LMFDB - Embedded newform 8021.2.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8021,2,Mod(1,8021)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8021, 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("8021.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8021 = 13 \cdot 617 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8021.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:	$64.0480074613$
Analytic rank:	$0$
Dimension:	$169$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	8021.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.81845 q^{2} -2.05603 q^{3} +5.94365 q^{4} -2.67963 q^{5} +5.79481 q^{6} -3.26986 q^{7} -11.1150 q^{8} +1.22725 q^{9} +O(q^{10})$	\(q-2.81845 q^{2} -2.05603 q^{3} +5.94365 q^{4} -2.67963 q^{5} +5.79481 q^{6} -3.26986 q^{7} -11.1150 q^{8} +1.22725 q^{9} +7.55241 q^{10} +3.81690 q^{11} -12.2203 q^{12} -1.00000 q^{13} +9.21595 q^{14} +5.50940 q^{15} +19.4397 q^{16} -6.98971 q^{17} -3.45893 q^{18} +5.83611 q^{19} -15.9268 q^{20} +6.72293 q^{21} -10.7578 q^{22} +1.80157 q^{23} +22.8527 q^{24} +2.18043 q^{25} +2.81845 q^{26} +3.64483 q^{27} -19.4349 q^{28} -0.500124 q^{29} -15.5279 q^{30} -6.88329 q^{31} -32.5599 q^{32} -7.84766 q^{33} +19.7001 q^{34} +8.76204 q^{35} +7.29432 q^{36} +9.15331 q^{37} -16.4488 q^{38} +2.05603 q^{39} +29.7841 q^{40} +8.46407 q^{41} -18.9482 q^{42} -1.57883 q^{43} +22.6864 q^{44} -3.28857 q^{45} -5.07763 q^{46} +1.75756 q^{47} -39.9686 q^{48} +3.69202 q^{49} -6.14543 q^{50} +14.3710 q^{51} -5.94365 q^{52} +5.90555 q^{53} -10.2728 q^{54} -10.2279 q^{55} +36.3445 q^{56} -11.9992 q^{57} +1.40957 q^{58} -4.21383 q^{59} +32.7459 q^{60} -5.11382 q^{61} +19.4002 q^{62} -4.01293 q^{63} +52.8889 q^{64} +2.67963 q^{65} +22.1182 q^{66} +10.3802 q^{67} -41.5444 q^{68} -3.70407 q^{69} -24.6953 q^{70} -6.98551 q^{71} -13.6408 q^{72} +7.38465 q^{73} -25.7981 q^{74} -4.48302 q^{75} +34.6878 q^{76} -12.4808 q^{77} -5.79481 q^{78} +4.87480 q^{79} -52.0913 q^{80} -11.1756 q^{81} -23.8555 q^{82} -9.69052 q^{83} +39.9588 q^{84} +18.7298 q^{85} +4.44984 q^{86} +1.02827 q^{87} -42.4248 q^{88} +13.8339 q^{89} +9.26866 q^{90} +3.26986 q^{91} +10.7079 q^{92} +14.1522 q^{93} -4.95359 q^{94} -15.6386 q^{95} +66.9439 q^{96} +15.0944 q^{97} -10.4058 q^{98} +4.68428 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 169 q + 9 q^{2} + 9 q^{3} + 199 q^{4} + 12 q^{5} + 22 q^{6} + 36 q^{7} + 30 q^{8} + 198 q^{9}+O(q^{10}) $ 169 * q + 9 * q^2 + 9 * q^3 + 199 * q^4 + 12 * q^5 + 22 * q^6 + 36 * q^7 + 30 * q^8 + 198 * q^9	\( 169 q + 9 q^{2} + 9 q^{3} + 199 q^{4} + 12 q^{5} + 22 q^{6} + 36 q^{7} + 30 q^{8} + 198 q^{9} - 3 q^{10} + 59 q^{11} + 11 q^{12} - 169 q^{13} + 30 q^{14} + 50 q^{15} + 267 q^{16} + q^{17} + 53 q^{18} + 107 q^{19} + 48 q^{20} + 36 q^{21} + 14 q^{22} + 12 q^{23} + 78 q^{24} + 217 q^{25} - 9 q^{26} + 39 q^{27} + 99 q^{28} + 30 q^{29} - q^{30} + 106 q^{31} + 74 q^{32} + 16 q^{33} + 56 q^{34} + 46 q^{35} + 271 q^{36} + 73 q^{37} + 2 q^{38} - 9 q^{39} - 16 q^{40} + 52 q^{41} - 2 q^{42} + 64 q^{43} + 124 q^{44} + 84 q^{45} + 105 q^{46} + 55 q^{47} + 26 q^{48} + 257 q^{49} + 60 q^{50} + 117 q^{51} - 199 q^{52} + 7 q^{53} + 78 q^{54} - 4 q^{55} + 63 q^{56} + 51 q^{57} + 84 q^{58} + 98 q^{59} + 94 q^{60} + 32 q^{61} - 25 q^{62} + 128 q^{63} + 380 q^{64} - 12 q^{65} + 16 q^{66} + 170 q^{67} - 10 q^{68} + 55 q^{69} + 70 q^{70} + 124 q^{71} + 173 q^{72} + 81 q^{73} + 54 q^{74} + 120 q^{75} + 212 q^{76} + 20 q^{77} - 22 q^{78} + 92 q^{79} + 66 q^{80} + 265 q^{81} + 21 q^{82} + 62 q^{83} + 98 q^{84} + 139 q^{85} + 51 q^{86} - 33 q^{87} + 31 q^{88} + 58 q^{89} + 16 q^{90} - 36 q^{91} + 40 q^{92} + 37 q^{93} + 55 q^{94} + 23 q^{95} + 164 q^{96} + 78 q^{97} + 69 q^{98} + 307 q^{99}+O(q^{100}) \) 169 * q + 9 * q^2 + 9 * q^3 + 199 * q^4 + 12 * q^5 + 22 * q^6 + 36 * q^7 + 30 * q^8 + 198 * q^9 - 3 * q^10 + 59 * q^11 + 11 * q^12 - 169 * q^13 + 30 * q^14 + 50 * q^15 + 267 * q^16 + q^17 + 53 * q^18 + 107 * q^19 + 48 * q^20 + 36 * q^21 + 14 * q^22 + 12 * q^23 + 78 * q^24 + 217 * q^25 - 9 * q^26 + 39 * q^27 + 99 * q^28 + 30 * q^29 - q^30 + 106 * q^31 + 74 * q^32 + 16 * q^33 + 56 * q^34 + 46 * q^35 + 271 * q^36 + 73 * q^37 + 2 * q^38 - 9 * q^39 - 16 * q^40 + 52 * q^41 - 2 * q^42 + 64 * q^43 + 124 * q^44 + 84 * q^45 + 105 * q^46 + 55 * q^47 + 26 * q^48 + 257 * q^49 + 60 * q^50 + 117 * q^51 - 199 * q^52 + 7 * q^53 + 78 * q^54 - 4 * q^55 + 63 * q^56 + 51 * q^57 + 84 * q^58 + 98 * q^59 + 94 * q^60 + 32 * q^61 - 25 * q^62 + 128 * q^63 + 380 * q^64 - 12 * q^65 + 16 * q^66 + 170 * q^67 - 10 * q^68 + 55 * q^69 + 70 * q^70 + 124 * q^71 + 173 * q^72 + 81 * q^73 + 54 * q^74 + 120 * q^75 + 212 * q^76 + 20 * q^77 - 22 * q^78 + 92 * q^79 + 66 * q^80 + 265 * q^81 + 21 * q^82 + 62 * q^83 + 98 * q^84 + 139 * q^85 + 51 * q^86 - 33 * q^87 + 31 * q^88 + 58 * q^89 + 16 * q^90 - 36 * q^91 + 40 * q^92 + 37 * q^93 + 55 * q^94 + 23 * q^95 + 164 * q^96 + 78 * q^97 + 69 * q^98 + 307 * 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 $

$2$	−2.81845	−1.99294	−0.996472	−	0.0839244i	$-0.973255\pi$
$2$	−2.81845	−1.99294	−0.996472	+	0.0839244i	$0.973255\pi$
$3$	−2.05603	−1.18705	−0.593524	−	0.804816i	$-0.702264\pi$
$3$	−2.05603	−1.18705	−0.593524	+	0.804816i	$0.702264\pi$
$4$	5.94365	2.97183
$5$	−2.67963	−1.19837	−0.599184	−	0.800611i	$-0.704508\pi$
$5$	−2.67963	−1.19837	−0.599184	+	0.800611i	$0.704508\pi$
$6$	5.79481	2.36572
$7$	−3.26986	−1.23589	−0.617946	−	0.786220i	$-0.712035\pi$
$7$	−3.26986	−1.23589	−0.617946	+	0.786220i	$0.712035\pi$
$8$	−11.1150	−3.92974
$9$	1.22725	0.409082
$10$	7.55241	2.38828
$11$	3.81690	1.15084	0.575420	−	0.817858i	$-0.304839\pi$
$11$	3.81690	1.15084	0.575420	+	0.817858i	$0.304839\pi$
$12$	−12.2203	−3.52770
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	9.21595	2.46307
$15$	5.50940	1.42252
$16$	19.4397	4.85993
$17$	−6.98971	−1.69525	−0.847626	−	0.530593i	$-0.821969\pi$
$17$	−6.98971	−1.69525	−0.847626	+	0.530593i	$0.821969\pi$
$18$	−3.45893	−0.815277
$19$	5.83611	1.33890	0.669448	−	0.742859i	$-0.266531\pi$
$19$	5.83611	1.33890	0.669448	+	0.742859i	$0.266531\pi$
$20$	−15.9268	−3.56134
$21$	6.72293	1.46706
$22$	−10.7578	−2.29356
