LMFDB - Embedded newform 4033.2.a.c.1.20

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:	$1$
Dimension:	$77$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
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)

$f(q)$	$=$	$q-1.67758 q^{2} +0.712654 q^{3} +0.814260 q^{4} +2.97956 q^{5} -1.19553 q^{6} +2.13168 q^{7} +1.98917 q^{8} -2.49212 q^{9} +O(q^{10})$	\(q-1.67758 q^{2} +0.712654 q^{3} +0.814260 q^{4} +2.97956 q^{5} -1.19553 q^{6} +2.13168 q^{7} +1.98917 q^{8} -2.49212 q^{9} -4.99844 q^{10} -0.287924 q^{11} +0.580285 q^{12} -4.06633 q^{13} -3.57605 q^{14} +2.12340 q^{15} -4.96550 q^{16} -0.936117 q^{17} +4.18073 q^{18} -6.89538 q^{19} +2.42614 q^{20} +1.51915 q^{21} +0.483015 q^{22} +6.25818 q^{23} +1.41759 q^{24} +3.87780 q^{25} +6.82158 q^{26} -3.91398 q^{27} +1.73574 q^{28} +9.31637 q^{29} -3.56216 q^{30} -9.22921 q^{31} +4.35166 q^{32} -0.205190 q^{33} +1.57041 q^{34} +6.35146 q^{35} -2.02924 q^{36} +1.00000 q^{37} +11.5675 q^{38} -2.89789 q^{39} +5.92686 q^{40} +3.12738 q^{41} -2.54848 q^{42} -6.98779 q^{43} -0.234445 q^{44} -7.42544 q^{45} -10.4986 q^{46} -8.58905 q^{47} -3.53868 q^{48} -2.45596 q^{49} -6.50530 q^{50} -0.667128 q^{51} -3.31105 q^{52} +9.21104 q^{53} +6.56600 q^{54} -0.857889 q^{55} +4.24026 q^{56} -4.91402 q^{57} -15.6289 q^{58} -1.60262 q^{59} +1.72900 q^{60} -15.0180 q^{61} +15.4827 q^{62} -5.31240 q^{63} +2.63075 q^{64} -12.1159 q^{65} +0.344222 q^{66} -4.06675 q^{67} -0.762242 q^{68} +4.45992 q^{69} -10.6551 q^{70} -14.4076 q^{71} -4.95726 q^{72} -10.1892 q^{73} -1.67758 q^{74} +2.76353 q^{75} -5.61463 q^{76} -0.613761 q^{77} +4.86143 q^{78} -2.73071 q^{79} -14.7950 q^{80} +4.68706 q^{81} -5.24642 q^{82} +6.26225 q^{83} +1.23698 q^{84} -2.78922 q^{85} +11.7225 q^{86} +6.63935 q^{87} -0.572730 q^{88} -4.74793 q^{89} +12.4567 q^{90} -8.66810 q^{91} +5.09578 q^{92} -6.57723 q^{93} +14.4088 q^{94} -20.5452 q^{95} +3.10123 q^{96} +18.4976 q^{97} +4.12005 q^{98} +0.717543 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 77 q - 9 q^{2} - 27 q^{3} + 73 q^{4} - 16 q^{5} - 2 q^{6} - 23 q^{7} - 24 q^{8} + 66 q^{9}+O(q^{10}) $ 77 * q - 9 * q^2 - 27 * q^3 + 73 * q^4 - 16 * q^5 - 2 * q^6 - 23 * q^7 - 24 * q^8 + 66 * q^9	\( 77 q - 9 q^{2} - 27 q^{3} + 73 q^{4} - 16 q^{5} - 2 q^{6} - 23 q^{7} - 24 q^{8} + 66 q^{9} - 11 q^{10} - 33 q^{11} - 52 q^{12} - 10 q^{13} - 18 q^{14} - 33 q^{15} + 53 q^{16} - 44 q^{17} - 27 q^{18} - 9 q^{19} - 45 q^{20} - 7 q^{21} - 3 q^{22} - 74 q^{23} + 21 q^{24} + 59 q^{25} - 47 q^{26} - 99 q^{27} - 49 q^{28} - 9 q^{29} - 39 q^{30} - 27 q^{31} - 47 q^{32} - 28 q^{33} - 23 q^{34} - 48 q^{35} + 77 q^{36} + 77 q^{37} - 66 q^{38} - 11 q^{39} - 2 q^{40} - 37 q^{41} - 24 q^{42} - 44 q^{43} - 54 q^{44} - 36 q^{45} - 41 q^{46} - 150 q^{47} - 135 q^{48} + 64 q^{49} + 4 q^{50} + 3 q^{51} - 57 q^{52} - 72 q^{53} + 21 q^{54} - 65 q^{55} - 92 q^{56} - 13 q^{57} - 12 q^{58} - 70 q^{59} - 22 q^{60} + 15 q^{61} - 86 q^{62} - 108 q^{63} + 10 q^{64} - 53 q^{65} - 55 q^{66} - 48 q^{67} - 70 q^{68} - 2 q^{69} + 11 q^{70} - 127 q^{71} - 12 q^{72} - 33 q^{73} - 9 q^{74} - 115 q^{75} - 24 q^{76} - 40 q^{77} + 81 q^{78} - 7 q^{79} - 62 q^{80} + 53 q^{81} - 68 q^{82} - 164 q^{83} + 7 q^{84} - 9 q^{85} - 50 q^{86} - 75 q^{87} - 82 q^{88} - 26 q^{89} + 23 q^{90} + 16 q^{91} - 117 q^{92} + 19 q^{93} + 23 q^{94} - 92 q^{95} - 35 q^{96} - 19 q^{97} - 10 q^{98} - 19 q^{99}+O(q^{100}) \) 77 * q - 9 * q^2 - 27 * q^3 + 73 * q^4 - 16 * q^5 - 2 * q^6 - 23 * q^7 - 24 * q^8 + 66 * q^9 - 11 * q^10 - 33 * q^11 - 52 * q^12 - 10 * q^13 - 18 * q^14 - 33 * q^15 + 53 * q^16 - 44 * q^17 - 27 * q^18 - 9 * q^19 - 45 * q^20 - 7 * q^21 - 3 * q^22 - 74 * q^23 + 21 * q^24 + 59 * q^25 - 47 * q^26 - 99 * q^27 - 49 * q^28 - 9 * q^29 - 39 * q^30 - 27 * q^31 - 47 * q^32 - 28 * q^33 - 23 * q^34 - 48 * q^35 + 77 * q^36 + 77 * q^37 - 66 * q^38 - 11 * q^39 - 2 * q^40 - 37 * q^41 - 24 * q^42 - 44 * q^43 - 54 * q^44 - 36 * q^45 - 41 * q^46 - 150 * q^47 - 135 * q^48 + 64 * q^49 + 4 * q^50 + 3 * q^51 - 57 * q^52 - 72 * q^53 + 21 * q^54 - 65 * q^55 - 92 * q^56 - 13 * q^57 - 12 * q^58 - 70 * q^59 - 22 * q^60 + 15 * q^61 - 86 * q^62 - 108 * q^63 + 10 * q^64 - 53 * q^65 - 55 * q^66 - 48 * q^67 - 70 * q^68 - 2 * q^69 + 11 * q^70 - 127 * q^71 - 12 * q^72 - 33 * q^73 - 9 * q^74 - 115 * q^75 - 24 * q^76 - 40 * q^77 + 81 * q^78 - 7 * q^79 - 62 * q^80 + 53 * q^81 - 68 * q^82 - 164 * q^83 + 7 * q^84 - 9 * q^85 - 50 * q^86 - 75 * q^87 - 82 * q^88 - 26 * q^89 + 23 * q^90 + 16 * q^91 - 117 * q^92 + 19 * q^93 + 23 * q^94 - 92 * q^95 - 35 * q^96 - 19 * q^97 - 10 * q^98 - 19 * 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 $

$2$	−1.67758	−1.18623	−0.593113	−	0.805120i	$-0.702101\pi$
$2$	−1.67758	−1.18623	−0.593113	+	0.805120i	$0.702101\pi$
$3$	0.712654	0.411451	0.205725	−	0.978610i	$-0.434045\pi$
$3$	0.712654	0.411451	0.205725	+	0.978610i	$0.434045\pi$
$4$	0.814260	0.407130
$5$	2.97956	1.33250	0.666251	−	0.745728i	$-0.267898\pi$
$5$	2.97956	1.33250	0.666251	+	0.745728i	$0.267898\pi$
$6$	−1.19553	−0.488073
$7$	2.13168	0.805698	0.402849	−	0.915267i	$-0.368020\pi$
$7$	2.13168	0.805698	0.402849	+	0.915267i	$0.368020\pi$
$8$	1.98917	0.703277
$9$	−2.49212	−0.830708
$10$	−4.99844	−1.58065
$11$	−0.287924	−0.0868124	−0.0434062	−	0.999058i	$-0.513821\pi$
$11$	−0.287924	−0.0868124	−0.0434062	+	0.999058i	$0.513821\pi$
$12$	0.580285	0.167514
$13$	−4.06633	−1.12780	−0.563899	−	0.825844i	$-0.690699\pi$
$13$	−4.06633	−1.12780	−0.563899	+	0.825844i	$0.690699\pi$
$14$	−3.57605	−0.955739
$15$	2.12340	0.548259
$16$	−4.96550	−1.24138
$17$	−0.936117	−0.227042	−0.113521	−	0.993536i	$-0.536213\pi$
$17$	−0.936117	−0.227042	−0.113521	+	0.993536i	$0.536213\pi$
$18$	4.18073	0.985407
$19$	−6.89538	−1.58191	−0.790954	−	0.611875i	$-0.790416\pi$
$19$	−6.89538	−1.58191	−0.790954	+	0.611875i	$0.790416\pi$
$20$	2.42614	0.542501
$21$	1.51915	0.331505
$22$	0.483015	0.102979
$23$	6.25818	1.30492	0.652460	−	0.757823i	$-0.273737\pi$
$23$	6.25818	1.30492	0.652460	+	0.757823i	$0.273737\pi$
$24$	1.41759	0.289364
$25$	3.87780	0.775560
$26$	6.82158	1.33782
$27$	−3.91398	−0.753247
$28$	1.73574	0.328024
$29$	9.31637	1.73001	0.865003	−	0.501767i	$-0.167316\pi$
