LMFDB - Embedded newform 6007.2.a.b.1.9

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			1.9
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)

$f(q)$	$=$	$q-2.71184 q^{2} +0.480935 q^{3} +5.35409 q^{4} -1.73647 q^{5} -1.30422 q^{6} +3.65301 q^{7} -9.09575 q^{8} -2.76870 q^{9} +O(q^{10})$	\(q-2.71184 q^{2} +0.480935 q^{3} +5.35409 q^{4} -1.73647 q^{5} -1.30422 q^{6} +3.65301 q^{7} -9.09575 q^{8} -2.76870 q^{9} +4.70903 q^{10} -1.74435 q^{11} +2.57497 q^{12} +0.499202 q^{13} -9.90639 q^{14} -0.835129 q^{15} +13.9581 q^{16} -7.63934 q^{17} +7.50828 q^{18} +0.781149 q^{19} -9.29721 q^{20} +1.75686 q^{21} +4.73041 q^{22} +1.05606 q^{23} -4.37446 q^{24} -1.98467 q^{25} -1.35376 q^{26} -2.77437 q^{27} +19.5585 q^{28} +2.31039 q^{29} +2.26474 q^{30} +5.33930 q^{31} -19.6605 q^{32} -0.838920 q^{33} +20.7167 q^{34} -6.34335 q^{35} -14.8239 q^{36} -6.57451 q^{37} -2.11835 q^{38} +0.240083 q^{39} +15.7945 q^{40} +11.8571 q^{41} -4.76433 q^{42} +9.85833 q^{43} -9.33941 q^{44} +4.80777 q^{45} -2.86386 q^{46} +6.51684 q^{47} +6.71292 q^{48} +6.34450 q^{49} +5.38211 q^{50} -3.67403 q^{51} +2.67277 q^{52} -1.32343 q^{53} +7.52365 q^{54} +3.02902 q^{55} -33.2269 q^{56} +0.375682 q^{57} -6.26541 q^{58} -10.3953 q^{59} -4.47135 q^{60} +8.21193 q^{61} -14.4793 q^{62} -10.1141 q^{63} +25.4002 q^{64} -0.866849 q^{65} +2.27502 q^{66} +3.10360 q^{67} -40.9017 q^{68} +0.507895 q^{69} +17.2022 q^{70} +3.30629 q^{71} +25.1834 q^{72} +3.36131 q^{73} +17.8290 q^{74} -0.954497 q^{75} +4.18234 q^{76} -6.37214 q^{77} -0.651068 q^{78} +5.47829 q^{79} -24.2378 q^{80} +6.97181 q^{81} -32.1546 q^{82} +9.66933 q^{83} +9.40638 q^{84} +13.2655 q^{85} -26.7342 q^{86} +1.11115 q^{87} +15.8662 q^{88} -7.67236 q^{89} -13.0379 q^{90} +1.82359 q^{91} +5.65422 q^{92} +2.56785 q^{93} -17.6726 q^{94} -1.35644 q^{95} -9.45544 q^{96} -17.5483 q^{97} -17.2053 q^{98} +4.82959 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.71184	−1.91756	−0.958781	−	0.284147i	$-0.908290\pi$
$2$	−2.71184	−1.91756	−0.958781	+	0.284147i	$0.908290\pi$
$3$	0.480935	0.277668	0.138834	−	0.990316i	$-0.455665\pi$
$3$	0.480935	0.277668	0.138834	+	0.990316i	$0.455665\pi$
$4$	5.35409	2.67704
$5$	−1.73647	−0.776573	−0.388287	−	0.921539i	$-0.626933\pi$
$5$	−1.73647	−0.776573	−0.388287	+	0.921539i	$0.626933\pi$
$6$	−1.30422	−0.532445
$7$	3.65301	1.38071	0.690354	−	0.723471i	$-0.257455\pi$
$7$	3.65301	1.38071	0.690354	+	0.723471i	$0.257455\pi$
$8$	−9.09575	−3.21583
$9$	−2.76870	−0.922901
$10$	4.70903	1.48913
$11$	−1.74435	−0.525942	−0.262971	−	0.964804i	$-0.584702\pi$
$11$	−1.74435	−0.525942	−0.262971	+	0.964804i	$0.584702\pi$
$12$	2.57497	0.743329
$13$	0.499202	0.138454	0.0692268	−	0.997601i	$-0.477947\pi$
$13$	0.499202	0.138454	0.0692268	+	0.997601i	$0.477947\pi$
$14$	−9.90639	−2.64759
$15$	−0.835129	−0.215629
$16$	13.9581	3.48951
$17$	−7.63934	−1.85281	−0.926406	−	0.376525i	$-0.877119\pi$
$17$	−7.63934	−1.85281	−0.926406	+	0.376525i	$0.877119\pi$
$18$	7.50828	1.76972
$19$	0.781149	0.179208	0.0896039	−	0.995977i	$-0.471440\pi$
$19$	0.781149	0.179208	0.0896039	+	0.995977i	$0.471440\pi$
$20$	−9.29721	−2.07892
$21$	1.75686	0.383378
$22$	4.73041	1.00853
$23$	1.05606	0.220203	0.110102	−	0.993920i	$-0.464882\pi$
$23$	1.05606	0.220203	0.110102	+	0.993920i	$0.464882\pi$
$24$	−4.37446	−0.892933
$25$	−1.98467	−0.396934
$26$	−1.35376	−0.265493
$27$	−2.77437	−0.533928
$28$	19.5585	3.69622
$29$	2.31039	0.429029	0.214514	−	0.976721i	$-0.431183\pi$
$29$	2.31039	0.429029	0.214514	+	0.976721i	$0.431183\pi$
$30$	2.26474	0.413483
$31$	5.33930	0.958966	0.479483	−	0.877551i	$-0.340824\pi$
$31$	5.33930	0.958966	0.479483	+	0.877551i	$0.340824\pi$
$32$	−19.6605	−3.47553
$33$	−0.838920	−0.146037
$34$	20.7167	3.55288
$35$	−6.34335	−1.07222
$36$	−14.8239	−2.47064
$37$	−6.57451	−1.08084	−0.540422	−	0.841394i	$-0.681735\pi$
$37$	−6.57451	−1.08084	−0.540422	+	0.841394i	$0.681735\pi$
$38$	−2.11835	−0.343642
$39$	0.240083	0.0384441
$40$	15.7945	2.49733
$41$	11.8571	1.85177	0.925884	−	0.377808i	$-0.123322\pi$
$41$	11.8571	1.85177	0.925884	+	0.377808i	$0.123322\pi$
$42$	−4.76433	−0.735152
$43$	9.85833	1.50338	0.751691	−	0.659516i	$-0.229239\pi$
$43$	9.85833	1.50338	0.751691	+	0.659516i	$0.229239\pi$
$44$	−9.33941	−1.40797
$45$	4.80777	0.716700
$46$	−2.86386	−0.422253
$47$	6.51684	0.950579	0.475290	−	0.879829i	$-0.342343\pi$
$47$	6.51684	0.950579	0.475290	+	0.879829i	$0.342343\pi$
$48$	6.71292	0.968926
$49$	6.34450	0.906356
$50$	5.38211	0.761145
$51$	−3.67403	−0.514467
$52$	2.67277	0.370646
$53$	−1.32343	−0.181787	−0.0908937	−	0.995861i	$-0.528972\pi$
$53$	−1.32343	−0.181787	−0.0908937	+	0.995861i	$0.528972\pi$
$54$	7.52365	1.02384
$55$	3.02902	0.408432
$56$	−33.2269	−4.44013
$57$	0.375682	0.0497603
$58$	−6.26541	−0.822689
$59$	−10.3953	−1.35335	−0.676674	−	0.736283i	$-0.736579\pi$
$59$	−10.3953	−1.35335	−0.676674	+	0.736283i	$0.736579\pi$
$60$	−4.47135	−0.577249
$61$	8.21193	1.05143	0.525715	−	0.850661i	$-0.323798\pi$
$61$	8.21193	1.05143	0.525715	+	0.850661i	$0.323798\pi$
$62$	−14.4793	−1.83888
$63$	−10.1141	−1.27426
$64$	25.4002	3.17502
$65$	−0.866849	−0.107519
$66$	2.27502	0.280035
$67$	3.10360	0.379165	0.189583	−	0.981865i	$-0.439287\pi$
$67$	3.10360	0.379165	0.189583	+	0.981865i	$0.439287\pi$
$68$	−40.9017	−4.96006
$69$	0.507895	0.0611434
$70$	17.2022	2.05605
$71$	3.30629	0.392384	0.196192	−	0.980565i	$-0.437142\pi$
$71$	3.30629	0.392384	0.196192	+	0.980565i	$0.437142\pi$
$72$	25.1834	2.96789
$73$	3.36131	0.393411	0.196706	−	0.980463i	$-0.436976\pi$