$23$	1.80157	0.375653	0.187826	−	0.982202i	$-0.439856\pi$
$23$	1.80157	0.375653	0.187826	+	0.982202i	$0.439856\pi$
$24$	22.8527	4.66479
$25$	2.18043	0.436086
$26$	2.81845	0.552743
$27$	3.64483	0.701448
$28$	−19.4349	−3.67286
$29$	−0.500124	−0.0928707	−0.0464354	−	0.998921i	$-0.514786\pi$
$29$	−0.500124	−0.0928707	−0.0464354	+	0.998921i	$0.514786\pi$
$30$	−15.5279	−2.83500
$31$	−6.88329	−1.23628	−0.618138	−	0.786070i	$-0.712113\pi$
$31$	−6.88329	−1.23628	−0.618138	+	0.786070i	$0.712113\pi$
$32$	−32.5599	−5.75582
$33$	−7.84766	−1.36610
$34$	19.7001	3.37854
$35$	8.76204	1.48105
$36$	7.29432	1.21572
$37$	9.15331	1.50480	0.752398	−	0.658709i	$-0.228897\pi$
$37$	9.15331	1.50480	0.752398	+	0.658709i	$0.228897\pi$
$38$	−16.4488	−2.66835
$39$	2.05603	0.329228
$40$	29.7841	4.70928
$41$	8.46407	1.32186	0.660932	−	0.750445i	$-0.270161\pi$
$41$	8.46407	1.32186	0.660932	+	0.750445i	$0.270161\pi$
$42$	−18.9482	−2.92378
$43$	−1.57883	−0.240769	−0.120384	−	0.992727i	$-0.538413\pi$
$43$	−1.57883	−0.240769	−0.120384	+	0.992727i	$0.538413\pi$
$44$	22.6864	3.42010
$45$	−3.28857	−0.490231
$46$	−5.07763	−0.748655
$47$	1.75756	0.256366	0.128183	−	0.991751i	$-0.459085\pi$
$47$	1.75756	0.256366	0.128183	+	0.991751i	$0.459085\pi$
$48$	−39.9686	−5.76897
$49$	3.69202	0.527431
$50$	−6.14543	−0.869095
$51$	14.3710	2.01235
$52$	−5.94365	−0.824236
$53$	5.90555	0.811190	0.405595	−	0.914053i	$-0.367064\pi$
$53$	5.90555	0.811190	0.405595	+	0.914053i	$0.367064\pi$
$54$	−10.2728	−1.39795
$55$	−10.2279	−1.37913
$56$	36.3445	4.85674
$57$	−11.9992	−1.58933
$58$	1.40957	0.185086
$59$	−4.21383	−0.548594	−0.274297	−	0.961645i	$-0.588445\pi$
$59$	−4.21383	−0.548594	−0.274297	+	0.961645i	$0.588445\pi$
$60$	32.7459	4.22748
$61$	−5.11382	−0.654758	−0.327379	−	0.944893i	$-0.606165\pi$
$61$	−5.11382	−0.654758	−0.327379	+	0.944893i	$0.606165\pi$
$62$	19.4002	2.46383
$63$	−4.01293	−0.505581
$64$	52.8889	6.61111
$65$	2.67963	0.332367
$66$	22.1182	2.72256
$67$	10.3802	1.26815	0.634073	−	0.773273i	$-0.281382\pi$
$67$	10.3802	1.26815	0.634073	+	0.773273i	$0.281382\pi$
$68$	−41.5444	−5.03800
$69$	−3.70407	−0.445918
$70$	−24.6953	−2.95166
$71$	−6.98551	−0.829028	−0.414514	−	0.910043i	$-0.636048\pi$
$71$	−6.98551	−0.829028	−0.414514	+	0.910043i	$0.636048\pi$
$72$	−13.6408	−1.60759
$73$	7.38465	0.864308	0.432154	−	0.901800i	$-0.357754\pi$
$73$	7.38465	0.864308	0.432154	+	0.901800i	$0.357754\pi$
$74$	−25.7981	−2.99897
$75$	−4.48302	−0.517655
$76$	34.6878	3.97897
$77$	−12.4808	−1.42231
$78$	−5.79481	−0.656133
$79$	4.87480	0.548458	0.274229	−	0.961664i	$-0.411577\pi$
$79$	4.87480	0.548458	0.274229	+	0.961664i	$0.411577\pi$
$80$	−52.0913	−5.82398
$81$	−11.1756	−1.24173
$82$	−23.8555	−2.63440
$83$	−9.69052	−1.06367	−0.531836	−	0.846847i	$-0.678498\pi$
$83$	−9.69052	−1.06367	−0.531836	+	0.846847i	$0.678498\pi$
$84$	39.9588	4.35986
$85$	18.7298	2.03154
$86$	4.44984	0.479839
$87$	1.02827	0.110242
$88$	−42.4248	−4.52250
$89$	13.8339	1.46639	0.733197	−	0.680017i	$-0.238028\pi$
$89$	13.8339	1.46639	0.733197	+	0.680017i	$0.238028\pi$
$90$	9.26866	0.977002
$91$	3.26986	0.342775
$92$	10.7079	1.11638
$93$	14.1522	1.46752
$94$	−4.95359	−0.510924
$95$	−15.6386	−1.60449
$96$	66.9439	6.83244
$97$	15.0944	1.53260	0.766301	−	0.642482i	$-0.222095\pi$
$97$	15.0944	1.53260	0.766301	+	0.642482i	$0.222095\pi$
$98$	−10.4058	−1.05114
$99$	4.68428	0.470788
$100$	12.9597	1.29597
$101$	−7.16136	−0.712582	−0.356291	−	0.934375i	$-0.615959\pi$
$101$	−7.16136	−0.712582	−0.356291	+	0.934375i	$0.615959\pi$
$102$	−40.5040	−4.01049
$103$	16.0203	1.57853	0.789265	−	0.614052i	$-0.210462\pi$
$103$	16.0203	1.57853	0.789265	+	0.614052i	$0.210462\pi$
$104$	11.1150	1.08991
$105$	−18.0150	−1.75808
$106$	−16.6445	−1.61666
$107$	−12.2017	−1.17958	−0.589792	−	0.807555i	$-0.700790\pi$
$107$	−12.2017	−1.17958	−0.589792	+	0.807555i	$0.700790\pi$
$108$	21.6636	2.08458
$109$	−5.59046	−0.535469	−0.267734	−	0.963493i	$-0.586275\pi$
$109$	−5.59046	−0.535469	−0.267734	+	0.963493i	$0.586275\pi$
$110$	28.8268	2.74853
$111$	−18.8195	−1.78626
$112$	−63.5652	−6.00635
$113$	−5.66469	−0.532889	−0.266444	−	0.963850i	$-0.585849\pi$
$113$	−5.66469	−0.532889	−0.266444	+	0.963850i	$0.585849\pi$
$114$	33.8191	3.16745
$115$	−4.82754	−0.450170
$116$	−2.97256	−0.275996
$117$	−1.22725	−0.113459
$118$	11.8765	1.09332
$119$	22.8554	2.09515
$120$	−61.2369	−5.59013
$121$	3.56876	0.324433
$122$	14.4131	1.30490
$123$	−17.4023	−1.56912
$124$	−40.9119	−3.67400
$125$	7.55541	0.675777
$126$	11.3102	1.00760
$127$	−20.2967	−1.80104	−0.900522	−	0.434810i	$-0.856815\pi$
$127$	−20.2967	−1.80104	−0.900522	+	0.434810i	$0.856815\pi$
$128$	−83.9449	−7.41975
$129$	3.24611	0.285804
$130$	−7.55241	−0.662390
$131$	−19.4684	−1.70096	−0.850482	−	0.526004i	$-0.823690\pi$
$131$	−19.4684	−1.70096	−0.850482	+	0.526004i	$0.823690\pi$
$132$	−46.6438	−4.05982
$133$	−19.0833	−1.65473
$134$	−29.2561	−2.52735
$135$	−9.76680	−0.840593
$136$	77.6905	6.66190
$137$	8.16256	0.697374	0.348687	−	0.937239i	$-0.386628\pi$
$137$	8.16256	0.697374	0.348687	+	0.937239i	$0.386628\pi$
$138$	10.4397	0.888689
$139$	−8.39456	−0.712017	−0.356009	−	0.934483i	$-0.615863\pi$
$139$	−8.39456	−0.712017	−0.356009	+	0.934483i	$0.615863\pi$
$140$	52.0785	4.40144
$141$	−3.61359	−0.304319
$142$	19.6883	1.65221
$143$	−3.81690	−0.319186
$144$	23.8573	1.98811
$145$	1.34015	0.111293
$146$	−20.8133	−1.72252
$147$	−7.59088	−0.626085
$148$	54.4041	4.47199
$149$	−8.33243	−0.682619	−0.341310	−	0.939951i	$-0.610870\pi$
$149$	−8.33243	−0.682619	−0.341310	+	0.939951i	$0.610870\pi$
$150$	12.6352	1.03166
$151$	−3.66143	−0.297963	−0.148981	−	0.988840i	$-0.547599\pi$
$151$	−3.66143	−0.297963	−0.148981	+	0.988840i	$0.547599\pi$
$152$	−64.8683	−5.26151
$153$	−8.57809	−0.693497
$154$	35.1764	2.83459
$155$	18.4447	1.48151
$156$	12.2203	0.978408
$157$	0.863009	0.0688756	0.0344378	−	0.999407i	$-0.489036\pi$
$157$	0.863009	0.0688756	0.0344378	+	0.999407i	$0.489036\pi$
$158$	−13.7394	−1.09305
$159$	−12.1420	−0.962921
$160$	87.2484	6.89760
$161$	−5.89088	−0.464267
$162$	31.4979	2.47471
$163$	3.45678	0.270756	0.135378	−	0.990794i	$-0.456775\pi$
$163$	3.45678	0.270756	0.135378	+	0.990794i	$0.456775\pi$
$164$	50.3075	3.92835
