LMFDB - Embedded newform 8027.2.a.c.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8027,2,Mod(1,8027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8027, 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("8027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8027 = 23 \cdot 349 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8027.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:	$64.0959177025$
Analytic rank:	$1$
Dimension:	$143$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	8027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.56363 q^{2} +3.26823 q^{3} +4.57221 q^{4} -1.87479 q^{5} -8.37854 q^{6} -1.87590 q^{7} -6.59421 q^{8} +7.68132 q^{9} +O(q^{10})$	\(q-2.56363 q^{2} +3.26823 q^{3} +4.57221 q^{4} -1.87479 q^{5} -8.37854 q^{6} -1.87590 q^{7} -6.59421 q^{8} +7.68132 q^{9} +4.80627 q^{10} +2.14779 q^{11} +14.9430 q^{12} +6.01154 q^{13} +4.80913 q^{14} -6.12723 q^{15} +7.76072 q^{16} +4.57944 q^{17} -19.6921 q^{18} -2.40321 q^{19} -8.57193 q^{20} -6.13088 q^{21} -5.50613 q^{22} +1.00000 q^{23} -21.5514 q^{24} -1.48517 q^{25} -15.4114 q^{26} +15.2996 q^{27} -8.57703 q^{28} -10.0394 q^{29} +15.7080 q^{30} -9.82464 q^{31} -6.70720 q^{32} +7.01946 q^{33} -11.7400 q^{34} +3.51692 q^{35} +35.1207 q^{36} -11.8040 q^{37} +6.16094 q^{38} +19.6471 q^{39} +12.3627 q^{40} -10.9386 q^{41} +15.7173 q^{42} +2.68805 q^{43} +9.82014 q^{44} -14.4008 q^{45} -2.56363 q^{46} +1.43160 q^{47} +25.3638 q^{48} -3.48099 q^{49} +3.80744 q^{50} +14.9667 q^{51} +27.4860 q^{52} -2.26905 q^{53} -39.2227 q^{54} -4.02664 q^{55} +12.3701 q^{56} -7.85423 q^{57} +25.7373 q^{58} -9.79751 q^{59} -28.0150 q^{60} -11.9703 q^{61} +25.1868 q^{62} -14.4094 q^{63} +1.67337 q^{64} -11.2703 q^{65} -17.9953 q^{66} +2.21842 q^{67} +20.9382 q^{68} +3.26823 q^{69} -9.01609 q^{70} +1.76796 q^{71} -50.6523 q^{72} -12.9857 q^{73} +30.2611 q^{74} -4.85389 q^{75} -10.9880 q^{76} -4.02904 q^{77} -50.3679 q^{78} -6.06876 q^{79} -14.5497 q^{80} +26.9588 q^{81} +28.0425 q^{82} +5.29995 q^{83} -28.0317 q^{84} -8.58548 q^{85} -6.89118 q^{86} -32.8111 q^{87} -14.1630 q^{88} +5.18780 q^{89} +36.9185 q^{90} -11.2771 q^{91} +4.57221 q^{92} -32.1092 q^{93} -3.67009 q^{94} +4.50550 q^{95} -21.9207 q^{96} -8.41319 q^{97} +8.92398 q^{98} +16.4978 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 143 q - 17 q^{2} - 17 q^{3} + 121 q^{4} - 22 q^{5} - 11 q^{6} - 33 q^{7} - 45 q^{8} + 104 q^{9}+O(q^{10}) $ 143 * q - 17 * q^2 - 17 * q^3 + 121 * q^4 - 22 * q^5 - 11 * q^6 - 33 * q^7 - 45 * q^8 + 104 * q^9	\( 143 q - 17 q^{2} - 17 q^{3} + 121 q^{4} - 22 q^{5} - 11 q^{6} - 33 q^{7} - 45 q^{8} + 104 q^{9} - 22 q^{10} - 14 q^{11} - 36 q^{12} - 87 q^{13} - 18 q^{14} - 19 q^{15} + 81 q^{16} - 14 q^{17} - 60 q^{18} - 18 q^{19} - 25 q^{20} - 26 q^{21} - 62 q^{22} + 143 q^{23} - 21 q^{24} + 67 q^{25} - 5 q^{26} - 47 q^{27} - 76 q^{28} - 54 q^{29} - 22 q^{30} - 62 q^{31} - 117 q^{32} - 59 q^{33} - 35 q^{34} - 52 q^{35} + 52 q^{36} - 190 q^{37} - 19 q^{38} - 43 q^{39} - 41 q^{40} - 50 q^{41} + 8 q^{42} - 50 q^{43} - 18 q^{44} - 75 q^{45} - 17 q^{46} - 63 q^{47} - 35 q^{48} + 74 q^{49} - 53 q^{50} - 33 q^{51} - 124 q^{52} - 100 q^{53} - 46 q^{54} - 61 q^{55} - 3 q^{56} - 80 q^{57} - 112 q^{58} - 109 q^{59} - 55 q^{60} - 76 q^{61} - 6 q^{62} - 93 q^{63} + 57 q^{64} - 17 q^{65} + 50 q^{66} - 120 q^{67} + 26 q^{68} - 17 q^{69} - 109 q^{71} - 153 q^{72} - 94 q^{73} + 35 q^{74} - 105 q^{75} - 16 q^{76} - 52 q^{77} - 59 q^{78} - 29 q^{79} - 30 q^{80} + 39 q^{81} - 65 q^{82} + 8 q^{83} + 11 q^{84} - 155 q^{85} - 15 q^{86} - 25 q^{87} - 139 q^{88} + 6 q^{89} + 82 q^{90} - 34 q^{91} + 121 q^{92} - 151 q^{93} - 3 q^{94} - 70 q^{95} - 23 q^{96} - 203 q^{97} - 18 q^{98} - 49 q^{99}+O(q^{100}) \) 143 * q - 17 * q^2 - 17 * q^3 + 121 * q^4 - 22 * q^5 - 11 * q^6 - 33 * q^7 - 45 * q^8 + 104 * q^9 - 22 * q^10 - 14 * q^11 - 36 * q^12 - 87 * q^13 - 18 * q^14 - 19 * q^15 + 81 * q^16 - 14 * q^17 - 60 * q^18 - 18 * q^19 - 25 * q^20 - 26 * q^21 - 62 * q^22 + 143 * q^23 - 21 * q^24 + 67 * q^25 - 5 * q^26 - 47 * q^27 - 76 * q^28 - 54 * q^29 - 22 * q^30 - 62 * q^31 - 117 * q^32 - 59 * q^33 - 35 * q^34 - 52 * q^35 + 52 * q^36 - 190 * q^37 - 19 * q^38 - 43 * q^39 - 41 * q^40 - 50 * q^41 + 8 * q^42 - 50 * q^43 - 18 * q^44 - 75 * q^45 - 17 * q^46 - 63 * q^47 - 35 * q^48 + 74 * q^49 - 53 * q^50 - 33 * q^51 - 124 * q^52 - 100 * q^53 - 46 * q^54 - 61 * q^55 - 3 * q^56 - 80 * q^57 - 112 * q^58 - 109 * q^59 - 55 * q^60 - 76 * q^61 - 6 * q^62 - 93 * q^63 + 57 * q^64 - 17 * q^65 + 50 * q^66 - 120 * q^67 + 26 * q^68 - 17 * q^69 - 109 * q^71 - 153 * q^72 - 94 * q^73 + 35 * q^74 - 105 * q^75 - 16 * q^76 - 52 * q^77 - 59 * q^78 - 29 * q^79 - 30 * q^80 + 39 * q^81 - 65 * q^82 + 8 * q^83 + 11 * q^84 - 155 * q^85 - 15 * q^86 - 25 * q^87 - 139 * q^88 + 6 * q^89 + 82 * q^90 - 34 * q^91 + 121 * q^92 - 151 * q^93 - 3 * q^94 - 70 * q^95 - 23 * q^96 - 203 * q^97 - 18 * q^98 - 49 * 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 $

$2$	−2.56363	−1.81276	−0.906381	−	0.422461i	$-0.861166\pi$
$2$	−2.56363	−1.81276	−0.906381	+	0.422461i	$0.861166\pi$
$3$	3.26823	1.88691	0.943457	−	0.331496i	$-0.107553\pi$
$3$	3.26823	1.88691	0.943457	+	0.331496i	$0.107553\pi$
$4$	4.57221	2.28611
$5$	−1.87479	−0.838430	−0.419215	−	0.907887i	$-0.637695\pi$
$5$	−1.87479	−0.838430	−0.419215	+	0.907887i	$0.637695\pi$
$6$	−8.37854	−3.42053
$7$	−1.87590	−0.709025	−0.354512	−	0.935051i	$-0.615353\pi$
$7$	−1.87590	−0.709025	−0.354512	+	0.935051i	$0.615353\pi$
$8$	−6.59421	−2.33141
$9$	7.68132	2.56044
$10$	4.80627	1.51987
$11$	2.14779	0.647582	0.323791	−	0.946129i	$-0.395043\pi$
$11$	2.14779	0.647582	0.323791	+	0.946129i	$0.395043\pi$
$12$	14.9430	4.31369
$13$	6.01154	1.66730	0.833650	−	0.552293i	$-0.186247\pi$
$13$	6.01154	1.66730	0.833650	+	0.552293i	$0.186247\pi$
$14$	4.80913	1.28529
$15$	−6.12723	−1.58204
$16$	7.76072	1.94018
$17$	4.57944	1.11068	0.555339	−	0.831624i	$-0.312589\pi$
$17$	4.57944	1.11068	0.555339	+	0.831624i	$0.312589\pi$
$18$	−19.6921	−4.64147
$19$	−2.40321	−0.551333	−0.275667	−	0.961253i	$-0.588899\pi$
$19$	−2.40321	−0.551333	−0.275667	+	0.961253i	$0.588899\pi$
$20$	−8.57193	−1.91674
