LMFDB - Embedded newform 2645.2.a.l.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2645,2,Mod(1,2645)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2645, 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("2645.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2645 = 5 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2645.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:	$21.1204313346$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.2777.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 4x^{2} + x + 2 $ x^4 - x^3 - 4*x^2 + x + 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$0.825785$ of defining polynomial
Character	$\chi$	$=$	2645.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.825785 q^{2} +2.96965 q^{3} -1.31808 q^{4} +1.00000 q^{5} -2.45229 q^{6} -4.36652 q^{7} +2.74002 q^{8} +5.81882 q^{9} +O(q^{10})$	\(q-0.825785 q^{2} +2.96965 q^{3} -1.31808 q^{4} +1.00000 q^{5} -2.45229 q^{6} -4.36652 q^{7} +2.74002 q^{8} +5.81882 q^{9} -0.825785 q^{10} -1.82578 q^{11} -3.91423 q^{12} +3.08845 q^{13} +3.60581 q^{14} +2.96965 q^{15} +0.373494 q^{16} -0.413499 q^{17} -4.80509 q^{18} -8.44003 q^{19} -1.31808 q^{20} -12.9670 q^{21} +1.50770 q^{22} +8.13689 q^{24} +1.00000 q^{25} -2.55039 q^{26} +8.37089 q^{27} +5.75543 q^{28} -7.15352 q^{29} -2.45229 q^{30} -8.11351 q^{31} -5.78846 q^{32} -5.42194 q^{33} +0.341461 q^{34} -4.36652 q^{35} -7.66966 q^{36} +0.929644 q^{37} +6.96965 q^{38} +9.17161 q^{39} +2.74002 q^{40} -3.80072 q^{41} +10.7080 q^{42} -4.10386 q^{43} +2.40653 q^{44} +5.81882 q^{45} -1.69036 q^{47} +1.10915 q^{48} +12.0665 q^{49} -0.825785 q^{50} -1.22795 q^{51} -4.07082 q^{52} +7.66269 q^{53} -6.91255 q^{54} -1.82578 q^{55} -11.9644 q^{56} -25.0639 q^{57} +5.90727 q^{58} -1.15927 q^{59} -3.91423 q^{60} +1.28773 q^{61} +6.70001 q^{62} -25.4080 q^{63} +4.03304 q^{64} +3.08845 q^{65} +4.47735 q^{66} +6.07619 q^{67} +0.545025 q^{68} +3.60581 q^{70} +3.35540 q^{71} +15.9437 q^{72} -1.25423 q^{73} -0.767686 q^{74} +2.96965 q^{75} +11.1246 q^{76} +7.97233 q^{77} -7.57378 q^{78} +6.68776 q^{79} +0.373494 q^{80} +7.40216 q^{81} +3.13858 q^{82} +1.63087 q^{83} +17.0916 q^{84} -0.413499 q^{85} +3.38890 q^{86} -21.2434 q^{87} -5.00268 q^{88} +5.03350 q^{89} -4.80509 q^{90} -13.4858 q^{91} -24.0943 q^{93} +1.39587 q^{94} -8.44003 q^{95} -17.1897 q^{96} -7.28504 q^{97} -9.96436 q^{98} -10.6239 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} + q^{3} + q^{4} + 4 q^{5} - 10 q^{6} - 3 q^{7} - 6 q^{8} + 9 q^{9}+O(q^{10}) $ 4 * q - q^2 + q^3 + q^4 + 4 * q^5 - 10 * q^6 - 3 * q^7 - 6 * q^8 + 9 * q^9	$ 4 q - q^{2} + q^{3} + q^{4} + 4 q^{5} - 10 q^{6} - 3 q^{7} - 6 q^{8} + 9 q^{9} - q^{10} - 5 q^{11} - q^{12} - 9 q^{14} + q^{15} - q^{16} + 5 q^{17} + 9 q^{18} - 4 q^{19} + q^{20} + 4 q^{21} + 10 q^{22} + 12 q^{24} + 4 q^{25} + 17 q^{26} - 14 q^{27} + 14 q^{28} - 5 q^{29} - 10 q^{30} - 13 q^{31} + 2 q^{32} - 11 q^{33} - 6 q^{34} - 3 q^{35} - 7 q^{36} - 3 q^{37} + 17 q^{38} - 6 q^{39} - 6 q^{40} - 20 q^{41} + 21 q^{42} - 12 q^{43} - 9 q^{44} + 9 q^{45} - 9 q^{47} + 18 q^{48} + 21 q^{49} - q^{50} - 17 q^{51} - 28 q^{52} - 5 q^{53} - 19 q^{54} - 5 q^{55} - 19 q^{56} - 28 q^{57} - 3 q^{58} - 4 q^{59} - q^{60} - 12 q^{61} + 14 q^{62} - 67 q^{63} + 11 q^{66} - 18 q^{67} + 29 q^{68} - 9 q^{70} + 30 q^{71} + 9 q^{72} + q^{73} - 24 q^{74} + q^{75} - 6 q^{76} - 6 q^{77} - 2 q^{78} - 16 q^{79} - q^{80} + 44 q^{81} - 14 q^{82} - 24 q^{83} + 34 q^{84} + 5 q^{85} + 19 q^{86} - 33 q^{87} + 7 q^{88} + 9 q^{89} + 9 q^{90} - 43 q^{91} - 35 q^{93} + 23 q^{94} - 4 q^{95} - 7 q^{96} - 39 q^{97} - 11 q^{98}+O(q^{100}) $ 4 * q - q^2 + q^3 + q^4 + 4 * q^5 - 10 * q^6 - 3 * q^7 - 6 * q^8 + 9 * q^9 - q^10 - 5 * q^11 - q^12 - 9 * q^14 + q^15 - q^16 + 5 * q^17 + 9 * q^18 - 4 * q^19 + q^20 + 4 * q^21 + 10 * q^22 + 12 * q^24 + 4 * q^25 + 17 * q^26 - 14 * q^27 + 14 * q^28 - 5 * q^29 - 10 * q^30 - 13 * q^31 + 2 * q^32 - 11 * q^33 - 6 * q^34 - 3 * q^35 - 7 * q^36 - 3 * q^37 + 17 * q^38 - 6 * q^39 - 6 * q^40 - 20 * q^41 + 21 * q^42 - 12 * q^43 - 9 * q^44 + 9 * q^45 - 9 * q^47 + 18 * q^48 + 21 * q^49 - q^50 - 17 * q^51 - 28 * q^52 - 5 * q^53 - 19 * q^54 - 5 * q^55 - 19 * q^56 - 28 * q^57 - 3 * q^58 - 4 * q^59 - q^60 - 12 * q^61 + 14 * q^62 - 67 * q^63 + 11 * q^66 - 18 * q^67 + 29 * q^68 - 9 * q^70 + 30 * q^71 + 9 * q^72 + q^73 - 24 * q^74 + q^75 - 6 * q^76 - 6 * q^77 - 2 * q^78 - 16 * q^79 - q^80 + 44 * q^81 - 14 * q^82 - 24 * q^83 + 34 * q^84 + 5 * q^85 + 19 * q^86 - 33 * q^87 + 7 * q^88 + 9 * q^89 + 9 * q^90 - 43 * q^91 - 35 * q^93 + 23 * q^94 - 4 * q^95 - 7 * q^96 - 39 * q^97 - 11 * 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 $

$2$	−0.825785	−0.583918	−0.291959	−	0.956431i	$-0.594307\pi$
$2$	−0.825785	−0.583918	−0.291959	+	0.956431i	$0.594307\pi$
$3$	2.96965	1.71453	0.857264	−	0.514877i	$-0.172163\pi$
$3$	2.96965	1.71453	0.857264	+	0.514877i	$0.172163\pi$
$4$	−1.31808	−0.659040
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−2.45229	−1.00114
$7$	−4.36652	−1.65039	−0.825196	−	0.564847i	$-0.808935\pi$
$7$	−4.36652	−1.65039	−0.825196	+	0.564847i	$0.808935\pi$
$8$	2.74002	0.968743
$9$	5.81882	1.93961
$10$	−0.825785	−0.261136
$11$	−1.82578	−0.550495	−0.275247	−	0.961373i	$-0.588760\pi$
$11$	−1.82578	−0.550495	−0.275247	+	0.961373i	$0.588760\pi$
$12$	−3.91423	−1.12994
$13$	3.08845	0.856582	0.428291	−	0.903641i	$-0.359116\pi$
$13$	3.08845	0.856582	0.428291	+	0.903641i	$0.359116\pi$
$14$	3.60581	0.963693
$15$	2.96965	0.766760
$16$	0.373494	0.0933736
$17$	−0.413499	−0.100288	−0.0501442	−	0.998742i	$-0.515968\pi$
$17$	−0.413499	−0.100288	−0.0501442	+	0.998742i	$0.515968\pi$
$18$	−4.80509	−1.13257
$19$	−8.44003	−1.93628	−0.968138	−	0.250417i	$-0.919432\pi$
$19$	−8.44003	−1.93628	−0.968138	+	0.250417i	$0.919432\pi$
$20$	−1.31808	−0.294732
$21$	−12.9670	−2.82964
$22$	1.50770	0.321444
$23$	0	0
$23$	0	0
$24$	8.13689	1.66094
$25$	1.00000	0.200000
$26$	−2.55039	−0.500173
$27$	8.37089	1.61098
$28$	5.75543	1.08767
$29$	−7.15352	−1.32838	−0.664188	−	0.747566i	$-0.731222\pi$
