LMFDB - Embedded newform 4015.2.a.h.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4015,2,Mod(1,4015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4015, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4015 = 5 \cdot 11 \cdot 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4015.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:	$32.0599364115$
Analytic rank:	$0$
Dimension:	$37$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	4015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.421939 q^{2} -2.05594 q^{3} -1.82197 q^{4} +1.00000 q^{5} +0.867482 q^{6} -0.0580639 q^{7} +1.61264 q^{8} +1.22690 q^{9} +O(q^{10})$	\(q-0.421939 q^{2} -2.05594 q^{3} -1.82197 q^{4} +1.00000 q^{5} +0.867482 q^{6} -0.0580639 q^{7} +1.61264 q^{8} +1.22690 q^{9} -0.421939 q^{10} +1.00000 q^{11} +3.74586 q^{12} +6.32922 q^{13} +0.0244994 q^{14} -2.05594 q^{15} +2.96350 q^{16} +5.86865 q^{17} -0.517676 q^{18} +0.796345 q^{19} -1.82197 q^{20} +0.119376 q^{21} -0.421939 q^{22} +8.29329 q^{23} -3.31549 q^{24} +1.00000 q^{25} -2.67054 q^{26} +3.64539 q^{27} +0.105790 q^{28} -1.17504 q^{29} +0.867482 q^{30} -0.271039 q^{31} -4.47569 q^{32} -2.05594 q^{33} -2.47621 q^{34} -0.0580639 q^{35} -2.23537 q^{36} +3.31240 q^{37} -0.336009 q^{38} -13.0125 q^{39} +1.61264 q^{40} +1.75836 q^{41} -0.0503693 q^{42} -1.18574 q^{43} -1.82197 q^{44} +1.22690 q^{45} -3.49926 q^{46} -11.5364 q^{47} -6.09279 q^{48} -6.99663 q^{49} -0.421939 q^{50} -12.0656 q^{51} -11.5316 q^{52} +3.80653 q^{53} -1.53813 q^{54} +1.00000 q^{55} -0.0936359 q^{56} -1.63724 q^{57} +0.495794 q^{58} +1.80051 q^{59} +3.74586 q^{60} +7.32347 q^{61} +0.114362 q^{62} -0.0712385 q^{63} -4.03854 q^{64} +6.32922 q^{65} +0.867482 q^{66} +11.5619 q^{67} -10.6925 q^{68} -17.0505 q^{69} +0.0244994 q^{70} -2.43721 q^{71} +1.97854 q^{72} +1.00000 q^{73} -1.39763 q^{74} -2.05594 q^{75} -1.45091 q^{76} -0.0580639 q^{77} +5.49048 q^{78} +10.1837 q^{79} +2.96350 q^{80} -11.1754 q^{81} -0.741920 q^{82} +1.69280 q^{83} -0.217499 q^{84} +5.86865 q^{85} +0.500309 q^{86} +2.41581 q^{87} +1.61264 q^{88} +10.5321 q^{89} -0.517676 q^{90} -0.367499 q^{91} -15.1101 q^{92} +0.557240 q^{93} +4.86764 q^{94} +0.796345 q^{95} +9.20176 q^{96} -17.3837 q^{97} +2.95215 q^{98} +1.22690 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9}+O(q^{10}) $ 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9	\( 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9} + 5 q^{10} + 37 q^{11} + 6 q^{12} + 11 q^{13} + 11 q^{14} + 3 q^{15} + 43 q^{16} + 38 q^{17} + 11 q^{18} + 34 q^{19} + 43 q^{20} + 39 q^{21} + 5 q^{22} + 4 q^{23} + 25 q^{24} + 37 q^{25} - 9 q^{26} + 3 q^{27} + 14 q^{28} + 58 q^{29} + 9 q^{30} + 8 q^{31} + 14 q^{32} + 3 q^{33} + 8 q^{34} + 6 q^{35} + 20 q^{36} + 2 q^{37} + 15 q^{38} + 14 q^{39} + 12 q^{40} + 62 q^{41} - 13 q^{42} + 30 q^{43} + 43 q^{44} + 50 q^{45} + 31 q^{46} + 5 q^{47} - 25 q^{48} + 59 q^{49} + 5 q^{50} + 23 q^{51} - q^{52} + 18 q^{53} + 13 q^{54} + 37 q^{55} + 22 q^{56} + 5 q^{57} - 40 q^{58} + 15 q^{59} + 6 q^{60} + 57 q^{61} + 20 q^{62} - 29 q^{63} + 10 q^{64} + 11 q^{65} + 9 q^{66} - 14 q^{67} + 53 q^{68} + 24 q^{69} + 11 q^{70} + 8 q^{71} + 15 q^{72} + 37 q^{73} + 7 q^{74} + 3 q^{75} + 59 q^{76} + 6 q^{77} + q^{78} + 42 q^{79} + 43 q^{80} + 61 q^{81} - 22 q^{82} + 44 q^{83} + 66 q^{84} + 38 q^{85} - q^{86} - 26 q^{87} + 12 q^{88} + 69 q^{89} + 11 q^{90} - 10 q^{91} - 21 q^{92} - 26 q^{93} + 29 q^{94} + 34 q^{95} - 9 q^{96} + 37 q^{97} - 15 q^{98} + 50 q^{99}+O(q^{100}) \) 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9 + 5 * q^10 + 37 * q^11 + 6 * q^12 + 11 * q^13 + 11 * q^14 + 3 * q^15 + 43 * q^16 + 38 * q^17 + 11 * q^18 + 34 * q^19 + 43 * q^20 + 39 * q^21 + 5 * q^22 + 4 * q^23 + 25 * q^24 + 37 * q^25 - 9 * q^26 + 3 * q^27 + 14 * q^28 + 58 * q^29 + 9 * q^30 + 8 * q^31 + 14 * q^32 + 3 * q^33 + 8 * q^34 + 6 * q^35 + 20 * q^36 + 2 * q^37 + 15 * q^38 + 14 * q^39 + 12 * q^40 + 62 * q^41 - 13 * q^42 + 30 * q^43 + 43 * q^44 + 50 * q^45 + 31 * q^46 + 5 * q^47 - 25 * q^48 + 59 * q^49 + 5 * q^50 + 23 * q^51 - q^52 + 18 * q^53 + 13 * q^54 + 37 * q^55 + 22 * q^56 + 5 * q^57 - 40 * q^58 + 15 * q^59 + 6 * q^60 + 57 * q^61 + 20 * q^62 - 29 * q^63 + 10 * q^64 + 11 * q^65 + 9 * q^66 - 14 * q^67 + 53 * q^68 + 24 * q^69 + 11 * q^70 + 8 * q^71 + 15 * q^72 + 37 * q^73 + 7 * q^74 + 3 * q^75 + 59 * q^76 + 6 * q^77 + q^78 + 42 * q^79 + 43 * q^80 + 61 * q^81 - 22 * q^82 + 44 * q^83 + 66 * q^84 + 38 * q^85 - q^86 - 26 * q^87 + 12 * q^88 + 69 * q^89 + 11 * q^90 - 10 * q^91 - 21 * q^92 - 26 * q^93 + 29 * q^94 + 34 * q^95 - 9 * q^96 + 37 * q^97 - 15 * q^98 + 50 * 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 $

$2$	−0.421939	−0.298356	−0.149178	−	0.988810i	$-0.547663\pi$
$2$	−0.421939	−0.298356	−0.149178	+	0.988810i	$0.547663\pi$
$3$	−2.05594	−1.18700	−0.593499	−	0.804834i	$-0.702254\pi$
$3$	−2.05594	−1.18700	−0.593499	+	0.804834i	$0.702254\pi$
$4$	−1.82197	−0.910984
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.867482	0.354148
$7$	−0.0580639	−0.0219461	−0.0109730	−	0.999940i	$-0.503493\pi$
$7$	−0.0580639	−0.0219461	−0.0109730	+	0.999940i	$0.503493\pi$
$8$	1.61264	0.570153
$9$	1.22690	0.408967
$10$	−0.421939	−0.133429
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	3.74586	1.08134
$13$	6.32922	1.75541	0.877704	−	0.479202i	$-0.159074\pi$
$13$	6.32922	1.75541	0.877704	+	0.479202i	$0.159074\pi$
$14$	0.0244994	0.00654774
$15$	−2.05594	−0.530842
$16$	2.96350	0.740875
$17$	5.86865	1.42336	0.711678	−	0.702506i	$-0.247936\pi$
$17$	5.86865	1.42336	0.711678	+	0.702506i	$0.247936\pi$
$18$	−0.517676	−0.122018
$19$	0.796345	0.182694	0.0913470	−	0.995819i	$-0.470883\pi$
$19$	0.796345	0.182694	0.0913470	+	0.995819i	$0.470883\pi$
$20$	−1.82197	−0.407404
$21$	0.119376	0.0260500
$22$	−0.421939	−0.0899576
$23$	8.29329	1.72927	0.864635	−	0.502400i	$-0.167549\pi$
$23$	8.29329	1.72927	0.864635	+	0.502400i	$0.167549\pi$
$24$	−3.31549	−0.676771
$25$	1.00000	0.200000
$26$	−2.67054	−0.523736
$27$	3.64539	0.701556
$28$	0.105790	0.0199925
$29$	−1.17504	−0.218199	−0.109099	−	0.994031i	$-0.534797\pi$
$29$	−1.17504	−0.218199	−0.109099	+	0.994031i	$0.534797\pi$
$30$	0.867482	0.158380
$31$	−0.271039	−0.0486800	−0.0243400	−	0.999704i	$-0.507748\pi$
