LMFDB - Embedded newform 4013.2.a.b.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4013,2,Mod(1,4013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4013, 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("4013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4013 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4013.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:	$32.0439663311$
Analytic rank:	$1$
Dimension:	$157$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	4013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.68953 q^{2} +2.61392 q^{3} +5.23356 q^{4} +1.08630 q^{5} -7.03022 q^{6} -3.47806 q^{7} -8.69675 q^{8} +3.83259 q^{9} +O(q^{10})$	\(q-2.68953 q^{2} +2.61392 q^{3} +5.23356 q^{4} +1.08630 q^{5} -7.03022 q^{6} -3.47806 q^{7} -8.69675 q^{8} +3.83259 q^{9} -2.92162 q^{10} +0.184213 q^{11} +13.6801 q^{12} -3.02638 q^{13} +9.35435 q^{14} +2.83949 q^{15} +12.9230 q^{16} -3.23366 q^{17} -10.3079 q^{18} +3.22238 q^{19} +5.68519 q^{20} -9.09139 q^{21} -0.495445 q^{22} +7.46180 q^{23} -22.7326 q^{24} -3.81996 q^{25} +8.13955 q^{26} +2.17632 q^{27} -18.2027 q^{28} -5.47961 q^{29} -7.63689 q^{30} +6.68243 q^{31} -17.3634 q^{32} +0.481517 q^{33} +8.69701 q^{34} -3.77820 q^{35} +20.0581 q^{36} -5.07301 q^{37} -8.66667 q^{38} -7.91073 q^{39} -9.44724 q^{40} -4.24459 q^{41} +24.4515 q^{42} -4.05089 q^{43} +0.964088 q^{44} +4.16332 q^{45} -20.0687 q^{46} +3.38125 q^{47} +33.7798 q^{48} +5.09693 q^{49} +10.2739 q^{50} -8.45252 q^{51} -15.8388 q^{52} -10.3048 q^{53} -5.85328 q^{54} +0.200109 q^{55} +30.2479 q^{56} +8.42304 q^{57} +14.7376 q^{58} -2.92183 q^{59} +14.8607 q^{60} +10.1661 q^{61} -17.9726 q^{62} -13.3300 q^{63} +20.8532 q^{64} -3.28755 q^{65} -1.29505 q^{66} +2.80569 q^{67} -16.9235 q^{68} +19.5046 q^{69} +10.1616 q^{70} +10.2172 q^{71} -33.3311 q^{72} -1.45377 q^{73} +13.6440 q^{74} -9.98508 q^{75} +16.8645 q^{76} -0.640703 q^{77} +21.2761 q^{78} -16.4158 q^{79} +14.0382 q^{80} -5.80903 q^{81} +11.4159 q^{82} +16.5516 q^{83} -47.5803 q^{84} -3.51270 q^{85} +10.8950 q^{86} -14.3233 q^{87} -1.60205 q^{88} +2.88151 q^{89} -11.1974 q^{90} +10.5260 q^{91} +39.0518 q^{92} +17.4674 q^{93} -9.09397 q^{94} +3.50045 q^{95} -45.3865 q^{96} -8.86871 q^{97} -13.7083 q^{98} +0.706011 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 157 q - 15 q^{2} - 51 q^{3} + 137 q^{4} - 13 q^{5} - 15 q^{6} - 49 q^{7} - 42 q^{8} + 144 q^{9}+O(q^{10}) $ 157 * q - 15 * q^2 - 51 * q^3 + 137 * q^4 - 13 * q^5 - 15 * q^6 - 49 * q^7 - 42 * q^8 + 144 * q^9	\( 157 q - 15 q^{2} - 51 q^{3} + 137 q^{4} - 13 q^{5} - 15 q^{6} - 49 q^{7} - 42 q^{8} + 144 q^{9} - 61 q^{10} - 27 q^{11} - 93 q^{12} - 97 q^{13} - 12 q^{14} - 36 q^{15} + 105 q^{16} - 45 q^{17} - 68 q^{18} - 128 q^{19} - 30 q^{20} - 26 q^{21} - 68 q^{22} - 41 q^{23} - 40 q^{24} + 102 q^{25} - 5 q^{26} - 189 q^{27} - 115 q^{28} - 26 q^{29} - 12 q^{30} - 88 q^{31} - 89 q^{32} - 52 q^{33} - 61 q^{34} - 87 q^{35} + 110 q^{36} - 62 q^{37} - 37 q^{38} - 20 q^{39} - 161 q^{40} - 34 q^{41} - 53 q^{42} - 254 q^{43} - 19 q^{44} - 46 q^{45} - 52 q^{46} - 76 q^{47} - 162 q^{48} + 96 q^{49} - 54 q^{50} - 76 q^{51} - 259 q^{52} - 48 q^{53} - 12 q^{54} - 194 q^{55} - 10 q^{56} - 30 q^{57} - 52 q^{58} - 64 q^{59} - 31 q^{60} - 107 q^{61} - 51 q^{62} - 106 q^{63} + 54 q^{64} - 17 q^{65} - 13 q^{66} - 193 q^{67} - 118 q^{68} - 55 q^{69} - 86 q^{70} - 11 q^{71} - 172 q^{72} - 173 q^{73} - 11 q^{74} - 209 q^{75} - 213 q^{76} - 84 q^{77} - 30 q^{78} - 111 q^{79} - 6 q^{80} + 157 q^{81} - 117 q^{82} - 154 q^{83} - 6 q^{84} - 91 q^{85} + 28 q^{86} - 165 q^{87} - 165 q^{88} - 32 q^{89} - 103 q^{90} - 200 q^{91} - 86 q^{92} - 39 q^{93} - 118 q^{94} - 22 q^{95} - 28 q^{96} - 151 q^{97} - 38 q^{98} - 91 q^{99}+O(q^{100}) \) 157 * q - 15 * q^2 - 51 * q^3 + 137 * q^4 - 13 * q^5 - 15 * q^6 - 49 * q^7 - 42 * q^8 + 144 * q^9 - 61 * q^10 - 27 * q^11 - 93 * q^12 - 97 * q^13 - 12 * q^14 - 36 * q^15 + 105 * q^16 - 45 * q^17 - 68 * q^18 - 128 * q^19 - 30 * q^20 - 26 * q^21 - 68 * q^22 - 41 * q^23 - 40 * q^24 + 102 * q^25 - 5 * q^26 - 189 * q^27 - 115 * q^28 - 26 * q^29 - 12 * q^30 - 88 * q^31 - 89 * q^32 - 52 * q^33 - 61 * q^34 - 87 * q^35 + 110 * q^36 - 62 * q^37 - 37 * q^38 - 20 * q^39 - 161 * q^40 - 34 * q^41 - 53 * q^42 - 254 * q^43 - 19 * q^44 - 46 * q^45 - 52 * q^46 - 76 * q^47 - 162 * q^48 + 96 * q^49 - 54 * q^50 - 76 * q^51 - 259 * q^52 - 48 * q^53 - 12 * q^54 - 194 * q^55 - 10 * q^56 - 30 * q^57 - 52 * q^58 - 64 * q^59 - 31 * q^60 - 107 * q^61 - 51 * q^62 - 106 * q^63 + 54 * q^64 - 17 * q^65 - 13 * q^66 - 193 * q^67 - 118 * q^68 - 55 * q^69 - 86 * q^70 - 11 * q^71 - 172 * q^72 - 173 * q^73 - 11 * q^74 - 209 * q^75 - 213 * q^76 - 84 * q^77 - 30 * q^78 - 111 * q^79 - 6 * q^80 + 157 * q^81 - 117 * q^82 - 154 * q^83 - 6 * q^84 - 91 * q^85 + 28 * q^86 - 165 * q^87 - 165 * q^88 - 32 * q^89 - 103 * q^90 - 200 * q^91 - 86 * q^92 - 39 * q^93 - 118 * q^94 - 22 * q^95 - 28 * q^96 - 151 * q^97 - 38 * q^98 - 91 * 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 $

$2$	−2.68953	−1.90178	−0.950892	−	0.309524i	$-0.899830\pi$
$2$	−2.68953	−1.90178	−0.950892	+	0.309524i	$0.899830\pi$
$3$	2.61392	1.50915	0.754574	−	0.656215i	$-0.227843\pi$
$3$	2.61392	1.50915	0.754574	+	0.656215i	$0.227843\pi$
$4$	5.23356	2.61678
$5$	1.08630	0.485806	0.242903	−	0.970051i	$-0.421900\pi$
$5$	1.08630	0.485806	0.242903	+	0.970051i	$0.421900\pi$
$6$	−7.03022	−2.87007
$7$	−3.47806	−1.31458	−0.657292	−	0.753636i	$-0.728298\pi$
$7$	−3.47806	−1.31458	−0.657292	+	0.753636i	$0.728298\pi$
$8$	−8.69675	−3.07477
$9$	3.83259	1.27753
$10$	−2.92162	−0.923898
$11$	0.184213	0.0555422	0.0277711	−	0.999614i	$-0.491159\pi$
$11$	0.184213	0.0555422	0.0277711	+	0.999614i	$0.491159\pi$
$12$	13.6801	3.94911
$13$	−3.02638	−0.839368	−0.419684	−	0.907670i	$-0.637859\pi$
$13$	−3.02638	−0.839368	−0.419684	+	0.907670i	$0.637859\pi$
$14$	9.35435	2.50006
$15$	2.83949	0.733153
$16$	12.9230	3.23076
$17$	−3.23366	−0.784277	−0.392138	−	0.919906i	$-0.628265\pi$
$17$	−3.23366	−0.784277	−0.392138	+	0.919906i	$0.628265\pi$
$18$	−10.3079	−2.42958
$19$	3.22238	0.739264	0.369632	−	0.929178i	$-0.379484\pi$
$19$	3.22238	0.739264	0.369632	+	0.929178i	$0.379484\pi$
$20$	5.68519	1.27125