$21$	−6.13088	−1.33787
$22$	−5.50613	−1.17391
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−21.5514	−4.39916
$25$	−1.48517	−0.297035
$26$	−15.4114	−3.02242
$27$	15.2996	2.94442
$28$	−8.57703	−1.62091
$29$	−10.0394	−1.86427	−0.932135	−	0.362112i	$-0.882056\pi$
$29$	−10.0394	−1.86427	−0.932135	+	0.362112i	$0.882056\pi$
$30$	15.7080	2.86787
$31$	−9.82464	−1.76456	−0.882279	−	0.470727i	$-0.843992\pi$
$31$	−9.82464	−1.76456	−0.882279	+	0.470727i	$0.843992\pi$
$32$	−6.70720	−1.18568
$33$	7.01946	1.22193
$34$	−11.7400	−2.01339
$35$	3.51692	0.594468
$36$	35.1207	5.85344
$37$	−11.8040	−1.94056	−0.970282	−	0.241978i	$-0.922204\pi$
$37$	−11.8040	−1.94056	−0.970282	+	0.241978i	$0.922204\pi$
$38$	6.16094	0.999437
$39$	19.6471	3.14605
$40$	12.3627	1.95472
$41$	−10.9386	−1.70832	−0.854158	−	0.520013i	$-0.825927\pi$
$41$	−10.9386	−1.70832	−0.854158	+	0.520013i	$0.825927\pi$
$42$	15.7173	2.42524
$43$	2.68805	0.409924	0.204962	−	0.978770i	$-0.434293\pi$
$43$	2.68805	0.409924	0.204962	+	0.978770i	$0.434293\pi$
$44$	9.82014	1.48044
$45$	−14.4008	−2.14675
$46$	−2.56363	−0.377987
$47$	1.43160	0.208820	0.104410	−	0.994534i	$-0.466705\pi$
$47$	1.43160	0.208820	0.104410	+	0.994534i	$0.466705\pi$
$48$	25.3638	3.66095
$49$	−3.48099	−0.497284
$50$	3.80744	0.538454
$51$	14.9667	2.09575
$52$	27.4860	3.81163
$53$	−2.26905	−0.311678	−0.155839	−	0.987783i	$-0.549808\pi$
$53$	−2.26905	−0.311678	−0.155839	+	0.987783i	$0.549808\pi$
$54$	−39.2227	−5.33753
$55$	−4.02664	−0.542952
$56$	12.3701	1.65302
$57$	−7.85423	−1.04032
$58$	25.7373	3.37948
$59$	−9.79751	−1.27553	−0.637763	−	0.770232i	$-0.720140\pi$
$59$	−9.79751	−1.27553	−0.637763	+	0.770232i	$0.720140\pi$
$60$	−28.0150	−3.61672
$61$	−11.9703	−1.53264	−0.766322	−	0.642456i	$-0.777915\pi$
$61$	−11.9703	−1.53264	−0.766322	+	0.642456i	$0.777915\pi$
$62$	25.1868	3.19872
$63$	−14.4094	−1.81542
$64$	1.67337	0.209172
$65$	−11.2703	−1.39791
$66$	−17.9953	−2.21507
$67$	2.21842	0.271023	0.135512	−	0.990776i	$-0.456732\pi$
$67$	2.21842	0.271023	0.135512	+	0.990776i	$0.456732\pi$
$68$	20.9382	2.53913
$69$	3.26823	0.393449
$70$	−9.01609	−1.07763
$71$	1.76796	0.209818	0.104909	−	0.994482i	$-0.466545\pi$
$71$	1.76796	0.209818	0.104909	+	0.994482i	$0.466545\pi$
$72$	−50.6523	−5.96943
$73$	−12.9857	−1.51987	−0.759933	−	0.650001i	$-0.774768\pi$
$73$	−12.9857	−1.51987	−0.759933	+	0.650001i	$0.774768\pi$
$74$	30.2611	3.51778
$75$	−4.85389	−0.560479
$76$	−10.9880	−1.26041
$77$	−4.02904	−0.459151
$78$	−50.3679	−5.70304
$79$	−6.06876	−0.682788	−0.341394	−	0.939920i	$-0.610899\pi$
$79$	−6.06876	−0.682788	−0.341394	+	0.939920i	$0.610899\pi$
$80$	−14.5497	−1.62671
$81$	26.9588	2.99542
$82$	28.0425	3.09677
$83$	5.29995	0.581745	0.290873	−	0.956762i	$-0.406054\pi$
$83$	5.29995	0.581745	0.290873	+	0.956762i	$0.406054\pi$
$84$	−28.0317	−3.05851
$85$	−8.58548	−0.931226
$86$	−6.89118	−0.743095
$87$	−32.8111	−3.51771
$88$	−14.1630	−1.50978
$89$	5.18780	0.549905	0.274953	−	0.961458i	$-0.411338\pi$
$89$	5.18780	0.549905	0.274953	+	0.961458i	$0.411338\pi$
$90$	36.9185	3.89155
$91$	−11.2771	−1.18216
$92$	4.57221	0.476686
$93$	−32.1092	−3.32957
$94$	−3.67009	−0.378540
$95$	4.50550	0.462255
$96$	−21.9207	−2.23727
$97$	−8.41319	−0.854230	−0.427115	−	0.904197i	$-0.640470\pi$
$97$	−8.41319	−0.854230	−0.427115	+	0.904197i	$0.640470\pi$
$98$	8.92398	0.901458
$99$	16.4978	1.65810
$100$	−6.79053	−0.679053
$101$	−2.63388	−0.262081	−0.131041	−	0.991377i	$-0.541832\pi$
$101$	−2.63388	−0.262081	−0.131041	+	0.991377i	$0.541832\pi$
$102$	−38.3690	−3.79910
$103$	−11.2215	−1.10569	−0.552843	−	0.833286i	$-0.686457\pi$
$103$	−11.2215	−1.10569	−0.552843	+	0.833286i	$0.686457\pi$
$104$	−39.6414	−3.88715
$105$	11.4941	1.12171
$106$	5.81700	0.564997
$107$	−9.16881	−0.886382	−0.443191	−	0.896427i	$-0.646154\pi$
$107$	−9.16881	−0.886382	−0.443191	+	0.896427i	$0.646154\pi$
$108$	69.9533	6.73125
$109$	−4.84158	−0.463739	−0.231870	−	0.972747i	$-0.574484\pi$
$109$	−4.84158	−0.463739	−0.231870	+	0.972747i	$0.574484\pi$
$110$	10.3228	0.984243
$111$	−38.5781	−3.66167
$112$	−14.5584	−1.37563
$113$	1.74665	0.164311	0.0821553	−	0.996620i	$-0.473820\pi$
$113$	1.74665	0.164311	0.0821553	+	0.996620i	$0.473820\pi$
$114$	20.1354	1.88585
$115$	−1.87479	−0.174825
$116$	−45.9023	−4.26192
$117$	46.1766	4.26902
$118$	25.1172	2.31223
$119$	−8.59059	−0.787498
$120$	40.4043	3.68839
$121$	−6.38702	−0.580638
$122$	30.6875	2.77832
$123$	−35.7497	−3.22345
$124$	−44.9204	−4.03397
$125$	12.1583	1.08747
$126$	36.9405	3.29092
$127$	15.6611	1.38970	0.694850	−	0.719154i	$-0.255471\pi$
$127$	15.6611	1.38970	0.694850	+	0.719154i	$0.255471\pi$
$128$	9.12449	0.806499
$129$	8.78517	0.773491
$130$	28.8930	2.53409
$131$	−5.05477	−0.441637	−0.220819	−	0.975315i	$-0.570873\pi$
$131$	−5.05477	−0.441637	−0.220819	+	0.975315i	$0.570873\pi$
$132$	32.0945	2.79346
$133$	4.50818	0.390909
$134$	−5.68721	−0.491300
$135$	−28.6836	−2.46869
$136$	−30.1978	−2.58944
$137$	16.0227	1.36891	0.684457	−	0.729053i	$-0.260039\pi$
$137$	16.0227	1.36891	0.684457	+	0.729053i	$0.260039\pi$
$138$	−8.37854	−0.713229
$139$	11.8288	1.00331	0.501655	−	0.865068i	$-0.332725\pi$
$139$	11.8288	1.00331	0.501655	+	0.865068i	$0.332725\pi$
$140$	16.0801	1.35902
$141$	4.67878	0.394025
$142$	−4.53239	−0.380350
$143$	12.9115	1.07971
$144$	59.6126	4.96772
$145$	18.8217	1.56306
$146$	33.2907	2.75516
$147$	−11.3767	−0.938332
$148$	−53.9704	−4.43634
$149$	21.6207	1.77124	0.885618	−	0.464415i	$-0.153735\pi$
$149$	21.6207	1.77124	0.885618	+	0.464415i	$0.153735\pi$
$150$	12.4436	1.01602
$151$	−8.04478	−0.654675	−0.327337	−	0.944908i	$-0.606151\pi$
$151$	−8.04478	−0.654675	−0.327337	+	0.944908i	$0.606151\pi$
$152$	15.8473	1.28538
$153$	35.1762	2.84383
$154$	10.3290	0.832332
$155$	18.4191	1.47946
$156$	89.8307	7.19221
$157$	15.7697	1.25856	0.629279	−	0.777180i	$-0.283350\pi$
$157$	15.7697	1.25856	0.629279	+	0.777180i	$0.283350\pi$
$158$	15.5581	1.23773
$159$	−7.41577	−0.588109
$160$	12.5746	0.994108
$161$	−1.87590	−0.147842
$162$	−69.1124	−5.42998
$163$	−3.03391	−0.237634	−0.118817	−	0.992916i	$-0.537910\pi$
$163$	−3.03391	−0.237634	−0.118817	+	0.992916i	$0.537910\pi$
$164$	−50.0135	−3.90540
$165$	−13.1600	−1.02450
