LMFDB - Embedded newform 2645.2.a.x.1.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2645, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2645.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2645 = 5 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2645.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$21.1204313346$
Analytic rank:	$0$
Dimension:	$25$
Twist minimal:	no (minimal twist has level 115)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.21
Character	$\chi$	$=$	2645.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.34901 q^{2} +2.25515 q^{3} +3.51786 q^{4} -1.00000 q^{5} +5.29738 q^{6} -0.494634 q^{7} +3.56547 q^{8} +2.08571 q^{9} +O(q^{10})$	\(q+2.34901 q^{2} +2.25515 q^{3} +3.51786 q^{4} -1.00000 q^{5} +5.29738 q^{6} -0.494634 q^{7} +3.56547 q^{8} +2.08571 q^{9} -2.34901 q^{10} -2.23243 q^{11} +7.93331 q^{12} +4.56220 q^{13} -1.16190 q^{14} -2.25515 q^{15} +1.33961 q^{16} +6.89177 q^{17} +4.89936 q^{18} +5.65825 q^{19} -3.51786 q^{20} -1.11547 q^{21} -5.24400 q^{22} +8.04067 q^{24} +1.00000 q^{25} +10.7167 q^{26} -2.06186 q^{27} -1.74005 q^{28} +9.72883 q^{29} -5.29738 q^{30} -4.25004 q^{31} -3.98418 q^{32} -5.03446 q^{33} +16.1888 q^{34} +0.494634 q^{35} +7.33724 q^{36} -2.00407 q^{37} +13.2913 q^{38} +10.2885 q^{39} -3.56547 q^{40} -2.18900 q^{41} -2.62026 q^{42} -5.95884 q^{43} -7.85336 q^{44} -2.08571 q^{45} -3.87797 q^{47} +3.02102 q^{48} -6.75534 q^{49} +2.34901 q^{50} +15.5420 q^{51} +16.0492 q^{52} -8.53595 q^{53} -4.84333 q^{54} +2.23243 q^{55} -1.76360 q^{56} +12.7602 q^{57} +22.8531 q^{58} +2.93429 q^{59} -7.93331 q^{60} +6.93009 q^{61} -9.98340 q^{62} -1.03166 q^{63} -12.0381 q^{64} -4.56220 q^{65} -11.8260 q^{66} +3.81733 q^{67} +24.2442 q^{68} +1.16190 q^{70} +2.76568 q^{71} +7.43654 q^{72} -11.0250 q^{73} -4.70759 q^{74} +2.25515 q^{75} +19.9049 q^{76} +1.10423 q^{77} +24.1677 q^{78} -14.9221 q^{79} -1.33961 q^{80} -10.9069 q^{81} -5.14200 q^{82} +9.39180 q^{83} -3.92408 q^{84} -6.89177 q^{85} -13.9974 q^{86} +21.9400 q^{87} -7.95964 q^{88} +4.63796 q^{89} -4.89936 q^{90} -2.25662 q^{91} -9.58450 q^{93} -9.10939 q^{94} -5.65825 q^{95} -8.98493 q^{96} +8.18195 q^{97} -15.8684 q^{98} -4.65620 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q + 3 q^{2} + 10 q^{3} + 33 q^{4} - 25 q^{5} + 22 q^{6} - 14 q^{7} + 21 q^{8} + 29 q^{9}+O(q^{10}) $ 25 * q + 3 * q^2 + 10 * q^3 + 33 * q^4 - 25 * q^5 + 22 * q^6 - 14 * q^7 + 21 * q^8 + 29 * q^9	\( 25 q + 3 q^{2} + 10 q^{3} + 33 q^{4} - 25 q^{5} + 22 q^{6} - 14 q^{7} + 21 q^{8} + 29 q^{9} - 3 q^{10} + 8 q^{11} + 34 q^{12} + 15 q^{13} + 6 q^{14} - 10 q^{15} + 41 q^{16} - 19 q^{17} + 23 q^{18} + 8 q^{19} - 33 q^{20} + 21 q^{21} - 3 q^{22} + 51 q^{24} + 25 q^{25} + 7 q^{26} + 64 q^{27} - 27 q^{28} + 3 q^{29} - 22 q^{30} + 34 q^{31} + 30 q^{32} + q^{33} + 21 q^{34} + 14 q^{35} + 31 q^{36} + q^{37} + 7 q^{38} + 49 q^{39} - 21 q^{40} + 29 q^{42} - 25 q^{43} + 33 q^{44} - 29 q^{45} - 5 q^{47} + 42 q^{48} + 33 q^{49} + 3 q^{50} - 23 q^{51} + 67 q^{52} - 24 q^{53} + 37 q^{54} - 8 q^{55} + 55 q^{56} + 19 q^{57} + 49 q^{58} + 41 q^{59} - 34 q^{60} + 31 q^{61} - 3 q^{62} - 37 q^{63} + 77 q^{64} - 15 q^{65} + 39 q^{66} + 5 q^{67} - 27 q^{68} - 6 q^{70} + 15 q^{71} + 48 q^{72} + 34 q^{73} + 29 q^{74} + 10 q^{75} + 24 q^{76} - 35 q^{77} - 45 q^{78} + 41 q^{79} - 41 q^{80} + 25 q^{81} + 33 q^{82} - 62 q^{83} + 126 q^{84} + 19 q^{85} + 10 q^{86} + 26 q^{87} + 50 q^{88} + 23 q^{89} - 23 q^{90} - 19 q^{91} + 50 q^{93} + 9 q^{94} - 8 q^{95} + 64 q^{96} - 37 q^{97} - 55 q^{98} + 48 q^{99}+O(q^{100}) \) 25 * q + 3 * q^2 + 10 * q^3 + 33 * q^4 - 25 * q^5 + 22 * q^6 - 14 * q^7 + 21 * q^8 + 29 * q^9 - 3 * q^10 + 8 * q^11 + 34 * q^12 + 15 * q^13 + 6 * q^14 - 10 * q^15 + 41 * q^16 - 19 * q^17 + 23 * q^18 + 8 * q^19 - 33 * q^20 + 21 * q^21 - 3 * q^22 + 51 * q^24 + 25 * q^25 + 7 * q^26 + 64 * q^27 - 27 * q^28 + 3 * q^29 - 22 * q^30 + 34 * q^31 + 30 * q^32 + q^33 + 21 * q^34 + 14 * q^35 + 31 * q^36 + q^37 + 7 * q^38 + 49 * q^39 - 21 * q^40 + 29 * q^42 - 25 * q^43 + 33 * q^44 - 29 * q^45 - 5 * q^47 + 42 * q^48 + 33 * q^49 + 3 * q^50 - 23 * q^51 + 67 * q^52 - 24 * q^53 + 37 * q^54 - 8 * q^55 + 55 * q^56 + 19 * q^57 + 49 * q^58 + 41 * q^59 - 34 * q^60 + 31 * q^61 - 3 * q^62 - 37 * q^63 + 77 * q^64 - 15 * q^65 + 39 * q^66 + 5 * q^67 - 27 * q^68 - 6 * q^70 + 15 * q^71 + 48 * q^72 + 34 * q^73 + 29 * q^74 + 10 * q^75 + 24 * q^76 - 35 * q^77 - 45 * q^78 + 41 * q^79 - 41 * q^80 + 25 * q^81 + 33 * q^82 - 62 * q^83 + 126 * q^84 + 19 * q^85 + 10 * q^86 + 26 * q^87 + 50 * q^88 + 23 * q^89 - 23 * q^90 - 19 * q^91 + 50 * q^93 + 9 * q^94 - 8 * q^95 + 64 * q^96 - 37 * q^97 - 55 * q^98 + 48 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.34901	1.66100	0.830501	−	0.557017i	$-0.188054\pi$
$2$	2.34901	1.66100	0.830501	+	0.557017i	$0.188054\pi$
$3$	2.25515	1.30201	0.651006	−	0.759072i	$-0.274347\pi$
$3$	2.25515	1.30201	0.651006	+	0.759072i	$0.274347\pi$
$4$	3.51786	1.75893
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	5.29738	2.16265
$7$	−0.494634	−0.186954	−0.0934770	−	0.995621i	$-0.529798\pi$
$7$	−0.494634	−0.186954	−0.0934770	+	0.995621i	$0.529798\pi$
$8$	3.56547	1.26058
$9$	2.08571	0.695238
$10$	−2.34901	−0.742823
$11$	−2.23243	−0.673102	−0.336551	−	0.941665i	$-0.609260\pi$
$11$	−2.23243	−0.673102	−0.336551	+	0.941665i	$0.609260\pi$
$12$	7.93331	2.29015
$13$	4.56220	1.26533	0.632663	−	0.774427i	$-0.281962\pi$
$13$	4.56220	1.26533	0.632663	+	0.774427i	$0.281962\pi$
$14$	−1.16190	−0.310531
$15$	−2.25515	−0.582278
$16$	1.33961	0.334901
$17$	6.89177	1.67150	0.835749	−	0.549111i	$-0.185034\pi$
$17$	6.89177	1.67150	0.835749	+	0.549111i	$0.185034\pi$
$18$	4.89936	1.15479
$19$	5.65825	1.29809	0.649046	−	0.760749i	$-0.275168\pi$
$19$	5.65825	1.29809	0.649046	+	0.760749i	$0.275168\pi$
$20$	−3.51786	−0.786617
$21$	−1.11547	−0.243417
$22$	−5.24400	−1.11802
$23$	0	0
$23$	0	0
$24$	8.04067	1.64129
$25$	1.00000	0.200000
$26$	10.7167	2.10171
$27$	−2.06186	−0.396805
$28$	−1.74005	−0.328839
$29$	9.72883	1.80660	0.903299	−	0.429012i	$-0.141138\pi$
$29$	9.72883	1.80660	0.903299	+	0.429012i	$0.141138\pi$
$30$	−5.29738	−0.967165
