LMFDB - Embedded newform 1334.2.a.i.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1334, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1334.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$10.6520436296$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 22x^{6} + 151x^{4} - 332x^{2} + 6 $ x^8 - 22x^6 + 151x^4 - 332*x^2 + 6
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			1.6
Root			$-0.134992$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.77365 q^{3} +1.00000 q^{4} +0.134992 q^{5} +1.77365 q^{6} +1.25283 q^{7} +1.00000 q^{8} +0.145840 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.77365 q^{3} +1.00000 q^{4} +0.134992 q^{5} +1.77365 q^{6} +1.25283 q^{7} +1.00000 q^{8} +0.145840 q^{9} +0.134992 q^{10} -4.38751 q^{11} +1.77365 q^{12} +5.80946 q^{13} +1.25283 q^{14} +0.239429 q^{15} +1.00000 q^{16} +3.23718 q^{17} +0.145840 q^{18} +5.70247 q^{19} +0.134992 q^{20} +2.22208 q^{21} -4.38751 q^{22} -1.00000 q^{23} +1.77365 q^{24} -4.98178 q^{25} +5.80946 q^{26} -5.06229 q^{27} +1.25283 q^{28} -1.00000 q^{29} +0.239429 q^{30} +8.77308 q^{31} +1.00000 q^{32} -7.78192 q^{33} +3.23718 q^{34} +0.169122 q^{35} +0.145840 q^{36} +8.65777 q^{37} +5.70247 q^{38} +10.3040 q^{39} +0.134992 q^{40} -9.04334 q^{41} +2.22208 q^{42} +6.33456 q^{43} -4.38751 q^{44} +0.0196873 q^{45} -1.00000 q^{46} -6.20480 q^{47} +1.77365 q^{48} -5.43043 q^{49} -4.98178 q^{50} +5.74163 q^{51} +5.80946 q^{52} +2.72943 q^{53} -5.06229 q^{54} -0.592280 q^{55} +1.25283 q^{56} +10.1142 q^{57} -1.00000 q^{58} +5.21133 q^{59} +0.239429 q^{60} -1.88158 q^{61} +8.77308 q^{62} +0.182712 q^{63} +1.00000 q^{64} +0.784232 q^{65} -7.78192 q^{66} -5.13139 q^{67} +3.23718 q^{68} -1.77365 q^{69} +0.169122 q^{70} -9.21641 q^{71} +0.145840 q^{72} -16.1998 q^{73} +8.65777 q^{74} -8.83594 q^{75} +5.70247 q^{76} -5.49679 q^{77} +10.3040 q^{78} -2.83851 q^{79} +0.134992 q^{80} -9.41625 q^{81} -9.04334 q^{82} -10.1730 q^{83} +2.22208 q^{84} +0.436994 q^{85} +6.33456 q^{86} -1.77365 q^{87} -4.38751 q^{88} -12.0587 q^{89} +0.0196873 q^{90} +7.27824 q^{91} -1.00000 q^{92} +15.5604 q^{93} -6.20480 q^{94} +0.769790 q^{95} +1.77365 q^{96} -0.677219 q^{97} -5.43043 q^{98} -0.639875 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} + 4 q^{3} + 8 q^{4} + 4 q^{6} + 8 q^{7} + 8 q^{8} + 12 q^{9}+O(q^{10}) $ 8 * q + 8 * q^2 + 4 * q^3 + 8 * q^4 + 4 * q^6 + 8 * q^7 + 8 * q^8 + 12 * q^9	$ 8 q + 8 q^{2} + 4 q^{3} + 8 q^{4} + 4 q^{6} + 8 q^{7} + 8 q^{8} + 12 q^{9} + 8 q^{11} + 4 q^{12} + 4 q^{13} + 8 q^{14} + 8 q^{16} + 8 q^{17} + 12 q^{18} + 16 q^{19} - 4 q^{21} + 8 q^{22} - 8 q^{23} + 4 q^{24} + 4 q^{25} + 4 q^{26} + 4 q^{27} + 8 q^{28} - 8 q^{29} + 8 q^{31} + 8 q^{32} + 12 q^{33} + 8 q^{34} + 4 q^{35} + 12 q^{36} + 8 q^{37} + 16 q^{38} - 16 q^{39} + 8 q^{41} - 4 q^{42} + 32 q^{43} + 8 q^{44} - 8 q^{46} + 16 q^{47} + 4 q^{48} + 4 q^{49} + 4 q^{50} + 12 q^{51} + 4 q^{52} + 4 q^{54} + 8 q^{56} + 8 q^{57} - 8 q^{58} - 4 q^{59} + 8 q^{61} + 8 q^{62} + 24 q^{63} + 8 q^{64} - 4 q^{65} + 12 q^{66} + 20 q^{67} + 8 q^{68} - 4 q^{69} + 4 q^{70} - 24 q^{71} + 12 q^{72} - 4 q^{73} + 8 q^{74} - 16 q^{75} + 16 q^{76} - 16 q^{77} - 16 q^{78} + 4 q^{79} - 8 q^{81} + 8 q^{82} - 4 q^{83} - 4 q^{84} - 44 q^{85} + 32 q^{86} - 4 q^{87} + 8 q^{88} + 20 q^{89} - 8 q^{92} - 4 q^{93} + 16 q^{94} - 8 q^{95} + 4 q^{96} + 4 q^{97} + 4 q^{98}+O(q^{100}) $ 8 * q + 8 * q^2 + 4 * q^3 + 8 * q^4 + 4 * q^6 + 8 * q^7 + 8 * q^8 + 12 * q^9 + 8 * q^11 + 4 * q^12 + 4 * q^13 + 8 * q^14 + 8 * q^16 + 8 * q^17 + 12 * q^18 + 16 * q^19 - 4 * q^21 + 8 * q^22 - 8 * q^23 + 4 * q^24 + 4 * q^25 + 4 * q^26 + 4 * q^27 + 8 * q^28 - 8 * q^29 + 8 * q^31 + 8 * q^32 + 12 * q^33 + 8 * q^34 + 4 * q^35 + 12 * q^36 + 8 * q^37 + 16 * q^38 - 16 * q^39 + 8 * q^41 - 4 * q^42 + 32 * q^43 + 8 * q^44 - 8 * q^46 + 16 * q^47 + 4 * q^48 + 4 * q^49 + 4 * q^50 + 12 * q^51 + 4 * q^52 + 4 * q^54 + 8 * q^56 + 8 * q^57 - 8 * q^58 - 4 * q^59 + 8 * q^61 + 8 * q^62 + 24 * q^63 + 8 * q^64 - 4 * q^65 + 12 * q^66 + 20 * q^67 + 8 * q^68 - 4 * q^69 + 4 * q^70 - 24 * q^71 + 12 * q^72 - 4 * q^73 + 8 * q^74 - 16 * q^75 + 16 * q^76 - 16 * q^77 - 16 * q^78 + 4 * q^79 - 8 * q^81 + 8 * q^82 - 4 * q^83 - 4 * q^84 - 44 * q^85 + 32 * q^86 - 4 * q^87 + 8 * q^88 + 20 * q^89 - 8 * q^92 - 4 * q^93 + 16 * q^94 - 8 * q^95 + 4 * q^96 + 4 * q^97 + 4 * q^98

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
$3$	1.77365	1.02402	0.512009	−	0.858980i	$-0.328901\pi$
$3$	1.77365	1.02402	0.512009	+	0.858980i	$0.328901\pi$
$4$	1.00000	0.500000
$5$	0.134992	0.0603704	0.0301852	−	0.999544i	$-0.490390\pi$
$5$	0.134992	0.0603704	0.0301852	+	0.999544i	$0.490390\pi$
$6$	1.77365	0.724090
$7$	1.25283	0.473523	0.236762	−	0.971568i	$-0.423914\pi$
$7$	1.25283	0.473523	0.236762	+	0.971568i	$0.423914\pi$
$8$	1.00000	0.353553
$9$	0.145840	0.0486134
$10$	0.134992	0.0426883
$11$	−4.38751	−1.32288	−0.661442	−	0.749996i	$-0.730055\pi$
$11$	−4.38751	−1.32288	−0.661442	+	0.749996i	$0.730055\pi$
$12$	1.77365	0.512009
$13$	5.80946	1.61125	0.805627	−	0.592423i	$-0.201829\pi$
$13$	5.80946	1.61125	0.805627	+	0.592423i	$0.201829\pi$
$14$	1.25283	0.334832
$15$	0.239429	0.0618204
$16$	1.00000	0.250000
$17$	3.23718	0.785131	0.392566	−	0.919724i	$-0.371588\pi$
$17$	3.23718	0.785131	0.392566	+	0.919724i	$0.371588\pi$
$18$	0.145840	0.0343748
$19$	5.70247	1.30824	0.654119	−	0.756392i	$-0.273040\pi$
$19$	5.70247	1.30824	0.654119	+	0.756392i	$0.273040\pi$
$20$	0.134992	0.0301852
$21$	2.22208	0.484897
$22$	−4.38751	−0.935421
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	1.77365	0.362045
$25$	−4.98178	−0.996355
$26$	5.80946	1.13933
$27$	−5.06229	−0.974237
$28$	1.25283	0.236762
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	0.239429	0.0437136
$31$	8.77308	1.57569	0.787846	−	0.615872i	$-0.211196\pi$
$31$	8.77308	1.57569	0.787846	+	0.615872i	$0.211196\pi$
$32$	1.00000	0.176777
$33$	−7.78192	−1.35466
$34$	3.23718	0.555172
$35$	0.169122	0.0285868
$36$	0.145840	0.0243067
$37$	8.65777	1.42333	0.711665	−	0.702519i	$-0.247942\pi$
$37$	8.65777	1.42333	0.711665	+	0.702519i	$0.247942\pi$
$38$	5.70247	0.925064