$31$	−0.271039	−0.0486800	−0.0243400	+	0.999704i	$0.507748\pi$
$32$	−4.47569	−0.791197
$33$	−2.05594	−0.357894
$34$	−2.47621	−0.424666
$35$	−0.0580639	−0.00981458
$36$	−2.23537	−0.372562
$37$	3.31240	0.544556	0.272278	−	0.962219i	$-0.412223\pi$
$37$	3.31240	0.544556	0.272278	+	0.962219i	$0.412223\pi$
$38$	−0.336009	−0.0545078
$39$	−13.0125	−2.08367
$40$	1.61264	0.254980
$41$	1.75836	0.274610	0.137305	−	0.990529i	$-0.456156\pi$
$41$	1.75836	0.274610	0.137305	+	0.990529i	$0.456156\pi$
$42$	−0.0503693	−0.00777216
$43$	−1.18574	−0.180823	−0.0904117	−	0.995904i	$-0.528818\pi$
$43$	−1.18574	−0.180823	−0.0904117	+	0.995904i	$0.528818\pi$
$44$	−1.82197	−0.274672
$45$	1.22690	0.182895
$46$	−3.49926	−0.515938
$47$	−11.5364	−1.68275	−0.841376	−	0.540450i	$-0.818254\pi$
$47$	−11.5364	−1.68275	−0.841376	+	0.540450i	$0.818254\pi$
$48$	−6.09279	−0.879418
$49$	−6.99663	−0.999518
$50$	−0.421939	−0.0596711
$51$	−12.0656	−1.68952
$52$	−11.5316	−1.59915
$53$	3.80653	0.522867	0.261433	−	0.965222i	$-0.415805\pi$
$53$	3.80653	0.522867	0.261433	+	0.965222i	$0.415805\pi$
$54$	−1.53813	−0.209313
$55$	1.00000	0.134840
$56$	−0.0936359	−0.0125126
$57$	−1.63724	−0.216858
$58$	0.495794	0.0651009
$59$	1.80051	0.234406	0.117203	−	0.993108i	$-0.462607\pi$
$59$	1.80051	0.234406	0.117203	+	0.993108i	$0.462607\pi$
$60$	3.74586	0.483589
$61$	7.32347	0.937674	0.468837	−	0.883285i	$-0.344673\pi$
$61$	7.32347	0.937674	0.468837	+	0.883285i	$0.344673\pi$
$62$	0.114362	0.0145240
$63$	−0.0712385	−0.00897521
$64$	−4.03854	−0.504817
$65$	6.32922	0.785043
$66$	0.867482	0.106780
$67$	11.5619	1.41251	0.706257	−	0.707955i	$-0.250382\pi$
$67$	11.5619	1.41251	0.706257	+	0.707955i	$0.250382\pi$
$68$	−10.6925	−1.29665
$69$	−17.0505	−2.05264
$70$	0.0244994	0.00292824
$71$	−2.43721	−0.289244	−0.144622	−	0.989487i	$-0.546197\pi$
$71$	−2.43721	−0.289244	−0.144622	+	0.989487i	$0.546197\pi$
$72$	1.97854	0.233173
$73$	1.00000	0.117041
$73$	1.00000	0.117041
$74$	−1.39763	−0.162471
$75$	−2.05594	−0.237400
$76$	−1.45091	−0.166431
$77$	−0.0580639	−0.00661699
$78$	5.49048	0.621674
$79$	10.1837	1.14575	0.572876	−	0.819642i	$-0.305828\pi$
$79$	10.1837	1.14575	0.572876	+	0.819642i	$0.305828\pi$
$80$	2.96350	0.331330
$81$	−11.1754	−1.24171
$82$	−0.741920	−0.0819314
$83$	1.69280	0.185809	0.0929043	−	0.995675i	$-0.470385\pi$
$83$	1.69280	0.185809	0.0929043	+	0.995675i	$0.470385\pi$
$84$	−0.217499	−0.0237311
$85$	5.86865	0.636544
$86$	0.500309	0.0539497
$87$	2.41581	0.259002
$88$	1.61264	0.171908
$89$	10.5321	1.11640	0.558198	−	0.829708i	$-0.311493\pi$
$89$	10.5321	1.11640	0.558198	+	0.829708i	$0.311493\pi$
$90$	−0.517676	−0.0545679
$91$	−0.367499	−0.0385243
$92$	−15.1101	−1.57534
$93$	0.557240	0.0577831
$94$	4.86764	0.502059
$95$	0.796345	0.0817033
$96$	9.20176	0.939151
$97$	−17.3837	−1.76505	−0.882524	−	0.470268i	$-0.844157\pi$
$97$	−17.3837	−1.76505	−0.882524	+	0.470268i	$0.844157\pi$
$98$	2.95215	0.298212
$99$	1.22690	0.123308
$100$	−1.82197	−0.182197
$101$	17.1524	1.70673	0.853363	−	0.521318i	$-0.174559\pi$
$101$	17.1524	1.70673	0.853363	+	0.521318i	$0.174559\pi$
$102$	5.09094	0.504078
$103$	−7.46160	−0.735213	−0.367607	−	0.929981i	$-0.619823\pi$
$103$	−7.46160	−0.735213	−0.367607	+	0.929981i	$0.619823\pi$
$104$	10.2067	1.00085
$105$	0.119376	0.0116499
$106$	−1.60612	−0.156000
$107$	−5.35473	−0.517661	−0.258831	−	0.965923i	$-0.583337\pi$
$107$	−5.35473	−0.517661	−0.258831	+	0.965923i	$0.583337\pi$
$108$	−6.64179	−0.639106
$109$	−3.32627	−0.318599	−0.159300	−	0.987230i	$-0.550924\pi$
$109$	−3.32627	−0.318599	−0.159300	+	0.987230i	$0.550924\pi$
$110$	−0.421939	−0.0402303
$111$	−6.81011	−0.646387
$112$	−0.172072	−0.0162593
$113$	−4.97691	−0.468189	−0.234094	−	0.972214i	$-0.575212\pi$
$113$	−4.97691	−0.468189	−0.234094	+	0.972214i	$0.575212\pi$
$114$	0.690815	0.0647007
$115$	8.29329	0.773353
$116$	2.14088	0.198776
$117$	7.76531	0.717903
$118$	−0.759705	−0.0699365
$119$	−0.340756	−0.0312371
$120$	−3.31549	−0.302661
$121$	1.00000	0.0909091
$122$	−3.09006	−0.279761
$123$	−3.61509	−0.325961
$124$	0.493824	0.0443467
$125$	1.00000	0.0894427
$126$	0.0300583	0.00267781
$127$	−9.98530	−0.886052	−0.443026	−	0.896509i	$-0.646095\pi$
$127$	−9.98530	−0.886052	−0.443026	+	0.896509i	$0.646095\pi$
$128$	10.6554	0.941813
$129$	2.43781	0.214637
$130$	−2.67054	−0.234222
$131$	−15.7333	−1.37463	−0.687314	−	0.726361i	$-0.741210\pi$
$131$	−15.7333	−1.37463	−0.687314	+	0.726361i	$0.741210\pi$
$132$	3.74586	0.326035
$133$	−0.0462389	−0.00400942
$134$	−4.87843	−0.421432
$135$	3.64539	0.313745
$136$	9.46399	0.811530
$137$	−0.359744	−0.0307350	−0.0153675	−	0.999882i	$-0.504892\pi$
$137$	−0.359744	−0.0307350	−0.0153675	+	0.999882i	$0.504892\pi$
$138$	7.19428	0.612418
$139$	3.22965	0.273935	0.136968	−	0.990576i	$-0.456264\pi$
$139$	3.22965	0.273935	0.136968	+	0.990576i	$0.456264\pi$
$140$	0.105790	0.00894093
$141$	23.7181	1.99742
$142$	1.02836	0.0862976
$143$	6.32922	0.529276
$144$	3.63592	0.302993
$145$	−1.17504	−0.0975815
$146$	−0.421939	−0.0349199
$147$	14.3847	1.18643
$148$	−6.03509	−0.496082
$149$	−3.54582	−0.290485	−0.145242	−	0.989396i	$-0.546396\pi$
$149$	−3.54582	−0.290485	−0.145242	+	0.989396i	$0.546396\pi$
$150$	0.867482	0.0708296
$151$	−13.4361	−1.09342	−0.546709	−	0.837323i	$-0.684120\pi$
$151$	−13.4361	−1.09342	−0.546709	+	0.837323i	$0.684120\pi$
$152$	1.28421	0.104164
$153$	7.20024	0.582105
$154$	0.0244994	0.00197422
$155$	−0.271039	−0.0217704
$156$	23.7084	1.89819
$157$	1.13284	0.0904102	0.0452051	−	0.998978i	$-0.485606\pi$
$157$	1.13284	0.0904102	0.0452051	+	0.998978i	$0.485606\pi$
$158$	−4.29688	−0.341841
$159$	−7.82600	−0.620642
$160$	−4.47569	−0.353834
$161$	−0.481541	−0.0379507
$162$	4.71534	0.370472
$163$	3.66846	0.287336	0.143668	−	0.989626i	$-0.454110\pi$
$163$	3.66846	0.287336	0.143668	+	0.989626i	$0.454110\pi$
$164$	−3.20367	−0.250165
$165$	−2.05594	−0.160055
$166$	−0.714256	−0.0554371
$167$	−13.5067	−1.04518	−0.522589	−	0.852585i	$-0.675034\pi$
$167$	−13.5067	−1.04518	−0.522589	+	0.852585i	$0.675034\pi$
$168$	0.192510	0.0148525
$169$	27.0590	2.08146
$170$	−2.47621	−0.189917
$171$	0.977035	0.0747158
$172$	2.16038	0.164727
$173$	8.10928	0.616537	0.308269	−	0.951299i	$-0.400250\pi$
$173$	8.10928	0.616537	0.308269	+	0.951299i	$0.400250\pi$
