LMFDB - Embedded newform 1805.2.a.i.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1805,2,Mod(1,1805)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1805, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1805.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1805 = 5 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1805.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:	$14.4129975648$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.7537.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 5x^{2} + 4x + 3 $ x^4 - x^3 - 5x^2 + 4x + 3
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-0.491918$ of defining polynomial
Character	$\chi$	$=$	1805.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.75802 q^{2} -1.49192 q^{3} +5.60665 q^{4} +1.00000 q^{5} +4.11474 q^{6} -2.84864 q^{7} -9.94721 q^{8} -0.774179 q^{9} +O(q^{10})$	\(q-2.75802 q^{2} -1.49192 q^{3} +5.60665 q^{4} +1.00000 q^{5} +4.11474 q^{6} -2.84864 q^{7} -9.94721 q^{8} -0.774179 q^{9} -2.75802 q^{10} -0.864801 q^{11} -8.36467 q^{12} -0.643281 q^{13} +7.85659 q^{14} -1.49192 q^{15} +16.2213 q^{16} +3.74185 q^{17} +2.13520 q^{18} +5.60665 q^{20} +4.24993 q^{21} +2.38513 q^{22} +0.417460 q^{23} +14.8404 q^{24} +1.00000 q^{25} +1.77418 q^{26} +5.63077 q^{27} -15.9713 q^{28} +9.70523 q^{29} +4.11474 q^{30} -4.93349 q^{31} -24.8441 q^{32} +1.29021 q^{33} -10.3201 q^{34} -2.84864 q^{35} -4.34056 q^{36} -6.36467 q^{37} +0.959723 q^{39} -9.94721 q^{40} +4.01372 q^{41} -11.7214 q^{42} -2.05829 q^{43} -4.84864 q^{44} -0.774179 q^{45} -1.15136 q^{46} -3.95396 q^{47} -24.2008 q^{48} +1.11474 q^{49} -2.75802 q^{50} -5.58254 q^{51} -3.60665 q^{52} +10.9875 q^{53} -15.5297 q^{54} -0.864801 q^{55} +28.3360 q^{56} -26.7672 q^{58} -2.45959 q^{59} -8.36467 q^{60} +6.33479 q^{61} +13.6067 q^{62} +2.20536 q^{63} +36.0778 q^{64} -0.643281 q^{65} -3.55843 q^{66} +2.53220 q^{67} +20.9793 q^{68} -0.622817 q^{69} +7.85659 q^{70} +1.78213 q^{71} +7.70092 q^{72} -7.13090 q^{73} +17.5539 q^{74} -1.49192 q^{75} +2.46350 q^{77} -2.64693 q^{78} -1.82452 q^{79} +16.2213 q^{80} -6.07811 q^{81} -11.0699 q^{82} -7.43913 q^{83} +23.8279 q^{84} +3.74185 q^{85} +5.67681 q^{86} -14.4794 q^{87} +8.60235 q^{88} -4.44588 q^{89} +2.13520 q^{90} +1.83247 q^{91} +2.34056 q^{92} +7.36037 q^{93} +10.9051 q^{94} +37.0653 q^{96} +10.8541 q^{97} -3.07446 q^{98} +0.669511 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} - 3 q^{3} + 5 q^{4} + 4 q^{5} + 2 q^{6} - 4 q^{7} - 12 q^{8} + q^{9}+O(q^{10}) $ 4 * q - q^2 - 3 * q^3 + 5 * q^4 + 4 * q^5 + 2 * q^6 - 4 * q^7 - 12 * q^8 + q^9	$ 4 q - q^{2} - 3 q^{3} + 5 q^{4} + 4 q^{5} + 2 q^{6} - 4 q^{7} - 12 q^{8} + q^{9} - q^{10} - 2 q^{11} - 6 q^{12} - 7 q^{13} + q^{14} - 3 q^{15} + 7 q^{16} - q^{17} + 10 q^{18} + 5 q^{20} + 4 q^{21} - 2 q^{22} + 2 q^{23} + 23 q^{24} + 4 q^{25} + 3 q^{26} - 12 q^{27} - 19 q^{28} + q^{29} + 2 q^{30} - 30 q^{32} - 19 q^{33} - 15 q^{34} - 4 q^{35} - 7 q^{36} + 2 q^{37} + 15 q^{39} - 12 q^{40} + 8 q^{41} - 15 q^{42} + q^{43} - 12 q^{44} + q^{45} - 12 q^{46} - 12 q^{47} - 23 q^{48} - 10 q^{49} - q^{50} - 22 q^{51} + 3 q^{52} + 5 q^{53} - 34 q^{54} - 2 q^{55} + 41 q^{56} - 27 q^{58} + 5 q^{59} - 6 q^{60} + 37 q^{62} - 3 q^{63} + 56 q^{64} - 7 q^{65} - 31 q^{66} - 4 q^{67} + 16 q^{68} + 9 q^{69} + q^{70} - 20 q^{71} - 17 q^{72} - 20 q^{73} + 25 q^{74} - 3 q^{75} + 14 q^{77} + 18 q^{78} - 17 q^{79} + 7 q^{80} + 12 q^{81} + 21 q^{82} + q^{83} + 20 q^{84} - q^{85} - 8 q^{86} - 16 q^{87} + 7 q^{88} - 11 q^{89} + 10 q^{90} - 6 q^{91} - q^{92} - 8 q^{93} + 31 q^{94} + 21 q^{96} - q^{97} - 9 q^{98} + 38 q^{99}+O(q^{100}) $ 4 * q - q^2 - 3 * q^3 + 5 * q^4 + 4 * q^5 + 2 * q^6 - 4 * q^7 - 12 * q^8 + q^9 - q^10 - 2 * q^11 - 6 * q^12 - 7 * q^13 + q^14 - 3 * q^15 + 7 * q^16 - q^17 + 10 * q^18 + 5 * q^20 + 4 * q^21 - 2 * q^22 + 2 * q^23 + 23 * q^24 + 4 * q^25 + 3 * q^26 - 12 * q^27 - 19 * q^28 + q^29 + 2 * q^30 - 30 * q^32 - 19 * q^33 - 15 * q^34 - 4 * q^35 - 7 * q^36 + 2 * q^37 + 15 * q^39 - 12 * q^40 + 8 * q^41 - 15 * q^42 + q^43 - 12 * q^44 + q^45 - 12 * q^46 - 12 * q^47 - 23 * q^48 - 10 * q^49 - q^50 - 22 * q^51 + 3 * q^52 + 5 * q^53 - 34 * q^54 - 2 * q^55 + 41 * q^56 - 27 * q^58 + 5 * q^59 - 6 * q^60 + 37 * q^62 - 3 * q^63 + 56 * q^64 - 7 * q^65 - 31 * q^66 - 4 * q^67 + 16 * q^68 + 9 * q^69 + q^70 - 20 * q^71 - 17 * q^72 - 20 * q^73 + 25 * q^74 - 3 * q^75 + 14 * q^77 + 18 * q^78 - 17 * q^79 + 7 * q^80 + 12 * q^81 + 21 * q^82 + q^83 + 20 * q^84 - q^85 - 8 * q^86 - 16 * q^87 + 7 * q^88 - 11 * q^89 + 10 * q^90 - 6 * q^91 - q^92 - 8 * q^93 + 31 * q^94 + 21 * q^96 - q^97 - 9 * q^98 + 38 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.75802	−1.95021	−0.975106	−	0.221739i	$-0.928827\pi$
$2$	−2.75802	−1.95021	−0.975106	+	0.221739i	$0.928827\pi$
$3$	−1.49192	−0.861360	−0.430680	−	0.902505i	$-0.641726\pi$
$3$	−1.49192	−0.861360	−0.430680	+	0.902505i	$0.641726\pi$
$4$	5.60665	2.80333
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	4.11474	1.67983
$7$	−2.84864	−1.07668	−0.538342	−	0.842727i	$-0.680949\pi$
$7$	−2.84864	−1.07668	−0.538342	+	0.842727i	$0.680949\pi$
$8$	−9.94721	−3.51687
$9$	−0.774179	−0.258060
$10$	−2.75802	−0.872161
$11$	−0.864801	−0.260747	−0.130374	−	0.991465i	$-0.541618\pi$
$11$	−0.864801	−0.260747	−0.130374	+	0.991465i	$0.541618\pi$
$12$	−8.36467	−2.41467
$13$	−0.643281	−0.178414	−0.0892070	−	0.996013i	$-0.528433\pi$
$13$	−0.643281	−0.178414	−0.0892070	+	0.996013i	$0.528433\pi$
$14$	7.85659	2.09976
$15$	−1.49192	−0.385212
$16$	16.2213	4.05531
$17$	3.74185	0.907533	0.453766	−	0.891121i	$-0.350080\pi$
$17$	3.74185	0.907533	0.453766	+	0.891121i	$0.350080\pi$
$18$	2.13520	0.503271
$19$	0	0
$19$	0	0
$20$	5.60665	1.25369
$21$	4.24993	0.927412
$22$	2.38513	0.508512
$23$	0.417460	0.0870465	0.0435233	−	0.999052i	$-0.486142\pi$
$23$	0.417460	0.0870465	0.0435233	+	0.999052i	$0.486142\pi$
$24$	14.8404	3.02929
$25$	1.00000	0.200000
$26$	1.77418	0.347945
$27$	5.63077	1.08364
$28$	−15.9713	−3.01830
$29$	9.70523	1.80222	0.901108	−	0.433596i	$-0.142755\pi$
$29$	9.70523	1.80222	0.901108	+	0.433596i	$0.142755\pi$
$30$	4.11474	0.751244
$31$	−4.93349	−0.886081	−0.443041	−	0.896501i	$-0.646100\pi$