$21$	−9.09139	−1.98390
$22$	−0.495445	−0.105629
$23$	7.46180	1.55589	0.777947	−	0.628330i	$-0.216261\pi$
$23$	7.46180	1.55589	0.777947	+	0.628330i	$0.216261\pi$
$24$	−22.7326	−4.64028
$25$	−3.81996	−0.763993
$26$	8.13955	1.59630
$27$	2.17632	0.418833
$28$	−18.2027	−3.43998
$29$	−5.47961	−1.01754	−0.508769	−	0.860903i	$-0.669899\pi$
$29$	−5.47961	−1.01754	−0.508769	+	0.860903i	$0.669899\pi$
$30$	−7.63689	−1.39430
$31$	6.68243	1.20020	0.600100	−	0.799925i	$-0.295127\pi$
$31$	6.68243	1.20020	0.600100	+	0.799925i	$0.295127\pi$
$32$	−17.3634	−3.06944
$33$	0.481517	0.0838214
$34$	8.69701	1.49152
$35$	−3.77820	−0.638633
$36$	20.0581	3.34301
$37$	−5.07301	−0.833997	−0.416999	−	0.908907i	$-0.636918\pi$
$37$	−5.07301	−0.833997	−0.416999	+	0.908907i	$0.636918\pi$
$38$	−8.66667	−1.40592
$39$	−7.91073	−1.26673
$40$	−9.44724	−1.49374
$41$	−4.24459	−0.662894	−0.331447	−	0.943474i	$-0.607537\pi$
$41$	−4.24459	−0.662894	−0.331447	+	0.943474i	$0.607537\pi$
$42$	24.4515	3.77296
$43$	−4.05089	−0.617754	−0.308877	−	0.951102i	$-0.599953\pi$
$43$	−4.05089	−0.617754	−0.308877	+	0.951102i	$0.599953\pi$
$44$	0.964088	0.145342
$45$	4.16332	0.620632
$46$	−20.0687	−2.95897
$47$	3.38125	0.493206	0.246603	−	0.969117i	$-0.420686\pi$
$47$	3.38125	0.493206	0.246603	+	0.969117i	$0.420686\pi$
$48$	33.7798	4.87570
$49$	5.09693	0.728133
$50$	10.2739	1.45295
$51$	−8.45252	−1.18359
$52$	−15.8388	−2.19644
$53$	−10.3048	−1.41548	−0.707738	−	0.706475i	$-0.750284\pi$
$53$	−10.3048	−1.41548	−0.707738	+	0.706475i	$0.750284\pi$
$54$	−5.85328	−0.796530
$55$	0.200109	0.0269827
$56$	30.2479	4.04204
$57$	8.42304	1.11566
$58$	14.7376	1.93514
$59$	−2.92183	−0.380390	−0.190195	−	0.981746i	$-0.560912\pi$
$59$	−2.92183	−0.380390	−0.190195	+	0.981746i	$0.560912\pi$
$60$	14.8607	1.91850
$61$	10.1661	1.30163	0.650816	−	0.759236i	$-0.274427\pi$
$61$	10.1661	1.30163	0.650816	+	0.759236i	$0.274427\pi$
$62$	−17.9726	−2.28252
$63$	−13.3300	−1.67942
$64$	20.8532	2.60665
$65$	−3.28755	−0.407770
$66$	−1.29505	−0.159410
$67$	2.80569	0.342770	0.171385	−	0.985204i	$-0.445176\pi$
$67$	2.80569	0.342770	0.171385	+	0.985204i	$0.445176\pi$
$68$	−16.9235	−2.05228
$69$	19.5046	2.34807
$70$	10.1616	1.21454
$71$	10.2172	1.21256	0.606280	−	0.795251i	$-0.292661\pi$
$71$	10.2172	1.21256	0.606280	+	0.795251i	$0.292661\pi$
$72$	−33.3311	−3.92810
$73$	−1.45377	−0.170151	−0.0850755	−	0.996375i	$-0.527113\pi$
$73$	−1.45377	−0.170151	−0.0850755	+	0.996375i	$0.527113\pi$
$74$	13.6440	1.58608
$75$	−9.98508	−1.15298
$76$	16.8645	1.93449
$77$	−0.640703	−0.0730149
$78$	21.2761	2.40905
$79$	−16.4158	−1.84692	−0.923459	−	0.383696i	$-0.874651\pi$
$79$	−16.4158	−1.84692	−0.923459	+	0.383696i	$0.874651\pi$
$80$	14.0382	1.56952
$81$	−5.80903	−0.645448
$82$	11.4159	1.26068
$83$	16.5516	1.81677	0.908385	−	0.418134i	$-0.137316\pi$
$83$	16.5516	1.81677	0.908385	+	0.418134i	$0.137316\pi$
$84$	−47.5803	−5.19144
$85$	−3.51270	−0.381006
$86$	10.8950	1.17483
$87$	−14.3233	−1.53562
$88$	−1.60205	−0.170779
$89$	2.88151	0.305439	0.152720	−	0.988270i	$-0.451197\pi$
$89$	2.88151	0.305439	0.152720	+	0.988270i	$0.451197\pi$
$90$	−11.1974	−1.18031
$91$	10.5260	1.10342
$92$	39.0518	4.07143
$93$	17.4674	1.81128
$94$	−9.09397	−0.937971
$95$	3.50045	0.359139
$96$	−45.3865	−4.63224
$97$	−8.86871	−0.900481	−0.450240	−	0.892907i	$-0.648662\pi$
$97$	−8.86871	−0.900481	−0.450240	+	0.892907i	$0.648662\pi$
$98$	−13.7083	−1.38475
$99$	0.706011	0.0709568
$100$	−19.9920	−1.99920
$101$	−9.81836	−0.976963	−0.488482	−	0.872574i	$-0.662449\pi$
$101$	−9.81836	−0.976963	−0.488482	+	0.872574i	$0.662449\pi$
$102$	22.7333	2.25093
$103$	−9.41351	−0.927540	−0.463770	−	0.885956i	$-0.653504\pi$
$103$	−9.41351	−0.927540	−0.463770	+	0.885956i	$0.653504\pi$
$104$	26.3197	2.58086
$105$	−9.87593	−0.963792
$106$	27.7151	2.69193
$107$	−0.557198	−0.0538663	−0.0269332	−	0.999637i	$-0.508574\pi$
$107$	−0.557198	−0.0538663	−0.0269332	+	0.999637i	$0.508574\pi$
$108$	11.3899	1.09599
$109$	−7.53221	−0.721455	−0.360728	−	0.932671i	$-0.617472\pi$
$109$	−7.53221	−0.721455	−0.360728	+	0.932671i	$0.617472\pi$
$110$	−0.538200	−0.0513153
$111$	−13.2604	−1.25863
$112$	−44.9472	−4.24711
$113$	−5.90363	−0.555366	−0.277683	−	0.960673i	$-0.589567\pi$
$113$	−5.90363	−0.555366	−0.277683	+	0.960673i	$0.589567\pi$
$114$	−22.6540	−2.12174
$115$	8.10572	0.755862
$116$	−28.6779	−2.66267
$117$	−11.5989	−1.07232
$118$	7.85834	0.723419
$119$	11.2469	1.03100
$120$	−24.6944	−2.25428
$121$	−10.9661	−0.996915
$122$	−27.3419	−2.47542
$123$	−11.0950	−1.00041
$124$	34.9729	3.14066
$125$	−9.58108	−0.856958
$126$	35.8514	3.19389
$127$	−15.8657	−1.40786	−0.703928	−	0.710271i	$-0.748572\pi$
$127$	−15.8657	−1.40786	−0.703928	+	0.710271i	$0.748572\pi$
$128$	−21.3585	−1.88784
$129$	−10.5887	−0.932283
$130$	8.84195	0.775490
$131$	−14.5326	−1.26972	−0.634860	−	0.772627i	$-0.718942\pi$
$131$	−14.5326	−1.26972	−0.634860	+	0.772627i	$0.718942\pi$
$132$	2.52005	0.219342
$133$	−11.2076	−0.971825
$134$	−7.54599	−0.651874
$135$	2.36413	0.203472
$136$	28.1223	2.41147
$137$	−22.0263	−1.88183	−0.940916	−	0.338639i	$-0.890033\pi$
$137$	−22.0263	−1.88183	−0.940916	+	0.338639i	$0.890033\pi$
$138$	−52.4581	−4.46553
$139$	−3.43188	−0.291088	−0.145544	−	0.989352i	$-0.546493\pi$
$139$	−3.43188	−0.291088	−0.145544	+	0.989352i	$0.546493\pi$
$140$	−19.7735	−1.67116
$141$	8.83833	0.744321
$142$	−27.4795	−2.30603
$143$	−0.557498	−0.0466203
$144$	49.5287	4.12739
$145$	−5.95248	−0.494326
$146$	3.90996	0.323590
$147$	13.3230	1.09886
$148$	−26.5499	−2.18239
$149$	8.69384	0.712227	0.356114	−	0.934443i	$-0.384102\pi$
$149$	8.69384	0.712227	0.356114	+	0.934443i	$0.384102\pi$
$150$	26.8552	2.19271
$151$	14.7513	1.20044	0.600222	−	0.799834i	$-0.295079\pi$
$151$	14.7513	1.20044	0.600222	+	0.799834i	$0.295079\pi$
$152$	−28.0242	−2.27306
$153$	−12.3933	−1.00194
$154$	1.72319	0.138859
$155$	7.25909	0.583064
$156$	−41.4013	−3.31476
$157$	−17.7925	−1.42000	−0.709998	−	0.704204i	$-0.751304\pi$
$157$	−17.7925	−1.42000	−0.709998	+	0.704204i	$0.751304\pi$
$158$	44.1507	3.51244
$159$	−26.9360	−2.13616
$160$	−18.8617	−1.49115
$161$	−25.9526	−2.04535
$162$	15.6235	1.22750
$163$	−11.9213	−0.933749	−0.466875	−	0.884323i	$-0.654620\pi$
$163$	−11.9213	−0.933749	−0.466875	+	0.884323i	$0.654620\pi$
