LMFDB - Embedded newform 6018.2.a.y.1.1

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:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} - 33x^{8} + 53x^{7} + 356x^{6} - 433x^{5} - 1296x^{4} + 1135x^{3} + 930x^{2} - 186x - 104 $ x^10 - 2x^9 - 33x^8 + 53x^7 + 356x^6 - 433x^5 - 1296x^4 + 1135x^3 + 930x^2 - 186*x - 104
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$4.05993$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -4.05993 q^{5} -1.00000 q^{6} +4.32251 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -4.05993 q^{5} -1.00000 q^{6} +4.32251 q^{7} -1.00000 q^{8} +1.00000 q^{9} +4.05993 q^{10} -0.174683 q^{11} +1.00000 q^{12} -3.57932 q^{13} -4.32251 q^{14} -4.05993 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} +4.32911 q^{19} -4.05993 q^{20} +4.32251 q^{21} +0.174683 q^{22} -0.966068 q^{23} -1.00000 q^{24} +11.4830 q^{25} +3.57932 q^{26} +1.00000 q^{27} +4.32251 q^{28} -2.78244 q^{29} +4.05993 q^{30} -8.94938 q^{31} -1.00000 q^{32} -0.174683 q^{33} +1.00000 q^{34} -17.5491 q^{35} +1.00000 q^{36} +9.05465 q^{37} -4.32911 q^{38} -3.57932 q^{39} +4.05993 q^{40} -1.49587 q^{41} -4.32251 q^{42} -7.81727 q^{43} -0.174683 q^{44} -4.05993 q^{45} +0.966068 q^{46} -10.9910 q^{47} +1.00000 q^{48} +11.6841 q^{49} -11.4830 q^{50} -1.00000 q^{51} -3.57932 q^{52} +8.25436 q^{53} -1.00000 q^{54} +0.709201 q^{55} -4.32251 q^{56} +4.32911 q^{57} +2.78244 q^{58} +1.00000 q^{59} -4.05993 q^{60} -13.2963 q^{61} +8.94938 q^{62} +4.32251 q^{63} +1.00000 q^{64} +14.5318 q^{65} +0.174683 q^{66} +10.6386 q^{67} -1.00000 q^{68} -0.966068 q^{69} +17.5491 q^{70} -11.5730 q^{71} -1.00000 q^{72} +15.4034 q^{73} -9.05465 q^{74} +11.4830 q^{75} +4.32911 q^{76} -0.755069 q^{77} +3.57932 q^{78} -10.6346 q^{79} -4.05993 q^{80} +1.00000 q^{81} +1.49587 q^{82} +13.5213 q^{83} +4.32251 q^{84} +4.05993 q^{85} +7.81727 q^{86} -2.78244 q^{87} +0.174683 q^{88} +6.06380 q^{89} +4.05993 q^{90} -15.4717 q^{91} -0.966068 q^{92} -8.94938 q^{93} +10.9910 q^{94} -17.5759 q^{95} -1.00000 q^{96} -12.2431 q^{97} -11.6841 q^{98} -0.174683 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{2} + 10 q^{3} + 10 q^{4} - 2 q^{5} - 10 q^{6} - 6 q^{7} - 10 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q - 10 * q^2 + 10 * q^3 + 10 * q^4 - 2 * q^5 - 10 * q^6 - 6 * q^7 - 10 * q^8 + 10 * q^9	\( 10 q - 10 q^{2} + 10 q^{3} + 10 q^{4} - 2 q^{5} - 10 q^{6} - 6 q^{7} - 10 q^{8} + 10 q^{9} + 2 q^{10} - 3 q^{11} + 10 q^{12} - 10 q^{13} + 6 q^{14} - 2 q^{15} + 10 q^{16} - 10 q^{17} - 10 q^{18} + 8 q^{19} - 2 q^{20} - 6 q^{21} + 3 q^{22} - 9 q^{23} - 10 q^{24} + 20 q^{25} + 10 q^{26} + 10 q^{27} - 6 q^{28} - 24 q^{29} + 2 q^{30} - 7 q^{31} - 10 q^{32} - 3 q^{33} + 10 q^{34} - 22 q^{35} + 10 q^{36} - 4 q^{37} - 8 q^{38} - 10 q^{39} + 2 q^{40} - 9 q^{41} + 6 q^{42} - 11 q^{43} - 3 q^{44} - 2 q^{45} + 9 q^{46} - 18 q^{47} + 10 q^{48} + 6 q^{49} - 20 q^{50} - 10 q^{51} - 10 q^{52} - 9 q^{53} - 10 q^{54} + q^{55} + 6 q^{56} + 8 q^{57} + 24 q^{58} + 10 q^{59} - 2 q^{60} - 25 q^{61} + 7 q^{62} - 6 q^{63} + 10 q^{64} - 28 q^{65} + 3 q^{66} + 2 q^{67} - 10 q^{68} - 9 q^{69} + 22 q^{70} - 30 q^{71} - 10 q^{72} - 11 q^{73} + 4 q^{74} + 20 q^{75} + 8 q^{76} + 4 q^{77} + 10 q^{78} + 3 q^{79} - 2 q^{80} + 10 q^{81} + 9 q^{82} - q^{83} - 6 q^{84} + 2 q^{85} + 11 q^{86} - 24 q^{87} + 3 q^{88} - 14 q^{89} + 2 q^{90} - 13 q^{91} - 9 q^{92} - 7 q^{93} + 18 q^{94} - 35 q^{95} - 10 q^{96} - 10 q^{97} - 6 q^{98} - 3 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 + 10 * q^3 + 10 * q^4 - 2 * q^5 - 10 * q^6 - 6 * q^7 - 10 * q^8 + 10 * q^9 + 2 * q^10 - 3 * q^11 + 10 * q^12 - 10 * q^13 + 6 * q^14 - 2 * q^15 + 10 * q^16 - 10 * q^17 - 10 * q^18 + 8 * q^19 - 2 * q^20 - 6 * q^21 + 3 * q^22 - 9 * q^23 - 10 * q^24 + 20 * q^25 + 10 * q^26 + 10 * q^27 - 6 * q^28 - 24 * q^29 + 2 * q^30 - 7 * q^31 - 10 * q^32 - 3 * q^33 + 10 * q^34 - 22 * q^35 + 10 * q^36 - 4 * q^37 - 8 * q^38 - 10 * q^39 + 2 * q^40 - 9 * q^41 + 6 * q^42 - 11 * q^43 - 3 * q^44 - 2 * q^45 + 9 * q^46 - 18 * q^47 + 10 * q^48 + 6 * q^49 - 20 * q^50 - 10 * q^51 - 10 * q^52 - 9 * q^53 - 10 * q^54 + q^55 + 6 * q^56 + 8 * q^57 + 24 * q^58 + 10 * q^59 - 2 * q^60 - 25 * q^61 + 7 * q^62 - 6 * q^63 + 10 * q^64 - 28 * q^65 + 3 * q^66 + 2 * q^67 - 10 * q^68 - 9 * q^69 + 22 * q^70 - 30 * q^71 - 10 * q^72 - 11 * q^73 + 4 * q^74 + 20 * q^75 + 8 * q^76 + 4 * q^77 + 10 * q^78 + 3 * q^79 - 2 * q^80 + 10 * q^81 + 9 * q^82 - q^83 - 6 * q^84 + 2 * q^85 + 11 * q^86 - 24 * q^87 + 3 * q^88 - 14 * q^89 + 2 * q^90 - 13 * q^91 - 9 * q^92 - 7 * q^93 + 18 * q^94 - 35 * q^95 - 10 * q^96 - 10 * q^97 - 6 * q^98 - 3 * 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
$5$	−4.05993	−1.81566	−0.907828	−	0.419343i	$-0.862261\pi$
$5$	−4.05993	−1.81566	−0.907828	+	0.419343i	$0.862261\pi$
$6$	−1.00000	−0.408248
$7$	4.32251	1.63376	0.816878	−	0.576811i	$-0.195703\pi$
$7$	4.32251	1.63376	0.816878	+	0.576811i	$0.195703\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	4.05993	1.28386
$11$	−0.174683	−0.0526689	−0.0263344	−	0.999653i	$-0.508383\pi$
$11$	−0.174683	−0.0526689	−0.0263344	+	0.999653i	$0.508383\pi$
$12$	1.00000	0.288675
$13$	−3.57932	−0.992726	−0.496363	−	0.868115i	$-0.665331\pi$
$13$	−3.57932	−0.992726	−0.496363	+	0.868115i	$0.665331\pi$
$14$	−4.32251	−1.15524
$15$	−4.05993	−1.04827
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−1.00000	−0.235702
$19$	4.32911	0.993167	0.496583	−	0.867989i	$-0.334588\pi$
$19$	4.32911	0.993167	0.496583	+	0.867989i	$0.334588\pi$
$20$	−4.05993	−0.907828
$21$	4.32251	0.943249
$22$	0.174683	0.0372425
$23$	−0.966068	−0.201439	−0.100720	−	0.994915i	$-0.532114\pi$
$23$	−0.966068	−0.201439	−0.100720	+	0.994915i	$0.532114\pi$
$24$	−1.00000	−0.204124
$25$	11.4830	2.29661
$26$	3.57932	0.701963
$27$	1.00000	0.192450
$28$	4.32251	0.816878
$29$	−2.78244	−0.516686	−0.258343	−	0.966053i	$-0.583176\pi$
$29$	−2.78244	−0.516686	−0.258343	+	0.966053i	$0.583176\pi$
$30$	4.05993	0.741238
$31$	−8.94938	−1.60736	−0.803678	−	0.595064i	$-0.797127\pi$
$31$	−8.94938	−1.60736	−0.803678	+	0.595064i	$0.797127\pi$
$32$	−1.00000	−0.176777
$33$	−0.174683	−0.0304084
