LMFDB - Embedded newform 4641.2.a.w.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4641,2,Mod(1,4641)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4641, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4641.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4641 = 3 \cdot 7 \cdot 13 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4641.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:	$37.0585715781$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - x^{13} - 22 x^{12} + 19 x^{11} + 187 x^{10} - 135 x^{9} - 776 x^{8} + 443 x^{7} + 1636 x^{6} + \cdots - 19 $ x^14 - x^13 - 22x^12 + 19x^11 + 187x^10 - 135x^9 - 776x^8 + 443x^7 + 1636x^6 - 648x^5 - 1635x^4 + 306x^3 + 604x^2 + 8x - 19
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$-0.724018$ of defining polynomial
Character	$\chi$	$=$	4641.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.724018 q^{2} -1.00000 q^{3} -1.47580 q^{4} -0.789548 q^{5} -0.724018 q^{6} +1.00000 q^{7} -2.51654 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.724018 q^{2} -1.00000 q^{3} -1.47580 q^{4} -0.789548 q^{5} -0.724018 q^{6} +1.00000 q^{7} -2.51654 q^{8} +1.00000 q^{9} -0.571646 q^{10} +4.73322 q^{11} +1.47580 q^{12} +1.00000 q^{13} +0.724018 q^{14} +0.789548 q^{15} +1.12958 q^{16} +1.00000 q^{17} +0.724018 q^{18} -1.88881 q^{19} +1.16521 q^{20} -1.00000 q^{21} +3.42694 q^{22} -2.75694 q^{23} +2.51654 q^{24} -4.37661 q^{25} +0.724018 q^{26} -1.00000 q^{27} -1.47580 q^{28} +4.76446 q^{29} +0.571646 q^{30} -2.81730 q^{31} +5.85091 q^{32} -4.73322 q^{33} +0.724018 q^{34} -0.789548 q^{35} -1.47580 q^{36} +1.28402 q^{37} -1.36753 q^{38} -1.00000 q^{39} +1.98693 q^{40} +3.27909 q^{41} -0.724018 q^{42} -3.85937 q^{43} -6.98529 q^{44} -0.789548 q^{45} -1.99607 q^{46} +8.50080 q^{47} -1.12958 q^{48} +1.00000 q^{49} -3.16875 q^{50} -1.00000 q^{51} -1.47580 q^{52} -10.1456 q^{53} -0.724018 q^{54} -3.73711 q^{55} -2.51654 q^{56} +1.88881 q^{57} +3.44955 q^{58} -0.185274 q^{59} -1.16521 q^{60} -8.87418 q^{61} -2.03977 q^{62} +1.00000 q^{63} +1.97701 q^{64} -0.789548 q^{65} -3.42694 q^{66} +5.26312 q^{67} -1.47580 q^{68} +2.75694 q^{69} -0.571646 q^{70} -11.3864 q^{71} -2.51654 q^{72} +13.9605 q^{73} +0.929654 q^{74} +4.37661 q^{75} +2.78750 q^{76} +4.73322 q^{77} -0.724018 q^{78} -3.88905 q^{79} -0.891856 q^{80} +1.00000 q^{81} +2.37412 q^{82} +15.9895 q^{83} +1.47580 q^{84} -0.789548 q^{85} -2.79425 q^{86} -4.76446 q^{87} -11.9113 q^{88} +6.54006 q^{89} -0.571646 q^{90} +1.00000 q^{91} +4.06869 q^{92} +2.81730 q^{93} +6.15473 q^{94} +1.49130 q^{95} -5.85091 q^{96} -8.31071 q^{97} +0.724018 q^{98} +4.73322 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - q^{2} - 14 q^{3} + 17 q^{4} - q^{5} + q^{6} + 14 q^{7} - 6 q^{8} + 14 q^{9}+O(q^{10}) $ 14 * q - q^2 - 14 * q^3 + 17 * q^4 - q^5 + q^6 + 14 * q^7 - 6 * q^8 + 14 * q^9	\( 14 q - q^{2} - 14 q^{3} + 17 q^{4} - q^{5} + q^{6} + 14 q^{7} - 6 q^{8} + 14 q^{9} + 11 q^{10} - 4 q^{11} - 17 q^{12} + 14 q^{13} - q^{14} + q^{15} + 19 q^{16} + 14 q^{17} - q^{18} + 6 q^{19} + q^{20} - 14 q^{21} + 12 q^{22} + 7 q^{23} + 6 q^{24} + 19 q^{25} - q^{26} - 14 q^{27} + 17 q^{28} - 4 q^{29} - 11 q^{30} + 31 q^{31} - 18 q^{32} + 4 q^{33} - q^{34} - q^{35} + 17 q^{36} + 2 q^{37} + 9 q^{38} - 14 q^{39} + 50 q^{40} + 4 q^{41} + q^{42} + 14 q^{43} - 8 q^{44} - q^{45} - 17 q^{46} - q^{47} - 19 q^{48} + 14 q^{49} - 3 q^{50} - 14 q^{51} + 17 q^{52} - 43 q^{53} + q^{54} + 23 q^{55} - 6 q^{56} - 6 q^{57} - 10 q^{58} + 11 q^{59} - q^{60} + 25 q^{61} - 3 q^{62} + 14 q^{63} + 36 q^{64} - q^{65} - 12 q^{66} + 11 q^{67} + 17 q^{68} - 7 q^{69} + 11 q^{70} + 20 q^{71} - 6 q^{72} + 14 q^{73} - 24 q^{74} - 19 q^{75} + 9 q^{76} - 4 q^{77} + q^{78} + 42 q^{79} + 13 q^{80} + 14 q^{81} + 2 q^{82} + 15 q^{83} - 17 q^{84} - q^{85} - 11 q^{86} + 4 q^{87} + 63 q^{88} + 21 q^{89} + 11 q^{90} + 14 q^{91} + 30 q^{92} - 31 q^{93} - 29 q^{94} + 16 q^{95} + 18 q^{96} + 15 q^{97} - q^{98} - 4 q^{99}+O(q^{100}) \) 14 * q - q^2 - 14 * q^3 + 17 * q^4 - q^5 + q^6 + 14 * q^7 - 6 * q^8 + 14 * q^9 + 11 * q^10 - 4 * q^11 - 17 * q^12 + 14 * q^13 - q^14 + q^15 + 19 * q^16 + 14 * q^17 - q^18 + 6 * q^19 + q^20 - 14 * q^21 + 12 * q^22 + 7 * q^23 + 6 * q^24 + 19 * q^25 - q^26 - 14 * q^27 + 17 * q^28 - 4 * q^29 - 11 * q^30 + 31 * q^31 - 18 * q^32 + 4 * q^33 - q^34 - q^35 + 17 * q^36 + 2 * q^37 + 9 * q^38 - 14 * q^39 + 50 * q^40 + 4 * q^41 + q^42 + 14 * q^43 - 8 * q^44 - q^45 - 17 * q^46 - q^47 - 19 * q^48 + 14 * q^49 - 3 * q^50 - 14 * q^51 + 17 * q^52 - 43 * q^53 + q^54 + 23 * q^55 - 6 * q^56 - 6 * q^57 - 10 * q^58 + 11 * q^59 - q^60 + 25 * q^61 - 3 * q^62 + 14 * q^63 + 36 * q^64 - q^65 - 12 * q^66 + 11 * q^67 + 17 * q^68 - 7 * q^69 + 11 * q^70 + 20 * q^71 - 6 * q^72 + 14 * q^73 - 24 * q^74 - 19 * q^75 + 9 * q^76 - 4 * q^77 + q^78 + 42 * q^79 + 13 * q^80 + 14 * q^81 + 2 * q^82 + 15 * q^83 - 17 * q^84 - q^85 - 11 * q^86 + 4 * q^87 + 63 * q^88 + 21 * q^89 + 11 * q^90 + 14 * q^91 + 30 * q^92 - 31 * q^93 - 29 * q^94 + 16 * q^95 + 18 * q^96 + 15 * q^97 - q^98 - 4 * 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 $

$2$	0.724018	0.511958	0.255979	−	0.966682i	$-0.417602\pi$
$2$	0.724018	0.511958	0.255979	+	0.966682i	$0.417602\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.47580	−0.737899
$5$	−0.789548	−0.353096	−0.176548	−	0.984292i	$-0.556493\pi$
$5$	−0.789548	−0.353096	−0.176548	+	0.984292i	$0.556493\pi$
$6$	−0.724018	−0.295579
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−2.51654	−0.889731
$9$	1.00000	0.333333
$10$	−0.571646	−0.180770
$11$	4.73322	1.42712	0.713560	−	0.700594i	$-0.247081\pi$
$11$	4.73322	1.42712	0.713560	+	0.700594i	$0.247081\pi$
$12$	1.47580	0.426026
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	0.724018	0.193502
$15$	0.789548	0.203860
$16$	1.12958	0.282395
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	0.724018	0.170653
$19$	−1.88881	−0.433322	−0.216661	−	0.976247i	$-0.569517\pi$
$19$	−1.88881	−0.433322	−0.216661	+	0.976247i	$0.569517\pi$
$20$	1.16521	0.260550
$21$	−1.00000	−0.218218
$22$	3.42694	0.730626
$23$	−2.75694	−0.574862	−0.287431	−	0.957801i	$-0.592801\pi$
$23$	−2.75694	−0.574862	−0.287431	+	0.957801i	$0.592801\pi$
$24$	2.51654	0.513686
$25$	−4.37661	−0.875323
