LMFDB - Embedded newform 799.2.a.d.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [799,2,Mod(1,799)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(799, 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("799.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 799 = 17 \cdot 47 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	799.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$6.38004712150$
Analytic rank:	$1$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 8x^{6} + 3x^{5} + 18x^{4} - 10x^{2} - x + 1 $ x^8 - x^7 - 8x^6 + 3x^5 + 18x^4 - 10x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$0.289520$ of defining polynomial
Character	$\chi$	$=$	799.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.32352 q^{2} -0.710480 q^{3} -0.248291 q^{4} +2.07080 q^{5} -0.940335 q^{6} -1.47833 q^{7} -2.97566 q^{8} -2.49522 q^{9} +O(q^{10})$	\(q+1.32352 q^{2} -0.710480 q^{3} -0.248291 q^{4} +2.07080 q^{5} -0.940335 q^{6} -1.47833 q^{7} -2.97566 q^{8} -2.49522 q^{9} +2.74075 q^{10} -1.77171 q^{11} +0.176406 q^{12} -4.88029 q^{13} -1.95660 q^{14} -1.47126 q^{15} -3.44177 q^{16} +1.00000 q^{17} -3.30248 q^{18} -6.75619 q^{19} -0.514162 q^{20} +1.05032 q^{21} -2.34490 q^{22} +5.04805 q^{23} +2.11415 q^{24} -0.711774 q^{25} -6.45916 q^{26} +3.90424 q^{27} +0.367056 q^{28} +9.00268 q^{29} -1.94725 q^{30} +3.43036 q^{31} +1.39607 q^{32} +1.25876 q^{33} +1.32352 q^{34} -3.06133 q^{35} +0.619541 q^{36} -7.73939 q^{37} -8.94197 q^{38} +3.46734 q^{39} -6.16201 q^{40} -9.93882 q^{41} +1.39012 q^{42} -0.977814 q^{43} +0.439900 q^{44} -5.16711 q^{45} +6.68120 q^{46} +1.00000 q^{47} +2.44531 q^{48} -4.81455 q^{49} -0.942048 q^{50} -0.710480 q^{51} +1.21173 q^{52} -8.51679 q^{53} +5.16735 q^{54} -3.66886 q^{55} +4.39900 q^{56} +4.80014 q^{57} +11.9152 q^{58} +13.6317 q^{59} +0.365302 q^{60} -9.05732 q^{61} +4.54016 q^{62} +3.68875 q^{63} +8.73126 q^{64} -10.1061 q^{65} +1.66600 q^{66} -0.823786 q^{67} -0.248291 q^{68} -3.58654 q^{69} -4.05173 q^{70} -8.07323 q^{71} +7.42493 q^{72} -1.38603 q^{73} -10.2433 q^{74} +0.505701 q^{75} +1.67750 q^{76} +2.61917 q^{77} +4.58910 q^{78} +4.72287 q^{79} -7.12723 q^{80} +4.71177 q^{81} -13.1542 q^{82} +15.2674 q^{83} -0.260786 q^{84} +2.07080 q^{85} -1.29416 q^{86} -6.39622 q^{87} +5.27201 q^{88} +4.04402 q^{89} -6.83878 q^{90} +7.21466 q^{91} -1.25339 q^{92} -2.43720 q^{93} +1.32352 q^{94} -13.9907 q^{95} -0.991878 q^{96} +6.64689 q^{97} -6.37215 q^{98} +4.42080 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} - 7 q^{3} + 7 q^{4} - 10 q^{5} + 2 q^{6} - 9 q^{7} - q^{9}+O(q^{10}) $ 8 * q + q^2 - 7 * q^3 + 7 * q^4 - 10 * q^5 + 2 * q^6 - 9 * q^7 - q^9	\( 8 q + q^{2} - 7 q^{3} + 7 q^{4} - 10 q^{5} + 2 q^{6} - 9 q^{7} - q^{9} + 2 q^{10} - 2 q^{11} - 11 q^{12} - 3 q^{13} - 9 q^{14} + 14 q^{15} - 7 q^{16} + 8 q^{17} - 5 q^{18} - 8 q^{19} - 20 q^{20} + 4 q^{21} - 20 q^{22} - 9 q^{23} - 4 q^{24} + 14 q^{25} - 20 q^{26} + 2 q^{27} - 21 q^{28} - 2 q^{29} - 27 q^{30} - 7 q^{31} + 21 q^{32} - 23 q^{33} + q^{34} + 7 q^{35} - 17 q^{36} - 13 q^{37} - 7 q^{38} + 9 q^{39} - 16 q^{40} - 39 q^{41} + 11 q^{42} + 35 q^{43} - 17 q^{44} - 13 q^{45} + 19 q^{46} + 8 q^{47} + 9 q^{48} + q^{49} - 30 q^{50} - 7 q^{51} - 17 q^{52} - 6 q^{53} - 4 q^{54} + 22 q^{55} - 48 q^{56} + 5 q^{57} + 3 q^{58} - 19 q^{59} + 32 q^{60} - 15 q^{61} + 15 q^{62} + 17 q^{63} - 8 q^{64} - 29 q^{65} - 5 q^{66} + 15 q^{67} + 7 q^{68} - 12 q^{69} + 35 q^{70} - 7 q^{71} + q^{72} - 22 q^{73} - 43 q^{74} - 29 q^{75} + 52 q^{76} + 2 q^{77} + 43 q^{78} - 43 q^{79} + 6 q^{80} - 16 q^{81} + 19 q^{82} - 3 q^{83} + 34 q^{84} - 10 q^{85} - 19 q^{86} + q^{87} + 5 q^{88} - 53 q^{89} + 42 q^{90} + 5 q^{91} + 28 q^{92} + 44 q^{93} + q^{94} - 53 q^{95} - 41 q^{96} - 40 q^{97} + 30 q^{98} + 45 q^{99}+O(q^{100}) \) 8 * q + q^2 - 7 * q^3 + 7 * q^4 - 10 * q^5 + 2 * q^6 - 9 * q^7 - q^9 + 2 * q^10 - 2 * q^11 - 11 * q^12 - 3 * q^13 - 9 * q^14 + 14 * q^15 - 7 * q^16 + 8 * q^17 - 5 * q^18 - 8 * q^19 - 20 * q^20 + 4 * q^21 - 20 * q^22 - 9 * q^23 - 4 * q^24 + 14 * q^25 - 20 * q^26 + 2 * q^27 - 21 * q^28 - 2 * q^29 - 27 * q^30 - 7 * q^31 + 21 * q^32 - 23 * q^33 + q^34 + 7 * q^35 - 17 * q^36 - 13 * q^37 - 7 * q^38 + 9 * q^39 - 16 * q^40 - 39 * q^41 + 11 * q^42 + 35 * q^43 - 17 * q^44 - 13 * q^45 + 19 * q^46 + 8 * q^47 + 9 * q^48 + q^49 - 30 * q^50 - 7 * q^51 - 17 * q^52 - 6 * q^53 - 4 * q^54 + 22 * q^55 - 48 * q^56 + 5 * q^57 + 3 * q^58 - 19 * q^59 + 32 * q^60 - 15 * q^61 + 15 * q^62 + 17 * q^63 - 8 * q^64 - 29 * q^65 - 5 * q^66 + 15 * q^67 + 7 * q^68 - 12 * q^69 + 35 * q^70 - 7 * q^71 + q^72 - 22 * q^73 - 43 * q^74 - 29 * q^75 + 52 * q^76 + 2 * q^77 + 43 * q^78 - 43 * q^79 + 6 * q^80 - 16 * q^81 + 19 * q^82 - 3 * q^83 + 34 * q^84 - 10 * q^85 - 19 * q^86 + q^87 + 5 * q^88 - 53 * q^89 + 42 * q^90 + 5 * q^91 + 28 * q^92 + 44 * q^93 + q^94 - 53 * q^95 - 41 * q^96 - 40 * q^97 + 30 * q^98 + 45 * 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 $

$2$	1.32352	0.935871	0.467935	−	0.883763i	$-0.344998\pi$
$2$	1.32352	0.935871	0.467935	+	0.883763i	$0.344998\pi$
$3$	−0.710480	−0.410196	−0.205098	−	0.978741i	$-0.565751\pi$
$3$	−0.710480	−0.410196	−0.205098	+	0.978741i	$0.565751\pi$
$4$	−0.248291	−0.124146
$5$	2.07080	0.926091	0.463046	−	0.886334i	$-0.346757\pi$
$5$	2.07080	0.926091	0.463046	+	0.886334i	$0.346757\pi$
$6$	−0.940335	−0.383890
$7$	−1.47833	−0.558755	−0.279378	−	0.960181i	$-0.590128\pi$
$7$	−1.47833	−0.558755	−0.279378	+	0.960181i	$0.590128\pi$
$8$	−2.97566	−1.05206
$9$	−2.49522	−0.831740
$10$	2.74075	0.866702
$11$	−1.77171	−0.534191	−0.267095	−	0.963670i	$-0.586064\pi$
$11$	−1.77171	−0.534191	−0.267095	+	0.963670i	$0.586064\pi$
$12$	0.176406	0.0509240
$13$	−4.88029	−1.35355	−0.676774	−	0.736191i	$-0.736623\pi$
$13$	−4.88029	−1.35355	−0.676774	+	0.736191i	$0.736623\pi$
$14$	−1.95660	−0.522923
$15$	−1.47126	−0.379879
$16$	−3.44177	−0.860442
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−3.30248	−0.778401
$19$	−6.75619	−1.54998	−0.774989	−	0.631975i	$-0.782244\pi$
$19$	−6.75619	−1.54998	−0.774989	+	0.631975i	$0.782244\pi$
$20$	−0.514162	−0.114970
$21$	1.05032	0.229199
$22$	−2.34490	−0.499934
$23$	5.04805	1.05259	0.526295	−	0.850302i	$-0.323581\pi$
