LMFDB - Embedded newform 4022.2.a.f.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4022,2,Mod(1,4022)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4022, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4022 = 2 \cdot 2011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4022.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$32.1158316930$
Analytic rank:	$0$
Dimension:	$50$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	4022.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -0.445408 q^{3} +1.00000 q^{4} -2.87764 q^{5} -0.445408 q^{6} -1.74390 q^{7} +1.00000 q^{8} -2.80161 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.445408 q^{3} +1.00000 q^{4} -2.87764 q^{5} -0.445408 q^{6} -1.74390 q^{7} +1.00000 q^{8} -2.80161 q^{9} -2.87764 q^{10} -3.03924 q^{11} -0.445408 q^{12} -0.0734694 q^{13} -1.74390 q^{14} +1.28172 q^{15} +1.00000 q^{16} -7.52885 q^{17} -2.80161 q^{18} +1.09061 q^{19} -2.87764 q^{20} +0.776750 q^{21} -3.03924 q^{22} +8.07322 q^{23} -0.445408 q^{24} +3.28080 q^{25} -0.0734694 q^{26} +2.58409 q^{27} -1.74390 q^{28} -1.39452 q^{29} +1.28172 q^{30} -2.92741 q^{31} +1.00000 q^{32} +1.35370 q^{33} -7.52885 q^{34} +5.01833 q^{35} -2.80161 q^{36} +8.81127 q^{37} +1.09061 q^{38} +0.0327239 q^{39} -2.87764 q^{40} -3.43677 q^{41} +0.776750 q^{42} -11.6425 q^{43} -3.03924 q^{44} +8.06202 q^{45} +8.07322 q^{46} +6.32504 q^{47} -0.445408 q^{48} -3.95880 q^{49} +3.28080 q^{50} +3.35341 q^{51} -0.0734694 q^{52} +12.7165 q^{53} +2.58409 q^{54} +8.74583 q^{55} -1.74390 q^{56} -0.485767 q^{57} -1.39452 q^{58} +3.82842 q^{59} +1.28172 q^{60} +11.9757 q^{61} -2.92741 q^{62} +4.88574 q^{63} +1.00000 q^{64} +0.211418 q^{65} +1.35370 q^{66} -4.65959 q^{67} -7.52885 q^{68} -3.59588 q^{69} +5.01833 q^{70} -1.93328 q^{71} -2.80161 q^{72} +2.22351 q^{73} +8.81127 q^{74} -1.46130 q^{75} +1.09061 q^{76} +5.30014 q^{77} +0.0327239 q^{78} -13.1879 q^{79} -2.87764 q^{80} +7.25386 q^{81} -3.43677 q^{82} +1.52394 q^{83} +0.776750 q^{84} +21.6653 q^{85} -11.6425 q^{86} +0.621130 q^{87} -3.03924 q^{88} +1.15465 q^{89} +8.06202 q^{90} +0.128124 q^{91} +8.07322 q^{92} +1.30389 q^{93} +6.32504 q^{94} -3.13838 q^{95} -0.445408 q^{96} +11.0269 q^{97} -3.95880 q^{98} +8.51477 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q + 50 q^{2} + 18 q^{3} + 50 q^{4} + 11 q^{5} + 18 q^{6} + 30 q^{7} + 50 q^{8} + 66 q^{9}+O(q^{10}) $ 50 * q + 50 * q^2 + 18 * q^3 + 50 * q^4 + 11 * q^5 + 18 * q^6 + 30 * q^7 + 50 * q^8 + 66 * q^9	\( 50 q + 50 q^{2} + 18 q^{3} + 50 q^{4} + 11 q^{5} + 18 q^{6} + 30 q^{7} + 50 q^{8} + 66 q^{9} + 11 q^{10} + 21 q^{11} + 18 q^{12} + 26 q^{13} + 30 q^{14} + 17 q^{15} + 50 q^{16} + 24 q^{17} + 66 q^{18} + 39 q^{19} + 11 q^{20} - q^{21} + 21 q^{22} + 28 q^{23} + 18 q^{24} + 79 q^{25} + 26 q^{26} + 66 q^{27} + 30 q^{28} - 5 q^{29} + 17 q^{30} + 60 q^{31} + 50 q^{32} + 37 q^{33} + 24 q^{34} + 38 q^{35} + 66 q^{36} + 35 q^{37} + 39 q^{38} + 37 q^{39} + 11 q^{40} + 42 q^{41} - q^{42} + 44 q^{43} + 21 q^{44} + 31 q^{45} + 28 q^{46} + 60 q^{47} + 18 q^{48} + 92 q^{49} + 79 q^{50} + 26 q^{51} + 26 q^{52} - 2 q^{53} + 66 q^{54} + 33 q^{55} + 30 q^{56} + 15 q^{57} - 5 q^{58} + 65 q^{59} + 17 q^{60} + 15 q^{61} + 60 q^{62} + 56 q^{63} + 50 q^{64} + 6 q^{65} + 37 q^{66} + 48 q^{67} + 24 q^{68} - 9 q^{69} + 38 q^{70} + 34 q^{71} + 66 q^{72} + 91 q^{73} + 35 q^{74} + 54 q^{75} + 39 q^{76} - 6 q^{77} + 37 q^{78} + 29 q^{79} + 11 q^{80} + 66 q^{81} + 42 q^{82} + 43 q^{83} - q^{84} + 44 q^{86} + 32 q^{87} + 21 q^{88} + 38 q^{89} + 31 q^{90} + 55 q^{91} + 28 q^{92} - 15 q^{93} + 60 q^{94} + 9 q^{95} + 18 q^{96} + 80 q^{97} + 92 q^{98} + 20 q^{99}+O(q^{100}) \) 50 * q + 50 * q^2 + 18 * q^3 + 50 * q^4 + 11 * q^5 + 18 * q^6 + 30 * q^7 + 50 * q^8 + 66 * q^9 + 11 * q^10 + 21 * q^11 + 18 * q^12 + 26 * q^13 + 30 * q^14 + 17 * q^15 + 50 * q^16 + 24 * q^17 + 66 * q^18 + 39 * q^19 + 11 * q^20 - q^21 + 21 * q^22 + 28 * q^23 + 18 * q^24 + 79 * q^25 + 26 * q^26 + 66 * q^27 + 30 * q^28 - 5 * q^29 + 17 * q^30 + 60 * q^31 + 50 * q^32 + 37 * q^33 + 24 * q^34 + 38 * q^35 + 66 * q^36 + 35 * q^37 + 39 * q^38 + 37 * q^39 + 11 * q^40 + 42 * q^41 - q^42 + 44 * q^43 + 21 * q^44 + 31 * q^45 + 28 * q^46 + 60 * q^47 + 18 * q^48 + 92 * q^49 + 79 * q^50 + 26 * q^51 + 26 * q^52 - 2 * q^53 + 66 * q^54 + 33 * q^55 + 30 * q^56 + 15 * q^57 - 5 * q^58 + 65 * q^59 + 17 * q^60 + 15 * q^61 + 60 * q^62 + 56 * q^63 + 50 * q^64 + 6 * q^65 + 37 * q^66 + 48 * q^67 + 24 * q^68 - 9 * q^69 + 38 * q^70 + 34 * q^71 + 66 * q^72 + 91 * q^73 + 35 * q^74 + 54 * q^75 + 39 * q^76 - 6 * q^77 + 37 * q^78 + 29 * q^79 + 11 * q^80 + 66 * q^81 + 42 * q^82 + 43 * q^83 - q^84 + 44 * q^86 + 32 * q^87 + 21 * q^88 + 38 * q^89 + 31 * q^90 + 55 * q^91 + 28 * q^92 - 15 * q^93 + 60 * q^94 + 9 * q^95 + 18 * q^96 + 80 * q^97 + 92 * q^98 + 20 * 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
$3$	−0.445408	−0.257157	−0.128578	−	0.991699i	$-0.541041\pi$
$3$	−0.445408	−0.257157	−0.128578	+	0.991699i	$0.541041\pi$
$4$	1.00000	0.500000
$5$	−2.87764	−1.28692	−0.643459	−	0.765480i	$-0.722501\pi$
$5$	−2.87764	−1.28692	−0.643459	+	0.765480i	$0.722501\pi$
$6$	−0.445408	−0.181837
$7$	−1.74390	−0.659134	−0.329567	−	0.944132i	$-0.606903\pi$
$7$	−1.74390	−0.659134	−0.329567	+	0.944132i	$0.606903\pi$
$8$	1.00000	0.353553
$9$	−2.80161	−0.933870
$10$	−2.87764	−0.909989
$11$	−3.03924	−0.916365	−0.458182	−	0.888858i	$-0.651499\pi$
$11$	−3.03924	−0.916365	−0.458182	+	0.888858i	$0.651499\pi$
$12$	−0.445408	−0.128578
$13$	−0.0734694	−0.0203767	−0.0101884	−	0.999948i	$-0.503243\pi$
$13$	−0.0734694	−0.0203767	−0.0101884	+	0.999948i	$0.503243\pi$
$14$	−1.74390	−0.466078
$15$	1.28172	0.330940
$16$	1.00000	0.250000
$17$	−7.52885	−1.82601	−0.913007	−	0.407943i	$-0.866246\pi$
$17$	−7.52885	−1.82601	−0.913007	+	0.407943i	$0.866246\pi$
$18$	−2.80161	−0.660346
$19$	1.09061	0.250203	0.125102	−	0.992144i	$-0.460074\pi$
$19$	1.09061	0.250203	0.125102	+	0.992144i	$0.460074\pi$
$20$	−2.87764	−0.643459
$21$	0.776750	0.169501
$22$	−3.03924	−0.647968
$23$	8.07322	1.68338	0.841692	−	0.539958i	$-0.181560\pi$
$23$	8.07322	1.68338	0.841692	+	0.539958i	$0.181560\pi$
$24$	−0.445408	−0.0909186
$25$	3.28080	0.656160
$26$	−0.0734694	−0.0144085
$27$	2.58409	0.497308
