LMFDB - Embedded newform 805.2.a.l.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [805,2,Mod(1,805)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(805, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("805.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 805 = 5 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	805.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:	$6.42795736271$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.255877.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 6x^{3} + 6x^{2} + 6x - 5 $ x^5 - x^4 - 6x^3 + 6x^2 + 6*x - 5
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			$1.45275$ of defining polynomial
Character	$\chi$	$=$	805.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.45275 q^{2} +2.09827 q^{3} +0.110473 q^{4} -1.00000 q^{5} -3.04825 q^{6} +1.00000 q^{7} +2.74500 q^{8} +1.40273 q^{9} +O(q^{10})$	\(q-1.45275 q^{2} +2.09827 q^{3} +0.110473 q^{4} -1.00000 q^{5} -3.04825 q^{6} +1.00000 q^{7} +2.74500 q^{8} +1.40273 q^{9} +1.45275 q^{10} -3.31921 q^{11} +0.231801 q^{12} -5.28005 q^{13} -1.45275 q^{14} -2.09827 q^{15} -4.20874 q^{16} -6.61026 q^{17} -2.03781 q^{18} +1.66149 q^{19} -0.110473 q^{20} +2.09827 q^{21} +4.82198 q^{22} +1.00000 q^{23} +5.75976 q^{24} +1.00000 q^{25} +7.67058 q^{26} -3.35150 q^{27} +0.110473 q^{28} +4.74877 q^{29} +3.04825 q^{30} -2.40273 q^{31} +0.624225 q^{32} -6.96460 q^{33} +9.60303 q^{34} -1.00000 q^{35} +0.154963 q^{36} -1.97183 q^{37} -2.41372 q^{38} -11.0790 q^{39} -2.74500 q^{40} -8.26906 q^{41} -3.04825 q^{42} +7.03605 q^{43} -0.366682 q^{44} -1.40273 q^{45} -1.45275 q^{46} +1.69377 q^{47} -8.83107 q^{48} +1.00000 q^{49} -1.45275 q^{50} -13.8701 q^{51} -0.583302 q^{52} -9.69930 q^{53} +4.86888 q^{54} +3.31921 q^{55} +2.74500 q^{56} +3.48625 q^{57} -6.89875 q^{58} -9.83228 q^{59} -0.231801 q^{60} -4.79623 q^{61} +3.49056 q^{62} +1.40273 q^{63} +7.51064 q^{64} +5.28005 q^{65} +10.1178 q^{66} +11.8299 q^{67} -0.730253 q^{68} +2.09827 q^{69} +1.45275 q^{70} -2.62368 q^{71} +3.85050 q^{72} -6.49445 q^{73} +2.86457 q^{74} +2.09827 q^{75} +0.183549 q^{76} -3.31921 q^{77} +16.0949 q^{78} +0.525407 q^{79} +4.20874 q^{80} -11.2405 q^{81} +12.0129 q^{82} +10.4463 q^{83} +0.231801 q^{84} +6.61026 q^{85} -10.2216 q^{86} +9.96419 q^{87} -9.11126 q^{88} -8.27083 q^{89} +2.03781 q^{90} -5.28005 q^{91} +0.110473 q^{92} -5.04157 q^{93} -2.46062 q^{94} -1.66149 q^{95} +1.30979 q^{96} +11.6268 q^{97} -1.45275 q^{98} -4.65596 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - q^{2} - 4 q^{3} + 3 q^{4} - 5 q^{5} - 5 q^{6} + 5 q^{7} + 3 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q - q^2 - 4 * q^3 + 3 * q^4 - 5 * q^5 - 5 * q^6 + 5 * q^7 + 3 * q^8 + 5 * q^9	\( 5 q - q^{2} - 4 q^{3} + 3 q^{4} - 5 q^{5} - 5 q^{6} + 5 q^{7} + 3 q^{8} + 5 q^{9} + q^{10} - 7 q^{11} - 10 q^{12} - 5 q^{13} - q^{14} + 4 q^{15} - 9 q^{16} - 7 q^{17} + 11 q^{18} - 10 q^{19} - 3 q^{20} - 4 q^{21} + 4 q^{22} + 5 q^{23} - 4 q^{24} + 5 q^{25} - 2 q^{26} - 7 q^{27} + 3 q^{28} - 14 q^{29} + 5 q^{30} - 10 q^{31} + 4 q^{33} - 10 q^{34} - 5 q^{35} + 20 q^{36} - 3 q^{37} - 15 q^{38} - 13 q^{39} - 3 q^{40} - 15 q^{41} - 5 q^{42} + 8 q^{43} - 27 q^{44} - 5 q^{45} - q^{46} - 10 q^{47} - 2 q^{48} + 5 q^{49} - q^{50} - 18 q^{51} + 18 q^{52} - 9 q^{53} - 39 q^{54} + 7 q^{55} + 3 q^{56} + 23 q^{57} - 31 q^{58} - 19 q^{59} + 10 q^{60} - 21 q^{61} - 10 q^{62} + 5 q^{63} - 7 q^{64} + 5 q^{65} + 25 q^{66} + 5 q^{67} - 15 q^{68} - 4 q^{69} + q^{70} - 16 q^{71} + 26 q^{72} + q^{73} - 16 q^{74} - 4 q^{75} - 7 q^{77} + 28 q^{78} + 20 q^{79} + 9 q^{80} - 3 q^{81} + 11 q^{82} - 31 q^{83} - 10 q^{84} + 7 q^{85} + 10 q^{86} + 38 q^{87} - 3 q^{88} - 21 q^{89} - 11 q^{90} - 5 q^{91} + 3 q^{92} + 23 q^{93} + 28 q^{94} + 10 q^{95} + 24 q^{96} + 19 q^{97} - q^{98} - 26 q^{99}+O(q^{100}) \) 5 * q - q^2 - 4 * q^3 + 3 * q^4 - 5 * q^5 - 5 * q^6 + 5 * q^7 + 3 * q^8 + 5 * q^9 + q^10 - 7 * q^11 - 10 * q^12 - 5 * q^13 - q^14 + 4 * q^15 - 9 * q^16 - 7 * q^17 + 11 * q^18 - 10 * q^19 - 3 * q^20 - 4 * q^21 + 4 * q^22 + 5 * q^23 - 4 * q^24 + 5 * q^25 - 2 * q^26 - 7 * q^27 + 3 * q^28 - 14 * q^29 + 5 * q^30 - 10 * q^31 + 4 * q^33 - 10 * q^34 - 5 * q^35 + 20 * q^36 - 3 * q^37 - 15 * q^38 - 13 * q^39 - 3 * q^40 - 15 * q^41 - 5 * q^42 + 8 * q^43 - 27 * q^44 - 5 * q^45 - q^46 - 10 * q^47 - 2 * q^48 + 5 * q^49 - q^50 - 18 * q^51 + 18 * q^52 - 9 * q^53 - 39 * q^54 + 7 * q^55 + 3 * q^56 + 23 * q^57 - 31 * q^58 - 19 * q^59 + 10 * q^60 - 21 * q^61 - 10 * q^62 + 5 * q^63 - 7 * q^64 + 5 * q^65 + 25 * q^66 + 5 * q^67 - 15 * q^68 - 4 * q^69 + q^70 - 16 * q^71 + 26 * q^72 + q^73 - 16 * q^74 - 4 * q^75 - 7 * q^77 + 28 * q^78 + 20 * q^79 + 9 * q^80 - 3 * q^81 + 11 * q^82 - 31 * q^83 - 10 * q^84 + 7 * q^85 + 10 * q^86 + 38 * q^87 - 3 * q^88 - 21 * q^89 - 11 * q^90 - 5 * q^91 + 3 * q^92 + 23 * q^93 + 28 * q^94 + 10 * q^95 + 24 * q^96 + 19 * q^97 - q^98 - 26 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.45275	−1.02725	−0.513623	−	0.858016i	$-0.671697\pi$
$2$	−1.45275	−1.02725	−0.513623	+	0.858016i	$0.671697\pi$
$3$	2.09827	1.21144	0.605718	−	0.795679i	$-0.292886\pi$
$3$	2.09827	1.21144	0.605718	+	0.795679i	$0.292886\pi$
$4$	0.110473	0.0552363
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−3.04825	−1.24444
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	2.74500	0.970506
$9$	1.40273	0.467577
$10$	1.45275	0.459399
$11$	−3.31921	−1.00078	−0.500390	−	0.865800i	$-0.666810\pi$
$11$	−3.31921	−1.00078	−0.500390	+	0.865800i	$0.666810\pi$
$12$	0.231801	0.0669153
$13$	−5.28005	−1.46442	−0.732212	−	0.681077i	$-0.761512\pi$
$13$	−5.28005	−1.46442	−0.732212	+	0.681077i	$0.761512\pi$
$14$	−1.45275	−0.388263
$15$	−2.09827	−0.541771
$16$	−4.20874	−1.05219
$17$	−6.61026	−1.60322	−0.801611	−	0.597845i	$-0.796024\pi$
$17$	−6.61026	−1.60322	−0.801611	+	0.597845i	$0.796024\pi$
$18$	−2.03781	−0.480317
$19$	1.66149	0.381171	0.190586	−	0.981671i	$-0.438961\pi$
$19$	1.66149	0.381171	0.190586	+	0.981671i	$0.438961\pi$
$20$	−0.110473	−0.0247024
$21$	2.09827	0.457880
$22$	4.82198	1.02805
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	5.75976	1.17571
$25$	1.00000	0.200000
$26$	7.67058	1.50432
$27$	−3.35150	−0.644997
$28$	0.110473	0.0208774
