LMFDB - Embedded newform 6023.2.a.c.1.101

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6023,2,Mod(1,6023)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6023, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6023.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6023 = 19 \cdot 317 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6023.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.0938971374$
Analytic rank:	$0$
Dimension:	$138$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.101
Character	$\chi$	$=$	6023.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.61656 q^{2} -2.64019 q^{3} +0.613280 q^{4} -1.92836 q^{5} -4.26804 q^{6} +2.89651 q^{7} -2.24172 q^{8} +3.97063 q^{9} +O(q^{10})$	\(q+1.61656 q^{2} -2.64019 q^{3} +0.613280 q^{4} -1.92836 q^{5} -4.26804 q^{6} +2.89651 q^{7} -2.24172 q^{8} +3.97063 q^{9} -3.11732 q^{10} -4.55345 q^{11} -1.61918 q^{12} +6.09910 q^{13} +4.68239 q^{14} +5.09125 q^{15} -4.85045 q^{16} +6.78606 q^{17} +6.41877 q^{18} +1.00000 q^{19} -1.18263 q^{20} -7.64734 q^{21} -7.36095 q^{22} -4.93547 q^{23} +5.91858 q^{24} -1.28143 q^{25} +9.85958 q^{26} -2.56264 q^{27} +1.77637 q^{28} -8.05329 q^{29} +8.23033 q^{30} -6.40433 q^{31} -3.35762 q^{32} +12.0220 q^{33} +10.9701 q^{34} -5.58551 q^{35} +2.43511 q^{36} +4.58345 q^{37} +1.61656 q^{38} -16.1028 q^{39} +4.32285 q^{40} +6.03021 q^{41} -12.3624 q^{42} +0.806627 q^{43} -2.79254 q^{44} -7.65680 q^{45} -7.97850 q^{46} -3.58284 q^{47} +12.8061 q^{48} +1.38975 q^{49} -2.07151 q^{50} -17.9165 q^{51} +3.74045 q^{52} -2.26612 q^{53} -4.14267 q^{54} +8.78070 q^{55} -6.49316 q^{56} -2.64019 q^{57} -13.0187 q^{58} -1.61892 q^{59} +3.12236 q^{60} +3.47826 q^{61} -10.3530 q^{62} +11.5009 q^{63} +4.27309 q^{64} -11.7613 q^{65} +19.4343 q^{66} -12.4922 q^{67} +4.16176 q^{68} +13.0306 q^{69} -9.02934 q^{70} -7.42148 q^{71} -8.90104 q^{72} +10.3933 q^{73} +7.40944 q^{74} +3.38321 q^{75} +0.613280 q^{76} -13.1891 q^{77} -26.0312 q^{78} +9.77344 q^{79} +9.35341 q^{80} -5.14601 q^{81} +9.74822 q^{82} -16.6010 q^{83} -4.68996 q^{84} -13.0860 q^{85} +1.30396 q^{86} +21.2622 q^{87} +10.2076 q^{88} +4.76681 q^{89} -12.3777 q^{90} +17.6661 q^{91} -3.02682 q^{92} +16.9087 q^{93} -5.79189 q^{94} -1.92836 q^{95} +8.86476 q^{96} +7.10148 q^{97} +2.24662 q^{98} -18.0801 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 138 q + 11 q^{2} + 29 q^{3} + 157 q^{4} + 12 q^{5} + 8 q^{6} + 18 q^{7} + 33 q^{8} + 171 q^{9}+O(q^{10}) $ 138 * q + 11 * q^2 + 29 * q^3 + 157 * q^4 + 12 * q^5 + 8 * q^6 + 18 * q^7 + 33 * q^8 + 171 * q^9	\( 138 q + 11 q^{2} + 29 q^{3} + 157 q^{4} + 12 q^{5} + 8 q^{6} + 18 q^{7} + 33 q^{8} + 171 q^{9} + 40 q^{10} + 4 q^{11} + 69 q^{12} + 72 q^{13} + 3 q^{14} + 30 q^{15} + 191 q^{16} + 31 q^{17} + 31 q^{18} + 138 q^{19} + 16 q^{20} + 16 q^{21} + 95 q^{22} + 34 q^{23} + 3 q^{24} + 244 q^{25} - 13 q^{26} + 107 q^{27} + 43 q^{28} + 30 q^{29} - 14 q^{30} + 60 q^{31} + 62 q^{32} + 77 q^{33} + 36 q^{34} + 2 q^{35} + 205 q^{36} + 142 q^{37} + 11 q^{38} + 20 q^{39} + 76 q^{40} + 46 q^{41} - 21 q^{42} + 69 q^{43} - 7 q^{44} + 30 q^{45} + 39 q^{46} + 8 q^{47} + 116 q^{48} + 236 q^{49} + 34 q^{51} + 165 q^{52} + 49 q^{53} + 6 q^{55} - 33 q^{56} + 29 q^{57} + 75 q^{58} + 8 q^{59} - 24 q^{60} + 38 q^{61} - 10 q^{62} + 2 q^{63} + 251 q^{64} + 72 q^{65} - 15 q^{66} + 158 q^{67} - 19 q^{68} + 33 q^{69} + 48 q^{70} + 23 q^{71} + 88 q^{72} + 134 q^{73} + 4 q^{74} + 118 q^{75} + 157 q^{76} + 13 q^{77} + 12 q^{78} + 78 q^{79} - 48 q^{80} + 254 q^{81} + 89 q^{82} - 27 q^{83} - 15 q^{84} + 37 q^{85} + 66 q^{86} + 43 q^{87} + 224 q^{88} + 26 q^{89} + 38 q^{90} + 108 q^{91} + 113 q^{92} + 83 q^{93} + 48 q^{94} + 12 q^{95} + 40 q^{96} + 254 q^{97} + 47 q^{98} + 11 q^{99}+O(q^{100}) \) 138 * q + 11 * q^2 + 29 * q^3 + 157 * q^4 + 12 * q^5 + 8 * q^6 + 18 * q^7 + 33 * q^8 + 171 * q^9 + 40 * q^10 + 4 * q^11 + 69 * q^12 + 72 * q^13 + 3 * q^14 + 30 * q^15 + 191 * q^16 + 31 * q^17 + 31 * q^18 + 138 * q^19 + 16 * q^20 + 16 * q^21 + 95 * q^22 + 34 * q^23 + 3 * q^24 + 244 * q^25 - 13 * q^26 + 107 * q^27 + 43 * q^28 + 30 * q^29 - 14 * q^30 + 60 * q^31 + 62 * q^32 + 77 * q^33 + 36 * q^34 + 2 * q^35 + 205 * q^36 + 142 * q^37 + 11 * q^38 + 20 * q^39 + 76 * q^40 + 46 * q^41 - 21 * q^42 + 69 * q^43 - 7 * q^44 + 30 * q^45 + 39 * q^46 + 8 * q^47 + 116 * q^48 + 236 * q^49 + 34 * q^51 + 165 * q^52 + 49 * q^53 + 6 * q^55 - 33 * q^56 + 29 * q^57 + 75 * q^58 + 8 * q^59 - 24 * q^60 + 38 * q^61 - 10 * q^62 + 2 * q^63 + 251 * q^64 + 72 * q^65 - 15 * q^66 + 158 * q^67 - 19 * q^68 + 33 * q^69 + 48 * q^70 + 23 * q^71 + 88 * q^72 + 134 * q^73 + 4 * q^74 + 118 * q^75 + 157 * q^76 + 13 * q^77 + 12 * q^78 + 78 * q^79 - 48 * q^80 + 254 * q^81 + 89 * q^82 - 27 * q^83 - 15 * q^84 + 37 * q^85 + 66 * q^86 + 43 * q^87 + 224 * q^88 + 26 * q^89 + 38 * q^90 + 108 * q^91 + 113 * q^92 + 83 * q^93 + 48 * q^94 + 12 * q^95 + 40 * q^96 + 254 * q^97 + 47 * q^98 + 11 * 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 $

$2$	1.61656	1.14308	0.571542	−	0.820573i	$-0.306346\pi$
$2$	1.61656	1.14308	0.571542	+	0.820573i	$0.306346\pi$
$3$	−2.64019	−1.52432	−0.762158	−	0.647391i	$-0.775860\pi$
$3$	−2.64019	−1.52432	−0.762158	+	0.647391i	$0.775860\pi$
$4$	0.613280	0.306640
$5$	−1.92836	−0.862389	−0.431195	−	0.902259i	$-0.641908\pi$
$5$	−1.92836	−0.862389	−0.431195	+	0.902259i	$0.641908\pi$
$6$	−4.26804	−1.74242
$7$	2.89651	1.09478	0.547388	−	0.836879i	$-0.315622\pi$
$7$	2.89651	1.09478	0.547388	+	0.836879i	$0.315622\pi$
$8$	−2.24172	−0.792568
$9$	3.97063	1.32354
$10$	−3.11732	−0.985783
$11$	−4.55345	−1.37292	−0.686459	−	0.727169i	$-0.740836\pi$
$11$	−4.55345	−1.37292	−0.686459	+	0.727169i	$0.740836\pi$
$12$	−1.61918	−0.467417
$13$	6.09910	1.69158	0.845792	−	0.533512i	$-0.179128\pi$
$13$	6.09910	1.69158	0.845792	+	0.533512i	$0.179128\pi$
$14$	4.68239	1.25142
$15$	5.09125	1.31455
$16$	−4.85045	−1.21261
$17$	6.78606	1.64586	0.822931	−	0.568142i	$-0.192338\pi$
$17$	6.78606	1.64586	0.822931	+	0.568142i	$0.192338\pi$
$18$	6.41877	1.51292
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−1.18263	−0.264443
$21$	−7.64734	−1.66879
$22$	−7.36095	−1.56936
$23$	−4.93547	−1.02912	−0.514558	−	0.857456i	$-0.672044\pi$
