LMFDB - Embedded newform 1805.2.a.q.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1805,2,Mod(1,1805)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1805, 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("1805.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1805 = 5 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1805.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:	$14.4129975648$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.5822000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 8x^{4} + 5x^{3} + 14x^{2} + x - 1 $ x^6 - x^5 - 8x^4 + 5x^3 + 14*x^2 + x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-2.31247$ of defining polynomial
Character	$\chi$	$=$	1805.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.69444 q^{2} +0.918335 q^{3} +0.871115 q^{4} -1.00000 q^{5} -1.55606 q^{6} +3.12687 q^{7} +1.91282 q^{8} -2.15666 q^{9} +O(q^{10})$	\(q-1.69444 q^{2} +0.918335 q^{3} +0.871115 q^{4} -1.00000 q^{5} -1.55606 q^{6} +3.12687 q^{7} +1.91282 q^{8} -2.15666 q^{9} +1.69444 q^{10} +5.68692 q^{11} +0.799975 q^{12} +5.35443 q^{13} -5.29829 q^{14} -0.918335 q^{15} -4.98339 q^{16} +7.27477 q^{17} +3.65433 q^{18} -0.871115 q^{20} +2.87152 q^{21} -9.63612 q^{22} +1.74790 q^{23} +1.75661 q^{24} +1.00000 q^{25} -9.07274 q^{26} -4.73554 q^{27} +2.72387 q^{28} -7.78826 q^{29} +1.55606 q^{30} +2.11836 q^{31} +4.61839 q^{32} +5.22249 q^{33} -12.3266 q^{34} -3.12687 q^{35} -1.87870 q^{36} -4.72949 q^{37} +4.91716 q^{39} -1.91282 q^{40} -0.302311 q^{41} -4.86560 q^{42} +3.54915 q^{43} +4.95396 q^{44} +2.15666 q^{45} -2.96170 q^{46} -0.288923 q^{47} -4.57642 q^{48} +2.77734 q^{49} -1.69444 q^{50} +6.68068 q^{51} +4.66432 q^{52} -9.14589 q^{53} +8.02407 q^{54} -5.68692 q^{55} +5.98116 q^{56} +13.1967 q^{58} +0.589838 q^{59} -0.799975 q^{60} +7.80981 q^{61} -3.58943 q^{62} -6.74361 q^{63} +2.14121 q^{64} -5.35443 q^{65} -8.84918 q^{66} +11.7935 q^{67} +6.33717 q^{68} +1.60515 q^{69} +5.29829 q^{70} -11.7066 q^{71} -4.12531 q^{72} -1.03058 q^{73} +8.01381 q^{74} +0.918335 q^{75} +17.7823 q^{77} -8.33181 q^{78} -5.70778 q^{79} +4.98339 q^{80} +2.12117 q^{81} +0.512247 q^{82} -3.71429 q^{83} +2.50142 q^{84} -7.27477 q^{85} -6.01381 q^{86} -7.15223 q^{87} +10.8781 q^{88} +5.54914 q^{89} -3.65433 q^{90} +16.7426 q^{91} +1.52262 q^{92} +1.94536 q^{93} +0.489562 q^{94} +4.24123 q^{96} +6.81742 q^{97} -4.70603 q^{98} -12.2648 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{2} - 4 q^{3} + 8 q^{4} - 6 q^{5} + 8 q^{6} + 7 q^{7} + 10 q^{9}+O(q^{10}) $ 6 * q - 2 * q^2 - 4 * q^3 + 8 * q^4 - 6 * q^5 + 8 * q^6 + 7 * q^7 + 10 * q^9	\( 6 q - 2 q^{2} - 4 q^{3} + 8 q^{4} - 6 q^{5} + 8 q^{6} + 7 q^{7} + 10 q^{9} + 2 q^{10} + 15 q^{11} + 20 q^{12} - 6 q^{13} - 20 q^{14} + 4 q^{15} + 20 q^{16} + 5 q^{17} + 8 q^{18} - 8 q^{20} - 7 q^{21} - 14 q^{22} + 18 q^{24} + 6 q^{25} - 22 q^{26} - 28 q^{27} + 10 q^{28} + 20 q^{29} - 8 q^{30} - 12 q^{31} + 8 q^{32} - q^{33} - 7 q^{35} - 14 q^{36} - 20 q^{37} + 16 q^{39} - 8 q^{41} - 30 q^{42} + 27 q^{43} + 46 q^{44} - 10 q^{45} - 16 q^{46} - 8 q^{47} + 24 q^{48} + 11 q^{49} - 2 q^{50} + 11 q^{51} - 4 q^{52} - 19 q^{53} + 30 q^{54} - 15 q^{55} - 62 q^{56} + 20 q^{58} + 41 q^{59} - 20 q^{60} + 6 q^{61} - 30 q^{62} - 18 q^{63} + 48 q^{64} + 6 q^{65} + 46 q^{66} + 15 q^{67} - 14 q^{68} + 10 q^{69} + 20 q^{70} - 2 q^{71} + 68 q^{72} + 8 q^{73} + 2 q^{74} - 4 q^{75} + 21 q^{77} - 46 q^{78} - 18 q^{79} - 20 q^{80} + 50 q^{81} - 18 q^{82} - 10 q^{83} - 4 q^{84} - 5 q^{85} + 10 q^{86} - 14 q^{87} + 52 q^{88} - 17 q^{89} - 8 q^{90} + 23 q^{91} + 28 q^{92} + 10 q^{93} + 28 q^{94} + 26 q^{96} + 4 q^{97} - 50 q^{98} + 58 q^{99}+O(q^{100}) \) 6 * q - 2 * q^2 - 4 * q^3 + 8 * q^4 - 6 * q^5 + 8 * q^6 + 7 * q^7 + 10 * q^9 + 2 * q^10 + 15 * q^11 + 20 * q^12 - 6 * q^13 - 20 * q^14 + 4 * q^15 + 20 * q^16 + 5 * q^17 + 8 * q^18 - 8 * q^20 - 7 * q^21 - 14 * q^22 + 18 * q^24 + 6 * q^25 - 22 * q^26 - 28 * q^27 + 10 * q^28 + 20 * q^29 - 8 * q^30 - 12 * q^31 + 8 * q^32 - q^33 - 7 * q^35 - 14 * q^36 - 20 * q^37 + 16 * q^39 - 8 * q^41 - 30 * q^42 + 27 * q^43 + 46 * q^44 - 10 * q^45 - 16 * q^46 - 8 * q^47 + 24 * q^48 + 11 * q^49 - 2 * q^50 + 11 * q^51 - 4 * q^52 - 19 * q^53 + 30 * q^54 - 15 * q^55 - 62 * q^56 + 20 * q^58 + 41 * q^59 - 20 * q^60 + 6 * q^61 - 30 * q^62 - 18 * q^63 + 48 * q^64 + 6 * q^65 + 46 * q^66 + 15 * q^67 - 14 * q^68 + 10 * q^69 + 20 * q^70 - 2 * q^71 + 68 * q^72 + 8 * q^73 + 2 * q^74 - 4 * q^75 + 21 * q^77 - 46 * q^78 - 18 * q^79 - 20 * q^80 + 50 * q^81 - 18 * q^82 - 10 * q^83 - 4 * q^84 - 5 * q^85 + 10 * q^86 - 14 * q^87 + 52 * q^88 - 17 * q^89 - 8 * q^90 + 23 * q^91 + 28 * q^92 + 10 * q^93 + 28 * q^94 + 26 * q^96 + 4 * q^97 - 50 * q^98 + 58 * 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 $

$2$	−1.69444	−1.19815	−0.599074	−	0.800694i	$-0.704464\pi$
$2$	−1.69444	−1.19815	−0.599074	+	0.800694i	$0.704464\pi$
$3$	0.918335	0.530201	0.265100	−	0.964221i	$-0.414595\pi$
$3$	0.918335	0.530201	0.265100	+	0.964221i	$0.414595\pi$
$4$	0.871115	0.435558
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.55606	−0.635259
$7$	3.12687	1.18185	0.590924	−	0.806727i	$-0.298763\pi$
$7$	3.12687	1.18185	0.590924	+	0.806727i	$0.298763\pi$
$8$	1.91282	0.676285
$9$	−2.15666	−0.718887
$10$	1.69444	0.535828
$11$	5.68692	1.71467	0.857335	−	0.514759i	$-0.172119\pi$
$11$	5.68692	1.71467	0.857335	+	0.514759i	$0.172119\pi$
$12$	0.799975	0.230933
$13$	5.35443	1.48505	0.742525	−	0.669818i	$-0.233628\pi$
$13$	5.35443	1.48505	0.742525	+	0.669818i	$0.233628\pi$
$14$	−5.29829	−1.41603
$15$	−0.918335	−0.237113
$16$	−4.98339	−1.24585
$17$	7.27477	1.76439	0.882196	−	0.470883i	$-0.156065\pi$
$17$	7.27477	1.76439	0.882196	+	0.470883i	$0.156065\pi$
$18$	3.65433	0.861333
$19$	0	0
$19$	0	0
$20$	−0.871115	−0.194787
$21$	2.87152	0.626616
$22$	−9.63612	−2.05443
$23$	1.74790	0.364461	0.182231	−	0.983256i	$-0.441668\pi$
$23$	1.74790	0.364461	0.182231	+	0.983256i	$0.441668\pi$
$24$	1.75661	0.358567
$25$	1.00000	0.200000
$26$	−9.07274	−1.77931
$27$	−4.73554	−0.911355
$28$	2.72387	0.514763
$29$	−7.78826	−1.44624	−0.723122	−	0.690720i	$-0.757294\pi$
