LMFDB - Embedded newform 717.4.a.b.1.27

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [717,4,Mod(1,717)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(717, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("717.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 717 = 3 \cdot 239 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	717.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:	$42.3043694741$
Analytic rank:	$1$
Dimension:	$28$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.27
Character	$\chi$	$=$	717.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.86739 q^{2} -3.00000 q^{3} +15.6914 q^{4} -12.8877 q^{5} -14.6022 q^{6} +25.7021 q^{7} +37.4372 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+4.86739 q^{2} -3.00000 q^{3} +15.6914 q^{4} -12.8877 q^{5} -14.6022 q^{6} +25.7021 q^{7} +37.4372 q^{8} +9.00000 q^{9} -62.7292 q^{10} -53.1026 q^{11} -47.0743 q^{12} -81.7543 q^{13} +125.102 q^{14} +38.6630 q^{15} +56.6898 q^{16} +36.6803 q^{17} +43.8065 q^{18} +7.96807 q^{19} -202.226 q^{20} -77.1062 q^{21} -258.471 q^{22} -53.4635 q^{23} -112.312 q^{24} +41.0919 q^{25} -397.930 q^{26} -27.0000 q^{27} +403.302 q^{28} +104.112 q^{29} +188.188 q^{30} +18.8604 q^{31} -23.5667 q^{32} +159.308 q^{33} +178.537 q^{34} -331.240 q^{35} +141.223 q^{36} -258.224 q^{37} +38.7837 q^{38} +245.263 q^{39} -482.478 q^{40} -136.879 q^{41} -375.306 q^{42} -430.798 q^{43} -833.256 q^{44} -115.989 q^{45} -260.228 q^{46} +11.3640 q^{47} -170.069 q^{48} +317.596 q^{49} +200.010 q^{50} -110.041 q^{51} -1282.84 q^{52} -307.139 q^{53} -131.419 q^{54} +684.368 q^{55} +962.213 q^{56} -23.9042 q^{57} +506.752 q^{58} +706.161 q^{59} +606.678 q^{60} -507.467 q^{61} +91.8008 q^{62} +231.319 q^{63} -568.226 q^{64} +1053.62 q^{65} +775.412 q^{66} -552.177 q^{67} +575.566 q^{68} +160.391 q^{69} -1612.27 q^{70} +986.525 q^{71} +336.935 q^{72} +144.680 q^{73} -1256.88 q^{74} -123.276 q^{75} +125.031 q^{76} -1364.85 q^{77} +1193.79 q^{78} -507.444 q^{79} -730.599 q^{80} +81.0000 q^{81} -666.242 q^{82} -502.367 q^{83} -1209.91 q^{84} -472.723 q^{85} -2096.86 q^{86} -312.335 q^{87} -1988.01 q^{88} +1430.11 q^{89} -564.563 q^{90} -2101.26 q^{91} -838.920 q^{92} -56.5812 q^{93} +55.3129 q^{94} -102.690 q^{95} +70.7001 q^{96} -1299.67 q^{97} +1545.86 q^{98} -477.923 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 5 q^{2} - 84 q^{3} + 103 q^{4} + 6 q^{5} + 15 q^{6} - 68 q^{7} - 39 q^{8} + 252 q^{9}+O(q^{10}) $ 28 * q - 5 * q^2 - 84 * q^3 + 103 * q^4 + 6 * q^5 + 15 * q^6 - 68 * q^7 - 39 * q^8 + 252 * q^9	\( 28 q - 5 q^{2} - 84 q^{3} + 103 q^{4} + 6 q^{5} + 15 q^{6} - 68 q^{7} - 39 q^{8} + 252 q^{9} - 88 q^{10} - 110 q^{11} - 309 q^{12} - 82 q^{13} + 126 q^{14} - 18 q^{15} + 271 q^{16} + 100 q^{17} - 45 q^{18} - 292 q^{19} - 52 q^{20} + 204 q^{21} - 351 q^{22} - 276 q^{23} + 117 q^{24} + 386 q^{25} + 84 q^{26} - 756 q^{27} - 1010 q^{28} - 38 q^{29} + 264 q^{30} - 432 q^{31} - 452 q^{32} + 330 q^{33} - 524 q^{34} - 166 q^{35} + 927 q^{36} - 936 q^{37} - 41 q^{38} + 246 q^{39} - 1183 q^{40} + 1054 q^{41} - 378 q^{42} - 1804 q^{43} - 341 q^{44} + 54 q^{45} - 888 q^{46} - 560 q^{47} - 813 q^{48} + 1074 q^{49} - 1054 q^{50} - 300 q^{51} - 632 q^{52} - 160 q^{53} + 135 q^{54} - 842 q^{55} + 509 q^{56} + 876 q^{57} - 1266 q^{58} + 846 q^{59} + 156 q^{60} - 2220 q^{61} + 82 q^{62} - 612 q^{63} - 1565 q^{64} + 296 q^{65} + 1053 q^{66} - 4752 q^{67} - 1719 q^{68} + 828 q^{69} - 5601 q^{70} - 802 q^{71} - 351 q^{72} - 2732 q^{73} - 4581 q^{74} - 1158 q^{75} - 5614 q^{76} - 1008 q^{77} - 252 q^{78} - 3172 q^{79} - 732 q^{80} + 2268 q^{81} - 9709 q^{82} - 4780 q^{83} + 3030 q^{84} - 4624 q^{85} - 2009 q^{86} + 114 q^{87} - 9331 q^{88} + 4372 q^{89} - 792 q^{90} - 7398 q^{91} - 6138 q^{92} + 1296 q^{93} - 7068 q^{94} - 3160 q^{95} + 1356 q^{96} - 4846 q^{97} - 3772 q^{98} - 990 q^{99}+O(q^{100}) \) 28 * q - 5 * q^2 - 84 * q^3 + 103 * q^4 + 6 * q^5 + 15 * q^6 - 68 * q^7 - 39 * q^8 + 252 * q^9 - 88 * q^10 - 110 * q^11 - 309 * q^12 - 82 * q^13 + 126 * q^14 - 18 * q^15 + 271 * q^16 + 100 * q^17 - 45 * q^18 - 292 * q^19 - 52 * q^20 + 204 * q^21 - 351 * q^22 - 276 * q^23 + 117 * q^24 + 386 * q^25 + 84 * q^26 - 756 * q^27 - 1010 * q^28 - 38 * q^29 + 264 * q^30 - 432 * q^31 - 452 * q^32 + 330 * q^33 - 524 * q^34 - 166 * q^35 + 927 * q^36 - 936 * q^37 - 41 * q^38 + 246 * q^39 - 1183 * q^40 + 1054 * q^41 - 378 * q^42 - 1804 * q^43 - 341 * q^44 + 54 * q^45 - 888 * q^46 - 560 * q^47 - 813 * q^48 + 1074 * q^49 - 1054 * q^50 - 300 * q^51 - 632 * q^52 - 160 * q^53 + 135 * q^54 - 842 * q^55 + 509 * q^56 + 876 * q^57 - 1266 * q^58 + 846 * q^59 + 156 * q^60 - 2220 * q^61 + 82 * q^62 - 612 * q^63 - 1565 * q^64 + 296 * q^65 + 1053 * q^66 - 4752 * q^67 - 1719 * q^68 + 828 * q^69 - 5601 * q^70 - 802 * q^71 - 351 * q^72 - 2732 * q^73 - 4581 * q^74 - 1158 * q^75 - 5614 * q^76 - 1008 * q^77 - 252 * q^78 - 3172 * q^79 - 732 * q^80 + 2268 * q^81 - 9709 * q^82 - 4780 * q^83 + 3030 * q^84 - 4624 * q^85 - 2009 * q^86 + 114 * q^87 - 9331 * q^88 + 4372 * q^89 - 792 * q^90 - 7398 * q^91 - 6138 * q^92 + 1296 * q^93 - 7068 * q^94 - 3160 * q^95 + 1356 * q^96 - 4846 * q^97 - 3772 * q^98 - 990 * 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 $

$2$	4.86739	1.72088	0.860440	−	0.509551i	$-0.170189\pi$
$2$	4.86739	1.72088	0.860440	+	0.509551i	$0.170189\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	15.6914	1.96143
$5$	−12.8877	−1.15271	−0.576354	−	0.817200i	$-0.695525\pi$
$5$	−12.8877	−1.15271	−0.576354	+	0.817200i	$0.695525\pi$
$6$	−14.6022	−0.993551
$7$	25.7021	1.38778	0.693891	−	0.720080i	$-0.255895\pi$
$7$	25.7021	1.38778	0.693891	+	0.720080i	$0.255895\pi$
$8$	37.4372	1.65451
$9$	9.00000	0.333333
$10$	−62.7292	−1.98367
$11$	−53.1026	−1.45555	−0.727774	−	0.685817i	$-0.759445\pi$
$11$	−53.1026	−1.45555	−0.727774	+	0.685817i	$0.759445\pi$
$12$	−47.0743	−1.13243
$13$	−81.7543	−1.74420	−0.872099	−	0.489329i	$-0.837242\pi$
$13$	−81.7543	−1.74420	−0.872099	+	0.489329i	$0.837242\pi$
$14$	125.102	2.38821
$15$	38.6630	0.665516
$16$	56.6898	0.885777
$17$	36.6803	0.523310	0.261655	−	0.965161i	$-0.415732\pi$
$17$	36.6803	0.523310	0.261655	+	0.965161i	$0.415732\pi$
$18$	43.8065	0.573627
$19$	7.96807	0.0962106	0.0481053	−	0.998842i	$-0.484682\pi$
