LMFDB - Embedded newform 8018.2.a.d.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8018,2,Mod(1,8018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8018, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("8018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8018 = 2 \cdot 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8018.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:	$64.0240523407$
Analytic rank:	$1$
Dimension:	$30$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	8018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.74076 q^{3} +1.00000 q^{4} +0.116951 q^{5} -2.74076 q^{6} -0.997196 q^{7} +1.00000 q^{8} +4.51179 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.74076 q^{3} +1.00000 q^{4} +0.116951 q^{5} -2.74076 q^{6} -0.997196 q^{7} +1.00000 q^{8} +4.51179 q^{9} +0.116951 q^{10} +3.52284 q^{11} -2.74076 q^{12} +1.83864 q^{13} -0.997196 q^{14} -0.320535 q^{15} +1.00000 q^{16} -2.74753 q^{17} +4.51179 q^{18} +1.00000 q^{19} +0.116951 q^{20} +2.73308 q^{21} +3.52284 q^{22} +3.51262 q^{23} -2.74076 q^{24} -4.98632 q^{25} +1.83864 q^{26} -4.14345 q^{27} -0.997196 q^{28} -2.84490 q^{29} -0.320535 q^{30} -7.76519 q^{31} +1.00000 q^{32} -9.65527 q^{33} -2.74753 q^{34} -0.116623 q^{35} +4.51179 q^{36} +1.28081 q^{37} +1.00000 q^{38} -5.03929 q^{39} +0.116951 q^{40} -5.75259 q^{41} +2.73308 q^{42} -9.54966 q^{43} +3.52284 q^{44} +0.527657 q^{45} +3.51262 q^{46} -12.0470 q^{47} -2.74076 q^{48} -6.00560 q^{49} -4.98632 q^{50} +7.53034 q^{51} +1.83864 q^{52} -1.96674 q^{53} -4.14345 q^{54} +0.411999 q^{55} -0.997196 q^{56} -2.74076 q^{57} -2.84490 q^{58} +13.5938 q^{59} -0.320535 q^{60} +13.4735 q^{61} -7.76519 q^{62} -4.49913 q^{63} +1.00000 q^{64} +0.215031 q^{65} -9.65527 q^{66} +8.40618 q^{67} -2.74753 q^{68} -9.62726 q^{69} -0.116623 q^{70} +5.48242 q^{71} +4.51179 q^{72} +10.8422 q^{73} +1.28081 q^{74} +13.6663 q^{75} +1.00000 q^{76} -3.51296 q^{77} -5.03929 q^{78} +2.10807 q^{79} +0.116951 q^{80} -2.17914 q^{81} -5.75259 q^{82} +0.895937 q^{83} +2.73308 q^{84} -0.321326 q^{85} -9.54966 q^{86} +7.79720 q^{87} +3.52284 q^{88} +4.04750 q^{89} +0.527657 q^{90} -1.83349 q^{91} +3.51262 q^{92} +21.2825 q^{93} -12.0470 q^{94} +0.116951 q^{95} -2.74076 q^{96} +2.54927 q^{97} -6.00560 q^{98} +15.8943 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 30 q^{2} - 10 q^{3} + 30 q^{4} - 12 q^{5} - 10 q^{6} - 15 q^{7} + 30 q^{8} + 10 q^{9}+O(q^{10}) $ 30 * q + 30 * q^2 - 10 * q^3 + 30 * q^4 - 12 * q^5 - 10 * q^6 - 15 * q^7 + 30 * q^8 + 10 * q^9	\( 30 q + 30 q^{2} - 10 q^{3} + 30 q^{4} - 12 q^{5} - 10 q^{6} - 15 q^{7} + 30 q^{8} + 10 q^{9} - 12 q^{10} - 17 q^{11} - 10 q^{12} - 19 q^{13} - 15 q^{14} - 8 q^{15} + 30 q^{16} - 18 q^{17} + 10 q^{18} + 30 q^{19} - 12 q^{20} - 14 q^{21} - 17 q^{22} - 15 q^{23} - 10 q^{24} - 4 q^{25} - 19 q^{26} - 37 q^{27} - 15 q^{28} - 37 q^{29} - 8 q^{30} - 11 q^{31} + 30 q^{32} + 6 q^{33} - 18 q^{34} - 4 q^{35} + 10 q^{36} - 46 q^{37} + 30 q^{38} - 12 q^{40} - 28 q^{41} - 14 q^{42} - 61 q^{43} - 17 q^{44} - 14 q^{45} - 15 q^{46} - 4 q^{47} - 10 q^{48} - q^{49} - 4 q^{50} - 8 q^{51} - 19 q^{52} - 19 q^{53} - 37 q^{54} - 17 q^{55} - 15 q^{56} - 10 q^{57} - 37 q^{58} - 6 q^{59} - 8 q^{60} - 32 q^{61} - 11 q^{62} - 24 q^{63} + 30 q^{64} - 24 q^{65} + 6 q^{66} - 44 q^{67} - 18 q^{68} - 2 q^{69} - 4 q^{70} + 10 q^{71} + 10 q^{72} - 58 q^{73} - 46 q^{74} - 42 q^{75} + 30 q^{76} - 32 q^{77} - 42 q^{79} - 12 q^{80} - 38 q^{81} - 28 q^{82} - 25 q^{83} - 14 q^{84} - 48 q^{85} - 61 q^{86} - 15 q^{87} - 17 q^{88} - 39 q^{89} - 14 q^{90} - 21 q^{91} - 15 q^{92} - 45 q^{93} - 4 q^{94} - 12 q^{95} - 10 q^{96} - 33 q^{97} - q^{98} - 38 q^{99}+O(q^{100}) \) 30 * q + 30 * q^2 - 10 * q^3 + 30 * q^4 - 12 * q^5 - 10 * q^6 - 15 * q^7 + 30 * q^8 + 10 * q^9 - 12 * q^10 - 17 * q^11 - 10 * q^12 - 19 * q^13 - 15 * q^14 - 8 * q^15 + 30 * q^16 - 18 * q^17 + 10 * q^18 + 30 * q^19 - 12 * q^20 - 14 * q^21 - 17 * q^22 - 15 * q^23 - 10 * q^24 - 4 * q^25 - 19 * q^26 - 37 * q^27 - 15 * q^28 - 37 * q^29 - 8 * q^30 - 11 * q^31 + 30 * q^32 + 6 * q^33 - 18 * q^34 - 4 * q^35 + 10 * q^36 - 46 * q^37 + 30 * q^38 - 12 * q^40 - 28 * q^41 - 14 * q^42 - 61 * q^43 - 17 * q^44 - 14 * q^45 - 15 * q^46 - 4 * q^47 - 10 * q^48 - q^49 - 4 * q^50 - 8 * q^51 - 19 * q^52 - 19 * q^53 - 37 * q^54 - 17 * q^55 - 15 * q^56 - 10 * q^57 - 37 * q^58 - 6 * q^59 - 8 * q^60 - 32 * q^61 - 11 * q^62 - 24 * q^63 + 30 * q^64 - 24 * q^65 + 6 * q^66 - 44 * q^67 - 18 * q^68 - 2 * q^69 - 4 * q^70 + 10 * q^71 + 10 * q^72 - 58 * q^73 - 46 * q^74 - 42 * q^75 + 30 * q^76 - 32 * q^77 - 42 * q^79 - 12 * q^80 - 38 * q^81 - 28 * q^82 - 25 * q^83 - 14 * q^84 - 48 * q^85 - 61 * q^86 - 15 * q^87 - 17 * q^88 - 39 * q^89 - 14 * q^90 - 21 * q^91 - 15 * q^92 - 45 * q^93 - 4 * q^94 - 12 * q^95 - 10 * q^96 - 33 * q^97 - q^98 - 38 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.74076	−1.58238	−0.791190	−	0.611570i	$-0.790538\pi$
$3$	−2.74076	−1.58238	−0.791190	+	0.611570i	$0.790538\pi$
$4$	1.00000	0.500000
$5$	0.116951	0.0523020	0.0261510	−	0.999658i	$-0.491675\pi$
$5$	0.116951	0.0523020	0.0261510	+	0.999658i	$0.491675\pi$
$6$	−2.74076	−1.11891
$7$	−0.997196	−0.376905	−0.188452	−	0.982082i	$-0.560347\pi$
$7$	−0.997196	−0.376905	−0.188452	+	0.982082i	$0.560347\pi$
$8$	1.00000	0.353553
$9$	4.51179	1.50393
$10$	0.116951	0.0369831
$11$	3.52284	1.06218	0.531088	−	0.847317i	$-0.321783\pi$
$11$	3.52284	1.06218	0.531088	+	0.847317i	$0.321783\pi$
$12$	−2.74076	−0.791190
$13$	1.83864	0.509948	0.254974	−	0.966948i	$-0.417933\pi$
$13$	1.83864	0.509948	0.254974	+	0.966948i	$0.417933\pi$
$14$	−0.997196	−0.266512
$15$	−0.320535	−0.0827617
$16$	1.00000	0.250000
$17$	−2.74753	−0.666375	−0.333187	−	0.942861i	$-0.608124\pi$
$17$	−2.74753	−0.666375	−0.333187	+	0.942861i	$0.608124\pi$
$18$	4.51179	1.06344
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	0.116951	0.0261510
$21$	2.73308	0.596407
$22$	3.52284	0.751072
$23$	3.51262	0.732432	0.366216	−	0.930530i	$-0.380653\pi$
$23$	3.51262	0.732432	0.366216	+	0.930530i	$0.380653\pi$
$24$	−2.74076	−0.559456
$25$	−4.98632	−0.997265
$26$	1.83864	0.360588
$27$	−4.14345	−0.797408
$28$	−0.997196	−0.188452
$29$	−2.84490	−0.528285	−0.264142	−	0.964484i	$-0.585089\pi$