$34$	1.00000	0.171499
$35$	−17.5491	−2.96634
$36$	1.00000	0.166667
$37$	9.05465	1.48858	0.744288	−	0.667859i	$-0.232789\pi$
$37$	9.05465	1.48858	0.744288	+	0.667859i	$0.232789\pi$
$38$	−4.32911	−0.702275
$39$	−3.57932	−0.573150
$40$	4.05993	0.641931
$41$	−1.49587	−0.233616	−0.116808	−	0.993155i	$-0.537266\pi$
$41$	−1.49587	−0.233616	−0.116808	+	0.993155i	$0.537266\pi$
$42$	−4.32251	−0.666978
$43$	−7.81727	−1.19212	−0.596062	−	0.802939i	$-0.703269\pi$
$43$	−7.81727	−1.19212	−0.596062	+	0.802939i	$0.703269\pi$
$44$	−0.174683	−0.0263344
$45$	−4.05993	−0.605219
$46$	0.966068	0.142439
$47$	−10.9910	−1.60320	−0.801602	−	0.597857i	$-0.796019\pi$
$47$	−10.9910	−1.60320	−0.801602	+	0.597857i	$0.796019\pi$
$48$	1.00000	0.144338
$49$	11.6841	1.66916
$50$	−11.4830	−1.62395
$51$	−1.00000	−0.140028
$52$	−3.57932	−0.496363
$53$	8.25436	1.13382	0.566912	−	0.823779i	$-0.308138\pi$
$53$	8.25436	1.13382	0.566912	+	0.823779i	$0.308138\pi$
$54$	−1.00000	−0.136083
$55$	0.709201	0.0956286
$56$	−4.32251	−0.577620
$57$	4.32911	0.573405
$58$	2.78244	0.365352
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	−4.05993	−0.524135
$61$	−13.2963	−1.70242	−0.851208	−	0.524828i	$-0.824130\pi$
$61$	−13.2963	−1.70242	−0.851208	+	0.524828i	$0.824130\pi$
$62$	8.94938	1.13657
$63$	4.32251	0.544585
$64$	1.00000	0.125000
$65$	14.5318	1.80245
$66$	0.174683	0.0215020
$67$	10.6386	1.29971	0.649857	−	0.760057i	$-0.274829\pi$
$67$	10.6386	1.29971	0.649857	+	0.760057i	$0.274829\pi$
$68$	−1.00000	−0.121268
$69$	−0.966068	−0.116301
$70$	17.5491	2.09752
$71$	−11.5730	−1.37346	−0.686730	−	0.726912i	$-0.740955\pi$
$71$	−11.5730	−1.37346	−0.686730	+	0.726912i	$0.740955\pi$
$72$	−1.00000	−0.117851
$73$	15.4034	1.80283	0.901413	−	0.432959i	$-0.142531\pi$
$73$	15.4034	1.80283	0.901413	+	0.432959i	$0.142531\pi$
$74$	−9.05465	−1.05258
$75$	11.4830	1.32595
$76$	4.32911	0.496583
$77$	−0.755069	−0.0860481
$78$	3.57932	0.405279
$79$	−10.6346	−1.19648	−0.598241	−	0.801316i	$-0.704133\pi$
$79$	−10.6346	−1.19648	−0.598241	+	0.801316i	$0.704133\pi$
$80$	−4.05993	−0.453914
$81$	1.00000	0.111111
$82$	1.49587	0.165191
$83$	13.5213	1.48416	0.742080	−	0.670311i	$-0.233839\pi$
$83$	13.5213	1.48416	0.742080	+	0.670311i	$0.233839\pi$
$84$	4.32251	0.471625
$85$	4.05993	0.440361
$86$	7.81727	0.842958
$87$	−2.78244	−0.298309
$88$	0.174683	0.0186213
$89$	6.06380	0.642761	0.321381	−	0.946950i	$-0.395853\pi$
$89$	6.06380	0.642761	0.321381	+	0.946950i	$0.395853\pi$
$90$	4.05993	0.427954
$91$	−15.4717	−1.62187
$92$	−0.966068	−0.100720
$93$	−8.94938	−0.928008
$94$	10.9910	1.13364
$95$	−17.5759	−1.80325
$96$	−1.00000	−0.102062
$97$	−12.2431	−1.24310	−0.621551	−	0.783374i	$-0.713497\pi$
$97$	−12.2431	−1.24310	−0.621551	+	0.783374i	$0.713497\pi$
$98$	−11.6841	−1.18027
$99$	−0.174683	−0.0175563
$100$	11.4830	1.14830
$101$	12.6064	1.25438	0.627192	−	0.778865i	$-0.284204\pi$
$101$	12.6064	1.25438	0.627192	+	0.778865i	$0.284204\pi$
$102$	1.00000	0.0990148
$103$	5.09638	0.502161	0.251080	−	0.967966i	$-0.419214\pi$
$103$	5.09638	0.502161	0.251080	+	0.967966i	$0.419214\pi$
$104$	3.57932	0.350982
$105$	−17.5491	−1.71262
$106$	−8.25436	−0.801734
$107$	−12.2482	−1.18408	−0.592038	−	0.805910i	$-0.701676\pi$
$107$	−12.2482	−1.18408	−0.592038	+	0.805910i	$0.701676\pi$
$108$	1.00000	0.0962250
$109$	−16.4156	−1.57233	−0.786164	−	0.618018i	$-0.787936\pi$
$109$	−16.4156	−1.57233	−0.786164	+	0.618018i	$0.787936\pi$
$110$	−0.709201	−0.0676196
$111$	9.05465	0.859429
$112$	4.32251	0.408439
$113$	−10.7707	−1.01323	−0.506613	−	0.862174i	$-0.669103\pi$
$113$	−10.7707	−1.01323	−0.506613	+	0.862174i	$0.669103\pi$
$114$	−4.32911	−0.405459
$115$	3.92217	0.365744
$116$	−2.78244	−0.258343
$117$	−3.57932	−0.330909
$118$	−1.00000	−0.0920575
$119$	−4.32251	−0.396244
$120$	4.05993	0.370619
$121$	−10.9695	−0.997226
$122$	13.2963	1.20379
$123$	−1.49587	−0.134878
$124$	−8.94938	−0.803678
$125$	−26.3207	−2.35419
$126$	−4.32251	−0.385080
$127$	−2.14110	−0.189992	−0.0949959	−	0.995478i	$-0.530284\pi$
$127$	−2.14110	−0.189992	−0.0949959	+	0.995478i	$0.530284\pi$
$128$	−1.00000	−0.0883883
$129$	−7.81727	−0.688273
$130$	−14.5318	−1.27452
$131$	13.7267	1.19931	0.599653	−	0.800260i	$-0.295305\pi$
$131$	13.7267	1.19931	0.599653	+	0.800260i	$0.295305\pi$
$132$	−0.174683	−0.0152042
$133$	18.7126	1.62259
$134$	−10.6386	−0.919036
$135$	−4.05993	−0.349423
$136$	1.00000	0.0857493
$137$	10.8186	0.924296	0.462148	−	0.886803i	$-0.347079\pi$
$137$	10.8186	0.924296	0.462148	+	0.886803i	$0.347079\pi$
$138$	0.966068	0.0822372
$139$	−3.78704	−0.321212	−0.160606	−	0.987019i	$-0.551345\pi$
$139$	−3.78704	−0.321212	−0.160606	+	0.987019i	$0.551345\pi$
$140$	−17.5491	−1.48317
$141$	−10.9910	−0.925611
$142$	11.5730	0.971183
$143$	0.625247	0.0522858
$144$	1.00000	0.0833333
$145$	11.2965	0.938123
$146$	−15.4034	−1.27479
$147$	11.6841	0.963688
$148$	9.05465	0.744288
$149$	−21.9080	−1.79478	−0.897388	−	0.441242i	$-0.854538\pi$
$149$	−21.9080	−1.79478	−0.897388	+	0.441242i	$0.854538\pi$
$150$	−11.4830	−0.937586
$151$	−5.89511	−0.479737	−0.239869	−	0.970805i	$-0.577104\pi$
$151$	−5.89511	−0.479737	−0.239869	+	0.970805i	$0.577104\pi$
$152$	−4.32911	−0.351138
$153$	−1.00000	−0.0808452
$154$	0.755069	0.0608452
$155$	36.3339	2.91841
$156$	−3.57932	−0.286575
$157$	2.64550	0.211134	0.105567	−	0.994412i	$-0.466334\pi$
$157$	2.64550	0.211134	0.105567	+	0.994412i	$0.466334\pi$
$158$	10.6346	0.846040
$159$	8.25436	0.654613
$160$	4.05993	0.320966
$161$	−4.17584	−0.329102
$162$	−1.00000	−0.0785674
$163$	−7.83285	−0.613516	−0.306758	−	0.951788i	$-0.599244\pi$
$163$	−7.83285	−0.613516	−0.306758	+	0.951788i	$0.599244\pi$
$164$	−1.49587	−0.116808
$165$	0.709201	0.0552112
$166$	−13.5213	−1.04946
$167$	−11.8583	−0.917623	−0.458811	−	0.888534i	$-0.651725\pi$
$167$	−11.8583	−0.917623	−0.458811	+	0.888534i	$0.651725\pi$
$168$	−4.32251	−0.333489
$169$	−0.188447	−0.0144959
$170$	−4.05993	−0.311382
$171$	4.32911	0.331056
$172$	−7.81727	−0.596062
$173$	−5.47185	−0.416017	−0.208008	−	0.978127i	$-0.566698\pi$
$173$	−5.47185	−0.416017	−0.208008	+	0.978127i	$0.566698\pi$
$174$	2.78244	0.210936
$175$	49.6355	3.75209
$176$	−0.174683	−0.0131672