$31$	−4.93349	−0.886081	−0.443041	+	0.896501i	$0.646100\pi$
$32$	−24.8441	−4.39185
$33$	1.29021	0.224597
$34$	−10.3201	−1.76988
$35$	−2.84864	−0.481508
$36$	−4.34056	−0.723426
$37$	−6.36467	−1.04635	−0.523173	−	0.852227i	$-0.675252\pi$
$37$	−6.36467	−1.04635	−0.523173	+	0.852227i	$0.675252\pi$
$38$	0	0
$39$	0.959723	0.153679
$40$	−9.94721	−1.57279
$41$	4.01372	0.626837	0.313419	−	0.949615i	$-0.398526\pi$
$41$	4.01372	0.626837	0.313419	+	0.949615i	$0.398526\pi$
$42$	−11.7214	−1.80865
$43$	−2.05829	−0.313887	−0.156944	−	0.987608i	$-0.550164\pi$
$43$	−2.05829	−0.313887	−0.156944	+	0.987608i	$0.550164\pi$
$44$	−4.84864	−0.730960
$45$	−0.774179	−0.115408
$46$	−1.15136	−0.169759
$47$	−3.95396	−0.576744	−0.288372	−	0.957518i	$-0.593114\pi$
$47$	−3.95396	−0.576744	−0.288372	+	0.957518i	$0.593114\pi$
$48$	−24.2008	−3.49308
$49$	1.11474	0.159248
$50$	−2.75802	−0.390042
$51$	−5.58254	−0.781712
$52$	−3.60665	−0.500153
$53$	10.9875	1.50925	0.754624	−	0.656158i	$-0.227819\pi$
$53$	10.9875	1.50925	0.754624	+	0.656158i	$0.227819\pi$
$54$	−15.5297	−2.11333
$55$	−0.864801	−0.116610
$56$	28.3360	3.78656
$57$	0	0
$58$	−26.7672	−3.51470
$59$	−2.45959	−0.320212	−0.160106	−	0.987100i	$-0.551184\pi$
$59$	−2.45959	−0.320212	−0.160106	+	0.987100i	$0.551184\pi$
$60$	−8.36467	−1.07987
$61$	6.33479	0.811087	0.405543	−	0.914076i	$-0.367082\pi$
$61$	6.33479	0.811087	0.405543	+	0.914076i	$0.367082\pi$
$62$	13.6067	1.72805
$63$	2.20536	0.277849
$64$	36.0778	4.50973
$65$	−0.643281	−0.0797892
$66$	−3.55843	−0.438012
$67$	2.53220	0.309357	0.154678	−	0.987965i	$-0.450566\pi$
$67$	2.53220	0.309357	0.154678	+	0.987965i	$0.450566\pi$
$68$	20.9793	2.54411
$69$	−0.622817	−0.0749783
$70$	7.85659	0.939042
$71$	1.78213	0.211500	0.105750	−	0.994393i	$-0.466276\pi$
$71$	1.78213	0.211500	0.105750	+	0.994393i	$0.466276\pi$
$72$	7.70092	0.907563
$73$	−7.13090	−0.834609	−0.417304	−	0.908767i	$-0.637025\pi$
$73$	−7.13090	−0.834609	−0.417304	+	0.908767i	$0.637025\pi$
$74$	17.5539	2.04060
$75$	−1.49192	−0.172272
$76$	0	0
$77$	2.46350	0.280742
$78$	−2.64693	−0.299706
$79$	−1.82452	−0.205275	−0.102637	−	0.994719i	$-0.532728\pi$
$79$	−1.82452	−0.205275	−0.102637	+	0.994719i	$0.532728\pi$
$80$	16.2213	1.81359
$81$	−6.07811	−0.675345
$82$	−11.0699	−1.22247
$83$	−7.43913	−0.816550	−0.408275	−	0.912859i	$-0.633870\pi$
$83$	−7.43913	−0.816550	−0.408275	+	0.912859i	$0.633870\pi$
$84$	23.8279	2.59984
$85$	3.74185	0.405861
$86$	5.67681	0.612146
$87$	−14.4794	−1.55236
$88$	8.60235	0.917014
$89$	−4.44588	−0.471262	−0.235631	−	0.971843i	$-0.575716\pi$
$89$	−4.44588	−0.471262	−0.235631	+	0.971843i	$0.575716\pi$
$90$	2.13520	0.225070
$91$	1.83247	0.192096
$92$	2.34056	0.244020
$93$	7.36037	0.763235
$94$	10.9051	1.12477
$95$	0	0
$96$	37.0653	3.78296
$97$	10.8541	1.10207	0.551036	−	0.834482i	$-0.314233\pi$
$97$	10.8541	1.10207	0.551036	+	0.834482i	$0.314233\pi$
$98$	−3.07446	−0.310567
$99$	0.669511	0.0672884
$100$	5.60665	0.560665
$101$	−5.29598	−0.526969	−0.263485	−	0.964664i	$-0.584872\pi$
$101$	−5.29598	−0.526969	−0.263485	+	0.964664i	$0.584872\pi$
$102$	15.3967	1.52450
$103$	0.385134	0.0379484	0.0189742	−	0.999820i	$-0.493960\pi$
$103$	0.385134	0.0379484	0.0189742	+	0.999820i	$0.493960\pi$
$104$	6.39885	0.627459
$105$	4.24993	0.414751
$106$	−30.3037	−2.94335
$107$	6.43336	0.621937	0.310968	−	0.950420i	$-0.399347\pi$
$107$	6.43336	0.621937	0.310968	+	0.950420i	$0.399347\pi$
$108$	31.5698	3.03780
$109$	−6.56882	−0.629179	−0.314590	−	0.949228i	$-0.601867\pi$
$109$	−6.56882	−0.629179	−0.314590	+	0.949228i	$0.601867\pi$
$110$	2.38513	0.227414
$111$	9.49557	0.901279
$112$	−46.2085	−4.36629
$113$	−0.294513	−0.0277054	−0.0138527	−	0.999904i	$-0.504410\pi$
$113$	−0.294513	−0.0277054	−0.0138527	+	0.999904i	$0.504410\pi$
$114$	0	0
$115$	0.417460	0.0389284
$116$	54.4138	5.05220
$117$	0.498015	0.0460415
$118$	6.78360	0.624481
$119$	−10.6592	−0.977126
$120$	14.8404	1.35474
$121$	−10.2521	−0.932011
$122$	−17.4715	−1.58179
$123$	−5.98814	−0.539932
$124$	−27.6604	−2.48398
$125$	1.00000	0.0894427
$126$	−6.08241	−0.541864
$127$	−8.83492	−0.783972	−0.391986	−	0.919971i	$-0.628212\pi$
$127$	−8.83492	−0.783972	−0.391986	+	0.919971i	$0.628212\pi$
$128$	−49.8151	−4.40308
$129$	3.07081	0.270370
$130$	1.77418	0.155606
$131$	20.9128	1.82716	0.913578	−	0.406662i	$-0.133307\pi$
$131$	20.9128	1.82716	0.913578	+	0.406662i	$0.133307\pi$
$132$	7.23377	0.629619
$133$	0	0
$134$	−6.98384	−0.603312
$135$	5.63077	0.484619
$136$	−37.2210	−3.19167
$137$	5.21477	0.445528	0.222764	−	0.974872i	$-0.428492\pi$
$137$	5.21477	0.445528	0.222764	+	0.974872i	$0.428492\pi$
$138$	1.71774	0.146224
$139$	−10.7238	−0.909584	−0.454792	−	0.890598i	$-0.650286\pi$
$139$	−10.7238	−0.909584	−0.454792	+	0.890598i	$0.650286\pi$
$140$	−15.9713	−1.34982
$141$	5.89898	0.496784
$142$	−4.91514	−0.412470
$143$	0.556310	0.0465210
$144$	−12.5582	−1.04651
$145$	9.70523	0.805975
$146$	19.6671	1.62766
$147$	−1.66309	−0.137170
$148$	−35.6845	−2.93325
$149$	−14.9116	−1.22160	−0.610801	−	0.791784i	$-0.709153\pi$
$149$	−14.9116	−1.22160	−0.610801	+	0.791784i	$0.709153\pi$
$150$	4.11474	0.335967
$151$	−21.4589	−1.74630	−0.873152	−	0.487448i	$-0.837928\pi$
$151$	−21.4589	−1.74630	−0.873152	+	0.487448i	$0.837928\pi$
$152$	0	0
$153$	−2.89687	−0.234198
$154$	−6.79438	−0.547507
$155$	−4.93349	−0.396268
$156$	5.38083	0.430811
$157$	−2.43118	−0.194029	−0.0970145	−	0.995283i	$-0.530929\pi$
$157$	−2.43118	−0.194029	−0.0970145	+	0.995283i	$0.530929\pi$
$158$	5.03207	0.400330
$159$	−16.3924	−1.30000
$160$	−24.8441	−1.96410
$161$	−1.18919	−0.0937216
$162$	16.7635	1.31707
$163$	17.8175	1.39558	0.697788	−	0.716305i	$-0.254168\pi$
$163$	17.8175	1.39558	0.697788	+	0.716305i	$0.254168\pi$
$164$	22.5035	1.75723
$165$	1.29021	0.100443
$166$	20.5172	1.59245
$167$	0.405598	0.0313861	0.0156931	−	0.999877i	$-0.495005\pi$
$167$	0.405598	0.0313861	0.0156931	+	0.999877i	$0.495005\pi$
$168$	−42.2750	−3.26159
$169$	−12.5862	−0.968168
$170$	−10.3201	−0.791515
$171$	0	0
$172$	−11.5401	−0.879928
$173$	−18.0210	−1.37011	−0.685056	−	0.728490i	$-0.740222\pi$
$173$	−18.0210	−1.37011	−0.685056	+	0.728490i	$0.740222\pi$
$174$	39.9344	3.02742
