LMFDB - Embedded newform 6011.2.a.f.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6011,2,Mod(1,6011)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6011, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6011.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6011.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:	$47.9980766550$
Analytic rank:	$0$
Dimension:	$275$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	6011.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.52281 q^{2} +0.402729 q^{3} +4.36459 q^{4} +0.845770 q^{5} -1.01601 q^{6} -3.10596 q^{7} -5.96541 q^{8} -2.83781 q^{9} +O(q^{10})$	\(q-2.52281 q^{2} +0.402729 q^{3} +4.36459 q^{4} +0.845770 q^{5} -1.01601 q^{6} -3.10596 q^{7} -5.96541 q^{8} -2.83781 q^{9} -2.13372 q^{10} +4.17716 q^{11} +1.75774 q^{12} -5.44152 q^{13} +7.83577 q^{14} +0.340616 q^{15} +6.32044 q^{16} +1.63875 q^{17} +7.15926 q^{18} -8.06535 q^{19} +3.69144 q^{20} -1.25086 q^{21} -10.5382 q^{22} -2.52474 q^{23} -2.40244 q^{24} -4.28467 q^{25} +13.7279 q^{26} -2.35105 q^{27} -13.5562 q^{28} -1.89667 q^{29} -0.859310 q^{30} -0.161842 q^{31} -4.01447 q^{32} +1.68226 q^{33} -4.13426 q^{34} -2.62693 q^{35} -12.3859 q^{36} +0.826376 q^{37} +20.3474 q^{38} -2.19146 q^{39} -5.04537 q^{40} +7.06595 q^{41} +3.15569 q^{42} -10.0327 q^{43} +18.2316 q^{44} -2.40013 q^{45} +6.36945 q^{46} +4.30657 q^{47} +2.54542 q^{48} +2.64701 q^{49} +10.8094 q^{50} +0.659972 q^{51} -23.7500 q^{52} -7.85446 q^{53} +5.93127 q^{54} +3.53292 q^{55} +18.5283 q^{56} -3.24815 q^{57} +4.78494 q^{58} -12.2138 q^{59} +1.48665 q^{60} +14.3346 q^{61} +0.408298 q^{62} +8.81414 q^{63} -2.51312 q^{64} -4.60228 q^{65} -4.24403 q^{66} -3.21099 q^{67} +7.15247 q^{68} -1.01679 q^{69} +6.62726 q^{70} -5.85452 q^{71} +16.9287 q^{72} +2.86686 q^{73} -2.08479 q^{74} -1.72556 q^{75} -35.2019 q^{76} -12.9741 q^{77} +5.52863 q^{78} +6.90061 q^{79} +5.34564 q^{80} +7.56659 q^{81} -17.8261 q^{82} -1.40212 q^{83} -5.45949 q^{84} +1.38601 q^{85} +25.3106 q^{86} -0.763843 q^{87} -24.9185 q^{88} +13.3155 q^{89} +6.05509 q^{90} +16.9012 q^{91} -11.0195 q^{92} -0.0651785 q^{93} -10.8647 q^{94} -6.82143 q^{95} -1.61674 q^{96} -6.85470 q^{97} -6.67792 q^{98} -11.8540 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 275 q + 16 q^{2} + 9 q^{3} + 316 q^{4} + 36 q^{5} + 30 q^{6} + 41 q^{7} + 36 q^{8} + 322 q^{9}+O(q^{10}) $ 275 * q + 16 * q^2 + 9 * q^3 + 316 * q^4 + 36 * q^5 + 30 * q^6 + 41 * q^7 + 36 * q^8 + 322 * q^9	\( 275 q + 16 q^{2} + 9 q^{3} + 316 q^{4} + 36 q^{5} + 30 q^{6} + 41 q^{7} + 36 q^{8} + 322 q^{9} + 44 q^{10} + 42 q^{11} + 26 q^{12} + 97 q^{13} + 24 q^{14} + 46 q^{15} + 386 q^{16} + 35 q^{17} + 47 q^{18} + 101 q^{19} + 60 q^{20} + 187 q^{21} + 72 q^{22} + 35 q^{23} + 73 q^{24} + 373 q^{25} + 21 q^{26} + 27 q^{27} + 97 q^{28} + 162 q^{29} + 13 q^{30} + 113 q^{31} + 58 q^{32} + 16 q^{33} + 52 q^{34} + 23 q^{35} + 426 q^{36} + 257 q^{37} + 8 q^{38} + 87 q^{39} + 126 q^{40} + 77 q^{41} - 7 q^{42} + 107 q^{43} + 133 q^{44} + 140 q^{45} + 207 q^{46} + 24 q^{47} + 4 q^{48} + 418 q^{49} + 65 q^{50} + 94 q^{51} + 142 q^{52} + 81 q^{53} + 79 q^{54} + 26 q^{55} + 62 q^{56} + 112 q^{57} + 44 q^{58} + 30 q^{59} + 83 q^{60} + 347 q^{61} + 5 q^{62} + 97 q^{63} + 508 q^{64} + 94 q^{65} + 4 q^{66} + 98 q^{67} + 28 q^{68} + 91 q^{69} + 17 q^{70} + 58 q^{71} + 99 q^{72} + 157 q^{73} + 80 q^{74} + 83 q^{75} + 264 q^{76} + 61 q^{77} + 5 q^{78} + 282 q^{79} + 49 q^{80} + 403 q^{81} + 46 q^{82} + 43 q^{83} + 318 q^{84} + 396 q^{85} + 57 q^{86} + 31 q^{87} + 180 q^{88} + 98 q^{89} + 67 q^{90} + 195 q^{91} + 97 q^{92} + 83 q^{93} + 96 q^{94} + 28 q^{95} + 127 q^{96} + 167 q^{97} + 24 q^{98} + 133 q^{99}+O(q^{100}) \) 275 * q + 16 * q^2 + 9 * q^3 + 316 * q^4 + 36 * q^5 + 30 * q^6 + 41 * q^7 + 36 * q^8 + 322 * q^9 + 44 * q^10 + 42 * q^11 + 26 * q^12 + 97 * q^13 + 24 * q^14 + 46 * q^15 + 386 * q^16 + 35 * q^17 + 47 * q^18 + 101 * q^19 + 60 * q^20 + 187 * q^21 + 72 * q^22 + 35 * q^23 + 73 * q^24 + 373 * q^25 + 21 * q^26 + 27 * q^27 + 97 * q^28 + 162 * q^29 + 13 * q^30 + 113 * q^31 + 58 * q^32 + 16 * q^33 + 52 * q^34 + 23 * q^35 + 426 * q^36 + 257 * q^37 + 8 * q^38 + 87 * q^39 + 126 * q^40 + 77 * q^41 - 7 * q^42 + 107 * q^43 + 133 * q^44 + 140 * q^45 + 207 * q^46 + 24 * q^47 + 4 * q^48 + 418 * q^49 + 65 * q^50 + 94 * q^51 + 142 * q^52 + 81 * q^53 + 79 * q^54 + 26 * q^55 + 62 * q^56 + 112 * q^57 + 44 * q^58 + 30 * q^59 + 83 * q^60 + 347 * q^61 + 5 * q^62 + 97 * q^63 + 508 * q^64 + 94 * q^65 + 4 * q^66 + 98 * q^67 + 28 * q^68 + 91 * q^69 + 17 * q^70 + 58 * q^71 + 99 * q^72 + 157 * q^73 + 80 * q^74 + 83 * q^75 + 264 * q^76 + 61 * q^77 + 5 * q^78 + 282 * q^79 + 49 * q^80 + 403 * q^81 + 46 * q^82 + 43 * q^83 + 318 * q^84 + 396 * q^85 + 57 * q^86 + 31 * q^87 + 180 * q^88 + 98 * q^89 + 67 * q^90 + 195 * q^91 + 97 * q^92 + 83 * q^93 + 96 * q^94 + 28 * q^95 + 127 * q^96 + 167 * q^97 + 24 * q^98 + 133 * 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 $

$2$	−2.52281	−1.78390	−0.891949	−	0.452136i	$-0.850662\pi$
$2$	−2.52281	−1.78390	−0.891949	+	0.452136i	$0.850662\pi$
$3$	0.402729	0.232515	0.116258	−	0.993219i	$-0.462910\pi$
$3$	0.402729	0.232515	0.116258	+	0.993219i	$0.462910\pi$
$4$	4.36459	2.18229
$5$	0.845770	0.378240	0.189120	−	0.981954i	$-0.439436\pi$
$5$	0.845770	0.378240	0.189120	+	0.981954i	$0.439436\pi$
$6$	−1.01601	−0.414784
$7$	−3.10596	−1.17394	−0.586972	−	0.809607i	$-0.699680\pi$
$7$	−3.10596	−1.17394	−0.586972	+	0.809607i	$0.699680\pi$
$8$	−5.96541	−2.10909
$9$	−2.83781	−0.945937
$10$	−2.13372	−0.674742
$11$	4.17716	1.25946	0.629730	−	0.776814i	$-0.283165\pi$
$11$	4.17716	1.25946	0.629730	+	0.776814i	$0.283165\pi$
$12$	1.75774	0.507417
$13$	−5.44152	−1.50921	−0.754603	−	0.656182i	$-0.772171\pi$
$13$	−5.44152	−1.50921	−0.754603	+	0.656182i	$0.772171\pi$
$14$	7.83577	2.09420
$15$	0.340616	0.0879466
$16$	6.32044	1.58011
$17$	1.63875	0.397455	0.198728	−	0.980055i	$-0.436319\pi$
$17$	1.63875	0.397455	0.198728	+	0.980055i	$0.436319\pi$
$18$	7.15926	1.68745
$19$	−8.06535	−1.85032	−0.925159	−	0.379580i	$-0.876069\pi$
$19$	−8.06535	−1.85032	−0.925159	+	0.379580i	$0.876069\pi$
$20$	3.69144	0.825430
$21$	−1.25086	−0.272960
$22$	−10.5382	−2.24675
