LMFDB - Embedded newform 8023.2.a.b.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8023,2,Mod(1,8023)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8023, 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("8023.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8023 = 71 \cdot 113 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8023.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:	$64.0639775417$
Analytic rank:	$1$
Dimension:	$155$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	8023.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.68312 q^{2} -1.89873 q^{3} +5.19916 q^{4} -4.03080 q^{5} +5.09454 q^{6} +2.89742 q^{7} -8.58374 q^{8} +0.605189 q^{9} +O(q^{10})$	\(q-2.68312 q^{2} -1.89873 q^{3} +5.19916 q^{4} -4.03080 q^{5} +5.09454 q^{6} +2.89742 q^{7} -8.58374 q^{8} +0.605189 q^{9} +10.8151 q^{10} +4.37119 q^{11} -9.87182 q^{12} -7.11541 q^{13} -7.77414 q^{14} +7.65341 q^{15} +12.6329 q^{16} -5.62071 q^{17} -1.62380 q^{18} +4.41329 q^{19} -20.9568 q^{20} -5.50143 q^{21} -11.7285 q^{22} -1.65643 q^{23} +16.2982 q^{24} +11.2473 q^{25} +19.0915 q^{26} +4.54711 q^{27} +15.0642 q^{28} -8.49738 q^{29} -20.5351 q^{30} +1.05840 q^{31} -16.7283 q^{32} -8.29973 q^{33} +15.0811 q^{34} -11.6789 q^{35} +3.14648 q^{36} +0.261035 q^{37} -11.8414 q^{38} +13.5103 q^{39} +34.5993 q^{40} -7.57547 q^{41} +14.7610 q^{42} +8.95195 q^{43} +22.7265 q^{44} -2.43940 q^{45} +4.44441 q^{46} +5.62870 q^{47} -23.9866 q^{48} +1.39505 q^{49} -30.1780 q^{50} +10.6722 q^{51} -36.9942 q^{52} +6.41130 q^{53} -12.2005 q^{54} -17.6194 q^{55} -24.8707 q^{56} -8.37966 q^{57} +22.7995 q^{58} +0.488914 q^{59} +39.7913 q^{60} -8.30795 q^{61} -2.83982 q^{62} +1.75349 q^{63} +19.6181 q^{64} +28.6808 q^{65} +22.2692 q^{66} -10.6531 q^{67} -29.2229 q^{68} +3.14512 q^{69} +31.3360 q^{70} +1.00000 q^{71} -5.19479 q^{72} +10.8446 q^{73} -0.700389 q^{74} -21.3557 q^{75} +22.9454 q^{76} +12.6652 q^{77} -36.2498 q^{78} +11.2629 q^{79} -50.9208 q^{80} -10.4493 q^{81} +20.3259 q^{82} -2.42078 q^{83} -28.6028 q^{84} +22.6559 q^{85} -24.0192 q^{86} +16.1343 q^{87} -37.5212 q^{88} -2.70177 q^{89} +6.54521 q^{90} -20.6164 q^{91} -8.61205 q^{92} -2.00962 q^{93} -15.1025 q^{94} -17.7891 q^{95} +31.7625 q^{96} -13.9368 q^{97} -3.74310 q^{98} +2.64540 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 155 q - 21 q^{2} - 16 q^{3} + 151 q^{4} - 26 q^{5} - 10 q^{6} - 40 q^{7} - 57 q^{8} + 135 q^{9}+O(q^{10}) $ 155 * q - 21 * q^2 - 16 * q^3 + 151 * q^4 - 26 * q^5 - 10 * q^6 - 40 * q^7 - 57 * q^8 + 135 * q^9	\( 155 q - 21 q^{2} - 16 q^{3} + 151 q^{4} - 26 q^{5} - 10 q^{6} - 40 q^{7} - 57 q^{8} + 135 q^{9} - 2 q^{10} - 24 q^{11} - 32 q^{12} - 62 q^{13} - 18 q^{14} - 12 q^{15} + 155 q^{16} - 129 q^{17} - 42 q^{18} - 18 q^{19} - 59 q^{20} - 45 q^{21} - 17 q^{22} - 38 q^{23} - 27 q^{24} + 129 q^{25} - 44 q^{26} - 43 q^{27} - 100 q^{28} - 52 q^{29} - 39 q^{30} - 56 q^{31} - 145 q^{32} - 126 q^{33} - q^{34} - 49 q^{35} + 131 q^{36} - 30 q^{37} - 91 q^{38} - 29 q^{39} - 5 q^{40} - 163 q^{41} - 80 q^{42} - 15 q^{43} - 118 q^{44} - 66 q^{45} + 2 q^{46} - 111 q^{47} - 89 q^{48} + 101 q^{49} - 121 q^{50} + 5 q^{51} - 111 q^{52} - 93 q^{53} - 68 q^{54} - 60 q^{55} - 27 q^{56} - 106 q^{57} + 16 q^{58} - 79 q^{59} - 103 q^{60} - 74 q^{61} - 102 q^{62} - 118 q^{63} + 175 q^{64} - 109 q^{65} + 65 q^{66} - 18 q^{67} - 346 q^{68} - 39 q^{69} + 32 q^{70} + 155 q^{71} - 203 q^{72} - 108 q^{73} - 87 q^{74} - 22 q^{75} - 16 q^{76} - 121 q^{77} - 75 q^{78} - 6 q^{79} - 136 q^{80} + 107 q^{81} - 30 q^{82} - 116 q^{83} - 5 q^{84} - 53 q^{85} + 8 q^{86} - 100 q^{87} - 43 q^{88} - 189 q^{89} - 76 q^{90} + 14 q^{91} - 99 q^{92} - 72 q^{93} + 17 q^{94} - 18 q^{95} - 50 q^{96} - 184 q^{97} - 249 q^{98} - 114 q^{99}+O(q^{100}) \) 155 * q - 21 * q^2 - 16 * q^3 + 151 * q^4 - 26 * q^5 - 10 * q^6 - 40 * q^7 - 57 * q^8 + 135 * q^9 - 2 * q^10 - 24 * q^11 - 32 * q^12 - 62 * q^13 - 18 * q^14 - 12 * q^15 + 155 * q^16 - 129 * q^17 - 42 * q^18 - 18 * q^19 - 59 * q^20 - 45 * q^21 - 17 * q^22 - 38 * q^23 - 27 * q^24 + 129 * q^25 - 44 * q^26 - 43 * q^27 - 100 * q^28 - 52 * q^29 - 39 * q^30 - 56 * q^31 - 145 * q^32 - 126 * q^33 - q^34 - 49 * q^35 + 131 * q^36 - 30 * q^37 - 91 * q^38 - 29 * q^39 - 5 * q^40 - 163 * q^41 - 80 * q^42 - 15 * q^43 - 118 * q^44 - 66 * q^45 + 2 * q^46 - 111 * q^47 - 89 * q^48 + 101 * q^49 - 121 * q^50 + 5 * q^51 - 111 * q^52 - 93 * q^53 - 68 * q^54 - 60 * q^55 - 27 * q^56 - 106 * q^57 + 16 * q^58 - 79 * q^59 - 103 * q^60 - 74 * q^61 - 102 * q^62 - 118 * q^63 + 175 * q^64 - 109 * q^65 + 65 * q^66 - 18 * q^67 - 346 * q^68 - 39 * q^69 + 32 * q^70 + 155 * q^71 - 203 * q^72 - 108 * q^73 - 87 * q^74 - 22 * q^75 - 16 * q^76 - 121 * q^77 - 75 * q^78 - 6 * q^79 - 136 * q^80 + 107 * q^81 - 30 * q^82 - 116 * q^83 - 5 * q^84 - 53 * q^85 + 8 * q^86 - 100 * q^87 - 43 * q^88 - 189 * q^89 - 76 * q^90 + 14 * q^91 - 99 * q^92 - 72 * q^93 + 17 * q^94 - 18 * q^95 - 50 * q^96 - 184 * q^97 - 249 * q^98 - 114 * 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 $

$2$	−2.68312	−1.89726	−0.948628	−	0.316394i	$-0.897528\pi$
$2$	−2.68312	−1.89726	−0.948628	+	0.316394i	$0.897528\pi$
$3$	−1.89873	−1.09623	−0.548117	−	0.836402i	$-0.684655\pi$
$3$	−1.89873	−1.09623	−0.548117	+	0.836402i	$0.684655\pi$
$4$	5.19916	2.59958
$5$	−4.03080	−1.80263	−0.901314	−	0.433166i	$-0.857396\pi$
$5$	−4.03080	−1.80263	−0.901314	+	0.433166i	$0.857396\pi$
$6$	5.09454	2.07984
$7$	2.89742	1.09512	0.547561	−	0.836766i	$-0.315556\pi$
$7$	2.89742	1.09512	0.547561	+	0.836766i	$0.315556\pi$
$8$	−8.58374	−3.03481
$9$	0.605189	0.201730
$10$	10.8151	3.42005
$11$	4.37119	1.31796	0.658982	−	0.752159i	$-0.270987\pi$
$11$	4.37119	1.31796	0.658982	+	0.752159i	$0.270987\pi$
$12$	−9.87182	−2.84975
$13$	−7.11541	−1.97346	−0.986730	−	0.162369i	$-0.948087\pi$
$13$	−7.11541	−1.97346	−0.986730	+	0.162369i	$0.948087\pi$
$14$	−7.77414	−2.07773
$15$	7.65341	1.97610
$16$	12.6329	3.15823
$17$	−5.62071	−1.36322	−0.681611	−	0.731715i	$-0.738720\pi$
$17$	−5.62071	−1.36322	−0.681611	+	0.731715i	$0.738720\pi$
$18$	−1.62380	−0.382733
$19$	4.41329	1.01248	0.506239	−	0.862393i	$-0.331035\pi$
$19$	4.41329	1.01248	0.506239	+	0.862393i	$0.331035\pi$
