LMFDB - Embedded newform 8018.2.a.f.1.28

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:	$34$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.28
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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.86746 q^{3} +1.00000 q^{4} -2.09397 q^{5} -1.86746 q^{6} +2.42790 q^{7} -1.00000 q^{8} +0.487417 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.86746 q^{3} +1.00000 q^{4} -2.09397 q^{5} -1.86746 q^{6} +2.42790 q^{7} -1.00000 q^{8} +0.487417 q^{9} +2.09397 q^{10} +2.99461 q^{11} +1.86746 q^{12} -5.37284 q^{13} -2.42790 q^{14} -3.91041 q^{15} +1.00000 q^{16} +0.964069 q^{17} -0.487417 q^{18} -1.00000 q^{19} -2.09397 q^{20} +4.53401 q^{21} -2.99461 q^{22} +3.99152 q^{23} -1.86746 q^{24} -0.615290 q^{25} +5.37284 q^{26} -4.69216 q^{27} +2.42790 q^{28} -0.375299 q^{29} +3.91041 q^{30} -4.16611 q^{31} -1.00000 q^{32} +5.59232 q^{33} -0.964069 q^{34} -5.08395 q^{35} +0.487417 q^{36} +7.39092 q^{37} +1.00000 q^{38} -10.0336 q^{39} +2.09397 q^{40} +0.401844 q^{41} -4.53401 q^{42} +1.78574 q^{43} +2.99461 q^{44} -1.02064 q^{45} -3.99152 q^{46} -4.63226 q^{47} +1.86746 q^{48} -1.10531 q^{49} +0.615290 q^{50} +1.80036 q^{51} -5.37284 q^{52} -8.02571 q^{53} +4.69216 q^{54} -6.27063 q^{55} -2.42790 q^{56} -1.86746 q^{57} +0.375299 q^{58} -10.7511 q^{59} -3.91041 q^{60} +12.8044 q^{61} +4.16611 q^{62} +1.18340 q^{63} +1.00000 q^{64} +11.2506 q^{65} -5.59232 q^{66} +10.4904 q^{67} +0.964069 q^{68} +7.45401 q^{69} +5.08395 q^{70} -8.96856 q^{71} -0.487417 q^{72} +3.29220 q^{73} -7.39092 q^{74} -1.14903 q^{75} -1.00000 q^{76} +7.27061 q^{77} +10.0336 q^{78} -15.5108 q^{79} -2.09397 q^{80} -10.2247 q^{81} -0.401844 q^{82} +0.126446 q^{83} +4.53401 q^{84} -2.01873 q^{85} -1.78574 q^{86} -0.700857 q^{87} -2.99461 q^{88} +11.2811 q^{89} +1.02064 q^{90} -13.0447 q^{91} +3.99152 q^{92} -7.78006 q^{93} +4.63226 q^{94} +2.09397 q^{95} -1.86746 q^{96} -16.1334 q^{97} +1.10531 q^{98} +1.45962 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9}+O(q^{10}) $ 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9	\( 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9} - 7 q^{10} + 4 q^{11} - 10 q^{12} - 5 q^{13} + 6 q^{14} - 17 q^{15} + 34 q^{16} + 8 q^{17} - 38 q^{18} - 34 q^{19} + 7 q^{20} - 4 q^{22} - 24 q^{23} + 10 q^{24} + 5 q^{25} + 5 q^{26} - 31 q^{27} - 6 q^{28} + 24 q^{29} + 17 q^{30} - 28 q^{31} - 34 q^{32} - 16 q^{33} - 8 q^{34} + 2 q^{35} + 38 q^{36} - 36 q^{37} + 34 q^{38} - 9 q^{39} - 7 q^{40} + 9 q^{41} - 24 q^{43} + 4 q^{44} + 22 q^{45} + 24 q^{46} - 29 q^{47} - 10 q^{48} + 22 q^{49} - 5 q^{50} - 21 q^{51} - 5 q^{52} - 9 q^{53} + 31 q^{54} - 28 q^{55} + 6 q^{56} + 10 q^{57} - 24 q^{58} - 28 q^{59} - 17 q^{60} + 23 q^{61} + 28 q^{62} - 27 q^{63} + 34 q^{64} - 6 q^{65} + 16 q^{66} - 51 q^{67} + 8 q^{68} - 17 q^{69} - 2 q^{70} - 31 q^{71} - 38 q^{72} - 26 q^{73} + 36 q^{74} - 109 q^{75} - 34 q^{76} - 28 q^{77} + 9 q^{78} - 36 q^{79} + 7 q^{80} + 6 q^{81} - 9 q^{82} - 10 q^{83} - 32 q^{85} + 24 q^{86} - 8 q^{87} - 4 q^{88} - 34 q^{89} - 22 q^{90} - 41 q^{91} - 24 q^{92} - 33 q^{93} + 29 q^{94} - 7 q^{95} + 10 q^{96} - 56 q^{97} - 22 q^{98} - 28 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9 - 7 * q^10 + 4 * q^11 - 10 * q^12 - 5 * q^13 + 6 * q^14 - 17 * q^15 + 34 * q^16 + 8 * q^17 - 38 * q^18 - 34 * q^19 + 7 * q^20 - 4 * q^22 - 24 * q^23 + 10 * q^24 + 5 * q^25 + 5 * q^26 - 31 * q^27 - 6 * q^28 + 24 * q^29 + 17 * q^30 - 28 * q^31 - 34 * q^32 - 16 * q^33 - 8 * q^34 + 2 * q^35 + 38 * q^36 - 36 * q^37 + 34 * q^38 - 9 * q^39 - 7 * q^40 + 9 * q^41 - 24 * q^43 + 4 * q^44 + 22 * q^45 + 24 * q^46 - 29 * q^47 - 10 * q^48 + 22 * q^49 - 5 * q^50 - 21 * q^51 - 5 * q^52 - 9 * q^53 + 31 * q^54 - 28 * q^55 + 6 * q^56 + 10 * q^57 - 24 * q^58 - 28 * q^59 - 17 * q^60 + 23 * q^61 + 28 * q^62 - 27 * q^63 + 34 * q^64 - 6 * q^65 + 16 * q^66 - 51 * q^67 + 8 * q^68 - 17 * q^69 - 2 * q^70 - 31 * q^71 - 38 * q^72 - 26 * q^73 + 36 * q^74 - 109 * q^75 - 34 * q^76 - 28 * q^77 + 9 * q^78 - 36 * q^79 + 7 * q^80 + 6 * q^81 - 9 * q^82 - 10 * q^83 - 32 * q^85 + 24 * q^86 - 8 * q^87 - 4 * q^88 - 34 * q^89 - 22 * q^90 - 41 * q^91 - 24 * q^92 - 33 * q^93 + 29 * q^94 - 7 * q^95 + 10 * q^96 - 56 * q^97 - 22 * q^98 - 28 * 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
$3$	1.86746	1.07818	0.539090	−	0.842248i	$-0.318768\pi$
$3$	1.86746	1.07818	0.539090	+	0.842248i	$0.318768\pi$
$4$	1.00000	0.500000
$5$	−2.09397	−0.936452	−0.468226	−	0.883609i	$-0.655107\pi$
$5$	−2.09397	−0.936452	−0.468226	+	0.883609i	$0.655107\pi$
$6$	−1.86746	−0.762388
$7$	2.42790	0.917659	0.458830	−	0.888524i	$-0.348269\pi$
$7$	2.42790	0.917659	0.458830	+	0.888524i	$0.348269\pi$
$8$	−1.00000	−0.353553
$9$	0.487417	0.162472
$10$	2.09397	0.662171
$11$	2.99461	0.902909	0.451455	−	0.892294i	$-0.350905\pi$
$11$	2.99461	0.902909	0.451455	+	0.892294i	$0.350905\pi$
$12$	1.86746	0.539090
$13$	−5.37284	−1.49016	−0.745079	−	0.666976i	$-0.767588\pi$
$13$	−5.37284	−1.49016	−0.745079	+	0.666976i	$0.767588\pi$
$14$	−2.42790	−0.648883
$15$	−3.91041	−1.00966
$16$	1.00000	0.250000
$17$	0.964069	0.233821	0.116911	−	0.993142i	$-0.462701\pi$
$17$	0.964069	0.233821	0.116911	+	0.993142i	$0.462701\pi$
$18$	−0.487417	−0.114885
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−2.09397	−0.468226
$21$	4.53401	0.989402
$22$	−2.99461	−0.638453
$23$	3.99152	0.832289	0.416144	−	0.909299i	$-0.363381\pi$
$23$	3.99152	0.832289	0.416144	+	0.909299i	$0.363381\pi$
$24$	−1.86746	−0.381194
$25$	−0.615290	−0.123058
$26$	5.37284	1.05370
$27$	−4.69216	−0.903006
$28$	2.42790	0.458830
$29$	−0.375299	−0.0696913	−0.0348456	−	0.999393i	$-0.511094\pi$
$29$	−0.375299	−0.0696913	−0.0348456	+	0.999393i	$0.511094\pi$
$30$	3.91041	0.713940
$31$	−4.16611	−0.748256	−0.374128	−	0.927377i	$-0.622058\pi$
$31$	−4.16611	−0.748256	−0.374128	+	0.927377i	$0.622058\pi$
$32$	−1.00000	−0.176777
$33$	5.59232	0.973499
$34$	−0.964069	−0.165337
$35$	−5.08395	−0.859344
$36$	0.487417	0.0812361
$37$	7.39092	1.21506	0.607530	−	0.794297i	$-0.292161\pi$
$37$	7.39092	1.21506	0.607530	+	0.794297i	$0.292161\pi$