$174$	−1.01932	−0.0772747
$175$	−0.0580639	−0.00438922
$176$	2.96350	0.223382
$177$	−3.70174	−0.278240
$178$	−4.44389	−0.333083
$179$	−16.7291	−1.25039	−0.625196	−	0.780467i	$-0.714981\pi$
$179$	−16.7291	−1.25039	−0.625196	+	0.780467i	$0.714981\pi$
$180$	−2.23537	−0.166615
$181$	25.8052	1.91809	0.959044	−	0.283256i	$-0.0914145\pi$
$181$	25.8052	1.91809	0.959044	+	0.283256i	$0.0914145\pi$
$182$	0.155062	0.0114940
$183$	−15.0566	−1.11302
$184$	13.3741	0.985949
$185$	3.31240	0.243533
$186$	−0.235121	−0.0172399
$187$	5.86865	0.429158
$188$	21.0189	1.53296
$189$	−0.211666	−0.0153964
$190$	−0.336009	−0.0243766
$191$	21.0196	1.52093	0.760464	−	0.649380i	$-0.224972\pi$
$191$	21.0196	1.52093	0.760464	+	0.649380i	$0.224972\pi$
$192$	8.30300	0.599217
$193$	12.1296	0.873110	0.436555	−	0.899678i	$-0.356198\pi$
$193$	12.1296	0.873110	0.436555	+	0.899678i	$0.356198\pi$
$194$	7.33486	0.526612
$195$	−13.0125	−0.931845
$196$	12.7476	0.910545
$197$	−18.0668	−1.28721	−0.643605	−	0.765358i	$-0.722562\pi$
$197$	−18.0668	−1.28721	−0.643605	+	0.765358i	$0.722562\pi$
$198$	−0.517676	−0.0367897
$199$	11.8000	0.836482	0.418241	−	0.908336i	$-0.362647\pi$
$199$	11.8000	0.836482	0.418241	+	0.908336i	$0.362647\pi$
$200$	1.61264	0.114031
$201$	−23.7707	−1.67665
$202$	−7.23725	−0.509211
$203$	0.0682272	0.00478861
$204$	21.9831	1.53913
$205$	1.75836	0.122809
$206$	3.14834	0.219355
$207$	10.1750	0.707214
$208$	18.7566	1.30054
$209$	0.796345	0.0550843
$210$	−0.0503693	−0.00347581
$211$	−11.5382	−0.794322	−0.397161	−	0.917749i	$-0.630005\pi$
$211$	−11.5382	−0.794322	−0.397161	+	0.917749i	$0.630005\pi$
$212$	−6.93537	−0.476323
$213$	5.01077	0.343332
$214$	2.25937	0.154447
$215$	−1.18574	−0.0808667
$216$	5.87869	0.399994
$217$	0.0157376	0.00106833
$218$	1.40348	0.0950559
$219$	−2.05594	−0.138928
$220$	−1.82197	−0.122837
$221$	37.1439	2.49857
$222$	2.87345	0.192853
$223$	13.1748	0.882252	0.441126	−	0.897445i	$-0.354579\pi$
$223$	13.1748	0.882252	0.441126	+	0.897445i	$0.354579\pi$
$224$	0.259876	0.0173637
$225$	1.22690	0.0817933
$226$	2.09995	0.139687
$227$	2.72086	0.180590	0.0902949	−	0.995915i	$-0.471219\pi$
$227$	2.72086	0.180590	0.0902949	+	0.995915i	$0.471219\pi$
$228$	2.98300	0.197554
$229$	−4.38186	−0.289562	−0.144781	−	0.989464i	$-0.546248\pi$
$229$	−4.38186	−0.289562	−0.144781	+	0.989464i	$0.546248\pi$
$230$	−3.49926	−0.230734
$231$	0.119376	0.00785436
$232$	−1.89491	−0.124407
$233$	−16.0203	−1.04952	−0.524761	−	0.851250i	$-0.675845\pi$
$233$	−16.0203	−1.04952	−0.524761	+	0.851250i	$0.675845\pi$
$234$	−3.27649	−0.214191
$235$	−11.5364	−0.752550
$236$	−3.28047	−0.213540
$237$	−20.9370	−1.36001
$238$	0.143778	0.00931976
$239$	−5.87473	−0.380004	−0.190002	−	0.981784i	$-0.560850\pi$
$239$	−5.87473	−0.380004	−0.190002	+	0.981784i	$0.560850\pi$
$240$	−6.09279	−0.393288
$241$	18.3559	1.18241	0.591205	−	0.806521i	$-0.298652\pi$
$241$	18.3559	1.18241	0.591205	+	0.806521i	$0.298652\pi$
$242$	−0.421939	−0.0271232
$243$	12.0398	0.772356
$244$	−13.3431	−0.854206
$245$	−6.99663	−0.446998
$246$	1.52535	0.0972524
$247$	5.04024	0.320703
$248$	−0.437087	−0.0277550
$249$	−3.48029	−0.220555
$250$	−0.421939	−0.0266857
$251$	14.5307	0.917167	0.458584	−	0.888651i	$-0.348357\pi$
$251$	14.5307	0.917167	0.458584	+	0.888651i	$0.348357\pi$
$252$	0.129794	0.00817627
$253$	8.29329	0.521395
$254$	4.21319	0.264359
$255$	−12.0656	−0.755577
$256$	3.58115	0.223822
$257$	10.8262	0.675318	0.337659	−	0.941269i	$-0.390365\pi$
$257$	10.8262	0.675318	0.337659	+	0.941269i	$0.390365\pi$
$258$	−1.02861	−0.0640382
$259$	−0.192331	−0.0119509
$260$	−11.5316	−0.715161
$261$	−1.44165	−0.0892360
$262$	6.63850	0.410128
$263$	15.7384	0.970470	0.485235	−	0.874384i	$-0.338734\pi$
$263$	15.7384	0.970470	0.485235	+	0.874384i	$0.338734\pi$
$264$	−3.31549	−0.204054
$265$	3.80653	0.233833
$266$	0.0195100	0.00119623
$267$	−21.6533	−1.32516
$268$	−21.0655	−1.28678
$269$	−5.28552	−0.322264	−0.161132	−	0.986933i	$-0.551514\pi$
$269$	−5.28552	−0.322264	−0.161132	+	0.986933i	$0.551514\pi$
$270$	−1.53813	−0.0936077
$271$	−25.1431	−1.52734	−0.763668	−	0.645610i	$-0.776603\pi$
$271$	−25.1431	−1.52734	−0.763668	+	0.645610i	$0.776603\pi$
$272$	17.3917	1.05453
$273$	0.755556	0.0457283
$274$	0.151790	0.00916998
$275$	1.00000	0.0603023
$276$	31.0655	1.86992
$277$	18.6561	1.12094	0.560468	−	0.828176i	$-0.310621\pi$
$277$	18.6561	1.12094	0.560468	+	0.828176i	$0.310621\pi$
$278$	−1.36271	−0.0817302
$279$	−0.332537	−0.0199085
$280$	−0.0936359	−0.00559581
$281$	14.3401	0.855457	0.427729	−	0.903907i	$-0.359314\pi$
$281$	14.3401	0.855457	0.427729	+	0.903907i	$0.359314\pi$
$282$	−10.0076	−0.595943
$283$	−16.0739	−0.955496	−0.477748	−	0.878497i	$-0.658547\pi$
$283$	−16.0739	−0.955496	−0.477748	+	0.878497i	$0.658547\pi$
$284$	4.44053	0.263497
$285$	−1.63724	−0.0969817
$286$	−2.67054	−0.157912
$287$	−0.102097	−0.00602660
$288$	−5.49122	−0.323573
$289$	17.4410	1.02594
$290$	0.495794	0.0291140
$291$	35.7399	2.09511
$292$	−1.82197	−0.106623
$293$	−2.29458	−0.134051	−0.0670254	−	0.997751i	$-0.521351\pi$
$293$	−2.29458	−0.134051	−0.0670254	+	0.997751i	$0.521351\pi$
$294$	−6.06945	−0.353977
$295$	1.80051	0.104830
$296$	5.34170	0.310480
$297$	3.64539	0.211527
$298$	1.49612	0.0866678
$299$	52.4900	3.03558
$300$	3.74586	0.216267
$301$	0.0688485	0.00396836
$302$	5.66923	0.326228
$303$	−35.2643	−2.02588
$304$	2.35997	0.135354
$305$	7.32347	0.419341
$306$	−3.03806	−0.173674
$307$	−29.5989	−1.68930	−0.844650	−	0.535318i	$-0.820192\pi$
$307$	−29.5989	−1.68930	−0.844650	+	0.535318i	$0.820192\pi$
$308$	0.105790	0.00602797
$309$	15.3406	0.872697
$310$	0.114362	0.00649531
$311$	7.86269	0.445852	0.222926	−	0.974835i	$-0.428439\pi$
$311$	7.86269	0.445852	0.222926	+	0.974835i	$0.428439\pi$
$312$	−20.9844	−1.18801
$313$	17.4585	0.986815	0.493408	−	0.869798i	$-0.335751\pi$
$313$	17.4585	0.986815	0.493408	+	0.869798i	$0.335751\pi$
$314$	−0.477988	−0.0269744
$315$	−0.0712385	−0.00401384
$316$	−18.5543	−1.04376
$317$	−0.269093	−0.0151138	−0.00755689	−	0.999971i	$-0.502405\pi$
$317$	−0.269093	−0.0151138	−0.00755689	+	0.999971i	$0.502405\pi$
$318$	3.30209	0.185172
$319$	−1.17504	−0.0657894
$320$	−4.03854	−0.225761
$321$	11.0090	0.614463
$322$	0.203181	0.0113228