$26$	0.724018	0.141992
$27$	−1.00000	−0.192450
$28$	−1.47580	−0.278900
$29$	4.76446	0.884738	0.442369	−	0.896833i	$-0.354138\pi$
$29$	4.76446	0.884738	0.442369	+	0.896833i	$0.354138\pi$
$30$	0.571646	0.104368
$31$	−2.81730	−0.506001	−0.253001	−	0.967466i	$-0.581417\pi$
$31$	−2.81730	−0.506001	−0.253001	+	0.967466i	$0.581417\pi$
$32$	5.85091	1.03431
$33$	−4.73322	−0.823949
$34$	0.724018	0.124168
$35$	−0.789548	−0.133458
$36$	−1.47580	−0.245966
$37$	1.28402	0.211092	0.105546	−	0.994414i	$-0.466341\pi$
$37$	1.28402	0.211092	0.105546	+	0.994414i	$0.466341\pi$
$38$	−1.36753	−0.221843
$39$	−1.00000	−0.160128
$40$	1.98693	0.314161
$41$	3.27909	0.512108	0.256054	−	0.966662i	$-0.417578\pi$
$41$	3.27909	0.512108	0.256054	+	0.966662i	$0.417578\pi$
$42$	−0.724018	−0.111718
$43$	−3.85937	−0.588549	−0.294275	−	0.955721i	$-0.595078\pi$
$43$	−3.85937	−0.588549	−0.294275	+	0.955721i	$0.595078\pi$
$44$	−6.98529	−1.05307
$45$	−0.789548	−0.117699
$46$	−1.99607	−0.294305
$47$	8.50080	1.23997	0.619985	−	0.784614i	$-0.287139\pi$
$47$	8.50080	1.23997	0.619985	+	0.784614i	$0.287139\pi$
$48$	−1.12958	−0.163041
$49$	1.00000	0.142857
$50$	−3.16875	−0.448128
$51$	−1.00000	−0.140028
$52$	−1.47580	−0.204656
$53$	−10.1456	−1.39361	−0.696804	−	0.717261i	$-0.745395\pi$
$53$	−10.1456	−1.39361	−0.696804	+	0.717261i	$0.745395\pi$
$54$	−0.724018	−0.0985263
$55$	−3.73711	−0.503911
$56$	−2.51654	−0.336287
$57$	1.88881	0.250179
$58$	3.44955	0.452949
$59$	−0.185274	−0.0241206	−0.0120603	−	0.999927i	$-0.503839\pi$
$59$	−0.185274	−0.0241206	−0.0120603	+	0.999927i	$0.503839\pi$
$60$	−1.16521	−0.150428
$61$	−8.87418	−1.13622	−0.568111	−	0.822952i	$-0.692326\pi$
$61$	−8.87418	−1.13622	−0.568111	+	0.822952i	$0.692326\pi$
$62$	−2.03977	−0.259051
$63$	1.00000	0.125988
$64$	1.97701	0.247126
$65$	−0.789548	−0.0979313
$66$	−3.42694	−0.421827
$67$	5.26312	0.642993	0.321496	−	0.946911i	$-0.395814\pi$
$67$	5.26312	0.642993	0.321496	+	0.946911i	$0.395814\pi$
$68$	−1.47580	−0.178967
$69$	2.75694	0.331897
$70$	−0.571646	−0.0683248
$71$	−11.3864	−1.35132	−0.675660	−	0.737213i	$-0.736141\pi$
$71$	−11.3864	−1.35132	−0.675660	+	0.737213i	$0.736141\pi$
$72$	−2.51654	−0.296577
$73$	13.9605	1.63395	0.816974	−	0.576675i	$-0.195650\pi$
$73$	13.9605	1.63395	0.816974	+	0.576675i	$0.195650\pi$
$74$	0.929654	0.108070
$75$	4.37661	0.505368
$76$	2.78750	0.319748
$77$	4.73322	0.539401
$78$	−0.724018	−0.0819788
$79$	−3.88905	−0.437553	−0.218776	−	0.975775i	$-0.570207\pi$
$79$	−3.88905	−0.437553	−0.218776	+	0.975775i	$0.570207\pi$
$80$	−0.891856	−0.0997125
$81$	1.00000	0.111111
$82$	2.37412	0.262178
$83$	15.9895	1.75508	0.877539	−	0.479506i	$-0.159184\pi$
$83$	15.9895	1.75508	0.877539	+	0.479506i	$0.159184\pi$
$84$	1.47580	0.161023
$85$	−0.789548	−0.0856385
$86$	−2.79425	−0.301312
$87$	−4.76446	−0.510804
$88$	−11.9113	−1.26975
$89$	6.54006	0.693245	0.346623	−	0.938005i	$-0.387328\pi$
$89$	6.54006	0.693245	0.346623	+	0.938005i	$0.387328\pi$
$90$	−0.571646	−0.0602568
$91$	1.00000	0.104828
$92$	4.06869	0.424190
$93$	2.81730	0.292140
$94$	6.15473	0.634812
$95$	1.49130	0.153005
$96$	−5.85091	−0.597156
$97$	−8.31071	−0.843825	−0.421913	−	0.906637i	$-0.638641\pi$
$97$	−8.31071	−0.843825	−0.421913	+	0.906637i	$0.638641\pi$
$98$	0.724018	0.0731368
$99$	4.73322	0.475707
$100$	6.45900	0.645900
$101$	−2.03466	−0.202456	−0.101228	−	0.994863i	$-0.532277\pi$
$101$	−2.03466	−0.202456	−0.101228	+	0.994863i	$0.532277\pi$
$102$	−0.724018	−0.0716884
$103$	5.79000	0.570505	0.285253	−	0.958452i	$-0.407923\pi$
$103$	5.79000	0.570505	0.285253	+	0.958452i	$0.407923\pi$
$104$	−2.51654	−0.246767
$105$	0.789548	0.0770520
$106$	−7.34561	−0.713469
$107$	−5.65393	−0.546586	−0.273293	−	0.961931i	$-0.588113\pi$
$107$	−5.65393	−0.546586	−0.273293	+	0.961931i	$0.588113\pi$
$108$	1.47580	0.142009
$109$	10.0012	0.957942	0.478971	−	0.877831i	$-0.341010\pi$
$109$	10.0012	0.957942	0.478971	+	0.877831i	$0.341010\pi$
$110$	−2.70573	−0.257981
$111$	−1.28402	−0.121874
$112$	1.12958	0.106735
$113$	−7.02766	−0.661107	−0.330553	−	0.943787i	$-0.607235\pi$
$113$	−7.02766	−0.661107	−0.330553	+	0.943787i	$0.607235\pi$
$114$	1.36753	0.128081
$115$	2.17674	0.202982
$116$	−7.03139	−0.652848
$117$	1.00000	0.0924500
$118$	−0.134141	−0.0123487
$119$	1.00000	0.0916698
$120$	−1.98693	−0.181381
$121$	11.4034	1.03667
$122$	−6.42506	−0.581698
$123$	−3.27909	−0.295666
$124$	4.15776	0.373378
$125$	7.40328	0.662170
$126$	0.724018	0.0645006
$127$	11.1103	0.985878	0.492939	−	0.870064i	$-0.335923\pi$
$127$	11.1103	0.985878	0.492939	+	0.870064i	$0.335923\pi$
$128$	−10.2704	−0.907787
$129$	3.85937	0.339799
$130$	−0.571646	−0.0501367
$131$	5.15154	0.450092	0.225046	−	0.974348i	$-0.427747\pi$
$131$	5.15154	0.450092	0.225046	+	0.974348i	$0.427747\pi$
$132$	6.98529	0.607991
$133$	−1.88881	−0.163780
$134$	3.81059	0.329185
$135$	0.789548	0.0679534
$136$	−2.51654	−0.215791
$137$	1.41659	0.121027	0.0605137	−	0.998167i	$-0.480726\pi$
$137$	1.41659	0.121027	0.0605137	+	0.998167i	$0.480726\pi$
$138$	1.99607	0.169917
$139$	−1.62890	−0.138161	−0.0690807	−	0.997611i	$-0.522007\pi$
$139$	−1.62890	−0.138161	−0.0690807	+	0.997611i	$0.522007\pi$
$140$	1.16521	0.0984785
$141$	−8.50080	−0.715897
$142$	−8.24398	−0.691819
$143$	4.73322	0.395812
$144$	1.12958	0.0941315
$145$	−3.76177	−0.312398
$146$	10.1076	0.836512
$147$	−1.00000	−0.0824786
$148$	−1.89496	−0.155765
$149$	−2.68493	−0.219958	−0.109979	−	0.993934i	$-0.535078\pi$
$149$	−2.68493	−0.219958	−0.109979	+	0.993934i	$0.535078\pi$
$150$	3.16875	0.258727
$151$	12.6922	1.03288	0.516440	−	0.856323i	$-0.327257\pi$
$151$	12.6922	1.03288	0.516440	+	0.856323i	$0.327257\pi$
$152$	4.75326	0.385540
$153$	1.00000	0.0808452
$154$	3.42694	0.276150
$155$	2.22439	0.178667
$156$	1.47580	0.118158
$157$	15.3363	1.22397	0.611983	−	0.790871i	$-0.290372\pi$
$157$	15.3363	1.22397	0.611983	+	0.790871i	$0.290372\pi$
$158$	−2.81574	−0.224009
$159$	10.1456	0.804600
$160$	−4.61957	−0.365209
$161$	−2.75694	−0.217277
$162$	0.724018	0.0568842
$163$	3.14718	0.246506	0.123253	−	0.992375i	$-0.460667\pi$
$163$	3.14718	0.246506	0.123253	+	0.992375i	$0.460667\pi$
$164$	−4.83928	−0.377884
$165$	3.73711	0.290933
$166$	11.5767	0.898526
$167$	19.3076	1.49407	0.747034	−	0.664786i	$-0.231477\pi$
$167$	19.3076	1.49407	0.747034	+	0.664786i	$0.231477\pi$