$29$	4.74877	0.881824	0.440912	−	0.897550i	$-0.354655\pi$
$29$	4.74877	0.881824	0.440912	+	0.897550i	$0.354655\pi$
$30$	3.04825	0.556532
$31$	−2.40273	−0.431543	−0.215772	−	0.976444i	$-0.569227\pi$
$31$	−2.40273	−0.431543	−0.215772	+	0.976444i	$0.569227\pi$
$32$	0.624225	0.110349
$33$	−6.96460	−1.21238
$34$	9.60303	1.64691
$35$	−1.00000	−0.169031
$36$	0.154963	0.0258272
$37$	−1.97183	−0.324167	−0.162083	−	0.986777i	$-0.551821\pi$
$37$	−1.97183	−0.324167	−0.162083	+	0.986777i	$0.551821\pi$
$38$	−2.41372	−0.391557
$39$	−11.0790	−1.77405
$40$	−2.74500	−0.434023
$41$	−8.26906	−1.29141	−0.645705	−	0.763587i	$-0.723437\pi$
$41$	−8.26906	−1.29141	−0.645705	+	0.763587i	$0.723437\pi$
$42$	−3.04825	−0.470356
$43$	7.03605	1.07299	0.536494	−	0.843904i	$-0.319749\pi$
$43$	7.03605	1.07299	0.536494	+	0.843904i	$0.319749\pi$
$44$	−0.366682	−0.0552794
$45$	−1.40273	−0.209107
$46$	−1.45275	−0.214196
$47$	1.69377	0.247062	0.123531	−	0.992341i	$-0.460578\pi$
$47$	1.69377	0.247062	0.123531	+	0.992341i	$0.460578\pi$
$48$	−8.83107	−1.27465
$49$	1.00000	0.142857
$50$	−1.45275	−0.205449
$51$	−13.8701	−1.94220
$52$	−0.583302	−0.0808894
$53$	−9.69930	−1.33230	−0.666151	−	0.745817i	$-0.732059\pi$
$53$	−9.69930	−1.33230	−0.666151	+	0.745817i	$0.732059\pi$
$54$	4.86888	0.662571
$55$	3.31921	0.447563
$56$	2.74500	0.366817
$57$	3.48625	0.461765
$58$	−6.89875	−0.905851
$59$	−9.83228	−1.28005	−0.640027	−	0.768352i	$-0.721077\pi$
$59$	−9.83228	−1.28005	−0.640027	+	0.768352i	$0.721077\pi$
$60$	−0.231801	−0.0299254
$61$	−4.79623	−0.614095	−0.307047	−	0.951694i	$-0.599341\pi$
$61$	−4.79623	−0.614095	−0.307047	+	0.951694i	$0.599341\pi$
$62$	3.49056	0.443301
$63$	1.40273	0.176727
$64$	7.51064	0.938830
$65$	5.28005	0.654910
$66$	10.1178	1.24542
$67$	11.8299	1.44525	0.722623	−	0.691242i	$-0.242936\pi$
$67$	11.8299	1.44525	0.722623	+	0.691242i	$0.242936\pi$
$68$	−0.730253	−0.0885561
$69$	2.09827	0.252602
$70$	1.45275	0.173636
$71$	−2.62368	−0.311373	−0.155687	−	0.987807i	$-0.549759\pi$
$71$	−2.62368	−0.311373	−0.155687	+	0.987807i	$0.549759\pi$
$72$	3.85050	0.453786
$73$	−6.49445	−0.760118	−0.380059	−	0.924962i	$-0.624096\pi$
$73$	−6.49445	−0.760118	−0.380059	+	0.924962i	$0.624096\pi$
$74$	2.86457	0.332999
$75$	2.09827	0.242287
$76$	0.183549	0.0210545
$77$	−3.31921	−0.378260
$78$	16.0949	1.82239
$79$	0.525407	0.0591129	0.0295565	−	0.999563i	$-0.490591\pi$
$79$	0.525407	0.0591129	0.0295565	+	0.999563i	$0.490591\pi$
$80$	4.20874	0.470552
$81$	−11.2405	−1.24895
$82$	12.0129	1.32660
$83$	10.4463	1.14663	0.573315	−	0.819335i	$-0.305657\pi$
$83$	10.4463	1.14663	0.573315	+	0.819335i	$0.305657\pi$
$84$	0.231801	0.0252916
$85$	6.61026	0.716983
$86$	−10.2216	−1.10222
$87$	9.96419	1.06827
$88$	−9.11126	−0.971263
$89$	−8.27083	−0.876706	−0.438353	−	0.898803i	$-0.644438\pi$
$89$	−8.27083	−0.876706	−0.438353	+	0.898803i	$0.644438\pi$
$90$	2.03781	0.214804
$91$	−5.28005	−0.553500
$92$	0.110473	0.0115176
$93$	−5.04157	−0.522787
$94$	−2.46062	−0.253794
$95$	−1.66149	−0.170465
$96$	1.30979	0.133680
$97$	11.6268	1.18052	0.590259	−	0.807214i	$-0.299026\pi$
$97$	11.6268	1.18052	0.590259	+	0.807214i	$0.299026\pi$
$98$	−1.45275	−0.146750
$99$	−4.65596	−0.467942
$100$	0.110473	0.0110473
$101$	−11.0064	−1.09518	−0.547591	−	0.836746i	$-0.684455\pi$
$101$	−11.0064	−1.09518	−0.547591	+	0.836746i	$0.684455\pi$
$102$	20.1497	1.99512
$103$	−8.87520	−0.874500	−0.437250	−	0.899340i	$-0.644047\pi$
$103$	−8.87520	−0.874500	−0.437250	+	0.899340i	$0.644047\pi$
$104$	−14.4938	−1.42123
$105$	−2.09827	−0.204770
$106$	14.0906	1.36860
$107$	0.280737	0.0271399	0.0135700	−	0.999908i	$-0.495680\pi$
$107$	0.280737	0.0271399	0.0135700	+	0.999908i	$0.495680\pi$
$108$	−0.370249	−0.0356272
$109$	−5.75211	−0.550952	−0.275476	−	0.961308i	$-0.588836\pi$
$109$	−5.75211	−0.550952	−0.275476	+	0.961308i	$0.588836\pi$
$110$	−4.82198	−0.459757
$111$	−4.13743	−0.392707
$112$	−4.20874	−0.397689
$113$	−0.696202	−0.0654932	−0.0327466	−	0.999464i	$-0.510425\pi$
$113$	−0.696202	−0.0654932	−0.0327466	+	0.999464i	$0.510425\pi$
$114$	−5.06463	−0.474346
$115$	−1.00000	−0.0932505
$116$	0.524609	0.0487087
$117$	−7.40649	−0.684730
$118$	14.2838	1.31493
$119$	−6.61026	−0.605961
$120$	−5.75976	−0.525791
$121$	0.0171799	0.00156181
$122$	6.96771	0.630827
$123$	−17.3507	−1.56446
$124$	−0.265436	−0.0238369
$125$	−1.00000	−0.0894427
$126$	−2.03781	−0.181543
$127$	0.107261	0.00951785	0.00475892	−	0.999989i	$-0.498485\pi$
$127$	0.107261	0.00951785	0.00475892	+	0.999989i	$0.498485\pi$
$128$	−12.1595	−1.07476
$129$	14.7635	1.29986
$130$	−7.67058	−0.672754
$131$	6.13631	0.536132	0.268066	−	0.963401i	$-0.413615\pi$
$131$	6.13631	0.536132	0.268066	+	0.963401i	$0.413615\pi$
$132$	−0.769398	−0.0669675
$133$	1.66149	0.144069
$134$	−17.1858	−1.48463
$135$	3.35150	0.288451
$136$	−18.1452	−1.55594
$137$	−8.52982	−0.728752	−0.364376	−	0.931252i	$-0.618718\pi$
$137$	−8.52982	−0.728752	−0.364376	+	0.931252i	$0.618718\pi$
$138$	−3.04825	−0.259484
$139$	10.8545	0.920666	0.460333	−	0.887746i	$-0.347730\pi$
$139$	10.8545	0.920666	0.460333	+	0.887746i	$0.347730\pi$
$140$	−0.110473	−0.00933664
$141$	3.55399	0.299300
$142$	3.81154	0.319857
$143$	17.5256	1.46557
$144$	−5.90373	−0.491977
$145$	−4.74877	−0.394364
$146$	9.43480	0.780829
$147$	2.09827	0.173062
$148$	−0.217833	−0.0179058
$149$	20.5497	1.68350	0.841748	−	0.539871i	$-0.181527\pi$
$149$	20.5497	1.68350	0.841748	+	0.539871i	$0.181527\pi$
$150$	−3.04825	−0.248889
$151$	−7.61888	−0.620015	−0.310008	−	0.950734i	$-0.600332\pi$
$151$	−7.61888	−0.620015	−0.310008	+	0.950734i	$0.600332\pi$
$152$	4.56079	0.369929
$153$	−9.27241	−0.749630
$154$	4.82198	0.388566
$155$	2.40273	0.192992
$156$	−1.22392	−0.0979923
$157$	16.2659	1.29816	0.649079	−	0.760721i	$-0.275155\pi$
$157$	16.2659	1.29816	0.649079	+	0.760721i	$0.275155\pi$
$158$	−0.763284	−0.0607236
$159$	−20.3517	−1.61400
$160$	−0.624225	−0.0493494
$161$	1.00000	0.0788110
$162$	16.3297	1.28298
$163$	4.59482	0.359894	0.179947	−	0.983676i	$-0.442407\pi$
$163$	4.59482	0.359894	0.179947	+	0.983676i	$0.442407\pi$
$164$	−0.913505	−0.0713328
$165$	6.96460	0.542193
$166$	−15.1758	−1.17787
$167$	9.34124	0.722846	0.361423	−	0.932402i	$-0.382291\pi$
$167$	9.34124	0.722846	0.361423	+	0.932402i	$0.382291\pi$
$168$	5.75976	0.444375
$169$	14.8790	1.14454
