LMFDB - Embedded newform 6026.2.a.k.1.27

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6026,2,Mod(1,6026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6026, 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("6026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6026 = 2 \cdot 23 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6026.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.1178522580$
Analytic rank:	$0$
Dimension:	$35$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.27
Character	$\chi$	$=$	6026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +2.12884 q^{3} +1.00000 q^{4} -4.38597 q^{5} +2.12884 q^{6} +4.48136 q^{7} +1.00000 q^{8} +1.53195 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.12884 q^{3} +1.00000 q^{4} -4.38597 q^{5} +2.12884 q^{6} +4.48136 q^{7} +1.00000 q^{8} +1.53195 q^{9} -4.38597 q^{10} -4.38348 q^{11} +2.12884 q^{12} -4.60233 q^{13} +4.48136 q^{14} -9.33703 q^{15} +1.00000 q^{16} +2.76331 q^{17} +1.53195 q^{18} +5.48767 q^{19} -4.38597 q^{20} +9.54009 q^{21} -4.38348 q^{22} -1.00000 q^{23} +2.12884 q^{24} +14.2367 q^{25} -4.60233 q^{26} -3.12523 q^{27} +4.48136 q^{28} -4.34897 q^{29} -9.33703 q^{30} +9.33631 q^{31} +1.00000 q^{32} -9.33172 q^{33} +2.76331 q^{34} -19.6551 q^{35} +1.53195 q^{36} -1.50182 q^{37} +5.48767 q^{38} -9.79761 q^{39} -4.38597 q^{40} +1.93108 q^{41} +9.54009 q^{42} +9.47514 q^{43} -4.38348 q^{44} -6.71911 q^{45} -1.00000 q^{46} +13.4937 q^{47} +2.12884 q^{48} +13.0826 q^{49} +14.2367 q^{50} +5.88264 q^{51} -4.60233 q^{52} +9.83158 q^{53} -3.12523 q^{54} +19.2258 q^{55} +4.48136 q^{56} +11.6824 q^{57} -4.34897 q^{58} -11.0061 q^{59} -9.33703 q^{60} +5.85973 q^{61} +9.33631 q^{62} +6.86523 q^{63} +1.00000 q^{64} +20.1857 q^{65} -9.33172 q^{66} -0.491136 q^{67} +2.76331 q^{68} -2.12884 q^{69} -19.6551 q^{70} -2.58104 q^{71} +1.53195 q^{72} +6.24874 q^{73} -1.50182 q^{74} +30.3077 q^{75} +5.48767 q^{76} -19.6439 q^{77} -9.79761 q^{78} +7.64063 q^{79} -4.38597 q^{80} -11.2490 q^{81} +1.93108 q^{82} +9.49073 q^{83} +9.54009 q^{84} -12.1198 q^{85} +9.47514 q^{86} -9.25825 q^{87} -4.38348 q^{88} -10.0731 q^{89} -6.71911 q^{90} -20.6247 q^{91} -1.00000 q^{92} +19.8755 q^{93} +13.4937 q^{94} -24.0688 q^{95} +2.12884 q^{96} +5.89350 q^{97} +13.0826 q^{98} -6.71529 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 35 q + 35 q^{2} - 3 q^{3} + 35 q^{4} + 10 q^{5} - 3 q^{6} + 14 q^{7} + 35 q^{8} + 54 q^{9}+O(q^{10}) $ 35 * q + 35 * q^2 - 3 * q^3 + 35 * q^4 + 10 * q^5 - 3 * q^6 + 14 * q^7 + 35 * q^8 + 54 * q^9	\( 35 q + 35 q^{2} - 3 q^{3} + 35 q^{4} + 10 q^{5} - 3 q^{6} + 14 q^{7} + 35 q^{8} + 54 q^{9} + 10 q^{10} + 9 q^{11} - 3 q^{12} + 19 q^{13} + 14 q^{14} + 14 q^{15} + 35 q^{16} + 28 q^{17} + 54 q^{18} + 21 q^{19} + 10 q^{20} + 28 q^{21} + 9 q^{22} - 35 q^{23} - 3 q^{24} + 81 q^{25} + 19 q^{26} - 21 q^{27} + 14 q^{28} + 35 q^{29} + 14 q^{30} + 5 q^{31} + 35 q^{32} + 26 q^{33} + 28 q^{34} - 7 q^{35} + 54 q^{36} + 51 q^{37} + 21 q^{38} + 21 q^{39} + 10 q^{40} + 3 q^{41} + 28 q^{42} + 43 q^{43} + 9 q^{44} + 2 q^{45} - 35 q^{46} + 10 q^{47} - 3 q^{48} + 85 q^{49} + 81 q^{50} + 26 q^{51} + 19 q^{52} + 39 q^{53} - 21 q^{54} + 2 q^{55} + 14 q^{56} + 50 q^{57} + 35 q^{58} - 42 q^{59} + 14 q^{60} + 47 q^{61} + 5 q^{62} + 23 q^{63} + 35 q^{64} + 61 q^{65} + 26 q^{66} + 22 q^{67} + 28 q^{68} + 3 q^{69} - 7 q^{70} + 54 q^{72} + 30 q^{73} + 51 q^{74} - 26 q^{75} + 21 q^{76} + 2 q^{77} + 21 q^{78} + 55 q^{79} + 10 q^{80} + 67 q^{81} + 3 q^{82} + 20 q^{83} + 28 q^{84} + 28 q^{85} + 43 q^{86} + 29 q^{87} + 9 q^{88} - 31 q^{89} + 2 q^{90} + 32 q^{91} - 35 q^{92} + 11 q^{93} + 10 q^{94} + 16 q^{95} - 3 q^{96} + 36 q^{97} + 85 q^{98} - 9 q^{99}+O(q^{100}) \) 35 * q + 35 * q^2 - 3 * q^3 + 35 * q^4 + 10 * q^5 - 3 * q^6 + 14 * q^7 + 35 * q^8 + 54 * q^9 + 10 * q^10 + 9 * q^11 - 3 * q^12 + 19 * q^13 + 14 * q^14 + 14 * q^15 + 35 * q^16 + 28 * q^17 + 54 * q^18 + 21 * q^19 + 10 * q^20 + 28 * q^21 + 9 * q^22 - 35 * q^23 - 3 * q^24 + 81 * q^25 + 19 * q^26 - 21 * q^27 + 14 * q^28 + 35 * q^29 + 14 * q^30 + 5 * q^31 + 35 * q^32 + 26 * q^33 + 28 * q^34 - 7 * q^35 + 54 * q^36 + 51 * q^37 + 21 * q^38 + 21 * q^39 + 10 * q^40 + 3 * q^41 + 28 * q^42 + 43 * q^43 + 9 * q^44 + 2 * q^45 - 35 * q^46 + 10 * q^47 - 3 * q^48 + 85 * q^49 + 81 * q^50 + 26 * q^51 + 19 * q^52 + 39 * q^53 - 21 * q^54 + 2 * q^55 + 14 * q^56 + 50 * q^57 + 35 * q^58 - 42 * q^59 + 14 * q^60 + 47 * q^61 + 5 * q^62 + 23 * q^63 + 35 * q^64 + 61 * q^65 + 26 * q^66 + 22 * q^67 + 28 * q^68 + 3 * q^69 - 7 * q^70 + 54 * q^72 + 30 * q^73 + 51 * q^74 - 26 * q^75 + 21 * q^76 + 2 * q^77 + 21 * q^78 + 55 * q^79 + 10 * q^80 + 67 * q^81 + 3 * q^82 + 20 * q^83 + 28 * q^84 + 28 * q^85 + 43 * q^86 + 29 * q^87 + 9 * q^88 - 31 * q^89 + 2 * q^90 + 32 * q^91 - 35 * q^92 + 11 * q^93 + 10 * q^94 + 16 * q^95 - 3 * q^96 + 36 * q^97 + 85 * q^98 - 9 * 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
$3$	2.12884	1.22909	0.614543	−	0.788884i	$-0.289341\pi$
$3$	2.12884	1.22909	0.614543	+	0.788884i	$0.289341\pi$
$4$	1.00000	0.500000
$5$	−4.38597	−1.96147	−0.980733	−	0.195352i	$-0.937415\pi$
$5$	−4.38597	−1.96147	−0.980733	+	0.195352i	$0.937415\pi$
$6$	2.12884	0.869095
$7$	4.48136	1.69379	0.846897	−	0.531757i	$-0.178468\pi$
$7$	4.48136	1.69379	0.846897	+	0.531757i	$0.178468\pi$
$8$	1.00000	0.353553
$9$	1.53195	0.510651
$10$	−4.38597	−1.38697
$11$	−4.38348	−1.32167	−0.660834	−	0.750532i	$-0.729797\pi$
$11$	−4.38348	−1.32167	−0.660834	+	0.750532i	$0.729797\pi$
$12$	2.12884	0.614543
$13$	−4.60233	−1.27646	−0.638228	−	0.769848i	$-0.720332\pi$
$13$	−4.60233	−1.27646	−0.638228	+	0.769848i	$0.720332\pi$
$14$	4.48136	1.19769
$15$	−9.33703	−2.41081
$16$	1.00000	0.250000
$17$	2.76331	0.670202	0.335101	−	0.942182i	$-0.391230\pi$
$17$	2.76331	0.670202	0.335101	+	0.942182i	$0.391230\pi$
$18$	1.53195	0.361085
$19$	5.48767	1.25896	0.629479	−	0.777018i	$-0.283269\pi$
$19$	5.48767	1.25896	0.629479	+	0.777018i	$0.283269\pi$
$20$	−4.38597	−0.980733
$21$	9.54009	2.08182
$22$	−4.38348	−0.934561
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	2.12884	0.434547
$25$	14.2367	2.84735
$26$	−4.60233	−0.902590
$27$	−3.12523	−0.601451