$29$	−7.15352	−1.32838	−0.664188	+	0.747566i	$0.731222\pi$
$30$	−2.45229	−0.447725
$31$	−8.11351	−1.45723	−0.728615	−	0.684923i	$-0.759836\pi$
$31$	−8.11351	−1.45723	−0.728615	+	0.684923i	$0.759836\pi$
$32$	−5.78846	−1.02327
$33$	−5.42194	−0.943838
$34$	0.341461	0.0585601
$35$	−4.36652	−0.738077
$36$	−7.66966	−1.27828
$37$	0.929644	0.152833	0.0764163	−	0.997076i	$-0.475652\pi$
$37$	0.929644	0.152833	0.0764163	+	0.997076i	$0.475652\pi$
$38$	6.96965	1.13063
$39$	9.17161	1.46863
$40$	2.74002	0.433235
$41$	−3.80072	−0.593573	−0.296786	−	0.954944i	$-0.595915\pi$
$41$	−3.80072	−0.593573	−0.296786	+	0.954944i	$0.595915\pi$
$42$	10.7080	1.65228
$43$	−4.10386	−0.625833	−0.312916	−	0.949781i	$-0.601306\pi$
$43$	−4.10386	−0.625833	−0.312916	+	0.949781i	$0.601306\pi$
$44$	2.40653	0.362798
$45$	5.81882	0.867418
$46$	0	0
$47$	−1.69036	−0.246564	−0.123282	−	0.992372i	$-0.539342\pi$
$47$	−1.69036	−0.246564	−0.123282	+	0.992372i	$0.539342\pi$
$48$	1.10915	0.160092
$49$	12.0665	1.72379
$50$	−0.825785	−0.116784
$51$	−1.22795	−0.171947
$52$	−4.07082	−0.564522
$53$	7.66269	1.05255	0.526276	−	0.850314i	$-0.323588\pi$
$53$	7.66269	1.05255	0.526276	+	0.850314i	$0.323588\pi$
$54$	−6.91255	−0.940679
$55$	−1.82578	−0.246189
$56$	−11.9644	−1.59881
$57$	−25.0639	−3.31980
$58$	5.90727	0.775662
$59$	−1.15927	−0.150925	−0.0754623	−	0.997149i	$-0.524043\pi$
$59$	−1.15927	−0.150925	−0.0754623	+	0.997149i	$0.524043\pi$
$60$	−3.91423	−0.505326
$61$	1.28773	0.164877	0.0824384	−	0.996596i	$-0.473729\pi$
$61$	1.28773	0.164877	0.0824384	+	0.996596i	$0.473729\pi$
$62$	6.70001	0.850903
$63$	−25.4080	−3.20111
$64$	4.03304	0.504129
$65$	3.08845	0.383075
$66$	4.47735	0.551124
$67$	6.07619	0.742325	0.371163	−	0.928568i	$-0.378959\pi$
$67$	6.07619	0.742325	0.371163	+	0.928568i	$0.378959\pi$
$68$	0.545025	0.0660940
$69$	0	0
$70$	3.60581	0.430977
$71$	3.35540	0.398213	0.199106	−	0.979978i	$-0.436196\pi$
$71$	3.35540	0.398213	0.199106	+	0.979978i	$0.436196\pi$
$72$	15.9437	1.87898
$73$	−1.25423	−0.146796	−0.0733980	−	0.997303i	$-0.523384\pi$
$73$	−1.25423	−0.146796	−0.0733980	+	0.997303i	$0.523384\pi$
$74$	−0.767686	−0.0892416
$75$	2.96965	0.342906
$76$	11.1246	1.27608
$77$	7.97233	0.908532
$78$	−7.57378	−0.857561
$79$	6.68776	0.752431	0.376216	−	0.926532i	$-0.377225\pi$
$79$	6.68776	0.752431	0.376216	+	0.926532i	$0.377225\pi$
$80$	0.373494	0.0417579
$81$	7.40216	0.822463
$82$	3.13858	0.346598
$83$	1.63087	0.179011	0.0895057	−	0.995986i	$-0.471471\pi$
$83$	1.63087	0.179011	0.0895057	+	0.995986i	$0.471471\pi$
$84$	17.0916	1.86485
$85$	−0.413499	−0.0448503
$86$	3.38890	0.365435
$87$	−21.2434	−2.27754
$88$	−5.00268	−0.533288
$89$	5.03350	0.533550	0.266775	−	0.963759i	$-0.414042\pi$
$89$	5.03350	0.533550	0.266775	+	0.963759i	$0.414042\pi$
$90$	−4.80509	−0.506501
$91$	−13.4858	−1.41370
$92$	0	0
$93$	−24.0943	−2.49846
$94$	1.39587	0.143973
$95$	−8.44003	−0.865929
$96$	−17.1897	−1.75442
$97$	−7.28504	−0.739684	−0.369842	−	0.929095i	$-0.620588\pi$
$97$	−7.28504	−0.739684	−0.369842	+	0.929095i	$0.620588\pi$
$98$	−9.96436	−1.00655
$99$	−10.6239	−1.06774
$100$	−1.31808	−0.131808
$101$	−15.2451	−1.51695	−0.758473	−	0.651704i	$-0.774054\pi$
$101$	−15.2451	−1.51695	−0.758473	+	0.651704i	$0.774054\pi$
$102$	1.01402	0.100403
$103$	−5.49398	−0.541338	−0.270669	−	0.962673i	$-0.587245\pi$
$103$	−5.49398	−0.541338	−0.270669	+	0.962673i	$0.587245\pi$
$104$	8.46241	0.829808
$105$	−12.9670	−1.26545
$106$	−6.32773	−0.614604
$107$	−13.9654	−1.35008	−0.675041	−	0.737780i	$-0.735874\pi$
$107$	−13.9654	−1.35008	−0.675041	+	0.737780i	$0.735874\pi$
$108$	−11.0335	−1.06170
$109$	−4.48961	−0.430027	−0.215013	−	0.976611i	$-0.568980\pi$
$109$	−4.48961	−0.430027	−0.215013	+	0.976611i	$0.568980\pi$
$110$	1.50770	0.143754
$111$	2.76072	0.262036
$112$	−1.63087	−0.154103
$113$	−15.6627	−1.47342	−0.736711	−	0.676208i	$-0.763622\pi$
$113$	−15.6627	−1.47342	−0.736711	+	0.676208i	$0.763622\pi$
$114$	20.6974	1.93849
$115$	0	0
$116$	9.42891	0.875452
$117$	17.9711	1.66143
$118$	0.957310	0.0881276
$119$	1.80556	0.165515
$120$	8.13689	0.742793
$121$	−7.66651	−0.696956
$122$	−1.06339	−0.0962745
$123$	−11.2868	−1.01770
$124$	10.6943	0.960373
$125$	1.00000	0.0894427
$126$	20.9815	1.86918
$127$	21.1659	1.87817	0.939083	−	0.343690i	$-0.111677\pi$
$127$	21.1659	1.87817	0.939083	+	0.343690i	$0.111677\pi$
$128$	8.24651	0.728895
$129$	−12.1870	−1.07301
$130$	−2.55039	−0.223684
$131$	−20.0490	−1.75169	−0.875844	−	0.482594i	$-0.839695\pi$
$131$	−20.0490	−1.75169	−0.875844	+	0.482594i	$0.839695\pi$
$132$	7.14655	0.622027
$133$	36.8536	3.19561
$134$	−5.01763	−0.433457
$135$	8.37089	0.720452
$136$	−1.13300	−0.0971536
$137$	−0.0387909	−0.00331413	−0.00165706	−	0.999999i	$-0.500527\pi$
$137$	−0.0387909	−0.00331413	−0.00165706	+	0.999999i	$0.500527\pi$
$138$	0	0
$139$	0.729151	0.0618458	0.0309229	−	0.999522i	$-0.490155\pi$
$139$	0.729151	0.0618458	0.0309229	+	0.999522i	$0.490155\pi$
$140$	5.75543	0.486422
$141$	−5.01978	−0.422741
$142$	−2.77084	−0.232524
$143$	−5.63884	−0.471544
$144$	2.17329	0.181108
$145$	−7.15352	−0.594067
$146$	1.03572	0.0857168
$147$	35.8334	2.95549
$148$	−1.22534	−0.100723
$149$	−13.7981	−1.13039	−0.565193	−	0.824959i	$-0.691198\pi$
$149$	−13.7981	−1.13039	−0.565193	+	0.824959i	$0.691198\pi$
$150$	−2.45229	−0.200229
$151$	−12.3875	−1.00808	−0.504041	−	0.863680i	$-0.668154\pi$
$151$	−12.3875	−1.00808	−0.504041	+	0.863680i	$0.668154\pi$
$152$	−23.1259	−1.87575
$153$	−2.40608	−0.194520
$154$	−6.58343	−0.530508
$155$	−8.11351	−0.651693
$156$	−12.0889	−0.967888
$157$	7.26556	0.579855	0.289927	−	0.957049i	$-0.406369\pi$
$157$	7.26556	0.579855	0.289927	+	0.957049i	$0.406369\pi$
$158$	−5.52265	−0.439358
$159$	22.7555	1.80463
$160$	−5.78846	−0.457618
$161$	0	0
$162$	−6.11259	−0.480251
$163$	7.04966	0.552172	0.276086	−	0.961133i	$-0.410963\pi$
$163$	7.04966	0.552172	0.276086	+	0.961133i	$0.410963\pi$
$164$	5.00965	0.391188
$165$	−5.42194	−0.422097
$166$	−1.34675	−0.104528
$167$	−14.8188	−1.14671	−0.573357	−	0.819306i	$-0.694359\pi$
$167$	−14.8188	−1.14671	−0.573357	+	0.819306i	$0.694359\pi$
$168$	−35.5300	−2.74120
