LMFDB - Embedded newform 799.2.a.e.1.9

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:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} - 8 x^{10} + 44 x^{9} + 11 x^{8} - 168 x^{7} + 41 x^{6} + 272 x^{5} - 111 x^{4} + \cdots - 17 $ x^12 - 4x^11 - 8x^10 + 44x^9 + 11x^8 - 168x^7 + 41x^6 + 272x^5 - 111x^4 - 181x^3 + 77x^2 + 39*x - 17
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			1.9
Root			$-0.829033$ 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)

$f(q)$	$=$	$q+0.829033 q^{2} -0.269629 q^{3} -1.31270 q^{4} -1.24530 q^{5} -0.223531 q^{6} +4.95448 q^{7} -2.74634 q^{8} -2.92730 q^{9} +O(q^{10})$	\(q+0.829033 q^{2} -0.269629 q^{3} -1.31270 q^{4} -1.24530 q^{5} -0.223531 q^{6} +4.95448 q^{7} -2.74634 q^{8} -2.92730 q^{9} -1.03240 q^{10} -4.14710 q^{11} +0.353943 q^{12} +0.518411 q^{13} +4.10743 q^{14} +0.335769 q^{15} +0.348601 q^{16} -1.00000 q^{17} -2.42683 q^{18} -1.45645 q^{19} +1.63471 q^{20} -1.33587 q^{21} -3.43808 q^{22} -4.30503 q^{23} +0.740493 q^{24} -3.44923 q^{25} +0.429780 q^{26} +1.59817 q^{27} -6.50377 q^{28} -2.92743 q^{29} +0.278364 q^{30} -6.03755 q^{31} +5.78168 q^{32} +1.11818 q^{33} -0.829033 q^{34} -6.16982 q^{35} +3.84268 q^{36} +4.49198 q^{37} -1.20744 q^{38} -0.139779 q^{39} +3.42002 q^{40} -12.5007 q^{41} -1.10748 q^{42} -4.00859 q^{43} +5.44391 q^{44} +3.64537 q^{45} -3.56901 q^{46} -1.00000 q^{47} -0.0939930 q^{48} +17.5469 q^{49} -2.85952 q^{50} +0.269629 q^{51} -0.680520 q^{52} -8.32916 q^{53} +1.32494 q^{54} +5.16439 q^{55} -13.6067 q^{56} +0.392700 q^{57} -2.42693 q^{58} +7.17036 q^{59} -0.440766 q^{60} +11.2550 q^{61} -5.00533 q^{62} -14.5033 q^{63} +4.09600 q^{64} -0.645577 q^{65} +0.927007 q^{66} -6.87647 q^{67} +1.31270 q^{68} +1.16076 q^{69} -5.11498 q^{70} -10.9760 q^{71} +8.03936 q^{72} +7.99250 q^{73} +3.72400 q^{74} +0.930012 q^{75} +1.91188 q^{76} -20.5467 q^{77} -0.115881 q^{78} -2.54734 q^{79} -0.434113 q^{80} +8.35099 q^{81} -10.3635 q^{82} +0.605016 q^{83} +1.75361 q^{84} +1.24530 q^{85} -3.32326 q^{86} +0.789319 q^{87} +11.3893 q^{88} -1.58474 q^{89} +3.02213 q^{90} +2.56846 q^{91} +5.65123 q^{92} +1.62790 q^{93} -0.829033 q^{94} +1.81371 q^{95} -1.55891 q^{96} -15.7955 q^{97} +14.5470 q^{98} +12.1398 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{2} - q^{3} + 8 q^{4} - 11 q^{5} - q^{6} + q^{7} - 12 q^{8} - 3 q^{9}+O(q^{10}) $ 12 * q - 4 * q^2 - q^3 + 8 * q^4 - 11 * q^5 - q^6 + q^7 - 12 * q^8 - 3 * q^9	\( 12 q - 4 q^{2} - q^{3} + 8 q^{4} - 11 q^{5} - q^{6} + q^{7} - 12 q^{8} - 3 q^{9} - 2 q^{10} - 6 q^{11} - 4 q^{12} - 13 q^{13} - 15 q^{14} - 15 q^{15} + 4 q^{16} - 12 q^{17} - 9 q^{18} - 9 q^{19} - 23 q^{20} - 6 q^{21} + 11 q^{22} - 2 q^{23} - 6 q^{24} + q^{25} - 9 q^{26} + 2 q^{27} + 23 q^{28} - 14 q^{29} + 25 q^{30} - 18 q^{31} - 28 q^{32} - 17 q^{33} + 4 q^{34} - 15 q^{35} - 13 q^{36} + 8 q^{37} - 13 q^{38} - 9 q^{39} + 21 q^{40} - 43 q^{41} - 21 q^{42} - 7 q^{43} + 4 q^{44} - q^{45} - 24 q^{46} - 12 q^{47} - 2 q^{48} - 19 q^{49} + 8 q^{50} + q^{51} - 14 q^{52} + 5 q^{53} - q^{54} - 7 q^{55} - 26 q^{56} + 2 q^{57} + 27 q^{58} - 25 q^{59} - 13 q^{60} - q^{61} + 5 q^{62} - 13 q^{63} + 34 q^{64} - 8 q^{65} + 2 q^{66} - 2 q^{67} - 8 q^{68} - 27 q^{69} + 31 q^{70} - 5 q^{71} + 27 q^{72} + 6 q^{73} + 21 q^{74} + 14 q^{75} - 41 q^{76} - 22 q^{77} + 40 q^{78} - 10 q^{79} - 24 q^{80} - 4 q^{81} + 9 q^{82} - 45 q^{83} + 24 q^{84} + 11 q^{85} - 48 q^{86} + 7 q^{87} + 25 q^{88} - 65 q^{89} + 32 q^{90} + 7 q^{91} - 8 q^{92} - 15 q^{93} + 4 q^{94} + 44 q^{95} + 12 q^{96} - 21 q^{97} + 41 q^{98} - 41 q^{99}+O(q^{100}) \) 12 * q - 4 * q^2 - q^3 + 8 * q^4 - 11 * q^5 - q^6 + q^7 - 12 * q^8 - 3 * q^9 - 2 * q^10 - 6 * q^11 - 4 * q^12 - 13 * q^13 - 15 * q^14 - 15 * q^15 + 4 * q^16 - 12 * q^17 - 9 * q^18 - 9 * q^19 - 23 * q^20 - 6 * q^21 + 11 * q^22 - 2 * q^23 - 6 * q^24 + q^25 - 9 * q^26 + 2 * q^27 + 23 * q^28 - 14 * q^29 + 25 * q^30 - 18 * q^31 - 28 * q^32 - 17 * q^33 + 4 * q^34 - 15 * q^35 - 13 * q^36 + 8 * q^37 - 13 * q^38 - 9 * q^39 + 21 * q^40 - 43 * q^41 - 21 * q^42 - 7 * q^43 + 4 * q^44 - q^45 - 24 * q^46 - 12 * q^47 - 2 * q^48 - 19 * q^49 + 8 * q^50 + q^51 - 14 * q^52 + 5 * q^53 - q^54 - 7 * q^55 - 26 * q^56 + 2 * q^57 + 27 * q^58 - 25 * q^59 - 13 * q^60 - q^61 + 5 * q^62 - 13 * q^63 + 34 * q^64 - 8 * q^65 + 2 * q^66 - 2 * q^67 - 8 * q^68 - 27 * q^69 + 31 * q^70 - 5 * q^71 + 27 * q^72 + 6 * q^73 + 21 * q^74 + 14 * q^75 - 41 * q^76 - 22 * q^77 + 40 * q^78 - 10 * q^79 - 24 * q^80 - 4 * q^81 + 9 * q^82 - 45 * q^83 + 24 * q^84 + 11 * q^85 - 48 * q^86 + 7 * q^87 + 25 * q^88 - 65 * q^89 + 32 * q^90 + 7 * q^91 - 8 * q^92 - 15 * q^93 + 4 * q^94 + 44 * q^95 + 12 * q^96 - 21 * q^97 + 41 * q^98 - 41 * 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 $

