LMFDB - Embedded newform 1334.2.a.h.1.2

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:	$1$
Dimension:	$5$
Coefficient field:	5.5.179024.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 8x^{3} + 6x - 2 $ x^5 - 8x^3 + 6x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.69767$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.81085 q^{3} +1.00000 q^{4} -2.65571 q^{5} -1.81085 q^{6} +1.95629 q^{7} +1.00000 q^{8} +0.279165 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.81085 q^{3} +1.00000 q^{4} -2.65571 q^{5} -1.81085 q^{6} +1.95629 q^{7} +1.00000 q^{8} +0.279165 q^{9} -2.65571 q^{10} +4.97507 q^{11} -1.81085 q^{12} -3.40406 q^{13} +1.95629 q^{14} +4.80909 q^{15} +1.00000 q^{16} -5.22935 q^{17} +0.279165 q^{18} -0.209700 q^{19} -2.65571 q^{20} -3.54253 q^{21} +4.97507 q^{22} -1.00000 q^{23} -1.81085 q^{24} +2.05281 q^{25} -3.40406 q^{26} +4.92701 q^{27} +1.95629 q^{28} +1.00000 q^{29} +4.80909 q^{30} -4.04195 q^{31} +1.00000 q^{32} -9.00909 q^{33} -5.22935 q^{34} -5.19533 q^{35} +0.279165 q^{36} -1.47015 q^{37} -0.209700 q^{38} +6.16422 q^{39} -2.65571 q^{40} -5.85714 q^{41} -3.54253 q^{42} -8.66480 q^{43} +4.97507 q^{44} -0.741381 q^{45} -1.00000 q^{46} +5.67536 q^{47} -1.81085 q^{48} -3.17295 q^{49} +2.05281 q^{50} +9.46955 q^{51} -3.40406 q^{52} -2.58767 q^{53} +4.92701 q^{54} -13.2124 q^{55} +1.95629 q^{56} +0.379734 q^{57} +1.00000 q^{58} -7.48710 q^{59} +4.80909 q^{60} -13.9217 q^{61} -4.04195 q^{62} +0.546126 q^{63} +1.00000 q^{64} +9.04019 q^{65} -9.00909 q^{66} +6.04532 q^{67} -5.22935 q^{68} +1.81085 q^{69} -5.19533 q^{70} -14.4535 q^{71} +0.279165 q^{72} -8.47565 q^{73} -1.47015 q^{74} -3.71731 q^{75} -0.209700 q^{76} +9.73266 q^{77} +6.16422 q^{78} -4.27528 q^{79} -2.65571 q^{80} -9.75956 q^{81} -5.85714 q^{82} +2.51936 q^{83} -3.54253 q^{84} +13.8876 q^{85} -8.66480 q^{86} -1.81085 q^{87} +4.97507 q^{88} -14.7012 q^{89} -0.741381 q^{90} -6.65931 q^{91} -1.00000 q^{92} +7.31936 q^{93} +5.67536 q^{94} +0.556903 q^{95} -1.81085 q^{96} +6.35521 q^{97} -3.17295 q^{98} +1.38887 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 5 q^{2} - 3 q^{3} + 5 q^{4} - 5 q^{5} - 3 q^{6} - 6 q^{7} + 5 q^{8} + 2 q^{9}+O(q^{10}) $ 5 * q + 5 * q^2 - 3 * q^3 + 5 * q^4 - 5 * q^5 - 3 * q^6 - 6 * q^7 + 5 * q^8 + 2 * q^9	\( 5 q + 5 q^{2} - 3 q^{3} + 5 q^{4} - 5 q^{5} - 3 q^{6} - 6 q^{7} + 5 q^{8} + 2 q^{9} - 5 q^{10} - 9 q^{11} - 3 q^{12} - 5 q^{13} - 6 q^{14} - 3 q^{15} + 5 q^{16} - 6 q^{17} + 2 q^{18} - 10 q^{19} - 5 q^{20} - 2 q^{21} - 9 q^{22} - 5 q^{23} - 3 q^{24} - 4 q^{25} - 5 q^{26} - 9 q^{27} - 6 q^{28} + 5 q^{29} - 3 q^{30} - 15 q^{31} + 5 q^{32} - 15 q^{33} - 6 q^{34} - 2 q^{35} + 2 q^{36} - 10 q^{38} + 3 q^{39} - 5 q^{40} - 2 q^{41} - 2 q^{42} - 5 q^{43} - 9 q^{44} - 6 q^{45} - 5 q^{46} - 9 q^{47} - 3 q^{48} - 3 q^{49} - 4 q^{50} - 2 q^{51} - 5 q^{52} + 3 q^{53} - 9 q^{54} - 3 q^{55} - 6 q^{56} - 2 q^{57} + 5 q^{58} - 26 q^{59} - 3 q^{60} - 8 q^{61} - 15 q^{62} - 6 q^{63} + 5 q^{64} + 19 q^{65} - 15 q^{66} + 12 q^{67} - 6 q^{68} + 3 q^{69} - 2 q^{70} - 12 q^{71} + 2 q^{72} + 2 q^{73} + 24 q^{75} - 10 q^{76} + 36 q^{77} + 3 q^{78} - 25 q^{79} - 5 q^{80} + 9 q^{81} - 2 q^{82} - 16 q^{83} - 2 q^{84} + 4 q^{85} - 5 q^{86} - 3 q^{87} - 9 q^{88} - 20 q^{89} - 6 q^{90} - 32 q^{91} - 5 q^{92} + 11 q^{93} - 9 q^{94} + 20 q^{95} - 3 q^{96} - 4 q^{97} - 3 q^{98} + 20 q^{99}+O(q^{100}) \) 5 * q + 5 * q^2 - 3 * q^3 + 5 * q^4 - 5 * q^5 - 3 * q^6 - 6 * q^7 + 5 * q^8 + 2 * q^9 - 5 * q^10 - 9 * q^11 - 3 * q^12 - 5 * q^13 - 6 * q^14 - 3 * q^15 + 5 * q^16 - 6 * q^17 + 2 * q^18 - 10 * q^19 - 5 * q^20 - 2 * q^21 - 9 * q^22 - 5 * q^23 - 3 * q^24 - 4 * q^25 - 5 * q^26 - 9 * q^27 - 6 * q^28 + 5 * q^29 - 3 * q^30 - 15 * q^31 + 5 * q^32 - 15 * q^33 - 6 * q^34 - 2 * q^35 + 2 * q^36 - 10 * q^38 + 3 * q^39 - 5 * q^40 - 2 * q^41 - 2 * q^42 - 5 * q^43 - 9 * q^44 - 6 * q^45 - 5 * q^46 - 9 * q^47 - 3 * q^48 - 3 * q^49 - 4 * q^50 - 2 * q^51 - 5 * q^52 + 3 * q^53 - 9 * q^54 - 3 * q^55 - 6 * q^56 - 2 * q^57 + 5 * q^58 - 26 * q^59 - 3 * q^60 - 8 * q^61 - 15 * q^62 - 6 * q^63 + 5 * q^64 + 19 * q^65 - 15 * q^66 + 12 * q^67 - 6 * q^68 + 3 * q^69 - 2 * q^70 - 12 * q^71 + 2 * q^72 + 2 * q^73 + 24 * q^75 - 10 * q^76 + 36 * q^77 + 3 * q^78 - 25 * q^79 - 5 * q^80 + 9 * q^81 - 2 * q^82 - 16 * q^83 - 2 * q^84 + 4 * q^85 - 5 * q^86 - 3 * q^87 - 9 * q^88 - 20 * q^89 - 6 * q^90 - 32 * q^91 - 5 * q^92 + 11 * q^93 - 9 * q^94 + 20 * q^95 - 3 * q^96 - 4 * q^97 - 3 * q^98 + 20 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.81085	−1.04549	−0.522746	−	0.852488i	$-0.675093\pi$
$3$	−1.81085	−1.04549	−0.522746	+	0.852488i	$0.675093\pi$
$4$	1.00000	0.500000
$5$	−2.65571	−1.18767	−0.593835	−	0.804587i	$-0.702387\pi$
$5$	−2.65571	−1.18767	−0.593835	+	0.804587i	$0.702387\pi$
$6$	−1.81085	−0.739275
$7$	1.95629	0.739406	0.369703	−	0.929150i	$-0.379459\pi$
$7$	1.95629	0.739406	0.369703	+	0.929150i	$0.379459\pi$
$8$	1.00000	0.353553
$9$	0.279165	0.0930550
$10$	−2.65571	−0.839810
$11$	4.97507	1.50004	0.750020	−	0.661415i	$-0.230044\pi$
$11$	4.97507	1.50004	0.750020	+	0.661415i	$0.230044\pi$
$12$	−1.81085	−0.522746
$13$	−3.40406	−0.944116	−0.472058	−	0.881568i	$-0.656489\pi$
$13$	−3.40406	−0.944116	−0.472058	+	0.881568i	$0.656489\pi$
$14$	1.95629	0.522839
$15$	4.80909	1.24170
$16$	1.00000	0.250000
$17$	−5.22935	−1.26830	−0.634152	−	0.773209i	$-0.718650\pi$
$17$	−5.22935	−1.26830	−0.634152	+	0.773209i	$0.718650\pi$
$18$	0.279165	0.0657998
$19$	−0.209700	−0.0481085	−0.0240542	−	0.999711i	$-0.507657\pi$
$19$	−0.209700	−0.0481085	−0.0240542	+	0.999711i	$0.507657\pi$
$20$	−2.65571	−0.593835
$21$	−3.54253	−0.773044
$22$	4.97507	1.06069
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−1.81085	−0.369637
$25$	2.05281	0.410561
$26$	−3.40406	−0.667591
$27$	4.92701	0.948204
$28$	1.95629	0.369703
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	4.80909	0.878015
$31$	−4.04195	−0.725957	−0.362978	−	0.931798i	$-0.618240\pi$
$31$	−4.04195	−0.725957	−0.362978	+	0.931798i	$0.618240\pi$
$32$	1.00000	0.176777
$33$	−9.00909	−1.56828
$34$	−5.22935	−0.896826
$35$	−5.19533	−0.878171
$36$	0.279165	0.0465275