$28$	4.48136	0.846897
$29$	−4.34897	−0.807583	−0.403792	−	0.914851i	$-0.632308\pi$
$29$	−4.34897	−0.807583	−0.403792	+	0.914851i	$0.632308\pi$
$30$	−9.33703	−1.70470
$31$	9.33631	1.67685	0.838426	−	0.545016i	$-0.183476\pi$
$31$	9.33631	1.67685	0.838426	+	0.545016i	$0.183476\pi$
$32$	1.00000	0.176777
$33$	−9.33172	−1.62444
$34$	2.76331	0.473904
$35$	−19.6551	−3.32232
$36$	1.53195	0.255326
$37$	−1.50182	−0.246898	−0.123449	−	0.992351i	$-0.539396\pi$
$37$	−1.50182	−0.246898	−0.123449	+	0.992351i	$0.539396\pi$
$38$	5.48767	0.890217
$39$	−9.79761	−1.56887
$40$	−4.38597	−0.693483
$41$	1.93108	0.301584	0.150792	−	0.988566i	$-0.451818\pi$
$41$	1.93108	0.301584	0.150792	+	0.988566i	$0.451818\pi$
$42$	9.54009	1.47207
$43$	9.47514	1.44495	0.722473	−	0.691399i	$-0.243006\pi$
$43$	9.47514	1.44495	0.722473	+	0.691399i	$0.243006\pi$
$44$	−4.38348	−0.660834
$45$	−6.71911	−1.00163
$46$	−1.00000	−0.147442
$47$	13.4937	1.96825	0.984126	−	0.177471i	$-0.0567916\pi$
$47$	13.4937	1.96825	0.984126	+	0.177471i	$0.0567916\pi$
$48$	2.12884	0.307271
$49$	13.0826	1.86894
$50$	14.2367	2.01338
$51$	5.88264	0.823735
$52$	−4.60233	−0.638228
$53$	9.83158	1.35047	0.675236	−	0.737602i	$-0.264042\pi$
$53$	9.83158	1.35047	0.675236	+	0.737602i	$0.264042\pi$
$54$	−3.12523	−0.425290
$55$	19.2258	2.59241
$56$	4.48136	0.598847
$57$	11.6824	1.54737
$58$	−4.34897	−0.571048
$59$	−11.0061	−1.43287	−0.716433	−	0.697656i	$-0.754227\pi$
$59$	−11.0061	−1.43287	−0.716433	+	0.697656i	$0.754227\pi$
$60$	−9.33703	−1.20540
$61$	5.85973	0.750261	0.375131	−	0.926972i	$-0.377598\pi$
$61$	5.85973	0.750261	0.375131	+	0.926972i	$0.377598\pi$
$62$	9.33631	1.18571
$63$	6.86523	0.864938
$64$	1.00000	0.125000
$65$	20.1857	2.50372
$66$	−9.33172	−1.14866
$67$	−0.491136	−0.0600019	−0.0300009	−	0.999550i	$-0.509551\pi$
$67$	−0.491136	−0.0600019	−0.0300009	+	0.999550i	$0.509551\pi$
$68$	2.76331	0.335101
$69$	−2.12884	−0.256282
$70$	−19.6551	−2.34923
$71$	−2.58104	−0.306314	−0.153157	−	0.988202i	$-0.548944\pi$
$71$	−2.58104	−0.306314	−0.153157	+	0.988202i	$0.548944\pi$
$72$	1.53195	0.180542
$73$	6.24874	0.731360	0.365680	−	0.930741i	$-0.380836\pi$
$73$	6.24874	0.731360	0.365680	+	0.930741i	$0.380836\pi$
$74$	−1.50182	−0.174583
$75$	30.3077	3.49964
$76$	5.48767	0.629479
$77$	−19.6439	−2.23863
$78$	−9.79761	−1.10936
$79$	7.64063	0.859638	0.429819	−	0.902915i	$-0.358577\pi$
$79$	7.64063	0.859638	0.429819	+	0.902915i	$0.358577\pi$
$80$	−4.38597	−0.490367
$81$	−11.2490	−1.24989
$82$	1.93108	0.213252
$83$	9.49073	1.04174	0.520871	−	0.853635i	$-0.325607\pi$
$83$	9.49073	1.04174	0.520871	+	0.853635i	$0.325607\pi$
$84$	9.54009	1.04091
$85$	−12.1198	−1.31458
$86$	9.47514	1.02173
$87$	−9.25825	−0.992589
$88$	−4.38348	−0.467281
$89$	−10.0731	−1.06775	−0.533875	−	0.845563i	$-0.679265\pi$
$89$	−10.0731	−1.06775	−0.533875	+	0.845563i	$0.679265\pi$
$90$	−6.71911	−0.708256
$91$	−20.6247	−2.16205
$92$	−1.00000	−0.104257
$93$	19.8755	2.06099
$94$	13.4937	1.39176
$95$	−24.0688	−2.46940
$96$	2.12884	0.217274
$97$	5.89350	0.598395	0.299197	−	0.954191i	$-0.403281\pi$
$97$	5.89350	0.598395	0.299197	+	0.954191i	$0.403281\pi$
$98$	13.0826	1.32154
$99$	−6.71529	−0.674912
$100$	14.2367	1.42367
$101$	18.2567	1.81661	0.908307	−	0.418304i	$-0.137375\pi$
$101$	18.2567	1.81661	0.908307	+	0.418304i	$0.137375\pi$
$102$	5.88264	0.582469
$103$	0.209800	0.0206722	0.0103361	−	0.999947i	$-0.496710\pi$
$103$	0.209800	0.0206722	0.0103361	+	0.999947i	$0.496710\pi$
$104$	−4.60233	−0.451295
$105$	−41.8425	−4.08341
$106$	9.83158	0.954928
$107$	−18.4626	−1.78485	−0.892423	−	0.451201i	$-0.850996\pi$
$107$	−18.4626	−1.78485	−0.892423	+	0.451201i	$0.850996\pi$
$108$	−3.12523	−0.300726
$109$	6.05047	0.579530	0.289765	−	0.957098i	$-0.406423\pi$
$109$	6.05047	0.579530	0.289765	+	0.957098i	$0.406423\pi$
$110$	19.2258	1.83311
$111$	−3.19714	−0.303459
$112$	4.48136	0.423448
$113$	2.92313	0.274985	0.137493	−	0.990503i	$-0.456096\pi$
$113$	2.92313	0.274985	0.137493	+	0.990503i	$0.456096\pi$
$114$	11.6824	1.09415
$115$	4.38597	0.408994
$116$	−4.34897	−0.403792
$117$	−7.05055	−0.651824
$118$	−11.0061	−1.01319
$119$	12.3834	1.13518
$120$	−9.33703	−0.852350
$121$	8.21490	0.746809
$122$	5.85973	0.530515
$123$	4.11096	0.370672
$124$	9.33631	0.838426
$125$	−40.5121	−3.62351
$126$	6.86523	0.611603
$127$	−15.8703	−1.40826	−0.704129	−	0.710072i	$-0.748662\pi$
$127$	−15.8703	−1.40826	−0.704129	+	0.710072i	$0.748662\pi$
$128$	1.00000	0.0883883
$129$	20.1710	1.77596
$130$	20.1857	1.77040
$131$	−1.00000	−0.0873704
$131$	−1.00000	−0.0873704
$132$	−9.33172	−0.812222
$133$	24.5922	2.13241
$134$	−0.491136	−0.0424277
$135$	13.7072	1.17973
$136$	2.76331	0.236952
$137$	10.1148	0.864165	0.432082	−	0.901834i	$-0.357779\pi$
$137$	10.1148	0.864165	0.432082	+	0.901834i	$0.357779\pi$
$138$	−2.12884	−0.181219
$139$	−10.7579	−0.912470	−0.456235	−	0.889859i	$-0.650802\pi$
$139$	−10.7579	−0.912470	−0.456235	+	0.889859i	$0.650802\pi$
$140$	−19.6551	−1.66116
$141$	28.7258	2.41915
$142$	−2.58104	−0.216596
$143$	20.1742	1.68705
$144$	1.53195	0.127663
$145$	19.0745	1.58405
$146$	6.24874	0.517150
$147$	27.8507	2.29708
$148$	−1.50182	−0.123449
$149$	−1.75577	−0.143839	−0.0719193	−	0.997410i	$-0.522912\pi$
$149$	−1.75577	−0.143839	−0.0719193	+	0.997410i	$0.522912\pi$
$150$	30.3077	2.47462
$151$	5.70455	0.464230	0.232115	−	0.972688i	$-0.425435\pi$
$151$	5.70455	0.464230	0.232115	+	0.972688i	$0.425435\pi$
$152$	5.48767	0.445109
$153$	4.23327	0.342239
$154$	−19.6439	−1.58295
$155$	−40.9488	−3.28909
$156$	−9.79761	−0.784437
$157$	13.8985	1.10922	0.554611	−	0.832110i	$-0.312867\pi$
$157$	13.8985	1.10922	0.554611	+	0.832110i	$0.312867\pi$
$158$	7.64063	0.607856
$159$	20.9299	1.65985
$160$	−4.38597	−0.346742
$161$	−4.48136	−0.353180
$162$	−11.2490	−0.883803
$163$	−10.2213	−0.800593	−0.400296	−	0.916386i	$-0.631093\pi$
$163$	−10.2213	−0.800593	−0.400296	+	0.916386i	$0.631093\pi$
$164$	1.93108	0.150792
$165$	40.9287	3.18629
$166$	9.49073	0.736623
$167$	−1.71062	−0.132372	−0.0661860	−	0.997807i	$-0.521083\pi$
$167$	−1.71062	−0.132372	−0.0661860	+	0.997807i	$0.521083\pi$
$168$	9.54009	0.736034
$169$	8.18141	0.629339
$170$	−12.1198	−0.929547
$171$	8.40685	0.642888