$175$	−2.84864	−0.215337
$176$	−14.0282	−1.05741
$177$	3.66951	0.275817
$178$	12.2618	0.919061
$179$	−20.1523	−1.50625	−0.753127	−	0.657875i	$-0.771455\pi$
$179$	−20.1523	−1.50625	−0.753127	+	0.657875i	$0.771455\pi$
$180$	−4.34056	−0.323526
$181$	17.1108	1.27184	0.635919	−	0.771756i	$-0.280621\pi$
$181$	17.1108	1.27184	0.635919	+	0.771756i	$0.280621\pi$
$182$	−5.05399	−0.374627
$183$	−9.45099	−0.698637
$184$	−4.15257	−0.306131
$185$	−6.36467	−0.467940
$186$	−20.3000	−1.48847
$187$	−3.23596	−0.236637
$188$	−22.1685	−1.61680
$189$	−16.0400	−1.16674
$190$	0	0
$191$	5.28080	0.382105	0.191053	−	0.981580i	$-0.438810\pi$
$191$	5.28080	0.382105	0.191053	+	0.981580i	$0.438810\pi$
$192$	−53.8252	−3.88450
$193$	−18.0036	−1.29593	−0.647966	−	0.761670i	$-0.724380\pi$
$193$	−18.0036	−1.29593	−0.647966	+	0.761670i	$0.724380\pi$
$194$	−29.9359	−2.14927
$195$	0.959723	0.0687272
$196$	6.24993	0.446424
$197$	8.07785	0.575523	0.287761	−	0.957702i	$-0.407089\pi$
$197$	8.07785	0.575523	0.287761	+	0.957702i	$0.407089\pi$
$198$	−1.84652	−0.131227
$199$	1.40374	0.0995088	0.0497544	−	0.998761i	$-0.484156\pi$
$199$	1.40374	0.0995088	0.0497544	+	0.998761i	$0.484156\pi$
$200$	−9.94721	−0.703374
$201$	−3.77783	−0.266468
$202$	14.6064	1.02770
$203$	−27.6467	−1.94042
$204$	−31.2994	−2.19139
$205$	4.01372	0.280330
$206$	−1.06221	−0.0740074
$207$	−0.323189	−0.0224632
$208$	−10.4348	−0.723525
$209$	0	0
$210$	−11.7214	−0.808853
$211$	−18.9163	−1.30226	−0.651128	−	0.758968i	$-0.725704\pi$
$211$	−18.9163	−1.30226	−0.651128	+	0.758968i	$0.725704\pi$
$212$	61.6030	4.23091
$213$	−2.65879	−0.182178
$214$	−17.7433	−1.21291
$215$	−2.05829	−0.140375
$216$	−56.0104	−3.81103
$217$	14.0537	0.954030
$218$	18.1169	1.22703
$219$	10.6387	0.718898
$220$	−4.84864	−0.326895
$221$	−2.40706	−0.161917
$222$	−26.1889	−1.75769
$223$	16.1480	1.08135	0.540675	−	0.841231i	$-0.318169\pi$
$223$	16.1480	1.08135	0.540675	+	0.841231i	$0.318169\pi$
$224$	70.7718	4.72864
$225$	−0.774179	−0.0516120
$226$	0.812271	0.0540315
$227$	−26.3186	−1.74683	−0.873414	−	0.486978i	$-0.838099\pi$
$227$	−26.3186	−1.74683	−0.873414	+	0.486978i	$0.838099\pi$
$228$	0	0
$229$	−13.3323	−0.881026	−0.440513	−	0.897746i	$-0.645203\pi$
$229$	−13.3323	−0.881026	−0.440513	+	0.897746i	$0.645203\pi$
$230$	−1.15136	−0.0759186
$231$	−3.67535	−0.241820
$232$	−96.5399	−6.33816
$233$	25.3094	1.65808	0.829038	−	0.559192i	$-0.188889\pi$
$233$	25.3094	1.65808	0.829038	+	0.559192i	$0.188889\pi$
$234$	−1.37353	−0.0897907
$235$	−3.95396	−0.257928
$236$	−13.7901	−0.897658
$237$	2.72204	0.176815
$238$	29.3982	1.90560
$239$	−23.5500	−1.52332	−0.761660	−	0.647977i	$-0.775615\pi$
$239$	−23.5500	−1.52332	−0.761660	+	0.647977i	$0.775615\pi$
$240$	−24.2008	−1.56215
$241$	−8.38415	−0.540071	−0.270035	−	0.962850i	$-0.587035\pi$
$241$	−8.38415	−0.540071	−0.270035	+	0.962850i	$0.587035\pi$
$242$	28.2755	1.81762
$243$	−7.82426	−0.501927
$244$	35.5170	2.27374
$245$	1.11474	0.0712178
$246$	16.5154	1.05298
$247$	0	0
$248$	49.0745	3.11623
$249$	11.0986	0.703343
$250$	−2.75802	−0.174432
$251$	18.2478	1.15179	0.575896	−	0.817523i	$-0.304653\pi$
$251$	18.2478	1.15179	0.575896	+	0.817523i	$0.304653\pi$
$252$	12.3647	0.778901
$253$	−0.361020	−0.0226971
$254$	24.3669	1.52891
$255$	−5.58254	−0.349592
$256$	65.2353	4.07720
$257$	−14.0998	−0.879520	−0.439760	−	0.898115i	$-0.644936\pi$
$257$	−14.0998	−0.879520	−0.439760	+	0.898115i	$0.644936\pi$
$258$	−8.46934	−0.527278
$259$	18.1306	1.12658
$260$	−3.60665	−0.223675
$261$	−7.51359	−0.465079
$262$	−57.6778	−3.56334
$263$	−6.41071	−0.395301	−0.197651	−	0.980273i	$-0.563331\pi$
$263$	−6.41071	−0.395301	−0.197651	+	0.980273i	$0.563331\pi$
$264$	−12.8340	−0.789879
$265$	10.9875	0.674956
$266$	0	0
$267$	6.63288	0.405926
$268$	14.1971	0.867229
$269$	−17.9911	−1.09694	−0.548469	−	0.836171i	$-0.684789\pi$
$269$	−17.9911	−1.09694	−0.548469	+	0.836171i	$0.684789\pi$
$270$	−15.5297	−0.945110
$271$	11.8819	0.721774	0.360887	−	0.932609i	$-0.382474\pi$
$271$	11.8819	0.721774	0.360887	+	0.932609i	$0.382474\pi$
$272$	60.6976	3.68033
$273$	−2.73390	−0.165463
$274$	−14.3824	−0.868874
$275$	−0.864801	−0.0521494
$276$	−3.49192	−0.210189
$277$	23.6240	1.41943	0.709715	−	0.704489i	$-0.248824\pi$
$277$	23.6240	1.41943	0.709715	+	0.704489i	$0.248824\pi$
$278$	29.5765	1.77388
$279$	3.81941	0.228662
$280$	28.3360	1.69340
$281$	−13.8093	−0.823794	−0.411897	−	0.911230i	$-0.635134\pi$
$281$	−13.8093	−0.823794	−0.411897	+	0.911230i	$0.635134\pi$
$282$	−16.2695	−0.968834
$283$	−11.7574	−0.698903	−0.349451	−	0.936954i	$-0.613632\pi$
$283$	−11.7574	−0.698903	−0.349451	+	0.936954i	$0.613632\pi$
$284$	9.99179	0.592904
$285$	0	0
$286$	−1.53431	−0.0907257
$287$	−11.4336	−0.674905
$288$	19.2338	1.13336
$289$	−2.99854	−0.176384
$290$	−26.7672	−1.57182
$291$	−16.1935	−0.949279
$292$	−39.9805	−2.33968
$293$	27.0576	1.58072	0.790362	−	0.612640i	$-0.209892\pi$
$293$	27.0576	1.58072	0.790362	+	0.612640i	$0.209892\pi$
$294$	4.58684	0.267510
$295$	−2.45959	−0.143203
$296$	63.3107	3.67986
$297$	−4.86949	−0.282557
$298$	41.1263	2.38238
$299$	−0.268544	−0.0155303
$300$	−8.36467	−0.482934
$301$	5.86334	0.337957
$302$	59.1841	3.40566
$303$	7.90117	0.453910
$304$	0	0
$305$	6.33479	0.362729
$306$	7.98960	0.456735
$307$	−8.83824	−0.504425	−0.252212	−	0.967672i	$-0.581158\pi$
$307$	−8.83824	−0.504425	−0.252212	+	0.967672i	$0.581158\pi$
$308$	13.8120	0.787012
$309$	−0.574589	−0.0326872
$310$	13.6067	0.772806
$311$	−0.651493	−0.0369428	−0.0184714	−	0.999829i	$-0.505880\pi$
$311$	−0.651493	−0.0369428	−0.0184714	+	0.999829i	$0.505880\pi$
$312$	−9.54656	−0.540468
$313$	−2.96556	−0.167623	−0.0838116	−	0.996482i	$-0.526709\pi$
$313$	−2.96556	−0.167623	−0.0838116	+	0.996482i	$0.526709\pi$
$314$	6.70523	0.378398
$315$	2.20536	0.124258
$316$	−10.2295	−0.575453
$317$	10.3799	0.582991	0.291495	−	0.956572i	$-0.405847\pi$
$317$	10.3799	0.582991	0.291495	+	0.956572i	$0.405847\pi$
$318$	45.2106	2.53528
$319$	−8.39309	−0.469923
$320$	36.0778	2.01681
$321$	−9.59805	−0.535711
$322$	3.27981	0.182777
$323$	0	0
$324$	−34.0778	−1.89321
$325$	−0.643281	−0.0356828
$326$	−49.1410	−2.72167
$327$	9.80015	0.541949
$328$	−39.9253	−2.20450