$323$	4.67347	0.260039
$324$	20.3612	1.13118
$325$	6.32922	0.351082
$326$	−1.54787	−0.0857283
$327$	6.83862	0.378177
$328$	2.83559	0.156570
$329$	0.669846	0.0369298
$330$	0.867482	0.0477533
$331$	23.9116	1.31430	0.657149	−	0.753760i	$-0.271762\pi$
$331$	23.9116	1.31430	0.657149	+	0.753760i	$0.271762\pi$
$332$	−3.08422	−0.169269
$333$	4.06399	0.222705
$334$	5.69899	0.311835
$335$	11.5619	0.631696
$336$	0.353771	0.0192998
$337$	24.3953	1.32890	0.664448	−	0.747334i	$-0.268667\pi$
$337$	24.3953	1.32890	0.664448	+	0.747334i	$0.268667\pi$
$338$	−11.4172	−0.621016
$339$	10.2322	0.555739
$340$	−10.6925	−0.579881
$341$	−0.271039	−0.0146776
$342$	−0.412249	−0.0222919
$343$	0.812698	0.0438816
$344$	−1.91216	−0.103097
$345$	−17.0505	−0.917970
$346$	−3.42162	−0.183947
$347$	−6.25222	−0.335637	−0.167818	−	0.985818i	$-0.553672\pi$
$347$	−6.25222	−0.335637	−0.167818	+	0.985818i	$0.553672\pi$
$348$	−4.40152	−0.235946
$349$	−0.727597	−0.0389474	−0.0194737	−	0.999810i	$-0.506199\pi$
$349$	−0.727597	−0.0389474	−0.0194737	+	0.999810i	$0.506199\pi$
$350$	0.0244994	0.00130955
$351$	23.0725	1.23152
$352$	−4.47569	−0.238555
$353$	2.69860	0.143632	0.0718160	−	0.997418i	$-0.477121\pi$
$353$	2.69860	0.143632	0.0718160	+	0.997418i	$0.477121\pi$
$354$	1.56191	0.0830145
$355$	−2.43721	−0.129354
$356$	−19.1891	−1.01702
$357$	0.700575	0.0370784
$358$	7.05866	0.373062
$359$	−8.46936	−0.446996	−0.223498	−	0.974704i	$-0.571748\pi$
$359$	−8.46936	−0.446996	−0.223498	+	0.974704i	$0.571748\pi$
$360$	1.97854	0.104278
$361$	−18.3658	−0.966623
$362$	−10.8882	−0.572273
$363$	−2.05594	−0.107909
$364$	0.669571	0.0350950
$365$	1.00000	0.0523424
$366$	6.35298	0.332075
$367$	−12.1939	−0.636515	−0.318257	−	0.948004i	$-0.603098\pi$
$367$	−12.1939	−0.636515	−0.318257	+	0.948004i	$0.603098\pi$
$368$	24.5772	1.28117
$369$	2.15733	0.112306
$370$	−1.39763	−0.0726594
$371$	−0.221022	−0.0114749
$372$	−1.01527	−0.0526395
$373$	26.5346	1.37391	0.686955	−	0.726700i	$-0.258947\pi$
$373$	26.5346	1.37391	0.686955	+	0.726700i	$0.258947\pi$
$374$	−2.47621	−0.128042
$375$	−2.05594	−0.106168
$376$	−18.6040	−0.959426
$377$	−7.43706	−0.383028
$378$	0.0893099	0.00459361
$379$	−11.4594	−0.588629	−0.294314	−	0.955709i	$-0.595091\pi$
$379$	−11.4594	−0.588629	−0.294314	+	0.955709i	$0.595091\pi$
$380$	−1.45091	−0.0744304
$381$	20.5292	1.05174
$382$	−8.86900	−0.453778
$383$	−12.5491	−0.641230	−0.320615	−	0.947210i	$-0.603890\pi$
$383$	−12.5491	−0.641230	−0.320615	+	0.947210i	$0.603890\pi$
$384$	−21.9069	−1.11793
$385$	−0.0580639	−0.00295921
$386$	−5.11796	−0.260497
$387$	−1.45478	−0.0739507
$388$	31.6725	1.60793
$389$	−25.3120	−1.28337	−0.641683	−	0.766970i	$-0.721764\pi$
$389$	−25.3120	−1.28337	−0.641683	+	0.766970i	$0.721764\pi$
$390$	5.49048	0.278021
$391$	48.6704	2.46137
$392$	−11.2830	−0.569878
$393$	32.3468	1.63168
$394$	7.62310	0.384046
$395$	10.1837	0.512396
$396$	−2.23537	−0.112332
$397$	−20.5408	−1.03092	−0.515458	−	0.856915i	$-0.672378\pi$
$397$	−20.5408	−1.03092	−0.515458	+	0.856915i	$0.672378\pi$
$398$	−4.97889	−0.249569
$399$	0.0950645	0.00475918
$400$	2.96350	0.148175
$401$	2.76198	0.137927	0.0689633	−	0.997619i	$-0.478031\pi$
$401$	2.76198	0.137927	0.0689633	+	0.997619i	$0.478031\pi$
$402$	10.0298	0.500239
$403$	−1.71546	−0.0854533
$404$	−31.2511	−1.55480
$405$	−11.1754	−0.555311
$406$	−0.0287877	−0.00142871
$407$	3.31240	0.164190
$408$	−19.4574	−0.963286
$409$	12.6883	0.627397	0.313698	−	0.949523i	$-0.398432\pi$
$409$	12.6883	0.627397	0.313698	+	0.949523i	$0.398432\pi$
$410$	−0.741920	−0.0366408
$411$	0.739614	0.0364825
$412$	13.5948	0.669767
$413$	−0.104545	−0.00514430
$414$	−4.29324	−0.211001
$415$	1.69280	0.0830961
$416$	−28.3276	−1.38888
$417$	−6.63998	−0.325161
$418$	−0.336009	−0.0164347
$419$	−9.15123	−0.447067	−0.223533	−	0.974696i	$-0.571759\pi$
$419$	−9.15123	−0.447067	−0.223533	+	0.974696i	$0.571759\pi$
$420$	−0.217499	−0.0106129
$421$	−13.8899	−0.676950	−0.338475	−	0.940975i	$-0.609911\pi$
$421$	−13.8899	−0.676950	−0.338475	+	0.940975i	$0.609911\pi$
$422$	4.86841	0.236991
$423$	−14.1540	−0.688189
$424$	6.13854	0.298114
$425$	5.86865	0.284671
$426$	−2.11424	−0.102435
$427$	−0.425229	−0.0205783
$428$	9.75614	0.471581
$429$	−13.0125	−0.628250
$430$	0.500309	0.0241270
$431$	−9.50354	−0.457769	−0.228885	−	0.973454i	$-0.573508\pi$
$431$	−9.50354	−0.457769	−0.228885	+	0.973454i	$0.573508\pi$
$432$	10.8031	0.519766
$433$	−34.4609	−1.65609	−0.828043	−	0.560664i	$-0.810546\pi$
$433$	−34.4609	−1.65609	−0.828043	+	0.560664i	$0.810546\pi$
$434$	−0.00664028	−0.000318744 0
$435$	2.41581	0.115829
$436$	6.06036	0.290239
$437$	6.60432	0.315928
$438$	0.867482	0.0414499
$439$	−24.1079	−1.15061	−0.575303	−	0.817940i	$-0.695116\pi$
$439$	−24.1079	−1.15061	−0.575303	+	0.817940i	$0.695116\pi$
$440$	1.61264	0.0768794
$441$	−8.58416	−0.408770
$442$	−15.6725	−0.745463
$443$	30.4108	1.44486	0.722430	−	0.691444i	$-0.243025\pi$
$443$	30.4108	1.44486	0.722430	+	0.691444i	$0.243025\pi$
$444$	12.4078	0.588848
$445$	10.5321	0.499268
$446$	−5.55897	−0.263225
$447$	7.29000	0.344805
$448$	0.234493	0.0110788
$449$	8.93383	0.421614	0.210807	−	0.977528i	$-0.432391\pi$
$449$	8.93383	0.421614	0.210807	+	0.977528i	$0.432391\pi$
$450$	−0.517676	−0.0244035
$451$	1.75836	0.0827979
$452$	9.06777	0.426512
$453$	27.6239	1.29789
$454$	−1.14804	−0.0538800
$455$	−0.367499	−0.0172286
$456$	−2.64027	−0.123642
$457$	−18.0465	−0.844178	−0.422089	−	0.906554i	$-0.638703\pi$
$457$	−18.0465	−0.844178	−0.422089	+	0.906554i	$0.638703\pi$
$458$	1.84888	0.0863924
$459$	21.3935	0.998564
$460$	−15.1101	−0.704513
$461$	−21.9323	−1.02149	−0.510744	−	0.859733i	$-0.670630\pi$
$461$	−21.9323	−1.02149	−0.510744	+	0.859733i	$0.670630\pi$
$462$	−0.0503693	−0.00234339
$463$	11.7722	0.547100	0.273550	−	0.961858i	$-0.411802\pi$
$463$	11.7722	0.547100	0.273550	+	0.961858i	$0.411802\pi$
$464$	−3.48222	−0.161658
$465$	0.557240	0.0258414
$466$	6.75957	0.313131
$467$	−7.31958	−0.338710	−0.169355	−	0.985555i	$-0.554168\pi$
$467$	−7.31958	−0.338710	−0.169355	+	0.985555i	$0.554168\pi$
$468$	−14.1482	−0.653998
$469$	−0.671330	−0.0309992
$470$	4.86764	0.224527
$471$	−2.32905	−0.107317
$472$	2.90357	0.133647
$473$	−1.18574	−0.0545203
$474$	8.83414	0.405765
$475$	0.796345	0.0365388