$37$	−1.47015	−0.241692	−0.120846	−	0.992671i	$-0.538561\pi$
$37$	−1.47015	−0.241692	−0.120846	+	0.992671i	$0.538561\pi$
$38$	−0.209700	−0.0340178
$39$	6.16422	0.987066
$40$	−2.65571	−0.419905
$41$	−5.85714	−0.914732	−0.457366	−	0.889279i	$-0.651207\pi$
$41$	−5.85714	−0.914732	−0.457366	+	0.889279i	$0.651207\pi$
$42$	−3.54253	−0.546625
$43$	−8.66480	−1.32137	−0.660685	−	0.750663i	$-0.729734\pi$
$43$	−8.66480	−1.32137	−0.660685	+	0.750663i	$0.729734\pi$
$44$	4.97507	0.750020
$45$	−0.741381	−0.110519
$46$	−1.00000	−0.147442
$47$	5.67536	0.827836	0.413918	−	0.910314i	$-0.364160\pi$
$47$	5.67536	0.827836	0.413918	+	0.910314i	$0.364160\pi$
$48$	−1.81085	−0.261373
$49$	−3.17295	−0.453278
$50$	2.05281	0.290310
$51$	9.46955	1.32600
$52$	−3.40406	−0.472058
$53$	−2.58767	−0.355444	−0.177722	−	0.984081i	$-0.556873\pi$
$53$	−2.58767	−0.355444	−0.177722	+	0.984081i	$0.556873\pi$
$54$	4.92701	0.670482
$55$	−13.2124	−1.78155
$56$	1.95629	0.261420
$57$	0.379734	0.0502970
$58$	1.00000	0.131306
$59$	−7.48710	−0.974738	−0.487369	−	0.873196i	$-0.662043\pi$
$59$	−7.48710	−0.974738	−0.487369	+	0.873196i	$0.662043\pi$
$60$	4.80909	0.620850
$61$	−13.9217	−1.78249	−0.891243	−	0.453526i	$-0.850166\pi$
$61$	−13.9217	−1.78249	−0.891243	+	0.453526i	$0.850166\pi$
$62$	−4.04195	−0.513329
$63$	0.546126	0.0688054
$64$	1.00000	0.125000
$65$	9.04019	1.12130
$66$	−9.00909	−1.10894
$67$	6.04532	0.738554	0.369277	−	0.929319i	$-0.379605\pi$
$67$	6.04532	0.738554	0.369277	+	0.929319i	$0.379605\pi$
$68$	−5.22935	−0.634152
$69$	1.81085	0.218000
$70$	−5.19533	−0.620961
$71$	−14.4535	−1.71531	−0.857655	−	0.514226i	$-0.828079\pi$
$71$	−14.4535	−1.71531	−0.857655	+	0.514226i	$0.828079\pi$
$72$	0.279165	0.0328999
$73$	−8.47565	−0.992000	−0.496000	−	0.868323i	$-0.665198\pi$
$73$	−8.47565	−0.992000	−0.496000	+	0.868323i	$0.665198\pi$
$74$	−1.47015	−0.170902
$75$	−3.71731	−0.429239
$76$	−0.209700	−0.0240542
$77$	9.73266	1.10914
$78$	6.16422	0.697961
$79$	−4.27528	−0.481006	−0.240503	−	0.970648i	$-0.577312\pi$
$79$	−4.27528	−0.481006	−0.240503	+	0.970648i	$0.577312\pi$
$80$	−2.65571	−0.296918
$81$	−9.75956	−1.08440
$82$	−5.85714	−0.646813
$83$	2.51936	0.276536	0.138268	−	0.990395i	$-0.455846\pi$
$83$	2.51936	0.276536	0.138268	+	0.990395i	$0.455846\pi$
$84$	−3.54253	−0.386522
$85$	13.8876	1.50633
$86$	−8.66480	−0.934350
$87$	−1.81085	−0.194143
$88$	4.97507	0.530344
$89$	−14.7012	−1.55833	−0.779163	−	0.626821i	$-0.784356\pi$
$89$	−14.7012	−1.55833	−0.779163	+	0.626821i	$0.784356\pi$
$90$	−0.741381	−0.0781485
$91$	−6.65931	−0.698085
$92$	−1.00000	−0.104257
$93$	7.31936	0.758982
$94$	5.67536	0.585369
$95$	0.556903	0.0571370
$96$	−1.81085	−0.184819
$97$	6.35521	0.645274	0.322637	−	0.946523i	$-0.395431\pi$
$97$	6.35521	0.645274	0.322637	+	0.946523i	$0.395431\pi$
$98$	−3.17295	−0.320516
$99$	1.38887	0.139586
$100$	2.05281	0.205281
$101$	7.77375	0.773517	0.386759	−	0.922181i	$-0.373595\pi$
$101$	7.77375	0.773517	0.386759	+	0.922181i	$0.373595\pi$
$102$	9.46955	0.937625
$103$	12.4456	1.22630	0.613150	−	0.789966i	$-0.289902\pi$
$103$	12.4456	1.22630	0.613150	+	0.789966i	$0.289902\pi$
$104$	−3.40406	−0.333795
$105$	9.40794	0.918121
$106$	−2.58767	−0.251337
$107$	4.31027	0.416689	0.208345	−	0.978055i	$-0.433192\pi$
$107$	4.31027	0.416689	0.208345	+	0.978055i	$0.433192\pi$
$108$	4.92701	0.474102
$109$	−17.5426	−1.68028	−0.840138	−	0.542372i	$-0.817526\pi$
$109$	−17.5426	−1.68028	−0.840138	+	0.542372i	$0.817526\pi$
$110$	−13.2124	−1.25975
$111$	2.66222	0.252687
$112$	1.95629	0.184852
$113$	14.8476	1.39675	0.698374	−	0.715733i	$-0.253907\pi$
$113$	14.8476	1.39675	0.698374	+	0.715733i	$0.253907\pi$
$114$	0.379734	0.0355654
$115$	2.65571	0.247646
$116$	1.00000	0.0928477
$117$	−0.950293	−0.0878546
$118$	−7.48710	−0.689244
$119$	−10.2301	−0.937791
$120$	4.80909	0.439008
$121$	13.7513	1.25012
$122$	−13.9217	−1.26041
$123$	10.6064	0.956346
$124$	−4.04195	−0.362978
$125$	7.82690	0.700059
$126$	0.546126	0.0486528
$127$	4.59590	0.407820	0.203910	−	0.978990i	$-0.434635\pi$
$127$	4.59590	0.407820	0.203910	+	0.978990i	$0.434635\pi$
$128$	1.00000	0.0883883
$129$	15.6906	1.38148
$130$	9.04019	0.792878
$131$	3.15068	0.275276	0.137638	−	0.990483i	$-0.456049\pi$
$131$	3.15068	0.275276	0.137638	+	0.990483i	$0.456049\pi$
$132$	−9.00909	−0.784141
$133$	−0.410233	−0.0355717
$134$	6.04532	0.522236
$135$	−13.0847	−1.12615
$136$	−5.22935	−0.448413
$137$	3.51285	0.300123	0.150062	−	0.988677i	$-0.452053\pi$
$137$	3.51285	0.300123	0.150062	+	0.988677i	$0.452053\pi$
$138$	1.81085	0.154149
$139$	−4.96530	−0.421151	−0.210576	−	0.977578i	$-0.567534\pi$
$139$	−4.96530	−0.421151	−0.210576	+	0.977578i	$0.567534\pi$
$140$	−5.19533	−0.439085
$141$	−10.2772	−0.865497
$142$	−14.4535	−1.21291
$143$	−16.9354	−1.41621
$144$	0.279165	0.0232637
$145$	−2.65571	−0.220545
$146$	−8.47565	−0.701450
$147$	5.74572	0.473899
$148$	−1.47015	−0.120846
$149$	23.7437	1.94516	0.972581	−	0.232565i	$-0.0747119\pi$
$149$	23.7437	1.94516	0.972581	+	0.232565i	$0.0747119\pi$
$150$	−3.71731	−0.303517
$151$	6.93524	0.564382	0.282191	−	0.959358i	$-0.408939\pi$
$151$	6.93524	0.564382	0.282191	+	0.959358i	$0.408939\pi$
$152$	−0.209700	−0.0170089
$153$	−1.45985	−0.118022
$154$	9.73266	0.784280
$155$	10.7343	0.862197
$156$	6.16422	0.493533
$157$	9.00247	0.718475	0.359238	−	0.933246i	$-0.383037\pi$
$157$	9.00247	0.718475	0.359238	+	0.933246i	$0.383037\pi$
$158$	−4.27528	−0.340123
$159$	4.68588	0.371614
$160$	−2.65571	−0.209952
$161$	−1.95629	−0.154177
$162$	−9.75956	−0.766784
$163$	10.1406	0.794273	0.397137	−	0.917760i	$-0.370004\pi$
$163$	10.1406	0.794273	0.397137	+	0.917760i	$0.370004\pi$
$164$	−5.85714	−0.457366
$165$	23.9255	1.86260
$166$	2.51936	0.195541
$167$	−8.16995	−0.632209	−0.316105	−	0.948724i	$-0.602375\pi$
$167$	−8.16995	−0.632209	−0.316105	+	0.948724i	$0.602375\pi$
$168$	−3.54253	−0.273312
$169$	−1.41240	−0.108646
$170$	13.8876	1.06513
$171$	−0.0585409	−0.00447673
$172$	−8.66480	−0.660685
$173$	11.4967	0.874077	0.437039	−	0.899443i	$-0.356027\pi$
$173$	11.4967	0.874077	0.437039	+	0.899443i	$0.356027\pi$
$174$	−1.81085	−0.137280
$175$	4.01587	0.303571
$176$	4.97507	0.375010
$177$	13.5580	1.01908