$38$	1.00000	0.162221
$39$	−10.0336	−1.60666
$40$	2.09397	0.331086
$41$	0.401844	0.0627575	0.0313787	−	0.999508i	$-0.490010\pi$
$41$	0.401844	0.0627575	0.0313787	+	0.999508i	$0.490010\pi$
$42$	−4.53401	−0.699613
$43$	1.78574	0.272324	0.136162	−	0.990687i	$-0.456523\pi$
$43$	1.78574	0.272324	0.136162	+	0.990687i	$0.456523\pi$
$44$	2.99461	0.451455
$45$	−1.02064	−0.152147
$46$	−3.99152	−0.588517
$47$	−4.63226	−0.675685	−0.337843	−	0.941203i	$-0.609697\pi$
$47$	−4.63226	−0.675685	−0.337843	+	0.941203i	$0.609697\pi$
$48$	1.86746	0.269545
$49$	−1.10531	−0.157901
$50$	0.615290	0.0870152
$51$	1.80036	0.252101
$52$	−5.37284	−0.745079
$53$	−8.02571	−1.10242	−0.551208	−	0.834368i	$-0.685833\pi$
$53$	−8.02571	−1.10242	−0.551208	+	0.834368i	$0.685833\pi$
$54$	4.69216	0.638521
$55$	−6.27063	−0.845531
$56$	−2.42790	−0.324442
$57$	−1.86746	−0.247351
$58$	0.375299	0.0492792
$59$	−10.7511	−1.39968	−0.699839	−	0.714301i	$-0.746745\pi$
$59$	−10.7511	−1.39968	−0.699839	+	0.714301i	$0.746745\pi$
$60$	−3.91041	−0.504832
$61$	12.8044	1.63944	0.819720	−	0.572764i	$-0.194129\pi$
$61$	12.8044	1.63944	0.819720	+	0.572764i	$0.194129\pi$
$62$	4.16611	0.529097
$63$	1.18340	0.149094
$64$	1.00000	0.125000
$65$	11.2506	1.39546
$66$	−5.59232	−0.688368
$67$	10.4904	1.28160	0.640802	−	0.767706i	$-0.278602\pi$
$67$	10.4904	1.28160	0.640802	+	0.767706i	$0.278602\pi$
$68$	0.964069	0.116911
$69$	7.45401	0.897357
$70$	5.08395	0.607648
$71$	−8.96856	−1.06437	−0.532186	−	0.846627i	$-0.678629\pi$
$71$	−8.96856	−1.06437	−0.532186	+	0.846627i	$0.678629\pi$
$72$	−0.487417	−0.0574426
$73$	3.29220	0.385323	0.192662	−	0.981265i	$-0.438288\pi$
$73$	3.29220	0.385323	0.192662	+	0.981265i	$0.438288\pi$
$74$	−7.39092	−0.859177
$75$	−1.14903	−0.132679
$76$	−1.00000	−0.114708
$77$	7.27061	0.828563
$78$	10.0336	1.13608
$79$	−15.5108	−1.74510	−0.872549	−	0.488526i	$-0.837535\pi$
$79$	−15.5108	−1.74510	−0.872549	+	0.488526i	$0.837535\pi$
$80$	−2.09397	−0.234113
$81$	−10.2247	−1.13607
$82$	−0.401844	−0.0443762
$83$	0.126446	0.0138792	0.00693962	−	0.999976i	$-0.497791\pi$
$83$	0.126446	0.0138792	0.00693962	+	0.999976i	$0.497791\pi$
$84$	4.53401	0.494701
$85$	−2.01873	−0.218962
$86$	−1.78574	−0.192562
$87$	−0.700857	−0.0751397
$88$	−2.99461	−0.319227
$89$	11.2811	1.19579	0.597896	−	0.801574i	$-0.296004\pi$
$89$	11.2811	1.19579	0.597896	+	0.801574i	$0.296004\pi$
$90$	1.02064	0.107584
$91$	−13.0447	−1.36746
$92$	3.99152	0.416144
$93$	−7.78006	−0.806755
$94$	4.63226	0.477781
$95$	2.09397	0.214837
$96$	−1.86746	−0.190597
$97$	−16.1334	−1.63810	−0.819051	−	0.573721i	$-0.805500\pi$
$97$	−16.1334	−1.63810	−0.819051	+	0.573721i	$0.805500\pi$
$98$	1.10531	0.111653
$99$	1.45962	0.146698
$100$	−0.615290	−0.0615290
$101$	−8.95826	−0.891381	−0.445690	−	0.895187i	$-0.647042\pi$
$101$	−8.95826	−0.891381	−0.445690	+	0.895187i	$0.647042\pi$
$102$	−1.80036	−0.178263
$103$	−2.26337	−0.223017	−0.111508	−	0.993764i	$-0.535568\pi$
$103$	−2.26337	−0.223017	−0.111508	+	0.993764i	$0.535568\pi$
$104$	5.37284	0.526851
$105$	−9.49408	−0.926527
$106$	8.02571	0.779526
$107$	19.8844	1.92230	0.961151	−	0.276023i	$-0.0890166\pi$
$107$	19.8844	1.92230	0.961151	+	0.276023i	$0.0890166\pi$
$108$	−4.69216	−0.451503
$109$	−12.7976	−1.22579	−0.612895	−	0.790165i	$-0.709995\pi$
$109$	−12.7976	−1.22579	−0.612895	+	0.790165i	$0.709995\pi$
$110$	6.27063	0.597881
$111$	13.8023	1.31005
$112$	2.42790	0.229415
$113$	4.13237	0.388740	0.194370	−	0.980928i	$-0.437734\pi$
$113$	4.13237	0.388740	0.194370	+	0.980928i	$0.437734\pi$
$114$	1.86746	0.174904
$115$	−8.35812	−0.779398
$116$	−0.375299	−0.0348456
$117$	−2.61881	−0.242109
$118$	10.7511	0.989721
$119$	2.34066	0.214568
$120$	3.91041	0.356970
$121$	−2.03230	−0.184755
$122$	−12.8044	−1.15926
$123$	0.750428	0.0676638
$124$	−4.16611	−0.374128
$125$	11.7582	1.05169
$126$	−1.18340	−0.105425
$127$	−1.69186	−0.150128	−0.0750640	−	0.997179i	$-0.523916\pi$
$127$	−1.69186	−0.150128	−0.0750640	+	0.997179i	$0.523916\pi$
$128$	−1.00000	−0.0883883
$129$	3.33481	0.293614
$130$	−11.2506	−0.986740
$131$	−16.2229	−1.41740	−0.708699	−	0.705511i	$-0.750718\pi$
$131$	−16.2229	−1.41740	−0.708699	+	0.705511i	$0.750718\pi$
$132$	5.59232	0.486749
$133$	−2.42790	−0.210525
$134$	−10.4904	−0.906231
$135$	9.82523	0.845621
$136$	−0.964069	−0.0826683
$137$	0.435069	0.0371705	0.0185852	−	0.999827i	$-0.494084\pi$
$137$	0.435069	0.0371705	0.0185852	+	0.999827i	$0.494084\pi$
$138$	−7.45401	−0.634527
$139$	2.09364	0.177580	0.0887900	−	0.996050i	$-0.471700\pi$
$139$	2.09364	0.177580	0.0887900	+	0.996050i	$0.471700\pi$
$140$	−5.08395	−0.429672
$141$	−8.65058	−0.728510
$142$	8.96856	0.752625
$143$	−16.0896	−1.34548
$144$	0.487417	0.0406180
$145$	0.785865	0.0652625
$146$	−3.29220	−0.272465
$147$	−2.06412	−0.170246
$148$	7.39092	0.607530
$149$	−0.419334	−0.0343532	−0.0171766	−	0.999852i	$-0.505468\pi$
$149$	−0.419334	−0.0343532	−0.0171766	+	0.999852i	$0.505468\pi$
$150$	1.14903	0.0938180
$151$	−13.9905	−1.13853	−0.569265	−	0.822154i	$-0.692772\pi$
$151$	−13.9905	−1.13853	−0.569265	+	0.822154i	$0.692772\pi$
$152$	1.00000	0.0811107
$153$	0.469903	0.0379894
$154$	−7.27061	−0.585883
$155$	8.72372	0.700706
$156$	−10.0336	−0.803330
$157$	−9.24471	−0.737808	−0.368904	−	0.929467i	$-0.620267\pi$
$157$	−9.24471	−0.737808	−0.368904	+	0.929467i	$0.620267\pi$
$158$	15.5108	1.23397
$159$	−14.9877	−1.18860
$160$	2.09397	0.165543
$161$	9.69100	0.763758
$162$	10.2247	0.803326
$163$	−3.14077	−0.246004	−0.123002	−	0.992406i	$-0.539252\pi$
$163$	−3.14077	−0.246004	−0.123002	+	0.992406i	$0.539252\pi$
$164$	0.401844	0.0313787
$165$	−11.7102	−0.911635
$166$	−0.126446	−0.00981410
$167$	13.3722	1.03478	0.517388	−	0.855751i	$-0.326904\pi$
$167$	13.3722	1.03478	0.517388	+	0.855751i	$0.326904\pi$
$168$	−4.53401	−0.349806
$169$	15.8674	1.22057
$170$	2.01873	0.154830
$171$	−0.487417	−0.0372737
$172$	1.78574	0.136162
$173$	−14.1459	−1.07550	−0.537748	−	0.843106i	$-0.680725\pi$
$173$	−14.1459	−1.07550	−0.537748	+	0.843106i	$0.680725\pi$
$174$	0.700857	0.0531318
$175$	−1.49386	−0.112925
$176$	2.99461	0.225727
$177$	−20.0773	−1.50910
$178$	−11.2811	−0.845552
