LMFDB - Embedded newform 4009.2.a.c.1.30

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4009,2,Mod(1,4009)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4009, 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("4009.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4009 = 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4009.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:	$32.0120261703$
Analytic rank:	$1$
Dimension:	$71$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.30
Character	$\chi$	$=$	4009.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00678 q^{2} -2.96425 q^{3} -0.986402 q^{4} +0.219154 q^{5} +2.98434 q^{6} +3.36402 q^{7} +3.00664 q^{8} +5.78680 q^{9} +O(q^{10})$	\(q-1.00678 q^{2} -2.96425 q^{3} -0.986402 q^{4} +0.219154 q^{5} +2.98434 q^{6} +3.36402 q^{7} +3.00664 q^{8} +5.78680 q^{9} -0.220639 q^{10} +3.87533 q^{11} +2.92395 q^{12} +0.532354 q^{13} -3.38681 q^{14} -0.649629 q^{15} -1.05421 q^{16} +4.77500 q^{17} -5.82601 q^{18} +1.00000 q^{19} -0.216174 q^{20} -9.97181 q^{21} -3.90159 q^{22} -8.92669 q^{23} -8.91244 q^{24} -4.95197 q^{25} -0.535962 q^{26} -8.26079 q^{27} -3.31828 q^{28} +0.0766535 q^{29} +0.654031 q^{30} -7.44890 q^{31} -4.95193 q^{32} -11.4875 q^{33} -4.80736 q^{34} +0.737239 q^{35} -5.70812 q^{36} -4.23988 q^{37} -1.00678 q^{38} -1.57803 q^{39} +0.658918 q^{40} +2.36046 q^{41} +10.0394 q^{42} +8.04888 q^{43} -3.82264 q^{44} +1.26820 q^{45} +8.98717 q^{46} +1.28540 q^{47} +3.12493 q^{48} +4.31662 q^{49} +4.98553 q^{50} -14.1543 q^{51} -0.525116 q^{52} +0.910239 q^{53} +8.31677 q^{54} +0.849296 q^{55} +10.1144 q^{56} -2.96425 q^{57} -0.0771729 q^{58} -4.76522 q^{59} +0.640796 q^{60} -10.5292 q^{61} +7.49937 q^{62} +19.4669 q^{63} +7.09389 q^{64} +0.116668 q^{65} +11.5653 q^{66} -4.37216 q^{67} -4.71007 q^{68} +26.4610 q^{69} -0.742235 q^{70} +5.72851 q^{71} +17.3988 q^{72} +2.94773 q^{73} +4.26861 q^{74} +14.6789 q^{75} -0.986402 q^{76} +13.0367 q^{77} +1.58873 q^{78} -1.93676 q^{79} -0.231034 q^{80} +7.12668 q^{81} -2.37645 q^{82} -12.5882 q^{83} +9.83621 q^{84} +1.04646 q^{85} -8.10342 q^{86} -0.227220 q^{87} +11.6517 q^{88} -5.58994 q^{89} -1.27680 q^{90} +1.79085 q^{91} +8.80530 q^{92} +22.0804 q^{93} -1.29411 q^{94} +0.219154 q^{95} +14.6788 q^{96} +2.37302 q^{97} -4.34587 q^{98} +22.4258 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 71 q - 15 q^{2} - 8 q^{3} + 69 q^{4} - 18 q^{5} - 9 q^{6} - 19 q^{7} - 39 q^{8} + 63 q^{9}+O(q^{10}) $ 71 * q - 15 * q^2 - 8 * q^3 + 69 * q^4 - 18 * q^5 - 9 * q^6 - 19 * q^7 - 39 * q^8 + 63 * q^9	\( 71 q - 15 q^{2} - 8 q^{3} + 69 q^{4} - 18 q^{5} - 9 q^{6} - 19 q^{7} - 39 q^{8} + 63 q^{9} - 10 q^{10} - 52 q^{11} - 9 q^{12} - 15 q^{13} - 53 q^{14} - 33 q^{15} + 53 q^{16} - 10 q^{17} - 35 q^{18} + 71 q^{19} - 33 q^{20} - 38 q^{21} - 6 q^{22} - 65 q^{23} - 30 q^{24} + 51 q^{25} - 4 q^{26} - 23 q^{27} - 29 q^{28} - 97 q^{29} - 27 q^{30} - 53 q^{31} - 78 q^{32} - 17 q^{33} - 24 q^{34} - 38 q^{35} + 24 q^{36} - 33 q^{37} - 15 q^{38} - 86 q^{39} + 25 q^{40} - 69 q^{41} + 64 q^{42} - 10 q^{43} - 94 q^{44} - 34 q^{45} - 6 q^{46} - 37 q^{47} - q^{48} + 74 q^{49} - 41 q^{50} - 46 q^{51} - 30 q^{52} - 50 q^{53} - 17 q^{54} - 30 q^{55} - 116 q^{56} - 8 q^{57} + 11 q^{58} - 93 q^{59} - 56 q^{60} - 18 q^{61} - q^{62} - 84 q^{63} + 93 q^{64} - 78 q^{65} - 53 q^{66} - 5 q^{67} - 9 q^{68} - 69 q^{69} - 10 q^{70} - 221 q^{71} - 73 q^{72} - 34 q^{73} - 58 q^{74} - 70 q^{75} + 69 q^{76} - 2 q^{77} + 7 q^{78} - 68 q^{79} - 71 q^{80} + 39 q^{81} + 26 q^{82} - 45 q^{83} - 10 q^{84} - 44 q^{85} - 80 q^{86} - 7 q^{87} - 46 q^{88} - 143 q^{89} + 41 q^{90} - 30 q^{91} - 46 q^{92} + 32 q^{93} + 41 q^{94} - 18 q^{95} - 140 q^{96} - 18 q^{97} - 97 q^{98} - 142 q^{99}+O(q^{100}) \) 71 * q - 15 * q^2 - 8 * q^3 + 69 * q^4 - 18 * q^5 - 9 * q^6 - 19 * q^7 - 39 * q^8 + 63 * q^9 - 10 * q^10 - 52 * q^11 - 9 * q^12 - 15 * q^13 - 53 * q^14 - 33 * q^15 + 53 * q^16 - 10 * q^17 - 35 * q^18 + 71 * q^19 - 33 * q^20 - 38 * q^21 - 6 * q^22 - 65 * q^23 - 30 * q^24 + 51 * q^25 - 4 * q^26 - 23 * q^27 - 29 * q^28 - 97 * q^29 - 27 * q^30 - 53 * q^31 - 78 * q^32 - 17 * q^33 - 24 * q^34 - 38 * q^35 + 24 * q^36 - 33 * q^37 - 15 * q^38 - 86 * q^39 + 25 * q^40 - 69 * q^41 + 64 * q^42 - 10 * q^43 - 94 * q^44 - 34 * q^45 - 6 * q^46 - 37 * q^47 - q^48 + 74 * q^49 - 41 * q^50 - 46 * q^51 - 30 * q^52 - 50 * q^53 - 17 * q^54 - 30 * q^55 - 116 * q^56 - 8 * q^57 + 11 * q^58 - 93 * q^59 - 56 * q^60 - 18 * q^61 - q^62 - 84 * q^63 + 93 * q^64 - 78 * q^65 - 53 * q^66 - 5 * q^67 - 9 * q^68 - 69 * q^69 - 10 * q^70 - 221 * q^71 - 73 * q^72 - 34 * q^73 - 58 * q^74 - 70 * q^75 + 69 * q^76 - 2 * q^77 + 7 * q^78 - 68 * q^79 - 71 * q^80 + 39 * q^81 + 26 * q^82 - 45 * q^83 - 10 * q^84 - 44 * q^85 - 80 * q^86 - 7 * q^87 - 46 * q^88 - 143 * q^89 + 41 * q^90 - 30 * q^91 - 46 * q^92 + 32 * q^93 + 41 * q^94 - 18 * q^95 - 140 * q^96 - 18 * q^97 - 97 * q^98 - 142 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00678	−0.711898	−0.355949	−	0.934505i	$-0.615842\pi$
$2$	−1.00678	−0.711898	−0.355949	+	0.934505i	$0.615842\pi$
$3$	−2.96425	−1.71141	−0.855707	−	0.517461i	$-0.826877\pi$
$3$	−2.96425	−1.71141	−0.855707	+	0.517461i	$0.826877\pi$
$4$	−0.986402	−0.493201
$5$	0.219154	0.0980088	0.0490044	−	0.998799i	$-0.484395\pi$
$5$	0.219154	0.0980088	0.0490044	+	0.998799i	$0.484395\pi$
$6$	2.98434	1.21835
$7$	3.36402	1.27148	0.635740	−	0.771904i	$-0.280695\pi$
$7$	3.36402	1.27148	0.635740	+	0.771904i	$0.280695\pi$
$8$	3.00664	1.06301
$9$	5.78680	1.92893
$10$	−0.220639	−0.0697723
$11$	3.87533	1.16846	0.584228	−	0.811589i	$-0.301397\pi$
$11$	3.87533	1.16846	0.584228	+	0.811589i	$0.301397\pi$
$12$	2.92395	0.844071
$13$	0.532354	0.147649	0.0738243	−	0.997271i	$-0.476480\pi$
$13$	0.532354	0.147649	0.0738243	+	0.997271i	$0.476480\pi$
$14$	−3.38681	−0.905164
$15$	−0.649629	−0.167734
$16$	−1.05421	−0.263551
$17$	4.77500	1.15811	0.579054	−	0.815289i	$-0.303422\pi$
$17$	4.77500	1.15811	0.579054	+	0.815289i	$0.303422\pi$
$18$	−5.82601	−1.37320
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−0.216174	−0.0483381
$21$	−9.97181	−2.17603
$22$	−3.90159	−0.831822
$23$	−8.92669	−1.86134	−0.930671	−	0.365856i	$-0.880776\pi$
$23$	−8.92669	−1.86134	−0.930671	+	0.365856i	$0.880776\pi$
