LMFDB - Embedded newform 4021.2.a.c.1.13

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			1.13
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)

$f(q)$	$=$	$q-2.51665 q^{2} +0.669973 q^{3} +4.33353 q^{4} +4.29318 q^{5} -1.68609 q^{6} +3.31221 q^{7} -5.87268 q^{8} -2.55114 q^{9} +O(q^{10})$	\(q-2.51665 q^{2} +0.669973 q^{3} +4.33353 q^{4} +4.29318 q^{5} -1.68609 q^{6} +3.31221 q^{7} -5.87268 q^{8} -2.55114 q^{9} -10.8044 q^{10} +5.56759 q^{11} +2.90335 q^{12} +0.352569 q^{13} -8.33569 q^{14} +2.87631 q^{15} +6.11242 q^{16} +2.51378 q^{17} +6.42032 q^{18} +0.980083 q^{19} +18.6046 q^{20} +2.21909 q^{21} -14.0117 q^{22} -6.39136 q^{23} -3.93453 q^{24} +13.4314 q^{25} -0.887294 q^{26} -3.71911 q^{27} +14.3536 q^{28} +3.42581 q^{29} -7.23868 q^{30} +0.661238 q^{31} -3.63746 q^{32} +3.73014 q^{33} -6.32630 q^{34} +14.2199 q^{35} -11.0554 q^{36} -5.41895 q^{37} -2.46653 q^{38} +0.236212 q^{39} -25.2125 q^{40} -7.11652 q^{41} -5.58468 q^{42} -1.59969 q^{43} +24.1273 q^{44} -10.9525 q^{45} +16.0848 q^{46} -6.60217 q^{47} +4.09515 q^{48} +3.97077 q^{49} -33.8021 q^{50} +1.68416 q^{51} +1.52787 q^{52} -1.65555 q^{53} +9.35970 q^{54} +23.9027 q^{55} -19.4516 q^{56} +0.656629 q^{57} -8.62156 q^{58} +12.3907 q^{59} +12.4646 q^{60} +8.27888 q^{61} -1.66411 q^{62} -8.44991 q^{63} -3.07062 q^{64} +1.51364 q^{65} -9.38745 q^{66} +5.86924 q^{67} +10.8935 q^{68} -4.28204 q^{69} -35.7866 q^{70} -1.97588 q^{71} +14.9820 q^{72} -8.50101 q^{73} +13.6376 q^{74} +8.99866 q^{75} +4.24722 q^{76} +18.4411 q^{77} -0.594463 q^{78} +3.28607 q^{79} +26.2417 q^{80} +5.16170 q^{81} +17.9098 q^{82} +5.32295 q^{83} +9.61651 q^{84} +10.7921 q^{85} +4.02585 q^{86} +2.29520 q^{87} -32.6967 q^{88} -5.13366 q^{89} +27.5636 q^{90} +1.16779 q^{91} -27.6971 q^{92} +0.443012 q^{93} +16.6153 q^{94} +4.20767 q^{95} -2.43700 q^{96} +13.2327 q^{97} -9.99303 q^{98} -14.2037 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.51665	−1.77954	−0.889770	−	0.456409i	$-0.849136\pi$
$2$	−2.51665	−1.77954	−0.889770	+	0.456409i	$0.849136\pi$
$3$	0.669973	0.386809	0.193405	−	0.981119i	$-0.438047\pi$
$3$	0.669973	0.386809	0.193405	+	0.981119i	$0.438047\pi$
$4$	4.33353	2.16676
$5$	4.29318	1.91997	0.959984	−	0.280055i	$-0.0903527\pi$
$5$	4.29318	1.91997	0.959984	+	0.280055i	$0.0903527\pi$
$6$	−1.68609	−0.688342
$7$	3.31221	1.25190	0.625950	−	0.779863i	$-0.284712\pi$
$7$	3.31221	1.25190	0.625950	+	0.779863i	$0.284712\pi$
$8$	−5.87268	−2.07630
$9$	−2.55114	−0.850379
$10$	−10.8044	−3.41666
$11$	5.56759	1.67869	0.839346	−	0.543597i	$-0.182938\pi$
$11$	5.56759	1.67869	0.839346	+	0.543597i	$0.182938\pi$
$12$	2.90335	0.838124
$13$	0.352569	0.0977851	0.0488926	−	0.998804i	$-0.484431\pi$
$13$	0.352569	0.0977851	0.0488926	+	0.998804i	$0.484431\pi$
$14$	−8.33569	−2.22781
$15$	2.87631	0.742661
$16$	6.11242	1.52810
$17$	2.51378	0.609681	0.304840	−	0.952403i	$-0.401397\pi$
$17$	2.51378	0.609681	0.304840	+	0.952403i	$0.401397\pi$
$18$	6.42032	1.51328
$19$	0.980083	0.224847	0.112423	−	0.993660i	$-0.464139\pi$
$19$	0.980083	0.224847	0.112423	+	0.993660i	$0.464139\pi$
$20$	18.6046	4.16012
$21$	2.21909	0.484246
$22$	−14.0117	−2.98730
$23$	−6.39136	−1.33269	−0.666345	−	0.745643i	$-0.732142\pi$
$23$	−6.39136	−1.33269	−0.666345	+	0.745643i	$0.732142\pi$
$24$	−3.93453	−0.803134
$25$	13.4314	2.68628
$26$	−0.887294	−0.174013
$27$	−3.71911	−0.715743
$28$	14.3536	2.71257
$29$	3.42581	0.636157	0.318078	−	0.948064i	$-0.396963\pi$
$29$	3.42581	0.636157	0.318078	+	0.948064i	$0.396963\pi$
$30$	−7.23868	−1.32160
$31$	0.661238	0.118762	0.0593810	−	0.998235i	$-0.481087\pi$
$31$	0.661238	0.118762	0.0593810	+	0.998235i	$0.481087\pi$
$32$	−3.63746	−0.643018
$33$	3.73014	0.649333
$34$	−6.32630	−1.08495
$35$	14.2199	2.40361
$36$	−11.0554	−1.84257
$37$	−5.41895	−0.890871	−0.445435	−	0.895314i	$-0.646951\pi$
$37$	−5.41895	−0.890871	−0.445435	+	0.895314i	$0.646951\pi$
$38$	−2.46653	−0.400123
$39$	0.236212	0.0378242
$40$	−25.2125	−3.98644
$41$	−7.11652	−1.11141	−0.555707	−	0.831378i	$-0.687552\pi$
$41$	−7.11652	−1.11141	−0.555707	+	0.831378i	$0.687552\pi$
$42$	−5.58468	−0.861736
$43$	−1.59969	−0.243950	−0.121975	−	0.992533i	$-0.538923\pi$
$43$	−1.59969	−0.243950	−0.121975	+	0.992533i	$0.538923\pi$
$44$	24.1273	3.63733
$45$	−10.9525	−1.63270
$46$	16.0848	2.37158
$47$	−6.60217	−0.963025	−0.481512	−	0.876439i	$-0.659912\pi$
$47$	−6.60217	−0.963025	−0.481512	+	0.876439i	$0.659912\pi$
$48$	4.09515	0.591084
$49$	3.97077	0.567252
$50$	−33.8021	−4.78034
$51$	1.68416	0.235830
$52$	1.52787	0.211877
$53$	−1.65555	−0.227407	−0.113703	−	0.993515i	$-0.536271\pi$
$53$	−1.65555	−0.227407	−0.113703	+	0.993515i	$0.536271\pi$
$54$	9.35970	1.27369
$55$	23.9027	3.22304
$56$	−19.4516	−2.59932
$57$	0.656629	0.0869727
$58$	−8.62156	−1.13207
$59$	12.3907	1.61313	0.806565	−	0.591145i	$-0.201324\pi$
$59$	12.3907	1.61313	0.806565	+	0.591145i	$0.201324\pi$
$60$	12.4646	1.60917
$61$	8.27888	1.06000	0.530001	−	0.847997i	$-0.322192\pi$
$61$	8.27888	1.06000	0.530001	+	0.847997i	$0.322192\pi$
$62$	−1.66411	−0.211342
$63$	−8.44991	−1.06459
$64$	−3.07062	−0.383827
$65$	1.51364	0.187744
$66$	−9.38745	−1.15552
$67$	5.86924	0.717041	0.358521	−	0.933522i	$-0.383281\pi$
$67$	5.86924	0.717041	0.358521	+	0.933522i	$0.383281\pi$
$68$	10.8935	1.32103
$69$	−4.28204	−0.515497
$70$	−35.7866	−4.27732
$71$	−1.97588	−0.234493	−0.117247	−	0.993103i	$-0.537407\pi$
$71$	−1.97588	−0.234493	−0.117247	+	0.993103i	$0.537407\pi$
$72$	14.9820	1.76565
$73$	−8.50101	−0.994968	−0.497484	−	0.867473i	$-0.665743\pi$
