * q^94 - 55 * q^95 - 49 * q^96 - 140 * q^97 - 4 * q^98 - 101 * 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 $

$2$	−2.33650	−1.65216	−0.826078	−	0.563556i	$-0.809433\pi$
$2$	−2.33650	−1.65216	−0.826078	+	0.563556i	$0.809433\pi$
$3$	−1.34355	−0.775697	−0.387849	−	0.921723i	$-0.626782\pi$
$3$	−1.34355	−0.775697	−0.387849	+	0.921723i	$0.626782\pi$
$4$	3.45924	1.72962
$5$	−2.97087	−1.32861	−0.664307	−	0.747460i	$-0.731273\pi$
$5$	−2.97087	−1.32861	−0.664307	+	0.747460i	$0.731273\pi$
$6$	3.13920	1.28157
$7$	1.58277	0.598231	0.299116	−	0.954217i	$-0.403308\pi$
$7$	1.58277	0.598231	0.299116	+	0.954217i	$0.403308\pi$
$8$	−3.40951	−1.20544
$9$	−1.19488	−0.398294
$10$	6.94144	2.19508
$11$	2.50527	0.755369	0.377684	−	0.925934i	$-0.376720\pi$
$11$	2.50527	0.755369	0.377684	+	0.925934i	$0.376720\pi$
$12$	−4.64765	−1.34166
$13$	6.58035	1.82506	0.912531	−	0.409008i	$-0.134125\pi$
$13$	6.58035	1.82506	0.912531	+	0.409008i	$0.134125\pi$
$14$	−3.69815	−0.988371
$15$	3.99150	1.03060
$16$	1.04784	0.261961
$17$	2.65118	0.643006	0.321503	−	0.946909i	$-0.395812\pi$
$17$	2.65118	0.643006	0.321503	+	0.946909i	$0.395812\pi$
$18$	2.79184	0.658043
$19$	−2.86001	−0.656132	−0.328066	−	0.944655i	$-0.606397\pi$
$19$	−2.86001	−0.656132	−0.328066	+	0.944655i	$0.606397\pi$
$20$	−10.2769	−2.29799
$21$	−2.12653	−0.464046
$22$	−5.85358	−1.24799
$23$	8.89786	1.85533	0.927666	−	0.373410i	$-0.121812\pi$
$23$	8.89786	1.85533	0.927666	+	0.373410i	$0.121812\pi$
$24$	4.58083	0.935059
$25$	3.82607	0.765214
$26$	−15.3750	−3.01529
$27$	5.63602	1.08465
$28$	5.47518	1.03471
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	−9.32615	−1.70271
$31$	−5.31724	−0.955004	−0.477502	−	0.878631i	$-0.658458\pi$
$31$	−5.31724	−0.955004	−0.477502	+	0.878631i	$0.658458\pi$
$32$	4.37073	0.772643
$33$	−3.36595	−0.585937
$34$	−6.19449	−1.06235
$35$	−4.70221	−0.794818
$36$	−4.13338	−0.688896
$37$	−6.33551	−1.04155	−0.520775	−	0.853694i	$-0.674357\pi$
$37$	−6.33551	−1.04155	−0.520775	+	0.853694i	$0.674357\pi$
$38$	6.68242	1.08403
$39$	−8.84102	−1.41570
$40$	10.1292	1.60157
$41$	−6.27673	−0.980261	−0.490130	−	0.871649i	$-0.663051\pi$
$41$	−6.27673	−0.980261	−0.490130	+	0.871649i	$0.663051\pi$
$42$	4.96863	0.766677
$43$	−1.10472	−0.168469	−0.0842344	−	0.996446i	$-0.526844\pi$
$43$	−1.10472	−0.168469	−0.0842344	+	0.996446i	$0.526844\pi$
$44$	8.66634	1.30650
$45$	3.54984	0.529179
$46$	−20.7899	−3.06530
$47$	0.737109	0.107518	0.0537592	−	0.998554i	$-0.482880\pi$
$47$	0.737109	0.107518	0.0537592	+	0.998554i	$0.482880\pi$
$48$	−1.40783	−0.203202
$49$	−4.49483	−0.642119
$50$	−8.93961	−1.26425
$51$	−3.56199	−0.498778
$52$	22.7630	3.15666
$53$	6.51598	0.895039	0.447519	−	0.894274i	$-0.352308\pi$
$53$	6.51598	0.895039	0.447519	+	0.894274i	$0.352308\pi$
$54$	−13.1686	−1.79201
$55$	−7.44284	−1.00359
$56$	−5.39647	−0.721134
$57$	3.84256	0.508960
$58$	−2.33650	−0.306798
$59$	−2.37244	−0.308865	−0.154433	−	0.988003i	$-0.549355\pi$
$59$	−2.37244	−0.308865	−0.154433	+	0.988003i	$0.549355\pi$
$60$	13.8076	1.78255
$61$	−9.80125	−1.25492	−0.627461	−	0.778648i	$-0.715906\pi$
$61$	−9.80125	−1.25492	−0.627461	+	0.778648i	$0.715906\pi$
$62$	12.4237	1.57782
$63$	−1.89122	−0.238272
$64$	−12.3079	−1.53849
$65$	−19.5494	−2.42480
$66$	7.86455	0.968060
$67$	0.744514	0.0909568	0.0454784	−	0.998965i	$-0.485519\pi$
$67$	0.744514	0.0909568	0.0454784	+	0.998965i	$0.485519\pi$
$68$	9.17106	1.11215
$69$	−11.9547	−1.43918
$70$	10.9867	1.31316
$71$	5.95688	0.706951	0.353476	−	0.935444i	$-0.385000\pi$
$71$	5.95688	0.706951	0.353476	+	0.935444i	$0.385000\pi$
$72$	4.07396	0.480120
$73$	−13.8133	−1.61673	−0.808363	−	0.588685i	$-0.799646\pi$
$73$	−13.8133	−1.61673	−0.808363	+	0.588685i	$0.799646\pi$
$74$	14.8029	1.72080
$75$	−5.14050	−0.593574
$76$	−9.89346	−1.13486
$77$	3.96528	0.451885
$78$	20.6570	2.33895
$79$	5.98764	0.673662	0.336831	−	0.941565i	$-0.390645\pi$
$79$	5.98764	0.673662	0.336831	+	0.941565i	$0.390645\pi$
$80$	−3.11301	−0.348045
$81$	−3.98761	−0.443068
$82$	14.6656	1.61954
$83$	−1.38215	−0.151711	−0.0758554	−	0.997119i	$-0.524169\pi$
$83$	−1.38215	−0.151711	−0.0758554	+	0.997119i	$0.524169\pi$
$84$	−7.35616	−0.802623
$85$	−7.87632	−0.854306
$86$	2.58119	0.278337
$87$	−1.34355	−0.144043
$88$	−8.54175	−0.910554
$89$	−6.69829	−0.710017	−0.355009	−	0.934863i	$-0.615522\pi$
$89$	−6.69829	−0.710017	−0.355009	+	0.934863i	$0.615522\pi$
$90$	−8.29420	−0.874285
$91$	10.4152	1.09181
$92$	30.7798	3.20902
$93$	7.14396	0.740794
$94$	−1.72226	−0.177637
$95$	8.49673	0.871746
$96$	−5.87228	−0.599337
$97$	−4.80332	−0.487704	−0.243852	−	0.969813i	$-0.578411\pi$
$97$	−4.80332	−0.487704	−0.243852	+	0.969813i	$0.578411\pi$
$98$	10.5022	1.06088
$99$	−2.99351	−0.300859
$100$	13.2353	1.32353
$101$	8.08075	0.804065	0.402032	−	0.915625i	$-0.368304\pi$
$101$	8.08075	0.804065	0.402032	+	0.915625i	$0.368304\pi$
$102$	8.32259	0.824059
$103$	0.261898	0.0258056	0.0129028	−	0.999917i	$-0.495893\pi$
$103$	0.261898	0.0258056	0.0129028	+	0.999917i	$0.495893\pi$
$104$	−22.4358	−2.20001
$105$	6.31764	0.616538
$106$	−15.2246	−1.47874
$107$	−6.98668	−0.675427	−0.337714	−	0.941249i	$-0.609654\pi$
$107$	−6.98668	−0.675427	−0.337714	+	0.941249i	$0.609654\pi$
$108$	19.4963	1.87603
$109$	3.15826	0.302506	0.151253	−	0.988495i	$-0.451669\pi$
$109$	3.15826	0.302506	0.151253	+	0.988495i	$0.451669\pi$
$110$	17.3902	1.65809
$111$	8.51205	0.807928
$112$	1.65850	0.156713
$113$	−5.83699	−0.549098	−0.274549	−	0.961573i	$-0.588528\pi$
$113$	−5.83699	−0.549098	−0.274549	+	0.961573i	$0.588528\pi$
$114$	−8.97815	−0.840881
$115$	−26.4344	−2.46502
$116$	3.45924	0.321182