$19$	7.96807	0.0962106	0.0481053	+	0.998842i	$0.484682\pi$
$20$	−202.226	−2.26096
$21$	−77.1062	−0.801236
$22$	−258.471	−2.50482
$23$	−53.4635	−0.484692	−0.242346	−	0.970190i	$-0.577917\pi$
$23$	−53.4635	−0.484692	−0.242346	+	0.970190i	$0.577917\pi$
$24$	−112.312	−0.955230
$25$	41.0919	0.328735
$26$	−397.930	−3.00156
$27$	−27.0000	−0.192450
$28$	403.302	2.72204
$29$	104.112	0.666657	0.333329	−	0.942811i	$-0.391828\pi$
$29$	104.112	0.666657	0.333329	+	0.942811i	$0.391828\pi$
$30$	188.188	1.14527
$31$	18.8604	0.109272	0.0546359	−	0.998506i	$-0.482600\pi$
$31$	18.8604	0.109272	0.0546359	+	0.998506i	$0.482600\pi$
$32$	−23.5667	−0.130189
$33$	159.308	0.840361
$34$	178.537	0.900554
$35$	−331.240	−1.59971
$36$	141.223	0.653810
$37$	−258.224	−1.14734	−0.573672	−	0.819085i	$-0.694482\pi$
$37$	−258.224	−1.14734	−0.573672	+	0.819085i	$0.694482\pi$
$38$	38.7837	0.165567
$39$	245.263	1.00701
$40$	−482.478	−1.90716
$41$	−136.879	−0.521388	−0.260694	−	0.965422i	$-0.583951\pi$
$41$	−136.879	−0.521388	−0.260694	+	0.965422i	$0.583951\pi$
$42$	−375.306	−1.37883
$43$	−430.798	−1.52782	−0.763908	−	0.645325i	$-0.776722\pi$
$43$	−430.798	−1.52782	−0.763908	+	0.645325i	$0.776722\pi$
$44$	−833.256	−2.85496
$45$	−115.989	−0.384236
$46$	−260.228	−0.834097
$47$	11.3640	0.0352682	0.0176341	−	0.999845i	$-0.494387\pi$
$47$	11.3640	0.0352682	0.0176341	+	0.999845i	$0.494387\pi$
$48$	−170.069	−0.511404
$49$	317.596	0.925937
$50$	200.010	0.565714
$51$	−110.041	−0.302133
$52$	−1282.84	−3.42112
$53$	−307.139	−0.796015	−0.398008	−	0.917382i	$-0.630298\pi$
$53$	−307.139	−0.796015	−0.398008	+	0.917382i	$0.630298\pi$
$54$	−131.419	−0.331184
$55$	684.368	1.67782
$56$	962.213	2.29609
$57$	−23.9042	−0.0555472
$58$	506.752	1.14724
$59$	706.161	1.55821	0.779105	−	0.626894i	$-0.215674\pi$
$59$	706.161	1.55821	0.779105	+	0.626894i	$0.215674\pi$
$60$	606.678	1.30536
$61$	−507.467	−1.06516	−0.532578	−	0.846381i	$-0.678777\pi$
$61$	−507.467	−1.06516	−0.532578	+	0.846381i	$0.678777\pi$
$62$	91.8008	0.188044
$63$	231.319	0.462594
$64$	−568.226	−1.10982
$65$	1053.62	2.01055
$66$	775.412	1.44616
$67$	−552.177	−1.00685	−0.503426	−	0.864038i	$-0.667928\pi$
$67$	−552.177	−1.00685	−0.503426	+	0.864038i	$0.667928\pi$
$68$	575.566	1.02644
$69$	160.391	0.279837
$70$	−1612.27	−2.75290
$71$	986.525	1.64900	0.824500	−	0.565862i	$-0.191456\pi$
$71$	986.525	1.64900	0.824500	+	0.565862i	$0.191456\pi$
$72$	336.935	0.551502
$73$	144.680	0.231966	0.115983	−	0.993251i	$-0.462998\pi$
$73$	144.680	0.231966	0.115983	+	0.993251i	$0.462998\pi$
$74$	−1256.88	−1.97444
$75$	−123.276	−0.189795
$76$	125.031	0.188710
$77$	−1364.85	−2.01998
$78$	1193.79	1.73295
$79$	−507.444	−0.722683	−0.361341	−	0.932434i	$-0.617681\pi$
$79$	−507.444	−0.722683	−0.361341	+	0.932434i	$0.617681\pi$
$80$	−730.599	−1.02104
$81$	81.0000	0.111111
$82$	−666.242	−0.897246
$83$	−502.367	−0.664361	−0.332180	−	0.943216i	$-0.607784\pi$
$83$	−502.367	−0.664361	−0.332180	+	0.943216i	$0.607784\pi$
$84$	−1209.91	−1.57157
$85$	−472.723	−0.603223
$86$	−2096.86	−2.62919
$87$	−312.335	−0.384895
$88$	−1988.01	−2.40821
$89$	1430.11	1.70327	0.851635	−	0.524135i	$-0.175611\pi$
$89$	1430.11	1.70327	0.851635	+	0.524135i	$0.175611\pi$
$90$	−564.563	−0.661224
$91$	−2101.26	−2.42057
$92$	−838.920	−0.950689
$93$	−56.5812	−0.0630881
$94$	55.3129	0.0606924
$95$	−102.690	−0.110903
$96$	70.7001	0.0751646
$97$	−1299.67	−1.36043	−0.680215	−	0.733012i	$-0.738114\pi$
$97$	−1299.67	−1.36043	−0.680215	+	0.733012i	$0.738114\pi$
$98$	1545.86	1.59343
$99$	−477.923	−0.485183
$100$	644.791	0.644791
$101$	753.294	0.742134	0.371067	−	0.928606i	$-0.378992\pi$
$101$	753.294	0.742134	0.371067	+	0.928606i	$0.378992\pi$
$102$	−535.611	−0.519935
$103$	295.212	0.282409	0.141204	−	0.989980i	$-0.454903\pi$
$103$	295.212	0.282409	0.141204	+	0.989980i	$0.454903\pi$
$104$	−3060.65	−2.88579
$105$	993.719	0.923591
$106$	−1494.97	−1.36985
$107$	−176.010	−0.159024	−0.0795120	−	0.996834i	$-0.525336\pi$
$107$	−176.010	−0.159024	−0.0795120	+	0.996834i	$0.525336\pi$
$108$	−423.669	−0.377477
$109$	−616.259	−0.541532	−0.270766	−	0.962645i	$-0.587277\pi$
$109$	−616.259	−0.541532	−0.270766	+	0.962645i	$0.587277\pi$
$110$	3331.08	2.88733
$111$	774.672	0.662420
$112$	1457.04	1.22927
$113$	−1678.42	−1.39728	−0.698639	−	0.715475i	$-0.746210\pi$
$113$	−1678.42	−1.39728	−0.698639	+	0.715475i	$0.746210\pi$
$114$	−116.351	−0.0955901
$115$	689.020	0.558708
$116$	1633.66	1.30760
$117$	−735.789	−0.581399
$118$	3437.16	2.68149
$119$	942.758	0.726240
$120$	1447.43	1.10110
$121$	1488.88	1.11862
$122$	−2470.04	−1.83301
$123$	410.637	0.301023
$124$	295.947	0.214329
$125$	1081.38	0.773772
$126$	1125.92	0.796069
$127$	165.496	0.115633	0.0578164	−	0.998327i	$-0.481586\pi$
$127$	165.496	0.115633	0.0578164	+	0.998327i	$0.481586\pi$
$128$	−2577.24	−1.77967
$129$	1292.39	0.882085
$130$	5128.39	3.45992
$131$	2867.31	1.91235	0.956177	−	0.292789i	$-0.0945833\pi$
$131$	2867.31	1.91235	0.956177	+	0.292789i	$0.0945833\pi$
$132$	2499.77	1.64831
$133$	204.796	0.133519
$134$	−2687.66	−1.73267
$135$	347.967	0.221839
$136$	1373.21	0.865819
$137$	933.866	0.582377	0.291188	−	0.956666i	$-0.405949\pi$
$137$	933.866	0.582377	0.291188	+	0.956666i	$0.405949\pi$
$138$	780.683	0.481566
$139$	−1152.86	−0.703486	−0.351743	−	0.936097i	$-0.614411\pi$
$139$	−1152.86	−0.703486	−0.351743	+	0.936097i	$0.614411\pi$
$140$	−5197.63	−3.13771
$141$	−34.0919	−0.0203621
$142$	4801.80	2.83773
$143$	4341.37	2.53876
$144$	510.208	0.295259
$145$	−1341.76	−0.768461
$146$	704.214	0.399186
$147$	−952.789	−0.534590
$148$	−4051.91	−2.25044
$149$	−1155.04	−0.635064	−0.317532	−	0.948248i	$-0.602854\pi$
$149$	−1155.04	−0.635064	−0.317532	+	0.948248i	$0.602854\pi$
$150$	−600.030	−0.326615
$151$	−418.063	−0.225308	−0.112654	−	0.993634i	$-0.535935\pi$
$151$	−418.063	−0.225308	−0.112654	+	0.993634i	$0.535935\pi$
$152$	298.302	0.159181
$153$	330.122	0.174437
$154$	−6643.23	−3.47615
$155$	−243.066	−0.125958
$156$	3848.53	1.97519
$157$	786.803	0.399960	0.199980	−	0.979800i	$-0.435912\pi$
$157$	786.803	0.399960	0.199980	+	0.979800i	$0.435912\pi$
$158$	−2469.93	−1.24365
$159$	921.418	0.459580
$160$	303.720	0.150070
$161$	−1374.12	−0.672646
$162$	394.258	0.191209
$163$	3169.51	1.52304	0.761518	−	0.648143i	$-0.224454\pi$
$163$	3169.51	1.52304	0.761518	+	0.648143i	$0.224454\pi$