$168$	2.51654	0.194155
$169$	1.00000	0.0769231
$170$	−0.571646	−0.0438433
$171$	−1.88881	−0.144441
$172$	5.69566	0.434290
$173$	−2.76579	−0.210279	−0.105140	−	0.994457i	$-0.533529\pi$
$173$	−2.76579	−0.210279	−0.105140	+	0.994457i	$0.533529\pi$
$174$	−3.44955	−0.261510
$175$	−4.37661	−0.330841
$176$	5.34655	0.403011
$177$	0.185274	0.0139260
$178$	4.73512	0.354912
$179$	18.7932	1.40467	0.702336	−	0.711846i	$-0.252141\pi$
$179$	18.7932	1.40467	0.702336	+	0.711846i	$0.252141\pi$
$180$	1.16521	0.0868499
$181$	3.76790	0.280066	0.140033	−	0.990147i	$-0.455279\pi$
$181$	3.76790	0.280066	0.140033	+	0.990147i	$0.455279\pi$
$182$	0.724018	0.0536678
$183$	8.87418	0.655998
$184$	6.93795	0.511472
$185$	−1.01380	−0.0745358
$186$	2.03977	0.149563
$187$	4.73322	0.346128
$188$	−12.5455	−0.914973
$189$	−1.00000	−0.0727393
$190$	1.07973	0.0783319
$191$	6.04658	0.437515	0.218757	−	0.975779i	$-0.429800\pi$
$191$	6.04658	0.437515	0.218757	+	0.975779i	$0.429800\pi$
$192$	−1.97701	−0.142678
$193$	16.3988	1.18041	0.590205	−	0.807253i	$-0.299047\pi$
$193$	16.3988	1.18041	0.590205	+	0.807253i	$0.299047\pi$
$194$	−6.01710	−0.432003
$195$	0.789548	0.0565407
$196$	−1.47580	−0.105414
$197$	18.9381	1.34929	0.674643	−	0.738145i	$-0.264298\pi$
$197$	18.9381	1.34929	0.674643	+	0.738145i	$0.264298\pi$
$198$	3.42694	0.243542
$199$	16.0691	1.13911	0.569555	−	0.821953i	$-0.307115\pi$
$199$	16.0691	1.13911	0.569555	+	0.821953i	$0.307115\pi$
$200$	11.0139	0.778802
$201$	−5.26312	−0.371232
$202$	−1.47313	−0.103649
$203$	4.76446	0.334400
$204$	1.47580	0.103327
$205$	−2.58900	−0.180823
$206$	4.19206	0.292075
$207$	−2.75694	−0.191621
$208$	1.12958	0.0783222
$209$	−8.94015	−0.618403
$210$	0.571646	0.0394473
$211$	−9.96507	−0.686024	−0.343012	−	0.939331i	$-0.611447\pi$
$211$	−9.96507	−0.686024	−0.343012	+	0.939331i	$0.611447\pi$
$212$	14.9729	1.02834
$213$	11.3864	0.780185
$214$	−4.09355	−0.279829
$215$	3.04716	0.207815
$216$	2.51654	0.171229
$217$	−2.81730	−0.191250
$218$	7.24105	0.490426
$219$	−13.9605	−0.943360
$220$	5.51522	0.371836
$221$	1.00000	0.0672673
$222$	−0.929654	−0.0623943
$223$	−9.75788	−0.653436	−0.326718	−	0.945122i	$-0.605943\pi$
$223$	−9.75788	−0.653436	−0.326718	+	0.945122i	$0.605943\pi$
$224$	5.85091	0.390931
$225$	−4.37661	−0.291774
$226$	−5.08815	−0.338459
$227$	−17.3471	−1.15137	−0.575685	−	0.817672i	$-0.695264\pi$
$227$	−17.3471	−1.15137	−0.575685	+	0.817672i	$0.695264\pi$
$228$	−2.78750	−0.184607
$229$	28.9451	1.91275	0.956374	−	0.292144i	$-0.0943688\pi$
$229$	28.9451	1.91275	0.956374	+	0.292144i	$0.0943688\pi$
$230$	1.57599	0.103918
$231$	−4.73322	−0.311423
$232$	−11.9900	−0.787179
$233$	7.00084	0.458641	0.229320	−	0.973351i	$-0.426350\pi$
$233$	7.00084	0.458641	0.229320	+	0.973351i	$0.426350\pi$
$234$	0.724018	0.0473305
$235$	−6.71179	−0.437829
$236$	0.273426	0.0177985
$237$	3.88905	0.252621
$238$	0.724018	0.0469311
$239$	25.8123	1.66966	0.834831	−	0.550507i	$-0.185566\pi$
$239$	25.8123	1.66966	0.834831	+	0.550507i	$0.185566\pi$
$240$	0.891856	0.0575691
$241$	4.73774	0.305184	0.152592	−	0.988289i	$-0.451238\pi$
$241$	4.73774	0.305184	0.152592	+	0.988289i	$0.451238\pi$
$242$	8.25627	0.530733
$243$	−1.00000	−0.0641500
$244$	13.0965	0.838417
$245$	−0.789548	−0.0504423
$246$	−2.37412	−0.151368
$247$	−1.88881	−0.120182
$248$	7.08983	0.450205
$249$	−15.9895	−1.01329
$250$	5.36011	0.339003
$251$	−7.70532	−0.486355	−0.243178	−	0.969982i	$-0.578190\pi$
$251$	−7.70532	−0.486355	−0.243178	+	0.969982i	$0.578190\pi$
$252$	−1.47580	−0.0929666
$253$	−13.0492	−0.820397
$254$	8.04404	0.504728
$255$	0.789548	0.0494434
$256$	−11.3900	−0.711875
$257$	0.356418	0.0222328	0.0111164	−	0.999938i	$-0.496461\pi$
$257$	0.356418	0.0222328	0.0111164	+	0.999938i	$0.496461\pi$
$258$	2.79425	0.173963
$259$	1.28402	0.0797852
$260$	1.16521	0.0722635
$261$	4.76446	0.294913
$262$	3.72981	0.230428
$263$	−14.4367	−0.890206	−0.445103	−	0.895479i	$-0.646833\pi$
$263$	−14.4367	−0.890206	−0.445103	+	0.895479i	$0.646833\pi$
$264$	11.9113	0.733093
$265$	8.01045	0.492078
$266$	−1.36753	−0.0838486
$267$	−6.54006	−0.400245
$268$	−7.76731	−0.474464
$269$	24.3241	1.48307	0.741533	−	0.670917i	$-0.234099\pi$
$269$	24.3241	1.48307	0.741533	+	0.670917i	$0.234099\pi$
$270$	0.571646	0.0347893
$271$	−2.03234	−0.123456	−0.0617279	−	0.998093i	$-0.519661\pi$
$271$	−2.03234	−0.123456	−0.0617279	+	0.998093i	$0.519661\pi$
$272$	1.12958	0.0684907
$273$	−1.00000	−0.0605228
$274$	1.02564	0.0619609
$275$	−20.7155	−1.24919
$276$	−4.06869	−0.244906
$277$	26.2103	1.57482	0.787411	−	0.616428i	$-0.211421\pi$
$277$	26.2103	1.57482	0.787411	+	0.616428i	$0.211421\pi$
$278$	−1.17935	−0.0707328
$279$	−2.81730	−0.168667
$280$	1.98693	0.118742
$281$	−11.4656	−0.683983	−0.341991	−	0.939703i	$-0.611101\pi$
$281$	−11.4656	−0.683983	−0.341991	+	0.939703i	$0.611101\pi$
$282$	−6.15473	−0.366509
$283$	12.9590	0.770332	0.385166	−	0.922847i	$-0.374144\pi$
$283$	12.9590	0.770332	0.385166	+	0.922847i	$0.374144\pi$
$284$	16.8041	0.997138
$285$	−1.49130	−0.0883372
$286$	3.42694	0.202639
$287$	3.27909	0.193559
$288$	5.85091	0.344768
$289$	1.00000	0.0588235
$290$	−2.72359	−0.159935
$291$	8.31071	0.487183
$292$	−20.6028	−1.20569
$293$	15.2267	0.889551	0.444775	−	0.895642i	$-0.353284\pi$
$293$	15.2267	0.889551	0.444775	+	0.895642i	$0.353284\pi$
$294$	−0.724018	−0.0422256
$295$	0.146282	0.00851689
$296$	−3.23129	−0.187815
$297$	−4.73322	−0.274650
$298$	−1.94394	−0.112609
$299$	−2.75694	−0.159438
$300$	−6.45900	−0.372911
$301$	−3.85937	−0.222451
$302$	9.18941	0.528791
$303$	2.03466	0.116888
$304$	−2.13356	−0.122368
$305$	7.00658	0.401196
$306$	0.724018	0.0413893
$307$	−4.71856	−0.269302	−0.134651	−	0.990893i	$-0.542991\pi$
$307$	−4.71856	−0.269302	−0.134651	+	0.990893i	$0.542991\pi$
$308$	−6.98529	−0.398024
$309$	−5.79000	−0.329381
$310$	1.61050	0.0914701
$311$	−15.8211	−0.897130	−0.448565	−	0.893750i	$-0.648065\pi$
$311$	−15.8211	−0.897130	−0.448565	+	0.893750i	$0.648065\pi$
$312$	2.51654	0.142471
$313$	1.24401	0.0703155	0.0351577	−	0.999382i	$-0.488807\pi$
$313$	1.24401	0.0703155	0.0351577	+	0.999382i	$0.488807\pi$
$314$	11.1037	0.626619
$315$	−0.789548	−0.0444860
$316$	5.73946	0.322870
$317$	−7.25147	−0.407283	−0.203641	−	0.979046i	$-0.565278\pi$