$177$	1.00000	0.0751646
$178$	−6.06380	−0.454501
$179$	21.4193	1.60095	0.800476	−	0.599365i	$-0.204580\pi$
$179$	21.4193	1.60095	0.800476	+	0.599365i	$0.204580\pi$
$180$	−4.05993	−0.302609
$181$	21.9957	1.63493	0.817464	−	0.575980i	$-0.195380\pi$
$181$	21.9957	1.63493	0.817464	+	0.575980i	$0.195380\pi$
$182$	15.4717	1.14684
$183$	−13.2963	−0.982891
$184$	0.966068	0.0712195
$185$	−36.7613	−2.70274
$186$	8.94938	0.656201
$187$	0.174683	0.0127741
$188$	−10.9910	−0.801602
$189$	4.32251	0.314416
$190$	17.5759	1.27509
$191$	−7.81869	−0.565740	−0.282870	−	0.959158i	$-0.591287\pi$
$191$	−7.81869	−0.565740	−0.282870	+	0.959158i	$0.591287\pi$
$192$	1.00000	0.0721688
$193$	2.50888	0.180593	0.0902964	−	0.995915i	$-0.471219\pi$
$193$	2.50888	0.180593	0.0902964	+	0.995915i	$0.471219\pi$
$194$	12.2431	0.879005
$195$	14.5318	1.04064
$196$	11.6841	0.834579
$197$	18.4106	1.31170	0.655852	−	0.754889i	$-0.272309\pi$
$197$	18.4106	1.31170	0.655852	+	0.754889i	$0.272309\pi$
$198$	0.174683	0.0124142
$199$	6.35539	0.450522	0.225261	−	0.974299i	$-0.427677\pi$
$199$	6.35539	0.450522	0.225261	+	0.974299i	$0.427677\pi$
$200$	−11.4830	−0.811973
$201$	10.6386	0.750390
$202$	−12.6064	−0.886983
$203$	−12.0271	−0.844138
$204$	−1.00000	−0.0700140
$205$	6.07313	0.424166
$206$	−5.09638	−0.355081
$207$	−0.966068	−0.0671464
$208$	−3.57932	−0.248181
$209$	−0.756222	−0.0523090
$210$	17.5491	1.21100
$211$	−13.0469	−0.898183	−0.449091	−	0.893486i	$-0.648252\pi$
$211$	−13.0469	−0.898183	−0.449091	+	0.893486i	$0.648252\pi$
$212$	8.25436	0.566912
$213$	−11.5730	−0.792968
$214$	12.2482	0.837268
$215$	31.7376	2.16449
$216$	−1.00000	−0.0680414
$217$	−38.6838	−2.62603
$218$	16.4156	1.11180
$219$	15.4034	1.04086
$220$	0.709201	0.0478143
$221$	3.57932	0.240771
$222$	−9.05465	−0.607708
$223$	−3.72942	−0.249740	−0.124870	−	0.992173i	$-0.539851\pi$
$223$	−3.72942	−0.249740	−0.124870	+	0.992173i	$0.539851\pi$
$224$	−4.32251	−0.288810
$225$	11.4830	0.765536
$226$	10.7707	0.716458
$227$	−19.9745	−1.32575	−0.662877	−	0.748729i	$-0.730665\pi$
$227$	−19.9745	−1.32575	−0.662877	+	0.748729i	$0.730665\pi$
$228$	4.32911	0.286703
$229$	−18.9899	−1.25489	−0.627445	−	0.778661i	$-0.715899\pi$
$229$	−18.9899	−1.25489	−0.627445	+	0.778661i	$0.715899\pi$
$230$	−3.92217	−0.258620
$231$	−0.755069	−0.0496799
$232$	2.78244	0.182676
$233$	−28.4041	−1.86081	−0.930406	−	0.366530i	$-0.880546\pi$
$233$	−28.4041	−1.86081	−0.930406	+	0.366530i	$0.880546\pi$
$234$	3.57932	0.233988
$235$	44.6228	2.91087
$236$	1.00000	0.0650945
$237$	−10.6346	−0.690789
$238$	4.32251	0.280187
$239$	−8.49338	−0.549391	−0.274696	−	0.961531i	$-0.588577\pi$
$239$	−8.49338	−0.549391	−0.274696	+	0.961531i	$0.588577\pi$
$240$	−4.05993	−0.262067
$241$	12.2957	0.792038	0.396019	−	0.918242i	$-0.370391\pi$
$241$	12.2957	0.792038	0.396019	+	0.918242i	$0.370391\pi$
$242$	10.9695	0.705145
$243$	1.00000	0.0641500
$244$	−13.2963	−0.851208
$245$	−47.4366	−3.03062
$246$	1.49587	0.0953732
$247$	−15.4953	−0.985942
$248$	8.94938	0.568286
$249$	13.5213	0.856881
$250$	26.3207	1.66466
$251$	9.25024	0.583870	0.291935	−	0.956438i	$-0.405701\pi$
$251$	9.25024	0.583870	0.291935	+	0.956438i	$0.405701\pi$
$252$	4.32251	0.272293
$253$	0.168756	0.0106096
$254$	2.14110	0.134345
$255$	4.05993	0.254243
$256$	1.00000	0.0625000
$257$	−23.1257	−1.44254	−0.721270	−	0.692654i	$-0.756441\pi$
$257$	−23.1257	−1.44254	−0.721270	+	0.692654i	$0.756441\pi$
$258$	7.81727	0.486682
$259$	39.1388	2.43197
$260$	14.5318	0.901224
$261$	−2.78244	−0.172229
$262$	−13.7267	−0.848038
$263$	−16.1148	−0.993681	−0.496840	−	0.867842i	$-0.665507\pi$
$263$	−16.1148	−0.993681	−0.496840	+	0.867842i	$0.665507\pi$
$264$	0.174683	0.0107510
$265$	−33.5121	−2.05863
$266$	−18.7126	−1.14735
$267$	6.06380	0.371098
$268$	10.6386	0.649857
$269$	18.7529	1.14339	0.571693	−	0.820467i	$-0.306287\pi$
$269$	18.7529	1.14339	0.571693	+	0.820467i	$0.306287\pi$
$270$	4.05993	0.247079
$271$	−7.10047	−0.431323	−0.215661	−	0.976468i	$-0.569191\pi$
$271$	−7.10047	−0.431323	−0.215661	+	0.976468i	$0.569191\pi$
$272$	−1.00000	−0.0606339
$273$	−15.4717	−0.936388
$274$	−10.8186	−0.653576
$275$	−2.00589	−0.120960
$276$	−0.966068	−0.0581504
$277$	−9.73472	−0.584903	−0.292451	−	0.956280i	$-0.594471\pi$
$277$	−9.73472	−0.584903	−0.292451	+	0.956280i	$0.594471\pi$
$278$	3.78704	0.227131
$279$	−8.94938	−0.535786
$280$	17.5491	1.04876
$281$	−11.3620	−0.677799	−0.338899	−	0.940823i	$-0.610055\pi$
$281$	−11.3620	−0.677799	−0.338899	+	0.940823i	$0.610055\pi$
$282$	10.9910	0.654506
$283$	−2.28586	−0.135880	−0.0679402	−	0.997689i	$-0.521643\pi$
$283$	−2.28586	−0.135880	−0.0679402	+	0.997689i	$0.521643\pi$
$284$	−11.5730	−0.686730
$285$	−17.5759	−1.04111
$286$	−0.625247	−0.0369716
$287$	−6.46591	−0.381671
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	−11.2965	−0.663353
$291$	−12.2431	−0.717705
$292$	15.4034	0.901413
$293$	−11.8171	−0.690362	−0.345181	−	0.938536i	$-0.612182\pi$
$293$	−11.8171	−0.690362	−0.345181	+	0.938536i	$0.612182\pi$
$294$	−11.6841	−0.681431
$295$	−4.05993	−0.236378
$296$	−9.05465	−0.526291
$297$	−0.174683	−0.0101361
$298$	21.9080	1.26910
$299$	3.45787	0.199974
$300$	11.4830	0.662973
$301$	−33.7903	−1.94764
$302$	5.89511	0.339225
$303$	12.6064	0.724219
$304$	4.32911	0.248292
$305$	53.9821	3.09100
$306$	1.00000	0.0571662
$307$	−21.0755	−1.20284	−0.601422	−	0.798932i	$-0.705399\pi$
$307$	−21.0755	−1.20284	−0.601422	+	0.798932i	$0.705399\pi$
$308$	−0.755069	−0.0430240
$309$	5.09638	0.289923
$310$	−36.3339	−2.06363
$311$	2.89958	0.164420	0.0822101	−	0.996615i	$-0.473802\pi$
$311$	2.89958	0.164420	0.0822101	+	0.996615i	$0.473802\pi$
$312$	3.57932	0.202639
$313$	13.0246	0.736192	0.368096	−	0.929788i	$-0.380010\pi$
$313$	13.0246	0.736192	0.368096	+	0.929788i	$0.380010\pi$
$314$	−2.64550	−0.149294
$315$	−17.5491	−0.988779
$316$	−10.6346	−0.598241
$317$	8.38129	0.470740	0.235370	−	0.971906i	$-0.424370\pi$
$317$	8.38129	0.470740	0.235370	+	0.971906i	$0.424370\pi$
$318$	−8.25436	−0.462881
$319$	0.486044	0.0272133
$320$	−4.05993	−0.226957
$321$	−12.2482	−0.683626
$322$	4.17584	0.232710
$323$	−4.32911	−0.240878
$324$	1.00000	0.0555556
$325$	−41.1015	−2.27990