$39$	10.3040	1.64995
$40$	0.134992	0.0213442
$41$	−9.04334	−1.41233	−0.706166	−	0.708046i	$-0.749577\pi$
$41$	−9.04334	−1.41233	−0.706166	+	0.708046i	$0.749577\pi$
$42$	2.22208	0.342874
$43$	6.33456	0.966011	0.483006	−	0.875617i	$-0.339545\pi$
$43$	6.33456	0.966011	0.483006	+	0.875617i	$0.339545\pi$
$44$	−4.38751	−0.661442
$45$	0.0196873	0.00293481
$46$	−1.00000	−0.147442
$47$	−6.20480	−0.905063	−0.452532	−	0.891748i	$-0.649479\pi$
$47$	−6.20480	−0.905063	−0.452532	+	0.891748i	$0.649479\pi$
$48$	1.77365	0.256005
$49$	−5.43043	−0.775776
$50$	−4.98178	−0.704530
$51$	5.74163	0.803989
$52$	5.80946	0.805627
$53$	2.72943	0.374917	0.187458	−	0.982273i	$-0.439975\pi$
$53$	2.72943	0.374917	0.187458	+	0.982273i	$0.439975\pi$
$54$	−5.06229	−0.688890
$55$	−0.592280	−0.0798631
$56$	1.25283	0.167416
$57$	10.1142	1.33966
$58$	−1.00000	−0.131306
$59$	5.21133	0.678458	0.339229	−	0.940704i	$-0.389834\pi$
$59$	5.21133	0.678458	0.339229	+	0.940704i	$0.389834\pi$
$60$	0.239429	0.0309102
$61$	−1.88158	−0.240912	−0.120456	−	0.992719i	$-0.538436\pi$
$61$	−1.88158	−0.240912	−0.120456	+	0.992719i	$0.538436\pi$
$62$	8.77308	1.11418
$63$	0.182712	0.0230196
$64$	1.00000	0.125000
$65$	0.784232	0.0972721
$66$	−7.78192	−0.957888
$67$	−5.13139	−0.626899	−0.313450	−	0.949605i	$-0.601485\pi$
$67$	−5.13139	−0.626899	−0.313450	+	0.949605i	$0.601485\pi$
$68$	3.23718	0.392566
$69$	−1.77365	−0.213523
$70$	0.169122	0.0202139
$71$	−9.21641	−1.09379	−0.546893	−	0.837202i	$-0.684190\pi$
$71$	−9.21641	−1.09379	−0.546893	+	0.837202i	$0.684190\pi$
$72$	0.145840	0.0171874
$73$	−16.1998	−1.89604	−0.948020	−	0.318211i	$-0.896918\pi$
$73$	−16.1998	−1.89604	−0.948020	+	0.318211i	$0.896918\pi$
$74$	8.65777	1.00645
$75$	−8.83594	−1.02029
$76$	5.70247	0.654119
$77$	−5.49679	−0.626417
$78$	10.3040	1.16669
$79$	−2.83851	−0.319358	−0.159679	−	0.987169i	$-0.551046\pi$
$79$	−2.83851	−0.319358	−0.159679	+	0.987169i	$0.551046\pi$
$80$	0.134992	0.0150926
$81$	−9.41625	−1.04625
$82$	−9.04334	−0.998670
$83$	−10.1730	−1.11664	−0.558318	−	0.829627i	$-0.688553\pi$
$83$	−10.1730	−1.11664	−0.558318	+	0.829627i	$0.688553\pi$
$84$	2.22208	0.242448
$85$	0.436994	0.0473987
$86$	6.33456	0.683073
$87$	−1.77365	−0.190155
$88$	−4.38751	−0.467710
$89$	−12.0587	−1.27821	−0.639107	−	0.769117i	$-0.720696\pi$
$89$	−12.0587	−1.27821	−0.639107	+	0.769117i	$0.720696\pi$
$90$	0.0196873	0.00207522
$91$	7.27824	0.762967
$92$	−1.00000	−0.104257
$93$	15.5604	1.61354
$94$	−6.20480	−0.639976
$95$	0.769790	0.0789788
$96$	1.77365	0.181023
$97$	−0.677219	−0.0687612	−0.0343806	−	0.999409i	$-0.510946\pi$
$97$	−0.677219	−0.0687612	−0.0343806	+	0.999409i	$0.510946\pi$
$98$	−5.43043	−0.548556
$99$	−0.639875	−0.0643099
$100$	−4.98178	−0.498178
$101$	−6.61819	−0.658534	−0.329267	−	0.944237i	$-0.606802\pi$
$101$	−6.61819	−0.658534	−0.329267	+	0.944237i	$0.606802\pi$
$102$	5.74163	0.568506
$103$	11.3531	1.11865	0.559326	−	0.828948i	$-0.311060\pi$
$103$	11.3531	1.11865	0.559326	+	0.828948i	$0.311060\pi$
$104$	5.80946	0.569664
$105$	0.299963	0.0292734
$106$	2.72943	0.265106
$107$	7.73978	0.748233	0.374116	−	0.927382i	$-0.377946\pi$
$107$	7.73978	0.748233	0.374116	+	0.927382i	$0.377946\pi$
$108$	−5.06229	−0.487119
$109$	−4.80109	−0.459861	−0.229930	−	0.973207i	$-0.573850\pi$
$109$	−4.80109	−0.459861	−0.229930	+	0.973207i	$0.573850\pi$
$110$	−0.592280	−0.0564717
$111$	15.3559	1.45752
$112$	1.25283	0.118381
$113$	10.6653	1.00331	0.501654	−	0.865068i	$-0.332725\pi$
$113$	10.6653	1.00331	0.501654	+	0.865068i	$0.332725\pi$
$114$	10.1142	0.947282
$115$	−0.134992	−0.0125881
$116$	−1.00000	−0.0928477
$117$	0.847252	0.0783285
$118$	5.21133	0.479742
$119$	4.05562	0.371778
$120$	0.239429	0.0218568
$121$	8.25027	0.750025
$122$	−1.88158	−0.170351
$123$	−16.0397	−1.44625
$124$	8.77308	0.787846
$125$	−1.34746	−0.120521
$126$	0.182712	0.0162773
$127$	−13.7905	−1.22371	−0.611855	−	0.790970i	$-0.709576\pi$
$127$	−13.7905	−1.22371	−0.611855	+	0.790970i	$0.709576\pi$
$128$	1.00000	0.0883883
$129$	11.2353	0.989213
$130$	0.784232	0.0687817
$131$	−20.3940	−1.78183	−0.890915	−	0.454170i	$-0.849936\pi$
$131$	−20.3940	−1.78183	−0.890915	+	0.454170i	$0.849936\pi$
$132$	−7.78192	−0.677329
$133$	7.14420	0.619481
$134$	−5.13139	−0.443285
$135$	−0.683370	−0.0588151
$136$	3.23718	0.277586
$137$	13.2830	1.13485	0.567423	−	0.823427i	$-0.307941\pi$
$137$	13.2830	1.13485	0.567423	+	0.823427i	$0.307941\pi$
$138$	−1.77365	−0.150983
$139$	13.7556	1.16674	0.583368	−	0.812208i	$-0.301734\pi$
$139$	13.7556	1.16674	0.583368	+	0.812208i	$0.301734\pi$
$140$	0.169122	0.0142934
$141$	−11.0052	−0.926801
$142$	−9.21641	−0.773424
$143$	−25.4891	−2.13150
$144$	0.145840	0.0121533
$145$	−0.134992	−0.0112105
$146$	−16.1998	−1.34070
$147$	−9.63169	−0.794408
$148$	8.65777	0.711665
$149$	8.21740	0.673196	0.336598	−	0.941649i	$-0.390724\pi$
$149$	8.21740	0.673196	0.336598	+	0.941649i	$0.390724\pi$
$150$	−8.83594	−0.721451
$151$	2.46908	0.200931	0.100466	−	0.994941i	$-0.467967\pi$
$151$	2.46908	0.200931	0.100466	+	0.994941i	$0.467967\pi$
$152$	5.70247	0.462532
$153$	0.472110	0.0381679
$154$	−5.49679	−0.442944
$155$	1.18430	0.0951251
$156$	10.3040	0.824977
$157$	3.67018	0.292913	0.146456	−	0.989217i	$-0.453213\pi$
$157$	3.67018	0.292913	0.146456	+	0.989217i	$0.453213\pi$
$158$	−2.83851	−0.225820
$159$	4.84106	0.383921
$160$	0.134992	0.0106721
$161$	−1.25283	−0.0987365
$162$	−9.41625	−0.739811
$163$	4.88506	0.382627	0.191314	−	0.981529i	$-0.438725\pi$
$163$	4.88506	0.382627	0.191314	+	0.981529i	$0.438725\pi$
$164$	−9.04334	−0.706166
$165$	−1.05050	−0.0817813
$166$	−10.1730	−0.789580
$167$	−0.401990	−0.0311069	−0.0155535	−	0.999879i	$-0.504951\pi$
$167$	−0.401990	−0.0311069	−0.0155535	+	0.999879i	$0.504951\pi$
$168$	2.22208	0.171437
$169$	20.7498	1.59614
$170$	0.436994	0.0335159
$171$	0.831649	0.0635978
$172$	6.33456	0.483006
$173$	9.22224	0.701154	0.350577	−	0.936534i	$-0.385986\pi$
$173$	9.22224	0.701154	0.350577	+	0.936534i	$0.385986\pi$
$174$	−1.77365	−0.134460
$175$	−6.24130	−0.471798
$176$	−4.38751	−0.330721
$177$	9.24309	0.694753
$178$	−12.0587	−0.903834
$179$	−4.81089	−0.359583	−0.179791	−	0.983705i	$-0.557542\pi$