$28$	−1.74390	−0.329567
$29$	−1.39452	−0.258955	−0.129478	−	0.991582i	$-0.541330\pi$
$29$	−1.39452	−0.258955	−0.129478	+	0.991582i	$0.541330\pi$
$30$	1.28172	0.234010
$31$	−2.92741	−0.525778	−0.262889	−	0.964826i	$-0.584675\pi$
$31$	−2.92741	−0.525778	−0.262889	+	0.964826i	$0.584675\pi$
$32$	1.00000	0.176777
$33$	1.35370	0.235649
$34$	−7.52885	−1.29119
$35$	5.01833	0.848252
$36$	−2.80161	−0.466935
$37$	8.81127	1.44856	0.724282	−	0.689504i	$-0.242171\pi$
$37$	8.81127	1.44856	0.724282	+	0.689504i	$0.242171\pi$
$38$	1.09061	0.176920
$39$	0.0327239	0.00524002
$40$	−2.87764	−0.454994
$41$	−3.43677	−0.536733	−0.268366	−	0.963317i	$-0.586484\pi$
$41$	−3.43677	−0.536733	−0.268366	+	0.963317i	$0.586484\pi$
$42$	0.776750	0.119855
$43$	−11.6425	−1.77546	−0.887732	−	0.460360i	$-0.847720\pi$
$43$	−11.6425	−1.77546	−0.887732	+	0.460360i	$0.847720\pi$
$44$	−3.03924	−0.458182
$45$	8.06202	1.20182
$46$	8.07322	1.19033
$47$	6.32504	0.922601	0.461301	−	0.887244i	$-0.347383\pi$
$47$	6.32504	0.922601	0.461301	+	0.887244i	$0.347383\pi$
$48$	−0.445408	−0.0642892
$49$	−3.95880	−0.565542
$50$	3.28080	0.463975
$51$	3.35341	0.469572
$52$	−0.0734694	−0.0101884
$53$	12.7165	1.74675	0.873376	−	0.487047i	$-0.161926\pi$
$53$	12.7165	1.74675	0.873376	+	0.487047i	$0.161926\pi$
$54$	2.58409	0.351650
$55$	8.74583	1.17929
$56$	−1.74390	−0.233039
$57$	−0.485767	−0.0643414
$58$	−1.39452	−0.183109
$59$	3.82842	0.498418	0.249209	−	0.968450i	$-0.419829\pi$
$59$	3.82842	0.498418	0.249209	+	0.968450i	$0.419829\pi$
$60$	1.28172	0.165470
$61$	11.9757	1.53333	0.766665	−	0.642047i	$-0.221915\pi$
$61$	11.9757	1.53333	0.766665	+	0.642047i	$0.221915\pi$
$62$	−2.92741	−0.371781
$63$	4.88574	0.615546
$64$	1.00000	0.125000
$65$	0.211418	0.0262232
$66$	1.35370	0.166629
$67$	−4.65959	−0.569260	−0.284630	−	0.958638i	$-0.591871\pi$
$67$	−4.65959	−0.569260	−0.284630	+	0.958638i	$0.591871\pi$
$68$	−7.52885	−0.913007
$69$	−3.59588	−0.432893
$70$	5.01833	0.599805
$71$	−1.93328	−0.229439	−0.114719	−	0.993398i	$-0.536597\pi$
$71$	−1.93328	−0.229439	−0.114719	+	0.993398i	$0.536597\pi$
$72$	−2.80161	−0.330173
$73$	2.22351	0.260243	0.130121	−	0.991498i	$-0.458463\pi$
$73$	2.22351	0.260243	0.130121	+	0.991498i	$0.458463\pi$
$74$	8.81127	1.02429
$75$	−1.46130	−0.168736
$76$	1.09061	0.125102
$77$	5.30014	0.604007
$78$	0.0327239	0.00370525
$79$	−13.1879	−1.48375	−0.741876	−	0.670537i	$-0.766064\pi$
$79$	−13.1879	−1.48375	−0.741876	+	0.670537i	$0.766064\pi$
$80$	−2.87764	−0.321730
$81$	7.25386	0.805984
$82$	−3.43677	−0.379527
$83$	1.52394	0.167275	0.0836373	−	0.996496i	$-0.473346\pi$
$83$	1.52394	0.167275	0.0836373	+	0.996496i	$0.473346\pi$
$84$	0.776750	0.0847504
$85$	21.6653	2.34993
$86$	−11.6425	−1.25544
$87$	0.621130	0.0665921
$88$	−3.03924	−0.323984
$89$	1.15465	0.122392	0.0611962	−	0.998126i	$-0.480508\pi$
$89$	1.15465	0.122392	0.0611962	+	0.998126i	$0.480508\pi$
$90$	8.06202	0.849812
$91$	0.128124	0.0134310
$92$	8.07322	0.841692
$93$	1.30389	0.135207
$94$	6.32504	0.652378
$95$	−3.13838	−0.321991
$96$	−0.445408	−0.0454593
$97$	11.0269	1.11961	0.559807	−	0.828623i	$-0.310875\pi$
$97$	11.0269	1.11961	0.559807	+	0.828623i	$0.310875\pi$
$98$	−3.95880	−0.399899
$99$	8.51477	0.855766
$100$	3.28080	0.328080
$101$	17.7125	1.76246	0.881228	−	0.472692i	$-0.156718\pi$
$101$	17.7125	1.76246	0.881228	+	0.472692i	$0.156718\pi$
$102$	3.35341	0.332037
$103$	5.37048	0.529169	0.264585	−	0.964362i	$-0.414765\pi$
$103$	5.37048	0.529169	0.264585	+	0.964362i	$0.414765\pi$
$104$	−0.0734694	−0.00720427
$105$	−2.23520	−0.218134
$106$	12.7165	1.23514
$107$	−16.8179	−1.62585	−0.812923	−	0.582371i	$-0.802125\pi$
$107$	−16.8179	−1.62585	−0.812923	+	0.582371i	$0.802125\pi$
$108$	2.58409	0.248654
$109$	18.3277	1.75548	0.877738	−	0.479141i	$-0.159052\pi$
$109$	18.3277	1.75548	0.877738	+	0.479141i	$0.159052\pi$
$110$	8.74583	0.833882
$111$	−3.92462	−0.372508
$112$	−1.74390	−0.164783
$113$	−8.88737	−0.836054	−0.418027	−	0.908435i	$-0.637278\pi$
$113$	−8.88737	−0.836054	−0.418027	+	0.908435i	$0.637278\pi$
$114$	−0.485767	−0.0454962
$115$	−23.2318	−2.16638
$116$	−1.39452	−0.129478
$117$	0.205833	0.0190292
$118$	3.82842	0.352434
$119$	13.1296	1.20359
$120$	1.28172	0.117005
$121$	−1.76303	−0.160275
$122$	11.9757	1.08423
$123$	1.53076	0.138024
$124$	−2.92741	−0.262889
$125$	4.94724	0.442495
$126$	4.88574	0.435257
$127$	5.63767	0.500262	0.250131	−	0.968212i	$-0.419526\pi$
$127$	5.63767	0.500262	0.250131	+	0.968212i	$0.419526\pi$
$128$	1.00000	0.0883883
$129$	5.18567	0.456573
$130$	0.211418	0.0185426
$131$	18.7713	1.64005	0.820027	−	0.572324i	$-0.193958\pi$
$131$	18.7713	1.64005	0.820027	+	0.572324i	$0.193958\pi$
$132$	1.35370	0.117825
$133$	−1.90192	−0.164917
$134$	−4.65959	−0.402527
$135$	−7.43607	−0.639995
$136$	−7.52885	−0.645594
$137$	−17.1275	−1.46330	−0.731649	−	0.681682i	$-0.761249\pi$
$137$	−17.1275	−1.46330	−0.731649	+	0.681682i	$0.761249\pi$
$138$	−3.59588	−0.306102
$139$	2.98357	0.253063	0.126531	−	0.991963i	$-0.459616\pi$
$139$	2.98357	0.253063	0.126531	+	0.991963i	$0.459616\pi$
$140$	5.01833	0.424126
$141$	−2.81722	−0.237253
$142$	−1.93328	−0.162238
$143$	0.223291	0.0186725
$144$	−2.80161	−0.233468
$145$	4.01292	0.333255
$146$	2.22351	0.184019
$147$	1.76328	0.145433
$148$	8.81127	0.724282
$149$	−14.9779	−1.22704	−0.613521	−	0.789679i	$-0.710247\pi$
$149$	−14.9779	−1.22704	−0.613521	+	0.789679i	$0.710247\pi$
$150$	−1.46130	−0.119314
$151$	7.45114	0.606365	0.303183	−	0.952932i	$-0.401951\pi$
$151$	7.45114	0.606365	0.303183	+	0.952932i	$0.401951\pi$
$152$	1.09061	0.0884601
$153$	21.0929	1.70526
$154$	5.30014	0.427098
$155$	8.42402	0.676634
$156$	0.0327239	0.00262001
$157$	−2.26163	−0.180498	−0.0902490	−	0.995919i	$-0.528766\pi$
$157$	−2.26163	−0.180498	−0.0902490	+	0.995919i	$0.528766\pi$
$158$	−13.1879	−1.04917
$159$	−5.66406	−0.449189
$160$	−2.87764	−0.227497
$161$	−14.0789	−1.10958
$162$	7.25386	0.569917
$163$	−8.33263	−0.652662	−0.326331	−	0.945256i	$-0.605812\pi$
$163$	−8.33263	−0.652662	−0.326331	+	0.945256i	$0.605812\pi$
$164$	−3.43677	−0.268366
$165$	−3.89547	−0.303262
$166$	1.52394	0.118281
$167$	−13.4134	−1.03796	−0.518979	−	0.854787i	$-0.673688\pi$
$167$	−13.4134	−1.03796	−0.518979	+	0.854787i	$0.673688\pi$
$168$	0.776750	0.0599276
$169$	−12.9946	−0.999585