$169$	−3.46148	−0.266267
$170$	0.341461	0.0261889
$171$	−49.1110	−3.75561
$172$	5.40921	0.412449
$173$	−12.5342	−0.952961	−0.476480	−	0.879185i	$-0.658088\pi$
$173$	−12.5342	−0.952961	−0.476480	+	0.879185i	$0.658088\pi$
$174$	17.5425	1.32989
$175$	−4.36652	−0.330078
$176$	−0.681920	−0.0514017
$177$	−3.44264	−0.258764
$178$	−4.15659	−0.311550
$179$	10.7986	0.807124	0.403562	−	0.914952i	$-0.367772\pi$
$179$	10.7986	0.807124	0.403562	+	0.914952i	$0.367772\pi$
$180$	−7.66966	−0.571663
$181$	19.4897	1.44866	0.724329	−	0.689455i	$-0.242150\pi$
$181$	19.4897	1.44866	0.724329	+	0.689455i	$0.242150\pi$
$182$	11.1364	0.825482
$183$	3.82410	0.282686
$184$	0	0
$185$	0.929644	0.0683488
$186$	19.8967	1.45890
$187$	0.754961	0.0552082
$188$	2.22803	0.162496
$189$	−36.5517	−2.65875
$190$	6.96965	0.505631
$191$	−7.42609	−0.537333	−0.268667	−	0.963233i	$-0.586583\pi$
$191$	−7.42609	−0.537333	−0.268667	+	0.963233i	$0.586583\pi$
$192$	11.9767	0.864344
$193$	7.37236	0.530674	0.265337	−	0.964156i	$-0.414517\pi$
$193$	7.37236	0.530674	0.265337	+	0.964156i	$0.414517\pi$
$194$	6.01588	0.431915
$195$	9.17161	0.656793
$196$	−15.9047	−1.13605
$197$	12.9591	0.923296	0.461648	−	0.887063i	$-0.347258\pi$
$197$	12.9591	0.923296	0.461648	+	0.887063i	$0.347258\pi$
$198$	8.77305	0.623474
$199$	−4.04529	−0.286763	−0.143382	−	0.989667i	$-0.545798\pi$
$199$	−4.04529	−0.286763	−0.143382	+	0.989667i	$0.545798\pi$
$200$	2.74002	0.193749
$201$	18.0442	1.27274
$202$	12.5892	0.885772
$203$	31.2360	2.19234
$204$	1.61853	0.113320
$205$	−3.80072	−0.265454
$206$	4.53684	0.316097
$207$	0	0
$208$	1.15352	0.0799821
$209$	15.4097	1.06591
$210$	10.7080	0.738921
$211$	4.86411	0.334859	0.167429	−	0.985884i	$-0.446453\pi$
$211$	4.86411	0.334859	0.167429	+	0.985884i	$0.446453\pi$
$212$	−10.1000	−0.693674
$213$	9.96436	0.682747
$214$	11.5324	0.788337
$215$	−4.10386	−0.279881
$216$	22.9364	1.56062
$217$	35.4279	2.40500
$218$	3.70745	0.251100
$219$	−3.72461	−0.251686
$220$	2.40653	0.162248
$221$	−1.27707	−0.0859052
$222$	−2.27976	−0.153007
$223$	−17.4275	−1.16703	−0.583517	−	0.812101i	$-0.698324\pi$
$223$	−17.4275	−1.16703	−0.583517	+	0.812101i	$0.698324\pi$
$224$	25.2755	1.68879
$225$	5.81882	0.387921
$226$	12.9340	0.860358
$227$	−21.1885	−1.40633	−0.703165	−	0.711027i	$-0.748230\pi$
$227$	−21.1885	−1.40633	−0.703165	+	0.711027i	$0.748230\pi$
$228$	33.0363	2.18788
$229$	−8.25738	−0.545663	−0.272831	−	0.962062i	$-0.587960\pi$
$229$	−8.25738	−0.545663	−0.272831	+	0.962062i	$0.587960\pi$
$230$	0	0
$231$	23.6750	1.55770
$232$	−19.6008	−1.28685
$233$	15.6709	1.02663	0.513317	−	0.858199i	$-0.328417\pi$
$233$	15.6709	1.02663	0.513317	+	0.858199i	$0.328417\pi$
$234$	−14.8403	−0.970139
$235$	−1.69036	−0.110267
$236$	1.52802	0.0994653
$237$	19.8603	1.29006
$238$	−1.49100	−0.0966472
$239$	−21.9131	−1.41744	−0.708720	−	0.705490i	$-0.750727\pi$
$239$	−21.9131	−1.41744	−0.708720	+	0.705490i	$0.750727\pi$
$240$	1.10915	0.0715951
$241$	16.8259	1.08385	0.541925	−	0.840427i	$-0.317696\pi$
$241$	16.8259	1.08385	0.541925	+	0.840427i	$0.317696\pi$
$242$	6.33089	0.406965
$243$	−3.13085	−0.200844
$244$	−1.69733	−0.108660
$245$	12.0665	0.770903
$246$	9.32047	0.594252
$247$	−26.0666	−1.65858
$248$	−22.2312	−1.41168
$249$	4.84312	0.306920
$250$	−0.825785	−0.0522272
$251$	2.92675	0.184735	0.0923673	−	0.995725i	$-0.470557\pi$
$251$	2.92675	0.184735	0.0923673	+	0.995725i	$0.470557\pi$
$252$	33.4898	2.10966
$253$	0	0
$254$	−17.4784	−1.09669
$255$	−1.22795	−0.0768971
$256$	−14.8759	−0.929744
$257$	12.0708	0.752957	0.376479	−	0.926425i	$-0.377135\pi$
$257$	12.0708	0.752957	0.376479	+	0.926425i	$0.377135\pi$
$258$	10.0639	0.626548
$259$	−4.05931	−0.252233
$260$	−4.07082	−0.252462
$261$	−41.6250	−2.57652
$262$	16.5561	1.02284
$263$	26.7466	1.64927	0.824633	−	0.565668i	$-0.191382\pi$
$263$	26.7466	1.64927	0.824633	+	0.565668i	$0.191382\pi$
$264$	−14.8562	−0.914337
$265$	7.66269	0.470716
$266$	−30.4331	−1.86598
$267$	14.9477	0.914787
$268$	−8.00891	−0.489222
$269$	17.0292	1.03829	0.519145	−	0.854686i	$-0.326251\pi$
$269$	17.0292	1.03829	0.519145	+	0.854686i	$0.326251\pi$
$270$	−6.91255	−0.420685
$271$	16.2201	0.985298	0.492649	−	0.870228i	$-0.336029\pi$
$271$	16.2201	0.985298	0.492649	+	0.870228i	$0.336029\pi$
$272$	−0.154440	−0.00936428
$273$	−40.0481	−2.42382
$274$	0.0320329	0.00193518
$275$	−1.82578	−0.110099
$276$	0	0
$277$	9.68776	0.582081	0.291040	−	0.956711i	$-0.405999\pi$
$277$	9.68776	0.582081	0.291040	+	0.956711i	$0.405999\pi$
$278$	−0.602122	−0.0361128
$279$	−47.2110	−2.82645
$280$	−11.9644	−0.715007
$281$	31.9435	1.90559	0.952796	−	0.303612i	$-0.0981927\pi$
$281$	31.9435	1.90559	0.952796	+	0.303612i	$0.0981927\pi$
$282$	4.14525	0.246846
$283$	4.38777	0.260826	0.130413	−	0.991460i	$-0.458370\pi$
$283$	4.38777	0.260826	0.130413	+	0.991460i	$0.458370\pi$
$284$	−4.42269	−0.262438
$285$	−25.0639	−1.48466
$286$	4.65647	0.275343
$287$	16.5959	0.979628
$288$	−33.6820	−1.98473
$289$	−16.8290	−0.989942
$290$	5.90727	0.346887
$291$	−21.6340	−1.26821
$292$	1.65317	0.0967444
$293$	16.3808	0.956977	0.478488	−	0.878094i	$-0.341185\pi$
$293$	16.3808	0.956977	0.478488	+	0.878094i	$0.341185\pi$
$294$	−29.5907	−1.72576
$295$	−1.15927	−0.0674955
$296$	2.54724	0.148055
$297$	−15.2834	−0.886835
$298$	11.3943	0.660052
$299$	0	0
$300$	−3.91423	−0.225988
$301$	17.9196	1.03287
$302$	10.2294	0.588637
$303$	−45.2727	−2.60085
$304$	−3.15230	−0.180797
$305$	1.28773	0.0737351
$306$	1.98690	0.113584
$307$	−14.6210	−0.834465	−0.417232	−	0.908800i	$-0.637000\pi$
$307$	−14.6210	−0.834465	−0.417232	+	0.908800i	$0.637000\pi$
$308$	−10.5082	−0.598759
$309$	−16.3152	−0.928138
$310$	6.70001	0.380535
$311$	29.3767	1.66580	0.832901	−	0.553422i	$-0.186678\pi$
$311$	29.3767	1.66580	0.832901	+	0.553422i	$0.186678\pi$
$312$	25.1304	1.42273
$313$	−10.5690	−0.597397	−0.298699	−	0.954347i	$-0.596553\pi$
$313$	−10.5690	−0.597397	−0.298699	+	0.954347i	$0.596553\pi$
$314$	−5.99979	−0.338588
$315$	−25.4080	−1.43158
$316$	−8.81500	−0.495882
$317$	16.9413	0.951519	0.475760	−	0.879575i	$-0.342173\pi$