$329$	11.2634	0.620971
$330$	−3.55843	−0.195885
$331$	−15.0922	−0.829543	−0.414772	−	0.909926i	$-0.636139\pi$
$331$	−15.0922	−0.829543	−0.414772	+	0.909926i	$0.636139\pi$
$332$	−41.7086	−2.28906
$333$	4.92740	0.270020
$334$	−1.11865	−0.0612096
$335$	2.53220	0.138349
$336$	68.9393	3.76095
$337$	−15.7974	−0.860541	−0.430271	−	0.902700i	$-0.641582\pi$
$337$	−15.7974	−0.860541	−0.430271	+	0.902700i	$0.641582\pi$
$338$	34.7129	1.88813
$339$	0.439389	0.0238643
$340$	20.9793	1.13776
$341$	4.26649	0.231043
$342$	0	0
$343$	16.7650	0.905224
$344$	20.4743	1.10390
$345$	−0.622817	−0.0335313
$346$	49.7023	2.67201
$347$	−21.3522	−1.14624	−0.573122	−	0.819470i	$-0.694268\pi$
$347$	−21.3522	−1.14624	−0.573122	+	0.819470i	$0.694268\pi$
$348$	−81.1810	−4.35176
$349$	−32.3897	−1.73378	−0.866891	−	0.498497i	$-0.833885\pi$
$349$	−32.3897	−1.73378	−0.866891	+	0.498497i	$0.833885\pi$
$350$	7.85659	0.419952
$351$	−3.62217	−0.193337
$352$	21.4852	1.14516
$353$	0.730583	0.0388850	0.0194425	−	0.999811i	$-0.493811\pi$
$353$	0.730583	0.0388850	0.0194425	+	0.999811i	$0.493811\pi$
$354$	−10.1206	−0.537902
$355$	1.78213	0.0945857
$356$	−24.9265	−1.32110
$357$	15.9026	0.841657
$358$	55.5804	2.93751
$359$	−26.8496	−1.41707	−0.708533	−	0.705677i	$-0.750643\pi$
$359$	−26.8496	−1.41707	−0.708533	+	0.705677i	$0.750643\pi$
$360$	7.70092	0.405874
$361$	0	0
$362$	−47.1919	−2.48035
$363$	15.2953	0.802796
$364$	10.2740	0.538506
$365$	−7.13090	−0.373248
$366$	26.0660	1.36249
$367$	−22.9643	−1.19873	−0.599364	−	0.800477i	$-0.704580\pi$
$367$	−22.9643	−1.19873	−0.599364	+	0.800477i	$0.704580\pi$
$368$	6.77173	0.353001
$369$	−3.10734	−0.161761
$370$	17.5539	0.912582
$371$	−31.2994	−1.62498
$372$	41.2670	2.13960
$373$	−29.5305	−1.52903	−0.764515	−	0.644606i	$-0.777021\pi$
$373$	−29.5305	−1.52903	−0.764515	+	0.644606i	$0.777021\pi$
$374$	8.92482	0.461492
$375$	−1.49192	−0.0770423
$376$	39.3308	2.02833
$377$	−6.24319	−0.321541
$378$	44.2386	2.27539
$379$	−17.5117	−0.899517	−0.449759	−	0.893150i	$-0.648490\pi$
$379$	−17.5117	−0.899517	−0.449759	+	0.893150i	$0.648490\pi$
$380$	0	0
$381$	13.1810	0.675282
$382$	−14.5645	−0.745186
$383$	−8.10652	−0.414224	−0.207112	−	0.978317i	$-0.566406\pi$
$383$	−8.10652	−0.414224	−0.207112	+	0.978317i	$0.566406\pi$
$384$	74.3201	3.79263
$385$	2.46350	0.125552
$386$	49.6544	2.52734
$387$	1.59349	0.0810016
$388$	60.8554	3.08947
$389$	17.3078	0.877542	0.438771	−	0.898599i	$-0.355414\pi$
$389$	17.3078	0.877542	0.438771	+	0.898599i	$0.355414\pi$
$390$	−2.64693	−0.134033
$391$	1.56208	0.0789976
$392$	−11.0885	−0.560054
$393$	−31.2001	−1.57384
$394$	−22.2788	−1.12239
$395$	−1.82452	−0.0918017
$396$	3.75372	0.188631
$397$	−11.3894	−0.571619	−0.285810	−	0.958286i	$-0.592263\pi$
$397$	−11.3894	−0.571619	−0.285810	+	0.958286i	$0.592263\pi$
$398$	−3.87155	−0.194063
$399$	0	0
$400$	16.2213	0.811063
$401$	8.93861	0.446373	0.223186	−	0.974776i	$-0.428354\pi$
$401$	8.93861	0.446373	0.223186	+	0.974776i	$0.428354\pi$
$402$	10.4193	0.519668
$403$	3.17362	0.158089
$404$	−29.6927	−1.47727
$405$	−6.07811	−0.302024
$406$	76.2500	3.78422
$407$	5.50417	0.272832
$408$	55.5307	2.74918
$409$	6.54471	0.323615	0.161808	−	0.986822i	$-0.448268\pi$
$409$	6.54471	0.323615	0.161808	+	0.986822i	$0.448268\pi$
$410$	−11.0699	−0.546703
$411$	−7.78001	−0.383760
$412$	2.15931	0.106382
$413$	7.00649	0.344767
$414$	0.891361	0.0438080
$415$	−7.43913	−0.365172
$416$	15.9817	0.783568
$417$	15.9991	0.783479
$418$	0	0
$419$	21.8441	1.06715	0.533576	−	0.845752i	$-0.320848\pi$
$419$	21.8441	1.06715	0.533576	+	0.845752i	$0.320848\pi$
$420$	23.8279	1.16268
$421$	29.3434	1.43011	0.715054	−	0.699069i	$-0.246402\pi$
$421$	29.3434	1.43011	0.715054	+	0.699069i	$0.246402\pi$
$422$	52.1716	2.53967
$423$	3.06107	0.148834
$424$	−109.295	−5.30783
$425$	3.74185	0.181507
$426$	7.33299	0.355285
$427$	−18.0455	−0.873284
$428$	36.0696	1.74349
$429$	−0.829969	−0.0400713
$430$	5.67681	0.273760
$431$	12.8867	0.620732	0.310366	−	0.950617i	$-0.399548\pi$
$431$	12.8867	0.620732	0.310366	+	0.950617i	$0.399548\pi$
$432$	91.3381	4.39451
$433$	13.8429	0.665246	0.332623	−	0.943060i	$-0.392066\pi$
$433$	13.8429	0.665246	0.332623	+	0.943060i	$0.392066\pi$
$434$	−38.7604	−1.86056
$435$	−14.4794	−0.694234
$436$	−36.8291	−1.76379
$437$	0	0
$438$	−29.3418	−1.40200
$439$	0.0708081	0.00337948	0.00168974	−	0.999999i	$-0.499462\pi$
$439$	0.0708081	0.00337948	0.00168974	+	0.999999i	$0.499462\pi$
$440$	8.60235	0.410101
$441$	−0.863005	−0.0410955
$442$	6.63872	0.315772
$443$	−3.78914	−0.180027	−0.0900137	−	0.995941i	$-0.528691\pi$
$443$	−3.78914	−0.180027	−0.0900137	+	0.995941i	$0.528691\pi$
$444$	53.2384	2.52658
$445$	−4.44588	−0.210755
$446$	−44.5365	−2.10886
$447$	22.2468	1.05224
$448$	−102.773	−4.85555
$449$	26.5765	1.25422	0.627112	−	0.778929i	$-0.284237\pi$
$449$	26.5765	1.25422	0.627112	+	0.778929i	$0.284237\pi$
$450$	2.13520	0.100654
$451$	−3.47106	−0.163446
$452$	−1.65123	−0.0776674
$453$	32.0150	1.50420
$454$	72.5872	3.40669
$455$	1.83247	0.0859077
$456$	0	0
$457$	−33.1523	−1.55080	−0.775400	−	0.631471i	$-0.782452\pi$
$457$	−33.1523	−1.55080	−0.775400	+	0.631471i	$0.782452\pi$
$458$	36.7708	1.71819
$459$	21.0695	0.983440
$460$	2.34056	0.109129
$461$	−19.2536	−0.896729	−0.448364	−	0.893851i	$-0.647993\pi$
$461$	−19.2536	−0.896729	−0.448364	+	0.893851i	$0.647993\pi$
$462$	10.1367	0.471600
$463$	39.1713	1.82044	0.910222	−	0.414120i	$-0.135911\pi$
$463$	39.1713	1.82044	0.910222	+	0.414120i	$0.135911\pi$
$464$	157.431	7.30855
$465$	7.36037	0.341329
$466$	−69.8038	−3.23360
$467$	−39.0650	−1.80771	−0.903856	−	0.427836i	$-0.859276\pi$
$467$	−39.0650	−1.80771	−0.903856	+	0.427836i	$0.859276\pi$
$468$	2.79220	0.129069
$469$	−7.21331	−0.333080
$470$	10.9051	0.503014
$471$	3.62712	0.167129
$472$	24.4661	1.12614
$473$	1.78001	0.0818452
$474$	−7.50743	−0.344828
$475$	0	0
$476$	−59.7623	−2.73920
$477$	−8.50629	−0.389476
$478$	64.9512	2.97080
$479$	−24.7550	−1.13109	−0.565543	−	0.824718i	$-0.691334\pi$
$479$	−24.7550	−1.13109	−0.565543	+	0.824718i	$0.691334\pi$
$480$	37.0653	1.69179
$481$	4.09427	0.186683
$482$	23.1236	1.05325
$483$	1.77418	0.0807280
$484$	−57.4801	−2.61273
$485$	10.8541	0.492861