$164$	−22.2143	−1.73465
$165$	0.523070	0.0407210
$166$	−44.5159	−3.45510
$167$	9.27339	0.717596	0.358798	−	0.933415i	$-0.383187\pi$
$167$	9.27339	0.717596	0.358798	+	0.933415i	$0.383187\pi$
$168$	79.0656	6.10004
$169$	−3.84100	−0.295461
$170$	9.44752	0.724592
$171$	12.3500	0.944432
$172$	−21.2006	−1.61653
$173$	17.6561	1.34237	0.671183	−	0.741292i	$-0.265786\pi$
$173$	17.6561	1.34237	0.671183	+	0.741292i	$0.265786\pi$
$174$	38.5229	2.92041
$175$	13.2861	1.00433
$176$	2.38059	0.179443
$177$	−7.63743	−0.574065
$178$	−7.74990	−0.580879
$179$	10.0443	0.750750	0.375375	−	0.926873i	$-0.377514\pi$
$179$	10.0443	0.750750	0.375375	+	0.926873i	$0.377514\pi$
$180$	21.7890	1.62406
$181$	2.31872	0.172349	0.0861744	−	0.996280i	$-0.472536\pi$
$181$	2.31872	0.172349	0.0861744	+	0.996280i	$0.472536\pi$
$182$	−28.3099	−2.09847
$183$	26.5733	1.96436
$184$	−64.8934	−4.78401
$185$	−5.51078	−0.405161
$186$	−46.9789	−3.44466
$187$	−0.595680	−0.0435604
$188$	17.6960	1.29061
$189$	−7.56939	−0.550592
$190$	−9.41457	−0.683004
$191$	2.27900	0.164902	0.0824512	−	0.996595i	$-0.473725\pi$
$191$	2.27900	0.164902	0.0824512	+	0.996595i	$0.473725\pi$
$192$	54.5086	3.93382
$193$	−15.2704	−1.09919	−0.549594	−	0.835432i	$-0.685218\pi$
$193$	−15.2704	−1.09919	−0.549594	+	0.835432i	$0.685218\pi$
$194$	23.8526	1.71252
$195$	−8.59339	−0.615386
$196$	26.6751	1.90536
$197$	−10.5770	−0.753582	−0.376791	−	0.926298i	$-0.622973\pi$
$197$	−10.5770	−0.753582	−0.376791	+	0.926298i	$0.622973\pi$
$198$	−1.89884	−0.134944
$199$	−1.23074	−0.0872447	−0.0436223	−	0.999048i	$-0.513890\pi$
$199$	−1.23074	−0.0872447	−0.0436223	+	0.999048i	$0.513890\pi$
$200$	33.2213	2.34910
$201$	7.33387	0.517291
$202$	26.4068	1.85797
$203$	19.0584	1.33764
$204$	−44.2368	−3.09720
$205$	−4.61088	−0.322038
$206$	25.3179	1.76398
$207$	28.5980	1.98770
$208$	−39.1101	−2.71180
$209$	0.593603	0.0410603
$210$	26.5616	1.83292
$211$	3.30599	0.227594	0.113797	−	0.993504i	$-0.463699\pi$
$211$	3.30599	0.227594	0.113797	+	0.993504i	$0.463699\pi$
$212$	−53.9309	−3.70399
$213$	26.7070	1.82993
$214$	1.49860	0.102442
$215$	−4.40046	−0.300109
$216$	−18.9269	−1.28781
$217$	−23.2419	−1.57776
$218$	20.2581	1.37205
$219$	−3.80004	−0.256783
$220$	1.04728	0.0706079
$221$	9.78628	0.658297
$222$	35.6643	2.39363
$223$	−3.29060	−0.220355	−0.110177	−	0.993912i	$-0.535142\pi$
$223$	−3.29060	−0.220355	−0.110177	+	0.993912i	$0.535142\pi$
$224$	60.3909	4.03504
$225$	−14.6403	−0.976023
$226$	15.8780	1.05619
$227$	4.70043	0.311978	0.155989	−	0.987759i	$-0.450144\pi$
$227$	4.70043	0.311978	0.155989	+	0.987759i	$0.450144\pi$
$228$	44.0825	2.91944
$229$	−18.4886	−1.22176	−0.610880	−	0.791723i	$-0.709184\pi$
$229$	−18.4886	−1.22176	−0.610880	+	0.791723i	$0.709184\pi$
$230$	−21.8006	−1.43749
$231$	−1.67475	−0.110190
$232$	47.6548	3.12869
$233$	18.9840	1.24368	0.621840	−	0.783144i	$-0.286385\pi$
$233$	18.9840	1.24368	0.621840	+	0.783144i	$0.286385\pi$
$234$	31.1955	2.03932
$235$	3.67304	0.239603
$236$	−15.2916	−0.995396
$237$	−42.9096	−2.78728
$238$	−30.2487	−1.96074
$239$	15.7975	1.02186	0.510929	−	0.859623i	$-0.329301\pi$
$239$	15.7975	1.02186	0.510929	+	0.859623i	$0.329301\pi$
$240$	36.6949	2.36864
$241$	−0.856820	−0.0551926	−0.0275963	−	0.999619i	$-0.508785\pi$
$241$	−0.856820	−0.0551926	−0.0275963	+	0.999619i	$0.508785\pi$
$242$	29.4935	1.89592
$243$	−21.7133	−1.39291
$244$	53.2047	3.40608
$245$	5.53677	0.353731
$246$	29.8404	1.90255
$247$	−9.75215	−0.620515
$248$	−58.1154	−3.69033
$249$	43.2645	2.74178
$250$	25.7686	1.62975
$251$	6.33977	0.400163	0.200081	−	0.979779i	$-0.435879\pi$
$251$	6.33977	0.400163	0.200081	+	0.979779i	$0.435879\pi$
$252$	−69.7633	−4.39468
$253$	1.37456	0.0864177
$254$	42.6713	2.67744
$255$	−9.18194	−0.574995
$256$	15.7379	0.983619
$257$	4.09104	0.255192	0.127596	−	0.991826i	$-0.459274\pi$
$257$	4.09104	0.255192	0.127596	+	0.991826i	$0.459274\pi$
$258$	28.4786	1.77300
$259$	17.6442	1.09636
$260$	−17.2056	−1.06704
$261$	−21.0011	−1.29994
$262$	39.0859	2.41473
$263$	−13.6829	−0.843725	−0.421863	−	0.906660i	$-0.638624\pi$
$263$	−13.6829	−0.843725	−0.421863	+	0.906660i	$0.638624\pi$
$264$	−4.18764	−0.257731
$265$	−11.1941	−0.687646
$266$	30.1432	1.84820
$267$	7.53204	0.460953
$268$	14.6838	0.896954
$269$	−20.2765	−1.23628	−0.618139	−	0.786068i	$-0.712113\pi$
$269$	−20.2765	−1.23628	−0.618139	+	0.786068i	$0.712113\pi$
$270$	−6.35839	−0.386959
$271$	0.757059	0.0459881	0.0229940	−	0.999736i	$-0.492680\pi$
$271$	0.757059	0.0459881	0.0229940	+	0.999736i	$0.492680\pi$
$272$	−41.7887	−2.53381
$273$	27.5140	1.66523
$274$	59.2403	3.57884
$275$	−0.703685	−0.0424338
$276$	102.078	6.14439
$277$	−17.1957	−1.03319	−0.516595	−	0.856230i	$-0.672801\pi$
$277$	−17.1957	−1.03319	−0.516595	+	0.856230i	$0.672801\pi$
$278$	9.23013	0.553587
$279$	25.6110	1.53329
$280$	32.8581	1.96365
$281$	13.7083	0.817770	0.408885	−	0.912586i	$-0.365918\pi$
$281$	13.7083	0.817770	0.408885	+	0.912586i	$0.365918\pi$
$282$	−23.7709	−1.41554
$283$	7.29513	0.433651	0.216825	−	0.976210i	$-0.430430\pi$
$283$	7.29513	0.433651	0.216825	+	0.976210i	$0.430430\pi$
$284$	53.4724	3.17300
$285$	9.14991	0.541994
$286$	1.49941	0.0886618
$287$	14.7630	0.871430
$288$	−66.5466	−3.92130
$289$	−6.54347	−0.384910
$290$	16.0094	0.940102
$291$	−23.1821	−1.35896
$292$	−7.60840	−0.445248
$293$	−17.9967	−1.05138	−0.525689	−	0.850677i	$-0.676192\pi$
$293$	−17.9967	−1.05138	−0.525689	+	0.850677i	$0.676192\pi$
$294$	−35.8325	−2.08980
$295$	−3.17397	−0.184796
$296$	44.1187	2.56435
$297$	0.400906	0.0232629
$298$	−23.3823	−1.35450
$299$	−22.5823	−1.30597
$300$	−52.2575	−3.01709
$301$	14.0892	0.812090
$302$	−39.6740	−2.28298
$303$	−25.6644	−1.47438
$304$	41.6429	2.38838
$305$	11.0433	0.632340
$306$	33.3320	1.90547
$307$	−10.2071	−0.582549	−0.291274	−	0.956640i	$-0.594079\pi$
$307$	−10.2071	−0.582549	−0.291274	+	0.956640i	$0.594079\pi$
$308$	−3.35316	−0.191064
$309$	−24.6062	−1.39980
$310$	−19.5235	−1.10886
$311$	29.9842	1.70025	0.850124	−	0.526582i	$-0.176527\pi$
$311$	29.9842	1.70025	0.850124	+	0.526582i	$0.176527\pi$
$312$	68.7977	3.89490
$313$	19.9597	1.12819	0.564094	−	0.825710i	$-0.309226\pi$
$313$	19.9597	1.12819	0.564094	+	0.825710i	$0.309226\pi$
$314$	47.8534	2.70053