$172$	9.47514	0.722473
$173$	−17.9779	−1.36683	−0.683417	−	0.730028i	$-0.739507\pi$
$173$	−17.9779	−1.36683	−0.683417	+	0.730028i	$0.739507\pi$
$174$	−9.25825	−0.701866
$175$	63.8000	4.82282
$176$	−4.38348	−0.330417
$177$	−23.4301	−1.76112
$178$	−10.0731	−0.755013
$179$	22.2441	1.66260	0.831299	−	0.555825i	$-0.187598\pi$
$179$	22.2441	1.66260	0.831299	+	0.555825i	$0.187598\pi$
$180$	−6.71911	−0.500813
$181$	−15.7787	−1.17282	−0.586410	−	0.810015i	$-0.699459\pi$
$181$	−15.7787	−1.17282	−0.586410	+	0.810015i	$0.699459\pi$
$182$	−20.6247	−1.52880
$183$	12.4744	0.922136
$184$	−1.00000	−0.0737210
$185$	6.58695	0.484282
$186$	19.8755	1.45734
$187$	−12.1129	−0.885785
$188$	13.4937	0.984126
$189$	−14.0053	−1.01873
$190$	−24.0688	−1.74613
$191$	−16.6139	−1.20214	−0.601070	−	0.799197i	$-0.705259\pi$
$191$	−16.6139	−1.20214	−0.601070	+	0.799197i	$0.705259\pi$
$192$	2.12884	0.153636
$193$	−8.24167	−0.593248	−0.296624	−	0.954994i	$-0.595861\pi$
$193$	−8.24167	−0.593248	−0.296624	+	0.954994i	$0.595861\pi$
$194$	5.89350	0.423129
$195$	42.9720	3.07729
$196$	13.0826	0.934469
$197$	15.9992	1.13990	0.569949	−	0.821680i	$-0.306963\pi$
$197$	15.9992	1.13990	0.569949	+	0.821680i	$0.306963\pi$
$198$	−6.71529	−0.477235
$199$	14.7360	1.04461	0.522304	−	0.852759i	$-0.325073\pi$
$199$	14.7360	1.04461	0.522304	+	0.852759i	$0.325073\pi$
$200$	14.2367	1.00669
$201$	−1.04555	−0.0737474
$202$	18.2567	1.28454
$203$	−19.4893	−1.36788
$204$	5.88264	0.411868
$205$	−8.46966	−0.591547
$206$	0.209800	0.0146174
$207$	−1.53195	−0.106478
$208$	−4.60233	−0.319114
$209$	−24.0551	−1.66392
$210$	−41.8425	−2.88741
$211$	−7.11568	−0.489864	−0.244932	−	0.969540i	$-0.578766\pi$
$211$	−7.11568	−0.489864	−0.244932	+	0.969540i	$0.578766\pi$
$212$	9.83158	0.675236
$213$	−5.49463	−0.376486
$214$	−18.4626	−1.26208
$215$	−41.5577	−2.83421
$216$	−3.12523	−0.212645
$217$	41.8394	2.84024
$218$	6.05047	0.409789
$219$	13.3026	0.898904
$220$	19.2258	1.29620
$221$	−12.7177	−0.855483
$222$	−3.19714	−0.214578
$223$	1.72594	0.115577	0.0577886	−	0.998329i	$-0.481595\pi$
$223$	1.72594	0.115577	0.0577886	+	0.998329i	$0.481595\pi$
$224$	4.48136	0.299423
$225$	21.8100	1.45400
$226$	2.92313	0.194444
$227$	23.0680	1.53108	0.765539	−	0.643390i	$-0.222472\pi$
$227$	23.0680	1.53108	0.765539	+	0.643390i	$0.222472\pi$
$228$	11.6824	0.773683
$229$	4.44534	0.293756	0.146878	−	0.989155i	$-0.453078\pi$
$229$	4.44534	0.293756	0.146878	+	0.989155i	$0.453078\pi$
$230$	4.38597	0.289202
$231$	−41.8188	−2.75147
$232$	−4.34897	−0.285524
$233$	−26.2382	−1.71892	−0.859462	−	0.511200i	$-0.829201\pi$
$233$	−26.2382	−1.71892	−0.859462	+	0.511200i	$0.829201\pi$
$234$	−7.05055	−0.460909
$235$	−59.1828	−3.86066
$236$	−11.0061	−0.716433
$237$	16.2657	1.05657
$238$	12.3834	0.802696
$239$	11.1125	0.718806	0.359403	−	0.933182i	$-0.382980\pi$
$239$	11.1125	0.718806	0.359403	+	0.933182i	$0.382980\pi$
$240$	−9.33703	−0.602702
$241$	−26.5802	−1.71218	−0.856089	−	0.516828i	$-0.827113\pi$
$241$	−26.5802	−1.71218	−0.856089	+	0.516828i	$0.827113\pi$
$242$	8.21490	0.528074
$243$	−14.5716	−0.934766
$244$	5.85973	0.375131
$245$	−57.3797	−3.66586
$246$	4.11096	0.262105
$247$	−25.2560	−1.60700
$248$	9.33631	0.592857
$249$	20.2042	1.28039
$250$	−40.5121	−2.56221
$251$	9.70569	0.612618	0.306309	−	0.951932i	$-0.400906\pi$
$251$	9.70569	0.612618	0.306309	+	0.951932i	$0.400906\pi$
$252$	6.86523	0.432469
$253$	4.38348	0.275587
$254$	−15.8703	−0.995788
$255$	−25.8011	−1.61573
$256$	1.00000	0.0625000
$257$	7.80596	0.486923	0.243461	−	0.969911i	$-0.421717\pi$
$257$	7.80596	0.486923	0.243461	+	0.969911i	$0.421717\pi$
$258$	20.1710	1.25579
$259$	−6.73020	−0.418194
$260$	20.1857	1.25186
$261$	−6.66242	−0.412393
$262$	−1.00000	−0.0617802
$263$	14.6337	0.902350	0.451175	−	0.892436i	$-0.351005\pi$
$263$	14.6337	0.902350	0.451175	+	0.892436i	$0.351005\pi$
$264$	−9.33172	−0.574328
$265$	−43.1210	−2.64890
$266$	24.5922	1.50784
$267$	−21.4441	−1.31236
$268$	−0.491136	−0.0300009
$269$	−8.01704	−0.488807	−0.244404	−	0.969674i	$-0.578592\pi$
$269$	−8.01704	−0.488807	−0.244404	+	0.969674i	$0.578592\pi$
$270$	13.7072	0.834193
$271$	−4.72587	−0.287076	−0.143538	−	0.989645i	$-0.545848\pi$
$271$	−4.72587	−0.287076	−0.143538	+	0.989645i	$0.545848\pi$
$272$	2.76331	0.167550
$273$	−43.9066	−2.65735
$274$	10.1148	0.611057
$275$	−62.4065	−3.76325
$276$	−2.12884	−0.128141
$277$	24.8162	1.49106	0.745530	−	0.666472i	$-0.232197\pi$
$277$	24.8162	1.49106	0.745530	+	0.666472i	$0.232197\pi$
$278$	−10.7579	−0.645213
$279$	14.3028	0.856286
$280$	−19.6551	−1.17462
$281$	−22.9246	−1.36756	−0.683782	−	0.729686i	$-0.739666\pi$
$281$	−22.9246	−1.36756	−0.683782	+	0.729686i	$0.739666\pi$
$282$	28.7258	1.71060
$283$	−10.2964	−0.612059	−0.306029	−	0.952022i	$-0.599001\pi$
$283$	−10.2964	−0.612059	−0.306029	+	0.952022i	$0.599001\pi$
$284$	−2.58104	−0.153157
$285$	−51.2385	−3.03511
$286$	20.1742	1.19293
$287$	8.65385	0.510821
$288$	1.53195	0.0902712
$289$	−9.36411	−0.550830
$290$	19.0745	1.12009
$291$	12.5463	0.735478
$292$	6.24874	0.365680
$293$	14.2492	0.832448	0.416224	−	0.909262i	$-0.363353\pi$
$293$	14.2492	0.832448	0.416224	+	0.909262i	$0.363353\pi$
$294$	27.8507	1.62428
$295$	48.2723	2.81052
$296$	−1.50182	−0.0872916
$297$	13.6994	0.794920
$298$	−1.75577	−0.101709
$299$	4.60233	0.266159
$300$	30.3077	1.74982
$301$	42.4615	2.44744
$302$	5.70455	0.328260
$303$	38.8657	2.23277
$304$	5.48767	0.314739
$305$	−25.7006	−1.47161
$306$	4.23327	0.242000
$307$	−22.4146	−1.27927	−0.639635	−	0.768679i	$-0.720915\pi$
$307$	−22.4146	−1.27927	−0.639635	+	0.768679i	$0.720915\pi$
$308$	−19.6439	−1.11932
$309$	0.446630	0.0254079
$310$	−40.9488	−2.32574
$311$	18.4805	1.04793	0.523965	−	0.851740i	$-0.324452\pi$
$311$	18.4805	1.04793	0.523965	+	0.851740i	$0.324452\pi$
$312$	−9.79761	−0.554680
$313$	−6.93322	−0.391889	−0.195944	−	0.980615i	$-0.562777\pi$
$313$	−6.93322	−0.391889	−0.195944	+	0.980615i	$0.562777\pi$
$314$	13.8985	0.784338
$315$	−30.1107	−1.69655
$316$	7.64063	0.429819
$317$	−21.6012	−1.21325	−0.606623	−	0.794990i	$-0.707476\pi$
$317$	−21.6012	−1.21325	−0.606623	+	0.794990i	$0.707476\pi$
$318$	20.9299	1.17369
$319$	19.0636	1.06736
$320$	−4.38597	−0.245183