$117$	−7.86274	−0.726911
$118$	5.54321	0.510294
$119$	4.19621	0.384666
$120$	−13.6091	−1.24233
$121$	−4.72360	−0.429418
$122$	22.9006	2.07333
$123$	8.43308	0.760386
$124$	−18.3936	−1.65179
$125$	3.48760	0.311940
$126$	4.41885	0.393662
$127$	−6.27603	−0.556907	−0.278454	−	0.960450i	$-0.589822\pi$
$127$	−6.27603	−0.556907	−0.278454	+	0.960450i	$0.589822\pi$
$128$	20.0160	1.76918
$129$	1.48425	0.130681
$130$	45.6771	4.00615
$131$	−2.95763	−0.258410	−0.129205	−	0.991618i	$-0.541242\pi$
$131$	−2.95763	−0.258410	−0.129205	+	0.991618i	$0.541242\pi$
$132$	−11.6436	−1.01345
$133$	−4.52675	−0.392519
$134$	−1.73956	−0.150275
$135$	−16.7439	−1.44108
$136$	−9.03922	−0.775107
$137$	6.41498	0.548069	0.274034	−	0.961720i	$-0.411642\pi$
$137$	6.41498	0.548069	0.274034	+	0.961720i	$0.411642\pi$
$138$	27.9322	2.37774
$139$	−9.87281	−0.837401	−0.418700	−	0.908124i	$-0.637514\pi$
$139$	−9.87281	−0.837401	−0.418700	+	0.908124i	$0.637514\pi$
$140$	−16.2661	−1.37473
$141$	−0.990340	−0.0834017
$142$	−13.9183	−1.16799
$143$	16.4856	1.37859
$144$	−1.25205	−0.104337
$145$	−2.97087	−0.246717
$146$	32.2748	2.67108
$147$	6.03902	0.498090
$148$	−21.9160	−1.80149
$149$	−14.9650	−1.22598	−0.612990	−	0.790090i	$-0.710034\pi$
$149$	−14.9650	−1.22598	−0.612990	+	0.790090i	$0.710034\pi$
$150$	12.0108	0.980677
$151$	0.339210	0.0276045	0.0138023	−	0.999905i	$-0.495606\pi$
$151$	0.339210	0.0276045	0.0138023	+	0.999905i	$0.495606\pi$
$152$	9.75123	0.790930
$153$	−3.16785	−0.256105
$154$	−9.26487	−0.746585
$155$	15.7968	1.26883
$156$	−30.5832	−2.44861
$157$	8.52609	0.680456	0.340228	−	0.940343i	$-0.389496\pi$
$157$	8.52609	0.680456	0.340228	+	0.940343i	$0.389496\pi$
$158$	−13.9901	−1.11299
$159$	−8.75452	−0.694279
$160$	−12.9849	−1.02654
$161$	14.0833	1.10992
$162$	9.31706	0.732018
$163$	3.13174	0.245297	0.122648	−	0.992450i	$-0.460861\pi$
$163$	3.13174	0.245297	0.122648	+	0.992450i	$0.460861\pi$
$164$	−21.7127	−1.69548
$165$	9.99981	0.778484
$166$	3.22940	0.250650
$167$	23.5434	1.82184	0.910922	−	0.412578i	$-0.135372\pi$
$167$	23.5434	1.82184	0.910922	+	0.412578i	$0.135372\pi$
$168$	7.25041	0.559382
$169$	30.3011	2.33085
$170$	18.4030	1.41145
$171$	3.41738	0.261333
$172$	−3.82150	−0.291387
$173$	−22.5096	−1.71137	−0.855685	−	0.517497i	$-0.826864\pi$
$173$	−22.5096	−1.71137	−0.855685	+	0.517497i	$0.826864\pi$
$174$	3.13920	0.237982
$175$	6.05579	0.457775
$176$	2.62514	0.197877
$177$	3.18748	0.239586
$178$	15.6506	1.17306
$179$	16.2274	1.21289	0.606447	−	0.795124i	$-0.292594\pi$
$179$	16.2274	1.21289	0.606447	+	0.795124i	$0.292594\pi$
$180$	12.2797	0.915277
$181$	−9.81290	−0.729387	−0.364694	−	0.931128i	$-0.618826\pi$
$181$	−9.81290	−0.729387	−0.364694	+	0.931128i	$0.618826\pi$
$182$	−24.3351	−1.80384
$183$	13.1684	0.973439
$184$	−30.3373	−2.23650
$185$	18.8220	1.38382
$186$	−16.6919	−1.22391
$187$	6.64194	0.485706
$188$	2.54983	0.185966
$189$	8.92053	0.648873
$190$	−19.8526	−1.44026
$191$	−14.1460	−1.02357	−0.511785	−	0.859113i	$-0.671016\pi$
$191$	−14.1460	−1.02357	−0.511785	+	0.859113i	$0.671016\pi$
$192$	16.5362	1.19340
$193$	3.29799	0.237395	0.118697	−	0.992930i	$-0.462128\pi$
$193$	3.29799	0.237395	0.118697	+	0.992930i	$0.462128\pi$
$194$	11.2230	0.805762
$195$	26.2655	1.88091
$196$	−15.5487	−1.11062
$197$	3.55657	0.253395	0.126698	−	0.991941i	$-0.459562\pi$
$197$	3.55657	0.253395	0.126698	+	0.991941i	$0.459562\pi$
$198$	6.99433	0.497065
$199$	−0.310471	−0.0220087	−0.0110044	−	0.999939i	$-0.503503\pi$
$199$	−0.310471	−0.0220087	−0.0110044	+	0.999939i	$0.503503\pi$
$200$	−13.0450	−0.922422
$201$	−1.00029	−0.0705550
$202$	−18.8807	−1.32844
$203$	1.58277	0.111089
$204$	−12.3218	−0.862695
$205$	18.6474	1.30239
$206$	−0.611926	−0.0426349
$207$	−10.6319	−0.738967
$208$	6.89518	0.478095
$209$	−7.16512	−0.495621
$210$	−14.7612	−1.01862
$211$	−10.0567	−0.692329	−0.346165	−	0.938174i	$-0.612516\pi$
$211$	−10.0567	−0.692329	−0.346165	+	0.938174i	$0.612516\pi$
$212$	22.5403	1.54807
$213$	−8.00335	−0.548380
$214$	16.3244	1.11591
$215$	3.28199	0.223830
$216$	−19.2161	−1.30749
$217$	−8.41597	−0.571313
$218$	−7.37927	−0.499787
$219$	18.5588	1.25409
$220$	−25.7466	−1.73583
$221$	17.4457	1.17353
$222$	−19.8884	−1.33482
$223$	−8.38992	−0.561831	−0.280915	−	0.959733i	$-0.590638\pi$
$223$	−8.38992	−0.561831	−0.280915	+	0.959733i	$0.590638\pi$
$224$	6.91786	0.462219
$225$	−4.57170	−0.304780
$226$	13.6381	0.907195
$227$	−2.09864	−0.139291	−0.0696457	−	0.997572i	$-0.522187\pi$
$227$	−2.09864	−0.139291	−0.0696457	+	0.997572i	$0.522187\pi$
$228$	13.2923	0.880306
$229$	23.3032	1.53992	0.769959	−	0.638094i	$-0.220277\pi$
$229$	23.3032	1.53992	0.769959	+	0.638094i	$0.220277\pi$
$230$	61.7640	4.07260
$231$	−5.32754	−0.350526
$232$	−3.40951	−0.223845
$233$	14.5256	0.951602	0.475801	−	0.879553i	$-0.342158\pi$
$233$	14.5256	0.951602	0.475801	+	0.879553i	$0.342158\pi$
$234$	18.3713	1.20097
$235$	−2.18985	−0.142850
$236$	−8.20683	−0.534219
$237$	−8.04467	−0.522558
$238$	−9.80446	−0.635529
$239$	3.47791	0.224967	0.112484	−	0.993654i	$-0.464119\pi$
$239$	3.47791	0.224967	0.112484	+	0.993654i	$0.464119\pi$
$240$	4.18247	0.269978
$241$	−6.57478	−0.423519	−0.211759	−	0.977322i	$-0.567919\pi$
$241$	−6.57478	−0.423519	−0.211759	+	0.977322i	$0.567919\pi$
$242$	11.0367	0.709466
$243$	−11.5505	−0.740966
$244$	−33.9048	−2.17054
$245$	13.3536	0.853128
$246$	−19.7039	−1.25628
$247$	−18.8199	−1.19748
$248$	18.1292	1.15120
$249$	1.85699	0.117682
$250$	−8.14877	−0.515373
$251$	−26.4988	−1.67259	−0.836295	−	0.548280i	$-0.815283\pi$
$251$	−26.4988	−1.67259	−0.836295	+	0.548280i	$0.815283\pi$
$252$	−6.54219	−0.412119
$253$	22.2916	1.40146