$23$	−4.93547	−1.02912	−0.514558	+	0.857456i	$0.672044\pi$
$24$	5.91858	1.20813
$25$	−1.28143	−0.256285
$26$	9.85958	1.93362
$27$	−2.56264	−0.493181
$28$	1.77637	0.335702
$29$	−8.05329	−1.49546	−0.747729	−	0.664004i	$-0.768856\pi$
$29$	−8.05329	−1.49546	−0.747729	+	0.664004i	$0.768856\pi$
$30$	8.23033	1.50265
$31$	−6.40433	−1.15025	−0.575126	−	0.818065i	$-0.695047\pi$
$31$	−6.40433	−1.15025	−0.575126	+	0.818065i	$0.695047\pi$
$32$	−3.35762	−0.593548
$33$	12.0220	2.09276
$34$	10.9701	1.88136
$35$	−5.58551	−0.944123
$36$	2.43511	0.405851
$37$	4.58345	0.753514	0.376757	−	0.926312i	$-0.377039\pi$
$37$	4.58345	0.753514	0.376757	+	0.926312i	$0.377039\pi$
$38$	1.61656	0.262241
$39$	−16.1028	−2.57851
$40$	4.32285	0.683502
$41$	6.03021	0.941761	0.470880	−	0.882197i	$-0.343936\pi$
$41$	6.03021	0.941761	0.470880	+	0.882197i	$0.343936\pi$
$42$	−12.3624	−1.90756
$43$	0.806627	0.123009	0.0615047	−	0.998107i	$-0.480410\pi$
$43$	0.806627	0.123009	0.0615047	+	0.998107i	$0.480410\pi$
$44$	−2.79254	−0.420992
$45$	−7.65680	−1.14141
$46$	−7.97850	−1.17637
$47$	−3.58284	−0.522611	−0.261305	−	0.965256i	$-0.584153\pi$
$47$	−3.58284	−0.522611	−0.261305	+	0.965256i	$0.584153\pi$
$48$	12.8061	1.84840
$49$	1.38975	0.198536
$50$	−2.07151	−0.292955
$51$	−17.9165	−2.50881
$52$	3.74045	0.518708
$53$	−2.26612	−0.311276	−0.155638	−	0.987814i	$-0.549743\pi$
$53$	−2.26612	−0.311276	−0.155638	+	0.987814i	$0.549743\pi$
$54$	−4.14267	−0.563747
$55$	8.78070	1.18399
$56$	−6.49316	−0.867685
$57$	−2.64019	−0.349702
$58$	−13.0187	−1.70943
$59$	−1.61892	−0.210765	−0.105382	−	0.994432i	$-0.533607\pi$
$59$	−1.61892	−0.210765	−0.105382	+	0.994432i	$0.533607\pi$
$60$	3.12236	0.403095
$61$	3.47826	0.445345	0.222673	−	0.974893i	$-0.428522\pi$
$61$	3.47826	0.445345	0.222673	+	0.974893i	$0.428522\pi$
$62$	−10.3530	−1.31483
$63$	11.5009	1.44898
$64$	4.27309	0.534136
$65$	−11.7613	−1.45880
$66$	19.4343	2.39220
$67$	−12.4922	−1.52616	−0.763081	−	0.646303i	$-0.776314\pi$
$67$	−12.4922	−1.52616	−0.763081	+	0.646303i	$0.776314\pi$
$68$	4.16176	0.504687
$69$	13.0306	1.56870
$70$	−9.02934	−1.07921
$71$	−7.42148	−0.880767	−0.440384	−	0.897810i	$-0.645158\pi$
$71$	−7.42148	−0.880767	−0.440384	+	0.897810i	$0.645158\pi$
$72$	−8.90104	−1.04900
$73$	10.3933	1.21644	0.608222	−	0.793767i	$-0.291883\pi$
$73$	10.3933	1.21644	0.608222	+	0.793767i	$0.291883\pi$
$74$	7.40944	0.861329
$75$	3.38321	0.390660
$76$	0.613280	0.0703481
$77$	−13.1891	−1.50304
$78$	−26.0312	−2.94745
$79$	9.77344	1.09960	0.549799	−	0.835297i	$-0.314704\pi$
$79$	9.77344	1.09960	0.549799	+	0.835297i	$0.314704\pi$
$80$	9.35341	1.04574
$81$	−5.14601	−0.571779
$82$	9.74822	1.07651
$83$	−16.6010	−1.82220	−0.911098	−	0.412189i	$-0.864764\pi$
$83$	−16.6010	−1.82220	−0.911098	+	0.412189i	$0.864764\pi$
$84$	−4.68996	−0.511717
$85$	−13.0860	−1.41937
$86$	1.30396	0.140610
$87$	21.2622	2.27955
$88$	10.2076	1.08813
$89$	4.76681	0.505281	0.252641	−	0.967560i	$-0.418701\pi$
$89$	4.76681	0.505281	0.252641	+	0.967560i	$0.418701\pi$
$90$	−12.3777	−1.30472
$91$	17.6661	1.85191
$92$	−3.02682	−0.315568
$93$	16.9087	1.75335
$94$	−5.79189	−0.597388
$95$	−1.92836	−0.197846
$96$	8.86476	0.904756
$97$	7.10148	0.721046	0.360523	−	0.932750i	$-0.382598\pi$
$97$	7.10148	0.721046	0.360523	+	0.932750i	$0.382598\pi$
$98$	2.24662	0.226943
$99$	−18.0801	−1.81711
$100$	−0.785873	−0.0785873
$101$	17.7473	1.76592	0.882961	−	0.469446i	$-0.155546\pi$
$101$	17.7473	1.76592	0.882961	+	0.469446i	$0.155546\pi$
$102$	−28.9632	−2.86778
$103$	7.38292	0.727461	0.363730	−	0.931504i	$-0.381503\pi$
$103$	7.38292	0.727461	0.363730	+	0.931504i	$0.381503\pi$
$104$	−13.6725	−1.34070
$105$	14.7468	1.43914
$106$	−3.66334	−0.355815
$107$	−3.63569	−0.351475	−0.175737	−	0.984437i	$-0.556231\pi$
$107$	−3.63569	−0.351475	−0.175737	+	0.984437i	$0.556231\pi$
$108$	−1.57162	−0.151229
$109$	0.856725	0.0820594	0.0410297	−	0.999158i	$-0.486936\pi$
$109$	0.856725	0.0820594	0.0410297	+	0.999158i	$0.486936\pi$
$110$	14.1946	1.35340
$111$	−12.1012	−1.14859
$112$	−14.0494	−1.32754
$113$	−0.825569	−0.0776630	−0.0388315	−	0.999246i	$-0.512364\pi$
$113$	−0.825569	−0.0776630	−0.0388315	+	0.999246i	$0.512364\pi$
$114$	−4.26804	−0.399739
$115$	9.51736	0.887498
$116$	−4.93892	−0.458567
$117$	24.2172	2.23888
$118$	−2.61708	−0.240922
$119$	19.6559	1.80185
$120$	−11.4132	−1.04187
$121$	9.73394	0.884904
$122$	5.62283	0.509067
$123$	−15.9209	−1.43554
$124$	−3.92765	−0.352713
$125$	12.1129	1.08341
$126$	18.5920	1.65631
$127$	9.60616	0.852409	0.426204	−	0.904627i	$-0.359850\pi$
$127$	9.60616	0.852409	0.426204	+	0.904627i	$0.359850\pi$
$128$	13.6230	1.20411
$129$	−2.12965	−0.187505
$130$	−19.0128	−1.66754
$131$	13.0250	1.13800	0.568999	−	0.822338i	$-0.307331\pi$
$131$	13.0250	1.13800	0.568999	+	0.822338i	$0.307331\pi$
$132$	7.37286	0.641725
$133$	2.89651	0.251159
$134$	−20.1944	−1.74453
$135$	4.94170	0.425314
$136$	−15.2125	−1.30446
$137$	11.7547	1.00427	0.502134	−	0.864790i	$-0.332548\pi$
$137$	11.7547	1.00427	0.502134	+	0.864790i	$0.332548\pi$
$138$	21.0648	1.79315
$139$	10.1948	0.864716	0.432358	−	0.901702i	$-0.357682\pi$
$139$	10.1948	0.864716	0.432358	+	0.901702i	$0.357682\pi$
$140$	−3.42548	−0.289506
$141$	9.45939	0.796624
$142$	−11.9973	−1.00679
$143$	−27.7720	−2.32241
$144$	−19.2593	−1.60494
$145$	15.5296	1.28967
$146$	16.8015	1.39050
$147$	−3.66921	−0.302632
$148$	2.81094	0.231058
$149$	−2.18657	−0.179131	−0.0895654	−	0.995981i	$-0.528548\pi$
$149$	−2.18657	−0.179131	−0.0895654	+	0.995981i	$0.528548\pi$
$150$	5.46918	0.446557
$151$	−3.72578	−0.303199	−0.151600	−	0.988442i	$-0.548442\pi$
$151$	−3.72578	−0.303199	−0.151600	+	0.988442i	$0.548442\pi$
$152$	−2.24172	−0.181828
$153$	26.9449	2.17837
$154$	−21.3210	−1.71810
$155$	12.3499	0.991964
$156$	−9.87553	−0.790675
$157$	−19.3866	−1.54722	−0.773610	−	0.633662i	$-0.781551\pi$
$157$	−19.3866	−1.54722	−0.773610	+	0.633662i	$0.781551\pi$
$158$	15.7994	1.25693
$159$	5.98301	0.474483
$160$	6.47470	0.511870
$161$	−14.2956	−1.12665
$162$	−8.31885	−0.653591
$163$	13.5119	1.05833	0.529166	−	0.848518i	$-0.322505\pi$
$163$	13.5119	1.05833	0.529166	+	0.848518i	$0.322505\pi$
$164$	3.69821	0.288782
$165$	−23.1828	−1.80478
$166$	−26.8366	−2.08292