$20$	−20.9568	−4.68608
$21$	−5.50143	−1.20051
$22$	−11.7285	−2.50051
$23$	−1.65643	−0.345390	−0.172695	−	0.984975i	$-0.555247\pi$
$23$	−1.65643	−0.345390	−0.172695	+	0.984975i	$0.555247\pi$
$24$	16.2982	3.32687
$25$	11.2473	2.24947
$26$	19.0915	3.74416
$27$	4.54711	0.875091
$28$	15.0642	2.84686
$29$	−8.49738	−1.57792	−0.788961	−	0.614443i	$-0.789381\pi$
$29$	−8.49738	−1.57792	−0.788961	+	0.614443i	$0.789381\pi$
$30$	−20.5351	−3.74917
$31$	1.05840	0.190095	0.0950473	−	0.995473i	$-0.469700\pi$
$31$	1.05840	0.190095	0.0950473	+	0.995473i	$0.469700\pi$
$32$	−16.7283	−2.95717
$33$	−8.29973	−1.44480
$34$	15.0811	2.58638
$35$	−11.6789	−1.97410
$36$	3.14648	0.524413
$37$	0.261035	0.0429138	0.0214569	−	0.999770i	$-0.493170\pi$
$37$	0.261035	0.0429138	0.0214569	+	0.999770i	$0.493170\pi$
$38$	−11.8414	−1.92093
$39$	13.5103	2.16338
$40$	34.5993	5.47064
$41$	−7.57547	−1.18309	−0.591545	−	0.806272i	$-0.701482\pi$
$41$	−7.57547	−1.18309	−0.591545	+	0.806272i	$0.701482\pi$
$42$	14.7610	2.27768
$43$	8.95195	1.36516	0.682580	−	0.730811i	$-0.260858\pi$
$43$	8.95195	1.36516	0.682580	+	0.730811i	$0.260858\pi$
$44$	22.7265	3.42615
$45$	−2.43940	−0.363644
$46$	4.44441	0.655293
$47$	5.62870	0.821030	0.410515	−	0.911854i	$-0.365349\pi$
$47$	5.62870	0.821030	0.410515	+	0.911854i	$0.365349\pi$
$48$	−23.9866	−3.46217
$49$	1.39505	0.199293
$50$	−30.1780	−4.26782
$51$	10.6722	1.49441
$52$	−36.9942	−5.13017
$53$	6.41130	0.880659	0.440330	−	0.897836i	$-0.354862\pi$
$53$	6.41130	0.880659	0.440330	+	0.897836i	$0.354862\pi$
$54$	−12.2005	−1.66027
$55$	−17.6194	−2.37580
$56$	−24.8707	−3.32349
$57$	−8.37966	−1.10991
$58$	22.7995	2.99372
$59$	0.488914	0.0636511	0.0318256	−	0.999493i	$-0.489868\pi$
$59$	0.488914	0.0636511	0.0318256	+	0.999493i	$0.489868\pi$
$60$	39.7913	5.13704
$61$	−8.30795	−1.06372	−0.531862	−	0.846831i	$-0.678508\pi$
$61$	−8.30795	−1.06372	−0.531862	+	0.846831i	$0.678508\pi$
$62$	−2.83982	−0.360658
$63$	1.75349	0.220919
$64$	19.6181	2.45227
$65$	28.6808	3.55741
$66$	22.2692	2.74115
$67$	−10.6531	−1.30149	−0.650744	−	0.759297i	$-0.725543\pi$
$67$	−10.6531	−1.30149	−0.650744	+	0.759297i	$0.725543\pi$
$68$	−29.2229	−3.54380
$69$	3.14512	0.378628
$70$	31.3360	3.74537
$71$	1.00000	0.118678
$71$	1.00000	0.118678
$72$	−5.19479	−0.612212
$73$	10.8446	1.26926	0.634631	−	0.772815i	$-0.281152\pi$
$73$	10.8446	1.26926	0.634631	+	0.772815i	$0.281152\pi$
$74$	−0.700389	−0.0814185
$75$	−21.3557	−2.46594
$76$	22.9454	2.63202
$77$	12.6652	1.44333
$78$	−36.2498	−4.10448
$79$	11.2629	1.26718	0.633589	−	0.773670i	$-0.281581\pi$
$79$	11.2629	1.26718	0.633589	+	0.773670i	$0.281581\pi$
$80$	−50.9208	−5.69312
$81$	−10.4493	−1.16103
$82$	20.3259	2.24463
$83$	−2.42078	−0.265716	−0.132858	−	0.991135i	$-0.542415\pi$
$83$	−2.42078	−0.265716	−0.132858	+	0.991135i	$0.542415\pi$
$84$	−28.6028	−3.12082
$85$	22.6559	2.45738
$86$	−24.0192	−2.59006
$87$	16.1343	1.72977
$88$	−37.5212	−3.99977
$89$	−2.70177	−0.286387	−0.143193	−	0.989695i	$-0.545737\pi$
$89$	−2.70177	−0.286387	−0.143193	+	0.989695i	$0.545737\pi$
$90$	6.54521	0.689925
$91$	−20.6164	−2.16118
$92$	−8.61205	−0.897868
$93$	−2.00962	−0.208388
$94$	−15.1025	−1.55770
$95$	−17.7891	−1.82512
$96$	31.7625	3.24175
$97$	−13.9368	−1.41507	−0.707535	−	0.706678i	$-0.750193\pi$
$97$	−13.9368	−1.41507	−0.707535	+	0.706678i	$0.750193\pi$
$98$	−3.74310	−0.378110
$99$	2.64540	0.265873
$100$	58.4767	5.84767
$101$	11.9493	1.18900	0.594501	−	0.804095i	$-0.297350\pi$
$101$	11.9493	1.18900	0.594501	+	0.804095i	$0.297350\pi$
$102$	−28.6349	−2.83528
$103$	−14.7727	−1.45559	−0.727797	−	0.685793i	$-0.759456\pi$
$103$	−14.7727	−1.45559	−0.727797	+	0.685793i	$0.759456\pi$
$104$	61.0769	5.98908
$105$	22.1752	2.16407
$106$	−17.2023	−1.67084
$107$	−0.272866	−0.0263790	−0.0131895	−	0.999913i	$-0.504198\pi$
$107$	−0.272866	−0.0263790	−0.0131895	+	0.999913i	$0.504198\pi$
$108$	23.6411	2.27487
$109$	8.34647	0.799447	0.399723	−	0.916636i	$-0.369106\pi$
$109$	8.34647	0.799447	0.399723	+	0.916636i	$0.369106\pi$
$110$	47.2750	4.50750
$111$	−0.495635	−0.0470436
$112$	36.6030	3.45865
$113$	1.00000	0.0940721
$113$	1.00000	0.0940721
$114$	22.4837	2.10579
$115$	6.67674	0.622609
$116$	−44.1792	−4.10194
$117$	−4.30617	−0.398106
$118$	−1.31182	−0.120763
$119$	−16.2856	−1.49289
$120$	−65.6949	−5.99710
$121$	8.10732	0.737029
$122$	22.2913	2.01816
$123$	14.3838	1.29694
$124$	5.50280	0.494166
$125$	−25.1818	−2.25233
$126$	−4.70483	−0.419140
$127$	−21.4812	−1.90615	−0.953074	−	0.302738i	$-0.902099\pi$
$127$	−21.4812	−1.90615	−0.953074	+	0.302738i	$0.902099\pi$
$128$	−19.1814	−1.69541
$129$	−16.9974	−1.49653
$130$	−76.9542	−6.74933
$131$	11.5068	1.00535	0.502676	−	0.864475i	$-0.332349\pi$
$131$	11.5068	1.00535	0.502676	+	0.864475i	$0.332349\pi$
$132$	−43.1516	−3.75587
$133$	12.7872	1.10879
$134$	28.5837	2.46926
$135$	−18.3285	−1.57746
$136$	48.2467	4.13712
$137$	−21.6005	−1.84545	−0.922726	−	0.385457i	$-0.874044\pi$
$137$	−21.6005	−1.84545	−0.922726	+	0.385457i	$0.874044\pi$
$138$	−8.43875	−0.718354
$139$	−3.48722	−0.295782	−0.147891	−	0.989004i	$-0.547249\pi$
$139$	−3.48722	−0.295782	−0.147891	+	0.989004i	$0.547249\pi$
$140$	−60.7206	−5.13183
$141$	−10.6874	−0.900041
$142$	−2.68312	−0.225163
$143$	−31.1028	−2.60095
$144$	7.64532	0.637110
$145$	34.2512	2.84441
$146$	−29.0974	−2.40812
$147$	−2.64883	−0.218472
$148$	1.35716	0.111558
$149$	15.6532	1.28236	0.641180	−	0.767391i	$-0.278445\pi$
$149$	15.6532	1.28236	0.641180	+	0.767391i	$0.278445\pi$
$150$	57.3000	4.67853
$151$	0.534149	0.0434685	0.0217342	−	0.999764i	$-0.493081\pi$
$151$	0.534149	0.0434685	0.0217342	+	0.999764i	$0.493081\pi$
$152$	−37.8825	−3.07268
$153$	−3.40159	−0.275002
$154$	−33.9823	−2.73837
$155$	−4.26620	−0.342670
$156$	70.2421	5.62387
$157$	−6.74222	−0.538088	−0.269044	−	0.963128i	$-0.586708\pi$
$157$	−6.74222	−0.538088	−0.269044	+	0.963128i	$0.586708\pi$
$158$	−30.2198	−2.40416
$159$	−12.1733	−0.965409
$160$	67.4283	5.33067
$161$	−4.79938	−0.378244
$162$	28.0368	2.20278
$163$	14.0139	1.09766	0.548828	−	0.835935i	$-0.315074\pi$
$163$	14.0139	1.09766	0.548828	+	0.835935i	$0.315074\pi$
$164$	−39.3861	−3.07554
$165$	33.4545	2.60443
$166$	6.49527	0.504130