$476$	0.620847	0.0284565
$477$	4.67023	0.213835
$478$	2.47877	0.113376
$479$	32.6962	1.49393	0.746964	−	0.664864i	$-0.231511\pi$
$479$	32.6962	1.49393	0.746964	+	0.664864i	$0.231511\pi$
$480$	9.20176	0.420001
$481$	20.9649	0.955918
$482$	−7.74508	−0.352779
$483$	0.990020	0.0450475
$484$	−1.82197	−0.0828167
$485$	−17.3837	−0.789353
$486$	−5.08007	−0.230437
$487$	30.1482	1.36615	0.683074	−	0.730350i	$-0.260643\pi$
$487$	30.1482	1.36615	0.683074	+	0.730350i	$0.260643\pi$
$488$	11.8101	0.534618
$489$	−7.54214	−0.341068
$490$	2.95215	0.133364
$491$	39.3210	1.77453	0.887267	−	0.461256i	$-0.152601\pi$
$491$	39.3210	1.77453	0.887267	+	0.461256i	$0.152601\pi$
$492$	6.58657	0.296946
$493$	−6.89587	−0.310575
$494$	−2.12667	−0.0956835
$495$	1.22690	0.0551450
$496$	−0.803224	−0.0360658
$497$	0.141514	0.00634777
$498$	1.46847	0.0658037
$499$	−7.48890	−0.335249	−0.167625	−	0.985851i	$-0.553610\pi$
$499$	−7.48890	−0.335249	−0.167625	+	0.985851i	$0.553610\pi$
$500$	−1.82197	−0.0814809
$501$	27.7690	1.24063
$502$	−6.13105	−0.273642
$503$	−9.35534	−0.417134	−0.208567	−	0.978008i	$-0.566880\pi$
$503$	−9.35534	−0.417134	−0.208567	+	0.978008i	$0.566880\pi$
$504$	−0.114882	−0.00511724
$505$	17.1524	0.763271
$506$	−3.49926	−0.155561
$507$	−55.6317	−2.47069
$508$	18.1929	0.807179
$509$	13.4172	0.594707	0.297353	−	0.954768i	$-0.403896\pi$
$509$	13.4172	0.594707	0.297353	+	0.954768i	$0.403896\pi$
$510$	5.09094	0.225431
$511$	−0.0580639	−0.00256859
$512$	−22.8218	−1.00859
$513$	2.90299	0.128170
$514$	−4.56798	−0.201485
$515$	−7.46160	−0.328797
$516$	−4.44161	−0.195531
$517$	−11.5364	−0.507369
$518$	0.0811519	0.00356561
$519$	−16.6722	−0.731829
$520$	10.2067	0.447594
$521$	−5.77327	−0.252932	−0.126466	−	0.991971i	$-0.540363\pi$
$521$	−5.77327	−0.252932	−0.126466	+	0.991971i	$0.540363\pi$
$522$	0.608289	0.0266241
$523$	−10.3779	−0.453793	−0.226896	−	0.973919i	$-0.572858\pi$
$523$	−10.3779	−0.453793	−0.226896	+	0.973919i	$0.572858\pi$
$524$	28.6656	1.25226
$525$	0.119376	0.00520999
$526$	−6.64063	−0.289545
$527$	−1.59063	−0.0692889
$528$	−6.09279	−0.265155
$529$	45.7787	1.99038
$530$	−1.60612	−0.0697654
$531$	2.20904	0.0958644
$532$	0.0842457	0.00365252
$533$	11.1290	0.482052
$534$	9.13637	0.395370
$535$	−5.35473	−0.231505
$536$	18.6452	0.805349
$537$	34.3941	1.48421
$538$	2.23017	0.0961493
$539$	−6.99663	−0.301366
$540$	−6.64179	−0.285817
$541$	−3.11922	−0.134106	−0.0670529	−	0.997749i	$-0.521360\pi$
$541$	−3.11922	−0.134106	−0.0670529	+	0.997749i	$0.521360\pi$
$542$	10.6089	0.455689
$543$	−53.0541	−2.27677
$544$	−26.2662	−1.12616
$545$	−3.32627	−0.142482
$546$	−0.318798	−0.0136433
$547$	−33.8721	−1.44827	−0.724134	−	0.689659i	$-0.757760\pi$
$547$	−33.8721	−1.44827	−0.724134	+	0.689659i	$0.757760\pi$
$548$	0.655443	0.0279991
$549$	8.98516	0.383477
$550$	−0.421939	−0.0179915
$551$	−0.935735	−0.0398636
$552$	−27.4963	−1.17032
$553$	−0.591303	−0.0251447
$554$	−7.87173	−0.334438
$555$	−6.81011	−0.289073
$556$	−5.88432	−0.249551
$557$	7.61945	0.322847	0.161423	−	0.986885i	$-0.448392\pi$
$557$	7.61945	0.322847	0.161423	+	0.986885i	$0.448392\pi$
$558$	0.140310	0.00593981
$559$	−7.50479	−0.317419
$560$	−0.172072	−0.00727138
$561$	−12.0656	−0.509410
$562$	−6.05063	−0.255231
$563$	−12.1437	−0.511797	−0.255899	−	0.966704i	$-0.582371\pi$
$563$	−12.1437	−0.511797	−0.255899	+	0.966704i	$0.582371\pi$
$564$	−43.2136	−1.81962
$565$	−4.97691	−0.209380
$566$	6.78221	0.285078
$567$	0.648888	0.0272507
$568$	−3.93034	−0.164913
$569$	−42.0698	−1.76366	−0.881830	−	0.471568i	$-0.843688\pi$
$569$	−42.0698	−1.76366	−0.881830	+	0.471568i	$0.843688\pi$
$570$	0.690815	0.0289350
$571$	1.39958	0.0585708	0.0292854	−	0.999571i	$-0.490677\pi$
$571$	1.39958	0.0585708	0.0292854	+	0.999571i	$0.490677\pi$
$572$	−11.5316	−0.482162
$573$	−43.2152	−1.80534
$574$	0.0430787	0.00179807
$575$	8.29329	0.345854
$576$	−4.95488	−0.206453
$577$	28.8807	1.20232	0.601159	−	0.799129i	$-0.294706\pi$
$577$	28.8807	1.20232	0.601159	+	0.799129i	$0.294706\pi$
$578$	−7.35903	−0.306095
$579$	−24.9378	−1.03638
$580$	2.14088	0.0888952
$581$	−0.0982903	−0.00407777
$582$	−15.0800	−0.625088
$583$	3.80653	0.157650
$584$	1.61264	0.0667314
$585$	7.76531	0.321056
$586$	0.968172	0.0399948
$587$	−33.1395	−1.36781	−0.683907	−	0.729569i	$-0.739721\pi$
$587$	−33.1395	−1.36781	−0.683907	+	0.729569i	$0.739721\pi$
$588$	−26.2084	−1.08082
$589$	−0.215840	−0.00889355
$590$	−0.759705	−0.0312765
$591$	37.1444	1.52792
$592$	9.81631	0.403448
$593$	−20.3765	−0.836763	−0.418382	−	0.908271i	$-0.637403\pi$
$593$	−20.3765	−0.836763	−0.418382	+	0.908271i	$0.637403\pi$
$594$	−1.53813	−0.0631103
$595$	−0.340756	−0.0139696
$596$	6.46036	0.264627
$597$	−24.2602	−0.992903
$598$	−22.1476	−0.905682
$599$	−36.4738	−1.49028	−0.745140	−	0.666908i	$-0.767618\pi$
$599$	−36.4738	−1.49028	−0.745140	+	0.666908i	$0.767618\pi$
$600$	−3.31549	−0.135354
$601$	1.23151	0.0502345	0.0251172	−	0.999685i	$-0.492004\pi$
$601$	1.23151	0.0502345	0.0251172	+	0.999685i	$0.492004\pi$
$602$	−0.0290499	−0.00118398
$603$	14.1853	0.577671
$604$	24.4802	0.996086
$605$	1.00000	0.0406558
$606$	14.8794	0.604433
$607$	−45.9718	−1.86594	−0.932968	−	0.359958i	$-0.882791\pi$
$607$	−45.9718	−1.86594	−0.932968	+	0.359958i	$0.882791\pi$
$608$	−3.56419	−0.144547
$609$	−0.140271	−0.00568407
$610$	−3.09006	−0.125113
$611$	−73.0162	−2.95392
$612$	−13.1186	−0.530288
$613$	12.5456	0.506710	0.253355	−	0.967373i	$-0.418466\pi$
$613$	12.5456	0.506710	0.253355	+	0.967373i	$0.418466\pi$
$614$	12.4889	0.504013
$615$	−3.61509	−0.145774
$616$	−0.0936359	−0.00377270
$617$	12.3123	0.495674	0.247837	−	0.968802i	$-0.420280\pi$
$617$	12.3123	0.495674	0.247837	+	0.968802i	$0.420280\pi$
$618$	−6.47280	−0.260374
$619$	26.5602	1.06754	0.533772	−	0.845629i	$-0.320774\pi$
$619$	26.5602	1.06754	0.533772	+	0.845629i	$0.320774\pi$
$620$	0.493824	0.0198324
$621$	30.2323	1.21318
$622$	−3.31757	−0.133023
$623$	−0.611532	−0.0245005
$624$	−38.5626	−1.54374
$625$	1.00000	0.0400000
$626$	−7.36644	−0.294422
$627$	−1.63724	−0.0653851
$628$	−2.06399	−0.0823623
$629$	19.4393	0.775097
$630$	0.0300583	0.00119755
$631$	−23.2148	−0.924166	−0.462083	−	0.886837i	$-0.652898\pi$
$631$	−23.2148	−0.924166	−0.462083	+	0.886837i	$0.652898\pi$
$632$	16.4225	0.653254