$179$	−17.4010	−1.30061	−0.650306	−	0.759672i	$-0.725359\pi$
$179$	−17.4010	−1.30061	−0.650306	+	0.759672i	$0.725359\pi$
$180$	−1.02064	−0.0760737
$181$	−0.364013	−0.0270569	−0.0135284	−	0.999908i	$-0.504306\pi$
$181$	−0.364013	−0.0270569	−0.0135284	+	0.999908i	$0.504306\pi$
$182$	13.0447	0.966939
$183$	23.9118	1.76761
$184$	−3.99152	−0.294259
$185$	−15.4764	−1.13784
$186$	7.78006	0.570462
$187$	2.88701	0.211119
$188$	−4.63226	−0.337843
$189$	−11.3921	−0.828652
$190$	−2.09397	−0.151913
$191$	8.11910	0.587478	0.293739	−	0.955886i	$-0.405100\pi$
$191$	8.11910	0.587478	0.293739	+	0.955886i	$0.405100\pi$
$192$	1.86746	0.134773
$193$	−12.5336	−0.902188	−0.451094	−	0.892476i	$-0.648966\pi$
$193$	−12.5336	−0.902188	−0.451094	+	0.892476i	$0.648966\pi$
$194$	16.1334	1.15831
$195$	21.0100	1.50456
$196$	−1.10531	−0.0789507
$197$	−20.4311	−1.45566	−0.727828	−	0.685760i	$-0.759470\pi$
$197$	−20.4311	−1.45566	−0.727828	+	0.685760i	$0.759470\pi$
$198$	−1.45962	−0.103731
$199$	−8.81027	−0.624544	−0.312272	−	0.949993i	$-0.601090\pi$
$199$	−8.81027	−0.624544	−0.312272	+	0.949993i	$0.601090\pi$
$200$	0.615290	0.0435076
$201$	19.5904	1.38180
$202$	8.95826	0.630301
$203$	−0.911188	−0.0639528
$204$	1.80036	0.126051
$205$	−0.841449	−0.0587693
$206$	2.26337	0.157697
$207$	1.94553	0.135224
$208$	−5.37284	−0.372540
$209$	−2.99461	−0.207142
$210$	9.49408	0.655154
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	−8.02571	−0.551208
$213$	−16.7484	−1.14758
$214$	−19.8844	−1.35927
$215$	−3.73930	−0.255018
$216$	4.69216	0.319261
$217$	−10.1149	−0.686644
$218$	12.7976	0.866764
$219$	6.14807	0.415448
$220$	−6.27063	−0.422765
$221$	−5.17979	−0.348431
$222$	−13.8023	−0.926347
$223$	16.6311	1.11370	0.556849	−	0.830614i	$-0.312010\pi$
$223$	16.6311	1.11370	0.556849	+	0.830614i	$0.312010\pi$
$224$	−2.42790	−0.162221
$225$	−0.299903	−0.0199935
$226$	−4.13237	−0.274881
$227$	2.00730	0.133229	0.0666145	−	0.997779i	$-0.478780\pi$
$227$	2.00730	0.133229	0.0666145	+	0.997779i	$0.478780\pi$
$228$	−1.86746	−0.123676
$229$	4.84829	0.320384	0.160192	−	0.987086i	$-0.448789\pi$
$229$	4.84829	0.320384	0.160192	+	0.987086i	$0.448789\pi$
$230$	8.35812	0.551118
$231$	13.5776	0.893340
$232$	0.375299	0.0246396
$233$	−4.50535	−0.295155	−0.147578	−	0.989050i	$-0.547148\pi$
$233$	−4.50535	−0.295155	−0.147578	+	0.989050i	$0.547148\pi$
$234$	2.61881	0.171197
$235$	9.69982	0.632746
$236$	−10.7511	−0.699839
$237$	−28.9658	−1.88153
$238$	−2.34066	−0.151723
$239$	−16.3783	−1.05942	−0.529712	−	0.848178i	$-0.677700\pi$
$239$	−16.3783	−1.05942	−0.529712	+	0.848178i	$0.677700\pi$
$240$	−3.91041	−0.252416
$241$	−5.09404	−0.328136	−0.164068	−	0.986449i	$-0.552462\pi$
$241$	−5.09404	−0.328136	−0.164068	+	0.986449i	$0.552462\pi$
$242$	2.03230	0.130641
$243$	−5.01773	−0.321888
$244$	12.8044	0.819720
$245$	2.31449	0.147867
$246$	−0.750428	−0.0478456
$247$	5.37284	0.341866
$248$	4.16611	0.264549
$249$	0.236133	0.0149643
$250$	−11.7582	−0.743657
$251$	19.0310	1.20123	0.600615	−	0.799539i	$-0.294923\pi$
$251$	19.0310	1.20123	0.600615	+	0.799539i	$0.294923\pi$
$252$	1.18340	0.0745471
$253$	11.9530	0.751481
$254$	1.69186	0.106156
$255$	−3.76991	−0.236081
$256$	1.00000	0.0625000
$257$	28.4451	1.77435	0.887177	−	0.461429i	$-0.152663\pi$
$257$	28.4451	1.77435	0.887177	+	0.461429i	$0.152663\pi$
$258$	−3.33481	−0.207616
$259$	17.9444	1.11501
$260$	11.2506	0.697731
$261$	−0.182927	−0.0113229
$262$	16.2229	1.00225
$263$	22.6952	1.39945	0.699724	−	0.714414i	$-0.253306\pi$
$263$	22.6952	1.39945	0.699724	+	0.714414i	$0.253306\pi$
$264$	−5.59232	−0.344184
$265$	16.8056	1.03236
$266$	2.42790	0.148864
$267$	21.0670	1.28928
$268$	10.4904	0.640802
$269$	6.64859	0.405372	0.202686	−	0.979244i	$-0.435033\pi$
$269$	6.64859	0.405372	0.202686	+	0.979244i	$0.435033\pi$
$270$	−9.82523	−0.597945
$271$	11.9577	0.726378	0.363189	−	0.931716i	$-0.381688\pi$
$271$	11.9577	0.726378	0.363189	+	0.931716i	$0.381688\pi$
$272$	0.964069	0.0584553
$273$	−24.3605	−1.47437
$274$	−0.435069	−0.0262835
$275$	−1.84255	−0.111110
$276$	7.45401	0.448679
$277$	1.97569	0.118707	0.0593537	−	0.998237i	$-0.481096\pi$
$277$	1.97569	0.118707	0.0593537	+	0.998237i	$0.481096\pi$
$278$	−2.09364	−0.125568
$279$	−2.03063	−0.121571
$280$	5.08395	0.303824
$281$	2.98499	0.178070	0.0890348	−	0.996029i	$-0.471622\pi$
$281$	2.98499	0.178070	0.0890348	+	0.996029i	$0.471622\pi$
$282$	8.65058	0.515134
$283$	3.16290	0.188015	0.0940073	−	0.995572i	$-0.470032\pi$
$283$	3.16290	0.188015	0.0940073	+	0.995572i	$0.470032\pi$
$284$	−8.96856	−0.532186
$285$	3.91041	0.231633
$286$	16.0896	0.951397
$287$	0.975636	0.0575900
$288$	−0.487417	−0.0287213
$289$	−16.0706	−0.945328
$290$	−0.785865	−0.0461476
$291$	−30.1286	−1.76617
$292$	3.29220	0.192662
$293$	−19.9890	−1.16777	−0.583886	−	0.811836i	$-0.698469\pi$
$293$	−19.9890	−1.16777	−0.583886	+	0.811836i	$0.698469\pi$
$294$	2.06412	0.120382
$295$	22.5125	1.31073
$296$	−7.39092	−0.429588
$297$	−14.0512	−0.815332
$298$	0.419334	0.0242914
$299$	−21.4458	−1.24024
$300$	−1.14903	−0.0663394
$301$	4.33561	0.249900
$302$	13.9905	0.805063
$303$	−16.7292	−0.961069
$304$	−1.00000	−0.0573539
$305$	−26.8121	−1.53526
$306$	−0.469903	−0.0268626
$307$	−17.7402	−1.01249	−0.506244	−	0.862390i	$-0.668967\pi$
$307$	−17.7402	−1.01249	−0.506244	+	0.862390i	$0.668967\pi$
$308$	7.27061	0.414282
$309$	−4.22676	−0.240452
$310$	−8.72372	−0.495474
$311$	32.7628	1.85781	0.928903	−	0.370322i	$-0.120753\pi$
$311$	32.7628	1.85781	0.928903	+	0.370322i	$0.120753\pi$
$312$	10.0336	0.568040
$313$	15.3335	0.866702	0.433351	−	0.901225i	$-0.357331\pi$
$313$	15.3335	0.866702	0.433351	+	0.901225i	$0.357331\pi$
$314$	9.24471	0.521709
$315$	−2.47800	−0.139619
$316$	−15.5108	−0.872549
$317$	−18.6875	−1.04959	−0.524797	−	0.851227i	$-0.675859\pi$
$317$	−18.6875	−1.04959	−0.524797	+	0.851227i	$0.675859\pi$
$318$	14.9877	0.840470
$319$	−1.12387	−0.0629249
$320$	−2.09397	−0.117056
$321$	37.1335	2.07259
$322$	−9.69100	−0.540058
$323$	−0.964069	−0.0536423
$324$	−10.2247	−0.568037
$325$	3.30586	0.183376
$326$	3.14077	0.173951
$327$	−23.8991	−1.32162
$328$	−0.401844	−0.0221881
