LMFDB - Embedded newform 8027.2.a.f.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8027,2,Mod(1,8027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8027, 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("8027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8027 = 23 \cdot 349 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8027.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:	$64.0959177025$
Analytic rank:	$0$
Dimension:	$176$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	8027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.41247 q^{2} +2.73531 q^{3} +3.82000 q^{4} -4.06212 q^{5} -6.59885 q^{6} +3.23940 q^{7} -4.39069 q^{8} +4.48192 q^{9} +O(q^{10})$	\(q-2.41247 q^{2} +2.73531 q^{3} +3.82000 q^{4} -4.06212 q^{5} -6.59885 q^{6} +3.23940 q^{7} -4.39069 q^{8} +4.48192 q^{9} +9.79973 q^{10} -4.16401 q^{11} +10.4489 q^{12} +5.20045 q^{13} -7.81494 q^{14} -11.1112 q^{15} +2.95241 q^{16} +6.42329 q^{17} -10.8125 q^{18} +5.14494 q^{19} -15.5173 q^{20} +8.86075 q^{21} +10.0456 q^{22} +1.00000 q^{23} -12.0099 q^{24} +11.5008 q^{25} -12.5459 q^{26} +4.05351 q^{27} +12.3745 q^{28} +0.970739 q^{29} +26.8053 q^{30} +5.78906 q^{31} +1.65880 q^{32} -11.3899 q^{33} -15.4960 q^{34} -13.1588 q^{35} +17.1209 q^{36} +9.74412 q^{37} -12.4120 q^{38} +14.2248 q^{39} +17.8355 q^{40} +9.09773 q^{41} -21.3763 q^{42} -5.13587 q^{43} -15.9065 q^{44} -18.2061 q^{45} -2.41247 q^{46} +6.94159 q^{47} +8.07575 q^{48} +3.49369 q^{49} -27.7454 q^{50} +17.5697 q^{51} +19.8657 q^{52} +1.05253 q^{53} -9.77897 q^{54} +16.9147 q^{55} -14.2232 q^{56} +14.0730 q^{57} -2.34188 q^{58} -2.55339 q^{59} -42.4446 q^{60} -12.3008 q^{61} -13.9659 q^{62} +14.5187 q^{63} -9.90662 q^{64} -21.1248 q^{65} +27.4777 q^{66} +0.828885 q^{67} +24.5370 q^{68} +2.73531 q^{69} +31.7452 q^{70} -11.4798 q^{71} -19.6787 q^{72} -10.0341 q^{73} -23.5074 q^{74} +31.4583 q^{75} +19.6537 q^{76} -13.4889 q^{77} -34.3170 q^{78} -1.85268 q^{79} -11.9930 q^{80} -2.35814 q^{81} -21.9480 q^{82} +7.22276 q^{83} +33.8481 q^{84} -26.0922 q^{85} +12.3901 q^{86} +2.65527 q^{87} +18.2829 q^{88} -13.5713 q^{89} +43.9216 q^{90} +16.8463 q^{91} +3.82000 q^{92} +15.8349 q^{93} -16.7464 q^{94} -20.8993 q^{95} +4.53734 q^{96} +17.9077 q^{97} -8.42842 q^{98} -18.6628 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q + 19 q^{2} + 22 q^{3} + 203 q^{4} + 28 q^{5} + 9 q^{6} + 30 q^{7} + 51 q^{8} + 204 q^{9}+O(q^{10}) $ 176 * q + 19 * q^2 + 22 * q^3 + 203 * q^4 + 28 * q^5 + 9 * q^6 + 30 * q^7 + 51 * q^8 + 204 * q^9	\( 176 q + 19 q^{2} + 22 q^{3} + 203 q^{4} + 28 q^{5} + 9 q^{6} + 30 q^{7} + 51 q^{8} + 204 q^{9} + 18 q^{10} + 11 q^{11} + 46 q^{12} + 87 q^{13} - 6 q^{14} + 29 q^{15} + 257 q^{16} + 14 q^{17} + 72 q^{18} + 34 q^{19} + 45 q^{20} + 23 q^{21} + 62 q^{22} + 176 q^{23} + 33 q^{24} + 272 q^{25} + 31 q^{26} + 82 q^{27} + 80 q^{28} + 75 q^{29} - 30 q^{30} + 73 q^{31} + 71 q^{32} + 30 q^{33} + 23 q^{34} + 44 q^{35} + 264 q^{36} + 236 q^{37} - 21 q^{38} + 17 q^{39} + 43 q^{40} + 51 q^{41} + 38 q^{42} + 51 q^{43} + 12 q^{44} + 127 q^{45} + 19 q^{46} + 45 q^{47} + 61 q^{48} + 268 q^{49} + 55 q^{50} - 3 q^{51} + 166 q^{52} + 63 q^{53} - 32 q^{54} + 11 q^{55} - 9 q^{56} + 72 q^{57} + 98 q^{58} + 95 q^{59} - 7 q^{60} + 73 q^{61} + 12 q^{62} + 19 q^{63} + 365 q^{64} + 19 q^{65} - 28 q^{66} + 138 q^{67} + 16 q^{68} + 22 q^{69} + 100 q^{70} + 85 q^{71} + 129 q^{72} + 118 q^{73} - 21 q^{74} - 12 q^{75} + 52 q^{76} + 75 q^{77} + 97 q^{78} + 74 q^{79} + 8 q^{80} + 280 q^{81} + 67 q^{82} + 10 q^{83} - 51 q^{84} + 169 q^{85} - 39 q^{86} - 6 q^{87} + 159 q^{88} + 38 q^{89} + 22 q^{90} + 90 q^{91} + 203 q^{92} + 230 q^{93} + 63 q^{94} + 30 q^{95} + 107 q^{96} + 161 q^{97} + 58 q^{98} + 7 q^{99}+O(q^{100}) \) 176 * q + 19 * q^2 + 22 * q^3 + 203 * q^4 + 28 * q^5 + 9 * q^6 + 30 * q^7 + 51 * q^8 + 204 * q^9 + 18 * q^10 + 11 * q^11 + 46 * q^12 + 87 * q^13 - 6 * q^14 + 29 * q^15 + 257 * q^16 + 14 * q^17 + 72 * q^18 + 34 * q^19 + 45 * q^20 + 23 * q^21 + 62 * q^22 + 176 * q^23 + 33 * q^24 + 272 * q^25 + 31 * q^26 + 82 * q^27 + 80 * q^28 + 75 * q^29 - 30 * q^30 + 73 * q^31 + 71 * q^32 + 30 * q^33 + 23 * q^34 + 44 * q^35 + 264 * q^36 + 236 * q^37 - 21 * q^38 + 17 * q^39 + 43 * q^40 + 51 * q^41 + 38 * q^42 + 51 * q^43 + 12 * q^44 + 127 * q^45 + 19 * q^46 + 45 * q^47 + 61 * q^48 + 268 * q^49 + 55 * q^50 - 3 * q^51 + 166 * q^52 + 63 * q^53 - 32 * q^54 + 11 * q^55 - 9 * q^56 + 72 * q^57 + 98 * q^58 + 95 * q^59 - 7 * q^60 + 73 * q^61 + 12 * q^62 + 19 * q^63 + 365 * q^64 + 19 * q^65 - 28 * q^66 + 138 * q^67 + 16 * q^68 + 22 * q^69 + 100 * q^70 + 85 * q^71 + 129 * q^72 + 118 * q^73 - 21 * q^74 - 12 * q^75 + 52 * q^76 + 75 * q^77 + 97 * q^78 + 74 * q^79 + 8 * q^80 + 280 * q^81 + 67 * q^82 + 10 * q^83 - 51 * q^84 + 169 * q^85 - 39 * q^86 - 6 * q^87 + 159 * q^88 + 38 * q^89 + 22 * q^90 + 90 * q^91 + 203 * q^92 + 230 * q^93 + 63 * q^94 + 30 * q^95 + 107 * q^96 + 161 * q^97 + 58 * q^98 + 7 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.41247	−1.70587	−0.852936	−	0.522015i	$-0.825180\pi$
$2$	−2.41247	−1.70587	−0.852936	+	0.522015i	$0.825180\pi$
$3$	2.73531	1.57923	0.789616	−	0.613601i	$-0.210280\pi$
$3$	2.73531	1.57923	0.789616	+	0.613601i	$0.210280\pi$
$4$	3.82000	1.91000
$5$	−4.06212	−1.81664	−0.908318	−	0.418281i	$-0.862633\pi$
$5$	−4.06212	−1.81664	−0.908318	+	0.418281i	$0.862633\pi$
$6$	−6.59885	−2.69397
$7$	3.23940	1.22438	0.612188	−	0.790712i	$-0.290289\pi$
$7$	3.23940	1.22438	0.612188	+	0.790712i	$0.290289\pi$
$8$	−4.39069	−1.55234
$9$	4.48192	1.49397
$10$	9.79973	3.09895
$11$	−4.16401	−1.25550	−0.627749	−	0.778416i	$-0.716024\pi$
$11$	−4.16401	−1.25550	−0.627749	+	0.778416i	$0.716024\pi$
$12$	10.4489	3.01633
$13$	5.20045	1.44234	0.721172	−	0.692756i	$-0.243604\pi$
$13$	5.20045	1.44234	0.721172	+	0.692756i	$0.243604\pi$
$14$	−7.81494	−2.08863
$15$	−11.1112	−2.86889
$16$	2.95241	0.738102
$17$	6.42329	1.55788	0.778938	−	0.627100i	$-0.215758\pi$
$17$	6.42329	1.55788	0.778938	+	0.627100i	$0.215758\pi$
$18$	−10.8125	−2.54853
$19$	5.14494	1.18033	0.590165	−	0.807283i	$-0.299063\pi$
$19$	5.14494	1.18033	0.590165	+	0.807283i	$0.299063\pi$
$20$	−15.5173	−3.46977
