LMFDB - Embedded newform 6018.2.a.o.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6018,2,Mod(1,6018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6018, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("6018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6018 = 2 \cdot 3 \cdot 17 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6018.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:	$48.0539719364$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.725.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 3x^{2} + x + 1 $ x^4 - x^3 - 3*x^2 + x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-0.477260$ of defining polynomial
Character	$\chi$	$=$	6018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.140774 q^{5} +1.00000 q^{6} -1.43574 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.140774 q^{5} +1.00000 q^{6} -1.43574 q^{7} +1.00000 q^{8} +1.00000 q^{9} +0.140774 q^{10} -1.70504 q^{11} +1.00000 q^{12} -5.85410 q^{13} -1.43574 q^{14} +0.140774 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} +1.78051 q^{19} +0.140774 q^{20} -1.43574 q^{21} -1.70504 q^{22} -0.440861 q^{23} +1.00000 q^{24} -4.98018 q^{25} -5.85410 q^{26} +1.00000 q^{27} -1.43574 q^{28} +5.52463 q^{29} +0.140774 q^{30} -9.59426 q^{31} +1.00000 q^{32} -1.70504 q^{33} +1.00000 q^{34} -0.202114 q^{35} +1.00000 q^{36} +6.81296 q^{37} +1.78051 q^{38} -5.85410 q^{39} +0.140774 q^{40} -3.27759 q^{41} -1.43574 q^{42} -3.73315 q^{43} -1.70504 q^{44} +0.140774 q^{45} -0.440861 q^{46} -1.32307 q^{47} +1.00000 q^{48} -4.93866 q^{49} -4.98018 q^{50} +1.00000 q^{51} -5.85410 q^{52} -6.32741 q^{53} +1.00000 q^{54} -0.240025 q^{55} -1.43574 q^{56} +1.78051 q^{57} +5.52463 q^{58} +1.00000 q^{59} +0.140774 q^{60} -2.22137 q^{61} -9.59426 q^{62} -1.43574 q^{63} +1.00000 q^{64} -0.824105 q^{65} -1.70504 q^{66} -8.22967 q^{67} +1.00000 q^{68} -0.440861 q^{69} -0.202114 q^{70} -0.429334 q^{71} +1.00000 q^{72} -1.75052 q^{73} +6.81296 q^{74} -4.98018 q^{75} +1.78051 q^{76} +2.44798 q^{77} -5.85410 q^{78} -0.426656 q^{79} +0.140774 q^{80} +1.00000 q^{81} -3.27759 q^{82} +7.32473 q^{83} -1.43574 q^{84} +0.140774 q^{85} -3.73315 q^{86} +5.52463 q^{87} -1.70504 q^{88} +4.66913 q^{89} +0.140774 q^{90} +8.40495 q^{91} -0.440861 q^{92} -9.59426 q^{93} -1.32307 q^{94} +0.250650 q^{95} +1.00000 q^{96} -19.0720 q^{97} -4.93866 q^{98} -1.70504 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} - q^{5} + 4 q^{6} - q^{7} + 4 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 - q^5 + 4 * q^6 - q^7 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} - q^{5} + 4 q^{6} - q^{7} + 4 q^{8} + 4 q^{9} - q^{10} - 10 q^{11} + 4 q^{12} - 10 q^{13} - q^{14} - q^{15} + 4 q^{16} + 4 q^{17} + 4 q^{18} - 14 q^{19} - q^{20} - q^{21} - 10 q^{22} - 12 q^{23} + 4 q^{24} - 3 q^{25} - 10 q^{26} + 4 q^{27} - q^{28} - 7 q^{29} - q^{30} - 13 q^{31} + 4 q^{32} - 10 q^{33} + 4 q^{34} - 18 q^{35} + 4 q^{36} - 11 q^{37} - 14 q^{38} - 10 q^{39} - q^{40} - 6 q^{41} - q^{42} - 20 q^{43} - 10 q^{44} - q^{45} - 12 q^{46} - 4 q^{47} + 4 q^{48} - q^{49} - 3 q^{50} + 4 q^{51} - 10 q^{52} - 5 q^{53} + 4 q^{54} + 4 q^{55} - q^{56} - 14 q^{57} - 7 q^{58} + 4 q^{59} - q^{60} + 2 q^{61} - 13 q^{62} - q^{63} + 4 q^{64} - 20 q^{65} - 10 q^{66} - 7 q^{67} + 4 q^{68} - 12 q^{69} - 18 q^{70} + 20 q^{71} + 4 q^{72} - 16 q^{73} - 11 q^{74} - 3 q^{75} - 14 q^{76} - 6 q^{77} - 10 q^{78} + 22 q^{79} - q^{80} + 4 q^{81} - 6 q^{82} + 7 q^{83} - q^{84} - q^{85} - 20 q^{86} - 7 q^{87} - 10 q^{88} + 3 q^{89} - q^{90} + 25 q^{91} - 12 q^{92} - 13 q^{93} - 4 q^{94} + 3 q^{95} + 4 q^{96} - 16 q^{97} - q^{98} - 10 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 - q^5 + 4 * q^6 - q^7 + 4 * q^8 + 4 * q^9 - q^10 - 10 * q^11 + 4 * q^12 - 10 * q^13 - q^14 - q^15 + 4 * q^16 + 4 * q^17 + 4 * q^18 - 14 * q^19 - q^20 - q^21 - 10 * q^22 - 12 * q^23 + 4 * q^24 - 3 * q^25 - 10 * q^26 + 4 * q^27 - q^28 - 7 * q^29 - q^30 - 13 * q^31 + 4 * q^32 - 10 * q^33 + 4 * q^34 - 18 * q^35 + 4 * q^36 - 11 * q^37 - 14 * q^38 - 10 * q^39 - q^40 - 6 * q^41 - q^42 - 20 * q^43 - 10 * q^44 - q^45 - 12 * q^46 - 4 * q^47 + 4 * q^48 - q^49 - 3 * q^50 + 4 * q^51 - 10 * q^52 - 5 * q^53 + 4 * q^54 + 4 * q^55 - q^56 - 14 * q^57 - 7 * q^58 + 4 * q^59 - q^60 + 2 * q^61 - 13 * q^62 - q^63 + 4 * q^64 - 20 * q^65 - 10 * q^66 - 7 * q^67 + 4 * q^68 - 12 * q^69 - 18 * q^70 + 20 * q^71 + 4 * q^72 - 16 * q^73 - 11 * q^74 - 3 * q^75 - 14 * q^76 - 6 * q^77 - 10 * q^78 + 22 * q^79 - q^80 + 4 * q^81 - 6 * q^82 + 7 * q^83 - q^84 - q^85 - 20 * q^86 - 7 * q^87 - 10 * q^88 + 3 * q^89 - q^90 + 25 * q^91 - 12 * q^92 - 13 * q^93 - 4 * q^94 + 3 * q^95 + 4 * q^96 - 16 * q^97 - q^98 - 10 * 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
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	0.140774	0.0629560	0.0314780	−	0.999504i	$-0.489979\pi$
$5$	0.140774	0.0629560	0.0314780	+	0.999504i	$0.489979\pi$
$6$	1.00000	0.408248
$7$	−1.43574	−0.542658	−0.271329	−	0.962487i	$-0.587463\pi$
$7$	−1.43574	−0.542658	−0.271329	+	0.962487i	$0.587463\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	0.140774	0.0445166
$11$	−1.70504	−0.514088	−0.257044	−	0.966400i	$-0.582749\pi$
$11$	−1.70504	−0.514088	−0.257044	+	0.966400i	$0.582749\pi$
$12$	1.00000	0.288675
$13$	−5.85410	−1.62364	−0.811818	−	0.583911i	$-0.801522\pi$
$13$	−5.85410	−1.62364	−0.811818	+	0.583911i	$0.801522\pi$
$14$	−1.43574	−0.383717
$15$	0.140774	0.0363477
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	1.00000	0.235702
$19$	1.78051	0.408478	0.204239	−	0.978921i	$-0.434528\pi$
$19$	1.78051	0.408478	0.204239	+	0.978921i	$0.434528\pi$
$20$	0.140774	0.0314780
$21$	−1.43574	−0.313303
$22$	−1.70504	−0.363515
$23$	−0.440861	−0.0919259	−0.0459629	−	0.998943i	$-0.514636\pi$
$23$	−0.440861	−0.0919259	−0.0459629	+	0.998943i	$0.514636\pi$
$24$	1.00000	0.204124
$25$	−4.98018	−0.996037
$26$	−5.85410	−1.14808
$27$	1.00000	0.192450
$28$	−1.43574	−0.271329
$29$	5.52463	1.02590	0.512949	−	0.858419i	$-0.328553\pi$
$29$	5.52463	1.02590	0.512949	+	0.858419i	$0.328553\pi$
$30$	0.140774	0.0257017
$31$	−9.59426	−1.72318	−0.861590	−	0.507605i	$-0.830531\pi$
$31$	−9.59426	−1.72318	−0.861590	+	0.507605i	$0.830531\pi$