$315$	−14.4803	−0.815873
$316$	−85.9130	−4.83298
$317$	−19.6303	−1.10255	−0.551274	−	0.834324i	$-0.685858\pi$
$317$	−19.6303	−1.10255	−0.551274	+	0.834324i	$0.685858\pi$
$318$	72.4451	4.06252
$319$	−1.00941	−0.0565163
$320$	22.6527	1.26633
$321$	−1.45647	−0.0812923
$322$	69.8003	3.88982
$323$	−10.4201	−0.579788
$324$	−30.4019	−1.68900
$325$	11.5607	0.641271
$326$	32.0627	1.77579
$327$	−19.6886	−1.08878
$328$	36.9142	2.03824
$329$	−11.7602	−0.648361
$330$	−1.40681	−0.0774424
$331$	−13.2984	−0.730946	−0.365473	−	0.930822i	$-0.619093\pi$
$331$	−13.2984	−0.730946	−0.365473	+	0.930822i	$0.619093\pi$
$332$	86.6236	4.75409
$333$	−19.4427	−1.06546
$334$	−24.9410	−1.36471
$335$	3.04781	0.166520
$336$	−117.488	−6.40952
$337$	11.4276	0.622501	0.311250	−	0.950328i	$-0.399252\pi$
$337$	11.4276	0.622501	0.311250	+	0.950328i	$0.399252\pi$
$338$	10.3305	0.561904
$339$	−15.4316	−0.838130
$340$	−18.3840	−0.997010
$341$	1.23099	0.0666617
$342$	−33.2158	−1.79610
$343$	6.61900	0.357392
$344$	35.2296	1.89945
$345$	21.1877	1.14071
$346$	−47.4865	−2.55289
$347$	−25.4944	−1.36861	−0.684304	−	0.729197i	$-0.739894\pi$
$347$	−25.4944	−1.36861	−0.684304	+	0.729197i	$0.739894\pi$
$348$	−74.9618	−4.01837
$349$	21.4999	1.15086	0.575431	−	0.817850i	$-0.304834\pi$
$349$	21.4999	1.15086	0.575431	+	0.817850i	$0.304834\pi$
$350$	−35.7333	−1.91002
$351$	−6.58639	−0.351555
$352$	−3.19855	−0.170483
$353$	29.0248	1.54483	0.772417	−	0.635116i	$-0.219048\pi$
$353$	29.0248	1.54483	0.772417	+	0.635116i	$0.219048\pi$
$354$	20.5411	1.09175
$355$	11.0989	0.589069
$356$	15.0805	0.799267
$357$	29.3984	1.55593
$358$	−27.0146	−1.42776
$359$	−0.538340	−0.0284125	−0.0142063	−	0.999899i	$-0.504522\pi$
$359$	−0.538340	−0.0284125	−0.0142063	+	0.999899i	$0.504522\pi$
$360$	−36.2074	−1.90830
$361$	−8.61628	−0.453489
$362$	−6.23625	−0.327770
$363$	−28.6644	−1.50449
$364$	55.0882	2.88741
$365$	−1.57922	−0.0826604
$366$	−71.4696	−3.73578
$367$	−19.9535	−1.04156	−0.520781	−	0.853690i	$-0.674359\pi$
$367$	−19.9535	−1.04156	−0.520781	+	0.853690i	$0.674359\pi$
$368$	96.4291	5.02672
$369$	−16.2678	−0.846866
$370$	14.8214	0.770528
$371$	35.8408	1.86076
$372$	91.4165	4.73972
$373$	19.0627	0.987028	0.493514	−	0.869738i	$-0.335712\pi$
$373$	19.0627	0.987028	0.493514	+	0.869738i	$0.335712\pi$
$374$	1.60210	0.0828425
$375$	−25.0442	−1.29328
$376$	−29.4059	−1.51649
$377$	16.5834	0.854089
$378$	20.3581	1.04711
$379$	1.69785	0.0872126	0.0436063	−	0.999049i	$-0.486115\pi$
$379$	1.69785	0.0872126	0.0436063	+	0.999049i	$0.486115\pi$
$380$	18.3198	0.939788
$381$	−41.4718	−2.12466
$382$	−6.12943	−0.313609
$383$	15.9767	0.816372	0.408186	−	0.912899i	$-0.366162\pi$
$383$	15.9767	0.816372	0.408186	+	0.912899i	$0.366162\pi$
$384$	−55.8294	−2.84903
$385$	−0.695993	−0.0354711
$386$	41.0702	2.09042
$387$	−15.5254	−0.789199
$388$	−46.4149	−2.35636
$389$	14.2415	0.722074	0.361037	−	0.932552i	$-0.382423\pi$
$389$	14.2415	0.722074	0.361037	+	0.932552i	$0.382423\pi$
$390$	23.1122	1.17033
$391$	−24.1289	−1.22025
$392$	−44.3267	−2.23884
$393$	−37.9871	−1.91620
$394$	28.4472	1.43315
$395$	−17.8324	−0.897244
$396$	3.69495	0.185678
$397$	11.4011	0.572205	0.286103	−	0.958199i	$-0.407640\pi$
$397$	11.4011	0.572205	0.286103	+	0.958199i	$0.407640\pi$
$398$	3.31010	0.165921
$399$	−29.2959	−1.46663
$400$	−49.3655	−2.46828
$401$	−29.4780	−1.47206	−0.736031	−	0.676948i	$-0.763302\pi$
$401$	−29.4780	−1.47206	−0.736031	+	0.676948i	$0.763302\pi$
$402$	−19.7246	−0.983775
$403$	−20.2236	−1.00741
$404$	−51.3850	−2.55650
$405$	−6.31032	−0.313562
$406$	−51.2582	−2.54390
$407$	−0.934512	−0.0463220
$408$	73.5095	3.63926
$409$	−19.9824	−0.988068	−0.494034	−	0.869443i	$-0.664478\pi$
$409$	−19.9824	−0.988068	−0.494034	+	0.869443i	$0.664478\pi$
$410$	12.4011	0.612446
$411$	−57.5750	−2.83996
$412$	−49.2662	−2.42717
$413$	10.1623	0.500054
$414$	−76.9152	−3.78017
$415$	17.9799	0.882598
$416$	52.5482	2.57639
$417$	−8.97066	−0.439295
$418$	−1.59651	−0.0780879
$419$	35.2650	1.72281	0.861404	−	0.507920i	$-0.169585\pi$
$419$	35.2650	1.72281	0.861404	+	0.507920i	$0.169585\pi$
$420$	−51.6863	−2.52203
$421$	4.41266	0.215060	0.107530	−	0.994202i	$-0.465706\pi$
$421$	4.41266	0.215060	0.107530	+	0.994202i	$0.465706\pi$
$422$	−8.89155	−0.432834
$423$	12.9589	0.630086
$424$	89.6184	4.35226
$425$	12.3524	0.599181
$426$	−71.8292	−3.48014
$427$	−35.3582	−1.71110
$428$	−2.91613	−0.140956
$429$	−1.45726	−0.0703570
$430$	11.8352	0.570742
$431$	−12.2863	−0.591809	−0.295904	−	0.955218i	$-0.595621\pi$
$431$	−12.2863	−0.591809	−0.295904	+	0.955218i	$0.595621\pi$
$432$	28.1247	1.35315
$433$	−18.3412	−0.881421	−0.440710	−	0.897649i	$-0.645273\pi$
$433$	−18.3412	−0.881421	−0.440710	+	0.897649i	$0.645273\pi$
$434$	62.5098	3.00057
$435$	−15.5593	−0.746012
$436$	−39.4203	−1.88789
$437$	24.0447	1.15022
$438$	10.2203	0.488346
$439$	27.7563	1.32474	0.662368	−	0.749179i	$-0.269552\pi$
$439$	27.7563	1.32474	0.662368	+	0.749179i	$0.269552\pi$
$440$	−1.74030	−0.0829656
$441$	19.5344	0.930211
$442$	−26.3205	−1.25194
$443$	17.0287	0.809060	0.404530	−	0.914525i	$-0.367435\pi$
$443$	17.0287	0.809060	0.404530	+	0.914525i	$0.367435\pi$
$444$	−69.3993	−3.29355
$445$	3.13017	0.148384
$446$	8.85016	0.419067
$447$	22.7250	1.07486
$448$	−72.5287	−3.42666
$449$	−1.77700	−0.0838618	−0.0419309	−	0.999121i	$-0.513351\pi$
$449$	−1.77700	−0.0838618	−0.0419309	+	0.999121i	$0.513351\pi$
$450$	39.3756	1.85618
$451$	−0.781907	−0.0368186
$452$	−30.8970	−1.45327
$453$	38.5587	1.81165
$454$	−12.6419	−0.593315
$455$	11.4343	0.536048
$456$	−73.2531	−3.43039
$457$	7.04477	0.329541	0.164770	−	0.986332i	$-0.447312\pi$
$457$	7.04477	0.329541	0.164770	+	0.986332i	$0.447312\pi$
$458$	49.7256	2.32352
$459$	−7.03747	−0.328481
$460$	42.4218	1.97793
$461$	−3.68983	−0.171852	−0.0859262	−	0.996302i	$-0.527385\pi$
$461$	−3.68983	−0.171852	−0.0859262	+	0.996302i	$0.527385\pi$
$462$	4.50428	0.209558
$463$	3.43878	0.159814	0.0799068	−	0.996802i	$-0.474538\pi$
$463$	3.43878	0.159814	0.0799068	+	0.996802i	$0.474538\pi$
$464$	−70.8132	−3.28742
$465$	18.9747	0.879931
$466$	−51.0579	−2.36521
$467$	−7.87148	−0.364249	−0.182124	−	0.983276i	$-0.558297\pi$
$467$	−7.87148	−0.364249	−0.182124	+	0.983276i	$0.558297\pi$
$468$	−60.7035	−2.80602