$164$	−2147.83	−1.02267
$165$	−2053.10	−0.968691
$166$	−2445.21	−1.14329
$167$	3646.16	1.68951	0.844757	−	0.535151i	$-0.179745\pi$
$167$	3646.16	1.68951	0.844757	+	0.535151i	$0.179745\pi$
$168$	−2886.64	−1.32565
$169$	4486.77	2.04223
$170$	−2300.92	−1.03808
$171$	71.7126	0.0320702
$172$	−6759.84	−2.99670
$173$	2371.65	1.04227	0.521137	−	0.853473i	$-0.325508\pi$
$173$	2371.65	1.04227	0.521137	+	0.853473i	$0.325508\pi$
$174$	−1520.26	−0.662358
$175$	1056.15	0.456213
$176$	−3010.37	−1.28929
$177$	−2118.48	−0.899633
$178$	6960.88	2.93113
$179$	547.509	0.228618	0.114309	−	0.993445i	$-0.463535\pi$
$179$	547.509	0.228618	0.114309	+	0.993445i	$0.463535\pi$
$180$	−1820.03	−0.753652
$181$	−4221.82	−1.73373	−0.866866	−	0.498541i	$-0.833869\pi$
$181$	−4221.82	−1.73373	−0.866866	+	0.498541i	$0.833869\pi$
$182$	−10227.6	−4.16550
$183$	1522.40	0.614968
$184$	−2001.52	−0.801926
$185$	3327.90	1.32255
$186$	−275.402	−0.108567
$187$	−1947.82	−0.761703
$188$	178.317	0.0691762
$189$	−693.956	−0.267079
$190$	−499.831	−0.190850
$191$	668.362	0.253199	0.126599	−	0.991954i	$-0.459594\pi$
$191$	668.362	0.253199	0.126599	+	0.991954i	$0.459594\pi$
$192$	1704.68	0.640753
$193$	713.345	0.266050	0.133025	−	0.991113i	$-0.457531\pi$
$193$	713.345	0.266050	0.133025	+	0.991113i	$0.457531\pi$
$194$	−6326.01	−2.34114
$195$	−3160.87	−1.16079
$196$	4983.54	1.81616
$197$	−4019.98	−1.45387	−0.726933	−	0.686708i	$-0.759055\pi$
$197$	−4019.98	−1.45387	−0.726933	+	0.686708i	$0.759055\pi$
$198$	−2326.24	−0.834942
$199$	5076.26	1.80827	0.904136	−	0.427244i	$-0.140515\pi$
$199$	5076.26	1.80827	0.904136	+	0.427244i	$0.140515\pi$
$200$	1538.37	0.543894
$201$	1656.53	0.581307
$202$	3666.57	1.27712
$203$	2675.89	0.925175
$204$	−1726.70	−0.592613
$205$	1764.05	0.601007
$206$	1436.91	0.485992
$207$	−481.172	−0.161564
$208$	−4634.63	−1.54497
$209$	−423.125	−0.140039
$210$	4836.81	1.58939
$211$	3896.66	1.27136	0.635681	−	0.771952i	$-0.280719\pi$
$211$	3896.66	1.27136	0.635681	+	0.771952i	$0.280719\pi$
$212$	−4819.46	−1.56133
$213$	−2959.58	−0.952051
$214$	−856.710	−0.273661
$215$	5551.98	1.76113
$216$	−1010.80	−0.318410
$217$	484.751	0.151645
$218$	−2999.57	−0.931911
$219$	−434.041	−0.133926
$220$	10738.7	3.29093
$221$	−2998.77	−0.912756
$222$	3770.63	1.13995
$223$	−3340.77	−1.00320	−0.501601	−	0.865099i	$-0.667256\pi$
$223$	−3340.77	−1.00320	−0.501601	+	0.865099i	$0.667256\pi$
$224$	−605.713	−0.180674
$225$	369.827	0.109578
$226$	−8169.51	−2.40455
$227$	−5858.55	−1.71298	−0.856488	−	0.516166i	$-0.827359\pi$
$227$	−5858.55	−1.71298	−0.856488	+	0.516166i	$0.827359\pi$
$228$	−375.092	−0.108952
$229$	3218.01	0.928613	0.464306	−	0.885675i	$-0.346304\pi$
$229$	3218.01	0.928613	0.464306	+	0.885675i	$0.346304\pi$
$230$	3353.73	0.961470
$231$	4094.54	1.16624
$232$	3897.65	1.10299
$233$	88.1635	0.0247888	0.0123944	−	0.999923i	$-0.496055\pi$
$233$	88.1635	0.0247888	0.0123944	+	0.999923i	$0.496055\pi$
$234$	−3581.37	−1.00052
$235$	−146.455	−0.0406540
$236$	11080.7	3.05632
$237$	1522.33	0.417241
$238$	4588.77	1.24977
$239$	239.000	0.0646846
$239$	239.000	0.0646846
$240$	2191.80	0.589499
$241$	2475.88	0.661766	0.330883	−	0.943672i	$-0.392653\pi$
$241$	2475.88	0.661766	0.330883	+	0.943672i	$0.392653\pi$
$242$	7246.97	1.92501
$243$	−243.000	−0.0641500
$244$	−7962.89	−2.08923
$245$	−4093.08	−1.06733
$246$	1998.73	0.518025
$247$	−651.424	−0.167810
$248$	706.080	0.180791
$249$	1507.10	0.383569
$250$	5263.49	1.33157
$251$	4657.91	1.17133	0.585667	−	0.810552i	$-0.300833\pi$
$251$	4657.91	1.17133	0.585667	+	0.810552i	$0.300833\pi$
$252$	3629.72	0.907345
$253$	2839.05	0.705493
$254$	805.531	0.198990
$255$	1418.17	0.348271
$256$	−7998.62	−1.95279
$257$	−5892.92	−1.43031	−0.715156	−	0.698965i	$-0.753644\pi$
$257$	−5892.92	−1.43031	−0.715156	+	0.698965i	$0.753644\pi$
$258$	6290.58	1.51796
$259$	−6636.89	−1.59226
$260$	16532.9	3.94355
$261$	937.006	0.222219
$262$	13956.3	3.29093
$263$	−4062.87	−0.952575	−0.476288	−	0.879289i	$-0.658018\pi$
$263$	−4062.87	−0.952575	−0.476288	+	0.879289i	$0.658018\pi$
$264$	5964.04	1.39038
$265$	3958.31	0.917573
$266$	996.821	0.229771
$267$	−4290.32	−0.983384
$268$	−8664.45	−1.97487
$269$	−2492.51	−0.564949	−0.282474	−	0.959275i	$-0.591155\pi$
$269$	−2492.51	−0.564949	−0.282474	+	0.959275i	$0.591155\pi$
$270$	1693.69	0.381758
$271$	−5129.98	−1.14990	−0.574952	−	0.818187i	$-0.694979\pi$
$271$	−5129.98	−1.14990	−0.574952	+	0.818187i	$0.694979\pi$
$272$	2079.39	0.463536
$273$	6303.77	1.39751
$274$	4545.49	1.00220
$275$	−2182.09	−0.478490
$276$	2516.76	0.548881
$277$	7795.14	1.69085	0.845423	−	0.534097i	$-0.179348\pi$
$277$	7795.14	1.69085	0.845423	+	0.534097i	$0.179348\pi$
$278$	−5611.43	−1.21062
$279$	169.743	0.0364239
$280$	−12400.7	−2.64672
$281$	−1814.02	−0.385109	−0.192555	−	0.981286i	$-0.561677\pi$
$281$	−1814.02	−0.385109	−0.192555	+	0.981286i	$0.561677\pi$
$282$	−165.939	−0.0350408
$283$	−281.625	−0.0591550	−0.0295775	−	0.999562i	$-0.509416\pi$
$283$	−281.625	−0.0591550	−0.0295775	+	0.999562i	$0.509416\pi$
$284$	15480.0	3.23440
$285$	308.070	0.0640297
$286$	21131.1	4.36891
$287$	−3518.07	−0.723572
$288$	−212.100	−0.0433963
$289$	−3567.56	−0.726147
$290$	−6530.85	−1.32243
$291$	3899.02	0.785445
$292$	2270.24	0.454986
$293$	−625.851	−0.124787	−0.0623936	−	0.998052i	$-0.519873\pi$
$293$	−625.851	−0.124787	−0.0623936	+	0.998052i	$0.519873\pi$
$294$	−4637.59	−0.919965
$295$	−9100.77	−1.79616
$296$	−9667.18	−1.89829
$297$	1433.77	0.280120
$298$	−5622.03	−1.09287
$299$	4370.88	0.845399
$300$	−1934.37	−0.372270
$301$	−11072.4	−2.12027
$302$	−2034.88	−0.387728
$303$	−2259.88	−0.428471
$304$	451.708	0.0852212
$305$	6540.07	1.22781
$306$	1606.83	0.300185
$307$	3498.07	0.650311	0.325155	−	0.945661i	$-0.394583\pi$
$307$	3498.07	0.650311	0.325155	+	0.945661i	$0.394583\pi$
$308$	−21416.4	−3.96205
$309$	−885.636	−0.163049
$310$	−1183.10	−0.216759
$311$	−43.1419	−0.00786609	−0.00393304	−	0.999992i	$-0.501252\pi$
$311$	−43.1419	−0.00786609	−0.00393304	+	0.999992i	$0.501252\pi$
$312$	9181.96	1.66611
$313$	−11030.1	−1.99188	−0.995942	−	0.0900000i	$-0.971313\pi$
$313$	−11030.1	−1.99188	−0.995942	+	0.0900000i	$0.971313\pi$
$314$	3829.67	0.688283
$315$	−2981.16	−0.533235
$316$	−7962.53	−1.41749
$317$	1750.06	0.310073	0.155036	−	0.987909i	$-0.450450\pi$
