LMFDB - Embedded newform 4033.2.a.f.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4033,2,Mod(1,4033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4033, 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("4033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4033 = 37 \cdot 109 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4033.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:	$32.2036671352$
Analytic rank:	$0$
Dimension:	$85$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	4033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.92648 q^{2} -3.23973 q^{3} +1.71134 q^{4} +1.34988 q^{5} +6.24129 q^{6} +3.96616 q^{7} +0.556094 q^{8} +7.49587 q^{9} +O(q^{10})$	\(q-1.92648 q^{2} -3.23973 q^{3} +1.71134 q^{4} +1.34988 q^{5} +6.24129 q^{6} +3.96616 q^{7} +0.556094 q^{8} +7.49587 q^{9} -2.60052 q^{10} -2.26646 q^{11} -5.54429 q^{12} -1.74141 q^{13} -7.64075 q^{14} -4.37325 q^{15} -4.49399 q^{16} +2.07799 q^{17} -14.4407 q^{18} -0.0556045 q^{19} +2.31011 q^{20} -12.8493 q^{21} +4.36630 q^{22} +2.13566 q^{23} -1.80160 q^{24} -3.17782 q^{25} +3.35480 q^{26} -14.5654 q^{27} +6.78746 q^{28} -1.24737 q^{29} +8.42500 q^{30} +6.48541 q^{31} +7.54542 q^{32} +7.34272 q^{33} -4.00321 q^{34} +5.35384 q^{35} +12.8280 q^{36} +1.00000 q^{37} +0.107121 q^{38} +5.64170 q^{39} +0.750660 q^{40} +9.82822 q^{41} +24.7540 q^{42} +5.56260 q^{43} -3.87869 q^{44} +10.1185 q^{45} -4.11431 q^{46} -4.31048 q^{47} +14.5593 q^{48} +8.73042 q^{49} +6.12203 q^{50} -6.73212 q^{51} -2.98015 q^{52} -3.11563 q^{53} +28.0600 q^{54} -3.05945 q^{55} +2.20556 q^{56} +0.180144 q^{57} +2.40305 q^{58} +4.26046 q^{59} -7.48413 q^{60} -5.43610 q^{61} -12.4941 q^{62} +29.7298 q^{63} -5.54815 q^{64} -2.35070 q^{65} -14.1456 q^{66} +0.851420 q^{67} +3.55615 q^{68} -6.91896 q^{69} -10.3141 q^{70} +13.0363 q^{71} +4.16841 q^{72} -1.26557 q^{73} -1.92648 q^{74} +10.2953 q^{75} -0.0951583 q^{76} -8.98914 q^{77} -10.8687 q^{78} -2.32278 q^{79} -6.06635 q^{80} +24.7004 q^{81} -18.9339 q^{82} -0.341132 q^{83} -21.9896 q^{84} +2.80503 q^{85} -10.7163 q^{86} +4.04116 q^{87} -1.26036 q^{88} -10.6367 q^{89} -19.4932 q^{90} -6.90671 q^{91} +3.65484 q^{92} -21.0110 q^{93} +8.30407 q^{94} -0.0750594 q^{95} -24.4451 q^{96} +0.0238378 q^{97} -16.8190 q^{98} -16.9891 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 85 q + 11 q^{2} + 21 q^{3} + 93 q^{4} + 12 q^{5} + 4 q^{6} + 17 q^{7} + 30 q^{8} + 98 q^{9}+O(q^{10}) $ 85 * q + 11 * q^2 + 21 * q^3 + 93 * q^4 + 12 * q^5 + 4 * q^6 + 17 * q^7 + 30 * q^8 + 98 * q^9	\( 85 q + 11 q^{2} + 21 q^{3} + 93 q^{4} + 12 q^{5} + 4 q^{6} + 17 q^{7} + 30 q^{8} + 98 q^{9} + 9 q^{10} + 37 q^{11} + 44 q^{12} + 14 q^{13} + 26 q^{14} + 27 q^{15} + 85 q^{16} + 34 q^{17} + 3 q^{18} + 15 q^{19} + 15 q^{20} + 17 q^{21} + q^{22} + 72 q^{23} + 15 q^{24} + 85 q^{25} + 33 q^{26} + 69 q^{27} + 7 q^{28} + 19 q^{29} - 9 q^{30} + 23 q^{31} + 51 q^{32} + 32 q^{33} + 49 q^{34} + 40 q^{35} + 121 q^{36} + 85 q^{37} + 84 q^{38} + 39 q^{39} + 22 q^{40} + 55 q^{41} - 28 q^{42} + 78 q^{44} + 28 q^{45} + 17 q^{46} + 184 q^{47} + 97 q^{48} + 88 q^{49} + 26 q^{50} + 27 q^{51} + 73 q^{52} + 64 q^{53} + 31 q^{54} + 39 q^{55} + 68 q^{56} - 33 q^{57} + 28 q^{58} + 60 q^{59} - 22 q^{60} + 7 q^{61} + 70 q^{62} + 28 q^{63} + 102 q^{64} + 17 q^{65} - 15 q^{66} + 82 q^{67} + 92 q^{68} + 22 q^{69} - 41 q^{70} + 113 q^{71} - 19 q^{73} + 11 q^{74} + 45 q^{75} + 34 q^{76} + 64 q^{77} + 29 q^{78} + 23 q^{79} + 54 q^{80} + 149 q^{81} + 4 q^{82} + 100 q^{83} - 49 q^{84} - 5 q^{85} - 24 q^{86} + 65 q^{87} + 14 q^{88} + 84 q^{89} - 21 q^{90} + 32 q^{91} + 95 q^{92} + 19 q^{93} - 47 q^{94} + 102 q^{95} + 29 q^{96} + 7 q^{97} + 26 q^{98} + 107 q^{99}+O(q^{100}) \) 85 * q + 11 * q^2 + 21 * q^3 + 93 * q^4 + 12 * q^5 + 4 * q^6 + 17 * q^7 + 30 * q^8 + 98 * q^9 + 9 * q^10 + 37 * q^11 + 44 * q^12 + 14 * q^13 + 26 * q^14 + 27 * q^15 + 85 * q^16 + 34 * q^17 + 3 * q^18 + 15 * q^19 + 15 * q^20 + 17 * q^21 + q^22 + 72 * q^23 + 15 * q^24 + 85 * q^25 + 33 * q^26 + 69 * q^27 + 7 * q^28 + 19 * q^29 - 9 * q^30 + 23 * q^31 + 51 * q^32 + 32 * q^33 + 49 * q^34 + 40 * q^35 + 121 * q^36 + 85 * q^37 + 84 * q^38 + 39 * q^39 + 22 * q^40 + 55 * q^41 - 28 * q^42 + 78 * q^44 + 28 * q^45 + 17 * q^46 + 184 * q^47 + 97 * q^48 + 88 * q^49 + 26 * q^50 + 27 * q^51 + 73 * q^52 + 64 * q^53 + 31 * q^54 + 39 * q^55 + 68 * q^56 - 33 * q^57 + 28 * q^58 + 60 * q^59 - 22 * q^60 + 7 * q^61 + 70 * q^62 + 28 * q^63 + 102 * q^64 + 17 * q^65 - 15 * q^66 + 82 * q^67 + 92 * q^68 + 22 * q^69 - 41 * q^70 + 113 * q^71 - 19 * q^73 + 11 * q^74 + 45 * q^75 + 34 * q^76 + 64 * q^77 + 29 * q^78 + 23 * q^79 + 54 * q^80 + 149 * q^81 + 4 * q^82 + 100 * q^83 - 49 * q^84 - 5 * q^85 - 24 * q^86 + 65 * q^87 + 14 * q^88 + 84 * q^89 - 21 * q^90 + 32 * q^91 + 95 * q^92 + 19 * q^93 - 47 * q^94 + 102 * q^95 + 29 * q^96 + 7 * q^97 + 26 * q^98 + 107 * 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 $

$2$	−1.92648	−1.36223	−0.681115	−	0.732176i	$-0.738505\pi$
$2$	−1.92648	−1.36223	−0.681115	+	0.732176i	$0.738505\pi$
$3$	−3.23973	−1.87046	−0.935230	−	0.354040i	$-0.884808\pi$
$3$	−3.23973	−1.87046	−0.935230	+	0.354040i	$0.884808\pi$
$4$	1.71134	0.855671
$5$	1.34988	0.603685	0.301842	−	0.953358i	$-0.402398\pi$
$5$	1.34988	0.603685	0.301842	+	0.953358i	$0.402398\pi$
$6$	6.24129	2.54800
$7$	3.96616	1.49907	0.749534	−	0.661966i	$-0.230278\pi$
$7$	3.96616	1.49907	0.749534	+	0.661966i	$0.230278\pi$
$8$	0.556094	0.196609
$9$	7.49587	2.49862
$10$	−2.60052	−0.822358
$11$	−2.26646	−0.683363	−0.341682	−	0.939816i	$-0.610996\pi$
$11$	−2.26646	−0.683363	−0.341682	+	0.939816i	$0.610996\pi$
$12$	−5.54429	−1.60050
$13$	−1.74141	−0.482980	−0.241490	−	0.970403i	$-0.577636\pi$
$13$	−1.74141	−0.482980	−0.241490	+	0.970403i	$0.577636\pi$
$14$	−7.64075	−2.04208
$15$	−4.37325	−1.12917
$16$	−4.49399	−1.12350
$17$	2.07799	0.503986	0.251993	−	0.967729i	$-0.418914\pi$
$17$	2.07799	0.503986	0.251993	+	0.967729i	$0.418914\pi$
$18$	−14.4407	−3.40370
$19$	−0.0556045	−0.0127565	−0.00637827	−	0.999980i	$-0.502030\pi$
$19$	−0.0556045	−0.0127565	−0.00637827	+	0.999980i	$0.502030\pi$
$20$	2.31011	0.516556
$21$	−12.8493	−2.80395
$22$	4.36630	0.930898
$23$	2.13566	0.445316	0.222658	−	0.974897i	$-0.428527\pi$