$167$	6.15734	0.476469	0.238235	−	0.971208i	$-0.423431\pi$
$167$	6.15734	0.476469	0.238235	+	0.971208i	$0.423431\pi$
$168$	47.2229	3.64332
$169$	37.6291	2.89455
$170$	−60.7887	−4.66228
$171$	2.67088	0.204247
$172$	46.5426	3.54884
$173$	3.11260	0.236647	0.118323	−	0.992975i	$-0.462248\pi$
$173$	3.11260	0.236647	0.118323	+	0.992975i	$0.462248\pi$
$174$	−43.2902	−3.28182
$175$	32.5883	2.46344
$176$	55.2210	4.16244
$177$	−0.928317	−0.0697766
$178$	7.24918	0.543349
$179$	11.0599	0.826655	0.413327	−	0.910582i	$-0.364366\pi$
$179$	11.0599	0.826655	0.413327	+	0.910582i	$0.364366\pi$
$180$	−12.6828	−0.945321
$181$	−1.40536	−0.104460	−0.0522298	−	0.998635i	$-0.516633\pi$
$181$	−1.40536	−0.104460	−0.0522298	+	0.998635i	$0.516633\pi$
$182$	55.3162	4.10031
$183$	15.7746	1.16609
$184$	14.2184	1.04819
$185$	−1.05218	−0.0773577
$186$	5.39207	0.395366
$187$	−24.5692	−1.79668
$188$	29.2645	2.13433
$189$	13.1749	0.958332
$190$	47.7303	3.46272
$191$	7.08443	0.512611	0.256306	−	0.966596i	$-0.417495\pi$
$191$	7.08443	0.512611	0.256306	+	0.966596i	$0.417495\pi$
$192$	−37.2496	−2.68826
$193$	8.96123	0.645043	0.322522	−	0.946562i	$-0.395470\pi$
$193$	8.96123	0.645043	0.322522	+	0.946562i	$0.395470\pi$
$194$	37.3942	2.68475
$195$	−54.4572	−3.89976
$196$	7.25310	0.518079
$197$	16.3366	1.16393	0.581967	−	0.813212i	$-0.302283\pi$
$197$	16.3366	1.16393	0.581967	+	0.813212i	$0.302283\pi$
$198$	−7.09794	−0.504428
$199$	16.1215	1.14282	0.571412	−	0.820664i	$-0.306396\pi$
$199$	16.1215	1.14282	0.571412	+	0.820664i	$0.306396\pi$
$200$	−96.5443	−6.82671
$201$	20.2275	1.42674
$202$	−32.0615	−2.25584
$203$	−24.6205	−1.72802
$204$	55.4866	3.88484
$205$	30.5352	2.13267
$206$	39.6369	2.76163
$207$	−1.00245	−0.0696754
$208$	−89.8886	−6.23265
$209$	19.2913	1.33441
$210$	−59.4987	−4.10580
$211$	9.91358	0.682479	0.341239	−	0.939976i	$-0.389153\pi$
$211$	9.91358	0.682479	0.341239	+	0.939976i	$0.389153\pi$
$212$	33.3334	2.28934
$213$	−1.89873	−0.130099
$214$	0.732135	0.0500477
$215$	−36.0835	−2.46087
$216$	−39.0312	−2.65574
$217$	3.06664	0.208177
$218$	−22.3946	−1.51676
$219$	−20.5910	−1.39141
$220$	−91.6060	−6.17608
$221$	39.9936	2.69026
$222$	1.32985	0.0892538
$223$	6.92418	0.463677	0.231839	−	0.972754i	$-0.425526\pi$
$223$	6.92418	0.463677	0.231839	+	0.972754i	$0.425526\pi$
$224$	−48.4688	−3.23846
$225$	6.80677	0.453785
$226$	−2.68312	−0.178479
$227$	−9.37278	−0.622093	−0.311047	−	0.950395i	$-0.600680\pi$
$227$	−9.37278	−0.622093	−0.311047	+	0.950395i	$0.600680\pi$
$228$	−43.5672	−2.88531
$229$	15.7793	1.04273	0.521364	−	0.853334i	$-0.325423\pi$
$229$	15.7793	1.04273	0.521364	+	0.853334i	$0.325423\pi$
$230$	−17.9145	−1.18125
$231$	−24.0478	−1.58223
$232$	72.9393	4.78870
$233$	−10.2629	−0.672344	−0.336172	−	0.941801i	$-0.609132\pi$
$233$	−10.2629	−0.672344	−0.336172	+	0.941801i	$0.609132\pi$
$234$	11.5540	0.755309
$235$	−22.6881	−1.48001
$236$	2.54194	0.165466
$237$	−21.3853	−1.38912
$238$	43.6962	2.83240
$239$	16.1622	1.04544	0.522722	−	0.852503i	$-0.324916\pi$
$239$	16.1622	1.04544	0.522722	+	0.852503i	$0.324916\pi$
$240$	96.6851	6.24100
$241$	−4.25546	−0.274118	−0.137059	−	0.990563i	$-0.543765\pi$
$241$	−4.25546	−0.274118	−0.137059	+	0.990563i	$0.543765\pi$
$242$	−21.7529	−1.39833
$243$	6.19914	0.397675
$244$	−43.1944	−2.76524
$245$	−5.62318	−0.359252
$246$	−38.5936	−2.46064
$247$	−31.4024	−1.99809
$248$	−9.08505	−0.576901
$249$	4.59642	0.291287
$250$	67.5658	4.27324
$251$	5.33926	0.337011	0.168505	−	0.985701i	$-0.446106\pi$
$251$	5.33926	0.337011	0.168505	+	0.985701i	$0.446106\pi$
$252$	9.11667	0.574296
$253$	−7.24058	−0.455211
$254$	57.6367	3.61645
$255$	−43.0176	−2.69387
$256$	12.2298	0.764364
$257$	−21.7093	−1.35419	−0.677095	−	0.735895i	$-0.736762\pi$
$257$	−21.7093	−1.35419	−0.677095	+	0.735895i	$0.736762\pi$
$258$	45.6061	2.83931
$259$	0.756327	0.0469959
$260$	149.116	9.24778
$261$	−5.14252	−0.318314
$262$	−30.8741	−1.90741
$263$	10.4685	0.645514	0.322757	−	0.946482i	$-0.395390\pi$
$263$	10.4685	0.645514	0.322757	+	0.946482i	$0.395390\pi$
$264$	71.2427	4.38469
$265$	−25.8426	−1.58750
$266$	−34.3095	−2.10365
$267$	5.12994	0.313947
$268$	−55.3874	−3.38332
$269$	−28.3784	−1.73026	−0.865129	−	0.501549i	$-0.832764\pi$
$269$	−28.3784	−1.73026	−0.865129	+	0.501549i	$0.832764\pi$
$270$	49.1776	2.99285
$271$	16.3569	0.993613	0.496806	−	0.867861i	$-0.334506\pi$
$271$	16.3569	0.993613	0.496806	+	0.867861i	$0.334506\pi$
$272$	−71.0060	−4.30537
$273$	39.1450	2.36916
$274$	57.9567	3.50129
$275$	49.1643	2.96472
$276$	16.3520	0.984274
$277$	2.99216	0.179781	0.0898906	−	0.995952i	$-0.471348\pi$
$277$	2.99216	0.179781	0.0898906	+	0.995952i	$0.471348\pi$
$278$	9.35665	0.561175
$279$	0.640533	0.0383477
$280$	100.249	5.99102
$281$	−23.4790	−1.40064	−0.700318	−	0.713831i	$-0.746959\pi$
$281$	−23.4790	−1.40064	−0.700318	+	0.713831i	$0.746959\pi$
$282$	28.6756	1.70761
$283$	−26.2876	−1.56263	−0.781316	−	0.624135i	$-0.785451\pi$
$283$	−26.2876	−1.56263	−0.781316	+	0.624135i	$0.785451\pi$
$284$	5.19916	0.308513
$285$	33.7767	2.00076
$286$	83.4528	4.93467
$287$	−21.9493	−1.29563
$288$	−10.1238	−0.596549
$289$	14.5923	0.858372
$290$	−91.9003	−5.39657
$291$	26.4623	1.55125
$292$	56.3827	3.29955
$293$	5.17317	0.302220	0.151110	−	0.988517i	$-0.451715\pi$
$293$	5.17317	0.302220	0.151110	+	0.988517i	$0.451715\pi$
$294$	7.10715	0.414498
$295$	−1.97071	−0.114739
$296$	−2.24065	−0.130235
$297$	19.8763	1.15334
$298$	−41.9995	−2.43296
$299$	11.7862	0.681613
$300$	−111.032	−6.41042
$301$	25.9376	1.49502
$302$	−1.43319	−0.0824708
$303$	−22.6886	−1.30343
$304$	55.7528	3.19764
$305$	33.4877	1.91750
$306$	9.12690	0.521750
$307$	24.2620	1.38471	0.692353	−	0.721559i	$-0.256574\pi$
$307$	24.2620	1.38471	0.692353	+	0.721559i	$0.256574\pi$
$308$	65.8483	3.75206
$309$	28.0493	1.59567
$310$	11.4468	0.650132
$311$	12.4491	0.705924	0.352962	−	0.935638i	$-0.385174\pi$
$311$	12.4491	0.705924	0.352962	+	0.935638i	$0.385174\pi$
$312$	−115.969	−6.56544
$313$	−18.0836	−1.02214	−0.511072	−	0.859538i	$-0.670751\pi$
$313$	−18.0836	−1.02214	−0.511072	+	0.859538i	$0.670751\pi$
$314$	18.0902	1.02089
$315$	−7.06796	−0.398235
$316$	58.5577	3.29413
$317$	30.9549	1.73860	0.869300	−	0.494285i	$-0.164570\pi$
$317$	30.9549	1.73860	0.869300	+	0.494285i	$0.164570\pi$