$165$	21.0288	1.63709
$166$	27.3122	2.11984
$167$	7.20864	0.557822	0.278911	−	0.960317i	$-0.410027\pi$
$167$	7.20864	0.557822	0.278911	+	0.960317i	$0.410027\pi$
$168$	−74.7253	−5.76518
$169$	1.00000	0.0769231
$170$	−52.7891	−4.04874
$171$	7.16234	0.547718
$172$	−9.38400	−0.715523
$173$	−20.0303	−1.52287	−0.761437	−	0.648239i	$-0.775506\pi$
$173$	−20.0303	−1.52287	−0.761437	+	0.648239i	$0.775506\pi$
$174$	−2.89812	−0.219706
$175$	−7.12971	−0.538955
$176$	74.1995	5.59300
$177$	8.66375	0.651207
$178$	−38.9902	−2.92244
$179$	11.1404	0.832674	0.416337	−	0.909210i	$-0.363314\pi$
$179$	11.1404	0.832674	0.416337	+	0.909210i	$0.363314\pi$
$180$	−19.5461	−1.45688
$181$	−6.45545	−0.479830	−0.239915	−	0.970794i	$-0.577120\pi$
$181$	−6.45545	−0.479830	−0.239915	+	0.970794i	$0.577120\pi$
$182$	−9.21595	−0.683131
$183$	10.5142	0.777229
$184$	−20.0244	−1.47622
$185$	−24.5275	−1.80330
$186$	−39.8873	−2.92468
$187$	−26.6790	−1.95096
$188$	10.4463	0.761876
$189$	−11.9181	−0.866914
$190$	44.0767	3.19766
$191$	0.472736	0.0342060	0.0171030	−	0.999854i	$-0.494556\pi$
$191$	0.472736	0.0342060	0.0171030	+	0.999854i	$0.494556\pi$
$192$	−108.741	−7.84770
$193$	−7.46198	−0.537125	−0.268562	−	0.963262i	$-0.586549\pi$
$193$	−7.46198	−0.537125	−0.268562	+	0.963262i	$0.586549\pi$
$194$	−42.5427	−3.05439
$195$	−5.50940	−0.394536
$196$	21.9441	1.56743
$197$	4.89252	0.348578	0.174289	−	0.984695i	$-0.444237\pi$
$197$	4.89252	0.348578	0.174289	+	0.984695i	$0.444237\pi$
$198$	−13.2024	−0.938254
$199$	14.4273	1.02273	0.511364	−	0.859364i	$-0.329140\pi$
$199$	14.4273	1.02273	0.511364	+	0.859364i	$0.329140\pi$
$200$	−24.2354	−1.71370
$201$	−21.3420	−1.50535
$202$	20.1839	1.42014
$203$	1.63534	0.114778
$204$	85.4164	5.98034
$205$	−22.6806	−1.58408
$206$	−45.1525	−3.14592
$207$	2.21097	0.153673
$208$	−19.4397	−1.34790
$209$	22.2759	1.54086
$210$	50.7743	3.50376
$211$	23.0754	1.58858	0.794288	−	0.607542i	$-0.207844\pi$
$211$	23.0754	1.58858	0.794288	+	0.607542i	$0.207844\pi$
$212$	35.1006	2.41072
$213$	14.3624	0.984095
$214$	34.3899	2.35084
$215$	4.23068	0.288530
$216$	−40.5122	−2.75651
$217$	22.5074	1.52790
$218$	15.7564	1.06716
$219$	−15.1830	−1.02597
$220$	−60.7911	−4.09854
$221$	6.98971	0.470179
$222$	53.0417	3.55992
$223$	7.29522	0.488524	0.244262	−	0.969709i	$-0.421454\pi$
$223$	7.29522	0.488524	0.244262	+	0.969709i	$0.421454\pi$
$224$	106.466	7.11358
$225$	2.67592	0.178395
$226$	15.9656	1.06202
$227$	−3.20215	−0.212534	−0.106267	−	0.994338i	$-0.533890\pi$
$227$	−3.20215	−0.212534	−0.106267	+	0.994338i	$0.533890\pi$
$228$	−71.3191	−4.72322
$229$	−13.9019	−0.918664	−0.459332	−	0.888265i	$-0.651911\pi$
$229$	−13.9019	−0.918664	−0.459332	+	0.888265i	$0.651911\pi$
$230$	13.6062	0.897165
$231$	25.6608	1.68836
$232$	5.55887	0.364958
$233$	−15.5554	−1.01907	−0.509534	−	0.860450i	$-0.670182\pi$
$233$	−15.5554	−1.01907	−0.509534	+	0.860450i	$0.670182\pi$
$234$	3.45893	0.226117
$235$	−4.70961	−0.307221
$236$	−25.0456	−1.63033
$237$	−10.0227	−0.651046
$238$	−64.4168	−4.17552
$239$	20.9639	1.35604	0.678021	−	0.735042i	$-0.262838\pi$
$239$	20.9639	1.35604	0.678021	+	0.735042i	$0.262838\pi$
$240$	107.101	6.91334
$241$	19.8648	1.27960	0.639801	−	0.768540i	$-0.279017\pi$
$241$	19.8648	1.27960	0.639801	+	0.768540i	$0.279017\pi$
$242$	−10.0584	−0.646577
$243$	12.0429	0.772549
$244$	−30.3948	−1.94583
$245$	−9.89324	−0.632056
$246$	49.0476	3.12716
$247$	−5.83611	−0.371343
$248$	76.5077	4.85824
$249$	19.9240	1.26263
$250$	−21.2945	−1.34678
$251$	−14.4517	−0.912184	−0.456092	−	0.889933i	$-0.650751\pi$
$251$	−14.4517	−0.912184	−0.456092	+	0.889933i	$0.650751\pi$
$252$	−23.8515	−1.50250
$253$	6.87641	0.432316
$254$	57.2053	3.58938
$255$	−38.5091	−2.41153
$256$	130.817	8.17603
$257$	18.2557	1.13876	0.569380	−	0.822074i	$-0.307183\pi$
$257$	18.2557	1.13876	0.569380	+	0.822074i	$0.307183\pi$
$258$	−9.14900	−0.569592
$259$	−29.9301	−1.85977
$260$	15.9268	0.987739
$261$	−0.613775	−0.0379917
$262$	54.8708	3.38993
$263$	−6.82695	−0.420968	−0.210484	−	0.977597i	$-0.567504\pi$
$263$	−6.82695	−0.420968	−0.210484	+	0.977597i	$0.567504\pi$
$264$	87.2266	5.36843
$265$	−15.8247	−0.972104
$266$	53.7853	3.29779
$267$	−28.4429	−1.74068
$268$	61.6965	3.76871
$269$	−9.67854	−0.590111	−0.295056	−	0.955480i	$-0.595338\pi$
$269$	−9.67854	−0.590111	−0.295056	+	0.955480i	$0.595338\pi$
$270$	27.5272	1.67525
$271$	−9.09832	−0.552684	−0.276342	−	0.961059i	$-0.589122\pi$
$271$	−9.09832	−0.552684	−0.276342	+	0.961059i	$0.589122\pi$
$272$	−135.878	−8.23881
$273$	−6.72293	−0.406890
$274$	−23.0057	−1.38983
$275$	8.32249	0.501865
$276$	−22.0157	−1.32519
$277$	14.3772	0.863840	0.431920	−	0.901912i	$-0.357836\pi$
$277$	14.3772	0.863840	0.431920	+	0.901912i	$0.357836\pi$
$278$	23.6596	1.41901
$279$	−8.44749	−0.505738
$280$	−97.3899	−5.82016
$281$	−21.2557	−1.26801	−0.634005	−	0.773329i	$-0.718590\pi$
$281$	−21.2557	−1.26801	−0.634005	+	0.773329i	$0.718590\pi$
$282$	10.1847	0.606491
$283$	−4.22051	−0.250883	−0.125442	−	0.992101i	$-0.540035\pi$
$283$	−4.22051	−0.250883	−0.125442	+	0.992101i	$0.540035\pi$
$284$	−41.5195	−2.46373
$285$	32.1535	1.90461
$286$	10.7578	0.636119
$287$	−27.6763	−1.63368
$288$	−39.9589	−2.35460
$289$	31.8560	1.87388
$290$	−3.77714	−0.221801
$291$	−31.0344	−1.81927
$292$	43.8918	2.56857
$293$	8.75817	0.511658	0.255829	−	0.966722i	$-0.417652\pi$
$293$	8.75817	0.511658	0.255829	+	0.966722i	$0.417652\pi$
$294$	21.3945	1.24775
$295$	11.2915	0.657418
$296$	−101.739	−5.91346
$297$	13.9120	0.807254
$298$	23.4845	1.36042
$299$	−1.80157	−0.104187
$300$	−26.6455	−1.53838
$301$	5.16255	0.297565
$302$	10.3195	0.593823
$303$	14.7239	0.845868
$304$	113.452	6.50694
$305$	13.7032	0.784641
$306$	24.1769	1.38210
$307$	6.32483	0.360977	0.180489	−	0.983577i	$-0.442232\pi$
$307$	6.32483	0.360977	0.180489	+	0.983577i	$0.442232\pi$
$308$	−74.1813	−4.22687
$309$	−32.9382	−1.87379
$310$	−51.9854	−2.95257
$311$	−11.7475	−0.666142	−0.333071	−	0.942902i	$-0.608085\pi$
$311$	−11.7475	−0.666142	−0.333071	+	0.942902i	$0.608085\pi$
$312$	−22.8527	−1.29378
$313$	−5.95312	−0.336490	−0.168245	−	0.985745i	$-0.553810\pi$
$313$	−5.95312	−0.336490	−0.168245	+	0.985745i	$0.553810\pi$
$314$	−2.43235	−0.137265
