LMFDB - Embedded newform 1334.2.a.k.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1334,2,Mod(1,1334)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1334, 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("1334.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1334 = 2 \cdot 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1334.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:	$10.6520436296$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 5x^{9} - 8x^{8} + 60x^{7} + 13x^{6} - 241x^{5} + 6x^{4} + 346x^{3} + 16x^{2} - 64x - 12 $ x^10 - 5x^9 - 8x^8 + 60x^7 + 13x^6 - 241x^5 + 6x^4 + 346x^3 + 16x^2 - 64*x - 12
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$-1.74474$ of defining polynomial
Character	$\chi$	$=$	1334.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +2.74474 q^{3} +1.00000 q^{4} +1.89466 q^{5} +2.74474 q^{6} +2.43465 q^{7} +1.00000 q^{8} +4.53361 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.74474 q^{3} +1.00000 q^{4} +1.89466 q^{5} +2.74474 q^{6} +2.43465 q^{7} +1.00000 q^{8} +4.53361 q^{9} +1.89466 q^{10} -4.99698 q^{11} +2.74474 q^{12} -1.80301 q^{13} +2.43465 q^{14} +5.20036 q^{15} +1.00000 q^{16} +1.87629 q^{17} +4.53361 q^{18} -7.01905 q^{19} +1.89466 q^{20} +6.68248 q^{21} -4.99698 q^{22} +1.00000 q^{23} +2.74474 q^{24} -1.41025 q^{25} -1.80301 q^{26} +4.20938 q^{27} +2.43465 q^{28} +1.00000 q^{29} +5.20036 q^{30} +4.50779 q^{31} +1.00000 q^{32} -13.7154 q^{33} +1.87629 q^{34} +4.61283 q^{35} +4.53361 q^{36} -5.69526 q^{37} -7.01905 q^{38} -4.94880 q^{39} +1.89466 q^{40} -3.91861 q^{41} +6.68248 q^{42} +1.45005 q^{43} -4.99698 q^{44} +8.58967 q^{45} +1.00000 q^{46} +4.23415 q^{47} +2.74474 q^{48} -1.07250 q^{49} -1.41025 q^{50} +5.14993 q^{51} -1.80301 q^{52} -7.14175 q^{53} +4.20938 q^{54} -9.46759 q^{55} +2.43465 q^{56} -19.2655 q^{57} +1.00000 q^{58} -6.11561 q^{59} +5.20036 q^{60} -1.81767 q^{61} +4.50779 q^{62} +11.0377 q^{63} +1.00000 q^{64} -3.41610 q^{65} -13.7154 q^{66} +1.34182 q^{67} +1.87629 q^{68} +2.74474 q^{69} +4.61283 q^{70} +10.7697 q^{71} +4.53361 q^{72} +5.94574 q^{73} -5.69526 q^{74} -3.87077 q^{75} -7.01905 q^{76} -12.1659 q^{77} -4.94880 q^{78} +2.34832 q^{79} +1.89466 q^{80} -2.04719 q^{81} -3.91861 q^{82} +4.40900 q^{83} +6.68248 q^{84} +3.55494 q^{85} +1.45005 q^{86} +2.74474 q^{87} -4.99698 q^{88} +1.05775 q^{89} +8.58967 q^{90} -4.38969 q^{91} +1.00000 q^{92} +12.3727 q^{93} +4.23415 q^{94} -13.2987 q^{95} +2.74474 q^{96} +5.62532 q^{97} -1.07250 q^{98} -22.6544 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 10 q^{2} + 5 q^{3} + 10 q^{4} - q^{5} + 5 q^{6} + 2 q^{7} + 10 q^{8} + 11 q^{9}+O(q^{10}) $ 10 * q + 10 * q^2 + 5 * q^3 + 10 * q^4 - q^5 + 5 * q^6 + 2 * q^7 + 10 * q^8 + 11 * q^9	\( 10 q + 10 q^{2} + 5 q^{3} + 10 q^{4} - q^{5} + 5 q^{6} + 2 q^{7} + 10 q^{8} + 11 q^{9} - q^{10} + q^{11} + 5 q^{12} + 9 q^{13} + 2 q^{14} + 5 q^{15} + 10 q^{16} + 11 q^{18} + 20 q^{19} - q^{20} + 14 q^{21} + q^{22} + 10 q^{23} + 5 q^{24} + 23 q^{25} + 9 q^{26} + 23 q^{27} + 2 q^{28} + 10 q^{29} + 5 q^{30} + 21 q^{31} + 10 q^{32} + q^{33} + 2 q^{35} + 11 q^{36} - 8 q^{37} + 20 q^{38} + 23 q^{39} - q^{40} - 4 q^{41} + 14 q^{42} - 3 q^{43} + q^{44} - 18 q^{45} + 10 q^{46} - q^{47} + 5 q^{48} + 18 q^{49} + 23 q^{50} - 6 q^{51} + 9 q^{52} - 13 q^{53} + 23 q^{54} + 13 q^{55} + 2 q^{56} - 22 q^{57} + 10 q^{58} + 14 q^{59} + 5 q^{60} + 12 q^{61} + 21 q^{62} - 26 q^{63} + 10 q^{64} - 25 q^{65} + q^{66} + 6 q^{67} + 5 q^{69} + 2 q^{70} + 8 q^{71} + 11 q^{72} + 16 q^{73} - 8 q^{74} + 8 q^{75} + 20 q^{76} - 16 q^{77} + 23 q^{78} + 7 q^{79} - q^{80} - 2 q^{81} - 4 q^{82} + 18 q^{83} + 14 q^{84} + 8 q^{85} - 3 q^{86} + 5 q^{87} + q^{88} + 2 q^{89} - 18 q^{90} + 8 q^{91} + 10 q^{92} - 41 q^{93} - q^{94} - 16 q^{95} + 5 q^{96} + 6 q^{97} + 18 q^{98} - 22 q^{99}+O(q^{100}) \) 10 * q + 10 * q^2 + 5 * q^3 + 10 * q^4 - q^5 + 5 * q^6 + 2 * q^7 + 10 * q^8 + 11 * q^9 - q^10 + q^11 + 5 * q^12 + 9 * q^13 + 2 * q^14 + 5 * q^15 + 10 * q^16 + 11 * q^18 + 20 * q^19 - q^20 + 14 * q^21 + q^22 + 10 * q^23 + 5 * q^24 + 23 * q^25 + 9 * q^26 + 23 * q^27 + 2 * q^28 + 10 * q^29 + 5 * q^30 + 21 * q^31 + 10 * q^32 + q^33 + 2 * q^35 + 11 * q^36 - 8 * q^37 + 20 * q^38 + 23 * q^39 - q^40 - 4 * q^41 + 14 * q^42 - 3 * q^43 + q^44 - 18 * q^45 + 10 * q^46 - q^47 + 5 * q^48 + 18 * q^49 + 23 * q^50 - 6 * q^51 + 9 * q^52 - 13 * q^53 + 23 * q^54 + 13 * q^55 + 2 * q^56 - 22 * q^57 + 10 * q^58 + 14 * q^59 + 5 * q^60 + 12 * q^61 + 21 * q^62 - 26 * q^63 + 10 * q^64 - 25 * q^65 + q^66 + 6 * q^67 + 5 * q^69 + 2 * q^70 + 8 * q^71 + 11 * q^72 + 16 * q^73 - 8 * q^74 + 8 * q^75 + 20 * q^76 - 16 * q^77 + 23 * q^78 + 7 * q^79 - q^80 - 2 * q^81 - 4 * q^82 + 18 * q^83 + 14 * q^84 + 8 * q^85 - 3 * q^86 + 5 * q^87 + q^88 + 2 * q^89 - 18 * q^90 + 8 * q^91 + 10 * q^92 - 41 * q^93 - q^94 - 16 * q^95 + 5 * q^96 + 6 * q^97 + 18 * q^98 - 22 * 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
$3$	2.74474	1.58468	0.792339	−	0.610081i	$-0.208863\pi$
$3$	2.74474	1.58468	0.792339	+	0.610081i	$0.208863\pi$
$4$	1.00000	0.500000
$5$	1.89466	0.847319	0.423660	−	0.905821i	$-0.360745\pi$
$5$	1.89466	0.847319	0.423660	+	0.905821i	$0.360745\pi$
$6$	2.74474	1.12054
$7$	2.43465	0.920209	0.460105	−	0.887865i	$-0.347812\pi$
$7$	2.43465	0.920209	0.460105	+	0.887865i	$0.347812\pi$
$8$	1.00000	0.353553
$9$	4.53361	1.51120
$10$	1.89466	0.599145
$11$	−4.99698	−1.50665	−0.753323	−	0.657651i	$-0.771550\pi$
$11$	−4.99698	−1.50665	−0.753323	+	0.657651i	$0.771550\pi$
$12$	2.74474	0.792339
$13$	−1.80301	−0.500065	−0.250033	−	0.968237i	$-0.580441\pi$
$13$	−1.80301	−0.500065	−0.250033	+	0.968237i	$0.580441\pi$
$14$	2.43465	0.650686
$15$	5.20036	1.34273
$16$	1.00000	0.250000
$17$	1.87629	0.455067	0.227533	−	0.973770i	$-0.426934\pi$
$17$	1.87629	0.455067	0.227533	+	0.973770i	$0.426934\pi$
$18$	4.53361	1.06858
$19$	−7.01905	−1.61028	−0.805140	−	0.593084i	$-0.797910\pi$
$19$	−7.01905	−1.61028	−0.805140	+	0.593084i	$0.797910\pi$
$20$	1.89466	0.423660
$21$	6.68248	1.45824
$22$	−4.99698	−1.06536
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	2.74474	0.560268
$25$	−1.41025	−0.282050