$326$	7.83285	0.433821
$327$	−16.4156	−0.907784
$328$	1.49587	0.0825956
$329$	−47.5088	−2.61924
$330$	−0.709201	−0.0390402
$331$	17.9828	0.988427	0.494213	−	0.869341i	$-0.335456\pi$
$331$	17.9828	0.988427	0.494213	+	0.869341i	$0.335456\pi$
$332$	13.5213	0.742080
$333$	9.05465	0.496192
$334$	11.8583	0.648857
$335$	−43.1920	−2.35983
$336$	4.32251	0.235812
$337$	−2.98634	−0.162676	−0.0813382	−	0.996687i	$-0.525919\pi$
$337$	−2.98634	−0.162676	−0.0813382	+	0.996687i	$0.525919\pi$
$338$	0.188447	0.0102501
$339$	−10.7707	−0.584986
$340$	4.05993	0.220181
$341$	1.56330	0.0846577
$342$	−4.32911	−0.234092
$343$	20.2471	1.09324
$344$	7.81727	0.421479
$345$	3.92217	0.211162
$346$	5.47185	0.294168
$347$	−0.244347	−0.0131172	−0.00655861	−	0.999978i	$-0.502088\pi$
$347$	−0.244347	−0.0131172	−0.00655861	+	0.999978i	$0.502088\pi$
$348$	−2.78244	−0.149154
$349$	−21.9939	−1.17731	−0.588654	−	0.808385i	$-0.700342\pi$
$349$	−21.9939	−1.17731	−0.588654	+	0.808385i	$0.700342\pi$
$350$	−49.6355	−2.65313
$351$	−3.57932	−0.191050
$352$	0.174683	0.00931063
$353$	−31.3154	−1.66675	−0.833375	−	0.552708i	$-0.813595\pi$
$353$	−31.3154	−1.66675	−0.833375	+	0.552708i	$0.813595\pi$
$354$	−1.00000	−0.0531494
$355$	46.9855	2.49373
$356$	6.06380	0.321381
$357$	−4.32251	−0.228772
$358$	−21.4193	−1.13204
$359$	12.1113	0.639213	0.319606	−	0.947550i	$-0.396449\pi$
$359$	12.1113	0.639213	0.319606	+	0.947550i	$0.396449\pi$
$360$	4.05993	0.213977
$361$	−0.258768	−0.0136194
$362$	−21.9957	−1.15607
$363$	−10.9695	−0.575749
$364$	−15.4717	−0.810936
$365$	−62.5366	−3.27331
$366$	13.2963	0.695009
$367$	−16.1209	−0.841505	−0.420752	−	0.907176i	$-0.638234\pi$
$367$	−16.1209	−0.841505	−0.420752	+	0.907176i	$0.638234\pi$
$368$	−0.966068	−0.0503598
$369$	−1.49587	−0.0778719
$370$	36.7613	1.91113
$371$	35.6795	1.85239
$372$	−8.94938	−0.464004
$373$	14.4822	0.749859	0.374930	−	0.927053i	$-0.377667\pi$
$373$	14.4822	0.749859	0.374930	+	0.927053i	$0.377667\pi$
$374$	−0.174683	−0.00903264
$375$	−26.3207	−1.35919
$376$	10.9910	0.566819
$377$	9.95924	0.512927
$378$	−4.32251	−0.222326
$379$	−29.1541	−1.49755	−0.748773	−	0.662827i	$-0.769357\pi$
$379$	−29.1541	−1.49755	−0.748773	+	0.662827i	$0.769357\pi$
$380$	−17.5759	−0.901625
$381$	−2.14110	−0.109692
$382$	7.81869	0.400039
$383$	−4.49641	−0.229756	−0.114878	−	0.993380i	$-0.536648\pi$
$383$	−4.49641	−0.229756	−0.114878	+	0.993380i	$0.536648\pi$
$384$	−1.00000	−0.0510310
$385$	3.06553	0.156234
$386$	−2.50888	−0.127698
$387$	−7.81727	−0.397374
$388$	−12.2431	−0.621551
$389$	15.4343	0.782552	0.391276	−	0.920273i	$-0.372034\pi$
$389$	15.4343	0.782552	0.391276	+	0.920273i	$0.372034\pi$
$390$	−14.5318	−0.735846
$391$	0.966068	0.0488561
$392$	−11.6841	−0.590136
$393$	13.7267	0.692420
$394$	−18.4106	−0.927515
$395$	43.1756	2.17240
$396$	−0.174683	−0.00877815
$397$	−6.00696	−0.301481	−0.150740	−	0.988573i	$-0.548166\pi$
$397$	−6.00696	−0.301481	−0.150740	+	0.988573i	$0.548166\pi$
$398$	−6.35539	−0.318567
$399$	18.7126	0.936804
$400$	11.4830	0.574152
$401$	−12.5444	−0.626435	−0.313218	−	0.949681i	$-0.601407\pi$
$401$	−12.5444	−0.626435	−0.313218	+	0.949681i	$0.601407\pi$
$402$	−10.6386	−0.530606
$403$	32.0327	1.59566
$404$	12.6064	0.627192
$405$	−4.05993	−0.201740
$406$	12.0271	0.596896
$407$	−1.58169	−0.0784016
$408$	1.00000	0.0495074
$409$	−13.1148	−0.648487	−0.324244	−	0.945974i	$-0.605110\pi$
$409$	−13.1148	−0.648487	−0.324244	+	0.945974i	$0.605110\pi$
$410$	−6.07313	−0.299930
$411$	10.8186	0.533642
$412$	5.09638	0.251080
$413$	4.32251	0.212697
$414$	0.966068	0.0474796
$415$	−54.8957	−2.69473
$416$	3.57932	0.175491
$417$	−3.78704	−0.185452
$418$	0.756222	0.0369880
$419$	−9.76811	−0.477203	−0.238602	−	0.971118i	$-0.576689\pi$
$419$	−9.76811	−0.477203	−0.238602	+	0.971118i	$0.576689\pi$
$420$	−17.5491	−0.856308
$421$	−24.1206	−1.17556	−0.587782	−	0.809019i	$-0.699999\pi$
$421$	−24.1206	−1.17556	−0.587782	+	0.809019i	$0.699999\pi$
$422$	13.0469	0.635111
$423$	−10.9910	−0.534402
$424$	−8.25436	−0.400867
$425$	−11.4830	−0.557009
$426$	11.5730	0.560713
$427$	−57.4734	−2.78133
$428$	−12.2482	−0.592038
$429$	0.625247	0.0301872
$430$	−31.7376	−1.53052
$431$	−37.0961	−1.78686	−0.893429	−	0.449204i	$-0.851708\pi$
$431$	−37.0961	−1.78686	−0.893429	+	0.449204i	$0.851708\pi$
$432$	1.00000	0.0481125
$433$	17.3365	0.833137	0.416569	−	0.909104i	$-0.363233\pi$
$433$	17.3365	0.833137	0.416569	+	0.909104i	$0.363233\pi$
$434$	38.6838	1.85688
$435$	11.2965	0.541626
$436$	−16.4156	−0.786164
$437$	−4.18222	−0.200063
$438$	−15.4034	−0.736001
$439$	12.8971	0.615544	0.307772	−	0.951460i	$-0.400417\pi$
$439$	12.8971	0.615544	0.307772	+	0.951460i	$0.400417\pi$
$440$	−0.709201	−0.0338098
$441$	11.6841	0.556386
$442$	−3.57932	−0.170251
$443$	−1.74694	−0.0829998	−0.0414999	−	0.999139i	$-0.513214\pi$
$443$	−1.74694	−0.0829998	−0.0414999	+	0.999139i	$0.513214\pi$
$444$	9.05465	0.429715
$445$	−24.6186	−1.16703
$446$	3.72942	0.176593
$447$	−21.9080	−1.03621
$448$	4.32251	0.204219
$449$	34.4503	1.62581	0.812905	−	0.582397i	$-0.197885\pi$
$449$	34.4503	1.62581	0.812905	+	0.582397i	$0.197885\pi$
$450$	−11.4830	−0.541315
$451$	0.261303	0.0123043
$452$	−10.7707	−0.506613
$453$	−5.89511	−0.276976
$454$	19.9745	0.937449
$455$	62.8139	2.94476
$456$	−4.32911	−0.202729
$457$	−29.6667	−1.38775	−0.693874	−	0.720096i	$-0.744098\pi$
$457$	−29.6667	−1.38775	−0.693874	+	0.720096i	$0.744098\pi$
$458$	18.9899	0.887341
$459$	−1.00000	−0.0466760
$460$	3.92217	0.182872
$461$	12.1391	0.565373	0.282686	−	0.959212i	$-0.408774\pi$
$461$	12.1391	0.565373	0.282686	+	0.959212i	$0.408774\pi$
$462$	0.755069	0.0351290
$463$	−8.82748	−0.410248	−0.205124	−	0.978736i	$-0.565760\pi$
$463$	−8.82748	−0.410248	−0.205124	+	0.978736i	$0.565760\pi$
$464$	−2.78244	−0.129171
$465$	36.3339	1.68494
$466$	28.4041	1.31579
$467$	−5.50907	−0.254929	−0.127465	−	0.991843i	$-0.540684\pi$
$467$	−5.50907	−0.254929	−0.127465	+	0.991843i	$0.540684\pi$
$468$	−3.57932	−0.165454
$469$	45.9855	2.12341
$470$	−44.6228	−2.05829
$471$	2.64550	0.121898
$472$	−1.00000	−0.0460287
$473$	1.36554	0.0627878
$474$	10.6346	0.488462
$475$	49.7114	2.28091
$476$	−4.32251	−0.198122