$315$	10.7532	0.605873
$316$	28.9741	1.62992
$317$	−12.7796	−0.717776	−0.358888	−	0.933381i	$-0.616844\pi$
$317$	−12.7796	−0.717776	−0.358888	+	0.933381i	$0.616844\pi$
$318$	34.2215	1.91905
$319$	−1.90893	−0.106879
$320$	−141.723	−7.92254
$321$	25.0870	1.40022
$322$	16.6032	0.925258
$323$	−40.7927	−2.26977
$324$	−66.4239	−3.69022
$325$	−2.18043	−0.120948
$326$	−9.74277	−0.539602
$327$	11.4941	0.635627
$328$	−94.0780	−5.19459
$329$	−5.74698	−0.316841
$330$	−59.2687	−3.26263
$331$	−8.13377	−0.447072	−0.223536	−	0.974696i	$-0.571760\pi$
$331$	−8.13377	−0.447072	−0.223536	+	0.974696i	$0.571760\pi$
$332$	−57.5971	−3.16105
$333$	11.2334	0.615585
$334$	−20.3172	−1.11171
$335$	−27.8152	−1.51971
$336$	130.692	7.12982
$337$	−32.1383	−1.75068	−0.875342	−	0.483505i	$-0.839364\pi$
$337$	−32.1383	−1.75068	−0.875342	+	0.483505i	$0.839364\pi$
$338$	−2.81845	−0.153303
$339$	11.6467	0.632565
$340$	111.324	6.03738
$341$	−26.2729	−1.42276
$342$	−20.1867	−1.09157
$343$	10.8167	0.584045
$344$	17.5486	0.946159
$345$	9.92555	0.534374
$346$	56.4543	3.03500
$347$	−27.9837	−1.50224	−0.751122	−	0.660163i	$-0.770487\pi$
$347$	−27.9837	−1.50224	−0.751122	+	0.660163i	$0.770487\pi$
$348$	6.11167	0.327620
$349$	−32.5215	−1.74084	−0.870418	−	0.492314i	$-0.836151\pi$
$349$	−32.5215	−1.74084	−0.870418	+	0.492314i	$0.836151\pi$
$350$	20.0947	1.07411
$351$	−3.64483	−0.194547
$352$	−124.278	−6.62403
$353$	−12.0135	−0.639413	−0.319707	−	0.947517i	$-0.603584\pi$
$353$	−12.0135	−0.639413	−0.319707	+	0.947517i	$0.603584\pi$
$354$	−24.4183	−1.29782
$355$	18.7186	0.993480
$356$	82.2241	4.35787
$357$	−46.9913	−2.48704
$358$	−31.3987	−1.65947
$359$	−26.7014	−1.40924	−0.704622	−	0.709583i	$-0.748883\pi$
$359$	−26.7014	−1.40924	−0.704622	+	0.709583i	$0.748883\pi$
$360$	36.5524	1.92648
$361$	15.0602	0.792643
$362$	18.1944	0.956275
$363$	−7.33747	−0.385117
$364$	19.4349	1.01867
$365$	−19.7881	−1.03576
$366$	−29.6336	−1.54897
$367$	−11.8846	−0.620371	−0.310185	−	0.950676i	$-0.600391\pi$
$367$	−11.8846	−0.620371	−0.310185	+	0.950676i	$0.600391\pi$
$368$	35.0220	1.82565
$369$	10.3875	0.540751
$370$	69.1296	3.59387
$371$	−19.3104	−1.00254
$372$	84.1160	4.36121
$373$	2.03763	0.105504	0.0527522	−	0.998608i	$-0.483201\pi$
$373$	2.03763	0.105504	0.0527522	+	0.998608i	$0.483201\pi$
$374$	75.1935	3.88816
$375$	−15.5341	−0.802179
$376$	−19.5352	−1.00745
$377$	0.500124	0.0257577
$378$	33.5906	1.72771
$379$	−15.0902	−0.775132	−0.387566	−	0.921842i	$-0.626684\pi$
$379$	−15.0902	−0.775132	−0.387566	+	0.921842i	$0.626684\pi$
$380$	−92.9506	−4.76827
$381$	41.7306	2.13792
$382$	−1.33238	−0.0681706
$383$	−25.2379	−1.28960	−0.644798	−	0.764353i	$-0.723058\pi$
$383$	−25.2379	−1.28960	−0.644798	+	0.764353i	$0.723058\pi$
$384$	172.593	8.80759
$385$	33.4439	1.70446
$386$	21.0312	1.07046
$387$	−1.93761	−0.0984942
$388$	89.7157	4.55463
$389$	30.4883	1.54582	0.772908	−	0.634518i	$-0.218801\pi$
$389$	30.4883	1.54582	0.772908	+	0.634518i	$0.218801\pi$
$390$	15.5279	0.786288
$391$	−12.5924	−0.636827
$392$	−41.0367	−2.07267
$393$	40.0276	2.01913
$394$	−13.7893	−0.694696
$395$	−13.0627	−0.657255
$396$	27.8417	1.39910
$397$	−23.4826	−1.17856	−0.589278	−	0.807930i	$-0.700588\pi$
$397$	−23.4826	−1.17856	−0.589278	+	0.807930i	$0.700588\pi$
$398$	−40.6627	−2.03824
$399$	39.2358	1.96425
$400$	42.3869	2.11935
$401$	27.8080	1.38867	0.694334	−	0.719653i	$-0.255699\pi$
$401$	27.8080	1.38867	0.694334	+	0.719653i	$0.255699\pi$
$402$	60.1514	3.00008
$403$	6.88329	0.342881
$404$	−42.5646	−2.11767
$405$	29.9465	1.48805
$406$	−4.60912	−0.228747
$407$	34.9373	1.73178
$408$	−159.734	−7.90800
$409$	−33.1899	−1.64113	−0.820567	−	0.571551i	$-0.806342\pi$
$409$	−33.1899	−1.64113	−0.820567	+	0.571551i	$0.806342\pi$
$410$	63.9241	3.15698
$411$	−16.7824	−0.827816
$412$	95.2193	4.69112
$413$	13.7787	0.678003
$414$	−6.23150	−0.306261
$415$	25.9670	1.27467
$416$	32.5599	1.59638
$417$	17.2594	0.845198
$418$	−62.7834	−3.07084
$419$	9.64997	0.471432	0.235716	−	0.971822i	$-0.424257\pi$
$419$	9.64997	0.471432	0.235716	+	0.971822i	$0.424257\pi$
$420$	−107.075	−5.22471
$421$	−22.0905	−1.07662	−0.538311	−	0.842746i	$-0.680938\pi$
$421$	−22.0905	−1.07662	−0.538311	+	0.842746i	$0.680938\pi$
$422$	−65.0368	−3.16594
$423$	2.15696	0.104875
$424$	−65.6401	−3.18777
$425$	−15.2406	−0.739276
$426$	−40.4797	−1.96125
$427$	16.7215	0.809211
$428$	−72.5227	−3.50552
$429$	7.84766	0.378888
$430$	−11.9239	−0.575024
$431$	−33.5826	−1.61762	−0.808809	−	0.588072i	$-0.799887\pi$
$431$	−33.5826	−1.61762	−0.808809	+	0.588072i	$0.799887\pi$
$432$	70.8544	3.40899
$433$	−32.1954	−1.54721	−0.773606	−	0.633667i	$-0.781549\pi$
$433$	−32.1954	−1.54721	−0.773606	+	0.633667i	$0.781549\pi$
$434$	−63.4360	−3.04503
$435$	−2.75538	−0.132110
$436$	−33.2277	−1.59132
$437$	10.5142	0.502960
$438$	42.7926	2.04471
$439$	2.81509	0.134357	0.0671784	−	0.997741i	$-0.478600\pi$
$439$	2.81509	0.134357	0.0671784	+	0.997741i	$0.478600\pi$
$440$	113.683	5.41962
$441$	4.53101	0.215762
$442$	−19.7001	−0.937040
$443$	12.2841	0.583633	0.291817	−	0.956474i	$-0.405740\pi$
$443$	12.2841	0.583633	0.291817	+	0.956474i	$0.405740\pi$
$444$	−111.856	−5.30847
$445$	−37.0698	−1.75728
$446$	−20.5612	−0.973602
$447$	17.1317	0.810302
$448$	−172.939	−8.17062
$449$	7.65530	0.361276	0.180638	−	0.983550i	$-0.442184\pi$
$449$	7.65530	0.361276	0.180638	+	0.983550i	$0.442184\pi$
$450$	−7.54195	−0.355531
$451$	32.3065	1.52126
$452$	−33.6689	−1.58365
$453$	7.52799	0.353696
$454$	9.02509	0.423569
$455$	−8.76204	−0.410771
$456$	133.371	6.24567
$457$	29.3102	1.37107	0.685537	−	0.728038i	$-0.259567\pi$
$457$	29.3102	1.37107	0.685537	+	0.728038i	$0.259567\pi$
$458$	39.1818	1.83085
$459$	−25.4763	−1.18913
$460$	−28.6932	−1.33783
$461$	30.9376	1.44091	0.720454	−	0.693503i	$-0.243933\pi$
$461$	30.9376	1.44091	0.720454	+	0.693503i	$0.243933\pi$
$462$	−72.3236	−3.36480
$463$	−21.6172	−1.00463	−0.502317	−	0.864683i	$-0.667519\pi$
$463$	−21.6172	−1.00463	−0.502317	+	0.864683i	$0.667519\pi$
$464$	−9.72227	−0.451345
$465$	−37.9228	−1.75863
$466$	43.8421	2.03095
$467$	−29.6666	−1.37281	−0.686404	−	0.727221i	$-0.740812\pi$
$467$	−29.6666	−1.37281	−0.686404	+	0.727221i	$0.740812\pi$
$468$	−7.29432	−0.337180