$73$	−8.50101	−0.994968	−0.497484	+	0.867473i	$0.665743\pi$
$74$	13.6376	1.58534
$75$	8.99866	1.03908
$76$	4.24722	0.487189
$77$	18.4411	2.10155
$78$	−0.594463	−0.0673097
$79$	3.28607	0.369712	0.184856	−	0.982766i	$-0.440818\pi$
$79$	3.28607	0.369712	0.184856	+	0.982766i	$0.440818\pi$
$80$	26.2417	2.93391
$81$	5.16170	0.573523
$82$	17.9098	1.97781
$83$	5.32295	0.584270	0.292135	−	0.956377i	$-0.405634\pi$
$83$	5.32295	0.584270	0.292135	+	0.956377i	$0.405634\pi$
$84$	9.61651	1.04925
$85$	10.7921	1.17057
$86$	4.02585	0.434119
$87$	2.29520	0.246071
$88$	−32.6967	−3.48548
$89$	−5.13366	−0.544167	−0.272084	−	0.962274i	$-0.587713\pi$
$89$	−5.13366	−0.544167	−0.272084	+	0.962274i	$0.587713\pi$
$90$	27.5636	2.90546
$91$	1.16779	0.122417
$92$	−27.6971	−2.88763
$93$	0.443012	0.0459382
$94$	16.6153	1.71374
$95$	4.20767	0.431698
$96$	−2.43700	−0.248725
$97$	13.2327	1.34357	0.671787	−	0.740744i	$-0.265527\pi$
$97$	13.2327	1.34357	0.671787	+	0.740744i	$0.265527\pi$
$98$	−9.99303	−1.00945
$99$	−14.2037	−1.42752
$100$	58.2053	5.82053
$101$	14.5172	1.44451	0.722257	−	0.691624i	$-0.243105\pi$
$101$	14.5172	1.44451	0.722257	+	0.691624i	$0.243105\pi$
$102$	−4.23845	−0.419669
$103$	13.6897	1.34889	0.674443	−	0.738327i	$-0.264384\pi$
$103$	13.6897	1.34889	0.674443	+	0.738327i	$0.264384\pi$
$104$	−2.07053	−0.203032
$105$	9.52697	0.929737
$106$	4.16643	0.404680
$107$	−10.9251	−1.05617	−0.528086	−	0.849191i	$-0.677090\pi$
$107$	−10.9251	−1.05617	−0.528086	+	0.849191i	$0.677090\pi$
$108$	−16.1169	−1.55085
$109$	−19.3608	−1.85443	−0.927215	−	0.374529i	$-0.877804\pi$
$109$	−19.3608	−1.85443	−0.927215	+	0.374529i	$0.877804\pi$
$110$	−60.1547	−5.73552
$111$	−3.63055	−0.344597
$112$	20.2456	1.91303
$113$	11.7214	1.10266	0.551330	−	0.834287i	$-0.314121\pi$
$113$	11.7214	1.10266	0.551330	+	0.834287i	$0.314121\pi$
$114$	−1.65251	−0.154771
$115$	−27.4392	−2.55872
$116$	14.8458	1.37840
$117$	−0.899452	−0.0831544
$118$	−31.1830	−2.87063
$119$	8.32617	0.763259
$120$	−16.8917	−1.54199
$121$	19.9981	1.81801
$122$	−20.8350	−1.88632
$123$	−4.76788	−0.429905
$124$	2.86550	0.257329
$125$	36.1974	3.23760
$126$	21.2655	1.89448
$127$	−14.0169	−1.24380	−0.621900	−	0.783097i	$-0.713639\pi$
$127$	−14.0169	−1.24380	−0.621900	+	0.783097i	$0.713639\pi$
$128$	15.0026	1.32605
$129$	−1.07175	−0.0943621
$130$	−3.80931	−0.334099
$131$	12.8707	1.12452	0.562260	−	0.826961i	$-0.309932\pi$
$131$	12.8707	1.12452	0.562260	+	0.826961i	$0.309932\pi$
$132$	16.1647	1.40695
$133$	3.24625	0.281485
$134$	−14.7708	−1.27600
$135$	−15.9668	−1.37420
$136$	−14.7626	−1.26588
$137$	11.0586	0.944799	0.472399	−	0.881385i	$-0.343388\pi$
$137$	11.0586	0.944799	0.472399	+	0.881385i	$0.343388\pi$
$138$	10.7764	0.917347
$139$	8.64019	0.732851	0.366426	−	0.930447i	$-0.380581\pi$
$139$	8.64019	0.732851	0.366426	+	0.930447i	$0.380581\pi$
$140$	61.6225	5.20805
$141$	−4.42327	−0.372507
$142$	4.97259	0.417290
$143$	1.96296	0.164151
$144$	−15.5936	−1.29947
$145$	14.7076	1.22140
$146$	21.3941	1.77059
$147$	2.66031	0.219418
$148$	−23.4832	−1.93031
$149$	12.9939	1.06450	0.532251	−	0.846587i	$-0.321346\pi$
$149$	12.9939	1.06450	0.532251	+	0.846587i	$0.321346\pi$
$150$	−22.6465	−1.84908
$151$	−10.6118	−0.863579	−0.431789	−	0.901975i	$-0.642118\pi$
$151$	−10.6118	−0.863579	−0.431789	+	0.901975i	$0.642118\pi$
$152$	−5.75571	−0.466850
$153$	−6.41299	−0.518459
$154$	−46.4097	−3.73980
$155$	2.83881	0.228019
$156$	1.02363	0.0819561
$157$	−20.6568	−1.64859	−0.824296	−	0.566159i	$-0.808429\pi$
$157$	−20.6568	−1.64859	−0.824296	+	0.566159i	$0.808429\pi$
$158$	−8.26989	−0.657917
$159$	−1.10917	−0.0879630
$160$	−15.6163	−1.23457
$161$	−21.1696	−1.66839
$162$	−12.9902	−1.02061
$163$	10.1224	0.792848	0.396424	−	0.918068i	$-0.370251\pi$
$163$	10.1224	0.792848	0.396424	+	0.918068i	$0.370251\pi$
$164$	−30.8397	−2.40817
$165$	16.0141	1.24670
$166$	−13.3960	−1.03973
$167$	−1.52847	−0.118276	−0.0591382	−	0.998250i	$-0.518835\pi$
$167$	−1.52847	−0.118276	−0.0591382	+	0.998250i	$0.518835\pi$
$168$	−13.0320	−1.00544
$169$	−12.8757	−0.990438
$170$	−27.1599	−2.08307
$171$	−2.50033	−0.191205
$172$	−6.93229	−0.528582
$173$	7.47218	0.568100	0.284050	−	0.958810i	$-0.408322\pi$
$173$	7.47218	0.568100	0.284050	+	0.958810i	$0.408322\pi$
$174$	−5.77621	−0.437894
$175$	44.4876	3.36295
$176$	34.0314	2.56522
$177$	8.30143	0.623974
$178$	12.9196	0.968368
$179$	−13.8670	−1.03647	−0.518236	−	0.855238i	$-0.673411\pi$
$179$	−13.8670	−1.03647	−0.518236	+	0.855238i	$0.673411\pi$
$180$	−47.4629	−3.53768
$181$	−14.8242	−1.10187	−0.550937	−	0.834547i	$-0.685730\pi$
$181$	−14.8242	−1.10187	−0.550937	+	0.834547i	$0.685730\pi$
$182$	−2.93891	−0.217846
$183$	5.54662	0.410018
$184$	37.5344	2.76707
$185$	−23.2645	−1.71044
$186$	−1.11491	−0.0817489
$187$	13.9957	1.02347
$188$	−28.6107	−2.08665
$189$	−12.3185	−0.896039
$190$	−10.5892	−0.768224
$191$	−17.8632	−1.29254	−0.646268	−	0.763110i	$-0.723671\pi$
$191$	−17.8632	−1.29254	−0.646268	+	0.763110i	$0.723671\pi$
$192$	−2.05723	−0.148468
$193$	11.2879	0.812524	0.406262	−	0.913757i	$-0.366832\pi$
$193$	11.2879	0.812524	0.406262	+	0.913757i	$0.366832\pi$
$194$	−33.3020	−2.39095
$195$	1.01410	0.0726212
$196$	17.2074	1.22910
$197$	−11.5649	−0.823967	−0.411984	−	0.911191i	$-0.635164\pi$
$197$	−11.5649	−0.823967	−0.411984	+	0.911191i	$0.635164\pi$
$198$	35.7457	2.54034
$199$	−19.0057	−1.34728	−0.673639	−	0.739061i	$-0.735270\pi$
$199$	−19.0057	−1.34728	−0.673639	+	0.739061i	$0.735270\pi$
$200$	−78.8782	−5.57753
$201$	3.93223	0.277358
$202$	−36.5347	−2.57057