$23$	5.04805	1.05259	0.526295	+	0.850302i	$0.323581\pi$
$24$	2.11415	0.431548
$25$	−0.711774	−0.142355
$26$	−6.45916	−1.26675
$27$	3.90424	0.751372
$28$	0.367056	0.0693670
$29$	9.00268	1.67176	0.835878	−	0.548916i	$-0.184959\pi$
$29$	9.00268	1.67176	0.835878	+	0.548916i	$0.184959\pi$
$30$	−1.94725	−0.355517
$31$	3.43036	0.616111	0.308056	−	0.951368i	$-0.400322\pi$
$31$	3.43036	0.616111	0.308056	+	0.951368i	$0.400322\pi$
$32$	1.39607	0.246792
$33$	1.25876	0.219123
$34$	1.32352	0.226982
$35$	−3.06133	−0.517459
$36$	0.619541	0.103257
$37$	−7.73939	−1.27235	−0.636174	−	0.771545i	$-0.719484\pi$
$37$	−7.73939	−1.27235	−0.636174	+	0.771545i	$0.719484\pi$
$38$	−8.94197	−1.45058
$39$	3.46734	0.555219
$40$	−6.16201	−0.974299
$41$	−9.93882	−1.55218	−0.776091	−	0.630621i	$-0.782800\pi$
$41$	−9.93882	−1.55218	−0.776091	+	0.630621i	$0.782800\pi$
$42$	1.39012	0.214501
$43$	−0.977814	−0.149115	−0.0745576	−	0.997217i	$-0.523754\pi$
$43$	−0.977814	−0.149115	−0.0745576	+	0.997217i	$0.523754\pi$
$44$	0.439900	0.0663174
$45$	−5.16711	−0.770267
$46$	6.68120	0.985089
$47$	1.00000	0.145865
$47$	1.00000	0.145865
$48$	2.44531	0.352950
$49$	−4.81455	−0.687792
$50$	−0.942048	−0.133226
$51$	−0.710480	−0.0994871
$52$	1.21173	0.168037
$53$	−8.51679	−1.16987	−0.584936	−	0.811080i	$-0.698880\pi$
$53$	−8.51679	−1.16987	−0.584936	+	0.811080i	$0.698880\pi$
$54$	5.16735	0.703187
$55$	−3.66886	−0.494709
$56$	4.39900	0.587842
$57$	4.80014	0.635794
$58$	11.9152	1.56455
$59$	13.6317	1.77470	0.887349	−	0.461099i	$-0.152545\pi$
$59$	13.6317	1.77470	0.887349	+	0.461099i	$0.152545\pi$
$60$	0.365302	0.0471603
$61$	−9.05732	−1.15967	−0.579836	−	0.814734i	$-0.696883\pi$
$61$	−9.05732	−1.15967	−0.579836	+	0.814734i	$0.696883\pi$
$62$	4.54016	0.576601
$63$	3.68875	0.464739
$64$	8.73126	1.09141
$65$	−10.1061	−1.25351
$66$	1.66600	0.205071
$67$	−0.823786	−0.100641	−0.0503207	−	0.998733i	$-0.516024\pi$
$67$	−0.823786	−0.100641	−0.0503207	+	0.998733i	$0.516024\pi$
$68$	−0.248291	−0.0301097
$69$	−3.58654	−0.431768
$70$	−4.05173	−0.484274
$71$	−8.07323	−0.958116	−0.479058	−	0.877783i	$-0.659022\pi$
$71$	−8.07323	−0.958116	−0.479058	+	0.877783i	$0.659022\pi$
$72$	7.42493	0.875036
$73$	−1.38603	−0.162223	−0.0811113	−	0.996705i	$-0.525847\pi$
$73$	−1.38603	−0.162223	−0.0811113	+	0.996705i	$0.525847\pi$
$74$	−10.2433	−1.19075
$75$	0.505701	0.0583933
$76$	1.67750	0.192423
$77$	2.61917	0.298482
$78$	4.58910	0.519614
$79$	4.72287	0.531364	0.265682	−	0.964061i	$-0.414403\pi$
$79$	4.72287	0.531364	0.265682	+	0.964061i	$0.414403\pi$
$80$	−7.12723	−0.796848
$81$	4.71177	0.523530
$82$	−13.1542	−1.45264
$83$	15.2674	1.67581	0.837906	−	0.545815i	$-0.183780\pi$
$83$	15.2674	1.67581	0.837906	+	0.545815i	$0.183780\pi$
$84$	−0.260786	−0.0284541
$85$	2.07080	0.224610
$86$	−1.29416	−0.139553
$87$	−6.39622	−0.685747
$88$	5.27201	0.561998
$89$	4.04402	0.428666	0.214333	−	0.976761i	$-0.431242\pi$
$89$	4.04402	0.428666	0.214333	+	0.976761i	$0.431242\pi$
$90$	−6.83878	−0.720870
$91$	7.21466	0.756302
$92$	−1.25339	−0.130675
$93$	−2.43720	−0.252726
$94$	1.32352	0.136511
$95$	−13.9907	−1.43542
$96$	−0.991878	−0.101233
$97$	6.64689	0.674889	0.337445	−	0.941345i	$-0.390437\pi$
$97$	6.64689	0.674889	0.337445	+	0.941345i	$0.390437\pi$
$98$	−6.37215	−0.643685
$99$	4.42080	0.444308
$100$	0.176727	0.0176727
$101$	6.31436	0.628302	0.314151	−	0.949373i	$-0.398280\pi$
$101$	6.31436	0.628302	0.314151	+	0.949373i	$0.398280\pi$
$102$	−0.940335	−0.0931070
$103$	−12.4982	−1.23148	−0.615740	−	0.787950i	$-0.711143\pi$
$103$	−12.4982	−1.23148	−0.615740	+	0.787950i	$0.711143\pi$
$104$	14.5221	1.42401
$105$	2.17501	0.212259
$106$	−11.2722	−1.09485
$107$	5.18761	0.501505	0.250753	−	0.968051i	$-0.419322\pi$
$107$	5.18761	0.501505	0.250753	+	0.968051i	$0.419322\pi$
$108$	−0.969389	−0.0932795
$109$	1.59094	0.152384	0.0761921	−	0.997093i	$-0.475724\pi$
$109$	1.59094	0.152384	0.0761921	+	0.997093i	$0.475724\pi$
$110$	−4.85582	−0.462984
$111$	5.49868	0.521912
$112$	5.08806	0.480777
$113$	−6.93924	−0.652788	−0.326394	−	0.945234i	$-0.605834\pi$
$113$	−6.93924	−0.652788	−0.326394	+	0.945234i	$0.605834\pi$
$114$	6.35309	0.595021
$115$	10.4535	0.974795
$116$	−2.23529	−0.207541
$117$	12.1774	1.12580
$118$	18.0419	1.66089
$119$	−1.47833	−0.135518
$120$	4.37798	0.399653
$121$	−7.86104	−0.714640
$122$	−11.9876	−1.08530
$123$	7.06133	0.636698
$124$	−0.851729	−0.0764875
$125$	−11.8280	−1.05792
$126$	4.88214	0.434936
$127$	−15.6672	−1.39024	−0.695118	−	0.718895i	$-0.744648\pi$
$127$	−15.6672	−1.39024	−0.695118	+	0.718895i	$0.744648\pi$
$128$	8.76388	0.774625
$129$	0.694717	0.0611664
$130$	−13.3757	−1.17312
$131$	7.90717	0.690853	0.345426	−	0.938446i	$-0.387734\pi$
$131$	7.90717	0.690853	0.345426	+	0.938446i	$0.387734\pi$
$132$	−0.312540	−0.0272031
$133$	9.98787	0.866058
$134$	−1.09030	−0.0941874
$135$	8.08492	0.695839
$136$	−2.97566	−0.255161
$137$	6.74137	0.575954	0.287977	−	0.957637i	$-0.407017\pi$
$137$	6.74137	0.575954	0.287977	+	0.957637i	$0.407017\pi$
$138$	−4.74686	−0.404079
$139$	−0.659595	−0.0559461	−0.0279731	−	0.999609i	$-0.508905\pi$
$139$	−0.659595	−0.0559461	−0.0279731	+	0.999609i	$0.508905\pi$
$140$	0.760100	0.0642402
$141$	−0.710480	−0.0598332
$142$	−10.6851	−0.896672
$143$	8.64645	0.723053
$144$	8.58797	0.715664
$145$	18.6428	1.54820
$146$	−1.83444	−0.151819
$147$	3.42064	0.282129
$148$	1.92162	0.157956
$149$	24.0700	1.97189	0.985945	−	0.167070i	$-0.0534307\pi$
$149$	24.0700	1.97189	0.985945	+	0.167070i	$0.0534307\pi$
$150$	0.669306	0.0546486
$151$	−17.0738	−1.38944	−0.694722	−	0.719278i	$-0.744473\pi$
$151$	−17.0738	−1.38944	−0.694722	+	0.719278i	$0.744473\pi$
$152$	20.1041	1.63066
$153$	−2.49522	−0.201726
$154$	3.46653	0.279341
$155$	7.10361	0.570575
$156$	−0.860911	−0.0689281
$157$	−7.73483	−0.617307	−0.308654	−	0.951175i	$-0.599878\pi$
$157$	−7.73483	−0.617307	−0.308654	+	0.951175i	$0.599878\pi$
$158$	6.25081	0.497288
$159$	6.05101	0.479876
$160$	2.89098	0.228552
$161$	−7.46267	−0.588141
$162$	6.23613	0.489957
$163$	0.667053	0.0522476	0.0261238	−	0.999659i	$-0.491684\pi$
$163$	0.667053	0.0522476	0.0261238	+	0.999659i	$0.491684\pi$
$164$	2.46772	0.192697
$165$	2.60665	0.202928
$166$	20.2067	1.56834
$167$	10.0284	0.776022	0.388011	−	0.921655i	$-0.373162\pi$