$477$	8.25436	0.377941
$478$	8.49338	0.388478
$479$	36.9263	1.68721	0.843603	−	0.536967i	$-0.180430\pi$
$479$	36.9263	1.68721	0.843603	+	0.536967i	$0.180430\pi$
$480$	4.05993	0.185310
$481$	−32.4095	−1.47775
$482$	−12.2957	−0.560055
$483$	−4.17584	−0.190007
$484$	−10.9695	−0.498613
$485$	49.7062	2.25704
$486$	−1.00000	−0.0453609
$487$	−2.28081	−0.103353	−0.0516766	−	0.998664i	$-0.516457\pi$
$487$	−2.28081	−0.103353	−0.0516766	+	0.998664i	$0.516457\pi$
$488$	13.2963	0.601895
$489$	−7.83285	−0.354214
$490$	47.4366	2.14297
$491$	−31.6406	−1.42792	−0.713959	−	0.700187i	$-0.753100\pi$
$491$	−31.6406	−1.42792	−0.713959	+	0.700187i	$0.753100\pi$
$492$	−1.49587	−0.0674390
$493$	2.78244	0.125315
$494$	15.4953	0.697166
$495$	0.709201	0.0318762
$496$	−8.94938	−0.401839
$497$	−50.0244	−2.24390
$498$	−13.5213	−0.605906
$499$	−23.7710	−1.06414	−0.532068	−	0.846701i	$-0.678585\pi$
$499$	−23.7710	−1.06414	−0.532068	+	0.846701i	$0.678585\pi$
$500$	−26.3207	−1.17710
$501$	−11.8583	−0.529790
$502$	−9.25024	−0.412859
$503$	13.4171	0.598240	0.299120	−	0.954216i	$-0.403307\pi$
$503$	13.4171	0.598240	0.299120	+	0.954216i	$0.403307\pi$
$504$	−4.32251	−0.192540
$505$	−51.1811	−2.27753
$506$	−0.168756	−0.00750210
$507$	−0.188447	−0.00836921
$508$	−2.14110	−0.0949959
$509$	30.4803	1.35101	0.675507	−	0.737354i	$-0.263925\pi$
$509$	30.4803	1.35101	0.675507	+	0.737354i	$0.263925\pi$
$510$	−4.05993	−0.179777
$511$	66.5812	2.94538
$512$	−1.00000	−0.0441942
$513$	4.32911	0.191135
$514$	23.1257	1.02003
$515$	−20.6909	−0.911751
$516$	−7.81727	−0.344136
$517$	1.91994	0.0844390
$518$	−39.1388	−1.71966
$519$	−5.47185	−0.240188
$520$	−14.5318	−0.637262
$521$	6.64178	0.290982	0.145491	−	0.989360i	$-0.453524\pi$
$521$	6.64178	0.290982	0.145491	+	0.989360i	$0.453524\pi$
$522$	2.78244	0.121784
$523$	44.3127	1.93766	0.968829	−	0.247732i	$-0.0796853\pi$
$523$	44.3127	1.93766	0.968829	+	0.247732i	$0.0796853\pi$
$524$	13.7267	0.599653
$525$	49.6355	2.16627
$526$	16.1148	0.702638
$527$	8.94938	0.389841
$528$	−0.174683	−0.00760210
$529$	−22.0667	−0.959422
$530$	33.5121	1.45567
$531$	1.00000	0.0433963
$532$	18.7126	0.811296
$533$	5.35420	0.231916
$534$	−6.06380	−0.262406
$535$	49.7267	2.14987
$536$	−10.6386	−0.459518
$537$	21.4193	0.924310
$538$	−18.7529	−0.808497
$539$	−2.04101	−0.0879127
$540$	−4.05993	−0.174712
$541$	−12.3021	−0.528908	−0.264454	−	0.964398i	$-0.585192\pi$
$541$	−12.3021	−0.528908	−0.264454	+	0.964398i	$0.585192\pi$
$542$	7.10047	0.304991
$543$	21.9957	0.943926
$544$	1.00000	0.0428746
$545$	66.6461	2.85481
$546$	15.4717	0.662126
$547$	−27.4914	−1.17545	−0.587723	−	0.809062i	$-0.699975\pi$
$547$	−27.4914	−1.17545	−0.587723	+	0.809062i	$0.699975\pi$
$548$	10.8186	0.462148
$549$	−13.2963	−0.567472
$550$	2.00589	0.0855314
$551$	−12.0455	−0.513155
$552$	0.966068	0.0411186
$553$	−45.9680	−1.95476
$554$	9.73472	0.413589
$555$	−36.7613	−1.56043
$556$	−3.78704	−0.160606
$557$	4.85946	0.205902	0.102951	−	0.994686i	$-0.467172\pi$
$557$	4.85946	0.205902	0.102951	+	0.994686i	$0.467172\pi$
$558$	8.94938	0.378858
$559$	27.9805	1.18345
$560$	−17.5491	−0.741585
$561$	0.174683	0.00737512
$562$	11.3620	0.479276
$563$	−4.05063	−0.170714	−0.0853568	−	0.996350i	$-0.527203\pi$
$563$	−4.05063	−0.170714	−0.0853568	+	0.996350i	$0.527203\pi$
$564$	−10.9910	−0.462805
$565$	43.7284	1.83967
$566$	2.28586	0.0960819
$567$	4.32251	0.181528
$568$	11.5730	0.485592
$569$	−34.7391	−1.45634	−0.728168	−	0.685398i	$-0.759628\pi$
$569$	−34.7391	−1.45634	−0.728168	+	0.685398i	$0.759628\pi$
$570$	17.5759	0.736174
$571$	−18.6043	−0.778565	−0.389283	−	0.921118i	$-0.627277\pi$
$571$	−18.6043	−0.778565	−0.389283	+	0.921118i	$0.627277\pi$
$572$	0.625247	0.0261429
$573$	−7.81869	−0.326630
$574$	6.46591	0.269882
$575$	−11.0934	−0.462626
$576$	1.00000	0.0416667
$577$	−8.88899	−0.370054	−0.185027	−	0.982733i	$-0.559237\pi$
$577$	−8.88899	−0.370054	−0.185027	+	0.982733i	$0.559237\pi$
$578$	−1.00000	−0.0415945
$579$	2.50888	0.104265
$580$	11.2965	0.469062
$581$	58.4462	2.42476
$582$	12.2431	0.507494
$583$	−1.44190	−0.0597172
$584$	−15.4034	−0.637396
$585$	14.5318	0.600816
$586$	11.8171	0.488160
$587$	−15.6963	−0.647854	−0.323927	−	0.946082i	$-0.605003\pi$
$587$	−15.6963	−0.647854	−0.323927	+	0.946082i	$0.605003\pi$
$588$	11.6841	0.481844
$589$	−38.7429	−1.59637
$590$	4.05993	0.167145
$591$	18.4106	0.757313
$592$	9.05465	0.372144
$593$	2.75499	0.113134	0.0565668	−	0.998399i	$-0.481985\pi$
$593$	2.75499	0.113134	0.0565668	+	0.998399i	$0.481985\pi$
$594$	0.174683	0.00716733
$595$	17.5491	0.719443
$596$	−21.9080	−0.897388
$597$	6.35539	0.260109
$598$	−3.45787	−0.141403
$599$	−34.9824	−1.42934	−0.714671	−	0.699461i	$-0.753423\pi$
$599$	−34.9824	−1.42934	−0.714671	+	0.699461i	$0.753423\pi$
$600$	−11.4830	−0.468793
$601$	−33.4111	−1.36287	−0.681434	−	0.731879i	$-0.738643\pi$
$601$	−33.4111	−1.36287	−0.681434	+	0.731879i	$0.738643\pi$
$602$	33.7903	1.37719
$603$	10.6386	0.433238
$604$	−5.89511	−0.239869
$605$	44.5353	1.81062
$606$	−12.6064	−0.512100
$607$	40.1724	1.63055	0.815274	−	0.579076i	$-0.196586\pi$
$607$	40.1724	1.63055	0.815274	+	0.579076i	$0.196586\pi$
$608$	−4.32911	−0.175569
$609$	−12.0271	−0.487363
$610$	−53.9821	−2.18567
$611$	39.3404	1.59154
$612$	−1.00000	−0.0404226
$613$	27.2179	1.09932	0.549661	−	0.835388i	$-0.314757\pi$
$613$	27.2179	1.09932	0.549661	+	0.835388i	$0.314757\pi$
$614$	21.0755	0.850539
$615$	6.07313	0.244892
$616$	0.755069	0.0304226
$617$	5.10001	0.205319	0.102659	−	0.994717i	$-0.467265\pi$
$617$	5.10001	0.205319	0.102659	+	0.994717i	$0.467265\pi$
$618$	−5.09638	−0.205006
$619$	−47.9346	−1.92665	−0.963327	−	0.268331i	$-0.913528\pi$
$619$	−47.9346	−1.92665	−0.963327	+	0.268331i	$0.913528\pi$
$620$	36.3339	1.45920
$621$	−0.966068	−0.0387670
$622$	−2.89958	−0.116263
$623$	26.2108	1.05011
$624$	−3.57932	−0.143288
$625$	49.4449	1.97780
$626$	−13.0246	−0.520567
$627$	−0.756222	−0.0302006
$628$	2.64550	0.105567
$629$	−9.05465	−0.361033
$630$	17.5491	0.699173
$631$	−14.0892	−0.560880	−0.280440	−	0.959871i	$-0.590480\pi$
$631$	−14.0892	−0.560880	−0.280440	+	0.959871i	$0.590480\pi$
$632$	10.6346	0.423020
$633$	−13.0469	−0.518566