$317$	1750.06	0.310073	0.155036	+	0.987909i	$0.450450\pi$
$318$	4484.90	0.790882
$319$	−5528.60	−0.970352
$320$	7323.11	1.27929
$321$	528.031	0.0918125
$322$	−6688.39	−1.15754
$323$	292.271	0.0503480
$324$	1271.01	0.217937
$325$	−3359.44	−0.573379
$326$	15427.2	2.62096
$327$	1848.78	0.312653
$328$	−5124.36	−0.862639
$329$	292.078	0.0489446
$330$	−9993.25	−1.66700
$331$	2650.32	0.440105	0.220052	−	0.975488i	$-0.429377\pi$
$331$	2650.32	0.440105	0.220052	+	0.975488i	$0.429377\pi$
$332$	−7882.86	−1.30310
$333$	−2324.02	−0.382448
$334$	17747.3	2.90745
$335$	7116.27	1.16061
$336$	−4371.13	−0.709717
$337$	−4402.78	−0.711677	−0.355838	−	0.934548i	$-0.615805\pi$
$337$	−4402.78	−0.711677	−0.355838	+	0.934548i	$0.615805\pi$
$338$	21838.9	3.51443
$339$	5035.25	0.806718
$340$	−7417.70	−1.18318
$341$	−1001.54	−0.159050
$342$	349.053	0.0551890
$343$	−652.927	−0.102783
$344$	−16127.9	−2.52778
$345$	−2067.06	−0.322570
$346$	11543.8	1.79363
$347$	−9750.61	−1.50847	−0.754237	−	0.656602i	$-0.771993\pi$
$347$	−9750.61	−1.50847	−0.754237	+	0.656602i	$0.771993\pi$
$348$	−4900.99	−0.754944
$349$	3046.79	0.467309	0.233655	−	0.972320i	$-0.424932\pi$
$349$	3046.79	0.467309	0.233655	+	0.972320i	$0.424932\pi$
$350$	5140.67	0.785087
$351$	2207.37	0.335671
$352$	1251.45	0.189496
$353$	−5209.64	−0.785499	−0.392750	−	0.919645i	$-0.628476\pi$
$353$	−5209.64	−0.785499	−0.392750	+	0.919645i	$0.628476\pi$
$354$	−10311.5	−1.54816
$355$	−12714.0	−1.90082
$356$	22440.4	3.34085
$357$	−2828.28	−0.419295
$358$	2664.93	0.393425
$359$	−5418.81	−0.796641	−0.398320	−	0.917246i	$-0.630407\pi$
$359$	−5418.81	−0.796641	−0.398320	+	0.917246i	$0.630407\pi$
$360$	−4342.30	−0.635721
$361$	−6795.51	−0.990744
$362$	−20549.2	−2.98355
$363$	−4466.65	−0.645836
$364$	−32971.7	−4.74777
$365$	−1864.59	−0.267389
$366$	7410.11	1.05829
$367$	−7155.67	−1.01777	−0.508887	−	0.860833i	$-0.669943\pi$
$367$	−7155.67	−1.01777	−0.508887	+	0.860833i	$0.669943\pi$
$368$	−3030.83	−0.429329
$369$	−1231.91	−0.173796
$370$	16198.2	2.27596
$371$	−7894.11	−1.10470
$372$	−887.840	−0.123743
$373$	12097.4	1.67930	0.839650	−	0.543128i	$-0.182760\pi$
$373$	12097.4	1.67930	0.839650	+	0.543128i	$0.182760\pi$
$374$	−9480.77	−1.31080
$375$	−3244.14	−0.446738
$376$	425.436	0.0583515
$377$	−8511.59	−1.16278
$378$	−3377.75	−0.459610
$379$	−3039.72	−0.411978	−0.205989	−	0.978554i	$-0.566041\pi$
$379$	−3039.72	−0.411978	−0.205989	+	0.978554i	$0.566041\pi$
$380$	−1611.35	−0.217528
$381$	−496.487	−0.0667606
$382$	3253.18	0.435725
$383$	10410.1	1.38886	0.694430	−	0.719560i	$-0.255657\pi$
$383$	10410.1	1.38886	0.694430	+	0.719560i	$0.255657\pi$
$384$	7731.73	1.02750
$385$	17589.7	2.32845
$386$	3472.12	0.457841
$387$	−3877.18	−0.509272
$388$	−20393.7	−2.66839
$389$	−12584.0	−1.64020	−0.820098	−	0.572223i	$-0.806081\pi$
$389$	−12584.0	−1.64020	−0.820098	+	0.572223i	$0.806081\pi$
$390$	−15385.2	−1.99758
$391$	−1961.06	−0.253644
$392$	11889.9	1.53197
$393$	−8601.94	−1.10410
$394$	−19566.8	−2.50193
$395$	6539.77	0.833042
$396$	−7499.30	−0.951652
$397$	−5015.82	−0.634098	−0.317049	−	0.948409i	$-0.602692\pi$
$397$	−5015.82	−0.634098	−0.317049	+	0.948409i	$0.602692\pi$
$398$	24708.1	3.11182
$399$	−614.388	−0.0770874
$400$	2329.49	0.291186
$401$	−10100.5	−1.25784	−0.628922	−	0.777469i	$-0.716503\pi$
$401$	−10100.5	−1.25784	−0.628922	+	0.777469i	$0.716503\pi$
$402$	8062.97	1.00036
$403$	−1541.92	−0.190592
$404$	11820.3	1.45564
$405$	−1043.90	−0.128079
$406$	13024.6	1.59212
$407$	13712.4	1.67002
$408$	−4119.62	−0.499881
$409$	−3088.69	−0.373413	−0.186706	−	0.982416i	$-0.559781\pi$
$409$	−3088.69	−0.373413	−0.186706	+	0.982416i	$0.559781\pi$
$410$	8586.31	1.03426
$411$	−2801.60	−0.336235
$412$	4632.30	0.553925
$413$	18149.8	2.16245
$414$	−2342.05	−0.278032
$415$	6474.34	0.765814
$416$	1926.68	0.227075
$417$	3458.59	0.406158
$418$	−2059.51	−0.240991
$419$	10633.0	1.23976	0.619879	−	0.784698i	$-0.287182\pi$
$419$	10633.0	1.23976	0.619879	+	0.784698i	$0.287182\pi$
$420$	15592.9	1.81156
$421$	−883.014	−0.102222	−0.0511110	−	0.998693i	$-0.516276\pi$
$421$	−883.014	−0.102222	−0.0511110	+	0.998693i	$0.516276\pi$
$422$	18966.6	2.18786
$423$	102.276	0.0117561
$424$	−11498.4	−1.31701
$425$	1507.26	0.172030
$426$	−14405.4	−1.63837
$427$	−13043.0	−1.47820
$428$	−2761.86	−0.311914
$429$	−13024.1	−1.46576
$430$	27023.6	3.03069
$431$	−1832.00	−0.204743	−0.102372	−	0.994746i	$-0.532643\pi$
$431$	−1832.00	−0.204743	−0.102372	+	0.994746i	$0.532643\pi$
$432$	−1530.62	−0.170468
$433$	11930.2	1.32409	0.662044	−	0.749465i	$-0.269689\pi$
$433$	11930.2	1.32409	0.662044	+	0.749465i	$0.269689\pi$
$434$	2359.47	0.260964
$435$	4025.27	0.443671
$436$	−9670.00	−1.06218
$437$	−426.001	−0.0466325
$438$	−2112.64	−0.230470
$439$	−13299.9	−1.44594	−0.722972	−	0.690877i	$-0.757224\pi$
$439$	−13299.9	−1.44594	−0.722972	+	0.690877i	$0.757224\pi$
$440$	25620.8	2.77597
$441$	2858.37	0.308646
$442$	−14596.2	−1.57074
$443$	8646.60	0.927341	0.463671	−	0.886008i	$-0.346532\pi$
$443$	8646.60	0.927341	0.463671	+	0.886008i	$0.346532\pi$
$444$	12155.7	1.29929
$445$	−18430.7	−1.96337
$446$	−16260.8	−1.72639
$447$	3465.12	0.366655
$448$	−14604.6	−1.54018
$449$	3986.26	0.418983	0.209492	−	0.977810i	$-0.432819\pi$
$449$	3986.26	0.418983	0.209492	+	0.977810i	$0.432819\pi$
$450$	1800.09	0.188571
$451$	7268.62	0.758905
$452$	−26336.8	−2.74066
$453$	1254.19	0.130082
$454$	−28515.8	−2.94783
$455$	27080.3	2.79020
$456$	−894.907	−0.0919032
$457$	−2207.34	−0.225941	−0.112970	−	0.993598i	$-0.536037\pi$
$457$	−2207.34	−0.225941	−0.112970	+	0.993598i	$0.536037\pi$
$458$	15663.3	1.59803
$459$	−990.367	−0.100711
$460$	10811.7	1.09587
$461$	762.547	0.0770398	0.0385199	−	0.999258i	$-0.487736\pi$
$461$	762.547	0.0770398	0.0385199	+	0.999258i	$0.487736\pi$
$462$	19929.7	2.00696
$463$	−10833.6	−1.08743	−0.543717	−	0.839268i	$-0.682984\pi$
$463$	−10833.6	−1.08743	−0.543717	+	0.839268i	$0.682984\pi$
$464$	5902.07	0.590510
$465$	729.199	0.0727221
$466$	429.126	0.0426585
$467$	−837.565	−0.0829933	−0.0414967	−	0.999139i	$-0.513213\pi$
$467$	−837.565	−0.0829933	−0.0414967	+	0.999139i	$0.513213\pi$
$468$	−11545.6	−1.14037
$469$	−14192.1	−1.39729
$470$	−712.854	−0.0699606
$471$	−2360.41	−0.230917
$472$	26436.7	2.57807
$473$	22876.5	2.22381
$474$	7409.78	0.718022
$475$	327.423	0.0316278
