LMFDB - Embedded newform 2645.2.a.k.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:	$0$
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	$-0.191065\pi$
$7$	4.36652	1.65039	0.825196	+	0.564847i	$0.191065\pi$
$8$	2.74002	0.968743
$9$	5.81882	1.93961
$10$	0.825785	0.261136
$11$	1.82578	0.550495	0.275247	−	0.961373i	$-0.411240\pi$
$11$	1.82578	0.550495	0.275247	+	0.961373i	$0.411240\pi$
$12$	−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	$-0.484032\pi$
$17$	0.413499	0.100288	0.0501442	+	0.998742i	$0.484032\pi$
$18$	−4.80509	−1.13257
$19$	8.44003	1.93628	0.968138	−	0.250417i	$-0.0805676\pi$
$19$	8.44003	1.93628	0.968138	+	0.250417i	$0.0805676\pi$
$20$	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	$-0.524348\pi$
$37$	−0.929644	−0.152833	−0.0764163	+	0.997076i	$0.524348\pi$
$38$	−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	$-0.398694\pi$
$43$	4.10386	0.625833	0.312916	+	0.949781i	$0.398694\pi$
$44$	−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	$-0.676412\pi$
$53$	−7.66269	−1.05255	−0.526276	+	0.850314i	$0.676412\pi$
$54$	−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	$-0.526271\pi$
$61$	−1.28773	−0.164877	−0.0824384	+	0.996596i	$0.526271\pi$
$62$	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	$-0.621041\pi$
$67$	−6.07619	−0.742325	−0.371163	+	0.928568i	$0.621041\pi$
$68$	−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	$-0.622775\pi$
$79$	−6.68776	−0.752431	−0.376216	+	0.926532i	$0.622775\pi$
$80$	−0.373494	−0.0417579
$81$	7.40216	0.822463
$82$	3.13858	0.346598
$83$	−1.63087	−0.179011	−0.0895057	−	0.995986i	$-0.528529\pi$
$83$	−1.63087	−0.179011	−0.0895057	+	0.995986i	$0.528529\pi$
$84$	−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	$-0.585958\pi$
$89$	−5.03350	−0.533550	−0.266775	+	0.963759i	$0.585958\pi$
$90$	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	$-0.379412\pi$
$97$	7.28504	0.739684	0.369842	+	0.929095i	$0.379412\pi$
$98$	−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	$-0.412755\pi$
$103$	5.49398	0.541338	0.270669	+	0.962673i	$0.412755\pi$
$104$	8.46241	0.829808
$105$	−12.9670	−1.26545
$106$	6.32773	0.614604
$107$	13.9654	1.35008	0.675041	−	0.737780i	$-0.264126\pi$
$107$	13.9654	1.35008	0.675041	+	0.737780i	$0.264126\pi$
$108$	−11.0335	−1.06170
$109$	4.48961	0.430027	0.215013	−	0.976611i	$-0.431020\pi$
$109$	4.48961	0.430027	0.215013	+	0.976611i	$0.431020\pi$
$110$	1.50770	0.143754
$111$	−2.76072	−0.262036
$112$	1.63087	0.154103
$113$	15.6627	1.47342	0.736711	−	0.676208i	$-0.236378\pi$
$113$	15.6627	1.47342	0.736711	+	0.676208i	$0.236378\pi$
$114$	−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	$-0.499473\pi$
$137$	0.0387909	0.00331413	0.00165706	+	0.999999i	$0.499473\pi$
$138$	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	$-0.308802\pi$
$149$	13.7981	1.13039	0.565193	+	0.824959i	$0.308802\pi$
$150$	−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	$-0.593631\pi$
$157$	−7.26556	−0.579855	−0.289927	+	0.957049i	$0.593631\pi$
$158$	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	$-0.757850\pi$
$181$	−19.4897	−1.44866	−0.724329	+	0.689455i	$0.757850\pi$
$182$	−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	$-0.413417\pi$
$191$	7.42609	0.537333	0.268667	+	0.963233i	$0.413417\pi$
$192$	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	$-0.454202\pi$
$199$	4.04529	0.286763	0.143382	+	0.989667i	$0.454202\pi$
$200$	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	$-0.251770\pi$
$227$	21.1885	1.40633	0.703165	+	0.711027i	$0.251770\pi$
$228$	−33.0363	−2.18788
$229$	8.25738	0.545663	0.272831	−	0.962062i	$-0.412040\pi$
$229$	8.25738	0.545663	0.272831	+	0.962062i	$0.412040\pi$
$230$	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	$-0.682304\pi$
$241$	−16.8259	−1.08385	−0.541925	+	0.840427i	$0.682304\pi$
$242$	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	$-0.529443\pi$
$251$	−2.92675	−0.184735	−0.0923673	+	0.995725i	$0.529443\pi$
$252$	−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	$-0.808618\pi$
$263$	−26.7466	−1.64927	−0.824633	+	0.565668i	$0.808618\pi$
$264$	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	$-0.901807\pi$