$203$	11.3470	0.796404
$204$	7.29837	0.510988
$205$	−30.5525	−2.13388
$206$	−34.4522	−2.40040
$207$	16.3052	1.13329
$208$	2.15505	0.149426
$209$	5.45670	0.377448
$210$	−23.9760	−1.65450
$211$	−11.4580	−0.788798	−0.394399	−	0.918939i	$-0.629047\pi$
$211$	−11.4580	−0.788798	−0.394399	+	0.918939i	$0.629047\pi$
$212$	−7.17436	−0.492737
$213$	−1.32378	−0.0907042
$214$	27.4947	1.87950
$215$	−6.86774	−0.468376
$216$	21.8411	1.48610
$217$	2.19016	0.148678
$218$	48.7244	3.30003
$219$	−5.69545	−0.384863
$220$	103.583	6.98356
$221$	0.886281	0.0596177
$222$	9.13683	0.613224
$223$	−1.68139	−0.112594	−0.0562972	−	0.998414i	$-0.517929\pi$
$223$	−1.68139	−0.112594	−0.0562972	+	0.998414i	$0.517929\pi$
$224$	−12.0480	−0.804994
$225$	−34.2653	−2.28435
$226$	−29.4987	−1.96223
$227$	5.73235	0.380469	0.190235	−	0.981739i	$-0.439075\pi$
$227$	5.73235	0.380469	0.190235	+	0.981739i	$0.439075\pi$
$228$	2.84552	0.188449
$229$	0.0584392	0.00386177	0.00193089	−	0.999998i	$-0.499385\pi$
$229$	0.0584392	0.00386177	0.00193089	+	0.999998i	$0.499385\pi$
$230$	69.0550	4.55335
$231$	12.3550	0.812900
$232$	−20.1187	−1.32085
$233$	−6.06571	−0.397378	−0.198689	−	0.980063i	$-0.563668\pi$
$233$	−6.06571	−0.397378	−0.198689	+	0.980063i	$0.563668\pi$
$234$	2.26361	0.147977
$235$	−28.3443	−1.84898
$236$	53.6954	3.49527
$237$	2.20158	0.143008
$238$	−20.9541	−1.35825
$239$	−18.2321	−1.17934	−0.589669	−	0.807645i	$-0.700742\pi$
$239$	−18.2321	−1.17934	−0.589669	+	0.807645i	$0.700742\pi$
$240$	17.5812	1.13486
$241$	3.07384	0.198003	0.0990016	−	0.995087i	$-0.468435\pi$
$241$	3.07384	0.198003	0.0990016	+	0.995087i	$0.468435\pi$
$242$	−50.3282	−3.23522
$243$	14.6155	0.937587
$244$	35.8768	2.29677
$245$	17.0472	1.08911
$246$	11.9991	0.765033
$247$	0.345547	0.0219866
$248$	−3.88324	−0.246586
$249$	3.56623	0.226001
$250$	−91.0963	−5.76144
$251$	21.0849	1.33087	0.665435	−	0.746456i	$-0.268246\pi$
$251$	21.0849	1.33087	0.665435	+	0.746456i	$0.268246\pi$
$252$	−36.6179	−2.30671
$253$	−35.5845	−2.23718
$254$	35.2756	2.21339
$255$	7.23041	0.452786
$256$	−31.6150	−1.97594
$257$	10.0817	0.628880	0.314440	−	0.949277i	$-0.398183\pi$
$257$	10.0817	0.628880	0.314440	+	0.949277i	$0.398183\pi$
$258$	2.69721	0.167921
$259$	−17.9487	−1.11528
$260$	6.55942	0.406798
$261$	−8.73970	−0.540974
$262$	−32.3911	−2.00113
$263$	−9.32676	−0.575113	−0.287556	−	0.957764i	$-0.592843\pi$
$263$	−9.32676	−0.575113	−0.287556	+	0.957764i	$0.592843\pi$
$264$	−21.9059	−1.34821
$265$	−7.10756	−0.436614
$266$	−8.16967	−0.500914
$267$	−3.43942	−0.210489
$268$	25.4345	1.55366
$269$	−15.7860	−0.962489	−0.481244	−	0.876586i	$-0.659815\pi$
$269$	−15.7860	−0.962489	−0.481244	+	0.876586i	$0.659815\pi$
$270$	40.1829	2.44545
$271$	4.45742	0.270769	0.135384	−	0.990793i	$-0.456773\pi$
$271$	4.45742	0.270769	0.135384	+	0.990793i	$0.456773\pi$
$272$	15.3653	0.931655
$273$	0.782384	0.0473521
$274$	−27.8306	−1.68131
$275$	74.7805	4.50943
$276$	−18.5563	−1.11696
$277$	−27.4427	−1.64887	−0.824435	−	0.565956i	$-0.808507\pi$
$277$	−27.4427	−1.64887	−0.824435	+	0.565956i	$0.808507\pi$
$278$	−21.7443	−1.30414
$279$	−1.68691	−0.100993
$280$	−83.5090	−4.99062
$281$	24.9040	1.48565	0.742825	−	0.669486i	$-0.233485\pi$
$281$	24.9040	1.48565	0.742825	+	0.669486i	$0.233485\pi$
$282$	11.1318	0.662891
$283$	21.9262	1.30337	0.651687	−	0.758488i	$-0.274061\pi$
$283$	21.9262	1.30337	0.651687	+	0.758488i	$0.274061\pi$
$284$	−8.56252	−0.508092
$285$	2.81903	0.166985
$286$	−4.94009	−0.292114
$287$	−23.5714	−1.39138
$288$	9.27965	0.546809
$289$	−10.6809	−0.628290
$290$	−37.0139	−2.17353
$291$	8.86553	0.519707
$292$	−36.8394	−2.15586
$293$	−32.6041	−1.90475	−0.952377	−	0.304924i	$-0.901369\pi$
$293$	−32.6041	−1.90475	−0.952377	+	0.304924i	$0.901369\pi$
$294$	−6.69506	−0.390464
$295$	53.1955	3.09716
$296$	31.8238	1.84972
$297$	−20.7065	−1.20151
$298$	−32.7011	−1.89432
$299$	−2.25340	−0.130317
$300$	38.9960	2.25143
$301$	−5.29851	−0.305401
$302$	26.7063	1.53677
$303$	9.72613	0.558751
$304$	5.99068	0.343589
$305$	35.5427	2.03517
$306$	16.1393	0.922620
$307$	−19.3232	−1.10283	−0.551416	−	0.834230i	$-0.685912\pi$
$307$	−19.3232	−1.10283	−0.551416	+	0.834230i	$0.685912\pi$
$308$	79.9149	4.55357
$309$	9.17173	0.521762
$310$	−7.14430	−0.405769
$311$	13.2452	0.751066	0.375533	−	0.926809i	$-0.377460\pi$
$311$	13.2452	0.751066	0.375533	+	0.926809i	$0.377460\pi$
$312$	−1.38720	−0.0785345
$313$	8.38867	0.474156	0.237078	−	0.971491i	$-0.423810\pi$
$313$	8.38867	0.474156	0.237078	+	0.971491i	$0.423810\pi$
$314$	51.9859	2.93374
$315$	−36.2770	−2.04398
$316$	14.2403	0.801078
$317$	12.4405	0.698730	0.349365	−	0.936987i	$-0.386397\pi$
$317$	12.4405	0.698730	0.349365	+	0.936987i	$0.386397\pi$
$318$	2.79140	0.156534
$319$	19.0735	1.06791
$320$	−13.1827	−0.736936
$321$	−7.31954	−0.408537
$322$	53.2764	2.96898
$323$	2.46371	0.137085
$324$	22.3684	1.24269
$325$	4.73549	0.262678
$326$	−25.4746	−1.41090
$327$	−12.9712	−0.717310
$328$	41.7930	2.30763
$329$	−21.8678	−1.20561
$330$	−40.3020	−2.21855
$331$	−21.4418	−1.17855	−0.589274	−	0.807933i	$-0.700586\pi$
$331$	−21.4418	−1.17855	−0.589274	+	0.807933i	$0.700586\pi$
$332$	23.0672	1.26597
$333$	13.8245	0.757577
$334$	3.84662	0.210478
$335$	25.1977	1.37670
$336$	13.5640	0.739978
$337$	−24.5762	−1.33875	−0.669375	−	0.742925i	$-0.733438\pi$
$337$	−24.5762	−1.33875	−0.669375	+	0.742925i	$0.733438\pi$
$338$	32.4036	1.76252
$339$	7.85304	0.426519
$340$	46.7679	2.53634
$341$	3.68151	0.199365
$342$	6.29245	0.340257
$343$	−10.0335	−0.541757
$344$	9.39444	0.506515