$486$	21.5794	0.978863
$487$	−21.8871	−0.991797	−0.495899	−	0.868380i	$-0.665161\pi$
$487$	−21.8871	−0.991797	−0.495899	+	0.868380i	$0.665161\pi$
$488$	−63.0135	−2.85249
$489$	−26.5823	−1.20209
$490$	−3.07446	−0.138890
$491$	9.39553	0.424014	0.212007	−	0.977268i	$-0.432000\pi$
$491$	9.39553	0.424014	0.212007	+	0.977268i	$0.432000\pi$
$492$	−33.5734	−1.51361
$493$	36.3155	1.63557
$494$	0	0
$495$	0.669511	0.0300923
$496$	−80.0275	−3.59334
$497$	−5.07664	−0.227719
$498$	−30.6100	−1.37167
$499$	24.9115	1.11519	0.557596	−	0.830112i	$-0.311724\pi$
$499$	24.9115	1.11519	0.557596	+	0.830112i	$0.311724\pi$
$500$	5.60665	0.250737
$501$	−0.605119	−0.0270347
$502$	−50.3278	−2.24624
$503$	−31.3180	−1.39640	−0.698200	−	0.715903i	$-0.746015\pi$
$503$	−31.3180	−1.39640	−0.698200	+	0.715903i	$0.746015\pi$
$504$	−21.9371	−0.977158
$505$	−5.29598	−0.235668
$506$	0.995699	0.0442642
$507$	18.7776	0.833941
$508$	−49.5343	−2.19773
$509$	9.66619	0.428446	0.214223	−	0.976785i	$-0.431278\pi$
$509$	9.66619	0.428446	0.214223	+	0.976785i	$0.431278\pi$
$510$	15.3967	0.681779
$511$	20.3133	0.898609
$512$	−80.2896	−3.54833
$513$	0	0
$514$	38.8874	1.71525
$515$	0.385134	0.0169710
$516$	17.2170	0.757934
$517$	3.41938	0.150384
$518$	−50.0046	−2.19708
$519$	26.8859	1.18016
$520$	6.39885	0.280608
$521$	0.982633	0.0430499	0.0215250	−	0.999768i	$-0.493148\pi$
$521$	0.982633	0.0430499	0.0215250	+	0.999768i	$0.493148\pi$
$522$	20.7226	0.907003
$523$	−39.7209	−1.73687	−0.868436	−	0.495801i	$-0.834875\pi$
$523$	−39.7209	−1.73687	−0.868436	+	0.495801i	$0.834875\pi$
$524$	117.251	5.12212
$525$	4.24993	0.185482
$526$	17.6809	0.770922
$527$	−18.4604	−0.804148
$528$	20.9289	0.910812
$529$	−22.8257	−0.992423
$530$	−30.3037	−1.31631
$531$	1.90417	0.0826337
$532$	0	0
$533$	−2.58195	−0.111837
$534$	−18.2936	−0.791642
$535$	6.43336	0.278139
$536$	−25.1883	−1.08797
$537$	30.0656	1.29743
$538$	49.6198	2.13926
$539$	−0.964024	−0.0415234
$540$	31.5698	1.35855
$541$	30.7775	1.32323	0.661614	−	0.749845i	$-0.269872\pi$
$541$	30.7775	1.32323	0.661614	+	0.749845i	$0.269872\pi$
$542$	−32.7705	−1.40761
$543$	−25.5280	−1.09551
$544$	−92.9629	−3.98575
$545$	−6.56882	−0.281377
$546$	7.54015	0.322688
$547$	17.8657	0.763884	0.381942	−	0.924186i	$-0.375255\pi$
$547$	17.8657	0.763884	0.381942	+	0.924186i	$0.375255\pi$
$548$	29.2374	1.24896
$549$	−4.90426	−0.209309
$550$	2.38513	0.101702
$551$	0	0
$552$	6.19529	0.263689
$553$	5.19741	0.221016
$554$	−65.1554	−2.76819
$555$	9.49557	0.403064
$556$	−60.1248	−2.54986
$557$	−10.6576	−0.451575	−0.225787	−	0.974177i	$-0.572495\pi$
$557$	−10.6576	−0.451575	−0.225787	+	0.974177i	$0.572495\pi$
$558$	−10.5340	−0.445939
$559$	1.32406	0.0560019
$560$	−46.2085	−1.95266
$561$	4.82778	0.203829
$562$	38.0863	1.60657
$563$	−7.75961	−0.327029	−0.163514	−	0.986541i	$-0.552283\pi$
$563$	−7.75961	−0.327029	−0.163514	+	0.986541i	$0.552283\pi$
$564$	33.0735	1.39265
$565$	−0.294513	−0.0123903
$566$	32.4270	1.36301
$567$	17.3143	0.727133
$568$	−17.7272	−0.743818
$569$	−5.72754	−0.240111	−0.120056	−	0.992767i	$-0.538307\pi$
$569$	−5.72754	−0.240111	−0.120056	+	0.992767i	$0.538307\pi$
$570$	0	0
$571$	−20.8347	−0.871903	−0.435952	−	0.899970i	$-0.643588\pi$
$571$	−20.8347	−0.871903	−0.435952	+	0.899970i	$0.643588\pi$
$572$	3.11904	0.130413
$573$	−7.87852	−0.329130
$574$	31.5341	1.31621
$575$	0.417460	0.0174093
$576$	−27.9307	−1.16378
$577$	−5.11190	−0.212811	−0.106406	−	0.994323i	$-0.533934\pi$
$577$	−5.11190	−0.212811	−0.106406	+	0.994323i	$0.533934\pi$
$578$	8.27001	0.343987
$579$	26.8600	1.11626
$580$	54.4138	2.25941
$581$	21.1914	0.879167
$582$	44.6619	1.85130
$583$	−9.50199	−0.393532
$584$	70.9325	2.93521
$585$	0.498015	0.0205904
$586$	−74.6254	−3.08275
$587$	−10.6692	−0.440367	−0.220184	−	0.975458i	$-0.570666\pi$
$587$	−10.6692	−0.440367	−0.220184	+	0.975458i	$0.570666\pi$
$588$	−9.32439	−0.384531
$589$	0	0
$590$	6.78360	0.279276
$591$	−12.0515	−0.495732
$592$	−103.243	−4.24326
$593$	−17.0027	−0.698216	−0.349108	−	0.937083i	$-0.613515\pi$
$593$	−17.0027	−0.698216	−0.349108	+	0.937083i	$0.613515\pi$
$594$	13.4301	0.551045
$595$	−10.6592	−0.436984
$596$	−83.6040	−3.42455
$597$	−2.09427	−0.0857128
$598$	0.740650	0.0302874
$599$	−28.6751	−1.17163	−0.585816	−	0.810444i	$-0.699226\pi$
$599$	−28.6751	−1.17163	−0.585816	+	0.810444i	$0.699226\pi$
$600$	14.8404	0.605858
$601$	−27.4370	−1.11918	−0.559590	−	0.828770i	$-0.689041\pi$
$601$	−27.4370	−1.11918	−0.559590	+	0.828770i	$0.689041\pi$
$602$	−16.1712	−0.659088
$603$	−1.96037	−0.0798326
$604$	−120.313	−4.89546
$605$	−10.2521	−0.416808
$606$	−21.7915	−0.885221
$607$	17.7547	0.720639	0.360320	−	0.932829i	$-0.382668\pi$
$607$	17.7547	0.720639	0.360320	+	0.932829i	$0.382668\pi$
$608$	0	0
$609$	41.2466	1.67140
$610$	−17.4715	−0.707399
$611$	2.54351	0.102899
$612$	−16.2417	−0.656533
$613$	34.6391	1.39906	0.699530	−	0.714603i	$-0.253393\pi$
$613$	34.6391	1.39906	0.699530	+	0.714603i	$0.253393\pi$
$614$	24.3760	0.983736
$615$	−5.98814	−0.241465
$616$	−24.5050	−0.987334
$617$	4.46569	0.179782	0.0898909	−	0.995952i	$-0.471348\pi$
$617$	4.46569	0.179782	0.0898909	+	0.995952i	$0.471348\pi$
$618$	1.58472	0.0637470
$619$	−17.9112	−0.719913	−0.359957	−	0.932969i	$-0.617209\pi$
$619$	−17.9112	−0.719913	−0.359957	+	0.932969i	$0.617209\pi$
$620$	−27.6604	−1.11087
$621$	2.35062	0.0943272
$622$	1.79683	0.0720463
$623$	12.6647	0.507400
$624$	15.5679	0.623215
$625$	1.00000	0.0400000
$626$	8.17906	0.326901
$627$	0	0
$628$	−13.6308	−0.543927
$629$	−23.8157	−0.949593
$630$	−6.08241	−0.242329
$631$	4.96881	0.197805	0.0989026	−	0.995097i	$-0.468467\pi$
$631$	4.96881	0.197805	0.0989026	+	0.995097i	$0.468467\pi$
$632$	18.1489	0.721925
$633$	28.2216	1.12171
$634$	−28.6278	−1.13696
$635$	−8.83492	−0.350603
$636$	−91.9067	−3.64434
$637$	−0.717088	−0.0284121
$638$	23.1483	0.916449
$639$	−1.37969	−0.0545796
$640$	−49.8151	−1.96912
$641$	37.9521	1.49902	0.749508	−	0.661995i	$-0.230290\pi$
$641$	37.9521	1.49902	0.749508	+	0.661995i	$0.230290\pi$
$642$	26.4716	1.04475
$643$	35.2502	1.39013	0.695067	−	0.718945i	$-0.255375\pi$
$643$	35.2502	1.39013	0.695067	+	0.718945i	$0.255375\pi$
$644$	−6.66740	−0.262732