$321$	−39.3039	−2.19373
$322$	−4.48136	−0.249736
$323$	15.1641	0.843755
$324$	−11.2490	−0.624943
$325$	−65.5222	−3.63452
$326$	−10.2213	−0.566105
$327$	12.8805	0.712291
$328$	1.93108	0.106626
$329$	60.4699	3.33381
$330$	40.9287	2.25305
$331$	−14.4765	−0.795701	−0.397851	−	0.917450i	$-0.630244\pi$
$331$	−14.4765	−0.795701	−0.397851	+	0.917450i	$0.630244\pi$
$332$	9.49073	0.520871
$333$	−2.30072	−0.126079
$334$	−1.71062	−0.0936011
$335$	2.15411	0.117692
$336$	9.54009	0.520454
$337$	3.37344	0.183763	0.0918815	−	0.995770i	$-0.470712\pi$
$337$	3.37344	0.183763	0.0918815	+	0.995770i	$0.470712\pi$
$338$	8.18141	0.445010
$339$	6.22288	0.337980
$340$	−12.1198	−0.657289
$341$	−40.9255	−2.21624
$342$	8.40685	0.454591
$343$	27.2581	1.47180
$344$	9.47514	0.510865
$345$	9.33703	0.502689
$346$	−17.9779	−0.966498
$347$	13.9040	0.746405	0.373203	−	0.927750i	$-0.378260\pi$
$347$	13.9040	0.746405	0.373203	+	0.927750i	$0.378260\pi$
$348$	−9.25825	−0.496294
$349$	−8.53760	−0.457007	−0.228504	−	0.973543i	$-0.573383\pi$
$349$	−8.53760	−0.457007	−0.228504	+	0.973543i	$0.573383\pi$
$350$	63.8000	3.41025
$351$	14.3833	0.767726
$352$	−4.38348	−0.233640
$353$	15.1807	0.807987	0.403994	−	0.914762i	$-0.367622\pi$
$353$	15.1807	0.807987	0.403994	+	0.914762i	$0.367622\pi$
$354$	−23.4301	−1.24530
$355$	11.3204	0.600824
$356$	−10.0731	−0.533875
$357$	26.3622	1.39524
$358$	22.2441	1.17563
$359$	16.9228	0.893149	0.446575	−	0.894746i	$-0.352644\pi$
$359$	16.9228	0.893149	0.446575	+	0.894746i	$0.352644\pi$
$360$	−6.71911	−0.354128
$361$	11.1145	0.584973
$362$	−15.7787	−0.829308
$363$	17.4882	0.917892
$364$	−20.6247	−1.08103
$365$	−27.4068	−1.43454
$366$	12.4744	0.652048
$367$	31.9695	1.66880	0.834398	−	0.551162i	$-0.185815\pi$
$367$	31.9695	1.66880	0.834398	+	0.551162i	$0.185815\pi$
$368$	−1.00000	−0.0521286
$369$	2.95832	0.154004
$370$	6.58695	0.342439
$371$	44.0588	2.28742
$372$	19.8755	1.03050
$373$	6.72390	0.348150	0.174075	−	0.984732i	$-0.444306\pi$
$373$	6.72390	0.348150	0.174075	+	0.984732i	$0.444306\pi$
$374$	−12.1129	−0.626344
$375$	−86.2438	−4.45361
$376$	13.4937	0.695882
$377$	20.0154	1.03084
$378$	−14.0053	−0.720354
$379$	8.36796	0.429833	0.214917	−	0.976632i	$-0.431052\pi$
$379$	8.36796	0.429833	0.214917	+	0.976632i	$0.431052\pi$
$380$	−24.0688	−1.23470
$381$	−33.7852	−1.73087
$382$	−16.6139	−0.850041
$383$	22.3260	1.14080	0.570402	−	0.821366i	$-0.306788\pi$
$383$	22.3260	1.14080	0.570402	+	0.821366i	$0.306788\pi$
$384$	2.12884	0.108637
$385$	86.1578	4.39101
$386$	−8.24167	−0.419490
$387$	14.5155	0.737863
$388$	5.89350	0.299197
$389$	14.7618	0.748454	0.374227	−	0.927337i	$-0.377908\pi$
$389$	14.7618	0.748454	0.374227	+	0.927337i	$0.377908\pi$
$390$	42.9720	2.17597
$391$	−2.76331	−0.139747
$392$	13.0826	0.660769
$393$	−2.12884	−0.107386
$394$	15.9992	0.806030
$395$	−33.5116	−1.68615
$396$	−6.71529	−0.337456
$397$	−32.5136	−1.63181	−0.815906	−	0.578184i	$-0.803761\pi$
$397$	−32.5136	−1.63181	−0.815906	+	0.578184i	$0.803761\pi$
$398$	14.7360	0.738650
$399$	52.3528	2.62092
$400$	14.2367	0.711837
$401$	−1.13193	−0.0565257	−0.0282629	−	0.999601i	$-0.508998\pi$
$401$	−1.13193	−0.0565257	−0.0282629	+	0.999601i	$0.508998\pi$
$402$	−1.04555	−0.0521473
$403$	−42.9688	−2.14043
$404$	18.2567	0.908307
$405$	49.3377	2.45161
$406$	−19.4893	−0.967237
$407$	6.58321	0.326317
$408$	5.88264	0.291234
$409$	−30.1520	−1.49092	−0.745460	−	0.666550i	$-0.767770\pi$
$409$	−30.1520	−1.49092	−0.745460	+	0.666550i	$0.767770\pi$
$410$	−8.46966	−0.418287
$411$	21.5328	1.06213
$412$	0.209800	0.0103361
$413$	−49.3221	−2.42698
$414$	−1.53195	−0.0752914
$415$	−41.6261	−2.04334
$416$	−4.60233	−0.225648
$417$	−22.9017	−1.12150
$418$	−24.0551	−1.17657
$419$	9.58233	0.468128	0.234064	−	0.972221i	$-0.424798\pi$
$419$	9.58233	0.468128	0.234064	+	0.972221i	$0.424798\pi$
$420$	−41.8425	−2.04171
$421$	−15.7434	−0.767287	−0.383644	−	0.923481i	$-0.625331\pi$
$421$	−15.7434	−0.767287	−0.383644	+	0.923481i	$0.625331\pi$
$422$	−7.11568	−0.346386
$423$	20.6717	1.00509
$424$	9.83158	0.477464
$425$	39.3406	1.90830
$426$	−5.49463	−0.266215
$427$	26.2595	1.27079
$428$	−18.4626	−0.892423
$429$	42.9476	2.07353
$430$	−41.5577	−2.00409
$431$	36.6246	1.76415	0.882073	−	0.471113i	$-0.156148\pi$
$431$	36.6246	1.76415	0.882073	+	0.471113i	$0.156148\pi$
$432$	−3.12523	−0.150363
$433$	−41.5245	−1.99554	−0.997769	−	0.0667580i	$-0.978734\pi$
$433$	−41.5245	−1.99554	−0.997769	+	0.0667580i	$0.978734\pi$
$434$	41.8394	2.00835
$435$	40.6064	1.94693
$436$	6.05047	0.289765
$437$	−5.48767	−0.262511
$438$	13.3026	0.635621
$439$	−7.20466	−0.343860	−0.171930	−	0.985109i	$-0.555000\pi$
$439$	−7.20466	−0.343860	−0.171930	+	0.985109i	$0.555000\pi$
$440$	19.2258	0.916555
$441$	20.0419	0.954375
$442$	−12.7177	−0.604918
$443$	−21.9655	−1.04361	−0.521806	−	0.853064i	$-0.674741\pi$
$443$	−21.9655	−1.04361	−0.521806	+	0.853064i	$0.674741\pi$
$444$	−3.19714	−0.151729
$445$	44.1805	2.09436
$446$	1.72594	0.0817254
$447$	−3.73776	−0.176790
$448$	4.48136	0.211724
$449$	8.68603	0.409919	0.204960	−	0.978770i	$-0.434294\pi$
$449$	8.68603	0.409919	0.204960	+	0.978770i	$0.434294\pi$
$450$	21.8100	1.02814
$451$	−8.46485	−0.398594
$452$	2.92313	0.137493
$453$	12.1441	0.570578
$454$	23.0680	1.08264
$455$	90.4592	4.24079
$456$	11.6824	0.547077
$457$	22.4249	1.04899	0.524497	−	0.851412i	$-0.324253\pi$
$457$	22.4249	1.04899	0.524497	+	0.851412i	$0.324253\pi$
$458$	4.44534	0.207717
$459$	−8.63599	−0.403094
$460$	4.38597	0.204497
$461$	−28.3632	−1.32101	−0.660504	−	0.750823i	$-0.729657\pi$
$461$	−28.3632	−1.32101	−0.660504	+	0.750823i	$0.729657\pi$
$462$	−41.8188	−1.94559
$463$	−6.98396	−0.324572	−0.162286	−	0.986744i	$-0.551887\pi$
$463$	−6.98396	−0.324572	−0.162286	+	0.986744i	$0.551887\pi$
$464$	−4.34897	−0.201896
$465$	−87.1734	−4.04257
$466$	−26.2382	−1.21546
$467$	17.0703	0.789919	0.394959	−	0.918699i	$-0.370759\pi$
$467$	17.0703	0.789919	0.394959	+	0.918699i	$0.370759\pi$
$468$	−7.05055	−0.325912
$469$	−2.20096	−0.101631
$470$	−59.1828	−2.72990
$471$	29.5877	1.36333
$472$	−11.0061	−0.506595
$473$	−41.5341	−1.90974
$474$	16.2657	0.747107
$475$	78.1265	3.58469
$476$	12.3834	0.567592
$477$	15.0615	0.689620