$2$	0.829033	0.586215	0.293107	−	0.956080i	$-0.405311\pi$
$2$	0.829033	0.586215	0.293107	+	0.956080i	$0.405311\pi$
$3$	−0.269629	−0.155670	−0.0778352	−	0.996966i	$-0.524801\pi$
$3$	−0.269629	−0.155670	−0.0778352	+	0.996966i	$0.524801\pi$
$4$	−1.31270	−0.656352
$5$	−1.24530	−0.556915	−0.278458	−	0.960448i	$-0.589823\pi$
$5$	−1.24530	−0.556915	−0.278458	+	0.960448i	$0.589823\pi$
$6$	−0.223531	−0.0912563
$7$	4.95448	1.87262	0.936309	−	0.351177i	$-0.114218\pi$
$7$	4.95448	1.87262	0.936309	+	0.351177i	$0.114218\pi$
$8$	−2.74634	−0.970978
$9$	−2.92730	−0.975767
$10$	−1.03240	−0.326472
$11$	−4.14710	−1.25040	−0.625199	−	0.780466i	$-0.714982\pi$
$11$	−4.14710	−1.25040	−0.625199	+	0.780466i	$0.714982\pi$
$12$	0.353943	0.102175
$13$	0.518411	0.143781	0.0718906	−	0.997413i	$-0.477097\pi$
$13$	0.518411	0.143781	0.0718906	+	0.997413i	$0.477097\pi$
$14$	4.10743	1.09776
$15$	0.335769	0.0866953
$16$	0.348601	0.0871503
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−2.42683	−0.572009
$19$	−1.45645	−0.334131	−0.167066	−	0.985946i	$-0.553429\pi$
$19$	−1.45645	−0.334131	−0.167066	+	0.985946i	$0.553429\pi$
$20$	1.63471	0.365533
$21$	−1.33587	−0.291511
$22$	−3.43808	−0.733002
$23$	−4.30503	−0.897660	−0.448830	−	0.893617i	$-0.648159\pi$
$23$	−4.30503	−0.897660	−0.448830	+	0.893617i	$0.648159\pi$
$24$	0.740493	0.151153
$25$	−3.44923	−0.689845
$26$	0.429780	0.0842867
$27$	1.59817	0.307568
$28$	−6.50377	−1.22910
$29$	−2.92743	−0.543609	−0.271805	−	0.962352i	$-0.587620\pi$
$29$	−2.92743	−0.543609	−0.271805	+	0.962352i	$0.587620\pi$
$30$	0.278364	0.0508220
$31$	−6.03755	−1.08438	−0.542188	−	0.840257i	$-0.682404\pi$
$31$	−6.03755	−1.08438	−0.542188	+	0.840257i	$0.682404\pi$
$32$	5.78168	1.02207
$33$	1.11818	0.194650
$34$	−0.829033	−0.142178
$35$	−6.16982	−1.04289
$36$	3.84268	0.640447
$37$	4.49198	0.738477	0.369239	−	0.929335i	$-0.379619\pi$
$37$	4.49198	0.738477	0.369239	+	0.929335i	$0.379619\pi$
$38$	−1.20744	−0.195873
$39$	−0.139779	−0.0223825
$40$	3.42002	0.540753
$41$	−12.5007	−1.95229	−0.976143	−	0.217126i	$-0.930332\pi$
$41$	−12.5007	−1.95229	−0.976143	+	0.217126i	$0.930332\pi$
$42$	−1.10748	−0.170888
$43$	−4.00859	−0.611305	−0.305652	−	0.952143i	$-0.598875\pi$
$43$	−4.00859	−0.611305	−0.305652	+	0.952143i	$0.598875\pi$
$44$	5.44391	0.820701
$45$	3.64537	0.543420
$46$	−3.56901	−0.526222
$47$	−1.00000	−0.145865
$47$	−1.00000	−0.145865
$48$	−0.0939930	−0.0135667
$49$	17.5469	2.50670
$50$	−2.85952	−0.404398
$51$	0.269629	0.0377556
$52$	−0.680520	−0.0943711
$53$	−8.32916	−1.14410	−0.572049	−	0.820219i	$-0.693851\pi$
$53$	−8.32916	−1.14410	−0.572049	+	0.820219i	$0.693851\pi$
$54$	1.32494	0.180301
$55$	5.16439	0.696366
$56$	−13.6067	−1.81827
$57$	0.392700	0.0520144
$58$	−2.42693	−0.318672
$59$	7.17036	0.933502	0.466751	−	0.884389i	$-0.345424\pi$
$59$	7.17036	0.933502	0.466751	+	0.884389i	$0.345424\pi$
$60$	−0.440766	−0.0569026
$61$	11.2550	1.44105	0.720525	−	0.693429i	$-0.243901\pi$
$61$	11.2550	1.44105	0.720525	+	0.693429i	$0.243901\pi$
$62$	−5.00533	−0.635677
$63$	−14.5033	−1.82724
$64$	4.09600	0.512001
$65$	−0.645577	−0.0800740
$66$	0.927007	0.114107
$67$	−6.87647	−0.840094	−0.420047	−	0.907502i	$-0.637986\pi$
$67$	−6.87647	−0.840094	−0.420047	+	0.907502i	$0.637986\pi$
$68$	1.31270	0.159189
$69$	1.16076	0.139739
$70$	−5.11498	−0.611358
$71$	−10.9760	−1.30261	−0.651306	−	0.758815i	$-0.725779\pi$
$71$	−10.9760	−1.30261	−0.651306	+	0.758815i	$0.725779\pi$
$72$	8.03936	0.947448
$73$	7.99250	0.935451	0.467726	−	0.883874i	$-0.345074\pi$
$73$	7.99250	0.935451	0.467726	+	0.883874i	$0.345074\pi$
$74$	3.72400	0.432906
$75$	0.930012	0.107389
$76$	1.91188	0.219308
$77$	−20.5467	−2.34152
$78$	−0.115881	−0.0131209
$79$	−2.54734	−0.286598	−0.143299	−	0.989679i	$-0.545771\pi$
$79$	−2.54734	−0.286598	−0.143299	+	0.989679i	$0.545771\pi$
$80$	−0.434113	−0.0485354
$81$	8.35099	0.927887
$82$	−10.3635	−1.14446
$83$	0.605016	0.0664092	0.0332046	−	0.999449i	$-0.489429\pi$
$83$	0.605016	0.0664092	0.0332046	+	0.999449i	$0.489429\pi$
$84$	1.75361	0.191334
$85$	1.24530	0.135072
$86$	−3.32326	−0.358356
$87$	0.789319	0.0846239
$88$	11.3893	1.21411
$89$	−1.58474	−0.167982	−0.0839912	−	0.996466i	$-0.526767\pi$
$89$	−1.58474	−0.167982	−0.0839912	+	0.996466i	$0.526767\pi$
$90$	3.02213	0.318561
$91$	2.56846	0.269247
$92$	5.65123	0.589181
$93$	1.62790	0.168805
$94$	−0.829033	−0.0855082
$95$	1.81371	0.186083
$96$	−1.55891	−0.159106
$97$	−15.7955	−1.60379	−0.801895	−	0.597465i	$-0.796175\pi$
$97$	−15.7955	−1.60379	−0.801895	+	0.597465i	$0.796175\pi$