$634$	−8.38129	−0.332864
$635$	8.69271	0.344960
$636$	8.25436	0.327307
$637$	−41.8212	−1.65702
$638$	−0.486044	−0.0192427
$639$	−11.5730	−0.457820
$640$	4.05993	0.160483
$641$	34.5870	1.36611	0.683053	−	0.730369i	$-0.260652\pi$
$641$	34.5870	1.36611	0.683053	+	0.730369i	$0.260652\pi$
$642$	12.2482	0.483397
$643$	42.9143	1.69238	0.846188	−	0.532884i	$-0.178892\pi$
$643$	42.9143	1.69238	0.846188	+	0.532884i	$0.178892\pi$
$644$	−4.17584	−0.164551
$645$	31.7376	1.24967
$646$	4.32911	0.170327
$647$	11.6391	0.457578	0.228789	−	0.973476i	$-0.426523\pi$
$647$	11.6391	0.457578	0.228789	+	0.973476i	$0.426523\pi$
$648$	−1.00000	−0.0392837
$649$	−0.174683	−0.00685691
$650$	41.1015	1.61213
$651$	−38.6838	−1.51614
$652$	−7.83285	−0.306758
$653$	−20.8139	−0.814511	−0.407256	−	0.913314i	$-0.633514\pi$
$653$	−20.8139	−0.814511	−0.407256	+	0.913314i	$0.633514\pi$
$654$	16.4156	0.641900
$655$	−55.7294	−2.17753
$656$	−1.49587	−0.0584039
$657$	15.4034	0.600942
$658$	47.5088	1.85209
$659$	−29.1730	−1.13642	−0.568209	−	0.822884i	$-0.692364\pi$
$659$	−29.1730	−1.13642	−0.568209	+	0.822884i	$0.692364\pi$
$660$	0.709201	0.0276056
$661$	47.5780	1.85057	0.925286	−	0.379271i	$-0.123825\pi$
$661$	47.5780	1.85057	0.925286	+	0.379271i	$0.123825\pi$
$662$	−17.9828	−0.698923
$663$	3.57932	0.139009
$664$	−13.5213	−0.524730
$665$	−75.9720	−2.94607
$666$	−9.05465	−0.350861
$667$	2.68802	0.104081
$668$	−11.8583	−0.458811
$669$	−3.72942	−0.144188
$670$	43.1920	1.66865
$671$	2.32264	0.0896644
$672$	−4.32251	−0.166744
$673$	30.4302	1.17300	0.586499	−	0.809950i	$-0.300506\pi$
$673$	30.4302	1.17300	0.586499	+	0.809950i	$0.300506\pi$
$674$	2.98634	0.115030
$675$	11.4830	0.441982
$676$	−0.188447	−0.00724794
$677$	−37.7621	−1.45131	−0.725657	−	0.688056i	$-0.758464\pi$
$677$	−37.7621	−1.45131	−0.725657	+	0.688056i	$0.758464\pi$
$678$	10.7707	0.413647
$679$	−52.9211	−2.03092
$680$	−4.05993	−0.155691
$681$	−19.9745	−0.765424
$682$	−1.56330	−0.0598620
$683$	8.07878	0.309126	0.154563	−	0.987983i	$-0.450603\pi$
$683$	8.07878	0.309126	0.154563	+	0.987983i	$0.450603\pi$
$684$	4.32911	0.165528
$685$	−43.9228	−1.67820
$686$	−20.2471	−0.773037
$687$	−18.9899	−0.724511
$688$	−7.81727	−0.298031
$689$	−29.5450	−1.12558
$690$	−3.92217	−0.149314
$691$	11.6530	0.443300	0.221650	−	0.975126i	$-0.428856\pi$
$691$	11.6530	0.443300	0.221650	+	0.975126i	$0.428856\pi$
$692$	−5.47185	−0.208008
$693$	−0.755069	−0.0286827
$694$	0.244347	0.00927527
$695$	15.3751	0.583211
$696$	2.78244	0.105468
$697$	1.49587	0.0566601
$698$	21.9939	0.832483
$699$	−28.4041	−1.07434
$700$	49.6355	1.87605
$701$	5.88109	0.222126	0.111063	−	0.993813i	$-0.464574\pi$
$701$	5.88109	0.222126	0.111063	+	0.993813i	$0.464574\pi$
$702$	3.57932	0.135093
$703$	39.1986	1.47840
$704$	−0.174683	−0.00658361
$705$	44.6228	1.68059
$706$	31.3154	1.17857
$707$	54.4913	2.04936
$708$	1.00000	0.0375823
$709$	−19.6916	−0.739535	−0.369768	−	0.929124i	$-0.620563\pi$
$709$	−19.6916	−0.739535	−0.369768	+	0.929124i	$0.620563\pi$
$710$	−46.9855	−1.76334
$711$	−10.6346	−0.398827
$712$	−6.06380	−0.227250
$713$	8.64571	0.323784
$714$	4.32251	0.161766
$715$	−2.53846	−0.0949329
$716$	21.4193	0.800476
$717$	−8.49338	−0.317191
$718$	−12.1113	−0.451992
$719$	−35.7611	−1.33366	−0.666832	−	0.745208i	$-0.732350\pi$
$719$	−35.7611	−1.33366	−0.666832	+	0.745208i	$0.732350\pi$
$720$	−4.05993	−0.151305
$721$	22.0291	0.820408
$722$	0.258768	0.00963034
$723$	12.2957	0.457283
$724$	21.9957	0.817464
$725$	−31.9508	−1.18662
$726$	10.9695	0.407116
$727$	−21.5900	−0.800728	−0.400364	−	0.916356i	$-0.631116\pi$
$727$	−21.5900	−0.800728	−0.400364	+	0.916356i	$0.631116\pi$
$728$	15.4717	0.573418
$729$	1.00000	0.0370370
$730$	62.5366	2.31458
$731$	7.81727	0.289132
$732$	−13.2963	−0.491445
$733$	−8.04904	−0.297298	−0.148649	−	0.988890i	$-0.547492\pi$
$733$	−8.04904	−0.297298	−0.148649	+	0.988890i	$0.547492\pi$
$734$	16.1209	0.595034
$735$	−47.4366	−1.74973
$736$	0.966068	0.0356097
$737$	−1.85838	−0.0684545
$738$	1.49587	0.0550637
$739$	9.69286	0.356558	0.178279	−	0.983980i	$-0.442947\pi$
$739$	9.69286	0.356558	0.178279	+	0.983980i	$0.442947\pi$
$740$	−36.7613	−1.35137
$741$	−15.4953	−0.569234
$742$	−35.6795	−1.30984
$743$	1.09730	0.0402560	0.0201280	−	0.999797i	$-0.493593\pi$
$743$	1.09730	0.0402560	0.0201280	+	0.999797i	$0.493593\pi$
$744$	8.94938	0.328100
$745$	88.9451	3.25870
$746$	−14.4822	−0.530231
$747$	13.5213	0.494720
$748$	0.174683	0.00638704
$749$	−52.9428	−1.93449
$750$	26.3207	0.961095
$751$	−50.7608	−1.85229	−0.926144	−	0.377170i	$-0.876897\pi$
$751$	−50.7608	−1.85229	−0.926144	+	0.377170i	$0.876897\pi$
$752$	−10.9910	−0.400801
$753$	9.25024	0.337098
$754$	−9.95924	−0.362694
$755$	23.9337	0.871037
$756$	4.32251	0.157208
$757$	−33.1847	−1.20612	−0.603058	−	0.797697i	$-0.706051\pi$
$757$	−33.1847	−1.20612	−0.603058	+	0.797697i	$0.706051\pi$
$758$	29.1541	1.05892
$759$	0.168756	0.00612544
$760$	17.5759	0.637545
$761$	−26.2199	−0.950472	−0.475236	−	0.879858i	$-0.657637\pi$
$761$	−26.2199	−0.950472	−0.475236	+	0.879858i	$0.657637\pi$
$762$	2.14110	0.0775638
$763$	−70.9565	−2.56880
$764$	−7.81869	−0.282870
$765$	4.05993	0.146787
$766$	4.49641	0.162462
$767$	−3.57932	−0.129242
$768$	1.00000	0.0360844
$769$	21.1662	0.763272	0.381636	−	0.924313i	$-0.375361\pi$
$769$	21.1662	0.763272	0.381636	+	0.924313i	$0.375361\pi$
$770$	−3.06553	−0.110474
$771$	−23.1257	−0.832851
$772$	2.50888	0.0902964
$773$	5.77405	0.207678	0.103839	−	0.994594i	$-0.466887\pi$
$773$	5.77405	0.207678	0.103839	+	0.994594i	$0.466887\pi$
$774$	7.81727	0.280986
$775$	−102.766	−3.69147
$776$	12.2431	0.439503
$777$	39.1388	1.40410
$778$	−15.4343	−0.553348
$779$	−6.47579	−0.232019
$780$	14.5318	0.520322
$781$	2.02160	0.0723387
$782$	−0.966068	−0.0345465
$783$	−2.78244	−0.0994362
$784$	11.6841	0.417289
$785$	−10.7405	−0.383346
$786$	−13.7267	−0.489615
$787$	−6.03223	−0.215026	−0.107513	−	0.994204i	$-0.534289\pi$
$787$	−6.03223	−0.215026	−0.107513	+	0.994204i	$0.534289\pi$
$788$	18.4106	0.655852
$789$	−16.1148	−0.573702
$790$	−43.1756	−1.53612
$791$	−46.5566	−1.65536
$792$	0.174683	0.00620709
$793$	47.5918	1.69003
$794$	6.00696	0.213179
$795$	−33.5121	−1.18855