$254$	14.6639	0.920098
$255$	10.5822	0.662683
$256$	−22.1515	−1.38447
$257$	5.23119	0.326313	0.163156	−	0.986600i	$-0.447833\pi$
$257$	5.23119	0.326313	0.163156	+	0.986600i	$0.447833\pi$
$258$	−3.46795	−0.215905
$259$	−10.0277	−0.623088
$260$	−67.6259	−4.19398
$261$	−1.19488	−0.0739613
$262$	6.91051	0.426933
$263$	−1.17082	−0.0721957	−0.0360979	−	0.999348i	$-0.511493\pi$
$263$	−1.17082	−0.0721957	−0.0360979	+	0.999348i	$0.511493\pi$
$264$	11.4762	0.706314
$265$	−19.3581	−1.18916
$266$	10.5767	0.648502
$267$	8.99946	0.550758
$268$	2.57545	0.157321
$269$	−4.60716	−0.280904	−0.140452	−	0.990088i	$-0.544856\pi$
$269$	−4.60716	−0.280904	−0.140452	+	0.990088i	$0.544856\pi$
$270$	39.1221	2.38090
$271$	27.6139	1.67743	0.838713	−	0.544574i	$-0.183309\pi$
$271$	27.6139	1.67743	0.838713	+	0.544574i	$0.183309\pi$
$272$	2.77802	0.168442
$273$	−13.9933	−0.846914
$274$	−14.9886	−0.905495
$275$	9.58535	0.578019
$276$	−41.3541	−2.48923
$277$	1.00000	0.0600842
$277$	1.00000	0.0600842
$278$	23.0678	1.38352
$279$	6.35347	0.380372
$280$	16.0322	0.958108
$281$	−12.0020	−0.715982	−0.357991	−	0.933725i	$-0.616538\pi$
$281$	−12.0020	−0.715982	−0.357991	+	0.933725i	$0.616538\pi$
$282$	2.31393	0.137793
$283$	−25.1427	−1.49458	−0.747290	−	0.664498i	$-0.768645\pi$
$283$	−25.1427	−1.49458	−0.747290	+	0.664498i	$0.768645\pi$
$284$	20.6063	1.22276
$285$	−11.4158	−0.676211
$286$	−38.5186	−2.27765
$287$	−9.93463	−0.586423
$288$	−5.22250	−0.307739
$289$	−9.97124	−0.586543
$290$	6.94144	0.407615
$291$	6.45349	0.378310
$292$	−47.7835	−2.79632
$293$	−19.9512	−1.16556	−0.582780	−	0.812630i	$-0.698035\pi$
$293$	−19.9512	−1.16556	−0.582780	+	0.812630i	$0.698035\pi$
$294$	−14.1102	−0.822922
$295$	7.04821	0.410363
$296$	21.6010	1.25553
$297$	14.1198	0.819313
$298$	34.9657	2.02551
$299$	58.5511	3.38610
$300$	−17.7822	−1.02666
$301$	−1.74853	−0.100783
$302$	−0.792564	−0.0456069
$303$	−10.8569	−0.623711
$304$	−2.99685	−0.171881
$305$	29.1182	1.66731
$306$	7.40168	0.423126
$307$	−7.11026	−0.405804	−0.202902	−	0.979199i	$-0.565037\pi$
$307$	−7.11026	−0.405804	−0.202902	+	0.979199i	$0.565037\pi$
$308$	13.7168	0.781589
$309$	−0.351873	−0.0200173
$310$	−36.9093	−2.09631
$311$	−0.147058	−0.00833887	−0.00416944	−	0.999991i	$-0.501327\pi$
$311$	−0.147058	−0.00833887	−0.00416944	+	0.999991i	$0.501327\pi$
$312$	30.1435	1.70654
$313$	3.73689	0.211222	0.105611	−	0.994408i	$-0.466320\pi$
$313$	3.73689	0.211222	0.105611	+	0.994408i	$0.466320\pi$
$314$	−19.9212	−1.12422
$315$	5.61858	0.316571
$316$	20.7127	1.16518
$317$	18.2867	1.02708	0.513541	−	0.858065i	$-0.328333\pi$
$317$	18.2867	1.02708	0.513541	+	0.858065i	$0.328333\pi$
$318$	20.4550	1.14706
$319$	2.50527	0.140268
$320$	36.5652	2.04405
$321$	9.38693	0.523927
$322$	−32.9056	−1.83376
$323$	−7.58241	−0.421897
$324$	−13.7941	−0.766339
$325$	25.1769	1.39656
$326$	−7.31731	−0.405268
$327$	−4.24327	−0.234653
$328$	21.4006	1.18165
$329$	1.16668	0.0643209
$330$	−23.3646	−1.28618
$331$	−10.7465	−0.590679	−0.295340	−	0.955392i	$-0.595433\pi$
$331$	−10.7465	−0.590679	−0.295340	+	0.955392i	$0.595433\pi$
$332$	−4.78119	−0.262402
$333$	7.57018	0.414843
$334$	−55.0092	−3.00997
$335$	−2.21185	−0.120846
$336$	−2.22827	−0.121562
$337$	−5.75801	−0.313659	−0.156829	−	0.987626i	$-0.550127\pi$
$337$	−5.75801	−0.313659	−0.156829	+	0.987626i	$0.550127\pi$
$338$	−70.7985	−3.85093
$339$	7.84227	0.425933
$340$	−27.2460	−1.47762
$341$	−13.3211	−0.721380
$342$	−7.98470	−0.431763
$343$	−18.1937	−0.982367
$344$	3.76657	0.203080
$345$	35.5158	1.91211
$346$	52.5936	2.82745
$347$	−3.98495	−0.213923	−0.106962	−	0.994263i	$-0.534112\pi$
$347$	−3.98495	−0.213923	−0.106962	+	0.994263i	$0.534112\pi$
$348$	−4.64765	−0.249140
$349$	4.87575	0.260993	0.130497	−	0.991449i	$-0.458343\pi$
$349$	4.87575	0.260993	0.130497	+	0.991449i	$0.458343\pi$
$350$	−14.1494	−0.756316
$351$	37.0870	1.97956
$352$	10.9499	0.583630
$353$	−7.14356	−0.380213	−0.190107	−	0.981763i	$-0.560883\pi$
$353$	−7.14356	−0.380213	−0.190107	+	0.981763i	$0.560883\pi$
$354$	−7.44756	−0.395833
$355$	−17.6971	−0.939265
$356$	−23.1710	−1.22806
$357$	−5.63781	−0.298385
$358$	−37.9154	−2.00389
$359$	−5.11877	−0.270158	−0.135079	−	0.990835i	$-0.543129\pi$
$359$	−5.11877	−0.270158	−0.135079	+	0.990835i	$0.543129\pi$
$360$	−12.1032	−0.637894
$361$	−10.8203	−0.569491
$362$	22.9278	1.20506
$363$	6.34638	0.333099
$364$	36.0286	1.88841
$365$	41.0375	2.14800
$366$	−30.7681	−1.60827
$367$	36.7594	1.91883	0.959413	−	0.282004i	$-0.0909992\pi$
$367$	36.7594	1.91883	0.959413	+	0.282004i	$0.0909992\pi$
$368$	9.32357	0.486025
$369$	7.49995	0.390432
$370$	−43.9775	−2.28628
$371$	10.3133	0.535440
$372$	24.7126	1.28129
$373$	−29.6428	−1.53485	−0.767424	−	0.641140i	$-0.778462\pi$
$373$	−29.6428	−1.53485	−0.767424	+	0.641140i	$0.778462\pi$
$374$	−15.5189	−0.802463
$375$	−4.68575	−0.241971
$376$	−2.51318	−0.129607
$377$	6.58035	0.338905
$378$	−20.8428	−1.07204
$379$	36.5267	1.87625	0.938126	−	0.346293i	$-0.112560\pi$
$379$	36.5267	1.87625	0.938126	+	0.346293i	$0.112560\pi$
$380$	29.3922	1.50779
$381$	8.43214	0.431992
$382$	33.0522	1.69110
$383$	−11.5070	−0.587979	−0.293989	−	0.955809i	$-0.594983\pi$
$383$	−11.5070	−0.587979	−0.293989	+	0.955809i	$0.594983\pi$
$384$	−26.8924	−1.37235
$385$	−11.7803	−0.600381
$386$	−7.70576	−0.392213
$387$	1.32001	0.0671001
$388$	−16.6158	−0.843541
$389$	−22.4427	−1.13789	−0.568945	−	0.822375i	$-0.692648\pi$
$389$	−22.4427	−1.13789	−0.568945	+	0.822375i	$0.692648\pi$
$390$	−61.3694	−3.10756
$391$	23.5898	1.19299
$392$	15.3252	0.774038
$393$	3.97372	0.200448
$394$	−8.30993	−0.418648
$395$	−17.7885	−0.895036