$73$	3.36131	0.393411	0.196706	+	0.980463i	$0.436976\pi$
$74$	17.8290	2.07258
$75$	−0.954497	−0.110216
$76$	4.18234	0.479747
$77$	−6.37214	−0.726173
$78$	−0.651068	−0.0737190
$79$	5.47829	0.616356	0.308178	−	0.951329i	$-0.400281\pi$
$79$	5.47829	0.616356	0.308178	+	0.951329i	$0.400281\pi$
$80$	−24.2378	−2.70986
$81$	6.97181	0.774646
$82$	−32.1546	−3.55088
$83$	9.66933	1.06135	0.530673	−	0.847576i	$-0.321939\pi$
$83$	9.66933	1.06135	0.530673	+	0.847576i	$0.321939\pi$
$84$	9.40638	1.02632
$85$	13.2655	1.43885
$86$	−26.7342	−2.88283
$87$	1.11115	0.119127
$88$	15.8662	1.69134
$89$	−7.67236	−0.813269	−0.406634	−	0.913591i	$-0.633298\pi$
$89$	−7.67236	−0.813269	−0.406634	+	0.913591i	$0.633298\pi$
$90$	−13.0379	−1.37432
$91$	1.82359	0.191164
$92$	5.65422	0.589494
$93$	2.56785	0.266274
$94$	−17.6726	−1.82279
$95$	−1.35644	−0.139168
$96$	−9.45544	−0.965042
$97$	−17.5483	−1.78176	−0.890880	−	0.454238i	$-0.849911\pi$
$97$	−17.5483	−1.78176	−0.890880	+	0.454238i	$0.849911\pi$
$98$	−17.2053	−1.73799
$99$	4.82959	0.485392
$100$	−10.6261	−1.06261
$101$	14.1832	1.41128	0.705640	−	0.708570i	$-0.250660\pi$
$101$	14.1832	1.41128	0.705640	+	0.708570i	$0.250660\pi$
$102$	9.96338	0.986521
$103$	−5.24536	−0.516841	−0.258420	−	0.966033i	$-0.583202\pi$
$103$	−5.24536	−0.516841	−0.258420	+	0.966033i	$0.583202\pi$
$104$	−4.54061	−0.445244
$105$	−3.05074	−0.297722
$106$	3.58894	0.348588
$107$	13.3119	1.28691	0.643454	−	0.765484i	$-0.277501\pi$
$107$	13.3119	1.28691	0.643454	+	0.765484i	$0.277501\pi$
$108$	−14.8542	−1.42935
$109$	−11.1251	−1.06559	−0.532797	−	0.846243i	$-0.678859\pi$
$109$	−11.1251	−1.06559	−0.532797	+	0.846243i	$0.678859\pi$
$110$	−8.21421	−0.783194
$111$	−3.16191	−0.300115
$112$	50.9889	4.81800
$113$	7.33945	0.690437	0.345219	−	0.938522i	$-0.387805\pi$
$113$	7.33945	0.690437	0.345219	+	0.938522i	$0.387805\pi$
$114$	−1.01879	−0.0954184
$115$	−1.83381	−0.171004
$116$	12.3700	1.14853
$117$	−1.38214	−0.127779
$118$	28.1903	2.59513
$119$	−27.9066	−2.55819
$120$	7.59613	0.693428
$121$	−7.95724	−0.723385
$122$	−22.2695	−2.01618
$123$	5.70249	0.514177
$124$	28.5871	2.56719
$125$	12.1287	1.08482
$126$	27.4278	2.44347
$127$	−11.2463	−0.997943	−0.498972	−	0.866618i	$-0.666289\pi$
$127$	−11.2463	−0.997943	−0.498972	+	0.866618i	$0.666289\pi$
$128$	−29.5601	−2.61277
$129$	4.74121	0.417441
$130$	2.35076	0.206175
$131$	−15.1750	−1.32584	−0.662922	−	0.748689i	$-0.730684\pi$
$131$	−15.1750	−1.32584	−0.662922	+	0.748689i	$0.730684\pi$
$132$	−4.49165	−0.390948
$133$	2.85355	0.247434
$134$	−8.41648	−0.727073
$135$	4.81761	0.414634
$136$	69.4855	5.95834
$137$	−11.7207	−1.00136	−0.500682	−	0.865631i	$-0.666918\pi$
$137$	−11.7207	−1.00136	−0.500682	+	0.865631i	$0.666918\pi$
$138$	−1.37733	−0.117246
$139$	−17.3417	−1.47090	−0.735452	−	0.677577i	$-0.763030\pi$
$139$	−17.3417	−1.47090	−0.735452	+	0.677577i	$0.763030\pi$
$140$	−33.9628	−2.87038
$141$	3.13418	0.263945
$142$	−8.96613	−0.752421
$143$	−0.870783	−0.0728186
$144$	−38.6457	−3.22047
$145$	−4.01192	−0.333172
$146$	−9.11534	−0.754391
$147$	3.05129	0.251666
$148$	−35.2005	−2.89346
$149$	−16.2215	−1.32891	−0.664457	−	0.747326i	$-0.731337\pi$
$149$	−16.2215	−1.32891	−0.664457	+	0.747326i	$0.731337\pi$
$150$	2.58844	0.211346
$151$	19.2564	1.56707	0.783533	−	0.621350i	$-0.213415\pi$
$151$	19.2564	1.56707	0.783533	+	0.621350i	$0.213415\pi$
$152$	−7.10513	−0.576302
$153$	21.1511	1.70996
$154$	17.2802	1.39248
$155$	−9.27153	−0.744708
$156$	1.28543	0.102917
$157$	−19.9507	−1.59224	−0.796121	−	0.605138i	$-0.793118\pi$
$157$	−19.9507	−1.59224	−0.796121	+	0.605138i	$0.793118\pi$
$158$	−14.8563	−1.18190
$159$	−0.636485	−0.0504765
$160$	34.1400	2.69900
$161$	3.85779	0.304037
$162$	−18.9065	−1.48543
$163$	−17.9621	−1.40690	−0.703450	−	0.710745i	$-0.748358\pi$
$163$	−17.9621	−1.40690	−0.703450	+	0.710745i	$0.748358\pi$
$164$	63.4839	4.95726
$165$	1.45676	0.113409
$166$	−26.2217	−2.03520
$167$	−11.4604	−0.886836	−0.443418	−	0.896315i	$-0.646234\pi$
$167$	−11.4604	−0.886836	−0.443418	+	0.896315i	$0.646234\pi$
$168$	−15.9800	−1.23288
$169$	−12.7508	−0.980831
$170$	−35.9739	−2.75907
$171$	−2.16277	−0.165391
$172$	52.7823	4.02461
$173$	23.2906	1.77075	0.885375	−	0.464878i	$-0.153902\pi$
$173$	23.2906	1.77075	0.885375	+	0.464878i	$0.153902\pi$
$174$	−3.01325	−0.228434
$175$	−7.25002	−0.548050
$176$	−24.3478	−1.83528
$177$	−4.99945	−0.375781
$178$	20.8062	1.55949
$179$	5.06220	0.378367	0.189183	−	0.981942i	$-0.439416\pi$
$179$	5.06220	0.378367	0.189183	+	0.981942i	$0.439416\pi$
$180$	25.7412	1.91864
$181$	−2.18084	−0.162101	−0.0810504	−	0.996710i	$-0.525827\pi$
$181$	−2.18084	−0.162101	−0.0810504	+	0.996710i	$0.525827\pi$
$182$	−4.94529	−0.366569
$183$	3.94941	0.291948
$184$	−9.60564	−0.708137
$185$	11.4164	0.839354
$186$	−6.96361	−0.510597
$187$	13.3257	0.974472
$188$	34.8917	2.54474
$189$	−10.1348	−0.737199
$190$	3.67846	0.266863
$191$	−3.74438	−0.270934	−0.135467	−	0.990782i	$-0.543253\pi$
$191$	−3.74438	−0.270934	−0.135467	+	0.990782i	$0.543253\pi$
$192$	12.2158	0.881601
$193$	−18.8299	−1.35541	−0.677704	−	0.735335i	$-0.737025\pi$
$193$	−18.8299	−1.35541	−0.677704	+	0.735335i	$0.737025\pi$
$194$	47.5882	3.41664
$195$	−0.416898	−0.0298547
$196$	33.9690	2.42635
$197$	−22.9220	−1.63313	−0.816564	−	0.577255i	$-0.804124\pi$
$197$	−22.9220	−1.63313	−0.816564	+	0.577255i	$0.804124\pi$
$198$	−13.0971	−0.930769
$199$	−15.9219	−1.12868	−0.564339	−	0.825543i	$-0.690869\pi$
$199$	−15.9219	−1.12868	−0.564339	+	0.825543i	$0.690869\pi$
$200$	18.0520	1.27647
$201$	1.49263	0.105282
$202$	−38.4626	−2.70622