$329$	−11.2467	−0.620049
$330$	11.7102	0.644623
$331$	−16.6770	−0.916649	−0.458325	−	0.888785i	$-0.651550\pi$
$331$	−16.6770	−0.916649	−0.458325	+	0.888785i	$0.651550\pi$
$332$	0.126446	0.00693962
$333$	3.60246	0.197413
$334$	−13.3722	−0.731697
$335$	−21.9666	−1.20016
$336$	4.53401	0.247350
$337$	−35.5532	−1.93671	−0.968354	−	0.249580i	$-0.919707\pi$
$337$	−35.5532	−1.93671	−0.968354	+	0.249580i	$0.919707\pi$
$338$	−15.8674	−0.863075
$339$	7.71704	0.419132
$340$	−2.01873	−0.109481
$341$	−12.4759	−0.675607
$342$	0.487417	0.0263565
$343$	−19.6789	−1.06256
$344$	−1.78574	−0.0962809
$345$	−15.6085	−0.840332
$346$	14.1459	0.760490
$347$	−11.1846	−0.600423	−0.300212	−	0.953873i	$-0.597057\pi$
$347$	−11.1846	−0.600423	−0.300212	+	0.953873i	$0.597057\pi$
$348$	−0.700857	−0.0375699
$349$	−27.3848	−1.46587	−0.732936	−	0.680298i	$-0.761851\pi$
$349$	−27.3848	−1.46587	−0.732936	+	0.680298i	$0.761851\pi$
$350$	1.49386	0.0798503
$351$	25.2102	1.34562
$352$	−2.99461	−0.159613
$353$	−0.141064	−0.00750805	−0.00375403	−	0.999993i	$-0.501195\pi$
$353$	−0.141064	−0.00750805	−0.00375403	+	0.999993i	$0.501195\pi$
$354$	20.0773	1.06710
$355$	18.7799	0.996733
$356$	11.2811	0.597896
$357$	4.37110	0.231343
$358$	17.4010	0.919672
$359$	13.8050	0.728601	0.364300	−	0.931282i	$-0.381308\pi$
$359$	13.8050	0.728601	0.364300	+	0.931282i	$0.381308\pi$
$360$	1.02064	0.0537922
$361$	1.00000	0.0526316
$362$	0.364013	0.0191321
$363$	−3.79525	−0.199199
$364$	−13.0447	−0.683729
$365$	−6.89378	−0.360837
$366$	−23.9118	−1.24989
$367$	−29.6810	−1.54934	−0.774668	−	0.632368i	$-0.782083\pi$
$367$	−29.6810	−1.54934	−0.774668	+	0.632368i	$0.782083\pi$
$368$	3.99152	0.208072
$369$	0.195865	0.0101963
$370$	15.4764	0.804578
$371$	−19.4856	−1.01164
$372$	−7.78006	−0.403377
$373$	−10.2793	−0.532244	−0.266122	−	0.963939i	$-0.585742\pi$
$373$	−10.2793	−0.532244	−0.266122	+	0.963939i	$0.585742\pi$
$374$	−2.88701	−0.149284
$375$	21.9581	1.13391
$376$	4.63226	0.238891
$377$	2.01642	0.103851
$378$	11.3921	0.585945
$379$	−15.5494	−0.798718	−0.399359	−	0.916795i	$-0.630767\pi$
$379$	−15.5494	−0.798718	−0.399359	+	0.916795i	$0.630767\pi$
$380$	2.09397	0.107418
$381$	−3.15948	−0.161865
$382$	−8.11910	−0.415409
$383$	−15.5545	−0.794798	−0.397399	−	0.917646i	$-0.630087\pi$
$383$	−15.5545	−0.794798	−0.397399	+	0.917646i	$0.630087\pi$
$384$	−1.86746	−0.0952986
$385$	−15.2244	−0.775909
$386$	12.5336	0.637943
$387$	0.870402	0.0442450
$388$	−16.1334	−0.819051
$389$	−14.6363	−0.742089	−0.371044	−	0.928615i	$-0.621000\pi$
$389$	−14.6363	−0.742089	−0.371044	+	0.928615i	$0.621000\pi$
$390$	−21.0100	−1.06388
$391$	3.84810	0.194607
$392$	1.10531	0.0558266
$393$	−30.2956	−1.52821
$394$	20.4311	1.02930
$395$	32.4791	1.63420
$396$	1.45962	0.0733488
$397$	−28.3225	−1.42147	−0.710733	−	0.703461i	$-0.751637\pi$
$397$	−28.3225	−1.42147	−0.710733	+	0.703461i	$0.751637\pi$
$398$	8.81027	0.441619
$399$	−4.53401	−0.226984
$400$	−0.615290	−0.0307645
$401$	15.5235	0.775204	0.387602	−	0.921827i	$-0.373303\pi$
$401$	15.5235	0.775204	0.387602	+	0.921827i	$0.373303\pi$
$402$	−19.5904	−0.977081
$403$	22.3839	1.11502
$404$	−8.95826	−0.445690
$405$	21.4102	1.06388
$406$	0.911188	0.0452215
$407$	22.1329	1.09709
$408$	−1.80036	−0.0891313
$409$	11.4530	0.566316	0.283158	−	0.959073i	$-0.408618\pi$
$409$	11.4530	0.566316	0.283158	+	0.959073i	$0.408618\pi$
$410$	0.841449	0.0415562
$411$	0.812476	0.0400765
$412$	−2.26337	−0.111508
$413$	−26.1026	−1.28443
$414$	−1.94553	−0.0956177
$415$	−0.264774	−0.0129972
$416$	5.37284	0.263425
$417$	3.90979	0.191463
$418$	2.99461	0.146471
$419$	−11.5468	−0.564096	−0.282048	−	0.959400i	$-0.591014\pi$
$419$	−11.5468	−0.564096	−0.282048	+	0.959400i	$0.591014\pi$
$420$	−9.49408	−0.463264
$421$	−12.0447	−0.587021	−0.293510	−	0.955956i	$-0.594823\pi$
$421$	−12.0447	−0.587021	−0.293510	+	0.955956i	$0.594823\pi$
$422$	1.00000	0.0486792
$423$	−2.25784	−0.109780
$424$	8.02571	0.389763
$425$	−0.593182	−0.0287736
$426$	16.7484	0.811465
$427$	31.0879	1.50445
$428$	19.8844	0.961151
$429$	−30.0467	−1.45067
$430$	3.73930	0.180325
$431$	13.3053	0.640896	0.320448	−	0.947266i	$-0.396167\pi$
$431$	13.3053	0.640896	0.320448	+	0.947266i	$0.396167\pi$
$432$	−4.69216	−0.225751
$433$	−8.69871	−0.418033	−0.209017	−	0.977912i	$-0.567026\pi$
$433$	−8.69871	−0.418033	−0.209017	+	0.977912i	$0.567026\pi$
$434$	10.1149	0.485531
$435$	1.46757	0.0703647
$436$	−12.7976	−0.612895
$437$	−3.99152	−0.190940
$438$	−6.14807	−0.293766
$439$	−9.52532	−0.454619	−0.227309	−	0.973823i	$-0.572993\pi$
$439$	−9.52532	−0.454619	−0.227309	+	0.973823i	$0.572993\pi$
$440$	6.27063	0.298940
$441$	−0.538746	−0.0256546
$442$	5.17979	0.246378
$443$	−18.0208	−0.856194	−0.428097	−	0.903733i	$-0.640816\pi$
$443$	−18.0208	−0.856194	−0.428097	+	0.903733i	$0.640816\pi$
$444$	13.8023	0.655027
$445$	−23.6222	−1.11980
$446$	−16.6311	−0.787504
$447$	−0.783090	−0.0370389
$448$	2.42790	0.114707
$449$	−36.7586	−1.73475	−0.867374	−	0.497657i	$-0.834194\pi$
$449$	−36.7586	−1.73475	−0.867374	+	0.497657i	$0.834194\pi$
$450$	0.299903	0.0141375
$451$	1.20337	0.0566643
$452$	4.13237	0.194370
$453$	−26.1267	−1.22754
$454$	−2.00730	−0.0942072
$455$	27.3152	1.28056
$456$	1.86746	0.0874519
$457$	−19.2563	−0.900770	−0.450385	−	0.892835i	$-0.648713\pi$
$457$	−19.2563	−0.900770	−0.450385	+	0.892835i	$0.648713\pi$
$458$	−4.84829	−0.226546
$459$	−4.52356	−0.211142
$460$	−8.35812	−0.389699
$461$	42.1892	1.96495	0.982475	−	0.186397i	$-0.0596809\pi$
$461$	42.1892	1.96495	0.982475	+	0.186397i	$0.0596809\pi$
$462$	−13.5776	−0.631687
$463$	13.3878	0.622182	0.311091	−	0.950380i	$-0.399306\pi$
$463$	13.3878	0.622182	0.311091	+	0.950380i	$0.399306\pi$
$464$	−0.375299	−0.0174228
$465$	16.2912	0.755487
$466$	4.50535	0.208706
$467$	23.1031	1.06909	0.534543	−	0.845141i	$-0.320484\pi$
$467$	23.1031	1.06909	0.534543	+	0.845141i	$0.320484\pi$
$468$	−2.61881	−0.121055
$469$	25.4696	1.17608
$470$	−9.69982	−0.447419
$471$	−17.2642	−0.795490
$472$	10.7511	0.494861
$473$	5.34761	0.245883
$474$	28.9658	1.33044
$475$	0.615290	0.0282314
$476$	2.34066	0.107284
$477$	−3.91187	−0.179112
$478$	16.3783	0.749125
