LMFDB - Embedded newform 670.2.a.g.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [670,2,Mod(1,670)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(670, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("670.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 670 = 2 \cdot 5 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	670.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:	$5.34997693543$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.148.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 3x + 1 $ x^3 - x^2 - 3*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$0.311108$ of defining polynomial
Character	$\chi$	$=$	670.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.31111 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.31111 q^{6} +0.311108 q^{7} -1.00000 q^{8} -1.28100 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.31111 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.31111 q^{6} +0.311108 q^{7} -1.00000 q^{8} -1.28100 q^{9} -1.00000 q^{10} +1.00000 q^{11} +1.31111 q^{12} -0.836535 q^{13} -0.311108 q^{14} +1.31111 q^{15} +1.00000 q^{16} +7.11753 q^{17} +1.28100 q^{18} +6.23506 q^{19} +1.00000 q^{20} +0.407896 q^{21} -1.00000 q^{22} +3.37778 q^{23} -1.31111 q^{24} +1.00000 q^{25} +0.836535 q^{26} -5.61285 q^{27} +0.311108 q^{28} -2.83654 q^{29} -1.31111 q^{30} -2.21432 q^{31} -1.00000 q^{32} +1.31111 q^{33} -7.11753 q^{34} +0.311108 q^{35} -1.28100 q^{36} -2.45875 q^{37} -6.23506 q^{38} -1.09679 q^{39} -1.00000 q^{40} +8.36196 q^{41} -0.407896 q^{42} +11.3526 q^{43} +1.00000 q^{44} -1.28100 q^{45} -3.37778 q^{46} -4.02074 q^{47} +1.31111 q^{48} -6.90321 q^{49} -1.00000 q^{50} +9.33185 q^{51} -0.836535 q^{52} +10.7763 q^{53} +5.61285 q^{54} +1.00000 q^{55} -0.311108 q^{56} +8.17484 q^{57} +2.83654 q^{58} -14.5970 q^{59} +1.31111 q^{60} -10.0716 q^{61} +2.21432 q^{62} -0.398528 q^{63} +1.00000 q^{64} -0.836535 q^{65} -1.31111 q^{66} -1.00000 q^{67} +7.11753 q^{68} +4.42864 q^{69} -0.311108 q^{70} +15.4494 q^{71} +1.28100 q^{72} -3.54617 q^{73} +2.45875 q^{74} +1.31111 q^{75} +6.23506 q^{76} +0.311108 q^{77} +1.09679 q^{78} -17.2859 q^{79} +1.00000 q^{80} -3.51606 q^{81} -8.36196 q^{82} +3.66815 q^{83} +0.407896 q^{84} +7.11753 q^{85} -11.3526 q^{86} -3.71900 q^{87} -1.00000 q^{88} +8.05086 q^{89} +1.28100 q^{90} -0.260253 q^{91} +3.37778 q^{92} -2.90321 q^{93} +4.02074 q^{94} +6.23506 q^{95} -1.31111 q^{96} +11.7239 q^{97} +6.90321 q^{98} -1.28100 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} + 4 q^{3} + 3 q^{4} + 3 q^{5} - 4 q^{6} + q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 + 4 * q^3 + 3 * q^4 + 3 * q^5 - 4 * q^6 + q^7 - 3 * q^8 + 3 * q^9	\( 3 q - 3 q^{2} + 4 q^{3} + 3 q^{4} + 3 q^{5} - 4 q^{6} + q^{7} - 3 q^{8} + 3 q^{9} - 3 q^{10} + 3 q^{11} + 4 q^{12} + 4 q^{13} - q^{14} + 4 q^{15} + 3 q^{16} + 8 q^{17} - 3 q^{18} - 8 q^{19} + 3 q^{20} + 8 q^{21} - 3 q^{22} + 10 q^{23} - 4 q^{24} + 3 q^{25} - 4 q^{26} + 10 q^{27} + q^{28} - 2 q^{29} - 4 q^{30} - 3 q^{32} + 4 q^{33} - 8 q^{34} + q^{35} + 3 q^{36} - q^{37} + 8 q^{38} - 10 q^{39} - 3 q^{40} + 12 q^{41} - 8 q^{42} - 6 q^{43} + 3 q^{44} + 3 q^{45} - 10 q^{46} + 8 q^{47} + 4 q^{48} - 14 q^{49} - 3 q^{50} + 8 q^{51} + 4 q^{52} + 12 q^{53} - 10 q^{54} + 3 q^{55} - q^{56} - 16 q^{57} + 2 q^{58} - 4 q^{59} + 4 q^{60} + 3 q^{61} + 19 q^{63} + 3 q^{64} + 4 q^{65} - 4 q^{66} - 3 q^{67} + 8 q^{68} - q^{70} + 13 q^{71} - 3 q^{72} + 16 q^{73} + q^{74} + 4 q^{75} - 8 q^{76} + q^{77} + 10 q^{78} - 12 q^{79} + 3 q^{80} + 23 q^{81} - 12 q^{82} + 31 q^{83} + 8 q^{84} + 8 q^{85} + 6 q^{86} - 18 q^{87} - 3 q^{88} + 11 q^{89} - 3 q^{90} - 14 q^{91} + 10 q^{92} - 2 q^{93} - 8 q^{94} - 8 q^{95} - 4 q^{96} + 9 q^{97} + 14 q^{98} + 3 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 + 4 * q^3 + 3 * q^4 + 3 * q^5 - 4 * q^6 + q^7 - 3 * q^8 + 3 * q^9 - 3 * q^10 + 3 * q^11 + 4 * q^12 + 4 * q^13 - q^14 + 4 * q^15 + 3 * q^16 + 8 * q^17 - 3 * q^18 - 8 * q^19 + 3 * q^20 + 8 * q^21 - 3 * q^22 + 10 * q^23 - 4 * q^24 + 3 * q^25 - 4 * q^26 + 10 * q^27 + q^28 - 2 * q^29 - 4 * q^30 - 3 * q^32 + 4 * q^33 - 8 * q^34 + q^35 + 3 * q^36 - q^37 + 8 * q^38 - 10 * q^39 - 3 * q^40 + 12 * q^41 - 8 * q^42 - 6 * q^43 + 3 * q^44 + 3 * q^45 - 10 * q^46 + 8 * q^47 + 4 * q^48 - 14 * q^49 - 3 * q^50 + 8 * q^51 + 4 * q^52 + 12 * q^53 - 10 * q^54 + 3 * q^55 - q^56 - 16 * q^57 + 2 * q^58 - 4 * q^59 + 4 * q^60 + 3 * q^61 + 19 * q^63 + 3 * q^64 + 4 * q^65 - 4 * q^66 - 3 * q^67 + 8 * q^68 - q^70 + 13 * q^71 - 3 * q^72 + 16 * q^73 + q^74 + 4 * q^75 - 8 * q^76 + q^77 + 10 * q^78 - 12 * q^79 + 3 * q^80 + 23 * q^81 - 12 * q^82 + 31 * q^83 + 8 * q^84 + 8 * q^85 + 6 * q^86 - 18 * q^87 - 3 * q^88 + 11 * q^89 - 3 * q^90 - 14 * q^91 + 10 * q^92 - 2 * q^93 - 8 * q^94 - 8 * q^95 - 4 * q^96 + 9 * q^97 + 14 * 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
$3$	1.31111	0.756968	0.378484	−	0.925608i	$-0.376445\pi$
$3$	1.31111	0.756968	0.378484	+	0.925608i	$0.376445\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.31111	−0.535258
$7$	0.311108	0.117588	0.0587939	−	0.998270i	$-0.481275\pi$
$7$	0.311108	0.117588	0.0587939	+	0.998270i	$0.481275\pi$
$8$	−1.00000	−0.353553
$9$	−1.28100	−0.426999
$10$	−1.00000	−0.316228
$11$	1.00000	0.301511	0.150756	−	0.988571i	$-0.451829\pi$
$11$	1.00000	0.301511	0.150756	+	0.988571i	$0.451829\pi$
$12$	1.31111	0.378484
$13$	−0.836535	−0.232013	−0.116007	−	0.993248i	$-0.537009\pi$
$13$	−0.836535	−0.232013	−0.116007	+	0.993248i	$0.537009\pi$
$14$	−0.311108	−0.0831471
$15$	1.31111	0.338527
$16$	1.00000	0.250000
$17$	7.11753	1.72625	0.863127	−	0.504986i	$-0.168502\pi$
$17$	7.11753	1.72625	0.863127	+	0.504986i	$0.168502\pi$
$18$	1.28100	0.301934
$19$	6.23506	1.43042	0.715211	−	0.698909i	$-0.246331\pi$
$19$	6.23506	1.43042	0.715211	+	0.698909i	$0.246331\pi$
$20$	1.00000	0.223607
$21$	0.407896	0.0890102
$22$	−1.00000	−0.213201
$23$	3.37778	0.704317	0.352158	−	0.935940i	$-0.385448\pi$
$23$	3.37778	0.704317	0.352158	+	0.935940i	$0.385448\pi$
$24$	−1.31111	−0.267629
$25$	1.00000	0.200000
$26$	0.836535	0.164058
$27$	−5.61285	−1.08019
$28$	0.311108	0.0587939
$29$	−2.83654	−0.526731	−0.263366	−	0.964696i	$-0.584833\pi$
$29$	−2.83654	−0.526731	−0.263366	+	0.964696i	$0.584833\pi$