$203$	8.43988	0.592363
$204$	−19.6711	−1.37725
$205$	−20.5895	−1.43803
$206$	14.2246	0.991074
$207$	−2.92391	−0.203226
$208$	6.96788	0.483136
$209$	−1.36260	−0.0942529
$210$	8.27312	0.570899
$211$	5.13200	0.353301	0.176651	−	0.984274i	$-0.443474\pi$
$211$	5.13200	0.353301	0.176651	+	0.984274i	$0.443474\pi$
$212$	−7.08577	−0.486652
$213$	1.59011	0.108952
$214$	−36.0997	−2.46773
$215$	−17.1187	−1.16749
$216$	25.2350	1.71702
$217$	19.5045	1.32405
$218$	30.1696	2.04334
$219$	1.61657	0.109238
$220$	16.2176	1.09339
$221$	−3.81357	−0.256529
$222$	8.57461	0.575490
$223$	−11.3676	−0.761234	−0.380617	−	0.924733i	$-0.624288\pi$
$223$	−11.3676	−0.761234	−0.380617	+	0.924733i	$0.624288\pi$
$224$	−71.8202	−4.79869
$225$	5.49496	0.366330
$226$	−19.9034	−1.32396
$227$	−8.53379	−0.566407	−0.283204	−	0.959060i	$-0.591397\pi$
$227$	−8.53379	−0.566407	−0.283204	+	0.959060i	$0.591397\pi$
$228$	2.01143	0.133210
$229$	26.1636	1.72894	0.864470	−	0.502684i	$-0.167654\pi$
$229$	26.1636	1.72894	0.864470	+	0.502684i	$0.167654\pi$
$230$	4.97301	0.327911
$231$	−3.06458	−0.201635
$232$	−21.0147	−1.37968
$233$	25.3098	1.65810	0.829050	−	0.559174i	$-0.188882\pi$
$233$	25.3098	1.65810	0.829050	+	0.559174i	$0.188882\pi$
$234$	3.74815	0.245024
$235$	−11.3163	−0.738194
$236$	−55.6571	−3.62297
$237$	2.63470	0.171142
$238$	75.6783	4.90550
$239$	−13.2810	−0.859076	−0.429538	−	0.903049i	$-0.641324\pi$
$239$	−13.2810	−0.859076	−0.429538	+	0.903049i	$0.641324\pi$
$240$	−11.6568	−0.752442
$241$	−12.9254	−0.832599	−0.416300	−	0.909228i	$-0.636673\pi$
$241$	−12.9254	−0.832599	−0.416300	+	0.909228i	$0.636673\pi$
$242$	21.5788	1.38714
$243$	11.6761	0.749022
$244$	43.9674	2.81472
$245$	−11.0170	−0.703852
$246$	−15.4643	−0.985965
$247$	0.389951	0.0248120
$248$	−48.5649	−3.08387
$249$	4.65032	0.294702
$250$	−32.8910	−2.08021
$251$	−10.7349	−0.677578	−0.338789	−	0.940862i	$-0.610017\pi$
$251$	−10.7349	−0.677578	−0.338789	+	0.940862i	$0.610017\pi$
$252$	−54.1517	−3.41124
$253$	−1.84214	−0.115814
$254$	30.4981	1.91362
$255$	6.37984	0.399521
$256$	29.3621	1.83513
$257$	13.9658	0.871165	0.435583	−	0.900149i	$-0.356542\pi$
$257$	13.9658	0.871165	0.435583	+	0.900149i	$0.356542\pi$
$258$	−12.8574	−0.800468
$259$	−24.0168	−1.49233
$260$	−4.64118	−0.287834
$261$	−6.39678	−0.395951
$262$	41.1521	2.54239
$263$	−15.4574	−0.953144	−0.476572	−	0.879135i	$-0.658121\pi$
$263$	−15.4574	−0.953144	−0.476572	+	0.879135i	$0.658121\pi$
$264$	7.63060	0.469631
$265$	2.29810	0.141171
$266$	−7.73836	−0.474469
$267$	−3.68991	−0.225819
$268$	16.6169	1.01504
$269$	−20.4832	−1.24888	−0.624440	−	0.781073i	$-0.714673\pi$
$269$	−20.4832	−1.24888	−0.624440	+	0.781073i	$0.714673\pi$
$270$	−13.0646	−0.795086
$271$	−0.158086	−0.00960307	−0.00480153	−	0.999988i	$-0.501528\pi$
$271$	−0.158086	−0.00960307	−0.00480153	+	0.999988i	$0.501528\pi$
$272$	−106.630	−6.46542
$273$	0.877028	0.0530801
$274$	31.7846	1.92018
$275$	3.46196	0.208764
$276$	2.71931	0.163683
$277$	−6.95620	−0.417958	−0.208979	−	0.977920i	$-0.567014\pi$
$277$	−6.95620	−0.417958	−0.208979	+	0.977920i	$0.567014\pi$
$278$	47.0279	2.82055
$279$	−14.7829	−0.885030
$280$	57.6975	3.44808
$281$	−2.40544	−0.143497	−0.0717484	−	0.997423i	$-0.522858\pi$
$281$	−2.40544	−0.143497	−0.0717484	+	0.997423i	$0.522858\pi$
$282$	−8.49939	−0.506131
$283$	18.6097	1.10623	0.553116	−	0.833104i	$-0.313439\pi$
$283$	18.6097	1.10623	0.553116	+	0.833104i	$0.313439\pi$
$284$	17.7021	1.05043
$285$	−0.652360	−0.0386425
$286$	2.36143	0.139634
$287$	43.3141	2.55675
$288$	54.4342	3.20756
$289$	41.3596	2.43292
$290$	10.8797	0.638878
$291$	−8.43959	−0.494738
$292$	17.9967	1.05318
$293$	−19.5303	−1.14097	−0.570486	−	0.821307i	$-0.693245\pi$
$293$	−19.5303	−1.14097	−0.570486	+	0.821307i	$0.693245\pi$
$294$	−8.27461	−0.482585
$295$	18.0511	1.05097
$296$	59.8001	3.47581
$297$	4.83948	0.280815
$298$	43.9901	2.54828
$299$	0.527186	0.0304879
$300$	−5.11046	−0.295052
$301$	36.0126	2.07573
$302$	−52.2204	−3.00495
$303$	6.82119	0.391867
$304$	10.9033	0.625348
$305$	−14.2598	−0.816513
$306$	−57.3583	−3.27896
$307$	−17.4992	−0.998731	−0.499366	−	0.866391i	$-0.666434\pi$
$307$	−17.4992	−0.998731	−0.499366	+	0.866391i	$0.666434\pi$
$308$	−34.1170	−1.94399
$309$	−2.52268	−0.143510
$310$	25.1429	1.42802
$311$	−15.7934	−0.895561	−0.447781	−	0.894143i	$-0.647785\pi$
$311$	−15.7934	−0.895561	−0.447781	+	0.894143i	$0.647785\pi$
$312$	−2.18374	−0.123630
$313$	−5.20550	−0.294232	−0.147116	−	0.989119i	$-0.546999\pi$
$313$	−5.20550	−0.294232	−0.147116	+	0.989119i	$0.546999\pi$
$314$	54.1032	3.05322
$315$	17.5628	0.989554
$316$	29.3312	1.65001
$317$	−9.30088	−0.522389	−0.261195	−	0.965286i	$-0.584116\pi$
$317$	−9.30088	−0.522389	−0.261195	+	0.965286i	$0.584116\pi$
$318$	1.72605	0.0967918
$319$	−4.03013	−0.225644
$320$	−44.1067	−2.46564
$321$	6.40215	0.357333
$322$	−10.4617	−0.583009
$323$	−5.96746	−0.332039
$324$	37.3277	2.07376
$325$	−0.990750	−0.0549569
$326$	48.7104	2.69782
$327$	−5.35046	−0.295881
$328$	−107.849	−5.95498
$329$	23.8061	1.31247
$330$	−3.95050	−0.217468
$331$	16.7946	0.923115	0.461558	−	0.887110i	$-0.347291\pi$
$331$	16.7946	0.923115	0.461558	+	0.887110i	$0.347291\pi$
$332$	51.7704	2.84127
$333$	18.2029	0.997511
$334$	31.0789	1.70056
$335$	−5.38931	−0.294450
$336$	24.5224	1.33780
$337$	22.4665	1.22383	0.611914	−	0.790924i	$-0.290400\pi$
$337$	22.4665	1.22383	0.611914	+	0.790924i	$0.290400\pi$
$338$	34.5781	1.88080
$339$	3.52980	0.191712
$340$	71.0246	3.85185
$341$	−9.31361	−0.504360
$342$	5.86508	0.317147
$343$	−2.39457	−0.129294
$344$	−89.6689	−4.83462