$23$	−2.52474	−0.526445	−0.263223	−	0.964735i	$-0.584785\pi$
$23$	−2.52474	−0.526445	−0.263223	+	0.964735i	$0.584785\pi$
$24$	−2.40244	−0.490396
$25$	−4.28467	−0.856935
$26$	13.7279	2.69227
$27$	−2.35105	−0.452460
$28$	−13.5562	−2.56189
$29$	−1.89667	−0.352202	−0.176101	−	0.984372i	$-0.556349\pi$
$29$	−1.89667	−0.352202	−0.176101	+	0.984372i	$0.556349\pi$
$30$	−0.859310	−0.156888
$31$	−0.161842	−0.0290677	−0.0145339	−	0.999894i	$-0.504626\pi$
$31$	−0.161842	−0.0290677	−0.0145339	+	0.999894i	$0.504626\pi$
$32$	−4.01447	−0.709665
$33$	1.68226	0.292844
$34$	−4.13426	−0.709020
$35$	−2.62693	−0.444033
$36$	−12.3859	−2.06431
$37$	0.826376	0.135855	0.0679277	−	0.997690i	$-0.478361\pi$
$37$	0.826376	0.135855	0.0679277	+	0.997690i	$0.478361\pi$
$38$	20.3474	3.30078
$39$	−2.19146	−0.350914
$40$	−5.04537	−0.797742
$41$	7.06595	1.10352	0.551758	−	0.834004i	$-0.313957\pi$
$41$	7.06595	1.10352	0.551758	+	0.834004i	$0.313957\pi$
$42$	3.15569	0.486933
$43$	−10.0327	−1.52997	−0.764985	−	0.644048i	$-0.777254\pi$
$43$	−10.0327	−1.52997	−0.764985	+	0.644048i	$0.777254\pi$
$44$	18.2316	2.74851
$45$	−2.40013	−0.357791
$46$	6.36945	0.939125
$47$	4.30657	0.628178	0.314089	−	0.949393i	$-0.398301\pi$
$47$	4.30657	0.628178	0.314089	+	0.949393i	$0.398301\pi$
$48$	2.54542	0.367400
$49$	2.64701	0.378145
$50$	10.8094	1.52868
$51$	0.659972	0.0924145
$52$	−23.7500	−3.29353
$53$	−7.85446	−1.07889	−0.539447	−	0.842020i	$-0.681367\pi$
$53$	−7.85446	−1.07889	−0.539447	+	0.842020i	$0.681367\pi$
$54$	5.93127	0.807143
$55$	3.53292	0.476378
$56$	18.5283	2.47595
$57$	−3.24815	−0.430228
$58$	4.78494	0.628293
$59$	−12.2138	−1.59010	−0.795051	−	0.606542i	$-0.792556\pi$
$59$	−12.2138	−1.59010	−0.795051	+	0.606542i	$0.792556\pi$
$60$	1.48665	0.191925
$61$	14.3346	1.83536	0.917678	−	0.397324i	$-0.130061\pi$
$61$	14.3346	1.83536	0.917678	+	0.397324i	$0.130061\pi$
$62$	0.408298	0.0518539
$63$	8.81414	1.11048
$64$	−2.51312	−0.314140
$65$	−4.60228	−0.570842
$66$	−4.24403	−0.522404
$67$	−3.21099	−0.392285	−0.196142	−	0.980575i	$-0.562841\pi$
$67$	−3.21099	−0.392285	−0.196142	+	0.980575i	$0.562841\pi$
$68$	7.15247	0.867364
$69$	−1.01679	−0.122407
$70$	6.62726	0.792109
$71$	−5.85452	−0.694803	−0.347402	−	0.937716i	$-0.612936\pi$
$71$	−5.85452	−0.694803	−0.347402	+	0.937716i	$0.612936\pi$
$72$	16.9287	1.99507
$73$	2.86686	0.335540	0.167770	−	0.985826i	$-0.446343\pi$
$73$	2.86686	0.335540	0.167770	+	0.985826i	$0.446343\pi$
$74$	−2.08479	−0.242352
$75$	−1.72556	−0.199251
$76$	−35.2019	−4.03794
$77$	−12.9741	−1.47854
$78$	5.52863	0.625995
$79$	6.90061	0.776380	0.388190	−	0.921579i	$-0.373100\pi$
$79$	6.90061	0.776380	0.388190	+	0.921579i	$0.373100\pi$
$80$	5.34564	0.597661
$81$	7.56659	0.840733
$82$	−17.8261	−1.96856
$83$	−1.40212	−0.153902	−0.0769511	−	0.997035i	$-0.524519\pi$
$83$	−1.40212	−0.153902	−0.0769511	+	0.997035i	$0.524519\pi$
$84$	−5.45949	−0.595679
$85$	1.38601	0.150333
$86$	25.3106	2.72931
$87$	−0.763843	−0.0818925
$88$	−24.9185	−2.65632
$89$	13.3155	1.41144	0.705720	−	0.708491i	$-0.250624\pi$
$89$	13.3155	1.41144	0.705720	+	0.708491i	$0.250624\pi$
$90$	6.05509	0.638263
$91$	16.9012	1.77172
$92$	−11.0195	−1.14886
$93$	−0.0651785	−0.00675870
$94$	−10.8647	−1.12061
$95$	−6.82143	−0.699864
$96$	−1.61674	−0.165008
$97$	−6.85470	−0.695989	−0.347995	−	0.937497i	$-0.613137\pi$
$97$	−6.85470	−0.695989	−0.347995	+	0.937497i	$0.613137\pi$
$98$	−6.67792	−0.674572
$99$	−11.8540	−1.19137
$100$	−18.7008	−1.87008
$101$	5.34846	0.532191	0.266096	−	0.963947i	$-0.414266\pi$
$101$	5.34846	0.532191	0.266096	+	0.963947i	$0.414266\pi$
$102$	−1.66499	−0.164858
$103$	−13.9654	−1.37605	−0.688024	−	0.725688i	$-0.741522\pi$
$103$	−13.9654	−1.37605	−0.688024	+	0.725688i	$0.741522\pi$
$104$	32.4609	3.18305
$105$	−1.05794	−0.103244
$106$	19.8153	1.92464
$107$	−7.62853	−0.737478	−0.368739	−	0.929533i	$-0.620210\pi$
$107$	−7.62853	−0.737478	−0.368739	+	0.929533i	$0.620210\pi$
$108$	−10.2614	−0.987401
$109$	−16.9840	−1.62677	−0.813385	−	0.581726i	$-0.802378\pi$
$109$	−16.9840	−1.62677	−0.813385	+	0.581726i	$0.802378\pi$
$110$	−8.91289	−0.849810
$111$	0.332805	0.0315885
$112$	−19.6311	−1.85496
$113$	10.8646	1.02206	0.511028	−	0.859564i	$-0.329265\pi$
$113$	10.8646	1.02206	0.511028	+	0.859564i	$0.329265\pi$
$114$	8.19447	0.767482
$115$	−2.13535	−0.199123
$116$	−8.27817	−0.768609
$117$	15.4420	1.42761
$118$	30.8132	2.83658
$119$	−5.08990	−0.466590
$120$	−2.03191	−0.185487
$121$	6.44865	0.586241
$122$	−36.1635	−3.27409
$123$	2.84566	0.256585
$124$	−0.706375	−0.0634343
$125$	−7.85270	−0.702367
$126$	−22.2364	−1.98098
$127$	16.0541	1.42457	0.712284	−	0.701891i	$-0.247661\pi$
$127$	16.0541	1.42457	0.712284	+	0.701891i	$0.247661\pi$
$128$	14.3691	1.27006
$129$	−4.04045	−0.355742
$130$	11.6107	1.01832
$131$	19.4020	1.69516	0.847582	−	0.530664i	$-0.178057\pi$
$131$	19.4020	1.69516	0.847582	+	0.530664i	$0.178057\pi$
$132$	7.34237	0.639072
$133$	25.0507	2.17217
$134$	8.10072	0.699796
$135$	−1.98845	−0.171139
$136$	−9.77582	−0.838269
$137$	−22.7741	−1.94573	−0.972863	−	0.231381i	$-0.925676\pi$
$137$	−22.7741	−1.94573	−0.972863	+	0.231381i	$0.925676\pi$
$138$	2.56516	0.218361
$139$	−1.86273	−0.157995	−0.0789973	−	0.996875i	$-0.525172\pi$
$139$	−1.86273	−0.157995	−0.0789973	+	0.996875i	$0.525172\pi$
$140$	−11.4655	−0.969009
$141$	1.73438	0.146061
$142$	14.7699	1.23946
$143$	−22.7301	−1.90079
$144$	−17.9362	−1.49468
$145$	−1.60415	−0.133217
$146$	−7.23254	−0.598570
$147$	1.06603	0.0879245
$148$	3.60679	0.296476
$149$	16.8589	1.38113	0.690567	−	0.723269i	$-0.257361\pi$
$149$	16.8589	1.38113	0.690567	+	0.723269i	$0.257361\pi$
$150$	4.35327	0.355443
$151$	−3.45732	−0.281353	−0.140676	−	0.990056i	$-0.544928\pi$
$151$	−3.45732	−0.281353	−0.140676	+	0.990056i	$0.544928\pi$
$152$	48.1131	3.90249
$153$	−4.65046	−0.375968
$154$	32.7312	2.63756
$155$	−0.136881	−0.0109946
$156$	−9.56480	−0.765797
$157$	9.19200	0.733601	0.366801	−	0.930300i	$-0.380453\pi$
$157$	9.19200	0.733601	0.366801	+	0.930300i	$0.380453\pi$
$158$	−17.4090	−1.38498
$159$	−3.16322	−0.250859
$160$	−3.39532	−0.268424
$161$	7.84176	0.618017
$162$	−19.0891	−1.49978
$163$	9.64301	0.755299	0.377649	−	0.925949i	$-0.376732\pi$
$163$	9.64301	0.755299	0.377649	+	0.925949i	$0.376732\pi$
$164$	30.8399	2.40819
$165$	1.42281	0.110765