$633$	23.7219	0.942860
$634$	0.113541	0.00450928
$635$	−9.98530	−0.396255
$636$	14.2587	0.565395
$637$	−44.2832	−1.75456
$638$	0.495794	0.0196287
$639$	−2.99022	−0.118291
$640$	10.6554	0.421191
$641$	−2.79433	−0.110369	−0.0551847	−	0.998476i	$-0.517575\pi$
$641$	−2.79433	−0.110369	−0.0551847	+	0.998476i	$0.517575\pi$
$642$	−4.64513	−0.183329
$643$	−47.9516	−1.89103	−0.945513	−	0.325586i	$-0.894439\pi$
$643$	−47.9516	−1.89103	−0.945513	+	0.325586i	$0.894439\pi$
$644$	0.877351	0.0345725
$645$	2.43781	0.0959887
$646$	−1.97192	−0.0775840
$647$	42.0348	1.65256	0.826279	−	0.563261i	$-0.190453\pi$
$647$	42.0348	1.65256	0.826279	+	0.563261i	$0.190453\pi$
$648$	−18.0219	−0.707966
$649$	1.80051	0.0706762
$650$	−2.67054	−0.104747
$651$	−0.0323555	−0.00126811
$652$	−6.68382	−0.261758
$653$	32.3619	1.26642	0.633209	−	0.773981i	$-0.281738\pi$
$653$	32.3619	1.26642	0.633209	+	0.773981i	$0.281738\pi$
$654$	−2.88548	−0.112831
$655$	−15.7333	−0.614752
$656$	5.21090	0.203452
$657$	1.22690	0.0478659
$658$	−0.282634	−0.0110182
$659$	−13.5290	−0.527014	−0.263507	−	0.964657i	$-0.584879\pi$
$659$	−13.5290	−0.527014	−0.263507	+	0.964657i	$0.584879\pi$
$660$	3.74586	0.145807
$661$	10.6160	0.412915	0.206457	−	0.978456i	$-0.433807\pi$
$661$	10.6160	0.412915	0.206457	+	0.978456i	$0.433807\pi$
$662$	−10.0892	−0.392129
$663$	−76.3658	−2.96580
$664$	2.72987	0.105939
$665$	−0.0462389	−0.00179307
$666$	−1.71475	−0.0664453
$667$	−9.74492	−0.377325
$668$	24.6087	0.952141
$669$	−27.0867	−1.04723
$670$	−4.87843	−0.188470
$671$	7.32347	0.282719
$672$	−0.534290	−0.0206107
$673$	−27.0125	−1.04125	−0.520627	−	0.853784i	$-0.674302\pi$
$673$	−27.0125	−1.04125	−0.520627	+	0.853784i	$0.674302\pi$
$674$	−10.2933	−0.396484
$675$	3.64539	0.140311
$676$	−49.3006	−1.89618
$677$	1.25101	0.0480803	0.0240402	−	0.999711i	$-0.492347\pi$
$677$	1.25101	0.0480803	0.0240402	+	0.999711i	$0.492347\pi$
$678$	−4.31738	−0.165808
$679$	1.00936	0.0387359
$680$	9.46399	0.362927
$681$	−5.59393	−0.214360
$682$	0.114362	0.00437914
$683$	27.9142	1.06811	0.534053	−	0.845451i	$-0.320668\pi$
$683$	27.9142	1.06811	0.534053	+	0.845451i	$0.320668\pi$
$684$	−1.78013	−0.0680649
$685$	−0.359744	−0.0137451
$686$	−0.342909	−0.0130923
$687$	9.00886	0.343709
$688$	−3.51394	−0.133968
$689$	24.0923	0.917845
$690$	7.19428	0.273882
$691$	10.0972	0.384115	0.192057	−	0.981384i	$-0.438484\pi$
$691$	10.0972	0.384115	0.192057	+	0.981384i	$0.438484\pi$
$692$	−14.7748	−0.561655
$693$	−0.0712385	−0.00270613
$694$	2.63805	0.100139
$695$	3.22965	0.122508
$696$	3.89582	0.147671
$697$	10.3192	0.390867
$698$	0.307001	0.0116202
$699$	32.9367	1.24578
$700$	0.105790	0.00399850
$701$	24.0837	0.909630	0.454815	−	0.890586i	$-0.349705\pi$
$701$	24.0837	0.909630	0.454815	+	0.890586i	$0.349705\pi$
$702$	−9.73517	−0.367430
$703$	2.63782	0.0994871
$704$	−4.03854	−0.152208
$705$	23.7181	0.893275
$706$	−1.13864	−0.0428535
$707$	−0.995933	−0.0374559
$708$	6.74446	0.253472
$709$	18.6612	0.700834	0.350417	−	0.936594i	$-0.386040\pi$
$709$	18.6612	0.700834	0.350417	+	0.936594i	$0.386040\pi$
$710$	1.02836	0.0385935
$711$	12.4943	0.468574
$712$	16.9844	0.636517
$713$	−2.24780	−0.0841809
$714$	−0.295600	−0.0110625
$715$	6.32922	0.236699
$716$	30.4799	1.13909
$717$	12.0781	0.451065
$718$	3.57355	0.133364
$719$	−41.7871	−1.55839	−0.779197	−	0.626779i	$-0.784373\pi$
$719$	−41.7871	−1.55839	−0.779197	+	0.626779i	$0.784373\pi$
$720$	3.63592	0.135503
$721$	0.433249	0.0161350
$722$	7.74926	0.288397
$723$	−37.7388	−1.40352
$724$	−47.0163	−1.74735
$725$	−1.17504	−0.0436398
$726$	0.867482	0.0321953
$727$	−4.24284	−0.157358	−0.0786791	−	0.996900i	$-0.525070\pi$
$727$	−4.24284	−0.157358	−0.0786791	+	0.996900i	$0.525070\pi$
$728$	−0.592642	−0.0219648
$729$	8.77304	0.324927
$730$	−0.421939	−0.0156167
$731$	−6.95868	−0.257376
$732$	27.4327	1.01394
$733$	−1.98876	−0.0734566	−0.0367283	−	0.999325i	$-0.511694\pi$
$733$	−1.98876	−0.0734566	−0.0367283	+	0.999325i	$0.511694\pi$
$734$	5.14507	0.189908
$735$	14.3847	0.530586
$736$	−37.1182	−1.36819
$737$	11.5619	0.425889
$738$	−0.910261	−0.0335072
$739$	36.6734	1.34905	0.674526	−	0.738251i	$-0.264348\pi$
$739$	36.6734	1.34905	0.674526	+	0.738251i	$0.264348\pi$
$740$	−6.03509	−0.221854
$741$	−10.3624	−0.380674
$742$	0.0932576	0.00342359
$743$	20.5285	0.753116	0.376558	−	0.926393i	$-0.377108\pi$
$743$	20.5285	0.753116	0.376558	+	0.926393i	$0.377108\pi$
$744$	0.898625	0.0329452
$745$	−3.54582	−0.129909
$746$	−11.1960	−0.409914
$747$	2.07689	0.0759895
$748$	−10.6925	−0.390956
$749$	0.310916	0.0113606
$750$	0.867482	0.0316760
$751$	28.2983	1.03262	0.516310	−	0.856402i	$-0.327305\pi$
$751$	28.2983	1.03262	0.516310	+	0.856402i	$0.327305\pi$
$752$	−34.1880	−1.24671
$753$	−29.8742	−1.08868
$754$	3.13798	0.114279
$755$	−13.4361	−0.488991
$756$	0.385648	0.0140259
$757$	−20.7624	−0.754622	−0.377311	−	0.926087i	$-0.623151\pi$
$757$	−20.7624	−0.754622	−0.377311	+	0.926087i	$0.623151\pi$
$758$	4.83515	0.175621
$759$	−17.0505	−0.618895
$760$	1.28421	0.0465834
$761$	−7.83255	−0.283930	−0.141965	−	0.989872i	$-0.545342\pi$
$761$	−7.83255	−0.283930	−0.141965	+	0.989872i	$0.545342\pi$
$762$	−8.66207	−0.313794
$763$	0.193136	0.00699200
$764$	−38.2971	−1.38554
$765$	7.20024	0.260325
$766$	5.29496	0.191315
$767$	11.3958	0.411479
$768$	−7.36264	−0.265676
$769$	5.47033	0.197265	0.0986326	−	0.995124i	$-0.468553\pi$
$769$	5.47033	0.197265	0.0986326	+	0.995124i	$0.468553\pi$
$770$	0.0244994	0.000882897 0
$771$	−22.2580	−0.801602
$772$	−22.0998	−0.795389
$773$	1.72694	0.0621139	0.0310569	−	0.999518i	$-0.490113\pi$
$773$	1.72694	0.0621139	0.0310569	+	0.999518i	$0.490113\pi$
$774$	0.613829	0.0220636
$775$	−0.271039	−0.00973600
$776$	−28.0336	−1.00635
$777$	0.395421	0.0141857
$778$	10.6801	0.382900
$779$	1.40026	0.0501696
$780$	23.7084	0.848896
$781$	−2.43721	−0.0872104
$782$	−20.5359	−0.734363
$783$	−4.28347	−0.153079
$784$	−20.7345	−0.740519
$785$	1.13284	0.0404327
$786$	−13.6484	−0.486822
$787$	−44.3928	−1.58243	−0.791216	−	0.611537i	$-0.790551\pi$
$787$	−44.3928	−1.58243	−0.791216	+	0.611537i	$0.790551\pi$
$788$	32.9172	1.17263
$789$	−32.3572	−1.15195
$790$	−4.29688	−0.152876
$791$	0.288979	0.0102749
$792$	1.97854	0.0703045
$793$	46.3518	1.64600
$794$	8.66698	0.307579
$795$	−7.82600	−0.277560