$396$	−10.3552	−0.520371
$397$	23.6060	1.18475	0.592375	−	0.805662i	$-0.298190\pi$
$397$	23.6060	1.18475	0.592375	+	0.805662i	$0.298190\pi$
$398$	0.725417	0.0363619
$399$	6.08190	0.304476
$400$	4.00912	0.200456
$401$	9.08015	0.453441	0.226721	−	0.973960i	$-0.427200\pi$
$401$	9.08015	0.453441	0.226721	+	0.973960i	$0.427200\pi$
$402$	2.33718	0.116568
$403$	−34.9893	−1.74294
$404$	27.9532	1.39072
$405$	11.8467	0.588667
$406$	−3.69815	−0.183536
$407$	−15.8722	−0.786755
$408$	12.1446	0.601248
$409$	8.68995	0.429690	0.214845	−	0.976648i	$-0.431075\pi$
$409$	8.68995	0.429690	0.214845	+	0.976648i	$0.431075\pi$
$410$	−43.5696	−2.15175
$411$	−8.61883	−0.425135
$412$	0.905968	0.0446339
$413$	−3.75503	−0.184773
$414$	24.8414	1.22089
$415$	4.10619	0.201565
$416$	28.7609	1.41012
$417$	13.2646	0.649570
$418$	16.7413	0.818844
$419$	8.33286	0.407087	0.203543	−	0.979066i	$-0.434754\pi$
$419$	8.33286	0.407087	0.203543	+	0.979066i	$0.434754\pi$
$420$	21.8542	1.06638
$421$	29.3682	1.43132	0.715660	−	0.698449i	$-0.246126\pi$
$421$	29.3682	1.43132	0.715660	+	0.698449i	$0.246126\pi$
$422$	23.4974	1.14384
$423$	−0.880758	−0.0428239
$424$	−22.2163	−1.07892
$425$	10.1436	0.492037
$426$	18.6998	0.906010
$427$	−15.5131	−0.750734
$428$	−24.1686	−1.16823
$429$	−22.1492	−1.06937
$430$	−7.66838	−0.369802
$431$	28.9041	1.39226	0.696130	−	0.717915i	$-0.254904\pi$
$431$	28.9041	1.39226	0.696130	+	0.717915i	$0.254904\pi$
$432$	5.90567	0.284137
$433$	−1.73721	−0.0834850	−0.0417425	−	0.999128i	$-0.513291\pi$
$433$	−1.73721	−0.0834850	−0.0417425	+	0.999128i	$0.513291\pi$
$434$	19.6639	0.943899
$435$	3.99150	0.191378
$436$	10.9252	0.523220
$437$	−25.4480	−1.21734
$438$	−43.3627	−2.07195
$439$	−25.8598	−1.23422	−0.617110	−	0.786877i	$-0.711697\pi$
$439$	−25.8598	−1.23422	−0.617110	+	0.786877i	$0.711697\pi$
$440$	25.3764	1.20977
$441$	5.37079	0.255752
$442$	−40.7619	−1.93885
$443$	18.7413	0.890425	0.445213	−	0.895425i	$-0.353128\pi$
$443$	18.7413	0.890425	0.445213	+	0.895425i	$0.353128\pi$
$444$	29.4452	1.39741
$445$	19.8997	0.943338
$446$	19.6031	0.928232
$447$	20.1062	0.950990
$448$	−19.4806	−0.920371
$449$	−8.48236	−0.400307	−0.200154	−	0.979765i	$-0.564144\pi$
$449$	−8.48236	−0.400307	−0.200154	+	0.979765i	$0.564144\pi$
$450$	10.6818	0.503544
$451$	−15.7249	−0.740458
$452$	−20.1915	−0.949729
$453$	−0.455744	−0.0214127
$454$	4.90346	0.230131
$455$	−30.9422	−1.45059
$456$	−13.1012	−0.613522
$457$	−23.6399	−1.10583	−0.552915	−	0.833238i	$-0.686485\pi$
$457$	−23.6399	−1.10583	−0.552915	+	0.833238i	$0.686485\pi$
$458$	−54.4479	−2.54418
$459$	14.9421	0.697438
$460$	−91.4428	−4.26354
$461$	13.6234	0.634507	0.317253	−	0.948341i	$-0.397239\pi$
$461$	13.6234	0.634507	0.317253	+	0.948341i	$0.397239\pi$
$462$	12.4478	0.579124
$463$	5.23848	0.243453	0.121726	−	0.992564i	$-0.461157\pi$
$463$	5.23848	0.243453	0.121726	+	0.992564i	$0.461157\pi$
$464$	1.04784	0.0486449
$465$	−21.2238	−0.984229
$466$	−33.9390	−1.57219
$467$	15.1233	0.699824	0.349912	−	0.936783i	$-0.386212\pi$
$467$	15.1233	0.699824	0.349912	+	0.936783i	$0.386212\pi$
$468$	−27.1991	−1.25728
$469$	1.17840	0.0544132
$470$	5.11660	0.236011
$471$	−11.4552	−0.527828
$472$	8.08885	0.372320
$473$	−2.76764	−0.127256
$474$	18.7964	0.863347
$475$	−10.9426	−0.502081
$476$	14.5157	0.665326
$477$	−7.78582	−0.356488
$478$	−8.12614	−0.371681
$479$	−36.8145	−1.68210	−0.841048	−	0.540961i	$-0.818061\pi$
$479$	−36.8145	−1.68210	−0.841048	+	0.540961i	$0.818061\pi$
$480$	17.4458	0.796287
$481$	−41.6899	−1.90089
$482$	15.3620	0.699719
$483$	−18.9216	−0.860961
$484$	−16.3401	−0.742730
$485$	14.2700	0.647970
$486$	26.9878	1.22419
$487$	36.3206	1.64584	0.822922	−	0.568154i	$-0.192342\pi$
$487$	36.3206	1.64584	0.822922	+	0.568154i	$0.192342\pi$
$488$	33.4174	1.51274
$489$	−4.20764	−0.190276
$490$	−31.2006	−1.40950
$491$	8.74066	0.394460	0.197230	−	0.980357i	$-0.436805\pi$
$491$	8.74066	0.394460	0.197230	+	0.980357i	$0.436805\pi$
$492$	29.1720	1.31518
$493$	2.65118	0.119403
$494$	43.9727	1.97843
$495$	8.89332	0.399725
$496$	−5.57164	−0.250174
$497$	9.42838	0.422921
$498$	−4.33885	−0.194428
$499$	−10.6687	−0.477599	−0.238799	−	0.971069i	$-0.576754\pi$
$499$	−10.6687	−0.477599	−0.238799	+	0.971069i	$0.576754\pi$
$500$	12.0644	0.539537
$501$	−31.6317	−1.41320
$502$	61.9145	2.76338
$503$	18.1257	0.808183	0.404091	−	0.914719i	$-0.367588\pi$
$503$	18.1257	0.808183	0.404091	+	0.914719i	$0.367588\pi$
$504$	6.44814	0.287223
$505$	−24.0069	−1.06829
$506$	−52.0843	−2.31543
$507$	−40.7109	−1.80803
$508$	−21.7103	−0.963237
$509$	6.92608	0.306993	0.153497	−	0.988149i	$-0.450947\pi$
$509$	6.92608	0.306993	0.153497	+	0.988149i	$0.450947\pi$
$510$	−24.7253	−1.09486
$511$	−21.8633	−0.967176
$512$	11.7251	0.518181
$513$	−16.1191	−0.711675
$514$	−12.2227	−0.539119
$515$	−0.778066	−0.0342857
$516$	5.13437	0.226028
$517$	1.84666	0.0812160
$518$	23.4296	1.02944
$519$	30.2426	1.32750
$520$	66.6537	2.92296
$521$	−4.38017	−0.191899	−0.0959493	−	0.995386i	$-0.530589\pi$
$521$	−4.38017	−0.191899	−0.0959493	+	0.995386i	$0.530589\pi$
$522$	2.79184	0.122196
$523$	−28.8666	−1.26225	−0.631124	−	0.775682i	$-0.717406\pi$
$523$	−28.8666	−1.26225	−0.631124	+	0.775682i	$0.717406\pi$
$524$	−10.2312	−0.446950
$525$	−8.13624	−0.355095
$526$	2.73562	0.119279
$527$	−14.0970	−0.614073
$528$	−3.52699	−0.153493
$529$	56.1719	2.44226
$530$	45.2303	1.96468
$531$	2.83478	0.123019
$532$	−15.6591	−0.678908
$533$	−41.3031	−1.78904
$534$	−21.0273	−0.909938
$535$	20.7565	0.897382
$536$	−2.53843	−0.109643
$537$	−21.8023	−0.940839
$538$	10.7646	0.464097
$539$	−11.2608	−0.485037
$540$	−57.9211	−2.49253