$26$	−1.80301	−0.353600
$27$	4.20938	0.810095
$28$	2.43465	0.460105
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	5.20036	0.949452
$31$	4.50779	0.809622	0.404811	−	0.914400i	$-0.367337\pi$
$31$	4.50779	0.809622	0.404811	+	0.914400i	$0.367337\pi$
$32$	1.00000	0.176777
$33$	−13.7154	−2.38755
$34$	1.87629	0.321781
$35$	4.61283	0.779711
$36$	4.53361	0.755602
$37$	−5.69526	−0.936295	−0.468147	−	0.883650i	$-0.655078\pi$
$37$	−5.69526	−0.936295	−0.468147	+	0.883650i	$0.655078\pi$
$38$	−7.01905	−1.13864
$39$	−4.94880	−0.792442
$40$	1.89466	0.299573
$41$	−3.91861	−0.611983	−0.305992	−	0.952034i	$-0.598988\pi$
$41$	−3.91861	−0.611983	−0.305992	+	0.952034i	$0.598988\pi$
$42$	6.68248	1.03113
$43$	1.45005	0.221131	0.110565	−	0.993869i	$-0.464734\pi$
$43$	1.45005	0.221131	0.110565	+	0.993869i	$0.464734\pi$
$44$	−4.99698	−0.753323
$45$	8.58967	1.28047
$46$	1.00000	0.147442
$47$	4.23415	0.617614	0.308807	−	0.951125i	$-0.400070\pi$
$47$	4.23415	0.617614	0.308807	+	0.951125i	$0.400070\pi$
$48$	2.74474	0.396170
$49$	−1.07250	−0.153215
$50$	−1.41025	−0.199440
$51$	5.14993	0.721135
$52$	−1.80301	−0.250033
$53$	−7.14175	−0.980995	−0.490497	−	0.871443i	$-0.663185\pi$
$53$	−7.14175	−0.980995	−0.490497	+	0.871443i	$0.663185\pi$
$54$	4.20938	0.572824
$55$	−9.46759	−1.27661
$56$	2.43465	0.325343
$57$	−19.2655	−2.55178
$58$	1.00000	0.131306
$59$	−6.11561	−0.796185	−0.398092	−	0.917345i	$-0.630328\pi$
$59$	−6.11561	−0.796185	−0.398092	+	0.917345i	$0.630328\pi$
$60$	5.20036	0.671364
$61$	−1.81767	−0.232729	−0.116365	−	0.993207i	$-0.537124\pi$
$61$	−1.81767	−0.232729	−0.116365	+	0.993207i	$0.537124\pi$
$62$	4.50779	0.572489
$63$	11.0377	1.39062
$64$	1.00000	0.125000
$65$	−3.41610	−0.423715
$66$	−13.7154	−1.68825
$67$	1.34182	0.163929	0.0819647	−	0.996635i	$-0.473881\pi$
$67$	1.34182	0.163929	0.0819647	+	0.996635i	$0.473881\pi$
$68$	1.87629	0.227533
$69$	2.74474	0.330428
$70$	4.61283	0.551339
$71$	10.7697	1.27812	0.639062	−	0.769155i	$-0.279323\pi$
$71$	10.7697	1.27812	0.639062	+	0.769155i	$0.279323\pi$
$72$	4.53361	0.534292
$73$	5.94574	0.695897	0.347948	−	0.937514i	$-0.386878\pi$
$73$	5.94574	0.695897	0.347948	+	0.937514i	$0.386878\pi$
$74$	−5.69526	−0.662060
$75$	−3.87077	−0.446959
$76$	−7.01905	−0.805140
$77$	−12.1659	−1.38643
$78$	−4.94880	−0.560341
$79$	2.34832	0.264207	0.132103	−	0.991236i	$-0.457827\pi$
$79$	2.34832	0.264207	0.132103	+	0.991236i	$0.457827\pi$
$80$	1.89466	0.211830
$81$	−2.04719	−0.227465
$82$	−3.91861	−0.432738
$83$	4.40900	0.483951	0.241976	−	0.970282i	$-0.422205\pi$
$83$	4.40900	0.483951	0.241976	+	0.970282i	$0.422205\pi$
$84$	6.68248	0.729118
$85$	3.55494	0.385587
$86$	1.45005	0.156363
$87$	2.74474	0.294267
$88$	−4.99698	−0.532680
$89$	1.05775	0.112121	0.0560606	−	0.998427i	$-0.482146\pi$
$89$	1.05775	0.112121	0.0560606	+	0.998427i	$0.482146\pi$
$90$	8.58967	0.905431
$91$	−4.38969	−0.460165
$92$	1.00000	0.104257
$93$	12.3727	1.28299
$94$	4.23415	0.436719
$95$	−13.2987	−1.36442
$96$	2.74474	0.280134
$97$	5.62532	0.571165	0.285582	−	0.958354i	$-0.407813\pi$
$97$	5.62532	0.571165	0.285582	+	0.958354i	$0.407813\pi$
$98$	−1.07250	−0.108339
$99$	−22.6544	−2.27685
$100$	−1.41025	−0.141025
$101$	9.27039	0.922438	0.461219	−	0.887286i	$-0.347412\pi$
$101$	9.27039	0.922438	0.461219	+	0.887286i	$0.347412\pi$
$102$	5.14993	0.509919
$103$	−1.98893	−0.195976	−0.0979878	−	0.995188i	$-0.531241\pi$
$103$	−1.98893	−0.195976	−0.0979878	+	0.995188i	$0.531241\pi$
$104$	−1.80301	−0.176800
$105$	12.6610	1.23559
$106$	−7.14175	−0.693668
$107$	−2.68686	−0.259748	−0.129874	−	0.991530i	$-0.541457\pi$
$107$	−2.68686	−0.259748	−0.129874	+	0.991530i	$0.541457\pi$
$108$	4.20938	0.405047
$109$	14.4068	1.37992	0.689962	−	0.723846i	$-0.257627\pi$
$109$	14.4068	1.37992	0.689962	+	0.723846i	$0.257627\pi$
$110$	−9.46759	−0.902700
$111$	−15.6320	−1.48373
$112$	2.43465	0.230052
$113$	8.12697	0.764521	0.382261	−	0.924055i	$-0.375146\pi$
$113$	8.12697	0.764521	0.382261	+	0.924055i	$0.375146\pi$
$114$	−19.2655	−1.80438
$115$	1.89466	0.176678
$116$	1.00000	0.0928477
$117$	−8.17416	−0.755701
$118$	−6.11561	−0.562988
$119$	4.56810	0.418757
$120$	5.20036	0.474726
$121$	13.9698	1.26998
$122$	−1.81767	−0.164564
$123$	−10.7556	−0.969797
$124$	4.50779	0.404811
$125$	−12.1453	−1.08631
$126$	11.0377	0.983320
$127$	20.9559	1.85953	0.929767	−	0.368149i	$-0.120008\pi$
$127$	20.9559	1.85953	0.929767	+	0.368149i	$0.120008\pi$
$128$	1.00000	0.0883883
$129$	3.98002	0.350421
$130$	−3.41610	−0.299612
$131$	−8.27720	−0.723182	−0.361591	−	0.932337i	$-0.617766\pi$
$131$	−8.27720	−0.723182	−0.361591	+	0.932337i	$0.617766\pi$
$132$	−13.7154	−1.19377
$133$	−17.0889	−1.48180
$134$	1.34182	0.115916
$135$	7.97535	0.686409
$136$	1.87629	0.160890
$137$	−3.52022	−0.300753	−0.150376	−	0.988629i	$-0.548049\pi$
$137$	−3.52022	−0.300753	−0.150376	+	0.988629i	$0.548049\pi$
$138$	2.74474	0.233648
$139$	20.5782	1.74542	0.872711	−	0.488238i	$-0.162360\pi$
$139$	20.5782	1.74542	0.872711	+	0.488238i	$0.162360\pi$
$140$	4.61283	0.389856
$141$	11.6216	0.978719
$142$	10.7697	0.903770
$143$	9.00961	0.753421
$144$	4.53361	0.377801
$145$	1.89466	0.157343
$146$	5.94574	0.492073
$147$	−2.94374	−0.242796
$148$	−5.69526	−0.468147
$149$	−10.3841	−0.850699	−0.425350	−	0.905029i	$-0.639849\pi$
$149$	−10.3841	−0.850699	−0.425350	+	0.905029i	$0.639849\pi$
$150$	−3.87077	−0.316047
$151$	−2.18653	−0.177937	−0.0889685	−	0.996034i	$-0.528357\pi$
$151$	−2.18653	−0.177937	−0.0889685	+	0.996034i	$0.528357\pi$
$152$	−7.01905	−0.569320
$153$	8.50637	0.687699
$154$	−12.1659	−0.980354
$155$	8.54074	0.686008
$156$	−4.94880	−0.396221
$157$	5.12422	0.408958	0.204479	−	0.978871i	$-0.434450\pi$
$157$	5.12422	0.408958	0.204479	+	0.978871i	$0.434450\pi$
$158$	2.34832	0.186822
$159$	−19.6023	−1.55456
$160$	1.89466	0.149786
$161$	2.43465	0.191877
$162$	−2.04719	−0.160842
$163$	9.24998	0.724514	0.362257	−	0.932078i	$-0.382006\pi$
$163$	9.24998	0.724514	0.362257	+	0.932078i	$0.382006\pi$
$164$	−3.91861	−0.305992
$165$	−25.9861	−2.02302
$166$	4.40900	0.342205
$167$	1.90173	0.147160	0.0735801	−	0.997289i	$-0.476558\pi$
$167$	1.90173	0.147160	0.0735801	+	0.997289i	$0.476558\pi$
$168$	6.68248	0.515564