$345$	−18.3836	−0.989737
$346$	−18.8049	−1.01096
$347$	−10.3760	−0.557012	−0.278506	−	0.960434i	$-0.589839\pi$
$347$	−10.3760	−0.557012	−0.278506	+	0.960434i	$0.589839\pi$
$348$	9.94631	0.533178
$349$	29.9858	1.60510	0.802552	−	0.596582i	$-0.203475\pi$
$349$	29.9858	1.60510	0.802552	+	0.596582i	$0.203475\pi$
$350$	−111.960	−5.98450
$351$	−1.31124	−0.0699890
$352$	−20.2519	−1.07943
$353$	34.7240	1.84817	0.924086	−	0.382183i	$-0.124828\pi$
$353$	34.7240	1.84817	0.924086	+	0.382183i	$0.124828\pi$
$354$	−20.8918	−1.11039
$355$	−8.48279	−0.450220
$356$	−22.2469	−1.17908
$357$	5.57831	0.295235
$358$	34.8985	1.84444
$359$	15.7118	0.829237	0.414618	−	0.909995i	$-0.363915\pi$
$359$	15.7118	0.829237	0.414618	+	0.909995i	$0.363915\pi$
$360$	64.3204	3.38998
$361$	−18.0394	−0.949444
$362$	37.3073	1.96083
$363$	13.3982	0.703222
$364$	5.06063	0.265249
$365$	−36.4964	−1.91031
$366$	−13.9589	−0.729644
$367$	−4.28167	−0.223502	−0.111751	−	0.993736i	$-0.535646\pi$
$367$	−4.28167	−0.223502	−0.111751	+	0.993736i	$0.535646\pi$
$368$	−39.0666	−2.03649
$369$	18.1552	0.945123
$370$	58.5487	3.04380
$371$	−5.48353	−0.284690
$372$	1.91980	0.0995372
$373$	−28.0175	−1.45069	−0.725346	−	0.688384i	$-0.758320\pi$
$373$	−28.0175	−1.45069	−0.725346	+	0.688384i	$0.758320\pi$
$374$	−35.2223	−1.82130
$375$	24.2513	1.25233
$376$	38.7724	1.99953
$377$	1.20783	0.0622066
$378$	31.0013	1.59454
$379$	6.57543	0.337757	0.168879	−	0.985637i	$-0.445985\pi$
$379$	6.57543	0.337757	0.168879	+	0.985637i	$0.445985\pi$
$380$	18.2341	0.935388
$381$	−9.39095	−0.481113
$382$	44.9555	2.30012
$383$	−5.79976	−0.296354	−0.148177	−	0.988961i	$-0.547341\pi$
$383$	−5.79976	−0.296354	−0.148177	+	0.988961i	$0.547341\pi$
$384$	10.0513	0.512930
$385$	79.1708	4.03492
$386$	−28.4078	−1.44592
$387$	4.08102	0.207450
$388$	57.3442	2.91121
$389$	−3.16618	−0.160532	−0.0802659	−	0.996773i	$-0.525577\pi$
$389$	−3.16618	−0.160532	−0.0802659	+	0.996773i	$0.525577\pi$
$390$	−2.55213	−0.129232
$391$	−16.0665	−0.812516
$392$	−23.3190	−1.17779
$393$	8.62303	0.434974
$394$	29.1049	1.46628
$395$	14.1077	0.709834
$396$	−61.5521	−3.09311
$397$	−4.31139	−0.216383	−0.108191	−	0.994130i	$-0.534506\pi$
$397$	−4.31139	−0.216383	−0.108191	+	0.994130i	$0.534506\pi$
$398$	47.8307	2.39753
$399$	2.17490	0.108881
$400$	82.0982	4.10491
$401$	32.1438	1.60519	0.802593	−	0.596528i	$-0.203453\pi$
$401$	32.1438	1.60519	0.802593	+	0.596528i	$0.203453\pi$
$402$	−9.89605	−0.493570
$403$	0.233132	0.0116131
$404$	62.9107	3.12992
$405$	22.1601	1.10115
$406$	−28.5565	−1.41723
$407$	−30.1705	−1.49550
$408$	−9.89055	−0.489655
$409$	−3.85014	−0.190377	−0.0951887	−	0.995459i	$-0.530345\pi$
$409$	−3.85014	−0.190377	−0.0951887	+	0.995459i	$0.530345\pi$
$410$	76.8900	3.79732
$411$	7.40895	0.365457
$412$	59.3247	2.92272
$413$	41.0406	2.01948
$414$	−41.0346	−2.01674
$415$	22.8524	1.12178
$416$	−1.28246	−0.0628776
$417$	5.78869	0.283474
$418$	−13.7326	−0.671684
$419$	24.4785	1.19585	0.597925	−	0.801552i	$-0.295992\pi$
$419$	24.4785	1.19585	0.597925	+	0.801552i	$0.295992\pi$
$420$	41.2854	2.01452
$421$	34.5524	1.68398	0.841991	−	0.539492i	$-0.181384\pi$
$421$	34.5524	1.68398	0.841991	+	0.539492i	$0.181384\pi$
$422$	28.8357	1.40370
$423$	16.8430	0.818936
$424$	9.72249	0.472166
$425$	33.7635	1.63777
$426$	3.33150	0.161412
$427$	27.4214	1.32702
$428$	−47.3444	−2.28848
$429$	1.31513	0.0634952
$430$	17.2837	0.833494
$431$	7.71448	0.371593	0.185797	−	0.982588i	$-0.440513\pi$
$431$	7.71448	0.371593	0.185797	+	0.982588i	$0.440513\pi$
$432$	−22.7328	−1.09373
$433$	−5.12979	−0.246522	−0.123261	−	0.992374i	$-0.539335\pi$
$433$	−5.12979	−0.246522	−0.123261	+	0.992374i	$0.539335\pi$
$434$	−5.51187	−0.264578
$435$	9.85370	0.472449
$436$	−83.9007	−4.01811
$437$	−6.26406	−0.299651
$438$	14.3335	0.684879
$439$	−2.71981	−0.129809	−0.0649047	−	0.997891i	$-0.520674\pi$
$439$	−2.71981	−0.129809	−0.0649047	+	0.997891i	$0.520674\pi$
$440$	−140.373	−6.69200
$441$	−10.1300	−0.482379
$442$	−2.23046	−0.106092
$443$	2.07371	0.0985247	0.0492624	−	0.998786i	$-0.484313\pi$
$443$	2.07371	0.0985247	0.0492624	+	0.998786i	$0.484313\pi$
$444$	−15.7331	−0.746660
$445$	−22.0397	−1.04478
$446$	4.23148	0.200366
$447$	8.70556	0.411759
$448$	−10.1705	−0.480513
$449$	−20.9324	−0.987860	−0.493930	−	0.869502i	$-0.664440\pi$
$449$	−20.9324	−0.987860	−0.493930	+	0.869502i	$0.664440\pi$
$450$	86.2338	4.06510
$451$	−39.6219	−1.86572
$452$	50.7952	2.38920
$453$	−7.10964	−0.334040
$454$	−14.4263	−0.677061
$455$	5.01351	0.235037
$456$	−3.85617	−0.180582
$457$	−22.6530	−1.05966	−0.529831	−	0.848103i	$-0.677745\pi$
$457$	−22.6530	−1.05966	−0.529831	+	0.848103i	$0.677745\pi$
$458$	−0.147071	−0.00687218
$459$	−9.34902	−0.436375
$460$	−118.909	−5.54415
$461$	23.6430	1.10116	0.550581	−	0.834782i	$-0.314406\pi$
$461$	23.6430	1.10116	0.550581	+	0.834782i	$0.314406\pi$
$462$	−31.0932	−1.44659
$463$	−38.4367	−1.78630	−0.893151	−	0.449756i	$-0.851511\pi$
$463$	−38.4367	−1.78630	−0.893151	+	0.449756i	$0.851511\pi$
$464$	20.9400	0.972113
$465$	1.90193	0.0881998
$466$	15.2653	0.707150
$467$	1.14331	0.0529062	0.0264531	−	0.999650i	$-0.491579\pi$
$467$	1.14331	0.0529062	0.0264531	+	0.999650i	$0.491579\pi$
$468$	−3.89780	−0.180176
$469$	19.4402	0.897663
$470$	71.3326	3.29033
$471$	−13.8395	−0.637690
$472$	−72.7665	−3.34935
$473$	−8.90641	−0.409517
$474$	−5.54060	−0.254488
$475$	13.1639	0.604000
$476$	36.0817	1.65380
$477$	4.22352	0.193382
$478$	45.8839	2.09868
$479$	11.3147	0.516983	0.258492	−	0.966014i	$-0.416775\pi$
$479$	11.3147	0.516983	0.258492	+	0.966014i	$0.416775\pi$