$178$	−14.7012	−1.10190
$179$	0.213932	0.0159900	0.00799500	−	0.999968i	$-0.497455\pi$
$179$	0.213932	0.0159900	0.00799500	+	0.999968i	$0.497455\pi$
$180$	−0.741381	−0.0552593
$181$	14.1009	1.04811	0.524057	−	0.851683i	$-0.324418\pi$
$181$	14.1009	1.04811	0.524057	+	0.851683i	$0.324418\pi$
$182$	−6.65931	−0.493621
$183$	25.2100	1.86358
$184$	−1.00000	−0.0737210
$185$	3.90430	0.287050
$186$	7.31936	0.536681
$187$	−26.0164	−1.90251
$188$	5.67536	0.413918
$189$	9.63865	0.701108
$190$	0.556903	0.0404020
$191$	−1.79756	−0.130067	−0.0650333	−	0.997883i	$-0.520715\pi$
$191$	−1.79756	−0.130067	−0.0650333	+	0.997883i	$0.520715\pi$
$192$	−1.81085	−0.130687
$193$	−17.5053	−1.26006	−0.630029	−	0.776572i	$-0.716957\pi$
$193$	−17.5053	−1.26006	−0.630029	+	0.776572i	$0.716957\pi$
$194$	6.35521	0.456278
$195$	−16.3704	−1.17231
$196$	−3.17295	−0.226639
$197$	23.6299	1.68356	0.841780	−	0.539821i	$-0.181508\pi$
$197$	23.6299	1.68356	0.841780	+	0.539821i	$0.181508\pi$
$198$	1.38887	0.0987024
$199$	1.00662	0.0713573	0.0356787	−	0.999363i	$-0.488641\pi$
$199$	1.00662	0.0713573	0.0356787	+	0.999363i	$0.488641\pi$
$200$	2.05281	0.145155
$201$	−10.9472	−0.772153
$202$	7.77375	0.546959
$203$	1.95629	0.137304
$204$	9.46955	0.663001
$205$	15.5549	1.08640
$206$	12.4456	0.867125
$207$	−0.279165	−0.0194033
$208$	−3.40406	−0.236029
$209$	−1.04327	−0.0721646
$210$	9.40794	0.649210
$211$	−21.2163	−1.46059	−0.730296	−	0.683131i	$-0.760618\pi$
$211$	−21.2163	−1.46059	−0.730296	+	0.683131i	$0.760618\pi$
$212$	−2.58767	−0.177722
$213$	26.1730	1.79334
$214$	4.31027	0.294644
$215$	23.0112	1.56935
$216$	4.92701	0.335241
$217$	−7.90722	−0.536777
$218$	−17.5426	−1.18814
$219$	15.3481	1.03713
$220$	−13.2124	−0.890777
$221$	17.8010	1.19742
$222$	2.66222	0.178677
$223$	−27.2709	−1.82619	−0.913097	−	0.407743i	$-0.866316\pi$
$223$	−27.2709	−1.82619	−0.913097	+	0.407743i	$0.866316\pi$
$224$	1.95629	0.130710
$225$	0.573071	0.0382047
$226$	14.8476	0.987650
$227$	−9.09263	−0.603499	−0.301750	−	0.953387i	$-0.597571\pi$
$227$	−9.09263	−0.603499	−0.301750	+	0.953387i	$0.597571\pi$
$228$	0.379734	0.0251485
$229$	−23.2235	−1.53465	−0.767326	−	0.641257i	$-0.778413\pi$
$229$	−23.2235	−1.53465	−0.767326	+	0.641257i	$0.778413\pi$
$230$	2.65571	0.175112
$231$	−17.6243	−1.15960
$232$	1.00000	0.0656532
$233$	−1.27501	−0.0835284	−0.0417642	−	0.999127i	$-0.513298\pi$
$233$	−1.27501	−0.0835284	−0.0417642	+	0.999127i	$0.513298\pi$
$234$	−0.950293	−0.0621226
$235$	−15.0721	−0.983197
$236$	−7.48710	−0.487369
$237$	7.74187	0.502889
$238$	−10.2301	−0.663119
$239$	−3.97850	−0.257348	−0.128674	−	0.991687i	$-0.541072\pi$
$239$	−3.97850	−0.257348	−0.128674	+	0.991687i	$0.541072\pi$
$240$	4.80909	0.310425
$241$	−4.38703	−0.282594	−0.141297	−	0.989967i	$-0.545127\pi$
$241$	−4.38703	−0.282594	−0.141297	+	0.989967i	$0.545127\pi$
$242$	13.7513	0.883969
$243$	2.89202	0.185523
$244$	−13.9217	−0.891243
$245$	8.42644	0.538345
$246$	10.6064	0.676238
$247$	0.713830	0.0454199
$248$	−4.04195	−0.256664
$249$	−4.56218	−0.289116
$250$	7.82690	0.495017
$251$	−11.8382	−0.747221	−0.373610	−	0.927586i	$-0.621880\pi$
$251$	−11.8382	−0.747221	−0.373610	+	0.927586i	$0.621880\pi$
$252$	0.546126	0.0344027
$253$	−4.97507	−0.312780
$254$	4.59590	0.288373
$255$	−25.1484	−1.57485
$256$	1.00000	0.0625000
$257$	11.0000	0.686163	0.343082	−	0.939306i	$-0.388529\pi$
$257$	11.0000	0.686163	0.343082	+	0.939306i	$0.388529\pi$
$258$	15.6906	0.976856
$259$	−2.87604	−0.178708
$260$	9.04019	0.560649
$261$	0.279165	0.0172799
$262$	3.15068	0.194650
$263$	−5.86171	−0.361448	−0.180724	−	0.983534i	$-0.557844\pi$
$263$	−5.86171	−0.361448	−0.180724	+	0.983534i	$0.557844\pi$
$264$	−9.00909	−0.554471
$265$	6.87212	0.422151
$266$	−0.410233	−0.0251530
$267$	26.6217	1.62922
$268$	6.04532	0.369277
$269$	30.6818	1.87070	0.935352	−	0.353718i	$-0.115083\pi$
$269$	30.6818	1.87070	0.935352	+	0.353718i	$0.115083\pi$
$270$	−13.0847	−0.796311
$271$	−3.61143	−0.219379	−0.109689	−	0.993966i	$-0.534986\pi$
$271$	−3.61143	−0.219379	−0.109689	+	0.993966i	$0.534986\pi$
$272$	−5.22935	−0.317076
$273$	12.0590	0.729843
$274$	3.51285	0.212219
$275$	10.2129	0.615858
$276$	1.81085	0.109000
$277$	−25.9604	−1.55981	−0.779905	−	0.625897i	$-0.784733\pi$
$277$	−25.9604	−1.55981	−0.779905	+	0.625897i	$0.784733\pi$
$278$	−4.96530	−0.297799
$279$	−1.12837	−0.0675539
$280$	−5.19533	−0.310480
$281$	−25.9055	−1.54539	−0.772696	−	0.634776i	$-0.781092\pi$
$281$	−25.9055	−1.54539	−0.772696	+	0.634776i	$0.781092\pi$
$282$	−10.2772	−0.611999
$283$	9.28582	0.551985	0.275992	−	0.961160i	$-0.410994\pi$
$283$	9.28582	0.551985	0.275992	+	0.961160i	$0.410994\pi$
$284$	−14.4535	−0.857655
$285$	−1.00846	−0.0597363
$286$	−16.9354	−1.00141
$287$	−11.4582	−0.676359
$288$	0.279165	0.0164499
$289$	10.3461	0.608593
$290$	−2.65571	−0.155949
$291$	−11.5083	−0.674629
$292$	−8.47565	−0.496000
$293$	−14.5441	−0.849678	−0.424839	−	0.905269i	$-0.639669\pi$
$293$	−14.5441	−0.849678	−0.424839	+	0.905269i	$0.639669\pi$
$294$	5.74572	0.335097
$295$	19.8836	1.15767
$296$	−1.47015	−0.0854509
$297$	24.5122	1.42234
$298$	23.7437	1.37544
$299$	3.40406	0.196862
$300$	−3.71731	−0.214619
$301$	−16.9508	−0.977029
$302$	6.93524	0.399078
$303$	−14.0771	−0.808706
$304$	−0.209700	−0.0120271
$305$	36.9719	2.11701
$306$	−1.45985	−0.0834541
$307$	14.0496	0.801851	0.400925	−	0.916111i	$-0.368689\pi$
$307$	14.0496	0.801851	0.400925	+	0.916111i	$0.368689\pi$
$308$	9.73266	0.554570
$309$	−22.5371	−1.28209
$310$	10.7343	0.609665
$311$	11.9226	0.676066	0.338033	−	0.941134i	$-0.390238\pi$
$311$	11.9226	0.676066	0.338033	+	0.941134i	$0.390238\pi$
$312$	6.16422	0.348981
$313$	7.60356	0.429779	0.214889	−	0.976638i	$-0.431061\pi$
$313$	7.60356	0.429779	0.214889	+	0.976638i	$0.431061\pi$
$314$	9.00247	0.508039
$315$	−1.45035	−0.0817182
$316$	−4.27528	−0.240503
$317$	28.2665	1.58760	0.793802	−	0.608176i	$-0.208098\pi$
$317$	28.2665	1.58760	0.793802	+	0.608176i	$0.208098\pi$
$318$	4.68588	0.262771
$319$	4.97507	0.278551
$320$	−2.65571	−0.148459
$321$	−7.80524	−0.435646
$322$	−1.95629	−0.109020
$323$	1.09659	0.0610161
$324$	−9.75956	−0.542198
$325$	−6.98787	−0.387617