$170$	21.6653	1.66165
$171$	−3.05546	−0.233657
$172$	−11.6425	−0.887732
$173$	−22.6549	−1.72242	−0.861209	−	0.508251i	$-0.830292\pi$
$173$	−22.6549	−1.72242	−0.861209	+	0.508251i	$0.830292\pi$
$174$	0.621130	0.0470877
$175$	−5.72140	−0.432497
$176$	−3.03924	−0.229091
$177$	−1.70521	−0.128171
$178$	1.15465	0.0865445
$179$	−2.24324	−0.167667	−0.0838337	−	0.996480i	$-0.526716\pi$
$179$	−2.24324	−0.167667	−0.0838337	+	0.996480i	$0.526716\pi$
$180$	8.06202	0.600908
$181$	6.19988	0.460833	0.230417	−	0.973092i	$-0.425991\pi$
$181$	6.19988	0.460833	0.230417	+	0.973092i	$0.425991\pi$
$182$	0.128124	0.00949716
$183$	−5.33407	−0.394306
$184$	8.07322	0.595166
$185$	−25.3556	−1.86418
$186$	1.30389	0.0956060
$187$	22.8820	1.67330
$188$	6.32504	0.461301
$189$	−4.50640	−0.327792
$190$	−3.13838	−0.227682
$191$	13.5886	0.983239	0.491619	−	0.870810i	$-0.336405\pi$
$191$	13.5886	0.983239	0.491619	+	0.870810i	$0.336405\pi$
$192$	−0.445408	−0.0321446
$193$	12.0930	0.870476	0.435238	−	0.900315i	$-0.356664\pi$
$193$	12.0930	0.870476	0.435238	+	0.900315i	$0.356664\pi$
$194$	11.0269	0.791687
$195$	−0.0941675	−0.00674347
$196$	−3.95880	−0.282771
$197$	−14.1326	−1.00691	−0.503454	−	0.864022i	$-0.667938\pi$
$197$	−14.1326	−1.00691	−0.503454	+	0.864022i	$0.667938\pi$
$198$	8.51477	0.605118
$199$	23.3606	1.65599	0.827994	−	0.560737i	$-0.189482\pi$
$199$	23.3606	1.65599	0.827994	+	0.560737i	$0.189482\pi$
$200$	3.28080	0.231987
$201$	2.07542	0.146389
$202$	17.7125	1.24624
$203$	2.43191	0.170686
$204$	3.35341	0.234786
$205$	9.88977	0.690731
$206$	5.37048	0.374179
$207$	−22.6180	−1.57206
$208$	−0.0734694	−0.00509419
$209$	−3.31462	−0.229277
$210$	−2.23520	−0.154244
$211$	15.4539	1.06389	0.531944	−	0.846780i	$-0.321462\pi$
$211$	15.4539	1.06389	0.531944	+	0.846780i	$0.321462\pi$
$212$	12.7165	0.873376
$213$	0.861101	0.0590017
$214$	−16.8179	−1.14965
$215$	33.5029	2.28488
$216$	2.58409	0.175825
$217$	5.10512	0.346558
$218$	18.3277	1.24131
$219$	−0.990372	−0.0669231
$220$	8.74583	0.589644
$221$	0.553140	0.0372082
$222$	−3.92462	−0.263403
$223$	17.0776	1.14360	0.571800	−	0.820393i	$-0.306245\pi$
$223$	17.0776	1.14360	0.571800	+	0.820393i	$0.306245\pi$
$224$	−1.74390	−0.116520
$225$	−9.19152	−0.612768
$226$	−8.88737	−0.591179
$227$	−12.2670	−0.814187	−0.407093	−	0.913387i	$-0.633458\pi$
$227$	−12.2670	−0.814187	−0.407093	+	0.913387i	$0.633458\pi$
$228$	−0.485767	−0.0321707
$229$	12.9337	0.854681	0.427341	−	0.904091i	$-0.359451\pi$
$229$	12.9337	0.854681	0.427341	+	0.904091i	$0.359451\pi$
$230$	−23.2318	−1.53186
$231$	−2.36073	−0.155325
$232$	−1.39452	−0.0915546
$233$	−13.5169	−0.885519	−0.442760	−	0.896640i	$-0.646001\pi$
$233$	−13.5169	−0.885519	−0.442760	+	0.896640i	$0.646001\pi$
$234$	0.205833	0.0134557
$235$	−18.2012	−1.18731
$236$	3.82842	0.249209
$237$	5.87399	0.381557
$238$	13.1296	0.851065
$239$	−3.47884	−0.225028	−0.112514	−	0.993650i	$-0.535890\pi$
$239$	−3.47884	−0.225028	−0.112514	+	0.993650i	$0.535890\pi$
$240$	1.28172	0.0827349
$241$	17.9255	1.15468	0.577340	−	0.816504i	$-0.304091\pi$
$241$	17.9255	1.15468	0.577340	+	0.816504i	$0.304091\pi$
$242$	−1.76303	−0.113332
$243$	−10.9832	−0.704572
$244$	11.9757	0.766665
$245$	11.3920	0.727807
$246$	1.53076	0.0975980
$247$	−0.0801264	−0.00509832
$248$	−2.92741	−0.185891
$249$	−0.678778	−0.0430158
$250$	4.94724	0.312891
$251$	−5.09393	−0.321526	−0.160763	−	0.986993i	$-0.551396\pi$
$251$	−5.09393	−0.321526	−0.160763	+	0.986993i	$0.551396\pi$
$252$	4.88574	0.307773
$253$	−24.5365	−1.54259
$254$	5.63767	0.353739
$255$	−9.64991	−0.604301
$256$	1.00000	0.0625000
$257$	22.3590	1.39472	0.697358	−	0.716723i	$-0.254359\pi$
$257$	22.3590	1.39472	0.697358	+	0.716723i	$0.254359\pi$
$258$	5.18567	0.322846
$259$	−15.3660	−0.954798
$260$	0.211418	0.0131116
$261$	3.90690	0.241831
$262$	18.7713	1.15969
$263$	5.54494	0.341916	0.170958	−	0.985278i	$-0.445314\pi$
$263$	5.54494	0.341916	0.170958	+	0.985278i	$0.445314\pi$
$264$	1.35370	0.0833146
$265$	−36.5936	−2.24793
$266$	−1.90192	−0.116614
$267$	−0.514290	−0.0314740
$268$	−4.65959	−0.284630
$269$	−16.7355	−1.02038	−0.510190	−	0.860062i	$-0.670425\pi$
$269$	−16.7355	−1.02038	−0.510190	+	0.860062i	$0.670425\pi$
$270$	−7.43607	−0.452545
$271$	−0.841467	−0.0511155	−0.0255577	−	0.999673i	$-0.508136\pi$
$271$	−0.841467	−0.0511155	−0.0255577	+	0.999673i	$0.508136\pi$
$272$	−7.52885	−0.456504
$273$	−0.0570673	−0.00345387
$274$	−17.1275	−1.03471
$275$	−9.97113	−0.601282
$276$	−3.59588	−0.216447
$277$	15.5055	0.931633	0.465816	−	0.884881i	$-0.345761\pi$
$277$	15.5055	0.931633	0.465816	+	0.884881i	$0.345761\pi$
$278$	2.98357	0.178942
$279$	8.20146	0.491009
$280$	5.01833	0.299902
$281$	13.2082	0.787934	0.393967	−	0.919125i	$-0.371102\pi$
$281$	13.2082	0.787934	0.393967	+	0.919125i	$0.371102\pi$
$282$	−2.81722	−0.167763
$283$	−2.55154	−0.151673	−0.0758365	−	0.997120i	$-0.524163\pi$
$283$	−2.55154	−0.151673	−0.0758365	+	0.997120i	$0.524163\pi$
$284$	−1.93328	−0.114719
$285$	1.39786	0.0828021
$286$	0.223291	0.0132035
$287$	5.99339	0.353779
$288$	−2.80161	−0.165087
$289$	39.6836	2.33433
$290$	4.01292	0.235647
$291$	−4.91148	−0.287916
$292$	2.22351	0.130121
$293$	−30.7227	−1.79484	−0.897421	−	0.441175i	$-0.854562\pi$
$293$	−30.7227	−1.79484	−0.897421	+	0.441175i	$0.854562\pi$
$294$	1.76328	0.102837
$295$	−11.0168	−0.641423
$296$	8.81127	0.512145
$297$	−7.85366	−0.455715
$298$	−14.9779	−0.867649
$299$	−0.593135	−0.0343019
$300$	−1.46130	−0.0843679
$301$	20.3034	1.17027
$302$	7.45114	0.428765
$303$	−7.88928	−0.453227
$304$	1.09061	0.0625508
$305$	−34.4617	−1.97327
$306$	21.0929	1.20580
$307$	5.22420	0.298161	0.149080	−	0.988825i	$-0.452369\pi$
$307$	5.22420	0.298161	0.149080	+	0.988825i	$0.452369\pi$
$308$	5.30014	0.302004
$309$	−2.39206	−0.136079
$310$	8.42402	0.478452
$311$	−2.25340	−0.127779	−0.0638893	−	0.997957i	$-0.520350\pi$
$311$	−2.25340	−0.127779	−0.0638893	+	0.997957i	$0.520350\pi$
$312$	0.0327239	0.00185263
$313$	−6.42938	−0.363410	−0.181705	−	0.983353i	$-0.558162\pi$
$313$	−6.42938	−0.363410	−0.181705	+	0.983353i	$0.558162\pi$
$314$	−2.26163	−0.127631
$315$	−14.0594	−0.792157
$316$	−13.1879	−0.741876
$317$	−4.10054	−0.230309	−0.115155	−	0.993348i	$-0.536736\pi$
$317$	−4.10054	−0.230309	−0.115155	+	0.993348i	$0.536736\pi$
$318$	−5.66406	−0.317624
