LMFDB - Embedded newform 6033.2.a.e.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6033,2,Mod(1,6033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6033, 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("6033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6033 = 3 \cdot 2011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6033.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:	$48.1737475394$
Analytic rank:	$0$
Dimension:	$97$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	6033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.77569 q^{2} +1.00000 q^{3} +5.70444 q^{4} -4.08383 q^{5} -2.77569 q^{6} +2.32651 q^{7} -10.2824 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.77569 q^{2} +1.00000 q^{3} +5.70444 q^{4} -4.08383 q^{5} -2.77569 q^{6} +2.32651 q^{7} -10.2824 q^{8} +1.00000 q^{9} +11.3354 q^{10} -2.73819 q^{11} +5.70444 q^{12} -0.956206 q^{13} -6.45766 q^{14} -4.08383 q^{15} +17.1318 q^{16} +5.05272 q^{17} -2.77569 q^{18} -1.73945 q^{19} -23.2960 q^{20} +2.32651 q^{21} +7.60038 q^{22} +4.18079 q^{23} -10.2824 q^{24} +11.6777 q^{25} +2.65413 q^{26} +1.00000 q^{27} +13.2714 q^{28} +4.88585 q^{29} +11.3354 q^{30} +3.41494 q^{31} -26.9878 q^{32} -2.73819 q^{33} -14.0248 q^{34} -9.50107 q^{35} +5.70444 q^{36} -6.66497 q^{37} +4.82816 q^{38} -0.956206 q^{39} +41.9915 q^{40} +6.69417 q^{41} -6.45766 q^{42} +6.76241 q^{43} -15.6199 q^{44} -4.08383 q^{45} -11.6046 q^{46} +3.39380 q^{47} +17.1318 q^{48} -1.58736 q^{49} -32.4136 q^{50} +5.05272 q^{51} -5.45462 q^{52} -1.86028 q^{53} -2.77569 q^{54} +11.1823 q^{55} -23.9221 q^{56} -1.73945 q^{57} -13.5616 q^{58} -14.6633 q^{59} -23.2960 q^{60} +3.04585 q^{61} -9.47881 q^{62} +2.32651 q^{63} +40.6460 q^{64} +3.90498 q^{65} +7.60038 q^{66} -9.48304 q^{67} +28.8229 q^{68} +4.18079 q^{69} +26.3720 q^{70} +8.47417 q^{71} -10.2824 q^{72} -8.74415 q^{73} +18.4999 q^{74} +11.6777 q^{75} -9.92258 q^{76} -6.37043 q^{77} +2.65413 q^{78} -15.4663 q^{79} -69.9634 q^{80} +1.00000 q^{81} -18.5809 q^{82} -3.42088 q^{83} +13.2714 q^{84} -20.6345 q^{85} -18.7703 q^{86} +4.88585 q^{87} +28.1552 q^{88} +13.8738 q^{89} +11.3354 q^{90} -2.22462 q^{91} +23.8491 q^{92} +3.41494 q^{93} -9.42013 q^{94} +7.10361 q^{95} -26.9878 q^{96} +13.8435 q^{97} +4.40601 q^{98} -2.73819 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 97 q + 12 q^{2} + 97 q^{3} + 120 q^{4} + 6 q^{5} + 12 q^{6} + 50 q^{7} + 30 q^{8} + 97 q^{9}+O(q^{10}) $ 97 * q + 12 * q^2 + 97 * q^3 + 120 * q^4 + 6 * q^5 + 12 * q^6 + 50 * q^7 + 30 * q^8 + 97 * q^9	\( 97 q + 12 q^{2} + 97 q^{3} + 120 q^{4} + 6 q^{5} + 12 q^{6} + 50 q^{7} + 30 q^{8} + 97 q^{9} + 35 q^{10} + 18 q^{11} + 120 q^{12} + 67 q^{13} - q^{14} + 6 q^{15} + 158 q^{16} + 25 q^{17} + 12 q^{18} + 51 q^{19} + 10 q^{20} + 50 q^{21} + 39 q^{22} + 87 q^{23} + 30 q^{24} + 149 q^{25} + 14 q^{26} + 97 q^{27} + 83 q^{28} + 23 q^{29} + 35 q^{30} + 72 q^{31} + 57 q^{32} + 18 q^{33} + 28 q^{34} + 45 q^{35} + 120 q^{36} + 72 q^{37} + 3 q^{38} + 67 q^{39} + 90 q^{40} + 5 q^{41} - q^{42} + 122 q^{43} + 11 q^{44} + 6 q^{45} + 56 q^{46} + 49 q^{47} + 158 q^{48} + 167 q^{49} + 13 q^{50} + 25 q^{51} + 128 q^{52} + 30 q^{53} + 12 q^{54} + 120 q^{55} - 21 q^{56} + 51 q^{57} + 37 q^{58} + 2 q^{59} + 10 q^{60} + 158 q^{61} + 17 q^{62} + 50 q^{63} + 212 q^{64} + q^{65} + 39 q^{66} + 77 q^{67} + 56 q^{68} + 87 q^{69} + 9 q^{70} + 38 q^{71} + 30 q^{72} + 82 q^{73} - 6 q^{74} + 149 q^{75} + 93 q^{76} + 49 q^{77} + 14 q^{78} + 134 q^{79} - 25 q^{80} + 97 q^{81} + 53 q^{82} + 69 q^{83} + 83 q^{84} + 72 q^{85} + 23 q^{87} + 107 q^{88} + 35 q^{90} + 84 q^{91} + 108 q^{92} + 72 q^{93} + 65 q^{94} + 89 q^{95} + 57 q^{96} + 65 q^{97} + 18 q^{99}+O(q^{100}) \) 97 * q + 12 * q^2 + 97 * q^3 + 120 * q^4 + 6 * q^5 + 12 * q^6 + 50 * q^7 + 30 * q^8 + 97 * q^9 + 35 * q^10 + 18 * q^11 + 120 * q^12 + 67 * q^13 - q^14 + 6 * q^15 + 158 * q^16 + 25 * q^17 + 12 * q^18 + 51 * q^19 + 10 * q^20 + 50 * q^21 + 39 * q^22 + 87 * q^23 + 30 * q^24 + 149 * q^25 + 14 * q^26 + 97 * q^27 + 83 * q^28 + 23 * q^29 + 35 * q^30 + 72 * q^31 + 57 * q^32 + 18 * q^33 + 28 * q^34 + 45 * q^35 + 120 * q^36 + 72 * q^37 + 3 * q^38 + 67 * q^39 + 90 * q^40 + 5 * q^41 - q^42 + 122 * q^43 + 11 * q^44 + 6 * q^45 + 56 * q^46 + 49 * q^47 + 158 * q^48 + 167 * q^49 + 13 * q^50 + 25 * q^51 + 128 * q^52 + 30 * q^53 + 12 * q^54 + 120 * q^55 - 21 * q^56 + 51 * q^57 + 37 * q^58 + 2 * q^59 + 10 * q^60 + 158 * q^61 + 17 * q^62 + 50 * q^63 + 212 * q^64 + q^65 + 39 * q^66 + 77 * q^67 + 56 * q^68 + 87 * q^69 + 9 * q^70 + 38 * q^71 + 30 * q^72 + 82 * q^73 - 6 * q^74 + 149 * q^75 + 93 * q^76 + 49 * q^77 + 14 * q^78 + 134 * q^79 - 25 * q^80 + 97 * q^81 + 53 * q^82 + 69 * q^83 + 83 * q^84 + 72 * q^85 + 23 * q^87 + 107 * q^88 + 35 * q^90 + 84 * q^91 + 108 * q^92 + 72 * q^93 + 65 * q^94 + 89 * q^95 + 57 * q^96 + 65 * q^97 + 18 * 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 $

$2$	−2.77569	−1.96271	−0.981354	−	0.192209i	$-0.938435\pi$
$2$	−2.77569	−1.96271	−0.981354	+	0.192209i	$0.938435\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	5.70444	2.85222
$5$	−4.08383	−1.82635	−0.913173	−	0.407573i	$-0.866375\pi$
$5$	−4.08383	−1.82635	−0.913173	+	0.407573i	$0.866375\pi$
$6$	−2.77569	−1.13317
$7$	2.32651	0.879338	0.439669	−	0.898160i	$-0.355096\pi$
$7$	2.32651	0.879338	0.439669	+	0.898160i	$0.355096\pi$
$8$	−10.2824	−3.63537
$9$	1.00000	0.333333
$10$	11.3354	3.58458
$11$	−2.73819	−0.825597	−0.412798	−	0.910822i	$-0.635449\pi$
$11$	−2.73819	−0.825597	−0.412798	+	0.910822i	$0.635449\pi$
$12$	5.70444	1.64673
$13$	−0.956206	−0.265204	−0.132602	−	0.991169i	$-0.542333\pi$
$13$	−0.956206	−0.265204	−0.132602	+	0.991169i	$0.542333\pi$
$14$	−6.45766	−1.72588
$15$	−4.08383	−1.05444
$16$	17.1318	4.28295
$17$	5.05272	1.22546	0.612732	−	0.790291i	$-0.290071\pi$
$17$	5.05272	1.22546	0.612732	+	0.790291i	$0.290071\pi$
$18$	−2.77569	−0.654236
$19$	−1.73945	−0.399057	−0.199528	−	0.979892i	$-0.563941\pi$
$19$	−1.73945	−0.399057	−0.199528	+	0.979892i	$0.563941\pi$
$20$	−23.2960	−5.20914
$21$	2.32651	0.507686
$22$	7.60038	1.62041
$23$	4.18079	0.871756	0.435878	−	0.900006i	$-0.356438\pi$