$167$	10.0284	0.776022	0.388011	+	0.921655i	$0.373162\pi$
$168$	−3.12540	−0.241130
$169$	10.8172	0.832092
$170$	2.74075	0.210206
$171$	16.8582	1.28918
$172$	0.242783	0.0185120
$173$	−19.4301	−1.47725	−0.738623	−	0.674119i	$-0.764524\pi$
$173$	−19.4301	−1.47725	−0.738623	+	0.674119i	$0.764524\pi$
$174$	−8.46554	−0.641771
$175$	1.05224	0.0795415
$176$	6.09782	0.459640
$177$	−9.68505	−0.727973
$178$	5.35235	0.401176
$179$	−19.8408	−1.48297	−0.741486	−	0.670969i	$-0.765879\pi$
$179$	−19.8408	−1.48297	−0.741486	+	0.670969i	$0.765879\pi$
$180$	1.28295	0.0956252
$181$	−20.6414	−1.53426	−0.767131	−	0.641491i	$-0.778316\pi$
$181$	−20.6414	−1.53426	−0.767131	+	0.641491i	$0.778316\pi$
$182$	9.54876	0.707801
$183$	6.43504	0.475692
$184$	−15.0213	−1.10738
$185$	−16.0268	−1.17831
$186$	−3.22569	−0.236519
$187$	−1.77171	−0.129560
$188$	−0.248291	−0.0181085
$189$	−5.77175	−0.419833
$190$	−18.5171	−1.34337
$191$	5.07499	0.367213	0.183607	−	0.983000i	$-0.441223\pi$
$191$	5.07499	0.367213	0.183607	+	0.983000i	$0.441223\pi$
$192$	−6.20339	−0.447691
$193$	−7.94185	−0.571667	−0.285833	−	0.958279i	$-0.592270\pi$
$193$	−7.94185	−0.571667	−0.285833	+	0.958279i	$0.592270\pi$
$194$	8.79730	0.631609
$195$	7.18019	0.514184
$196$	1.19541	0.0853864
$197$	15.4822	1.10306	0.551532	−	0.834154i	$-0.314043\pi$
$197$	15.4822	1.10306	0.551532	+	0.834154i	$0.314043\pi$
$198$	5.85103	0.415814
$199$	19.1899	1.36034	0.680168	−	0.733056i	$-0.261907\pi$
$199$	19.1899	1.36034	0.680168	+	0.733056i	$0.261907\pi$
$200$	2.11800	0.149765
$201$	0.585283	0.0412827
$202$	8.35719	0.588010
$203$	−13.3089	−0.934103
$204$	0.176406	0.0123509
$205$	−20.5813	−1.43746
$206$	−16.5416	−1.15251
$207$	−12.5960	−0.875481
$208$	16.7968	1.16465
$209$	11.9700	0.827983
$210$	2.87867	0.198647
$211$	4.44229	0.305820	0.152910	−	0.988240i	$-0.451136\pi$
$211$	4.44229	0.305820	0.152910	+	0.988240i	$0.451136\pi$
$212$	2.11464	0.145234
$213$	5.73586	0.393015
$214$	6.86591	0.469344
$215$	−2.02486	−0.138094
$216$	−11.6177	−0.790484
$217$	−5.07120	−0.344256
$218$	2.10564	0.142612
$219$	0.984747	0.0665430
$220$	0.910946	0.0614160
$221$	−4.88029	−0.328284
$222$	7.27762	0.488442
$223$	1.38508	0.0927519	0.0463759	−	0.998924i	$-0.485233\pi$
$223$	1.38508	0.0927519	0.0463759	+	0.998924i	$0.485233\pi$
$224$	−2.06385	−0.137897
$225$	1.77603	0.118402
$226$	−9.18423	−0.610926
$227$	−6.44655	−0.427873	−0.213936	−	0.976848i	$-0.568628\pi$
$227$	−6.44655	−0.427873	−0.213936	+	0.976848i	$0.568628\pi$
$228$	−1.19183	−0.0789310
$229$	−23.8613	−1.57680	−0.788401	−	0.615162i	$-0.789091\pi$
$229$	−23.8613	−1.57680	−0.788401	+	0.615162i	$0.789091\pi$
$230$	13.8354	0.912282
$231$	−1.86087	−0.122436
$232$	−26.7889	−1.75878
$233$	7.75474	0.508030	0.254015	−	0.967200i	$-0.418249\pi$
$233$	7.75474	0.508030	0.254015	+	0.967200i	$0.418249\pi$
$234$	16.1170	1.05360
$235$	2.07080	0.135084
$236$	−3.38463	−0.220321
$237$	−3.35550	−0.217963
$238$	−1.95660	−0.126827
$239$	−22.2525	−1.43940	−0.719698	−	0.694288i	$-0.755720\pi$
$239$	−22.2525	−1.43940	−0.719698	+	0.694288i	$0.755720\pi$
$240$	5.06375	0.326864
$241$	−11.0821	−0.713864	−0.356932	−	0.934130i	$-0.616177\pi$
$241$	−11.0821	−0.713864	−0.356932	+	0.934130i	$0.616177\pi$
$242$	−10.4043	−0.668811
$243$	−15.0603	−0.966121
$244$	2.24885	0.143968
$245$	−9.96998	−0.636959
$246$	9.34582	0.595868
$247$	32.9722	2.09797
$248$	−10.2076	−0.648183
$249$	−10.8472	−0.687410
$250$	−15.6546	−0.990081
$251$	−19.3777	−1.22311	−0.611555	−	0.791202i	$-0.709456\pi$
$251$	−19.3777	−1.22311	−0.611555	+	0.791202i	$0.709456\pi$
$252$	−0.915885	−0.0576953
$253$	−8.94368	−0.562284
$254$	−20.7358	−1.30108
$255$	−1.47126	−0.0921341
$256$	−5.86335	−0.366459
$257$	24.4690	1.52633	0.763167	−	0.646201i	$-0.223643\pi$
$257$	24.4690	1.52633	0.763167	+	0.646201i	$0.223643\pi$
$258$	0.919473	0.0572439
$259$	11.4414	0.710932
$260$	2.50926	0.155618
$261$	−22.4637	−1.39047
$262$	10.4653	0.646549
$263$	8.97151	0.553207	0.276604	−	0.960984i	$-0.410791\pi$
$263$	8.97151	0.553207	0.276604	+	0.960984i	$0.410791\pi$
$264$	−3.74566	−0.230529
$265$	−17.6366	−1.08341
$266$	13.2192	0.810519
$267$	−2.87320	−0.175837
$268$	0.204539	0.0124942
$269$	−10.6006	−0.646330	−0.323165	−	0.946343i	$-0.604747\pi$
$269$	−10.6006	−0.646330	−0.323165	+	0.946343i	$0.604747\pi$
$270$	10.7006	0.651215
$271$	26.9840	1.63916	0.819581	−	0.572964i	$-0.194206\pi$
$271$	26.9840	1.63916	0.819581	+	0.572964i	$0.194206\pi$
$272$	−3.44177	−0.208688
$273$	−5.12587	−0.310232
$274$	8.92235	0.539019
$275$	1.26106	0.0760446
$276$	0.890505	0.0536021
$277$	−9.97771	−0.599502	−0.299751	−	0.954017i	$-0.596904\pi$
$277$	−9.97771	−0.599502	−0.299751	+	0.954017i	$0.596904\pi$
$278$	−0.872988	−0.0523584
$279$	−8.55951	−0.512444
$280$	9.10947	0.544395
$281$	−22.7686	−1.35826	−0.679132	−	0.734017i	$-0.737643\pi$
$281$	−22.7686	−1.35826	−0.679132	+	0.734017i	$0.737643\pi$
$282$	−0.940335	−0.0559961
$283$	−3.89979	−0.231819	−0.115909	−	0.993260i	$-0.536978\pi$
$283$	−3.89979	−0.231819	−0.115909	+	0.993260i	$0.536978\pi$
$284$	2.00451	0.118946
$285$	9.94014	0.588803
$286$	11.4438	0.676684
$287$	14.6928	0.867290
$288$	−3.48349	−0.205267
$289$	1.00000	0.0588235
$290$	24.6741	1.44891
$291$	−4.72248	−0.276837
$292$	0.344139	0.0201392
$293$	−5.83329	−0.340784	−0.170392	−	0.985376i	$-0.554503\pi$
$293$	−5.83329	−0.340784	−0.170392	+	0.985376i	$0.554503\pi$
$294$	4.52729	0.264037
$295$	28.2286	1.64353
$296$	23.0298	1.33858
$297$	−6.91718	−0.401376
$298$	31.8571	1.84543
$299$	−24.6359	−1.42473
$300$	−0.125561	−0.00724927
$301$	1.44553	0.0833190
$302$	−22.5975	−1.30034
$303$	−4.48623	−0.257727
$304$	23.2533	1.33367
$305$	−18.7559	−1.07396
$306$	−3.30248	−0.188790
$307$	15.2936	0.872849	0.436425	−	0.899741i	$-0.356245\pi$
$307$	15.2936	0.872849	0.436425	+	0.899741i	$0.356245\pi$
$308$	−0.650317	−0.0370552
$309$	8.87968	0.505147
$310$	9.40178	0.533985
$311$	−27.7535	−1.57376	−0.786879	−	0.617107i	$-0.788304\pi$
$311$	−27.7535	−1.57376	−0.786879	+	0.617107i	$0.788304\pi$
$312$	−10.3176	−0.584122
$313$	1.25693	0.0710460	0.0355230	−	0.999369i	$-0.488690\pi$
$313$	1.25693	0.0710460	0.0355230	+	0.999369i	$0.488690\pi$
$314$	−10.2372	−0.577720
$315$	7.63868	0.430391
$316$	−1.17265	−0.0659665
