LMFDB - Embedded newform 4021.2.a.c.1.10

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			1.10
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)

$f(q)$	$=$	$q-2.57672 q^{2} -1.91417 q^{3} +4.63947 q^{4} -2.65404 q^{5} +4.93228 q^{6} -2.26992 q^{7} -6.80118 q^{8} +0.664061 q^{9} +O(q^{10})$	\(q-2.57672 q^{2} -1.91417 q^{3} +4.63947 q^{4} -2.65404 q^{5} +4.93228 q^{6} -2.26992 q^{7} -6.80118 q^{8} +0.664061 q^{9} +6.83870 q^{10} +4.73227 q^{11} -8.88076 q^{12} -2.48260 q^{13} +5.84893 q^{14} +5.08029 q^{15} +8.24577 q^{16} +6.94871 q^{17} -1.71110 q^{18} +6.99836 q^{19} -12.3133 q^{20} +4.34501 q^{21} -12.1937 q^{22} -1.86740 q^{23} +13.0186 q^{24} +2.04391 q^{25} +6.39697 q^{26} +4.47139 q^{27} -10.5312 q^{28} +4.00495 q^{29} -13.0905 q^{30} +7.17667 q^{31} -7.64466 q^{32} -9.05839 q^{33} -17.9049 q^{34} +6.02444 q^{35} +3.08089 q^{36} +1.89761 q^{37} -18.0328 q^{38} +4.75214 q^{39} +18.0506 q^{40} +11.5731 q^{41} -11.1959 q^{42} +0.0405043 q^{43} +21.9553 q^{44} -1.76244 q^{45} +4.81176 q^{46} -5.73327 q^{47} -15.7838 q^{48} -1.84748 q^{49} -5.26658 q^{50} -13.3010 q^{51} -11.5180 q^{52} +0.0902283 q^{53} -11.5215 q^{54} -12.5596 q^{55} +15.4381 q^{56} -13.3961 q^{57} -10.3196 q^{58} -8.79942 q^{59} +23.5699 q^{60} +4.59972 q^{61} -18.4922 q^{62} -1.50736 q^{63} +3.20659 q^{64} +6.58892 q^{65} +23.3409 q^{66} -3.60761 q^{67} +32.2384 q^{68} +3.57452 q^{69} -15.5233 q^{70} +1.18514 q^{71} -4.51640 q^{72} +8.77763 q^{73} -4.88961 q^{74} -3.91240 q^{75} +32.4687 q^{76} -10.7419 q^{77} -12.2449 q^{78} -3.43149 q^{79} -21.8846 q^{80} -10.5512 q^{81} -29.8206 q^{82} +9.53079 q^{83} +20.1586 q^{84} -18.4421 q^{85} -0.104368 q^{86} -7.66618 q^{87} -32.1850 q^{88} +13.7694 q^{89} +4.54131 q^{90} +5.63530 q^{91} -8.66374 q^{92} -13.7374 q^{93} +14.7730 q^{94} -18.5739 q^{95} +14.6332 q^{96} -10.7704 q^{97} +4.76045 q^{98} +3.14252 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.57672	−1.82201	−0.911007	−	0.412390i	$-0.864694\pi$
$2$	−2.57672	−1.82201	−0.911007	+	0.412390i	$0.864694\pi$
$3$	−1.91417	−1.10515	−0.552574	−	0.833464i	$-0.686354\pi$
$3$	−1.91417	−1.10515	−0.552574	+	0.833464i	$0.686354\pi$
$4$	4.63947	2.31974
$5$	−2.65404	−1.18692	−0.593461	−	0.804863i	$-0.702239\pi$
$5$	−2.65404	−1.18692	−0.593461	+	0.804863i	$0.702239\pi$
$6$	4.93228	2.01360
$7$	−2.26992	−0.857947	−0.428974	−	0.903317i	$-0.641125\pi$
$7$	−2.26992	−0.857947	−0.428974	+	0.903317i	$0.641125\pi$
$8$	−6.80118	−2.40458
$9$	0.664061	0.221354
$10$	6.83870	2.16259
$11$	4.73227	1.42683	0.713417	−	0.700740i	$-0.247147\pi$
$11$	4.73227	1.42683	0.713417	+	0.700740i	$0.247147\pi$
$12$	−8.88076	−2.56365
$13$	−2.48260	−0.688551	−0.344275	−	0.938869i	$-0.611875\pi$
$13$	−2.48260	−0.688551	−0.344275	+	0.938869i	$0.611875\pi$
$14$	5.84893	1.56319
$15$	5.08029	1.31172
$16$	8.24577	2.06144
$17$	6.94871	1.68531	0.842655	−	0.538453i	$-0.180991\pi$
$17$	6.94871	1.68531	0.842655	+	0.538453i	$0.180991\pi$
$18$	−1.71110	−0.403309
$19$	6.99836	1.60553	0.802767	−	0.596293i	$-0.203360\pi$
$19$	6.99836	1.60553	0.802767	+	0.596293i	$0.203360\pi$
$20$	−12.3133	−2.75334
$21$	4.34501	0.948159
$22$	−12.1937	−2.59971
$23$	−1.86740	−0.389379	−0.194690	−	0.980865i	$-0.562370\pi$
$23$	−1.86740	−0.389379	−0.194690	+	0.980865i	$0.562370\pi$
$24$	13.0186	2.65742
$25$	2.04391	0.408782
$26$	6.39697	1.25455
$27$	4.47139	0.860520
$28$	−10.5312	−1.99021
$29$	4.00495	0.743701	0.371851	−	0.928293i	$-0.378723\pi$
$29$	4.00495	0.743701	0.371851	+	0.928293i	$0.378723\pi$
$30$	−13.0905	−2.38998
$31$	7.17667	1.28897	0.644484	−	0.764618i	$-0.277072\pi$
$31$	7.17667	1.28897	0.644484	+	0.764618i	$0.277072\pi$
$32$	−7.64466	−1.35140
$33$	−9.05839	−1.57686
$34$	−17.9049	−3.07066
$35$	6.02444	1.01832
$36$	3.08089	0.513482
$37$	1.89761	0.311966	0.155983	−	0.987760i	$-0.450146\pi$
$37$	1.89761	0.311966	0.155983	+	0.987760i	$0.450146\pi$
$38$	−18.0328	−2.92531
$39$	4.75214	0.760951
$40$	18.0506	2.85405
$41$	11.5731	1.80741	0.903706	−	0.428153i	$-0.140835\pi$
$41$	11.5731	1.80741	0.903706	+	0.428153i	$0.140835\pi$
$42$	−11.1959	−1.72756
$43$	0.0405043	0.00617684	0.00308842	−	0.999995i	$-0.499017\pi$
$43$	0.0405043	0.00617684	0.00308842	+	0.999995i	$0.499017\pi$
$44$	21.9553	3.30988
$45$	−1.76244	−0.262729
$46$	4.81176	0.709455
$47$	−5.73327	−0.836284	−0.418142	−	0.908382i	$-0.637319\pi$
$47$	−5.73327	−0.836284	−0.418142	+	0.908382i	$0.637319\pi$
$48$	−15.7838	−2.27820
$49$	−1.84748	−0.263926
$50$	−5.26658	−0.744807
$51$	−13.3010	−1.86252
$52$	−11.5180	−1.59726
$53$	0.0902283	0.0123938	0.00619690	−	0.999981i	$-0.498027\pi$
$53$	0.0902283	0.0123938	0.00619690	+	0.999981i	$0.498027\pi$
$54$	−11.5215	−1.56788
$55$	−12.5596	−1.69354
$56$	15.4381	2.06300
$57$	−13.3961	−1.77435
$58$	−10.3196	−1.35503
$59$	−8.79942	−1.14559	−0.572794	−	0.819700i	$-0.694140\pi$
$59$	−8.79942	−1.14559	−0.572794	+	0.819700i	$0.694140\pi$
$60$	23.5699	3.04286
$61$	4.59972	0.588934	0.294467	−	0.955662i	$-0.404858\pi$
$61$	4.59972	0.588934	0.294467	+	0.955662i	$0.404858\pi$
$62$	−18.4922	−2.34852
$63$	−1.50736	−0.189910
$64$	3.20659	0.400824
$65$	6.58892	0.817255
$66$	23.3409	2.87307
$67$	−3.60761	−0.440739	−0.220370	−	0.975416i	$-0.570726\pi$
$67$	−3.60761	−0.440739	−0.220370	+	0.975416i	$0.570726\pi$
$68$	32.2384	3.90948
$69$	3.57452	0.430322
$70$	−15.5233	−1.85539
$71$	1.18514	0.140650	0.0703250	−	0.997524i	$-0.477596\pi$
$71$	1.18514	0.140650	0.0703250	+	0.997524i	$0.477596\pi$
$72$	−4.51640	−0.532262
$73$	8.77763	1.02734	0.513672	−	0.857987i	$-0.328285\pi$