$98$	14.5470	1.46946
$99$	12.1398	1.22010
$100$	4.52781	0.452781
$101$	14.3615	1.42902	0.714512	−	0.699623i	$-0.246649\pi$
$101$	14.3615	1.42902	0.714512	+	0.699623i	$0.246649\pi$
$102$	0.223531	0.0221329
$103$	10.0756	0.992777	0.496389	−	0.868100i	$-0.334659\pi$
$103$	10.0756	0.992777	0.496389	+	0.868100i	$0.334659\pi$
$104$	−1.42373	−0.139608
$105$	1.66356	0.162347
$106$	−6.90515	−0.670687
$107$	5.68927	0.550002	0.275001	−	0.961444i	$-0.411322\pi$
$107$	5.68927	0.550002	0.275001	+	0.961444i	$0.411322\pi$
$108$	−2.09793	−0.201873
$109$	3.66641	0.351178	0.175589	−	0.984464i	$-0.443817\pi$
$109$	3.66641	0.351178	0.175589	+	0.984464i	$0.443817\pi$
$110$	4.28145	0.408220
$111$	−1.21117	−0.114959
$112$	1.72714	0.163199
$113$	9.16543	0.862212	0.431106	−	0.902301i	$-0.358124\pi$
$113$	9.16543	0.862212	0.431106	+	0.902301i	$0.358124\pi$
$114$	0.325561	0.0304916
$115$	5.36105	0.499921
$116$	3.84285	0.356799
$117$	−1.51754	−0.140297
$118$	5.94447	0.547233
$119$	−4.95448	−0.454177
$120$	−0.922137	−0.0841792
$121$	6.19843	0.563494
$122$	9.33073	0.844765
$123$	3.37056	0.303913
$124$	7.92552	0.711732
$125$	10.5218	0.941101
$126$	−12.0237	−1.07115
$127$	−5.84153	−0.518352	−0.259176	−	0.965830i	$-0.583451\pi$
$127$	−5.84153	−0.518352	−0.259176	+	0.965830i	$0.583451\pi$
$128$	−8.16765	−0.721925
$129$	1.08083	0.0951621
$130$	−0.535205	−0.0469406
$131$	18.4670	1.61347	0.806733	−	0.590916i	$-0.201233\pi$
$131$	18.4670	1.61347	0.806733	+	0.590916i	$0.201233\pi$
$132$	−1.46784	−0.127759
$133$	−7.21593	−0.625701
$134$	−5.70082	−0.492476
$135$	−1.99021	−0.171290
$136$	2.74634	0.235497
$137$	17.8488	1.52492	0.762462	−	0.647033i	$-0.223990\pi$
$137$	17.8488	1.52492	0.762462	+	0.647033i	$0.223990\pi$
$138$	0.962308	0.0819171
$139$	20.3121	1.72285	0.861426	−	0.507884i	$-0.169572\pi$
$139$	20.3121	1.72285	0.861426	+	0.507884i	$0.169572\pi$
$140$	8.09915	0.684503
$141$	0.269629	0.0227069
$142$	−9.09947	−0.763610
$143$	−2.14990	−0.179784
$144$	−1.02046	−0.0850384
$145$	3.64553	0.302744
$146$	6.62604	0.548375
$147$	−4.73115	−0.390219
$148$	−5.89664	−0.484701
$149$	−4.42996	−0.362917	−0.181458	−	0.983399i	$-0.558082\pi$
$149$	−4.42996	−0.362917	−0.181458	+	0.983399i	$0.558082\pi$
$150$	0.771010	0.0629527
$151$	−10.7737	−0.876750	−0.438375	−	0.898792i	$-0.644446\pi$
$151$	−10.7737	−0.876750	−0.438375	+	0.898792i	$0.644446\pi$
$152$	3.99989	0.324434
$153$	2.92730	0.236658
$154$	−17.0339	−1.37263
$155$	7.51856	0.603906
$156$	0.183488	0.0146908
$157$	−8.62668	−0.688484	−0.344242	−	0.938881i	$-0.611864\pi$
$157$	−8.62668	−0.688484	−0.344242	+	0.938881i	$0.611864\pi$
$158$	−2.11183	−0.168008
$159$	2.24578	0.178102
$160$	−7.19994	−0.569205
$161$	−21.3292	−1.68097
$162$	6.92324	0.543941
$163$	−16.0804	−1.25951	−0.629756	−	0.776793i	$-0.716845\pi$
$163$	−16.0804	−1.25951	−0.629756	+	0.776793i	$0.716845\pi$
$164$	16.4098	1.28139
$165$	−1.39247	−0.108404
$166$	0.501578	0.0389300
$167$	−7.55280	−0.584453	−0.292227	−	0.956349i	$-0.594396\pi$
$167$	−7.55280	−0.584453	−0.292227	+	0.956349i	$0.594396\pi$
$168$	3.66876	0.283051
$169$	−12.7313	−0.979327
$170$	1.03240	0.0791811
$171$	4.26345	0.326034
$172$	5.26210	0.401231
$173$	−12.5494	−0.954113	−0.477056	−	0.878873i	$-0.658296\pi$
$173$	−12.5494	−0.954113	−0.477056	+	0.878873i	$0.658296\pi$
$174$	0.654372	0.0496078
$175$	−17.0891	−1.29182
$176$	−1.44568	−0.108973
$177$	−1.93334	−0.145319
$178$	−1.31380	−0.0984737
$179$	−13.9654	−1.04383	−0.521913	−	0.852999i	$-0.674781\pi$
$179$	−13.9654	−1.04383	−0.521913	+	0.852999i	$0.674781\pi$
$180$	−4.78529	−0.356675
$181$	−10.8867	−0.809206	−0.404603	−	0.914493i	$-0.632590\pi$
$181$	−10.8867	−0.809206	−0.404603	+	0.914493i	$0.632590\pi$
$182$	2.12933	0.157837
$183$	−3.03466	−0.224329
$184$	11.8231	0.871608
$185$	−5.59387	−0.411269
$186$	1.34958	0.0989561
$187$	4.14710	0.303266
$188$	1.31270	0.0957388
$189$	7.91812	0.575958
$190$	1.50363	0.109085
$191$	−12.2177	−0.884044	−0.442022	−	0.897004i	$-0.645739\pi$
$191$	−12.2177	−0.884044	−0.442022	+	0.897004i	$0.645739\pi$
$192$	−1.10440	−0.0797033
$193$	17.8168	1.28248	0.641239	−	0.767341i	$-0.278421\pi$
$193$	17.8168	1.28248	0.641239	+	0.767341i	$0.278421\pi$
$194$	−13.0950	−0.940165
$195$	0.174066	0.0124652
$196$	−23.0339	−1.64528
$197$	−8.35176	−0.595038	−0.297519	−	0.954716i	$-0.596159\pi$
$197$	−8.35176	−0.595038	−0.297519	+	0.954716i	$0.596159\pi$
$198$	10.0643	0.715238
$199$	21.7885	1.54455	0.772273	−	0.635291i	$-0.219120\pi$
$199$	21.7885	1.54455	0.772273	+	0.635291i	$0.219120\pi$
$200$	9.47275	0.669825
$201$	1.85410	0.130778
$202$	11.9062	0.837715
$203$	−14.5039	−1.01797
$204$	−0.353943	−0.0247810