$31$	−4.25004	−0.763330	−0.381665	−	0.924301i	$-0.624649\pi$
$31$	−4.25004	−0.763330	−0.381665	+	0.924301i	$0.624649\pi$
$32$	−3.98418	−0.704310
$33$	−5.03446	−0.876388
$34$	16.1888	2.77636
$35$	0.494634	0.0836084
$36$	7.33724	1.22287
$37$	−2.00407	−0.329468	−0.164734	−	0.986338i	$-0.552676\pi$
$37$	−2.00407	−0.329468	−0.164734	+	0.986338i	$0.552676\pi$
$38$	13.2913	2.15613
$39$	10.2885	1.64747
$40$	−3.56547	−0.563750
$41$	−2.18900	−0.341865	−0.170933	−	0.985283i	$-0.554678\pi$
$41$	−2.18900	−0.341865	−0.170933	+	0.985283i	$0.554678\pi$
$42$	−2.62026	−0.404315
$43$	−5.95884	−0.908715	−0.454357	−	0.890820i	$-0.650131\pi$
$43$	−5.95884	−0.908715	−0.454357	+	0.890820i	$0.650131\pi$
$44$	−7.85336	−1.18394
$45$	−2.08571	−0.310920
$46$	0	0
$47$	−3.87797	−0.565660	−0.282830	−	0.959170i	$-0.591273\pi$
$47$	−3.87797	−0.565660	−0.282830	+	0.959170i	$0.591273\pi$
$48$	3.02102	0.436046
$49$	−6.75534	−0.965048
$50$	2.34901	0.332200
$51$	15.5420	2.17631
$52$	16.0492	2.22562
$53$	−8.53595	−1.17250	−0.586251	−	0.810129i	$-0.699397\pi$
$53$	−8.53595	−1.17250	−0.586251	+	0.810129i	$0.699397\pi$
$54$	−4.84333	−0.659093
$55$	2.23243	0.301020
$56$	−1.76360	−0.235671
$57$	12.7602	1.69013
$58$	22.8531	3.00076
$59$	2.93429	0.382013	0.191006	−	0.981589i	$-0.438825\pi$
$59$	2.93429	0.382013	0.191006	+	0.981589i	$0.438825\pi$
$60$	−7.93331	−1.02419
$61$	6.93009	0.887307	0.443654	−	0.896198i	$-0.353682\pi$
$61$	6.93009	0.887307	0.443654	+	0.896198i	$0.353682\pi$
$62$	−9.98340	−1.26789
$63$	−1.03166	−0.129977
$64$	−12.0381	−1.50476
$65$	−4.56220	−0.565871
$66$	−11.8260	−1.45568
$67$	3.81733	0.466361	0.233180	−	0.972434i	$-0.425087\pi$
$67$	3.81733	0.466361	0.233180	+	0.972434i	$0.425087\pi$
$68$	24.2442	2.94005
$69$	0	0
$70$	1.16190	0.138874
$71$	2.76568	0.328225	0.164113	−	0.986442i	$-0.447524\pi$
$71$	2.76568	0.328225	0.164113	+	0.986442i	$0.447524\pi$
$72$	7.43654	0.876404
$73$	−11.0250	−1.29038	−0.645189	−	0.764023i	$-0.723221\pi$
$73$	−11.0250	−1.29038	−0.645189	+	0.764023i	$0.723221\pi$
$74$	−4.70759	−0.547246
$75$	2.25515	0.260403
$76$	19.9049	2.28325
$77$	1.10423	0.125839
$78$	24.1677	2.73645
$79$	−14.9221	−1.67887	−0.839434	−	0.543462i	$-0.817113\pi$
$79$	−14.9221	−1.67887	−0.839434	+	0.543462i	$0.817113\pi$
$80$	−1.33961	−0.149772
$81$	−10.9069	−1.21188
$82$	−5.14200	−0.567839
$83$	9.39180	1.03088	0.515442	−	0.856924i	$-0.327628\pi$
$83$	9.39180	1.03088	0.515442	+	0.856924i	$0.327628\pi$
$84$	−3.92408	−0.428152
$85$	−6.89177	−0.747517
$86$	−13.9974	−1.50938
$87$	21.9400	2.35221
$88$	−7.95964	−0.848501
$89$	4.63796	0.491622	0.245811	−	0.969318i	$-0.420946\pi$
$89$	4.63796	0.491622	0.245811	+	0.969318i	$0.420946\pi$
$90$	−4.89936	−0.516438
$91$	−2.25662	−0.236558
$92$	0	0
$93$	−9.58450	−0.993866
$94$	−9.10939	−0.939562
$95$	−5.65825	−0.580524
$96$	−8.98493	−0.917021
$97$	8.18195	0.830751	0.415375	−	0.909650i	$-0.363650\pi$
$97$	8.18195	0.830751	0.415375	+	0.909650i	$0.363650\pi$
$98$	−15.8684	−1.60295
$99$	−4.65620	−0.467966
$100$	3.51786	0.351786
$101$	−5.44489	−0.541787	−0.270894	−	0.962609i	$-0.587319\pi$
$101$	−5.44489	−0.541787	−0.270894	+	0.962609i	$0.587319\pi$
$102$	36.5083	3.61486
$103$	3.02400	0.297964	0.148982	−	0.988840i	$-0.452400\pi$
$103$	3.02400	0.297964	0.148982	+	0.988840i	$0.452400\pi$
$104$	16.2664	1.59505
$105$	1.11547	0.108859
$106$	−20.0511	−1.94753
$107$	−7.20154	−0.696199	−0.348100	−	0.937458i	$-0.613173\pi$
$107$	−7.20154	−0.696199	−0.348100	+	0.937458i	$0.613173\pi$
$108$	−7.25332	−0.697951
$109$	−5.61499	−0.537818	−0.268909	−	0.963166i	$-0.586663\pi$
$109$	−5.61499	−0.537818	−0.268909	+	0.963166i	$0.586663\pi$
$110$	5.24400	0.499996
$111$	−4.51949	−0.428971
$112$	−0.662614	−0.0626112
$113$	0.0343555	0.00323189	0.00161594	−	0.999999i	$-0.499486\pi$
$113$	0.0343555	0.00323189	0.00161594	+	0.999999i	$0.499486\pi$
$114$	29.9739	2.80731
$115$	0	0
$116$	34.2246	3.17768
$117$	9.51544	0.879702
$118$	6.89269	0.634524
$119$	−3.40890	−0.312493
$120$	−8.04067	−0.734009
$121$	−6.01627	−0.546934
$122$	16.2789	1.47382
$123$	−4.93654	−0.445113
$124$	−14.9510	−1.34264
$125$	−1.00000	−0.0894427
$126$	−2.42339	−0.215893
$127$	8.76703	0.777948	0.388974	−	0.921249i	$-0.372830\pi$
$127$	8.76703	0.777948	0.388974	+	0.921249i	$0.372830\pi$
$128$	−20.3093	−1.79510
$129$	−13.4381	−1.18316
$130$	−10.7167	−0.939913
$131$	9.10796	0.795766	0.397883	−	0.917436i	$-0.369745\pi$
$131$	9.10796	0.795766	0.397883	+	0.917436i	$0.369745\pi$
$132$	−17.7105	−1.54150
$133$	−2.79876	−0.242683
$134$	8.96694	0.774626
$135$	2.06186	0.177456
$136$	24.5723	2.10706
$137$	−7.97171	−0.681069	−0.340535	−	0.940232i	$-0.610608\pi$
$137$	−7.97171	−0.681069	−0.340535	+	0.940232i	$0.610608\pi$
$138$	0	0
$139$	−6.13056	−0.519987	−0.259994	−	0.965610i	$-0.583720\pi$
$139$	−6.13056	−0.519987	−0.259994	+	0.965610i	$0.583720\pi$
$140$	1.74005	0.147061
$141$	−8.74541	−0.736496
$142$	6.49661	0.545183
$143$	−10.1848	−0.851694
$144$	2.79403	0.232836
$145$	−9.72883	−0.807935
$146$	−25.8978	−2.14332
$147$	−15.2343	−1.25651
$148$	−7.05004	−0.579510
$149$	−19.2302	−1.57540	−0.787702	−	0.616057i	$-0.788729\pi$
$149$	−19.2302	−1.57540	−0.787702	+	0.616057i	$0.788729\pi$
$150$	5.29738	0.432529
$151$	3.67088	0.298732	0.149366	−	0.988782i	$-0.452277\pi$
$151$	3.67088	0.298732	0.149366	+	0.988782i	$0.452277\pi$
$152$	20.1743	1.63635
$153$	14.3742	1.16209
$154$	2.59386	0.209019
$155$	4.25004	0.341372
$156$	36.1933	2.89778
$157$	−19.1117	−1.52528	−0.762641	−	0.646822i	$-0.776098\pi$
$157$	−19.1117	−1.52528	−0.762641	+	0.646822i	$0.776098\pi$
$158$	−35.0522	−2.78860
$159$	−19.2499	−1.52661
$160$	3.98418	0.314977
$161$	0	0
$162$	−25.6205	−2.01294
$163$	20.0727	1.57221	0.786107	−	0.618090i	$-0.212093\pi$
$163$	20.0727	1.57221	0.786107	+	0.618090i	$0.212093\pi$
$164$	−7.70061	−0.601316
$165$	5.03446	0.391932
$166$	22.0615	1.71230
$167$	21.7829	1.68561	0.842805	−	0.538220i	$-0.180903\pi$
$167$	21.7829	1.68561	0.842805	+	0.538220i	$0.180903\pi$
$168$	−3.97719	−0.306847
$169$	7.81366	0.601051
$170$	−16.1888	−1.24163
$171$	11.8015	0.902482
$172$	−20.9624	−1.59836
$173$	−19.9043	−1.51330	−0.756649	−	0.653821i	$-0.773165\pi$