$23$	4.18079	0.871756	0.435878	+	0.900006i	$0.356438\pi$
$24$	−10.2824	−2.09888
$25$	11.6777	2.33554
$26$	2.65413	0.520518
$27$	1.00000	0.192450
$28$	13.2714	2.50807
$29$	4.88585	0.907279	0.453639	−	0.891185i	$-0.350125\pi$
$29$	4.88585	0.907279	0.453639	+	0.891185i	$0.350125\pi$
$30$	11.3354	2.06956
$31$	3.41494	0.613342	0.306671	−	0.951816i	$-0.400785\pi$
$31$	3.41494	0.613342	0.306671	+	0.951816i	$0.400785\pi$
$32$	−26.9878	−4.77081
$33$	−2.73819	−0.476659
$34$	−14.0248	−2.40523
$35$	−9.50107	−1.60597
$36$	5.70444	0.950741
$37$	−6.66497	−1.09571	−0.547857	−	0.836572i	$-0.684556\pi$
$37$	−6.66497	−1.09571	−0.547857	+	0.836572i	$0.684556\pi$
$38$	4.82816	0.783232
$39$	−0.956206	−0.153115
$40$	41.9915	6.63944
$41$	6.69417	1.04545	0.522727	−	0.852500i	$-0.324915\pi$
$41$	6.69417	1.04545	0.522727	+	0.852500i	$0.324915\pi$
$42$	−6.45766	−0.996439
$43$	6.76241	1.03126	0.515629	−	0.856812i	$-0.327558\pi$
$43$	6.76241	1.03126	0.515629	+	0.856812i	$0.327558\pi$
$44$	−15.6199	−2.35479
$45$	−4.08383	−0.608782
$46$	−11.6046	−1.71100
$47$	3.39380	0.495037	0.247518	−	0.968883i	$-0.420385\pi$
$47$	3.39380	0.495037	0.247518	+	0.968883i	$0.420385\pi$
$48$	17.1318	2.47276
$49$	−1.58736	−0.226765
$50$	−32.4136	−4.58398
$51$	5.05272	0.707522
$52$	−5.45462	−0.756420
$53$	−1.86028	−0.255530	−0.127765	−	0.991804i	$-0.540780\pi$
$53$	−1.86028	−0.255530	−0.127765	+	0.991804i	$0.540780\pi$
$54$	−2.77569	−0.377723
$55$	11.1823	1.50783
$56$	−23.9221	−3.19672
$57$	−1.73945	−0.230395
$58$	−13.5616	−1.78072
$59$	−14.6633	−1.90900	−0.954499	−	0.298215i	$-0.903609\pi$
$59$	−14.6633	−1.90900	−0.954499	+	0.298215i	$0.903609\pi$
$60$	−23.2960	−3.00750
$61$	3.04585	0.389982	0.194991	−	0.980805i	$-0.437532\pi$
$61$	3.04585	0.389982	0.194991	+	0.980805i	$0.437532\pi$
$62$	−9.47881	−1.20381
$63$	2.32651	0.293113
$64$	40.6460	5.08075
$65$	3.90498	0.484354
$66$	7.60038	0.935542
$67$	−9.48304	−1.15854	−0.579269	−	0.815137i	$-0.696662\pi$
$67$	−9.48304	−1.15854	−0.579269	+	0.815137i	$0.696662\pi$
$68$	28.8229	3.49530
$69$	4.18079	0.503308
$70$	26.3720	3.15206
$71$	8.47417	1.00570	0.502849	−	0.864374i	$-0.332285\pi$
$71$	8.47417	1.00570	0.502849	+	0.864374i	$0.332285\pi$
$72$	−10.2824	−1.21179
$73$	−8.74415	−1.02343	−0.511713	−	0.859157i	$-0.670989\pi$
$73$	−8.74415	−1.02343	−0.511713	+	0.859157i	$0.670989\pi$
$74$	18.4999	2.15057
$75$	11.6777	1.34842
$76$	−9.92258	−1.13820
$77$	−6.37043	−0.725978
$78$	2.65413	0.300521
$79$	−15.4663	−1.74009	−0.870046	−	0.492971i	$-0.835911\pi$
$79$	−15.4663	−1.74009	−0.870046	+	0.492971i	$0.835911\pi$
$80$	−69.9634	−7.82215
$81$	1.00000	0.111111
$82$	−18.5809	−2.05192
$83$	−3.42088	−0.375490	−0.187745	−	0.982218i	$-0.560118\pi$
$83$	−3.42088	−0.375490	−0.187745	+	0.982218i	$0.560118\pi$
$84$	13.2714	1.44803
$85$	−20.6345	−2.23812
$86$	−18.7703	−2.02406
$87$	4.88585	0.523818
$88$	28.1552	3.00135
$89$	13.8738	1.47062	0.735311	−	0.677730i	$-0.237036\pi$
$89$	13.8738	1.47062	0.735311	+	0.677730i	$0.237036\pi$
$90$	11.3354	1.19486
$91$	−2.22462	−0.233204
$92$	23.8491	2.48644
$93$	3.41494	0.354113
$94$	−9.42013	−0.971612
$95$	7.10361	0.728815
$96$	−26.9878	−2.75443
$97$	13.8435	1.40559	0.702796	−	0.711392i	$-0.251935\pi$
$97$	13.8435	1.40559	0.702796	+	0.711392i	$0.251935\pi$
$98$	4.40601	0.445074
$99$	−2.73819	−0.275199
$100$	66.6147	6.66147
$101$	−0.548237	−0.0545516	−0.0272758	−	0.999628i	$-0.508683\pi$
$101$	−0.548237	−0.0545516	−0.0272758	+	0.999628i	$0.508683\pi$
$102$	−14.0248	−1.38866
$103$	6.67617	0.657823	0.328911	−	0.944361i	$-0.393318\pi$
$103$	6.67617	0.657823	0.328911	+	0.944361i	$0.393318\pi$
$104$	9.83207	0.964114
$105$	−9.50107	−0.927210
$106$	5.16357	0.501530
$107$	−13.7636	−1.33058	−0.665290	−	0.746585i	$-0.731692\pi$
$107$	−13.7636	−1.33058	−0.665290	+	0.746585i	$0.731692\pi$
$108$	5.70444	0.548910
$109$	−10.0722	−0.964742	−0.482371	−	0.875967i	$-0.660224\pi$
$109$	−10.0722	−0.964742	−0.482371	+	0.875967i	$0.660224\pi$
$110$	−31.0387	−2.95942
$111$	−6.66497	−0.632611
$112$	39.8573	3.76616
$113$	−0.941776	−0.0885948	−0.0442974	−	0.999018i	$-0.514105\pi$
$113$	−0.941776	−0.0885948	−0.0442974	+	0.999018i	$0.514105\pi$
$114$	4.82816	0.452199
$115$	−17.0737	−1.59213
$116$	27.8710	2.58776
$117$	−0.956206	−0.0884013
$118$	40.7007	3.74680
$119$	11.7552	1.07760
$120$	41.9915	3.83328
$121$	−3.50229	−0.318390
$122$	−8.45434	−0.765420
$123$	6.69417	0.603593
$124$	19.4803	1.74939
$125$	−27.2706	−2.43915
$126$	−6.45766	−0.575294
$127$	−15.2536	−1.35354	−0.676771	−	0.736194i	$-0.736621\pi$
$127$	−15.2536	−1.35354	−0.676771	+	0.736194i	$0.736621\pi$
$128$	−58.8452	−5.20123
$129$	6.76241	0.595397
$130$	−10.8390	−0.950645
$131$	4.06563	0.355216	0.177608	−	0.984101i	$-0.443164\pi$
$131$	4.06563	0.355216	0.177608	+	0.984101i	$0.443164\pi$
$132$	−15.6199	−1.35954
$133$	−4.04684	−0.350906
$134$	26.3220	2.27387
$135$	−4.08383	−0.351480
$136$	−51.9540	−4.45502
$137$	−16.3179	−1.39413	−0.697064	−	0.717009i	$-0.745511\pi$
$137$	−16.3179	−1.39413	−0.697064	+	0.717009i	$0.745511\pi$
$138$	−11.6046	−0.987847
$139$	11.6177	0.985403	0.492702	−	0.870198i	$-0.336009\pi$
$139$	11.6177	0.985403	0.492702	+	0.870198i	$0.336009\pi$
$140$	−54.1983	−4.58060
$141$	3.39380	0.285810
$142$	−23.5216	−1.97389
$143$	2.61828	0.218951
$144$	17.1318	1.42765
$145$	−19.9530	−1.65700
$146$	24.2710	2.00869
$147$	−1.58736	−0.130923
$148$	−38.0200	−3.12522
$149$	−9.73767	−0.797741	−0.398870	−	0.917007i	$-0.630598\pi$
$149$	−9.73767	−0.797741	−0.398870	+	0.917007i	$0.630598\pi$
$150$	−32.4136	−2.64656
$151$	9.72349	0.791287	0.395643	−	0.918404i	$-0.370522\pi$
$151$	9.72349	0.791287	0.395643	+	0.918404i	$0.370522\pi$
$152$	17.8857	1.45072
$153$	5.05272	0.408488
$154$	17.6823	1.42488
$155$	−13.9460	−1.12017
$156$	−5.45462	−0.436719
$157$	6.54493	0.522342	0.261171	−	0.965293i	$-0.415891\pi$
$157$	6.54493	0.522342	0.261171	+	0.965293i	$0.415891\pi$
$158$	42.9296	3.41529
$159$	−1.86028	−0.147530
$160$	110.214	8.71314
$161$	9.72665	0.766567
$162$	−2.77569	−0.218079
$163$	23.0313	1.80395	0.901976	−	0.431785i	$-0.142116\pi$
$163$	23.0313	1.80395	0.901976	+	0.431785i	$0.142116\pi$
$164$	38.1865	2.98186
$165$	11.1823	0.870543
$166$	9.49529	0.736978
