LMFDB - Embedded newform 6007.2.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6007,2,Mod(1,6007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6007, 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("6007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6007 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6007.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:	$47.9661364942$
Analytic rank:	$1$
Dimension:	$237$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	6007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.79278 q^{2} +2.70470 q^{3} +5.79960 q^{4} +2.04099 q^{5} -7.55362 q^{6} -2.59733 q^{7} -10.6114 q^{8} +4.31540 q^{9} +O(q^{10})$	\(q-2.79278 q^{2} +2.70470 q^{3} +5.79960 q^{4} +2.04099 q^{5} -7.55362 q^{6} -2.59733 q^{7} -10.6114 q^{8} +4.31540 q^{9} -5.70003 q^{10} -0.699263 q^{11} +15.6862 q^{12} -6.81399 q^{13} +7.25377 q^{14} +5.52026 q^{15} +18.0362 q^{16} -5.32691 q^{17} -12.0519 q^{18} +5.65212 q^{19} +11.8369 q^{20} -7.02500 q^{21} +1.95289 q^{22} +4.91564 q^{23} -28.7008 q^{24} -0.834365 q^{25} +19.0299 q^{26} +3.55776 q^{27} -15.0635 q^{28} +3.49298 q^{29} -15.4169 q^{30} +3.07578 q^{31} -29.1482 q^{32} -1.89130 q^{33} +14.8769 q^{34} -5.30112 q^{35} +25.0276 q^{36} -4.64934 q^{37} -15.7851 q^{38} -18.4298 q^{39} -21.6578 q^{40} +6.73132 q^{41} +19.6193 q^{42} -2.80003 q^{43} -4.05545 q^{44} +8.80768 q^{45} -13.7283 q^{46} +1.71226 q^{47} +48.7825 q^{48} -0.253874 q^{49} +2.33020 q^{50} -14.4077 q^{51} -39.5184 q^{52} -3.80882 q^{53} -9.93602 q^{54} -1.42719 q^{55} +27.5614 q^{56} +15.2873 q^{57} -9.75511 q^{58} -7.95123 q^{59} +32.0153 q^{60} -6.31070 q^{61} -8.58998 q^{62} -11.2085 q^{63} +45.3320 q^{64} -13.9073 q^{65} +5.28197 q^{66} +2.51519 q^{67} -30.8940 q^{68} +13.2953 q^{69} +14.8049 q^{70} -14.6307 q^{71} -45.7926 q^{72} +10.4588 q^{73} +12.9846 q^{74} -2.25671 q^{75} +32.7800 q^{76} +1.81622 q^{77} +51.4703 q^{78} -2.22840 q^{79} +36.8117 q^{80} -3.32354 q^{81} -18.7991 q^{82} -2.26372 q^{83} -40.7422 q^{84} -10.8722 q^{85} +7.81986 q^{86} +9.44746 q^{87} +7.42020 q^{88} +1.35585 q^{89} -24.5979 q^{90} +17.6982 q^{91} +28.5088 q^{92} +8.31907 q^{93} -4.78197 q^{94} +11.5359 q^{95} -78.8371 q^{96} +1.17228 q^{97} +0.709015 q^{98} -3.01760 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 237 q - 26 q^{2} - 24 q^{3} + 226 q^{4} - 67 q^{5} - 30 q^{6} - 37 q^{7} - 75 q^{8} + 189 q^{9}+O(q^{10}) $ 237 * q - 26 * q^2 - 24 * q^3 + 226 * q^4 - 67 * q^5 - 30 * q^6 - 37 * q^7 - 75 * q^8 + 189 * q^9	\( 237 q - 26 q^{2} - 24 q^{3} + 226 q^{4} - 67 q^{5} - 30 q^{6} - 37 q^{7} - 75 q^{8} + 189 q^{9} - 39 q^{10} - 38 q^{11} - 67 q^{12} - 52 q^{13} - 54 q^{14} - 24 q^{15} + 208 q^{16} - 255 q^{17} - 71 q^{18} - 24 q^{19} - 154 q^{20} - 60 q^{21} - 39 q^{22} - 118 q^{23} - 85 q^{24} + 170 q^{25} - 61 q^{26} - 87 q^{27} - 99 q^{28} - 87 q^{29} - 30 q^{30} - 28 q^{31} - 156 q^{32} - 173 q^{33} - 4 q^{34} - 113 q^{35} + 152 q^{36} - 49 q^{37} - 145 q^{38} - 49 q^{39} - 91 q^{40} - 197 q^{41} - 61 q^{42} - 63 q^{43} - 106 q^{44} - 181 q^{45} - 2 q^{46} - 119 q^{47} - 142 q^{48} + 150 q^{49} - 89 q^{50} - 40 q^{51} - 97 q^{52} - 190 q^{53} - 97 q^{54} - 55 q^{55} - 154 q^{56} - 202 q^{57} - 27 q^{58} - 86 q^{59} - 48 q^{60} - 96 q^{61} - 239 q^{62} - 149 q^{63} + 183 q^{64} - 259 q^{65} - 72 q^{66} - 28 q^{67} - 482 q^{68} - 83 q^{69} + 20 q^{70} - 63 q^{71} - 193 q^{72} - 206 q^{73} - 132 q^{74} - 89 q^{75} - 11 q^{76} - 179 q^{77} - 58 q^{78} - 32 q^{79} - 320 q^{80} + 57 q^{81} - 77 q^{82} - 245 q^{83} - 133 q^{84} + q^{85} - 39 q^{86} - 179 q^{87} - 104 q^{88} - 227 q^{89} - 146 q^{90} - 36 q^{91} - 315 q^{92} - 87 q^{93} - 48 q^{94} - 111 q^{95} - 134 q^{96} - 221 q^{97} - 161 q^{98} - 68 q^{99}+O(q^{100}) \) 237 * q - 26 * q^2 - 24 * q^3 + 226 * q^4 - 67 * q^5 - 30 * q^6 - 37 * q^7 - 75 * q^8 + 189 * q^9 - 39 * q^10 - 38 * q^11 - 67 * q^12 - 52 * q^13 - 54 * q^14 - 24 * q^15 + 208 * q^16 - 255 * q^17 - 71 * q^18 - 24 * q^19 - 154 * q^20 - 60 * q^21 - 39 * q^22 - 118 * q^23 - 85 * q^24 + 170 * q^25 - 61 * q^26 - 87 * q^27 - 99 * q^28 - 87 * q^29 - 30 * q^30 - 28 * q^31 - 156 * q^32 - 173 * q^33 - 4 * q^34 - 113 * q^35 + 152 * q^36 - 49 * q^37 - 145 * q^38 - 49 * q^39 - 91 * q^40 - 197 * q^41 - 61 * q^42 - 63 * q^43 - 106 * q^44 - 181 * q^45 - 2 * q^46 - 119 * q^47 - 142 * q^48 + 150 * q^49 - 89 * q^50 - 40 * q^51 - 97 * q^52 - 190 * q^53 - 97 * q^54 - 55 * q^55 - 154 * q^56 - 202 * q^57 - 27 * q^58 - 86 * q^59 - 48 * q^60 - 96 * q^61 - 239 * q^62 - 149 * q^63 + 183 * q^64 - 259 * q^65 - 72 * q^66 - 28 * q^67 - 482 * q^68 - 83 * q^69 + 20 * q^70 - 63 * q^71 - 193 * q^72 - 206 * q^73 - 132 * q^74 - 89 * q^75 - 11 * q^76 - 179 * q^77 - 58 * q^78 - 32 * q^79 - 320 * q^80 + 57 * q^81 - 77 * q^82 - 245 * q^83 - 133 * q^84 + q^85 - 39 * q^86 - 179 * q^87 - 104 * q^88 - 227 * q^89 - 146 * q^90 - 36 * q^91 - 315 * q^92 - 87 * q^93 - 48 * q^94 - 111 * q^95 - 134 * q^96 - 221 * q^97 - 161 * q^98 - 68 * 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 $

$2$	−2.79278	−1.97479	−0.987396	−	0.158270i	$-0.949408\pi$
$2$	−2.79278	−1.97479	−0.987396	+	0.158270i	$0.949408\pi$
$3$	2.70470	1.56156	0.780779	−	0.624807i	$-0.214822\pi$
$3$	2.70470	1.56156	0.780779	+	0.624807i	$0.214822\pi$
$4$	5.79960	2.89980
$5$	2.04099	0.912758	0.456379	−	0.889786i	$-0.349146\pi$
$5$	2.04099	0.912758	0.456379	+	0.889786i	$0.349146\pi$
$6$	−7.55362	−3.08375
$7$	−2.59733	−0.981699	−0.490849	−	0.871244i	$-0.663313\pi$
$7$	−2.59733	−0.981699	−0.490849	+	0.871244i	$0.663313\pi$
$8$	−10.6114	−3.75171
$9$	4.31540	1.43847
$10$	−5.70003	−1.80251
$11$	−0.699263	−0.210836	−0.105418	−	0.994428i	$-0.533618\pi$
$11$	−0.699263	−0.210836	−0.105418	+	0.994428i	$0.533618\pi$
$12$	15.6862	4.52821
$13$	−6.81399	−1.88986	−0.944930	−	0.327273i	$-0.893870\pi$
$13$	−6.81399	−1.88986	−0.944930	+	0.327273i	$0.893870\pi$
$14$	7.25377	1.93865
$15$	5.52026	1.42533
$16$	18.0362	4.50905
$17$	−5.32691	−1.29197	−0.645983	−	0.763352i	$-0.723552\pi$
$17$	−5.32691	−1.29197	−0.645983	+	0.763352i	$0.723552\pi$
$18$	−12.0519	−2.84067
$19$	5.65212	1.29668	0.648342	−	0.761349i	$-0.275463\pi$
$19$	5.65212	1.29668	0.648342	+	0.761349i	$0.275463\pi$