$30$	−1.31111	−0.239374
$31$	−2.21432	−0.397704	−0.198852	−	0.980030i	$-0.563721\pi$
$31$	−2.21432	−0.397704	−0.198852	+	0.980030i	$0.563721\pi$
$32$	−1.00000	−0.176777
$33$	1.31111	0.228235
$34$	−7.11753	−1.22065
$35$	0.311108	0.0525868
$36$	−1.28100	−0.213499
$37$	−2.45875	−0.404216	−0.202108	−	0.979363i	$-0.564779\pi$
$37$	−2.45875	−0.404216	−0.202108	+	0.979363i	$0.564779\pi$
$38$	−6.23506	−1.01146
$39$	−1.09679	−0.175627
$40$	−1.00000	−0.158114
$41$	8.36196	1.30592	0.652960	−	0.757393i	$-0.273527\pi$
$41$	8.36196	1.30592	0.652960	+	0.757393i	$0.273527\pi$
$42$	−0.407896	−0.0629397
$43$	11.3526	1.73125	0.865627	−	0.500689i	$-0.166920\pi$
$43$	11.3526	1.73125	0.865627	+	0.500689i	$0.166920\pi$
$44$	1.00000	0.150756
$45$	−1.28100	−0.190960
$46$	−3.37778	−0.498027
$47$	−4.02074	−0.586486	−0.293243	−	0.956038i	$-0.594734\pi$
$47$	−4.02074	−0.586486	−0.293243	+	0.956038i	$0.594734\pi$
$48$	1.31111	0.189242
$49$	−6.90321	−0.986173
$50$	−1.00000	−0.141421
$51$	9.33185	1.30672
$52$	−0.836535	−0.116007
$53$	10.7763	1.48024	0.740120	−	0.672475i	$-0.234769\pi$
$53$	10.7763	1.48024	0.740120	+	0.672475i	$0.234769\pi$
$54$	5.61285	0.763812
$55$	1.00000	0.134840
$56$	−0.311108	−0.0415735
$57$	8.17484	1.08278
$58$	2.83654	0.372455
$59$	−14.5970	−1.90037	−0.950185	−	0.311685i	$-0.899107\pi$
$59$	−14.5970	−1.90037	−0.950185	+	0.311685i	$0.899107\pi$
$60$	1.31111	0.169263
$61$	−10.0716	−1.28954	−0.644768	−	0.764378i	$-0.723046\pi$
$61$	−10.0716	−1.28954	−0.644768	+	0.764378i	$0.723046\pi$
$62$	2.21432	0.281219
$63$	−0.398528	−0.0502098
$64$	1.00000	0.125000
$65$	−0.836535	−0.103759
$66$	−1.31111	−0.161386
$67$	−1.00000	−0.122169
$67$	−1.00000	−0.122169
$68$	7.11753	0.863127
$69$	4.42864	0.533146
$70$	−0.311108	−0.0371845
$71$	15.4494	1.83350	0.916752	−	0.399456i	$-0.130801\pi$
$71$	15.4494	1.83350	0.916752	+	0.399456i	$0.130801\pi$
$72$	1.28100	0.150967
$73$	−3.54617	−0.415048	−0.207524	−	0.978230i	$-0.566540\pi$
$73$	−3.54617	−0.415048	−0.207524	+	0.978230i	$0.566540\pi$
$74$	2.45875	0.285824
$75$	1.31111	0.151394
$76$	6.23506	0.715211
$77$	0.311108	0.0354540
$78$	1.09679	0.124187
$79$	−17.2859	−1.94482	−0.972409	−	0.233283i	$-0.925053\pi$
$79$	−17.2859	−1.94482	−0.972409	+	0.233283i	$0.925053\pi$
$80$	1.00000	0.111803
$81$	−3.51606	−0.390673
$82$	−8.36196	−0.923424
$83$	3.66815	0.402632	0.201316	−	0.979526i	$-0.435478\pi$
$83$	3.66815	0.402632	0.201316	+	0.979526i	$0.435478\pi$
$84$	0.407896	0.0445051
$85$	7.11753	0.772005
$86$	−11.3526	−1.22418
$87$	−3.71900	−0.398719
$88$	−1.00000	−0.106600
$89$	8.05086	0.853389	0.426694	−	0.904396i	$-0.359678\pi$
$89$	8.05086	0.853389	0.426694	+	0.904396i	$0.359678\pi$
$90$	1.28100	0.135029
$91$	−0.260253	−0.0272819
$92$	3.37778	0.352158
$93$	−2.90321	−0.301049
$94$	4.02074	0.414708
$95$	6.23506	0.639704
$96$	−1.31111	−0.133814
$97$	11.7239	1.19038	0.595192	−	0.803583i	$-0.297076\pi$
$97$	11.7239	1.19038	0.595192	+	0.803583i	$0.297076\pi$
$98$	6.90321	0.697330
$99$	−1.28100	−0.128745
$100$	1.00000	0.100000
$101$	11.1082	1.10530	0.552652	−	0.833412i	$-0.313616\pi$
$101$	11.1082	1.10530	0.552652	+	0.833412i	$0.313616\pi$
$102$	−9.33185	−0.923991
$103$	4.70318	0.463418	0.231709	−	0.972785i	$-0.425568\pi$
$103$	4.70318	0.463418	0.231709	+	0.972785i	$0.425568\pi$
$104$	0.836535	0.0820290
$105$	0.407896	0.0398066
$106$	−10.7763	−1.04669
$107$	−7.65878	−0.740402	−0.370201	−	0.928952i	$-0.620711\pi$
$107$	−7.65878	−0.740402	−0.370201	+	0.928952i	$0.620711\pi$
$108$	−5.61285	−0.540097
$109$	−9.98418	−0.956311	−0.478155	−	0.878275i	$-0.658694\pi$
$109$	−9.98418	−0.956311	−0.478155	+	0.878275i	$0.658694\pi$
$110$	−1.00000	−0.0953463
$111$	−3.22369	−0.305979
$112$	0.311108	0.0293969
$113$	−2.46520	−0.231907	−0.115953	−	0.993255i	$-0.536992\pi$
$113$	−2.46520	−0.231907	−0.115953	+	0.993255i	$0.536992\pi$
$114$	−8.17484	−0.765644
$115$	3.37778	0.314980
$116$	−2.83654	−0.263366
$117$	1.07160	0.0990693
$118$	14.5970	1.34377
$119$	2.21432	0.202986
$120$	−1.31111	−0.119687
$121$	−10.0000	−0.909091
$122$	10.0716	0.911840
$123$	10.9634	0.988540
$124$	−2.21432	−0.198852
$125$	1.00000	0.0894427
$126$	0.398528	0.0355037
$127$	−9.16346	−0.813126	−0.406563	−	0.913623i	$-0.633273\pi$
$127$	−9.16346	−0.813126	−0.406563	+	0.913623i	$0.633273\pi$
$128$	−1.00000	−0.0883883
$129$	14.8845	1.31051
$130$	0.836535	0.0733690
$131$	−19.0923	−1.66811	−0.834053	−	0.551685i	$-0.813985\pi$
$131$	−19.0923	−1.66811	−0.834053	+	0.551685i	$0.813985\pi$
$132$	1.31111	0.114117
$133$	1.93978	0.168200
$134$	1.00000	0.0863868
$135$	−5.61285	−0.483077
$136$	−7.11753	−0.610323
$137$	−8.56691	−0.731921	−0.365960	−	0.930630i	$-0.619259\pi$
$137$	−8.56691	−0.731921	−0.365960	+	0.930630i	$0.619259\pi$
$138$	−4.42864	−0.376991
$139$	−5.42372	−0.460034	−0.230017	−	0.973187i	$-0.573878\pi$
$139$	−5.42372	−0.460034	−0.230017	+	0.973187i	$0.573878\pi$
$140$	0.311108	0.0262934
$141$	−5.27163	−0.443951
$142$	−15.4494	−1.29648
$143$	−0.836535	−0.0699546
$144$	−1.28100	−0.106750
$145$	−2.83654	−0.235561
$146$	3.54617	0.293483
$147$	−9.05086	−0.746502
$148$	−2.45875	−0.202108
$149$	−10.0000	−0.819232	−0.409616	−	0.912258i	$-0.634337\pi$
$149$	−10.0000	−0.819232	−0.409616	+	0.912258i	$0.634337\pi$
$150$	−1.31111	−0.107052
$151$	−21.2558	−1.72977	−0.864887	−	0.501967i	$-0.832610\pi$
$151$	−21.2558	−1.72977	−0.864887	+	0.501967i	$0.832610\pi$
$152$	−6.23506	−0.505730
$153$	−9.11753	−0.737109
$154$	−0.311108	−0.0250698
$155$	−2.21432	−0.177858
$156$	−1.09679	−0.0878133
$157$	−2.14764	−0.171401	−0.0857003	−	0.996321i	$-0.527313\pi$
$157$	−2.14764	−0.171401	−0.0857003	+	0.996321i	$0.527313\pi$
$158$	17.2859	1.37519
$159$	14.1289	1.12050
$160$	−1.00000	−0.0790569
$161$	1.05086	0.0828190
$162$	3.51606	0.276248
$163$	1.99063	0.155918	0.0779592	−	0.996957i	$-0.475160\pi$
$163$	1.99063	0.155918	0.0779592	+	0.996957i	$0.475160\pi$
$164$	8.36196	0.652960
$165$	1.31111	0.102070
$166$	−3.66815	−0.284704
$167$	−2.32693	−0.180063	−0.0900316	−	0.995939i	$-0.528697\pi$
$167$	−2.32693	−0.180063	−0.0900316	+	0.995939i	$0.528697\pi$
$168$	−0.407896	−0.0314699
$169$	−12.3002	−0.946170
$170$	−7.11753	−0.545890
$171$	−7.98709	−0.610788
$172$	11.3526	0.865627
$173$	20.7669	1.57888	0.789441	−	0.613827i	$-0.210371\pi$