$169$	−9.74915	−0.749935
$170$	3.55494	0.272651
$171$	−31.8217	−2.43346
$172$	1.45005	0.110565
$173$	−7.04378	−0.535529	−0.267764	−	0.963484i	$-0.586285\pi$
$173$	−7.04378	−0.535529	−0.267764	+	0.963484i	$0.586285\pi$
$174$	2.74474	0.208078
$175$	−3.43346	−0.259545
$176$	−4.99698	−0.376662
$177$	−16.7858	−1.26170
$178$	1.05775	0.0792816
$179$	−17.4349	−1.30314	−0.651572	−	0.758587i	$-0.725890\pi$
$179$	−17.4349	−1.30314	−0.651572	+	0.758587i	$0.725890\pi$
$180$	8.58967	0.640236
$181$	−14.5250	−1.07964	−0.539819	−	0.841781i	$-0.681507\pi$
$181$	−14.5250	−1.07964	−0.539819	+	0.841781i	$0.681507\pi$
$182$	−4.38969	−0.325386
$183$	−4.98905	−0.368801
$184$	1.00000	0.0737210
$185$	−10.7906	−0.793340
$186$	12.3727	0.907211
$187$	−9.37578	−0.685625
$188$	4.23415	0.308807
$189$	10.2483	0.745457
$190$	−13.2987	−0.964792
$191$	−18.7402	−1.35600	−0.677998	−	0.735063i	$-0.737152\pi$
$191$	−18.7402	−1.35600	−0.677998	+	0.735063i	$0.737152\pi$
$192$	2.74474	0.198085
$193$	13.5834	0.977751	0.488876	−	0.872354i	$-0.337407\pi$
$193$	13.5834	0.977751	0.488876	+	0.872354i	$0.337407\pi$
$194$	5.62532	0.403875
$195$	−9.37631	−0.671452
$196$	−1.07250	−0.0766073
$197$	4.50849	0.321217	0.160608	−	0.987018i	$-0.448654\pi$
$197$	4.50849	0.321217	0.160608	+	0.987018i	$0.448654\pi$
$198$	−22.6544	−1.60998
$199$	17.3617	1.23074	0.615370	−	0.788238i	$-0.289007\pi$
$199$	17.3617	1.23074	0.615370	+	0.788238i	$0.289007\pi$
$200$	−1.41025	−0.0997198
$201$	3.68295	0.259775
$202$	9.27039	0.652262
$203$	2.43465	0.170879
$204$	5.14993	0.360567
$205$	−7.42444	−0.518545
$206$	−1.98893	−0.138576
$207$	4.53361	0.315108
$208$	−1.80301	−0.125016
$209$	35.0740	2.42612
$210$	12.6610	0.873695
$211$	−12.9000	−0.888076	−0.444038	−	0.896008i	$-0.646454\pi$
$211$	−12.9000	−0.888076	−0.444038	+	0.896008i	$0.646454\pi$
$212$	−7.14175	−0.490497
$213$	29.5600	2.02542
$214$	−2.68686	−0.183670
$215$	2.74736	0.187369
$216$	4.20938	0.286412
$217$	10.9749	0.745022
$218$	14.4068	0.975754
$219$	16.3195	1.10277
$220$	−9.46759	−0.638305
$221$	−3.38297	−0.227563
$222$	−15.6320	−1.04915
$223$	19.5661	1.31024	0.655121	−	0.755524i	$-0.272618\pi$
$223$	19.5661	1.31024	0.655121	+	0.755524i	$0.272618\pi$
$224$	2.43465	0.162672
$225$	−6.39353	−0.426235
$226$	8.12697	0.540598
$227$	5.32845	0.353662	0.176831	−	0.984241i	$-0.443415\pi$
$227$	5.32845	0.353662	0.176831	+	0.984241i	$0.443415\pi$
$228$	−19.2655	−1.27589
$229$	−19.7557	−1.30549	−0.652747	−	0.757576i	$-0.726383\pi$
$229$	−19.7557	−1.30549	−0.652747	+	0.757576i	$0.726383\pi$
$230$	1.89466	0.124930
$231$	−33.3922	−2.19704
$232$	1.00000	0.0656532
$233$	24.0162	1.57335	0.786675	−	0.617367i	$-0.211801\pi$
$233$	24.0162	1.57335	0.786675	+	0.617367i	$0.211801\pi$
$234$	−8.17416	−0.534361
$235$	8.02228	0.523316
$236$	−6.11561	−0.398092
$237$	6.44554	0.418683
$238$	4.56810	0.296106
$239$	0.727468	0.0470560	0.0235280	−	0.999723i	$-0.492510\pi$
$239$	0.727468	0.0470560	0.0235280	+	0.999723i	$0.492510\pi$
$240$	5.20036	0.335682
$241$	4.18369	0.269495	0.134747	−	0.990880i	$-0.456978\pi$
$241$	4.18369	0.269495	0.134747	+	0.990880i	$0.456978\pi$
$242$	13.9698	0.898013
$243$	−18.2471	−1.17055
$244$	−1.81767	−0.116365
$245$	−2.03203	−0.129822
$246$	−10.7556	−0.685750
$247$	12.6554	0.805245
$248$	4.50779	0.286245
$249$	12.1016	0.766907
$250$	−12.1453	−0.768134
$251$	−21.8177	−1.37712	−0.688560	−	0.725179i	$-0.741757\pi$
$251$	−21.8177	−1.37712	−0.688560	+	0.725179i	$0.741757\pi$
$252$	11.0377	0.695312
$253$	−4.99698	−0.314157
$254$	20.9559	1.31489
$255$	9.75739	0.611031
$256$	1.00000	0.0625000
$257$	13.3952	0.835568	0.417784	−	0.908546i	$-0.362807\pi$
$257$	13.3952	0.835568	0.417784	+	0.908546i	$0.362807\pi$
$258$	3.98002	0.247785
$259$	−13.8659	−0.861587
$260$	−3.41610	−0.211857
$261$	4.53361	0.280624
$262$	−8.27720	−0.511367
$263$	−1.98730	−0.122542	−0.0612711	−	0.998121i	$-0.519515\pi$
$263$	−1.98730	−0.122542	−0.0612711	+	0.998121i	$0.519515\pi$
$264$	−13.7154	−0.844126
$265$	−13.5312	−0.831216
$266$	−17.0889	−1.04779
$267$	2.90325	0.177676
$268$	1.34182	0.0819647
$269$	−1.12684	−0.0687048	−0.0343524	−	0.999410i	$-0.510937\pi$
$269$	−1.12684	−0.0687048	−0.0343524	+	0.999410i	$0.510937\pi$
$270$	7.97535	0.485364
$271$	21.5148	1.30693	0.653466	−	0.756956i	$-0.273314\pi$
$271$	21.5148	1.30693	0.653466	+	0.756956i	$0.273314\pi$
$272$	1.87629	0.113767
$273$	−12.0486	−0.729213
$274$	−3.52022	−0.212664
$275$	7.04699	0.424950
$276$	2.74474	0.165214
$277$	−23.8122	−1.43074	−0.715368	−	0.698748i	$-0.753741\pi$
$277$	−23.8122	−1.43074	−0.715368	+	0.698748i	$0.753741\pi$
$278$	20.5782	1.23420
$279$	20.4366	1.22350
$280$	4.61283	0.275670
$281$	14.6231	0.872342	0.436171	−	0.899864i	$-0.356334\pi$
$281$	14.6231	0.872342	0.436171	+	0.899864i	$0.356334\pi$
$282$	11.6216	0.692059
$283$	24.3702	1.44866	0.724329	−	0.689455i	$-0.242150\pi$
$283$	24.3702	1.44866	0.724329	+	0.689455i	$0.242150\pi$
$284$	10.7697	0.639062
$285$	−36.5016	−2.16217
$286$	9.00961	0.532749
$287$	−9.54041	−0.563153
$288$	4.53361	0.267146
$289$	−13.4795	−0.792914
$290$	1.89466	0.111258
$291$	15.4401	0.905113
$292$	5.94574	0.347948
$293$	−8.43978	−0.493057	−0.246529	−	0.969136i	$-0.579290\pi$
$293$	−8.43978	−0.493057	−0.246529	+	0.969136i	$0.579290\pi$
$294$	−2.94374	−0.171683
$295$	−11.5870	−0.674623
$296$	−5.69526	−0.331030
$297$	−21.0342	−1.22053
$298$	−10.3841	−0.601535
$299$	−1.80301	−0.104271
$300$	−3.87077	−0.223479
$301$	3.53036	0.203487
$302$	−2.18653	−0.125821
$303$	25.4448	1.46177
$304$	−7.01905	−0.402570
$305$	−3.44388	−0.197196
$306$	8.50637	0.486277
$307$	−13.8412	−0.789957	−0.394978	−	0.918690i	$-0.629248\pi$
$307$	−13.8412	−0.789957	−0.394978	+	0.918690i	$0.629248\pi$
$308$	−12.1659	−0.693215
$309$	−5.45911	−0.310558
$310$	8.54074	0.485081
$311$	−20.1727	−1.14389	−0.571945	−	0.820292i	$-0.693811\pi$
$311$	−20.1727	−1.14389	−0.571945	+	0.820292i	$0.693811\pi$
$312$	−4.94880	−0.280171
$313$	−1.52291	−0.0860798	−0.0430399	−	0.999073i	$-0.513704\pi$
$313$	−1.52291	−0.0860798	−0.0430399	+	0.999073i	$0.513704\pi$
$314$	5.12422	0.289177
$315$	20.9128	1.17830
$316$	2.34832	0.132103
$317$	9.31793	0.523347	0.261674	−	0.965156i	$-0.415726\pi$