$29$	−2.84490	−0.528285	−0.264142	+	0.964484i	$0.585089\pi$
$30$	−0.320535	−0.0585213
$31$	−7.76519	−1.39467	−0.697335	−	0.716746i	$-0.745631\pi$
$31$	−7.76519	−1.39467	−0.697335	+	0.716746i	$0.745631\pi$
$32$	1.00000	0.176777
$33$	−9.65527	−1.68077
$34$	−2.74753	−0.471198
$35$	−0.116623	−0.0197129
$36$	4.51179	0.751964
$37$	1.28081	0.210563	0.105282	−	0.994442i	$-0.466426\pi$
$37$	1.28081	0.210563	0.105282	+	0.994442i	$0.466426\pi$
$38$	1.00000	0.162221
$39$	−5.03929	−0.806932
$40$	0.116951	0.0184915
$41$	−5.75259	−0.898403	−0.449201	−	0.893430i	$-0.648291\pi$
$41$	−5.75259	−0.898403	−0.449201	+	0.893430i	$0.648291\pi$
$42$	2.73308	0.421723
$43$	−9.54966	−1.45631	−0.728155	−	0.685412i	$-0.759622\pi$
$43$	−9.54966	−1.45631	−0.728155	+	0.685412i	$0.759622\pi$
$44$	3.52284	0.531088
$45$	0.527657	0.0786585
$46$	3.51262	0.517907
$47$	−12.0470	−1.75723	−0.878614	−	0.477532i	$-0.841532\pi$
$47$	−12.0470	−1.75723	−0.878614	+	0.477532i	$0.841532\pi$
$48$	−2.74076	−0.395595
$49$	−6.00560	−0.857943
$50$	−4.98632	−0.705172
$51$	7.53034	1.05446
$52$	1.83864	0.254974
$53$	−1.96674	−0.270153	−0.135076	−	0.990835i	$-0.543128\pi$
$53$	−1.96674	−0.270153	−0.135076	+	0.990835i	$0.543128\pi$
$54$	−4.14345	−0.563852
$55$	0.411999	0.0555539
$56$	−0.997196	−0.133256
$57$	−2.74076	−0.363023
$58$	−2.84490	−0.373554
$59$	13.5938	1.76976	0.884878	−	0.465823i	$-0.154242\pi$
$59$	13.5938	1.76976	0.884878	+	0.465823i	$0.154242\pi$
$60$	−0.320535	−0.0413808
$61$	13.4735	1.72510	0.862550	−	0.505972i	$-0.168866\pi$
$61$	13.4735	1.72510	0.862550	+	0.505972i	$0.168866\pi$
$62$	−7.76519	−0.986180
$63$	−4.49913	−0.566838
$64$	1.00000	0.125000
$65$	0.215031	0.0266713
$66$	−9.65527	−1.18848
$67$	8.40618	1.02698	0.513489	−	0.858096i	$-0.328353\pi$
$67$	8.40618	1.02698	0.513489	+	0.858096i	$0.328353\pi$
$68$	−2.74753	−0.333187
$69$	−9.62726	−1.15899
$70$	−0.116623	−0.0139391
$71$	5.48242	0.650643	0.325322	−	0.945603i	$-0.394527\pi$
$71$	5.48242	0.650643	0.325322	+	0.945603i	$0.394527\pi$
$72$	4.51179	0.531719
$73$	10.8422	1.26898	0.634491	−	0.772930i	$-0.281210\pi$
$73$	10.8422	1.26898	0.634491	+	0.772930i	$0.281210\pi$
$74$	1.28081	0.148891
$75$	13.6663	1.57805
$76$	1.00000	0.114708
$77$	−3.51296	−0.400339
$78$	−5.03929	−0.570587
$79$	2.10807	0.237176	0.118588	−	0.992944i	$-0.462163\pi$
$79$	2.10807	0.237176	0.118588	+	0.992944i	$0.462163\pi$
$80$	0.116951	0.0130755
$81$	−2.17914	−0.242127
$82$	−5.75259	−0.635267
$83$	0.895937	0.0983419	0.0491709	−	0.998790i	$-0.484342\pi$
$83$	0.895937	0.0983419	0.0491709	+	0.998790i	$0.484342\pi$
$84$	2.73308	0.298203
$85$	−0.321326	−0.0348527
$86$	−9.54966	−1.02977
$87$	7.79720	0.835948
$88$	3.52284	0.375536
$89$	4.04750	0.429035	0.214517	−	0.976720i	$-0.431182\pi$
$89$	4.04750	0.429035	0.214517	+	0.976720i	$0.431182\pi$
$90$	0.527657	0.0556199
$91$	−1.83349	−0.192202
$92$	3.51262	0.366216
$93$	21.2825	2.20690
$94$	−12.0470	−1.24255
$95$	0.116951	0.0119989
$96$	−2.74076	−0.279728
$97$	2.54927	0.258839	0.129420	−	0.991590i	$-0.458689\pi$
$97$	2.54927	0.258839	0.129420	+	0.991590i	$0.458689\pi$
$98$	−6.00560	−0.606657
$99$	15.8943	1.59744
$100$	−4.98632	−0.498632
$101$	15.7207	1.56427	0.782136	−	0.623107i	$-0.214130\pi$
$101$	15.7207	1.56427	0.782136	+	0.623107i	$0.214130\pi$
$102$	7.53034	0.745615
$103$	6.84497	0.674455	0.337228	−	0.941423i	$-0.390511\pi$
$103$	6.84497	0.674455	0.337228	+	0.941423i	$0.390511\pi$
$104$	1.83864	0.180294
$105$	0.319636	0.0311932
$106$	−1.96674	−0.191027
$107$	−2.33219	−0.225461	−0.112730	−	0.993626i	$-0.535960\pi$
$107$	−2.33219	−0.225461	−0.112730	+	0.993626i	$0.535960\pi$
$108$	−4.14345	−0.398704
$109$	−10.7889	−1.03339	−0.516694	−	0.856170i	$-0.672838\pi$
$109$	−10.7889	−1.03339	−0.516694	+	0.856170i	$0.672838\pi$
$110$	0.411999	0.0392826
$111$	−3.51039	−0.333191
$112$	−0.997196	−0.0942261
$113$	−11.2605	−1.05930	−0.529650	−	0.848216i	$-0.677677\pi$
$113$	−11.2605	−1.05930	−0.529650	+	0.848216i	$0.677677\pi$
$114$	−2.74076	−0.256696
$115$	0.410804	0.0383076
$116$	−2.84490	−0.264142
$117$	8.29557	0.766925
$118$	13.5938	1.25141
$119$	2.73983	0.251160
$120$	−0.320535	−0.0292607
$121$	1.41040	0.128218
$122$	13.4735	1.21983
$123$	15.7665	1.42162
$124$	−7.76519	−0.697335
$125$	−1.16791	−0.104461
$126$	−4.49913	−0.400815
$127$	−17.4328	−1.54692	−0.773458	−	0.633848i	$-0.781474\pi$
$127$	−17.4328	−1.54692	−0.773458	+	0.633848i	$0.781474\pi$
$128$	1.00000	0.0883883
$129$	26.1734	2.30444
$130$	0.215031	0.0188594
$131$	−11.1103	−0.970708	−0.485354	−	0.874318i	$-0.661309\pi$
$131$	−11.1103	−0.970708	−0.485354	+	0.874318i	$0.661309\pi$
$132$	−9.65527	−0.840384
$133$	−0.997196	−0.0864678
$134$	8.40618	0.726183
$135$	−0.484580	−0.0417060
$136$	−2.74753	−0.235599
$137$	−15.9828	−1.36550	−0.682750	−	0.730652i	$-0.739216\pi$
$137$	−15.9828	−1.36550	−0.682750	+	0.730652i	$0.739216\pi$
$138$	−9.62726	−0.819527
$139$	3.16160	0.268163	0.134082	−	0.990970i	$-0.457192\pi$
$139$	3.16160	0.268163	0.134082	+	0.990970i	$0.457192\pi$
$140$	−0.116623	−0.00985643
$141$	33.0179	2.78061
$142$	5.48242	0.460074
$143$	6.47725	0.541654
$144$	4.51179	0.375982
$145$	−0.332713	−0.0276303
$146$	10.8422	0.897306
$147$	16.4599	1.35759
$148$	1.28081	0.105282
$149$	−11.7345	−0.961331	−0.480665	−	0.876904i	$-0.659605\pi$
$149$	−11.7345	−0.961331	−0.480665	+	0.876904i	$0.659605\pi$
$150$	13.6663	1.11585
$151$	−20.0544	−1.63201	−0.816004	−	0.578047i	$-0.803815\pi$
$151$	−20.0544	−1.63201	−0.816004	+	0.578047i	$0.803815\pi$
$152$	1.00000	0.0811107
$153$	−12.3963	−1.00218
$154$	−3.51296	−0.283082
$155$	−0.908145	−0.0729440
$156$	−5.03929	−0.403466
$157$	17.2770	1.37885	0.689427	−	0.724355i	$-0.257862\pi$
$157$	17.2770	1.37885	0.689427	+	0.724355i	$0.257862\pi$
$158$	2.10807	0.167709
$159$	5.39037	0.427484
$160$	0.116951	0.00924577
$161$	−3.50277	−0.276057
$162$	−2.17914	−0.171209
$163$	−17.8246	−1.39613	−0.698065	−	0.716034i	$-0.745956\pi$
$163$	−17.8246	−1.39613	−0.698065	+	0.716034i	$0.745956\pi$
$164$	−5.75259	−0.449201
$165$	−1.12919	−0.0879075
$166$	0.895937	0.0695382
$167$	−11.4034	−0.882424	−0.441212	−	0.897403i	$-0.645451\pi$
$167$	−11.4034	−0.882424	−0.441212	+	0.897403i	$0.645451\pi$
$168$	2.73308	0.210862
$169$	−9.61939	−0.739953