$166$	3.53728	0.274546
$167$	18.5435	1.43494	0.717471	−	0.696588i	$-0.245299\pi$
$167$	18.5435	1.43494	0.717471	+	0.696588i	$0.245299\pi$
$168$	7.46190	0.575698
$169$	16.6101	1.27770
$170$	−3.49663	−0.268180
$171$	22.8879	1.75028
$172$	−43.7885	−3.33884
$173$	0.435350	0.0330990	0.0165495	−	0.999863i	$-0.494732\pi$
$173$	0.435350	0.0330990	0.0165495	+	0.999863i	$0.494732\pi$
$174$	1.92703	0.146088
$175$	13.3080	1.00599
$176$	26.4015	1.99009
$177$	−4.91885	−0.369723
$178$	−33.5925	−2.51786
$179$	5.91569	0.442160	0.221080	−	0.975256i	$-0.429042\pi$
$179$	5.91569	0.442160	0.221080	+	0.975256i	$0.429042\pi$
$180$	−10.4756	−0.780805
$181$	3.69447	0.274608	0.137304	−	0.990529i	$-0.456156\pi$
$181$	3.69447	0.274608	0.137304	+	0.990529i	$0.456156\pi$
$182$	−42.6385	−3.16058
$183$	5.77295	0.426749
$184$	15.0611	1.11032
$185$	0.698924	0.0513859
$186$	0.164433	0.0120568
$187$	6.84532	0.500579
$188$	18.7964	1.37087
$189$	7.30229	0.531163
$190$	17.2092	1.24849
$191$	−7.81446	−0.565435	−0.282717	−	0.959203i	$-0.591236\pi$
$191$	−7.81446	−0.565435	−0.282717	+	0.959203i	$0.591236\pi$
$192$	−1.01210	−0.0730423
$193$	−1.64813	−0.118635	−0.0593175	−	0.998239i	$-0.518892\pi$
$193$	−1.64813	−0.118635	−0.0593175	+	0.998239i	$0.518892\pi$
$194$	17.2931	1.24157
$195$	−1.85347	−0.132730
$196$	11.5531	0.825223
$197$	11.1581	0.794978	0.397489	−	0.917607i	$-0.369882\pi$
$197$	11.1581	0.794978	0.397489	+	0.917607i	$0.369882\pi$
$198$	29.9054	2.12528
$199$	1.10353	0.0782273	0.0391137	−	0.999235i	$-0.487547\pi$
$199$	1.10353	0.0782273	0.0391137	+	0.999235i	$0.487547\pi$
$200$	25.5598	1.80735
$201$	−1.29316	−0.0912122
$202$	−13.4932	−0.949375
$203$	5.89098	0.413466
$204$	2.88050	0.201676
$205$	5.97617	0.417394
$206$	35.2320	2.45473
$207$	7.16474	0.497984
$208$	−34.3928	−2.38471
$209$	−33.6902	−2.33040
$210$	2.66899	0.184178
$211$	6.72094	0.462689	0.231344	−	0.972872i	$-0.425688\pi$
$211$	6.72094	0.462689	0.231344	+	0.972872i	$0.425688\pi$
$212$	−34.2815	−2.35446
$213$	−2.35778	−0.161553
$214$	19.2454	1.31559
$215$	−8.48535	−0.578696
$216$	14.0250	0.954280
$217$	0.502676	0.0341239
$218$	42.8474	2.90199
$219$	1.15457	0.0780183
$220$	15.4197	1.03960
$221$	−8.91729	−0.599842
$222$	−0.839606	−0.0563507
$223$	13.0251	0.872226	0.436113	−	0.899892i	$-0.356355\pi$
$223$	13.0251	0.872226	0.436113	+	0.899892i	$0.356355\pi$
$224$	12.4688	0.833108
$225$	12.1591	0.810606
$226$	−27.4094	−1.82324
$227$	14.7319	0.977791	0.488895	−	0.872342i	$-0.337400\pi$
$227$	14.7319	0.977791	0.488895	+	0.872342i	$0.337400\pi$
$228$	−14.1768	−0.938883
$229$	−26.3906	−1.74394	−0.871971	−	0.489557i	$-0.837158\pi$
$229$	−26.3906	−1.74394	−0.871971	+	0.489557i	$0.837158\pi$
$230$	5.38709	0.355214
$231$	−5.22504	−0.343783
$232$	11.3144	0.742827
$233$	7.39517	0.484474	0.242237	−	0.970217i	$-0.422119\pi$
$233$	7.39517	0.484474	0.242237	+	0.970217i	$0.422119\pi$
$234$	−38.9573	−2.54672
$235$	3.64237	0.237602
$236$	−53.3082	−3.47007
$237$	2.77907	0.180520
$238$	12.8409	0.832350
$239$	6.04872	0.391259	0.195630	−	0.980678i	$-0.437325\pi$
$239$	6.04872	0.391259	0.195630	+	0.980678i	$0.437325\pi$
$240$	2.15284	0.138965
$241$	26.7811	1.72512	0.862562	−	0.505951i	$-0.168859\pi$
$241$	26.7811	1.72512	0.862562	+	0.505951i	$0.168859\pi$
$242$	−16.2687	−1.04579
$243$	10.1004	0.647944
$244$	62.5646	4.00529
$245$	2.23877	0.143029
$246$	−7.17907	−0.457721
$247$	43.8878	2.79251
$248$	0.965455	0.0613065
$249$	−0.564673	−0.0357847
$250$	19.8109	1.25295
$251$	−6.75133	−0.426140	−0.213070	−	0.977037i	$-0.568346\pi$
$251$	−6.75133	−0.426140	−0.213070	+	0.977037i	$0.568346\pi$
$252$	38.4701	2.42339
$253$	−10.5463	−0.663037
$254$	−40.5014	−2.54128
$255$	0.558184	0.0349549
$256$	−31.2242	−1.95152
$257$	−11.2571	−0.702202	−0.351101	−	0.936338i	$-0.614193\pi$
$257$	−11.2571	−0.702202	−0.351101	+	0.936338i	$0.614193\pi$
$258$	10.1933	0.634607
$259$	−2.56670	−0.159487
$260$	−20.0870	−1.24574
$261$	5.38238	0.333161
$262$	−48.9477	−3.02400
$263$	−19.9575	−1.23063	−0.615317	−	0.788280i	$-0.710972\pi$
$263$	−19.9575	−1.23063	−0.615317	+	0.788280i	$0.710972\pi$
$264$	−10.0354	−0.617635
$265$	−6.64307	−0.408081
$266$	−63.1982	−3.87493
$267$	5.36253	0.328182
$268$	−14.0146	−0.856080
$269$	25.6162	1.56185	0.780923	−	0.624627i	$-0.214749\pi$
$269$	25.6162	1.56185	0.780923	+	0.624627i	$0.214749\pi$
$270$	5.01649	0.305294
$271$	−22.8808	−1.38991	−0.694955	−	0.719053i	$-0.744576\pi$
$271$	−22.8808	−1.38991	−0.694955	+	0.719053i	$0.744576\pi$
$272$	10.3576	0.628023
$273$	6.80658	0.411953
$274$	57.4549	3.47098
$275$	−17.8978	−1.07928
$276$	−4.43785	−0.267127
$277$	−9.87504	−0.593334	−0.296667	−	0.954981i	$-0.595875\pi$
$277$	−9.87504	−0.593334	−0.296667	+	0.954981i	$0.595875\pi$
$278$	4.69931	0.281846
$279$	0.459278	0.0274962
$280$	15.6707	0.936505
$281$	−15.2745	−0.911198	−0.455599	−	0.890185i	$-0.650575\pi$
$281$	−15.2745	−0.911198	−0.455599	+	0.890185i	$0.650575\pi$
$282$	−4.37552	−0.260558
$283$	26.0827	1.55046	0.775228	−	0.631682i	$-0.217635\pi$
$283$	26.0827	1.55046	0.775228	+	0.631682i	$0.217635\pi$
$284$	−25.5525	−1.51626
$285$	−2.74719	−0.162729
$286$	57.3438	3.39081
$287$	−21.9466	−1.29547
$288$	11.3923	0.671298
$289$	−14.3145	−0.842029
$290$	4.04696	0.237646
$291$	−2.76058	−0.161828
$292$	12.5126	0.732247
$293$	−30.5632	−1.78552	−0.892760	−	0.450533i	$-0.851234\pi$
$293$	−30.5632	−1.78552	−0.892760	+	0.450533i	$0.851234\pi$
$294$	−2.68939	−0.156848
$295$	−10.3301	−0.601440
$296$	−4.92967	−0.286531
$297$	−9.82072	−0.569856
$298$	−42.5318	−2.46380
$299$	13.7384	0.794514
$300$	−7.53136	−0.434823
$301$	31.1612	1.79610
$302$	8.72217	0.501904
$303$	2.15398	0.123743
$304$	−50.9766	−2.92371
$305$	12.1238	0.694205
$306$	11.7322	0.670688
$307$	18.9161	1.07960	0.539799	−	0.841794i	$-0.318500\pi$
$307$	18.9161	1.07960	0.539799	+	0.841794i	$0.318500\pi$
$308$	−56.6266	−3.22660
$309$	−5.62425	−0.319953
$310$	0.345326	0.0196132
$311$	−5.40493	−0.306486	−0.153243	−	0.988189i	$-0.548972\pi$
$311$	−5.40493	−0.306486	−0.153243	+	0.988189i	$0.548972\pi$
$312$	13.0729	0.740109
$313$	−15.3068	−0.865189	−0.432594	−	0.901589i	$-0.642402\pi$
$313$	−15.3068	−0.865189	−0.432594	+	0.901589i	$0.642402\pi$
$314$	−23.1897	−1.30867
$315$	7.45473	0.420027
$316$	30.1183	1.69429