$73$	8.77763	1.02734	0.513672	+	0.857987i	$0.328285\pi$
$74$	−4.88961	−0.568406
$75$	−3.91240	−0.451765
$76$	32.4687	3.72442
$77$	−10.7419	−1.22415
$78$	−12.2449	−1.38646
$79$	−3.43149	−0.386073	−0.193036	−	0.981192i	$-0.561834\pi$
$79$	−3.43149	−0.386073	−0.193036	+	0.981192i	$0.561834\pi$
$80$	−21.8846	−2.44677
$81$	−10.5512	−1.17236
$82$	−29.8206	−3.29313
$83$	9.53079	1.04614	0.523070	−	0.852290i	$-0.324787\pi$
$83$	9.53079	1.04614	0.523070	+	0.852290i	$0.324787\pi$
$84$	20.1586	2.19948
$85$	−18.4421	−2.00033
$86$	−0.104368	−0.0112543
$87$	−7.66618	−0.821900
$88$	−32.1850	−3.43094
$89$	13.7694	1.45955	0.729776	−	0.683687i	$-0.239625\pi$
$89$	13.7694	1.45955	0.729776	+	0.683687i	$0.239625\pi$
$90$	4.54131	0.478697
$91$	5.63530	0.590740
$92$	−8.66374	−0.903257
$93$	−13.7374	−1.42450
$94$	14.7730	1.52372
$95$	−18.5739	−1.90564
$96$	14.6332	1.49350
$97$	−10.7704	−1.09357	−0.546785	−	0.837273i	$-0.684149\pi$
$97$	−10.7704	−1.09357	−0.546785	+	0.837273i	$0.684149\pi$
$98$	4.76045	0.480878
$99$	3.14252	0.315835
$100$	9.48267	0.948267
$101$	−9.34439	−0.929801	−0.464901	−	0.885363i	$-0.653910\pi$
$101$	−9.34439	−0.929801	−0.464901	+	0.885363i	$0.653910\pi$
$102$	34.2730	3.39354
$103$	1.23116	0.121309	0.0606547	−	0.998159i	$-0.480681\pi$
$103$	1.23116	0.121309	0.0606547	+	0.998159i	$0.480681\pi$
$104$	16.8846	1.65567
$105$	−11.5318	−1.12539
$106$	−0.232493	−0.0225817
$107$	17.7459	1.71556	0.857781	−	0.514015i	$-0.171843\pi$
$107$	17.7459	1.71556	0.857781	+	0.514015i	$0.171843\pi$
$108$	20.7449	1.99618
$109$	−4.36145	−0.417751	−0.208876	−	0.977942i	$-0.566980\pi$
$109$	−4.36145	−0.417751	−0.208876	+	0.977942i	$0.566980\pi$
$110$	32.3626	3.08565
$111$	−3.63236	−0.344768
$112$	−18.7172	−1.76861
$113$	19.3105	1.81658	0.908292	−	0.418338i	$-0.137387\pi$
$113$	19.3105	1.81658	0.908292	+	0.418338i	$0.137387\pi$
$114$	34.5179	3.23290
$115$	4.95614	0.462163
$116$	18.5809	1.72519
$117$	−1.64860	−0.152413
$118$	22.6736	2.08728
$119$	−15.7730	−1.44591
$120$	−34.5519	−3.15415
$121$	11.3944	1.03585
$122$	−11.8522	−1.07305
$123$	−22.1529	−1.99746
$124$	33.2960	2.99007
$125$	7.84557	0.701729
$126$	3.88405	0.346018
$127$	−5.35836	−0.475478	−0.237739	−	0.971329i	$-0.576406\pi$
$127$	−5.35836	−0.475478	−0.237739	+	0.971329i	$0.576406\pi$
$128$	7.02683	0.621090
$129$	−0.0775322	−0.00682633
$130$	−16.9778	−1.48905
$131$	4.35598	0.380584	0.190292	−	0.981728i	$-0.439057\pi$
$131$	4.35598	0.380584	0.190292	+	0.981728i	$0.439057\pi$
$132$	−42.0262	−3.65791
$133$	−15.8857	−1.37746
$134$	9.29578	0.803033
$135$	−11.8672	−1.02137
$136$	−47.2594	−4.05246
$137$	−10.7159	−0.915520	−0.457760	−	0.889076i	$-0.651348\pi$
$137$	−10.7159	−0.915520	−0.457760	+	0.889076i	$0.651348\pi$
$138$	−9.21054	−0.784053
$139$	7.91755	0.671558	0.335779	−	0.941941i	$-0.391001\pi$
$139$	7.91755	0.671558	0.335779	+	0.941941i	$0.391001\pi$
$140$	27.9502	2.36223
$141$	10.9745	0.924218
$142$	−3.05377	−0.256267
$143$	−11.7484	−0.982447
$144$	5.47569	0.456308
$145$	−10.6293	−0.882715
$146$	−22.6175	−1.87183
$147$	3.53641	0.291678
$148$	8.80392	0.723678
$149$	5.94316	0.486883	0.243441	−	0.969916i	$-0.421724\pi$
$149$	5.94316	0.486883	0.243441	+	0.969916i	$0.421724\pi$
$150$	10.0811	0.823122
$151$	−10.1332	−0.824629	−0.412314	−	0.911042i	$-0.635279\pi$
$151$	−10.1332	−0.824629	−0.412314	+	0.911042i	$0.635279\pi$
$152$	−47.5971	−3.86063
$153$	4.61437	0.373050
$154$	27.6787	2.23042
$155$	−19.0471	−1.52990
$156$	22.0474	1.76521
$157$	−22.6114	−1.80459	−0.902295	−	0.431119i	$-0.858119\pi$
$157$	−22.6114	−1.80459	−0.902295	+	0.431119i	$0.858119\pi$
$158$	8.84198	0.703430
$159$	−0.172713	−0.0136970
$160$	20.2892	1.60400
$161$	4.23883	0.334067
$162$	27.1875	2.13605
$163$	3.01022	0.235779	0.117889	−	0.993027i	$-0.462387\pi$
$163$	3.01022	0.235779	0.117889	+	0.993027i	$0.462387\pi$
$164$	53.6930	4.19272
$165$	24.0413	1.87161
$166$	−24.5582	−1.90608
$167$	12.7493	0.986570	0.493285	−	0.869868i	$-0.335796\pi$
$167$	12.7493	0.986570	0.493285	+	0.869868i	$0.335796\pi$
$168$	−29.5512	−2.27992
$169$	−6.83667	−0.525898
$170$	47.5202	3.64463
$171$	4.64734	0.355391
$172$	0.187919	0.0143287
$173$	15.5816	1.18465	0.592325	−	0.805699i	$-0.298210\pi$
$173$	15.5816	1.18465	0.592325	+	0.805699i	$0.298210\pi$
$174$	19.7536	1.49751
$175$	−4.63950	−0.350714
$176$	39.0212	2.94134
$177$	16.8436	1.26604
$178$	−35.4798	−2.65932
$179$	−20.3759	−1.52297	−0.761484	−	0.648184i	$-0.775529\pi$
$179$	−20.3759	−1.52297	−0.761484	+	0.648184i	$0.775529\pi$
$180$	−8.17680	−0.609463
$181$	−19.7765	−1.46997	−0.734987	−	0.678081i	$-0.762812\pi$
$181$	−19.7765	−1.46997	−0.734987	+	0.678081i	$0.762812\pi$
$182$	−14.5206	−1.07634
$183$	−8.80467	−0.650860
$184$	12.7005	0.936293
$185$	−5.03633	−0.370278
$186$	35.3974	2.59546
$187$	32.8832	2.40466
$188$	−26.5994	−1.93996
$189$	−10.1497	−0.738281
$190$	47.8597	3.47211
$191$	−0.857870	−0.0620733	−0.0310367	−	0.999518i	$-0.509881\pi$
$191$	−0.857870	−0.0620733	−0.0310367	+	0.999518i	$0.509881\pi$
$192$	−6.13798	−0.442970
$193$	19.4475	1.39986	0.699930	−	0.714211i	$-0.253214\pi$
$193$	19.4475	1.39986	0.699930	+	0.714211i	$0.253214\pi$
$194$	27.7523	1.99250
$195$	−12.6123	−0.903189
$196$	−8.57136	−0.612240
$197$	−23.9929	−1.70943	−0.854713	−	0.519101i	$-0.826267\pi$
$197$	−23.9929	−1.70943	−0.854713	+	0.519101i	$0.826267\pi$
$198$	−8.09738	−0.575455
$199$	−14.4351	−1.02328	−0.511639	−	0.859201i	$-0.670961\pi$
$199$	−14.4351	−1.02328	−0.511639	+	0.859201i	$0.670961\pi$
$200$	−13.9010	−0.982949
$201$	6.90559	0.487082