$318$	32.6626	1.83163
$319$	−37.1437	−2.07965
$320$	−79.0768	−4.42053
$321$	0.518101	0.0289176
$322$	12.8773	0.717626
$323$	−24.8058	−1.38023
$324$	−54.3276	−3.01820
$325$	−80.0295	−4.43924
$326$	−37.6011	−2.08253
$327$	−15.8477	−0.876381
$328$	65.0259	3.59046
$329$	16.3087	0.899128
$330$	−89.7627	−4.94127
$331$	32.3319	1.77712	0.888561	−	0.458758i	$-0.151706\pi$
$331$	32.3319	1.77712	0.888561	+	0.458758i	$0.151706\pi$
$332$	−12.5860	−0.690749
$333$	0.157975	0.00865700
$334$	−16.5209	−0.903984
$335$	42.9407	2.34610
$336$	−69.4993	−3.79150
$337$	24.6750	1.34413	0.672066	−	0.740491i	$-0.265407\pi$
$337$	24.6750	1.34413	0.672066	+	0.740491i	$0.265407\pi$
$338$	−100.964	−5.49169
$339$	−1.89873	−0.103125
$340$	117.792	6.38816
$341$	4.62648	0.250538
$342$	−7.16629	−0.387509
$343$	−16.2399	−0.876872
$344$	−76.8412	−4.14300
$345$	−12.6773	−0.682526
$346$	−8.35150	−0.448979
$347$	−3.86435	−0.207449	−0.103725	−	0.994606i	$-0.533076\pi$
$347$	−3.86435	−0.207449	−0.103725	+	0.994606i	$0.533076\pi$
$348$	83.8845	4.49668
$349$	14.1708	0.758543	0.379272	−	0.925285i	$-0.376175\pi$
$349$	14.1708	0.758543	0.379272	+	0.925285i	$0.376175\pi$
$350$	−87.4384	−4.67378
$351$	−32.3545	−1.72696
$352$	−73.1224	−3.89744
$353$	7.15123	0.380621	0.190311	−	0.981724i	$-0.439050\pi$
$353$	7.15123	0.380621	0.190311	+	0.981724i	$0.439050\pi$
$354$	2.49079	0.132384
$355$	−4.03080	−0.213933
$356$	−14.0469	−0.744485
$357$	30.9219	1.63656
$358$	−29.6751	−1.56838
$359$	8.86323	0.467783	0.233892	−	0.972263i	$-0.424854\pi$
$359$	8.86323	0.467783	0.233892	+	0.972263i	$0.424854\pi$
$360$	20.9392	1.10359
$361$	0.477122	0.0251117
$362$	3.77076	0.198187
$363$	−15.3936	−0.807956
$364$	−107.188	−5.61816
$365$	−43.7123	−2.28801
$366$	−42.3252	−2.21237
$367$	4.18075	0.218233	0.109117	−	0.994029i	$-0.465198\pi$
$367$	4.18075	0.218233	0.109117	+	0.994029i	$0.465198\pi$
$368$	−20.9256	−1.09082
$369$	−4.58460	−0.238665
$370$	2.82313	0.146767
$371$	18.5762	0.964430
$372$	−10.4483	−0.541722
$373$	−23.0331	−1.19261	−0.596305	−	0.802758i	$-0.703365\pi$
$373$	−23.0331	−1.19261	−0.596305	+	0.802758i	$0.703365\pi$
$374$	65.9222	3.40875
$375$	47.8135	2.46908
$376$	−48.3153	−2.49167
$377$	60.4623	3.11397
$378$	−35.3499	−1.81820
$379$	−23.6161	−1.21308	−0.606539	−	0.795053i	$-0.707443\pi$
$379$	−23.6161	−1.21308	−0.606539	+	0.795053i	$0.707443\pi$
$380$	−92.4883	−4.74455
$381$	40.7871	2.08958
$382$	−19.0084	−0.972554
$383$	11.5305	0.589180	0.294590	−	0.955624i	$-0.404817\pi$
$383$	11.5305	0.589180	0.294590	+	0.955624i	$0.404817\pi$
$384$	36.4204	1.85857
$385$	−51.0508	−2.60179
$386$	−24.0441	−1.22381
$387$	5.41763	0.275393
$388$	−72.4598	−3.67859
$389$	25.6639	1.30121	0.650606	−	0.759415i	$-0.274515\pi$
$389$	25.6639	1.30121	0.650606	+	0.759415i	$0.274515\pi$
$390$	146.115	7.39884
$391$	9.31031	0.470843
$392$	−11.9748	−0.604818
$393$	−21.8483	−1.10210
$394$	−43.8331	−2.20828
$395$	−45.3986	−2.28425
$396$	13.7539	0.691157
$397$	27.9804	1.40430	0.702149	−	0.712030i	$-0.252224\pi$
$397$	27.9804	1.40430	0.702149	+	0.712030i	$0.252224\pi$
$398$	−43.2560	−2.16823
$399$	−24.2794	−1.21549
$400$	142.087	7.10435
$401$	36.1227	1.80388	0.901940	−	0.431860i	$-0.142143\pi$
$401$	36.1227	1.80388	0.901940	+	0.431860i	$0.142143\pi$
$402$	−54.2728	−2.70688
$403$	−7.53096	−0.375144
$404$	62.1265	3.09091
$405$	42.1191	2.09291
$406$	66.0598	3.27849
$407$	1.14103	0.0565589
$408$	−91.6076	−4.53525
$409$	10.4228	0.515376	0.257688	−	0.966228i	$-0.417039\pi$
$409$	10.4228	0.515376	0.257688	+	0.966228i	$0.417039\pi$
$410$	−81.9298	−4.04622
$411$	41.0135	2.02305
$412$	−76.8054	−3.78393
$413$	1.41659	0.0697058
$414$	2.68971	0.132192
$415$	9.75769	0.478986
$416$	119.029	5.83585
$417$	6.62130	0.324247
$418$	−51.7611	−2.53172
$419$	−11.4459	−0.559170	−0.279585	−	0.960121i	$-0.590197\pi$
$419$	−11.4459	−0.559170	−0.279585	+	0.960121i	$0.590197\pi$
$420$	115.292	5.62568
$421$	12.6869	0.618323	0.309162	−	0.951010i	$-0.399952\pi$
$421$	12.6869	0.618323	0.309162	+	0.951010i	$0.399952\pi$
$422$	−26.5994	−1.29484
$423$	3.40643	0.165626
$424$	−55.0329	−2.67264
$425$	−63.2180	−3.06652
$426$	5.09454	0.246831
$427$	−24.0716	−1.16491
$428$	−1.41868	−0.0685743
$429$	59.0560	2.85125
$430$	96.8166	4.66891
$431$	2.55155	0.122904	0.0614520	−	0.998110i	$-0.480427\pi$
$431$	2.55155	0.122904	0.0614520	+	0.998110i	$0.480427\pi$
$432$	57.4433	2.76374
$433$	18.4170	0.885063	0.442531	−	0.896753i	$-0.354081\pi$
$433$	18.4170	0.885063	0.442531	+	0.896753i	$0.354081\pi$
$434$	−8.22817	−0.394965
$435$	−65.0339	−3.11814
$436$	43.3946	2.07823
$437$	−7.31031	−0.349699
$438$	55.2482	2.63986
$439$	−2.68467	−0.128132	−0.0640661	−	0.997946i	$-0.520407\pi$
$439$	−2.68467	−0.128132	−0.0640661	+	0.997946i	$0.520407\pi$
$440$	151.240	7.21010
$441$	0.844271	0.0402034
$442$	−107.308	−5.10412
$443$	19.7893	0.940219	0.470109	−	0.882608i	$-0.344214\pi$
$443$	19.7893	0.940219	0.470109	+	0.882608i	$0.344214\pi$
$444$	−2.57689	−0.122294
$445$	10.8903	0.516249
$446$	−18.5784	−0.879714
$447$	−29.7212	−1.40577
$448$	56.8420	2.68553
$449$	−21.8176	−1.02964	−0.514818	−	0.857300i	$-0.672140\pi$
$449$	−21.8176	−1.02964	−0.514818	+	0.857300i	$0.672140\pi$
$450$	−18.2634	−0.860946
$451$	−33.1139	−1.55927
$452$	5.19916	0.244548
$453$	−1.01421	−0.0476516
$454$	25.1483	1.18027
$455$	83.1004	3.89581
$456$	71.9289	3.36838
$457$	−2.87076	−0.134289	−0.0671443	−	0.997743i	$-0.521389\pi$
$457$	−2.87076	−0.134289	−0.0671443	+	0.997743i	$0.521389\pi$
$458$	−42.3379	−1.97832
$459$	−25.5580	−1.19294
$460$	34.7134	1.61852
$461$	6.46628	0.301165	0.150582	−	0.988597i	$-0.451885\pi$
$461$	6.46628	0.301165	0.150582	+	0.988597i	$0.451885\pi$
$462$	64.5233	3.00190
$463$	19.7523	0.917967	0.458983	−	0.888445i	$-0.348214\pi$
$463$	19.7523	0.917967	0.458983	+	0.888445i	$0.348214\pi$
$464$	−107.347	−4.98345
$465$	8.10038	0.375646
$466$	27.5366	1.27561
$467$	17.6221	0.815452	0.407726	−	0.913104i	$-0.366322\pi$
$467$	17.6221	0.815452	0.407726	+	0.913104i	$0.366322\pi$
$468$	−22.3885	−1.03491
$469$	−30.8666	−1.42529
$470$	60.8751	2.80796
$471$	12.8017	0.589871
$472$	−4.19671	−0.193169
$473$	39.1307	1.79923
$474$	57.3794	2.63552
$475$	49.6378	2.27754
$476$	−84.6712	−3.88090