$29$	9.31637	1.73001	0.865003	+	0.501767i	$0.167316\pi$
$30$	−3.56216	−0.650359
$31$	−9.22921	−1.65761	−0.828807	−	0.559534i	$-0.810980\pi$
$31$	−9.22921	−1.65761	−0.828807	+	0.559534i	$0.810980\pi$
$32$	4.35166	0.769273
$33$	−0.205190	−0.0357191
$34$	1.57041	0.269323
$35$	6.35146	1.07359
$36$	−2.02924	−0.338206
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	11.5675	1.87650
$39$	−2.89789	−0.464033
$40$	5.92686	0.937118
$41$	3.12738	0.488415	0.244207	−	0.969723i	$-0.421472\pi$
$41$	3.12738	0.488415	0.244207	+	0.969723i	$0.421472\pi$
$42$	−2.54848	−0.393240
$43$	−6.98779	−1.06563	−0.532814	−	0.846233i	$-0.678865\pi$
$43$	−6.98779	−1.06563	−0.532814	+	0.846233i	$0.678865\pi$
$44$	−0.234445	−0.0353439
$45$	−7.42544	−1.10692
$46$	−10.4986	−1.54793
$47$	−8.58905	−1.25284	−0.626421	−	0.779485i	$-0.715481\pi$
$47$	−8.58905	−1.25284	−0.626421	+	0.779485i	$0.715481\pi$
$48$	−3.53868	−0.510765
$49$	−2.45596	−0.350851
$50$	−6.50530	−0.919989
$51$	−0.667128	−0.0934165
$52$	−3.31105	−0.459160
$53$	9.21104	1.26523	0.632617	−	0.774465i	$-0.281981\pi$
$53$	9.21104	1.26523	0.632617	+	0.774465i	$0.281981\pi$
$54$	6.56600	0.893520
$55$	−0.857889	−0.115678
$56$	4.24026	0.566629
$57$	−4.91402	−0.650878
$58$	−15.6289	−2.05218
$59$	−1.60262	−0.208643	−0.104322	−	0.994544i	$-0.533267\pi$
$59$	−1.60262	−0.208643	−0.104322	+	0.994544i	$0.533267\pi$
$60$	1.72900	0.223213
$61$	−15.0180	−1.92286	−0.961431	−	0.275046i	$-0.911307\pi$
$61$	−15.0180	−1.92286	−0.961431	+	0.275046i	$0.911307\pi$
$62$	15.4827	1.96630
$63$	−5.31240	−0.669300
$64$	2.63075	0.328844
$65$	−12.1159	−1.50279
$66$	0.344222	0.0423708
$67$	−4.06675	−0.496832	−0.248416	−	0.968653i	$-0.579910\pi$
$67$	−4.06675	−0.496832	−0.248416	+	0.968653i	$0.579910\pi$
$68$	−0.762242	−0.0924355
$69$	4.45992	0.536911
$70$	−10.6551	−1.27352
$71$	−14.4076	−1.70987	−0.854935	−	0.518736i	$-0.826403\pi$
$71$	−14.4076	−1.70987	−0.854935	+	0.518736i	$0.826403\pi$
$72$	−4.95726	−0.584218
$73$	−10.1892	−1.19255	−0.596277	−	0.802779i	$-0.703354\pi$
$73$	−10.1892	−1.19255	−0.596277	+	0.802779i	$0.703354\pi$
$74$	−1.67758	−0.195014
$75$	2.76353	0.319105
$76$	−5.61463	−0.644042
$77$	−0.613761	−0.0699446
$78$	4.86143	0.550448
$79$	−2.73071	−0.307228	−0.153614	−	0.988131i	$-0.549091\pi$
$79$	−2.73071	−0.307228	−0.153614	+	0.988131i	$0.549091\pi$
$80$	−14.7950	−1.65413
$81$	4.68706	0.520784
$82$	−5.24642	−0.579370
$83$	6.26225	0.687371	0.343685	−	0.939085i	$-0.388325\pi$
$83$	6.26225	0.687371	0.343685	+	0.939085i	$0.388325\pi$
$84$	1.23698	0.134966
$85$	−2.78922	−0.302533
$86$	11.7225	1.26407
$87$	6.63935	0.711813
$88$	−0.572730	−0.0610532
$89$	−4.74793	−0.503279	−0.251640	−	0.967821i	$-0.580970\pi$
$89$	−4.74793	−0.503279	−0.251640	+	0.967821i	$0.580970\pi$
$90$	12.4567	1.31306
$91$	−8.66810	−0.908664
$92$	5.09578	0.531272
$93$	−6.57723	−0.682027
$94$	14.4088	1.48615
$95$	−20.5452	−2.10790
$96$	3.10123	0.316518
$97$	18.4976	1.87814	0.939072	−	0.343721i	$-0.111688\pi$
$97$	18.4976	1.87814	0.939072	+	0.343721i	$0.111688\pi$
$98$	4.12005	0.416188
$99$	0.717543	0.0721158
$100$	3.15754	0.315754
$101$	−5.58318	−0.555548	−0.277774	−	0.960647i	$-0.589597\pi$
$101$	−5.58318	−0.555548	−0.277774	+	0.960647i	$0.589597\pi$
$102$	1.11916	0.110813
$103$	2.30520	0.227138	0.113569	−	0.993530i	$-0.463772\pi$
$103$	2.30520	0.227138	0.113569	+	0.993530i	$0.463772\pi$
$104$	−8.08862	−0.793154
$105$	4.52640	0.441731
$106$	−15.4522	−1.50085
$107$	−4.25182	−0.411039	−0.205520	−	0.978653i	$-0.565888\pi$
$107$	−4.25182	−0.411039	−0.205520	+	0.978653i	$0.565888\pi$
$108$	−3.18700	−0.306669
$109$	1.00000	0.0957826
$109$	1.00000	0.0957826
$110$	1.43917	0.137220
$111$	0.712654	0.0676421
$112$	−10.5848	−1.00017
$113$	−4.05793	−0.381738	−0.190869	−	0.981616i	$-0.561131\pi$
$113$	−4.05793	−0.381738	−0.190869	+	0.981616i	$0.561131\pi$
$114$	8.24364	0.772088
$115$	18.6466	1.73881
$116$	7.58594	0.704337
$117$	10.1338	0.936870
$118$	2.68852	0.247498
$119$	−1.99550	−0.182927
$120$	4.22380	0.385578
$121$	−10.9171	−0.992464
$122$	25.1939	2.28095
$123$	2.22874	0.200959
$124$	−7.51497	−0.674864
$125$	−3.34367	−0.299067
$126$	8.91195	0.793940
$127$	8.81929	0.782586	0.391293	−	0.920266i	$-0.372028\pi$
$127$	8.81929	0.782586	0.391293	+	0.920266i	$0.372028\pi$
$128$	−13.1166	−1.15936
$129$	−4.97987	−0.438453
$130$	20.3253	1.78265
$131$	15.7251	1.37390	0.686952	−	0.726702i	$-0.258948\pi$
$131$	15.7251	1.37390	0.686952	+	0.726702i	$0.258948\pi$
$132$	−0.167078	−0.0145423
$133$	−14.6987	−1.27454
$134$	6.82228	0.589355
$135$	−11.6620	−1.00370
$136$	−1.86209	−0.159673
$137$	6.27035	0.535713	0.267856	−	0.963459i	$-0.413685\pi$
$137$	6.27035	0.535713	0.267856	+	0.963459i	$0.413685\pi$
$138$	−7.48185	−0.636897
$139$	−15.2973	−1.29750	−0.648748	−	0.761003i	$-0.724707\pi$
$139$	−15.2973	−1.29750	−0.648748	+	0.761003i	$0.724707\pi$
$140$	5.17174	0.437092
$141$	−6.12102	−0.515483
$142$	24.1699	2.02829
$143$	1.17080	0.0979068
$144$	12.3746	1.03122
$145$	27.7587	2.30524
$146$	17.0931	1.41464
$147$	−1.75025	−0.144358
$148$	0.814260	0.0669317
$149$	−16.9051	−1.38492	−0.692458	−	0.721458i	$-0.743472\pi$
$149$	−16.9051	−1.38492	−0.692458	+	0.721458i	$0.743472\pi$
$150$	−4.63603	−0.378530
$151$	17.2560	1.40428	0.702138	−	0.712041i	$-0.252229\pi$
$151$	17.2560	1.40428	0.702138	+	0.712041i	$0.252229\pi$
$152$	−13.7161	−1.11252
$153$	2.33292	0.188605
$154$	1.02963	0.0829700
$155$	−27.4990	−2.20877
$156$	−2.35963	−0.188922
$157$	14.3788	1.14755	0.573776	−	0.819013i	$-0.305478\pi$
$157$	14.3788	1.14755	0.573776	+	0.819013i	$0.305478\pi$
$158$	4.58096	0.364442
$159$	6.56428	0.520582
$160$	12.9661	1.02506
$161$	13.3404	1.05137
$162$	−7.86289	−0.617767
$163$	−10.3996	−0.814556	−0.407278	−	0.913304i	$-0.633522\pi$
$163$	−10.3996	−0.814556	−0.407278	+	0.913304i	$0.633522\pi$
$164$	2.54650	0.198848
$165$	−0.611378	−0.0475957
$166$	−10.5054	−0.815377
$167$	10.3091	0.797742	0.398871	−	0.917007i	$-0.369402\pi$
$167$	10.3091	0.797742	0.398871	+	0.917007i	$0.369402\pi$
$168$	3.02184	0.233140
$169$	3.53505	0.271927
$170$	4.67913	0.358873
$171$	17.1841	1.31410
$172$	−5.68987	−0.433849
$173$	2.31535	0.176033	0.0880164	−	0.996119i	$-0.471947\pi$