$20$	11.8369	2.64682
$21$	−7.02500	−1.53298
$22$	1.95289	0.416357
$23$	4.91564	1.02498	0.512491	−	0.858693i	$-0.328723\pi$
$23$	4.91564	1.02498	0.512491	+	0.858693i	$0.328723\pi$
$24$	−28.7008	−5.85852
$25$	−0.834365	−0.166873
$26$	19.0299	3.73208
$27$	3.55776	0.684690
$28$	−15.0635	−2.84673
$29$	3.49298	0.648630	0.324315	−	0.945949i	$-0.394866\pi$
$29$	3.49298	0.648630	0.324315	+	0.945949i	$0.394866\pi$
$30$	−15.4169	−2.81472
$31$	3.07578	0.552427	0.276214	−	0.961096i	$-0.410920\pi$
$31$	3.07578	0.552427	0.276214	+	0.961096i	$0.410920\pi$
$32$	−29.1482	−5.15272
$33$	−1.89130	−0.329233
$34$	14.8769	2.55136
$35$	−5.30112	−0.896053
$36$	25.0276	4.17127
$37$	−4.64934	−0.764347	−0.382174	−	0.924091i	$-0.624824\pi$
$37$	−4.64934	−0.764347	−0.382174	+	0.924091i	$0.624824\pi$
$38$	−15.7851	−2.56068
$39$	−18.4298	−2.95113
$40$	−21.6578	−3.42441
$41$	6.73132	1.05125	0.525627	−	0.850715i	$-0.323831\pi$
$41$	6.73132	1.05125	0.525627	+	0.850715i	$0.323831\pi$
$42$	19.6193	3.02732
$43$	−2.80003	−0.427001	−0.213500	−	0.976943i	$-0.568486\pi$
$43$	−2.80003	−0.427001	−0.213500	+	0.976943i	$0.568486\pi$
$44$	−4.05545	−0.611382
$45$	8.80768	1.31297
$46$	−13.7283	−2.02412
$47$	1.71226	0.249759	0.124880	−	0.992172i	$-0.460146\pi$
$47$	1.71226	0.249759	0.124880	+	0.992172i	$0.460146\pi$
$48$	48.7825	7.04115
$49$	−0.253874	−0.0362678
$50$	2.33020	0.329539
$51$	−14.4077	−2.01748
$52$	−39.5184	−5.48022
$53$	−3.80882	−0.523181	−0.261591	−	0.965179i	$-0.584247\pi$
$53$	−3.80882	−0.523181	−0.261591	+	0.965179i	$0.584247\pi$
$54$	−9.93602	−1.35212
$55$	−1.42719	−0.192442
$56$	27.5614	3.68305
$57$	15.2873	2.02485
$58$	−9.75511	−1.28091
$59$	−7.95123	−1.03516	−0.517581	−	0.855634i	$-0.673167\pi$
$59$	−7.95123	−1.03516	−0.517581	+	0.855634i	$0.673167\pi$
$60$	32.0153	4.13316
$61$	−6.31070	−0.808003	−0.404001	−	0.914758i	$-0.632381\pi$
$61$	−6.31070	−0.808003	−0.404001	+	0.914758i	$0.632381\pi$
$62$	−8.58998	−1.09093
$63$	−11.2085	−1.41214
$64$	45.3320	5.66650
$65$	−13.9073	−1.72498
$66$	5.28197	0.650166
$67$	2.51519	0.307279	0.153640	−	0.988127i	$-0.450901\pi$
$67$	2.51519	0.307279	0.153640	+	0.988127i	$0.450901\pi$
$68$	−30.8940	−3.74645
$69$	13.2953	1.60057
$70$	14.8049	1.76952
$71$	−14.6307	−1.73635	−0.868174	−	0.496260i	$-0.834706\pi$
$71$	−14.6307	−1.73635	−0.868174	+	0.496260i	$0.834706\pi$
$72$	−45.7926	−5.39671
$73$	10.4588	1.22411	0.612056	−	0.790814i	$-0.290343\pi$
$73$	10.4588	1.22411	0.612056	+	0.790814i	$0.290343\pi$
$74$	12.9846	1.50943
$75$	−2.25671	−0.260582
$76$	32.7800	3.76013
$77$	1.81622	0.206977
$78$	51.4703	5.82786
$79$	−2.22840	−0.250714	−0.125357	−	0.992112i	$-0.540008\pi$
$79$	−2.22840	−0.250714	−0.125357	+	0.992112i	$0.540008\pi$
$80$	36.8117	4.11567
$81$	−3.32354	−0.369282
$82$	−18.7991	−2.07601
$83$	−2.26372	−0.248475	−0.124238	−	0.992253i	$-0.539648\pi$
$83$	−2.26372	−0.248475	−0.124238	+	0.992253i	$0.539648\pi$
$84$	−40.7422	−4.44534
$85$	−10.8722	−1.17925
$86$	7.81986	0.843237
$87$	9.44746	1.01287
$88$	7.42020	0.790996
$89$	1.35585	0.143720	0.0718601	−	0.997415i	$-0.477106\pi$
$89$	1.35585	0.143720	0.0718601	+	0.997415i	$0.477106\pi$
$90$	−24.5979	−2.59284
$91$	17.6982	1.85527
$92$	28.5088	2.97224
$93$	8.31907	0.862647
$94$	−4.78197	−0.493222
$95$	11.5359	1.18356
$96$	−78.8371	−8.04628
$97$	1.17228	0.119027	0.0595136	−	0.998227i	$-0.481045\pi$
$97$	1.17228	0.119027	0.0595136	+	0.998227i	$0.481045\pi$
$98$	0.709015	0.0716213
$99$	−3.01760	−0.303280
$100$	−4.83899	−0.483899
$101$	−0.897242	−0.0892789	−0.0446395	−	0.999003i	$-0.514214\pi$
$101$	−0.897242	−0.0892789	−0.0446395	+	0.999003i	$0.514214\pi$
$102$	40.2375	3.98411
$103$	11.8457	1.16719	0.583596	−	0.812044i	$-0.301645\pi$
$103$	11.8457	1.16719	0.583596	+	0.812044i	$0.301645\pi$
$104$	72.3063	7.09021
$105$	−14.3379	−1.39924
$106$	10.6372	1.03317
$107$	−13.8414	−1.33810	−0.669050	−	0.743218i	$-0.733299\pi$
$107$	−13.8414	−1.33810	−0.669050	+	0.743218i	$0.733299\pi$
$108$	20.6336	1.98547
$109$	20.0478	1.92023	0.960117	−	0.279600i	$-0.0902018\pi$
$109$	20.0478	1.92023	0.960117	+	0.279600i	$0.0902018\pi$
$110$	3.98582	0.380033
$111$	−12.5751	−1.19357
$112$	−46.8460	−4.42653
$113$	−10.7595	−1.01217	−0.506085	−	0.862484i	$-0.668908\pi$
$113$	−10.7595	−1.01217	−0.506085	+	0.862484i	$0.668908\pi$
$114$	−42.6940	−3.99866
$115$	10.0328	0.935560
$116$	20.2579	1.88090
$117$	−29.4051	−2.71850
$118$	22.2060	2.04423
$119$	13.8358	1.26832
$120$	−58.5780	−5.34741
$121$	−10.5110	−0.955548
$122$	17.6244	1.59564
$123$	18.2062	1.64160
$124$	17.8383	1.60193
$125$	−11.9079	−1.06507
$126$	31.3029	2.78868
$127$	3.46437	0.307413	0.153706	−	0.988117i	$-0.450879\pi$
$127$	3.46437	0.307413	0.153706	+	0.988117i	$0.450879\pi$
$128$	−68.3058	−6.03744
$129$	−7.57324	−0.666787
$130$	38.8399	3.40649
$131$	−16.1111	−1.40764	−0.703818	−	0.710381i	$-0.748523\pi$
$131$	−16.1111	−1.40764	−0.703818	+	0.710381i	$0.748523\pi$
$132$	−10.9688	−0.954709
$133$	−14.6804	−1.27295
$134$	−7.02436	−0.606812
$135$	7.26134	0.624957
$136$	56.5263	4.84709
$137$	6.15596	0.525939	0.262969	−	0.964804i	$-0.415298\pi$
$137$	6.15596	0.525939	0.262969	+	0.964804i	$0.415298\pi$
$138$	−37.1309	−3.16079
$139$	−7.53991	−0.639526	−0.319763	−	0.947497i	$-0.603603\pi$
$139$	−7.53991	−0.639526	−0.319763	+	0.947497i	$0.603603\pi$
$140$	−30.7444	−2.59838
$141$	4.63116	0.390014
$142$	40.8604	3.42893
$143$	4.76477	0.398450
$144$	77.8334	6.48612
$145$	7.12913	0.592042
$146$	−29.2092	−2.41737
$147$	−0.686654	−0.0566343
$148$	−26.9643	−2.21646
$149$	8.09447	0.663125	0.331562	−	0.943433i	$-0.392424\pi$
$149$	8.09447	0.663125	0.331562	+	0.943433i	$0.392424\pi$
$150$	6.30248	0.514595
$151$	−22.4258	−1.82499	−0.912495	−	0.409089i	$-0.865847\pi$
$151$	−22.4258	−1.82499	−0.912495	+	0.409089i	$0.865847\pi$
$152$	−59.9772	−4.86479
$153$	−22.9878	−1.85845
$154$	−5.07229	−0.408737
$155$	6.27764	0.504232
$156$	−106.885	−8.55769
$157$	−17.6857	−1.41148	−0.705738	−	0.708473i	$-0.749384\pi$
$157$	−17.6857	−1.41148	−0.705738	+	0.708473i	$0.749384\pi$
$158$	6.22341	0.495108
$159$	−10.3017	−0.816978
$160$	−59.4911	−4.70319
$161$	−12.7675	−1.00622
$162$	9.28189	0.729254
$163$	−13.5834	−1.06393	−0.531966	−	0.846766i	$-0.678547\pi$
$163$	−13.5834	−1.06393	−0.531966	+	0.846766i	$0.678547\pi$