$477$	3.88005	0.177655
$478$	−43.3651	−1.98348
$479$	23.6884	1.08235	0.541175	−	0.840910i	$-0.317980\pi$
$479$	23.6884	1.08235	0.541175	+	0.840910i	$0.317980\pi$
$480$	−128.028	−5.84367
$481$	−1.85737	−0.0846887
$482$	11.4179	0.520073
$483$	9.11274	0.414644
$484$	42.1512	1.91596
$485$	56.1765	2.55084
$486$	−16.6331	−0.754492
$487$	−25.6824	−1.16378	−0.581891	−	0.813267i	$-0.697687\pi$
$487$	−25.6824	−1.16378	−0.581891	+	0.813267i	$0.697687\pi$
$488$	71.3133	3.22820
$489$	−26.6087	−1.20329
$490$	15.0877	0.681592
$491$	6.40598	0.289098	0.144549	−	0.989498i	$-0.453827\pi$
$491$	6.40598	0.289098	0.144549	+	0.989498i	$0.453827\pi$
$492$	74.7837	3.37151
$493$	47.7612	2.15106
$494$	84.2565	3.79088
$495$	−10.6631	−0.479269
$496$	13.3707	0.600363
$497$	2.89742	0.129967
$498$	−12.3328	−0.552645
$499$	−40.4860	−1.81240	−0.906201	−	0.422848i	$-0.861030\pi$
$499$	−40.4860	−1.81240	−0.906201	+	0.422848i	$0.861030\pi$
$500$	−130.924	−5.85510
$501$	−11.6912	−0.522322
$502$	−14.3259	−0.639396
$503$	−6.00757	−0.267864	−0.133932	−	0.990990i	$-0.542760\pi$
$503$	−6.00757	−0.267864	−0.133932	+	0.990990i	$0.542760\pi$
$504$	−15.0515	−0.670447
$505$	−48.1653	−2.14333
$506$	19.4274	0.863652
$507$	−71.4476	−3.17310
$508$	−111.684	−4.95518
$509$	−11.5806	−0.513300	−0.256650	−	0.966504i	$-0.582619\pi$
$509$	−11.5806	−0.513300	−0.256650	+	0.966504i	$0.582619\pi$
$510$	115.422	5.11095
$511$	31.4213	1.39000
$512$	5.54868	0.245219
$513$	20.0677	0.886011
$514$	58.2488	2.56925
$515$	59.5456	2.62389
$516$	−88.3720	−3.89036
$517$	24.6041	1.08209
$518$	−2.02932	−0.0891632
$519$	−5.91000	−0.259420
$520$	−246.189	−10.7961
$521$	10.1265	0.443652	0.221826	−	0.975086i	$-0.428798\pi$
$521$	10.1265	0.443652	0.221826	+	0.975086i	$0.428798\pi$
$522$	13.7980	0.603923
$523$	1.05552	0.0461545	0.0230773	−	0.999734i	$-0.492654\pi$
$523$	1.05552	0.0461545	0.0230773	+	0.999734i	$0.492654\pi$
$524$	59.8255	2.61349
$525$	−61.8765	−2.70051
$526$	−28.0882	−1.22470
$527$	−5.94896	−0.259141
$528$	−104.850	−4.56301
$529$	−20.2562	−0.880706
$530$	69.3390	3.01190
$531$	0.295885	0.0128403
$532$	66.4825	2.88238
$533$	53.9026	2.33478
$534$	−13.7643	−0.595638
$535$	1.09987	0.0475515
$536$	91.4438	3.94977
$537$	−20.9998	−0.906208
$538$	76.1427	3.28274
$539$	6.09804	0.262661
$540$	−95.2927	−4.10074
$541$	−38.5840	−1.65885	−0.829427	−	0.558615i	$-0.811333\pi$
$541$	−38.5840	−1.65885	−0.829427	+	0.558615i	$0.811333\pi$
$542$	−43.8877	−1.88514
$543$	2.66841	0.114512
$544$	94.0246	4.03127
$545$	−33.6429	−1.44111
$546$	−105.031	−4.49490
$547$	−9.67459	−0.413656	−0.206828	−	0.978377i	$-0.566314\pi$
$547$	−9.67459	−0.413656	−0.206828	+	0.978377i	$0.566314\pi$
$548$	−112.304	−4.79740
$549$	−5.02788	−0.214585
$550$	−131.914	−5.62483
$551$	−37.5014	−1.59761
$552$	−26.9969	−1.14906
$553$	32.6334	1.38771
$554$	−8.02833	−0.341091
$555$	1.99781	0.0848021
$556$	−18.1306	−0.768910
$557$	−1.65147	−0.0699751	−0.0349876	−	0.999388i	$-0.511139\pi$
$557$	−1.65147	−0.0699751	−0.0349876	+	0.999388i	$0.511139\pi$
$558$	−1.71863	−0.0727555
$559$	−63.6968	−2.69409
$560$	−147.539	−6.23467
$561$	46.6503	1.96958
$562$	62.9970	2.65737
$563$	−25.1024	−1.05794	−0.528971	−	0.848640i	$-0.677422\pi$
$563$	−25.1024	−1.05794	−0.528971	+	0.848640i	$0.677422\pi$
$564$	−55.5655	−2.33973
$565$	−4.03080	−0.169577
$566$	70.5328	2.96471
$567$	−30.2761	−1.27148
$568$	−8.58374	−0.360166
$569$	−26.9947	−1.13167	−0.565837	−	0.824517i	$-0.691447\pi$
$569$	−26.9947	−1.13167	−0.565837	+	0.824517i	$0.691447\pi$
$570$	−90.6272	−3.79595
$571$	41.3086	1.72871	0.864355	−	0.502882i	$-0.167727\pi$
$571$	41.3086	1.72871	0.864355	+	0.502882i	$0.167727\pi$
$572$	−161.709	−6.76138
$573$	−13.4514	−0.561942
$574$	58.8928	2.45814
$575$	−18.6304	−0.776943
$576$	11.8727	0.494696
$577$	−25.3220	−1.05417	−0.527085	−	0.849812i	$-0.676715\pi$
$577$	−25.3220	−1.05417	−0.527085	+	0.849812i	$0.676715\pi$
$578$	−39.1530	−1.62855
$579$	−17.0150	−0.707118
$580$	178.077	7.39427
$581$	−7.01403	−0.290991
$582$	−71.0017	−2.94312
$583$	28.0250	1.16068
$584$	−93.0871	−3.85197
$585$	17.3573	0.717637
$586$	−13.8803	−0.573388
$587$	−42.2175	−1.74250	−0.871251	−	0.490838i	$-0.836691\pi$
$587$	−42.2175	−1.74250	−0.871251	+	0.490838i	$0.836691\pi$
$588$	−13.7717	−0.567936
$589$	4.67103	0.192467
$590$	5.28767	0.217690
$591$	−31.0189	−1.27595
$592$	3.29763	0.135532
$593$	−39.4111	−1.61842	−0.809210	−	0.587519i	$-0.800105\pi$
$593$	−39.4111	−1.61842	−0.809210	+	0.587519i	$0.800105\pi$
$594$	−53.3305	−2.18818
$595$	65.6438	2.69113
$596$	81.3834	3.33360
$597$	−30.6104	−1.25280
$598$	−31.6238	−1.29319
$599$	−18.3343	−0.749117	−0.374559	−	0.927203i	$-0.622206\pi$
$599$	−18.3343	−0.749117	−0.374559	+	0.927203i	$0.622206\pi$
$600$	183.312	7.48368
$601$	−17.3879	−0.709266	−0.354633	−	0.935006i	$-0.615394\pi$
$601$	−17.3879	−0.709266	−0.354633	+	0.935006i	$0.615394\pi$
$602$	−69.5938	−2.83643
$603$	−6.44717	−0.262549
$604$	2.77713	0.113000
$605$	−32.6790	−1.32859
$606$	60.8763	2.47293
$607$	34.9978	1.42052	0.710259	−	0.703940i	$-0.248578\pi$
$607$	34.9978	1.42052	0.710259	+	0.703940i	$0.248578\pi$
$608$	−73.8267	−2.99407
$609$	46.7477	1.89431
$610$	−89.8516	−3.63799
$611$	−40.0505	−1.62027
$612$	−17.6854	−0.714891
$613$	8.12896	0.328326	0.164163	−	0.986433i	$-0.447508\pi$
$613$	8.12896	0.328326	0.164163	+	0.986433i	$0.447508\pi$
$614$	−65.0980	−2.62714
$615$	−57.9782	−2.33791
$616$	−108.715	−4.38024
$617$	18.1680	0.731415	0.365707	−	0.930730i	$-0.380827\pi$
$617$	18.1680	0.731415	0.365707	+	0.930730i	$0.380827\pi$
$618$	−75.2599	−3.02740
$619$	−2.92712	−0.117651	−0.0588254	−	0.998268i	$-0.518736\pi$
$619$	−2.92712	−0.117651	−0.0588254	+	0.998268i	$0.518736\pi$
$620$	−22.1807	−0.890797
$621$	−7.53197	−0.302247
$622$	−33.4025	−1.33932
$623$	−7.82816	−0.313629
$624$	170.674	6.83245
$625$	45.2659	1.81064
$626$	48.5205	1.93927
$627$	−36.6291	−1.46283
$628$	−35.0539	−1.39880
$629$	−1.46720	−0.0585010
$630$	18.9642	0.755553
$631$	34.9933	1.39306	0.696530	−	0.717527i	$-0.254726\pi$
$631$	34.9933	1.39306	0.696530	+	0.717527i	$0.254726\pi$
$632$	−96.6780	−3.84565
$633$	−18.8232	−0.748157
$634$	−83.0558	−3.29857
$635$	86.5864	3.43607
$636$	−63.2912	−2.50966
$637$	−9.92638	−0.393297