$479$	−15.7786	−0.720941	−0.360470	−	0.932771i	$-0.617384\pi$
$479$	−15.7786	−0.720941	−0.360470	+	0.932771i	$0.617384\pi$
$480$	3.91041	0.178485
$481$	−39.7103	−1.81063
$482$	5.09404	0.232027
$483$	18.0976	0.823468
$484$	−2.03230	−0.0923775
$485$	33.7829	1.53400
$486$	5.01773	0.227609
$487$	−8.38884	−0.380135	−0.190067	−	0.981771i	$-0.560871\pi$
$487$	−8.38884	−0.380135	−0.190067	+	0.981771i	$0.560871\pi$
$488$	−12.8044	−0.579630
$489$	−5.86528	−0.265237
$490$	−2.31449	−0.104558
$491$	8.05244	0.363402	0.181701	−	0.983354i	$-0.441840\pi$
$491$	8.05244	0.363402	0.181701	+	0.983354i	$0.441840\pi$
$492$	0.750428	0.0338319
$493$	−0.361814	−0.0162953
$494$	−5.37284	−0.241736
$495$	−3.05641	−0.137375
$496$	−4.16611	−0.187064
$497$	−21.7748	−0.976731
$498$	−0.236133	−0.0105814
$499$	38.5305	1.72486	0.862431	−	0.506175i	$-0.168941\pi$
$499$	38.5305	1.72486	0.862431	+	0.506175i	$0.168941\pi$
$500$	11.7582	0.525845
$501$	24.9722	1.11567
$502$	−19.0310	−0.849397
$503$	13.9605	0.622467	0.311233	−	0.950334i	$-0.399258\pi$
$503$	13.9605	0.622467	0.311233	+	0.950334i	$0.399258\pi$
$504$	−1.18340	−0.0527127
$505$	18.7583	0.834735
$506$	−11.9530	−0.531377
$507$	29.6319	1.31600
$508$	−1.69186	−0.0750640
$509$	19.5808	0.867905	0.433953	−	0.900936i	$-0.357119\pi$
$509$	19.5808	0.867905	0.433953	+	0.900936i	$0.357119\pi$
$510$	3.76991	0.166934
$511$	7.99314	0.353596
$512$	−1.00000	−0.0441942
$513$	4.69216	0.207164
$514$	−28.4451	−1.25466
$515$	4.73943	0.208844
$516$	3.33481	0.146807
$517$	−13.8718	−0.610082
$518$	−17.9444	−0.788432
$519$	−26.4170	−1.15958
$520$	−11.2506	−0.493370
$521$	−13.8347	−0.606108	−0.303054	−	0.952973i	$-0.598006\pi$
$521$	−13.8347	−0.606108	−0.303054	+	0.952973i	$0.598006\pi$
$522$	0.182927	0.00800649
$523$	−28.9476	−1.26579	−0.632896	−	0.774237i	$-0.718134\pi$
$523$	−28.9476	−1.26579	−0.632896	+	0.774237i	$0.718134\pi$
$524$	−16.2229	−0.708699
$525$	−2.78973	−0.121754
$526$	−22.6952	−0.989559
$527$	−4.01642	−0.174958
$528$	5.59232	0.243375
$529$	−7.06779	−0.307295
$530$	−16.8056	−0.729989
$531$	−5.24028	−0.227409
$532$	−2.42790	−0.105263
$533$	−2.15904	−0.0935186
$534$	−21.0670	−0.911657
$535$	−41.6374	−1.80014
$536$	−10.4904	−0.453116
$537$	−32.4957	−1.40229
$538$	−6.64859	−0.286641
$539$	−3.30997	−0.142571
$540$	9.82523	0.422811
$541$	21.4461	0.922039	0.461019	−	0.887390i	$-0.347484\pi$
$541$	21.4461	0.922039	0.461019	+	0.887390i	$0.347484\pi$
$542$	−11.9577	−0.513627
$543$	−0.679781	−0.0291722
$544$	−0.964069	−0.0413341
$545$	26.7978	1.14789
$546$	24.3605	1.04253
$547$	−11.0313	−0.471665	−0.235832	−	0.971794i	$-0.575782\pi$
$547$	−11.0313	−0.471665	−0.235832	+	0.971794i	$0.575782\pi$
$548$	0.435069	0.0185852
$549$	6.24109	0.266363
$550$	1.84255	0.0785668
$551$	0.375299	0.0159883
$552$	−7.45401	−0.317264
$553$	−37.6586	−1.60141
$554$	−1.97569	−0.0839388
$555$	−28.9015	−1.22680
$556$	2.09364	0.0887900
$557$	−1.12703	−0.0477538	−0.0238769	−	0.999715i	$-0.507601\pi$
$557$	−1.12703	−0.0477538	−0.0238769	+	0.999715i	$0.507601\pi$
$558$	2.03063	0.0859636
$559$	−9.59453	−0.405805
$560$	−5.08395	−0.214836
$561$	5.39139	0.227625
$562$	−2.98499	−0.125914
$563$	22.2535	0.937874	0.468937	−	0.883232i	$-0.344637\pi$
$563$	22.2535	0.937874	0.468937	+	0.883232i	$0.344637\pi$
$564$	−8.65058	−0.364255
$565$	−8.65305	−0.364037
$566$	−3.16290	−0.132946
$567$	−24.8245	−1.04253
$568$	8.96856	0.376312
$569$	9.05170	0.379467	0.189734	−	0.981836i	$-0.439238\pi$
$569$	9.05170	0.379467	0.189734	+	0.981836i	$0.439238\pi$
$570$	−3.91041	−0.163789
$571$	5.69746	0.238431	0.119216	−	0.992868i	$-0.461962\pi$
$571$	5.69746	0.238431	0.119216	+	0.992868i	$0.461962\pi$
$572$	−16.0896	−0.672739
$573$	15.1621	0.633407
$574$	−0.975636	−0.0407223
$575$	−2.45594	−0.102420
$576$	0.487417	0.0203090
$577$	40.7320	1.69570	0.847848	−	0.530239i	$-0.177898\pi$
$577$	40.7320	1.69570	0.847848	+	0.530239i	$0.177898\pi$
$578$	16.0706	0.668448
$579$	−23.4060	−0.972721
$580$	0.785865	0.0326313
$581$	0.306998	0.0127364
$582$	30.1286	1.24887
$583$	−24.0339	−0.995382
$584$	−3.29220	−0.136232
$585$	5.48372	0.226724
$586$	19.9890	0.825740
$587$	37.2971	1.53942	0.769708	−	0.638396i	$-0.220402\pi$
$587$	37.2971	1.53942	0.769708	+	0.638396i	$0.220402\pi$
$588$	−2.06412	−0.0851231
$589$	4.16611	0.171662
$590$	−22.5125	−0.926826
$591$	−38.1543	−1.56946
$592$	7.39092	0.303765
$593$	30.8351	1.26624	0.633122	−	0.774052i	$-0.281773\pi$
$593$	30.8351	1.26624	0.633122	+	0.774052i	$0.281773\pi$
$594$	14.0512	0.576527
$595$	−4.90128	−0.200933
$596$	−0.419334	−0.0171766
$597$	−16.4529	−0.673370
$598$	21.4458	0.876984
$599$	14.8196	0.605511	0.302755	−	0.953068i	$-0.402094\pi$
$599$	14.8196	0.605511	0.302755	+	0.953068i	$0.402094\pi$
$600$	1.14903	0.0469090
$601$	17.4585	0.712147	0.356074	−	0.934458i	$-0.384115\pi$
$601$	17.4585	0.712147	0.356074	+	0.934458i	$0.384115\pi$
$602$	−4.33561	−0.176706
$603$	5.11319	0.208225
$604$	−13.9905	−0.569265
$605$	4.25558	0.173014
$606$	16.7292	0.679578
$607$	1.74531	0.0708400	0.0354200	−	0.999373i	$-0.488723\pi$
$607$	1.74531	0.0708400	0.0354200	+	0.999373i	$0.488723\pi$
$608$	1.00000	0.0405554
$609$	−1.70161	−0.0689527
$610$	26.8121	1.08559
$611$	24.8884	1.00688
$612$	0.469903	0.0189947
$613$	−24.5454	−0.991379	−0.495689	−	0.868500i	$-0.665085\pi$
$613$	−24.5454	−0.991379	−0.495689	+	0.868500i	$0.665085\pi$
$614$	17.7402	0.715937
$615$	−1.57137	−0.0633639
$616$	−7.27061	−0.292941
$617$	43.0375	1.73262	0.866312	−	0.499503i	$-0.166484\pi$
$617$	43.0375	1.73262	0.866312	+	0.499503i	$0.166484\pi$
$618$	4.22676	0.170025
$619$	−35.7257	−1.43594	−0.717968	−	0.696076i	$-0.754928\pi$
$619$	−35.7257	−1.43594	−0.717968	+	0.696076i	$0.754928\pi$
$620$	8.72372	0.350353
$621$	−18.7288	−0.751562
$622$	−32.7628	−1.31367
$623$	27.3893	1.09733
$624$	−10.0336	−0.401665
$625$	−21.5450	−0.861799
$626$	−15.3335	−0.612851
$627$	−5.59232	−0.223336
$628$	−9.24471	−0.368904
$629$	7.12536	0.284107
$630$	2.47800	0.0987259
$631$	−32.6807	−1.30100	−0.650499	−	0.759507i	$-0.725440\pi$
$631$	−32.6807	−1.30100	−0.650499	+	0.759507i	$0.725440\pi$
$632$	15.5108	0.616986
$633$	−1.86746	−0.0742250