$23$	2.13566	0.445316	0.222658	+	0.974897i	$0.428527\pi$
$24$	−1.80160	−0.367749
$25$	−3.17782	−0.635565
$26$	3.35480	0.657931
$27$	−14.5654	−2.80311
$28$	6.78746	1.28271
$29$	−1.24737	−0.231632	−0.115816	−	0.993271i	$-0.536948\pi$
$29$	−1.24737	−0.231632	−0.115816	+	0.993271i	$0.536948\pi$
$30$	8.42500	1.53819
$31$	6.48541	1.16481	0.582407	−	0.812897i	$-0.302111\pi$
$31$	6.48541	1.16481	0.582407	+	0.812897i	$0.302111\pi$
$32$	7.54542	1.33385
$33$	7.34272	1.27820
$34$	−4.00321	−0.686545
$35$	5.35384	0.904964
$36$	12.8280	2.13800
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	0.107121	0.0173773
$39$	5.64170	0.903396
$40$	0.750660	0.118690
$41$	9.82822	1.53491	0.767455	−	0.641103i	$-0.221523\pi$
$41$	9.82822	1.53491	0.767455	+	0.641103i	$0.221523\pi$
$42$	24.7540	3.81962
$43$	5.56260	0.848288	0.424144	−	0.905595i	$-0.360575\pi$
$43$	5.56260	0.848288	0.424144	+	0.905595i	$0.360575\pi$
$44$	−3.87869	−0.584734
$45$	10.1185	1.50838
$46$	−4.11431	−0.606622
$47$	−4.31048	−0.628748	−0.314374	−	0.949299i	$-0.601795\pi$
$47$	−4.31048	−0.628748	−0.314374	+	0.949299i	$0.601795\pi$
$48$	14.5593	2.10146
$49$	8.73042	1.24720
$50$	6.12203	0.865785
$51$	−6.73212	−0.942685
$52$	−2.98015	−0.413272
$53$	−3.11563	−0.427964	−0.213982	−	0.976838i	$-0.568643\pi$
$53$	−3.11563	−0.427964	−0.213982	+	0.976838i	$0.568643\pi$
$54$	28.0600	3.81849
$55$	−3.05945	−0.412536
$56$	2.20556	0.294730
$57$	0.180144	0.0238606
$58$	2.40305	0.315536
$59$	4.26046	0.554664	0.277332	−	0.960774i	$-0.410550\pi$
$59$	4.26046	0.554664	0.277332	+	0.960774i	$0.410550\pi$
$60$	−7.48413	−0.966197
$61$	−5.43610	−0.696022	−0.348011	−	0.937491i	$-0.613143\pi$
$61$	−5.43610	−0.696022	−0.348011	+	0.937491i	$0.613143\pi$
$62$	−12.4941	−1.58675
$63$	29.7298	3.74560
$64$	−5.54815	−0.693518
$65$	−2.35070	−0.291568
$66$	−14.1456	−1.74121
$67$	0.851420	0.104018	0.0520088	−	0.998647i	$-0.483438\pi$
$67$	0.851420	0.104018	0.0520088	+	0.998647i	$0.483438\pi$
$68$	3.55615	0.431246
$69$	−6.91896	−0.832945
$70$	−10.3141	−1.23277
$71$	13.0363	1.54712	0.773560	−	0.633723i	$-0.218474\pi$
$71$	13.0363	1.54712	0.773560	+	0.633723i	$0.218474\pi$
$72$	4.16841	0.491251
$73$	−1.26557	−0.148123	−0.0740616	−	0.997254i	$-0.523596\pi$
$73$	−1.26557	−0.148123	−0.0740616	+	0.997254i	$0.523596\pi$
$74$	−1.92648	−0.223949
$75$	10.2953	1.18880
$76$	−0.0951583	−0.0109154
$77$	−8.98914	−1.02441
$78$	−10.8687	−1.23063
$79$	−2.32278	−0.261334	−0.130667	−	0.991426i	$-0.541712\pi$
$79$	−2.32278	−0.261334	−0.130667	+	0.991426i	$0.541712\pi$
$80$	−6.06635	−0.678239
$81$	24.7004	2.74449
$82$	−18.9339	−2.09090
$83$	−0.341132	−0.0374441	−0.0187220	−	0.999825i	$-0.505960\pi$
$83$	−0.341132	−0.0374441	−0.0187220	+	0.999825i	$0.505960\pi$
$84$	−21.9896	−2.39926
$85$	2.80503	0.304249
$86$	−10.7163	−1.15556
$87$	4.04116	0.433258
$88$	−1.26036	−0.134355
$89$	−10.6367	−1.12748	−0.563742	−	0.825951i	$-0.690639\pi$
$89$	−10.6367	−1.12748	−0.563742	+	0.825951i	$0.690639\pi$
$90$	−19.4932	−2.05476
$91$	−6.90671	−0.724020
$92$	3.65484	0.381044
$93$	−21.0110	−2.17874
$94$	8.30407	0.856499
$95$	−0.0750594	−0.00770093
$96$	−24.4451	−2.49492
$97$	0.0238378	0.00242036	0.00121018	−	0.999999i	$-0.499615\pi$
$97$	0.0238378	0.00242036	0.00121018	+	0.999999i	$0.499615\pi$
$98$	−16.8190	−1.69898
$99$	−16.9891	−1.70747
$100$	−5.43834	−0.543834
$101$	−2.07023	−0.205995	−0.102998	−	0.994682i	$-0.532843\pi$
$101$	−2.07023	−0.205995	−0.102998	+	0.994682i	$0.532843\pi$
$102$	12.9693	1.28415
$103$	6.35658	0.626332	0.313166	−	0.949698i	$-0.398610\pi$
$103$	6.35658	0.626332	0.313166	+	0.949698i	$0.398610\pi$
$104$	−0.968388	−0.0949582
$105$	−17.3450	−1.69270
$106$	6.00220	0.582986
$107$	6.15416	0.594945	0.297473	−	0.954730i	$-0.403856\pi$
$107$	6.15416	0.594945	0.297473	+	0.954730i	$0.403856\pi$
$108$	−24.9264	−2.39854
$109$	−1.00000	−0.0957826
$109$	−1.00000	−0.0957826
$110$	5.89398	0.561969
$111$	−3.23973	−0.307502
$112$	−17.8239	−1.68420
$113$	16.6497	1.56627	0.783134	−	0.621853i	$-0.213620\pi$
$113$	16.6497	1.56627	0.783134	+	0.621853i	$0.213620\pi$
$114$	−0.347044	−0.0325036
$115$	2.88288	0.268830
$116$	−2.13468	−0.198201
$117$	−13.0534	−1.20679
$118$	−8.20771	−0.755581
$119$	8.24163	0.755509
$120$	−2.43194	−0.222005
$121$	−5.86316	−0.533015
$122$	10.4726	0.948142
$123$	−31.8408	−2.87099
$124$	11.0988	0.996699
$125$	−11.0391	−0.987366
$126$	−57.2740	−5.10237
$127$	5.64587	0.500990	0.250495	−	0.968118i	$-0.419407\pi$
$127$	5.64587	0.500990	0.250495	+	0.968118i	$0.419407\pi$
$128$	−4.40242	−0.389122
$129$	−18.0213	−1.58669
$130$	4.52858	0.397183
$131$	13.1502	1.14894	0.574469	−	0.818526i	$-0.305208\pi$
$131$	13.1502	1.14894	0.574469	+	0.818526i	$0.305208\pi$
$132$	12.5659	1.09372
$133$	−0.220536	−0.0191229
$134$	−1.64025	−0.141696
$135$	−19.6616	−1.69220
$136$	1.15556	0.0990881
$137$	−4.51177	−0.385467	−0.192733	−	0.981251i	$-0.561735\pi$
$137$	−4.51177	−0.385467	−0.192733	+	0.981251i	$0.561735\pi$
$138$	13.3293	1.13466
$139$	−1.93497	−0.164122	−0.0820610	−	0.996627i	$-0.526150\pi$
$139$	−1.93497	−0.164122	−0.0820610	+	0.996627i	$0.526150\pi$
$140$	9.16226	0.774352
$141$	13.9648	1.17605
$142$	−25.1142	−2.10753
$143$	3.94684	0.330051
$144$	−33.6864	−2.80720
$145$	−1.68381	−0.139832
$146$	2.43809	0.201778
$147$	−28.2842	−2.33284
$148$	1.71134	0.140671
$149$	13.5228	1.10783	0.553917	−	0.832572i	$-0.313132\pi$
$149$	13.5228	1.10783	0.553917	+	0.832572i	$0.313132\pi$
$150$	−19.8337	−1.61942
$151$	−8.03719	−0.654058	−0.327029	−	0.945014i	$-0.606047\pi$
$151$	−8.03719	−0.654058	−0.327029	+	0.945014i	$0.606047\pi$
$152$	−0.0309213	−0.00250805
$153$	15.5763	1.25927
$154$	17.3174	1.39548
$155$	8.75453	0.703181
$156$	9.65489	0.773010
$157$	5.49841	0.438821	0.219410	−	0.975633i	$-0.429587\pi$
$157$	5.49841	0.438821	0.219410	+	0.975633i	$0.429587\pi$
$158$	4.47481	0.355997
$159$	10.0938	0.800490
$160$	10.1854	0.805227
$161$	8.47036	0.667558
$162$	−47.5850	−3.73863
$163$	3.77403	0.295605	0.147802	−	0.989017i	$-0.452780\pi$
$163$	3.77403	0.295605	0.147802	+	0.989017i	$0.452780\pi$
$164$	16.8194	1.31338
$165$	9.91180	0.771632
$166$	0.657185	0.0510075
$167$	22.0558	1.70673	0.853366	−	0.521313i	$-0.174558\pi$
$167$	22.0558	1.70673	0.853366	+	0.521313i	$0.174558\pi$
