LMFDB - Embedded newform 4015.2.a.f.1.14

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:	$1$
Dimension:	$31$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
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)

$f(q)$	$=$	$q-0.602631 q^{2} -3.44000 q^{3} -1.63684 q^{4} -1.00000 q^{5} +2.07305 q^{6} -0.349257 q^{7} +2.19167 q^{8} +8.83357 q^{9} +O(q^{10})$	\(q-0.602631 q^{2} -3.44000 q^{3} -1.63684 q^{4} -1.00000 q^{5} +2.07305 q^{6} -0.349257 q^{7} +2.19167 q^{8} +8.83357 q^{9} +0.602631 q^{10} +1.00000 q^{11} +5.63071 q^{12} -6.76394 q^{13} +0.210473 q^{14} +3.44000 q^{15} +1.95290 q^{16} -3.51529 q^{17} -5.32338 q^{18} -2.53829 q^{19} +1.63684 q^{20} +1.20144 q^{21} -0.602631 q^{22} -1.89790 q^{23} -7.53934 q^{24} +1.00000 q^{25} +4.07616 q^{26} -20.0674 q^{27} +0.571676 q^{28} +9.67848 q^{29} -2.07305 q^{30} -4.30320 q^{31} -5.56022 q^{32} -3.44000 q^{33} +2.11842 q^{34} +0.349257 q^{35} -14.4591 q^{36} -7.66685 q^{37} +1.52965 q^{38} +23.2679 q^{39} -2.19167 q^{40} +2.98885 q^{41} -0.724026 q^{42} +9.34941 q^{43} -1.63684 q^{44} -8.83357 q^{45} +1.14373 q^{46} +0.371265 q^{47} -6.71798 q^{48} -6.87802 q^{49} -0.602631 q^{50} +12.0926 q^{51} +11.0715 q^{52} +5.85330 q^{53} +12.0933 q^{54} -1.00000 q^{55} -0.765456 q^{56} +8.73169 q^{57} -5.83255 q^{58} +14.8054 q^{59} -5.63071 q^{60} -2.51737 q^{61} +2.59324 q^{62} -3.08518 q^{63} -0.555043 q^{64} +6.76394 q^{65} +2.07305 q^{66} +8.73441 q^{67} +5.75395 q^{68} +6.52876 q^{69} -0.210473 q^{70} -4.53863 q^{71} +19.3603 q^{72} +1.00000 q^{73} +4.62028 q^{74} -3.44000 q^{75} +4.15476 q^{76} -0.349257 q^{77} -14.0220 q^{78} -5.87149 q^{79} -1.95290 q^{80} +42.5312 q^{81} -1.80118 q^{82} +14.7196 q^{83} -1.96656 q^{84} +3.51529 q^{85} -5.63425 q^{86} -33.2939 q^{87} +2.19167 q^{88} -3.71724 q^{89} +5.32338 q^{90} +2.36235 q^{91} +3.10655 q^{92} +14.8030 q^{93} -0.223736 q^{94} +2.53829 q^{95} +19.1271 q^{96} -3.94924 q^{97} +4.14491 q^{98} +8.83357 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q - 7 q^{2} - 4 q^{3} + 39 q^{4} - 31 q^{5} - 5 q^{6} - 11 q^{7} - 24 q^{8} + 31 q^{9}+O(q^{10}) $ 31 * q - 7 * q^2 - 4 * q^3 + 39 * q^4 - 31 * q^5 - 5 * q^6 - 11 * q^7 - 24 * q^8 + 31 * q^9	\( 31 q - 7 q^{2} - 4 q^{3} + 39 q^{4} - 31 q^{5} - 5 q^{6} - 11 q^{7} - 24 q^{8} + 31 q^{9} + 7 q^{10} + 31 q^{11} - 4 q^{12} - 24 q^{13} - 9 q^{14} + 4 q^{15} + 43 q^{16} - 49 q^{17} - 35 q^{18} - 22 q^{19} - 39 q^{20} - 8 q^{21} - 7 q^{22} - q^{23} - 13 q^{24} + 31 q^{25} - 9 q^{26} - 22 q^{27} - 34 q^{28} - 12 q^{29} + 5 q^{30} + 4 q^{31} - 45 q^{32} - 4 q^{33} + 2 q^{34} + 11 q^{35} + 34 q^{36} - 18 q^{37} - 7 q^{38} - q^{39} + 24 q^{40} - 58 q^{41} - 21 q^{42} - 41 q^{43} + 39 q^{44} - 31 q^{45} + 23 q^{46} - 31 q^{47} - 29 q^{48} + 44 q^{49} - 7 q^{50} + 8 q^{51} - 89 q^{52} - 46 q^{53} - 47 q^{54} - 31 q^{55} + 10 q^{56} - 47 q^{57} - 34 q^{58} - 9 q^{59} + 4 q^{60} - 5 q^{61} - 50 q^{62} - 61 q^{63} + 78 q^{64} + 24 q^{65} - 5 q^{66} + q^{67} - 115 q^{68} - 19 q^{69} + 9 q^{70} - 8 q^{71} - 93 q^{72} + 31 q^{73} - 19 q^{74} - 4 q^{75} - 7 q^{76} - 11 q^{77} + 57 q^{78} - 43 q^{80} + 43 q^{81} + 20 q^{82} - 29 q^{83} - 32 q^{84} + 49 q^{85} + 25 q^{86} - 62 q^{87} - 24 q^{88} - 77 q^{89} + 35 q^{90} - 11 q^{91} - 25 q^{92} - 38 q^{94} + 22 q^{95} - 23 q^{96} - 39 q^{97} - 65 q^{98} + 31 q^{99}+O(q^{100}) \) 31 * q - 7 * q^2 - 4 * q^3 + 39 * q^4 - 31 * q^5 - 5 * q^6 - 11 * q^7 - 24 * q^8 + 31 * q^9 + 7 * q^10 + 31 * q^11 - 4 * q^12 - 24 * q^13 - 9 * q^14 + 4 * q^15 + 43 * q^16 - 49 * q^17 - 35 * q^18 - 22 * q^19 - 39 * q^20 - 8 * q^21 - 7 * q^22 - q^23 - 13 * q^24 + 31 * q^25 - 9 * q^26 - 22 * q^27 - 34 * q^28 - 12 * q^29 + 5 * q^30 + 4 * q^31 - 45 * q^32 - 4 * q^33 + 2 * q^34 + 11 * q^35 + 34 * q^36 - 18 * q^37 - 7 * q^38 - q^39 + 24 * q^40 - 58 * q^41 - 21 * q^42 - 41 * q^43 + 39 * q^44 - 31 * q^45 + 23 * q^46 - 31 * q^47 - 29 * q^48 + 44 * q^49 - 7 * q^50 + 8 * q^51 - 89 * q^52 - 46 * q^53 - 47 * q^54 - 31 * q^55 + 10 * q^56 - 47 * q^57 - 34 * q^58 - 9 * q^59 + 4 * q^60 - 5 * q^61 - 50 * q^62 - 61 * q^63 + 78 * q^64 + 24 * q^65 - 5 * q^66 + q^67 - 115 * q^68 - 19 * q^69 + 9 * q^70 - 8 * q^71 - 93 * q^72 + 31 * q^73 - 19 * q^74 - 4 * q^75 - 7 * q^76 - 11 * q^77 + 57 * q^78 - 43 * q^80 + 43 * q^81 + 20 * q^82 - 29 * q^83 - 32 * q^84 + 49 * q^85 + 25 * q^86 - 62 * q^87 - 24 * q^88 - 77 * q^89 + 35 * q^90 - 11 * q^91 - 25 * q^92 - 38 * q^94 + 22 * q^95 - 23 * q^96 - 39 * q^97 - 65 * q^98 + 31 * 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 $

$2$	−0.602631	−0.426125	−0.213062	−	0.977039i	$-0.568344\pi$
$2$	−0.602631	−0.426125	−0.213062	+	0.977039i	$0.568344\pi$
$3$	−3.44000	−1.98608	−0.993041	−	0.117768i	$-0.962426\pi$
$3$	−3.44000	−1.98608	−0.993041	+	0.117768i	$0.962426\pi$
$4$	−1.63684	−0.818418
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	2.07305	0.846318
$7$	−0.349257	−0.132007	−0.0660033	−	0.997819i	$-0.521025\pi$
$7$	−0.349257	−0.132007	−0.0660033	+	0.997819i	$0.521025\pi$
$8$	2.19167	0.774873
$9$	8.83357	2.94452
$10$	0.602631	0.190569
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	5.63071	1.62545
$13$	−6.76394	−1.87598	−0.937989	−	0.346664i	$-0.887315\pi$
$13$	−6.76394	−1.87598	−0.937989	+	0.346664i	$0.887315\pi$
$14$	0.210473	0.0562513
$15$	3.44000	0.888203
$16$	1.95290	0.488226
$17$	−3.51529	−0.852583	−0.426291	−	0.904586i	$-0.640180\pi$
$17$	−3.51529	−0.852583	−0.426291	+	0.904586i	$0.640180\pi$
$18$	−5.32338	−1.25473
$19$	−2.53829	−0.582323	−0.291161	−	0.956674i	$-0.594042\pi$
$19$	−2.53829	−0.582323	−0.291161	+	0.956674i	$0.594042\pi$
$20$	1.63684	0.366008
$21$	1.20144	0.262176
$22$	−0.602631	−0.128481
$23$	−1.89790	−0.395739	−0.197869	−	0.980228i	$-0.563402\pi$
$23$	−1.89790	−0.395739	−0.197869	+	0.980228i	$0.563402\pi$
$24$	−7.53934	−1.53896
$25$	1.00000	0.200000
$26$	4.07616	0.799401
$27$	−20.0674	−3.86198
$28$	0.571676	0.108037
$29$	9.67848	1.79725	0.898624	−	0.438719i	$-0.144568\pi$
$29$	9.67848	1.79725	0.898624	+	0.438719i	$0.144568\pi$
$30$	−2.07305	−0.378485
$31$	−4.30320	−0.772877	−0.386438	−	0.922315i	$-0.626295\pi$
$31$	−4.30320	−0.772877	−0.386438	+	0.922315i	$0.626295\pi$