$24$	−8.91244	−1.81924
$25$	−4.95197	−0.990394
$26$	−0.535962	−0.105111
$27$	−8.26079	−1.58979
$28$	−3.31828	−0.627095
$29$	0.0766535	0.0142342	0.00711710	−	0.999975i	$-0.497735\pi$
$29$	0.0766535	0.0142342	0.00711710	+	0.999975i	$0.497735\pi$
$30$	0.654031	0.119409
$31$	−7.44890	−1.33786	−0.668931	−	0.743325i	$-0.733248\pi$
$31$	−7.44890	−1.33786	−0.668931	+	0.743325i	$0.733248\pi$
$32$	−4.95193	−0.875385
$33$	−11.4875	−1.99971
$34$	−4.80736	−0.824455
$35$	0.737239	0.124616
$36$	−5.70812	−0.951353
$37$	−4.23988	−0.697032	−0.348516	−	0.937303i	$-0.613314\pi$
$37$	−4.23988	−0.697032	−0.348516	+	0.937303i	$0.613314\pi$
$38$	−1.00678	−0.163321
$39$	−1.57803	−0.252688
$40$	0.658918	0.104184
$41$	2.36046	0.368641	0.184321	−	0.982866i	$-0.440992\pi$
$41$	2.36046	0.368641	0.184321	+	0.982866i	$0.440992\pi$
$42$	10.0394	1.54911
$43$	8.04888	1.22744	0.613721	−	0.789523i	$-0.289672\pi$
$43$	8.04888	1.22744	0.613721	+	0.789523i	$0.289672\pi$
$44$	−3.82264	−0.576284
$45$	1.26820	0.189053
$46$	8.98717	1.32509
$47$	1.28540	0.187495	0.0937475	−	0.995596i	$-0.470115\pi$
$47$	1.28540	0.187495	0.0937475	+	0.995596i	$0.470115\pi$
$48$	3.12493	0.451045
$49$	4.31662	0.616660
$50$	4.98553	0.705060
$51$	−14.1543	−1.98200
$52$	−0.525116	−0.0728204
$53$	0.910239	0.125031	0.0625155	−	0.998044i	$-0.480088\pi$
$53$	0.910239	0.125031	0.0625155	+	0.998044i	$0.480088\pi$
$54$	8.31677	1.13177
$55$	0.849296	0.114519
$56$	10.1144	1.35159
$57$	−2.96425	−0.392625
$58$	−0.0771729	−0.0101333
$59$	−4.76522	−0.620379	−0.310189	−	0.950675i	$-0.600392\pi$
$59$	−4.76522	−0.620379	−0.310189	+	0.950675i	$0.600392\pi$
$60$	0.640796	0.0827264
$61$	−10.5292	−1.34813	−0.674065	−	0.738672i	$-0.735453\pi$
$61$	−10.5292	−1.34813	−0.674065	+	0.738672i	$0.735453\pi$
$62$	7.49937	0.952421
$63$	19.4669	2.45260
$64$	7.09389	0.886736
$65$	0.116668	0.0144709
$66$	11.5653	1.42359
$67$	−4.37216	−0.534145	−0.267072	−	0.963677i	$-0.586056\pi$
$67$	−4.37216	−0.534145	−0.267072	+	0.963677i	$0.586056\pi$
$68$	−4.71007	−0.571180
$69$	26.4610	3.18553
$70$	−0.742235	−0.0887140
$71$	5.72851	0.679849	0.339924	−	0.940453i	$-0.389599\pi$
$71$	5.72851	0.679849	0.339924	+	0.940453i	$0.389599\pi$
$72$	17.3988	2.05047
$73$	2.94773	0.345006	0.172503	−	0.985009i	$-0.444815\pi$
$73$	2.94773	0.345006	0.172503	+	0.985009i	$0.444815\pi$
$74$	4.26861	0.496216
$75$	14.6789	1.69497
$76$	−0.986402	−0.113148
$77$	13.0367	1.48567
$78$	1.58873	0.179888
$79$	−1.93676	−0.217903	−0.108951	−	0.994047i	$-0.534749\pi$
$79$	−1.93676	−0.217903	−0.108951	+	0.994047i	$0.534749\pi$
$80$	−0.231034	−0.0258304
$81$	7.12668	0.791854
$82$	−2.37645	−0.262435
$83$	−12.5882	−1.38174	−0.690868	−	0.722981i	$-0.742771\pi$
$83$	−12.5882	−1.38174	−0.690868	+	0.722981i	$0.742771\pi$
$84$	9.83621	1.07322
$85$	1.04646	0.113505
$86$	−8.10342	−0.873814
$87$	−0.227220	−0.0243606
$88$	11.6517	1.24208
$89$	−5.58994	−0.592533	−0.296266	−	0.955105i	$-0.595742\pi$
$89$	−5.58994	−0.592533	−0.296266	+	0.955105i	$0.595742\pi$
$90$	−1.27680	−0.134586
$91$	1.79085	0.187732
$92$	8.80530	0.918016
$93$	22.0804	2.28963
$94$	−1.29411	−0.133477
$95$	0.219154	0.0224848
$96$	14.6788	1.49815
$97$	2.37302	0.240943	0.120472	−	0.992717i	$-0.461559\pi$
$97$	2.37302	0.240943	0.120472	+	0.992717i	$0.461559\pi$
$98$	−4.34587	−0.438999
$99$	22.4258	2.25388
$100$	4.88464	0.488464
$101$	−5.79827	−0.576950	−0.288475	−	0.957487i	$-0.593148\pi$
$101$	−5.79827	−0.576950	−0.288475	+	0.957487i	$0.593148\pi$
$102$	14.2502	1.41098
$103$	−7.35963	−0.725165	−0.362583	−	0.931952i	$-0.618105\pi$
$103$	−7.35963	−0.725165	−0.362583	+	0.931952i	$0.618105\pi$
$104$	1.60060	0.156951
$105$	−2.18536	−0.213270
$106$	−0.916407	−0.0890093
$107$	−7.20318	−0.696358	−0.348179	−	0.937428i	$-0.613200\pi$
$107$	−7.20318	−0.696358	−0.348179	+	0.937428i	$0.613200\pi$
$108$	8.14847	0.784087
$109$	−12.2441	−1.17277	−0.586387	−	0.810031i	$-0.699450\pi$
$109$	−12.2441	−1.17277	−0.586387	+	0.810031i	$0.699450\pi$
$110$	−0.855051	−0.0815259
$111$	12.5681	1.19291
$112$	−3.54637	−0.335100
$113$	−14.6760	−1.38060	−0.690300	−	0.723523i	$-0.742522\pi$
$113$	−14.6760	−1.38060	−0.690300	+	0.723523i	$0.742522\pi$
$114$	2.98434	0.279509
$115$	−1.95632	−0.182428
$116$	−0.0756112	−0.00702032
$117$	3.08063	0.284804
$118$	4.79751	0.441646
$119$	16.0632	1.47251
$120$	−1.95320	−0.178302
$121$	4.01820	0.365290
$122$	10.6006	0.959731
$123$	−6.99699	−0.630898
$124$	7.34761	0.659835
$125$	−2.18102	−0.195076
$126$	−19.5988	−1.74600
$127$	−22.3897	−1.98676	−0.993382	−	0.114860i	$-0.963358\pi$
$127$	−22.3897	−1.98676	−0.993382	+	0.114860i	$0.963358\pi$
$128$	2.76189	0.244119
$129$	−23.8589	−2.10066
$130$	−0.117458	−0.0103018
$131$	−14.9038	−1.30215	−0.651076	−	0.759013i	$-0.725682\pi$
$131$	−14.9038	−1.30215	−0.651076	+	0.759013i	$0.725682\pi$
$132$	11.3313	0.986260
$133$	3.36402	0.291697
$134$	4.40179	0.380256
$135$	−1.81039	−0.155813
$136$	14.3567	1.23108
$137$	16.1103	1.37639	0.688197	−	0.725524i	$-0.258402\pi$
$137$	16.1103	1.37639	0.688197	+	0.725524i	$0.258402\pi$
$138$	−26.6403	−2.26777
$139$	−0.917608	−0.0778305	−0.0389153	−	0.999243i	$-0.512390\pi$
$139$	−0.917608	−0.0778305	−0.0389153	+	0.999243i	$0.512390\pi$
$140$	−0.727215	−0.0614608
$141$	−3.81025	−0.320881
$142$	−5.76732	−0.483983
$143$	2.06305	0.172521
$144$	−6.10048	−0.508373
$145$	0.0167989	0.00139508
$146$	−2.96771	−0.245609
$147$	−12.7956	−1.05536
$148$	4.18223	0.343777
$149$	4.80273	0.393455	0.196727	−	0.980458i	$-0.436969\pi$
$149$	4.80273	0.393455	0.196727	+	0.980458i	$0.436969\pi$
$150$	−14.7784	−1.20665
$151$	−4.63589	−0.377263	−0.188631	−	0.982048i	$-0.560405\pi$
$151$	−4.63589	−0.377263	−0.188631	+	0.982048i	$0.560405\pi$
$152$	3.00664	0.243871
$153$	27.6320	2.23391
$154$	−13.1250	−1.05764
$155$	−1.63246	−0.131122
$156$	1.55658	0.124626
$157$	10.9446	0.873478	0.436739	−	0.899588i	$-0.356133\pi$
$157$	10.9446	0.873478	0.436739	+	0.899588i	$0.356133\pi$
$158$	1.94988	0.155124
$159$	−2.69818	−0.213980
$160$	−1.08524	−0.0857955
$161$	−30.0295	−2.36666
$162$	−7.17497	−0.563719
$163$	−9.35849	−0.733014	−0.366507	−	0.930415i	$-0.619446\pi$
$163$	−9.35849	−0.733014	−0.366507	+	0.930415i	$0.619446\pi$
$164$	−2.32836	−0.181814
$165$	−2.51753	−0.195989
$166$	12.6735	0.983655