$168$	−7.14542	−0.551281
$169$	−9.96749	−0.766730
$170$	−5.40385	−0.414457
$171$	−0.416804	−0.0318738
$172$	9.51951	0.725856
$173$	−18.6692	−1.41939	−0.709696	−	0.704508i	$-0.751168\pi$
$173$	−18.6692	−1.41939	−0.709696	+	0.704508i	$0.751168\pi$
$174$	−7.78523	−0.590197
$175$	−12.6038	−0.952754
$176$	10.1855	0.767757
$177$	−13.8027	−1.03748
$178$	20.4914	1.53589
$179$	−12.9707	−0.969474	−0.484737	−	0.874660i	$-0.661085\pi$
$179$	−12.9707	−0.969474	−0.484737	+	0.874660i	$0.661085\pi$
$180$	17.3163	1.29068
$181$	−20.5983	−1.53106	−0.765531	−	0.643399i	$-0.777523\pi$
$181$	−20.5983	−1.53106	−0.765531	+	0.643399i	$0.777523\pi$
$182$	13.3057	0.986282
$183$	17.6115	1.30188
$184$	1.18763	0.0875530
$185$	1.34988	0.0992452
$186$	40.4774	2.96795
$187$	−4.70967	−0.344405
$188$	−7.37670	−0.538001
$189$	−57.7687	−4.20206
$190$	0.144601	0.0104904
$191$	5.17869	0.374717	0.187358	−	0.982292i	$-0.440007\pi$
$191$	5.17869	0.374717	0.187358	+	0.982292i	$0.440007\pi$
$192$	17.9745	1.29720
$193$	14.4871	1.04280	0.521401	−	0.853312i	$-0.325410\pi$
$193$	14.4871	1.04280	0.521401	+	0.853312i	$0.325410\pi$
$194$	−0.0459231	−0.00329709
$195$	7.61563	0.545366
$196$	14.9407	1.06720
$197$	0.161692	0.0115201	0.00576005	−	0.999983i	$-0.498167\pi$
$197$	0.161692	0.0115201	0.00576005	+	0.999983i	$0.498167\pi$
$198$	32.7292	2.32596
$199$	−3.85590	−0.273337	−0.136669	−	0.990617i	$-0.543640\pi$
$199$	−3.85590	−0.273337	−0.136669	+	0.990617i	$0.543640\pi$
$200$	−1.76717	−0.124958
$201$	−2.75837	−0.194561
$202$	3.98826	0.280613
$203$	−4.94729	−0.347231
$204$	−11.5210	−0.806629
$205$	13.2669	0.926602
$206$	−12.2458	−0.853209
$207$	16.0086	1.11268
$208$	7.82588	0.542627
$209$	0.126025	0.00871735
$210$	33.4149	2.30585
$211$	−4.80857	−0.331036	−0.165518	−	0.986207i	$-0.552930\pi$
$211$	−4.80857	−0.331036	−0.165518	+	0.986207i	$0.552930\pi$
$212$	−5.33190	−0.366197
$213$	−42.2340	−2.89383
$214$	−11.8559	−0.810453
$215$	7.50884	0.512099
$216$	−8.09974	−0.551117
$217$	25.7222	1.74614
$218$	1.92648	0.130478
$219$	4.10009	0.277059
$220$	−5.23577	−0.352995
$221$	−3.61863	−0.243415
$222$	6.24129	0.418888
$223$	12.8924	0.863337	0.431669	−	0.902032i	$-0.357925\pi$
$223$	12.8924	0.863337	0.431669	+	0.902032i	$0.357925\pi$
$224$	29.9263	1.99954
$225$	−23.8205	−1.58804
$226$	−32.0753	−2.13362
$227$	25.3867	1.68497	0.842487	−	0.538717i	$-0.181091\pi$
$227$	25.3867	1.68497	0.842487	+	0.538717i	$0.181091\pi$
$228$	0.308288	0.0204168
$229$	−11.8144	−0.780720	−0.390360	−	0.920662i	$-0.627650\pi$
$229$	−11.8144	−0.780720	−0.390360	+	0.920662i	$0.627650\pi$
$230$	−5.55383	−0.366209
$231$	29.1224	1.91611
$232$	−0.693657	−0.0455408
$233$	−28.9936	−1.89943	−0.949716	−	0.313112i	$-0.898628\pi$
$233$	−28.9936	−1.89943	−0.949716	+	0.313112i	$0.898628\pi$
$234$	25.1471	1.64392
$235$	−5.81863	−0.379565
$236$	7.29110	0.474610
$237$	7.52520	0.488814
$238$	−15.8774	−1.02918
$239$	−1.92586	−0.124573	−0.0622867	−	0.998058i	$-0.519839\pi$
$239$	−1.92586	−0.124573	−0.0622867	+	0.998058i	$0.519839\pi$
$240$	19.6534	1.26862
$241$	2.04690	0.131852	0.0659261	−	0.997825i	$-0.479000\pi$
$241$	2.04690	0.131852	0.0659261	+	0.997825i	$0.479000\pi$
$242$	11.2953	0.726089
$243$	−36.3266	−2.33035
$244$	−9.30303	−0.595566
$245$	11.7850	0.752918
$246$	61.3408	3.91095
$247$	0.0968302	0.00616116
$248$	3.60650	0.229013
$249$	1.10518	0.0700377
$250$	21.2666	1.34502
$251$	8.84677	0.558403	0.279202	−	0.960232i	$-0.409930\pi$
$251$	8.84677	0.558403	0.279202	+	0.960232i	$0.409930\pi$
$252$	50.8779	3.20501
$253$	−4.84038	−0.304312
$254$	−10.8767	−0.682464
$255$	−9.08756	−0.569085
$256$	19.5775	1.22359
$257$	25.9731	1.62016	0.810079	−	0.586321i	$-0.199424\pi$
$257$	25.9731	1.62016	0.810079	+	0.586321i	$0.199424\pi$
$258$	34.7178	2.16144
$259$	3.96616	0.246445
$260$	−4.02285	−0.249486
$261$	−9.35015	−0.578760
$262$	−25.3337	−1.56512
$263$	0.803203	0.0495276	0.0247638	−	0.999693i	$-0.492117\pi$
$263$	0.803203	0.0495276	0.0247638	+	0.999693i	$0.492117\pi$
$264$	4.08324	0.251306
$265$	−4.20572	−0.258355
$266$	0.424860	0.0260498
$267$	34.4599	2.10891
$268$	1.45707	0.0890048
$269$	22.4963	1.37162	0.685812	−	0.727779i	$-0.259447\pi$
$269$	22.4963	1.37162	0.685812	+	0.727779i	$0.259447\pi$
$270$	37.8777	2.30516
$271$	−23.2444	−1.41200	−0.706000	−	0.708212i	$-0.749502\pi$
$271$	−23.2444	−1.41200	−0.706000	+	0.708212i	$0.749502\pi$
$272$	−9.33845	−0.566227
$273$	22.3759	1.35425
$274$	8.69186	0.525094
$275$	7.20241	0.434322
$276$	−11.8407	−0.712727
$277$	−23.4400	−1.40838	−0.704188	−	0.710014i	$-0.748689\pi$
$277$	−23.4400	−1.40838	−0.704188	+	0.710014i	$0.748689\pi$
$278$	3.72769	0.223572
$279$	48.6138	2.91043
$280$	2.97724	0.177924
$281$	−0.318088	−0.0189755	−0.00948777	−	0.999955i	$-0.503020\pi$
$281$	−0.318088	−0.0189755	−0.00948777	+	0.999955i	$0.503020\pi$
$282$	−26.9030	−1.60205
$283$	−23.9981	−1.42654	−0.713270	−	0.700889i	$-0.752787\pi$
$283$	−23.9981	−1.42654	−0.713270	+	0.700889i	$0.752787\pi$
$284$	22.3095	1.32383
$285$	0.243172	0.0144043
$286$	−7.60352	−0.449606
$287$	38.9803	2.30093
$288$	56.5595	3.33280
$289$	−12.6820	−0.745998
$290$	3.24383	0.190484
$291$	−0.0772280	−0.00452718
$292$	−2.16582	−0.126745
$293$	11.7660	0.687376	0.343688	−	0.939084i	$-0.388324\pi$
$293$	11.7660	0.687376	0.343688	+	0.939084i	$0.388324\pi$
$294$	54.4891	3.17787
$295$	5.75111	0.334842
$296$	0.556094	0.0323223
$297$	33.0119	1.91555
$298$	−26.0515	−1.50913
$299$	−3.71906	−0.215079
$300$	17.6188	1.01722
$301$	22.0621	1.27164
$302$	15.4835	0.890977
$303$	6.70699	0.385306
$304$	0.249886	0.0143319
$305$	−7.33809	−0.420178
$306$	−30.0075	−1.71542
$307$	33.1856	1.89400	0.947002	−	0.321227i	$-0.104095\pi$
$307$	33.1856	1.89400	0.947002	+	0.321227i	$0.104095\pi$
$308$	−15.3835	−0.876556
$309$	−20.5936	−1.17153
$310$	−16.8655	−0.957894
$311$	−19.9194	−1.12952	−0.564761	−	0.825254i	$-0.691032\pi$
$311$	−19.9194	−1.12952	−0.564761	+	0.825254i	$0.691032\pi$
$312$	3.13732	0.177616
$313$	12.6244	0.713573	0.356786	−	0.934186i	$-0.383872\pi$
$313$	12.6244	0.713573	0.356786	+	0.934186i	$0.383872\pi$
$314$	−10.5926	−0.597775
$315$	40.1317	2.26116
$316$	−3.97508	−0.223616
$317$	31.4879	1.76854	0.884268	−	0.466979i	$-0.154658\pi$
$317$	31.4879	1.76854	0.884268	+	0.466979i	$0.154658\pi$