$173$	20.7669	1.57888	0.789441	+	0.613827i	$0.210371\pi$
$174$	3.71900	0.281937
$175$	0.311108	0.0235175
$176$	1.00000	0.0753778
$177$	−19.1383	−1.43852
$178$	−8.05086	−0.603437
$179$	8.38271	0.626553	0.313276	−	0.949662i	$-0.398573\pi$
$179$	8.38271	0.626553	0.313276	+	0.949662i	$0.398573\pi$
$180$	−1.28100	−0.0954798
$181$	10.9382	0.813033	0.406517	−	0.913643i	$-0.366743\pi$
$181$	10.9382	0.813033	0.406517	+	0.913643i	$0.366743\pi$
$182$	0.260253	0.0192912
$183$	−13.2050	−0.976138
$184$	−3.37778	−0.249014
$185$	−2.45875	−0.180771
$186$	2.90321	0.212874
$187$	7.11753	0.520485
$188$	−4.02074	−0.293243
$189$	−1.74620	−0.127017
$190$	−6.23506	−0.452339
$191$	−5.65233	−0.408988	−0.204494	−	0.978868i	$-0.565555\pi$
$191$	−5.65233	−0.408988	−0.204494	+	0.978868i	$0.565555\pi$
$192$	1.31111	0.0946211
$193$	10.1684	0.731936	0.365968	−	0.930627i	$-0.380738\pi$
$193$	10.1684	0.731936	0.365968	+	0.930627i	$0.380738\pi$
$194$	−11.7239	−0.841729
$195$	−1.09679	−0.0785426
$196$	−6.90321	−0.493087
$197$	−16.6035	−1.18295	−0.591474	−	0.806324i	$-0.701454\pi$
$197$	−16.6035	−1.18295	−0.591474	+	0.806324i	$0.701454\pi$
$198$	1.28100	0.0910364
$199$	−23.9240	−1.69592	−0.847962	−	0.530057i	$-0.822171\pi$
$199$	−23.9240	−1.69592	−0.847962	+	0.530057i	$0.822171\pi$
$200$	−1.00000	−0.0707107
$201$	−1.31111	−0.0924784
$202$	−11.1082	−0.781568
$203$	−0.882468	−0.0619371
$204$	9.33185	0.653360
$205$	8.36196	0.584025
$206$	−4.70318	−0.327686
$207$	−4.32693	−0.300742
$208$	−0.836535	−0.0580033
$209$	6.23506	0.431288
$210$	−0.407896	−0.0281475
$211$	−1.44446	−0.0994408	−0.0497204	−	0.998763i	$-0.515833\pi$
$211$	−1.44446	−0.0994408	−0.0497204	+	0.998763i	$0.515833\pi$
$212$	10.7763	0.740120
$213$	20.2558	1.38791
$214$	7.65878	0.523543
$215$	11.3526	0.774241
$216$	5.61285	0.381906
$217$	−0.688892	−0.0467650
$218$	9.98418	0.676214
$219$	−4.64941	−0.314178
$220$	1.00000	0.0674200
$221$	−5.95407	−0.400514
$222$	3.22369	0.216360
$223$	−2.85728	−0.191338	−0.0956688	−	0.995413i	$-0.530499\pi$
$223$	−2.85728	−0.191338	−0.0956688	+	0.995413i	$0.530499\pi$
$224$	−0.311108	−0.0207868
$225$	−1.28100	−0.0853998
$226$	2.46520	0.163983
$227$	8.99063	0.596729	0.298365	−	0.954452i	$-0.403559\pi$
$227$	8.99063	0.596729	0.298365	+	0.954452i	$0.403559\pi$
$228$	8.17484	0.541392
$229$	−8.69381	−0.574503	−0.287252	−	0.957855i	$-0.592742\pi$
$229$	−8.69381	−0.574503	−0.287252	+	0.957855i	$0.592742\pi$
$230$	−3.37778	−0.222725
$231$	0.407896	0.0268376
$232$	2.83654	0.186228
$233$	−15.5303	−1.01743	−0.508714	−	0.860936i	$-0.669879\pi$
$233$	−15.5303	−1.01743	−0.508714	+	0.860936i	$0.669879\pi$
$234$	−1.07160	−0.0700526
$235$	−4.02074	−0.262284
$236$	−14.5970	−0.950185
$237$	−22.6637	−1.47217
$238$	−2.21432	−0.143533
$239$	5.93978	0.384212	0.192106	−	0.981374i	$-0.438468\pi$
$239$	5.93978	0.384212	0.192106	+	0.981374i	$0.438468\pi$
$240$	1.31111	0.0846316
$241$	−2.79213	−0.179857	−0.0899286	−	0.995948i	$-0.528664\pi$
$241$	−2.79213	−0.179857	−0.0899286	+	0.995948i	$0.528664\pi$
$242$	10.0000	0.642824
$243$	12.2286	0.784466
$244$	−10.0716	−0.644768
$245$	−6.90321	−0.441030
$246$	−10.9634	−0.699003
$247$	−5.21585	−0.331877
$248$	2.21432	0.140609
$249$	4.80934	0.304779
$250$	−1.00000	−0.0632456
$251$	−19.6178	−1.23826	−0.619131	−	0.785287i	$-0.712515\pi$
$251$	−19.6178	−1.23826	−0.619131	+	0.785287i	$0.712515\pi$
$252$	−0.398528	−0.0251049
$253$	3.37778	0.212359
$254$	9.16346	0.574967
$255$	9.33185	0.584383
$256$	1.00000	0.0625000
$257$	25.4859	1.58977	0.794885	−	0.606760i	$-0.207531\pi$
$257$	25.4859	1.58977	0.794885	+	0.606760i	$0.207531\pi$
$258$	−14.8845	−0.926667
$259$	−0.764937	−0.0475309
$260$	−0.836535	−0.0518797
$261$	3.63359	0.224914
$262$	19.0923	1.17953
$263$	−24.7862	−1.52838	−0.764190	−	0.644991i	$-0.776861\pi$
$263$	−24.7862	−1.52838	−0.764190	+	0.644991i	$0.776861\pi$
$264$	−1.31111	−0.0806931
$265$	10.7763	0.661984
$266$	−1.93978	−0.118935
$267$	10.5555	0.645989
$268$	−1.00000	−0.0610847
$269$	26.0415	1.58778	0.793889	−	0.608063i	$-0.208053\pi$
$269$	26.0415	1.58778	0.793889	+	0.608063i	$0.208053\pi$
$270$	5.61285	0.341587
$271$	5.12399	0.311260	0.155630	−	0.987815i	$-0.450259\pi$
$271$	5.12399	0.311260	0.155630	+	0.987815i	$0.450259\pi$
$272$	7.11753	0.431564
$273$	−0.341219	−0.0206515
$274$	8.56691	0.517546
$275$	1.00000	0.0603023
$276$	4.42864	0.266573
$277$	13.5368	0.813348	0.406674	−	0.913573i	$-0.366689\pi$
$277$	13.5368	0.813348	0.406674	+	0.913573i	$0.366689\pi$
$278$	5.42372	0.325293
$279$	2.83654	0.169819
$280$	−0.311108	−0.0185922
$281$	26.3970	1.57471	0.787356	−	0.616498i	$-0.211449\pi$
$281$	26.3970	1.57471	0.787356	+	0.616498i	$0.211449\pi$
$282$	5.27163	0.313921
$283$	−14.5986	−0.867794	−0.433897	−	0.900962i	$-0.642862\pi$
$283$	−14.5986	−0.867794	−0.433897	+	0.900962i	$0.642862\pi$
$284$	15.4494	0.916752
$285$	8.17484	0.484236
$286$	0.836535	0.0494654
$287$	2.60147	0.153560
$288$	1.28100	0.0754834
$289$	33.6593	1.97996
$290$	2.83654	0.166567
$291$	15.3713	0.901083
$292$	−3.54617	−0.207524
$293$	−26.2005	−1.53065	−0.765325	−	0.643644i	$-0.777422\pi$
$293$	−26.2005	−1.53065	−0.765325	+	0.643644i	$0.777422\pi$
$294$	9.05086	0.527857
$295$	−14.5970	−0.849872
$296$	2.45875	0.142912
$297$	−5.61285	−0.325690
$298$	10.0000	0.579284
$299$	−2.82564	−0.163411
$300$	1.31111	0.0756968
$301$	3.53188	0.203574
$302$	21.2558	1.22313
$303$	14.5640	0.836680
$304$	6.23506	0.357605
$305$	−10.0716	−0.576698
$306$	9.11753	0.521215
$307$	−15.6780	−0.894790	−0.447395	−	0.894336i	$-0.647648\pi$
$307$	−15.6780	−0.894790	−0.447395	+	0.894336i	$0.647648\pi$
$308$	0.311108	0.0177270
$309$	6.16638	0.350793
$310$	2.21432	0.125765
$311$	−14.6430	−0.830326	−0.415163	−	0.909747i	$-0.636275\pi$
$311$	−14.6430	−0.830326	−0.415163	+	0.909747i	$0.636275\pi$
$312$	1.09679	0.0620934
$313$	−5.64941	−0.319324	−0.159662	−	0.987172i	$-0.551040\pi$
$313$	−5.64941	−0.319324	−0.159662	+	0.987172i	$0.551040\pi$
$314$	2.14764	0.121199
$315$	−0.398528	−0.0224545
$316$	−17.2859	−0.972409
$317$	−1.02227	−0.0574167	−0.0287083	−	0.999588i	$-0.509139\pi$
$317$	−1.02227	−0.0574167	−0.0287083	+	0.999588i	$0.509139\pi$
$318$	−14.1289	−0.792310
$319$	−2.83654	−0.158815
$320$	1.00000	0.0559017
$321$	−10.0415	−0.560461
$322$	−1.05086	−0.0585619
$323$	44.3783	2.46927