$179$	−4.81089	−0.359583	−0.179791	+	0.983705i	$0.557542\pi$
$180$	0.0196873	0.00146740
$181$	−21.4966	−1.59783	−0.798915	−	0.601444i	$-0.794592\pi$
$181$	−21.4966	−1.59783	−0.798915	+	0.601444i	$0.794592\pi$
$182$	7.27824	0.539499
$183$	−3.33728	−0.246699
$184$	−1.00000	−0.0737210
$185$	1.16873	0.0859270
$186$	15.5604	1.14094
$187$	−14.2032	−1.03864
$188$	−6.20480	−0.452532
$189$	−6.34216	−0.461324
$190$	0.769790	0.0558465
$191$	−1.68863	−0.122185	−0.0610926	−	0.998132i	$-0.519458\pi$
$191$	−1.68863	−0.122185	−0.0610926	+	0.998132i	$0.519458\pi$
$192$	1.77365	0.128002
$193$	11.9427	0.859652	0.429826	−	0.902912i	$-0.358575\pi$
$193$	11.9427	0.859652	0.429826	+	0.902912i	$0.358575\pi$
$194$	−0.677219	−0.0486215
$195$	1.39096	0.0996084
$196$	−5.43043	−0.387888
$197$	6.44607	0.459263	0.229632	−	0.973278i	$-0.426248\pi$
$197$	6.44607	0.459263	0.229632	+	0.973278i	$0.426248\pi$
$198$	−0.639875	−0.0454740
$199$	−20.4551	−1.45002	−0.725010	−	0.688738i	$-0.758165\pi$
$199$	−20.4551	−1.45002	−0.725010	+	0.688738i	$0.758165\pi$
$200$	−4.98178	−0.352265
$201$	−9.10130	−0.641956
$202$	−6.61819	−0.465654
$203$	−1.25283	−0.0879311
$204$	5.74163	0.401994
$205$	−1.22078	−0.0852631
$206$	11.3531	0.791006
$207$	−0.145840	−0.0101366
$208$	5.80946	0.402814
$209$	−25.0197	−1.73065
$210$	0.299963	0.0206994
$211$	−8.43819	−0.580909	−0.290455	−	0.956889i	$-0.593807\pi$
$211$	−8.43819	−0.580909	−0.290455	+	0.956889i	$0.593807\pi$
$212$	2.72943	0.187458
$213$	−16.3467	−1.12006
$214$	7.73978	0.529081
$215$	0.855117	0.0583185
$216$	−5.06229	−0.344445
$217$	10.9911	0.746127
$218$	−4.80109	−0.325171
$219$	−28.7327	−1.94158
$220$	−0.592280	−0.0399315
$221$	18.8063	1.26505
$222$	15.3559	1.03062
$223$	5.53263	0.370492	0.185246	−	0.982692i	$-0.440692\pi$
$223$	5.53263	0.370492	0.185246	+	0.982692i	$0.440692\pi$
$224$	1.25283	0.0837079
$225$	−0.726543	−0.0484362
$226$	10.6653	0.709446
$227$	29.4875	1.95716	0.978578	−	0.205879i	$-0.0660053\pi$
$227$	29.4875	1.95716	0.978578	+	0.205879i	$0.0660053\pi$
$228$	10.1142	0.669830
$229$	−25.5103	−1.68577	−0.842883	−	0.538097i	$-0.819143\pi$
$229$	−25.5103	−1.68577	−0.842883	+	0.538097i	$0.819143\pi$
$230$	−0.134992	−0.00890113
$231$	−9.74939	−0.641462
$232$	−1.00000	−0.0656532
$233$	−18.6385	−1.22105	−0.610523	−	0.791999i	$-0.709041\pi$
$233$	−18.6385	−1.22105	−0.610523	+	0.791999i	$0.709041\pi$
$234$	0.847252	0.0553866
$235$	−0.837600	−0.0546390
$236$	5.21133	0.339229
$237$	−5.03453	−0.327028
$238$	4.05562	0.262887
$239$	9.73828	0.629917	0.314959	−	0.949105i	$-0.398009\pi$
$239$	9.73828	0.629917	0.314959	+	0.949105i	$0.398009\pi$
$240$	0.239429	0.0154551
$241$	−1.49045	−0.0960086	−0.0480043	−	0.998847i	$-0.515286\pi$
$241$	−1.49045	−0.0960086	−0.0480043	+	0.998847i	$0.515286\pi$
$242$	8.25027	0.530347
$243$	−1.51429	−0.0971419
$244$	−1.88158	−0.120456
$245$	−0.733066	−0.0468339
$246$	−16.0397	−1.02266
$247$	33.1283	2.10790
$248$	8.77308	0.557091
$249$	−18.0434	−1.14345
$250$	−1.34746	−0.0852210
$251$	4.35278	0.274745	0.137373	−	0.990519i	$-0.456134\pi$
$251$	4.35278	0.274745	0.137373	+	0.990519i	$0.456134\pi$
$252$	0.182712	0.0115098
$253$	4.38751	0.275841
$254$	−13.7905	−0.865294
$255$	0.775076	0.0485371
$256$	1.00000	0.0625000
$257$	18.8633	1.17666	0.588331	−	0.808620i	$-0.299785\pi$
$257$	18.8633	1.17666	0.588331	+	0.808620i	$0.299785\pi$
$258$	11.2353	0.699479
$259$	10.8467	0.673980
$260$	0.784232	0.0486360
$261$	−0.145840	−0.00902727
$262$	−20.3940	−1.25994
$263$	20.8960	1.28850	0.644252	−	0.764813i	$-0.277169\pi$
$263$	20.8960	1.28850	0.644252	+	0.764813i	$0.277169\pi$
$264$	−7.78192	−0.478944
$265$	0.368453	0.0226339
$266$	7.14420	0.438039
$267$	−21.3879	−1.30892
$268$	−5.13139	−0.313450
$269$	10.3037	0.628226	0.314113	−	0.949386i	$-0.398293\pi$
$269$	10.3037	0.628226	0.314113	+	0.949386i	$0.398293\pi$
$270$	−0.683370	−0.0415885
$271$	−14.2571	−0.866060	−0.433030	−	0.901380i	$-0.642556\pi$
$271$	−14.2571	−0.866060	−0.433030	+	0.901380i	$0.642556\pi$
$272$	3.23718	0.196283
$273$	12.9091	0.781292
$274$	13.2830	0.802457
$275$	21.8576	1.31806
$276$	−1.77365	−0.106761
$277$	−14.3972	−0.865045	−0.432523	−	0.901623i	$-0.642376\pi$
$277$	−14.3972	−0.865045	−0.432523	+	0.901623i	$0.642376\pi$
$278$	13.7556	0.825007
$279$	1.27947	0.0765997
$280$	0.169122	0.0101070
$281$	−25.2457	−1.50603	−0.753015	−	0.658003i	$-0.771401\pi$
$281$	−25.2457	−1.50603	−0.753015	+	0.658003i	$0.771401\pi$
$282$	−11.0052	−0.655347
$283$	24.3693	1.44860	0.724302	−	0.689483i	$-0.242162\pi$
$283$	24.3693	1.44860	0.724302	+	0.689483i	$0.242162\pi$
$284$	−9.21641	−0.546893
$285$	1.36534	0.0808757
$286$	−25.4891	−1.50720
$287$	−11.3297	−0.668773
$288$	0.145840	0.00859371
$289$	−6.52067	−0.383569
$290$	−0.134992	−0.00792702
$291$	−1.20115	−0.0704127
$292$	−16.1998	−0.948020
$293$	−6.43928	−0.376187	−0.188093	−	0.982151i	$-0.560231\pi$
$293$	−6.43928	−0.376187	−0.188093	+	0.982151i	$0.560231\pi$
$294$	−9.63169	−0.561731
$295$	0.703490	0.0409588
$296$	8.65777	0.503223
$297$	22.2108	1.28880
$298$	8.21740	0.476021
$299$	−5.80946	−0.335970
$300$	−8.83594	−0.510143
$301$	7.93610	0.457429
$302$	2.46908	0.142080
$303$	−11.7384	−0.674351
$304$	5.70247	0.327059
$305$	−0.253999	−0.0145440
$306$	0.472110	0.0269888
$307$	−20.4131	−1.16504	−0.582520	−	0.812817i	$-0.697933\pi$
$307$	−20.4131	−1.16504	−0.582520	+	0.812817i	$0.697933\pi$
$308$	−5.49679	−0.313209
$309$	20.1364	1.14552
$310$	1.18430	0.0672636
$311$	26.3809	1.49593	0.747963	−	0.663741i	$-0.231032\pi$
$311$	26.3809	1.49593	0.747963	+	0.663741i	$0.231032\pi$
$312$	10.3040	0.583347
$313$	−25.5483	−1.44407	−0.722037	−	0.691854i	$-0.756794\pi$
$313$	−25.5483	−1.44407	−0.722037	+	0.691854i	$0.756794\pi$
$314$	3.67018	0.207121
$315$	0.0246647	0.00138970
$316$	−2.83851	−0.159679
$317$	12.5784	0.706472	0.353236	−	0.935534i	$-0.385081\pi$
$317$	12.5784	0.706472	0.353236	+	0.935534i	$0.385081\pi$
$318$	4.84106	0.271473
$319$	4.38751	0.245654
$320$	0.134992	0.00754630
$321$	13.7277	0.766204
$322$	−1.25283	−0.0698172
$323$	18.4599	1.02714
$324$	−9.41625	−0.523125
$325$	−28.9414	−1.60538