$345$	−0.881945	−0.0474823
$346$	−63.1603	−3.39552
$347$	−31.4195	−1.68669	−0.843344	−	0.537374i	$-0.819416\pi$
$347$	−31.4195	−1.68669	−0.843344	+	0.537374i	$0.819416\pi$
$348$	5.94918	0.318909
$349$	19.4896	1.04325	0.521626	−	0.853174i	$-0.325326\pi$
$349$	19.4896	1.04325	0.521626	+	0.853174i	$0.325326\pi$
$350$	19.6609	1.05092
$351$	−1.38497	−0.0739242
$352$	34.2949	1.82792
$353$	31.8628	1.69589	0.847943	−	0.530087i	$-0.177841\pi$
$353$	31.8628	1.69589	0.847943	+	0.530087i	$0.177841\pi$
$354$	13.5577	0.720584
$355$	−5.74127	−0.304715
$356$	−41.0785	−2.17716
$357$	−13.4213	−0.710329
$358$	−13.7279	−0.725541
$359$	30.0291	1.58487	0.792437	−	0.609954i	$-0.208812\pi$
$359$	30.0291	1.58487	0.792437	+	0.609954i	$0.208812\pi$
$360$	−43.7303	−2.30479
$361$	−18.3898	−0.967885
$362$	5.91410	0.310838
$363$	−3.82691	−0.200861
$364$	9.76365	0.511754
$365$	−5.83681	−0.305513
$366$	−10.7102	−0.559829
$367$	−7.58940	−0.396163	−0.198082	−	0.980186i	$-0.563471\pi$
$367$	−7.58940	−0.396163	−0.198082	+	0.980186i	$0.563471\pi$
$368$	14.7405	0.768402
$369$	−32.8288	−1.70900
$370$	−30.9596	−1.60951
$371$	−4.83451	−0.250995
$372$	13.7485	0.712827
$373$	−33.6058	−1.74004	−0.870020	−	0.493017i	$-0.835894\pi$
$373$	−33.6058	−1.74004	−0.870020	+	0.493017i	$0.835894\pi$
$374$	−36.1372	−1.86861
$375$	5.83310	0.301220
$376$	−59.2755	−3.05690
$377$	1.15335	0.0594006
$378$	27.4840	1.41362
$379$	−21.3914	−1.09880	−0.549401	−	0.835559i	$-0.685144\pi$
$379$	−21.3914	−1.09880	−0.549401	+	0.835559i	$0.685144\pi$
$380$	−7.26251	−0.372559
$381$	−5.40871	−0.277097
$382$	10.1542	0.519533
$383$	−13.1963	−0.674301	−0.337151	−	0.941451i	$-0.609463\pi$
$383$	−13.1963	−0.674301	−0.337151	+	0.941451i	$0.609463\pi$
$384$	−14.2165	−0.725483
$385$	11.0650	0.563926
$386$	51.0638	2.59908
$387$	−27.2948	−1.38747
$388$	−93.9551	−4.76985
$389$	−2.29137	−0.116177	−0.0580885	−	0.998311i	$-0.518501\pi$
$389$	−2.29137	−0.116177	−0.0580885	+	0.998311i	$0.518501\pi$
$390$	1.13056	0.0572482
$391$	−8.06759	−0.407995
$392$	−57.7079	−2.91469
$393$	−7.29817	−0.368144
$394$	62.1609	3.13162
$395$	−9.51290	−0.478646
$396$	25.8580	1.29942
$397$	20.1019	1.00889	0.504443	−	0.863445i	$-0.331698\pi$
$397$	20.1019	1.00889	0.504443	+	0.863445i	$0.331698\pi$
$398$	43.1778	2.16431
$399$	1.37237	0.0687044
$400$	−27.7021	−1.38511
$401$	−4.03853	−0.201674	−0.100837	−	0.994903i	$-0.532152\pi$
$401$	−4.03853	−0.201674	−0.100837	+	0.994903i	$0.532152\pi$
$402$	−4.04778	−0.201885
$403$	2.66539	0.132772
$404$	75.9380	3.77806
$405$	−12.1064	−0.601569
$406$	−22.8876	−1.13589
$407$	11.4683	0.568461
$408$	33.4180	1.65444
$409$	−6.17257	−0.305214	−0.152607	−	0.988287i	$-0.548767\pi$
$409$	−6.17257	−0.305214	−0.152607	+	0.988287i	$0.548767\pi$
$410$	55.8355	2.75752
$411$	−5.63688	−0.278047
$412$	−28.0841	−1.38360
$413$	−37.9740	−1.86858
$414$	7.92918	0.389698
$415$	−16.7905	−0.824214
$416$	−9.81458	−0.481199
$417$	−8.34023	−0.408423
$418$	3.69515	0.180736
$419$	−9.10843	−0.444976	−0.222488	−	0.974935i	$-0.571418\pi$
$419$	−9.10843	−0.444976	−0.222488	+	0.974935i	$0.571418\pi$
$420$	−16.3339	−0.797013
$421$	13.8284	0.673957	0.336979	−	0.941512i	$-0.390595\pi$
$421$	13.8284	0.673957	0.336979	+	0.941512i	$0.390595\pi$
$422$	−13.9172	−0.677477
$423$	−18.0432	−0.877290
$424$	12.0376	0.584598
$425$	15.1616	0.735444
$426$	−4.31212	−0.208923
$427$	29.9983	1.45172
$428$	71.2730	3.44511
$429$	−0.418790	−0.0202194
$430$	46.4232	2.23873
$431$	−5.70847	−0.274967	−0.137484	−	0.990504i	$-0.543901\pi$
$431$	−5.70847	−0.274967	−0.137484	+	0.990504i	$0.543901\pi$
$432$	−38.7248	−1.86315
$433$	4.84556	0.232863	0.116431	−	0.993199i	$-0.462854\pi$
$433$	4.84556	0.232863	0.116431	+	0.993199i	$0.462854\pi$
$434$	−52.8932	−2.53895
$435$	−1.92947	−0.0925112
$436$	−59.5649	−2.85264
$437$	0.824938	0.0394621
$438$	−4.38388	−0.209470
$439$	−9.34571	−0.446046	−0.223023	−	0.974813i	$-0.571593\pi$
$439$	−9.34571	−0.446046	−0.223023	+	0.974813i	$0.571593\pi$
$440$	−27.5512	−1.31345
$441$	−17.5660	−0.836477
$442$	10.3418	0.491909
$443$	0.451243	0.0214392	0.0107196	−	0.999943i	$-0.496588\pi$
$443$	0.451243	0.0214392	0.0107196	+	0.999943i	$0.496588\pi$
$444$	−16.9291	−0.803422
$445$	13.3228	0.631563
$446$	30.8273	1.45971
$447$	−7.80147	−0.368997
$448$	92.7871	4.38378
$449$	33.3983	1.57616	0.788082	−	0.615571i	$-0.211074\pi$
$449$	33.3983	1.57616	0.788082	+	0.615571i	$0.211074\pi$
$450$	−14.9015	−0.702461
$451$	−20.6830	−0.973923
$452$	39.2960	1.84833
$453$	9.26109	0.435124
$454$	23.1423	1.08612
$455$	−3.16661	−0.148453
$456$	−3.41711	−0.160021
$457$	23.4338	1.09619	0.548094	−	0.836417i	$-0.315354\pi$
$457$	23.4338	1.09619	0.548094	+	0.836417i	$0.315354\pi$
$458$	−70.9516	−3.31535
$459$	21.1944	0.989268
$460$	−9.81839	−0.457785
$461$	35.3506	1.64644	0.823221	−	0.567721i	$-0.192175\pi$
$461$	35.3506	1.64644	0.823221	+	0.567721i	$0.192175\pi$
$462$	8.31067	0.386647
$463$	15.7777	0.733250	0.366625	−	0.930369i	$-0.380513\pi$
$463$	15.7777	0.733250	0.366625	+	0.930369i	$0.380513\pi$
$464$	32.2485	1.49710
$465$	−4.45900	−0.206781
$466$	−68.6362	−3.17951
$467$	17.7420	0.821004	0.410502	−	0.911860i	$-0.365354\pi$
$467$	17.7420	0.821004	0.410502	+	0.911860i	$0.365354\pi$
$468$	−7.40010	−0.342070
$469$	11.3375	0.523517
$470$	30.6880	1.41553
$471$	−9.59500	−0.442114
$472$	94.5527	4.35214
$473$	−17.1964	−0.790691
$474$	−7.14490	−0.328176
$475$	−1.55032	−0.0711336
$476$	−149.414	−6.84840
$477$	3.66419	0.167772
$478$	36.0160	1.64733
$479$	−33.2339	−1.51849	−0.759247	−	0.650802i	$-0.774433\pi$