$645$	3.07081	0.120913
$646$	0	0
$647$	35.5219	1.39651	0.698254	−	0.715850i	$-0.253960\pi$
$647$	35.5219	1.39651	0.698254	+	0.715850i	$0.253960\pi$
$648$	60.4602	2.37510
$649$	2.12706	0.0834943
$650$	1.77418	0.0695890
$651$	−20.9670	−0.821762
$652$	99.8966	3.91225
$653$	8.02411	0.314008	0.157004	−	0.987598i	$-0.449816\pi$
$653$	8.02411	0.314008	0.157004	+	0.987598i	$0.449816\pi$
$654$	−27.0290	−1.05692
$655$	20.9128	0.817129
$656$	65.1075	2.54202
$657$	5.52059	0.215379
$658$	−31.0646	−1.21102
$659$	47.2195	1.83941	0.919706	−	0.392608i	$-0.128427\pi$
$659$	47.2195	1.83941	0.919706	+	0.392608i	$0.128427\pi$
$660$	7.23377	0.281574
$661$	26.1159	1.01579	0.507896	−	0.861418i	$-0.330423\pi$
$661$	26.1159	1.01579	0.507896	+	0.861418i	$0.330423\pi$
$662$	41.6246	1.61778
$663$	3.59114	0.139468
$664$	73.9986	2.87170
$665$	0	0
$666$	−13.5898	−0.526596
$667$	4.05155	0.156877
$668$	2.27405	0.0879856
$669$	−24.0915	−0.931431
$670$	−6.98384	−0.269809
$671$	−5.47833	−0.211489
$672$	−105.586	−4.07306
$673$	−15.3820	−0.592931	−0.296466	−	0.955044i	$-0.595808\pi$
$673$	−15.3820	−0.592931	−0.296466	+	0.955044i	$0.595808\pi$
$674$	43.5696	1.67824
$675$	5.63077	0.216728
$676$	−70.5664	−2.71409
$677$	−24.4763	−0.940701	−0.470350	−	0.882480i	$-0.655872\pi$
$677$	−24.4763	−0.940701	−0.470350	+	0.882480i	$0.655872\pi$
$678$	−1.21184	−0.0465405
$679$	−30.9195	−1.18658
$680$	−37.2210	−1.42736
$681$	39.2652	1.50465
$682$	−11.7670	−0.450583
$683$	17.8502	0.683018	0.341509	−	0.939879i	$-0.389062\pi$
$683$	17.8502	0.683018	0.341509	+	0.939879i	$0.389062\pi$
$684$	0	0
$685$	5.21477	0.199246
$686$	−46.2381	−1.76538
$687$	19.8908	0.758880
$688$	−33.3881	−1.27291
$689$	−7.06804	−0.269271
$690$	1.71774	0.0653932
$691$	−9.27242	−0.352739	−0.176370	−	0.984324i	$-0.556435\pi$
$691$	−9.27242	−0.352739	−0.176370	+	0.984324i	$0.556435\pi$
$692$	−101.038	−3.84087
$693$	−1.90719	−0.0724483
$694$	58.8896	2.23542
$695$	−10.7238	−0.406778
$696$	144.030	5.45943
$697$	15.0187	0.568875
$698$	89.3314	3.38124
$699$	−37.7596	−1.42820
$700$	−15.9713	−0.603659
$701$	−7.68906	−0.290412	−0.145206	−	0.989401i	$-0.546384\pi$
$701$	−7.68906	−0.290412	−0.145206	+	0.989401i	$0.546384\pi$
$702$	9.98999	0.377048
$703$	0	0
$704$	−31.2001	−1.17590
$705$	5.89898	0.222168
$706$	−2.01496	−0.0758340
$707$	15.0863	0.567379
$708$	20.5737	0.773206
$709$	24.4375	0.917769	0.458885	−	0.888496i	$-0.348249\pi$
$709$	24.4375	0.917769	0.458885	+	0.888496i	$0.348249\pi$
$710$	−4.91514	−0.184462
$711$	1.41251	0.0529732
$712$	44.2241	1.65737
$713$	−2.05954	−0.0771303
$714$	−43.8597	−1.64141
$715$	0.556310	0.0208048
$716$	−112.987	−4.22252
$717$	35.1346	1.31213
$718$	74.0516	2.76358
$719$	−22.1126	−0.824662	−0.412331	−	0.911034i	$-0.635285\pi$
$719$	−22.1126	−0.824662	−0.412331	+	0.911034i	$0.635285\pi$
$720$	−12.5582	−0.468015
$721$	−1.09711	−0.0408584
$722$	0	0
$723$	12.5085	0.465195
$724$	95.9345	3.56538
$725$	9.70523	0.360443
$726$	−42.1848	−1.56562
$727$	−29.0494	−1.07738	−0.538692	−	0.842503i	$-0.681081\pi$
$727$	−29.0494	−1.07738	−0.538692	+	0.842503i	$0.681081\pi$
$728$	−18.2280	−0.675575
$729$	29.9075	1.10768
$730$	19.6671	0.727913
$731$	−7.70184	−0.284863
$732$	−52.9884	−1.95851
$733$	14.5428	0.537151	0.268576	−	0.963259i	$-0.413447\pi$
$733$	14.5428	0.537151	0.268576	+	0.963259i	$0.413447\pi$
$734$	63.3360	2.33777
$735$	−1.66309	−0.0613442
$736$	−10.3714	−0.382296
$737$	−2.18984	−0.0806640
$738$	8.57009	0.315469
$739$	−4.75596	−0.174951	−0.0874754	−	0.996167i	$-0.527880\pi$
$739$	−4.75596	−0.174951	−0.0874754	+	0.996167i	$0.527880\pi$
$740$	−35.6845	−1.31179
$741$	0	0
$742$	86.3242	3.16906
$743$	−5.87705	−0.215608	−0.107804	−	0.994172i	$-0.534382\pi$
$743$	−5.87705	−0.215608	−0.107804	+	0.994172i	$0.534382\pi$
$744$	−73.2151	−2.68420
$745$	−14.9116	−0.546317
$746$	81.4455	2.98193
$747$	5.75922	0.210719
$748$	−18.1429	−0.663370
$749$	−18.3263	−0.669629
$750$	4.11474	0.150249
$751$	−1.62096	−0.0591498	−0.0295749	−	0.999563i	$-0.509415\pi$
$751$	−1.62096	−0.0591498	−0.0295749	+	0.999563i	$0.509415\pi$
$752$	−64.1382	−2.33888
$753$	−27.2243	−0.992107
$754$	17.2188	0.627072
$755$	−21.4589	−0.780971
$756$	−89.9308	−3.27075
$757$	−28.1135	−1.02180	−0.510901	−	0.859639i	$-0.670688\pi$
$757$	−28.1135	−1.02180	−0.510901	+	0.859639i	$0.670688\pi$
$758$	48.2976	1.75425
$759$	0.538612	0.0195504
$760$	0	0
$761$	20.1663	0.731027	0.365514	−	0.930806i	$-0.380893\pi$
$761$	20.1663	0.731027	0.365514	+	0.930806i	$0.380893\pi$
$762$	−36.3534	−1.31694
$763$	18.7122	0.677427
$764$	29.6076	1.07117
$765$	−2.89687	−0.104736
$766$	22.3579	0.807825
$767$	1.58221	0.0571303
$768$	−97.3257	−3.51194
$769$	45.3047	1.63373	0.816865	−	0.576829i	$-0.195710\pi$
$769$	45.3047	1.63373	0.816865	+	0.576829i	$0.195710\pi$
$770$	−6.79438	−0.244853
$771$	21.0357	0.757583
$772$	−100.940	−3.63292
$773$	20.1762	0.725686	0.362843	−	0.931850i	$-0.381806\pi$
$773$	20.1762	0.725686	0.362843	+	0.931850i	$0.381806\pi$
$774$	−4.39487	−0.157970
$775$	−4.93349	−0.177216
$776$	−107.968	−3.87584
$777$	−27.0494	−0.970393
$778$	−47.7353	−1.71139
$779$	0	0
$780$	5.38083	0.192665
$781$	−1.54119	−0.0551480
$782$	−4.30823	−0.154062
$783$	54.6479	1.95296
$784$	18.0824	0.645800
$785$	−2.43118	−0.0867724
$786$	86.0505	3.06932
$787$	46.1385	1.64466	0.822331	−	0.569010i	$-0.192673\pi$
$787$	46.1385	1.64466	0.822331	+	0.569010i	$0.192673\pi$
$788$	45.2897	1.61338
$789$	9.56426	0.340497
$790$	5.03207	0.179033
$791$	0.838961	0.0298300
$792$	−6.65976	−0.236644
$793$	−4.07505	−0.144709
$794$	31.4122	1.11478
$795$	−16.3924	−0.581380
$796$	7.87031	0.278956
$797$	1.86497	0.0660606	0.0330303	−	0.999454i	$-0.489484\pi$
$797$	1.86497	0.0660606	0.0330303	+	0.999454i	$0.489484\pi$
$798$	0	0
$799$	−14.7951	−0.523414
$800$	−24.8441	−0.878371
$801$	3.44191	0.121614
$802$	−24.6528	−0.870522
$803$	6.16681	0.217622
$804$	−21.1810	−0.746996
$805$	−1.18919	−0.0419136
$806$	−8.75290	−0.308308
$807$	26.8413	0.944859
$808$	52.6802	1.85328
$809$	18.2267	0.640816	0.320408	−	0.947280i	$-0.396180\pi$
$809$	18.2267	0.640816	0.320408	+	0.947280i	$0.396180\pi$
$810$	16.7635	0.589010
$811$	20.9779	0.736634	0.368317	−	0.929700i	$-0.379934\pi$