$32$	−5.56022	−0.982917
$33$	−3.44000	−0.598826
$34$	2.11842	0.363306
$35$	0.349257	0.0590352
$36$	−14.4591	−2.40985
$37$	−7.66685	−1.26042	−0.630211	−	0.776424i	$-0.717032\pi$
$37$	−7.66685	−1.26042	−0.630211	+	0.776424i	$0.717032\pi$
$38$	1.52965	0.248142
$39$	23.2679	3.72585
$40$	−2.19167	−0.346534
$41$	2.98885	0.466780	0.233390	−	0.972383i	$-0.425018\pi$
$41$	2.98885	0.466780	0.233390	+	0.972383i	$0.425018\pi$
$42$	−0.724026	−0.111720
$43$	9.34941	1.42577	0.712886	−	0.701280i	$-0.247388\pi$
$43$	9.34941	1.42577	0.712886	+	0.701280i	$0.247388\pi$
$44$	−1.63684	−0.246762
$45$	−8.83357	−1.31683
$46$	1.14373	0.168634
$47$	0.371265	0.0541546	0.0270773	−	0.999633i	$-0.491380\pi$
$47$	0.371265	0.0541546	0.0270773	+	0.999633i	$0.491380\pi$
$48$	−6.71798	−0.969656
$49$	−6.87802	−0.982574
$50$	−0.602631	−0.0852249
$51$	12.0926	1.69330
$52$	11.0715	1.53533
$53$	5.85330	0.804013	0.402006	−	0.915637i	$-0.368313\pi$
$53$	5.85330	0.804013	0.402006	+	0.915637i	$0.368313\pi$
$54$	12.0933	1.64569
$55$	−1.00000	−0.134840
$56$	−0.765456	−0.102288
$57$	8.73169	1.15654
$58$	−5.83255	−0.765852
$59$	14.8054	1.92750	0.963751	−	0.266804i	$-0.0859678\pi$
$59$	14.8054	1.92750	0.963751	+	0.266804i	$0.0859678\pi$
$60$	−5.63071	−0.726921
$61$	−2.51737	−0.322316	−0.161158	−	0.986929i	$-0.551523\pi$
$61$	−2.51737	−0.322316	−0.161158	+	0.986929i	$0.551523\pi$
$62$	2.59324	0.329342
$63$	−3.08518	−0.388697
$64$	−0.555043	−0.0693803
$65$	6.76394	0.838963
$66$	2.07305	0.255175
$67$	8.73441	1.06708	0.533539	−	0.845775i	$-0.320862\pi$
$67$	8.73441	1.06708	0.533539	+	0.845775i	$0.320862\pi$
$68$	5.75395	0.697769
$69$	6.52876	0.785970
$70$	−0.210473	−0.0251563
$71$	−4.53863	−0.538636	−0.269318	−	0.963051i	$-0.586798\pi$
$71$	−4.53863	−0.538636	−0.269318	+	0.963051i	$0.586798\pi$
$72$	19.3603	2.28163
$73$	1.00000	0.117041
$73$	1.00000	0.117041
$74$	4.62028	0.537097
$75$	−3.44000	−0.397216
$76$	4.15476	0.476583
$77$	−0.349257	−0.0398015
$78$	−14.0220	−1.58768
$79$	−5.87149	−0.660594	−0.330297	−	0.943877i	$-0.607149\pi$
$79$	−5.87149	−0.660594	−0.330297	+	0.943877i	$0.607149\pi$
$80$	−1.95290	−0.218341
$81$	42.5312	4.72569
$82$	−1.80118	−0.198907
$83$	14.7196	1.61568	0.807841	−	0.589400i	$-0.200636\pi$
$83$	14.7196	1.61568	0.807841	+	0.589400i	$0.200636\pi$
$84$	−1.96656	−0.214570
$85$	3.51529	0.381287
$86$	−5.63425	−0.607556
$87$	−33.2939	−3.56948
$88$	2.19167	0.233633
$89$	−3.71724	−0.394026	−0.197013	−	0.980401i	$-0.563124\pi$
$89$	−3.71724	−0.394026	−0.197013	+	0.980401i	$0.563124\pi$
$90$	5.32338	0.561134
$91$	2.36235	0.247642
$92$	3.10655	0.323880
$93$	14.8030	1.53500
$94$	−0.223736	−0.0230766
$95$	2.53829	0.260423
$96$	19.1271	1.95215
$97$	−3.94924	−0.400984	−0.200492	−	0.979695i	$-0.564254\pi$
$97$	−3.94924	−0.400984	−0.200492	+	0.979695i	$0.564254\pi$
$98$	4.14491	0.418699
$99$	8.83357	0.887807
$100$	−1.63684	−0.163684
$101$	19.0558	1.89612	0.948062	−	0.318087i	$-0.103040\pi$
$101$	19.0558	1.89612	0.948062	+	0.318087i	$0.103040\pi$
$102$	−7.28736	−0.721556
$103$	11.8351	1.16615	0.583073	−	0.812420i	$-0.301850\pi$
$103$	11.8351	1.16615	0.583073	+	0.812420i	$0.301850\pi$
$104$	−14.8243	−1.45364
$105$	−1.20144	−0.117249
$106$	−3.52738	−0.342610
$107$	−2.04137	−0.197347	−0.0986736	−	0.995120i	$-0.531460\pi$
$107$	−2.04137	−0.197347	−0.0986736	+	0.995120i	$0.531460\pi$
$108$	32.8471	3.16071
$109$	−8.90406	−0.852854	−0.426427	−	0.904522i	$-0.640228\pi$
$109$	−8.90406	−0.852854	−0.426427	+	0.904522i	$0.640228\pi$
$110$	0.602631	0.0574586
$111$	26.3739	2.50330
$112$	−0.682065	−0.0644490
$113$	−6.21773	−0.584914	−0.292457	−	0.956279i	$-0.594473\pi$
$113$	−6.21773	−0.584914	−0.292457	+	0.956279i	$0.594473\pi$
$114$	−5.26199	−0.492830
$115$	1.89790	0.176980
$116$	−15.8421	−1.47090
$117$	−59.7497	−5.52386
$118$	−8.92221	−0.821356
$119$	1.22774	0.112547
$120$	7.53934	0.688244
$121$	1.00000	0.0909091
$122$	1.51705	0.137347
$123$	−10.2816	−0.927064
$124$	7.04363	0.632536
$125$	−1.00000	−0.0894427
$126$	1.85923	0.165633
$127$	10.9741	0.973792	0.486896	−	0.873460i	$-0.338129\pi$
$127$	10.9741	0.973792	0.486896	+	0.873460i	$0.338129\pi$
$128$	11.4549	1.01248
$129$	−32.1619	−2.83170
$130$	−4.07616	−0.357503
$131$	−6.19508	−0.541267	−0.270633	−	0.962682i	$-0.587233\pi$
$131$	−6.19508	−0.541267	−0.270633	+	0.962682i	$0.587233\pi$
$132$	5.63071	0.490090
$133$	0.886514	0.0768705
$134$	−5.26363	−0.454708
$135$	20.0674	1.72713
$136$	−7.70435	−0.660643
$137$	−14.8227	−1.26638	−0.633192	−	0.773994i	$-0.718256\pi$
$137$	−14.8227	−1.26638	−0.633192	+	0.773994i	$0.718256\pi$
$138$	−3.93443	−0.334921
$139$	12.7165	1.07860	0.539300	−	0.842114i	$-0.318689\pi$
$139$	12.7165	1.07860	0.539300	+	0.842114i	$0.318689\pi$
$140$	−0.571676	−0.0483155
$141$	−1.27715	−0.107555
$142$	2.73512	0.229526
$143$	−6.76394	−0.565629
$144$	17.2511	1.43759
$145$	−9.67848	−0.803754
$146$	−0.602631	−0.0498741
$147$	23.6604	1.95147
$148$	12.5494	1.03155
$149$	4.85463	0.397707	0.198853	−	0.980029i	$-0.436278\pi$
$149$	4.85463	0.397707	0.198853	+	0.980029i	$0.436278\pi$
$150$	2.07305	0.169264
$151$	−2.64043	−0.214875	−0.107438	−	0.994212i	$-0.534265\pi$
$151$	−2.64043	−0.214875	−0.107438	+	0.994212i	$0.534265\pi$
$152$	−5.56309	−0.451226
$153$	−31.0525	−2.51045
$154$	0.210473	0.0169604
$155$	4.30320	0.345641
$156$	−38.0858	−3.04930
$157$	10.3770	0.828171	0.414086	−	0.910238i	$-0.364101\pi$
$157$	10.3770	0.828171	0.414086	+	0.910238i	$0.364101\pi$
$158$	3.53834	0.281495
$159$	−20.1353	−1.59684
$160$	5.56022	0.439574
$161$	0.662854	0.0522402
$162$	−25.6306	−2.01373
$163$	17.0865	1.33831	0.669157	−	0.743121i	$-0.266655\pi$
$163$	17.0865	1.33831	0.669157	+	0.743121i	$0.266655\pi$
$164$	−4.89226	−0.382021
$165$	3.44000	0.267803
$166$	−8.87047	−0.688482
$167$	1.11461	0.0862512	0.0431256	−	0.999070i	$-0.486268\pi$
$167$	1.11461	0.0862512	0.0431256	+	0.999070i	$0.486268\pi$
$168$	2.63317	0.203153
$169$	32.7509	2.51930
$170$	−2.11842	−0.162476
$171$	−22.4221	−1.71466
$172$	−15.3034	−1.16688
$173$	9.66870	0.735098	0.367549	−	0.930004i	$-0.380197\pi$
$173$	9.66870	0.735098	0.367549	+	0.930004i	$0.380197\pi$
$174$	20.0640	1.52104
$175$	−0.349257	−0.0264013
$176$	1.95290	0.147206