$317$	−7.25147	−0.407283	−0.203641	+	0.979046i	$0.565278\pi$
$318$	7.34561	0.411921
$319$	22.5513	1.26263
$320$	−1.56094	−0.0872593
$321$	5.65393	0.315572
$322$	−1.99607	−0.111237
$323$	−1.88881	−0.105096
$324$	−1.47580	−0.0819888
$325$	−4.37661	−0.242771
$326$	2.27861	0.126201
$327$	−10.0012	−0.553068
$328$	−8.25196	−0.455638
$329$	8.50080	0.468664
$330$	2.70573	0.148946
$331$	5.52098	0.303460	0.151730	−	0.988422i	$-0.451516\pi$
$331$	5.52098	0.303460	0.151730	+	0.988422i	$0.451516\pi$
$332$	−23.5973	−1.29507
$333$	1.28402	0.0703639
$334$	13.9791	0.764900
$335$	−4.15549	−0.227038
$336$	−1.12958	−0.0616235
$337$	−34.4589	−1.87710	−0.938548	−	0.345148i	$-0.887829\pi$
$337$	−34.4589	−1.87710	−0.938548	+	0.345148i	$0.887829\pi$
$338$	0.724018	0.0393814
$339$	7.02766	0.381690
$340$	1.16521	0.0631926
$341$	−13.3349	−0.722125
$342$	−1.36753	−0.0739476
$343$	1.00000	0.0539949
$344$	9.71227	0.523650
$345$	−2.17674	−0.117191
$346$	−2.00248	−0.107654
$347$	−0.693872	−0.0372490	−0.0186245	−	0.999827i	$-0.505929\pi$
$347$	−0.693872	−0.0372490	−0.0186245	+	0.999827i	$0.505929\pi$
$348$	7.03139	0.376922
$349$	2.80617	0.150211	0.0751054	−	0.997176i	$-0.476071\pi$
$349$	2.80617	0.150211	0.0751054	+	0.997176i	$0.476071\pi$
$350$	−3.16875	−0.169377
$351$	−1.00000	−0.0533761
$352$	27.6937	1.47608
$353$	3.21855	0.171306	0.0856530	−	0.996325i	$-0.472702\pi$
$353$	3.21855	0.171306	0.0856530	+	0.996325i	$0.472702\pi$
$354$	0.134141	0.00712953
$355$	8.99013	0.477146
$356$	−9.65181	−0.511545
$357$	−1.00000	−0.0529256
$358$	13.6066	0.719132
$359$	−35.3596	−1.86621	−0.933105	−	0.359605i	$-0.882911\pi$
$359$	−35.3596	−1.86621	−0.933105	+	0.359605i	$0.882911\pi$
$360$	1.98693	0.104720
$361$	−15.4324	−0.812232
$362$	2.72803	0.143382
$363$	−11.4034	−0.598524
$364$	−1.47580	−0.0773529
$365$	−11.0224	−0.576941
$366$	6.42506	0.335843
$367$	13.7855	0.719597	0.359799	−	0.933030i	$-0.382845\pi$
$367$	13.7855	0.719597	0.359799	+	0.933030i	$0.382845\pi$
$368$	−3.11418	−0.162338
$369$	3.27909	0.170703
$370$	−0.734006	−0.0381592
$371$	−10.1456	−0.526734
$372$	−4.15776	−0.215570
$373$	3.93182	0.203582	0.101791	−	0.994806i	$-0.467543\pi$
$373$	3.93182	0.203582	0.101791	+	0.994806i	$0.467543\pi$
$374$	3.42694	0.177203
$375$	−7.40328	−0.382304
$376$	−21.3926	−1.10324
$377$	4.76446	0.245382
$378$	−0.724018	−0.0372394
$379$	30.3734	1.56018	0.780088	−	0.625670i	$-0.215174\pi$
$379$	30.3734	1.56018	0.780088	+	0.625670i	$0.215174\pi$
$380$	−2.20086	−0.112902
$381$	−11.1103	−0.569197
$382$	4.37783	0.223989
$383$	0.694605	0.0354927	0.0177463	−	0.999843i	$-0.494351\pi$
$383$	0.694605	0.0354927	0.0177463	+	0.999843i	$0.494351\pi$
$384$	10.2704	0.524111
$385$	−3.73711	−0.190461
$386$	11.8730	0.604320
$387$	−3.85937	−0.196183
$388$	12.2649	0.622658
$389$	−30.5182	−1.54733	−0.773667	−	0.633593i	$-0.781580\pi$
$389$	−30.5182	−1.54733	−0.773667	+	0.633593i	$0.781580\pi$
$390$	0.571646	0.0289464
$391$	−2.75694	−0.139424
$392$	−2.51654	−0.127104
$393$	−5.15154	−0.259861
$394$	13.7115	0.690777
$395$	3.07059	0.154498
$396$	−6.98529	−0.351024
$397$	−37.0461	−1.85929	−0.929646	−	0.368455i	$-0.879887\pi$
$397$	−37.0461	−1.85929	−0.929646	+	0.368455i	$0.879887\pi$
$398$	11.6343	0.583177
$399$	1.88881	0.0945587
$400$	−4.94373	−0.247186
$401$	−10.4835	−0.523519	−0.261759	−	0.965133i	$-0.584303\pi$
$401$	−10.4835	−0.523519	−0.261759	+	0.965133i	$0.584303\pi$
$402$	−3.81059	−0.190055
$403$	−2.81730	−0.140339
$404$	3.00274	0.149392
$405$	−0.789548	−0.0392329
$406$	3.44955	0.171199
$407$	6.07756	0.301254
$408$	2.51654	0.124587
$409$	24.5237	1.21262	0.606309	−	0.795229i	$-0.292649\pi$
$409$	24.5237	1.21262	0.606309	+	0.795229i	$0.292649\pi$
$410$	−1.87448	−0.0925740
$411$	−1.41659	−0.0698752
$412$	−8.54487	−0.420975
$413$	−0.185274	−0.00911672
$414$	−1.99607	−0.0981016
$415$	−12.6245	−0.619712
$416$	5.85091	0.286865
$417$	1.62890	0.0797675
$418$	−6.47283	−0.316596
$419$	−13.4846	−0.658767	−0.329383	−	0.944196i	$-0.606841\pi$
$419$	−13.4846	−0.658767	−0.329383	+	0.944196i	$0.606841\pi$
$420$	−1.16521	−0.0568566
$421$	8.43079	0.410892	0.205446	−	0.978668i	$-0.434136\pi$
$421$	8.43079	0.410892	0.205446	+	0.978668i	$0.434136\pi$
$422$	−7.21489	−0.351215
$423$	8.50080	0.413323
$424$	25.5319	1.23994
$425$	−4.37661	−0.212297
$426$	8.24398	0.399422
$427$	−8.87418	−0.429451
$428$	8.34407	0.403326
$429$	−4.73322	−0.228522
$430$	2.20620	0.106392
$431$	40.2083	1.93677	0.968383	−	0.249469i	$-0.0802562\pi$
$431$	40.2083	1.93677	0.968383	+	0.249469i	$0.0802562\pi$
$432$	−1.12958	−0.0543469
$433$	−6.83537	−0.328487	−0.164243	−	0.986420i	$-0.552518\pi$
$433$	−6.83537	−0.328487	−0.164243	+	0.986420i	$0.552518\pi$
$434$	−2.03977	−0.0979122
$435$	3.76177	0.180363
$436$	−14.7598	−0.706865
$437$	5.20733	0.249100
$438$	−10.1076	−0.482960
$439$	−12.0444	−0.574848	−0.287424	−	0.957803i	$-0.592799\pi$
$439$	−12.0444	−0.574848	−0.287424	+	0.957803i	$0.592799\pi$
$440$	9.40457	0.448345
$441$	1.00000	0.0476190
$442$	0.724018	0.0344380
$443$	−37.5639	−1.78472	−0.892358	−	0.451327i	$-0.850951\pi$
$443$	−37.5639	−1.78472	−0.892358	+	0.451327i	$0.850951\pi$
$444$	1.89496	0.0899307
$445$	−5.16369	−0.244782
$446$	−7.06488	−0.334532
$447$	2.68493	0.126993
$448$	1.97701	0.0934048
$449$	10.7221	0.506006	0.253003	−	0.967466i	$-0.418582\pi$
$449$	10.7221	0.506006	0.253003	+	0.967466i	$0.418582\pi$
$450$	−3.16875	−0.149376
$451$	15.5207	0.730840
$452$	10.3714	0.487830
$453$	−12.6922	−0.596334
$454$	−12.5596	−0.589453
$455$	−0.789548	−0.0370146
$456$	−4.75326	−0.222592
$457$	−21.0380	−0.984115	−0.492057	−	0.870563i	$-0.663755\pi$
$457$	−21.0380	−0.984115	−0.492057	+	0.870563i	$0.663755\pi$
$458$	20.9568	0.979246
$459$	−1.00000	−0.0466760
$460$	−3.21242	−0.149780
$461$	−4.76313	−0.221841	−0.110921	−	0.993829i	$-0.535380\pi$
$461$	−4.76313	−0.221841	−0.110921	+	0.993829i	$0.535380\pi$
$462$	−3.42694	−0.159436
$463$	−16.2719	−0.756217	−0.378109	−	0.925761i	$-0.623425\pi$
$463$	−16.2719	−0.756217	−0.378109	+	0.925761i	$0.623425\pi$
$464$	5.38183	0.249845
$465$	−2.22439	−0.103154
$466$	5.06873	0.234805
$467$	1.03821	0.0480427	0.0240214	−	0.999711i	$-0.492353\pi$
$467$	1.03821	0.0480427	0.0240214	+	0.999711i	$0.492353\pi$
$468$	−1.47580	−0.0682188
$469$	5.26312	0.243028
$470$	−4.85945	−0.224150