$170$	−9.60303	−0.736519
$171$	2.33062	0.178227
$172$	0.777291	0.0592679
$173$	−3.82920	−0.291129	−0.145565	−	0.989349i	$-0.546500\pi$
$173$	−3.82920	−0.291129	−0.145565	+	0.989349i	$0.546500\pi$
$174$	−14.4754	−1.09738
$175$	1.00000	0.0755929
$176$	13.9697	1.05301
$177$	−20.6308	−1.55070
$178$	12.0154	0.900594
$179$	−22.5742	−1.68727	−0.843637	−	0.536915i	$-0.819590\pi$
$179$	−22.5742	−1.68727	−0.843637	+	0.536915i	$0.819590\pi$
$180$	−0.154963	−0.0115503
$181$	2.06622	0.153581	0.0767903	−	0.997047i	$-0.475533\pi$
$181$	2.06622	0.153581	0.0767903	+	0.997047i	$0.475533\pi$
$182$	7.67058	0.568581
$183$	−10.0638	−0.743937
$184$	2.74500	0.202364
$185$	1.97183	0.144972
$186$	7.32413	0.537031
$187$	21.9409	1.60447
$188$	0.187116	0.0136468
$189$	−3.35150	−0.243786
$190$	2.41372	0.175110
$191$	3.83228	0.277294	0.138647	−	0.990342i	$-0.455725\pi$
$191$	3.83228	0.277294	0.138647	+	0.990342i	$0.455725\pi$
$192$	15.7593	1.13733
$193$	17.0988	1.23080	0.615400	−	0.788215i	$-0.288994\pi$
$193$	17.0988	1.23080	0.615400	+	0.788215i	$0.288994\pi$
$194$	−16.8907	−1.21268
$195$	11.0790	0.793382
$196$	0.110473	0.00789090
$197$	−11.5906	−0.825796	−0.412898	−	0.910777i	$-0.635483\pi$
$197$	−11.5906	−0.825796	−0.412898	+	0.910777i	$0.635483\pi$
$198$	6.76393	0.480692
$199$	24.3947	1.72930	0.864648	−	0.502379i	$-0.167542\pi$
$199$	24.3947	1.72930	0.864648	+	0.502379i	$0.167542\pi$
$200$	2.74500	0.194101
$201$	24.8222	1.75082
$202$	15.9896	1.12502
$203$	4.74877	0.333298
$204$	−1.53227	−0.107280
$205$	8.26906	0.577536
$206$	12.8934	0.898327
$207$	1.40273	0.0974965
$208$	22.2224	1.54084
$209$	−5.51483	−0.381469
$210$	3.04825	0.210349
$211$	−7.72982	−0.532143	−0.266071	−	0.963953i	$-0.585726\pi$
$211$	−7.72982	−0.532143	−0.266071	+	0.963953i	$0.585726\pi$
$212$	−1.07151	−0.0735914
$213$	−5.50518	−0.377208
$214$	−0.407840	−0.0278794
$215$	−7.03605	−0.479854
$216$	−9.19988	−0.625973
$217$	−2.40273	−0.163108
$218$	8.35636	0.565964
$219$	−13.6271	−0.920835
$220$	0.366682	0.0247217
$221$	34.9025	2.34780
$222$	6.01064	0.403407
$223$	27.5492	1.84483	0.922417	−	0.386195i	$-0.126211\pi$
$223$	27.5492	1.84483	0.922417	+	0.386195i	$0.126211\pi$
$224$	0.624225	0.0417078
$225$	1.40273	0.0935154
$226$	1.01141	0.0672777
$227$	10.3353	0.685978	0.342989	−	0.939339i	$-0.388561\pi$
$227$	10.3353	0.685978	0.342989	+	0.939339i	$0.388561\pi$
$228$	0.385135	0.0255062
$229$	−4.83708	−0.319643	−0.159822	−	0.987146i	$-0.551092\pi$
$229$	−4.83708	−0.319643	−0.159822	+	0.987146i	$0.551092\pi$
$230$	1.45275	0.0957913
$231$	−6.96460	−0.458237
$232$	13.0354	0.855815
$233$	3.05676	0.200255	0.100127	−	0.994975i	$-0.468075\pi$
$233$	3.05676	0.200255	0.100127	+	0.994975i	$0.468075\pi$
$234$	10.7598	0.703387
$235$	−1.69377	−0.110490
$236$	−1.08620	−0.0707055
$237$	1.10245	0.0716115
$238$	9.60303	0.622472
$239$	21.2082	1.37184	0.685921	−	0.727676i	$-0.259400\pi$
$239$	21.2082	1.37184	0.685921	+	0.727676i	$0.259400\pi$
$240$	8.83107	0.570043
$241$	−21.0627	−1.35677	−0.678385	−	0.734706i	$-0.737320\pi$
$241$	−21.0627	−1.35677	−0.678385	+	0.734706i	$0.737320\pi$
$242$	−0.0249581	−0.00160437
$243$	−13.5312	−0.868025
$244$	−0.529853	−0.0339203
$245$	−1.00000	−0.0638877
$246$	25.2062	1.60709
$247$	−8.77274	−0.558196
$248$	−6.59551	−0.418815
$249$	21.9191	1.38907
$250$	1.45275	0.0918798
$251$	−17.6608	−1.11474	−0.557370	−	0.830264i	$-0.688190\pi$
$251$	−17.6608	−1.11474	−0.557370	+	0.830264i	$0.688190\pi$
$252$	0.154963	0.00976177
$253$	−3.31921	−0.208677
$254$	−0.155823	−0.00977718
$255$	13.8701	0.868579
$256$	2.64340	0.165213
$257$	−26.0924	−1.62760	−0.813798	−	0.581148i	$-0.802604\pi$
$257$	−26.0924	−1.62760	−0.813798	+	0.581148i	$0.802604\pi$
$258$	−21.4477	−1.33527
$259$	−1.97183	−0.122524
$260$	0.583302	0.0361748
$261$	6.66124	0.412320
$262$	−8.91451	−0.550740
$263$	2.30822	0.142331	0.0711656	−	0.997465i	$-0.477328\pi$
$263$	2.30822	0.142331	0.0711656	+	0.997465i	$0.477328\pi$
$264$	−19.1179	−1.17662
$265$	9.69930	0.595823
$266$	−2.41372	−0.147995
$267$	−17.3544	−1.06207
$268$	1.30688	0.0798301
$269$	−27.8775	−1.69972	−0.849859	−	0.527010i	$-0.823313\pi$
$269$	−27.8775	−1.69972	−0.849859	+	0.527010i	$0.823313\pi$
$270$	−4.86888	−0.296311
$271$	25.6283	1.55681	0.778405	−	0.627763i	$-0.216029\pi$
$271$	25.6283	1.55681	0.778405	+	0.627763i	$0.216029\pi$
$272$	27.8209	1.68689
$273$	−11.0790	−0.670530
$274$	12.3917	0.748608
$275$	−3.31921	−0.200156
$276$	0.231801	0.0139528
$277$	20.9048	1.25605	0.628024	−	0.778194i	$-0.283864\pi$
$277$	20.9048	1.25605	0.628024	+	0.778194i	$0.283864\pi$
$278$	−15.7688	−0.945752
$279$	−3.37038	−0.201780
$280$	−2.74500	−0.164045
$281$	−30.3572	−1.81096	−0.905481	−	0.424387i	$-0.860489\pi$
$281$	−30.3572	−1.81096	−0.905481	+	0.424387i	$0.860489\pi$
$282$	−5.16305	−0.307455
$283$	−4.28389	−0.254651	−0.127325	−	0.991861i	$-0.540639\pi$
$283$	−4.28389	−0.254651	−0.127325	+	0.991861i	$0.540639\pi$
$284$	−0.289844	−0.0171991
$285$	−3.48625	−0.206507
$286$	−25.4603	−1.50550
$287$	−8.26906	−0.488107
$288$	0.875620	0.0515964
$289$	26.6955	1.57032
$290$	6.89875	0.405109
$291$	24.3961	1.43012
$292$	−0.717460	−0.0419861
$293$	18.7329	1.09439	0.547194	−	0.837006i	$-0.315696\pi$
$293$	18.7329	1.09439	0.547194	+	0.837006i	$0.315696\pi$
$294$	−3.04825	−0.177778
$295$	9.83228	0.572458
$296$	−5.41268	−0.314606
$297$	11.1243	0.645500
$298$	−29.8535	−1.72937
$299$	−5.28005	−0.305353
$300$	0.231801	0.0133831
$301$	7.03605	0.405551
$302$	11.0683	0.636909
$303$	−23.0945	−1.32674
$304$	−6.99277	−0.401063
$305$	4.79623	0.274632
$306$	13.4705	0.770055
$307$	−20.9113	−1.19347	−0.596737	−	0.802437i	$-0.703536\pi$
$307$	−20.9113	−1.19347	−0.596737	+	0.802437i	$0.703536\pi$
$308$	−0.366682	−0.0208937
$309$	−18.6226	−1.05940
$310$	−3.49056	−0.198250
$311$	18.4854	1.04821	0.524106	−	0.851653i	$-0.324399\pi$
$311$	18.4854	1.04821	0.524106	+	0.851653i	$0.324399\pi$
$312$	−30.4118	−1.72173
$313$	13.3781	0.756174	0.378087	−	0.925770i	$-0.376582\pi$
$313$	13.3781	0.756174	0.378087	+	0.925770i	$0.376582\pi$
$314$	−23.6302	−1.33353
$315$	−1.40273	−0.0790349
$316$	0.0580431	0.00326518
$317$	−22.2803	−1.25139	−0.625693	−	0.780070i	$-0.715184\pi$
$317$	−22.2803	−1.25139	−0.625693	+	0.780070i	$0.715184\pi$
$318$	29.5659	1.65797
$319$	−15.7622	−0.882512