$326$	10.1406	0.561636
$327$	31.7670	1.75672
$328$	−5.85714	−0.323407
$329$	11.1026	0.612107
$330$	23.9255	1.31706
$331$	19.4790	1.07066	0.535331	−	0.844642i	$-0.320187\pi$
$331$	19.4790	1.07066	0.535331	+	0.844642i	$0.320187\pi$
$332$	2.51936	0.138268
$333$	−0.410415	−0.0224906
$334$	−8.16995	−0.447040
$335$	−16.0546	−0.877159
$336$	−3.54253	−0.193261
$337$	−14.3251	−0.780339	−0.390169	−	0.920743i	$-0.627584\pi$
$337$	−14.3251	−0.780339	−0.390169	+	0.920743i	$0.627584\pi$
$338$	−1.41240	−0.0768242
$339$	−26.8868	−1.46029
$340$	13.8876	0.753163
$341$	−20.1090	−1.08896
$342$	−0.0585409	−0.00316553
$343$	−19.9012	−1.07456
$344$	−8.66480	−0.467175
$345$	−4.80909	−0.258913
$346$	11.4967	0.618066
$347$	−2.21498	−0.118906	−0.0594531	−	0.998231i	$-0.518936\pi$
$347$	−2.21498	−0.118906	−0.0594531	+	0.998231i	$0.518936\pi$
$348$	−1.81085	−0.0970716
$349$	9.36562	0.501330	0.250665	−	0.968074i	$-0.419351\pi$
$349$	9.36562	0.501330	0.250665	+	0.968074i	$0.419351\pi$
$350$	4.01587	0.214657
$351$	−16.7718	−0.895215
$352$	4.97507	0.265172
$353$	−2.27051	−0.120847	−0.0604237	−	0.998173i	$-0.519245\pi$
$353$	−2.27051	−0.120847	−0.0604237	+	0.998173i	$0.519245\pi$
$354$	13.5580	0.720599
$355$	38.3842	2.03722
$356$	−14.7012	−0.779163
$357$	18.5251	0.980454
$358$	0.213932	0.0113066
$359$	9.51806	0.502344	0.251172	−	0.967942i	$-0.419184\pi$
$359$	9.51806	0.502344	0.251172	+	0.967942i	$0.419184\pi$
$360$	−0.741381	−0.0390742
$361$	−18.9560	−0.997686
$362$	14.1009	0.741129
$363$	−24.9016	−1.30699
$364$	−6.65931	−0.349042
$365$	22.5089	1.17817
$366$	25.2100	1.31775
$367$	−26.8545	−1.40179	−0.700896	−	0.713263i	$-0.747216\pi$
$367$	−26.8545	−1.40179	−0.700896	+	0.713263i	$0.747216\pi$
$368$	−1.00000	−0.0521286
$369$	−1.63511	−0.0851204
$370$	3.90430	0.202975
$371$	−5.06223	−0.262818
$372$	7.31936	0.379491
$373$	−7.46053	−0.386291	−0.193146	−	0.981170i	$-0.561869\pi$
$373$	−7.46053	−0.386291	−0.193146	+	0.981170i	$0.561869\pi$
$374$	−26.0164	−1.34527
$375$	−14.1733	−0.731907
$376$	5.67536	0.292684
$377$	−3.40406	−0.175318
$378$	9.63865	0.495758
$379$	2.19553	0.112777	0.0563883	−	0.998409i	$-0.482042\pi$
$379$	2.19553	0.112777	0.0563883	+	0.998409i	$0.482042\pi$
$380$	0.556903	0.0285685
$381$	−8.32247	−0.426373
$382$	−1.79756	−0.0919710
$383$	33.5072	1.71214	0.856068	−	0.516864i	$-0.172901\pi$
$383$	33.5072	1.71214	0.856068	+	0.516864i	$0.172901\pi$
$384$	−1.81085	−0.0924094
$385$	−25.8471	−1.31729
$386$	−17.5053	−0.890996
$387$	−2.41891	−0.122960
$388$	6.35521	0.322637
$389$	−20.6351	−1.04624	−0.523121	−	0.852259i	$-0.675232\pi$
$389$	−20.6351	−1.04624	−0.523121	+	0.852259i	$0.675232\pi$
$390$	−16.3704	−0.828948
$391$	5.22935	0.264460
$392$	−3.17295	−0.160258
$393$	−5.70539	−0.287799
$394$	23.6299	1.19046
$395$	11.3539	0.571277
$396$	1.38887	0.0697931
$397$	35.3762	1.77548	0.887740	−	0.460345i	$-0.152274\pi$
$397$	35.3762	1.77548	0.887740	+	0.460345i	$0.152274\pi$
$398$	1.00662	0.0504572
$399$	0.742869	0.0371899
$400$	2.05281	0.102640
$401$	−16.8591	−0.841903	−0.420951	−	0.907083i	$-0.638304\pi$
$401$	−16.8591	−0.841903	−0.420951	+	0.907083i	$0.638304\pi$
$402$	−10.9472	−0.545994
$403$	13.7590	0.685387
$404$	7.77375	0.386759
$405$	25.9186	1.28790
$406$	1.95629	0.0970888
$407$	−7.31411	−0.362547
$408$	9.46955	0.468812
$409$	13.4269	0.663920	0.331960	−	0.943294i	$-0.392290\pi$
$409$	13.4269	0.663920	0.331960	+	0.943294i	$0.392290\pi$
$410$	15.5549	0.768201
$411$	−6.36124	−0.313777
$412$	12.4456	0.613150
$413$	−14.6469	−0.720727
$414$	−0.279165	−0.0137202
$415$	−6.69070	−0.328434
$416$	−3.40406	−0.166898
$417$	8.99140	0.440311
$418$	−1.04327	−0.0510281
$419$	10.1052	0.493673	0.246836	−	0.969057i	$-0.420609\pi$
$419$	10.1052	0.493673	0.246836	+	0.969057i	$0.420609\pi$
$420$	9.40794	0.459061
$421$	−10.8309	−0.527868	−0.263934	−	0.964541i	$-0.585020\pi$
$421$	−10.8309	−0.527868	−0.263934	+	0.964541i	$0.585020\pi$
$422$	−21.2163	−1.03279
$423$	1.58436	0.0770343
$424$	−2.58767	−0.125669
$425$	−10.7348	−0.520716
$426$	26.1730	1.26809
$427$	−27.2347	−1.31798
$428$	4.31027	0.208345
$429$	30.6675	1.48064
$430$	23.0112	1.10970
$431$	−16.6403	−0.801535	−0.400767	−	0.916180i	$-0.631256\pi$
$431$	−16.6403	−0.801535	−0.400767	+	0.916180i	$0.631256\pi$
$432$	4.92701	0.237051
$433$	−15.1946	−0.730207	−0.365104	−	0.930967i	$-0.618966\pi$
$433$	−15.1946	−0.730207	−0.365104	+	0.930967i	$0.618966\pi$
$434$	−7.90722	−0.379558
$435$	4.80909	0.230578
$436$	−17.5426	−0.840138
$437$	0.209700	0.0100313
$438$	15.3481	0.733360
$439$	−27.9970	−1.33622	−0.668112	−	0.744061i	$-0.732897\pi$
$439$	−27.9970	−1.33622	−0.668112	+	0.744061i	$0.732897\pi$
$440$	−13.2124	−0.629874
$441$	−0.885776	−0.0421798
$442$	17.8010	0.846707
$443$	17.8961	0.850269	0.425135	−	0.905130i	$-0.360227\pi$
$443$	17.8961	0.850269	0.425135	+	0.905130i	$0.360227\pi$
$444$	2.66222	0.126343
$445$	39.0422	1.85078
$446$	−27.2709	−1.29131
$447$	−42.9962	−2.03365
$448$	1.95629	0.0924258
$449$	21.7437	1.02615	0.513074	−	0.858345i	$-0.328507\pi$
$449$	21.7437	1.02615	0.513074	+	0.858345i	$0.328507\pi$
$450$	0.573071	0.0270148
$451$	−29.1397	−1.37214
$452$	14.8476	0.698374
$453$	−12.5587	−0.590057
$454$	−9.09263	−0.426738
$455$	17.6852	0.829095
$456$	0.379734	0.0177827
$457$	−30.0788	−1.40703	−0.703514	−	0.710682i	$-0.748387\pi$
$457$	−30.0788	−1.40703	−0.703514	+	0.710682i	$0.748387\pi$
$458$	−23.2235	−1.08516
$459$	−25.7651	−1.20261
$460$	2.65571	0.123823
$461$	−9.01406	−0.419827	−0.209913	−	0.977720i	$-0.567318\pi$
$461$	−9.01406	−0.419827	−0.209913	+	0.977720i	$0.567318\pi$
$462$	−17.6243	−0.819959
$463$	21.1032	0.980751	0.490375	−	0.871511i	$-0.336860\pi$
$463$	21.1032	0.980751	0.490375	+	0.871511i	$0.336860\pi$
$464$	1.00000	0.0464238
$465$	−19.4381	−0.901421
$466$	−1.27501	−0.0590635
$467$	−35.9244	−1.66238	−0.831190	−	0.555988i	$-0.812340\pi$
$467$	−35.9244	−1.66238	−0.831190	+	0.555988i	$0.812340\pi$
$468$	−0.950293	−0.0439273
$469$	11.8264	0.546091
$470$	−15.0721	−0.695225
$471$	−16.3021	−0.751161
$472$	−7.48710	−0.344622
$473$	−43.1080	−1.98211
$474$	7.74187	0.355596
$475$	−0.430473	−0.0197515
$476$	−10.2301	−0.468896
$477$	−0.722388	−0.0330759