$173$	−19.9043	−1.51330	−0.756649	+	0.653821i	$0.773165\pi$
$174$	51.5373	3.90703
$175$	−0.494634	−0.0373908
$176$	−2.99057	−0.225423
$177$	6.61728	0.497385
$178$	10.8946	0.816586
$179$	−13.9205	−1.04047	−0.520234	−	0.854024i	$-0.674155\pi$
$179$	−13.9205	−1.04047	−0.520234	+	0.854024i	$0.674155\pi$
$180$	−7.33724	−0.546886
$181$	−4.70635	−0.349820	−0.174910	−	0.984584i	$-0.555963\pi$
$181$	−4.70635	−0.349820	−0.174910	+	0.984584i	$0.555963\pi$
$182$	−5.30082	−0.392923
$183$	15.6284	1.15529
$184$	0	0
$185$	2.00407	0.147342
$186$	−22.5141	−1.65081
$187$	−15.3854	−1.12509
$188$	−13.6421	−0.994955
$189$	1.01986	0.0741842
$190$	−13.2913	−0.964252
$191$	−1.54440	−0.111749	−0.0558746	−	0.998438i	$-0.517795\pi$
$191$	−1.54440	−0.111749	−0.0558746	+	0.998438i	$0.517795\pi$
$192$	−27.1477	−1.95922
$193$	8.99982	0.647821	0.323911	−	0.946088i	$-0.395002\pi$
$193$	8.99982	0.647821	0.323911	+	0.946088i	$0.395002\pi$
$194$	19.2195	1.37988
$195$	−10.2885	−0.736771
$196$	−23.7643	−1.69745
$197$	−24.1665	−1.72179	−0.860897	−	0.508779i	$-0.830097\pi$
$197$	−24.1665	−1.72179	−0.860897	+	0.508779i	$0.830097\pi$
$198$	−10.9375	−0.777292
$199$	16.8860	1.19702	0.598509	−	0.801116i	$-0.295760\pi$
$199$	16.8860	1.19702	0.598509	+	0.801116i	$0.295760\pi$
$200$	3.56547	0.252116
$201$	8.60865	0.607208
$202$	−12.7901	−0.899910
$203$	−4.81221	−0.337751
$204$	54.6745	3.82798
$205$	2.18900	0.152887
$206$	7.10341	0.494918
$207$	0	0
$208$	6.11155	0.423760
$209$	−12.6316	−0.873748
$210$	2.62026	0.180815
$211$	3.39715	0.233869	0.116935	−	0.993140i	$-0.462693\pi$
$211$	3.39715	0.233869	0.116935	+	0.993140i	$0.462693\pi$
$212$	−30.0283	−2.06235
$213$	6.23702	0.427354
$214$	−16.9165	−1.15639
$215$	5.95884	0.406390
$216$	−7.35148	−0.500205
$217$	2.10222	0.142708
$218$	−13.1897	−0.893318
$219$	−24.8630	−1.68009
$220$	7.85336	0.529473
$221$	31.4416	2.11499
$222$	−10.6163	−0.712522
$223$	20.8599	1.39688	0.698442	−	0.715667i	$-0.253877\pi$
$223$	20.8599	1.39688	0.698442	+	0.715667i	$0.253877\pi$
$224$	1.97071	0.131674
$225$	2.08571	0.139048
$226$	0.0807014	0.00536818
$227$	1.65140	0.109608	0.0548038	−	0.998497i	$-0.482547\pi$
$227$	1.65140	0.109608	0.0548038	+	0.998497i	$0.482547\pi$
$228$	44.8886	2.97282
$229$	−9.29749	−0.614395	−0.307198	−	0.951646i	$-0.599391\pi$
$229$	−9.29749	−0.614395	−0.307198	+	0.951646i	$0.599391\pi$
$230$	0	0
$231$	2.49022	0.163844
$232$	34.6878	2.27737
$233$	−17.0042	−1.11398	−0.556991	−	0.830519i	$-0.688044\pi$
$233$	−17.0042	−1.11398	−0.556991	+	0.830519i	$0.688044\pi$
$234$	22.3519	1.46119
$235$	3.87797	0.252971
$236$	10.3224	0.671933
$237$	−33.6516	−2.18591
$238$	−8.00755	−0.519052
$239$	−13.1206	−0.848699	−0.424350	−	0.905498i	$-0.639497\pi$
$239$	−13.1206	−0.848699	−0.424350	+	0.905498i	$0.639497\pi$
$240$	−3.02102	−0.195006
$241$	7.71024	0.496660	0.248330	−	0.968675i	$-0.420118\pi$
$241$	7.71024	0.496660	0.248330	+	0.968675i	$0.420118\pi$
$242$	−14.1323	−0.908458
$243$	−18.4112	−1.18108
$244$	24.3791	1.56071
$245$	6.75534	0.431583
$246$	−11.5960	−0.739333
$247$	25.8141	1.64251
$248$	−15.1534	−0.962241
$249$	21.1799	1.34222
$250$	−2.34901	−0.148565
$251$	19.9137	1.25694	0.628472	−	0.777832i	$-0.283681\pi$
$251$	19.9137	1.25694	0.628472	+	0.777832i	$0.283681\pi$
$252$	−3.62925	−0.228621
$253$	0	0
$254$	20.5939	1.29217
$255$	−15.5420	−0.973277
$256$	−23.6305	−1.47691
$257$	17.1958	1.07265	0.536324	−	0.844012i	$-0.319813\pi$
$257$	17.1958	1.07265	0.536324	+	0.844012i	$0.319813\pi$
$258$	−31.5662	−1.96523
$259$	0.991282	0.0615953
$260$	−16.0492	−0.995327
$261$	20.2915	1.25601
$262$	21.3947	1.32177
$263$	−1.33839	−0.0825284	−0.0412642	−	0.999148i	$-0.513139\pi$
$263$	−1.33839	−0.0825284	−0.0412642	+	0.999148i	$0.513139\pi$
$264$	−17.9502	−1.10476
$265$	8.53595	0.524359
$266$	−6.57433	−0.403098
$267$	10.4593	0.640099
$268$	13.4288	0.820295
$269$	2.41213	0.147070	0.0735352	−	0.997293i	$-0.476572\pi$
$269$	2.41213	0.147070	0.0735352	+	0.997293i	$0.476572\pi$
$270$	4.84333	0.294755
$271$	−2.74558	−0.166782	−0.0833909	−	0.996517i	$-0.526575\pi$
$271$	−2.74558	−0.166782	−0.0833909	+	0.996517i	$0.526575\pi$
$272$	9.23225	0.559787
$273$	−5.08902	−0.308001
$274$	−18.7256	−1.13126
$275$	−2.23243	−0.134620
$276$	0	0
$277$	7.60821	0.457133	0.228566	−	0.973528i	$-0.426596\pi$
$277$	7.60821	0.457133	0.228566	+	0.973528i	$0.426596\pi$
$278$	−14.4008	−0.863700
$279$	−8.86437	−0.530696
$280$	1.76360	0.105395
$281$	−24.7509	−1.47652	−0.738258	−	0.674519i	$-0.764351\pi$
$281$	−24.7509	−1.47652	−0.738258	+	0.674519i	$0.764351\pi$
$282$	−20.5431	−1.22332
$283$	22.8015	1.35541	0.677705	−	0.735334i	$-0.262975\pi$
$283$	22.8015	1.35541	0.677705	+	0.735334i	$0.262975\pi$
$284$	9.72925	0.577325
$285$	−12.7602	−0.755850
$286$	−23.9242	−1.41467
$287$	1.08276	0.0639130
$288$	−8.30986	−0.489663
$289$	30.4964	1.79391
$290$	−22.8531	−1.34198
$291$	18.4515	1.08165
$292$	−38.7844	−2.26968
$293$	6.73722	0.393593	0.196796	−	0.980444i	$-0.436946\pi$
$293$	6.73722	0.393593	0.196796	+	0.980444i	$0.436946\pi$
$294$	−35.7856	−2.08706
$295$	−2.93429	−0.170841
$296$	−7.14545	−0.415321
$297$	4.60295	0.267090
$298$	−45.1721	−2.61675
$299$	0	0
$300$	7.93331	0.458030
$301$	2.94744	0.169888
$302$	8.62294	0.496195
$303$	−12.2791	−0.705414
$304$	7.57983	0.434733
$305$	−6.93009	−0.396816
$306$	33.7653	1.93023
$307$	−3.68462	−0.210292	−0.105146	−	0.994457i	$-0.533531\pi$
$307$	−3.68462	−0.210292	−0.105146	+	0.994457i	$0.533531\pi$
$308$	3.88454	0.221342
$309$	6.81958	0.387953
$310$	9.98340	0.567019
$311$	13.8857	0.787387	0.393694	−	0.919242i	$-0.371197\pi$
$311$	13.8857	0.787387	0.393694	+	0.919242i	$0.371197\pi$
$312$	36.6831	2.07677
$313$	5.61143	0.317177	0.158589	−	0.987345i	$-0.449306\pi$
$313$	5.61143	0.317177	0.158589	+	0.987345i	$0.449306\pi$
$314$	−44.8937	−2.53350
$315$	1.03166	0.0581277
$316$	−52.4938	−2.95301
$317$	−10.8680	−0.610410	−0.305205	−	0.952287i	$-0.598725\pi$
$317$	−10.8680	−0.610410	−0.305205	+	0.952287i	$0.598725\pi$
$318$	−45.2182	−2.53571
$319$	−21.7189	−1.21602
$320$	12.0381	0.672950
$321$	−16.2406	−0.906460
$322$	0	0
$323$	38.9953	2.16976
$324$	−38.3691	−2.13161
$325$	4.56220	0.253065
$326$	47.1510	2.61145