$164$	39.0390	3.04843
$165$	−3.86012	−0.300510
$166$	6.32205	0.490686
$167$	4.33221	0.335237	0.167618	−	0.985852i	$-0.446392\pi$
$167$	4.33221	0.335237	0.167618	+	0.985852i	$0.446392\pi$
$168$	74.5454	5.75130
$169$	33.4304	2.57157
$170$	30.3635	2.32878
$171$	24.3911	1.86524
$172$	−16.2391	−1.23822
$173$	−19.4624	−1.47970	−0.739850	−	0.672771i	$-0.765104\pi$
$173$	−19.4624	−1.47970	−0.739850	+	0.672771i	$0.765104\pi$
$174$	−26.3846	−2.00021
$175$	2.16712	0.163819
$176$	−12.6121	−0.950670
$177$	−21.5057	−1.61647
$178$	−3.78660	−0.283817
$179$	−3.60456	−0.269417	−0.134709	−	0.990885i	$-0.543010\pi$
$179$	−3.60456	−0.269417	−0.134709	+	0.990885i	$0.543010\pi$
$180$	51.0810	3.80736
$181$	8.38854	0.623515	0.311758	−	0.950162i	$-0.399082\pi$
$181$	8.38854	0.623515	0.311758	+	0.950162i	$0.399082\pi$
$182$	−49.4271	−3.66378
$183$	−17.0686	−1.26174
$184$	−52.1620	−3.84544
$185$	−9.48926	−0.697664
$186$	−23.2333	−1.70355
$187$	3.72492	0.272393
$188$	9.93045	0.724252
$189$	−9.24067	−0.672160
$190$	−32.2172	−2.33728
$191$	4.37593	0.316631	0.158316	−	0.987389i	$-0.449394\pi$
$191$	4.37593	0.316631	0.158316	+	0.987389i	$0.449394\pi$
$192$	122.609	8.84858
$193$	−20.3385	−1.46400	−0.732000	−	0.681304i	$-0.761413\pi$
$193$	−20.3385	−1.46400	−0.732000	+	0.681304i	$0.761413\pi$
$194$	−3.27392	−0.235054
$195$	−37.6150	−2.69366
$196$	−1.47237	−0.105169
$197$	−13.6007	−0.969011	−0.484505	−	0.874788i	$-0.661000\pi$
$197$	−13.6007	−0.969011	−0.484505	+	0.874788i	$0.661000\pi$
$198$	8.42748	0.598915
$199$	−12.4327	−0.881330	−0.440665	−	0.897672i	$-0.645257\pi$
$199$	−12.4327	−0.881330	−0.440665	+	0.897672i	$0.645257\pi$
$200$	8.85382	0.626060
$201$	6.80283	0.479834
$202$	2.50580	0.176307
$203$	−9.07242	−0.636759
$204$	−83.5589	−5.85030
$205$	13.7385	0.959541
$206$	−33.0824	−2.30496
$207$	21.2129	1.47440
$208$	−122.898	−8.52147
$209$	−3.95232	−0.273388
$210$	40.0427	2.76321
$211$	−7.18169	−0.494408	−0.247204	−	0.968963i	$-0.579512\pi$
$211$	−7.18169	−0.494408	−0.247204	+	0.968963i	$0.579512\pi$
$212$	−22.0896	−1.51712
$213$	−39.5717	−2.71141
$214$	38.6560	2.64247
$215$	−5.71483	−0.389748
$216$	−37.7529	−2.56876
$217$	−7.98883	−0.542317
$218$	−55.9891	−3.79206
$219$	28.2880	1.91152
$220$	−8.27713	−0.558044
$221$	36.2975	2.44164
$222$	35.1194	2.35706
$223$	−3.14033	−0.210292	−0.105146	−	0.994457i	$-0.533531\pi$
$223$	−3.14033	−0.210292	−0.105146	+	0.994457i	$0.533531\pi$
$224$	75.7075	5.05842
$225$	−3.60062	−0.240041
$226$	30.0489	1.99882
$227$	2.07622	0.137803	0.0689016	−	0.997623i	$-0.478051\pi$
$227$	2.07622	0.137803	0.0689016	+	0.997623i	$0.478051\pi$
$228$	88.6602	5.87166
$229$	6.01138	0.397243	0.198621	−	0.980076i	$-0.436354\pi$
$229$	6.01138	0.397243	0.198621	+	0.980076i	$0.436354\pi$
$230$	−28.0193	−1.84754
$231$	4.91232	0.323207
$232$	−37.0656	−2.43347
$233$	−12.9811	−0.850418	−0.425209	−	0.905095i	$-0.639799\pi$
$233$	−12.9811	−0.850418	−0.425209	+	0.905095i	$0.639799\pi$
$234$	82.1218	5.36847
$235$	3.49471	0.227970
$236$	−46.1140	−3.00176
$237$	−6.02714	−0.391505
$238$	−38.6402	−2.50467
$239$	−14.6366	−0.946764	−0.473382	−	0.880857i	$-0.656967\pi$
$239$	−14.6366	−0.946764	−0.473382	+	0.880857i	$0.656967\pi$
$240$	99.5645	6.42686
$241$	17.6053	1.13406	0.567028	−	0.823699i	$-0.308093\pi$
$241$	17.6053	1.13406	0.567028	+	0.823699i	$0.308093\pi$
$242$	29.3550	1.88701
$243$	−19.6624	−1.26135
$244$	−36.5996	−2.34305
$245$	−0.518155	−0.0331037
$246$	−50.8458	−3.24181
$247$	−38.5135	−2.45055
$248$	−32.6385	−2.07255
$249$	−6.12267	−0.388008
$250$	33.2560	2.10330
$251$	−25.2692	−1.59498	−0.797490	−	0.603332i	$-0.793839\pi$
$251$	−25.2692	−1.59498	−0.797490	+	0.603332i	$0.793839\pi$
$252$	−65.0049	−4.09493
$253$	−3.43733	−0.216103
$254$	−9.67521	−0.607076
$255$	−29.4059	−1.84147
$256$	100.099	6.25618
$257$	−12.2593	−0.764716	−0.382358	−	0.924014i	$-0.624888\pi$
$257$	−12.2593	−0.764716	−0.382358	+	0.924014i	$0.624888\pi$
$258$	21.1504	1.31676
$259$	12.0759	0.750359
$260$	−80.6567	−5.00211
$261$	15.0736	0.933032
$262$	44.9948	2.77979
$263$	−14.3500	−0.884859	−0.442429	−	0.896803i	$-0.645883\pi$
$263$	−14.3500	−0.884859	−0.442429	+	0.896803i	$0.645883\pi$
$264$	20.0694	1.23519
$265$	−7.77375	−0.477538
$266$	40.9991	2.51382
$267$	3.66718	0.224428
$268$	14.5871	0.891049
$269$	−6.04419	−0.368521	−0.184260	−	0.982877i	$-0.558989\pi$
$269$	−6.04419	−0.368521	−0.184260	+	0.982877i	$0.558989\pi$
$270$	−20.2793	−1.23416
$271$	9.25088	0.561951	0.280976	−	0.959715i	$-0.409342\pi$
$271$	9.25088	0.561951	0.280976	+	0.959715i	$0.409342\pi$
$272$	−96.0773	−5.82554
$273$	47.8682	2.89712
$274$	−17.1922	−1.03862
$275$	0.583441	0.0351828
$276$	77.1076	4.64133
$277$	18.1720	1.09185	0.545926	−	0.837834i	$-0.316178\pi$
$277$	18.1720	1.09185	0.545926	+	0.837834i	$0.316178\pi$
$278$	21.0573	1.26293
$279$	13.2732	0.794648
$280$	56.2526	3.36173
$281$	2.98198	0.177890	0.0889450	−	0.996037i	$-0.471650\pi$
$281$	2.98198	0.177890	0.0889450	+	0.996037i	$0.471650\pi$
$282$	−12.9338	−0.770196
$283$	−31.5428	−1.87502	−0.937512	−	0.347952i	$-0.886877\pi$
$283$	−31.5428	−1.87502	−0.937512	+	0.347952i	$0.886877\pi$
$284$	−84.8524	−5.03507
$285$	31.2012	1.84820
$286$	−13.3069	−0.786856
$287$	−17.4835	−1.03202
$288$	−125.786	−7.41201
$289$	11.3760	0.669177
$290$	−19.9101	−1.16916
$291$	3.17067	0.185868
$292$	60.6570	3.54968
$293$	31.7435	1.85448	0.927238	−	0.374472i	$-0.122176\pi$
$293$	31.7435	1.85448	0.927238	+	0.374472i	$0.122176\pi$
$294$	1.91767	0.111841
$295$	−16.2284	−0.944852
$296$	49.3363	2.86761
$297$	−2.48781	−0.144357
$298$	−22.6060	−1.30953
$299$	−33.4951	−1.93707
$300$	−13.0880	−0.755636
$301$	7.27260	0.419186
$302$	62.6304	3.60397
$303$	−2.42677	−0.139414
$304$	101.943	5.84682
$305$	−12.8801	−0.737511
$306$	64.1997	3.67005
$307$	19.2767	1.10018	0.550089	−	0.835106i	$-0.314594\pi$
$307$	19.2767	1.10018	0.550089	+	0.835106i	$0.314594\pi$
$308$	10.5333	0.600193
$309$	32.0391	1.82264
$310$	−17.5321	−0.995754
$311$	−7.94170	−0.450333	−0.225166	−	0.974320i	$-0.572293\pi$
$311$	−7.94170	−0.450333	−0.225166	+	0.974320i	$0.572293\pi$
$312$	195.567	11.0718
$313$	32.2383	1.82222	0.911108	−	0.412167i	$-0.135228\pi$
$313$	32.2383	1.82222	0.911108	+	0.412167i	$0.135228\pi$
$314$	49.3924	2.78737