$318$	−19.4455	−1.09045
$319$	2.82712	0.158289
$320$	−7.48933	−0.418666
$321$	−19.9378	−1.11282
$322$	−16.3180	−0.909368
$323$	−0.115545	−0.00642912
$324$	42.2709	2.34838
$325$	5.53390	0.306965
$326$	−7.27061	−0.402682
$327$	3.23973	0.179158
$328$	5.46541	0.301777
$329$	−17.0960	−0.942535
$330$	−19.0949	−1.05114
$331$	−19.0817	−1.04882	−0.524412	−	0.851465i	$-0.675715\pi$
$331$	−19.0817	−1.04882	−0.524412	+	0.851465i	$0.675715\pi$
$332$	−0.583794	−0.0320398
$333$	7.49587	0.410771
$334$	−42.4902	−2.32496
$335$	1.14932	0.0627938
$336$	57.7446	3.15023
$337$	29.6681	1.61612	0.808062	−	0.589097i	$-0.200517\pi$
$337$	29.6681	1.61612	0.808062	+	0.589097i	$0.200517\pi$
$338$	19.2022	1.04446
$339$	−53.9404	−2.92964
$340$	4.80037	0.260337
$341$	−14.6989	−0.795992
$342$	0.802966	0.0434194
$343$	6.86313	0.370574
$344$	3.09333	0.166781
$345$	−9.33977	−0.502836
$346$	35.9659	1.93354
$347$	−9.89584	−0.531237	−0.265618	−	0.964078i	$-0.585576\pi$
$347$	−9.89584	−0.531237	−0.265618	+	0.964078i	$0.585576\pi$
$348$	6.91581	0.370726
$349$	3.30139	0.176719	0.0883597	−	0.996089i	$-0.471837\pi$
$349$	3.30139	0.176719	0.0883597	+	0.996089i	$0.471837\pi$
$350$	24.2809	1.29787
$351$	25.3644	1.35385
$352$	−17.1014	−0.911507
$353$	11.0858	0.590036	0.295018	−	0.955492i	$-0.404674\pi$
$353$	11.0858	0.590036	0.295018	+	0.955492i	$0.404674\pi$
$354$	26.5908	1.41328
$355$	17.5974	0.933973
$356$	−18.2030	−0.964755
$357$	−26.7007	−1.41315
$358$	24.9878	1.32065
$359$	6.34740	0.335003	0.167502	−	0.985872i	$-0.446430\pi$
$359$	6.34740	0.335003	0.167502	+	0.985872i	$0.446430\pi$
$360$	5.62685	0.296561
$361$	−18.9969	−0.999837
$362$	39.6824	2.08566
$363$	18.9951	0.996983
$364$	−11.8198	−0.619523
$365$	−1.70836	−0.0894197
$366$	−33.9283	−1.77346
$367$	32.5563	1.69942	0.849712	−	0.527247i	$-0.176776\pi$
$367$	32.5563	1.69942	0.849712	+	0.527247i	$0.176776\pi$
$368$	−9.59763	−0.500311
$369$	73.6710	3.83516
$370$	−2.60052	−0.135195
$371$	−12.3571	−0.641547
$372$	−35.9570	−1.86429
$373$	3.47387	0.179870	0.0899350	−	0.995948i	$-0.471334\pi$
$373$	3.47387	0.179870	0.0899350	+	0.995948i	$0.471334\pi$
$374$	9.07311	0.469159
$375$	35.7637	1.84683
$376$	−2.39703	−0.123617
$377$	2.17219	0.111874
$378$	111.291	5.72417
$379$	−9.28610	−0.476995	−0.238497	−	0.971143i	$-0.576655\pi$
$379$	−9.28610	−0.476995	−0.238497	+	0.971143i	$0.576655\pi$
$380$	−0.128452	−0.00658947
$381$	−18.2911	−0.937083
$382$	−9.97667	−0.510451
$383$	−28.2878	−1.44544	−0.722720	−	0.691141i	$-0.757108\pi$
$383$	−28.2878	−1.44544	−0.722720	+	0.691141i	$0.757108\pi$
$384$	14.2627	0.727838
$385$	−12.1343	−0.618419
$386$	−27.9091	−1.42054
$387$	41.6965	2.11955
$388$	0.0407946	0.00207103
$389$	−1.02205	−0.0518202	−0.0259101	−	0.999664i	$-0.508248\pi$
$389$	−1.02205	−0.0518202	−0.0259101	+	0.999664i	$0.508248\pi$
$390$	−14.6714	−0.742914
$391$	4.43787	0.224433
$392$	4.85493	0.245211
$393$	−42.6032	−2.14904
$394$	−0.311498	−0.0156930
$395$	−3.13548	−0.157763
$396$	−29.0741	−1.46103
$397$	−8.22353	−0.412727	−0.206364	−	0.978475i	$-0.566163\pi$
$397$	−8.22353	−0.412727	−0.206364	+	0.978475i	$0.566163\pi$
$398$	7.42833	0.372348
$399$	0.714478	0.0357687
$400$	14.2811	0.714056
$401$	−11.1475	−0.556681	−0.278341	−	0.960482i	$-0.589784\pi$
$401$	−11.1475	−0.556681	−0.278341	+	0.960482i	$0.589784\pi$
$402$	5.31397	0.265037
$403$	−11.2938	−0.562583
$404$	−3.54287	−0.176264
$405$	33.3426	1.65681
$406$	9.53087	0.473009
$407$	−2.26646	−0.112344
$408$	−3.74369	−0.185340
$409$	−22.8940	−1.13204	−0.566018	−	0.824393i	$-0.691517\pi$
$409$	−22.8940	−1.13204	−0.566018	+	0.824393i	$0.691517\pi$
$410$	−25.5585	−1.26224
$411$	14.6169	0.721000
$412$	10.8783	0.535934
$413$	16.8977	0.831479
$414$	−30.8403	−1.51572
$415$	−0.460487	−0.0226044
$416$	−13.1397	−0.644225
$417$	6.26878	0.306984
$418$	−0.242786	−0.0118750
$419$	−0.628840	−0.0307208	−0.0153604	−	0.999882i	$-0.504890\pi$
$419$	−0.628840	−0.0307208	−0.0153604	+	0.999882i	$0.504890\pi$
$420$	−29.6833	−1.44839
$421$	9.90182	0.482585	0.241293	−	0.970452i	$-0.422429\pi$
$421$	9.90182	0.482585	0.241293	+	0.970452i	$0.422429\pi$
$422$	9.26364	0.450947
$423$	−32.3108	−1.57100
$424$	−1.73258	−0.0841415
$425$	−6.60347	−0.320316
$426$	81.3632	3.94206
$427$	−21.5604	−1.04338
$428$	10.5319	0.509078
$429$	−12.7867	−0.617347
$430$	−14.4657	−0.697596
$431$	13.9722	0.673015	0.336507	−	0.941681i	$-0.390754\pi$
$431$	13.9722	0.673015	0.336507	+	0.941681i	$0.390754\pi$
$432$	65.4568	3.14929
$433$	−8.97314	−0.431222	−0.215611	−	0.976479i	$-0.569174\pi$
$433$	−8.97314	−0.431222	−0.215611	+	0.976479i	$0.569174\pi$
$434$	−49.5534	−2.37864
$435$	5.45508	0.261551
$436$	−1.71134	−0.0819584
$437$	−0.118752	−0.00568069
$438$	−7.89877	−0.377418
$439$	−35.1841	−1.67925	−0.839623	−	0.543169i	$-0.817224\pi$
$439$	−35.1841	−1.67925	−0.839623	+	0.543169i	$0.817224\pi$
$440$	−1.70134	−0.0811083
$441$	65.4421	3.11629
$442$	6.97123	0.331588
$443$	−1.42393	−0.0676531	−0.0338266	−	0.999428i	$-0.510769\pi$
$443$	−1.42393	−0.0676531	−0.0338266	+	0.999428i	$0.510769\pi$
$444$	−5.54429	−0.263120
$445$	−14.3582	−0.680645
$446$	−24.8370	−1.17606
$447$	−43.8104	−2.07216
$448$	−22.0048	−1.03963
$449$	−17.0025	−0.802398	−0.401199	−	0.915991i	$-0.631406\pi$
$449$	−17.0025	−0.802398	−0.401199	+	0.915991i	$0.631406\pi$
$450$	45.8899	2.16327
$451$	−22.2753	−1.04890
$452$	28.4933	1.34021
$453$	26.0384	1.22339
$454$	−48.9071	−2.29532
$455$	−9.32323	−0.437080
$456$	0.100177	0.00469121
$457$	3.03418	0.141933	0.0709665	−	0.997479i	$-0.477392\pi$
$457$	3.03418	0.141933	0.0709665	+	0.997479i	$0.477392\pi$
$458$	22.7603	1.06352
$459$	−30.2667	−1.41273
$460$	4.93360	0.230030
$461$	33.7244	1.57070	0.785350	−	0.619051i	$-0.212483\pi$
$461$	33.7244	1.57070	0.785350	+	0.619051i	$0.212483\pi$
$462$	−56.1039	−2.61019
$463$	17.8786	0.830891	0.415446	−	0.909618i	$-0.363626\pi$
$463$	17.8786	0.830891	0.415446	+	0.909618i	$0.363626\pi$
$464$	5.60569	0.260238
$465$	−28.3623	−1.31527
$466$	55.8557	2.58746
$467$	−17.1965	−0.795758	−0.397879	−	0.917438i	$-0.630254\pi$
$467$	−17.1965	−0.795758	−0.397879	+	0.917438i	$0.630254\pi$
$468$	−22.3388	−1.03261
$469$	3.37687	0.155929
$470$	11.2095	0.517055
$471$	−17.8134	−0.820797
$472$	2.36921	0.109052