$326$	4.88506	0.270558
$327$	−8.51546	−0.470906
$328$	−9.04334	−0.499335
$329$	−7.77353	−0.428569
$330$	−1.05050	−0.0578281
$331$	21.7642	1.19627	0.598135	−	0.801396i	$-0.295909\pi$
$331$	21.7642	1.19627	0.598135	+	0.801396i	$0.295909\pi$
$332$	−10.1730	−0.558318
$333$	1.26265	0.0691928
$334$	−0.401990	−0.0219959
$335$	−0.692698	−0.0378462
$336$	2.22208	0.121224
$337$	26.2873	1.43196	0.715979	−	0.698122i	$-0.245981\pi$
$337$	26.2873	1.43196	0.715979	+	0.698122i	$0.245981\pi$
$338$	20.7498	1.12864
$339$	18.9166	1.02741
$340$	0.436994	0.0236993
$341$	−38.4920	−2.08446
$342$	0.831649	0.0449704
$343$	−15.5732	−0.840871
$344$	6.33456	0.341537
$345$	−0.239429	−0.0128904
$346$	9.22224	0.495791
$347$	−13.2512	−0.711364	−0.355682	−	0.934607i	$-0.615751\pi$
$347$	−13.2512	−0.711364	−0.355682	+	0.934607i	$0.615751\pi$
$348$	−1.77365	−0.0950777
$349$	−9.99892	−0.535230	−0.267615	−	0.963526i	$-0.586236\pi$
$349$	−9.99892	−0.535230	−0.267615	+	0.963526i	$0.586236\pi$
$350$	−6.24130	−0.333611
$351$	−29.4091	−1.56974
$352$	−4.38751	−0.233855
$353$	22.9034	1.21902	0.609512	−	0.792777i	$-0.291366\pi$
$353$	22.9034	1.21902	0.609512	+	0.792777i	$0.291366\pi$
$354$	9.24309	0.491265
$355$	−1.24414	−0.0660323
$356$	−12.0587	−0.639107
$357$	7.19326	0.380707
$358$	−4.81089	−0.254263
$359$	−31.6917	−1.67262	−0.836311	−	0.548256i	$-0.815292\pi$
$359$	−31.6917	−1.67262	−0.836311	+	0.548256i	$0.815292\pi$
$360$	0.0196873	0.00103761
$361$	13.5182	0.711485
$362$	−21.4966	−1.12984
$363$	14.6331	0.768039
$364$	7.27824	0.381483
$365$	−2.18684	−0.114465
$366$	−3.33728	−0.174442
$367$	26.4829	1.38240	0.691198	−	0.722666i	$-0.257083\pi$
$367$	26.4829	1.38240	0.691198	+	0.722666i	$0.257083\pi$
$368$	−1.00000	−0.0521286
$369$	−1.31888	−0.0686582
$370$	1.16873	0.0607595
$371$	3.41950	0.177532
$372$	15.5604	0.806769
$373$	−20.0888	−1.04016	−0.520079	−	0.854118i	$-0.674098\pi$
$373$	−20.0888	−1.04016	−0.520079	+	0.854118i	$0.674098\pi$
$374$	−14.2032	−0.734428
$375$	−2.38993	−0.123415
$376$	−6.20480	−0.319988
$377$	−5.80946	−0.299202
$378$	−6.34216	−0.326205
$379$	29.3128	1.50570	0.752850	−	0.658193i	$-0.228679\pi$
$379$	29.3128	1.50570	0.752850	+	0.658193i	$0.228679\pi$
$380$	0.769790	0.0394894
$381$	−24.4596	−1.25310
$382$	−1.68863	−0.0863980
$383$	4.80258	0.245400	0.122700	−	0.992444i	$-0.460845\pi$
$383$	4.80258	0.245400	0.122700	+	0.992444i	$0.460845\pi$
$384$	1.77365	0.0905113
$385$	−0.742024	−0.0378170
$386$	11.9427	0.607866
$387$	0.923833	0.0469611
$388$	−0.677219	−0.0343806
$389$	−12.3676	−0.627063	−0.313531	−	0.949578i	$-0.601512\pi$
$389$	−12.3676	−0.627063	−0.313531	+	0.949578i	$0.601512\pi$
$390$	1.39096	0.0704337
$391$	−3.23718	−0.163711
$392$	−5.43043	−0.274278
$393$	−36.1718	−1.82463
$394$	6.44607	0.324748
$395$	−0.383177	−0.0192798
$396$	−0.639875	−0.0321549
$397$	4.78066	0.239935	0.119967	−	0.992778i	$-0.461721\pi$
$397$	4.78066	0.239935	0.119967	+	0.992778i	$0.461721\pi$
$398$	−20.4551	−1.02532
$399$	12.6713	0.634360
$400$	−4.98178	−0.249089
$401$	−13.7838	−0.688332	−0.344166	−	0.938909i	$-0.611838\pi$
$401$	−13.7838	−0.688332	−0.344166	+	0.938909i	$0.611838\pi$
$402$	−9.10130	−0.453932
$403$	50.9669	2.53884
$404$	−6.61819	−0.329267
$405$	−1.27112	−0.0631625
$406$	−1.25283	−0.0621767
$407$	−37.9861	−1.88290
$408$	5.74163	0.284253
$409$	−33.1575	−1.63953	−0.819765	−	0.572700i	$-0.805896\pi$
$409$	−33.1575	−1.63953	−0.819765	+	0.572700i	$0.805896\pi$
$410$	−1.22078	−0.0602901
$411$	23.5595	1.16210
$412$	11.3531	0.559326
$413$	6.52889	0.321266
$414$	−0.145840	−0.00716765
$415$	−1.37328	−0.0674117
$416$	5.80946	0.284832
$417$	24.3977	1.19476
$418$	−25.0197	−1.22375
$419$	−37.2654	−1.82053	−0.910267	−	0.414022i	$-0.864124\pi$
$419$	−37.2654	−1.82053	−0.910267	+	0.414022i	$0.864124\pi$
$420$	0.299963	0.0146367
$421$	−26.1202	−1.27302	−0.636510	−	0.771268i	$-0.719623\pi$
$421$	−26.1202	−1.27302	−0.636510	+	0.771268i	$0.719623\pi$
$422$	−8.43819	−0.410765
$423$	−0.904909	−0.0439982
$424$	2.72943	0.132553
$425$	−16.1269	−0.782270
$426$	−16.3467	−0.792000
$427$	−2.35730	−0.114078
$428$	7.73978	0.374116
$429$	−45.2088	−2.18270
$430$	0.855117	0.0412374
$431$	4.08526	0.196780	0.0983900	−	0.995148i	$-0.468631\pi$
$431$	4.08526	0.196780	0.0983900	+	0.995148i	$0.468631\pi$
$432$	−5.06229	−0.243559
$433$	15.0211	0.721867	0.360934	−	0.932592i	$-0.382458\pi$
$433$	15.0211	0.721867	0.360934	+	0.932592i	$0.382458\pi$
$434$	10.9911	0.527591
$435$	−0.239429	−0.0114798
$436$	−4.80109	−0.229930
$437$	−5.70247	−0.272786
$438$	−28.7327	−1.37290
$439$	−1.20675	−0.0575950	−0.0287975	−	0.999585i	$-0.509168\pi$
$439$	−1.20675	−0.0575950	−0.0287975	+	0.999585i	$0.509168\pi$
$440$	−0.592280	−0.0282359
$441$	−0.791974	−0.0377131
$442$	18.8063	0.894523
$443$	−34.9981	−1.66281	−0.831404	−	0.555668i	$-0.812462\pi$
$443$	−34.9981	−1.66281	−0.831404	+	0.555668i	$0.812462\pi$
$444$	15.3559	0.728758
$445$	−1.62783	−0.0771663
$446$	5.53263	0.261978
$447$	14.5748	0.689365
$448$	1.25283	0.0591904
$449$	−13.0071	−0.613845	−0.306922	−	0.951735i	$-0.599299\pi$
$449$	−13.0071	−0.613845	−0.306922	+	0.951735i	$0.599299\pi$
$450$	−0.726543	−0.0342496
$451$	39.6778	1.86835
$452$	10.6653	0.501654
$453$	4.37930	0.205757
$454$	29.4875	1.38392
$455$	0.982506	0.0460606
$456$	10.1142	0.473641
$457$	31.7080	1.48324	0.741620	−	0.670820i	$-0.234058\pi$
$457$	31.7080	1.48324	0.741620	+	0.670820i	$0.234058\pi$
$458$	−25.5103	−1.19202
$459$	−16.3875	−0.764904
$460$	−0.134992	−0.00629405
$461$	29.6841	1.38253	0.691264	−	0.722602i	$-0.257054\pi$
$461$	29.6841	1.38253	0.691264	+	0.722602i	$0.257054\pi$
$462$	−9.74939	−0.453582
$463$	36.0371	1.67478	0.837392	−	0.546603i	$-0.184079\pi$
$463$	36.0371	1.67478	0.837392	+	0.546603i	$0.184079\pi$
$464$	−1.00000	−0.0464238
$465$	2.10053	0.0974099
$466$	−18.6385	−0.863410
$467$	17.3258	0.801743	0.400871	−	0.916134i	$-0.368707\pi$
$467$	17.3258	0.801743	0.400871	+	0.916134i	$0.368707\pi$
$468$	0.847252	0.0391642
$469$	−6.42874	−0.296851
$470$	−0.837600	−0.0386356
$471$	6.50963	0.299948
$472$	5.21133	0.239871
$473$	−27.7930	−1.27792
$474$	−5.03453	−0.231244
$475$	−28.4085	−1.30347