$476$	14793.2	1.42447
$477$	−2764.25	−0.265338
$478$	1163.31	0.111315
$479$	−12686.8	−1.21017	−0.605086	−	0.796160i	$-0.706861\pi$
$479$	−12686.8	−1.21017	−0.605086	+	0.796160i	$0.706861\pi$
$480$	−911.159	−0.0866428
$481$	21110.9	2.00120
$482$	12051.1	1.13882
$483$	4122.37	0.388353
$484$	23362.7	2.19410
$485$	16749.7	1.56818
$486$	−1182.77	−0.110395
$487$	17683.6	1.64542	0.822710	−	0.568461i	$-0.192461\pi$
$487$	17683.6	1.64542	0.822710	+	0.568461i	$0.192461\pi$
$488$	−18998.2	−1.76231
$489$	−9508.52	−0.879326
$490$	−19922.6	−1.83676
$491$	−18906.9	−1.73779	−0.868896	−	0.494995i	$-0.835170\pi$
$491$	−18906.9	−1.73779	−0.868896	+	0.494995i	$0.835170\pi$
$492$	6443.48	0.590436
$493$	3818.85	0.348868
$494$	−3170.73	−0.288781
$495$	6159.31	0.559274
$496$	1069.19	0.0967905
$497$	25355.7	2.28845
$498$	7335.64	0.660076
$499$	−4634.53	−0.415772	−0.207886	−	0.978153i	$-0.566658\pi$
$499$	−4634.53	−0.415772	−0.207886	+	0.978153i	$0.566658\pi$
$500$	16968.4	1.51770
$501$	−10938.5	−0.975441
$502$	22671.9	2.01573
$503$	−1706.15	−0.151239	−0.0756196	−	0.997137i	$-0.524093\pi$
$503$	−1706.15	−0.151239	−0.0756196	+	0.997137i	$0.524093\pi$
$504$	8659.92	0.765364
$505$	−9708.20	−0.855464
$506$	13818.8	1.21407
$507$	−13460.3	−1.17908
$508$	2596.86	0.226806
$509$	2176.83	0.189560	0.0947801	−	0.995498i	$-0.469785\pi$
$509$	2176.83	0.189560	0.0947801	+	0.995498i	$0.469785\pi$
$510$	6902.77	0.599333
$511$	3718.58	0.321918
$512$	−18314.4	−1.58084
$513$	−215.138	−0.0185157
$514$	−28683.1	−2.46140
$515$	−3804.59	−0.325535
$516$	20279.5	1.73015
$517$	−603.457	−0.0513346
$518$	−32304.3	−2.74010
$519$	−7114.96	−0.601757
$520$	39444.7	3.32647
$521$	−4692.38	−0.394581	−0.197291	−	0.980345i	$-0.563214\pi$
$521$	−4692.38	−0.394581	−0.197291	+	0.980345i	$0.563214\pi$
$522$	4560.77	0.382413
$523$	8435.46	0.705271	0.352636	−	0.935761i	$-0.385286\pi$
$523$	8435.46	0.705271	0.352636	+	0.935761i	$0.385286\pi$
$524$	44992.3	3.75095
$525$	−3168.44	−0.263394
$526$	−19775.6	−1.63927
$527$	691.804	0.0571830
$528$	9031.12	0.744373
$529$	−9308.65	−0.765074
$530$	19266.6	1.57903
$531$	6355.45	0.519403
$532$	3213.54	0.261889
$533$	11190.4	0.909403
$534$	−20882.6	−1.69229
$535$	2268.36	0.183308
$536$	−20672.0	−1.66584
$537$	−1642.53	−0.131993
$538$	−12132.0	−0.972210
$539$	−16865.2	−1.34775
$540$	5460.10	0.435121
$541$	4631.19	0.368042	0.184021	−	0.982922i	$-0.441089\pi$
$541$	4631.19	0.368042	0.184021	+	0.982922i	$0.441089\pi$
$542$	−24969.6	−1.97885
$543$	12665.5	1.00097
$544$	−864.433	−0.0681291
$545$	7942.14	0.624228
$546$	30682.9	2.40495
$547$	−15790.1	−1.23425	−0.617127	−	0.786864i	$-0.711703\pi$
$547$	−15790.1	−1.23425	−0.617127	+	0.786864i	$0.711703\pi$
$548$	14653.7	1.14229
$549$	−4567.20	−0.355052
$550$	−10621.1	−0.823424
$551$	829.570	0.0641395
$552$	6004.57	0.462992
$553$	−13042.4	−1.00293
$554$	37942.0	2.90975
$555$	−9983.71	−0.763577
$556$	−18090.1	−1.37984
$557$	−9551.34	−0.726577	−0.363288	−	0.931677i	$-0.618346\pi$
$557$	−9551.34	−0.726577	−0.363288	+	0.931677i	$0.618346\pi$
$558$	826.207	0.0626812
$559$	35219.6	2.66481
$560$	−18777.9	−1.41698
$561$	5843.45	0.439769
$562$	−8829.56	−0.662727
$563$	11113.4	0.831923	0.415962	−	0.909382i	$-0.363445\pi$
$563$	11113.4	0.831923	0.415962	+	0.909382i	$0.363445\pi$
$564$	−534.952	−0.0399389
$565$	21630.9	1.61065
$566$	−1370.78	−0.101799
$567$	2081.87	0.154198
$568$	36932.7	2.72828
$569$	−14314.8	−1.05467	−0.527336	−	0.849657i	$-0.676809\pi$
$569$	−14314.8	−1.05467	−0.527336	+	0.849657i	$0.676809\pi$
$570$	1499.49	0.110187
$571$	−176.918	−0.0129663	−0.00648317	−	0.999979i	$-0.502064\pi$
$571$	−176.918	−0.0129663	−0.00648317	+	0.999979i	$0.502064\pi$
$572$	68122.3	4.97961
$573$	−2005.09	−0.146184
$574$	−17123.8	−1.24518
$575$	−2196.92	−0.159335
$576$	−5114.04	−0.369939
$577$	20581.3	1.48494	0.742471	−	0.669878i	$-0.233654\pi$
$577$	20581.3	1.48494	0.742471	+	0.669878i	$0.233654\pi$
$578$	−17364.7	−1.24961
$579$	−2140.03	−0.153604
$580$	−21054.1	−1.50728
$581$	−12911.9	−0.921988
$582$	18978.0	1.35166
$583$	16309.9	1.15864
$584$	5416.42	0.383790
$585$	9482.60	0.670184
$586$	−3046.26	−0.214744
$587$	−22471.3	−1.58005	−0.790026	−	0.613073i	$-0.789933\pi$
$587$	−22471.3	−1.58005	−0.790026	+	0.613073i	$0.789933\pi$
$588$	−14950.6	−1.04856
$589$	150.281	0.0105131
$590$	−44296.9	−3.09098
$591$	12059.9	0.839390
$592$	−14638.7	−1.01629
$593$	−7523.03	−0.520967	−0.260484	−	0.965478i	$-0.583882\pi$
$593$	−7523.03	−0.520967	−0.260484	+	0.965478i	$0.583882\pi$
$594$	6978.71	0.482054
$595$	−12150.0	−0.837142
$596$	−18124.2	−1.24563
$597$	−15228.8	−1.04401
$598$	21274.7	1.45483
$599$	−15953.6	−1.08822	−0.544112	−	0.839013i	$-0.683133\pi$
$599$	−15953.6	−1.08822	−0.544112	+	0.839013i	$0.683133\pi$
$600$	−4615.10	−0.314018
$601$	953.599	0.0647223	0.0323612	−	0.999476i	$-0.489697\pi$
$601$	953.599	0.0647223	0.0323612	+	0.999476i	$0.489697\pi$
$602$	−53893.6	−3.64874
$603$	−4969.59	−0.335618
$604$	−6560.02	−0.441926
$605$	−19188.2	−1.28944
$606$	−10999.7	−0.737348
$607$	−27189.4	−1.81809	−0.909046	−	0.416696i	$-0.863188\pi$
$607$	−27189.4	−1.81809	−0.909046	+	0.416696i	$0.863188\pi$
$608$	−187.781	−0.0125255
$609$	−8027.66	−0.534150
$610$	31833.0	2.11292
$611$	−929.055	−0.0615148
$612$	5180.09	0.342145
$613$	26386.6	1.73857	0.869286	−	0.494309i	$-0.164579\pi$
$613$	26386.6	1.73857	0.869286	+	0.494309i	$0.164579\pi$
$614$	17026.5	1.11911
$615$	−5292.15	−0.346992
$616$	−51096.0	−3.34207
$617$	8097.91	0.528379	0.264189	−	0.964471i	$-0.414896\pi$
$617$	8097.91	0.528379	0.264189	+	0.964471i	$0.414896\pi$
$618$	−4310.73	−0.280588
$619$	−3529.62	−0.229188	−0.114594	−	0.993412i	$-0.536557\pi$
$619$	−3529.62	−0.229188	−0.114594	+	0.993412i	$0.536557\pi$
$620$	−3814.06	−0.247059
$621$	1443.52	0.0932790
$622$	−209.988	−0.0135366
$623$	36756.7	2.36377
$624$	13903.9	0.891990
$625$	−19072.9	−1.22067
$626$	−53687.9	−3.42779
$627$	1269.38	0.0808516
$628$	12346.1	0.784494
$629$	−9471.72	−0.600417
$630$	−14510.4	−0.917634
$631$	−7380.71	−0.465644	−0.232822	−	0.972519i	$-0.574796\pi$
$631$	−7380.71	−0.465644	−0.232822	+	0.972519i	$0.574796\pi$
$632$	−18997.3	−1.19568
$633$	−11690.0	−0.734021
$634$	8518.21	0.533598
$635$	−2132.85	−0.133291
$636$	14458.4	0.901433
$637$	−25964.9	−1.61502
$638$	−26909.8	−1.66986