$173$	2.31535	0.176033	0.0880164	+	0.996119i	$0.471947\pi$
$174$	−11.1380	−0.844370
$175$	8.26621	0.624867
$176$	1.42969	0.107767
$177$	−1.14211	−0.0858465
$178$	7.96501	0.597003
$179$	−5.18036	−0.387198	−0.193599	−	0.981081i	$-0.562016\pi$
$179$	−5.18036	−0.387198	−0.193599	+	0.981081i	$0.562016\pi$
$180$	−6.04624	−0.450660
$181$	−3.20018	−0.237867	−0.118934	−	0.992902i	$-0.537948\pi$
$181$	−3.20018	−0.237867	−0.118934	+	0.992902i	$0.537948\pi$
$182$	14.5414	1.07788
$183$	−10.7027	−0.791164
$184$	12.4486	0.917721
$185$	2.97956	0.219062
$186$	11.0338	0.809038
$187$	0.269531	0.0197100
$188$	−6.99371	−0.510069
$189$	−8.34335	−0.606889
$190$	34.4662	2.50044
$191$	−14.2661	−1.03226	−0.516129	−	0.856511i	$-0.672627\pi$
$191$	−14.2661	−1.03226	−0.516129	+	0.856511i	$0.672627\pi$
$192$	1.87482	0.135303
$193$	−4.68456	−0.337202	−0.168601	−	0.985684i	$-0.553925\pi$
$193$	−4.68456	−0.337202	−0.168601	+	0.985684i	$0.553925\pi$
$194$	−31.0311	−2.22790
$195$	−8.63444	−0.618325
$196$	−1.99979	−0.142842
$197$	14.5749	1.03842	0.519208	−	0.854648i	$-0.326227\pi$
$197$	14.5749	1.03842	0.519208	+	0.854648i	$0.326227\pi$
$198$	−1.20373	−0.0855456
$199$	−5.66633	−0.401676	−0.200838	−	0.979625i	$-0.564366\pi$
$199$	−5.66633	−0.401676	−0.200838	+	0.979625i	$0.564366\pi$
$200$	7.71360	0.545434
$201$	−2.89818	−0.204422
$202$	9.36621	0.659004
$203$	19.8595	1.39386
$204$	−0.543215	−0.0380327
$205$	9.31823	0.650814
$206$	−3.86714	−0.269437
$207$	−15.5962	−1.08401
$208$	20.1914	1.40002
$209$	1.98535	0.137329
$210$	−7.59337	−0.523992
$211$	−14.6463	−1.00829	−0.504145	−	0.863619i	$-0.668192\pi$
$211$	−14.6463	−1.00829	−0.504145	+	0.863619i	$0.668192\pi$
$212$	7.50018	0.515114
$213$	−10.2676	−0.703527
$214$	7.13275	0.487585
$215$	−20.8206	−1.41995
$216$	−7.78558	−0.529741
$217$	−19.6737	−1.33554
$218$	−1.67758	−0.113620
$219$	−7.26136	−0.490678
$220$	−0.698544	−0.0470958
$221$	3.80656	0.256057
$222$	−1.19553	−0.0802388
$223$	−13.6416	−0.913509	−0.456755	−	0.889593i	$-0.650988\pi$
$223$	−13.6416	−0.913509	−0.456755	+	0.889593i	$0.650988\pi$
$224$	9.27634	0.619801
$225$	−9.66396	−0.644264
$226$	6.80749	0.452827
$227$	−1.64206	−0.108988	−0.0544938	−	0.998514i	$-0.517355\pi$
$227$	−1.64206	−0.108988	−0.0544938	+	0.998514i	$0.517355\pi$
$228$	−4.00129	−0.264992
$229$	5.00740	0.330898	0.165449	−	0.986218i	$-0.447093\pi$
$229$	5.00740	0.330898	0.165449	+	0.986218i	$0.447093\pi$
$230$	−31.2812	−2.06262
$231$	−0.437399	−0.0287788
$232$	18.5318	1.21667
$233$	0.523373	0.0342873	0.0171436	−	0.999853i	$-0.494543\pi$
$233$	0.523373	0.0342873	0.0171436	+	0.999853i	$0.494543\pi$
$234$	−17.0002	−1.11134
$235$	−25.5916	−1.66941
$236$	−1.30495	−0.0849450
$237$	−1.94605	−0.126409
$238$	3.34760	0.216993
$239$	22.9789	1.48638	0.743190	−	0.669081i	$-0.233312\pi$
$239$	22.9789	1.48638	0.743190	+	0.669081i	$0.233312\pi$
$240$	−10.5437	−0.680595
$241$	3.46416	0.223146	0.111573	−	0.993756i	$-0.464411\pi$
$241$	3.46416	0.223146	0.111573	+	0.993756i	$0.464411\pi$
$242$	18.3143	1.17729
$243$	15.0822	0.967524
$244$	−12.2286	−0.782855
$245$	−7.31768	−0.467510
$246$	−3.73888	−0.238382
$247$	28.0389	1.78407
$248$	−18.3585	−1.16576
$249$	4.46282	0.282819
$250$	5.60925	0.354760
$251$	1.64117	0.103590	0.0517948	−	0.998658i	$-0.483506\pi$
$251$	1.64117	0.103590	0.0517948	+	0.998658i	$0.483506\pi$
$252$	−4.32567	−0.272492
$253$	−1.80188	−0.113283
$254$	−14.7950	−0.928323
$255$	−1.98775	−0.124478
$256$	16.7426	1.04641
$257$	6.83437	0.426316	0.213158	−	0.977018i	$-0.431625\pi$
$257$	6.83437	0.426316	0.213158	+	0.977018i	$0.431625\pi$
$258$	8.35411	0.520104
$259$	2.13168	0.132456
$260$	−9.86549	−0.611831
$261$	−23.2175	−1.43713
$262$	−26.3800	−1.62976
$263$	10.9252	0.673676	0.336838	−	0.941563i	$-0.390642\pi$
$263$	10.9252	0.673676	0.336838	+	0.941563i	$0.390642\pi$
$264$	−0.408158	−0.0251204
$265$	27.4449	1.68593
$266$	24.6582	1.51189
$267$	−3.38363	−0.207075
$268$	−3.31139	−0.202275
$269$	−28.8302	−1.75781	−0.878904	−	0.476999i	$-0.841725\pi$
$269$	−28.8302	−1.75781	−0.878904	+	0.476999i	$0.841725\pi$
$270$	19.5638	1.19062
$271$	2.96197	0.179927	0.0899633	−	0.995945i	$-0.471325\pi$
$271$	2.96197	0.179927	0.0899633	+	0.995945i	$0.471325\pi$
$272$	4.64829	0.281844
$273$	−6.17736	−0.373871
$274$	−10.5190	−0.635476
$275$	−1.11651	−0.0673282
$276$	3.63153	0.218593
$277$	−20.2000	−1.21370	−0.606851	−	0.794816i	$-0.707567\pi$
$277$	−20.2000	−1.21370	−0.606851	+	0.794816i	$0.707567\pi$
$278$	25.6623	1.53912
$279$	23.0003	1.37699
$280$	12.6341	0.755034
$281$	−17.8743	−1.06629	−0.533147	−	0.846023i	$-0.678991\pi$
$281$	−17.8743	−1.06629	−0.533147	+	0.846023i	$0.678991\pi$
$282$	10.2685	0.611479
$283$	−7.99727	−0.475388	−0.237694	−	0.971340i	$-0.576392\pi$
$283$	−7.99727	−0.475388	−0.237694	+	0.971340i	$0.576392\pi$
$284$	−11.7315	−0.696139
$285$	−14.6416	−0.867296
$286$	−1.96410	−0.116140
$287$	6.66656	0.393515
$288$	−10.8449	−0.639041
$289$	−16.1237	−0.948452
$290$	−46.5673	−2.73453
$291$	13.1824	0.772764
$292$	−8.29664	−0.485524
$293$	25.9447	1.51571	0.757854	−	0.652424i	$-0.226248\pi$
$293$	25.9447	1.51571	0.757854	+	0.652424i	$0.226248\pi$
$294$	2.93617	0.171241
$295$	−4.77511	−0.278018
$296$	1.98917	0.115618
$297$	1.12693	0.0653912
$298$	28.3595	1.64282
$299$	−25.4478	−1.47169
$300$	2.25023	0.129917
$301$	−14.8957	−0.858574
$302$	−28.9483	−1.66579
$303$	−3.97888	−0.228581
$304$	34.2390	1.96374
$305$	−44.7472	−2.56222
$306$	−3.91365	−0.223728
$307$	−2.15003	−0.122709	−0.0613544	−	0.998116i	$-0.519542\pi$
$307$	−2.15003	−0.122709	−0.0613544	+	0.998116i	$0.519542\pi$
$308$	−0.499761	−0.0284765
$309$	1.64281	0.0934561
$310$	46.1317	2.62010
$311$	11.3895	0.645839	0.322919	−	0.946427i	$-0.395336\pi$
$311$	11.3895	0.645839	0.322919	+	0.946427i	$0.395336\pi$
$312$	−5.76439	−0.326344
$313$	−13.8453	−0.782580	−0.391290	−	0.920267i	$-0.627971\pi$
$313$	−13.8453	−0.782580	−0.391290	+	0.920267i	$0.627971\pi$
$314$	−24.1215	−1.36125
$315$	−15.8286	−0.891843
$316$	−2.22350	−0.125082
$317$	32.0677	1.80110	0.900551	−	0.434751i	$-0.143164\pi$
$317$	32.0677	1.80110	0.900551	+	0.434751i	$0.143164\pi$
$318$	−11.0121	−0.617527
$319$	−2.68241	−0.150186
$320$	7.83850	0.438186
$321$	−3.03008	−0.169122