$29$	−7.78826	−1.44624	−0.723122	+	0.690720i	$0.757294\pi$
$30$	1.55606	0.284096
$31$	2.11836	0.380469	0.190234	−	0.981739i	$-0.439075\pi$
$31$	2.11836	0.380469	0.190234	+	0.981739i	$0.439075\pi$
$32$	4.61839	0.816424
$33$	5.22249	0.909119
$34$	−12.3266	−2.11400
$35$	−3.12687	−0.528538
$36$	−1.87870	−0.313117
$37$	−4.72949	−0.777523	−0.388761	−	0.921338i	$-0.627097\pi$
$37$	−4.72949	−0.777523	−0.388761	+	0.921338i	$0.627097\pi$
$38$	0	0
$39$	4.91716	0.787375
$40$	−1.91282	−0.302444
$41$	−0.302311	−0.0472130	−0.0236065	−	0.999721i	$-0.507515\pi$
$41$	−0.302311	−0.0472130	−0.0236065	+	0.999721i	$0.507515\pi$
$42$	−4.86560	−0.750779
$43$	3.54915	0.541241	0.270620	−	0.962686i	$-0.412771\pi$
$43$	3.54915	0.541241	0.270620	+	0.962686i	$0.412771\pi$
$44$	4.95396	0.746837
$45$	2.15666	0.321496
$46$	−2.96170	−0.436679
$47$	−0.288923	−0.0421438	−0.0210719	−	0.999778i	$-0.506708\pi$
$47$	−0.288923	−0.0421438	−0.0210719	+	0.999778i	$0.506708\pi$
$48$	−4.57642	−0.660549
$49$	2.77734	0.396763
$50$	−1.69444	−0.239630
$51$	6.68068	0.935482
$52$	4.66432	0.646825
$53$	−9.14589	−1.25628	−0.628142	−	0.778099i	$-0.716184\pi$
$53$	−9.14589	−1.25628	−0.628142	+	0.778099i	$0.716184\pi$
$54$	8.02407	1.09194
$55$	−5.68692	−0.766823
$56$	5.98116	0.799266
$57$	0	0
$58$	13.1967	1.73281
$59$	0.589838	0.0767904	0.0383952	−	0.999263i	$-0.487775\pi$
$59$	0.589838	0.0767904	0.0383952	+	0.999263i	$0.487775\pi$
$60$	−0.799975	−0.103276
$61$	7.80981	0.999944	0.499972	−	0.866042i	$-0.333344\pi$
$61$	7.80981	0.999944	0.499972	+	0.866042i	$0.333344\pi$
$62$	−3.58943	−0.455857
$63$	−6.74361	−0.849615
$64$	2.14121	0.267651
$65$	−5.35443	−0.664135
$66$	−8.84918	−1.08926
$67$	11.7935	1.44081	0.720404	−	0.693555i	$-0.243956\pi$
$67$	11.7935	1.44081	0.720404	+	0.693555i	$0.243956\pi$
$68$	6.33717	0.768494
$69$	1.60515	0.193238
$70$	5.29829	0.633267
$71$	−11.7066	−1.38932	−0.694661	−	0.719337i	$-0.744446\pi$
$71$	−11.7066	−1.38932	−0.694661	+	0.719337i	$0.744446\pi$
$72$	−4.12531	−0.486173
$73$	−1.03058	−0.120620	−0.0603101	−	0.998180i	$-0.519209\pi$
$73$	−1.03058	−0.120620	−0.0603101	+	0.998180i	$0.519209\pi$
$74$	8.01381	0.931587
$75$	0.918335	0.106040
$76$	0	0
$77$	17.7823	2.02648
$78$	−8.33181	−0.943392
$79$	−5.70778	−0.642176	−0.321088	−	0.947049i	$-0.604049\pi$
$79$	−5.70778	−0.642176	−0.321088	+	0.947049i	$0.604049\pi$
$80$	4.98339	0.557160
$81$	2.12117	0.235686
$82$	0.512247	0.0565682
$83$	−3.71429	−0.407696	−0.203848	−	0.979003i	$-0.565345\pi$
$83$	−3.71429	−0.407696	−0.203848	+	0.979003i	$0.565345\pi$
$84$	2.50142	0.272928
$85$	−7.27477	−0.789060
$86$	−6.01381	−0.648486
$87$	−7.15223	−0.766800
$88$	10.8781	1.15961
$89$	5.54914	0.588208	0.294104	−	0.955773i	$-0.404979\pi$
$89$	5.54914	0.588208	0.294104	+	0.955773i	$0.404979\pi$
$90$	−3.65433	−0.385200
$91$	16.7426	1.75510
$92$	1.52262	0.158744
$93$	1.94536	0.201725
$94$	0.489562	0.0504945
$95$	0	0
$96$	4.24123	0.432868
$97$	6.81742	0.692204	0.346102	−	0.938197i	$-0.387505\pi$
$97$	6.81742	0.692204	0.346102	+	0.938197i	$0.387505\pi$
$98$	−4.70603	−0.475381
$99$	−12.2648	−1.23265
$100$	0.871115	0.0871115
$101$	16.0519	1.59722	0.798610	−	0.601849i	$-0.205569\pi$
$101$	16.0519	1.59722	0.798610	+	0.601849i	$0.205569\pi$
$102$	−11.3200	−1.12085
$103$	−0.228184	−0.0224836	−0.0112418	−	0.999937i	$-0.503578\pi$
$103$	−0.228184	−0.0224836	−0.0112418	+	0.999937i	$0.503578\pi$
$104$	10.2421	1.00432
$105$	−2.87152	−0.280231
$106$	15.4971	1.50521
$107$	−5.66185	−0.547351	−0.273676	−	0.961822i	$-0.588240\pi$
$107$	−5.66185	−0.547351	−0.273676	+	0.961822i	$0.588240\pi$
$108$	−4.12520	−0.396948
$109$	5.64821	0.541000	0.270500	−	0.962720i	$-0.412811\pi$
$109$	5.64821	0.541000	0.270500	+	0.962720i	$0.412811\pi$
$110$	9.63612	0.918768
$111$	−4.34325	−0.412243
$112$	−15.5824	−1.47240
$113$	−4.26203	−0.400938	−0.200469	−	0.979700i	$-0.564247\pi$
$113$	−4.26203	−0.400938	−0.200469	+	0.979700i	$0.564247\pi$
$114$	0	0
$115$	−1.74790	−0.162992
$116$	−6.78447	−0.629923
$117$	−11.5477	−1.06758
$118$	−0.999443	−0.0920062
$119$	22.7473	2.08524
$120$	−1.75661	−0.160356
$121$	21.3410	1.94009
$122$	−13.2332	−1.19808
$123$	−0.277623	−0.0250324
$124$	1.84534	0.165716
$125$	−1.00000	−0.0894427
$126$	11.4266	1.01796
$127$	0.302950	0.0268824	0.0134412	−	0.999910i	$-0.495721\pi$
$127$	0.302950	0.0268824	0.0134412	+	0.999910i	$0.495721\pi$
$128$	−12.8649	−1.13711
$129$	3.25931	0.286966
$130$	9.07274	0.795732
$131$	−15.2113	−1.32902	−0.664509	−	0.747280i	$-0.731359\pi$
$131$	−15.2113	−1.32902	−0.664509	+	0.747280i	$0.731359\pi$
$132$	4.54939	0.395974
$133$	0	0
$134$	−19.9834	−1.72630
$135$	4.73554	0.407570
$136$	13.9154	1.19323
$137$	−16.8460	−1.43925	−0.719626	−	0.694362i	$-0.755687\pi$
$137$	−16.8460	−1.43925	−0.719626	+	0.694362i	$0.755687\pi$
$138$	−2.71983	−0.231527
$139$	1.04207	0.0883876	0.0441938	−	0.999023i	$-0.485928\pi$
$139$	1.04207	0.0883876	0.0441938	+	0.999023i	$0.485928\pi$
$140$	−2.72387	−0.230209
$141$	−0.265328	−0.0223447
$142$	19.8362	1.66461
$143$	30.4502	2.54637
$144$	10.7475	0.895623
$145$	7.78826	0.646780
$146$	1.74625	0.144521
$147$	2.55053	0.210364
$148$	−4.11993	−0.338656
$149$	−14.9135	−1.22177	−0.610883	−	0.791721i	$-0.709185\pi$
$149$	−14.9135	−1.22177	−0.610883	+	0.791721i	$0.709185\pi$
$150$	−1.55606	−0.127052
$151$	7.78392	0.633446	0.316723	−	0.948518i	$-0.397417\pi$
$151$	7.78392	0.633446	0.316723	+	0.948518i	$0.397417\pi$
$152$	0	0
$153$	−15.6892	−1.26840
$154$	−30.1309	−2.42802
$155$	−2.11836	−0.170151
$156$	4.28341	0.342947
$157$	5.77297	0.460733	0.230367	−	0.973104i	$-0.426007\pi$
$157$	5.77297	0.460733	0.230367	+	0.973104i	$0.426007\pi$
$158$	9.67148	0.769422
$159$	−8.39899	−0.666083
$160$	−4.61839	−0.365116
$161$	5.46545	0.430738
$162$	−3.59419	−0.282386
$163$	3.08268	0.241454	0.120727	−	0.992686i	$-0.461477\pi$
$163$	3.08268	0.241454	0.120727	+	0.992686i	$0.461477\pi$
$164$	−0.263348	−0.0205640
$165$	−5.22249	−0.406570
$166$	6.29363	0.488480
$167$	−9.69093	−0.749907	−0.374953	−	0.927044i	$-0.622341\pi$
$167$	−9.69093	−0.749907	−0.374953	+	0.927044i	$0.622341\pi$