$638$	99.6611	3.94562
$639$	0.605189	0.0239409
$640$	77.3164	3.05620
$641$	19.7603	0.780486	0.390243	−	0.920712i	$-0.372391\pi$
$641$	19.7603	0.780486	0.390243	+	0.920712i	$0.372391\pi$
$642$	−1.39013	−0.0548640
$643$	−15.9234	−0.627958	−0.313979	−	0.949430i	$-0.601662\pi$
$643$	−15.9234	−0.627958	−0.313979	+	0.949430i	$0.601662\pi$
$644$	−24.9527	−0.983275
$645$	68.5130	2.69770
$646$	66.5571	2.61865
$647$	21.7455	0.854902	0.427451	−	0.904039i	$-0.359412\pi$
$647$	21.7455	0.854902	0.427451	+	0.904039i	$0.359412\pi$
$648$	89.6942	3.52352
$649$	2.13714	0.0838899
$650$	214.729	8.42237
$651$	−5.82272	−0.228211
$652$	72.8607	2.85344
$653$	−12.3655	−0.483899	−0.241949	−	0.970289i	$-0.577787\pi$
$653$	−12.3655	−0.483899	−0.241949	+	0.970289i	$0.577787\pi$
$654$	42.5214	1.66272
$655$	−46.3815	−1.81227
$656$	−95.7005	−3.73648
$657$	6.56303	0.256048
$658$	−43.7583	−1.70588
$659$	12.0873	0.470855	0.235428	−	0.971892i	$-0.424351\pi$
$659$	12.0873	0.470855	0.235428	+	0.971892i	$0.424351\pi$
$660$	173.935	6.77043
$661$	25.8125	1.00399	0.501994	−	0.864871i	$-0.332600\pi$
$661$	25.8125	1.00399	0.501994	+	0.864871i	$0.332600\pi$
$662$	−86.7505	−3.37166
$663$	−75.9373	−2.94916
$664$	20.7794	0.806397
$665$	−51.5425	−1.99873
$666$	−0.423868	−0.0164245
$667$	14.0753	0.544998
$668$	32.0130	1.23862
$669$	−13.1472	−0.508299
$670$	−115.215	−4.45115
$671$	−36.3156	−1.40195
$672$	92.0294	3.55011
$673$	18.8563	0.726857	0.363428	−	0.931622i	$-0.381606\pi$
$673$	18.8563	0.726857	0.363428	+	0.931622i	$0.381606\pi$
$674$	−66.2060	−2.55016
$675$	51.1429	1.96849
$676$	195.640	7.52460
$677$	17.1486	0.659073	0.329536	−	0.944143i	$-0.393108\pi$
$677$	17.1486	0.659073	0.329536	+	0.944143i	$0.393108\pi$
$678$	5.09454	0.195655
$679$	−40.3809	−1.54968
$680$	−194.473	−7.45769
$681$	17.7964	0.681960
$682$	−12.4134	−0.475334
$683$	18.8610	0.721695	0.360847	−	0.932625i	$-0.382488\pi$
$683$	18.8610	0.721695	0.360847	+	0.932625i	$0.382488\pi$
$684$	13.8863	0.530956
$685$	87.0671	3.32666
$686$	43.5737	1.66365
$687$	−29.9608	−1.14307
$688$	113.089	4.31149
$689$	−45.6190	−1.73795
$690$	34.0149	1.29493
$691$	35.1805	1.33833	0.669165	−	0.743114i	$-0.266652\pi$
$691$	35.1805	1.33833	0.669165	+	0.743114i	$0.266652\pi$
$692$	16.1829	0.615182
$693$	7.66484	0.291163
$694$	10.3685	0.393584
$695$	14.0563	0.533185
$696$	−138.492	−5.24954
$697$	42.5795	1.61281
$698$	−38.0219	−1.43915
$699$	19.4865	0.737047
$700$	169.432	6.40392
$701$	−18.5883	−0.702072	−0.351036	−	0.936362i	$-0.614171\pi$
$701$	−18.5883	−0.702072	−0.351036	+	0.936362i	$0.614171\pi$
$702$	86.8113	3.27648
$703$	1.15202	0.0434493
$704$	85.7547	3.23200
$705$	43.0787	1.62244
$706$	−19.1876	−0.722136
$707$	34.6222	1.30210
$708$	−4.82647	−0.181390
$709$	−33.8787	−1.27234	−0.636171	−	0.771548i	$-0.719483\pi$
$709$	−33.8787	−1.27234	−0.636171	+	0.771548i	$0.719483\pi$
$710$	10.8151	0.405885
$711$	6.81620	0.255628
$712$	23.1913	0.869130
$713$	−1.75317	−0.0656567
$714$	−82.9674	−3.10498
$715$	125.369	4.68854
$716$	57.5021	2.14896
$717$	−30.6877	−1.14605
$718$	−23.7812	−0.887505
$719$	−45.0352	−1.67953	−0.839766	−	0.542949i	$-0.817308\pi$
$719$	−45.0352	−1.67953	−0.839766	+	0.542949i	$0.817308\pi$
$720$	−30.8168	−1.14847
$721$	−42.8026	−1.59405
$722$	−1.28018	−0.0476433
$723$	8.07999	0.300498
$724$	−7.30670	−0.271551
$725$	−95.5729	−3.54949
$726$	41.3030	1.53290
$727$	−24.7995	−0.919764	−0.459882	−	0.887980i	$-0.652108\pi$
$727$	−24.7995	−0.919764	−0.459882	+	0.887980i	$0.652108\pi$
$728$	176.965	6.55878
$729$	19.5774	0.725090
$730$	117.286	4.34094
$731$	−50.3163	−1.86101
$732$	82.0146	3.03135
$733$	−0.589721	−0.0217818	−0.0108909	−	0.999941i	$-0.503467\pi$
$733$	−0.589721	−0.0217818	−0.0108909	+	0.999941i	$0.503467\pi$
$734$	−11.2175	−0.414045
$735$	10.6769	0.393824
$736$	27.7092	1.02138
$737$	−46.5669	−1.71531
$738$	12.3010	0.452808
$739$	−22.1267	−0.813945	−0.406972	−	0.913440i	$-0.633415\pi$
$739$	−22.1267	−0.813945	−0.406972	+	0.913440i	$0.633415\pi$
$740$	−5.47044	−0.201097
$741$	59.6247	2.19037
$742$	−49.8423	−1.82977
$743$	16.2040	0.594468	0.297234	−	0.954805i	$-0.403936\pi$
$743$	16.2040	0.594468	0.297234	+	0.954805i	$0.403936\pi$
$744$	17.2501	0.632419
$745$	−63.0949	−2.31162
$746$	61.8008	2.26269
$747$	−1.46503	−0.0536027
$748$	−127.739	−4.67060
$749$	−0.790609	−0.0288882
$750$	−128.289	−4.68447
$751$	−13.8144	−0.504093	−0.252047	−	0.967715i	$-0.581104\pi$
$751$	−13.8144	−0.504093	−0.252047	+	0.967715i	$0.581104\pi$
$752$	71.1070	2.59301
$753$	−10.1378	−0.369443
$754$	−162.228	−5.90799
$755$	−2.15305	−0.0783575
$756$	68.4983	2.49126
$757$	−28.9698	−1.05293	−0.526463	−	0.850198i	$-0.676482\pi$
$757$	−28.9698	−1.05293	−0.526463	+	0.850198i	$0.676482\pi$
$758$	63.3650	2.30152
$759$	13.7479	0.499018
$760$	152.697	5.53890
$761$	−30.9654	−1.12250	−0.561248	−	0.827648i	$-0.689678\pi$
$761$	−30.9654	−1.12250	−0.561248	+	0.827648i	$0.689678\pi$
$762$	−109.437	−3.96448
$763$	24.1832	0.875492
$764$	36.8331	1.33257
$765$	13.7111	0.495727
$766$	−30.9377	−1.11783
$767$	−3.47882	−0.125613
$768$	−23.2212	−0.837922
$769$	−48.6711	−1.75513	−0.877563	−	0.479461i	$-0.840832\pi$
$769$	−48.6711	−1.75513	−0.877563	+	0.479461i	$0.840832\pi$
$770$	136.976	4.93626
$771$	41.2202	1.48451
$772$	46.5908	1.67684
$773$	−48.8527	−1.75711	−0.878554	−	0.477643i	$-0.841491\pi$
$773$	−48.8527	−1.75711	−0.878554	+	0.477643i	$0.841491\pi$
$774$	−14.5362	−0.522492
$775$	11.9042	0.427611
$776$	119.630	4.29447
$777$	−1.43606	−0.0515185
$778$	−68.8595	−2.46873
$779$	−33.4328	−1.19785
$780$	−283.132	−10.1377
$781$	4.37119	0.156414
$782$	−24.9807	−0.893309
$783$	−38.6385	−1.38083
$784$	17.6236	0.629415
$785$	27.1765	0.969972
$786$	58.6217	2.09097
$787$	37.2424	1.32755	0.663775	−	0.747933i	$-0.268953\pi$
$787$	37.2424	1.32755	0.663775	+	0.747933i	$0.268953\pi$
$788$	84.9366	3.02574
$789$	−19.8768	−0.707634
$790$	121.810	4.33381
$791$	2.89742	0.103020
$792$	−22.7074	−0.806873
$793$	59.1145	2.09922
$794$	−75.0750	−2.66431
$795$	49.0683	1.74027
$796$	83.8183	2.97086
$797$	36.4265	1.29029	0.645146	−	0.764059i	$-0.276797\pi$
$797$	36.4265	1.29029	0.645146	+	0.764059i	$0.276797\pi$
$798$	65.1447	2.30610
$799$	−31.6373	−1.11925
$800$	−188.148	−6.65205