$21$	8.86075	1.93358
$22$	10.0456	2.14172
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−12.0099	−2.45151
$25$	11.5008	2.30016
$26$	−12.5459	−2.46046
$27$	4.05351	0.780099
$28$	12.3745	2.33856
$29$	0.970739	0.180262	0.0901308	−	0.995930i	$-0.471271\pi$
$29$	0.970739	0.180262	0.0901308	+	0.995930i	$0.471271\pi$
$30$	26.8053	4.89396
$31$	5.78906	1.03975	0.519873	−	0.854244i	$-0.325979\pi$
$31$	5.78906	1.03975	0.519873	+	0.854244i	$0.325979\pi$
$32$	1.65880	0.293238
$33$	−11.3899	−1.98272
$34$	−15.4960	−2.65754
$35$	−13.1588	−2.22425
$36$	17.1209	2.85349
$37$	9.74412	1.60192	0.800961	−	0.598716i	$-0.204322\pi$
$37$	9.74412	1.60192	0.800961	+	0.598716i	$0.204322\pi$
$38$	−12.4120	−2.01349
$39$	14.2248	2.27780
$40$	17.8355	2.82004
$41$	9.09773	1.42083	0.710413	−	0.703785i	$-0.248508\pi$
$41$	9.09773	1.42083	0.710413	+	0.703785i	$0.248508\pi$
$42$	−21.3763	−3.29843
$43$	−5.13587	−0.783213	−0.391606	−	0.920133i	$-0.628081\pi$
$43$	−5.13587	−0.783213	−0.391606	+	0.920133i	$0.628081\pi$
$44$	−15.9065	−2.39800
$45$	−18.2061	−2.71401
$46$	−2.41247	−0.355699
$47$	6.94159	1.01254	0.506268	−	0.862376i	$-0.331025\pi$
$47$	6.94159	1.01254	0.506268	+	0.862376i	$0.331025\pi$
$48$	8.07575	1.16563
$49$	3.49369	0.499099
$50$	−27.7454	−3.92379
$51$	17.5697	2.46025
$52$	19.8657	2.75488
$53$	1.05253	0.144576	0.0722878	−	0.997384i	$-0.476970\pi$
$53$	1.05253	0.144576	0.0722878	+	0.997384i	$0.476970\pi$
$54$	−9.77897	−1.33075
$55$	16.9147	2.28078
$56$	−14.2232	−1.90066
$57$	14.0730	1.86401
$58$	−2.34188	−0.307503
$59$	−2.55339	−0.332423	−0.166212	−	0.986090i	$-0.553153\pi$
$59$	−2.55339	−0.332423	−0.166212	+	0.986090i	$0.553153\pi$
$60$	−42.4446	−5.47958
$61$	−12.3008	−1.57495	−0.787476	−	0.616346i	$-0.788612\pi$
$61$	−12.3008	−1.57495	−0.787476	+	0.616346i	$0.788612\pi$
$62$	−13.9659	−1.77367
$63$	14.5187	1.82919
$64$	−9.90662	−1.23833
$65$	−21.1248	−2.62021
$66$	27.4777	3.38227
$67$	0.828885	0.101264	0.0506322	−	0.998717i	$-0.483876\pi$
$67$	0.828885	0.101264	0.0506322	+	0.998717i	$0.483876\pi$
$68$	24.5370	2.97555
$69$	2.73531	0.329293
$70$	31.7452	3.79428
$71$	−11.4798	−1.36240	−0.681202	−	0.732095i	$-0.738543\pi$
$71$	−11.4798	−1.36240	−0.681202	+	0.732095i	$0.738543\pi$
$72$	−19.6787	−2.31916
$73$	−10.0341	−1.17440	−0.587200	−	0.809442i	$-0.699770\pi$
$73$	−10.0341	−1.17440	−0.587200	+	0.809442i	$0.699770\pi$
$74$	−23.5074	−2.73268
$75$	31.4583	3.63249
$76$	19.6537	2.25443
$77$	−13.4889	−1.53720
$78$	−34.3170	−3.88563
$79$	−1.85268	−0.208443	−0.104222	−	0.994554i	$-0.533235\pi$
$79$	−1.85268	−0.208443	−0.104222	+	0.994554i	$0.533235\pi$
$80$	−11.9930	−1.34086
$81$	−2.35814	−0.262016
$82$	−21.9480	−2.42375
$83$	7.22276	0.792801	0.396401	−	0.918078i	$-0.370259\pi$
$83$	7.22276	0.792801	0.396401	+	0.918078i	$0.370259\pi$
$84$	33.8481	3.69313
$85$	−26.0922	−2.83009
$86$	12.3901	1.33606
$87$	2.65527	0.284675
$88$	18.2829	1.94897
$89$	−13.5713	−1.43855	−0.719276	−	0.694725i	$-0.755526\pi$
$89$	−13.5713	−1.43855	−0.719276	+	0.694725i	$0.755526\pi$
$90$	43.9216	4.62975
$91$	16.8463	1.76597
$92$	3.82000	0.398263
$93$	15.8349	1.64200
$94$	−16.7464	−1.72726
$95$	−20.8993	−2.14423
$96$	4.53734	0.463090
$97$	17.9077	1.81825	0.909126	−	0.416522i	$-0.136751\pi$
$97$	17.9077	1.81825	0.909126	+	0.416522i	$0.136751\pi$
$98$	−8.42842	−0.851399
$99$	−18.6628	−1.87568
$100$	43.9331	4.39331
$101$	18.7030	1.86101	0.930507	−	0.366274i	$-0.119367\pi$
$101$	18.7030	1.86101	0.930507	+	0.366274i	$0.119367\pi$
$102$	−42.3863	−4.19687
$103$	−16.1531	−1.59161	−0.795804	−	0.605554i	$-0.792952\pi$
$103$	−16.1531	−1.59161	−0.795804	+	0.605554i	$0.792952\pi$
$104$	−22.8336	−2.23902
$105$	−35.9934	−3.51260
$106$	−2.53919	−0.246628
$107$	9.54927	0.923162	0.461581	−	0.887098i	$-0.347282\pi$
$107$	9.54927	0.923162	0.461581	+	0.887098i	$0.347282\pi$
$108$	15.4844	1.48999
$109$	2.67242	0.255971	0.127986	−	0.991776i	$-0.459149\pi$
$109$	2.67242	0.255971	0.127986	+	0.991776i	$0.459149\pi$
$110$	−40.8062	−3.89072
$111$	26.6532	2.52981
$112$	9.56402	0.903715
$113$	−6.75437	−0.635398	−0.317699	−	0.948192i	$-0.602910\pi$
$113$	−6.75437	−0.635398	−0.317699	+	0.948192i	$0.602910\pi$
$114$	−33.9506	−3.17977
$115$	−4.06212	−0.378795
$116$	3.70822	0.344300
$117$	23.3080	2.15482
$118$	6.15998	0.567072
$119$	20.8076	1.90743
$120$	48.7857	4.45350
$121$	6.33902	0.576274
$122$	29.6752	2.68667
$123$	24.8851	2.24382
$124$	22.1142	1.98591
$125$	−26.4071	−2.36192
$126$	−35.0259	−3.12036
$127$	−16.8356	−1.49392	−0.746959	−	0.664871i	$-0.768487\pi$
$127$	−16.8356	−1.49392	−0.746959	+	0.664871i	$0.768487\pi$
$128$	20.5818	1.81919
$129$	−14.0482	−1.23687
$130$	50.9630	4.46975
$131$	−3.14113	−0.274442	−0.137221	−	0.990540i	$-0.543817\pi$
$131$	−3.14113	−0.274442	−0.137221	+	0.990540i	$0.543817\pi$
$132$	−43.5093	−3.78700
$133$	16.6665	1.44517
$134$	−1.99966	−0.172744
$135$	−16.4659	−1.41716
$136$	−28.2027	−2.41836
$137$	−22.9360	−1.95955	−0.979777	−	0.200092i	$-0.935876\pi$
$137$	−22.9360	−1.95955	−0.979777	+	0.200092i	$0.935876\pi$
$138$	−6.59885	−0.561731
$139$	9.44831	0.801396	0.400698	−	0.916210i	$-0.368768\pi$
$139$	9.44831	0.801396	0.400698	+	0.916210i	$0.368768\pi$
$140$	−50.2667	−4.24831
$141$	18.9874	1.59903
$142$	27.6947	2.32409
$143$	−21.6547	−1.81086
$144$	13.2325	1.10270
$145$	−3.94326	−0.327470
$146$	24.2069	2.00338
$147$	9.55633	0.788192
$148$	37.2225	3.05967
$149$	20.6974	1.69560	0.847799	−	0.530318i	$-0.177927\pi$
$149$	20.6974	1.69560	0.847799	+	0.530318i	$0.177927\pi$
$150$	−75.8922	−6.19657
$151$	3.43764	0.279751	0.139875	−	0.990169i	$-0.455330\pi$
$151$	3.43764	0.279751	0.139875	+	0.990169i	$0.455330\pi$
$152$	−22.5898	−1.83228
$153$	28.7887	2.32743
$154$	32.5415	2.62227
$155$	−23.5159	−1.88884
$156$	54.3389	4.35059
$157$	−18.4152	−1.46969	−0.734846	−	0.678234i	$-0.762746\pi$
$157$	−18.4152	−1.46969	−0.734846	+	0.678234i	$0.762746\pi$
$158$	4.46954	0.355577
$159$	2.87899	0.228319
$160$	−6.73826	−0.532706
$161$	3.23940	0.255300
$162$	5.68895	0.446966
$163$	13.0090	1.01894	0.509472	−	0.860487i	$-0.329841\pi$
$163$	13.0090	1.01894	0.509472	+	0.860487i	$0.329841\pi$
$164$	34.7533	2.71378
$165$	46.2670	3.60188
$166$	−17.4247	−1.35242
