LMFDB - Embedded newform 8017.2.a.a.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8017,2,Mod(1,8017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8017, 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("8017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8017 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8017.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:	$64.0160673005$
Analytic rank:	$1$
Dimension:	$327$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	8017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.70756 q^{2} -2.54523 q^{3} +5.33088 q^{4} +0.896657 q^{5} +6.89137 q^{6} +3.68403 q^{7} -9.01856 q^{8} +3.47821 q^{9} +O(q^{10})$	\(q-2.70756 q^{2} -2.54523 q^{3} +5.33088 q^{4} +0.896657 q^{5} +6.89137 q^{6} +3.68403 q^{7} -9.01856 q^{8} +3.47821 q^{9} -2.42775 q^{10} +0.131595 q^{11} -13.5683 q^{12} -1.14664 q^{13} -9.97474 q^{14} -2.28220 q^{15} +13.7565 q^{16} -3.70851 q^{17} -9.41746 q^{18} +7.09439 q^{19} +4.77997 q^{20} -9.37672 q^{21} -0.356301 q^{22} -6.05252 q^{23} +22.9543 q^{24} -4.19601 q^{25} +3.10459 q^{26} -1.21715 q^{27} +19.6391 q^{28} -8.90498 q^{29} +6.17919 q^{30} +5.69980 q^{31} -19.2095 q^{32} -0.334940 q^{33} +10.0410 q^{34} +3.30331 q^{35} +18.5419 q^{36} -3.39502 q^{37} -19.2085 q^{38} +2.91846 q^{39} -8.08655 q^{40} +4.92679 q^{41} +25.3880 q^{42} -0.617800 q^{43} +0.701517 q^{44} +3.11876 q^{45} +16.3875 q^{46} +2.91641 q^{47} -35.0136 q^{48} +6.57209 q^{49} +11.3609 q^{50} +9.43901 q^{51} -6.11259 q^{52} -1.35520 q^{53} +3.29552 q^{54} +0.117996 q^{55} -33.2247 q^{56} -18.0569 q^{57} +24.1108 q^{58} +4.24968 q^{59} -12.1661 q^{60} +4.52818 q^{61} -15.4326 q^{62} +12.8138 q^{63} +24.4978 q^{64} -1.02814 q^{65} +0.906869 q^{66} +14.0652 q^{67} -19.7696 q^{68} +15.4051 q^{69} -8.94392 q^{70} +11.5404 q^{71} -31.3684 q^{72} -10.4208 q^{73} +9.19223 q^{74} +10.6798 q^{75} +37.8193 q^{76} +0.484800 q^{77} -7.90190 q^{78} -8.13357 q^{79} +12.3349 q^{80} -7.33669 q^{81} -13.3396 q^{82} -6.68019 q^{83} -49.9862 q^{84} -3.32526 q^{85} +1.67273 q^{86} +22.6652 q^{87} -1.18680 q^{88} +6.91674 q^{89} -8.44423 q^{90} -4.22425 q^{91} -32.2652 q^{92} -14.5073 q^{93} -7.89636 q^{94} +6.36123 q^{95} +48.8926 q^{96} -8.20895 q^{97} -17.7943 q^{98} +0.457715 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 327 q - 23 q^{2} - 48 q^{3} + 315 q^{4} - 55 q^{5} - 38 q^{6} - 87 q^{7} - 69 q^{8} + 303 q^{9}+O(q^{10}) $ 327 * q - 23 * q^2 - 48 * q^3 + 315 * q^4 - 55 * q^5 - 38 * q^6 - 87 * q^7 - 69 * q^8 + 303 * q^9	\( 327 q - 23 q^{2} - 48 q^{3} + 315 q^{4} - 55 q^{5} - 38 q^{6} - 87 q^{7} - 69 q^{8} + 303 q^{9} - 48 q^{10} - 70 q^{11} - 120 q^{12} - 53 q^{13} - 52 q^{14} - 77 q^{15} + 295 q^{16} - 164 q^{17} - 58 q^{18} - 47 q^{19} - 153 q^{20} - 39 q^{21} - 68 q^{22} - 256 q^{23} - 107 q^{24} + 288 q^{25} - 95 q^{26} - 189 q^{27} - 167 q^{28} - 99 q^{29} - 81 q^{30} - 71 q^{31} - 146 q^{32} - 95 q^{33} - 40 q^{34} - 192 q^{35} + 261 q^{36} - 54 q^{37} - 179 q^{38} - 115 q^{39} - 121 q^{40} - 111 q^{41} - 62 q^{42} - 110 q^{43} - 157 q^{44} - 137 q^{45} - 11 q^{46} - 324 q^{47} - 236 q^{48} + 296 q^{49} - 73 q^{50} - 88 q^{51} - 138 q^{52} - 170 q^{53} - 127 q^{54} - 151 q^{55} - 151 q^{56} - 106 q^{57} - 81 q^{58} - 123 q^{59} - 83 q^{60} - 62 q^{61} - 287 q^{62} - 400 q^{63} + 263 q^{64} - 143 q^{65} - 64 q^{66} - 95 q^{67} - 442 q^{68} - 22 q^{69} - 26 q^{70} - 210 q^{71} - 129 q^{72} - 121 q^{73} - 159 q^{74} - 194 q^{75} - 86 q^{76} - 178 q^{77} - 68 q^{78} - 145 q^{79} - 338 q^{80} + 259 q^{81} - 103 q^{82} - 418 q^{83} - 102 q^{84} - 40 q^{85} - 89 q^{86} - 372 q^{87} - 186 q^{88} - 100 q^{89} - 150 q^{90} - 69 q^{91} - 458 q^{92} - 81 q^{93} - 46 q^{94} - 377 q^{95} - 190 q^{96} - 87 q^{97} - 147 q^{98} - 171 q^{99}+O(q^{100}) \) 327 * q - 23 * q^2 - 48 * q^3 + 315 * q^4 - 55 * q^5 - 38 * q^6 - 87 * q^7 - 69 * q^8 + 303 * q^9 - 48 * q^10 - 70 * q^11 - 120 * q^12 - 53 * q^13 - 52 * q^14 - 77 * q^15 + 295 * q^16 - 164 * q^17 - 58 * q^18 - 47 * q^19 - 153 * q^20 - 39 * q^21 - 68 * q^22 - 256 * q^23 - 107 * q^24 + 288 * q^25 - 95 * q^26 - 189 * q^27 - 167 * q^28 - 99 * q^29 - 81 * q^30 - 71 * q^31 - 146 * q^32 - 95 * q^33 - 40 * q^34 - 192 * q^35 + 261 * q^36 - 54 * q^37 - 179 * q^38 - 115 * q^39 - 121 * q^40 - 111 * q^41 - 62 * q^42 - 110 * q^43 - 157 * q^44 - 137 * q^45 - 11 * q^46 - 324 * q^47 - 236 * q^48 + 296 * q^49 - 73 * q^50 - 88 * q^51 - 138 * q^52 - 170 * q^53 - 127 * q^54 - 151 * q^55 - 151 * q^56 - 106 * q^57 - 81 * q^58 - 123 * q^59 - 83 * q^60 - 62 * q^61 - 287 * q^62 - 400 * q^63 + 263 * q^64 - 143 * q^65 - 64 * q^66 - 95 * q^67 - 442 * q^68 - 22 * q^69 - 26 * q^70 - 210 * q^71 - 129 * q^72 - 121 * q^73 - 159 * q^74 - 194 * q^75 - 86 * q^76 - 178 * q^77 - 68 * q^78 - 145 * q^79 - 338 * q^80 + 259 * q^81 - 103 * q^82 - 418 * q^83 - 102 * q^84 - 40 * q^85 - 89 * q^86 - 372 * q^87 - 186 * q^88 - 100 * q^89 - 150 * q^90 - 69 * q^91 - 458 * q^92 - 81 * q^93 - 46 * q^94 - 377 * q^95 - 190 * q^96 - 87 * q^97 - 147 * q^98 - 171 * 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 $

$2$	−2.70756	−1.91453	−0.957267	−	0.289206i	$-0.906609\pi$
$2$	−2.70756	−1.91453	−0.957267	+	0.289206i	$0.906609\pi$
$3$	−2.54523	−1.46949	−0.734745	−	0.678343i	$-0.762698\pi$
$3$	−2.54523	−1.46949	−0.734745	+	0.678343i	$0.762698\pi$
$4$	5.33088	2.66544
$5$	0.896657	0.400997	0.200499	−	0.979694i	$-0.435744\pi$
$5$	0.896657	0.400997	0.200499	+	0.979694i	$0.435744\pi$
$6$	6.89137	2.81339
$7$	3.68403	1.39243	0.696217	−	0.717832i	$-0.254865\pi$
$7$	3.68403	1.39243	0.696217	+	0.717832i	$0.254865\pi$
$8$	−9.01856	−3.18854
$9$	3.47821	1.15940
$10$	−2.42775	−0.767723
$11$	0.131595	0.0396774	0.0198387	−	0.999803i	$-0.493685\pi$
$11$	0.131595	0.0396774	0.0198387	+	0.999803i	$0.493685\pi$
$12$	−13.5683	−3.91684
$13$	−1.14664	−0.318020	−0.159010	−	0.987277i	$-0.550830\pi$
$13$	−1.14664	−0.318020	−0.159010	+	0.987277i	$0.550830\pi$
$14$	−9.97474	−2.66586
$15$	−2.28220	−0.589262
$16$	13.7565	3.43913
$17$	−3.70851	−0.899445	−0.449723	−	0.893168i	$-0.648477\pi$
$17$	−3.70851	−0.899445	−0.449723	+	0.893168i	$0.648477\pi$
$18$	−9.41746	−2.21972
$19$	7.09439	1.62756	0.813782	−	0.581170i	$-0.197405\pi$
$19$	7.09439	1.62756	0.813782	+	0.581170i	$0.197405\pi$