$167$	−8.59402	−0.665025	−0.332513	−	0.943099i	$-0.607896\pi$
$167$	−8.59402	−0.665025	−0.332513	+	0.943099i	$0.607896\pi$
$168$	17.1432	1.32263
$169$	24.1990	1.86146
$170$	−21.1543	−1.62246
$171$	3.97063	0.303641
$172$	0.494688	0.0377196
$173$	20.5270	1.56064	0.780318	−	0.625383i	$-0.215057\pi$
$173$	20.5270	1.56064	0.780318	+	0.625383i	$0.215057\pi$
$174$	34.3718	2.60572
$175$	−3.71166	−0.280575
$176$	22.0863	1.66482
$177$	4.27425	0.321273
$178$	7.70586	0.577579
$179$	4.60863	0.344465	0.172233	−	0.985056i	$-0.444902\pi$
$179$	4.60863	0.344465	0.172233	+	0.985056i	$0.444902\pi$
$180$	−4.69576	−0.350002
$181$	−6.43120	−0.478027	−0.239014	−	0.971016i	$-0.576824\pi$
$181$	−6.43120	−0.478027	−0.239014	+	0.971016i	$0.576824\pi$
$182$	28.5583	2.11689
$183$	−9.18327	−0.678847
$184$	11.0639	0.815645
$185$	−8.83854	−0.649822
$186$	27.3340	2.00422
$187$	−30.9000	−2.25963
$188$	−2.19728	−0.160253
$189$	−7.42271	−0.539923
$190$	−3.11732	−0.226154
$191$	7.88128	0.570270	0.285135	−	0.958487i	$-0.407962\pi$
$191$	7.88128	0.570270	0.285135	+	0.958487i	$0.407962\pi$
$192$	−11.2818	−0.814193
$193$	5.39247	0.388158	0.194079	−	0.980986i	$-0.437828\pi$
$193$	5.39247	0.388158	0.194079	+	0.980986i	$0.437828\pi$
$194$	11.4800	0.824215
$195$	31.0520	2.22368
$196$	0.852307	0.0608791
$197$	−20.9582	−1.49321	−0.746604	−	0.665269i	$-0.768317\pi$
$197$	−20.9582	−1.49321	−0.746604	+	0.665269i	$0.768317\pi$
$198$	−29.2276	−2.07711
$199$	20.4528	1.44986	0.724931	−	0.688821i	$-0.241871\pi$
$199$	20.4528	1.44986	0.724931	+	0.688821i	$0.241871\pi$
$200$	2.87260	0.203123
$201$	32.9818	2.32635
$202$	28.6897	2.01860
$203$	−23.3264	−1.63719
$204$	−10.9878	−0.769303
$205$	−11.6284	−0.812164
$206$	11.9350	0.831548
$207$	−19.5969	−1.36208
$208$	−29.5833	−2.05124
$209$	−4.55345	−0.314969
$210$	23.8392	1.64506
$211$	0.507708	0.0349520	0.0174760	−	0.999847i	$-0.494437\pi$
$211$	0.507708	0.0349520	0.0174760	+	0.999847i	$0.494437\pi$
$212$	−1.38977	−0.0954497
$213$	19.5941	1.34257
$214$	−5.87732	−0.401765
$215$	−1.55547	−0.106082
$216$	5.74473	0.390879
$217$	−18.5502	−1.25927
$218$	1.38495	0.0938008
$219$	−27.4404	−1.85425
$220$	5.38503	0.363059
$221$	41.3888	2.78411
$222$	−19.5624	−1.31294
$223$	−0.726278	−0.0486352	−0.0243176	−	0.999704i	$-0.507741\pi$
$223$	−0.726278	−0.0486352	−0.0243176	+	0.999704i	$0.507741\pi$
$224$	−9.72536	−0.649803
$225$	−5.08806	−0.339204
$226$	−1.33459	−0.0887753
$227$	28.9652	1.92249	0.961243	−	0.275702i	$-0.0889102\pi$
$227$	28.9652	1.92249	0.961243	+	0.275702i	$0.0889102\pi$
$228$	−1.61918	−0.107233
$229$	−24.5372	−1.62146	−0.810730	−	0.585420i	$-0.800930\pi$
$229$	−24.5372	−1.62146	−0.810730	+	0.585420i	$0.800930\pi$
$230$	15.3854	1.01448
$231$	34.8218	2.29111
$232$	18.0532	1.18525
$233$	8.16551	0.534940	0.267470	−	0.963566i	$-0.413812\pi$
$233$	8.16551	0.534940	0.267470	+	0.963566i	$0.413812\pi$
$234$	39.1487	2.55923
$235$	6.90900	0.450694
$236$	−0.992849	−0.0646290
$237$	−25.8038	−1.67614
$238$	31.7750	2.05967
$239$	−21.1517	−1.36819	−0.684095	−	0.729393i	$-0.739803\pi$
$239$	−21.1517	−1.36819	−0.684095	+	0.729393i	$0.739803\pi$
$240$	−24.6948	−1.59404
$241$	21.4174	1.37962	0.689809	−	0.723992i	$-0.257695\pi$
$241$	21.4174	1.37962	0.689809	+	0.723992i	$0.257695\pi$
$242$	15.7355	1.01152
$243$	21.2744	1.36475
$244$	2.13315	0.136561
$245$	−2.67994	−0.171215
$246$	−25.7372	−1.64094
$247$	6.09910	0.388076
$248$	14.3567	0.911653
$249$	43.8299	2.77760
$250$	19.5812	1.23842
$251$	11.5335	0.727991	0.363996	−	0.931401i	$-0.381412\pi$
$251$	11.5335	0.727991	0.363996	+	0.931401i	$0.381412\pi$
$252$	7.05330	0.444316
$253$	22.4734	1.41289
$254$	15.5290	0.974374
$255$	34.5495	2.16357
$256$	13.4762	0.842263
$257$	−6.55922	−0.409153	−0.204576	−	0.978851i	$-0.565582\pi$
$257$	−6.55922	−0.409153	−0.204576	+	0.978851i	$0.565582\pi$
$258$	−3.44272	−0.214334
$259$	13.2760	0.824929
$260$	−7.21295	−0.447328
$261$	−31.9766	−1.97930
$262$	21.0557	1.30083
$263$	11.6774	0.720058	0.360029	−	0.932941i	$-0.382767\pi$
$263$	11.6774	0.720058	0.360029	+	0.932941i	$0.382767\pi$
$264$	−26.9500	−1.65866
$265$	4.36990	0.268441
$266$	4.68239	0.287096
$267$	−12.5853	−0.770209
$268$	−7.66120	−0.467982
$269$	−12.4632	−0.759896	−0.379948	−	0.925008i	$-0.624058\pi$
$269$	−12.4632	−0.759896	−0.379948	+	0.925008i	$0.624058\pi$
$270$	7.98857	0.486169
$271$	26.4528	1.60689	0.803446	−	0.595378i	$-0.202998\pi$
$271$	26.4528	1.60689	0.803446	+	0.595378i	$0.202998\pi$
$272$	−32.9154	−1.99579
$273$	−46.6419	−2.82289
$274$	19.0022	1.14796
$275$	5.83491	0.351858
$276$	7.99140	0.481026
$277$	13.9776	0.839833	0.419916	−	0.907563i	$-0.362059\pi$
$277$	13.9776	0.839833	0.419916	+	0.907563i	$0.362059\pi$
$278$	16.4806	0.988442
$279$	−25.4292	−1.52241
$280$	12.5212	0.748282
$281$	6.83104	0.407506	0.203753	−	0.979022i	$-0.434686\pi$
$281$	6.83104	0.407506	0.203753	+	0.979022i	$0.434686\pi$
$282$	15.2917	0.910608
$283$	−12.7872	−0.760121	−0.380060	−	0.924962i	$-0.624097\pi$
$283$	−12.7872	−0.760121	−0.380060	+	0.924962i	$0.624097\pi$
$284$	−4.55144	−0.270079
$285$	5.09125	0.301579
$286$	−44.8951	−2.65471
$287$	17.4665	1.03102
$288$	−13.3318	−0.785586
$289$	29.0506	1.70886
$290$	25.1047	1.47420
$291$	−18.7493	−1.09910
$292$	6.37401	0.373011
$293$	27.4412	1.60313	0.801565	−	0.597908i	$-0.204001\pi$
$293$	27.4412	1.60313	0.801565	+	0.597908i	$0.204001\pi$
$294$	−5.93152	−0.345933
$295$	3.12185	0.181761
$296$	−10.2748	−0.597211
$297$	11.6689	0.677096
$298$	−3.53473	−0.204761
$299$	−30.1019	−1.74084
$300$	2.07486	0.119792
$301$	2.33640	0.134668
$302$	−6.02296	−0.346582
$303$	−46.8563	−2.69183
$304$	−4.85045	−0.278192
$305$	−6.70733	−0.384061
$306$	43.5582	2.49005
$307$	−18.8767	−1.07735	−0.538674	−	0.842514i	$-0.681075\pi$
$307$	−18.8767	−1.07735	−0.538674	+	0.842514i	$0.681075\pi$
$308$	−8.08862	−0.460892
$309$	−19.4923	−1.10888
$310$	19.9643	1.13390
$311$	16.0295	0.908949	0.454474	−	0.890760i	$-0.349827\pi$
$311$	16.0295	0.908949	0.454474	+	0.890760i	$0.349827\pi$
$312$	36.0980	2.04365
$313$	27.0799	1.53065	0.765324	−	0.643645i	$-0.222579\pi$
$313$	27.0799	1.53065	0.765324	+	0.643645i	$0.222579\pi$
$314$	−31.3397	−1.76860
$315$	−22.1780	−1.24959
$316$	5.99386	0.337181
$317$	−1.00000	−0.0561656