$167$	−2.65845	−0.205717	−0.102858	−	0.994696i	$-0.532799\pi$
$167$	−2.65845	−0.205717	−0.102858	+	0.994696i	$0.532799\pi$
$168$	−38.9049	−3.00158
$169$	14.0447	1.08036
$170$	62.9465	4.82778
$171$	23.0592	1.76338
$172$	−19.6190	−1.49594
$173$	−7.77900	−0.591427	−0.295713	−	0.955277i	$-0.595557\pi$
$173$	−7.77900	−0.591427	−0.295713	+	0.955277i	$0.595557\pi$
$174$	−6.40576	−0.485619
$175$	37.2557	2.81627
$176$	−12.2939	−0.926685
$177$	−6.98432	−0.524974
$178$	32.7402	2.45399
$179$	−13.8881	−1.03805	−0.519023	−	0.854760i	$-0.673704\pi$
$179$	−13.8881	−1.03805	−0.519023	+	0.854760i	$0.673704\pi$
$180$	−69.5473	−5.18375
$181$	7.84090	0.582810	0.291405	−	0.956600i	$-0.405877\pi$
$181$	7.84090	0.582810	0.291405	+	0.956600i	$0.405877\pi$
$182$	−40.6412	−3.01252
$183$	−33.6464	−2.48721
$184$	−4.39069	−0.323686
$185$	−39.5818	−2.91011
$186$	−38.2011	−2.80104
$187$	−26.7467	−1.95591
$188$	26.5169	1.93394
$189$	13.1309	0.955136
$190$	50.4190	3.65778
$191$	2.44333	0.176793	0.0883965	−	0.996085i	$-0.471826\pi$
$191$	2.44333	0.176793	0.0883965	+	0.996085i	$0.471826\pi$
$192$	−27.0977	−1.95561
$193$	−13.7548	−0.990094	−0.495047	−	0.868866i	$-0.664849\pi$
$193$	−13.7548	−0.990094	−0.495047	+	0.868866i	$0.664849\pi$
$194$	−43.2018	−3.10171
$195$	−57.7830	−4.13793
$196$	13.3459	0.953279
$197$	9.87868	0.703827	0.351914	−	0.936033i	$-0.385531\pi$
$197$	9.87868	0.703827	0.351914	+	0.936033i	$0.385531\pi$
$198$	45.0234	3.19967
$199$	−19.9664	−1.41538	−0.707690	−	0.706523i	$-0.750263\pi$
$199$	−19.9664	−1.41538	−0.707690	+	0.706523i	$0.750263\pi$
$200$	−50.4966	−3.57065
$201$	2.26726	0.159920
$202$	−45.1203	−3.17465
$203$	3.14461	0.220708
$204$	67.1162	4.69908
$205$	−36.9561	−2.58112
$206$	38.9687	2.71508
$207$	4.48192	0.311515
$208$	15.3538	1.06460
$209$	−21.4236	−1.48190
$210$	86.8330	5.99205
$211$	17.5786	1.21016	0.605082	−	0.796163i	$-0.293140\pi$
$211$	17.5786	1.21016	0.605082	+	0.796163i	$0.293140\pi$
$212$	4.02065	0.276140
$213$	−31.4009	−2.15155
$214$	−23.0373	−1.57480
$215$	20.8625	1.42281
$216$	−17.7977	−1.21098
$217$	18.7531	1.27304
$218$	−6.44713	−0.436655
$219$	−27.4463	−1.85465
$220$	64.6143	4.35629
$221$	33.4040	2.24700
$222$	−64.2999	−4.31553
$223$	−12.4494	−0.833671	−0.416835	−	0.908982i	$-0.636861\pi$
$223$	−12.4494	−0.833671	−0.416835	+	0.908982i	$0.636861\pi$
$224$	5.37352	0.359033
$225$	51.5458	3.43639
$226$	16.2947	1.08391
$227$	16.2664	1.07964	0.539818	−	0.841782i	$-0.318493\pi$
$227$	16.2664	1.07964	0.539818	+	0.841782i	$0.318493\pi$
$228$	53.7589	3.56027
$229$	−4.47918	−0.295992	−0.147996	−	0.988988i	$-0.547282\pi$
$229$	−4.47918	−0.295992	−0.147996	+	0.988988i	$0.547282\pi$
$230$	9.79973	0.646175
$231$	−36.8963	−2.42760
$232$	−4.26222	−0.279828
$233$	9.37580	0.614229	0.307115	−	0.951673i	$-0.400637\pi$
$233$	9.37580	0.614229	0.307115	+	0.951673i	$0.400637\pi$
$234$	−56.2298	−3.67586
$235$	−28.1976	−1.83941
$236$	−9.75396	−0.634929
$237$	−5.06766	−0.329180
$238$	−50.1976	−3.25383
$239$	22.5974	1.46171	0.730853	−	0.682535i	$-0.239123\pi$
$239$	22.5974	1.46171	0.730853	+	0.682535i	$0.239123\pi$
$240$	−32.8047	−2.11753
$241$	5.90408	0.380315	0.190158	−	0.981754i	$-0.439100\pi$
$241$	5.90408	0.380315	0.190158	+	0.981754i	$0.439100\pi$
$242$	−15.2927	−0.983051
$243$	−18.6108	−1.19388
$244$	−46.9889	−3.00816
$245$	−14.1918	−0.906680
$246$	−60.0345	−3.82766
$247$	26.7560	1.70244
$248$	−25.4180	−1.61404
$249$	19.7565	1.25202
$250$	63.7063	4.02914
$251$	−16.2071	−1.02298	−0.511492	−	0.859288i	$-0.670907\pi$
$251$	−16.2071	−1.02298	−0.511492	+	0.859288i	$0.670907\pi$
$252$	55.4615	3.49375
$253$	−4.16401	−0.261789
$254$	40.6153	2.54843
$255$	−71.3702	−4.46938
$256$	−29.8397	−1.86498
$257$	18.5326	1.15603	0.578015	−	0.816026i	$-0.303827\pi$
$257$	18.5326	1.15603	0.578015	+	0.816026i	$0.303827\pi$
$258$	33.8908	2.10995
$259$	31.5651	1.96136
$260$	−80.6969	−5.00461
$261$	4.35078	0.269306
$262$	7.57788	0.468163
$263$	−4.80820	−0.296486	−0.148243	−	0.988951i	$-0.547362\pi$
$263$	−4.80820	−0.296486	−0.148243	+	0.988951i	$0.547362\pi$
$264$	50.0094	3.07787
$265$	−4.27549	−0.262641
$266$	−40.2074	−2.46527
$267$	−37.1216	−2.27181
$268$	3.16634	0.193415
$269$	−5.86660	−0.357693	−0.178846	−	0.983877i	$-0.557237\pi$
$269$	−5.86660	−0.357693	−0.178846	+	0.983877i	$0.557237\pi$
$270$	39.7234	2.41749
$271$	22.1165	1.34348	0.671742	−	0.740785i	$-0.265546\pi$
$271$	22.1165	1.34348	0.671742	+	0.740785i	$0.265546\pi$
$272$	18.9642	1.14987
$273$	46.0799	2.78888
$274$	55.3324	3.34275
$275$	−47.8896	−2.88785
$276$	10.4489	0.628949
$277$	−3.87553	−0.232858	−0.116429	−	0.993199i	$-0.537145\pi$
$277$	−3.87553	−0.232858	−0.116429	+	0.993199i	$0.537145\pi$
$278$	−22.7938	−1.36708
$279$	25.9461	1.55335
$280$	57.7763	3.45280
$281$	20.2207	1.20627	0.603133	−	0.797641i	$-0.293919\pi$
$281$	20.2207	1.20627	0.603133	+	0.797641i	$0.293919\pi$
$282$	−45.8065	−2.72774
$283$	9.83391	0.584565	0.292283	−	0.956332i	$-0.405585\pi$
$283$	9.83391	0.584565	0.292283	+	0.956332i	$0.405585\pi$
$284$	−43.8530	−2.60219
$285$	−57.1662	−3.38623
$286$	52.2414	3.08910
$287$	29.4712	1.73963
$288$	7.43462	0.438089
$289$	24.2587	1.42698
$290$	9.51298	0.558622
$291$	48.9831	2.87144
$292$	−38.3302	−2.24310
$293$	25.1644	1.47012	0.735059	−	0.678003i	$-0.237154\pi$
$293$	25.1644	1.47012	0.735059	+	0.678003i	$0.237154\pi$
$294$	−23.0543	−1.34456
$295$	10.3722	0.603892
$296$	−42.7834	−2.48674
$297$	−16.8789	−0.979413
$298$	−49.9318	−2.89247
$299$	5.20045	0.300750
$300$	120.171	6.93806
$301$	−16.6371	−0.958948
$302$	−8.29319	−0.477219
$303$	51.1584	2.93897
$304$	15.1899	0.871203
$305$	49.9672	2.86111
$306$	−69.4518	−3.97029
$307$	1.92498	0.109864	0.0549321	−	0.998490i	$-0.482506\pi$
$307$	1.92498	0.109864	0.0549321	+	0.998490i	$0.482506\pi$
$308$	−51.5276	−2.93606
$309$	−44.1836	−2.51352
$310$	56.7312	3.22212
$311$	−4.08616	−0.231705	−0.115852	−	0.993266i	$-0.536960\pi$
$311$	−4.08616	−0.231705	−0.115852	+	0.993266i	$0.536960\pi$
$312$	−62.4569	−3.53593
$313$	0.436524	0.0246738	0.0123369	−	0.999924i	$-0.496073\pi$
$313$	0.436524	0.0246738	0.0123369	+	0.999924i	$0.496073\pi$
$314$	44.4261	2.50711
$315$	−58.9768	−3.32297
$316$	−7.07725	−0.398126