$473$	−12.6074	−0.579689
$474$	−14.4972	−0.665878
$475$	0.176701	0.00810761
$476$	14.1042	0.646467
$477$	−23.3543	−1.06932
$478$	3.71013	0.169698
$479$	4.32679	0.197696	0.0988480	−	0.995103i	$-0.468484\pi$
$479$	4.32679	0.197696	0.0988480	+	0.995103i	$0.468484\pi$
$480$	−32.9980	−1.50615
$481$	−1.74141	−0.0794015
$482$	−3.94331	−0.179613
$483$	−27.4417	−1.24864
$484$	−10.0339	−0.456085
$485$	0.0321781	0.00146113
$486$	69.9826	3.17447
$487$	8.43485	0.382220	0.191110	−	0.981569i	$-0.438791\pi$
$487$	8.43485	0.382220	0.191110	+	0.981569i	$0.438791\pi$
$488$	−3.02298	−0.136844
$489$	−12.2268	−0.552917
$490$	−22.7037	−1.02565
$491$	−15.3908	−0.694577	−0.347288	−	0.937758i	$-0.612898\pi$
$491$	−15.3908	−0.694577	−0.347288	+	0.937758i	$0.612898\pi$
$492$	−54.4905	−2.45662
$493$	−2.59203	−0.116739
$494$	−0.186542	−0.00839292
$495$	−22.9332	−1.03077
$496$	−29.1454	−1.30867
$497$	51.7039	2.31924
$498$	−2.12911	−0.0954075
$499$	34.6105	1.54938	0.774688	−	0.632343i	$-0.217907\pi$
$499$	34.6105	1.54938	0.774688	+	0.632343i	$0.217907\pi$
$500$	−18.8917	−0.844860
$501$	−71.4550	−3.19237
$502$	−17.0432	−0.760674
$503$	33.0545	1.47383	0.736913	−	0.675988i	$-0.236283\pi$
$503$	33.0545	1.47383	0.736913	+	0.675988i	$0.236283\pi$
$504$	16.5326	0.736419
$505$	−2.79456	−0.124356
$506$	9.32493	0.414543
$507$	32.2920	1.43414
$508$	9.66203	0.428683
$509$	−17.6100	−0.780550	−0.390275	−	0.920698i	$-0.627620\pi$
$509$	−17.6100	−0.780550	−0.390275	+	0.920698i	$0.627620\pi$
$510$	17.5070	0.775225
$511$	−5.01943	−0.222047
$512$	−28.9109	−1.27769
$513$	0.809902	0.0357580
$514$	−50.0368	−2.20703
$515$	8.58062	0.378107
$516$	−30.8407	−1.35768
$517$	9.76952	0.429663
$518$	−7.64075	−0.335715
$519$	60.4832	2.65492
$520$	−1.30721	−0.0573248
$521$	19.9261	0.872978	0.436489	−	0.899710i	$-0.356222\pi$
$521$	19.9261	0.872978	0.436489	+	0.899710i	$0.356222\pi$
$522$	18.0129	0.788404
$523$	14.0995	0.616530	0.308265	−	0.951301i	$-0.400252\pi$
$523$	14.0995	0.616530	0.308265	+	0.951301i	$0.400252\pi$
$524$	22.5045	0.983114
$525$	40.8328	1.78209
$526$	−1.54736	−0.0674680
$527$	13.4766	0.587050
$528$	−32.9981	−1.43606
$529$	−18.4390	−0.801694
$530$	8.10226	0.351940
$531$	31.9358	1.38590
$532$	−0.377413	−0.0163629
$533$	−17.1150	−0.741331
$534$	−66.3865	−2.87283
$535$	8.30738	0.359159
$536$	0.473470	0.0204508
$537$	42.0215	1.81336
$538$	−43.3388	−1.86847
$539$	−19.7872	−0.852293
$540$	−33.6477	−1.44796
$541$	0.421224	0.0181098	0.00905491	−	0.999959i	$-0.497118\pi$
$541$	0.421224	0.0181098	0.00905491	+	0.999959i	$0.497118\pi$
$542$	44.7801	1.92347
$543$	66.7331	2.86379
$544$	15.6793	0.672243
$545$	−1.34988	−0.0578225
$546$	−43.1068	−1.84480
$547$	3.06417	0.131014	0.0655072	−	0.997852i	$-0.479133\pi$
$547$	3.06417	0.131014	0.0655072	+	0.997852i	$0.479133\pi$
$548$	−7.72118	−0.329833
$549$	−40.7483	−1.73910
$550$	−13.8753	−0.591646
$551$	0.0693596	0.00295482
$552$	−3.84759	−0.163764
$553$	−9.21253	−0.391757
$554$	45.1569	1.91853
$555$	−4.37325	−0.185634
$556$	−3.31140	−0.140434
$557$	36.6361	1.55232	0.776161	−	0.630534i	$-0.217164\pi$
$557$	36.6361	1.55232	0.776161	+	0.630534i	$0.217164\pi$
$558$	−93.6537	−3.96468
$559$	−9.68676	−0.409706
$560$	−24.0601	−1.01673
$561$	15.2581	0.644197
$562$	0.612792	0.0258491
$563$	−40.4196	−1.70348	−0.851741	−	0.523964i	$-0.824453\pi$
$563$	−40.4196	−1.70348	−0.851741	+	0.523964i	$0.824453\pi$
$564$	23.8985	1.00631
$565$	22.4750	0.945532
$566$	46.2320	1.94328
$567$	97.9658	4.11418
$568$	7.24939	0.304178
$569$	36.6620	1.53695	0.768475	−	0.639879i	$-0.221016\pi$
$569$	36.6620	1.53695	0.768475	+	0.639879i	$0.221016\pi$
$570$	−0.468468	−0.0196220
$571$	−6.54264	−0.273801	−0.136900	−	0.990585i	$-0.543714\pi$
$571$	−6.54264	−0.273801	−0.136900	+	0.990585i	$0.543714\pi$
$572$	6.75439	0.282415
$573$	−16.7776	−0.700893
$574$	−75.0949	−3.13440
$575$	−6.78675	−0.283027
$576$	−41.5882	−1.73284
$577$	−9.21807	−0.383753	−0.191877	−	0.981419i	$-0.561457\pi$
$577$	−9.21807	−0.383753	−0.191877	+	0.981419i	$0.561457\pi$
$578$	24.4316	1.01622
$579$	−46.9342	−1.95052
$580$	−2.88157	−0.119651
$581$	−1.35298	−0.0561312
$582$	0.148779	0.00616707
$583$	7.06144	0.292455
$584$	−0.703773	−0.0291223
$585$	−17.6205	−0.728518
$586$	−22.6670	−0.936364
$587$	19.6619	0.811535	0.405767	−	0.913976i	$-0.367004\pi$
$587$	19.6619	0.811535	0.405767	+	0.913976i	$0.367004\pi$
$588$	−48.4040	−1.99615
$589$	−0.360618	−0.0148590
$590$	−11.0794	−0.456132
$591$	−0.523840	−0.0215479
$592$	−4.49399	−0.184702
$593$	3.16157	0.129830	0.0649151	−	0.997891i	$-0.479322\pi$
$593$	3.16157	0.129830	0.0649151	+	0.997891i	$0.479322\pi$
$594$	−63.5969	−2.60941
$595$	11.1252	0.456089
$596$	23.1422	0.947942
$597$	12.4921	0.511267
$598$	7.16471	0.292987
$599$	19.3669	0.791308	0.395654	−	0.918400i	$-0.370518\pi$
$599$	19.3669	0.791308	0.395654	+	0.918400i	$0.370518\pi$
$600$	5.72515	0.233728
$601$	32.6005	1.32980	0.664901	−	0.746932i	$-0.268474\pi$
$601$	32.6005	1.32980	0.664901	+	0.746932i	$0.268474\pi$
$602$	−42.5024	−1.73227
$603$	6.38214	0.259901
$604$	−13.7544	−0.559658
$605$	−7.91456	−0.321773
$606$	−12.9209	−0.524876
$607$	37.3475	1.51589	0.757945	−	0.652319i	$-0.226204\pi$
$607$	37.3475	1.51589	0.757945	+	0.652319i	$0.226204\pi$
$608$	−0.419559	−0.0170154
$609$	16.0279	0.649483
$610$	14.1367	0.572379
$611$	7.50631	0.303673
$612$	26.6564	1.07752
$613$	19.4375	0.785072	0.392536	−	0.919737i	$-0.371598\pi$
$613$	19.4375	0.785072	0.392536	+	0.919737i	$0.371598\pi$
$614$	−63.9316	−2.58007
$615$	−42.9813	−1.73317
$616$	−4.99881	−0.201408
$617$	−10.5770	−0.425813	−0.212906	−	0.977073i	$-0.568293\pi$
$617$	−10.5770	−0.425813	−0.212906	+	0.977073i	$0.568293\pi$
$618$	39.6733	1.59589
$619$	−32.7979	−1.31826	−0.659129	−	0.752030i	$-0.729075\pi$
$619$	−32.7979	−1.31826	−0.659129	+	0.752030i	$0.729075\pi$
$620$	14.9820	0.601692
$621$	−31.1067	−1.24827
$622$	38.3743	1.53867
$623$	−42.1867	−1.69017
$624$	−25.3538	−1.01496
$625$	0.987677	0.0395071
$626$	−24.3207	−0.972050
$627$	−0.408288	−0.0163055
$628$	9.40966	0.375486
$629$	2.07799	0.0828547
$630$	−77.3131	−3.08023
$631$	−18.5308	−0.737699	−0.368850	−	0.929489i	$-0.620248\pi$
$631$	−18.5308	−0.737699	−0.368850	+	0.929489i	$0.620248\pi$
$632$	−1.29169	−0.0513805
$633$	15.5785	0.619189