$541$	3.83211	0.164755	0.0823777	−	0.996601i	$-0.473749\pi$
$541$	3.83211	0.164755	0.0823777	+	0.996601i	$0.473749\pi$
$542$	−64.5199	−2.77137
$543$	13.1841	0.565784
$544$	11.5876	0.496814
$545$	−9.38277	−0.401914
$546$	32.6954	1.39923
$547$	25.7986	1.10307	0.551534	−	0.834152i	$-0.314043\pi$
$547$	25.7986	1.10307	0.551534	+	0.834152i	$0.314043\pi$
$548$	22.1909	0.947949
$549$	11.7113	0.499827
$550$	−22.3962	−0.954977
$551$	−2.86001	−0.121841
$552$	40.7596	1.73484
$553$	9.47706	0.403006
$554$	−2.33650	−0.0992684
$555$	−25.2882	−1.07342
$556$	−34.1524	−1.44838
$557$	46.3089	1.96217	0.981086	−	0.193572i	$-0.0620072\pi$
$557$	46.3089	1.96217	0.981086	+	0.193572i	$0.0620072\pi$
$558$	−14.8449	−0.628434
$559$	−7.26948	−0.307466
$560$	−4.92718	−0.208211
$561$	−8.92375	−0.376761
$562$	28.0428	1.18291
$563$	−36.1235	−1.52242	−0.761212	−	0.648503i	$-0.775395\pi$
$563$	−36.1235	−1.52242	−0.761212	+	0.648503i	$0.775395\pi$
$564$	−3.42582	−0.144253
$565$	17.3409	0.729538
$566$	58.7460	2.46928
$567$	−6.31148	−0.265057
$568$	−20.3100	−0.852190
$569$	−42.9553	−1.80078	−0.900390	−	0.435083i	$-0.856719\pi$
$569$	−42.9553	−1.80078	−0.900390	+	0.435083i	$0.856719\pi$
$570$	26.6729	1.11721
$571$	−25.1774	−1.05364	−0.526820	−	0.849977i	$-0.676616\pi$
$571$	−25.1774	−1.05364	−0.526820	+	0.849977i	$0.676616\pi$
$572$	57.0276	2.38444
$573$	19.0059	0.793981
$574$	23.2123	0.968862
$575$	34.0438	1.41973
$576$	14.7065	0.612770
$577$	−36.3437	−1.51301	−0.756504	−	0.653989i	$-0.773094\pi$
$577$	−36.3437	−1.51301	−0.756504	+	0.653989i	$0.773094\pi$
$578$	23.2978	0.969061
$579$	−4.43101	−0.184146
$580$	−10.2769	−0.426727
$581$	−2.18763	−0.0907582
$582$	−15.0786	−0.625028
$583$	16.3243	0.676084
$584$	47.0966	1.94887
$585$	23.3592	0.965783
$586$	46.6159	1.92569
$587$	9.37902	0.387114	0.193557	−	0.981089i	$-0.437998\pi$
$587$	9.37902	0.387114	0.193557	+	0.981089i	$0.437998\pi$
$588$	20.8904	0.861506
$589$	15.2074	0.626609
$590$	−16.4682	−0.677983
$591$	−4.77842	−0.196558
$592$	−6.63862	−0.272846
$593$	−12.9337	−0.531124	−0.265562	−	0.964094i	$-0.585557\pi$
$593$	−12.9337	−0.531124	−0.265562	+	0.964094i	$0.585557\pi$
$594$	−32.9909	−1.35363
$595$	−12.4664	−0.511073
$596$	−51.7675	−2.12048
$597$	0.417133	0.0170721
$598$	−136.805	−5.59436
$599$	42.1151	1.72078	0.860388	−	0.509639i	$-0.170221\pi$
$599$	42.1151	1.72078	0.860388	+	0.509639i	$0.170221\pi$
$600$	17.5266	0.715520
$601$	−47.5093	−1.93795	−0.968973	−	0.247168i	$-0.920500\pi$
$601$	−47.5093	−1.93795	−0.968973	+	0.247168i	$0.920500\pi$
$602$	4.08543	0.166510
$603$	−0.889606	−0.0362275
$604$	1.17341	0.0477453
$605$	14.0332	0.570531
$606$	25.3671	1.03047
$607$	−30.9844	−1.25762	−0.628809	−	0.777560i	$-0.716457\pi$
$607$	−30.9844	−1.25762	−0.628809	+	0.777560i	$0.716457\pi$
$608$	−12.5003	−0.506955
$609$	−2.12653	−0.0861713
$610$	−68.0348	−2.75465
$611$	4.85044	0.196228
$612$	−10.9583	−0.442964
$613$	3.13698	0.126701	0.0633507	−	0.997991i	$-0.479821\pi$
$613$	3.13698	0.126701	0.0633507	+	0.997991i	$0.479821\pi$
$614$	16.6131	0.670451
$615$	−25.0536	−1.01026
$616$	−13.5196	−0.544722
$617$	−44.9728	−1.81054	−0.905269	−	0.424839i	$-0.860331\pi$
$617$	−44.9728	−1.81054	−0.905269	+	0.424839i	$0.860331\pi$
$618$	0.822151	0.0330718
$619$	8.49112	0.341287	0.170644	−	0.985333i	$-0.445415\pi$
$619$	8.49112	0.341287	0.170644	+	0.985333i	$0.445415\pi$
$620$	54.6449	2.19459
$621$	50.1485	2.01239
$622$	0.343600	0.0137771
$623$	−10.6019	−0.424755
$624$	−9.26401	−0.370857
$625$	−29.4915	−1.17966
$626$	−8.73126	−0.348971
$627$	9.62667	0.384452
$628$	29.4938	1.17693
$629$	−16.7966	−0.669723
$630$	−13.1278	−0.523025
$631$	8.56088	0.340803	0.170402	−	0.985375i	$-0.445493\pi$
$631$	8.56088	0.340803	0.170402	+	0.985375i	$0.445493\pi$
$632$	−20.4149	−0.812061
$633$	13.5116	0.537038
$634$	−42.7269	−1.69690
$635$	18.6453	0.739915
$636$	−30.2840	−1.20084
$637$	−29.5776	−1.17191
$638$	−5.85358	−0.231745
$639$	−7.11776	−0.281574
$640$	−59.4648	−2.35055
$641$	−21.5390	−0.850738	−0.425369	−	0.905020i	$-0.639856\pi$
$641$	−21.5390	−0.850738	−0.425369	+	0.905020i	$0.639856\pi$
$642$	−21.9326	−0.865609
$643$	7.22872	0.285073	0.142537	−	0.989790i	$-0.454474\pi$
$643$	7.22872	0.285073	0.142537	+	0.989790i	$0.454474\pi$
$644$	48.7174	1.91973
$645$	−4.40951	−0.173624
$646$	17.7163	0.697039
$647$	19.9136	0.782883	0.391442	−	0.920203i	$-0.371977\pi$
$647$	19.9136	0.782883	0.391442	+	0.920203i	$0.371977\pi$
$648$	13.5958	0.534094
$649$	−5.94361	−0.233307
$650$	−58.8258	−2.30734
$651$	11.3073	0.443166
$652$	10.8334	0.424270
$653$	−29.9773	−1.17310	−0.586551	−	0.809912i	$-0.699515\pi$
$653$	−29.9773	−1.17310	−0.586551	+	0.809912i	$0.699515\pi$
$654$	9.91440	0.387684
$655$	8.78675	0.343327
$656$	−6.57704	−0.256790
$657$	16.5053	0.643932
$658$	−2.72594	−0.106268
$659$	−27.7874	−1.08244	−0.541222	−	0.840880i	$-0.682038\pi$
$659$	−27.7874	−1.08244	−0.541222	+	0.840880i	$0.682038\pi$
$660$	34.5917	1.34648
$661$	33.7400	1.31233	0.656167	−	0.754615i	$-0.272177\pi$
$661$	33.7400	1.31233	0.656167	+	0.754615i	$0.272177\pi$
$662$	25.1091	0.975894
$663$	−23.4391	−0.910301
$664$	4.71245	0.182879
$665$	13.4484	0.521506
$666$	−17.6877	−0.685386
$667$	8.89786	0.344527
$668$	81.4422	3.15109
$669$	11.2723	0.435811
$670$	5.16800	0.199657
$671$	−24.5548	−0.947928
$672$	−9.29447	−0.358542
$673$	7.45694	0.287444	0.143722	−	0.989618i	$-0.454093\pi$
$673$	7.45694	0.287444	0.143722	+	0.989618i	$0.454093\pi$
$674$	13.4536	0.518213
$675$	21.5638	0.829991
$676$	104.819	4.03148
$677$	25.2752	0.971406	0.485703	−	0.874124i	$-0.338564\pi$
$677$	25.2752	0.971406	0.485703	+	0.874124i	$0.338564\pi$
$678$	−18.3235	−0.703708