$471$	−15.3363	−0.706657
$472$	0.466248	0.0214608
$473$	−18.2673	−0.839930
$474$	2.81574	0.129331
$475$	8.26658	0.379297
$476$	−1.47580	−0.0676431
$477$	−10.1456	−0.464536
$478$	18.6886	0.854796
$479$	36.3219	1.65959	0.829795	−	0.558069i	$-0.188457\pi$
$479$	36.3219	1.65959	0.829795	+	0.558069i	$0.188457\pi$
$480$	4.61957	0.210854
$481$	1.28402	0.0585463
$482$	3.43020	0.156242
$483$	2.75694	0.125445
$484$	−16.8291	−0.764961
$485$	6.56171	0.297952
$486$	−0.724018	−0.0328421
$487$	−16.8109	−0.761774	−0.380887	−	0.924622i	$-0.624381\pi$
$487$	−16.8109	−0.761774	−0.380887	+	0.924622i	$0.624381\pi$
$488$	22.3322	1.01093
$489$	−3.14718	−0.142320
$490$	−0.571646	−0.0258244
$491$	11.5544	0.521441	0.260720	−	0.965414i	$-0.416040\pi$
$491$	11.5544	0.521441	0.260720	+	0.965414i	$0.416040\pi$
$492$	4.83928	0.218171
$493$	4.76446	0.214581
$494$	−1.36753	−0.0615281
$495$	−3.73711	−0.167970
$496$	−3.18236	−0.142892
$497$	−11.3864	−0.510751
$498$	−11.5767	−0.518764
$499$	−14.6717	−0.656796	−0.328398	−	0.944539i	$-0.606509\pi$
$499$	−14.6717	−0.656796	−0.328398	+	0.944539i	$0.606509\pi$
$500$	−10.9258	−0.488615
$501$	−19.3076	−0.862601
$502$	−5.57878	−0.248993
$503$	16.3821	0.730443	0.365222	−	0.930921i	$-0.380993\pi$
$503$	16.3821	0.730443	0.365222	+	0.930921i	$0.380993\pi$
$504$	−2.51654	−0.112096
$505$	1.60646	0.0714865
$506$	−9.44786	−0.420009
$507$	−1.00000	−0.0444116
$508$	−16.3965	−0.727479
$509$	20.8689	0.924997	0.462498	−	0.886620i	$-0.346953\pi$
$509$	20.8689	0.924997	0.462498	+	0.886620i	$0.346953\pi$
$510$	0.571646	0.0253129
$511$	13.9605	0.617574
$512$	12.2943	0.543337
$513$	1.88881	0.0833929
$514$	0.258053	0.0113822
$515$	−4.57148	−0.201443
$516$	−5.69566	−0.250737
$517$	40.2362	1.76959
$518$	0.929654	0.0408467
$519$	2.76579	0.121405
$520$	1.98693	0.0871325
$521$	−2.31681	−0.101501	−0.0507507	−	0.998711i	$-0.516161\pi$
$521$	−2.31681	−0.101501	−0.0507507	+	0.998711i	$0.516161\pi$
$522$	3.44955	0.150983
$523$	16.8834	0.738257	0.369129	−	0.929378i	$-0.379656\pi$
$523$	16.8834	0.738257	0.369129	+	0.929378i	$0.379656\pi$
$524$	−7.60264	−0.332123
$525$	4.37661	0.191011
$526$	−10.4524	−0.455748
$527$	−2.81730	−0.122723
$528$	−5.34655	−0.232679
$529$	−15.3993	−0.669534
$530$	5.79971	0.251923
$531$	−0.185274	−0.00804019
$532$	2.78750	0.120853
$533$	3.27909	0.142033
$534$	−4.73512	−0.204909
$535$	4.46405	0.192998
$536$	−13.2449	−0.572091
$537$	−18.7932	−0.810987
$538$	17.6111	0.759267
$539$	4.73322	0.203874
$540$	−1.16521	−0.0501428
$541$	43.6514	1.87672	0.938359	−	0.345661i	$-0.112345\pi$
$541$	43.6514	1.87672	0.938359	+	0.345661i	$0.112345\pi$
$542$	−1.47145	−0.0632042
$543$	−3.76790	−0.161696
$544$	5.85091	0.250856
$545$	−7.89643	−0.338246
$546$	−0.724018	−0.0309851
$547$	−27.6785	−1.18345	−0.591724	−	0.806141i	$-0.701553\pi$
$547$	−27.6785	−1.18345	−0.591724	+	0.806141i	$0.701553\pi$
$548$	−2.09060	−0.0893060
$549$	−8.87418	−0.378741
$550$	−14.9984	−0.639533
$551$	−8.99915	−0.383377
$552$	−6.93795	−0.295299
$553$	−3.88905	−0.165379
$554$	18.9767	0.806242
$555$	1.01380	0.0430333
$556$	2.40393	0.101949
$557$	−46.7188	−1.97954	−0.989769	−	0.142677i	$-0.954429\pi$
$557$	−46.7188	−1.97954	−0.989769	+	0.142677i	$0.954429\pi$
$558$	−2.03977	−0.0863504
$559$	−3.85937	−0.163234
$560$	−0.891856	−0.0376878
$561$	−4.73322	−0.199837
$562$	−8.30132	−0.350170
$563$	−31.2636	−1.31760	−0.658801	−	0.752317i	$-0.728936\pi$
$563$	−31.2636	−1.31760	−0.658801	+	0.752317i	$0.728936\pi$
$564$	12.5455	0.528260
$565$	5.54867	0.233434
$566$	9.38254	0.394378
$567$	1.00000	0.0419961
$568$	28.6544	1.20231
$569$	−1.52740	−0.0640318	−0.0320159	−	0.999487i	$-0.510193\pi$
$569$	−1.52740	−0.0640318	−0.0320159	+	0.999487i	$0.510193\pi$
$570$	−1.07973	−0.0452249
$571$	8.88483	0.371819	0.185909	−	0.982567i	$-0.440477\pi$
$571$	8.88483	0.371819	0.185909	+	0.982567i	$0.440477\pi$
$572$	−6.98529	−0.292069
$573$	−6.04658	−0.252599
$574$	2.37412	0.0990938
$575$	12.0661	0.503190
$576$	1.97701	0.0823753
$577$	15.7228	0.654549	0.327275	−	0.944929i	$-0.393870\pi$
$577$	15.7228	0.654549	0.327275	+	0.944929i	$0.393870\pi$
$578$	0.724018	0.0301152
$579$	−16.3988	−0.681510
$580$	5.55161	0.230518
$581$	15.9895	0.663357
$582$	6.01710	0.249417
$583$	−48.0215	−1.98885
$584$	−35.1320	−1.45377
$585$	−0.789548	−0.0326438
$586$	11.0244	0.455412
$587$	7.49714	0.309440	0.154720	−	0.987958i	$-0.450552\pi$
$587$	7.49714	0.309440	0.154720	+	0.987958i	$0.450552\pi$
$588$	1.47580	0.0608609
$589$	5.32133	0.219262
$590$	0.105911	0.00436029
$591$	−18.9381	−0.779010
$592$	1.45040	0.0596112
$593$	−19.0300	−0.781469	−0.390735	−	0.920503i	$-0.627779\pi$
$593$	−19.0300	−0.781469	−0.390735	+	0.920503i	$0.627779\pi$
$594$	−3.42694	−0.140609
$595$	−0.789548	−0.0323683
$596$	3.96241	0.162307
$597$	−16.0691	−0.657666
$598$	−1.99607	−0.0816255
$599$	−16.5857	−0.677672	−0.338836	−	0.940845i	$-0.610033\pi$
$599$	−16.5857	−0.677672	−0.338836	+	0.940845i	$0.610033\pi$
$600$	−11.0139	−0.449641
$601$	30.6270	1.24930	0.624650	−	0.780905i	$-0.285242\pi$
$601$	30.6270	1.24930	0.624650	+	0.780905i	$0.285242\pi$
$602$	−2.79425	−0.113885
$603$	5.26312	0.214331
$604$	−18.7312	−0.762161
$605$	−9.00354	−0.366046
$606$	1.47313	0.0598417
$607$	−4.95253	−0.201017	−0.100509	−	0.994936i	$-0.532047\pi$
$607$	−4.95253	−0.201017	−0.100509	+	0.994936i	$0.532047\pi$
$608$	−11.0513	−0.448187
$609$	−4.76446	−0.193066
$610$	5.07289	0.205395
$611$	8.50080	0.343906
$612$	−1.47580	−0.0596556
$613$	0.813988	0.0328767	0.0164383	−	0.999865i	$-0.494767\pi$
$613$	0.813988	0.0328767	0.0164383	+	0.999865i	$0.494767\pi$
$614$	−3.41632	−0.137871
$615$	2.58900	0.104398
$616$	−11.9113	−0.479922
$617$	8.45649	0.340446	0.170223	−	0.985406i	$-0.445551\pi$
$617$	8.45649	0.340446	0.170223	+	0.985406i	$0.445551\pi$
$618$	−4.19206	−0.168629
$619$	29.9315	1.20305	0.601523	−	0.798855i	$-0.294561\pi$
$619$	29.9315	1.20305	0.601523	+	0.798855i	$0.294561\pi$
$620$	−3.28275	−0.131838
$621$	2.75694	0.110632
$622$	−11.4547	−0.459292
$623$	6.54006	0.262022
$624$	−1.12958	−0.0452193
$625$	16.0378	0.641513
$626$	0.900684	0.0359986
$627$	8.94015	0.357035
$628$	−22.6332	−0.903164
$629$	1.28402	0.0511973
$630$	−0.571646	−0.0227749
$631$	13.4280	0.534560	0.267280	−	0.963619i	$-0.413875\pi$
$631$	13.4280	0.534560	0.267280	+	0.963619i	$0.413875\pi$