$796$	6.35539	0.225261
$797$	43.2926	1.53350	0.766751	−	0.641944i	$-0.221872\pi$
$797$	43.2926	1.53350	0.766751	+	0.641944i	$0.221872\pi$
$798$	−18.7126	−0.662420
$799$	10.9910	0.388834
$800$	−11.4830	−0.405987
$801$	6.06380	0.214254
$802$	12.5444	0.442957
$803$	−2.69070	−0.0949529
$804$	10.6386	0.375195
$805$	16.9536	0.597536
$806$	−32.0327	−1.12830
$807$	18.7529	0.660135
$808$	−12.6064	−0.443492
$809$	19.3752	0.681196	0.340598	−	0.940209i	$-0.389371\pi$
$809$	19.3752	0.681196	0.340598	+	0.940209i	$0.389371\pi$
$810$	4.05993	0.142651
$811$	−0.993961	−0.0349027	−0.0174513	−	0.999848i	$-0.505555\pi$
$811$	−0.993961	−0.0349027	−0.0174513	+	0.999848i	$0.505555\pi$
$812$	−12.0271	−0.422069
$813$	−7.10047	−0.249024
$814$	1.58169	0.0554383
$815$	31.8008	1.11393
$816$	−1.00000	−0.0350070
$817$	−33.8419	−1.18398
$818$	13.1148	0.458550
$819$	−15.4717	−0.540624
$820$	6.07313	0.212083
$821$	47.2114	1.64769	0.823845	−	0.566815i	$-0.191825\pi$
$821$	47.2114	1.64769	0.823845	+	0.566815i	$0.191825\pi$
$822$	−10.8186	−0.377342
$823$	−0.437840	−0.0152621	−0.00763107	−	0.999971i	$-0.502429\pi$
$823$	−0.437840	−0.0152621	−0.00763107	+	0.999971i	$0.502429\pi$
$824$	−5.09638	−0.177541
$825$	−2.00589	−0.0698361
$826$	−4.32251	−0.150399
$827$	13.0771	0.454734	0.227367	−	0.973809i	$-0.426988\pi$
$827$	13.0771	0.454734	0.227367	+	0.973809i	$0.426988\pi$
$828$	−0.966068	−0.0335732
$829$	19.7507	0.685971	0.342985	−	0.939341i	$-0.388562\pi$
$829$	19.7507	0.685971	0.342985	+	0.939341i	$0.388562\pi$
$830$	54.8957	1.90546
$831$	−9.73472	−0.337694
$832$	−3.57932	−0.124091
$833$	−11.6841	−0.404830
$834$	3.78704	0.131134
$835$	48.1439	1.66609
$836$	−0.756222	−0.0261545
$837$	−8.94938	−0.309336
$838$	9.76811	0.337434
$839$	5.25854	0.181545	0.0907724	−	0.995872i	$-0.471066\pi$
$839$	5.25854	0.181545	0.0907724	+	0.995872i	$0.471066\pi$
$840$	17.5491	0.605501
$841$	−21.2580	−0.733036
$842$	24.1206	0.831250
$843$	−11.3620	−0.391327
$844$	−13.0469	−0.449091
$845$	0.765080	0.0263195
$846$	10.9910	0.377879
$847$	−47.4157	−1.62922
$848$	8.25436	0.283456
$849$	−2.28586	−0.0784506
$850$	11.4830	0.393865
$851$	−8.74741	−0.299857
$852$	−11.5730	−0.396484
$853$	17.0886	0.585101	0.292551	−	0.956250i	$-0.405496\pi$
$853$	17.0886	0.585101	0.292551	+	0.956250i	$0.405496\pi$
$854$	57.4734	1.96670
$855$	−17.5759	−0.601083
$856$	12.2482	0.418634
$857$	−6.88810	−0.235293	−0.117647	−	0.993056i	$-0.537535\pi$
$857$	−6.88810	−0.235293	−0.117647	+	0.993056i	$0.537535\pi$
$858$	−0.625247	−0.0213456
$859$	21.2091	0.723645	0.361822	−	0.932247i	$-0.382155\pi$
$859$	21.2091	0.723645	0.361822	+	0.932247i	$0.382155\pi$
$860$	31.7376	1.08224
$861$	−6.46591	−0.220358
$862$	37.0961	1.26350
$863$	24.6734	0.839893	0.419947	−	0.907549i	$-0.362049\pi$
$863$	24.6734	0.839893	0.419947	+	0.907549i	$0.362049\pi$
$864$	−1.00000	−0.0340207
$865$	22.2153	0.755344
$866$	−17.3365	−0.589117
$867$	1.00000	0.0339618
$868$	−38.6838	−1.31301
$869$	1.85768	0.0630174
$870$	−11.2965	−0.382987
$871$	−38.0790	−1.29026
$872$	16.4156	0.555902
$873$	−12.2431	−0.414367
$874$	4.18222	0.141466
$875$	−113.771	−3.84617
$876$	15.4034	0.520431
$877$	−16.4095	−0.554109	−0.277054	−	0.960854i	$-0.589358\pi$
$877$	−16.4095	−0.554109	−0.277054	+	0.960854i	$0.589358\pi$
$878$	−12.8971	−0.435255
$879$	−11.8171	−0.398581
$880$	0.709201	0.0239071
$881$	29.4247	0.991344	0.495672	−	0.868510i	$-0.334922\pi$
$881$	29.4247	0.991344	0.495672	+	0.868510i	$0.334922\pi$
$882$	−11.6841	−0.393424
$883$	−9.91701	−0.333734	−0.166867	−	0.985979i	$-0.553365\pi$
$883$	−9.91701	−0.333734	−0.166867	+	0.985979i	$0.553365\pi$
$884$	3.57932	0.120386
$885$	−4.05993	−0.136473
$886$	1.74694	0.0586897
$887$	−9.92272	−0.333172	−0.166586	−	0.986027i	$-0.553274\pi$
$887$	−9.92272	−0.333172	−0.166586	+	0.986027i	$0.553274\pi$
$888$	−9.05465	−0.303854
$889$	−9.25493	−0.310400
$890$	24.6186	0.825217
$891$	−0.174683	−0.00585210
$892$	−3.72942	−0.124870
$893$	−47.5814	−1.59225
$894$	21.9080	0.732714
$895$	−86.9608	−2.90678
$896$	−4.32251	−0.144405
$897$	3.45787	0.115455
$898$	−34.4503	−1.14962
$899$	24.9011	0.830498
$900$	11.4830	0.382768
$901$	−8.25436	−0.274993
$902$	−0.261303	−0.00870044
$903$	−33.7903	−1.12447
$904$	10.7707	0.358229
$905$	−89.3010	−2.96847
$906$	5.89511	0.195852
$907$	37.0105	1.22891	0.614457	−	0.788950i	$-0.289375\pi$
$907$	37.0105	1.22891	0.614457	+	0.788950i	$0.289375\pi$
$908$	−19.9745	−0.662877
$909$	12.6064	0.418128
$910$	−62.8139	−2.08226
$911$	38.7884	1.28512	0.642559	−	0.766236i	$-0.277873\pi$
$911$	38.7884	1.28512	0.642559	+	0.766236i	$0.277873\pi$
$912$	4.32911	0.143351
$913$	−2.36195	−0.0781691
$914$	29.6667	0.981286
$915$	53.9821	1.78459
$916$	−18.9899	−0.627445
$917$	59.3338	1.95937
$918$	1.00000	0.0330049
$919$	−35.8518	−1.18264	−0.591321	−	0.806436i	$-0.701393\pi$
$919$	−35.8518	−1.18264	−0.591321	+	0.806436i	$0.701393\pi$
$920$	−3.92217	−0.129310
$921$	−21.0755	−0.694462
$922$	−12.1391	−0.399779
$923$	41.4235	1.36347
$924$	−0.755069	−0.0248399
$925$	103.975	3.41867
$926$	8.82748	0.290089
$927$	5.09638	0.167387
$928$	2.78244	0.0913380
$929$	29.3173	0.961871	0.480935	−	0.876756i	$-0.340297\pi$
$929$	29.3173	0.961871	0.480935	+	0.876756i	$0.340297\pi$
$930$	−36.3339	−1.19143
$931$	50.5818	1.65775
$932$	−28.4041	−0.930406
$933$	2.89958	0.0949280
$934$	5.50907	0.180262
$935$	−0.709201	−0.0231933
$936$	3.57932	0.116994
$937$	−6.99549	−0.228533	−0.114266	−	0.993450i	$-0.536452\pi$
$937$	−6.99549	−0.228533	−0.114266	+	0.993450i	$0.536452\pi$
$938$	−45.9855	−1.50148
$939$	13.0246	0.425041
$940$	44.6228	1.45543
$941$	−22.1704	−0.722733	−0.361367	−	0.932424i	$-0.617690\pi$
$941$	−22.1704	−0.722733	−0.361367	+	0.932424i	$0.617690\pi$
$942$	−2.64550	−0.0861950
$943$	1.44511	0.0470593
$944$	1.00000	0.0325472
$945$	−17.5491	−0.570872
$946$	−1.36554	−0.0443977
$947$	10.6628	0.346496	0.173248	−	0.984878i	$-0.444574\pi$
$947$	10.6628	0.346496	0.173248	+	0.984878i	$0.444574\pi$
$948$	−10.6346	−0.345395
$949$	−55.1336	−1.78971
$950$	−49.7114	−1.61285
$951$	8.38129	0.271782
$952$	4.32251	0.140093
$953$	−55.5462	−1.79932	−0.899659	−	0.436593i	$-0.856185\pi$