$478$	11.1125	0.508273
$479$	7.59890	0.347203	0.173601	−	0.984816i	$-0.444460\pi$
$479$	7.59890	0.347203	0.173601	+	0.984816i	$0.444460\pi$
$480$	−9.33703	−0.426175
$481$	6.91188	0.315154
$482$	−26.5802	−1.21069
$483$	−9.54009	−0.434089
$484$	8.21490	0.373404
$485$	−25.8487	−1.17373
$486$	−14.5716	−0.660979
$487$	−23.7255	−1.07511	−0.537553	−	0.843230i	$-0.680651\pi$
$487$	−23.7255	−1.07511	−0.537553	+	0.843230i	$0.680651\pi$
$488$	5.85973	0.265257
$489$	−21.7595	−0.983997
$490$	−57.3797	−2.59215
$491$	13.8061	0.623059	0.311529	−	0.950237i	$-0.399159\pi$
$491$	13.8061	0.623059	0.311529	+	0.950237i	$0.399159\pi$
$492$	4.11096	0.185336
$493$	−12.0176	−0.541244
$494$	−25.2560	−1.13632
$495$	29.4531	1.32382
$496$	9.33631	0.419213
$497$	−11.5666	−0.518832
$498$	20.2042	0.905373
$499$	−6.25483	−0.280005	−0.140002	−	0.990151i	$-0.544711\pi$
$499$	−6.25483	−0.280005	−0.140002	+	0.990151i	$0.544711\pi$
$500$	−40.5121	−1.81176
$501$	−3.64164	−0.162696
$502$	9.70569	0.433186
$503$	−12.7942	−0.570463	−0.285232	−	0.958459i	$-0.592071\pi$
$503$	−12.7942	−0.570463	−0.285232	+	0.958459i	$0.592071\pi$
$504$	6.86523	0.305802
$505$	−80.0736	−3.56323
$506$	4.38348	0.194869
$507$	17.4169	0.773512
$508$	−15.8703	−0.704129
$509$	−18.1850	−0.806037	−0.403018	−	0.915192i	$-0.632039\pi$
$509$	−18.1850	−0.806037	−0.403018	+	0.915192i	$0.632039\pi$
$510$	−25.8011	−1.14249
$511$	28.0028	1.23877
$512$	1.00000	0.0441942
$513$	−17.1502	−0.757202
$514$	7.80596	0.344306
$515$	−0.920176	−0.0405478
$516$	20.1710	0.887981
$517$	−59.1492	−2.60138
$518$	−6.73020	−0.295708
$519$	−38.2720	−1.67996
$520$	20.1857	0.885200
$521$	−11.9604	−0.523996	−0.261998	−	0.965068i	$-0.584381\pi$
$521$	−11.9604	−0.523996	−0.261998	+	0.965068i	$0.584381\pi$
$522$	−6.66242	−0.291606
$523$	37.2066	1.62693	0.813467	−	0.581612i	$-0.197578\pi$
$523$	37.2066	1.62693	0.813467	+	0.581612i	$0.197578\pi$
$524$	−1.00000	−0.0436852
$525$	135.820	5.92766
$526$	14.6337	0.638058
$527$	25.7991	1.12383
$528$	−9.33172	−0.406111
$529$	1.00000	0.0434783
$530$	−43.1210	−1.87306
$531$	−16.8608	−0.731695
$532$	24.5922	1.06621
$533$	−8.88746	−0.384958
$534$	−21.4441	−0.927976
$535$	80.9764	3.50091
$536$	−0.491136	−0.0212139
$537$	47.3540	2.04348
$538$	−8.01704	−0.345639
$539$	−57.3471	−2.47012
$540$	13.7072	0.589863
$541$	39.8642	1.71390	0.856948	−	0.515402i	$-0.172358\pi$
$541$	39.8642	1.71390	0.856948	+	0.515402i	$0.172358\pi$
$542$	−4.72587	−0.202994
$543$	−33.5902	−1.44150
$544$	2.76331	0.118476
$545$	−26.5372	−1.13673
$546$	−43.9066	−1.87903
$547$	−20.3698	−0.870951	−0.435476	−	0.900201i	$-0.643420\pi$
$547$	−20.3698	−0.870951	−0.435476	+	0.900201i	$0.643420\pi$
$548$	10.1148	0.432082
$549$	8.97683	0.383122
$550$	−62.4065	−2.66102
$551$	−23.8657	−1.01671
$552$	−2.12884	−0.0906094
$553$	34.2404	1.45605
$554$	24.8162	1.05434
$555$	14.0226	0.595224
$556$	−10.7579	−0.456235
$557$	17.6371	0.747310	0.373655	−	0.927568i	$-0.378104\pi$
$557$	17.6371	0.747310	0.373655	+	0.927568i	$0.378104\pi$
$558$	14.3028	0.605486
$559$	−43.6077	−1.84441
$560$	−19.6551	−0.830580
$561$	−25.7865	−1.08871
$562$	−22.9246	−0.967014
$563$	9.20452	0.387924	0.193962	−	0.981009i	$-0.437866\pi$
$563$	9.20452	0.387924	0.193962	+	0.981009i	$0.437866\pi$
$564$	28.7258	1.20958
$565$	−12.8208	−0.539374
$566$	−10.2964	−0.432791
$567$	−50.4107	−2.11705
$568$	−2.58104	−0.108298
$569$	16.6599	0.698418	0.349209	−	0.937045i	$-0.386450\pi$
$569$	16.6599	0.698418	0.349209	+	0.937045i	$0.386450\pi$
$570$	−51.2385	−2.14614
$571$	12.1923	0.510231	0.255116	−	0.966911i	$-0.417886\pi$
$571$	12.1923	0.510231	0.255116	+	0.966911i	$0.417886\pi$
$572$	20.1742	0.843526
$573$	−35.3683	−1.47753
$574$	8.65385	0.361205
$575$	−14.2367	−0.593713
$576$	1.53195	0.0638314
$577$	−27.9687	−1.16435	−0.582176	−	0.813063i	$-0.697798\pi$
$577$	−27.9687	−1.16435	−0.582176	+	0.813063i	$0.697798\pi$
$578$	−9.36411	−0.389496
$579$	−17.5452	−0.729153
$580$	19.0745	0.792024
$581$	42.5313	1.76450
$582$	12.5463	0.520062
$583$	−43.0965	−1.78488
$584$	6.24874	0.258575
$585$	30.9235	1.27853
$586$	14.2492	0.588629
$587$	40.7365	1.68137	0.840687	−	0.541521i	$-0.182152\pi$
$587$	40.7365	1.68137	0.840687	+	0.541521i	$0.182152\pi$
$588$	27.8507	1.14854
$589$	51.2346	2.11108
$590$	48.2723	1.98734
$591$	34.0598	1.40103
$592$	−1.50182	−0.0617245
$593$	25.5470	1.04909	0.524545	−	0.851383i	$-0.324235\pi$
$593$	25.5470	1.04909	0.524545	+	0.851383i	$0.324235\pi$
$594$	13.6994	0.562093
$595$	−54.3132	−2.22662
$596$	−1.75577	−0.0719193
$597$	31.3706	1.28391
$598$	4.60233	0.188203
$599$	34.9901	1.42966	0.714829	−	0.699300i	$-0.246505\pi$
$599$	34.9901	1.42966	0.714829	+	0.699300i	$0.246505\pi$
$600$	30.3077	1.23731
$601$	−23.6874	−0.966230	−0.483115	−	0.875557i	$-0.660495\pi$
$601$	−23.6874	−0.966230	−0.483115	+	0.875557i	$0.660495\pi$
$602$	42.4615	1.73060
$603$	−0.752398	−0.0306400
$604$	5.70455	0.232115
$605$	−36.0303	−1.46484
$606$	38.8657	1.57881
$607$	−33.0146	−1.34002	−0.670010	−	0.742352i	$-0.733710\pi$
$607$	−33.0146	−1.34002	−0.670010	+	0.742352i	$0.733710\pi$
$608$	5.48767	0.222554
$609$	−41.4895	−1.68124
$610$	−25.7006	−1.04059
$611$	−62.1022	−2.51239
$612$	4.23327	0.171120
$613$	17.4449	0.704594	0.352297	−	0.935888i	$-0.385401\pi$
$613$	17.4449	0.704594	0.352297	+	0.935888i	$0.385401\pi$
$614$	−22.4146	−0.904581
$615$	−18.0305	−0.727061
$616$	−19.6439	−0.791477
$617$	20.3518	0.819332	0.409666	−	0.912236i	$-0.365645\pi$
$617$	20.3518	0.819332	0.409666	+	0.912236i	$0.365645\pi$
$618$	0.446630	0.0179661
$619$	−12.1334	−0.487681	−0.243840	−	0.969815i	$-0.578407\pi$
$619$	−12.1334	−0.487681	−0.243840	+	0.969815i	$0.578407\pi$
$620$	−40.9488	−1.64454
$621$	3.12523	0.125411
$622$	18.4805	0.740999
$623$	−45.1413	−1.80855
$624$	−9.79761	−0.392218
$625$	106.501	4.26005
$626$	−6.93322	−0.277107
$627$	−51.2094	−2.04511
$628$	13.8985	0.554611
$629$	−4.15000	−0.165471
$630$	−30.1107	−1.19964
$631$	21.1513	0.842018	0.421009	−	0.907056i	$-0.361676\pi$
$631$	21.1513	0.842018	0.421009	+	0.907056i	$0.361676\pi$
$632$	7.64063	0.303928
$633$	−15.1481	−0.602084
$634$	−21.6012	−0.857894
$635$	69.6065	2.76225
$636$	20.9299	0.829923
$637$	−60.2102	−2.38562
$638$	19.0636	0.754736