$170$	−0.321326	−0.0246446
$171$	4.51179	0.345025
$172$	−9.54966	−0.728155
$173$	−24.0155	−1.82587	−0.912933	−	0.408109i	$-0.866188\pi$
$173$	−24.0155	−1.82587	−0.912933	+	0.408109i	$0.866188\pi$
$174$	7.79720	0.591104
$175$	4.97234	0.375874
$176$	3.52284	0.265544
$177$	−37.2573	−2.80043
$178$	4.04750	0.303373
$179$	8.40847	0.628479	0.314239	−	0.949344i	$-0.398251\pi$
$179$	8.40847	0.628479	0.314239	+	0.949344i	$0.398251\pi$
$180$	0.527657	0.0393292
$181$	4.80991	0.357518	0.178759	−	0.983893i	$-0.442792\pi$
$181$	4.80991	0.357518	0.178759	+	0.983893i	$0.442792\pi$
$182$	−1.83349	−0.135907
$183$	−36.9276	−2.72977
$184$	3.51262	0.258954
$185$	0.149791	0.0110129
$186$	21.2825	1.56051
$187$	−9.67912	−0.707808
$188$	−12.0470	−0.878614
$189$	4.13183	0.300547
$190$	0.116951	0.00848450
$191$	16.7800	1.21415	0.607077	−	0.794643i	$-0.292342\pi$
$191$	16.7800	1.21415	0.607077	+	0.794643i	$0.292342\pi$
$192$	−2.74076	−0.197798
$193$	2.87542	0.206977	0.103488	−	0.994631i	$-0.467000\pi$
$193$	2.87542	0.206977	0.103488	+	0.994631i	$0.467000\pi$
$194$	2.54927	0.183027
$195$	−0.589349	−0.0422041
$196$	−6.00560	−0.428971
$197$	−18.6932	−1.33184	−0.665919	−	0.746024i	$-0.731960\pi$
$197$	−18.6932	−1.33184	−0.665919	+	0.746024i	$0.731960\pi$
$198$	15.8943	1.12956
$199$	14.1949	1.00625	0.503125	−	0.864214i	$-0.332184\pi$
$199$	14.1949	1.00625	0.503125	+	0.864214i	$0.332184\pi$
$200$	−4.98632	−0.352586
$201$	−23.0394	−1.62507
$202$	15.7207	1.10611
$203$	2.83692	0.199113
$204$	7.53034	0.527229
$205$	−0.672769	−0.0469883
$206$	6.84497	0.476912
$207$	15.8482	1.10153
$208$	1.83864	0.127487
$209$	3.52284	0.243680
$210$	0.319636	0.0220570
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	−1.96674	−0.135076
$213$	−15.0260	−1.02957
$214$	−2.33219	−0.159425
$215$	−1.11684	−0.0761679
$216$	−4.14345	−0.281926
$217$	7.74341	0.525657
$218$	−10.7889	−0.730716
$219$	−29.7159	−2.00801
$220$	0.411999	0.0277770
$221$	−5.05173	−0.339816
$222$	−3.51039	−0.235602
$223$	14.2168	0.952026	0.476013	−	0.879438i	$-0.342081\pi$
$223$	14.2168	0.952026	0.476013	+	0.879438i	$0.342081\pi$
$224$	−0.997196	−0.0666279
$225$	−22.4972	−1.49981
$226$	−11.2605	−0.749038
$227$	−0.421693	−0.0279887	−0.0139944	−	0.999902i	$-0.504455\pi$
$227$	−0.421693	−0.0279887	−0.0139944	+	0.999902i	$0.504455\pi$
$228$	−2.74076	−0.181512
$229$	−22.4671	−1.48467	−0.742335	−	0.670029i	$-0.766282\pi$
$229$	−22.4671	−1.48467	−0.742335	+	0.670029i	$0.766282\pi$
$230$	0.410804	0.0270876
$231$	9.62820	0.633489
$232$	−2.84490	−0.186777
$233$	9.30220	0.609407	0.304704	−	0.952447i	$-0.401443\pi$
$233$	9.30220	0.609407	0.304704	+	0.952447i	$0.401443\pi$
$234$	8.29557	0.542298
$235$	−1.40890	−0.0919066
$236$	13.5938	0.884878
$237$	−5.77772	−0.375304
$238$	2.73983	0.177597
$239$	−1.20314	−0.0778247	−0.0389123	−	0.999243i	$-0.512389\pi$
$239$	−1.20314	−0.0778247	−0.0389123	+	0.999243i	$0.512389\pi$
$240$	−0.320535	−0.0206904
$241$	−7.81685	−0.503528	−0.251764	−	0.967789i	$-0.581011\pi$
$241$	−7.81685	−0.503528	−0.251764	+	0.967789i	$0.581011\pi$
$242$	1.41040	0.0906641
$243$	18.4029	1.18054
$244$	13.4735	0.862550
$245$	−0.702360	−0.0448721
$246$	15.7665	1.00523
$247$	1.83864	0.116990
$248$	−7.76519	−0.493090
$249$	−2.45555	−0.155614
$250$	−1.16791	−0.0738650
$251$	14.7296	0.929726	0.464863	−	0.885383i	$-0.346104\pi$
$251$	14.7296	0.929726	0.464863	+	0.885383i	$0.346104\pi$
$252$	−4.49913	−0.283419
$253$	12.3744	0.777972
$254$	−17.4328	−1.09383
$255$	0.880679	0.0551503
$256$	1.00000	0.0625000
$257$	−22.9435	−1.43118	−0.715588	−	0.698522i	$-0.753841\pi$
$257$	−22.9435	−1.43118	−0.715588	+	0.698522i	$0.753841\pi$
$258$	26.1734	1.62948
$259$	−1.27722	−0.0793623
$260$	0.215031	0.0133356
$261$	−12.8356	−0.794503
$262$	−11.1103	−0.686394
$263$	−24.7062	−1.52345	−0.761724	−	0.647901i	$-0.775647\pi$
$263$	−24.7062	−1.52345	−0.761724	+	0.647901i	$0.775647\pi$
$264$	−9.65527	−0.594241
$265$	−0.230012	−0.0141295
$266$	−0.997196	−0.0611420
$267$	−11.0933	−0.678896
$268$	8.40618	0.513489
$269$	−11.1971	−0.682702	−0.341351	−	0.939936i	$-0.610884\pi$
$269$	−11.1971	−0.682702	−0.341351	+	0.939936i	$0.610884\pi$
$270$	−0.484580	−0.0294906
$271$	−20.0777	−1.21963	−0.609816	−	0.792543i	$-0.708757\pi$
$271$	−20.0777	−1.21963	−0.609816	+	0.792543i	$0.708757\pi$
$272$	−2.74753	−0.166594
$273$	5.02515	0.304136
$274$	−15.9828	−0.965555
$275$	−17.5660	−1.05927
$276$	−9.62726	−0.579493
$277$	−14.1896	−0.852571	−0.426286	−	0.904589i	$-0.640178\pi$
$277$	−14.1896	−0.852571	−0.426286	+	0.904589i	$0.640178\pi$
$278$	3.16160	0.189620
$279$	−35.0349	−2.09748
$280$	−0.116623	−0.00696955
$281$	−17.2940	−1.03167	−0.515837	−	0.856687i	$-0.672519\pi$
$281$	−17.2940	−1.03167	−0.515837	+	0.856687i	$0.672519\pi$
$282$	33.0179	1.96618
$283$	6.98404	0.415158	0.207579	−	0.978218i	$-0.433442\pi$
$283$	6.98404	0.415158	0.207579	+	0.978218i	$0.433442\pi$
$284$	5.48242	0.325322
$285$	−0.320535	−0.0189868
$286$	6.47725	0.383008
$287$	5.73645	0.338612
$288$	4.51179	0.265860
$289$	−9.45106	−0.555945
$290$	−0.332713	−0.0195376
$291$	−6.98695	−0.409582
$292$	10.8422	0.634491
$293$	21.5432	1.25857	0.629283	−	0.777176i	$-0.283349\pi$
$293$	21.5432	1.25857	0.629283	+	0.777176i	$0.283349\pi$
$294$	16.4599	0.959963
$295$	1.58980	0.0925618
$296$	1.28081	0.0744454
$297$	−14.5967	−0.846987
$298$	−11.7345	−0.679763
$299$	6.45845	0.373502
$300$	13.6663	0.789026
$301$	9.52288	0.548890
$302$	−20.0544	−1.15400
$303$	−43.0868	−2.47527
$304$	1.00000	0.0573539
$305$	1.57573	0.0902262
$306$	−12.3963	−0.708649
$307$	34.7514	1.98337	0.991684	−	0.128694i	$-0.0410784\pi$
$307$	34.7514	1.98337	0.991684	+	0.128694i	$0.0410784\pi$
$308$	−3.51296	−0.200170
$309$	−18.7605	−1.06724
$310$	−0.908145	−0.0515792
$311$	19.8701	1.12673	0.563365	−	0.826208i	$-0.309507\pi$
$311$	19.8701	1.12673	0.563365	+	0.826208i	$0.309507\pi$
$312$	−5.03929	−0.285293
$313$	−8.40056	−0.474828	−0.237414	−	0.971409i	$-0.576300\pi$
$313$	−8.40056	−0.474828	−0.237414	+	0.971409i	$0.576300\pi$
$314$	17.2770	0.974997
$315$	−0.526177	−0.0296467
$316$	2.10807	0.118588
$317$	−11.8208	−0.663921	−0.331961	−	0.943293i	$-0.607710\pi$
$317$	−11.8208	−0.663921	−0.331961	+	0.943293i	$0.607710\pi$
$318$	5.39037	0.302277
$319$	−10.0221	−0.561131
$320$	0.116951	0.00653775