$20$	4.77997	1.06883
$21$	−9.37672	−2.04617
$22$	−0.356301	−0.0759637
$23$	−6.05252	−1.26204	−0.631018	−	0.775768i	$-0.717363\pi$
$23$	−6.05252	−1.26204	−0.631018	+	0.775768i	$0.717363\pi$
$24$	22.9543	4.68553
$25$	−4.19601	−0.839201
$26$	3.10459	0.608860
$27$	−1.21715	−0.234241
$28$	19.6391	3.71145
$29$	−8.90498	−1.65361	−0.826807	−	0.562486i	$-0.809845\pi$
$29$	−8.90498	−1.65361	−0.826807	+	0.562486i	$0.809845\pi$
$30$	6.17919	1.12816
$31$	5.69980	1.02372	0.511858	−	0.859070i	$-0.328958\pi$
$31$	5.69980	1.02372	0.511858	+	0.859070i	$0.328958\pi$
$32$	−19.2095	−3.39579
$33$	−0.334940	−0.0583055
$34$	10.0410	1.72202
$35$	3.30331	0.558362
$36$	18.5419	3.09032
$37$	−3.39502	−0.558139	−0.279069	−	0.960271i	$-0.590026\pi$
$37$	−3.39502	−0.558139	−0.279069	+	0.960271i	$0.590026\pi$
$38$	−19.2085	−3.11603
$39$	2.91846	0.467328
$40$	−8.08655	−1.27860
$41$	4.92679	0.769435	0.384718	−	0.923034i	$-0.374299\pi$
$41$	4.92679	0.769435	0.384718	+	0.923034i	$0.374299\pi$
$42$	25.3880	3.91746
$43$	−0.617800	−0.0942137	−0.0471068	−	0.998890i	$-0.515000\pi$
$43$	−0.617800	−0.0942137	−0.0471068	+	0.998890i	$0.515000\pi$
$44$	0.701517	0.105758
$45$	3.11876	0.464917
$46$	16.3875	2.41621
$47$	2.91641	0.425402	0.212701	−	0.977117i	$-0.431774\pi$
$47$	2.91641	0.425402	0.212701	+	0.977117i	$0.431774\pi$
$48$	−35.0136	−5.05377
$49$	6.57209	0.938870
$50$	11.3609	1.60668
$51$	9.43901	1.32173
$52$	−6.11259	−0.847663
$53$	−1.35520	−0.186152	−0.0930758	−	0.995659i	$-0.529670\pi$
$53$	−1.35520	−0.186152	−0.0930758	+	0.995659i	$0.529670\pi$
$54$	3.29552	0.448463
$55$	0.117996	0.0159105
$56$	−33.2247	−4.43983
$57$	−18.0569	−2.39169
$58$	24.1108	3.16590
$59$	4.24968	0.553261	0.276631	−	0.960976i	$-0.410782\pi$
$59$	4.24968	0.553261	0.276631	+	0.960976i	$0.410782\pi$
$60$	−12.1661	−1.57064
$61$	4.52818	0.579774	0.289887	−	0.957061i	$-0.406382\pi$
$61$	4.52818	0.579774	0.289887	+	0.957061i	$0.406382\pi$
$62$	−15.4326	−1.95994
$63$	12.8138	1.61439
$64$	24.4978	3.06223
$65$	−1.02814	−0.127525
$66$	0.906869	0.111628
$67$	14.0652	1.71834	0.859169	−	0.511691i	$-0.170981\pi$
$67$	14.0652	1.71834	0.859169	+	0.511691i	$0.170981\pi$
$68$	−19.7696	−2.39742
$69$	15.4051	1.85455
$70$	−8.94392	−1.06900
$71$	11.5404	1.36959	0.684796	−	0.728734i	$-0.259891\pi$
$71$	11.5404	1.36959	0.684796	+	0.728734i	$0.259891\pi$
$72$	−31.3684	−3.69680
$73$	−10.4208	−1.21966	−0.609832	−	0.792531i	$-0.708763\pi$
$73$	−10.4208	−1.21966	−0.609832	+	0.792531i	$0.708763\pi$
$74$	9.19223	1.06858
$75$	10.6798	1.23320
$76$	37.8193	4.33818
$77$	0.484800	0.0552481
$78$	−7.90190	−0.894714
$79$	−8.13357	−0.915098	−0.457549	−	0.889185i	$-0.651272\pi$
$79$	−8.13357	−0.915098	−0.457549	+	0.889185i	$0.651272\pi$
$80$	12.3349	1.37908
$81$	−7.33669	−0.815188
$82$	−13.3396	−1.47311
$83$	−6.68019	−0.733246	−0.366623	−	0.930370i	$-0.619486\pi$
$83$	−6.68019	−0.733246	−0.366623	+	0.930370i	$0.619486\pi$
$84$	−49.9862	−5.45394
$85$	−3.32526	−0.360675
$86$	1.67273	0.180375
$87$	22.6652	2.42997
$88$	−1.18680	−0.126513
$89$	6.91674	0.733173	0.366586	−	0.930384i	$-0.380526\pi$
$89$	6.91674	0.733173	0.366586	+	0.930384i	$0.380526\pi$
$90$	−8.44423	−0.890100
$91$	−4.22425	−0.442822
$92$	−32.2652	−3.36388
$93$	−14.5073	−1.50434
$94$	−7.89636	−0.814447
$95$	6.36123	0.652649
$96$	48.8926	4.99008
$97$	−8.20895	−0.833492	−0.416746	−	0.909023i	$-0.636830\pi$
$97$	−8.20895	−0.833492	−0.416746	+	0.909023i	$0.636830\pi$
$98$	−17.7943	−1.79750
$99$	0.457715	0.0460021
$100$	−22.3684	−2.23684
$101$	−0.213290	−0.0212231	−0.0106116	−	0.999944i	$-0.503378\pi$
$101$	−0.213290	−0.0212231	−0.0106116	+	0.999944i	$0.503378\pi$
$102$	−25.5567	−2.53049
$103$	7.69091	0.757808	0.378904	−	0.925436i	$-0.376301\pi$
$103$	7.69091	0.757808	0.378904	+	0.925436i	$0.376301\pi$
$104$	10.3410	1.01402
$105$	−8.40770	−0.820507
$106$	3.66930	0.356394
$107$	−13.7428	−1.32856	−0.664281	−	0.747483i	$-0.731262\pi$
$107$	−13.7428	−1.32856	−0.664281	+	0.747483i	$0.731262\pi$
$108$	−6.48850	−0.624356
$109$	7.25888	0.695275	0.347637	−	0.937629i	$-0.386984\pi$
$109$	7.25888	0.695275	0.347637	+	0.937629i	$0.386984\pi$
$110$	−0.319480	−0.0304612
$111$	8.64113	0.820180
$112$	50.6795	4.78876
$113$	9.01682	0.848231	0.424115	−	0.905608i	$-0.360585\pi$
$113$	9.01682	0.848231	0.424115	+	0.905608i	$0.360585\pi$
$114$	48.8901	4.57897
$115$	−5.42703	−0.506073
$116$	−47.4714	−4.40761
$117$	−3.98825	−0.368713
$118$	−11.5063	−1.05924
$119$	−13.6623	−1.25242
$120$	20.5822	1.87889
$121$	−10.9827	−0.998426
$122$	−12.2603	−1.11000
$123$	−12.5398	−1.13068
$124$	30.3850	2.72865
$125$	−8.24566	−0.737515
$126$	−34.6942	−3.09081
$127$	−2.61930	−0.232426	−0.116213	−	0.993224i	$-0.537075\pi$
$127$	−2.61930	−0.232426	−0.116213	+	0.993224i	$0.537075\pi$
$128$	−27.9103	−2.46695
$129$	1.57245	0.138446
$130$	2.78375	0.244151
$131$	−19.1527	−1.67338	−0.836690	−	0.547676i	$-0.815513\pi$
$131$	−19.1527	−1.67338	−0.836690	+	0.547676i	$0.815513\pi$
$132$	−1.78552	−0.155410
$133$	26.1360	2.26627
$134$	−38.0824	−3.28982
$135$	−1.09137	−0.0939301
$136$	33.4454	2.86792
$137$	−0.370896	−0.0316878	−0.0158439	−	0.999874i	$-0.505043\pi$
$137$	−0.370896	−0.0316878	−0.0158439	+	0.999874i	$0.505043\pi$
$138$	−41.7101	−3.55060
$139$	−4.17501	−0.354120	−0.177060	−	0.984200i	$-0.556659\pi$
$139$	−4.17501	−0.354120	−0.177060	+	0.984200i	$0.556659\pi$
$140$	17.6096	1.48828
$141$	−7.42294	−0.625125
$142$	−31.2463	−2.62213
$143$	−0.150892	−0.0126182
$144$	47.8481	3.98734
$145$	−7.98471	−0.663094
$146$	28.2150	2.33509
$147$	−16.7275	−1.37966
$148$	−18.0985	−1.48769
$149$	−1.52491	−0.124925	−0.0624627	−	0.998047i	$-0.519895\pi$
$149$	−1.52491	−0.124925	−0.0624627	+	0.998047i	$0.519895\pi$
$150$	−28.9162	−2.36100
$151$	−12.6706	−1.03112	−0.515559	−	0.856854i	$-0.672416\pi$
$151$	−12.6706	−1.03112	−0.515559	+	0.856854i	$0.672416\pi$
$152$	−63.9812	−5.18956
$153$	−12.8990	−1.04282
$154$	−1.31263	−0.105774
$155$	5.11077	0.410507
$156$	15.5580	1.24563
$157$	7.79082	0.621775	0.310888	−	0.950447i	$-0.399374\pi$
$157$	7.79082	0.621775	0.310888	+	0.950447i	$0.399374\pi$
$158$	22.0221	1.75199
$159$	3.44931	0.273548
$160$	−17.2243	−1.36170
$161$	−22.2977	−1.75730
$162$	19.8645	1.56070
$163$	−6.06082	−0.474720	−0.237360	−	0.971422i	$-0.576282\pi$