$317$	32.3086	1.81463	0.907315	−	0.420452i	$-0.138129\pi$
$317$	32.3086	1.81463	0.907315	+	0.420452i	$0.138129\pi$
$318$	8.00864	0.449102
$319$	−15.9501	−0.893036
$320$	18.0807	1.01074
$321$	−3.68569	−0.205715
$322$	−9.87700	−0.550424
$323$	−6.75619	−0.375925
$324$	−1.16989	−0.0649940
$325$	3.47366	0.192684
$326$	0.882859	0.0488970
$327$	−1.13033	−0.0625074
$328$	29.5746	1.63298
$329$	−1.47833	−0.0815029
$330$	3.44996	0.189914
$331$	2.42048	0.133042	0.0665209	−	0.997785i	$-0.478810\pi$
$331$	2.42048	0.133042	0.0665209	+	0.997785i	$0.478810\pi$
$332$	−3.79075	−0.208045
$333$	19.3115	1.05826
$334$	13.2728	0.726257
$335$	−1.70590	−0.0932032
$336$	−3.61497	−0.197213
$337$	2.98082	0.162375	0.0811877	−	0.996699i	$-0.474129\pi$
$337$	2.98082	0.162375	0.0811877	+	0.996699i	$0.474129\pi$
$338$	14.3168	0.778731
$339$	4.93019	0.267771
$340$	−0.514162	−0.0278844
$341$	−6.07761	−0.329121
$342$	22.3122	1.20650
$343$	17.4658	0.943063
$344$	2.90964	0.156877
$345$	−7.42701	−0.399857
$346$	−25.7162	−1.38251
$347$	−1.47320	−0.0790854	−0.0395427	−	0.999218i	$-0.512590\pi$
$347$	−1.47320	−0.0790854	−0.0395427	+	0.999218i	$0.512590\pi$
$348$	1.58813	0.0851325
$349$	4.34182	0.232412	0.116206	−	0.993225i	$-0.462927\pi$
$349$	4.34182	0.232412	0.116206	+	0.993225i	$0.462927\pi$
$350$	1.39266	0.0744406
$351$	−19.0538	−1.01702
$352$	−2.47343	−0.131834
$353$	−35.2864	−1.87810	−0.939052	−	0.343774i	$-0.888295\pi$
$353$	−35.2864	−1.87810	−0.939052	+	0.343774i	$0.888295\pi$
$354$	−12.8184	−0.681289
$355$	−16.7181	−0.887303
$356$	−1.00410	−0.0532170
$357$	1.05032	0.0555889
$358$	−26.2597	−1.38787
$359$	15.9248	0.840477	0.420239	−	0.907414i	$-0.361946\pi$
$359$	15.9248	0.840477	0.420239	+	0.907414i	$0.361946\pi$
$360$	15.3756	0.810363
$361$	26.6461	1.40243
$362$	−27.3193	−1.43587
$363$	5.58511	0.293142
$364$	−1.79134	−0.0938916
$365$	−2.87020	−0.150233
$366$	8.51692	0.445186
$367$	−18.3999	−0.960466	−0.480233	−	0.877141i	$-0.659448\pi$
$367$	−18.3999	−0.960466	−0.480233	+	0.877141i	$0.659448\pi$
$368$	−17.3742	−0.905694
$369$	24.7995	1.29101
$370$	−21.2118	−1.10275
$371$	12.5906	0.653672
$372$	0.605136	0.0313748
$373$	12.6038	0.652602	0.326301	−	0.945266i	$-0.394198\pi$
$373$	12.6038	0.652602	0.326301	+	0.945266i	$0.394198\pi$
$374$	−2.34490	−0.121252
$375$	8.40353	0.433956
$376$	−2.97566	−0.153458
$377$	−43.9357	−2.26280
$378$	−7.63903	−0.392910
$379$	−19.2525	−0.988937	−0.494468	−	0.869196i	$-0.664637\pi$
$379$	−19.2525	−0.988937	−0.494468	+	0.869196i	$0.664637\pi$
$380$	3.47378	0.178201
$381$	11.1312	0.570269
$382$	6.71686	0.343664
$383$	−14.0238	−0.716581	−0.358291	−	0.933610i	$-0.616640\pi$
$383$	−14.0238	−0.716581	−0.358291	+	0.933610i	$0.616640\pi$
$384$	−6.22656	−0.317748
$385$	5.42378	0.276422
$386$	−10.5112	−0.535006
$387$	2.43986	0.124025
$388$	−1.65036	−0.0837846
$389$	−20.0205	−1.01508	−0.507539	−	0.861629i	$-0.669445\pi$
$389$	−20.0205	−1.01508	−0.507539	+	0.861629i	$0.669445\pi$
$390$	9.50313	0.481210
$391$	5.04805	0.255291
$392$	14.3265	0.723595
$393$	−5.61788	−0.283385
$394$	20.4911	1.03233
$395$	9.78012	0.492091
$396$	−1.09765	−0.0551588
$397$	−18.5985	−0.933431	−0.466716	−	0.884407i	$-0.654563\pi$
$397$	−18.5985	−0.933431	−0.466716	+	0.884407i	$0.654563\pi$
$398$	25.3982	1.27310
$399$	−7.09618	−0.355253
$400$	2.44976	0.122488
$401$	−2.00967	−0.100358	−0.0501790	−	0.998740i	$-0.515979\pi$
$401$	−2.00967	−0.100358	−0.0501790	+	0.998740i	$0.515979\pi$
$402$	0.774634	0.0386353
$403$	−16.7412	−0.833936
$404$	−1.56780	−0.0780010
$405$	9.75715	0.484837
$406$	−17.6146	−0.874200
$407$	13.7120	0.679677
$408$	2.11415	0.104666
$409$	−34.9287	−1.72711	−0.863557	−	0.504251i	$-0.831769\pi$
$409$	−34.9287	−1.72711	−0.863557	+	0.504251i	$0.831769\pi$
$410$	−27.2398	−1.34528
$411$	−4.78961	−0.236254
$412$	3.10318	0.152883
$413$	−20.1521	−0.991622
$414$	−16.6711	−0.819338
$415$	31.6157	1.55195
$416$	−6.81321	−0.334045
$417$	0.468629	0.0229489
$418$	15.8426	0.774886
$419$	13.9520	0.681599	0.340799	−	0.940136i	$-0.389302\pi$
$419$	13.9520	0.681599	0.340799	+	0.940136i	$0.389302\pi$
$420$	−0.540036	−0.0263511
$421$	26.3739	1.28539	0.642694	−	0.766123i	$-0.277817\pi$
$421$	26.3739	1.28539	0.642694	+	0.766123i	$0.277817\pi$
$422$	5.87946	0.286208
$423$	−2.49522	−0.121322
$424$	25.3431	1.23077
$425$	−0.711774	−0.0345261
$426$	7.59154	0.367811
$427$	13.3897	0.647973
$428$	−1.28804	−0.0622596
$429$	−6.14313	−0.296593
$430$	−2.67995	−0.129239
$431$	26.4251	1.27285	0.636425	−	0.771338i	$-0.280412\pi$
$431$	26.4251	1.27285	0.636425	+	0.771338i	$0.280412\pi$
$432$	−13.4375	−0.646512
$433$	34.7773	1.67129	0.835646	−	0.549269i	$-0.185094\pi$
$433$	34.7773	1.67129	0.835646	+	0.549269i	$0.185094\pi$
$434$	−6.71184	−0.322179
$435$	−13.2453	−0.635064
$436$	−0.395016	−0.0189178
$437$	−34.1056	−1.63149
$438$	1.30333	0.0622757
$439$	37.4353	1.78669	0.893345	−	0.449371i	$-0.148352\pi$
$439$	37.4353	1.78669	0.893345	+	0.449371i	$0.148352\pi$
$440$	10.9173	0.520462
$441$	12.0133	0.572064
$442$	−6.45916	−0.307231
$443$	−9.25703	−0.439815	−0.219907	−	0.975521i	$-0.570576\pi$
$443$	−9.25703	−0.439815	−0.219907	+	0.975521i	$0.570576\pi$
$444$	−1.36527	−0.0647930
$445$	8.37438	0.396984
$446$	1.83318	0.0868038
$447$	−17.1012	−0.808861
$448$	−12.9077	−0.609830
$449$	−19.0633	−0.899651	−0.449826	−	0.893116i	$-0.648514\pi$
$449$	−19.0633	−0.899651	−0.449826	+	0.893116i	$0.648514\pi$
$450$	2.35062	0.110809
$451$	17.6087	0.829161
$452$	1.72295	0.0810408
$453$	12.1306	0.569944
$454$	−8.53215	−0.400433
$455$	14.9402	0.700405
$456$	−14.2836	−0.668890
$457$	24.7981	1.16000	0.580002	−	0.814615i	$-0.303052\pi$
$457$	24.7981	1.16000	0.580002	+	0.814615i	$0.303052\pi$
$458$	−31.5810	−1.47568
$459$	3.90424	0.182234
$460$	−2.59552	−0.121017
$461$	−24.0864	−1.12181	−0.560907	−	0.827879i	$-0.689548\pi$
$461$	−24.0864	−1.12181	−0.560907	+	0.827879i	$0.689548\pi$
$462$	−2.46290	−0.114584
$463$	−29.3847	−1.36562	−0.682812	−	0.730594i	$-0.739243\pi$
$463$	−29.3847	−1.36562	−0.682812	+	0.730594i	$0.739243\pi$
$464$	−30.9851	−1.43845
$465$	−5.04697	−0.234048
$466$	10.2636	0.475450
$467$	2.68261	0.124137	0.0620683	−	0.998072i	$-0.480230\pi$
$467$	2.68261	0.124137	0.0620683	+	0.998072i	$0.480230\pi$
$468$	−3.02354	−0.139763
$469$	1.21783	0.0562339