$319$	4.23827	0.237298
$320$	−2.87764	−0.160865
$321$	7.49083	0.418097
$322$	−14.0789	−0.784588
$323$	−8.21104	−0.456874
$324$	7.25386	0.402992
$325$	−0.241038	−0.0133704
$326$	−8.33263	−0.461501
$327$	−8.16332	−0.451432
$328$	−3.43677	−0.189764
$329$	−11.0303	−0.608118
$330$	−3.89547	−0.214438
$331$	18.4734	1.01539	0.507696	−	0.861536i	$-0.330497\pi$
$331$	18.4734	1.01539	0.507696	+	0.861536i	$0.330497\pi$
$332$	1.52394	0.0836373
$333$	−24.6858	−1.35277
$334$	−13.4134	−0.733948
$335$	13.4086	0.732591
$336$	0.776750	0.0423752
$337$	21.0476	1.14654	0.573268	−	0.819368i	$-0.305675\pi$
$337$	21.0476	1.14654	0.573268	+	0.819368i	$0.305675\pi$
$338$	−12.9946	−0.706813
$339$	3.95851	0.214997
$340$	21.6653	1.17497
$341$	8.89709	0.481805
$342$	−3.05546	−0.165221
$343$	19.1111	1.03190
$344$	−11.6425	−0.627722
$345$	10.3476	0.557098
$346$	−22.6549	−1.21793
$347$	1.81901	0.0976496	0.0488248	−	0.998807i	$-0.484452\pi$
$347$	1.81901	0.0976496	0.0488248	+	0.998807i	$0.484452\pi$
$348$	0.621130	0.0332961
$349$	−13.5812	−0.726987	−0.363494	−	0.931597i	$-0.618416\pi$
$349$	−13.5812	−0.726987	−0.363494	+	0.931597i	$0.618416\pi$
$350$	−5.72140	−0.305822
$351$	−0.189851	−0.0101335
$352$	−3.03924	−0.161992
$353$	35.1651	1.87165	0.935825	−	0.352464i	$-0.114656\pi$
$353$	35.1651	1.87165	0.935825	+	0.352464i	$0.114656\pi$
$354$	−1.70521	−0.0906309
$355$	5.56329	0.295269
$356$	1.15465	0.0611962
$357$	−5.84803	−0.309511
$358$	−2.24324	−0.118559
$359$	−10.4510	−0.551583	−0.275791	−	0.961218i	$-0.588940\pi$
$359$	−10.4510	−0.551583	−0.275791	+	0.961218i	$0.588940\pi$
$360$	8.06202	0.424906
$361$	−17.8106	−0.937398
$362$	6.19988	0.325858
$363$	0.785268	0.0412159
$364$	0.128124	0.00671550
$365$	−6.39847	−0.334911
$366$	−5.33407	−0.278816
$367$	31.7647	1.65810	0.829051	−	0.559173i	$-0.188881\pi$
$367$	31.7647	1.65810	0.829051	+	0.559173i	$0.188881\pi$
$368$	8.07322	0.420846
$369$	9.62848	0.501239
$370$	−25.3556	−1.31818
$371$	−22.1764	−1.15134
$372$	1.30389	0.0676037
$373$	−18.8559	−0.976322	−0.488161	−	0.872754i	$-0.662332\pi$
$373$	−18.8559	−0.976322	−0.488161	+	0.872754i	$0.662332\pi$
$374$	22.8820	1.18320
$375$	−2.20354	−0.113790
$376$	6.32504	0.326189
$377$	0.102454	0.00527667
$378$	−4.50640	−0.231784
$379$	−7.64112	−0.392498	−0.196249	−	0.980554i	$-0.562876\pi$
$379$	−7.64112	−0.392498	−0.196249	+	0.980554i	$0.562876\pi$
$380$	−3.13838	−0.160995
$381$	−2.51107	−0.128646
$382$	13.5886	0.695255
$383$	2.32518	0.118811	0.0594056	−	0.998234i	$-0.481079\pi$
$383$	2.32518	0.118811	0.0594056	+	0.998234i	$0.481079\pi$
$384$	−0.445408	−0.0227297
$385$	−15.2519	−0.777308
$386$	12.0930	0.615520
$387$	32.6178	1.65805
$388$	11.0269	0.559807
$389$	−6.42149	−0.325582	−0.162791	−	0.986661i	$-0.552050\pi$
$389$	−6.42149	−0.325582	−0.162791	+	0.986661i	$0.552050\pi$
$390$	−0.0941675	−0.00476836
$391$	−60.7821	−3.07388
$392$	−3.95880	−0.199949
$393$	−8.36089	−0.421751
$394$	−14.1326	−0.711991
$395$	37.9499	1.90947
$396$	8.51477	0.427883
$397$	3.91329	0.196402	0.0982012	−	0.995167i	$-0.468691\pi$
$397$	3.91329	0.196402	0.0982012	+	0.995167i	$0.468691\pi$
$398$	23.3606	1.17096
$399$	0.847131	0.0424096
$400$	3.28080	0.164040
$401$	−39.5658	−1.97582	−0.987911	−	0.155020i	$-0.950456\pi$
$401$	−39.5658	−1.97582	−0.987911	+	0.155020i	$0.950456\pi$
$402$	2.07542	0.103513
$403$	0.215075	0.0107136
$404$	17.7125	0.881228
$405$	−20.8740	−1.03724
$406$	2.43191	0.120693
$407$	−26.7796	−1.32741
$408$	3.35341	0.166019
$409$	4.25369	0.210332	0.105166	−	0.994455i	$-0.466463\pi$
$409$	4.25369	0.210332	0.105166	+	0.994455i	$0.466463\pi$
$410$	9.88977	0.488421
$411$	7.62871	0.376297
$412$	5.37048	0.264585
$413$	−6.67640	−0.328524
$414$	−22.6180	−1.11162
$415$	−4.38536	−0.215269
$416$	−0.0734694	−0.00360213
$417$	−1.32891	−0.0650768
$418$	−3.31462	−0.162124
$419$	−10.0892	−0.492890	−0.246445	−	0.969157i	$-0.579262\pi$
$419$	−10.0892	−0.492890	−0.246445	+	0.969157i	$0.579262\pi$
$420$	−2.23520	−0.109067
$421$	−24.1453	−1.17677	−0.588386	−	0.808580i	$-0.700236\pi$
$421$	−24.1453	−1.17677	−0.588386	+	0.808580i	$0.700236\pi$
$422$	15.4539	0.752282
$423$	−17.7203	−0.861590
$424$	12.7165	0.617570
$425$	−24.7006	−1.19816
$426$	0.861101	0.0417205
$427$	−20.8845	−1.01067
$428$	−16.8179	−0.812923
$429$	−0.0994557	−0.00480177
$430$	33.5029	1.61565
$431$	37.3793	1.80050	0.900248	−	0.435377i	$-0.143385\pi$
$431$	37.3793	1.80050	0.900248	+	0.435377i	$0.143385\pi$
$432$	2.58409	0.124327
$433$	−14.7224	−0.707514	−0.353757	−	0.935337i	$-0.615096\pi$
$433$	−14.7224	−0.707514	−0.353757	+	0.935337i	$0.615096\pi$
$434$	5.10512	0.245054
$435$	−1.78739	−0.0856986
$436$	18.3277	0.877738
$437$	8.80474	0.421188
$438$	−0.990372	−0.0473218
$439$	−4.48637	−0.214123	−0.107061	−	0.994252i	$-0.534144\pi$
$439$	−4.48637	−0.214123	−0.107061	+	0.994252i	$0.534144\pi$
$440$	8.74583	0.416941
$441$	11.0910	0.528143
$442$	0.553140	0.0263102
$443$	30.0626	1.42832	0.714159	−	0.699983i	$-0.246809\pi$
$443$	30.0626	1.42832	0.714159	+	0.699983i	$0.246809\pi$
$444$	−3.92462	−0.186254
$445$	−3.32266	−0.157509
$446$	17.0776	0.808647
$447$	6.67131	0.315542
$448$	−1.74390	−0.0823917
$449$	12.9647	0.611840	0.305920	−	0.952057i	$-0.401036\pi$
$449$	12.9647	0.611840	0.305920	+	0.952057i	$0.401036\pi$
$450$	−9.19152	−0.433292
$451$	10.4452	0.491843
$452$	−8.88737	−0.418027
$453$	−3.31880	−0.155931
$454$	−12.2670	−0.575717
$455$	−0.368693	−0.0172846
$456$	−0.485767	−0.0227481
$457$	−3.18035	−0.148771	−0.0743853	−	0.997230i	$-0.523699\pi$
$457$	−3.18035	−0.148771	−0.0743853	+	0.997230i	$0.523699\pi$
$458$	12.9337	0.604351
$459$	−19.4552	−0.908091
$460$	−23.2318	−1.08319
$461$	21.4150	0.997394	0.498697	−	0.866776i	$-0.333812\pi$
$461$	21.4150	0.997394	0.498697	+	0.866776i	$0.333812\pi$
$462$	−2.36073	−0.109831
$463$	−5.75274	−0.267353	−0.133676	−	0.991025i	$-0.542678\pi$
$463$	−5.75274	−0.267353	−0.133676	+	0.991025i	$0.542678\pi$
$464$	−1.39452	−0.0647389
$465$	−3.75213	−0.174001
$466$	−13.5169	−0.626157
$467$	3.24870	0.150332	0.0751660	−	0.997171i	$-0.476051\pi$
$467$	3.24870	0.150332	0.0751660	+	0.997171i	$0.476051\pi$
$468$	0.205833	0.00951462
$469$	8.12588	0.375218
$470$	−18.2012	−0.839557
$471$	1.00735	0.0464162
$472$	3.82842	0.176217
$473$	35.3843	1.62697
$474$	5.87399	0.269802
