LMFDB - Embedded newform 4021.2.a.c.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4021,2,Mod(1,4021)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4021, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4021.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4021 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4021.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:	$32.1078466528$
Analytic rank:	$0$
Dimension:	$182$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	4021.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.53727 q^{2} +1.21389 q^{3} +4.43775 q^{4} -4.40547 q^{5} -3.07998 q^{6} -1.31615 q^{7} -6.18523 q^{8} -1.52646 q^{9} +O(q^{10})$	\(q-2.53727 q^{2} +1.21389 q^{3} +4.43775 q^{4} -4.40547 q^{5} -3.07998 q^{6} -1.31615 q^{7} -6.18523 q^{8} -1.52646 q^{9} +11.1779 q^{10} +5.70308 q^{11} +5.38696 q^{12} +4.84673 q^{13} +3.33943 q^{14} -5.34777 q^{15} +6.81812 q^{16} +7.47823 q^{17} +3.87305 q^{18} -7.58170 q^{19} -19.5504 q^{20} -1.59766 q^{21} -14.4703 q^{22} +2.56363 q^{23} -7.50822 q^{24} +14.4082 q^{25} -12.2975 q^{26} -5.49464 q^{27} -5.84074 q^{28} +4.91361 q^{29} +13.5687 q^{30} -8.67382 q^{31} -4.92896 q^{32} +6.92293 q^{33} -18.9743 q^{34} +5.79825 q^{35} -6.77406 q^{36} -1.99947 q^{37} +19.2368 q^{38} +5.88342 q^{39} +27.2489 q^{40} +4.03710 q^{41} +4.05371 q^{42} +1.75689 q^{43} +25.3088 q^{44} +6.72478 q^{45} -6.50462 q^{46} +10.9742 q^{47} +8.27648 q^{48} -5.26775 q^{49} -36.5574 q^{50} +9.07778 q^{51} +21.5086 q^{52} -11.6937 q^{53} +13.9414 q^{54} -25.1247 q^{55} +8.14068 q^{56} -9.20337 q^{57} -12.4672 q^{58} -2.92239 q^{59} -23.7321 q^{60} -2.87812 q^{61} +22.0078 q^{62} +2.00905 q^{63} -1.13012 q^{64} -21.3521 q^{65} -17.5654 q^{66} +7.00109 q^{67} +33.1865 q^{68} +3.11197 q^{69} -14.7117 q^{70} -4.93369 q^{71} +9.44153 q^{72} +1.52889 q^{73} +5.07320 q^{74} +17.4900 q^{75} -33.6457 q^{76} -7.50609 q^{77} -14.9278 q^{78} +2.68056 q^{79} -30.0370 q^{80} -2.09053 q^{81} -10.2432 q^{82} -8.53882 q^{83} -7.09003 q^{84} -32.9451 q^{85} -4.45771 q^{86} +5.96460 q^{87} -35.2749 q^{88} -4.98383 q^{89} -17.0626 q^{90} -6.37902 q^{91} +11.3767 q^{92} -10.5291 q^{93} -27.8446 q^{94} +33.4009 q^{95} -5.98324 q^{96} +9.89884 q^{97} +13.3657 q^{98} -8.70553 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 182 q + 18 q^{2} + 28 q^{3} + 208 q^{4} + 22 q^{5} + 18 q^{6} + 14 q^{7} + 54 q^{8} + 238 q^{9}+O(q^{10}) $ 182 * q + 18 * q^2 + 28 * q^3 + 208 * q^4 + 22 * q^5 + 18 * q^6 + 14 * q^7 + 54 * q^8 + 238 * q^9	\( 182 q + 18 q^{2} + 28 q^{3} + 208 q^{4} + 22 q^{5} + 18 q^{6} + 14 q^{7} + 54 q^{8} + 238 q^{9} + 7 q^{10} + 138 q^{11} + 47 q^{12} + 5 q^{13} + 72 q^{14} + 41 q^{15} + 256 q^{16} + 29 q^{17} + 35 q^{18} + 48 q^{19} + 56 q^{20} + 22 q^{21} + 19 q^{22} + 91 q^{23} + 46 q^{24} + 230 q^{25} + 88 q^{26} + 103 q^{27} + 15 q^{28} + 75 q^{29} + 18 q^{30} + 43 q^{31} + 116 q^{32} + 15 q^{33} + 13 q^{34} + 185 q^{35} + 364 q^{36} + 15 q^{37} + 53 q^{38} + 80 q^{39} - 13 q^{40} + 68 q^{41} + 32 q^{42} + 82 q^{43} + 259 q^{44} + 37 q^{45} + 13 q^{46} + 121 q^{47} + 53 q^{48} + 244 q^{49} + 93 q^{50} + 144 q^{51} - 16 q^{52} + 101 q^{53} + 47 q^{54} + 49 q^{55} + 199 q^{56} + 3 q^{57} + 4 q^{58} + 254 q^{59} + 24 q^{60} + 8 q^{61} + 37 q^{62} + 19 q^{63} + 326 q^{64} + 65 q^{65} + 41 q^{66} + 91 q^{67} + 50 q^{68} + 50 q^{69} + 5 q^{70} + 212 q^{71} + 77 q^{72} + 5 q^{73} + 101 q^{74} + 127 q^{75} + 22 q^{76} + 87 q^{77} - 20 q^{78} + 86 q^{79} + 71 q^{80} + 358 q^{81} - 20 q^{82} + 139 q^{83} - 30 q^{84} + 25 q^{85} + 82 q^{86} + 36 q^{87} - 8 q^{88} + 100 q^{89} - 87 q^{90} + 74 q^{91} + 171 q^{92} + 50 q^{93} - 13 q^{94} + 217 q^{95} + 42 q^{96} + 20 q^{97} + 47 q^{98} + 389 q^{99}+O(q^{100}) \) 182 * q + 18 * q^2 + 28 * q^3 + 208 * q^4 + 22 * q^5 + 18 * q^6 + 14 * q^7 + 54 * q^8 + 238 * q^9 + 7 * q^10 + 138 * q^11 + 47 * q^12 + 5 * q^13 + 72 * q^14 + 41 * q^15 + 256 * q^16 + 29 * q^17 + 35 * q^18 + 48 * q^19 + 56 * q^20 + 22 * q^21 + 19 * q^22 + 91 * q^23 + 46 * q^24 + 230 * q^25 + 88 * q^26 + 103 * q^27 + 15 * q^28 + 75 * q^29 + 18 * q^30 + 43 * q^31 + 116 * q^32 + 15 * q^33 + 13 * q^34 + 185 * q^35 + 364 * q^36 + 15 * q^37 + 53 * q^38 + 80 * q^39 - 13 * q^40 + 68 * q^41 + 32 * q^42 + 82 * q^43 + 259 * q^44 + 37 * q^45 + 13 * q^46 + 121 * q^47 + 53 * q^48 + 244 * q^49 + 93 * q^50 + 144 * q^51 - 16 * q^52 + 101 * q^53 + 47 * q^54 + 49 * q^55 + 199 * q^56 + 3 * q^57 + 4 * q^58 + 254 * q^59 + 24 * q^60 + 8 * q^61 + 37 * q^62 + 19 * q^63 + 326 * q^64 + 65 * q^65 + 41 * q^66 + 91 * q^67 + 50 * q^68 + 50 * q^69 + 5 * q^70 + 212 * q^71 + 77 * q^72 + 5 * q^73 + 101 * q^74 + 127 * q^75 + 22 * q^76 + 87 * q^77 - 20 * q^78 + 86 * q^79 + 71 * q^80 + 358 * q^81 - 20 * q^82 + 139 * q^83 - 30 * q^84 + 25 * q^85 + 82 * q^86 + 36 * q^87 - 8 * q^88 + 100 * q^89 - 87 * q^90 + 74 * q^91 + 171 * q^92 + 50 * q^93 - 13 * q^94 + 217 * q^95 + 42 * q^96 + 20 * q^97 + 47 * q^98 + 389 * 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 $

$2$	−2.53727	−1.79412	−0.897061	−	0.441906i	$-0.854302\pi$
$2$	−2.53727	−1.79412	−0.897061	+	0.441906i	$0.854302\pi$
$3$	1.21389	0.700842	0.350421	−	0.936592i	$-0.386039\pi$
$3$	1.21389	0.700842	0.350421	+	0.936592i	$0.386039\pi$
$4$	4.43775	2.21887
$5$	−4.40547	−1.97019	−0.985093	−	0.172024i	$-0.944969\pi$
$5$	−4.40547	−1.97019	−0.985093	+	0.172024i	$0.944969\pi$
$6$	−3.07998	−1.25740
$7$	−1.31615	−0.497457	−0.248729	−	0.968573i	$-0.580013\pi$
$7$	−1.31615	−0.497457	−0.248729	+	0.968573i	$0.580013\pi$
$8$	−6.18523	−2.18681
$9$	−1.52646	−0.508821
$10$	11.1779	3.53475
$11$	5.70308	1.71954	0.859771	−	0.510679i	$-0.170606\pi$
$11$	5.70308	1.71954	0.859771	+	0.510679i	$0.170606\pi$
$12$	5.38696	1.55508
$13$	4.84673	1.34424	0.672121	−	0.740442i	$-0.265384\pi$
$13$	4.84673	1.34424	0.672121	+	0.740442i	$0.265384\pi$
$14$	3.33943	0.892499
$15$	−5.34777	−1.38079
$16$	6.81812	1.70453
$17$	7.47823	1.81374	0.906869	−	0.421413i	$-0.138466\pi$
$17$	7.47823	1.81374	0.906869	+	0.421413i	$0.138466\pi$
$18$	3.87305	0.912887
$19$	−7.58170	−1.73936	−0.869680	−	0.493615i	$-0.835675\pi$
$19$	−7.58170	−1.73936	−0.869680	+	0.493615i	$0.835675\pi$
$20$	−19.5504	−4.37160