$469$	−33.9419	−1.56729
$470$	13.2738	0.612275
$471$	−1.77437	−0.0817587
$472$	46.8367	2.15583
$473$	−6.02623	−0.277086
$474$	28.2485	1.29750
$475$	12.7252	0.583874
$476$	135.845	6.22642
$477$	7.24757	0.331843
$478$	−59.0857	−2.70252
$479$	−25.6307	−1.17110	−0.585548	−	0.810638i	$-0.699121\pi$
$479$	−25.6307	−1.17110	−0.585548	+	0.810638i	$0.699121\pi$
$480$	−179.385	−8.18777
$481$	−9.15331	−0.417355
$482$	−55.9879	−2.55018
$483$	12.1118	0.551107
$484$	21.2115	0.964158
$485$	−40.4474	−1.83662
$486$	−33.9422	−1.53965
$487$	17.4062	0.788751	0.394375	−	0.918949i	$-0.370961\pi$
$487$	17.4062	0.788751	0.394375	+	0.918949i	$0.370961\pi$
$488$	56.8401	2.57303
$489$	−7.10724	−0.321401
$490$	27.8836	1.25965
$491$	20.1827	0.910833	0.455417	−	0.890278i	$-0.349490\pi$
$491$	20.1827	0.910833	0.455417	+	0.890278i	$0.349490\pi$
$492$	−103.434	−4.66314
$493$	3.49572	0.157439
$494$	16.4488	0.740066
$495$	−12.5521	−0.564177
$496$	−133.809	−6.00821
$497$	22.8417	1.02459
$498$	−56.1547	−2.51635
$499$	11.5650	0.517721	0.258861	−	0.965915i	$-0.416653\pi$
$499$	11.5650	0.517721	0.258861	+	0.965915i	$0.416653\pi$
$500$	44.9067	2.00829
$501$	−14.8212	−0.662161
$502$	40.7314	1.81793
$503$	7.50140	0.334471	0.167235	−	0.985917i	$-0.446516\pi$
$503$	7.50140	0.334471	0.167235	+	0.985917i	$0.446516\pi$
$504$	44.6036	1.98680
$505$	19.1898	0.853935
$506$	−19.3808	−0.861582
$507$	−2.05603	−0.0913114
$508$	−120.637	−5.35239
$509$	−4.18536	−0.185513	−0.0927564	−	0.995689i	$-0.529568\pi$
$509$	−4.18536	−0.185513	−0.0927564	+	0.995689i	$0.529568\pi$
$510$	108.536	4.80605
$511$	−24.1468	−1.06819
$512$	−200.810	−8.87463
$513$	21.2716	0.939166
$514$	−51.4528	−2.26949
$515$	−42.9286	−1.89166
$516$	19.2938	0.849360
$517$	6.70843	0.295037
$518$	84.3565	3.70641
$519$	41.1828	1.80772
$520$	−29.7841	−1.30612
$521$	11.6023	0.508307	0.254153	−	0.967164i	$-0.418203\pi$
$521$	11.6023	0.508307	0.254153	+	0.967164i	$0.418203\pi$
$522$	1.72989	0.0757154
$523$	1.65002	0.0721505	0.0360752	−	0.999349i	$-0.488514\pi$
$523$	1.65002	0.0721505	0.0360752	+	0.999349i	$0.488514\pi$
$524$	−115.714	−5.05497
$525$	14.6589	0.639766
$526$	19.2414	0.838966
$527$	48.1122	2.09580
$528$	−152.556	−6.63916
$529$	−19.7544	−0.858885
$530$	44.6011	1.93735
$531$	−5.17141	−0.224420
$532$	−113.425	−4.91758
$533$	−8.46407	−0.366619
$534$	80.1649	3.46907
$535$	32.6961	1.41358
$536$	−115.376	−4.98349
$537$	−22.9050	−0.988423
$538$	27.2785	1.17606
$539$	14.0921	0.606989
$540$	−58.0505	−2.49810
$541$	27.3076	1.17405	0.587023	−	0.809570i	$-0.300300\pi$
$541$	27.3076	1.17405	0.587023	+	0.809570i	$0.300300\pi$
$542$	25.6432	1.10147
$543$	13.2726	0.569581
$544$	227.584	9.75758
$545$	14.9804	0.641688
$546$	18.9482	0.810909
$547$	20.9802	0.897047	0.448524	−	0.893771i	$-0.351950\pi$
$547$	20.9802	0.897047	0.448524	+	0.893771i	$0.351950\pi$
$548$	48.5154	2.07248
$549$	−6.27592	−0.267850
$550$	−23.4565	−1.00019
$551$	−2.91878	−0.124344
$552$	41.1707	1.75234
$553$	−15.9399	−0.677835
$554$	−40.5213	−1.72158
$555$	50.4292	2.14060
$556$	−49.8944	−2.11599
$557$	13.8289	0.585951	0.292975	−	0.956120i	$-0.405355\pi$
$557$	13.8289	0.585951	0.292975	+	0.956120i	$0.405355\pi$
$558$	23.8088	1.00791
$559$	1.57883	0.0667773
$560$	170.331	7.19782
$561$	54.8528	2.31589
$562$	59.9082	2.52708
$563$	38.9465	1.64140	0.820699	−	0.571361i	$-0.193584\pi$
$563$	38.9465	1.64140	0.820699	+	0.571361i	$0.193584\pi$
$564$	−21.4779	−0.904383
$565$	15.1793	0.638597
$566$	11.8953	0.499996
$567$	36.5427	1.53465
$568$	77.6438	3.25786
$569$	44.3309	1.85845	0.929223	−	0.369519i	$-0.120478\pi$
$569$	44.3309	1.85845	0.929223	+	0.369519i	$0.120478\pi$
$570$	−90.6229	−3.79577
$571$	31.0245	1.29834	0.649168	−	0.760645i	$-0.275117\pi$
$571$	31.0245	1.29834	0.649168	+	0.760645i	$0.275117\pi$
$572$	−22.6864	−0.948564
$573$	−0.971957	−0.0406041
$574$	78.0044	3.25584
$575$	3.92819	0.163817
$576$	64.9076	2.70448
$577$	29.7554	1.23873	0.619367	−	0.785102i	$-0.287389\pi$
$577$	29.7554	1.23873	0.619367	+	0.785102i	$0.287389\pi$
$578$	−89.7845	−3.73454
$579$	15.3420	0.637593
$580$	7.96538	0.330744
$581$	31.6867	1.31459
$582$	87.4690	3.62571
$583$	22.5409	0.933550
$584$	−82.0803	−3.39651
$585$	3.28857	0.135966
$586$	−24.6845	−1.01971
$587$	−43.8565	−1.81015	−0.905076	−	0.425249i	$-0.860186\pi$
$587$	−43.8565	−1.81015	−0.905076	+	0.425249i	$0.860186\pi$
$588$	−45.1176	−1.86062
$589$	−40.1717	−1.65524
$590$	−31.8246	−1.31020
$591$	−10.0591	−0.413778
$592$	177.938	7.31320
$593$	34.5572	1.41909	0.709547	−	0.704658i	$-0.248899\pi$
$593$	34.5572	1.41909	0.709547	+	0.704658i	$0.248899\pi$
$594$	−39.2102	−1.60881
$595$	−61.2441	−2.51076
$596$	−49.5251	−2.02863
$597$	−29.6630	−1.21403
$598$	5.07763	0.207640
$599$	5.81717	0.237683	0.118842	−	0.992913i	$-0.462082\pi$
$599$	5.81717	0.237683	0.118842	+	0.992913i	$0.462082\pi$
$600$	49.8287	2.03425
$601$	−11.5367	−0.470592	−0.235296	−	0.971924i	$-0.575606\pi$
$601$	−11.5367	−0.470592	−0.235296	+	0.971924i	$0.575606\pi$
$602$	−14.5504	−0.593030
$603$	12.7391	0.518776
$604$	−21.7623	−0.885494
$605$	−9.56297	−0.388790
$606$	−41.4987	−1.68577
$607$	−10.9174	−0.443123	−0.221561	−	0.975146i	$-0.571115\pi$
$607$	−10.9174	−0.443123	−0.221561	+	0.975146i	$0.571115\pi$
$608$	−190.023	−7.70645
$609$	−3.36230	−0.136247
$610$	−38.6217	−1.56375
$611$	−1.75756	−0.0711032
$612$	−50.9852	−2.06095
$613$	23.0836	0.932338	0.466169	−	0.884696i	$-0.345634\pi$
$613$	23.0836	0.932338	0.466169	+	0.884696i	$0.345634\pi$
$614$	−17.8262	−0.719408
$615$	46.6319	1.88038
$616$	138.723	5.58933
$617$	1.00000	0.0402585
$617$	1.00000	0.0402585
$618$	92.8348	3.73436
$619$	0.780752	0.0313811	0.0156905	−	0.999877i	$-0.495005\pi$
$619$	0.780752	0.0313811	0.0156905	+	0.999877i	$0.495005\pi$
$620$	109.629	4.40280
$621$	6.56641	0.263501
$622$	33.1099	1.32758
$623$	−45.2351	−1.81230
$624$	39.9686	1.60002
$625$	−31.1479	−1.24591
$626$	16.7786	0.670607
$627$	−45.7998	−1.82907
$628$	5.12943	0.204686
$629$	−63.9790	−2.55101
$630$	−30.3073	−1.20747
$631$	22.6809	0.902914	0.451457	−	0.892293i	$-0.350904\pi$
$631$	22.6809	0.902914	0.451457	+	0.892293i	$0.350904\pi$
$632$	−54.1834	−2.15530
$633$	−47.4436	−1.88571
$634$	36.0187	1.43049