$32$	1.00000	0.176777
$33$	−1.70504	−0.296809
$34$	1.00000	0.171499
$35$	−0.202114	−0.0341636
$36$	1.00000	0.166667
$37$	6.81296	1.12004	0.560022	−	0.828478i	$-0.310793\pi$
$37$	6.81296	1.12004	0.560022	+	0.828478i	$0.310793\pi$
$38$	1.78051	0.288837
$39$	−5.85410	−0.937407
$40$	0.140774	0.0222583
$41$	−3.27759	−0.511874	−0.255937	−	0.966693i	$-0.582384\pi$
$41$	−3.27759	−0.511874	−0.255937	+	0.966693i	$0.582384\pi$
$42$	−1.43574	−0.221539
$43$	−3.73315	−0.569299	−0.284650	−	0.958632i	$-0.591877\pi$
$43$	−3.73315	−0.569299	−0.284650	+	0.958632i	$0.591877\pi$
$44$	−1.70504	−0.257044
$45$	0.140774	0.0209853
$46$	−0.440861	−0.0650014
$47$	−1.32307	−0.192990	−0.0964949	−	0.995333i	$-0.530763\pi$
$47$	−1.32307	−0.192990	−0.0964949	+	0.995333i	$0.530763\pi$
$48$	1.00000	0.144338
$49$	−4.93866	−0.705523
$50$	−4.98018	−0.704304
$51$	1.00000	0.140028
$52$	−5.85410	−0.811818
$53$	−6.32741	−0.869136	−0.434568	−	0.900639i	$-0.643099\pi$
$53$	−6.32741	−0.869136	−0.434568	+	0.900639i	$0.643099\pi$
$54$	1.00000	0.136083
$55$	−0.240025	−0.0323649
$56$	−1.43574	−0.191858
$57$	1.78051	0.235835
$58$	5.52463	0.725419
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	0.140774	0.0181738
$61$	−2.22137	−0.284418	−0.142209	−	0.989837i	$-0.545420\pi$
$61$	−2.22137	−0.284418	−0.142209	+	0.989837i	$0.545420\pi$
$62$	−9.59426	−1.21847
$63$	−1.43574	−0.180886
$64$	1.00000	0.125000
$65$	−0.824105	−0.102218
$66$	−1.70504	−0.209876
$67$	−8.22967	−1.00541	−0.502707	−	0.864457i	$-0.667662\pi$
$67$	−8.22967	−1.00541	−0.502707	+	0.864457i	$0.667662\pi$
$68$	1.00000	0.121268
$69$	−0.440861	−0.0530734
$70$	−0.202114	−0.0241573
$71$	−0.429334	−0.0509526	−0.0254763	−	0.999675i	$-0.508110\pi$
$71$	−0.429334	−0.0509526	−0.0254763	+	0.999675i	$0.508110\pi$
$72$	1.00000	0.117851
$73$	−1.75052	−0.204883	−0.102441	−	0.994739i	$-0.532665\pi$
$73$	−1.75052	−0.204883	−0.102441	+	0.994739i	$0.532665\pi$
$74$	6.81296	0.791990
$75$	−4.98018	−0.575062
$76$	1.78051	0.204239
$77$	2.44798	0.278974
$78$	−5.85410	−0.662847
$79$	−0.426656	−0.0480025	−0.0240013	−	0.999712i	$-0.507641\pi$
$79$	−0.426656	−0.0480025	−0.0240013	+	0.999712i	$0.507641\pi$
$80$	0.140774	0.0157390
$81$	1.00000	0.111111
$82$	−3.27759	−0.361949
$83$	7.32473	0.803993	0.401997	−	0.915641i	$-0.368316\pi$
$83$	7.32473	0.803993	0.401997	+	0.915641i	$0.368316\pi$
$84$	−1.43574	−0.156652
$85$	0.140774	0.0152691
$86$	−3.73315	−0.402555
$87$	5.52463	0.592302
$88$	−1.70504	−0.181758
$89$	4.66913	0.494926	0.247463	−	0.968897i	$-0.420403\pi$
$89$	4.66913	0.494926	0.247463	+	0.968897i	$0.420403\pi$
$90$	0.140774	0.0148389
$91$	8.40495	0.881078
$92$	−0.440861	−0.0459629
$93$	−9.59426	−0.994878
$94$	−1.32307	−0.136464
$95$	0.250650	0.0257162
$96$	1.00000	0.102062
$97$	−19.0720	−1.93647	−0.968235	−	0.250044i	$-0.919555\pi$
$97$	−19.0720	−1.93647	−0.968235	+	0.250044i	$0.919555\pi$
$98$	−4.93866	−0.498880
$99$	−1.70504	−0.171363
$100$	−4.98018	−0.498018
$101$	−6.22650	−0.619560	−0.309780	−	0.950808i	$-0.600255\pi$
$101$	−6.22650	−0.619560	−0.309780	+	0.950808i	$0.600255\pi$
$102$	1.00000	0.0990148
$103$	8.28856	0.816696	0.408348	−	0.912826i	$-0.366105\pi$
$103$	8.28856	0.816696	0.408348	+	0.912826i	$0.366105\pi$
$104$	−5.85410	−0.574042
$105$	−0.202114	−0.0197243
$106$	−6.32741	−0.614572
$107$	−5.76197	−0.557031	−0.278516	−	0.960432i	$-0.589842\pi$
$107$	−5.76197	−0.557031	−0.278516	+	0.960432i	$0.589842\pi$
$108$	1.00000	0.0962250
$109$	−11.6078	−1.11182	−0.555912	−	0.831241i	$-0.687631\pi$
$109$	−11.6078	−1.11182	−0.555912	+	0.831241i	$0.687631\pi$
$110$	−0.240025	−0.0228855
$111$	6.81296	0.646657
$112$	−1.43574	−0.135664
$113$	−17.8188	−1.67625	−0.838126	−	0.545477i	$-0.816349\pi$
$113$	−17.8188	−1.67625	−0.838126	+	0.545477i	$0.816349\pi$
$114$	1.78051	0.166760
$115$	−0.0620618	−0.00578729
$116$	5.52463	0.512949
$117$	−5.85410	−0.541212
$118$	1.00000	0.0920575
$119$	−1.43574	−0.131614
$120$	0.140774	0.0128508
$121$	−8.09285	−0.735713
$122$	−2.22137	−0.201114
$123$	−3.27759	−0.295530
$124$	−9.59426	−0.861590
$125$	−1.40495	−0.125663
$126$	−1.43574	−0.127906
$127$	12.1485	1.07801	0.539003	−	0.842304i	$-0.318801\pi$
$127$	12.1485	1.07801	0.539003	+	0.842304i	$0.318801\pi$
$128$	1.00000	0.0883883
$129$	−3.73315	−0.328685
$130$	−0.824105	−0.0722788
$131$	−11.6441	−1.01735	−0.508674	−	0.860959i	$-0.669864\pi$
$131$	−11.6441	−1.01735	−0.508674	+	0.860959i	$0.669864\pi$
$132$	−1.70504	−0.148404
$133$	−2.55635	−0.221664
$134$	−8.22967	−0.710935
$135$	0.140774	0.0121159
$136$	1.00000	0.0857493
$137$	8.99164	0.768208	0.384104	−	0.923290i	$-0.374510\pi$
$137$	8.99164	0.768208	0.384104	+	0.923290i	$0.374510\pi$
$138$	−0.440861	−0.0375286
$139$	18.1296	1.53773	0.768867	−	0.639408i	$-0.220821\pi$
$139$	18.1296	1.53773	0.768867	+	0.639408i	$0.220821\pi$
$140$	−0.202114	−0.0170818
$141$	−1.32307	−0.111423
$142$	−0.429334	−0.0360289
$143$	9.98146	0.834692
$144$	1.00000	0.0833333
$145$	0.777724	0.0645865
$146$	−1.75052	−0.144874
$147$	−4.93866	−0.407334
$148$	6.81296	0.560022
$149$	5.21753	0.427437	0.213718	−	0.976895i	$-0.431443\pi$
$149$	5.21753	0.427437	0.213718	+	0.976895i	$0.431443\pi$
$150$	−4.98018	−0.406630
$151$	−11.0505	−0.899280	−0.449640	−	0.893210i	$-0.648448\pi$
$151$	−11.0505	−0.899280	−0.449640	+	0.893210i	$0.648448\pi$
$152$	1.78051	0.144419
$153$	1.00000	0.0808452
$154$	2.44798	0.197264
$155$	−1.35062	−0.108485
$156$	−5.85410	−0.468703
$157$	5.93636	0.473773	0.236886	−	0.971537i	$-0.423873\pi$
$157$	5.93636	0.473773	0.236886	+	0.971537i	$0.423873\pi$
$158$	−0.426656	−0.0339429
$159$	−6.32741	−0.501796
$160$	0.140774	0.0111292
$161$	0.632960	0.0498843
$162$	1.00000	0.0785674
$163$	−22.7905	−1.78509	−0.892543	−	0.450962i	$-0.851081\pi$
$163$	−22.7905	−1.78509	−0.892543	+	0.450962i	$0.851081\pi$
$164$	−3.27759	−0.255937
$165$	−0.240025	−0.0186859
$166$	7.32473	0.568509
$167$	−14.5110	−1.12289	−0.561447	−	0.827513i	$-0.689755\pi$
$167$	−14.5110	−1.12289	−0.561447	+	0.827513i	$0.689755\pi$
$168$	−1.43574	−0.110770
$169$	21.2705	1.63619
$170$	0.140774	0.0107969
$171$	1.78051	0.136159
$172$	−3.73315	−0.284650
$173$	6.90787	0.525196	0.262598	−	0.964905i	$-0.415421\pi$
$173$	6.90787	0.525196	0.262598	+	0.964905i	$0.415421\pi$