$166$	−13.5871	−1.05457
$167$	−20.3061	−1.57133	−0.785666	−	0.618651i	$-0.787680\pi$
$167$	−20.3061	−1.57133	−0.785666	+	0.618651i	$0.787680\pi$
$168$	40.4283	3.11911
$169$	23.1386	1.77989
$170$	22.0100	1.68809
$171$	−18.4598	−1.41166
$172$	12.2903	0.937130
$173$	15.5180	1.17981	0.589904	−	0.807473i	$-0.299165\pi$
$173$	15.5180	1.17981	0.589904	+	0.807473i	$0.299165\pi$
$174$	84.1155	6.37678
$175$	2.78604	0.210605
$176$	16.6684	1.25642
$177$	−32.0205	−2.40681
$178$	−13.2996	−0.996848
$179$	5.81583	0.434695	0.217348	−	0.976094i	$-0.430259\pi$
$179$	5.81583	0.434695	0.217348	+	0.976094i	$0.430259\pi$
$180$	−65.8438	−4.90770
$181$	−8.64684	−0.642715	−0.321357	−	0.946958i	$-0.604139\pi$
$181$	−8.64684	−0.642715	−0.321357	+	0.946958i	$0.604139\pi$
$182$	28.9102	2.14297
$183$	−39.1218	−2.89197
$184$	−6.59421	−0.486132
$185$	22.1300	1.62703
$186$	82.3162	6.03572
$187$	9.83566	0.719255
$188$	6.54556	0.477384
$189$	−28.7006	−2.08766
$190$	−11.5505	−0.837958
$191$	−1.57225	−0.113764	−0.0568818	−	0.998381i	$-0.518116\pi$
$191$	−1.57225	−0.113764	−0.0568818	+	0.998381i	$0.518116\pi$
$192$	5.46897	0.394689
$193$	8.55230	0.615608	0.307804	−	0.951450i	$-0.400406\pi$
$193$	8.55230	0.615608	0.307804	+	0.951450i	$0.400406\pi$
$194$	21.5683	1.54852
$195$	−36.8341	−2.63774
$196$	−15.9158	−1.13685
$197$	−7.94358	−0.565957	−0.282978	−	0.959126i	$-0.591322\pi$
$197$	−7.94358	−0.565957	−0.282978	+	0.959126i	$0.591322\pi$
$198$	−42.2944	−3.00573
$199$	2.79630	0.198224	0.0991121	−	0.995076i	$-0.468400\pi$
$199$	2.79630	0.198224	0.0991121	+	0.995076i	$0.468400\pi$
$200$	9.79356	0.692509
$201$	7.25030	0.511397
$202$	6.75231	0.475091
$203$	18.8329	1.32181
$204$	68.4308	4.79112
$205$	20.5075	1.43230
$206$	28.7678	2.00434
$207$	7.68132	0.533889
$208$	46.6538	3.23486
$209$	−5.16157	−0.357034
$210$	−29.4666	−2.03339
$211$	0.703229	0.0484123	0.0242061	−	0.999707i	$-0.492294\pi$
$211$	0.703229	0.0484123	0.0242061	+	0.999707i	$0.492294\pi$
$212$	−10.3746	−0.712528
$213$	5.77809	0.395908
$214$	23.5055	1.60680
$215$	−5.03952	−0.343693
$216$	−100.889	−6.86464
$217$	18.4301	1.25112
$218$	12.4120	0.840649
$219$	−42.4404	−2.86786
$220$	−18.4107	−1.24125
$221$	27.5295	1.85183
$222$	98.9002	6.63775
$223$	−11.0253	−0.738309	−0.369155	−	0.929368i	$-0.620353\pi$
$223$	−11.0253	−0.738309	−0.369155	+	0.929368i	$0.620353\pi$
$224$	12.5821	0.840674
$225$	−11.4081	−0.760540
$226$	−4.47776	−0.297856
$227$	10.1309	0.672411	0.336205	−	0.941789i	$-0.390856\pi$
$227$	10.1309	0.672411	0.336205	+	0.941789i	$0.390856\pi$
$228$	−35.9112	−2.37828
$229$	−8.71565	−0.575946	−0.287973	−	0.957638i	$-0.592981\pi$
$229$	−8.71565	−0.575946	−0.287973	+	0.957638i	$0.592981\pi$
$230$	4.80627	0.316916
$231$	−13.1678	−0.866379
$232$	66.2019	4.34637
$233$	10.3192	0.676035	0.338018	−	0.941140i	$-0.390244\pi$
$233$	10.3192	0.676035	0.338018	+	0.941140i	$0.390244\pi$
$234$	−118.380	−7.73873
$235$	−2.68394	−0.175081
$236$	−44.7963	−2.91599
$237$	−19.8341	−1.28836
$238$	22.0231	1.42755
$239$	−0.660024	−0.0426934	−0.0213467	−	0.999772i	$-0.506795\pi$
$239$	−0.660024	−0.0426934	−0.0213467	+	0.999772i	$0.506795\pi$
$240$	−47.5517	−3.06945
$241$	5.54497	0.357183	0.178591	−	0.983923i	$-0.442846\pi$
$241$	5.54497	0.357183	0.178591	+	0.983923i	$0.442846\pi$
$242$	16.3740	1.05256
$243$	42.2085	2.70768
$244$	−54.7309	−3.50379
$245$	6.52611	0.416938
$246$	91.6492	5.84334
$247$	−14.4470	−0.919238
$248$	64.7858	4.11390
$249$	17.3215	1.09770
$250$	−31.1695	−1.97133
$251$	12.4901	0.788369	0.394185	−	0.919031i	$-0.371027\pi$
$251$	12.4901	0.788369	0.394185	+	0.919031i	$0.371027\pi$
$252$	−65.8829	−4.15024
$253$	2.14779	0.135030
$254$	−40.1494	−2.51920
$255$	−28.0593	−1.75714
$256$	−26.7386	−1.67116
$257$	−10.2907	−0.641917	−0.320958	−	0.947093i	$-0.604005\pi$
$257$	−10.2907	−0.641917	−0.320958	+	0.947093i	$0.604005\pi$
$258$	−22.5220	−1.40216
$259$	22.1431	1.37591
$260$	−51.5304	−3.19578
$261$	−77.1159	−4.77335
$262$	12.9586	0.800583
$263$	−14.3173	−0.882845	−0.441422	−	0.897299i	$-0.645526\pi$
$263$	−14.3173	−0.882845	−0.441422	+	0.897299i	$0.645526\pi$
$264$	−46.2878	−2.84882
$265$	4.25398	0.261320
$266$	−11.5573	−0.708625
$267$	16.9549	1.03762
$268$	10.1431	0.619588
$269$	−6.06718	−0.369923	−0.184961	−	0.982746i	$-0.559216\pi$
$269$	−6.06718	−0.369923	−0.184961	+	0.982746i	$0.559216\pi$
$270$	73.5341	4.47515
$271$	−2.25583	−0.137032	−0.0685160	−	0.997650i	$-0.521826\pi$
$271$	−2.25583	−0.137032	−0.0685160	+	0.997650i	$0.521826\pi$
$272$	35.5398	2.15491
$273$	−36.8560	−2.23063
$274$	−41.0764	−2.48151
$275$	−3.18984	−0.192354
$276$	14.9430	0.899466
$277$	9.53695	0.573020	0.286510	−	0.958077i	$-0.407505\pi$
$277$	9.53695	0.573020	0.286510	+	0.958077i	$0.407505\pi$
$278$	−30.3248	−1.81876
$279$	−75.4663	−4.51805
$280$	−23.1913	−1.38595
$281$	16.2820	0.971303	0.485652	−	0.874152i	$-0.338582\pi$
$281$	16.2820	0.971303	0.485652	+	0.874152i	$0.338582\pi$
$282$	−11.9947	−0.714273
$283$	−2.05516	−0.122167	−0.0610833	−	0.998133i	$-0.519456\pi$
$283$	−2.05516	−0.122167	−0.0610833	+	0.998133i	$0.519456\pi$
$284$	8.08348	0.479666
$285$	14.7250	0.872234
$286$	−33.1003	−1.95726
$287$	20.5197	1.21124
$288$	−51.5202	−3.03586
$289$	3.97129	0.233605
$290$	−48.2520	−2.83346
$291$	−27.4962	−1.61186
$292$	−59.3736	−3.47458
$293$	15.9755	0.933300	0.466650	−	0.884442i	$-0.345461\pi$
$293$	15.9755	0.933300	0.466650	+	0.884442i	$0.345461\pi$
$294$	29.1656	1.70097
$295$	18.3682	1.06944
$296$	77.8380	4.52424
$297$	32.8604	1.90675
$298$	−55.4275	−3.21083
$299$	6.01154	0.347656
$300$	−22.1930	−1.28132
$301$	−5.04252	−0.290646
$302$	20.6239	1.18677
$303$	−8.60813	−0.494524
$304$	−18.6506	−1.06969
$305$	22.4418	1.28502
$306$	−90.1788	−5.15518
$307$	15.6159	0.891246	0.445623	−	0.895221i	$-0.352982\pi$
$307$	15.6159	0.891246	0.445623	+	0.895221i	$0.352982\pi$
$308$	−18.4216	−1.04967
$309$	−36.6744	−2.08633
$310$	−47.2199	−2.68191
$311$	−24.3750	−1.38218	−0.691091	−	0.722768i	$-0.742870\pi$
$311$	−24.3750	−1.38218	−0.691091	+	0.722768i	$0.742870\pi$
$312$	−129.557	−7.33472
$313$	−6.61690	−0.374009	−0.187005	−	0.982359i	$-0.559878\pi$
$313$	−6.61690	−0.374009	−0.187005	+	0.982359i	$0.559878\pi$
$314$	−40.4277	−2.28147