$322$	−22.3796	−1.24716
$323$	6.45488	0.359159
$324$	3.81648	0.212027
$325$	−15.7684	−0.874675
$326$	17.4460	0.966247
$327$	0.712654	0.0394099
$328$	6.22089	0.343491
$329$	−18.3091	−1.00941
$330$	1.02563	0.0564592
$331$	−21.8295	−1.19986	−0.599928	−	0.800054i	$-0.704804\pi$
$331$	−21.8295	−1.19986	−0.599928	+	0.800054i	$0.704804\pi$
$332$	5.09910	0.279849
$333$	−2.49212	−0.136568
$334$	−17.2943	−0.946301
$335$	−12.1171	−0.662030
$336$	−7.54333	−0.411522
$337$	−21.6311	−1.17832	−0.589162	−	0.808015i	$-0.700542\pi$
$337$	−21.6311	−1.17832	−0.589162	+	0.808015i	$0.700542\pi$
$338$	−5.93032	−0.322567
$339$	−2.89190	−0.157066
$340$	−2.27115	−0.123170
$341$	2.65731	0.143902
$342$	−28.8277	−1.55882
$343$	−20.1570	−1.08838
$344$	−13.8999	−0.749432
$345$	13.2886	0.715435
$346$	−3.88417	−0.208814
$347$	18.8601	1.01246	0.506230	−	0.862398i	$-0.331039\pi$
$347$	18.8601	1.01246	0.506230	+	0.862398i	$0.331039\pi$
$348$	5.40615	0.289800
$349$	−7.58683	−0.406114	−0.203057	−	0.979167i	$-0.565088\pi$
$349$	−7.58683	−0.406114	−0.203057	+	0.979167i	$0.565088\pi$
$350$	−13.8672	−0.741233
$351$	15.9156	0.849510
$352$	−1.25295	−0.0667825
$353$	−22.1292	−1.17782	−0.588908	−	0.808200i	$-0.700442\pi$
$353$	−22.1292	−1.17782	−0.588908	+	0.808200i	$0.700442\pi$
$354$	1.91598	0.101833
$355$	−42.9284	−2.27840
$356$	−3.86605	−0.204900
$357$	−1.42210	−0.0752655
$358$	8.69045	0.459304
$359$	6.56537	0.346507	0.173253	−	0.984877i	$-0.444572\pi$
$359$	6.56537	0.346507	0.173253	+	0.984877i	$0.444572\pi$
$360$	−14.7705	−0.778472
$361$	28.5463	1.50244
$362$	5.36854	0.282164
$363$	−7.78011	−0.408350
$364$	−7.05809	−0.369944
$365$	−30.3593	−1.58908
$366$	17.9545	0.938498
$367$	16.4395	0.858134	0.429067	−	0.903273i	$-0.358842\pi$
$367$	16.4395	0.858134	0.429067	+	0.903273i	$0.358842\pi$
$368$	−31.0750	−1.61990
$369$	−7.79382	−0.405730
$370$	−4.99844	−0.259857
$371$	19.6350	1.01940
$372$	−5.35558	−0.277674
$373$	28.8575	1.49419	0.747093	−	0.664719i	$-0.231449\pi$
$373$	28.8575	1.49419	0.747093	+	0.664719i	$0.231449\pi$
$374$	−0.452158	−0.0233805
$375$	−2.38288	−0.123051
$376$	−17.0851	−0.881095
$377$	−37.8834	−1.95110
$378$	13.9966	0.719907
$379$	21.8722	1.12350	0.561750	−	0.827307i	$-0.310128\pi$
$379$	21.8722	1.12350	0.561750	+	0.827307i	$0.310128\pi$
$380$	−16.7292	−0.858187
$381$	6.28510	0.321996
$382$	23.9324	1.22449
$383$	7.72986	0.394977	0.197489	−	0.980305i	$-0.436721\pi$
$383$	7.72986	0.394977	0.197489	+	0.980305i	$0.436721\pi$
$384$	−9.34761	−0.477018
$385$	−1.82874	−0.0932013
$386$	7.85870	0.399998
$387$	17.4144	0.885225
$388$	15.0618	0.764648
$389$	34.5534	1.75193	0.875963	−	0.482378i	$-0.160227\pi$
$389$	34.5534	1.75193	0.875963	+	0.482378i	$0.160227\pi$
$390$	14.4849	0.733473
$391$	−5.85839	−0.296272
$392$	−4.88531	−0.246746
$393$	11.2065	0.565294
$394$	−24.4504	−1.23180
$395$	−8.13631	−0.409382
$396$	0.584266	0.0293605
$397$	26.5320	1.33160	0.665801	−	0.746129i	$-0.268090\pi$
$397$	26.5320	1.33160	0.665801	+	0.746129i	$0.268090\pi$
$398$	9.50570	0.476478
$399$	−10.4751	−0.524411
$400$	−19.2552	−0.962761
$401$	37.1126	1.85331	0.926657	−	0.375907i	$-0.122669\pi$
$401$	37.1126	1.85331	0.926657	+	0.375907i	$0.122669\pi$
$402$	4.86192	0.242491
$403$	37.5290	1.86945
$404$	−4.54616	−0.226180
$405$	13.9654	0.693945
$406$	−33.3158	−1.65343
$407$	−0.287924	−0.0142719
$408$	−1.32703	−0.0656977
$409$	−31.0516	−1.53540	−0.767701	−	0.640808i	$-0.778599\pi$
$409$	−31.0516	−1.53540	−0.767701	+	0.640808i	$0.778599\pi$
$410$	−15.6320	−0.772011
$411$	4.46859	0.220419
$412$	1.87703	0.0924746
$413$	−3.41627	−0.168104
$414$	26.1637	1.28588
$415$	18.6588	0.915923
$416$	−17.6953	−0.867584
$417$	−10.9016	−0.533856
$418$	−3.33057	−0.162904
$419$	−9.06959	−0.443078	−0.221539	−	0.975151i	$-0.571108\pi$
$419$	−9.06959	−0.443078	−0.221539	+	0.975151i	$0.571108\pi$
$420$	3.68566	0.179842
$421$	−31.9283	−1.55609	−0.778045	−	0.628208i	$-0.783789\pi$
$421$	−31.9283	−1.55609	−0.778045	+	0.628208i	$0.783789\pi$
$422$	24.5702	1.19606
$423$	21.4050	1.04075
$424$	18.3223	0.889810
$425$	−3.63007	−0.176084
$426$	17.2247	0.834542
$427$	−32.0136	−1.54925
$428$	−3.46209	−0.167346
$429$	0.834372	0.0402839
$430$	34.9281	1.68438
$431$	−5.32507	−0.256500	−0.128250	−	0.991742i	$-0.540936\pi$
$431$	−5.32507	−0.256500	−0.128250	+	0.991742i	$0.540936\pi$
$432$	19.4349	0.935062
$433$	11.5239	0.553802	0.276901	−	0.960898i	$-0.410693\pi$
$433$	11.5239	0.553802	0.276901	+	0.960898i	$0.410693\pi$
$434$	33.0041	1.58425
$435$	19.7824	0.948491
$436$	0.814260	0.0389960
$437$	−43.1525	−2.06427
$438$	12.1815	0.582054
$439$	−3.07330	−0.146681	−0.0733404	−	0.997307i	$-0.523366\pi$
$439$	−3.07330	−0.146681	−0.0733404	+	0.997307i	$0.523366\pi$
$440$	−1.70649	−0.0813535
$441$	6.12055	0.291455
$442$	−6.38580	−0.303741
$443$	−22.7261	−1.07975	−0.539874	−	0.841746i	$-0.681528\pi$
$443$	−22.7261	−1.07975	−0.539874	+	0.841746i	$0.681528\pi$
$444$	0.580285	0.0275391
$445$	−14.1468	−0.670621
$446$	22.8848	1.08363
$447$	−12.0475	−0.569825
$448$	5.60792	0.264949
$449$	−39.4856	−1.86344	−0.931721	−	0.363176i	$-0.881692\pi$
$449$	−39.4856	−1.86344	−0.931721	+	0.363176i	$0.881692\pi$
$450$	16.2120	0.764242
$451$	−0.900449	−0.0424005
$452$	−3.30421	−0.155417
$453$	12.2976	0.577791
$454$	2.75469	0.129284
$455$	−25.8272	−1.21080
$456$	−9.77482	−0.457748
$457$	−5.79383	−0.271024	−0.135512	−	0.990776i	$-0.543268\pi$
$457$	−5.79383	−0.271024	−0.135512	+	0.990776i	$0.543268\pi$
$458$	−8.40029	−0.392520
$459$	3.66395	0.171018
$460$	15.1832	0.707921
$461$	3.49254	0.162664	0.0813318	−	0.996687i	$-0.474083\pi$
$461$	3.49254	0.162664	0.0813318	+	0.996687i	$0.474083\pi$
$462$	0.733771	0.0341381
$463$	16.0530	0.746048	0.373024	−	0.927822i	$-0.378321\pi$
$463$	16.0530	0.746048	0.373024	+	0.927822i	$0.378321\pi$
$464$	−46.2604	−2.14759
$465$	−19.5973	−0.908802
$466$	−0.877997	−0.0406724
$467$	−32.7578	−1.51585	−0.757925	−	0.652341i	$-0.773787\pi$
$467$	−32.7578	−1.51585	−0.757925	+	0.652341i	$0.773787\pi$
$468$	8.25155	0.381428
$469$	−8.66899	−0.400297
$470$	42.9319	1.98030
$471$	10.2471	0.472161
$472$	−3.18788	−0.146734
$473$	2.01195	0.0925097
$474$	3.26464	0.149950
$475$	−26.7389	−1.22687
$476$	−1.62485	−0.0744751