$317$	−10.4113	−0.584756	−0.292378	−	0.956303i	$-0.594447\pi$
$317$	−10.4113	−0.584756	−0.292378	+	0.956303i	$0.594447\pi$
$318$	7.98021	0.447508
$319$	−7.92268	−0.443585
$320$	−2.12552	−0.118820
$321$	−3.07223	−0.171475
$322$	−19.7833	−1.10248
$323$	−13.2171	−0.735419
$324$	33.0250	1.83472
$325$	23.3151	1.29329
$326$	−24.3275	−1.34738
$327$	−6.83993	−0.378249
$328$	−42.1513	−2.32741
$329$	−13.3761	−0.737446
$330$	−3.58947	−0.197594
$331$	1.55723	0.0855929	0.0427965	−	0.999084i	$-0.486373\pi$
$331$	1.55723	0.0855929	0.0427965	+	0.999084i	$0.486373\pi$
$332$	−6.11966	−0.335860
$333$	−2.34510	−0.128511
$334$	−46.7819	−2.55979
$335$	−2.71576	−0.148378
$336$	−7.90599	−0.431307
$337$	−15.7306	−0.856903	−0.428451	−	0.903565i	$-0.640941\pi$
$337$	−15.7306	−0.856903	−0.428451	+	0.903565i	$0.640941\pi$
$338$	−41.9043	−2.27929
$339$	4.37549	0.237644
$340$	6.04934	0.328072
$341$	−0.676041	−0.0366097
$342$	−57.7420	−3.12233
$343$	13.5202	0.730023
$344$	59.8491	3.22685
$345$	−0.859967	−0.0462991
$346$	−1.09831	−0.0590453
$347$	−28.3292	−1.52079	−0.760395	−	0.649461i	$-0.774995\pi$
$347$	−28.3292	−1.52079	−0.760395	+	0.649461i	$0.774995\pi$
$348$	−3.33386	−0.178713
$349$	4.05340	0.216974	0.108487	−	0.994098i	$-0.465399\pi$
$349$	4.05340	0.216974	0.108487	+	0.994098i	$0.465399\pi$
$350$	−33.5737	−1.79459
$351$	12.7933	0.682856
$352$	−16.7691	−0.893796
$353$	−14.2531	−0.758617	−0.379309	−	0.925270i	$-0.623838\pi$
$353$	−14.2531	−0.758617	−0.379309	+	0.925270i	$0.623838\pi$
$354$	12.4093	0.659549
$355$	−4.95158	−0.262802
$356$	58.1166	3.08017
$357$	−2.04985	−0.108489
$358$	−14.9242	−0.788768
$359$	−29.5213	−1.55807	−0.779037	−	0.626978i	$-0.784291\pi$
$359$	−29.5213	−1.55807	−0.779037	+	0.626978i	$0.784291\pi$
$360$	14.3178	0.754614
$361$	46.0499	2.42368
$362$	−9.32047	−0.489873
$363$	2.59706	0.136310
$364$	73.7666	3.86642
$365$	2.42470	0.126915
$366$	−14.5641	−0.761277
$367$	−16.3873	−0.855408	−0.427704	−	0.903919i	$-0.640677\pi$
$367$	−16.3873	−0.855408	−0.427704	+	0.903919i	$0.640677\pi$
$368$	−15.9575	−0.831842
$369$	−20.0518	−1.04386
$370$	−1.76326	−0.0916673
$371$	24.3957	1.26656
$372$	−0.284477	−0.0147495
$373$	24.3513	1.26086	0.630431	−	0.776246i	$-0.282878\pi$
$373$	24.3513	1.26086	0.630431	+	0.776246i	$0.282878\pi$
$374$	−17.2695	−0.892983
$375$	−3.16251	−0.163311
$376$	−25.6905	−1.32489
$377$	10.3208	0.531546
$378$	−18.4223	−0.947541
$379$	−8.70830	−0.447316	−0.223658	−	0.974668i	$-0.571800\pi$
$379$	−8.70830	−0.447316	−0.223658	+	0.974668i	$0.571800\pi$
$380$	−29.7727	−1.52731
$381$	6.46543	0.331234
$382$	19.7144	1.00868
$383$	−6.69726	−0.342214	−0.171107	−	0.985252i	$-0.554734\pi$
$383$	−6.69726	−0.342214	−0.171107	+	0.985252i	$0.554734\pi$
$384$	5.78684	0.295308
$385$	−10.9731	−0.559241
$386$	4.15792	0.211633
$387$	28.4709	1.44726
$388$	−29.9179	−1.51885
$389$	2.57365	0.130489	0.0652447	−	0.997869i	$-0.479217\pi$
$389$	2.57365	0.130489	0.0652447	+	0.997869i	$0.479217\pi$
$390$	4.67595	0.236776
$391$	−4.13742	−0.209238
$392$	−15.7905	−0.797542
$393$	7.81376	0.394152
$394$	−28.1497	−1.41816
$395$	5.83633	0.293658
$396$	−51.7377	−2.59992
$397$	−18.0711	−0.906961	−0.453481	−	0.891266i	$-0.649818\pi$
$397$	−18.0711	−0.906961	−0.453481	+	0.891266i	$0.649818\pi$
$398$	−2.78401	−0.139550
$399$	10.0886	0.505063
$400$	−27.0810	−1.35405
$401$	3.03824	0.151723	0.0758613	−	0.997118i	$-0.475829\pi$
$401$	3.03824	0.151723	0.0758613	+	0.997118i	$0.475829\pi$
$402$	3.26239	0.162713
$403$	0.880668	0.0438692
$404$	23.3438	1.16140
$405$	6.39960	0.317999
$406$	−14.8618	−0.737581
$407$	3.45190	0.171105
$408$	−3.93700	−0.194911
$409$	2.61076	0.129094	0.0645470	−	0.997915i	$-0.479440\pi$
$409$	2.61076	0.129094	0.0645470	+	0.997915i	$0.479440\pi$
$410$	−15.0768	−0.744588
$411$	−9.17180	−0.452412
$412$	−60.9531	−3.00294
$413$	37.9357	1.86669
$414$	−18.0753	−0.888353
$415$	−1.18587	−0.0582120
$416$	21.8448	1.07103
$417$	−0.750174	−0.0367362
$418$	84.9942	4.15720
$419$	4.54141	0.221862	0.110931	−	0.993828i	$-0.464617\pi$
$419$	4.54141	0.221862	0.110931	+	0.993828i	$0.464617\pi$
$420$	−4.61747	−0.225310
$421$	−3.84856	−0.187567	−0.0937837	−	0.995593i	$-0.529896\pi$
$421$	−3.84856	−0.187567	−0.0937837	+	0.995593i	$0.529896\pi$
$422$	−16.9557	−0.825390
$423$	−12.2212	−0.594217
$424$	46.8551	2.27548
$425$	−7.02151	−0.340593
$426$	5.94824	0.288193
$427$	−44.5227	−2.15461
$428$	−33.2954	−1.60939
$429$	−9.15406	−0.441962
$430$	21.4069	1.03233
$431$	12.5927	0.606571	0.303285	−	0.952900i	$-0.401916\pi$
$431$	12.5927	0.606571	0.303285	+	0.952900i	$0.401916\pi$
$432$	−14.8597	−0.714937
$433$	38.0662	1.82934	0.914672	−	0.404198i	$-0.132449\pi$
$433$	38.0662	1.82934	0.914672	+	0.404198i	$0.132449\pi$
$434$	−1.26816	−0.0608735
$435$	−0.646035	−0.0309750
$436$	−74.1280	−3.55009
$437$	20.3629	0.974091
$438$	−2.91275	−0.139177
$439$	13.1534	0.627777	0.313889	−	0.949460i	$-0.398368\pi$
$439$	13.1534	0.627777	0.313889	+	0.949460i	$0.398368\pi$
$440$	−21.0753	−1.00473
$441$	−7.51172	−0.357701
$442$	22.4967	1.07006
$443$	−17.3540	−0.824513	−0.412256	−	0.911068i	$-0.635259\pi$
$443$	−17.3540	−0.824513	−0.412256	+	0.911068i	$0.635259\pi$
$444$	1.45256	0.0689353
$445$	11.2618	0.533863
$446$	−32.8599	−1.55596
$447$	6.78955	0.321135
$448$	7.80565	0.368782
$449$	27.7475	1.30949	0.654744	−	0.755851i	$-0.272777\pi$
$449$	27.7475	1.30949	0.654744	+	0.755851i	$0.272777\pi$
$450$	−30.6751	−1.44604
$451$	29.5156	1.38983
$452$	47.4195	2.23043
$453$	−1.39236	−0.0654188
$454$	−37.1658	−1.74428
$455$	14.2945	0.670137
$456$	19.3765	0.907389
$457$	−10.4033	−0.486645	−0.243322	−	0.969945i	$-0.578237\pi$
$457$	−10.4033	−0.486645	−0.243322	+	0.969945i	$0.578237\pi$
$458$	66.5786	3.11102
$459$	−3.85279	−0.179833
$460$	−9.31993	−0.434544
$461$	−9.30702	−0.433471	−0.216735	−	0.976230i	$-0.569541\pi$
$461$	−9.30702	−0.433471	−0.216735	+	0.976230i	$0.569541\pi$
$462$	13.1818	0.613273
$463$	−17.3301	−0.805400	−0.402700	−	0.915332i	$-0.631928\pi$
$463$	−17.3301	−0.805400	−0.402700	+	0.915332i	$0.631928\pi$
$464$	−11.9878	−0.556519
$465$	−0.0551260	−0.00255641
$466$	−18.6566	−0.864252
$467$	25.2813	1.16988	0.584939	−	0.811077i	$-0.301118\pi$
$467$	25.2813	1.16988	0.584939	+	0.811077i	$0.301118\pi$
$468$	67.3979	3.11547
$469$	9.97321	0.460520