$317$	14.5111	0.815025	0.407513	−	0.913200i	$-0.366396\pi$
$317$	14.5111	0.815025	0.407513	+	0.913200i	$0.366396\pi$
$318$	−6.94546	−0.389482
$319$	−4.04217	−0.226318
$320$	40.2419	2.24959
$321$	26.1202	1.45789
$322$	−7.81494	−0.435510
$323$	33.0474	1.83881
$324$	−9.00811	−0.500451
$325$	59.8094	3.31763
$326$	−31.3838	−1.73819
$327$	7.30990	0.404238
$328$	−39.9454	−2.20561
$329$	22.4866	1.23972
$330$	−111.618	−6.14435
$331$	15.4684	0.850221	0.425110	−	0.905141i	$-0.360235\pi$
$331$	15.4684	0.850221	0.425110	+	0.905141i	$0.360235\pi$
$332$	27.5910	1.51425
$333$	43.6724	2.39323
$334$	6.41341	0.350926
$335$	−3.36703	−0.183961
$336$	26.1606	1.42718
$337$	18.6319	1.01495	0.507473	−	0.861668i	$-0.330580\pi$
$337$	18.6319	1.01495	0.507473	+	0.861668i	$0.330580\pi$
$338$	−33.8823	−1.84295
$339$	−18.4753	−1.00344
$340$	−99.6722	−5.40548
$341$	−24.1057	−1.30540
$342$	−55.6296	−3.00810
$343$	−11.3583	−0.613292
$344$	22.5500	1.21582
$345$	−11.1112	−0.598205
$346$	18.7666	1.00890
$347$	−30.0257	−1.61186	−0.805932	−	0.592008i	$-0.798335\pi$
$347$	−30.0257	−1.61186	−0.805932	+	0.592008i	$0.798335\pi$
$348$	10.1431	0.543729
$349$	−1.00000	−0.0535288
$349$	−1.00000	−0.0535288
$350$	−89.8782	−4.80419
$351$	21.0801	1.12517
$352$	−6.90728	−0.368159
$353$	−4.94774	−0.263342	−0.131671	−	0.991293i	$-0.542034\pi$
$353$	−4.94774	−0.263342	−0.131671	+	0.991293i	$0.542034\pi$
$354$	16.8494	0.895538
$355$	46.6324	2.47499
$356$	−51.8423	−2.74763
$357$	56.9152	3.01227
$358$	33.5046	1.77077
$359$	−15.3734	−0.811378	−0.405689	−	0.914011i	$-0.632968\pi$
$359$	−15.3734	−0.811378	−0.405689	+	0.914011i	$0.632968\pi$
$360$	79.9374	4.21307
$361$	7.47036	0.393177
$362$	−18.9159	−0.994199
$363$	17.3392	0.910071
$364$	64.3529	3.37301
$365$	40.7596	2.13346
$366$	81.1709	4.24287
$367$	0.276065	0.0144105	0.00720525	−	0.999974i	$-0.497706\pi$
$367$	0.276065	0.0144105	0.00720525	+	0.999974i	$0.497706\pi$
$368$	2.95241	0.153905
$369$	40.7753	2.12268
$370$	95.4898	4.96428
$371$	3.40955	0.177015
$372$	60.4892	3.13622
$373$	17.8704	0.925295	0.462648	−	0.886542i	$-0.346900\pi$
$373$	17.8704	0.925295	0.462648	+	0.886542i	$0.346900\pi$
$374$	64.5255	3.33653
$375$	−72.2317	−3.73003
$376$	−30.4784	−1.57180
$377$	5.04828	0.259999
$378$	−31.6780	−1.62934
$379$	−19.8777	−1.02105	−0.510524	−	0.859864i	$-0.670549\pi$
$379$	−19.8777	−1.02105	−0.510524	+	0.859864i	$0.670549\pi$
$380$	−79.8355	−4.09548
$381$	−46.0506	−2.35924
$382$	−5.89445	−0.301586
$383$	−13.0261	−0.665603	−0.332801	−	0.942997i	$-0.607994\pi$
$383$	−13.0261	−0.665603	−0.332801	+	0.942997i	$0.607994\pi$
$384$	56.2976	2.87293
$385$	54.7935	2.79254
$386$	33.1831	1.68897
$387$	−23.0186	−1.17010
$388$	68.4074	3.47286
$389$	−5.98493	−0.303448	−0.151724	−	0.988423i	$-0.548482\pi$
$389$	−5.98493	−0.303448	−0.151724	+	0.988423i	$0.548482\pi$
$390$	139.400	7.05877
$391$	6.42329	0.324840
$392$	−15.3397	−0.774773
$393$	−8.59197	−0.433407
$394$	−23.8320	−1.20064
$395$	7.52582	0.378665
$396$	−71.2919	−3.58255
$397$	−0.0600055	−0.00301159	−0.00150580	−	0.999999i	$-0.500479\pi$
$397$	−0.0600055	−0.00301159	−0.00150580	+	0.999999i	$0.500479\pi$
$398$	48.1683	2.41446
$399$	45.5880	2.28225
$400$	33.9551	1.69776
$401$	15.1341	0.755762	0.377881	−	0.925854i	$-0.376653\pi$
$401$	15.1341	0.755762	0.377881	+	0.925854i	$0.376653\pi$
$402$	−5.46969	−0.272803
$403$	30.1057	1.49967
$404$	71.4453	3.55454
$405$	9.57906	0.475988
$406$	−7.58627	−0.376500
$407$	−40.5746	−2.01121
$408$	−77.1432	−3.81916
$409$	1.63048	0.0806221	0.0403111	−	0.999187i	$-0.487165\pi$
$409$	1.63048	0.0806221	0.0403111	+	0.999187i	$0.487165\pi$
$410$	89.1553	4.40307
$411$	−62.7371	−3.09459
$412$	−61.7047	−3.03997
$413$	−8.27145	−0.407011
$414$	−10.8125	−0.531405
$415$	−29.3397	−1.44023
$416$	8.62651	0.422950
$417$	25.8441	1.26559
$418$	51.6837	2.52793
$419$	−28.8894	−1.41134	−0.705669	−	0.708542i	$-0.749353\pi$
$419$	−28.8894	−1.41134	−0.705669	+	0.708542i	$0.749353\pi$
$420$	−137.495	−6.70907
$421$	−18.5307	−0.903133	−0.451567	−	0.892237i	$-0.649135\pi$
$421$	−18.5307	−0.903133	−0.451567	+	0.892237i	$0.649135\pi$
$422$	−42.4079	−2.06439
$423$	31.1117	1.51270
$424$	−4.62132	−0.224431
$425$	73.8731	3.58337
$426$	75.7536	3.67028
$427$	−39.8470	−1.92833
$428$	36.4782	1.76324
$429$	−59.2324	−2.85977
$430$	−50.3302	−2.42714
$431$	−17.5469	−0.845206	−0.422603	−	0.906315i	$-0.638883\pi$
$431$	−17.5469	−0.845206	−0.422603	+	0.906315i	$0.638883\pi$
$432$	11.9676	0.575793
$433$	−9.79065	−0.470508	−0.235254	−	0.971934i	$-0.575592\pi$
$433$	−9.79065	−0.470508	−0.235254	+	0.971934i	$0.575592\pi$
$434$	−45.2411	−2.17164
$435$	−10.7860	−0.517151
$436$	10.2086	0.488906
$437$	5.14494	0.246116
$438$	66.2133	3.16380
$439$	40.0509	1.91152	0.955762	−	0.294141i	$-0.0950336\pi$
$439$	40.0509	1.91152	0.955762	+	0.294141i	$0.0950336\pi$
$440$	−74.2674	−3.54056
$441$	15.6584	0.745640
$442$	−80.5860	−3.83309
$443$	−31.1380	−1.47941	−0.739706	−	0.672930i	$-0.765036\pi$
$443$	−31.1380	−1.47941	−0.739706	+	0.672930i	$0.765036\pi$
$444$	101.815	4.83193
$445$	55.1281	2.61332
$446$	30.0337	1.42214
$447$	56.6138	2.67774
$448$	−32.0915	−1.51618
$449$	21.4661	1.01305	0.506523	−	0.862226i	$-0.330930\pi$
$449$	21.4661	1.01305	0.506523	+	0.862226i	$0.330930\pi$
$450$	−124.353	−5.86203
$451$	−37.8831	−1.78384
$452$	−25.8017	−1.21361
$453$	9.40300	0.441791
$454$	−39.2421	−1.84172
$455$	−68.4317	−3.20813
$456$	−61.7902	−2.89359
$457$	15.4413	0.722315	0.361157	−	0.932505i	$-0.382382\pi$
$457$	15.4413	0.722315	0.361157	+	0.932505i	$0.382382\pi$
$458$	10.8059	0.504925
$459$	26.0369	1.21530
$460$	−15.5173	−0.723498
$461$	33.5834	1.56413	0.782066	−	0.623195i	$-0.214166\pi$
$461$	33.5834	1.56413	0.782066	+	0.623195i	$0.214166\pi$
$462$	89.0112	4.14117
$463$	0.0989485	0.00459853	0.00229926	−	0.999997i	$-0.499268\pi$
$463$	0.0989485	0.00459853	0.00229926	+	0.999997i	$0.499268\pi$
$464$	2.86602	0.133051
$465$	−64.3231	−2.98291
$466$	−22.6188	−1.04780
$467$	36.6133	1.69426	0.847131	−	0.531384i	$-0.178328\pi$
$467$	36.6133	1.69426	0.847131	+	0.531384i	$0.178328\pi$
$468$	89.0366	4.11572
$469$	2.68509	0.123986
$470$	68.0258	3.13779
$471$	−50.3713	−2.32099
$472$	11.2112	0.516036
$473$	21.3858	0.983322
$474$	12.2256	0.561539