$174$	5.52463	0.418821
$175$	7.15023	0.540507
$176$	−1.70504	−0.128522
$177$	1.00000	0.0751646
$178$	4.66913	0.349966
$179$	10.4970	0.784583	0.392292	−	0.919841i	$-0.371682\pi$
$179$	10.4970	0.784583	0.392292	+	0.919841i	$0.371682\pi$
$180$	0.140774	0.0104927
$181$	−0.314780	−0.0233974	−0.0116987	−	0.999932i	$-0.503724\pi$
$181$	−0.314780	−0.0233974	−0.0116987	+	0.999932i	$0.503724\pi$
$182$	8.40495	0.623016
$183$	−2.22137	−0.164209
$184$	−0.440861	−0.0325007
$185$	0.959087	0.0705135
$186$	−9.59426	−0.703485
$187$	−1.70504	−0.124685
$188$	−1.32307	−0.0964949
$189$	−1.43574	−0.104434
$190$	0.250650	0.0181841
$191$	−20.2517	−1.46537	−0.732683	−	0.680571i	$-0.761732\pi$
$191$	−20.2517	−1.46537	−0.732683	+	0.680571i	$0.761732\pi$
$192$	1.00000	0.0721688
$193$	4.81186	0.346365	0.173183	−	0.984890i	$-0.444595\pi$
$193$	4.81186	0.346365	0.173183	+	0.984890i	$0.444595\pi$
$194$	−19.0720	−1.36929
$195$	−0.824105	−0.0590154
$196$	−4.93866	−0.352761
$197$	13.0292	0.928293	0.464146	−	0.885759i	$-0.346361\pi$
$197$	13.0292	0.928293	0.464146	+	0.885759i	$0.346361\pi$
$198$	−1.70504	−0.121172
$199$	5.09096	0.360889	0.180444	−	0.983585i	$-0.442246\pi$
$199$	5.09096	0.360889	0.180444	+	0.983585i	$0.442246\pi$
$200$	−4.98018	−0.352152
$201$	−8.22967	−0.580476
$202$	−6.22650	−0.438095
$203$	−7.93191	−0.556711
$204$	1.00000	0.0700140
$205$	−0.461400	−0.0322255
$206$	8.28856	0.577491
$207$	−0.440861	−0.0306420
$208$	−5.85410	−0.405909
$209$	−3.03584	−0.209994
$210$	−0.202114	−0.0139472
$211$	11.6386	0.801232	0.400616	−	0.916246i	$-0.368796\pi$
$211$	11.6386	0.801232	0.400616	+	0.916246i	$0.368796\pi$
$212$	−6.32741	−0.434568
$213$	−0.429334	−0.0294175
$214$	−5.76197	−0.393880
$215$	−0.525530	−0.0358408
$216$	1.00000	0.0680414
$217$	13.7748	0.935097
$218$	−11.6078	−0.786178
$219$	−1.75052	−0.118289
$220$	−0.240025	−0.0161825
$221$	−5.85410	−0.393790
$222$	6.81296	0.457256
$223$	−17.8294	−1.19394	−0.596972	−	0.802262i	$-0.703630\pi$
$223$	−17.8294	−1.19394	−0.596972	+	0.802262i	$0.703630\pi$
$224$	−1.43574	−0.0959292
$225$	−4.98018	−0.332012
$226$	−17.8188	−1.18529
$227$	9.37440	0.622201	0.311100	−	0.950377i	$-0.399302\pi$
$227$	9.37440	0.622201	0.311100	+	0.950377i	$0.399302\pi$
$228$	1.78051	0.117917
$229$	19.3027	1.27556	0.637779	−	0.770219i	$-0.279853\pi$
$229$	19.3027	1.27556	0.637779	+	0.770219i	$0.279853\pi$
$230$	−0.0620618	−0.00409223
$231$	2.44798	0.161066
$232$	5.52463	0.362710
$233$	4.83088	0.316482	0.158241	−	0.987401i	$-0.449418\pi$
$233$	4.83088	0.316482	0.158241	+	0.987401i	$0.449418\pi$
$234$	−5.85410	−0.382695
$235$	−0.186254	−0.0121499
$236$	1.00000	0.0650945
$237$	−0.426656	−0.0277143
$238$	−1.43574	−0.0930650
$239$	−16.6341	−1.07597	−0.537984	−	0.842955i	$-0.680814\pi$
$239$	−16.6341	−1.07597	−0.537984	+	0.842955i	$0.680814\pi$
$240$	0.140774	0.00908692
$241$	6.45800	0.415996	0.207998	−	0.978129i	$-0.433305\pi$
$241$	6.45800	0.415996	0.207998	+	0.978129i	$0.433305\pi$
$242$	−8.09285	−0.520228
$243$	1.00000	0.0641500
$244$	−2.22137	−0.142209
$245$	−0.695235	−0.0444169
$246$	−3.27759	−0.208972
$247$	−10.4233	−0.663219
$248$	−9.59426	−0.609236
$249$	7.32473	0.464186
$250$	−1.40495	−0.0888569
$251$	7.06395	0.445873	0.222936	−	0.974833i	$-0.428436\pi$
$251$	7.06395	0.445873	0.222936	+	0.974833i	$0.428436\pi$
$252$	−1.43574	−0.0904429
$253$	0.751684	0.0472580
$254$	12.1485	0.762265
$255$	0.140774	0.00881561
$256$	1.00000	0.0625000
$257$	−17.3885	−1.08467	−0.542333	−	0.840163i	$-0.682459\pi$
$257$	−17.3885	−1.08467	−0.542333	+	0.840163i	$0.682459\pi$
$258$	−3.73315	−0.232415
$259$	−9.78161	−0.607800
$260$	−0.824105	−0.0511088
$261$	5.52463	0.341966
$262$	−11.6441	−0.719373
$263$	27.0337	1.66697	0.833483	−	0.552545i	$-0.186343\pi$
$263$	27.0337	1.66697	0.833483	+	0.552545i	$0.186343\pi$
$264$	−1.70504	−0.104938
$265$	−0.890734	−0.0547174
$266$	−2.55635	−0.156740
$267$	4.66913	0.285746
$268$	−8.22967	−0.502707
$269$	13.1645	0.802654	0.401327	−	0.915935i	$-0.368549\pi$
$269$	13.1645	0.802654	0.401327	+	0.915935i	$0.368549\pi$
$270$	0.140774	0.00856723
$271$	7.89635	0.479669	0.239834	−	0.970814i	$-0.422907\pi$
$271$	7.89635	0.479669	0.239834	+	0.970814i	$0.422907\pi$
$272$	1.00000	0.0606339
$273$	8.40495	0.508691
$274$	8.99164	0.543205
$275$	8.49140	0.512050
$276$	−0.440861	−0.0265367
$277$	26.5485	1.59514	0.797572	−	0.603224i	$-0.206118\pi$
$277$	26.5485	1.59514	0.797572	+	0.603224i	$0.206118\pi$
$278$	18.1296	1.08734
$279$	−9.59426	−0.574393
$280$	−0.202114	−0.0120786
$281$	−7.09171	−0.423056	−0.211528	−	0.977372i	$-0.567844\pi$
$281$	−7.09171	−0.423056	−0.211528	+	0.977372i	$0.567844\pi$
$282$	−1.32307	−0.0787877
$283$	−11.4136	−0.678469	−0.339235	−	0.940702i	$-0.610168\pi$
$283$	−11.4136	−0.678469	−0.339235	+	0.940702i	$0.610168\pi$
$284$	−0.429334	−0.0254763
$285$	0.250650	0.0148472
$286$	9.98146	0.590216
$287$	4.70576	0.277772
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	0.777724	0.0456695
$291$	−19.0720	−1.11802
$292$	−1.75052	−0.102441
$293$	−8.55646	−0.499874	−0.249937	−	0.968262i	$-0.580410\pi$
$293$	−8.55646	−0.499874	−0.249937	+	0.968262i	$0.580410\pi$
$294$	−4.93866	−0.288028
$295$	0.140774	0.00819618
$296$	6.81296	0.395995
$297$	−1.70504	−0.0989363
$298$	5.21753	0.302243
$299$	2.58084	0.149254
$300$	−4.98018	−0.287531
$301$	5.35981	0.308935
$302$	−11.0505	−0.635887
$303$	−6.22650	−0.357703
$304$	1.78051	0.102119
$305$	−0.312712	−0.0179058
$306$	1.00000	0.0571662
$307$	25.7900	1.47191	0.735956	−	0.677030i	$-0.236733\pi$
$307$	25.7900	1.47191	0.735956	+	0.677030i	$0.236733\pi$
$308$	2.44798	0.139487
$309$	8.28856	0.471520
$310$	−1.35062	−0.0767102
$311$	4.55376	0.258220	0.129110	−	0.991630i	$-0.458788\pi$
$311$	4.55376	0.258220	0.129110	+	0.991630i	$0.458788\pi$
$312$	−5.85410	−0.331423
$313$	0.102451	0.00579085	0.00289542	−	0.999996i	$-0.499078\pi$
$313$	0.102451	0.00579085	0.00289542	+	0.999996i	$0.499078\pi$
$314$	5.93636	0.335008
$315$	−0.202114	−0.0113879
$316$	−0.426656	−0.0240013
$317$	0.807455	0.0453512	0.0226756	−	0.999743i	$-0.492782\pi$
$317$	0.807455	0.0453512	0.0226756	+	0.999743i	$0.492782\pi$
$318$	−6.32741	−0.354823
$319$	−9.41970	−0.527402
$320$	0.140774	0.00786951
$321$	−5.76197	−0.321602