$639$	8878.73	0.549667
$640$	33214.6	2.05144
$641$	9645.99	0.594374	0.297187	−	0.954819i	$-0.403951\pi$
$641$	9645.99	0.594374	0.297187	+	0.954819i	$0.403951\pi$
$642$	2570.13	0.157998
$643$	−27664.9	−1.69673	−0.848364	−	0.529413i	$-0.822412\pi$
$643$	−27664.9	−1.69673	−0.848364	+	0.529413i	$0.822412\pi$
$644$	−21562.0	−1.31935
$645$	−16655.9	−1.01679
$646$	1422.60	0.0866428
$647$	−15623.4	−0.949334	−0.474667	−	0.880165i	$-0.657432\pi$
$647$	−15623.4	−0.949334	−0.474667	+	0.880165i	$0.657432\pi$
$648$	3032.41	0.183834
$649$	−37499.0	−2.26805
$650$	−16351.7	−0.986717
$651$	−1454.25	−0.0875525
$652$	49734.1	2.98733
$653$	−156.806	−0.00939706	−0.00469853	−	0.999989i	$-0.501496\pi$
$653$	−156.806	−0.00939706	−0.00469853	+	0.999989i	$0.501496\pi$
$654$	8998.71	0.538039
$655$	−36953.0	−2.20439
$656$	−7759.63	−0.461833
$657$	1302.12	0.0773221
$658$	1421.66	0.0842278
$659$	6405.08	0.378614	0.189307	−	0.981918i	$-0.439376\pi$
$659$	6405.08	0.378614	0.189307	+	0.981918i	$0.439376\pi$
$660$	−32216.2	−1.90002
$661$	32471.6	1.91074	0.955369	−	0.295416i	$-0.0954582\pi$
$661$	32471.6	1.91074	0.955369	+	0.295416i	$0.0954582\pi$
$662$	12900.1	0.757368
$663$	8996.31	0.526980
$664$	−18807.2	−1.09919
$665$	−2639.34	−0.153909
$666$	−11311.9	−0.658148
$667$	−5566.18	−0.323124
$668$	57213.6	3.31386
$669$	10022.3	0.579199
$670$	34637.6	1.99727
$671$	26947.8	1.55039
$672$	1817.14	0.104312
$673$	−3967.84	−0.227264	−0.113632	−	0.993523i	$-0.536249\pi$
$673$	−3967.84	−0.227264	−0.113632	+	0.993523i	$0.536249\pi$
$674$	−21430.1	−1.22471
$675$	−1109.48	−0.0632651
$676$	70403.9	4.00569
$677$	−18433.7	−1.04648	−0.523238	−	0.852187i	$-0.675276\pi$
$677$	−18433.7	−1.04648	−0.523238	+	0.852187i	$0.675276\pi$
$678$	24508.5	1.38827
$679$	−33404.3	−1.88798
$680$	−17697.4	−0.998037
$681$	17575.7	0.988988
$682$	−4874.86	−0.273707
$683$	−10157.3	−0.569043	−0.284522	−	0.958670i	$-0.591835\pi$
$683$	−10157.3	−0.569043	−0.284522	+	0.958670i	$0.591835\pi$
$684$	1125.27	0.0629034
$685$	−12035.4	−0.671310
$686$	−3178.05	−0.176878
$687$	−9654.04	−0.536135
$688$	−24421.8	−1.35330
$689$	25110.0	1.38841
$690$	−10061.2	−0.555105
$691$	−201.380	−0.0110866	−0.00554331	−	0.999985i	$-0.501764\pi$
$691$	−201.380	−0.0110866	−0.00554331	+	0.999985i	$0.501764\pi$
$692$	37214.7	2.04435
$693$	−12283.6	−0.673328
$694$	−47460.0	−2.59590
$695$	14857.7	0.810914
$696$	−11693.0	−0.636811
$697$	−5020.75	−0.272847
$698$	14829.9	0.804183
$699$	−264.491	−0.0143118
$700$	16572.5	0.894829
$701$	−2141.29	−0.115372	−0.0576859	−	0.998335i	$-0.518372\pi$
$701$	−2141.29	−0.115372	−0.0576859	+	0.998335i	$0.518372\pi$
$702$	10744.1	0.577650
$703$	−2057.55	−0.110387
$704$	30174.3	1.61539
$705$	439.366	0.0234716
$706$	−25357.3	−1.35175
$707$	19361.2	1.02992
$708$	−33242.1	−1.76457
$709$	19332.5	1.02405	0.512023	−	0.858972i	$-0.328896\pi$
$709$	19332.5	1.02405	0.512023	+	0.858972i	$0.328896\pi$
$710$	−61884.0	−3.27108
$711$	−4567.00	−0.240894
$712$	53539.2	2.81807
$713$	−1008.34	−0.0529632
$714$	−13766.3	−0.721556
$715$	−55950.1	−2.92645
$716$	8591.20	0.448419
$717$	−717.000	−0.0373457
$718$	−26375.5	−1.37092
$719$	−15337.0	−0.795513	−0.397756	−	0.917491i	$-0.630211\pi$
$719$	−15337.0	−0.795513	−0.397756	+	0.917491i	$0.630211\pi$
$720$	−6575.39	−0.340348
$721$	7587.56	0.391922
$722$	−33076.4	−1.70495
$723$	−7427.65	−0.382071
$724$	−66246.5	−3.40059
$725$	4278.15	0.219154
$726$	−21740.9	−1.11141
$727$	20925.8	1.06753	0.533766	−	0.845632i	$-0.320776\pi$
$727$	20925.8	1.06753	0.533766	+	0.845632i	$0.320776\pi$
$728$	−78665.1	−4.00484
$729$	729.000	0.0370370
$730$	−9075.68	−0.460145
$731$	−15801.8	−0.799521
$732$	23888.7	1.20622
$733$	−21879.2	−1.10249	−0.551247	−	0.834342i	$-0.685848\pi$
$733$	−21879.2	−1.10249	−0.551247	+	0.834342i	$0.685848\pi$
$734$	−34829.4	−1.75147
$735$	12279.2	0.616226
$736$	1259.96	0.0631015
$737$	29322.0	1.46552
$738$	−5996.18	−0.299082
$739$	27062.8	1.34712	0.673560	−	0.739132i	$-0.264764\pi$
$739$	27062.8	1.34712	0.673560	+	0.739132i	$0.264764\pi$
$740$	52219.6	2.59410
$741$	1954.27	0.0968853
$742$	−38423.7	−1.90105
$743$	22905.7	1.13100	0.565498	−	0.824750i	$-0.308684\pi$
$743$	22905.7	1.13100	0.565498	+	0.824750i	$0.308684\pi$
$744$	−2118.24	−0.104380
$745$	14885.8	0.732043
$746$	58882.6	2.88987
$747$	−4521.30	−0.221454
$748$	−30564.0	−1.49403
$749$	−4523.83	−0.220690
$750$	−15790.5	−0.768782
$751$	−9357.07	−0.454653	−0.227326	−	0.973819i	$-0.572998\pi$
$751$	−9357.07	−0.454653	−0.227326	+	0.973819i	$0.572998\pi$
$752$	644.221	0.0312398
$753$	−13973.7	−0.676270
$754$	−41429.2	−2.00101
$755$	5387.86	0.259714
$756$	−10889.2	−0.523856
$757$	6910.90	0.331811	0.165906	−	0.986142i	$-0.446945\pi$
$757$	6910.90	0.331811	0.165906	+	0.986142i	$0.446945\pi$
$758$	−14795.5	−0.708965
$759$	−8517.15	−0.407316
$760$	−3844.42	−0.183489
$761$	28790.3	1.37142	0.685708	−	0.727877i	$-0.259493\pi$
$761$	28790.3	1.37142	0.685708	+	0.727877i	$0.259493\pi$
$762$	−2416.59	−0.114887
$763$	−15839.1	−0.751527
$764$	10487.6	0.496632
$765$	−4254.51	−0.201074
$766$	50670.2	2.39006
$767$	−57731.7	−2.71783
$768$	23995.9	1.12744
$769$	1494.77	0.0700945	0.0350472	−	0.999386i	$-0.488842\pi$
$769$	1494.77	0.0700945	0.0350472	+	0.999386i	$0.488842\pi$
$770$	85615.8	4.00698
$771$	17678.8	0.825791
$772$	11193.4	0.521839
$773$	−18782.4	−0.873943	−0.436971	−	0.899475i	$-0.643949\pi$
$773$	−18782.4	−0.873943	−0.436971	+	0.899475i	$0.643949\pi$
$774$	−18871.7	−0.876396
$775$	775.009	0.0359215
$776$	−48656.1	−2.25084
$777$	19910.7	0.919294
$778$	−61251.4	−2.82258
$779$	−1090.66	−0.0501630
$780$	−49598.6	−2.27681
$781$	−52387.0	−2.40020
$782$	−9545.21	−0.436491
$783$	−2811.02	−0.128298
$784$	18004.5	0.820174
$785$	−10140.1	−0.461037
$786$	−41869.0	−1.90002
$787$	−3311.15	−0.149974	−0.0749872	−	0.997184i	$-0.523892\pi$
$787$	−3311.15	−0.149974	−0.0749872	+	0.997184i	$0.523892\pi$
$788$	−63079.3	−2.85166
$789$	12188.6	0.549970
$790$	31831.6	1.43357
$791$	−43138.8	−1.93911
$792$	−17892.1	−0.802738
$793$	41487.6	1.85784
$794$	−24413.9	−1.09121
$795$	−11874.9	−0.529761
$796$	79653.8	3.54680
$797$	−18230.4	−0.810231	−0.405115	−	0.914266i	$-0.632769\pi$
$797$	−18230.4	−0.810231	−0.405115	+	0.914266i	$0.632769\pi$
$798$	−2990.46	−0.132658
$799$	416.834	0.0184562
$800$	−968.401	−0.0427977
$801$	12871.0	0.567757