$320$	−7.51064	−0.419858
$321$	0.589062	0.0328783
$322$	−1.45275	−0.0809584
$323$	−10.9829	−0.611103
$324$	−1.24177	−0.0689873
$325$	−5.28005	−0.292885
$326$	−6.67511	−0.369700
$327$	−12.0695	−0.667444
$328$	−22.6986	−1.25332
$329$	1.69377	0.0933808
$330$	−10.1178	−0.556967
$331$	−19.3933	−1.06595	−0.532977	−	0.846130i	$-0.678927\pi$
$331$	−19.3933	−1.06595	−0.532977	+	0.846130i	$0.678927\pi$
$332$	1.15403	0.0633357
$333$	−2.76595	−0.151573
$334$	−13.5704	−0.742542
$335$	−11.8299	−0.646334
$336$	−8.83107	−0.481774
$337$	14.2181	0.774507	0.387254	−	0.921973i	$-0.373424\pi$
$337$	14.2181	0.774507	0.387254	+	0.921973i	$0.373424\pi$
$338$	−21.6154	−1.17572
$339$	−1.46082	−0.0793408
$340$	0.730253	0.0396035
$341$	7.97518	0.431880
$342$	−3.38580	−0.183083
$343$	1.00000	0.0539949
$344$	19.3140	1.04134
$345$	−2.09827	−0.112967
$346$	5.56286	0.299061
$347$	4.62325	0.248189	0.124094	−	0.992270i	$-0.460397\pi$
$347$	4.62325	0.248189	0.124094	+	0.992270i	$0.460397\pi$
$348$	1.10077	0.0590075
$349$	−24.1593	−1.29322	−0.646609	−	0.762822i	$-0.723813\pi$
$349$	−24.1593	−1.29322	−0.646609	+	0.762822i	$0.723813\pi$
$350$	−1.45275	−0.0776526
$351$	17.6961	0.944548
$352$	−2.07194	−0.110435
$353$	28.8245	1.53417	0.767087	−	0.641543i	$-0.221705\pi$
$353$	28.8245	1.53417	0.767087	+	0.641543i	$0.221705\pi$
$354$	29.9713	1.59296
$355$	2.62368	0.139250
$356$	−0.913700	−0.0484260
$357$	−13.8701	−0.734083
$358$	32.7946	1.73325
$359$	23.8211	1.25723	0.628615	−	0.777717i	$-0.283622\pi$
$359$	23.8211	1.25723	0.628615	+	0.777717i	$0.283622\pi$
$360$	−3.85050	−0.202939
$361$	−16.2395	−0.854708
$362$	−3.00169	−0.157765
$363$	0.0360481	0.00189204
$364$	−0.583302	−0.0305733
$365$	6.49445	0.339935
$366$	14.6201	0.764207
$367$	−0.854244	−0.0445912	−0.0222956	−	0.999751i	$-0.507097\pi$
$367$	−0.854244	−0.0445912	−0.0222956	+	0.999751i	$0.507097\pi$
$368$	−4.20874	−0.219396
$369$	−11.5993	−0.603834
$370$	−2.86457	−0.148922
$371$	−9.69930	−0.503563
$372$	−0.556956	−0.0288768
$373$	9.66426	0.500396	0.250198	−	0.968195i	$-0.419504\pi$
$373$	9.66426	0.500396	0.250198	+	0.968195i	$0.419504\pi$
$374$	−31.8745	−1.64819
$375$	−2.09827	−0.108354
$376$	4.64942	0.239775
$377$	−25.0737	−1.29136
$378$	4.86888	0.250428
$379$	−24.4119	−1.25396	−0.626979	−	0.779036i	$-0.715709\pi$
$379$	−24.4119	−1.25396	−0.626979	+	0.779036i	$0.715709\pi$
$380$	−0.183549	−0.00941586
$381$	0.225062	0.0115303
$382$	−5.56734	−0.284850
$383$	8.61668	0.440292	0.220146	−	0.975467i	$-0.429347\pi$
$383$	8.61668	0.440292	0.220146	+	0.975467i	$0.429347\pi$
$384$	−25.5139	−1.30200
$385$	3.31921	0.169163
$386$	−24.8403	−1.26434
$387$	9.86968	0.501704
$388$	1.28444	0.0652075
$389$	33.6320	1.70521	0.852606	−	0.522554i	$-0.175021\pi$
$389$	33.6320	1.70521	0.852606	+	0.522554i	$0.175021\pi$
$390$	−16.0949	−0.814999
$391$	−6.61026	−0.334295
$392$	2.74500	0.138644
$393$	12.8756	0.649490
$394$	16.8382	0.848297
$395$	−0.525407	−0.0264361
$396$	−0.514357	−0.0258474
$397$	−32.5324	−1.63276	−0.816378	−	0.577518i	$-0.804021\pi$
$397$	−32.5324	−1.63276	−0.816378	+	0.577518i	$0.804021\pi$
$398$	−35.4393	−1.77641
$399$	3.48625	0.174531
$400$	−4.20874	−0.210437
$401$	6.21203	0.310214	0.155107	−	0.987898i	$-0.450428\pi$
$401$	6.21203	0.310214	0.155107	+	0.987898i	$0.450428\pi$
$402$	−36.0604	−1.79853
$403$	12.6865	0.631962
$404$	−1.21591	−0.0604938
$405$	11.2405	0.558547
$406$	−6.89875	−0.342379
$407$	6.54493	0.324420
$408$	−38.0735	−1.88492
$409$	−38.2397	−1.89083	−0.945415	−	0.325870i	$-0.894343\pi$
$409$	−38.2397	−1.89083	−0.945415	+	0.325870i	$0.894343\pi$
$410$	−12.0129	−0.593273
$411$	−17.8978	−0.882836
$412$	−0.980467	−0.0483042
$413$	−9.83228	−0.483815
$414$	−2.03781	−0.100153
$415$	−10.4463	−0.512789
$416$	−3.29594	−0.161597
$417$	22.7756	1.11533
$418$	8.01165	0.391863
$419$	−33.6848	−1.64561	−0.822806	−	0.568322i	$-0.807593\pi$
$419$	−33.6848	−1.64561	−0.822806	+	0.568322i	$0.807593\pi$
$420$	−0.231801	−0.0113107
$421$	14.7234	0.717574	0.358787	−	0.933420i	$-0.383191\pi$
$421$	14.7234	0.717574	0.358787	+	0.933420i	$0.383191\pi$
$422$	11.2295	0.546642
$423$	2.37591	0.115521
$424$	−26.6246	−1.29301
$425$	−6.61026	−0.320645
$426$	7.99763	0.387486
$427$	−4.79623	−0.232106
$428$	0.0310138	0.00149911
$429$	36.7735	1.77544
$430$	10.2216	0.492929
$431$	29.1446	1.40384	0.701922	−	0.712254i	$-0.252325\pi$
$431$	29.1446	1.40384	0.701922	+	0.712254i	$0.252325\pi$
$432$	14.1056	0.678656
$433$	9.11790	0.438178	0.219089	−	0.975705i	$-0.429691\pi$
$433$	9.11790	0.438178	0.219089	+	0.975705i	$0.429691\pi$
$434$	3.49056	0.167552
$435$	−9.96419	−0.477746
$436$	−0.635451	−0.0304326
$437$	1.66149	0.0794797
$438$	19.7967	0.945925
$439$	−27.1610	−1.29632	−0.648161	−	0.761503i	$-0.724462\pi$
$439$	−27.1610	−1.29632	−0.648161	+	0.761503i	$0.724462\pi$
$440$	9.11126	0.434362
$441$	1.40273	0.0667967
$442$	−50.7045	−2.41177
$443$	3.28815	0.156225	0.0781125	−	0.996945i	$-0.475111\pi$
$443$	3.28815	0.156225	0.0781125	+	0.996945i	$0.475111\pi$
$444$	−0.457073	−0.0216917
$445$	8.27083	0.392075
$446$	−40.0221	−1.89510
$447$	43.1187	2.03945
$448$	7.51064	0.354844
$449$	3.22909	0.152390	0.0761951	−	0.997093i	$-0.475723\pi$
$449$	3.22909	0.152390	0.0761951	+	0.997093i	$0.475723\pi$
$450$	−2.03781	−0.0960634
$451$	27.4468	1.29242
$452$	−0.0769113	−0.00361760
$453$	−15.9864	−0.751109
$454$	−15.0146	−0.704669
$455$	5.28005	0.247533
$456$	9.56976	0.448145
$457$	−39.6940	−1.85681	−0.928404	−	0.371572i	$-0.878819\pi$
$457$	−39.6940	−1.85681	−0.928404	+	0.371572i	$0.878819\pi$
$458$	7.02706	0.328353
$459$	22.1543	1.03407
$460$	−0.110473	−0.00515081
$461$	1.38385	0.0644522	0.0322261	−	0.999481i	$-0.489740\pi$
$461$	1.38385	0.0644522	0.0322261	+	0.999481i	$0.489740\pi$
$462$	10.1178	0.470723
$463$	25.9498	1.20599	0.602994	−	0.797746i	$-0.293974\pi$
$463$	25.9498	1.20599	0.602994	+	0.797746i	$0.293974\pi$
$464$	−19.9863	−0.927842
$465$	5.04157	0.233797
$466$	−4.44069	−0.205711
$467$	−35.7835	−1.65586	−0.827931	−	0.560830i	$-0.810482\pi$
$467$	−35.7835	−1.65586	−0.827931	+	0.560830i	$0.810482\pi$
$468$	−0.818215	−0.0378220
$469$	11.8299	0.546252
$470$	2.46062	0.113500
$471$	34.1302	1.57263
$472$	−26.9897	−1.24230
$473$	−23.3541	−1.07382
$474$	−1.60157	−0.0735627
$475$	1.66149	0.0762343