$202$	24.0778	1.69411
$203$	−9.09091	−0.638057
$204$	−61.7098	−4.32055
$205$	−30.7154	−2.14526
$206$	−3.17234	−0.221028
$207$	−1.24007	−0.0861905
$208$	−20.4710	−1.41941
$209$	33.1181	2.29083
$210$	29.7142	2.05048
$211$	2.01506	0.138722	0.0693611	−	0.997592i	$-0.477904\pi$
$211$	2.01506	0.138722	0.0693611	+	0.997592i	$0.477904\pi$
$212$	0.418612	0.0287504
$213$	−2.26856	−0.155439
$214$	−45.7262	−3.12578
$215$	−0.107500	−0.00733143
$216$	−30.4107	−2.06919
$217$	−16.2904	−1.10587
$218$	11.2382	0.761149
$219$	−16.8019	−1.13537
$220$	−58.2700	−3.92857
$221$	−17.2509	−1.16042
$222$	9.35956	0.628173
$223$	−12.5923	−0.843242	−0.421621	−	0.906772i	$-0.638539\pi$
$223$	−12.5923	−0.843242	−0.421621	+	0.906772i	$0.638539\pi$
$224$	17.3527	1.15943
$225$	1.35728	0.0904854
$226$	−49.7578	−3.30984
$227$	−15.6280	−1.03727	−0.518635	−	0.854996i	$-0.673560\pi$
$227$	−15.6280	−1.03727	−0.518635	+	0.854996i	$0.673560\pi$
$228$	−62.1507	−4.11603
$229$	15.0188	0.992470	0.496235	−	0.868188i	$-0.334716\pi$
$229$	15.0188	0.992470	0.496235	+	0.868188i	$0.334716\pi$
$230$	−12.7706	−0.842067
$231$	20.5618	1.35287
$232$	−27.2384	−1.78829
$233$	11.1846	0.732728	0.366364	−	0.930472i	$-0.380602\pi$
$233$	11.1846	0.732728	0.366364	+	0.930472i	$0.380602\pi$
$234$	4.24798	0.277699
$235$	15.2163	0.992603
$236$	−40.8247	−2.65746
$237$	6.56846	0.426668
$238$	40.6425	2.63446
$239$	24.5933	1.59081	0.795405	−	0.606079i	$-0.207258\pi$
$239$	24.5933	1.59081	0.795405	+	0.606079i	$0.207258\pi$
$240$	41.8909	2.70404
$241$	−17.6948	−1.13982	−0.569911	−	0.821706i	$-0.693022\pi$
$241$	−17.6948	−1.13982	−0.569911	+	0.821706i	$0.693022\pi$
$242$	−29.3601	−1.88734
$243$	6.78266	0.435108
$244$	21.3403	1.36617
$245$	4.90329	0.313260
$246$	57.0818	3.63940
$247$	−17.3742	−1.10549
$248$	−48.8098	−3.09943
$249$	−18.2436	−1.15614
$250$	−20.2158	−1.27856
$251$	8.95633	0.565318	0.282659	−	0.959220i	$-0.408783\pi$
$251$	8.95633	0.565318	0.282659	+	0.959220i	$0.408783\pi$
$252$	−6.99336	−0.440541
$253$	−8.83703	−0.555579
$254$	13.8070	0.866328
$255$	35.3015	2.21066
$256$	−24.5194	−1.53246
$257$	4.93425	0.307790	0.153895	−	0.988087i	$-0.450818\pi$
$257$	4.93425	0.307790	0.153895	+	0.988087i	$0.450818\pi$
$258$	0.199779	0.0124377
$259$	−4.30742	−0.267650
$260$	30.5691	1.89582
$261$	2.65953	0.164621
$262$	−11.2241	−0.693429
$263$	−25.4726	−1.57071	−0.785353	−	0.619048i	$-0.787518\pi$
$263$	−25.4726	−1.57071	−0.785353	+	0.619048i	$0.787518\pi$
$264$	61.6077	3.79169
$265$	−0.239469	−0.0147105
$266$	40.9329	2.50976
$267$	−26.3570	−1.61302
$268$	−16.7374	−1.02240
$269$	18.5852	1.13316	0.566579	−	0.824007i	$-0.308267\pi$
$269$	18.5852	1.13316	0.566579	+	0.824007i	$0.308267\pi$
$270$	30.5785	1.86095
$271$	21.3047	1.29417	0.647084	−	0.762419i	$-0.275988\pi$
$271$	21.3047	1.29417	0.647084	+	0.762419i	$0.275988\pi$
$272$	57.2975	3.47417
$273$	−10.7869	−0.652856
$274$	27.6118	1.66809
$275$	9.67234	0.583264
$276$	16.5839	0.998234
$277$	2.91881	0.175374	0.0876872	−	0.996148i	$-0.472052\pi$
$277$	2.91881	0.175374	0.0876872	+	0.996148i	$0.472052\pi$
$278$	−20.4013	−1.22359
$279$	4.76574	0.285318
$280$	−40.9733	−2.44862
$281$	4.11840	0.245683	0.122841	−	0.992426i	$-0.460799\pi$
$281$	4.11840	0.245683	0.122841	+	0.992426i	$0.460799\pi$
$282$	−28.2781	−1.68394
$283$	4.42704	0.263160	0.131580	−	0.991306i	$-0.457995\pi$
$283$	4.42704	0.263160	0.131580	+	0.991306i	$0.457995\pi$
$284$	5.49842	0.326271
$285$	35.5537	2.10602
$286$	30.2722	1.79003
$287$	−26.2699	−1.55067
$288$	−5.07652	−0.299137
$289$	31.2846	1.84027
$290$	27.3887	1.60832
$291$	20.6164	1.20856
$292$	40.7236	2.38317
$293$	−3.27044	−0.191061	−0.0955307	−	0.995426i	$-0.530455\pi$
$293$	−3.27044	−0.191061	−0.0955307	+	0.995426i	$0.530455\pi$
$294$	−9.11232	−0.531441
$295$	23.3540	1.35972
$296$	−12.9060	−0.750146
$297$	21.1598	1.22782
$298$	−15.3138	−0.887107
$299$	4.63601	0.268107
$300$	−18.1515	−1.04798
$301$	−0.0919413	−0.00529941
$302$	26.1104	1.50249
$303$	17.8868	1.02757
$304$	57.7068	3.30971
$305$	−12.2078	−0.699019
$306$	−11.8899	−0.679702
$307$	−17.6483	−1.00724	−0.503622	−	0.863924i	$-0.667999\pi$
$307$	−17.6483	−1.00724	−0.503622	+	0.863924i	$0.667999\pi$
$308$	−49.8366	−2.83970
$309$	−2.35665	−0.134065
$310$	49.0791	2.78751
$311$	18.9064	1.07208	0.536042	−	0.844191i	$-0.319919\pi$
$311$	18.9064	1.07208	0.536042	+	0.844191i	$0.319919\pi$
$312$	−32.3201	−1.82977
$313$	−4.04392	−0.228576	−0.114288	−	0.993448i	$-0.536459\pi$
$313$	−4.04392	−0.228576	−0.114288	+	0.993448i	$0.536459\pi$
$314$	58.2633	3.28799
$315$	4.00059	0.225408
$316$	−15.9203	−0.895587
$317$	17.5345	0.984835	0.492417	−	0.870359i	$-0.336113\pi$
$317$	17.5345	0.984835	0.492417	+	0.870359i	$0.336113\pi$
$318$	0.445032	0.0249561
$319$	18.9525	1.06114
$320$	−8.51042	−0.475747
$321$	−33.9688	−1.89595
$322$	−10.9223	−0.608675
$323$	48.6296	2.70582
$324$	−48.9520	−2.71956
$325$	−5.07422	−0.281467
$326$	−7.75648	−0.429592
$327$	8.34857	0.461677
$328$	−78.7106	−4.34607
$329$	13.0140	0.717487
$330$	−61.9476	−3.41011
$331$	−21.0337	−1.15612	−0.578058	−	0.815996i	$-0.696189\pi$
$331$	−21.0337	−1.15612	−0.578058	+	0.815996i	$0.696189\pi$
$332$	44.2178	2.42677
$333$	1.26013	0.0690547
$334$	−32.8513	−1.79754
$335$	9.57472	0.523123
$336$	35.8280	1.95458
$337$	31.8176	1.73322	0.866608	−	0.498990i	$-0.166296\pi$
$337$	31.8176	1.73322	0.866608	+	0.498990i	$0.166296\pi$
$338$	17.6162	0.958194
$339$	−36.9637	−2.00759
$340$	−85.5618	−4.64024
$341$	33.9619	1.83914
$342$	−11.9749	−0.647527
$343$	20.0830	1.08438
$344$	−0.275477	−0.0148527