$21$	−1.59766	−0.348639
$22$	−14.4703	−3.08507
$23$	2.56363	0.534553	0.267277	−	0.963620i	$-0.413876\pi$
$23$	2.56363	0.534553	0.267277	+	0.963620i	$0.413876\pi$
$24$	−7.50822	−1.53261
$25$	14.4082	2.88163
$26$	−12.2975	−2.41173
$27$	−5.49464	−1.05744
$28$	−5.84074	−1.10380
$29$	4.91361	0.912434	0.456217	−	0.889868i	$-0.349204\pi$
$29$	4.91361	0.912434	0.456217	+	0.889868i	$0.349204\pi$
$30$	13.5687	2.47730
$31$	−8.67382	−1.55786	−0.778932	−	0.627108i	$-0.784238\pi$
$31$	−8.67382	−1.55786	−0.778932	+	0.627108i	$0.784238\pi$
$32$	−4.92896	−0.871326
$33$	6.92293	1.20513
$34$	−18.9743	−3.25407
$35$	5.79825	0.980083
$36$	−6.77406	−1.12901
$37$	−1.99947	−0.328711	−0.164355	−	0.986401i	$-0.552554\pi$
$37$	−1.99947	−0.328711	−0.164355	+	0.986401i	$0.552554\pi$
$38$	19.2368	3.12063
$39$	5.88342	0.942101
$40$	27.2489	4.30842
$41$	4.03710	0.630488	0.315244	−	0.949011i	$-0.397914\pi$
$41$	4.03710	0.630488	0.315244	+	0.949011i	$0.397914\pi$
$42$	4.05371	0.625501
$43$	1.75689	0.267923	0.133962	−	0.990987i	$-0.457230\pi$
$43$	1.75689	0.267923	0.133962	+	0.990987i	$0.457230\pi$
$44$	25.3088	3.81545
$45$	6.72478	1.00247
$46$	−6.50462	−0.959054
$47$	10.9742	1.60076	0.800378	−	0.599495i	$-0.204632\pi$
$47$	10.9742	1.60076	0.800378	+	0.599495i	$0.204632\pi$
$48$	8.27648	1.19461
$49$	−5.26775	−0.752536
$50$	−36.5574	−5.17000
$51$	9.07778	1.27114
$52$	21.5086	2.98270
$53$	−11.6937	−1.60626	−0.803130	−	0.595804i	$-0.796833\pi$
$53$	−11.6937	−1.60626	−0.803130	+	0.595804i	$0.796833\pi$
$54$	13.9414	1.89719
$55$	−25.1247	−3.38782
$56$	8.14068	1.08784
$57$	−9.20337	−1.21902
$58$	−12.4672	−1.63702
$59$	−2.92239	−0.380463	−0.190232	−	0.981739i	$-0.560924\pi$
$59$	−2.92239	−0.380463	−0.190232	+	0.981739i	$0.560924\pi$
$60$	−23.7321	−3.06380
$61$	−2.87812	−0.368506	−0.184253	−	0.982879i	$-0.558987\pi$
$61$	−2.87812	−0.368506	−0.184253	+	0.982879i	$0.558987\pi$
$62$	22.0078	2.79500
$63$	2.00905	0.253117
$64$	−1.13012	−0.141265
$65$	−21.3521	−2.64841
$66$	−17.5654	−2.16215
$67$	7.00109	0.855319	0.427660	−	0.903940i	$-0.359338\pi$
$67$	7.00109	0.855319	0.427660	+	0.903940i	$0.359338\pi$
$68$	33.1865	4.02446
$69$	3.11197	0.374637
$70$	−14.7117	−1.75839
$71$	−4.93369	−0.585521	−0.292761	−	0.956186i	$-0.594574\pi$
$71$	−4.93369	−0.585521	−0.292761	+	0.956186i	$0.594574\pi$
$72$	9.44153	1.11269
$73$	1.52889	0.178943	0.0894714	−	0.995989i	$-0.471482\pi$
$73$	1.52889	0.178943	0.0894714	+	0.995989i	$0.471482\pi$
$74$	5.07320	0.589747
$75$	17.4900	2.01957
$76$	−33.6457	−3.85942
$77$	−7.50609	−0.855399
$78$	−14.9278	−1.69024
$79$	2.68056	0.301586	0.150793	−	0.988565i	$-0.451817\pi$
$79$	2.68056	0.301586	0.150793	+	0.988565i	$0.451817\pi$
$80$	−30.0370	−3.35824
$81$	−2.09053	−0.232281
$82$	−10.2432	−1.13117
$83$	−8.53882	−0.937258	−0.468629	−	0.883395i	$-0.655252\pi$
$83$	−8.53882	−0.937258	−0.468629	+	0.883395i	$0.655252\pi$
$84$	−7.09003	−0.773586
$85$	−32.9451	−3.57340
$86$	−4.45771	−0.480687
$87$	5.96460	0.639472
$88$	−35.2749	−3.76031
$89$	−4.98383	−0.528285	−0.264142	−	0.964484i	$-0.585089\pi$
$89$	−4.98383	−0.528285	−0.264142	+	0.964484i	$0.585089\pi$
$90$	−17.0626	−1.79856
$91$	−6.37902	−0.668703
$92$	11.3767	1.18611
$93$	−10.5291	−1.09182
$94$	−27.8446	−2.87195
$95$	33.4009	3.42686
$96$	−5.98324	−0.610662
$97$	9.89884	1.00507	0.502537	−	0.864556i	$-0.332400\pi$
$97$	9.89884	1.00507	0.502537	+	0.864556i	$0.332400\pi$
$98$	13.3657	1.35014
$99$	−8.70553	−0.874939
$100$	63.9398	6.39398
$101$	8.55752	0.851505	0.425753	−	0.904840i	$-0.360009\pi$
$101$	8.55752	0.851505	0.425753	+	0.904840i	$0.360009\pi$
$102$	−23.0328	−2.28059
$103$	−4.24613	−0.418384	−0.209192	−	0.977875i	$-0.567083\pi$
$103$	−4.24613	−0.418384	−0.209192	+	0.977875i	$0.567083\pi$
$104$	−29.9782	−2.93960
$105$	7.03846	0.686883
$106$	29.6702	2.88183
$107$	−6.73424	−0.651024	−0.325512	−	0.945538i	$-0.605537\pi$
$107$	−6.73424	−0.651024	−0.325512	+	0.945538i	$0.605537\pi$
$108$	−24.3839	−2.34634
$109$	−5.97268	−0.572079	−0.286040	−	0.958218i	$-0.592339\pi$
$109$	−5.97268	−0.572079	−0.286040	+	0.958218i	$0.592339\pi$
$110$	63.7483	6.07816
$111$	−2.42714	−0.230374
$112$	−8.97366	−0.847931
$113$	−12.6327	−1.18839	−0.594193	−	0.804322i	$-0.702528\pi$
$113$	−12.6327	−1.18839	−0.594193	+	0.804322i	$0.702528\pi$
$114$	23.3515	2.18707
$115$	−11.2940	−1.05317
$116$	21.8054	2.02458
$117$	−7.39835	−0.683978
$118$	7.41491	0.682598
$119$	−9.84246	−0.902257
$120$	33.0772	3.01952
$121$	21.5251	1.95683
$122$	7.30259	0.661145
$123$	4.90061	0.441873
$124$	−38.4922	−3.45671
$125$	−41.4473	−3.70716
$126$	−5.09751	−0.454122
$127$	−2.97840	−0.264290	−0.132145	−	0.991230i	$-0.542186\pi$
$127$	−2.97840	−0.264290	−0.132145	+	0.991230i	$0.542186\pi$
$128$	12.7254	1.12477
$129$	2.13268	0.187772
$130$	54.1761	4.75156
$131$	16.6370	1.45358	0.726791	−	0.686859i	$-0.241011\pi$
$131$	16.6370	1.45358	0.726791	+	0.686859i	$0.241011\pi$
$132$	30.7222	2.67403
$133$	9.97864	0.865257
$134$	−17.7637	−1.53455
$135$	24.2065	2.08336
$136$	−46.2546	−3.96630
$137$	6.59412	0.563374	0.281687	−	0.959506i	$-0.409106\pi$
$137$	6.59412	0.563374	0.281687	+	0.959506i	$0.409106\pi$
$138$	−7.89592	−0.672145
$139$	18.3923	1.56001	0.780007	−	0.625771i	$-0.215216\pi$
$139$	18.3923	1.56001	0.780007	+	0.625771i	$0.215216\pi$
$140$	25.7312	2.17468
$141$	13.3216	1.12188
$142$	12.5181	1.05050
$143$	27.6413	2.31148
$144$	−10.4076	−0.867300
$145$	−21.6468	−1.79767
$146$	−3.87920	−0.321045
$147$	−6.39449	−0.527409
$148$	−8.87315	−0.729368
$149$	20.0700	1.64420	0.822101	−	0.569342i	$-0.192802\pi$
$149$	20.0700	1.64420	0.822101	+	0.569342i	$0.192802\pi$
$150$	−44.3768	−3.62335
$151$	0.0927361	0.00754675	0.00377338	−	0.999993i	$-0.498799\pi$
$151$	0.0927361	0.00754675	0.00377338	+	0.999993i	$0.498799\pi$
$152$	46.8946	3.80365
$153$	−11.4152	−0.922867
$154$	19.0450	1.53469
$155$	38.2122	3.06928
$156$	26.1091	2.09040
$157$	−6.87124	−0.548384	−0.274192	−	0.961675i	$-0.588410\pi$
$157$	−6.87124	−0.548384	−0.274192	+	0.961675i	$0.588410\pi$
$158$	−6.80130	−0.541083
$159$	−14.1950	−1.12573
$160$	21.7144	1.71667
$161$	−3.37411	−0.265917
$162$	5.30424	0.416740
$163$	−6.62711	−0.519075	−0.259538	−	0.965733i	$-0.583570\pi$
$163$	−6.62711	−0.519075	−0.259538	+	0.965733i	$0.583570\pi$