$315$	27.0146	1.52210
$316$	−27.7477	−1.56093
$317$	−8.44114	−0.474102	−0.237051	−	0.971497i	$-0.576181\pi$
$317$	−8.44114	−0.474102	−0.237051	+	0.971497i	$0.576181\pi$
$318$	19.0113	1.06610
$319$	−21.5625	−1.20727
$320$	−3.13722	−0.175376
$321$	−29.9658	−1.67253
$322$	4.80913	0.268002
$323$	−11.0053	−0.612354
$324$	123.261	6.84785
$325$	−8.92818	−0.495246
$326$	7.77784	0.430775
$327$	−15.8234	−0.875036
$328$	72.1312	3.98278
$329$	−2.68553	−0.148058
$330$	33.7374	1.85718
$331$	−14.3464	−0.788549	−0.394274	−	0.918993i	$-0.629004\pi$
$331$	−14.3464	−0.788549	−0.394274	+	0.918993i	$0.629004\pi$
$332$	24.2325	1.32993
$333$	−90.6702	−4.96870
$334$	52.0574	2.84845
$335$	−4.15906	−0.227234
$336$	−47.5800	−2.59570
$337$	31.7547	1.72979	0.864894	−	0.501954i	$-0.167385\pi$
$337$	31.7547	1.72979	0.864894	+	0.501954i	$0.167385\pi$
$338$	−59.3188	−3.22652
$339$	5.70844	0.310040
$340$	−39.2546	−2.12888
$341$	−21.1012	−1.14270
$342$	47.3242	2.55900
$343$	19.6613	1.06161
$344$	−17.7256	−0.955700
$345$	−6.12723	−0.329879
$346$	−39.7824	−2.13871
$347$	13.0826	0.702313	0.351156	−	0.936317i	$-0.385789\pi$
$347$	13.0826	0.702313	0.351156	+	0.936317i	$0.385789\pi$
$348$	−150.019	−8.04187
$349$	1.00000	0.0535288
$349$	1.00000	0.0535288
$350$	−7.14239	−0.381777
$351$	91.9743	4.90923
$352$	−14.4056	−0.767823
$353$	−13.5775	−0.722657	−0.361329	−	0.932439i	$-0.617677\pi$
$353$	−13.5775	−0.722657	−0.361329	+	0.932439i	$0.617677\pi$
$354$	82.0888	4.36297
$355$	−3.31454	−0.175918
$356$	23.7197	1.25714
$357$	−28.0760	−1.48594
$358$	−14.9097	−0.788000
$359$	−13.0604	−0.689299	−0.344650	−	0.938731i	$-0.612002\pi$
$359$	−13.0604	−0.689299	−0.344650	+	0.938731i	$0.612002\pi$
$360$	94.9623	5.00495
$361$	−13.2246	−0.696031
$362$	22.1673	1.16509
$363$	−20.8742	−1.09561
$364$	−51.5611	−2.70254
$365$	24.3455	1.27430
$366$	100.294	5.24245
$367$	23.7382	1.23912	0.619562	−	0.784947i	$-0.287310\pi$
$367$	23.7382	1.23912	0.619562	+	0.784947i	$0.287310\pi$
$368$	7.76072	0.404555
$369$	−84.0227	−4.37405
$370$	−56.7331	−2.94941
$371$	4.25651	0.220987
$372$	−146.810	−7.61175
$373$	−25.5406	−1.32244	−0.661222	−	0.750190i	$-0.729962\pi$
$373$	−25.5406	−1.32244	−0.661222	+	0.750190i	$0.729962\pi$
$374$	−25.2150	−1.30384
$375$	39.7362	2.05197
$376$	−9.44025	−0.486844
$377$	−60.3522	−3.10830
$378$	73.5779	3.78444
$379$	−20.8320	−1.07007	−0.535034	−	0.844830i	$-0.679701\pi$
$379$	−20.8320	−1.07007	−0.535034	+	0.844830i	$0.679701\pi$
$380$	20.6001	1.05676
$381$	51.1842	2.62224
$382$	4.03066	0.206226
$383$	−29.3108	−1.49771	−0.748855	−	0.662734i	$-0.769396\pi$
$383$	−29.3108	−1.49771	−0.748855	+	0.662734i	$0.769396\pi$
$384$	29.8209	1.52179
$385$	7.55359	0.384966
$386$	−21.9250	−1.11595
$387$	20.6478	1.04959
$388$	−38.4669	−1.95286
$389$	18.0836	0.916877	0.458439	−	0.888726i	$-0.348409\pi$
$389$	18.0836	0.916877	0.458439	+	0.888726i	$0.348409\pi$
$390$	94.4291	4.78160
$391$	4.57944	0.231592
$392$	22.9544	1.15937
$393$	−16.5201	−0.833331
$394$	20.3644	1.02595
$395$	11.3776	0.572470
$396$	75.4317	3.79058
$397$	−28.0089	−1.40573	−0.702863	−	0.711326i	$-0.748095\pi$
$397$	−28.0089	−1.40573	−0.702863	+	0.711326i	$0.748095\pi$
$398$	−7.16868	−0.359334
$399$	14.7338	0.737611
$400$	−11.5260	−0.576301
$401$	−27.4961	−1.37309	−0.686545	−	0.727087i	$-0.740873\pi$
$401$	−27.4961	−1.37309	−0.686545	+	0.727087i	$0.740873\pi$
$402$	−18.5871	−0.927041
$403$	−59.0612	−2.94205
$404$	−12.0427	−0.599146
$405$	−50.5420	−2.51145
$406$	−48.2807	−2.39613
$407$	−25.3524	−1.25667
$408$	−98.6934	−4.88605
$409$	16.1454	0.798339	0.399170	−	0.916877i	$-0.369298\pi$
$409$	16.1454	0.798339	0.399170	+	0.916877i	$0.369298\pi$
$410$	−52.5736	−2.59643
$411$	52.3659	2.58302
$412$	−51.3070	−2.52772
$413$	18.3792	0.904380
$414$	−19.6921	−0.967814
$415$	−9.93628	−0.487753
$416$	−40.3206	−1.97688
$417$	38.6594	1.89316
$418$	13.2324	0.647217
$419$	39.2601	1.91798	0.958991	−	0.283437i	$-0.0914747\pi$
$419$	39.2601	1.91798	0.958991	+	0.283437i	$0.0914747\pi$
$420$	52.5535	2.56435
$421$	26.6692	1.29978	0.649888	−	0.760030i	$-0.274816\pi$
$421$	26.6692	1.29978	0.649888	+	0.760030i	$0.274816\pi$
$422$	−1.80282	−0.0877599
$423$	10.9966	0.534671
$424$	14.9626	0.726647
$425$	−6.80127	−0.329910
$426$	−14.8129	−0.717687
$427$	22.4552	1.08668
$428$	−41.9218	−2.02636
$429$	42.1977	2.03732
$430$	12.9195	0.623033
$431$	10.7025	0.515522	0.257761	−	0.966209i	$-0.417015\pi$
$431$	10.7025	0.515522	0.257761	+	0.966209i	$0.417015\pi$
$432$	118.736	5.71270
$433$	10.6998	0.514201	0.257101	−	0.966385i	$-0.417233\pi$
$433$	10.6998	0.514201	0.257101	+	0.966385i	$0.417233\pi$
$434$	−47.2480	−2.26797
$435$	61.5137	2.94936
$436$	−22.1367	−1.06016
$437$	−2.40321	−0.114961
$438$	108.802	5.19874
$439$	−9.71922	−0.463873	−0.231937	−	0.972731i	$-0.574506\pi$
$439$	−9.71922	−0.463873	−0.231937	+	0.972731i	$0.574506\pi$
$440$	26.5525	1.26584
$441$	−26.7386	−1.27327
$442$	−70.5755	−3.35693
$443$	−22.1284	−1.05135	−0.525675	−	0.850685i	$-0.676187\pi$
$443$	−22.1284	−1.05135	−0.525675	+	0.850685i	$0.676187\pi$
$444$	−176.388	−8.37098
$445$	−9.72601	−0.461057
$446$	28.2648	1.33838
$447$	70.6614	3.34217
$448$	−3.13909	−0.148308
$449$	20.5334	0.969030	0.484515	−	0.874783i	$-0.338996\pi$
$449$	20.5334	0.969030	0.484515	+	0.874783i	$0.338996\pi$
$450$	29.2462	1.37868
$451$	−23.4937	−1.10627
$452$	7.98604	0.375632
$453$	−26.2922	−1.23531
$454$	−25.9719	−1.21892
$455$	21.1421	0.991156
$456$	51.7925	2.42541
$457$	42.6701	1.99602	0.998012	−	0.0630215i	$-0.0200737\pi$
$457$	42.6701	1.99602	0.998012	+	0.0630215i	$0.0200737\pi$
$458$	22.3437	1.04405
$459$	70.0638	3.27030
$460$	−8.57193	−0.399668
$461$	27.0826	1.26136	0.630681	−	0.776043i	$-0.282776\pi$
$461$	27.0826	1.26136	0.630681	+	0.776043i	$0.282776\pi$
$462$	33.7575	1.57054
$463$	13.7324	0.638200	0.319100	−	0.947721i	$-0.396619\pi$
$463$	13.7324	0.638200	0.319100	+	0.947721i	$0.396619\pi$
$464$	−77.9129	−3.61702
$465$	60.1979	2.79161
$466$	−26.4547	−1.22549
$467$	−8.00908	−0.370616	−0.185308	−	0.982680i	$-0.559328\pi$
$467$	−8.00908	−0.370616	−0.185308	+	0.982680i	$0.559328\pi$
$468$	211.129	9.75945
$469$	−4.16154	−0.192162
$470$	6.88063	0.317380
$471$	51.5390	2.37479
$472$	64.6069	2.97377