$168$	5.49271	0.423771
$169$	15.6699	1.20538
$170$	12.3266	0.945410
$171$	0	0
$172$	3.09172	0.235742
$173$	−5.42562	−0.412503	−0.206251	−	0.978499i	$-0.566126\pi$
$173$	−5.42562	−0.412503	−0.206251	+	0.978499i	$0.566126\pi$
$174$	12.1190	0.918739
$175$	3.12687	0.236369
$176$	−28.3401	−2.13622
$177$	0.541669	0.0407143
$178$	−9.40267	−0.704760
$179$	4.14592	0.309880	0.154940	−	0.987924i	$-0.450482\pi$
$179$	4.14592	0.309880	0.154940	+	0.987924i	$0.450482\pi$
$180$	1.87870	0.140030
$181$	6.90928	0.513563	0.256781	−	0.966470i	$-0.417338\pi$
$181$	6.90928	0.513563	0.256781	+	0.966470i	$0.417338\pi$
$182$	−28.3693	−2.10287
$183$	7.17202	0.530171
$184$	3.34342	0.246480
$185$	4.72949	0.347719
$186$	−3.29629	−0.241696
$187$	41.3710	3.02535
$188$	−0.251685	−0.0183560
$189$	−14.8074	−1.07708
$190$	0	0
$191$	1.50338	0.108781	0.0543903	−	0.998520i	$-0.482678\pi$
$191$	1.50338	0.108781	0.0543903	+	0.998520i	$0.482678\pi$
$192$	1.96635	0.141909
$193$	10.6727	0.768239	0.384119	−	0.923283i	$-0.374505\pi$
$193$	10.6727	0.768239	0.384119	+	0.923283i	$0.374505\pi$
$194$	−11.5517	−0.829363
$195$	−4.91716	−0.352125
$196$	2.41939	0.172813
$197$	1.12058	0.0798379	0.0399190	−	0.999203i	$-0.487290\pi$
$197$	1.12058	0.0798379	0.0399190	+	0.999203i	$0.487290\pi$
$198$	20.7818	1.47690
$199$	−19.3704	−1.37313	−0.686564	−	0.727069i	$-0.740882\pi$
$199$	−19.3704	−1.37313	−0.686564	+	0.727069i	$0.740882\pi$
$200$	1.91282	0.135257
$201$	10.8304	0.763918
$202$	−27.1989	−1.91370
$203$	−24.3529	−1.70924
$204$	5.81964	0.407456
$205$	0.302311	0.0211143
$206$	0.386643	0.0269387
$207$	−3.76962	−0.262007
$208$	−26.6832	−1.85015
$209$	0	0
$210$	4.86560	0.335759
$211$	14.3318	0.986644	0.493322	−	0.869847i	$-0.335782\pi$
$211$	14.3318	0.986644	0.493322	+	0.869847i	$0.335782\pi$
$212$	−7.96712	−0.547184
$213$	−10.7506	−0.736620
$214$	9.59364	0.655808
$215$	−3.54915	−0.242050
$216$	−9.05825	−0.616336
$217$	6.62384	0.449656
$218$	−9.57054	−0.648198
$219$	−0.946417	−0.0639529
$220$	−4.95396	−0.333996
$221$	38.9522	2.62021
$222$	7.35936	0.493928
$223$	9.87573	0.661328	0.330664	−	0.943749i	$-0.392727\pi$
$223$	9.87573	0.661328	0.330664	+	0.943749i	$0.392727\pi$
$224$	14.4411	0.964888
$225$	−2.15666	−0.143777
$226$	7.22174	0.480383
$227$	−0.345546	−0.0229347	−0.0114673	−	0.999934i	$-0.503650\pi$
$227$	−0.345546	−0.0229347	−0.0114673	+	0.999934i	$0.503650\pi$
$228$	0	0
$229$	6.12864	0.404992	0.202496	−	0.979283i	$-0.435095\pi$
$229$	6.12864	0.404992	0.202496	+	0.979283i	$0.435095\pi$
$230$	2.96170	0.195289
$231$	16.3301	1.07444
$232$	−14.8976	−0.978073
$233$	16.5333	1.08313	0.541566	−	0.840658i	$-0.317832\pi$
$233$	16.5333	1.08313	0.541566	+	0.840658i	$0.317832\pi$
$234$	19.5668	1.27912
$235$	0.288923	0.0188473
$236$	0.513817	0.0334466
$237$	−5.24166	−0.340482
$238$	−38.5439	−2.49843
$239$	−24.1926	−1.56489	−0.782444	−	0.622721i	$-0.786027\pi$
$239$	−24.1926	−1.56489	−0.782444	+	0.622721i	$0.786027\pi$
$240$	4.57642	0.295407
$241$	−14.3057	−0.921510	−0.460755	−	0.887527i	$-0.652421\pi$
$241$	−14.3057	−0.921510	−0.460755	+	0.887527i	$0.652421\pi$
$242$	−36.1610	−2.32452
$243$	16.1546	1.03632
$244$	6.80324	0.435533
$245$	−2.77734	−0.177438
$246$	0.470414	0.0299925
$247$	0	0
$248$	4.05205	0.257305
$249$	−3.41096	−0.216161
$250$	1.69444	0.107166
$251$	26.0310	1.64306	0.821530	−	0.570165i	$-0.193121\pi$
$251$	26.0310	1.64306	0.821530	+	0.570165i	$0.193121\pi$
$252$	−5.87446	−0.370056
$253$	9.94013	0.624931
$254$	−0.513329	−0.0322091
$255$	−6.68068	−0.418360
$256$	17.5164	1.09477
$257$	22.3381	1.39342	0.696708	−	0.717355i	$-0.254647\pi$
$257$	22.3381	1.39342	0.696708	+	0.717355i	$0.254647\pi$
$258$	−5.52269	−0.343828
$259$	−14.7885	−0.918913
$260$	−4.66432	−0.289269
$261$	16.7966	1.03969
$262$	25.7746	1.59236
$263$	−20.5510	−1.26723	−0.633614	−	0.773649i	$-0.718429\pi$
$263$	−20.5510	−1.26723	−0.633614	+	0.773649i	$0.718429\pi$
$264$	9.98970	0.614824
$265$	9.14589	0.561827
$266$	0	0
$267$	5.09597	0.311868
$268$	10.2735	0.627555
$269$	30.8947	1.88368	0.941841	−	0.336059i	$-0.109094\pi$
$269$	30.8947	1.88368	0.941841	+	0.336059i	$0.109094\pi$
$270$	−8.02407	−0.488330
$271$	17.1363	1.04095	0.520477	−	0.853876i	$-0.325754\pi$
$271$	17.1363	1.04095	0.520477	+	0.853876i	$0.325754\pi$
$272$	−36.2530	−2.19816
$273$	15.3753	0.930557
$274$	28.5445	1.72444
$275$	5.68692	0.342934
$276$	1.39827	0.0841662
$277$	−16.5131	−0.992174	−0.496087	−	0.868273i	$-0.665230\pi$
$277$	−16.5131	−0.992174	−0.496087	+	0.868273i	$0.665230\pi$
$278$	−1.76573	−0.105901
$279$	−4.56858	−0.273514
$280$	−5.98116	−0.357443
$281$	2.46908	0.147293	0.0736466	−	0.997284i	$-0.476536\pi$
$281$	2.46908	0.147293	0.0736466	+	0.997284i	$0.476536\pi$
$282$	0.449582	0.0267722
$283$	−5.79496	−0.344475	−0.172237	−	0.985055i	$-0.555100\pi$
$283$	−5.79496	−0.344475	−0.172237	+	0.985055i	$0.555100\pi$
$284$	−10.1978	−0.605130
$285$	0	0
$286$	−51.5959	−3.05093
$287$	−0.945288	−0.0557986
$288$	−9.96030	−0.586916
$289$	35.9223	2.11308
$290$	−13.1967	−0.774938
$291$	6.26067	0.367007
$292$	−0.897753	−0.0525370
$293$	9.77443	0.571028	0.285514	−	0.958374i	$-0.407836\pi$
$293$	9.77443	0.571028	0.285514	+	0.958374i	$0.407836\pi$
$294$	−4.32171	−0.252047
$295$	−0.589838	−0.0343417
$296$	−9.04667	−0.525827
$297$	−26.9306	−1.56267
$298$	25.2701	1.46386
$299$	9.35898	0.541244
$300$	0.799975	0.0461866
$301$	11.0978	0.639664
$302$	−13.1894	−0.758962
$303$	14.7410	0.846847
$304$	0	0
$305$	−7.80981	−0.447188
$306$	26.5844	1.51973
$307$	−7.51685	−0.429009	−0.214505	−	0.976723i	$-0.568814\pi$
$307$	−7.51685	−0.429009	−0.214505	+	0.976723i	$0.568814\pi$
$308$	15.4904	0.882648
$309$	−0.209549	−0.0119208
$310$	3.58943	0.203866
$311$	−7.37315	−0.418093	−0.209047	−	0.977906i	$-0.567036\pi$
$311$	−7.37315	−0.418093	−0.209047	+	0.977906i	$0.567036\pi$
$312$	9.40565	0.532490
$313$	11.2358	0.635085	0.317543	−	0.948244i	$-0.397142\pi$
$313$	11.2358	0.635085	0.317543	+	0.948244i	$0.397142\pi$
$314$	−9.78194	−0.552027
$315$	6.74361	0.379959
$316$	−4.97214	−0.279705
$317$	10.1851	0.572055	0.286027	−	0.958221i	$-0.407665\pi$
$317$	10.1851	0.572055	0.286027	+	0.958221i	$0.407665\pi$