$470$	2.74075	0.126421
$471$	5.49544	0.253217
$472$	−40.5633	−1.86708
$473$	1.73240	0.0796560
$474$	−4.44108	−0.203985
$475$	4.80888	0.220647
$476$	0.367056	0.0168240
$477$	21.2513	0.973028
$478$	−29.4517	−1.34709
$479$	−11.7154	−0.535289	−0.267644	−	0.963518i	$-0.586245\pi$
$479$	−11.7154	−0.535289	−0.267644	+	0.963518i	$0.586245\pi$
$480$	−2.05398	−0.0937511
$481$	37.7705	1.72218
$482$	−14.6675	−0.668084
$483$	5.30208	0.241253
$484$	1.95183	0.0887195
$485$	13.7644	0.625009
$486$	−19.9327	−0.904165
$487$	−17.0613	−0.773121	−0.386560	−	0.922264i	$-0.626337\pi$
$487$	−17.0613	−0.773121	−0.386560	+	0.922264i	$0.626337\pi$
$488$	26.9515	1.22004
$489$	−0.473928	−0.0214318
$490$	−13.1955	−0.596111
$491$	28.2460	1.27472	0.637361	−	0.770565i	$-0.280026\pi$
$491$	28.2460	1.27472	0.637361	+	0.770565i	$0.280026\pi$
$492$	−1.75327	−0.0790433
$493$	9.00268	0.405460
$494$	43.6394	1.96343
$495$	9.15461	0.411469
$496$	−11.8065	−0.530128
$497$	11.9349	0.535352
$498$	−14.3564	−0.643327
$499$	−13.7326	−0.614756	−0.307378	−	0.951587i	$-0.599452\pi$
$499$	−13.7326	−0.614756	−0.307378	+	0.951587i	$0.599452\pi$
$500$	2.93678	0.131337
$501$	−7.12499	−0.318321
$502$	−25.6468	−1.14467
$503$	−39.4009	−1.75680	−0.878399	−	0.477928i	$-0.841388\pi$
$503$	−39.4009	−1.75680	−0.878399	+	0.477928i	$0.841388\pi$
$504$	−10.9765	−0.488931
$505$	13.0758	0.581865
$506$	−11.8371	−0.526225
$507$	−7.68540	−0.341321
$508$	3.89002	0.172592
$509$	−1.38275	−0.0612894	−0.0306447	−	0.999530i	$-0.509756\pi$
$509$	−1.38275	−0.0612894	−0.0306447	+	0.999530i	$0.509756\pi$
$510$	−1.94725	−0.0862256
$511$	2.04901	0.0906428
$512$	−25.2880	−1.11758
$513$	−26.3778	−1.16461
$514$	32.3853	1.42845
$515$	−25.8812	−1.14046
$516$	−0.172492	−0.00759354
$517$	−1.77171	−0.0779197
$518$	15.1429	0.665340
$519$	13.8047	0.605960
$520$	30.0724	1.31876
$521$	−36.5617	−1.60180	−0.800898	−	0.598801i	$-0.795644\pi$
$521$	−36.5617	−1.60180	−0.800898	+	0.598801i	$0.795644\pi$
$522$	−29.7311	−1.30130
$523$	−0.776369	−0.0339482	−0.0169741	−	0.999856i	$-0.505403\pi$
$523$	−0.776369	−0.0339482	−0.0169741	+	0.999856i	$0.505403\pi$
$524$	−1.96328	−0.0857663
$525$	−0.747592	−0.0326276
$526$	11.8740	0.517731
$527$	3.43036	0.149429
$528$	−4.33238	−0.188542
$529$	2.48279	0.107947
$530$	−23.3424	−1.01393
$531$	−34.0141	−1.47609
$532$	−2.47990	−0.107517
$533$	48.5043	2.10095
$534$	−3.80274	−0.164561
$535$	10.7425	0.464439
$536$	2.45131	0.105880
$537$	14.0965	0.608309
$538$	−14.0301	−0.604881
$539$	8.52998	0.367412
$540$	−2.00741	−0.0863853
$541$	−35.6164	−1.53127	−0.765635	−	0.643275i	$-0.777575\pi$
$541$	−35.6164	−1.53127	−0.765635	+	0.643275i	$0.777575\pi$
$542$	35.7139	1.53404
$543$	14.6653	0.629347
$544$	1.39607	0.0598559
$545$	3.29452	0.141122
$546$	−6.78420	−0.290337
$547$	−30.3294	−1.29679	−0.648395	−	0.761304i	$-0.724559\pi$
$547$	−30.3294	−1.29679	−0.648395	+	0.761304i	$0.724559\pi$
$548$	−1.67382	−0.0715022
$549$	22.6000	0.964544
$550$	1.66904	0.0711679
$551$	−60.8238	−2.59118
$552$	10.6723	0.454244
$553$	−6.98194	−0.296902
$554$	−13.2057	−0.561057
$555$	11.3867	0.483338
$556$	0.163772	0.00694547
$557$	31.4769	1.33372	0.666860	−	0.745183i	$-0.267638\pi$
$557$	31.4769	1.33372	0.666860	+	0.745183i	$0.267638\pi$
$558$	−11.3287	−0.479582
$559$	4.77201	0.201835
$560$	10.5364	0.445243
$561$	1.25876	0.0531451
$562$	−30.1348	−1.27116
$563$	4.36284	0.183872	0.0919360	−	0.995765i	$-0.470694\pi$
$563$	4.36284	0.183872	0.0919360	+	0.995765i	$0.470694\pi$
$564$	0.176406	0.00742803
$565$	−14.3698	−0.604542
$566$	−5.16146	−0.216952
$567$	−6.96554	−0.292525
$568$	24.0232	1.00799
$569$	12.4533	0.522070	0.261035	−	0.965329i	$-0.415936\pi$
$569$	12.4533	0.522070	0.261035	+	0.965329i	$0.415936\pi$
$570$	13.1560	0.551044
$571$	17.9243	0.750109	0.375055	−	0.927003i	$-0.377624\pi$
$571$	17.9243	0.750109	0.375055	+	0.927003i	$0.377624\pi$
$572$	−2.14684	−0.0897638
$573$	−3.60568	−0.150629
$574$	19.4463	0.811672
$575$	−3.59307	−0.149841
$576$	−21.7864	−0.907767
$577$	16.8231	0.700355	0.350177	−	0.936683i	$-0.386121\pi$
$577$	16.8231	0.700355	0.350177	+	0.936683i	$0.386121\pi$
$578$	1.32352	0.0550512
$579$	5.64252	0.234495
$580$	−4.62884	−0.192202
$581$	−22.5702	−0.936369
$582$	−6.25030	−0.259083
$583$	15.0893	0.624934
$584$	4.12436	0.170667
$585$	25.2170	1.04259
$586$	−7.72048	−0.318930
$587$	24.7054	1.01970	0.509850	−	0.860263i	$-0.329701\pi$
$587$	24.7054	1.01970	0.509850	+	0.860263i	$0.329701\pi$
$588$	−0.849314	−0.0350251
$589$	−23.1762	−0.954959
$590$	37.3611	1.53813
$591$	−10.9998	−0.452472
$592$	26.6372	1.09478
$593$	2.97360	0.122111	0.0610556	−	0.998134i	$-0.480553\pi$
$593$	2.97360	0.122111	0.0610556	+	0.998134i	$0.480553\pi$
$594$	−9.15504	−0.375636
$595$	−3.06133	−0.125502
$596$	−5.97637	−0.244801
$597$	−13.6340	−0.558004
$598$	−32.6062	−1.33337
$599$	9.77731	0.399490	0.199745	−	0.979848i	$-0.435989\pi$
$599$	9.77731	0.399490	0.199745	+	0.979848i	$0.435989\pi$
$600$	−1.50479	−0.0614330
$601$	−30.1162	−1.22846	−0.614232	−	0.789126i	$-0.710534\pi$
$601$	−30.1162	−1.22846	−0.614232	+	0.789126i	$0.710534\pi$
$602$	1.91319	0.0779758
$603$	2.05553	0.0837075
$604$	4.23927	0.172493
$605$	−16.2787	−0.661822
$606$	−5.93762	−0.241199
$607$	10.3732	0.421037	0.210519	−	0.977590i	$-0.432485\pi$
$607$	10.3732	0.421037	0.210519	+	0.977590i	$0.432485\pi$
$608$	−9.43211	−0.382522
$609$	9.45571	0.383165
$610$	−24.8239	−1.00509
$611$	−4.88029	−0.197435
$612$	0.619541	0.0250435
$613$	29.8246	1.20460	0.602302	−	0.798268i	$-0.294250\pi$
$613$	29.8246	1.20460	0.602302	+	0.798268i	$0.294250\pi$
$614$	20.2413	0.816874
$615$	14.6226	0.589641
$616$	−7.79376	−0.314020
$617$	−34.8361	−1.40245	−0.701225	−	0.712940i	$-0.747363\pi$
$617$	−34.8361	−1.40245	−0.701225	+	0.712940i	$0.747363\pi$
$618$	11.7524	0.472753
$619$	30.1325	1.21113	0.605563	−	0.795797i	$-0.292948\pi$
$619$	30.1325	1.21113	0.605563	+	0.795797i	$0.292948\pi$
$620$	−1.76376	−0.0708344
$621$	19.7088	0.790887
$622$	−36.7324	−1.47283
$623$	−5.97839	−0.239519
$624$	−11.9338	−0.477734
$625$	−20.9345	−0.837380
$626$	1.66358	0.0664899
$627$	−8.50445	−0.339635
$628$	1.92049	0.0766360
$629$	−7.73939	−0.308590
$630$	10.1100	0.402790
$631$	−5.56614	−0.221585	−0.110792	−	0.993844i	$-0.535339\pi$