$163$	−6.06082	−0.474720	−0.237360	+	0.971422i	$0.576282\pi$
$164$	26.2641	2.05088
$165$	−0.300326	−0.0233804
$166$	18.0870	1.40382
$167$	3.99360	0.309034	0.154517	−	0.987990i	$-0.450618\pi$
$167$	3.99360	0.309034	0.154517	+	0.987990i	$0.450618\pi$
$168$	84.5645	6.52429
$169$	−11.6852	−0.898863
$170$	9.00334	0.690524
$171$	24.6758	1.88700
$172$	−3.29342	−0.251121
$173$	10.9817	0.834926	0.417463	−	0.908694i	$-0.362919\pi$
$173$	10.9817	0.834926	0.417463	+	0.908694i	$0.362919\pi$
$174$	−61.3675	−4.65226
$175$	−15.4582	−1.16853
$176$	1.81029	0.136456
$177$	−10.8164	−0.813012
$178$	−18.7275	−1.40368
$179$	−23.6109	−1.76476	−0.882381	−	0.470535i	$-0.844061\pi$
$179$	−23.6109	−1.76476	−0.882381	+	0.470535i	$0.844061\pi$
$180$	16.6257	1.23921
$181$	13.8930	1.03266	0.516330	−	0.856390i	$-0.327298\pi$
$181$	13.8930	1.03266	0.516330	+	0.856390i	$0.327298\pi$
$182$	11.4374	0.847797
$183$	−11.5253	−0.851973
$184$	54.5850	4.02406
$185$	−3.04417	−0.223812
$186$	39.2795	2.88011
$187$	−0.488021	−0.0356876
$188$	15.5470	1.13388
$189$	−4.48403	−0.326165
$190$	−17.2234	−1.24952
$191$	7.81000	0.565112	0.282556	−	0.959251i	$-0.408818\pi$
$191$	7.81000	0.565112	0.282556	+	0.959251i	$0.408818\pi$
$192$	−62.3526	−4.49991
$193$	−20.7292	−1.49212	−0.746059	−	0.665880i	$-0.768056\pi$
$193$	−20.7292	−1.49212	−0.746059	+	0.665880i	$0.768056\pi$
$194$	22.2262	1.59575
$195$	2.61686	0.187397
$196$	35.0350	2.50250
$197$	−20.9659	−1.49376	−0.746878	−	0.664961i	$-0.768448\pi$
$197$	−20.9659	−1.49376	−0.746878	+	0.664961i	$0.768448\pi$
$198$	−1.23929	−0.0880725
$199$	5.53690	0.392501	0.196250	−	0.980554i	$-0.437123\pi$
$199$	5.53690	0.392501	0.196250	+	0.980554i	$0.437123\pi$
$200$	37.8419	2.67583
$201$	−35.7992	−2.52508
$202$	0.577494	0.0406324
$203$	−32.8062	−2.30255
$204$	50.3182	3.52298
$205$	4.41764	0.308541
$206$	−20.8236	−1.45085
$207$	−21.0519	−1.46321
$208$	−15.7737	−1.09371
$209$	0.933586	0.0645775
$210$	22.7644	1.57089
$211$	−4.41872	−0.304197	−0.152099	−	0.988365i	$-0.548603\pi$
$211$	−4.41872	−0.304197	−0.152099	+	0.988365i	$0.548603\pi$
$212$	−7.22443	−0.496176
$213$	−29.3730	−2.01260
$214$	37.2093	2.54358
$215$	−0.553955	−0.0377794
$216$	10.9770	0.746888
$217$	20.9983	1.42545
$218$	−19.6539	−1.33113
$219$	26.5234	1.79228
$220$	0.629020	0.0424085
$221$	4.25231	0.286042
$222$	−23.3964	−1.57026
$223$	18.2469	1.22190	0.610952	−	0.791668i	$-0.290787\pi$
$223$	18.2469	1.22190	0.610952	+	0.791668i	$0.290787\pi$
$224$	−70.7684	−4.72841
$225$	−14.5946	−0.972972
$226$	−24.4136	−1.62397
$227$	20.1605	1.33810	0.669048	−	0.743219i	$-0.266702\pi$
$227$	20.1605	1.33810	0.669048	+	0.743219i	$0.266702\pi$
$228$	−96.2590	−6.37491
$229$	−11.3690	−0.751283	−0.375642	−	0.926765i	$-0.622578\pi$
$229$	−11.3690	−0.751283	−0.375642	+	0.926765i	$0.622578\pi$
$230$	14.6940	0.968894
$231$	−1.23393	−0.0811866
$232$	80.3101	5.27261
$233$	−4.77099	−0.312558	−0.156279	−	0.987713i	$-0.549950\pi$
$233$	−4.77099	−0.312558	−0.156279	+	0.987713i	$0.549950\pi$
$234$	10.7984	0.705914
$235$	2.61502	0.170585
$236$	22.6545	1.47469
$237$	20.7018	1.34473
$238$	36.9914	2.39780
$239$	18.6244	1.20471	0.602357	−	0.798227i	$-0.294228\pi$
$239$	18.6244	1.20471	0.602357	+	0.798227i	$0.294228\pi$
$240$	−31.3951	−2.02655
$241$	−25.1490	−1.61999	−0.809995	−	0.586437i	$-0.800530\pi$
$241$	−25.1490	−1.61999	−0.809995	+	0.586437i	$0.800530\pi$
$242$	29.7363	1.91152
$243$	22.3250	1.43215
$244$	24.1392	1.54535
$245$	5.89291	0.376484
$246$	33.9523	2.16472
$247$	−8.13469	−0.517598
$248$	−51.4040	−3.26416
$249$	17.0026	1.07750
$250$	22.3256	1.41200
$251$	11.6007	0.732231	0.366116	−	0.930569i	$-0.380687\pi$
$251$	11.6007	0.732231	0.366116	+	0.930569i	$0.380687\pi$
$252$	68.3090	4.30306
$253$	−0.796481	−0.0500743
$254$	7.09192	0.444987
$255$	8.46356	0.530008
$256$	26.5732	1.66082
$257$	12.5442	0.782485	0.391242	−	0.920288i	$-0.372045\pi$
$257$	12.5442	0.782485	0.391242	+	0.920288i	$0.372045\pi$
$258$	−4.25749	−0.265060
$259$	−12.5074	−0.777171
$260$	−5.48089	−0.339911
$261$	−30.9734	−1.91720
$262$	51.8571	3.20374
$263$	11.6553	0.718697	0.359348	−	0.933204i	$-0.382999\pi$
$263$	11.6553	0.718697	0.359348	+	0.933204i	$0.382999\pi$
$264$	3.02067	0.185910
$265$	−1.21515	−0.0746463
$266$	−70.7647	−4.33886
$267$	−17.6047	−1.07739
$268$	74.9799	4.58013
$269$	−5.27597	−0.321681	−0.160841	−	0.986980i	$-0.551421\pi$
$269$	−5.27597	−0.321681	−0.160841	+	0.986980i	$0.551421\pi$
$270$	2.95495	0.179832
$271$	15.0392	0.913565	0.456782	−	0.889578i	$-0.349002\pi$
$271$	15.0392	0.913565	0.456782	+	0.889578i	$0.349002\pi$
$272$	−51.0162	−3.09331
$273$	10.7517	0.650722
$274$	1.00422	0.0606674
$275$	−0.552173	−0.0332973
$276$	82.1225	4.94320
$277$	2.50764	0.150669	0.0753347	−	0.997158i	$-0.475997\pi$
$277$	2.50764	0.150669	0.0753347	+	0.997158i	$0.475997\pi$
$278$	11.3041	0.677974
$279$	19.8251	1.18690
$280$	−29.7911	−1.78036
$281$	−12.5353	−0.747792	−0.373896	−	0.927471i	$-0.621978\pi$
$281$	−12.5353	−0.747792	−0.373896	+	0.927471i	$0.621978\pi$
$282$	20.0981	1.19682
$283$	−5.67926	−0.337597	−0.168799	−	0.985651i	$-0.553989\pi$
$283$	−5.67926	−0.337597	−0.168799	+	0.985651i	$0.553989\pi$
$284$	61.5205	3.65057
$285$	−16.1908	−0.959061
$286$	0.408548	0.0241580
$287$	18.1504	1.07139
$288$	−66.8146	−3.93709
$289$	−3.24698	−0.190999
$290$	21.6191	1.26952
$291$	20.8937	1.22481
$292$	−55.5521	−3.25094
$293$	13.7857	0.805372	0.402686	−	0.915338i	$-0.368077\pi$
$293$	13.7857	0.805372	0.402686	+	0.915338i	$0.368077\pi$
$294$	45.2907	2.64141
$295$	3.81051	0.221856
$296$	30.6182	1.77965
$297$	−0.160171	−0.00929408
$298$	4.12878	0.239174
$299$	6.94004	0.401353
$300$	56.9328	3.28702
$301$	−2.27600	−0.131186
$302$	34.3064	1.97411
$303$	0.542872	0.0311872
$304$	97.5941	5.59741
$305$	4.06022	0.232488
$306$	34.9247	1.99651
$307$	−1.77928	−0.101549	−0.0507744	−	0.998710i	$-0.516169\pi$
$307$	−1.77928	−0.101549	−0.0507744	+	0.998710i	$0.516169\pi$
$308$	2.58441	0.147260
$309$	−19.5752	−1.11359
$310$	−13.8377	−0.785929
$311$	18.4438	1.04585	0.522925	−	0.852379i	$-0.324841\pi$
$311$	18.4438	1.04585	0.522925	+	0.852379i	$0.324841\pi$
$312$	−26.3203	−1.49009
$313$	−23.9453	−1.35347	−0.676734	−	0.736228i	$-0.736605\pi$
$313$	−23.9453	−1.35347	−0.676734	+	0.736228i	$0.736605\pi$
$314$	−21.0941	−1.19041
$315$	11.4896	0.647366