$322$	0.632960	0.0352735
$323$	1.78051	0.0990704
$324$	1.00000	0.0555556
$325$	29.1545	1.61720
$326$	−22.7905	−1.26225
$327$	−11.6078	−0.641912
$328$	−3.27759	−0.180975
$329$	1.89958	0.104727
$330$	−0.240025	−0.0132129
$331$	−9.59950	−0.527636	−0.263818	−	0.964572i	$-0.584982\pi$
$331$	−9.59950	−0.527636	−0.263818	+	0.964572i	$0.584982\pi$
$332$	7.32473	0.401997
$333$	6.81296	0.373348
$334$	−14.5110	−0.794006
$335$	−1.15852	−0.0632969
$336$	−1.43574	−0.0783259
$337$	−18.0633	−0.983973	−0.491986	−	0.870603i	$-0.663729\pi$
$337$	−18.0633	−0.983973	−0.491986	+	0.870603i	$0.663729\pi$
$338$	21.2705	1.15696
$339$	−17.8188	−0.967784
$340$	0.140774	0.00763454
$341$	16.3586	0.885866
$342$	1.78051	0.0962792
$343$	17.1408	0.925515
$344$	−3.73315	−0.201278
$345$	−0.0620618	−0.00334129
$346$	6.90787	0.371370
$347$	1.70693	0.0916326	0.0458163	−	0.998950i	$-0.485411\pi$
$347$	1.70693	0.0916326	0.0458163	+	0.998950i	$0.485411\pi$
$348$	5.52463	0.296151
$349$	−13.0732	−0.699791	−0.349896	−	0.936789i	$-0.613783\pi$
$349$	−13.0732	−0.699791	−0.349896	+	0.936789i	$0.613783\pi$
$350$	7.15023	0.382196
$351$	−5.85410	−0.312469
$352$	−1.70504	−0.0908788
$353$	32.7844	1.74494	0.872468	−	0.488671i	$-0.162518\pi$
$353$	32.7844	1.74494	0.872468	+	0.488671i	$0.162518\pi$
$354$	1.00000	0.0531494
$355$	−0.0604391	−0.00320778
$356$	4.66913	0.247463
$357$	−1.43574	−0.0759873
$358$	10.4970	0.554784
$359$	10.7275	0.566178	0.283089	−	0.959094i	$-0.408641\pi$
$359$	10.7275	0.566178	0.283089	+	0.959094i	$0.408641\pi$
$360$	0.140774	0.00741944
$361$	−15.8298	−0.833146
$362$	−0.314780	−0.0165445
$363$	−8.09285	−0.424764
$364$	8.40495	0.440539
$365$	−0.246427	−0.0128986
$366$	−2.22137	−0.116113
$367$	−5.97981	−0.312143	−0.156072	−	0.987746i	$-0.549883\pi$
$367$	−5.97981	−0.312143	−0.156072	+	0.987746i	$0.549883\pi$
$368$	−0.440861	−0.0229815
$369$	−3.27759	−0.170625
$370$	0.959087	0.0498606
$371$	9.08449	0.471643
$372$	−9.59426	−0.497439
$373$	−24.8232	−1.28530	−0.642649	−	0.766160i	$-0.722165\pi$
$373$	−24.8232	−1.28530	−0.642649	+	0.766160i	$0.722165\pi$
$374$	−1.70504	−0.0881654
$375$	−1.40495	−0.0725513
$376$	−1.32307	−0.0682322
$377$	−32.3417	−1.66568
$378$	−1.43574	−0.0738463
$379$	32.3102	1.65966	0.829832	−	0.558014i	$-0.188436\pi$
$379$	32.3102	1.65966	0.829832	+	0.558014i	$0.188436\pi$
$380$	0.250650	0.0128581
$381$	12.1485	0.622387
$382$	−20.2517	−1.03617
$383$	16.8537	0.861185	0.430593	−	0.902546i	$-0.358305\pi$
$383$	16.8537	0.861185	0.430593	+	0.902546i	$0.358305\pi$
$384$	1.00000	0.0510310
$385$	0.344613	0.0175631
$386$	4.81186	0.244917
$387$	−3.73315	−0.189766
$388$	−19.0720	−0.968235
$389$	−6.97799	−0.353798	−0.176899	−	0.984229i	$-0.556607\pi$
$389$	−6.97799	−0.353798	−0.176899	+	0.984229i	$0.556607\pi$
$390$	−0.824105	−0.0417302
$391$	−0.440861	−0.0222953
$392$	−4.93866	−0.249440
$393$	−11.6441	−0.587366
$394$	13.0292	0.656402
$395$	−0.0600621	−0.00302205
$396$	−1.70504	−0.0856813
$397$	27.1704	1.36364	0.681821	−	0.731519i	$-0.261188\pi$
$397$	27.1704	1.36364	0.681821	+	0.731519i	$0.261188\pi$
$398$	5.09096	0.255187
$399$	−2.55635	−0.127978
$400$	−4.98018	−0.249009
$401$	−31.0620	−1.55116	−0.775581	−	0.631248i	$-0.782543\pi$
$401$	−31.0620	−1.55116	−0.775581	+	0.631248i	$0.782543\pi$
$402$	−8.22967	−0.410458
$403$	56.1658	2.79782
$404$	−6.22650	−0.309780
$405$	0.140774	0.00699512
$406$	−7.93191	−0.393654
$407$	−11.6163	−0.575801
$408$	1.00000	0.0495074
$409$	25.4877	1.26029	0.630144	−	0.776478i	$-0.282996\pi$
$409$	25.4877	1.26029	0.630144	+	0.776478i	$0.282996\pi$
$410$	−0.461400	−0.0227869
$411$	8.99164	0.443525
$412$	8.28856	0.408348
$413$	−1.43574	−0.0706480
$414$	−0.440861	−0.0216671
$415$	1.03113	0.0506162
$416$	−5.85410	−0.287021
$417$	18.1296	0.887812
$418$	−3.03584	−0.148488
$419$	25.0826	1.22536	0.612682	−	0.790330i	$-0.290091\pi$
$419$	25.0826	1.22536	0.612682	+	0.790330i	$0.290091\pi$
$420$	−0.202114	−0.00986217
$421$	−37.2707	−1.81646	−0.908230	−	0.418471i	$-0.862566\pi$
$421$	−37.2707	−1.81646	−0.908230	+	0.418471i	$0.862566\pi$
$422$	11.6386	0.566557
$423$	−1.32307	−0.0643299
$424$	−6.32741	−0.307286
$425$	−4.98018	−0.241574
$426$	−0.429334	−0.0208013
$427$	3.18931	0.154342
$428$	−5.76197	−0.278516
$429$	9.98146	0.481909
$430$	−0.525530	−0.0253433
$431$	21.8924	1.05452	0.527260	−	0.849704i	$-0.323220\pi$
$431$	21.8924	1.05452	0.527260	+	0.849704i	$0.323220\pi$
$432$	1.00000	0.0481125
$433$	−7.74192	−0.372053	−0.186027	−	0.982545i	$-0.559561\pi$
$433$	−7.74192	−0.372053	−0.186027	+	0.982545i	$0.559561\pi$
$434$	13.7748	0.661213
$435$	0.777724	0.0372890
$436$	−11.6078	−0.555912
$437$	−0.784959	−0.0375497
$438$	−1.75052	−0.0836429
$439$	27.1752	1.29700	0.648501	−	0.761214i	$-0.275396\pi$
$439$	27.1752	1.29700	0.648501	+	0.761214i	$0.275396\pi$
$440$	−0.240025	−0.0114427
$441$	−4.93866	−0.235174
$442$	−5.85410	−0.278451
$443$	−36.3213	−1.72568	−0.862839	−	0.505479i	$-0.831316\pi$
$443$	−36.3213	−1.72568	−0.862839	+	0.505479i	$0.831316\pi$
$444$	6.81296	0.323329
$445$	0.657292	0.0311586
$446$	−17.8294	−0.844246
$447$	5.21753	0.246781
$448$	−1.43574	−0.0678322
$449$	−32.5662	−1.53690	−0.768448	−	0.639913i	$-0.778971\pi$
$449$	−32.5662	−1.53690	−0.768448	+	0.639913i	$0.778971\pi$
$450$	−4.98018	−0.234768
$451$	5.58841	0.263148
$452$	−17.8188	−0.838126
$453$	−11.0505	−0.519199
$454$	9.37440	0.439962
$455$	1.18320	0.0554692
$456$	1.78051	0.0833802
$457$	−19.0632	−0.891740	−0.445870	−	0.895098i	$-0.647106\pi$
$457$	−19.0632	−0.891740	−0.445870	+	0.895098i	$0.647106\pi$
$458$	19.3027	0.901956
$459$	1.00000	0.0466760
$460$	−0.0620618	−0.00289364
$461$	−14.1322	−0.658201	−0.329101	−	0.944295i	$-0.606746\pi$
$461$	−14.1322	−0.658201	−0.329101	+	0.944295i	$0.606746\pi$
$462$	2.44798	0.113891
$463$	36.7512	1.70797	0.853987	−	0.520295i	$-0.174178\pi$
$463$	36.7512	1.70797	0.853987	+	0.520295i	$0.174178\pi$
$464$	5.52463	0.256474
$465$	−1.35062	−0.0626336
$466$	4.83088	0.223786
$467$	−33.4836	−1.54944	−0.774719	−	0.632305i	$-0.782109\pi$
$467$	−33.4836	−1.54944	−0.774719	+	0.632305i	$0.782109\pi$
$468$	−5.85410	−0.270606
$469$	11.8156	0.545595
$470$	−0.186254	−0.00859126
$471$	5.93636	0.273533
$472$	1.00000	0.0460287
$473$	6.36515	0.292670
$474$	−0.426656	−0.0195970