$327$	−12.6627	−0.700246
$328$	−7.80482	−0.430949
$329$	1.91817	0.105752
$330$	11.8260	0.651001
$331$	2.84712	0.156492	0.0782460	−	0.996934i	$-0.475068\pi$
$331$	2.84712	0.156492	0.0782460	+	0.996934i	$0.475068\pi$
$332$	33.0390	1.81325
$333$	−4.17992	−0.229058
$334$	51.1682	2.79980
$335$	−3.81733	−0.208563
$336$	−1.49430	−0.0815206
$337$	1.72210	0.0938085	0.0469042	−	0.998899i	$-0.485064\pi$
$337$	1.72210	0.0938085	0.0469042	+	0.998899i	$0.485064\pi$
$338$	18.3544	0.998346
$339$	0.0774768	0.00420796
$340$	−24.2442	−1.31483
$341$	9.48791	0.513799
$342$	27.7218	1.49903
$343$	6.80385	0.367374
$344$	−21.2460	−1.14551
$345$	0	0
$346$	−46.7555	−2.51359
$347$	−18.8964	−1.01441	−0.507207	−	0.861824i	$-0.669322\pi$
$347$	−18.8964	−1.01441	−0.507207	+	0.861824i	$0.669322\pi$
$348$	77.1818	4.13738
$349$	19.6153	1.04998	0.524992	−	0.851107i	$-0.324068\pi$
$349$	19.6153	1.04998	0.524992	+	0.851107i	$0.324068\pi$
$350$	−1.16190	−0.0621062
$351$	−9.40660	−0.502087
$352$	8.89439	0.474073
$353$	2.72168	0.144860	0.0724302	−	0.997373i	$-0.476925\pi$
$353$	2.72168	0.144860	0.0724302	+	0.997373i	$0.476925\pi$
$354$	15.5441	0.826158
$355$	−2.76568	−0.146787
$356$	16.3157	0.864729
$357$	−7.68759	−0.406870
$358$	−32.6995	−1.72822
$359$	19.7911	1.04453	0.522266	−	0.852783i	$-0.325087\pi$
$359$	19.7911	1.04453	0.522266	+	0.852783i	$0.325087\pi$
$360$	−7.43654	−0.391940
$361$	13.0158	0.685042
$362$	−11.0553	−0.581052
$363$	−13.5676	−0.712115
$364$	−7.93846	−0.416088
$365$	11.0250	0.577074
$366$	36.7113	1.91893
$367$	−2.51429	−0.131245	−0.0656223	−	0.997845i	$-0.520903\pi$
$367$	−2.51429	−0.131245	−0.0656223	+	0.997845i	$0.520903\pi$
$368$	0	0
$369$	−4.56564	−0.237677
$370$	4.70759	0.244736
$371$	4.22217	0.219204
$372$	−33.7169	−1.74814
$373$	31.6115	1.63678	0.818391	−	0.574661i	$-0.194866\pi$
$373$	31.6115	1.63678	0.818391	+	0.574661i	$0.194866\pi$
$374$	−36.1404	−1.86878
$375$	−2.25515	−0.116456
$376$	−13.8268	−0.713061
$377$	44.3848	2.28594
$378$	2.39567	0.123220
$379$	2.11571	0.108677	0.0543385	−	0.998523i	$-0.482695\pi$
$379$	2.11571	0.108677	0.0543385	+	0.998523i	$0.482695\pi$
$380$	−19.9049	−1.02110
$381$	19.7710	1.01290
$382$	−3.62782	−0.185616
$383$	−5.79494	−0.296108	−0.148054	−	0.988979i	$-0.547301\pi$
$383$	−5.79494	−0.296108	−0.148054	+	0.988979i	$0.547301\pi$
$384$	−45.8005	−2.33725
$385$	−1.10423	−0.0562770
$386$	21.1407	1.07603
$387$	−12.4284	−0.631773
$388$	28.7829	1.46123
$389$	−29.2573	−1.48340	−0.741701	−	0.670731i	$-0.765981\pi$
$389$	−29.2573	−1.48340	−0.741701	+	0.670731i	$0.765981\pi$
$390$	−24.1677	−1.22378
$391$	0	0
$392$	−24.0859	−1.21652
$393$	20.5398	1.03610
$394$	−56.7675	−2.85990
$395$	14.9221	0.750813
$396$	−16.3799	−0.823119
$397$	9.24976	0.464232	0.232116	−	0.972688i	$-0.425435\pi$
$397$	9.24976	0.464232	0.232116	+	0.972688i	$0.425435\pi$
$398$	39.6655	1.98825
$399$	−6.31163	−0.315977
$400$	1.33961	0.0669803
$401$	11.6359	0.581070	0.290535	−	0.956864i	$-0.406167\pi$
$401$	11.6359	0.581070	0.290535	+	0.956864i	$0.406167\pi$
$402$	20.2218	1.00857
$403$	−19.3895	−0.965862
$404$	−19.1544	−0.952965
$405$	10.9069	0.541970
$406$	−11.3039	−0.561005
$407$	4.47395	0.221765
$408$	55.4144	2.74342
$409$	−13.3198	−0.658622	−0.329311	−	0.944221i	$-0.606817\pi$
$409$	−13.3198	−0.658622	−0.329311	+	0.944221i	$0.606817\pi$
$410$	5.14200	0.253945
$411$	−17.9774	−0.886761
$412$	10.6380	0.524097
$413$	−1.45140	−0.0714188
$414$	0	0
$415$	−9.39180	−0.461025
$416$	−18.1766	−0.891182
$417$	−13.8253	−0.677030
$418$	−29.6719	−1.45130
$419$	−34.7010	−1.69525	−0.847626	−	0.530594i	$-0.821969\pi$
$419$	−34.7010	−1.69525	−0.847626	+	0.530594i	$0.821969\pi$
$420$	3.92408	0.191476
$421$	−13.8992	−0.677406	−0.338703	−	0.940893i	$-0.609988\pi$
$421$	−13.8992	−0.677406	−0.338703	+	0.940893i	$0.609988\pi$
$422$	7.97994	0.388457
$423$	−8.08833	−0.393268
$424$	−30.4346	−1.47804
$425$	6.89177	0.334300
$426$	14.6508	0.709835
$427$	−3.42786	−0.165886
$428$	−25.3340	−1.22456
$429$	−22.9682	−1.10892
$430$	13.9974	0.675014
$431$	19.0719	0.918659	0.459329	−	0.888266i	$-0.348090\pi$
$431$	19.0719	0.918659	0.459329	+	0.888266i	$0.348090\pi$
$432$	−2.76208	−0.132890
$433$	−11.9976	−0.576567	−0.288283	−	0.957545i	$-0.593085\pi$
$433$	−11.9976	−0.576567	−0.288283	+	0.957545i	$0.593085\pi$
$434$	4.93813	0.237038
$435$	−21.9400	−1.05194
$436$	−19.7527	−0.945984
$437$	0	0
$438$	−58.4036	−2.79063
$439$	12.9772	0.619369	0.309685	−	0.950839i	$-0.399777\pi$
$439$	12.9772	0.619369	0.309685	+	0.950839i	$0.399777\pi$
$440$	7.95964	0.379461
$441$	−14.0897	−0.670938
$442$	73.8567	3.51300
$443$	−17.1214	−0.813464	−0.406732	−	0.913547i	$-0.633332\pi$
$443$	−17.1214	−0.813464	−0.406732	+	0.913547i	$0.633332\pi$
$444$	−15.8989	−0.754529
$445$	−4.63796	−0.219860
$446$	49.0002	2.32023
$447$	−43.3671	−2.05120
$448$	5.95445	0.281321
$449$	−19.1333	−0.902956	−0.451478	−	0.892282i	$-0.649103\pi$
$449$	−19.1333	−0.902956	−0.451478	+	0.892282i	$0.649103\pi$
$450$	4.89936	0.230958
$451$	4.88679	0.230110
$452$	0.120858	0.00568466
$453$	8.27840	0.388953
$454$	3.87917	0.182058
$455$	2.25662	0.105792
$456$	45.4961	2.13055
$457$	10.6979	0.500426	0.250213	−	0.968191i	$-0.419499\pi$
$457$	10.6979	0.500426	0.250213	+	0.968191i	$0.419499\pi$
$458$	−21.8399	−1.02051
$459$	−14.2098	−0.663258
$460$	0	0
$461$	−28.0303	−1.30550	−0.652751	−	0.757573i	$-0.726385\pi$
$461$	−28.0303	−1.30550	−0.652751	+	0.757573i	$0.726385\pi$
$462$	5.84955	0.272146
$463$	23.4454	1.08960	0.544800	−	0.838566i	$-0.316606\pi$
$463$	23.4454	1.08960	0.544800	+	0.838566i	$0.316606\pi$
$464$	13.0328	0.605032
$465$	9.58450	0.444470
$466$	−39.9431	−1.85033
$467$	27.3912	1.26751	0.633756	−	0.773533i	$-0.281512\pi$
$467$	27.3912	1.26751	0.633756	+	0.773533i	$0.281512\pi$
$468$	33.4739	1.54733
$469$	−1.88818	−0.0871880
$470$	9.10939	0.420185
$471$	−43.0999	−1.98594
$472$	10.4621	0.481558
$473$	13.3027	0.611658
$474$	−79.0481	−3.63080
$475$	5.65825	0.259618
$476$	−11.9920	−0.549653
$477$	−17.8035	−0.815168
$478$	−30.8204	−1.40969
$479$	−21.2126	−0.969230	−0.484615	−	0.874728i	$-0.661040\pi$
$479$	−21.2126	−0.969230	−0.484615	+	0.874728i	$0.661040\pi$
$480$	8.98493	0.410104