$635$	54.3878	2.15831
$636$	−72.1677	−2.86164
$637$	−3.69202	−0.146283
$638$	5.38021	0.213005
$639$	−8.57294	−0.339140
$640$	224.941	8.89159
$641$	−13.6064	−0.537419	−0.268710	−	0.963221i	$-0.586597\pi$
$641$	−13.6064	−0.537419	−0.268710	+	0.963221i	$0.586597\pi$
$642$	−70.7065	−2.79056
$643$	33.9789	1.34000	0.669999	−	0.742362i	$-0.266295\pi$
$643$	33.9789	1.34000	0.669999	+	0.742362i	$0.266295\pi$
$644$	−35.0134	−1.37972
$645$	−8.69838	−0.342499
$646$	114.972	4.52352
$647$	36.0993	1.41921	0.709605	−	0.704600i	$-0.248873\pi$
$647$	36.0993	1.41921	0.709605	+	0.704600i	$0.248873\pi$
$648$	124.217	4.87969
$649$	−16.0838	−0.631344
$650$	6.14543	0.241044
$651$	−46.2759	−1.81369
$652$	20.5459	0.804641
$653$	18.2980	0.716055	0.358028	−	0.933711i	$-0.383449\pi$
$653$	18.2980	0.716055	0.358028	+	0.933711i	$0.383449\pi$
$654$	−32.3956	−1.26677
$655$	52.1682	2.03838
$656$	164.539	6.42417
$657$	9.06278	0.353573
$658$	16.1976	0.631447
$659$	−32.8157	−1.27832	−0.639159	−	0.769075i	$-0.720717\pi$
$659$	−32.8157	−1.27832	−0.639159	+	0.769075i	$0.720717\pi$
$660$	124.988	4.86516
$661$	6.93174	0.269613	0.134807	−	0.990872i	$-0.456959\pi$
$661$	6.93174	0.269613	0.134807	+	0.990872i	$0.456959\pi$
$662$	22.9246	0.890990
$663$	−14.3710	−0.558124
$664$	107.710	4.17996
$665$	51.1362	1.98298
$666$	−31.6607	−1.22683
$667$	−0.901007	−0.0348871
$668$	42.8457	1.65775
$669$	−14.9992	−0.579902
$670$	78.3957	3.02869
$671$	−19.5190	−0.753522
$672$	−218.898	−8.44416
$673$	17.5158	0.675184	0.337592	−	0.941292i	$-0.390388\pi$
$673$	17.5158	0.675184	0.337592	+	0.941292i	$0.390388\pi$
$674$	90.5801	3.48901
$675$	7.94730	0.305892
$676$	5.94365	0.228602
$677$	21.6850	0.833420	0.416710	−	0.909039i	$-0.363183\pi$
$677$	21.6850	0.833420	0.416710	+	0.909039i	$0.363183\pi$
$678$	−32.8258	−1.26067
$679$	−49.3566	−1.89413
$680$	−208.182	−7.98341
$681$	6.58370	0.252288
$682$	74.0487	2.83547
$683$	23.9056	0.914721	0.457361	−	0.889281i	$-0.348795\pi$
$683$	23.9056	0.914721	0.457361	+	0.889281i	$0.348795\pi$
$684$	42.5705	1.62772
$685$	−21.8726	−0.835711
$686$	−30.4862	−1.16397
$687$	28.5827	1.09050
$688$	−30.6919	−1.17012
$689$	−5.90555	−0.224984
$690$	−27.9747	−1.06498
$691$	8.21038	0.312338	0.156169	−	0.987730i	$-0.450086\pi$
$691$	8.21038	0.312338	0.156169	+	0.987730i	$0.450086\pi$
$692$	−119.053	−4.52572
$693$	−15.3170	−0.581843
$694$	78.8707	2.99389
$695$	22.4943	0.853259
$696$	−11.4292	−0.433222
$697$	−59.1613	−2.24090
$698$	91.6601	3.46939
$699$	31.9823	1.20968
$700$	−42.3765	−1.60168
$701$	−35.7243	−1.34929	−0.674644	−	0.738143i	$-0.735703\pi$
$701$	−35.7243	−1.34929	−0.674644	+	0.738143i	$0.735703\pi$
$702$	10.2728	0.387721
$703$	53.4198	2.01476
$704$	201.872	7.60833
$705$	9.68309	0.364686
$706$	33.8594	1.27431
$707$	23.4167	0.880675
$708$	51.4943	1.93528
$709$	−28.6737	−1.07686	−0.538432	−	0.842669i	$-0.680983\pi$
$709$	−28.6737	−1.07686	−0.538432	+	0.842669i	$0.680983\pi$
$710$	−52.7574	−1.97995
$711$	5.98258	0.224364
$712$	−153.764	−5.76254
$713$	−12.4007	−0.464411
$714$	132.443	4.95654
$715$	10.2279	0.382502
$716$	66.2148	2.47456
$717$	−43.1024	−1.60969
$718$	75.2564	2.80854
$719$	1.13547	0.0423460	0.0211730	−	0.999776i	$-0.493260\pi$
$719$	1.13547	0.0423460	0.0211730	+	0.999776i	$0.493260\pi$
$720$	−63.9288	−2.38249
$721$	−52.3843	−1.95089
$722$	−42.4464	−1.57969
$723$	−40.8425	−1.51895
$724$	−38.3690	−1.42597
$725$	−1.09049	−0.0404996
$726$	20.6803	0.767517
$727$	−35.0014	−1.29813	−0.649064	−	0.760734i	$-0.724839\pi$
$727$	−35.0014	−1.29813	−0.649064	+	0.760734i	$0.724839\pi$
$728$	−36.3445	−1.34702
$729$	8.76639	0.324681
$730$	55.7719	2.06421
$731$	11.0355	0.408164
$732$	62.4925	2.30979
$733$	−27.2796	−1.00759	−0.503797	−	0.863822i	$-0.668064\pi$
$733$	−27.2796	−1.00759	−0.503797	+	0.863822i	$0.668064\pi$
$734$	33.4961	1.23636
$735$	20.3408	0.750281
$736$	−58.6588	−2.16219
$737$	39.6203	1.45943
$738$	−29.2766	−1.07769
$739$	−4.84706	−0.178302	−0.0891510	−	0.996018i	$-0.528415\pi$
$739$	−4.84706	−0.178302	−0.0891510	+	0.996018i	$0.528415\pi$
$740$	−145.783	−5.35909
$741$	11.9992	0.440802
$742$	54.4253	1.99801
$743$	30.9289	1.13467	0.567335	−	0.823487i	$-0.307974\pi$
$743$	30.9289	1.13467	0.567335	+	0.823487i	$0.307974\pi$
$744$	−157.302	−5.76697
$745$	22.3279	0.818029
$746$	−5.74296	−0.210265
$747$	−11.8926	−0.435129
$748$	−158.571	−5.79793
$749$	39.8979	1.45784
$750$	43.7821	1.59870
$751$	14.4259	0.526408	0.263204	−	0.964740i	$-0.415221\pi$
$751$	14.4259	0.526408	0.263204	+	0.964740i	$0.415221\pi$
$752$	34.1664	1.24592
$753$	29.7131	1.08281
$754$	−1.40957	−0.0513337
$755$	9.81128	0.357069
$756$	−70.8371	−2.57632
$757$	24.1988	0.879520	0.439760	−	0.898115i	$-0.355064\pi$
$757$	24.1988	0.879520	0.439760	+	0.898115i	$0.355064\pi$
$758$	42.5310	1.54479
$759$	−14.1381	−0.513180
$760$	173.823	6.30523
$761$	37.4959	1.35922	0.679612	−	0.733571i	$-0.262148\pi$
$761$	37.4959	1.35922	0.679612	+	0.733571i	$0.262148\pi$
$762$	−117.616	−4.26077
$763$	18.2800	0.661782
$764$	2.80978	0.101654
$765$	22.9861	0.831065
$766$	71.1317	2.57009
$767$	4.21383	0.152153
$768$	−268.962	−9.70534
$769$	−9.94279	−0.358546	−0.179273	−	0.983799i	$-0.557375\pi$
$769$	−9.94279	−0.358546	−0.179273	+	0.983799i	$0.557375\pi$
$770$	−94.2598	−3.39689
$771$	−37.5343	−1.35176
$772$	−44.3514	−1.59624
$773$	−34.2275	−1.23108	−0.615539	−	0.788107i	$-0.711061\pi$
$773$	−34.2275	−1.23108	−0.615539	+	0.788107i	$0.711061\pi$
$774$	5.46105	0.196293
$775$	−15.0085	−0.539122
$776$	−167.774	−6.02273
$777$	61.5371	2.20763
$778$	−85.9296	−3.08072
$779$	49.3972	1.76984
$780$	−32.7459	−1.17249
$781$	−26.6630	−0.954078
$782$	35.4911	1.26916
$783$	−1.82287	−0.0651440
$784$	71.7717	2.56328
$785$	−2.31255	−0.0825384
$786$	−112.816	−4.02400
$787$	30.6405	1.09221	0.546107	−	0.837715i	$-0.316109\pi$
$787$	30.6405	1.09221	0.546107	+	0.837715i	$0.316109\pi$
$788$	29.0794	1.03591
$789$	14.0364	0.499709
$790$	36.8165	1.30987
$791$	18.5228	0.658594
$792$	−52.0657	−1.85007
$793$	5.11382	0.181597
$794$	66.1845	2.34880
$795$	32.5360	1.15393
$796$	85.7511	3.03937
$797$	−30.2476	−1.07143	−0.535713	−	0.844400i	$-0.679957\pi$
$797$	−30.2476	−1.07143	−0.535713	+	0.844400i	$0.679957\pi$
$798$	−110.584	−3.91463