$324$	−3.51606	−0.195337
$325$	−0.836535	−0.0464026
$326$	−1.99063	−0.110251
$327$	−13.0903	−0.723897
$328$	−8.36196	−0.461712
$329$	−1.25088	−0.0689635
$330$	−1.31111	−0.0721741
$331$	12.8938	0.708710	0.354355	−	0.935111i	$-0.384700\pi$
$331$	12.8938	0.708710	0.354355	+	0.935111i	$0.384700\pi$
$332$	3.66815	0.201316
$333$	3.14965	0.172600
$334$	2.32693	0.127324
$335$	−1.00000	−0.0546358
$336$	0.407896	0.0222525
$337$	−10.8113	−0.588932	−0.294466	−	0.955662i	$-0.595142\pi$
$337$	−10.8113	−0.588932	−0.294466	+	0.955662i	$0.595142\pi$
$338$	12.3002	0.669043
$339$	−3.23215	−0.175546
$340$	7.11753	0.386002
$341$	−2.21432	−0.119912
$342$	7.98709	0.431893
$343$	−4.32540	−0.233550
$344$	−11.3526	−0.612091
$345$	4.42864	0.238430
$346$	−20.7669	−1.11644
$347$	24.7654	1.32948	0.664739	−	0.747076i	$-0.268543\pi$
$347$	24.7654	1.32948	0.664739	+	0.747076i	$0.268543\pi$
$348$	−3.71900	−0.199360
$349$	19.6414	1.05138	0.525691	−	0.850676i	$-0.323807\pi$
$349$	19.6414	1.05138	0.525691	+	0.850676i	$0.323807\pi$
$350$	−0.311108	−0.0166294
$351$	4.69535	0.250619
$352$	−1.00000	−0.0533002
$353$	15.8020	0.841054	0.420527	−	0.907280i	$-0.361845\pi$
$353$	15.8020	0.841054	0.420527	+	0.907280i	$0.361845\pi$
$354$	19.1383	1.01719
$355$	15.4494	0.819968
$356$	8.05086	0.426694
$357$	2.90321	0.153654
$358$	−8.38271	−0.443040
$359$	−17.3477	−0.915575	−0.457788	−	0.889062i	$-0.651358\pi$
$359$	−17.3477	−0.915575	−0.457788	+	0.889062i	$0.651358\pi$
$360$	1.28100	0.0675144
$361$	19.8760	1.04611
$362$	−10.9382	−0.574901
$363$	−13.1111	−0.688153
$364$	−0.260253	−0.0136409
$365$	−3.54617	−0.185615
$366$	13.2050	0.690234
$367$	21.4050	1.11733	0.558665	−	0.829393i	$-0.311314\pi$
$367$	21.4050	1.11733	0.558665	+	0.829393i	$0.311314\pi$
$368$	3.37778	0.176079
$369$	−10.7116	−0.557626
$370$	2.45875	0.127824
$371$	3.35260	0.174058
$372$	−2.90321	−0.150525
$373$	−33.1655	−1.71724	−0.858622	−	0.512610i	$-0.828679\pi$
$373$	−33.1655	−1.71724	−0.858622	+	0.512610i	$0.828679\pi$
$374$	−7.11753	−0.368039
$375$	1.31111	0.0677053
$376$	4.02074	0.207354
$377$	2.37286	0.122209
$378$	1.74620	0.0898149
$379$	−25.3319	−1.30121	−0.650605	−	0.759416i	$-0.725485\pi$
$379$	−25.3319	−1.30121	−0.650605	+	0.759416i	$0.725485\pi$
$380$	6.23506	0.319852
$381$	−12.0143	−0.615511
$382$	5.65233	0.289198
$383$	13.6844	0.699243	0.349621	−	0.936891i	$-0.386310\pi$
$383$	13.6844	0.699243	0.349621	+	0.936891i	$0.386310\pi$
$384$	−1.31111	−0.0669072
$385$	0.311108	0.0158555
$386$	−10.1684	−0.517557
$387$	−14.5426	−0.739244
$388$	11.7239	0.595192
$389$	6.19358	0.314027	0.157013	−	0.987596i	$-0.449813\pi$
$389$	6.19358	0.314027	0.157013	+	0.987596i	$0.449813\pi$
$390$	1.09679	0.0555380
$391$	24.0415	1.21583
$392$	6.90321	0.348665
$393$	−25.0321	−1.26270
$394$	16.6035	0.836471
$395$	−17.2859	−0.869749
$396$	−1.28100	−0.0643725
$397$	4.37133	0.219391	0.109695	−	0.993965i	$-0.465012\pi$
$397$	4.37133	0.219391	0.109695	+	0.993965i	$0.465012\pi$
$398$	23.9240	1.19920
$399$	2.54326	0.127322
$400$	1.00000	0.0500000
$401$	18.6287	0.930271	0.465136	−	0.885239i	$-0.346006\pi$
$401$	18.6287	0.930271	0.465136	+	0.885239i	$0.346006\pi$
$402$	1.31111	0.0653921
$403$	1.85236	0.0922725
$404$	11.1082	0.552652
$405$	−3.51606	−0.174714
$406$	0.882468	0.0437962
$407$	−2.45875	−0.121876
$408$	−9.33185	−0.461995
$409$	24.9971	1.23603	0.618013	−	0.786168i	$-0.287938\pi$
$409$	24.9971	1.23603	0.618013	+	0.786168i	$0.287938\pi$
$410$	−8.36196	−0.412968
$411$	−11.2321	−0.554041
$412$	4.70318	0.231709
$413$	−4.54125	−0.223460
$414$	4.32693	0.212657
$415$	3.66815	0.180062
$416$	0.836535	0.0410145
$417$	−7.11108	−0.348231
$418$	−6.23506	−0.304967
$419$	−3.93978	−0.192471	−0.0962353	−	0.995359i	$-0.530680\pi$
$419$	−3.93978	−0.192471	−0.0962353	+	0.995359i	$0.530680\pi$
$420$	0.407896	0.0199033
$421$	30.3892	1.48108	0.740539	−	0.672014i	$-0.234571\pi$
$421$	30.3892	1.48108	0.740539	+	0.672014i	$0.234571\pi$
$422$	1.44446	0.0703153
$423$	5.15056	0.250429
$424$	−10.7763	−0.523344
$425$	7.11753	0.345251
$426$	−20.2558	−0.981397
$427$	−3.13335	−0.151634
$428$	−7.65878	−0.370201
$429$	−1.09679	−0.0529534
$430$	−11.3526	−0.547471
$431$	8.03011	0.386797	0.193398	−	0.981120i	$-0.438049\pi$
$431$	8.03011	0.386797	0.193398	+	0.981120i	$0.438049\pi$
$432$	−5.61285	−0.270048
$433$	27.7605	1.33408	0.667042	−	0.745020i	$-0.267560\pi$
$433$	27.7605	1.33408	0.667042	+	0.745020i	$0.267560\pi$
$434$	0.688892	0.0330679
$435$	−3.71900	−0.178313
$436$	−9.98418	−0.478155
$437$	21.0607	1.00747
$438$	4.64941	0.222158
$439$	−18.0158	−0.859848	−0.429924	−	0.902865i	$-0.641460\pi$
$439$	−18.0158	−0.859848	−0.429924	+	0.902865i	$0.641460\pi$
$440$	−1.00000	−0.0476731
$441$	8.84299	0.421095
$442$	5.95407	0.283206
$443$	4.02858	0.191404	0.0957018	−	0.995410i	$-0.469490\pi$
$443$	4.02858	0.191404	0.0957018	+	0.995410i	$0.469490\pi$
$444$	−3.22369	−0.152989
$445$	8.05086	0.381647
$446$	2.85728	0.135296
$447$	−13.1111	−0.620133
$448$	0.311108	0.0146985
$449$	30.6271	1.44538	0.722692	−	0.691170i	$-0.242905\pi$
$449$	30.6271	1.44538	0.722692	+	0.691170i	$0.242905\pi$
$450$	1.28100	0.0603867
$451$	8.36196	0.393749
$452$	−2.46520	−0.115953
$453$	−27.8687	−1.30938
$454$	−8.99063	−0.421951
$455$	−0.260253	−0.0122008
$456$	−8.17484	−0.382822
$457$	−26.3368	−1.23198	−0.615991	−	0.787753i	$-0.711244\pi$
$457$	−26.3368	−1.23198	−0.615991	+	0.787753i	$0.711244\pi$
$458$	8.69381	0.406235
$459$	−39.9496	−1.86469
$460$	3.37778	0.157490
$461$	−20.3082	−0.945847	−0.472923	−	0.881104i	$-0.656801\pi$
$461$	−20.3082	−0.945847	−0.472923	+	0.881104i	$0.656801\pi$
$462$	−0.407896	−0.0189770
$463$	−22.8256	−1.06080	−0.530399	−	0.847748i	$-0.677958\pi$
$463$	−22.8256	−1.06080	−0.530399	+	0.847748i	$0.677958\pi$
$464$	−2.83654	−0.131683
$465$	−2.90321	−0.134633
$466$	15.5303	0.719430
$467$	−10.9857	−0.508358	−0.254179	−	0.967157i	$-0.581805\pi$
$467$	−10.9857	−0.508358	−0.254179	+	0.967157i	$0.581805\pi$
$468$	1.07160	0.0495347
$469$	−0.311108	−0.0143656
$470$	4.02074	0.185463
$471$	−2.81579	−0.129745
$472$	14.5970	0.671883
$473$	11.3526	0.521993
$474$	22.6637	1.04098
$475$	6.23506	0.286084
$476$	2.21432	0.101493
$477$	−13.8044	−0.632061
$478$	−5.93978	−0.271679
$479$	−9.09526	−0.415573	−0.207786	−	0.978174i	$-0.566626\pi$