$315$	−22.8765	−1.28894
$316$	−12.9238	−0.727021
$317$	1.04334	0.0585999	0.0292999	−	0.999571i	$-0.490672\pi$
$317$	1.04334	0.0585999	0.0292999	+	0.999571i	$0.490672\pi$
$318$	28.7704	1.61336
$319$	−2.44251	−0.136754
$320$	92.5221	5.17214
$321$	−37.4368	−2.08952
$322$	35.6569	1.98708
$323$	−30.1083	−1.67527
$324$	−19.2752	−1.07084
$325$	5.68535	0.315367
$326$	37.9354	2.10104
$327$	54.2233	2.99856
$328$	−71.4290	−3.94401
$329$	−4.44731	−0.245188
$330$	10.7804	0.593444
$331$	−28.4777	−1.56527	−0.782637	−	0.622478i	$-0.786126\pi$
$331$	−28.4777	−1.56527	−0.782637	+	0.622478i	$0.786126\pi$
$332$	−13.1287	−0.720529
$333$	−20.0638	−1.09949
$334$	−12.0989	−0.662023
$335$	5.13347	0.280471
$336$	−126.704	−6.91228
$337$	6.67269	0.363485	0.181742	−	0.983346i	$-0.441826\pi$
$337$	6.67269	0.363485	0.181742	+	0.983346i	$0.441826\pi$
$338$	−93.3637	−5.07832
$339$	−29.1013	−1.58056
$340$	−63.0543	−3.41960
$341$	−2.15078	−0.116471
$342$	−68.1190	−3.68345
$343$	18.8407	1.01730
$344$	29.7124	1.60198
$345$	27.1356	1.46093
$346$	54.3542	2.92210
$347$	−4.91200	−0.263690	−0.131845	−	0.991270i	$-0.542090\pi$
$347$	−4.91200	−0.263690	−0.131845	+	0.991270i	$0.542090\pi$
$348$	54.7915	2.93713
$349$	36.7539	1.96739	0.983695	−	0.179847i	$-0.0575604\pi$
$349$	36.7539	1.96739	0.983695	+	0.179847i	$0.0575604\pi$
$350$	−6.05229	−0.323508
$351$	−24.2425	−1.29397
$352$	20.3823	1.08638
$353$	−34.1116	−1.81558	−0.907790	−	0.419425i	$-0.862232\pi$
$353$	−34.1116	−1.81558	−0.907790	+	0.419425i	$0.862232\pi$
$354$	60.0606	3.19218
$355$	−29.8612	−1.58487
$356$	7.86341	0.416760
$357$	37.4216	1.98056
$358$	10.0667	0.532043
$359$	8.32935	0.439606	0.219803	−	0.975544i	$-0.429458\pi$
$359$	8.32935	0.439606	0.219803	+	0.975544i	$0.429458\pi$
$360$	−93.4622	−4.92589
$361$	12.9464	0.681391
$362$	−23.4273	−1.23131
$363$	−28.4292	−1.49214
$364$	102.642	5.37992
$365$	21.3463	1.11732
$366$	47.6687	2.49168
$367$	−14.6232	−0.763325	−0.381663	−	0.924302i	$-0.624648\pi$
$367$	−14.6232	−0.763325	−0.381663	+	0.924302i	$0.624648\pi$
$368$	88.6594	4.62169
$369$	29.0483	1.51219
$370$	26.5014	1.37774
$371$	9.89275	0.513606
$372$	48.2473	2.50151
$373$	20.5213	1.06255	0.531276	−	0.847199i	$-0.321713\pi$
$373$	20.5213	1.06255	0.531276	+	0.847199i	$0.321713\pi$
$374$	−10.4029	−0.537919
$375$	−32.2072	−1.66317
$376$	−18.1696	−0.937025
$377$	−23.8011	−1.22582
$378$	25.8071	1.32738
$379$	26.0360	1.33738	0.668691	−	0.743541i	$-0.266855\pi$
$379$	26.0360	1.33738	0.668691	+	0.743541i	$0.266855\pi$
$380$	66.9037	3.43209
$381$	9.37007	0.480043
$382$	−12.2210	−0.625280
$383$	16.6698	0.851788	0.425894	−	0.904773i	$-0.359960\pi$
$383$	16.6698	0.851788	0.425894	+	0.904773i	$0.359960\pi$
$384$	−184.747	−9.42782
$385$	3.70688	0.188920
$386$	56.8010	2.89110
$387$	−12.0832	−0.614226
$388$	6.79877	0.345155
$389$	19.9762	1.01283	0.506417	−	0.862289i	$-0.330970\pi$
$389$	19.9762	1.01283	0.506417	+	0.862289i	$0.330970\pi$
$390$	105.050	5.31943
$391$	−26.1852	−1.32424
$392$	2.69397	0.136066
$393$	−43.5757	−2.19810
$394$	37.9838	1.91359
$395$	−4.54813	−0.228841
$396$	−17.5009	−0.879453
$397$	−22.2146	−1.11492	−0.557458	−	0.830205i	$-0.688223\pi$
$397$	−22.2146	−1.11492	−0.557458	+	0.830205i	$0.688223\pi$
$398$	34.7217	1.74044
$399$	−39.7061	−1.98779
$400$	−15.0488	−0.752439
$401$	−6.38548	−0.318875	−0.159438	−	0.987208i	$-0.550968\pi$
$401$	−6.38548	−0.318875	−0.159438	+	0.987208i	$0.550968\pi$
$402$	−18.9988	−0.947573
$403$	−20.9584	−1.04401
$404$	−5.20365	−0.258891
$405$	−6.78330	−0.337065
$406$	25.3373	1.25747
$407$	3.25112	0.161152
$408$	152.887	7.56901
$409$	−29.9074	−1.47882	−0.739412	−	0.673253i	$-0.764897\pi$
$409$	−29.9074	−1.47882	−0.739412	+	0.673253i	$0.764897\pi$
$410$	−38.3687	−1.89489
$411$	16.6500	0.821284
$412$	68.7004	3.38463
$413$	20.6520	1.01622
$414$	−59.2430	−2.91163
$415$	−4.62022	−0.226798
$416$	198.615	9.73792
$417$	−20.3932	−0.998658
$418$	11.0379	0.539884
$419$	−14.5318	−0.709926	−0.354963	−	0.934880i	$-0.615507\pi$
$419$	−14.5318	−0.709926	−0.354963	+	0.934880i	$0.615507\pi$
$420$	−83.1544	−4.05752
$421$	−14.1905	−0.691604	−0.345802	−	0.938308i	$-0.612393\pi$
$421$	−14.1905	−0.691604	−0.345802	+	0.938308i	$0.612393\pi$
$422$	20.0569	0.976352
$423$	7.38910	0.359270
$424$	40.4171	1.96283
$425$	4.44459	0.215594
$426$	110.515	5.35447
$427$	16.3910	0.793215
$428$	−80.2747	−3.88022
$429$	12.8873	0.622203
$430$	15.9602	0.769671
$431$	−24.5867	−1.18430	−0.592149	−	0.805828i	$-0.701720\pi$
$431$	−24.5867	−1.18430	−0.592149	+	0.805828i	$0.701720\pi$
$432$	64.1684	3.08730
$433$	−1.11820	−0.0537371	−0.0268686	−	0.999639i	$-0.508554\pi$
$433$	−1.11820	−0.0537371	−0.0268686	+	0.999639i	$0.508554\pi$
$434$	22.3110	1.07096
$435$	19.2822	0.924509
$436$	116.269	5.56830
$437$	27.7838	1.32908
$438$	−79.0020	−3.77486
$439$	13.4716	0.642963	0.321481	−	0.946916i	$-0.395819\pi$
$439$	13.4716	0.642963	0.321481	+	0.946916i	$0.395819\pi$
$440$	15.1445	0.721988
$441$	−1.09557	−0.0521700
$442$	−101.371	−4.82172
$443$	26.3824	1.25346	0.626732	−	0.779235i	$-0.284392\pi$
$443$	26.3824	1.25346	0.626732	+	0.779235i	$0.284392\pi$
$444$	−72.9305	−3.46113
$445$	2.76728	0.131182
$446$	8.77024	0.415283
$447$	21.8931	1.03551
$448$	−117.742	−5.56280
$449$	−26.0751	−1.23056	−0.615280	−	0.788308i	$-0.710957\pi$
$449$	−26.0751	−1.23056	−0.615280	+	0.788308i	$0.710957\pi$
$450$	10.0557	0.474031
$451$	−4.70696	−0.221642
$452$	−62.4009	−2.93509
$453$	−60.6552	−2.84983
$454$	−5.79841	−0.272133
$455$	36.1218	1.69341
$456$	−162.220	−7.59665
$457$	11.1780	0.522885	0.261443	−	0.965219i	$-0.415802\pi$
$457$	11.1780	0.522885	0.261443	+	0.965219i	$0.415802\pi$
$458$	−16.7884	−0.784472
$459$	−18.9519	−0.884597
$460$	58.1861	2.71294
$461$	19.8410	0.924085	0.462043	−	0.886858i	$-0.347117\pi$
$461$	19.8410	0.924085	0.462043	+	0.886858i	$0.347117\pi$
$462$	−13.7190	−0.638267
$463$	14.9746	0.695929	0.347964	−	0.937508i	$-0.386873\pi$
$463$	14.9746	0.695929	0.347964	+	0.937508i	$0.386873\pi$
$464$	63.0001	2.92471
$465$	16.9791	0.787388
$466$	36.2532	1.67940
$467$	8.96696	0.414941	0.207471	−	0.978241i	$-0.433477\pi$
$467$	8.96696	0.414941	0.207471	+	0.978241i	$0.433477\pi$
$468$	−170.538	−7.88311
$469$	−6.53277	−0.301655
$470$	−9.75994	−0.450193