$799$	−12.2848	−0.434606
$800$	−70.9945	−2.51003
$801$	16.9776	0.599875
$802$	−78.3756	−2.76754
$803$	28.1865	0.994680
$804$	−126.850	−4.47364
$805$	15.7854	0.556362
$806$	−19.4002	−0.683343
$807$	19.8993	0.700490
$808$	79.5984	2.80026
$809$	−16.2357	−0.570817	−0.285408	−	0.958406i	$-0.592129\pi$
$809$	−16.2357	−0.570817	−0.285408	+	0.958406i	$0.592129\pi$
$810$	−84.4027	−2.96561
$811$	1.26772	0.0445156	0.0222578	−	0.999752i	$-0.492915\pi$
$811$	1.26772	0.0445156	0.0222578	+	0.999752i	$0.492915\pi$
$812$	9.71988	0.341101
$813$	18.7064	0.656062
$814$	−98.4691	−3.45134
$815$	−9.26291	−0.324466
$816$	279.369	9.77985
$817$	−9.21421	−0.322365
$818$	93.5440	3.27069
$819$	4.01293	0.140223
$820$	−134.806	−4.70761
$821$	35.2625	1.23067	0.615335	−	0.788266i	$-0.289021\pi$
$821$	35.2625	1.23067	0.615335	+	0.788266i	$0.289021\pi$
$822$	47.3004	1.64979
$823$	17.2938	0.602823	0.301412	−	0.953494i	$-0.402542\pi$
$823$	17.2938	0.602823	0.301412	+	0.953494i	$0.402542\pi$
$824$	−178.066	−6.20322
$825$	−17.1113	−0.595738
$826$	−38.8344	−1.35122
$827$	47.7569	1.66067	0.830334	−	0.557265i	$-0.188149\pi$
$827$	47.7569	1.66067	0.830334	+	0.557265i	$0.188149\pi$
$828$	13.1412	0.456689
$829$	−44.6521	−1.55083	−0.775416	−	0.631451i	$-0.782460\pi$
$829$	−44.6521	−1.55083	−0.775416	+	0.631451i	$0.782460\pi$
$830$	−73.1867	−2.54035
$831$	−29.5598	−1.02542
$832$	−52.8889	−1.83359
$833$	−25.8061	−0.894129
$834$	−48.6448	−1.68443
$835$	−19.3165	−0.668476
$836$	132.400	4.57915
$837$	−25.0884	−0.867183
$838$	−27.1979	−0.939537
$839$	−22.3440	−0.771399	−0.385700	−	0.922624i	$-0.626040\pi$
$839$	−22.3440	−0.771399	−0.385700	+	0.922624i	$0.626040\pi$
$840$	200.236	6.90881
$841$	−28.7499	−0.991375
$842$	62.2608	2.14565
$843$	43.7024	1.50519
$844$	137.152	4.72097
$845$	−2.67963	−0.0921822
$846$	−6.07927	−0.209010
$847$	−11.6694	−0.400964
$848$	114.802	3.94233
$849$	8.67748	0.297810
$850$	42.9548	1.47334
$851$	16.4903	0.565281
$852$	85.3651	2.92456
$853$	1.80562	0.0618234	0.0309117	−	0.999522i	$-0.490159\pi$
$853$	1.80562	0.0618234	0.0309117	+	0.999522i	$0.490159\pi$
$854$	−47.1287	−1.61271
$855$	−19.1924	−0.656368
$856$	135.622	4.63546
$857$	−44.5770	−1.52272	−0.761361	−	0.648328i	$-0.775469\pi$
$857$	−44.5770	−1.52272	−0.761361	+	0.648328i	$0.775469\pi$
$858$	−22.1182	−0.755104
$859$	−34.8069	−1.18760	−0.593798	−	0.804614i	$-0.702372\pi$
$859$	−34.8069	−1.18760	−0.593798	+	0.804614i	$0.702372\pi$
$860$	25.1457	0.857460
$861$	56.9033	1.93926
$862$	94.6508	3.22382
$863$	−45.3024	−1.54211	−0.771055	−	0.636768i	$-0.780271\pi$
$863$	−45.3024	−1.54211	−0.771055	+	0.636768i	$0.780271\pi$
$864$	−118.675	−4.03741
$865$	53.6738	1.82496
$866$	90.7410	3.08351
$867$	−65.4968	−2.22439
$868$	133.776	4.54067
$869$	18.6067	0.631187
$870$	7.76590	0.263289
$871$	−10.3802	−0.351721
$872$	62.1378	2.10425
$873$	18.5245	0.626959
$874$	−29.6336	−1.00237
$875$	−24.7052	−0.835187
$876$	−90.2427	−3.04902
$877$	41.1676	1.39013	0.695065	−	0.718946i	$-0.255375\pi$
$877$	41.1676	1.39013	0.695065	+	0.718946i	$0.255375\pi$
$878$	−7.93418	−0.267766
$879$	−18.0070	−0.607362
$880$	−198.827	−6.70247
$881$	14.6397	0.493222	0.246611	−	0.969115i	$-0.420683\pi$
$881$	14.6397	0.493222	0.246611	+	0.969115i	$0.420683\pi$
$882$	−12.7704	−0.430002
$883$	35.2221	1.18532	0.592659	−	0.805454i	$-0.298078\pi$
$883$	35.2221	1.18532	0.592659	+	0.805454i	$0.298078\pi$
$884$	41.5444	1.39729
$885$	−23.2157	−0.780386
$886$	−34.6220	−1.16315
$887$	36.4542	1.22401	0.612005	−	0.790854i	$-0.290363\pi$
$887$	36.4542	1.22401	0.612005	+	0.790854i	$0.290363\pi$
$888$	209.178	7.01955
$889$	66.3676	2.22590
$890$	104.479	3.50216
$891$	−42.6562	−1.42904
$892$	43.3603	1.45181
$893$	10.2573	0.343248
$894$	−48.2848	−1.61489
$895$	−29.8522	−0.997850
$896$	274.488	9.17001
$897$	3.70407	0.123675
$898$	−21.5761	−0.720003
$899$	3.44250	0.114814
$900$	15.9048	0.530159
$901$	−41.2781	−1.37517
$902$	−91.0543	−3.03178
$903$	−10.6143	−0.353223
$904$	62.9629	2.09412
$905$	17.2982	0.575013
$906$	−21.2173	−0.704896
$907$	−37.9752	−1.26094	−0.630472	−	0.776212i	$-0.717139\pi$
$907$	−37.9752	−1.26094	−0.630472	+	0.776212i	$0.717139\pi$
$908$	−19.0325	−0.631614
$909$	−8.78875	−0.291504
$910$	24.6953	0.818643
$911$	59.3736	1.96714	0.983568	−	0.180539i	$-0.0577843\pi$
$911$	59.3736	1.96714	0.983568	+	0.180539i	$0.0577843\pi$
$912$	−233.261	−7.72405
$913$	−36.9878	−1.22412
$914$	−82.6094	−2.73247
$915$	−28.1741	−0.931406
$916$	−82.6281	−2.73011
$917$	63.6591	2.10221
$918$	71.8036	2.36987
$919$	37.5876	1.23990	0.619950	−	0.784641i	$-0.287153\pi$
$919$	37.5876	1.23990	0.619950	+	0.784641i	$0.287153\pi$
$920$	53.6580	1.76905
$921$	−13.0040	−0.428497
$922$	−87.1961	−2.87165
$923$	6.98551	0.229931
$924$	152.519	5.01750
$925$	19.9582	0.656220
$926$	60.9268	2.00218
$927$	19.6609	0.645748
$928$	16.2840	0.534547
$929$	−18.3653	−0.602544	−0.301272	−	0.953538i	$-0.597411\pi$
$929$	−18.3653	−0.602544	−0.301272	+	0.953538i	$0.597411\pi$
$930$	106.883	3.50485
$931$	21.5470	0.706175
$932$	−92.4559	−3.02849
$933$	24.1533	0.790743
$934$	83.6139	2.73593
$935$	71.4900	2.33797
$936$	13.6408	0.445864
$937$	14.6323	0.478017	0.239009	−	0.971017i	$-0.423178\pi$
$937$	14.6323	0.478017	0.239009	+	0.971017i	$0.423178\pi$
$938$	95.6636	3.12353
$939$	12.2398	0.399430
$940$	−27.9923	−0.913008
$941$	0.982057	0.0320141	0.0160071	−	0.999872i	$-0.494905\pi$
$941$	0.982057	0.0320141	0.0160071	+	0.999872i	$0.494905\pi$
$942$	5.00097	0.162940
$943$	15.2486	0.496562
$944$	−81.9157	−2.66613
$945$	31.9361	1.03888
$946$	16.9846	0.552218
$947$	18.5356	0.602325	0.301163	−	0.953573i	$-0.402625\pi$
$947$	18.5356	0.602325	0.301163	+	0.953573i	$0.402625\pi$
$948$	−59.5716	−1.93480
$949$	−7.38465	−0.239716
$950$	−35.8654	−1.16363
$951$	26.2753	0.852034
$952$	−254.037	−8.23340
$953$	54.8708	1.77744	0.888720	−	0.458451i	$-0.151596\pi$
$953$	54.8708	1.77744	0.888720	+	0.458451i	$0.151596\pi$
$954$	−20.4269	−0.661345
$955$	−1.26676	−0.0409913
$956$	124.602	4.02992
$957$	3.92480	0.126871
$958$	72.2388	2.33393
$959$	−26.6905	−0.861880
$960$	291.386	9.40443
$961$	16.3797	0.528378
$962$	25.7981	0.831766
$963$	−14.9745	−0.482546
$964$	118.069	3.80276
$965$	19.9954	0.643673