$634$	−60.6609	−2.40915
$635$	7.62125	0.302440
$636$	17.2739	0.684956
$637$	−15.2033	−0.602375
$638$	−5.44641	−0.215625
$639$	97.7181	3.86567
$640$	−5.94273	−0.234907
$641$	13.2777	0.524437	0.262218	−	0.965009i	$-0.415546\pi$
$641$	13.2777	0.524437	0.262218	+	0.965009i	$0.415546\pi$
$642$	38.4099	1.51592
$643$	31.1781	1.22954	0.614772	−	0.788705i	$-0.289248\pi$
$643$	31.1781	1.22954	0.614772	+	0.788705i	$0.289248\pi$
$644$	14.4957	0.571210
$645$	−24.3266	−0.957860
$646$	0.222596	0.00875794
$647$	9.16297	0.360234	0.180117	−	0.983645i	$-0.442352\pi$
$647$	9.16297	0.360234	0.180117	+	0.983645i	$0.442352\pi$
$648$	13.7358	0.539592
$649$	−9.65615	−0.379037
$650$	−10.6610	−0.418157
$651$	−83.3330	−3.26608
$652$	6.45866	0.252940
$653$	12.6327	0.494354	0.247177	−	0.968970i	$-0.420497\pi$
$653$	12.6327	0.494354	0.247177	+	0.968970i	$0.420497\pi$
$654$	−6.24129	−0.244054
$655$	17.7512	0.693597
$656$	−44.1679	−1.72447
$657$	−9.48651	−0.370104
$658$	32.9353	1.28395
$659$	50.5499	1.96914	0.984572	−	0.174983i	$-0.0559869\pi$
$659$	50.5499	1.96914	0.984572	+	0.174983i	$0.0559869\pi$
$660$	16.9625	0.660264
$661$	−15.2491	−0.593121	−0.296561	−	0.955014i	$-0.595840\pi$
$661$	−15.2491	−0.593121	−0.296561	+	0.955014i	$0.595840\pi$
$662$	36.7605	1.42874
$663$	11.7234	0.455299
$664$	−0.189701	−0.00736184
$665$	−0.297698	−0.0115442
$666$	−14.4407	−0.559565
$667$	−2.66397	−0.103149
$668$	37.7451	1.46040
$669$	−41.7679	−1.61484
$670$	−2.21414	−0.0855396
$671$	12.3207	0.475636
$672$	−96.9533	−3.74006
$673$	−43.3797	−1.67217	−0.836083	−	0.548603i	$-0.815160\pi$
$673$	−43.3797	−1.67217	−0.836083	+	0.548603i	$0.815160\pi$
$674$	−57.1551	−2.20153
$675$	46.2863	1.78156
$676$	−17.0578	−0.656069
$677$	−33.5075	−1.28780	−0.643898	−	0.765111i	$-0.722684\pi$
$677$	−33.5075	−1.28780	−0.643898	+	0.765111i	$0.722684\pi$
$678$	103.915	3.99085
$679$	0.0945444	0.00362828
$680$	1.55986	0.0598180
$681$	−82.2461	−3.15168
$682$	28.3173	1.08432
$683$	28.2494	1.08093	0.540467	−	0.841365i	$-0.318248\pi$
$683$	28.2494	1.08093	0.540467	+	0.841365i	$0.318248\pi$
$684$	−0.713294	−0.0272735
$685$	−6.09035	−0.232700
$686$	−13.2217	−0.504808
$687$	38.2756	1.46031
$688$	−24.9983	−0.953050
$689$	5.42558	0.206698
$690$	17.9929	0.684979
$691$	25.7424	0.979288	0.489644	−	0.871922i	$-0.337127\pi$
$691$	25.7424	0.979288	0.489644	+	0.871922i	$0.337127\pi$
$692$	−31.9494	−1.21453
$693$	−67.3814	−2.55961
$694$	19.0642	0.723666
$695$	−2.61198	−0.0990779
$696$	2.24726	0.0851823
$697$	20.4229	0.773573
$698$	−6.36008	−0.240733
$699$	93.9314	3.55281
$700$	−21.5693	−0.815245
$701$	12.6667	0.478416	0.239208	−	0.970968i	$-0.423112\pi$
$701$	12.6667	0.478416	0.239208	+	0.970968i	$0.423112\pi$
$702$	−48.8640	−1.84425
$703$	−0.0556045	−0.00209716
$704$	12.5747	0.473925
$705$	18.8508	0.709962
$706$	−21.3566	−0.803765
$707$	−8.21086	−0.308801
$708$	−23.6212	−0.887740
$709$	24.1517	0.907035	0.453518	−	0.891247i	$-0.350169\pi$
$709$	24.1517	0.907035	0.453518	+	0.891247i	$0.350169\pi$
$710$	−33.9011	−1.27229
$711$	−17.4113	−0.652974
$712$	−5.91498	−0.221673
$713$	13.8506	0.518710
$714$	51.4384	1.92503
$715$	5.32776	0.199247
$716$	−22.1973	−0.829551
$717$	6.23926	0.233010
$718$	−12.2282	−0.456351
$719$	21.0475	0.784941	0.392471	−	0.919765i	$-0.371620\pi$
$719$	21.0475	0.784941	0.392471	+	0.919765i	$0.371620\pi$
$720$	−45.4726	−1.69466
$721$	25.2112	0.938914
$722$	36.5972	1.36201
$723$	−6.63140	−0.246624
$724$	−35.2508	−1.31009
$725$	3.96394	0.147217
$726$	−36.5937	−1.35812
$727$	47.2143	1.75108	0.875541	−	0.483144i	$-0.160505\pi$
$727$	47.2143	1.75108	0.875541	+	0.483144i	$0.160505\pi$
$728$	−3.84078	−0.142349
$729$	43.5871	1.61434
$730$	3.29113	0.121810
$731$	11.5590	0.427525
$732$	30.1393	1.11398
$733$	−18.8782	−0.697282	−0.348641	−	0.937256i	$-0.613357\pi$
$733$	−18.8782	−0.697282	−0.348641	+	0.937256i	$0.613357\pi$
$734$	−62.7192	−2.31501
$735$	−38.1803	−1.40830
$736$	16.1144	0.593986
$737$	−1.92971	−0.0710818
$738$	−141.926	−5.22437
$739$	27.2012	1.00061	0.500306	−	0.865849i	$-0.333221\pi$
$739$	27.2012	1.00061	0.500306	+	0.865849i	$0.333221\pi$
$740$	2.31011	0.0849212
$741$	−0.313704	−0.0115242
$742$	23.8057	0.873935
$743$	39.7775	1.45929	0.729647	−	0.683824i	$-0.239684\pi$
$743$	39.7775	1.45929	0.729647	+	0.683824i	$0.239684\pi$
$744$	−11.6841	−0.428360
$745$	18.2542	0.668783
$746$	−6.69235	−0.245024
$747$	−2.55708	−0.0935587
$748$	−8.05986	−0.294698
$749$	24.4084	0.891863
$750$	−68.8982	−2.51581
$751$	43.7727	1.59729	0.798644	−	0.601804i	$-0.205551\pi$
$751$	43.7727	1.59729	0.798644	+	0.601804i	$0.205551\pi$
$752$	19.3712	0.706397
$753$	−28.6612	−1.04447
$754$	−4.18469	−0.152397
$755$	−10.8492	−0.394845
$756$	−98.8621	−3.59558
$757$	−28.3539	−1.03054	−0.515270	−	0.857028i	$-0.672308\pi$
$757$	−28.3539	−1.03054	−0.515270	+	0.857028i	$0.672308\pi$
$758$	17.8895	0.649777
$759$	15.6816	0.569204
$760$	−0.0417401	−0.00151407
$761$	−21.0154	−0.761809	−0.380904	−	0.924614i	$-0.624387\pi$
$761$	−21.0154	−0.761809	−0.380904	+	0.924614i	$0.624387\pi$
$762$	35.2376	1.27652
$763$	−3.96616	−0.143585
$764$	8.86251	0.320634
$765$	21.0262	0.760202
$766$	54.4960	1.96902
$767$	−7.41921	−0.267892
$768$	−63.4258	−2.28868
$769$	−35.5062	−1.28039	−0.640193	−	0.768214i	$-0.721146\pi$
$769$	−35.5062	−1.28039	−0.640193	+	0.768214i	$0.721146\pi$
$770$	23.3765	0.842430
$771$	−84.1459	−3.03044
$772$	24.7923	0.892295
$773$	−8.93550	−0.321387	−0.160694	−	0.987004i	$-0.551373\pi$
$773$	−8.93550	−0.321387	−0.160694	+	0.987004i	$0.551373\pi$
$774$	−80.3276	−2.88732
$775$	−20.6095	−0.740315
$776$	0.0132560	0.000475864 0
$777$	−12.8493	−0.460966
$778$	1.96897	0.0705910
$779$	−0.546493	−0.0195801
$780$	13.0329	0.466654
$781$	−29.5462	−1.05725
$782$	−8.54949	−0.305729
$783$	18.1685	0.649290
$784$	−39.2344	−1.40123
$785$	7.42219	0.264909
$786$	82.0743	2.92749
$787$	−4.74107	−0.169001	−0.0845005	−	0.996423i	$-0.526929\pi$
$787$	−4.74107	−0.169001	−0.0845005	+	0.996423i	$0.526929\pi$
$788$	0.276711	0.00985743
$789$	−2.60216	−0.0926395
$790$	6.04045	0.214910
$791$	66.0352	2.34794
$792$	−9.44752	−0.335703
$793$	9.46649	0.336165
$794$	15.8425	0.562229
$795$	13.6254	0.483244
$796$	−6.59876	−0.233887
$797$	−13.3979	−0.474579	−0.237290	−	0.971439i	$-0.576259\pi$