$316$	−43.3591	−2.43914
$317$	−3.11688	−0.175061	−0.0875306	−	0.996162i	$-0.527898\pi$
$317$	−3.11688	−0.175061	−0.0875306	+	0.996162i	$0.527898\pi$
$318$	−9.33921	−0.523717
$319$	−1.17185	−0.0656110
$320$	21.9661	1.22794
$321$	34.9785	1.95231
$322$	60.3723	3.36441
$323$	−26.3096	−1.46390
$324$	−39.1110	−2.17283
$325$	4.81130	0.266883
$326$	16.4100	0.908867
$327$	−18.4755	−1.02170
$328$	−44.4325	−2.45338
$329$	10.7442	0.592344
$330$	0.813151	0.0447625
$331$	10.3198	0.567229	0.283614	−	0.958938i	$-0.408466\pi$
$331$	10.3198	0.567229	0.283614	+	0.958938i	$0.408466\pi$
$332$	−35.6113	−1.95442
$333$	−11.8086	−0.647108
$334$	−10.8129	−0.591656
$335$	12.6117	0.689049
$336$	−128.991	−7.03704
$337$	6.17114	0.336163	0.168082	−	0.985773i	$-0.446243\pi$
$337$	6.17114	0.336163	0.168082	+	0.985773i	$0.446243\pi$
$338$	31.6384	1.72090
$339$	−22.9499	−1.24647
$340$	−17.7266	−0.961357
$341$	0.750065	0.0406183
$342$	−66.8111	−3.61273
$343$	−1.57643	−0.0851190
$344$	5.57167	0.300404
$345$	13.8131	0.743670
$346$	−29.7337	−1.59849
$347$	−31.7407	−1.70393	−0.851964	−	0.523601i	$-0.824588\pi$
$347$	−31.7407	−1.70393	−0.851964	+	0.523601i	$0.824588\pi$
$348$	120.826	6.47694
$349$	−10.4283	−0.558215	−0.279107	−	0.960260i	$-0.590039\pi$
$349$	−10.4283	−0.558215	−0.279107	+	0.960260i	$0.590039\pi$
$350$	41.8541	2.23719
$351$	1.39563	0.0744934
$352$	−2.52787	−0.134736
$353$	4.16072	0.221453	0.110726	−	0.993851i	$-0.464682\pi$
$353$	4.16072	0.221453	0.110726	+	0.993851i	$0.464682\pi$
$354$	29.2861	1.55654
$355$	10.3478	0.549203
$356$	36.8723	1.95423
$357$	34.7736	1.84042
$358$	63.9280	3.37870
$359$	2.45412	0.129524	0.0647618	−	0.997901i	$-0.479371\pi$
$359$	2.45412	0.129524	0.0647618	+	0.997901i	$0.479371\pi$
$360$	−28.1267	−1.48241
$361$	31.3304	1.64897
$362$	−37.6162	−1.97706
$363$	27.9535	1.46718
$364$	−22.5190	−1.18031
$365$	−9.34390	−0.489082
$366$	31.2054	1.63113
$367$	−5.38117	−0.280895	−0.140447	−	0.990088i	$-0.544854\pi$
$367$	−5.38117	−0.280895	−0.140447	+	0.990088i	$0.544854\pi$
$368$	−83.2616	−4.34031
$369$	17.1364	0.892085
$370$	8.24228	0.428496
$371$	−4.99262	−0.259204
$372$	−77.3368	−4.00973
$373$	1.53218	0.0793331	0.0396665	−	0.999213i	$-0.487370\pi$
$373$	1.53218	0.0793331	0.0396665	+	0.999213i	$0.487370\pi$
$374$	1.32135	0.0683251
$375$	20.9871	1.08377
$376$	−26.3018	−1.35641
$377$	10.2108	0.525882
$378$	12.1408	0.624455
$379$	−29.6586	−1.52346	−0.761729	−	0.647896i	$-0.775649\pi$
$379$	−29.6586	−1.52346	−0.761729	+	0.647896i	$0.775649\pi$
$380$	33.9110	1.73960
$381$	6.66674	0.341547
$382$	−21.1460	−1.08193
$383$	−22.5297	−1.15121	−0.575607	−	0.817726i	$-0.695234\pi$
$383$	−22.5297	−1.15121	−0.575607	+	0.817726i	$0.695234\pi$
$384$	71.0382	3.62515
$385$	0.434699	0.0221543
$386$	56.1254	2.85671
$387$	−2.14884	−0.109232
$388$	−43.7609	−2.22162
$389$	31.4147	1.59279	0.796394	−	0.604778i	$-0.206738\pi$
$389$	31.4147	1.59279	0.796394	+	0.604778i	$0.206738\pi$
$390$	−7.08530	−0.358778
$391$	22.4458	1.13513
$392$	−59.2708	−2.99363
$393$	48.7481	2.45902
$394$	56.7664	2.85985
$395$	−7.29302	−0.366952
$396$	2.44002	0.122616
$397$	15.9450	0.800258	0.400129	−	0.916459i	$-0.368965\pi$
$397$	15.9450	0.800258	0.400129	+	0.916459i	$0.368965\pi$
$398$	−14.9915	−0.751456
$399$	−66.5221	−3.33027
$400$	−57.7225	−2.88612
$401$	−21.9552	−1.09639	−0.548196	−	0.836350i	$-0.684685\pi$
$401$	−21.9552	−1.09639	−0.548196	+	0.836350i	$0.684685\pi$
$402$	96.9285	4.83436
$403$	−6.53561	−0.325562
$404$	−1.13702	−0.0565689
$405$	−6.57849	−0.326888
$406$	88.8248	4.40830
$407$	−0.446768	−0.0221455
$408$	−85.1263	−4.21438
$409$	20.7656	1.02679	0.513396	−	0.858152i	$-0.328387\pi$
$409$	20.7656	1.02679	0.513396	+	0.858152i	$0.328387\pi$
$410$	−11.9610	−0.590713
$411$	0.944017	0.0465649
$412$	40.9993	2.01989
$413$	15.6560	0.770380
$414$	56.9993	2.80136
$415$	−5.98984	−0.294030
$416$	22.0263	1.07993
$417$	10.6264	0.520376
$418$	−2.52774	−0.123636
$419$	13.4276	0.655981	0.327990	−	0.944681i	$-0.393629\pi$
$419$	13.4276	0.655981	0.327990	+	0.944681i	$0.393629\pi$
$420$	−44.8204	−2.18701
$421$	14.4546	0.704476	0.352238	−	0.935911i	$-0.385421\pi$
$421$	14.4546	0.704476	0.352238	+	0.935911i	$0.385421\pi$
$422$	11.9640	0.582396
$423$	10.1439	0.493213
$424$	12.2220	0.593552
$425$	15.5609	0.754815
$426$	79.5291	3.85320
$427$	16.6820	0.807297
$428$	−73.2610	−3.54120
$429$	0.384055	0.0185423
$430$	1.49987	0.0723300
$431$	16.8202	0.810198	0.405099	−	0.914273i	$-0.367237\pi$
$431$	16.8202	0.810198	0.405099	+	0.914273i	$0.367237\pi$
$432$	−16.7438	−0.805586
$433$	7.23500	0.347692	0.173846	−	0.984773i	$-0.444381\pi$
$433$	7.23500	0.347692	0.173846	+	0.984773i	$0.444381\pi$
$434$	−56.8540	−2.72908
$435$	20.3229	0.974411
$436$	38.6962	1.85321
$437$	−42.9389	−2.05405
$438$	−71.8137	−3.43139
$439$	17.9525	0.856827	0.428414	−	0.903583i	$-0.359073\pi$
$439$	17.9525	0.856827	0.428414	+	0.903583i	$0.359073\pi$
$440$	−1.06415	−0.0507313
$441$	22.8591	1.08853
$442$	−11.5134	−0.547636
$443$	−5.16979	−0.245624	−0.122812	−	0.992430i	$-0.539191\pi$
$443$	−5.16979	−0.245624	−0.122812	+	0.992430i	$0.539191\pi$
$444$	46.0648	2.18614
$445$	6.20194	0.294000
$446$	−49.4046	−2.33938
$447$	3.88125	0.183577
$448$	90.2507	4.26395
$449$	9.16113	0.432341	0.216170	−	0.976356i	$-0.430643\pi$
$449$	9.16113	0.432341	0.216170	+	0.976356i	$0.430643\pi$
$450$	39.5157	1.86279
$451$	0.648341	0.0305292
$452$	48.0676	2.26091
$453$	32.2496	1.51522
$454$	−54.5856	−2.56183
$455$	−3.78770	−0.177570
$456$	162.847	7.62601
$457$	−23.5616	−1.10216	−0.551082	−	0.834451i	$-0.685785\pi$
$457$	−23.5616	−1.10216	−0.551082	+	0.834451i	$0.685785\pi$
$458$	30.7822	1.43836
$459$	4.51382	0.210687
$460$	−28.9308	−1.34891
$461$	−24.7857	−1.15439	−0.577193	−	0.816607i	$-0.695852\pi$
$461$	−24.7857	−1.15439	−0.577193	+	0.816607i	$0.695852\pi$
$462$	3.34094	0.155434
$463$	−18.7637	−0.872023	−0.436012	−	0.899941i	$-0.643609\pi$
$463$	−18.7637	−0.872023	−0.436012	+	0.899941i	$0.643609\pi$
$464$	−122.502	−5.68699
$465$	−13.0081	−0.603236
$466$	12.9177	0.598402
$467$	−28.2399	−1.30679	−0.653394	−	0.757018i	$-0.726655\pi$
$467$	−28.2399	−1.30679	−0.653394	+	0.757018i	$0.726655\pi$
$468$	−21.2609	−0.982784
$469$	51.8167	2.39267
$470$	−7.08032	−0.326591
$471$	−19.8295	−0.913693