$476$	4.05562	0.185889
$477$	0.398061	0.0182260
$478$	9.73828	0.445419
$479$	−1.92324	−0.0878751	−0.0439376	−	0.999034i	$-0.513990\pi$
$479$	−1.92324	−0.0878751	−0.0439376	+	0.999034i	$0.513990\pi$
$480$	0.239429	0.0109284
$481$	50.2970	2.29335
$482$	−1.49045	−0.0678883
$483$	−2.22208	−0.101108
$484$	8.25027	0.375012
$485$	−0.0914194	−0.00415114
$486$	−1.51429	−0.0686897
$487$	4.86805	0.220592	0.110296	−	0.993899i	$-0.464820\pi$
$487$	4.86805	0.220592	0.110296	+	0.993899i	$0.464820\pi$
$488$	−1.88158	−0.0851753
$489$	8.66439	0.391817
$490$	−0.733066	−0.0331166
$491$	25.9551	1.17134	0.585668	−	0.810551i	$-0.300832\pi$
$491$	25.9551	1.17134	0.585668	+	0.810551i	$0.300832\pi$
$492$	−16.0397	−0.723127
$493$	−3.23718	−0.145795
$494$	33.1283	1.49051
$495$	−0.0863782	−0.00388241
$496$	8.77308	0.393923
$497$	−11.5465	−0.517933
$498$	−18.0434	−0.808545
$499$	−26.7130	−1.19584	−0.597918	−	0.801557i	$-0.704005\pi$
$499$	−26.7130	−1.19584	−0.597918	+	0.801557i	$0.704005\pi$
$500$	−1.34746	−0.0602604
$501$	−0.712990	−0.0318541
$502$	4.35278	0.194274
$503$	31.1526	1.38903	0.694513	−	0.719480i	$-0.255620\pi$
$503$	31.1526	1.38903	0.694513	+	0.719480i	$0.255620\pi$
$504$	0.182712	0.00813865
$505$	−0.893404	−0.0397560
$506$	4.38751	0.195049
$507$	36.8030	1.63448
$508$	−13.7905	−0.611855
$509$	23.1044	1.02409	0.512043	−	0.858960i	$-0.328889\pi$
$509$	23.1044	1.02409	0.512043	+	0.858960i	$0.328889\pi$
$510$	0.775076	0.0343209
$511$	−20.2955	−0.897819
$512$	1.00000	0.0441942
$513$	−28.8676	−1.27453
$514$	18.8633	0.832026
$515$	1.53258	0.0675335
$516$	11.2353	0.494607
$517$	27.2236	1.19729
$518$	10.8467	0.476576
$519$	16.3570	0.717994
$520$	0.784232	0.0343909
$521$	24.4968	1.07323	0.536613	−	0.843829i	$-0.319704\pi$
$521$	24.4968	1.07323	0.536613	+	0.843829i	$0.319704\pi$
$522$	−0.145840	−0.00638325
$523$	−22.0326	−0.963419	−0.481710	−	0.876331i	$-0.659984\pi$
$523$	−22.0326	−0.963419	−0.481710	+	0.876331i	$0.659984\pi$
$524$	−20.3940	−0.890915
$525$	−11.0699	−0.483129
$526$	20.8960	0.911110
$527$	28.4000	1.23712
$528$	−7.78192	−0.338665
$529$	1.00000	0.0434783
$530$	0.368453	0.0160046
$531$	0.760021	0.0329821
$532$	7.14420	0.309741
$533$	−52.5369	−2.27563
$534$	−21.3879	−0.925543
$535$	1.04481	0.0451711
$536$	−5.13139	−0.221642
$537$	−8.53284	−0.368219
$538$	10.3037	0.444223
$539$	23.8261	1.02626
$540$	−0.683370	−0.0294075
$541$	−10.9701	−0.471643	−0.235821	−	0.971796i	$-0.575778\pi$
$541$	−10.9701	−0.471643	−0.235821	+	0.971796i	$0.575778\pi$
$542$	−14.2571	−0.612397
$543$	−38.1275	−1.63621
$544$	3.23718	0.138793
$545$	−0.648110	−0.0277620
$546$	12.9091	0.552457
$547$	0.949453	0.0405957	0.0202978	−	0.999794i	$-0.493539\pi$
$547$	0.949453	0.0405957	0.0202978	+	0.999794i	$0.493539\pi$
$548$	13.2830	0.567423
$549$	−0.274410	−0.0117116
$550$	21.8576	0.932012
$551$	−5.70247	−0.242934
$552$	−1.77365	−0.0754916
$553$	−3.55616	−0.151223
$554$	−14.3972	−0.611679
$555$	2.07293	0.0879908
$556$	13.7556	0.583368
$557$	3.28481	0.139182	0.0695910	−	0.997576i	$-0.477831\pi$
$557$	3.28481	0.139182	0.0695910	+	0.997576i	$0.477831\pi$
$558$	1.27947	0.0541641
$559$	36.8004	1.55649
$560$	0.169122	0.00714670
$561$	−25.1915	−1.06358
$562$	−25.2457	−1.06492
$563$	38.5666	1.62539	0.812695	−	0.582690i	$-0.198000\pi$
$563$	38.5666	1.62539	0.812695	+	0.582690i	$0.198000\pi$
$564$	−11.0052	−0.463401
$565$	1.43974	0.0605701
$566$	24.3693	1.02432
$567$	−11.7969	−0.495424
$568$	−9.21641	−0.386712
$569$	6.22141	0.260815	0.130408	−	0.991460i	$-0.458371\pi$
$569$	6.22141	0.260815	0.130408	+	0.991460i	$0.458371\pi$
$570$	1.36534	0.0571878
$571$	20.7171	0.866983	0.433491	−	0.901158i	$-0.357281\pi$
$571$	20.7171	0.866983	0.433491	+	0.901158i	$0.357281\pi$
$572$	−25.4891	−1.06575
$573$	−2.99505	−0.125120
$574$	−11.3297	−0.472894
$575$	4.98178	0.207754
$576$	0.145840	0.00607667
$577$	9.53612	0.396994	0.198497	−	0.980102i	$-0.436394\pi$
$577$	9.53612	0.396994	0.198497	+	0.980102i	$0.436394\pi$
$578$	−6.52067	−0.271224
$579$	21.1821	0.880299
$580$	−0.134992	−0.00560525
$581$	−12.7450	−0.528753
$582$	−1.20115	−0.0497893
$583$	−11.9754	−0.495971
$584$	−16.1998	−0.670351
$585$	0.114373	0.00472872
$586$	−6.43928	−0.266004
$587$	41.3958	1.70859	0.854293	−	0.519792i	$-0.173990\pi$
$587$	41.3958	1.70859	0.854293	+	0.519792i	$0.173990\pi$
$588$	−9.63169	−0.397204
$589$	50.0283	2.06138
$590$	0.703490	0.0289622
$591$	11.4331	0.470294
$592$	8.65777	0.355832
$593$	−1.82216	−0.0748273	−0.0374136	−	0.999300i	$-0.511912\pi$
$593$	−1.82216	−0.0748273	−0.0374136	+	0.999300i	$0.511912\pi$
$594$	22.2108	0.911322
$595$	0.547477	0.0224444
$596$	8.21740	0.336598
$597$	−36.2801	−1.48485
$598$	−5.80946	−0.237566
$599$	19.9757	0.816185	0.408092	−	0.912941i	$-0.366194\pi$
$599$	19.9757	0.816185	0.408092	+	0.912941i	$0.366194\pi$
$600$	−8.83594	−0.360726
$601$	7.61359	0.310565	0.155282	−	0.987870i	$-0.450371\pi$
$601$	7.61359	0.310565	0.155282	+	0.987870i	$0.450371\pi$
$602$	7.93610	0.323451
$603$	−0.748362	−0.0304757
$604$	2.46908	0.100466
$605$	1.11372	0.0452793
$606$	−11.7384	−0.476838
$607$	3.00490	0.121965	0.0609825	−	0.998139i	$-0.480577\pi$
$607$	3.00490	0.121965	0.0609825	+	0.998139i	$0.480577\pi$
$608$	5.70247	0.231266
$609$	−2.22208	−0.0900430
$610$	−0.253999	−0.0102841
$611$	−36.0465	−1.45829
$612$	0.472110	0.0190839
$613$	−34.9743	−1.41260	−0.706299	−	0.707914i	$-0.749637\pi$
$613$	−34.9743	−1.41260	−0.706299	+	0.707914i	$0.749637\pi$
$614$	−20.4131	−0.823807
$615$	−2.16524	−0.0873110
$616$	−5.49679	−0.221472
$617$	−25.3760	−1.02160	−0.510799	−	0.859700i	$-0.670650\pi$
$617$	−25.3760	−1.02160	−0.510799	+	0.859700i	$0.670650\pi$
$618$	20.1364	0.810005
$619$	−18.9378	−0.761173	−0.380586	−	0.924745i	$-0.624278\pi$
$619$	−18.9378	−0.761173	−0.380586	+	0.924745i	$0.624278\pi$
$620$	1.18430	0.0475626
$621$	5.06229	0.203143
$622$	26.3809	1.05778
$623$	−15.1074	−0.605265
$624$	10.3040	0.412488
$625$	24.7270	0.989080
$626$	−25.5483	−1.02111
$627$	−44.3762	−1.77221
$628$	3.67018	0.146456
$629$	28.0268	1.11750
$630$	0.0246647	0.000982667 0
$631$	33.4678	1.33233	0.666166	−	0.745804i	$-0.267934\pi$
$631$	33.4678	1.33233	0.666166	+	0.745804i	$0.267934\pi$