$321$	6.39197	0.356765
$322$	−3.50277	−0.195202
$323$	−2.74753	−0.152877
$324$	−2.17914	−0.121063
$325$	−9.16807	−0.508553
$326$	−17.8246	−0.987214
$327$	29.5698	1.63521
$328$	−5.75259	−0.317633
$329$	12.0132	0.662308
$330$	−1.12919	−0.0621600
$331$	10.1127	0.555845	0.277923	−	0.960603i	$-0.410354\pi$
$331$	10.1127	0.555845	0.277923	+	0.960603i	$0.410354\pi$
$332$	0.895937	0.0491709
$333$	5.77873	0.316672
$334$	−11.4034	−0.623968
$335$	0.983109	0.0537130
$336$	2.73308	0.149102
$337$	8.19049	0.446165	0.223082	−	0.974800i	$-0.428388\pi$
$337$	8.19049	0.446165	0.223082	+	0.974800i	$0.428388\pi$
$338$	−9.61939	−0.523226
$339$	30.8624	1.67622
$340$	−0.321326	−0.0174264
$341$	−27.3555	−1.48138
$342$	4.51179	0.243969
$343$	12.9691	0.700267
$344$	−9.54966	−0.514883
$345$	−1.12592	−0.0606173
$346$	−24.0155	−1.29108
$347$	−10.5382	−0.565722	−0.282861	−	0.959161i	$-0.591284\pi$
$347$	−10.5382	−0.565722	−0.282861	+	0.959161i	$0.591284\pi$
$348$	7.79720	0.417974
$349$	15.8770	0.849876	0.424938	−	0.905222i	$-0.360296\pi$
$349$	15.8770	0.849876	0.424938	+	0.905222i	$0.360296\pi$
$350$	4.97234	0.265783
$351$	−7.61833	−0.406636
$352$	3.52284	0.187768
$353$	−18.0927	−0.962977	−0.481489	−	0.876452i	$-0.659904\pi$
$353$	−18.0927	−0.962977	−0.481489	+	0.876452i	$0.659904\pi$
$354$	−37.2573	−1.98020
$355$	0.641173	0.0340299
$356$	4.04750	0.214517
$357$	−7.50922	−0.397430
$358$	8.40847	0.444402
$359$	24.9033	1.31435	0.657173	−	0.753740i	$-0.271752\pi$
$359$	24.9033	1.31435	0.657173	+	0.753740i	$0.271752\pi$
$360$	0.527657	0.0278100
$361$	1.00000	0.0526316
$362$	4.80991	0.252803
$363$	−3.86558	−0.202890
$364$	−1.83349	−0.0961008
$365$	1.26800	0.0663703
$366$	−36.9276	−1.93024
$367$	22.6852	1.18416	0.592078	−	0.805881i	$-0.298308\pi$
$367$	22.6852	1.18416	0.592078	+	0.805881i	$0.298308\pi$
$368$	3.51262	0.183108
$369$	−25.9544	−1.35113
$370$	0.149791	0.00778728
$371$	1.96123	0.101822
$372$	21.2825	1.10345
$373$	0.627435	0.0324874	0.0162437	−	0.999868i	$-0.494829\pi$
$373$	0.627435	0.0324874	0.0162437	+	0.999868i	$0.494829\pi$
$374$	−9.67912	−0.500495
$375$	3.20096	0.165297
$376$	−12.0470	−0.621274
$377$	−5.23076	−0.269398
$378$	4.13183	0.212518
$379$	−25.4763	−1.30863	−0.654314	−	0.756223i	$-0.727043\pi$
$379$	−25.4763	−1.30863	−0.654314	+	0.756223i	$0.727043\pi$
$380$	0.116951	0.00599945
$381$	47.7793	2.44781
$382$	16.7800	0.858537
$383$	10.8886	0.556381	0.278191	−	0.960526i	$-0.410265\pi$
$383$	10.8886	0.556381	0.278191	+	0.960526i	$0.410265\pi$
$384$	−2.74076	−0.139864
$385$	−0.410844	−0.0209385
$386$	2.87542	0.146355
$387$	−43.0860	−2.19019
$388$	2.54927	0.129420
$389$	−33.1823	−1.68241	−0.841203	−	0.540719i	$-0.818152\pi$
$389$	−33.1823	−1.68241	−0.841203	+	0.540719i	$0.818152\pi$
$390$	−0.589349	−0.0298428
$391$	−9.65104	−0.488074
$392$	−6.00560	−0.303329
$393$	30.4506	1.53603
$394$	−18.6932	−0.941751
$395$	0.246541	0.0124048
$396$	15.8943	0.798719
$397$	−35.0174	−1.75747	−0.878737	−	0.477305i	$-0.841614\pi$
$397$	−35.0174	−1.75747	−0.878737	+	0.477305i	$0.841614\pi$
$398$	14.1949	0.711526
$399$	2.73308	0.136825
$400$	−4.98632	−0.249316
$401$	−2.43149	−0.121423	−0.0607114	−	0.998155i	$-0.519337\pi$
$401$	−2.43149	−0.121423	−0.0607114	+	0.998155i	$0.519337\pi$
$402$	−23.0394	−1.14910
$403$	−14.2774	−0.711208
$404$	15.7207	0.782136
$405$	−0.254852	−0.0126637
$406$	2.83692	0.140794
$407$	4.51208	0.223655
$408$	7.53034	0.372807
$409$	17.4603	0.863358	0.431679	−	0.902027i	$-0.357921\pi$
$409$	17.4603	0.863358	0.431679	+	0.902027i	$0.357921\pi$
$410$	−0.672769	−0.0332257
$411$	43.8050	2.16074
$412$	6.84497	0.337228
$413$	−13.5556	−0.667029
$414$	15.8482	0.778896
$415$	0.104781	0.00514348
$416$	1.83864	0.0901469
$417$	−8.66520	−0.424336
$418$	3.52284	0.172308
$419$	3.78517	0.184918	0.0924588	−	0.995717i	$-0.470527\pi$
$419$	3.78517	0.184918	0.0924588	+	0.995717i	$0.470527\pi$
$420$	0.319636	0.0155966
$421$	−15.4466	−0.752824	−0.376412	−	0.926452i	$-0.622842\pi$
$421$	−15.4466	−0.752824	−0.376412	+	0.926452i	$0.622842\pi$
$422$	−1.00000	−0.0486792
$423$	−54.3533	−2.64275
$424$	−1.96674	−0.0955134
$425$	13.7001	0.664552
$426$	−15.0260	−0.728012
$427$	−13.4357	−0.650198
$428$	−2.33219	−0.112730
$429$	−17.7526	−0.857104
$430$	−1.11684	−0.0538588
$431$	7.72797	0.372243	0.186122	−	0.982527i	$-0.440408\pi$
$431$	7.72797	0.372243	0.186122	+	0.982527i	$0.440408\pi$
$432$	−4.14345	−0.199352
$433$	−8.93362	−0.429322	−0.214661	−	0.976689i	$-0.568865\pi$
$433$	−8.93362	−0.429322	−0.214661	+	0.976689i	$0.568865\pi$
$434$	7.74341	0.371696
$435$	0.911889	0.0437217
$436$	−10.7889	−0.516694
$437$	3.51262	0.168031
$438$	−29.7159	−1.41988
$439$	−3.21929	−0.153648	−0.0768241	−	0.997045i	$-0.524478\pi$
$439$	−3.21929	−0.153648	−0.0768241	+	0.997045i	$0.524478\pi$
$440$	0.411999	0.0196413
$441$	−27.0960	−1.29029
$442$	−5.05173	−0.240286
$443$	−10.2920	−0.488986	−0.244493	−	0.969651i	$-0.578622\pi$
$443$	−10.2920	−0.488986	−0.244493	+	0.969651i	$0.578622\pi$
$444$	−3.51039	−0.166596
$445$	0.473359	0.0224394
$446$	14.2168	0.673184
$447$	32.1616	1.52119
$448$	−0.997196	−0.0471131
$449$	−18.7701	−0.885818	−0.442909	−	0.896567i	$-0.646054\pi$
$449$	−18.7701	−0.885818	−0.442909	+	0.896567i	$0.646054\pi$
$450$	−22.4972	−1.06053
$451$	−20.2654	−0.954262
$452$	−11.2605	−0.529650
$453$	54.9645	2.58246
$454$	−0.421693	−0.0197910
$455$	−0.214428	−0.0100525
$456$	−2.74076	−0.128348
$457$	0.823220	0.0385086	0.0192543	−	0.999815i	$-0.493871\pi$
$457$	0.823220	0.0385086	0.0192543	+	0.999815i	$0.493871\pi$
$458$	−22.4671	−1.04982
$459$	11.3843	0.531372
$460$	0.410804	0.0191538
$461$	39.0053	1.81666	0.908328	−	0.418258i	$-0.137359\pi$
$461$	39.0053	1.81666	0.908328	+	0.418258i	$0.137359\pi$
$462$	9.62820	0.447944
$463$	−25.6145	−1.19041	−0.595203	−	0.803575i	$-0.702928\pi$
$463$	−25.6145	−1.19041	−0.595203	+	0.803575i	$0.702928\pi$
$464$	−2.84490	−0.132071
$465$	2.48901	0.115425
$466$	9.30220	0.430916
$467$	−11.2528	−0.520720	−0.260360	−	0.965512i	$-0.583841\pi$
$467$	−11.2528	−0.520720	−0.260360	+	0.965512i	$0.583841\pi$
$468$	8.29557	0.383463
$469$	−8.38261	−0.387073
$470$	−1.40890	−0.0649878
$471$	−47.3521	−2.18187
$472$	13.5938	0.625703
$473$	−33.6419	−1.54686
$474$	−5.77772	−0.265380
$475$	−4.98632	−0.228788