$177$	−50.9306	−3.82818
$178$	2.24012	0.167904
$179$	−12.3904	−0.926102	−0.463051	−	0.886332i	$-0.653245\pi$
$179$	−12.3904	−0.926102	−0.463051	+	0.886332i	$0.653245\pi$
$180$	14.4591	1.07772
$181$	−21.5794	−1.60398	−0.801992	−	0.597334i	$-0.796227\pi$
$181$	−21.5794	−1.60398	−0.801992	+	0.597334i	$0.796227\pi$
$182$	−1.42363	−0.105526
$183$	8.65974	0.640146
$184$	−4.15956	−0.306647
$185$	7.66685	0.563678
$186$	−8.92073	−0.654100
$187$	−3.51529	−0.257063
$188$	−0.607700	−0.0443211
$189$	7.00869	0.509807
$190$	−1.52965	−0.110972
$191$	11.9279	0.863076	0.431538	−	0.902095i	$-0.357971\pi$
$191$	11.9279	0.863076	0.431538	+	0.902095i	$0.357971\pi$
$192$	1.90934	0.137795
$193$	−17.2084	−1.23868	−0.619342	−	0.785121i	$-0.712601\pi$
$193$	−17.2084	−1.23868	−0.619342	+	0.785121i	$0.712601\pi$
$194$	2.37993	0.170869
$195$	−23.2679	−1.66625
$196$	11.2582	0.804156
$197$	7.79112	0.555095	0.277547	−	0.960712i	$-0.410478\pi$
$197$	7.79112	0.555095	0.277547	+	0.960712i	$0.410478\pi$
$198$	−5.32338	−0.378316
$199$	1.14027	0.0808316	0.0404158	−	0.999183i	$-0.487132\pi$
$199$	1.14027	0.0808316	0.0404158	+	0.999183i	$0.487132\pi$
$200$	2.19167	0.154975
$201$	−30.0463	−2.11930
$202$	−11.4836	−0.807985
$203$	−3.38028	−0.237249
$204$	−19.7936	−1.38583
$205$	−2.98885	−0.208750
$206$	−7.13219	−0.496924
$207$	−16.7652	−1.16526
$208$	−13.2093	−0.915901
$209$	−2.53829	−0.175577
$210$	0.724026	0.0499626
$211$	−20.9118	−1.43963	−0.719815	−	0.694166i	$-0.755773\pi$
$211$	−20.9118	−1.43963	−0.719815	+	0.694166i	$0.755773\pi$
$212$	−9.58089	−0.658019
$213$	15.6129	1.06978
$214$	1.23020	0.0840945
$215$	−9.34941	−0.637624
$216$	−43.9812	−2.99254
$217$	1.50292	0.102025
$218$	5.36586	0.363422
$219$	−3.44000	−0.232453
$220$	1.63684	0.110355
$221$	23.7772	1.59943
$222$	−15.8937	−1.06672
$223$	9.94501	0.665967	0.332984	−	0.942933i	$-0.391945\pi$
$223$	9.94501	0.665967	0.332984	+	0.942933i	$0.391945\pi$
$224$	1.94195	0.129752
$225$	8.83357	0.588905
$226$	3.74700	0.249246
$227$	−18.3846	−1.22023	−0.610113	−	0.792314i	$-0.708876\pi$
$227$	−18.3846	−1.22023	−0.610113	+	0.792314i	$0.708876\pi$
$228$	−14.2923	−0.946534
$229$	−18.8008	−1.24239	−0.621196	−	0.783655i	$-0.713353\pi$
$229$	−18.8008	−1.24239	−0.621196	+	0.783655i	$0.713353\pi$
$230$	−1.14373	−0.0754154
$231$	1.20144	0.0790491
$232$	21.2120	1.39264
$233$	20.2351	1.32564	0.662822	−	0.748777i	$-0.269358\pi$
$233$	20.2351	1.32564	0.662822	+	0.748777i	$0.269358\pi$
$234$	36.0070	2.35385
$235$	−0.371265	−0.0242187
$236$	−24.2340	−1.57750
$237$	20.1979	1.31199
$238$	−0.739874	−0.0479589
$239$	−3.23590	−0.209313	−0.104657	−	0.994508i	$-0.533374\pi$
$239$	−3.23590	−0.209313	−0.104657	+	0.994508i	$0.533374\pi$
$240$	6.71798	0.433643
$241$	−17.7106	−1.14084	−0.570419	−	0.821354i	$-0.693219\pi$
$241$	−17.7106	−1.14084	−0.570419	+	0.821354i	$0.693219\pi$
$242$	−0.602631	−0.0387386
$243$	−86.1048	−5.52363
$244$	4.12052	0.263789
$245$	6.87802	0.439421
$246$	6.19603	0.395045
$247$	17.1688	1.09243
$248$	−9.43119	−0.598881
$249$	−50.6352	−3.20888
$250$	0.602631	0.0381137
$251$	20.5581	1.29762	0.648809	−	0.760951i	$-0.275267\pi$
$251$	20.5581	1.29762	0.648809	+	0.760951i	$0.275267\pi$
$252$	5.04994	0.318116
$253$	−1.89790	−0.119320
$254$	−6.61332	−0.414957
$255$	−12.0926	−0.757267
$256$	−5.79301	−0.362063
$257$	−29.2020	−1.82157	−0.910786	−	0.412880i	$-0.864523\pi$
$257$	−29.2020	−1.82157	−0.910786	+	0.412880i	$0.864523\pi$
$258$	19.3818	1.20666
$259$	2.67770	0.166384
$260$	−11.0715	−0.686623
$261$	85.4955	5.29204
$262$	3.73335	0.230647
$263$	−9.41873	−0.580784	−0.290392	−	0.956908i	$-0.593786\pi$
$263$	−9.41873	−0.580784	−0.290392	+	0.956908i	$0.593786\pi$
$264$	−7.53934	−0.464014
$265$	−5.85330	−0.359566
$266$	−0.534241	−0.0327564
$267$	12.7873	0.782569
$268$	−14.2968	−0.873316
$269$	11.7076	0.713826	0.356913	−	0.934138i	$-0.383829\pi$
$269$	11.7076	0.713826	0.356913	+	0.934138i	$0.383829\pi$
$270$	−12.0933	−0.735973
$271$	−12.4788	−0.758036	−0.379018	−	0.925389i	$-0.623738\pi$
$271$	−12.4788	−0.758036	−0.379018	+	0.925389i	$0.623738\pi$
$272$	−6.86502	−0.416253
$273$	−8.12648	−0.491837
$274$	8.93259	0.539638
$275$	1.00000	0.0603023
$276$	−10.6865	−0.643252
$277$	−16.5404	−0.993815	−0.496908	−	0.867803i	$-0.665531\pi$
$277$	−16.5404	−0.993815	−0.496908	+	0.867803i	$0.665531\pi$
$278$	−7.66336	−0.459618
$279$	−38.0126	−2.27575
$280$	0.765456	0.0457447
$281$	6.70102	0.399749	0.199875	−	0.979821i	$-0.435947\pi$
$281$	6.70102	0.399749	0.199875	+	0.979821i	$0.435947\pi$
$282$	0.769651	0.0458320
$283$	−6.52780	−0.388038	−0.194019	−	0.980998i	$-0.562152\pi$
$283$	−6.52780	−0.388038	−0.194019	+	0.980998i	$0.562152\pi$
$284$	7.42899	0.440829
$285$	−8.73169	−0.517221
$286$	4.07616	0.241028
$287$	−1.04388	−0.0616181
$288$	−49.1166	−2.89422
$289$	−4.64275	−0.273103
$290$	5.83255	0.342499
$291$	13.5854	0.796388
$292$	−1.63684	−0.0957886
$293$	17.4272	1.01811	0.509053	−	0.860735i	$-0.329996\pi$
$293$	17.4272	1.01811	0.509053	+	0.860735i	$0.329996\pi$
$294$	−14.2585	−0.831571
$295$	−14.8054	−0.862005
$296$	−16.8032	−0.976666
$297$	−20.0674	−1.16443
$298$	−2.92555	−0.169473
$299$	12.8373	0.742398
$300$	5.63071	0.325089
$301$	−3.26535	−0.188211
$302$	1.59121	0.0915637
$303$	−65.5519	−3.76586
$304$	−4.95703	−0.284305
$305$	2.51737	0.144144
$306$	18.7132	1.06976
$307$	10.3633	0.591467	0.295733	−	0.955270i	$-0.404436\pi$
$307$	10.3633	0.591467	0.295733	+	0.955270i	$0.404436\pi$
$308$	0.571676	0.0325743
$309$	−40.7127	−2.31606
$310$	−2.59324	−0.147286
$311$	6.53180	0.370384	0.185192	−	0.982702i	$-0.440709\pi$
$311$	6.53180	0.370384	0.185192	+	0.982702i	$0.440709\pi$
$312$	50.9956	2.88706
$313$	−18.1182	−1.02410	−0.512051	−	0.858955i	$-0.671114\pi$
$313$	−18.1182	−1.02410	−0.512051	+	0.858955i	$0.671114\pi$
$314$	−6.25348	−0.352904
$315$	3.08518	0.173830
$316$	9.61066	0.540642
$317$	3.97159	0.223067	0.111533	−	0.993761i	$-0.464424\pi$
$317$	3.97159	0.223067	0.111533	+	0.993761i	$0.464424\pi$
$318$	12.1342	0.680451
$319$	9.67848	0.541891
$320$	0.555043	0.0310278
$321$	7.02232	0.391948
$322$	−0.399456	−0.0222608
$323$	8.92281	0.496478
$324$	−69.6166	−3.86759
$325$	−6.76394	−0.375196