$471$	−47.8346	−2.20410
$472$	84.3740	3.88363
$473$	1.95796	0.0900270
$474$	16.8325	0.773140
$475$	−4.71593	−0.216382
$476$	80.2419	3.67788
$477$	−16.4366	−0.752578
$478$	40.8768	1.86966
$479$	−16.1158	−0.736348	−0.368174	−	0.929757i	$-0.620017\pi$
$479$	−16.1158	−0.736348	−0.368174	+	0.929757i	$0.620017\pi$
$480$	−160.906	−7.34430
$481$	31.6806	1.44451
$482$	−49.1676	−2.23952
$483$	−34.5323	−1.57128
$484$	−60.9598	−2.77090
$485$	2.39261	0.108643
$486$	54.9128	2.49089
$487$	42.2675	1.91532	0.957661	−	0.287897i	$-0.0929562\pi$
$487$	42.2675	1.91532	0.957661	+	0.287897i	$0.0929562\pi$
$488$	66.9657	3.03139
$489$	−36.7390	−1.66139
$490$	1.44709	0.0653729
$491$	−13.8932	−0.626992	−0.313496	−	0.949590i	$-0.601500\pi$
$491$	−13.8932	−0.626992	−0.313496	+	0.949590i	$0.601500\pi$
$492$	105.589	4.76030
$493$	−18.6068	−0.838008
$494$	107.559	4.83933
$495$	−6.15889	−0.276821
$496$	55.4755	2.49092
$497$	38.0008	1.70457
$498$	17.0993	0.766236
$499$	16.0229	0.717285	0.358643	−	0.933475i	$-0.383240\pi$
$499$	16.0229	0.717285	0.358643	+	0.933475i	$0.383240\pi$
$500$	−69.0610	−3.08850
$501$	11.7173	0.523492
$502$	70.5714	3.14975
$503$	0.278875	0.0124344	0.00621721	−	0.999981i	$-0.498021\pi$
$503$	0.278875	0.0124344	0.00621721	+	0.999981i	$0.498021\pi$
$504$	118.939	5.29794
$505$	−1.83126	−0.0814900
$506$	9.59969	0.426758
$507$	90.4192	4.01566
$508$	20.0920	0.891437
$509$	−7.65389	−0.339253	−0.169626	−	0.985508i	$-0.554256\pi$
$509$	−7.65389	−0.339253	−0.169626	+	0.985508i	$0.554256\pi$
$510$	82.1243	3.63652
$511$	−27.1650	−1.20171
$512$	−142.942	−6.31722
$513$	20.1089	0.887828
$514$	34.2376	1.51015
$515$	24.1770	1.06536
$516$	−43.9218	−1.93355
$517$	−1.19732	−0.0526582
$518$	−33.7252	−1.48180
$519$	−52.6400	−2.31064
$520$	147.576	6.47165
$521$	37.2139	1.63037	0.815186	−	0.579200i	$-0.196635\pi$
$521$	37.2139	1.63037	0.815186	+	0.579200i	$0.196635\pi$
$522$	−42.0972	−1.84254
$523$	36.8031	1.60929	0.804643	−	0.593759i	$-0.202357\pi$
$523$	36.8031	1.60929	0.804643	+	0.593759i	$0.202357\pi$
$524$	−93.4381	−4.08186
$525$	5.86141	0.255813
$526$	40.0764	1.74741
$527$	−16.3844	−0.713717
$528$	−34.1118	−1.48453
$529$	1.16350	0.0505870
$530$	21.7104	0.943037
$531$	−34.3127	−1.48904
$532$	−85.1406	−3.69131
$533$	−45.8671	−1.98672
$534$	−10.2416	−0.443198
$535$	−28.2502	−1.22136
$536$	−26.6898	−1.15282
$537$	−9.74925	−0.420711
$538$	16.8801	0.727752
$539$	0.177525	0.00764655
$540$	42.1129	1.81225
$541$	−41.7436	−1.79470	−0.897348	−	0.441323i	$-0.854509\pi$
$541$	−41.7436	−1.79470	−0.897348	+	0.441323i	$0.854509\pi$
$542$	−25.8357	−1.10974
$543$	22.6885	0.973656
$544$	155.270	6.65714
$545$	40.9174	1.75271
$546$	−133.685	−5.72120
$547$	−2.63377	−0.112612	−0.0563059	−	0.998414i	$-0.517932\pi$
$547$	−2.63377	−0.112612	−0.0563059	+	0.998414i	$0.517932\pi$
$548$	35.7021	1.52512
$549$	−27.2332	−1.16228
$550$	−1.62942	−0.0694787
$551$	19.7427	0.841069
$552$	−141.083	−6.00488
$553$	5.78788	0.246126
$554$	−50.7504	−2.15618
$555$	−25.6656	−1.08944
$556$	−43.7285	−1.85450
$557$	13.1715	0.558094	0.279047	−	0.960277i	$-0.409982\pi$
$557$	13.1715	0.558094	0.279047	+	0.960277i	$0.409982\pi$
$558$	−37.0692	−1.56926
$559$	19.0794	0.806971
$560$	−95.6121	−4.04035
$561$	10.0748	0.425357
$562$	−8.32800	−0.351296
$563$	−0.888791	−0.0374581	−0.0187290	−	0.999825i	$-0.505962\pi$
$563$	−0.888791	−0.0374581	−0.0187290	+	0.999825i	$0.505962\pi$
$564$	26.8589	1.13096
$565$	−21.9600	−0.923866
$566$	88.0920	3.70278
$567$	8.63232	0.362523
$568$	155.253	6.51428
$569$	10.6189	0.445168	0.222584	−	0.974914i	$-0.428551\pi$
$569$	10.6189	0.445168	0.222584	+	0.974914i	$0.428551\pi$
$570$	−87.1379	−3.64980
$571$	10.4127	0.435756	0.217878	−	0.975976i	$-0.430086\pi$
$571$	10.4127	0.435756	0.217878	+	0.975976i	$0.430086\pi$
$572$	27.6338	1.15543
$573$	11.8356	0.494438
$574$	48.8274	2.03802
$575$	−4.10144	−0.171042
$576$	195.626	8.15107
$577$	15.2457	0.634686	0.317343	−	0.948311i	$-0.397209\pi$
$577$	15.2457	0.634686	0.317343	+	0.948311i	$0.397209\pi$
$578$	−31.7706	−1.32148
$579$	−55.0096	−2.28612
$580$	41.3461	1.71680
$581$	5.87962	0.243928
$582$	−8.85497	−0.367050
$583$	2.66337	0.110305
$584$	−110.983	−4.59252
$585$	−60.0154	−2.48133
$586$	−88.6526	−3.66220
$587$	−41.4016	−1.70883	−0.854414	−	0.519592i	$-0.826084\pi$
$587$	−41.4016	−1.70883	−0.854414	+	0.519592i	$0.826084\pi$
$588$	−3.98232	−0.164228
$589$	17.3847	0.716324
$590$	45.3222	1.86589
$591$	−36.7858	−1.51317
$592$	−83.8565	−3.44648
$593$	12.5582	0.515704	0.257852	−	0.966184i	$-0.416985\pi$
$593$	12.5582	0.515704	0.257852	+	0.966184i	$0.416985\pi$
$594$	6.94789	0.285076
$595$	28.2386	1.15767
$596$	46.9447	1.92293
$597$	−33.6267	−1.37625
$598$	93.5443	3.82531
$599$	−11.0752	−0.452520	−0.226260	−	0.974067i	$-0.572650\pi$
$599$	−11.0752	−0.452520	−0.226260	+	0.974067i	$0.572650\pi$
$600$	23.9469	0.977629
$601$	−46.9798	−1.91635	−0.958173	−	0.286188i	$-0.907612\pi$
$601$	−46.9798	−1.91635	−0.958173	+	0.286188i	$0.907612\pi$
$602$	−20.3108	−0.827805
$603$	10.8540	0.442010
$604$	−130.061	−5.29211
$605$	−21.4529	−0.872184
$606$	6.77743	0.275314
$607$	28.2571	1.14692	0.573460	−	0.819234i	$-0.305601\pi$
$607$	28.2571	1.14692	0.573460	+	0.819234i	$0.305601\pi$
$608$	−164.749	−6.68146
$609$	−24.5382	−0.994337
$610$	35.9712	1.45643
$611$	−11.6673	−0.472010
$612$	−133.320	−5.38914
$613$	3.57236	0.144286	0.0721432	−	0.997394i	$-0.477016\pi$
$613$	3.57236	0.144286	0.0721432	+	0.997394i	$0.477016\pi$
$614$	−53.8354	−2.17262
$615$	37.1586	1.49838
$616$	−19.2727	−0.776519
$617$	34.2409	1.37849	0.689244	−	0.724530i	$-0.257943\pi$
$617$	34.2409	1.37849	0.689244	+	0.724530i	$0.257943\pi$
$618$	−89.4780	−3.59933
$619$	36.4615	1.46551	0.732756	−	0.680491i	$-0.238233\pi$
$619$	36.4615	1.46551	0.732756	+	0.680491i	$0.238233\pi$
$620$	36.4078	1.46217
$621$	17.4886	0.701795
$622$	22.1794	0.889313
$623$	−3.52160	−0.141090
$624$	−332.403	−13.3068
$625$	−20.1320	−0.805280
$626$	−90.0344	−3.59850
$627$	−10.6898	−0.426911
$628$	−102.570	−4.09300
$629$	24.7666	0.987511
$630$	63.8888	2.54539
$631$	15.0740	0.600087	0.300044	−	0.953925i	$-0.402999\pi$
$631$	15.0740	0.600087	0.300044	+	0.953925i	$0.402999\pi$
$632$	23.6465	0.940607
$633$	−19.4243	−0.772047
$634$	−2.91382	−0.115723