$345$	−9.48691	−0.510758
$346$	−40.1495	−2.15845
$347$	25.5560	1.37192	0.685959	−	0.727640i	$-0.259383\pi$
$347$	25.5560	1.37192	0.685959	+	0.727640i	$0.259383\pi$
$348$	−35.5670	−1.90659
$349$	−6.35171	−0.339999	−0.170000	−	0.985444i	$-0.554377\pi$
$349$	−6.35171	−0.339999	−0.170000	+	0.985444i	$0.554377\pi$
$350$	11.9547	0.639005
$351$	−11.1007	−0.592512
$352$	−36.1766	−1.92822
$353$	23.2340	1.23662	0.618310	−	0.785935i	$-0.287818\pi$
$353$	23.2340	1.23662	0.618310	+	0.785935i	$0.287818\pi$
$354$	−43.4013	−2.30675
$355$	−3.14540	−0.166941
$356$	63.8827	3.38577
$357$	30.1922	1.59794
$358$	52.5030	2.77487
$359$	−5.78782	−0.305470	−0.152735	−	0.988267i	$-0.548808\pi$
$359$	−5.78782	−0.305470	−0.152735	+	0.988267i	$0.548808\pi$
$360$	11.9867	0.631753
$361$	29.9770	1.57774
$362$	50.9584	2.67832
$363$	−21.8109	−1.14477
$364$	26.1448	1.37036
$365$	−23.2961	−1.21938
$366$	22.6872	1.18588
$367$	4.71983	0.246373	0.123186	−	0.992384i	$-0.460689\pi$
$367$	4.71983	0.246373	0.123186	+	0.992384i	$0.460689\pi$
$368$	−15.3981	−0.802683
$369$	7.68523	0.400077
$370$	12.9772	0.674653
$371$	−0.204811	−0.0106332
$372$	−63.7343	−3.30447
$373$	34.1382	1.76761	0.883805	−	0.467856i	$-0.154973\pi$
$373$	34.1382	1.76761	0.883805	+	0.467856i	$0.154973\pi$
$374$	−84.7307	−4.38132
$375$	−15.0178	−0.775515
$376$	38.9930	2.01091
$377$	−9.94272	−0.512076
$378$	26.1529	1.34516
$379$	−4.91206	−0.252316	−0.126158	−	0.992010i	$-0.540265\pi$
$379$	−4.91206	−0.252316	−0.126158	+	0.992010i	$0.540265\pi$
$380$	−86.1731	−4.42059
$381$	10.2568	0.525474
$382$	2.21049	0.113098
$383$	−13.9987	−0.715298	−0.357649	−	0.933856i	$-0.616422\pi$
$383$	−13.9987	−0.715298	−0.357649	+	0.933856i	$0.616422\pi$
$384$	−13.4506	−0.686397
$385$	28.5093	1.45297
$386$	−50.1107	−2.55057
$387$	0.0268973	0.00136727
$388$	−49.9691	−2.53679
$389$	−1.90056	−0.0963621	−0.0481810	−	0.998839i	$-0.515342\pi$
$389$	−1.90056	−0.0963621	−0.0481810	+	0.998839i	$0.515342\pi$
$390$	32.4984	1.64562
$391$	−12.9760	−0.656225
$392$	12.5651	0.634632
$393$	−8.33811	−0.420602
$394$	61.8230	3.11460
$395$	9.10730	0.458238
$396$	14.5796	0.732653
$397$	10.8753	0.545814	0.272907	−	0.962040i	$-0.412015\pi$
$397$	10.8753	0.545814	0.272907	+	0.962040i	$0.412015\pi$
$398$	37.1952	1.86443
$399$	30.4080	1.52230
$400$	16.8536	0.842681
$401$	−17.0903	−0.853447	−0.426724	−	0.904382i	$-0.640332\pi$
$401$	−17.0903	−0.853447	−0.426724	+	0.904382i	$0.640332\pi$
$402$	−17.7937	−0.887471
$403$	−17.8168	−0.887520
$404$	−43.3530	−2.15689
$405$	28.0033	1.39149
$406$	23.4247	1.16255
$407$	8.98002	0.445123
$408$	90.4628	4.47857
$409$	−32.0950	−1.58700	−0.793499	−	0.608572i	$-0.791743\pi$
$409$	−32.0950	−1.58700	−0.793499	+	0.608572i	$0.791743\pi$
$410$	79.1449	3.90869
$411$	20.5121	1.01179
$412$	5.71192	0.281406
$413$	19.9739	0.982854
$414$	3.19530	0.157040
$415$	−25.2951	−1.24169
$416$	18.9787	0.930506
$417$	−15.1556	−0.742171
$418$	−85.3361	−4.17392
$419$	−38.4446	−1.87814	−0.939072	−	0.343722i	$-0.888312\pi$
$419$	−38.4446	−1.87814	−0.939072	+	0.343722i	$0.888312\pi$
$420$	−53.5016	−2.61061
$421$	−15.5038	−0.755607	−0.377804	−	0.925886i	$-0.623321\pi$
$421$	−15.5038	−0.755607	−0.377804	+	0.925886i	$0.623321\pi$
$422$	−5.19223	−0.252754
$423$	−3.80724	−0.185114
$424$	−0.613659	−0.0298019
$425$	14.2025	0.688925
$426$	5.84544	0.283213
$427$	−10.4410	−0.505275
$428$	82.3317	3.97965
$429$	22.4884	1.08575
$430$	0.276997	0.0133580
$431$	4.48230	0.215905	0.107952	−	0.994156i	$-0.465571\pi$
$431$	4.48230	0.215905	0.107952	+	0.994156i	$0.465571\pi$
$432$	36.8701	1.77391
$433$	−24.2286	−1.16435	−0.582177	−	0.813062i	$-0.697799\pi$
$433$	−24.2286	−1.16435	−0.582177	+	0.813062i	$0.697799\pi$
$434$	41.9758	2.01490
$435$	20.3463	0.975531
$436$	−20.2348	−0.969073
$437$	−13.0687	−0.625161
$438$	43.2937	2.06866
$439$	34.8132	1.66154	0.830772	−	0.556614i	$-0.187900\pi$
$439$	34.8132	1.66154	0.830772	+	0.556614i	$0.187900\pi$
$440$	85.4202	4.07225
$441$	−1.22684	−0.0584210
$442$	44.4507	2.11431
$443$	14.7812	0.702276	0.351138	−	0.936324i	$-0.385795\pi$
$443$	14.7812	0.702276	0.351138	+	0.936324i	$0.385795\pi$
$444$	−16.8522	−0.799772
$445$	−36.5444	−1.73237
$446$	32.4468	1.53640
$447$	−11.3762	−0.538078
$448$	−7.27870	−0.343886
$449$	−15.4273	−0.728058	−0.364029	−	0.931388i	$-0.618599\pi$
$449$	−15.4273	−0.728058	−0.364029	+	0.931388i	$0.618599\pi$
$450$	−3.49733	−0.164866
$451$	54.7670	2.57888
$452$	89.5908	4.21399
$453$	19.3967	0.911337
$454$	40.2691	1.88992
$455$	−14.9563	−0.701162
$456$	91.1091	4.26657
$457$	−29.5467	−1.38214	−0.691068	−	0.722789i	$-0.742860\pi$
$457$	−29.5467	−1.38214	−0.691068	+	0.722789i	$0.742860\pi$
$458$	−38.6992	−1.80829
$459$	31.0704	1.45024
$460$	22.9939	1.07210
$461$	12.9564	0.603438	0.301719	−	0.953397i	$-0.402440\pi$
$461$	12.9564	0.603438	0.301719	+	0.953397i	$0.402440\pi$
$462$	−52.9819	−2.46494
$463$	11.9852	0.556998	0.278499	−	0.960437i	$-0.410163\pi$
$463$	11.9852	0.556998	0.278499	+	0.960437i	$0.410163\pi$
$464$	33.0239	1.53310
$465$	36.4595	1.69077
$466$	−28.8196	−1.33504
$467$	−5.44812	−0.252109	−0.126055	−	0.992023i	$-0.540231\pi$
$467$	−5.44812	−0.252109	−0.126055	+	0.992023i	$0.540231\pi$
$468$	−7.64864	−0.353558
$469$	8.18896	0.378131
$470$	−39.2081	−1.80854
$471$	43.2822	1.99434
$472$	59.8464	2.75466
$473$	0.191677	0.00881333
$474$	−16.9251	−0.777395
$475$	14.3040	0.656313
$476$	−73.1784	−3.35413
$477$	0.0599171	0.00274341
$478$	−63.3700	−2.89848
$479$	−1.06431	−0.0486295	−0.0243147	−	0.999704i	$-0.507740\pi$