$317$	9.31793	0.523347	0.261674	+	0.965156i	$0.415726\pi$
$318$	−19.6023	−1.09924
$319$	−4.99698	−0.279777
$320$	1.89466	0.105915
$321$	−7.37473	−0.411617
$322$	2.43465	0.135677
$323$	−13.1698	−0.732786
$324$	−2.04719	−0.113733
$325$	2.54270	0.141043
$326$	9.24998	0.512309
$327$	39.5430	2.18674
$328$	−3.91861	−0.216369
$329$	10.3086	0.568334
$330$	−25.9861	−1.43049
$331$	−21.3847	−1.17541	−0.587706	−	0.809075i	$-0.699969\pi$
$331$	−21.3847	−1.17541	−0.587706	+	0.809075i	$0.699969\pi$
$332$	4.40900	0.241976
$333$	−25.8201	−1.41493
$334$	1.90173	0.104058
$335$	2.54230	0.138900
$336$	6.68248	0.364559
$337$	−31.7334	−1.72863	−0.864314	−	0.502953i	$-0.832247\pi$
$337$	−31.7334	−1.72863	−0.864314	+	0.502953i	$0.832247\pi$
$338$	−9.74915	−0.530284
$339$	22.3064	1.21152
$340$	3.55494	0.192794
$341$	−22.5253	−1.21981
$342$	−31.8217	−1.72072
$343$	−19.6537	−1.06120
$344$	1.45005	0.0781816
$345$	5.20036	0.279978
$346$	−7.04378	−0.378676
$347$	33.5782	1.80257	0.901287	−	0.433223i	$-0.142624\pi$
$347$	33.5782	1.80257	0.901287	+	0.433223i	$0.142624\pi$
$348$	2.74474	0.147134
$349$	6.89024	0.368826	0.184413	−	0.982849i	$-0.440962\pi$
$349$	6.89024	0.368826	0.184413	+	0.982849i	$0.440962\pi$
$350$	−3.43346	−0.183526
$351$	−7.58955	−0.405100
$352$	−4.99698	−0.266340
$353$	−18.9674	−1.00953	−0.504765	−	0.863257i	$-0.668421\pi$
$353$	−18.9674	−1.00953	−0.504765	+	0.863257i	$0.668421\pi$
$354$	−16.7858	−0.892154
$355$	20.4049	1.08298
$356$	1.05775	0.0560606
$357$	12.5383	0.663595
$358$	−17.4349	−0.921462
$359$	20.2427	1.06837	0.534184	−	0.845368i	$-0.320619\pi$
$359$	20.2427	1.06837	0.534184	+	0.845368i	$0.320619\pi$
$360$	8.58967	0.452716
$361$	30.2671	1.59300
$362$	−14.5250	−0.763419
$363$	38.3435	2.01251
$364$	−4.38969	−0.230082
$365$	11.2652	0.589647
$366$	−4.98905	−0.260782
$367$	−16.6957	−0.871509	−0.435754	−	0.900066i	$-0.643518\pi$
$367$	−16.6957	−0.871509	−0.435754	+	0.900066i	$0.643518\pi$
$368$	1.00000	0.0521286
$369$	−17.7654	−0.924832
$370$	−10.7906	−0.560976
$371$	−17.3876	−0.902721
$372$	12.3727	0.641495
$373$	−16.7367	−0.866593	−0.433296	−	0.901251i	$-0.642650\pi$
$373$	−16.7367	−0.866593	−0.433296	+	0.901251i	$0.642650\pi$
$374$	−9.37578	−0.484810
$375$	−33.3356	−1.72144
$376$	4.23415	0.218359
$377$	−1.80301	−0.0928598
$378$	10.2483	0.527118
$379$	1.53851	0.0790277	0.0395139	−	0.999219i	$-0.487419\pi$
$379$	1.53851	0.0790277	0.0395139	+	0.999219i	$0.487419\pi$
$380$	−13.2987	−0.682211
$381$	57.5185	2.94676
$382$	−18.7402	−0.958834
$383$	−25.7298	−1.31473	−0.657366	−	0.753571i	$-0.728329\pi$
$383$	−25.7298	−1.31473	−0.657366	+	0.753571i	$0.728329\pi$
$384$	2.74474	0.140067
$385$	−23.0502	−1.17475
$386$	13.5834	0.691374
$387$	6.57398	0.334174
$388$	5.62532	0.285582
$389$	−24.3809	−1.23616	−0.618080	−	0.786116i	$-0.712089\pi$
$389$	−24.3809	−1.23616	−0.618080	+	0.786116i	$0.712089\pi$
$390$	−9.37631	−0.474788
$391$	1.87629	0.0948880
$392$	−1.07250	−0.0541696
$393$	−22.7188	−1.14601
$394$	4.50849	0.227135
$395$	4.44928	0.223867
$396$	−22.6544	−1.13843
$397$	12.8583	0.645339	0.322669	−	0.946512i	$-0.395420\pi$
$397$	12.8583	0.645339	0.322669	+	0.946512i	$0.395420\pi$
$398$	17.3617	0.870265
$399$	−46.9046	−2.34817
$400$	−1.41025	−0.0705125
$401$	38.8426	1.93971	0.969853	−	0.243692i	$-0.0783587\pi$
$401$	38.8426	1.93971	0.969853	+	0.243692i	$0.0783587\pi$
$402$	3.68295	0.183689
$403$	−8.12759	−0.404864
$404$	9.27039	0.461219
$405$	−3.87873	−0.192736
$406$	2.43465	0.120829
$407$	28.4591	1.41066
$408$	5.14993	0.254960
$409$	0.560516	0.0277157	0.0138579	−	0.999904i	$-0.495589\pi$
$409$	0.560516	0.0277157	0.0138579	+	0.999904i	$0.495589\pi$
$410$	−7.42444	−0.366667
$411$	−9.66210	−0.476596
$412$	−1.98893	−0.0979878
$413$	−14.8893	−0.732657
$414$	4.53361	0.222815
$415$	8.35358	0.410061
$416$	−1.80301	−0.0883999
$417$	56.4819	2.76593
$418$	35.0740	1.71553
$419$	−33.1665	−1.62029	−0.810145	−	0.586229i	$-0.800612\pi$
$419$	−33.1665	−1.62029	−0.810145	+	0.586229i	$0.800612\pi$
$420$	12.6610	0.617796
$421$	−3.42900	−0.167119	−0.0835596	−	0.996503i	$-0.526629\pi$
$421$	−3.42900	−0.167119	−0.0835596	+	0.996503i	$0.526629\pi$
$422$	−12.9000	−0.627965
$423$	19.1960	0.933341
$424$	−7.14175	−0.346834
$425$	−2.64604	−0.128352
$426$	29.5600	1.43218
$427$	−4.42539	−0.214160
$428$	−2.68686	−0.129874
$429$	24.7291	1.19393
$430$	2.74736	0.132490
$431$	−8.90505	−0.428941	−0.214470	−	0.976730i	$-0.568803\pi$
$431$	−8.90505	−0.428941	−0.214470	+	0.976730i	$0.568803\pi$
$432$	4.20938	0.202524
$433$	−13.6940	−0.658094	−0.329047	−	0.944314i	$-0.606727\pi$
$433$	−13.6940	−0.658094	−0.329047	+	0.944314i	$0.606727\pi$
$434$	10.9749	0.526810
$435$	5.20036	0.249338
$436$	14.4068	0.689962
$437$	−7.01905	−0.335767
$438$	16.3195	0.779778
$439$	−30.2202	−1.44233	−0.721165	−	0.692764i	$-0.756393\pi$
$439$	−30.2202	−1.44233	−0.721165	+	0.692764i	$0.756393\pi$
$440$	−9.46759	−0.451350
$441$	−4.86231	−0.231539
$442$	−3.38297	−0.160911
$443$	4.46384	0.212084	0.106042	−	0.994362i	$-0.466182\pi$
$443$	4.46384	0.212084	0.106042	+	0.994362i	$0.466182\pi$
$444$	−15.6320	−0.741863
$445$	2.00408	0.0950024
$446$	19.5661	0.926481
$447$	−28.5017	−1.34808
$448$	2.43465	0.115026
$449$	−32.2231	−1.52070	−0.760350	−	0.649513i	$-0.774973\pi$
$449$	−32.2231	−1.52070	−0.760350	+	0.649513i	$0.774973\pi$
$450$	−6.39353	−0.301394
$451$	19.5812	0.922042
$452$	8.12697	0.382261
$453$	−6.00146	−0.281973
$454$	5.32845	0.250077
$455$	−8.31699	−0.389906
$456$	−19.2655	−0.902189
$457$	−1.21309	−0.0567459	−0.0283730	−	0.999597i	$-0.509033\pi$
$457$	−1.21309	−0.0567459	−0.0283730	+	0.999597i	$0.509033\pi$
$458$	−19.7557	−0.923123
$459$	7.89801	0.368647
$460$	1.89466	0.0883391
$461$	−38.8929	−1.81142	−0.905711	−	0.423895i	$-0.860662\pi$
$461$	−38.8929	−1.81142	−0.905711	+	0.423895i	$0.860662\pi$
$462$	−33.3922	−1.55355
$463$	22.4937	1.04537	0.522684	−	0.852526i	$-0.324931\pi$
$463$	22.4937	1.04537	0.522684	+	0.852526i	$0.324931\pi$
$464$	1.00000	0.0464238
$465$	23.4421	1.08710
$466$	24.0162	1.11253
$467$	14.3794	0.665400	0.332700	−	0.943033i	$-0.392040\pi$
$467$	14.3794	0.665400	0.332700	+	0.943033i	$0.392040\pi$
$468$	−8.17416	−0.377850
$469$	3.26685	0.150849
$470$	8.02228	0.370040