$801$	−1.63508	−0.0577728
$802$	−96.9217	−3.42242
$803$	47.4037	1.67284
$804$	105.166	3.70891
$805$	19.3453	0.681833
$806$	20.2065	0.711744
$807$	53.8829	1.89677
$808$	−102.570	−3.60840
$809$	−30.1492	−1.05999	−0.529994	−	0.848001i	$-0.677806\pi$
$809$	−30.1492	−1.05999	−0.529994	+	0.848001i	$0.677806\pi$
$810$	−113.011	−3.97079
$811$	−39.7184	−1.39470	−0.697350	−	0.716731i	$-0.745638\pi$
$811$	−39.7184	−1.39470	−0.697350	+	0.716731i	$0.745638\pi$
$812$	−128.006	−4.49212
$813$	−31.0574	−1.08923
$814$	−3.06153	−0.107307
$815$	−56.4874	−1.97867
$816$	134.822	4.71970
$817$	39.5075	1.38219
$818$	−27.9657	−0.977799
$819$	−12.4768	−0.435975
$820$	158.757	5.54405
$821$	14.4365	0.503838	0.251919	−	0.967748i	$-0.418938\pi$
$821$	14.4365	0.503838	0.251919	+	0.967748i	$0.418938\pi$
$822$	−110.044	−3.83824
$823$	−42.0193	−1.46470	−0.732351	−	0.680927i	$-0.761577\pi$
$823$	−42.0193	−1.46470	−0.732351	+	0.680927i	$0.761577\pi$
$824$	126.805	4.41745
$825$	−93.3499	−3.25002
$826$	−3.80089	−0.132250
$827$	−8.41665	−0.292676	−0.146338	−	0.989235i	$-0.546749\pi$
$827$	−8.41665	−0.292676	−0.146338	+	0.989235i	$0.546749\pi$
$828$	−5.21192	−0.181127
$829$	6.26413	0.217562	0.108781	−	0.994066i	$-0.465305\pi$
$829$	6.26413	0.217562	0.108781	+	0.994066i	$0.465305\pi$
$830$	−26.1811	−0.908760
$831$	−5.68131	−0.197082
$832$	−139.591	−4.83945
$833$	−7.84118	−0.271681
$834$	−17.7658	−0.615179
$835$	−24.8190	−0.858897
$836$	100.299	3.46890
$837$	4.81266	0.166350
$838$	30.7108	1.06089
$839$	38.0699	1.31432	0.657160	−	0.753751i	$-0.271758\pi$
$839$	38.0699	1.31432	0.657160	+	0.753751i	$0.271758\pi$
$840$	−190.346	−6.56756
$841$	43.2054	1.48984
$842$	−34.0406	−1.17312
$843$	44.5803	1.53543
$844$	51.5423	1.77416
$845$	−151.675	−5.21779
$846$	−9.13987	−0.314235
$847$	23.4903	0.807137
$848$	80.9935	2.78133
$849$	49.9131	1.71301
$850$	169.622	5.81798
$851$	−0.432386	−0.0148220
$852$	−9.87182	−0.338203
$853$	−9.02574	−0.309035	−0.154518	−	0.987990i	$-0.549382\pi$
$853$	−9.02574	−0.309035	−0.154518	+	0.987990i	$0.549382\pi$
$854$	64.5872	2.21013
$855$	−10.7658	−0.368181
$856$	2.34222	0.0800553
$857$	−3.42024	−0.116833	−0.0584165	−	0.998292i	$-0.518605\pi$
$857$	−3.42024	−0.116833	−0.0584165	+	0.998292i	$0.518605\pi$
$858$	−158.455	−5.40955
$859$	12.7793	0.436024	0.218012	−	0.975946i	$-0.430043\pi$
$859$	12.7793	0.436024	0.218012	+	0.975946i	$0.430043\pi$
$860$	−187.604	−6.39724
$861$	41.6760	1.42031
$862$	−6.84614	−0.233180
$863$	11.4374	0.389335	0.194667	−	0.980869i	$-0.437637\pi$
$863$	11.4374	0.389335	0.194667	+	0.980869i	$0.437637\pi$
$864$	−76.0652	−2.58779
$865$	−12.5463	−0.426586
$866$	−49.4150	−1.67919
$867$	−27.7069	−0.940977
$868$	15.9439	0.541172
$869$	49.2324	1.67009
$870$	174.494	5.91591
$871$	75.8015	2.56844
$872$	−71.6440	−2.42617
$873$	−8.43442	−0.285462
$874$	19.6145	0.663469
$875$	−72.9622	−2.46657
$876$	−107.056	−3.61708
$877$	−34.2139	−1.15532	−0.577660	−	0.816277i	$-0.696034\pi$
$877$	−34.2139	−1.15532	−0.577660	+	0.816277i	$0.696034\pi$
$878$	7.20330	0.243100
$879$	−9.82247	−0.331304
$880$	−222.585	−7.50333
$881$	−41.8188	−1.40891	−0.704456	−	0.709747i	$-0.748809\pi$
$881$	−41.8188	−1.40891	−0.704456	+	0.709747i	$0.748809\pi$
$882$	−2.26529	−0.0762761
$883$	7.23016	0.243314	0.121657	−	0.992572i	$-0.461179\pi$
$883$	7.23016	0.243314	0.121657	+	0.992572i	$0.461179\pi$
$884$	207.933	6.99355
$885$	3.74186	0.125781
$886$	−53.0972	−1.78384
$887$	−32.9105	−1.10503	−0.552513	−	0.833505i	$-0.686331\pi$
$887$	−32.9105	−1.10503	−0.552513	+	0.833505i	$0.686331\pi$
$888$	4.25441	0.142769
$889$	−62.2401	−2.08746
$890$	−29.2200	−0.979456
$891$	−45.6760	−1.53020
$892$	35.9999	1.20537
$893$	24.8411	0.831275
$894$	79.7458	2.66710
$895$	−44.5802	−1.49015
$896$	−55.5766	−1.85668
$897$	−22.3788	−0.747207
$898$	58.5393	1.95348
$899$	−8.99363	−0.299954
$900$	35.3895	1.17965
$901$	−36.0360	−1.20053
$902$	88.8486	2.95833
$903$	−49.2485	−1.63889
$904$	−8.58374	−0.285491
$905$	5.66473	0.188302
$906$	2.72125	0.0904073
$907$	33.0856	1.09859	0.549294	−	0.835629i	$-0.314897\pi$
$907$	33.0856	1.09859	0.549294	+	0.835629i	$0.314897\pi$
$908$	−48.7306	−1.61718
$909$	7.23161	0.239857
$910$	−222.969	−7.39134
$911$	−37.7599	−1.25104	−0.625521	−	0.780208i	$-0.715113\pi$
$911$	−37.7599	−1.25104	−0.625521	+	0.780208i	$0.715113\pi$
$912$	−105.860	−3.50537
$913$	−10.5817	−0.350203
$914$	7.70262	0.254780
$915$	−63.5842	−2.10203
$916$	82.0393	2.71065
$917$	33.3400	1.10098
$918$	68.5752	2.26332
$919$	−51.0443	−1.68380	−0.841899	−	0.539636i	$-0.818562\pi$
$919$	−51.0443	−1.68380	−0.841899	+	0.539636i	$0.818562\pi$
$920$	−57.3114	−1.88950
$921$	−46.0671	−1.51796
$922$	−17.3498	−0.571386
$923$	−7.11541	−0.234207
$924$	−125.028	−4.11313
$925$	2.93595	0.0965333
$926$	−52.9979	−1.74162
$927$	−8.94026	−0.293637
$928$	142.146	4.66618
$929$	−39.4908	−1.29565	−0.647825	−	0.761789i	$-0.724321\pi$
$929$	−39.4908	−1.29565	−0.647825	+	0.761789i	$0.724321\pi$
$930$	−21.7343	−0.712697
$931$	6.15677	0.201780
$932$	−53.3584	−1.74781
$933$	−23.6375	−0.773858
$934$	−47.2822	−1.54712
$935$	99.0334	3.23874
$936$	36.9631	1.20818
$937$	−13.4188	−0.438374	−0.219187	−	0.975683i	$-0.570341\pi$
$937$	−13.4188	−0.438374	−0.219187	+	0.975683i	$0.570341\pi$
$938$	82.8190	2.70414
$939$	34.3359	1.12051
$940$	−117.959	−3.84741
$941$	10.7838	0.351543	0.175771	−	0.984431i	$-0.443758\pi$
$941$	10.7838	0.351543	0.175771	+	0.984431i	$0.443758\pi$
$942$	−34.3485	−1.11914
$943$	12.5482	0.408627
$944$	6.17642	0.201025
$945$	−53.1053	−1.72752
$946$	−104.993	−3.41360
$947$	17.8726	0.580782	0.290391	−	0.956908i	$-0.406215\pi$
$947$	17.8726	0.580782	0.290391	+	0.956908i	$0.406215\pi$
$948$	−111.186	−3.61114
$949$	−77.1637	−2.50484
$950$	−133.184	−4.32107
$951$	−58.7751	−1.90591
$952$	139.791	4.53065
$953$	−23.3878	−0.757606	−0.378803	−	0.925477i	$-0.623664\pi$
$953$	−23.3878	−0.757606	−0.378803	+	0.925477i	$0.623664\pi$
$954$	−10.4107	−0.337057
$955$	−28.5559	−0.924047
$956$	84.0297	2.71772
$957$	70.5259	2.27978
$958$	−63.5589	−2.05350
$959$	−62.5856	−2.02100
$960$	150.146	4.84593
$961$	−29.8798	−0.963864
$962$	4.98355	0.160676
$963$	−0.165136	−0.00532143
$964$	−22.1248	−0.712592
$965$	−36.1209	−1.16277