$281$	−31.9435	−1.90559	−0.952796	+	0.303612i	$0.901807\pi$
$282$	4.14525	0.246846
$283$	−4.38777	−0.260826	−0.130413	−	0.991460i	$-0.541630\pi$
$283$	−4.38777	−0.260826	−0.130413	+	0.991460i	$0.541630\pi$
$284$	−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	$-0.658815\pi$
$293$	−16.3808	−0.956977	−0.478488	+	0.878094i	$0.658815\pi$
$294$	−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	$-0.403447\pi$
$313$	10.5690	0.597397	0.298699	+	0.954347i	$0.403447\pi$
$314$	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	$-0.513013\pi$
$337$	−1.50052	−0.0817387	−0.0408694	+	0.999164i	$0.513013\pi$
$338$	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	$-0.575731\pi$
$359$	−8.93086	−0.471353	−0.235676	+	0.971832i	$0.575731\pi$
$360$	−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	$-0.314711\pi$
$367$	21.0646	1.09956	0.549782	+	0.835308i	$0.314711\pi$
$368$	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	$-0.614534\pi$
$373$	−13.6006	−0.704213	−0.352106	+	0.935960i	$0.614534\pi$
$374$	−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	$-0.228795\pi$
$379$	29.3035	1.50522	0.752609	+	0.658467i	$0.228795\pi$
$380$	11.1246	0.570682
$381$	62.8552	3.22017
$382$	−6.13235	−0.313759
$383$	−33.7584	−1.72497	−0.862487	−	0.506079i	$-0.831094\pi$
$383$	−33.7584	−1.72497	−0.862487	+	0.506079i	$0.831094\pi$
$384$	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	$-0.461031\pi$
$389$	4.81713	0.244238	0.122119	+	0.992515i	$0.461031\pi$
$390$	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	$-0.222422\pi$
$401$	30.6639	1.53128	0.765641	+	0.643268i	$0.222422\pi$
$402$	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	$-0.614774\pi$
$419$	−14.4437	−0.705620	−0.352810	+	0.935695i	$0.614774\pi$
$420$	17.0916	0.833985
$421$	−4.14139	−0.201839	−0.100920	−	0.994895i	$-0.532178\pi$
$421$	−4.14139	−0.201839	−0.100920	+	0.994895i	$0.532178\pi$
$422$	−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	$-0.723246\pi$
$431$	−26.7914	−1.29050	−0.645249	+	0.763972i	$0.723246\pi$
$432$	3.12648	0.150423
$433$	10.1606	0.488286	0.244143	−	0.969739i	$-0.421493\pi$
$433$	10.1606	0.488286	0.244143	+	0.969739i	$0.421493\pi$
$434$	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	$-0.347892\pi$
$457$	19.6622	0.919761	0.459880	+	0.887981i	$0.347892\pi$
$458$	−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	$-0.680374\pi$
$467$	−23.2015	−1.07364	−0.536819	+	0.843698i	$0.680374\pi$
$468$	−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	$-0.354515\pi$
$479$	19.3169	0.882614	0.441307	+	0.897356i	$0.354515\pi$
$480$	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	$-0.509829\pi$
$503$	−1.38487	−0.0617485	−0.0308743	+	0.999523i	$0.509829\pi$
$504$	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	$-0.729392\pi$
$521$	−30.1240	−1.31976	−0.659878	+	0.751373i	$0.729392\pi$
$522$	34.3733	1.50448
$523$	2.12698	0.0930065	0.0465033	−	0.998918i	$-0.485192\pi$
$523$	2.12698	0.0930065	0.0465033	+	0.998918i	$0.485192\pi$
$524$	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	$-0.344559\pi$
$557$	22.1449	0.938308	0.469154	+	0.883116i	$0.344559\pi$
$558$	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	$-0.269881\pi$
$563$	31.3960	1.32319	0.661593	+	0.749863i	$0.269881\pi$
$564$	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	$-0.425145\pi$
$569$	11.1160	0.466006	0.233003	+	0.972476i	$0.425145\pi$
$570$	20.6974	0.866919
$571$	−8.63624	−0.361415	−0.180708	−	0.983537i	$-0.557839\pi$
$571$	−8.63624	−0.361415	−0.180708	+	0.983537i	$0.557839\pi$
$572$	−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	$-0.514572\pi$
$613$	−2.26603	−0.0915241	−0.0457620	+	0.998952i	$0.514572\pi$
$614$	12.0738	0.487259
$615$	11.2868	0.455128
$616$	21.8443	0.880134
$617$	14.1254	0.568667	0.284333	−	0.958726i	$-0.408228\pi$
$617$	14.1254	0.568667	0.284333	+	0.958726i	$0.408228\pi$
$618$	−13.4728	−0.541957
$619$	−31.2057	−1.25426	−0.627131	−	0.778914i	$-0.715771\pi$
$619$	−31.2057	−1.25426	−0.627131	+	0.778914i	$0.715771\pi$
$620$	−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	$-0.571953\pi$
$631$	−11.2601	−0.448256	−0.224128	+	0.974560i	$0.571953\pi$
$632$	−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	$-0.502221\pi$