$634$	18.6875	0.742175
$635$	3.54270	0.140588
$636$	−14.9877	−0.594302
$637$	5.93866	0.235298
$638$	1.12387	0.0444946
$639$	−4.37142	−0.172931
$640$	2.09397	0.0827714
$641$	−8.98273	−0.354797	−0.177398	−	0.984139i	$-0.556768\pi$
$641$	−8.98273	−0.354797	−0.177398	+	0.984139i	$0.556768\pi$
$642$	−37.1335	−1.46554
$643$	31.0171	1.22319	0.611597	−	0.791169i	$-0.290527\pi$
$643$	31.0171	1.22319	0.611597	+	0.791169i	$0.290527\pi$
$644$	9.69100	0.381879
$645$	−6.98299	−0.274955
$646$	0.964069	0.0379308
$647$	−12.5082	−0.491748	−0.245874	−	0.969302i	$-0.579075\pi$
$647$	−12.5082	−0.491748	−0.245874	+	0.969302i	$0.579075\pi$
$648$	10.2247	0.401663
$649$	−32.1954	−1.26378
$650$	−3.30586	−0.129666
$651$	−18.8892	−0.740326
$652$	−3.14077	−0.123002
$653$	34.9403	1.36732	0.683660	−	0.729800i	$-0.260387\pi$
$653$	34.9403	1.36732	0.683660	+	0.729800i	$0.260387\pi$
$654$	23.8991	0.934528
$655$	33.9702	1.32733
$656$	0.401844	0.0156894
$657$	1.60467	0.0626043
$658$	11.2467	0.438441
$659$	−6.04976	−0.235665	−0.117833	−	0.993033i	$-0.537595\pi$
$659$	−6.04976	−0.235665	−0.117833	+	0.993033i	$0.537595\pi$
$660$	−11.7102	−0.455817
$661$	18.5019	0.719641	0.359821	−	0.933021i	$-0.382838\pi$
$661$	18.5019	0.719641	0.359821	+	0.933021i	$0.382838\pi$
$662$	16.6770	0.648169
$663$	−9.67307	−0.375671
$664$	−0.126446	−0.00490705
$665$	5.08395	0.197147
$666$	−3.60246	−0.139592
$667$	−1.49801	−0.0580033
$668$	13.3722	0.517388
$669$	31.0579	1.20077
$670$	21.9666	0.848642
$671$	38.3443	1.48027
$672$	−4.53401	−0.174903
$673$	−32.7178	−1.26118	−0.630589	−	0.776117i	$-0.717187\pi$
$673$	−32.7178	−1.26118	−0.630589	+	0.776117i	$0.717187\pi$
$674$	35.5532	1.36946
$675$	2.88704	0.111122
$676$	15.8674	0.610286
$677$	−46.4152	−1.78388	−0.891940	−	0.452153i	$-0.850656\pi$
$677$	−46.4152	−1.78388	−0.891940	+	0.452153i	$0.850656\pi$
$678$	−7.71704	−0.296371
$679$	−39.1703	−1.50322
$680$	2.01873	0.0774148
$681$	3.74855	0.143645
$682$	12.4759	0.477727
$683$	20.0111	0.765703	0.382851	−	0.923810i	$-0.374942\pi$
$683$	20.0111	0.765703	0.382851	+	0.923810i	$0.374942\pi$
$684$	−0.487417	−0.0186368
$685$	−0.911022	−0.0348084
$686$	19.6789	0.751343
$687$	9.05400	0.345432
$688$	1.78574	0.0680809
$689$	43.1209	1.64278
$690$	15.6085	0.594204
$691$	−10.2162	−0.388641	−0.194320	−	0.980938i	$-0.562250\pi$
$691$	−10.2162	−0.388641	−0.194320	+	0.980938i	$0.562250\pi$
$692$	−14.1459	−0.537748
$693$	3.54382	0.134618
$694$	11.1846	0.424563
$695$	−4.38401	−0.166295
$696$	0.700857	0.0265659
$697$	0.387405	0.0146740
$698$	27.3848	1.03653
$699$	−8.41358	−0.318231
$700$	−1.49386	−0.0564627
$701$	−16.9194	−0.639037	−0.319518	−	0.947580i	$-0.603521\pi$
$701$	−16.9194	−0.639037	−0.319518	+	0.947580i	$0.603521\pi$
$702$	−25.2102	−0.951498
$703$	−7.39092	−0.278754
$704$	2.99461	0.112864
$705$	18.1141	0.682215
$706$	0.141064	0.00530900
$707$	−21.7498	−0.817984
$708$	−20.0773	−0.754552
$709$	−23.3961	−0.878659	−0.439329	−	0.898326i	$-0.644784\pi$
$709$	−23.3961	−0.878659	−0.439329	+	0.898326i	$0.644784\pi$
$710$	−18.7799	−0.704797
$711$	−7.56021	−0.283530
$712$	−11.2811	−0.422776
$713$	−16.6291	−0.622765
$714$	−4.37110	−0.163584
$715$	33.6911	1.25998
$716$	−17.4010	−0.650306
$717$	−30.5858	−1.14225
$718$	−13.8050	−0.515198
$719$	2.77513	0.103495	0.0517474	−	0.998660i	$-0.483521\pi$
$719$	2.77513	0.103495	0.0517474	+	0.998660i	$0.483521\pi$
$720$	−1.02064	−0.0380368
$721$	−5.49524	−0.204653
$722$	−1.00000	−0.0372161
$723$	−9.51294	−0.353790
$724$	−0.364013	−0.0135284
$725$	0.230918	0.00857607
$726$	3.79525	0.140855
$727$	−25.9178	−0.961236	−0.480618	−	0.876930i	$-0.659588\pi$
$727$	−25.9178	−0.961236	−0.480618	+	0.876930i	$0.659588\pi$
$728$	13.0447	0.483469
$729$	21.3036	0.789022
$730$	6.89378	0.255150
$731$	1.72158	0.0636750
$732$	23.9118	0.883806
$733$	6.72301	0.248320	0.124160	−	0.992262i	$-0.460376\pi$
$733$	6.72301	0.248320	0.124160	+	0.992262i	$0.460376\pi$
$734$	29.6810	1.09555
$735$	4.32222	0.159427
$736$	−3.99152	−0.147129
$737$	31.4146	1.15717
$738$	−0.195865	−0.00720990
$739$	−0.961114	−0.0353552	−0.0176776	−	0.999844i	$-0.505627\pi$
$739$	−0.961114	−0.0353552	−0.0176776	+	0.999844i	$0.505627\pi$
$740$	−15.4764	−0.568922
$741$	10.0336	0.368593
$742$	19.4856	0.715340
$743$	−2.93354	−0.107621	−0.0538106	−	0.998551i	$-0.517137\pi$
$743$	−2.93354	−0.107621	−0.0538106	+	0.998551i	$0.517137\pi$
$744$	7.78006	0.285231
$745$	0.878072	0.0321701
$746$	10.2793	0.376353
$747$	0.0616318	0.00225499
$748$	2.88701	0.105560
$749$	48.2774	1.76402
$750$	−21.9581	−0.801796
$751$	−6.42443	−0.234431	−0.117215	−	0.993107i	$-0.537397\pi$
$751$	−6.42443	−0.234431	−0.117215	+	0.993107i	$0.537397\pi$
$752$	−4.63226	−0.168921
$753$	35.5398	1.29514
$754$	−2.01642	−0.0734338
$755$	29.2957	1.06618
$756$	−11.3921	−0.414326
$757$	−35.5238	−1.29114	−0.645568	−	0.763703i	$-0.723379\pi$
$757$	−35.5238	−1.29114	−0.645568	+	0.763703i	$0.723379\pi$
$758$	15.5494	0.564779
$759$	22.3219	0.810232
$760$	−2.09397	−0.0759563
$761$	0.933236	0.0338298	0.0169149	−	0.999857i	$-0.494616\pi$
$761$	0.933236	0.0338298	0.0169149	+	0.999857i	$0.494616\pi$
$762$	3.15948	0.114456
$763$	−31.0713	−1.12486
$764$	8.11910	0.293739
$765$	−0.983963	−0.0355753
$766$	15.5545	0.562007
$767$	57.7641	2.08574
$768$	1.86746	0.0673863
$769$	−3.33959	−0.120429	−0.0602144	−	0.998185i	$-0.519178\pi$
$769$	−3.33959	−0.120429	−0.0602144	+	0.998185i	$0.519178\pi$
$770$	15.2244	0.548651
$771$	53.1201	1.91307
$772$	−12.5336	−0.451094
$773$	−2.90723	−0.104566	−0.0522828	−	0.998632i	$-0.516650\pi$
$773$	−2.90723	−0.104566	−0.0522828	+	0.998632i	$0.516650\pi$
$774$	−0.870402	−0.0312859
$775$	2.56337	0.0920789
$776$	16.1334	0.579157
$777$	33.5105	1.20218
$778$	14.6363	0.524736
$779$	−0.401844	−0.0143976
$780$	21.0100	0.752279
$781$	−26.8573	−0.961031
$782$	−3.84810	−0.137608
$783$	1.76096	0.0629316
$784$	−1.10531	−0.0394754
$785$	19.3581	0.690922
$786$	30.2956	1.08061
$787$	1.95936	0.0698436	0.0349218	−	0.999390i	$-0.488882\pi$
$787$	1.95936	0.0698436	0.0349218	+	0.999390i	$0.488882\pi$
$788$	−20.4311	−0.727828
$789$	42.3825	1.50886
$790$	−32.4791	−1.15555
$791$	10.0330	0.356731