$475$	59.1710	2.71495
$476$	79.4850	3.64319
$477$	4.71734	0.215992
$478$	−54.5155	−2.49348
$479$	14.1938	0.648533	0.324267	−	0.945966i	$-0.394882\pi$
$479$	14.1938	0.648533	0.324267	+	0.945966i	$0.394882\pi$
$480$	−18.4312	−0.841266
$481$	50.6738	2.31052
$482$	−14.2434	−0.648769
$483$	8.86075	0.403178
$484$	24.2151	1.10068
$485$	−72.7432	−3.30310
$486$	44.8980	2.03661
$487$	−33.9233	−1.53721	−0.768605	−	0.639723i	$-0.779049\pi$
$487$	−33.9233	−1.53721	−0.768605	+	0.639723i	$0.779049\pi$
$488$	54.0089	2.44487
$489$	35.5837	1.60915
$490$	34.2372	1.54668
$491$	−10.5001	−0.473862	−0.236931	−	0.971526i	$-0.576142\pi$
$491$	−10.5001	−0.473862	−0.236931	+	0.971526i	$0.576142\pi$
$492$	95.0612	4.28569
$493$	6.23534	0.280825
$494$	−64.5479	−2.90415
$495$	75.8105	3.40743
$496$	17.0917	0.767438
$497$	−37.1877	−1.66810
$498$	−47.6619	−2.13578
$499$	4.94415	0.221331	0.110665	−	0.993858i	$-0.464702\pi$
$499$	4.94415	0.221331	0.110665	+	0.993858i	$0.464702\pi$
$500$	−100.875	−4.51128
$501$	−7.27167	−0.324874
$502$	39.0992	1.74508
$503$	−3.26214	−0.145452	−0.0727259	−	0.997352i	$-0.523170\pi$
$503$	−3.26214	−0.145452	−0.0727259	+	0.997352i	$0.523170\pi$
$504$	−63.7473	−2.83953
$505$	−75.9737	−3.38078
$506$	10.0456	0.446579
$507$	38.4165	1.70614
$508$	−64.3120	−2.85338
$509$	41.5852	1.84323	0.921615	−	0.388105i	$-0.126870\pi$
$509$	41.5852	1.84323	0.921615	+	0.388105i	$0.126870\pi$
$510$	172.178	7.62418
$511$	−32.5043	−1.43791
$512$	30.8237	1.36223
$513$	20.8551	0.920774
$514$	−44.7093	−1.97204
$515$	65.6157	2.89137
$516$	−53.6641	−2.36243
$517$	−28.9049	−1.27124
$518$	−76.1497	−3.34583
$519$	−21.2780	−0.934000
$520$	92.7527	4.06748
$521$	16.1396	0.707090	0.353545	−	0.935418i	$-0.384976\pi$
$521$	16.1396	0.707090	0.353545	+	0.935418i	$0.384976\pi$
$522$	−10.4961	−0.459402
$523$	−17.0067	−0.743653	−0.371827	−	0.928302i	$-0.621268\pi$
$523$	−17.0067	−0.743653	−0.371827	+	0.928302i	$0.621268\pi$
$524$	−11.9991	−0.524184
$525$	101.906	4.44754
$526$	11.5996	0.505768
$527$	37.1848	1.61980
$528$	−33.6275	−1.46345
$529$	1.00000	0.0434783
$530$	10.3145	0.448032
$531$	−11.4441	−0.496632
$532$	63.6660	2.76027
$533$	47.3123	2.04932
$534$	89.5547	3.87541
$535$	−38.7903	−1.67705
$536$	−3.63938	−0.157197
$537$	−37.9883	−1.63932
$538$	14.1530	0.610179
$539$	−14.5478	−0.626617
$540$	−62.8996	−2.70677
$541$	39.2315	1.68670	0.843348	−	0.537368i	$-0.180581\pi$
$541$	39.2315	1.68670	0.843348	+	0.537368i	$0.180581\pi$
$542$	−53.3554	−2.29181
$543$	21.4473	0.920391
$544$	10.6550	0.456828
$545$	−10.8557	−0.465007
$546$	−111.166	−4.75748
$547$	26.3033	1.12465	0.562325	−	0.826916i	$-0.309907\pi$
$547$	26.3033	1.12465	0.562325	+	0.826916i	$0.309907\pi$
$548$	−87.6155	−3.74275
$549$	−55.1310	−2.35294
$550$	115.532	4.92630
$551$	4.99439	0.212768
$552$	−12.0099	−0.511176
$553$	−6.00157	−0.255213
$554$	9.34959	0.397226
$555$	−108.268	−4.59574
$556$	36.0926	1.53067
$557$	−38.6045	−1.63572	−0.817862	−	0.575415i	$-0.804841\pi$
$557$	−38.6045	−1.63572	−0.817862	+	0.575415i	$0.804841\pi$
$558$	−62.5941	−2.64982
$559$	−26.7088	−1.12966
$560$	−38.8502	−1.64172
$561$	−73.1605	−3.08884
$562$	−48.7818	−2.05774
$563$	−14.9804	−0.631350	−0.315675	−	0.948867i	$-0.602231\pi$
$563$	−14.9804	−0.631350	−0.315675	+	0.948867i	$0.602231\pi$
$564$	72.5319	3.05414
$565$	27.4371	1.15429
$566$	−23.7240	−0.997194
$567$	−7.63896	−0.320806
$568$	50.4044	2.11492
$569$	4.10009	0.171885	0.0859424	−	0.996300i	$-0.472610\pi$
$569$	4.10009	0.171885	0.0859424	+	0.996300i	$0.472610\pi$
$570$	137.912	5.77648
$571$	−10.1251	−0.423724	−0.211862	−	0.977300i	$-0.567953\pi$
$571$	−10.1251	−0.423724	−0.211862	+	0.977300i	$0.567953\pi$
$572$	−82.7211	−3.45874
$573$	6.68326	0.279197
$574$	−71.0982	−2.96758
$575$	11.5008	0.479617
$576$	−44.4007	−1.85003
$577$	−31.0534	−1.29277	−0.646384	−	0.763012i	$-0.723720\pi$
$577$	−31.0534	−1.29277	−0.646384	+	0.763012i	$0.723720\pi$
$578$	−58.5233	−2.43425
$579$	−37.6237	−1.56359
$580$	−15.0632	−0.625467
$581$	23.3974	0.970688
$582$	−118.170	−4.89831
$583$	−4.38274	−0.181514
$584$	44.0566	1.82307
$585$	−94.6799	−3.91453
$586$	−60.7083	−2.50784
$587$	19.4674	0.803505	0.401753	−	0.915748i	$-0.368401\pi$
$587$	19.4674	0.803505	0.401753	+	0.915748i	$0.368401\pi$
$588$	36.5052	1.50545
$589$	29.7843	1.22724
$590$	−25.0226	−1.03016
$591$	27.0213	1.11151
$592$	28.7686	1.18238
$593$	−21.4563	−0.881105	−0.440552	−	0.897727i	$-0.645217\pi$
$593$	−21.4563	−0.881105	−0.440552	+	0.897727i	$0.645217\pi$
$594$	40.7198	1.67075
$595$	−84.5229	−3.46510
$596$	79.0641	3.23859
$597$	−54.6143	−2.23521
$598$	−12.5459	−0.513040
$599$	8.74498	0.357310	0.178655	−	0.983912i	$-0.442825\pi$
$599$	8.74498	0.357310	0.178655	+	0.983912i	$0.442825\pi$
$600$	−138.124	−5.63888
$601$	−29.4972	−1.20322	−0.601608	−	0.798792i	$-0.705473\pi$
$601$	−29.4972	−1.20322	−0.601608	+	0.798792i	$0.705473\pi$
$602$	40.1365	1.63584
$603$	3.71500	0.151286
$604$	13.1318	0.534324
$605$	−25.7499	−1.04688
$606$	−123.418	−5.01351
$607$	−32.1118	−1.30338	−0.651690	−	0.758486i	$-0.725940\pi$
$607$	−32.1118	−1.30338	−0.651690	+	0.758486i	$0.725940\pi$
$608$	8.53443	0.346117
$609$	8.60148	0.348549
$610$	−120.544	−4.88069
$611$	36.0994	1.46042
$612$	109.973	4.44539
$613$	−7.54526	−0.304750	−0.152375	−	0.988323i	$-0.548692\pi$
$613$	−7.54526	−0.304750	−0.152375	+	0.988323i	$0.548692\pi$
$614$	−4.64394	−0.187414
$615$	−101.086	−4.07619
$616$	59.2256	2.38627
$617$	−19.9929	−0.804883	−0.402441	−	0.915446i	$-0.631838\pi$
$617$	−19.9929	−0.804883	−0.402441	+	0.915446i	$0.631838\pi$
$618$	106.592	4.28774
$619$	−34.5889	−1.39024	−0.695122	−	0.718892i	$-0.744650\pi$
$619$	−34.5889	−1.39024	−0.695122	+	0.718892i	$0.744650\pi$
$620$	−89.8306	−3.60768
$621$	4.05351	0.162662
$622$	9.85773	0.395259
$623$	−43.9627	−1.76133
$624$	41.9975	1.68125
$625$	49.7648	1.99059
$626$	−1.05310	−0.0420903
$627$	−58.6002	−2.34026
$628$	−70.3461	−2.80711
$629$	62.5893	2.49560
$630$	142.280	5.66856
$631$	−23.3604	−0.929963	−0.464981	−	0.885320i	$-0.653939\pi$
$631$	−23.3604	−0.929963	−0.464981	+	0.885320i	$0.653939\pi$
$632$	8.13456	0.323576
$633$	48.0831	1.91113
$634$	−35.0076	−1.39033
$635$	68.3882	2.71390
$636$	10.9977	0.436089