$164$	17.9156	1.39897
$165$	−30.4988	−2.37432
$166$	21.6653	1.68155
$167$	−0.262923	−0.0203456	−0.0101728	−	0.999948i	$-0.503238\pi$
$167$	−0.262923	−0.0203456	−0.0101728	+	0.999948i	$0.503238\pi$
$168$	9.88192	0.762407
$169$	10.4908	0.806985
$170$	83.5907	6.41112
$171$	11.5732	0.885023
$172$	7.79663	0.594488
$173$	5.74330	0.436655	0.218328	−	0.975876i	$-0.429940\pi$
$173$	5.74330	0.436655	0.218328	+	0.975876i	$0.429940\pi$
$174$	−15.1338	−1.14729
$175$	−18.9633	−1.43349
$176$	38.8843	2.93101
$177$	−3.54748	−0.266645
$178$	12.6453	0.947807
$179$	25.9416	1.93896	0.969482	−	0.245161i	$-0.0788407\pi$
$179$	25.9416	1.93896	0.969482	+	0.245161i	$0.0788407\pi$
$180$	29.8429	2.22436
$181$	12.3150	0.915366	0.457683	−	0.889115i	$-0.348679\pi$
$181$	12.3150	0.915366	0.457683	+	0.889115i	$0.348679\pi$
$182$	16.1853	1.19973
$183$	−3.49374	−0.258265
$184$	−15.8566	−1.16897
$185$	8.80860	0.647621
$186$	26.7152	1.95885
$187$	42.6489	3.11880
$188$	48.7009	3.55188
$189$	7.23176	0.526033
$190$	−84.7472	−6.14821
$191$	2.84768	0.206051	0.103026	−	0.994679i	$-0.467148\pi$
$191$	2.84768	0.206051	0.103026	+	0.994679i	$0.467148\pi$
$192$	−1.37185	−0.0990047
$193$	−12.5342	−0.902232	−0.451116	−	0.892465i	$-0.648974\pi$
$193$	−12.5342	−0.902232	−0.451116	+	0.892465i	$0.648974\pi$
$194$	−25.1160	−1.80323
$195$	−25.9192	−1.85611
$196$	−23.3770	−1.66978
$197$	5.04161	0.359200	0.179600	−	0.983740i	$-0.442520\pi$
$197$	5.04161	0.359200	0.179600	+	0.983740i	$0.442520\pi$
$198$	22.0883	1.56975
$199$	−10.9079	−0.773237	−0.386619	−	0.922240i	$-0.626357\pi$
$199$	−10.9079	−0.773237	−0.386619	+	0.922240i	$0.626357\pi$
$200$	−89.1178	−6.30158
$201$	8.49858	0.599444
$202$	−21.7128	−1.52770
$203$	−6.46704	−0.453897
$204$	40.2849	2.82051
$205$	−17.7853	−1.24218
$206$	10.7736	0.750632
$207$	−3.91328	−0.271992
$208$	33.0456	2.29130
$209$	−43.2390	−2.99090
$210$	−17.8585	−1.23235
$211$	15.3105	1.05402	0.527008	−	0.849860i	$-0.323314\pi$
$211$	15.3105	1.05402	0.527008	+	0.849860i	$0.323314\pi$
$212$	−51.8939	−3.56409
$213$	−5.98897	−0.410358
$214$	17.0866	1.16802
$215$	−7.73992	−0.527858
$216$	33.9857	2.31243
$217$	11.4160	0.774971
$218$	15.1543	1.02638
$219$	1.85591	0.125411
$220$	−111.497	−7.51714
$221$	36.2450	2.43810
$222$	6.15833	0.413320
$223$	−21.4693	−1.43769	−0.718844	−	0.695172i	$-0.755328\pi$
$223$	−21.4693	−1.43769	−0.718844	+	0.695172i	$0.755328\pi$
$224$	6.48725	0.433447
$225$	−21.9935	−1.46623
$226$	32.0526	2.13211
$227$	10.8357	0.719189	0.359594	−	0.933109i	$-0.382915\pi$
$227$	10.8357	0.719189	0.359594	+	0.933109i	$0.382915\pi$
$228$	−40.8423	−2.70485
$229$	−15.4040	−1.01792	−0.508962	−	0.860789i	$-0.669970\pi$
$229$	−15.4040	−1.01792	−0.508962	+	0.860789i	$0.669970\pi$
$230$	28.6559	1.88951
$231$	−9.11160	−0.599499
$232$	−30.3918	−1.99532
$233$	−17.6468	−1.15608	−0.578041	−	0.816008i	$-0.696183\pi$
$233$	−17.6468	−1.15608	−0.578041	+	0.816008i	$0.696183\pi$
$234$	18.7716	1.22714
$235$	−48.3466	−3.15379
$236$	−12.9689	−0.844201
$237$	3.25391	0.211364
$238$	24.9730	1.61876
$239$	22.3474	1.44553	0.722766	−	0.691093i	$-0.242871\pi$
$239$	22.3474	1.44553	0.722766	+	0.691093i	$0.242871\pi$
$240$	−36.4618	−2.35360
$241$	−12.0496	−0.776181	−0.388091	−	0.921621i	$-0.626865\pi$
$241$	−12.0496	−0.776181	−0.388091	+	0.921621i	$0.626865\pi$
$242$	−54.6150	−3.51079
$243$	13.9463	0.894653
$244$	−12.7724	−0.817669
$245$	23.2069	1.48264
$246$	−12.4342	−0.792774
$247$	−36.7464	−2.33812
$248$	53.6496	3.40675
$249$	−10.3652	−0.656869
$250$	105.163	6.65110
$251$	−1.11272	−0.0702345	−0.0351173	−	0.999383i	$-0.511180\pi$
$251$	−1.11272	−0.0702345	−0.0351173	+	0.999383i	$0.511180\pi$
$252$	8.91566	0.561634
$253$	14.6206	0.919187
$254$	7.55700	0.474168
$255$	−39.9919	−2.50439
$256$	−30.0274	−1.87672
$257$	3.52992	0.220190	0.110095	−	0.993921i	$-0.464884\pi$
$257$	3.52992	0.220190	0.110095	+	0.993921i	$0.464884\pi$
$258$	−5.41118	−0.336885
$259$	2.63160	0.163520
$260$	−94.7554	−5.87648
$261$	−7.50044	−0.464266
$262$	−42.2126	−2.60790
$263$	14.5347	0.896247	0.448124	−	0.893972i	$-0.352092\pi$
$263$	14.5347	0.896247	0.448124	+	0.893972i	$0.352092\pi$
$264$	−42.8199	−2.63539
$265$	51.5164	3.16463
$266$	−25.3185	−1.55238
$267$	−6.04984	−0.370244
$268$	31.0691	1.89785
$269$	7.14872	0.435865	0.217933	−	0.975964i	$-0.430069\pi$
$269$	7.14872	0.435865	0.217933	+	0.975964i	$0.430069\pi$
$270$	−61.4184	−3.73781
$271$	23.3869	1.42065	0.710326	−	0.703873i	$-0.248548\pi$
$271$	23.3869	1.42065	0.710326	+	0.703873i	$0.248548\pi$
$272$	50.9875	3.09157
$273$	−7.74345	−0.468655
$274$	−16.7311	−1.01076
$275$	82.1708	4.95509
$276$	13.8101	0.831273
$277$	16.3749	0.983871	0.491936	−	0.870632i	$-0.336290\pi$
$277$	16.3749	0.983871	0.491936	+	0.870632i	$0.336290\pi$
$278$	−46.6662	−2.79886
$279$	13.2403	0.792674
$280$	−35.8635	−2.14326
$281$	3.51555	0.209720	0.104860	−	0.994487i	$-0.466561\pi$
$281$	3.51555	0.209720	0.104860	+	0.994487i	$0.466561\pi$
$282$	−33.8004	−2.01278
$283$	7.21955	0.429158	0.214579	−	0.976707i	$-0.431162\pi$
$283$	7.21955	0.429158	0.214579	+	0.976707i	$0.431162\pi$
$284$	−21.8945	−1.29920
$285$	40.5452	2.40169
$286$	−70.1335	−4.14708
$287$	−5.31342	−0.313641
$288$	7.52388	0.443349
$289$	38.9239	2.28964
$290$	54.9237	3.22523
$291$	12.0161	0.704398
$292$	6.78482	0.397052
$293$	−3.13245	−0.183000	−0.0914999	−	0.995805i	$-0.529166\pi$
$293$	−3.13245	−0.183000	−0.0914999	+	0.995805i	$0.529166\pi$
$294$	16.2246	0.946236
$295$	12.8745	0.749583
$296$	12.3672	0.718828
$297$	−31.3364	−1.81832
$298$	−50.9232	−2.94990
$299$	12.4252	0.718569
$300$	77.6161	4.48117
$301$	−2.31233	−0.133280
$302$	−0.235297	−0.0135398
$303$	10.3879	0.596771
$304$	−51.6929	−2.96479
$305$	12.6795	0.726025
$306$	28.9636	1.65574
$307$	23.7345	1.35460	0.677300	−	0.735707i	$-0.263150\pi$
$307$	23.7345	1.35460	0.677300	+	0.735707i	$0.263150\pi$
$308$	−33.3102	−1.89802
$309$	−5.15435	−0.293221
$310$	−96.9549	−5.50667
$311$	−12.0478	−0.683170	−0.341585	−	0.939851i	$-0.610964\pi$
$311$	−12.0478	−0.683170	−0.341585	+	0.939851i	$0.610964\pi$
$312$	−36.3903	−2.06020
$313$	16.3525	0.924297	0.462149	−	0.886802i	$-0.347079\pi$
$313$	16.3525	0.924297	0.462149	+	0.886802i	$0.347079\pi$
$314$	17.4342	0.983869