$318$	14.2315	0.798066
$319$	−44.2912	−2.47983
$320$	−2.14121	−0.119697
$321$	−5.19947	−0.290206
$322$	−9.26086	−0.516087
$323$	0	0
$324$	1.84779	0.102655
$325$	5.35443	0.297010
$326$	−5.22341	−0.289298
$327$	5.18695	0.286839
$328$	−0.578267	−0.0319295
$329$	−0.903426	−0.0498075
$330$	8.84918	0.487131
$331$	−33.2603	−1.82815	−0.914075	−	0.405545i	$-0.867082\pi$
$331$	−33.2603	−1.82815	−0.914075	+	0.405545i	$0.867082\pi$
$332$	−3.23557	−0.177575
$333$	10.1999	0.558951
$334$	16.4207	0.898499
$335$	−11.7935	−0.644349
$336$	−14.3099	−0.780668
$337$	−6.28046	−0.342119	−0.171059	−	0.985261i	$-0.554719\pi$
$337$	−6.28046	−0.342119	−0.171059	+	0.985261i	$0.554719\pi$
$338$	−26.5516	−1.44422
$339$	−3.91397	−0.212578
$340$	−6.33717	−0.343681
$341$	12.0469	0.652378
$342$	0	0
$343$	−13.2037	−0.712934
$344$	6.78890	0.366033
$345$	−1.60515	−0.0864185
$346$	9.19338	0.494239
$347$	−19.3237	−1.03735	−0.518674	−	0.854972i	$-0.673574\pi$
$347$	−19.3237	−1.03735	−0.518674	+	0.854972i	$0.673574\pi$
$348$	−6.23042	−0.333985
$349$	7.95037	0.425573	0.212787	−	0.977099i	$-0.431746\pi$
$349$	7.95037	0.425573	0.212787	+	0.977099i	$0.431746\pi$
$350$	−5.29829	−0.283206
$351$	−25.3561	−1.35341
$352$	26.2644	1.39990
$353$	−14.7026	−0.782540	−0.391270	−	0.920276i	$-0.627964\pi$
$353$	−14.7026	−0.782540	−0.391270	+	0.920276i	$0.627964\pi$
$354$	−0.917823	−0.0487818
$355$	11.7066	0.621324
$356$	4.83394	0.256198
$357$	20.8896	1.10560
$358$	−7.02499	−0.371282
$359$	13.7186	0.724038	0.362019	−	0.932171i	$-0.382088\pi$
$359$	13.7186	0.724038	0.362019	+	0.932171i	$0.382088\pi$
$360$	4.12531	0.217423
$361$	0	0
$362$	−11.7073	−0.615324
$363$	19.5982	1.02864
$364$	14.5848	0.764449
$365$	1.03058	0.0539430
$366$	−12.1525	−0.635223
$367$	−29.9263	−1.56214	−0.781071	−	0.624442i	$-0.785326\pi$
$367$	−29.9263	−1.56214	−0.781071	+	0.624442i	$0.785326\pi$
$368$	−8.71044	−0.454063
$369$	0.651982	0.0339408
$370$	−8.01381	−0.416618
$371$	−28.5980	−1.48474
$372$	1.69464	0.0878628
$373$	−30.9973	−1.60498	−0.802491	−	0.596665i	$-0.796492\pi$
$373$	−30.9973	−1.60498	−0.802491	+	0.596665i	$0.796492\pi$
$374$	−70.1006	−3.62481
$375$	−0.918335	−0.0474226
$376$	−0.552659	−0.0285012
$377$	−41.7017	−2.14775
$378$	25.0903	1.29050
$379$	−18.8321	−0.967339	−0.483669	−	0.875251i	$-0.660696\pi$
$379$	−18.8321	−0.967339	−0.483669	+	0.875251i	$0.660696\pi$
$380$	0	0
$381$	0.278209	0.0142531
$382$	−2.54738	−0.130335
$383$	8.63306	0.441129	0.220564	−	0.975372i	$-0.429210\pi$
$383$	8.63306	0.441129	0.220564	+	0.975372i	$0.429210\pi$
$384$	−11.8143	−0.602896
$385$	−17.7823	−0.906268
$386$	−18.0842	−0.920463
$387$	−7.65432	−0.389091
$388$	5.93876	0.301495
$389$	−3.75614	−0.190444	−0.0952220	−	0.995456i	$-0.530356\pi$
$389$	−3.75614	−0.190444	−0.0952220	+	0.995456i	$0.530356\pi$
$390$	8.33181	0.421898
$391$	12.7155	0.643053
$392$	5.31257	0.268325
$393$	−13.9691	−0.704646
$394$	−1.89875	−0.0956576
$395$	5.70778	0.287190
$396$	−10.6840	−0.536892
$397$	−8.02713	−0.402870	−0.201435	−	0.979502i	$-0.564561\pi$
$397$	−8.02713	−0.402870	−0.201435	+	0.979502i	$0.564561\pi$
$398$	32.8218	1.64521
$399$	0	0
$400$	−4.98339	−0.249169
$401$	−30.1897	−1.50760	−0.753800	−	0.657104i	$-0.771781\pi$
$401$	−30.1897	−1.50760	−0.753800	+	0.657104i	$0.771781\pi$
$402$	−18.3514	−0.915286
$403$	11.3426	0.565015
$404$	13.9830	0.695681
$405$	−2.12117	−0.105402
$406$	41.2645	2.04792
$407$	−26.8962	−1.33319
$408$	12.7790	0.632652
$409$	0.747844	0.0369785	0.0184893	−	0.999829i	$-0.494114\pi$
$409$	0.747844	0.0369785	0.0184893	+	0.999829i	$0.494114\pi$
$410$	−0.512247	−0.0252981
$411$	−15.4703	−0.763093
$412$	−0.198775	−0.00979292
$413$	1.84435	0.0907545
$414$	6.38738	0.313923
$415$	3.71429	0.182327
$416$	24.7288	1.21243
$417$	0.956973	0.0468632
$418$	0	0
$419$	23.7597	1.16074	0.580368	−	0.814354i	$-0.302909\pi$
$419$	23.7597	1.16074	0.580368	+	0.814354i	$0.302909\pi$
$420$	−2.50142	−0.122057
$421$	−13.4572	−0.655862	−0.327931	−	0.944702i	$-0.606351\pi$
$421$	−13.4572	−0.655862	−0.327931	+	0.944702i	$0.606351\pi$
$422$	−24.2844	−1.18215
$423$	0.623109	0.0302966
$424$	−17.4945	−0.849606
$425$	7.27477	0.352878
$426$	18.2162	0.882579
$427$	24.4203	1.18178
$428$	−4.93212	−0.238403
$429$	27.9635	1.35009
$430$	6.01381	0.290012
$431$	−18.2970	−0.881337	−0.440669	−	0.897670i	$-0.645259\pi$
$431$	−18.2970	−0.881337	−0.440669	+	0.897670i	$0.645259\pi$
$432$	23.5990	1.13541
$433$	30.5829	1.46972	0.734861	−	0.678218i	$-0.237248\pi$
$433$	30.5829	1.46972	0.734861	+	0.678218i	$0.237248\pi$
$434$	−11.2237	−0.538754
$435$	7.15223	0.342923
$436$	4.92024	0.235637
$437$	0	0
$438$	1.60364	0.0766250
$439$	40.0429	1.91115	0.955573	−	0.294756i	$-0.0952383\pi$
$439$	40.0429	1.91115	0.955573	+	0.294756i	$0.0952383\pi$
$440$	−10.8781	−0.518591
$441$	−5.98979	−0.285228
$442$	−66.0021	−3.13940
$443$	22.0122	1.04583	0.522915	−	0.852385i	$-0.324844\pi$
$443$	22.0122	1.04583	0.522915	+	0.852385i	$0.324844\pi$
$444$	−3.78347	−0.179556
$445$	−5.54914	−0.263055
$446$	−16.7338	−0.792369
$447$	−13.6956	−0.647781
$448$	6.69529	0.316323
$449$	−31.5101	−1.48705	−0.743527	−	0.668705i	$-0.766849\pi$
$449$	−31.5101	−1.48705	−0.743527	+	0.668705i	$0.766849\pi$
$450$	3.65433	0.172267
$451$	−1.71922	−0.0809547
$452$	−3.71272	−0.174632
$453$	7.14824	0.335854
$454$	0.585506	0.0274791
$455$	−16.7426	−0.784906
$456$	0	0
$457$	−11.9174	−0.557472	−0.278736	−	0.960368i	$-0.589916\pi$
$457$	−11.9174	−0.557472	−0.278736	+	0.960368i	$0.589916\pi$
$458$	−10.3846	−0.485240
$459$	−34.4500	−1.60799
$460$	−1.52262	−0.0709925
$461$	−0.693591	−0.0323038	−0.0161519	−	0.999870i	$-0.505142\pi$
$461$	−0.693591	−0.0323038	−0.0161519	+	0.999870i	$0.505142\pi$
$462$	−27.6703	−1.28734
$463$	17.5684	0.816474	0.408237	−	0.912876i	$-0.366144\pi$
$463$	17.5684	0.816474	0.408237	+	0.912876i	$0.366144\pi$
$464$	38.8119	1.80180
$465$	−1.94536	−0.0902140
$466$	−28.0146	−1.29775
$467$	−35.5547	−1.64528	−0.822638	−	0.568566i	$-0.807498\pi$
$467$	−35.5547	−1.64528	−0.822638	+	0.568566i	$0.807498\pi$
$468$	−10.0594	−0.464994
$469$	36.8769	1.70282
$470$	−0.489562	−0.0225818
$471$	5.30152	0.244281