$479$	−1.06431	−0.0486295	−0.0243147	+	0.999704i	$0.507740\pi$
$480$	−38.8371	−1.77266
$481$	−4.71102	−0.214804
$482$	45.5945	2.07677
$483$	−8.11386	−0.369194
$484$	52.8640	2.40291
$485$	28.5851	1.29798
$486$	−17.4770	−0.792773
$487$	22.2238	1.00706	0.503529	−	0.863978i	$-0.332035\pi$
$487$	22.2238	1.00706	0.503529	+	0.863978i	$0.332035\pi$
$488$	−31.2835	−1.41614
$489$	−5.76208	−0.260570
$490$	−12.6344	−0.570764
$491$	25.0065	1.12853	0.564263	−	0.825595i	$-0.309160\pi$
$491$	25.0065	1.12853	0.564263	+	0.825595i	$0.309160\pi$
$492$	−102.778	−4.63358
$493$	27.8293	1.25337
$494$	44.7683	2.01422
$495$	−8.34035	−0.374871
$496$	59.1771	2.65713
$497$	−2.69016	−0.120670
$498$	47.0086	2.10650
$499$	16.8169	0.752829	0.376415	−	0.926451i	$-0.377157\pi$
$499$	16.8169	0.752829	0.376415	+	0.926451i	$0.377157\pi$
$500$	36.3993	1.62783
$501$	−24.4044	−1.09031
$502$	−23.0779	−1.03002
$503$	8.55031	0.381239	0.190620	−	0.981664i	$-0.438950\pi$
$503$	8.55031	0.381239	0.190620	+	0.981664i	$0.438950\pi$
$504$	10.2518	0.456653
$505$	24.8003	1.10360
$506$	22.7705	1.01227
$507$	13.0866	0.581196
$508$	−24.8600	−1.10298
$509$	−15.4007	−0.682624	−0.341312	−	0.939950i	$-0.610871\pi$
$509$	−15.4007	−0.682624	−0.341312	+	0.939950i	$0.610871\pi$
$510$	−90.9619	−4.02786
$511$	−19.9245	−0.881407
$512$	49.1258	2.17107
$513$	31.2924	1.38159
$514$	−12.7142	−0.560798
$515$	−3.26754	−0.143985
$516$	−0.359709	−0.0158353
$517$	−27.1314	−1.19324
$518$	11.0990	0.487662
$519$	−29.8260	−1.30921
$520$	−44.8124	−1.96516
$521$	−21.3467	−0.935216	−0.467608	−	0.883936i	$-0.654884\pi$
$521$	−21.3467	−0.935216	−0.467608	+	0.883936i	$0.654884\pi$
$522$	−6.85286	−0.299942
$523$	13.4031	0.586075	0.293037	−	0.956101i	$-0.405334\pi$
$523$	13.4031	0.586075	0.293037	+	0.956101i	$0.405334\pi$
$524$	20.2095	0.882854
$525$	8.88082	0.387591
$526$	65.6356	2.86185
$527$	49.8686	2.17231
$528$	−74.6934	−3.25061
$529$	−19.5128	−0.848384
$530$	0.617044	0.0268027
$531$	−5.84335	−0.253580
$532$	−73.7012	−3.19535
$533$	−28.7314	−1.24450
$534$	67.9145	2.93895
$535$	−47.0983	−2.03624
$536$	24.5360	1.05979
$537$	39.0030	1.68311
$538$	−47.8888	−2.06463
$539$	−8.74280	−0.376579
$540$	−55.0578	−2.36931
$541$	37.8026	1.62526	0.812631	−	0.582778i	$-0.198034\pi$
$541$	37.8026	1.62526	0.812631	+	0.582778i	$0.198034\pi$
$542$	−54.8961	−2.35799
$543$	37.8556	1.62454
$544$	−53.1206	−2.27753
$545$	11.5754	0.495838
$546$	27.7949	1.18951
$547$	31.9069	1.36424	0.682121	−	0.731240i	$-0.261058\pi$
$547$	31.9069	1.36424	0.682121	+	0.731240i	$0.261058\pi$
$548$	−49.7161	−2.12376
$549$	3.05450	0.130363
$550$	−24.9229	−1.06272
$551$	28.0281	1.19404
$552$	−24.3110	−1.03474
$553$	7.78919	0.331230
$554$	−7.52096	−0.319535
$555$	9.64041	0.409213
$556$	36.7333	1.55784
$557$	−31.0592	−1.31602	−0.658010	−	0.753010i	$-0.728601\pi$
$557$	−31.0592	−1.31602	−0.658010	+	0.753010i	$0.728601\pi$
$558$	−12.2800	−0.519853
$559$	−0.100556	−0.00425307
$560$	49.6761	2.09920
$561$	−62.9442	−2.65750
$562$	−10.6119	−0.447638
$563$	7.01223	0.295530	0.147765	−	0.989022i	$-0.452792\pi$
$563$	7.01223	0.295530	0.147765	+	0.989022i	$0.452792\pi$
$564$	50.9158	2.14394
$565$	−51.2509	−2.15614
$566$	−11.4072	−0.479482
$567$	23.9503	1.00582
$568$	−8.06034	−0.338204
$569$	10.7364	0.450093	0.225047	−	0.974348i	$-0.427747\pi$
$569$	10.7364	0.450093	0.225047	+	0.974348i	$0.427747\pi$
$570$	−91.6118	−3.83719
$571$	37.3744	1.56407	0.782035	−	0.623235i	$-0.214182\pi$
$571$	37.3744	1.56407	0.782035	+	0.623235i	$0.214182\pi$
$572$	−54.5062	−2.27902
$573$	1.64211	0.0686002
$574$	67.6902	2.82533
$575$	−3.81679	−0.159171
$576$	2.12937	0.0887239
$577$	−26.9211	−1.12074	−0.560370	−	0.828242i	$-0.689341\pi$
$577$	−26.9211	−1.12074	−0.560370	+	0.828242i	$0.689341\pi$
$578$	−80.6116	−3.35300
$579$	−37.2259	−1.54705
$580$	−49.3143	−2.04767
$581$	−21.6341	−0.897533
$582$	−53.1228	−2.20201
$583$	0.426985	0.0176839
$584$	−59.6982	−2.47033
$585$	4.37545	0.180902
$586$	8.42701	0.348117
$587$	6.38712	0.263625	0.131812	−	0.991275i	$-0.457920\pi$
$587$	6.38712	0.263625	0.131812	+	0.991275i	$0.457920\pi$
$588$	16.4071	0.676616
$589$	50.2249	2.06948
$590$	−60.1766	−2.47743
$591$	45.9266	1.88917
$592$	15.6473	0.643099
$593$	−9.97703	−0.409708	−0.204854	−	0.978793i	$-0.565672\pi$
$593$	−9.97703	−0.409708	−0.204854	+	0.978793i	$0.565672\pi$
$594$	−54.5230	−2.23710
$595$	41.8621	1.71618
$596$	27.5731	1.12944
$597$	27.6313	1.13087
$598$	−11.9457	−0.488495
$599$	39.5902	1.61761	0.808806	−	0.588076i	$-0.200114\pi$
$599$	39.5902	1.61761	0.808806	+	0.588076i	$0.200114\pi$
$600$	26.6089	1.08630
$601$	20.9390	0.854122	0.427061	−	0.904223i	$-0.359549\pi$
$601$	20.9390	0.854122	0.427061	+	0.904223i	$0.359549\pi$
$602$	0.236907	0.00965560
$603$	−2.39567	−0.0975592
$604$	−47.0128	−1.91292
$605$	−30.2411	−1.22948
$606$	−46.0892	−1.87225
$607$	−26.0358	−1.05676	−0.528381	−	0.849008i	$-0.677201\pi$
$607$	−26.0358	−1.05676	−0.528381	+	0.849008i	$0.677201\pi$
$608$	−53.5001	−2.16971
$609$	17.4016	0.705147
$610$	31.4561	1.27362
$611$	14.2334	0.575824
$612$	21.4082	0.865377
$613$	26.8998	1.08647	0.543236	−	0.839580i	$-0.317199\pi$
$613$	26.8998	1.08647	0.543236	+	0.839580i	$0.317199\pi$
$614$	45.4748	1.83521
$615$	58.7946	2.37083
$616$	73.0573	2.94356
$617$	−20.9015	−0.841464	−0.420732	−	0.907185i	$-0.638227\pi$
$617$	−20.9015	−0.841464	−0.420732	+	0.907185i	$0.638227\pi$
$618$	6.07242	0.244268
$619$	8.34078	0.335244	0.167622	−	0.985851i	$-0.446391\pi$
$619$	8.34078	0.335244	0.167622	+	0.985851i	$0.446391\pi$
$620$	−88.3687	−3.54897