$477$	−22.9551	−1.05104
$478$	−38.5488	−1.76318
$479$	27.3466	1.24950	0.624749	−	0.780826i	$-0.285201\pi$
$479$	27.3466	1.24950	0.624749	+	0.780826i	$0.285201\pi$
$480$	9.24032	0.421761
$481$	−4.06633	−0.185409
$482$	−5.81139	−0.264701
$483$	9.50710	0.432588
$484$	−8.88936	−0.404062
$485$	55.1147	2.50263
$486$	−25.3015	−1.14770
$487$	−0.484198	−0.0219411	−0.0109705	−	0.999940i	$-0.503492\pi$
$487$	−0.484198	−0.0219411	−0.0109705	+	0.999940i	$0.503492\pi$
$488$	−29.8734	−1.35231
$489$	−7.41129	−0.335150
$490$	12.2760	0.554572
$491$	−12.9205	−0.583094	−0.291547	−	0.956557i	$-0.594170\pi$
$491$	−12.9205	−0.583094	−0.291547	+	0.956557i	$0.594170\pi$
$492$	1.81477	0.0818163
$493$	−8.72121	−0.392784
$494$	−47.0374	−2.11631
$495$	2.13797	0.0960944
$496$	45.8276	2.05772
$497$	−30.7124	−1.37764
$498$	−7.48671	−0.335488
$499$	−20.2671	−0.907282	−0.453641	−	0.891185i	$-0.649875\pi$
$499$	−20.2671	−0.907282	−0.453641	+	0.891185i	$0.649875\pi$
$500$	−2.72261	−0.121759
$501$	7.34682	0.328232
$502$	−2.75318	−0.122880
$503$	−1.85015	−0.0824941	−0.0412471	−	0.999149i	$-0.513133\pi$
$503$	−1.85015	−0.0824941	−0.0412471	+	0.999149i	$0.513133\pi$
$504$	−10.5673	−0.470703
$505$	−16.6355	−0.740268
$506$	3.02279	0.134380
$507$	2.51927	0.111885
$508$	7.18119	0.318614
$509$	−26.7844	−1.18720	−0.593598	−	0.804762i	$-0.702293\pi$
$509$	−26.7844	−1.18720	−0.593598	+	0.804762i	$0.702293\pi$
$510$	3.33460	0.147659
$511$	−21.7200	−0.960838
$512$	−1.85376	−0.0819252
$513$	26.9884	1.19157
$514$	−11.4652	−0.505707
$515$	6.86848	0.302662
$516$	−4.05491	−0.178507
$517$	2.47299	0.108762
$518$	−3.57605	−0.157123
$519$	1.65004	0.0724288
$520$	−24.1006	−1.05688
$521$	15.7539	0.690189	0.345095	−	0.938568i	$-0.387847\pi$
$521$	15.7539	0.690189	0.345095	+	0.938568i	$0.387847\pi$
$522$	38.9492	1.70476
$523$	−9.51380	−0.416010	−0.208005	−	0.978128i	$-0.566697\pi$
$523$	−9.51380	−0.416010	−0.208005	+	0.978128i	$0.566697\pi$
$524$	12.8043	0.559358
$525$	5.89095	0.257102
$526$	−18.3278	−0.799132
$527$	8.63962	0.376348
$528$	1.01887	0.0443408
$529$	16.1648	0.702819
$530$	−46.0409	−1.99989
$531$	3.99393	0.173322
$532$	−11.9686	−0.518904
$533$	−12.7170	−0.550833
$534$	5.67630	0.245637
$535$	−12.6686	−0.547710
$536$	−8.08945	−0.349411
$537$	−3.69181	−0.159313
$538$	48.3648	2.08516
$539$	0.707130	0.0304582
$540$	−9.49587	−0.408637
$541$	−17.9585	−0.772095	−0.386047	−	0.922479i	$-0.626160\pi$
$541$	−17.9585	−0.772095	−0.386047	+	0.922479i	$0.626160\pi$
$542$	−4.96892	−0.213433
$543$	−2.28062	−0.0978707
$544$	−4.07367	−0.174657
$545$	2.97956	0.127630
$546$	10.3630	0.443495
$547$	25.7553	1.10122	0.550608	−	0.834764i	$-0.314396\pi$
$547$	25.7553	1.10122	0.550608	+	0.834764i	$0.314396\pi$
$548$	5.10570	0.218105
$549$	37.4268	1.59734
$550$	1.87303	0.0798665
$551$	−64.2399	−2.73671
$552$	8.87153	0.377597
$553$	−5.82098	−0.247533
$554$	33.8871	1.43972
$555$	2.12340	0.0901332
$556$	−12.4559	−0.528249
$557$	10.4023	0.440761	0.220381	−	0.975414i	$-0.429270\pi$
$557$	10.4023	0.440761	0.220381	+	0.975414i	$0.429270\pi$
$558$	−38.5848	−1.63342
$559$	28.4147	1.20181
$560$	−31.5382	−1.33273
$561$	0.192082	0.00810972
$562$	29.9856	1.26486
$563$	−18.4333	−0.776870	−0.388435	−	0.921476i	$-0.626984\pi$
$563$	−18.4333	−0.776870	−0.388435	+	0.921476i	$0.626984\pi$
$564$	−4.98410	−0.209868
$565$	−12.0909	−0.508666
$566$	13.4160	0.563917
$567$	9.99128	0.419595
$568$	−28.6592	−1.20251
$569$	−0.982307	−0.0411805	−0.0205902	−	0.999788i	$-0.506555\pi$
$569$	−0.982307	−0.0411805	−0.0205902	+	0.999788i	$0.506555\pi$
$570$	24.5625	1.02881
$571$	−33.4177	−1.39849	−0.699243	−	0.714884i	$-0.746479\pi$
$571$	−33.4177	−1.39849	−0.699243	+	0.714884i	$0.746479\pi$
$572$	0.953332	0.0398608
$573$	−10.1668	−0.424723
$574$	−11.1837	−0.466797
$575$	24.2680	1.01204
$576$	−6.55617	−0.273174
$577$	31.8728	1.32688	0.663441	−	0.748229i	$-0.269095\pi$
$577$	31.8728	1.32688	0.663441	+	0.748229i	$0.269095\pi$
$578$	27.0487	1.12508
$579$	−3.33847	−0.138742
$580$	22.6028	0.938530
$581$	13.3491	0.553813
$582$	−22.1144	−0.916672
$583$	−2.65208	−0.109838
$584$	−20.2680	−0.838696
$585$	30.1943	1.24838
$586$	−43.5243	−1.79797
$587$	−33.9888	−1.40287	−0.701434	−	0.712735i	$-0.747456\pi$
$587$	−33.9888	−1.40287	−0.701434	+	0.712735i	$0.747456\pi$
$588$	−1.42516	−0.0587725
$589$	63.6389	2.62220
$590$	8.01061	0.329791
$591$	10.3868	0.427258
$592$	−4.96550	−0.204081
$593$	−28.0865	−1.15337	−0.576687	−	0.816965i	$-0.695655\pi$
$593$	−28.0865	−1.15337	−0.576687	+	0.816965i	$0.695655\pi$
$594$	−1.89051	−0.0775686
$595$	−5.94571	−0.243751
$596$	−13.7651	−0.563841
$597$	−4.03813	−0.165270
$598$	42.6907	1.74575
$599$	−13.5898	−0.555264	−0.277632	−	0.960687i	$-0.589550\pi$
$599$	−13.5898	−0.555264	−0.277632	+	0.960687i	$0.589550\pi$
$600$	5.49713	0.224419
$601$	36.5332	1.49022	0.745111	−	0.666940i	$-0.232396\pi$
$601$	36.5332	1.49022	0.745111	+	0.666940i	$0.232396\pi$
$602$	24.9887	1.01846
$603$	10.1348	0.412723
$604$	14.0509	0.571723
$605$	−32.5282	−1.32246
$606$	6.67487	0.271148
$607$	4.26694	0.173190	0.0865948	−	0.996244i	$-0.472401\pi$
$607$	4.26694	0.173190	0.0865948	+	0.996244i	$0.472401\pi$
$608$	−30.0064	−1.21692
$609$	14.1529	0.573506
$610$	75.0668	3.03937
$611$	34.9259	1.41295
$612$	1.89960	0.0767869
$613$	33.8142	1.36574	0.682871	−	0.730539i	$-0.260731\pi$
$613$	33.8142	1.36574	0.682871	+	0.730539i	$0.260731\pi$
$614$	3.60684	0.145560
$615$	6.64068	0.267778
$616$	−1.22087	−0.0491904
$617$	−11.2709	−0.453750	−0.226875	−	0.973924i	$-0.572851\pi$
$617$	−11.2709	−0.453750	−0.226875	+	0.973924i	$0.572851\pi$
$618$	−2.75594	−0.110860
$619$	−19.4879	−0.783285	−0.391642	−	0.920117i	$-0.628093\pi$
$619$	−19.4879	−0.783285	−0.391642	+	0.920117i	$0.628093\pi$
$620$	−22.3913	−0.899258
$621$	−24.4944	−0.982927
$622$	−19.1067	−0.766110
$623$	−10.1210	−0.405491
$624$	14.3895	0.576040
$625$	−29.3517	−1.17407
$626$	23.2265	0.928316
$627$	1.41487	0.0565043
$628$	11.7081	0.467202
$629$	−0.936117	−0.0373254
$630$	26.5537	1.05793
$631$	15.4270	0.614138	0.307069	−	0.951687i	$-0.400652\pi$
$631$	15.4270	0.614138	0.307069	+	0.951687i	$0.400652\pi$
$632$	−5.43183	−0.216067
$633$	−10.4377	−0.414862
$634$	−53.7960	−2.13651