$470$	−9.18902	−0.423858
$471$	3.70188	0.170574
$472$	72.8604	3.35367
$473$	−41.9081	−1.92694
$474$	−7.01109	−0.322030
$475$	34.5574	1.58560
$476$	−22.2153	−1.01824
$477$	22.2895	1.02056
$478$	−15.2598	−0.697967
$479$	8.21335	0.375277	0.187639	−	0.982238i	$-0.439917\pi$
$479$	8.21335	0.375277	0.187639	+	0.982238i	$0.439917\pi$
$480$	−1.36739	−0.0624127
$481$	−4.49674	−0.205034
$482$	−67.5638	−3.07745
$483$	3.15810	0.143699
$484$	28.1457	1.27935
$485$	−5.79750	−0.263251
$486$	−25.4815	−1.15587
$487$	7.34571	0.332866	0.166433	−	0.986053i	$-0.446775\pi$
$487$	7.34571	0.332866	0.166433	+	0.986053i	$0.446775\pi$
$488$	−85.5117	−3.87093
$489$	3.88352	0.175619
$490$	−5.64799	−0.255150
$491$	−6.49590	−0.293156	−0.146578	−	0.989199i	$-0.546826\pi$
$491$	−6.49590	−0.293156	−0.146578	+	0.989199i	$0.546826\pi$
$492$	12.4201	0.559943
$493$	−3.10817	−0.139985
$494$	−110.721	−4.98156
$495$	−10.0257	−0.450624
$496$	−1.02291	−0.0459302
$497$	18.1839	0.815660
$498$	1.42456	0.0638362
$499$	22.1376	0.991016	0.495508	−	0.868603i	$-0.334982\pi$
$499$	22.1376	0.991016	0.495508	+	0.868603i	$0.334982\pi$
$500$	−34.2738	−1.53277
$501$	7.46802	0.333646
$502$	17.0323	0.760190
$503$	29.6772	1.32324	0.661620	−	0.749839i	$-0.269869\pi$
$503$	29.6772	1.32324	0.661620	+	0.749839i	$0.269869\pi$
$504$	−52.5799	−2.34210
$505$	4.52356	0.201296
$506$	26.6062	1.18279
$507$	6.68938	0.297086
$508$	70.0694	3.10883
$509$	19.6435	0.870682	0.435341	−	0.900266i	$-0.356628\pi$
$509$	19.6435	0.870682	0.435341	+	0.900266i	$0.356628\pi$
$510$	−1.40819	−0.0623559
$511$	−8.90436	−0.393906
$512$	50.0348	2.21125
$513$	18.9621	0.837196
$514$	28.3997	1.25266
$515$	−11.8115	−0.520477
$516$	−17.6349	−0.776333
$517$	17.9892	0.791166
$518$	6.47529	0.284508
$519$	0.175328	0.00769604
$520$	27.4545	1.20396
$521$	−3.04319	−0.133324	−0.0666622	−	0.997776i	$-0.521235\pi$
$521$	−3.04319	−0.133324	−0.0666622	+	0.997776i	$0.521235\pi$
$522$	−13.5787	−0.594326
$523$	−25.1025	−1.09765	−0.548827	−	0.835936i	$-0.684925\pi$
$523$	−25.1025	−1.09765	−0.548827	+	0.835936i	$0.684925\pi$
$524$	84.6819	3.69935
$525$	5.35953	0.233909
$526$	50.3491	2.19533
$527$	−0.265219	−0.0115531
$528$	10.6326	0.462726
$529$	−16.6257	−0.722855
$530$	16.7592	0.727974
$531$	34.6605	1.50414
$532$	109.336	4.74031
$533$	−38.4495	−1.66543
$534$	−13.5287	−0.585442
$535$	−6.45199	−0.278944
$536$	19.1549	0.827364
$537$	2.38242	0.102809
$538$	−64.6248	−2.78617
$539$	11.0570	0.476259
$540$	−8.67876	−0.373475
$541$	33.9460	1.45945	0.729726	−	0.683740i	$-0.239648\pi$
$541$	33.9460	1.45945	0.729726	+	0.683740i	$0.239648\pi$
$542$	57.7240	2.47946
$543$	1.48787	0.0638506
$544$	−6.57872	−0.282060
$545$	−14.3645	−0.615309
$546$	−17.1717	−0.734883
$547$	10.5976	0.453119	0.226560	−	0.973997i	$-0.427252\pi$
$547$	10.5976	0.453119	0.226560	+	0.973997i	$0.427252\pi$
$548$	−99.3997	−4.24615
$549$	−40.6789	−1.73613
$550$	45.1527	1.92532
$551$	15.2973	0.651686
$552$	6.06555	0.258167
$553$	−21.4331	−0.911426
$554$	24.9129	1.05845
$555$	0.281477	0.0119480
$556$	−8.13004	−0.344790
$557$	−27.5883	−1.16895	−0.584476	−	0.811411i	$-0.698700\pi$
$557$	−27.5883	−1.16895	−0.584476	+	0.811411i	$0.698700\pi$
$558$	−1.15867	−0.0490505
$559$	54.5931	2.30904
$560$	−16.6034	−0.701620
$561$	2.75681	0.116392
$562$	38.5346	1.62548
$563$	17.7117	0.746460	0.373230	−	0.927739i	$-0.378250\pi$
$563$	17.7117	0.746460	0.373230	+	0.927739i	$0.378250\pi$
$564$	7.56985	0.318748
$565$	9.18896	0.386583
$566$	−65.8018	−2.76586
$567$	−23.5016	−0.986973
$568$	34.9246	1.46540
$569$	31.5391	1.32219	0.661095	−	0.750303i	$-0.270092\pi$
$569$	31.5391	1.32219	0.661095	+	0.750303i	$0.270092\pi$
$570$	6.93064	0.290292
$571$	10.5869	0.443046	0.221523	−	0.975155i	$-0.428897\pi$
$571$	10.5869	0.443046	0.221523	+	0.975155i	$0.428897\pi$
$572$	−99.2074	−4.14807
$573$	−3.14711	−0.131472
$574$	55.3671	2.31098
$575$	10.8177	0.451129
$576$	7.13174	0.297156
$577$	−22.6324	−0.942200	−0.471100	−	0.882080i	$-0.656143\pi$
$577$	−22.6324	−0.942200	−0.471100	+	0.882080i	$0.656143\pi$
$578$	36.1128	1.50209
$579$	−0.663749	−0.0275845
$580$	−7.00143	−0.290719
$581$	4.35492	0.180673
$582$	6.96444	0.288685
$583$	−32.8093	−1.35882
$584$	−17.1020	−0.707685
$585$	13.0604	0.539980
$586$	77.1052	3.18519
$587$	−16.4914	−0.680674	−0.340337	−	0.940304i	$-0.610541\pi$
$587$	−16.4914	−0.680674	−0.340337	+	0.940304i	$0.610541\pi$
$588$	4.65277	0.191877
$589$	1.30531	0.0537845
$590$	26.0608	1.07291
$591$	4.49367	0.184845
$592$	5.22306	0.214667
$593$	−35.0713	−1.44020	−0.720102	−	0.693868i	$-0.755905\pi$
$593$	−35.0713	−1.44020	−0.720102	+	0.693868i	$0.755905\pi$
$594$	24.7758	1.01657
$595$	−4.30489	−0.176483
$596$	73.5821	3.01404
$597$	0.444424	0.0181891
$598$	−34.6595	−1.41733
$599$	−18.2225	−0.744553	−0.372277	−	0.928122i	$-0.621423\pi$
$599$	−18.2225	−0.744553	−0.372277	+	0.928122i	$0.621423\pi$
$600$	10.2937	0.420238
$601$	11.3606	0.463409	0.231705	−	0.972786i	$-0.425570\pi$
$601$	11.3606	0.463409	0.231705	+	0.972786i	$0.425570\pi$
$602$	−78.6138	−3.20406
$603$	9.11217	0.371076
$604$	−15.0898	−0.613994
$605$	5.45408	0.221740
$606$	−5.43408	−0.220744
$607$	−33.9066	−1.37623	−0.688113	−	0.725604i	$-0.741561\pi$
$607$	−33.9066	−1.37623	−0.688113	+	0.725604i	$0.741561\pi$
$608$	32.3781	1.31311
$609$	2.37247	0.0961372
$610$	−30.5860	−1.23839
$611$	−23.4343	−0.948051
$612$	−20.2973	−0.820471
$613$	38.3741	1.54991	0.774957	−	0.632013i	$-0.217771\pi$
$613$	38.3741	1.54991	0.774957	+	0.632013i	$0.217771\pi$
$614$	−47.7217	−1.92589
$615$	2.40677	0.0970505
$616$	77.3958	3.11837
$617$	4.95531	0.199493	0.0997466	−	0.995013i	$-0.468197\pi$
$617$	4.95531	0.199493	0.0997466	+	0.995013i	$0.468197\pi$
$618$	14.1889	0.570763
$619$	38.7970	1.55939	0.779693	−	0.626163i	$-0.215375\pi$
$619$	38.7970	1.55939	0.779693	+	0.626163i	$0.215375\pi$
$620$	−0.597430	−0.0239934
$621$	5.93580	0.238196
$622$	13.6356	0.546739
$623$	−41.3574	−1.65695
$624$	−13.8510	−0.554483
$625$	14.7818	0.591271
$626$	38.6161	1.54341
$627$	−13.5680	−0.541855
$628$	40.1193	1.60093
$629$	1.35422	0.0539965
$630$	−18.8069	−0.749285
$631$	15.1327	0.602422	0.301211	−	0.953557i	$-0.402609\pi$
$631$	15.1327	0.602422	0.301211	+	0.953557i	$0.402609\pi$
$632$	−41.1650	−1.63746
$633$	2.70672	0.107582