$471$	14.0647	0.648066
$472$	−6.11561	−0.281494
$473$	−7.24588	−0.333166
$474$	6.44554	0.296053
$475$	9.89862	0.454180
$476$	4.56810	0.209378
$477$	−32.3779	−1.48248
$478$	0.727468	0.0332736
$479$	−1.50483	−0.0687573	−0.0343786	−	0.999409i	$-0.510945\pi$
$479$	−1.50483	−0.0687573	−0.0343786	+	0.999409i	$0.510945\pi$
$480$	5.20036	0.237363
$481$	10.2686	0.468208
$482$	4.18369	0.190562
$483$	6.68248	0.304063
$484$	13.9698	0.634991
$485$	10.6581	0.483959
$486$	−18.2471	−0.827707
$487$	26.6267	1.20657	0.603286	−	0.797525i	$-0.293858\pi$
$487$	26.6267	1.20657	0.603286	+	0.797525i	$0.293858\pi$
$488$	−1.81767	−0.0822822
$489$	25.3888	1.14812
$490$	−2.03203	−0.0917978
$491$	35.1332	1.58554	0.792770	−	0.609521i	$-0.208638\pi$
$491$	35.1332	1.58554	0.792770	+	0.609521i	$0.208638\pi$
$492$	−10.7556	−0.484898
$493$	1.87629	0.0845038
$494$	12.6554	0.569394
$495$	−42.9224	−1.92922
$496$	4.50779	0.202406
$497$	26.2203	1.17614
$498$	12.1016	0.542285
$499$	38.4437	1.72098	0.860489	−	0.509470i	$-0.170158\pi$
$499$	38.4437	1.72098	0.860489	+	0.509470i	$0.170158\pi$
$500$	−12.1453	−0.543153
$501$	5.21976	0.233202
$502$	−21.8177	−0.973772
$503$	−44.0080	−1.96222	−0.981110	−	0.193448i	$-0.938033\pi$
$503$	−44.0080	−1.96222	−0.981110	+	0.193448i	$0.938033\pi$
$504$	11.0377	0.491660
$505$	17.5643	0.781600
$506$	−4.99698	−0.222143
$507$	−26.7589	−1.18841
$508$	20.9559	0.929767
$509$	10.4740	0.464251	0.232126	−	0.972686i	$-0.425432\pi$
$509$	10.4740	0.464251	0.232126	+	0.972686i	$0.425432\pi$
$510$	9.75739	0.432064
$511$	14.4758	0.640371
$512$	1.00000	0.0441942
$513$	−29.5458	−1.30448
$514$	13.3952	0.590836
$515$	−3.76836	−0.166054
$516$	3.98002	0.175211
$517$	−21.1579	−0.930525
$518$	−13.8659	−0.609234
$519$	−19.3334	−0.848641
$520$	−3.41610	−0.149806
$521$	−27.0338	−1.18437	−0.592187	−	0.805801i	$-0.701735\pi$
$521$	−27.0338	−1.18437	−0.592187	+	0.805801i	$0.701735\pi$
$522$	4.53361	0.198431
$523$	35.5539	1.55466	0.777332	−	0.629091i	$-0.216573\pi$
$523$	35.5539	1.55466	0.777332	+	0.629091i	$0.216573\pi$
$524$	−8.27720	−0.361591
$525$	−9.42396	−0.411295
$526$	−1.98730	−0.0866505
$527$	8.45791	0.368432
$528$	−13.7154	−0.596887
$529$	1.00000	0.0434783
$530$	−13.5312	−0.587758
$531$	−27.7258	−1.20320
$532$	−17.0889	−0.740898
$533$	7.06529	0.306032
$534$	2.90325	0.125636
$535$	−5.09069	−0.220090
$536$	1.34182	0.0579578
$537$	−47.8542	−2.06506
$538$	−1.12684	−0.0485816
$539$	5.35927	0.230840
$540$	7.97535	0.343204
$541$	−24.6818	−1.06115	−0.530577	−	0.847637i	$-0.678025\pi$
$541$	−24.6818	−1.06115	−0.530577	+	0.847637i	$0.678025\pi$
$542$	21.5148	0.924141
$543$	−39.8675	−1.71088
$544$	1.87629	0.0804452
$545$	27.2961	1.16924
$546$	−12.0486	−0.515631
$547$	30.6897	1.31220	0.656098	−	0.754676i	$-0.272206\pi$
$547$	30.6897	1.31220	0.656098	+	0.754676i	$0.272206\pi$
$548$	−3.52022	−0.150376
$549$	−8.24063	−0.351702
$550$	7.04699	0.300485
$551$	−7.01905	−0.299022
$552$	2.74474	0.116824
$553$	5.71733	0.243125
$554$	−23.8122	−1.01168
$555$	−29.6174	−1.25719
$556$	20.5782	0.872711
$557$	46.8025	1.98308	0.991542	−	0.129788i	$-0.0414296\pi$
$557$	46.8025	1.98308	0.991542	+	0.129788i	$0.0414296\pi$
$558$	20.4366	0.865149
$559$	−2.61446	−0.110580
$560$	4.61283	0.194928
$561$	−25.7341	−1.08649
$562$	14.6231	0.616839
$563$	−22.7220	−0.957620	−0.478810	−	0.877919i	$-0.658932\pi$
$563$	−22.7220	−0.957620	−0.478810	+	0.877919i	$0.658932\pi$
$564$	11.6216	0.489359
$565$	15.3979	0.647793
$566$	24.3702	1.02436
$567$	−4.98417	−0.209316
$568$	10.7697	0.451885
$569$	−42.4953	−1.78150	−0.890748	−	0.454497i	$-0.849819\pi$
$569$	−42.4953	−1.78150	−0.890748	+	0.454497i	$0.849819\pi$
$570$	−36.5016	−1.52888
$571$	25.4832	1.06644	0.533219	−	0.845977i	$-0.320982\pi$
$571$	25.4832	1.06644	0.533219	+	0.845977i	$0.320982\pi$
$572$	9.00961	0.376711
$573$	−51.4372	−2.14882
$574$	−9.54041	−0.398209
$575$	−1.41025	−0.0588115
$576$	4.53361	0.188901
$577$	3.27473	0.136329	0.0681644	−	0.997674i	$-0.478286\pi$
$577$	3.27473	0.136329	0.0681644	+	0.997674i	$0.478286\pi$
$578$	−13.4795	−0.560675
$579$	37.2828	1.54942
$580$	1.89466	0.0786716
$581$	10.7344	0.445336
$582$	15.4401	0.640011
$583$	35.6872	1.47801
$584$	5.94574	0.246037
$585$	−15.4873	−0.640320
$586$	−8.43978	−0.348644
$587$	33.5795	1.38598	0.692988	−	0.720949i	$-0.256294\pi$
$587$	33.5795	1.38598	0.692988	+	0.720949i	$0.256294\pi$
$588$	−2.94374	−0.121398
$589$	−31.6404	−1.30372
$590$	−11.5870	−0.477030
$591$	12.3746	0.509025
$592$	−5.69526	−0.234074
$593$	−27.5419	−1.13101	−0.565505	−	0.824745i	$-0.691319\pi$
$593$	−27.5419	−1.13101	−0.565505	+	0.824745i	$0.691319\pi$
$594$	−21.0342	−0.863042
$595$	8.65501	0.354821
$596$	−10.3841	−0.425350
$597$	47.6535	1.95033
$598$	−1.80301	−0.0737306
$599$	−42.5562	−1.73880	−0.869400	−	0.494110i	$-0.835494\pi$
$599$	−42.5562	−1.73880	−0.869400	+	0.494110i	$0.835494\pi$
$600$	−3.87077	−0.158024
$601$	15.0828	0.615240	0.307620	−	0.951509i	$-0.400467\pi$
$601$	15.0828	0.615240	0.307620	+	0.951509i	$0.400467\pi$
$602$	3.53036	0.143887
$603$	6.08329	0.247731
$604$	−2.18653	−0.0889685
$605$	26.4681	1.07608
$606$	25.4448	1.03363
$607$	32.2515	1.30905	0.654524	−	0.756041i	$-0.272869\pi$
$607$	32.2515	1.30905	0.654524	+	0.756041i	$0.272869\pi$
$608$	−7.01905	−0.284660
$609$	6.68248	0.270788
$610$	−3.44388	−0.139439
$611$	−7.63421	−0.308847
$612$	8.50637	0.343850
$613$	29.0984	1.17527	0.587637	−	0.809125i	$-0.300058\pi$
$613$	29.0984	1.17527	0.587637	+	0.809125i	$0.300058\pi$
$614$	−13.8412	−0.558584
$615$	−20.3782	−0.821727
$616$	−12.1659	−0.490177
$617$	21.2615	0.855954	0.427977	−	0.903790i	$-0.359226\pi$
$617$	21.2615	0.855954	0.427977	+	0.903790i	$0.359226\pi$
$618$	−5.45911	−0.219598
$619$	−9.51887	−0.382596	−0.191298	−	0.981532i	$-0.561270\pi$
$619$	−9.51887	−0.382596	−0.191298	+	0.981532i	$0.561270\pi$
$620$	8.54074	0.343004
$621$	4.20938	0.168916
$622$	−20.1727	−0.808852
$623$	2.57524	0.103175
$624$	−4.94880	−0.198111
$625$	−15.9599	−0.638398
$626$	−1.52291	−0.0608676
$627$	96.2693	3.84462
$628$	5.12422	0.204479
$629$	−10.6860	−0.426077
$630$	20.9128	0.833186
$631$	−41.3154	−1.64474	−0.822370	−	0.568953i	$-0.807348\pi$