$792$	−1.45962	−0.0518654
$793$	−68.7962	−2.44303
$794$	28.3225	1.00513
$795$	31.3838	1.11307
$796$	−8.81027	−0.312272
$797$	−15.1878	−0.537981	−0.268991	−	0.963143i	$-0.586690\pi$
$797$	−15.1878	−0.537981	−0.268991	+	0.963143i	$0.586690\pi$
$798$	4.53401	0.160502
$799$	−4.46582	−0.157989
$800$	0.615290	0.0217538
$801$	5.49858	0.194283
$802$	−15.5235	−0.548152
$803$	9.85887	0.347912
$804$	19.5904	0.690900
$805$	−20.2927	−0.715222
$806$	−22.3839	−0.788439
$807$	12.4160	0.437064
$808$	8.95826	0.315151
$809$	−32.9322	−1.15783	−0.578917	−	0.815387i	$-0.696524\pi$
$809$	−32.9322	−1.15783	−0.578917	+	0.815387i	$0.696524\pi$
$810$	−21.4102	−0.752276
$811$	34.3532	1.20631	0.603153	−	0.797626i	$-0.293911\pi$
$811$	34.3532	1.20631	0.603153	+	0.797626i	$0.293911\pi$
$812$	−0.911188	−0.0319764
$813$	22.3305	0.783166
$814$	−22.1329	−0.775759
$815$	6.57669	0.230371
$816$	1.80036	0.0630253
$817$	−1.78574	−0.0624753
$818$	−11.4530	−0.400446
$819$	−6.35821	−0.222174
$820$	−0.841449	−0.0293847
$821$	27.6694	0.965668	0.482834	−	0.875712i	$-0.339608\pi$
$821$	27.6694	0.965668	0.482834	+	0.875712i	$0.339608\pi$
$822$	−0.812476	−0.0283383
$823$	−16.0488	−0.559425	−0.279713	−	0.960084i	$-0.590239\pi$
$823$	−16.0488	−0.559425	−0.279713	+	0.960084i	$0.590239\pi$
$824$	2.26337	0.0788483
$825$	−3.44090	−0.119797
$826$	26.1026	0.908227
$827$	3.57700	0.124385	0.0621923	−	0.998064i	$-0.480191\pi$
$827$	3.57700	0.124385	0.0621923	+	0.998064i	$0.480191\pi$
$828$	1.94553	0.0676119
$829$	18.7819	0.652322	0.326161	−	0.945314i	$-0.394245\pi$
$829$	18.7819	0.652322	0.326161	+	0.945314i	$0.394245\pi$
$830$	0.264774	0.00919043
$831$	3.68952	0.127988
$832$	−5.37284	−0.186270
$833$	−1.06560	−0.0369207
$834$	−3.90979	−0.135385
$835$	−28.0011	−0.969018
$836$	−2.99461	−0.103571
$837$	19.5481	0.675680
$838$	11.5468	0.398876
$839$	49.6259	1.71328	0.856639	−	0.515917i	$-0.172549\pi$
$839$	49.6259	1.71328	0.856639	+	0.515917i	$0.172549\pi$
$840$	9.49408	0.327577
$841$	−28.8592	−0.995143
$842$	12.0447	0.415086
$843$	5.57436	0.191991
$844$	−1.00000	−0.0344214
$845$	−33.2260	−1.14301
$846$	2.25784	0.0776262
$847$	−4.93423	−0.169542
$848$	−8.02571	−0.275604
$849$	5.90659	0.202714
$850$	0.593182	0.0203460
$851$	29.5010	1.01128
$852$	−16.7484	−0.573792
$853$	−20.6880	−0.708343	−0.354172	−	0.935180i	$-0.615237\pi$
$853$	−20.6880	−0.708343	−0.354172	+	0.935180i	$0.615237\pi$
$854$	−31.0879	−1.06380
$855$	1.02064	0.0349050
$856$	−19.8844	−0.679636
$857$	28.5224	0.974308	0.487154	−	0.873316i	$-0.338035\pi$
$857$	28.5224	0.974308	0.487154	+	0.873316i	$0.338035\pi$
$858$	30.0467	1.02578
$859$	2.68533	0.0916222	0.0458111	−	0.998950i	$-0.485413\pi$
$859$	2.68533	0.0916222	0.0458111	+	0.998950i	$0.485413\pi$
$860$	−3.73930	−0.127509
$861$	1.82196	0.0620924
$862$	−13.3053	−0.453182
$863$	−55.8931	−1.90262	−0.951312	−	0.308231i	$-0.900263\pi$
$863$	−55.8931	−1.90262	−0.951312	+	0.308231i	$0.900263\pi$
$864$	4.69216	0.159630
$865$	29.6212	1.00715
$866$	8.69871	0.295594
$867$	−30.0112	−1.01923
$868$	−10.1149	−0.343322
$869$	−46.4487	−1.57567
$870$	−1.46757	−0.0497554
$871$	−56.3632	−1.90979
$872$	12.7976	0.433382
$873$	−7.86370	−0.266146
$874$	3.99152	0.135015
$875$	28.5478	0.965093
$876$	6.14807	0.207724
$877$	−18.9838	−0.641039	−0.320519	−	0.947242i	$-0.603857\pi$
$877$	−18.9838	−0.641039	−0.320519	+	0.947242i	$0.603857\pi$
$878$	9.52532	0.321464
$879$	−37.3288	−1.25907
$880$	−6.27063	−0.211383
$881$	11.0715	0.373007	0.186504	−	0.982454i	$-0.440284\pi$
$881$	11.0715	0.373007	0.186504	+	0.982454i	$0.440284\pi$
$882$	0.538746	0.0181405
$883$	4.18182	0.140729	0.0703647	−	0.997521i	$-0.477584\pi$
$883$	4.18182	0.140729	0.0703647	+	0.997521i	$0.477584\pi$
$884$	−5.17979	−0.174215
$885$	42.0413	1.41320
$886$	18.0208	0.605421
$887$	19.8008	0.664846	0.332423	−	0.943130i	$-0.392134\pi$
$887$	19.8008	0.664846	0.332423	+	0.943130i	$0.392134\pi$
$888$	−13.8023	−0.463174
$889$	−4.10765	−0.137766
$890$	23.6222	0.791819
$891$	−30.6189	−1.02577
$892$	16.6311	0.556849
$893$	4.63226	0.155013
$894$	0.783090	0.0261905
$895$	36.4372	1.21796
$896$	−2.42790	−0.0811104
$897$	−40.0492	−1.33720
$898$	36.7586	1.22665
$899$	1.56354	0.0521469
$900$	−0.299903	−0.00999675
$901$	−7.73734	−0.257768
$902$	−1.20337	−0.0400677
$903$	8.09658	0.269437
$904$	−4.13237	−0.137440
$905$	0.762233	0.0253375
$906$	26.1267	0.868002
$907$	56.7435	1.88414	0.942068	−	0.335422i	$-0.108879\pi$
$907$	56.7435	1.88414	0.942068	+	0.335422i	$0.108879\pi$
$908$	2.00730	0.0666145
$909$	−4.36641	−0.144825
$910$	−27.3152	−0.905492
$911$	−27.1315	−0.898905	−0.449453	−	0.893304i	$-0.648381\pi$
$911$	−27.1315	−0.898905	−0.449453	+	0.893304i	$0.648381\pi$
$912$	−1.86746	−0.0618379
$913$	0.378656	0.0125317
$914$	19.2563	0.636940
$915$	−50.0706	−1.65528
$916$	4.84829	0.160192
$917$	−39.3875	−1.30069
$918$	4.52356	0.149300
$919$	13.8016	0.455272	0.227636	−	0.973746i	$-0.426900\pi$
$919$	13.8016	0.455272	0.227636	+	0.973746i	$0.426900\pi$
$920$	8.35812	0.275559
$921$	−33.1292	−1.09164
$922$	−42.1892	−1.38943
$923$	48.1867	1.58608
$924$	13.5776	0.446670
$925$	−4.54756	−0.149523
$926$	−13.3878	−0.439949
$927$	−1.10320	−0.0362340
$928$	0.375299	0.0123198
$929$	−43.7337	−1.43486	−0.717428	−	0.696633i	$-0.754681\pi$
$929$	−43.7337	−1.43486	−0.717428	+	0.696633i	$0.754681\pi$
$930$	−16.2912	−0.534210
$931$	1.10531	0.0362251
$932$	−4.50535	−0.147578
$933$	61.1833	2.00305
$934$	−23.1031	−0.755958
$935$	−6.04532	−0.197703
$936$	2.61881	0.0855986
$937$	50.0395	1.63472	0.817360	−	0.576127i	$-0.195437\pi$
$937$	50.0395	1.63472	0.817360	+	0.576127i	$0.195437\pi$
$938$	−25.4696	−0.831612
$939$	28.6348	0.934460
$940$	9.69982	0.316373
$941$	42.6911	1.39169	0.695845	−	0.718192i	$-0.255030\pi$
$941$	42.6911	1.39169	0.695845	+	0.718192i	$0.255030\pi$
$942$	17.2642	0.562496
$943$	1.60397	0.0522323
$944$	−10.7511	−0.349919
$945$	23.8547	0.775992
$946$	−5.34761	−0.173866
$947$	−29.2813	−0.951515	−0.475758	−	0.879576i	$-0.657826\pi$
$947$	−29.2813	−0.951515	−0.475758	+	0.879576i	$0.657826\pi$
$948$	−28.9658	−0.940765
$949$	−17.6885	−0.574193
$950$	−0.615290	−0.0199626