$476$	2.73983	0.125580
$477$	−8.87351	−0.406290
$478$	−1.20314	−0.0550303
$479$	−25.9292	−1.18473	−0.592367	−	0.805668i	$-0.701807\pi$
$479$	−25.9292	−1.18473	−0.592367	+	0.805668i	$0.701807\pi$
$480$	−0.320535	−0.0146303
$481$	2.35495	0.107376
$482$	−7.81685	−0.356048
$483$	9.60026	0.436827
$484$	1.41040	0.0641092
$485$	0.298139	0.0135378
$486$	18.4029	0.834771
$487$	34.5869	1.56728	0.783642	−	0.621213i	$-0.213360\pi$
$487$	34.5869	1.56728	0.783642	+	0.621213i	$0.213360\pi$
$488$	13.4735	0.609915
$489$	48.8530	2.20921
$490$	−0.702360	−0.0317294
$491$	28.2296	1.27399	0.636993	−	0.770870i	$-0.280178\pi$
$491$	28.2296	1.27399	0.636993	+	0.770870i	$0.280178\pi$
$492$	15.7665	0.710808
$493$	7.81646	0.352036
$494$	1.83864	0.0827245
$495$	1.85885	0.0835492
$496$	−7.76519	−0.348667
$497$	−5.46704	−0.245230
$498$	−2.45555	−0.110036
$499$	2.64444	0.118381	0.0591907	−	0.998247i	$-0.481148\pi$
$499$	2.64444	0.118381	0.0591907	+	0.998247i	$0.481148\pi$
$500$	−1.16791	−0.0522305
$501$	31.2541	1.39633
$502$	14.7296	0.657415
$503$	−22.0493	−0.983131	−0.491565	−	0.870841i	$-0.663575\pi$
$503$	−22.0493	−0.983131	−0.491565	+	0.870841i	$0.663575\pi$
$504$	−4.49913	−0.200407
$505$	1.83855	0.0818146
$506$	12.3744	0.550109
$507$	26.3645	1.17089
$508$	−17.4328	−0.773458
$509$	4.65666	0.206403	0.103201	−	0.994660i	$-0.467091\pi$
$509$	4.65666	0.206403	0.103201	+	0.994660i	$0.467091\pi$
$510$	0.880679	0.0389971
$511$	−10.8118	−0.478285
$512$	1.00000	0.0441942
$513$	−4.14345	−0.182938
$514$	−22.9435	−1.01199
$515$	0.800525	0.0352753
$516$	26.1734	1.15222
$517$	−42.4395	−1.86649
$518$	−1.27722	−0.0561176
$519$	65.8209	2.88922
$520$	0.215031	0.00942972
$521$	−30.8508	−1.35160	−0.675798	−	0.737086i	$-0.736201\pi$
$521$	−30.8508	−1.35160	−0.675798	+	0.737086i	$0.736201\pi$
$522$	−12.8356	−0.561798
$523$	−36.3519	−1.58956	−0.794778	−	0.606900i	$-0.792413\pi$
$523$	−36.3519	−1.58956	−0.794778	+	0.606900i	$0.792413\pi$
$524$	−11.1103	−0.485354
$525$	−13.6280	−0.594775
$526$	−24.7062	−1.07724
$527$	21.3351	0.929372
$528$	−9.65527	−0.420192
$529$	−10.6615	−0.463544
$530$	−0.230012	−0.00999108
$531$	61.3321	2.66159
$532$	−0.997196	−0.0432339
$533$	−10.5770	−0.458139
$534$	−11.0933	−0.480052
$535$	−0.272751	−0.0117921
$536$	8.40618	0.363092
$537$	−23.0456	−0.994493
$538$	−11.1971	−0.482743
$539$	−21.1568	−0.911287
$540$	−0.484580	−0.0208530
$541$	14.3989	0.619058	0.309529	−	0.950890i	$-0.399829\pi$
$541$	14.3989	0.619058	0.309529	+	0.950890i	$0.399829\pi$
$542$	−20.0777	−0.862410
$543$	−13.1828	−0.565730
$544$	−2.74753	−0.117800
$545$	−1.26177	−0.0540483
$546$	5.02515	0.215057
$547$	−2.98632	−0.127686	−0.0638428	−	0.997960i	$-0.520336\pi$
$547$	−2.98632	−0.127686	−0.0638428	+	0.997960i	$0.520336\pi$
$548$	−15.9828	−0.682750
$549$	60.7894	2.59443
$550$	−17.5660	−0.749017
$551$	−2.84490	−0.121197
$552$	−9.62726	−0.409763
$553$	−2.10216	−0.0893929
$554$	−14.1896	−0.602859
$555$	−0.410543	−0.0174266
$556$	3.16160	0.134082
$557$	−45.7883	−1.94011	−0.970057	−	0.242877i	$-0.921909\pi$
$557$	−45.7883	−1.94011	−0.970057	+	0.242877i	$0.921909\pi$
$558$	−35.0349	−1.48314
$559$	−17.5584	−0.742642
$560$	−0.116623	−0.00492821
$561$	26.5282	1.12002
$562$	−17.2940	−0.729504
$563$	−10.7441	−0.452809	−0.226404	−	0.974033i	$-0.572697\pi$
$563$	−10.7441	−0.452809	−0.226404	+	0.974033i	$0.572697\pi$
$564$	33.0179	1.39030
$565$	−1.31693	−0.0554035
$566$	6.98404	0.293561
$567$	2.17303	0.0912586
$568$	5.48242	0.230037
$569$	24.7561	1.03783	0.518916	−	0.854825i	$-0.326336\pi$
$569$	24.7561	1.03783	0.518916	+	0.854825i	$0.326336\pi$
$570$	−0.320535	−0.0134257
$571$	−39.3234	−1.64563	−0.822817	−	0.568306i	$-0.807599\pi$
$571$	−39.3234	−1.64563	−0.822817	+	0.568306i	$0.807599\pi$
$572$	6.47725	0.270827
$573$	−45.9899	−1.92126
$574$	5.73645	0.239435
$575$	−17.5151	−0.730428
$576$	4.51179	0.187991
$577$	−44.3664	−1.84700	−0.923498	−	0.383604i	$-0.874683\pi$
$577$	−44.3664	−1.84700	−0.923498	+	0.383604i	$0.874683\pi$
$578$	−9.45106	−0.393112
$579$	−7.88083	−0.327516
$580$	−0.332713	−0.0138152
$581$	−0.893425	−0.0370655
$582$	−6.98695	−0.289618
$583$	−6.92851	−0.286950
$584$	10.8422	0.448653
$585$	0.970173	0.0401117
$586$	21.5432	0.889941
$587$	−27.7204	−1.14414	−0.572072	−	0.820204i	$-0.693860\pi$
$587$	−27.7204	−1.14414	−0.572072	+	0.820204i	$0.693860\pi$
$588$	16.4599	0.678796
$589$	−7.76519	−0.319959
$590$	1.58980	0.0654510
$591$	51.2337	2.10747
$592$	1.28081	0.0526408
$593$	23.1732	0.951611	0.475805	−	0.879551i	$-0.342157\pi$
$593$	23.1732	0.951611	0.475805	+	0.879551i	$0.342157\pi$
$594$	−14.5967	−0.598910
$595$	0.320425	0.0131362
$596$	−11.7345	−0.480665
$597$	−38.9049	−1.59227
$598$	6.45845	0.264106
$599$	16.6771	0.681406	0.340703	−	0.940171i	$-0.389335\pi$
$599$	16.6771	0.681406	0.340703	+	0.940171i	$0.389335\pi$
$600$	13.6663	0.557926
$601$	−34.6691	−1.41418	−0.707092	−	0.707122i	$-0.749993\pi$
$601$	−34.6691	−1.41418	−0.707092	+	0.707122i	$0.749993\pi$
$602$	9.52288	0.388124
$603$	37.9269	1.54450
$604$	−20.0544	−0.816004
$605$	0.164948	0.00670607
$606$	−43.0868	−1.75028
$607$	−38.2887	−1.55409	−0.777045	−	0.629445i	$-0.783282\pi$
$607$	−38.2887	−1.55409	−0.777045	+	0.629445i	$0.783282\pi$
$608$	1.00000	0.0405554
$609$	−7.77533	−0.315072
$610$	1.57573	0.0637995
$611$	−22.1500	−0.896095
$612$	−12.3963	−0.501090
$613$	−30.2695	−1.22257	−0.611286	−	0.791409i	$-0.709348\pi$
$613$	−30.2695	−1.22257	−0.611286	+	0.791409i	$0.709348\pi$
$614$	34.7514	1.40245
$615$	1.84390	0.0743533
$616$	−3.51296	−0.141541
$617$	21.0103	0.845842	0.422921	−	0.906167i	$-0.361005\pi$
$617$	21.0103	0.845842	0.422921	+	0.906167i	$0.361005\pi$
$618$	−18.7605	−0.754656
$619$	14.1126	0.567232	0.283616	−	0.958938i	$-0.408466\pi$
$619$	14.1126	0.567232	0.283616	+	0.958938i	$0.408466\pi$
$620$	−0.908145	−0.0364720
$621$	−14.5544	−0.584047
$622$	19.8701	0.796718
$623$	−4.03615	−0.161705
$624$	−5.03929	−0.201733
$625$	24.7950	0.991801
$626$	−8.40056	−0.335754
$627$	−9.65527	−0.385594
$628$	17.2770	0.689427
$629$	−3.51906	−0.140314
$630$	−0.526177	−0.0209634
$631$	−1.93725	−0.0771209	−0.0385604	−	0.999256i	$-0.512277\pi$
$631$	−1.93725	−0.0771209	−0.0385604	+	0.999256i	$0.512277\pi$
$632$	2.10807	0.0838546
$633$	2.74076	0.108936