$167$	−0.908613	−0.0703106	−0.0351553	−	0.999382i	$-0.511193\pi$
$167$	−0.908613	−0.0703106	−0.0351553	+	0.999382i	$0.511193\pi$
$168$	−29.9816	−2.31313
$169$	−12.7166	−0.978200
$170$	−1.05355	−0.0808039
$171$	5.78680	0.442528
$172$	−7.93943	−0.605376
$173$	−24.1945	−1.83947	−0.919735	−	0.392540i	$-0.871597\pi$
$173$	−24.1945	−1.83947	−0.919735	+	0.392540i	$0.871597\pi$
$174$	0.228760	0.0173422
$175$	−16.6585	−1.25927
$176$	−4.08540	−0.307948
$177$	14.1253	1.06172
$178$	5.62782	0.421823
$179$	14.4827	1.08249	0.541243	−	0.840866i	$-0.317954\pi$
$179$	14.4827	1.08249	0.541243	+	0.840866i	$0.317954\pi$
$180$	−1.25096	−0.0932410
$181$	12.1219	0.901012	0.450506	−	0.892773i	$-0.351244\pi$
$181$	12.1219	0.901012	0.450506	+	0.892773i	$0.351244\pi$
$182$	−1.80298	−0.133646
$183$	31.2113	2.30721
$184$	−26.8393	−1.97862
$185$	−0.929189	−0.0683153
$186$	−22.2300	−1.62999
$187$	18.5047	1.35320
$188$	−1.26792	−0.0924727
$189$	−27.7895	−2.02139
$190$	−0.220639	−0.0160069
$191$	−3.24219	−0.234596	−0.117298	−	0.993097i	$-0.537423\pi$
$191$	−3.24219	−0.234596	−0.117298	+	0.993097i	$0.537423\pi$
$192$	−21.0281	−1.51757
$193$	15.9111	1.14530	0.572652	−	0.819799i	$-0.305915\pi$
$193$	15.9111	1.14530	0.572652	+	0.819799i	$0.305915\pi$
$194$	−2.38910	−0.171527
$195$	−0.345833	−0.0247656
$196$	−4.25792	−0.304137
$197$	26.6087	1.89579	0.947894	−	0.318585i	$-0.103208\pi$
$197$	26.6087	1.89579	0.947894	+	0.318585i	$0.103208\pi$
$198$	−22.5777	−1.60453
$199$	22.4825	1.59374	0.796869	−	0.604152i	$-0.206488\pi$
$199$	22.4825	1.59374	0.796869	+	0.604152i	$0.206488\pi$
$200$	−14.8888	−1.05280
$201$	12.9602	0.914142
$202$	5.83756	0.410729
$203$	0.257864	0.0180985
$204$	13.9619	0.977525
$205$	0.517304	0.0361301
$206$	7.40949	0.516244
$207$	−51.6570	−3.59041
$208$	−0.561211	−0.0389130
$209$	3.87533	0.268062
$210$	2.20017	0.151826
$211$	1.00000	0.0688428
$211$	1.00000	0.0688428
$212$	−0.897862	−0.0616654
$213$	−16.9807	−1.16350
$214$	7.25199	0.495736
$215$	1.76395	0.120300
$216$	−24.8372	−1.68996
$217$	−25.0582	−1.70106
$218$	12.3271	0.834895
$219$	−8.73784	−0.590448
$220$	−0.837747	−0.0564809
$221$	2.54199	0.170993
$222$	−12.6532	−0.849230
$223$	23.4010	1.56705	0.783523	−	0.621363i	$-0.213421\pi$
$223$	23.4010	1.56705	0.783523	+	0.621363i	$0.213421\pi$
$224$	−16.6584	−1.11303
$225$	−28.6561	−1.91041
$226$	14.7754	0.982847
$227$	18.0894	1.20064	0.600319	−	0.799761i	$-0.295040\pi$
$227$	18.0894	1.20064	0.600319	+	0.799761i	$0.295040\pi$
$228$	2.92395	0.193643
$229$	25.6722	1.69647	0.848234	−	0.529622i	$-0.177666\pi$
$229$	25.6722	1.69647	0.848234	+	0.529622i	$0.177666\pi$
$230$	1.96958	0.129870
$231$	−38.6441	−2.54259
$232$	0.230469	0.0151310
$233$	18.5566	1.21568	0.607841	−	0.794059i	$-0.292036\pi$
$233$	18.5566	1.21568	0.607841	+	0.794059i	$0.292036\pi$
$234$	−3.10150	−0.202752
$235$	0.281701	0.0183762
$236$	4.70042	0.305972
$237$	5.74105	0.372921
$238$	−16.1720	−1.04828
$239$	−14.7326	−0.952972	−0.476486	−	0.879182i	$-0.658090\pi$
$239$	−14.7326	−0.952972	−0.476486	+	0.879182i	$0.658090\pi$
$240$	0.684843	0.0442064
$241$	−1.36021	−0.0876189	−0.0438094	−	0.999040i	$-0.513949\pi$
$241$	−1.36021	−0.0876189	−0.0438094	+	0.999040i	$0.513949\pi$
$242$	−4.04542	−0.260050
$243$	3.65708	0.234602
$244$	10.3861	0.664899
$245$	0.946006	0.0604381
$246$	7.04440	0.449135
$247$	0.532354	0.0338729
$248$	−22.3961	−1.42216
$249$	37.3147	2.36472
$250$	2.19580	0.138874
$251$	−24.6628	−1.55670	−0.778351	−	0.627830i	$-0.783943\pi$
$251$	−24.6628	−1.55670	−0.778351	+	0.627830i	$0.783943\pi$
$252$	−19.2022	−1.20963
$253$	−34.5939	−2.17490
$254$	22.5414	1.41437
$255$	−3.10198	−0.194254
$256$	−16.9684	−1.06052
$257$	−21.2877	−1.32789	−0.663944	−	0.747783i	$-0.731118\pi$
$257$	−21.2877	−1.32789	−0.663944	+	0.747783i	$0.731118\pi$
$258$	24.0206	1.49546
$259$	−14.2630	−0.886262
$260$	−0.115081	−0.00713704
$261$	0.443579	0.0274568
$262$	15.0048	0.926999
$263$	1.43201	0.0883015	0.0441507	−	0.999025i	$-0.485942\pi$
$263$	1.43201	0.0883015	0.0441507	+	0.999025i	$0.485942\pi$
$264$	−34.5387	−2.12571
$265$	0.199483	0.0122541
$266$	−3.38681	−0.207659
$267$	16.5700	1.01407
$268$	4.31271	0.263441
$269$	5.96072	0.363432	0.181716	−	0.983351i	$-0.441835\pi$
$269$	5.96072	0.363432	0.181716	+	0.983351i	$0.441835\pi$
$270$	1.82266	0.110923
$271$	−9.95801	−0.604906	−0.302453	−	0.953164i	$-0.597806\pi$
$271$	−9.95801	−0.604906	−0.302453	+	0.953164i	$0.597806\pi$
$272$	−5.03383	−0.305221
$273$	−5.30853	−0.321287
$274$	−16.2194	−0.979852
$275$	−19.1905	−1.15723
$276$	−26.1012	−1.57111
$277$	−8.73311	−0.524722	−0.262361	−	0.964970i	$-0.584501\pi$
$277$	−8.73311	−0.524722	−0.262361	+	0.964970i	$0.584501\pi$
$278$	0.923826	0.0554074
$279$	−43.1053	−2.58065
$280$	2.21661	0.132468
$281$	−20.3185	−1.21210	−0.606049	−	0.795427i	$-0.707246\pi$
$281$	−20.3185	−1.21210	−0.606049	+	0.795427i	$0.707246\pi$
$282$	3.83607	0.228435
$283$	−13.6810	−0.813248	−0.406624	−	0.913596i	$-0.633294\pi$
$283$	−13.6810	−0.813248	−0.406624	+	0.913596i	$0.633294\pi$
$284$	−5.65061	−0.335302
$285$	−0.649629	−0.0384807
$286$	−2.07703	−0.122817
$287$	7.94062	0.468720
$288$	−28.6558	−1.68856
$289$	5.80065	0.341215
$290$	−0.0169128	−0.000993152 0
$291$	−7.03423	−0.412354
$292$	−2.90765	−0.170157
$293$	−0.340888	−0.0199149	−0.00995745	−	0.999950i	$-0.503170\pi$
$293$	−0.340888	−0.0199149	−0.00995745	+	0.999950i	$0.503170\pi$
$294$	12.8823	0.751308
$295$	−1.04432	−0.0608026
$296$	−12.7478	−0.740950
$297$	−32.0133	−1.85760
$298$	−4.83527	−0.280100
$299$	−4.75216	−0.274825
$300$	−14.4793	−0.835963
$301$	27.0766	1.56067
$302$	4.66730	0.268573
$303$	17.1876	0.987399
$304$	−1.05421	−0.0604628
$305$	−2.30753	−0.132129
$306$	−27.8192	−1.59032
$307$	−21.7811	−1.24312	−0.621558	−	0.783368i	$-0.713500\pi$
$307$	−21.7811	−1.24312	−0.621558	+	0.783368i	$0.713500\pi$
$308$	−12.8594	−0.732733
$309$	21.8158	1.24106
$310$	1.64352	0.0933456
$311$	−22.1123	−1.25387	−0.626936	−	0.779071i	$-0.715691\pi$
$311$	−22.1123	−1.25387	−0.626936	+	0.779071i	$0.715691\pi$
$312$	−4.74458	−0.268609
$313$	−6.05305	−0.342138	−0.171069	−	0.985259i	$-0.554722\pi$
$313$	−6.05305	−0.342138	−0.171069	+	0.985259i	$0.554722\pi$
$314$	−11.0188	−0.621827
$315$	4.26626	0.240376
$316$	1.91043	0.107470
$317$	−20.1198	−1.13004	−0.565019	−	0.825078i	$-0.691131\pi$