$475$	−8.86728	−0.406859
$476$	−1.43574	−0.0658069
$477$	−6.32741	−0.289712
$478$	−16.6341	−0.760824
$479$	3.83720	0.175326	0.0876630	−	0.996150i	$-0.472060\pi$
$479$	3.83720	0.175326	0.0876630	+	0.996150i	$0.472060\pi$
$480$	0.140774	0.00642542
$481$	−39.8837	−1.81854
$482$	6.45800	0.294154
$483$	0.632960	0.0288007
$484$	−8.09285	−0.367857
$485$	−2.68484	−0.121912
$486$	1.00000	0.0453609
$487$	37.7041	1.70853	0.854267	−	0.519834i	$-0.174006\pi$
$487$	37.7041	1.70853	0.854267	+	0.519834i	$0.174006\pi$
$488$	−2.22137	−0.100557
$489$	−22.7905	−1.03062
$490$	−0.695235	−0.0314075
$491$	−35.3879	−1.59703	−0.798516	−	0.601974i	$-0.794381\pi$
$491$	−35.3879	−1.59703	−0.798516	+	0.601974i	$0.794381\pi$
$492$	−3.27759	−0.147765
$493$	5.52463	0.248817
$494$	−10.4233	−0.468967
$495$	−0.240025	−0.0107883
$496$	−9.59426	−0.430795
$497$	0.616411	0.0276498
$498$	7.32473	0.328229
$499$	−10.4432	−0.467504	−0.233752	−	0.972296i	$-0.575100\pi$
$499$	−10.4432	−0.467504	−0.233752	+	0.972296i	$0.575100\pi$
$500$	−1.40495	−0.0628313
$501$	−14.5110	−0.648303
$502$	7.06395	0.315280
$503$	−44.7314	−1.99447	−0.997236	−	0.0742963i	$-0.976329\pi$
$503$	−44.7314	−1.99447	−0.997236	+	0.0742963i	$0.976329\pi$
$504$	−1.43574	−0.0639528
$505$	−0.876529	−0.0390050
$506$	0.751684	0.0334164
$507$	21.2705	0.944657
$508$	12.1485	0.539003
$509$	42.4435	1.88127	0.940637	−	0.339414i	$-0.110229\pi$
$509$	42.4435	1.88127	0.940637	+	0.339414i	$0.110229\pi$
$510$	0.140774	0.00623358
$511$	2.51328	0.111181
$512$	1.00000	0.0441942
$513$	1.78051	0.0786116
$514$	−17.3885	−0.766975
$515$	1.16681	0.0514160
$516$	−3.73315	−0.164343
$517$	2.25589	0.0992137
$518$	−9.78161	−0.429779
$519$	6.90787	0.303222
$520$	−0.824105	−0.0361394
$521$	7.83466	0.343243	0.171621	−	0.985163i	$-0.445099\pi$
$521$	7.83466	0.343243	0.171621	+	0.985163i	$0.445099\pi$
$522$	5.52463	0.241806
$523$	−22.9515	−1.00360	−0.501800	−	0.864984i	$-0.667329\pi$
$523$	−22.9515	−1.00360	−0.501800	+	0.864984i	$0.667329\pi$
$524$	−11.6441	−0.508674
$525$	7.15023	0.312062
$526$	27.0337	1.17872
$527$	−9.59426	−0.417933
$528$	−1.70504	−0.0742022
$529$	−22.8056	−0.991550
$530$	−0.890734	−0.0386910
$531$	1.00000	0.0433963
$532$	−2.55635	−0.110832
$533$	19.1874	0.831096
$534$	4.66913	0.202053
$535$	−0.811136	−0.0350685
$536$	−8.22967	−0.355467
$537$	10.4970	0.452979
$538$	13.1645	0.567562
$539$	8.42060	0.362701
$540$	0.140774	0.00605795
$541$	−12.4583	−0.535622	−0.267811	−	0.963471i	$-0.586300\pi$
$541$	−12.4583	−0.535622	−0.267811	+	0.963471i	$0.586300\pi$
$542$	7.89635	0.339177
$543$	−0.314780	−0.0135085
$544$	1.00000	0.0428746
$545$	−1.63407	−0.0699961
$546$	8.40495	0.359699
$547$	−0.112020	−0.00478962	−0.00239481	−	0.999997i	$-0.500762\pi$
$547$	−0.112020	−0.00478962	−0.00239481	+	0.999997i	$0.500762\pi$
$548$	8.99164	0.384104
$549$	−2.22137	−0.0948060
$550$	8.49140	0.362074
$551$	9.83668	0.419057
$552$	−0.440861	−0.0187643
$553$	0.612566	0.0260489
$554$	26.5485	1.12794
$555$	0.959087	0.0407110
$556$	18.1296	0.768867
$557$	−7.77501	−0.329438	−0.164719	−	0.986341i	$-0.552672\pi$
$557$	−7.77501	−0.329438	−0.164719	+	0.986341i	$0.552672\pi$
$558$	−9.59426	−0.406157
$559$	21.8542	0.924335
$560$	−0.202114	−0.00854089
$561$	−1.70504	−0.0719867
$562$	−7.09171	−0.299146
$563$	−19.8684	−0.837352	−0.418676	−	0.908136i	$-0.637506\pi$
$563$	−19.8684	−0.837352	−0.418676	+	0.908136i	$0.637506\pi$
$564$	−1.32307	−0.0557113
$565$	−2.50842	−0.105530
$566$	−11.4136	−0.479750
$567$	−1.43574	−0.0602953
$568$	−0.429334	−0.0180145
$569$	−36.9615	−1.54951	−0.774753	−	0.632265i	$-0.782126\pi$
$569$	−36.9615	−1.54951	−0.774753	+	0.632265i	$0.782126\pi$
$570$	0.250650	0.0104986
$571$	−12.3120	−0.515239	−0.257620	−	0.966246i	$-0.582938\pi$
$571$	−12.3120	−0.515239	−0.257620	+	0.966246i	$0.582938\pi$
$572$	9.98146	0.417346
$573$	−20.2517	−0.846029
$574$	4.70576	0.196415
$575$	2.19557	0.0915615
$576$	1.00000	0.0416667
$577$	13.0222	0.542121	0.271061	−	0.962562i	$-0.412626\pi$
$577$	13.0222	0.542121	0.271061	+	0.962562i	$0.412626\pi$
$578$	1.00000	0.0415945
$579$	4.81186	0.199974
$580$	0.777724	0.0322932
$581$	−10.5164	−0.436293
$582$	−19.0720	−0.790560
$583$	10.7885	0.446812
$584$	−1.75052	−0.0724369
$585$	−0.824105	−0.0340726
$586$	−8.55646	−0.353464
$587$	−11.1991	−0.462237	−0.231118	−	0.972926i	$-0.574238\pi$
$587$	−11.1991	−0.462237	−0.231118	+	0.972926i	$0.574238\pi$
$588$	−4.93866	−0.203667
$589$	−17.0827	−0.703881
$590$	0.140774	0.00579557
$591$	13.0292	0.535950
$592$	6.81296	0.280011
$593$	21.8497	0.897260	0.448630	−	0.893718i	$-0.351912\pi$
$593$	21.8497	0.897260	0.448630	+	0.893718i	$0.351912\pi$
$594$	−1.70504	−0.0699585
$595$	−0.202114	−0.00828588
$596$	5.21753	0.213718
$597$	5.09096	0.208359
$598$	2.58084	0.105539
$599$	−26.2684	−1.07330	−0.536648	−	0.843806i	$-0.680310\pi$
$599$	−26.2684	−1.07330	−0.536648	+	0.843806i	$0.680310\pi$
$600$	−4.98018	−0.203315
$601$	45.6025	1.86016	0.930082	−	0.367352i	$-0.119736\pi$
$601$	45.6025	1.86016	0.930082	+	0.367352i	$0.119736\pi$
$602$	5.35981	0.218450
$603$	−8.22967	−0.335138
$604$	−11.0505	−0.449640
$605$	−1.13926	−0.0463176
$606$	−6.22650	−0.252934
$607$	−35.5510	−1.44297	−0.721485	−	0.692430i	$-0.756540\pi$
$607$	−35.5510	−1.44297	−0.721485	+	0.692430i	$0.756540\pi$
$608$	1.78051	0.0722094
$609$	−7.93191	−0.321417
$610$	−0.312712	−0.0126613
$611$	7.74539	0.313345
$612$	1.00000	0.0404226
$613$	16.5873	0.669955	0.334977	−	0.942226i	$-0.391271\pi$
$613$	16.5873	0.669955	0.334977	+	0.942226i	$0.391271\pi$
$614$	25.7900	1.04080
$615$	−0.461400	−0.0186054
$616$	2.44798	0.0986321
$617$	39.3027	1.58227	0.791134	−	0.611643i	$-0.209491\pi$
$617$	39.3027	1.58227	0.791134	+	0.611643i	$0.209491\pi$
$618$	8.28856	0.333415
$619$	22.6500	0.910382	0.455191	−	0.890394i	$-0.349571\pi$
$619$	22.6500	0.910382	0.455191	+	0.890394i	$0.349571\pi$
$620$	−1.35062	−0.0542423
$621$	−0.440861	−0.0176911
$622$	4.55376	0.182589
$623$	−6.70364	−0.268576
$624$	−5.85410	−0.234352
$625$	24.7031	0.988125
$626$	0.102451	0.00409475
$627$	−3.03584	−0.121240
$628$	5.93636	0.236886
$629$	6.81296	0.271650
$630$	−0.202114	−0.00805243
$631$	44.0513	1.75365	0.876826	−	0.480807i	$-0.159656\pi$