$802$	−49163.1	−2.16460
$803$	−7682.89	−0.337638
$804$	25993.3	1.14019
$805$	17709.2	0.775365
$806$	−7505.11	−0.327985
$807$	7477.54	0.326173
$808$	28201.2	1.22787
$809$	30301.8	1.31688	0.658439	−	0.752634i	$-0.271217\pi$
$809$	30301.8	1.31688	0.658439	+	0.752634i	$0.271217\pi$
$810$	−5081.07	−0.220408
$811$	−20841.4	−0.902395	−0.451197	−	0.892424i	$-0.649003\pi$
$811$	−20841.4	−0.902395	−0.451197	+	0.892424i	$0.649003\pi$
$812$	41988.5	1.81467
$813$	15389.9	0.663897
$814$	66743.3	2.87390
$815$	−40847.5	−1.75562
$816$	−6238.18	−0.267623
$817$	−3432.63	−0.146992
$818$	−15033.8	−0.642599
$819$	−18911.3	−0.806855
$820$	27680.5	1.17883
$821$	1849.97	0.0786410	0.0393205	−	0.999227i	$-0.487481\pi$
$821$	1849.97	0.0786410	0.0393205	+	0.999227i	$0.487481\pi$
$822$	−13636.5	−0.578621
$823$	13233.2	0.560485	0.280243	−	0.959929i	$-0.409585\pi$
$823$	13233.2	0.560485	0.280243	+	0.959929i	$0.409585\pi$
$824$	11051.9	0.467247
$825$	6546.26	0.276256
$826$	88342.1	3.72132
$827$	4575.83	0.192403	0.0962015	−	0.995362i	$-0.469331\pi$
$827$	4575.83	0.192403	0.0962015	+	0.995362i	$0.469331\pi$
$828$	−7550.28	−0.316896
$829$	25481.5	1.06756	0.533781	−	0.845623i	$-0.320771\pi$
$829$	25481.5	1.06756	0.533781	+	0.845623i	$0.320771\pi$
$830$	31513.1	1.31787
$831$	−23385.4	−0.976211
$832$	46455.0	1.93574
$833$	11649.5	0.484552
$834$	16834.3	0.698950
$835$	−46990.6	−1.94752
$836$	−6639.44	−0.274677
$837$	−509.230	−0.0210294
$838$	51755.1	2.13347
$839$	−12457.9	−0.512626	−0.256313	−	0.966594i	$-0.582508\pi$
$839$	−12457.9	−0.512626	−0.256313	+	0.966594i	$0.582508\pi$
$840$	37202.1	1.52809
$841$	−13549.7	−0.555568
$842$	−4297.97	−0.175912
$843$	5442.07	0.222343
$844$	61144.3	2.49369
$845$	−57824.0	−2.35409
$846$	497.816	0.0202308
$847$	38267.4	1.55240
$848$	−17411.7	−0.705093
$849$	844.875	0.0341532
$850$	7336.42	0.296044
$851$	13805.6	0.556109
$852$	−46440.0	−1.86738
$853$	−4017.73	−0.161271	−0.0806357	−	0.996744i	$-0.525695\pi$
$853$	−4017.73	−0.161271	−0.0806357	+	0.996744i	$0.525695\pi$
$854$	−63485.1	−2.54381
$855$	−924.209	−0.0369676
$856$	−6589.33	−0.263106
$857$	−5839.09	−0.232742	−0.116371	−	0.993206i	$-0.537126\pi$
$857$	−5839.09	−0.232742	−0.116371	+	0.993206i	$0.537126\pi$
$858$	−63393.3	−2.52239
$859$	38284.1	1.52065	0.760323	−	0.649545i	$-0.225041\pi$
$859$	38284.1	1.52065	0.760323	+	0.649545i	$0.225041\pi$
$860$	87118.6	3.45432
$861$	10554.2	0.417754
$862$	−8917.05	−0.352338
$863$	35942.8	1.41774	0.708869	−	0.705340i	$-0.249206\pi$
$863$	35942.8	1.41774	0.708869	+	0.705340i	$0.249206\pi$
$864$	636.301	0.0250549
$865$	−30565.1	−1.20144
$866$	58069.0	2.27860
$867$	10702.7	0.419241
$868$	7606.44	0.297442
$869$	26946.6	1.05190
$870$	19592.5	0.763505
$871$	45142.9	1.75615
$872$	−23071.0	−0.895967
$873$	−11697.1	−0.453477
$874$	−2073.51	−0.0802490
$875$	27793.7	1.07383
$876$	−6810.72	−0.262686
$877$	37783.3	1.45479	0.727396	−	0.686218i	$-0.240730\pi$
$877$	37783.3	1.45479	0.727396	+	0.686218i	$0.240730\pi$
$878$	−64735.7	−2.48830
$879$	1877.55	0.0720459
$880$	38796.7	1.48618
$881$	46281.4	1.76987	0.884937	−	0.465710i	$-0.154201\pi$
$881$	46281.4	1.76987	0.884937	+	0.465710i	$0.154201\pi$
$882$	13912.8	0.531142
$883$	8154.17	0.310770	0.155385	−	0.987854i	$-0.450338\pi$
$883$	8154.17	0.310770	0.155385	+	0.987854i	$0.450338\pi$
$884$	−47055.0	−1.79031
$885$	27302.3	1.03701
$886$	42086.3	1.59584
$887$	21950.9	0.830934	0.415467	−	0.909608i	$-0.363618\pi$
$887$	21950.9	0.830934	0.415467	+	0.909608i	$0.363618\pi$
$888$	29001.5	1.09598
$889$	4253.58	0.160473
$890$	−89709.5	−3.37873
$891$	−4301.31	−0.161728
$892$	−52421.4	−1.96771
$893$	90.5490	0.00339318
$894$	16866.1	0.630969
$895$	−7056.11	−0.263530
$896$	−66240.5	−2.46980
$897$	−13112.6	−0.488091
$898$	19402.7	0.721020
$899$	1963.59	0.0728469
$900$	5803.12	0.214930
$901$	−11265.9	−0.416563
$902$	35379.2	1.30598
$903$	33217.2	1.22414
$904$	−62835.3	−2.31180
$905$	54409.4	1.99849
$906$	6104.63	0.223855
$907$	−35884.5	−1.31370	−0.656850	−	0.754021i	$-0.728112\pi$
$907$	−35884.5	−1.31370	−0.656850	+	0.754021i	$0.728112\pi$
$908$	−91929.1	−3.35988
$909$	6779.65	0.247378
$910$	131810.	4.80161
$911$	−3990.76	−0.145137	−0.0725685	−	0.997363i	$-0.523120\pi$
$911$	−3990.76	−0.145137	−0.0725685	+	0.997363i	$0.523120\pi$
$912$	−1355.12	−0.0492025
$913$	26677.0	0.967009
$914$	−10744.0	−0.388817
$915$	−19620.2	−0.708879
$916$	50495.3	1.82141
$917$	73695.9	2.65393
$918$	−4820.50	−0.173312
$919$	−16836.4	−0.604334	−0.302167	−	0.953255i	$-0.597710\pi$
$919$	−16836.4	−0.604334	−0.302167	+	0.953255i	$0.597710\pi$
$920$	25795.0	0.924386
$921$	−10494.2	−0.375457
$922$	3711.61	0.132576
$923$	−80652.7	−2.87618
$924$	64249.2	2.28749
$925$	−10610.9	−0.377173
$926$	−52731.5	−1.87135
$927$	2656.91	0.0941363
$928$	−2453.57	−0.0867914
$929$	−12626.5	−0.445922	−0.222961	−	0.974827i	$-0.571572\pi$
$929$	−12626.5	−0.445922	−0.222961	+	0.974827i	$0.571572\pi$
$930$	3549.29	0.125146
$931$	2530.63	0.0890849
$932$	1383.41	0.0486214
$933$	129.426	0.00454149
$934$	−4076.75	−0.142822
$935$	25102.8	0.878021
$936$	−27545.9	−0.961929
$937$	21058.2	0.734196	0.367098	−	0.930182i	$-0.380351\pi$
$937$	21058.2	0.734196	0.367098	+	0.930182i	$0.380351\pi$
$938$	−69078.4	−2.40457
$939$	33090.4	1.15001
$940$	−2298.09	−0.0797399
$941$	−23153.1	−0.802094	−0.401047	−	0.916057i	$-0.631354\pi$
$941$	−23153.1	−0.802094	−0.401047	+	0.916057i	$0.631354\pi$
$942$	−11489.0	−0.397381
$943$	7318.03	0.252712
$944$	40032.1	1.38023
$945$	8943.47	0.307864
$946$	111349.	3.82691
$947$	6504.63	0.223202	0.111601	−	0.993753i	$-0.464402\pi$
$947$	6504.63	0.223202	0.111601	+	0.993753i	$0.464402\pi$
$948$	23887.6	0.818389
$949$	−11828.2	−0.404595
$950$	1593.70	0.0544277
$951$	−5250.18	−0.179021
$952$	35294.2	1.20157
$953$	15332.1	0.521148	0.260574	−	0.965454i	$-0.416088\pi$
$953$	15332.1	0.521148	0.260574	+	0.965454i	$0.416088\pi$
$954$	−13454.7	−0.456616
$955$	−8613.63	−0.291864
$956$	3750.25	0.126874
$957$	16585.8	0.560233
$958$	−61751.3	−2.08256
$959$	24002.3	0.808211
$960$	−21969.3	−0.738601
$961$	−29435.3	−0.988060
$962$	102755.	3.44382
$963$	−1584.09	−0.0530080
$964$	38850.2	1.29801
$965$	−9193.35	−0.306678
$966$	20065.2	0.668308
$967$	−18370.9	−0.610927	−0.305464	−	0.952204i	$-0.598811\pi$
$967$	−18370.9	−0.610927	−0.305464	+	0.952204i	$0.598811\pi$