$326$	−10.2968	−0.570289
$327$	30.6299	1.69384
$328$	6.55058	0.361695
$329$	−0.129667	−0.00714877
$330$	−2.07305	−0.114118
$331$	25.8067	1.41846	0.709232	−	0.704975i	$-0.249042\pi$
$331$	25.8067	1.41846	0.709232	+	0.704975i	$0.249042\pi$
$332$	−24.0935	−1.32230
$333$	−67.7256	−3.71134
$334$	−0.671699	−0.0367538
$335$	−8.73441	−0.477212
$336$	2.34630	0.128001
$337$	23.0305	1.25455	0.627276	−	0.778797i	$-0.284170\pi$
$337$	23.0305	1.25455	0.627276	+	0.778797i	$0.284170\pi$
$338$	−19.7367	−1.07353
$339$	21.3889	1.16169
$340$	−5.75395	−0.312052
$341$	−4.30320	−0.233031
$342$	13.5123	0.730660
$343$	4.84699	0.261713
$344$	20.4908	1.10479
$345$	−6.52876	−0.351496
$346$	−5.82666	−0.313243
$347$	−11.1118	−0.596511	−0.298256	−	0.954486i	$-0.596405\pi$
$347$	−11.1118	−0.596511	−0.298256	+	0.954486i	$0.596405\pi$
$348$	54.4967	2.92133
$349$	17.9285	0.959693	0.479847	−	0.877352i	$-0.340692\pi$
$349$	17.9285	0.959693	0.479847	+	0.877352i	$0.340692\pi$
$350$	0.210473	0.0112503
$351$	135.735	7.24500
$352$	−5.56022	−0.296361
$353$	3.23179	0.172011	0.0860053	−	0.996295i	$-0.472590\pi$
$353$	3.23179	0.172011	0.0860053	+	0.996295i	$0.472590\pi$
$354$	30.6923	1.63128
$355$	4.53863	0.240885
$356$	6.08451	0.322478
$357$	−4.22342	−0.223527
$358$	7.46684	0.394635
$359$	12.6120	0.665638	0.332819	−	0.942991i	$-0.392000\pi$
$359$	12.6120	0.665638	0.332819	+	0.942991i	$0.392000\pi$
$360$	−19.3603	−1.02038
$361$	−12.5571	−0.660900
$362$	13.0044	0.683497
$363$	−3.44000	−0.180553
$364$	−3.86678	−0.202674
$365$	−1.00000	−0.0523424
$366$	−5.21863	−0.272782
$367$	−4.49050	−0.234402	−0.117201	−	0.993108i	$-0.537392\pi$
$367$	−4.49050	−0.234402	−0.117201	+	0.993108i	$0.537392\pi$
$368$	−3.70641	−0.193210
$369$	26.4022	1.37444
$370$	−4.62028	−0.240197
$371$	−2.04431	−0.106135
$372$	−24.2300	−1.25627
$373$	−6.67732	−0.345738	−0.172869	−	0.984945i	$-0.555304\pi$
$373$	−6.67732	−0.345738	−0.172869	+	0.984945i	$0.555304\pi$
$374$	2.11842	0.109541
$375$	3.44000	0.177641
$376$	0.813691	0.0419629
$377$	−65.4646	−3.37160
$378$	−4.22366	−0.217241
$379$	−17.2222	−0.884647	−0.442323	−	0.896856i	$-0.645846\pi$
$379$	−17.2222	−0.884647	−0.442323	+	0.896856i	$0.645846\pi$
$380$	−4.15476	−0.213135
$381$	−37.7508	−1.93403
$382$	−7.18815	−0.367778
$383$	−22.0092	−1.12462	−0.562308	−	0.826928i	$-0.690086\pi$
$383$	−22.0092	−1.12462	−0.562308	+	0.826928i	$0.690086\pi$
$384$	−39.4049	−2.01087
$385$	0.349257	0.0177998
$386$	10.3703	0.527834
$387$	82.5886	4.19822
$388$	6.46425	0.328173
$389$	21.0242	1.06597	0.532985	−	0.846125i	$-0.321070\pi$
$389$	21.0242	1.06597	0.532985	+	0.846125i	$0.321070\pi$
$390$	14.0220	0.710030
$391$	6.67166	0.337400
$392$	−15.0744	−0.761370
$393$	21.3111	1.07500
$394$	−4.69517	−0.236539
$395$	5.87149	0.295427
$396$	−14.4591	−0.726597
$397$	−3.47207	−0.174258	−0.0871291	−	0.996197i	$-0.527769\pi$
$397$	−3.47207	−0.174258	−0.0871291	+	0.996197i	$0.527769\pi$
$398$	−0.687162	−0.0344443
$399$	−3.04960	−0.152671
$400$	1.95290	0.0976451
$401$	−16.5695	−0.827441	−0.413721	−	0.910404i	$-0.635771\pi$
$401$	−16.5695	−0.827441	−0.413721	+	0.910404i	$0.635771\pi$
$402$	18.1069	0.903088
$403$	29.1066	1.44990
$404$	−31.1912	−1.55182
$405$	−42.5312	−2.11339
$406$	2.03706	0.101098
$407$	−7.66685	−0.380031
$408$	26.5029	1.31209
$409$	−3.52052	−0.174078	−0.0870392	−	0.996205i	$-0.527741\pi$
$409$	−3.52052	−0.174078	−0.0870392	+	0.996205i	$0.527741\pi$
$410$	1.80118	0.0889537
$411$	50.9899	2.51514
$412$	−19.3721	−0.954395
$413$	−5.17089	−0.254443
$414$	10.1032	0.496547
$415$	−14.7196	−0.722555
$416$	37.6090	1.84393
$417$	−43.7447	−2.14219
$418$	1.52965	0.0748176
$419$	−6.46492	−0.315832	−0.157916	−	0.987453i	$-0.550478\pi$
$419$	−6.46492	−0.315832	−0.157916	+	0.987453i	$0.550478\pi$
$420$	1.96656	0.0959585
$421$	31.8324	1.55142	0.775708	−	0.631092i	$-0.217393\pi$
$421$	31.8324	1.55142	0.775708	+	0.631092i	$0.217393\pi$
$422$	12.6021	0.613461
$423$	3.27960	0.159459
$424$	12.8285	0.623008
$425$	−3.51529	−0.170517
$426$	−9.40880	−0.455858
$427$	0.879209	0.0425479
$428$	3.34139	0.161512
$429$	23.2679	1.12339
$430$	5.63425	0.271707
$431$	10.9048	0.525267	0.262634	−	0.964896i	$-0.415409\pi$
$431$	10.9048	0.525267	0.262634	+	0.964896i	$0.415409\pi$
$432$	−39.1898	−1.88552
$433$	28.9486	1.39118	0.695591	−	0.718438i	$-0.255143\pi$
$433$	28.9486	1.39118	0.695591	+	0.718438i	$0.255143\pi$
$434$	−0.905707	−0.0434753
$435$	33.2939	1.59632
$436$	14.5745	0.697991
$437$	4.81740	0.230448
$438$	2.07305	0.0990541
$439$	24.4670	1.16775	0.583874	−	0.811844i	$-0.301536\pi$
$439$	24.4670	1.16775	0.583874	+	0.811844i	$0.301536\pi$
$440$	−2.19167	−0.104484
$441$	−60.7575	−2.89321
$442$	−14.3289	−0.681555
$443$	27.0288	1.28418	0.642089	−	0.766630i	$-0.278068\pi$
$443$	27.0288	1.28418	0.642089	+	0.766630i	$0.278068\pi$
$444$	−43.1698	−2.04875
$445$	3.71724	0.176214
$446$	−5.99317	−0.283785
$447$	−16.6999	−0.789878
$448$	0.193852	0.00915867
$449$	3.56355	0.168174	0.0840872	−	0.996458i	$-0.473203\pi$
$449$	3.56355	0.168174	0.0840872	+	0.996458i	$0.473203\pi$
$450$	−5.32338	−0.250947
$451$	2.98885	0.140740
$452$	10.1774	0.478704
$453$	9.08308	0.426760
$454$	11.0791	0.519968
$455$	−2.36235	−0.110749
$456$	19.1370	0.896172
$457$	−8.43500	−0.394572	−0.197286	−	0.980346i	$-0.563213\pi$
$457$	−8.43500	−0.394572	−0.197286	+	0.980346i	$0.563213\pi$
$458$	11.3300	0.529414
$459$	70.5429	3.29266
$460$	−3.10655	−0.144843
$461$	−37.7754	−1.75938	−0.879688	−	0.475551i	$-0.842249\pi$
$461$	−37.7754	−1.75938	−0.879688	+	0.475551i	$0.842249\pi$
$462$	−0.724026	−0.0336848
$463$	36.5820	1.70011	0.850054	−	0.526695i	$-0.176569\pi$
$463$	36.5820	1.70011	0.850054	+	0.526695i	$0.176569\pi$
$464$	18.9011	0.877463
$465$	−14.8030	−0.686472
$466$	−12.1943	−0.564890
$467$	−9.29965	−0.430336	−0.215168	−	0.976577i	$-0.569030\pi$
$467$	−9.29965	−0.430336	−0.215168	+	0.976577i	$0.569030\pi$
$468$	97.8005	4.52083
$469$	−3.05055	−0.140861
$470$	0.223736	0.0103202
$471$	−35.6967	−1.64482
$472$	32.4486	1.49357
$473$	9.34941	0.429886
$474$	−12.1719	−0.559073
$475$	−2.53829	−0.116465
$476$	−2.00961	−0.0921102
$477$	51.7055	2.36743
$478$	1.95006	0.0891935
$479$	4.71558	0.215460	0.107730	−	0.994180i	$-0.465642\pi$