$811$	20.9779	0.736634	0.368317	+	0.929700i	$0.379934\pi$
$812$	−155.005	−5.43962
$813$	−17.7268	−0.621707
$814$	−15.1806	−0.532079
$815$	17.8175	0.624120
$816$	−90.5558	−3.17009
$817$	0	0
$818$	−18.0504	−0.631118
$819$	−1.41866	−0.0495721
$820$	22.5035	0.785857
$821$	−22.0867	−0.770829	−0.385415	−	0.922743i	$-0.625942\pi$
$821$	−22.0867	−0.770829	−0.385415	+	0.922743i	$0.625942\pi$
$822$	21.4574	0.748413
$823$	15.9769	0.556921	0.278461	−	0.960448i	$-0.410176\pi$
$823$	15.9769	0.556921	0.278461	+	0.960448i	$0.410176\pi$
$824$	−3.83101	−0.133460
$825$	1.29021	0.0449194
$826$	−19.3240	−0.672368
$827$	−49.2009	−1.71088	−0.855441	−	0.517901i	$-0.826714\pi$
$827$	−49.2009	−1.71088	−0.855441	+	0.517901i	$0.826714\pi$
$828$	−1.81201	−0.0629717
$829$	35.8564	1.24534	0.622672	−	0.782483i	$-0.286047\pi$
$829$	35.8564	1.24534	0.622672	+	0.782483i	$0.286047\pi$
$830$	20.5172	0.712164
$831$	−35.2451	−1.22264
$832$	−23.2082	−0.804599
$833$	4.17118	0.144523
$834$	−44.1257	−1.52795
$835$	0.405598	0.0140363
$836$	0	0
$837$	−27.7794	−0.960195
$838$	−60.2463	−2.08117
$839$	25.4830	0.879770	0.439885	−	0.898054i	$-0.355019\pi$
$839$	25.4830	0.879770	0.439885	+	0.898054i	$0.355019\pi$
$840$	−42.2750	−1.45863
$841$	65.1914	2.24798
$842$	−80.9294	−2.78901
$843$	20.6024	0.709583
$844$	−106.057	−3.65065
$845$	−12.5862	−0.432978
$846$	−8.44249	−0.290259
$847$	29.2046	1.00348
$848$	178.231	6.12047
$849$	17.5410	0.602007
$850$	−10.3201	−0.353976
$851$	−2.65700	−0.0910807
$852$	−14.9069	−0.510703
$853$	−57.1622	−1.95720	−0.978598	−	0.205782i	$-0.934026\pi$
$853$	−57.1622	−1.95720	−0.978598	+	0.205782i	$0.934026\pi$
$854$	49.7698	1.70309
$855$	0	0
$856$	−63.9940	−2.18727
$857$	−26.1974	−0.894885	−0.447442	−	0.894313i	$-0.647665\pi$
$857$	−26.1974	−0.894885	−0.447442	+	0.894313i	$0.647665\pi$
$858$	2.28907	0.0781475
$859$	−17.7449	−0.605449	−0.302724	−	0.953078i	$-0.597896\pi$
$859$	−17.7449	−0.605449	−0.302724	+	0.953078i	$0.597896\pi$
$860$	−11.5401	−0.393516
$861$	17.0580	0.581336
$862$	−35.5418	−1.21056
$863$	−25.0867	−0.853960	−0.426980	−	0.904261i	$-0.640422\pi$
$863$	−25.0867	−0.853960	−0.426980	+	0.904261i	$0.640422\pi$
$864$	−139.891	−4.75920
$865$	−18.0210	−0.612733
$866$	−38.1789	−1.29737
$867$	4.47357	0.151930
$868$	78.7944	2.67446
$869$	1.57785	0.0535249
$870$	39.9344	1.35390
$871$	−1.62891	−0.0551936
$872$	65.3415	2.21274
$873$	−8.40305	−0.284400
$874$	0	0
$875$	−2.84864	−0.0963015
$876$	59.6476	2.01531
$877$	−10.0157	−0.338205	−0.169103	−	0.985598i	$-0.554087\pi$
$877$	−10.0157	−0.338205	−0.169103	+	0.985598i	$0.554087\pi$
$878$	−0.195290	−0.00659071
$879$	−40.3678	−1.36157
$880$	−14.0282	−0.472889
$881$	33.3473	1.12350	0.561750	−	0.827307i	$-0.310128\pi$
$881$	33.3473	1.12350	0.561750	+	0.827307i	$0.310128\pi$
$882$	2.38018	0.0801449
$883$	−27.3570	−0.920638	−0.460319	−	0.887754i	$-0.652265\pi$
$883$	−27.3570	−0.920638	−0.460319	+	0.887754i	$0.652265\pi$
$884$	−13.4956	−0.453905
$885$	3.66951	0.123349
$886$	10.4505	0.351092
$887$	−17.1634	−0.576292	−0.288146	−	0.957586i	$-0.593039\pi$
$887$	−17.1634	−0.576292	−0.288146	+	0.957586i	$0.593039\pi$
$888$	−94.4544	−3.16968
$889$	25.1675	0.844090
$890$	12.2618	0.411016
$891$	5.25635	0.176094
$892$	90.5363	3.03138
$893$	0	0
$894$	−61.3571	−2.05209
$895$	−20.1523	−0.673617
$896$	141.905	4.74072
$897$	0.400646	0.0133772
$898$	−73.2985	−2.44600
$899$	−47.8807	−1.59691
$900$	−4.34056	−0.144685
$901$	41.1136	1.36969
$902$	9.57325	0.318754
$903$	−8.74762	−0.291103
$904$	2.92958	0.0974364
$905$	17.1108	0.568783
$906$	−88.2979	−2.93350
$907$	−3.02106	−0.100313	−0.0501563	−	0.998741i	$-0.515972\pi$
$907$	−3.02106	−0.100313	−0.0501563	+	0.998741i	$0.515972\pi$
$908$	−147.559	−4.89693
$909$	4.10004	0.135990
$910$	−5.05399	−0.167538
$911$	19.5682	0.648324	0.324162	−	0.946002i	$-0.394918\pi$
$911$	19.5682	0.648324	0.324162	+	0.946002i	$0.394918\pi$
$912$	0	0
$913$	6.43336	0.212913
$914$	91.4346	3.02439
$915$	−9.45099	−0.312440
$916$	−74.7498	−2.46980
$917$	−59.5729	−1.96727
$918$	−58.1100	−1.91792
$919$	−1.81420	−0.0598448	−0.0299224	−	0.999552i	$-0.509526\pi$
$919$	−1.81420	−0.0598448	−0.0299224	+	0.999552i	$0.509526\pi$
$920$	−4.15257	−0.136906
$921$	13.1859	0.434491
$922$	53.1017	1.74881
$923$	−1.14641	−0.0377346
$924$	−20.6064	−0.677901
$925$	−6.36467	−0.209269
$926$	−108.035	−3.55025
$927$	−0.298163	−0.00979295
$928$	−241.117	−7.91507
$929$	−22.4754	−0.737395	−0.368698	−	0.929549i	$-0.620196\pi$
$929$	−22.4754	−0.737395	−0.368698	+	0.929549i	$0.620196\pi$
$930$	−20.3000	−0.665664
$931$	0	0
$932$	141.901	4.64813
$933$	0.971975	0.0318210
$934$	107.742	3.52542
$935$	−3.23596	−0.105827
$936$	−4.95386	−0.161922
$937$	55.0385	1.79803	0.899015	−	0.437918i	$-0.144284\pi$
$937$	55.0385	1.79803	0.899015	+	0.437918i	$0.144284\pi$
$938$	19.8944	0.649576
$939$	4.42437	0.144384
$940$	−22.1685	−0.723056
$941$	12.1956	0.397566	0.198783	−	0.980044i	$-0.436301\pi$
$941$	12.1956	0.397566	0.198783	+	0.980044i	$0.436301\pi$
$942$	−10.0036	−0.325937
$943$	1.67557	0.0545640
$944$	−39.8977	−1.29856
$945$	−16.0400	−0.521782
$946$	−4.90931	−0.159615
$947$	30.4307	0.988863	0.494432	−	0.869216i	$-0.335376\pi$
$947$	30.4307	0.988863	0.494432	+	0.869216i	$0.335376\pi$
$948$	15.2615	0.495672
$949$	4.58717	0.148906
$950$	0	0
$951$	−15.4859	−0.502164
$952$	106.029	3.43642
$953$	−15.7378	−0.509798	−0.254899	−	0.966968i	$-0.582042\pi$
$953$	−15.7378	−0.509798	−0.254899	+	0.966968i	$0.582042\pi$
$954$	23.4605	0.759561
$955$	5.28080	0.170883
$956$	−132.036	−4.27036
$957$	12.5218	0.404772
$958$	68.2748	2.20586
$959$	−14.8550	−0.479693
$960$	−53.8252	−1.73720
$961$	−6.66065	−0.214860
$962$	−11.2921	−0.364071
$963$	−4.98058	−0.160497
$964$	−47.0070	−1.51399
$965$	−18.0036	−0.579558
$966$	−4.89322	−0.157437
$967$	30.6373	0.985228	0.492614	−	0.870248i	$-0.336042\pi$
$967$	30.6373	0.985228	0.492614	+	0.870248i	$0.336042\pi$
$968$	101.980	3.27776
$969$	0	0
$970$	−29.9359	−0.961184
$971$	−16.4765	−0.528755	−0.264378	−	0.964419i	$-0.585167\pi$
$971$	−16.4765	−0.528755	−0.264378	+	0.964419i	$0.585167\pi$
$972$	−43.8679	−1.40706
$973$	30.5483	0.979334
$974$	60.3649	1.93422
$975$	0.959723	0.0307357
$976$	102.758	3.28921