$796$	−21.4993	−0.762021
$797$	31.4065	1.11247	0.556237	−	0.831024i	$-0.312245\pi$
$797$	31.4065	1.11247	0.556237	+	0.831024i	$0.312245\pi$
$798$	−0.0401114	−0.00141993
$799$	−67.7028	−2.39515
$800$	−4.47569	−0.158239
$801$	12.9218	0.456569
$802$	−1.16539	−0.0411512
$803$	1.00000	0.0352892
$804$	43.3094	1.52740
$805$	−0.481541	−0.0169721
$806$	0.723820	0.0254955
$807$	10.8667	0.382527
$808$	27.6605	0.973095
$809$	0.367867	0.0129335	0.00646675	−	0.999979i	$-0.497942\pi$
$809$	0.367867	0.0129335	0.00646675	+	0.999979i	$0.497942\pi$
$810$	4.71534	0.165680
$811$	−13.9338	−0.489283	−0.244642	−	0.969614i	$-0.578670\pi$
$811$	−13.9338	−0.489283	−0.244642	+	0.969614i	$0.578670\pi$
$812$	−0.124308	−0.00436235
$813$	51.6928	1.81295
$814$	−1.39763	−0.0489870
$815$	3.66846	0.128501
$816$	−35.7564	−1.25173
$817$	−0.944257	−0.0330354
$818$	−5.35369	−0.187187
$819$	−0.450884	−0.0157552
$820$	−3.20367	−0.111877
$821$	−6.97646	−0.243480	−0.121740	−	0.992562i	$-0.538847\pi$
$821$	−6.97646	−0.243480	−0.121740	+	0.992562i	$0.538847\pi$
$822$	−0.312072	−0.0108848
$823$	25.5197	0.889561	0.444781	−	0.895640i	$-0.353282\pi$
$823$	25.5197	0.889561	0.444781	+	0.895640i	$0.353282\pi$
$824$	−12.0328	−0.419184
$825$	−2.05594	−0.0715787
$826$	0.0441114	0.00153483
$827$	−13.1983	−0.458951	−0.229476	−	0.973314i	$-0.573701\pi$
$827$	−13.1983	−0.458951	−0.229476	+	0.973314i	$0.573701\pi$
$828$	−18.5386	−0.644260
$829$	−18.0657	−0.627448	−0.313724	−	0.949514i	$-0.601577\pi$
$829$	−18.0657	−0.627448	−0.313724	+	0.949514i	$0.601577\pi$
$830$	−0.714256	−0.0247922
$831$	−38.3558	−1.33055
$832$	−25.5608	−0.886161
$833$	−41.0607	−1.42267
$834$	2.80166	0.0970137
$835$	−13.5067	−0.467418
$836$	−1.45091	−0.0501809
$837$	−0.988043	−0.0341517
$838$	3.86126	0.133385
$839$	0.449001	0.0155012	0.00775062	−	0.999970i	$-0.497533\pi$
$839$	0.449001	0.0155012	0.00775062	+	0.999970i	$0.497533\pi$
$840$	0.192510	0.00664223
$841$	−27.6193	−0.952389
$842$	5.86067	0.201972
$843$	−29.4824	−1.01543
$844$	21.0222	0.723615
$845$	27.0590	0.930857
$846$	5.97210	0.205325
$847$	−0.0580639	−0.00199510
$848$	11.2806	0.387379
$849$	33.0471	1.13417
$850$	−2.47621	−0.0849333
$851$	27.4707	0.941685
$852$	−9.12946	−0.312770
$853$	−15.9855	−0.547335	−0.273667	−	0.961824i	$-0.588237\pi$
$853$	−15.9855	−0.547335	−0.273667	+	0.961824i	$0.588237\pi$
$854$	0.179421	0.00613965
$855$	0.977035	0.0334139
$856$	−8.63523	−0.295146
$857$	9.41864	0.321735	0.160867	−	0.986976i	$-0.448571\pi$
$857$	9.41864	0.321735	0.160867	+	0.986976i	$0.448571\pi$
$858$	5.49048	0.187442
$859$	−30.8026	−1.05097	−0.525485	−	0.850803i	$-0.676116\pi$
$859$	−30.8026	−1.05097	−0.525485	+	0.850803i	$0.676116\pi$
$860$	2.16038	0.0736682
$861$	0.209906	0.00715357
$862$	4.00991	0.136578
$863$	36.6797	1.24859	0.624295	−	0.781189i	$-0.285386\pi$
$863$	36.6797	1.24859	0.624295	+	0.781189i	$0.285386\pi$
$864$	−16.3156	−0.555069
$865$	8.10928	0.275724
$866$	14.5404	0.494103
$867$	−35.8577	−1.21779
$868$	−0.0286733	−0.000973236 0
$869$	10.1837	0.345457
$870$	−1.01932	−0.0345583
$871$	73.1780	2.47954
$872$	−5.36407	−0.181650
$873$	−21.3281	−0.721845
$874$	−2.78662	−0.0942588
$875$	−0.0580639	−0.00196292
$876$	3.74586	0.126561
$877$	7.05155	0.238114	0.119057	−	0.992887i	$-0.462013\pi$
$877$	7.05155	0.238114	0.119057	+	0.992887i	$0.462013\pi$
$878$	10.1720	0.343290
$879$	4.71753	0.159118
$880$	2.96350	0.0998996
$881$	−10.9248	−0.368067	−0.184034	−	0.982920i	$-0.558916\pi$
$881$	−10.9248	−0.368067	−0.184034	+	0.982920i	$0.558916\pi$
$882$	3.62199	0.121959
$883$	43.6605	1.46929	0.734646	−	0.678451i	$-0.237348\pi$
$883$	43.6605	1.46929	0.734646	+	0.678451i	$0.237348\pi$
$884$	−67.6750	−2.27616
$885$	−3.70174	−0.124433
$886$	−12.8315	−0.431082
$887$	−25.6433	−0.861018	−0.430509	−	0.902586i	$-0.641666\pi$
$887$	−25.6433	−0.861018	−0.430509	+	0.902586i	$0.641666\pi$
$888$	−10.9822	−0.368540
$889$	0.579785	0.0194454
$890$	−4.44389	−0.148959
$891$	−11.1754	−0.374391
$892$	−24.0041	−0.803718
$893$	−9.18693	−0.307429
$894$	−3.07593	−0.102875
$895$	−16.7291	−0.559193
$896$	−0.618693	−0.0206691
$897$	−107.917	−3.60323
$898$	−3.76953	−0.125791
$899$	0.318480	0.0106219
$900$	−2.23537	−0.0745124
$901$	22.3392	0.744225
$902$	−0.741920	−0.0247032
$903$	−0.141549	−0.00471044
$904$	−8.02595	−0.266939
$905$	25.8052	0.857795
$906$	−11.6556	−0.387232
$907$	29.5453	0.981034	0.490517	−	0.871432i	$-0.336808\pi$
$907$	29.5453	0.981034	0.490517	+	0.871432i	$0.336808\pi$
$908$	−4.95732	−0.164514
$909$	21.0442	0.697994
$910$	0.155062	0.00514025
$911$	26.3096	0.871677	0.435838	−	0.900025i	$-0.356452\pi$
$911$	26.3096	0.871677	0.435838	+	0.900025i	$0.356452\pi$
$912$	−4.85196	−0.160665
$913$	1.69280	0.0560234
$914$	7.61450	0.251865
$915$	−15.0566	−0.497757
$916$	7.98362	0.263786
$917$	0.913538	0.0301677
$918$	−9.02675	−0.297927
$919$	53.2713	1.75726	0.878629	−	0.477505i	$-0.158459\pi$
$919$	53.2713	1.75726	0.878629	+	0.477505i	$0.158459\pi$
$920$	13.3741	0.440930
$921$	60.8537	2.00520
$922$	9.25408	0.304767
$923$	−15.4257	−0.507742
$924$	−0.217499	−0.00715520
$925$	3.31240	0.108911
$926$	−4.96714	−0.163230
$927$	−9.15463	−0.300678
$928$	5.25910	0.172638
$929$	38.9317	1.27731	0.638654	−	0.769494i	$-0.279492\pi$
$929$	38.9317	1.27731	0.638654	+	0.769494i	$0.279492\pi$
$930$	−0.235121	−0.00770993
$931$	−5.57173	−0.182606
$932$	29.1884	0.956098
$933$	−16.1652	−0.529226
$934$	3.08842	0.101056
$935$	5.86865	0.191925
$936$	12.5226	0.409315
$937$	46.6511	1.52403	0.762013	−	0.647562i	$-0.224211\pi$
$937$	46.6511	1.52403	0.762013	+	0.647562i	$0.224211\pi$
$938$	0.283260	0.00924878
$939$	−35.8938	−1.17135
$940$	21.0189	0.685560
$941$	50.3438	1.64116	0.820581	−	0.571530i	$-0.193650\pi$
$941$	50.3438	1.64116	0.820581	+	0.571530i	$0.193650\pi$
$942$	0.982716	0.0320186
$943$	14.5826	0.474875
$944$	5.33581	0.173666
$945$	−0.211666	−0.00688548
$946$	0.500309	0.0162664
$947$	25.3314	0.823162	0.411581	−	0.911373i	$-0.364977\pi$
$947$	25.3314	0.823162	0.411581	+	0.911373i	$0.364977\pi$
$948$	38.1466	1.23894
$949$	6.32922	0.205455
$950$	−0.336009	−0.0109016
$951$	0.553240	0.0179400
$952$	−0.549516	−0.0178099
$953$	39.2750	1.27224	0.636120	−	0.771590i	$-0.280538\pi$
$953$	39.2750	1.27224	0.636120	+	0.771590i	$0.280538\pi$