$315$	−8.85081	−0.498687
$316$	11.8956	0.669182
$317$	−10.5988	−0.595286	−0.297643	−	0.954677i	$-0.596201\pi$
$317$	−10.5988	−0.595286	−0.297643	+	0.954677i	$0.596201\pi$
$318$	36.0165	2.01970
$319$	28.0227	1.56897
$320$	4.97872	0.278319
$321$	−8.17465	−0.456265
$322$	8.56104	0.477088
$323$	−56.6977	−3.15474
$324$	−9.27724	−0.515402
$325$	69.8325	3.87361
$326$	16.8148	0.931285
$327$	−7.25020	−0.400937
$328$	−24.9704	−1.37876
$329$	−14.4437	−0.796308
$330$	77.3836	4.25983
$331$	1.06052	0.0582916	0.0291458	−	0.999575i	$-0.490721\pi$
$331$	1.06052	0.0582916	0.0291458	+	0.999575i	$0.490721\pi$
$332$	−37.8932	−2.07966
$333$	3.05212	0.167255
$334$	0.667107	0.0365025
$335$	−30.8431	−1.68514
$336$	−10.8931	−0.594266
$337$	11.8840	0.647364	0.323682	−	0.946166i	$-0.395079\pi$
$337$	11.8840	0.647364	0.323682	+	0.946166i	$0.395079\pi$
$338$	−26.6180	−1.44783
$339$	−15.3348	−0.832871
$340$	−146.202	−7.92893
$341$	−49.4675	−2.67881
$342$	−29.3643	−1.58784
$343$	16.1462	0.871812
$344$	−10.8668	−0.585897
$345$	−13.7097	−0.738105
$346$	−14.5723	−0.783413
$347$	26.3717	1.41571	0.707854	−	0.706359i	$-0.249663\pi$
$347$	26.3717	1.41571	0.707854	+	0.706359i	$0.249663\pi$
$348$	26.4694	1.41891
$349$	8.10312	0.433750	0.216875	−	0.976199i	$-0.430414\pi$
$349$	8.10312	0.433750	0.216875	+	0.976199i	$0.430414\pi$
$350$	48.1150	2.57185
$351$	−26.6311	−1.42146
$352$	−28.1103	−1.49828
$353$	−12.4716	−0.663798	−0.331899	−	0.943315i	$-0.607689\pi$
$353$	−12.4716	−0.663798	−0.331899	+	0.943315i	$0.607689\pi$
$354$	9.00091	0.478393
$355$	21.7352	1.15359
$356$	−22.1170	−1.17220
$357$	−11.9477	−0.632339
$358$	−65.8209	−3.47874
$359$	−12.6203	−0.666073	−0.333037	−	0.942914i	$-0.608073\pi$
$359$	−12.6203	−0.666073	−0.333037	+	0.942914i	$0.608073\pi$
$360$	−41.5943	−2.19221
$361$	38.4821	2.02538
$362$	−31.2465	−1.64228
$363$	26.1292	1.37143
$364$	−28.3085	−1.48377
$365$	−6.73547	−0.352550
$366$	8.86456	0.463358
$367$	−16.2279	−0.847087	−0.423544	−	0.905876i	$-0.639214\pi$
$367$	−16.2279	−0.847087	−0.423544	+	0.905876i	$0.639214\pi$
$368$	17.4791	0.911162
$369$	−6.16247	−0.320806
$370$	−22.3498	−1.16191
$371$	15.3907	0.799045
$372$	−46.7255	−2.42260
$373$	−31.2069	−1.61583	−0.807915	−	0.589299i	$-0.799404\pi$
$373$	−31.2069	−1.61583	−0.807915	+	0.589299i	$0.799404\pi$
$374$	−108.212	−5.59551
$375$	−50.3127	−2.59813
$376$	−67.8782	−3.50055
$377$	23.8149	1.22653
$378$	−18.3490	−0.943768
$379$	−0.673580	−0.0345995	−0.0172998	−	0.999850i	$-0.505507\pi$
$379$	−0.673580	−0.0345995	−0.0172998	+	0.999850i	$0.505507\pi$
$380$	148.225	7.60378
$381$	−3.61546	−0.185225
$382$	−7.22535	−0.369681
$383$	−12.9236	−0.660366	−0.330183	−	0.943917i	$-0.607111\pi$
$383$	−12.9236	−0.660366	−0.330183	+	0.943917i	$0.607111\pi$
$384$	15.4472	0.788288
$385$	33.0679	1.68529
$386$	31.8027	1.61872
$387$	−2.68182	−0.136325
$388$	43.9286	2.23013
$389$	23.5198	1.19250	0.596252	−	0.802798i	$-0.296656\pi$
$389$	23.5198	1.19250	0.596252	+	0.802798i	$0.296656\pi$
$390$	65.7641	3.33009
$391$	19.1714	0.969539
$392$	32.5823	1.64565
$393$	20.1956	1.01873
$394$	−12.7919	−0.644449
$395$	−11.8091	−0.594181
$396$	−38.6330	−1.94138
$397$	7.33816	0.368292	0.184146	−	0.982899i	$-0.441048\pi$
$397$	7.33816	0.368292	0.184146	+	0.982899i	$0.441048\pi$
$398$	27.6762	1.38728
$399$	12.1130	0.606409
$400$	98.2366	4.91183
$401$	−2.69125	−0.134395	−0.0671973	−	0.997740i	$-0.521406\pi$
$401$	−2.69125	−0.134395	−0.0671973	+	0.997740i	$0.521406\pi$
$402$	−21.5632	−1.07548
$403$	−42.0397	−2.09415
$404$	37.9761	1.88938
$405$	9.20975	0.457636
$406$	16.4086	0.814347
$407$	−11.4031	−0.565232
$408$	−56.1482	−2.77975
$409$	34.4709	1.70448	0.852238	−	0.523154i	$-0.175245\pi$
$409$	34.4709	1.70448	0.852238	+	0.523154i	$0.175245\pi$
$410$	45.1261	2.22862
$411$	8.00456	0.394836
$412$	−18.8433	−0.928342
$413$	3.84630	0.189264
$414$	9.92906	0.487986
$415$	37.6175	1.84657
$416$	−23.8894	−1.17127
$417$	22.3263	1.09332
$418$	109.709	5.36605
$419$	27.9342	1.36468	0.682338	−	0.731037i	$-0.260963\pi$
$419$	27.9342	1.36468	0.682338	+	0.731037i	$0.260963\pi$
$420$	31.2349	1.52411
$421$	−34.4035	−1.67672	−0.838362	−	0.545114i	$-0.816486\pi$
$421$	−34.4035	−1.67672	−0.838362	+	0.545114i	$0.816486\pi$
$422$	−38.8468	−1.89103
$423$	−16.7518	−0.814498
$424$	72.3285	3.51258
$425$	107.748	5.22652
$426$	15.1957	0.736232
$427$	3.78804	0.183316
$428$	−29.8849	−1.44454
$429$	33.5536	1.61998
$430$	19.6383	0.947042
$431$	−21.1310	−1.01785	−0.508923	−	0.860812i	$-0.669956\pi$
$431$	−21.1310	−1.01785	−0.508923	+	0.860812i	$0.669956\pi$
$432$	−37.4632	−1.80245
$433$	−23.9539	−1.15115	−0.575576	−	0.817748i	$-0.695222\pi$
$433$	−23.9539	−1.15115	−0.575576	+	0.817748i	$0.695222\pi$
$434$	−28.9656	−1.39039
$435$	−26.2769	−1.25988
$436$	−26.5053	−1.26937
$437$	−19.4366	−0.929781
$438$	−4.70894	−0.225002
$439$	35.8583	1.71143	0.855713	−	0.517451i	$-0.173119\pi$
$439$	35.8583	1.71143	0.855713	+	0.517451i	$0.173119\pi$
$440$	155.402	7.40852
$441$	8.04103	0.382906
$442$	−91.9634	−4.37425
$443$	21.3835	1.01596	0.507981	−	0.861368i	$-0.330392\pi$
$443$	21.3835	1.01596	0.507981	+	0.861368i	$0.330392\pi$
$444$	−10.7711	−0.511172
$445$	21.9561	1.04082
$446$	54.4733	2.57939
$447$	24.3629	1.15233
$448$	1.48741	0.0702735
$449$	−7.19891	−0.339737	−0.169869	−	0.985467i	$-0.554334\pi$
$449$	−7.19891	−0.339737	−0.169869	+	0.985467i	$0.554334\pi$
$450$	55.8035	2.63060
$451$	23.0239	1.08415
$452$	−56.0608	−2.63688
$453$	0.112572	0.00528908
$454$	−27.4931	−1.29031
$455$	28.1026	1.31747
$456$	56.9250	2.66576
$457$	−8.81272	−0.412242	−0.206121	−	0.978527i	$-0.566084\pi$
$457$	−8.81272	−0.412242	−0.206121	+	0.978527i	$0.566084\pi$
$458$	39.0841	1.82628
$459$	−41.0902	−1.91793
$460$	−50.1199	−2.33685
$461$	2.45118	0.114163	0.0570813	−	0.998370i	$-0.481821\pi$
$461$	2.45118	0.114163	0.0570813	+	0.998370i	$0.481821\pi$
$462$	23.1186	1.07558
$463$	19.5521	0.908664	0.454332	−	0.890832i	$-0.349878\pi$
$463$	19.5521	0.908664	0.454332	+	0.890832i	$0.349878\pi$
$464$	33.5016	1.55527
$465$	46.3856	2.15108
$466$	44.7748	2.07415
$467$	11.6542	0.539292	0.269646	−	0.962959i	$-0.413093\pi$
$467$	11.6542	0.539292	0.269646	+	0.962959i	$0.413093\pi$
$468$	−32.8320	−1.51766
$469$	−9.21447	−0.425485