$478$	−3.97850	−0.181972
$479$	19.9594	0.911969	0.455985	−	0.889988i	$-0.349287\pi$
$479$	19.9594	0.911969	0.455985	+	0.889988i	$0.349287\pi$
$480$	4.80909	0.219504
$481$	5.00448	0.228185
$482$	−4.38703	−0.199824
$483$	3.54253	0.161191
$484$	13.7513	0.625061
$485$	−16.8776	−0.766373
$486$	2.89202	0.131185
$487$	32.3703	1.46684	0.733418	−	0.679778i	$-0.237924\pi$
$487$	32.3703	1.46684	0.733418	+	0.679778i	$0.237924\pi$
$488$	−13.9217	−0.630204
$489$	−18.3631	−0.830407
$490$	8.42644	0.380668
$491$	12.1884	0.550056	0.275028	−	0.961436i	$-0.411313\pi$
$491$	12.1884	0.550056	0.275028	+	0.961436i	$0.411313\pi$
$492$	10.6064	0.478173
$493$	−5.22935	−0.235518
$494$	0.713830	0.0321168
$495$	−3.68843	−0.165782
$496$	−4.04195	−0.181489
$497$	−28.2751	−1.26831
$498$	−4.56218	−0.204436
$499$	42.8229	1.91702	0.958509	−	0.285064i	$-0.0920147\pi$
$499$	42.8229	1.91702	0.958509	+	0.285064i	$0.0920147\pi$
$500$	7.82690	0.350030
$501$	14.7945	0.660970
$502$	−11.8382	−0.528365
$503$	−12.4627	−0.555684	−0.277842	−	0.960627i	$-0.589619\pi$
$503$	−12.4627	−0.555684	−0.277842	+	0.960627i	$0.589619\pi$
$504$	0.546126	0.0243264
$505$	−20.6448	−0.918683
$506$	−4.97507	−0.221169
$507$	2.55763	0.113588
$508$	4.59590	0.203910
$509$	27.1082	1.20155	0.600774	−	0.799419i	$-0.294859\pi$
$509$	27.1082	1.20155	0.600774	+	0.799419i	$0.294859\pi$
$510$	−25.1484	−1.11359
$511$	−16.5808	−0.733491
$512$	1.00000	0.0441942
$513$	−1.03319	−0.0456167
$514$	11.0000	0.485191
$515$	−33.0519	−1.45644
$516$	15.6906	0.690741
$517$	28.2353	1.24179
$518$	−2.87604	−0.126366
$519$	−20.8187	−0.913841
$520$	9.04019	0.396439
$521$	−40.2546	−1.76359	−0.881794	−	0.471635i	$-0.843664\pi$
$521$	−40.2546	−1.76359	−0.881794	+	0.471635i	$0.843664\pi$
$522$	0.279165	0.0122187
$523$	−23.6485	−1.03407	−0.517037	−	0.855963i	$-0.672965\pi$
$523$	−23.6485	−1.03407	−0.517037	+	0.855963i	$0.672965\pi$
$524$	3.15068	0.137638
$525$	−7.27213	−0.317382
$526$	−5.86171	−0.255583
$527$	21.1368	0.920733
$528$	−9.00909	−0.392070
$529$	1.00000	0.0434783
$530$	6.87212	0.298506
$531$	−2.09014	−0.0907042
$532$	−0.410233	−0.0177858
$533$	19.9380	0.863613
$534$	26.6217	1.15203
$535$	−11.4468	−0.494890
$536$	6.04532	0.261118
$537$	−0.387397	−0.0167174
$538$	30.6818	1.32279
$539$	−15.7856	−0.679936
$540$	−13.0847	−0.563077
$541$	29.3366	1.26128	0.630639	−	0.776076i	$-0.282793\pi$
$541$	29.3366	1.26128	0.630639	+	0.776076i	$0.282793\pi$
$542$	−3.61143	−0.155124
$543$	−25.5346	−1.09580
$544$	−5.22935	−0.224206
$545$	46.5881	1.99562
$546$	12.0590	0.516077
$547$	13.4751	0.576155	0.288078	−	0.957607i	$-0.406984\pi$
$547$	13.4751	0.576155	0.288078	+	0.957607i	$0.406984\pi$
$548$	3.51285	0.150062
$549$	−3.88644	−0.165869
$550$	10.2129	0.435477
$551$	−0.209700	−0.00893352
$552$	1.81085	0.0770747
$553$	−8.36366	−0.355659
$554$	−25.9604	−1.10295
$555$	−7.07009	−0.300109
$556$	−4.96530	−0.210576
$557$	9.62008	0.407616	0.203808	−	0.979011i	$-0.434668\pi$
$557$	9.62008	0.407616	0.203808	+	0.979011i	$0.434668\pi$
$558$	−1.12837	−0.0477678
$559$	29.4955	1.24753
$560$	−5.19533	−0.219543
$561$	47.1117	1.98906
$562$	−25.9055	−1.09276
$563$	4.09476	0.172574	0.0862868	−	0.996270i	$-0.472500\pi$
$563$	4.09476	0.172574	0.0862868	+	0.996270i	$0.472500\pi$
$564$	−10.2772	−0.432748
$565$	−39.4310	−1.65888
$566$	9.28582	0.390312
$567$	−19.0925	−0.801809
$568$	−14.4535	−0.606453
$569$	−18.4219	−0.772284	−0.386142	−	0.922439i	$-0.626193\pi$
$569$	−18.4219	−0.772284	−0.386142	+	0.922439i	$0.626193\pi$
$570$	−1.00846	−0.0422399
$571$	38.0241	1.59126	0.795629	−	0.605784i	$-0.207141\pi$
$571$	38.0241	1.59126	0.795629	+	0.605784i	$0.207141\pi$
$572$	−16.9354	−0.708106
$573$	3.25510	0.135984
$574$	−11.4582	−0.478258
$575$	−2.05281	−0.0856079
$576$	0.279165	0.0116319
$577$	33.5976	1.39869	0.699344	−	0.714786i	$-0.253476\pi$
$577$	33.5976	1.39869	0.699344	+	0.714786i	$0.253476\pi$
$578$	10.3461	0.430340
$579$	31.6994	1.31738
$580$	−2.65571	−0.110272
$581$	4.92859	0.204472
$582$	−11.5083	−0.477035
$583$	−12.8739	−0.533181
$584$	−8.47565	−0.350725
$585$	2.52370	0.104342
$586$	−14.5441	−0.600813
$587$	4.00277	0.165212	0.0826059	−	0.996582i	$-0.473676\pi$
$587$	4.00277	0.165212	0.0826059	+	0.996582i	$0.473676\pi$
$588$	5.74572	0.236950
$589$	0.847598	0.0349246
$590$	19.8836	0.818595
$591$	−42.7901	−1.76015
$592$	−1.47015	−0.0604229
$593$	−46.9070	−1.92624	−0.963119	−	0.269076i	$-0.913282\pi$
$593$	−46.9070	−1.92624	−0.963119	+	0.269076i	$0.913282\pi$
$594$	24.5122	1.00575
$595$	27.1682	1.11379
$596$	23.7437	0.972581
$597$	−1.82283	−0.0746035
$598$	3.40406	0.139202
$599$	−13.9782	−0.571133	−0.285566	−	0.958359i	$-0.592182\pi$
$599$	−13.9782	−0.571133	−0.285566	+	0.958359i	$0.592182\pi$
$600$	−3.71731	−0.151759
$601$	27.8083	1.13432	0.567162	−	0.823606i	$-0.308041\pi$
$601$	27.8083	1.13432	0.567162	+	0.823606i	$0.308041\pi$
$602$	−16.9508	−0.690864
$603$	1.68764	0.0687261
$604$	6.93524	0.282191
$605$	−36.5196	−1.48473
$606$	−14.0771	−0.571842
$607$	−22.7392	−0.922954	−0.461477	−	0.887152i	$-0.652680\pi$
$607$	−22.7392	−0.922954	−0.461477	+	0.887152i	$0.652680\pi$
$608$	−0.209700	−0.00850445
$609$	−3.54253	−0.143551
$610$	36.9719	1.49695
$611$	−19.3192	−0.781573
$612$	−1.45985	−0.0590110
$613$	−41.9108	−1.69276	−0.846380	−	0.532580i	$-0.821223\pi$
$613$	−41.9108	−1.69276	−0.846380	+	0.532580i	$0.821223\pi$
$614$	14.0496	0.566994
$615$	−28.1675	−1.13582
$616$	9.73266	0.392140
$617$	16.2073	0.652483	0.326241	−	0.945286i	$-0.394218\pi$
$617$	16.2073	0.652483	0.326241	+	0.945286i	$0.394218\pi$
$618$	−22.5371	−0.906573
$619$	−22.8907	−0.920056	−0.460028	−	0.887904i	$-0.652161\pi$
$619$	−22.8907	−0.920056	−0.460028	+	0.887904i	$0.652161\pi$
$620$	10.7343	0.431099
$621$	−4.92701	−0.197714
$622$	11.9226	0.478051
$623$	−28.7598	−1.15224
$624$	6.16422	0.246766
$625$	−31.0500	−1.24200
$626$	7.60356	0.303900
$627$	1.88921	0.0754476
$628$	9.00247	0.359238
$629$	7.68794	0.306538
$630$	−1.45035	−0.0577835
$631$	−17.0441	−0.678513	−0.339257	−	0.940694i	$-0.610176\pi$
$631$	−17.0441	−0.678513	−0.339257	+	0.940694i	$0.610176\pi$
$632$	−4.27528	−0.170061
$633$	38.4195	1.52704
$634$	28.2665	1.12261
$635$	−12.2054	−0.484356