$167$	22.0812	1.70870	0.854348	−	0.519701i	$-0.173957\pi$
$167$	22.0812	1.70870	0.854348	+	0.519701i	$0.173957\pi$
$168$	−23.9221	−1.84563
$169$	−12.0857	−0.929667
$170$	57.2748	4.39278
$171$	−1.73945	−0.133019
$172$	38.5758	2.94138
$173$	−2.49723	−0.189861	−0.0949305	−	0.995484i	$-0.530263\pi$
$173$	−2.49723	−0.189861	−0.0949305	+	0.995484i	$0.530263\pi$
$174$	−13.5616	−1.02810
$175$	27.1682	2.05373
$176$	−46.9102	−3.53599
$177$	−14.6633	−1.10216
$178$	−38.5094	−2.88640
$179$	−8.29464	−0.619970	−0.309985	−	0.950741i	$-0.600324\pi$
$179$	−8.29464	−0.619970	−0.309985	+	0.950741i	$0.600324\pi$
$180$	−23.2960	−1.73638
$181$	−19.0154	−1.41340	−0.706700	−	0.707513i	$-0.749817\pi$
$181$	−19.0154	−1.41340	−0.706700	+	0.707513i	$0.749817\pi$
$182$	6.17485	0.457711
$183$	3.04585	0.225156
$184$	−42.9885	−3.16916
$185$	27.2186	2.00115
$186$	−9.47881	−0.695020
$187$	−13.8353	−1.01174
$188$	19.3597	1.41195
$189$	2.32651	0.169229
$190$	−19.7174	−1.43045
$191$	−2.19091	−0.158529	−0.0792643	−	0.996854i	$-0.525257\pi$
$191$	−2.19091	−0.158529	−0.0792643	+	0.996854i	$0.525257\pi$
$192$	40.6460	2.93337
$193$	23.2132	1.67092	0.835461	−	0.549549i	$-0.185201\pi$
$193$	23.2132	1.67092	0.835461	+	0.549549i	$0.185201\pi$
$194$	−38.4252	−2.75877
$195$	3.90498	0.279642
$196$	−9.05499	−0.646785
$197$	6.74285	0.480408	0.240204	−	0.970722i	$-0.422786\pi$
$197$	6.74285	0.480408	0.240204	+	0.970722i	$0.422786\pi$
$198$	7.60038	0.540135
$199$	22.4683	1.59273	0.796367	−	0.604814i	$-0.206753\pi$
$199$	22.4683	1.59273	0.796367	+	0.604814i	$0.206753\pi$
$200$	−120.074	−8.49055
$201$	−9.48304	−0.668882
$202$	1.52174	0.107069
$203$	11.3670	0.797804
$204$	28.8229	2.01801
$205$	−27.3379	−1.90936
$206$	−18.5310	−1.29111
$207$	4.18079	0.290585
$208$	−16.3815	−1.13585
$209$	4.76295	0.329460
$210$	26.3720	1.81984
$211$	14.5833	1.00396	0.501979	−	0.864880i	$-0.332606\pi$
$211$	14.5833	1.00396	0.501979	+	0.864880i	$0.332606\pi$
$212$	−10.6119	−0.728827
$213$	8.47417	0.580640
$214$	38.2035	2.61154
$215$	−27.6165	−1.88343
$216$	−10.2824	−0.699628
$217$	7.94489	0.539334
$218$	27.9573	1.89351
$219$	−8.74415	−0.590875
$220$	63.7890	4.30065
$221$	−4.83144	−0.324998
$222$	18.4999	1.24163
$223$	10.4363	0.698870	0.349435	−	0.936961i	$-0.386374\pi$
$223$	10.4363	0.698870	0.349435	+	0.936961i	$0.386374\pi$
$224$	−62.7873	−4.19515
$225$	11.6777	0.778513
$226$	2.61408	0.173886
$227$	20.8084	1.38110	0.690552	−	0.723283i	$-0.257368\pi$
$227$	20.8084	1.38110	0.690552	+	0.723283i	$0.257368\pi$
$228$	−9.92258	−0.657139
$229$	14.2109	0.939080	0.469540	−	0.882911i	$-0.344420\pi$
$229$	14.2109	0.939080	0.469540	+	0.882911i	$0.344420\pi$
$230$	47.3911	3.12488
$231$	−6.37043	−0.419144
$232$	−50.2381	−3.29830
$233$	22.4183	1.46867	0.734337	−	0.678785i	$-0.237493\pi$
$233$	22.4183	1.46867	0.734337	+	0.678785i	$0.237493\pi$
$234$	2.65413	0.173506
$235$	−13.8597	−0.904108
$236$	−83.6459	−5.44488
$237$	−15.4663	−1.00464
$238$	−32.6287	−2.11501
$239$	14.1302	0.914004	0.457002	−	0.889466i	$-0.348923\pi$
$239$	14.1302	0.914004	0.457002	+	0.889466i	$0.348923\pi$
$240$	−69.9634	−4.51612
$241$	16.4544	1.05992	0.529961	−	0.848022i	$-0.322207\pi$
$241$	16.4544	1.05992	0.529961	+	0.848022i	$0.322207\pi$
$242$	9.72126	0.624906
$243$	1.00000	0.0641500
$244$	17.3749	1.11231
$245$	6.48250	0.414152
$246$	−18.5809	−1.18468
$247$	1.66327	0.105831
$248$	−35.1137	−2.22972
$249$	−3.42088	−0.216789
$250$	75.6946	4.78734
$251$	9.67787	0.610862	0.305431	−	0.952214i	$-0.401199\pi$
$251$	9.67787	0.610862	0.305431	+	0.952214i	$0.401199\pi$
$252$	13.2714	0.836022
$253$	−11.4478	−0.719719
$254$	42.3394	2.65661
$255$	−20.6345	−1.29218
$256$	82.0438	5.12774
$257$	−18.7539	−1.16983	−0.584917	−	0.811093i	$-0.698873\pi$
$257$	−18.7539	−1.16983	−0.584917	+	0.811093i	$0.698873\pi$
$258$	−18.7703	−1.16859
$259$	−15.5061	−0.963503
$260$	22.2758	1.38148
$261$	4.88585	0.302426
$262$	−11.2849	−0.697185
$263$	18.5785	1.14560	0.572798	−	0.819696i	$-0.305858\pi$
$263$	18.5785	1.14560	0.572798	+	0.819696i	$0.305858\pi$
$264$	28.1552	1.73283
$265$	7.59709	0.466685
$266$	11.2328	0.688725
$267$	13.8738	0.849064
$268$	−54.0955	−3.30441
$269$	17.4955	1.06672	0.533359	−	0.845889i	$-0.320929\pi$
$269$	17.4955	1.06672	0.533359	+	0.845889i	$0.320929\pi$
$270$	11.3354	0.689853
$271$	−12.0433	−0.731576	−0.365788	−	0.930698i	$-0.619200\pi$
$271$	−12.0433	−0.731576	−0.365788	+	0.930698i	$0.619200\pi$
$272$	86.5621	5.24860
$273$	−2.22462	−0.134640
$274$	45.2933	2.73627
$275$	−31.9758	−1.92821
$276$	23.8491	1.43555
$277$	6.13440	0.368580	0.184290	−	0.982872i	$-0.441001\pi$
$277$	6.13440	0.368580	0.184290	+	0.982872i	$0.441001\pi$
$278$	−32.2472	−1.93406
$279$	3.41494	0.204447
$280$	97.6937	5.83831
$281$	−9.53343	−0.568717	−0.284358	−	0.958718i	$-0.591781\pi$
$281$	−9.53343	−0.568717	−0.284358	+	0.958718i	$0.591781\pi$
$282$	−9.42013	−0.560961
$283$	−21.4421	−1.27460	−0.637302	−	0.770615i	$-0.719949\pi$
$283$	−21.4421	−1.27460	−0.637302	+	0.770615i	$0.719949\pi$
$284$	48.3404	2.86848
$285$	7.10361	0.420782
$286$	−7.26752	−0.429738
$287$	15.5740	0.919306
$288$	−26.9878	−1.59027
$289$	8.52995	0.501762
$290$	55.3832	3.25222
$291$	13.8435	0.811519
$292$	−49.8805	−2.91904
$293$	−11.4097	−0.666563	−0.333282	−	0.942827i	$-0.608156\pi$
$293$	−11.4097	−0.666563	−0.333282	+	0.942827i	$0.608156\pi$
$294$	4.40601	0.256964
$295$	59.8824	3.48649
$296$	68.5318	3.98333
$297$	−2.73819	−0.158886
$298$	27.0287	1.56573
$299$	−3.99770	−0.231193
$300$	66.6147	3.84600
$301$	15.7328	0.906824
$302$	−26.9894	−1.55306
$303$	−0.548237	−0.0314954
$304$	−29.7999	−1.70914
$305$	−12.4388	−0.712241
$306$	−14.0248	−0.801743
$307$	7.26834	0.414826	0.207413	−	0.978253i	$-0.433496\pi$
$307$	7.26834	0.414826	0.207413	+	0.978253i	$0.433496\pi$
$308$	−36.3398	−2.07065
$309$	6.67617	0.379794
$310$	38.7099	2.19857
$311$	7.74549	0.439206	0.219603	−	0.975589i	$-0.429524\pi$
$311$	7.74549	0.439206	0.219603	+	0.975589i	$0.429524\pi$
$312$	9.83207	0.556632
$313$	−8.33629	−0.471195	−0.235598	−	0.971851i	$-0.575705\pi$
$313$	−8.33629	−0.471195	−0.235598	+	0.971851i	$0.575705\pi$
$314$	−18.1667	−1.02521
$315$	−9.50107	−0.535325
$316$	−88.2265	−4.96313
$317$	26.4511	1.48564	0.742821	−	0.669490i	$-0.233487\pi$