$205$	15.5672	1.08726
$206$	8.35300	0.581981
$207$	12.6021	0.875907
$208$	0.180719	0.0125306
$209$	6.04002	0.417797
$210$	1.37915	0.0951703
$211$	−7.87121	−0.541876	−0.270938	−	0.962597i	$-0.587334\pi$
$211$	−7.87121	−0.541876	−0.270938	+	0.962597i	$0.587334\pi$
$212$	10.9337	0.750931
$213$	2.95945	0.202778
$214$	4.71659	0.322420
$215$	4.99190	0.340445
$216$	−4.38913	−0.298642
$217$	−29.9129	−2.03062
$218$	3.03957	0.205866
$219$	−2.15501	−0.145622
$220$	−6.77931	−0.457061
$221$	−0.518411	−0.0348721
$222$	−1.00410	−0.0673907
$223$	−23.1031	−1.54710	−0.773548	−	0.633738i	$-0.781520\pi$
$223$	−23.1031	−1.54710	−0.773548	+	0.633738i	$0.781520\pi$
$224$	28.6453	1.91394
$225$	10.0969	0.673128
$226$	7.59845	0.505441
$227$	11.2918	0.749462	0.374731	−	0.927134i	$-0.377735\pi$
$227$	11.2918	0.749462	0.374731	+	0.927134i	$0.377735\pi$
$228$	−0.515499	−0.0341397
$229$	1.99346	0.131732	0.0658658	−	0.997828i	$-0.479019\pi$
$229$	1.99346	0.131732	0.0658658	+	0.997828i	$0.479019\pi$
$230$	4.44449	0.293061
$231$	5.54000	0.364505
$232$	8.03971	0.527833
$233$	−10.6788	−0.699592	−0.349796	−	0.936826i	$-0.613749\pi$
$233$	−10.6788	−0.699592	−0.349796	+	0.936826i	$0.613749\pi$
$234$	−1.25809	−0.0822442
$235$	1.24530	0.0812345
$236$	−9.41257	−0.612706
$237$	0.686836	0.0446148
$238$	−4.10743	−0.266245
$239$	27.0269	1.74823	0.874113	−	0.485723i	$-0.161444\pi$
$239$	27.0269	1.74823	0.874113	+	0.485723i	$0.161444\pi$
$240$	0.117050	0.00755552
$241$	−4.93156	−0.317670	−0.158835	−	0.987305i	$-0.550774\pi$
$241$	−4.93156	−0.317670	−0.158835	+	0.987305i	$0.550774\pi$
$242$	5.13870	0.330328
$243$	−7.04619	−0.452013
$244$	−14.7744	−0.945836
$245$	−21.8512	−1.39602
$246$	2.79431	0.178159
$247$	−0.755037	−0.0480418
$248$	16.5812	1.05291
$249$	−0.163130	−0.0103379
$250$	8.72294	0.551687
$251$	17.5500	1.10774	0.553872	−	0.832602i	$-0.313150\pi$
$251$	17.5500	1.10774	0.553872	+	0.832602i	$0.313150\pi$
$252$	19.0385	1.19931
$253$	17.8534	1.12243
$254$	−4.84282	−0.303866
$255$	−0.335769	−0.0210267
$256$	−14.9633	−0.935204
$257$	−14.7262	−0.918595	−0.459298	−	0.888282i	$-0.651899\pi$
$257$	−14.7262	−0.918595	−0.459298	+	0.888282i	$0.651899\pi$
$258$	0.896046	0.0557854
$259$	22.2554	1.38289
$260$	0.847452	0.0525567
$261$	8.56946	0.530436
$262$	15.3097	0.945838
$263$	−25.3038	−1.56030	−0.780149	−	0.625594i	$-0.784857\pi$
$263$	−25.3038	−1.56030	−0.780149	+	0.625594i	$0.784857\pi$
$264$	−3.07090	−0.189001
$265$	10.3723	0.637166
$266$	−5.98224	−0.366795
$267$	0.427293	0.0261499
$268$	9.02677	0.551398
$269$	−16.3238	−0.995278	−0.497639	−	0.867384i	$-0.665800\pi$
$269$	−16.3238	−0.995278	−0.497639	+	0.867384i	$0.665800\pi$
$270$	−1.64995	−0.100413
$271$	1.18959	0.0722627	0.0361313	−	0.999347i	$-0.488497\pi$
$271$	1.18959	0.0722627	0.0361313	+	0.999347i	$0.488497\pi$
$272$	−0.348601	−0.0211371
$273$	−0.692531	−0.0419139
$274$	14.7972	0.893933
$275$	14.3043	0.862581
$276$	−1.52373	−0.0917181
$277$	−4.13787	−0.248620	−0.124310	−	0.992243i	$-0.539672\pi$
$277$	−4.13787	−0.248620	−0.124310	+	0.992243i	$0.539672\pi$
$278$	16.8394	1.00996
$279$	17.6737	1.05810
$280$	16.9444	1.01262
$281$	3.43543	0.204941	0.102470	−	0.994736i	$-0.467325\pi$
$281$	3.43543	0.204941	0.102470	+	0.994736i	$0.467325\pi$
$282$	0.223531	0.0133111
$283$	17.9668	1.06801	0.534007	−	0.845480i	$-0.320686\pi$
$283$	17.9668	1.06801	0.534007	+	0.845480i	$0.320686\pi$
$284$	14.4082	0.854972
$285$	−0.489030	−0.0289676
$286$	−1.78234	−0.105392
$287$	−61.9347	−3.65589
$288$	−16.9247	−0.997299
$289$	1.00000	0.0588235
$290$	3.02226	0.177473
$291$	4.25893	0.249663
$292$	−10.4918	−0.613985
$293$	−25.2037	−1.47241	−0.736207	−	0.676756i	$-0.763385\pi$
$293$	−25.2037	−1.47241	−0.736207	+	0.676756i	$0.763385\pi$
$294$	−3.92228	−0.228752
$295$	−8.92926	−0.519882
$296$	−12.3365	−0.717045
$297$	−6.62778	−0.384583
$298$	−3.67259	−0.212747
$299$	−2.23177	−0.129067
$300$	−1.22083	−0.0704847
$301$	−19.8605	−1.14474
$302$	−8.93174	−0.513964
$303$	−3.87228	−0.222457
$304$	−0.507719	−0.0291197
$305$	−14.0158	−0.802543
$306$	2.42683	0.138733
$307$	−26.2145	−1.49614	−0.748071	−	0.663619i	$-0.769020\pi$
$307$	−26.2145	−1.49614	−0.748071	+	0.663619i	$0.769020\pi$
$308$	26.9718	1.53686
$309$	−2.71667	−0.154546
$310$	6.23314	0.354018
$311$	21.0813	1.19541	0.597704	−	0.801717i	$-0.296080\pi$
$311$	21.0813	1.19541	0.597704	+	0.801717i	$0.296080\pi$
$312$	0.383880	0.0217329
$313$	−26.7443	−1.51168	−0.755840	−	0.654757i	$-0.772771\pi$
$313$	−26.7443	−1.51168	−0.755840	+	0.654757i	$0.772771\pi$
$314$	−7.15180	−0.403599
$315$	18.0609	1.01762
$316$	3.34390	0.188109
$317$	22.4255	1.25954	0.629771	−	0.776780i	$-0.283149\pi$