$479$	4.71558	0.215460	0.107730	+	0.994180i	$0.465642\pi$
$480$	−19.1271	−0.873030
$481$	51.8581	2.36452
$482$	10.6729	0.486139
$483$	−2.28021	−0.103753
$484$	−1.63684	−0.0744016
$485$	3.94924	0.179326
$486$	51.8895	2.35375
$487$	11.2546	0.509994	0.254997	−	0.966942i	$-0.417926\pi$
$487$	11.2546	0.509994	0.254997	+	0.966942i	$0.417926\pi$
$488$	−5.51725	−0.249754
$489$	−58.7773	−2.65800
$490$	−4.14491	−0.187248
$491$	−3.01056	−0.135865	−0.0679323	−	0.997690i	$-0.521640\pi$
$491$	−3.01056	−0.135865	−0.0679323	+	0.997690i	$0.521640\pi$
$492$	16.8293	0.758726
$493$	−34.0226	−1.53230
$494$	−10.3465	−0.465509
$495$	−8.83357	−0.397039
$496$	−8.40372	−0.377338
$497$	1.58515	0.0711036
$498$	30.5144	1.36738
$499$	−15.8626	−0.710105	−0.355053	−	0.934846i	$-0.615537\pi$
$499$	−15.8626	−0.710105	−0.355053	+	0.934846i	$0.615537\pi$
$500$	1.63684	0.0732015
$501$	−3.83426	−0.171302
$502$	−12.3890	−0.552947
$503$	−19.1738	−0.854916	−0.427458	−	0.904035i	$-0.640591\pi$
$503$	−19.1738	−0.854916	−0.427458	+	0.904035i	$0.640591\pi$
$504$	−6.76171	−0.301190
$505$	−19.0558	−0.847972
$506$	1.14373	0.0508451
$507$	−112.663	−5.00353
$508$	−17.9628	−0.796968
$509$	8.82633	0.391220	0.195610	−	0.980682i	$-0.437331\pi$
$509$	8.82633	0.391220	0.195610	+	0.980682i	$0.437331\pi$
$510$	7.28736	0.322690
$511$	−0.349257	−0.0154502
$512$	−19.4188	−0.858198
$513$	50.9369	2.24892
$514$	17.5980	0.776216
$515$	−11.8351	−0.521516
$516$	52.6438	2.31751
$517$	0.371265	0.0163282
$518$	−1.61366	−0.0709004
$519$	−33.2603	−1.45996
$520$	14.8243	0.650090
$521$	−35.6678	−1.56264	−0.781318	−	0.624134i	$-0.785452\pi$
$521$	−35.6678	−1.56264	−0.781318	+	0.624134i	$0.785452\pi$
$522$	−51.5222	−2.25507
$523$	−37.4570	−1.63788	−0.818940	−	0.573879i	$-0.805438\pi$
$523$	−37.4570	−1.63788	−0.818940	+	0.573879i	$0.805438\pi$
$524$	10.1403	0.442983
$525$	1.20144	0.0524352
$526$	5.67602	0.247486
$527$	15.1270	0.658941
$528$	−6.71798	−0.292362
$529$	−19.3980	−0.843391
$530$	3.52738	0.153220
$531$	130.785	5.67557
$532$	−1.45108	−0.0629122
$533$	−20.2164	−0.875670
$534$	−7.70601	−0.333472
$535$	2.04137	0.0882563
$536$	19.1430	0.826850
$537$	42.6229	1.83931
$538$	−7.05538	−0.304179
$539$	−6.87802	−0.296257
$540$	−32.8471	−1.41351
$541$	24.5192	1.05416	0.527082	−	0.849815i	$-0.323286\pi$
$541$	24.5192	1.05416	0.527082	+	0.849815i	$0.323286\pi$
$542$	7.52014	0.323018
$543$	74.2331	3.18565
$544$	19.5458	0.838018
$545$	8.90406	0.381408
$546$	4.89727	0.209584
$547$	2.10185	0.0898688	0.0449344	−	0.998990i	$-0.485692\pi$
$547$	2.10185	0.0898688	0.0449344	+	0.998990i	$0.485692\pi$
$548$	24.2622	1.03643
$549$	−22.2374	−0.949067
$550$	−0.602631	−0.0256963
$551$	−24.5667	−1.04658
$552$	14.3089	0.609026
$553$	2.05066	0.0872028
$554$	9.96775	0.423489
$555$	−26.3739	−1.11951
$556$	−20.8148	−0.882746
$557$	−5.73434	−0.242972	−0.121486	−	0.992593i	$-0.538766\pi$
$557$	−5.73434	−0.242972	−0.121486	+	0.992593i	$0.538766\pi$
$558$	22.9076	0.969754
$559$	−63.2388	−2.67472
$560$	0.682065	0.0288225
$561$	12.0926	0.510549
$562$	−4.03824	−0.170343
$563$	−8.23680	−0.347140	−0.173570	−	0.984822i	$-0.555530\pi$
$563$	−8.23680	−0.347140	−0.173570	+	0.984822i	$0.555530\pi$
$564$	2.09049	0.0880253
$565$	6.21773	0.261582
$566$	3.93386	0.165352
$567$	−14.8543	−0.623823
$568$	−9.94718	−0.417374
$569$	−39.0907	−1.63877	−0.819385	−	0.573244i	$-0.805685\pi$
$569$	−39.0907	−1.63877	−0.819385	+	0.573244i	$0.805685\pi$
$570$	5.26199	0.220400
$571$	−3.33447	−0.139543	−0.0697716	−	0.997563i	$-0.522227\pi$
$571$	−3.33447	−0.139543	−0.0697716	+	0.997563i	$0.522227\pi$
$572$	11.0715	0.462921
$573$	−41.0321	−1.71414
$574$	0.629073	0.0262570
$575$	−1.89790	−0.0791478
$576$	−4.90301	−0.204292
$577$	−24.2773	−1.01068	−0.505339	−	0.862921i	$-0.668632\pi$
$577$	−24.2773	−1.01068	−0.505339	+	0.862921i	$0.668632\pi$
$578$	2.79786	0.116376
$579$	59.1967	2.46013
$580$	15.8421	0.657807
$581$	−5.14091	−0.213281
$582$	−8.18696	−0.339360
$583$	5.85330	0.242419
$584$	2.19167	0.0906920
$585$	59.7497	2.47035
$586$	−10.5021	−0.433840
$587$	−20.4711	−0.844935	−0.422467	−	0.906378i	$-0.638836\pi$
$587$	−20.4711	−0.844935	−0.422467	+	0.906378i	$0.638836\pi$
$588$	−38.7281	−1.59712
$589$	10.9227	0.450064
$590$	8.92221	0.367321
$591$	−26.8014	−1.10246
$592$	−14.9726	−0.615370
$593$	−34.6867	−1.42441	−0.712205	−	0.701971i	$-0.752303\pi$
$593$	−34.6867	−1.42441	−0.712205	+	0.701971i	$0.752303\pi$
$594$	12.0933	0.496193
$595$	−1.22774	−0.0503324
$596$	−7.94623	−0.325490
$597$	−3.92252	−0.160538
$598$	−7.73613	−0.316354
$599$	−23.6338	−0.965652	−0.482826	−	0.875716i	$-0.660390\pi$
$599$	−23.6338	−0.965652	−0.482826	+	0.875716i	$0.660390\pi$
$600$	−7.53934	−0.307792
$601$	45.9772	1.87545	0.937725	−	0.347379i	$-0.112928\pi$
$601$	45.9772	1.87545	0.937725	+	0.347379i	$0.112928\pi$
$602$	1.96780	0.0802015
$603$	77.1560	3.14204
$604$	4.32196	0.175858
$605$	−1.00000	−0.0406558
$606$	39.5036	1.60472
$607$	−27.1422	−1.10167	−0.550834	−	0.834615i	$-0.685690\pi$
$607$	−27.1422	−1.10167	−0.550834	+	0.834615i	$0.685690\pi$
$608$	14.1134	0.572375
$609$	11.6281	0.471196
$610$	−1.51705	−0.0614234
$611$	−2.51121	−0.101593
$612$	50.8279	2.05460
$613$	−18.2804	−0.738337	−0.369168	−	0.929363i	$-0.620357\pi$
$613$	−18.2804	−0.738337	−0.369168	+	0.929363i	$0.620357\pi$
$614$	−6.24527	−0.252039
$615$	10.2816	0.414596
$616$	−0.765456	−0.0308411
$617$	3.21940	0.129608	0.0648041	−	0.997898i	$-0.479358\pi$
$617$	3.21940	0.129608	0.0648041	+	0.997898i	$0.479358\pi$
$618$	24.5347	0.986931
$619$	−3.22480	−0.129615	−0.0648077	−	0.997898i	$-0.520643\pi$
$619$	−3.22480	−0.129615	−0.0648077	+	0.997898i	$0.520643\pi$
$620$	−7.04363	−0.282879
$621$	38.0859	1.52834
$622$	−3.93627	−0.157830
$623$	1.29827	0.0520141
$624$	45.4400	1.81905
$625$	1.00000	0.0400000
$626$	10.9186	0.436395
$627$	8.73169	0.348710
$628$	−16.9854	−0.677790
$629$	26.9512	1.07461
$630$	−1.85923	−0.0740734
$631$	−40.1910	−1.59998	−0.799989	−	0.600014i	$-0.795162\pi$
$631$	−40.1910	−1.59998	−0.799989	+	0.600014i	$0.795162\pi$
$632$	−12.8684	−0.511876
$633$	71.9366	2.85922
$634$	−2.39340	−0.0950542
$635$	−10.9741	−0.435493
$636$	32.9582	1.30688
$637$	46.5225	1.84329