$317$	−20.1198	−1.13004	−0.565019	+	0.825078i	$0.691131\pi$
$318$	2.71646	0.152332
$319$	0.297058	0.0166320
$320$	1.55466	0.0869080
$321$	21.3521	1.19176
$322$	30.2330	1.68482
$323$	4.77500	0.265688
$324$	−7.02978	−0.390543
$325$	−2.63620	−0.146230
$326$	9.42191	0.521831
$327$	36.2947	2.00710
$328$	7.09704	0.391868
$329$	4.32411	0.238396
$330$	2.53459	0.139524
$331$	1.16922	0.0642663	0.0321331	−	0.999484i	$-0.489770\pi$
$331$	1.16922	0.0642663	0.0321331	+	0.999484i	$0.489770\pi$
$332$	12.4170	0.681474
$333$	−24.5354	−1.34453
$334$	0.914769	0.0500540
$335$	−0.958178	−0.0523509
$336$	10.5123	0.573495
$337$	−34.8916	−1.90067	−0.950333	−	0.311235i	$-0.899257\pi$
$337$	−34.8916	−1.90067	−0.950333	+	0.311235i	$0.899257\pi$
$338$	12.8028	0.696379
$339$	43.5034	2.36278
$340$	−1.03223	−0.0559807
$341$	−28.8669	−1.56323
$342$	−5.82601	−0.315035
$343$	−9.02694	−0.487409
$344$	24.2001	1.30478
$345$	5.79904	0.312210
$346$	24.3584	1.30952
$347$	8.97452	0.481778	0.240889	−	0.970553i	$-0.422561\pi$
$347$	8.97452	0.481778	0.240889	+	0.970553i	$0.422561\pi$
$348$	0.224131	0.0120147
$349$	23.6938	1.26830	0.634151	−	0.773210i	$-0.281350\pi$
$349$	23.6938	1.26830	0.634151	+	0.773210i	$0.281350\pi$
$350$	16.7714	0.896469
$351$	−4.39767	−0.234730
$352$	−19.1904	−1.02285
$353$	15.1458	0.806129	0.403065	−	0.915171i	$-0.367945\pi$
$353$	15.1458	0.806129	0.403065	+	0.915171i	$0.367945\pi$
$354$	−14.2210	−0.755839
$355$	1.25543	0.0666311
$356$	5.51393	0.292238
$357$	−47.6154	−2.52007
$358$	−14.5808	−0.770619
$359$	−10.1025	−0.533190	−0.266595	−	0.963809i	$-0.585899\pi$
$359$	−10.1025	−0.533190	−0.266595	+	0.963809i	$0.585899\pi$
$360$	3.81303	0.200964
$361$	1.00000	0.0526316
$362$	−12.2040	−0.641429
$363$	−11.9110	−0.625163
$364$	−1.76650	−0.0925897
$365$	0.646009	0.0338137
$366$	−31.4228	−1.64250
$367$	27.0608	1.41256	0.706282	−	0.707931i	$-0.250371\pi$
$367$	27.0608	1.41256	0.706282	+	0.707931i	$0.250371\pi$
$368$	9.41056	0.490560
$369$	13.6595	0.711085
$370$	0.935485	0.0486335
$371$	3.06206	0.158974
$372$	−21.7802	−1.12925
$373$	29.2847	1.51630	0.758152	−	0.652078i	$-0.226102\pi$
$373$	29.2847	1.51630	0.758152	+	0.652078i	$0.226102\pi$
$374$	−18.6301	−0.963340
$375$	6.46509	0.333856
$376$	3.86473	0.199308
$377$	0.0408068	0.00210166
$378$	27.9778	1.43902
$379$	−17.5139	−0.899631	−0.449816	−	0.893121i	$-0.648510\pi$
$379$	−17.5139	−0.899631	−0.449816	+	0.893121i	$0.648510\pi$
$380$	−0.216174	−0.0110895
$381$	66.3687	3.40017
$382$	3.26415	0.167009
$383$	−12.6100	−0.644338	−0.322169	−	0.946682i	$-0.604412\pi$
$383$	−12.6100	−0.644338	−0.322169	+	0.946682i	$0.604412\pi$
$384$	−8.18696	−0.417789
$385$	2.85705	0.145609
$386$	−16.0189	−0.815340
$387$	46.5773	2.36766
$388$	−2.34075	−0.118834
$389$	20.3298	1.03076	0.515380	−	0.856961i	$-0.327651\pi$
$389$	20.3298	1.03076	0.515380	+	0.856961i	$0.327651\pi$
$390$	0.348176	0.0176306
$391$	−42.6249	−2.15564
$392$	12.9785	0.655514
$393$	44.1787	2.22852
$394$	−26.7890	−1.34961
$395$	−0.424450	−0.0213564
$396$	−22.1208	−1.11161
$397$	9.18653	0.461059	0.230529	−	0.973065i	$-0.425954\pi$
$397$	9.18653	0.461059	0.230529	+	0.973065i	$0.425954\pi$
$398$	−22.6348	−1.13458
$399$	−9.97181	−0.499215
$400$	5.22040	0.261020
$401$	−37.7390	−1.88459	−0.942297	−	0.334778i	$-0.891339\pi$
$401$	−37.7390	−1.88459	−0.942297	+	0.334778i	$0.891339\pi$
$402$	−13.0480	−0.650776
$403$	−3.96545	−0.197533
$404$	5.71943	0.284552
$405$	1.56184	0.0776086
$406$	−0.259611	−0.0128843
$407$	−16.4309	−0.814452
$408$	−42.5569	−2.10688
$409$	3.23343	0.159883	0.0799415	−	0.996800i	$-0.474527\pi$
$409$	3.23343	0.159883	0.0799415	+	0.996800i	$0.474527\pi$
$410$	−0.520810	−0.0257209
$411$	−47.7550	−2.35558
$412$	7.25955	0.357652
$413$	−16.0303	−0.788799
$414$	52.0070	2.55600
$415$	−2.75876	−0.135422
$416$	−2.63618	−0.129249
$417$	2.72002	0.133200
$418$	−3.90159	−0.190833
$419$	14.2582	0.696558	0.348279	−	0.937391i	$-0.386766\pi$
$419$	14.2582	0.696558	0.348279	+	0.937391i	$0.386766\pi$
$420$	2.15565	0.105185
$421$	−4.08172	−0.198931	−0.0994654	−	0.995041i	$-0.531713\pi$
$421$	−4.08172	−0.198931	−0.0994654	+	0.995041i	$0.531713\pi$
$422$	−1.00678	−0.0490091
$423$	7.43836	0.361665
$424$	2.73676	0.132909
$425$	−23.6457	−1.14698
$426$	17.0958	0.828295
$427$	−35.4205	−1.71412
$428$	7.10524	0.343445
$429$	−6.11540	−0.295254
$430$	−1.77590	−0.0856415
$431$	−8.88733	−0.428087	−0.214044	−	0.976824i	$-0.568663\pi$
$431$	−8.88733	−0.428087	−0.214044	+	0.976824i	$0.568663\pi$
$432$	8.70858	0.418992
$433$	9.47465	0.455323	0.227661	−	0.973740i	$-0.426892\pi$
$433$	9.47465	0.455323	0.227661	+	0.973740i	$0.426892\pi$
$434$	25.2280	1.21098
$435$	−0.0497963	−0.00238755
$436$	12.0776	0.578413
$437$	−8.92669	−0.427021
$438$	8.79704	0.420339
$439$	−7.64850	−0.365043	−0.182522	−	0.983202i	$-0.558426\pi$
$439$	−7.64850	−0.365043	−0.182522	+	0.983202i	$0.558426\pi$
$440$	2.55353	0.121735
$441$	24.9794	1.18950
$442$	−2.55922	−0.121730
$443$	13.6636	0.649179	0.324589	−	0.945855i	$-0.394774\pi$
$443$	13.6636	0.649179	0.324589	+	0.945855i	$0.394774\pi$
$444$	−12.3972	−0.588345
$445$	−1.22506	−0.0580734
$446$	−23.5596	−1.11558
$447$	−14.2365	−0.673364
$448$	23.8640	1.12747
$449$	−4.45943	−0.210454	−0.105227	−	0.994448i	$-0.533557\pi$
$449$	−4.45943	−0.210454	−0.105227	+	0.994448i	$0.533557\pi$
$450$	28.8503	1.36001
$451$	9.14755	0.430741
$452$	14.4764	0.680914
$453$	13.7419	0.645653
$454$	−18.2120	−0.854732
$455$	0.392473	0.0183994
$456$	−8.91244	−0.417363
$457$	16.1642	0.756130	0.378065	−	0.925779i	$-0.376590\pi$
$457$	16.1642	0.756130	0.378065	+	0.925779i	$0.376590\pi$
$458$	−25.8462	−1.20771
$459$	−39.4453	−1.84115
$460$	1.92972	0.0899737
$461$	1.64588	0.0766565	0.0383282	−	0.999265i	$-0.487797\pi$
$461$	1.64588	0.0766565	0.0383282	+	0.999265i	$0.487797\pi$
$462$	38.9059	1.81007
$463$	−16.6545	−0.773999	−0.386999	−	0.922080i	$-0.626488\pi$
$463$	−16.6545	−0.773999	−0.386999	+	0.922080i	$0.626488\pi$
$464$	−0.0808085	−0.00375144
$465$	4.83902	0.224404
$466$	−18.6823	−0.865441
$467$	−26.7319	−1.23700	−0.618502	−	0.785784i	$-0.712260\pi$
$467$	−26.7319	−1.23700	−0.618502	+	0.785784i	$0.712260\pi$
$468$	−3.03874	−0.140466
$469$	−14.7080	−0.679154
$470$	−0.283610	−0.0130819
$471$	−32.4427	−1.49488
$472$	−14.3273	−0.659467