$636$	4.68588	0.185807
$637$	10.8009	0.427947
$638$	4.97507	0.196965
$639$	−4.03490	−0.159618
$640$	−2.65571	−0.104976
$641$	13.4563	0.531493	0.265747	−	0.964043i	$-0.414382\pi$
$641$	13.4563	0.531493	0.265747	+	0.964043i	$0.414382\pi$
$642$	−7.80524	−0.308048
$643$	0.730600	0.0288121	0.0144060	−	0.999896i	$-0.495414\pi$
$643$	0.730600	0.0288121	0.0144060	+	0.999896i	$0.495414\pi$
$644$	−1.95629	−0.0770884
$645$	−41.6698	−1.64075
$646$	1.09659	0.0431449
$647$	−2.28258	−0.0897373	−0.0448686	−	0.998993i	$-0.514287\pi$
$647$	−2.28258	−0.0897373	−0.0448686	+	0.998993i	$0.514287\pi$
$648$	−9.75956	−0.383392
$649$	−37.2489	−1.46215
$650$	−6.98787	−0.274087
$651$	14.3188	0.561196
$652$	10.1406	0.397137
$653$	−3.93427	−0.153960	−0.0769800	−	0.997033i	$-0.524528\pi$
$653$	−3.93427	−0.153960	−0.0769800	+	0.997033i	$0.524528\pi$
$654$	31.7670	1.24219
$655$	−8.36729	−0.326937
$656$	−5.85714	−0.228683
$657$	−2.36610	−0.0923105
$658$	11.1026	0.432825
$659$	30.3118	1.18078	0.590391	−	0.807118i	$-0.298974\pi$
$659$	30.3118	1.18078	0.590391	+	0.807118i	$0.298974\pi$
$660$	23.9255	0.931301
$661$	−2.90561	−0.113015	−0.0565076	−	0.998402i	$-0.517997\pi$
$661$	−2.90561	−0.113015	−0.0565076	+	0.998402i	$0.517997\pi$
$662$	19.4790	0.757073
$663$	−32.2349	−1.25190
$664$	2.51936	0.0977703
$665$	1.08946	0.0422474
$666$	−0.410415	−0.0159033
$667$	−1.00000	−0.0387202
$668$	−8.16995	−0.316105
$669$	49.3834	1.90927
$670$	−16.0546	−0.620245
$671$	−69.2613	−2.67380
$672$	−3.54253	−0.136656
$673$	−12.1674	−0.469019	−0.234509	−	0.972114i	$-0.575348\pi$
$673$	−12.1674	−0.469019	−0.234509	+	0.972114i	$0.575348\pi$
$674$	−14.3251	−0.551783
$675$	10.1142	0.389296
$676$	−1.41240	−0.0543229
$677$	10.4766	0.402647	0.201323	−	0.979525i	$-0.435476\pi$
$677$	10.4766	0.402647	0.201323	+	0.979525i	$0.435476\pi$
$678$	−26.8868	−1.03258
$679$	12.4326	0.477120
$680$	13.8876	0.532567
$681$	16.4654	0.630954
$682$	−20.1090	−0.770014
$683$	−1.29122	−0.0494071	−0.0247035	−	0.999695i	$-0.507864\pi$
$683$	−1.29122	−0.0494071	−0.0247035	+	0.999695i	$0.507864\pi$
$684$	−0.0585409	−0.00223837
$685$	−9.32913	−0.356448
$686$	−19.9012	−0.759831
$687$	42.0542	1.60447
$688$	−8.66480	−0.330342
$689$	8.80859	0.335581
$690$	−4.80909	−0.183079
$691$	24.6456	0.937563	0.468781	−	0.883314i	$-0.344693\pi$
$691$	24.6456	0.937563	0.468781	+	0.883314i	$0.344693\pi$
$692$	11.4967	0.437039
$693$	2.71702	0.103211
$694$	−2.21498	−0.0840794
$695$	13.1864	0.500189
$696$	−1.81085	−0.0686400
$697$	30.6290	1.16016
$698$	9.36562	0.354494
$699$	2.30884	0.0873283
$700$	4.01587	0.151786
$701$	−2.60971	−0.0985674	−0.0492837	−	0.998785i	$-0.515694\pi$
$701$	−2.60971	−0.0985674	−0.0492837	+	0.998785i	$0.515694\pi$
$702$	−16.7718	−0.633012
$703$	0.308291	0.0116274
$704$	4.97507	0.187505
$705$	27.2933	1.02792
$706$	−2.27051	−0.0854519
$707$	15.2077	0.571943
$708$	13.5580	0.509541
$709$	−30.2155	−1.13477	−0.567383	−	0.823454i	$-0.692044\pi$
$709$	−30.2155	−1.13477	−0.567383	+	0.823454i	$0.692044\pi$
$710$	38.3842	1.44053
$711$	−1.19351	−0.0447600
$712$	−14.7012	−0.550952
$713$	4.04195	0.151372
$714$	18.5251	0.693286
$715$	44.9756	1.68199
$716$	0.213932	0.00799500
$717$	7.20446	0.269055
$718$	9.51806	0.355211
$719$	14.7138	0.548732	0.274366	−	0.961625i	$-0.411532\pi$
$719$	14.7138	0.548732	0.274366	+	0.961625i	$0.411532\pi$
$720$	−0.741381	−0.0276297
$721$	24.3471	0.906734
$722$	−18.9560	−0.705470
$723$	7.94424	0.295449
$724$	14.1009	0.524057
$725$	2.05281	0.0762393
$726$	−24.9016	−0.924183
$727$	50.7584	1.88253	0.941263	−	0.337674i	$-0.109640\pi$
$727$	50.7584	1.88253	0.941263	+	0.337674i	$0.109640\pi$
$728$	−6.65931	−0.246810
$729$	24.0417	0.890432
$730$	22.5089	0.833091
$731$	45.3113	1.67590
$732$	25.2100	0.931788
$733$	25.7732	0.951956	0.475978	−	0.879457i	$-0.342094\pi$
$733$	25.7732	0.951956	0.475978	+	0.879457i	$0.342094\pi$
$734$	−26.8545	−0.991217
$735$	−15.2590	−0.562836
$736$	−1.00000	−0.0368605
$737$	30.0759	1.10786
$738$	−1.63511	−0.0601892
$739$	19.3668	0.712418	0.356209	−	0.934406i	$-0.384069\pi$
$739$	19.3668	0.712418	0.356209	+	0.934406i	$0.384069\pi$
$740$	3.90430	0.143525
$741$	−1.29264	−0.0474862
$742$	−5.06223	−0.185840
$743$	33.3360	1.22298	0.611490	−	0.791252i	$-0.290571\pi$
$743$	33.3360	1.22298	0.611490	+	0.791252i	$0.290571\pi$
$744$	7.31936	0.268341
$745$	−63.0565	−2.31021
$746$	−7.46053	−0.273149
$747$	0.703318	0.0257331
$748$	−26.0164	−0.951253
$749$	8.43212	0.308103
$750$	−14.1733	−0.517536
$751$	4.05611	0.148009	0.0740047	−	0.997258i	$-0.476422\pi$
$751$	4.05611	0.148009	0.0740047	+	0.997258i	$0.476422\pi$
$752$	5.67536	0.206959
$753$	21.4372	0.781214
$754$	−3.40406	−0.123968
$755$	−18.4180	−0.670300
$756$	9.63865	0.350554
$757$	0.0727471	0.00264404	0.00132202	−	0.999999i	$-0.499579\pi$
$757$	0.0727471	0.00264404	0.00132202	+	0.999999i	$0.499579\pi$
$758$	2.19553	0.0797451
$759$	9.00909	0.327009
$760$	0.556903	0.0202010
$761$	−19.6933	−0.713881	−0.356940	−	0.934127i	$-0.616180\pi$
$761$	−19.6933	−0.713881	−0.356940	+	0.934127i	$0.616180\pi$
$762$	−8.32247	−0.301491
$763$	−34.3183	−1.24241
$764$	−1.79756	−0.0650333
$765$	3.87694	0.140171
$766$	33.5072	1.21066
$767$	25.4865	0.920265
$768$	−1.81085	−0.0653433
$769$	23.0518	0.831271	0.415635	−	0.909531i	$-0.363559\pi$
$769$	23.0518	0.831271	0.415635	+	0.909531i	$0.363559\pi$
$770$	−25.8471	−0.931466
$771$	−19.9194	−0.717379
$772$	−17.5053	−0.630029
$773$	14.0650	0.505883	0.252942	−	0.967482i	$-0.418602\pi$
$773$	14.0650	0.505883	0.252942	+	0.967482i	$0.418602\pi$
$774$	−2.41891	−0.0869459
$775$	−8.29735	−0.298049
$776$	6.35521	0.228139
$777$	5.20806	0.186838
$778$	−20.6351	−0.739805
$779$	1.22824	0.0440063
$780$	−16.3704	−0.586154
$781$	−71.9070	−2.57303
$782$	5.22935	0.187001
$783$	4.92701	0.176077
$784$	−3.17295	−0.113320
$785$	−23.9080	−0.853312
$786$	−5.70539	−0.203505
$787$	−50.4436	−1.79812	−0.899060	−	0.437825i	$-0.855749\pi$
$787$	−50.4436	−1.79812	−0.899060	+	0.437825i	$0.855749\pi$
$788$	23.6299	0.841780
$789$	10.6147	0.377892
$790$	11.3539	0.403954
$791$	29.0462	1.03276
$792$	1.38887	0.0493512
$793$	47.3901	1.68287
$794$	35.3762	1.25545
$795$	−12.4443	−0.441356