$639$	−3.95404	−0.156419
$640$	−4.38597	−0.173371
$641$	17.5278	0.692308	0.346154	−	0.938178i	$-0.387487\pi$
$641$	17.5278	0.692308	0.346154	+	0.938178i	$0.387487\pi$
$642$	−39.3039	−1.55120
$643$	−16.1495	−0.636873	−0.318436	−	0.947944i	$-0.603158\pi$
$643$	−16.1495	−0.636873	−0.318436	+	0.947944i	$0.603158\pi$
$644$	−4.48136	−0.176590
$645$	−88.4696	−3.48349
$646$	15.1641	0.596625
$647$	−43.3707	−1.70508	−0.852539	−	0.522663i	$-0.824939\pi$
$647$	−43.3707	−1.70508	−0.852539	+	0.522663i	$0.824939\pi$
$648$	−11.2490	−0.441902
$649$	48.2448	1.89378
$650$	−65.5222	−2.56999
$651$	89.0692	3.49090
$652$	−10.2213	−0.400296
$653$	−32.5710	−1.27460	−0.637302	−	0.770615i	$-0.719949\pi$
$653$	−32.5710	−1.27460	−0.637302	+	0.770615i	$0.719949\pi$
$654$	12.8805	0.503666
$655$	4.38597	0.171374
$656$	1.93108	0.0753960
$657$	9.57278	0.373470
$658$	60.4699	2.35736
$659$	0.355944	0.0138656	0.00693281	−	0.999976i	$-0.497793\pi$
$659$	0.355944	0.0138656	0.00693281	+	0.999976i	$0.497793\pi$
$660$	40.9287	1.59315
$661$	30.0296	1.16802	0.584009	−	0.811747i	$-0.301483\pi$
$661$	30.0296	1.16802	0.584009	+	0.811747i	$0.301483\pi$
$662$	−14.4765	−0.562646
$663$	−27.0739	−1.05146
$664$	9.49073	0.368312
$665$	−107.861	−4.18266
$666$	−2.30072	−0.0891512
$667$	4.34897	0.168393
$668$	−1.71062	−0.0661860
$669$	3.67424	0.142054
$670$	2.15411	0.0832206
$671$	−25.6860	−0.991597
$672$	9.54009	0.368017
$673$	−11.6654	−0.449668	−0.224834	−	0.974397i	$-0.572184\pi$
$673$	−11.6654	−0.449668	−0.224834	+	0.974397i	$0.572184\pi$
$674$	3.37344	0.129940
$675$	−44.4932	−1.71254
$676$	8.18141	0.314670
$677$	25.9711	0.998151	0.499075	−	0.866559i	$-0.333673\pi$
$677$	25.9711	0.998151	0.499075	+	0.866559i	$0.333673\pi$
$678$	6.22288	0.238988
$679$	26.4109	1.01356
$680$	−12.1198	−0.464773
$681$	49.1081	1.88183
$682$	−40.9255	−1.56712
$683$	19.3221	0.739341	0.369670	−	0.929163i	$-0.379471\pi$
$683$	19.3221	0.739341	0.369670	+	0.929163i	$0.379471\pi$
$684$	8.40685	0.321444
$685$	−44.3632	−1.69503
$686$	27.2581	1.04072
$687$	9.46340	0.361051
$688$	9.47514	0.361236
$689$	−45.2481	−1.72382
$690$	9.33703	0.355455
$691$	9.67864	0.368193	0.184096	−	0.982908i	$-0.441064\pi$
$691$	9.67864	0.368193	0.184096	+	0.982908i	$0.441064\pi$
$692$	−17.9779	−0.683417
$693$	−30.0936	−1.14316
$694$	13.9040	0.527788
$695$	47.1837	1.78978
$696$	−9.25825	−0.350933
$697$	5.33617	0.202122
$698$	−8.53760	−0.323153
$699$	−55.8570	−2.11270
$700$	63.8000	2.41141
$701$	−25.9286	−0.979312	−0.489656	−	0.871916i	$-0.662878\pi$
$701$	−25.9286	−0.979312	−0.489656	+	0.871916i	$0.662878\pi$
$702$	14.3833	0.542864
$703$	−8.24150	−0.310834
$704$	−4.38348	−0.165209
$705$	−125.991	−4.74508
$706$	15.1807	0.571333
$707$	81.8150	3.07697
$708$	−23.4301	−0.880558
$709$	−27.8732	−1.04680	−0.523399	−	0.852088i	$-0.675336\pi$
$709$	−27.8732	−1.04680	−0.523399	+	0.852088i	$0.675336\pi$
$710$	11.3204	0.424846
$711$	11.7051	0.438975
$712$	−10.0731	−0.377507
$713$	−9.33631	−0.349648
$714$	26.3622	0.986582
$715$	−88.4835	−3.30910
$716$	22.2441	0.831299
$717$	23.6567	0.883474
$718$	16.9228	0.631552
$719$	−4.93565	−0.184069	−0.0920344	−	0.995756i	$-0.529337\pi$
$719$	−4.93565	−0.184069	−0.0920344	+	0.995756i	$0.529337\pi$
$720$	−6.71911	−0.250406
$721$	0.940188	0.0350144
$722$	11.1145	0.413639
$723$	−56.5849	−2.10441
$724$	−15.7787	−0.586410
$725$	−61.9152	−2.29947
$726$	17.4882	0.649048
$727$	0.747446	0.0277213	0.0138606	−	0.999904i	$-0.495588\pi$
$727$	0.747446	0.0277213	0.0138606	+	0.999904i	$0.495588\pi$
$728$	−20.6247	−0.764401
$729$	2.72644	0.100979
$730$	−27.4068	−1.01437
$731$	26.1828	0.968405
$732$	12.4744	0.461068
$733$	−34.0747	−1.25858	−0.629290	−	0.777171i	$-0.716654\pi$
$733$	−34.0747	−1.25858	−0.629290	+	0.777171i	$0.716654\pi$
$734$	31.9695	1.18002
$735$	−122.152	−4.50565
$736$	−1.00000	−0.0368605
$737$	2.15289	0.0793026
$738$	2.95832	0.108897
$739$	33.1527	1.21954	0.609771	−	0.792577i	$-0.291261\pi$
$739$	33.1527	1.21954	0.609771	+	0.792577i	$0.291261\pi$
$740$	6.58695	0.242141
$741$	−53.7660	−1.97514
$742$	44.0588	1.61745
$743$	−15.5089	−0.568965	−0.284483	−	0.958681i	$-0.591822\pi$
$743$	−15.5089	−0.568965	−0.284483	+	0.958681i	$0.591822\pi$
$744$	19.8755	0.728671
$745$	7.70077	0.282134
$746$	6.72390	0.246179
$747$	14.5394	0.531967
$748$	−12.1129	−0.442892
$749$	−82.7374	−3.02316
$750$	−86.2438	−3.14918
$751$	−26.2470	−0.957768	−0.478884	−	0.877878i	$-0.658959\pi$
$751$	−26.2470	−0.957768	−0.478884	+	0.877878i	$0.658959\pi$
$752$	13.4937	0.492063
$753$	20.6619	0.752960
$754$	20.0154	0.728917
$755$	−25.0200	−0.910571
$756$	−14.0053	−0.509367
$757$	−10.0832	−0.366480	−0.183240	−	0.983068i	$-0.558659\pi$
$757$	−10.0832	−0.366480	−0.183240	+	0.983068i	$0.558659\pi$
$758$	8.36796	0.303938
$759$	9.33172	0.338720
$760$	−24.0688	−0.873065
$761$	−41.2254	−1.49442	−0.747210	−	0.664588i	$-0.768607\pi$
$761$	−41.2254	−1.49442	−0.747210	+	0.664588i	$0.768607\pi$
$762$	−33.7852	−1.22391
$763$	27.1143	0.981603
$764$	−16.6139	−0.601070
$765$	−18.5670	−0.671291
$766$	22.3260	0.806670
$767$	50.6535	1.82899
$768$	2.12884	0.0768178
$769$	23.1805	0.835911	0.417955	−	0.908468i	$-0.362747\pi$
$769$	23.1805	0.835911	0.417955	+	0.908468i	$0.362747\pi$
$770$	86.1578	3.10491
$771$	16.6176	0.598469
$772$	−8.24167	−0.296624
$773$	7.45648	0.268191	0.134095	−	0.990968i	$-0.457187\pi$
$773$	7.45648	0.268191	0.134095	+	0.990968i	$0.457187\pi$
$774$	14.5155	0.521748
$775$	132.919	4.77458
$776$	5.89350	0.211564
$777$	−14.3275	−0.513997
$778$	14.7618	0.529237
$779$	10.5971	0.379681
$780$	42.9720	1.53865
$781$	11.3140	0.404845
$782$	−2.76331	−0.0988158
$783$	13.5915	0.485722
$784$	13.0826	0.467234
$785$	−60.9584	−2.17570
$786$	−2.12884	−0.0759332
$787$	−39.8333	−1.41990	−0.709952	−	0.704250i	$-0.751284\pi$
$787$	−39.8333	−1.41990	−0.709952	+	0.704250i	$0.751284\pi$
$788$	15.9992	0.569949
$789$	31.1527	1.10906
$790$	−33.5116	−1.19229
$791$	13.0996	0.465768
$792$	−6.71529	−0.238617
$793$	−26.9684	−0.957676
$794$	−32.5136	−1.15387
$795$	−91.7977	−3.25573
$796$	14.7360	0.522304
$797$	−1.12825	−0.0399647	−0.0199823	−	0.999800i	$-0.506361\pi$
$797$	−1.12825	−0.0399647	−0.0199823	+	0.999800i	$0.506361\pi$