$631$	−5.56614	−0.221585	−0.110792	+	0.993844i	$0.535339\pi$
$632$	−14.0536	−0.559024
$633$	−3.15615	−0.125446
$634$	42.7611	1.69826
$635$	−32.4436	−1.28749
$636$	−1.50241	−0.0595745
$637$	23.4964	0.930960
$638$	−21.1103	−0.835767
$639$	20.1445	0.796903
$640$	18.1483	0.717373
$641$	26.6031	1.05076	0.525379	−	0.850869i	$-0.323924\pi$
$641$	26.6031	1.05076	0.525379	+	0.850869i	$0.323924\pi$
$642$	−4.87809	−0.192523
$643$	−4.07812	−0.160825	−0.0804127	−	0.996762i	$-0.525624\pi$
$643$	−4.07812	−0.160825	−0.0804127	+	0.996762i	$0.525624\pi$
$644$	1.85292	0.0730151
$645$	1.43862	0.0566457
$646$	−8.94197	−0.351817
$647$	−31.8345	−1.25154	−0.625772	−	0.780006i	$-0.715216\pi$
$647$	−31.8345	−1.25154	−0.625772	+	0.780006i	$0.715216\pi$
$648$	−14.0206	−0.550783
$649$	−24.1514	−0.948027
$650$	4.59746	0.180327
$651$	3.60299	0.141212
$652$	−0.165623	−0.00648631
$653$	23.4069	0.915983	0.457991	−	0.888957i	$-0.348569\pi$
$653$	23.4069	0.915983	0.457991	+	0.888957i	$0.348569\pi$
$654$	−1.49602	−0.0584988
$655$	16.3742	0.639793
$656$	34.2071	1.33556
$657$	3.45845	0.134927
$658$	−1.95660	−0.0762762
$659$	4.26587	0.166175	0.0830873	−	0.996542i	$-0.473522\pi$
$659$	4.26587	0.166175	0.0830873	+	0.996542i	$0.473522\pi$
$660$	−0.647209	−0.0251926
$661$	−46.2817	−1.80015	−0.900074	−	0.435737i	$-0.856488\pi$
$661$	−46.2817	−1.80015	−0.900074	+	0.435737i	$0.856488\pi$
$662$	3.20356	0.124510
$663$	3.46734	0.134661
$664$	−45.4305	−1.76305
$665$	20.6829	0.802049
$666$	25.5592	0.990397
$667$	45.4460	1.75967
$668$	−2.48997	−0.0963397
$669$	−0.984072	−0.0380464
$670$	−2.25779	−0.0872261
$671$	16.0469	0.619486
$672$	1.46632	0.0565646
$673$	2.83373	0.109232	0.0546160	−	0.998507i	$-0.482607\pi$
$673$	2.83373	0.109232	0.0546160	+	0.998507i	$0.482607\pi$
$674$	3.94517	0.151962
$675$	−2.77894	−0.106961
$676$	−2.68581	−0.103301
$677$	33.5949	1.29116	0.645578	−	0.763694i	$-0.276617\pi$
$677$	33.5949	1.29116	0.645578	+	0.763694i	$0.276617\pi$
$678$	6.52521	0.250599
$679$	−9.82628	−0.377098
$680$	−6.16201	−0.236302
$681$	4.58014	0.175511
$682$	−8.04385	−0.308015
$683$	48.6214	1.86045	0.930224	−	0.366993i	$-0.119613\pi$
$683$	48.6214	1.86045	0.930224	+	0.366993i	$0.119613\pi$
$684$	−4.18574	−0.160046
$685$	13.9600	0.533386
$686$	23.1163	0.882585
$687$	16.9530	0.646797
$688$	3.36541	0.128305
$689$	41.5644	1.58348
$690$	−9.82981	−0.374214
$691$	−23.2600	−0.884854	−0.442427	−	0.896805i	$-0.645882\pi$
$691$	−23.2600	−0.884854	−0.442427	+	0.896805i	$0.645882\pi$
$692$	4.82433	0.183394
$693$	−6.53540	−0.248259
$694$	−1.94981	−0.0740137
$695$	−1.36589	−0.0518112
$696$	19.0330	0.721444
$697$	−9.93882	−0.376460
$698$	5.74649	0.217508
$699$	−5.50958	−0.208392
$700$	−0.261261	−0.00987473
$701$	8.22492	0.310651	0.155325	−	0.987863i	$-0.450357\pi$
$701$	8.22492	0.310651	0.155325	+	0.987863i	$0.450357\pi$
$702$	−25.2181	−0.951797
$703$	52.2888	1.97211
$704$	−15.4693	−0.583020
$705$	−1.47126	−0.0554110
$706$	−46.7023	−1.75766
$707$	−9.33470	−0.351067
$708$	2.40471	0.0903746
$709$	0.898457	0.0337423	0.0168711	−	0.999858i	$-0.494629\pi$
$709$	0.898457	0.0337423	0.0168711	+	0.999858i	$0.494629\pi$
$710$	−22.1267	−0.830401
$711$	−11.7846	−0.441956
$712$	−12.0336	−0.450980
$713$	17.3166	0.648513
$714$	1.39012	0.0520241
$715$	17.9051	0.669613
$716$	4.92630	0.184104
$717$	15.8100	0.590434
$718$	21.0768	0.786578
$719$	18.0042	0.671442	0.335721	−	0.941961i	$-0.391020\pi$
$719$	18.0042	0.671442	0.335721	+	0.941961i	$0.391020\pi$
$720$	17.7840	0.662770
$721$	18.4764	0.688096
$722$	35.2667	1.31249
$723$	7.87364	0.292824
$724$	5.12507	0.190472
$725$	−6.40787	−0.237982
$726$	7.39201	0.274343
$727$	−40.5744	−1.50482	−0.752410	−	0.658695i	$-0.771109\pi$
$727$	−40.5744	−1.50482	−0.752410	+	0.658695i	$0.771109\pi$
$728$	−21.4684	−0.795672
$729$	−3.43525	−0.127231
$730$	−3.79877	−0.140599
$731$	−0.977814	−0.0361658
$732$	−1.59776	−0.0590551
$733$	−20.6546	−0.762896	−0.381448	−	0.924390i	$-0.624574\pi$
$733$	−20.6546	−0.762896	−0.381448	+	0.924390i	$0.624574\pi$
$734$	−24.3526	−0.898872
$735$	7.08347	0.261278
$736$	7.04742	0.259771
$737$	1.45951	0.0537617
$738$	32.8227	1.20822
$739$	1.90134	0.0699418	0.0349709	−	0.999388i	$-0.488866\pi$
$739$	1.90134	0.0699418	0.0349709	+	0.999388i	$0.488866\pi$
$740$	3.97930	0.146282
$741$	−23.4261	−0.860577
$742$	16.6639	0.611753
$743$	47.7771	1.75277	0.876386	−	0.481610i	$-0.159948\pi$
$743$	47.7771	1.75277	0.876386	+	0.481610i	$0.159948\pi$
$744$	7.25229	0.265882
$745$	49.8442	1.82615
$746$	16.6815	0.610752
$747$	−38.0954	−1.39384
$748$	0.439900	0.0160843
$749$	−7.66899	−0.280219
$750$	11.1222	0.406127
$751$	30.5515	1.11484	0.557420	−	0.830231i	$-0.311791\pi$
$751$	30.5515	1.11484	0.557420	+	0.830231i	$0.311791\pi$
$752$	−3.44177	−0.125508
$753$	13.7675	0.501714
$754$	−58.1498	−2.11769
$755$	−35.3564	−1.28675
$756$	1.43307	0.0521204
$757$	16.3755	0.595179	0.297589	−	0.954694i	$-0.403817\pi$
$757$	16.3755	0.595179	0.297589	+	0.954694i	$0.403817\pi$
$758$	−25.4812	−0.925517
$759$	6.35430	0.230647
$760$	41.6317	1.51014
$761$	−46.3309	−1.67949	−0.839747	−	0.542979i	$-0.817296\pi$
$761$	−46.3309	−1.67949	−0.839747	+	0.542979i	$0.817296\pi$
$762$	14.7324	0.533698
$763$	−2.35193	−0.0851456
$764$	−1.26008	−0.0455879
$765$	−5.16711	−0.186817
$766$	−18.5608	−0.670628
$767$	−66.5266	−2.40214
$768$	4.16579	0.150320
$769$	25.9153	0.934531	0.467266	−	0.884117i	$-0.345239\pi$
$769$	25.9153	0.934531	0.467266	+	0.884117i	$0.345239\pi$
$770$	7.17849	0.258695
$771$	−17.3847	−0.626096
$772$	1.97189	0.0709699
$773$	16.8869	0.607378	0.303689	−	0.952771i	$-0.401782\pi$
$773$	16.8869	0.607378	0.303689	+	0.952771i	$0.401782\pi$
$774$	3.22921	0.116071
$775$	−2.44164	−0.0877064
$776$	−19.7789	−0.710021
$777$	−8.12886	−0.291621
$778$	−26.4975	−0.949983
$779$	67.1486	2.40585
$780$	−1.78278	−0.0638337
$781$	14.3034	0.511816
$782$	6.68120	0.238919
$783$	35.1486	1.25611
$784$	16.5706	0.591806
$785$	−16.0173	−0.571683
$786$	−7.43539	−0.265212
$787$	15.2856	0.544873	0.272436	−	0.962174i	$-0.412171\pi$
$787$	15.2856	0.544873	0.272436	+	0.962174i	$0.412171\pi$
$788$	−3.84410	−0.136941
$789$	−6.37408	−0.226923
$790$	12.9442	0.460534
$791$	10.2585	0.364749
$792$	−13.1548	−0.467436
$793$	44.2023	1.56967
$794$	−24.6155	−0.873571