$635$	7.07074	0.280594
$636$	−59.7458	−2.36907
$637$	1.72990	0.0685410
$638$	6.82139	0.270062
$639$	−63.1374	−2.49768
$640$	−139.411	−5.51072
$641$	33.7551	1.33325	0.666624	−	0.745394i	$-0.267739\pi$
$641$	33.7551	1.33325	0.666624	+	0.745394i	$0.267739\pi$
$642$	104.553	4.12637
$643$	21.2876	0.839499	0.419750	−	0.907640i	$-0.362118\pi$
$643$	21.2876	0.839499	0.419750	+	0.907640i	$0.362118\pi$
$644$	−74.0467	−2.91785
$645$	−15.4569	−0.608615
$646$	84.0859	3.30831
$647$	0.173478	0.00682011	0.00341006	−	0.999994i	$-0.498915\pi$
$647$	0.173478	0.00682011	0.00341006	+	0.999994i	$0.498915\pi$
$648$	35.2675	1.38544
$649$	5.56000	0.218249
$650$	−15.8779	−0.622783
$651$	−21.6074	−0.846860
$652$	−78.7782	−3.08519
$653$	−45.5728	−1.78340	−0.891702	−	0.452624i	$-0.850488\pi$
$653$	−45.5728	−1.78340	−0.891702	+	0.452624i	$0.850488\pi$
$654$	−151.434	−5.92153
$655$	−32.8826	−1.28483
$656$	121.407	4.74016
$657$	45.1340	1.76084
$658$	12.4204	0.484196
$659$	−37.6151	−1.46528	−0.732639	−	0.680618i	$-0.761711\pi$
$659$	−37.6151	−1.46528	−0.732639	+	0.680618i	$0.761711\pi$
$660$	−22.3871	−0.871419
$661$	−20.6688	−0.803921	−0.401961	−	0.915657i	$-0.631671\pi$
$661$	−20.6688	−0.803921	−0.401961	+	0.915657i	$0.631671\pi$
$662$	79.5318	3.09109
$663$	98.1739	3.81276
$664$	24.0213	0.932207
$665$	−29.9626	−1.16190
$666$	56.0336	2.17126
$667$	17.1702	0.664834
$668$	25.1251	0.972120
$669$	−8.49365	−0.328383
$670$	−14.3366	−0.553873
$671$	4.41284	0.170356
$672$	204.766	7.89902
$673$	−7.52550	−0.290087	−0.145043	−	0.989425i	$-0.546332\pi$
$673$	−7.52550	−0.290087	−0.145043	+	0.989425i	$0.546332\pi$
$674$	−18.6353	−0.717806
$675$	−2.96847	−0.114256
$676$	193.883	7.45705
$677$	0.265341	0.0101979	0.00509894	−	0.999987i	$-0.498377\pi$
$677$	0.265341	0.0101979	0.00509894	+	0.999987i	$0.498377\pi$
$678$	81.2733	3.12128
$679$	−3.04480	−0.116849
$680$	115.369	4.42422
$681$	5.61554	0.215188
$682$	6.00666	0.230007
$683$	22.6896	0.868192	0.434096	−	0.900867i	$-0.357068\pi$
$683$	22.6896	0.868192	0.434096	+	0.900867i	$0.357068\pi$
$684$	141.459	5.40882
$685$	12.5642	0.480055
$686$	−52.6179	−2.00896
$687$	16.2590	0.620318
$688$	−50.5019	−1.92537
$689$	25.9532	0.988739
$690$	−75.7837	−2.88504
$691$	0.193628	0.00736594	0.00368297	−	0.999993i	$-0.498828\pi$
$691$	0.193628	0.00736594	0.00368297	+	0.999993i	$0.498828\pi$
$692$	−112.874	−4.29084
$693$	7.83770	0.297730
$694$	13.7181	0.520733
$695$	−15.3889	−0.583733
$696$	−100.251	−3.80001
$697$	−35.8571	−1.35819
$698$	−102.645	−3.88518
$699$	−35.1099	−1.32798
$700$	12.5684	0.475043
$701$	47.8062	1.80561	0.902807	−	0.430046i	$-0.141503\pi$
$701$	47.8062	1.80561	0.902807	+	0.430046i	$0.141503\pi$
$702$	67.7039	2.55532
$703$	−26.2786	−0.991117
$704$	−31.6990	−1.19470
$705$	9.45214	0.355988
$706$	95.2662	3.58539
$707$	2.33043	0.0876450
$708$	−124.724	−4.68743
$709$	−39.9561	−1.50058	−0.750291	−	0.661107i	$-0.770087\pi$
$709$	−39.9561	−1.50058	−0.750291	+	0.661107i	$0.770087\pi$
$710$	83.3955	3.12978
$711$	−9.61641	−0.360644
$712$	−14.3876	−0.539197
$713$	15.1194	0.566228
$714$	−104.510	−3.91119
$715$	9.72485	0.363689
$716$	−20.9050	−0.781257
$717$	−39.5876	−1.47843
$718$	−23.2620	−0.868131
$719$	28.7908	1.07372	0.536858	−	0.843673i	$-0.319611\pi$
$719$	28.7908	1.07372	0.536858	+	0.843673i	$0.319611\pi$
$720$	158.857	5.92025
$721$	−30.7672	−1.14583
$722$	−36.1565	−1.34561
$723$	47.6170	1.77089
$724$	48.6502	1.80807
$725$	−2.91442	−0.108239
$726$	79.3964	2.94668
$727$	41.6782	1.54576	0.772879	−	0.634553i	$-0.218816\pi$
$727$	41.6782	1.54576	0.772879	+	0.634553i	$0.218816\pi$
$728$	−187.803	−6.96045
$729$	−43.2104	−1.60038
$730$	−59.6156	−2.20647
$731$	14.9155	0.551670
$732$	−98.9909	−3.65881
$733$	18.1021	0.668615	0.334307	−	0.942464i	$-0.391498\pi$
$733$	18.1021	0.668615	0.334307	+	0.942464i	$0.391498\pi$
$734$	40.8394	1.50741
$735$	−1.40145	−0.0516934
$736$	−143.282	−5.28144
$737$	−1.75878	−0.0647854
$738$	−81.1254	−2.98627
$739$	−47.4340	−1.74489	−0.872443	−	0.488715i	$-0.837466\pi$
$739$	−47.4340	−1.74489	−0.872443	+	0.488715i	$0.837466\pi$
$740$	−55.0339	−2.02309
$741$	−104.167	−3.82668
$742$	−27.6283	−1.01427
$743$	−44.5649	−1.63493	−0.817464	−	0.575980i	$-0.804621\pi$
$743$	−44.5649	−1.63493	−0.817464	+	0.575980i	$0.804621\pi$
$744$	−88.2774	−3.23641
$745$	16.5207	0.605272
$746$	−57.3114	−2.09832
$747$	−9.76883	−0.357423
$748$	21.6030	0.789885
$749$	35.9507	1.31361
$750$	89.9476	3.28442
$751$	8.56324	0.312477	0.156239	−	0.987719i	$-0.450063\pi$
$751$	8.56324	0.312477	0.156239	+	0.987719i	$0.450063\pi$
$752$	30.8827	1.12618
$753$	−68.3457	−2.49066
$754$	66.4712	2.42074
$755$	−45.7709	−1.66577
$756$	−53.5922	−1.94913
$757$	−54.5316	−1.98198	−0.990992	−	0.133921i	$-0.957243\pi$
$757$	−54.5316	−1.98198	−0.990992	+	0.133921i	$0.957243\pi$
$758$	−72.7129	−2.64105
$759$	−9.29693	−0.337457
$760$	−122.413	−4.44038
$761$	−28.4268	−1.03047	−0.515235	−	0.857049i	$-0.672295\pi$
$761$	−28.4268	−1.03047	−0.515235	+	0.857049i	$0.672295\pi$
$762$	−26.1685	−0.947986
$763$	−52.0708	−1.88509
$764$	25.3786	0.918167
$765$	−46.9177	−1.69631
$766$	−46.5551	−1.68210
$767$	54.1796	1.95631
$768$	270.737	9.76940
$769$	−41.3206	−1.49006	−0.745030	−	0.667031i	$-0.767565\pi$
$769$	−41.3206	−1.49006	−0.745030	+	0.667031i	$0.767565\pi$
$770$	−10.3525	−0.373078
$771$	−33.1578	−1.19415
$772$	−117.956	−4.24531
$773$	40.8152	1.46802	0.734010	−	0.679138i	$-0.237646\pi$
$773$	40.8152	1.46802	0.734010	+	0.679138i	$0.237646\pi$
$774$	33.7458	1.21297
$775$	−2.56633	−0.0921852
$776$	−12.4396	−0.446556
$777$	32.6616	1.17173
$778$	−55.7891	−2.00014
$779$	38.0462	1.36315
$780$	−218.152	−7.81110
$781$	10.2307	0.366084
$782$	73.1294	2.61510
$783$	12.4272	0.444111
$784$	−4.57893	−0.163533
$785$	−36.0964	−1.28834
$786$	121.697	4.34080
$787$	28.6656	1.02182	0.510909	−	0.859635i	$-0.329309\pi$
$787$	28.6656	1.02182	0.510909	+	0.859635i	$0.329309\pi$
$788$	−78.8788	−2.80994
$789$	−38.8124	−1.38176
$790$	12.7019	0.451914
$791$	27.9460	0.993646
$792$	32.0211	1.13782
$793$	43.0010	1.52701
$794$	62.0403	2.20173
$795$	−21.0257	−0.745703
$796$	−72.1047	−2.55568
$797$	−0.265018	−0.00938742	−0.00469371	−	0.999989i	$-0.501494\pi$
$797$	−0.265018	−0.00938742	−0.00469371	+	0.999989i	$0.501494\pi$