$472$	1.12826	0.0519322
$473$	20.1837	0.928049
$474$	8.88166	0.407948
$475$	0	0
$476$	19.8155	0.908243
$477$	19.7246	0.903127
$478$	40.9928	1.87497
$479$	20.6519	0.943610	0.471805	−	0.881703i	$-0.343603\pi$
$479$	20.6519	0.943610	0.471805	+	0.881703i	$0.343603\pi$
$480$	−4.24123	−0.193585
$481$	−25.3237	−1.15466
$482$	24.2401	1.10411
$483$	5.01911	0.228378
$484$	18.5905	0.845022
$485$	−6.81742	−0.309563
$486$	−27.3729	−1.24166
$487$	16.4082	0.743526	0.371763	−	0.928328i	$-0.378753\pi$
$487$	16.4082	0.743526	0.371763	+	0.928328i	$0.378753\pi$
$488$	14.9388	0.676247
$489$	2.83093	0.128019
$490$	4.70603	0.212597
$491$	−14.8115	−0.668433	−0.334217	−	0.942496i	$-0.608472\pi$
$491$	−14.8115	−0.668433	−0.334217	+	0.942496i	$0.608472\pi$
$492$	−0.241841	−0.0109030
$493$	−56.6578	−2.55174
$494$	0	0
$495$	12.2648	0.551260
$496$	−10.5566	−0.474006
$497$	−36.6052	−1.64197
$498$	5.77966	0.258993
$499$	6.52515	0.292106	0.146053	−	0.989277i	$-0.453343\pi$
$499$	6.52515	0.292106	0.146053	+	0.989277i	$0.453343\pi$
$500$	−0.871115	−0.0389575
$501$	−8.89952	−0.397601
$502$	−44.1078	−1.96863
$503$	4.73899	0.211301	0.105651	−	0.994403i	$-0.466308\pi$
$503$	4.73899	0.211301	0.105651	+	0.994403i	$0.466308\pi$
$504$	−12.8993	−0.574582
$505$	−16.0519	−0.714298
$506$	−16.8429	−0.748759
$507$	14.3902	0.639091
$508$	0.263904	0.0117088
$509$	−24.4240	−1.08257	−0.541287	−	0.840838i	$-0.682063\pi$
$509$	−24.4240	−1.08257	−0.541287	+	0.840838i	$0.682063\pi$
$510$	11.3200	0.501257
$511$	−3.22249	−0.142555
$512$	−3.95054	−0.174591
$513$	0	0
$514$	−37.8506	−1.66952
$515$	0.228184	0.0100550
$516$	2.83924	0.124990
$517$	−1.64308	−0.0722626
$518$	25.0582	1.10099
$519$	−4.98254	−0.218709
$520$	−10.2421	−0.449145
$521$	24.8753	1.08981	0.544903	−	0.838499i	$-0.316566\pi$
$521$	24.8753	1.08981	0.544903	+	0.838499i	$0.316566\pi$
$522$	−28.4608	−1.24570
$523$	−38.8691	−1.69963	−0.849813	−	0.527084i	$-0.823285\pi$
$523$	−38.8691	−1.69963	−0.849813	+	0.527084i	$0.823285\pi$
$524$	−13.2508	−0.578864
$525$	2.87152	0.125323
$526$	34.8224	1.51833
$527$	15.4106	0.671295
$528$	−26.0257	−1.13262
$529$	−19.9449	−0.867168
$530$	−15.4971	−0.673152
$531$	−1.27208	−0.0552036
$532$	0	0
$533$	−1.61870	−0.0701138
$534$	−8.63480	−0.373664
$535$	5.66185	0.244783
$536$	22.5589	0.974397
$537$	3.80734	0.164299
$538$	−52.3491	−2.25693
$539$	15.7945	0.680318
$540$	4.12520	0.177520
$541$	−0.866332	−0.0372465	−0.0186233	−	0.999827i	$-0.505928\pi$
$541$	−0.866332	−0.0372465	−0.0186233	+	0.999827i	$0.505928\pi$
$542$	−29.0363	−1.24722
$543$	6.34503	0.272291
$544$	33.5977	1.44049
$545$	−5.64821	−0.241943
$546$	−26.0525	−1.11495
$547$	−35.8930	−1.53467	−0.767337	−	0.641244i	$-0.778419\pi$
$547$	−35.8930	−1.53467	−0.767337	+	0.641244i	$0.778419\pi$
$548$	−14.6748	−0.626877
$549$	−16.8431	−0.718847
$550$	−9.63612	−0.410885
$551$	0	0
$552$	3.07037	0.130684
$553$	−17.8475	−0.758954
$554$	27.9803	1.18877
$555$	4.34325	0.184361
$556$	0.907767	0.0384979
$557$	41.8808	1.77455	0.887273	−	0.461244i	$-0.152597\pi$
$557$	41.8808	1.77455	0.887273	+	0.461244i	$0.152597\pi$
$558$	7.74118	0.327710
$559$	19.0037	0.803770
$560$	15.5824	0.658478
$561$	37.9924	1.60404
$562$	−4.18371	−0.176479
$563$	−7.49458	−0.315859	−0.157929	−	0.987450i	$-0.550482\pi$
$563$	−7.49458	−0.315859	−0.157929	+	0.987450i	$0.550482\pi$
$564$	−0.231131	−0.00973239
$565$	4.26203	0.179305
$566$	9.81919	0.412731
$567$	6.63264	0.278545
$568$	−22.3927	−0.939578
$569$	10.4307	0.437276	0.218638	−	0.975806i	$-0.429839\pi$
$569$	10.4307	0.437276	0.218638	+	0.975806i	$0.429839\pi$
$570$	0	0
$571$	40.2388	1.68394	0.841970	−	0.539524i	$-0.181396\pi$
$571$	40.2388	1.68394	0.841970	+	0.539524i	$0.181396\pi$
$572$	26.5256	1.10909
$573$	1.38060	0.0576755
$574$	1.60173	0.0668550
$575$	1.74790	0.0728923
$576$	−4.61786	−0.192411
$577$	−5.34053	−0.222329	−0.111165	−	0.993802i	$-0.535458\pi$
$577$	−5.34053	−0.222329	−0.111165	+	0.993802i	$0.535458\pi$
$578$	−60.8681	−2.53178
$579$	9.80112	0.407321
$580$	6.78447	0.281710
$581$	−11.6141	−0.481835
$582$	−10.6083	−0.439729
$583$	−52.0119	−2.15411
$584$	−1.97132	−0.0815736
$585$	11.5477	0.477438
$586$	−16.5622	−0.684176
$587$	−9.87644	−0.407644	−0.203822	−	0.979008i	$-0.565336\pi$
$587$	−9.87644	−0.407644	−0.203822	+	0.979008i	$0.565336\pi$
$588$	2.22181	0.0916258
$589$	0	0
$590$	0.999443	0.0411464
$591$	1.02907	0.0423301
$592$	23.5689	0.968675
$593$	−12.5122	−0.513813	−0.256906	−	0.966436i	$-0.582703\pi$
$593$	−12.5122	−0.513813	−0.256906	+	0.966436i	$0.582703\pi$
$594$	45.6322	1.87231
$595$	−22.7473	−0.932548
$596$	−12.9914	−0.532149
$597$	−17.7885	−0.728034
$598$	−15.8582	−0.648490
$599$	−39.7759	−1.62520	−0.812599	−	0.582823i	$-0.801948\pi$
$599$	−39.7759	−1.62520	−0.812599	+	0.582823i	$0.801948\pi$
$600$	1.75661	0.0717134
$601$	−12.2234	−0.498603	−0.249301	−	0.968426i	$-0.580201\pi$
$601$	−12.2234	−0.498603	−0.249301	+	0.968426i	$0.580201\pi$
$602$	−18.8044	−0.766412
$603$	−25.4346	−1.03578
$604$	6.78069	0.275902
$605$	−21.3410	−0.867635
$606$	−24.9777	−1.01465
$607$	36.5608	1.48396	0.741979	−	0.670424i	$-0.233888\pi$
$607$	36.5608	1.48396	0.741979	+	0.670424i	$0.233888\pi$
$608$	0	0
$609$	−22.3641	−0.906240
$610$	13.2332	0.535798
$611$	−1.54702	−0.0625857
$612$	−13.6671	−0.552461
$613$	−30.2527	−1.22189	−0.610947	−	0.791672i	$-0.709211\pi$
$613$	−30.2527	−1.22189	−0.610947	+	0.791672i	$0.709211\pi$
$614$	12.7368	0.514016
$615$	0.277623	0.0111948
$616$	34.0143	1.37048
$617$	−23.2875	−0.937519	−0.468760	−	0.883326i	$-0.655299\pi$
$617$	−23.2875	−0.937519	−0.468760	+	0.883326i	$0.655299\pi$
$618$	0.355068	0.0142829
$619$	39.9577	1.60604	0.803018	−	0.595955i	$-0.203226\pi$
$619$	39.9577	1.60604	0.803018	+	0.595955i	$0.203226\pi$
$620$	−1.84534	−0.0741104
$621$	−8.27723	−0.332154
$622$	12.4933	0.500937
$623$	17.3515	0.695172
$624$	−24.5041	−0.980949
$625$	1.00000	0.0400000
$626$	−19.0384	−0.760926
$627$	0	0
$628$	5.02893	0.200676
$629$	−34.4059	−1.37185
$630$	−11.4266	−0.455247
$631$	−42.0068	−1.67226	−0.836132	−	0.548529i	$-0.815188\pi$
$631$	−42.0068	−1.67226	−0.836132	+	0.548529i	$0.815188\pi$