$634$	26.2657	1.04315
$635$	13.5781	0.538829
$636$	−13.8061	−0.547449
$637$	−14.4038	−0.570699
$638$	19.9874	0.791311
$639$	16.6140	0.657240
$640$	12.1529	0.480387
$641$	0.285628	0.0112816	0.00564081	−	0.999984i	$-0.498204\pi$
$641$	0.285628	0.0112816	0.00564081	+	0.999984i	$0.498204\pi$
$642$	7.75066	0.305894
$643$	17.4932	0.689865	0.344933	−	0.938627i	$-0.387902\pi$
$643$	17.4932	0.689865	0.344933	+	0.938627i	$0.387902\pi$
$644$	34.2260	1.34870
$645$	−3.41729	−0.134556
$646$	33.3443	1.31191
$647$	29.8588	1.17387	0.586935	−	0.809634i	$-0.300334\pi$
$647$	29.8588	1.17387	0.586935	+	0.809634i	$0.300334\pi$
$648$	−45.1378	−1.77318
$649$	−51.0190	−2.00267
$650$	−58.8197	−2.30710
$651$	0.202442	0.00793433
$652$	42.0878	1.64828
$653$	−17.5107	−0.685247	−0.342623	−	0.939473i	$-0.611315\pi$
$653$	−17.5107	−0.685247	−0.342623	+	0.939473i	$0.611315\pi$
$654$	17.2559	0.674758
$655$	16.4097	0.641179
$656$	44.6599	1.74368
$657$	−8.13559	−0.317400
$658$	33.7453	1.31553
$659$	25.4748	0.992356	0.496178	−	0.868221i	$-0.334736\pi$
$659$	25.4748	0.992356	0.496178	+	0.868221i	$0.334736\pi$
$660$	6.20996	0.241722
$661$	1.94240	0.0755508	0.0377754	−	0.999286i	$-0.487973\pi$
$661$	1.94240	0.0755508	0.0377754	+	0.999286i	$0.487973\pi$
$662$	−3.92859	−0.152689
$663$	−3.59125	−0.139473
$664$	8.36420	0.324594
$665$	21.1871	0.821601
$666$	5.91625	0.229250
$667$	4.78860	0.185415
$668$	80.9349	3.13147
$669$	5.24559	0.202806
$670$	6.85135	0.264691
$671$	59.8779	2.31156
$672$	5.02155	0.193710
$673$	8.83823	0.340689	0.170344	−	0.985385i	$-0.445512\pi$
$673$	8.83823	0.340689	0.170344	+	0.985385i	$0.445512\pi$
$674$	39.6855	1.52863
$675$	10.0735	0.387729
$676$	72.4964	2.78832
$677$	33.1263	1.27315	0.636574	−	0.771215i	$-0.280351\pi$
$677$	33.1263	1.27315	0.636574	+	0.771215i	$0.280351\pi$
$678$	−11.0385	−0.423933
$679$	21.2904	0.817052
$680$	−8.26809	−0.317067
$681$	5.93296	0.227351
$682$	1.70552	0.0653079
$683$	38.6501	1.47890	0.739452	−	0.673210i	$-0.235085\pi$
$683$	38.6501	1.47890	0.739452	+	0.673210i	$0.235085\pi$
$684$	99.8963	3.81963
$685$	−19.2617	−0.735951
$686$	−34.1090	−1.30229
$687$	−10.6283	−0.405494
$688$	−63.4110	−2.41752
$689$	42.7402	1.62827
$690$	2.16954	0.0825929
$691$	−23.8800	−0.908438	−0.454219	−	0.890890i	$-0.650082\pi$
$691$	−23.8800	−0.908438	−0.454219	+	0.890890i	$0.650082\pi$
$692$	1.90012	0.0722318
$693$	36.8180	1.39860
$694$	71.4692	2.71293
$695$	−1.57544	−0.0597598
$696$	4.55663	0.172719
$697$	11.5793	0.438598
$698$	−10.2260	−0.387059
$699$	2.97825	0.112648
$700$	58.0841	2.19537
$701$	37.3665	1.41131	0.705656	−	0.708554i	$-0.250652\pi$
$701$	37.3665	1.41131	0.705656	+	0.708554i	$0.250652\pi$
$702$	−32.2751	−1.21815
$703$	−6.66501	−0.251376
$704$	−10.4977	−0.395646
$705$	1.46689	0.0552462
$706$	35.9580	1.35330
$707$	−16.6121	−0.624763
$708$	−21.4687	−0.806845
$709$	16.6562	0.625536	0.312768	−	0.949830i	$-0.398744\pi$
$709$	16.6562	0.625536	0.312768	+	0.949830i	$0.398744\pi$
$710$	12.4919	0.468813
$711$	−19.5826	−0.734406
$712$	−79.4324	−2.97685
$713$	0.408610	0.0153026
$714$	5.17138	0.193534
$715$	−19.2244	−0.718953
$716$	25.8196	0.964922
$717$	2.43599	0.0909739
$718$	74.4767	2.77944
$719$	50.9982	1.90191	0.950957	−	0.309324i	$-0.100103\pi$
$719$	50.9982	1.90191	0.950957	+	0.309324i	$0.100103\pi$
$720$	−15.1699	−0.565349
$721$	43.3759	1.61540
$722$	−116.175	−4.32359
$723$	10.7855	0.401118
$724$	16.1249	0.599275
$725$	8.12660	0.301814
$726$	−6.55189	−0.243163
$727$	−13.1678	−0.488367	−0.244184	−	0.969729i	$-0.578520\pi$
$727$	−13.1678	−0.488367	−0.244184	+	0.969729i	$0.578520\pi$
$728$	−100.822	−3.73673
$729$	−18.6320	−0.690076
$730$	−6.11707	−0.226403
$731$	−16.4411	−0.608095
$732$	25.1965	0.931291
$733$	−20.4107	−0.753886	−0.376943	−	0.926237i	$-0.623025\pi$
$733$	−20.4107	−0.753886	−0.376943	+	0.926237i	$0.623025\pi$
$734$	41.3420	1.52596
$735$	0.901615	0.0332566
$736$	10.1355	0.373600
$737$	−13.4128	−0.494067
$738$	50.5870	1.86213
$739$	21.2343	0.781117	0.390558	−	0.920578i	$-0.372282\pi$
$739$	21.2343	0.781117	0.390558	+	0.920578i	$0.372282\pi$
$740$	3.05052	0.112139
$741$	17.6749	0.649302
$742$	−61.5458	−2.25942
$743$	−10.6591	−0.391045	−0.195523	−	0.980699i	$-0.562640\pi$
$743$	−10.6591	−0.391045	−0.195523	+	0.980699i	$0.562640\pi$
$744$	0.388817	0.0142547
$745$	14.2587	0.522400
$746$	−61.4337	−2.24925
$747$	3.97894	0.145582
$748$	29.8770	1.09241
$749$	23.6940	0.865758
$750$	7.97841	0.291330
$751$	−36.0308	−1.31478	−0.657391	−	0.753549i	$-0.728340\pi$
$751$	−36.0308	−1.31478	−0.657391	+	0.753549i	$0.728340\pi$
$752$	27.2194	0.992591
$753$	−2.71895	−0.0990841
$754$	−26.0373	−0.948224
$755$	−2.92410	−0.106419
$756$	31.8715	1.15915
$757$	−39.6125	−1.43974	−0.719870	−	0.694109i	$-0.755799\pi$
$757$	−39.6125	−1.43974	−0.719870	+	0.694109i	$0.755799\pi$
$758$	21.9694	0.797965
$759$	−4.24728	−0.154166
$760$	40.6926	1.47608
$761$	−16.4618	−0.596739	−0.298370	−	0.954450i	$-0.596443\pi$
$761$	−16.4618	−0.596739	−0.298370	+	0.954450i	$0.596443\pi$
$762$	−16.3111	−0.590888
$763$	52.7516	1.90974
$764$	−34.1069	−1.23394
$765$	−3.93322	−0.142206
$766$	16.8959	0.610475
$767$	66.4617	2.39979
$768$	−12.5749	−0.453758
$769$	48.8368	1.76110	0.880550	−	0.473952i	$-0.157173\pi$
$769$	48.8368	1.76110	0.880550	+	0.473952i	$0.157173\pi$
$770$	27.6831	0.997630
$771$	−4.53358	−0.163273
$772$	−7.19340	−0.258896
$773$	−8.95582	−0.322118	−0.161059	−	0.986945i	$-0.551491\pi$
$773$	−8.95582	−0.322118	−0.161059	+	0.986945i	$0.551491\pi$
$774$	−71.8267	−2.58176
$775$	0.693441	0.0249091
$776$	40.8911	1.46790
$777$	−1.03368	−0.0370831
$778$	−6.49285	−0.232780
$779$	−56.9893	−2.04186
$780$	−8.08962	−0.289655
$781$	−24.4552	−0.875078
$782$	10.4379	0.373260
$783$	4.45917	0.159358
$784$	16.7303	0.597511
$785$	7.77432	0.277477
$786$	−19.7127	−0.703127
$787$	30.7057	1.09454	0.547271	−	0.836956i	$-0.315667\pi$
$787$	30.7057	1.09454	0.547271	+	0.836956i	$0.315667\pi$
$788$	48.7003	1.73488
$789$	−8.03747	−0.286141
$790$	−14.7240	−0.523856
$791$	−33.7451	−1.19984
$792$	70.7138	2.51271
$793$	−78.0020	−2.76993
$794$	45.5900	1.61793
$795$	−2.67535	−0.0948851
$796$	4.81646	0.170715
$797$	3.01974	0.106965	0.0534823	−	0.998569i	$-0.482968\pi$
$797$	3.01974	0.106965	0.0534823	+	0.998569i	$0.482968\pi$