$317$	−1.00000	−0.0561656
$318$	9.67192	0.542374
$319$	36.6703	2.05314
$320$	−8.24006	−0.460633
$321$	9.59892	0.535759
$322$	−23.1098	−1.28786
$323$	6.78606	0.377586
$324$	−3.15594	−0.175330
$325$	−7.81553	−0.433528
$326$	21.8428	1.20976
$327$	−2.26192	−0.125085
$328$	−13.5181	−0.746410
$329$	−10.3777	−0.572142
$330$	−37.4764	−2.06301
$331$	−3.86327	−0.212344	−0.106172	−	0.994348i	$-0.533859\pi$
$331$	−3.86327	−0.212344	−0.106172	+	0.994348i	$0.533859\pi$
$332$	−10.1811	−0.558758
$333$	18.1992	0.997307
$334$	−13.8928	−0.760179
$335$	24.0894	1.31615
$336$	37.0930	2.02359
$337$	−9.91252	−0.539970	−0.269985	−	0.962865i	$-0.587019\pi$
$337$	−9.91252	−0.539970	−0.269985	+	0.962865i	$0.587019\pi$
$338$	39.1192	2.12780
$339$	2.17966	0.118383
$340$	−8.02537	−0.435237
$341$	29.1618	1.57920
$342$	6.41877	0.347087
$343$	−16.2501	−0.877424
$344$	−1.80823	−0.0974934
$345$	−25.1277	−1.35283
$346$	33.1832	1.78394
$347$	−32.8863	−1.76543	−0.882716	−	0.469907i	$-0.844287\pi$
$347$	−32.8863	−1.76543	−0.882716	+	0.469907i	$0.844287\pi$
$348$	13.0397	0.699002
$349$	19.3222	1.03429	0.517147	−	0.855896i	$-0.326994\pi$
$349$	19.3222	1.03429	0.517147	+	0.855896i	$0.326994\pi$
$350$	−6.00013	−0.320721
$351$	−15.6298	−0.834257
$352$	15.2888	0.814893
$353$	21.5531	1.14716	0.573578	−	0.819151i	$-0.305555\pi$
$353$	21.5531	1.14716	0.573578	+	0.819151i	$0.305555\pi$
$354$	6.90961	0.367241
$355$	14.3113	0.759564
$356$	2.92339	0.154940
$357$	−51.8953	−2.74659
$358$	7.45015	0.393752
$359$	−13.4982	−0.712406	−0.356203	−	0.934409i	$-0.615929\pi$
$359$	−13.4982	−0.712406	−0.356203	+	0.934409i	$0.615929\pi$
$360$	17.1644	0.904644
$361$	1.00000	0.0526316
$362$	−10.3965	−0.546425
$363$	−25.6995	−1.34887
$364$	10.8343	0.567869
$365$	−20.0421	−1.04905
$366$	−14.8454	−0.775979
$367$	10.1042	0.527435	0.263718	−	0.964600i	$-0.415051\pi$
$367$	10.1042	0.527435	0.263718	+	0.964600i	$0.415051\pi$
$368$	23.9392	1.24792
$369$	23.9437	1.24646
$370$	−14.2881	−0.742801
$371$	−6.56384	−0.340778
$372$	10.3698	0.537647
$373$	2.98888	0.154758	0.0773791	−	0.997002i	$-0.475345\pi$
$373$	2.98888	0.154758	0.0773791	+	0.997002i	$0.475345\pi$
$374$	−49.9518	−2.58295
$375$	−31.9803	−1.65145
$376$	8.03173	0.414205
$377$	−49.1178	−2.52969
$378$	−11.9993	−0.617177
$379$	17.8721	0.918029	0.459015	−	0.888429i	$-0.348203\pi$
$379$	17.8721	0.918029	0.459015	+	0.888429i	$0.348203\pi$
$380$	−1.18263	−0.0606674
$381$	−25.3621	−1.29934
$382$	12.7406	0.651866
$383$	−22.2698	−1.13794	−0.568968	−	0.822360i	$-0.692657\pi$
$383$	−22.2698	−1.13794	−0.568968	+	0.822360i	$0.692657\pi$
$384$	−35.9673	−1.83545
$385$	25.4334	1.29620
$386$	8.71727	0.443697
$387$	3.20281	0.162808
$388$	4.35519	0.221101
$389$	7.23307	0.366731	0.183366	−	0.983045i	$-0.441301\pi$
$389$	7.23307	0.366731	0.183366	+	0.983045i	$0.441301\pi$
$390$	50.1976	2.54185
$391$	−33.4924	−1.69378
$392$	−3.11544	−0.157353
$393$	−34.3885	−1.73467
$394$	−33.8802	−1.70686
$395$	−18.8467	−0.948281
$396$	−11.0881	−0.557200
$397$	−25.9066	−1.30021	−0.650107	−	0.759842i	$-0.725276\pi$
$397$	−25.9066	−1.30021	−0.650107	+	0.759842i	$0.725276\pi$
$398$	33.0633	1.65731
$399$	−7.64734	−0.382846
$400$	6.21549	0.310774
$401$	−13.8672	−0.692494	−0.346247	−	0.938143i	$-0.612544\pi$
$401$	−13.8672	−0.692494	−0.346247	+	0.938143i	$0.612544\pi$
$402$	53.3171	2.65922
$403$	−39.0606	−1.94575
$404$	10.8841	0.541503
$405$	9.92336	0.493096
$406$	−37.7086	−1.87145
$407$	−20.8705	−1.03451
$408$	40.1638	1.98841
$409$	2.17124	0.107361	0.0536806	−	0.998558i	$-0.482905\pi$
$409$	2.17124	0.107361	0.0536806	+	0.998558i	$0.482905\pi$
$410$	−18.7981	−0.928371
$411$	−31.0346	−1.53082
$412$	4.52780	0.223069
$413$	−4.68920	−0.230741
$414$	−31.6796	−1.55697
$415$	32.0127	1.57144
$416$	−20.4784	−1.00404
$417$	−26.9164	−1.31810
$418$	−7.36095	−0.360036
$419$	−29.7251	−1.45216	−0.726082	−	0.687608i	$-0.758661\pi$
$419$	−29.7251	−1.45216	−0.726082	+	0.687608i	$0.758661\pi$
$420$	9.04394	0.441299
$421$	−13.6691	−0.666191	−0.333095	−	0.942893i	$-0.608093\pi$
$421$	−13.6691	−0.666191	−0.333095	+	0.942893i	$0.608093\pi$
$422$	0.820742	0.0399531
$423$	−14.2261	−0.691697
$424$	5.08002	0.246708
$425$	−8.69583	−0.421810
$426$	31.6752	1.53467
$427$	10.0748	0.487553
$428$	−2.22969	−0.107776
$429$	73.3233	3.54008
$430$	−2.51451	−0.121261
$431$	11.4358	0.550844	0.275422	−	0.961323i	$-0.411182\pi$
$431$	11.4358	0.550844	0.275422	+	0.961323i	$0.411182\pi$
$432$	12.4300	0.598037
$433$	16.9220	0.813220	0.406610	−	0.913602i	$-0.366711\pi$
$433$	16.9220	0.813220	0.406610	+	0.913602i	$0.366711\pi$
$434$	−29.9876	−1.43945
$435$	−41.0013	−1.96586
$436$	0.525413	0.0251627
$437$	−4.93547	−0.236095
$438$	−44.3591	−2.11956
$439$	7.69315	0.367174	0.183587	−	0.983003i	$-0.441229\pi$
$439$	7.69315	0.367174	0.183587	+	0.983003i	$0.441229\pi$
$440$	−19.6839	−0.938393
$441$	5.51818	0.262771
$442$	66.9077	3.18247
$443$	14.7697	0.701728	0.350864	−	0.936427i	$-0.385888\pi$
$443$	14.7697	0.701728	0.350864	+	0.936427i	$0.385888\pi$
$444$	−7.42142	−0.352205
$445$	−9.19214	−0.435749
$446$	−1.17408	−0.0555941
$447$	5.77297	0.273052
$448$	12.3770	0.584760
$449$	22.4879	1.06127	0.530635	−	0.847601i	$-0.321954\pi$
$449$	22.4879	1.06127	0.530635	+	0.847601i	$0.321954\pi$
$450$	−8.22518	−0.387739
$451$	−27.4583	−1.29296
$452$	−0.506305	−0.0238146
$453$	9.83677	0.462172
$454$	46.8241	2.19756
$455$	−34.0666	−1.59706
$456$	5.91858	0.277163
$457$	5.54054	0.259175	0.129588	−	0.991568i	$-0.458635\pi$
$457$	5.54054	0.259175	0.129588	+	0.991568i	$0.458635\pi$
$458$	−39.6659	−1.85347
$459$	−17.3902	−0.811707
$460$	5.83681	0.272143
$461$	7.91739	0.368750	0.184375	−	0.982856i	$-0.440974\pi$
$461$	7.91739	0.368750	0.184375	+	0.982856i	$0.440974\pi$
$462$	56.2917	2.61893
$463$	7.50910	0.348978	0.174489	−	0.984659i	$-0.444173\pi$
$463$	7.50910	0.348978	0.174489	+	0.984659i	$0.444173\pi$
$464$	39.0621	1.81341
$465$	−32.6060	−1.51207
$466$	13.2001	0.611481
$467$	33.4836	1.54944	0.774718	−	0.632307i	$-0.217892\pi$
$467$	33.4836	1.54944	0.774718	+	0.632307i	$0.217892\pi$
$468$	14.8519	0.686531
$469$	−36.1837	−1.67081
$470$	11.1689	0.515181
$471$	51.1844	2.35845
$472$	3.62916	0.167046
$473$	−3.67294	−0.168882
$474$	−41.7135	−1.91596