$481$	−9.14298	−0.416884
$482$	18.1114	0.824953
$483$	0	0
$484$	−21.1644	−0.962017
$485$	−8.18195	−0.371523
$486$	−43.2482	−1.96178
$487$	40.9912	1.85749	0.928745	−	0.370719i	$-0.120889\pi$
$487$	40.9912	1.85749	0.928745	+	0.370719i	$0.120889\pi$
$488$	24.7090	1.11852
$489$	45.2670	2.04704
$490$	15.8684	0.716860
$491$	26.7388	1.20670	0.603352	−	0.797475i	$-0.293831\pi$
$491$	26.7388	1.20670	0.603352	+	0.797475i	$0.293831\pi$
$492$	−17.3660	−0.782922
$493$	67.0488	3.01973
$494$	60.6375	2.72821
$495$	4.65620	0.209281
$496$	−5.69338	−0.255641
$497$	−1.36800	−0.0613630
$498$	49.7519	2.22944
$499$	27.6800	1.23913	0.619564	−	0.784946i	$-0.287309\pi$
$499$	27.6800	1.23913	0.619564	+	0.784946i	$0.287309\pi$
$500$	−3.51786	−0.157323
$501$	49.1237	2.19469
$502$	46.7776	2.08779
$503$	−17.4957	−0.780094	−0.390047	−	0.920795i	$-0.627541\pi$
$503$	−17.4957	−0.780094	−0.390047	+	0.920795i	$0.627541\pi$
$504$	−3.67836	−0.163847
$505$	5.44489	0.242295
$506$	0	0
$507$	17.6210	0.782576
$508$	30.8412	1.36836
$509$	23.5959	1.04587	0.522936	−	0.852372i	$-0.324837\pi$
$509$	23.5959	1.04587	0.522936	+	0.852372i	$0.324837\pi$
$510$	−36.5083	−1.61661
$511$	5.45333	0.241241
$512$	−14.8899	−0.658045
$513$	−11.6665	−0.515089
$514$	40.3932	1.78167
$515$	−3.02400	−0.133253
$516$	−47.2733	−2.08109
$517$	8.65728	0.380747
$518$	2.32853	0.102310
$519$	−44.8873	−1.97033
$520$	−16.2664	−0.713327
$521$	37.3615	1.63684	0.818419	−	0.574622i	$-0.194851\pi$
$521$	37.3615	1.63684	0.818419	+	0.574622i	$0.194851\pi$
$522$	47.6651	2.08624
$523$	29.1713	1.27557	0.637786	−	0.770213i	$-0.279850\pi$
$523$	29.1713	1.27557	0.637786	+	0.770213i	$0.279850\pi$
$524$	32.0405	1.39970
$525$	−1.11547	−0.0486833
$526$	−3.14389	−0.137080
$527$	−29.2903	−1.27591
$528$	−6.74420	−0.293504
$529$	0	0
$530$	20.0511	0.870962
$531$	6.12010	0.265590
$532$	−9.84565	−0.426863
$533$	−9.98668	−0.432571
$534$	24.5690	1.06321
$535$	7.20154	0.311350
$536$	13.6105	0.587886
$537$	−31.3929	−1.35470
$538$	5.66613	0.244284
$539$	15.0808	0.649576
$540$	7.25332	0.312133
$541$	2.28159	0.0980932	0.0490466	−	0.998796i	$-0.484382\pi$
$541$	2.28159	0.0980932	0.0490466	+	0.998796i	$0.484382\pi$
$542$	−6.44939	−0.277025
$543$	−10.6135	−0.455470
$544$	−27.4580	−1.17725
$545$	5.61499	0.240520
$546$	−11.9542	−0.511591
$547$	10.2325	0.437508	0.218754	−	0.975780i	$-0.429801\pi$
$547$	10.2325	0.437508	0.218754	+	0.975780i	$0.429801\pi$
$548$	−28.0433	−1.19795
$549$	14.4542	0.616889
$550$	−5.24400	−0.223605
$551$	55.0481	2.34513
$552$	0	0
$553$	7.38098	0.313871
$554$	17.8718	0.759299
$555$	4.51949	0.191842
$556$	−21.5664	−0.914620
$557$	0.427459	0.0181120	0.00905600	−	0.999959i	$-0.497117\pi$
$557$	0.427459	0.0181120	0.00905600	+	0.999959i	$0.497117\pi$
$558$	−20.8225	−0.881487
$559$	−27.1854	−1.14982
$560$	0.662614	0.0280006
$561$	−34.6963	−1.46488
$562$	−58.1402	−2.45250
$563$	−13.6979	−0.577299	−0.288650	−	0.957435i	$-0.593206\pi$
$563$	−13.6979	−0.577299	−0.288650	+	0.957435i	$0.593206\pi$
$564$	−30.7651	−1.29544
$565$	−0.0343555	−0.00144534
$566$	53.5611	2.25134
$567$	5.39494	0.226566
$568$	9.86092	0.413755
$569$	−40.5548	−1.70014	−0.850072	−	0.526667i	$-0.823442\pi$
$569$	−40.5548	−1.70014	−0.850072	+	0.526667i	$0.823442\pi$
$570$	−29.9739	−1.25547
$571$	34.5903	1.44756	0.723780	−	0.690031i	$-0.242403\pi$
$571$	34.5903	1.44756	0.723780	+	0.690031i	$0.242403\pi$
$572$	−35.8286	−1.49807
$573$	−3.48287	−0.145499
$574$	2.54341	0.106160
$575$	0	0
$576$	−25.1080	−1.04617
$577$	−23.7472	−0.988609	−0.494304	−	0.869289i	$-0.664577\pi$
$577$	−23.7472	−0.988609	−0.494304	+	0.869289i	$0.664577\pi$
$578$	71.6365	2.97968
$579$	20.2960	0.843472
$580$	−34.2246	−1.42110
$581$	−4.64550	−0.192728
$582$	43.3429	1.79662
$583$	19.0559	0.789214
$584$	−39.3092	−1.62663
$585$	−9.51544	−0.393415
$586$	15.8258	0.653758
$587$	24.0024	0.990684	0.495342	−	0.868698i	$-0.335043\pi$
$587$	24.0024	0.990684	0.495342	+	0.868698i	$0.335043\pi$
$588$	−53.5922	−2.21010
$589$	−24.0478	−0.990873
$590$	−6.89269	−0.283768
$591$	−54.4992	−2.24180
$592$	−2.68467	−0.110339
$593$	33.9593	1.39454	0.697272	−	0.716807i	$-0.254397\pi$
$593$	33.9593	1.39454	0.697272	+	0.716807i	$0.254397\pi$
$594$	10.8124	0.443637
$595$	3.40890	0.139751
$596$	−67.6493	−2.77102
$597$	38.0806	1.55853
$598$	0	0
$599$	2.55000	0.104190	0.0520950	−	0.998642i	$-0.483410\pi$
$599$	2.55000	0.104190	0.0520950	+	0.998642i	$0.483410\pi$
$600$	8.04067	0.328259
$601$	29.6098	1.20781	0.603905	−	0.797057i	$-0.293611\pi$
$601$	29.6098	1.20781	0.603905	+	0.797057i	$0.293611\pi$
$602$	6.92358	0.282184
$603$	7.96185	0.324231
$604$	12.9136	0.525448
$605$	6.01627	0.244596
$606$	−28.8437	−1.17169
$607$	−24.9533	−1.01282	−0.506412	−	0.862292i	$-0.669028\pi$
$607$	−24.9533	−1.01282	−0.506412	+	0.862292i	$0.669028\pi$
$608$	−22.5435	−0.914259
$609$	−10.8523	−0.439756
$610$	−16.2789	−0.659112
$611$	−17.6921	−0.715744
$612$	50.5665	2.04403
$613$	6.41643	0.259157	0.129579	−	0.991569i	$-0.458638\pi$
$613$	6.41643	0.259157	0.129579	+	0.991569i	$0.458638\pi$
$614$	−8.65521	−0.349296
$615$	4.93654	0.199060
$616$	3.93711	0.158631
$617$	38.0734	1.53278	0.766389	−	0.642376i	$-0.222051\pi$
$617$	38.0734	1.53278	0.766389	+	0.642376i	$0.222051\pi$
$618$	16.0193	0.644390
$619$	5.71345	0.229643	0.114822	−	0.993386i	$-0.463370\pi$
$619$	5.71345	0.229643	0.114822	+	0.993386i	$0.463370\pi$
$620$	14.9510	0.600449
$621$	0	0
$622$	32.6177	1.30785
$623$	−2.29409	−0.0919108
$624$	13.7825	0.551741
$625$	1.00000	0.0400000
$626$	13.1813	0.526832
$627$	−28.4863	−1.13763
$628$	−67.2323	−2.68286
$629$	−13.8116	−0.550705
$630$	2.42339	0.0965502
$631$	7.64585	0.304377	0.152188	−	0.988352i	$-0.451368\pi$
$631$	7.64585	0.304377	0.152188	+	0.988352i	$0.451368\pi$
$632$	−53.2042	−2.11635
$633$	7.66109	0.304501
$634$	−25.5292	−1.01389
$635$	−8.76703	−0.347909
$636$	−67.7183	−2.68521
$637$	−30.8192	−1.22110
$638$	−51.0180	−2.01982
$639$	5.76841	0.228195
$640$	20.3093	0.802795
$641$	17.9279	0.708111	0.354056	−	0.935224i	$-0.384802\pi$
$641$	17.9279	0.708111	0.354056	+	0.935224i	$0.384802\pi$
$642$	−38.1493	−1.50563
$643$	−46.9101	−1.84995	−0.924977	−	0.380024i	$-0.875916\pi$