$317$	16.9413	0.951519	0.475760	+	0.879575i	$0.342173\pi$
$318$	−18.7911	−1.05376
$319$	13.0608	0.731263
$320$	4.03304	0.225454
$321$	−41.4722	−2.31475
$322$	0	0
$323$	3.48995	0.194186
$324$	−9.75664	−0.542036
$325$	3.08845	0.171316
$326$	−5.82150	−0.322423
$327$	−13.3326	−0.737293
$328$	−10.4140	−0.575020
$329$	7.38100	0.406928
$330$	4.47735	0.246470
$331$	−14.3391	−0.788149	−0.394075	−	0.919078i	$-0.628935\pi$
$331$	−14.3391	−0.788149	−0.394075	+	0.919078i	$0.628935\pi$
$332$	−2.14962	−0.117976
$333$	5.40943	0.296435
$334$	12.2371	0.669587
$335$	6.07619	0.331978
$336$	−4.84312	−0.264214
$337$	1.50052	0.0817387	0.0408694	−	0.999164i	$-0.486987\pi$
$337$	1.50052	0.0817387	0.0408694	+	0.999164i	$0.486987\pi$
$338$	2.85843	0.155478
$339$	−46.5127	−2.52622
$340$	0.545025	0.0295581
$341$	14.8135	0.802197
$342$	40.5551	2.19297
$343$	−22.1232	−1.19454
$344$	−11.2447	−0.606271
$345$	0	0
$346$	10.3506	0.556451
$347$	−31.5637	−1.69443	−0.847215	−	0.531249i	$-0.821723\pi$
$347$	−31.5637	−1.69443	−0.847215	+	0.531249i	$0.821723\pi$
$348$	28.0005	1.50099
$349$	20.9378	1.12078	0.560388	−	0.828230i	$-0.310652\pi$
$349$	20.9378	1.12078	0.560388	+	0.828230i	$0.310652\pi$
$350$	3.60581	0.192739
$351$	25.8531	1.37994
$352$	10.5685	0.563302
$353$	7.58456	0.403686	0.201843	−	0.979418i	$-0.435307\pi$
$353$	7.58456	0.403686	0.201843	+	0.979418i	$0.435307\pi$
$354$	2.84288	0.151097
$355$	3.35540	0.178086
$356$	−6.63456	−0.351631
$357$	5.36187	0.283780
$358$	−8.91731	−0.471294
$359$	8.93086	0.471353	0.235676	−	0.971832i	$-0.424269\pi$
$359$	8.93086	0.471353	0.235676	+	0.971832i	$0.424269\pi$
$360$	15.9437	0.840305
$361$	52.2342	2.74917
$362$	−16.0943	−0.845897
$363$	−22.7668	−1.19495
$364$	17.7754	0.931682
$365$	−1.25423	−0.0656492
$366$	−3.15788	−0.165065
$367$	−21.0646	−1.09956	−0.549782	−	0.835308i	$-0.685289\pi$
$367$	−21.0646	−1.09956	−0.549782	+	0.835308i	$0.685289\pi$
$368$	0	0
$369$	−22.1157	−1.15130
$370$	−0.767686	−0.0399101
$371$	−33.4593	−1.73712
$372$	31.7582	1.64659
$373$	13.6006	0.704213	0.352106	−	0.935960i	$-0.385466\pi$
$373$	13.6006	0.704213	0.352106	+	0.935960i	$0.385466\pi$
$374$	−0.623435	−0.0322371
$375$	2.96965	0.153352
$376$	−4.63162	−0.238857
$377$	−22.0933	−1.13786
$378$	30.1838	1.55249
$379$	−29.3035	−1.50522	−0.752609	−	0.658467i	$-0.771205\pi$
$379$	−29.3035	−1.50522	−0.752609	+	0.658467i	$0.771205\pi$
$380$	11.1246	0.570682
$381$	62.8552	3.22017
$382$	6.13235	0.313759
$383$	33.7584	1.72497	0.862487	−	0.506079i	$-0.168906\pi$
$383$	33.7584	1.72497	0.862487	+	0.506079i	$0.168906\pi$
$384$	24.4892	1.24971
$385$	7.97233	0.406308
$386$	−6.08798	−0.309870
$387$	−23.8796	−1.21387
$388$	9.60227	0.487481
$389$	−4.81713	−0.244238	−0.122119	−	0.992515i	$-0.538969\pi$
$389$	−4.81713	−0.244238	−0.122119	+	0.992515i	$0.538969\pi$
$390$	−7.57378	−0.383513
$391$	0	0
$392$	33.0625	1.66991
$393$	−59.5385	−3.00332
$394$	−10.7014	−0.539129
$395$	6.68776	0.336498
$396$	14.0032	0.703685
$397$	−15.0836	−0.757026	−0.378513	−	0.925596i	$-0.623564\pi$
$397$	−15.0836	−0.757026	−0.378513	+	0.925596i	$0.623564\pi$
$398$	3.34054	0.167446
$399$	109.442	5.47897
$400$	0.373494	0.0186747
$401$	−30.6639	−1.53128	−0.765641	−	0.643268i	$-0.777578\pi$
$401$	−30.6639	−1.53128	−0.765641	+	0.643268i	$0.777578\pi$
$402$	−14.9006	−0.743174
$403$	−25.0582	−1.24824
$404$	20.0943	0.999728
$405$	7.40216	0.367816
$406$	−25.7942	−1.28015
$407$	−1.69733	−0.0841335
$408$	−3.36460	−0.166573
$409$	−11.3324	−0.560353	−0.280176	−	0.959949i	$-0.590393\pi$
$409$	−11.3324	−0.560353	−0.280176	+	0.959949i	$0.590393\pi$
$410$	3.13858	0.155003
$411$	−0.115195	−0.00568216
$412$	7.24150	0.356763
$413$	5.06200	0.249085
$414$	0	0
$415$	1.63087	0.0800564
$416$	−17.8774	−0.876511
$417$	2.16532	0.106036
$418$	−12.7251	−0.622404
$419$	14.4437	0.705620	0.352810	−	0.935695i	$-0.385226\pi$
$419$	14.4437	0.705620	0.352810	+	0.935695i	$0.385226\pi$
$420$	17.0916	0.833985
$421$	4.14139	0.201839	0.100920	−	0.994895i	$-0.467822\pi$
$421$	4.14139	0.201839	0.100920	+	0.994895i	$0.467822\pi$
$422$	−4.01671	−0.195530
$423$	−9.83589	−0.478237
$424$	20.9959	1.01965
$425$	−0.413499	−0.0200577
$426$	−8.22842	−0.398668
$427$	−5.62290	−0.272111
$428$	18.4075	0.889758
$429$	−16.7454	−0.808475
$430$	3.38890	0.163427
$431$	26.7914	1.29050	0.645249	−	0.763972i	$-0.276754\pi$
$431$	26.7914	1.29050	0.645249	+	0.763972i	$0.276754\pi$
$432$	3.12648	0.150423
$433$	−10.1606	−0.488286	−0.244143	−	0.969739i	$-0.578507\pi$
$433$	−10.1606	−0.488286	−0.244143	+	0.969739i	$0.578507\pi$
$434$	−29.2558	−1.40432
$435$	−21.2434	−1.01854
$436$	5.91767	0.283405
$437$	0	0
$438$	3.07573	0.146964
$439$	24.0931	1.14990	0.574950	−	0.818189i	$-0.305022\pi$
$439$	24.0931	1.14990	0.574950	+	0.818189i	$0.305022\pi$
$440$	−5.00268	−0.238494
$441$	70.2130	3.34347
$442$	1.05459	0.0501616
$443$	17.9911	0.854783	0.427391	−	0.904067i	$-0.359433\pi$
$443$	17.9911	0.854783	0.427391	+	0.904067i	$0.359433\pi$
$444$	−3.63884	−0.172692
$445$	5.03350	0.238611
$446$	14.3914	0.681451
$447$	−40.9756	−1.93808
$448$	−17.6103	−0.832011
$449$	−5.27111	−0.248759	−0.124379	−	0.992235i	$-0.539694\pi$
$449$	−5.27111	−0.248759	−0.124379	+	0.992235i	$0.539694\pi$
$450$	−4.80509	−0.226514
$451$	6.93930	0.326759
$452$	20.6447	0.971044
$453$	−36.7866	−1.72838
$454$	17.4971	0.821181
$455$	−13.4858	−0.632224
$456$	−68.6757	−3.21603
$457$	−19.6622	−0.919761	−0.459880	−	0.887981i	$-0.652108\pi$
$457$	−19.6622	−0.919761	−0.459880	+	0.887981i	$0.652108\pi$
$458$	6.81882	0.318622
$459$	−3.46136	−0.161562
$460$	0	0
$461$	−6.18312	−0.287977	−0.143988	−	0.989579i	$-0.545993\pi$
$461$	−6.18312	−0.287977	−0.143988	+	0.989579i	$0.545993\pi$
$462$	−19.5505	−0.909570
$463$	−28.6960	−1.33362	−0.666809	−	0.745229i	$-0.732340\pi$
$463$	−28.6960	−1.33362	−0.666809	+	0.745229i	$0.732340\pi$
$464$	−2.67180	−0.124035
$465$	−24.0943	−1.11735
$466$	−12.9408	−0.599470
$467$	23.2015	1.07364	0.536819	−	0.843698i	$-0.319626\pi$
$467$	23.2015	1.07364	0.536819	+	0.843698i	$0.319626\pi$
$468$	−23.6874	−1.09495
$469$	−26.5318	−1.22513
$470$	1.39587	0.0643868