$798$	−25.4517	−0.900981
$799$	7.05740	0.249673
$800$	17.2007	0.608137
$801$	−37.7868	−1.33513
$802$	−7.66492	−0.270658
$803$	11.9753	0.422600
$804$	−5.64409	−0.199052
$805$	6.63233	0.233759
$806$	−2.22176	−0.0782582
$807$	10.3164	0.363153
$808$	−31.9057	−1.12244
$809$	−45.0750	−1.58475	−0.792377	−	0.610032i	$-0.791156\pi$
$809$	−45.0750	−1.58475	−0.792377	+	0.610032i	$0.791156\pi$
$810$	−16.1450	−0.567277
$811$	−22.4789	−0.789340	−0.394670	−	0.918823i	$-0.629141\pi$
$811$	−22.4789	−0.789340	−0.394670	+	0.918823i	$0.629141\pi$
$812$	25.7117	0.902304
$813$	−9.21476	−0.323176
$814$	−8.70851	−0.305233
$815$	8.15577	0.285684
$816$	4.17131	0.146025
$817$	80.9171	2.83093
$818$	−6.58647	−0.230291
$819$	−47.9623	−1.67594
$820$	26.0835	0.910875
$821$	29.9768	1.04620	0.523098	−	0.852273i	$-0.324776\pi$
$821$	29.9768	1.04620	0.523098	+	0.852273i	$0.324776\pi$
$822$	23.1387	0.807056
$823$	−54.8637	−1.91243	−0.956214	−	0.292669i	$-0.905457\pi$
$823$	−54.8637	−1.91243	−0.956214	+	0.292669i	$0.905457\pi$
$824$	83.3092	2.90221
$825$	−7.20794	−0.250948
$826$	−95.7046	−3.32999
$827$	25.1881	0.875876	0.437938	−	0.899005i	$-0.355709\pi$
$827$	25.1881	0.875876	0.437938	+	0.899005i	$0.355709\pi$
$828$	31.2711	1.08675
$829$	−13.2582	−0.460477	−0.230239	−	0.973134i	$-0.573951\pi$
$829$	−13.2582	−0.460477	−0.230239	+	0.973134i	$0.573951\pi$
$830$	2.99172	0.103844
$831$	−3.97696	−0.137959
$832$	13.6752	0.474101
$833$	4.33780	0.150296
$834$	1.89255	0.0655336
$835$	15.6836	0.542753
$836$	−147.044	−5.08562
$837$	0.380500	0.0131520
$838$	−11.4571	−0.395780
$839$	0.832092	0.0287270	0.0143635	−	0.999897i	$-0.495428\pi$
$839$	0.832092	0.0287270	0.0143635	+	0.999897i	$0.495428\pi$
$840$	6.31105	0.217752
$841$	−25.4027	−0.875953
$842$	9.70920	0.334601
$843$	−6.15146	−0.211868
$844$	29.3341	1.00972
$845$	14.0484	0.483278
$846$	30.8319	1.06002
$847$	−20.0293	−0.688214
$848$	−49.6437	−1.70477
$849$	10.5043	0.360505
$850$	17.7140	0.607584
$851$	−2.08639	−0.0715205
$852$	−10.2907	−0.352555
$853$	−13.9023	−0.476007	−0.238003	−	0.971264i	$-0.576493\pi$
$853$	−13.9023	−0.476007	−0.238003	+	0.971264i	$0.576493\pi$
$854$	112.323	3.84360
$855$	19.3579	0.662027
$856$	45.5073	1.55541
$857$	−34.3949	−1.17491	−0.587454	−	0.809257i	$-0.699870\pi$
$857$	−34.3949	−1.17491	−0.587454	+	0.809257i	$0.699870\pi$
$858$	23.0940	0.788415
$859$	−44.9837	−1.53482	−0.767411	−	0.641155i	$-0.778456\pi$
$859$	−44.9837	−1.53482	−0.767411	+	0.641155i	$0.778456\pi$
$860$	−37.0350	−1.26288
$861$	−8.83852	−0.301216
$862$	−31.7691	−1.08206
$863$	16.8349	0.573067	0.286533	−	0.958070i	$-0.407497\pi$
$863$	16.8349	0.573067	0.286533	+	0.958070i	$0.407497\pi$
$864$	9.43824	0.321095
$865$	0.368206	0.0125194
$866$	−96.0338	−3.26336
$867$	−5.76486	−0.195785
$868$	2.19397	0.0744683
$869$	28.8250	0.977820
$870$	1.62983	0.0552563
$871$	17.4727	0.592038
$872$	101.316	3.43100
$873$	19.4523	0.658362
$874$	−51.3719	−1.73768
$875$	24.3902	0.824539
$876$	5.03920	0.170259
$877$	21.6425	0.730815	0.365407	−	0.930848i	$-0.380930\pi$
$877$	21.6425	0.730815	0.365407	+	0.930848i	$0.380930\pi$
$878$	−33.1836	−1.11989
$879$	−12.3087	−0.415161
$880$	22.3296	0.752730
$881$	17.8811	0.602430	0.301215	−	0.953556i	$-0.402608\pi$
$881$	17.8811	0.602430	0.301215	+	0.953556i	$0.402608\pi$
$882$	18.9507	0.638102
$883$	−41.6215	−1.40067	−0.700337	−	0.713812i	$-0.746967\pi$
$883$	−41.6215	−1.40067	−0.700337	+	0.713812i	$0.746967\pi$
$884$	−38.9203	−1.30903
$885$	−4.16022	−0.139844
$886$	43.7809	1.47085
$887$	10.0556	0.337635	0.168818	−	0.985647i	$-0.446005\pi$
$887$	10.0556	0.337635	0.168818	+	0.985647i	$0.446005\pi$
$888$	−1.98532	−0.0666230
$889$	−49.8634	−1.67236
$890$	−28.4115	−0.952357
$891$	31.6069	1.05887
$892$	56.8493	1.90345
$893$	−34.7340	−1.16233
$894$	−17.1288	−0.572872
$895$	5.00332	0.167242
$896$	−44.6298	−1.49098
$897$	5.53286	0.184737
$898$	−70.0018	−2.33599
$899$	0.306961	0.0102377
$900$	53.0694	1.76898
$901$	−12.8715	−0.428812
$902$	−74.4623	−2.47932
$903$	12.5495	0.417621
$904$	−64.8118	−2.15561
$905$	3.12468	0.103868
$906$	3.51267	0.116701
$907$	−18.1919	−0.604052	−0.302026	−	0.953300i	$-0.597663\pi$
$907$	−18.1919	−0.604052	−0.302026	+	0.953300i	$0.597663\pi$
$908$	64.2987	2.13383
$909$	−15.1779	−0.503419
$910$	−36.0624	−1.19546
$911$	0.965263	0.0319806	0.0159903	−	0.999872i	$-0.494910\pi$
$911$	0.965263	0.0319806	0.0159903	+	0.999872i	$0.494910\pi$
$912$	−20.5297	−0.679807
$913$	−5.85686	−0.193834
$914$	26.2455	0.868125
$915$	4.88259	0.161413
$916$	−115.184	−3.80579
$917$	−60.2620	−1.99003
$918$	9.71987	0.320803
$919$	−53.3039	−1.75833	−0.879167	−	0.476514i	$-0.841900\pi$
$919$	−53.3039	−1.75833	−0.879167	+	0.476514i	$0.841900\pi$
$920$	12.7383	0.419968
$921$	7.61804	0.251023
$922$	23.4799	0.773268
$923$	31.8575	1.04860
$924$	−22.8052	−0.750234
$925$	−3.54075	−0.116419
$926$	43.7207	1.43675
$927$	39.6311	1.30165
$928$	7.61412	0.249946
$929$	56.0134	1.83774	0.918870	−	0.394561i	$-0.129103\pi$
$929$	56.0134	1.83774	0.918870	+	0.394561i	$0.129103\pi$
$930$	0.139073	0.00456037
$931$	−21.3491	−0.699688
$932$	32.2769	1.05726
$933$	−2.17672	−0.0712626
$934$	−63.7800	−2.08694
$935$	5.78957	0.189339
$936$	−92.1178	−3.01097
$937$	22.4628	0.733829	0.366914	−	0.930255i	$-0.380414\pi$
$937$	22.4628	0.733829	0.366914	+	0.930255i	$0.380414\pi$
$938$	−25.1606	−0.821521
$939$	−6.16447	−0.201170
$940$	15.8974	0.518517
$941$	35.2672	1.14968	0.574839	−	0.818267i	$-0.305065\pi$
$941$	35.2672	1.14968	0.574839	+	0.818267i	$0.305065\pi$
$942$	−9.33915	−0.304286
$943$	−17.8397	−0.580941
$944$	−77.1967	−2.51254
$945$	6.17606	0.200907
$946$	105.726	3.43746
$947$	−8.15096	−0.264871	−0.132435	−	0.991192i	$-0.542280\pi$
$947$	−8.15096	−0.264871	−0.132435	+	0.991192i	$0.542280\pi$
$948$	12.1295	0.393948
$949$	−15.6001	−0.506399
$950$	−87.1818	−2.82855
$951$	−4.19292	−0.135965
$952$	30.3633	0.984081
$953$	−2.83771	−0.0919223	−0.0459611	−	0.998943i	$-0.514635\pi$
$953$	−2.83771	−0.0919223	−0.0459611	+	0.998943i	$0.514635\pi$
$954$	−56.2322	−1.82058
$955$	−6.60924	−0.213870
$956$	26.4002	0.853843
$957$	−3.19069	−0.103140
$958$	−20.7207	−0.669457
$959$	70.7357	2.28417
$960$	−0.856007	−0.0276275
$961$	−30.9738	−0.999155
$962$	11.3444	0.365760
$963$	21.6483	0.697608
$964$	116.889	3.76473