$475$	3.57807	0.164173
$476$	13.1296	0.601794
$477$	−35.6268	−1.63124
$478$	−3.47884	−0.159119
$479$	9.39599	0.429314	0.214657	−	0.976690i	$-0.431137\pi$
$479$	9.39599	0.429314	0.214657	+	0.976690i	$0.431137\pi$
$480$	1.28172	0.0585024
$481$	−0.647359	−0.0295170
$482$	17.9255	0.816482
$483$	6.27088	0.285335
$484$	−1.76303	−0.0801376
$485$	−31.7315	−1.44085
$486$	−10.9832	−0.498208
$487$	−20.6028	−0.933603	−0.466801	−	0.884362i	$-0.654594\pi$
$487$	−20.6028	−0.933603	−0.466801	+	0.884362i	$0.654594\pi$
$488$	11.9757	0.542114
$489$	3.71142	0.167836
$490$	11.3920	0.514637
$491$	−17.2024	−0.776335	−0.388168	−	0.921589i	$-0.626892\pi$
$491$	−17.2024	−0.776335	−0.388168	+	0.921589i	$0.626892\pi$
$492$	1.53076	0.0690122
$493$	10.4991	0.472856
$494$	−0.0801264	−0.00360506
$495$	−24.5024	−1.10130
$496$	−2.92741	−0.131445
$497$	3.37146	0.151231
$498$	−0.678778	−0.0304168
$499$	11.2045	0.501580	0.250790	−	0.968041i	$-0.419310\pi$
$499$	11.2045	0.501580	0.250790	+	0.968041i	$0.419310\pi$
$500$	4.94724	0.221247
$501$	5.97444	0.266918
$502$	−5.09393	−0.227353
$503$	0.131614	0.00586838	0.00293419	−	0.999996i	$-0.499066\pi$
$503$	0.131614	0.00586838	0.00293419	+	0.999996i	$0.499066\pi$
$504$	4.88574	0.217628
$505$	−50.9700	−2.26814
$506$	−24.5365	−1.09078
$507$	5.78791	0.257050
$508$	5.63767	0.250131
$509$	−32.2425	−1.42912	−0.714561	−	0.699573i	$-0.753374\pi$
$509$	−32.2425	−1.42912	−0.714561	+	0.699573i	$0.753374\pi$
$510$	−9.64991	−0.427305
$511$	−3.87760	−0.171535
$512$	1.00000	0.0441942
$513$	2.81823	0.124428
$514$	22.3590	0.986213
$515$	−15.4543	−0.680998
$516$	5.18567	0.228286
$517$	−19.2233	−0.845439
$518$	−15.3660	−0.675144
$519$	10.0907	0.442931
$520$	0.211418	0.00927131
$521$	6.24900	0.273774	0.136887	−	0.990587i	$-0.456290\pi$
$521$	6.24900	0.273774	0.136887	+	0.990587i	$0.456290\pi$
$522$	3.90690	0.171000
$523$	31.4517	1.37529	0.687643	−	0.726049i	$-0.258646\pi$
$523$	31.4517	1.37529	0.687643	+	0.726049i	$0.258646\pi$
$524$	18.7713	0.820027
$525$	2.54836	0.111220
$526$	5.54494	0.241771
$527$	22.0400	0.960078
$528$	1.35370	0.0589123
$529$	42.1769	1.83378
$530$	−36.5936	−1.58952
$531$	−10.7257	−0.465458
$532$	−1.90192	−0.0824587
$533$	0.252497	0.0109369
$534$	−0.514290	−0.0222555
$535$	48.3958	2.09233
$536$	−4.65959	−0.201264
$537$	0.999157	0.0431168
$538$	−16.7355	−0.721517
$539$	12.0317	0.518243
$540$	−7.43607	−0.319997
$541$	20.2658	0.871296	0.435648	−	0.900117i	$-0.356519\pi$
$541$	20.2658	0.871296	0.435648	+	0.900117i	$0.356519\pi$
$542$	−0.841467	−0.0361441
$543$	−2.76148	−0.118506
$544$	−7.52885	−0.322797
$545$	−52.7405	−2.25915
$546$	−0.0570673	−0.00244226
$547$	41.2652	1.76437	0.882187	−	0.470899i	$-0.156070\pi$
$547$	41.2652	1.76437	0.882187	+	0.470899i	$0.156070\pi$
$548$	−17.1275	−0.731649
$549$	−33.5512	−1.43193
$550$	−9.97113	−0.425170
$551$	−1.52087	−0.0647914
$552$	−3.59588	−0.153051
$553$	22.9984	0.977992
$554$	15.5055	0.658764
$555$	11.2936	0.479387
$556$	2.98357	0.126531
$557$	3.53472	0.149771	0.0748855	−	0.997192i	$-0.476141\pi$
$557$	3.53472	0.149771	0.0748855	+	0.997192i	$0.476141\pi$
$558$	8.20146	0.347196
$559$	0.855367	0.0361782
$560$	5.01833	0.212063
$561$	−10.1918	−0.430299
$562$	13.2082	0.557153
$563$	3.53376	0.148930	0.0744651	−	0.997224i	$-0.476275\pi$
$563$	3.53376	0.148930	0.0744651	+	0.997224i	$0.476275\pi$
$564$	−2.81722	−0.118627
$565$	25.5746	1.07593
$566$	−2.55154	−0.107249
$567$	−12.6500	−0.531252
$568$	−1.93328	−0.0811188
$569$	−9.86844	−0.413706	−0.206853	−	0.978372i	$-0.566322\pi$
$569$	−9.86844	−0.413706	−0.206853	+	0.978372i	$0.566322\pi$
$570$	1.39786	0.0585499
$571$	−33.7782	−1.41358	−0.706788	−	0.707426i	$-0.749856\pi$
$571$	−33.7782	−1.41358	−0.706788	+	0.707426i	$0.749856\pi$
$572$	0.223291	0.00933627
$573$	−6.05249	−0.252846
$574$	5.99339	0.250159
$575$	26.4866	1.10457
$576$	−2.80161	−0.116734
$577$	19.9783	0.831705	0.415853	−	0.909432i	$-0.363483\pi$
$577$	19.9783	0.831705	0.415853	+	0.909432i	$0.363483\pi$
$578$	39.6836	1.65062
$579$	−5.38634	−0.223849
$580$	4.01292	0.166627
$581$	−2.65761	−0.110256
$582$	−4.91148	−0.203588
$583$	−38.6486	−1.60066
$584$	2.22351	0.0920097
$585$	−0.592312	−0.0244891
$586$	−30.7227	−1.26915
$587$	−2.29857	−0.0948721	−0.0474360	−	0.998874i	$-0.515105\pi$
$587$	−2.29857	−0.0948721	−0.0474360	+	0.998874i	$0.515105\pi$
$588$	1.76328	0.0727165
$589$	−3.19266	−0.131551
$590$	−11.0168	−0.453555
$591$	6.29479	0.258933
$592$	8.81127	0.362141
$593$	6.41056	0.263250	0.131625	−	0.991300i	$-0.457981\pi$
$593$	6.41056	0.263250	0.131625	+	0.991300i	$0.457981\pi$
$594$	−7.85366	−0.322239
$595$	−37.7822	−1.54892
$596$	−14.9779	−0.613521
$597$	−10.4050	−0.425848
$598$	−0.593135	−0.0242551
$599$	−12.4646	−0.509290	−0.254645	−	0.967035i	$-0.581959\pi$
$599$	−12.4646	−0.509290	−0.254645	+	0.967035i	$0.581959\pi$
$600$	−1.46130	−0.0596571
$601$	0.886430	0.0361582	0.0180791	−	0.999837i	$-0.494245\pi$
$601$	0.886430	0.0361582	0.0180791	+	0.999837i	$0.494245\pi$
$602$	20.3034	0.827505
$603$	13.0544	0.531615
$604$	7.45114	0.303183
$605$	5.07336	0.206261
$606$	−7.88928	−0.320480
$607$	25.0956	1.01860	0.509300	−	0.860589i	$-0.329904\pi$
$607$	25.0956	1.01860	0.509300	+	0.860589i	$0.329904\pi$
$608$	1.09061	0.0442301
$609$	−1.08319	−0.0438931
$610$	−34.4617	−1.39531
$611$	−0.464697	−0.0187996
$612$	21.0929	0.852631
$613$	−12.3004	−0.496808	−0.248404	−	0.968657i	$-0.579906\pi$
$613$	−12.3004	−0.496808	−0.248404	+	0.968657i	$0.579906\pi$
$614$	5.22420	0.210832
$615$	−4.40499	−0.177626
$616$	5.30014	0.213549
$617$	38.7848	1.56142	0.780709	−	0.624894i	$-0.214858\pi$
$617$	38.7848	1.56142	0.780709	+	0.624894i	$0.214858\pi$
$618$	−2.39206	−0.0962227
$619$	−23.2380	−0.934014	−0.467007	−	0.884254i	$-0.654668\pi$
$619$	−23.2380	−0.934014	−0.467007	+	0.884254i	$0.654668\pi$
$620$	8.42402	0.338317
$621$	20.8619	0.837160
$622$	−2.25340	−0.0903532
$623$	−2.01360	−0.0806730
$624$	0.0327239	0.00131000
$625$	−30.6404	−1.22561
$626$	−6.42938	−0.256970
$627$	1.47636	0.0589602
$628$	−2.26163	−0.0902490
$629$	−66.3388	−2.64510
$630$	−14.0594	−0.560140
$631$	16.8522	0.670877	0.335438	−	0.942062i	$-0.391116\pi$
$631$	16.8522	0.670877	0.335438	+	0.942062i	$0.391116\pi$
$632$	−13.1879	−0.524586
$633$	−6.88328	−0.273586
$634$	−4.10054	−0.162853