$632$	−10.9180	−0.434294
$633$	13.1614	0.523120
$634$	−17.2581	−0.685406
$635$	−0.302950	−0.0120222
$636$	−7.31649	−0.290118
$637$	14.8711	0.589214
$638$	75.0486	2.97120
$639$	25.2472	0.998766
$640$	12.8649	0.508531
$641$	11.8819	0.469307	0.234653	−	0.972079i	$-0.424604\pi$
$641$	11.8819	0.469307	0.234653	+	0.972079i	$0.424604\pi$
$642$	8.81017	0.347710
$643$	39.1686	1.54466	0.772329	−	0.635223i	$-0.219092\pi$
$643$	39.1686	1.54466	0.772329	+	0.635223i	$0.219092\pi$
$644$	4.76104	0.187611
$645$	−3.25931	−0.128335
$646$	0	0
$647$	1.59402	0.0626675	0.0313337	−	0.999509i	$-0.490025\pi$
$647$	1.59402	0.0626675	0.0313337	+	0.999509i	$0.490025\pi$
$648$	4.05743	0.159391
$649$	3.35436	0.131670
$650$	−9.07274	−0.355862
$651$	6.08291	0.238408
$652$	2.68537	0.105167
$653$	−32.3959	−1.26775	−0.633874	−	0.773436i	$-0.718536\pi$
$653$	−32.3959	−1.26775	−0.633874	+	0.773436i	$0.718536\pi$
$654$	−8.78895	−0.343675
$655$	15.2113	0.594355
$656$	1.50653	0.0588202
$657$	2.22261	0.0867123
$658$	1.53080	0.0596768
$659$	−43.1666	−1.68153	−0.840766	−	0.541399i	$-0.817895\pi$
$659$	−43.1666	−1.68153	−0.840766	+	0.541399i	$0.817895\pi$
$660$	−4.54939	−0.177085
$661$	−32.6606	−1.27035	−0.635174	−	0.772369i	$-0.719072\pi$
$661$	−32.6606	−1.27035	−0.635174	+	0.772369i	$0.719072\pi$
$662$	56.3574	2.19039
$663$	35.7712	1.38924
$664$	−7.10478	−0.275719
$665$	0	0
$666$	−17.2831	−0.669706
$667$	−13.6131	−0.527100
$668$	−8.44192	−0.326628
$669$	9.06923	0.350637
$670$	19.9834	0.772025
$671$	44.4137	1.71457
$672$	13.2618	0.511584
$673$	15.2048	0.586101	0.293051	−	0.956097i	$-0.405330\pi$
$673$	15.2048	0.586101	0.293051	+	0.956097i	$0.405330\pi$
$674$	10.6418	0.409908
$675$	−4.73554	−0.182271
$676$	13.6503	0.525011
$677$	8.82561	0.339196	0.169598	−	0.985513i	$-0.445753\pi$
$677$	8.82561	0.339196	0.169598	+	0.985513i	$0.445753\pi$
$678$	6.63197	0.254699
$679$	21.3172	0.818080
$680$	−13.9154	−0.533630
$681$	−0.317327	−0.0121600
$682$	−20.4128	−0.781645
$683$	10.9999	0.420898	0.210449	−	0.977605i	$-0.432507\pi$
$683$	10.9999	0.420898	0.210449	+	0.977605i	$0.432507\pi$
$684$	0	0
$685$	16.8460	0.643653
$686$	22.3729	0.854200
$687$	5.62814	0.214727
$688$	−17.6868	−0.674303
$689$	−48.9710	−1.86565
$690$	2.71983	0.103542
$691$	−37.4842	−1.42597	−0.712983	−	0.701181i	$-0.752656\pi$
$691$	−37.4842	−1.42597	−0.712983	+	0.701181i	$0.752656\pi$
$692$	−4.72634	−0.179669
$693$	−38.3503	−1.45681
$694$	32.7427	1.24290
$695$	−1.04207	−0.0395281
$696$	−13.6810	−0.518575
$697$	−2.19924	−0.0833023
$698$	−13.4714	−0.509900
$699$	15.1831	0.574278
$700$	2.72387	0.102953
$701$	2.97731	0.112452	0.0562258	−	0.998418i	$-0.482093\pi$
$701$	2.97731	0.112452	0.0562258	+	0.998418i	$0.482093\pi$
$702$	42.9643	1.62158
$703$	0	0
$704$	12.1769	0.458933
$705$	0.265328	0.00999284
$706$	24.9126	0.937598
$707$	50.1921	1.88767
$708$	0.471856	0.0177334
$709$	21.7087	0.815286	0.407643	−	0.913141i	$-0.366351\pi$
$709$	21.7087	0.815286	0.407643	+	0.913141i	$0.366351\pi$
$710$	−19.8362	−0.744437
$711$	12.3098	0.461652
$712$	10.6145	0.397796
$713$	3.70267	0.138666
$714$	−35.3962	−1.32467
$715$	−30.4502	−1.13877
$716$	3.61157	0.134971
$717$	−22.2169	−0.829705
$718$	−23.2452	−0.867505
$719$	−6.77952	−0.252834	−0.126417	−	0.991977i	$-0.540348\pi$
$719$	−6.77952	−0.252834	−0.126417	+	0.991977i	$0.540348\pi$
$720$	−10.7475	−0.400535
$721$	−0.713503	−0.0265722
$722$	0	0
$723$	−13.1374	−0.488585
$724$	6.01878	0.223686
$725$	−7.78826	−0.289249
$726$	−33.2079	−1.23246
$727$	27.6811	1.02664	0.513318	−	0.858199i	$-0.328416\pi$
$727$	27.6811	1.02664	0.513318	+	0.858199i	$0.328416\pi$
$728$	32.0257	1.18695
$729$	8.47178	0.313770
$730$	−1.74625	−0.0646316
$731$	25.8193	0.954960
$732$	6.24766	0.230920
$733$	−31.4103	−1.16017	−0.580084	−	0.814557i	$-0.696980\pi$
$733$	−31.4103	−1.16017	−0.580084	+	0.814557i	$0.696980\pi$
$734$	50.7083	1.87168
$735$	−2.55053	−0.0940778
$736$	8.07246	0.297555
$737$	67.0688	2.47051
$738$	−1.10474	−0.0406661
$739$	45.0375	1.65673	0.828365	−	0.560188i	$-0.189271\pi$
$739$	45.0375	1.65673	0.828365	+	0.560188i	$0.189271\pi$
$740$	4.11993	0.151452
$741$	0	0
$742$	48.4576	1.77893
$743$	8.82369	0.323710	0.161855	−	0.986815i	$-0.448252\pi$
$743$	8.82369	0.323710	0.161855	+	0.986815i	$0.448252\pi$
$744$	3.72114	0.136423
$745$	14.9135	0.546390
$746$	52.5230	1.92300
$747$	8.01047	0.293088
$748$	36.0389	1.31771
$749$	−17.7039	−0.646886
$750$	1.55606	0.0568193
$751$	39.3104	1.43446	0.717228	−	0.696838i	$-0.245411\pi$
$751$	39.3104	1.43446	0.717228	+	0.696838i	$0.245411\pi$
$752$	1.43982	0.0525047
$753$	23.9051	0.871152
$754$	70.6608	2.57332
$755$	−7.78392	−0.283286
$756$	−12.8990	−0.469132
$757$	7.20750	0.261961	0.130980	−	0.991385i	$-0.458187\pi$
$757$	7.20750	0.261961	0.130980	+	0.991385i	$0.458187\pi$
$758$	31.9098	1.15901
$759$	9.12837	0.331339
$760$	0	0
$761$	−13.9525	−0.505777	−0.252888	−	0.967495i	$-0.581381\pi$
$761$	−13.9525	−0.505777	−0.252888	+	0.967495i	$0.581381\pi$
$762$	−0.471408	−0.0170773
$763$	17.6612	0.639380
$764$	1.30961	0.0473802
$765$	15.6892	0.567245
$766$	−14.6282	−0.528537
$767$	3.15825	0.114038
$768$	16.0859	0.580450
$769$	41.8518	1.50922	0.754608	−	0.656176i	$-0.227827\pi$
$769$	41.8518	1.50922	0.754608	+	0.656176i	$0.227827\pi$
$770$	30.1309	1.08584
$771$	20.5139	0.738790
$772$	9.29716	0.334612
$773$	46.2210	1.66245	0.831226	−	0.555934i	$-0.187639\pi$
$773$	46.2210	1.66245	0.831226	+	0.555934i	$0.187639\pi$
$774$	12.9698	0.466188
$775$	2.11836	0.0760937
$776$	13.0405	0.468127
$777$	−13.5808	−0.487209
$778$	6.36454	0.228180
$779$	0	0
$780$	−4.28341	−0.153371
$781$	−66.5746	−2.38223
$782$	−21.5457	−0.770472
$783$	36.8816	1.31804
$784$	−13.8406	−0.494307
$785$	−5.77297	−0.206046
$786$	23.6697	0.844270
$787$	10.1042	0.360175	0.180088	−	0.983651i	$-0.442362\pi$
$787$	10.1042	0.360175	0.180088	+	0.983651i	$0.442362\pi$
$788$	0.976153	0.0347740
$789$	−18.8727	−0.671886
$790$	−9.67148	−0.344096
$791$	−13.3268	−0.473847
$792$	−23.4603	−0.833626
$793$	41.8171	1.48497
$794$	13.6015	0.482698
$795$	8.39899	0.297881
$796$	−16.8738	−0.598076
$797$	13.0320	0.461616	0.230808	−	0.972999i	$-0.425863\pi$