$632$	9.78696	0.389304
$633$	9.96507	0.396076
$634$	−5.25019	−0.208512
$635$	−8.77209	−0.348110
$636$	−14.9729	−0.593714
$637$	1.00000	0.0396214
$638$	16.3275	0.646412
$639$	−11.3864	−0.450440
$640$	8.10900	0.320536
$641$	−18.3886	−0.726307	−0.363154	−	0.931729i	$-0.618300\pi$
$641$	−18.3886	−0.726307	−0.363154	+	0.931729i	$0.618300\pi$
$642$	4.09355	0.161559
$643$	19.5098	0.769393	0.384697	−	0.923043i	$-0.374306\pi$
$643$	19.5098	0.769393	0.384697	+	0.923043i	$0.374306\pi$
$644$	4.06869	0.160329
$645$	−3.04716	−0.119982
$646$	−1.36753	−0.0538048
$647$	40.8933	1.60768	0.803841	−	0.594845i	$-0.202787\pi$
$647$	40.8933	1.60768	0.803841	+	0.594845i	$0.202787\pi$
$648$	−2.51654	−0.0988590
$649$	−0.876941	−0.0344230
$650$	−3.16875	−0.124288
$651$	2.81730	0.110419
$652$	−4.64460	−0.181897
$653$	−15.3025	−0.598835	−0.299417	−	0.954122i	$-0.596792\pi$
$653$	−15.3025	−0.598835	−0.299417	+	0.954122i	$0.596792\pi$
$654$	−7.24105	−0.283148
$655$	−4.06739	−0.158926
$656$	3.70399	0.144616
$657$	13.9605	0.544649
$658$	6.15473	0.239936
$659$	41.0699	1.59985	0.799927	−	0.600097i	$-0.204871\pi$
$659$	41.0699	1.59985	0.799927	+	0.600097i	$0.204871\pi$
$660$	−5.51522	−0.214679
$661$	28.9278	1.12516	0.562581	−	0.826742i	$-0.309809\pi$
$661$	28.9278	1.12516	0.562581	+	0.826742i	$0.309809\pi$
$662$	3.99729	0.155359
$663$	−1.00000	−0.0388368
$664$	−40.2382	−1.56155
$665$	1.49130	0.0578303
$666$	0.929654	0.0360234
$667$	−13.1353	−0.508602
$668$	−28.4941	−1.10247
$669$	9.75788	0.377262
$670$	−3.00864	−0.116234
$671$	−42.0035	−1.62153
$672$	−5.85091	−0.225704
$673$	48.0239	1.85118	0.925592	−	0.378522i	$-0.123568\pi$
$673$	48.0239	1.85118	0.925592	+	0.378522i	$0.123568\pi$
$674$	−24.9489	−0.960994
$675$	4.37661	0.168456
$676$	−1.47580	−0.0567615
$677$	−10.2414	−0.393609	−0.196805	−	0.980443i	$-0.563056\pi$
$677$	−10.2414	−0.393609	−0.196805	+	0.980443i	$0.563056\pi$
$678$	5.08815	0.195409
$679$	−8.31071	−0.318936
$680$	1.98693	0.0761952
$681$	17.3471	0.664744
$682$	−9.65470	−0.369697
$683$	−13.3901	−0.512356	−0.256178	−	0.966630i	$-0.582463\pi$
$683$	−13.3901	−0.512356	−0.256178	+	0.966630i	$0.582463\pi$
$684$	2.78750	0.106583
$685$	−1.11846	−0.0427343
$686$	0.724018	0.0276431
$687$	−28.9451	−1.10433
$688$	−4.35947	−0.166203
$689$	−10.1456	−0.386517
$690$	−1.57599	−0.0599971
$691$	−38.0237	−1.44649	−0.723245	−	0.690591i	$-0.757350\pi$
$691$	−38.0237	−1.44649	−0.723245	+	0.690591i	$0.757350\pi$
$692$	4.08175	0.155165
$693$	4.73322	0.179800
$694$	−0.502375	−0.0190699
$695$	1.28609	0.0487843
$696$	11.9900	0.454478
$697$	3.27909	0.124204
$698$	2.03172	0.0769016
$699$	−7.00084	−0.264796
$700$	6.45900	0.244127
$701$	27.6096	1.04280	0.521400	−	0.853313i	$-0.325410\pi$
$701$	27.6096	1.04280	0.521400	+	0.853313i	$0.325410\pi$
$702$	−0.724018	−0.0273263
$703$	−2.42527	−0.0914708
$704$	9.35762	0.352679
$705$	6.71179	0.252781
$706$	2.33029	0.0877015
$707$	−2.03466	−0.0765211
$708$	−0.273426	−0.0102760
$709$	8.36669	0.314218	0.157109	−	0.987581i	$-0.449783\pi$
$709$	8.36669	0.314218	0.157109	+	0.987581i	$0.449783\pi$
$710$	6.50901	0.244279
$711$	−3.88905	−0.145851
$712$	−16.4583	−0.616802
$713$	7.76711	0.290881
$714$	−0.724018	−0.0270957
$715$	−3.73711	−0.139760
$716$	−27.7350	−1.03651
$717$	−25.8123	−0.963979
$718$	−25.6010	−0.955420
$719$	−21.8962	−0.816592	−0.408296	−	0.912850i	$-0.633877\pi$
$719$	−21.8962	−0.816592	−0.408296	+	0.912850i	$0.633877\pi$
$720$	−0.891856	−0.0332375
$721$	5.79000	0.215631
$722$	−11.1733	−0.415828
$723$	−4.73774	−0.176198
$724$	−5.56066	−0.206660
$725$	−20.8522	−0.774432
$726$	−8.25627	−0.306419
$727$	23.3113	0.864568	0.432284	−	0.901737i	$-0.357708\pi$
$727$	23.3113	0.864568	0.432284	+	0.901737i	$0.357708\pi$
$728$	−2.51654	−0.0932692
$729$	1.00000	0.0370370
$730$	−7.98044	−0.295369
$731$	−3.85937	−0.142744
$732$	−13.0965	−0.484060
$733$	−40.0508	−1.47931	−0.739655	−	0.672986i	$-0.765011\pi$
$733$	−40.0508	−1.47931	−0.739655	+	0.672986i	$0.765011\pi$
$734$	9.98094	0.368403
$735$	0.789548	0.0291229
$736$	−16.1306	−0.594582
$737$	24.9115	0.917628
$738$	2.37412	0.0873925
$739$	−10.3515	−0.380787	−0.190394	−	0.981708i	$-0.560976\pi$
$739$	−10.3515	−0.380787	−0.190394	+	0.981708i	$0.560976\pi$
$740$	1.49616	0.0549999
$741$	1.88881	0.0693871
$742$	−7.34561	−0.269666
$743$	20.1791	0.740301	0.370151	−	0.928972i	$-0.379306\pi$
$743$	20.1791	0.740301	0.370151	+	0.928972i	$0.379306\pi$
$744$	−7.08983	−0.259926
$745$	2.11988	0.0776664
$746$	2.84671	0.104225
$747$	15.9895	0.585026
$748$	−6.98529	−0.255407
$749$	−5.65393	−0.206590
$750$	−5.36011	−0.195723
$751$	6.85505	0.250144	0.125072	−	0.992148i	$-0.460084\pi$
$751$	6.85505	0.250144	0.125072	+	0.992148i	$0.460084\pi$
$752$	9.60232	0.350161
$753$	7.70532	0.280797
$754$	3.44955	0.125625
$755$	−10.0211	−0.364706
$756$	1.47580	0.0536743
$757$	4.40938	0.160262	0.0801308	−	0.996784i	$-0.474466\pi$
$757$	4.40938	0.160262	0.0801308	+	0.996784i	$0.474466\pi$
$758$	21.9909	0.798744
$759$	13.0492	0.473656
$760$	−3.75292	−0.136133
$761$	37.9925	1.37723	0.688613	−	0.725129i	$-0.258220\pi$
$761$	37.9925	1.37723	0.688613	+	0.725129i	$0.258220\pi$
$762$	−8.04404	−0.291405
$763$	10.0012	0.362068
$764$	−8.92353	−0.322842
$765$	−0.789548	−0.0285462
$766$	0.502906	0.0181707
$767$	−0.185274	−0.00668984
$768$	11.3900	0.411001
$769$	12.6784	0.457195	0.228597	−	0.973521i	$-0.426586\pi$
$769$	12.6784	0.457195	0.228597	+	0.973521i	$0.426586\pi$
$770$	−2.70573	−0.0975078
$771$	−0.356418	−0.0128361
$772$	−24.2013	−0.871024
$773$	15.2694	0.549202	0.274601	−	0.961558i	$-0.411454\pi$
$773$	15.2694	0.549202	0.274601	+	0.961558i	$0.411454\pi$
$774$	−2.79425	−0.100437
$775$	12.3302	0.442914
$776$	20.9142	0.750777
$777$	−1.28402	−0.0460640
$778$	−22.0957	−0.792170
$779$	−6.19357	−0.221908
$780$	−1.16521	−0.0417213
$781$	−53.8945	−1.92850
$782$	−1.99607	−0.0713794
$783$	−4.76446	−0.170268
$784$	1.12958	0.0403421
$785$	−12.1087	−0.432178
$786$	−3.72981	−0.133038
$787$	29.5873	1.05467	0.527336	−	0.849657i	$-0.323191\pi$
$787$	29.5873	1.05467	0.527336	+	0.849657i	$0.323191\pi$
$788$	−27.9488	−0.995637
$789$	14.4367	0.513960
$790$	2.22316	0.0790966
$791$	−7.02766	−0.249875
$792$	−11.9113	−0.423251
$793$	−8.87418	−0.315131
$794$	−26.8220	−0.951879