$479$	−9.09526	−0.415573	−0.207786	+	0.978174i	$0.566626\pi$
$480$	−1.31111	−0.0598436
$481$	2.05683	0.0937835
$482$	2.79213	0.127178
$483$	1.37778	0.0626914
$484$	−10.0000	−0.454545
$485$	11.7239	0.532356
$486$	−12.2286	−0.554701
$487$	−2.67952	−0.121421	−0.0607104	−	0.998155i	$-0.519337\pi$
$487$	−2.67952	−0.121421	−0.0607104	+	0.998155i	$0.519337\pi$
$488$	10.0716	0.455920
$489$	2.60993	0.118025
$490$	6.90321	0.311855
$491$	−36.5970	−1.65160	−0.825800	−	0.563963i	$-0.809276\pi$
$491$	−36.5970	−1.65160	−0.825800	+	0.563963i	$0.809276\pi$
$492$	10.9634	0.494270
$493$	−20.1891	−0.909273
$494$	5.21585	0.234672
$495$	−1.28100	−0.0575765
$496$	−2.21432	−0.0994259
$497$	4.80642	0.215598
$498$	−4.80934	−0.215512
$499$	−6.09234	−0.272731	−0.136365	−	0.990659i	$-0.543542\pi$
$499$	−6.09234	−0.272731	−0.136365	+	0.990659i	$0.543542\pi$
$500$	1.00000	0.0447214
$501$	−3.05086	−0.136302
$502$	19.6178	0.875584
$503$	−14.7540	−0.657850	−0.328925	−	0.944356i	$-0.606686\pi$
$503$	−14.7540	−0.657850	−0.328925	+	0.944356i	$0.606686\pi$
$504$	0.398528	0.0177518
$505$	11.1082	0.494307
$506$	−3.37778	−0.150161
$507$	−16.1269	−0.716221
$508$	−9.16346	−0.406563
$509$	−10.1225	−0.448670	−0.224335	−	0.974512i	$-0.572021\pi$
$509$	−10.1225	−0.448670	−0.224335	+	0.974512i	$0.572021\pi$
$510$	−9.33185	−0.413221
$511$	−1.10324	−0.0488045
$512$	−1.00000	−0.0441942
$513$	−34.9965	−1.54513
$514$	−25.4859	−1.12414
$515$	4.70318	0.207247
$516$	14.8845	0.655253
$517$	−4.02074	−0.176832
$518$	0.764937	0.0336094
$519$	27.2277	1.19516
$520$	0.836535	0.0366845
$521$	20.1497	0.882772	0.441386	−	0.897317i	$-0.354487\pi$
$521$	20.1497	0.882772	0.441386	+	0.897317i	$0.354487\pi$
$522$	−3.63359	−0.159038
$523$	5.28544	0.231116	0.115558	−	0.993301i	$-0.463134\pi$
$523$	5.28544	0.231116	0.115558	+	0.993301i	$0.463134\pi$
$524$	−19.0923	−0.834053
$525$	0.407896	0.0178020
$526$	24.7862	1.08073
$527$	−15.7605	−0.686538
$528$	1.31111	0.0570586
$529$	−11.5906	−0.503938
$530$	−10.7763	−0.468093
$531$	18.6987	0.811456
$532$	1.93978	0.0841000
$533$	−6.99508	−0.302990
$534$	−10.5555	−0.456783
$535$	−7.65878	−0.331118
$536$	1.00000	0.0431934
$537$	10.9906	0.474281
$538$	−26.0415	−1.12273
$539$	−6.90321	−0.297342
$540$	−5.61285	−0.241539
$541$	−4.81135	−0.206856	−0.103428	−	0.994637i	$-0.532981\pi$
$541$	−4.81135	−0.206856	−0.103428	+	0.994637i	$0.532981\pi$
$542$	−5.12399	−0.220094
$543$	14.3412	0.615441
$544$	−7.11753	−0.305162
$545$	−9.98418	−0.427675
$546$	0.341219	0.0146028
$547$	−2.10171	−0.0898626	−0.0449313	−	0.998990i	$-0.514307\pi$
$547$	−2.10171	−0.0898626	−0.0449313	+	0.998990i	$0.514307\pi$
$548$	−8.56691	−0.365960
$549$	12.9017	0.550630
$550$	−1.00000	−0.0426401
$551$	−17.6860	−0.753448
$552$	−4.42864	−0.188495
$553$	−5.37778	−0.228687
$554$	−13.5368	−0.575124
$555$	−3.22369	−0.136838
$556$	−5.42372	−0.230017
$557$	−2.47013	−0.104663	−0.0523313	−	0.998630i	$-0.516665\pi$
$557$	−2.47013	−0.104663	−0.0523313	+	0.998630i	$0.516665\pi$
$558$	−2.83654	−0.120080
$559$	−9.49685	−0.401674
$560$	0.311108	0.0131467
$561$	9.33185	0.393991
$562$	−26.3970	−1.11349
$563$	−31.0386	−1.30812	−0.654060	−	0.756443i	$-0.726936\pi$
$563$	−31.0386	−1.30812	−0.654060	+	0.756443i	$0.726936\pi$
$564$	−5.27163	−0.221976
$565$	−2.46520	−0.103712
$566$	14.5986	0.613623
$567$	−1.09387	−0.0459384
$568$	−15.4494	−0.648242
$569$	24.9857	1.04746	0.523728	−	0.851886i	$-0.324541\pi$
$569$	24.9857	1.04746	0.523728	+	0.851886i	$0.324541\pi$
$570$	−8.17484	−0.342406
$571$	15.8415	0.662944	0.331472	−	0.943465i	$-0.392455\pi$
$571$	15.8415	0.662944	0.331472	+	0.943465i	$0.392455\pi$
$572$	−0.836535	−0.0349773
$573$	−7.41081	−0.309591
$574$	−2.60147	−0.108583
$575$	3.37778	0.140863
$576$	−1.28100	−0.0533748
$577$	29.5714	1.23107	0.615536	−	0.788109i	$-0.288940\pi$
$577$	29.5714	1.23107	0.615536	+	0.788109i	$0.288940\pi$
$578$	−33.6593	−1.40004
$579$	13.3319	0.554053
$580$	−2.83654	−0.117781
$581$	1.14119	0.0473445
$582$	−15.3713	−0.637162
$583$	10.7763	0.446309
$584$	3.54617	0.146742
$585$	1.07160	0.0443052
$586$	26.2005	1.08233
$587$	−7.82516	−0.322979	−0.161489	−	0.986874i	$-0.551630\pi$
$587$	−7.82516	−0.322979	−0.161489	+	0.986874i	$0.551630\pi$
$588$	−9.05086	−0.373251
$589$	−13.8064	−0.568884
$590$	14.5970	0.600950
$591$	−21.7690	−0.895455
$592$	−2.45875	−0.101054
$593$	4.44785	0.182651	0.0913257	−	0.995821i	$-0.470890\pi$
$593$	4.44785	0.182651	0.0913257	+	0.995821i	$0.470890\pi$
$594$	5.61285	0.230298
$595$	2.21432	0.0907783
$596$	−10.0000	−0.409616
$597$	−31.3669	−1.28376
$598$	2.82564	0.115549
$599$	23.7067	0.968630	0.484315	−	0.874894i	$-0.339069\pi$
$599$	23.7067	0.968630	0.484315	+	0.874894i	$0.339069\pi$
$600$	−1.31111	−0.0535258
$601$	6.66862	0.272019	0.136009	−	0.990708i	$-0.456572\pi$
$601$	6.66862	0.272019	0.136009	+	0.990708i	$0.456572\pi$
$602$	−3.53188	−0.143949
$603$	1.28100	0.0521662
$604$	−21.2558	−0.864887
$605$	−10.0000	−0.406558
$606$	−14.5640	−0.591622
$607$	31.8064	1.29098	0.645491	−	0.763767i	$-0.276653\pi$
$607$	31.8064	1.29098	0.645491	+	0.763767i	$0.276653\pi$
$608$	−6.23506	−0.252865
$609$	−1.15701	−0.0468845
$610$	10.0716	0.407787
$611$	3.36349	0.136072
$612$	−9.11753	−0.368554
$613$	47.3832	1.91379	0.956894	−	0.290436i	$-0.0938004\pi$
$613$	47.3832	1.91379	0.956894	+	0.290436i	$0.0938004\pi$
$614$	15.6780	0.632712
$615$	10.9634	0.442088
$616$	−0.311108	−0.0125349
$617$	−38.3432	−1.54364	−0.771820	−	0.635841i	$-0.780653\pi$
$617$	−38.3432	−1.54364	−0.771820	+	0.635841i	$0.780653\pi$
$618$	−6.16638	−0.248048
$619$	23.1941	0.932248	0.466124	−	0.884719i	$-0.345650\pi$
$619$	23.1941	0.932248	0.466124	+	0.884719i	$0.345650\pi$
$620$	−2.21432	−0.0889292
$621$	−18.9590	−0.760798
$622$	14.6430	0.587129
$623$	2.50468	0.100348
$624$	−1.09679	−0.0439067
$625$	1.00000	0.0400000
$626$	5.64941	0.225796
$627$	8.17484	0.326472
$628$	−2.14764	−0.0857003
$629$	−17.5002	−0.697780
$630$	0.398528	0.0158777
$631$	6.92840	0.275815	0.137908	−	0.990445i	$-0.455962\pi$
$631$	6.92840	0.275815	0.137908	+	0.990445i	$0.455962\pi$
$632$	17.2859	0.687597
$633$	−1.89384	−0.0752735
$634$	1.02227	0.0405997
$635$	−9.16346	−0.363641
$636$	14.1289	0.560248
$637$	5.77478	0.228805
$638$	2.83654	0.112300
$639$	−19.7906	−0.782904
$640$	−1.00000	−0.0395285