$475$	−1.28143	−0.0587958
$476$	12.0546	0.552519
$477$	−8.99793	−0.411987
$478$	−34.1931	−1.56396
$479$	−18.4707	−0.843946	−0.421973	−	0.906608i	$-0.638662\pi$
$479$	−18.4707	−0.843946	−0.421973	+	0.906608i	$0.638662\pi$
$480$	−17.0945	−0.780252
$481$	27.9549	1.27463
$482$	34.6226	1.57702
$483$	37.7432	1.71738
$484$	5.96963	0.271347
$485$	−13.6942	−0.621822
$486$	34.3914	1.56003
$487$	−30.0538	−1.36187	−0.680933	−	0.732345i	$-0.738426\pi$
$487$	−30.0538	−1.36187	−0.680933	+	0.732345i	$0.738426\pi$
$488$	−7.79728	−0.352966
$489$	−35.6740	−1.61323
$490$	−4.33230	−0.195713
$491$	8.93907	0.403414	0.201707	−	0.979446i	$-0.435351\pi$
$491$	8.93907	0.403414	0.201707	+	0.979446i	$0.435351\pi$
$492$	−9.76399	−0.440195
$493$	−54.6501	−2.46132
$494$	9.85958	0.443603
$495$	34.8649	1.56706
$496$	31.0639	1.39481
$497$	−21.4964	−0.964243
$498$	70.8538	3.17503
$499$	40.1671	1.79813	0.899063	−	0.437819i	$-0.144249\pi$
$499$	40.1671	1.79813	0.899063	+	0.437819i	$0.144249\pi$
$500$	7.42857	0.332216
$501$	22.6899	1.01371
$502$	18.6447	0.832155
$503$	36.0591	1.60779	0.803897	−	0.594768i	$-0.202756\pi$
$503$	36.0591	1.60779	0.803897	+	0.594768i	$0.202756\pi$
$504$	−25.7819	−1.14842
$505$	−34.2232	−1.52291
$506$	36.3297	1.61505
$507$	−63.8900	−2.83745
$508$	5.89127	0.261383
$509$	4.65734	0.206433	0.103216	−	0.994659i	$-0.467087\pi$
$509$	4.65734	0.206433	0.103216	+	0.994659i	$0.467087\pi$
$510$	55.8515	2.47315
$511$	30.1043	1.33174
$512$	−5.46076	−0.241334
$513$	−2.56264	−0.113143
$514$	−10.6034	−0.467696
$515$	−14.2369	−0.627354
$516$	−1.30607	−0.0574967
$517$	16.3143	0.717502
$518$	21.4615	0.942963
$519$	−54.1952	−2.37890
$520$	26.3655	1.15620
$521$	−20.4107	−0.894210	−0.447105	−	0.894482i	$-0.647545\pi$
$521$	−20.4107	−0.894210	−0.447105	+	0.894482i	$0.647545\pi$
$522$	−51.6922	−2.26251
$523$	−18.2114	−0.796329	−0.398165	−	0.917314i	$-0.630353\pi$
$523$	−18.2114	−0.796329	−0.398165	+	0.917314i	$0.630353\pi$
$524$	7.98796	0.348956
$525$	9.79949	0.427685
$526$	18.8772	0.823086
$527$	−43.4602	−1.89315
$528$	−58.3121	−2.53771
$529$	1.35884	0.0590799
$530$	7.06423	0.306851
$531$	−6.42811	−0.278956
$532$	1.77637	0.0770154
$533$	36.7788	1.59307
$534$	−20.3450	−0.880413
$535$	7.01091	0.303108
$536$	28.0040	1.20959
$537$	−12.1677	−0.525074
$538$	−20.1476	−0.868624
$539$	−6.32817	−0.272574
$540$	3.03064	0.130418
$541$	25.8433	1.11109	0.555544	−	0.831487i	$-0.312510\pi$
$541$	25.8433	1.11109	0.555544	+	0.831487i	$0.312510\pi$
$542$	42.7626	1.83681
$543$	16.9796	0.728665
$544$	−22.7850	−0.976898
$545$	−1.65208	−0.0707671
$546$	−75.3996	−3.22680
$547$	20.9470	0.895630	0.447815	−	0.894126i	$-0.352202\pi$
$547$	20.9470	0.895630	0.447815	+	0.894126i	$0.352202\pi$
$548$	7.20890	0.307949
$549$	13.8109	0.589433
$550$	9.43251	0.402203
$551$	−8.05329	−0.343082
$552$	−29.2110	−1.24330
$553$	28.3088	1.20381
$554$	22.5957	0.959999
$555$	23.3355	0.990535
$556$	6.25230	0.265157
$557$	−29.2942	−1.24124	−0.620618	−	0.784113i	$-0.713118\pi$
$557$	−29.2942	−1.24124	−0.620618	+	0.784113i	$0.713118\pi$
$558$	−41.1079	−1.74024
$559$	4.91970	0.208081
$560$	27.0922	1.14486
$561$	81.5820	3.44440
$562$	11.0428	0.465813
$563$	32.5297	1.37096	0.685482	−	0.728089i	$-0.259591\pi$
$563$	32.5297	1.37096	0.685482	+	0.728089i	$0.259591\pi$
$564$	5.80126	0.244277
$565$	1.59200	0.0669757
$566$	−20.6714	−0.868882
$567$	−14.9054	−0.625970
$568$	16.6369	0.698068
$569$	22.1264	0.927587	0.463794	−	0.885943i	$-0.346488\pi$
$569$	22.1264	0.927587	0.463794	+	0.885943i	$0.346488\pi$
$570$	8.23033	0.344731
$571$	36.4318	1.52462	0.762311	−	0.647211i	$-0.224065\pi$
$571$	36.4318	1.52462	0.762311	+	0.647211i	$0.224065\pi$
$572$	−17.0320	−0.712143
$573$	−20.8081	−0.869271
$574$	28.2358	1.17854
$575$	6.32443	0.263747
$576$	16.9668	0.706952
$577$	−9.35759	−0.389562	−0.194781	−	0.980847i	$-0.562400\pi$
$577$	−9.35759	−0.389562	−0.194781	+	0.980847i	$0.562400\pi$
$578$	46.9622	1.95337
$579$	−14.2372	−0.591676
$580$	9.52402	0.395464
$581$	−48.0849	−1.99490
$582$	−30.3094	−1.25637
$583$	10.3187	0.427357
$584$	−23.2989	−0.964116
$585$	−46.6995	−1.93079
$586$	44.3604	1.83251
$587$	−17.3769	−0.717220	−0.358610	−	0.933488i	$-0.616749\pi$
$587$	−17.3769	−0.717220	−0.358610	+	0.933488i	$0.616749\pi$
$588$	−2.25026	−0.0927990
$589$	−6.40433	−0.263886
$590$	5.04668	0.207768
$591$	55.3336	2.27612
$592$	−22.2318	−0.913720
$593$	−43.6831	−1.79385	−0.896925	−	0.442183i	$-0.854204\pi$
$593$	−43.6831	−1.79385	−0.896925	+	0.442183i	$0.854204\pi$
$594$	18.8635	0.773978
$595$	−37.9036	−1.55390
$596$	−1.34098	−0.0549287
$597$	−53.9994	−2.21005
$598$	−48.6616	−1.98992
$599$	21.0681	0.860819	0.430410	−	0.902634i	$-0.358369\pi$
$599$	21.0681	0.860819	0.430410	+	0.902634i	$0.358369\pi$
$600$	−7.58422	−0.309624
$601$	−1.84589	−0.0752956	−0.0376478	−	0.999291i	$-0.511986\pi$
$601$	−1.84589	−0.0752956	−0.0376478	+	0.999291i	$0.511986\pi$
$602$	3.77694	0.153937
$603$	−49.6017	−2.01994
$604$	−2.28495	−0.0929731
$605$	−18.7706	−0.763131
$606$	−75.7463	−3.07698
$607$	45.8864	1.86247	0.931236	−	0.364418i	$-0.118732\pi$
$607$	45.8864	1.86247	0.931236	+	0.364418i	$0.118732\pi$
$608$	−3.35762	−0.136169
$609$	61.5862	2.49560
$610$	−10.8428	−0.439014
$611$	−21.8521	−0.884040
$612$	16.5248	0.667974
$613$	−32.6081	−1.31703	−0.658515	−	0.752568i	$-0.728815\pi$
$613$	−32.6081	−1.31703	−0.658515	+	0.752568i	$0.728815\pi$
$614$	−30.5153	−1.23150
$615$	30.7013	1.23800
$616$	29.5663	1.19126
$617$	−16.9170	−0.681053	−0.340526	−	0.940235i	$-0.610605\pi$
$617$	−16.9170	−0.681053	−0.340526	+	0.940235i	$0.610605\pi$
$618$	−31.5106	−1.26754
$619$	−1.43454	−0.0576591	−0.0288296	−	0.999584i	$-0.509178\pi$
$619$	−1.43454	−0.0576591	−0.0288296	+	0.999584i	$0.509178\pi$
$620$	7.57392	0.304176
$621$	12.6478	0.507540
$622$	25.9127	1.03900
$623$	13.8071	0.553170
$624$	78.1058	3.12673
$625$	−16.9508	−0.678033
$626$	43.7765	1.74966
$627$	12.0220	0.480113
$628$	−11.8894	−0.474440
$629$	31.1035	1.24018
$630$	−35.8521	−1.42838
$631$	33.7470	1.34345	0.671724	−	0.740801i	$-0.265554\pi$
$631$	33.7470	1.34345	0.671724	+	0.740801i	$0.265554\pi$
$632$	−21.9093	−0.871506
$633$	−1.34045	−0.0532780
$634$	−1.61656	−0.0642020
$635$	−18.5241	−0.735108
$636$	3.66926	0.145496