$480$	−10.4625	−0.477544
$481$	−1.91056	−0.0871139
$482$	−7.73577	−0.352355
$483$	−14.1830	−0.645350
$484$	86.6623	3.93920
$485$	56.8102	2.57962
$486$	−36.7822	−1.66847
$487$	−19.4341	−0.880645	−0.440322	−	0.897840i	$-0.645136\pi$
$487$	−19.4341	−0.880645	−0.440322	+	0.897840i	$0.645136\pi$
$488$	−48.6192	−2.20089
$489$	6.78174	0.306681
$490$	−42.9019	−1.93811
$491$	−4.95833	−0.223766	−0.111883	−	0.993721i	$-0.535688\pi$
$491$	−4.95833	−0.223766	−0.111883	+	0.993721i	$0.535688\pi$
$492$	−20.6617	−0.931503
$493$	8.61172	0.387852
$494$	−0.869622	−0.0391261
$495$	−60.9790	−2.74080
$496$	4.04176	0.181481
$497$	−6.54453	−0.293562
$498$	−8.97496	−0.402178
$499$	27.0114	1.20920	0.604598	−	0.796531i	$-0.293334\pi$
$499$	27.0114	1.20920	0.604598	+	0.796531i	$0.293334\pi$
$500$	156.863	7.01511
$501$	−1.02403	−0.0457504
$502$	−53.0634	−2.36834
$503$	−35.2040	−1.56967	−0.784834	−	0.619706i	$-0.787252\pi$
$503$	−35.2040	−1.56967	−0.784834	+	0.619706i	$0.787252\pi$
$504$	49.6236	2.21041
$505$	62.3249	2.77342
$506$	89.5537	3.98115
$507$	−8.62637	−0.383110
$508$	−60.7427	−2.69502
$509$	−24.8338	−1.10074	−0.550369	−	0.834922i	$-0.685513\pi$
$509$	−24.8338	−1.10074	−0.550369	+	0.834922i	$0.685513\pi$
$510$	−18.1964	−0.805751
$511$	−28.1572	−1.24560
$512$	49.5588	2.19021
$513$	−3.64504	−0.160932
$514$	−25.3722	−1.11912
$515$	58.7723	2.58982
$516$	−4.64445	−0.204460
$517$	−36.7582	−1.61662
$518$	45.1707	1.98469
$519$	5.00616	0.219746
$520$	−8.88914	−0.389814
$521$	16.9448	0.742367	0.371183	−	0.928560i	$-0.378952\pi$
$521$	16.9448	0.742367	0.371183	+	0.928560i	$0.378952\pi$
$522$	21.9948	0.962685
$523$	−35.3255	−1.54468	−0.772338	−	0.635211i	$-0.780913\pi$
$523$	−35.3255	−1.54468	−0.772338	+	0.635211i	$0.780913\pi$
$524$	55.7756	2.43657
$525$	29.8055	1.30082
$526$	23.4722	1.02344
$527$	1.66221	0.0724068
$528$	22.8001	0.992249
$529$	17.8495	0.776064
$530$	17.8872	0.776972
$531$	−31.6103	−1.37177
$532$	14.0677	0.609912
$533$	−2.50907	−0.108680
$534$	8.65581	0.374573
$535$	−46.9035	−2.02782
$536$	−34.4681	−1.48880
$537$	−9.29055	−0.400917
$538$	39.7278	1.71279
$539$	22.1076	0.952242
$540$	−69.1926	−2.97758
$541$	−5.72675	−0.246212	−0.123106	−	0.992394i	$-0.539286\pi$
$541$	−5.72675	−0.246212	−0.123106	+	0.992394i	$0.539286\pi$
$542$	−11.2178	−0.481844
$543$	−9.93182	−0.426215
$544$	−9.14376	−0.392036
$545$	−83.1195	−3.56045
$546$	−1.96899	−0.0842649
$547$	−29.7313	−1.27122	−0.635609	−	0.772011i	$-0.719251\pi$
$547$	−29.7313	−1.27122	−0.635609	+	0.772011i	$0.719251\pi$
$548$	47.9227	2.04716
$549$	−21.1205	−0.901403
$550$	−188.196	−8.02472
$551$	3.35758	0.143038
$552$	25.1470	1.07033
$553$	10.8842	0.462842
$554$	69.0636	2.93423
$555$	−15.5866	−0.661615
$556$	37.4425	1.58792
$557$	−22.5934	−0.957311	−0.478656	−	0.878003i	$-0.658876\pi$
$557$	−22.5934	−0.957311	−0.478656	+	0.878003i	$0.658876\pi$
$558$	4.24536	0.179720
$559$	−0.564000	−0.0238547
$560$	86.9181	3.67296
$561$	9.37673	0.395886
$562$	−62.6748	−2.64377
$563$	−6.71807	−0.283133	−0.141566	−	0.989929i	$-0.545214\pi$
$563$	−6.71807	−0.283133	−0.141566	+	0.989929i	$0.545214\pi$
$564$	−19.1684	−0.807135
$565$	50.3222	2.11707
$566$	−55.1805	−2.31941
$567$	17.0967	0.717993
$568$	11.6037	0.486880
$569$	−20.2554	−0.849149	−0.424575	−	0.905393i	$-0.639576\pi$
$569$	−20.2554	−0.849149	−0.424575	+	0.905393i	$0.639576\pi$
$570$	−7.09451	−0.297156
$571$	34.6194	1.44878	0.724389	−	0.689391i	$-0.242122\pi$
$571$	34.6194	1.44878	0.724389	+	0.689391i	$0.242122\pi$
$572$	8.50655	0.355677
$573$	−11.9679	−0.499965
$574$	59.3211	2.47601
$575$	−85.8448	−3.57998
$576$	7.83356	0.326398
$577$	24.2753	1.01059	0.505296	−	0.862946i	$-0.331383\pi$
$577$	24.2753	1.01059	0.505296	+	0.862946i	$0.331383\pi$
$578$	26.8801	1.11807
$579$	7.56262	0.314292
$580$	63.7358	2.64649
$581$	17.6307	0.731447
$582$	−22.3114	−0.924839
$583$	−9.21741	−0.381746
$584$	49.9237	2.06586
$585$	−3.86151	−0.159654
$586$	82.0532	3.38959
$587$	−14.2438	−0.587904	−0.293952	−	0.955820i	$-0.594971\pi$
$587$	−14.2438	−0.587904	−0.293952	+	0.955820i	$0.594971\pi$
$588$	11.5285	0.475428
$589$	0.648069	0.0267032
$590$	−133.874	−5.51152
$591$	−7.74819	−0.318718
$592$	−33.1229	−1.36134
$593$	−32.8020	−1.34702	−0.673508	−	0.739180i	$-0.735213\pi$
$593$	−32.8020	−1.34702	−0.673508	+	0.739180i	$0.735213\pi$
$594$	52.1110	2.13814
$595$	35.7457	1.46543
$596$	56.3094	2.30652
$597$	−12.7333	−0.521139
$598$	5.67101	0.231905
$599$	15.9457	0.651526	0.325763	−	0.945452i	$-0.394379\pi$
$599$	15.9457	0.651526	0.325763	+	0.945452i	$0.394379\pi$
$600$	−52.8462	−2.15744
$601$	−11.9000	−0.485411	−0.242706	−	0.970100i	$-0.578035\pi$
$601$	−11.9000	−0.485411	−0.242706	+	0.970100i	$0.578035\pi$
$602$	13.3345	0.543473
$603$	−14.9732	−0.609757
$604$	−45.9867	−1.87117
$605$	85.8554	3.49052
$606$	−24.4773	−0.994321
$607$	20.9663	0.850994	0.425497	−	0.904960i	$-0.360099\pi$
$607$	20.9663	0.850994	0.425497	+	0.904960i	$0.360099\pi$
$608$	−3.56501	−0.144580
$609$	7.60219	0.308056
$610$	−89.4486	−3.62167
$611$	−2.32772	−0.0941695
$612$	−27.7909	−1.12338
$613$	−35.4601	−1.43222	−0.716110	−	0.697988i	$-0.754079\pi$
$613$	−35.4601	−1.43222	−0.716110	+	0.697988i	$0.754079\pi$
$614$	48.6297	1.96254
$615$	−20.4694	−0.825404
$616$	−108.298	−4.36347
$617$	48.1991	1.94042	0.970212	−	0.242258i	$-0.0778881\pi$
$617$	48.1991	1.94042	0.970212	+	0.242258i	$0.0778881\pi$
$618$	−23.0820	−0.928496
$619$	−30.6122	−1.23041	−0.615203	−	0.788369i	$-0.710926\pi$
$619$	−30.6122	−1.23041	−0.615203	+	0.788369i	$0.710926\pi$