$637$	18.1688	0.719872
$638$	9.75161	0.386070
$639$	−51.4517	−2.03540
$640$	−83.6057	−3.30481
$641$	−24.8137	−0.980082	−0.490041	−	0.871699i	$-0.663018\pi$
$641$	−24.8137	−0.980082	−0.490041	+	0.871699i	$0.663018\pi$
$642$	−63.0141	−2.48697
$643$	−15.8611	−0.625500	−0.312750	−	0.949835i	$-0.601250\pi$
$643$	−15.8611	−0.625500	−0.312750	+	0.949835i	$0.601250\pi$
$644$	12.3745	0.487624
$645$	57.0655	2.24695
$646$	−79.7258	−3.13677
$647$	37.7695	1.48487	0.742437	−	0.669916i	$-0.233670\pi$
$647$	37.7695	1.48487	0.742437	+	0.669916i	$0.233670\pi$
$648$	10.3539	0.406739
$649$	10.6324	0.417357
$650$	−144.288	−5.65945
$651$	51.2954	2.01043
$652$	49.6944	1.94618
$653$	−26.0114	−1.01790	−0.508952	−	0.860795i	$-0.669967\pi$
$653$	−26.0114	−1.01790	−0.508952	+	0.860795i	$0.669967\pi$
$654$	−17.6349	−0.689579
$655$	12.7597	0.498561
$656$	26.8602	1.04871
$657$	−44.9719	−1.75452
$658$	−54.2481	−2.11481
$659$	−25.4702	−0.992180	−0.496090	−	0.868271i	$-0.665231\pi$
$659$	−25.4702	−0.992180	−0.496090	+	0.868271i	$0.665231\pi$
$660$	176.740	6.87960
$661$	8.78925	0.341862	0.170931	−	0.985283i	$-0.445322\pi$
$661$	8.78925	0.341862	0.170931	+	0.985283i	$0.445322\pi$
$662$	−37.3170	−1.45037
$663$	91.3703	3.54853
$664$	−31.7130	−1.23070
$665$	−67.7013	−2.62534
$666$	−105.358	−4.08255
$667$	0.970739	0.0375872
$668$	−10.1553	−0.392919
$669$	−34.0529	−1.31656
$670$	8.12286	0.313813
$671$	51.2206	1.97735
$672$	14.6982	0.566997
$673$	−10.3021	−0.397118	−0.198559	−	0.980089i	$-0.563626\pi$
$673$	−10.3021	−0.397118	−0.198559	+	0.980089i	$0.563626\pi$
$674$	−44.9489	−1.73137
$675$	46.6187	1.79436
$676$	53.6506	2.06348
$677$	−16.9300	−0.650673	−0.325336	−	0.945598i	$-0.605478\pi$
$677$	−16.9300	−0.650673	−0.325336	+	0.945598i	$0.605478\pi$
$678$	44.5711	1.71174
$679$	58.0101	2.22623
$680$	114.563	4.39328
$681$	44.4935	1.70500
$682$	58.1543	2.22684
$683$	−5.38235	−0.205950	−0.102975	−	0.994684i	$-0.532836\pi$
$683$	−5.38235	−0.205950	−0.102975	+	0.994684i	$0.532836\pi$
$684$	88.0862	3.36806
$685$	93.1688	3.55980
$686$	27.4016	1.04620
$687$	−12.2519	−0.467441
$688$	−15.1632	−0.578091
$689$	5.47361	0.208528
$690$	26.8053	1.02046
$691$	3.22259	0.122593	0.0612965	−	0.998120i	$-0.480476\pi$
$691$	3.22259	0.122593	0.0612965	+	0.998120i	$0.480476\pi$
$692$	−29.7158	−1.12963
$693$	−60.4562	−2.29654
$694$	72.4360	2.74963
$695$	−38.3802	−1.45584
$696$	−11.6585	−0.441914
$697$	58.4374	2.21347
$698$	2.41247	0.0913133
$699$	25.6457	0.970010
$700$	142.317	5.37907
$701$	6.50385	0.245647	0.122824	−	0.992429i	$-0.460805\pi$
$701$	6.50385	0.245647	0.122824	+	0.992429i	$0.460805\pi$
$702$	−50.8550	−1.91940
$703$	50.1328	1.89080
$704$	41.2513	1.55472
$705$	−77.1291	−2.90485
$706$	11.9363	0.449227
$707$	60.5863	2.27858
$708$	−26.6801	−1.00270
$709$	7.58839	0.284988	0.142494	−	0.989796i	$-0.454488\pi$
$709$	7.58839	0.284988	0.142494	+	0.989796i	$0.454488\pi$
$710$	−112.499	−4.22202
$711$	−8.30358	−0.311409
$712$	59.5873	2.23313
$713$	5.78906	0.216802
$714$	−137.306	−5.13855
$715$	87.9642	3.28967
$716$	−53.0526	−1.98267
$717$	61.8109	2.30837
$718$	37.0879	1.38411
$719$	6.98428	0.260470	0.130235	−	0.991483i	$-0.458427\pi$
$719$	6.98428	0.260470	0.130235	+	0.991483i	$0.458427\pi$
$720$	−53.7518	−2.00321
$721$	−52.3262	−1.94873
$722$	−18.0220	−0.670709
$723$	16.1495	0.600606
$724$	29.9522	1.11317
$725$	11.1643	0.414631
$726$	−41.8302	−1.55247
$727$	−11.4897	−0.426130	−0.213065	−	0.977038i	$-0.568345\pi$
$727$	−11.4897	−0.426130	−0.213065	+	0.977038i	$0.568345\pi$
$728$	−73.9670	−2.74140
$729$	−43.8319	−1.62340
$730$	−98.3313	−3.63940
$731$	−32.9892	−1.22015
$732$	−128.529	−4.75058
$733$	44.6480	1.64911	0.824556	−	0.565780i	$-0.191425\pi$
$733$	44.6480	1.64911	0.824556	+	0.565780i	$0.191425\pi$
$734$	−0.665999	−0.0245825
$735$	−38.8189	−1.43186
$736$	1.65880	0.0611443
$737$	−3.45149	−0.127137
$738$	−98.3691	−3.62102
$739$	−43.3474	−1.59456	−0.797280	−	0.603610i	$-0.793729\pi$
$739$	−43.3474	−1.59456	−0.797280	+	0.603610i	$0.793729\pi$
$740$	−151.202	−5.55831
$741$	73.1859	2.68855
$742$	−8.22543	−0.301965
$743$	−16.1598	−0.592847	−0.296424	−	0.955057i	$-0.595794\pi$
$743$	−16.1598	−0.592847	−0.296424	+	0.955057i	$0.595794\pi$
$744$	−69.5261	−2.54895
$745$	−84.0754	−3.08028
$746$	−43.1118	−1.57844
$747$	32.3719	1.18442
$748$	−102.172	−3.73579
$749$	30.9339	1.13030
$750$	174.257	6.36295
$751$	−3.80297	−0.138772	−0.0693862	−	0.997590i	$-0.522104\pi$
$751$	−3.80297	−0.138772	−0.0693862	+	0.997590i	$0.522104\pi$
$752$	20.4944	0.747354
$753$	−44.3315	−1.61553
$754$	−12.1788	−0.443526
$755$	−13.9641	−0.508205
$756$	50.1602	1.82431
$757$	−43.6685	−1.58716	−0.793579	−	0.608467i	$-0.791785\pi$
$757$	−43.6685	−1.58716	−0.793579	+	0.608467i	$0.791785\pi$
$758$	47.9543	1.74178
$759$	−11.3899	−0.413426
$760$	91.7626	3.32858
$761$	−11.3502	−0.411445	−0.205722	−	0.978610i	$-0.565954\pi$
$761$	−11.3502	−0.411445	−0.205722	+	0.978610i	$0.565954\pi$
$762$	111.095	4.02457
$763$	8.65703	0.313405
$764$	9.33351	0.337675
$765$	−116.943	−4.22809
$766$	31.4251	1.13543
$767$	−13.2788	−0.479469
$768$	−81.6208	−2.94524
$769$	−37.3619	−1.34730	−0.673652	−	0.739049i	$-0.735275\pi$
$769$	−37.3619	−1.34730	−0.673652	+	0.739049i	$0.735275\pi$
$770$	−132.188	−4.76371
$771$	50.6924	1.82564
$772$	−52.5434	−1.89108
$773$	−36.1849	−1.30148	−0.650740	−	0.759301i	$-0.725541\pi$
$773$	−36.1849	−1.30148	−0.650740	+	0.759301i	$0.725541\pi$
$774$	55.5316	1.99604
$775$	66.5789	2.39159
$776$	−78.6272	−2.82255
$777$	86.3402	3.09744
$778$	14.4384	0.517643
$779$	46.8072	1.67704
$780$	−220.731	−7.90344
$781$	47.8022	1.71050
$782$	−15.4960	−0.554135
$783$	3.93490	0.140622
$784$	10.3148	0.368386
$785$	74.8047	2.66990
$786$	20.7278	0.739338
$787$	28.7584	1.02513	0.512564	−	0.858649i	$-0.328696\pi$
$787$	28.7584	1.02513	0.512564	+	0.858649i	$0.328696\pi$
$788$	37.7366	1.34431
$789$	−13.1519	−0.468220
$790$	−18.1558	−0.645954
$791$	−21.8801	−0.777967
$792$	81.9426	2.91170
$793$	−63.9695	−2.27162
$794$	0.144761	0.00513739
$795$	−11.6948	−0.414772
$796$	−76.2717	−2.70338
$797$	8.20781	0.290736	0.145368	−	0.989378i	$-0.453563\pi$
$797$	8.20781	0.290736	0.145368	+	0.989378i	$0.453563\pi$