$635$	26.2776	1.04280
$636$	5.34503	0.211944
$637$	9.98674	0.395689
$638$	4.49994	0.178154
$639$	35.9056	1.42040
$640$	−39.0818	−1.54484
$641$	3.70352	0.146280	0.0731402	−	0.997322i	$-0.476698\pi$
$641$	3.70352	0.146280	0.0731402	+	0.997322i	$0.476698\pi$
$642$	5.08319	0.200617
$643$	29.4450	1.16120	0.580599	−	0.814190i	$-0.302818\pi$
$643$	29.4450	1.16120	0.580599	+	0.814190i	$0.302818\pi$
$644$	10.8626	0.428045
$645$	−14.8379	−0.584240
$646$	−10.8286	−0.426044
$647$	−22.9379	−0.901782	−0.450891	−	0.892579i	$-0.648894\pi$
$647$	−22.9379	−0.901782	−0.450891	+	0.892579i	$0.648894\pi$
$648$	9.32335	0.366256
$649$	0.461433	0.0181128
$650$	26.4527	1.03756
$651$	−14.0205	−0.549508
$652$	−8.46794	−0.331630
$653$	30.5536	1.19565	0.597827	−	0.801625i	$-0.296031\pi$
$653$	30.5536	1.19565	0.597827	+	0.801625i	$0.296031\pi$
$654$	−1.19553	−0.0467490
$655$	46.8538	1.83073
$656$	−15.5290	−0.606306
$657$	25.3927	0.990664
$658$	30.7148	1.19739
$659$	−30.5887	−1.19157	−0.595784	−	0.803145i	$-0.703158\pi$
$659$	−30.5887	−1.19157	−0.595784	+	0.803145i	$0.703158\pi$
$660$	−0.497820	−0.0193776
$661$	0.809167	0.0314730	0.0157365	−	0.999876i	$-0.494991\pi$
$661$	0.809167	0.0314730	0.0157365	+	0.999876i	$0.494991\pi$
$662$	36.6206	1.42330
$663$	2.71276	0.105355
$664$	12.4567	0.483412
$665$	−43.7958	−1.69833
$666$	4.18073	0.162000
$667$	58.3035	2.25752
$668$	8.39428	0.324785
$669$	−9.72174	−0.375864
$670$	20.3274	0.785316
$671$	4.32406	0.166928
$672$	6.61082	0.255018
$673$	−35.7122	−1.37661	−0.688303	−	0.725424i	$-0.741644\pi$
$673$	−35.7122	−1.37661	−0.688303	+	0.725424i	$0.741644\pi$
$674$	36.2879	1.39776
$675$	−15.1776	−0.584188
$676$	2.87845	0.110710
$677$	45.1096	1.73370	0.866852	−	0.498566i	$-0.166140\pi$
$677$	45.1096	1.73370	0.866852	+	0.498566i	$0.166140\pi$
$678$	4.85138	0.186316
$679$	39.4308	1.51322
$680$	−5.54823	−0.212765
$681$	−1.17022	−0.0448430
$682$	−4.45784	−0.170700
$683$	23.5168	0.899846	0.449923	−	0.893067i	$-0.351451\pi$
$683$	23.5168	0.899846	0.449923	+	0.893067i	$0.351451\pi$
$684$	13.9924	0.535011
$685$	18.6829	0.713838
$686$	33.8150	1.29106
$687$	3.56854	0.136148
$688$	34.6979	1.32284
$689$	−37.4551	−1.42693
$690$	−22.2926	−0.848667
$691$	10.5838	0.402626	0.201313	−	0.979527i	$-0.435479\pi$
$691$	10.5838	0.402626	0.201313	+	0.979527i	$0.435479\pi$
$692$	1.88530	0.0716682
$693$	1.52957	0.0581035
$694$	−31.6392	−1.20101
$695$	−45.5791	−1.72892
$696$	13.2068	0.500602
$697$	−2.92760	−0.110891
$698$	12.7275	0.481742
$699$	0.372984	0.0141075
$700$	6.73084	0.254402
$701$	13.4860	0.509358	0.254679	−	0.967026i	$-0.418030\pi$
$701$	13.4860	0.509358	0.254679	+	0.967026i	$0.418030\pi$
$702$	−26.6996	−1.00771
$703$	−6.89538	−0.260064
$704$	−0.757458	−0.0285478
$705$	−18.2380	−0.686881
$706$	37.1233	1.39715
$707$	−11.9015	−0.447603
$708$	−0.929977	−0.0349507
$709$	25.6855	0.964641	0.482320	−	0.875995i	$-0.339794\pi$
$709$	25.6855	0.964641	0.482320	+	0.875995i	$0.339794\pi$
$710$	72.0156	2.70270
$711$	6.80526	0.255217
$712$	−9.44443	−0.353945
$713$	−57.7580	−2.16306
$714$	2.38568	0.0892818
$715$	3.48846	0.130461
$716$	−4.21816	−0.157640
$717$	16.3760	0.611572
$718$	−11.0139	−0.411035
$719$	13.2044	0.492441	0.246221	−	0.969214i	$-0.420811\pi$
$719$	13.2044	0.492441	0.246221	+	0.969214i	$0.420811\pi$
$720$	36.8710	1.37410
$721$	4.91394	0.183005
$722$	−47.8885	−1.78223
$723$	2.46875	0.0918136
$724$	−2.60578	−0.0968429
$725$	36.1270	1.34172
$726$	13.0517	0.484395
$727$	−14.3440	−0.531989	−0.265995	−	0.963975i	$-0.585700\pi$
$727$	−14.3440	−0.531989	−0.265995	+	0.963975i	$0.585700\pi$
$728$	−17.2423	−0.639043
$729$	−3.31278	−0.122695
$730$	50.9301	1.88501
$731$	6.54139	0.241942
$732$	−8.71475	−0.322106
$733$	−39.9325	−1.47494	−0.737470	−	0.675380i	$-0.763980\pi$
$733$	−39.9325	−1.47494	−0.737470	+	0.675380i	$0.763980\pi$
$734$	−27.5785	−1.01794
$735$	−5.21498	−0.192357
$736$	27.2335	1.00384
$737$	1.17092	0.0431312
$738$	13.0747	0.481287
$739$	17.0352	0.626650	0.313325	−	0.949646i	$-0.398557\pi$
$739$	17.0352	0.626650	0.313325	+	0.949646i	$0.398557\pi$
$740$	2.42614	0.0891866
$741$	19.9820	0.734059
$742$	−32.9391	−1.20923
$743$	16.2335	0.595551	0.297775	−	0.954636i	$-0.403755\pi$
$743$	16.2335	0.595551	0.297775	+	0.954636i	$0.403755\pi$
$744$	−13.0832	−0.479654
$745$	−50.3697	−1.84540
$746$	−48.4107	−1.77244
$747$	−15.6063	−0.571005
$748$	0.219468	0.00802455
$749$	−9.06351	−0.331173
$750$	3.99746	0.145966
$751$	−53.4566	−1.95066	−0.975330	−	0.220751i	$-0.929149\pi$
$751$	−53.4566	−1.95066	−0.975330	+	0.220751i	$0.929149\pi$
$752$	42.6489	1.55525
$753$	1.16958	0.0426220
$754$	63.5523	2.31444
$755$	51.4155	1.87120
$756$	−6.79365	−0.247083
$757$	−19.3395	−0.702908	−0.351454	−	0.936205i	$-0.614313\pi$
$757$	−19.3395	−0.702908	−0.351454	+	0.936205i	$0.614313\pi$
$758$	−36.6923	−1.33272
$759$	−1.28412	−0.0466105
$760$	−40.8679	−1.48244
$761$	−53.7297	−1.94770	−0.973850	−	0.227193i	$-0.927045\pi$
$761$	−53.7297	−1.94770	−0.973850	+	0.227193i	$0.927045\pi$
$762$	−10.5437	−0.381959
$763$	2.13168	0.0771718
$764$	−11.6163	−0.420263
$765$	6.95108	0.251317
$766$	−12.9674	−0.468532
$767$	6.51679	0.235307
$768$	11.9317	0.430548
$769$	−37.3510	−1.34691	−0.673456	−	0.739227i	$-0.735191\pi$
$769$	−37.3510	−1.34691	−0.673456	+	0.739227i	$0.735191\pi$
$770$	3.06785	0.110558
$771$	4.87054	0.175408
$772$	−3.81445	−0.137285
$773$	−36.0943	−1.29822	−0.649111	−	0.760693i	$-0.724859\pi$
$773$	−36.0943	−1.29822	−0.649111	+	0.760693i	$0.724859\pi$
$774$	−29.2140	−1.05008
$775$	−35.7890	−1.28558
$776$	36.7948	1.32086
$777$	1.51915	0.0544991
$778$	−57.9659	−2.07818
$779$	−21.5645	−0.772628
$780$	−7.03068	−0.251739
$781$	4.14830	0.148438
$782$	9.82789	0.351445
$783$	−36.4641	−1.30312
$784$	12.1951	0.435538
$785$	42.8425	1.52911
$786$	−18.7998	−0.670566
$787$	6.55742	0.233747	0.116873	−	0.993147i	$-0.462713\pi$
$787$	6.55742	0.233747	0.116873	+	0.993147i	$0.462713\pi$
$788$	11.8677	0.422770
$789$	7.78588	0.277185
$790$	13.6493	0.485619
$791$	−8.65019	−0.307565
$792$	1.42731	0.0507174
$793$	61.0683	2.16860
$794$	−44.5094	−1.57958
$795$	19.5587	0.693676
$796$	−4.61387	−0.163534
$797$	33.1241	1.17332	0.586658	−	0.809835i	$-0.300443\pi$