$470$	122.669	5.65828
$471$	−8.34095	−0.384331
$472$	18.0757	0.832001
$473$	10.0197	0.460705
$474$	−8.25606	−0.379213
$475$	−109.238	−5.01220
$476$	−43.6784	−2.00199
$477$	17.8501	0.817298
$478$	−56.7014	−2.59346
$479$	3.66376	0.167401	0.0837006	−	0.996491i	$-0.473326\pi$
$479$	3.66376	0.167401	0.0837006	+	0.996491i	$0.473326\pi$
$480$	26.3590	1.20312
$481$	−9.69089	−0.441867
$482$	30.5730	1.39256
$483$	−4.09581	−0.186366
$484$	95.5230	4.34195
$485$	−43.6090	−1.98018
$486$	−35.3854	−1.60512
$487$	−11.0151	−0.499142	−0.249571	−	0.968356i	$-0.580290\pi$
$487$	−11.0151	−0.499142	−0.249571	+	0.968356i	$0.580290\pi$
$488$	17.8019	0.805853
$489$	−8.04461	−0.363790
$490$	−58.8823	−2.66003
$491$	11.1952	0.505232	0.252616	−	0.967567i	$-0.418709\pi$
$491$	11.1952	0.505232	0.252616	+	0.967567i	$0.418709\pi$
$492$	21.7477	0.980460
$493$	36.7451	1.65492
$494$	93.2357	4.19487
$495$	38.3520	1.72379
$496$	−59.1392	−2.65543
$497$	6.49346	0.291272
$498$	26.2994	1.17850
$499$	−13.5176	−0.605132	−0.302566	−	0.953128i	$-0.597843\pi$
$499$	−13.5176	−0.605132	−0.302566	+	0.953128i	$0.597843\pi$
$500$	−183.933	−8.22573
$501$	−0.319160	−0.0142590
$502$	2.82328	0.126009
$503$	−1.29230	−0.0576206	−0.0288103	−	0.999585i	$-0.509172\pi$
$503$	−1.29230	−0.0576206	−0.0288103	+	0.999585i	$0.509172\pi$
$504$	−12.4264	−0.553518
$505$	−37.6999	−1.67762
$506$	−37.0964	−1.64913
$507$	12.7347	0.565569
$508$	−13.2174	−0.586426
$509$	−15.6682	−0.694482	−0.347241	−	0.937776i	$-0.612881\pi$
$509$	−15.6682	−0.694482	−0.347241	+	0.937776i	$0.612881\pi$
$510$	101.470	4.49318
$511$	−2.01224	−0.0890164
$512$	50.7371	2.24228
$513$	41.6587	1.83928
$514$	−8.95636	−0.395048
$515$	18.7062	0.824294
$516$	9.46429	0.416642
$517$	62.5869	2.75257
$518$	−6.67708	−0.293374
$519$	6.97176	0.306026
$520$	132.068	5.79156
$521$	23.0654	1.01051	0.505256	−	0.862969i	$-0.331398\pi$
$521$	23.0654	1.01051	0.505256	+	0.862969i	$0.331398\pi$
$522$	19.0307	0.832949
$523$	−11.5841	−0.506538	−0.253269	−	0.967396i	$-0.581506\pi$
$523$	−11.5841	−0.506538	−0.253269	+	0.967396i	$0.581506\pi$
$524$	73.8308	3.22532
$525$	−23.0194	−1.00465
$526$	−36.8785	−1.60798
$527$	−64.8648	−2.82556
$528$	47.2014	2.05418
$529$	−16.4278	−0.714253
$530$	−130.711	−5.67773
$531$	4.46092	0.193588
$532$	44.2827	1.91990
$533$	19.5667	0.847529
$534$	15.3501	0.664263
$535$	29.6675	1.28264
$536$	−43.3034	−1.87042
$537$	31.4903	1.35891
$538$	−18.1382	−0.781995
$539$	−30.0424	−1.29402
$540$	107.422	4.62272
$541$	9.14254	0.393069	0.196534	−	0.980497i	$-0.437031\pi$
$541$	9.14254	0.393069	0.196534	+	0.980497i	$0.437031\pi$
$542$	−59.3388	−2.54882
$543$	14.9491	0.641527
$544$	−36.8599	−1.58036
$545$	26.3125	1.12710
$546$	19.6472	0.840824
$547$	−42.3058	−1.80887	−0.904433	−	0.426615i	$-0.859706\pi$
$547$	−42.3058	−1.80887	−0.904433	+	0.426615i	$0.859706\pi$
$548$	29.2630	1.25006
$549$	4.39335	0.187504
$550$	−208.490	−8.89003
$551$	−37.2535	−1.58705
$552$	−19.2483	−0.819261
$553$	−3.52801	−0.150026
$554$	−41.5475	−1.76519
$555$	10.6927	0.453880
$556$	81.6204	3.46147
$557$	18.0584	0.765158	0.382579	−	0.923923i	$-0.375036\pi$
$557$	18.0584	0.765158	0.382579	+	0.923923i	$0.375036\pi$
$558$	−33.5941	−1.42215
$559$	8.51517	0.360153
$560$	39.5332	1.67058
$561$	51.7713	2.18578
$562$	−8.91990	−0.376263
$563$	−40.4696	−1.70559	−0.852795	−	0.522246i	$-0.825094\pi$
$563$	−40.4696	−1.70559	−0.852795	+	0.522246i	$0.825094\pi$
$564$	59.1177	2.48930
$565$	55.6530	2.34134
$566$	−18.3180	−0.769961
$567$	2.75144	0.115550
$568$	30.5160	1.28042
$569$	1.56030	0.0654114	0.0327057	−	0.999465i	$-0.489588\pi$
$569$	1.56030	0.0654114	0.0327057	+	0.999465i	$0.489588\pi$
$570$	−102.874	−4.30892
$571$	4.63111	0.193806	0.0969029	−	0.995294i	$-0.469106\pi$
$571$	4.63111	0.193806	0.0969029	+	0.995294i	$0.469106\pi$
$572$	122.665	5.12889
$573$	3.45678	0.144409
$574$	13.4816	0.562710
$575$	36.9371	1.54039
$576$	1.72509	0.0718787
$577$	14.0643	0.585505	0.292753	−	0.956188i	$-0.405429\pi$
$577$	14.0643	0.585505	0.292753	+	0.956188i	$0.405429\pi$
$578$	−98.7606	−4.10790
$579$	−15.2152	−0.632322
$580$	−96.0629	−3.98879
$581$	11.2384	0.466246
$582$	−30.4882	−1.26378
$583$	−66.6903	−2.76203
$584$	−9.45653	−0.391314
$585$	32.5932	1.34756
$586$	7.94788	0.328324
$587$	33.0743	1.36512	0.682560	−	0.730829i	$-0.260866\pi$
$587$	33.0743	1.36512	0.682560	+	0.730829i	$0.260866\pi$
$588$	−28.3772	−1.17025
$589$	65.7623	2.70969
$590$	−32.6662	−1.34484
$591$	6.11998	0.251742
$592$	−13.6326	−0.560298
$593$	7.32768	0.300912	0.150456	−	0.988617i	$-0.451926\pi$
$593$	7.32768	0.300912	0.150456	+	0.988617i	$0.451926\pi$
$594$	79.5089	3.26229
$595$	43.3606	1.77761
$596$	89.0658	3.64828
$597$	−13.2410	−0.541917
$598$	−31.5261	−1.28920
$599$	4.98219	0.203567	0.101783	−	0.994807i	$-0.467545\pi$
$599$	4.98219	0.203567	0.101783	+	0.994807i	$0.467545\pi$
$600$	−108.180	−4.41641
$601$	13.5715	0.553594	0.276797	−	0.960928i	$-0.410727\pi$
$601$	13.5715	0.553594	0.276797	+	0.960928i	$0.410727\pi$
$602$	5.86700	0.239121
$603$	−10.6869	−0.435204
$604$	0.411539	0.0167453
$605$	−94.8281	−3.85531
$606$	−26.3570	−1.07068
$607$	−1.78984	−0.0726474	−0.0363237	−	0.999340i	$-0.511565\pi$
$607$	−1.78984	−0.0726474	−0.0363237	+	0.999340i	$0.511565\pi$
$608$	37.3699	1.51555
$609$	−7.85030	−0.318110
$610$	−32.1713	−1.30258
$611$	53.1892	2.15180
$612$	−50.6580	−2.04773
$613$	42.2032	1.70457	0.852285	−	0.523077i	$-0.175216\pi$
$613$	42.2032	1.70457	0.852285	+	0.523077i	$0.175216\pi$
$614$	−60.2209	−2.43032
$615$	−21.5895	−0.870571
$616$	46.4270	1.87060
$617$	38.3865	1.54538	0.772692	−	0.634781i	$-0.218910\pi$
$617$	38.3865	1.54538	0.772692	+	0.634781i	$0.218910\pi$
$618$	13.0780	0.526074
$619$	26.9262	1.08225	0.541127	−	0.840941i	$-0.317998\pi$
$619$	26.9262	1.08225	0.541127	+	0.840941i	$0.317998\pi$
$620$	169.576	6.81035
$621$	−14.0862	−0.565261
$622$	30.5686	1.22569
$623$	6.55945	0.262799
$624$	40.1139	1.60584
$625$	110.554	4.42217
$626$	−41.4907	−1.65830
$627$	−52.4876	−2.09615
$628$	−30.4928	−1.21680
$629$	−14.9525	−0.596195
$630$	22.4569	0.894705
$631$	10.6874	0.425460	0.212730	−	0.977111i	$-0.431765\pi$
$631$	10.6874	0.425460	0.212730	+	0.977111i	$0.431765\pi$
$632$	−16.5799	−0.659512
$633$	18.5853	0.738699