$473$	31.1921	1.43421
$474$	−5.77995	−0.265482
$475$	−4.95197	−0.227212
$476$	−15.8448	−0.726244
$477$	5.26738	0.241177
$478$	14.8324	0.678419
$479$	−33.5688	−1.53380	−0.766899	−	0.641768i	$-0.778201\pi$
$479$	−33.5688	−1.53380	−0.766899	+	0.641768i	$0.778201\pi$
$480$	3.21692	0.146831
$481$	−2.25712	−0.102916
$482$	1.36943	0.0623757
$483$	89.0152	4.05033
$484$	−3.96356	−0.180162
$485$	0.520057	0.0236146
$486$	−3.68186	−0.167013
$487$	32.8297	1.48766	0.743828	−	0.668371i	$-0.233008\pi$
$487$	32.8297	1.48766	0.743828	+	0.668371i	$0.233008\pi$
$488$	−31.6576	−1.43307
$489$	27.7410	1.25449
$490$	−0.952416	−0.0430258
$491$	7.57165	0.341704	0.170852	−	0.985297i	$-0.445348\pi$
$491$	7.57165	0.341704	0.170852	+	0.985297i	$0.445348\pi$
$492$	6.90185	0.311159
$493$	0.366020	0.0164847
$494$	−0.535962	−0.0241140
$495$	4.91471	0.220900
$496$	7.85267	0.352595
$497$	19.2708	0.864413
$498$	−37.5675	−1.68344
$499$	1.23780	0.0554114	0.0277057	−	0.999616i	$-0.491180\pi$
$499$	1.23780	0.0554114	0.0277057	+	0.999616i	$0.491180\pi$
$500$	2.15136	0.0962118
$501$	2.69336	0.120330
$502$	24.8299	1.10821
$503$	−3.59668	−0.160368	−0.0801840	−	0.996780i	$-0.525551\pi$
$503$	−3.59668	−0.160368	−0.0801840	+	0.996780i	$0.525551\pi$
$504$	58.5300	2.60713
$505$	−1.27072	−0.0565462
$506$	34.8283	1.54831
$507$	37.6952	1.67410
$508$	22.0852	0.979874
$509$	−11.0110	−0.488053	−0.244026	−	0.969769i	$-0.578468\pi$
$509$	−11.0110	−0.488053	−0.244026	+	0.969769i	$0.578468\pi$
$510$	3.12300	0.138289
$511$	9.91623	0.438668
$512$	11.5596	0.510866
$513$	−8.26079	−0.364723
$514$	21.4319	0.945320
$515$	−1.61289	−0.0710726
$516$	23.5345	1.03605
$517$	4.98135	0.219080
$518$	14.3597	0.630928
$519$	71.7185	3.14809
$520$	0.350778	0.0153826
$521$	22.1752	0.971513	0.485756	−	0.874094i	$-0.338544\pi$
$521$	22.1752	0.971513	0.485756	+	0.874094i	$0.338544\pi$
$522$	−0.446584	−0.0195465
$523$	7.04521	0.308066	0.154033	−	0.988066i	$-0.450774\pi$
$523$	7.04521	0.308066	0.154033	+	0.988066i	$0.450774\pi$
$524$	14.7012	0.642223
$525$	49.3801	2.15512
$526$	−1.44171	−0.0628617
$527$	−35.5685	−1.54939
$528$	12.1102	0.527027
$529$	56.6857	2.46460
$530$	−0.200835	−0.00872370
$531$	−27.5754	−1.19667
$532$	−3.31828	−0.143865
$533$	1.25660	0.0544294
$534$	−16.6823	−0.721913
$535$	−1.57861	−0.0682492
$536$	−13.1455	−0.567799
$537$	−42.9303	−1.85258
$538$	−6.00111	−0.258726
$539$	16.7283	0.720540
$540$	1.78577	0.0768474
$541$	−29.3751	−1.26294	−0.631468	−	0.775402i	$-0.717547\pi$
$541$	−29.3751	−1.26294	−0.631468	+	0.775402i	$0.717547\pi$
$542$	10.0255	0.430632
$543$	−35.9323	−1.54200
$544$	−23.6455	−1.01379
$545$	−2.68335	−0.114942
$546$	5.34450	0.228724
$547$	14.1026	0.602985	0.301492	−	0.953469i	$-0.402515\pi$
$547$	14.1026	0.602985	0.301492	+	0.953469i	$0.402515\pi$
$548$	−15.8912	−0.678839
$549$	−60.9306	−2.60045
$550$	19.3206	0.823832
$551$	0.0766535	0.00326555
$552$	79.5585	3.38624
$553$	−6.51530	−0.277059
$554$	8.79229	0.373548
$555$	2.75435	0.116916
$556$	0.905131	0.0383861
$557$	13.5361	0.573542	0.286771	−	0.957999i	$-0.407418\pi$
$557$	13.5361	0.573542	0.286771	+	0.957999i	$0.407418\pi$
$558$	43.3974	1.83716
$559$	4.28486	0.181230
$560$	−0.777202	−0.0328428
$561$	−54.8527	−2.31588
$562$	20.4561	0.862890
$563$	7.60170	0.320373	0.160187	−	0.987087i	$-0.448790\pi$
$563$	7.60170	0.320373	0.160187	+	0.987087i	$0.448790\pi$
$564$	3.75844	0.158259
$565$	−3.21631	−0.135311
$566$	13.7737	0.578950
$567$	23.9743	1.00683
$568$	17.2235	0.722684
$569$	0.749024	0.0314007	0.0157004	−	0.999877i	$-0.495002\pi$
$569$	0.749024	0.0314007	0.0157004	+	0.999877i	$0.495002\pi$
$570$	0.654031	0.0273943
$571$	27.3272	1.14361	0.571805	−	0.820390i	$-0.306244\pi$
$571$	27.3272	1.14361	0.571805	+	0.820390i	$0.306244\pi$
$572$	−2.03500	−0.0850875
$573$	9.61066	0.401491
$574$	−7.99442	−0.333681
$575$	44.2047	1.84346
$576$	41.0510	1.71046
$577$	23.2451	0.967706	0.483853	−	0.875149i	$-0.339237\pi$
$577$	23.2451	0.967706	0.483853	+	0.875149i	$0.339237\pi$
$578$	−5.83995	−0.242910
$579$	−47.1645	−1.96009
$580$	−0.0165705	−0.000688053 0
$581$	−42.3470	−1.75685
$582$	7.08189	0.293554
$583$	3.52748	0.146093
$584$	8.86277	0.366744
$585$	0.675134	0.0279133
$586$	0.343198	0.0141774
$587$	6.02522	0.248688	0.124344	−	0.992239i	$-0.460317\pi$
$587$	6.02522	0.248688	0.124344	+	0.992239i	$0.460317\pi$
$588$	12.6216	0.520505
$589$	−7.44890	−0.306926
$590$	1.05139	0.0432852
$591$	−78.8748	−3.24448
$592$	4.46971	0.183704
$593$	−31.0631	−1.27561	−0.637804	−	0.770199i	$-0.720157\pi$
$593$	−31.0631	−1.27561	−0.637804	+	0.770199i	$0.720157\pi$
$594$	32.2302	1.32242
$595$	3.52032	0.144319
$596$	−4.73742	−0.194052
$597$	−66.6437	−2.72755
$598$	4.78436	0.195647
$599$	−5.55977	−0.227166	−0.113583	−	0.993529i	$-0.536233\pi$
$599$	−5.55977	−0.227166	−0.113583	+	0.993529i	$0.536233\pi$
$600$	44.1341	1.80177
$601$	26.1337	1.06602	0.533008	−	0.846110i	$-0.321062\pi$
$601$	26.1337	1.06602	0.533008	+	0.846110i	$0.321062\pi$
$602$	−27.2600	−1.11104
$603$	−25.3008	−1.03033
$604$	4.57285	0.186067
$605$	0.880605	0.0358017
$606$	−17.3040	−0.702928
$607$	−16.2732	−0.660509	−0.330254	−	0.943892i	$-0.607135\pi$
$607$	−16.2732	−0.660509	−0.330254	+	0.943892i	$0.607135\pi$
$608$	−4.95193	−0.200827
$609$	−0.764373	−0.0309740
$610$	2.32316	0.0940621
$611$	0.684288	0.0276833
$612$	−27.2563	−1.10177
$613$	15.6183	0.630817	0.315409	−	0.948956i	$-0.397858\pi$
$613$	15.6183	0.630817	0.315409	+	0.948956i	$0.397858\pi$
$614$	21.9287	0.884972
$615$	−1.53342	−0.0618335
$616$	39.1966	1.57928
$617$	−5.09278	−0.205028	−0.102514	−	0.994732i	$-0.532689\pi$
$617$	−5.09278	−0.205028	−0.102514	+	0.994732i	$0.532689\pi$
$618$	−21.9636	−0.883506
$619$	−28.5499	−1.14752	−0.573758	−	0.819025i	$-0.694515\pi$
$619$	−28.5499	−1.14752	−0.573758	+	0.819025i	$0.694515\pi$
$620$	1.61026	0.0646696
$621$	73.7415	2.95915
$622$	22.2621	0.892629
$623$	−18.8047	−0.753393
$624$	1.66357	0.0665962
$625$	24.2819	0.971275
$626$	6.09406	0.243568
$627$	−11.4875	−0.458765
$628$	−10.7958	−0.430800
$629$	−20.2454	−0.807239
$630$	−4.29517	−0.171124
$631$	−36.5863	−1.45648	−0.728239	−	0.685323i	$-0.759661\pi$
$631$	−36.5863	−1.45648	−0.728239	+	0.685323i	$0.759661\pi$
$632$	−5.82314	−0.231632
$633$	−2.96425	−0.117819
$634$	20.2561	0.804472