$643$	−46.9101	−1.84995	−0.924977	+	0.380024i	$0.875916\pi$
$644$	0	0
$645$	13.4381	0.529124
$646$	91.6005	3.60397
$647$	−28.5017	−1.12052	−0.560259	−	0.828317i	$-0.689298\pi$
$647$	−28.5017	−1.12052	−0.560259	+	0.828317i	$0.689298\pi$
$648$	−38.8883	−1.52768
$649$	−6.55060	−0.257134
$650$	10.7167	0.420342
$651$	4.74082	0.185807
$652$	70.6129	2.76541
$653$	−30.3319	−1.18698	−0.593490	−	0.804841i	$-0.702250\pi$
$653$	−30.3319	−1.18698	−0.593490	+	0.804841i	$0.702250\pi$
$654$	−29.7447	−1.16311
$655$	−9.10796	−0.355877
$656$	−2.93240	−0.114491
$657$	−22.9950	−0.897119
$658$	4.50581	0.175655
$659$	−13.2694	−0.516901	−0.258450	−	0.966025i	$-0.583212\pi$
$659$	−13.2694	−0.516901	−0.258450	+	0.966025i	$0.583212\pi$
$660$	17.7105	0.689381
$661$	−17.8102	−0.692736	−0.346368	−	0.938099i	$-0.612585\pi$
$661$	−17.8102	−0.692736	−0.346368	+	0.938099i	$0.612585\pi$
$662$	6.68792	0.259934
$663$	70.9056	2.75375
$664$	33.4861	1.29951
$665$	2.79876	0.108531
$666$	−9.81868	−0.380466
$667$	0	0
$668$	76.6290	2.96487
$669$	47.0423	1.81876
$670$	−8.96694	−0.346423
$671$	−15.4709	−0.597248
$672$	4.44425	0.171441
$673$	37.3809	1.44093	0.720465	−	0.693492i	$-0.243929\pi$
$673$	37.3809	1.44093	0.720465	+	0.693492i	$0.243929\pi$
$674$	4.04522	0.155816
$675$	−2.06186	−0.0793609
$676$	27.4873	1.05721
$677$	−35.2861	−1.35616	−0.678078	−	0.734990i	$-0.737187\pi$
$677$	−35.2861	−1.35616	−0.678078	+	0.734990i	$0.737187\pi$
$678$	0.181994	0.00698943
$679$	−4.04707	−0.155312
$680$	−24.5723	−0.942307
$681$	3.72417	0.142710
$682$	22.2872	0.853422
$683$	−34.3529	−1.31448	−0.657240	−	0.753682i	$-0.728276\pi$
$683$	−34.3529	−1.31448	−0.657240	+	0.753682i	$0.728276\pi$
$684$	41.5159	1.58740
$685$	7.97171	0.304583
$686$	15.9823	0.610208
$687$	−20.9673	−0.799951
$688$	−7.98250	−0.304330
$689$	−38.9427	−1.48360
$690$	0	0
$691$	47.3016	1.79944	0.899719	−	0.436470i	$-0.143772\pi$
$691$	47.3016	1.79944	0.899719	+	0.436470i	$0.143772\pi$
$692$	−70.0206	−2.66178
$693$	2.30311	0.0874881
$694$	−44.3879	−1.68494
$695$	6.13056	0.232545
$696$	78.2263	2.96516
$697$	−15.0861	−0.571427
$698$	46.0766	1.74403
$699$	−38.3471	−1.45042
$700$	−1.74005	−0.0657677
$701$	14.0290	0.529867	0.264933	−	0.964267i	$-0.414650\pi$
$701$	14.0290	0.529867	0.264933	+	0.964267i	$0.414650\pi$
$702$	−22.0962	−0.833968
$703$	−11.3395	−0.427679
$704$	26.8742	1.01286
$705$	8.74541	0.329371
$706$	6.39326	0.240613
$707$	2.69323	0.101289
$708$	23.2787	0.874865
$709$	7.04046	0.264410	0.132205	−	0.991222i	$-0.457794\pi$
$709$	7.04046	0.264410	0.132205	+	0.991222i	$0.457794\pi$
$710$	−6.49661	−0.243813
$711$	−31.1232	−1.16721
$712$	16.5365	0.619731
$713$	0	0
$714$	−18.0582	−0.675813
$715$	10.1848	0.380889
$716$	−48.9704	−1.83011
$717$	−29.5889	−1.10502
$718$	46.4894	1.73497
$719$	17.0649	0.636413	0.318207	−	0.948021i	$-0.396919\pi$
$719$	17.0649	0.636413	0.318207	+	0.948021i	$0.396919\pi$
$720$	−2.79403	−0.104127
$721$	−1.49577	−0.0557055
$722$	30.5743	1.13786
$723$	17.3878	0.646658
$724$	−16.5563	−0.615308
$725$	9.72883	0.361320
$726$	−31.8705	−1.18282
$727$	−3.42967	−0.127199	−0.0635996	−	0.997975i	$-0.520258\pi$
$727$	−3.42967	−0.127199	−0.0635996	+	0.997975i	$0.520258\pi$
$728$	−8.04589	−0.298201
$729$	−8.79934	−0.325902
$730$	25.8978	0.958522
$731$	−41.0669	−1.51892
$732$	54.9785	2.03206
$733$	−8.77340	−0.324053	−0.162027	−	0.986786i	$-0.551803\pi$
$733$	−8.77340	−0.324053	−0.162027	+	0.986786i	$0.551803\pi$
$734$	−5.90609	−0.217998
$735$	15.2343	0.561926
$736$	0	0
$737$	−8.52190	−0.313908
$738$	−10.7247	−0.394783
$739$	12.7296	0.468267	0.234134	−	0.972204i	$-0.424775\pi$
$739$	12.7296	0.468267	0.234134	+	0.972204i	$0.424775\pi$
$740$	7.05004	0.259165
$741$	58.2147	2.13857
$742$	9.91793	0.364099
$743$	−5.36184	−0.196707	−0.0983535	−	0.995152i	$-0.531358\pi$
$743$	−5.36184	−0.196707	−0.0983535	+	0.995152i	$0.531358\pi$
$744$	−34.1732	−1.25285
$745$	19.2302	0.704542
$746$	74.2559	2.71870
$747$	19.5886	0.716709
$748$	−54.1235	−1.97895
$749$	3.56213	0.130157
$750$	−5.29738	−0.193433
$751$	−13.7796	−0.502825	−0.251412	−	0.967880i	$-0.580895\pi$
$751$	−13.7796	−0.502825	−0.251412	+	0.967880i	$0.580895\pi$
$752$	−5.19495	−0.189440
$753$	44.9085	1.63656
$754$	104.261	3.79694
$755$	−3.67088	−0.133597
$756$	3.58774	0.130485
$757$	39.0506	1.41932	0.709658	−	0.704546i	$-0.248849\pi$
$757$	39.0506	1.41932	0.709658	+	0.704546i	$0.248849\pi$
$758$	4.96984	0.180513
$759$	0	0
$760$	−20.1743	−0.731799
$761$	7.33796	0.266001	0.133000	−	0.991116i	$-0.457539\pi$
$761$	7.33796	0.266001	0.133000	+	0.991116i	$0.457539\pi$
$762$	46.4423	1.68243
$763$	2.77736	0.100547
$764$	−5.43299	−0.196559
$765$	−14.3742	−0.519702
$766$	−13.6124	−0.491836
$767$	13.3868	0.483371
$768$	−53.2905	−1.92295
$769$	−37.9449	−1.36833	−0.684165	−	0.729327i	$-0.739833\pi$
$769$	−37.9449	−1.36833	−0.684165	+	0.729327i	$0.739833\pi$
$770$	−2.59386	−0.0934762
$771$	38.7792	1.39660
$772$	31.6601	1.13947
$773$	−42.9259	−1.54394	−0.771969	−	0.635660i	$-0.780728\pi$
$773$	−42.9259	−1.54394	−0.771969	+	0.635660i	$0.780728\pi$
$774$	−29.1945	−1.04938
$775$	−4.25004	−0.152666
$776$	29.1724	1.04723
$777$	2.23549	0.0801978
$778$	−68.7257	−2.46393
$779$	−12.3859	−0.443772
$780$	−36.1933	−1.29593
$781$	−6.17417	−0.220929
$782$	0	0
$783$	−20.0595	−0.716866
$784$	−9.04949	−0.323196
$785$	19.1117	0.682127
$786$	48.2483	1.72096
$787$	−42.7050	−1.52227	−0.761134	−	0.648595i	$-0.775357\pi$
$787$	−42.7050	−1.52227	−0.761134	+	0.648595i	$0.775357\pi$
$788$	−85.0144	−3.02851
$789$	−3.01827	−0.107453
$790$	35.0522	1.24710
$791$	−0.0169934	−0.000604215 0
$792$	−16.6015	−0.589910
$793$	31.6164	1.12273
$794$	21.7278	0.771091
$795$	19.2499	0.682723
$796$	59.4026	2.10547
$797$	30.7951	1.09082	0.545409	−	0.838170i	$-0.316374\pi$
$797$	30.7951	1.09082	0.545409	+	0.838170i	$0.316374\pi$
$798$	−14.8261	−0.524838
$799$	−26.7260	−0.945499
$800$	−3.98418	−0.140862
$801$	9.67345	0.341794
$802$	27.3329	0.965158
$803$	24.6125	0.868556
$804$	30.2840	1.06803
$805$	0	0
$806$	−45.5463	−1.60430
$807$	5.43973	0.191488
$808$	−19.4136	−0.682967
$809$	−4.11424	−0.144649	−0.0723246	−	0.997381i	$-0.523042\pi$
$809$	−4.11424	−0.144649	−0.0723246	+	0.997381i	$0.523042\pi$