$476$	−0.730253	−0.0334711
$477$	−13.6055	−0.622953
$478$	−30.8101	−1.40922
$479$	−19.1174	−0.873497	−0.436748	−	0.899584i	$-0.643870\pi$
$479$	−19.1174	−0.873497	−0.436748	+	0.899584i	$0.643870\pi$
$480$	−1.30979	−0.0597836
$481$	10.4114	0.474718
$482$	30.5988	1.39374
$483$	2.09827	0.0954745
$484$	0.00189791	8.62688e−5 0
$485$	−11.6268	−0.527944
$486$	19.6574	0.891676
$487$	9.05777	0.410447	0.205223	−	0.978715i	$-0.434208\pi$
$487$	9.05777	0.410447	0.205223	+	0.978715i	$0.434208\pi$
$488$	−13.1657	−0.595983
$489$	9.64117	0.435989
$490$	1.45275	0.0656284
$491$	−34.9052	−1.57525	−0.787625	−	0.616155i	$-0.788690\pi$
$491$	−34.9052	−1.57525	−0.787625	+	0.616155i	$0.788690\pi$
$492$	−1.91678	−0.0864151
$493$	−31.3906	−1.41376
$494$	12.7446	0.573405
$495$	4.65596	0.209270
$496$	10.1125	0.454063
$497$	−2.62368	−0.117688
$498$	−31.8430	−1.42692
$499$	−1.28244	−0.0574099	−0.0287050	−	0.999588i	$-0.509138\pi$
$499$	−1.28244	−0.0574099	−0.0287050	+	0.999588i	$0.509138\pi$
$500$	−0.110473	−0.00494049
$501$	19.6004	0.875682
$502$	25.6567	1.14511
$503$	−37.1760	−1.65760	−0.828798	−	0.559548i	$-0.810975\pi$
$503$	−37.1760	−1.65760	−0.828798	+	0.559548i	$0.810975\pi$
$504$	3.85050	0.171515
$505$	11.0064	0.489780
$506$	4.82198	0.214363
$507$	31.2201	1.38653
$508$	0.0118494	0.000525731 0
$509$	1.47758	0.0654928	0.0327464	−	0.999464i	$-0.489575\pi$
$509$	1.47758	0.0654928	0.0327464	+	0.999464i	$0.489575\pi$
$510$	−20.1497	−0.892245
$511$	−6.49445	−0.287298
$512$	20.4788	0.905045
$513$	−5.56848	−0.245854
$514$	37.9056	1.67194
$515$	8.87520	0.391088
$516$	1.63096	0.0717992
$517$	−5.62200	−0.247255
$518$	2.86457	0.125862
$519$	−8.03470	−0.352684
$520$	14.4938	0.635594
$521$	−23.5197	−1.03042	−0.515208	−	0.857065i	$-0.672286\pi$
$521$	−23.5197	−1.03042	−0.515208	+	0.857065i	$0.672286\pi$
$522$	−9.67709	−0.423555
$523$	−2.74010	−0.119816	−0.0599082	−	0.998204i	$-0.519081\pi$
$523$	−2.74010	−0.119816	−0.0599082	+	0.998204i	$0.519081\pi$
$524$	0.677895	0.0296140
$525$	2.09827	0.0915759
$526$	−3.35326	−0.146209
$527$	15.8827	0.691860
$528$	29.3122	1.27565
$529$	1.00000	0.0434783
$530$	−14.0906	−0.612058
$531$	−13.7920	−0.598524
$532$	0.183549	0.00795786
$533$	43.6611	1.89117
$534$	25.2116	1.09101
$535$	−0.280737	−0.0121373
$536$	32.4730	1.40262
$537$	−47.3667	−2.04402
$538$	40.4989	1.74603
$539$	−3.31921	−0.142969
$540$	0.370249	0.0159330
$541$	13.6576	0.587185	0.293592	−	0.955931i	$-0.405149\pi$
$541$	13.6576	0.587185	0.293592	+	0.955931i	$0.405149\pi$
$542$	−37.2315	−1.59923
$543$	4.33548	0.186053
$544$	−4.12629	−0.176913
$545$	5.75211	0.246393
$546$	16.0949	0.688800
$547$	−40.5614	−1.73428	−0.867140	−	0.498064i	$-0.834044\pi$
$547$	−40.5614	−1.73428	−0.867140	+	0.498064i	$0.834044\pi$
$548$	−0.942312	−0.0402536
$549$	−6.72782	−0.287137
$550$	4.82198	0.205610
$551$	7.89002	0.336126
$552$	5.75976	0.245152
$553$	0.525407	0.0223426
$554$	−30.3694	−1.29027
$555$	4.13743	0.175624
$556$	1.19913	0.0508542
$557$	−3.24586	−0.137531	−0.0687657	−	0.997633i	$-0.521906\pi$
$557$	−3.24586	−0.137531	−0.0687657	+	0.997633i	$0.521906\pi$
$558$	4.89631	0.207277
$559$	−37.1507	−1.57131
$560$	4.20874	0.177852
$561$	46.0378	1.94372
$562$	44.1014	1.86030
$563$	−7.62791	−0.321478	−0.160739	−	0.986997i	$-0.551388\pi$
$563$	−7.62791	−0.321478	−0.160739	+	0.986997i	$0.551388\pi$
$564$	0.392619	0.0165322
$565$	0.696202	0.0292895
$566$	6.22341	0.261589
$567$	−11.2405	−0.472058
$568$	−7.20200	−0.302189
$569$	29.1581	1.22237	0.611185	−	0.791488i	$-0.290693\pi$
$569$	29.1581	1.22237	0.611185	+	0.791488i	$0.290693\pi$
$570$	5.06463	0.212134
$571$	−22.6249	−0.946822	−0.473411	−	0.880842i	$-0.656977\pi$
$571$	−22.6249	−0.946822	−0.473411	+	0.880842i	$0.656977\pi$
$572$	1.93610	0.0809525
$573$	8.04116	0.335924
$574$	12.0129	0.501407
$575$	1.00000	0.0417029
$576$	10.5354	0.438975
$577$	12.6370	0.526087	0.263044	−	0.964784i	$-0.415274\pi$
$577$	12.6370	0.526087	0.263044	+	0.964784i	$0.415274\pi$
$578$	−38.7818	−1.61311
$579$	35.8779	1.49104
$580$	−0.524609	−0.0217832
$581$	10.4463	0.433386
$582$	−35.4413	−1.46909
$583$	32.1940	1.33334
$584$	−17.8273	−0.737699
$585$	7.40649	0.306221
$586$	−27.2142	−1.12421
$587$	−30.1722	−1.24534	−0.622670	−	0.782485i	$-0.713952\pi$
$587$	−30.1722	−1.24534	−0.622670	+	0.782485i	$0.713952\pi$
$588$	0.231801	0.00955932
$589$	−3.99211	−0.164492
$590$	−14.2838	−0.588055
$591$	−24.3202	−1.00040
$592$	8.29892	0.341084
$593$	43.2243	1.77501	0.887505	−	0.460798i	$-0.152437\pi$
$593$	43.2243	1.77501	0.887505	+	0.460798i	$0.152437\pi$
$594$	−16.1609	−0.663088
$595$	6.61026	0.270994
$596$	2.27018	0.0929901
$597$	51.1867	2.09493
$598$	7.67058	0.313673
$599$	−33.4145	−1.36528	−0.682639	−	0.730755i	$-0.739168\pi$
$599$	−33.4145	−1.36528	−0.682639	+	0.730755i	$0.739168\pi$
$600$	5.75976	0.235141
$601$	12.8460	0.524000	0.262000	−	0.965068i	$-0.415618\pi$
$601$	12.8460	0.524000	0.262000	+	0.965068i	$0.415618\pi$
$602$	−10.2216	−0.416601
$603$	16.5941	0.675764
$604$	−0.841677	−0.0342474
$605$	−0.0171799	−0.000698464 0
$606$	33.5504	1.36289
$607$	14.5177	0.589256	0.294628	−	0.955612i	$-0.404804\pi$
$607$	14.5177	0.589256	0.294628	+	0.955612i	$0.404804\pi$
$608$	1.03714	0.0420617
$609$	9.96419	0.403769
$610$	−6.96771	−0.282114
$611$	−8.94322	−0.361804
$612$	−1.02435	−0.0414068
$613$	20.4453	0.825778	0.412889	−	0.910781i	$-0.364520\pi$
$613$	20.4453	0.825778	0.412889	+	0.910781i	$0.364520\pi$
$614$	30.3789	1.22599
$615$	17.3507	0.699648
$616$	−9.11126	−0.367103
$617$	47.4858	1.91171	0.955853	−	0.293847i	$-0.0949356\pi$
$617$	47.4858	1.91171	0.955853	+	0.293847i	$0.0949356\pi$
$618$	27.0539	1.08827
$619$	−7.17447	−0.288366	−0.144183	−	0.989551i	$-0.546055\pi$
$619$	−7.17447	−0.288366	−0.144183	+	0.989551i	$0.546055\pi$
$620$	0.265436	0.0106602
$621$	−3.35150	−0.134491
$622$	−26.8546	−1.07677
$623$	−8.27083	−0.331364
$624$	46.6285	1.86663
$625$	1.00000	0.0400000
$626$	−19.4350	−0.776778
$627$	−11.5716	−0.462125
$628$	1.79693	0.0717054
$629$	13.0343	0.519712
$630$	2.03781	0.0811884
$631$	−31.5381	−1.25551	−0.627756	−	0.778410i	$-0.716026\pi$
$631$	−31.5381	−1.25551	−0.627756	+	0.778410i	$0.716026\pi$
$632$	1.44225	0.0573694
$633$	−16.2192	−0.644657
$634$	32.3676	1.28548
$635$	−0.107261	−0.00425651
$636$	−2.24831	−0.0891513