$620$	12.3021	0.494064
$621$	23.7702	0.953864
$622$	−33.3335	−1.33655
$623$	−17.0038	−0.681243
$624$	1.44383	0.0577993
$625$	88.2452	3.52981
$626$	−21.1114	−0.843780
$627$	3.65584	0.146000
$628$	−89.5168	−3.57211
$629$	−13.6220	−0.543147
$630$	91.2965	3.63734
$631$	−5.68540	−0.226332	−0.113166	−	0.993576i	$-0.536099\pi$
$631$	−5.68540	−0.226332	−0.113166	+	0.993576i	$0.536099\pi$
$632$	−19.2980	−0.767634
$633$	−7.67652	−0.305114
$634$	−31.3085	−1.24342
$635$	−60.1771	−2.38805
$636$	−4.80663	−0.190595
$637$	1.39997	0.0554688
$638$	−48.0013	−1.90039
$639$	5.04073	0.199408
$640$	64.4088	2.54598
$641$	−16.2344	−0.641220	−0.320610	−	0.947211i	$-0.603888\pi$
$641$	−16.2344	−0.641220	−0.320610	+	0.947211i	$0.603888\pi$
$642$	18.4207	0.727008
$643$	37.9573	1.49689	0.748445	−	0.663197i	$-0.230801\pi$
$643$	37.9573	1.49689	0.748445	+	0.663197i	$0.230801\pi$
$644$	−91.7389	−3.61502
$645$	−4.60120	−0.181172
$646$	−6.20030	−0.243948
$647$	9.05177	0.355862	0.177931	−	0.984043i	$-0.443060\pi$
$647$	9.05177	0.355862	0.177931	+	0.984043i	$0.443060\pi$
$648$	−30.3130	−1.19081
$649$	68.9863	2.70795
$650$	−11.9176	−0.467446
$651$	1.46735	0.0575100
$652$	43.8657	1.71791
$653$	21.7508	0.851174	0.425587	−	0.904918i	$-0.360068\pi$
$653$	21.7508	0.851174	0.425587	+	0.904918i	$0.360068\pi$
$654$	32.6440	1.27648
$655$	55.2563	2.15904
$656$	−43.4991	−1.69836
$657$	21.6872	0.846100
$658$	55.0336	2.14543
$659$	5.83129	0.227155	0.113577	−	0.993529i	$-0.463769\pi$
$659$	5.83129	0.227155	0.113577	+	0.993529i	$0.463769\pi$
$660$	69.3978	2.70130
$661$	−16.7516	−0.651560	−0.325780	−	0.945446i	$-0.605627\pi$
$661$	−16.7516	−0.651560	−0.325780	+	0.945446i	$0.605627\pi$
$662$	53.9615	2.09727
$663$	0.593784	0.0230607
$664$	−31.2600	−1.21312
$665$	13.9367	0.540443
$666$	−34.7914	−1.34814
$667$	−21.8956	−0.847800
$668$	−6.62366	−0.256277
$669$	−1.12649	−0.0435526
$670$	−63.4137	−2.44989
$671$	46.0934	1.77942
$672$	−8.07187	−0.311379
$673$	−37.0635	−1.42869	−0.714347	−	0.699791i	$-0.753276\pi$
$673$	−37.0635	−1.42869	−0.714347	+	0.699791i	$0.753276\pi$
$674$	61.8497	2.38236
$675$	−49.9528	−1.92268
$676$	−55.7972	−2.14605
$677$	−30.1134	−1.15735	−0.578676	−	0.815557i	$-0.696431\pi$
$677$	−30.1134	−1.15735	−0.578676	+	0.815557i	$0.696431\pi$
$678$	−19.7634	−0.759007
$679$	43.8295	1.68202
$680$	−63.3785	−2.43045
$681$	3.84052	0.147169
$682$	−9.26506	−0.354778
$683$	23.0996	0.883881	0.441940	−	0.897044i	$-0.354290\pi$
$683$	23.0996	0.883881	0.441940	+	0.897044i	$0.354290\pi$
$684$	−10.8352	−0.414296
$685$	47.4765	1.81398
$686$	25.2507	0.964078
$687$	0.0391527	0.00149377
$688$	−9.77795	−0.372781
$689$	−0.583695	−0.0222370
$690$	46.2650	1.76128
$691$	39.3108	1.49545	0.747726	−	0.664007i	$-0.231146\pi$
$691$	39.3108	1.49545	0.747726	+	0.664007i	$0.231146\pi$
$692$	32.3809	1.23094
$693$	−47.0457	−1.78712
$694$	26.1127	0.991225
$695$	37.0939	1.40705
$696$	−13.4790	−0.510919
$697$	−17.8894	−0.677608
$698$	−75.4638	−2.85635
$699$	−4.06386	−0.153709
$700$	192.788	7.28672
$701$	−16.8257	−0.635496	−0.317748	−	0.948175i	$-0.602927\pi$
$701$	−16.8257	−0.635496	−0.317748	+	0.948175i	$0.602927\pi$
$702$	3.29994	0.124548
$703$	−5.31103	−0.200309
$704$	−17.0959	−0.644328
$705$	−18.9899	−0.715201
$706$	−87.3882	−3.28890
$707$	48.0841	1.80839
$708$	35.9745	1.35200
$709$	41.9252	1.57454	0.787268	−	0.616611i	$-0.211495\pi$
$709$	41.9252	1.57454	0.787268	+	0.616611i	$0.211495\pi$
$710$	21.3482	0.801184
$711$	−8.38321	−0.314395
$712$	30.1483	1.12986
$713$	−4.22621	−0.158273
$714$	−14.0387	−0.525383
$715$	8.42735	0.315165
$716$	−60.0933	−2.24579
$717$	−12.2150	−0.456178
$718$	−39.5411	−1.47566
$719$	−14.1887	−0.529148	−0.264574	−	0.964365i	$-0.585231\pi$
$719$	−14.1887	−0.529148	−0.264574	+	0.964365i	$0.585231\pi$
$720$	−66.9461	−2.49494
$721$	45.3432	1.68867
$722$	45.3990	1.68957
$723$	2.05939	0.0765894
$724$	−64.2411	−2.38750
$725$	46.0133	1.70889
$726$	−33.7185	−1.25141
$727$	29.5495	1.09593	0.547966	−	0.836501i	$-0.315402\pi$
$727$	29.5495	1.09593	0.547966	+	0.836501i	$0.315402\pi$
$728$	−6.85802	−0.254175
$729$	−5.69310	−0.210856
$730$	91.8486	3.39947
$731$	−4.02126	−0.148732
$732$	24.0365	0.888413
$733$	39.0055	1.44070	0.720351	−	0.693609i	$-0.243981\pi$
$733$	39.0055	1.44070	0.720351	+	0.693609i	$0.243981\pi$
$734$	10.7755	0.397730
$735$	11.4212	0.421276
$736$	23.2483	0.856944
$737$	32.6775	1.20369
$738$	−45.6903	−1.68188
$739$	−5.78845	−0.212932	−0.106466	−	0.994316i	$-0.533953\pi$
$739$	−5.78845	−0.212932	−0.106466	+	0.994316i	$0.533953\pi$
$740$	−100.818	−3.70613
$741$	0.231507	0.00850463
$742$	13.8001	0.506618
$743$	12.1846	0.447011	0.223505	−	0.974703i	$-0.428250\pi$
$743$	12.1846	0.447011	0.223505	+	0.974703i	$0.428250\pi$
$744$	−2.60166	−0.0953817
$745$	55.7851	2.04381
$746$	70.5103	2.58157
$747$	−13.5796	−0.496850
$748$	60.6507	2.21761
$749$	−36.1864	−1.32222
$750$	−61.0321	−2.22858
$751$	50.4635	1.84144	0.920720	−	0.390223i	$-0.127602\pi$
$751$	50.4635	1.84144	0.920720	+	0.390223i	$0.127602\pi$
$752$	−40.3552	−1.47160
$753$	14.1263	0.514792
$754$	−3.03970	−0.110699
$755$	−45.5585	−1.65804
$756$	−53.3826	−1.94150
$757$	−18.1777	−0.660679	−0.330340	−	0.943862i	$-0.607163\pi$
$757$	−18.1777	−0.660679	−0.330340	+	0.943862i	$0.607163\pi$
$758$	−16.5481	−0.601052
$759$	−23.8406	−0.865361
$760$	−24.7103	−0.896337
$761$	8.66178	0.313989	0.156995	−	0.987599i	$-0.449819\pi$
$761$	8.66178	0.313989	0.156995	+	0.987599i	$0.449819\pi$
$762$	23.6337	0.856160
$763$	−64.1272	−2.32156
$764$	−77.4107	−2.80062