$471$	21.5762	0.994177
$472$	−3.17643	−0.146207
$473$	7.49276	0.344518
$474$	−16.4003	−0.753292
$475$	−8.44003	−0.387255
$476$	−2.37987	−0.109081
$477$	44.5878	2.04153
$478$	18.0955	0.827669
$479$	−19.3169	−0.882614	−0.441307	−	0.897356i	$-0.645485\pi$
$479$	−19.3169	−0.882614	−0.441307	+	0.897356i	$0.645485\pi$
$480$	−17.1897	−0.784599
$481$	2.87116	0.130914
$482$	−13.8945	−0.632879
$483$	0	0
$484$	10.1051	0.459322
$485$	−7.28504	−0.330797
$486$	2.58540	0.117276
$487$	8.99035	0.407391	0.203696	−	0.979034i	$-0.434705\pi$
$487$	8.99035	0.407391	0.203696	+	0.979034i	$0.434705\pi$
$488$	3.52840	0.159723
$489$	20.9350	0.946714
$490$	−9.96436	−0.450144
$491$	21.9831	0.992084	0.496042	−	0.868298i	$-0.334786\pi$
$491$	21.9831	0.992084	0.496042	+	0.868298i	$0.334786\pi$
$492$	14.8769	0.670703
$493$	2.95798	0.133221
$494$	21.5254	0.968474
$495$	−10.6239	−0.477509
$496$	−3.03035	−0.136067
$497$	−14.6514	−0.657207
$498$	−3.99937	−0.179216
$499$	−24.6905	−1.10530	−0.552650	−	0.833414i	$-0.686383\pi$
$499$	−24.6905	−1.10530	−0.552650	+	0.833414i	$0.686383\pi$
$500$	−1.31808	−0.0589463
$501$	−44.0067	−1.96607
$502$	−2.41686	−0.107870
$503$	1.38487	0.0617485	0.0308743	−	0.999523i	$-0.490171\pi$
$503$	1.38487	0.0617485	0.0308743	+	0.999523i	$0.490171\pi$
$504$	−69.6184	−3.10105
$505$	−15.2451	−0.678399
$506$	0	0
$507$	−10.2794	−0.456523
$508$	−27.8983	−1.23779
$509$	31.6175	1.40142	0.700710	−	0.713446i	$-0.252867\pi$
$509$	31.6175	1.40142	0.700710	+	0.713446i	$0.252867\pi$
$510$	1.01402	0.0449016
$511$	5.47661	0.242271
$512$	−4.20872	−0.186001
$513$	−70.6506	−3.11930
$514$	−9.96790	−0.439665
$515$	−5.49398	−0.242094
$516$	16.0635	0.707155
$517$	3.08623	0.135732
$518$	3.35212	0.147284
$519$	−37.2223	−1.63388
$520$	8.46241	0.371101
$521$	30.1240	1.31976	0.659878	−	0.751373i	$-0.270608\pi$
$521$	30.1240	1.31976	0.659878	+	0.751373i	$0.270608\pi$
$522$	34.3733	1.50448
$523$	−2.12698	−0.0930065	−0.0465033	−	0.998918i	$-0.514808\pi$
$523$	−2.12698	−0.0930065	−0.0465033	+	0.998918i	$0.514808\pi$
$524$	26.4262	1.15443
$525$	−12.9670	−0.565928
$526$	−22.0869	−0.963036
$527$	3.35493	0.146143
$528$	−2.02506	−0.0881296
$529$	0	0
$530$	−6.32773	−0.274859
$531$	−6.74560	−0.292734
$532$	−48.5760	−2.10604
$533$	−11.7383	−0.508444
$534$	−12.3436	−0.534160
$535$	−13.9654	−0.603775
$536$	16.6489	0.719122
$537$	32.0680	1.38384
$538$	−14.0625	−0.606276
$539$	−22.0309	−0.948938
$540$	−11.0335	−0.474806
$541$	−9.53739	−0.410044	−0.205022	−	0.978757i	$-0.565727\pi$
$541$	−9.53739	−0.410044	−0.205022	+	0.978757i	$0.565727\pi$
$542$	−13.3943	−0.575333
$543$	57.8775	2.48376
$544$	2.39353	0.102622
$545$	−4.48961	−0.192314
$546$	33.0711	1.41531
$547$	−24.1957	−1.03453	−0.517267	−	0.855824i	$-0.673051\pi$
$547$	−24.1957	−1.03453	−0.517267	+	0.855824i	$0.673051\pi$
$548$	0.0511295	0.00218414
$549$	7.49306	0.319796
$550$	1.50770	0.0642887
$551$	60.3759	2.57210
$552$	0	0
$553$	−29.2023	−1.24181
$554$	−8.00000	−0.339887
$555$	2.76072	0.117186
$556$	−0.961079	−0.0407588
$557$	−22.1449	−0.938308	−0.469154	−	0.883116i	$-0.655441\pi$
$557$	−22.1449	−0.938308	−0.469154	+	0.883116i	$0.655441\pi$
$558$	38.9861	1.65042
$559$	−12.6746	−0.536077
$560$	−1.63087	−0.0689169
$561$	2.24197	0.0946560
$562$	−26.3785	−1.11271
$563$	−31.3960	−1.32319	−0.661593	−	0.749863i	$-0.730119\pi$
$563$	−31.3960	−1.32319	−0.661593	+	0.749863i	$0.730119\pi$
$564$	6.61647	0.278603
$565$	−15.6627	−0.658934
$566$	−3.62335	−0.152301
$567$	−32.3217	−1.35739
$568$	9.19386	0.385766
$569$	−11.1160	−0.466006	−0.233003	−	0.972476i	$-0.574855\pi$
$569$	−11.1160	−0.466006	−0.233003	+	0.972476i	$0.574855\pi$
$570$	20.6974	0.866919
$571$	8.63624	0.361415	0.180708	−	0.983537i	$-0.442161\pi$
$571$	8.63624	0.361415	0.180708	+	0.983537i	$0.442161\pi$
$572$	7.43245	0.310766
$573$	−22.0529	−0.921273
$574$	−13.7047	−0.572022
$575$	0	0
$576$	23.4675	0.977812
$577$	39.9115	1.66154	0.830769	−	0.556617i	$-0.187901\pi$
$577$	39.9115	1.66154	0.830769	+	0.556617i	$0.187901\pi$
$578$	13.8971	0.578045
$579$	21.8933	0.909856
$580$	9.42891	0.391514
$581$	−7.12124	−0.295439
$582$	17.8650	0.740530
$583$	−13.9904	−0.579424
$584$	−3.43660	−0.142208
$585$	17.9711	0.743014
$586$	−13.5270	−0.558796
$587$	−45.7611	−1.88876	−0.944382	−	0.328850i	$-0.893339\pi$
$587$	−45.7611	−1.88876	−0.944382	+	0.328850i	$0.893339\pi$
$588$	−47.2313	−1.94778
$589$	68.4783	2.82160
$590$	0.957310	0.0394118
$591$	38.4839	1.58302
$592$	0.347217	0.0142705
$593$	27.2788	1.12021	0.560104	−	0.828422i	$-0.310761\pi$
$593$	27.2788	1.12021	0.560104	+	0.828422i	$0.310761\pi$
$594$	12.6208	0.517839
$595$	1.80556	0.0740205
$596$	18.1870	0.744969
$597$	−12.0131	−0.491663
$598$	0	0
$599$	28.5604	1.16695	0.583473	−	0.812133i	$-0.301693\pi$
$599$	28.5604	1.16695	0.583473	+	0.812133i	$0.301693\pi$
$600$	8.13689	0.332187
$601$	26.6765	1.08816	0.544079	−	0.839034i	$-0.316879\pi$
$601$	26.6765	1.08816	0.544079	+	0.839034i	$0.316879\pi$
$602$	−14.7977	−0.603111
$603$	35.3562	1.43982
$604$	16.3277	0.664366
$605$	−7.66651	−0.311688
$606$	37.3855	1.51868
$607$	21.5827	0.876014	0.438007	−	0.898972i	$-0.355684\pi$
$607$	21.5827	0.876014	0.438007	+	0.898972i	$0.355684\pi$
$608$	48.8548	1.98132
$609$	92.7600	3.75882
$610$	−1.06339	−0.0430553
$611$	−5.22059	−0.211203
$612$	3.17140	0.128196
$613$	2.26603	0.0915241	0.0457620	−	0.998952i	$-0.485428\pi$
$613$	2.26603	0.0915241	0.0457620	+	0.998952i	$0.485428\pi$
$614$	12.0738	0.487259
$615$	−11.2868	−0.455128
$616$	21.8443	0.880134
$617$	−14.1254	−0.568667	−0.284333	−	0.958726i	$-0.591772\pi$
$617$	−14.1254	−0.568667	−0.284333	+	0.958726i	$0.591772\pi$
$618$	13.4728	0.541957
$619$	31.2057	1.25426	0.627131	−	0.778914i	$-0.284229\pi$
$619$	31.2057	1.25426	0.627131	+	0.778914i	$0.284229\pi$
$620$	10.6943	0.429492
$621$	0	0
$622$	−24.2588	−0.972691
$623$	−21.9789	−0.880567
$624$	3.42554	0.137132
$625$	1.00000	0.0400000
$626$	8.72775	0.348831
$627$	45.7613	1.82753
$628$	−9.57659	−0.382148
$629$	−0.384407	−0.0153273
$630$	20.9815	0.835924
$631$	11.2601	0.448256	0.224128	−	0.974560i	$-0.428047\pi$