$637$	−5.28005	−0.209203
$638$	22.8984	0.906558
$639$	−3.68031	−0.145591
$640$	12.1595	0.480647
$641$	−39.3307	−1.55347	−0.776734	−	0.629829i	$-0.783125\pi$
$641$	−39.3307	−1.55347	−0.776734	+	0.629829i	$0.783125\pi$
$642$	−0.855758	−0.0337741
$643$	−21.8077	−0.860010	−0.430005	−	0.902826i	$-0.641488\pi$
$643$	−21.8077	−0.860010	−0.430005	+	0.902826i	$0.641488\pi$
$644$	0.110473	0.00435323
$645$	−14.7635	−0.581313
$646$	15.9553	0.627753
$647$	−21.4809	−0.844500	−0.422250	−	0.906480i	$-0.638759\pi$
$647$	−21.4809	−0.844500	−0.422250	+	0.906480i	$0.638759\pi$
$648$	−30.8553	−1.21211
$649$	32.6354	1.28105
$650$	7.67058	0.300865
$651$	−5.04157	−0.197595
$652$	0.507602	0.0198792
$653$	−11.8548	−0.463912	−0.231956	−	0.972726i	$-0.574513\pi$
$653$	−11.8548	−0.463912	−0.231956	+	0.972726i	$0.574513\pi$
$654$	17.5339	0.685629
$655$	−6.13631	−0.239766
$656$	34.8023	1.35880
$657$	−9.10997	−0.355414
$658$	−2.46062	−0.0959251
$659$	27.5069	1.07152	0.535758	−	0.844371i	$-0.320026\pi$
$659$	27.5069	1.07152	0.535758	+	0.844371i	$0.320026\pi$
$660$	0.769398	0.0299488
$661$	−32.1476	−1.25040	−0.625199	−	0.780466i	$-0.714982\pi$
$661$	−32.1476	−1.25040	−0.625199	+	0.780466i	$0.714982\pi$
$662$	28.1736	1.09500
$663$	73.2348	2.84421
$664$	28.6751	1.11281
$665$	−1.66149	−0.0644297
$666$	4.01822	0.155703
$667$	4.74877	0.183873
$668$	1.03195	0.0399274
$669$	57.8057	2.23490
$670$	17.1858	0.663945
$671$	15.9197	0.614574
$672$	1.30979	0.0505263
$673$	−46.7331	−1.80143	−0.900714	−	0.434413i	$-0.856956\pi$
$673$	−46.7331	−1.80143	−0.900714	+	0.434413i	$0.856956\pi$
$674$	−20.6552	−0.795610
$675$	−3.35150	−0.128999
$676$	1.64372	0.0632200
$677$	41.8886	1.60991	0.804956	−	0.593335i	$-0.202189\pi$
$677$	41.8886	1.60991	0.804956	+	0.593335i	$0.202189\pi$
$678$	2.12220	0.0815026
$679$	11.6268	0.446194
$680$	18.1452	0.695836
$681$	21.6862	0.831018
$682$	−11.5859	−0.443647
$683$	−28.9163	−1.10645	−0.553227	−	0.833031i	$-0.686604\pi$
$683$	−28.9163	−1.10645	−0.553227	+	0.833031i	$0.686604\pi$
$684$	0.257470	0.00984460
$685$	8.52982	0.325908
$686$	−1.45275	−0.0554661
$687$	−10.1495	−0.387228
$688$	−29.6129	−1.12898
$689$	51.2128	1.95105
$690$	3.04825	0.116045
$691$	−6.80368	−0.258824	−0.129412	−	0.991591i	$-0.541309\pi$
$691$	−6.80368	−0.258824	−0.129412	+	0.991591i	$0.541309\pi$
$692$	−0.423022	−0.0160809
$693$	−4.65596	−0.176865
$694$	−6.71640	−0.254951
$695$	−10.8545	−0.411735
$696$	27.3517	1.03676
$697$	54.6606	2.07042
$698$	35.0973	1.32845
$699$	6.41389	0.242596
$700$	0.110473	0.00417547
$701$	19.1275	0.722437	0.361219	−	0.932481i	$-0.382361\pi$
$701$	19.1275	0.722437	0.361219	+	0.932481i	$0.382361\pi$
$702$	−25.7080	−0.970284
$703$	−3.27617	−0.123563
$704$	−24.9294	−0.939563
$705$	−3.55399	−0.133851
$706$	−41.8747	−1.57598
$707$	−11.0064	−0.413940
$708$	−2.27914	−0.0856552
$709$	35.6571	1.33913	0.669566	−	0.742753i	$-0.266480\pi$
$709$	35.6571	1.33913	0.669566	+	0.742753i	$0.266480\pi$
$710$	−3.81154	−0.143044
$711$	0.737005	0.0276398
$712$	−22.7035	−0.850848
$713$	−2.40273	−0.0899830
$714$	20.1497	0.754085
$715$	−17.5256	−0.655421
$716$	−2.49383	−0.0931988
$717$	44.5004	1.66190
$718$	−34.6060	−1.29149
$719$	−11.8756	−0.442884	−0.221442	−	0.975174i	$-0.571076\pi$
$719$	−11.8756	−0.442884	−0.221442	+	0.975174i	$0.571076\pi$
$720$	5.90373	0.220019
$721$	−8.87520	−0.330530
$722$	23.5918	0.877997
$723$	−44.1953	−1.64364
$724$	0.228260	0.00848323
$725$	4.74877	0.176365
$726$	−0.0523688	−0.00194359
$727$	−32.0090	−1.18715	−0.593574	−	0.804779i	$-0.702284\pi$
$727$	−32.0090	−1.18715	−0.593574	+	0.804779i	$0.702284\pi$
$728$	−14.4938	−0.537175
$729$	5.32960	0.197392
$730$	−9.43480	−0.349197
$731$	−46.5101	−1.72024
$732$	−1.11177	−0.0410923
$733$	−13.6867	−0.505529	−0.252764	−	0.967528i	$-0.581340\pi$
$733$	−13.6867	−0.505529	−0.252764	+	0.967528i	$0.581340\pi$
$734$	1.24100	0.0458061
$735$	−2.09827	−0.0773958
$736$	0.624225	0.0230093
$737$	−39.2658	−1.44637
$738$	16.8508	0.620286
$739$	24.0419	0.884396	0.442198	−	0.896918i	$-0.354199\pi$
$739$	24.0419	0.884396	0.442198	+	0.896918i	$0.354199\pi$
$740$	0.217833	0.00800771
$741$	−18.4076	−0.676219
$742$	14.0906	0.517283
$743$	24.7571	0.908251	0.454125	−	0.890938i	$-0.349952\pi$
$743$	24.7571	0.908251	0.454125	+	0.890938i	$0.349952\pi$
$744$	−13.8391	−0.507368
$745$	−20.5497	−0.752882
$746$	−14.0397	−0.514030
$747$	14.6533	0.536138
$748$	2.42386	0.0886253
$749$	0.280737	0.0102579
$750$	3.04825	0.111306
$751$	−15.1725	−0.553652	−0.276826	−	0.960920i	$-0.589283\pi$
$751$	−15.1725	−0.553652	−0.276826	+	0.960920i	$0.589283\pi$
$752$	−7.12866	−0.259955
$753$	−37.0571	−1.35044
$754$	36.4258	1.32655
$755$	7.61888	0.277279
$756$	−0.370249	−0.0134658
$757$	−16.9049	−0.614418	−0.307209	−	0.951642i	$-0.599395\pi$
$757$	−16.9049	−0.614418	−0.307209	+	0.951642i	$0.599395\pi$
$758$	35.4644	1.28812
$759$	−6.96460	−0.252799
$760$	−4.56079	−0.165437
$761$	−23.5417	−0.853386	−0.426693	−	0.904396i	$-0.640322\pi$
$761$	−23.5417	−0.853386	−0.426693	+	0.904396i	$0.640322\pi$
$762$	−0.326958	−0.0118444
$763$	−5.75211	−0.208240
$764$	0.423362	0.0153167
$765$	9.27241	0.335245
$766$	−12.5179	−0.452288
$767$	51.9150	1.87454
$768$	5.54657	0.200145
$769$	28.8749	1.04125	0.520627	−	0.853784i	$-0.325698\pi$
$769$	28.8749	1.04125	0.520627	+	0.853784i	$0.325698\pi$
$770$	−4.82198	−0.173772
$771$	−54.7488	−1.97173
$772$	1.88895	0.0679849
$773$	−34.3839	−1.23670	−0.618352	−	0.785901i	$-0.712199\pi$
$773$	−34.3839	−1.23670	−0.618352	+	0.785901i	$0.712199\pi$
$774$	−14.3381	−0.515374
$775$	−2.40273	−0.0863086
$776$	31.9155	1.14570
$777$	−4.13743	−0.148429
$778$	−48.8588	−1.75167
$779$	−13.7389	−0.492249
$780$	1.22392	0.0438235
$781$	8.70854	0.311616
$782$	9.60303	0.343404
$783$	−15.9155	−0.568773
$784$	−4.20874	−0.150312
$785$	−16.2659	−0.580554
$786$	−18.7050	−0.667186
$787$	−9.08385	−0.323804	−0.161902	−	0.986807i	$-0.551763\pi$
$787$	−9.08385	−0.323804	−0.161902	+	0.986807i	$0.551763\pi$
$788$	−1.28044	−0.0456140
$789$	4.84327	0.172425
$790$	0.763284	0.0271564
$791$	−0.696202	−0.0247541
$792$	−12.7806	−0.454140
$793$	25.3244	0.899295
$794$	47.2614	1.67724
$795$	20.3517	0.721802
$796$	2.69495	0.0955199
$797$	49.5232	1.75420	0.877101	−	0.480306i	$-0.159474\pi$
$797$	49.5232	1.75420	0.877101	+	0.480306i	$0.159474\pi$