$641$	−0.353265	−0.0139531	−0.00697656	+	0.999976i	$0.502221\pi$
$642$	−34.2471	−1.35163
$643$	25.6832	1.01285	0.506424	−	0.862285i	$-0.330967\pi$
$643$	25.6832	1.01285	0.506424	+	0.862285i	$0.330967\pi$
$644$	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	$-0.804147\pi$
$659$	−41.9262	−1.63321	−0.816606	+	0.577196i	$0.804147\pi$
$660$	7.14655	0.278179
$661$	0.743639	0.0289242	0.0144621	−	0.999895i	$-0.495396\pi$
$661$	0.743639	0.0289242	0.0144621	+	0.999895i	$0.495396\pi$
$662$	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	$-0.540109\pi$
$677$	−6.53978	−0.251344	−0.125672	+	0.992072i	$0.540109\pi$
$678$	−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	$-0.515676\pi$
$701$	−2.60677	−0.0984562	−0.0492281	+	0.998788i	$0.515676\pi$
$702$	−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	$-0.430532\pi$
$709$	11.5302	0.433024	0.216512	+	0.976280i	$0.430532\pi$
$710$	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	$-0.590999\pi$
$727$	−15.2073	−0.564006	−0.282003	+	0.959414i	$0.590999\pi$
$728$	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	$-0.493105\pi$
$733$	1.17283	0.0433193	0.0216597	+	0.999765i	$0.493105\pi$
$734$	−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	$-0.733489\pi$
$743$	−36.4982	−1.33899	−0.669495	+	0.742817i	$0.733489\pi$
$744$	−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	$-0.147989\pi$
$751$	48.9912	1.78771	0.893857	+	0.448353i	$0.147989\pi$
$752$	−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	$-0.320675\pi$
$757$	29.3865	1.06807	0.534035	+	0.845462i	$0.320675\pi$
$758$	−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	$-0.521520\pi$
$769$	−3.74678	−0.135112	−0.0675561	+	0.997715i	$0.521520\pi$
$770$	6.58343	0.237250
$771$	35.8461	1.29097
$772$	−9.71736	−0.349735
$773$	33.2884	1.19730	0.598650	−	0.801011i	$-0.295704\pi$
$773$	33.2884	1.19730	0.598650	+	0.801011i	$0.295704\pi$
$774$	−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	$-0.863898\pi$
$787$	−51.0559	−1.81995	−0.909973	+	0.414667i	$0.863898\pi$
$788$	−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	$-0.458272\pi$
$797$	7.38055	0.261432	0.130716	+	0.991420i	$0.458272\pi$
$798$	−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	$-0.203536\pi$
$827$	46.1524	1.60488	0.802438	+	0.596736i	$0.203536\pi$
$828$	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	$-0.729305\pi$
$839$	−38.2155	−1.31935	−0.659673	+	0.751552i	$0.729305\pi$
$840$	−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	$-0.619758\pi$
$881$	−21.8111	−0.734835	−0.367417	+	0.930056i	$0.619758\pi$
$882$	−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	$-0.448490\pi$
$907$	9.70464	0.322237	0.161119	+	0.986935i	$0.448490\pi$
$908$	−27.9281	−0.926827
$909$	−88.7085	−2.94228
$910$	11.1364	0.369167
$911$	−37.5165	−1.24298	−0.621488	−	0.783423i	$-0.713472\pi$
$911$	−37.5165	−1.24298	−0.621488	+	0.783423i	$0.713472\pi$
$912$	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	$-0.315907\pi$
$919$	33.1428	1.09328	0.546640	+	0.837368i	$0.315907\pi$
$920$	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	$-0.718525\pi$
$937$	−38.8046	−1.26769	−0.633846	+	0.773459i	$0.718525\pi$
$938$	21.9096	0.715373
$939$	31.3863	1.02425
$940$	−2.22803	−0.0726703
$941$	4.96176	0.161749	0.0808743	−	0.996724i	$-0.474229\pi$
$941$	4.96176	0.161749	0.0808743	+	0.996724i	$0.474229\pi$
$942$	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	$-0.101499\pi$
$953$	58.6291	1.89918	0.949591	+	0.313492i	$0.101499\pi$
$954$	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	$-0.389097\pi$
$971$	21.2770	0.682812	0.341406	+	0.939916i	$0.389097\pi$
$972$	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	$-0.831471\pi$
$977$	−53.9550	−1.72617	−0.863086	+	0.505057i	$0.831471\pi$
$978$	−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	$-0.340632\pi$
$983$	30.0995	0.960025	0.480012	+	0.877262i	$0.340632\pi$
$984$	−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.k.1.2	✓	4
23.22	odd	2		2645.2.a.l.1.2	yes	4

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

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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