$641$	36.9842	1.46079	0.730394	−	0.683026i	$-0.239337\pi$
$641$	36.9842	1.46079	0.730394	+	0.683026i	$0.239337\pi$
$642$	10.0415	0.396306
$643$	24.0370	0.947928	0.473964	−	0.880544i	$-0.342823\pi$
$643$	24.0370	0.947928	0.473964	+	0.880544i	$0.342823\pi$
$644$	1.05086	0.0414095
$645$	14.8845	0.586076
$646$	−44.3783	−1.74604
$647$	−25.3575	−0.996907	−0.498453	−	0.866916i	$-0.666099\pi$
$647$	−25.3575	−0.996907	−0.498453	+	0.866916i	$0.666099\pi$
$648$	3.51606	0.138124
$649$	−14.5970	−0.572983
$650$	0.836535	0.0328116
$651$	−0.903212	−0.0353997
$652$	1.99063	0.0779592
$653$	−39.9891	−1.56489	−0.782447	−	0.622717i	$-0.786029\pi$
$653$	−39.9891	−1.56489	−0.782447	+	0.622717i	$0.786029\pi$
$654$	13.0903	0.511873
$655$	−19.0923	−0.746000
$656$	8.36196	0.326480
$657$	4.54263	0.177225
$658$	1.25088	0.0487646
$659$	35.1876	1.37071	0.685357	−	0.728207i	$-0.259646\pi$
$659$	35.1876	1.37071	0.685357	+	0.728207i	$0.259646\pi$
$660$	1.31111	0.0510348
$661$	−5.18421	−0.201642	−0.100821	−	0.994905i	$-0.532147\pi$
$661$	−5.18421	−0.201642	−0.100821	+	0.994905i	$0.532147\pi$
$662$	−12.8938	−0.501133
$663$	−7.80642	−0.303176
$664$	−3.66815	−0.142352
$665$	1.93978	0.0752213
$666$	−3.14965	−0.122046
$667$	−9.58120	−0.370986
$668$	−2.32693	−0.0900316
$669$	−3.74620	−0.144836
$670$	1.00000	0.0386334
$671$	−10.0716	−0.388810
$672$	−0.407896	−0.0157349
$673$	16.6049	0.640070	0.320035	−	0.947406i	$-0.396305\pi$
$673$	16.6049	0.640070	0.320035	+	0.947406i	$0.396305\pi$
$674$	10.8113	0.416437
$675$	−5.61285	−0.216039
$676$	−12.3002	−0.473085
$677$	15.2257	0.585171	0.292586	−	0.956239i	$-0.405484\pi$
$677$	15.2257	0.585171	0.292586	+	0.956239i	$0.405484\pi$
$678$	3.23215	0.124130
$679$	3.64740	0.139975
$680$	−7.11753	−0.272945
$681$	11.7877	0.451705
$682$	2.21432	0.0847907
$683$	26.4889	1.01357	0.506784	−	0.862073i	$-0.330834\pi$
$683$	26.4889	1.01357	0.506784	+	0.862073i	$0.330834\pi$
$684$	−7.98709	−0.305394
$685$	−8.56691	−0.327325
$686$	4.32540	0.165144
$687$	−11.3985	−0.434881
$688$	11.3526	0.432814
$689$	−9.01477	−0.343435
$690$	−4.42864	−0.168595
$691$	36.3017	1.38098	0.690492	−	0.723340i	$-0.257394\pi$
$691$	36.3017	1.38098	0.690492	+	0.723340i	$0.257394\pi$
$692$	20.7669	0.789441
$693$	−0.398528	−0.0151388
$694$	−24.7654	−0.940082
$695$	−5.42372	−0.205733
$696$	3.71900	0.140968
$697$	59.5165	2.25435
$698$	−19.6414	−0.743439
$699$	−20.3620	−0.770160
$700$	0.311108	0.0117588
$701$	13.4538	0.508144	0.254072	−	0.967185i	$-0.418230\pi$
$701$	13.4538	0.508144	0.254072	+	0.967185i	$0.418230\pi$
$702$	−4.69535	−0.177214
$703$	−15.3305	−0.578200
$704$	1.00000	0.0376889
$705$	−5.27163	−0.198541
$706$	−15.8020	−0.594715
$707$	3.45584	0.129970
$708$	−19.1383	−0.719260
$709$	−5.36995	−0.201673	−0.100836	−	0.994903i	$-0.532152\pi$
$709$	−5.36995	−0.201673	−0.100836	+	0.994903i	$0.532152\pi$
$710$	−15.4494	−0.579805
$711$	22.1432	0.830435
$712$	−8.05086	−0.301719
$713$	−7.47949	−0.280109
$714$	−2.90321	−0.108650
$715$	−0.836535	−0.0312846
$716$	8.38271	0.313276
$717$	7.78769	0.290837
$718$	17.3477	0.647409
$719$	5.44785	0.203171	0.101585	−	0.994827i	$-0.467609\pi$
$719$	5.44785	0.203171	0.101585	+	0.994827i	$0.467609\pi$
$720$	−1.28100	−0.0477399
$721$	1.46320	0.0544923
$722$	−19.8760	−0.739709
$723$	−3.66079	−0.136146
$724$	10.9382	0.406517
$725$	−2.83654	−0.105346
$726$	13.1111	0.486598
$727$	2.17929	0.0808252	0.0404126	−	0.999183i	$-0.487133\pi$
$727$	2.17929	0.0808252	0.0404126	+	0.999183i	$0.487133\pi$
$728$	0.260253	0.00964561
$729$	26.5812	0.984489
$730$	3.54617	0.131250
$731$	80.8025	2.98859
$732$	−13.2050	−0.488069
$733$	−0.528342	−0.0195148	−0.00975738	−	0.999952i	$-0.503106\pi$
$733$	−0.528342	−0.0195148	−0.00975738	+	0.999952i	$0.503106\pi$
$734$	−21.4050	−0.790072
$735$	−9.05086	−0.333846
$736$	−3.37778	−0.124507
$737$	−1.00000	−0.0368355
$738$	10.7116	0.394301
$739$	−6.84299	−0.251723	−0.125862	−	0.992048i	$-0.540170\pi$
$739$	−6.84299	−0.251723	−0.125862	+	0.992048i	$0.540170\pi$
$740$	−2.45875	−0.0903855
$741$	−6.83854	−0.251220
$742$	−3.35260	−0.123078
$743$	2.67460	0.0981216	0.0490608	−	0.998796i	$-0.484377\pi$
$743$	2.67460	0.0981216	0.0490608	+	0.998796i	$0.484377\pi$
$744$	2.90321	0.106437
$745$	−10.0000	−0.366372
$746$	33.1655	1.21427
$747$	−4.69888	−0.171923
$748$	7.11753	0.260243
$749$	−2.38271	−0.0870622
$750$	−1.31111	−0.0478749
$751$	14.7141	0.536924	0.268462	−	0.963290i	$-0.413485\pi$
$751$	14.7141	0.536924	0.268462	+	0.963290i	$0.413485\pi$
$752$	−4.02074	−0.146621
$753$	−25.7210	−0.937326
$754$	−2.37286	−0.0864145
$755$	−21.2558	−0.773578
$756$	−1.74620	−0.0635087
$757$	−41.7768	−1.51840	−0.759202	−	0.650856i	$-0.774410\pi$
$757$	−41.7768	−1.51840	−0.759202	+	0.650856i	$0.774410\pi$
$758$	25.3319	0.920094
$759$	4.42864	0.160749
$760$	−6.23506	−0.226170
$761$	−30.5714	−1.10821	−0.554105	−	0.832446i	$-0.686940\pi$
$761$	−30.5714	−1.10821	−0.554105	+	0.832446i	$0.686940\pi$
$762$	12.0143	0.435232
$763$	−3.10616	−0.112450
$764$	−5.65233	−0.204494
$765$	−9.11753	−0.329645
$766$	−13.6844	−0.494439
$767$	12.2109	0.440911
$768$	1.31111	0.0473105
$769$	48.5150	1.74950	0.874748	−	0.484578i	$-0.161027\pi$
$769$	48.5150	1.74950	0.874748	+	0.484578i	$0.161027\pi$
$770$	−0.311108	−0.0112115
$771$	33.4148	1.20341
$772$	10.1684	0.365968
$773$	−53.1037	−1.91001	−0.955004	−	0.296593i	$-0.904150\pi$
$773$	−53.1037	−1.91001	−0.955004	+	0.296593i	$0.904150\pi$
$774$	14.5426	0.522724
$775$	−2.21432	−0.0795407
$776$	−11.7239	−0.420864
$777$	−1.00291	−0.0359794
$778$	−6.19358	−0.222050
$779$	52.1374	1.86802
$780$	−1.09679	−0.0392713
$781$	15.4494	0.552822
$782$	−24.0415	−0.859722
$783$	15.9210	0.568972
$784$	−6.90321	−0.246543
$785$	−2.14764	−0.0766527
$786$	25.0321	0.892866
$787$	−28.3718	−1.01135	−0.505673	−	0.862725i	$-0.668756\pi$
$787$	−28.3718	−1.01135	−0.505673	+	0.862725i	$0.668756\pi$
$788$	−16.6035	−0.591474
$789$	−32.4973	−1.15694
$790$	17.2859	0.615005
$791$	−0.766944	−0.0272694
$792$	1.28100	0.0455182
$793$	8.42525	0.299189
$794$	−4.37133	−0.155133
$795$	14.1289	0.501101
$796$	−23.9240	−0.847962
$797$	−8.44891	−0.299276	−0.149638	−	0.988741i	$-0.547811\pi$
$797$	−8.44891	−0.299276	−0.149638	+	0.988741i	$0.547811\pi$
$798$	−2.54326	−0.0900303
$799$	−28.6178	−1.01242
$800$	−1.00000	−0.0353553