$798$	−5.06463	−0.179286
$799$	−11.1963	−0.396096
$800$	0.624225	0.0220697
$801$	−11.6017	−0.409927
$802$	−9.02450	−0.318666
$803$	21.5565	0.760712
$804$	2.74218	0.0967091
$805$	−1.00000	−0.0352454
$806$	−18.4303	−0.649181
$807$	−58.4944	−2.05910
$808$	−30.2127	−1.06288
$809$	5.63141	0.197990	0.0989949	−	0.995088i	$-0.468437\pi$
$809$	5.63141	0.197990	0.0989949	+	0.995088i	$0.468437\pi$
$810$	−16.3297	−0.573766
$811$	37.2815	1.30913	0.654565	−	0.756006i	$-0.272852\pi$
$811$	37.2815	1.30913	0.654565	+	0.756006i	$0.272852\pi$
$812$	0.524609	0.0184102
$813$	53.7751	1.88598
$814$	−9.50812	−0.333259
$815$	−4.59482	−0.160950
$816$	58.3756	2.04356
$817$	11.6903	0.408992
$818$	55.5525	1.94235
$819$	−7.40649	−0.258804
$820$	0.913505	0.0319010
$821$	−5.45135	−0.190253	−0.0951267	−	0.995465i	$-0.530326\pi$
$821$	−5.45135	−0.190253	−0.0951267	+	0.995465i	$0.530326\pi$
$822$	26.0010	0.906890
$823$	−52.6766	−1.83619	−0.918095	−	0.396361i	$-0.870273\pi$
$823$	−52.6766	−1.83619	−0.918095	+	0.396361i	$0.870273\pi$
$824$	−24.3625	−0.848707
$825$	−6.96460	−0.242476
$826$	14.2838	0.496997
$827$	−32.9785	−1.14678	−0.573388	−	0.819284i	$-0.694371\pi$
$827$	−32.9785	−1.14678	−0.573388	+	0.819284i	$0.694371\pi$
$828$	0.154963	0.00538535
$829$	16.4900	0.572720	0.286360	−	0.958122i	$-0.407555\pi$
$829$	16.4900	0.572720	0.286360	+	0.958122i	$0.407555\pi$
$830$	15.1758	0.526761
$831$	43.8639	1.52162
$832$	−39.6566	−1.37484
$833$	−6.61026	−0.229032
$834$	−33.0872	−1.14572
$835$	−9.34124	−0.323267
$836$	−0.609238	−0.0210709
$837$	8.05275	0.278344
$838$	48.9355	1.69045
$839$	−4.40899	−0.152215	−0.0761077	−	0.997100i	$-0.524249\pi$
$839$	−4.40899	−0.152215	−0.0761077	+	0.997100i	$0.524249\pi$
$840$	−5.75976	−0.198730
$841$	−6.44922	−0.222387
$842$	−21.3893	−0.737125
$843$	−63.6976	−2.19386
$844$	−0.853934	−0.0293936
$845$	−14.8790	−0.511852
$846$	−3.45159	−0.118668
$847$	0.0171799	0.000590310 0
$848$	40.8218	1.40183
$849$	−8.98875	−0.308493
$850$	9.60303	0.329381
$851$	−1.97183	−0.0675935
$852$	−0.608171	−0.0208356
$853$	44.8473	1.53554	0.767772	−	0.640723i	$-0.221365\pi$
$853$	44.8473	1.53554	0.767772	+	0.640723i	$0.221365\pi$
$854$	6.96771	0.238430
$855$	−2.33062	−0.0797055
$856$	0.770625	0.0263394
$857$	−41.6071	−1.42127	−0.710637	−	0.703559i	$-0.751593\pi$
$857$	−41.6071	−1.42127	−0.710637	+	0.703559i	$0.751593\pi$
$858$	−53.4225	−1.82382
$859$	−21.6016	−0.737036	−0.368518	−	0.929621i	$-0.620135\pi$
$859$	−21.6016	−0.737036	−0.368518	+	0.929621i	$0.620135\pi$
$860$	−0.777291	−0.0265054
$861$	−17.3507	−0.591311
$862$	−42.3397	−1.44209
$863$	13.5068	0.459777	0.229888	−	0.973217i	$-0.426164\pi$
$863$	13.5068	0.459777	0.229888	+	0.973217i	$0.426164\pi$
$864$	−2.09209	−0.0711744
$865$	3.82920	0.130197
$866$	−13.2460	−0.450117
$867$	56.0143	1.90235
$868$	−0.265436	−0.00900949
$869$	−1.74394	−0.0591591
$870$	14.4754	0.490763
$871$	−62.4623	−2.11645
$872$	−15.7896	−0.534702
$873$	16.3092	0.551983
$874$	−2.41372	−0.0816453
$875$	−1.00000	−0.0338062
$876$	−1.50542	−0.0508635
$877$	−53.2430	−1.79789	−0.898944	−	0.438064i	$-0.855664\pi$
$877$	−53.2430	−1.79789	−0.898944	+	0.438064i	$0.855664\pi$
$878$	39.4580	1.33164
$879$	39.3067	1.32578
$880$	−13.9697	−0.470919
$881$	4.55419	0.153434	0.0767172	−	0.997053i	$-0.475556\pi$
$881$	4.55419	0.153434	0.0767172	+	0.997053i	$0.475556\pi$
$882$	−2.03781	−0.0686167
$883$	−13.9181	−0.468381	−0.234190	−	0.972191i	$-0.575244\pi$
$883$	−13.9181	−0.468381	−0.234190	+	0.972191i	$0.575244\pi$
$884$	3.85577	0.129684
$885$	20.6308	0.693496
$886$	−4.77686	−0.160482
$887$	−10.5236	−0.353347	−0.176674	−	0.984269i	$-0.556534\pi$
$887$	−10.5236	−0.353347	−0.176674	+	0.984269i	$0.556534\pi$
$888$	−11.3573	−0.381125
$889$	0.107261	0.00359741
$890$	−12.0154	−0.402758
$891$	37.3098	1.24992
$892$	3.04344	0.101902
$893$	2.81418	0.0941731
$894$	−62.6406	−2.09502
$895$	22.5742	0.754571
$896$	−12.1595	−0.406221
$897$	−11.0790	−0.369916
$898$	−4.69105	−0.156542
$899$	−11.4100	−0.380545
$900$	0.154963	0.00516545
$901$	64.1149	2.13598
$902$	−39.8732	−1.32763
$903$	14.7635	0.491299
$904$	−1.91108	−0.0635615
$905$	−2.06622	−0.0686833
$906$	23.2243	0.771574
$907$	52.2444	1.73475	0.867373	−	0.497658i	$-0.165807\pi$
$907$	52.2444	1.73475	0.867373	+	0.497658i	$0.165807\pi$
$908$	1.14177	0.0378909
$909$	−15.4391	−0.512082
$910$	−7.67058	−0.254277
$911$	46.9232	1.55464	0.777318	−	0.629108i	$-0.216580\pi$
$911$	46.9232	1.55464	0.777318	+	0.629108i	$0.216580\pi$
$912$	−14.6727	−0.485862
$913$	−34.6735	−1.14753
$914$	57.6654	1.90740
$915$	10.0638	0.332699
$916$	−0.534365	−0.0176559
$917$	6.13631	0.202639
$918$	−32.1846	−1.06225
$919$	−47.9596	−1.58204	−0.791020	−	0.611790i	$-0.790450\pi$
$919$	−47.9596	−1.58204	−0.791020	+	0.611790i	$0.790450\pi$
$920$	−2.74500	−0.0905001
$921$	−43.8776	−1.44582
$922$	−2.01038	−0.0662083
$923$	13.8531	0.455982
$924$	−0.769398	−0.0253113
$925$	−1.97183	−0.0648334
$926$	−37.6984	−1.23885
$927$	−12.4495	−0.408896
$928$	2.96430	0.0973079
$929$	10.6872	0.350634	0.175317	−	0.984512i	$-0.443905\pi$
$929$	10.6872	0.350634	0.175317	+	0.984512i	$0.443905\pi$
$930$	−7.32413	−0.240168
$931$	1.66149	0.0544531
$932$	0.337688	0.0110613
$933$	38.7874	1.26984
$934$	51.9843	1.70098
$935$	−21.9409	−0.717543
$936$	−20.3309	−0.664535
$937$	3.88361	0.126872	0.0634360	−	0.997986i	$-0.479794\pi$
$937$	3.88361	0.126872	0.0634360	+	0.997986i	$0.479794\pi$
$938$	−17.1858	−0.561136
$939$	28.0708	0.916057
$940$	−0.187116	−0.00610304
$941$	18.5753	0.605537	0.302769	−	0.953064i	$-0.402089\pi$
$941$	18.5753	0.605537	0.302769	+	0.953064i	$0.402089\pi$
$942$	−49.5825	−1.61548
$943$	−8.26906	−0.269278
$944$	41.3815	1.34685
$945$	3.35150	0.109024
$946$	33.9277	1.10308
$947$	45.0111	1.46267	0.731333	−	0.682021i	$-0.238899\pi$
$947$	45.0111	1.46267	0.731333	+	0.682021i	$0.238899\pi$
$948$	0.121790	0.00395556
$949$	34.2911	1.11314
$950$	−2.41372	−0.0783114
$951$	−46.7500	−1.51597
$952$	−18.1452	−0.588089
$953$	27.9422	0.905135	0.452568	−	0.891730i	$-0.350508\pi$
$953$	27.9422	0.905135	0.452568	+	0.891730i	$0.350508\pi$
$954$	19.7653	0.639927
$955$	−3.83228	−0.124010
$956$	2.34292	0.0757755
$957$	−33.0733	−1.06911
$958$	27.7728	0.897297
$959$	−8.52982	−0.275442
$960$	−15.7593	−0.508631