$638$	−5.83255	−0.230913
$639$	−40.0923	−1.58603
$640$	−11.4549	−0.452796
$641$	−27.7704	−1.09686	−0.548432	−	0.836195i	$-0.684775\pi$
$641$	−27.7704	−1.09686	−0.548432	+	0.836195i	$0.684775\pi$
$642$	−4.23187	−0.167018
$643$	30.3183	1.19564	0.597819	−	0.801631i	$-0.296034\pi$
$643$	30.3183	1.19564	0.597819	+	0.801631i	$0.296034\pi$
$644$	−1.08498	−0.0427543
$645$	32.1619	1.26637
$646$	−5.37716	−0.211562
$647$	18.5566	0.729536	0.364768	−	0.931099i	$-0.381148\pi$
$647$	18.5566	0.729536	0.364768	+	0.931099i	$0.381148\pi$
$648$	93.2144	3.66181
$649$	14.8054	0.581164
$650$	4.07616	0.159880
$651$	−5.17004	−0.202630
$652$	−27.9677	−1.09530
$653$	13.4272	0.525446	0.262723	−	0.964871i	$-0.415379\pi$
$653$	13.4272	0.525446	0.262723	+	0.964871i	$0.415379\pi$
$654$	−18.4585	−0.721786
$655$	6.19508	0.242062
$656$	5.83694	0.227894
$657$	8.83357	0.344630
$658$	0.0781413	0.00304627
$659$	−5.98226	−0.233036	−0.116518	−	0.993189i	$-0.537173\pi$
$659$	−5.98226	−0.233036	−0.116518	+	0.993189i	$0.537173\pi$
$660$	−5.63071	−0.219175
$661$	−6.70581	−0.260826	−0.130413	−	0.991460i	$-0.541630\pi$
$661$	−6.70581	−0.260826	−0.130413	+	0.991460i	$0.541630\pi$
$662$	−15.5519	−0.604442
$663$	−81.7934	−3.17659
$664$	32.2604	1.25195
$665$	−0.886514	−0.0343775
$666$	40.8136	1.58149
$667$	−18.3688	−0.711241
$668$	−1.82444	−0.0705895
$669$	−34.2108	−1.32267
$670$	5.26363	0.203352
$671$	−2.51737	−0.0971820
$672$	−6.68028	−0.257698
$673$	−3.42215	−0.131914	−0.0659570	−	0.997822i	$-0.521010\pi$
$673$	−3.42215	−0.131914	−0.0659570	+	0.997822i	$0.521010\pi$
$674$	−13.8789	−0.534596
$675$	−20.0674	−0.772396
$676$	−53.6078	−2.06184
$677$	−39.8690	−1.53229	−0.766145	−	0.642668i	$-0.777827\pi$
$677$	−39.8690	−1.53229	−0.766145	+	0.642668i	$0.777827\pi$
$678$	−12.8896	−0.495024
$679$	1.37930	0.0529326
$680$	7.70435	0.295449
$681$	63.2428	2.42347
$682$	2.59324	0.0993003
$683$	−14.0211	−0.536501	−0.268250	−	0.963349i	$-0.586445\pi$
$683$	−14.0211	−0.536501	−0.268250	+	0.963349i	$0.586445\pi$
$684$	36.7013	1.40331
$685$	14.8227	0.566344
$686$	−2.92095	−0.111522
$687$	64.6747	2.46749
$688$	18.2585	0.696098
$689$	−39.5914	−1.50831
$690$	3.93443	0.149781
$691$	43.3482	1.64904	0.824522	−	0.565830i	$-0.191444\pi$
$691$	43.3482	1.64904	0.824522	+	0.565830i	$0.191444\pi$
$692$	−15.8261	−0.601617
$693$	−3.08518	−0.117196
$694$	6.69630	0.254188
$695$	−12.7165	−0.482365
$696$	−72.9693	−2.76589
$697$	−10.5067	−0.397969
$698$	−10.8043	−0.408949
$699$	−69.6086	−2.63284
$700$	0.571676	0.0216073
$701$	24.9672	0.942998	0.471499	−	0.881867i	$-0.343713\pi$
$701$	24.9672	0.942998	0.471499	+	0.881867i	$0.343713\pi$
$702$	−81.7981	−3.08727
$703$	19.4606	0.733972
$704$	−0.555043	−0.0209190
$705$	1.27715	0.0481003
$706$	−1.94758	−0.0732980
$707$	−6.65537	−0.250301
$708$	83.3650	3.13305
$709$	−34.6852	−1.30263	−0.651316	−	0.758807i	$-0.725783\pi$
$709$	−34.6852	−1.30263	−0.651316	+	0.758807i	$0.725783\pi$
$710$	−2.73512	−0.102647
$711$	−51.8662	−1.94513
$712$	−8.14696	−0.305320
$713$	8.16702	0.305857
$714$	2.54516	0.0952503
$715$	6.76394	0.252957
$716$	20.2810	0.757938
$717$	11.1315	0.415713
$718$	−7.60041	−0.283645
$719$	9.88647	0.368703	0.184352	−	0.982860i	$-0.440981\pi$
$719$	9.88647	0.368703	0.184352	+	0.982860i	$0.440981\pi$
$720$	−17.2511	−0.642910
$721$	−4.13349	−0.153939
$722$	7.56730	0.281626
$723$	60.9242	2.26580
$724$	35.3219	1.31273
$725$	9.67848	0.359450
$726$	2.07305	0.0769380
$727$	−44.2158	−1.63987	−0.819937	−	0.572454i	$-0.805991\pi$
$727$	−44.2158	−1.63987	−0.819937	+	0.572454i	$0.805991\pi$
$728$	5.17750	0.191891
$729$	168.607	6.24469
$730$	0.602631	0.0223044
$731$	−32.8659	−1.21559
$732$	−14.1746	−0.523907
$733$	−0.833512	−0.0307865	−0.0153932	−	0.999882i	$-0.504900\pi$
$733$	−0.833512	−0.0307865	−0.0153932	+	0.999882i	$0.504900\pi$
$734$	2.70612	0.0998845
$735$	−23.6604	−0.872725
$736$	10.5527	0.388979
$737$	8.73441	0.321736
$738$	−15.9108	−0.585685
$739$	−16.0771	−0.591406	−0.295703	−	0.955280i	$-0.595554\pi$
$739$	−16.0771	−0.591406	−0.295703	+	0.955280i	$0.595554\pi$
$740$	−12.5494	−0.461324
$741$	−59.0606	−2.16965
$742$	1.23196	0.0452268
$743$	−5.53428	−0.203033	−0.101517	−	0.994834i	$-0.532369\pi$
$743$	−5.53428	−0.203033	−0.101517	+	0.994834i	$0.532369\pi$
$744$	32.4432	1.18943
$745$	−4.85463	−0.177860
$746$	4.02396	0.147328
$747$	130.026	4.75741
$748$	5.75395	0.210385
$749$	0.712964	0.0260511
$750$	−2.07305	−0.0756970
$751$	21.4001	0.780902	0.390451	−	0.920624i	$-0.372319\pi$
$751$	21.4001	0.780902	0.390451	+	0.920624i	$0.372319\pi$
$752$	0.725045	0.0264397
$753$	−70.7199	−2.57718
$754$	39.4510	1.43672
$755$	2.64043	0.0960952
$756$	−11.4721	−0.417235
$757$	−40.3631	−1.46702	−0.733511	−	0.679678i	$-0.762120\pi$
$757$	−40.3631	−1.46702	−0.733511	+	0.679678i	$0.762120\pi$
$758$	10.3787	0.376970
$759$	6.52876	0.236979
$760$	5.56309	0.201794
$761$	−52.6077	−1.90703	−0.953513	−	0.301351i	$-0.902562\pi$
$761$	−52.6077	−1.90703	−0.953513	+	0.301351i	$0.902562\pi$
$762$	22.7498	0.824138
$763$	3.10980	0.112582
$764$	−19.5241	−0.706357
$765$	31.0525	1.12271
$766$	13.2634	0.479226
$767$	−100.143	−3.61595
$768$	19.9279	0.719087
$769$	−30.5566	−1.10190	−0.550950	−	0.834538i	$-0.685735\pi$
$769$	−30.5566	−1.10190	−0.550950	+	0.834538i	$0.685735\pi$
$770$	−0.210473	−0.00758492
$771$	100.455	3.61779
$772$	28.1673	1.01376
$773$	−28.5937	−1.02844	−0.514221	−	0.857657i	$-0.671919\pi$
$773$	−28.5937	−1.02844	−0.514221	+	0.857657i	$0.671919\pi$
$774$	−49.7705	−1.78896
$775$	−4.30320	−0.154575
$776$	−8.65543	−0.310712
$777$	−9.21127	−0.330453
$778$	−12.6698	−0.454236
$779$	−7.58656	−0.271817
$780$	38.0858	1.36369
$781$	−4.53863	−0.162405
$782$	−4.02055	−0.143774
$783$	−194.222	−6.94094
$784$	−13.4321	−0.479718
$785$	−10.3770	−0.370369
$786$	−12.8427	−0.458084
$787$	11.5623	0.412153	0.206077	−	0.978536i	$-0.433930\pi$
$787$	11.5623	0.412153	0.206077	+	0.978536i	$0.433930\pi$
$788$	−12.7528	−0.454299
$789$	32.4004	1.15348
$790$	−3.53834	−0.125889
$791$	2.17158	0.0772126
$792$	19.3603	0.687937
$793$	17.0273	0.604658
$794$	2.09238	0.0742557
$795$	20.1353	0.714127
$796$	−1.86643	−0.0661540
$797$	32.8675	1.16423	0.582114	−	0.813107i	$-0.302226\pi$