$801$	−10.3131	−0.364396
$802$	−18.6287	−0.657801
$803$	−3.54617	−0.125142
$804$	−1.31111	−0.0462392
$805$	1.05086	0.0370378
$806$	−1.85236	−0.0652465
$807$	34.1432	1.20190
$808$	−11.1082	−0.390784
$809$	−5.81288	−0.204370	−0.102185	−	0.994765i	$-0.532583\pi$
$809$	−5.81288	−0.204370	−0.102185	+	0.994765i	$0.532583\pi$
$810$	3.51606	0.123542
$811$	43.9447	1.54311	0.771554	−	0.636164i	$-0.219480\pi$
$811$	43.9447	1.54311	0.771554	+	0.636164i	$0.219480\pi$
$812$	−0.882468	−0.0309686
$813$	6.71810	0.235614
$814$	2.45875	0.0861792
$815$	1.99063	0.0697288
$816$	9.33185	0.326680
$817$	70.7841	2.47642
$818$	−24.9971	−0.874003
$819$	0.333383	0.0116493
$820$	8.36196	0.292012
$821$	−43.0716	−1.50321	−0.751605	−	0.659614i	$-0.770720\pi$
$821$	−43.0716	−1.50321	−0.751605	+	0.659614i	$0.770720\pi$
$822$	11.2321	0.391766
$823$	5.91903	0.206325	0.103162	−	0.994665i	$-0.467104\pi$
$823$	5.91903	0.206325	0.103162	+	0.994665i	$0.467104\pi$
$824$	−4.70318	−0.163843
$825$	1.31111	0.0456469
$826$	4.54125	0.158010
$827$	36.4608	1.26786	0.633932	−	0.773388i	$-0.281440\pi$
$827$	36.4608	1.26786	0.633932	+	0.773388i	$0.281440\pi$
$828$	−4.32693	−0.150371
$829$	−16.7841	−0.582938	−0.291469	−	0.956580i	$-0.594144\pi$
$829$	−16.7841	−0.582938	−0.291469	+	0.956580i	$0.594144\pi$
$830$	−3.66815	−0.127323
$831$	17.7482	0.615679
$832$	−0.836535	−0.0290016
$833$	−49.1338	−1.70239
$834$	7.11108	0.246236
$835$	−2.32693	−0.0805267
$836$	6.23506	0.215644
$837$	12.4286	0.429597
$838$	3.93978	0.136097
$839$	−20.6450	−0.712743	−0.356372	−	0.934344i	$-0.615986\pi$
$839$	−20.6450	−0.712743	−0.356372	+	0.934344i	$0.615986\pi$
$840$	−0.407896	−0.0140737
$841$	−20.9541	−0.722554
$842$	−30.3892	−1.04728
$843$	34.6093	1.19201
$844$	−1.44446	−0.0497204
$845$	−12.3002	−0.423140
$846$	−5.15056	−0.177080
$847$	−3.11108	−0.106898
$848$	10.7763	0.370060
$849$	−19.1403	−0.656893
$850$	−7.11753	−0.244129
$851$	−8.30513	−0.284696
$852$	20.2558	0.693953
$853$	−8.67259	−0.296944	−0.148472	−	0.988917i	$-0.547435\pi$
$853$	−8.67259	−0.296944	−0.148472	+	0.988917i	$0.547435\pi$
$854$	3.13335	0.107221
$855$	−7.98709	−0.273153
$856$	7.65878	0.261772
$857$	18.9210	0.646330	0.323165	−	0.946343i	$-0.395253\pi$
$857$	18.9210	0.646330	0.323165	+	0.946343i	$0.395253\pi$
$858$	1.09679	0.0374437
$859$	−33.4445	−1.14111	−0.570555	−	0.821259i	$-0.693272\pi$
$859$	−33.4445	−1.14111	−0.570555	+	0.821259i	$0.693272\pi$
$860$	11.3526	0.387120
$861$	3.41081	0.116240
$862$	−8.03011	−0.273507
$863$	16.7052	0.568651	0.284326	−	0.958728i	$-0.408230\pi$
$863$	16.7052	0.568651	0.284326	+	0.958728i	$0.408230\pi$
$864$	5.61285	0.190953
$865$	20.7669	0.706097
$866$	−27.7605	−0.943340
$867$	44.1309	1.49876
$868$	−0.688892	−0.0233825
$869$	−17.2859	−0.586385
$870$	3.71900	0.126086
$871$	0.836535	0.0283449
$872$	9.98418	0.338107
$873$	−15.0183	−0.508293
$874$	−21.0607	−0.712389
$875$	0.311108	0.0105174
$876$	−4.64941	−0.157089
$877$	16.7841	0.566760	0.283380	−	0.959008i	$-0.408544\pi$
$877$	16.7841	0.566760	0.283380	+	0.959008i	$0.408544\pi$
$878$	18.0158	0.608005
$879$	−34.3517	−1.15865
$880$	1.00000	0.0337100
$881$	−21.0558	−0.709387	−0.354694	−	0.934983i	$-0.615415\pi$
$881$	−21.0558	−0.709387	−0.354694	+	0.934983i	$0.615415\pi$
$882$	−8.84299	−0.297759
$883$	27.6258	0.929681	0.464840	−	0.885395i	$-0.346112\pi$
$883$	27.6258	0.929681	0.464840	+	0.885395i	$0.346112\pi$
$884$	−5.95407	−0.200257
$885$	−19.1383	−0.643326
$886$	−4.02858	−0.135343
$887$	−20.7950	−0.698229	−0.349115	−	0.937080i	$-0.613518\pi$
$887$	−20.7950	−0.698229	−0.349115	+	0.937080i	$0.613518\pi$
$888$	3.22369	0.108180
$889$	−2.85083	−0.0956136
$890$	−8.05086	−0.269865
$891$	−3.51606	−0.117792
$892$	−2.85728	−0.0956688
$893$	−25.0696	−0.838922
$894$	13.1111	0.438500
$895$	8.38271	0.280203
$896$	−0.311108	−0.0103934
$897$	−3.70471	−0.123697
$898$	−30.6271	−1.02204
$899$	6.28100	0.209483
$900$	−1.28100	−0.0426999
$901$	76.7007	2.55527
$902$	−8.36196	−0.278423
$903$	4.63068	0.154099
$904$	2.46520	0.0819915
$905$	10.9382	0.363600
$906$	27.8687	0.925874
$907$	−27.7382	−0.921032	−0.460516	−	0.887651i	$-0.652336\pi$
$907$	−27.7382	−0.921032	−0.460516	+	0.887651i	$0.652336\pi$
$908$	8.99063	0.298365
$909$	−14.2295	−0.471963
$910$	0.260253	0.00862729
$911$	1.09387	0.0362417	0.0181208	−	0.999836i	$-0.494232\pi$
$911$	1.09387	0.0362417	0.0181208	+	0.999836i	$0.494232\pi$
$912$	8.17484	0.270696
$913$	3.66815	0.121398
$914$	26.3368	0.871143
$915$	−13.2050	−0.436542
$916$	−8.69381	−0.287252
$917$	−5.93978	−0.196149
$918$	39.9496	1.31853
$919$	5.18421	0.171011	0.0855056	−	0.996338i	$-0.472749\pi$
$919$	5.18421	0.171011	0.0855056	+	0.996338i	$0.472749\pi$
$920$	−3.37778	−0.111362
$921$	−20.5555	−0.677328
$922$	20.3082	0.668815
$923$	−12.9240	−0.425397
$924$	0.407896	0.0134188
$925$	−2.45875	−0.0808432
$926$	22.8256	0.750097
$927$	−6.02476	−0.197879
$928$	2.83654	0.0931138
$929$	30.0830	0.986990	0.493495	−	0.869749i	$-0.335719\pi$
$929$	30.0830	0.986990	0.493495	+	0.869749i	$0.335719\pi$
$930$	2.90321	0.0952001
$931$	−43.0420	−1.41064
$932$	−15.5303	−0.508714
$933$	−19.1985	−0.628531
$934$	10.9857	0.359463
$935$	7.11753	0.232768
$936$	−1.07160	−0.0350263
$937$	39.0384	1.27533	0.637665	−	0.770314i	$-0.279900\pi$
$937$	39.0384	1.27533	0.637665	+	0.770314i	$0.279900\pi$
$938$	0.311108	0.0101580
$939$	−7.40699	−0.241718
$940$	−4.02074	−0.131142
$941$	20.7467	0.676322	0.338161	−	0.941088i	$-0.390195\pi$
$941$	20.7467	0.676322	0.338161	+	0.941088i	$0.390195\pi$
$942$	2.81579	0.0917435
$943$	28.2449	0.919781
$944$	−14.5970	−0.475093
$945$	−1.74620	−0.0568039
$946$	−11.3526	−0.369105
$947$	−13.3511	−0.433851	−0.216926	−	0.976188i	$-0.569603\pi$
$947$	−13.3511	−0.433851	−0.216926	+	0.976188i	$0.569603\pi$
$948$	−22.6637	−0.736083
$949$	2.96650	0.0962966
$950$	−6.23506	−0.202292
$951$	−1.34031	−0.0434626
$952$	−2.21432	−0.0717665
$953$	−35.5714	−1.15227	−0.576135	−	0.817355i	$-0.695440\pi$
$953$	−35.5714	−1.15227	−0.576135	+	0.817355i	$0.695440\pi$
$954$	13.8044	0.446934
$955$	−5.65233	−0.182905
$956$	5.93978	0.192106
$957$	−3.71900	−0.120218
$958$	9.09526	0.293854
$959$	−2.66523	−0.0860649
$960$	1.31111	0.0423158
$961$	−26.0968	−0.841832
$962$	−2.05683	−0.0663149
$963$	9.81087	0.316151
$964$	−2.79213	−0.0899286