$631$	−41.3154	−1.64474	−0.822370	+	0.568953i	$0.807348\pi$
$632$	2.34832	0.0934112
$633$	−35.4073	−1.40731
$634$	9.31793	0.370062
$635$	39.7043	1.57562
$636$	−19.6023	−0.777280
$637$	1.93373	0.0766173
$638$	−4.99698	−0.197832
$639$	48.8255	1.93151
$640$	1.89466	0.0748931
$641$	37.1611	1.46778	0.733888	−	0.679270i	$-0.237704\pi$
$641$	37.1611	1.46778	0.733888	+	0.679270i	$0.237704\pi$
$642$	−7.37473	−0.291057
$643$	16.5745	0.653633	0.326816	−	0.945088i	$-0.394024\pi$
$643$	16.5745	0.653633	0.326816	+	0.945088i	$0.394024\pi$
$644$	2.43465	0.0959385
$645$	7.54080	0.296919
$646$	−13.1698	−0.518158
$647$	13.9891	0.549970	0.274985	−	0.961448i	$-0.411327\pi$
$647$	13.9891	0.549970	0.274985	+	0.961448i	$0.411327\pi$
$648$	−2.04719	−0.0804211
$649$	30.5596	1.19957
$650$	2.54270	0.0997328
$651$	30.1232	1.18062
$652$	9.24998	0.362257
$653$	−29.5360	−1.15583	−0.577916	−	0.816097i	$-0.696134\pi$
$653$	−29.5360	−1.15583	−0.577916	+	0.816097i	$0.696134\pi$
$654$	39.5430	1.54626
$655$	−15.6825	−0.612766
$656$	−3.91861	−0.152996
$657$	26.9557	1.05164
$658$	10.3086	0.401873
$659$	−7.18000	−0.279693	−0.139847	−	0.990173i	$-0.544661\pi$
$659$	−7.18000	−0.279693	−0.139847	+	0.990173i	$0.544661\pi$
$660$	−25.9861	−1.01151
$661$	44.9517	1.74842	0.874209	−	0.485549i	$-0.161380\pi$
$661$	44.9517	1.74842	0.874209	+	0.485549i	$0.161380\pi$
$662$	−21.3847	−0.831141
$663$	−9.28538	−0.360614
$664$	4.40900	0.171103
$665$	−32.3777	−1.25555
$666$	−25.8201	−1.00051
$667$	1.00000	0.0387202
$668$	1.90173	0.0735801
$669$	53.7039	2.07631
$670$	2.54230	0.0982175
$671$	9.08288	0.350641
$672$	6.68248	0.257782
$673$	13.1859	0.508278	0.254139	−	0.967168i	$-0.418208\pi$
$673$	13.1859	0.508278	0.254139	+	0.967168i	$0.418208\pi$
$674$	−31.7334	−1.22232
$675$	−5.93627	−0.228487
$676$	−9.74915	−0.374967
$677$	−23.9031	−0.918672	−0.459336	−	0.888263i	$-0.651913\pi$
$677$	−23.9031	−0.918672	−0.459336	+	0.888263i	$0.651913\pi$
$678$	22.3064	0.856674
$679$	13.6957	0.525591
$680$	3.55494	0.136326
$681$	14.6252	0.560440
$682$	−22.5253	−0.862539
$683$	7.13825	0.273137	0.136569	−	0.990631i	$-0.456393\pi$
$683$	7.13825	0.273137	0.136569	+	0.990631i	$0.456393\pi$
$684$	−31.8217	−1.21673
$685$	−6.66963	−0.254833
$686$	−19.6537	−0.750381
$687$	−54.2243	−2.06879
$688$	1.45005	0.0552827
$689$	12.8767	0.490561
$690$	5.20036	0.197974
$691$	50.0625	1.90447	0.952233	−	0.305372i	$-0.0987808\pi$
$691$	50.0625	1.90447	0.952233	+	0.305372i	$0.0987808\pi$
$692$	−7.04378	−0.267764
$693$	−55.1554	−2.09518
$694$	33.5782	1.27461
$695$	38.9888	1.47893
$696$	2.74474	0.104039
$697$	−7.35244	−0.278493
$698$	6.89024	0.260800
$699$	65.9182	2.49325
$700$	−3.43346	−0.129773
$701$	−37.0415	−1.39904	−0.699519	−	0.714614i	$-0.746602\pi$
$701$	−37.0415	−1.39904	−0.699519	+	0.714614i	$0.746602\pi$
$702$	−7.58955	−0.286449
$703$	39.9753	1.50770
$704$	−4.99698	−0.188331
$705$	22.0191	0.829287
$706$	−18.9674	−0.713846
$707$	22.5701	0.848836
$708$	−16.7858	−0.630848
$709$	39.3301	1.47707	0.738536	−	0.674214i	$-0.235518\pi$
$709$	39.3301	1.47707	0.738536	+	0.674214i	$0.235518\pi$
$710$	20.4049	0.765782
$711$	10.6464	0.399270
$712$	1.05775	0.0396408
$713$	4.50779	0.168818
$714$	12.5383	0.469232
$715$	17.0702	0.638388
$716$	−17.4349	−0.651572
$717$	1.99671	0.0745686
$718$	20.2427	0.755450
$719$	42.6692	1.59129	0.795646	−	0.605762i	$-0.207132\pi$
$719$	42.6692	1.59129	0.795646	+	0.605762i	$0.207132\pi$
$720$	8.58967	0.320118
$721$	−4.84235	−0.180339
$722$	30.2671	1.12642
$723$	11.4831	0.427063
$724$	−14.5250	−0.539819
$725$	−1.41025	−0.0523754
$726$	38.3435	1.42306
$727$	3.67284	0.136218	0.0681091	−	0.997678i	$-0.478303\pi$
$727$	3.67284	0.136218	0.0681091	+	0.997678i	$0.478303\pi$
$728$	−4.38969	−0.162693
$729$	−43.9421	−1.62749
$730$	11.2652	0.416943
$731$	2.72072	0.100629
$732$	−4.98905	−0.184401
$733$	2.13702	0.0789326	0.0394663	−	0.999221i	$-0.487434\pi$
$733$	2.13702	0.0789326	0.0394663	+	0.999221i	$0.487434\pi$
$734$	−16.6957	−0.616250
$735$	−5.57741	−0.205726
$736$	1.00000	0.0368605
$737$	−6.70504	−0.246983
$738$	−17.7654	−0.653955
$739$	−15.8495	−0.583032	−0.291516	−	0.956566i	$-0.594160\pi$
$739$	−15.8495	−0.583032	−0.291516	+	0.956566i	$0.594160\pi$
$740$	−10.7906	−0.396670
$741$	34.7359	1.27605
$742$	−17.3876	−0.638320
$743$	47.7073	1.75021	0.875106	−	0.483931i	$-0.160792\pi$
$743$	47.7073	1.75021	0.875106	+	0.483931i	$0.160792\pi$
$744$	12.3727	0.453606
$745$	−19.6744	−0.720814
$746$	−16.7367	−0.612774
$747$	19.9887	0.731349
$748$	−9.37578	−0.342812
$749$	−6.54154	−0.239023
$750$	−33.3356	−1.21725
$751$	18.1935	0.663888	0.331944	−	0.943299i	$-0.392295\pi$
$751$	18.1935	0.663888	0.331944	+	0.943299i	$0.392295\pi$
$752$	4.23415	0.154403
$753$	−59.8840	−2.18229
$754$	−1.80301	−0.0656618
$755$	−4.14273	−0.150770
$756$	10.2483	0.372728
$757$	9.62891	0.349969	0.174984	−	0.984571i	$-0.444013\pi$
$757$	9.62891	0.349969	0.174984	+	0.984571i	$0.444013\pi$
$758$	1.53851	0.0558810
$759$	−13.7154	−0.497838
$760$	−13.2987	−0.482396
$761$	−42.9269	−1.55610	−0.778049	−	0.628203i	$-0.783791\pi$
$761$	−42.9269	−1.55610	−0.778049	+	0.628203i	$0.783791\pi$
$762$	57.5185	2.08368
$763$	35.0755	1.26982
$764$	−18.7402	−0.677998
$765$	16.1167	0.582701
$766$	−25.7298	−0.929656
$767$	11.0265	0.398144
$768$	2.74474	0.0990424
$769$	−4.98963	−0.179931	−0.0899653	−	0.995945i	$-0.528676\pi$
$769$	−4.98963	−0.179931	−0.0899653	+	0.995945i	$0.528676\pi$
$770$	−23.0502	−0.830673
$771$	36.7663	1.32411
$772$	13.5834	0.488876
$773$	−49.1282	−1.76702	−0.883510	−	0.468412i	$-0.844826\pi$
$773$	−49.1282	−1.76702	−0.883510	+	0.468412i	$0.844826\pi$
$774$	6.57398	0.236297
$775$	−6.35711	−0.228354
$776$	5.62532	0.201937
$777$	−38.0584	−1.36534
$778$	−24.3809	−0.874096
$779$	27.5049	0.985465
$780$	−9.37631	−0.335726
$781$	−53.8158	−1.92568
$782$	1.87629	0.0670960
$783$	4.20938	0.150431
$784$	−1.07250	−0.0383037
$785$	9.70868	0.346518
$786$	−22.7188	−0.810352
$787$	3.36989	0.120124	0.0600618	−	0.998195i	$-0.480870\pi$
$787$	3.36989	0.120124	0.0600618	+	0.998195i	$0.480870\pi$
$788$	4.50849	0.160608
$789$	−5.45463	−0.194190
$790$	4.44928	0.158298
$791$	19.7863	0.703519
$792$	−22.6544	−0.804988
$793$	3.27729	0.116380
$794$	12.8583	0.456324