$679$	−7.60256	−0.291760
$680$	26.8544	1.02982
$681$	2.81962	0.108048
$682$	31.1248	1.19183
$683$	24.0299	0.919477	0.459738	−	0.888054i	$-0.347943\pi$
$683$	24.0299	0.919477	0.459738	+	0.888054i	$0.347943\pi$
$684$	11.8215	0.452007
$685$	−19.0581	−0.728171
$686$	42.5096	1.62302
$687$	−31.3089	−1.19451
$688$	−1.15758	−0.0441323
$689$	42.8774	1.63350
$690$	−82.9828	−3.15910
$691$	3.64369	0.138612	0.0693062	−	0.997595i	$-0.477921\pi$
$691$	3.64369	0.138612	0.0693062	+	0.997595i	$0.477921\pi$
$692$	−77.8659	−2.96002
$693$	−4.73804	−0.179983
$694$	9.31084	0.353435
$695$	29.3308	1.11258
$696$	4.58083	0.173636
$697$	−16.6408	−0.630314
$698$	−11.3922	−0.431201
$699$	−19.5158	−0.738155
$700$	20.9484	0.791776
$701$	8.96201	0.338490	0.169245	−	0.985574i	$-0.445867\pi$
$701$	8.96201	0.338490	0.169245	+	0.985574i	$0.445867\pi$
$702$	−86.6538	−3.27054
$703$	18.1196	0.683395
$704$	−30.8346	−1.16212
$705$	2.94217	0.110809
$706$	16.6909	0.628172
$707$	12.7900	0.481017
$708$	11.0263	0.414392
$709$	−32.3658	−1.21552	−0.607762	−	0.794119i	$-0.707933\pi$
$709$	−32.3658	−1.21552	−0.607762	+	0.794119i	$0.707933\pi$
$710$	41.3493	1.55181
$711$	−7.15452	−0.268315
$712$	22.8379	0.855885
$713$	−47.3120	−1.77185
$714$	13.1728	0.492978
$715$	−48.9765	−1.83162
$716$	56.1345	2.09784
$717$	−4.67273	−0.174506
$718$	11.9600	0.446344
$719$	10.4245	0.388770	0.194385	−	0.980925i	$-0.437729\pi$
$719$	10.4245	0.388770	0.194385	+	0.980925i	$0.437729\pi$
$720$	3.71968	0.138624
$721$	0.414525	0.0154377
$722$	25.2817	0.940888
$723$	8.83353	0.328523
$724$	−33.9451	−1.26156
$725$	3.82607	0.142097
$726$	−14.8283	−0.550331
$727$	−4.91239	−0.182190	−0.0910952	−	0.995842i	$-0.529037\pi$
$727$	−4.91239	−0.182190	−0.0910952	+	0.995842i	$0.529037\pi$
$728$	−35.5107	−1.31611
$729$	27.4815	1.01783
$730$	−95.8843	−3.54884
$731$	−2.92882	−0.108326
$732$	45.5528	1.68368
$733$	−35.3520	−1.30575	−0.652877	−	0.757464i	$-0.726438\pi$
$733$	−35.3520	−1.30575	−0.652877	+	0.757464i	$0.726438\pi$
$734$	−85.8884	−3.17020
$735$	−17.9411	−0.661769
$736$	38.8901	1.43351
$737$	1.86521	0.0687059
$738$	−17.5236	−0.645054
$739$	−8.00175	−0.294349	−0.147175	−	0.989111i	$-0.547018\pi$
$739$	−8.00175	−0.294349	−0.147175	+	0.989111i	$0.547018\pi$
$740$	65.1096	2.39348
$741$	25.2854	0.928883
$742$	−24.0971	−0.884631
$743$	34.9538	1.28233	0.641165	−	0.767403i	$-0.278451\pi$
$743$	34.9538	1.28233	0.641165	+	0.767403i	$0.278451\pi$
$744$	−24.3574	−0.892985
$745$	44.4591	1.62885
$746$	69.2605	2.53581
$747$	1.65151	0.0604255
$748$	22.9760	0.840087
$749$	−11.0583	−0.404062
$750$	10.9483	0.399774
$751$	26.1636	0.954723	0.477361	−	0.878707i	$-0.341593\pi$
$751$	26.1636	0.954723	0.477361	+	0.878707i	$0.341593\pi$
$752$	0.772375	0.0281656
$753$	35.6024	1.29742
$754$	−15.3750	−0.559925
$755$	−1.00775	−0.0366757
$756$	30.8582	1.12230
$757$	−24.9302	−0.906104	−0.453052	−	0.891484i	$-0.649665\pi$
$757$	−24.9302	−0.906104	−0.453052	+	0.891484i	$0.649665\pi$
$758$	−85.3448	−3.09986
$759$	−29.9498	−1.08711
$760$	−28.9697	−1.05084
$761$	19.8547	0.719733	0.359867	−	0.933004i	$-0.382822\pi$
$761$	19.8547	0.719733	0.359867	+	0.933004i	$0.382822\pi$
$762$	−19.7017	−0.713717
$763$	4.99880	0.180969
$764$	−48.9345	−1.77039
$765$	9.41126	0.340265
$766$	26.8860	0.971432
$767$	−15.6115	−0.563698
$768$	29.7616	1.07393
$769$	−16.2372	−0.585527	−0.292764	−	0.956185i	$-0.594575\pi$
$769$	−16.2372	−0.585527	−0.292764	+	0.956185i	$0.594575\pi$
$770$	27.5247	0.991923
$771$	−7.02835	−0.253120
$772$	11.4085	0.410602
$773$	−43.5182	−1.56524	−0.782620	−	0.622499i	$-0.786117\pi$
$773$	−43.5182	−1.56524	−0.782620	+	0.622499i	$0.786117\pi$
$774$	−3.08421	−0.110860
$775$	−20.3441	−0.730782
$776$	16.3770	0.587899
$777$	13.4726	0.483328
$778$	52.4374	1.87997
$779$	17.9515	0.643180
$780$	90.8586	3.25326
$781$	14.9236	0.534009
$782$	−55.1177	−1.97100
$783$	5.63602	0.201415
$784$	−4.70989	−0.168210
$785$	−25.3299	−0.904064
$786$	−9.28460	−0.331171
$787$	9.53164	0.339766	0.169883	−	0.985464i	$-0.445661\pi$
$787$	9.53164	0.339766	0.169883	+	0.985464i	$0.445661\pi$
$788$	12.3030	0.438277
$789$	1.57305	0.0560020
$790$	41.5628	1.47874
$791$	−9.23862	−0.328487
$792$	10.2064	0.362668
$793$	−64.4957	−2.29031
$794$	−55.1554	−1.95739
$795$	26.0086	0.922428
$796$	−1.07399	−0.0380667
$797$	−37.1828	−1.31708	−0.658541	−	0.752544i	$-0.728826\pi$
$797$	−37.1828	−1.31708	−0.658541	+	0.752544i	$0.728826\pi$
$798$	−14.2104	−0.503041
$799$	1.95421	0.0691350
$800$	16.7227	0.591237
$801$	8.00366	0.282795
$802$	−21.2158	−0.749155
$803$	−34.6061	−1.22122
$804$	−3.46024	−0.122033
$805$	−41.8396	−1.47465
$806$	81.7525	2.87961
$807$	6.18994	0.217896
$808$	−27.5514	−0.969254
$809$	−5.28853	−0.185935	−0.0929674	−	0.995669i	$-0.529635\pi$
$809$	−5.28853	−0.185935	−0.0929674	+	0.995669i	$0.529635\pi$
$810$	−27.6798	−0.972569
$811$	36.9798	1.29854	0.649268	−	0.760559i	$-0.275075\pi$
$811$	36.9798	1.29854	0.649268	+	0.760559i	$0.275075\pi$
$812$	5.47518	0.192141
$813$	−37.1006	−1.30117
$814$	37.0854	1.29984
$815$	−9.30399	−0.325905
$816$	−3.73241	−0.130660
$817$	3.15953	0.110538
$818$	−20.3041	−0.709915
$819$	−12.4449	−0.434861
$820$	64.5056	2.25263
$821$	−55.3439	−1.93151	−0.965757	−	0.259448i	$-0.916459\pi$
$821$	−55.3439	−1.93151	−0.965757	+	0.259448i	$0.916459\pi$
$822$	20.1379	0.702390
$823$	33.5847	1.17069	0.585345	−	0.810784i	$-0.300959\pi$
$823$	33.5847	1.17069	0.585345	+	0.810784i	$0.300959\pi$
$824$	−0.892944	−0.0311072
$825$	−12.8784	−0.448367
$826$	8.77363	0.305274
$827$	10.5173	0.365722	0.182861	−	0.983139i	$-0.441464\pi$
$827$	10.5173	0.365722	0.182861	+	0.983139i	$0.441464\pi$