$798$	110.890	3.92547
$799$	−9.12108	−0.322680
$800$	24.3202	0.859850
$801$	5.85105	0.206737
$802$	17.8332	0.629713
$803$	−7.31347	−0.258087
$804$	39.4537	1.39142
$805$	−26.0584	−0.918438
$806$	58.5320	2.06170
$807$	−16.3477	−0.575467
$808$	9.52104	0.334949
$809$	10.7725	0.378742	0.189371	−	0.981906i	$-0.439355\pi$
$809$	10.7725	0.378742	0.189371	+	0.981906i	$0.439355\pi$
$810$	18.9442	0.665633
$811$	43.1058	1.51365	0.756825	−	0.653618i	$-0.226750\pi$
$811$	43.1058	1.51365	0.756825	+	0.653618i	$0.226750\pi$
$812$	−52.6165	−1.84648
$813$	25.0209	0.877520
$814$	−9.07964	−0.318241
$815$	−27.7235	−0.971113
$816$	−259.860	−9.09692
$817$	−15.8261	−0.553685
$818$	83.5246	2.92037
$819$	76.3747	2.66875
$820$	79.6781	2.78248
$821$	31.2387	1.09024	0.545118	−	0.838359i	$-0.316485\pi$
$821$	31.2387	1.09024	0.545118	+	0.838359i	$0.316485\pi$
$822$	−46.4998	−1.62187
$823$	−6.95205	−0.242333	−0.121167	−	0.992632i	$-0.538664\pi$
$823$	−6.95205	−0.242333	−0.121167	+	0.992632i	$0.538664\pi$
$824$	−125.700	−4.37897
$825$	1.57803	0.0549400
$826$	−57.6763	−2.00682
$827$	11.4405	0.397827	0.198913	−	0.980017i	$-0.436259\pi$
$827$	11.4405	0.397827	0.198913	+	0.980017i	$0.436259\pi$
$828$	123.027	4.27547
$829$	50.3637	1.74920	0.874601	−	0.484842i	$-0.161123\pi$
$829$	50.3637	1.74920	0.874601	+	0.484842i	$0.161123\pi$
$830$	12.9032	0.447878
$831$	49.1499	1.70499
$832$	−308.892	−10.7089
$833$	1.35237	0.0468567
$834$	56.9536	1.97214
$835$	8.84200	0.305990
$836$	−22.9219	−0.792770
$837$	10.9429	0.378242
$838$	40.5841	1.40196
$839$	51.7597	1.78694	0.893471	−	0.449121i	$-0.148263\pi$
$839$	51.7597	1.78694	0.893471	+	0.449121i	$0.148263\pi$
$840$	152.146	5.24955
$841$	−16.7991	−0.579279
$842$	39.6310	1.36577
$843$	8.06535	0.277786
$844$	−41.6509	−1.43368
$845$	68.2311	2.34722
$846$	−20.6361	−0.709484
$847$	27.3006	0.938060
$848$	−68.6966	−2.35905
$849$	−85.3138	−2.92796
$850$	−12.4128	−0.425754
$851$	−22.8545	−0.783442
$852$	−229.500	−7.86255
$853$	−1.93371	−0.0662091	−0.0331045	−	0.999452i	$-0.510539\pi$
$853$	−1.93371	−0.0662091	−0.0331045	+	0.999452i	$0.510539\pi$
$854$	−45.7764	−1.56643
$855$	49.7820	1.70251
$856$	146.877	5.02016
$857$	−23.1803	−0.791825	−0.395912	−	0.918288i	$-0.629572\pi$
$857$	−23.1803	−0.791825	−0.395912	+	0.918288i	$0.629572\pi$
$858$	−35.9913	−1.22872
$859$	29.4401	1.00448	0.502241	−	0.864728i	$-0.332509\pi$
$859$	29.4401	1.00448	0.502241	+	0.864728i	$0.332509\pi$
$860$	−33.1438	−1.13019
$861$	−47.2875	−1.61155
$862$	68.6651	2.33874
$863$	−48.5794	−1.65366	−0.826831	−	0.562451i	$-0.809859\pi$
$863$	−48.5794	−1.65366	−0.826831	+	0.562451i	$0.809859\pi$
$864$	−103.702	−3.52802
$865$	−39.7226	−1.35061
$866$	3.12288	0.106120
$867$	30.7687	1.04496
$868$	−46.3320	−1.57261
$869$	1.55824	0.0528595
$870$	−53.8508	−1.82571
$871$	−17.1385	−0.580714
$872$	−212.736	−7.20416
$873$	5.05886	0.171217
$874$	−77.5939	−2.62465
$875$	30.9287	1.04558
$876$	164.059	5.54304
$877$	−15.9851	−0.539779	−0.269890	−	0.962891i	$-0.586987\pi$
$877$	−15.9851	−0.539779	−0.269890	+	0.962891i	$0.586987\pi$
$878$	−37.6231	−1.26972
$879$	85.8567	2.89587
$880$	−25.7411	−0.867731
$881$	7.71118	0.259796	0.129898	−	0.991527i	$-0.458535\pi$
$881$	7.71118	0.259796	0.129898	+	0.991527i	$0.458535\pi$
$882$	3.05968	0.103025
$883$	7.42474	0.249862	0.124931	−	0.992165i	$-0.460129\pi$
$883$	7.42474	0.249862	0.124931	+	0.992165i	$0.460129\pi$
$884$	210.511	7.08026
$885$	−43.8928	−1.47544
$886$	−73.6801	−2.47533
$887$	−0.455289	−0.0152871	−0.00764356	−	0.999971i	$-0.502433\pi$
$887$	−0.455289	−0.0152871	−0.00764356	+	0.999971i	$0.502433\pi$
$888$	133.440	4.47794
$889$	−8.99811	−0.301787
$890$	−7.72840	−0.259057
$891$	2.32403	0.0778578
$892$	−18.2127	−0.609805
$893$	9.67791	0.323859
$894$	−61.1426	−2.04491
$895$	−7.35687	−0.245913
$896$	177.413	5.92695
$897$	−90.5942	−3.02485
$898$	72.8220	2.43010
$899$	10.7436	0.358321
$900$	−20.8822	−0.696072
$901$	20.2892	0.675932
$902$	13.1455	0.437697
$903$	19.6702	0.654583
$904$	114.174	3.79737
$905$	17.1209	0.569119
$906$	169.396	5.62782
$907$	53.8440	1.78786	0.893930	−	0.448207i	$-0.147937\pi$
$907$	53.8440	1.78786	0.893930	+	0.448207i	$0.147937\pi$
$908$	12.0412	0.399602
$909$	−3.87196	−0.128425
$910$	−100.880	−3.34414
$911$	−45.5209	−1.50818	−0.754088	−	0.656774i	$-0.771921\pi$
$911$	−45.5209	−1.50818	−0.754088	+	0.656774i	$0.771921\pi$
$912$	275.724	9.13015
$913$	1.58293	0.0523875
$914$	−31.2177	−1.03259
$915$	−34.8367	−1.15167
$916$	34.8636	1.15193
$917$	41.8459	1.38187
$918$	52.9283	1.74689
$919$	−25.3148	−0.835060	−0.417530	−	0.908663i	$-0.637104\pi$
$919$	−25.3148	−0.835060	−0.417530	+	0.908663i	$0.637104\pi$
$920$	−106.462	−3.50995
$921$	52.1376	1.71799
$922$	−55.4114	−1.82488
$923$	99.6936	3.28145
$924$	28.4895	0.937237
$925$	3.87925	0.127549
$926$	−41.8207	−1.37431
$927$	51.1189	1.67897
$928$	−101.814	−3.34221
$929$	−54.4341	−1.78592	−0.892962	−	0.450132i	$-0.851377\pi$
$929$	−54.4341	−1.78592	−0.892962	+	0.450132i	$0.851377\pi$
$930$	−47.4189	−1.55493
$931$	−1.43493	−0.0470279
$932$	−75.2851	−2.46605
$933$	−21.4799	−0.703221
$934$	−25.0427	−0.819422
$935$	7.60251	0.248629
$936$	312.030	10.1990
$937$	10.4144	0.340223	0.170111	−	0.985425i	$-0.445587\pi$
$937$	10.4144	0.340223	0.170111	+	0.985425i	$0.445587\pi$
$938$	18.2446	0.595707
$939$	87.1949	2.84550
$940$	20.2679	0.661067
$941$	15.4922	0.505031	0.252516	−	0.967593i	$-0.418742\pi$
$941$	15.4922	0.505031	0.252516	+	0.967593i	$0.418742\pi$
$942$	133.591	4.35264
$943$	33.0887	1.07752
$944$	−143.410	−4.66760
$945$	−18.8601	−0.613519
$946$	−5.46814	−0.177785
$947$	6.76757	0.219917	0.109958	−	0.993936i	$-0.464928\pi$
$947$	6.76757	0.219917	0.109958	+	0.993936i	$0.464928\pi$
$948$	−34.9550	−1.13529
$949$	−71.2663	−2.31340
$950$	13.1705	0.427309
$951$	2.82192	0.0915072
$952$	−146.817	−4.75838
$953$	25.0654	0.811949	0.405975	−	0.913884i	$-0.366932\pi$
$953$	25.0654	0.811949	0.405975	+	0.913884i	$0.366932\pi$
$954$	45.9036	1.48619
$955$	8.93122	0.289007
$956$	−84.8866	−2.74543
$957$	−6.60626	−0.213550
$958$	45.0077	1.45413
$959$	−15.9891	−0.516313
$960$	250.245	8.07661
$961$	−21.5396	−0.694824
$962$	−88.4767	−2.85260
$963$	−59.7312	−1.92481
$964$	102.104	3.28854
$965$	−41.5107	−1.33628