$634$	−11.8208	−0.469463
$635$	−2.03879	−0.0809067
$636$	5.39037	0.213742
$637$	−11.0422	−0.437506
$638$	−10.0221	−0.396780
$639$	24.7355	0.978521
$640$	0.116951	0.00462289
$641$	−18.4449	−0.728528	−0.364264	−	0.931296i	$-0.618679\pi$
$641$	−18.4449	−0.728528	−0.364264	+	0.931296i	$0.618679\pi$
$642$	6.39197	0.252271
$643$	20.1818	0.795891	0.397946	−	0.917409i	$-0.369723\pi$
$643$	20.1818	0.795891	0.397946	+	0.917409i	$0.369723\pi$
$644$	−3.50277	−0.138028
$645$	3.06100	0.120527
$646$	−2.74753	−0.108100
$647$	−10.2365	−0.402440	−0.201220	−	0.979546i	$-0.564491\pi$
$647$	−10.2365	−0.402440	−0.201220	+	0.979546i	$0.564491\pi$
$648$	−2.17914	−0.0856047
$649$	47.8886	1.87979
$650$	−9.16807	−0.359601
$651$	−21.2229	−0.831790
$652$	−17.8246	−0.698065
$653$	−34.5819	−1.35330	−0.676648	−	0.736307i	$-0.736568\pi$
$653$	−34.5819	−1.35330	−0.676648	+	0.736307i	$0.736568\pi$
$654$	29.5698	1.15627
$655$	−1.29935	−0.0507699
$656$	−5.75259	−0.224601
$657$	48.9176	1.90846
$658$	12.0132	0.468322
$659$	47.6677	1.85687	0.928435	−	0.371495i	$-0.121155\pi$
$659$	47.6677	1.85687	0.928435	+	0.371495i	$0.121155\pi$
$660$	−1.12919	−0.0439537
$661$	−9.67695	−0.376390	−0.188195	−	0.982132i	$-0.560264\pi$
$661$	−9.67695	−0.376390	−0.188195	+	0.982132i	$0.560264\pi$
$662$	10.1127	0.393042
$663$	13.8456	0.537719
$664$	0.895937	0.0347691
$665$	−0.116623	−0.00452244
$666$	5.77873	0.223921
$667$	−9.99305	−0.386932
$668$	−11.4034	−0.441212
$669$	−38.9649	−1.50647
$670$	0.983109	0.0379808
$671$	47.4649	1.83236
$672$	2.73308	0.105431
$673$	25.4400	0.980639	0.490319	−	0.871543i	$-0.336880\pi$
$673$	25.4400	0.980639	0.490319	+	0.871543i	$0.336880\pi$
$674$	8.19049	0.315486
$675$	20.6606	0.795226
$676$	−9.61939	−0.369977
$677$	10.1150	0.388752	0.194376	−	0.980927i	$-0.437732\pi$
$677$	10.1150	0.388752	0.194376	+	0.980927i	$0.437732\pi$
$678$	30.8624	1.18526
$679$	−2.54212	−0.0975577
$680$	−0.321326	−0.0123223
$681$	1.15576	0.0442888
$682$	−27.3555	−1.04750
$683$	48.3321	1.84938	0.924688	−	0.380725i	$-0.124326\pi$
$683$	48.3321	1.84938	0.924688	+	0.380725i	$0.124326\pi$
$684$	4.51179	0.172512
$685$	−1.86920	−0.0714184
$686$	12.9691	0.495164
$687$	61.5771	2.34931
$688$	−9.54966	−0.364078
$689$	−3.61613	−0.137764
$690$	−1.12592	−0.0428629
$691$	−31.0727	−1.18206	−0.591030	−	0.806649i	$-0.701279\pi$
$691$	−31.0727	−1.18206	−0.591030	+	0.806649i	$0.701279\pi$
$692$	−24.0155	−0.912933
$693$	−15.8497	−0.602081
$694$	−10.5382	−0.400026
$695$	0.369752	0.0140255
$696$	7.79720	0.295552
$697$	15.8054	0.598673
$698$	15.8770	0.600953
$699$	−25.4951	−0.964314
$700$	4.97234	0.187937
$701$	−30.7180	−1.16020	−0.580101	−	0.814545i	$-0.696987\pi$
$701$	−30.7180	−1.16020	−0.580101	+	0.814545i	$0.696987\pi$
$702$	−7.61833	−0.287535
$703$	1.28081	0.0483065
$704$	3.52284	0.132772
$705$	3.86146	0.145431
$706$	−18.0927	−0.680928
$707$	−15.6767	−0.589581
$708$	−37.2573	−1.40021
$709$	4.71652	0.177133	0.0885663	−	0.996070i	$-0.471771\pi$
$709$	4.71652	0.177133	0.0885663	+	0.996070i	$0.471771\pi$
$710$	0.641173	0.0240628
$711$	9.51117	0.356697
$712$	4.04750	0.151687
$713$	−27.2762	−1.02150
$714$	−7.50922	−0.281026
$715$	0.757519	0.0283296
$716$	8.40847	0.314239
$717$	3.29752	0.123148
$718$	24.9033	0.929383
$719$	−4.46961	−0.166688	−0.0833442	−	0.996521i	$-0.526560\pi$
$719$	−4.46961	−0.166688	−0.0833442	+	0.996521i	$0.526560\pi$
$720$	0.527657	0.0196646
$721$	−6.82578	−0.254205
$722$	1.00000	0.0372161
$723$	21.4241	0.796773
$724$	4.80991	0.178759
$725$	14.1856	0.526840
$726$	−3.86558	−0.143465
$727$	5.63650	0.209046	0.104523	−	0.994522i	$-0.466668\pi$
$727$	5.63650	0.209046	0.104523	+	0.994522i	$0.466668\pi$
$728$	−1.83349	−0.0679535
$729$	−43.9005	−1.62594
$730$	1.26800	0.0469309
$731$	26.2380	0.970448
$732$	−36.9276	−1.36488
$733$	−35.1414	−1.29798	−0.648988	−	0.760799i	$-0.724808\pi$
$733$	−35.1414	−1.29798	−0.648988	+	0.760799i	$0.724808\pi$
$734$	22.6852	0.837325
$735$	1.92500	0.0710048
$736$	3.51262	0.129477
$737$	29.6136	1.09083
$738$	−25.9544	−0.955396
$739$	41.0747	1.51096	0.755478	−	0.655174i	$-0.227405\pi$
$739$	41.0747	1.51096	0.755478	+	0.655174i	$0.227405\pi$
$740$	0.149791	0.00550644
$741$	−5.03929	−0.185123
$742$	1.96123	0.0719988
$743$	50.3060	1.84555	0.922775	−	0.385340i	$-0.125916\pi$
$743$	50.3060	1.84555	0.922775	+	0.385340i	$0.125916\pi$
$744$	21.2825	0.780256
$745$	−1.37236	−0.0502795
$746$	0.627435	0.0229720
$747$	4.04228	0.147899
$748$	−9.67912	−0.353904
$749$	2.32565	0.0849773
$750$	3.20096	0.116883
$751$	9.37159	0.341974	0.170987	−	0.985273i	$-0.445304\pi$
$751$	9.37159	0.341974	0.170987	+	0.985273i	$0.445304\pi$
$752$	−12.0470	−0.439307
$753$	−40.3704	−1.47118
$754$	−5.23076	−0.190493
$755$	−2.34538	−0.0853572
$756$	4.13183	0.150273
$757$	−26.6216	−0.967580	−0.483790	−	0.875184i	$-0.660740\pi$
$757$	−26.6216	−0.967580	−0.483790	+	0.875184i	$0.660740\pi$
$758$	−25.4763	−0.925340
$759$	−33.9153	−1.23105
$760$	0.116951	0.00424225
$761$	−32.0753	−1.16273	−0.581363	−	0.813644i	$-0.697481\pi$
$761$	−32.0753	−1.16273	−0.581363	+	0.813644i	$0.697481\pi$
$762$	47.7793	1.73086
$763$	10.7586	0.389489
$764$	16.7800	0.607077
$765$	−1.44976	−0.0524160
$766$	10.8886	0.393421
$767$	24.9941	0.902483
$768$	−2.74076	−0.0988988
$769$	−23.1112	−0.833412	−0.416706	−	0.909041i	$-0.636816\pi$
$769$	−23.1112	−0.833412	−0.416706	+	0.909041i	$0.636816\pi$
$770$	−0.410844	−0.0148058
$771$	62.8827	2.26467
$772$	2.87542	0.103488
$773$	13.1814	0.474100	0.237050	−	0.971497i	$-0.423819\pi$
$773$	13.1814	0.474100	0.237050	+	0.971497i	$0.423819\pi$
$774$	−43.0860	−1.54870
$775$	38.7197	1.39085
$776$	2.54927	0.0915135
$777$	3.50055	0.125581
$778$	−33.1823	−1.18964
$779$	−5.75259	−0.206108
$780$	−0.589349	−0.0211021
$781$	19.3137	0.691098
$782$	−9.65104	−0.345121
$783$	11.7877	0.421258
$784$	−6.00560	−0.214486
$785$	2.02056	0.0721168
$786$	30.4506	1.08614
$787$	45.1276	1.60863	0.804313	−	0.594207i	$-0.202534\pi$
$787$	45.1276	1.60863	0.804313	+	0.594207i	$0.202534\pi$
$788$	−18.6932	−0.665919
$789$	67.7138	2.41068
$790$	0.246541	0.00877152
$791$	11.2289	0.399255
$792$	15.8943	0.564779
$793$	24.7729	0.879711
$794$	−35.0174	−1.24272
$795$	0.630408	0.0223583
$796$	14.1949	0.503125
$797$	7.39822	0.262058	0.131029	−	0.991379i	$-0.458172\pi$