$828$	−36.7782	−1.27813
$829$	−25.2674	−0.877572	−0.438786	−	0.898592i	$-0.644591\pi$
$829$	−25.2674	−0.877572	−0.438786	+	0.898592i	$0.644591\pi$
$830$	−9.59412	−0.333017
$831$	−1.34355	−0.0466071
$832$	−80.9903	−2.80783
$833$	−11.9166	−0.412886
$834$	−30.9927	−1.07319
$835$	−69.9444	−2.42053
$836$	−24.7858	−0.857236
$837$	−29.9681	−1.03585
$838$	−19.4697	−0.672570
$839$	−39.9473	−1.37914	−0.689568	−	0.724221i	$-0.742199\pi$
$839$	−39.9473	−1.37914	−0.689568	+	0.724221i	$0.742199\pi$
$840$	−21.5400	−0.743202
$841$	1.00000	0.0344828
$842$	−68.6189	−2.36476
$843$	16.1253	0.555385
$844$	−34.7884	−1.19746
$845$	−90.0205	−3.09680
$846$	2.05789	0.0707518
$847$	−7.47638	−0.256892
$848$	6.82773	0.234465
$849$	33.7804	1.15934
$850$	−23.7005	−0.812922
$851$	−56.3725	−1.93242
$852$	−27.6855	−0.948489
$853$	39.0598	1.33738	0.668691	−	0.743541i	$-0.266855\pi$
$853$	39.0598	1.33738	0.668691	+	0.743541i	$0.266855\pi$
$854$	36.2465	1.24033
$855$	−10.1526	−0.347211
$856$	23.8211	0.814189
$857$	−43.2040	−1.47582	−0.737910	−	0.674900i	$-0.764187\pi$
$857$	−43.2040	−1.47582	−0.737910	+	0.674900i	$0.764187\pi$
$858$	51.7515	1.76677
$859$	−6.19261	−0.211289	−0.105645	−	0.994404i	$-0.533691\pi$
$859$	−6.19261	−0.211289	−0.105645	+	0.994404i	$0.533691\pi$
$860$	11.3532	0.387140
$861$	13.3476	0.454887
$862$	−67.5344	−2.30023
$863$	−29.7617	−1.01310	−0.506550	−	0.862210i	$-0.669080\pi$
$863$	−29.7617	−1.01310	−0.506550	+	0.862210i	$0.669080\pi$
$864$	24.6335	0.838049
$865$	66.8730	2.27375
$866$	4.05900	0.137930
$867$	13.3968	0.454980
$868$	−29.1128	−0.988154
$869$	15.0007	0.508863
$870$	−9.32615	−0.316186
$871$	4.89916	0.166002
$872$	−10.7681	−0.364654
$873$	5.73940	0.194249
$874$	59.4593	2.01124
$875$	5.52007	0.186612
$876$	64.1994	2.16910
$877$	49.4095	1.66844	0.834220	−	0.551431i	$-0.185918\pi$
$877$	49.4095	1.66844	0.834220	+	0.551431i	$0.185918\pi$
$878$	60.4214	2.03912
$879$	26.8053	0.904121
$880$	−7.79894	−0.262902
$881$	−52.5747	−1.77129	−0.885644	−	0.464365i	$-0.846283\pi$
$881$	−52.5747	−1.77129	−0.885644	+	0.464365i	$0.846283\pi$
$882$	−12.5489	−0.422542
$883$	−48.6496	−1.63719	−0.818594	−	0.574373i	$-0.805246\pi$
$883$	−48.6496	−1.63719	−0.818594	+	0.574373i	$0.805246\pi$
$884$	60.3488	2.02975
$885$	−9.46960	−0.318317
$886$	−43.7890	−1.47112
$887$	−13.2028	−0.443307	−0.221654	−	0.975125i	$-0.571145\pi$
$887$	−13.2028	−0.443307	−0.221654	+	0.975125i	$0.571145\pi$
$888$	−29.0219	−0.973911
$889$	−9.93352	−0.333160
$890$	−46.4958	−1.55854
$891$	−9.99007	−0.334680
$892$	−29.0227	−0.971753
$893$	−2.10814	−0.0705462
$894$	−46.9781	−1.57118
$895$	−48.2096	−1.61147
$896$	31.6807	1.05838
$897$	−78.6661	−2.62659
$898$	19.8190	0.661370
$899$	−5.31724	−0.177340
$900$	−15.8146	−0.527153
$901$	17.2750	0.575515
$902$	36.7413	1.22335
$903$	2.34923	0.0781774
$904$	19.9012	0.661906
$905$	29.1529	0.969074
$906$	1.06485	0.0353772
$907$	−50.3113	−1.67056	−0.835280	−	0.549825i	$-0.814694\pi$
$907$	−50.3113	−1.67056	−0.835280	+	0.549825i	$0.814694\pi$
$908$	−7.25968	−0.240921
$909$	−9.65554	−0.320254
$910$	72.2965	2.39660
$911$	13.0881	0.433628	0.216814	−	0.976213i	$-0.430433\pi$
$911$	13.0881	0.433628	0.216814	+	0.976213i	$0.430433\pi$
$912$	4.02641	0.133328
$913$	−3.46267	−0.114598
$914$	55.2348	1.82700
$915$	−39.1217	−1.29332
$916$	80.6112	2.66347
$917$	−4.68126	−0.154589
$918$	−34.9123	−1.15228
$919$	1.08684	0.0358514	0.0179257	−	0.999839i	$-0.494294\pi$
$919$	1.08684	0.0358514	0.0179257	+	0.999839i	$0.494294\pi$
$920$	90.1283	2.97144
$921$	9.55297	0.314781
$922$	−31.8312	−1.04830
$923$	39.1984	1.29023
$924$	−18.4292	−0.606276
$925$	−24.2401	−0.797009
$926$	−12.2397	−0.402222
$927$	−0.312937	−0.0102782
$928$	4.37073	0.143476
$929$	−46.8910	−1.53844	−0.769222	−	0.638981i	$-0.779356\pi$
$929$	−46.8910	−1.53844	−0.769222	+	0.638981i	$0.779356\pi$
$930$	49.5894	1.62610
$931$	12.8553	0.421315
$932$	50.2474	1.64591
$933$	0.197579	0.00646844
$934$	−35.3356	−1.15622
$935$	−19.7323	−0.645316
$936$	26.8081	0.876249
$937$	−18.1674	−0.593504	−0.296752	−	0.954955i	$-0.595904\pi$
$937$	−18.1674	−0.593504	−0.296752	+	0.954955i	$0.595904\pi$
$938$	−2.75332	−0.0898991
$939$	−5.02069	−0.163844
$940$	−7.57523	−0.247077
$941$	0.364056	0.0118679	0.00593394	−	0.999982i	$-0.498111\pi$
$941$	0.364056	0.0118679	0.00593394	+	0.999982i	$0.498111\pi$
$942$	26.7651	0.872054
$943$	−55.8495	−1.81871
$944$	−2.48595	−0.0809107
$945$	−26.5017	−0.862102
$946$	6.46659	0.210247
$947$	27.8330	0.904451	0.452226	−	0.891904i	$-0.350630\pi$
$947$	27.8330	0.904451	0.452226	+	0.891904i	$0.350630\pi$
$948$	−27.8284	−0.903825
$949$	−90.8965	−2.95062
$950$	25.5674	0.829516
$951$	−24.5690	−0.796705
$952$	−14.3070	−0.463693
$953$	−9.47685	−0.306985	−0.153493	−	0.988150i	$-0.549052\pi$
$953$	−9.47685	−0.306985	−0.153493	+	0.988150i	$0.549052\pi$
$954$	18.1916	0.588974
$955$	42.0260	1.35993
$956$	12.0309	0.389107
$957$	−3.36595	−0.108806
$958$	86.0170	2.77908
$959$	10.1534	0.327872
$960$	−49.1270	−1.58557
$961$	−2.72699	−0.0879674
$962$	97.4084	3.14057
$963$	8.34825	0.269019
$964$	−22.7437	−0.732526
$965$	−9.79791	−0.315406
$966$	44.2102	1.42244
$967$	−41.2928	−1.32789	−0.663943	−	0.747783i	$-0.731118\pi$
$967$	−41.2928	−1.32789	−0.663943	+	0.747783i	$0.731118\pi$
$968$	16.1052	0.517639
$969$	10.1873	0.327264
$970$	−33.3420	−1.07055
$971$	−6.82234	−0.218939	−0.109470	−	0.993990i	$-0.534915\pi$
$971$	−6.82234	−0.218939	−0.109470	+	0.993990i	$0.534915\pi$
$972$	−39.9560	−1.28159
$973$	−15.6264	−0.500960
$974$	−84.8631	−2.71919
$975$	−33.8263	−1.08331
$976$	−10.2702	−0.328741
$977$	18.0333	0.576937	0.288468	−	0.957489i	$-0.406854\pi$