$966$	−34.1365	−1.09832
$967$	−27.9945	−0.900242	−0.450121	−	0.892967i	$-0.648619\pi$
$967$	−27.9945	−0.900242	−0.450121	+	0.892967i	$0.648619\pi$
$968$	−39.6667	−1.27494
$969$	83.8709	2.69432
$970$	113.999	3.66028
$971$	−30.8335	−0.989495	−0.494747	−	0.869037i	$-0.664739\pi$
$971$	−30.8335	−0.989495	−0.494747	+	0.869037i	$0.664739\pi$
$972$	71.5785	2.29588
$973$	27.4491	0.879977
$974$	−49.0585	−1.57194
$975$	4.48302	0.143572
$976$	−99.4113	−3.18208
$977$	−58.2110	−1.86233	−0.931167	−	0.364593i	$-0.881208\pi$
$977$	−58.2110	−1.86233	−0.931167	+	0.364593i	$0.881208\pi$
$978$	20.0314	0.640533
$979$	52.8028	1.68758
$980$	−58.8020	−1.87836
$981$	−6.86086	−0.219051
$982$	−56.8840	−1.81524
$983$	−40.5570	−1.29357	−0.646784	−	0.762673i	$-0.723887\pi$
$983$	−40.5570	−1.29357	−0.646784	+	0.762673i	$0.723887\pi$
$984$	193.427	6.16622
$985$	−13.1102	−0.417724
$986$	−9.85251	−0.313768
$987$	11.8159	0.376106
$988$	−34.6878	−1.10357
$989$	−2.84436	−0.0904455
$990$	35.3776	1.12437
$991$	−53.5449	−1.70091	−0.850454	−	0.526049i	$-0.823673\pi$
$991$	−53.5449	−1.70091	−0.850454	+	0.526049i	$0.823673\pi$
$992$	224.119	7.11579
$993$	16.7232	0.530696
$994$	−64.3781	−2.04195
$995$	−38.6600	−1.22560
$996$	118.421	3.75232
$997$	−18.5362	−0.587049	−0.293524	−	0.955952i	$-0.594828\pi$
$997$	−18.5362	−0.587049	−0.293524	+	0.955952i	$0.594828\pi$
$998$	−32.5954	−1.03179
$999$	33.3623	1.05554

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8021.2.a.c.1.1	✓	169

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8021.2.a.c.1.1	✓	169	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:	\( N \)	\(=\)	\( 8021 = 13 \cdot 617 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8021.a (trivial)

\(f(q)\)	\(=\)	\(q-2.81845 q^{2} -2.05603 q^{3} +5.94365 q^{4} -2.67963 q^{5} +5.79481 q^{6} -3.26986 q^{7} -11.1150 q^{8} +1.22725 q^{9} +O(q^{10})\)	\(q-2.81845 q^{2} -2.05603 q^{3} +5.94365 q^{4} -2.67963 q^{5} +5.79481 q^{6} -3.26986 q^{7} -11.1150 q^{8} +1.22725 q^{9} +7.55241 q^{10} +3.81690 q^{11} -12.2203 q^{12} -1.00000 q^{13} +9.21595 q^{14} +5.50940 q^{15} +19.4397 q^{16} -6.98971 q^{17} -3.45893 q^{18} +5.83611 q^{19} -15.9268 q^{20} +6.72293 q^{21} -10.7578 q^{22} +1.80157 q^{23} +22.8527 q^{24} +2.18043 q^{25} +2.81845 q^{26} +3.64483 q^{27} -19.4349 q^{28} -0.500124 q^{29} -15.5279 q^{30} -6.88329 q^{31} -32.5599 q^{32} -7.84766 q^{33} +19.7001 q^{34} +8.76204 q^{35} +7.29432 q^{36} +9.15331 q^{37} -16.4488 q^{38} +2.05603 q^{39} +29.7841 q^{40} +8.46407 q^{41} -18.9482 q^{42} -1.57883 q^{43} +22.6864 q^{44} -3.28857 q^{45} -5.07763 q^{46} +1.75756 q^{47} -39.9686 q^{48} +3.69202 q^{49} -6.14543 q^{50} +14.3710 q^{51} -5.94365 q^{52} +5.90555 q^{53} -10.2728 q^{54} -10.2279 q^{55} +36.3445 q^{56} -11.9992 q^{57} +1.40957 q^{58} -4.21383 q^{59} +32.7459 q^{60} -5.11382 q^{61} +19.4002 q^{62} -4.01293 q^{63} +52.8889 q^{64} +2.67963 q^{65} +22.1182 q^{66} +10.3802 q^{67} -41.5444 q^{68} -3.70407 q^{69} -24.6953 q^{70} -6.98551 q^{71} -13.6408 q^{72} +7.38465 q^{73} -25.7981 q^{74} -4.48302 q^{75} +34.6878 q^{76} -12.4808 q^{77} -5.79481 q^{78} +4.87480 q^{79} -52.0913 q^{80} -11.1756 q^{81} -23.8555 q^{82} -9.69052 q^{83} +39.9588 q^{84} +18.7298 q^{85} +4.44984 q^{86} +1.02827 q^{87} -42.4248 q^{88} +13.8339 q^{89} +9.26866 q^{90} +3.26986 q^{91} +10.7079 q^{92} +14.1522 q^{93} -4.95359 q^{94} -15.6386 q^{95} +66.9439 q^{96} +15.0944 q^{97} -10.4058 q^{98} +4.68428 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 169 q + 9 q^{2} + 9 q^{3} + 199 q^{4} + 12 q^{5} + 22 q^{6} + 36 q^{7} + 30 q^{8} + 198 q^{9}+O(q^{10}) \) 169 * q + 9 * q^2 + 9 * q^3 + 199 * q^4 + 12 * q^5 + 22 * q^6 + 36 * q^7 + 30 * q^8 + 198 * q^9	\( 169 q + 9 q^{2} + 9 q^{3} + 199 q^{4} + 12 q^{5} + 22 q^{6} + 36 q^{7} + 30 q^{8} + 198 q^{9} - 3 q^{10} + 59 q^{11} + 11 q^{12} - 169 q^{13} + 30 q^{14} + 50 q^{15} + 267 q^{16} + q^{17} + 53 q^{18} + 107 q^{19} + 48 q^{20} + 36 q^{21} + 14 q^{22} + 12 q^{23} + 78 q^{24} + 217 q^{25} - 9 q^{26} + 39 q^{27} + 99 q^{28} + 30 q^{29} - q^{30} + 106 q^{31} + 74 q^{32} + 16 q^{33} + 56 q^{34} + 46 q^{35} + 271 q^{36} + 73 q^{37} + 2 q^{38} - 9 q^{39} - 16 q^{40} + 52 q^{41} - 2 q^{42} + 64 q^{43} + 124 q^{44} + 84 q^{45} + 105 q^{46} + 55 q^{47} + 26 q^{48} + 257 q^{49} + 60 q^{50} + 117 q^{51} - 199 q^{52} + 7 q^{53} + 78 q^{54} - 4 q^{55} + 63 q^{56} + 51 q^{57} + 84 q^{58} + 98 q^{59} + 94 q^{60} + 32 q^{61} - 25 q^{62} + 128 q^{63} + 380 q^{64} - 12 q^{65} + 16 q^{66} + 170 q^{67} - 10 q^{68} + 55 q^{69} + 70 q^{70} + 124 q^{71} + 173 q^{72} + 81 q^{73} + 54 q^{74} + 120 q^{75} + 212 q^{76} + 20 q^{77} - 22 q^{78} + 92 q^{79} + 66 q^{80} + 265 q^{81} + 21 q^{82} + 62 q^{83} + 98 q^{84} + 139 q^{85} + 51 q^{86} - 33 q^{87} + 31 q^{88} + 58 q^{89} + 16 q^{90} - 36 q^{91} + 40 q^{92} + 37 q^{93} + 55 q^{94} + 23 q^{95} + 164 q^{96} + 78 q^{97} + 69 q^{98} + 307 q^{99}+O(q^{100}) \) 169 * q + 9 * q^2 + 9 * q^3 + 199 * q^4 + 12 * q^5 + 22 * q^6 + 36 * q^7 + 30 * q^8 + 198 * q^9 - 3 * q^10 + 59 * q^11 + 11 * q^12 - 169 * q^13 + 30 * q^14 + 50 * q^15 + 267 * q^16 + q^17 + 53 * q^18 + 107 * q^19 + 48 * q^20 + 36 * q^21 + 14 * q^22 + 12 * q^23 + 78 * q^24 + 217 * q^25 - 9 * q^26 + 39 * q^27 + 99 * q^28 + 30 * q^29 - q^30 + 106 * q^31 + 74 * q^32 + 16 * q^33 + 56 * q^34 + 46 * q^35 + 271 * q^36 + 73 * q^37 + 2 * q^38 - 9 * q^39 - 16 * q^40 + 52 * q^41 - 2 * q^42 + 64 * q^43 + 124 * q^44 + 84 * q^45 + 105 * q^46 + 55 * q^47 + 26 * q^48 + 257 * q^49 + 60 * q^50 + 117 * q^51 - 199 * q^52 + 7 * q^53 + 78 * q^54 - 4 * q^55 + 63 * q^56 + 51 * q^57 + 84 * q^58 + 98 * q^59 + 94 * q^60 + 32 * q^61 - 25 * q^62 + 128 * q^63 + 380 * q^64 - 12 * q^65 + 16 * q^66 + 170 * q^67 - 10 * q^68 + 55 * q^69 + 70 * q^70 + 124 * q^71 + 173 * q^72 + 81 * q^73 + 54 * q^74 + 120 * q^75 + 212 * q^76 + 20 * q^77 - 22 * q^78 + 92 * q^79 + 66 * q^80 + 265 * q^81 + 21 * q^82 + 62 * q^83 + 98 * q^84 + 139 * q^85 + 51 * q^86 - 33 * q^87 + 31 * q^88 + 58 * q^89 + 16 * q^90 - 36 * q^91 + 40 * q^92 + 37 * q^93 + 55 * q^94 + 23 * q^95 + 164 * q^96 + 78 * q^97 + 69 * q^98 + 307 * q^99

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