$795$	−8.01045	−0.284101
$796$	−23.7148	−0.840549
$797$	−36.9501	−1.30884	−0.654420	−	0.756131i	$-0.727087\pi$
$797$	−36.9501	−1.30884	−0.654420	+	0.756131i	$0.727087\pi$
$798$	1.36753	0.0484100
$799$	8.50080	0.300737
$800$	−25.6072	−0.905351
$801$	6.54006	0.231082
$802$	−7.59021	−0.268020
$803$	66.0779	2.33184
$804$	7.76731	0.273932
$805$	2.17674	0.0767198
$806$	−2.03977	−0.0718479
$807$	−24.3241	−0.856248
$808$	5.12029	0.180131
$809$	−45.0092	−1.58244	−0.791220	−	0.611531i	$-0.790554\pi$
$809$	−45.0092	−1.58244	−0.791220	+	0.611531i	$0.790554\pi$
$810$	−0.571646	−0.0200856
$811$	55.1810	1.93767	0.968833	−	0.247715i	$-0.0796796\pi$
$811$	55.1810	1.93767	0.968833	+	0.247715i	$0.0796796\pi$
$812$	−7.03139	−0.246753
$813$	2.03234	0.0712773
$814$	4.40026	0.154229
$815$	−2.48485	−0.0870404
$816$	−1.12958	−0.0395432
$817$	7.28962	0.255031
$818$	17.7556	0.620810
$819$	1.00000	0.0349428
$820$	3.82084	0.133430
$821$	−3.12206	−0.108961	−0.0544803	−	0.998515i	$-0.517350\pi$
$821$	−3.12206	−0.108961	−0.0544803	+	0.998515i	$0.517350\pi$
$822$	−1.02564	−0.0357732
$823$	−12.6623	−0.441381	−0.220691	−	0.975344i	$-0.570831\pi$
$823$	−12.6623	−0.441381	−0.220691	+	0.975344i	$0.570831\pi$
$824$	−14.5708	−0.507596
$825$	20.7155	0.721221
$826$	−0.134141	−0.00466737
$827$	39.7868	1.38352	0.691762	−	0.722126i	$-0.256835\pi$
$827$	39.7868	1.38352	0.691762	+	0.722126i	$0.256835\pi$
$828$	4.06869	0.141397
$829$	−16.8436	−0.585001	−0.292501	−	0.956265i	$-0.594487\pi$
$829$	−16.8436	−0.585001	−0.292501	+	0.956265i	$0.594487\pi$
$830$	−9.14035	−0.317266
$831$	−26.2103	−0.909224
$832$	1.97701	0.0685404
$833$	1.00000	0.0346479
$834$	1.17935	0.0408376
$835$	−15.2443	−0.527550
$836$	13.1939	0.456319
$837$	2.81730	0.0973800
$838$	−9.76310	−0.337261
$839$	−9.65267	−0.333247	−0.166624	−	0.986021i	$-0.553286\pi$
$839$	−9.65267	−0.333247	−0.166624	+	0.986021i	$0.553286\pi$
$840$	−1.98693	−0.0685555
$841$	−6.29990	−0.217238
$842$	6.10404	0.210359
$843$	11.4656	0.394898
$844$	14.7064	0.506217
$845$	−0.789548	−0.0271613
$846$	6.15473	0.211604
$847$	11.4034	0.391826
$848$	−11.4603	−0.393547
$849$	−12.9590	−0.444752
$850$	−3.16875	−0.108687
$851$	−3.53997	−0.121349
$852$	−16.8041	−0.575698
$853$	−9.40579	−0.322048	−0.161024	−	0.986950i	$-0.551480\pi$
$853$	−9.40579	−0.322048	−0.161024	+	0.986950i	$0.551480\pi$
$854$	−6.42506	−0.219861
$855$	1.49130	0.0510015
$856$	14.2283	0.486315
$857$	50.4964	1.72492	0.862462	−	0.506122i	$-0.168921\pi$
$857$	50.4964	1.72492	0.862462	+	0.506122i	$0.168921\pi$
$858$	−3.42694	−0.116994
$859$	20.2249	0.690065	0.345032	−	0.938591i	$-0.387868\pi$
$859$	20.2249	0.690065	0.345032	+	0.938591i	$0.387868\pi$
$860$	−4.49699	−0.153346
$861$	−3.27909	−0.111751
$862$	29.1115	0.991542
$863$	−47.3992	−1.61349	−0.806743	−	0.590902i	$-0.798772\pi$
$863$	−47.3992	−1.61349	−0.806743	+	0.590902i	$0.798772\pi$
$864$	−5.85091	−0.199052
$865$	2.18372	0.0742488
$866$	−4.94893	−0.168171
$867$	−1.00000	−0.0339618
$868$	4.15776	0.141124
$869$	−18.4078	−0.624441
$870$	2.72359	0.0923383
$871$	5.26312	0.178334
$872$	−25.1684	−0.852311
$873$	−8.31071	−0.281275
$874$	3.77020	0.127529
$875$	7.40328	0.250277
$876$	20.6028	0.696105
$877$	−29.5726	−0.998596	−0.499298	−	0.866430i	$-0.666409\pi$
$877$	−29.5726	−0.998596	−0.499298	+	0.866430i	$0.666409\pi$
$878$	−8.72037	−0.294298
$879$	−15.2267	−0.513582
$880$	−4.22135	−0.142302
$881$	−56.0282	−1.88764	−0.943819	−	0.330464i	$-0.892795\pi$
$881$	−56.0282	−1.88764	−0.943819	+	0.330464i	$0.892795\pi$
$882$	0.724018	0.0243789
$883$	2.77768	0.0934765	0.0467382	−	0.998907i	$-0.485117\pi$
$883$	2.77768	0.0934765	0.0467382	+	0.998907i	$0.485117\pi$
$884$	−1.47580	−0.0496365
$885$	−0.146282	−0.00491723
$886$	−27.1970	−0.913700
$887$	−33.2367	−1.11598	−0.557989	−	0.829848i	$-0.688427\pi$
$887$	−33.2367	−1.11598	−0.557989	+	0.829848i	$0.688427\pi$
$888$	3.23129	0.108435
$889$	11.1103	0.372627
$890$	−3.73860	−0.125318
$891$	4.73322	0.158569
$892$	14.4007	0.482170
$893$	−16.0564	−0.537306
$894$	1.94394	0.0650149
$895$	−14.8381	−0.495984
$896$	−10.2704	−0.343111
$897$	2.75694	0.0920515
$898$	7.76297	0.259054
$899$	−13.4229	−0.447679
$900$	6.45900	0.215300
$901$	−10.1456	−0.338000
$902$	11.2372	0.374159
$903$	3.85937	0.128432
$904$	17.6854	0.588207
$905$	−2.97494	−0.0988902
$906$	−9.18941	−0.305298
$907$	17.3788	0.577055	0.288527	−	0.957472i	$-0.406834\pi$
$907$	17.3788	0.577055	0.288527	+	0.957472i	$0.406834\pi$
$908$	25.6009	0.849595
$909$	−2.03466	−0.0674853
$910$	−0.571646	−0.0189499
$911$	−25.7970	−0.854693	−0.427346	−	0.904088i	$-0.640552\pi$
$911$	−25.7970	−0.854693	−0.427346	+	0.904088i	$0.640552\pi$
$912$	2.13356	0.0706491
$913$	75.6820	2.50471
$914$	−15.2319	−0.503825
$915$	−7.00658	−0.231631
$916$	−42.7172	−1.41142
$917$	5.15154	0.170119
$918$	−0.724018	−0.0238961
$919$	28.9919	0.956353	0.478177	−	0.878264i	$-0.341298\pi$
$919$	28.9919	0.956353	0.478177	+	0.878264i	$0.341298\pi$
$920$	−5.47784	−0.180599
$921$	4.71856	0.155482
$922$	−3.44859	−0.113573
$923$	−11.3864	−0.374789
$924$	6.98529	0.229799
$925$	−5.61967	−0.184774
$926$	−11.7811	−0.387151
$927$	5.79000	0.190168
$928$	27.8765	0.915089
$929$	−49.3595	−1.61943	−0.809717	−	0.586821i	$-0.800379\pi$
$929$	−49.3595	−1.61943	−0.809717	+	0.586821i	$0.800379\pi$
$930$	−1.61050	−0.0528103
$931$	−1.88881	−0.0619032
$932$	−10.3318	−0.338431
$933$	15.8211	0.517958
$934$	0.751684	0.0245958
$935$	−3.73711	−0.122216
$936$	−2.51654	−0.0822557
$937$	−39.0349	−1.27521	−0.637607	−	0.770361i	$-0.720076\pi$
$937$	−39.0349	−1.27521	−0.637607	+	0.770361i	$0.720076\pi$
$938$	3.81059	0.124420
$939$	−1.24401	−0.0405967
$940$	9.90525	0.323074
$941$	−16.8165	−0.548203	−0.274101	−	0.961701i	$-0.588380\pi$
$941$	−16.8165	−0.548203	−0.274101	+	0.961701i	$0.588380\pi$
$942$	−11.1037	−0.361779
$943$	−9.04026	−0.294391
$944$	−0.209281	−0.00681152
$945$	0.789548	0.0256840
$946$	−13.2258	−0.430009
$947$	−27.2129	−0.884300	−0.442150	−	0.896941i	$-0.645784\pi$
$947$	−27.2129	−0.884300	−0.442150	+	0.896941i	$0.645784\pi$
$948$	−5.73946	−0.186409
$949$	13.9605	0.453175
$950$	5.98515	0.194184
$951$	7.25147	0.235145
$952$	−2.51654	−0.0815615
$953$	15.3350	0.496750	0.248375	−	0.968664i	$-0.420103\pi$
$953$	15.3350	0.496750	0.248375	+	0.968664i	$0.420103\pi$