$317$	26.4511	1.48564	0.742821	+	0.669490i	$0.233487\pi$
$318$	5.16357	0.289558
$319$	−13.3784	−0.749047
$320$	−165.992	−9.27921
$321$	−13.7636	−0.768211
$322$	−26.9981	−1.50455
$323$	−8.78894	−0.489030
$324$	5.70444	0.316914
$325$	−11.1663	−0.619393
$326$	−63.9278	−3.54063
$327$	−10.0722	−0.556994
$328$	−68.8320	−3.80061
$329$	7.89571	0.435304
$330$	−31.0387	−1.70862
$331$	−23.7414	−1.30494	−0.652471	−	0.757813i	$-0.726268\pi$
$331$	−23.7414	−1.30494	−0.652471	+	0.757813i	$0.726268\pi$
$332$	−19.5142	−1.07098
$333$	−6.66497	−0.365238
$334$	−61.2906	−3.35367
$335$	38.7271	2.11589
$336$	39.8573	2.17439
$337$	−12.3743	−0.674071	−0.337036	−	0.941492i	$-0.609424\pi$
$337$	−12.3743	−0.674071	−0.337036	+	0.941492i	$0.609424\pi$
$338$	33.5461	1.82466
$339$	−0.941776	−0.0511502
$340$	−117.708	−6.38362
$341$	−9.35078	−0.506373
$342$	4.82816	0.261077
$343$	−19.9786	−1.07874
$344$	−69.5337	−3.74901
$345$	−17.0737	−0.919215
$346$	6.93154	0.372642
$347$	−8.52017	−0.457386	−0.228693	−	0.973499i	$-0.573445\pi$
$347$	−8.52017	−0.457386	−0.228693	+	0.973499i	$0.573445\pi$
$348$	27.8710	1.49404
$349$	−19.8990	−1.06517	−0.532585	−	0.846376i	$-0.678780\pi$
$349$	−19.8990	−1.06517	−0.532585	+	0.846376i	$0.678780\pi$
$350$	−75.4106	−4.03086
$351$	−0.956206	−0.0510385
$352$	73.8978	3.93876
$353$	20.2668	1.07869	0.539346	−	0.842084i	$-0.318671\pi$
$353$	20.2668	1.07869	0.539346	+	0.842084i	$0.318671\pi$
$354$	40.7007	2.16322
$355$	−34.6071	−1.83675
$356$	79.1424	4.19454
$357$	11.7552	0.622151
$358$	23.0233	1.21682
$359$	−11.2556	−0.594047	−0.297024	−	0.954870i	$-0.595994\pi$
$359$	−11.2556	−0.594047	−0.297024	+	0.954870i	$0.595994\pi$
$360$	41.9915	2.21315
$361$	−15.9743	−0.840754
$362$	52.7807	2.77409
$363$	−3.50229	−0.183822
$364$	−12.6902	−0.665149
$365$	35.7097	1.86913
$366$	−8.45434	−0.441916
$367$	11.4481	0.597585	0.298793	−	0.954318i	$-0.403416\pi$
$367$	11.4481	0.597585	0.298793	+	0.954318i	$0.403416\pi$
$368$	71.6245	3.73369
$369$	6.69417	0.348484
$370$	−75.5504	−3.92768
$371$	−4.32797	−0.224697
$372$	19.4803	1.01001
$373$	11.7326	0.607490	0.303745	−	0.952753i	$-0.401763\pi$
$373$	11.7326	0.607490	0.303745	+	0.952753i	$0.401763\pi$
$374$	38.4025	1.98575
$375$	−27.2706	−1.40825
$376$	−34.8964	−1.79964
$377$	−4.67187	−0.240614
$378$	−6.45766	−0.332146
$379$	−0.461152	−0.0236878	−0.0118439	−	0.999930i	$-0.503770\pi$
$379$	−0.461152	−0.0236878	−0.0118439	+	0.999930i	$0.503770\pi$
$380$	40.5222	2.07874
$381$	−15.2536	−0.781468
$382$	6.08128	0.311145
$383$	−26.0474	−1.33096	−0.665481	−	0.746415i	$-0.731774\pi$
$383$	−26.0474	−1.33096	−0.665481	+	0.746415i	$0.731774\pi$
$384$	−58.8452	−3.00293
$385$	26.0158	1.32589
$386$	−64.4326	−3.27953
$387$	6.76241	0.343753
$388$	78.9693	4.00906
$389$	19.7168	0.999682	0.499841	−	0.866117i	$-0.333392\pi$
$389$	19.7168	0.999682	0.499841	+	0.866117i	$0.333392\pi$
$390$	−10.8390	−0.548855
$391$	21.1244	1.06830
$392$	16.3218	0.824376
$393$	4.06563	0.205084
$394$	−18.7161	−0.942901
$395$	63.1617	3.17801
$396$	−15.6199	−0.784929
$397$	22.8455	1.14658	0.573292	−	0.819351i	$-0.305666\pi$
$397$	22.8455	1.14658	0.573292	+	0.819351i	$0.305666\pi$
$398$	−62.3649	−3.12607
$399$	−4.04684	−0.202595
$400$	200.060	10.0030
$401$	7.88291	0.393654	0.196827	−	0.980438i	$-0.436936\pi$
$401$	7.88291	0.393654	0.196827	+	0.980438i	$0.436936\pi$
$402$	26.3220	1.31282
$403$	−3.26539	−0.162661
$404$	−3.12739	−0.155593
$405$	−4.08383	−0.202927
$406$	−31.5511	−1.56586
$407$	18.2500	0.904619
$408$	−51.9540	−2.57211
$409$	−2.57947	−0.127547	−0.0637734	−	0.997964i	$-0.520313\pi$
$409$	−2.57947	−0.127547	−0.0637734	+	0.997964i	$0.520313\pi$
$410$	75.8814	3.74751
$411$	−16.3179	−0.804901
$412$	38.0838	1.87626
$413$	−34.1143	−1.67865
$414$	−11.6046	−0.570334
$415$	13.9703	0.685775
$416$	25.8059	1.26524
$417$	11.6177	0.568923
$418$	−13.2205	−0.646634
$419$	35.0191	1.71079	0.855397	−	0.517973i	$-0.173313\pi$
$419$	35.0191	1.71079	0.855397	+	0.517973i	$0.173313\pi$
$420$	−54.1983	−2.64461
$421$	−21.0346	−1.02516	−0.512582	−	0.858638i	$-0.671311\pi$
$421$	−21.0346	−1.02516	−0.512582	+	0.858638i	$0.671311\pi$
$422$	−40.4788	−1.97047
$423$	3.39380	0.165012
$424$	19.1281	0.928945
$425$	59.0041	2.86212
$426$	−23.5216	−1.13963
$427$	7.08621	0.342926
$428$	−78.5138	−3.79511
$429$	2.61828	0.126412
$430$	76.6549	3.69663
$431$	−11.0733	−0.533380	−0.266690	−	0.963782i	$-0.585930\pi$
$431$	−11.0733	−0.533380	−0.266690	+	0.963782i	$0.585930\pi$
$432$	17.1318	0.824254
$433$	−9.10843	−0.437723	−0.218862	−	0.975756i	$-0.570234\pi$
$433$	−9.10843	−0.437723	−0.218862	+	0.975756i	$0.570234\pi$
$434$	−22.0525	−1.05856
$435$	−19.9530	−0.956672
$436$	−57.4563	−2.75166
$437$	−7.27227	−0.347880
$438$	24.2710	1.15972
$439$	9.32099	0.444867	0.222433	−	0.974948i	$-0.428600\pi$
$439$	9.32099	0.444867	0.222433	+	0.974948i	$0.428600\pi$
$440$	−114.981	−5.48150
$441$	−1.58736	−0.0755885
$442$	13.4106	0.637875
$443$	23.4776	1.11545	0.557727	−	0.830024i	$-0.311674\pi$
$443$	23.4776	1.11545	0.557727	+	0.830024i	$0.311674\pi$
$444$	−38.0200	−1.80435
$445$	−56.6584	−2.68586
$446$	−28.9681	−1.37168
$447$	−9.73767	−0.460576
$448$	94.5633	4.46770
$449$	3.00302	0.141721	0.0708605	−	0.997486i	$-0.477425\pi$
$449$	3.00302	0.141721	0.0708605	+	0.997486i	$0.477425\pi$
$450$	−32.4136	−1.52799
$451$	−18.3299	−0.863123
$452$	−5.37231	−0.252692
$453$	9.72349	0.456850
$454$	−57.7577	−2.71070
$455$	9.08498	0.425910
$456$	17.8857	0.837573
$457$	−6.33233	−0.296214	−0.148107	−	0.988971i	$-0.547318\pi$
$457$	−6.33233	−0.296214	−0.148107	+	0.988971i	$0.547318\pi$
$458$	−39.4449	−1.84314
$459$	5.05272	0.235841
$460$	−97.3957	−4.54110
$461$	13.3402	0.621314	0.310657	−	0.950522i	$-0.399451\pi$
$461$	13.3402	0.621314	0.310657	+	0.950522i	$0.399451\pi$
$462$	17.6823	0.822657
$463$	34.7712	1.61596	0.807978	−	0.589212i	$-0.200562\pi$
$463$	34.7712	1.61596	0.807978	+	0.589212i	$0.200562\pi$
$464$	83.7033	3.88583
$465$	−13.9460	−0.646733
$466$	−62.2263	−2.88258
$467$	−33.4049	−1.54579	−0.772896	−	0.634532i	$-0.781193\pi$
$467$	−33.4049	−1.54579	−0.772896	+	0.634532i	$0.781193\pi$
$468$	−5.45462	−0.252140
$469$	−22.0624	−1.01875
$470$	38.4702	1.77450
$471$	6.54493	0.301574