$472$	−38.3260	−1.76410
$473$	−0.0812994	−0.00373815
$474$	−56.0514	−2.57453
$475$	−29.7681	−1.36585
$476$	−72.8319	−3.33824
$477$	−4.71368	−0.215825
$478$	−50.4267	−2.30647
$479$	4.88422	0.223166	0.111583	−	0.993755i	$-0.464408\pi$
$479$	4.88422	0.223166	0.111583	+	0.993755i	$0.464408\pi$
$480$	43.8399	2.00101
$481$	3.89286	0.177499
$482$	68.0924	3.10152
$483$	56.7527	2.58234
$484$	−58.5474	−2.66124
$485$	−7.36061	−0.334228
$486$	−60.4464	−2.74190
$487$	−11.7178	−0.530984	−0.265492	−	0.964113i	$-0.585534\pi$
$487$	−11.7178	−0.530984	−0.265492	+	0.964113i	$0.585534\pi$
$488$	−40.8377	−1.84863
$489$	15.4262	0.697596
$490$	−15.9554	−0.720792
$491$	33.6758	1.51977	0.759884	−	0.650059i	$-0.225256\pi$
$491$	33.6758	1.51977	0.759884	+	0.650059i	$0.225256\pi$
$492$	−66.8483	−3.01375
$493$	33.0242	1.48733
$494$	22.0252	0.990959
$495$	0.410413	0.0184467
$496$	78.4095	3.52069
$497$	42.5152	1.90707
$498$	−46.0357	−2.06291
$499$	−30.2933	−1.35611	−0.678056	−	0.735010i	$-0.737177\pi$
$499$	−30.2933	−1.35611	−0.678056	+	0.735010i	$0.737177\pi$
$500$	−43.9566	−1.96580
$501$	−10.1646	−0.454122
$502$	−31.4097	−1.40188
$503$	30.8120	1.37384	0.686919	−	0.726734i	$-0.258963\pi$
$503$	30.8120	1.37384	0.686919	+	0.726734i	$0.258963\pi$
$504$	−115.562	−5.14755
$505$	−0.191248	−0.00851041
$506$	2.15652	0.0958689
$507$	29.7416	1.32087
$508$	−13.9632	−0.619517
$509$	28.9987	1.28534	0.642672	−	0.766141i	$-0.277826\pi$
$509$	28.9987	1.28534	0.642672	+	0.766141i	$0.277826\pi$
$510$	−22.9156	−1.01472
$511$	−38.3906	−1.69830
$512$	−16.1279	−0.712759
$513$	−8.63496	−0.381243
$514$	−33.9641	−1.49809
$515$	6.89611	0.303879
$516$	8.38252	0.369020
$517$	0.383785	0.0168788
$518$	33.8645	1.48792
$519$	−27.9511	−1.22692
$520$	9.27235	0.406619
$521$	−0.949456	−0.0415964	−0.0207982	−	0.999784i	$-0.506621\pi$
$521$	−0.949456	−0.0415964	−0.0207982	+	0.999784i	$0.506621\pi$
$522$	83.8623	3.67055
$523$	−21.5161	−0.940833	−0.470417	−	0.882444i	$-0.655896\pi$
$523$	−21.5161	−0.940833	−0.470417	+	0.882444i	$0.655896\pi$
$524$	−102.101	−4.46030
$525$	39.3448	1.71715
$526$	−31.5574	−1.37597
$527$	−21.1378	−0.920775
$528$	−4.60761	−0.200520
$529$	13.6329	0.592737
$530$	3.29010	0.142913
$531$	14.7813	0.641453
$532$	139.328	6.04062
$533$	−5.64924	−0.244696
$534$	47.6658	2.06270
$535$	−12.3225	−0.532750
$536$	−126.848	−5.47899
$537$	60.0953	2.59330
$538$	14.2850	0.615870
$539$	0.864854	0.0372519
$540$	−5.81796	−0.250365
$541$	−28.8007	−1.23824	−0.619118	−	0.785298i	$-0.712510\pi$
$541$	−28.8007	−1.23824	−0.619118	+	0.785298i	$0.712510\pi$
$542$	−40.7195	−1.74905
$543$	−35.3610	−1.51748
$544$	71.2385	3.05433
$545$	6.50873	0.278803
$546$	−29.1109	−1.24583
$547$	−30.4779	−1.30314	−0.651570	−	0.758588i	$-0.725889\pi$
$547$	−30.4779	−1.30314	−0.651570	+	0.758588i	$0.725889\pi$
$548$	−1.97720	−0.0844620
$549$	15.7500	0.672192
$550$	1.49504	0.0637488
$551$	−63.1754	−2.69136
$552$	−138.931	−5.91331
$553$	−29.9643	−1.27421
$554$	−6.78958	−0.288462
$555$	7.74813	0.328890
$556$	−22.2565	−0.943885
$557$	28.3508	1.20126	0.600631	−	0.799527i	$-0.294916\pi$
$557$	28.3508	1.20126	0.600631	+	0.799527i	$0.294916\pi$
$558$	−53.6777	−2.27236
$559$	0.708393	0.0299618
$560$	45.4421	1.92028
$561$	1.24213	0.0524426
$562$	33.9400	1.43167
$563$	2.45931	0.103648	0.0518238	−	0.998656i	$-0.483497\pi$
$563$	2.45931	0.103648	0.0518238	+	0.998656i	$0.483497\pi$
$564$	−39.5708	−1.66623
$565$	8.08499	0.340138
$566$	15.3769	0.646341
$567$	−27.0286	−1.13509
$568$	−104.078	−4.36700
$569$	−8.99475	−0.377080	−0.188540	−	0.982066i	$-0.560375\pi$
$569$	−8.99475	−0.377080	−0.188540	+	0.982066i	$0.560375\pi$
$570$	43.8376	1.83616
$571$	−42.5768	−1.78178	−0.890892	−	0.454216i	$-0.849920\pi$
$571$	−42.5768	−1.78178	−0.890892	+	0.454216i	$0.849920\pi$
$572$	−0.804386	−0.0336331
$573$	−19.8783	−0.830427
$574$	−49.1434	−2.05121
$575$	25.3964	1.05910
$576$	85.2085	3.55035
$577$	−14.0465	−0.584763	−0.292381	−	0.956302i	$-0.594448\pi$
$577$	−14.0465	−0.584763	−0.292381	+	0.956302i	$0.594448\pi$
$578$	8.79139	0.365673
$579$	52.7605	2.19265
$580$	−42.5655	−1.76744
$581$	−24.6100	−1.02100
$582$	−56.5709	−2.34494
$583$	−0.178338	−0.00738601
$584$	93.9807	3.88895
$585$	−3.57609	−0.147853
$586$	−37.3257	−1.54191
$587$	−16.9804	−0.700854	−0.350427	−	0.936590i	$-0.613964\pi$
$587$	−16.9804	−0.700854	−0.350427	+	0.936590i	$0.613964\pi$
$588$	−89.1723	−3.67740
$589$	40.4366	1.66616
$590$	−10.3172	−0.424751
$591$	53.3630	2.19506
$592$	−46.7037	−1.91951
$593$	−18.9024	−0.776227	−0.388113	−	0.921612i	$-0.626873\pi$
$593$	−18.9024	−0.776227	−0.388113	+	0.921612i	$0.626873\pi$
$594$	0.433673	0.0177938
$595$	−12.2504	−0.502216
$596$	−8.12911	−0.332981
$597$	−14.0927	−0.576776
$598$	−18.7906	−0.768404
$599$	10.7048	0.437386	0.218693	−	0.975794i	$-0.429821\pi$
$599$	10.7048	0.437386	0.218693	+	0.975794i	$0.429821\pi$
$600$	−96.3165	−3.93210
$601$	−1.16779	−0.0476350	−0.0238175	−	0.999716i	$-0.507582\pi$
$601$	−1.16779	−0.0476350	−0.0238175	+	0.999716i	$0.507582\pi$
$602$	6.16240	0.251161
$603$	48.9217	1.99225
$604$	−67.5454	−2.74838
$605$	−9.84770	−0.400366
$606$	−1.46986	−0.0597089
$607$	−9.39639	−0.381388	−0.190694	−	0.981650i	$-0.561074\pi$
$607$	−9.39639	−0.381388	−0.190694	+	0.981650i	$0.561074\pi$
$608$	−136.280	−5.52687
$609$	83.4995	3.38357
$610$	−10.9933	−0.445106
$611$	−3.34407	−0.135286
$612$	−68.7628	−2.77957
$613$	−25.8111	−1.04250	−0.521251	−	0.853404i	$-0.674534\pi$
$613$	−25.8111	−1.04250	−0.521251	+	0.853404i	$0.674534\pi$
$614$	4.81751	0.194419
$615$	−11.2439	−0.453399
$616$	−4.37220	−0.176161
$617$	−32.3539	−1.30252	−0.651259	−	0.758856i	$-0.725759\pi$
$617$	−32.3539	−1.30252	−0.651259	+	0.758856i	$0.725759\pi$
$618$	53.0009	2.13201
$619$	−19.7268	−0.792885	−0.396443	−	0.918059i	$-0.629755\pi$
$619$	−19.7268	−0.792885	−0.396443	+	0.918059i	$0.629755\pi$
$620$	27.2449	1.09418
$621$	7.36684	0.295621
$622$	−49.9376	−2.00231
$623$	25.4815	1.02089
$624$	40.1479	1.60720
$625$	13.5865	0.543460
$626$	64.8333	2.59126
$627$	−2.37619	−0.0948960
$628$	41.5319	1.65730
$629$	12.5905	0.502015
$630$	−31.1088	−1.23940
$631$	−40.1361	−1.59779	−0.798897	−	0.601468i	$-0.794583\pi$
$631$	−40.1361	−1.59779	−0.798897	+	0.601468i	$0.794583\pi$
$632$	73.3530	2.91783
$633$	11.2467	0.447015
$634$	8.43913	0.335161