$473$	5.77336	0.265459
$474$	50.8473	2.33550
$475$	3.56918	0.163765
$476$	−39.2780	−1.80030
$477$	−17.4293	−0.798032
$478$	1.69206	0.0773930
$479$	17.6461	0.806272	0.403136	−	0.915140i	$-0.367920\pi$
$479$	17.6461	0.806272	0.403136	+	0.915140i	$0.367920\pi$
$480$	41.0966	1.87580
$481$	−70.9601	−3.23550
$482$	−14.2153	−0.647487
$483$	−6.13088	−0.278965
$484$	−29.2028	−1.32740
$485$	15.7729	0.716212
$486$	−108.207	−4.90838
$487$	−35.5476	−1.61081	−0.805407	−	0.592722i	$-0.798053\pi$
$487$	−35.5476	−1.61081	−0.805407	+	0.592722i	$0.798053\pi$
$488$	78.9350	3.57322
$489$	−9.91552	−0.448395
$490$	−16.7306	−0.755810
$491$	9.99394	0.451020	0.225510	−	0.974241i	$-0.427595\pi$
$491$	9.99394	0.451020	0.225510	+	0.974241i	$0.427595\pi$
$492$	−163.455	−7.36914
$493$	−45.9748	−2.07060
$494$	37.0367	1.66636
$495$	−30.9299	−1.39020
$496$	−76.2463	−3.42356
$497$	−3.31651	−0.148766
$498$	−44.4059	−1.98987
$499$	−33.3674	−1.49373	−0.746864	−	0.664977i	$-0.768442\pi$
$499$	−33.3674	−1.49373	−0.746864	+	0.664977i	$0.768442\pi$
$500$	55.5904	2.48608
$501$	−66.3650	−2.96497
$502$	−32.0201	−1.42913
$503$	−15.4644	−0.689523	−0.344762	−	0.938690i	$-0.612040\pi$
$503$	−15.4644	−0.689523	−0.344762	+	0.938690i	$0.612040\pi$
$504$	95.0188	4.23247
$505$	4.93797	0.219737
$506$	−5.50613	−0.244778
$507$	75.6221	3.35850
$508$	71.6060	3.17700
$509$	29.5534	1.30993	0.654967	−	0.755658i	$-0.272683\pi$
$509$	29.5534	1.30993	0.654967	+	0.755658i	$0.272683\pi$
$510$	71.9338	3.18528
$511$	24.3600	1.07762
$512$	50.2990	2.22292
$513$	−36.7682	−1.62336
$514$	26.3816	1.16364
$515$	21.0379	0.927040
$516$	40.1677	1.76828
$517$	3.07476	0.135228
$518$	−56.7669	−2.49419
$519$	50.7163	2.22620
$520$	74.3191	3.25911
$521$	12.6500	0.554206	0.277103	−	0.960840i	$-0.410626\pi$
$521$	12.6500	0.554206	0.277103	+	0.960840i	$0.410626\pi$
$522$	197.697	8.65295
$523$	−2.14509	−0.0937984	−0.0468992	−	0.998900i	$-0.514934\pi$
$523$	−2.14509	−0.0937984	−0.0468992	+	0.998900i	$0.514934\pi$
$524$	−23.1115	−1.00963
$525$	9.10542	0.397393
$526$	36.7044	1.60039
$527$	−44.9914	−1.95986
$528$	54.4760	2.37076
$529$	1.00000	0.0434783
$530$	−10.9056	−0.473711
$531$	−75.2578	−3.26591
$532$	20.6124	0.893660
$533$	−65.7576	−2.84828
$534$	−43.4662	−1.88097
$535$	17.1896	0.743169
$536$	−14.6287	−0.631865
$537$	19.0075	0.820233
$538$	15.5540	0.670582
$539$	−7.47642	−0.322032
$540$	−131.147	−5.64369
$541$	−26.0351	−1.11934	−0.559668	−	0.828717i	$-0.689071\pi$
$541$	−26.0351	−1.11934	−0.559668	+	0.828717i	$0.689071\pi$
$542$	5.78312	0.248406
$543$	−28.2599	−1.21275
$544$	−30.7153	−1.31691
$545$	9.07693	0.388813
$546$	94.4853	4.04360
$547$	8.22148	0.351525	0.175762	−	0.984433i	$-0.443761\pi$
$547$	8.22148	0.351525	0.175762	+	0.984433i	$0.443761\pi$
$548$	73.2593	3.12948
$549$	−91.9480	−3.92425
$550$	8.17757	0.348693
$551$	24.1267	1.02783
$552$	−21.5514	−0.917289
$553$	11.3844	0.484114
$554$	−24.4492	−1.03875
$555$	72.3258	3.07006
$556$	54.0840	2.29367
$557$	38.3538	1.62510	0.812552	−	0.582888i	$-0.198077\pi$
$557$	38.3538	1.62510	0.812552	+	0.582888i	$0.198077\pi$
$558$	193.468	8.19015
$559$	16.1593	0.683466
$560$	27.2938	1.15337
$561$	32.1452	1.35717
$562$	−41.7411	−1.76074
$563$	−7.34035	−0.309359	−0.154679	−	0.987965i	$-0.549434\pi$
$563$	−7.34035	−0.309359	−0.154679	+	0.987965i	$0.549434\pi$
$564$	21.3924	0.900783
$565$	−3.27459	−0.137763
$566$	5.26868	0.221459
$567$	−50.5720	−2.12383
$568$	−11.6583	−0.489171
$569$	−31.6537	−1.32699	−0.663495	−	0.748180i	$-0.730928\pi$
$569$	−31.6537	−1.32699	−0.663495	+	0.748180i	$0.730928\pi$
$570$	−37.7495	−1.58115
$571$	22.4960	0.941428	0.470714	−	0.882286i	$-0.343996\pi$
$571$	22.4960	0.941428	0.470714	+	0.882286i	$0.343996\pi$
$572$	59.0341	2.46834
$573$	−5.13846	−0.214662
$574$	−52.6049	−2.19569
$575$	−1.48517	−0.0619360
$576$	12.8537	0.535572
$577$	22.0930	0.919744	0.459872	−	0.887985i	$-0.347895\pi$
$577$	22.0930	0.919744	0.459872	+	0.887985i	$0.347895\pi$
$578$	−10.1809	−0.423471
$579$	27.9509	1.16160
$580$	86.0570	3.57332
$581$	−9.94219	−0.412472
$582$	70.4903	2.92192
$583$	−4.87343	−0.201837
$584$	85.6308	3.54343
$585$	−86.5712	−3.57928
$586$	−40.9554	−1.69185
$587$	−6.98383	−0.288253	−0.144127	−	0.989559i	$-0.546037\pi$
$587$	−6.98383	−0.288253	−0.144127	+	0.989559i	$0.546037\pi$
$588$	−52.0166	−2.14513
$589$	23.6107	0.972860
$590$	−47.0894	−1.93864
$591$	−25.9614	−1.06791
$592$	−91.6074	−3.76504
$593$	14.2295	0.584337	0.292168	−	0.956367i	$-0.405623\pi$
$593$	14.2295	0.584337	0.292168	+	0.956367i	$0.405623\pi$
$594$	−84.2419	−3.45649
$595$	16.1055	0.660262
$596$	98.8544	4.04924
$597$	9.13894	0.374032
$598$	−15.4114	−0.630218
$599$	19.7233	0.805872	0.402936	−	0.915228i	$-0.367990\pi$
$599$	19.7233	0.805872	0.402936	+	0.915228i	$0.367990\pi$
$600$	32.0076	1.30670
$601$	−39.1149	−1.59553	−0.797766	−	0.602968i	$-0.793985\pi$
$601$	−39.1149	−1.59553	−0.797766	+	0.602968i	$0.793985\pi$
$602$	12.9272	0.526872
$603$	17.0404	0.693939
$604$	−36.7824	−1.49666
$605$	11.9743	0.486824
$606$	22.0681	0.896455
$607$	13.6285	0.553162	0.276581	−	0.960991i	$-0.410799\pi$
$607$	13.6285	0.553162	0.276581	+	0.960991i	$0.410799\pi$
$608$	16.1188	0.653704
$609$	61.5503	2.49415
$610$	−57.5326	−2.32943
$611$	8.60609	0.348165
$612$	160.833	6.50129
$613$	−18.0269	−0.728099	−0.364050	−	0.931380i	$-0.618606\pi$
$613$	−18.0269	−0.728099	−0.364050	+	0.931380i	$0.618606\pi$
$614$	−40.0334	−1.61562
$615$	67.0231	2.70263
$616$	26.5683	1.07047
$617$	−41.0943	−1.65439	−0.827197	−	0.561913i	$-0.810066\pi$
$617$	−41.0943	−1.65439	−0.827197	+	0.561913i	$0.810066\pi$
$618$	94.0196	3.78202
$619$	−34.3574	−1.38094	−0.690470	−	0.723361i	$-0.742596\pi$
$619$	−34.3574	−1.38094	−0.690470	+	0.723361i	$0.742596\pi$
$620$	84.2162	3.38220
$621$	15.2996	0.613954
$622$	62.4887	2.50557
$623$	−9.73180	−0.389896
$624$	152.475	6.10390
$625$	−15.3684	−0.614735
$626$	16.9633	0.677990
$627$	−16.8692	−0.673691
$628$	72.1024	2.87720
$629$	−54.0557	−2.15534
$630$	−69.2555	−2.75920
$631$	2.03467	0.0809990	0.0404995	−	0.999180i	$-0.487105\pi$
$631$	2.03467	0.0809990	0.0404995	+	0.999180i	$0.487105\pi$
$632$	40.0187	1.59186
$633$	2.29831	0.0913497
$634$	21.6400	0.859434
$635$	−29.3613	−1.16517