$797$	7.39822	0.262058	0.131029	+	0.991379i	$0.458172\pi$
$798$	2.73308	0.0967499
$799$	33.0994	1.17097
$800$	−4.98632	−0.176293
$801$	18.2615	0.645237
$802$	−2.43149	−0.0858589
$803$	38.1953	1.34788
$804$	−23.0394	−0.812535
$805$	−0.409652	−0.0144383
$806$	−14.2774	−0.502900
$807$	30.6887	1.08029
$808$	15.7207	0.553054
$809$	−23.0333	−0.809807	−0.404904	−	0.914359i	$-0.632695\pi$
$809$	−23.0333	−0.809807	−0.404904	+	0.914359i	$0.632695\pi$
$810$	−0.254852	−0.00895459
$811$	23.1348	0.812373	0.406187	−	0.913790i	$-0.366858\pi$
$811$	23.1348	0.812373	0.406187	+	0.913790i	$0.366858\pi$
$812$	2.83692	0.0995565
$813$	55.0282	1.92992
$814$	4.51208	0.158148
$815$	−2.08460	−0.0730204
$816$	7.53034	0.263615
$817$	−9.54966	−0.334100
$818$	17.4603	0.610486
$819$	−8.27230	−0.289058
$820$	−0.672769	−0.0234941
$821$	−33.0686	−1.15410	−0.577051	−	0.816708i	$-0.695797\pi$
$821$	−33.0686	−1.15410	−0.577051	+	0.816708i	$0.695797\pi$
$822$	43.8050	1.52788
$823$	−19.0969	−0.665677	−0.332839	−	0.942984i	$-0.608006\pi$
$823$	−19.0969	−0.665677	−0.332839	+	0.942984i	$0.608006\pi$
$824$	6.84497	0.238456
$825$	48.1443	1.67617
$826$	−13.5556	−0.471661
$827$	−11.8054	−0.410513	−0.205257	−	0.978708i	$-0.565803\pi$
$827$	−11.8054	−0.410513	−0.205257	+	0.978708i	$0.565803\pi$
$828$	15.8482	0.550763
$829$	35.9121	1.24728	0.623639	−	0.781712i	$-0.285653\pi$
$829$	35.9121	1.24728	0.623639	+	0.781712i	$0.285653\pi$
$830$	0.104781	0.00363699
$831$	38.8904	1.34909
$832$	1.83864	0.0637435
$833$	16.5006	0.571712
$834$	−8.66520	−0.300051
$835$	−1.33364	−0.0461525
$836$	3.52284	0.121840
$837$	32.1747	1.11212
$838$	3.78517	0.130756
$839$	−33.1393	−1.14410	−0.572048	−	0.820220i	$-0.693851\pi$
$839$	−33.1393	−1.14410	−0.572048	+	0.820220i	$0.693851\pi$
$840$	0.319636	0.0110285
$841$	−20.9065	−0.720915
$842$	−15.4466	−0.532327
$843$	47.3988	1.63250
$844$	−1.00000	−0.0344214
$845$	−1.12500	−0.0387010
$846$	−54.3533	−1.86870
$847$	−1.40645	−0.0483261
$848$	−1.96674	−0.0675381
$849$	−19.1416	−0.656939
$850$	13.7001	0.469909
$851$	4.49899	0.154223
$852$	−15.0260	−0.514783
$853$	−16.6918	−0.571517	−0.285759	−	0.958302i	$-0.592246\pi$
$853$	−16.6918	−0.571517	−0.285759	+	0.958302i	$0.592246\pi$
$854$	−13.4357	−0.459759
$855$	0.527657	0.0180455
$856$	−2.33219	−0.0797125
$857$	52.3734	1.78904	0.894520	−	0.447028i	$-0.147518\pi$
$857$	52.3734	1.78904	0.894520	+	0.447028i	$0.147518\pi$
$858$	−17.7526	−0.606064
$859$	14.8912	0.508081	0.254040	−	0.967194i	$-0.418240\pi$
$859$	14.8912	0.508081	0.254040	+	0.967194i	$0.418240\pi$
$860$	−1.11684	−0.0380840
$861$	−15.7223	−0.535813
$862$	7.72797	0.263216
$863$	16.7562	0.570388	0.285194	−	0.958470i	$-0.407942\pi$
$863$	16.7562	0.570388	0.285194	+	0.958470i	$0.407942\pi$
$864$	−4.14345	−0.140963
$865$	−2.80863	−0.0954964
$866$	−8.93362	−0.303577
$867$	25.9031	0.879716
$868$	7.74341	0.262829
$869$	7.42640	0.251923
$870$	0.911889	0.0309159
$871$	15.4560	0.523705
$872$	−10.7889	−0.365358
$873$	11.5018	0.389276
$874$	3.51262	0.118816
$875$	1.16463	0.0393718
$876$	−29.7159	−1.00401
$877$	51.5232	1.73981	0.869907	−	0.493216i	$-0.164179\pi$
$877$	51.5232	1.73981	0.869907	+	0.493216i	$0.164179\pi$
$878$	−3.21929	−0.108646
$879$	−59.0448	−1.99153
$880$	0.411999	0.0138885
$881$	54.1095	1.82299	0.911497	−	0.411306i	$-0.134927\pi$
$881$	54.1095	1.82299	0.911497	+	0.411306i	$0.134927\pi$
$882$	−27.0960	−0.912369
$883$	13.3154	0.448100	0.224050	−	0.974578i	$-0.428072\pi$
$883$	13.3154	0.448100	0.224050	+	0.974578i	$0.428072\pi$
$884$	−5.05173	−0.169908
$885$	−4.35727	−0.146468
$886$	−10.2920	−0.345766
$887$	−31.3735	−1.05342	−0.526709	−	0.850046i	$-0.676574\pi$
$887$	−31.3735	−1.05342	−0.526709	+	0.850046i	$0.676574\pi$
$888$	−3.51039	−0.117801
$889$	17.3840	0.583039
$890$	0.473359	0.0158670
$891$	−7.67676	−0.257181
$892$	14.2168	0.476013
$893$	−12.0470	−0.403136
$894$	32.1616	1.07564
$895$	0.983378	0.0328707
$896$	−0.997196	−0.0333140
$897$	−17.7011	−0.591022
$898$	−18.7701	−0.626368
$899$	22.0912	0.736782
$900$	−22.4972	−0.749907
$901$	5.40369	0.180023
$902$	−20.2654	−0.674765
$903$	−26.1000	−0.868553
$904$	−11.2605	−0.374519
$905$	0.562523	0.0186989
$906$	54.9645	1.82607
$907$	−7.36776	−0.244642	−0.122321	−	0.992491i	$-0.539034\pi$
$907$	−7.36776	−0.244642	−0.122321	+	0.992491i	$0.539034\pi$
$908$	−0.421693	−0.0139944
$909$	70.9286	2.35255
$910$	−0.214428	−0.00710821
$911$	−37.4948	−1.24226	−0.621129	−	0.783709i	$-0.713326\pi$
$911$	−37.4948	−1.24226	−0.621129	+	0.783709i	$0.713326\pi$
$912$	−2.74076	−0.0907558
$913$	3.15624	0.104456
$914$	0.823220	0.0272297
$915$	−4.31871	−0.142772
$916$	−22.4671	−0.742335
$917$	11.0791	0.365864
$918$	11.3843	0.375737
$919$	−38.0095	−1.25382	−0.626908	−	0.779093i	$-0.715680\pi$
$919$	−38.0095	−1.25382	−0.626908	+	0.779093i	$0.715680\pi$
$920$	0.410804	0.0135438
$921$	−95.2455	−3.13844
$922$	39.0053	1.28457
$923$	10.0802	0.331794
$924$	9.62820	0.316744
$925$	−6.38652	−0.209987
$926$	−25.6145	−0.841744
$927$	30.8831	1.01433
$928$	−2.84490	−0.0933884
$929$	43.9473	1.44186	0.720932	−	0.693006i	$-0.243714\pi$
$929$	43.9473	1.44186	0.720932	+	0.693006i	$0.243714\pi$
$930$	2.48901	0.0816179
$931$	−6.00560	−0.196826
$932$	9.30220	0.304704
$933$	−54.4592	−1.78291
$934$	−11.2528	−0.368204
$935$	−1.13198	−0.0370197
$936$	8.29557	0.271149
$937$	25.8418	0.844214	0.422107	−	0.906546i	$-0.361291\pi$
$937$	25.8418	0.844214	0.422107	+	0.906546i	$0.361291\pi$
$938$	−8.38261	−0.273702
$939$	23.0240	0.751359
$940$	−1.40890	−0.0459533
$941$	−23.6252	−0.770160	−0.385080	−	0.922883i	$-0.625826\pi$
$941$	−23.6252	−0.770160	−0.385080	+	0.922883i	$0.625826\pi$
$942$	−47.3521	−1.54282
$943$	−20.2066	−0.658019
$944$	13.5938	0.442439
$945$	0.483221	0.0157192
$946$	−33.6419	−1.09379
$947$	0.951940	0.0309339	0.0154669	−	0.999880i	$-0.495077\pi$
$947$	0.951940	0.0309339	0.0154669	+	0.999880i	$0.495077\pi$
$948$	−5.77772	−0.187652
$949$	19.9349	0.647115
$950$	−4.98632	−0.161778
$951$	32.3980	1.05058
$952$	2.73983	0.0887984
$953$	−3.80277	−0.123184	−0.0615918	−	0.998101i	$-0.519618\pi$
$953$	−3.80277	−0.123184	−0.0615918	+	0.998101i	$0.519618\pi$
$954$	−8.87351	−0.287291
$955$	1.96243	0.0635027
$956$	−1.20314	−0.0389123
$957$	27.4683	0.887924
$958$	−25.9292	−0.837734