$797$	−13.3979	−0.474579	−0.237290	+	0.971439i	$0.576259\pi$
$798$	−1.37643	−0.0487252
$799$	−8.95711	−0.316880
$800$	−23.9780	−0.847750
$801$	−79.7310	−2.81716
$802$	21.4755	0.758328
$803$	2.86835	0.101222
$804$	−4.72052	−0.166480
$805$	11.4340	0.402995
$806$	21.7573	0.766367
$807$	−72.8820	−2.56557
$808$	−1.15124	−0.0405005
$809$	44.5045	1.56469	0.782347	−	0.622843i	$-0.214022\pi$
$809$	44.5045	1.56469	0.782347	+	0.622843i	$0.214022\pi$
$810$	−64.2340	−2.25695
$811$	52.7827	1.85345	0.926726	−	0.375738i	$-0.122611\pi$
$811$	52.7827	1.85345	0.926726	+	0.375738i	$0.122611\pi$
$812$	−8.46650	−0.297116
$813$	75.3058	2.64109
$814$	4.36630	0.153039
$815$	5.09449	0.178452
$816$	30.2541	1.05911
$817$	−0.309305	−0.0108212
$818$	44.1050	1.54209
$819$	−51.7718	−1.80905
$820$	22.7042	0.792867
$821$	1.83938	0.0641949	0.0320974	−	0.999485i	$-0.489781\pi$
$821$	1.83938	0.0641949	0.0320974	+	0.999485i	$0.489781\pi$
$822$	−28.1593	−0.982168
$823$	22.1676	0.772714	0.386357	−	0.922349i	$-0.373733\pi$
$823$	22.1676	0.772714	0.386357	+	0.922349i	$0.373733\pi$
$824$	3.53485	0.123142
$825$	−23.3339	−0.812381
$826$	−32.5531	−1.13267
$827$	−1.42069	−0.0494021	−0.0247010	−	0.999695i	$-0.507863\pi$
$827$	−1.42069	−0.0494021	−0.0247010	+	0.999695i	$0.507863\pi$
$828$	27.3962	0.952085
$829$	−24.1328	−0.838168	−0.419084	−	0.907948i	$-0.637649\pi$
$829$	−24.1328	−0.838168	−0.419084	+	0.907948i	$0.637649\pi$
$830$	0.887122	0.0307924
$831$	75.9395	2.63431
$832$	9.66160	0.334956
$833$	18.1417	0.628573
$834$	−12.0767	−0.418182
$835$	29.7727	1.03033
$836$	0.215672	0.00745919
$837$	−94.4627	−3.26511
$838$	1.21145	0.0418488
$839$	5.86000	0.202310	0.101155	−	0.994871i	$-0.467746\pi$
$839$	5.86000	0.202310	0.101155	+	0.994871i	$0.467746\pi$
$840$	−9.64546	−0.332800
$841$	−27.4441	−0.946347
$842$	−19.0757	−0.657392
$843$	1.03052	0.0354930
$844$	−8.22911	−0.283258
$845$	−13.4549	−0.462863
$846$	62.2462	2.14007
$847$	−23.2542	−0.799025
$848$	14.0016	0.480817
$849$	77.7475	2.66829
$850$	12.7215	0.436343
$851$	2.13566	0.0732094
$852$	−72.2769	−2.47617
$853$	32.6845	1.11909	0.559547	−	0.828798i	$-0.310975\pi$
$853$	32.6845	1.11909	0.559547	+	0.828798i	$0.310975\pi$
$854$	41.5359	1.42133
$855$	−0.562635	−0.0192417
$856$	3.42229	0.116972
$857$	−31.8881	−1.08928	−0.544639	−	0.838671i	$-0.683333\pi$
$857$	−31.8881	−1.08928	−0.544639	+	0.838671i	$0.683333\pi$
$858$	24.6334	0.840969
$859$	−21.7249	−0.741244	−0.370622	−	0.928784i	$-0.620855\pi$
$859$	−21.7249	−0.741244	−0.370622	+	0.928784i	$0.620855\pi$
$860$	12.8502	0.438188
$861$	−126.286	−4.30381
$862$	−26.9171	−0.916801
$863$	−39.5074	−1.34485	−0.672424	−	0.740166i	$-0.734747\pi$
$863$	−39.5074	−1.34485	−0.672424	+	0.740166i	$0.734747\pi$
$864$	−109.902	−3.73895
$865$	−25.2012	−0.856865
$866$	17.2866	0.587423
$867$	41.0862	1.39536
$868$	44.0195	1.49412
$869$	5.26450	0.178586
$870$	−10.5091	−0.356293
$871$	−1.48267	−0.0502384
$872$	−0.556094	−0.0188317
$873$	0.178685	0.00604756
$874$	0.228774	0.00773840
$875$	−43.7828	−1.48013
$876$	7.01666	0.237071
$877$	−7.82967	−0.264389	−0.132195	−	0.991224i	$-0.542202\pi$
$877$	−7.82967	−0.264389	−0.132195	+	0.991224i	$0.542202\pi$
$878$	67.7817	2.28752
$879$	−38.1186	−1.28571
$880$	13.7491	0.463483
$881$	4.05232	0.136526	0.0682631	−	0.997667i	$-0.478254\pi$
$881$	4.05232	0.136526	0.0682631	+	0.997667i	$0.478254\pi$
$882$	−126.073	−4.24510
$883$	−30.9967	−1.04312	−0.521562	−	0.853214i	$-0.674650\pi$
$883$	−30.9967	−1.04312	−0.521562	+	0.853214i	$0.674650\pi$
$884$	−6.19271	−0.208283
$885$	−18.6321	−0.626310
$886$	2.74319	0.0921592
$887$	−16.4517	−0.552395	−0.276197	−	0.961101i	$-0.589074\pi$
$887$	−16.4517	−0.552395	−0.276197	+	0.961101i	$0.589074\pi$
$888$	−1.80160	−0.0604576
$889$	22.3924	0.751018
$890$	27.6609	0.927195
$891$	−55.9825	−1.87549
$892$	22.0633	0.738733
$893$	0.239682	0.00802065
$894$	84.4000	2.82276
$895$	−17.5089	−0.585257
$896$	−17.4607	−0.583321
$897$	12.0488	0.402296
$898$	32.7551	1.09305
$899$	−8.08974	−0.269808
$900$	−40.7651	−1.35884
$901$	−6.47423	−0.215688
$902$	42.9129	1.42884
$903$	−71.4754	−2.37855
$904$	9.25877	0.307942
$905$	−27.8053	−0.924279
$906$	−50.1625	−1.66654
$907$	21.4650	0.712733	0.356366	−	0.934346i	$-0.384015\pi$
$907$	21.4650	0.712733	0.356366	+	0.934346i	$0.384015\pi$
$908$	43.4453	1.44178
$909$	−15.5182	−0.514705
$910$	17.9611	0.595404
$911$	−33.0791	−1.09596	−0.547979	−	0.836492i	$-0.684603\pi$
$911$	−33.0791	−1.09596	−0.547979	+	0.836492i	$0.684603\pi$
$912$	−0.809564	−0.0268073
$913$	0.773162	0.0255879
$914$	−5.84530	−0.193345
$915$	23.7734	0.785926
$916$	−20.2186	−0.668040
$917$	52.1558	1.72234
$918$	58.3084	1.92446
$919$	18.7178	0.617442	0.308721	−	0.951153i	$-0.400099\pi$
$919$	18.7178	0.617442	0.308721	+	0.951153i	$0.400099\pi$
$920$	1.60315	0.0528544
$921$	−107.513	−3.54266
$922$	−64.9695	−2.13966
$923$	−22.7015	−0.747229
$924$	49.8384	1.63956
$925$	−3.17782	−0.104486
$926$	−34.4429	−1.13186
$927$	47.6481	1.56497
$928$	−9.41196	−0.308963
$929$	50.7241	1.66420	0.832102	−	0.554623i	$-0.187137\pi$
$929$	50.7241	1.66420	0.832102	+	0.554623i	$0.187137\pi$
$930$	54.6396	1.79170
$931$	−0.485451	−0.0159100
$932$	−49.6179	−1.62529
$933$	64.5334	2.11273
$934$	33.1288	1.08401
$935$	−6.35749	−0.207912
$936$	−7.25891	−0.237265
$937$	−22.8934	−0.747894	−0.373947	−	0.927450i	$-0.621996\pi$
$937$	−22.8934	−0.747894	−0.373947	+	0.927450i	$0.621996\pi$
$938$	−6.50549	−0.212412
$939$	−40.8996	−1.33471
$940$	−9.95766	−0.324783
$941$	35.0799	1.14357	0.571786	−	0.820403i	$-0.306251\pi$
$941$	35.0799	1.14357	0.571786	+	0.820403i	$0.306251\pi$
$942$	34.3172	1.11811
$943$	20.9897	0.683519
$944$	−19.1465	−0.623164
$945$	−77.9809	−2.53672
$946$	24.2880	0.789670
$947$	22.6453	0.735872	0.367936	−	0.929851i	$-0.380065\pi$
$947$	22.6453	0.735872	0.367936	+	0.929851i	$0.380065\pi$
$948$	12.8782	0.418264
$949$	2.20387	0.0715406
$950$	−0.340412	−0.0110444
$951$	−102.012	−3.30798
$952$	4.58312	0.148540
$953$	3.92428	0.127120	0.0635599	−	0.997978i	$-0.479755\pi$
$953$	3.92428	0.127120	0.0635599	+	0.997978i	$0.479755\pi$
$954$	44.9917	1.45666
$955$	6.99061	0.226211
$956$	−3.29580	−0.106594
$957$	−9.15912	−0.296072
$958$	−8.33549	−0.269307
$959$	−17.8944	−0.577840