$797$	13.0320	0.461616	0.230808	+	0.972999i	$0.425863\pi$
$798$	0	0
$799$	−2.10185	−0.0743581
$800$	4.61839	0.163285
$801$	−11.9676	−0.422855
$802$	51.1545	1.80633
$803$	−5.86082	−0.206824
$804$	9.43453	0.332730
$805$	−5.46545	−0.192632
$806$	−19.2193	−0.676972
$807$	28.3717	0.998730
$808$	30.7044	1.08018
$809$	24.1214	0.848063	0.424031	−	0.905648i	$-0.360615\pi$
$809$	24.1214	0.848063	0.424031	+	0.905648i	$0.360615\pi$
$810$	3.59419	0.126287
$811$	11.3131	0.397258	0.198629	−	0.980075i	$-0.436351\pi$
$811$	11.3131	0.397258	0.198629	+	0.980075i	$0.436351\pi$
$812$	−21.2142	−0.744472
$813$	15.7368	0.551915
$814$	45.5739	1.59736
$815$	−3.08268	−0.107982
$816$	−33.2924	−1.16547
$817$	0	0
$818$	−1.26717	−0.0443057
$819$	−36.1082	−1.26172
$820$	0.263348	0.00919650
$821$	−54.1667	−1.89043	−0.945215	−	0.326447i	$-0.894148\pi$
$821$	−54.1667	−1.89043	−0.945215	+	0.326447i	$0.894148\pi$
$822$	26.2134	0.914298
$823$	21.6843	0.755866	0.377933	−	0.925833i	$-0.376635\pi$
$823$	21.6843	0.755866	0.377933	+	0.925833i	$0.376635\pi$
$824$	−0.436476	−0.0152054
$825$	5.22249	0.181824
$826$	−3.12513	−0.108737
$827$	30.1997	1.05015	0.525074	−	0.851057i	$-0.324038\pi$
$827$	30.1997	1.05015	0.525074	+	0.851057i	$0.324038\pi$
$828$	−3.28377	−0.114119
$829$	52.0991	1.80948	0.904738	−	0.425968i	$-0.140066\pi$
$829$	52.0991	1.80948	0.904738	+	0.425968i	$0.140066\pi$
$830$	−6.29363	−0.218455
$831$	−15.1645	−0.526051
$832$	11.4650	0.397476
$833$	20.2045	0.700046
$834$	−1.62153	−0.0561490
$835$	9.69093	0.335369
$836$	0	0
$837$	−10.0316	−0.346742
$838$	−40.2593	−1.39073
$839$	−22.9039	−0.790730	−0.395365	−	0.918524i	$-0.629382\pi$
$839$	−22.9039	−0.790730	−0.395365	+	0.918524i	$0.629382\pi$
$840$	−5.49271	−0.189516
$841$	31.6570	1.09162
$842$	22.8023	0.785819
$843$	2.26745	0.0780950
$844$	12.4847	0.429740
$845$	−15.6699	−0.539061
$846$	−1.05582	−0.0362998
$847$	66.7306	2.29289
$848$	45.5775	1.56514
$849$	−5.32171	−0.182641
$850$	−12.3266	−0.422800
$851$	−8.26665	−0.283377
$852$	−9.36502	−0.320840
$853$	−54.5357	−1.86727	−0.933634	−	0.358229i	$-0.883381\pi$
$853$	−54.5357	−1.86727	−0.933634	+	0.358229i	$0.883381\pi$
$854$	−41.3786	−1.41595
$855$	0	0
$856$	−10.8301	−0.370166
$857$	−0.157483	−0.00537950	−0.00268975	−	0.999996i	$-0.500856\pi$
$857$	−0.157483	−0.00537950	−0.00268975	+	0.999996i	$0.500856\pi$
$858$	−47.3823	−1.61760
$859$	4.77861	0.163044	0.0815220	−	0.996672i	$-0.474022\pi$
$859$	4.77861	0.163044	0.0815220	+	0.996672i	$0.474022\pi$
$860$	−3.09172	−0.105427
$861$	−0.868091	−0.0295845
$862$	31.0032	1.05597
$863$	35.0915	1.19453	0.597265	−	0.802044i	$-0.296254\pi$
$863$	35.0915	1.19453	0.597265	+	0.802044i	$0.296254\pi$
$864$	−21.8706	−0.744052
$865$	5.42562	0.184477
$866$	−51.8208	−1.76094
$867$	32.9887	1.12036
$868$	5.77013	0.195851
$869$	−32.4597	−1.10112
$870$	−12.1190	−0.410873
$871$	63.1476	2.13967
$872$	10.8040	0.365871
$873$	−14.7029	−0.497617
$874$	0	0
$875$	−3.12687	−0.105708
$876$	−0.824438	−0.0278552
$877$	−2.62538	−0.0886528	−0.0443264	−	0.999017i	$-0.514114\pi$
$877$	−2.62538	−0.0886528	−0.0443264	+	0.999017i	$0.514114\pi$
$878$	−67.8502	−2.28983
$879$	8.97620	0.302760
$880$	28.3401	0.955345
$881$	−16.0534	−0.540854	−0.270427	−	0.962740i	$-0.587165\pi$
$881$	−16.0534	−0.540854	−0.270427	+	0.962740i	$0.587165\pi$
$882$	10.1493	0.341745
$883$	2.82768	0.0951590	0.0475795	−	0.998867i	$-0.484849\pi$
$883$	2.82768	0.0951590	0.0475795	+	0.998867i	$0.484849\pi$
$884$	33.9319	1.14125
$885$	−0.541669	−0.0182080
$886$	−37.2983	−1.25306
$887$	15.4425	0.518509	0.259255	−	0.965809i	$-0.416523\pi$
$887$	15.4425	0.518509	0.259255	+	0.965809i	$0.416523\pi$
$888$	−8.30787	−0.278794
$889$	0.947285	0.0317709
$890$	9.40267	0.315178
$891$	12.0629	0.404123
$892$	8.60290	0.288046
$893$	0	0
$894$	23.2064	0.776137
$895$	−4.14592	−0.138583
$896$	−40.2270	−1.34389
$897$	8.59468	0.286968
$898$	53.3919	1.78171
$899$	−16.4983	−0.550250
$900$	−1.87870	−0.0626234
$901$	−66.5342	−2.21658
$902$	2.91310	0.0969957
$903$	10.1915	0.339150
$904$	−8.15251	−0.271148
$905$	−6.90928	−0.229672
$906$	−12.1122	−0.402402
$907$	−7.96734	−0.264551	−0.132276	−	0.991213i	$-0.542228\pi$
$907$	−7.96734	−0.264551	−0.132276	+	0.991213i	$0.542228\pi$
$908$	−0.301010	−0.00998938
$909$	−34.6184	−1.14822
$910$	28.3693	0.940434
$911$	−20.1004	−0.665956	−0.332978	−	0.942935i	$-0.608054\pi$
$911$	−20.1004	−0.665956	−0.332978	+	0.942935i	$0.608054\pi$
$912$	0	0
$913$	−21.1229	−0.699064
$914$	20.1933	0.667934
$915$	−7.17202	−0.237100
$916$	5.33875	0.176397
$917$	−47.5638	−1.57070
$918$	58.3733	1.92661
$919$	−38.9475	−1.28476	−0.642380	−	0.766386i	$-0.722053\pi$
$919$	−38.9475	−1.28476	−0.642380	+	0.766386i	$0.722053\pi$
$920$	−3.34342	−0.110229
$921$	−6.90298	−0.227461
$922$	1.17525	0.0387047
$923$	−62.6823	−2.06321
$924$	14.2254	0.467981
$925$	−4.72949	−0.155505
$926$	−29.7686	−0.978256
$927$	0.492116	0.0161632
$928$	−35.9692	−1.18075
$929$	−30.9745	−1.01624	−0.508121	−	0.861286i	$-0.669660\pi$
$929$	−30.9745	−1.01624	−0.508121	+	0.861286i	$0.669660\pi$
$930$	3.29629	0.108090
$931$	0	0
$932$	14.4024	0.471766
$933$	−6.77102	−0.221673
$934$	60.2452	1.97128
$935$	−41.3710	−1.35298
$936$	−22.0887	−0.721991
$937$	15.9382	0.520678	0.260339	−	0.965517i	$-0.416166\pi$
$937$	15.9382	0.520678	0.260339	+	0.965517i	$0.416166\pi$
$938$	−62.4855	−2.04022
$939$	10.3182	0.336723
$940$	0.251685	0.00820907
$941$	18.3450	0.598030	0.299015	−	0.954248i	$-0.403342\pi$
$941$	18.3450	0.598030	0.299015	+	0.954248i	$0.403342\pi$
$942$	−8.98309	−0.292685
$943$	−0.528408	−0.0172073
$944$	−2.93939	−0.0956691
$945$	14.8074	0.481686
$946$	−34.2001	−1.11194
$947$	29.3184	0.952721	0.476360	−	0.879250i	$-0.341956\pi$
$947$	29.3184	0.952721	0.476360	+	0.879250i	$0.341956\pi$
$948$	−4.56609	−0.148300
$949$	−5.51816	−0.179127
$950$	0	0
$951$	9.35338	0.303304
$952$	43.5116	1.41022
$953$	33.8251	1.09570	0.547852	−	0.836576i	$-0.315446\pi$
$953$	33.8251	1.09570	0.547852	+	0.836576i	$0.315446\pi$
$954$	−33.4221	−1.08208
$955$	−1.50338	−0.0486481
$956$	−21.0745	−0.681599
$957$	−40.6741	−1.31481
$958$	−34.9934	−1.13058