$621$	−8.34987	−0.335069
$622$	−48.7165	−1.95335
$623$	−31.2553	−1.25222
$624$	39.1850	1.56866
$625$	−31.0420	−1.24168
$626$	10.4200	0.416469
$627$	−63.3939	−2.53171
$628$	−104.905	−4.18617
$629$	13.1860	0.525759
$630$	−10.3084	−0.410696
$631$	−23.9785	−0.954569	−0.477285	−	0.878749i	$-0.658379\pi$
$631$	−23.9785	−0.954569	−0.477285	+	0.878749i	$0.658379\pi$
$632$	23.3382	0.928342
$633$	−3.85717	−0.153309
$634$	−45.1814	−1.79438
$635$	14.2213	0.564355
$636$	−0.801295	−0.0317734
$637$	4.58657	0.181727
$638$	−48.8353	−1.93341
$639$	0.787004	0.0311334
$640$	−18.6495	−0.737185
$641$	6.25528	0.247069	0.123534	−	0.992340i	$-0.460577\pi$
$641$	6.25528	0.247069	0.123534	+	0.992340i	$0.460577\pi$
$642$	87.5279	3.45445
$643$	30.3958	1.19869	0.599346	−	0.800490i	$-0.295427\pi$
$643$	30.3958	1.19869	0.599346	+	0.800490i	$0.295427\pi$
$644$	19.6660	0.774947
$645$	0.205773	0.00810232
$646$	−125.305	−4.93005
$647$	−26.4583	−1.04018	−0.520092	−	0.854110i	$-0.674102\pi$
$647$	−26.4583	−1.04018	−0.520092	+	0.854110i	$0.674102\pi$
$648$	71.7606	2.81902
$649$	−41.6413	−1.63456
$650$	13.0748	0.512837
$651$	31.1827	1.22215
$652$	13.9658	0.546944
$653$	24.8499	0.972452	0.486226	−	0.873833i	$-0.338373\pi$
$653$	24.8499	0.972452	0.486226	+	0.873833i	$0.338373\pi$
$654$	−21.5119	−0.841182
$655$	−11.5609	−0.451723
$656$	95.4290	3.72588
$657$	5.82888	0.227406
$658$	−33.5335	−1.30727
$659$	−6.01352	−0.234253	−0.117127	−	0.993117i	$-0.537368\pi$
$659$	−6.01352	−0.234253	−0.117127	+	0.993117i	$0.537368\pi$
$660$	111.539	4.34165
$661$	−26.6630	−1.03707	−0.518535	−	0.855057i	$-0.673522\pi$
$661$	−26.6630	−1.03707	−0.518535	+	0.855057i	$0.673522\pi$
$662$	54.1978	2.10646
$663$	33.0212	1.28244
$664$	−64.8206	−2.51553
$665$	42.1612	1.63494
$666$	−3.24700	−0.125819
$667$	−7.47884	−0.289582
$668$	59.1500	2.28858
$669$	24.1038	0.931908
$670$	−24.6714	−0.953138
$671$	21.7671	0.840311
$672$	−33.2161	−1.28134
$673$	−30.7772	−1.18637	−0.593186	−	0.805065i	$-0.702130\pi$
$673$	−30.7772	−1.18637	−0.593186	+	0.805065i	$0.702130\pi$
$674$	−81.9850	−3.15794
$675$	9.13913	0.351765
$676$	−31.7186	−1.21995
$677$	−31.3691	−1.20561	−0.602806	−	0.797887i	$-0.705951\pi$
$677$	−31.3691	−1.20561	−0.602806	+	0.797887i	$0.705951\pi$
$678$	95.2451	3.65787
$679$	24.4479	0.938226
$680$	125.428	4.80996
$681$	29.9148	1.14634
$682$	−87.5103	−3.35094
$683$	48.8406	1.86883	0.934416	−	0.356183i	$-0.115922\pi$
$683$	48.8406	1.86883	0.934416	+	0.356183i	$0.115922\pi$
$684$	21.5612	0.824413
$685$	28.4403	1.08665
$686$	−51.7483	−1.97576
$687$	−28.7486	−1.09683
$688$	0.333989	0.0127332
$689$	−0.224001	−0.00853376
$690$	24.4451	0.930609
$691$	−15.7648	−0.599721	−0.299861	−	0.953983i	$-0.596940\pi$
$691$	−15.7648	−0.599721	−0.299861	+	0.953983i	$0.596940\pi$
$692$	72.2906	2.74808
$693$	−7.13325	−0.270970
$694$	−65.8506	−2.49966
$695$	−21.0135	−0.797086
$696$	52.1390	1.97633
$697$	80.4181	3.04605
$698$	16.3666	0.619483
$699$	−21.4093	−0.809774
$700$	−21.5249	−0.813563
$701$	11.1097	0.419607	0.209804	−	0.977744i	$-0.432718\pi$
$701$	11.1097	0.419607	0.209804	+	0.977744i	$0.432718\pi$
$702$	28.6034	1.07956
$703$	13.2802	0.500871
$704$	15.1745	0.571910
$705$	−29.1267	−1.09697
$706$	−59.8674	−2.25314
$707$	21.2110	0.797721
$708$	78.1455	2.93689
$709$	−2.95242	−0.110880	−0.0554401	−	0.998462i	$-0.517656\pi$
$709$	−2.95242	−0.110880	−0.0554401	+	0.998462i	$0.517656\pi$
$710$	8.10481	0.304168
$711$	−2.27872	−0.0854585
$712$	−93.6480	−3.50961
$713$	−13.4017	−0.501897
$714$	−77.7969	−2.91148
$715$	31.1806	1.16609
$716$	−94.5335	−3.53288
$717$	−47.0759	−1.75808
$718$	14.9136	0.556570
$719$	−3.71870	−0.138684	−0.0693421	−	0.997593i	$-0.522090\pi$
$719$	−3.71870	−0.138684	−0.0693421	+	0.997593i	$0.522090\pi$
$720$	−14.5327	−0.541601
$721$	−2.79462	−0.104077
$722$	−77.2423	−2.87466
$723$	33.8709	1.25967
$724$	−91.7525	−3.40995
$725$	8.18577	0.304012
$726$	56.2004	2.08579
$727$	−17.1367	−0.635564	−0.317782	−	0.948164i	$-0.602938\pi$
$727$	−17.1367	−0.635564	−0.317782	+	0.948164i	$0.602938\pi$
$728$	−38.3267	−1.42048
$729$	18.6704	0.691497
$730$	60.0276	2.22172
$731$	0.281453	0.0104099
$732$	−40.8490	−1.50982
$733$	8.31045	0.306954	0.153477	−	0.988152i	$-0.450953\pi$
$733$	8.31045	0.306954	0.153477	+	0.988152i	$0.450953\pi$
$734$	−12.1617	−0.448895
$735$	−9.38575	−0.346199
$736$	14.2756	0.526206
$737$	−17.0722	−0.628862
$738$	−19.8027	−0.728947
$739$	35.7576	1.31537	0.657683	−	0.753295i	$-0.271537\pi$
$739$	35.7576	1.31537	0.657683	+	0.753295i	$0.271537\pi$
$740$	−23.3659	−0.858949
$741$	33.2572	1.22173
$742$	0.527739	0.0193739
$743$	−37.9376	−1.39180	−0.695898	−	0.718140i	$-0.744994\pi$
$743$	−37.9376	−1.39180	−0.695898	+	0.718140i	$0.744994\pi$
$744$	93.4304	3.42533
$745$	−15.7734	−0.577891
$746$	−87.9645	−3.22061
$747$	6.32902	0.231567
$748$	152.561	5.57817
$749$	−40.2817	−1.47186
$750$	38.6966	1.41300
$751$	49.4956	1.80612	0.903060	−	0.429515i	$-0.141316\pi$
$751$	49.4956	1.80612	0.903060	+	0.429515i	$0.141316\pi$
$752$	−47.2752	−1.72395
$753$	−17.1440	−0.624761
$754$	25.6196	0.933010
$755$	26.8939	0.978769
$756$	−47.0892	−1.71262
$757$	−22.8003	−0.828690	−0.414345	−	0.910120i	$-0.635989\pi$
$757$	−22.8003	−0.828690	−0.414345	+	0.910120i	$0.635989\pi$
$758$	12.6570	0.459723
$759$	16.9156	0.613998
$760$	126.324	4.58227
$761$	−29.2756	−1.06124	−0.530619	−	0.847610i	$-0.678041\pi$
$761$	−29.2756	−1.06124	−0.530619	+	0.847610i	$0.678041\pi$
$762$	−26.4290	−0.957421
$763$	9.90012	0.358408
$764$	−3.98007	−0.143994
$765$	−12.2467	−0.442780
$766$	36.0706	1.30328