$954$	−1.97055	−0.0637989
$955$	21.0196	0.680180
$956$	10.7036	0.346178
$957$	2.41581	0.0780920
$958$	−13.7958	−0.445722
$959$	0.0208881	0.000674514 0
$960$	8.30300	0.267978
$961$	−30.9265	−0.997630
$962$	−8.84591	−0.285204
$963$	−6.56972	−0.211706
$964$	−33.4439	−1.07716
$965$	12.1296	0.390467
$966$	−0.417728	−0.0134402
$967$	35.6000	1.14482	0.572409	−	0.819968i	$-0.306009\pi$
$967$	35.6000	1.14482	0.572409	+	0.819968i	$0.306009\pi$
$968$	1.61264	0.0518321
$969$	−9.60838	−0.308666
$970$	7.33486	0.235508
$971$	5.02580	0.161286	0.0806428	−	0.996743i	$-0.474303\pi$
$971$	5.02580	0.161286	0.0806428	+	0.996743i	$0.474303\pi$
$972$	−21.9362	−0.703604
$973$	−0.187526	−0.00601181
$974$	−12.7207	−0.407598
$975$	−13.0125	−0.416734
$976$	21.7031	0.694700
$977$	−18.9735	−0.607015	−0.303507	−	0.952829i	$-0.598158\pi$
$977$	−18.9735	−0.607015	−0.303507	+	0.952829i	$0.598158\pi$
$978$	3.18232	0.101759
$979$	10.5321	0.336606
$980$	12.7476	0.407208
$981$	−4.08100	−0.130296
$982$	−16.5911	−0.529442
$983$	−31.2871	−0.997904	−0.498952	−	0.866630i	$-0.666282\pi$
$983$	−31.2871	−0.997904	−0.498952	+	0.866630i	$0.666282\pi$
$984$	−5.82982	−0.185848
$985$	−18.0668	−0.575657
$986$	2.90964	0.0926617
$987$	−1.37716	−0.0438356
$988$	−9.18316	−0.292155
$989$	−9.83367	−0.312693
$990$	−0.517676	−0.0164528
$991$	−20.8298	−0.661680	−0.330840	−	0.943687i	$-0.607332\pi$
$991$	−20.8298	−0.661680	−0.330840	+	0.943687i	$0.607332\pi$
$992$	1.21308	0.0385155
$993$	−49.1608	−1.56007
$994$	−0.0597103	−0.00189389
$995$	11.8000	0.374086
$996$	6.34098	0.200922
$997$	−34.4365	−1.09061	−0.545307	−	0.838236i	$-0.683587\pi$
$997$	−34.4365	−1.09061	−0.545307	+	0.838236i	$0.683587\pi$
$998$	3.15986	0.100023
$999$	12.0750	0.382036

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4015.2.a.h.1.16	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4015.2.a.h.1.16	✓	37	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:	\( N \)	\(=\)	\( 4015 = 5 \cdot 11 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4015.a (trivial)

\(f(q)\)	\(=\)	\(q-0.421939 q^{2} -2.05594 q^{3} -1.82197 q^{4} +1.00000 q^{5} +0.867482 q^{6} -0.0580639 q^{7} +1.61264 q^{8} +1.22690 q^{9} +O(q^{10})\)	\(q-0.421939 q^{2} -2.05594 q^{3} -1.82197 q^{4} +1.00000 q^{5} +0.867482 q^{6} -0.0580639 q^{7} +1.61264 q^{8} +1.22690 q^{9} -0.421939 q^{10} +1.00000 q^{11} +3.74586 q^{12} +6.32922 q^{13} +0.0244994 q^{14} -2.05594 q^{15} +2.96350 q^{16} +5.86865 q^{17} -0.517676 q^{18} +0.796345 q^{19} -1.82197 q^{20} +0.119376 q^{21} -0.421939 q^{22} +8.29329 q^{23} -3.31549 q^{24} +1.00000 q^{25} -2.67054 q^{26} +3.64539 q^{27} +0.105790 q^{28} -1.17504 q^{29} +0.867482 q^{30} -0.271039 q^{31} -4.47569 q^{32} -2.05594 q^{33} -2.47621 q^{34} -0.0580639 q^{35} -2.23537 q^{36} +3.31240 q^{37} -0.336009 q^{38} -13.0125 q^{39} +1.61264 q^{40} +1.75836 q^{41} -0.0503693 q^{42} -1.18574 q^{43} -1.82197 q^{44} +1.22690 q^{45} -3.49926 q^{46} -11.5364 q^{47} -6.09279 q^{48} -6.99663 q^{49} -0.421939 q^{50} -12.0656 q^{51} -11.5316 q^{52} +3.80653 q^{53} -1.53813 q^{54} +1.00000 q^{55} -0.0936359 q^{56} -1.63724 q^{57} +0.495794 q^{58} +1.80051 q^{59} +3.74586 q^{60} +7.32347 q^{61} +0.114362 q^{62} -0.0712385 q^{63} -4.03854 q^{64} +6.32922 q^{65} +0.867482 q^{66} +11.5619 q^{67} -10.6925 q^{68} -17.0505 q^{69} +0.0244994 q^{70} -2.43721 q^{71} +1.97854 q^{72} +1.00000 q^{73} -1.39763 q^{74} -2.05594 q^{75} -1.45091 q^{76} -0.0580639 q^{77} +5.49048 q^{78} +10.1837 q^{79} +2.96350 q^{80} -11.1754 q^{81} -0.741920 q^{82} +1.69280 q^{83} -0.217499 q^{84} +5.86865 q^{85} +0.500309 q^{86} +2.41581 q^{87} +1.61264 q^{88} +10.5321 q^{89} -0.517676 q^{90} -0.367499 q^{91} -15.1101 q^{92} +0.557240 q^{93} +4.86764 q^{94} +0.796345 q^{95} +9.20176 q^{96} -17.3837 q^{97} +2.95215 q^{98} +1.22690 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9}+O(q^{10}) \) 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9	\( 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9} + 5 q^{10} + 37 q^{11} + 6 q^{12} + 11 q^{13} + 11 q^{14} + 3 q^{15} + 43 q^{16} + 38 q^{17} + 11 q^{18} + 34 q^{19} + 43 q^{20} + 39 q^{21} + 5 q^{22} + 4 q^{23} + 25 q^{24} + 37 q^{25} - 9 q^{26} + 3 q^{27} + 14 q^{28} + 58 q^{29} + 9 q^{30} + 8 q^{31} + 14 q^{32} + 3 q^{33} + 8 q^{34} + 6 q^{35} + 20 q^{36} + 2 q^{37} + 15 q^{38} + 14 q^{39} + 12 q^{40} + 62 q^{41} - 13 q^{42} + 30 q^{43} + 43 q^{44} + 50 q^{45} + 31 q^{46} + 5 q^{47} - 25 q^{48} + 59 q^{49} + 5 q^{50} + 23 q^{51} - q^{52} + 18 q^{53} + 13 q^{54} + 37 q^{55} + 22 q^{56} + 5 q^{57} - 40 q^{58} + 15 q^{59} + 6 q^{60} + 57 q^{61} + 20 q^{62} - 29 q^{63} + 10 q^{64} + 11 q^{65} + 9 q^{66} - 14 q^{67} + 53 q^{68} + 24 q^{69} + 11 q^{70} + 8 q^{71} + 15 q^{72} + 37 q^{73} + 7 q^{74} + 3 q^{75} + 59 q^{76} + 6 q^{77} + q^{78} + 42 q^{79} + 43 q^{80} + 61 q^{81} - 22 q^{82} + 44 q^{83} + 66 q^{84} + 38 q^{85} - q^{86} - 26 q^{87} + 12 q^{88} + 69 q^{89} + 11 q^{90} - 10 q^{91} - 21 q^{92} - 26 q^{93} + 29 q^{94} + 34 q^{95} - 9 q^{96} + 37 q^{97} - 15 q^{98} + 50 q^{99}+O(q^{100}) \) 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9 + 5 * q^10 + 37 * q^11 + 6 * q^12 + 11 * q^13 + 11 * q^14 + 3 * q^15 + 43 * q^16 + 38 * q^17 + 11 * q^18 + 34 * q^19 + 43 * q^20 + 39 * q^21 + 5 * q^22 + 4 * q^23 + 25 * q^24 + 37 * q^25 - 9 * q^26 + 3 * q^27 + 14 * q^28 + 58 * q^29 + 9 * q^30 + 8 * q^31 + 14 * q^32 + 3 * q^33 + 8 * q^34 + 6 * q^35 + 20 * q^36 + 2 * q^37 + 15 * q^38 + 14 * q^39 + 12 * q^40 + 62 * q^41 - 13 * q^42 + 30 * q^43 + 43 * q^44 + 50 * q^45 + 31 * q^46 + 5 * q^47 - 25 * q^48 + 59 * q^49 + 5 * q^50 + 23 * q^51 - q^52 + 18 * q^53 + 13 * q^54 + 37 * q^55 + 22 * q^56 + 5 * q^57 - 40 * q^58 + 15 * q^59 + 6 * q^60 + 57 * q^61 + 20 * q^62 - 29 * q^63 + 10 * q^64 + 11 * q^65 + 9 * q^66 - 14 * q^67 + 53 * q^68 + 24 * q^69 + 11 * q^70 + 8 * q^71 + 15 * q^72 + 37 * q^73 + 7 * q^74 + 3 * q^75 + 59 * q^76 + 6 * q^77 + q^78 + 42 * q^79 + 43 * q^80 + 61 * q^81 - 22 * q^82 + 44 * q^83 + 66 * q^84 + 38 * q^85 - q^86 - 26 * q^87 + 12 * q^88 + 69 * q^89 + 11 * q^90 - 10 * q^91 - 21 * q^92 - 26 * q^93 + 29 * q^94 + 34 * q^95 - 9 * q^96 + 37 * q^97 - 15 * q^98 + 50 * q^99

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