$479$	−33.2339	−1.51849	−0.759247	+	0.650802i	$0.774433\pi$
$480$	16.4191	0.749426
$481$	−3.28201	−0.149647
$482$	35.0517	1.59656
$483$	1.85535	0.0844212
$484$	−42.6037	−1.93653
$485$	30.4721	1.38367
$486$	−31.6637	−1.43630
$487$	−7.48091	−0.338992	−0.169496	−	0.985531i	$-0.554214\pi$
$487$	−7.48091	−0.338992	−0.169496	+	0.985531i	$0.554214\pi$
$488$	−74.6937	−3.38122
$489$	−8.63860	−0.390651
$490$	29.8764	1.34968
$491$	37.9142	1.71105	0.855523	−	0.517765i	$-0.173236\pi$
$491$	37.9142	1.71105	0.855523	+	0.517765i	$0.173236\pi$
$492$	30.5316	1.37647
$493$	−17.6499	−0.794910
$494$	−1.05748	−0.0475785
$495$	−8.38644	−0.376943
$496$	74.5262	3.34633
$497$	12.0779	0.541768
$498$	−12.6109	−0.565109
$499$	−8.34475	−0.373562	−0.186781	−	0.982402i	$-0.559806\pi$
$499$	−8.34475	−0.373562	−0.186781	+	0.982402i	$0.559806\pi$
$500$	64.9380	2.90411
$501$	−5.51173	−0.246246
$502$	29.1112	1.29930
$503$	−37.8024	−1.68553	−0.842763	−	0.538285i	$-0.819072\pi$
$503$	−37.8024	−1.68553	−0.842763	+	0.538285i	$0.819072\pi$
$504$	91.9953	4.09780
$505$	−24.6287	−1.09596
$506$	4.99558	0.222081
$507$	−6.13230	−0.272345
$508$	−60.2134	−2.67154
$509$	14.2562	0.631897	0.315948	−	0.948776i	$-0.397677\pi$
$509$	14.2562	0.631897	0.315948	+	0.948776i	$0.397677\pi$
$510$	−17.3011	−0.766106
$511$	12.2789	0.543187
$512$	−20.5051	−0.906205
$513$	−2.16720	−0.0956840
$514$	−37.8732	−1.67051
$515$	9.10841	0.401365
$516$	25.3849	1.11751
$517$	−11.3677	−0.499949
$518$	65.1297	2.86163
$519$	11.2012	0.491680
$520$	7.88464	0.345764
$521$	26.7467	1.17180	0.585898	−	0.810385i	$-0.300742\pi$
$521$	26.7467	1.17180	0.585898	+	0.810385i	$0.300742\pi$
$522$	17.3471	0.759260
$523$	3.24307	0.141810	0.0709048	−	0.997483i	$-0.477411\pi$
$523$	3.24307	0.141810	0.0709048	+	0.997483i	$0.477411\pi$
$524$	−81.2481	−3.54934
$525$	−3.48679	−0.152176
$526$	41.9180	1.82771
$527$	−40.7887	−1.77678
$528$	−11.7097	−0.509599
$529$	−21.8847	−0.951511
$530$	−6.23209	−0.270704
$531$	28.7814	1.24901
$532$	15.2781	0.662391
$533$	5.91908	0.256384
$534$	10.0064	0.433021
$535$	−23.1157	−0.999379
$536$	−28.2296	−1.21933
$537$	2.43459	0.105060
$538$	55.5471	2.39480
$539$	−11.0670	−0.476691
$540$	25.7939	1.10999
$541$	−17.8257	−0.766385	−0.383192	−	0.923669i	$-0.625175\pi$
$541$	−17.8257	−0.766385	−0.383192	+	0.923669i	$0.625175\pi$
$542$	0.428705	0.0184145
$543$	−1.04884	−0.0450102
$544$	150.194	6.43950
$545$	19.3185	0.827512
$546$	−2.37836	−0.101784
$547$	27.8239	1.18966	0.594831	−	0.803851i	$-0.297219\pi$
$547$	27.8239	1.18966	0.594831	+	0.803851i	$0.297219\pi$
$548$	−62.7535	−2.68070
$549$	−22.7364	−0.970366
$550$	−9.38829	−0.400318
$551$	1.80476	0.0768853
$552$	−4.61969	−0.196627
$553$	20.0123	0.851008
$554$	18.8641	0.801459
$555$	5.49057	0.233062
$556$	−92.8489	−3.93767
$557$	−1.00871	−0.0427405	−0.0213703	−	0.999772i	$-0.506803\pi$
$557$	−1.00871	−0.0427405	−0.0213703	+	0.999772i	$0.506803\pi$
$558$	40.0889	1.69710
$559$	4.92129	0.208149
$560$	−88.5408	−3.74153
$561$	6.40880	0.270580
$562$	6.52319	0.275164
$563$	−28.8426	−1.21557	−0.607784	−	0.794102i	$-0.707942\pi$
$563$	−28.8426	−1.21557	−0.607784	+	0.794102i	$0.707942\pi$
$564$	16.7806	0.706593
$565$	−12.7447	−0.536175
$566$	−50.4666	−2.12127
$567$	25.4681	1.06956
$568$	−30.0731	−1.26184
$569$	−0.820891	−0.0344135	−0.0172068	−	0.999852i	$-0.505477\pi$
$569$	−0.820891	−0.0344135	−0.0172068	+	0.999852i	$0.505477\pi$
$570$	1.76910	0.0740993
$571$	−17.0584	−0.713873	−0.356937	−	0.934129i	$-0.616179\pi$
$571$	−17.0584	−0.713873	−0.356937	+	0.934129i	$0.616179\pi$
$572$	−4.66225	−0.194938
$573$	−1.80080	−0.0752297
$574$	−117.461	−4.90273
$575$	−2.09593	−0.0874061
$576$	−70.3255	−2.93023
$577$	−10.2396	−0.426279	−0.213139	−	0.977022i	$-0.568369\pi$
$577$	−10.2396	−0.426279	−0.213139	+	0.977022i	$0.568369\pi$
$578$	−112.161	−4.66526
$579$	−9.05597	−0.376353
$580$	−21.4802	−0.891916
$581$	35.3222	1.46541
$582$	22.8868	0.948690
$583$	2.30853	0.0956096
$584$	−30.5736	−1.26515
$585$	2.40005	0.0992297
$586$	52.9631	2.18789
$587$	33.3201	1.37527	0.687633	−	0.726059i	$-0.258650\pi$
$587$	33.3201	1.37527	0.687633	+	0.726059i	$0.258650\pi$
$588$	16.3369	0.673721
$589$	4.17079	0.171854
$590$	−48.9517	−2.01531
$591$	−11.0240	−0.453467
$592$	−91.7674	−3.77162
$593$	−18.4799	−0.758880	−0.379440	−	0.925216i	$-0.623883\pi$
$593$	−18.4799	−0.758880	−0.379440	+	0.925216i	$0.623883\pi$
$594$	−13.1239	−0.538480
$595$	48.4590	1.98663
$596$	−86.8511	−3.55756
$597$	−7.65742	−0.313397
$598$	−1.42964	−0.0584625
$599$	−25.0823	−1.02484	−0.512418	−	0.858736i	$-0.671250\pi$
$599$	−25.0823	−1.02484	−0.512418	+	0.858736i	$0.671250\pi$
$600$	8.68186	0.354435
$601$	−11.1229	−0.453714	−0.226857	−	0.973928i	$-0.572845\pi$
$601$	−11.1229	−0.453714	−0.226857	+	0.973928i	$0.572845\pi$
$602$	−97.6604	−3.98034
$603$	−8.59295	−0.349932
$604$	103.101	4.19510
$605$	13.8175	0.561762
$606$	−18.4980	−0.751430
$607$	−26.0593	−1.05771	−0.528856	−	0.848711i	$-0.677379\pi$
$607$	−26.0593	−1.05771	−0.528856	+	0.848711i	$0.677379\pi$
$608$	−15.3578	−0.622841
$609$	4.05903	0.164480
$610$	38.6703	1.56571
$611$	3.25322	0.131611
$612$	113.245	4.57764
$613$	0.545216	0.0220211	0.0110105	−	0.999939i	$-0.496495\pi$
$613$	0.545216	0.0220211	0.0110105	+	0.999939i	$0.496495\pi$
$614$	47.4550	1.91513
$615$	−9.90221	−0.399296
$616$	57.9594	2.33525
$617$	−6.34700	−0.255521	−0.127760	−	0.991805i	$-0.540779\pi$
$617$	−6.34700	−0.255521	−0.127760	+	0.991805i	$0.540779\pi$
$618$	6.84110	0.275189
$619$	22.7888	0.915959	0.457979	−	0.888963i	$-0.348573\pi$
$619$	22.7888	0.915959	0.457979	+	0.888963i	$0.348573\pi$