$631$	11.2601	0.448256	0.224128	+	0.974560i	$0.428047\pi$
$632$	18.3246	0.728913
$633$	14.4447	0.574125
$634$	−13.9899	−0.555609
$635$	21.1659	0.839941
$636$	−29.9936	−1.18932
$637$	37.2669	1.47657
$638$	−10.7854	−0.426998
$639$	19.5245	0.772375
$640$	8.24651	0.325972
$641$	0.353265	0.0139531	0.00697656	−	0.999976i	$-0.497779\pi$
$641$	0.353265	0.0139531	0.00697656	+	0.999976i	$0.497779\pi$
$642$	34.2471	1.35163
$643$	−25.6832	−1.01285	−0.506424	−	0.862285i	$-0.669033\pi$
$643$	−25.6832	−1.01285	−0.506424	+	0.862285i	$0.669033\pi$
$644$	0	0
$645$	−12.1870	−0.479864
$646$	−2.88195	−0.113389
$647$	10.2813	0.404200	0.202100	−	0.979365i	$-0.435223\pi$
$647$	10.2813	0.404200	0.202100	+	0.979365i	$0.435223\pi$
$648$	20.2821	0.796755
$649$	2.11658	0.0830832
$650$	−2.55039	−0.100035
$651$	105.208	4.12344
$652$	−9.29201	−0.363903
$653$	8.35574	0.326985	0.163493	−	0.986545i	$-0.447724\pi$
$653$	8.35574	0.326985	0.163493	+	0.986545i	$0.447724\pi$
$654$	11.0098	0.430518
$655$	−20.0490	−0.783379
$656$	−1.41955	−0.0554240
$657$	−7.29811	−0.284726
$658$	−6.09511	−0.237612
$659$	41.9262	1.63321	0.816606	−	0.577196i	$-0.195853\pi$
$659$	41.9262	1.63321	0.816606	+	0.577196i	$0.195853\pi$
$660$	7.14655	0.278179
$661$	−0.743639	−0.0289242	−0.0144621	−	0.999895i	$-0.504604\pi$
$661$	−0.743639	−0.0289242	−0.0144621	+	0.999895i	$0.504604\pi$
$662$	11.8410	0.460214
$663$	−3.79246	−0.147287
$664$	4.46862	0.173416
$665$	36.8536	1.42912
$666$	−4.46702	−0.173094
$667$	0	0
$668$	19.5324	0.755731
$669$	−51.7536	−2.00091
$670$	−5.01763	−0.193848
$671$	−2.35112	−0.0907638
$672$	75.0593	2.89547
$673$	14.8328	0.571761	0.285880	−	0.958265i	$-0.407714\pi$
$673$	14.8328	0.571761	0.285880	+	0.958265i	$0.407714\pi$
$674$	−1.23911	−0.0477287
$675$	8.37089	0.322196
$676$	4.56250	0.175481
$677$	6.53978	0.251344	0.125672	−	0.992072i	$-0.459891\pi$
$677$	6.53978	0.251344	0.125672	+	0.992072i	$0.459891\pi$
$678$	38.4095	1.47511
$679$	31.8103	1.22077
$680$	−1.13300	−0.0434484
$681$	−62.9224	−2.41119
$682$	−12.2328	−0.468417
$683$	−20.0422	−0.766892	−0.383446	−	0.923563i	$-0.625263\pi$
$683$	−20.0422	−0.766892	−0.383446	+	0.923563i	$0.625263\pi$
$684$	64.7322	2.47510
$685$	−0.0387909	−0.00148212
$686$	18.2690	0.697513
$687$	−24.5215	−0.935554
$688$	−1.53277	−0.0584362
$689$	23.6658	0.901597
$690$	0	0
$691$	−45.1654	−1.71817	−0.859087	−	0.511829i	$-0.828968\pi$
$691$	−45.1654	−1.71817	−0.859087	+	0.511829i	$0.828968\pi$
$692$	16.5211	0.628039
$693$	46.3895	1.76219
$694$	26.0649	0.989408
$695$	0.729151	0.0276583
$696$	−58.2074	−2.20635
$697$	1.57160	0.0595284
$698$	−17.2901	−0.654441
$699$	46.5370	1.76019
$700$	5.75543	0.217535
$701$	2.60677	0.0984562	0.0492281	−	0.998788i	$-0.484324\pi$
$701$	2.60677	0.0984562	0.0492281	+	0.998788i	$0.484324\pi$
$702$	−21.3491	−0.805769
$703$	−7.84623	−0.295926
$704$	−7.36345	−0.277521
$705$	−5.01978	−0.189056
$706$	−6.26321	−0.235719
$707$	66.5682	2.50355
$708$	4.53767	0.170536
$709$	−11.5302	−0.433024	−0.216512	−	0.976280i	$-0.569468\pi$
$709$	−11.5302	−0.433024	−0.216512	+	0.976280i	$0.569468\pi$
$710$	−2.77084	−0.103988
$711$	38.9148	1.45942
$712$	13.7919	0.516873
$713$	0	0
$714$	−4.42775	−0.165704
$715$	−5.63884	−0.210881
$716$	−14.2334	−0.531927
$717$	−65.0742	−2.43024
$718$	−7.37496	−0.275231
$719$	−1.54583	−0.0576498	−0.0288249	−	0.999584i	$-0.509177\pi$
$719$	−1.54583	−0.0576498	−0.0288249	+	0.999584i	$0.509177\pi$
$720$	2.17329	0.0809939
$721$	23.9896	0.893419
$722$	−43.1342	−1.60529
$723$	49.9669	1.85829
$724$	−25.6890	−0.954723
$725$	−7.15352	−0.265675
$726$	18.8005	0.697752
$727$	15.2073	0.564006	0.282003	−	0.959414i	$-0.409001\pi$
$727$	15.2073	0.564006	0.282003	+	0.959414i	$0.409001\pi$
$728$	−36.9513	−1.36951
$729$	−31.5040	−1.16682
$730$	1.03572	0.0383337
$731$	1.69694	0.0627637
$732$	−5.04047	−0.186301
$733$	−1.17283	−0.0433193	−0.0216597	−	0.999765i	$-0.506895\pi$
$733$	−1.17283	−0.0433193	−0.0216597	+	0.999765i	$0.506895\pi$
$734$	17.3948	0.642055
$735$	35.8334	1.32173
$736$	0	0
$737$	−11.0938	−0.408646
$738$	18.2628	0.672263
$739$	−4.85077	−0.178438	−0.0892192	−	0.996012i	$-0.528437\pi$
$739$	−4.85077	−0.178438	−0.0892192	+	0.996012i	$0.528437\pi$
$740$	−1.22534	−0.0450446
$741$	−77.4087	−2.84368
$742$	27.6302	1.01434
$743$	36.4982	1.33899	0.669495	−	0.742817i	$-0.266511\pi$
$743$	36.4982	1.33899	0.669495	+	0.742817i	$0.266511\pi$
$744$	−66.0188	−2.42037
$745$	−13.7981	−0.505524
$746$	−11.2312	−0.411202
$747$	9.48974	0.347212
$748$	−0.995099	−0.0363844
$749$	60.9801	2.22816
$750$	−2.45229	−0.0895450
$751$	−48.9912	−1.78771	−0.893857	−	0.448353i	$-0.852011\pi$
$751$	−48.9912	−1.78771	−0.893857	+	0.448353i	$0.852011\pi$
$752$	−0.631340	−0.0230226
$753$	8.69141	0.316733
$754$	18.2443	0.664418
$755$	−12.3875	−0.450828
$756$	48.1781	1.75222
$757$	−29.3865	−1.06807	−0.534035	−	0.845462i	$-0.679325\pi$
$757$	−29.3865	−1.06807	−0.534035	+	0.845462i	$0.679325\pi$
$758$	24.1984	0.878924
$759$	0	0
$760$	−23.1259	−0.838863
$761$	−23.0505	−0.835579	−0.417789	−	0.908544i	$-0.637195\pi$
$761$	−23.0505	−0.835579	−0.417789	+	0.908544i	$0.637195\pi$
$762$	−51.9048	−1.88031
$763$	19.6040	0.709712
$764$	9.78819	0.354124
$765$	−2.40608	−0.0869919
$766$	−27.8772	−1.00724
$767$	−3.58036	−0.129279
$768$	−44.1762	−1.59407
$769$	3.74678	0.135112	0.0675561	−	0.997715i	$-0.478480\pi$
$769$	3.74678	0.135112	0.0675561	+	0.997715i	$0.478480\pi$
$770$	−6.58343	−0.237250
$771$	35.8461	1.29097
$772$	−9.71736	−0.349735
$773$	−33.2884	−1.19730	−0.598650	−	0.801011i	$-0.704296\pi$
$773$	−33.2884	−1.19730	−0.598650	+	0.801011i	$0.704296\pi$
$774$	19.7194	0.708799
$775$	−8.11351	−0.291446
$776$	−19.9612	−0.716564
$777$	−12.0547	−0.432461
$778$	3.97791	0.142615
$779$	32.0782	1.14932
$780$	−12.0889	−0.432853
$781$	−6.12624	−0.219214
$782$	0	0
$783$	−59.8813	−2.13998
$784$	4.50678	0.160957
$785$	7.26556	0.259319
$786$	49.1660	1.75369
$787$	51.0559	1.81995	0.909973	−	0.414667i	$-0.136102\pi$
$787$	51.0559	1.81995	0.909973	+	0.414667i	$0.136102\pi$
$788$	−17.0811	−0.608489
$789$	79.4280	2.82771
$790$	−5.52265	−0.196487
$791$	68.3915	2.43172