$635$	−4.90680	−0.194720
$636$	2.66149	0.105535
$637$	2.29797	0.0910489
$638$	−0.299070	−0.0118403
$639$	33.1497	1.31138
$640$	0.605281	0.0239258
$641$	−18.8130	−0.743070	−0.371535	−	0.928419i	$-0.621168\pi$
$641$	−18.8130	−0.743070	−0.371535	+	0.928419i	$0.621168\pi$
$642$	−21.4967	−0.848409
$643$	18.0900	0.713399	0.356699	−	0.934219i	$-0.383902\pi$
$643$	18.0900	0.713399	0.356699	+	0.934219i	$0.383902\pi$
$644$	29.6212	1.16724
$645$	−5.22879	−0.205883
$646$	−4.80736	−0.189143
$647$	−14.8655	−0.584422	−0.292211	−	0.956354i	$-0.594391\pi$
$647$	−14.8655	−0.584422	−0.292211	+	0.956354i	$0.594391\pi$
$648$	21.4274	0.841746
$649$	−18.4668	−0.724886
$650$	2.65407	0.104101
$651$	74.2789	2.91122
$652$	9.23124	0.361523
$653$	−11.8140	−0.462317	−0.231159	−	0.972916i	$-0.574252\pi$
$653$	−11.8140	−0.462317	−0.231159	+	0.972916i	$0.574252\pi$
$654$	−36.5406	−1.42885
$655$	−3.26623	−0.127622
$656$	−2.48841	−0.0971560
$657$	17.0580	0.665494
$658$	−4.35341	−0.169714
$659$	41.6639	1.62299	0.811497	−	0.584356i	$-0.198653\pi$
$659$	41.6639	1.62299	0.811497	+	0.584356i	$0.198653\pi$
$660$	2.48330	0.0966622
$661$	25.1013	0.976328	0.488164	−	0.872752i	$-0.337667\pi$
$661$	25.1013	0.976328	0.488164	+	0.872752i	$0.337667\pi$
$662$	−1.17714	−0.0457510
$663$	−7.53512	−0.292640
$664$	−37.8482	−1.46880
$665$	0.737239	0.0285889
$666$	24.7016	0.957168
$667$	−0.684261	−0.0264947
$668$	0.896258	0.0346773
$669$	−69.3665	−2.68186
$670$	0.964671	0.0372685
$671$	−40.8043	−1.57523
$672$	49.3797	1.90486
$673$	49.5884	1.91149	0.955747	−	0.294191i	$-0.0950500\pi$
$673$	49.5884	1.91149	0.955747	+	0.294191i	$0.0950500\pi$
$674$	35.1280	1.35308
$675$	40.9072	1.57452
$676$	12.5437	0.482449
$677$	44.8155	1.72240	0.861200	−	0.508266i	$-0.169713\pi$
$677$	44.8155	1.72240	0.861200	+	0.508266i	$0.169713\pi$
$678$	−43.7981	−1.68206
$679$	7.98287	0.306355
$680$	3.14633	0.120656
$681$	−53.6217	−2.05479
$682$	29.0625	1.11286
$683$	−8.96281	−0.342952	−0.171476	−	0.985188i	$-0.554854\pi$
$683$	−8.96281	−0.342952	−0.171476	+	0.985188i	$0.554854\pi$
$684$	−5.70812	−0.218255
$685$	3.53064	0.134899
$686$	9.08811	0.346986
$687$	−76.0989	−2.90336
$688$	−8.48518	−0.323494
$689$	0.484570	0.0184606
$690$	−5.83833	−0.222261
$691$	−29.2728	−1.11359	−0.556794	−	0.830650i	$-0.687969\pi$
$691$	−29.2728	−1.11359	−0.556794	+	0.830650i	$0.687969\pi$
$692$	23.8655	0.907229
$693$	75.4407	2.86576
$694$	−9.03533	−0.342977
$695$	−0.201098	−0.00762808
$696$	−0.683169	−0.0258955
$697$	11.2712	0.426927
$698$	−23.8544	−0.902901
$699$	−55.0064	−2.08053
$700$	16.4320	0.621071
$701$	−20.2086	−0.763269	−0.381635	−	0.924313i	$-0.624639\pi$
$701$	−20.2086	−0.763269	−0.381635	+	0.924313i	$0.624639\pi$
$702$	4.42747	0.167104
$703$	−4.23988	−0.159910
$704$	27.4912	1.03611
$705$	−0.835034	−0.0314492
$706$	−15.2484	−0.573882
$707$	−19.5055	−0.733580
$708$	−13.9333	−0.523644
$709$	−49.4185	−1.85595	−0.927975	−	0.372643i	$-0.878452\pi$
$709$	−49.4185	−1.85595	−0.927975	+	0.372643i	$0.878452\pi$
$710$	−1.26393	−0.0474346
$711$	−11.2077	−0.420320
$712$	−16.8069	−0.629867
$713$	66.4940	2.49022
$714$	47.9380	1.79404
$715$	0.452126	0.0169086
$716$	−14.2857	−0.533883
$717$	43.6712	1.63093
$718$	10.1710	0.379577
$719$	−19.9759	−0.744976	−0.372488	−	0.928037i	$-0.621495\pi$
$719$	−19.9759	−0.744976	−0.372488	+	0.928037i	$0.621495\pi$
$720$	−1.33695	−0.0498251
$721$	−24.7579	−0.922033
$722$	−1.00678	−0.0374683
$723$	4.03201	0.149952
$724$	−11.9571	−0.444380
$725$	−0.379586	−0.0140975
$726$	11.9917	0.445052
$727$	−36.5532	−1.35568	−0.677842	−	0.735208i	$-0.737085\pi$
$727$	−36.5532	−1.35568	−0.677842	+	0.735208i	$0.737085\pi$
$728$	5.38444	0.199561
$729$	−32.2206	−1.19335
$730$	−0.650386	−0.0240719
$731$	38.4334	1.42151
$732$	−30.7869	−1.13792
$733$	13.2866	0.490752	0.245376	−	0.969428i	$-0.421089\pi$
$733$	13.2866	0.490752	0.245376	+	0.969428i	$0.421089\pi$
$734$	−27.2442	−1.00560
$735$	−2.80420	−0.103435
$736$	44.2043	1.62939
$737$	−16.9436	−0.624125
$738$	−13.7521	−0.506220
$739$	−6.48614	−0.238596	−0.119298	−	0.992858i	$-0.538064\pi$
$739$	−6.48614	−0.238596	−0.119298	+	0.992858i	$0.538064\pi$
$740$	0.916554	0.0336932
$741$	−1.57803	−0.0579705
$742$	−3.08281	−0.113174
$743$	−49.2702	−1.80755	−0.903774	−	0.428011i	$-0.859215\pi$
$743$	−49.2702	−1.80755	−0.903774	+	0.428011i	$0.859215\pi$
$744$	66.3878	2.43390
$745$	1.05254	0.0385620
$746$	−29.4831	−1.07945
$747$	−72.8455	−2.66528
$748$	−18.2531	−0.667399
$749$	−24.2316	−0.885405
$750$	−6.50890	−0.237671
$751$	−50.2925	−1.83520	−0.917600	−	0.397504i	$-0.869876\pi$
$751$	−50.2925	−1.83520	−0.917600	+	0.397504i	$0.869876\pi$
$752$	−1.35508	−0.0494145
$753$	73.1068	2.66416
$754$	−0.0410833	−0.00149617
$755$	−1.01597	−0.0369751
$756$	27.4116	0.996950
$757$	16.2072	0.589062	0.294531	−	0.955642i	$-0.404837\pi$
$757$	16.2072	0.589062	0.294531	+	0.955642i	$0.404837\pi$
$758$	17.6326	0.640446
$759$	102.545	3.72215
$760$	0.658918	0.0239015
$761$	10.7109	0.388270	0.194135	−	0.980975i	$-0.437810\pi$
$761$	10.7109	0.388270	0.194135	+	0.980975i	$0.437810\pi$
$762$	−66.8184	−2.42058
$763$	−41.1894	−1.49116
$764$	3.19810	0.115703
$765$	6.05567	0.218943
$766$	12.6954	0.458703
$767$	−2.53679	−0.0915980
$768$	50.2986	1.81500
$769$	−18.4924	−0.666853	−0.333426	−	0.942776i	$-0.608205\pi$
$769$	−18.4924	−0.666853	−0.333426	+	0.942776i	$0.608205\pi$
$770$	−2.87641	−0.103658
$771$	63.1020	2.27256
$772$	−15.6947	−0.564865
$773$	2.72045	0.0978478	0.0489239	−	0.998803i	$-0.484421\pi$
$773$	2.72045	0.0978478	0.0489239	+	0.998803i	$0.484421\pi$
$774$	−46.8929	−1.68553
$775$	36.8867	1.32501
$776$	7.13480	0.256125
$777$	42.2793	1.51676
$778$	−20.4675	−0.733797
$779$	2.36046	0.0845721
$780$	0.341130	0.0122144
$781$	22.1999	0.794373
$782$	42.9138	1.53459
$783$	−0.633218	−0.0226294
$784$	−4.55060	−0.162522
$785$	2.39857	0.0856085
$786$	−44.4780	−1.58648
$787$	4.86450	0.173401	0.0867003	−	0.996234i	$-0.472368\pi$
$787$	4.86450	0.173401	0.0867003	+	0.996234i	$0.472368\pi$
$788$	−26.2468	−0.935005
$789$	−4.24484	−0.151120
$790$	0.427326	0.0152036
$791$	−49.3703	−1.75541
$792$	67.4262	2.39589
$793$	−5.60528	−0.199049
$794$	−9.24878	−0.328227
$795$	−0.591318	−0.0209719
$796$	−22.1767	−0.786034
$797$	−47.7480	−1.69132	−0.845661	−	0.533721i	$-0.820793\pi$