$954$	−7.34561	−0.237823
$955$	−4.77406	−0.154485
$956$	−38.0938	−1.23204
$957$	−22.5513	−0.728979
$958$	26.2977	0.849640
$959$	1.41659	0.0457441
$960$	1.56094	0.0503792
$961$	−23.0628	−0.743963
$962$	0.929654	0.0299733
$963$	−5.65393	−0.182195
$964$	−6.99194	−0.225195
$965$	−12.9476	−0.416799
$966$	1.99607	0.0642226
$967$	24.0787	0.774320	0.387160	−	0.922013i	$-0.373456\pi$
$967$	24.0787	0.774320	0.387160	+	0.922013i	$0.373456\pi$
$968$	−28.6971	−0.922361
$969$	1.88881	0.0606772
$970$	4.75079	0.152539
$971$	−13.7431	−0.441037	−0.220518	−	0.975383i	$-0.570775\pi$
$971$	−13.7431	−0.441037	−0.220518	+	0.975383i	$0.570775\pi$
$972$	1.47580	0.0473363
$973$	−1.62890	−0.0522201
$974$	−12.1714	−0.389996
$975$	4.37661	0.140164
$976$	−10.0241	−0.320863
$977$	33.0309	1.05675	0.528376	−	0.849011i	$-0.322801\pi$
$977$	33.0309	1.05675	0.528376	+	0.849011i	$0.322801\pi$
$978$	−2.27861	−0.0728620
$979$	30.9556	0.989344
$980$	1.16521	0.0372214
$981$	10.0012	0.319314
$982$	8.36556	0.266956
$983$	40.0879	1.27861	0.639303	−	0.768955i	$-0.279223\pi$
$983$	40.0879	1.27861	0.639303	+	0.768955i	$0.279223\pi$
$984$	8.25196	0.263063
$985$	−14.9525	−0.476428
$986$	3.44955	0.109856
$987$	−8.50080	−0.270584
$988$	2.78750	0.0886822
$989$	10.6401	0.338334
$990$	−2.70573	−0.0859938
$991$	46.9985	1.49296	0.746478	−	0.665410i	$-0.231743\pi$
$991$	46.9985	1.49296	0.746478	+	0.665410i	$0.231743\pi$
$992$	−16.4838	−0.523360
$993$	−5.52098	−0.175203
$994$	−8.24398	−0.261483
$995$	−12.6873	−0.402216
$996$	23.5973	0.747709
$997$	−28.2099	−0.893416	−0.446708	−	0.894680i	$-0.647404\pi$
$997$	−28.2099	−0.893416	−0.446708	+	0.894680i	$0.647404\pi$
$998$	−10.6226	−0.336252
$999$	−1.28402	−0.0406246

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4641.2.a.w.1.9	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4641.2.a.w.1.9	✓	14	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:	\( N \)	\(=\)	\( 4641 = 3 \cdot 7 \cdot 13 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4641.a (trivial)

\(f(q)\)	\(=\)	\(q+0.724018 q^{2} -1.00000 q^{3} -1.47580 q^{4} -0.789548 q^{5} -0.724018 q^{6} +1.00000 q^{7} -2.51654 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.724018 q^{2} -1.00000 q^{3} -1.47580 q^{4} -0.789548 q^{5} -0.724018 q^{6} +1.00000 q^{7} -2.51654 q^{8} +1.00000 q^{9} -0.571646 q^{10} +4.73322 q^{11} +1.47580 q^{12} +1.00000 q^{13} +0.724018 q^{14} +0.789548 q^{15} +1.12958 q^{16} +1.00000 q^{17} +0.724018 q^{18} -1.88881 q^{19} +1.16521 q^{20} -1.00000 q^{21} +3.42694 q^{22} -2.75694 q^{23} +2.51654 q^{24} -4.37661 q^{25} +0.724018 q^{26} -1.00000 q^{27} -1.47580 q^{28} +4.76446 q^{29} +0.571646 q^{30} -2.81730 q^{31} +5.85091 q^{32} -4.73322 q^{33} +0.724018 q^{34} -0.789548 q^{35} -1.47580 q^{36} +1.28402 q^{37} -1.36753 q^{38} -1.00000 q^{39} +1.98693 q^{40} +3.27909 q^{41} -0.724018 q^{42} -3.85937 q^{43} -6.98529 q^{44} -0.789548 q^{45} -1.99607 q^{46} +8.50080 q^{47} -1.12958 q^{48} +1.00000 q^{49} -3.16875 q^{50} -1.00000 q^{51} -1.47580 q^{52} -10.1456 q^{53} -0.724018 q^{54} -3.73711 q^{55} -2.51654 q^{56} +1.88881 q^{57} +3.44955 q^{58} -0.185274 q^{59} -1.16521 q^{60} -8.87418 q^{61} -2.03977 q^{62} +1.00000 q^{63} +1.97701 q^{64} -0.789548 q^{65} -3.42694 q^{66} +5.26312 q^{67} -1.47580 q^{68} +2.75694 q^{69} -0.571646 q^{70} -11.3864 q^{71} -2.51654 q^{72} +13.9605 q^{73} +0.929654 q^{74} +4.37661 q^{75} +2.78750 q^{76} +4.73322 q^{77} -0.724018 q^{78} -3.88905 q^{79} -0.891856 q^{80} +1.00000 q^{81} +2.37412 q^{82} +15.9895 q^{83} +1.47580 q^{84} -0.789548 q^{85} -2.79425 q^{86} -4.76446 q^{87} -11.9113 q^{88} +6.54006 q^{89} -0.571646 q^{90} +1.00000 q^{91} +4.06869 q^{92} +2.81730 q^{93} +6.15473 q^{94} +1.49130 q^{95} -5.85091 q^{96} -8.31071 q^{97} +0.724018 q^{98} +4.73322 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - q^{2} - 14 q^{3} + 17 q^{4} - q^{5} + q^{6} + 14 q^{7} - 6 q^{8} + 14 q^{9}+O(q^{10}) \) 14 * q - q^2 - 14 * q^3 + 17 * q^4 - q^5 + q^6 + 14 * q^7 - 6 * q^8 + 14 * q^9	\( 14 q - q^{2} - 14 q^{3} + 17 q^{4} - q^{5} + q^{6} + 14 q^{7} - 6 q^{8} + 14 q^{9} + 11 q^{10} - 4 q^{11} - 17 q^{12} + 14 q^{13} - q^{14} + q^{15} + 19 q^{16} + 14 q^{17} - q^{18} + 6 q^{19} + q^{20} - 14 q^{21} + 12 q^{22} + 7 q^{23} + 6 q^{24} + 19 q^{25} - q^{26} - 14 q^{27} + 17 q^{28} - 4 q^{29} - 11 q^{30} + 31 q^{31} - 18 q^{32} + 4 q^{33} - q^{34} - q^{35} + 17 q^{36} + 2 q^{37} + 9 q^{38} - 14 q^{39} + 50 q^{40} + 4 q^{41} + q^{42} + 14 q^{43} - 8 q^{44} - q^{45} - 17 q^{46} - q^{47} - 19 q^{48} + 14 q^{49} - 3 q^{50} - 14 q^{51} + 17 q^{52} - 43 q^{53} + q^{54} + 23 q^{55} - 6 q^{56} - 6 q^{57} - 10 q^{58} + 11 q^{59} - q^{60} + 25 q^{61} - 3 q^{62} + 14 q^{63} + 36 q^{64} - q^{65} - 12 q^{66} + 11 q^{67} + 17 q^{68} - 7 q^{69} + 11 q^{70} + 20 q^{71} - 6 q^{72} + 14 q^{73} - 24 q^{74} - 19 q^{75} + 9 q^{76} - 4 q^{77} + q^{78} + 42 q^{79} + 13 q^{80} + 14 q^{81} + 2 q^{82} + 15 q^{83} - 17 q^{84} - q^{85} - 11 q^{86} + 4 q^{87} + 63 q^{88} + 21 q^{89} + 11 q^{90} + 14 q^{91} + 30 q^{92} - 31 q^{93} - 29 q^{94} + 16 q^{95} + 18 q^{96} + 15 q^{97} - q^{98} - 4 q^{99}+O(q^{100}) \) 14 * q - q^2 - 14 * q^3 + 17 * q^4 - q^5 + q^6 + 14 * q^7 - 6 * q^8 + 14 * q^9 + 11 * q^10 - 4 * q^11 - 17 * q^12 + 14 * q^13 - q^14 + q^15 + 19 * q^16 + 14 * q^17 - q^18 + 6 * q^19 + q^20 - 14 * q^21 + 12 * q^22 + 7 * q^23 + 6 * q^24 + 19 * q^25 - q^26 - 14 * q^27 + 17 * q^28 - 4 * q^29 - 11 * q^30 + 31 * q^31 - 18 * q^32 + 4 * q^33 - q^34 - q^35 + 17 * q^36 + 2 * q^37 + 9 * q^38 - 14 * q^39 + 50 * q^40 + 4 * q^41 + q^42 + 14 * q^43 - 8 * q^44 - q^45 - 17 * q^46 - q^47 - 19 * q^48 + 14 * q^49 - 3 * q^50 - 14 * q^51 + 17 * q^52 - 43 * q^53 + q^54 + 23 * q^55 - 6 * q^56 - 6 * q^57 - 10 * q^58 + 11 * q^59 - q^60 + 25 * q^61 - 3 * q^62 + 14 * q^63 + 36 * q^64 - q^65 - 12 * q^66 + 11 * q^67 + 17 * q^68 - 7 * q^69 + 11 * q^70 + 20 * q^71 - 6 * q^72 + 14 * q^73 - 24 * q^74 - 19 * q^75 + 9 * q^76 - 4 * q^77 + q^78 + 42 * q^79 + 13 * q^80 + 14 * q^81 + 2 * q^82 + 15 * q^83 - 17 * q^84 - q^85 - 11 * q^86 + 4 * q^87 + 63 * q^88 + 21 * q^89 + 11 * q^90 + 14 * q^91 + 30 * q^92 - 31 * q^93 - 29 * q^94 + 16 * q^95 + 18 * q^96 + 15 * q^97 - q^98 - 4 * q^99

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