$951$	−34.8982	−1.13165
$952$	−2.34066	−0.0758613
$953$	−33.0898	−1.07188	−0.535942	−	0.844255i	$-0.680044\pi$
$953$	−33.0898	−1.07188	−0.535942	+	0.844255i	$0.680044\pi$
$954$	3.91187	0.126651
$955$	−17.0012	−0.550144
$956$	−16.3783	−0.529712
$957$	−2.09879	−0.0678443
$958$	15.7786	0.509782
$959$	1.05630	0.0341098
$960$	−3.91041	−0.126208
$961$	−13.6435	−0.440113
$962$	39.7103	1.28031
$963$	9.69201	0.312321
$964$	−5.09404	−0.164068
$965$	26.2450	0.844856
$966$	−18.0976	−0.582280
$967$	39.8894	1.28276	0.641378	−	0.767225i	$-0.278363\pi$
$967$	39.8894	1.28276	0.641378	+	0.767225i	$0.278363\pi$
$968$	2.03230	0.0653207
$969$	−1.80036	−0.0578360
$970$	−33.7829	−1.08470
$971$	31.8640	1.02256	0.511282	−	0.859413i	$-0.329171\pi$
$971$	31.8640	1.02256	0.511282	+	0.859413i	$0.329171\pi$
$972$	−5.01773	−0.160944
$973$	5.08314	0.162958
$974$	8.38884	0.268796
$975$	6.17356	0.197712
$976$	12.8044	0.409860
$977$	−3.38665	−0.108349	−0.0541743	−	0.998531i	$-0.517253\pi$
$977$	−3.38665	−0.108349	−0.0541743	+	0.998531i	$0.517253\pi$
$978$	5.86528	0.187551
$979$	33.7824	1.07969
$980$	2.31449	0.0739335
$981$	−6.23777	−0.199157
$982$	−8.05244	−0.256964
$983$	−49.5689	−1.58100	−0.790501	−	0.612460i	$-0.790180\pi$
$983$	−49.5689	−1.58100	−0.790501	+	0.612460i	$0.790180\pi$
$984$	−0.750428	−0.0239228
$985$	42.7821	1.36315
$986$	0.361814	0.0115225
$987$	−21.0027	−0.668524
$988$	5.37284	0.170933
$989$	7.12783	0.226652
$990$	3.05641	0.0971390
$991$	−40.8624	−1.29804	−0.649018	−	0.760773i	$-0.724820\pi$
$991$	−40.8624	−1.29804	−0.649018	+	0.760773i	$0.724820\pi$
$992$	4.16611	0.132274
$993$	−31.1436	−0.988313
$994$	21.7748	0.690653
$995$	18.4484	0.584855
$996$	0.236133	0.00748216
$997$	−27.6049	−0.874255	−0.437127	−	0.899400i	$-0.644004\pi$
$997$	−27.6049	−0.874255	−0.437127	+	0.899400i	$0.644004\pi$
$998$	−38.5305	−1.21966
$999$	−34.6793	−1.09721

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.f.1.28	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.f.1.28	✓	34	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.86746 q^{3} +1.00000 q^{4} -2.09397 q^{5} -1.86746 q^{6} +2.42790 q^{7} -1.00000 q^{8} +0.487417 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.86746 q^{3} +1.00000 q^{4} -2.09397 q^{5} -1.86746 q^{6} +2.42790 q^{7} -1.00000 q^{8} +0.487417 q^{9} +2.09397 q^{10} +2.99461 q^{11} +1.86746 q^{12} -5.37284 q^{13} -2.42790 q^{14} -3.91041 q^{15} +1.00000 q^{16} +0.964069 q^{17} -0.487417 q^{18} -1.00000 q^{19} -2.09397 q^{20} +4.53401 q^{21} -2.99461 q^{22} +3.99152 q^{23} -1.86746 q^{24} -0.615290 q^{25} +5.37284 q^{26} -4.69216 q^{27} +2.42790 q^{28} -0.375299 q^{29} +3.91041 q^{30} -4.16611 q^{31} -1.00000 q^{32} +5.59232 q^{33} -0.964069 q^{34} -5.08395 q^{35} +0.487417 q^{36} +7.39092 q^{37} +1.00000 q^{38} -10.0336 q^{39} +2.09397 q^{40} +0.401844 q^{41} -4.53401 q^{42} +1.78574 q^{43} +2.99461 q^{44} -1.02064 q^{45} -3.99152 q^{46} -4.63226 q^{47} +1.86746 q^{48} -1.10531 q^{49} +0.615290 q^{50} +1.80036 q^{51} -5.37284 q^{52} -8.02571 q^{53} +4.69216 q^{54} -6.27063 q^{55} -2.42790 q^{56} -1.86746 q^{57} +0.375299 q^{58} -10.7511 q^{59} -3.91041 q^{60} +12.8044 q^{61} +4.16611 q^{62} +1.18340 q^{63} +1.00000 q^{64} +11.2506 q^{65} -5.59232 q^{66} +10.4904 q^{67} +0.964069 q^{68} +7.45401 q^{69} +5.08395 q^{70} -8.96856 q^{71} -0.487417 q^{72} +3.29220 q^{73} -7.39092 q^{74} -1.14903 q^{75} -1.00000 q^{76} +7.27061 q^{77} +10.0336 q^{78} -15.5108 q^{79} -2.09397 q^{80} -10.2247 q^{81} -0.401844 q^{82} +0.126446 q^{83} +4.53401 q^{84} -2.01873 q^{85} -1.78574 q^{86} -0.700857 q^{87} -2.99461 q^{88} +11.2811 q^{89} +1.02064 q^{90} -13.0447 q^{91} +3.99152 q^{92} -7.78006 q^{93} +4.63226 q^{94} +2.09397 q^{95} -1.86746 q^{96} -16.1334 q^{97} +1.10531 q^{98} +1.45962 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9}+O(q^{10}) \) 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9	\( 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9} - 7 q^{10} + 4 q^{11} - 10 q^{12} - 5 q^{13} + 6 q^{14} - 17 q^{15} + 34 q^{16} + 8 q^{17} - 38 q^{18} - 34 q^{19} + 7 q^{20} - 4 q^{22} - 24 q^{23} + 10 q^{24} + 5 q^{25} + 5 q^{26} - 31 q^{27} - 6 q^{28} + 24 q^{29} + 17 q^{30} - 28 q^{31} - 34 q^{32} - 16 q^{33} - 8 q^{34} + 2 q^{35} + 38 q^{36} - 36 q^{37} + 34 q^{38} - 9 q^{39} - 7 q^{40} + 9 q^{41} - 24 q^{43} + 4 q^{44} + 22 q^{45} + 24 q^{46} - 29 q^{47} - 10 q^{48} + 22 q^{49} - 5 q^{50} - 21 q^{51} - 5 q^{52} - 9 q^{53} + 31 q^{54} - 28 q^{55} + 6 q^{56} + 10 q^{57} - 24 q^{58} - 28 q^{59} - 17 q^{60} + 23 q^{61} + 28 q^{62} - 27 q^{63} + 34 q^{64} - 6 q^{65} + 16 q^{66} - 51 q^{67} + 8 q^{68} - 17 q^{69} - 2 q^{70} - 31 q^{71} - 38 q^{72} - 26 q^{73} + 36 q^{74} - 109 q^{75} - 34 q^{76} - 28 q^{77} + 9 q^{78} - 36 q^{79} + 7 q^{80} + 6 q^{81} - 9 q^{82} - 10 q^{83} - 32 q^{85} + 24 q^{86} - 8 q^{87} - 4 q^{88} - 34 q^{89} - 22 q^{90} - 41 q^{91} - 24 q^{92} - 33 q^{93} + 29 q^{94} - 7 q^{95} + 10 q^{96} - 56 q^{97} - 22 q^{98} - 28 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9 - 7 * q^10 + 4 * q^11 - 10 * q^12 - 5 * q^13 + 6 * q^14 - 17 * q^15 + 34 * q^16 + 8 * q^17 - 38 * q^18 - 34 * q^19 + 7 * q^20 - 4 * q^22 - 24 * q^23 + 10 * q^24 + 5 * q^25 + 5 * q^26 - 31 * q^27 - 6 * q^28 + 24 * q^29 + 17 * q^30 - 28 * q^31 - 34 * q^32 - 16 * q^33 - 8 * q^34 + 2 * q^35 + 38 * q^36 - 36 * q^37 + 34 * q^38 - 9 * q^39 - 7 * q^40 + 9 * q^41 - 24 * q^43 + 4 * q^44 + 22 * q^45 + 24 * q^46 - 29 * q^47 - 10 * q^48 + 22 * q^49 - 5 * q^50 - 21 * q^51 - 5 * q^52 - 9 * q^53 + 31 * q^54 - 28 * q^55 + 6 * q^56 + 10 * q^57 - 24 * q^58 - 28 * q^59 - 17 * q^60 + 23 * q^61 + 28 * q^62 - 27 * q^63 + 34 * q^64 - 6 * q^65 + 16 * q^66 - 51 * q^67 + 8 * q^68 - 17 * q^69 - 2 * q^70 - 31 * q^71 - 38 * q^72 - 26 * q^73 + 36 * q^74 - 109 * q^75 - 34 * q^76 - 28 * q^77 + 9 * q^78 - 36 * q^79 + 7 * q^80 + 6 * q^81 - 9 * q^82 - 10 * q^83 - 32 * q^85 + 24 * q^86 - 8 * q^87 - 4 * q^88 - 34 * q^89 - 22 * q^90 - 41 * q^91 - 24 * q^92 - 33 * q^93 + 29 * q^94 - 7 * q^95 + 10 * q^96 - 56 * q^97 - 22 * q^98 - 28 * q^99

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