$796$	1.00662	0.0356787
$797$	48.0846	1.70324	0.851622	−	0.524157i	$-0.175620\pi$
$797$	48.0846	1.70324	0.851622	+	0.524157i	$0.175620\pi$
$798$	0.742869	0.0262973
$799$	−29.6784	−1.04995
$800$	2.05281	0.0725776
$801$	−4.10406	−0.145010
$802$	−16.8591	−0.595315
$803$	−42.1670	−1.48804
$804$	−10.9472	−0.386076
$805$	5.19533	0.183111
$806$	13.7590	0.484642
$807$	−55.5601	−1.95581
$808$	7.77375	0.273480
$809$	−19.3824	−0.681450	−0.340725	−	0.940163i	$-0.610672\pi$
$809$	−19.3824	−0.681450	−0.340725	+	0.940163i	$0.610672\pi$
$810$	25.9186	0.910686
$811$	10.9022	0.382828	0.191414	−	0.981509i	$-0.438693\pi$
$811$	10.9022	0.382828	0.191414	+	0.981509i	$0.438693\pi$
$812$	1.95629	0.0686521
$813$	6.53974	0.229359
$814$	−7.31411	−0.256360
$815$	−26.9305	−0.943335
$816$	9.46955	0.331500
$817$	1.81701	0.0635691
$818$	13.4269	0.469462
$819$	−1.85904	−0.0649603
$820$	15.5549	0.543200
$821$	−48.0779	−1.67793	−0.838964	−	0.544186i	$-0.816838\pi$
$821$	−48.0779	−1.67793	−0.838964	+	0.544186i	$0.816838\pi$
$822$	−6.36124	−0.221874
$823$	−20.3511	−0.709394	−0.354697	−	0.934981i	$-0.615416\pi$
$823$	−20.3511	−0.709394	−0.354697	+	0.934981i	$0.615416\pi$
$824$	12.4456	0.433563
$825$	−18.4939	−0.643875
$826$	−14.6469	−0.509631
$827$	−30.8109	−1.07140	−0.535699	−	0.844409i	$-0.679952\pi$
$827$	−30.8109	−1.07140	−0.535699	+	0.844409i	$0.679952\pi$
$828$	−0.279165	−0.00970165
$829$	−40.8635	−1.41925	−0.709623	−	0.704581i	$-0.751135\pi$
$829$	−40.8635	−1.41925	−0.709623	+	0.704581i	$0.751135\pi$
$830$	−6.69070	−0.232238
$831$	47.0103	1.63077
$832$	−3.40406	−0.118014
$833$	16.5925	0.574894
$834$	8.99140	0.311347
$835$	21.6970	0.750856
$836$	−1.04327	−0.0360823
$837$	−19.9148	−0.688355
$838$	10.1052	0.349079
$839$	38.4741	1.32827	0.664137	−	0.747611i	$-0.268799\pi$
$839$	38.4741	1.32827	0.664137	+	0.747611i	$0.268799\pi$
$840$	9.40794	0.324605
$841$	1.00000	0.0344828
$842$	−10.8309	−0.373259
$843$	46.9109	1.61570
$844$	−21.2163	−0.730296
$845$	3.75091	0.129035
$846$	1.58436	0.0544715
$847$	26.9015	0.924347
$848$	−2.58767	−0.0888611
$849$	−16.8152	−0.577096
$850$	−10.7348	−0.368202
$851$	1.47015	0.0503962
$852$	26.1730	0.896672
$853$	−16.8742	−0.577760	−0.288880	−	0.957365i	$-0.593283\pi$
$853$	−16.8742	−0.577760	−0.288880	+	0.957365i	$0.593283\pi$
$854$	−27.2347	−0.931953
$855$	0.155468	0.00531688
$856$	4.31027	0.147322
$857$	−5.40296	−0.184561	−0.0922807	−	0.995733i	$-0.529416\pi$
$857$	−5.40296	−0.184561	−0.0922807	+	0.995733i	$0.529416\pi$
$858$	30.6675	1.04697
$859$	−24.2463	−0.827274	−0.413637	−	0.910442i	$-0.635742\pi$
$859$	−24.2463	−0.827274	−0.413637	+	0.910442i	$0.635742\pi$
$860$	23.0112	0.784676
$861$	20.7491	0.707128
$862$	−16.6403	−0.566771
$863$	−14.2053	−0.483554	−0.241777	−	0.970332i	$-0.577730\pi$
$863$	−14.2053	−0.483554	−0.241777	+	0.970332i	$0.577730\pi$
$864$	4.92701	0.167620
$865$	−30.5319	−1.03812
$866$	−15.1946	−0.516335
$867$	−18.7352	−0.636280
$868$	−7.90722	−0.268388
$869$	−21.2698	−0.721529
$870$	4.80909	0.163043
$871$	−20.5786	−0.697280
$872$	−17.5426	−0.594068
$873$	1.77415	0.0600460
$874$	0.209700	0.00709321
$875$	15.3116	0.517628
$876$	15.3481	0.518564
$877$	−20.7549	−0.700844	−0.350422	−	0.936592i	$-0.613962\pi$
$877$	−20.7549	−0.700844	−0.350422	+	0.936592i	$0.613962\pi$
$878$	−27.9970	−0.944853
$879$	26.3372	0.888332
$880$	−13.2124	−0.445388
$881$	3.17703	0.107037	0.0535185	−	0.998567i	$-0.482956\pi$
$881$	3.17703	0.107037	0.0535185	+	0.998567i	$0.482956\pi$
$882$	−0.885776	−0.0298256
$883$	−39.5294	−1.33027	−0.665136	−	0.746722i	$-0.731626\pi$
$883$	−39.5294	−1.33027	−0.665136	+	0.746722i	$0.731626\pi$
$884$	17.8010	0.598712
$885$	−36.0061	−1.21033
$886$	17.8961	0.601231
$887$	23.9720	0.804901	0.402451	−	0.915442i	$-0.368158\pi$
$887$	23.9720	0.804901	0.402451	+	0.915442i	$0.368158\pi$
$888$	2.66222	0.0893383
$889$	8.99089	0.301545
$890$	39.0422	1.30870
$891$	−48.5545	−1.62664
$892$	−27.2709	−0.913097
$893$	−1.19012	−0.0398259
$894$	−42.9962	−1.43801
$895$	−0.568140	−0.0189908
$896$	1.95629	0.0653549
$897$	−6.16422	−0.205817
$898$	21.7437	0.725596
$899$	−4.04195	−0.134807
$900$	0.573071	0.0191024
$901$	13.5318	0.450811
$902$	−29.1397	−0.970246
$903$	30.6953	1.02148
$904$	14.8476	0.493825
$905$	−37.4480	−1.24481
$906$	−12.5587	−0.417234
$907$	−35.6047	−1.18223	−0.591117	−	0.806586i	$-0.701313\pi$
$907$	−35.6047	−1.18223	−0.591117	+	0.806586i	$0.701313\pi$
$908$	−9.09263	−0.301750
$909$	2.17016	0.0719796
$910$	17.6852	0.586259
$911$	−33.3748	−1.10576	−0.552878	−	0.833262i	$-0.686471\pi$
$911$	−33.3748	−1.10576	−0.552878	+	0.833262i	$0.686471\pi$
$912$	0.379734	0.0125743
$913$	12.5340	0.414815
$914$	−30.0788	−0.994919
$915$	−66.9505	−2.21331
$916$	−23.2235	−0.767326
$917$	6.16363	0.203541
$918$	−25.7651	−0.850374
$919$	−50.9103	−1.67938	−0.839688	−	0.543070i	$-0.817262\pi$
$919$	−50.9103	−1.67938	−0.839688	+	0.543070i	$0.817262\pi$
$920$	2.65571	0.0875562
$921$	−25.4416	−0.838329
$922$	−9.01406	−0.296862
$923$	49.2004	1.61945
$924$	−17.6243	−0.579798
$925$	−3.01794	−0.0992291
$926$	21.1032	0.693496
$927$	3.47437	0.114113
$928$	1.00000	0.0328266
$929$	41.9125	1.37511	0.687553	−	0.726135i	$-0.258685\pi$
$929$	41.9125	1.37511	0.687553	+	0.726135i	$0.258685\pi$
$930$	−19.4381	−0.637401
$931$	0.665367	0.0218065
$932$	−1.27501	−0.0417642
$933$	−21.5899	−0.706822
$934$	−35.9244	−1.17548
$935$	69.0920	2.25955
$936$	−0.950293	−0.0310613
$937$	−44.8469	−1.46508	−0.732542	−	0.680721i	$-0.761666\pi$
$937$	−44.8469	−1.46508	−0.732542	+	0.680721i	$0.761666\pi$
$938$	11.8264	0.386145
$939$	−13.7689	−0.449331
$940$	−15.0721	−0.491598
$941$	−22.4953	−0.733325	−0.366663	−	0.930354i	$-0.619500\pi$
$941$	−22.4953	−0.733325	−0.366663	+	0.930354i	$0.619500\pi$
$942$	−16.3021	−0.531151
$943$	5.85714	0.190735
$944$	−7.48710	−0.243684
$945$	−25.5975	−0.832686
$946$	−43.1080	−1.40156
$947$	10.9117	0.354584	0.177292	−	0.984158i	$-0.443266\pi$
$947$	10.9117	0.354584	0.177292	+	0.984158i	$0.443266\pi$
$948$	7.74187	0.251444
$949$	28.8516	0.936562
$950$	−0.430473	−0.0139664
$951$	−51.1863	−1.65983
$952$	−10.2301	−0.331559
$953$	16.5142	0.534947	0.267474	−	0.963565i	$-0.413811\pi$