$792$	−29.1097	−1.03437
$793$	3.97709	0.141230
$794$	12.4558	0.442041
$795$	22.7555	0.807055
$796$	5.33202	0.188988
$797$	−7.38055	−0.261432	−0.130716	−	0.991420i	$-0.541728\pi$
$797$	−7.38055	−0.261432	−0.130716	+	0.991420i	$0.541728\pi$
$798$	−90.3758	−3.19927
$799$	0.698963	0.0247275
$800$	−5.78846	−0.204653
$801$	29.2890	1.03488
$802$	25.3218	0.894143
$803$	2.28995	0.0808104
$804$	−23.7836	−0.838784
$805$	0	0
$806$	20.6927	0.728868
$807$	50.5708	1.78018
$808$	−41.7719	−1.46953
$809$	5.99017	0.210603	0.105302	−	0.994440i	$-0.466419\pi$
$809$	5.99017	0.210603	0.105302	+	0.994440i	$0.466419\pi$
$810$	−6.11259	−0.214775
$811$	23.6468	0.830353	0.415176	−	0.909741i	$-0.363720\pi$
$811$	23.6468	0.830353	0.415176	+	0.909741i	$0.363720\pi$
$812$	−41.1716	−1.44484
$813$	48.1679	1.68932
$814$	1.40163	0.0491271
$815$	7.04966	0.246939
$816$	−0.458632	−0.0160553
$817$	34.6367	1.21179
$818$	9.35815	0.327200
$819$	−78.4713	−2.74201
$820$	5.00965	0.174945
$821$	−39.2433	−1.36960	−0.684800	−	0.728731i	$-0.740111\pi$
$821$	−39.2433	−1.36960	−0.684800	+	0.728731i	$0.740111\pi$
$822$	0.0951265	0.00331792
$823$	−10.5840	−0.368934	−0.184467	−	0.982839i	$-0.559056\pi$
$823$	−10.5840	−0.368934	−0.184467	+	0.982839i	$0.559056\pi$
$824$	−15.0536	−0.524417
$825$	−5.42194	−0.188768
$826$	−4.18012	−0.145445
$827$	−46.1524	−1.60488	−0.802438	−	0.596736i	$-0.796464\pi$
$827$	−46.1524	−1.60488	−0.802438	+	0.596736i	$0.796464\pi$
$828$	0	0
$829$	41.0069	1.42423	0.712115	−	0.702063i	$-0.247738\pi$
$829$	41.0069	1.42423	0.712115	+	0.702063i	$0.247738\pi$
$830$	−1.34675	−0.0467463
$831$	28.7692	0.997994
$832$	12.4558	0.431828
$833$	−4.98951	−0.172876
$834$	−1.78809	−0.0619165
$835$	−14.8188	−0.512826
$836$	−20.3112	−0.702477
$837$	−67.9173	−2.34757
$838$	−11.9274	−0.412024
$839$	38.2155	1.31935	0.659673	−	0.751552i	$-0.270695\pi$
$839$	38.2155	1.31935	0.659673	+	0.751552i	$0.270695\pi$
$840$	−35.5300	−1.22590
$841$	22.1728	0.764580
$842$	−3.41990	−0.117857
$843$	94.8611	3.26719
$844$	−6.41128	−0.220685
$845$	−3.46148	−0.119078
$846$	8.12233	0.279251
$847$	33.4760	1.15025
$848$	2.86197	0.0982805
$849$	13.0301	0.447193
$850$	0.341461	0.0117120
$851$	0	0
$852$	−13.1338	−0.449957
$853$	28.1611	0.964217	0.482109	−	0.876111i	$-0.339871\pi$
$853$	28.1611	0.964217	0.482109	+	0.876111i	$0.339871\pi$
$854$	4.64330	0.158891
$855$	−49.1110	−1.67956
$856$	−38.2654	−1.30788
$857$	−41.9309	−1.43233	−0.716167	−	0.697929i	$-0.754105\pi$
$857$	−41.9309	−1.43233	−0.716167	+	0.697929i	$0.754105\pi$
$858$	13.8281	0.472083
$859$	−37.6241	−1.28372	−0.641858	−	0.766823i	$-0.721836\pi$
$859$	−37.6241	−1.28372	−0.641858	+	0.766823i	$0.721836\pi$
$860$	5.40921	0.184453
$861$	49.2841	1.67960
$862$	−22.1240	−0.753545
$863$	22.5541	0.767749	0.383875	−	0.923385i	$-0.374590\pi$
$863$	22.5541	0.767749	0.383875	+	0.923385i	$0.374590\pi$
$864$	−48.4546	−1.64846
$865$	−12.5342	−0.426177
$866$	8.39044	0.285119
$867$	−49.9763	−1.69728
$868$	−46.6967	−1.58499
$869$	−12.2104	−0.414210
$870$	17.5425	0.594747
$871$	18.7660	0.635862
$872$	−12.3016	−0.416585
$873$	−42.3903	−1.43470
$874$	0	0
$875$	−4.36652	−0.147615
$876$	4.90933	0.165871
$877$	−54.3014	−1.83363	−0.916814	−	0.399314i	$-0.869248\pi$
$877$	−54.3014	−1.83363	−0.916814	+	0.399314i	$0.869248\pi$
$878$	−19.8957	−0.671447
$879$	48.6452	1.64076
$880$	−0.681920	−0.0229875
$881$	21.8111	0.734835	0.367417	−	0.930056i	$-0.380242\pi$
$881$	21.8111	0.734835	0.367417	+	0.930056i	$0.380242\pi$
$882$	−57.9808	−1.95231
$883$	6.21108	0.209020	0.104510	−	0.994524i	$-0.466673\pi$
$883$	6.21108	0.209020	0.104510	+	0.994524i	$0.466673\pi$
$884$	1.68328	0.0566149
$885$	−3.44264	−0.115723
$886$	−14.8568	−0.499123
$887$	−48.1015	−1.61509	−0.807545	−	0.589806i	$-0.799204\pi$
$887$	−48.1015	−1.61509	−0.807545	+	0.589806i	$0.799204\pi$
$888$	7.56441	0.253845
$889$	−92.4212	−3.09971
$890$	−4.15659	−0.139329
$891$	−13.5148	−0.452761
$892$	22.9709	0.769121
$893$	14.2667	0.477417
$894$	33.8370	1.13168
$895$	10.7986	0.360957
$896$	−36.0086	−1.20296
$897$	0	0
$898$	4.35280	0.145255
$899$	58.0402	1.93575
$900$	−7.66966	−0.255655
$901$	−3.16852	−0.105559
$902$	−5.73037	−0.190800
$903$	53.2149	1.77088
$904$	−42.9161	−1.42737
$905$	19.4897	0.647859
$906$	30.3778	1.00923
$907$	−9.70464	−0.322237	−0.161119	−	0.986935i	$-0.551510\pi$
$907$	−9.70464	−0.322237	−0.161119	+	0.986935i	$0.551510\pi$
$908$	27.9281	0.926827
$909$	−88.7085	−2.94228
$910$	11.1364	0.369167
$911$	37.5165	1.24298	0.621488	−	0.783423i	$-0.286528\pi$
$911$	37.5165	1.24298	0.621488	+	0.783423i	$0.286528\pi$
$912$	−9.36124	−0.309982
$913$	−2.97762	−0.0985449
$914$	16.2368	0.537065
$915$	3.82410	0.126421
$916$	10.8839	0.359614
$917$	87.5444	2.89097
$918$	2.85834	0.0943392
$919$	−33.1428	−1.09328	−0.546640	−	0.837368i	$-0.684093\pi$
$919$	−33.1428	−1.09328	−0.546640	+	0.837368i	$0.684093\pi$
$920$	0	0
$921$	−43.4193	−1.43071
$922$	5.10593	0.168155
$923$	10.3630	0.341102
$924$	−31.2056	−1.02659
$925$	0.929644	0.0305665
$926$	23.6967	0.778723
$927$	−31.9684	−1.04998
$928$	41.4079	1.35928
$929$	−16.7803	−0.550544	−0.275272	−	0.961366i	$-0.588768\pi$
$929$	−16.7803	−0.550544	−0.275272	+	0.961366i	$0.588768\pi$
$930$	19.8967	0.652438
$931$	−101.842	−3.33774
$932$	−20.6555	−0.676592
$933$	87.2386	2.85606
$934$	−19.1594	−0.626916
$935$	0.754961	0.0246899
$936$	49.2412	1.60950
$937$	38.8046	1.26769	0.633846	−	0.773459i	$-0.281475\pi$
$937$	38.8046	1.26769	0.633846	+	0.773459i	$0.281475\pi$
$938$	21.9096	0.715373
$939$	−31.3863	−1.02425
$940$	2.22803	0.0726703
$941$	−4.96176	−0.161749	−0.0808743	−	0.996724i	$-0.525771\pi$
$941$	−4.96176	−0.161749	−0.0808743	+	0.996724i	$0.525771\pi$
$942$	−17.8173	−0.580518
$943$	0	0
$944$	−0.432982	−0.0140924
$945$	−36.5517	−1.18903
$946$	−6.18741	−0.201170
$947$	−1.52806	−0.0496554	−0.0248277	−	0.999692i	$-0.507904\pi$
$947$	−1.52806	−0.0496554	−0.0248277	+	0.999692i	$0.507904\pi$
$948$	−26.1774	−0.850204
$949$	−3.87361	−0.125743
$950$	6.96965	0.226125
$951$	50.3098	1.63141
$952$	4.94726	0.160341
$953$	−58.6291	−1.89918	−0.949591	−	0.313492i	$-0.898501\pi$