$469$	−9.75838	−0.450600
$470$	−9.87874	−0.455672
$471$	−46.5082	−2.14299
$472$	25.4104	1.16961
$473$	−0.746224	−0.0343114
$474$	115.406	5.30079
$475$	−12.3094	−0.564792
$476$	58.8611	2.69790
$477$	−39.4941	−1.80831
$478$	−42.4879	−1.94335
$479$	36.4087	1.66355	0.831777	−	0.555110i	$-0.187324\pi$
$479$	36.4087	1.66355	0.831777	+	0.555110i	$0.187324\pi$
$480$	−49.3031	−2.25037
$481$	15.3529	0.700030
$482$	2.30444	0.104964
$483$	−67.8381	−3.08674
$484$	−57.3916	−2.60871
$485$	−9.63403	−0.437459
$486$	58.3986	2.64901
$487$	−10.3555	−0.469251	−0.234625	−	0.972086i	$-0.575386\pi$
$487$	−10.3555	−0.469251	−0.234625	+	0.972086i	$0.575386\pi$
$488$	−88.4118	−4.00221
$489$	−31.1614	−1.40917
$490$	−14.8913	−0.672720
$491$	−7.40008	−0.333961	−0.166981	−	0.985960i	$-0.553402\pi$
$491$	−7.40008	−0.333961	−0.166981	+	0.985960i	$0.553402\pi$
$492$	−58.0665	−2.61784
$493$	17.7192	0.798032
$494$	26.2287	1.18008
$495$	0.766937	0.0344712
$496$	86.3573	3.87756
$497$	−35.5361	−1.59401
$498$	−116.361	−5.21427
$499$	−33.4978	−1.49957	−0.749784	−	0.661683i	$-0.769842\pi$
$499$	−33.4978	−1.49957	−0.749784	+	0.661683i	$0.769842\pi$
$500$	−50.1432	−2.24247
$501$	24.2399	1.08296
$502$	−17.0510	−0.761022
$503$	14.4259	0.643218	0.321609	−	0.946873i	$-0.395776\pi$
$503$	14.4259	0.643218	0.321609	+	0.946873i	$0.395776\pi$
$504$	115.928	5.16383
$505$	−10.6656	−0.474615
$506$	−3.69691	−0.164348
$507$	−10.0401	−0.445895
$508$	−83.0343	−3.68405
$509$	−15.6294	−0.692759	−0.346379	−	0.938094i	$-0.612589\pi$
$509$	−15.6294	−0.692759	−0.346379	+	0.938094i	$0.612589\pi$
$510$	24.6951	1.09352
$511$	5.05631	0.223678
$512$	0.389469	0.0172122
$513$	7.01293	0.309628
$514$	−11.0030	−0.485320
$515$	−10.2258	−0.450605
$516$	−55.4166	−2.43958
$517$	0.622869	0.0273938
$518$	−47.4547	−2.08504
$519$	46.1516	2.02583
$520$	28.5910	1.25380
$521$	26.5180	1.16177	0.580887	−	0.813984i	$-0.302706\pi$
$521$	26.5180	1.16177	0.580887	+	0.813984i	$0.302706\pi$
$522$	56.4830	2.47220
$523$	−36.2662	−1.58581	−0.792906	−	0.609344i	$-0.791433\pi$
$523$	−36.2662	−1.58581	−0.792906	+	0.609344i	$0.791433\pi$
$524$	−76.0573	−3.32258
$525$	34.7288	1.51569
$526$	36.8006	1.60458
$527$	−21.6087	−0.941289
$528$	6.22267	0.270807
$529$	32.6785	1.42080
$530$	30.1068	1.30775
$531$	−11.1982	−0.485959
$532$	−58.6558	−2.54305
$533$	12.8458	0.556412
$534$	−20.2576	−0.876633
$535$	−0.605281	−0.0261686
$536$	−24.4004	−1.05394
$537$	26.2551	1.13299
$538$	54.5342	2.35113
$539$	0.938919	0.0404421
$540$	12.3728	0.532441
$541$	22.7539	0.978268	0.489134	−	0.872209i	$-0.337313\pi$
$541$	22.7539	0.978268	0.489134	+	0.872209i	$0.337313\pi$
$542$	−2.03613	−0.0874594
$543$	6.06094	0.260100
$544$	56.1471	2.40729
$545$	−8.18221	−0.350487
$546$	−73.9998	−3.16690
$547$	−31.1601	−1.33231	−0.666155	−	0.745813i	$-0.732061\pi$
$547$	−31.1601	−1.33231	−0.666155	+	0.745813i	$0.732061\pi$
$548$	−115.276	−4.92434
$549$	38.9623	1.66287
$550$	1.89258	0.0806999
$551$	−17.6574	−0.752230
$552$	−169.626	−7.21978
$553$	57.0951	2.42793
$554$	46.2483	1.96490
$555$	−14.4048	−0.611448
$556$	−17.9609	−0.761714
$557$	−1.47402	−0.0624564	−0.0312282	−	0.999512i	$-0.509942\pi$
$557$	−1.47402	−0.0624564	−0.0312282	+	0.999512i	$0.509942\pi$
$558$	−68.8815	−2.91599
$559$	12.2595	0.518523
$560$	−48.8259	−2.06327
$561$	−1.55706	−0.0657392
$562$	−36.8689	−1.55522
$563$	−10.4711	−0.441306	−0.220653	−	0.975352i	$-0.570819\pi$
$563$	−10.4711	−0.441306	−0.220653	+	0.975352i	$0.570819\pi$
$564$	46.2559	1.94773
$565$	−6.41308	−0.269800
$566$	−19.6205	−0.824710
$567$	20.2042	0.848496
$568$	−88.8566	−3.72834
$569$	34.3879	1.44162	0.720808	−	0.693135i	$-0.243771\pi$
$569$	34.3879	1.44162	0.720808	+	0.693135i	$0.243771\pi$
$570$	−24.6089	−1.03076
$571$	−34.1430	−1.42884	−0.714420	−	0.699718i	$-0.753309\pi$
$571$	−34.1430	−1.42884	−0.714420	+	0.699718i	$0.753309\pi$
$572$	−2.91770	−0.121995
$573$	5.95712	0.248862
$574$	−39.7054	−1.65727
$575$	−28.5038	−1.18869
$576$	79.9217	3.33007
$577$	−15.8371	−0.659309	−0.329655	−	0.944102i	$-0.606932\pi$
$577$	−15.8371	−0.659309	−0.329655	+	0.944102i	$0.606932\pi$
$578$	17.5989	0.732016
$579$	−39.9157	−1.65884
$580$	−31.1526	−1.29354
$581$	−57.5674	−2.38830
$582$	62.3489	2.58445
$583$	−1.89828	−0.0786186
$584$	12.6431	0.523174
$585$	−12.5998	−0.520938
$586$	48.4026	1.99949
$587$	14.3689	0.593067	0.296533	−	0.955022i	$-0.404169\pi$
$587$	14.3689	0.593067	0.296533	+	0.955022i	$0.404169\pi$
$588$	69.7266	2.87548
$589$	21.5333	0.887265
$590$	8.53648	0.351441
$591$	−27.6475	−1.13727
$592$	−65.5587	−2.69444
$593$	−0.632857	−0.0259883	−0.0129942	−	0.999916i	$-0.504136\pi$
$593$	−0.632857	−0.0259883	−0.0129942	+	0.999916i	$0.504136\pi$
$594$	−1.07825	−0.0442410
$595$	12.2174	0.500865
$596$	45.4998	1.86374
$597$	−3.21705	−0.131665
$598$	60.7357	2.48367
$599$	−25.3867	−1.03727	−0.518635	−	0.854996i	$-0.673560\pi$
$599$	−25.3867	−1.03727	−0.518635	+	0.854996i	$0.673560\pi$
$600$	86.8378	3.54514
$601$	31.1036	1.26874	0.634370	−	0.773029i	$-0.281259\pi$
$601$	31.1036	1.26874	0.634370	+	0.773029i	$0.281259\pi$
$602$	−37.8934	−1.54442
$603$	10.7531	0.437899
$604$	77.2018	3.14130
$605$	−11.9124	−0.484307
$606$	69.0252	2.80396
$607$	46.2303	1.87643	0.938215	−	0.346053i	$-0.112478\pi$
$607$	46.2303	1.87643	0.938215	+	0.346053i	$0.112478\pi$
$608$	−55.9513	−2.26913
$609$	49.8173	2.01870
$610$	−29.7014	−1.20257
$611$	−10.2330	−0.413982
$612$	−64.8609	−2.62185
$613$	29.3066	1.18368	0.591841	−	0.806055i	$-0.298401\pi$
$613$	29.3066	1.18368	0.591841	+	0.806055i	$0.298401\pi$
$614$	27.4522	1.10788
$615$	−12.0525	−0.486003
$616$	5.57204	0.224504
$617$	23.5949	0.949897	0.474948	−	0.880014i	$-0.342467\pi$
$617$	23.5949	0.949897	0.474948	+	0.880014i	$0.342467\pi$
$618$	66.1790	2.66211
$619$	43.5228	1.74933	0.874665	−	0.484728i	$-0.161081\pi$
$619$	43.5228	1.74933	0.874665	+	0.484728i	$0.161081\pi$
$620$	37.9909	1.52575
$621$	16.2393	0.651660
$622$	−80.6434	−3.23350
$623$	−10.0221	−0.401526
$624$	−102.231	−4.09250
$625$	8.69193	0.347677
$626$	−53.6821	−2.14557
$627$	1.55163	0.0619662
$628$	−93.1181	−3.71582
$629$	16.4044	0.654084
$630$	38.9452	1.55161
$631$	43.9770	1.75070	0.875348	−	0.483494i	$-0.160633\pi$
$631$	43.9770	1.75070	0.875348	+	0.483494i	$0.160633\pi$
$632$	142.764	5.67884