$966$	−24.4506	−0.786686
$967$	34.1715	1.09888	0.549441	−	0.835533i	$-0.314841\pi$
$967$	34.1715	1.09888	0.549441	+	0.835533i	$0.314841\pi$
$968$	−69.5911	−2.23674
$969$	47.0996	1.51306
$970$	−150.729	−4.83961
$971$	−1.27357	−0.0408707	−0.0204353	−	0.999791i	$-0.506505\pi$
$971$	−1.27357	−0.0408707	−0.0204353	+	0.999791i	$0.506505\pi$
$972$	32.2303	1.03379
$973$	−10.1040	−0.323918
$974$	68.9092	2.20799
$975$	151.955	4.86644
$976$	−104.954	−3.35949
$977$	−27.3758	−0.875829	−0.437914	−	0.899017i	$-0.644283\pi$
$977$	−27.3758	−0.875829	−0.437914	+	0.899017i	$0.644283\pi$
$978$	71.3946	2.28295
$979$	−11.8099	−0.377448
$980$	−29.2358	−0.933903
$981$	5.05120	0.161272
$982$	−17.1880	−0.548492
$983$	35.7493	1.14023	0.570113	−	0.821567i	$-0.306900\pi$
$983$	35.7493	1.14023	0.570113	+	0.821567i	$0.306900\pi$
$984$	−123.467	−3.93598
$985$	−65.8496	−2.09814
$986$	−128.149	−4.08111
$987$	−30.9659	−0.985655
$988$	−163.266	−5.19418
$989$	−14.8283	−0.471512
$990$	28.6104	0.909297
$991$	29.3406	0.932035	0.466017	−	0.884776i	$-0.345688\pi$
$991$	29.3406	0.932035	0.466017	+	0.884776i	$0.345688\pi$
$992$	−17.7052	−0.562141
$993$	−61.3897	−1.94814
$994$	−7.77414	−0.246581
$995$	−64.9825	−2.06009
$996$	23.8975	0.757222
$997$	12.1147	0.383676	0.191838	−	0.981427i	$-0.438555\pi$
$997$	12.1147	0.383676	0.191838	+	0.981427i	$0.438555\pi$
$998$	108.629	3.43859
$999$	1.18695	0.0375535

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8023.2.a.b.1.8	✓	155

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8023.2.a.b.1.8	✓	155	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:	\( N \)	\(=\)	\( 8023 = 71 \cdot 113 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8023.a (trivial)

\(f(q)\)	\(=\)	\(q-2.68312 q^{2} -1.89873 q^{3} +5.19916 q^{4} -4.03080 q^{5} +5.09454 q^{6} +2.89742 q^{7} -8.58374 q^{8} +0.605189 q^{9} +O(q^{10})\)	\(q-2.68312 q^{2} -1.89873 q^{3} +5.19916 q^{4} -4.03080 q^{5} +5.09454 q^{6} +2.89742 q^{7} -8.58374 q^{8} +0.605189 q^{9} +10.8151 q^{10} +4.37119 q^{11} -9.87182 q^{12} -7.11541 q^{13} -7.77414 q^{14} +7.65341 q^{15} +12.6329 q^{16} -5.62071 q^{17} -1.62380 q^{18} +4.41329 q^{19} -20.9568 q^{20} -5.50143 q^{21} -11.7285 q^{22} -1.65643 q^{23} +16.2982 q^{24} +11.2473 q^{25} +19.0915 q^{26} +4.54711 q^{27} +15.0642 q^{28} -8.49738 q^{29} -20.5351 q^{30} +1.05840 q^{31} -16.7283 q^{32} -8.29973 q^{33} +15.0811 q^{34} -11.6789 q^{35} +3.14648 q^{36} +0.261035 q^{37} -11.8414 q^{38} +13.5103 q^{39} +34.5993 q^{40} -7.57547 q^{41} +14.7610 q^{42} +8.95195 q^{43} +22.7265 q^{44} -2.43940 q^{45} +4.44441 q^{46} +5.62870 q^{47} -23.9866 q^{48} +1.39505 q^{49} -30.1780 q^{50} +10.6722 q^{51} -36.9942 q^{52} +6.41130 q^{53} -12.2005 q^{54} -17.6194 q^{55} -24.8707 q^{56} -8.37966 q^{57} +22.7995 q^{58} +0.488914 q^{59} +39.7913 q^{60} -8.30795 q^{61} -2.83982 q^{62} +1.75349 q^{63} +19.6181 q^{64} +28.6808 q^{65} +22.2692 q^{66} -10.6531 q^{67} -29.2229 q^{68} +3.14512 q^{69} +31.3360 q^{70} +1.00000 q^{71} -5.19479 q^{72} +10.8446 q^{73} -0.700389 q^{74} -21.3557 q^{75} +22.9454 q^{76} +12.6652 q^{77} -36.2498 q^{78} +11.2629 q^{79} -50.9208 q^{80} -10.4493 q^{81} +20.3259 q^{82} -2.42078 q^{83} -28.6028 q^{84} +22.6559 q^{85} -24.0192 q^{86} +16.1343 q^{87} -37.5212 q^{88} -2.70177 q^{89} +6.54521 q^{90} -20.6164 q^{91} -8.61205 q^{92} -2.00962 q^{93} -15.1025 q^{94} -17.7891 q^{95} +31.7625 q^{96} -13.9368 q^{97} -3.74310 q^{98} +2.64540 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 155 q - 21 q^{2} - 16 q^{3} + 151 q^{4} - 26 q^{5} - 10 q^{6} - 40 q^{7} - 57 q^{8} + 135 q^{9}+O(q^{10}) \) 155 * q - 21 * q^2 - 16 * q^3 + 151 * q^4 - 26 * q^5 - 10 * q^6 - 40 * q^7 - 57 * q^8 + 135 * q^9	\( 155 q - 21 q^{2} - 16 q^{3} + 151 q^{4} - 26 q^{5} - 10 q^{6} - 40 q^{7} - 57 q^{8} + 135 q^{9} - 2 q^{10} - 24 q^{11} - 32 q^{12} - 62 q^{13} - 18 q^{14} - 12 q^{15} + 155 q^{16} - 129 q^{17} - 42 q^{18} - 18 q^{19} - 59 q^{20} - 45 q^{21} - 17 q^{22} - 38 q^{23} - 27 q^{24} + 129 q^{25} - 44 q^{26} - 43 q^{27} - 100 q^{28} - 52 q^{29} - 39 q^{30} - 56 q^{31} - 145 q^{32} - 126 q^{33} - q^{34} - 49 q^{35} + 131 q^{36} - 30 q^{37} - 91 q^{38} - 29 q^{39} - 5 q^{40} - 163 q^{41} - 80 q^{42} - 15 q^{43} - 118 q^{44} - 66 q^{45} + 2 q^{46} - 111 q^{47} - 89 q^{48} + 101 q^{49} - 121 q^{50} + 5 q^{51} - 111 q^{52} - 93 q^{53} - 68 q^{54} - 60 q^{55} - 27 q^{56} - 106 q^{57} + 16 q^{58} - 79 q^{59} - 103 q^{60} - 74 q^{61} - 102 q^{62} - 118 q^{63} + 175 q^{64} - 109 q^{65} + 65 q^{66} - 18 q^{67} - 346 q^{68} - 39 q^{69} + 32 q^{70} + 155 q^{71} - 203 q^{72} - 108 q^{73} - 87 q^{74} - 22 q^{75} - 16 q^{76} - 121 q^{77} - 75 q^{78} - 6 q^{79} - 136 q^{80} + 107 q^{81} - 30 q^{82} - 116 q^{83} - 5 q^{84} - 53 q^{85} + 8 q^{86} - 100 q^{87} - 43 q^{88} - 189 q^{89} - 76 q^{90} + 14 q^{91} - 99 q^{92} - 72 q^{93} + 17 q^{94} - 18 q^{95} - 50 q^{96} - 184 q^{97} - 249 q^{98} - 114 q^{99}+O(q^{100}) \) 155 * q - 21 * q^2 - 16 * q^3 + 151 * q^4 - 26 * q^5 - 10 * q^6 - 40 * q^7 - 57 * q^8 + 135 * q^9 - 2 * q^10 - 24 * q^11 - 32 * q^12 - 62 * q^13 - 18 * q^14 - 12 * q^15 + 155 * q^16 - 129 * q^17 - 42 * q^18 - 18 * q^19 - 59 * q^20 - 45 * q^21 - 17 * q^22 - 38 * q^23 - 27 * q^24 + 129 * q^25 - 44 * q^26 - 43 * q^27 - 100 * q^28 - 52 * q^29 - 39 * q^30 - 56 * q^31 - 145 * q^32 - 126 * q^33 - q^34 - 49 * q^35 + 131 * q^36 - 30 * q^37 - 91 * q^38 - 29 * q^39 - 5 * q^40 - 163 * q^41 - 80 * q^42 - 15 * q^43 - 118 * q^44 - 66 * q^45 + 2 * q^46 - 111 * q^47 - 89 * q^48 + 101 * q^49 - 121 * q^50 + 5 * q^51 - 111 * q^52 - 93 * q^53 - 68 * q^54 - 60 * q^55 - 27 * q^56 - 106 * q^57 + 16 * q^58 - 79 * q^59 - 103 * q^60 - 74 * q^61 - 102 * q^62 - 118 * q^63 + 175 * q^64 - 109 * q^65 + 65 * q^66 - 18 * q^67 - 346 * q^68 - 39 * q^69 + 32 * q^70 + 155 * q^71 - 203 * q^72 - 108 * q^73 - 87 * q^74 - 22 * q^75 - 16 * q^76 - 121 * q^77 - 75 * q^78 - 6 * q^79 - 136 * q^80 + 107 * q^81 - 30 * q^82 - 116 * q^83 - 5 * q^84 - 53 * q^85 + 8 * q^86 - 100 * q^87 - 43 * q^88 - 189 * q^89 - 76 * q^90 + 14 * q^91 - 99 * q^92 - 72 * q^93 + 17 * q^94 - 18 * q^95 - 50 * q^96 - 184 * q^97 - 249 * q^98 - 114 * q^99

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