$637$	8.47623	0.335840
$638$	59.2799	2.34691
$639$	−29.4679	−1.16573
$640$	−26.2700	−1.03841
$641$	30.6721	1.21148	0.605738	−	0.795664i	$-0.292878\pi$
$641$	30.6721	1.21148	0.605738	+	0.795664i	$0.292878\pi$
$642$	15.5173	0.612418
$643$	−4.35083	−0.171580	−0.0857901	−	0.996313i	$-0.527341\pi$
$643$	−4.35083	−0.171580	−0.0857901	+	0.996313i	$0.527341\pi$
$644$	−8.76722	−0.345477
$645$	4.10674	0.161703
$646$	10.9701	0.431613
$647$	−10.5343	−0.414147	−0.207073	−	0.978325i	$-0.566394\pi$
$647$	−10.5343	−0.414147	−0.207073	+	0.978325i	$0.566394\pi$
$648$	11.5359	0.453174
$649$	7.37166	0.289363
$650$	−12.6343	−0.495559
$651$	48.9761	1.91952
$652$	8.28657	0.324527
$653$	−23.4265	−0.916751	−0.458375	−	0.888759i	$-0.651568\pi$
$653$	−23.4265	−0.916751	−0.458375	+	0.888759i	$0.651568\pi$
$654$	−3.65654	−0.142982
$655$	−25.1169	−0.981397
$656$	−29.2492	−1.14199
$657$	41.2679	1.61002
$658$	−16.7762	−0.654006
$659$	−31.9381	−1.24413	−0.622066	−	0.782965i	$-0.713707\pi$
$659$	−31.9381	−1.24413	−0.622066	+	0.782965i	$0.713707\pi$
$660$	−14.2175	−0.553416
$661$	−10.7582	−0.418445	−0.209222	−	0.977868i	$-0.567093\pi$
$661$	−10.7582	−0.418445	−0.209222	+	0.977868i	$0.567093\pi$
$662$	−6.24522	−0.242727
$663$	−109.275	−4.24387
$664$	37.2148	1.44422
$665$	−5.58551	−0.216597
$666$	29.4201	1.14001
$667$	39.7467	1.53900
$668$	−5.27054	−0.203923
$669$	1.91752	0.0741354
$670$	38.9421	1.50446
$671$	−15.8381	−0.611422
$672$	25.6768	0.990506
$673$	17.6587	0.680693	0.340347	−	0.940300i	$-0.389456\pi$
$673$	17.6587	0.680693	0.340347	+	0.940300i	$0.389456\pi$
$674$	−16.0242	−0.617230
$675$	3.28383	0.126395
$676$	14.8407	0.570798
$677$	−2.88732	−0.110969	−0.0554844	−	0.998460i	$-0.517670\pi$
$677$	−2.88732	−0.110969	−0.0554844	+	0.998460i	$0.517670\pi$
$678$	3.52357	0.135322
$679$	20.5695	0.789384
$680$	29.3351	1.12495
$681$	−76.4737	−2.93048
$682$	47.1419	1.80516
$683$	3.27380	0.125268	0.0626342	−	0.998037i	$-0.480050\pi$
$683$	3.27380	0.125268	0.0626342	+	0.998037i	$0.480050\pi$
$684$	2.43511	0.0931086
$685$	−22.6672	−0.866070
$686$	−26.2694	−1.00297
$687$	64.7829	2.47162
$688$	−3.91250	−0.149163
$689$	−13.8213	−0.526550
$690$	−40.6205	−1.54640
$691$	9.64940	0.367081	0.183540	−	0.983012i	$-0.441244\pi$
$691$	9.64940	0.367081	0.183540	+	0.983012i	$0.441244\pi$
$692$	12.5888	0.478554
$693$	−52.3690	−1.98933
$694$	−53.1629	−2.01804
$695$	−19.6593	−0.745722
$696$	−47.6640	−1.80670
$697$	40.9214	1.55001
$698$	31.2356	1.18229
$699$	−21.5585	−0.815418
$700$	−2.27629	−0.0860355
$701$	−39.4668	−1.49064	−0.745319	−	0.666708i	$-0.767703\pi$
$701$	−39.4668	−1.49064	−0.745319	+	0.666708i	$0.767703\pi$
$702$	−25.2666	−0.953625
$703$	4.58345	0.172868
$704$	−19.4573	−0.733326
$705$	−18.2411	−0.687000
$706$	34.8420	1.31129
$707$	51.4052	1.93329
$708$	2.62131	0.0985150
$709$	8.43917	0.316940	0.158470	−	0.987364i	$-0.449344\pi$
$709$	8.43917	0.316940	0.158470	+	0.987364i	$0.449344\pi$
$710$	23.1351	0.868245
$711$	38.8067	1.45536
$712$	−10.6859	−0.400470
$713$	31.6084	1.18374
$714$	−83.8921	−3.13958
$715$	53.5543	2.00282
$716$	2.82638	0.105627
$717$	55.8446	2.08556
$718$	−21.8207	−0.814340
$719$	46.2943	1.72649	0.863243	−	0.504788i	$-0.168429\pi$
$719$	46.2943	1.72649	0.863243	+	0.504788i	$0.168429\pi$
$720$	37.1389	1.38409
$721$	21.3847	0.796407
$722$	1.61656	0.0601623
$723$	−56.5461	−2.10297
$724$	−3.94413	−0.146582
$725$	10.3197	0.383264
$726$	−41.5449	−1.54188
$727$	−34.8414	−1.29220	−0.646099	−	0.763254i	$-0.723601\pi$
$727$	−34.8414	−1.29220	−0.646099	+	0.763254i	$0.723601\pi$
$728$	−39.6024	−1.46776
$729$	−40.7305	−1.50854
$730$	−32.3993	−1.19915
$731$	5.47382	0.202456
$732$	−5.63192	−0.208162
$733$	3.96852	0.146581	0.0732903	−	0.997311i	$-0.476650\pi$
$733$	3.96852	0.146581	0.0732903	+	0.997311i	$0.476650\pi$
$734$	16.3341	0.602902
$735$	7.07557	0.260986
$736$	16.5714	0.610830
$737$	56.8825	2.09529
$738$	38.7065	1.42481
$739$	−30.8278	−1.13402	−0.567010	−	0.823711i	$-0.691900\pi$
$739$	−30.8278	−1.13402	−0.567010	+	0.823711i	$0.691900\pi$
$740$	−5.42050	−0.199262
$741$	−16.1028	−0.591551
$742$	−10.6109	−0.389537
$743$	−12.4220	−0.455720	−0.227860	−	0.973694i	$-0.573173\pi$
$743$	−12.4220	−0.455720	−0.227860	+	0.973694i	$0.573173\pi$
$744$	−37.9045	−1.38965
$745$	4.21649	0.154480
$746$	4.83171	0.176902
$747$	−65.9164	−2.41175
$748$	−18.9504	−0.692894
$749$	−10.5308	−0.384787
$750$	−51.6982	−1.88775
$751$	13.6336	0.497496	0.248748	−	0.968568i	$-0.419981\pi$
$751$	13.6336	0.497496	0.248748	+	0.968568i	$0.419981\pi$
$752$	17.3784	0.633724
$753$	−30.4508	−1.10969
$754$	−79.4021	−2.89165
$755$	7.18464	0.261476
$756$	−4.55220	−0.165562
$757$	−42.4108	−1.54145	−0.770724	−	0.637169i	$-0.780105\pi$
$757$	−42.4108	−1.54145	−0.770724	+	0.637169i	$0.780105\pi$
$758$	28.8914	1.04938
$759$	−59.3342	−2.15370
$760$	4.32285	0.156806
$761$	19.8181	0.718407	0.359204	−	0.933259i	$-0.383048\pi$
$761$	19.8181	0.718407	0.359204	+	0.933259i	$0.383048\pi$
$762$	−40.9995	−1.48526
$763$	2.48151	0.0898367
$764$	4.83343	0.174867
$765$	−51.9595	−1.87860
$766$	−36.0006	−1.30076
$767$	−9.87393	−0.356527
$768$	−35.5798	−1.28388
$769$	17.1090	0.616968	0.308484	−	0.951230i	$-0.400178\pi$
$769$	17.1090	0.616968	0.308484	+	0.951230i	$0.400178\pi$
$770$	41.1147	1.48167
$771$	17.3176	0.623678
$772$	3.30709	0.119025
$773$	−2.65650	−0.0955477	−0.0477738	−	0.998858i	$-0.515213\pi$
$773$	−2.65650	−0.0955477	−0.0477738	+	0.998858i	$0.515213\pi$
$774$	5.17755	0.186103
$775$	8.20667	0.294792
$776$	−15.9195	−0.571478
$777$	−35.0512	−1.25745
$778$	11.6927	0.419205
$779$	6.03021	0.216055
$780$	19.0436	0.681869
$781$	33.7934	1.20922
$782$	−54.1426	−1.93613
$783$	20.6377	0.737531
$784$	−6.74092	−0.240747
$785$	37.3844	1.33431
$786$	−55.5912	−1.98287
$787$	22.0362	0.785504	0.392752	−	0.919644i	$-0.371523\pi$
$787$	22.0362	0.785504	0.392752	+	0.919644i	$0.371523\pi$
$788$	−12.8532	−0.457877
$789$	−30.8305	−1.09760
$790$	−30.4669	−1.08396
$791$	−2.39127	−0.0850237
$792$	40.5305	1.44019
$793$	21.2142	0.753339
$794$	−41.8797	−1.48625
$795$	−11.5374	−0.409189
$796$	12.5433	0.444586
$797$	16.7878	0.594653	0.297326	−	0.954776i	$-0.403905\pi$
$797$	16.7878	0.594653	0.297326	+	0.954776i	$0.403905\pi$
$798$	−12.3624	−0.437625