$965$	10.1684	0.327332
$966$	−1.37778	−0.0443295
$967$	45.3165	1.45728	0.728640	−	0.684897i	$-0.240153\pi$
$967$	45.3165	1.45728	0.728640	+	0.684897i	$0.240153\pi$
$968$	10.0000	0.321412
$969$	58.1847	1.86916
$970$	−11.7239	−0.376433
$971$	−54.5531	−1.75069	−0.875346	−	0.483497i	$-0.839367\pi$
$971$	−54.5531	−1.75069	−0.875346	+	0.483497i	$0.839367\pi$
$972$	12.2286	0.392233
$973$	−1.68736	−0.0540943
$974$	2.67952	0.0858575
$975$	−1.09679	−0.0351253
$976$	−10.0716	−0.322384
$977$	−25.2478	−0.807749	−0.403875	−	0.914814i	$-0.632337\pi$
$977$	−25.2478	−0.807749	−0.403875	+	0.914814i	$0.632337\pi$
$978$	−2.60993	−0.0834565
$979$	8.05086	0.257306
$980$	−6.90321	−0.220515
$981$	12.7897	0.408344
$982$	36.5970	1.16786
$983$	57.1022	1.82128	0.910638	−	0.413204i	$-0.135590\pi$
$983$	57.1022	1.82128	0.910638	+	0.413204i	$0.135590\pi$
$984$	−10.9634	−0.349502
$985$	−16.6035	−0.529031
$986$	20.1891	0.642953
$987$	−1.64004	−0.0522032
$988$	−5.21585	−0.165938
$989$	38.3466	1.21935
$990$	1.28100	0.0407127
$991$	30.1017	0.956212	0.478106	−	0.878302i	$-0.341323\pi$
$991$	30.1017	0.956212	0.478106	+	0.878302i	$0.341323\pi$
$992$	2.21432	0.0703047
$993$	16.9052	0.536471
$994$	−4.80642	−0.152451
$995$	−23.9240	−0.758440
$996$	4.80934	0.152390
$997$	−56.1086	−1.77698	−0.888489	−	0.458897i	$-0.848245\pi$
$997$	−56.1086	−1.77698	−0.888489	+	0.458897i	$0.848245\pi$
$998$	6.09234	0.192850
$999$	13.8006	0.436632

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	670.2.a.g.1.2	✓	3
3.2	odd	2		6030.2.a.br.1.2		3
4.3	odd	2		5360.2.a.x.1.2		3
5.2	odd	4		3350.2.c.h.2949.2		6
5.3	odd	4		3350.2.c.h.2949.5		6
5.4	even	2		3350.2.a.l.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
670.2.a.g.1.2	✓	3	1.1	even	1	trivial
3350.2.a.l.1.2		3	5.4	even	2
3350.2.c.h.2949.2		6	5.2	odd	4
3350.2.c.h.2949.5		6	5.3	odd	4
5360.2.a.x.1.2		3	4.3	odd	2
6030.2.a.br.1.2		3	3.2	odd	2

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:	\( N \)	\(=\)	\( 670 = 2 \cdot 5 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	670.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.31111 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.31111 q^{6} +0.311108 q^{7} -1.00000 q^{8} -1.28100 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.31111 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.31111 q^{6} +0.311108 q^{7} -1.00000 q^{8} -1.28100 q^{9} -1.00000 q^{10} +1.00000 q^{11} +1.31111 q^{12} -0.836535 q^{13} -0.311108 q^{14} +1.31111 q^{15} +1.00000 q^{16} +7.11753 q^{17} +1.28100 q^{18} +6.23506 q^{19} +1.00000 q^{20} +0.407896 q^{21} -1.00000 q^{22} +3.37778 q^{23} -1.31111 q^{24} +1.00000 q^{25} +0.836535 q^{26} -5.61285 q^{27} +0.311108 q^{28} -2.83654 q^{29} -1.31111 q^{30} -2.21432 q^{31} -1.00000 q^{32} +1.31111 q^{33} -7.11753 q^{34} +0.311108 q^{35} -1.28100 q^{36} -2.45875 q^{37} -6.23506 q^{38} -1.09679 q^{39} -1.00000 q^{40} +8.36196 q^{41} -0.407896 q^{42} +11.3526 q^{43} +1.00000 q^{44} -1.28100 q^{45} -3.37778 q^{46} -4.02074 q^{47} +1.31111 q^{48} -6.90321 q^{49} -1.00000 q^{50} +9.33185 q^{51} -0.836535 q^{52} +10.7763 q^{53} +5.61285 q^{54} +1.00000 q^{55} -0.311108 q^{56} +8.17484 q^{57} +2.83654 q^{58} -14.5970 q^{59} +1.31111 q^{60} -10.0716 q^{61} +2.21432 q^{62} -0.398528 q^{63} +1.00000 q^{64} -0.836535 q^{65} -1.31111 q^{66} -1.00000 q^{67} +7.11753 q^{68} +4.42864 q^{69} -0.311108 q^{70} +15.4494 q^{71} +1.28100 q^{72} -3.54617 q^{73} +2.45875 q^{74} +1.31111 q^{75} +6.23506 q^{76} +0.311108 q^{77} +1.09679 q^{78} -17.2859 q^{79} +1.00000 q^{80} -3.51606 q^{81} -8.36196 q^{82} +3.66815 q^{83} +0.407896 q^{84} +7.11753 q^{85} -11.3526 q^{86} -3.71900 q^{87} -1.00000 q^{88} +8.05086 q^{89} +1.28100 q^{90} -0.260253 q^{91} +3.37778 q^{92} -2.90321 q^{93} +4.02074 q^{94} +6.23506 q^{95} -1.31111 q^{96} +11.7239 q^{97} +6.90321 q^{98} -1.28100 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} + 4 q^{3} + 3 q^{4} + 3 q^{5} - 4 q^{6} + q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 + 4 * q^3 + 3 * q^4 + 3 * q^5 - 4 * q^6 + q^7 - 3 * q^8 + 3 * q^9	\( 3 q - 3 q^{2} + 4 q^{3} + 3 q^{4} + 3 q^{5} - 4 q^{6} + q^{7} - 3 q^{8} + 3 q^{9} - 3 q^{10} + 3 q^{11} + 4 q^{12} + 4 q^{13} - q^{14} + 4 q^{15} + 3 q^{16} + 8 q^{17} - 3 q^{18} - 8 q^{19} + 3 q^{20} + 8 q^{21} - 3 q^{22} + 10 q^{23} - 4 q^{24} + 3 q^{25} - 4 q^{26} + 10 q^{27} + q^{28} - 2 q^{29} - 4 q^{30} - 3 q^{32} + 4 q^{33} - 8 q^{34} + q^{35} + 3 q^{36} - q^{37} + 8 q^{38} - 10 q^{39} - 3 q^{40} + 12 q^{41} - 8 q^{42} - 6 q^{43} + 3 q^{44} + 3 q^{45} - 10 q^{46} + 8 q^{47} + 4 q^{48} - 14 q^{49} - 3 q^{50} + 8 q^{51} + 4 q^{52} + 12 q^{53} - 10 q^{54} + 3 q^{55} - q^{56} - 16 q^{57} + 2 q^{58} - 4 q^{59} + 4 q^{60} + 3 q^{61} + 19 q^{63} + 3 q^{64} + 4 q^{65} - 4 q^{66} - 3 q^{67} + 8 q^{68} - q^{70} + 13 q^{71} - 3 q^{72} + 16 q^{73} + q^{74} + 4 q^{75} - 8 q^{76} + q^{77} + 10 q^{78} - 12 q^{79} + 3 q^{80} + 23 q^{81} - 12 q^{82} + 31 q^{83} + 8 q^{84} + 8 q^{85} + 6 q^{86} - 18 q^{87} - 3 q^{88} + 11 q^{89} - 3 q^{90} - 14 q^{91} + 10 q^{92} - 2 q^{93} - 8 q^{94} - 8 q^{95} - 4 q^{96} + 9 q^{97} + 14 q^{98} + 3 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 + 4 * q^3 + 3 * q^4 + 3 * q^5 - 4 * q^6 + q^7 - 3 * q^8 + 3 * q^9 - 3 * q^10 + 3 * q^11 + 4 * q^12 + 4 * q^13 - q^14 + 4 * q^15 + 3 * q^16 + 8 * q^17 - 3 * q^18 - 8 * q^19 + 3 * q^20 + 8 * q^21 - 3 * q^22 + 10 * q^23 - 4 * q^24 + 3 * q^25 - 4 * q^26 + 10 * q^27 + q^28 - 2 * q^29 - 4 * q^30 - 3 * q^32 + 4 * q^33 - 8 * q^34 + q^35 + 3 * q^36 - q^37 + 8 * q^38 - 10 * q^39 - 3 * q^40 + 12 * q^41 - 8 * q^42 - 6 * q^43 + 3 * q^44 + 3 * q^45 - 10 * q^46 + 8 * q^47 + 4 * q^48 - 14 * q^49 - 3 * q^50 + 8 * q^51 + 4 * q^52 + 12 * q^53 - 10 * q^54 + 3 * q^55 - q^56 - 16 * q^57 + 2 * q^58 - 4 * q^59 + 4 * q^60 + 3 * q^61 + 19 * q^63 + 3 * q^64 + 4 * q^65 - 4 * q^66 - 3 * q^67 + 8 * q^68 - q^70 + 13 * q^71 - 3 * q^72 + 16 * q^73 + q^74 + 4 * q^75 - 8 * q^76 + q^77 + 10 * q^78 - 12 * q^79 + 3 * q^80 + 23 * q^81 - 12 * q^82 + 31 * q^83 + 8 * q^84 + 8 * q^85 + 6 * q^86 - 18 * q^87 - 3 * q^88 + 11 * q^89 - 3 * q^90 - 14 * q^91 + 10 * q^92 - 2 * q^93 - 8 * q^94 - 8 * q^95 - 4 * q^96 + 9 * q^97 + 14 * q^98 + 3 * q^99

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