$635$	−16.2232	−0.643797
$636$	−5.66406	−0.224594
$637$	0.290850	0.0115239
$638$	4.23827	0.167795
$639$	5.41631	0.214266
$640$	−2.87764	−0.113749
$641$	−14.5141	−0.573273	−0.286637	−	0.958039i	$-0.592537\pi$
$641$	−14.5141	−0.573273	−0.286637	+	0.958039i	$0.592537\pi$
$642$	7.49083	0.295639
$643$	33.2141	1.30984	0.654918	−	0.755700i	$-0.272703\pi$
$643$	33.2141	1.30984	0.654918	+	0.755700i	$0.272703\pi$
$644$	−14.0789	−0.554788
$645$	−14.9225	−0.587572
$646$	−8.21104	−0.323059
$647$	−11.2728	−0.443181	−0.221591	−	0.975140i	$-0.571125\pi$
$647$	−11.2728	−0.443181	−0.221591	+	0.975140i	$0.571125\pi$
$648$	7.25386	0.284959
$649$	−11.6355	−0.456732
$650$	−0.241038	−0.00945430
$651$	−2.27386	−0.0891198
$652$	−8.33263	−0.326331
$653$	−8.95219	−0.350326	−0.175163	−	0.984539i	$-0.556045\pi$
$653$	−8.95219	−0.350326	−0.175163	+	0.984539i	$0.556045\pi$
$654$	−8.16332	−0.319211
$655$	−54.0170	−2.11062
$656$	−3.43677	−0.134183
$657$	−6.22942	−0.243033
$658$	−11.0303	−0.430004
$659$	−43.0880	−1.67847	−0.839235	−	0.543769i	$-0.816997\pi$
$659$	−43.0880	−1.67847	−0.839235	+	0.543769i	$0.816997\pi$
$660$	−3.89547	−0.151631
$661$	−36.1770	−1.40712	−0.703560	−	0.710636i	$-0.748408\pi$
$661$	−36.1770	−1.40712	−0.703560	+	0.710636i	$0.748408\pi$
$662$	18.4734	0.717990
$663$	−0.246373	−0.00956835
$664$	1.52394	0.0591405
$665$	5.47303	0.212235
$666$	−24.6858	−0.956554
$667$	−11.2583	−0.435921
$668$	−13.4134	−0.518979
$669$	−7.60650	−0.294084
$670$	13.4086	0.518020
$671$	−36.3970	−1.40509
$672$	0.776750	0.0299638
$673$	10.6244	0.409540	0.204770	−	0.978810i	$-0.434355\pi$
$673$	10.6244	0.409540	0.204770	+	0.978810i	$0.434355\pi$
$674$	21.0476	0.810724
$675$	8.47787	0.326313
$676$	−12.9946	−0.499792
$677$	−22.0640	−0.847987	−0.423994	−	0.905665i	$-0.639372\pi$
$677$	−22.0640	−0.847987	−0.423994	+	0.905665i	$0.639372\pi$
$678$	3.95851	0.152026
$679$	−19.2299	−0.737976
$680$	21.6653	0.830827
$681$	5.46381	0.209374
$682$	8.89709	0.340687
$683$	−5.37390	−0.205627	−0.102813	−	0.994701i	$-0.532784\pi$
$683$	−5.37390	−0.205627	−0.102813	+	0.994701i	$0.532784\pi$
$684$	−3.05546	−0.116829
$685$	49.2866	1.88314
$686$	19.1111	0.729665
$687$	−5.76077	−0.219787
$688$	−11.6425	−0.443866
$689$	−0.934277	−0.0355931
$690$	10.3476	0.393928
$691$	8.55242	0.325349	0.162675	−	0.986680i	$-0.447988\pi$
$691$	8.55242	0.325349	0.162675	+	0.986680i	$0.447988\pi$
$692$	−22.6549	−0.861209
$693$	−14.8489	−0.564065
$694$	1.81901	0.0690487
$695$	−8.58562	−0.325671
$696$	0.621130	0.0235439
$697$	25.8749	0.980082
$698$	−13.5812	−0.514057
$699$	6.02053	0.227717
$700$	−5.72140	−0.216249
$701$	31.6269	1.19453	0.597265	−	0.802044i	$-0.296254\pi$
$701$	31.6269	1.19453	0.597265	+	0.802044i	$0.296254\pi$
$702$	−0.189851	−0.00716548
$703$	9.60966	0.362435
$704$	−3.03924	−0.114546
$705$	8.10695	0.305325
$706$	35.1651	1.32346
$707$	−30.8888	−1.16169
$708$	−1.70521	−0.0640857
$709$	27.0622	1.01634	0.508170	−	0.861257i	$-0.330322\pi$
$709$	27.0622	1.01634	0.508170	+	0.861257i	$0.330322\pi$
$710$	5.56329	0.208787
$711$	36.9473	1.38563
$712$	1.15465	0.0432723
$713$	−23.6336	−0.885086
$714$	−5.84803	−0.218857
$715$	−0.642551	−0.0240300
$716$	−2.24324	−0.0838337
$717$	1.54951	0.0578673
$718$	−10.4510	−0.390028
$719$	12.7976	0.477272	0.238636	−	0.971109i	$-0.423300\pi$
$719$	12.7976	0.477272	0.238636	+	0.971109i	$0.423300\pi$
$720$	8.06202	0.300454
$721$	−9.36561	−0.348794
$722$	−17.8106	−0.662841
$723$	−7.98415	−0.296934
$724$	6.19988	0.230417
$725$	−4.57513	−0.169916
$726$	0.785268	0.0291440
$727$	38.9410	1.44424	0.722120	−	0.691768i	$-0.243168\pi$
$727$	38.9410	1.44424	0.722120	+	0.691768i	$0.243168\pi$
$728$	0.128124	0.00474858
$729$	−16.8696	−0.624799
$730$	−6.39847	−0.236818
$731$	87.6546	3.24202
$732$	−5.33407	−0.197153
$733$	−16.4219	−0.606556	−0.303278	−	0.952902i	$-0.598081\pi$
$733$	−16.4219	−0.606556	−0.303278	+	0.952902i	$0.598081\pi$
$734$	31.7647	1.17246
$735$	−5.07409	−0.187160
$736$	8.07322	0.297583
$737$	14.1616	0.521650
$738$	9.62848	0.354429
$739$	−50.2615	−1.84890	−0.924450	−	0.381302i	$-0.875476\pi$
$739$	−50.2615	−1.84890	−0.924450	+	0.381302i	$0.875476\pi$
$740$	−25.3556	−0.932092
$741$	0.0356890	0.00131107
$742$	−22.1764	−0.814123
$743$	38.2473	1.40316	0.701579	−	0.712592i	$-0.252479\pi$
$743$	38.2473	1.40316	0.701579	+	0.712592i	$0.252479\pi$
$744$	1.30389	0.0478030
$745$	43.1011	1.57910
$746$	−18.8559	−0.690364
$747$	−4.26950	−0.156213
$748$	22.8820	0.836648
$749$	29.3288	1.07165
$750$	−2.20354	−0.0804620
$751$	−26.7893	−0.977554	−0.488777	−	0.872409i	$-0.662557\pi$
$751$	−26.7893	−0.977554	−0.488777	+	0.872409i	$0.662557\pi$
$752$	6.32504	0.230650
$753$	2.26888	0.0826826
$754$	0.102454	0.00373117
$755$	−21.4417	−0.780343
$756$	−4.50640	−0.163896
$757$	37.5615	1.36519	0.682597	−	0.730795i	$-0.260850\pi$
$757$	37.5615	1.36519	0.682597	+	0.730795i	$0.260850\pi$
$758$	−7.64112	−0.277538
$759$	10.9287	0.396688
$760$	−3.13838	−0.113841
$761$	−22.7663	−0.825278	−0.412639	−	0.910895i	$-0.635393\pi$
$761$	−22.7663	−0.825278	−0.412639	+	0.910895i	$0.635393\pi$
$762$	−2.51107	−0.0909663
$763$	−31.9618	−1.15709
$764$	13.5886	0.491619
$765$	−60.6978	−2.19453
$766$	2.32518	0.0840123
$767$	−0.281272	−0.0101561
$768$	−0.445408	−0.0160723
$769$	9.09983	0.328148	0.164074	−	0.986448i	$-0.447536\pi$
$769$	9.09983	0.328148	0.164074	+	0.986448i	$0.447536\pi$
$770$	−15.2519	−0.549640
$771$	−9.95888	−0.358660
$772$	12.0930	0.435238
$773$	−11.2480	−0.404563	−0.202282	−	0.979327i	$-0.564836\pi$
$773$	−11.2480	−0.404563	−0.202282	+	0.979327i	$0.564836\pi$
$774$	32.6178	1.17242
$775$	−9.60424	−0.344994
$776$	11.0269	0.395843
$777$	6.84415	0.245533
$778$	−6.42149	−0.230222
$779$	−3.74817	−0.134292
$780$	−0.0941675	−0.00337174
$781$	5.87571	0.210250
$782$	−60.7821	−2.17356
$783$	−3.60355	−0.128781
$784$	−3.95880	−0.141386
$785$	6.50816	0.232286
$786$	−8.36089	−0.298223
$787$	−53.6125	−1.91108	−0.955540	−	0.294863i	$-0.904726\pi$
$787$	−53.6125	−1.91108	−0.955540	+	0.294863i	$0.904726\pi$
$788$	−14.1326	−0.503454
$789$	−2.46976	−0.0879259
$790$	37.9499	1.35020
$791$	15.4987	0.551072
$792$	8.51477	0.302559
$793$	−0.879847	−0.0312443
$794$	3.91329	0.138877
$795$	16.2991	0.578069
$796$	23.3606	0.827994
$797$	43.7363	1.54922	0.774610	−	0.632439i	$-0.217946\pi$