$798$	−109.980	−3.89324
$799$	44.5879	1.57741
$800$	19.0776	0.674495
$801$	−60.8254	−2.14916
$802$	−36.5106	−1.28923
$803$	41.7820	1.47446
$804$	8.66093	0.305447
$805$	−13.1588	−0.463787
$806$	−72.6290	−2.55825
$807$	−16.0470	−0.564880
$808$	−82.1190	−2.88894
$809$	25.1631	0.884686	0.442343	−	0.896846i	$-0.354147\pi$
$809$	25.1631	0.884686	0.442343	+	0.896846i	$0.354147\pi$
$810$	−23.1092	−0.811974
$811$	−38.0882	−1.33746	−0.668729	−	0.743506i	$-0.733161\pi$
$811$	−38.0882	−1.33746	−0.668729	+	0.743506i	$0.733161\pi$
$812$	12.0124	0.421553
$813$	60.4956	2.12167
$814$	97.8850	3.43087
$815$	−52.8442	−1.85105
$816$	51.8729	1.81591
$817$	−26.4237	−0.924449
$818$	−3.93348	−0.137531
$819$	75.5038	2.63832
$820$	−141.172	−4.92995
$821$	39.2693	1.37051	0.685253	−	0.728305i	$-0.259691\pi$
$821$	39.2693	1.37051	0.685253	+	0.728305i	$0.259691\pi$
$822$	151.351	5.27898
$823$	21.9085	0.763683	0.381842	−	0.924228i	$-0.375290\pi$
$823$	21.9085	0.763683	0.381842	+	0.924228i	$0.375290\pi$
$824$	70.9232	2.47073
$825$	−130.993	−4.56059
$826$	19.9546	0.694309
$827$	−19.2256	−0.668540	−0.334270	−	0.942477i	$-0.608490\pi$
$827$	−19.2256	−0.668540	−0.334270	+	0.942477i	$0.608490\pi$
$828$	17.1209	0.594994
$829$	−14.5104	−0.503966	−0.251983	−	0.967732i	$-0.581083\pi$
$829$	−14.5104	−0.503966	−0.251983	+	0.967732i	$0.581083\pi$
$830$	70.7812	2.45685
$831$	−10.6008	−0.367737
$832$	−51.5189	−1.78610
$833$	22.4410	0.777534
$834$	−62.3480	−2.15893
$835$	10.7989	0.373712
$836$	−81.8381	−2.83043
$837$	23.4660	0.811105
$838$	69.6946	2.40756
$839$	14.7684	0.509861	0.254931	−	0.966959i	$-0.417947\pi$
$839$	14.7684	0.509861	0.254931	+	0.966959i	$0.417947\pi$
$840$	158.036	5.45277
$841$	−28.0577	−0.967506
$842$	44.7048	1.54063
$843$	55.3099	1.90497
$844$	67.1505	2.31141
$845$	−57.0511	−1.96262
$846$	−75.0559	−2.58048
$847$	20.5346	0.705577
$848$	3.10749	0.106712
$849$	26.8988	0.923164
$850$	−178.217	−6.11278
$851$	9.74412	0.334024
$852$	−119.951	−4.10947
$853$	40.0683	1.37191	0.685956	−	0.727643i	$-0.259384\pi$
$853$	40.0683	1.37191	0.685956	+	0.727643i	$0.259384\pi$
$854$	96.1297	3.28949
$855$	−93.6692	−3.20342
$856$	−41.9279	−1.43307
$857$	28.3928	0.969878	0.484939	−	0.874548i	$-0.338842\pi$
$857$	28.3928	0.969878	0.484939	+	0.874548i	$0.338842\pi$
$858$	142.896	4.87840
$859$	35.5608	1.21332	0.606660	−	0.794962i	$-0.292509\pi$
$859$	35.5608	1.21332	0.606660	+	0.794962i	$0.292509\pi$
$860$	79.6949	2.71757
$861$	80.6128	2.74728
$862$	42.3314	1.44181
$863$	−0.379248	−0.0129098	−0.00645488	−	0.999979i	$-0.502055\pi$
$863$	−0.379248	−0.0129098	−0.00645488	+	0.999979i	$0.502055\pi$
$864$	6.72398	0.228754
$865$	31.5992	1.07441
$866$	23.6196	0.802627
$867$	66.3550	2.25353
$868$	71.6367	2.43151
$869$	7.71460	0.261700
$870$	26.0210	0.882193
$871$	4.31057	0.146058
$872$	−11.7338	−0.397356
$873$	80.2609	2.71642
$874$	−12.4120	−0.419842
$875$	−85.5431	−2.89189
$876$	−104.845	−3.54238
$877$	−5.02229	−0.169591	−0.0847953	−	0.996398i	$-0.527024\pi$
$877$	−5.02229	−0.169591	−0.0847953	+	0.996398i	$0.527024\pi$
$878$	−96.6214	−3.26082
$879$	68.8324	2.32166
$880$	49.9392	1.68345
$881$	7.74970	0.261094	0.130547	−	0.991442i	$-0.458327\pi$
$881$	7.74970	0.261094	0.130547	+	0.991442i	$0.458327\pi$
$882$	−37.7755	−1.27197
$883$	25.6396	0.862840	0.431420	−	0.902151i	$-0.358013\pi$
$883$	25.6396	0.862840	0.431420	+	0.902151i	$0.358013\pi$
$884$	127.603	4.29176
$885$	28.3711	0.953685
$886$	75.1195	2.52369
$887$	18.8918	0.634323	0.317161	−	0.948372i	$-0.397270\pi$
$887$	18.8918	0.634323	0.317161	+	0.948372i	$0.397270\pi$
$888$	−117.026	−3.92713
$889$	−54.5372	−1.82912
$890$	−132.995	−4.45800
$891$	9.81935	0.328960
$892$	−47.5566	−1.59231
$893$	35.7140	1.19512
$894$	−136.579	−4.56789
$895$	56.4152	1.88575
$896$	66.6726	2.22738
$897$	14.2248	0.474953
$898$	−51.7862	−1.72813
$899$	5.61966	0.187426
$900$	196.905	6.56350
$901$	6.76069	0.225231
$902$	91.3917	3.04301
$903$	−45.5077	−1.51440
$904$	29.6564	0.986357
$905$	−31.8507	−1.05875
$906$	−22.6844	−0.753640
$907$	−20.9153	−0.694481	−0.347240	−	0.937776i	$-0.612881\pi$
$907$	−20.9153	−0.694481	−0.347240	+	0.937776i	$0.612881\pi$
$908$	62.1375	2.06211
$909$	83.8252	2.78031
$910$	165.089	5.47266
$911$	9.89733	0.327913	0.163957	−	0.986468i	$-0.447574\pi$
$911$	9.89733	0.327913	0.163957	+	0.986468i	$0.447574\pi$
$912$	41.5492	1.37583
$913$	−30.0757	−0.995360
$914$	−37.2517	−1.23218
$915$	136.676	4.51836
$916$	−17.1105	−0.565345
$917$	−10.1754	−0.336020
$918$	−62.8132	−2.07314
$919$	27.4954	0.906991	0.453495	−	0.891259i	$-0.350177\pi$
$919$	27.4954	0.906991	0.453495	+	0.891259i	$0.350177\pi$
$920$	17.8355	0.588020
$921$	5.26541	0.173501
$922$	−81.0188	−2.66821
$923$	−59.7002	−1.96506
$924$	−140.944	−4.63672
$925$	112.065	3.68469
$926$	−0.238710	−0.00784450
$927$	−72.3968	−2.37782
$928$	1.61026	0.0528595
$929$	−7.73922	−0.253916	−0.126958	−	0.991908i	$-0.540521\pi$
$929$	−7.73922	−0.253916	−0.126958	+	0.991908i	$0.540521\pi$
$930$	155.178	5.08847
$931$	17.9748	0.589101
$932$	35.8156	1.17318
$933$	−11.1769	−0.365916
$934$	−88.3285	−2.89020
$935$	108.648	3.55318
$936$	−102.338	−3.34503
$937$	36.4677	1.19135	0.595674	−	0.803227i	$-0.296885\pi$
$937$	36.4677	1.19135	0.595674	+	0.803227i	$0.296885\pi$
$938$	−6.47769	−0.211504
$939$	1.19403	0.0389656
$940$	−107.715	−3.51327
$941$	−22.1743	−0.722863	−0.361431	−	0.932399i	$-0.617712\pi$
$941$	−22.1743	−0.722863	−0.361431	+	0.932399i	$0.617712\pi$
$942$	121.519	3.95931
$943$	9.09773	0.296263
$944$	−7.53865	−0.245362
$945$	−53.3395	−1.73513
$946$	−51.5926	−1.67742
$947$	−24.9134	−0.809578	−0.404789	−	0.914410i	$-0.632655\pi$
$947$	−24.9134	−0.809578	−0.404789	+	0.914410i	$0.632655\pi$
$948$	−19.3585	−0.628734
$949$	−52.1817	−1.69389
$950$	−142.748	−4.63136
$951$	39.6924	1.28711
$952$	−91.3598	−2.96099
$953$	−13.7168	−0.444332	−0.222166	−	0.975009i	$-0.571313\pi$
$953$	−13.7168	−0.444332	−0.222166	+	0.975009i	$0.571313\pi$
$954$	−11.3804	−0.368455
$955$	−9.92509	−0.321168
$956$	86.3221	2.79186
$957$	−11.0566	−0.357409
$958$	−34.2422	−1.10632
$959$	−74.2988	−2.39923
$960$	110.074	3.55262
$961$	2.51320	0.0810710
$962$	−122.249	−3.94146
$963$	42.7991	1.37918
$964$	22.5536	0.726402