$965$	−1.39394	−0.0448725
$966$	−7.96730	−0.256344
$967$	−32.8006	−1.05480	−0.527399	−	0.849618i	$-0.676833\pi$
$967$	−32.8006	−1.05480	−0.527399	+	0.849618i	$0.676833\pi$
$968$	−38.4688	−1.23644
$969$	−5.32290	−0.170996
$970$	14.6260	0.469613
$971$	−30.3713	−0.974661	−0.487331	−	0.873218i	$-0.662029\pi$
$971$	−30.3713	−0.974661	−0.487331	+	0.873218i	$0.662029\pi$
$972$	44.0843	1.41400
$973$	5.78557	0.185477
$974$	−18.5318	−0.593799
$975$	9.38967	0.300710
$976$	90.6010	2.90007
$977$	−9.08680	−0.290712	−0.145356	−	0.989379i	$-0.546433\pi$
$977$	−9.08680	−0.290712	−0.145356	+	0.989379i	$0.546433\pi$
$978$	−9.79739	−0.313286
$979$	55.6209	1.77765
$980$	9.77129	0.312132
$981$	48.1973	1.53882
$982$	16.3879	0.522960
$983$	14.6669	0.467803	0.233901	−	0.972260i	$-0.424851\pi$
$983$	14.6669	0.467803	0.233901	+	0.972260i	$0.424851\pi$
$984$	−16.9755	−0.541160
$985$	9.43715	0.300692
$986$	7.84132	0.249719
$987$	−5.38692	−0.171468
$988$	191.552	6.09408
$989$	25.3300	0.805446
$990$	25.2931	0.803867
$991$	−22.0887	−0.701670	−0.350835	−	0.936437i	$-0.614102\pi$
$991$	−22.0887	−0.701670	−0.350835	+	0.936437i	$0.614102\pi$
$992$	0.649711	0.0206284
$993$	0.627140	0.0199017
$994$	−45.8746	−1.45506
$995$	0.933335	0.0295887
$996$	−2.46456	−0.0780926
$997$	50.4588	1.59805	0.799024	−	0.601299i	$-0.205350\pi$
$997$	50.4588	1.59805	0.799024	+	0.601299i	$0.205350\pi$
$998$	−55.8491	−1.76787
$999$	−1.94285	−0.0614692

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6011.2.a.f.1.20	✓	275

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6011.2.a.f.1.20	✓	275	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:	\( N \)	\(=\)	\( 6011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6011.a (trivial)

\(f(q)\)	\(=\)	\(q-2.52281 q^{2} +0.402729 q^{3} +4.36459 q^{4} +0.845770 q^{5} -1.01601 q^{6} -3.10596 q^{7} -5.96541 q^{8} -2.83781 q^{9} +O(q^{10})\)	\(q-2.52281 q^{2} +0.402729 q^{3} +4.36459 q^{4} +0.845770 q^{5} -1.01601 q^{6} -3.10596 q^{7} -5.96541 q^{8} -2.83781 q^{9} -2.13372 q^{10} +4.17716 q^{11} +1.75774 q^{12} -5.44152 q^{13} +7.83577 q^{14} +0.340616 q^{15} +6.32044 q^{16} +1.63875 q^{17} +7.15926 q^{18} -8.06535 q^{19} +3.69144 q^{20} -1.25086 q^{21} -10.5382 q^{22} -2.52474 q^{23} -2.40244 q^{24} -4.28467 q^{25} +13.7279 q^{26} -2.35105 q^{27} -13.5562 q^{28} -1.89667 q^{29} -0.859310 q^{30} -0.161842 q^{31} -4.01447 q^{32} +1.68226 q^{33} -4.13426 q^{34} -2.62693 q^{35} -12.3859 q^{36} +0.826376 q^{37} +20.3474 q^{38} -2.19146 q^{39} -5.04537 q^{40} +7.06595 q^{41} +3.15569 q^{42} -10.0327 q^{43} +18.2316 q^{44} -2.40013 q^{45} +6.36945 q^{46} +4.30657 q^{47} +2.54542 q^{48} +2.64701 q^{49} +10.8094 q^{50} +0.659972 q^{51} -23.7500 q^{52} -7.85446 q^{53} +5.93127 q^{54} +3.53292 q^{55} +18.5283 q^{56} -3.24815 q^{57} +4.78494 q^{58} -12.2138 q^{59} +1.48665 q^{60} +14.3346 q^{61} +0.408298 q^{62} +8.81414 q^{63} -2.51312 q^{64} -4.60228 q^{65} -4.24403 q^{66} -3.21099 q^{67} +7.15247 q^{68} -1.01679 q^{69} +6.62726 q^{70} -5.85452 q^{71} +16.9287 q^{72} +2.86686 q^{73} -2.08479 q^{74} -1.72556 q^{75} -35.2019 q^{76} -12.9741 q^{77} +5.52863 q^{78} +6.90061 q^{79} +5.34564 q^{80} +7.56659 q^{81} -17.8261 q^{82} -1.40212 q^{83} -5.45949 q^{84} +1.38601 q^{85} +25.3106 q^{86} -0.763843 q^{87} -24.9185 q^{88} +13.3155 q^{89} +6.05509 q^{90} +16.9012 q^{91} -11.0195 q^{92} -0.0651785 q^{93} -10.8647 q^{94} -6.82143 q^{95} -1.61674 q^{96} -6.85470 q^{97} -6.67792 q^{98} -11.8540 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 275 q + 16 q^{2} + 9 q^{3} + 316 q^{4} + 36 q^{5} + 30 q^{6} + 41 q^{7} + 36 q^{8} + 322 q^{9}+O(q^{10}) \) 275 * q + 16 * q^2 + 9 * q^3 + 316 * q^4 + 36 * q^5 + 30 * q^6 + 41 * q^7 + 36 * q^8 + 322 * q^9	\( 275 q + 16 q^{2} + 9 q^{3} + 316 q^{4} + 36 q^{5} + 30 q^{6} + 41 q^{7} + 36 q^{8} + 322 q^{9} + 44 q^{10} + 42 q^{11} + 26 q^{12} + 97 q^{13} + 24 q^{14} + 46 q^{15} + 386 q^{16} + 35 q^{17} + 47 q^{18} + 101 q^{19} + 60 q^{20} + 187 q^{21} + 72 q^{22} + 35 q^{23} + 73 q^{24} + 373 q^{25} + 21 q^{26} + 27 q^{27} + 97 q^{28} + 162 q^{29} + 13 q^{30} + 113 q^{31} + 58 q^{32} + 16 q^{33} + 52 q^{34} + 23 q^{35} + 426 q^{36} + 257 q^{37} + 8 q^{38} + 87 q^{39} + 126 q^{40} + 77 q^{41} - 7 q^{42} + 107 q^{43} + 133 q^{44} + 140 q^{45} + 207 q^{46} + 24 q^{47} + 4 q^{48} + 418 q^{49} + 65 q^{50} + 94 q^{51} + 142 q^{52} + 81 q^{53} + 79 q^{54} + 26 q^{55} + 62 q^{56} + 112 q^{57} + 44 q^{58} + 30 q^{59} + 83 q^{60} + 347 q^{61} + 5 q^{62} + 97 q^{63} + 508 q^{64} + 94 q^{65} + 4 q^{66} + 98 q^{67} + 28 q^{68} + 91 q^{69} + 17 q^{70} + 58 q^{71} + 99 q^{72} + 157 q^{73} + 80 q^{74} + 83 q^{75} + 264 q^{76} + 61 q^{77} + 5 q^{78} + 282 q^{79} + 49 q^{80} + 403 q^{81} + 46 q^{82} + 43 q^{83} + 318 q^{84} + 396 q^{85} + 57 q^{86} + 31 q^{87} + 180 q^{88} + 98 q^{89} + 67 q^{90} + 195 q^{91} + 97 q^{92} + 83 q^{93} + 96 q^{94} + 28 q^{95} + 127 q^{96} + 167 q^{97} + 24 q^{98} + 133 q^{99}+O(q^{100}) \) 275 * q + 16 * q^2 + 9 * q^3 + 316 * q^4 + 36 * q^5 + 30 * q^6 + 41 * q^7 + 36 * q^8 + 322 * q^9 + 44 * q^10 + 42 * q^11 + 26 * q^12 + 97 * q^13 + 24 * q^14 + 46 * q^15 + 386 * q^16 + 35 * q^17 + 47 * q^18 + 101 * q^19 + 60 * q^20 + 187 * q^21 + 72 * q^22 + 35 * q^23 + 73 * q^24 + 373 * q^25 + 21 * q^26 + 27 * q^27 + 97 * q^28 + 162 * q^29 + 13 * q^30 + 113 * q^31 + 58 * q^32 + 16 * q^33 + 52 * q^34 + 23 * q^35 + 426 * q^36 + 257 * q^37 + 8 * q^38 + 87 * q^39 + 126 * q^40 + 77 * q^41 - 7 * q^42 + 107 * q^43 + 133 * q^44 + 140 * q^45 + 207 * q^46 + 24 * q^47 + 4 * q^48 + 418 * q^49 + 65 * q^50 + 94 * q^51 + 142 * q^52 + 81 * q^53 + 79 * q^54 + 26 * q^55 + 62 * q^56 + 112 * q^57 + 44 * q^58 + 30 * q^59 + 83 * q^60 + 347 * q^61 + 5 * q^62 + 97 * q^63 + 508 * q^64 + 94 * q^65 + 4 * q^66 + 98 * q^67 + 28 * q^68 + 91 * q^69 + 17 * q^70 + 58 * q^71 + 99 * q^72 + 157 * q^73 + 80 * q^74 + 83 * q^75 + 264 * q^76 + 61 * q^77 + 5 * q^78 + 282 * q^79 + 49 * q^80 + 403 * q^81 + 46 * q^82 + 43 * q^83 + 318 * q^84 + 396 * q^85 + 57 * q^86 + 31 * q^87 + 180 * q^88 + 98 * q^89 + 67 * q^90 + 195 * q^91 + 97 * q^92 + 83 * q^93 + 96 * q^94 + 28 * q^95 + 127 * q^96 + 167 * q^97 + 24 * q^98 + 133 * q^99

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