$953$	16.5142	0.534947	0.267474	+	0.963565i	$0.413811\pi$
$954$	−0.722388	−0.0233882
$955$	4.77379	0.154476
$956$	−3.97850	−0.128674
$957$	−9.00909	−0.291223
$958$	19.9594	0.644860
$959$	6.87214	0.221913
$960$	4.80909	0.155213
$961$	−14.6626	−0.472987
$962$	5.00448	0.161351
$963$	1.20328	0.0387750
$964$	−4.38703	−0.141297
$965$	46.4890	1.49653
$966$	3.54253	0.113979
$967$	17.8811	0.575018	0.287509	−	0.957778i	$-0.407173\pi$
$967$	17.8811	0.575018	0.287509	+	0.957778i	$0.407173\pi$
$968$	13.7513	0.441985
$969$	−1.98576	−0.0637919
$970$	−16.8776	−0.541907
$971$	51.1641	1.64194	0.820968	−	0.570974i	$-0.193434\pi$
$971$	51.1641	1.64194	0.820968	+	0.570974i	$0.193434\pi$
$972$	2.89202	0.0927617
$973$	−9.71354	−0.311402
$974$	32.3703	1.03721
$975$	12.6540	0.405251
$976$	−13.9217	−0.445621
$977$	−39.8627	−1.27532	−0.637660	−	0.770318i	$-0.720097\pi$
$977$	−39.8627	−1.27532	−0.637660	+	0.770318i	$0.720097\pi$
$978$	−18.3631	−0.587186
$979$	−73.1396	−2.33755
$980$	8.42644	0.269173
$981$	−4.89728	−0.156358
$982$	12.1884	0.388949
$983$	−18.9362	−0.603972	−0.301986	−	0.953312i	$-0.597650\pi$
$983$	−18.9362	−0.603972	−0.301986	+	0.953312i	$0.597650\pi$
$984$	10.6064	0.338119
$985$	−62.7542	−1.99951
$986$	−5.22935	−0.166536
$987$	−20.1051	−0.639954
$988$	0.713830	0.0227100
$989$	8.66480	0.275525
$990$	−3.68843	−0.117226
$991$	29.3717	0.933024	0.466512	−	0.884515i	$-0.345510\pi$
$991$	29.3717	0.933024	0.466512	+	0.884515i	$0.345510\pi$
$992$	−4.04195	−0.128332
$993$	−35.2735	−1.11937
$994$	−28.2751	−0.896831
$995$	−2.67329	−0.0847490
$996$	−4.56218	−0.144558
$997$	−18.6900	−0.591917	−0.295959	−	0.955201i	$-0.595639\pi$
$997$	−18.6900	−0.591917	−0.295959	+	0.955201i	$0.595639\pi$
$998$	42.8229	1.35554
$999$	−7.24346	−0.229173

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1334.2.a.h.1.2	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1334.2.a.h.1.2	✓	5	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.81085 q^{3} +1.00000 q^{4} -2.65571 q^{5} -1.81085 q^{6} +1.95629 q^{7} +1.00000 q^{8} +0.279165 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.81085 q^{3} +1.00000 q^{4} -2.65571 q^{5} -1.81085 q^{6} +1.95629 q^{7} +1.00000 q^{8} +0.279165 q^{9} -2.65571 q^{10} +4.97507 q^{11} -1.81085 q^{12} -3.40406 q^{13} +1.95629 q^{14} +4.80909 q^{15} +1.00000 q^{16} -5.22935 q^{17} +0.279165 q^{18} -0.209700 q^{19} -2.65571 q^{20} -3.54253 q^{21} +4.97507 q^{22} -1.00000 q^{23} -1.81085 q^{24} +2.05281 q^{25} -3.40406 q^{26} +4.92701 q^{27} +1.95629 q^{28} +1.00000 q^{29} +4.80909 q^{30} -4.04195 q^{31} +1.00000 q^{32} -9.00909 q^{33} -5.22935 q^{34} -5.19533 q^{35} +0.279165 q^{36} -1.47015 q^{37} -0.209700 q^{38} +6.16422 q^{39} -2.65571 q^{40} -5.85714 q^{41} -3.54253 q^{42} -8.66480 q^{43} +4.97507 q^{44} -0.741381 q^{45} -1.00000 q^{46} +5.67536 q^{47} -1.81085 q^{48} -3.17295 q^{49} +2.05281 q^{50} +9.46955 q^{51} -3.40406 q^{52} -2.58767 q^{53} +4.92701 q^{54} -13.2124 q^{55} +1.95629 q^{56} +0.379734 q^{57} +1.00000 q^{58} -7.48710 q^{59} +4.80909 q^{60} -13.9217 q^{61} -4.04195 q^{62} +0.546126 q^{63} +1.00000 q^{64} +9.04019 q^{65} -9.00909 q^{66} +6.04532 q^{67} -5.22935 q^{68} +1.81085 q^{69} -5.19533 q^{70} -14.4535 q^{71} +0.279165 q^{72} -8.47565 q^{73} -1.47015 q^{74} -3.71731 q^{75} -0.209700 q^{76} +9.73266 q^{77} +6.16422 q^{78} -4.27528 q^{79} -2.65571 q^{80} -9.75956 q^{81} -5.85714 q^{82} +2.51936 q^{83} -3.54253 q^{84} +13.8876 q^{85} -8.66480 q^{86} -1.81085 q^{87} +4.97507 q^{88} -14.7012 q^{89} -0.741381 q^{90} -6.65931 q^{91} -1.00000 q^{92} +7.31936 q^{93} +5.67536 q^{94} +0.556903 q^{95} -1.81085 q^{96} +6.35521 q^{97} -3.17295 q^{98} +1.38887 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 5 q^{2} - 3 q^{3} + 5 q^{4} - 5 q^{5} - 3 q^{6} - 6 q^{7} + 5 q^{8} + 2 q^{9}+O(q^{10}) \) 5 * q + 5 * q^2 - 3 * q^3 + 5 * q^4 - 5 * q^5 - 3 * q^6 - 6 * q^7 + 5 * q^8 + 2 * q^9	\( 5 q + 5 q^{2} - 3 q^{3} + 5 q^{4} - 5 q^{5} - 3 q^{6} - 6 q^{7} + 5 q^{8} + 2 q^{9} - 5 q^{10} - 9 q^{11} - 3 q^{12} - 5 q^{13} - 6 q^{14} - 3 q^{15} + 5 q^{16} - 6 q^{17} + 2 q^{18} - 10 q^{19} - 5 q^{20} - 2 q^{21} - 9 q^{22} - 5 q^{23} - 3 q^{24} - 4 q^{25} - 5 q^{26} - 9 q^{27} - 6 q^{28} + 5 q^{29} - 3 q^{30} - 15 q^{31} + 5 q^{32} - 15 q^{33} - 6 q^{34} - 2 q^{35} + 2 q^{36} - 10 q^{38} + 3 q^{39} - 5 q^{40} - 2 q^{41} - 2 q^{42} - 5 q^{43} - 9 q^{44} - 6 q^{45} - 5 q^{46} - 9 q^{47} - 3 q^{48} - 3 q^{49} - 4 q^{50} - 2 q^{51} - 5 q^{52} + 3 q^{53} - 9 q^{54} - 3 q^{55} - 6 q^{56} - 2 q^{57} + 5 q^{58} - 26 q^{59} - 3 q^{60} - 8 q^{61} - 15 q^{62} - 6 q^{63} + 5 q^{64} + 19 q^{65} - 15 q^{66} + 12 q^{67} - 6 q^{68} + 3 q^{69} - 2 q^{70} - 12 q^{71} + 2 q^{72} + 2 q^{73} + 24 q^{75} - 10 q^{76} + 36 q^{77} + 3 q^{78} - 25 q^{79} - 5 q^{80} + 9 q^{81} - 2 q^{82} - 16 q^{83} - 2 q^{84} + 4 q^{85} - 5 q^{86} - 3 q^{87} - 9 q^{88} - 20 q^{89} - 6 q^{90} - 32 q^{91} - 5 q^{92} + 11 q^{93} - 9 q^{94} + 20 q^{95} - 3 q^{96} - 4 q^{97} - 3 q^{98} + 20 q^{99}+O(q^{100}) \) 5 * q + 5 * q^2 - 3 * q^3 + 5 * q^4 - 5 * q^5 - 3 * q^6 - 6 * q^7 + 5 * q^8 + 2 * q^9 - 5 * q^10 - 9 * q^11 - 3 * q^12 - 5 * q^13 - 6 * q^14 - 3 * q^15 + 5 * q^16 - 6 * q^17 + 2 * q^18 - 10 * q^19 - 5 * q^20 - 2 * q^21 - 9 * q^22 - 5 * q^23 - 3 * q^24 - 4 * q^25 - 5 * q^26 - 9 * q^27 - 6 * q^28 + 5 * q^29 - 3 * q^30 - 15 * q^31 + 5 * q^32 - 15 * q^33 - 6 * q^34 - 2 * q^35 + 2 * q^36 - 10 * q^38 + 3 * q^39 - 5 * q^40 - 2 * q^41 - 2 * q^42 - 5 * q^43 - 9 * q^44 - 6 * q^45 - 5 * q^46 - 9 * q^47 - 3 * q^48 - 3 * q^49 - 4 * q^50 - 2 * q^51 - 5 * q^52 + 3 * q^53 - 9 * q^54 - 3 * q^55 - 6 * q^56 - 2 * q^57 + 5 * q^58 - 26 * q^59 - 3 * q^60 - 8 * q^61 - 15 * q^62 - 6 * q^63 + 5 * q^64 + 19 * q^65 - 15 * q^66 + 12 * q^67 - 6 * q^68 + 3 * q^69 - 2 * q^70 - 12 * q^71 + 2 * q^72 + 2 * q^73 + 24 * q^75 - 10 * q^76 + 36 * q^77 + 3 * q^78 - 25 * q^79 - 5 * q^80 + 9 * q^81 - 2 * q^82 - 16 * q^83 - 2 * q^84 + 4 * q^85 - 5 * q^86 - 3 * q^87 - 9 * q^88 - 20 * q^89 - 6 * q^90 - 32 * q^91 - 5 * q^92 + 11 * q^93 - 9 * q^94 + 20 * q^95 - 3 * q^96 - 4 * q^97 - 3 * q^98 + 20 * q^99

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