$636$	−33.9065	−1.34448
$637$	−20.9261	−0.829122
$638$	55.2783	2.18849
$639$	13.5802	0.537226
$640$	−17.1065	−0.676193
$641$	39.9006	1.57598	0.787990	−	0.615688i	$-0.211122\pi$
$641$	39.9006	1.57598	0.787990	+	0.615688i	$0.211122\pi$
$642$	76.8212	3.03189
$643$	31.8764	1.25708	0.628540	−	0.777777i	$-0.283653\pi$
$643$	31.8764	1.25708	0.628540	+	0.777777i	$0.283653\pi$
$644$	−8.57703	−0.337982
$645$	−16.4703	−0.648518
$646$	28.2137	1.11005
$647$	11.0914	0.436046	0.218023	−	0.975944i	$-0.430039\pi$
$647$	11.0914	0.436046	0.218023	+	0.975944i	$0.430039\pi$
$648$	−177.772	−6.98354
$649$	−21.0429	−0.826008
$650$	22.8886	0.897763
$651$	60.2337	2.36075
$652$	−13.8717	−0.543258
$653$	−21.8914	−0.856675	−0.428338	−	0.903619i	$-0.640901\pi$
$653$	−21.8914	−0.856675	−0.428338	+	0.903619i	$0.640901\pi$
$654$	40.5654	1.58623
$655$	9.47662	0.370282
$656$	−84.8911	−3.31444
$657$	−99.7477	−3.89153
$658$	6.88472	0.268394
$659$	−41.7916	−1.62797	−0.813985	−	0.580886i	$-0.802706\pi$
$659$	−41.7916	−1.62797	−0.813985	+	0.580886i	$0.802706\pi$
$660$	−60.1703	−2.34213
$661$	25.7101	1.00001	0.500004	−	0.866023i	$-0.333332\pi$
$661$	25.7101	1.00001	0.500004	+	0.866023i	$0.333332\pi$
$662$	36.7789	1.42945
$663$	89.9726	3.49425
$664$	−34.9490	−1.35629
$665$	−8.45188	−0.327750
$666$	232.445	9.00707
$667$	−10.0394	−0.388727
$668$	−92.8438	−3.59223
$669$	−36.0332	−1.39313
$670$	10.6623	0.411921
$671$	−25.7097	−0.992513
$672$	41.1211	1.58628
$673$	−17.6307	−0.679615	−0.339807	−	0.940495i	$-0.610362\pi$
$673$	−17.6307	−0.679615	−0.339807	+	0.940495i	$0.610362\pi$
$674$	−81.4074	−3.13570
$675$	−22.7226	−0.874595
$676$	105.794	4.06902
$677$	11.8285	0.454605	0.227302	−	0.973824i	$-0.427009\pi$
$677$	11.8285	0.454605	0.227302	+	0.973824i	$0.427009\pi$
$678$	−14.6343	−0.562029
$679$	15.7823	0.605670
$680$	56.6145	2.17107
$681$	33.1101	1.26878
$682$	54.0958	2.07144
$683$	−37.2266	−1.42443	−0.712217	−	0.701959i	$-0.752309\pi$
$683$	−37.2266	−1.42443	−0.712217	+	0.701959i	$0.752309\pi$
$684$	−84.4022	−3.22720
$685$	−30.0392	−1.14774
$686$	−50.4044	−1.92445
$687$	−28.4848	−1.08676
$688$	20.8612	0.795326
$689$	−13.6405	−0.519660
$690$	15.7080	0.597993
$691$	−6.08494	−0.231482	−0.115741	−	0.993279i	$-0.536924\pi$
$691$	−6.08494	−0.231482	−0.115741	+	0.993279i	$0.536924\pi$
$692$	70.9514	2.69717
$693$	−30.9483	−1.17563
$694$	−33.5391	−1.27313
$695$	−22.1766	−0.841205
$696$	216.363	8.20122
$697$	−50.0925	−1.89739
$698$	−2.56363	−0.0970349
$699$	33.7256	1.27562
$700$	12.7384	0.481466
$701$	42.0610	1.58862	0.794311	−	0.607511i	$-0.207832\pi$
$701$	42.0610	1.58862	0.794311	+	0.607511i	$0.207832\pi$
$702$	−235.788	−8.89926
$703$	28.3674	1.06990
$704$	3.59405	0.135456
$705$	−8.77172	−0.330362
$706$	34.8077	1.31001
$707$	4.94091	0.185822
$708$	−146.405	−5.50222
$709$	9.11628	0.342369	0.171185	−	0.985239i	$-0.445241\pi$
$709$	9.11628	0.342369	0.171185	+	0.985239i	$0.445241\pi$
$710$	8.49727	0.318897
$711$	−46.6161	−1.74824
$712$	−34.2094	−1.28205
$713$	−9.82464	−0.367936
$714$	71.9766	2.69366
$715$	−24.2063	−0.905264
$716$	26.5912	0.993761
$717$	−2.15711	−0.0805588
$718$	33.4820	1.24954
$719$	32.2412	1.20239	0.601197	−	0.799101i	$-0.294691\pi$
$719$	32.2412	1.20239	0.601197	+	0.799101i	$0.294691\pi$
$720$	−111.761	−4.16508
$721$	21.0504	0.783958
$722$	33.9030	1.26174
$723$	18.1222	0.673973
$724$	−39.5352	−1.46931
$725$	14.9103	0.553753
$726$	53.5139	1.98609
$727$	−5.59182	−0.207389	−0.103695	−	0.994609i	$-0.533066\pi$
$727$	−5.59182	−0.207389	−0.103695	+	0.994609i	$0.533066\pi$
$728$	74.3633	2.75609
$729$	57.0708	2.11373
$730$	−62.4129	−2.31001
$731$	12.3098	0.455293
$732$	−178.873	−6.61135
$733$	−16.0245	−0.591878	−0.295939	−	0.955207i	$-0.595632\pi$
$733$	−16.0245	−0.591878	−0.295939	+	0.955207i	$0.595632\pi$
$734$	−60.8561	−2.24624
$735$	21.3288	0.786726
$736$	−6.70720	−0.247231
$737$	4.76469	0.175510
$738$	215.403	7.92910
$739$	−26.5545	−0.976824	−0.488412	−	0.872613i	$-0.662424\pi$
$739$	−26.5545	−0.976824	−0.488412	+	0.872613i	$0.662424\pi$
$740$	101.183	3.71956
$741$	−47.2160	−1.73452
$742$	−10.9121	−0.400597
$743$	−25.2866	−0.927674	−0.463837	−	0.885921i	$-0.653528\pi$
$743$	−25.2866	−0.927674	−0.463837	+	0.885921i	$0.653528\pi$
$744$	211.735	7.76258
$745$	−40.5342	−1.48506
$746$	65.4768	2.39728
$747$	40.7107	1.48952
$748$	44.9707	1.64429
$749$	17.1998	0.628467
$750$	−101.869	−3.71973
$751$	−51.3395	−1.87341	−0.936703	−	0.350126i	$-0.886139\pi$
$751$	−51.3395	−1.87341	−0.936703	+	0.350126i	$0.886139\pi$
$752$	11.1102	0.405148
$753$	40.8206	1.48758
$754$	154.721	5.63460
$755$	15.0822	0.548899
$756$	−131.225	−4.77262
$757$	−8.86106	−0.322061	−0.161030	−	0.986949i	$-0.551482\pi$
$757$	−8.86106	−0.322061	−0.161030	+	0.986949i	$0.551482\pi$
$758$	53.4056	1.93978
$759$	7.01946	0.254790
$760$	−29.7102	−1.07770
$761$	−52.0154	−1.88556	−0.942778	−	0.333422i	$-0.891797\pi$
$761$	−52.0154	−1.88556	−0.942778	+	0.333422i	$0.891797\pi$
$762$	−131.217	−4.75351
$763$	9.08233	0.328803
$764$	−7.18864	−0.260076
$765$	−65.9478	−2.38435
$766$	75.1421	2.71499
$767$	−58.8981	−2.12669
$768$	−87.3879	−3.15334
$769$	41.4219	1.49371	0.746856	−	0.664986i	$-0.231563\pi$
$769$	41.4219	1.49371	0.746856	+	0.664986i	$0.231563\pi$
$770$	−19.3646	−0.697853
$771$	−33.6324	−1.21124
$772$	39.1030	1.40735
$773$	55.0485	1.97996	0.989978	−	0.141220i	$-0.0451026\pi$
$773$	55.0485	1.97996	0.989978	+	0.141220i	$0.0451026\pi$
$774$	−52.9334	−1.90265
$775$	14.5913	0.524135
$776$	55.4784	1.99156
$777$	72.3688	2.59622
$778$	−46.3598	−1.66208
$779$	26.2876	0.941852
$780$	−168.413	−6.03016
$781$	3.79719	0.135874
$782$	−11.7400	−0.419822
$783$	−153.599	−5.48919
$784$	−27.0150	−0.964821
$785$	−29.5648	−1.05521
$786$	42.3516	1.51063
$787$	−16.5104	−0.588531	−0.294265	−	0.955724i	$-0.595075\pi$
$787$	−16.5104	−0.588531	−0.294265	+	0.955724i	$0.595075\pi$
$788$	−36.3198	−1.29384
$789$	−46.7923	−1.66585
$790$	−29.1681	−1.03775
$791$	−3.27654	−0.116500
$792$	−108.790	−3.86569
$793$	−71.9601	−2.55538
$794$	71.8045	2.54825
$795$	13.9030	0.493088
$796$	12.7853	0.453162
$797$	−38.3017	−1.35672	−0.678358	−	0.734732i	$-0.737308\pi$
$797$	−38.3017	−1.35672	−0.678358	+	0.734732i	$0.737308\pi$