$953$	−58.6291	−1.89918	−0.949591	+	0.313492i	$0.898501\pi$
$954$	−36.8199	−1.19209
$955$	−7.42609	−0.240303
$956$	28.8832	0.934150
$957$	38.7859	1.25377
$958$	15.9516	0.515374
$959$	0.169381	0.00546961
$960$	11.9767	0.386546
$961$	34.8291	1.12352
$962$	−2.37096	−0.0764428
$963$	−81.2619	−2.61863
$964$	−22.1778	−0.714300
$965$	7.37236	0.237325
$966$	0	0
$967$	−39.1526	−1.25906	−0.629532	−	0.776975i	$-0.716753\pi$
$967$	−39.1526	−1.25906	−0.629532	+	0.776975i	$0.716753\pi$
$968$	−21.0064	−0.675171
$969$	10.3639	0.332937
$970$	6.01588	0.193158
$971$	−21.2770	−0.682812	−0.341406	−	0.939916i	$-0.610903\pi$
$971$	−21.2770	−0.682812	−0.341406	+	0.939916i	$0.610903\pi$
$972$	4.12671	0.132364
$973$	−3.18386	−0.102070
$974$	−7.42409	−0.237883
$975$	9.17161	0.293727
$976$	0.480959	0.0153951
$977$	53.9550	1.72617	0.863086	−	0.505057i	$-0.168529\pi$
$977$	53.9550	1.72617	0.863086	+	0.505057i	$0.168529\pi$
$978$	−17.2878	−0.552803
$979$	−9.19009	−0.293717
$980$	−15.9047	−0.508056
$981$	−26.1242	−0.834082
$982$	−18.1533	−0.579296
$983$	−30.0995	−0.960025	−0.480012	−	0.877262i	$-0.659368\pi$
$983$	−30.0995	−0.960025	−0.480012	+	0.877262i	$0.659368\pi$
$984$	−30.9261	−0.985887
$985$	12.9591	0.412910
$986$	−2.44265	−0.0777898
$987$	21.9190	0.697689
$988$	34.3579	1.09307
$989$	0	0
$990$	8.77305	0.278826
$991$	−24.1201	−0.766199	−0.383100	−	0.923707i	$-0.625143\pi$
$991$	−24.1201	−0.766199	−0.383100	+	0.923707i	$0.625143\pi$
$992$	46.9648	1.49113
$993$	−42.5821	−1.35130
$994$	12.0989	0.383755
$995$	−4.04529	−0.128244
$996$	−6.38362	−0.202273
$997$	−17.9240	−0.567659	−0.283830	−	0.958875i	$-0.591605\pi$
$997$	−17.9240	−0.567659	−0.283830	+	0.958875i	$0.591605\pi$
$998$	20.3891	0.645404
$999$	7.78195	0.246210

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2645.2.a.l.1.2	yes	4
23.22	odd	2		2645.2.a.k.1.2	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2645.2.a.k.1.2	✓	4	23.22	odd	2
2645.2.a.l.1.2	yes	4	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:	\( N \)	\(=\)	\( 2645 = 5 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2645.a (trivial)

\(f(q)\)	\(=\)	\(q-0.825785 q^{2} +2.96965 q^{3} -1.31808 q^{4} +1.00000 q^{5} -2.45229 q^{6} -4.36652 q^{7} +2.74002 q^{8} +5.81882 q^{9} +O(q^{10})\)	\(q-0.825785 q^{2} +2.96965 q^{3} -1.31808 q^{4} +1.00000 q^{5} -2.45229 q^{6} -4.36652 q^{7} +2.74002 q^{8} +5.81882 q^{9} -0.825785 q^{10} -1.82578 q^{11} -3.91423 q^{12} +3.08845 q^{13} +3.60581 q^{14} +2.96965 q^{15} +0.373494 q^{16} -0.413499 q^{17} -4.80509 q^{18} -8.44003 q^{19} -1.31808 q^{20} -12.9670 q^{21} +1.50770 q^{22} +8.13689 q^{24} +1.00000 q^{25} -2.55039 q^{26} +8.37089 q^{27} +5.75543 q^{28} -7.15352 q^{29} -2.45229 q^{30} -8.11351 q^{31} -5.78846 q^{32} -5.42194 q^{33} +0.341461 q^{34} -4.36652 q^{35} -7.66966 q^{36} +0.929644 q^{37} +6.96965 q^{38} +9.17161 q^{39} +2.74002 q^{40} -3.80072 q^{41} +10.7080 q^{42} -4.10386 q^{43} +2.40653 q^{44} +5.81882 q^{45} -1.69036 q^{47} +1.10915 q^{48} +12.0665 q^{49} -0.825785 q^{50} -1.22795 q^{51} -4.07082 q^{52} +7.66269 q^{53} -6.91255 q^{54} -1.82578 q^{55} -11.9644 q^{56} -25.0639 q^{57} +5.90727 q^{58} -1.15927 q^{59} -3.91423 q^{60} +1.28773 q^{61} +6.70001 q^{62} -25.4080 q^{63} +4.03304 q^{64} +3.08845 q^{65} +4.47735 q^{66} +6.07619 q^{67} +0.545025 q^{68} +3.60581 q^{70} +3.35540 q^{71} +15.9437 q^{72} -1.25423 q^{73} -0.767686 q^{74} +2.96965 q^{75} +11.1246 q^{76} +7.97233 q^{77} -7.57378 q^{78} +6.68776 q^{79} +0.373494 q^{80} +7.40216 q^{81} +3.13858 q^{82} +1.63087 q^{83} +17.0916 q^{84} -0.413499 q^{85} +3.38890 q^{86} -21.2434 q^{87} -5.00268 q^{88} +5.03350 q^{89} -4.80509 q^{90} -13.4858 q^{91} -24.0943 q^{93} +1.39587 q^{94} -8.44003 q^{95} -17.1897 q^{96} -7.28504 q^{97} -9.96436 q^{98} -10.6239 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} + q^{3} + q^{4} + 4 q^{5} - 10 q^{6} - 3 q^{7} - 6 q^{8} + 9 q^{9}+O(q^{10}) \) 4 * q - q^2 + q^3 + q^4 + 4 * q^5 - 10 * q^6 - 3 * q^7 - 6 * q^8 + 9 * q^9	\( 4 q - q^{2} + q^{3} + q^{4} + 4 q^{5} - 10 q^{6} - 3 q^{7} - 6 q^{8} + 9 q^{9} - q^{10} - 5 q^{11} - q^{12} - 9 q^{14} + q^{15} - q^{16} + 5 q^{17} + 9 q^{18} - 4 q^{19} + q^{20} + 4 q^{21} + 10 q^{22} + 12 q^{24} + 4 q^{25} + 17 q^{26} - 14 q^{27} + 14 q^{28} - 5 q^{29} - 10 q^{30} - 13 q^{31} + 2 q^{32} - 11 q^{33} - 6 q^{34} - 3 q^{35} - 7 q^{36} - 3 q^{37} + 17 q^{38} - 6 q^{39} - 6 q^{40} - 20 q^{41} + 21 q^{42} - 12 q^{43} - 9 q^{44} + 9 q^{45} - 9 q^{47} + 18 q^{48} + 21 q^{49} - q^{50} - 17 q^{51} - 28 q^{52} - 5 q^{53} - 19 q^{54} - 5 q^{55} - 19 q^{56} - 28 q^{57} - 3 q^{58} - 4 q^{59} - q^{60} - 12 q^{61} + 14 q^{62} - 67 q^{63} + 11 q^{66} - 18 q^{67} + 29 q^{68} - 9 q^{70} + 30 q^{71} + 9 q^{72} + q^{73} - 24 q^{74} + q^{75} - 6 q^{76} - 6 q^{77} - 2 q^{78} - 16 q^{79} - q^{80} + 44 q^{81} - 14 q^{82} - 24 q^{83} + 34 q^{84} + 5 q^{85} + 19 q^{86} - 33 q^{87} + 7 q^{88} + 9 q^{89} + 9 q^{90} - 43 q^{91} - 35 q^{93} + 23 q^{94} - 4 q^{95} - 7 q^{96} - 39 q^{97} - 11 q^{98}+O(q^{100}) \) 4 * q - q^2 + q^3 + q^4 + 4 * q^5 - 10 * q^6 - 3 * q^7 - 6 * q^8 + 9 * q^9 - q^10 - 5 * q^11 - q^12 - 9 * q^14 + q^15 - q^16 + 5 * q^17 + 9 * q^18 - 4 * q^19 + q^20 + 4 * q^21 + 10 * q^22 + 12 * q^24 + 4 * q^25 + 17 * q^26 - 14 * q^27 + 14 * q^28 - 5 * q^29 - 10 * q^30 - 13 * q^31 + 2 * q^32 - 11 * q^33 - 6 * q^34 - 3 * q^35 - 7 * q^36 - 3 * q^37 + 17 * q^38 - 6 * q^39 - 6 * q^40 - 20 * q^41 + 21 * q^42 - 12 * q^43 - 9 * q^44 + 9 * q^45 - 9 * q^47 + 18 * q^48 + 21 * q^49 - q^50 - 17 * q^51 - 28 * q^52 - 5 * q^53 - 19 * q^54 - 5 * q^55 - 19 * q^56 - 28 * q^57 - 3 * q^58 - 4 * q^59 - q^60 - 12 * q^61 + 14 * q^62 - 67 * q^63 + 11 * q^66 - 18 * q^67 + 29 * q^68 - 9 * q^70 + 30 * q^71 + 9 * q^72 + q^73 - 24 * q^74 + q^75 - 6 * q^76 - 6 * q^77 - 2 * q^78 - 16 * q^79 - q^80 + 44 * q^81 - 14 * q^82 - 24 * q^83 + 34 * q^84 + 5 * q^85 + 19 * q^86 - 33 * q^87 + 7 * q^88 + 9 * q^89 + 9 * q^90 - 43 * q^91 - 35 * q^93 + 23 * q^94 - 4 * q^95 - 7 * q^96 - 39 * q^97 - 11 * q^98

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