$810$	25.6205	0.900214
$811$	22.6586	0.795651	0.397825	−	0.917461i	$-0.369765\pi$
$811$	22.6586	0.795651	0.397825	+	0.917461i	$0.369765\pi$
$812$	−16.9287	−0.594079
$813$	−6.19169	−0.217152
$814$	10.5094	0.368353
$815$	−20.0727	−0.703116
$816$	20.8201	0.728850
$817$	−33.7166	−1.17960
$818$	−31.2884	−1.09397
$819$	−4.70666	−0.164464
$820$	7.70061	0.268917
$821$	−39.1107	−1.36497	−0.682486	−	0.730898i	$-0.739101\pi$
$821$	−39.1107	−1.36497	−0.682486	+	0.730898i	$0.739101\pi$
$822$	−42.2292	−1.47291
$823$	−22.3911	−0.780506	−0.390253	−	0.920708i	$-0.627612\pi$
$823$	−22.3911	−0.780506	−0.390253	+	0.920708i	$0.627612\pi$
$824$	10.7820	0.375608
$825$	−5.03446	−0.175278
$826$	−3.40936	−0.118627
$827$	29.9594	1.04179	0.520896	−	0.853620i	$-0.325598\pi$
$827$	29.9594	1.04179	0.520896	+	0.853620i	$0.325598\pi$
$828$	0	0
$829$	−23.0543	−0.800709	−0.400354	−	0.916360i	$-0.631113\pi$
$829$	−23.0543	−0.800709	−0.400354	+	0.916360i	$0.631113\pi$
$830$	−22.0615	−0.765764
$831$	17.1577	0.595193
$832$	−54.9202	−1.90402
$833$	−46.5562	−1.61308
$834$	−32.4759	−1.12455
$835$	−21.7829	−0.753827
$836$	−44.4363	−1.53686
$837$	8.76298	0.302893
$838$	−81.5130	−2.81582
$839$	9.28384	0.320514	0.160257	−	0.987075i	$-0.448768\pi$
$839$	9.28384	0.320514	0.160257	+	0.987075i	$0.448768\pi$
$840$	3.97719	0.137226
$841$	65.6501	2.26380
$842$	−32.6494	−1.12517
$843$	−55.8171	−1.92244
$844$	11.9507	0.411359
$845$	−7.81366	−0.268798
$846$	−18.9996	−0.653219
$847$	2.97585	0.102251
$848$	−11.4348	−0.392673
$849$	51.4209	1.76476
$850$	16.1888	0.555273
$851$	0	0
$852$	21.9410	0.751685
$853$	−9.92931	−0.339973	−0.169987	−	0.985446i	$-0.554372\pi$
$853$	−9.92931	−0.339973	−0.169987	+	0.985446i	$0.554372\pi$
$854$	−8.05208	−0.275536
$855$	−11.8015	−0.403602
$856$	−25.6768	−0.877616
$857$	31.2213	1.06650	0.533249	−	0.845958i	$-0.320971\pi$
$857$	31.2213	1.06650	0.533249	+	0.845958i	$0.320971\pi$
$858$	−53.9526	−1.84191
$859$	−49.7545	−1.69760	−0.848800	−	0.528714i	$-0.822674\pi$
$859$	−49.7545	−1.69760	−0.848800	+	0.528714i	$0.822674\pi$
$860$	20.9624	0.714810
$861$	2.44178	0.0832156
$862$	44.8000	1.52589
$863$	7.75815	0.264090	0.132045	−	0.991244i	$-0.457846\pi$
$863$	7.75815	0.264090	0.132045	+	0.991244i	$0.457846\pi$
$864$	8.21481	0.279473
$865$	19.9043	0.676768
$866$	−28.1825	−0.957679
$867$	68.7741	2.33569
$868$	7.39529	0.251013
$869$	33.3125	1.13005
$870$	−51.5373	−1.74728
$871$	17.4154	0.590098
$872$	−20.0200	−0.677964
$873$	17.0652	0.577569
$874$	0	0
$875$	0.494634	0.0167217
$876$	−87.4646	−2.95516
$877$	−37.6296	−1.27066	−0.635331	−	0.772240i	$-0.719136\pi$
$877$	−37.6296	−1.27066	−0.635331	+	0.772240i	$0.719136\pi$
$878$	30.4837	1.02877
$879$	15.1935	0.512463
$880$	2.99057	0.100812
$881$	−10.7533	−0.362289	−0.181145	−	0.983456i	$-0.557980\pi$
$881$	−10.7533	−0.362289	−0.181145	+	0.983456i	$0.557980\pi$
$882$	−33.0969	−1.11443
$883$	31.3604	1.05536	0.527680	−	0.849443i	$-0.323062\pi$
$883$	31.3604	1.05536	0.527680	+	0.849443i	$0.323062\pi$
$884$	110.607	3.72012
$885$	−6.61728	−0.222438
$886$	−40.2185	−1.35117
$887$	−1.57763	−0.0529716	−0.0264858	−	0.999649i	$-0.508432\pi$
$887$	−1.57763	−0.0529716	−0.0264858	+	0.999649i	$0.508432\pi$
$888$	−16.1141	−0.540753
$889$	−4.33647	−0.145441
$890$	−10.8946	−0.365188
$891$	24.3490	0.815721
$892$	73.3822	2.45702
$893$	−21.9425	−0.734278
$894$	−101.870	−3.40704
$895$	13.9205	0.465312
$896$	10.0457	0.335602
$897$	0	0
$898$	−44.9444	−1.49981
$899$	−41.3479	−1.37903
$900$	7.33724	0.244575
$901$	−58.8278	−1.95984
$902$	11.4791	0.382213
$903$	6.64694	0.221196
$904$	0.122493	0.00407406
$905$	4.70635	0.156444
$906$	19.4461	0.646052
$907$	2.97740	0.0988629	0.0494315	−	0.998778i	$-0.484259\pi$
$907$	2.97740	0.0988629	0.0494315	+	0.998778i	$0.484259\pi$
$908$	5.80940	0.192792
$909$	−11.3565	−0.376671
$910$	5.30082	0.175721
$911$	19.1980	0.636058	0.318029	−	0.948081i	$-0.396979\pi$
$911$	19.1980	0.636058	0.318029	+	0.948081i	$0.396979\pi$
$912$	17.0937	0.566028
$913$	−20.9665	−0.693890
$914$	25.1295	0.831209
$915$	−15.6284	−0.516659
$916$	−32.7072	−1.08068
$917$	−4.50510	−0.148772
$918$	−33.3791	−1.10167
$919$	−35.3843	−1.16722	−0.583611	−	0.812034i	$-0.698361\pi$
$919$	−35.3843	−1.16722	−0.583611	+	0.812034i	$0.698361\pi$
$920$	0	0
$921$	−8.30938	−0.273803
$922$	−65.8435	−2.16844
$923$	12.6176	0.415312
$924$	8.76022	0.288190
$925$	−2.00407	−0.0658935
$926$	55.0735	1.80983
$927$	6.30720	0.207156
$928$	−38.7614	−1.27241
$929$	−4.06550	−0.133385	−0.0666923	−	0.997774i	$-0.521245\pi$
$929$	−4.06550	−0.133385	−0.0666923	+	0.997774i	$0.521245\pi$
$930$	22.5141	0.738266
$931$	−38.2234	−1.25272
$932$	−59.8183	−1.95941
$933$	31.3144	1.02519
$934$	64.3421	2.10534
$935$	15.3854	0.503155
$936$	33.9270	1.10894
$937$	27.2526	0.890303	0.445151	−	0.895455i	$-0.353150\pi$
$937$	27.2526	0.890303	0.445151	+	0.895455i	$0.353150\pi$
$938$	−4.43535	−0.144819
$939$	12.6546	0.412969
$940$	13.6421	0.444957
$941$	−25.2072	−0.821733	−0.410866	−	0.911696i	$-0.634774\pi$
$941$	−25.2072	−0.821733	−0.410866	+	0.911696i	$0.634774\pi$
$942$	−101.242	−3.29865
$943$	0	0
$944$	3.93080	0.127937
$945$	−1.01986	−0.0331762
$946$	31.2482	1.01596
$947$	−6.91551	−0.224724	−0.112362	−	0.993667i	$-0.535842\pi$
$947$	−6.91551	−0.224724	−0.112362	+	0.993667i	$0.535842\pi$
$948$	−118.382	−3.84486
$949$	−50.2982	−1.63275
$950$	13.2913	0.431227
$951$	−24.5091	−0.794762
$952$	−12.1543	−0.393924
$953$	−49.2862	−1.59654	−0.798269	−	0.602302i	$-0.794250\pi$
$953$	−49.2862	−1.59654	−0.798269	+	0.602302i	$0.794250\pi$
$954$	−41.8207	−1.35400
$955$	1.54440	0.0499758
$956$	−46.1563	−1.49280
$957$	−48.9794	−1.58328
$958$	−49.8287	−1.60989
$959$	3.94308	0.127329
$960$	27.1477	0.876190
$961$	−12.9371	−0.417327
$962$	−21.4770	−0.692445
$963$	−15.0203	−0.484024
$964$	27.1235	0.873590
$965$	−8.99982	−0.289715
$966$	0	0
$967$	31.3567	1.00836	0.504182	−	0.863598i	$-0.331794\pi$
$967$	31.3567	1.00836	0.504182	+	0.863598i	$0.331794\pi$
$968$	−21.4508	−0.689455
$969$	87.9404	2.82505
$970$	−19.2195	−0.617101
$971$	29.7345	0.954226	0.477113	−	0.878842i	$-0.341683\pi$
$971$	29.7345	0.954226	0.477113	+	0.878842i	$0.341683\pi$