$472$	150.774	6.93991
$473$	−18.5168	−0.851403
$474$	42.9296	1.97182
$475$	−20.3127	−0.932012
$476$	67.0568	3.07354
$477$	−1.86028	−0.0851765
$478$	−39.2209	−1.79392
$479$	−38.9711	−1.78064	−0.890318	−	0.455340i	$-0.849518\pi$
$479$	−38.9711	−1.78064	−0.890318	+	0.455340i	$0.849518\pi$
$480$	110.214	5.03054
$481$	6.37309	0.290588
$482$	−45.6723	−2.08032
$483$	9.72665	0.442578
$484$	−19.9786	−0.908119
$485$	−56.5344	−2.56710
$486$	−2.77569	−0.125908
$487$	32.1409	1.45644	0.728222	−	0.685342i	$-0.240347\pi$
$487$	32.1409	1.45644	0.728222	+	0.685342i	$0.240347\pi$
$488$	−31.3186	−1.41773
$489$	23.0313	1.04151
$490$	−17.9934	−0.812859
$491$	7.99020	0.360593	0.180296	−	0.983612i	$-0.442294\pi$
$491$	7.99020	0.360593	0.180296	+	0.983612i	$0.442294\pi$
$492$	38.1865	1.72158
$493$	24.6868	1.11184
$494$	−4.61672	−0.207716
$495$	11.1823	0.502608
$496$	58.5041	2.62691
$497$	19.7152	0.884349
$498$	9.49529	0.425494
$499$	−29.6416	−1.32694	−0.663470	−	0.748203i	$-0.730917\pi$
$499$	−29.6416	−1.32694	−0.663470	+	0.748203i	$0.730917\pi$
$500$	−155.563	−6.95701
$501$	22.0812	0.986516
$502$	−26.8628	−1.19894
$503$	−7.61840	−0.339688	−0.169844	−	0.985471i	$-0.554326\pi$
$503$	−7.61840	−0.339688	−0.169844	+	0.985471i	$0.554326\pi$
$504$	−23.9221	−1.06557
$505$	2.23891	0.0996301
$506$	31.7756	1.41260
$507$	−12.0857	−0.536743
$508$	−87.0136	−3.86060
$509$	12.7845	0.566661	0.283330	−	0.959022i	$-0.408561\pi$
$509$	12.7845	0.566661	0.283330	+	0.959022i	$0.408561\pi$
$510$	57.2748	2.53617
$511$	−20.3433	−0.899937
$512$	−110.038	−4.86302
$513$	−1.73945	−0.0767985
$514$	52.0549	2.29604
$515$	−27.2644	−1.20141
$516$	38.5758	1.69820
$517$	−9.29289	−0.408701
$518$	43.0401	1.89108
$519$	−2.49723	−0.109616
$520$	−40.1525	−1.76081
$521$	0.515321	0.0225766	0.0112883	−	0.999936i	$-0.496407\pi$
$521$	0.515321	0.0225766	0.0112883	+	0.999936i	$0.496407\pi$
$522$	−13.5616	−0.593575
$523$	23.2678	1.01743	0.508715	−	0.860935i	$-0.330121\pi$
$523$	23.2678	1.01743	0.508715	+	0.860935i	$0.330121\pi$
$524$	23.1922	1.01315
$525$	27.1682	1.18572
$526$	−51.5680	−2.24847
$527$	17.2547	0.751628
$528$	−46.9102	−2.04150
$529$	−5.52097	−0.240042
$530$	−21.0871	−0.915967
$531$	−14.6633	−0.636332
$532$	−23.0850	−1.00086
$533$	−6.40100	−0.277258
$534$	−38.5094	−1.66646
$535$	56.2083	2.43010
$536$	97.5082	4.21171
$537$	−8.29464	−0.357940
$538$	−48.5620	−2.09366
$539$	4.34649	0.187217
$540$	−23.2960	−1.00250
$541$	3.54982	0.152619	0.0763094	−	0.997084i	$-0.475686\pi$
$541$	3.54982	0.152619	0.0763094	+	0.997084i	$0.475686\pi$
$542$	33.4283	1.43587
$543$	−19.0154	−0.816027
$544$	−136.362	−5.84645
$545$	41.1332	1.76195
$546$	6.17485	0.264259
$547$	−28.2574	−1.20820	−0.604100	−	0.796909i	$-0.706467\pi$
$547$	−28.2574	−1.20820	−0.604100	+	0.796909i	$0.706467\pi$
$548$	−93.0843	−3.97636
$549$	3.04585	0.129994
$550$	88.7548	3.78452
$551$	−8.49867	−0.362056
$552$	−42.9885	−1.82971
$553$	−35.9824	−1.53013
$554$	−17.0272	−0.723416
$555$	27.2186	1.15537
$556$	66.2727	2.81059
$557$	25.9123	1.09794	0.548969	−	0.835843i	$-0.315020\pi$
$557$	25.9123	1.09794	0.548969	+	0.835843i	$0.315020\pi$
$558$	−9.47881	−0.401270
$559$	−6.46625	−0.273493
$560$	−162.770	−6.87831
$561$	−13.8353	−0.584128
$562$	26.4618	1.11622
$563$	−27.3503	−1.15268	−0.576339	−	0.817210i	$-0.695519\pi$
$563$	−27.3503	−1.15268	−0.576339	+	0.817210i	$0.695519\pi$
$564$	19.3597	0.815192
$565$	3.84605	0.161805
$566$	59.5167	2.50167
$567$	2.32651	0.0977042
$568$	−87.1346	−3.65609
$569$	17.6469	0.739796	0.369898	−	0.929072i	$-0.379393\pi$
$569$	17.6469	0.739796	0.369898	+	0.929072i	$0.379393\pi$
$570$	−19.7174	−0.825872
$571$	44.8612	1.87738	0.938692	−	0.344758i	$-0.112039\pi$
$571$	44.8612	1.87738	0.938692	+	0.344758i	$0.112039\pi$
$572$	14.9358	0.624498
$573$	−2.19091	−0.0915265
$574$	−43.2287	−1.80433
$575$	48.8220	2.03602
$576$	40.6460	1.69358
$577$	−4.67134	−0.194470	−0.0972352	−	0.995261i	$-0.531000\pi$
$577$	−4.67134	−0.194470	−0.0972352	+	0.995261i	$0.531000\pi$
$578$	−23.6765	−0.984812
$579$	23.2132	0.964708
$580$	−113.821	−4.72615
$581$	−7.95870	−0.330183
$582$	−38.4252	−1.59277
$583$	5.09382	0.210964
$584$	89.9107	3.72053
$585$	3.90498	0.161451
$586$	31.6698	1.30827
$587$	38.0493	1.57046	0.785232	−	0.619201i	$-0.212544\pi$
$587$	38.0493	1.57046	0.785232	+	0.619201i	$0.212544\pi$
$588$	−9.05499	−0.373422
$589$	−5.94011	−0.244758
$590$	−166.215	−6.84296
$591$	6.74285	0.277364
$592$	−114.183	−4.69289
$593$	−23.2712	−0.955632	−0.477816	−	0.878460i	$-0.658571\pi$
$593$	−23.2712	−0.955632	−0.477816	+	0.878460i	$0.658571\pi$
$594$	7.60038	0.311847
$595$	−48.0062	−1.96806
$596$	−55.5480	−2.27533
$597$	22.4683	0.919565
$598$	11.0964	0.453764
$599$	−34.6518	−1.41584	−0.707918	−	0.706295i	$-0.750365\pi$
$599$	−34.6518	−1.41584	−0.707918	+	0.706295i	$0.750365\pi$
$600$	−120.074	−4.90202
$601$	40.7468	1.66210	0.831048	−	0.556201i	$-0.187742\pi$
$601$	40.7468	1.66210	0.831048	+	0.556201i	$0.187742\pi$
$602$	−43.6694	−1.77983
$603$	−9.48304	−0.386179
$604$	55.4671	2.25693
$605$	14.3028	0.581490
$606$	1.52174	0.0618163
$607$	37.2495	1.51191	0.755955	−	0.654623i	$-0.227173\pi$
$607$	37.2495	1.51191	0.755955	+	0.654623i	$0.227173\pi$
$608$	46.9438	1.90382
$609$	11.3670	0.460613
$610$	34.5261	1.39792
$611$	−3.24517	−0.131286
$612$	28.8229	1.16510
$613$	10.9012	0.440296	0.220148	−	0.975466i	$-0.429346\pi$
$613$	10.9012	0.440296	0.220148	+	0.975466i	$0.429346\pi$
$614$	−20.1747	−0.814183
$615$	−27.3379	−1.10237
$616$	65.5032	2.63920
$617$	−0.836722	−0.0336852	−0.0168426	−	0.999858i	$-0.505361\pi$
$617$	−0.836722	−0.0336852	−0.0168426	+	0.999858i	$0.505361\pi$
$618$	−18.5310	−0.745425
$619$	−9.55828	−0.384180	−0.192090	−	0.981377i	$-0.561527\pi$
$619$	−9.55828	−0.384180	−0.192090	+	0.981377i	$0.561527\pi$
$620$	−79.5545	−3.19498
$621$	4.18079	0.167769
$622$	−21.4991	−0.862034
$623$	32.2776	1.29317
$624$	−16.3815	−0.655786
$625$	52.9800	2.11920
$626$	23.1389	0.924818
$627$	4.76295	0.190214
$628$	37.3352	1.48984
$629$	−33.6762	−1.34276
$630$	26.3720	1.05069
$631$	−18.2013	−0.724581	−0.362290	−	0.932065i	$-0.618005\pi$
$631$	−18.2013	−0.724581	−0.362290	+	0.932065i	$0.618005\pi$
$632$	159.030	6.32588