$960$	24.2634	0.783099
$961$	11.0606	0.356793
$962$	3.35480	0.108163
$963$	46.1308	1.48654
$964$	3.50294	0.112822
$965$	19.5558	0.629523
$966$	52.8660	1.70094
$967$	−15.2485	−0.490358	−0.245179	−	0.969478i	$-0.578847\pi$
$967$	−15.2485	−0.490358	−0.245179	+	0.969478i	$0.578847\pi$
$968$	−3.26047	−0.104795
$969$	0.374336	0.0120254
$970$	−0.0619907	−0.00199040
$971$	40.7839	1.30882	0.654409	−	0.756141i	$-0.272917\pi$
$971$	40.7839	1.30882	0.654409	+	0.756141i	$0.272917\pi$
$972$	−62.1672	−1.99401
$973$	−7.67440	−0.246030
$974$	−16.2496	−0.520671
$975$	−17.9283	−0.574166
$976$	24.4298	0.781979
$977$	−16.0448	−0.513318	−0.256659	−	0.966502i	$-0.582622\pi$
$977$	−16.0448	−0.513318	−0.256659	+	0.966502i	$0.582622\pi$
$978$	23.5548	0.753200
$979$	24.1076	0.770481
$980$	20.1682	0.644250
$981$	−7.49587	−0.239325
$982$	29.6501	0.946174
$983$	26.5463	0.846694	0.423347	−	0.905968i	$-0.360855\pi$
$983$	26.5463	0.846694	0.423347	+	0.905968i	$0.360855\pi$
$984$	−17.7065	−0.564462
$985$	0.218265	0.00695452
$986$	4.99350	0.159025
$987$	55.3866	1.76297
$988$	0.165710	0.00527193
$989$	11.8798	0.377756
$990$	44.1805	1.40415
$991$	−7.26308	−0.230719	−0.115360	−	0.993324i	$-0.536802\pi$
$991$	−7.26308	−0.230719	−0.115360	+	0.993324i	$0.536802\pi$
$992$	48.9352	1.55369
$993$	61.8195	1.96178
$994$	−99.6068	−3.15934
$995$	−5.20500	−0.165010
$996$	1.89134	0.0599293
$997$	2.34142	0.0741536	0.0370768	−	0.999312i	$-0.488195\pi$
$997$	2.34142	0.0741536	0.0370768	+	0.999312i	$0.488195\pi$
$998$	−66.6765	−2.11061
$999$	−14.5654	−0.460829

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4033.2.a.f.1.16	✓	85

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4033.2.a.f.1.16	✓	85	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4033 = 37 \cdot 109 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4033.a (trivial)

\(f(q)\)	\(=\)	\(q-1.92648 q^{2} -3.23973 q^{3} +1.71134 q^{4} +1.34988 q^{5} +6.24129 q^{6} +3.96616 q^{7} +0.556094 q^{8} +7.49587 q^{9} +O(q^{10})\)	\(q-1.92648 q^{2} -3.23973 q^{3} +1.71134 q^{4} +1.34988 q^{5} +6.24129 q^{6} +3.96616 q^{7} +0.556094 q^{8} +7.49587 q^{9} -2.60052 q^{10} -2.26646 q^{11} -5.54429 q^{12} -1.74141 q^{13} -7.64075 q^{14} -4.37325 q^{15} -4.49399 q^{16} +2.07799 q^{17} -14.4407 q^{18} -0.0556045 q^{19} +2.31011 q^{20} -12.8493 q^{21} +4.36630 q^{22} +2.13566 q^{23} -1.80160 q^{24} -3.17782 q^{25} +3.35480 q^{26} -14.5654 q^{27} +6.78746 q^{28} -1.24737 q^{29} +8.42500 q^{30} +6.48541 q^{31} +7.54542 q^{32} +7.34272 q^{33} -4.00321 q^{34} +5.35384 q^{35} +12.8280 q^{36} +1.00000 q^{37} +0.107121 q^{38} +5.64170 q^{39} +0.750660 q^{40} +9.82822 q^{41} +24.7540 q^{42} +5.56260 q^{43} -3.87869 q^{44} +10.1185 q^{45} -4.11431 q^{46} -4.31048 q^{47} +14.5593 q^{48} +8.73042 q^{49} +6.12203 q^{50} -6.73212 q^{51} -2.98015 q^{52} -3.11563 q^{53} +28.0600 q^{54} -3.05945 q^{55} +2.20556 q^{56} +0.180144 q^{57} +2.40305 q^{58} +4.26046 q^{59} -7.48413 q^{60} -5.43610 q^{61} -12.4941 q^{62} +29.7298 q^{63} -5.54815 q^{64} -2.35070 q^{65} -14.1456 q^{66} +0.851420 q^{67} +3.55615 q^{68} -6.91896 q^{69} -10.3141 q^{70} +13.0363 q^{71} +4.16841 q^{72} -1.26557 q^{73} -1.92648 q^{74} +10.2953 q^{75} -0.0951583 q^{76} -8.98914 q^{77} -10.8687 q^{78} -2.32278 q^{79} -6.06635 q^{80} +24.7004 q^{81} -18.9339 q^{82} -0.341132 q^{83} -21.9896 q^{84} +2.80503 q^{85} -10.7163 q^{86} +4.04116 q^{87} -1.26036 q^{88} -10.6367 q^{89} -19.4932 q^{90} -6.90671 q^{91} +3.65484 q^{92} -21.0110 q^{93} +8.30407 q^{94} -0.0750594 q^{95} -24.4451 q^{96} +0.0238378 q^{97} -16.8190 q^{98} -16.9891 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 85 q + 11 q^{2} + 21 q^{3} + 93 q^{4} + 12 q^{5} + 4 q^{6} + 17 q^{7} + 30 q^{8} + 98 q^{9}+O(q^{10}) \) 85 * q + 11 * q^2 + 21 * q^3 + 93 * q^4 + 12 * q^5 + 4 * q^6 + 17 * q^7 + 30 * q^8 + 98 * q^9	\( 85 q + 11 q^{2} + 21 q^{3} + 93 q^{4} + 12 q^{5} + 4 q^{6} + 17 q^{7} + 30 q^{8} + 98 q^{9} + 9 q^{10} + 37 q^{11} + 44 q^{12} + 14 q^{13} + 26 q^{14} + 27 q^{15} + 85 q^{16} + 34 q^{17} + 3 q^{18} + 15 q^{19} + 15 q^{20} + 17 q^{21} + q^{22} + 72 q^{23} + 15 q^{24} + 85 q^{25} + 33 q^{26} + 69 q^{27} + 7 q^{28} + 19 q^{29} - 9 q^{30} + 23 q^{31} + 51 q^{32} + 32 q^{33} + 49 q^{34} + 40 q^{35} + 121 q^{36} + 85 q^{37} + 84 q^{38} + 39 q^{39} + 22 q^{40} + 55 q^{41} - 28 q^{42} + 78 q^{44} + 28 q^{45} + 17 q^{46} + 184 q^{47} + 97 q^{48} + 88 q^{49} + 26 q^{50} + 27 q^{51} + 73 q^{52} + 64 q^{53} + 31 q^{54} + 39 q^{55} + 68 q^{56} - 33 q^{57} + 28 q^{58} + 60 q^{59} - 22 q^{60} + 7 q^{61} + 70 q^{62} + 28 q^{63} + 102 q^{64} + 17 q^{65} - 15 q^{66} + 82 q^{67} + 92 q^{68} + 22 q^{69} - 41 q^{70} + 113 q^{71} - 19 q^{73} + 11 q^{74} + 45 q^{75} + 34 q^{76} + 64 q^{77} + 29 q^{78} + 23 q^{79} + 54 q^{80} + 149 q^{81} + 4 q^{82} + 100 q^{83} - 49 q^{84} - 5 q^{85} - 24 q^{86} + 65 q^{87} + 14 q^{88} + 84 q^{89} - 21 q^{90} + 32 q^{91} + 95 q^{92} + 19 q^{93} - 47 q^{94} + 102 q^{95} + 29 q^{96} + 7 q^{97} + 26 q^{98} + 107 q^{99}+O(q^{100}) \) 85 * q + 11 * q^2 + 21 * q^3 + 93 * q^4 + 12 * q^5 + 4 * q^6 + 17 * q^7 + 30 * q^8 + 98 * q^9 + 9 * q^10 + 37 * q^11 + 44 * q^12 + 14 * q^13 + 26 * q^14 + 27 * q^15 + 85 * q^16 + 34 * q^17 + 3 * q^18 + 15 * q^19 + 15 * q^20 + 17 * q^21 + q^22 + 72 * q^23 + 15 * q^24 + 85 * q^25 + 33 * q^26 + 69 * q^27 + 7 * q^28 + 19 * q^29 - 9 * q^30 + 23 * q^31 + 51 * q^32 + 32 * q^33 + 49 * q^34 + 40 * q^35 + 121 * q^36 + 85 * q^37 + 84 * q^38 + 39 * q^39 + 22 * q^40 + 55 * q^41 - 28 * q^42 + 78 * q^44 + 28 * q^45 + 17 * q^46 + 184 * q^47 + 97 * q^48 + 88 * q^49 + 26 * q^50 + 27 * q^51 + 73 * q^52 + 64 * q^53 + 31 * q^54 + 39 * q^55 + 68 * q^56 - 33 * q^57 + 28 * q^58 + 60 * q^59 - 22 * q^60 + 7 * q^61 + 70 * q^62 + 28 * q^63 + 102 * q^64 + 17 * q^65 - 15 * q^66 + 82 * q^67 + 92 * q^68 + 22 * q^69 - 41 * q^70 + 113 * q^71 - 19 * q^73 + 11 * q^74 + 45 * q^75 + 34 * q^76 + 64 * q^77 + 29 * q^78 + 23 * q^79 + 54 * q^80 + 149 * q^81 + 4 * q^82 + 100 * q^83 - 49 * q^84 - 5 * q^85 - 24 * q^86 + 65 * q^87 + 14 * q^88 + 84 * q^89 - 21 * q^90 + 32 * q^91 + 95 * q^92 + 19 * q^93 - 47 * q^94 + 102 * q^95 + 29 * q^96 + 7 * q^97 + 26 * q^98 + 107 * q^99

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