$798$	−37.7720	−1.33711
$799$	6.55591	0.231931
$800$	9.96137	0.352187
$801$	39.8491	1.40800
$802$	70.4899	2.48909
$803$	−27.8906	−0.984238
$804$	33.1499	1.16911
$805$	3.51692	0.123955
$806$	151.411	5.33323
$807$	−19.8289	−0.698012
$808$	17.3684	0.611018
$809$	7.36059	0.258785	0.129392	−	0.991593i	$-0.458697\pi$
$809$	7.36059	0.258785	0.129392	+	0.991593i	$0.458697\pi$
$810$	129.571	4.55266
$811$	49.3127	1.73160	0.865802	−	0.500387i	$-0.166809\pi$
$811$	49.3127	1.73160	0.865802	+	0.500387i	$0.166809\pi$
$812$	86.1082	3.02181
$813$	−7.37258	−0.258568
$814$	64.9943	2.27805
$815$	5.68794	0.199240
$816$	116.152	4.06614
$817$	−6.45994	−0.226005
$818$	−41.3909	−1.44720
$819$	−86.6227	−3.02684
$820$	93.7646	3.27440
$821$	27.4086	0.956567	0.478283	−	0.878206i	$-0.341259\pi$
$821$	27.4086	0.956567	0.478283	+	0.878206i	$0.341259\pi$
$822$	−134.247	−4.68240
$823$	6.70085	0.233577	0.116789	−	0.993157i	$-0.462740\pi$
$823$	6.70085	0.233577	0.116789	+	0.993157i	$0.462740\pi$
$824$	73.9968	2.57780
$825$	−10.4251	−0.362956
$826$	−47.1175	−1.63943
$827$	32.3804	1.12598	0.562988	−	0.826465i	$-0.309652\pi$
$827$	32.3804	1.12598	0.562988	+	0.826465i	$0.309652\pi$
$828$	35.1207	1.22053
$829$	23.8250	0.827478	0.413739	−	0.910396i	$-0.364223\pi$
$829$	23.8250	0.827478	0.413739	+	0.910396i	$0.364223\pi$
$830$	25.4730	0.884180
$831$	31.1689	1.08124
$832$	10.0596	0.348752
$833$	−15.9410	−0.552322
$834$	−99.1085	−3.43185
$835$	38.0696	1.31745
$836$	−23.5998	−0.816217
$837$	−150.314	−5.19560
$838$	−100.649	−3.47685
$839$	37.0047	1.27754	0.638771	−	0.769397i	$-0.279443\pi$
$839$	37.0047	1.27754	0.638771	+	0.769397i	$0.279443\pi$
$840$	−75.7945	−2.61516
$841$	71.7895	2.47550
$842$	−68.3699	−2.35618
$843$	53.2134	1.83277
$844$	3.21531	0.110676
$845$	−43.3799	−1.49231
$846$	−28.1911	−0.969231
$847$	11.9814	0.411686
$848$	−17.6094	−0.604710
$849$	−6.71674	−0.230518
$850$	17.4360	0.598048
$851$	−11.8040	−0.404635
$852$	26.4187	0.905088
$853$	6.66526	0.228214	0.114107	−	0.993468i	$-0.463599\pi$
$853$	6.66526	0.228214	0.114107	+	0.993468i	$0.463599\pi$
$854$	−57.5669	−1.96990
$855$	34.6082	1.18358
$856$	60.4611	2.06652
$857$	37.6961	1.28767	0.643837	−	0.765163i	$-0.277341\pi$
$857$	37.6961	1.28767	0.643837	+	0.765163i	$0.277341\pi$
$858$	−108.179	−3.69319
$859$	−39.1305	−1.33512	−0.667558	−	0.744558i	$-0.732660\pi$
$859$	−39.1305	−1.33512	−0.667558	+	0.744558i	$0.732660\pi$
$860$	−23.0418	−0.785718
$861$	67.0630	2.28550
$862$	−27.4373	−0.934520
$863$	20.3804	0.693755	0.346878	−	0.937910i	$-0.387242\pi$
$863$	20.3804	0.693755	0.346878	+	0.937910i	$0.387242\pi$
$864$	−102.618	−3.49113
$865$	−29.0929	−0.989187
$866$	−27.4304	−0.932125
$867$	12.9791	0.440793
$868$	84.2663	2.86018
$869$	−13.0344	−0.442161
$870$	−157.699	−5.34648
$871$	13.3361	0.451877
$872$	31.9264	1.08116
$873$	−64.6245	−2.18721
$874$	6.16094	0.208397
$875$	−22.8078	−0.771045
$876$	−194.047	−6.55623
$877$	−10.4834	−0.353999	−0.176999	−	0.984211i	$-0.556639\pi$
$877$	−10.4834	−0.353999	−0.176999	+	0.984211i	$0.556639\pi$
$878$	24.9165	0.840892
$879$	52.2117	1.76106
$880$	−31.2496	−1.05342
$881$	10.1925	0.343394	0.171697	−	0.985150i	$-0.445075\pi$
$881$	10.1925	0.343394	0.171697	+	0.985150i	$0.445075\pi$
$882$	68.5480	2.30813
$883$	20.7058	0.696805	0.348402	−	0.937345i	$-0.386724\pi$
$883$	20.7058	0.696805	0.348402	+	0.937345i	$0.386724\pi$
$884$	125.871	4.23349
$885$	60.0316	2.01794
$886$	56.7290	1.90585
$887$	29.7295	0.998218	0.499109	−	0.866539i	$-0.333661\pi$
$887$	29.7295	0.998218	0.499109	+	0.866539i	$0.333661\pi$
$888$	254.393	8.53685
$889$	−29.3788	−0.985332
$890$	24.9339	0.835787
$891$	57.9017	1.93978
$892$	−50.4101	−1.68785
$893$	−3.44042	−0.115129
$894$	−181.150	−6.05856
$895$	−10.9034	−0.364462
$896$	−17.1167	−0.571827
$897$	19.6471	0.655997
$898$	−52.6400	−1.75662
$899$	98.6335	3.28961
$900$	−52.1603	−1.73868
$901$	−10.3910	−0.346173
$902$	60.2292	2.00541
$903$	−16.4801	−0.548424
$904$	−11.5178	−0.383075
$905$	16.2110	0.538871
$906$	67.4035	2.23933
$907$	−57.3966	−1.90582	−0.952912	−	0.303247i	$-0.901929\pi$
$907$	−57.3966	−1.90582	−0.952912	+	0.303247i	$0.901929\pi$
$908$	46.3206	1.53720
$909$	−20.2317	−0.671043
$910$	−54.2005	−1.79673
$911$	−2.40857	−0.0797995	−0.0398997	−	0.999204i	$-0.512704\pi$
$911$	−2.40857	−0.0797995	−0.0398997	+	0.999204i	$0.512704\pi$
$912$	−60.9545	−2.01840
$913$	11.3832	0.376728
$914$	−109.391	−3.61832
$915$	73.3450	2.42471
$916$	−39.8498	−1.31668
$917$	9.48226	0.313132
$918$	−179.618	−5.92828
$919$	−29.7420	−0.981098	−0.490549	−	0.871414i	$-0.663204\pi$
$919$	−29.7420	−0.981098	−0.490549	+	0.871414i	$0.663204\pi$
$920$	12.3627	0.407588
$921$	51.0363	1.68170
$922$	−69.4298	−2.28655
$923$	10.6281	0.349829
$924$	−60.2061	−1.98063
$925$	17.5310	0.576415
$926$	−35.2049	−1.15690
$927$	−86.1958	−2.83104
$928$	67.3363	2.21042
$929$	15.5248	0.509351	0.254675	−	0.967027i	$-0.418031\pi$
$929$	15.5248	0.509351	0.254675	+	0.967027i	$0.418031\pi$
$930$	−154.325	−5.06053
$931$	8.36554	0.274169
$932$	47.1818	1.54549
$933$	−79.6632	−2.60806
$934$	20.5323	0.671839
$935$	−18.4398	−0.603045
$936$	−304.498	−9.95283
$937$	6.61584	0.216130	0.108065	−	0.994144i	$-0.465535\pi$
$937$	6.61584	0.216130	0.108065	+	0.994144i	$0.465535\pi$
$938$	10.6687	0.348344
$939$	−21.6256	−0.705723
$940$	−12.2715	−0.400253
$941$	−15.8169	−0.515618	−0.257809	−	0.966196i	$-0.583000\pi$
$941$	−15.8169	−0.515618	−0.257809	+	0.966196i	$0.583000\pi$
$942$	−132.127	−4.30493
$943$	−10.9386	−0.356209
$944$	−76.0357	−2.47475
$945$	53.8076	1.75036
$946$	−14.8008	−0.481215
$947$	−28.0629	−0.911923	−0.455961	−	0.890000i	$-0.650704\pi$
$947$	−28.0629	−0.911923	−0.455961	+	0.890000i	$0.650704\pi$
$948$	−90.6857	−2.94534
$949$	−78.0643	−2.53407
$950$	−9.15007	−0.296867
$951$	−27.5876	−0.894589
$952$	56.6482	1.83598
$953$	−43.9925	−1.42506	−0.712529	−	0.701642i	$-0.752450\pi$
$953$	−43.9925	−1.42506	−0.712529	+	0.701642i	$0.752450\pi$
$954$	44.6823	1.44664
$955$	2.94762	0.0953829
$956$	−3.01777	−0.0976017
$957$	−70.4711	−2.27801
$958$	−45.2382	−1.46158
$959$	−30.0571	−0.970593
$960$	−10.2532	−0.330919
$961$	65.5236	2.11367
$962$	181.916	5.86519
$963$	−70.4286	−2.26953
$964$	25.3528	0.816558