$797$	43.7363	1.54922	0.774610	+	0.632439i	$0.217946\pi$
$798$	0.847131	0.0299881
$799$	−47.6202	−1.68468
$800$	3.28080	0.115994
$801$	−3.23487	−0.114299
$802$	−39.5658	−1.39712
$803$	−6.75779	−0.238477
$804$	2.07542	0.0731945
$805$	40.5141	1.42793
$806$	0.215075	0.00757569
$807$	7.45412	0.262397
$808$	17.7125	0.623122
$809$	34.7768	1.22269	0.611343	−	0.791366i	$-0.290630\pi$
$809$	34.7768	1.22269	0.611343	+	0.791366i	$0.290630\pi$
$810$	−20.8740	−0.733437
$811$	10.0424	0.352638	0.176319	−	0.984333i	$-0.443581\pi$
$811$	10.0424	0.352638	0.176319	+	0.984333i	$0.443581\pi$
$812$	2.43191	0.0853432
$813$	0.374797	0.0131447
$814$	−26.7796	−0.938623
$815$	23.9783	0.839922
$816$	3.35341	0.117393
$817$	−12.6974	−0.444227
$818$	4.25369	0.148727
$819$	−0.358953	−0.0125428
$820$	9.88977	0.345366
$821$	16.0968	0.561783	0.280891	−	0.959740i	$-0.409370\pi$
$821$	16.0968	0.561783	0.280891	+	0.959740i	$0.409370\pi$
$822$	7.62871	0.266082
$823$	37.4330	1.30483	0.652416	−	0.757861i	$-0.273756\pi$
$823$	37.4330	1.30483	0.652416	+	0.757861i	$0.273756\pi$
$824$	5.37048	0.187090
$825$	4.44123	0.154624
$826$	−6.67640	−0.232302
$827$	−50.5805	−1.75886	−0.879428	−	0.476032i	$-0.842075\pi$
$827$	−50.5805	−1.75886	−0.879428	+	0.476032i	$0.842075\pi$
$828$	−22.6180	−0.786031
$829$	20.2840	0.704494	0.352247	−	0.935907i	$-0.385418\pi$
$829$	20.2840	0.704494	0.352247	+	0.935907i	$0.385418\pi$
$830$	−4.38536	−0.152218
$831$	−6.90626	−0.239576
$832$	−0.0734694	−0.00254709
$833$	29.8052	1.03269
$834$	−1.32891	−0.0460162
$835$	38.5989	1.33577
$836$	−3.31462	−0.114639
$837$	−7.56468	−0.261473
$838$	−10.0892	−0.348526
$839$	0.241108	0.00832397	0.00416199	−	0.999991i	$-0.498675\pi$
$839$	0.241108	0.00832397	0.00416199	+	0.999991i	$0.498675\pi$
$840$	−2.23520	−0.0771219
$841$	−27.0553	−0.932942
$842$	−24.1453	−0.832103
$843$	−5.88303	−0.202622
$844$	15.4539	0.531944
$845$	37.3938	1.28638
$846$	−17.7203	−0.609236
$847$	3.07455	0.105643
$848$	12.7165	0.436688
$849$	1.13648	0.0390038
$850$	−24.7006	−0.847225
$851$	71.1354	2.43849
$852$	0.861101	0.0295008
$853$	28.5687	0.978173	0.489087	−	0.872235i	$-0.337330\pi$
$853$	28.5687	0.978173	0.489087	+	0.872235i	$0.337330\pi$
$854$	−20.8845	−0.714652
$855$	8.79252	0.300698
$856$	−16.8179	−0.574824
$857$	−9.32971	−0.318697	−0.159348	−	0.987222i	$-0.550939\pi$
$857$	−9.32971	−0.318697	−0.159348	+	0.987222i	$0.550939\pi$
$858$	−0.0994557	−0.00339536
$859$	46.2461	1.57790	0.788948	−	0.614460i	$-0.210626\pi$
$859$	46.2461	1.57790	0.788948	+	0.614460i	$0.210626\pi$
$860$	33.5029	1.14244
$861$	−2.66951	−0.0909766
$862$	37.3793	1.27314
$863$	14.3898	0.489834	0.244917	−	0.969544i	$-0.421239\pi$
$863$	14.3898	0.489834	0.244917	+	0.969544i	$0.421239\pi$
$864$	2.58409	0.0879124
$865$	65.1925	2.21661
$866$	−14.7224	−0.500288
$867$	−17.6754	−0.600288
$868$	5.10512	0.173279
$869$	40.0811	1.35966
$870$	−1.78739	−0.0605981
$871$	0.342337	0.0115997
$872$	18.3277	0.620654
$873$	−30.8931	−1.04557
$874$	8.80474	0.297825
$875$	−8.62751	−0.291663
$876$	−0.990372	−0.0334616
$877$	13.1558	0.444239	0.222119	−	0.975019i	$-0.428703\pi$
$877$	13.1558	0.444239	0.222119	+	0.975019i	$0.428703\pi$
$878$	−4.48637	−0.151407
$879$	13.6842	0.461556
$880$	8.74583	0.294822
$881$	26.2882	0.885673	0.442837	−	0.896602i	$-0.353972\pi$
$881$	26.2882	0.885673	0.442837	+	0.896602i	$0.353972\pi$
$882$	11.0910	0.373454
$883$	42.0671	1.41567	0.707835	−	0.706377i	$-0.249672\pi$
$883$	42.0671	1.41567	0.707835	+	0.706377i	$0.249672\pi$
$884$	0.553140	0.0186041
$885$	4.90698	0.164946
$886$	30.0626	1.00997
$887$	−39.2310	−1.31725	−0.658624	−	0.752472i	$-0.728861\pi$
$887$	−39.2310	−1.31725	−0.658624	+	0.752472i	$0.728861\pi$
$888$	−3.92462	−0.131701
$889$	−9.83156	−0.329740
$890$	−3.32266	−0.111376
$891$	−22.0462	−0.738576
$892$	17.0776	0.571800
$893$	6.89814	0.230838
$894$	6.67131	0.223122
$895$	6.45523	0.215774
$896$	−1.74390	−0.0582598
$897$	0.264187	0.00882096
$898$	12.9647	0.432636
$899$	4.08232	0.136153
$900$	−9.19152	−0.306384
$901$	−95.7410	−3.18959
$902$	10.4452	0.347786
$903$	−9.04331	−0.300943
$904$	−8.88737	−0.295590
$905$	−17.8410	−0.593055
$906$	−3.31880	−0.110260
$907$	6.58166	0.218540	0.109270	−	0.994012i	$-0.465149\pi$
$907$	6.58166	0.218540	0.109270	+	0.994012i	$0.465149\pi$
$908$	−12.2670	−0.407093
$909$	−49.6234	−1.64591
$910$	−0.368693	−0.0122221
$911$	17.8146	0.590223	0.295111	−	0.955463i	$-0.404643\pi$
$911$	17.8146	0.590223	0.295111	+	0.955463i	$0.404643\pi$
$912$	−0.485767	−0.0160853
$913$	−4.63163	−0.153285
$914$	−3.18035	−0.105197
$915$	15.3495	0.507440
$916$	12.9337	0.427341
$917$	−32.7353	−1.08102
$918$	−19.4552	−0.642117
$919$	−6.51062	−0.214766	−0.107383	−	0.994218i	$-0.534247\pi$
$919$	−6.51062	−0.214766	−0.107383	+	0.994218i	$0.534247\pi$
$920$	−23.2318	−0.765930
$921$	−2.32690	−0.0766740
$922$	21.4150	0.705264
$923$	0.142037	0.00467521
$924$	−2.36073	−0.0776623
$925$	28.9080	0.950489
$926$	−5.75274	−0.189047
$927$	−15.0460	−0.494176
$928$	−1.39452	−0.0457773
$929$	−7.90139	−0.259236	−0.129618	−	0.991564i	$-0.541375\pi$
$929$	−7.90139	−0.259236	−0.129618	+	0.991564i	$0.541375\pi$
$930$	−3.75213	−0.123037
$931$	−4.31750	−0.141500
$932$	−13.5169	−0.442760
$933$	1.00368	0.0328591
$934$	3.24870	0.106301
$935$	−65.8460	−2.15340
$936$	0.205833	0.00672785
$937$	19.0194	0.621338	0.310669	−	0.950518i	$-0.399447\pi$
$937$	19.0194	0.621338	0.310669	+	0.950518i	$0.399447\pi$
$938$	8.12588	0.265319
$939$	2.86370	0.0934534
$940$	−18.2012	−0.593656
$941$	1.03386	0.0337029	0.0168514	−	0.999858i	$-0.494636\pi$
$941$	1.03386	0.0337029	0.0168514	+	0.999858i	$0.494636\pi$
$942$	1.00735	0.0328212
$943$	−27.7458	−0.903527
$944$	3.82842	0.124604
$945$	12.9678	0.421842
$946$	35.3843	1.15044
$947$	27.2528	0.885598	0.442799	−	0.896621i	$-0.353985\pi$
$947$	27.2528	0.885598	0.442799	+	0.896621i	$0.353985\pi$
$948$	5.87399	0.190778
$949$	−0.163360	−0.00530290
$950$	3.57807	0.116088
$951$	1.82642	0.0592256
$952$	13.1296	0.425533
$953$	−40.6587	−1.31707	−0.658533	−	0.752552i	$-0.728823\pi$
$953$	−40.6587	−1.31707	−0.658533	+	0.752552i	$0.728823\pi$
$954$	−35.6268	−1.15346
$955$	−39.1032	−1.26535
$956$	−3.47884	−0.112514
$957$	−1.88776	−0.0610227
$958$	9.39599	0.303571
$959$	29.8686	0.964509
$960$	1.28172	0.0413675