$797$	32.8675	1.16423	0.582114	+	0.813107i	$0.302226\pi$
$798$	1.83779	0.0650569
$799$	−1.30510	−0.0461713
$800$	−5.56022	−0.196583
$801$	−32.8365	−1.16022
$802$	9.98530	0.352593
$803$	1.00000	0.0352892
$804$	49.1809	1.73448
$805$	−0.662854	−0.0233625
$806$	−17.5405	−0.617838
$807$	−40.2742	−1.41772
$808$	41.7640	1.46925
$809$	24.8120	0.872343	0.436172	−	0.899864i	$-0.356334\pi$
$809$	24.8120	0.872343	0.436172	+	0.899864i	$0.356334\pi$
$810$	25.6306	0.900569
$811$	−46.7850	−1.64284	−0.821422	−	0.570321i	$-0.806819\pi$
$811$	−46.7850	−1.64284	−0.821422	+	0.570321i	$0.806819\pi$
$812$	5.53296	0.194169
$813$	42.9272	1.50552
$814$	4.62028	0.161941
$815$	−17.0865	−0.598512
$816$	23.6156	0.826712
$817$	−23.7315	−0.830259
$818$	2.12157	0.0741791
$819$	20.8680	0.729187
$820$	4.89226	0.170845
$821$	−13.2869	−0.463714	−0.231857	−	0.972750i	$-0.574480\pi$
$821$	−13.2869	−0.463714	−0.231857	+	0.972750i	$0.574480\pi$
$822$	−30.7281	−1.07176
$823$	11.0841	0.386368	0.193184	−	0.981163i	$-0.438119\pi$
$823$	11.0841	0.386368	0.193184	+	0.981163i	$0.438119\pi$
$824$	25.9386	0.903615
$825$	−3.44000	−0.119765
$826$	3.11614	0.108424
$827$	7.00477	0.243580	0.121790	−	0.992556i	$-0.461137\pi$
$827$	7.00477	0.243580	0.121790	+	0.992556i	$0.461137\pi$
$828$	27.4419	0.953671
$829$	−9.00082	−0.312611	−0.156306	−	0.987709i	$-0.549958\pi$
$829$	−9.00082	−0.312611	−0.156306	+	0.987709i	$0.549958\pi$
$830$	8.87047	0.307899
$831$	56.8988	1.97380
$832$	3.75427	0.130156
$833$	24.1782	0.837726
$834$	26.3619	0.912839
$835$	−1.11461	−0.0385727
$836$	4.15476	0.143695
$837$	86.3542	2.98484
$838$	3.89596	0.134584
$839$	−5.26930	−0.181917	−0.0909583	−	0.995855i	$-0.528993\pi$
$839$	−5.26930	−0.181917	−0.0909583	+	0.995855i	$0.528993\pi$
$840$	−2.63317	−0.0908528
$841$	64.6729	2.23010
$842$	−19.1832	−0.661097
$843$	−23.0515	−0.793935
$844$	34.2292	1.17822
$845$	−32.7509	−1.12666
$846$	−1.97639	−0.0679496
$847$	−0.349257	−0.0120006
$848$	11.4309	0.392540
$849$	22.4556	0.770675
$850$	2.11842	0.0726613
$851$	14.5509	0.498798
$852$	−25.5557	−0.875523
$853$	−26.8778	−0.920278	−0.460139	−	0.887847i	$-0.652200\pi$
$853$	−26.8778	−0.920278	−0.460139	+	0.887847i	$0.652200\pi$
$854$	−0.529839	−0.0181307
$855$	22.4221	0.766820
$856$	−4.47402	−0.152919
$857$	−4.68923	−0.160181	−0.0800905	−	0.996788i	$-0.525521\pi$
$857$	−4.68923	−0.160181	−0.0800905	+	0.996788i	$0.525521\pi$
$858$	−14.0220	−0.478702
$859$	−0.663756	−0.0226471	−0.0113235	−	0.999936i	$-0.503604\pi$
$859$	−0.663756	−0.0226471	−0.0113235	+	0.999936i	$0.503604\pi$
$860$	15.3034	0.521843
$861$	3.59093	0.122379
$862$	−6.57159	−0.223829
$863$	48.7831	1.66060	0.830298	−	0.557320i	$-0.188170\pi$
$863$	48.7831	1.66060	0.830298	+	0.557320i	$0.188170\pi$
$864$	111.579	3.79601
$865$	−9.66870	−0.328746
$866$	−17.4453	−0.592817
$867$	15.9710	0.542404
$868$	−2.46003	−0.0834990
$869$	−5.87149	−0.199177
$870$	−20.0640	−0.680232
$871$	−59.0790	−2.00182
$872$	−19.5148	−0.660853
$873$	−34.8859	−1.18071
$874$	−2.90312	−0.0981994
$875$	0.349257	0.0118070
$876$	5.63071	0.190244
$877$	26.5226	0.895605	0.447802	−	0.894133i	$-0.352207\pi$
$877$	26.5226	0.895605	0.447802	+	0.894133i	$0.352207\pi$
$878$	−14.7446	−0.497606
$879$	−59.9493	−2.02204
$880$	−1.95290	−0.0658323
$881$	24.7406	0.833532	0.416766	−	0.909014i	$-0.363164\pi$
$881$	24.7406	0.833532	0.416766	+	0.909014i	$0.363164\pi$
$882$	36.6143	1.23287
$883$	−53.7749	−1.80967	−0.904835	−	0.425762i	$-0.860006\pi$
$883$	−53.7749	−1.80967	−0.904835	+	0.425762i	$0.860006\pi$
$884$	−38.9194	−1.30900
$885$	50.9306	1.71201
$886$	−16.2884	−0.547220
$887$	44.0831	1.48017	0.740083	−	0.672515i	$-0.234786\pi$
$887$	44.0831	1.48017	0.740083	+	0.672515i	$0.234786\pi$
$888$	57.8029	1.93974
$889$	−3.83277	−0.128547
$890$	−2.24012	−0.0750891
$891$	42.5312	1.42485
$892$	−16.2783	−0.545039
$893$	−0.942377	−0.0315355
$894$	10.0639	0.336586
$895$	12.3904	0.414165
$896$	−4.00071	−0.133654
$897$	−44.1601	−1.47446
$898$	−2.14751	−0.0716632
$899$	−41.6484	−1.38905
$900$	−14.4591	−0.481970
$901$	−20.5760	−0.685488
$902$	−1.80118	−0.0599726
$903$	11.2328	0.373803
$904$	−13.6272	−0.453234
$905$	21.5794	0.717324
$906$	−5.47375	−0.181853
$907$	55.0516	1.82796	0.913980	−	0.405759i	$-0.132993\pi$
$907$	55.0516	1.82796	0.913980	+	0.405759i	$0.132993\pi$
$908$	30.0925	0.998655
$909$	168.331	5.58318
$910$	1.42363	0.0471928
$911$	−39.8582	−1.32056	−0.660280	−	0.751019i	$-0.729563\pi$
$911$	−39.8582	−1.32056	−0.660280	+	0.751019i	$0.729563\pi$
$912$	17.0521	0.564653
$913$	14.7196	0.487147
$914$	5.08319	0.168137
$915$	−8.65974	−0.286282
$916$	30.7738	1.01680
$917$	2.16368	0.0714509
$918$	−42.5113	−1.40308
$919$	11.5348	0.380499	0.190250	−	0.981736i	$-0.439070\pi$
$919$	11.5348	0.380499	0.190250	+	0.981736i	$0.439070\pi$
$920$	4.15956	0.137137
$921$	−35.6498	−1.17470
$922$	22.7646	0.749714
$923$	30.6990	1.01047
$924$	−1.96656	−0.0646952
$925$	−7.66685	−0.252084
$926$	−22.0454	−0.724458
$927$	104.546	3.43374
$928$	−53.8145	−1.76655
$929$	6.18823	0.203029	0.101515	−	0.994834i	$-0.467631\pi$
$929$	6.18823	0.203029	0.101515	+	0.994834i	$0.467631\pi$
$930$	8.92073	0.292522
$931$	17.4584	0.572175
$932$	−33.1215	−1.08493
$933$	−22.4694	−0.735614
$934$	5.60426	0.183377
$935$	3.51529	0.114962
$936$	−130.952	−4.28029
$937$	5.01922	0.163971	0.0819854	−	0.996634i	$-0.473874\pi$
$937$	5.01922	0.163971	0.0819854	+	0.996634i	$0.473874\pi$
$938$	1.83836	0.0600245
$939$	62.3266	2.03395
$940$	0.607700	0.0198210
$941$	−13.1397	−0.428342	−0.214171	−	0.976796i	$-0.568705\pi$
$941$	−13.1397	−0.428342	−0.214171	+	0.976796i	$0.568705\pi$
$942$	21.5119	0.700896
$943$	−5.67253	−0.184723
$944$	28.9135	0.941056
$945$	−7.00869	−0.227993
$946$	−5.63425	−0.183185
$947$	49.7279	1.61594	0.807969	−	0.589224i	$-0.200567\pi$
$947$	49.7279	1.61594	0.807969	+	0.589224i	$0.200567\pi$
$948$	−33.0606	−1.07376
$949$	−6.76394	−0.219567
$950$	1.52965	0.0496284
$951$	−13.6622	−0.443029
$952$	2.69080	0.0872093
$953$	28.1320	0.911284	0.455642	−	0.890163i	$-0.349410\pi$
$953$	28.1320	0.911284	0.455642	+	0.890163i	$0.349410\pi$
$954$	−31.1594	−1.00882
$955$	−11.9279	−0.385979
$956$	5.29664	0.171306
$957$	−33.2939	−1.07624