$620$	−49.6406	−1.99361
$621$	−2.92990	−0.117573
$622$	42.8292	1.71729
$623$	−28.0272	−1.12289
$624$	3.35110	0.134151
$625$	−11.1377	−0.445510
$626$	14.1165	0.564208
$627$	−0.655321	−0.0261710
$628$	−106.818	−4.26250
$629$	50.2250	2.00260
$630$	−47.6276	−1.89753
$631$	12.3202	0.490459	0.245229	−	0.969465i	$-0.421137\pi$
$631$	12.3202	0.490459	0.245229	+	0.969465i	$0.421137\pi$
$632$	−49.8292	−1.98210
$633$	2.46816	0.0981004
$634$	25.2225	1.00171
$635$	19.5288	0.774976
$636$	−3.40779	−0.135128
$637$	3.16718	0.125488
$638$	10.9291	0.432686
$639$	−9.15412	−0.362131
$640$	51.3303	2.02901
$641$	−18.8388	−0.744087	−0.372043	−	0.928215i	$-0.621343\pi$
$641$	−18.8388	−0.744087	−0.372043	+	0.928215i	$0.621343\pi$
$642$	−17.3616	−0.685208
$643$	−23.3878	−0.922326	−0.461163	−	0.887316i	$-0.652568\pi$
$643$	−23.3878	−0.922326	−0.461163	+	0.887316i	$0.652568\pi$
$644$	20.6549	0.813919
$645$	−8.23298	−0.324173
$646$	16.1828	0.636704
$647$	−39.4422	−1.55063	−0.775316	−	0.631574i	$-0.782409\pi$
$647$	−39.4422	−1.55063	−0.775316	+	0.631574i	$0.782409\pi$
$648$	−63.4139	−2.49113
$649$	18.1330	0.711783
$650$	2.68676	0.105383
$651$	9.38040	0.367647
$652$	−96.1706	−3.76633
$653$	−28.3472	−1.10931	−0.554656	−	0.832080i	$-0.687150\pi$
$653$	−28.3472	−1.10931	−0.554656	+	0.832080i	$0.687150\pi$
$654$	14.5096	0.567371
$655$	26.3509	1.02961
$656$	165.502	6.46177
$657$	−9.30646	−0.363080
$658$	−64.5584	−2.51675
$659$	8.92020	0.347482	0.173741	−	0.984791i	$-0.444414\pi$
$659$	8.92020	0.347482	0.173741	+	0.984791i	$0.444414\pi$
$660$	7.79962	0.303600
$661$	21.3303	0.829652	0.414826	−	0.909901i	$-0.363842\pi$
$661$	21.3303	0.829652	0.414826	+	0.909901i	$0.363842\pi$
$662$	−45.5443	−1.77013
$663$	−1.83408	−0.0712298
$664$	−87.9498	−3.41311
$665$	−4.95510	−0.192150
$666$	−49.3633	−1.91279
$667$	2.43990	0.0944735
$668$	−61.3602	−2.37410
$669$	−5.46710	−0.211370
$670$	14.6150	0.564625
$671$	−14.3245	−0.552991
$672$	−34.5408	−1.33244
$673$	−41.7553	−1.60955	−0.804774	−	0.593581i	$-0.797714\pi$
$673$	−41.7553	−1.60955	−0.804774	+	0.593581i	$0.797714\pi$
$674$	−60.9256	−2.34677
$675$	5.50621	0.211934
$676$	−68.2689	−2.62573
$677$	−19.0221	−0.731080	−0.365540	−	0.930796i	$-0.619116\pi$
$677$	−19.0221	−0.731080	−0.365540	+	0.930796i	$0.619116\pi$
$678$	−9.57225	−0.367620
$679$	−64.1042	−2.46009
$680$	−120.660	−4.62708
$681$	−4.10420	−0.157273
$682$	25.2570	0.967142
$683$	−33.5941	−1.28544	−0.642721	−	0.766101i	$-0.722194\pi$
$683$	−33.5941	−1.28544	−0.642721	+	0.766101i	$0.722194\pi$
$684$	−11.5796	−0.442759
$685$	20.3526	0.777633
$686$	6.49369	0.247930
$687$	12.5830	0.480071
$688$	137.603	5.24607
$689$	−0.660659	−0.0251691
$690$	2.39169	0.0910503
$691$	13.1181	0.499036	0.249518	−	0.968370i	$-0.419728\pi$
$691$	13.1181	0.499036	0.249518	+	0.968370i	$0.419728\pi$
$692$	124.700	4.74037
$693$	17.6425	0.670185
$694$	85.2047	3.23433
$695$	30.1133	1.14226
$696$	−10.1067	−0.383094
$697$	−90.5805	−3.43098
$698$	−52.8526	−2.00050
$699$	12.1724	0.460401
$700$	−38.8172	−1.46715
$701$	2.80894	0.106092	0.0530460	−	0.998592i	$-0.483107\pi$
$701$	2.80894	0.106092	0.0530460	+	0.998592i	$0.483107\pi$
$702$	3.75582	0.141754
$703$	−5.13567	−0.193696
$704$	−44.3068	−1.66988
$705$	−5.44241	−0.204973
$706$	−86.4069	−3.25197
$707$	51.8114	1.94857
$708$	−26.7675	−1.00598
$709$	−19.9460	−0.749087	−0.374544	−	0.927209i	$-0.622201\pi$
$709$	−19.9460	−0.749087	−0.374544	+	0.927209i	$0.622201\pi$
$710$	15.5694	0.584310
$711$	−15.1678	−0.568835
$712$	69.7859	2.61534
$713$	5.63861	0.211167
$714$	36.3963	1.36210
$715$	1.51209	0.0565490
$716$	27.1034	1.01290
$717$	−6.38729	−0.238538
$718$	−81.4341	−3.03909
$719$	−47.7161	−1.77951	−0.889754	−	0.456440i	$-0.849124\pi$
$719$	−47.7161	−1.77951	−0.889754	+	0.456440i	$0.849124\pi$
$720$	67.1071	2.50093
$721$	−19.1614	−0.713606
$722$	49.8702	1.85598
$723$	−6.21628	−0.231186
$724$	−11.6764	−0.433951
$725$	−4.58536	−0.170296
$726$	10.3780	0.385163
$727$	−8.96375	−0.332447	−0.166224	−	0.986088i	$-0.553157\pi$
$727$	−8.96375	−0.332447	−0.166224	+	0.986088i	$0.553157\pi$
$728$	−16.5869	−0.614752
$729$	−15.3000	−0.566667
$730$	15.8285	0.585840
$731$	−75.3112	−2.78548
$732$	21.1455	0.781558
$733$	−19.8936	−0.734787	−0.367393	−	0.930066i	$-0.619750\pi$
$733$	−19.8936	−0.734787	−0.367393	+	0.930066i	$0.619750\pi$
$734$	20.5812	0.759668
$735$	−5.29847	−0.195437
$736$	−20.7627	−0.765322
$737$	−5.41377	−0.199419
$738$	89.0264	3.27711
$739$	14.0851	0.518130	0.259065	−	0.965860i	$-0.416586\pi$
$739$	14.0851	0.518130	0.259065	+	0.965860i	$0.416586\pi$
$740$	61.1246	2.24699
$741$	0.187541	0.00688949
$742$	13.1104	0.481299
$743$	−14.8058	−0.543173	−0.271586	−	0.962414i	$-0.587548\pi$
$743$	−14.8058	−0.543173	−0.271586	+	0.962414i	$0.587548\pi$
$744$	−23.3566	−0.856293
$745$	28.1681	1.03200
$746$	91.1335	3.33663
$747$	−26.7715	−0.979517
$748$	71.3469	2.60870
$749$	48.6285	1.77685
$750$	−15.8185	−0.577608
$751$	−31.2341	−1.13975	−0.569874	−	0.821732i	$-0.693008\pi$
$751$	−31.2341	−1.13975	−0.569874	+	0.821732i	$0.693008\pi$
$752$	90.9625	3.31706
$753$	−5.16277	−0.188142
$754$	−3.12770	−0.113904
$755$	−33.4382	−1.21694
$756$	−54.2626	−1.97351
$757$	−24.9839	−0.908055	−0.454028	−	0.890988i	$-0.650013\pi$
$757$	−24.9839	−0.908055	−0.454028	+	0.890988i	$0.650013\pi$
$758$	58.0100	2.10702
$759$	−0.885948	−0.0321579
$760$	12.3379	0.447541
$761$	12.8913	0.467310	0.233655	−	0.972320i	$-0.424931\pi$
$761$	12.8913	0.467310	0.233655	+	0.972320i	$0.424931\pi$
$762$	14.6676	0.531350
$763$	−40.6402	−1.47127