$634$	26.8920	1.06802
$635$	13.1212	0.520700
$636$	−62.9937	−2.49786
$637$	−25.5314	−1.01159
$638$	−71.1012	−2.81492
$639$	7.53109	0.297925
$640$	−56.0612	−2.21601
$641$	50.0486	1.97680	0.988400	−	0.151874i	$-0.0485307\pi$
$641$	50.0486	1.97680	0.988400	+	0.151874i	$0.0485307\pi$
$642$	20.7413	0.818595
$643$	−39.7694	−1.56835	−0.784176	−	0.620539i	$-0.786914\pi$
$643$	−39.7694	−1.56835	−0.784176	+	0.620539i	$0.786914\pi$
$644$	−14.9735	−0.590037
$645$	−9.39544	−0.369945
$646$	143.857	5.66000
$647$	−12.7983	−0.503154	−0.251577	−	0.967837i	$-0.580949\pi$
$647$	−12.7983	−0.503154	−0.251577	+	0.967837i	$0.580949\pi$
$648$	12.9304	0.507954
$649$	−16.6666	−0.654223
$650$	−177.184	−6.94973
$651$	13.8579	0.543132
$652$	−29.4095	−1.15176
$653$	−11.6790	−0.457034	−0.228517	−	0.973540i	$-0.573388\pi$
$653$	−11.6790	−0.457034	−0.228517	+	0.973540i	$0.573388\pi$
$654$	18.3957	0.719330
$655$	−73.2938	−2.86383
$656$	27.5254	1.07469
$657$	−2.33379	−0.0910498
$658$	36.6476	1.42867
$659$	10.7454	0.418579	0.209290	−	0.977854i	$-0.432885\pi$
$659$	10.7454	0.418579	0.209290	+	0.977854i	$0.432885\pi$
$660$	−135.346	−5.26833
$661$	−27.9466	−1.08700	−0.543499	−	0.839410i	$-0.682901\pi$
$661$	−27.9466	−1.08700	−0.543499	+	0.839410i	$0.682901\pi$
$662$	−2.69084	−0.104582
$663$	43.9975	1.70872
$664$	52.8146	2.04960
$665$	−43.9606	−1.70472
$666$	−7.74405	−0.300076
$667$	12.5967	0.487745
$668$	−1.16679	−0.0451443
$669$	−26.0614	−1.00759
$670$	78.2573	3.02334
$671$	−16.4142	−0.633662
$672$	7.87483	0.303778
$673$	10.9366	0.421573	0.210787	−	0.977532i	$-0.432397\pi$
$673$	10.9366	0.421573	0.210787	+	0.977532i	$0.432397\pi$
$674$	−30.1530	−1.16145
$675$	−79.1677	−3.04717
$676$	46.5556	1.79060
$677$	−42.9945	−1.65241	−0.826207	−	0.563367i	$-0.809506\pi$
$677$	−42.9945	−1.65241	−0.826207	+	0.563367i	$0.809506\pi$
$678$	38.9085	1.49427
$679$	−13.0283	−0.499982
$680$	203.773	7.81435
$681$	13.1534	0.504038
$682$	125.512	4.80612
$683$	11.8438	0.453191	0.226596	−	0.973989i	$-0.427240\pi$
$683$	11.8438	0.453191	0.226596	+	0.973989i	$0.427240\pi$
$684$	51.3588	1.96375
$685$	−29.0502	−1.10995
$686$	−40.9673	−1.56414
$687$	−18.6988	−0.713403
$688$	11.9787	0.456683
$689$	−56.6764	−2.15920
$690$	34.7852	1.32425
$691$	−35.2088	−1.33940	−0.669702	−	0.742630i	$-0.733578\pi$
$691$	−35.2088	−1.33940	−0.669702	+	0.742630i	$0.733578\pi$
$692$	25.4873	0.968884
$693$	11.4578	0.435245
$694$	−66.9122	−2.53995
$695$	−81.0267	−3.07352
$696$	−36.8924	−1.39840
$697$	30.1903	1.14354
$698$	−20.5598	−0.778200
$699$	−21.4214	−0.810230
$700$	−84.1542	−3.18073
$701$	24.0983	0.910181	0.455090	−	0.890445i	$-0.349607\pi$
$701$	24.0983	0.910181	0.455090	+	0.890445i	$0.349607\pi$
$702$	67.5703	2.55027
$703$	15.1594	0.571747
$704$	−6.44518	−0.242912
$705$	−58.6877	−2.21031
$706$	31.6439	1.19094
$707$	−11.2630	−0.423588
$708$	−15.7428	−0.591651
$709$	1.60886	0.0604221	0.0302110	−	0.999544i	$-0.490382\pi$
$709$	1.60886	0.0604221	0.0302110	+	0.999544i	$0.490382\pi$
$710$	−55.1481	−2.06967
$711$	−4.09177	−0.153453
$712$	30.8261	1.15526
$713$	−22.2364	−0.832761
$714$	30.3146	1.13449
$715$	−121.773	−4.55405
$716$	115.122	4.30232
$717$	27.1273	1.01309
$718$	32.0211	1.19502
$719$	18.9324	0.706060	0.353030	−	0.935612i	$-0.385151\pi$
$719$	18.9324	0.706060	0.353030	+	0.935612i	$0.385151\pi$
$720$	45.8504	1.70874
$721$	5.58854	0.208128
$722$	−97.6396	−3.63377
$723$	−14.6269	−0.543980
$724$	54.6509	2.03108
$725$	70.7961	2.62930
$726$	−66.2968	−2.46051
$727$	12.3011	0.456222	0.228111	−	0.973635i	$-0.426745\pi$
$727$	12.3011	0.456222	0.228111	+	0.973635i	$0.426745\pi$
$728$	39.4557	1.46233
$729$	23.2009	0.859291
$730$	17.0897	0.632519
$731$	13.1384	0.485942
$732$	−15.5043	−0.573057
$733$	1.49927	0.0553768	0.0276884	−	0.999617i	$-0.491185\pi$
$733$	1.49927	0.0553768	0.0276884	+	0.999617i	$0.491185\pi$
$734$	41.1745	1.51978
$735$	28.1707	1.03909
$736$	−12.6360	−0.465770
$737$	39.9278	1.47076
$738$	15.6359	0.575564
$739$	29.1088	1.07078	0.535392	−	0.844603i	$-0.320164\pi$
$739$	29.1088	1.07078	0.535392	+	0.844603i	$0.320164\pi$
$740$	39.0904	1.43699
$741$	−44.6063	−1.63865
$742$	−39.0504	−1.43358
$743$	−23.5572	−0.864230	−0.432115	−	0.901819i	$-0.642233\pi$
$743$	−23.5572	−0.864230	−0.432115	+	0.901819i	$0.642233\pi$
$744$	65.1249	2.38760
$745$	−88.4179	−3.23938
$746$	79.1803	2.89900
$747$	13.0342	0.476896
$748$	189.265	6.92022
$749$	8.86326	0.323856
$750$	127.657	4.66137
$751$	38.7457	1.41385	0.706925	−	0.707289i	$-0.250082\pi$
$751$	38.7457	1.41385	0.706925	+	0.707289i	$0.250082\pi$
$752$	74.8237	2.72854
$753$	−1.35073	−0.0492233
$754$	−60.4250	−2.20055
$755$	−0.408546	−0.0148685
$756$	32.0928	1.16720
$757$	31.1669	1.13278	0.566391	−	0.824137i	$-0.308339\pi$
$757$	31.1669	1.13278	0.566391	+	0.824137i	$0.308339\pi$
$758$	1.70906	0.0620757
$759$	17.7478	0.644205
$760$	−206.593	−7.49390
$761$	11.0633	0.401046	0.200523	−	0.979689i	$-0.435736\pi$
$761$	11.0633	0.401046	0.200523	+	0.979689i	$0.435736\pi$
$762$	9.17340	0.332317
$763$	7.86093	0.284585
$764$	12.6373	0.457202
$765$	50.2895	1.81822
$766$	32.7908	1.18478
$767$	−14.1641	−0.511435
$768$	−36.4501	−1.31528
$769$	−48.8529	−1.76168	−0.880840	−	0.473415i	$-0.843021\pi$
$769$	−48.8529	−1.76168	−0.880840	+	0.473415i	$0.843021\pi$
$770$	−83.9022	−3.02362
$771$	4.28495	0.154319
$772$	−55.6237	−2.00194
$773$	−36.2413	−1.30351	−0.651754	−	0.758430i	$-0.725967\pi$
$773$	−36.2413	−1.30351	−0.651754	+	0.758430i	$0.725967\pi$
$774$	6.80452	0.244583
$775$	−124.974	−4.48919
$776$	−61.2266	−2.19791
$777$	3.19448	0.114601
$778$	−59.6762	−2.13950
$779$	−30.6080	−1.09665
$780$	−115.023	−4.11848
$781$	−28.1372	−1.00683
$782$	−48.6431	−1.73947
$783$	−26.9985	−0.964849
$784$	−35.9162	−1.28272
$785$	30.2710	1.08042
$786$	−51.2416	−1.82773
$787$	20.3251	0.724512	0.362256	−	0.932079i	$-0.382007\pi$
$787$	20.3251	0.724512	0.362256	+	0.932079i	$0.382007\pi$
$788$	22.3734	0.797020
$789$	17.6436	0.628128
$790$	29.9629	1.06603
$791$	16.6265	0.591171
$792$	53.8458	1.91333
$793$	−13.9495	−0.495361
$794$	−18.6189	−0.660760
$795$	62.5355	2.21790
$796$	−48.4063	−1.71572
$797$	13.9619	0.494555	0.247278	−	0.968945i	$-0.420464\pi$
$797$	13.9619	0.494555	0.247278	+	0.968945i	$0.420464\pi$