$958$	−2.84175	−0.0918129
$959$	5.17691	0.167171
$960$	−1.90934	−0.0616238
$961$	−12.4825	−0.402661
$962$	−31.2513	−1.00758
$963$	−18.0326	−0.581093
$964$	28.9893	0.933681
$965$	17.2084	0.553957
$966$	1.37413	0.0442118
$967$	−7.11979	−0.228957	−0.114478	−	0.993426i	$-0.536520\pi$
$967$	−7.11979	−0.228957	−0.114478	+	0.993426i	$0.536520\pi$
$968$	2.19167	0.0704430
$969$	−30.6944	−0.986047
$970$	−2.37993	−0.0764151
$971$	−27.2568	−0.874712	−0.437356	−	0.899289i	$-0.644085\pi$
$971$	−27.2568	−0.874712	−0.437356	+	0.899289i	$0.644085\pi$
$972$	140.939	4.52064
$973$	−4.44133	−0.142382
$974$	−6.78236	−0.217321
$975$	23.2679	0.745170
$976$	−4.91618	−0.157363
$977$	−46.0918	−1.47461	−0.737304	−	0.675561i	$-0.763902\pi$
$977$	−46.0918	−1.47461	−0.737304	+	0.675561i	$0.763902\pi$
$978$	35.4210	1.13264
$979$	−3.71724	−0.118803
$980$	−11.2582	−0.359630
$981$	−78.6546	−2.51125
$982$	1.81426	0.0578952
$983$	3.05817	0.0975406	0.0487703	−	0.998810i	$-0.484470\pi$
$983$	3.05817	0.0975406	0.0487703	+	0.998810i	$0.484470\pi$
$984$	−22.5340	−0.718356
$985$	−7.79112	−0.248246
$986$	20.5031	0.652952
$987$	0.446054	0.0141980
$988$	−28.1025	−0.894060
$989$	−17.7442	−0.564233
$990$	5.32338	0.169188
$991$	60.6183	1.92561	0.962803	−	0.270206i	$-0.0870916\pi$
$991$	60.6183	1.92561	0.962803	+	0.270206i	$0.0870916\pi$
$992$	23.9267	0.759674
$993$	−88.7749	−2.81719
$994$	−0.955259	−0.0302990
$995$	−1.14027	−0.0361490
$996$	82.8816	2.62620
$997$	−0.606614	−0.0192117	−0.00960583	−	0.999954i	$-0.503058\pi$
$997$	−0.606614	−0.0192117	−0.00960583	+	0.999954i	$0.503058\pi$
$998$	9.55927	0.302593
$999$	153.854	4.86773

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4015.2.a.f.1.14	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4015.2.a.f.1.14	✓	31	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)

\(f(q)\)	\(=\)	\(q-0.602631 q^{2} -3.44000 q^{3} -1.63684 q^{4} -1.00000 q^{5} +2.07305 q^{6} -0.349257 q^{7} +2.19167 q^{8} +8.83357 q^{9} +O(q^{10})\)	\(q-0.602631 q^{2} -3.44000 q^{3} -1.63684 q^{4} -1.00000 q^{5} +2.07305 q^{6} -0.349257 q^{7} +2.19167 q^{8} +8.83357 q^{9} +0.602631 q^{10} +1.00000 q^{11} +5.63071 q^{12} -6.76394 q^{13} +0.210473 q^{14} +3.44000 q^{15} +1.95290 q^{16} -3.51529 q^{17} -5.32338 q^{18} -2.53829 q^{19} +1.63684 q^{20} +1.20144 q^{21} -0.602631 q^{22} -1.89790 q^{23} -7.53934 q^{24} +1.00000 q^{25} +4.07616 q^{26} -20.0674 q^{27} +0.571676 q^{28} +9.67848 q^{29} -2.07305 q^{30} -4.30320 q^{31} -5.56022 q^{32} -3.44000 q^{33} +2.11842 q^{34} +0.349257 q^{35} -14.4591 q^{36} -7.66685 q^{37} +1.52965 q^{38} +23.2679 q^{39} -2.19167 q^{40} +2.98885 q^{41} -0.724026 q^{42} +9.34941 q^{43} -1.63684 q^{44} -8.83357 q^{45} +1.14373 q^{46} +0.371265 q^{47} -6.71798 q^{48} -6.87802 q^{49} -0.602631 q^{50} +12.0926 q^{51} +11.0715 q^{52} +5.85330 q^{53} +12.0933 q^{54} -1.00000 q^{55} -0.765456 q^{56} +8.73169 q^{57} -5.83255 q^{58} +14.8054 q^{59} -5.63071 q^{60} -2.51737 q^{61} +2.59324 q^{62} -3.08518 q^{63} -0.555043 q^{64} +6.76394 q^{65} +2.07305 q^{66} +8.73441 q^{67} +5.75395 q^{68} +6.52876 q^{69} -0.210473 q^{70} -4.53863 q^{71} +19.3603 q^{72} +1.00000 q^{73} +4.62028 q^{74} -3.44000 q^{75} +4.15476 q^{76} -0.349257 q^{77} -14.0220 q^{78} -5.87149 q^{79} -1.95290 q^{80} +42.5312 q^{81} -1.80118 q^{82} +14.7196 q^{83} -1.96656 q^{84} +3.51529 q^{85} -5.63425 q^{86} -33.2939 q^{87} +2.19167 q^{88} -3.71724 q^{89} +5.32338 q^{90} +2.36235 q^{91} +3.10655 q^{92} +14.8030 q^{93} -0.223736 q^{94} +2.53829 q^{95} +19.1271 q^{96} -3.94924 q^{97} +4.14491 q^{98} +8.83357 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q - 7 q^{2} - 4 q^{3} + 39 q^{4} - 31 q^{5} - 5 q^{6} - 11 q^{7} - 24 q^{8} + 31 q^{9}+O(q^{10}) \) 31 * q - 7 * q^2 - 4 * q^3 + 39 * q^4 - 31 * q^5 - 5 * q^6 - 11 * q^7 - 24 * q^8 + 31 * q^9	\( 31 q - 7 q^{2} - 4 q^{3} + 39 q^{4} - 31 q^{5} - 5 q^{6} - 11 q^{7} - 24 q^{8} + 31 q^{9} + 7 q^{10} + 31 q^{11} - 4 q^{12} - 24 q^{13} - 9 q^{14} + 4 q^{15} + 43 q^{16} - 49 q^{17} - 35 q^{18} - 22 q^{19} - 39 q^{20} - 8 q^{21} - 7 q^{22} - q^{23} - 13 q^{24} + 31 q^{25} - 9 q^{26} - 22 q^{27} - 34 q^{28} - 12 q^{29} + 5 q^{30} + 4 q^{31} - 45 q^{32} - 4 q^{33} + 2 q^{34} + 11 q^{35} + 34 q^{36} - 18 q^{37} - 7 q^{38} - q^{39} + 24 q^{40} - 58 q^{41} - 21 q^{42} - 41 q^{43} + 39 q^{44} - 31 q^{45} + 23 q^{46} - 31 q^{47} - 29 q^{48} + 44 q^{49} - 7 q^{50} + 8 q^{51} - 89 q^{52} - 46 q^{53} - 47 q^{54} - 31 q^{55} + 10 q^{56} - 47 q^{57} - 34 q^{58} - 9 q^{59} + 4 q^{60} - 5 q^{61} - 50 q^{62} - 61 q^{63} + 78 q^{64} + 24 q^{65} - 5 q^{66} + q^{67} - 115 q^{68} - 19 q^{69} + 9 q^{70} - 8 q^{71} - 93 q^{72} + 31 q^{73} - 19 q^{74} - 4 q^{75} - 7 q^{76} - 11 q^{77} + 57 q^{78} - 43 q^{80} + 43 q^{81} + 20 q^{82} - 29 q^{83} - 32 q^{84} + 49 q^{85} + 25 q^{86} - 62 q^{87} - 24 q^{88} - 77 q^{89} + 35 q^{90} - 11 q^{91} - 25 q^{92} - 38 q^{94} + 22 q^{95} - 23 q^{96} - 39 q^{97} - 65 q^{98} + 31 q^{99}+O(q^{100}) \) 31 * q - 7 * q^2 - 4 * q^3 + 39 * q^4 - 31 * q^5 - 5 * q^6 - 11 * q^7 - 24 * q^8 + 31 * q^9 + 7 * q^10 + 31 * q^11 - 4 * q^12 - 24 * q^13 - 9 * q^14 + 4 * q^15 + 43 * q^16 - 49 * q^17 - 35 * q^18 - 22 * q^19 - 39 * q^20 - 8 * q^21 - 7 * q^22 - q^23 - 13 * q^24 + 31 * q^25 - 9 * q^26 - 22 * q^27 - 34 * q^28 - 12 * q^29 + 5 * q^30 + 4 * q^31 - 45 * q^32 - 4 * q^33 + 2 * q^34 + 11 * q^35 + 34 * q^36 - 18 * q^37 - 7 * q^38 - q^39 + 24 * q^40 - 58 * q^41 - 21 * q^42 - 41 * q^43 + 39 * q^44 - 31 * q^45 + 23 * q^46 - 31 * q^47 - 29 * q^48 + 44 * q^49 - 7 * q^50 + 8 * q^51 - 89 * q^52 - 46 * q^53 - 47 * q^54 - 31 * q^55 + 10 * q^56 - 47 * q^57 - 34 * q^58 - 9 * q^59 + 4 * q^60 - 5 * q^61 - 50 * q^62 - 61 * q^63 + 78 * q^64 + 24 * q^65 - 5 * q^66 + q^67 - 115 * q^68 - 19 * q^69 + 9 * q^70 - 8 * q^71 - 93 * q^72 + 31 * q^73 - 19 * q^74 - 4 * q^75 - 7 * q^76 - 11 * q^77 + 57 * q^78 - 43 * q^80 + 43 * q^81 + 20 * q^82 - 29 * q^83 - 32 * q^84 + 49 * q^85 + 25 * q^86 - 62 * q^87 - 24 * q^88 - 77 * q^89 + 35 * q^90 - 11 * q^91 - 25 * q^92 - 38 * q^94 + 22 * q^95 - 23 * q^96 - 39 * q^97 - 65 * q^98 + 31 * q^99

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