$795$	−37.1397	−1.31721
$796$	17.3617	0.615370
$797$	32.1994	1.14056	0.570281	−	0.821449i	$-0.306834\pi$
$797$	32.1994	1.14056	0.570281	+	0.821449i	$0.306834\pi$
$798$	−46.9046	−1.66041
$799$	7.94448	0.281056
$800$	−1.41025	−0.0498599
$801$	4.79542	0.169438
$802$	38.8426	1.37158
$803$	−29.7108	−1.04847
$804$	3.68295	0.129888
$805$	4.61283	0.162581
$806$	−8.12759	−0.286282
$807$	−3.09289	−0.108875
$808$	9.27039	0.326131
$809$	−19.4339	−0.683261	−0.341630	−	0.939834i	$-0.610979\pi$
$809$	−19.4339	−0.683261	−0.341630	+	0.939834i	$0.610979\pi$
$810$	−3.87873	−0.136285
$811$	23.3050	0.818351	0.409175	−	0.912456i	$-0.365816\pi$
$811$	23.3050	0.818351	0.409175	+	0.912456i	$0.365816\pi$
$812$	2.43465	0.0854393
$813$	59.0526	2.07107
$814$	28.4591	0.997490
$815$	17.5256	0.613895
$816$	5.14993	0.180284
$817$	−10.1780	−0.356083
$818$	0.560516	0.0195980
$819$	−19.9012	−0.695403
$820$	−7.42444	−0.259273
$821$	20.5577	0.717469	0.358735	−	0.933440i	$-0.383208\pi$
$821$	20.5577	0.717469	0.358735	+	0.933440i	$0.383208\pi$
$822$	−9.66210	−0.337004
$823$	9.35166	0.325978	0.162989	−	0.986628i	$-0.447886\pi$
$823$	9.35166	0.325978	0.162989	+	0.986628i	$0.447886\pi$
$824$	−1.98893	−0.0692878
$825$	19.3422	0.673408
$826$	−14.8893	−0.518067
$827$	38.2729	1.33088	0.665440	−	0.746451i	$-0.268244\pi$
$827$	38.2729	1.33088	0.665440	+	0.746451i	$0.268244\pi$
$828$	4.53361	0.157554
$829$	−25.5431	−0.887147	−0.443573	−	0.896238i	$-0.646289\pi$
$829$	−25.5431	−0.887147	−0.443573	+	0.896238i	$0.646289\pi$
$830$	8.35358	0.289957
$831$	−65.3583	−2.26726
$832$	−1.80301	−0.0625082
$833$	−2.01233	−0.0697229
$834$	56.4819	1.95581
$835$	3.60314	0.124692
$836$	35.0740	1.21306
$837$	18.9750	0.655871
$838$	−33.1665	−1.14572
$839$	14.2714	0.492702	0.246351	−	0.969181i	$-0.420768\pi$
$839$	14.2714	0.492702	0.246351	+	0.969181i	$0.420768\pi$
$840$	12.6610	0.436847
$841$	1.00000	0.0344828
$842$	−3.42900	−0.118171
$843$	40.1367	1.38238
$844$	−12.9000	−0.444038
$845$	−18.4714	−0.635434
$846$	19.1960	0.659972
$847$	34.0115	1.16865
$848$	−7.14175	−0.245249
$849$	66.8899	2.29566
$850$	−2.64604	−0.0907583
$851$	−5.69526	−0.195231
$852$	29.5600	1.01271
$853$	−18.7549	−0.642156	−0.321078	−	0.947053i	$-0.604045\pi$
$853$	−18.7549	−0.642156	−0.321078	+	0.947053i	$0.604045\pi$
$854$	−4.42539	−0.151434
$855$	−60.2913	−2.06192
$856$	−2.68686	−0.0918348
$857$	19.3534	0.661100	0.330550	−	0.943788i	$-0.392766\pi$
$857$	19.3534	0.661100	0.330550	+	0.943788i	$0.392766\pi$
$858$	24.7291	0.844236
$859$	23.4807	0.801151	0.400575	−	0.916264i	$-0.368810\pi$
$859$	23.4807	0.801151	0.400575	+	0.916264i	$0.368810\pi$
$860$	2.74736	0.0936843
$861$	−26.1860	−0.892416
$862$	−8.90505	−0.303307
$863$	−35.5259	−1.20932	−0.604658	−	0.796486i	$-0.706690\pi$
$863$	−35.5259	−1.20932	−0.604658	+	0.796486i	$0.706690\pi$
$864$	4.20938	0.143206
$865$	−13.3456	−0.453764
$866$	−13.6940	−0.465343
$867$	−36.9979	−1.25651
$868$	10.9749	0.372511
$869$	−11.7345	−0.398066
$870$	5.20036	0.176309
$871$	−2.41931	−0.0819753
$872$	14.4068	0.487877
$873$	25.5030	0.863147
$874$	−7.01905	−0.237423
$875$	−29.5694	−0.999629
$876$	16.3195	0.551386
$877$	24.4092	0.824239	0.412119	−	0.911130i	$-0.364789\pi$
$877$	24.4092	0.824239	0.412119	+	0.911130i	$0.364789\pi$
$878$	−30.2202	−1.01988
$879$	−23.1650	−0.781337
$880$	−9.46759	−0.319153
$881$	19.2294	0.647854	0.323927	−	0.946082i	$-0.394997\pi$
$881$	19.2294	0.647854	0.323927	+	0.946082i	$0.394997\pi$
$882$	−4.86231	−0.163723
$883$	−46.4810	−1.56421	−0.782106	−	0.623146i	$-0.785854\pi$
$883$	−46.4810	−1.56421	−0.782106	+	0.623146i	$0.785854\pi$
$884$	−3.38297	−0.113782
$885$	−31.8034	−1.06906
$886$	4.46384	0.149966
$887$	−3.39695	−0.114058	−0.0570292	−	0.998373i	$-0.518163\pi$
$887$	−3.39695	−0.114058	−0.0570292	+	0.998373i	$0.518163\pi$
$888$	−15.6320	−0.524576
$889$	51.0201	1.71116
$890$	2.00408	0.0671768
$891$	10.2297	0.342709
$892$	19.5661	0.655121
$893$	−29.7197	−0.994531
$894$	−28.5017	−0.953240
$895$	−33.0332	−1.10418
$896$	2.43465	0.0813358
$897$	−4.94880	−0.165236
$898$	−32.2231	−1.07530
$899$	4.50779	0.150343
$900$	−6.39353	−0.213118
$901$	−13.4000	−0.446418
$902$	19.5812	0.651982
$903$	9.68994	0.322461
$904$	8.12697	0.270299
$905$	−27.5201	−0.914798
$906$	−6.00146	−0.199385
$907$	49.8437	1.65503	0.827516	−	0.561443i	$-0.189753\pi$
$907$	49.8437	1.65503	0.827516	+	0.561443i	$0.189753\pi$
$908$	5.32845	0.176831
$909$	42.0284	1.39399
$910$	−8.31699	−0.275705
$911$	−37.3822	−1.23853	−0.619264	−	0.785183i	$-0.712569\pi$
$911$	−37.3822	−1.23853	−0.619264	+	0.785183i	$0.712569\pi$
$912$	−19.2655	−0.637944
$913$	−22.0317	−0.729143
$914$	−1.21309	−0.0401254
$915$	−9.45257	−0.312492
$916$	−19.7557	−0.652747
$917$	−20.1520	−0.665479
$918$	7.89801	0.260673
$919$	−53.6447	−1.76958	−0.884788	−	0.465993i	$-0.845697\pi$
$919$	−53.6447	−1.76958	−0.884788	+	0.465993i	$0.845697\pi$
$920$	1.89466	0.0624652
$921$	−37.9904	−1.25183
$922$	−38.8929	−1.28087
$923$	−19.4178	−0.639145
$924$	−33.3922	−1.09852
$925$	8.03174	0.264082
$926$	22.4937	0.739187
$927$	−9.01706	−0.296159
$928$	1.00000	0.0328266
$929$	−20.9841	−0.688465	−0.344233	−	0.938884i	$-0.611861\pi$
$929$	−20.9841	−0.688465	−0.344233	+	0.938884i	$0.611861\pi$
$930$	23.4421	0.768698
$931$	7.52795	0.246719
$932$	24.0162	0.786675
$933$	−55.3689	−1.81270
$934$	14.3794	0.470509
$935$	−17.7639	−0.580943
$936$	−8.17416	−0.267181
$937$	−1.32888	−0.0434127	−0.0217063	−	0.999764i	$-0.506910\pi$
$937$	−1.32888	−0.0434127	−0.0217063	+	0.999764i	$0.506910\pi$
$938$	3.26685	0.106667
$939$	−4.17999	−0.136409
$940$	8.02228	0.261658
$941$	−45.1962	−1.47336	−0.736678	−	0.676244i	$-0.763606\pi$
$941$	−45.1962	−1.47336	−0.736678	+	0.676244i	$0.763606\pi$
$942$	14.0647	0.458252
$943$	−3.91861	−0.127607
$944$	−6.11561	−0.199046
$945$	19.4172	0.631640
$946$	−7.24588	−0.235584
$947$	−14.7002	−0.477693	−0.238846	−	0.971057i	$-0.576769\pi$
$947$	−14.7002	−0.477693	−0.238846	+	0.971057i	$0.576769\pi$
$948$	6.44554	0.209341
$949$	−10.7202	−0.347994
$950$	9.89862	0.321154
$951$	25.5753	0.829337
$952$	4.56810	0.148053
$953$	16.4835	0.533954	0.266977	−	0.963703i	$-0.413975\pi$
$953$	16.4835	0.533954	0.266977	+	0.963703i	$0.413975\pi$