$631$	44.0513	1.75365	0.876826	+	0.480807i	$0.159656\pi$
$632$	−0.426656	−0.0169715
$633$	11.6386	0.462592
$634$	0.807455	0.0320681
$635$	1.71019	0.0678670
$636$	−6.32741	−0.250898
$637$	28.9114	1.14551
$638$	−9.41970	−0.372929
$639$	−0.429334	−0.0169842
$640$	0.140774	0.00556458
$641$	−3.02098	−0.119322	−0.0596609	−	0.998219i	$-0.519002\pi$
$641$	−3.02098	−0.119322	−0.0596609	+	0.998219i	$0.519002\pi$
$642$	−5.76197	−0.227407
$643$	20.1629	0.795145	0.397573	−	0.917571i	$-0.369853\pi$
$643$	20.1629	0.795145	0.397573	+	0.917571i	$0.369853\pi$
$644$	0.632960	0.0249421
$645$	−0.525530	−0.0206927
$646$	1.78051	0.0700534
$647$	0.873575	0.0343438	0.0171719	−	0.999853i	$-0.494534\pi$
$647$	0.873575	0.0343438	0.0171719	+	0.999853i	$0.494534\pi$
$648$	1.00000	0.0392837
$649$	−1.70504	−0.0669286
$650$	29.1545	1.14353
$651$	13.7748	0.539878
$652$	−22.7905	−0.892543
$653$	−24.8495	−0.972437	−0.486218	−	0.873837i	$-0.661624\pi$
$653$	−24.8495	−0.972437	−0.486218	+	0.873837i	$0.661624\pi$
$654$	−11.6078	−0.453900
$655$	−1.63918	−0.0640482
$656$	−3.27759	−0.127968
$657$	−1.75052	−0.0682942
$658$	1.89958	0.0740534
$659$	30.7036	1.19604	0.598021	−	0.801481i	$-0.295954\pi$
$659$	30.7036	1.19604	0.598021	+	0.801481i	$0.295954\pi$
$660$	−0.240025	−0.00934296
$661$	25.1758	0.979226	0.489613	−	0.871940i	$-0.337138\pi$
$661$	25.1758	0.979226	0.489613	+	0.871940i	$0.337138\pi$
$662$	−9.59950	−0.373095
$663$	−5.85410	−0.227354
$664$	7.32473	0.284255
$665$	−0.359867	−0.0139551
$666$	6.81296	0.263997
$667$	−2.43559	−0.0943065
$668$	−14.5110	−0.561447
$669$	−17.8294	−0.689324
$670$	−1.15852	−0.0447576
$671$	3.78753	0.146216
$672$	−1.43574	−0.0553848
$673$	−18.1576	−0.699924	−0.349962	−	0.936764i	$-0.613806\pi$
$673$	−18.1576	−0.699924	−0.349962	+	0.936764i	$0.613806\pi$
$674$	−18.0633	−0.695774
$675$	−4.98018	−0.191687
$676$	21.2705	0.818097
$677$	49.9805	1.92091	0.960454	−	0.278439i	$-0.0898169\pi$
$677$	49.9805	1.92091	0.960454	+	0.278439i	$0.0898169\pi$
$678$	−17.8188	−0.684327
$679$	27.3824	1.05084
$680$	0.140774	0.00539844
$681$	9.37440	0.359228
$682$	16.3586	0.626402
$683$	25.0390	0.958091	0.479046	−	0.877790i	$-0.340983\pi$
$683$	25.0390	0.958091	0.479046	+	0.877790i	$0.340983\pi$
$684$	1.78051	0.0680796
$685$	1.26579	0.0483633
$686$	17.1408	0.654438
$687$	19.3027	0.736444
$688$	−3.73315	−0.142325
$689$	37.0413	1.41116
$690$	−0.0620618	−0.00236265
$691$	−12.5935	−0.479078	−0.239539	−	0.970887i	$-0.576996\pi$
$691$	−12.5935	−0.479078	−0.239539	+	0.970887i	$0.576996\pi$
$692$	6.90787	0.262598
$693$	2.44798	0.0929912
$694$	1.70693	0.0647940
$695$	2.55218	0.0968097
$696$	5.52463	0.209411
$697$	−3.27759	−0.124148
$698$	−13.0732	−0.494827
$699$	4.83088	0.182721
$700$	7.15023	0.270253
$701$	40.7320	1.53842	0.769212	−	0.638993i	$-0.220649\pi$
$701$	40.7320	1.53842	0.769212	+	0.638993i	$0.220649\pi$
$702$	−5.85410	−0.220949
$703$	12.1306	0.457513
$704$	−1.70504	−0.0642610
$705$	−0.186254	−0.00701473
$706$	32.7844	1.23386
$707$	8.93961	0.336209
$708$	1.00000	0.0375823
$709$	−1.77614	−0.0667045	−0.0333522	−	0.999444i	$-0.510618\pi$
$709$	−1.77614	−0.0667045	−0.0333522	+	0.999444i	$0.510618\pi$
$710$	−0.0604391	−0.00226824
$711$	−0.426656	−0.0160008
$712$	4.66913	0.174983
$713$	4.22973	0.158405
$714$	−1.43574	−0.0537311
$715$	1.40513	0.0525489
$716$	10.4970	0.392292
$717$	−16.6341	−0.621210
$718$	10.7275	0.400348
$719$	6.69712	0.249761	0.124880	−	0.992172i	$-0.460145\pi$
$719$	6.69712	0.249761	0.124880	+	0.992172i	$0.460145\pi$
$720$	0.140774	0.00524634
$721$	−11.9002	−0.443186
$722$	−15.8298	−0.589123
$723$	6.45800	0.240176
$724$	−0.314780	−0.0116987
$725$	−27.5137	−1.02183
$726$	−8.09285	−0.300354
$727$	−31.9078	−1.18339	−0.591697	−	0.806160i	$-0.701542\pi$
$727$	−31.9078	−1.18339	−0.591697	+	0.806160i	$0.701542\pi$
$728$	8.40495	0.311508
$729$	1.00000	0.0370370
$730$	−0.246427	−0.00912068
$731$	−3.73315	−0.138075
$732$	−2.22137	−0.0821044
$733$	−41.5913	−1.53621	−0.768104	−	0.640325i	$-0.778800\pi$
$733$	−41.5913	−1.53621	−0.768104	+	0.640325i	$0.778800\pi$
$734$	−5.97981	−0.220719
$735$	−0.695235	−0.0256441
$736$	−0.440861	−0.0162503
$737$	14.0319	0.516871
$738$	−3.27759	−0.120650
$739$	−49.2336	−1.81109	−0.905543	−	0.424254i	$-0.860536\pi$
$739$	−49.2336	−1.81109	−0.905543	+	0.424254i	$0.860536\pi$
$740$	0.959087	0.0352567
$741$	−10.4233	−0.382910
$742$	9.08449	0.333502
$743$	8.70164	0.319232	0.159616	−	0.987179i	$-0.448974\pi$
$743$	8.70164	0.319232	0.159616	+	0.987179i	$0.448974\pi$
$744$	−9.59426	−0.351743
$745$	0.734492	0.0269097
$746$	−24.8232	−0.908844
$747$	7.32473	0.267998
$748$	−1.70504	−0.0623423
$749$	8.27268	0.302277
$750$	−1.40495	−0.0513015
$751$	49.7336	1.81480	0.907402	−	0.420264i	$-0.138063\pi$
$751$	49.7336	1.81480	0.907402	+	0.420264i	$0.138063\pi$
$752$	−1.32307	−0.0482474
$753$	7.06395	0.257425
$754$	−32.3417	−1.17782
$755$	−1.55563	−0.0566151
$756$	−1.43574	−0.0522172
$757$	−36.7151	−1.33443	−0.667216	−	0.744864i	$-0.732514\pi$
$757$	−36.7151	−1.33443	−0.667216	+	0.744864i	$0.732514\pi$
$758$	32.3102	1.17356
$759$	0.751684	0.0272844
$760$	0.250650	0.00909203
$761$	−42.3500	−1.53519	−0.767593	−	0.640937i	$-0.778546\pi$
$761$	−42.3500	−1.53519	−0.767593	+	0.640937i	$0.778546\pi$
$762$	12.1485	0.440094
$763$	16.6657	0.603340
$764$	−20.2517	−0.732683
$765$	0.140774	0.00508969
$766$	16.8537	0.608950
$767$	−5.85410	−0.211379
$768$	1.00000	0.0360844
$769$	4.77513	0.172196	0.0860979	−	0.996287i	$-0.472560\pi$
$769$	4.77513	0.172196	0.0860979	+	0.996287i	$0.472560\pi$
$770$	0.344613	0.0124190
$771$	−17.3885	−0.626233
$772$	4.81186	0.173183
$773$	−23.9124	−0.860068	−0.430034	−	0.902813i	$-0.641498\pi$
$773$	−23.9124	−0.860068	−0.430034	+	0.902813i	$0.641498\pi$
$774$	−3.73315	−0.134185
$775$	47.7812	1.71635
$776$	−19.0720	−0.684645
$777$	−9.78161	−0.350913
$778$	−6.97799	−0.250173
$779$	−5.83580	−0.209089
$780$	−0.824105	−0.0295077
$781$	0.732031	0.0261941
$782$	−0.440861	−0.0157652
$783$	5.52463	0.197434
$784$	−4.93866	−0.176381
$785$	0.835685	0.0298269
$786$	−11.6441	−0.415330
$787$	−29.1057	−1.03751	−0.518754	−	0.854924i	$-0.673604\pi$
$787$	−29.1057	−1.03751	−0.518754	+	0.854924i	$0.673604\pi$
$788$	13.0292	0.464146
$789$	27.0337	0.962423
$790$	−0.0600621	−0.00213691