$953$	−55.5462	−1.79932	−0.899659	+	0.436593i	$0.856185\pi$
$954$	−8.25436	−0.267245
$955$	31.7433	1.02719
$956$	−8.49338	−0.274696
$957$	0.486044	0.0157116
$958$	−36.9263	−1.19304
$959$	46.7635	1.51007
$960$	−4.05993	−0.131034
$961$	49.0914	1.58360
$962$	32.4095	1.04492
$963$	−12.2482	−0.394692
$964$	12.2957	0.396019
$965$	−10.1859	−0.327894
$966$	4.17584	0.134355
$967$	0.737989	0.0237321	0.0118661	−	0.999930i	$-0.496223\pi$
$967$	0.737989	0.0237321	0.0118661	+	0.999930i	$0.496223\pi$
$968$	10.9695	0.352573
$969$	−4.32911	−0.139071
$970$	−49.7062	−1.59597
$971$	35.3988	1.13600	0.568001	−	0.823028i	$-0.307717\pi$
$971$	35.3988	1.13600	0.568001	+	0.823028i	$0.307717\pi$
$972$	1.00000	0.0320750
$973$	−16.3695	−0.524782
$974$	2.28081	0.0730818
$975$	−41.1015	−1.31630
$976$	−13.2963	−0.425604
$977$	44.1495	1.41247	0.706233	−	0.707979i	$-0.250393\pi$
$977$	44.1495	1.41247	0.706233	+	0.707979i	$0.250393\pi$
$978$	7.83285	0.250467
$979$	−1.05924	−0.0338535
$980$	−47.4366	−1.51531
$981$	−16.4156	−0.524109
$982$	31.6406	1.00969
$983$	37.1477	1.18483	0.592413	−	0.805634i	$-0.298175\pi$
$983$	37.1477	1.18483	0.592413	+	0.805634i	$0.298175\pi$
$984$	1.49587	0.0476866
$985$	−74.7459	−2.38160
$986$	−2.78244	−0.0886108
$987$	−47.5088	−1.51222
$988$	−15.4953	−0.492971
$989$	7.55202	0.240140
$990$	−0.709201	−0.0225399
$991$	−44.9443	−1.42770	−0.713852	−	0.700297i	$-0.753051\pi$
$991$	−44.9443	−1.42770	−0.713852	+	0.700297i	$0.753051\pi$
$992$	8.94938	0.284143
$993$	17.9828	0.570668
$994$	50.0244	1.58668
$995$	−25.8024	−0.817992
$996$	13.5213	0.428440
$997$	−31.0541	−0.983492	−0.491746	−	0.870739i	$-0.663641\pi$
$997$	−31.0541	−0.983492	−0.491746	+	0.870739i	$0.663641\pi$
$998$	23.7710	0.752458
$999$	9.05465	0.286476

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.y.1.1	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.y.1.1	✓	10	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -4.05993 q^{5} -1.00000 q^{6} +4.32251 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -4.05993 q^{5} -1.00000 q^{6} +4.32251 q^{7} -1.00000 q^{8} +1.00000 q^{9} +4.05993 q^{10} -0.174683 q^{11} +1.00000 q^{12} -3.57932 q^{13} -4.32251 q^{14} -4.05993 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} +4.32911 q^{19} -4.05993 q^{20} +4.32251 q^{21} +0.174683 q^{22} -0.966068 q^{23} -1.00000 q^{24} +11.4830 q^{25} +3.57932 q^{26} +1.00000 q^{27} +4.32251 q^{28} -2.78244 q^{29} +4.05993 q^{30} -8.94938 q^{31} -1.00000 q^{32} -0.174683 q^{33} +1.00000 q^{34} -17.5491 q^{35} +1.00000 q^{36} +9.05465 q^{37} -4.32911 q^{38} -3.57932 q^{39} +4.05993 q^{40} -1.49587 q^{41} -4.32251 q^{42} -7.81727 q^{43} -0.174683 q^{44} -4.05993 q^{45} +0.966068 q^{46} -10.9910 q^{47} +1.00000 q^{48} +11.6841 q^{49} -11.4830 q^{50} -1.00000 q^{51} -3.57932 q^{52} +8.25436 q^{53} -1.00000 q^{54} +0.709201 q^{55} -4.32251 q^{56} +4.32911 q^{57} +2.78244 q^{58} +1.00000 q^{59} -4.05993 q^{60} -13.2963 q^{61} +8.94938 q^{62} +4.32251 q^{63} +1.00000 q^{64} +14.5318 q^{65} +0.174683 q^{66} +10.6386 q^{67} -1.00000 q^{68} -0.966068 q^{69} +17.5491 q^{70} -11.5730 q^{71} -1.00000 q^{72} +15.4034 q^{73} -9.05465 q^{74} +11.4830 q^{75} +4.32911 q^{76} -0.755069 q^{77} +3.57932 q^{78} -10.6346 q^{79} -4.05993 q^{80} +1.00000 q^{81} +1.49587 q^{82} +13.5213 q^{83} +4.32251 q^{84} +4.05993 q^{85} +7.81727 q^{86} -2.78244 q^{87} +0.174683 q^{88} +6.06380 q^{89} +4.05993 q^{90} -15.4717 q^{91} -0.966068 q^{92} -8.94938 q^{93} +10.9910 q^{94} -17.5759 q^{95} -1.00000 q^{96} -12.2431 q^{97} -11.6841 q^{98} -0.174683 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{2} + 10 q^{3} + 10 q^{4} - 2 q^{5} - 10 q^{6} - 6 q^{7} - 10 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q - 10 * q^2 + 10 * q^3 + 10 * q^4 - 2 * q^5 - 10 * q^6 - 6 * q^7 - 10 * q^8 + 10 * q^9	\( 10 q - 10 q^{2} + 10 q^{3} + 10 q^{4} - 2 q^{5} - 10 q^{6} - 6 q^{7} - 10 q^{8} + 10 q^{9} + 2 q^{10} - 3 q^{11} + 10 q^{12} - 10 q^{13} + 6 q^{14} - 2 q^{15} + 10 q^{16} - 10 q^{17} - 10 q^{18} + 8 q^{19} - 2 q^{20} - 6 q^{21} + 3 q^{22} - 9 q^{23} - 10 q^{24} + 20 q^{25} + 10 q^{26} + 10 q^{27} - 6 q^{28} - 24 q^{29} + 2 q^{30} - 7 q^{31} - 10 q^{32} - 3 q^{33} + 10 q^{34} - 22 q^{35} + 10 q^{36} - 4 q^{37} - 8 q^{38} - 10 q^{39} + 2 q^{40} - 9 q^{41} + 6 q^{42} - 11 q^{43} - 3 q^{44} - 2 q^{45} + 9 q^{46} - 18 q^{47} + 10 q^{48} + 6 q^{49} - 20 q^{50} - 10 q^{51} - 10 q^{52} - 9 q^{53} - 10 q^{54} + q^{55} + 6 q^{56} + 8 q^{57} + 24 q^{58} + 10 q^{59} - 2 q^{60} - 25 q^{61} + 7 q^{62} - 6 q^{63} + 10 q^{64} - 28 q^{65} + 3 q^{66} + 2 q^{67} - 10 q^{68} - 9 q^{69} + 22 q^{70} - 30 q^{71} - 10 q^{72} - 11 q^{73} + 4 q^{74} + 20 q^{75} + 8 q^{76} + 4 q^{77} + 10 q^{78} + 3 q^{79} - 2 q^{80} + 10 q^{81} + 9 q^{82} - q^{83} - 6 q^{84} + 2 q^{85} + 11 q^{86} - 24 q^{87} + 3 q^{88} - 14 q^{89} + 2 q^{90} - 13 q^{91} - 9 q^{92} - 7 q^{93} + 18 q^{94} - 35 q^{95} - 10 q^{96} - 10 q^{97} - 6 q^{98} - 3 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 + 10 * q^3 + 10 * q^4 - 2 * q^5 - 10 * q^6 - 6 * q^7 - 10 * q^8 + 10 * q^9 + 2 * q^10 - 3 * q^11 + 10 * q^12 - 10 * q^13 + 6 * q^14 - 2 * q^15 + 10 * q^16 - 10 * q^17 - 10 * q^18 + 8 * q^19 - 2 * q^20 - 6 * q^21 + 3 * q^22 - 9 * q^23 - 10 * q^24 + 20 * q^25 + 10 * q^26 + 10 * q^27 - 6 * q^28 - 24 * q^29 + 2 * q^30 - 7 * q^31 - 10 * q^32 - 3 * q^33 + 10 * q^34 - 22 * q^35 + 10 * q^36 - 4 * q^37 - 8 * q^38 - 10 * q^39 + 2 * q^40 - 9 * q^41 + 6 * q^42 - 11 * q^43 - 3 * q^44 - 2 * q^45 + 9 * q^46 - 18 * q^47 + 10 * q^48 + 6 * q^49 - 20 * q^50 - 10 * q^51 - 10 * q^52 - 9 * q^53 - 10 * q^54 + q^55 + 6 * q^56 + 8 * q^57 + 24 * q^58 + 10 * q^59 - 2 * q^60 - 25 * q^61 + 7 * q^62 - 6 * q^63 + 10 * q^64 - 28 * q^65 + 3 * q^66 + 2 * q^67 - 10 * q^68 - 9 * q^69 + 22 * q^70 - 30 * q^71 - 10 * q^72 - 11 * q^73 + 4 * q^74 + 20 * q^75 + 8 * q^76 + 4 * q^77 + 10 * q^78 + 3 * q^79 - 2 * q^80 + 10 * q^81 + 9 * q^82 - q^83 - 6 * q^84 + 2 * q^85 + 11 * q^86 - 24 * q^87 + 3 * q^88 - 14 * q^89 + 2 * q^90 - 13 * q^91 - 9 * q^92 - 7 * q^93 + 18 * q^94 - 35 * q^95 - 10 * q^96 - 10 * q^97 - 6 * q^98 - 3 * q^99

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