$764$	−20.0478	−0.725302
$765$	−36.7282	−1.32791
$766$	35.7864	1.29301
$767$	−5.18933	−0.187376
$768$	14.1213	0.509557
$769$	−16.5033	−0.595124	−0.297562	−	0.954703i	$-0.596173\pi$
$769$	−16.5033	−0.595124	−0.297562	+	0.954703i	$0.596173\pi$
$770$	−30.0066	−1.08136
$771$	6.71666	0.241895
$772$	−100.817	−3.62848
$773$	−28.7091	−1.03259	−0.516297	−	0.856409i	$-0.672690\pi$
$773$	−28.7091	−1.03259	−0.516297	+	0.856409i	$0.672690\pi$
$774$	74.0191	2.66056
$775$	−10.5967	−0.380646
$776$	159.615	5.72984
$777$	−11.5505	−0.414372
$778$	6.21383	0.222777
$779$	9.26216	0.331851
$780$	−2.23211	−0.0799223
$781$	−5.76733	−0.206371
$782$	21.8780	0.782356
$783$	−6.40987	−0.229070
$784$	88.5568	3.16274
$785$	34.6439	1.23649
$786$	19.7915	0.705939
$787$	2.32309	0.0828093	0.0414046	−	0.999142i	$-0.486817\pi$
$787$	2.32309	0.0828093	0.0414046	+	0.999142i	$0.486817\pi$
$788$	−122.727	−4.37195
$789$	−7.43401	−0.264658
$790$	25.7975	0.917833
$791$	26.8111	0.953293
$792$	−43.9287	−1.56094
$793$	4.09941	0.145574
$794$	−54.5132	−1.93460
$795$	1.10524	0.0391987
$796$	−85.2475	−3.02152
$797$	6.03933	0.213924	0.106962	−	0.994263i	$-0.465888\pi$
$797$	6.03933	0.213924	0.106962	+	0.994263i	$0.465888\pi$
$798$	−3.72165	−0.131745
$799$	−49.7844	−1.76125
$800$	39.0197	1.37955
$801$	21.2425	0.750566
$802$	10.9518	0.386723
$803$	−5.86331	−0.206912
$804$	7.99167	0.281844
$805$	−6.69894	−0.236107
$806$	−7.22810	−0.254599
$807$	−9.85106	−0.346774
$808$	−129.007	−4.53844
$809$	38.9890	1.37078	0.685389	−	0.728177i	$-0.259632\pi$
$809$	38.9890	1.37078	0.685389	+	0.728177i	$0.259632\pi$
$810$	32.8305	1.15355
$811$	−30.6528	−1.07636	−0.538182	−	0.842829i	$-0.680889\pi$
$811$	−30.6528	−1.07636	−0.538182	+	0.842829i	$0.680889\pi$
$812$	45.1878	1.58578
$813$	−0.0760293	−0.00266646
$814$	−31.1001	−1.09006
$815$	31.1907	1.09256
$816$	−51.2823	−1.79524
$817$	7.70082	0.269418
$818$	16.7390	0.585266
$819$	−5.04897	−0.176425
$820$	−110.238	−3.84968
$821$	−21.1418	−0.737853	−0.368927	−	0.929458i	$-0.620275\pi$
$821$	−21.1418	−0.737853	−0.368927	+	0.929458i	$0.620275\pi$
$822$	15.2863	0.533172
$823$	36.8356	1.28401	0.642005	−	0.766701i	$-0.278103\pi$
$823$	36.8356	1.28401	0.642005	+	0.766701i	$0.278103\pi$
$824$	47.7105	1.66207
$825$	1.66498	0.0579671
$826$	102.980	3.58312
$827$	−51.9127	−1.80518	−0.902590	−	0.430501i	$-0.858337\pi$
$827$	−51.9127	−1.80518	−0.902590	+	0.430501i	$0.858337\pi$
$828$	−15.6549	−0.544044
$829$	16.1154	0.559712	0.279856	−	0.960042i	$-0.409713\pi$
$829$	16.1154	0.559712	0.279856	+	0.960042i	$0.409713\pi$
$830$	45.5332	1.58048
$831$	−3.34548	−0.116053
$832$	12.6798	0.439593
$833$	−48.4678	−1.67931
$834$	22.6174	0.783176
$835$	19.9007	0.688693
$836$	−7.29547	−0.252319
$837$	−14.8132	−0.512019
$838$	24.7006	0.853269
$839$	15.4906	0.534795	0.267398	−	0.963586i	$-0.413836\pi$
$839$	15.4906	0.534795	0.267398	+	0.963586i	$0.413836\pi$
$840$	27.7487	0.957422
$841$	−23.6621	−0.815935
$842$	−37.5005	−1.29235
$843$	−1.15686	−0.0398445
$844$	27.4771	0.945802
$845$	22.1414	0.761687
$846$	48.9303	1.68226
$847$	−29.0679	−0.998784
$848$	−18.4725	−0.634350
$849$	8.95006	0.307165
$850$	−41.1158	−1.41026
$851$	−6.94307	−0.238005
$852$	8.51358	0.291670
$853$	35.7052	1.22252	0.611261	−	0.791429i	$-0.290663\pi$
$853$	35.7052	1.22252	0.611261	+	0.791429i	$0.290663\pi$
$854$	−81.3506	−2.78376
$855$	3.75558	0.128438
$856$	−121.082	−4.13848
$857$	−37.1761	−1.26991	−0.634955	−	0.772549i	$-0.718981\pi$
$857$	−37.1761	−1.26991	−0.634955	+	0.772549i	$0.718981\pi$
$858$	1.13569	0.0387719
$859$	−2.04499	−0.0697742	−0.0348871	−	0.999391i	$-0.511107\pi$
$859$	−2.04499	−0.0697742	−0.0348871	+	0.999391i	$0.511107\pi$
$860$	−91.6550	−3.12541
$861$	20.8313	0.709928
$862$	15.4805	0.527267
$863$	−10.0764	−0.343005	−0.171502	−	0.985184i	$-0.554862\pi$
$863$	−10.0764	−0.343005	−0.171502	+	0.985184i	$0.554862\pi$
$864$	54.5456	1.85568
$865$	−40.4434	−1.37512
$866$	−13.1404	−0.446529
$867$	19.8913	0.675542
$868$	104.429	3.54455
$869$	−9.55607	−0.324168
$870$	5.23243	0.177396
$871$	1.54932	0.0524968
$872$	101.191	3.42677
$873$	48.5860	1.64439
$874$	−2.23710	−0.0756711
$875$	44.3062	1.49782
$876$	8.65526	0.292434
$877$	−21.4964	−0.725882	−0.362941	−	0.931812i	$-0.618227\pi$
$877$	−21.4964	−0.725882	−0.362941	+	0.931812i	$0.618227\pi$
$878$	25.3441	0.855321
$879$	−9.39281	−0.316811
$880$	42.2792	1.42523
$881$	−4.82670	−0.162616	−0.0813078	−	0.996689i	$-0.525910\pi$
$881$	−4.82670	−0.162616	−0.0813078	+	0.996689i	$0.525910\pi$
$882$	47.6362	1.60400
$883$	−1.50222	−0.0505536	−0.0252768	−	0.999680i	$-0.508047\pi$
$883$	−1.50222	−0.0505536	−0.0252768	+	0.999680i	$0.508047\pi$
$884$	−20.4182	−0.686738
$885$	8.68139	0.291822
$886$	−1.22370	−0.0411110
$887$	49.9571	1.67740	0.838698	−	0.544597i	$-0.183317\pi$
$887$	49.9571	1.67740	0.838698	+	0.544597i	$0.183317\pi$
$888$	28.7600	0.965121
$889$	−41.0827	−1.37787
$890$	−36.1294	−1.21106
$891$	−12.1613	−0.407419
$892$	−60.8634	−2.03786
$893$	5.09062	0.170351
$894$	21.1564	0.707574
$895$	−8.79036	−0.293829
$896$	−107.984	−3.60748
$897$	0.253542	0.00846552
$898$	−90.5709	−3.02239
$899$	12.3359	0.411424
$900$	29.4205	0.980682
$901$	10.1101	0.336818
$902$	56.0889	1.86756
$903$	17.3197	0.576364
$904$	−66.7578	−2.22033
$905$	3.78697	0.125883
$906$	−25.1146	−0.834377
$907$	−10.8686	−0.360885	−0.180443	−	0.983586i	$-0.557753\pi$
$907$	−10.8686	−0.360885	−0.180443	+	0.983586i	$0.557753\pi$
$908$	−45.6906	−1.51630
$909$	−39.2690	−1.30247
$910$	8.58734	0.284668
$911$	24.8937	0.824766	0.412383	−	0.911011i	$-0.364697\pi$