$954$	−32.3779	−1.04827
$955$	−35.5065	−1.14896
$956$	0.727468	0.0235280
$957$	−13.7154	−0.443357
$958$	−1.50483	−0.0486187
$959$	−8.57048	−0.276755
$960$	5.20036	0.167841
$961$	−10.6799	−0.344512
$962$	10.2686	0.331073
$963$	−12.1812	−0.392533
$964$	4.18369	0.134747
$965$	25.7359	0.828467
$966$	6.68248	0.215005
$967$	52.0817	1.67483	0.837417	−	0.546565i	$-0.184065\pi$
$967$	52.0817	1.67483	0.837417	+	0.546565i	$0.184065\pi$
$968$	13.9698	0.449007
$969$	−36.1476	−1.16123
$970$	10.6581	0.342211
$971$	−14.9346	−0.479276	−0.239638	−	0.970862i	$-0.577029\pi$
$971$	−14.9346	−0.479276	−0.239638	+	0.970862i	$0.577029\pi$
$972$	−18.2471	−0.585277
$973$	50.1007	1.60615
$974$	26.6267	0.853176
$975$	6.97905	0.223508
$976$	−1.81767	−0.0581823
$977$	49.9326	1.59749	0.798743	−	0.601672i	$-0.205499\pi$
$977$	49.9326	1.59749	0.798743	+	0.601672i	$0.205499\pi$
$978$	25.3888	0.811845
$979$	−5.28555	−0.168927
$980$	−2.03203	−0.0649109
$981$	65.3150	2.08535
$982$	35.1332	1.12115
$983$	47.5489	1.51657	0.758287	−	0.651921i	$-0.226036\pi$
$983$	47.5489	1.51657	0.758287	+	0.651921i	$0.226036\pi$
$984$	−10.7556	−0.342875
$985$	8.54207	0.272173
$986$	1.87629	0.0597532
$987$	28.2946	0.900626
$988$	12.6554	0.402623
$989$	1.45005	0.0461090
$990$	−42.9224	−1.36416
$991$	−33.8178	−1.07426	−0.537129	−	0.843500i	$-0.680491\pi$
$991$	−33.8178	−1.07426	−0.537129	+	0.843500i	$0.680491\pi$
$992$	4.50779	0.143122
$993$	−58.6956	−1.86265
$994$	26.2203	0.831658
$995$	32.8946	1.04283
$996$	12.1016	0.383453
$997$	−35.4680	−1.12328	−0.561641	−	0.827381i	$-0.689830\pi$
$997$	−35.4680	−1.12328	−0.561641	+	0.827381i	$0.689830\pi$
$998$	38.4437	1.21691
$999$	−23.9735	−0.758487

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1334.2.a.k.1.9	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1334.2.a.k.1.9	✓	10	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1334 = 2 \cdot 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1334.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.74474 q^{3} +1.00000 q^{4} +1.89466 q^{5} +2.74474 q^{6} +2.43465 q^{7} +1.00000 q^{8} +4.53361 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.74474 q^{3} +1.00000 q^{4} +1.89466 q^{5} +2.74474 q^{6} +2.43465 q^{7} +1.00000 q^{8} +4.53361 q^{9} +1.89466 q^{10} -4.99698 q^{11} +2.74474 q^{12} -1.80301 q^{13} +2.43465 q^{14} +5.20036 q^{15} +1.00000 q^{16} +1.87629 q^{17} +4.53361 q^{18} -7.01905 q^{19} +1.89466 q^{20} +6.68248 q^{21} -4.99698 q^{22} +1.00000 q^{23} +2.74474 q^{24} -1.41025 q^{25} -1.80301 q^{26} +4.20938 q^{27} +2.43465 q^{28} +1.00000 q^{29} +5.20036 q^{30} +4.50779 q^{31} +1.00000 q^{32} -13.7154 q^{33} +1.87629 q^{34} +4.61283 q^{35} +4.53361 q^{36} -5.69526 q^{37} -7.01905 q^{38} -4.94880 q^{39} +1.89466 q^{40} -3.91861 q^{41} +6.68248 q^{42} +1.45005 q^{43} -4.99698 q^{44} +8.58967 q^{45} +1.00000 q^{46} +4.23415 q^{47} +2.74474 q^{48} -1.07250 q^{49} -1.41025 q^{50} +5.14993 q^{51} -1.80301 q^{52} -7.14175 q^{53} +4.20938 q^{54} -9.46759 q^{55} +2.43465 q^{56} -19.2655 q^{57} +1.00000 q^{58} -6.11561 q^{59} +5.20036 q^{60} -1.81767 q^{61} +4.50779 q^{62} +11.0377 q^{63} +1.00000 q^{64} -3.41610 q^{65} -13.7154 q^{66} +1.34182 q^{67} +1.87629 q^{68} +2.74474 q^{69} +4.61283 q^{70} +10.7697 q^{71} +4.53361 q^{72} +5.94574 q^{73} -5.69526 q^{74} -3.87077 q^{75} -7.01905 q^{76} -12.1659 q^{77} -4.94880 q^{78} +2.34832 q^{79} +1.89466 q^{80} -2.04719 q^{81} -3.91861 q^{82} +4.40900 q^{83} +6.68248 q^{84} +3.55494 q^{85} +1.45005 q^{86} +2.74474 q^{87} -4.99698 q^{88} +1.05775 q^{89} +8.58967 q^{90} -4.38969 q^{91} +1.00000 q^{92} +12.3727 q^{93} +4.23415 q^{94} -13.2987 q^{95} +2.74474 q^{96} +5.62532 q^{97} -1.07250 q^{98} -22.6544 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 10 q^{2} + 5 q^{3} + 10 q^{4} - q^{5} + 5 q^{6} + 2 q^{7} + 10 q^{8} + 11 q^{9}+O(q^{10}) \) 10 * q + 10 * q^2 + 5 * q^3 + 10 * q^4 - q^5 + 5 * q^6 + 2 * q^7 + 10 * q^8 + 11 * q^9	\( 10 q + 10 q^{2} + 5 q^{3} + 10 q^{4} - q^{5} + 5 q^{6} + 2 q^{7} + 10 q^{8} + 11 q^{9} - q^{10} + q^{11} + 5 q^{12} + 9 q^{13} + 2 q^{14} + 5 q^{15} + 10 q^{16} + 11 q^{18} + 20 q^{19} - q^{20} + 14 q^{21} + q^{22} + 10 q^{23} + 5 q^{24} + 23 q^{25} + 9 q^{26} + 23 q^{27} + 2 q^{28} + 10 q^{29} + 5 q^{30} + 21 q^{31} + 10 q^{32} + q^{33} + 2 q^{35} + 11 q^{36} - 8 q^{37} + 20 q^{38} + 23 q^{39} - q^{40} - 4 q^{41} + 14 q^{42} - 3 q^{43} + q^{44} - 18 q^{45} + 10 q^{46} - q^{47} + 5 q^{48} + 18 q^{49} + 23 q^{50} - 6 q^{51} + 9 q^{52} - 13 q^{53} + 23 q^{54} + 13 q^{55} + 2 q^{56} - 22 q^{57} + 10 q^{58} + 14 q^{59} + 5 q^{60} + 12 q^{61} + 21 q^{62} - 26 q^{63} + 10 q^{64} - 25 q^{65} + q^{66} + 6 q^{67} + 5 q^{69} + 2 q^{70} + 8 q^{71} + 11 q^{72} + 16 q^{73} - 8 q^{74} + 8 q^{75} + 20 q^{76} - 16 q^{77} + 23 q^{78} + 7 q^{79} - q^{80} - 2 q^{81} - 4 q^{82} + 18 q^{83} + 14 q^{84} + 8 q^{85} - 3 q^{86} + 5 q^{87} + q^{88} + 2 q^{89} - 18 q^{90} + 8 q^{91} + 10 q^{92} - 41 q^{93} - q^{94} - 16 q^{95} + 5 q^{96} + 6 q^{97} + 18 q^{98} - 22 q^{99}+O(q^{100}) \) 10 * q + 10 * q^2 + 5 * q^3 + 10 * q^4 - q^5 + 5 * q^6 + 2 * q^7 + 10 * q^8 + 11 * q^9 - q^10 + q^11 + 5 * q^12 + 9 * q^13 + 2 * q^14 + 5 * q^15 + 10 * q^16 + 11 * q^18 + 20 * q^19 - q^20 + 14 * q^21 + q^22 + 10 * q^23 + 5 * q^24 + 23 * q^25 + 9 * q^26 + 23 * q^27 + 2 * q^28 + 10 * q^29 + 5 * q^30 + 21 * q^31 + 10 * q^32 + q^33 + 2 * q^35 + 11 * q^36 - 8 * q^37 + 20 * q^38 + 23 * q^39 - q^40 - 4 * q^41 + 14 * q^42 - 3 * q^43 + q^44 - 18 * q^45 + 10 * q^46 - q^47 + 5 * q^48 + 18 * q^49 + 23 * q^50 - 6 * q^51 + 9 * q^52 - 13 * q^53 + 23 * q^54 + 13 * q^55 + 2 * q^56 - 22 * q^57 + 10 * q^58 + 14 * q^59 + 5 * q^60 + 12 * q^61 + 21 * q^62 - 26 * q^63 + 10 * q^64 - 25 * q^65 + q^66 + 6 * q^67 + 5 * q^69 + 2 * q^70 + 8 * q^71 + 11 * q^72 + 16 * q^73 - 8 * q^74 + 8 * q^75 + 20 * q^76 - 16 * q^77 + 23 * q^78 + 7 * q^79 - q^80 - 2 * q^81 - 4 * q^82 + 18 * q^83 + 14 * q^84 + 8 * q^85 - 3 * q^86 + 5 * q^87 + q^88 + 2 * q^89 - 18 * q^90 + 8 * q^91 + 10 * q^92 - 41 * q^93 - q^94 - 16 * q^95 + 5 * q^96 + 6 * q^97 + 18 * q^98 - 22 * q^99

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