$767$	21.8455	0.788795
$768$	46.9343	1.69360
$769$	30.2704	1.09158	0.545790	−	0.837922i	$-0.316230\pi$
$769$	30.2704	1.09158	0.545790	+	0.837922i	$0.316230\pi$
$770$	−73.4604	−2.64733
$771$	−9.44502	−0.340154
$772$	90.2261	3.24731
$773$	−1.52485	−0.0548451	−0.0274225	−	0.999624i	$-0.508730\pi$
$773$	−1.52485	−0.0548451	−0.0274225	+	0.999624i	$0.508730\pi$
$774$	−0.0693068	−0.00249118
$775$	14.6685	0.526907
$776$	73.2515	2.62958
$777$	8.24515	0.295793
$778$	4.89720	0.175573
$779$	80.9926	2.90186
$780$	−58.5146	−2.09516
$781$	5.60840	0.200684
$782$	33.4355	1.19565
$783$	17.9077	0.639970
$784$	−15.2339	−0.544069
$785$	60.0116	2.14191
$786$	21.4849	0.766343
$787$	−24.5821	−0.876259	−0.438129	−	0.898912i	$-0.644359\pi$
$787$	−24.5821	−0.876259	−0.438129	+	0.898912i	$0.644359\pi$
$788$	−111.315	−3.96542
$789$	48.7589	1.73586
$790$	−23.4669	−0.834916
$791$	−43.8333	−1.55853
$792$	−21.3728	−0.759450
$793$	−11.4193	−0.405511
$794$	−28.0225	−0.994481
$795$	0.458386	0.0162573
$796$	−66.9713	−2.37374
$797$	−47.8717	−1.69570	−0.847851	−	0.530235i	$-0.822104\pi$
$797$	−47.8717	−1.69570	−0.847851	+	0.530235i	$0.822104\pi$
$798$	−78.3527	−2.77366
$799$	−39.8389	−1.40940
$800$	−15.6250	−0.552427
$801$	9.14370	0.323077
$802$	44.0368	1.55499
$803$	41.5381	1.46585
$804$	32.0383	1.12990
$805$	−11.2500	−0.396511
$806$	45.9089	1.61707
$807$	−35.5753	−1.25231
$808$	63.5528	2.23578
$809$	−24.1519	−0.849137	−0.424569	−	0.905396i	$-0.639574\pi$
$809$	−24.1519	−0.849137	−0.424569	+	0.905396i	$0.639574\pi$
$810$	−72.1566	−2.53532
$811$	−36.6966	−1.28859	−0.644296	−	0.764776i	$-0.722849\pi$
$811$	−36.6966	−1.28859	−0.644296	+	0.764776i	$0.722849\pi$
$812$	−42.1770	−1.48012
$813$	−40.7809	−1.43025
$814$	−23.1390	−0.811020
$815$	−7.98923	−0.279851
$816$	−109.677	−3.83947
$817$	0.283463	0.00991713
$818$	82.6998	2.89153
$819$	3.74218	0.130762
$820$	−142.503	−4.97643
$821$	−40.0829	−1.39890	−0.699451	−	0.714680i	$-0.746572\pi$
$821$	−40.0829	−1.39890	−0.699451	+	0.714680i	$0.746572\pi$
$822$	−52.8538	−1.84349
$823$	26.2834	0.916180	0.458090	−	0.888906i	$-0.348534\pi$
$823$	26.2834	0.916180	0.458090	+	0.888906i	$0.348534\pi$
$824$	−8.37332	−0.291698
$825$	−18.5145	−0.644593
$826$	−51.4672	−1.79077
$827$	−40.9458	−1.42382	−0.711912	−	0.702269i	$-0.752170\pi$
$827$	−40.9458	−1.42382	−0.711912	+	0.702269i	$0.752170\pi$
$828$	−5.75325	−0.199939
$829$	−53.0947	−1.84406	−0.922028	−	0.387124i	$-0.873469\pi$
$829$	−53.0947	−1.84406	−0.922028	+	0.387124i	$0.873469\pi$
$830$	65.1782	2.26237
$831$	−5.58712	−0.193815
$832$	−7.96071	−0.275988
$833$	−12.8376	−0.444798
$834$	39.0516	1.35225
$835$	−33.8371	−1.17098
$836$	153.651	5.31412
$837$	32.0897	1.10918
$838$	99.0610	3.42200
$839$	−30.9315	−1.06788	−0.533938	−	0.845524i	$-0.679288\pi$
$839$	−30.9315	−1.06788	−0.533938	+	0.845524i	$0.679288\pi$
$840$	78.4300	2.70609
$841$	−12.9603	−0.446908
$842$	39.9488	1.37673
$843$	−7.88332	−0.271516
$844$	9.34881	0.321799
$845$	18.1448	0.624200
$846$	9.81019	0.337281
$847$	−25.8643	−0.888708
$848$	0.744001	0.0255491
$849$	−8.47413	−0.290831
$850$	−36.5960	−1.25523
$851$	−3.54360	−0.121473
$852$	−10.5249	−0.360578
$853$	18.3165	0.627146	0.313573	−	0.949564i	$-0.398474\pi$
$853$	18.3165	0.627146	0.313573	+	0.949564i	$0.398474\pi$
$854$	26.9035	0.920618
$855$	−12.3342	−0.421821
$856$	−120.693	−4.12521
$857$	−13.8660	−0.473655	−0.236827	−	0.971552i	$-0.576108\pi$
$857$	−13.8660	−0.473655	−0.236827	+	0.971552i	$0.576108\pi$
$858$	−57.9463	−1.97825
$859$	26.7169	0.911570	0.455785	−	0.890090i	$-0.349359\pi$
$859$	26.7169	0.911570	0.455785	+	0.890090i	$0.349359\pi$
$860$	−0.498743	−0.0170070
$861$	50.2852	1.71372
$862$	−11.5496	−0.393382
$863$	−31.9618	−1.08799	−0.543997	−	0.839087i	$-0.683090\pi$
$863$	−31.9618	−1.08799	−0.543997	+	0.839087i	$0.683090\pi$
$864$	−34.1823	−1.16290
$865$	−41.3543	−1.40609
$866$	62.4304	2.12147
$867$	−59.8842	−2.03377
$868$	−75.5790	−2.56532
$869$	−16.2387	−0.550861
$870$	−52.4267	−1.77743
$871$	8.95626	0.303471
$872$	29.6630	1.00452
$873$	−7.15221	−0.242066
$874$	33.6744	1.13905
$875$	−17.8088	−0.602047
$876$	−77.9520	−2.63375
$877$	24.8319	0.838513	0.419256	−	0.907868i	$-0.362291\pi$
$877$	24.8319	0.838513	0.419256	+	0.907868i	$0.362291\pi$
$878$	−89.7038	−3.02736
$879$	6.26020	0.211151
$880$	−103.564	−3.49113
$881$	−27.9991	−0.943314	−0.471657	−	0.881782i	$-0.656344\pi$
$881$	−27.9991	−0.943314	−0.471657	+	0.881782i	$0.656344\pi$
$882$	3.16123	0.106444
$883$	29.5070	0.992989	0.496495	−	0.868040i	$-0.334620\pi$
$883$	29.5070	0.992989	0.496495	+	0.868040i	$0.334620\pi$
$884$	−80.0351	−2.69187
$885$	−44.7036	−1.50269
$886$	−38.0870	−1.27956
$887$	10.9172	0.366563	0.183281	−	0.983061i	$-0.441328\pi$
$887$	10.9172	0.366563	0.183281	+	0.983061i	$0.441328\pi$
$888$	24.7043	0.829023
$889$	12.1630	0.407935
$890$	94.1647	3.15641
$891$	−49.9312	−1.67276
$892$	−58.4216	−1.95610
$893$	−40.1235	−1.34268
$894$	29.3134	0.980385
$895$	54.0784	1.80764
$896$	−15.9503	−0.532863
$897$	−8.87413	−0.296298
$898$	39.7517	1.32653
$899$	28.7422	0.958607
$900$	6.29707	0.209902
$901$	0.626970	0.0208874
$902$	−141.119	−4.69875
$903$	0.175992	0.00585663
$904$	−131.334	−4.36812
$905$	52.4875	1.74474
$906$	−49.9799	−1.66047
$907$	−16.2988	−0.541193	−0.270597	−	0.962693i	$-0.587221\pi$
$907$	−16.2988	−0.541193	−0.270597	+	0.962693i	$0.587221\pi$
$908$	−72.5059	−2.40619
$909$	−6.20524	−0.205815
$910$	38.5382	1.27753
$911$	37.3926	1.23887	0.619436	−	0.785047i	$-0.287361\pi$
$911$	37.3926	1.23887	0.619436	+	0.785047i	$0.287361\pi$