$791$	25.5831	0.909631
$792$	−1.70504	−0.0605859
$793$	13.0042	0.461791
$794$	27.1704	0.964241
$795$	−0.890734	−0.0315911
$796$	5.09096	0.180444
$797$	−20.0573	−0.710465	−0.355233	−	0.934778i	$-0.615598\pi$
$797$	−20.0573	−0.710465	−0.355233	+	0.934778i	$0.615598\pi$
$798$	−2.55635	−0.0904938
$799$	−1.32307	−0.0468069
$800$	−4.98018	−0.176076
$801$	4.66913	0.164975
$802$	−31.0620	−1.09684
$803$	2.98470	0.105328
$804$	−8.22967	−0.290238
$805$	0.0891043	0.00314052
$806$	56.1658	1.97836
$807$	13.1645	0.463413
$808$	−6.22650	−0.219047
$809$	−18.8144	−0.661480	−0.330740	−	0.943722i	$-0.607298\pi$
$809$	−18.8144	−0.661480	−0.330740	+	0.943722i	$0.607298\pi$
$810$	0.140774	0.00494629
$811$	39.7306	1.39513	0.697565	−	0.716522i	$-0.254267\pi$
$811$	39.7306	1.39513	0.697565	+	0.716522i	$0.254267\pi$
$812$	−7.93191	−0.278356
$813$	7.89635	0.276937
$814$	−11.6163	−0.407153
$815$	−3.20830	−0.112382
$816$	1.00000	0.0350070
$817$	−6.64692	−0.232546
$818$	25.4877	0.891158
$819$	8.40495	0.293693
$820$	−0.461400	−0.0161128
$821$	−25.3486	−0.884671	−0.442335	−	0.896850i	$-0.645850\pi$
$821$	−25.3486	−0.884671	−0.442335	+	0.896850i	$0.645850\pi$
$822$	8.99164	0.313619
$823$	−25.9142	−0.903313	−0.451656	−	0.892192i	$-0.649167\pi$
$823$	−25.9142	−0.903313	−0.451656	+	0.892192i	$0.649167\pi$
$824$	8.28856	0.288746
$825$	8.49140	0.295632
$826$	−1.43574	−0.0499557
$827$	−7.14766	−0.248549	−0.124274	−	0.992248i	$-0.539660\pi$
$827$	−7.14766	−0.248549	−0.124274	+	0.992248i	$0.539660\pi$
$828$	−0.440861	−0.0153210
$829$	46.7332	1.62311	0.811555	−	0.584276i	$-0.198622\pi$
$829$	46.7332	1.62311	0.811555	+	0.584276i	$0.198622\pi$
$830$	1.03113	0.0357911
$831$	26.5485	0.920956
$832$	−5.85410	−0.202954
$833$	−4.93866	−0.171114
$834$	18.1296	0.627778
$835$	−2.04277	−0.0706929
$836$	−3.03584	−0.104997
$837$	−9.59426	−0.331626
$838$	25.0826	0.866463
$839$	−39.2382	−1.35465	−0.677326	−	0.735683i	$-0.736862\pi$
$839$	−39.2382	−1.35465	−0.677326	+	0.735683i	$0.736862\pi$
$840$	−0.202114	−0.00697361
$841$	1.52152	0.0524662
$842$	−37.2707	−1.28443
$843$	−7.09171	−0.244252
$844$	11.6386	0.400616
$845$	2.99433	0.103008
$846$	−1.32307	−0.0454881
$847$	11.6192	0.399240
$848$	−6.32741	−0.217284
$849$	−11.4136	−0.391714
$850$	−4.98018	−0.170819
$851$	−3.00357	−0.102961
$852$	−0.429334	−0.0147088
$853$	11.1347	0.381244	0.190622	−	0.981664i	$-0.438950\pi$
$853$	11.1347	0.381244	0.190622	+	0.981664i	$0.438950\pi$
$854$	3.18931	0.109136
$855$	0.250650	0.00857205
$856$	−5.76197	−0.196940
$857$	22.4918	0.768307	0.384153	−	0.923269i	$-0.374493\pi$
$857$	22.4918	0.768307	0.384153	+	0.923269i	$0.374493\pi$
$858$	9.98146	0.340761
$859$	−4.28599	−0.146236	−0.0731181	−	0.997323i	$-0.523295\pi$
$859$	−4.28599	−0.146236	−0.0731181	+	0.997323i	$0.523295\pi$
$860$	−0.525530	−0.0179204
$861$	4.70576	0.160372
$862$	21.8924	0.745658
$863$	26.9998	0.919085	0.459542	−	0.888156i	$-0.348013\pi$
$863$	26.9998	0.919085	0.459542	+	0.888156i	$0.348013\pi$
$864$	1.00000	0.0340207
$865$	0.972449	0.0330643
$866$	−7.74192	−0.263081
$867$	1.00000	0.0339618
$868$	13.7748	0.467548
$869$	0.727464	0.0246775
$870$	0.777724	0.0263673
$871$	48.1773	1.63243
$872$	−11.6078	−0.393089
$873$	−19.0720	−0.645490
$874$	−0.784959	−0.0265516
$875$	2.01714	0.0681917
$876$	−1.75052	−0.0591445
$877$	−14.2488	−0.481147	−0.240574	−	0.970631i	$-0.577336\pi$
$877$	−14.2488	−0.481147	−0.240574	+	0.970631i	$0.577336\pi$
$878$	27.1752	0.917119
$879$	−8.55646	−0.288602
$880$	−0.240025	−0.00809124
$881$	−14.6980	−0.495188	−0.247594	−	0.968864i	$-0.579640\pi$
$881$	−14.6980	−0.495188	−0.247594	+	0.968864i	$0.579640\pi$
$882$	−4.93866	−0.166293
$883$	−36.0803	−1.21420	−0.607100	−	0.794626i	$-0.707667\pi$
$883$	−36.0803	−1.21420	−0.607100	+	0.794626i	$0.707667\pi$
$884$	−5.85410	−0.196895
$885$	0.140774	0.00473207
$886$	−36.3213	−1.22024
$887$	18.8596	0.633244	0.316622	−	0.948552i	$-0.397451\pi$
$887$	18.8596	0.633244	0.316622	+	0.948552i	$0.397451\pi$
$888$	6.81296	0.228628
$889$	−17.4421	−0.584988
$890$	0.657292	0.0220325
$891$	−1.70504	−0.0571209
$892$	−17.8294	−0.596972
$893$	−2.35575	−0.0788320
$894$	5.21753	0.174500
$895$	1.47771	0.0493943
$896$	−1.43574	−0.0479646
$897$	2.58084	0.0861719
$898$	−32.5662	−1.08675
$899$	−53.0047	−1.76781
$900$	−4.98018	−0.166006
$901$	−6.32741	−0.210796
$902$	5.58841	0.186074
$903$	5.35981	0.178363
$904$	−17.8188	−0.592645
$905$	−0.0443129	−0.00147301
$906$	−11.0505	−0.367129
$907$	15.4272	0.512250	0.256125	−	0.966644i	$-0.417554\pi$
$907$	15.4272	0.512250	0.256125	+	0.966644i	$0.417554\pi$
$908$	9.37440	0.311100
$909$	−6.22650	−0.206520
$910$	1.18320	0.0392226
$911$	35.3734	1.17197	0.585987	−	0.810320i	$-0.300707\pi$
$911$	35.3734	1.17197	0.585987	+	0.810320i	$0.300707\pi$
$912$	1.78051	0.0589587
$913$	−12.4889	−0.413323
$914$	−19.0632	−0.630556
$915$	−0.312712	−0.0103379
$916$	19.3027	0.637779
$917$	16.7178	0.552071
$918$	1.00000	0.0330049
$919$	−10.2061	−0.336670	−0.168335	−	0.985730i	$-0.553839\pi$
$919$	−10.2061	−0.336670	−0.168335	+	0.985730i	$0.553839\pi$
$920$	−0.0620618	−0.00204612
$921$	25.7900	0.849808
$922$	−14.1322	−0.465419
$923$	2.51337	0.0827285
$924$	2.44798	0.0805328
$925$	−33.9298	−1.11560
$926$	36.7512	1.20772
$927$	8.28856	0.272232
$928$	5.52463	0.181355
$929$	3.01228	0.0988297	0.0494149	−	0.998778i	$-0.484264\pi$
$929$	3.01228	0.0988297	0.0494149	+	0.998778i	$0.484264\pi$
$930$	−1.35062	−0.0442886
$931$	−8.79335	−0.288190
$932$	4.83088	0.158241
$933$	4.55376	0.149083
$934$	−33.4836	−1.09562
$935$	−0.240025	−0.00784965
$936$	−5.85410	−0.191347
$937$	−12.5932	−0.411402	−0.205701	−	0.978615i	$-0.565947\pi$
$937$	−12.5932	−0.411402	−0.205701	+	0.978615i	$0.565947\pi$
$938$	11.8156	0.385794
$939$	0.102451	0.00334335
$940$	−0.186254	−0.00607494
$941$	−25.3776	−0.827285	−0.413642	−	0.910439i	$-0.635744\pi$
$941$	−25.3776	−0.827285	−0.413642	+	0.910439i	$0.635744\pi$
$942$	5.93636	0.193417
$943$	1.44496	0.0470544
$944$	1.00000	0.0325472
$945$	−0.202114	−0.00657478
$946$	6.36515	0.206949
$947$	35.2367	1.14504	0.572520	−	0.819891i	$-0.305966\pi$
$947$	35.2367	1.14504	0.572520	+	0.819891i	$0.305966\pi$
$948$	−0.426656	−0.0138571
$949$	10.2477	0.332655
$950$	−8.86728	−0.287693