$632$	−2.83851	−0.112910
$633$	−14.9664	−0.594861
$634$	12.5784	0.499551
$635$	−1.86161	−0.0738759
$636$	4.84106	0.191961
$637$	−31.5479	−1.24997
$638$	4.38751	0.173703
$639$	−1.34412	−0.0531726
$640$	0.134992	0.00533604
$641$	−11.3272	−0.447397	−0.223698	−	0.974658i	$-0.571813\pi$
$641$	−11.3272	−0.447397	−0.223698	+	0.974658i	$0.571813\pi$
$642$	13.7277	0.541788
$643$	−18.8787	−0.744502	−0.372251	−	0.928132i	$-0.621414\pi$
$643$	−18.8787	−0.744502	−0.372251	+	0.928132i	$0.621414\pi$
$644$	−1.25283	−0.0493682
$645$	1.51668	0.0597192
$646$	18.4599	0.726296
$647$	40.7077	1.60039	0.800193	−	0.599742i	$-0.204730\pi$
$647$	40.7077	1.60039	0.800193	+	0.599742i	$0.204730\pi$
$648$	−9.41625	−0.369905
$649$	−22.8648	−0.897522
$650$	−28.9414	−1.13518
$651$	19.4944	0.764048
$652$	4.88506	0.191314
$653$	16.9495	0.663287	0.331644	−	0.943405i	$-0.392397\pi$
$653$	16.9495	0.663287	0.331644	+	0.943405i	$0.392397\pi$
$654$	−8.51546	−0.332981
$655$	−2.75303	−0.107570
$656$	−9.04334	−0.353083
$657$	−2.36258	−0.0921729
$658$	−7.77353	−0.303044
$659$	38.8172	1.51210	0.756052	−	0.654512i	$-0.227126\pi$
$659$	38.8172	1.51210	0.756052	+	0.654512i	$0.227126\pi$
$660$	−1.05050	−0.0408906
$661$	−7.10817	−0.276476	−0.138238	−	0.990399i	$-0.544144\pi$
$661$	−7.10817	−0.276476	−0.138238	+	0.990399i	$0.544144\pi$
$662$	21.7642	0.845890
$663$	33.3558	1.29543
$664$	−10.1730	−0.394790
$665$	0.964413	0.0373983
$666$	1.26265	0.0489267
$667$	1.00000	0.0387202
$668$	−0.401990	−0.0155535
$669$	9.81296	0.379391
$670$	−0.692698	−0.0267613
$671$	8.25548	0.318699
$672$	2.22208	0.0857184
$673$	−17.5285	−0.675673	−0.337837	−	0.941205i	$-0.609695\pi$
$673$	−17.5285	−0.675673	−0.337837	+	0.941205i	$0.609695\pi$
$674$	26.2873	1.01255
$675$	25.2192	0.970687
$676$	20.7498	0.798070
$677$	7.40314	0.284526	0.142263	−	0.989829i	$-0.454562\pi$
$677$	7.40314	0.284526	0.142263	+	0.989829i	$0.454562\pi$
$678$	18.9166	0.726486
$679$	−0.848438	−0.0325600
$680$	0.436994	0.0167580
$681$	52.3006	2.00416
$682$	−38.4920	−1.47393
$683$	−45.8664	−1.75503	−0.877514	−	0.479551i	$-0.840799\pi$
$683$	−45.8664	−1.75503	−0.877514	+	0.479551i	$0.840799\pi$
$684$	0.831649	0.0317989
$685$	1.79311	0.0685110
$686$	−15.5732	−0.594586
$687$	−45.2463	−1.72625
$688$	6.33456	0.241503
$689$	15.8565	0.604086
$690$	−0.239429	−0.00911492
$691$	25.5101	0.970451	0.485225	−	0.874389i	$-0.338738\pi$
$691$	25.5101	0.970451	0.485225	+	0.874389i	$0.338738\pi$
$692$	9.22224	0.350577
$693$	−0.801652	−0.0304522
$694$	−13.2512	−0.503010
$695$	1.85690	0.0704363
$696$	−1.77365	−0.0672301
$697$	−29.2749	−1.10887
$698$	−9.99892	−0.378465
$699$	−33.0581	−1.25037
$700$	−6.24130	−0.235899
$701$	−15.1313	−0.571501	−0.285750	−	0.958304i	$-0.592243\pi$
$701$	−15.1313	−0.571501	−0.285750	+	0.958304i	$0.592243\pi$
$702$	−29.4091	−1.10998
$703$	49.3707	1.86205
$704$	−4.38751	−0.165361
$705$	−1.48561	−0.0559514
$706$	22.9034	0.861980
$707$	−8.29143	−0.311831
$708$	9.24309	0.347377
$709$	30.2495	1.13605	0.568023	−	0.823013i	$-0.307709\pi$
$709$	30.2495	1.13605	0.568023	+	0.823013i	$0.307709\pi$
$710$	−1.24414	−0.0466919
$711$	−0.413969	−0.0155251
$712$	−12.0587	−0.451917
$713$	−8.77308	−0.328554
$714$	7.19326	0.269201
$715$	−3.44083	−0.128680
$716$	−4.81089	−0.179791
$717$	17.2723	0.645047
$718$	−31.6917	−1.18272
$719$	−37.0130	−1.38035	−0.690176	−	0.723641i	$-0.742467\pi$
$719$	−37.0130	−1.38035	−0.690176	+	0.723641i	$0.742467\pi$
$720$	0.0196873	0.000733702 0
$721$	14.2234	0.529708
$722$	13.5182	0.503096
$723$	−2.64355	−0.0983145
$724$	−21.4966	−0.798915
$725$	4.98178	0.185019
$726$	14.6331	0.543085
$727$	0.104259	0.00386676	0.00193338	−	0.999998i	$-0.499385\pi$
$727$	0.104259	0.00386676	0.00193338	+	0.999998i	$0.499385\pi$
$728$	7.27824	0.269749
$729$	25.5629	0.946775
$730$	−2.18684	−0.0809387
$731$	20.5061	0.758446
$732$	−3.33728	−0.123349
$733$	17.5963	0.649934	0.324967	−	0.945725i	$-0.394647\pi$
$733$	17.5963	0.649934	0.324967	+	0.945725i	$0.394647\pi$
$734$	26.4829	0.977501
$735$	−1.30020	−0.0479587
$736$	−1.00000	−0.0368605
$737$	22.5140	0.829315
$738$	−1.31888	−0.0485487
$739$	36.3887	1.33858	0.669290	−	0.743002i	$-0.266599\pi$
$739$	36.3887	1.33858	0.669290	+	0.743002i	$0.266599\pi$
$740$	1.16873	0.0429635
$741$	58.7581	2.15853
$742$	3.41950	0.125534
$743$	−26.3191	−0.965553	−0.482777	−	0.875743i	$-0.660372\pi$
$743$	−26.3191	−0.965553	−0.482777	+	0.875743i	$0.660372\pi$
$744$	15.5604	0.570471
$745$	1.10929	0.0406411
$746$	−20.0888	−0.735503
$747$	−1.48364	−0.0542834
$748$	−14.2032	−0.519319
$749$	9.69659	0.354306
$750$	−2.38993	−0.0872679
$751$	40.7688	1.48768	0.743838	−	0.668360i	$-0.233003\pi$
$751$	40.7688	1.48768	0.743838	+	0.668360i	$0.233003\pi$
$752$	−6.20480	−0.226266
$753$	7.72032	0.281344
$754$	−5.80946	−0.211568
$755$	0.333307	0.0121303
$756$	−6.34216	−0.230662
$757$	13.3667	0.485821	0.242911	−	0.970049i	$-0.421898\pi$
$757$	13.3667	0.485821	0.242911	+	0.970049i	$0.421898\pi$
$758$	29.3128	1.06469
$759$	7.78192	0.282466
$760$	0.769790	0.0279232
$761$	13.8165	0.500847	0.250424	−	0.968136i	$-0.419430\pi$
$761$	13.8165	0.500847	0.250424	+	0.968136i	$0.419430\pi$
$762$	−24.4596	−0.886077
$763$	−6.01492	−0.217755
$764$	−1.68863	−0.0610926
$765$	0.0637313	0.00230421
$766$	4.80258	0.173524
$767$	30.2750	1.09317
$768$	1.77365	0.0640011
$769$	−7.28211	−0.262600	−0.131300	−	0.991343i	$-0.541915\pi$
$769$	−7.28211	−0.262600	−0.131300	+	0.991343i	$0.541915\pi$
$770$	−0.742024	−0.0267407
$771$	33.4570	1.20492
$772$	11.9427	0.429826
$773$	−4.32911	−0.155707	−0.0778537	−	0.996965i	$-0.524807\pi$
$773$	−4.32911	−0.155707	−0.0778537	+	0.996965i	$0.524807\pi$
$774$	0.923833	0.0332065
$775$	−43.7055	−1.56995
$776$	−0.677219	−0.0243108
$777$	19.2382	0.690168
$778$	−12.3676	−0.443400
$779$	−51.5694	−1.84767
$780$	1.39096	0.0498042
$781$	40.4371	1.44695
$782$	−3.23718	−0.115761
$783$	5.06229	0.180911
$784$	−5.43043	−0.193944
$785$	0.495447	0.0176833
$786$	−36.1718	−1.29021
$787$	18.7172	0.667195	0.333598	−	0.942716i	$-0.391737\pi$
$787$	18.7172	0.667195	0.333598	+	0.942716i	$0.391737\pi$
$788$	6.44607	0.229632