$633$	14.5833	0.579635
$634$	−73.4200	−2.91588
$635$	62.2933	2.47204
$636$	−10.6119	−0.420789
$637$	1.51784	0.0601390
$638$	37.1343	1.47016
$639$	8.47417	0.335233
$640$	240.314	9.49924
$641$	−36.3364	−1.43520	−0.717601	−	0.696455i	$-0.754760\pi$
$641$	−36.3364	−1.43520	−0.717601	+	0.696455i	$0.754760\pi$
$642$	38.2035	1.50777
$643$	19.8436	0.782557	0.391278	−	0.920272i	$-0.372033\pi$
$643$	19.8436	0.782557	0.391278	+	0.920272i	$0.372033\pi$
$644$	55.4851	2.18642
$645$	−27.6165	−1.08740
$646$	24.3953	0.959822
$647$	25.6294	1.00759	0.503797	−	0.863822i	$-0.331936\pi$
$647$	25.6294	1.00759	0.503797	+	0.863822i	$0.331936\pi$
$648$	−10.2824	−0.403930
$649$	40.1509	1.57606
$650$	30.9941	1.21569
$651$	7.94489	0.311385
$652$	131.381	5.14527
$653$	39.3662	1.54052	0.770258	−	0.637732i	$-0.220127\pi$
$653$	39.3662	1.54052	0.770258	+	0.637732i	$0.220127\pi$
$654$	27.9573	1.09322
$655$	−16.6034	−0.648747
$656$	114.683	4.47762
$657$	−8.74415	−0.341142
$658$	−21.9160	−0.854375
$659$	13.0830	0.509640	0.254820	−	0.966988i	$-0.417984\pi$
$659$	13.0830	0.509640	0.254820	+	0.966988i	$0.417984\pi$
$660$	63.7890	2.48298
$661$	18.3325	0.713052	0.356526	−	0.934285i	$-0.383961\pi$
$661$	18.3325	0.713052	0.356526	+	0.934285i	$0.383961\pi$
$662$	65.8986	2.56122
$663$	−4.83144	−0.187637
$664$	35.1748	1.36505
$665$	16.5266	0.640875
$666$	18.4999	0.716856
$667$	20.4267	0.790925
$668$	125.961	4.87358
$669$	10.4363	0.403493
$670$	−107.494	−4.15287
$671$	−8.34014	−0.321968
$672$	−62.7873	−2.42207
$673$	44.3054	1.70785	0.853924	−	0.520398i	$-0.174216\pi$
$673$	44.3054	1.70785	0.853924	+	0.520398i	$0.174216\pi$
$674$	34.3472	1.32301
$675$	11.6777	0.449474
$676$	−68.9420	−2.65162
$677$	−30.7235	−1.18080	−0.590399	−	0.807111i	$-0.701030\pi$
$677$	−30.7235	−1.18080	−0.590399	+	0.807111i	$0.701030\pi$
$678$	2.61408	0.100393
$679$	32.2070	1.23599
$680$	212.171	8.13640
$681$	20.8084	0.797381
$682$	25.9548	0.993862
$683$	30.5279	1.16812	0.584059	−	0.811711i	$-0.301464\pi$
$683$	30.5279	1.16812	0.584059	+	0.811711i	$0.301464\pi$
$684$	−9.92258	−0.379399
$685$	66.6394	2.54616
$686$	55.4543	2.11725
$687$	14.2109	0.542178
$688$	115.852	4.41683
$689$	1.77881	0.0677674
$690$	47.3911	1.80415
$691$	−3.84677	−0.146338	−0.0731690	−	0.997320i	$-0.523311\pi$
$691$	−3.84677	−0.146338	−0.0731690	+	0.997320i	$0.523311\pi$
$692$	−14.2453	−0.541526
$693$	−6.37043	−0.241993
$694$	23.6493	0.897716
$695$	−47.4449	−1.79969
$696$	−50.2381	−1.90427
$697$	33.8237	1.28117
$698$	55.2335	2.09062
$699$	22.4183	0.847939
$700$	154.980	5.85768
$701$	−20.4557	−0.772599	−0.386300	−	0.922373i	$-0.626247\pi$
$701$	−20.4557	−0.772599	−0.386300	+	0.922373i	$0.626247\pi$
$702$	2.65413	0.100174
$703$	11.5934	0.437252
$704$	−111.297	−4.19465
$705$	−13.8597	−0.521987
$706$	−56.2543	−2.11716
$707$	−1.27548	−0.0479693
$708$	−83.6459	−3.14361
$709$	−9.14575	−0.343476	−0.171738	−	0.985143i	$-0.554938\pi$
$709$	−9.14575	−0.343476	−0.171738	+	0.985143i	$0.554938\pi$
$710$	96.0585	3.60501
$711$	−15.4663	−0.580031
$712$	−142.656	−5.34626
$713$	14.2772	0.534684
$714$	−32.6287	−1.22110
$715$	−10.6926	−0.399881
$716$	−47.3163	−1.76829
$717$	14.1302	0.527701
$718$	31.2420	1.16594
$719$	−35.8570	−1.33724	−0.668620	−	0.743604i	$-0.733115\pi$
$719$	−35.8570	−1.33724	−0.668620	+	0.743604i	$0.733115\pi$
$720$	−69.9634	−2.60738
$721$	15.5322	0.578448
$722$	44.3397	1.65015
$723$	16.4544	0.611946
$724$	−108.472	−4.03133
$725$	57.0554	2.11898
$726$	9.72126	0.360790
$727$	19.2816	0.715116	0.357558	−	0.933891i	$-0.383610\pi$
$727$	19.2816	0.715116	0.357558	+	0.933891i	$0.383610\pi$
$728$	22.8744	0.847782
$729$	1.00000	0.0370370
$730$	−99.1189	−3.66855
$731$	34.1685	1.26377
$732$	17.3749	0.642195
$733$	14.6735	0.541978	0.270989	−	0.962582i	$-0.412649\pi$
$733$	14.6735	0.541978	0.270989	+	0.962582i	$0.412649\pi$
$734$	−31.7763	−1.17289
$735$	6.48250	0.239111
$736$	−112.830	−4.15898
$737$	25.9664	0.956485
$738$	−18.5809	−0.683973
$739$	37.8607	1.39273	0.696364	−	0.717689i	$-0.254800\pi$
$739$	37.8607	1.39273	0.696364	+	0.717689i	$0.254800\pi$
$740$	155.267	5.70774
$741$	1.66327	0.0611017
$742$	12.0131	0.441014
$743$	−8.84628	−0.324539	−0.162269	−	0.986747i	$-0.551881\pi$
$743$	−8.84628	−0.324539	−0.162269	+	0.986747i	$0.551881\pi$
$744$	−35.1137	−1.28733
$745$	39.7670	1.45695
$746$	−32.5660	−1.19233
$747$	−3.42088	−0.125163
$748$	−78.9228	−2.88571
$749$	−32.0212	−1.17003
$750$	75.6946	2.76397
$751$	1.71932	0.0627390	0.0313695	−	0.999508i	$-0.490013\pi$
$751$	1.71932	0.0627390	0.0313695	+	0.999508i	$0.490013\pi$
$752$	58.1419	2.12022
$753$	9.67787	0.352681
$754$	12.9677	0.472255
$755$	−39.7091	−1.44516
$756$	13.2714	0.482678
$757$	28.8026	1.04685	0.523424	−	0.852072i	$-0.324654\pi$
$757$	28.8026	1.04685	0.523424	+	0.852072i	$0.324654\pi$
$758$	1.28001	0.0464922
$759$	−11.4478	−0.415530
$760$	−73.0421	−2.64951
$761$	21.4258	0.776684	0.388342	−	0.921515i	$-0.373048\pi$
$761$	21.4258	0.776684	0.388342	+	0.921515i	$0.373048\pi$
$762$	42.3394	1.53379
$763$	−23.4331	−0.848334
$764$	−12.4979	−0.452159
$765$	−20.6345	−0.746040
$766$	72.2996	2.61229
$767$	14.0211	0.506273
$768$	82.0438	2.96050
$769$	30.2712	1.09161	0.545804	−	0.837913i	$-0.316224\pi$
$769$	30.2712	1.09161	0.545804	+	0.837913i	$0.316224\pi$
$770$	−72.2117	−2.60233
$771$	−18.7539	−0.675404
$772$	132.418	4.76584
$773$	26.8727	0.966544	0.483272	−	0.875470i	$-0.339448\pi$
$773$	26.8727	0.966544	0.483272	+	0.875470i	$0.339448\pi$
$774$	−18.7703	−0.674686
$775$	39.8786	1.43248
$776$	−142.344	−5.10985
$777$	−15.5061	−0.556279
$778$	−54.7277	−1.96208
$779$	−11.6442	−0.417195
$780$	22.2758	0.797600
$781$	−23.2039	−0.830302
$782$	−58.6346	−2.09677
$783$	4.88585	0.174606
$784$	−27.1943	−0.971225
$785$	−26.7284	−0.953977
$786$	−11.2849	−0.402520
$787$	25.5746	0.911636	0.455818	−	0.890073i	$-0.349347\pi$
$787$	25.5746	0.911636	0.455818	+	0.890073i	$0.349347\pi$
$788$	38.4642	1.37023
$789$	18.5785	0.661410
$790$	−175.317	−6.23750
$791$	−2.19105	−0.0779047
$792$	28.1552	1.00045
$793$	−2.91246	−0.103425
$794$	−63.4120	−2.25041
$795$	7.59709	0.269441
$796$	128.169	4.54283
$797$	8.74785	0.309865	0.154932	−	0.987925i	$-0.450484\pi$