$797$	−47.7480	−1.69132	−0.845661	+	0.533721i	$0.820793\pi$
$798$	10.0394	0.355390
$799$	6.13779	0.217139
$800$	24.5218	0.866977
$801$	−32.3479	−1.14296
$802$	37.9947	1.34164
$803$	11.4234	0.403125
$804$	−12.7840	−0.450856
$805$	−6.58110	−0.231953
$806$	3.99232	0.140624
$807$	−17.6691	−0.621982
$808$	−17.4333	−0.613302
$809$	−4.06292	−0.142845	−0.0714223	−	0.997446i	$-0.522754\pi$
$809$	−4.06292	−0.142845	−0.0714223	+	0.997446i	$0.522754\pi$
$810$	−1.57243	−0.0552494
$811$	47.4956	1.66780	0.833899	−	0.551917i	$-0.186104\pi$
$811$	47.4956	1.66780	0.833899	+	0.551917i	$0.186104\pi$
$812$	−0.254357	−0.00892619
$813$	29.5181	1.03524
$814$	16.5423	0.579807
$815$	−2.05096	−0.0718418
$816$	14.9216	0.522359
$817$	8.04888	0.281595
$818$	−3.25534	−0.113820
$819$	10.3633	0.362123
$820$	−0.510270	−0.0178194
$821$	16.1922	0.565113	0.282556	−	0.959251i	$-0.408818\pi$
$821$	16.1922	0.565113	0.282556	+	0.959251i	$0.408818\pi$
$822$	48.0785	1.67693
$823$	−28.6419	−0.998395	−0.499198	−	0.866488i	$-0.666372\pi$
$823$	−28.6419	−0.998395	−0.499198	+	0.866488i	$0.666372\pi$
$824$	−22.1277	−0.770856
$825$	56.8856	1.98050
$826$	16.1389	0.561544
$827$	25.7575	0.895675	0.447837	−	0.894115i	$-0.352194\pi$
$827$	25.7575	0.895675	0.447837	+	0.894115i	$0.352194\pi$
$828$	50.9546	1.77079
$829$	−53.3786	−1.85391	−0.926957	−	0.375168i	$-0.877585\pi$
$829$	−53.3786	−1.85391	−0.926957	+	0.375168i	$0.877585\pi$
$830$	2.77746	0.0964069
$831$	25.8872	0.898016
$832$	3.77646	0.130925
$833$	20.6119	0.714159
$834$	−2.73846	−0.0948249
$835$	−0.199126	−0.00689106
$836$	−3.82264	−0.132209
$837$	61.5338	2.12692
$838$	−14.3548	−0.495878
$839$	41.7510	1.44140	0.720702	−	0.693245i	$-0.243819\pi$
$839$	41.7510	1.44140	0.720702	+	0.693245i	$0.243819\pi$
$840$	−6.57060	−0.226707
$841$	−28.9941	−0.999797
$842$	4.10938	0.141619
$843$	60.2291	2.07440
$844$	−0.986402	−0.0339534
$845$	−2.78690	−0.0958722
$846$	−7.48876	−0.257469
$847$	13.5173	0.464459
$848$	−0.959580	−0.0329521
$849$	40.5538	1.39180
$850$	23.8059	0.816535
$851$	37.8481	1.29742
$852$	16.7498	0.573840
$853$	49.5378	1.69614	0.848071	−	0.529883i	$-0.177764\pi$
$853$	49.5378	1.69614	0.848071	+	0.529883i	$0.177764\pi$
$854$	35.6605	1.22028
$855$	1.26820	0.0433716
$856$	−21.6574	−0.740233
$857$	−40.8576	−1.39567	−0.697835	−	0.716259i	$-0.745853\pi$
$857$	−40.8576	−1.39567	−0.697835	+	0.716259i	$0.745853\pi$
$858$	6.15684	0.210191
$859$	52.1249	1.77848	0.889239	−	0.457442i	$-0.151234\pi$
$859$	52.1249	1.77848	0.889239	+	0.457442i	$0.151234\pi$
$860$	−1.73996	−0.0593322
$861$	−23.5380	−0.802173
$862$	8.94754	0.304755
$863$	−2.62366	−0.0893104	−0.0446552	−	0.999002i	$-0.514219\pi$
$863$	−2.62366	−0.0893104	−0.0446552	+	0.999002i	$0.514219\pi$
$864$	40.9068	1.39168
$865$	−5.30232	−0.180284
$866$	−9.53885	−0.324143
$867$	−17.1946	−0.583959
$868$	24.7175	0.838966
$869$	−7.50559	−0.254610
$870$	0.0501337	0.00169969
$871$	−2.32754	−0.0788657
$872$	−36.8136	−1.24667
$873$	13.7322	0.464764
$874$	8.98717	0.303996
$875$	−7.33698	−0.248035
$876$	8.61902	0.291210
$877$	21.5330	0.727116	0.363558	−	0.931572i	$-0.381562\pi$
$877$	21.5330	0.727116	0.363558	+	0.931572i	$0.381562\pi$
$878$	7.70033	0.259873
$879$	1.01048	0.0340826
$880$	−0.895333	−0.0301817
$881$	2.78978	0.0939901	0.0469951	−	0.998895i	$-0.485035\pi$
$881$	2.78978	0.0939901	0.0469951	+	0.998895i	$0.485035\pi$
$882$	−25.1487	−0.846800
$883$	27.6052	0.928990	0.464495	−	0.885576i	$-0.346236\pi$
$883$	27.6052	0.928990	0.464495	+	0.885576i	$0.346236\pi$
$884$	−2.50743	−0.0843339
$885$	3.09563	0.104058
$886$	−13.7562	−0.462149
$887$	29.0632	0.975846	0.487923	−	0.872887i	$-0.337755\pi$
$887$	29.0632	0.975846	0.487923	+	0.872887i	$0.337755\pi$
$888$	37.7877	1.26807
$889$	−75.3193	−2.52613
$890$	1.23336	0.0413424
$891$	27.6183	0.925247
$892$	−23.0828	−0.772869
$893$	1.28540	0.0430143
$894$	14.3330	0.479366
$895$	3.17394	0.106093
$896$	9.29106	0.310393
$897$	14.0866	0.470338
$898$	4.48965	0.149822
$899$	−0.570984	−0.0190434
$900$	28.2664	0.942214
$901$	4.34640	0.144799
$902$	−9.20953	−0.306644
$903$	−80.2619	−2.67095
$904$	−44.1254	−1.46759
$905$	2.65656	0.0883071
$906$	−13.8351	−0.459639
$907$	10.6344	0.353109	0.176554	−	0.984291i	$-0.443505\pi$
$907$	10.6344	0.353109	0.176554	+	0.984291i	$0.443505\pi$
$908$	−17.8435	−0.592156
$909$	−33.5535	−1.11290
$910$	−0.395132	−0.0130985
$911$	−36.4874	−1.20888	−0.604440	−	0.796651i	$-0.706603\pi$
$911$	−36.4874	−1.20888	−0.604440	+	0.796651i	$0.706603\pi$
$912$	3.12493	0.103477
$913$	−48.7835	−1.61450
$914$	−16.2737	−0.538288
$915$	6.84009	0.226127
$916$	−25.3231	−0.836700
$917$	−50.1367	−1.65566
$918$	39.7126	1.31071
$919$	−18.0790	−0.596371	−0.298185	−	0.954508i	$-0.596381\pi$
$919$	−18.0790	−0.596371	−0.298185	+	0.954508i	$0.596381\pi$
$920$	−5.88195	−0.193922
$921$	64.5648	2.12748
$922$	−1.65704	−0.0545716
$923$	3.04960	0.100379
$924$	38.1186	1.25401
$925$	20.9958	0.690337
$926$	16.7673	0.551008
$927$	−42.5887	−1.39880
$928$	−0.379582	−0.0124604
$929$	39.0779	1.28210	0.641051	−	0.767498i	$-0.278499\pi$
$929$	39.0779	1.28210	0.641051	+	0.767498i	$0.278499\pi$
$930$	−4.87181	−0.159753
$931$	4.31662	0.141471
$932$	−18.3042	−0.599576
$933$	65.5464	2.14589
$934$	26.9130	0.880620
$935$	4.05539	0.132625
$936$	9.26234	0.302749
$937$	−10.4725	−0.342121	−0.171060	−	0.985261i	$-0.554719\pi$
$937$	−10.4725	−0.342121	−0.171060	+	0.985261i	$0.554719\pi$
$938$	14.8077	0.483488
$939$	17.9428	0.585540
$940$	−0.277871	−0.00906314
$941$	−48.3005	−1.57455	−0.787276	−	0.616601i	$-0.788509\pi$
$941$	−48.3005	−1.57455	−0.787276	+	0.616601i	$0.788509\pi$
$942$	32.6625	1.06420
$943$	−21.0711	−0.686168
$944$	5.02352	0.163502
$945$	−6.09018	−0.198114
$946$	−31.4034	−1.02101
$947$	−24.6313	−0.800409	−0.400204	−	0.916426i	$-0.631061\pi$
$947$	−24.6313	−0.800409	−0.400204	+	0.916426i	$0.631061\pi$
$948$	−5.66299	−0.183925
$949$	1.56924	0.0509397
$950$	4.98553	0.161752
$951$	59.6401	1.93396
$952$	48.2962	1.56529
$953$	−31.8629	−1.03214	−0.516070	−	0.856546i	$-0.672606\pi$
$953$	−31.8629	−1.03214	−0.516070	+	0.856546i	$0.672606\pi$
$954$	−5.30307	−0.171693
$955$	−0.710539	−0.0229925
$956$	14.5323	0.470007
$957$	−0.880554	−0.0284643
$958$	33.7963	1.09191
$959$	54.1953	1.75006
$960$	−4.60840	−0.148735
$961$	24.4861	0.789873