$972$	−64.7681	−2.07744
$973$	3.03238	0.0972136
$974$	96.2889	3.08530
$975$	10.2885	0.329494
$976$	9.28359	0.297160
$977$	3.29774	0.105504	0.0527521	−	0.998608i	$-0.483201\pi$
$977$	3.29774	0.105504	0.0527521	+	0.998608i	$0.483201\pi$
$978$	106.333	3.40014
$979$	−10.3539	−0.330912
$980$	23.7643	0.759123
$981$	−11.7113	−0.373912
$982$	62.8097	2.00434
$983$	−36.1905	−1.15430	−0.577148	−	0.816640i	$-0.695834\pi$
$983$	−36.1905	−1.15430	−0.577148	+	0.816640i	$0.695834\pi$
$984$	−17.6011	−0.561101
$985$	24.1665	0.770010
$986$	157.498	5.01577
$987$	4.32577	0.137691
$988$	90.8102	2.88906
$989$	0	0
$990$	10.9375	0.347616
$991$	−33.0860	−1.05101	−0.525505	−	0.850790i	$-0.676124\pi$
$991$	−33.0860	−1.05101	−0.525505	+	0.850790i	$0.676124\pi$
$992$	16.9329	0.537621
$993$	6.42070	0.203755
$994$	−3.21344	−0.101924
$995$	−16.8860	−0.535323
$996$	74.5080	2.36088
$997$	16.5898	0.525405	0.262703	−	0.964877i	$-0.415386\pi$
$997$	16.5898	0.525405	0.262703	+	0.964877i	$0.415386\pi$
$998$	65.0207	2.05819
$999$	4.13211	0.130734

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2645.2.a.x.1.21		25
23.11	odd	22		115.2.g.c.6.5	✓	50
23.21	odd	22		115.2.g.c.96.5	yes	50
23.22	odd	2		2645.2.a.y.1.21		25
115.34	odd	22		575.2.k.d.351.1		50
115.44	odd	22		575.2.k.d.326.1		50
115.57	even	44		575.2.p.d.374.9		100
115.67	even	44		575.2.p.d.349.2		100
115.103	even	44		575.2.p.d.374.2		100
115.113	even	44		575.2.p.d.349.9		100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.g.c.6.5	✓	50	23.11	odd	22
115.2.g.c.96.5	yes	50	23.21	odd	22
575.2.k.d.326.1		50	115.44	odd	22
575.2.k.d.351.1		50	115.34	odd	22
575.2.p.d.349.2		100	115.67	even	44
575.2.p.d.349.9		100	115.113	even	44
575.2.p.d.374.2		100	115.103	even	44
575.2.p.d.374.9		100	115.57	even	44
2645.2.a.x.1.21		25	1.1	even	1	trivial
2645.2.a.y.1.21		25	23.22	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2645 = 5 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2645.a (trivial)

\(f(q)\)	\(=\)	\(q+2.34901 q^{2} +2.25515 q^{3} +3.51786 q^{4} -1.00000 q^{5} +5.29738 q^{6} -0.494634 q^{7} +3.56547 q^{8} +2.08571 q^{9} +O(q^{10})\)	\(q+2.34901 q^{2} +2.25515 q^{3} +3.51786 q^{4} -1.00000 q^{5} +5.29738 q^{6} -0.494634 q^{7} +3.56547 q^{8} +2.08571 q^{9} -2.34901 q^{10} -2.23243 q^{11} +7.93331 q^{12} +4.56220 q^{13} -1.16190 q^{14} -2.25515 q^{15} +1.33961 q^{16} +6.89177 q^{17} +4.89936 q^{18} +5.65825 q^{19} -3.51786 q^{20} -1.11547 q^{21} -5.24400 q^{22} +8.04067 q^{24} +1.00000 q^{25} +10.7167 q^{26} -2.06186 q^{27} -1.74005 q^{28} +9.72883 q^{29} -5.29738 q^{30} -4.25004 q^{31} -3.98418 q^{32} -5.03446 q^{33} +16.1888 q^{34} +0.494634 q^{35} +7.33724 q^{36} -2.00407 q^{37} +13.2913 q^{38} +10.2885 q^{39} -3.56547 q^{40} -2.18900 q^{41} -2.62026 q^{42} -5.95884 q^{43} -7.85336 q^{44} -2.08571 q^{45} -3.87797 q^{47} +3.02102 q^{48} -6.75534 q^{49} +2.34901 q^{50} +15.5420 q^{51} +16.0492 q^{52} -8.53595 q^{53} -4.84333 q^{54} +2.23243 q^{55} -1.76360 q^{56} +12.7602 q^{57} +22.8531 q^{58} +2.93429 q^{59} -7.93331 q^{60} +6.93009 q^{61} -9.98340 q^{62} -1.03166 q^{63} -12.0381 q^{64} -4.56220 q^{65} -11.8260 q^{66} +3.81733 q^{67} +24.2442 q^{68} +1.16190 q^{70} +2.76568 q^{71} +7.43654 q^{72} -11.0250 q^{73} -4.70759 q^{74} +2.25515 q^{75} +19.9049 q^{76} +1.10423 q^{77} +24.1677 q^{78} -14.9221 q^{79} -1.33961 q^{80} -10.9069 q^{81} -5.14200 q^{82} +9.39180 q^{83} -3.92408 q^{84} -6.89177 q^{85} -13.9974 q^{86} +21.9400 q^{87} -7.95964 q^{88} +4.63796 q^{89} -4.89936 q^{90} -2.25662 q^{91} -9.58450 q^{93} -9.10939 q^{94} -5.65825 q^{95} -8.98493 q^{96} +8.18195 q^{97} -15.8684 q^{98} -4.65620 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 3 q^{2} + 10 q^{3} + 33 q^{4} - 25 q^{5} + 22 q^{6} - 14 q^{7} + 21 q^{8} + 29 q^{9}+O(q^{10}) \) 25 * q + 3 * q^2 + 10 * q^3 + 33 * q^4 - 25 * q^5 + 22 * q^6 - 14 * q^7 + 21 * q^8 + 29 * q^9	\( 25 q + 3 q^{2} + 10 q^{3} + 33 q^{4} - 25 q^{5} + 22 q^{6} - 14 q^{7} + 21 q^{8} + 29 q^{9} - 3 q^{10} + 8 q^{11} + 34 q^{12} + 15 q^{13} + 6 q^{14} - 10 q^{15} + 41 q^{16} - 19 q^{17} + 23 q^{18} + 8 q^{19} - 33 q^{20} + 21 q^{21} - 3 q^{22} + 51 q^{24} + 25 q^{25} + 7 q^{26} + 64 q^{27} - 27 q^{28} + 3 q^{29} - 22 q^{30} + 34 q^{31} + 30 q^{32} + q^{33} + 21 q^{34} + 14 q^{35} + 31 q^{36} + q^{37} + 7 q^{38} + 49 q^{39} - 21 q^{40} + 29 q^{42} - 25 q^{43} + 33 q^{44} - 29 q^{45} - 5 q^{47} + 42 q^{48} + 33 q^{49} + 3 q^{50} - 23 q^{51} + 67 q^{52} - 24 q^{53} + 37 q^{54} - 8 q^{55} + 55 q^{56} + 19 q^{57} + 49 q^{58} + 41 q^{59} - 34 q^{60} + 31 q^{61} - 3 q^{62} - 37 q^{63} + 77 q^{64} - 15 q^{65} + 39 q^{66} + 5 q^{67} - 27 q^{68} - 6 q^{70} + 15 q^{71} + 48 q^{72} + 34 q^{73} + 29 q^{74} + 10 q^{75} + 24 q^{76} - 35 q^{77} - 45 q^{78} + 41 q^{79} - 41 q^{80} + 25 q^{81} + 33 q^{82} - 62 q^{83} + 126 q^{84} + 19 q^{85} + 10 q^{86} + 26 q^{87} + 50 q^{88} + 23 q^{89} - 23 q^{90} - 19 q^{91} + 50 q^{93} + 9 q^{94} - 8 q^{95} + 64 q^{96} - 37 q^{97} - 55 q^{98} + 48 q^{99}+O(q^{100}) \) 25 * q + 3 * q^2 + 10 * q^3 + 33 * q^4 - 25 * q^5 + 22 * q^6 - 14 * q^7 + 21 * q^8 + 29 * q^9 - 3 * q^10 + 8 * q^11 + 34 * q^12 + 15 * q^13 + 6 * q^14 - 10 * q^15 + 41 * q^16 - 19 * q^17 + 23 * q^18 + 8 * q^19 - 33 * q^20 + 21 * q^21 - 3 * q^22 + 51 * q^24 + 25 * q^25 + 7 * q^26 + 64 * q^27 - 27 * q^28 + 3 * q^29 - 22 * q^30 + 34 * q^31 + 30 * q^32 + q^33 + 21 * q^34 + 14 * q^35 + 31 * q^36 + q^37 + 7 * q^38 + 49 * q^39 - 21 * q^40 + 29 * q^42 - 25 * q^43 + 33 * q^44 - 29 * q^45 - 5 * q^47 + 42 * q^48 + 33 * q^49 + 3 * q^50 - 23 * q^51 + 67 * q^52 - 24 * q^53 + 37 * q^54 - 8 * q^55 + 55 * q^56 + 19 * q^57 + 49 * q^58 + 41 * q^59 - 34 * q^60 + 31 * q^61 - 3 * q^62 - 37 * q^63 + 77 * q^64 - 15 * q^65 + 39 * q^66 + 5 * q^67 - 27 * q^68 - 6 * q^70 + 15 * q^71 + 48 * q^72 + 34 * q^73 + 29 * q^74 + 10 * q^75 + 24 * q^76 - 35 * q^77 - 45 * q^78 + 41 * q^79 - 41 * q^80 + 25 * q^81 + 33 * q^82 - 62 * q^83 + 126 * q^84 + 19 * q^85 + 10 * q^86 + 26 * q^87 + 50 * q^88 + 23 * q^89 - 23 * q^90 - 19 * q^91 + 50 * q^93 + 9 * q^94 - 8 * q^95 + 64 * q^96 - 37 * q^97 - 55 * q^98 + 48 * q^99

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