$799$	−24.3134	−0.860145
$800$	4.30254	0.152118
$801$	18.9272	0.668761
$802$	−22.4172	−0.791579
$803$	−47.3255	−1.67008
$804$	20.2271	0.713353
$805$	27.5671	0.971613
$806$	−63.1440	−2.22415
$807$	32.9053	1.15832
$808$	−39.7845	−1.39961
$809$	21.8917	0.769672	0.384836	−	0.922985i	$-0.374258\pi$
$809$	21.8917	0.769672	0.384836	+	0.922985i	$0.374258\pi$
$810$	16.0417	0.563650
$811$	0.435086	0.0152779	0.00763896	−	0.999971i	$-0.497568\pi$
$811$	0.435086	0.0152779	0.00763896	+	0.999971i	$0.497568\pi$
$812$	−14.3056	−0.502029
$813$	−69.8405	−2.44941
$814$	−33.7385	−1.18253
$815$	−26.0558	−0.912694
$816$	86.9031	3.04222
$817$	0.806627	0.0282203
$818$	3.50996	0.122723
$819$	70.1454	2.45108
$820$	−7.13148	−0.249042
$821$	−9.32417	−0.325416	−0.162708	−	0.986674i	$-0.552023\pi$
$821$	−9.32417	−0.325416	−0.162708	+	0.986674i	$0.552023\pi$
$822$	−50.1694	−1.74986
$823$	56.1617	1.95767	0.978837	−	0.204641i	$-0.0656027\pi$
$823$	56.1617	1.95767	0.978837	+	0.204641i	$0.0656027\pi$
$824$	−16.5505	−0.576562
$825$	−15.4053	−0.536344
$826$	−7.58040	−0.263756
$827$	−8.52636	−0.296491	−0.148245	−	0.988951i	$-0.547363\pi$
$827$	−8.52636	−0.296491	−0.148245	+	0.988951i	$0.547363\pi$
$828$	−12.0184	−0.417668
$829$	−32.6611	−1.13437	−0.567183	−	0.823592i	$-0.691967\pi$
$829$	−32.6611	−1.13437	−0.567183	+	0.823592i	$0.691967\pi$
$830$	51.7506	1.79629
$831$	−36.9036	−1.28017
$832$	26.0620	0.903537
$833$	9.43093	0.326763
$834$	−43.5121	−1.50670
$835$	16.5724	0.573510
$836$	−2.79254	−0.0965821
$837$	16.4120	0.567282
$838$	−48.0525	−1.65994
$839$	−28.1119	−0.970531	−0.485265	−	0.874367i	$-0.661277\pi$
$839$	−28.1119	−0.970531	−0.485265	+	0.874367i	$0.661277\pi$
$840$	−33.0583	−1.14062
$841$	35.8555	1.23640
$842$	−22.0970	−0.761512
$843$	−18.0353	−0.621168
$844$	0.311367	0.0107177
$845$	−46.6643	−1.60530
$846$	−22.9974	−0.790668
$847$	28.1944	0.968772
$848$	10.9917	0.377457
$849$	33.7607	1.15867
$850$	−14.0574	−0.482164
$851$	−22.6215	−0.775453
$852$	12.0167	0.411685
$853$	−14.4645	−0.495255	−0.247627	−	0.968855i	$-0.579651\pi$
$853$	−14.4645	−0.495255	−0.247627	+	0.968855i	$0.579651\pi$
$854$	16.2866	0.557314
$855$	−7.65680	−0.261857
$856$	8.15020	0.278568
$857$	−13.1808	−0.450249	−0.225124	−	0.974330i	$-0.572279\pi$
$857$	−13.1808	−0.450249	−0.225124	+	0.974330i	$0.572279\pi$
$858$	118.532	4.04661
$859$	−38.1161	−1.30050	−0.650252	−	0.759718i	$-0.725337\pi$
$859$	−38.1161	−1.30050	−0.650252	+	0.759718i	$0.725337\pi$
$860$	−0.953938	−0.0325290
$861$	−46.1151	−1.57160
$862$	18.4867	0.629661
$863$	−8.76534	−0.298376	−0.149188	−	0.988809i	$-0.547666\pi$
$863$	−8.76534	−0.298376	−0.149188	+	0.988809i	$0.547666\pi$
$864$	8.60437	0.292727
$865$	−39.5834	−1.34588
$866$	27.3555	0.929578
$867$	−76.6992	−2.60484
$868$	−11.3765	−0.386142
$869$	−44.5029	−1.50966
$870$	−66.2812	−2.24714
$871$	−76.1910	−2.58163
$872$	−1.92054	−0.0650377
$873$	28.1973	0.954334
$874$	−7.97850	−0.269877
$875$	35.0850	1.18609
$876$	−16.8286	−0.568587
$877$	0.574081	0.0193853	0.00969267	−	0.999953i	$-0.496915\pi$
$877$	0.574081	0.0193853	0.00969267	+	0.999953i	$0.496915\pi$
$878$	12.4365	0.419711
$879$	−72.4500	−2.44368
$880$	−42.5903	−1.43572
$881$	14.2875	0.481356	0.240678	−	0.970605i	$-0.422630\pi$
$881$	14.2875	0.481356	0.240678	+	0.970605i	$0.422630\pi$
$882$	8.92050	0.300369
$883$	44.4388	1.49548	0.747742	−	0.663990i	$-0.231138\pi$
$883$	44.4388	1.49548	0.747742	+	0.663990i	$0.231138\pi$
$884$	25.3829	0.853721
$885$	−8.24230	−0.277062
$886$	23.8761	0.802133
$887$	−26.2591	−0.881695	−0.440847	−	0.897582i	$-0.645322\pi$
$887$	−26.2591	−0.881695	−0.440847	+	0.897582i	$0.645322\pi$
$888$	27.1275	0.910339
$889$	27.8243	0.933197
$890$	−14.8597	−0.498098
$891$	23.4321	0.785005
$892$	−0.445412	−0.0149135
$893$	−3.58284	−0.119895
$894$	9.33237	0.312121
$895$	−8.88710	−0.297063
$896$	39.4590	1.31823
$897$	79.4748	2.65359
$898$	36.3531	1.21312
$899$	51.5759	1.72015
$900$	−3.12041	−0.104014
$901$	−15.3781	−0.512317
$902$	−44.3881	−1.47796
$903$	−6.16855	−0.205277
$904$	1.85070	0.0615532
$905$	12.4017	0.412246
$906$	15.9018	0.528301
$907$	44.8507	1.48924	0.744621	−	0.667487i	$-0.232630\pi$
$907$	44.8507	1.48924	0.744621	+	0.667487i	$0.232630\pi$
$908$	17.7638	0.589511
$909$	70.4679	2.33727
$910$	−55.0708	−1.82558
$911$	−34.9001	−1.15629	−0.578146	−	0.815934i	$-0.696223\pi$
$911$	−34.9001	−1.15629	−0.578146	+	0.815934i	$0.696223\pi$
$912$	12.8061	0.424053
$913$	75.5919	2.50173
$914$	8.95664	0.296259
$915$	17.7087	0.585430
$916$	−15.0481	−0.497205
$917$	37.7269	1.24585
$918$	−28.1124	−0.927848
$919$	47.2289	1.55794	0.778969	−	0.627063i	$-0.215743\pi$
$919$	47.2289	1.55794	0.778969	+	0.627063i	$0.215743\pi$
$920$	−21.3353	−0.703403
$921$	49.8380	1.64222
$922$	12.7990	0.421512
$923$	−45.2643	−1.48989
$924$	21.3555	0.702545
$925$	−5.87334	−0.193114
$926$	12.1389	0.398910
$927$	29.3148	0.962825
$928$	27.0399	0.887627
$929$	−55.9030	−1.83412	−0.917059	−	0.398751i	$-0.869444\pi$
$929$	−55.9030	−1.83412	−0.917059	+	0.398751i	$0.869444\pi$
$930$	−52.7097	−1.72842
$931$	1.38975	0.0455473
$932$	5.00774	0.164034
$933$	−42.3210	−1.38553
$934$	54.1284	1.77113
$935$	59.5864	1.94868
$936$	−54.2883	−1.77447
$937$	−14.2000	−0.463893	−0.231946	−	0.972729i	$-0.574509\pi$
$937$	−14.2000	−0.463893	−0.231946	+	0.972729i	$0.574509\pi$
$938$	−58.4932	−1.90987
$939$	−71.4963	−2.33319
$940$	4.23716	0.138201
$941$	−19.0354	−0.620537	−0.310268	−	0.950649i	$-0.600419\pi$
$941$	−19.0354	−0.620537	−0.310268	+	0.950649i	$0.600419\pi$
$942$	82.7429	2.69591
$943$	−29.7619	−0.969181
$944$	7.85247	0.255576
$945$	14.3137	0.465623
$946$	−5.93754	−0.193046
$947$	40.5491	1.31767	0.658834	−	0.752288i	$-0.271050\pi$
$947$	40.5491	1.31767	0.658834	+	0.752288i	$0.271050\pi$
$948$	−15.8249	−0.513970
$949$	63.3898	2.05772
$950$	−2.07151	−0.0672085
$951$	2.64019	0.0856142
$952$	−44.0630	−1.42809
$953$	−27.5816	−0.893456	−0.446728	−	0.894670i	$-0.647411\pi$
$953$	−27.5816	−0.893456	−0.446728	+	0.894670i	$0.647411\pi$
$954$	−14.5457	−0.470936
$955$	−15.1980	−0.491794
$956$	−12.9719	−0.419542
$957$	−96.8167	−3.12964
$958$	−29.8590	−0.964701
$959$	34.0474	1.09945
$960$	21.7554	0.702151
$961$	10.0154	0.323078
$962$	45.1909	1.45701