$965$	−16.0337	−0.516145
$966$	15.7173	0.505697
$967$	−4.24945	−0.136653	−0.0683265	−	0.997663i	$-0.521766\pi$
$967$	−4.24945	−0.136653	−0.0683265	+	0.997663i	$0.521766\pi$
$968$	42.1174	1.35370
$969$	−35.9680	−1.15546
$970$	−40.4360	−1.29832
$971$	60.0199	1.92613	0.963065	−	0.269269i	$-0.0867822\pi$
$971$	60.0199	1.92613	0.963065	+	0.269269i	$0.0867822\pi$
$972$	192.986	6.19004
$973$	−22.1898	−0.711371
$974$	91.1310	2.92002
$975$	−29.1793	−0.934486
$976$	−92.8984	−2.97361
$977$	−41.3474	−1.32282	−0.661410	−	0.750025i	$-0.730042\pi$
$977$	−41.3474	−1.32282	−0.661410	+	0.750025i	$0.730042\pi$
$978$	25.4198	0.812834
$979$	11.1423	0.356109
$980$	29.8388	0.953165
$981$	−37.1897	−1.18738
$982$	−25.6208	−0.817592
$983$	−43.1643	−1.37673	−0.688364	−	0.725366i	$-0.741671\pi$
$983$	−43.1643	−1.37673	−0.688364	+	0.725366i	$0.741671\pi$
$984$	235.741	7.51516
$985$	14.8925	0.474515
$986$	117.863	3.75351
$987$	−8.77694	−0.279373
$988$	−66.0546	−2.10148
$989$	2.68805	0.0854751
$990$	79.2930	2.52010
$991$	−4.37912	−0.139107	−0.0695537	−	0.997578i	$-0.522158\pi$
$991$	−4.37912	−0.139107	−0.0695537	+	0.997578i	$0.522158\pi$
$992$	65.8959	2.09220
$993$	−46.8873	−1.48792
$994$	8.50232	0.269677
$995$	−5.24246	−0.166197
$996$	79.1974	2.50947
$997$	28.5265	0.903444	0.451722	−	0.892159i	$-0.350810\pi$
$997$	28.5265	0.903444	0.451722	+	0.892159i	$0.350810\pi$
$998$	85.5417	2.70777
$999$	−180.597	−5.71383

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8027.2.a.c.1.9	✓	143

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8027.2.a.c.1.9	✓	143	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:	\( N \)	\(=\)	\( 8027 = 23 \cdot 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8027.a (trivial)

\(f(q)\)	\(=\)	\(q-2.56363 q^{2} +3.26823 q^{3} +4.57221 q^{4} -1.87479 q^{5} -8.37854 q^{6} -1.87590 q^{7} -6.59421 q^{8} +7.68132 q^{9} +O(q^{10})\)	\(q-2.56363 q^{2} +3.26823 q^{3} +4.57221 q^{4} -1.87479 q^{5} -8.37854 q^{6} -1.87590 q^{7} -6.59421 q^{8} +7.68132 q^{9} +4.80627 q^{10} +2.14779 q^{11} +14.9430 q^{12} +6.01154 q^{13} +4.80913 q^{14} -6.12723 q^{15} +7.76072 q^{16} +4.57944 q^{17} -19.6921 q^{18} -2.40321 q^{19} -8.57193 q^{20} -6.13088 q^{21} -5.50613 q^{22} +1.00000 q^{23} -21.5514 q^{24} -1.48517 q^{25} -15.4114 q^{26} +15.2996 q^{27} -8.57703 q^{28} -10.0394 q^{29} +15.7080 q^{30} -9.82464 q^{31} -6.70720 q^{32} +7.01946 q^{33} -11.7400 q^{34} +3.51692 q^{35} +35.1207 q^{36} -11.8040 q^{37} +6.16094 q^{38} +19.6471 q^{39} +12.3627 q^{40} -10.9386 q^{41} +15.7173 q^{42} +2.68805 q^{43} +9.82014 q^{44} -14.4008 q^{45} -2.56363 q^{46} +1.43160 q^{47} +25.3638 q^{48} -3.48099 q^{49} +3.80744 q^{50} +14.9667 q^{51} +27.4860 q^{52} -2.26905 q^{53} -39.2227 q^{54} -4.02664 q^{55} +12.3701 q^{56} -7.85423 q^{57} +25.7373 q^{58} -9.79751 q^{59} -28.0150 q^{60} -11.9703 q^{61} +25.1868 q^{62} -14.4094 q^{63} +1.67337 q^{64} -11.2703 q^{65} -17.9953 q^{66} +2.21842 q^{67} +20.9382 q^{68} +3.26823 q^{69} -9.01609 q^{70} +1.76796 q^{71} -50.6523 q^{72} -12.9857 q^{73} +30.2611 q^{74} -4.85389 q^{75} -10.9880 q^{76} -4.02904 q^{77} -50.3679 q^{78} -6.06876 q^{79} -14.5497 q^{80} +26.9588 q^{81} +28.0425 q^{82} +5.29995 q^{83} -28.0317 q^{84} -8.58548 q^{85} -6.89118 q^{86} -32.8111 q^{87} -14.1630 q^{88} +5.18780 q^{89} +36.9185 q^{90} -11.2771 q^{91} +4.57221 q^{92} -32.1092 q^{93} -3.67009 q^{94} +4.50550 q^{95} -21.9207 q^{96} -8.41319 q^{97} +8.92398 q^{98} +16.4978 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 143 q - 17 q^{2} - 17 q^{3} + 121 q^{4} - 22 q^{5} - 11 q^{6} - 33 q^{7} - 45 q^{8} + 104 q^{9}+O(q^{10}) \) 143 * q - 17 * q^2 - 17 * q^3 + 121 * q^4 - 22 * q^5 - 11 * q^6 - 33 * q^7 - 45 * q^8 + 104 * q^9	\( 143 q - 17 q^{2} - 17 q^{3} + 121 q^{4} - 22 q^{5} - 11 q^{6} - 33 q^{7} - 45 q^{8} + 104 q^{9} - 22 q^{10} - 14 q^{11} - 36 q^{12} - 87 q^{13} - 18 q^{14} - 19 q^{15} + 81 q^{16} - 14 q^{17} - 60 q^{18} - 18 q^{19} - 25 q^{20} - 26 q^{21} - 62 q^{22} + 143 q^{23} - 21 q^{24} + 67 q^{25} - 5 q^{26} - 47 q^{27} - 76 q^{28} - 54 q^{29} - 22 q^{30} - 62 q^{31} - 117 q^{32} - 59 q^{33} - 35 q^{34} - 52 q^{35} + 52 q^{36} - 190 q^{37} - 19 q^{38} - 43 q^{39} - 41 q^{40} - 50 q^{41} + 8 q^{42} - 50 q^{43} - 18 q^{44} - 75 q^{45} - 17 q^{46} - 63 q^{47} - 35 q^{48} + 74 q^{49} - 53 q^{50} - 33 q^{51} - 124 q^{52} - 100 q^{53} - 46 q^{54} - 61 q^{55} - 3 q^{56} - 80 q^{57} - 112 q^{58} - 109 q^{59} - 55 q^{60} - 76 q^{61} - 6 q^{62} - 93 q^{63} + 57 q^{64} - 17 q^{65} + 50 q^{66} - 120 q^{67} + 26 q^{68} - 17 q^{69} - 109 q^{71} - 153 q^{72} - 94 q^{73} + 35 q^{74} - 105 q^{75} - 16 q^{76} - 52 q^{77} - 59 q^{78} - 29 q^{79} - 30 q^{80} + 39 q^{81} - 65 q^{82} + 8 q^{83} + 11 q^{84} - 155 q^{85} - 15 q^{86} - 25 q^{87} - 139 q^{88} + 6 q^{89} + 82 q^{90} - 34 q^{91} + 121 q^{92} - 151 q^{93} - 3 q^{94} - 70 q^{95} - 23 q^{96} - 203 q^{97} - 18 q^{98} - 49 q^{99}+O(q^{100}) \) 143 * q - 17 * q^2 - 17 * q^3 + 121 * q^4 - 22 * q^5 - 11 * q^6 - 33 * q^7 - 45 * q^8 + 104 * q^9 - 22 * q^10 - 14 * q^11 - 36 * q^12 - 87 * q^13 - 18 * q^14 - 19 * q^15 + 81 * q^16 - 14 * q^17 - 60 * q^18 - 18 * q^19 - 25 * q^20 - 26 * q^21 - 62 * q^22 + 143 * q^23 - 21 * q^24 + 67 * q^25 - 5 * q^26 - 47 * q^27 - 76 * q^28 - 54 * q^29 - 22 * q^30 - 62 * q^31 - 117 * q^32 - 59 * q^33 - 35 * q^34 - 52 * q^35 + 52 * q^36 - 190 * q^37 - 19 * q^38 - 43 * q^39 - 41 * q^40 - 50 * q^41 + 8 * q^42 - 50 * q^43 - 18 * q^44 - 75 * q^45 - 17 * q^46 - 63 * q^47 - 35 * q^48 + 74 * q^49 - 53 * q^50 - 33 * q^51 - 124 * q^52 - 100 * q^53 - 46 * q^54 - 61 * q^55 - 3 * q^56 - 80 * q^57 - 112 * q^58 - 109 * q^59 - 55 * q^60 - 76 * q^61 - 6 * q^62 - 93 * q^63 + 57 * q^64 - 17 * q^65 + 50 * q^66 - 120 * q^67 + 26 * q^68 - 17 * q^69 - 109 * q^71 - 153 * q^72 - 94 * q^73 + 35 * q^74 - 105 * q^75 - 16 * q^76 - 52 * q^77 - 59 * q^78 - 29 * q^79 - 30 * q^80 + 39 * q^81 - 65 * q^82 + 8 * q^83 + 11 * q^84 - 155 * q^85 - 15 * q^86 - 25 * q^87 - 139 * q^88 + 6 * q^89 + 82 * q^90 - 34 * q^91 + 121 * q^92 - 151 * q^93 - 3 * q^94 - 70 * q^95 - 23 * q^96 - 203 * q^97 - 18 * q^98 - 49 * q^99

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