$961$	−22.4303	−0.723557
$962$	−0.647359	−0.0208717
$963$	47.1172	1.51833
$964$	17.9255	0.577340
$965$	−34.7994	−1.12023
$966$	6.27088	0.201762
$967$	16.2661	0.523081	0.261540	−	0.965193i	$-0.415770\pi$
$967$	16.2661	0.523081	0.261540	+	0.965193i	$0.415770\pi$
$968$	−1.76303	−0.0566659
$969$	3.65727	0.117488
$970$	−31.7315	−1.01884
$971$	31.4622	1.00967	0.504835	−	0.863216i	$-0.331553\pi$
$971$	31.4622	1.00967	0.504835	+	0.863216i	$0.331553\pi$
$972$	−10.9832	−0.352286
$973$	−5.20305	−0.166802
$974$	−20.6028	−0.660157
$975$	0.107360	0.00343829
$976$	11.9757	0.383332
$977$	−20.5802	−0.658419	−0.329210	−	0.944257i	$-0.606782\pi$
$977$	−20.5802	−0.658419	−0.329210	+	0.944257i	$0.606782\pi$
$978$	3.71142	0.118678
$979$	−3.50925	−0.112156
$980$	11.3920	0.363904
$981$	−51.3471	−1.63939
$982$	−17.2024	−0.548952
$983$	19.8675	0.633674	0.316837	−	0.948480i	$-0.397379\pi$
$983$	19.8675	0.633674	0.316837	+	0.948480i	$0.397379\pi$
$984$	1.53076	0.0487990
$985$	40.6686	1.29581
$986$	10.4991	0.334360
$987$	4.91297	0.156382
$988$	−0.0801264	−0.00254916
$989$	−93.9925	−2.98879
$990$	−24.5024	−0.778738
$991$	2.89041	0.0918169	0.0459084	−	0.998946i	$-0.485382\pi$
$991$	2.89041	0.0918169	0.0459084	+	0.998946i	$0.485382\pi$
$992$	−2.92741	−0.0929453
$993$	−8.22822	−0.261115
$994$	3.37146	0.106936
$995$	−67.2233	−2.13112
$996$	−0.678778	−0.0215079
$997$	42.7066	1.35253	0.676267	−	0.736657i	$-0.263597\pi$
$997$	42.7066	1.35253	0.676267	+	0.736657i	$0.263597\pi$
$998$	11.2045	0.354671
$999$	22.7691	0.720382

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4022.2.a.f.1.18	✓	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4022.2.a.f.1.18	✓	50	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:	\( N \)	\(=\)	\( 4022 = 2 \cdot 2011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4022.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.445408 q^{3} +1.00000 q^{4} -2.87764 q^{5} -0.445408 q^{6} -1.74390 q^{7} +1.00000 q^{8} -2.80161 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.445408 q^{3} +1.00000 q^{4} -2.87764 q^{5} -0.445408 q^{6} -1.74390 q^{7} +1.00000 q^{8} -2.80161 q^{9} -2.87764 q^{10} -3.03924 q^{11} -0.445408 q^{12} -0.0734694 q^{13} -1.74390 q^{14} +1.28172 q^{15} +1.00000 q^{16} -7.52885 q^{17} -2.80161 q^{18} +1.09061 q^{19} -2.87764 q^{20} +0.776750 q^{21} -3.03924 q^{22} +8.07322 q^{23} -0.445408 q^{24} +3.28080 q^{25} -0.0734694 q^{26} +2.58409 q^{27} -1.74390 q^{28} -1.39452 q^{29} +1.28172 q^{30} -2.92741 q^{31} +1.00000 q^{32} +1.35370 q^{33} -7.52885 q^{34} +5.01833 q^{35} -2.80161 q^{36} +8.81127 q^{37} +1.09061 q^{38} +0.0327239 q^{39} -2.87764 q^{40} -3.43677 q^{41} +0.776750 q^{42} -11.6425 q^{43} -3.03924 q^{44} +8.06202 q^{45} +8.07322 q^{46} +6.32504 q^{47} -0.445408 q^{48} -3.95880 q^{49} +3.28080 q^{50} +3.35341 q^{51} -0.0734694 q^{52} +12.7165 q^{53} +2.58409 q^{54} +8.74583 q^{55} -1.74390 q^{56} -0.485767 q^{57} -1.39452 q^{58} +3.82842 q^{59} +1.28172 q^{60} +11.9757 q^{61} -2.92741 q^{62} +4.88574 q^{63} +1.00000 q^{64} +0.211418 q^{65} +1.35370 q^{66} -4.65959 q^{67} -7.52885 q^{68} -3.59588 q^{69} +5.01833 q^{70} -1.93328 q^{71} -2.80161 q^{72} +2.22351 q^{73} +8.81127 q^{74} -1.46130 q^{75} +1.09061 q^{76} +5.30014 q^{77} +0.0327239 q^{78} -13.1879 q^{79} -2.87764 q^{80} +7.25386 q^{81} -3.43677 q^{82} +1.52394 q^{83} +0.776750 q^{84} +21.6653 q^{85} -11.6425 q^{86} +0.621130 q^{87} -3.03924 q^{88} +1.15465 q^{89} +8.06202 q^{90} +0.128124 q^{91} +8.07322 q^{92} +1.30389 q^{93} +6.32504 q^{94} -3.13838 q^{95} -0.445408 q^{96} +11.0269 q^{97} -3.95880 q^{98} +8.51477 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q + 50 q^{2} + 18 q^{3} + 50 q^{4} + 11 q^{5} + 18 q^{6} + 30 q^{7} + 50 q^{8} + 66 q^{9}+O(q^{10}) \) 50 * q + 50 * q^2 + 18 * q^3 + 50 * q^4 + 11 * q^5 + 18 * q^6 + 30 * q^7 + 50 * q^8 + 66 * q^9	\( 50 q + 50 q^{2} + 18 q^{3} + 50 q^{4} + 11 q^{5} + 18 q^{6} + 30 q^{7} + 50 q^{8} + 66 q^{9} + 11 q^{10} + 21 q^{11} + 18 q^{12} + 26 q^{13} + 30 q^{14} + 17 q^{15} + 50 q^{16} + 24 q^{17} + 66 q^{18} + 39 q^{19} + 11 q^{20} - q^{21} + 21 q^{22} + 28 q^{23} + 18 q^{24} + 79 q^{25} + 26 q^{26} + 66 q^{27} + 30 q^{28} - 5 q^{29} + 17 q^{30} + 60 q^{31} + 50 q^{32} + 37 q^{33} + 24 q^{34} + 38 q^{35} + 66 q^{36} + 35 q^{37} + 39 q^{38} + 37 q^{39} + 11 q^{40} + 42 q^{41} - q^{42} + 44 q^{43} + 21 q^{44} + 31 q^{45} + 28 q^{46} + 60 q^{47} + 18 q^{48} + 92 q^{49} + 79 q^{50} + 26 q^{51} + 26 q^{52} - 2 q^{53} + 66 q^{54} + 33 q^{55} + 30 q^{56} + 15 q^{57} - 5 q^{58} + 65 q^{59} + 17 q^{60} + 15 q^{61} + 60 q^{62} + 56 q^{63} + 50 q^{64} + 6 q^{65} + 37 q^{66} + 48 q^{67} + 24 q^{68} - 9 q^{69} + 38 q^{70} + 34 q^{71} + 66 q^{72} + 91 q^{73} + 35 q^{74} + 54 q^{75} + 39 q^{76} - 6 q^{77} + 37 q^{78} + 29 q^{79} + 11 q^{80} + 66 q^{81} + 42 q^{82} + 43 q^{83} - q^{84} + 44 q^{86} + 32 q^{87} + 21 q^{88} + 38 q^{89} + 31 q^{90} + 55 q^{91} + 28 q^{92} - 15 q^{93} + 60 q^{94} + 9 q^{95} + 18 q^{96} + 80 q^{97} + 92 q^{98} + 20 q^{99}+O(q^{100}) \) 50 * q + 50 * q^2 + 18 * q^3 + 50 * q^4 + 11 * q^5 + 18 * q^6 + 30 * q^7 + 50 * q^8 + 66 * q^9 + 11 * q^10 + 21 * q^11 + 18 * q^12 + 26 * q^13 + 30 * q^14 + 17 * q^15 + 50 * q^16 + 24 * q^17 + 66 * q^18 + 39 * q^19 + 11 * q^20 - q^21 + 21 * q^22 + 28 * q^23 + 18 * q^24 + 79 * q^25 + 26 * q^26 + 66 * q^27 + 30 * q^28 - 5 * q^29 + 17 * q^30 + 60 * q^31 + 50 * q^32 + 37 * q^33 + 24 * q^34 + 38 * q^35 + 66 * q^36 + 35 * q^37 + 39 * q^38 + 37 * q^39 + 11 * q^40 + 42 * q^41 - q^42 + 44 * q^43 + 21 * q^44 + 31 * q^45 + 28 * q^46 + 60 * q^47 + 18 * q^48 + 92 * q^49 + 79 * q^50 + 26 * q^51 + 26 * q^52 - 2 * q^53 + 66 * q^54 + 33 * q^55 + 30 * q^56 + 15 * q^57 - 5 * q^58 + 65 * q^59 + 17 * q^60 + 15 * q^61 + 60 * q^62 + 56 * q^63 + 50 * q^64 + 6 * q^65 + 37 * q^66 + 48 * q^67 + 24 * q^68 - 9 * q^69 + 38 * q^70 + 34 * q^71 + 66 * q^72 + 91 * q^73 + 35 * q^74 + 54 * q^75 + 39 * q^76 - 6 * q^77 + 37 * q^78 + 29 * q^79 + 11 * q^80 + 66 * q^81 + 42 * q^82 + 43 * q^83 - q^84 + 44 * q^86 + 32 * q^87 + 21 * q^88 + 38 * q^89 + 31 * q^90 + 55 * q^91 + 28 * q^92 - 15 * q^93 + 60 * q^94 + 9 * q^95 + 18 * q^96 + 80 * q^97 + 92 * q^98 + 20 * q^99

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