$635$	−2.34862	−0.0932020
$636$	18.3879	0.729126
$637$	−7.53581	−0.298580
$638$	3.17285	0.125615
$639$	40.1399	1.58791
$640$	−25.0260	−0.989238
$641$	−33.6539	−1.32925	−0.664624	−	0.747178i	$-0.731408\pi$
$641$	−33.6539	−1.32925	−0.664624	+	0.747178i	$0.731408\pi$
$642$	−94.7064	−3.73776
$643$	49.2251	1.94125	0.970625	−	0.240597i	$-0.0773432\pi$
$643$	49.2251	1.94125	0.970625	+	0.240597i	$0.0773432\pi$
$644$	−118.866	−4.68398
$645$	1.40994	0.0555165
$646$	71.2348	2.80270
$647$	−0.281426	−0.0110640	−0.00553200	−	0.999985i	$-0.501761\pi$
$647$	−0.281426	−0.0110640	−0.00553200	+	0.999985i	$0.501761\pi$
$648$	66.1664	2.59926
$649$	0.559237	0.0219520
$650$	−13.0269	−0.510956
$651$	−53.4455	−2.09469
$652$	−32.3095	−1.26534
$653$	−9.13377	−0.357432	−0.178716	−	0.983901i	$-0.557194\pi$
$653$	−9.13377	−0.357432	−0.178716	+	0.983901i	$0.557194\pi$
$654$	50.0236	1.95608
$655$	−17.1734	−0.671021
$656$	67.7755	2.64619
$657$	−36.2458	−1.41408
$658$	−29.0904	−1.13406
$659$	−43.3660	−1.68930	−0.844650	−	0.535319i	$-0.820191\pi$
$659$	−43.3660	−1.68930	−0.844650	+	0.535319i	$0.820191\pi$
$660$	−1.60100	−0.0623189
$661$	25.6436	0.997420	0.498710	−	0.866769i	$-0.333807\pi$
$661$	25.6436	0.997420	0.498710	+	0.866769i	$0.333807\pi$
$662$	−27.9415	−1.08598
$663$	−10.8231	−0.420335
$664$	60.2457	2.33799
$665$	23.4350	0.908770
$666$	31.9725	1.23891
$667$	53.8975	2.08692
$668$	21.2894	0.823711
$669$	−46.4426	−1.79558
$670$	−34.1468	−1.31921
$671$	0.595886	0.0230039
$672$	180.122	6.94836
$673$	−3.88692	−0.149830	−0.0749149	−	0.997190i	$-0.523869\pi$
$673$	−3.88692	−0.149830	−0.0749149	+	0.997190i	$0.523869\pi$
$674$	−16.7087	−0.643596
$675$	5.10718	0.196576
$676$	−62.2925	−2.39587
$677$	37.0153	1.42261	0.711306	−	0.702882i	$-0.248104\pi$
$677$	37.0153	1.42261	0.711306	+	0.702882i	$0.248104\pi$
$678$	62.1382	2.38640
$679$	−30.2420	−1.16058
$680$	29.9890	1.15003
$681$	−51.3130	−1.96632
$682$	−2.03085	−0.0777652
$683$	−22.3372	−0.854709	−0.427355	−	0.904084i	$-0.640554\pi$
$683$	−22.3372	−0.854709	−0.427355	+	0.904084i	$0.640554\pi$
$684$	131.544	5.02969
$685$	−0.332567	−0.0127067
$686$	4.26827	0.162963
$687$	28.9367	1.10400
$688$	−8.49879	−0.324013
$689$	1.55393	0.0591999
$690$	−37.3997	−1.42378
$691$	−22.3505	−0.850253	−0.425127	−	0.905134i	$-0.639770\pi$
$691$	−22.3505	−0.850253	−0.425127	+	0.905134i	$0.639770\pi$
$692$	58.5423	2.22545
$693$	1.68624	0.0640548
$694$	85.9397	3.26223
$695$	−3.74355	−0.142001
$696$	−204.408	−7.74806
$697$	−18.2710	−0.692065
$698$	28.2353	1.06872
$699$	12.1433	0.459301
$700$	−82.4059	−3.11465
$701$	12.9760	0.490098	0.245049	−	0.969511i	$-0.421196\pi$
$701$	12.9760	0.490098	0.245049	+	0.969511i	$0.421196\pi$
$702$	−3.77876	−0.142620
$703$	−24.0856	−0.908407
$704$	3.22379	0.121501
$705$	−6.65583	−0.250673
$706$	−11.2654	−0.423979
$707$	−0.785766	−0.0295518
$708$	−57.6611	−2.16704
$709$	18.3439	0.688920	0.344460	−	0.938801i	$-0.388062\pi$
$709$	18.3439	0.688920	0.344460	+	0.938801i	$0.388062\pi$
$710$	−28.0172	−1.05147
$711$	−28.2902	−1.06097
$712$	−62.3790	−2.33775
$713$	−34.4982	−1.29197
$714$	−94.1517	−3.52354
$715$	−0.135298	−0.00505986
$716$	−125.867	−4.70387
$717$	−47.4035	−1.77032
$718$	−6.64469	−0.247977
$719$	−36.3201	−1.35451	−0.677257	−	0.735747i	$-0.736831\pi$
$719$	−36.3201	−1.35451	−0.677257	+	0.735747i	$0.736831\pi$
$720$	42.9033	1.59891
$721$	28.3336	1.05520
$722$	−84.8288	−3.15700
$723$	64.0101	2.38056
$724$	74.0620	2.75249
$725$	37.3653	1.38771
$726$	−75.6857	−2.80896
$727$	−9.40217	−0.348707	−0.174354	−	0.984683i	$-0.555784\pi$
$727$	−9.40217	−0.348707	−0.174354	+	0.984683i	$0.555784\pi$
$728$	38.0966	1.41196
$729$	−34.8124	−1.28935
$730$	25.2992	0.936364
$731$	2.29112	0.0847400
$732$	−61.4398	−2.27088
$733$	−37.2500	−1.37586	−0.687931	−	0.725776i	$-0.741481\pi$
$733$	−37.2500	−1.37586	−0.687931	+	0.725776i	$0.741481\pi$
$734$	14.5698	0.537783
$735$	−14.9988	−0.553240
$736$	116.266	4.28561
$737$	1.85091	0.0681792
$738$	−46.3978	−1.70793
$739$	33.0744	1.21666	0.608331	−	0.793683i	$-0.291839\pi$
$739$	33.0744	1.21666	0.608331	+	0.793683i	$0.291839\pi$
$740$	−16.2281	−0.596558
$741$	20.7047	0.760606
$742$	13.5178	0.496254
$743$	−28.8113	−1.05698	−0.528492	−	0.848938i	$-0.677242\pi$
$743$	−28.8113	−1.05698	−0.528492	+	0.848938i	$0.677242\pi$
$744$	130.835	4.79665
$745$	−1.36732	−0.0500947
$746$	−4.14846	−0.151886
$747$	−23.2351	−0.850128
$748$	−2.60158	−0.0951232
$749$	−50.6287	−1.84993
$750$	−56.8239	−2.07492
$751$	38.8502	1.41766	0.708832	−	0.705377i	$-0.249222\pi$
$751$	38.8502	1.41766	0.708832	+	0.705377i	$0.249222\pi$
$752$	40.1197	1.46301
$753$	−29.5266	−1.07601
$754$	−27.6463	−1.00682
$755$	−11.3612	−0.413475
$756$	−23.9038	−0.869374
$757$	−9.77493	−0.355276	−0.177638	−	0.984096i	$-0.556846\pi$
$757$	−9.77493	−0.355276	−0.177638	+	0.984096i	$0.556846\pi$
$758$	80.3023	2.91671
$759$	2.02723	0.0735837
$760$	−57.3691	−2.08100
$761$	10.8780	0.394329	0.197164	−	0.980370i	$-0.436827\pi$
$761$	10.8780	0.394329	0.197164	+	0.980370i	$0.436827\pi$
$762$	−18.0506	−0.653904
$763$	26.7420	0.968124
$764$	41.6342	1.50627
$765$	−11.5659	−0.418168
$766$	61.0005	2.20404
$767$	−4.87284	−0.175948
$768$	−67.6349	−2.44057
$769$	51.2185	1.84699	0.923493	−	0.383615i	$-0.125321\pi$
$769$	51.2185	1.84699	0.923493	+	0.383615i	$0.125321\pi$
$770$	−1.17697	−0.0424152
$771$	−31.9279	−1.14985
$772$	−110.505	−3.97715
$773$	−37.5362	−1.35008	−0.675041	−	0.737780i	$-0.735874\pi$
$773$	−37.5362	−1.35008	−0.675041	+	0.737780i	$0.735874\pi$
$774$	5.81811	0.209128
$775$	−23.9164	−0.859103
$776$	74.0329	2.65762
$777$	31.8342	1.14205
$778$	−85.0572	−3.04945
$779$	34.9526	1.25231
$780$	13.9502	0.499496
$781$	1.51866	0.0543418
$782$	−60.7733	−2.17325
$783$	10.8387	0.387344
$784$	90.4091	3.22890
$785$	6.98569	0.249330
$786$	−131.988	−4.70787
$787$	43.7017	1.55780	0.778899	−	0.627149i	$-0.215778\pi$
$787$	43.7017	1.55780	0.778899	+	0.627149i	$0.215778\pi$
$788$	−111.767	−3.98152
$789$	−29.6655	−1.05612
$790$	19.7463	0.702541
$791$	33.2182	1.18110
$792$	−4.12793	−0.146679
$793$	−5.19218	−0.184380
$794$	−43.1721	−1.53212
$795$	3.09285	0.109692
$796$	29.5166	1.04619
$797$	52.5794	1.86246	0.931228	−	0.364437i	$-0.118739\pi$
$797$	52.5794	1.86246	0.931228	+	0.364437i	$0.118739\pi$
$798$	180.113	6.37591