$911$	24.8937	0.824766	0.412383	+	0.911011i	$0.364697\pi$
$912$	5.24379	0.173639
$913$	−16.8667	−0.558207
$914$	−63.5488	−2.10201
$915$	−6.85803	−0.226719
$916$	140.082	4.62845
$917$	−55.4343	−1.83060
$918$	−57.4758	−1.89698
$919$	−7.48714	−0.246978	−0.123489	−	0.992346i	$-0.539408\pi$
$919$	−7.48714	−0.246978	−0.123489	+	0.992346i	$0.539408\pi$
$920$	16.6799	0.549920
$921$	−8.41597	−0.277316
$922$	−95.8652	−3.15715
$923$	1.65050	0.0543270
$924$	−16.4080	−0.539785
$925$	13.0482	0.429023
$926$	−42.7865	−1.40605
$927$	14.5228	0.476992
$928$	−45.4235	−1.49110
$929$	40.6414	1.33340	0.666701	−	0.745326i	$-0.267706\pi$
$929$	40.6414	1.33340	0.666701	+	0.745326i	$0.267706\pi$
$930$	12.0921	0.396516
$931$	4.95599	0.162426
$932$	135.511	4.43881
$933$	−7.59559	−0.248669
$934$	−48.1136	−1.57433
$935$	−23.1397	−0.756749
$936$	12.5716	0.410916
$937$	−37.6202	−1.22900	−0.614500	−	0.788917i	$-0.710642\pi$
$937$	−37.6202	−1.22900	−0.614500	+	0.788917i	$0.710642\pi$
$938$	−30.7455	−1.00388
$939$	−2.50350	−0.0816988
$940$	−60.5885	−1.97618
$941$	6.27134	0.204440	0.102220	−	0.994762i	$-0.467405\pi$
$941$	6.27134	0.204440	0.102220	+	0.994762i	$0.467405\pi$
$942$	26.0201	0.847781
$943$	12.5218	0.407765
$944$	−145.098	−4.72253
$945$	17.5988	0.572489
$946$	46.6339	1.51620
$947$	−21.2182	−0.689500	−0.344750	−	0.938695i	$-0.612036\pi$
$947$	−21.2182	−0.689500	−0.344750	+	0.938695i	$0.612036\pi$
$948$	14.1064	0.458155
$949$	1.67797	0.0544692
$950$	4.20423	0.136403
$951$	−4.47312	−0.145051
$952$	253.831	8.22673
$953$	7.54963	0.244557	0.122278	−	0.992496i	$-0.460980\pi$
$953$	7.54963	0.244557	0.122278	+	0.992496i	$0.460980\pi$
$954$	−9.93670	−0.321712
$955$	6.50201	0.210400
$956$	−71.1076	−2.29978
$957$	−1.93823	−0.0626541
$958$	90.1250	2.91181
$959$	−42.8158	−1.38259
$960$	−21.2124	−0.684628
$961$	−2.49191	−0.0803840
$962$	8.90028	0.286957
$963$	−36.8566	−1.18769
$964$	−69.2038	−2.22890
$965$	32.6976	1.05257
$966$	−5.03141	−0.161883
$967$	−14.3232	−0.460602	−0.230301	−	0.973119i	$-0.573971\pi$
$967$	−14.3232	−0.460602	−0.230301	+	0.973119i	$0.573971\pi$
$968$	72.3770	2.32629
$969$	−2.86996	−0.0921964
$970$	−82.6356	−2.65327
$971$	50.9076	1.63370	0.816851	−	0.576849i	$-0.195718\pi$
$971$	50.9076	1.63370	0.816851	+	0.576849i	$0.195718\pi$
$972$	62.5148	2.00516
$973$	−63.3494	−2.03089
$974$	20.2870	0.650038
$975$	−0.476486	−0.0152598
$976$	114.623	3.66898
$977$	−17.6129	−0.563488	−0.281744	−	0.959490i	$-0.590913\pi$
$977$	−17.6129	−0.563488	−0.281744	+	0.959490i	$0.590913\pi$
$978$	23.4265	0.749097
$979$	13.3833	0.427732
$980$	−58.9861	−1.88424
$981$	30.8022	0.983437
$982$	−102.817	−3.28103
$983$	−11.6300	−0.370938	−0.185469	−	0.982650i	$-0.559380\pi$
$983$	−11.6300	−0.370938	−0.185469	+	0.982650i	$0.559380\pi$
$984$	−51.8684	−1.65351
$985$	39.8035	1.26824
$986$	47.8636	1.52429
$987$	11.4492	0.364432
$988$	2.08783	0.0664227
$989$	10.4110	0.331049
$990$	22.7427	0.722811
$991$	−10.3343	−0.328281	−0.164140	−	0.986437i	$-0.552485\pi$
$991$	−10.3343	−0.328281	−0.164140	+	0.986437i	$0.552485\pi$
$992$	−104.973	−3.33291
$993$	8.07711	0.256319
$994$	−32.7534	−1.03887
$995$	27.6480	0.876501
$996$	24.8982	0.788930
$997$	42.5294	1.34692	0.673459	−	0.739224i	$-0.264808\pi$
$997$	42.5294	1.34692	0.673459	+	0.739224i	$0.264808\pi$
$998$	22.6296	0.716329
$999$	18.2401	0.577092

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6007.2.a.b.1.9	✓	237

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6007.2.a.b.1.9	✓	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)

\(f(q)\)	\(=\)	\(q-2.71184 q^{2} +0.480935 q^{3} +5.35409 q^{4} -1.73647 q^{5} -1.30422 q^{6} +3.65301 q^{7} -9.09575 q^{8} -2.76870 q^{9} +O(q^{10})\)	\(q-2.71184 q^{2} +0.480935 q^{3} +5.35409 q^{4} -1.73647 q^{5} -1.30422 q^{6} +3.65301 q^{7} -9.09575 q^{8} -2.76870 q^{9} +4.70903 q^{10} -1.74435 q^{11} +2.57497 q^{12} +0.499202 q^{13} -9.90639 q^{14} -0.835129 q^{15} +13.9581 q^{16} -7.63934 q^{17} +7.50828 q^{18} +0.781149 q^{19} -9.29721 q^{20} +1.75686 q^{21} +4.73041 q^{22} +1.05606 q^{23} -4.37446 q^{24} -1.98467 q^{25} -1.35376 q^{26} -2.77437 q^{27} +19.5585 q^{28} +2.31039 q^{29} +2.26474 q^{30} +5.33930 q^{31} -19.6605 q^{32} -0.838920 q^{33} +20.7167 q^{34} -6.34335 q^{35} -14.8239 q^{36} -6.57451 q^{37} -2.11835 q^{38} +0.240083 q^{39} +15.7945 q^{40} +11.8571 q^{41} -4.76433 q^{42} +9.85833 q^{43} -9.33941 q^{44} +4.80777 q^{45} -2.86386 q^{46} +6.51684 q^{47} +6.71292 q^{48} +6.34450 q^{49} +5.38211 q^{50} -3.67403 q^{51} +2.67277 q^{52} -1.32343 q^{53} +7.52365 q^{54} +3.02902 q^{55} -33.2269 q^{56} +0.375682 q^{57} -6.26541 q^{58} -10.3953 q^{59} -4.47135 q^{60} +8.21193 q^{61} -14.4793 q^{62} -10.1141 q^{63} +25.4002 q^{64} -0.866849 q^{65} +2.27502 q^{66} +3.10360 q^{67} -40.9017 q^{68} +0.507895 q^{69} +17.2022 q^{70} +3.30629 q^{71} +25.1834 q^{72} +3.36131 q^{73} +17.8290 q^{74} -0.954497 q^{75} +4.18234 q^{76} -6.37214 q^{77} -0.651068 q^{78} +5.47829 q^{79} -24.2378 q^{80} +6.97181 q^{81} -32.1546 q^{82} +9.66933 q^{83} +9.40638 q^{84} +13.2655 q^{85} -26.7342 q^{86} +1.11115 q^{87} +15.8662 q^{88} -7.67236 q^{89} -13.0379 q^{90} +1.82359 q^{91} +5.65422 q^{92} +2.56785 q^{93} -17.6726 q^{94} -1.35644 q^{95} -9.45544 q^{96} -17.5483 q^{97} -17.2053 q^{98} +4.82959 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 237 q - 26 q^{2} - 24 q^{3} + 226 q^{4} - 67 q^{5} - 30 q^{6} - 37 q^{7} - 75 q^{8} + 189 q^{9}+O(q^{10}) \) 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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