$797$	33.1241	1.17332	0.586658	+	0.809835i	$0.300443\pi$
$798$	17.5728	0.622069
$799$	8.04035	0.284447
$800$	16.8749	0.596617
$801$	11.8324	0.418078
$802$	−62.2592	−2.19845
$803$	2.93371	0.103529
$804$	−2.35987	−0.0832264
$805$	39.7486	1.40095
$806$	−62.9578	−2.21759
$807$	−20.5460	−0.723252
$808$	−11.1059	−0.390704
$809$	−7.37005	−0.259117	−0.129559	−	0.991572i	$-0.541356\pi$
$809$	−7.37005	−0.259117	−0.129559	+	0.991572i	$0.541356\pi$
$810$	−23.4280	−0.823175
$811$	7.41796	0.260480	0.130240	−	0.991483i	$-0.458425\pi$
$811$	7.41796	0.260480	0.130240	+	0.991483i	$0.458425\pi$
$812$	16.1708	0.567483
$813$	2.11086	0.0740310
$814$	0.483015	0.0169297
$815$	−30.9861	−1.08540
$816$	3.31262	0.115965
$817$	48.1834	1.68573
$818$	52.0914	1.82133
$819$	21.6020	0.754834
$820$	7.58746	0.264966
$821$	27.1310	0.946879	0.473439	−	0.880826i	$-0.343012\pi$
$821$	27.1310	0.946879	0.473439	+	0.880826i	$0.343012\pi$
$822$	−7.49640	−0.261467
$823$	−46.6066	−1.62460	−0.812302	−	0.583237i	$-0.801786\pi$
$823$	−46.6066	−1.62460	−0.812302	+	0.583237i	$0.801786\pi$
$824$	4.58543	0.159741
$825$	−0.795687	−0.0277023
$826$	5.73105	0.199409
$827$	15.2656	0.530838	0.265419	−	0.964133i	$-0.414490\pi$
$827$	15.2656	0.530838	0.265419	+	0.964133i	$0.414490\pi$
$828$	−12.6993	−0.441332
$829$	3.07620	0.106841	0.0534203	−	0.998572i	$-0.482988\pi$
$829$	3.07620	0.106841	0.0534203	+	0.998572i	$0.482988\pi$
$830$	−31.3015	−1.08649
$831$	−14.3956	−0.499379
$832$	−10.6975	−0.370870
$833$	2.29906	0.0796578
$834$	18.2883	0.633273
$835$	30.7166	1.06299
$836$	1.61659	0.0559109
$837$	36.1230	1.24859
$838$	15.2149	0.525591
$839$	29.9429	1.03374	0.516871	−	0.856063i	$-0.327097\pi$
$839$	29.9429	1.03374	0.516871	+	0.856063i	$0.327097\pi$
$840$	9.00377	0.310659
$841$	57.7947	1.99292
$842$	53.5622	1.84587
$843$	−12.7382	−0.438728
$844$	−11.9259	−0.410505
$845$	10.5329	0.362343
$846$	−35.9085	−1.23456
$847$	−23.2717	−0.799626
$848$	−45.7374	−1.57063
$849$	−5.69929	−0.195599
$850$	6.08972	0.208876
$851$	6.25818	0.214528
$852$	−8.36053	−0.286427
$853$	−7.74013	−0.265017	−0.132509	−	0.991182i	$-0.542303\pi$
$853$	−7.74013	−0.265017	−0.132509	+	0.991182i	$0.542303\pi$
$854$	53.7052	1.83775
$855$	51.2013	1.75105
$856$	−8.45759	−0.289075
$857$	33.6548	1.14963	0.574814	−	0.818284i	$-0.305074\pi$
$857$	33.6548	1.14963	0.574814	+	0.818284i	$0.305074\pi$
$858$	−1.39972	−0.0477857
$859$	−13.2352	−0.451578	−0.225789	−	0.974176i	$-0.572496\pi$
$859$	−13.2352	−0.451578	−0.225789	+	0.974176i	$0.572496\pi$
$860$	−16.9533	−0.578104
$861$	4.75095	0.161912
$862$	8.93321	0.304266
$863$	−36.8396	−1.25403	−0.627017	−	0.779005i	$-0.715725\pi$
$863$	−36.8396	−1.25403	−0.627017	+	0.779005i	$0.715725\pi$
$864$	−17.0323	−0.579452
$865$	6.89873	0.234564
$866$	−19.3322	−0.656934
$867$	−11.4906	−0.390242
$868$	−16.0195	−0.543737
$869$	0.786236	0.0266712
$870$	−33.1864	−1.12512
$871$	16.5367	0.560326
$872$	1.98917	0.0673618
$873$	−46.0982	−1.56019
$874$	72.3916	2.44868
$875$	−7.12761	−0.240957
$876$	−5.91264	−0.199769
$877$	−55.0044	−1.85737	−0.928683	−	0.370874i	$-0.879058\pi$
$877$	−55.0044	−1.85737	−0.928683	+	0.370874i	$0.879058\pi$
$878$	5.15570	0.173996
$879$	18.4896	0.623640
$880$	4.25985	0.143599
$881$	56.7095	1.91059	0.955296	−	0.295653i	$-0.0955371\pi$
$881$	56.7095	1.91059	0.955296	+	0.295653i	$0.0955371\pi$
$882$	−10.2677	−0.345731
$883$	1.12152	0.0377421	0.0188711	−	0.999822i	$-0.493993\pi$
$883$	1.12152	0.0377421	0.0188711	+	0.999822i	$0.493993\pi$
$884$	3.09953	0.104248
$885$	−3.40300	−0.114391
$886$	38.1247	1.28083
$887$	−26.9238	−0.904011	−0.452006	−	0.892015i	$-0.649291\pi$
$887$	−26.9238	−0.904011	−0.452006	+	0.892015i	$0.649291\pi$
$888$	1.41759	0.0475712
$889$	18.7999	0.630527
$890$	23.7323	0.795507
$891$	−1.34952	−0.0452105
$892$	−11.1078	−0.371917
$893$	59.2247	1.98188
$894$	20.2105	0.675941
$895$	−15.4352	−0.515942
$896$	−27.9604	−0.934091
$897$	−18.1355	−0.605527
$898$	66.2401	2.21046
$899$	−85.9827	−2.86768
$900$	−7.86897	−0.262299
$901$	−8.62261	−0.287261
$902$	1.51057	0.0502965
$903$	−10.6155	−0.353261
$904$	−8.07191	−0.268468
$905$	−9.53513	−0.316959
$906$	−20.6301	−0.685390
$907$	−41.8302	−1.38895	−0.694475	−	0.719517i	$-0.744363\pi$
$907$	−41.8302	−1.38895	−0.694475	+	0.719517i	$0.744363\pi$
$908$	−1.33707	−0.0443721
$909$	13.9140	0.461498
$910$	43.3270	1.43628
$911$	−22.8713	−0.757759	−0.378879	−	0.925446i	$-0.623690\pi$
$911$	−22.8713	−0.757759	−0.378879	+	0.925446i	$0.623690\pi$
$912$	24.4006	0.807984
$913$	−1.80305	−0.0596723
$914$	9.71958	0.321495
$915$	−31.8893	−1.05423
$916$	4.07732	0.134719
$917$	33.5207	1.10695
$918$	−6.14655	−0.202866
$919$	55.2118	1.82127	0.910635	−	0.413213i	$-0.135593\pi$
$919$	55.2118	1.82127	0.910635	+	0.413213i	$0.135593\pi$
$920$	37.0913	1.22287
$921$	−1.53223	−0.0504886
$922$	−5.85900	−0.192956
$923$	58.5861	1.92839
$924$	−0.356157	−0.0117167
$925$	3.87780	0.127501
$926$	−26.9302	−0.884981
$927$	−5.74484	−0.188685
$928$	40.5417	1.33085
$929$	−8.86466	−0.290840	−0.145420	−	0.989370i	$-0.546453\pi$
$929$	−8.86466	−0.290840	−0.145420	+	0.989370i	$0.546453\pi$
$930$	32.8759	1.07804
$931$	16.9348	0.555015
$932$	0.426161	0.0139594
$933$	8.11676	0.265731
$934$	54.9537	1.79814
$935$	0.803084	0.0262637
$936$	20.1578	0.658880
$937$	−13.3080	−0.434753	−0.217377	−	0.976088i	$-0.569750\pi$
$937$	−13.3080	−0.434753	−0.217377	+	0.976088i	$0.569750\pi$
$938$	14.5429	0.474842
$939$	−9.86687	−0.321993
$940$	−20.8382	−0.679668
$941$	21.8580	0.712550	0.356275	−	0.934381i	$-0.384047\pi$
$941$	21.8580	0.712550	0.356275	+	0.934381i	$0.384047\pi$
$942$	−17.1903	−0.560089
$943$	19.5717	0.637343
$944$	7.95781	0.259005
$945$	−24.8595	−0.808681
$946$	−3.37520	−0.109737
$947$	−17.1692	−0.557924	−0.278962	−	0.960302i	$-0.589990\pi$
$947$	−17.1692	−0.557924	−0.278962	+	0.960302i	$0.589990\pi$
$948$	−1.58459	−0.0514651
$949$	41.4326	1.34496
$950$	44.8565	1.45534
$951$	22.8532	0.741065
$952$	−3.96938	−0.128648
$953$	15.7118	0.508954	0.254477	−	0.967079i	$-0.418097\pi$
$953$	15.7118	0.508954	0.254477	+	0.967079i	$0.418097\pi$
$954$	38.5088	1.24677
$955$	−42.5067	−1.37548
$956$	18.7108	0.605150
$957$	−1.91163	−0.0617942
$958$	−45.8760	−1.48219
$959$	13.3664	0.431622