$795$	12.5304	0.444409
$796$	−4.76468	−0.168880
$797$	1.25122	0.0443204	0.0221602	−	0.999754i	$-0.492946\pi$
$797$	1.25122	0.0443204	0.0221602	+	0.999754i	$0.492946\pi$
$798$	−9.39194	−0.332471
$799$	1.00000	0.0353775
$800$	−0.993685	−0.0351321
$801$	−10.0907	−0.356538
$802$	−2.65984	−0.0939222
$803$	2.45564	0.0866578
$804$	−0.145321	−0.00512506
$805$	−15.4537	−0.544672
$806$	−22.1573	−0.780457
$807$	7.53151	0.265122
$808$	−18.7894	−0.661009
$809$	53.6546	1.88640	0.943198	−	0.332230i	$-0.107801\pi$
$809$	53.6546	1.88640	0.943198	+	0.332230i	$0.107801\pi$
$810$	12.9138	0.453745
$811$	15.3216	0.538013	0.269007	−	0.963138i	$-0.413305\pi$
$811$	15.3216	0.538013	0.269007	+	0.963138i	$0.413305\pi$
$812$	3.30449	0.115965
$813$	−19.1716	−0.672377
$814$	18.1481	0.636090
$815$	1.38134	0.0483861
$816$	2.44531	0.0856029
$817$	6.60630	0.231125
$818$	−46.2289	−1.61636
$819$	−18.0022	−0.629047
$820$	5.11016	0.178455
$821$	14.7180	0.513662	0.256831	−	0.966456i	$-0.417322\pi$
$821$	14.7180	0.513662	0.256831	+	0.966456i	$0.417322\pi$
$822$	−6.33915	−0.221103
$823$	−43.5230	−1.51712	−0.758558	−	0.651605i	$-0.774096\pi$
$823$	−43.5230	−1.51712	−0.758558	+	0.651605i	$0.774096\pi$
$824$	37.1903	1.29558
$825$	−0.895956	−0.0311932
$826$	−26.6718	−0.928030
$827$	−39.4803	−1.37286	−0.686432	−	0.727194i	$-0.740824\pi$
$827$	−39.4803	−1.37286	−0.686432	+	0.727194i	$0.740824\pi$
$828$	3.12747	0.108687
$829$	10.1971	0.354161	0.177080	−	0.984196i	$-0.443335\pi$
$829$	10.1971	0.354161	0.177080	+	0.984196i	$0.443335\pi$
$830$	41.8441	1.45243
$831$	7.08896	0.245913
$832$	−42.6111	−1.47727
$833$	−4.81455	−0.166814
$834$	0.620240	0.0214772
$835$	20.7669	0.718667
$836$	−2.97205	−0.102790
$837$	13.3930	0.462929
$838$	18.4657	0.637889
$839$	−40.9166	−1.41260	−0.706299	−	0.707914i	$-0.749636\pi$
$839$	−40.9166	−1.41260	−0.706299	+	0.707914i	$0.749636\pi$
$840$	−6.47209	−0.223308
$841$	52.0482	1.79477
$842$	34.9065	1.20296
$843$	16.1767	0.557154
$844$	−1.10298	−0.0379662
$845$	22.4003	0.770593
$846$	−3.30248	−0.113541
$847$	11.6212	0.399309
$848$	29.3128	1.00661
$849$	2.77072	0.0950910
$850$	−0.942048	−0.0323120
$851$	−39.0688	−1.33926
$852$	−1.42416	−0.0487911
$853$	4.03873	0.138284	0.0691418	−	0.997607i	$-0.477974\pi$
$853$	4.03873	0.138284	0.0691418	+	0.997607i	$0.477974\pi$
$854$	17.7215	0.606419
$855$	34.9100	1.19390
$856$	−15.4366	−0.527611
$857$	−40.5609	−1.38554	−0.692768	−	0.721161i	$-0.743609\pi$
$857$	−40.5609	−1.38554	−0.692768	+	0.721161i	$0.743609\pi$
$858$	−8.13056	−0.277573
$859$	20.9090	0.713406	0.356703	−	0.934218i	$-0.383901\pi$
$859$	20.9090	0.713406	0.356703	+	0.934218i	$0.383901\pi$
$860$	0.502755	0.0171438
$861$	−10.4390	−0.355759
$862$	34.9741	1.19122
$863$	3.81476	0.129856	0.0649280	−	0.997890i	$-0.479318\pi$
$863$	3.81476	0.129856	0.0649280	+	0.997890i	$0.479318\pi$
$864$	5.45059	0.185433
$865$	−40.2360	−1.36806
$866$	46.0285	1.56411
$867$	−0.710480	−0.0241292
$868$	1.25913	0.0427378
$869$	−8.36755	−0.283850
$870$	−17.5305	−0.594338
$871$	4.02031	0.136223
$872$	−4.73409	−0.160317
$873$	−16.5854	−0.561332
$874$	−45.1395	−1.52687
$875$	17.4856	0.591121
$876$	−0.244504	−0.00826102
$877$	2.40867	0.0813351	0.0406676	−	0.999173i	$-0.487052\pi$
$877$	2.40867	0.0813351	0.0406676	+	0.999173i	$0.487052\pi$
$878$	49.5464	1.67211
$879$	4.14443	0.139788
$880$	12.6274	0.425669
$881$	1.74146	0.0586712	0.0293356	−	0.999570i	$-0.490661\pi$
$881$	1.74146	0.0586712	0.0293356	+	0.999570i	$0.490661\pi$
$882$	15.8999	0.535378
$883$	1.71237	0.0576259	0.0288130	−	0.999585i	$-0.490827\pi$
$883$	1.71237	0.0576259	0.0288130	+	0.999585i	$0.490827\pi$
$884$	1.21173	0.0407550
$885$	−20.0558	−0.674170
$886$	−12.2519	−0.411610
$887$	53.0108	1.77993	0.889964	−	0.456030i	$-0.150729\pi$
$887$	53.0108	1.77993	0.889964	+	0.456030i	$0.150729\pi$
$888$	−16.3622	−0.549080
$889$	23.1612	0.776803
$890$	11.0837	0.371525
$891$	−8.34789	−0.279665
$892$	−0.343903	−0.0115147
$893$	−6.75619	−0.226087
$894$	−22.6339	−0.756989
$895$	−41.0864	−1.37337
$896$	−12.9559	−0.432826
$897$	17.5033	0.584419
$898$	−25.2306	−0.841957
$899$	30.8825	1.02999
$900$	−0.440973	−0.0146991
$901$	−8.51679	−0.283735
$902$	23.3055	0.775988
$903$	−1.02702	−0.0341771
$904$	20.6488	0.686769
$905$	−42.7442	−1.42087
$906$	16.0551	0.533394
$907$	46.5810	1.54670	0.773348	−	0.633982i	$-0.218581\pi$
$907$	46.5810	1.54670	0.773348	+	0.633982i	$0.218581\pi$
$908$	1.60062	0.0531185
$909$	−15.7557	−0.522584
$910$	19.7736	0.655489
$911$	−29.2286	−0.968385	−0.484193	−	0.874961i	$-0.660887\pi$
$911$	−29.2286	−0.968385	−0.484193	+	0.874961i	$0.660887\pi$
$912$	−16.5210	−0.547064
$913$	−27.0493	−0.895203
$914$	32.8208	1.08561
$915$	13.3257	0.440534
$916$	5.92456	0.195753
$917$	−11.6894	−0.386018
$918$	5.16735	0.170548
$919$	15.8456	0.522698	0.261349	−	0.965244i	$-0.415833\pi$
$919$	15.8456	0.522698	0.261349	+	0.965244i	$0.415833\pi$
$920$	−31.1061	−1.02554
$921$	−10.8658	−0.358039
$922$	−31.8788	−1.04987
$923$	39.3997	1.29686
$924$	0.462037	0.0151999
$925$	5.50870	0.181125
$926$	−38.8913	−1.27805
$927$	31.1856	1.02427
$928$	12.5684	0.412576
$929$	−12.9203	−0.423901	−0.211950	−	0.977280i	$-0.567981\pi$
$929$	−12.9203	−0.423901	−0.211950	+	0.977280i	$0.567981\pi$
$930$	−6.67977	−0.219038
$931$	32.5280	1.06606
$932$	−1.92543	−0.0630696
$933$	19.7183	0.645549
$934$	3.55050	0.116176
$935$	−3.66886	−0.119985
$936$	−36.2358	−1.18440
$937$	18.0785	0.590598	0.295299	−	0.955405i	$-0.404581\pi$
$937$	18.0785	0.590598	0.295299	+	0.955405i	$0.404581\pi$
$938$	1.61182	0.0526277
$939$	−0.893025	−0.0291428
$940$	−0.514162	−0.0167701
$941$	34.2081	1.11515	0.557576	−	0.830126i	$-0.311731\pi$
$941$	34.2081	1.11515	0.557576	+	0.830126i	$0.311731\pi$
$942$	7.27334	0.236978
$943$	−50.1716	−1.63381
$944$	−46.9172	−1.52702
$945$	−11.9522	−0.388804
$946$	2.29287	0.0745477
$947$	−13.4096	−0.435753	−0.217877	−	0.975976i	$-0.569913\pi$
$947$	−13.4096	−0.435753	−0.217877	+	0.975976i	$0.569913\pi$
$948$	0.833141	0.0270592
$949$	6.76423	0.219576
$950$	6.36466	0.206497
$951$	−22.9546	−0.744353
$952$	4.39900	0.142573
$953$	11.1006	0.359584	0.179792	−	0.983705i	$-0.442457\pi$
$953$	11.1006	0.359584	0.179792	+	0.983705i	$0.442457\pi$
$954$	28.1265	0.910629
$955$	10.5093	0.340073