$798$	−30.7340	−1.08797
$799$	82.0678	2.90335
$800$	−71.0173	−2.51084
$801$	7.60762	0.268802
$802$	6.82843	0.241120
$803$	8.71936	0.307700
$804$	37.7146	1.33009
$805$	14.8646	0.523907
$806$	106.666	3.75715
$807$	8.67779	0.305473
$808$	−52.9303	−1.86208
$809$	−25.1461	−0.884089	−0.442044	−	0.896993i	$-0.645747\pi$
$809$	−25.1461	−0.884089	−0.442044	+	0.896993i	$0.645747\pi$
$810$	−23.3676	−0.821055
$811$	50.0949	1.75907	0.879534	−	0.475835i	$-0.157854\pi$
$811$	50.0949	1.75907	0.879534	+	0.475835i	$0.157854\pi$
$812$	−28.6991	−1.00714
$813$	28.3892	0.995652
$814$	28.9329	1.01410
$815$	29.1955	1.02267
$816$	61.8934	2.16670
$817$	−13.3202	−0.466015
$818$	−87.4621	−3.05804
$819$	9.73733	0.340250
$820$	−78.9267	−2.75624
$821$	−31.1410	−1.08683	−0.543414	−	0.839465i	$-0.682869\pi$
$821$	−31.1410	−1.08683	−0.543414	+	0.839465i	$0.682869\pi$
$822$	−20.3097	−0.708384
$823$	−3.24859	−0.113239	−0.0566193	−	0.998396i	$-0.518032\pi$
$823$	−3.24859	−0.113239	−0.0566193	+	0.998396i	$0.518032\pi$
$824$	26.2633	0.914926
$825$	99.7467	3.47273
$826$	−9.75912	−0.339563
$827$	29.2992	1.01883	0.509416	−	0.860520i	$-0.329862\pi$
$827$	29.2992	1.01883	0.509416	+	0.860520i	$0.329862\pi$
$828$	−17.3662	−0.603516
$829$	−13.6311	−0.473429	−0.236715	−	0.971579i	$-0.576071\pi$
$829$	−13.6311	−0.473429	−0.236715	+	0.971579i	$0.576071\pi$
$830$	−95.4459	−3.31297
$831$	19.8774	0.689538
$832$	−5.47740	−0.189895
$833$	−39.3935	−1.36490
$834$	−56.6479	−1.96155
$835$	1.15830	0.0400846
$836$	−191.884	−6.63644
$837$	47.6596	1.64736
$838$	−70.8767	−2.44839
$839$	−25.3836	−0.876340	−0.438170	−	0.898892i	$-0.644373\pi$
$839$	−25.3836	−0.876340	−0.438170	+	0.898892i	$0.644373\pi$
$840$	−43.5345	−1.50208
$841$	−4.85644	−0.167463
$842$	87.2910	3.00825
$843$	4.26750	0.146981
$844$	67.9440	2.33873
$845$	−46.2169	−1.58991
$846$	42.5037	1.46131
$847$	−28.3302	−0.973438
$848$	−79.7294	−2.73792
$849$	8.76376	0.300772
$850$	−273.385	−9.37702
$851$	−5.12590	−0.175713
$852$	−26.5776	−0.910532
$853$	26.1518	0.895421	0.447710	−	0.894179i	$-0.352240\pi$
$853$	26.1518	0.895421	0.447710	+	0.894179i	$0.352240\pi$
$854$	−9.61128	−0.328891
$855$	−50.9853	−1.74366
$856$	41.6529	1.42367
$857$	−48.9043	−1.67054	−0.835269	−	0.549842i	$-0.814688\pi$
$857$	−48.9043	−1.67054	−0.835269	+	0.549842i	$0.814688\pi$
$858$	−85.1346	−2.90645
$859$	26.2279	0.894885	0.447443	−	0.894313i	$-0.352335\pi$
$859$	26.2279	0.894885	0.447443	+	0.894313i	$0.352335\pi$
$860$	−34.3478	−1.17125
$861$	−6.44992	−0.219813
$862$	53.6151	1.82614
$863$	2.19216	0.0746220	0.0373110	−	0.999304i	$-0.488121\pi$
$863$	2.19216	0.0746220	0.0373110	+	0.999304i	$0.488121\pi$
$864$	27.0829	0.921379
$865$	−25.3020	−0.860292
$866$	60.7776	2.06531
$867$	47.2495	1.60468
$868$	50.6615	1.71956
$869$	15.2874	0.518590
$870$	66.6715	2.26038
$871$	33.9324	1.14976
$872$	36.9424	1.25103
$873$	−15.1102	−0.511403
$874$	49.3161	1.66814
$875$	54.5508	1.84415
$876$	8.23605	0.278270
$877$	7.75897	0.262002	0.131001	−	0.991382i	$-0.458181\pi$
$877$	7.75897	0.262002	0.131001	+	0.991382i	$0.458181\pi$
$878$	−90.9824	−3.07051
$879$	−3.80246	−0.128254
$880$	−171.304	−5.77464
$881$	−12.3907	−0.417452	−0.208726	−	0.977974i	$-0.566932\pi$
$881$	−12.3907	−0.417452	−0.208726	+	0.977974i	$0.566932\pi$
$882$	−20.4023	−0.686980
$883$	27.7293	0.933167	0.466583	−	0.884477i	$-0.345485\pi$
$883$	27.7293	0.933167	0.466583	+	0.884477i	$0.345485\pi$
$884$	160.846	5.40984
$885$	15.6283	0.525339
$886$	−54.2558	−1.82276
$887$	18.4824	0.620578	0.310289	−	0.950642i	$-0.399574\pi$
$887$	18.4824	0.620578	0.310289	+	0.950642i	$0.399574\pi$
$888$	15.0125	0.503785
$889$	3.92001	0.131473
$890$	−55.7086	−1.86736
$891$	−11.9224	−0.399417
$892$	−95.2752	−3.19005
$893$	−83.2033	−2.78429
$894$	−61.8153	−2.06741
$895$	−114.285	−3.82012
$896$	−16.7485	−0.559527
$897$	15.0829	0.503603
$898$	18.2656	0.609530
$899$	−42.6198	−1.42145
$900$	−97.6017	−3.25339
$901$	−87.4485	−2.91333
$902$	−58.4178	−1.94510
$903$	−2.80692	−0.0934084
$904$	78.1363	2.59877
$905$	−54.2533	−1.80344
$906$	−0.285625	−0.00948926
$907$	−26.3795	−0.875918	−0.437959	−	0.898995i	$-0.644299\pi$
$907$	−26.3795	−0.875918	−0.437959	+	0.898995i	$0.644299\pi$
$908$	48.0860	1.59579
$909$	−13.0627	−0.433264
$910$	−71.3038	−2.36370
$911$	20.4373	0.677118	0.338559	−	0.940945i	$-0.390060\pi$
$911$	20.4373	0.677118	0.338559	+	0.940945i	$0.390060\pi$
$912$	−62.7497	−2.07785
$913$	−48.6976	−1.61165
$914$	22.3603	0.739612
$915$	15.3916	0.508829
$916$	−68.3590	−2.25864
$917$	−21.8968	−0.723095
$918$	104.257	3.44100
$919$	9.27838	0.306066	0.153033	−	0.988221i	$-0.451096\pi$
$919$	9.27838	0.306066	0.153033	+	0.988221i	$0.451096\pi$
$920$	69.8559	2.30308
$921$	28.8112	0.949360
$922$	−6.21930	−0.204822
$923$	−23.9123	−0.787082
$924$	−40.4350	−1.33021
$925$	−28.8087	−0.947223
$926$	−49.6091	−1.63026
$927$	6.48156	0.212882
$928$	−24.2190	−0.795028
$929$	20.5080	0.672846	0.336423	−	0.941711i	$-0.390783\pi$
$929$	20.5080	0.672846	0.336423	+	0.941711i	$0.390783\pi$
$930$	−117.693	−3.85930
$931$	39.9385	1.30893
$932$	−78.3122	−2.56520
$933$	−14.6248	−0.478794
$934$	−29.5699	−0.967556
$935$	−187.889	−6.14461
$936$	45.7605	1.49573
$937$	53.9083	1.76111	0.880553	−	0.473948i	$-0.157171\pi$
$937$	53.9083	1.76111	0.880553	+	0.473948i	$0.157171\pi$
$938$	23.3796	0.763372
$939$	19.8502	0.647786
$940$	−214.550	−6.99786
$941$	17.4385	0.568478	0.284239	−	0.958754i	$-0.408259\pi$
$941$	17.4385	0.568478	0.284239	+	0.958754i	$0.408259\pi$
$942$	21.1633	0.689536
$943$	10.3496	0.337030
$944$	−19.9252	−0.648511
$945$	−31.8593	−1.03638
$946$	−25.4226	−0.826561
$947$	41.8504	1.35996	0.679978	−	0.733233i	$-0.261989\pi$
$947$	41.8504	1.35996	0.679978	+	0.733233i	$0.261989\pi$
$948$	14.4400	0.468991
$949$	7.41011	0.240542
$950$	277.167	8.99249
$951$	−12.8658	−0.417201
$952$	60.8779	1.97306
$953$	17.5543	0.568640	0.284320	−	0.958729i	$-0.408232\pi$
$953$	17.5543	0.568640	0.284320	+	0.958729i	$0.408232\pi$
$954$	−45.2904	−1.46633
$955$	−12.5454	−0.405959
$956$	99.1720	3.20745
$957$	34.0166	1.09960
$958$	−9.29595	−0.300338
$959$	−8.67884	−0.280254
$960$	6.04364	0.195058
$961$	44.2352	1.42694
$962$	24.5884	0.792763
$963$	10.2796	0.331254
$964$	−53.4730	−1.72225