$977$	18.0333	0.576937	0.288468	+	0.957489i	$0.406854\pi$
$978$	9.83115	0.314366
$979$	−16.7810	−0.536325
$980$	46.1931	1.47559
$981$	−3.77374	−0.120486
$982$	−20.4226	−0.651710
$983$	−14.1212	−0.450396	−0.225198	−	0.974313i	$-0.572303\pi$
$983$	−14.1212	−0.450396	−0.225198	+	0.974313i	$0.572303\pi$
$984$	−28.7527	−0.916601
$985$	−10.5661	−0.336664
$986$	−6.19449	−0.197273
$987$	−1.56748	−0.0498935
$988$	−65.1025	−2.07119
$989$	−9.82968	−0.312566
$990$	−20.7792	−0.660408
$991$	−48.7709	−1.54926	−0.774629	−	0.632416i	$-0.782063\pi$
$991$	−48.7709	−1.54926	−0.774629	+	0.632416i	$0.782063\pi$
$992$	−23.2402	−0.737877
$993$	14.4384	0.458188
$994$	−22.0294	−0.698731
$995$	0.922370	0.0292411
$996$	6.42375	0.203544
$997$	−58.0047	−1.83703	−0.918514	−	0.395389i	$-0.870610\pi$
$997$	−58.0047	−1.83703	−0.918514	+	0.395389i	$0.870610\pi$
$998$	24.9275	0.789068
$999$	−35.7070	−1.12972

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8033.2.a.c.1.18	✓	154

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8033.2.a.c.1.18	✓	154	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)

\(f(q)\)	\(=\)	\(q-2.33650 q^{2} -1.34355 q^{3} +3.45924 q^{4} -2.97087 q^{5} +3.13920 q^{6} +1.58277 q^{7} -3.40951 q^{8} -1.19488 q^{9} +O(q^{10})\)	\(q-2.33650 q^{2} -1.34355 q^{3} +3.45924 q^{4} -2.97087 q^{5} +3.13920 q^{6} +1.58277 q^{7} -3.40951 q^{8} -1.19488 q^{9} +6.94144 q^{10} +2.50527 q^{11} -4.64765 q^{12} +6.58035 q^{13} -3.69815 q^{14} +3.99150 q^{15} +1.04784 q^{16} +2.65118 q^{17} +2.79184 q^{18} -2.86001 q^{19} -10.2769 q^{20} -2.12653 q^{21} -5.85358 q^{22} +8.89786 q^{23} +4.58083 q^{24} +3.82607 q^{25} -15.3750 q^{26} +5.63602 q^{27} +5.47518 q^{28} +1.00000 q^{29} -9.32615 q^{30} -5.31724 q^{31} +4.37073 q^{32} -3.36595 q^{33} -6.19449 q^{34} -4.70221 q^{35} -4.13338 q^{36} -6.33551 q^{37} +6.68242 q^{38} -8.84102 q^{39} +10.1292 q^{40} -6.27673 q^{41} +4.96863 q^{42} -1.10472 q^{43} +8.66634 q^{44} +3.54984 q^{45} -20.7899 q^{46} +0.737109 q^{47} -1.40783 q^{48} -4.49483 q^{49} -8.93961 q^{50} -3.56199 q^{51} +22.7630 q^{52} +6.51598 q^{53} -13.1686 q^{54} -7.44284 q^{55} -5.39647 q^{56} +3.84256 q^{57} -2.33650 q^{58} -2.37244 q^{59} +13.8076 q^{60} -9.80125 q^{61} +12.4237 q^{62} -1.89122 q^{63} -12.3079 q^{64} -19.5494 q^{65} +7.86455 q^{66} +0.744514 q^{67} +9.17106 q^{68} -11.9547 q^{69} +10.9867 q^{70} +5.95688 q^{71} +4.07396 q^{72} -13.8133 q^{73} +14.8029 q^{74} -5.14050 q^{75} -9.89346 q^{76} +3.96528 q^{77} +20.6570 q^{78} +5.98764 q^{79} -3.11301 q^{80} -3.98761 q^{81} +14.6656 q^{82} -1.38215 q^{83} -7.35616 q^{84} -7.87632 q^{85} +2.58119 q^{86} -1.34355 q^{87} -8.54175 q^{88} -6.69829 q^{89} -8.29420 q^{90} +10.4152 q^{91} +30.7798 q^{92} +7.14396 q^{93} -1.72226 q^{94} +8.49673 q^{95} -5.87228 q^{96} -4.80332 q^{97} +10.5022 q^{98} -2.99351 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 154 q - 12 q^{2} - 36 q^{3} + 142 q^{4} - 9 q^{5} - 11 q^{6} - 68 q^{7} - 33 q^{8} + 146 q^{9}+O(q^{10}) \) 154 * q - 12 * q^2 - 36 * q^3 + 142 * q^4 - 9 * q^5 - 11 * q^6 - 68 * q^7 - 33 * q^8 + 146 * q^9	\( 154 q - 12 q^{2} - 36 q^{3} + 142 q^{4} - 9 q^{5} - 11 q^{6} - 68 q^{7} - 33 q^{8} + 146 q^{9} - 40 q^{10} - 36 q^{11} - 67 q^{12} - 51 q^{13} - 19 q^{14} - 48 q^{15} + 122 q^{16} - 54 q^{17} - 46 q^{18} - 73 q^{19} - 21 q^{20} - 8 q^{21} - 23 q^{22} - 38 q^{23} - 17 q^{24} + 133 q^{25} - 20 q^{26} - 129 q^{27} - 99 q^{28} + 154 q^{29} - 10 q^{30} - 91 q^{31} - 88 q^{32} - 39 q^{33} - 42 q^{34} - 36 q^{35} + 101 q^{36} - 50 q^{37} - 17 q^{38} - 33 q^{39} - 92 q^{40} - 31 q^{41} - 62 q^{42} - 154 q^{43} - 42 q^{44} - 14 q^{45} - 24 q^{46} - 140 q^{47} - 118 q^{48} + 126 q^{49} - 5 q^{50} - 16 q^{51} - 133 q^{52} - 40 q^{53} + 14 q^{54} - 203 q^{55} - 44 q^{56} - 16 q^{57} - 12 q^{58} + 5 q^{59} - 28 q^{60} - 106 q^{61} - 30 q^{62} - 145 q^{63} + 111 q^{64} - 15 q^{65} - 49 q^{66} - 78 q^{67} - 118 q^{68} - 32 q^{69} - 43 q^{70} - 4 q^{71} - 152 q^{72} - 137 q^{73} + 9 q^{74} - 129 q^{75} - 204 q^{76} - 76 q^{77} + 15 q^{78} - 141 q^{79} - 44 q^{80} + 122 q^{81} - 71 q^{82} - 90 q^{83} + 92 q^{84} - 41 q^{85} + 9 q^{86} - 36 q^{87} - 109 q^{88} - 51 q^{89} - 82 q^{90} - 22 q^{91} - 8 q^{92} - 10 q^{93} - 106 q^{94} - 55 q^{95} - 49 q^{96} - 140 q^{97} - 4 q^{98} - 101 q^{99}+O(q^{100}) \) 154 * q - 12 * q^2 - 36 * q^3 + 142 * q^4 - 9 * q^5 - 11 * q^6 - 68 * q^7 - 33 * q^8 + 146 * q^9 - 40 * q^10 - 36 * q^11 - 67 * q^12 - 51 * q^13 - 19 * q^14 - 48 * q^15 + 122 * q^16 - 54 * q^17 - 46 * q^18 - 73 * q^19 - 21 * q^20 - 8 * q^21 - 23 * q^22 - 38 * q^23 - 17 * q^24 + 133 * q^25 - 20 * q^26 - 129 * q^27 - 99 * q^28 + 154 * q^29 - 10 * q^30 - 91 * q^31 - 88 * q^32 - 39 * q^33 - 42 * q^34 - 36 * q^35 + 101 * q^36 - 50 * q^37 - 17 * q^38 - 33 * q^39 - 92 * q^40 - 31 * q^41 - 62 * q^42 - 154 * q^43 - 42 * q^44 - 14 * q^45 - 24 * q^46 - 140 * q^47 - 118 * q^48 + 126 * q^49 - 5 * q^50 - 16 * q^51 - 133 * q^52 - 40 * q^53 + 14 * q^54 - 203 * q^55 - 44 * q^56 - 16 * q^57 - 12 * q^58 + 5 * q^59 - 28 * q^60 - 106 * q^61 - 30 * q^62 - 145 * q^63 + 111 * q^64 - 15 * q^65 - 49 * q^66 - 78 * q^67 - 118 * q^68 - 32 * q^69 - 43 * q^70 - 4 * q^71 - 152 * q^72 - 137 * q^73 + 9 * q^74 - 129 * q^75 - 204 * q^76 - 76 * q^77 + 15 * q^78 - 141 * q^79 - 44 * q^80 + 122 * q^81 - 71 * q^82 - 90 * q^83 + 92 * q^84 - 41 * q^85 + 9 * q^86 - 36 * q^87 - 109 * q^88 - 51 * q^89 - 82 * q^90 - 22 * q^91 - 8 * q^92 - 10 * q^93 - 106 * q^94 - 55 * q^95 - 49 * q^96 - 140 * q^97 - 4 * q^98 - 101 * q^99

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