$797$	8.74785	0.309865	0.154932	+	0.987925i	$0.450484\pi$
$798$	11.2328	0.397636
$799$	17.1479	0.606650
$800$	−315.155	−11.1424
$801$	13.8738	0.490207
$802$	−21.8805	−0.772627
$803$	23.9432	0.844937
$804$	−54.0955	−1.90780
$805$	−39.7220	−1.40002
$806$	9.06370	0.319255
$807$	17.4955	0.615870
$808$	5.63718	0.198315
$809$	29.2645	1.02888	0.514442	−	0.857525i	$-0.327999\pi$
$809$	29.2645	1.02888	0.514442	+	0.857525i	$0.327999\pi$
$810$	11.3354	0.398287
$811$	41.1680	1.44560	0.722802	−	0.691055i	$-0.242854\pi$
$811$	41.1680	1.44560	0.722802	+	0.691055i	$0.242854\pi$
$812$	64.8422	2.27552
$813$	−12.0433	−0.422376
$814$	−50.6563	−1.77550
$815$	−94.0561	−3.29464
$816$	86.5621	3.03028
$817$	−11.7629	−0.411530
$818$	7.15981	0.250337
$819$	−2.22462	−0.0777345
$820$	−155.947	−5.44592
$821$	31.1913	1.08858	0.544291	−	0.838896i	$-0.316799\pi$
$821$	31.1913	1.08858	0.544291	+	0.838896i	$0.316799\pi$
$822$	45.2933	1.57978
$823$	25.5703	0.891324	0.445662	−	0.895201i	$-0.352968\pi$
$823$	25.5703	0.891324	0.445662	+	0.895201i	$0.352968\pi$
$824$	−68.6470	−2.39143
$825$	−31.9758	−1.11325
$826$	94.6905	3.29471
$827$	−23.1324	−0.804394	−0.402197	−	0.915553i	$-0.631753\pi$
$827$	−23.1324	−0.804394	−0.402197	+	0.915553i	$0.631753\pi$
$828$	23.8491	0.828814
$829$	16.7467	0.581636	0.290818	−	0.956778i	$-0.406073\pi$
$829$	16.7467	0.581636	0.290818	+	0.956778i	$0.406073\pi$
$830$	−38.7772	−1.34598
$831$	6.13440	0.212800
$832$	−38.8660	−1.34744
$833$	−8.02047	−0.277893
$834$	−32.2472	−1.11663
$835$	−90.1760	−3.12067
$836$	27.1700	0.939693
$837$	3.41494	0.118038
$838$	−97.2021	−3.35779
$839$	0.484174	0.0167155	0.00835777	−	0.999965i	$-0.497340\pi$
$839$	0.484174	0.0167155	0.00835777	+	0.999965i	$0.497340\pi$
$840$	97.6937	3.37075
$841$	−5.12850	−0.176845
$842$	58.3855	2.01210
$843$	−9.53343	−0.328349
$844$	83.1898	2.86351
$845$	49.3559	1.69789
$846$	−9.42013	−0.323871
$847$	−8.14810	−0.279972
$848$	−31.8700	−1.09442
$849$	−21.4421	−0.735892
$850$	−163.777	−5.61750
$851$	−27.8649	−0.955196
$852$	48.3404	1.65612
$853$	34.7875	1.19110	0.595550	−	0.803318i	$-0.296934\pi$
$853$	34.7875	1.19110	0.595550	+	0.803318i	$0.296934\pi$
$854$	−19.6691	−0.673063
$855$	7.10361	0.242938
$856$	141.523	4.83715
$857$	−14.6590	−0.500743	−0.250371	−	0.968150i	$-0.580553\pi$
$857$	−14.6590	−0.500743	−0.250371	+	0.968150i	$0.580553\pi$
$858$	−7.26752	−0.248109
$859$	−44.1545	−1.50653	−0.753266	−	0.657715i	$-0.771523\pi$
$859$	−44.1545	−1.50653	−0.753266	+	0.657715i	$0.771523\pi$
$860$	−157.537	−5.37197
$861$	15.5740	0.530762
$862$	30.7359	1.04687
$863$	41.7993	1.42287	0.711433	−	0.702754i	$-0.248047\pi$
$863$	41.7993	1.42287	0.711433	+	0.702754i	$0.248047\pi$
$864$	−26.9878	−0.918143
$865$	10.1983	0.346752
$866$	25.2822	0.859122
$867$	8.52995	0.289692
$868$	45.3212	1.53830
$869$	42.3497	1.43661
$870$	55.3832	1.87767
$871$	9.06774	0.307249
$872$	103.566	3.50719
$873$	13.8435	0.468531
$874$	20.1856	0.682787
$875$	−63.4452	−2.14484
$876$	−49.8805	−1.68531
$877$	38.5174	1.30064	0.650320	−	0.759661i	$-0.274635\pi$
$877$	38.5174	1.30064	0.650320	+	0.759661i	$0.274635\pi$
$878$	−25.8722	−0.873143
$879$	−11.4097	−0.384840
$880$	191.573	6.45794
$881$	−12.9008	−0.434640	−0.217320	−	0.976100i	$-0.569732\pi$
$881$	−12.9008	−0.434640	−0.217320	+	0.976100i	$0.569732\pi$
$882$	4.40601	0.148358
$883$	−13.4831	−0.453743	−0.226872	−	0.973925i	$-0.572850\pi$
$883$	−13.4831	−0.453743	−0.226872	+	0.973925i	$0.572850\pi$
$884$	−27.5607	−0.926966
$885$	59.8824	2.01292
$886$	−65.1665	−2.18931
$887$	−7.99609	−0.268482	−0.134241	−	0.990949i	$-0.542860\pi$
$887$	−7.99609	−0.268482	−0.134241	+	0.990949i	$0.542860\pi$
$888$	68.5318	2.29978
$889$	−35.4877	−1.19022
$890$	157.266	5.27157
$891$	−2.73819	−0.0917330
$892$	59.5336	1.99333
$893$	−5.90334	−0.197548
$894$	27.0287	0.903976
$895$	33.8739	1.13228
$896$	−136.904	−4.57363
$897$	−3.99770	−0.133479
$898$	−8.33544	−0.278157
$899$	16.6849	0.556472
$900$	66.6147	2.22049
$901$	−9.39949	−0.313142
$902$	50.8782	1.69406
$903$	15.7328	0.523555
$904$	9.68370	0.322075
$905$	77.6555	2.58136
$906$	−26.9894	−0.896662
$907$	−25.6621	−0.852096	−0.426048	−	0.904701i	$-0.640094\pi$
$907$	−25.6621	−0.852096	−0.426048	+	0.904701i	$0.640094\pi$
$908$	118.701	3.93922
$909$	−0.548237	−0.0181839
$910$	−25.2171	−0.835938
$911$	−21.9770	−0.728131	−0.364065	−	0.931373i	$-0.618612\pi$
$911$	−21.9770	−0.728131	−0.364065	+	0.931373i	$0.618612\pi$
$912$	−29.7999	−0.986772
$913$	9.36703	0.310004
$914$	17.5766	0.581381
$915$	−12.4388	−0.411213
$916$	81.0651	2.67847
$917$	9.45873	0.312355
$918$	−14.0248	−0.462886
$919$	−54.9788	−1.81358	−0.906792	−	0.421577i	$-0.861477\pi$
$919$	−54.9788	−1.81358	−0.906792	+	0.421577i	$0.861477\pi$
$920$	175.558	5.78797
$921$	7.26834	0.239500
$922$	−37.0282	−1.21946
$923$	−8.10305	−0.266715
$924$	−36.3398	−1.19549
$925$	−77.8315	−2.55908
$926$	−96.5141	−3.17165
$927$	6.67617	0.219274
$928$	−131.858	−4.32845
$929$	−28.6641	−0.940439	−0.470219	−	0.882550i	$-0.655825\pi$
$929$	−28.6641	−0.940439	−0.470219	+	0.882550i	$0.655825\pi$
$930$	38.7099	1.26935
$931$	2.76113	0.0904922
$932$	127.884	4.18898
$933$	7.74549	0.253576
$934$	92.7215	3.03394
$935$	56.5011	1.84779
$936$	9.83207	0.321371
$937$	−43.4744	−1.42025	−0.710124	−	0.704077i	$-0.751361\pi$
$937$	−43.4744	−1.42025	−0.710124	+	0.704077i	$0.751361\pi$
$938$	61.2383	1.99950
$939$	−8.33629	−0.272045
$940$	−79.0620	−2.57872
$941$	−32.9087	−1.07279	−0.536396	−	0.843966i	$-0.680215\pi$
$941$	−32.9087	−1.07279	−0.536396	+	0.843966i	$0.680215\pi$
$942$	−18.1667	−0.591903
$943$	27.9869	0.911380
$944$	−251.208	−8.17614
$945$	−9.50107	−0.309070
$946$	51.3968	1.67106
$947$	−5.02840	−0.163401	−0.0817005	−	0.996657i	$-0.526035\pi$
$947$	−5.02840	−0.163401	−0.0817005	+	0.996657i	$0.526035\pi$
$948$	−88.2265	−2.86546
$949$	8.36121	0.271416
$950$	56.3818	1.82927
$951$	26.4511	0.857736
$952$	−120.871	−3.91746
$953$	15.9115	0.515425	0.257712	−	0.966222i	$-0.417031\pi$
$953$	15.9115	0.515425	0.257712	+	0.966222i	$0.417031\pi$
$954$	5.16357	0.167177
$955$	8.94730	0.289528
$956$	80.6047	2.60694
$957$	−13.3784	−0.432462
$958$	108.172	3.49487
$959$	−37.9636	−1.22591
$960$	−165.992	−5.35736
$961$	−19.3382	−0.623812