$956$	5.52510	0.178695
$957$	11.3323	0.366320
$958$	−15.5055	−0.500961
$959$	−9.96595	−0.321817
$960$	−12.8460	−0.414603
$961$	−19.2326	−0.620407
$962$	49.9900	1.61174
$963$	−12.9442	−0.417122
$964$	2.75160	0.0886230
$965$	−16.4460	−0.529416
$966$	7.01741	0.225782
$967$	51.9614	1.67096	0.835482	−	0.549517i	$-0.185188\pi$
$967$	51.9614	1.67096	0.835482	+	0.549517i	$0.185188\pi$
$968$	23.3918	0.751841
$969$	4.80014	0.154203
$970$	18.2175	0.584928
$971$	3.42286	0.109845	0.0549224	−	0.998491i	$-0.482509\pi$
$971$	3.42286	0.109845	0.0549224	+	0.998491i	$0.482509\pi$
$972$	3.73935	0.119940
$973$	0.975098	0.0312602
$974$	−22.5810	−0.723541
$975$	−2.46797	−0.0790382
$976$	31.1732	0.997830
$977$	4.98880	0.159606	0.0798030	−	0.996811i	$-0.474571\pi$
$977$	4.98880	0.159606	0.0798030	+	0.996811i	$0.474571\pi$
$978$	−0.627253	−0.0200574
$979$	−7.16484	−0.228989
$980$	2.47546	0.0790756
$981$	−3.96974	−0.126744
$982$	37.3841	1.19298
$983$	5.20217	0.165923	0.0829617	−	0.996553i	$-0.473562\pi$
$983$	5.20217	0.165923	0.0829617	+	0.996553i	$0.473562\pi$
$984$	−21.0121	−0.669842
$985$	32.0607	1.02154
$986$	11.9152	0.379459
$987$	1.05032	0.0334321
$988$	−8.18670	−0.260454
$989$	−4.93605	−0.156957
$990$	12.1163	0.385082
$991$	−54.2309	−1.72270	−0.861350	−	0.508012i	$-0.830381\pi$
$991$	−54.2309	−1.72270	−0.861350	+	0.508012i	$0.830381\pi$
$992$	4.78902	0.152052
$993$	−1.71971	−0.0545732
$994$	15.7961	0.501021
$995$	39.7385	1.25980
$996$	2.69325	0.0853390
$997$	44.1849	1.39935	0.699674	−	0.714462i	$-0.253328\pi$
$997$	44.1849	1.39935	0.699674	+	0.714462i	$0.253328\pi$
$998$	−18.1754	−0.575333
$999$	−30.2165	−0.956006

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	799.2.a.d.1.6	✓	8
3.2	odd	2		7191.2.a.u.1.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
799.2.a.d.1.6	✓	8	1.1	even	1	trivial
7191.2.a.u.1.3		8	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 799 = 17 \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	799.a (trivial)

\(f(q)\)	\(=\)	\(q+1.32352 q^{2} -0.710480 q^{3} -0.248291 q^{4} +2.07080 q^{5} -0.940335 q^{6} -1.47833 q^{7} -2.97566 q^{8} -2.49522 q^{9} +O(q^{10})\)	\(q+1.32352 q^{2} -0.710480 q^{3} -0.248291 q^{4} +2.07080 q^{5} -0.940335 q^{6} -1.47833 q^{7} -2.97566 q^{8} -2.49522 q^{9} +2.74075 q^{10} -1.77171 q^{11} +0.176406 q^{12} -4.88029 q^{13} -1.95660 q^{14} -1.47126 q^{15} -3.44177 q^{16} +1.00000 q^{17} -3.30248 q^{18} -6.75619 q^{19} -0.514162 q^{20} +1.05032 q^{21} -2.34490 q^{22} +5.04805 q^{23} +2.11415 q^{24} -0.711774 q^{25} -6.45916 q^{26} +3.90424 q^{27} +0.367056 q^{28} +9.00268 q^{29} -1.94725 q^{30} +3.43036 q^{31} +1.39607 q^{32} +1.25876 q^{33} +1.32352 q^{34} -3.06133 q^{35} +0.619541 q^{36} -7.73939 q^{37} -8.94197 q^{38} +3.46734 q^{39} -6.16201 q^{40} -9.93882 q^{41} +1.39012 q^{42} -0.977814 q^{43} +0.439900 q^{44} -5.16711 q^{45} +6.68120 q^{46} +1.00000 q^{47} +2.44531 q^{48} -4.81455 q^{49} -0.942048 q^{50} -0.710480 q^{51} +1.21173 q^{52} -8.51679 q^{53} +5.16735 q^{54} -3.66886 q^{55} +4.39900 q^{56} +4.80014 q^{57} +11.9152 q^{58} +13.6317 q^{59} +0.365302 q^{60} -9.05732 q^{61} +4.54016 q^{62} +3.68875 q^{63} +8.73126 q^{64} -10.1061 q^{65} +1.66600 q^{66} -0.823786 q^{67} -0.248291 q^{68} -3.58654 q^{69} -4.05173 q^{70} -8.07323 q^{71} +7.42493 q^{72} -1.38603 q^{73} -10.2433 q^{74} +0.505701 q^{75} +1.67750 q^{76} +2.61917 q^{77} +4.58910 q^{78} +4.72287 q^{79} -7.12723 q^{80} +4.71177 q^{81} -13.1542 q^{82} +15.2674 q^{83} -0.260786 q^{84} +2.07080 q^{85} -1.29416 q^{86} -6.39622 q^{87} +5.27201 q^{88} +4.04402 q^{89} -6.83878 q^{90} +7.21466 q^{91} -1.25339 q^{92} -2.43720 q^{93} +1.32352 q^{94} -13.9907 q^{95} -0.991878 q^{96} +6.64689 q^{97} -6.37215 q^{98} +4.42080 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} - 7 q^{3} + 7 q^{4} - 10 q^{5} + 2 q^{6} - 9 q^{7} - q^{9}+O(q^{10}) \) 8 * q + q^2 - 7 * q^3 + 7 * q^4 - 10 * q^5 + 2 * q^6 - 9 * q^7 - q^9	\( 8 q + q^{2} - 7 q^{3} + 7 q^{4} - 10 q^{5} + 2 q^{6} - 9 q^{7} - q^{9} + 2 q^{10} - 2 q^{11} - 11 q^{12} - 3 q^{13} - 9 q^{14} + 14 q^{15} - 7 q^{16} + 8 q^{17} - 5 q^{18} - 8 q^{19} - 20 q^{20} + 4 q^{21} - 20 q^{22} - 9 q^{23} - 4 q^{24} + 14 q^{25} - 20 q^{26} + 2 q^{27} - 21 q^{28} - 2 q^{29} - 27 q^{30} - 7 q^{31} + 21 q^{32} - 23 q^{33} + q^{34} + 7 q^{35} - 17 q^{36} - 13 q^{37} - 7 q^{38} + 9 q^{39} - 16 q^{40} - 39 q^{41} + 11 q^{42} + 35 q^{43} - 17 q^{44} - 13 q^{45} + 19 q^{46} + 8 q^{47} + 9 q^{48} + q^{49} - 30 q^{50} - 7 q^{51} - 17 q^{52} - 6 q^{53} - 4 q^{54} + 22 q^{55} - 48 q^{56} + 5 q^{57} + 3 q^{58} - 19 q^{59} + 32 q^{60} - 15 q^{61} + 15 q^{62} + 17 q^{63} - 8 q^{64} - 29 q^{65} - 5 q^{66} + 15 q^{67} + 7 q^{68} - 12 q^{69} + 35 q^{70} - 7 q^{71} + q^{72} - 22 q^{73} - 43 q^{74} - 29 q^{75} + 52 q^{76} + 2 q^{77} + 43 q^{78} - 43 q^{79} + 6 q^{80} - 16 q^{81} + 19 q^{82} - 3 q^{83} + 34 q^{84} - 10 q^{85} - 19 q^{86} + q^{87} + 5 q^{88} - 53 q^{89} + 42 q^{90} + 5 q^{91} + 28 q^{92} + 44 q^{93} + q^{94} - 53 q^{95} - 41 q^{96} - 40 q^{97} + 30 q^{98} + 45 q^{99}+O(q^{100}) \) 8 * q + q^2 - 7 * q^3 + 7 * q^4 - 10 * q^5 + 2 * q^6 - 9 * q^7 - q^9 + 2 * q^10 - 2 * q^11 - 11 * q^12 - 3 * q^13 - 9 * q^14 + 14 * q^15 - 7 * q^16 + 8 * q^17 - 5 * q^18 - 8 * q^19 - 20 * q^20 + 4 * q^21 - 20 * q^22 - 9 * q^23 - 4 * q^24 + 14 * q^25 - 20 * q^26 + 2 * q^27 - 21 * q^28 - 2 * q^29 - 27 * q^30 - 7 * q^31 + 21 * q^32 - 23 * q^33 + q^34 + 7 * q^35 - 17 * q^36 - 13 * q^37 - 7 * q^38 + 9 * q^39 - 16 * q^40 - 39 * q^41 + 11 * q^42 + 35 * q^43 - 17 * q^44 - 13 * q^45 + 19 * q^46 + 8 * q^47 + 9 * q^48 + q^49 - 30 * q^50 - 7 * q^51 - 17 * q^52 - 6 * q^53 - 4 * q^54 + 22 * q^55 - 48 * q^56 + 5 * q^57 + 3 * q^58 - 19 * q^59 + 32 * q^60 - 15 * q^61 + 15 * q^62 + 17 * q^63 - 8 * q^64 - 29 * q^65 - 5 * q^66 + 15 * q^67 + 7 * q^68 - 12 * q^69 + 35 * q^70 - 7 * q^71 + q^72 - 22 * q^73 - 43 * q^74 - 29 * q^75 + 52 * q^76 + 2 * q^77 + 43 * q^78 - 43 * q^79 + 6 * q^80 - 16 * q^81 + 19 * q^82 - 3 * q^83 + 34 * q^84 - 10 * q^85 - 19 * q^86 + q^87 + 5 * q^88 - 53 * q^89 + 42 * q^90 + 5 * q^91 + 28 * q^92 + 44 * q^93 + q^94 - 53 * q^95 - 41 * q^96 - 40 * q^97 + 30 * q^98 + 45 * q^99

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