$963$	−14.4359	−0.465192
$964$	13.1349	0.423046
$965$	−10.3986	−0.334744
$966$	61.0143	1.96310
$967$	−24.1029	−0.775096	−0.387548	−	0.921849i	$-0.626678\pi$
$967$	−24.1029	−0.775096	−0.387548	+	0.921849i	$0.626678\pi$
$968$	−21.8208	−0.701347
$969$	−17.9165	−0.575561
$970$	−22.1376	−0.710794
$971$	−9.17940	−0.294581	−0.147290	−	0.989093i	$-0.547055\pi$
$971$	−9.17940	−0.294581	−0.147290	+	0.989093i	$0.547055\pi$
$972$	13.0472	0.418488
$973$	29.5294	0.946671
$974$	−48.5839	−1.55673
$975$	20.6345	0.660834
$976$	−16.8711	−0.540031
$977$	48.2240	1.54282	0.771412	−	0.636336i	$-0.219551\pi$
$977$	48.2240	1.54282	0.771412	+	0.636336i	$0.219551\pi$
$978$	−57.6693	−1.84406
$979$	−21.7055	−0.693710
$980$	−1.64356	−0.0525014
$981$	3.40174	0.108609
$982$	14.4506	0.461136
$983$	13.6256	0.434590	0.217295	−	0.976106i	$-0.430277\pi$
$983$	13.6256	0.434590	0.217295	+	0.976106i	$0.430277\pi$
$984$	35.6903	1.13776
$985$	40.4149	1.28773
$986$	−88.3454	−2.81349
$987$	27.3992	0.872126
$988$	3.74045	0.119000
$989$	−3.98108	−0.126591
$990$	56.3613	1.79128
$991$	7.02059	0.223016	0.111508	−	0.993764i	$-0.464432\pi$
$991$	7.02059	0.223016	0.111508	+	0.993764i	$0.464432\pi$
$992$	21.5033	0.682730
$993$	10.1998	0.323680
$994$	−34.7502	−1.10221
$995$	−39.4404	−1.25035
$996$	26.8800	0.851725
$997$	−48.2486	−1.52805	−0.764024	−	0.645188i	$-0.776779\pi$
$997$	−48.2486	−1.52805	−0.764024	+	0.645188i	$0.776779\pi$
$998$	64.9327	2.05541
$999$	−11.7457	−0.371618

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6023.2.a.c.1.101	✓	138

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6023.2.a.c.1.101	✓	138	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:	\( N \)	\(=\)	\( 6023 = 19 \cdot 317 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6023.a (trivial)

\(f(q)\)	\(=\)	\(q+1.61656 q^{2} -2.64019 q^{3} +0.613280 q^{4} -1.92836 q^{5} -4.26804 q^{6} +2.89651 q^{7} -2.24172 q^{8} +3.97063 q^{9} +O(q^{10})\)	\(q+1.61656 q^{2} -2.64019 q^{3} +0.613280 q^{4} -1.92836 q^{5} -4.26804 q^{6} +2.89651 q^{7} -2.24172 q^{8} +3.97063 q^{9} -3.11732 q^{10} -4.55345 q^{11} -1.61918 q^{12} +6.09910 q^{13} +4.68239 q^{14} +5.09125 q^{15} -4.85045 q^{16} +6.78606 q^{17} +6.41877 q^{18} +1.00000 q^{19} -1.18263 q^{20} -7.64734 q^{21} -7.36095 q^{22} -4.93547 q^{23} +5.91858 q^{24} -1.28143 q^{25} +9.85958 q^{26} -2.56264 q^{27} +1.77637 q^{28} -8.05329 q^{29} +8.23033 q^{30} -6.40433 q^{31} -3.35762 q^{32} +12.0220 q^{33} +10.9701 q^{34} -5.58551 q^{35} +2.43511 q^{36} +4.58345 q^{37} +1.61656 q^{38} -16.1028 q^{39} +4.32285 q^{40} +6.03021 q^{41} -12.3624 q^{42} +0.806627 q^{43} -2.79254 q^{44} -7.65680 q^{45} -7.97850 q^{46} -3.58284 q^{47} +12.8061 q^{48} +1.38975 q^{49} -2.07151 q^{50} -17.9165 q^{51} +3.74045 q^{52} -2.26612 q^{53} -4.14267 q^{54} +8.78070 q^{55} -6.49316 q^{56} -2.64019 q^{57} -13.0187 q^{58} -1.61892 q^{59} +3.12236 q^{60} +3.47826 q^{61} -10.3530 q^{62} +11.5009 q^{63} +4.27309 q^{64} -11.7613 q^{65} +19.4343 q^{66} -12.4922 q^{67} +4.16176 q^{68} +13.0306 q^{69} -9.02934 q^{70} -7.42148 q^{71} -8.90104 q^{72} +10.3933 q^{73} +7.40944 q^{74} +3.38321 q^{75} +0.613280 q^{76} -13.1891 q^{77} -26.0312 q^{78} +9.77344 q^{79} +9.35341 q^{80} -5.14601 q^{81} +9.74822 q^{82} -16.6010 q^{83} -4.68996 q^{84} -13.0860 q^{85} +1.30396 q^{86} +21.2622 q^{87} +10.2076 q^{88} +4.76681 q^{89} -12.3777 q^{90} +17.6661 q^{91} -3.02682 q^{92} +16.9087 q^{93} -5.79189 q^{94} -1.92836 q^{95} +8.86476 q^{96} +7.10148 q^{97} +2.24662 q^{98} -18.0801 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 138 q + 11 q^{2} + 29 q^{3} + 157 q^{4} + 12 q^{5} + 8 q^{6} + 18 q^{7} + 33 q^{8} + 171 q^{9}+O(q^{10}) \) 138 * q + 11 * q^2 + 29 * q^3 + 157 * q^4 + 12 * q^5 + 8 * q^6 + 18 * q^7 + 33 * q^8 + 171 * q^9	\( 138 q + 11 q^{2} + 29 q^{3} + 157 q^{4} + 12 q^{5} + 8 q^{6} + 18 q^{7} + 33 q^{8} + 171 q^{9} + 40 q^{10} + 4 q^{11} + 69 q^{12} + 72 q^{13} + 3 q^{14} + 30 q^{15} + 191 q^{16} + 31 q^{17} + 31 q^{18} + 138 q^{19} + 16 q^{20} + 16 q^{21} + 95 q^{22} + 34 q^{23} + 3 q^{24} + 244 q^{25} - 13 q^{26} + 107 q^{27} + 43 q^{28} + 30 q^{29} - 14 q^{30} + 60 q^{31} + 62 q^{32} + 77 q^{33} + 36 q^{34} + 2 q^{35} + 205 q^{36} + 142 q^{37} + 11 q^{38} + 20 q^{39} + 76 q^{40} + 46 q^{41} - 21 q^{42} + 69 q^{43} - 7 q^{44} + 30 q^{45} + 39 q^{46} + 8 q^{47} + 116 q^{48} + 236 q^{49} + 34 q^{51} + 165 q^{52} + 49 q^{53} + 6 q^{55} - 33 q^{56} + 29 q^{57} + 75 q^{58} + 8 q^{59} - 24 q^{60} + 38 q^{61} - 10 q^{62} + 2 q^{63} + 251 q^{64} + 72 q^{65} - 15 q^{66} + 158 q^{67} - 19 q^{68} + 33 q^{69} + 48 q^{70} + 23 q^{71} + 88 q^{72} + 134 q^{73} + 4 q^{74} + 118 q^{75} + 157 q^{76} + 13 q^{77} + 12 q^{78} + 78 q^{79} - 48 q^{80} + 254 q^{81} + 89 q^{82} - 27 q^{83} - 15 q^{84} + 37 q^{85} + 66 q^{86} + 43 q^{87} + 224 q^{88} + 26 q^{89} + 38 q^{90} + 108 q^{91} + 113 q^{92} + 83 q^{93} + 48 q^{94} + 12 q^{95} + 40 q^{96} + 254 q^{97} + 47 q^{98} + 11 q^{99}+O(q^{100}) \) 138 * q + 11 * q^2 + 29 * q^3 + 157 * q^4 + 12 * q^5 + 8 * q^6 + 18 * q^7 + 33 * q^8 + 171 * q^9 + 40 * q^10 + 4 * q^11 + 69 * q^12 + 72 * q^13 + 3 * q^14 + 30 * q^15 + 191 * q^16 + 31 * q^17 + 31 * q^18 + 138 * q^19 + 16 * q^20 + 16 * q^21 + 95 * q^22 + 34 * q^23 + 3 * q^24 + 244 * q^25 - 13 * q^26 + 107 * q^27 + 43 * q^28 + 30 * q^29 - 14 * q^30 + 60 * q^31 + 62 * q^32 + 77 * q^33 + 36 * q^34 + 2 * q^35 + 205 * q^36 + 142 * q^37 + 11 * q^38 + 20 * q^39 + 76 * q^40 + 46 * q^41 - 21 * q^42 + 69 * q^43 - 7 * q^44 + 30 * q^45 + 39 * q^46 + 8 * q^47 + 116 * q^48 + 236 * q^49 + 34 * q^51 + 165 * q^52 + 49 * q^53 + 6 * q^55 - 33 * q^56 + 29 * q^57 + 75 * q^58 + 8 * q^59 - 24 * q^60 + 38 * q^61 - 10 * q^62 + 2 * q^63 + 251 * q^64 + 72 * q^65 - 15 * q^66 + 158 * q^67 - 19 * q^68 + 33 * q^69 + 48 * q^70 + 23 * q^71 + 88 * q^72 + 134 * q^73 + 4 * q^74 + 118 * q^75 + 157 * q^76 + 13 * q^77 + 12 * q^78 + 78 * q^79 - 48 * q^80 + 254 * q^81 + 89 * q^82 - 27 * q^83 - 15 * q^84 + 37 * q^85 + 66 * q^86 + 43 * q^87 + 224 * q^88 + 26 * q^89 + 38 * q^90 + 108 * q^91 + 113 * q^92 + 83 * q^93 + 48 * q^94 + 12 * q^95 + 40 * q^96 + 254 * q^97 + 47 * q^98 + 11 * q^99

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