$951$	0.807455	0.0261835
$952$	−1.43574	−0.0465325
$953$	−54.7198	−1.77255	−0.886274	−	0.463162i	$-0.846715\pi$
$953$	−54.7198	−1.77255	−0.886274	+	0.463162i	$0.846715\pi$
$954$	−6.32741	−0.204857
$955$	−2.85092	−0.0922536
$956$	−16.6341	−0.537984
$957$	−9.41970	−0.304496
$958$	3.83720	0.123974
$959$	−12.9096	−0.416874
$960$	0.140774	0.00454346
$961$	61.0498	1.96935
$962$	−39.8837	−1.28590
$963$	−5.76197	−0.185677
$964$	6.45800	0.207998
$965$	0.677384	0.0218058
$966$	0.632960	0.0203652
$967$	18.3588	0.590379	0.295190	−	0.955439i	$-0.404617\pi$
$967$	18.3588	0.590379	0.295190	+	0.955439i	$0.404617\pi$
$968$	−8.09285	−0.260114
$969$	1.78051	0.0571983
$970$	−2.68484	−0.0862051
$971$	27.1030	0.869776	0.434888	−	0.900484i	$-0.356788\pi$
$971$	27.1030	0.869776	0.434888	+	0.900484i	$0.356788\pi$
$972$	1.00000	0.0320750
$973$	−26.0294	−0.834463
$974$	37.7041	1.20812
$975$	29.1545	0.933691
$976$	−2.22137	−0.0711045
$977$	−1.27455	−0.0407763	−0.0203882	−	0.999792i	$-0.506490\pi$
$977$	−1.27455	−0.0407763	−0.0203882	+	0.999792i	$0.506490\pi$
$978$	−22.7905	−0.728759
$979$	−7.96103	−0.254436
$980$	−0.695235	−0.0222085
$981$	−11.6078	−0.370608
$982$	−35.3879	−1.12927
$983$	−34.9689	−1.11534	−0.557668	−	0.830064i	$-0.688304\pi$
$983$	−34.9689	−1.11534	−0.557668	+	0.830064i	$0.688304\pi$
$984$	−3.27759	−0.104486
$985$	1.83417	0.0584416
$986$	5.52463	0.175940
$987$	1.89958	0.0604644
$988$	−10.4233	−0.331610
$989$	1.64580	0.0523333
$990$	−0.240025	−0.00762849
$991$	10.5714	0.335810	0.167905	−	0.985803i	$-0.446300\pi$
$991$	10.5714	0.335810	0.167905	+	0.985803i	$0.446300\pi$
$992$	−9.59426	−0.304618
$993$	−9.59950	−0.304631
$994$	0.616411	0.0195514
$995$	0.716675	0.0227201
$996$	7.32473	0.232093
$997$	−18.7273	−0.593099	−0.296550	−	0.955017i	$-0.595836\pi$
$997$	−18.7273	−0.593099	−0.296550	+	0.955017i	$0.595836\pi$
$998$	−10.4432	−0.330575
$999$	6.81296	0.215552

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.o.1.3	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.o.1.3	✓	4	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:	\( N \)	\(=\)	\( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6018.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.140774 q^{5} +1.00000 q^{6} -1.43574 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.140774 q^{5} +1.00000 q^{6} -1.43574 q^{7} +1.00000 q^{8} +1.00000 q^{9} +0.140774 q^{10} -1.70504 q^{11} +1.00000 q^{12} -5.85410 q^{13} -1.43574 q^{14} +0.140774 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} +1.78051 q^{19} +0.140774 q^{20} -1.43574 q^{21} -1.70504 q^{22} -0.440861 q^{23} +1.00000 q^{24} -4.98018 q^{25} -5.85410 q^{26} +1.00000 q^{27} -1.43574 q^{28} +5.52463 q^{29} +0.140774 q^{30} -9.59426 q^{31} +1.00000 q^{32} -1.70504 q^{33} +1.00000 q^{34} -0.202114 q^{35} +1.00000 q^{36} +6.81296 q^{37} +1.78051 q^{38} -5.85410 q^{39} +0.140774 q^{40} -3.27759 q^{41} -1.43574 q^{42} -3.73315 q^{43} -1.70504 q^{44} +0.140774 q^{45} -0.440861 q^{46} -1.32307 q^{47} +1.00000 q^{48} -4.93866 q^{49} -4.98018 q^{50} +1.00000 q^{51} -5.85410 q^{52} -6.32741 q^{53} +1.00000 q^{54} -0.240025 q^{55} -1.43574 q^{56} +1.78051 q^{57} +5.52463 q^{58} +1.00000 q^{59} +0.140774 q^{60} -2.22137 q^{61} -9.59426 q^{62} -1.43574 q^{63} +1.00000 q^{64} -0.824105 q^{65} -1.70504 q^{66} -8.22967 q^{67} +1.00000 q^{68} -0.440861 q^{69} -0.202114 q^{70} -0.429334 q^{71} +1.00000 q^{72} -1.75052 q^{73} +6.81296 q^{74} -4.98018 q^{75} +1.78051 q^{76} +2.44798 q^{77} -5.85410 q^{78} -0.426656 q^{79} +0.140774 q^{80} +1.00000 q^{81} -3.27759 q^{82} +7.32473 q^{83} -1.43574 q^{84} +0.140774 q^{85} -3.73315 q^{86} +5.52463 q^{87} -1.70504 q^{88} +4.66913 q^{89} +0.140774 q^{90} +8.40495 q^{91} -0.440861 q^{92} -9.59426 q^{93} -1.32307 q^{94} +0.250650 q^{95} +1.00000 q^{96} -19.0720 q^{97} -4.93866 q^{98} -1.70504 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} - q^{5} + 4 q^{6} - q^{7} + 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 - q^5 + 4 * q^6 - q^7 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} - q^{5} + 4 q^{6} - q^{7} + 4 q^{8} + 4 q^{9} - q^{10} - 10 q^{11} + 4 q^{12} - 10 q^{13} - q^{14} - q^{15} + 4 q^{16} + 4 q^{17} + 4 q^{18} - 14 q^{19} - q^{20} - q^{21} - 10 q^{22} - 12 q^{23} + 4 q^{24} - 3 q^{25} - 10 q^{26} + 4 q^{27} - q^{28} - 7 q^{29} - q^{30} - 13 q^{31} + 4 q^{32} - 10 q^{33} + 4 q^{34} - 18 q^{35} + 4 q^{36} - 11 q^{37} - 14 q^{38} - 10 q^{39} - q^{40} - 6 q^{41} - q^{42} - 20 q^{43} - 10 q^{44} - q^{45} - 12 q^{46} - 4 q^{47} + 4 q^{48} - q^{49} - 3 q^{50} + 4 q^{51} - 10 q^{52} - 5 q^{53} + 4 q^{54} + 4 q^{55} - q^{56} - 14 q^{57} - 7 q^{58} + 4 q^{59} - q^{60} + 2 q^{61} - 13 q^{62} - q^{63} + 4 q^{64} - 20 q^{65} - 10 q^{66} - 7 q^{67} + 4 q^{68} - 12 q^{69} - 18 q^{70} + 20 q^{71} + 4 q^{72} - 16 q^{73} - 11 q^{74} - 3 q^{75} - 14 q^{76} - 6 q^{77} - 10 q^{78} + 22 q^{79} - q^{80} + 4 q^{81} - 6 q^{82} + 7 q^{83} - q^{84} - q^{85} - 20 q^{86} - 7 q^{87} - 10 q^{88} + 3 q^{89} - q^{90} + 25 q^{91} - 12 q^{92} - 13 q^{93} - 4 q^{94} + 3 q^{95} + 4 q^{96} - 16 q^{97} - q^{98} - 10 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 - q^5 + 4 * q^6 - q^7 + 4 * q^8 + 4 * q^9 - q^10 - 10 * q^11 + 4 * q^12 - 10 * q^13 - q^14 - q^15 + 4 * q^16 + 4 * q^17 + 4 * q^18 - 14 * q^19 - q^20 - q^21 - 10 * q^22 - 12 * q^23 + 4 * q^24 - 3 * q^25 - 10 * q^26 + 4 * q^27 - q^28 - 7 * q^29 - q^30 - 13 * q^31 + 4 * q^32 - 10 * q^33 + 4 * q^34 - 18 * q^35 + 4 * q^36 - 11 * q^37 - 14 * q^38 - 10 * q^39 - q^40 - 6 * q^41 - q^42 - 20 * q^43 - 10 * q^44 - q^45 - 12 * q^46 - 4 * q^47 + 4 * q^48 - q^49 - 3 * q^50 + 4 * q^51 - 10 * q^52 - 5 * q^53 + 4 * q^54 + 4 * q^55 - q^56 - 14 * q^57 - 7 * q^58 + 4 * q^59 - q^60 + 2 * q^61 - 13 * q^62 - q^63 + 4 * q^64 - 20 * q^65 - 10 * q^66 - 7 * q^67 + 4 * q^68 - 12 * q^69 - 18 * q^70 + 20 * q^71 + 4 * q^72 - 16 * q^73 - 11 * q^74 - 3 * q^75 - 14 * q^76 - 6 * q^77 - 10 * q^78 + 22 * q^79 - q^80 + 4 * q^81 - 6 * q^82 + 7 * q^83 - q^84 - q^85 - 20 * q^86 - 7 * q^87 - 10 * q^88 + 3 * q^89 - q^90 + 25 * q^91 - 12 * q^92 - 13 * q^93 - 4 * q^94 + 3 * q^95 + 4 * q^96 - 16 * q^97 - q^98 - 10 * q^99

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