$317$	22.4255	1.25954	0.629771	+	0.776780i	$0.283149\pi$
$318$	1.86183	0.104406
$319$	12.1403	0.679728
$320$	−5.10076	−0.285141
$321$	−1.53399	−0.0856191
$322$	−17.6826	−0.985412
$323$	1.45645	0.0810388
$324$	−10.9624	−0.609021
$325$	−1.78812	−0.0991868
$326$	−13.3311	−0.738344
$327$	−0.988570	−0.0546680
$328$	34.3313	1.89563
$329$	−4.95448	−0.273149
$330$	−1.15440	−0.0635478
$331$	12.1898	0.670012	0.335006	−	0.942216i	$-0.391262\pi$
$331$	12.1898	0.670012	0.335006	+	0.942216i	$0.391262\pi$
$332$	−0.794207	−0.0435878
$333$	−13.1494	−0.720581
$334$	−6.26152	−0.342615
$335$	8.56327	0.467861
$336$	−0.465687	−0.0254053
$337$	−27.9457	−1.52230	−0.761149	−	0.648576i	$-0.775365\pi$
$337$	−27.9457	−1.52230	−0.761149	+	0.648576i	$0.775365\pi$
$338$	−10.5546	−0.574096
$339$	−2.47127	−0.134221
$340$	−1.63471	−0.0886547
$341$	25.0383	1.35590
$342$	3.53454	0.191126
$343$	52.2544	2.82147
$344$	11.0090	0.593564
$345$	−1.44550	−0.0778229
$346$	−10.4039	−0.559315
$347$	23.3281	1.25232	0.626160	−	0.779695i	$-0.284626\pi$
$347$	23.3281	1.25232	0.626160	+	0.779695i	$0.284626\pi$
$348$	−1.03614	−0.0555431
$349$	−37.0240	−1.98185	−0.990924	−	0.134425i	$-0.957081\pi$
$349$	−37.0240	−1.98185	−0.990924	+	0.134425i	$0.957081\pi$
$350$	−14.1675	−0.757282
$351$	0.828510	0.0442226
$352$	−23.9772	−1.27799
$353$	−13.6676	−0.727453	−0.363727	−	0.931506i	$-0.618496\pi$
$353$	−13.6676	−0.727453	−0.363727	+	0.931506i	$0.618496\pi$
$354$	−1.60280	−0.0851880
$355$	13.6684	0.725445
$356$	2.08030	0.110256
$357$	1.33587	0.0707019
$358$	−11.5778	−0.611906
$359$	−10.8398	−0.572102	−0.286051	−	0.958214i	$-0.592343\pi$
$359$	−10.8398	−0.572102	−0.286051	+	0.958214i	$0.592343\pi$
$360$	−10.0114	−0.527649
$361$	−16.8788	−0.888356
$362$	−9.02547	−0.474368
$363$	−1.67128	−0.0877193
$364$	−3.37162	−0.176721
$365$	−9.95306	−0.520967
$366$	−2.51584	−0.131505
$367$	−11.8663	−0.619414	−0.309707	−	0.950832i	$-0.600231\pi$
$367$	−11.8663	−0.619414	−0.309707	+	0.950832i	$0.600231\pi$
$368$	−1.50074	−0.0782313
$369$	36.5934	1.90498
$370$	−4.63750	−0.241092
$371$	−41.2667	−2.14246
$372$	−2.13695	−0.110796
$373$	33.7252	1.74623	0.873113	−	0.487518i	$-0.162097\pi$
$373$	33.7252	1.74623	0.873113	+	0.487518i	$0.162097\pi$
$374$	3.43808	0.177779
$375$	−2.83699	−0.146502
$376$	2.74634	0.141632
$377$	−1.51761	−0.0781608
$378$	6.56438	0.337635
$379$	15.3129	0.786573	0.393287	−	0.919416i	$-0.371338\pi$
$379$	15.3129	0.786573	0.393287	+	0.919416i	$0.371338\pi$
$380$	−2.38087	−0.122136
$381$	1.57505	0.0806920
$382$	−10.1289	−0.518240
$383$	−24.6100	−1.25751	−0.628756	−	0.777603i	$-0.716435\pi$
$383$	−24.6100	−1.25751	−0.628756	+	0.777603i	$0.716435\pi$
$384$	2.20223	0.112382
$385$	25.5869	1.30403
$386$	14.7707	0.751808
$387$	11.7344	0.596491
$388$	20.7348	1.05265
$389$	−5.59833	−0.283847	−0.141923	−	0.989878i	$-0.545329\pi$
$389$	−5.59833	−0.283847	−0.141923	+	0.989878i	$0.545329\pi$
$390$	0.144307	0.00730726
$391$	4.30503	0.217714
$392$	−48.1898	−2.43395
$393$	−4.97923	−0.251169
$394$	−6.92388	−0.348820
$395$	3.17220	0.159611
$396$	−15.9360	−0.800813
$397$	25.8995	1.29986	0.649931	−	0.759994i	$-0.274798\pi$
$397$	25.8995	1.29986	0.649931	+	0.759994i	$0.274798\pi$
$398$	18.0634	0.905436
$399$	1.94562	0.0974031
$400$	−1.20240	−0.0601202
$401$	−1.43339	−0.0715803	−0.0357901	−	0.999359i	$-0.511395\pi$
$401$	−1.43339	−0.0715803	−0.0357901	+	0.999359i	$0.511395\pi$
$402$	1.53711	0.0766639
$403$	−3.12993	−0.155913
$404$	−18.8524	−0.937943
$405$	−10.3995	−0.516755
$406$	−12.0242	−0.596751
$407$	−18.6287	−0.923390
$408$	−0.740493	−0.0366599
$409$	−9.64221	−0.476777	−0.238388	−	0.971170i	$-0.576619\pi$
$409$	−9.64221	−0.476777	−0.238388	+	0.971170i	$0.576619\pi$
$410$	12.9057	0.637367
$411$	−4.81255	−0.237386
$412$	−13.2263	−0.651612
$413$	35.5254	1.74809
$414$	10.4476	0.513469
$415$	−0.753427	−0.0369843
$416$	2.99729	0.146954
$417$	−5.47674	−0.268197
$418$	5.00738	0.244919
$419$	−2.31834	−0.113258	−0.0566291	−	0.998395i	$-0.518035\pi$
$419$	−2.31834	−0.113258	−0.0566291	+	0.998395i	$0.518035\pi$
$420$	−2.18377	−0.106557
$421$	−34.5803	−1.68534	−0.842671	−	0.538429i	$-0.819018\pi$
$421$	−34.5803	−1.68534	−0.842671	+	0.538429i	$0.819018\pi$
$422$	−6.52549	−0.317656
$423$	2.92730	0.142330
$424$	22.8747	1.11089
$425$	3.44923	0.167312
$426$	2.45348	0.118872
$427$	55.7625	2.69854
$428$	−7.46833	−0.360995
$429$	0.579676	0.0279870
$430$	4.13845	0.199574
$431$	−31.0797	−1.49706	−0.748529	−	0.663102i	$-0.769239\pi$
$431$	−31.0797	−1.49706	−0.748529	+	0.663102i	$0.769239\pi$
$432$	0.557125	0.0268047
$433$	−15.7398	−0.756408	−0.378204	−	0.925722i	$-0.623458\pi$