$765$	−27.5321	−0.995426
$766$	14.5960	0.527374
$767$	4.36858	0.157740
$768$	−21.1812	−0.764311
$769$	−7.45371	−0.268788	−0.134394	−	0.990928i	$-0.542909\pi$
$769$	−7.45371	−0.268788	−0.134394	+	0.990928i	$0.542909\pi$
$770$	−199.245	−7.18030
$771$	6.75448	0.243257
$772$	48.9166	1.76055
$773$	−30.3155	−1.09037	−0.545186	−	0.838315i	$-0.683541\pi$
$773$	−30.3155	−1.09037	−0.545186	+	0.838315i	$0.683541\pi$
$774$	−10.2705	−0.369165
$775$	8.88135	0.319027
$776$	−77.7112	−2.78967
$777$	−12.0252	−0.431401
$778$	7.96817	0.285673
$779$	−6.97478	−0.249898
$780$	4.39463	0.157353
$781$	−11.0009	−0.393642
$782$	40.4337	1.44590
$783$	−12.7410	−0.455325
$784$	24.2710	0.866820
$785$	−88.6833	−3.16524
$786$	−21.7012	−0.774054
$787$	20.8563	0.743445	0.371723	−	0.928344i	$-0.378767\pi$
$787$	20.8563	0.743445	0.371723	+	0.928344i	$0.378767\pi$
$788$	−50.1170	−1.78534
$789$	−6.24868	−0.222459
$790$	−35.5041	−1.26318
$791$	38.8239	1.38042
$792$	83.4137	2.96398
$793$	2.91888	0.103652
$794$	10.8503	0.385062
$795$	−4.76187	−0.168886
$796$	−82.3617	−2.91923
$797$	−40.1281	−1.42141	−0.710704	−	0.703491i	$-0.751624\pi$
$797$	−40.1281	−1.42141	−0.710704	+	0.703491i	$0.751624\pi$
$798$	−5.47346	−0.193758
$799$	−16.5964	−0.587138
$800$	−48.8561	−1.72732
$801$	13.0967	0.462748
$802$	−80.8947	−2.85649
$803$	−47.3302	−1.67025
$804$	17.0404	0.600970
$805$	−90.8847	−3.20326
$806$	−0.586712	−0.0206661
$807$	−10.5762	−0.372299
$808$	−85.2548	−2.99925
$809$	16.8398	0.592055	0.296027	−	0.955179i	$-0.404338\pi$
$809$	16.8398	0.592055	0.296027	+	0.955179i	$0.404338\pi$
$810$	−55.7693	−1.95953
$811$	−16.0238	−0.562672	−0.281336	−	0.959609i	$-0.590777\pi$
$811$	−16.0238	−0.562672	−0.281336	+	0.959609i	$0.590777\pi$
$812$	49.1726	1.72562
$813$	2.98635	0.104736
$814$	75.9287	2.66130
$815$	43.4573	1.52224
$816$	10.2943	0.360373
$817$	−1.56783	−0.0548513
$818$	9.68947	0.338784
$819$	−2.97918	−0.104101
$820$	−132.400	−4.62361
$821$	37.3781	1.30451	0.652253	−	0.758001i	$-0.273824\pi$
$821$	37.3781	1.30451	0.652253	+	0.758001i	$0.273824\pi$
$822$	−18.6457	−0.650345
$823$	18.2118	0.634825	0.317413	−	0.948288i	$-0.397186\pi$
$823$	18.2118	0.634825	0.317413	+	0.948288i	$0.397186\pi$
$824$	−80.3952	−2.80070
$825$	50.1009	1.74429
$826$	−103.285	−3.59374
$827$	−7.49992	−0.260798	−0.130399	−	0.991462i	$-0.541626\pi$
$827$	−7.49992	−0.260798	−0.130399	+	0.991462i	$0.541626\pi$
$828$	70.6592	2.45558
$829$	−44.4759	−1.54471	−0.772356	−	0.635190i	$-0.780922\pi$
$829$	−44.4759	−1.54471	−0.772356	+	0.635190i	$0.780922\pi$
$830$	−57.5114	−1.99625
$831$	−18.3859	−0.637798
$832$	−1.08261	−0.0375326
$833$	9.98162	0.345843
$834$	−14.5681	−0.504453
$835$	−6.56199	−0.227087
$836$	23.6468	0.817841
$837$	−2.45922	−0.0850030
$838$	−61.6037	−2.12806
$839$	47.2922	1.63271	0.816354	−	0.577552i	$-0.195992\pi$
$839$	47.2922	1.63271	0.816354	+	0.577552i	$0.195992\pi$
$840$	−55.9488	−1.93042
$841$	−17.2638	−0.595305
$842$	−86.9563	−2.99671
$843$	16.6850	0.574663
$844$	−49.6534	−1.70914
$845$	−55.2777	−1.90161
$846$	−42.3880	−1.45733
$847$	66.2380	2.27596
$848$	−10.1194	−0.347501
$849$	14.6899	0.504157
$850$	−84.9710	−2.91448
$851$	34.6345	1.18725
$852$	−5.73666	−0.196535
$853$	−27.9669	−0.957569	−0.478784	−	0.877933i	$-0.658922\pi$
$853$	−27.9669	−0.957569	−0.478784	+	0.877933i	$0.658922\pi$
$854$	−69.0101	−2.36148
$855$	−10.7343	−0.367107
$856$	64.1598	2.19294
$857$	26.4820	0.904610	0.452305	−	0.891863i	$-0.350602\pi$
$857$	26.4820	0.904610	0.452305	+	0.891863i	$0.350602\pi$
$858$	−3.30973	−0.112992
$859$	19.2127	0.655530	0.327765	−	0.944759i	$-0.393705\pi$
$859$	19.2127	0.655530	0.327765	+	0.944759i	$0.393705\pi$
$860$	−29.7616	−1.01486
$861$	−15.7922	−0.538198
$862$	−19.4146	−0.661266
$863$	−36.8097	−1.25302	−0.626508	−	0.779415i	$-0.715517\pi$
$863$	−36.8097	−1.25302	−0.626508	+	0.779415i	$0.715517\pi$
$864$	13.5281	0.460236
$865$	32.0794	1.09073
$866$	12.9099	0.438695
$867$	−7.15593	−0.243028
$868$	9.49114	0.322150
$869$	18.2955	0.620632
$870$	−24.7983	−0.840742
$871$	2.06931	0.0701160
$872$	113.700	3.85036
$873$	−33.7584	−1.14255
$874$	15.7645	0.533241
$875$	119.894	4.05315
$876$	−24.6814	−0.833907
$877$	−24.6091	−0.830992	−0.415496	−	0.909595i	$-0.636392\pi$
$877$	−24.6091	−0.830992	−0.415496	+	0.909595i	$0.636392\pi$
$878$	6.84481	0.231001
$879$	−21.8439	−0.736776
$880$	146.103	4.92513
$881$	18.9966	0.640011	0.320005	−	0.947416i	$-0.396315\pi$
$881$	18.9966	0.640011	0.320005	+	0.947416i	$0.396315\pi$
$882$	25.4936	0.858413
$883$	15.9611	0.537133	0.268566	−	0.963261i	$-0.413450\pi$
$883$	15.9611	0.537133	0.268566	+	0.963261i	$0.413450\pi$
$884$	3.84072	0.129178
$885$	35.6395	1.19801
$886$	−5.21879	−0.175329
$887$	12.8781	0.432405	0.216202	−	0.976349i	$-0.430633\pi$
$887$	12.8781	0.432405	0.216202	+	0.976349i	$0.430633\pi$
$888$	21.3211	0.715488
$889$	−46.4270	−1.55711
$890$	55.4663	1.85924
$891$	28.7383	0.962768
$892$	−7.28637	−0.243966
$893$	−6.47067	−0.216533
$894$	−21.9088	−0.732741
$895$	−59.5337	−1.98999
$896$	49.6918	1.66009
$897$	−1.50972	−0.0504079
$898$	52.6795	1.75794
$899$	2.26528	0.0755512
$900$	−148.490	−4.94965
$901$	−4.16168	−0.138646
$902$	99.7145	3.32013
$903$	−3.54986	−0.118132
$904$	−68.8362	−2.28946
$905$	−63.6430	−2.11556
$906$	17.8925	0.594438
$907$	59.9526	1.99069	0.995347	−	0.0963505i	$-0.0307170\pi$
$907$	59.9526	1.99069	0.995347	+	0.0963505i	$0.0307170\pi$
$908$	24.8413	0.824387
$909$	−37.0353	−1.22838
$910$	−12.6173	−0.418258
$911$	−26.7602	−0.886606	−0.443303	−	0.896372i	$-0.646193\pi$