$962$	2.27241	0.0732656
$963$	−41.6834	−1.34323
$964$	1.34172	0.0432137
$965$	3.48698	0.112250
$966$	−89.6183	−2.88342
$967$	−12.5180	−0.402553	−0.201277	−	0.979534i	$-0.564509\pi$
$967$	−12.5180	−0.402553	−0.201277	+	0.979534i	$0.564509\pi$
$968$	12.0813	0.388306
$969$	−14.1543	−0.454702
$970$	−0.523581	−0.0168112
$971$	−24.0610	−0.772156	−0.386078	−	0.922466i	$-0.626170\pi$
$971$	−24.0610	−0.772156	−0.386078	+	0.922466i	$0.626170\pi$
$972$	−3.60735	−0.115706
$973$	−3.08685	−0.0989599
$974$	−33.0521	−1.05906
$975$	7.81438	0.250260
$976$	11.1000	0.355301
$977$	27.7895	0.889064	0.444532	−	0.895763i	$-0.353370\pi$
$977$	27.7895	0.889064	0.444532	+	0.895763i	$0.353370\pi$
$978$	−27.9289	−0.893069
$979$	−21.6629	−0.692349
$980$	−0.933142	−0.0298081
$981$	−70.8543	−2.26220
$982$	−7.62295	−0.243258
$983$	−31.9361	−1.01860	−0.509301	−	0.860588i	$-0.670096\pi$
$983$	−31.9361	−1.01860	−0.509301	+	0.860588i	$0.670096\pi$
$984$	−21.0374	−0.670649
$985$	5.83140	0.185804
$986$	−0.368501	−0.0117354
$987$	−12.8178	−0.407994
$988$	−0.525116	−0.0167062
$989$	−71.8498	−2.28469
$990$	−4.94801	−0.157258
$991$	−34.2673	−1.08854	−0.544269	−	0.838911i	$-0.683193\pi$
$991$	−34.2673	−1.08854	−0.544269	+	0.838911i	$0.683193\pi$
$992$	36.8864	1.17114
$993$	−3.46587	−0.109986
$994$	−19.4014	−0.615374
$995$	4.92713	0.156200
$996$	−36.8073	−1.16628
$997$	57.0410	1.80651	0.903253	−	0.429108i	$-0.141172\pi$
$997$	57.0410	1.80651	0.903253	+	0.429108i	$0.141172\pi$
$998$	−1.24619	−0.0394473
$999$	35.0248	1.10814

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4009.2.a.c.1.30	✓	71

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4009.2.a.c.1.30	✓	71	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:	\( N \)	\(=\)	\( 4009 = 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4009.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00678 q^{2} -2.96425 q^{3} -0.986402 q^{4} +0.219154 q^{5} +2.98434 q^{6} +3.36402 q^{7} +3.00664 q^{8} +5.78680 q^{9} +O(q^{10})\)	\(q-1.00678 q^{2} -2.96425 q^{3} -0.986402 q^{4} +0.219154 q^{5} +2.98434 q^{6} +3.36402 q^{7} +3.00664 q^{8} +5.78680 q^{9} -0.220639 q^{10} +3.87533 q^{11} +2.92395 q^{12} +0.532354 q^{13} -3.38681 q^{14} -0.649629 q^{15} -1.05421 q^{16} +4.77500 q^{17} -5.82601 q^{18} +1.00000 q^{19} -0.216174 q^{20} -9.97181 q^{21} -3.90159 q^{22} -8.92669 q^{23} -8.91244 q^{24} -4.95197 q^{25} -0.535962 q^{26} -8.26079 q^{27} -3.31828 q^{28} +0.0766535 q^{29} +0.654031 q^{30} -7.44890 q^{31} -4.95193 q^{32} -11.4875 q^{33} -4.80736 q^{34} +0.737239 q^{35} -5.70812 q^{36} -4.23988 q^{37} -1.00678 q^{38} -1.57803 q^{39} +0.658918 q^{40} +2.36046 q^{41} +10.0394 q^{42} +8.04888 q^{43} -3.82264 q^{44} +1.26820 q^{45} +8.98717 q^{46} +1.28540 q^{47} +3.12493 q^{48} +4.31662 q^{49} +4.98553 q^{50} -14.1543 q^{51} -0.525116 q^{52} +0.910239 q^{53} +8.31677 q^{54} +0.849296 q^{55} +10.1144 q^{56} -2.96425 q^{57} -0.0771729 q^{58} -4.76522 q^{59} +0.640796 q^{60} -10.5292 q^{61} +7.49937 q^{62} +19.4669 q^{63} +7.09389 q^{64} +0.116668 q^{65} +11.5653 q^{66} -4.37216 q^{67} -4.71007 q^{68} +26.4610 q^{69} -0.742235 q^{70} +5.72851 q^{71} +17.3988 q^{72} +2.94773 q^{73} +4.26861 q^{74} +14.6789 q^{75} -0.986402 q^{76} +13.0367 q^{77} +1.58873 q^{78} -1.93676 q^{79} -0.231034 q^{80} +7.12668 q^{81} -2.37645 q^{82} -12.5882 q^{83} +9.83621 q^{84} +1.04646 q^{85} -8.10342 q^{86} -0.227220 q^{87} +11.6517 q^{88} -5.58994 q^{89} -1.27680 q^{90} +1.79085 q^{91} +8.80530 q^{92} +22.0804 q^{93} -1.29411 q^{94} +0.219154 q^{95} +14.6788 q^{96} +2.37302 q^{97} -4.34587 q^{98} +22.4258 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 71 q - 15 q^{2} - 8 q^{3} + 69 q^{4} - 18 q^{5} - 9 q^{6} - 19 q^{7} - 39 q^{8} + 63 q^{9}+O(q^{10}) \) 71 * q - 15 * q^2 - 8 * q^3 + 69 * q^4 - 18 * q^5 - 9 * q^6 - 19 * q^7 - 39 * q^8 + 63 * q^9	\( 71 q - 15 q^{2} - 8 q^{3} + 69 q^{4} - 18 q^{5} - 9 q^{6} - 19 q^{7} - 39 q^{8} + 63 q^{9} - 10 q^{10} - 52 q^{11} - 9 q^{12} - 15 q^{13} - 53 q^{14} - 33 q^{15} + 53 q^{16} - 10 q^{17} - 35 q^{18} + 71 q^{19} - 33 q^{20} - 38 q^{21} - 6 q^{22} - 65 q^{23} - 30 q^{24} + 51 q^{25} - 4 q^{26} - 23 q^{27} - 29 q^{28} - 97 q^{29} - 27 q^{30} - 53 q^{31} - 78 q^{32} - 17 q^{33} - 24 q^{34} - 38 q^{35} + 24 q^{36} - 33 q^{37} - 15 q^{38} - 86 q^{39} + 25 q^{40} - 69 q^{41} + 64 q^{42} - 10 q^{43} - 94 q^{44} - 34 q^{45} - 6 q^{46} - 37 q^{47} - q^{48} + 74 q^{49} - 41 q^{50} - 46 q^{51} - 30 q^{52} - 50 q^{53} - 17 q^{54} - 30 q^{55} - 116 q^{56} - 8 q^{57} + 11 q^{58} - 93 q^{59} - 56 q^{60} - 18 q^{61} - q^{62} - 84 q^{63} + 93 q^{64} - 78 q^{65} - 53 q^{66} - 5 q^{67} - 9 q^{68} - 69 q^{69} - 10 q^{70} - 221 q^{71} - 73 q^{72} - 34 q^{73} - 58 q^{74} - 70 q^{75} + 69 q^{76} - 2 q^{77} + 7 q^{78} - 68 q^{79} - 71 q^{80} + 39 q^{81} + 26 q^{82} - 45 q^{83} - 10 q^{84} - 44 q^{85} - 80 q^{86} - 7 q^{87} - 46 q^{88} - 143 q^{89} + 41 q^{90} - 30 q^{91} - 46 q^{92} + 32 q^{93} + 41 q^{94} - 18 q^{95} - 140 q^{96} - 18 q^{97} - 97 q^{98} - 142 q^{99}+O(q^{100}) \) 71 * q - 15 * q^2 - 8 * q^3 + 69 * q^4 - 18 * q^5 - 9 * q^6 - 19 * q^7 - 39 * q^8 + 63 * q^9 - 10 * q^10 - 52 * q^11 - 9 * q^12 - 15 * q^13 - 53 * q^14 - 33 * q^15 + 53 * q^16 - 10 * q^17 - 35 * q^18 + 71 * q^19 - 33 * q^20 - 38 * q^21 - 6 * q^22 - 65 * q^23 - 30 * q^24 + 51 * q^25 - 4 * q^26 - 23 * q^27 - 29 * q^28 - 97 * q^29 - 27 * q^30 - 53 * q^31 - 78 * q^32 - 17 * q^33 - 24 * q^34 - 38 * q^35 + 24 * q^36 - 33 * q^37 - 15 * q^38 - 86 * q^39 + 25 * q^40 - 69 * q^41 + 64 * q^42 - 10 * q^43 - 94 * q^44 - 34 * q^45 - 6 * q^46 - 37 * q^47 - q^48 + 74 * q^49 - 41 * q^50 - 46 * q^51 - 30 * q^52 - 50 * q^53 - 17 * q^54 - 30 * q^55 - 116 * q^56 - 8 * q^57 + 11 * q^58 - 93 * q^59 - 56 * q^60 - 18 * q^61 - q^62 - 84 * q^63 + 93 * q^64 - 78 * q^65 - 53 * q^66 - 5 * q^67 - 9 * q^68 - 69 * q^69 - 10 * q^70 - 221 * q^71 - 73 * q^72 - 34 * q^73 - 58 * q^74 - 70 * q^75 + 69 * q^76 - 2 * q^77 + 7 * q^78 - 68 * q^79 - 71 * q^80 + 39 * q^81 + 26 * q^82 - 45 * q^83 - 10 * q^84 - 44 * q^85 - 80 * q^86 - 7 * q^87 - 46 * q^88 - 143 * q^89 + 41 * q^90 - 30 * q^91 - 46 * q^92 + 32 * q^93 + 41 * q^94 - 18 * q^95 - 140 * q^96 - 18 * q^97 - 97 * q^98 - 142 * q^99

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