$433$	−15.7398	−0.756408	−0.378204	+	0.925722i	$0.623458\pi$
$434$	−24.7988	−1.19038
$435$	−0.982940	−0.0471284
$436$	−4.81291	−0.230496
$437$	6.27003	0.299936
$438$	−1.78657	−0.0853658
$439$	−11.4402	−0.546009	−0.273005	−	0.962013i	$-0.588017\pi$
$439$	−11.4402	−0.546009	−0.273005	+	0.962013i	$0.588017\pi$
$440$	−14.1832	−0.676156
$441$	−51.3650	−2.44595
$442$	−0.429780	−0.0204425
$443$	30.1528	1.43260	0.716302	−	0.697791i	$-0.245834\pi$
$443$	30.1528	1.43260	0.716302	+	0.697791i	$0.245834\pi$
$444$	1.58991	0.0754536
$445$	1.97348	0.0935519
$446$	−19.1532	−0.906931
$447$	1.19445	0.0564954
$448$	20.2936	0.958782
$449$	−9.31312	−0.439514	−0.219757	−	0.975555i	$-0.570526\pi$
$449$	−9.31312	−0.439514	−0.219757	+	0.975555i	$0.570526\pi$
$450$	8.37068	0.394598
$451$	51.8418	2.44113
$452$	−12.0315	−0.565914
$453$	2.90490	0.136484
$454$	9.36126	0.439346
$455$	−3.19850	−0.149948
$456$	−1.07849	−0.0505048
$457$	8.24218	0.385553	0.192776	−	0.981243i	$-0.438251\pi$
$457$	8.24218	0.385553	0.192776	+	0.981243i	$0.438251\pi$
$458$	1.65264	0.0772230
$459$	−1.59817	−0.0745963
$460$	−7.03748	−0.328124
$461$	−0.0632066	−0.00294383	−0.00147191	−	0.999999i	$-0.500469\pi$
$461$	−0.0632066	−0.00294383	−0.00147191	+	0.999999i	$0.500469\pi$
$462$	4.59284	0.213678
$463$	17.4627	0.811560	0.405780	−	0.913971i	$-0.367000\pi$
$463$	17.4627	0.811560	0.405780	+	0.913971i	$0.367000\pi$
$464$	−1.02050	−0.0473757
$465$	−2.02722	−0.0940102
$466$	−8.85309	−0.410111
$467$	19.2912	0.892692	0.446346	−	0.894861i	$-0.352725\pi$
$467$	19.2912	0.892692	0.446346	+	0.894861i	$0.352725\pi$
$468$	1.99209	0.0920842
$469$	−34.0693	−1.57318
$470$	1.03240	0.0476208
$471$	2.32600	0.107177
$472$	−19.6923	−0.906410
$473$	16.6240	0.764374
$474$	0.569410	0.0261538
$475$	5.02361	0.230499
$476$	6.50377	0.298100
$477$	24.3819	1.11637
$478$	22.4062	1.02484
$479$	−9.03364	−0.412757	−0.206379	−	0.978472i	$-0.566168\pi$
$479$	−9.03364	−0.412757	−0.206379	+	0.978472i	$0.566168\pi$
$480$	1.94131	0.0886084
$481$	2.32869	0.106179
$482$	−4.08843	−0.186223
$483$	5.75096	0.261678
$484$	−8.13671	−0.369850
$485$	19.6701	0.893175
$486$	−5.84152	−0.264977
$487$	43.3579	1.96473	0.982367	−	0.186965i	$-0.0598651\pi$
$487$	43.3579	1.96473	0.982367	+	0.186965i	$0.0598651\pi$
$488$	−30.9100	−1.39923
$489$	4.33573	0.196069
$490$	−18.1153	−0.818367
$491$	1.08170	0.0488166	0.0244083	−	0.999702i	$-0.492230\pi$
$491$	1.08170	0.0488166	0.0244083	+	0.999702i	$0.492230\pi$
$492$	−4.42455	−0.199474
$493$	2.92743	0.131845
$494$	−0.625950	−0.0281628
$495$	−15.1177	−0.679490
$496$	−2.10470	−0.0945037
$497$	−54.3804	−2.43929
$498$	−0.135240	−0.00606026
$499$	31.6489	1.41680	0.708399	−	0.705812i	$-0.249418\pi$
$499$	31.6489	1.41680	0.708399	+	0.705812i	$0.249418\pi$
$500$	−13.8120	−0.617694
$501$	2.03646	0.0909821
$502$	14.5495	0.649376
$503$	5.59232	0.249349	0.124675	−	0.992198i	$-0.460211\pi$
$503$	5.59232	0.249349	0.124675	+	0.992198i	$0.460211\pi$
$504$	39.8309	1.77421
$505$	−17.8844	−0.795846
$506$	14.8010	0.657986
$507$	3.43272	0.152452
$508$	7.66820	0.340221
$509$	−5.56347	−0.246596	−0.123298	−	0.992370i	$-0.539347\pi$
$509$	−5.56347	−0.246596	−0.123298	+	0.992370i	$0.539347\pi$
$510$	−0.278364	−0.0123262
$511$	39.5987	1.75174
$512$	3.93026	0.173695
$513$	−2.32765	−0.102768
$514$	−12.2085	−0.538494
$515$	−12.5471	−0.552893
$516$	−1.41881	−0.0624598
$517$	4.14710	0.182389
$518$	18.4505	0.810668
$519$	3.38368	0.148527
$520$	1.77298	0.0777501
$521$	−10.1274	−0.443688	−0.221844	−	0.975082i	$-0.571208\pi$
$521$	−10.1274	−0.443688	−0.221844	+	0.975082i	$0.571208\pi$
$522$	7.10436	0.310949
$523$	−7.38281	−0.322828	−0.161414	−	0.986887i	$-0.551605\pi$
$523$	−7.38281	−0.322828	−0.161414	+	0.986887i	$0.551605\pi$
$524$	−24.2417	−1.05900
$525$	4.60773	0.201098
$526$	−20.9777	−0.914670
$527$	6.03755	0.263000
$528$	0.389798	0.0169638
$529$	−4.46676	−0.194207
$530$	8.59898	0.373516
$531$	−20.9898	−0.910880
$532$	9.47238	0.410680
$533$	−6.48051	−0.280702
$534$	0.354240	0.0153294
$535$	−7.08485	−0.306305
$536$	18.8851	0.815713
$537$	3.76549	0.162493
$538$	−13.5329	−0.583447
$539$	−72.7687	−3.13437
$540$	2.61255	0.112426
$541$	−4.98278	−0.214227	−0.107113	−	0.994247i	$-0.534161\pi$
$541$	−4.98278	−0.214227	−0.107113	+	0.994247i	$0.534161\pi$
$542$	0.986212	0.0423614
$543$	2.93538	0.125969
$544$	−5.78168	−0.247888
$545$	−4.56578	−0.195576
$546$	−0.574131	−0.0245705
$547$	17.3536	0.741985	0.370992	−	0.928636i	$-0.379018\pi$
$547$	17.3536	0.741985	0.370992	+	0.928636i	$0.379018\pi$
$548$	−23.4302	−1.00089
$549$	−32.9466	−1.40613
$550$	11.8587	0.505658
$551$	4.26364	0.181637
$552$	−3.18784	−0.135684
$553$	−12.6207	−0.536688