$959$	−52.6754	−1.70098
$960$	−1.96635	−0.0634636
$961$	−26.5126	−0.855244
$962$	42.9094	1.38345
$963$	12.2107	0.393484
$964$	−12.4619	−0.401371
$965$	−10.6727	−0.343567
$966$	−8.50457	−0.273630
$967$	−41.5507	−1.33618	−0.668091	−	0.744080i	$-0.732888\pi$
$967$	−41.5507	−1.33618	−0.668091	+	0.744080i	$0.732888\pi$
$968$	40.8216	1.31206
$969$	0	0
$970$	11.5517	0.370902
$971$	7.03323	0.225707	0.112854	−	0.993612i	$-0.464001\pi$
$971$	7.03323	0.225707	0.112854	+	0.993612i	$0.464001\pi$
$972$	14.0725	0.451375
$973$	3.25843	0.104461
$974$	−27.8026	−0.890854
$975$	4.91716	0.157475
$976$	−38.9193	−1.24578
$977$	−23.2522	−0.743903	−0.371951	−	0.928252i	$-0.621311\pi$
$977$	−23.2522	−0.743903	−0.371951	+	0.928252i	$0.621311\pi$
$978$	−4.79684	−0.153386
$979$	31.5575	1.00858
$980$	−2.41939	−0.0772845
$981$	−12.1813	−0.388918
$982$	25.0971	0.800882
$983$	−15.8614	−0.505899	−0.252949	−	0.967480i	$-0.581401\pi$
$983$	−15.8614	−0.505899	−0.252949	+	0.967480i	$0.581401\pi$
$984$	−0.531043	−0.0169290
$985$	−1.12058	−0.0357046
$986$	96.0031	3.05736
$987$	−0.829648	−0.0264080
$988$	0	0
$989$	6.20355	0.197261
$990$	−20.7818	−0.660490
$991$	12.1053	0.384538	0.192269	−	0.981342i	$-0.438415\pi$
$991$	12.1053	0.384538	0.192269	+	0.981342i	$0.438415\pi$
$992$	9.78341	0.310623
$993$	−30.5441	−0.969287
$994$	62.0252	1.96732
$995$	19.3704	0.614082
$996$	−2.97134	−0.0941505
$997$	−31.5871	−1.00037	−0.500187	−	0.865918i	$-0.666735\pi$
$997$	−31.5871	−1.00037	−0.500187	+	0.865918i	$0.666735\pi$
$998$	−11.0564	−0.349986
$999$	22.3967	0.708599

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1805.2.a.q.1.2	✓	6
5.4	even	2		9025.2.a.ca.1.5		6
19.18	odd	2		1805.2.a.r.1.5	yes	6
95.94	odd	2		9025.2.a.bq.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1805.2.a.q.1.2	✓	6	1.1	even	1	trivial
1805.2.a.r.1.5	yes	6	19.18	odd	2
9025.2.a.bq.1.2		6	95.94	odd	2
9025.2.a.ca.1.5		6	5.4	even	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:	\( N \)	\(=\)	\( 1805 = 5 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1805.a (trivial)

\(f(q)\)	\(=\)	\(q-1.69444 q^{2} +0.918335 q^{3} +0.871115 q^{4} -1.00000 q^{5} -1.55606 q^{6} +3.12687 q^{7} +1.91282 q^{8} -2.15666 q^{9} +O(q^{10})\)	\(q-1.69444 q^{2} +0.918335 q^{3} +0.871115 q^{4} -1.00000 q^{5} -1.55606 q^{6} +3.12687 q^{7} +1.91282 q^{8} -2.15666 q^{9} +1.69444 q^{10} +5.68692 q^{11} +0.799975 q^{12} +5.35443 q^{13} -5.29829 q^{14} -0.918335 q^{15} -4.98339 q^{16} +7.27477 q^{17} +3.65433 q^{18} -0.871115 q^{20} +2.87152 q^{21} -9.63612 q^{22} +1.74790 q^{23} +1.75661 q^{24} +1.00000 q^{25} -9.07274 q^{26} -4.73554 q^{27} +2.72387 q^{28} -7.78826 q^{29} +1.55606 q^{30} +2.11836 q^{31} +4.61839 q^{32} +5.22249 q^{33} -12.3266 q^{34} -3.12687 q^{35} -1.87870 q^{36} -4.72949 q^{37} +4.91716 q^{39} -1.91282 q^{40} -0.302311 q^{41} -4.86560 q^{42} +3.54915 q^{43} +4.95396 q^{44} +2.15666 q^{45} -2.96170 q^{46} -0.288923 q^{47} -4.57642 q^{48} +2.77734 q^{49} -1.69444 q^{50} +6.68068 q^{51} +4.66432 q^{52} -9.14589 q^{53} +8.02407 q^{54} -5.68692 q^{55} +5.98116 q^{56} +13.1967 q^{58} +0.589838 q^{59} -0.799975 q^{60} +7.80981 q^{61} -3.58943 q^{62} -6.74361 q^{63} +2.14121 q^{64} -5.35443 q^{65} -8.84918 q^{66} +11.7935 q^{67} +6.33717 q^{68} +1.60515 q^{69} +5.29829 q^{70} -11.7066 q^{71} -4.12531 q^{72} -1.03058 q^{73} +8.01381 q^{74} +0.918335 q^{75} +17.7823 q^{77} -8.33181 q^{78} -5.70778 q^{79} +4.98339 q^{80} +2.12117 q^{81} +0.512247 q^{82} -3.71429 q^{83} +2.50142 q^{84} -7.27477 q^{85} -6.01381 q^{86} -7.15223 q^{87} +10.8781 q^{88} +5.54914 q^{89} -3.65433 q^{90} +16.7426 q^{91} +1.52262 q^{92} +1.94536 q^{93} +0.489562 q^{94} +4.24123 q^{96} +6.81742 q^{97} -4.70603 q^{98} -12.2648 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{2} - 4 q^{3} + 8 q^{4} - 6 q^{5} + 8 q^{6} + 7 q^{7} + 10 q^{9}+O(q^{10}) \) 6 * q - 2 * q^2 - 4 * q^3 + 8 * q^4 - 6 * q^5 + 8 * q^6 + 7 * q^7 + 10 * q^9	\( 6 q - 2 q^{2} - 4 q^{3} + 8 q^{4} - 6 q^{5} + 8 q^{6} + 7 q^{7} + 10 q^{9} + 2 q^{10} + 15 q^{11} + 20 q^{12} - 6 q^{13} - 20 q^{14} + 4 q^{15} + 20 q^{16} + 5 q^{17} + 8 q^{18} - 8 q^{20} - 7 q^{21} - 14 q^{22} + 18 q^{24} + 6 q^{25} - 22 q^{26} - 28 q^{27} + 10 q^{28} + 20 q^{29} - 8 q^{30} - 12 q^{31} + 8 q^{32} - q^{33} - 7 q^{35} - 14 q^{36} - 20 q^{37} + 16 q^{39} - 8 q^{41} - 30 q^{42} + 27 q^{43} + 46 q^{44} - 10 q^{45} - 16 q^{46} - 8 q^{47} + 24 q^{48} + 11 q^{49} - 2 q^{50} + 11 q^{51} - 4 q^{52} - 19 q^{53} + 30 q^{54} - 15 q^{55} - 62 q^{56} + 20 q^{58} + 41 q^{59} - 20 q^{60} + 6 q^{61} - 30 q^{62} - 18 q^{63} + 48 q^{64} + 6 q^{65} + 46 q^{66} + 15 q^{67} - 14 q^{68} + 10 q^{69} + 20 q^{70} - 2 q^{71} + 68 q^{72} + 8 q^{73} + 2 q^{74} - 4 q^{75} + 21 q^{77} - 46 q^{78} - 18 q^{79} - 20 q^{80} + 50 q^{81} - 18 q^{82} - 10 q^{83} - 4 q^{84} - 5 q^{85} + 10 q^{86} - 14 q^{87} + 52 q^{88} - 17 q^{89} - 8 q^{90} + 23 q^{91} + 28 q^{92} + 10 q^{93} + 28 q^{94} + 26 q^{96} + 4 q^{97} - 50 q^{98} + 58 q^{99}+O(q^{100}) \) 6 * q - 2 * q^2 - 4 * q^3 + 8 * q^4 - 6 * q^5 + 8 * q^6 + 7 * q^7 + 10 * q^9 + 2 * q^10 + 15 * q^11 + 20 * q^12 - 6 * q^13 - 20 * q^14 + 4 * q^15 + 20 * q^16 + 5 * q^17 + 8 * q^18 - 8 * q^20 - 7 * q^21 - 14 * q^22 + 18 * q^24 + 6 * q^25 - 22 * q^26 - 28 * q^27 + 10 * q^28 + 20 * q^29 - 8 * q^30 - 12 * q^31 + 8 * q^32 - q^33 - 7 * q^35 - 14 * q^36 - 20 * q^37 + 16 * q^39 - 8 * q^41 - 30 * q^42 + 27 * q^43 + 46 * q^44 - 10 * q^45 - 16 * q^46 - 8 * q^47 + 24 * q^48 + 11 * q^49 - 2 * q^50 + 11 * q^51 - 4 * q^52 - 19 * q^53 + 30 * q^54 - 15 * q^55 - 62 * q^56 + 20 * q^58 + 41 * q^59 - 20 * q^60 + 6 * q^61 - 30 * q^62 - 18 * q^63 + 48 * q^64 + 6 * q^65 + 46 * q^66 + 15 * q^67 - 14 * q^68 + 10 * q^69 + 20 * q^70 - 2 * q^71 + 68 * q^72 + 8 * q^73 + 2 * q^74 - 4 * q^75 + 21 * q^77 - 46 * q^78 - 18 * q^79 - 20 * q^80 + 50 * q^81 - 18 * q^82 - 10 * q^83 - 4 * q^84 - 5 * q^85 + 10 * q^86 - 14 * q^87 + 52 * q^88 - 17 * q^89 - 8 * q^90 + 23 * q^91 + 28 * q^92 + 10 * q^93 + 28 * q^94 + 26 * q^96 + 4 * q^97 - 50 * q^98 + 58 * q^99

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