$798$	52.3528	1.85327
$799$	37.2872	1.31913
$800$	14.2367	0.503345
$801$	−15.4316	−0.545248
$802$	−1.13193	−0.0399697
$803$	−27.3912	−0.966616
$804$	−1.04555	−0.0368737
$805$	19.6551	0.692751
$806$	−42.9688	−1.51351
$807$	−17.0670	−0.600786
$808$	18.2567	0.642270
$809$	−13.3453	−0.469197	−0.234599	−	0.972092i	$-0.575378\pi$
$809$	−13.3453	−0.469197	−0.234599	+	0.972092i	$0.575378\pi$
$810$	49.3377	1.73355
$811$	36.6694	1.28764	0.643818	−	0.765179i	$-0.277349\pi$
$811$	36.6694	1.28764	0.643818	+	0.765179i	$0.277349\pi$
$812$	−19.4893	−0.683940
$813$	−10.0606	−0.352841
$814$	6.58321	0.230741
$815$	44.8303	1.57034
$816$	5.88264	0.205934
$817$	51.9964	1.81912
$818$	−30.1520	−1.05424
$819$	−31.5960	−1.10405
$820$	−8.46966	−0.295773
$821$	−25.7999	−0.900424	−0.450212	−	0.892922i	$-0.648652\pi$
$821$	−25.7999	−0.900424	−0.450212	+	0.892922i	$0.648652\pi$
$822$	21.5328	0.751041
$823$	−15.7690	−0.549674	−0.274837	−	0.961491i	$-0.588624\pi$
$823$	−15.7690	−0.549674	−0.274837	+	0.961491i	$0.588624\pi$
$824$	0.209800	0.00730872
$825$	−132.853	−4.62536
$826$	−49.3221	−1.71613
$827$	27.4183	0.953426	0.476713	−	0.879059i	$-0.341828\pi$
$827$	27.4183	0.953426	0.476713	+	0.879059i	$0.341828\pi$
$828$	−1.53195	−0.0532391
$829$	18.1047	0.628801	0.314400	−	0.949290i	$-0.398197\pi$
$829$	18.1047	0.628801	0.314400	+	0.949290i	$0.398197\pi$
$830$	−41.6261	−1.44486
$831$	52.8296	1.83264
$832$	−4.60233	−0.159557
$833$	36.1512	1.25256
$834$	−22.9017	−0.793022
$835$	7.50274	0.259643
$836$	−24.0551	−0.831962
$837$	−29.1782	−1.00854
$838$	9.58233	0.331016
$839$	−0.502811	−0.0173589	−0.00867947	−	0.999962i	$-0.502763\pi$
$839$	−0.502811	−0.0173589	−0.00867947	+	0.999962i	$0.502763\pi$
$840$	−41.8425	−1.44371
$841$	−10.0865	−0.347809
$842$	−15.7434	−0.542554
$843$	−48.8027	−1.68085
$844$	−7.11568	−0.244932
$845$	−35.8834	−1.23443
$846$	20.6717	0.710706
$847$	36.8139	1.26494
$848$	9.83158	0.337618
$849$	−21.9194	−0.752273
$850$	39.3406	1.34937
$851$	1.50182	0.0514818
$852$	−5.49463	−0.188243
$853$	41.1878	1.41024	0.705122	−	0.709086i	$-0.250892\pi$
$853$	41.1878	1.41024	0.705122	+	0.709086i	$0.250892\pi$
$854$	26.2595	0.898583
$855$	−36.8722	−1.26100
$856$	−18.4626	−0.631038
$857$	−7.15739	−0.244492	−0.122246	−	0.992500i	$-0.539010\pi$
$857$	−7.15739	−0.244492	−0.122246	+	0.992500i	$0.539010\pi$
$858$	42.9476	1.46621
$859$	−57.6750	−1.96785	−0.983923	−	0.178591i	$-0.942846\pi$
$859$	−57.6750	−1.96785	−0.983923	+	0.178591i	$0.942846\pi$
$860$	−41.5577	−1.41711
$861$	18.4227	0.627843
$862$	36.6246	1.24744
$863$	−48.9007	−1.66460	−0.832300	−	0.554326i	$-0.812976\pi$
$863$	−48.9007	−1.66460	−0.832300	+	0.554326i	$0.812976\pi$
$864$	−3.12523	−0.106323
$865$	78.8506	2.68100
$866$	−41.5245	−1.41106
$867$	−19.9347	−0.677017
$868$	41.8394	1.42012
$869$	−33.4925	−1.13616
$870$	40.6064	1.37669
$871$	2.26037	0.0765897
$872$	6.05047	0.204895
$873$	9.02858	0.305571
$874$	−5.48767	−0.185623
$875$	−181.549	−6.13749
$876$	13.3026	0.449452
$877$	−22.6892	−0.766159	−0.383079	−	0.923715i	$-0.625136\pi$
$877$	−22.6892	−0.766159	−0.383079	+	0.923715i	$0.625136\pi$
$878$	−7.20466	−0.243145
$879$	30.3343	1.02315
$880$	19.2258	0.648102
$881$	−25.1012	−0.845680	−0.422840	−	0.906204i	$-0.638967\pi$
$881$	−25.1012	−0.845680	−0.422840	+	0.906204i	$0.638967\pi$
$882$	20.0419	0.674845
$883$	31.0168	1.04380	0.521900	−	0.853007i	$-0.325223\pi$
$883$	31.0168	1.04380	0.521900	+	0.853007i	$0.325223\pi$
$884$	−12.7177	−0.427741
$885$	102.764	3.45437
$886$	−21.9655	−0.737945
$887$	2.31434	0.0777081	0.0388540	−	0.999245i	$-0.487629\pi$
$887$	2.31434	0.0777081	0.0388540	+	0.999245i	$0.487629\pi$
$888$	−3.19714	−0.107289
$889$	−71.1203	−2.38530
$890$	44.1805	1.48093
$891$	49.3097	1.65194
$892$	1.72594	0.0577886
$893$	74.0487	2.47795
$894$	−3.73776	−0.125009
$895$	−97.5618	−3.26113
$896$	4.48136	0.149712
$897$	9.79761	0.327133
$898$	8.68603	0.289857
$899$	−40.6033	−1.35420
$900$	21.8100	0.727001
$901$	27.1677	0.905088
$902$	−8.46485	−0.281849
$903$	90.3937	3.00811
$904$	2.92313	0.0972220
$905$	69.2048	2.30045
$906$	12.1441	0.403460
$907$	22.2295	0.738117	0.369059	−	0.929406i	$-0.379680\pi$
$907$	22.2295	0.738117	0.369059	+	0.929406i	$0.379680\pi$
$908$	23.0680	0.765539
$909$	27.9685	0.927656
$910$	90.4592	2.99869
$911$	−42.7460	−1.41624	−0.708119	−	0.706093i	$-0.750456\pi$
$911$	−42.7460	−1.41624	−0.708119	+	0.706093i	$0.750456\pi$
$912$	11.6824	0.386842
$913$	−41.6024	−1.37684
$914$	22.4249	0.741751
$915$	−54.7124	−1.80874
$916$	4.44534	0.146878
$917$	−4.48136	−0.147987
$918$	−8.63599	−0.285030
$919$	3.90579	0.128840	0.0644200	−	0.997923i	$-0.479480\pi$
$919$	3.90579	0.128840	0.0644200	+	0.997923i	$0.479480\pi$
$920$	4.38597	0.144601
$921$	−47.7171	−1.57233
$922$	−28.3632	−0.934094
$923$	11.8788	0.390996
$924$	−41.8188	−1.37574
$925$	−21.3811	−0.703005
$926$	−6.98396	−0.229507
$927$	0.321404	0.0105563
$928$	−4.34897	−0.142762
$929$	−12.8352	−0.421108	−0.210554	−	0.977582i	$-0.567527\pi$
$929$	−12.8352	−0.421108	−0.210554	+	0.977582i	$0.567527\pi$
$930$	−87.1734	−2.85853
$931$	71.7927	2.35291
$932$	−26.2382	−0.859462
$933$	39.3419	1.28800
$934$	17.0703	0.558557
$935$	53.1269	1.73744
$936$	−7.05055	−0.230454
$937$	26.1094	0.852956	0.426478	−	0.904498i	$-0.359754\pi$
$937$	26.1094	0.852956	0.426478	+	0.904498i	$0.359754\pi$
$938$	−2.20096	−0.0718638
$939$	−14.7597	−0.481665
$940$	−59.1828	−1.93033
$941$	−15.2261	−0.496357	−0.248178	−	0.968714i	$-0.579832\pi$
$941$	−15.2261	−0.496357	−0.248178	+	0.968714i	$0.579832\pi$
$942$	29.5877	0.964018
$943$	−1.93108	−0.0628846
$944$	−11.0061	−0.358217
$945$	61.4268	1.99821
$946$	−41.5341	−1.35039
$947$	−27.6530	−0.898600	−0.449300	−	0.893381i	$-0.648327\pi$
$947$	−27.6530	−0.898600	−0.449300	+	0.893381i	$0.648327\pi$
$948$	16.2657	0.528284
$949$	−28.7588	−0.933549
$950$	78.1265	2.53476
$951$	−45.9855	−1.49118
$952$	12.3834	0.401348
$953$	−45.0304	−1.45868	−0.729339	−	0.684152i	$-0.760172\pi$
$953$	−45.0304	−1.45868	−0.729339	+	0.684152i	$0.760172\pi$
$954$	15.0615	0.487635
$955$	72.8681	2.35796
$956$	11.1125	0.359403
$957$	40.5834	1.31187
$958$	7.59890	0.245509
$959$	45.3280	1.46372
$960$	−9.33703	−0.301351
$961$	56.1668	1.81183