$554$	−3.43043	−0.145745
$555$	1.50827	0.0640225
$556$	−26.6638	−1.13080
$557$	−5.67571	−0.240488	−0.120244	−	0.992744i	$-0.538368\pi$
$557$	−5.67571	−0.240488	−0.120244	+	0.992744i	$0.538368\pi$
$558$	14.6521	0.620273
$559$	−2.07810	−0.0878942
$560$	−2.15081	−0.0908882
$561$	−1.11818	−0.0472095
$562$	2.84809	0.120139
$563$	−4.84406	−0.204153	−0.102076	−	0.994777i	$-0.532549\pi$
$563$	−4.84406	−0.204153	−0.102076	+	0.994777i	$0.532549\pi$
$564$	−0.353943	−0.0149037
$565$	−11.4137	−0.480179
$566$	14.8950	0.626086
$567$	41.3748	1.73758
$568$	30.1438	1.26481
$569$	1.13845	0.0477265	0.0238633	−	0.999715i	$-0.492403\pi$
$569$	1.13845	0.0477265	0.0238633	+	0.999715i	$0.492403\pi$
$570$	−0.405422	−0.0169812
$571$	−25.0424	−1.04799	−0.523996	−	0.851721i	$-0.675559\pi$
$571$	−25.0424	−1.04799	−0.523996	+	0.851721i	$0.675559\pi$
$572$	2.82218	0.118001
$573$	3.29426	0.137620
$574$	−51.3459	−2.14314
$575$	14.8490	0.619246
$576$	−11.9902	−0.499593
$577$	−30.1916	−1.25689	−0.628446	−	0.777853i	$-0.716309\pi$
$577$	−30.1916	−1.25689	−0.628446	+	0.777853i	$0.716309\pi$
$578$	0.829033	0.0344832
$579$	−4.80392	−0.199644
$580$	−4.78550	−0.198707
$581$	2.99754	0.124359
$582$	3.53079	0.146356
$583$	34.5418	1.43058
$584$	−21.9501	−0.908303
$585$	1.88980	0.0781335
$586$	−20.8947	−0.863151
$587$	−23.0988	−0.953388	−0.476694	−	0.879069i	$-0.658165\pi$
$587$	−23.0988	−0.953388	−0.476694	+	0.879069i	$0.658165\pi$
$588$	6.21060	0.256121
$589$	8.79336	0.362324
$590$	−7.40265	−0.304762
$591$	2.25188	0.0926298
$592$	1.56591	0.0643585
$593$	−35.1888	−1.44503	−0.722515	−	0.691355i	$-0.757014\pi$
$593$	−35.1888	−1.44503	−0.722515	+	0.691355i	$0.757014\pi$
$594$	−5.49465	−0.225448
$595$	6.16982	0.252938
$596$	5.81523	0.238201
$597$	−5.87481	−0.240440
$598$	−1.85021	−0.0756608
$599$	16.8631	0.689009	0.344505	−	0.938785i	$-0.388047\pi$
$599$	16.8631	0.689009	0.344505	+	0.938785i	$0.388047\pi$
$600$	−2.55413	−0.104272
$601$	11.8881	0.484925	0.242463	−	0.970161i	$-0.422045\pi$
$601$	11.8881	0.484925	0.242463	+	0.970161i	$0.422045\pi$
$602$	−16.4650	−0.671064
$603$	20.1295	0.819736
$604$	14.1427	0.575457
$605$	−7.71891	−0.313818
$606$	−3.21025	−0.130408
$607$	−22.1975	−0.900970	−0.450485	−	0.892784i	$-0.648749\pi$
$607$	−22.1975	−0.900970	−0.450485	+	0.892784i	$0.648749\pi$
$608$	−8.42071	−0.341505
$609$	3.91067	0.158468
$610$	−11.6196	−0.470463
$611$	−0.518411	−0.0209727
$612$	−3.84268	−0.155331
$613$	−11.6645	−0.471123	−0.235562	−	0.971859i	$-0.575693\pi$
$613$	−11.6645	−0.471123	−0.235562	+	0.971859i	$0.575693\pi$
$614$	−21.7327	−0.877061
$615$	−4.19736	−0.169254
$616$	56.4283	2.27356
$617$	23.8777	0.961280	0.480640	−	0.876918i	$-0.340404\pi$
$617$	23.8777	0.961280	0.480640	+	0.876918i	$0.340404\pi$
$618$	−2.25221	−0.0905972
$619$	5.31149	0.213487	0.106743	−	0.994287i	$-0.465958\pi$
$619$	5.31149	0.213487	0.106743	+	0.994287i	$0.465958\pi$
$620$	−9.86965	−0.396375
$621$	−6.88017	−0.276092
$622$	17.4771	0.700766
$623$	−7.85158	−0.314567
$624$	−0.0487270	−0.00195064
$625$	4.14329	0.165732
$626$	−22.1719	−0.886169
$627$	−1.62857	−0.0650386
$628$	11.3243	0.451888
$629$	−4.49198	−0.179107
$630$	14.9731	0.596542
$631$	31.7688	1.26469	0.632347	−	0.774685i	$-0.282092\pi$
$631$	31.7688	1.26469	0.632347	+	0.774685i	$0.282092\pi$
$632$	6.99585	0.278280
$633$	2.12231	0.0843541
$634$	18.5915	0.738363
$635$	7.27446	0.288678
$636$	−2.94805	−0.116898
$637$	9.09650	0.360416
$638$	10.0647	0.398467
$639$	32.1301	1.27105
$640$	10.1712	0.402051
$641$	22.4997	0.888684	0.444342	−	0.895857i	$-0.353437\pi$
$641$	22.4997	0.888684	0.444342	+	0.895857i	$0.353437\pi$
$642$	−1.27173	−0.0501912
$643$	5.43228	0.214228	0.107114	−	0.994247i	$-0.465839\pi$
$643$	5.43228	0.214228	0.107114	+	0.994247i	$0.465839\pi$
$644$	27.9989	1.10331
$645$	−1.34596	−0.0529972
$646$	1.20744	0.0475061
$647$	−22.5054	−0.884780	−0.442390	−	0.896823i	$-0.645869\pi$
$647$	−22.5054	−0.884780	−0.442390	+	0.896823i	$0.645869\pi$
$648$	−22.9347	−0.900958
$649$	−29.7362	−1.16725
$650$	−1.48241	−0.0581448
$651$	8.06540	0.316108
$652$	21.1088	0.826683
$653$	9.86200	0.385930	0.192965	−	0.981206i	$-0.438190\pi$
$653$	9.86200	0.385930	0.192965	+	0.981206i	$0.438190\pi$
$654$	−0.819557	−0.0320472
$655$	−22.9969	−0.898564
$656$	−4.35777	−0.170142
$657$	−23.3964	−0.912782
$658$	−4.10743	−0.160124
$659$	18.1291	0.706210	0.353105	−	0.935584i	$-0.385126\pi$
$659$	18.1291	0.706210	0.353105	+	0.935584i	$0.385126\pi$
$660$	1.82790	0.0711509
$661$	34.4992	1.34186	0.670931	−	0.741520i	$-0.265895\pi$
$661$	34.4992	1.34186	0.670931	+	0.741520i	$0.265895\pi$
$662$	10.1057	0.392771
$663$	0.139779	0.00542855
$664$	−1.66158	−0.0644818