$961$	−25.2269	−0.813771
$962$	−15.1251	−0.487652
$963$	0.393799	0.0126900
$964$	−2.32686	−0.0749430
$965$	−17.0988	−0.550431
$966$	−3.04825	−0.0980759
$967$	−26.5835	−0.854868	−0.427434	−	0.904047i	$-0.640582\pi$
$967$	−26.5835	−0.854868	−0.427434	+	0.904047i	$0.640582\pi$
$968$	0.0471590	0.00151575
$969$	−23.0450	−0.740312
$970$	16.8907	0.542329
$971$	4.59131	0.147342	0.0736711	−	0.997283i	$-0.476528\pi$
$971$	4.59131	0.147342	0.0736711	+	0.997283i	$0.476528\pi$
$972$	−1.49482	−0.0479465
$973$	10.8545	0.347979
$974$	−13.1587	−0.421630
$975$	−11.0790	−0.354811
$976$	20.1861	0.646142
$977$	20.6071	0.659279	0.329640	−	0.944107i	$-0.393073\pi$
$977$	20.6071	0.659279	0.329640	+	0.944107i	$0.393073\pi$
$978$	−14.0062	−0.447868
$979$	27.4526	0.877390
$980$	−0.110473	−0.00352892
$981$	−8.06866	−0.257613
$982$	50.7084	1.61817
$983$	−2.29695	−0.0732615	−0.0366307	−	0.999329i	$-0.511663\pi$
$983$	−2.29695	−0.0732615	−0.0366307	+	0.999329i	$0.511663\pi$
$984$	−47.6278	−1.51832
$985$	11.5906	0.369307
$986$	45.6025	1.45228
$987$	3.55399	0.113125
$988$	−0.969148	−0.0308327
$989$	7.03605	0.223733
$990$	−6.76393	−0.214972
$991$	−16.9645	−0.538895	−0.269447	−	0.963015i	$-0.586841\pi$
$991$	−16.9645	−0.538895	−0.269447	+	0.963015i	$0.586841\pi$
$992$	−1.49985	−0.0476201
$993$	−40.6924	−1.29134
$994$	3.81154	0.120895
$995$	−24.3947	−0.773365
$996$	2.42147	0.0767271
$997$	24.9468	0.790073	0.395036	−	0.918666i	$-0.370732\pi$
$997$	24.9468	0.790073	0.395036	+	0.918666i	$0.370732\pi$
$998$	1.86306	0.0589742
$999$	6.60859	0.209086

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	805.2.a.l.1.2	✓	5
3.2	odd	2		7245.2.a.bh.1.4		5
5.4	even	2		4025.2.a.q.1.4		5
7.6	odd	2		5635.2.a.y.1.2		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
805.2.a.l.1.2	✓	5	1.1	even	1	trivial
4025.2.a.q.1.4		5	5.4	even	2
5635.2.a.y.1.2		5	7.6	odd	2
7245.2.a.bh.1.4		5	3.2	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:	\( N \)	\(=\)	\( 805 = 5 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	805.a (trivial)

\(f(q)\)	\(=\)	\(q-1.45275 q^{2} +2.09827 q^{3} +0.110473 q^{4} -1.00000 q^{5} -3.04825 q^{6} +1.00000 q^{7} +2.74500 q^{8} +1.40273 q^{9} +O(q^{10})\)	\(q-1.45275 q^{2} +2.09827 q^{3} +0.110473 q^{4} -1.00000 q^{5} -3.04825 q^{6} +1.00000 q^{7} +2.74500 q^{8} +1.40273 q^{9} +1.45275 q^{10} -3.31921 q^{11} +0.231801 q^{12} -5.28005 q^{13} -1.45275 q^{14} -2.09827 q^{15} -4.20874 q^{16} -6.61026 q^{17} -2.03781 q^{18} +1.66149 q^{19} -0.110473 q^{20} +2.09827 q^{21} +4.82198 q^{22} +1.00000 q^{23} +5.75976 q^{24} +1.00000 q^{25} +7.67058 q^{26} -3.35150 q^{27} +0.110473 q^{28} +4.74877 q^{29} +3.04825 q^{30} -2.40273 q^{31} +0.624225 q^{32} -6.96460 q^{33} +9.60303 q^{34} -1.00000 q^{35} +0.154963 q^{36} -1.97183 q^{37} -2.41372 q^{38} -11.0790 q^{39} -2.74500 q^{40} -8.26906 q^{41} -3.04825 q^{42} +7.03605 q^{43} -0.366682 q^{44} -1.40273 q^{45} -1.45275 q^{46} +1.69377 q^{47} -8.83107 q^{48} +1.00000 q^{49} -1.45275 q^{50} -13.8701 q^{51} -0.583302 q^{52} -9.69930 q^{53} +4.86888 q^{54} +3.31921 q^{55} +2.74500 q^{56} +3.48625 q^{57} -6.89875 q^{58} -9.83228 q^{59} -0.231801 q^{60} -4.79623 q^{61} +3.49056 q^{62} +1.40273 q^{63} +7.51064 q^{64} +5.28005 q^{65} +10.1178 q^{66} +11.8299 q^{67} -0.730253 q^{68} +2.09827 q^{69} +1.45275 q^{70} -2.62368 q^{71} +3.85050 q^{72} -6.49445 q^{73} +2.86457 q^{74} +2.09827 q^{75} +0.183549 q^{76} -3.31921 q^{77} +16.0949 q^{78} +0.525407 q^{79} +4.20874 q^{80} -11.2405 q^{81} +12.0129 q^{82} +10.4463 q^{83} +0.231801 q^{84} +6.61026 q^{85} -10.2216 q^{86} +9.96419 q^{87} -9.11126 q^{88} -8.27083 q^{89} +2.03781 q^{90} -5.28005 q^{91} +0.110473 q^{92} -5.04157 q^{93} -2.46062 q^{94} -1.66149 q^{95} +1.30979 q^{96} +11.6268 q^{97} -1.45275 q^{98} -4.65596 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - q^{2} - 4 q^{3} + 3 q^{4} - 5 q^{5} - 5 q^{6} + 5 q^{7} + 3 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q - q^2 - 4 * q^3 + 3 * q^4 - 5 * q^5 - 5 * q^6 + 5 * q^7 + 3 * q^8 + 5 * q^9	\( 5 q - q^{2} - 4 q^{3} + 3 q^{4} - 5 q^{5} - 5 q^{6} + 5 q^{7} + 3 q^{8} + 5 q^{9} + q^{10} - 7 q^{11} - 10 q^{12} - 5 q^{13} - q^{14} + 4 q^{15} - 9 q^{16} - 7 q^{17} + 11 q^{18} - 10 q^{19} - 3 q^{20} - 4 q^{21} + 4 q^{22} + 5 q^{23} - 4 q^{24} + 5 q^{25} - 2 q^{26} - 7 q^{27} + 3 q^{28} - 14 q^{29} + 5 q^{30} - 10 q^{31} + 4 q^{33} - 10 q^{34} - 5 q^{35} + 20 q^{36} - 3 q^{37} - 15 q^{38} - 13 q^{39} - 3 q^{40} - 15 q^{41} - 5 q^{42} + 8 q^{43} - 27 q^{44} - 5 q^{45} - q^{46} - 10 q^{47} - 2 q^{48} + 5 q^{49} - q^{50} - 18 q^{51} + 18 q^{52} - 9 q^{53} - 39 q^{54} + 7 q^{55} + 3 q^{56} + 23 q^{57} - 31 q^{58} - 19 q^{59} + 10 q^{60} - 21 q^{61} - 10 q^{62} + 5 q^{63} - 7 q^{64} + 5 q^{65} + 25 q^{66} + 5 q^{67} - 15 q^{68} - 4 q^{69} + q^{70} - 16 q^{71} + 26 q^{72} + q^{73} - 16 q^{74} - 4 q^{75} - 7 q^{77} + 28 q^{78} + 20 q^{79} + 9 q^{80} - 3 q^{81} + 11 q^{82} - 31 q^{83} - 10 q^{84} + 7 q^{85} + 10 q^{86} + 38 q^{87} - 3 q^{88} - 21 q^{89} - 11 q^{90} - 5 q^{91} + 3 q^{92} + 23 q^{93} + 28 q^{94} + 10 q^{95} + 24 q^{96} + 19 q^{97} - q^{98} - 26 q^{99}+O(q^{100}) \) 5 * q - q^2 - 4 * q^3 + 3 * q^4 - 5 * q^5 - 5 * q^6 + 5 * q^7 + 3 * q^8 + 5 * q^9 + q^10 - 7 * q^11 - 10 * q^12 - 5 * q^13 - q^14 + 4 * q^15 - 9 * q^16 - 7 * q^17 + 11 * q^18 - 10 * q^19 - 3 * q^20 - 4 * q^21 + 4 * q^22 + 5 * q^23 - 4 * q^24 + 5 * q^25 - 2 * q^26 - 7 * q^27 + 3 * q^28 - 14 * q^29 + 5 * q^30 - 10 * q^31 + 4 * q^33 - 10 * q^34 - 5 * q^35 + 20 * q^36 - 3 * q^37 - 15 * q^38 - 13 * q^39 - 3 * q^40 - 15 * q^41 - 5 * q^42 + 8 * q^43 - 27 * q^44 - 5 * q^45 - q^46 - 10 * q^47 - 2 * q^48 + 5 * q^49 - q^50 - 18 * q^51 + 18 * q^52 - 9 * q^53 - 39 * q^54 + 7 * q^55 + 3 * q^56 + 23 * q^57 - 31 * q^58 - 19 * q^59 + 10 * q^60 - 21 * q^61 - 10 * q^62 + 5 * q^63 - 7 * q^64 + 5 * q^65 + 25 * q^66 + 5 * q^67 - 15 * q^68 - 4 * q^69 + q^70 - 16 * q^71 + 26 * q^72 + q^73 - 16 * q^74 - 4 * q^75 - 7 * q^77 + 28 * q^78 + 20 * q^79 + 9 * q^80 - 3 * q^81 + 11 * q^82 - 31 * q^83 - 10 * q^84 + 7 * q^85 + 10 * q^86 + 38 * q^87 - 3 * q^88 - 21 * q^89 - 11 * q^90 - 5 * q^91 + 3 * q^92 + 23 * q^93 + 28 * q^94 + 10 * q^95 + 24 * q^96 + 19 * q^97 - q^98 - 26 * q^99

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