$633$	8.64160	0.343473
$634$	52.7963	2.09681
$635$	−17.2349	−0.683945
$636$	−140.971	−5.58987
$637$	−15.4253	−0.611171
$638$	2.71485	0.107482
$639$	39.1584	1.54908
$640$	−23.2016	−0.917125
$641$	−21.7697	−0.859852	−0.429926	−	0.902864i	$-0.641460\pi$
$641$	−21.7697	−0.859852	−0.429926	+	0.902864i	$0.641460\pi$
$642$	3.91722	0.154600
$643$	−36.5837	−1.44272	−0.721360	−	0.692560i	$-0.756483\pi$
$643$	−36.5837	−1.44272	−0.721360	+	0.692560i	$0.756483\pi$
$644$	−135.825	−5.35224
$645$	−11.5025	−0.452909
$646$	28.0250	1.10263
$647$	38.7671	1.52409	0.762046	−	0.647522i	$-0.224195\pi$
$647$	38.7671	1.52409	0.762046	+	0.647522i	$0.224195\pi$
$648$	50.5197	1.98460
$649$	−0.538238	−0.0211277
$650$	−31.0928	−1.21956
$651$	−60.7526	−2.38108
$652$	−62.3909	−2.44342
$653$	−26.3235	−1.03012	−0.515060	−	0.857154i	$-0.672230\pi$
$653$	−26.3235	−1.03012	−0.515060	+	0.857154i	$0.672230\pi$
$654$	52.9531	2.07063
$655$	−15.7867	−0.616838
$656$	−54.8530	−2.14165
$657$	−5.57170	−0.217373
$658$	31.6294	1.23304
$659$	3.01661	0.117510	0.0587552	−	0.998272i	$-0.481287\pi$
$659$	3.01661	0.117510	0.0587552	+	0.998272i	$0.481287\pi$
$660$	2.73752	0.106558
$661$	6.80715	0.264768	0.132384	−	0.991199i	$-0.457737\pi$
$661$	6.80715	0.264768	0.132384	+	0.991199i	$0.457737\pi$
$662$	35.7664	1.39010
$663$	25.5806	0.993468
$664$	−143.945	−5.58615
$665$	−12.1748	−0.472119
$666$	52.2918	2.02627
$667$	−40.8878	−1.58318
$668$	48.5328	1.87779
$669$	−8.60137	−0.332548
$670$	−8.19718	−0.316685
$671$	1.87272	0.0722955
$672$	157.857	6.08947
$673$	−4.42234	−0.170468	−0.0852342	−	0.996361i	$-0.527164\pi$
$673$	−4.42234	−0.170468	−0.0852342	+	0.996361i	$0.527164\pi$
$674$	−30.7348	−1.18386
$675$	−8.31347	−0.319986
$676$	−20.1021	−0.773158
$677$	20.8725	0.802194	0.401097	−	0.916036i	$-0.368629\pi$
$677$	20.8725	0.802194	0.401097	+	0.916036i	$0.368629\pi$
$678$	41.5038	1.59394
$679$	30.8459	1.18376
$680$	30.5491	1.17151
$681$	12.2865	0.470822
$682$	−3.31078	−0.126776
$683$	−9.53546	−0.364864	−0.182432	−	0.983218i	$-0.558397\pi$
$683$	−9.53546	−0.364864	−0.182432	+	0.983218i	$0.558397\pi$
$684$	64.6347	2.47137
$685$	−23.9270	−0.914206
$686$	−17.8020	−0.679683
$687$	−48.3277	−1.84382
$688$	−52.3498	−1.99582
$689$	31.1863	1.18810
$690$	−56.9850	−2.16938
$691$	37.7842	1.43738	0.718689	−	0.695332i	$-0.244743\pi$
$691$	37.7842	1.43738	0.718689	+	0.695332i	$0.244743\pi$
$692$	92.4041	3.51268
$693$	−2.45555	−0.0932787
$694$	68.5678	2.60280
$695$	−3.72803	−0.141412
$696$	124.566	4.72166
$697$	13.7255	0.519892
$698$	−57.8245	−2.18869
$699$	49.6226	1.87690
$700$	69.5335	2.62812
$701$	−23.0571	−0.870855	−0.435427	−	0.900224i	$-0.643403\pi$
$701$	−23.0571	−0.870855	−0.435427	+	0.900224i	$0.643403\pi$
$702$	17.7143	0.668582
$703$	−16.3471	−0.616544
$704$	3.84142	0.144779
$705$	9.60103	0.361596
$706$	−78.0630	−2.93794
$707$	34.1489	1.28430
$708$	−39.9710	−1.50220
$709$	−4.16553	−0.156440	−0.0782199	−	0.996936i	$-0.524924\pi$
$709$	−4.16553	−0.156440	−0.0782199	+	0.996936i	$0.524924\pi$
$710$	−29.8508	−1.12028
$711$	−62.9149	−2.35949
$712$	−25.0598	−0.939154
$713$	49.8630	1.86738
$714$	−79.0679	−2.95904
$715$	−0.605608	−0.0226484
$716$	52.5677	1.96455
$717$	41.2936	1.54214
$718$	1.44788	0.0540345
$719$	11.1850	0.417129	0.208565	−	0.978009i	$-0.433121\pi$
$719$	11.1850	0.417129	0.208565	+	0.978009i	$0.433121\pi$
$720$	53.8028	2.00511
$721$	32.7408	1.21933
$722$	23.1737	0.862437
$723$	−2.23966	−0.0832938
$724$	12.1351	0.450999
$725$	20.9319	0.777392
$726$	77.0938	2.86122
$727$	−36.1834	−1.34197	−0.670983	−	0.741473i	$-0.734128\pi$
$727$	−36.1834	−1.34197	−0.670983	+	0.741473i	$0.734128\pi$
$728$	−91.5417	−3.39276
$729$	−39.3298	−1.45666
$730$	4.24737	0.157202
$731$	13.0992	0.484490
$732$	139.073	5.14029
$733$	39.2552	1.44993	0.724963	−	0.688788i	$-0.241857\pi$
$733$	39.2552	1.44993	0.724963	+	0.688788i	$0.241857\pi$
$734$	53.6654	1.98083
$735$	14.4727	0.533833
$736$	−129.562	−4.77572
$737$	0.516844	0.0190382
$738$	43.7526	1.61056
$739$	−11.8681	−0.436574	−0.218287	−	0.975885i	$-0.570047\pi$
$739$	−11.8681	−0.436574	−0.218287	+	0.975885i	$0.570047\pi$
$740$	−28.8410	−1.06022
$741$	−25.4914	−0.936449
$742$	−96.3949	−3.53877
$743$	23.8956	0.876645	0.438322	−	0.898818i	$-0.355573\pi$
$743$	23.8956	0.876645	0.438322	+	0.898818i	$0.355573\pi$
$744$	−151.909	−5.56926
$745$	9.44408	0.346004
$746$	−51.2696	−1.87711
$747$	63.4354	2.32098
$748$	−3.11753	−0.113988
$749$	1.93797	0.0708119
$750$	67.3571	2.45953
$751$	−28.7631	−1.04958	−0.524791	−	0.851231i	$-0.675857\pi$
$751$	−28.7631	−1.04958	−0.524791	+	0.851231i	$0.675857\pi$
$752$	43.6960	1.59343
$753$	16.5717	0.603905
$754$	−44.6015	−1.62429
$755$	16.0243	0.583183
$756$	−39.6148	−1.44078
$757$	46.5038	1.69021	0.845106	−	0.534599i	$-0.179537\pi$
$757$	46.5038	1.69021	0.845106	+	0.534599i	$0.179537\pi$
$758$	−4.56641	−0.165860
$759$	3.59299	0.130417
$760$	−30.4426	−1.10427
$761$	35.0835	1.27178	0.635888	−	0.771781i	$-0.280634\pi$
$761$	35.0835	1.27178	0.635888	+	0.771781i	$0.280634\pi$
$762$	111.540	4.04065
$763$	26.1975	0.948414
$764$	11.9273	0.431514
$765$	−13.4628	−0.486747
$766$	−42.9698	−1.55256
$767$	8.84258	0.319287
$768$	41.1376	1.48443
$769$	−41.4839	−1.49595	−0.747974	−	0.663728i	$-0.768973\pi$
$769$	−41.4839	−1.49595	−0.747974	+	0.663728i	$0.768973\pi$
$770$	1.87189	0.0674583
$771$	10.6937	0.385123
$772$	−79.9186	−2.87633
$773$	3.84438	0.138273	0.0691364	−	0.997607i	$-0.477976\pi$
$773$	3.84438	0.138273	0.0691364	+	0.997607i	$0.477976\pi$
$774$	41.7559	1.50089
$775$	−25.5266	−0.916944
$776$	77.1290	2.76877
$777$	46.1207	1.65457
$778$	−38.3030	−1.37323
$779$	−13.6777	−0.490054
$780$	−44.9740	−1.61033
$781$	1.88214	0.0673483
$782$	64.8953	2.32065
$783$	−11.9254	−0.426179
$784$	65.8678	2.35242
$785$	−19.3279	−0.689843
$786$	102.167	3.64419
$787$	29.1242	1.03816	0.519082	−	0.854724i	$-0.326274\pi$
$787$	29.1242	1.03816	0.519082	+	0.854724i	$0.326274\pi$
$788$	−55.3556	−1.97196
$789$	−35.7661	−1.27331
$790$	47.9607	1.70636
$791$	20.5332	0.730076
$792$	−6.14000	−0.218176
$793$	−30.7664	−1.09255
$794$	−30.6636	−1.08821
$795$	−29.2604	−1.03776
$796$	−6.44114	−0.228300
$797$	−50.6845	−1.79534	−0.897669	−	0.440670i	$-0.854741\pi$
$797$	−50.6845	−1.79534	−0.897669	+	0.440670i	$0.854741\pi$