$968$	55739.7	1.85076
$969$	−876.813	−0.0290684
$970$	81527.5	2.69865
$971$	41221.7	1.36238	0.681188	−	0.732109i	$-0.261464\pi$
$971$	41221.7	1.36238	0.681188	+	0.732109i	$0.261464\pi$
$972$	−3813.02	−0.125826
$973$	−29631.0	−0.976285
$974$	86072.8	2.83157
$975$	10078.3	0.331041
$976$	−28768.2	−0.943491
$977$	11406.9	0.373531	0.186765	−	0.982405i	$-0.440200\pi$
$977$	11406.9	0.373531	0.186765	+	0.982405i	$0.440200\pi$
$978$	−46281.6	−1.51321
$979$	−75942.4	−2.47919
$980$	−64226.2	−2.09350
$981$	−5546.33	−0.180511
$982$	−92027.1	−2.99053
$983$	−56720.7	−1.84040	−0.920198	−	0.391454i	$-0.871972\pi$
$983$	−56720.7	−1.84040	−0.920198	+	0.391454i	$0.871972\pi$
$984$	15373.1	0.498045
$985$	51808.1	1.67588
$986$	18587.8	0.600361
$987$	−876.233	−0.0282582
$988$	−10221.8	−0.329148
$989$	23032.0	0.740520
$990$	29979.8	0.962444
$991$	−53968.0	−1.72992	−0.864960	−	0.501842i	$-0.832656\pi$
$991$	−53968.0	−1.72992	−0.864960	+	0.501842i	$0.832656\pi$
$992$	−444.477	−0.0142260
$993$	−7950.96	−0.254095
$994$	123416.	3.93815
$995$	−65421.1	−2.08441
$996$	23648.6	0.752344
$997$	−6934.07	−0.220265	−0.110133	−	0.993917i	$-0.535128\pi$
$997$	−6934.07	−0.220265	−0.110133	+	0.993917i	$0.535128\pi$
$998$	−22558.0	−0.715493
$999$	6972.05	0.220807

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	717.4.a.b.1.27	✓	28
3.2	odd	2		2151.4.a.b.1.2		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
717.4.a.b.1.27	✓	28	1.1	even	1	trivial
2151.4.a.b.1.2		28	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 717 = 3 \cdot 239 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	717.a (trivial)

\(f(q)\)	\(=\)	\(q+4.86739 q^{2} -3.00000 q^{3} +15.6914 q^{4} -12.8877 q^{5} -14.6022 q^{6} +25.7021 q^{7} +37.4372 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+4.86739 q^{2} -3.00000 q^{3} +15.6914 q^{4} -12.8877 q^{5} -14.6022 q^{6} +25.7021 q^{7} +37.4372 q^{8} +9.00000 q^{9} -62.7292 q^{10} -53.1026 q^{11} -47.0743 q^{12} -81.7543 q^{13} +125.102 q^{14} +38.6630 q^{15} +56.6898 q^{16} +36.6803 q^{17} +43.8065 q^{18} +7.96807 q^{19} -202.226 q^{20} -77.1062 q^{21} -258.471 q^{22} -53.4635 q^{23} -112.312 q^{24} +41.0919 q^{25} -397.930 q^{26} -27.0000 q^{27} +403.302 q^{28} +104.112 q^{29} +188.188 q^{30} +18.8604 q^{31} -23.5667 q^{32} +159.308 q^{33} +178.537 q^{34} -331.240 q^{35} +141.223 q^{36} -258.224 q^{37} +38.7837 q^{38} +245.263 q^{39} -482.478 q^{40} -136.879 q^{41} -375.306 q^{42} -430.798 q^{43} -833.256 q^{44} -115.989 q^{45} -260.228 q^{46} +11.3640 q^{47} -170.069 q^{48} +317.596 q^{49} +200.010 q^{50} -110.041 q^{51} -1282.84 q^{52} -307.139 q^{53} -131.419 q^{54} +684.368 q^{55} +962.213 q^{56} -23.9042 q^{57} +506.752 q^{58} +706.161 q^{59} +606.678 q^{60} -507.467 q^{61} +91.8008 q^{62} +231.319 q^{63} -568.226 q^{64} +1053.62 q^{65} +775.412 q^{66} -552.177 q^{67} +575.566 q^{68} +160.391 q^{69} -1612.27 q^{70} +986.525 q^{71} +336.935 q^{72} +144.680 q^{73} -1256.88 q^{74} -123.276 q^{75} +125.031 q^{76} -1364.85 q^{77} +1193.79 q^{78} -507.444 q^{79} -730.599 q^{80} +81.0000 q^{81} -666.242 q^{82} -502.367 q^{83} -1209.91 q^{84} -472.723 q^{85} -2096.86 q^{86} -312.335 q^{87} -1988.01 q^{88} +1430.11 q^{89} -564.563 q^{90} -2101.26 q^{91} -838.920 q^{92} -56.5812 q^{93} +55.3129 q^{94} -102.690 q^{95} +70.7001 q^{96} -1299.67 q^{97} +1545.86 q^{98} -477.923 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 5 q^{2} - 84 q^{3} + 103 q^{4} + 6 q^{5} + 15 q^{6} - 68 q^{7} - 39 q^{8} + 252 q^{9}+O(q^{10}) \) 28 * q - 5 * q^2 - 84 * q^3 + 103 * q^4 + 6 * q^5 + 15 * q^6 - 68 * q^7 - 39 * q^8 + 252 * q^9	\( 28 q - 5 q^{2} - 84 q^{3} + 103 q^{4} + 6 q^{5} + 15 q^{6} - 68 q^{7} - 39 q^{8} + 252 q^{9} - 88 q^{10} - 110 q^{11} - 309 q^{12} - 82 q^{13} + 126 q^{14} - 18 q^{15} + 271 q^{16} + 100 q^{17} - 45 q^{18} - 292 q^{19} - 52 q^{20} + 204 q^{21} - 351 q^{22} - 276 q^{23} + 117 q^{24} + 386 q^{25} + 84 q^{26} - 756 q^{27} - 1010 q^{28} - 38 q^{29} + 264 q^{30} - 432 q^{31} - 452 q^{32} + 330 q^{33} - 524 q^{34} - 166 q^{35} + 927 q^{36} - 936 q^{37} - 41 q^{38} + 246 q^{39} - 1183 q^{40} + 1054 q^{41} - 378 q^{42} - 1804 q^{43} - 341 q^{44} + 54 q^{45} - 888 q^{46} - 560 q^{47} - 813 q^{48} + 1074 q^{49} - 1054 q^{50} - 300 q^{51} - 632 q^{52} - 160 q^{53} + 135 q^{54} - 842 q^{55} + 509 q^{56} + 876 q^{57} - 1266 q^{58} + 846 q^{59} + 156 q^{60} - 2220 q^{61} + 82 q^{62} - 612 q^{63} - 1565 q^{64} + 296 q^{65} + 1053 q^{66} - 4752 q^{67} - 1719 q^{68} + 828 q^{69} - 5601 q^{70} - 802 q^{71} - 351 q^{72} - 2732 q^{73} - 4581 q^{74} - 1158 q^{75} - 5614 q^{76} - 1008 q^{77} - 252 q^{78} - 3172 q^{79} - 732 q^{80} + 2268 q^{81} - 9709 q^{82} - 4780 q^{83} + 3030 q^{84} - 4624 q^{85} - 2009 q^{86} + 114 q^{87} - 9331 q^{88} + 4372 q^{89} - 792 q^{90} - 7398 q^{91} - 6138 q^{92} + 1296 q^{93} - 7068 q^{94} - 3160 q^{95} + 1356 q^{96} - 4846 q^{97} - 3772 q^{98} - 990 q^{99}+O(q^{100}) \) 28 * q - 5 * q^2 - 84 * q^3 + 103 * q^4 + 6 * q^5 + 15 * q^6 - 68 * q^7 - 39 * q^8 + 252 * q^9 - 88 * q^10 - 110 * q^11 - 309 * q^12 - 82 * q^13 + 126 * q^14 - 18 * q^15 + 271 * q^16 + 100 * q^17 - 45 * q^18 - 292 * q^19 - 52 * q^20 + 204 * q^21 - 351 * q^22 - 276 * q^23 + 117 * q^24 + 386 * q^25 + 84 * q^26 - 756 * q^27 - 1010 * q^28 - 38 * q^29 + 264 * q^30 - 432 * q^31 - 452 * q^32 + 330 * q^33 - 524 * q^34 - 166 * q^35 + 927 * q^36 - 936 * q^37 - 41 * q^38 + 246 * q^39 - 1183 * q^40 + 1054 * q^41 - 378 * q^42 - 1804 * q^43 - 341 * q^44 + 54 * q^45 - 888 * q^46 - 560 * q^47 - 813 * q^48 + 1074 * q^49 - 1054 * q^50 - 300 * q^51 - 632 * q^52 - 160 * q^53 + 135 * q^54 - 842 * q^55 + 509 * q^56 + 876 * q^57 - 1266 * q^58 + 846 * q^59 + 156 * q^60 - 2220 * q^61 + 82 * q^62 - 612 * q^63 - 1565 * q^64 + 296 * q^65 + 1053 * q^66 - 4752 * q^67 - 1719 * q^68 + 828 * q^69 - 5601 * q^70 - 802 * q^71 - 351 * q^72 - 2732 * q^73 - 4581 * q^74 - 1158 * q^75 - 5614 * q^76 - 1008 * q^77 - 252 * q^78 - 3172 * q^79 - 732 * q^80 + 2268 * q^81 - 9709 * q^82 - 4780 * q^83 + 3030 * q^84 - 4624 * q^85 - 2009 * q^86 + 114 * q^87 - 9331 * q^88 + 4372 * q^89 - 792 * q^90 - 7398 * q^91 - 6138 * q^92 + 1296 * q^93 - 7068 * q^94 - 3160 * q^95 + 1356 * q^96 - 4846 * q^97 - 3772 * q^98 - 990 * q^99

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