$977$	2.77995	0.0889383	0.0444692	−	0.999011i	$-0.485840\pi$
$977$	2.77995	0.0889383	0.0444692	+	0.999011i	$0.485840\pi$
$978$	73.3144	2.34433
$979$	3.84480	0.122880
$980$	6.24993	0.199647
$981$	5.08545	0.162366
$982$	−25.9130	−0.826918
$983$	1.71171	0.0545951	0.0272976	−	0.999627i	$-0.491310\pi$
$983$	1.71171	0.0545951	0.0272976	+	0.999627i	$0.491310\pi$
$984$	59.5653	1.89887
$985$	8.07785	0.257382
$986$	−100.159	−3.18971
$987$	−16.8041	−0.534879
$988$	0	0
$989$	−0.859257	−0.0273228
$990$	−1.84652	−0.0586863
$991$	9.67421	0.307311	0.153656	−	0.988124i	$-0.450895\pi$
$991$	9.67421	0.307311	0.153656	+	0.988124i	$0.450895\pi$
$992$	122.568	3.89154
$993$	22.5164	0.714535
$994$	14.0015	0.444099
$995$	1.40374	0.0445017
$996$	62.2259	1.97170
$997$	22.7311	0.719902	0.359951	−	0.932971i	$-0.382793\pi$
$997$	22.7311	0.719902	0.359951	+	0.932971i	$0.382793\pi$
$998$	−68.7064	−2.17486
$999$	−35.8380	−1.13386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1805.2.a.i.1.1		4
5.4	even	2		9025.2.a.bp.1.4		4
19.8	odd	6		95.2.e.c.26.1	yes	8
19.12	odd	6		95.2.e.c.11.1	✓	8
19.18	odd	2		1805.2.a.o.1.4		4
57.8	even	6		855.2.k.h.406.4		8
57.50	even	6		855.2.k.h.676.4		8
76.27	even	6		1520.2.q.o.881.3		8
76.31	even	6		1520.2.q.o.961.3		8
95.8	even	12		475.2.j.c.349.1		16
95.12	even	12		475.2.j.c.49.1		16
95.27	even	12		475.2.j.c.349.8		16
95.69	odd	6		475.2.e.e.201.4		8
95.84	odd	6		475.2.e.e.26.4		8
95.88	even	12		475.2.j.c.49.8		16
95.94	odd	2		9025.2.a.bg.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.e.c.11.1	✓	8	19.12	odd	6
95.2.e.c.26.1	yes	8	19.8	odd	6
475.2.e.e.26.4		8	95.84	odd	6
475.2.e.e.201.4		8	95.69	odd	6
475.2.j.c.49.1		16	95.12	even	12
475.2.j.c.49.8		16	95.88	even	12
475.2.j.c.349.1		16	95.8	even	12
475.2.j.c.349.8		16	95.27	even	12
855.2.k.h.406.4		8	57.8	even	6
855.2.k.h.676.4		8	57.50	even	6
1520.2.q.o.881.3		8	76.27	even	6
1520.2.q.o.961.3		8	76.31	even	6
1805.2.a.i.1.1		4	1.1	even	1	trivial
1805.2.a.o.1.4		4	19.18	odd	2
9025.2.a.bg.1.1		4	95.94	odd	2
9025.2.a.bp.1.4		4	5.4	even	2

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:	\( N \)	\(=\)	\( 1805 = 5 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1805.a (trivial)

\(f(q)\)	\(=\)	\(q-2.75802 q^{2} -1.49192 q^{3} +5.60665 q^{4} +1.00000 q^{5} +4.11474 q^{6} -2.84864 q^{7} -9.94721 q^{8} -0.774179 q^{9} +O(q^{10})\)	\(q-2.75802 q^{2} -1.49192 q^{3} +5.60665 q^{4} +1.00000 q^{5} +4.11474 q^{6} -2.84864 q^{7} -9.94721 q^{8} -0.774179 q^{9} -2.75802 q^{10} -0.864801 q^{11} -8.36467 q^{12} -0.643281 q^{13} +7.85659 q^{14} -1.49192 q^{15} +16.2213 q^{16} +3.74185 q^{17} +2.13520 q^{18} +5.60665 q^{20} +4.24993 q^{21} +2.38513 q^{22} +0.417460 q^{23} +14.8404 q^{24} +1.00000 q^{25} +1.77418 q^{26} +5.63077 q^{27} -15.9713 q^{28} +9.70523 q^{29} +4.11474 q^{30} -4.93349 q^{31} -24.8441 q^{32} +1.29021 q^{33} -10.3201 q^{34} -2.84864 q^{35} -4.34056 q^{36} -6.36467 q^{37} +0.959723 q^{39} -9.94721 q^{40} +4.01372 q^{41} -11.7214 q^{42} -2.05829 q^{43} -4.84864 q^{44} -0.774179 q^{45} -1.15136 q^{46} -3.95396 q^{47} -24.2008 q^{48} +1.11474 q^{49} -2.75802 q^{50} -5.58254 q^{51} -3.60665 q^{52} +10.9875 q^{53} -15.5297 q^{54} -0.864801 q^{55} +28.3360 q^{56} -26.7672 q^{58} -2.45959 q^{59} -8.36467 q^{60} +6.33479 q^{61} +13.6067 q^{62} +2.20536 q^{63} +36.0778 q^{64} -0.643281 q^{65} -3.55843 q^{66} +2.53220 q^{67} +20.9793 q^{68} -0.622817 q^{69} +7.85659 q^{70} +1.78213 q^{71} +7.70092 q^{72} -7.13090 q^{73} +17.5539 q^{74} -1.49192 q^{75} +2.46350 q^{77} -2.64693 q^{78} -1.82452 q^{79} +16.2213 q^{80} -6.07811 q^{81} -11.0699 q^{82} -7.43913 q^{83} +23.8279 q^{84} +3.74185 q^{85} +5.67681 q^{86} -14.4794 q^{87} +8.60235 q^{88} -4.44588 q^{89} +2.13520 q^{90} +1.83247 q^{91} +2.34056 q^{92} +7.36037 q^{93} +10.9051 q^{94} +37.0653 q^{96} +10.8541 q^{97} -3.07446 q^{98} +0.669511 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} - 3 q^{3} + 5 q^{4} + 4 q^{5} + 2 q^{6} - 4 q^{7} - 12 q^{8} + q^{9}+O(q^{10}) \) 4 * q - q^2 - 3 * q^3 + 5 * q^4 + 4 * q^5 + 2 * q^6 - 4 * q^7 - 12 * q^8 + q^9	\( 4 q - q^{2} - 3 q^{3} + 5 q^{4} + 4 q^{5} + 2 q^{6} - 4 q^{7} - 12 q^{8} + q^{9} - q^{10} - 2 q^{11} - 6 q^{12} - 7 q^{13} + q^{14} - 3 q^{15} + 7 q^{16} - q^{17} + 10 q^{18} + 5 q^{20} + 4 q^{21} - 2 q^{22} + 2 q^{23} + 23 q^{24} + 4 q^{25} + 3 q^{26} - 12 q^{27} - 19 q^{28} + q^{29} + 2 q^{30} - 30 q^{32} - 19 q^{33} - 15 q^{34} - 4 q^{35} - 7 q^{36} + 2 q^{37} + 15 q^{39} - 12 q^{40} + 8 q^{41} - 15 q^{42} + q^{43} - 12 q^{44} + q^{45} - 12 q^{46} - 12 q^{47} - 23 q^{48} - 10 q^{49} - q^{50} - 22 q^{51} + 3 q^{52} + 5 q^{53} - 34 q^{54} - 2 q^{55} + 41 q^{56} - 27 q^{58} + 5 q^{59} - 6 q^{60} + 37 q^{62} - 3 q^{63} + 56 q^{64} - 7 q^{65} - 31 q^{66} - 4 q^{67} + 16 q^{68} + 9 q^{69} + q^{70} - 20 q^{71} - 17 q^{72} - 20 q^{73} + 25 q^{74} - 3 q^{75} + 14 q^{77} + 18 q^{78} - 17 q^{79} + 7 q^{80} + 12 q^{81} + 21 q^{82} + q^{83} + 20 q^{84} - q^{85} - 8 q^{86} - 16 q^{87} + 7 q^{88} - 11 q^{89} + 10 q^{90} - 6 q^{91} - q^{92} - 8 q^{93} + 31 q^{94} + 21 q^{96} - q^{97} - 9 q^{98} + 38 q^{99}+O(q^{100}) \) 4 * q - q^2 - 3 * q^3 + 5 * q^4 + 4 * q^5 + 2 * q^6 - 4 * q^7 - 12 * q^8 + q^9 - q^10 - 2 * q^11 - 6 * q^12 - 7 * q^13 + q^14 - 3 * q^15 + 7 * q^16 - q^17 + 10 * q^18 + 5 * q^20 + 4 * q^21 - 2 * q^22 + 2 * q^23 + 23 * q^24 + 4 * q^25 + 3 * q^26 - 12 * q^27 - 19 * q^28 + q^29 + 2 * q^30 - 30 * q^32 - 19 * q^33 - 15 * q^34 - 4 * q^35 - 7 * q^36 + 2 * q^37 + 15 * q^39 - 12 * q^40 + 8 * q^41 - 15 * q^42 + q^43 - 12 * q^44 + q^45 - 12 * q^46 - 12 * q^47 - 23 * q^48 - 10 * q^49 - q^50 - 22 * q^51 + 3 * q^52 + 5 * q^53 - 34 * q^54 - 2 * q^55 + 41 * q^56 - 27 * q^58 + 5 * q^59 - 6 * q^60 + 37 * q^62 - 3 * q^63 + 56 * q^64 - 7 * q^65 - 31 * q^66 - 4 * q^67 + 16 * q^68 + 9 * q^69 + q^70 - 20 * q^71 - 17 * q^72 - 20 * q^73 + 25 * q^74 - 3 * q^75 + 14 * q^77 + 18 * q^78 - 17 * q^79 + 7 * q^80 + 12 * q^81 + 21 * q^82 + q^83 + 20 * q^84 - q^85 - 8 * q^86 - 16 * q^87 + 7 * q^88 - 11 * q^89 + 10 * q^90 - 6 * q^91 - q^92 - 8 * q^93 + 31 * q^94 + 21 * q^96 - q^97 - 9 * q^98 + 38 * q^99

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