$798$	78.7921	2.78921
$799$	−10.9338	−0.386810
$800$	66.3274	2.34503
$801$	11.0436	0.390208
$802$	79.2820	2.79954
$803$	−0.267803	−0.00945056
$804$	38.3822	1.35364
$805$	−28.1922	−0.993645
$806$	54.3919	1.91587
$807$	−53.0011	−1.86573
$808$	85.3878	3.00393
$809$	−45.9333	−1.61493	−0.807464	−	0.589917i	$-0.799160\pi$
$809$	−45.9333	−1.61493	−0.807464	+	0.589917i	$0.799160\pi$
$810$	16.9718	0.596328
$811$	−15.7293	−0.552332	−0.276166	−	0.961110i	$-0.589064\pi$
$811$	−15.7293	−0.552332	−0.276166	+	0.961110i	$0.589064\pi$
$812$	99.7435	3.50031
$813$	1.97889	0.0694028
$814$	2.51340	0.0880945
$815$	−12.9501	−0.453621
$816$	−109.232	−3.82389
$817$	−13.0535	−0.456684
$818$	53.7433	1.87909
$819$	40.3417	1.40965
$820$	−24.1313	−0.842702
$821$	−38.3149	−1.33720	−0.668600	−	0.743623i	$-0.733106\pi$
$821$	−38.3149	−1.33720	−0.668600	+	0.743623i	$0.733106\pi$
$822$	154.850	5.40100
$823$	−4.23167	−0.147507	−0.0737535	−	0.997277i	$-0.523498\pi$
$823$	−4.23167	−0.147507	−0.0737535	+	0.997277i	$0.523498\pi$
$824$	81.8669	2.85197
$825$	−1.83938	−0.0640389
$826$	−27.3318	−0.950995
$827$	−32.8601	−1.14266	−0.571329	−	0.820721i	$-0.693572\pi$
$827$	−32.8601	−1.14266	−0.571329	+	0.820721i	$0.693572\pi$
$828$	149.669	5.20137
$829$	28.8688	1.00266	0.501328	−	0.865258i	$-0.332845\pi$
$829$	28.8688	1.00266	0.501328	+	0.865258i	$0.332845\pi$
$830$	−48.3574	−1.67851
$831$	−44.9482	−1.55924
$832$	−63.1098	−2.18794
$833$	−16.4817	−0.571058
$834$	24.1269	0.835445
$835$	10.0736	0.348613
$836$	3.10666	0.107446
$837$	14.5431	0.502684
$838$	−94.8462	−3.27641
$839$	19.6198	0.677352	0.338676	−	0.940903i	$-0.390021\pi$
$839$	19.6198	0.677352	0.338676	+	0.940903i	$0.390021\pi$
$840$	85.8885	2.96344
$841$	1.02615	0.0353844
$842$	−11.8680	−0.408997
$843$	35.8325	1.23414
$844$	17.3021	0.595563
$845$	−4.17246	−0.143537
$846$	−34.8534	−1.19829
$847$	38.1407	1.31053
$848$	−133.170	−4.57306
$849$	19.0689	0.654443
$850$	−33.2222	−1.13951
$851$	−37.8538	−1.29761
$852$	139.773	4.78854
$853$	−28.8996	−0.989504	−0.494752	−	0.869034i	$-0.664741\pi$
$853$	−28.8996	−0.989504	−0.494752	+	0.869034i	$0.664741\pi$
$854$	95.0970	3.25415
$855$	13.4158	0.458811
$856$	4.84581	0.165626
$857$	10.9834	0.375187	0.187593	−	0.982247i	$-0.439931\pi$
$857$	10.9834	0.375187	0.187593	+	0.982247i	$0.439931\pi$
$858$	3.91933	0.133804
$859$	−25.7484	−0.878525	−0.439262	−	0.898359i	$-0.644760\pi$
$859$	−25.7484	−0.878525	−0.439262	+	0.898359i	$0.644760\pi$
$860$	−23.0301	−0.785319
$861$	38.5892	1.31512
$862$	33.0443	1.12549
$863$	−39.7170	−1.35198	−0.675992	−	0.736909i	$-0.736284\pi$
$863$	−39.7170	−1.35198	−0.675992	+	0.736909i	$0.736284\pi$
$864$	−37.7883	−1.28558
$865$	19.1797	0.652129
$866$	49.3291	1.67627
$867$	−17.1041	−0.580887
$868$	−121.638	−4.12866
$869$	−3.02399	−0.102582
$870$	41.8472	1.41875
$871$	−8.49111	−0.287710
$872$	65.5058	2.21831
$873$	−33.9901	−1.15039
$874$	−64.6690	−2.18746
$875$	33.3236	1.12654
$876$	−19.8878	−0.671945
$877$	36.5063	1.23273	0.616365	−	0.787460i	$-0.288604\pi$
$877$	36.5063	1.23273	0.616365	+	0.787460i	$0.288604\pi$
$878$	−74.6513	−2.51936
$879$	−47.0420	−1.58669
$880$	2.58602	0.0871747
$881$	−42.0841	−1.41785	−0.708925	−	0.705284i	$-0.750819\pi$
$881$	−42.0841	−1.41785	−0.708925	+	0.705284i	$0.750819\pi$
$882$	−52.5384	−1.76906
$883$	−10.0719	−0.338945	−0.169473	−	0.985535i	$-0.554206\pi$
$883$	−10.0719	−0.338945	−0.169473	+	0.985535i	$0.554206\pi$
$884$	51.2171	1.72262
$885$	−8.29651	−0.278884
$886$	−45.7993	−1.53866
$887$	9.93382	0.333545	0.166773	−	0.985995i	$-0.446665\pi$
$887$	9.93382	0.333545	0.166773	+	0.985995i	$0.446665\pi$
$888$	115.323	3.86998
$889$	55.1820	1.85075
$890$	−8.41868	−0.282195
$891$	−1.07010	−0.0358496
$892$	−17.2216	−0.576620
$893$	10.8957	0.364610
$894$	−61.1196	−2.04415
$895$	10.9111	0.364719
$896$	74.2862	2.48173
$897$	−59.0283	−1.97090
$898$	4.77929	0.159487
$899$	−36.6171	−1.22125
$900$	−76.6211	−2.55404
$901$	33.3222	1.11012
$902$	2.10296	0.0700210
$903$	36.8282	1.22557
$904$	51.3424	1.70762
$905$	2.51881	0.0837281
$906$	−103.705	−3.44536
$907$	41.0297	1.36237	0.681185	−	0.732112i	$-0.261465\pi$
$907$	41.0297	1.36237	0.681185	+	0.732112i	$0.261465\pi$
$908$	24.6000	0.816379
$909$	−37.6297	−1.24810
$910$	−30.7529	−1.01945
$911$	−45.6536	−1.51257	−0.756286	−	0.654241i	$-0.772988\pi$
$911$	−45.6536	−1.51257	−0.756286	+	0.654241i	$0.772988\pi$
$912$	108.851	3.60443
$913$	3.04901	0.100907
$914$	−18.9471	−0.626715
$915$	28.8665	0.954296
$916$	−96.7611	−3.19708
$917$	50.5453	1.66915
$918$	18.9275	0.624700
$919$	55.2098	1.82120	0.910601	−	0.413286i	$-0.135619\pi$
$919$	55.2098	1.82120	0.910601	+	0.413286i	$0.135619\pi$
$920$	−70.4934	−2.32410
$921$	−26.6805	−0.879153
$922$	9.92389	0.326826
$923$	−30.9212	−1.01778
$924$	−8.76490	−0.288344
$925$	19.3787	0.637168
$926$	−9.24869	−0.303931
$927$	−36.0781	−1.18496
$928$	95.1445	3.12327
$929$	43.9234	1.44108	0.720540	−	0.693414i	$-0.243894\pi$
$929$	43.9234	1.44108	0.720540	+	0.693414i	$0.243894\pi$
$930$	−51.0330	−1.67344
$931$	16.4242	0.538283
$932$	99.3537	3.25444
$933$	78.3764	2.56593
$934$	21.1706	0.692722
$935$	−0.647084	−0.0211619
$936$	100.873	3.29713
$937$	−43.9781	−1.43670	−0.718350	−	0.695682i	$-0.755102\pi$
$937$	−43.9781	−1.43670	−0.718350	+	0.695682i	$0.755102\pi$
$938$	26.2454	0.856944
$939$	52.1731	1.70260
$940$	19.2231	0.626987
$941$	−30.8464	−1.00556	−0.502782	−	0.864413i	$-0.667690\pi$
$941$	−30.8464	−1.00556	−0.502782	+	0.864413i	$0.667690\pi$
$942$	125.085	4.07549
$943$	−31.6723	−1.03139
$944$	−37.7589	−1.22895
$945$	−8.22259	−0.267481
$946$	2.00699	0.0652529
$947$	−20.7271	−0.673542	−0.336771	−	0.941587i	$-0.609335\pi$
$947$	−20.7271	−0.673542	−0.336771	+	0.941587i	$0.609335\pi$
$948$	−224.570	−7.29369
$949$	4.39967	0.142819
$950$	33.1064	1.07411
$951$	−51.3121	−1.66391
$952$	−97.8112	−3.17008
$953$	−27.7403	−0.898597	−0.449299	−	0.893382i	$-0.648326\pi$
$953$	−27.7403	−0.898597	−0.449299	+	0.893382i	$0.648326\pi$
$954$	106.221	3.43902
$955$	2.47566	0.0801106
$956$	82.6774	2.67398
$957$	−2.63853	−0.0852915
$958$	−97.9221	−3.16372
$959$	76.6088	2.47383
$960$	59.2124	1.91107
$961$	13.6549	0.440480
$962$	−41.2920	−1.33131
$963$	−2.13551	−0.0688158
$964$	−4.48422	−0.144427