$965$	55.8737	1.79864
$966$	−21.3763	−0.687771
$967$	33.8644	1.08900	0.544502	−	0.838759i	$-0.316719\pi$
$967$	33.8644	1.08900	0.544502	+	0.838759i	$0.316719\pi$
$968$	−27.8327	−0.894577
$969$	90.3949	2.90390
$970$	175.491	5.63467
$971$	28.6287	0.918738	0.459369	−	0.888246i	$-0.348076\pi$
$971$	28.6287	0.918738	0.459369	+	0.888246i	$0.348076\pi$
$972$	−71.0933	−2.28032
$973$	30.6068	0.981210
$974$	81.8388	2.62228
$975$	163.597	5.23931
$976$	−36.3169	−1.16247
$977$	−47.2993	−1.51324	−0.756620	−	0.653855i	$-0.773150\pi$
$977$	−47.2993	−1.51324	−0.756620	+	0.653855i	$0.773150\pi$
$978$	−85.8445	−2.74500
$979$	56.5110	1.80610
$980$	−54.2127	−1.73176
$981$	11.9776	0.382415
$982$	25.3311	0.808349
$983$	−6.00170	−0.191425	−0.0957123	−	0.995409i	$-0.530513\pi$
$983$	−6.00170	−0.191425	−0.0957123	+	0.995409i	$0.530513\pi$
$984$	−109.263	−3.48318
$985$	−40.1284	−1.27860
$986$	−15.0426	−0.479052
$987$	61.5077	1.95781
$988$	102.208	3.25166
$989$	−5.13587	−0.163311
$990$	−182.890	−5.81264
$991$	19.3602	0.614998	0.307499	−	0.951548i	$-0.400508\pi$
$991$	19.3602	0.614998	0.307499	+	0.951548i	$0.400508\pi$
$992$	9.60290	0.304893
$993$	42.3109	1.34270
$994$	89.7142	2.84556
$995$	81.1059	2.57123
$996$	75.4699	2.39135
$997$	59.2428	1.87624	0.938119	−	0.346312i	$-0.112566\pi$
$997$	59.2428	1.87624	0.938119	+	0.346312i	$0.112566\pi$
$998$	−11.9276	−0.377562
$999$	39.4979	1.24966

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8027.2.a.f.1.16	✓	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8027.2.a.f.1.16	✓	176	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:	\( N \)	\(=\)	\( 8027 = 23 \cdot 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8027.a (trivial)

\(f(q)\)	\(=\)	\(q-2.41247 q^{2} +2.73531 q^{3} +3.82000 q^{4} -4.06212 q^{5} -6.59885 q^{6} +3.23940 q^{7} -4.39069 q^{8} +4.48192 q^{9} +O(q^{10})\)	\(q-2.41247 q^{2} +2.73531 q^{3} +3.82000 q^{4} -4.06212 q^{5} -6.59885 q^{6} +3.23940 q^{7} -4.39069 q^{8} +4.48192 q^{9} +9.79973 q^{10} -4.16401 q^{11} +10.4489 q^{12} +5.20045 q^{13} -7.81494 q^{14} -11.1112 q^{15} +2.95241 q^{16} +6.42329 q^{17} -10.8125 q^{18} +5.14494 q^{19} -15.5173 q^{20} +8.86075 q^{21} +10.0456 q^{22} +1.00000 q^{23} -12.0099 q^{24} +11.5008 q^{25} -12.5459 q^{26} +4.05351 q^{27} +12.3745 q^{28} +0.970739 q^{29} +26.8053 q^{30} +5.78906 q^{31} +1.65880 q^{32} -11.3899 q^{33} -15.4960 q^{34} -13.1588 q^{35} +17.1209 q^{36} +9.74412 q^{37} -12.4120 q^{38} +14.2248 q^{39} +17.8355 q^{40} +9.09773 q^{41} -21.3763 q^{42} -5.13587 q^{43} -15.9065 q^{44} -18.2061 q^{45} -2.41247 q^{46} +6.94159 q^{47} +8.07575 q^{48} +3.49369 q^{49} -27.7454 q^{50} +17.5697 q^{51} +19.8657 q^{52} +1.05253 q^{53} -9.77897 q^{54} +16.9147 q^{55} -14.2232 q^{56} +14.0730 q^{57} -2.34188 q^{58} -2.55339 q^{59} -42.4446 q^{60} -12.3008 q^{61} -13.9659 q^{62} +14.5187 q^{63} -9.90662 q^{64} -21.1248 q^{65} +27.4777 q^{66} +0.828885 q^{67} +24.5370 q^{68} +2.73531 q^{69} +31.7452 q^{70} -11.4798 q^{71} -19.6787 q^{72} -10.0341 q^{73} -23.5074 q^{74} +31.4583 q^{75} +19.6537 q^{76} -13.4889 q^{77} -34.3170 q^{78} -1.85268 q^{79} -11.9930 q^{80} -2.35814 q^{81} -21.9480 q^{82} +7.22276 q^{83} +33.8481 q^{84} -26.0922 q^{85} +12.3901 q^{86} +2.65527 q^{87} +18.2829 q^{88} -13.5713 q^{89} +43.9216 q^{90} +16.8463 q^{91} +3.82000 q^{92} +15.8349 q^{93} -16.7464 q^{94} -20.8993 q^{95} +4.53734 q^{96} +17.9077 q^{97} -8.42842 q^{98} -18.6628 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q + 19 q^{2} + 22 q^{3} + 203 q^{4} + 28 q^{5} + 9 q^{6} + 30 q^{7} + 51 q^{8} + 204 q^{9}+O(q^{10}) \) 176 * q + 19 * q^2 + 22 * q^3 + 203 * q^4 + 28 * q^5 + 9 * q^6 + 30 * q^7 + 51 * q^8 + 204 * q^9	\( 176 q + 19 q^{2} + 22 q^{3} + 203 q^{4} + 28 q^{5} + 9 q^{6} + 30 q^{7} + 51 q^{8} + 204 q^{9} + 18 q^{10} + 11 q^{11} + 46 q^{12} + 87 q^{13} - 6 q^{14} + 29 q^{15} + 257 q^{16} + 14 q^{17} + 72 q^{18} + 34 q^{19} + 45 q^{20} + 23 q^{21} + 62 q^{22} + 176 q^{23} + 33 q^{24} + 272 q^{25} + 31 q^{26} + 82 q^{27} + 80 q^{28} + 75 q^{29} - 30 q^{30} + 73 q^{31} + 71 q^{32} + 30 q^{33} + 23 q^{34} + 44 q^{35} + 264 q^{36} + 236 q^{37} - 21 q^{38} + 17 q^{39} + 43 q^{40} + 51 q^{41} + 38 q^{42} + 51 q^{43} + 12 q^{44} + 127 q^{45} + 19 q^{46} + 45 q^{47} + 61 q^{48} + 268 q^{49} + 55 q^{50} - 3 q^{51} + 166 q^{52} + 63 q^{53} - 32 q^{54} + 11 q^{55} - 9 q^{56} + 72 q^{57} + 98 q^{58} + 95 q^{59} - 7 q^{60} + 73 q^{61} + 12 q^{62} + 19 q^{63} + 365 q^{64} + 19 q^{65} - 28 q^{66} + 138 q^{67} + 16 q^{68} + 22 q^{69} + 100 q^{70} + 85 q^{71} + 129 q^{72} + 118 q^{73} - 21 q^{74} - 12 q^{75} + 52 q^{76} + 75 q^{77} + 97 q^{78} + 74 q^{79} + 8 q^{80} + 280 q^{81} + 67 q^{82} + 10 q^{83} - 51 q^{84} + 169 q^{85} - 39 q^{86} - 6 q^{87} + 159 q^{88} + 38 q^{89} + 22 q^{90} + 90 q^{91} + 203 q^{92} + 230 q^{93} + 63 q^{94} + 30 q^{95} + 107 q^{96} + 161 q^{97} + 58 q^{98} + 7 q^{99}+O(q^{100}) \) 176 * q + 19 * q^2 + 22 * q^3 + 203 * q^4 + 28 * q^5 + 9 * q^6 + 30 * q^7 + 51 * q^8 + 204 * q^9 + 18 * q^10 + 11 * q^11 + 46 * q^12 + 87 * q^13 - 6 * q^14 + 29 * q^15 + 257 * q^16 + 14 * q^17 + 72 * q^18 + 34 * q^19 + 45 * q^20 + 23 * q^21 + 62 * q^22 + 176 * q^23 + 33 * q^24 + 272 * q^25 + 31 * q^26 + 82 * q^27 + 80 * q^28 + 75 * q^29 - 30 * q^30 + 73 * q^31 + 71 * q^32 + 30 * q^33 + 23 * q^34 + 44 * q^35 + 264 * q^36 + 236 * q^37 - 21 * q^38 + 17 * q^39 + 43 * q^40 + 51 * q^41 + 38 * q^42 + 51 * q^43 + 12 * q^44 + 127 * q^45 + 19 * q^46 + 45 * q^47 + 61 * q^48 + 268 * q^49 + 55 * q^50 - 3 * q^51 + 166 * q^52 + 63 * q^53 - 32 * q^54 + 11 * q^55 - 9 * q^56 + 72 * q^57 + 98 * q^58 + 95 * q^59 - 7 * q^60 + 73 * q^61 + 12 * q^62 + 19 * q^63 + 365 * q^64 + 19 * q^65 - 28 * q^66 + 138 * q^67 + 16 * q^68 + 22 * q^69 + 100 * q^70 + 85 * q^71 + 129 * q^72 + 118 * q^73 - 21 * q^74 - 12 * q^75 + 52 * q^76 + 75 * q^77 + 97 * q^78 + 74 * q^79 + 8 * q^80 + 280 * q^81 + 67 * q^82 + 10 * q^83 - 51 * q^84 + 169 * q^85 - 39 * q^86 - 6 * q^87 + 159 * q^88 + 38 * q^89 + 22 * q^90 + 90 * q^91 + 203 * q^92 + 230 * q^93 + 63 * q^94 + 30 * q^95 + 107 * q^96 + 161 * q^97 + 58 * q^98 + 7 * q^99

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