$959$	15.9380	0.514663
$960$	−0.320535	−0.0103452
$961$	29.2982	0.945102
$962$	2.35495	0.0759265
$963$	−10.5223	−0.339077
$964$	−7.81685	−0.251764
$965$	0.336282	0.0108253
$966$	9.60026	0.308883
$967$	59.5148	1.91387	0.956933	−	0.290308i	$-0.0937579\pi$
$967$	59.5148	1.91387	0.956933	+	0.290308i	$0.0937579\pi$
$968$	1.41040	0.0453320
$969$	7.53034	0.241909
$970$	0.298139	0.00957267
$971$	12.6012	0.404392	0.202196	−	0.979345i	$-0.435192\pi$
$971$	12.6012	0.404392	0.202196	+	0.979345i	$0.435192\pi$
$972$	18.4029	0.590272
$973$	−3.15273	−0.101072
$974$	34.5869	1.10824
$975$	25.1275	0.804724
$976$	13.4735	0.431275
$977$	25.1943	0.806036	0.403018	−	0.915192i	$-0.367961\pi$
$977$	25.1943	0.806036	0.403018	+	0.915192i	$0.367961\pi$
$978$	48.8530	1.56215
$979$	14.2587	0.455710
$980$	−0.702360	−0.0224361
$981$	−48.6772	−1.55414
$982$	28.2296	0.900844
$983$	−30.4475	−0.971123	−0.485562	−	0.874202i	$-0.661385\pi$
$983$	−30.4475	−0.971123	−0.485562	+	0.874202i	$0.661385\pi$
$984$	15.7665	0.502617
$985$	−2.18619	−0.0696577
$986$	7.81646	0.248927
$987$	−32.9253	−1.04802
$988$	1.83864	0.0584950
$989$	−33.5443	−1.06665
$990$	1.85885	0.0590782
$991$	50.2206	1.59531	0.797655	−	0.603114i	$-0.206074\pi$
$991$	50.2206	1.59531	0.797655	+	0.603114i	$0.206074\pi$
$992$	−7.76519	−0.246545
$993$	−27.7166	−0.879559
$994$	−5.46704	−0.173404
$995$	1.66011	0.0526289
$996$	−2.45555	−0.0778072
$997$	13.4416	0.425700	0.212850	−	0.977085i	$-0.431725\pi$
$997$	13.4416	0.425700	0.212850	+	0.977085i	$0.431725\pi$
$998$	2.64444	0.0837083
$999$	−5.30696	−0.167905

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.d.1.3	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.d.1.3	✓	30	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:	\( N \)	\(=\)	\( 8018 = 2 \cdot 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8018.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.74076 q^{3} +1.00000 q^{4} +0.116951 q^{5} -2.74076 q^{6} -0.997196 q^{7} +1.00000 q^{8} +4.51179 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.74076 q^{3} +1.00000 q^{4} +0.116951 q^{5} -2.74076 q^{6} -0.997196 q^{7} +1.00000 q^{8} +4.51179 q^{9} +0.116951 q^{10} +3.52284 q^{11} -2.74076 q^{12} +1.83864 q^{13} -0.997196 q^{14} -0.320535 q^{15} +1.00000 q^{16} -2.74753 q^{17} +4.51179 q^{18} +1.00000 q^{19} +0.116951 q^{20} +2.73308 q^{21} +3.52284 q^{22} +3.51262 q^{23} -2.74076 q^{24} -4.98632 q^{25} +1.83864 q^{26} -4.14345 q^{27} -0.997196 q^{28} -2.84490 q^{29} -0.320535 q^{30} -7.76519 q^{31} +1.00000 q^{32} -9.65527 q^{33} -2.74753 q^{34} -0.116623 q^{35} +4.51179 q^{36} +1.28081 q^{37} +1.00000 q^{38} -5.03929 q^{39} +0.116951 q^{40} -5.75259 q^{41} +2.73308 q^{42} -9.54966 q^{43} +3.52284 q^{44} +0.527657 q^{45} +3.51262 q^{46} -12.0470 q^{47} -2.74076 q^{48} -6.00560 q^{49} -4.98632 q^{50} +7.53034 q^{51} +1.83864 q^{52} -1.96674 q^{53} -4.14345 q^{54} +0.411999 q^{55} -0.997196 q^{56} -2.74076 q^{57} -2.84490 q^{58} +13.5938 q^{59} -0.320535 q^{60} +13.4735 q^{61} -7.76519 q^{62} -4.49913 q^{63} +1.00000 q^{64} +0.215031 q^{65} -9.65527 q^{66} +8.40618 q^{67} -2.74753 q^{68} -9.62726 q^{69} -0.116623 q^{70} +5.48242 q^{71} +4.51179 q^{72} +10.8422 q^{73} +1.28081 q^{74} +13.6663 q^{75} +1.00000 q^{76} -3.51296 q^{77} -5.03929 q^{78} +2.10807 q^{79} +0.116951 q^{80} -2.17914 q^{81} -5.75259 q^{82} +0.895937 q^{83} +2.73308 q^{84} -0.321326 q^{85} -9.54966 q^{86} +7.79720 q^{87} +3.52284 q^{88} +4.04750 q^{89} +0.527657 q^{90} -1.83349 q^{91} +3.51262 q^{92} +21.2825 q^{93} -12.0470 q^{94} +0.116951 q^{95} -2.74076 q^{96} +2.54927 q^{97} -6.00560 q^{98} +15.8943 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 30 q^{2} - 10 q^{3} + 30 q^{4} - 12 q^{5} - 10 q^{6} - 15 q^{7} + 30 q^{8} + 10 q^{9}+O(q^{10}) \) 30 * q + 30 * q^2 - 10 * q^3 + 30 * q^4 - 12 * q^5 - 10 * q^6 - 15 * q^7 + 30 * q^8 + 10 * q^9	\( 30 q + 30 q^{2} - 10 q^{3} + 30 q^{4} - 12 q^{5} - 10 q^{6} - 15 q^{7} + 30 q^{8} + 10 q^{9} - 12 q^{10} - 17 q^{11} - 10 q^{12} - 19 q^{13} - 15 q^{14} - 8 q^{15} + 30 q^{16} - 18 q^{17} + 10 q^{18} + 30 q^{19} - 12 q^{20} - 14 q^{21} - 17 q^{22} - 15 q^{23} - 10 q^{24} - 4 q^{25} - 19 q^{26} - 37 q^{27} - 15 q^{28} - 37 q^{29} - 8 q^{30} - 11 q^{31} + 30 q^{32} + 6 q^{33} - 18 q^{34} - 4 q^{35} + 10 q^{36} - 46 q^{37} + 30 q^{38} - 12 q^{40} - 28 q^{41} - 14 q^{42} - 61 q^{43} - 17 q^{44} - 14 q^{45} - 15 q^{46} - 4 q^{47} - 10 q^{48} - q^{49} - 4 q^{50} - 8 q^{51} - 19 q^{52} - 19 q^{53} - 37 q^{54} - 17 q^{55} - 15 q^{56} - 10 q^{57} - 37 q^{58} - 6 q^{59} - 8 q^{60} - 32 q^{61} - 11 q^{62} - 24 q^{63} + 30 q^{64} - 24 q^{65} + 6 q^{66} - 44 q^{67} - 18 q^{68} - 2 q^{69} - 4 q^{70} + 10 q^{71} + 10 q^{72} - 58 q^{73} - 46 q^{74} - 42 q^{75} + 30 q^{76} - 32 q^{77} - 42 q^{79} - 12 q^{80} - 38 q^{81} - 28 q^{82} - 25 q^{83} - 14 q^{84} - 48 q^{85} - 61 q^{86} - 15 q^{87} - 17 q^{88} - 39 q^{89} - 14 q^{90} - 21 q^{91} - 15 q^{92} - 45 q^{93} - 4 q^{94} - 12 q^{95} - 10 q^{96} - 33 q^{97} - q^{98} - 38 q^{99}+O(q^{100}) \) 30 * q + 30 * q^2 - 10 * q^3 + 30 * q^4 - 12 * q^5 - 10 * q^6 - 15 * q^7 + 30 * q^8 + 10 * q^9 - 12 * q^10 - 17 * q^11 - 10 * q^12 - 19 * q^13 - 15 * q^14 - 8 * q^15 + 30 * q^16 - 18 * q^17 + 10 * q^18 + 30 * q^19 - 12 * q^20 - 14 * q^21 - 17 * q^22 - 15 * q^23 - 10 * q^24 - 4 * q^25 - 19 * q^26 - 37 * q^27 - 15 * q^28 - 37 * q^29 - 8 * q^30 - 11 * q^31 + 30 * q^32 + 6 * q^33 - 18 * q^34 - 4 * q^35 + 10 * q^36 - 46 * q^37 + 30 * q^38 - 12 * q^40 - 28 * q^41 - 14 * q^42 - 61 * q^43 - 17 * q^44 - 14 * q^45 - 15 * q^46 - 4 * q^47 - 10 * q^48 - q^49 - 4 * q^50 - 8 * q^51 - 19 * q^52 - 19 * q^53 - 37 * q^54 - 17 * q^55 - 15 * q^56 - 10 * q^57 - 37 * q^58 - 6 * q^59 - 8 * q^60 - 32 * q^61 - 11 * q^62 - 24 * q^63 + 30 * q^64 - 24 * q^65 + 6 * q^66 - 44 * q^67 - 18 * q^68 - 2 * q^69 - 4 * q^70 + 10 * q^71 + 10 * q^72 - 58 * q^73 - 46 * q^74 - 42 * q^75 + 30 * q^76 - 32 * q^77 - 42 * q^79 - 12 * q^80 - 38 * q^81 - 28 * q^82 - 25 * q^83 - 14 * q^84 - 48 * q^85 - 61 * q^86 - 15 * q^87 - 17 * q^88 - 39 * q^89 - 14 * q^90 - 21 * q^91 - 15 * q^92 - 45 * q^93 - 4 * q^94 - 12 * q^95 - 10 * q^96 - 33 * q^97 - q^98 - 38 * q^99

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