$962$	−17.6897	−0.570339
$963$	−13.7636	−0.443527
$964$	93.8633	3.02313
$965$	−94.7988	−3.05168
$966$	−26.9981	−0.868651
$967$	−22.9993	−0.739609	−0.369804	−	0.929110i	$-0.620575\pi$
$967$	−22.9993	−0.739609	−0.369804	+	0.929110i	$0.620575\pi$
$968$	36.0119	1.15747
$969$	−8.78894	−0.282341
$970$	156.922	5.03846
$971$	28.2812	0.907587	0.453793	−	0.891107i	$-0.350070\pi$
$971$	28.2812	0.907587	0.453793	+	0.891107i	$0.350070\pi$
$972$	5.70444	0.182970
$973$	27.0288	0.866502
$974$	−89.2131	−2.85857
$975$	−11.1663	−0.357607
$976$	52.1810	1.67027
$977$	25.1331	0.804079	0.402040	−	0.915622i	$-0.368301\pi$
$977$	25.1331	0.804079	0.402040	+	0.915622i	$0.368301\pi$
$978$	−63.9278	−2.04419
$979$	−37.9892	−1.21414
$980$	36.9791	1.18125
$981$	−10.0722	−0.321581
$982$	−22.1783	−0.707738
$983$	−14.8037	−0.472166	−0.236083	−	0.971733i	$-0.575864\pi$
$983$	−14.8037	−0.472166	−0.236083	+	0.971733i	$0.575864\pi$
$984$	−68.8320	−2.19428
$985$	−27.5367	−0.877391
$986$	−68.5229	−2.18221
$987$	7.89571	0.251323
$988$	9.48803	0.301854
$989$	28.2722	0.899005
$990$	−31.0387	−0.986473
$991$	−16.9527	−0.538521	−0.269260	−	0.963067i	$-0.586779\pi$
$991$	−16.9527	−0.538521	−0.269260	+	0.963067i	$0.586779\pi$
$992$	−92.1617	−2.92614
$993$	−23.7414	−0.753409
$994$	−54.7233	−1.73572
$995$	−91.7567	−2.90888
$996$	−19.5142	−0.618331
$997$	42.6639	1.35118	0.675590	−	0.737278i	$-0.263889\pi$
$997$	42.6639	1.35118	0.675590	+	0.737278i	$0.263889\pi$
$998$	82.2758	2.60440
$999$	−6.66497	−0.210870

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6033.2.a.e.1.1	✓	97

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6033.2.a.e.1.1	✓	97	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:	\( N \)	\(=\)	\( 6033 = 3 \cdot 2011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6033.a (trivial)

\(f(q)\)	\(=\)	\(q-2.77569 q^{2} +1.00000 q^{3} +5.70444 q^{4} -4.08383 q^{5} -2.77569 q^{6} +2.32651 q^{7} -10.2824 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.77569 q^{2} +1.00000 q^{3} +5.70444 q^{4} -4.08383 q^{5} -2.77569 q^{6} +2.32651 q^{7} -10.2824 q^{8} +1.00000 q^{9} +11.3354 q^{10} -2.73819 q^{11} +5.70444 q^{12} -0.956206 q^{13} -6.45766 q^{14} -4.08383 q^{15} +17.1318 q^{16} +5.05272 q^{17} -2.77569 q^{18} -1.73945 q^{19} -23.2960 q^{20} +2.32651 q^{21} +7.60038 q^{22} +4.18079 q^{23} -10.2824 q^{24} +11.6777 q^{25} +2.65413 q^{26} +1.00000 q^{27} +13.2714 q^{28} +4.88585 q^{29} +11.3354 q^{30} +3.41494 q^{31} -26.9878 q^{32} -2.73819 q^{33} -14.0248 q^{34} -9.50107 q^{35} +5.70444 q^{36} -6.66497 q^{37} +4.82816 q^{38} -0.956206 q^{39} +41.9915 q^{40} +6.69417 q^{41} -6.45766 q^{42} +6.76241 q^{43} -15.6199 q^{44} -4.08383 q^{45} -11.6046 q^{46} +3.39380 q^{47} +17.1318 q^{48} -1.58736 q^{49} -32.4136 q^{50} +5.05272 q^{51} -5.45462 q^{52} -1.86028 q^{53} -2.77569 q^{54} +11.1823 q^{55} -23.9221 q^{56} -1.73945 q^{57} -13.5616 q^{58} -14.6633 q^{59} -23.2960 q^{60} +3.04585 q^{61} -9.47881 q^{62} +2.32651 q^{63} +40.6460 q^{64} +3.90498 q^{65} +7.60038 q^{66} -9.48304 q^{67} +28.8229 q^{68} +4.18079 q^{69} +26.3720 q^{70} +8.47417 q^{71} -10.2824 q^{72} -8.74415 q^{73} +18.4999 q^{74} +11.6777 q^{75} -9.92258 q^{76} -6.37043 q^{77} +2.65413 q^{78} -15.4663 q^{79} -69.9634 q^{80} +1.00000 q^{81} -18.5809 q^{82} -3.42088 q^{83} +13.2714 q^{84} -20.6345 q^{85} -18.7703 q^{86} +4.88585 q^{87} +28.1552 q^{88} +13.8738 q^{89} +11.3354 q^{90} -2.22462 q^{91} +23.8491 q^{92} +3.41494 q^{93} -9.42013 q^{94} +7.10361 q^{95} -26.9878 q^{96} +13.8435 q^{97} +4.40601 q^{98} -2.73819 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 97 q + 12 q^{2} + 97 q^{3} + 120 q^{4} + 6 q^{5} + 12 q^{6} + 50 q^{7} + 30 q^{8} + 97 q^{9}+O(q^{10}) \) 97 * q + 12 * q^2 + 97 * q^3 + 120 * q^4 + 6 * q^5 + 12 * q^6 + 50 * q^7 + 30 * q^8 + 97 * q^9	\( 97 q + 12 q^{2} + 97 q^{3} + 120 q^{4} + 6 q^{5} + 12 q^{6} + 50 q^{7} + 30 q^{8} + 97 q^{9} + 35 q^{10} + 18 q^{11} + 120 q^{12} + 67 q^{13} - q^{14} + 6 q^{15} + 158 q^{16} + 25 q^{17} + 12 q^{18} + 51 q^{19} + 10 q^{20} + 50 q^{21} + 39 q^{22} + 87 q^{23} + 30 q^{24} + 149 q^{25} + 14 q^{26} + 97 q^{27} + 83 q^{28} + 23 q^{29} + 35 q^{30} + 72 q^{31} + 57 q^{32} + 18 q^{33} + 28 q^{34} + 45 q^{35} + 120 q^{36} + 72 q^{37} + 3 q^{38} + 67 q^{39} + 90 q^{40} + 5 q^{41} - q^{42} + 122 q^{43} + 11 q^{44} + 6 q^{45} + 56 q^{46} + 49 q^{47} + 158 q^{48} + 167 q^{49} + 13 q^{50} + 25 q^{51} + 128 q^{52} + 30 q^{53} + 12 q^{54} + 120 q^{55} - 21 q^{56} + 51 q^{57} + 37 q^{58} + 2 q^{59} + 10 q^{60} + 158 q^{61} + 17 q^{62} + 50 q^{63} + 212 q^{64} + q^{65} + 39 q^{66} + 77 q^{67} + 56 q^{68} + 87 q^{69} + 9 q^{70} + 38 q^{71} + 30 q^{72} + 82 q^{73} - 6 q^{74} + 149 q^{75} + 93 q^{76} + 49 q^{77} + 14 q^{78} + 134 q^{79} - 25 q^{80} + 97 q^{81} + 53 q^{82} + 69 q^{83} + 83 q^{84} + 72 q^{85} + 23 q^{87} + 107 q^{88} + 35 q^{90} + 84 q^{91} + 108 q^{92} + 72 q^{93} + 65 q^{94} + 89 q^{95} + 57 q^{96} + 65 q^{97} + 18 q^{99}+O(q^{100}) \) 97 * q + 12 * q^2 + 97 * q^3 + 120 * q^4 + 6 * q^5 + 12 * q^6 + 50 * q^7 + 30 * q^8 + 97 * q^9 + 35 * q^10 + 18 * q^11 + 120 * q^12 + 67 * q^13 - q^14 + 6 * q^15 + 158 * q^16 + 25 * q^17 + 12 * q^18 + 51 * q^19 + 10 * q^20 + 50 * q^21 + 39 * q^22 + 87 * q^23 + 30 * q^24 + 149 * q^25 + 14 * q^26 + 97 * q^27 + 83 * q^28 + 23 * q^29 + 35 * q^30 + 72 * q^31 + 57 * q^32 + 18 * q^33 + 28 * q^34 + 45 * q^35 + 120 * q^36 + 72 * q^37 + 3 * q^38 + 67 * q^39 + 90 * q^40 + 5 * q^41 - q^42 + 122 * q^43 + 11 * q^44 + 6 * q^45 + 56 * q^46 + 49 * q^47 + 158 * q^48 + 167 * q^49 + 13 * q^50 + 25 * q^51 + 128 * q^52 + 30 * q^53 + 12 * q^54 + 120 * q^55 - 21 * q^56 + 51 * q^57 + 37 * q^58 + 2 * q^59 + 10 * q^60 + 158 * q^61 + 17 * q^62 + 50 * q^63 + 212 * q^64 + q^65 + 39 * q^66 + 77 * q^67 + 56 * q^68 + 87 * q^69 + 9 * q^70 + 38 * q^71 + 30 * q^72 + 82 * q^73 - 6 * q^74 + 149 * q^75 + 93 * q^76 + 49 * q^77 + 14 * q^78 + 134 * q^79 - 25 * q^80 + 97 * q^81 + 53 * q^82 + 69 * q^83 + 83 * q^84 + 72 * q^85 + 23 * q^87 + 107 * q^88 + 35 * q^90 + 84 * q^91 + 108 * q^92 + 72 * q^93 + 65 * q^94 + 89 * q^95 + 57 * q^96 + 65 * q^97 + 18 * q^99

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