$965$	−16.5882	−0.533992
$966$	182.453	5.87031
$967$	15.9521	0.512985	0.256492	−	0.966546i	$-0.417433\pi$
$967$	15.9521	0.512985	0.256492	+	0.966546i	$0.417433\pi$
$968$	95.3692	3.06528
$969$	−27.2372	−0.874986
$970$	25.9110	0.831952
$971$	20.1914	0.647973	0.323986	−	0.946062i	$-0.394977\pi$
$971$	20.1914	0.647973	0.323986	+	0.946062i	$0.394977\pi$
$972$	−113.638	−3.64494
$973$	11.9363	0.382660
$974$	27.8513	0.892413
$975$	30.2187	0.967773
$976$	131.376	4.20526
$977$	51.7834	1.65670	0.828348	−	0.560213i	$-0.189281\pi$
$977$	51.7834	1.65670	0.828348	+	0.560213i	$0.189281\pi$
$978$	83.8094	2.67993
$979$	0.530810	0.0169648
$980$	28.9770	0.925637
$981$	−28.8679	−0.921681
$982$	19.9027	0.635122
$983$	−51.3929	−1.63918	−0.819590	−	0.572950i	$-0.805799\pi$
$983$	−51.3929	−1.63918	−0.819590	+	0.572950i	$0.805799\pi$
$984$	96.4907	3.07601
$985$	−11.4898	−0.366095
$986$	−47.6562	−1.51768
$987$	−30.7403	−0.978474
$988$	−51.0385	−1.62375
$989$	−30.2269	−0.961160
$990$	−2.06270	−0.0655568
$991$	−20.3675	−0.646995	−0.323497	−	0.946229i	$-0.604859\pi$
$991$	−20.3675	−0.646995	−0.323497	+	0.946229i	$0.604859\pi$
$992$	−116.029	−3.68394
$993$	−34.7610	−1.10311
$994$	95.5754	3.03147
$995$	−1.33694	−0.0423840
$996$	226.427	7.17463
$997$	8.30790	0.263114	0.131557	−	0.991309i	$-0.458002\pi$
$997$	8.30790	0.263114	0.131557	+	0.991309i	$0.458002\pi$
$998$	90.0932	2.85185
$999$	−11.0405	−0.349306

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4013.2.a.b.1.4	✓	157

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4013.2.a.b.1.4	✓	157	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:	\( N \)	\(=\)	\( 4013 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4013.a (trivial)

\(f(q)\)	\(=\)	\(q-2.68953 q^{2} +2.61392 q^{3} +5.23356 q^{4} +1.08630 q^{5} -7.03022 q^{6} -3.47806 q^{7} -8.69675 q^{8} +3.83259 q^{9} +O(q^{10})\)	\(q-2.68953 q^{2} +2.61392 q^{3} +5.23356 q^{4} +1.08630 q^{5} -7.03022 q^{6} -3.47806 q^{7} -8.69675 q^{8} +3.83259 q^{9} -2.92162 q^{10} +0.184213 q^{11} +13.6801 q^{12} -3.02638 q^{13} +9.35435 q^{14} +2.83949 q^{15} +12.9230 q^{16} -3.23366 q^{17} -10.3079 q^{18} +3.22238 q^{19} +5.68519 q^{20} -9.09139 q^{21} -0.495445 q^{22} +7.46180 q^{23} -22.7326 q^{24} -3.81996 q^{25} +8.13955 q^{26} +2.17632 q^{27} -18.2027 q^{28} -5.47961 q^{29} -7.63689 q^{30} +6.68243 q^{31} -17.3634 q^{32} +0.481517 q^{33} +8.69701 q^{34} -3.77820 q^{35} +20.0581 q^{36} -5.07301 q^{37} -8.66667 q^{38} -7.91073 q^{39} -9.44724 q^{40} -4.24459 q^{41} +24.4515 q^{42} -4.05089 q^{43} +0.964088 q^{44} +4.16332 q^{45} -20.0687 q^{46} +3.38125 q^{47} +33.7798 q^{48} +5.09693 q^{49} +10.2739 q^{50} -8.45252 q^{51} -15.8388 q^{52} -10.3048 q^{53} -5.85328 q^{54} +0.200109 q^{55} +30.2479 q^{56} +8.42304 q^{57} +14.7376 q^{58} -2.92183 q^{59} +14.8607 q^{60} +10.1661 q^{61} -17.9726 q^{62} -13.3300 q^{63} +20.8532 q^{64} -3.28755 q^{65} -1.29505 q^{66} +2.80569 q^{67} -16.9235 q^{68} +19.5046 q^{69} +10.1616 q^{70} +10.2172 q^{71} -33.3311 q^{72} -1.45377 q^{73} +13.6440 q^{74} -9.98508 q^{75} +16.8645 q^{76} -0.640703 q^{77} +21.2761 q^{78} -16.4158 q^{79} +14.0382 q^{80} -5.80903 q^{81} +11.4159 q^{82} +16.5516 q^{83} -47.5803 q^{84} -3.51270 q^{85} +10.8950 q^{86} -14.3233 q^{87} -1.60205 q^{88} +2.88151 q^{89} -11.1974 q^{90} +10.5260 q^{91} +39.0518 q^{92} +17.4674 q^{93} -9.09397 q^{94} +3.50045 q^{95} -45.3865 q^{96} -8.86871 q^{97} -13.7083 q^{98} +0.706011 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 157 q - 15 q^{2} - 51 q^{3} + 137 q^{4} - 13 q^{5} - 15 q^{6} - 49 q^{7} - 42 q^{8} + 144 q^{9}+O(q^{10}) \) 157 * q - 15 * q^2 - 51 * q^3 + 137 * q^4 - 13 * q^5 - 15 * q^6 - 49 * q^7 - 42 * q^8 + 144 * q^9	\( 157 q - 15 q^{2} - 51 q^{3} + 137 q^{4} - 13 q^{5} - 15 q^{6} - 49 q^{7} - 42 q^{8} + 144 q^{9} - 61 q^{10} - 27 q^{11} - 93 q^{12} - 97 q^{13} - 12 q^{14} - 36 q^{15} + 105 q^{16} - 45 q^{17} - 68 q^{18} - 128 q^{19} - 30 q^{20} - 26 q^{21} - 68 q^{22} - 41 q^{23} - 40 q^{24} + 102 q^{25} - 5 q^{26} - 189 q^{27} - 115 q^{28} - 26 q^{29} - 12 q^{30} - 88 q^{31} - 89 q^{32} - 52 q^{33} - 61 q^{34} - 87 q^{35} + 110 q^{36} - 62 q^{37} - 37 q^{38} - 20 q^{39} - 161 q^{40} - 34 q^{41} - 53 q^{42} - 254 q^{43} - 19 q^{44} - 46 q^{45} - 52 q^{46} - 76 q^{47} - 162 q^{48} + 96 q^{49} - 54 q^{50} - 76 q^{51} - 259 q^{52} - 48 q^{53} - 12 q^{54} - 194 q^{55} - 10 q^{56} - 30 q^{57} - 52 q^{58} - 64 q^{59} - 31 q^{60} - 107 q^{61} - 51 q^{62} - 106 q^{63} + 54 q^{64} - 17 q^{65} - 13 q^{66} - 193 q^{67} - 118 q^{68} - 55 q^{69} - 86 q^{70} - 11 q^{71} - 172 q^{72} - 173 q^{73} - 11 q^{74} - 209 q^{75} - 213 q^{76} - 84 q^{77} - 30 q^{78} - 111 q^{79} - 6 q^{80} + 157 q^{81} - 117 q^{82} - 154 q^{83} - 6 q^{84} - 91 q^{85} + 28 q^{86} - 165 q^{87} - 165 q^{88} - 32 q^{89} - 103 q^{90} - 200 q^{91} - 86 q^{92} - 39 q^{93} - 118 q^{94} - 22 q^{95} - 28 q^{96} - 151 q^{97} - 38 q^{98} - 91 q^{99}+O(q^{100}) \) 157 * q - 15 * q^2 - 51 * q^3 + 137 * q^4 - 13 * q^5 - 15 * q^6 - 49 * q^7 - 42 * q^8 + 144 * q^9 - 61 * q^10 - 27 * q^11 - 93 * q^12 - 97 * q^13 - 12 * q^14 - 36 * q^15 + 105 * q^16 - 45 * q^17 - 68 * q^18 - 128 * q^19 - 30 * q^20 - 26 * q^21 - 68 * q^22 - 41 * q^23 - 40 * q^24 + 102 * q^25 - 5 * q^26 - 189 * q^27 - 115 * q^28 - 26 * q^29 - 12 * q^30 - 88 * q^31 - 89 * q^32 - 52 * q^33 - 61 * q^34 - 87 * q^35 + 110 * q^36 - 62 * q^37 - 37 * q^38 - 20 * q^39 - 161 * q^40 - 34 * q^41 - 53 * q^42 - 254 * q^43 - 19 * q^44 - 46 * q^45 - 52 * q^46 - 76 * q^47 - 162 * q^48 + 96 * q^49 - 54 * q^50 - 76 * q^51 - 259 * q^52 - 48 * q^53 - 12 * q^54 - 194 * q^55 - 10 * q^56 - 30 * q^57 - 52 * q^58 - 64 * q^59 - 31 * q^60 - 107 * q^61 - 51 * q^62 - 106 * q^63 + 54 * q^64 - 17 * q^65 - 13 * q^66 - 193 * q^67 - 118 * q^68 - 55 * q^69 - 86 * q^70 - 11 * q^71 - 172 * q^72 - 173 * q^73 - 11 * q^74 - 209 * q^75 - 213 * q^76 - 84 * q^77 - 30 * q^78 - 111 * q^79 - 6 * q^80 + 157 * q^81 - 117 * q^82 - 154 * q^83 - 6 * q^84 - 91 * q^85 + 28 * q^86 - 165 * q^87 - 165 * q^88 - 32 * q^89 - 103 * q^90 - 200 * q^91 - 86 * q^92 - 39 * q^93 - 118 * q^94 - 22 * q^95 - 28 * q^96 - 151 * q^97 - 38 * q^98 - 91 * q^99

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