$966$	96.4412	3.10294
$967$	−6.40947	−0.206115	−0.103057	−	0.994675i	$-0.532863\pi$
$967$	−6.40947	−0.206115	−0.103057	+	0.994675i	$0.532863\pi$
$968$	111.537	3.58494
$969$	−81.4340	−2.61604
$970$	−6.68204	−0.214547
$971$	11.1906	0.359122	0.179561	−	0.983747i	$-0.442532\pi$
$971$	11.1906	0.359122	0.179561	+	0.983747i	$0.442532\pi$
$972$	−114.034	−3.65765
$973$	19.5836	0.627822
$974$	−118.044	−3.78236
$975$	15.3772	0.492464
$976$	−113.821	−3.64333
$977$	7.83426	0.250640	0.125320	−	0.992116i	$-0.460004\pi$
$977$	7.83426	0.250640	0.125320	+	0.992116i	$0.460004\pi$
$978$	102.604	3.28091
$979$	−0.948099	−0.0303014
$980$	−3.00509	−0.0959942
$981$	86.5143	2.76219
$982$	38.8007	1.23818
$983$	0.414369	0.0132163	0.00660816	−	0.999978i	$-0.497897\pi$
$983$	0.414369	0.0132163	0.00660816	+	0.999978i	$0.497897\pi$
$984$	−193.194	−6.15880
$985$	−27.7589	−0.884472
$986$	51.9646	1.65489
$987$	−12.0286	−0.382876
$988$	−223.363	−7.10612
$989$	−13.7639	−0.437668
$990$	17.2004	0.546665
$991$	2.12624	0.0675424	0.0337712	−	0.999430i	$-0.489248\pi$
$991$	2.12624	0.0675424	0.0337712	+	0.999430i	$0.489248\pi$
$992$	−89.6536	−2.84650
$993$	−77.0236	−2.44427
$994$	−106.128	−3.36617
$995$	−25.3750	−0.804441
$996$	−35.5091	−1.12515
$997$	55.9996	1.77353	0.886763	−	0.462224i	$-0.152948\pi$
$997$	55.9996	1.77353	0.886763	+	0.462224i	$0.152948\pi$
$998$	−44.7485	−1.41649
$999$	−16.5412	−0.523341

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6007.2.a.b.1.1	✓	237

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6007.2.a.b.1.1	✓	237	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:	\( N \)	\(=\)	\( 6007 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6007.a (trivial)

\(f(q)\)	\(=\)	\(q-2.79278 q^{2} +2.70470 q^{3} +5.79960 q^{4} +2.04099 q^{5} -7.55362 q^{6} -2.59733 q^{7} -10.6114 q^{8} +4.31540 q^{9} +O(q^{10})\)	\(q-2.79278 q^{2} +2.70470 q^{3} +5.79960 q^{4} +2.04099 q^{5} -7.55362 q^{6} -2.59733 q^{7} -10.6114 q^{8} +4.31540 q^{9} -5.70003 q^{10} -0.699263 q^{11} +15.6862 q^{12} -6.81399 q^{13} +7.25377 q^{14} +5.52026 q^{15} +18.0362 q^{16} -5.32691 q^{17} -12.0519 q^{18} +5.65212 q^{19} +11.8369 q^{20} -7.02500 q^{21} +1.95289 q^{22} +4.91564 q^{23} -28.7008 q^{24} -0.834365 q^{25} +19.0299 q^{26} +3.55776 q^{27} -15.0635 q^{28} +3.49298 q^{29} -15.4169 q^{30} +3.07578 q^{31} -29.1482 q^{32} -1.89130 q^{33} +14.8769 q^{34} -5.30112 q^{35} +25.0276 q^{36} -4.64934 q^{37} -15.7851 q^{38} -18.4298 q^{39} -21.6578 q^{40} +6.73132 q^{41} +19.6193 q^{42} -2.80003 q^{43} -4.05545 q^{44} +8.80768 q^{45} -13.7283 q^{46} +1.71226 q^{47} +48.7825 q^{48} -0.253874 q^{49} +2.33020 q^{50} -14.4077 q^{51} -39.5184 q^{52} -3.80882 q^{53} -9.93602 q^{54} -1.42719 q^{55} +27.5614 q^{56} +15.2873 q^{57} -9.75511 q^{58} -7.95123 q^{59} +32.0153 q^{60} -6.31070 q^{61} -8.58998 q^{62} -11.2085 q^{63} +45.3320 q^{64} -13.9073 q^{65} +5.28197 q^{66} +2.51519 q^{67} -30.8940 q^{68} +13.2953 q^{69} +14.8049 q^{70} -14.6307 q^{71} -45.7926 q^{72} +10.4588 q^{73} +12.9846 q^{74} -2.25671 q^{75} +32.7800 q^{76} +1.81622 q^{77} +51.4703 q^{78} -2.22840 q^{79} +36.8117 q^{80} -3.32354 q^{81} -18.7991 q^{82} -2.26372 q^{83} -40.7422 q^{84} -10.8722 q^{85} +7.81986 q^{86} +9.44746 q^{87} +7.42020 q^{88} +1.35585 q^{89} -24.5979 q^{90} +17.6982 q^{91} +28.5088 q^{92} +8.31907 q^{93} -4.78197 q^{94} +11.5359 q^{95} -78.8371 q^{96} +1.17228 q^{97} +0.709015 q^{98} -3.01760 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 237 q - 26 q^{2} - 24 q^{3} + 226 q^{4} - 67 q^{5} - 30 q^{6} - 37 q^{7} - 75 q^{8} + 189 q^{9}+O(q^{10}) \) 237 * q - 26 * q^2 - 24 * q^3 + 226 * q^4 - 67 * q^5 - 30 * q^6 - 37 * q^7 - 75 * q^8 + 189 * q^9	\( 237 q - 26 q^{2} - 24 q^{3} + 226 q^{4} - 67 q^{5} - 30 q^{6} - 37 q^{7} - 75 q^{8} + 189 q^{9} - 39 q^{10} - 38 q^{11} - 67 q^{12} - 52 q^{13} - 54 q^{14} - 24 q^{15} + 208 q^{16} - 255 q^{17} - 71 q^{18} - 24 q^{19} - 154 q^{20} - 60 q^{21} - 39 q^{22} - 118 q^{23} - 85 q^{24} + 170 q^{25} - 61 q^{26} - 87 q^{27} - 99 q^{28} - 87 q^{29} - 30 q^{30} - 28 q^{31} - 156 q^{32} - 173 q^{33} - 4 q^{34} - 113 q^{35} + 152 q^{36} - 49 q^{37} - 145 q^{38} - 49 q^{39} - 91 q^{40} - 197 q^{41} - 61 q^{42} - 63 q^{43} - 106 q^{44} - 181 q^{45} - 2 q^{46} - 119 q^{47} - 142 q^{48} + 150 q^{49} - 89 q^{50} - 40 q^{51} - 97 q^{52} - 190 q^{53} - 97 q^{54} - 55 q^{55} - 154 q^{56} - 202 q^{57} - 27 q^{58} - 86 q^{59} - 48 q^{60} - 96 q^{61} - 239 q^{62} - 149 q^{63} + 183 q^{64} - 259 q^{65} - 72 q^{66} - 28 q^{67} - 482 q^{68} - 83 q^{69} + 20 q^{70} - 63 q^{71} - 193 q^{72} - 206 q^{73} - 132 q^{74} - 89 q^{75} - 11 q^{76} - 179 q^{77} - 58 q^{78} - 32 q^{79} - 320 q^{80} + 57 q^{81} - 77 q^{82} - 245 q^{83} - 133 q^{84} + q^{85} - 39 q^{86} - 179 q^{87} - 104 q^{88} - 227 q^{89} - 146 q^{90} - 36 q^{91} - 315 q^{92} - 87 q^{93} - 48 q^{94} - 111 q^{95} - 134 q^{96} - 221 q^{97} - 161 q^{98} - 68 q^{99}+O(q^{100}) \) 237 * q - 26 * q^2 - 24 * q^3 + 226 * q^4 - 67 * q^5 - 30 * q^6 - 37 * q^7 - 75 * q^8 + 189 * q^9 - 39 * q^10 - 38 * q^11 - 67 * q^12 - 52 * q^13 - 54 * q^14 - 24 * q^15 + 208 * q^16 - 255 * q^17 - 71 * q^18 - 24 * q^19 - 154 * q^20 - 60 * q^21 - 39 * q^22 - 118 * q^23 - 85 * q^24 + 170 * q^25 - 61 * q^26 - 87 * q^27 - 99 * q^28 - 87 * q^29 - 30 * q^30 - 28 * q^31 - 156 * q^32 - 173 * q^33 - 4 * q^34 - 113 * q^35 + 152 * q^36 - 49 * q^37 - 145 * q^38 - 49 * q^39 - 91 * q^40 - 197 * q^41 - 61 * q^42 - 63 * q^43 - 106 * q^44 - 181 * q^45 - 2 * q^46 - 119 * q^47 - 142 * q^48 + 150 * q^49 - 89 * q^50 - 40 * q^51 - 97 * q^52 - 190 * q^53 - 97 * q^54 - 55 * q^55 - 154 * q^56 - 202 * q^57 - 27 * q^58 - 86 * q^59 - 48 * q^60 - 96 * q^61 - 239 * q^62 - 149 * q^63 + 183 * q^64 - 259 * q^65 - 72 * q^66 - 28 * q^67 - 482 * q^68 - 83 * q^69 + 20 * q^70 - 63 * q^71 - 193 * q^72 - 206 * q^73 - 132 * q^74 - 89 * q^75 - 11 * q^76 - 179 * q^77 - 58 * q^78 - 32 * q^79 - 320 * q^80 + 57 * q^81 - 77 * q^82 - 245 * q^83 - 133 * q^84 + q^85 - 39 * q^86 - 179 * q^87 - 104 * q^88 - 227 * q^89 - 146 * q^90 - 36 * q^91 - 315 * q^92 - 87 * q^93 - 48 * q^94 - 111 * q^95 - 134 * q^96 - 221 * q^97 - 161 * q^98 - 68 * q^99

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