$960$	5.58614	0.180292
$961$	54.1783	1.74769
$962$	6.82158	0.219937
$963$	10.5961	0.341454
$964$	2.82072	0.0908494
$965$	−13.9579	−0.449322
$966$	−15.9489	−0.513147
$967$	10.0559	0.323376	0.161688	−	0.986842i	$-0.448306\pi$
$967$	10.0559	0.323376	0.161688	+	0.986842i	$0.448306\pi$
$968$	−21.7160	−0.697977
$969$	4.60010	0.147776
$970$	−92.4590	−2.96868
$971$	8.43555	0.270710	0.135355	−	0.990797i	$-0.456783\pi$
$971$	8.43555	0.270710	0.135355	+	0.990797i	$0.456783\pi$
$972$	12.2808	0.393908
$973$	−32.6088	−1.04539
$974$	0.812278	0.0260271
$975$	−11.2374	−0.359886
$976$	74.5721	2.38699
$977$	26.0530	0.833509	0.416755	−	0.909019i	$-0.363167\pi$
$977$	26.0530	0.833509	0.416755	+	0.909019i	$0.363167\pi$
$978$	12.4330	0.397563
$979$	1.36704	0.0436909
$980$	−5.95849	−0.190337
$981$	−2.49212	−0.0795674
$982$	21.6751	0.691680
$983$	−14.0206	−0.447187	−0.223593	−	0.974683i	$-0.571779\pi$
$983$	−14.0206	−0.447187	−0.223593	+	0.974683i	$0.571779\pi$
$984$	4.43334	0.141330
$985$	43.4268	1.38369
$986$	14.6305	0.465930
$987$	−13.0480	−0.415323
$988$	22.8310	0.726349
$989$	−43.7308	−1.39056
$990$	−3.58660	−0.113990
$991$	15.3816	0.488612	0.244306	−	0.969698i	$-0.421440\pi$
$991$	15.3816	0.488612	0.244306	+	0.969698i	$0.421440\pi$
$992$	−40.1624	−1.27516
$993$	−15.5569	−0.493682
$994$	51.5223	1.63419
$995$	−16.8832	−0.535233
$996$	3.63389	0.115144
$997$	16.9106	0.535563	0.267781	−	0.963480i	$-0.413710\pi$
$997$	16.9106	0.535563	0.267781	+	0.963480i	$0.413710\pi$
$998$	33.9997	1.07624
$999$	−3.91398	−0.123833

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4033.2.a.c.1.20	✓	77

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4033.2.a.c.1.20	✓	77	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)

\(f(q)\)	\(=\)	\(q-1.67758 q^{2} +0.712654 q^{3} +0.814260 q^{4} +2.97956 q^{5} -1.19553 q^{6} +2.13168 q^{7} +1.98917 q^{8} -2.49212 q^{9} +O(q^{10})\)	\(q-1.67758 q^{2} +0.712654 q^{3} +0.814260 q^{4} +2.97956 q^{5} -1.19553 q^{6} +2.13168 q^{7} +1.98917 q^{8} -2.49212 q^{9} -4.99844 q^{10} -0.287924 q^{11} +0.580285 q^{12} -4.06633 q^{13} -3.57605 q^{14} +2.12340 q^{15} -4.96550 q^{16} -0.936117 q^{17} +4.18073 q^{18} -6.89538 q^{19} +2.42614 q^{20} +1.51915 q^{21} +0.483015 q^{22} +6.25818 q^{23} +1.41759 q^{24} +3.87780 q^{25} +6.82158 q^{26} -3.91398 q^{27} +1.73574 q^{28} +9.31637 q^{29} -3.56216 q^{30} -9.22921 q^{31} +4.35166 q^{32} -0.205190 q^{33} +1.57041 q^{34} +6.35146 q^{35} -2.02924 q^{36} +1.00000 q^{37} +11.5675 q^{38} -2.89789 q^{39} +5.92686 q^{40} +3.12738 q^{41} -2.54848 q^{42} -6.98779 q^{43} -0.234445 q^{44} -7.42544 q^{45} -10.4986 q^{46} -8.58905 q^{47} -3.53868 q^{48} -2.45596 q^{49} -6.50530 q^{50} -0.667128 q^{51} -3.31105 q^{52} +9.21104 q^{53} +6.56600 q^{54} -0.857889 q^{55} +4.24026 q^{56} -4.91402 q^{57} -15.6289 q^{58} -1.60262 q^{59} +1.72900 q^{60} -15.0180 q^{61} +15.4827 q^{62} -5.31240 q^{63} +2.63075 q^{64} -12.1159 q^{65} +0.344222 q^{66} -4.06675 q^{67} -0.762242 q^{68} +4.45992 q^{69} -10.6551 q^{70} -14.4076 q^{71} -4.95726 q^{72} -10.1892 q^{73} -1.67758 q^{74} +2.76353 q^{75} -5.61463 q^{76} -0.613761 q^{77} +4.86143 q^{78} -2.73071 q^{79} -14.7950 q^{80} +4.68706 q^{81} -5.24642 q^{82} +6.26225 q^{83} +1.23698 q^{84} -2.78922 q^{85} +11.7225 q^{86} +6.63935 q^{87} -0.572730 q^{88} -4.74793 q^{89} +12.4567 q^{90} -8.66810 q^{91} +5.09578 q^{92} -6.57723 q^{93} +14.4088 q^{94} -20.5452 q^{95} +3.10123 q^{96} +18.4976 q^{97} +4.12005 q^{98} +0.717543 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 77 q - 9 q^{2} - 27 q^{3} + 73 q^{4} - 16 q^{5} - 2 q^{6} - 23 q^{7} - 24 q^{8} + 66 q^{9}+O(q^{10}) \) 77 * q - 9 * q^2 - 27 * q^3 + 73 * q^4 - 16 * q^5 - 2 * q^6 - 23 * q^7 - 24 * q^8 + 66 * q^9	\( 77 q - 9 q^{2} - 27 q^{3} + 73 q^{4} - 16 q^{5} - 2 q^{6} - 23 q^{7} - 24 q^{8} + 66 q^{9} - 11 q^{10} - 33 q^{11} - 52 q^{12} - 10 q^{13} - 18 q^{14} - 33 q^{15} + 53 q^{16} - 44 q^{17} - 27 q^{18} - 9 q^{19} - 45 q^{20} - 7 q^{21} - 3 q^{22} - 74 q^{23} + 21 q^{24} + 59 q^{25} - 47 q^{26} - 99 q^{27} - 49 q^{28} - 9 q^{29} - 39 q^{30} - 27 q^{31} - 47 q^{32} - 28 q^{33} - 23 q^{34} - 48 q^{35} + 77 q^{36} + 77 q^{37} - 66 q^{38} - 11 q^{39} - 2 q^{40} - 37 q^{41} - 24 q^{42} - 44 q^{43} - 54 q^{44} - 36 q^{45} - 41 q^{46} - 150 q^{47} - 135 q^{48} + 64 q^{49} + 4 q^{50} + 3 q^{51} - 57 q^{52} - 72 q^{53} + 21 q^{54} - 65 q^{55} - 92 q^{56} - 13 q^{57} - 12 q^{58} - 70 q^{59} - 22 q^{60} + 15 q^{61} - 86 q^{62} - 108 q^{63} + 10 q^{64} - 53 q^{65} - 55 q^{66} - 48 q^{67} - 70 q^{68} - 2 q^{69} + 11 q^{70} - 127 q^{71} - 12 q^{72} - 33 q^{73} - 9 q^{74} - 115 q^{75} - 24 q^{76} - 40 q^{77} + 81 q^{78} - 7 q^{79} - 62 q^{80} + 53 q^{81} - 68 q^{82} - 164 q^{83} + 7 q^{84} - 9 q^{85} - 50 q^{86} - 75 q^{87} - 82 q^{88} - 26 q^{89} + 23 q^{90} + 16 q^{91} - 117 q^{92} + 19 q^{93} + 23 q^{94} - 92 q^{95} - 35 q^{96} - 19 q^{97} - 10 q^{98} - 19 q^{99}+O(q^{100}) \) 77 * q - 9 * q^2 - 27 * q^3 + 73 * q^4 - 16 * q^5 - 2 * q^6 - 23 * q^7 - 24 * q^8 + 66 * q^9 - 11 * q^10 - 33 * q^11 - 52 * q^12 - 10 * q^13 - 18 * q^14 - 33 * q^15 + 53 * q^16 - 44 * q^17 - 27 * q^18 - 9 * q^19 - 45 * q^20 - 7 * q^21 - 3 * q^22 - 74 * q^23 + 21 * q^24 + 59 * q^25 - 47 * q^26 - 99 * q^27 - 49 * q^28 - 9 * q^29 - 39 * q^30 - 27 * q^31 - 47 * q^32 - 28 * q^33 - 23 * q^34 - 48 * q^35 + 77 * q^36 + 77 * q^37 - 66 * q^38 - 11 * q^39 - 2 * q^40 - 37 * q^41 - 24 * q^42 - 44 * q^43 - 54 * q^44 - 36 * q^45 - 41 * q^46 - 150 * q^47 - 135 * q^48 + 64 * q^49 + 4 * q^50 + 3 * q^51 - 57 * q^52 - 72 * q^53 + 21 * q^54 - 65 * q^55 - 92 * q^56 - 13 * q^57 - 12 * q^58 - 70 * q^59 - 22 * q^60 + 15 * q^61 - 86 * q^62 - 108 * q^63 + 10 * q^64 - 53 * q^65 - 55 * q^66 - 48 * q^67 - 70 * q^68 - 2 * q^69 + 11 * q^70 - 127 * q^71 - 12 * q^72 - 33 * q^73 - 9 * q^74 - 115 * q^75 - 24 * q^76 - 40 * q^77 + 81 * q^78 - 7 * q^79 - 62 * q^80 + 53 * q^81 - 68 * q^82 - 164 * q^83 + 7 * q^84 - 9 * q^85 - 50 * q^86 - 75 * q^87 - 82 * q^88 - 26 * q^89 + 23 * q^90 + 16 * q^91 - 117 * q^92 + 19 * q^93 + 23 * q^94 - 92 * q^95 - 35 * q^96 - 19 * q^97 - 10 * q^98 - 19 * q^99

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