$799$	−10.8155	−0.382626
$800$	80.6032	2.84975
$801$	24.0579	0.850043
$802$	59.4451	2.09908
$803$	−1.37133	−0.0483931
$804$	−190.841	−6.73046
$805$	−19.9934	−0.704673
$806$	17.6956	0.623299
$807$	13.4286	0.472708
$808$	1.92356	0.0676708
$809$	28.2827	0.994366	0.497183	−	0.867646i	$-0.334368\pi$
$809$	28.2827	0.994366	0.497183	+	0.867646i	$0.334368\pi$
$810$	17.8117	0.625838
$811$	38.5854	1.35492	0.677458	−	0.735561i	$-0.263081\pi$
$811$	38.5854	1.35492	0.677458	+	0.735561i	$0.263081\pi$
$812$	−174.886	−6.13730
$813$	−38.2782	−1.34248
$814$	1.20965	0.0423983
$815$	−5.43447	−0.190361
$816$	129.848	4.54559
$817$	−4.38292	−0.153339
$818$	−56.2241	−1.96583
$819$	−14.6928	−0.513409
$820$	23.5499	0.822398
$821$	2.99999	0.104701	0.0523503	−	0.998629i	$-0.483329\pi$
$821$	2.99999	0.104701	0.0523503	+	0.998629i	$0.483329\pi$
$822$	−2.55598	−0.0891502
$823$	−24.4577	−0.852543	−0.426271	−	0.904595i	$-0.640173\pi$
$823$	−24.4577	−0.852543	−0.426271	+	0.904595i	$0.640173\pi$
$824$	−69.3609	−2.41630
$825$	1.40541	0.0489301
$826$	−42.3895	−1.47492
$827$	30.5026	1.06068	0.530340	−	0.847785i	$-0.322064\pi$
$827$	30.5026	1.06068	0.530340	+	0.847785i	$0.322064\pi$
$828$	−112.225	−3.90010
$829$	44.9891	1.56254	0.781268	−	0.624196i	$-0.214573\pi$
$829$	44.9891	1.56254	0.781268	+	0.624196i	$0.214573\pi$
$830$	16.2178	0.562930
$831$	−6.38252	−0.221407
$832$	−28.0901	−0.973850
$833$	−24.3726	−0.844462
$834$	−28.7715	−0.996277
$835$	3.58089	0.123922
$836$	4.97683	0.172127
$837$	−6.93754	−0.239796
$838$	−36.3560	−1.25590
$839$	−36.3125	−1.25365	−0.626824	−	0.779161i	$-0.715646\pi$
$839$	−36.3125	−1.25365	−0.626824	+	0.779161i	$0.715646\pi$
$840$	75.8253	2.61622
$841$	50.2986	1.73444
$842$	−39.1368	−1.34874
$843$	31.9052	1.09887
$844$	−23.5557	−0.810820
$845$	−10.4776	−0.360442
$846$	−27.4652	−0.944272
$847$	−40.4606	−1.39024
$848$	−18.6429	−0.640200
$849$	14.4550	0.496096
$850$	−42.1321	−1.44512
$851$	20.5484	0.704391
$852$	−156.584	−5.36448
$853$	27.9212	0.956005	0.478002	−	0.878359i	$-0.341361\pi$
$853$	27.9212	0.956005	0.478002	+	0.878359i	$0.341361\pi$
$854$	−45.1674	−1.54560
$855$	22.1257	0.756683
$856$	123.940	4.23618
$857$	23.3304	0.796951	0.398475	−	0.917179i	$-0.369539\pi$
$857$	23.3304	0.796951	0.398475	+	0.917179i	$0.369539\pi$
$858$	−1.03985	−0.0354999
$859$	23.6293	0.806221	0.403110	−	0.915151i	$-0.367929\pi$
$859$	23.6293	0.806221	0.403110	+	0.915151i	$0.367929\pi$
$860$	−2.95307	−0.100699
$861$	−46.1971	−1.57439
$862$	−45.5416	−1.55115
$863$	−3.86902	−0.131703	−0.0658514	−	0.997829i	$-0.520976\pi$
$863$	−3.86902	−0.131703	−0.0658514	+	0.997829i	$0.520976\pi$
$864$	23.3809	0.795435
$865$	9.84685	0.334803
$866$	−19.5892	−0.665668
$867$	8.26431	0.280671
$868$	111.939	3.79946
$869$	−1.07034	−0.0363087
$870$	−55.0256	−1.86554
$871$	−16.1277	−0.546466
$872$	−65.4646	−2.21691
$873$	−28.5524	−0.966353
$874$	116.260	3.93254
$875$	−30.3773	−1.02694
$876$	141.393	4.77723
$877$	31.2652	1.05575	0.527876	−	0.849321i	$-0.322989\pi$
$877$	31.2652	1.05575	0.527876	+	0.849321i	$0.322989\pi$
$878$	−48.6075	−1.64042
$879$	−35.0879	−1.18349
$880$	1.62321	0.0547183
$881$	−44.0982	−1.48570	−0.742852	−	0.669455i	$-0.766528\pi$
$881$	−44.0982	−1.48570	−0.742852	+	0.669455i	$0.766528\pi$
$882$	−61.8924	−2.08403
$883$	−22.3215	−0.751179	−0.375590	−	0.926786i	$-0.622560\pi$
$883$	−22.3215	−0.751179	−0.375590	+	0.926786i	$0.622560\pi$
$884$	22.6686	0.762427
$885$	−9.69863	−0.326016
$886$	13.9975	0.470256
$887$	−51.5483	−1.73082	−0.865411	−	0.501063i	$-0.832942\pi$
$887$	−51.5483	−1.73082	−0.865411	+	0.501063i	$0.832942\pi$
$888$	−77.9305	−2.61518
$889$	−9.64960	−0.323637
$890$	−16.7921	−0.562874
$891$	−0.965471	−0.0323445
$892$	97.2721	3.25691
$893$	20.6902	0.692370
$894$	−10.5087	−0.351464
$895$	−21.1709	−0.707665
$896$	−102.822	−3.43506
$897$	−17.6640	−0.589785
$898$	−24.8043	−0.827731
$899$	−50.7566	−1.69283
$900$	−77.8020	−2.59340
$901$	5.02578	0.167433
$902$	−1.75542	−0.0584491
$903$	5.79294	0.192777
$904$	−81.3187	−2.70462
$905$	12.4573	0.414094
$906$	−87.3177	−2.90094
$907$	35.7895	1.18837	0.594186	−	0.804328i	$-0.297474\pi$
$907$	35.7895	1.18837	0.594186	+	0.804328i	$0.297474\pi$
$908$	107.473	3.56662
$909$	−0.741866	−0.0246061
$910$	10.2554	0.339964
$911$	−54.6335	−1.81009	−0.905045	−	0.425316i	$-0.860163\pi$
$911$	−54.6335	−1.81009	−0.905045	+	0.425316i	$0.860163\pi$
$912$	−248.400	−8.22534
$913$	−0.879079	−0.0290933
$914$	63.7944	2.11013
$915$	−10.3342	−0.341639
$916$	−60.6067	−2.00250
$917$	−70.5592	−2.33007
$918$	−12.2214	−0.403368
$919$	27.8685	0.919298	0.459649	−	0.888101i	$-0.347975\pi$
$919$	27.8685	0.919298	0.459649	+	0.888101i	$0.347975\pi$
$920$	48.9440	1.61364
$921$	4.52868	0.149225
$922$	67.1089	2.21011
$923$	−13.2327	−0.435558
$924$	−6.57793	−0.216398
$925$	14.2455	0.468391
$926$	50.8038	1.66952
$927$	26.7506	0.878605
$928$	171.060	5.61532
$929$	−39.3413	−1.29074	−0.645372	−	0.763868i	$-0.723298\pi$
$929$	−39.3413	−1.29074	−0.645372	+	0.763868i	$0.723298\pi$
$930$	35.2202	1.15492
$931$	46.6250	1.52807
$932$	−25.4336	−0.833104
$933$	−46.9437	−1.53687
$934$	76.4613	2.50189
$935$	−0.437587	−0.0143106
$936$	35.9682	1.17566
$937$	−4.63056	−0.151274	−0.0756369	−	0.997135i	$-0.524099\pi$
$937$	−4.63056	−0.151274	−0.0756369	+	0.997135i	$0.524099\pi$
$938$	−140.297	−4.58085
$939$	60.9463	1.98891
$940$	13.9404	0.454684
$941$	−46.5284	−1.51678	−0.758391	−	0.651800i	$-0.774014\pi$
$941$	−46.5284	−1.51678	−0.758391	+	0.651800i	$0.774014\pi$
$942$	53.6894	1.74930
$943$	−29.8195	−0.971056
$944$	58.4608	1.90274
$945$	−4.02064	−0.130791
$946$	0.220123	0.00715682
$947$	58.5130	1.90142	0.950709	−	0.310085i	$-0.100358\pi$
$947$	58.5130	1.90142	0.950709	+	0.310085i	$0.100358\pi$
$948$	110.359	3.58429
$949$	11.9489	0.387878
$950$	80.5989	2.61497
$951$	7.93317	0.257251
$952$	123.214	3.99338
$953$	24.6153	0.797369	0.398685	−	0.917088i	$-0.369467\pi$
$953$	24.6153	0.797369	0.398685	+	0.917088i	$0.369467\pi$
$954$	12.7626	0.413204
$955$	7.00289	0.226608
$956$	99.2846	3.21109
$957$	2.98263	0.0964148
$958$	−13.2243	−0.427259
$959$	−1.36639	−0.0441232
$960$	−55.9089	−1.80445
$961$	1.48777	0.0479925
$962$	−10.5402	−0.339828
$963$	−47.8002	−1.54034
$964$	−134.066	−4.31799
$965$	−18.5869	−0.598335
$966$	−153.661	−4.94398