$912$	−110.461	−3.65773
$913$	45.1023	1.49267
$914$	76.1335	2.51827
$915$	23.3679	0.772520
$916$	69.6793	2.30227
$917$	−9.88771	−0.326521
$918$	−80.0597	−2.64236
$919$	−1.61261	−0.0531950	−0.0265975	−	0.999646i	$-0.508467\pi$
$919$	−1.61261	−0.0531950	−0.0265975	+	0.999646i	$0.508467\pi$
$920$	−33.7076	−1.11131
$921$	33.7820	1.11315
$922$	−33.3849	−1.09947
$923$	−2.94223	−0.0968447
$924$	95.3958	3.13829
$925$	3.87855	0.127526
$926$	−30.8824	−1.01486
$927$	0.817563	0.0268523
$928$	−30.6165	−1.00504
$929$	−2.23013	−0.0731683	−0.0365842	−	0.999331i	$-0.511648\pi$
$929$	−2.23013	−0.0731683	−0.0365842	+	0.999331i	$0.511648\pi$
$930$	−93.9459	−3.08061
$931$	−12.9294	−0.423743
$932$	51.8907	1.69974
$933$	−36.1901	−1.18481
$934$	14.0383	0.459346
$935$	−87.2732	−2.85414
$936$	11.2124	0.366490
$937$	38.2604	1.24991	0.624957	−	0.780659i	$-0.285117\pi$
$937$	38.2604	1.24991	0.624957	+	0.780659i	$0.285117\pi$
$938$	−21.1006	−0.688960
$939$	7.74076	0.252610
$940$	70.5957	2.30258
$941$	−3.58632	−0.116911	−0.0584554	−	0.998290i	$-0.518618\pi$
$941$	−3.58632	−0.116911	−0.0584554	+	0.998290i	$0.518618\pi$
$942$	−111.526	−3.63372
$943$	−21.6116	−0.703769
$944$	−72.5580	−2.36156
$945$	26.9376	0.876281
$946$	−0.493898	−0.0160580
$947$	19.1578	0.622546	0.311273	−	0.950321i	$-0.399245\pi$
$947$	19.1578	0.622546	0.311273	+	0.950321i	$0.399245\pi$
$948$	30.4742	0.989757
$949$	−21.7914	−0.707378
$950$	−36.8574	−1.19581
$951$	−33.5640	−1.08839
$952$	107.275	3.47680
$953$	−18.7954	−0.608841	−0.304421	−	0.952538i	$-0.598463\pi$
$953$	−18.7954	−0.608841	−0.304421	+	0.952538i	$0.598463\pi$
$954$	−0.154389	−0.00499854
$955$	2.27682	0.0736761
$956$	114.100	3.69026
$957$	−36.2784	−1.17272
$958$	2.74242	0.0886036
$959$	24.3241	0.785468
$960$	16.2904	0.525771
$961$	20.5046	0.661438
$962$	12.1390	0.391376
$963$	11.7844	0.379746
$964$	−82.0946	−2.64409
$965$	−51.6143	−1.66152
$966$	20.9071	0.672676
$967$	−53.6211	−1.72434	−0.862169	−	0.506620i	$-0.830895\pi$
$967$	−53.6211	−1.72434	−0.862169	+	0.506620i	$0.830895\pi$
$968$	−77.4953	−2.49079
$969$	−93.0855	−2.99034
$970$	−73.6557	−2.36494
$971$	60.4535	1.94005	0.970023	−	0.243015i	$-0.0781364\pi$
$971$	60.4535	1.94005	0.970023	+	0.243015i	$0.0781364\pi$
$972$	31.4680	1.00934
$973$	−17.9722	−0.576161
$974$	−57.2645	−1.83487
$975$	9.71294	0.311063
$976$	37.9283	1.21405
$977$	−6.64655	−0.212642	−0.106321	−	0.994332i	$-0.533907\pi$
$977$	−6.64655	−0.212642	−0.106321	+	0.994332i	$0.533907\pi$
$978$	14.8473	0.474763
$979$	65.1604	2.08254
$980$	22.7487	0.726680
$981$	−2.89627	−0.0924707
$982$	−64.4346	−2.05619
$983$	−41.0547	−1.30944	−0.654721	−	0.755871i	$-0.727214\pi$
$983$	−41.0547	−1.30944	−0.654721	+	0.755871i	$0.727214\pi$
$984$	150.666	4.80305
$985$	63.6781	2.02895
$986$	−71.7082	−2.28365
$987$	−24.9111	−0.792930
$988$	−80.6069	−2.56445
$989$	−0.0756376	−0.00240514
$990$	21.4907	0.683020
$991$	−2.35477	−0.0748016	−0.0374008	−	0.999300i	$-0.511908\pi$
$991$	−2.35477	−0.0748016	−0.0374008	+	0.999300i	$0.511908\pi$
$992$	−54.8632	−1.74191
$993$	40.2621	1.27768
$994$	6.93179	0.219863
$995$	38.3113	1.21455
$996$	−84.6406	−2.68194
$997$	42.8665	1.35760	0.678798	−	0.734325i	$-0.262501\pi$
$997$	42.8665	1.35760	0.678798	+	0.734325i	$0.262501\pi$
$998$	−43.3325	−1.37167
$999$	8.48497	0.268453

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4021.2.a.c.1.10	✓	182

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4021.2.a.c.1.10	✓	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)

\(f(q)\)	\(=\)	\(q-2.57672 q^{2} -1.91417 q^{3} +4.63947 q^{4} -2.65404 q^{5} +4.93228 q^{6} -2.26992 q^{7} -6.80118 q^{8} +0.664061 q^{9} +O(q^{10})\)	\(q-2.57672 q^{2} -1.91417 q^{3} +4.63947 q^{4} -2.65404 q^{5} +4.93228 q^{6} -2.26992 q^{7} -6.80118 q^{8} +0.664061 q^{9} +6.83870 q^{10} +4.73227 q^{11} -8.88076 q^{12} -2.48260 q^{13} +5.84893 q^{14} +5.08029 q^{15} +8.24577 q^{16} +6.94871 q^{17} -1.71110 q^{18} +6.99836 q^{19} -12.3133 q^{20} +4.34501 q^{21} -12.1937 q^{22} -1.86740 q^{23} +13.0186 q^{24} +2.04391 q^{25} +6.39697 q^{26} +4.47139 q^{27} -10.5312 q^{28} +4.00495 q^{29} -13.0905 q^{30} +7.17667 q^{31} -7.64466 q^{32} -9.05839 q^{33} -17.9049 q^{34} +6.02444 q^{35} +3.08089 q^{36} +1.89761 q^{37} -18.0328 q^{38} +4.75214 q^{39} +18.0506 q^{40} +11.5731 q^{41} -11.1959 q^{42} +0.0405043 q^{43} +21.9553 q^{44} -1.76244 q^{45} +4.81176 q^{46} -5.73327 q^{47} -15.7838 q^{48} -1.84748 q^{49} -5.26658 q^{50} -13.3010 q^{51} -11.5180 q^{52} +0.0902283 q^{53} -11.5215 q^{54} -12.5596 q^{55} +15.4381 q^{56} -13.3961 q^{57} -10.3196 q^{58} -8.79942 q^{59} +23.5699 q^{60} +4.59972 q^{61} -18.4922 q^{62} -1.50736 q^{63} +3.20659 q^{64} +6.58892 q^{65} +23.3409 q^{66} -3.60761 q^{67} +32.2384 q^{68} +3.57452 q^{69} -15.5233 q^{70} +1.18514 q^{71} -4.51640 q^{72} +8.77763 q^{73} -4.88961 q^{74} -3.91240 q^{75} +32.4687 q^{76} -10.7419 q^{77} -12.2449 q^{78} -3.43149 q^{79} -21.8846 q^{80} -10.5512 q^{81} -29.8206 q^{82} +9.53079 q^{83} +20.1586 q^{84} -18.4421 q^{85} -0.104368 q^{86} -7.66618 q^{87} -32.1850 q^{88} +13.7694 q^{89} +4.54131 q^{90} +5.63530 q^{91} -8.66374 q^{92} -13.7374 q^{93} +14.7730 q^{94} -18.5739 q^{95} +14.6332 q^{96} -10.7704 q^{97} +4.76045 q^{98} +3.14252 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 182 q + 18 q^{2} + 28 q^{3} + 208 q^{4} + 22 q^{5} + 18 q^{6} + 14 q^{7} + 54 q^{8} + 238 q^{9}+O(q^{10}) \) 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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