$789$	37.0623	1.31945
$790$	−0.383177	−0.0136328
$791$	13.3618	0.475090
$792$	−0.639875	−0.0227370
$793$	−10.9310	−0.388171
$794$	4.78066	0.169659
$795$	0.653506	0.0231775
$796$	−20.4551	−0.725010
$797$	−9.44719	−0.334637	−0.167318	−	0.985903i	$-0.553511\pi$
$797$	−9.44719	−0.334637	−0.167318	+	0.985903i	$0.553511\pi$
$798$	12.6713	0.448560
$799$	−20.0860	−0.710593
$800$	−4.98178	−0.176132
$801$	−1.75864	−0.0621383
$802$	−13.7838	−0.486724
$803$	71.0767	2.50824
$804$	−9.10130	−0.320978
$805$	−0.169122	−0.00596076
$806$	50.9669	1.79523
$807$	18.2751	0.643315
$808$	−6.61819	−0.232827
$809$	−11.5733	−0.406896	−0.203448	−	0.979086i	$-0.565215\pi$
$809$	−11.5733	−0.406896	−0.203448	+	0.979086i	$0.565215\pi$
$810$	−1.27112	−0.0446627
$811$	32.4407	1.13915	0.569573	−	0.821941i	$-0.307108\pi$
$811$	32.4407	1.13915	0.569573	+	0.821941i	$0.307108\pi$
$812$	−1.25283	−0.0439655
$813$	−25.2872	−0.886861
$814$	−37.9861	−1.33141
$815$	0.659445	0.0230994
$816$	5.74163	0.200997
$817$	36.1227	1.26377
$818$	−33.1575	−1.15932
$819$	1.06146	0.0370904
$820$	−1.22078	−0.0426315
$821$	−34.9148	−1.21853	−0.609267	−	0.792965i	$-0.708536\pi$
$821$	−34.9148	−1.21853	−0.609267	+	0.792965i	$0.708536\pi$
$822$	23.5595	0.821730
$823$	−19.6793	−0.685976	−0.342988	−	0.939340i	$-0.611439\pi$
$823$	−19.6793	−0.685976	−0.342988	+	0.939340i	$0.611439\pi$
$824$	11.3531	0.395503
$825$	38.7678	1.34972
$826$	6.52889	0.227169
$827$	42.1318	1.46507	0.732533	−	0.680731i	$-0.238338\pi$
$827$	42.1318	1.46507	0.732533	+	0.680731i	$0.238338\pi$
$828$	−0.145840	−0.00506829
$829$	−12.6489	−0.439313	−0.219657	−	0.975577i	$-0.570494\pi$
$829$	−12.6489	−0.439313	−0.219657	+	0.975577i	$0.570494\pi$
$830$	−1.37328	−0.0476673
$831$	−25.5357	−0.885822
$832$	5.80946	0.201407
$833$	−17.5793	−0.609086
$834$	24.3977	0.844822
$835$	−0.0542656	−0.00187794
$836$	−25.0197	−0.865324
$837$	−44.4118	−1.53510
$838$	−37.2654	−1.28731
$839$	40.7489	1.40681	0.703405	−	0.710790i	$-0.251662\pi$
$839$	40.7489	1.40681	0.703405	+	0.710790i	$0.251662\pi$
$840$	0.299963	0.0103497
$841$	1.00000	0.0344828
$842$	−26.1202	−0.900161
$843$	−44.7770	−1.54220
$844$	−8.43819	−0.290455
$845$	2.80107	0.0963596
$846$	−0.904909	−0.0311114
$847$	10.3361	0.355154
$848$	2.72943	0.0937291
$849$	43.2226	1.48340
$850$	−16.1269	−0.553148
$851$	−8.65777	−0.296785
$852$	−16.3467	−0.560029
$853$	47.1111	1.61305	0.806527	−	0.591197i	$-0.201345\pi$
$853$	47.1111	1.61305	0.806527	+	0.591197i	$0.201345\pi$
$854$	−2.35730	−0.0806651
$855$	0.112266	0.00383943
$856$	7.73978	0.264540
$857$	−51.7146	−1.76654	−0.883268	−	0.468869i	$-0.844662\pi$
$857$	−51.7146	−1.76654	−0.883268	+	0.468869i	$0.844662\pi$
$858$	−45.2088	−1.54340
$859$	−4.56345	−0.155703	−0.0778515	−	0.996965i	$-0.524806\pi$
$859$	−4.56345	−0.155703	−0.0778515	+	0.996965i	$0.524806\pi$
$860$	0.855117	0.0291592
$861$	−20.0950	−0.684835
$862$	4.08526	0.139144
$863$	−18.2308	−0.620583	−0.310292	−	0.950641i	$-0.600427\pi$
$863$	−18.2308	−0.620583	−0.310292	+	0.950641i	$0.600427\pi$
$864$	−5.06229	−0.172222
$865$	1.24493	0.0423289
$866$	15.0211	0.510437
$867$	−11.5654	−0.392782
$868$	10.9911	0.373063
$869$	12.4540	0.422473
$870$	−0.239429	−0.00811741
$871$	−29.8106	−1.01009
$872$	−4.80109	−0.162585
$873$	−0.0987657	−0.00334271
$874$	−5.70247	−0.192889
$875$	−1.68814	−0.0570694
$876$	−28.7327	−0.970790
$877$	−14.5351	−0.490816	−0.245408	−	0.969420i	$-0.578922\pi$
$877$	−14.5351	−0.490816	−0.245408	+	0.969420i	$0.578922\pi$
$878$	−1.20675	−0.0407258
$879$	−11.4210	−0.385222
$880$	−0.592280	−0.0199658
$881$	−32.8847	−1.10791	−0.553957	−	0.832545i	$-0.686883\pi$
$881$	−32.8847	−1.10791	−0.553957	+	0.832545i	$0.686883\pi$
$882$	−0.791974	−0.0266672
$883$	17.0984	0.575408	0.287704	−	0.957719i	$-0.407108\pi$
$883$	17.0984	0.575408	0.287704	+	0.957719i	$0.407108\pi$
$884$	18.8063	0.632523
$885$	1.24775	0.0419425
$886$	−34.9981	−1.17578
$887$	−46.8476	−1.57299	−0.786493	−	0.617599i	$-0.788106\pi$
$887$	−46.8476	−1.57299	−0.786493	+	0.617599i	$0.788106\pi$
$888$	15.3559	0.515309
$889$	−17.2771	−0.579456
$890$	−1.62783	−0.0545648
$891$	41.3139	1.38407
$892$	5.53263	0.185246
$893$	−35.3827	−1.18404
$894$	14.5748	0.487454
$895$	−0.649433	−0.0217081
$896$	1.25283	0.0418540
$897$	−10.3040	−0.344039
$898$	−13.0071	−0.434054
$899$	−8.77308	−0.292599
$900$	−0.726543	−0.0242181
$901$	8.83566	0.294359
$902$	39.6778	1.32113
$903$	14.0759	0.468416
$904$	10.6653	0.354723
$905$	−2.90188	−0.0964616
$906$	4.37930	0.145492
$907$	13.5494	0.449901	0.224950	−	0.974370i	$-0.427778\pi$
$907$	13.5494	0.449901	0.224950	+	0.974370i	$0.427778\pi$
$908$	29.4875	0.978578
$909$	−0.965197	−0.0320136
$910$	0.982506	0.0325698
$911$	5.69371	0.188641	0.0943205	−	0.995542i	$-0.469932\pi$
$911$	5.69371	0.188641	0.0943205	+	0.995542i	$0.469932\pi$
$912$	10.1142	0.334915
$913$	44.6343	1.47718
$914$	31.7080	1.04881
$915$	−0.450507	−0.0148933
$916$	−25.5103	−0.842883
$917$	−25.5501	−0.843739
$918$	−16.3875	−0.540869
$919$	−36.6491	−1.20894	−0.604472	−	0.796627i	$-0.706616\pi$
$919$	−36.6491	−1.20894	−0.604472	+	0.796627i	$0.706616\pi$
$920$	−0.134992	−0.00445056
$921$	−36.2058	−1.19302
$922$	29.6841	0.977595
$923$	−53.5424	−1.76237
$924$	−9.74939	−0.320731
$925$	−43.1311	−1.41814
$926$	36.0371	1.18425
$927$	1.65573	0.0543814
$928$	−1.00000	−0.0328266
$929$	−14.7722	−0.484660	−0.242330	−	0.970194i	$-0.577912\pi$
$929$	−14.7722	−0.484660	−0.242330	+	0.970194i	$0.577912\pi$
$930$	2.10053	0.0688792
$931$	−30.9669	−1.01490
$932$	−18.6385	−0.610523
$933$	46.7906	1.53186
$934$	17.3258	0.566918
$935$	−1.91732	−0.0627030
$936$	0.847252	0.0276933
$937$	54.2434	1.77206	0.886028	−	0.463632i	$-0.153454\pi$
$937$	54.2434	1.77206	0.886028	+	0.463632i	$0.153454\pi$
$938$	−6.42874	−0.209906
$939$	−45.3138	−1.47876
$940$	−0.837600	−0.0273195
$941$	−46.9962	−1.53203	−0.766017	−	0.642820i	$-0.777764\pi$
$941$	−46.9962	−1.53203	−0.766017	+	0.642820i	$0.777764\pi$
$942$	6.50963	0.212095
$943$	9.04334	0.294492
$944$	5.21133	0.169614
$945$	−0.856143	−0.0278503
$946$	−27.7930	−0.903627
$947$	23.7849	0.772906	0.386453	−	0.922309i	$-0.373700\pi$