$967$	−2.05236	−0.0659996	−0.0329998	−	0.999455i	$-0.510506\pi$
$967$	−2.05236	−0.0659996	−0.0329998	+	0.999455i	$0.510506\pi$
$968$	99.0480	3.18352
$969$	66.9640	2.15119
$970$	19.9293	0.639891
$971$	−7.65293	−0.245594	−0.122797	−	0.992432i	$-0.539186\pi$
$971$	−7.65293	−0.245594	−0.122797	+	0.992432i	$0.539186\pi$
$972$	119.012	3.81732
$973$	−15.3809	−0.493088
$974$	31.7266	1.01659
$975$	−12.2459	−0.392182
$976$	62.2920	1.99392
$977$	−60.5225	−1.93629	−0.968143	−	0.250396i	$-0.919439\pi$
$977$	−60.5225	−1.93629	−0.968143	+	0.250396i	$0.919439\pi$
$978$	−41.7673	−1.33557
$979$	0.910208	0.0290904
$980$	31.4144	1.00350
$981$	25.2479	0.806104
$982$	−91.1792	−2.90965
$983$	−11.0982	−0.353977	−0.176989	−	0.984213i	$-0.556636\pi$
$983$	−11.0982	−0.353977	−0.176989	+	0.984213i	$0.556636\pi$
$984$	113.091	3.60521
$985$	−18.7992	−0.598992
$986$	−89.4149	−2.84755
$987$	−27.3464	−0.870444
$988$	−43.3651	−1.37963
$989$	3.73925	0.118901
$990$	−1.11122	−0.0353168
$991$	−36.6966	−1.16570	−0.582852	−	0.812578i	$-0.698063\pi$
$991$	−36.6966	−1.16570	−0.582852	+	0.812578i	$0.698063\pi$
$992$	−109.490	−3.47632
$993$	−26.2663	−0.833537
$994$	−115.112	−3.65114
$995$	4.96470	0.157392
$996$	90.6390	2.87201
$997$	13.2221	0.418748	0.209374	−	0.977836i	$-0.432857\pi$
$997$	13.2221	0.418748	0.209374	+	0.977836i	$0.432857\pi$
$998$	82.0208	2.59632
$999$	4.13227	0.130739

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8017.2.a.a.1.12	✓	327

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8017.2.a.a.1.12	✓	327	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:	\( N \)	\(=\)	\( 8017 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8017.a (trivial)

\(f(q)\)	\(=\)	\(q-2.70756 q^{2} -2.54523 q^{3} +5.33088 q^{4} +0.896657 q^{5} +6.89137 q^{6} +3.68403 q^{7} -9.01856 q^{8} +3.47821 q^{9} +O(q^{10})\)	\(q-2.70756 q^{2} -2.54523 q^{3} +5.33088 q^{4} +0.896657 q^{5} +6.89137 q^{6} +3.68403 q^{7} -9.01856 q^{8} +3.47821 q^{9} -2.42775 q^{10} +0.131595 q^{11} -13.5683 q^{12} -1.14664 q^{13} -9.97474 q^{14} -2.28220 q^{15} +13.7565 q^{16} -3.70851 q^{17} -9.41746 q^{18} +7.09439 q^{19} +4.77997 q^{20} -9.37672 q^{21} -0.356301 q^{22} -6.05252 q^{23} +22.9543 q^{24} -4.19601 q^{25} +3.10459 q^{26} -1.21715 q^{27} +19.6391 q^{28} -8.90498 q^{29} +6.17919 q^{30} +5.69980 q^{31} -19.2095 q^{32} -0.334940 q^{33} +10.0410 q^{34} +3.30331 q^{35} +18.5419 q^{36} -3.39502 q^{37} -19.2085 q^{38} +2.91846 q^{39} -8.08655 q^{40} +4.92679 q^{41} +25.3880 q^{42} -0.617800 q^{43} +0.701517 q^{44} +3.11876 q^{45} +16.3875 q^{46} +2.91641 q^{47} -35.0136 q^{48} +6.57209 q^{49} +11.3609 q^{50} +9.43901 q^{51} -6.11259 q^{52} -1.35520 q^{53} +3.29552 q^{54} +0.117996 q^{55} -33.2247 q^{56} -18.0569 q^{57} +24.1108 q^{58} +4.24968 q^{59} -12.1661 q^{60} +4.52818 q^{61} -15.4326 q^{62} +12.8138 q^{63} +24.4978 q^{64} -1.02814 q^{65} +0.906869 q^{66} +14.0652 q^{67} -19.7696 q^{68} +15.4051 q^{69} -8.94392 q^{70} +11.5404 q^{71} -31.3684 q^{72} -10.4208 q^{73} +9.19223 q^{74} +10.6798 q^{75} +37.8193 q^{76} +0.484800 q^{77} -7.90190 q^{78} -8.13357 q^{79} +12.3349 q^{80} -7.33669 q^{81} -13.3396 q^{82} -6.68019 q^{83} -49.9862 q^{84} -3.32526 q^{85} +1.67273 q^{86} +22.6652 q^{87} -1.18680 q^{88} +6.91674 q^{89} -8.44423 q^{90} -4.22425 q^{91} -32.2652 q^{92} -14.5073 q^{93} -7.89636 q^{94} +6.36123 q^{95} +48.8926 q^{96} -8.20895 q^{97} -17.7943 q^{98} +0.457715 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 327 q - 23 q^{2} - 48 q^{3} + 315 q^{4} - 55 q^{5} - 38 q^{6} - 87 q^{7} - 69 q^{8} + 303 q^{9}+O(q^{10}) \) 327 * q - 23 * q^2 - 48 * q^3 + 315 * q^4 - 55 * q^5 - 38 * q^6 - 87 * q^7 - 69 * q^8 + 303 * q^9	\( 327 q - 23 q^{2} - 48 q^{3} + 315 q^{4} - 55 q^{5} - 38 q^{6} - 87 q^{7} - 69 q^{8} + 303 q^{9} - 48 q^{10} - 70 q^{11} - 120 q^{12} - 53 q^{13} - 52 q^{14} - 77 q^{15} + 295 q^{16} - 164 q^{17} - 58 q^{18} - 47 q^{19} - 153 q^{20} - 39 q^{21} - 68 q^{22} - 256 q^{23} - 107 q^{24} + 288 q^{25} - 95 q^{26} - 189 q^{27} - 167 q^{28} - 99 q^{29} - 81 q^{30} - 71 q^{31} - 146 q^{32} - 95 q^{33} - 40 q^{34} - 192 q^{35} + 261 q^{36} - 54 q^{37} - 179 q^{38} - 115 q^{39} - 121 q^{40} - 111 q^{41} - 62 q^{42} - 110 q^{43} - 157 q^{44} - 137 q^{45} - 11 q^{46} - 324 q^{47} - 236 q^{48} + 296 q^{49} - 73 q^{50} - 88 q^{51} - 138 q^{52} - 170 q^{53} - 127 q^{54} - 151 q^{55} - 151 q^{56} - 106 q^{57} - 81 q^{58} - 123 q^{59} - 83 q^{60} - 62 q^{61} - 287 q^{62} - 400 q^{63} + 263 q^{64} - 143 q^{65} - 64 q^{66} - 95 q^{67} - 442 q^{68} - 22 q^{69} - 26 q^{70} - 210 q^{71} - 129 q^{72} - 121 q^{73} - 159 q^{74} - 194 q^{75} - 86 q^{76} - 178 q^{77} - 68 q^{78} - 145 q^{79} - 338 q^{80} + 259 q^{81} - 103 q^{82} - 418 q^{83} - 102 q^{84} - 40 q^{85} - 89 q^{86} - 372 q^{87} - 186 q^{88} - 100 q^{89} - 150 q^{90} - 69 q^{91} - 458 q^{92} - 81 q^{93} - 46 q^{94} - 377 q^{95} - 190 q^{96} - 87 q^{97} - 147 q^{98} - 171 q^{99}+O(q^{100}) \) 327 * q - 23 * q^2 - 48 * q^3 + 315 * q^4 - 55 * q^5 - 38 * q^6 - 87 * q^7 - 69 * q^8 + 303 * q^9 - 48 * q^10 - 70 * q^11 - 120 * q^12 - 53 * q^13 - 52 * q^14 - 77 * q^15 + 295 * q^16 - 164 * q^17 - 58 * q^18 - 47 * q^19 - 153 * q^20 - 39 * q^21 - 68 * q^22 - 256 * q^23 - 107 * q^24 + 288 * q^25 - 95 * q^26 - 189 * q^27 - 167 * q^28 - 99 * q^29 - 81 * q^30 - 71 * q^31 - 146 * q^32 - 95 * q^33 - 40 * q^34 - 192 * q^35 + 261 * q^36 - 54 * q^37 - 179 * q^38 - 115 * q^39 - 121 * q^40 - 111 * q^41 - 62 * q^42 - 110 * q^43 - 157 * q^44 - 137 * q^45 - 11 * q^46 - 324 * q^47 - 236 * q^48 + 296 * q^49 - 73 * q^50 - 88 * q^51 - 138 * q^52 - 170 * q^53 - 127 * q^54 - 151 * q^55 - 151 * q^56 - 106 * q^57 - 81 * q^58 - 123 * q^59 - 83 * q^60 - 62 * q^61 - 287 * q^62 - 400 * q^63 + 263 * q^64 - 143 * q^65 - 64 * q^66 - 95 * q^67 - 442 * q^68 - 22 * q^69 - 26 * q^70 - 210 * q^71 - 129 * q^72 - 121 * q^73 - 159 * q^74 - 194 * q^75 - 86 * q^76 - 178 * q^77 - 68 * q^78 - 145 * q^79 - 338 * q^80 + 259 * q^81 - 103 * q^82 - 418 * q^83 - 102 * q^84 - 40 * q^85 - 89 * q^86 - 372 * q^87 - 186 * q^88 - 100 * q^89 - 150 * q^90 - 69 * q^91 - 458 * q^92 - 81 * q^93 - 46 * q^94 - 377 * q^95 - 190 * q^96 - 87 * q^97 - 147 * q^98 - 171 * q^99

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