$965$	55.2191	1.77757
$966$	10.3922	0.334363
$967$	48.5318	1.56068	0.780339	−	0.625357i	$-0.215047\pi$
$967$	48.5318	1.56068	0.780339	+	0.625357i	$0.215047\pi$
$968$	−133.138	−4.27921
$969$	−68.8250	−2.21098
$970$	110.648	3.55269
$971$	−22.6765	−0.727725	−0.363862	−	0.931453i	$-0.618542\pi$
$971$	−22.6765	−0.727725	−0.363862	+	0.931453i	$0.618542\pi$
$972$	61.8900	1.98512
$973$	−24.2070	−0.776040
$974$	27.9483	0.895522
$975$	84.7692	2.71479
$976$	−19.6234	−0.628130
$977$	35.2019	1.12621	0.563104	−	0.826386i	$-0.309607\pi$
$977$	35.2019	1.12621	0.563104	+	0.826386i	$0.309607\pi$
$978$	20.4114	0.652683
$979$	−28.4232	−0.908408
$980$	102.987	3.28978
$981$	9.11707	0.291086
$982$	−28.4052	−0.906448
$983$	13.7160	0.437472	0.218736	−	0.975784i	$-0.429807\pi$
$983$	13.7160	0.437472	0.218736	+	0.975784i	$0.429807\pi$
$984$	−30.3114	−0.966292
$985$	−22.2107	−0.707691
$986$	−93.2323	−2.96912
$987$	−17.5331	−0.558086
$988$	−163.072	−5.18800
$989$	4.50401	0.143219
$990$	−97.3093	−3.09269
$991$	−22.8153	−0.724751	−0.362375	−	0.932032i	$-0.618034\pi$
$991$	−22.8153	−0.724751	−0.362375	+	0.932032i	$0.618034\pi$
$992$	42.7529	1.35741
$993$	1.28736	0.0408532
$994$	−16.4757	−0.522577
$995$	48.0542	1.52342
$996$	−45.9983	−1.45751
$997$	−17.2804	−0.547275	−0.273637	−	0.961833i	$-0.588227\pi$
$997$	−17.2804	−0.547275	−0.273637	+	0.961833i	$0.588227\pi$
$998$	34.2979	1.08568
$999$	10.9864	0.347594

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4021.2.a.c.1.12	✓	182

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4021.2.a.c.1.12	✓	182	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:	\( N \)	\(=\)	\( 4021 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4021.a (trivial)

\(f(q)\)	\(=\)	\(q-2.53727 q^{2} +1.21389 q^{3} +4.43775 q^{4} -4.40547 q^{5} -3.07998 q^{6} -1.31615 q^{7} -6.18523 q^{8} -1.52646 q^{9} +O(q^{10})\)	\(q-2.53727 q^{2} +1.21389 q^{3} +4.43775 q^{4} -4.40547 q^{5} -3.07998 q^{6} -1.31615 q^{7} -6.18523 q^{8} -1.52646 q^{9} +11.1779 q^{10} +5.70308 q^{11} +5.38696 q^{12} +4.84673 q^{13} +3.33943 q^{14} -5.34777 q^{15} +6.81812 q^{16} +7.47823 q^{17} +3.87305 q^{18} -7.58170 q^{19} -19.5504 q^{20} -1.59766 q^{21} -14.4703 q^{22} +2.56363 q^{23} -7.50822 q^{24} +14.4082 q^{25} -12.2975 q^{26} -5.49464 q^{27} -5.84074 q^{28} +4.91361 q^{29} +13.5687 q^{30} -8.67382 q^{31} -4.92896 q^{32} +6.92293 q^{33} -18.9743 q^{34} +5.79825 q^{35} -6.77406 q^{36} -1.99947 q^{37} +19.2368 q^{38} +5.88342 q^{39} +27.2489 q^{40} +4.03710 q^{41} +4.05371 q^{42} +1.75689 q^{43} +25.3088 q^{44} +6.72478 q^{45} -6.50462 q^{46} +10.9742 q^{47} +8.27648 q^{48} -5.26775 q^{49} -36.5574 q^{50} +9.07778 q^{51} +21.5086 q^{52} -11.6937 q^{53} +13.9414 q^{54} -25.1247 q^{55} +8.14068 q^{56} -9.20337 q^{57} -12.4672 q^{58} -2.92239 q^{59} -23.7321 q^{60} -2.87812 q^{61} +22.0078 q^{62} +2.00905 q^{63} -1.13012 q^{64} -21.3521 q^{65} -17.5654 q^{66} +7.00109 q^{67} +33.1865 q^{68} +3.11197 q^{69} -14.7117 q^{70} -4.93369 q^{71} +9.44153 q^{72} +1.52889 q^{73} +5.07320 q^{74} +17.4900 q^{75} -33.6457 q^{76} -7.50609 q^{77} -14.9278 q^{78} +2.68056 q^{79} -30.0370 q^{80} -2.09053 q^{81} -10.2432 q^{82} -8.53882 q^{83} -7.09003 q^{84} -32.9451 q^{85} -4.45771 q^{86} +5.96460 q^{87} -35.2749 q^{88} -4.98383 q^{89} -17.0626 q^{90} -6.37902 q^{91} +11.3767 q^{92} -10.5291 q^{93} -27.8446 q^{94} +33.4009 q^{95} -5.98324 q^{96} +9.89884 q^{97} +13.3657 q^{98} -8.70553 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 182 q + 18 q^{2} + 28 q^{3} + 208 q^{4} + 22 q^{5} + 18 q^{6} + 14 q^{7} + 54 q^{8} + 238 q^{9}+O(q^{10}) \) 182 * q + 18 * q^2 + 28 * q^3 + 208 * q^4 + 22 * q^5 + 18 * q^6 + 14 * q^7 + 54 * q^8 + 238 * q^9	\( 182 q + 18 q^{2} + 28 q^{3} + 208 q^{4} + 22 q^{5} + 18 q^{6} + 14 q^{7} + 54 q^{8} + 238 q^{9} + 7 q^{10} + 138 q^{11} + 47 q^{12} + 5 q^{13} + 72 q^{14} + 41 q^{15} + 256 q^{16} + 29 q^{17} + 35 q^{18} + 48 q^{19} + 56 q^{20} + 22 q^{21} + 19 q^{22} + 91 q^{23} + 46 q^{24} + 230 q^{25} + 88 q^{26} + 103 q^{27} + 15 q^{28} + 75 q^{29} + 18 q^{30} + 43 q^{31} + 116 q^{32} + 15 q^{33} + 13 q^{34} + 185 q^{35} + 364 q^{36} + 15 q^{37} + 53 q^{38} + 80 q^{39} - 13 q^{40} + 68 q^{41} + 32 q^{42} + 82 q^{43} + 259 q^{44} + 37 q^{45} + 13 q^{46} + 121 q^{47} + 53 q^{48} + 244 q^{49} + 93 q^{50} + 144 q^{51} - 16 q^{52} + 101 q^{53} + 47 q^{54} + 49 q^{55} + 199 q^{56} + 3 q^{57} + 4 q^{58} + 254 q^{59} + 24 q^{60} + 8 q^{61} + 37 q^{62} + 19 q^{63} + 326 q^{64} + 65 q^{65} + 41 q^{66} + 91 q^{67} + 50 q^{68} + 50 q^{69} + 5 q^{70} + 212 q^{71} + 77 q^{72} + 5 q^{73} + 101 q^{74} + 127 q^{75} + 22 q^{76} + 87 q^{77} - 20 q^{78} + 86 q^{79} + 71 q^{80} + 358 q^{81} - 20 q^{82} + 139 q^{83} - 30 q^{84} + 25 q^{85} + 82 q^{86} + 36 q^{87} - 8 q^{88} + 100 q^{89} - 87 q^{90} + 74 q^{91} + 171 q^{92} + 50 q^{93} - 13 q^{94} + 217 q^{95} + 42 q^{96} + 20 q^{97} + 47 q^{98} + 389 q^{99}+O(q^{100}) \) 182 * q + 18 * q^2 + 28 * q^3 + 208 * q^4 + 22 * q^5 + 18 * q^6 + 14 * q^7 + 54 * q^8 + 238 * q^9 + 7 * q^10 + 138 * q^11 + 47 * q^12 + 5 * q^13 + 72 * q^14 + 41 * q^15 + 256 * q^16 + 29 * q^17 + 35 * q^18 + 48 * q^19 + 56 * q^20 + 22 * q^21 + 19 * q^22 + 91 * q^23 + 46 * q^24 + 230 * q^25 + 88 * q^26 + 103 * q^27 + 15 * q^28 + 75 * q^29 + 18 * q^30 + 43 * q^31 + 116 * q^32 + 15 * q^33 + 13 * q^34 + 185 * q^35 + 364 * q^36 + 15 * q^37 + 53 * q^38 + 80 * q^39 - 13 * q^40 + 68 * q^41 + 32 * q^42 + 82 * q^43 + 259 * q^44 + 37 * q^45 + 13 * q^46 + 121 * q^47 + 53 * q^48 + 244 * q^49 + 93 * q^50 + 144 * q^51 - 16 * q^52 + 101 * q^53 + 47 * q^54 + 49 * q^55 + 199 * q^56 + 3 * q^57 + 4 * q^58 + 254 * q^59 + 24 * q^60 + 8 * q^61 + 37 * q^62 + 19 * q^63 + 326 * q^64 + 65 * q^65 + 41 * q^66 + 91 * q^67 + 50 * q^68 + 50 * q^69 + 5 * q^70 + 212 * q^71 + 77 * q^72 + 5 * q^73 + 101 * q^74 + 127 * q^75 + 22 * q^76 + 87 * q^77 - 20 * q^78 + 86 * q^79 + 71 * q^80 + 358 * q^81 - 20 * q^82 + 139 * q^83 - 30 * q^84 + 25 * q^85 + 82 * q^86 + 36 * q^87 - 8 * q^88 + 100 * q^89 - 87 * q^90 + 74 * q^91 + 171 * q^92 + 50 * q^93 - 13 * q^94 + 217 * q^95 + 42 * q^96 + 20 * q^97 + 47 * q^98 + 389 * q^99

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