$947$	23.7849	0.772906	0.386453	+	0.922309i	$0.373700\pi$
$948$	−5.03453	−0.163514
$949$	−94.1119	−3.05500
$950$	−28.4085	−0.921692
$951$	22.3097	0.723440
$952$	4.05562	0.131443
$953$	3.28460	0.106399	0.0531993	−	0.998584i	$-0.483058\pi$
$953$	3.28460	0.106399	0.0531993	+	0.998584i	$0.483058\pi$
$954$	0.398061	0.0128877
$955$	−0.227952	−0.00737637
$956$	9.73828	0.314959
$957$	7.78192	0.251554
$958$	−1.92324	−0.0621371
$959$	16.6413	0.537376
$960$	0.239429	0.00772755
$961$	45.9669	1.48280
$962$	50.2970	1.62164
$963$	1.12877	0.0363741
$964$	−1.49045	−0.0480043
$965$	1.61217	0.0518975
$966$	−2.22208	−0.0714941
$967$	42.2176	1.35763	0.678813	−	0.734312i	$-0.262495\pi$
$967$	42.2176	1.35763	0.678813	+	0.734312i	$0.262495\pi$
$968$	8.25027	0.265174
$969$	32.7415	1.05181
$970$	−0.0914194	−0.00293530
$971$	8.71784	0.279769	0.139884	−	0.990168i	$-0.455327\pi$
$971$	8.71784	0.279769	0.139884	+	0.990168i	$0.455327\pi$
$972$	−1.51429	−0.0485710
$973$	17.2334	0.552477
$974$	4.86805	0.155982
$975$	−51.3320	−1.64394
$976$	−1.88158	−0.0602281
$977$	61.0531	1.95326	0.976631	−	0.214925i	$-0.0689508\pi$
$977$	61.0531	1.95326	0.976631	+	0.214925i	$0.0689508\pi$
$978$	8.66439	0.277057
$979$	52.9075	1.69093
$980$	−0.733066	−0.0234169
$981$	−0.700191	−0.0223554
$982$	25.9551	0.828260
$983$	−9.10025	−0.290253	−0.145126	−	0.989413i	$-0.546359\pi$
$983$	−9.10025	−0.290253	−0.145126	+	0.989413i	$0.546359\pi$
$984$	−16.0397	−0.511328
$985$	0.870170	0.0277259
$986$	−3.23718	−0.103093
$987$	−13.7875	−0.438862
$988$	33.1283	1.05395
$989$	−6.33456	−0.201427
$990$	−0.0863782	−0.00274528
$991$	19.1706	0.608974	0.304487	−	0.952516i	$-0.401515\pi$
$991$	19.1706	0.608974	0.304487	+	0.952516i	$0.401515\pi$
$992$	8.77308	0.278546
$993$	38.6021	1.22500
$994$	−11.5465	−0.366234
$995$	−2.76128	−0.0875383
$996$	−18.0434	−0.571727
$997$	−39.9672	−1.26577	−0.632887	−	0.774244i	$-0.718130\pi$
$997$	−39.9672	−1.26577	−0.632887	+	0.774244i	$0.718130\pi$
$998$	−26.7130	−0.845584
$999$	−43.8281	−1.38666

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1334.2.a.i.1.6	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1334.2.a.i.1.6	✓	8	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.77365 q^{3} +1.00000 q^{4} +0.134992 q^{5} +1.77365 q^{6} +1.25283 q^{7} +1.00000 q^{8} +0.145840 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.77365 q^{3} +1.00000 q^{4} +0.134992 q^{5} +1.77365 q^{6} +1.25283 q^{7} +1.00000 q^{8} +0.145840 q^{9} +0.134992 q^{10} -4.38751 q^{11} +1.77365 q^{12} +5.80946 q^{13} +1.25283 q^{14} +0.239429 q^{15} +1.00000 q^{16} +3.23718 q^{17} +0.145840 q^{18} +5.70247 q^{19} +0.134992 q^{20} +2.22208 q^{21} -4.38751 q^{22} -1.00000 q^{23} +1.77365 q^{24} -4.98178 q^{25} +5.80946 q^{26} -5.06229 q^{27} +1.25283 q^{28} -1.00000 q^{29} +0.239429 q^{30} +8.77308 q^{31} +1.00000 q^{32} -7.78192 q^{33} +3.23718 q^{34} +0.169122 q^{35} +0.145840 q^{36} +8.65777 q^{37} +5.70247 q^{38} +10.3040 q^{39} +0.134992 q^{40} -9.04334 q^{41} +2.22208 q^{42} +6.33456 q^{43} -4.38751 q^{44} +0.0196873 q^{45} -1.00000 q^{46} -6.20480 q^{47} +1.77365 q^{48} -5.43043 q^{49} -4.98178 q^{50} +5.74163 q^{51} +5.80946 q^{52} +2.72943 q^{53} -5.06229 q^{54} -0.592280 q^{55} +1.25283 q^{56} +10.1142 q^{57} -1.00000 q^{58} +5.21133 q^{59} +0.239429 q^{60} -1.88158 q^{61} +8.77308 q^{62} +0.182712 q^{63} +1.00000 q^{64} +0.784232 q^{65} -7.78192 q^{66} -5.13139 q^{67} +3.23718 q^{68} -1.77365 q^{69} +0.169122 q^{70} -9.21641 q^{71} +0.145840 q^{72} -16.1998 q^{73} +8.65777 q^{74} -8.83594 q^{75} +5.70247 q^{76} -5.49679 q^{77} +10.3040 q^{78} -2.83851 q^{79} +0.134992 q^{80} -9.41625 q^{81} -9.04334 q^{82} -10.1730 q^{83} +2.22208 q^{84} +0.436994 q^{85} +6.33456 q^{86} -1.77365 q^{87} -4.38751 q^{88} -12.0587 q^{89} +0.0196873 q^{90} +7.27824 q^{91} -1.00000 q^{92} +15.5604 q^{93} -6.20480 q^{94} +0.769790 q^{95} +1.77365 q^{96} -0.677219 q^{97} -5.43043 q^{98} -0.639875 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} + 4 q^{3} + 8 q^{4} + 4 q^{6} + 8 q^{7} + 8 q^{8} + 12 q^{9}+O(q^{10}) \) 8 * q + 8 * q^2 + 4 * q^3 + 8 * q^4 + 4 * q^6 + 8 * q^7 + 8 * q^8 + 12 * q^9	\( 8 q + 8 q^{2} + 4 q^{3} + 8 q^{4} + 4 q^{6} + 8 q^{7} + 8 q^{8} + 12 q^{9} + 8 q^{11} + 4 q^{12} + 4 q^{13} + 8 q^{14} + 8 q^{16} + 8 q^{17} + 12 q^{18} + 16 q^{19} - 4 q^{21} + 8 q^{22} - 8 q^{23} + 4 q^{24} + 4 q^{25} + 4 q^{26} + 4 q^{27} + 8 q^{28} - 8 q^{29} + 8 q^{31} + 8 q^{32} + 12 q^{33} + 8 q^{34} + 4 q^{35} + 12 q^{36} + 8 q^{37} + 16 q^{38} - 16 q^{39} + 8 q^{41} - 4 q^{42} + 32 q^{43} + 8 q^{44} - 8 q^{46} + 16 q^{47} + 4 q^{48} + 4 q^{49} + 4 q^{50} + 12 q^{51} + 4 q^{52} + 4 q^{54} + 8 q^{56} + 8 q^{57} - 8 q^{58} - 4 q^{59} + 8 q^{61} + 8 q^{62} + 24 q^{63} + 8 q^{64} - 4 q^{65} + 12 q^{66} + 20 q^{67} + 8 q^{68} - 4 q^{69} + 4 q^{70} - 24 q^{71} + 12 q^{72} - 4 q^{73} + 8 q^{74} - 16 q^{75} + 16 q^{76} - 16 q^{77} - 16 q^{78} + 4 q^{79} - 8 q^{81} + 8 q^{82} - 4 q^{83} - 4 q^{84} - 44 q^{85} + 32 q^{86} - 4 q^{87} + 8 q^{88} + 20 q^{89} - 8 q^{92} - 4 q^{93} + 16 q^{94} - 8 q^{95} + 4 q^{96} + 4 q^{97} + 4 q^{98}+O(q^{100}) \) 8 * q + 8 * q^2 + 4 * q^3 + 8 * q^4 + 4 * q^6 + 8 * q^7 + 8 * q^8 + 12 * q^9 + 8 * q^11 + 4 * q^12 + 4 * q^13 + 8 * q^14 + 8 * q^16 + 8 * q^17 + 12 * q^18 + 16 * q^19 - 4 * q^21 + 8 * q^22 - 8 * q^23 + 4 * q^24 + 4 * q^25 + 4 * q^26 + 4 * q^27 + 8 * q^28 - 8 * q^29 + 8 * q^31 + 8 * q^32 + 12 * q^33 + 8 * q^34 + 4 * q^35 + 12 * q^36 + 8 * q^37 + 16 * q^38 - 16 * q^39 + 8 * q^41 - 4 * q^42 + 32 * q^43 + 8 * q^44 - 8 * q^46 + 16 * q^47 + 4 * q^48 + 4 * q^49 + 4 * q^50 + 12 * q^51 + 4 * q^52 + 4 * q^54 + 8 * q^56 + 8 * q^57 - 8 * q^58 - 4 * q^59 + 8 * q^61 + 8 * q^62 + 24 * q^63 + 8 * q^64 - 4 * q^65 + 12 * q^66 + 20 * q^67 + 8 * q^68 - 4 * q^69 + 4 * q^70 - 24 * q^71 + 12 * q^72 - 4 * q^73 + 8 * q^74 - 16 * q^75 + 16 * q^76 - 16 * q^77 - 16 * q^78 + 4 * q^79 - 8 * q^81 + 8 * q^82 - 4 * q^83 - 4 * q^84 - 44 * q^85 + 32 * q^86 - 4 * q^87 + 8 * q^88 + 20 * q^89 - 8 * q^92 - 4 * q^93 + 16 * q^94 - 8 * q^95 + 4 * q^96 + 4 * q^97 + 4 * q^98

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