$962$	6.91188	0.222848
$963$	−28.2838	−0.911433
$964$	−26.5802	−0.856089
$965$	36.1477	1.16364
$966$	−9.54009	−0.306947
$967$	12.6337	0.406273	0.203137	−	0.979150i	$-0.434886\pi$
$967$	12.6337	0.406273	0.203137	+	0.979150i	$0.434886\pi$
$968$	8.21490	0.264037
$969$	32.2820	1.03705
$970$	−25.8487	−0.829953
$971$	−35.3054	−1.13300	−0.566502	−	0.824060i	$-0.691704\pi$
$971$	−35.3054	−1.13300	−0.566502	+	0.824060i	$0.691704\pi$
$972$	−14.5716	−0.467383
$973$	−48.2098	−1.54554
$974$	−23.7255	−0.760215
$975$	−139.486	−4.46713
$976$	5.85973	0.187565
$977$	0.808523	0.0258669	0.0129335	−	0.999916i	$-0.495883\pi$
$977$	0.808523	0.0258669	0.0129335	+	0.999916i	$0.495883\pi$
$978$	−21.7595	−0.695791
$979$	44.1554	1.41121
$980$	−57.3797	−1.83293
$981$	9.26903	0.295937
$982$	13.8061	0.440569
$983$	−32.5552	−1.03835	−0.519176	−	0.854668i	$-0.673761\pi$
$983$	−32.5552	−1.03835	−0.519176	+	0.854668i	$0.673761\pi$
$984$	4.11096	0.131052
$985$	−70.1722	−2.23587
$986$	−12.0176	−0.382717
$987$	128.731	4.09754
$988$	−25.2560	−0.803502
$989$	−9.47514	−0.301292
$990$	29.4531	0.936080
$991$	6.74231	0.214177	0.107088	−	0.994250i	$-0.465847\pi$
$991$	6.74231	0.214177	0.107088	+	0.994250i	$0.465847\pi$
$992$	9.33631	0.296428
$993$	−30.8182	−0.977985
$994$	−11.5666	−0.366870
$995$	−64.6317	−2.04896
$996$	20.2042	0.640195
$997$	28.7682	0.911099	0.455549	−	0.890211i	$-0.349443\pi$
$997$	28.7682	0.911099	0.455549	+	0.890211i	$0.349443\pi$
$998$	−6.25483	−0.197993
$999$	4.69354	0.148497

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.k.1.27	✓	35

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.k.1.27	✓	35	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:	\( N \)	\(=\)	\( 6026 = 2 \cdot 23 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6026.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.12884 q^{3} +1.00000 q^{4} -4.38597 q^{5} +2.12884 q^{6} +4.48136 q^{7} +1.00000 q^{8} +1.53195 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.12884 q^{3} +1.00000 q^{4} -4.38597 q^{5} +2.12884 q^{6} +4.48136 q^{7} +1.00000 q^{8} +1.53195 q^{9} -4.38597 q^{10} -4.38348 q^{11} +2.12884 q^{12} -4.60233 q^{13} +4.48136 q^{14} -9.33703 q^{15} +1.00000 q^{16} +2.76331 q^{17} +1.53195 q^{18} +5.48767 q^{19} -4.38597 q^{20} +9.54009 q^{21} -4.38348 q^{22} -1.00000 q^{23} +2.12884 q^{24} +14.2367 q^{25} -4.60233 q^{26} -3.12523 q^{27} +4.48136 q^{28} -4.34897 q^{29} -9.33703 q^{30} +9.33631 q^{31} +1.00000 q^{32} -9.33172 q^{33} +2.76331 q^{34} -19.6551 q^{35} +1.53195 q^{36} -1.50182 q^{37} +5.48767 q^{38} -9.79761 q^{39} -4.38597 q^{40} +1.93108 q^{41} +9.54009 q^{42} +9.47514 q^{43} -4.38348 q^{44} -6.71911 q^{45} -1.00000 q^{46} +13.4937 q^{47} +2.12884 q^{48} +13.0826 q^{49} +14.2367 q^{50} +5.88264 q^{51} -4.60233 q^{52} +9.83158 q^{53} -3.12523 q^{54} +19.2258 q^{55} +4.48136 q^{56} +11.6824 q^{57} -4.34897 q^{58} -11.0061 q^{59} -9.33703 q^{60} +5.85973 q^{61} +9.33631 q^{62} +6.86523 q^{63} +1.00000 q^{64} +20.1857 q^{65} -9.33172 q^{66} -0.491136 q^{67} +2.76331 q^{68} -2.12884 q^{69} -19.6551 q^{70} -2.58104 q^{71} +1.53195 q^{72} +6.24874 q^{73} -1.50182 q^{74} +30.3077 q^{75} +5.48767 q^{76} -19.6439 q^{77} -9.79761 q^{78} +7.64063 q^{79} -4.38597 q^{80} -11.2490 q^{81} +1.93108 q^{82} +9.49073 q^{83} +9.54009 q^{84} -12.1198 q^{85} +9.47514 q^{86} -9.25825 q^{87} -4.38348 q^{88} -10.0731 q^{89} -6.71911 q^{90} -20.6247 q^{91} -1.00000 q^{92} +19.8755 q^{93} +13.4937 q^{94} -24.0688 q^{95} +2.12884 q^{96} +5.89350 q^{97} +13.0826 q^{98} -6.71529 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 35 q + 35 q^{2} - 3 q^{3} + 35 q^{4} + 10 q^{5} - 3 q^{6} + 14 q^{7} + 35 q^{8} + 54 q^{9}+O(q^{10}) \) 35 * q + 35 * q^2 - 3 * q^3 + 35 * q^4 + 10 * q^5 - 3 * q^6 + 14 * q^7 + 35 * q^8 + 54 * q^9	\( 35 q + 35 q^{2} - 3 q^{3} + 35 q^{4} + 10 q^{5} - 3 q^{6} + 14 q^{7} + 35 q^{8} + 54 q^{9} + 10 q^{10} + 9 q^{11} - 3 q^{12} + 19 q^{13} + 14 q^{14} + 14 q^{15} + 35 q^{16} + 28 q^{17} + 54 q^{18} + 21 q^{19} + 10 q^{20} + 28 q^{21} + 9 q^{22} - 35 q^{23} - 3 q^{24} + 81 q^{25} + 19 q^{26} - 21 q^{27} + 14 q^{28} + 35 q^{29} + 14 q^{30} + 5 q^{31} + 35 q^{32} + 26 q^{33} + 28 q^{34} - 7 q^{35} + 54 q^{36} + 51 q^{37} + 21 q^{38} + 21 q^{39} + 10 q^{40} + 3 q^{41} + 28 q^{42} + 43 q^{43} + 9 q^{44} + 2 q^{45} - 35 q^{46} + 10 q^{47} - 3 q^{48} + 85 q^{49} + 81 q^{50} + 26 q^{51} + 19 q^{52} + 39 q^{53} - 21 q^{54} + 2 q^{55} + 14 q^{56} + 50 q^{57} + 35 q^{58} - 42 q^{59} + 14 q^{60} + 47 q^{61} + 5 q^{62} + 23 q^{63} + 35 q^{64} + 61 q^{65} + 26 q^{66} + 22 q^{67} + 28 q^{68} + 3 q^{69} - 7 q^{70} + 54 q^{72} + 30 q^{73} + 51 q^{74} - 26 q^{75} + 21 q^{76} + 2 q^{77} + 21 q^{78} + 55 q^{79} + 10 q^{80} + 67 q^{81} + 3 q^{82} + 20 q^{83} + 28 q^{84} + 28 q^{85} + 43 q^{86} + 29 q^{87} + 9 q^{88} - 31 q^{89} + 2 q^{90} + 32 q^{91} - 35 q^{92} + 11 q^{93} + 10 q^{94} + 16 q^{95} - 3 q^{96} + 36 q^{97} + 85 q^{98} - 9 q^{99}+O(q^{100}) \) 35 * q + 35 * q^2 - 3 * q^3 + 35 * q^4 + 10 * q^5 - 3 * q^6 + 14 * q^7 + 35 * q^8 + 54 * q^9 + 10 * q^10 + 9 * q^11 - 3 * q^12 + 19 * q^13 + 14 * q^14 + 14 * q^15 + 35 * q^16 + 28 * q^17 + 54 * q^18 + 21 * q^19 + 10 * q^20 + 28 * q^21 + 9 * q^22 - 35 * q^23 - 3 * q^24 + 81 * q^25 + 19 * q^26 - 21 * q^27 + 14 * q^28 + 35 * q^29 + 14 * q^30 + 5 * q^31 + 35 * q^32 + 26 * q^33 + 28 * q^34 - 7 * q^35 + 54 * q^36 + 51 * q^37 + 21 * q^38 + 21 * q^39 + 10 * q^40 + 3 * q^41 + 28 * q^42 + 43 * q^43 + 9 * q^44 + 2 * q^45 - 35 * q^46 + 10 * q^47 - 3 * q^48 + 85 * q^49 + 81 * q^50 + 26 * q^51 + 19 * q^52 + 39 * q^53 - 21 * q^54 + 2 * q^55 + 14 * q^56 + 50 * q^57 + 35 * q^58 - 42 * q^59 + 14 * q^60 + 47 * q^61 + 5 * q^62 + 23 * q^63 + 35 * q^64 + 61 * q^65 + 26 * q^66 + 22 * q^67 + 28 * q^68 + 3 * q^69 - 7 * q^70 + 54 * q^72 + 30 * q^73 + 51 * q^74 - 26 * q^75 + 21 * q^76 + 2 * q^77 + 21 * q^78 + 55 * q^79 + 10 * q^80 + 67 * q^81 + 3 * q^82 + 20 * q^83 + 28 * q^84 + 28 * q^85 + 43 * q^86 + 29 * q^87 + 9 * q^88 - 31 * q^89 + 2 * q^90 + 32 * q^91 - 35 * q^92 + 11 * q^93 + 10 * q^94 + 16 * q^95 - 3 * q^96 + 36 * q^97 + 85 * q^98 - 9 * q^99

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