$911$	−26.7602	−0.886606	−0.443303	+	0.896372i	$0.646193\pi$
$912$	4.01359	0.132903
$913$	29.6360	0.980809
$914$	57.0097	1.88571
$915$	23.8127	0.787222
$916$	0.253248	0.00836755
$917$	42.6306	1.40779
$918$	23.5282	0.776547
$919$	−20.9103	−0.689768	−0.344884	−	0.938645i	$-0.612082\pi$
$919$	−20.9103	−0.689768	−0.344884	+	0.938645i	$0.612082\pi$
$920$	161.142	5.31269
$921$	−12.9460	−0.426586
$922$	−59.5011	−1.95956
$923$	−0.696633	−0.0229300
$924$	53.5408	1.76136
$925$	−72.7841	−2.39313
$926$	96.7316	3.17880
$927$	−34.9243	−1.14706
$928$	−12.4612	−0.409060
$929$	−34.5016	−1.13196	−0.565981	−	0.824418i	$-0.691503\pi$
$929$	−34.5016	−1.13196	−0.565981	+	0.824418i	$0.691503\pi$
$930$	−4.78649	−0.156955
$931$	3.89168	0.127545
$932$	−26.2859	−0.861024
$933$	8.87392	0.290519
$934$	−2.87732	−0.0941487
$935$	60.0860	1.96502
$936$	5.28219	0.172654
$937$	5.66707	0.185135	0.0925676	−	0.995706i	$-0.470493\pi$
$937$	5.66707	0.185135	0.0925676	+	0.995706i	$0.470493\pi$
$938$	−48.9241	−1.59743
$939$	5.62018	0.183408
$940$	−122.831	−4.00630
$941$	42.2590	1.37760	0.688802	−	0.724949i	$-0.258137\pi$
$941$	42.2590	1.37760	0.688802	+	0.724949i	$0.258137\pi$
$942$	34.8292	1.13480
$943$	45.4843	1.48117
$944$	75.7371	2.46503
$945$	−52.8855	−1.72037
$946$	22.4143	0.728752
$947$	−9.94841	−0.323280	−0.161640	−	0.986850i	$-0.551678\pi$
$947$	−9.94841	−0.323280	−0.161640	+	0.986850i	$0.551678\pi$
$948$	9.54060	0.309864
$949$	−2.99720	−0.0972931
$950$	−33.1289	−1.07484
$951$	8.33483	0.270275
$952$	−48.8969	−1.58476
$953$	−43.4689	−1.40810	−0.704048	−	0.710152i	$-0.748626\pi$
$953$	−43.4689	−1.40810	−0.704048	+	0.710152i	$0.748626\pi$
$954$	−10.6291	−0.344131
$955$	−76.6900	−2.48163
$956$	−79.0094	−2.55535
$957$	12.7787	0.413078
$958$	−28.4752	−0.919993
$959$	36.6284	1.18279
$960$	−8.83206	−0.285053
$961$	−30.5628	−0.985896
$962$	4.80820	0.155023
$963$	27.8715	0.898147
$964$	13.3206	0.429026
$965$	48.4612	1.56002
$966$	35.6937	1.14843
$967$	−49.2236	−1.58292	−0.791462	−	0.611218i	$-0.790680\pi$
$967$	−49.2236	−1.58292	−0.791462	+	0.611218i	$0.790680\pi$
$968$	−117.442	−3.77474
$969$	1.65062	0.0530256
$970$	−142.971	−4.59054
$971$	1.72535	0.0553692	0.0276846	−	0.999617i	$-0.491187\pi$
$971$	1.72535	0.0553692	0.0276846	+	0.999617i	$0.491187\pi$
$972$	63.3369	2.03153
$973$	28.6182	0.917456
$974$	48.9089	1.56714
$975$	3.17265	0.101606
$976$	50.6039	1.61979
$977$	−9.06542	−0.290028	−0.145014	−	0.989430i	$-0.546323\pi$
$977$	−9.06542	−0.290028	−0.145014	+	0.989430i	$0.546323\pi$
$978$	−17.0673	−0.545751
$979$	−28.5822	−0.913489
$980$	73.8746	2.35984
$981$	49.3921	1.57697
$982$	12.4784	0.398201
$983$	−33.6658	−1.07377	−0.536886	−	0.843655i	$-0.680400\pi$
$983$	−33.6658	−1.07377	−0.536886	+	0.843655i	$0.680400\pi$
$984$	28.0002	0.892614
$985$	−49.6503	−1.58199
$986$	−21.6727	−0.690199
$987$	−14.6508	−0.466341
$988$	1.49744	0.0476399
$989$	10.2242	0.325110
$990$	153.463	4.87737
$991$	31.6884	1.00662	0.503308	−	0.864107i	$-0.332116\pi$
$991$	31.6884	1.00662	0.503308	+	0.864107i	$0.332116\pi$
$992$	−2.40523	−0.0763660
$993$	−14.3654	−0.455873
$994$	16.4703	0.522406
$995$	−81.5948	−2.58673
$996$	15.4544	0.489690
$997$	5.60198	0.177417	0.0887083	−	0.996058i	$-0.471726\pi$
$997$	5.60198	0.177417	0.0887083	+	0.996058i	$0.471726\pi$
$998$	−67.9783	−2.15181
$999$	20.1537	0.637635

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4021.2.a.c.1.13	✓	182

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4021.2.a.c.1.13	✓	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)

\(f(q)\)	\(=\)	\(q-2.51665 q^{2} +0.669973 q^{3} +4.33353 q^{4} +4.29318 q^{5} -1.68609 q^{6} +3.31221 q^{7} -5.87268 q^{8} -2.55114 q^{9} +O(q^{10})\)	\(q-2.51665 q^{2} +0.669973 q^{3} +4.33353 q^{4} +4.29318 q^{5} -1.68609 q^{6} +3.31221 q^{7} -5.87268 q^{8} -2.55114 q^{9} -10.8044 q^{10} +5.56759 q^{11} +2.90335 q^{12} +0.352569 q^{13} -8.33569 q^{14} +2.87631 q^{15} +6.11242 q^{16} +2.51378 q^{17} +6.42032 q^{18} +0.980083 q^{19} +18.6046 q^{20} +2.21909 q^{21} -14.0117 q^{22} -6.39136 q^{23} -3.93453 q^{24} +13.4314 q^{25} -0.887294 q^{26} -3.71911 q^{27} +14.3536 q^{28} +3.42581 q^{29} -7.23868 q^{30} +0.661238 q^{31} -3.63746 q^{32} +3.73014 q^{33} -6.32630 q^{34} +14.2199 q^{35} -11.0554 q^{36} -5.41895 q^{37} -2.46653 q^{38} +0.236212 q^{39} -25.2125 q^{40} -7.11652 q^{41} -5.58468 q^{42} -1.59969 q^{43} +24.1273 q^{44} -10.9525 q^{45} +16.0848 q^{46} -6.60217 q^{47} +4.09515 q^{48} +3.97077 q^{49} -33.8021 q^{50} +1.68416 q^{51} +1.52787 q^{52} -1.65555 q^{53} +9.35970 q^{54} +23.9027 q^{55} -19.4516 q^{56} +0.656629 q^{57} -8.62156 q^{58} +12.3907 q^{59} +12.4646 q^{60} +8.27888 q^{61} -1.66411 q^{62} -8.44991 q^{63} -3.07062 q^{64} +1.51364 q^{65} -9.38745 q^{66} +5.86924 q^{67} +10.8935 q^{68} -4.28204 q^{69} -35.7866 q^{70} -1.97588 q^{71} +14.9820 q^{72} -8.50101 q^{73} +13.6376 q^{74} +8.99866 q^{75} +4.24722 q^{76} +18.4411 q^{77} -0.594463 q^{78} +3.28607 q^{79} +26.2417 q^{80} +5.16170 q^{81} +17.9098 q^{82} +5.32295 q^{83} +9.61651 q^{84} +10.7921 q^{85} +4.02585 q^{86} +2.29520 q^{87} -32.6967 q^{88} -5.13366 q^{89} +27.5636 q^{90} +1.16779 q^{91} -27.6971 q^{92} +0.443012 q^{93} +16.6153 q^{94} +4.20767 q^{95} -2.43700 q^{96} +13.2327 q^{97} -9.99303 q^{98} -14.2037 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 182 q + 18 q^{2} + 28 q^{3} + 208 q^{4} + 22 q^{5} + 18 q^{6} + 14 q^{7} + 54 q^{8} + 238 q^{9}+O(q^{10}) \) 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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