$665$	8.98600	0.348462
$666$	−10.9013	−0.422415
$667$	12.6026	0.487976
$668$	9.91460	0.383607
$669$	6.22926	0.240837
$670$	7.09923	0.274267
$671$	−46.6754	−1.80188
$672$	−7.72359	−0.297944
$673$	31.8140	1.22634	0.613170	−	0.789951i	$-0.289894\pi$
$673$	31.8140	1.22634	0.613170	+	0.789951i	$0.289894\pi$
$674$	−23.1679	−0.892394
$675$	−5.51246	−0.212175
$676$	16.7124	0.642783
$677$	18.9116	0.726831	0.363415	−	0.931627i	$-0.381611\pi$
$677$	18.9116	0.726831	0.363415	+	0.931627i	$0.381611\pi$
$678$	−2.04876	−0.0786822
$679$	−78.2585	−3.00329
$680$	−3.42002	−0.131152
$681$	−3.04459	−0.116669
$682$	20.7576	0.794849
$683$	38.3403	1.46705	0.733526	−	0.679661i	$-0.237873\pi$
$683$	38.3403	1.46705	0.733526	+	0.679661i	$0.237873\pi$
$684$	−5.59665	−0.213993
$685$	−22.2271	−0.849254
$686$	43.3206	1.65399
$687$	−0.537495	−0.0205067
$688$	−1.39740	−0.0532754
$689$	−4.31792	−0.164500
$690$	−1.19836	−0.0456209
$691$	−10.1861	−0.387498	−0.193749	−	0.981051i	$-0.562065\pi$
$691$	−10.1861	−0.387498	−0.193749	+	0.981051i	$0.562065\pi$
$692$	16.4736	0.626234
$693$	60.1464	2.28477
$694$	19.3398	0.734128
$695$	−25.2947	−0.959483
$696$	−2.16774	−0.0821680
$697$	12.5007	0.473499
$698$	−30.6941	−1.16179
$699$	2.87932	0.108906
$700$	22.4330	0.847887
$701$	−28.2197	−1.06584	−0.532921	−	0.846165i	$-0.678906\pi$
$701$	−28.2197	−1.06584	−0.532921	+	0.846165i	$0.678906\pi$
$702$	0.686862	0.0259239
$703$	−6.54232	−0.246748
$704$	−16.9865	−0.640204
$705$	−0.335769	−0.0126458
$706$	−11.3309	−0.426444
$707$	71.1539	2.67602
$708$	2.53790	0.0953802
$709$	−40.9675	−1.53857	−0.769283	−	0.638909i	$-0.779386\pi$
$709$	−40.9675	−1.53857	−0.769283	+	0.638909i	$0.779386\pi$
$710$	11.3316	0.425266
$711$	7.45682	0.279652
$712$	4.35224	0.163107
$713$	25.9918	0.973401
$714$	1.10748	0.0414465
$715$	2.67727	0.100124
$716$	18.3325	0.685117
$717$	−7.28724	−0.272147
$718$	−8.98653	−0.335374
$719$	−9.54506	−0.355971	−0.177985	−	0.984033i	$-0.556958\pi$
$719$	−9.54506	−0.355971	−0.177985	+	0.984033i	$0.556958\pi$
$720$	1.27078	0.0473592
$721$	49.9193	1.85909
$722$	−13.9931	−0.520768
$723$	1.32969	0.0494518
$724$	14.2911	0.531124
$725$	10.0974	0.375006
$726$	−1.38554	−0.0514224
$727$	19.8444	0.735988	0.367994	−	0.929828i	$-0.380045\pi$
$727$	19.8444	0.735988	0.367994	+	0.929828i	$0.380045\pi$
$728$	−7.05386	−0.261433
$729$	−23.1531	−0.857522
$730$	−8.25142	−0.305399
$731$	4.00859	0.148263
$732$	3.98362	0.147239
$733$	9.87019	0.364564	0.182282	−	0.983246i	$-0.441652\pi$
$733$	9.87019	0.364564	0.182282	+	0.983246i	$0.441652\pi$
$734$	−9.83753	−0.363110
$735$	5.89171	0.217319
$736$	−24.8903	−0.917469
$737$	28.5174	1.05045
$738$	30.3371	1.11673
$739$	11.3068	0.415928	0.207964	−	0.978137i	$-0.433316\pi$
$739$	11.3068	0.415928	0.207964	+	0.978137i	$0.433316\pi$
$740$	7.34309	0.269937
$741$	0.203580	0.00747869
$742$	−34.2114	−1.25594
$743$	−10.8740	−0.398927	−0.199464	−	0.979905i	$-0.563920\pi$
$743$	−10.8740	−0.398927	−0.199464	+	0.979905i	$0.563920\pi$
$744$	−4.47077	−0.163906
$745$	5.51664	0.202114
$746$	27.9593	1.02366
$747$	−1.77106	−0.0647998
$748$	−5.44391	−0.199049
$749$	28.1874	1.02994
$750$	−2.35196	−0.0858814
$751$	27.0467	0.986948	0.493474	−	0.869761i	$-0.335727\pi$
$751$	27.0467	0.986948	0.493474	+	0.869761i	$0.335727\pi$
$752$	−0.348601	−0.0127122
$753$	−4.73198	−0.172443
$754$	−1.25815	−0.0458190
$755$	13.4165	0.488276
$756$	−10.3941	−0.378031
$757$	−19.0468	−0.692268	−0.346134	−	0.938185i	$-0.612506\pi$
$757$	−19.0468	−0.692268	−0.346134	+	0.938185i	$0.612506\pi$
$758$	12.6949	0.461101
$759$	−4.81379	−0.174729
$760$	−4.98107	−0.180682
$761$	21.7954	0.790082	0.395041	−	0.918664i	$-0.370730\pi$
$761$	21.7954	0.790082	0.395041	+	0.918664i	$0.370730\pi$
$762$	1.30577	0.0473029
$763$	18.1651	0.657622
$764$	16.0383	0.580244
$765$	−3.64537	−0.131799
$766$	−20.4025	−0.737172
$767$	3.71719	0.134220
$768$	4.03453	0.145584
$769$	2.14491	0.0773473	0.0386736	−	0.999252i	$-0.487687\pi$
$769$	2.14491	0.0773473	0.0386736	+	0.999252i	$0.487687\pi$
$770$	21.2123	0.764440
$771$	3.97061	0.142998
$772$	−23.3881	−0.841757
$773$	12.2964	0.442272	0.221136	−	0.975243i	$-0.429024\pi$
$773$	12.2964	0.442272	0.221136	+	0.975243i	$0.429024\pi$
$774$	9.72817	0.349672
$775$	20.8249	0.748052
$776$	43.3798	1.55725
$777$	−6.00071	−0.215274
$778$	−4.64120	−0.166395
$779$	18.2066	0.652320
$780$	−0.228498	−0.00818153
$781$	45.5186	1.62878
$782$	3.56901	0.127627
$783$	−4.67853	−0.167197
$784$	6.11687	0.218460
$785$	10.7428	0.383427
$786$	−4.12795	−0.147239
$787$	−25.7603	−0.918256	−0.459128	−	0.888370i	$-0.651838\pi$
$787$	−25.7603	−0.918256	−0.459128	+	0.888370i	$0.651838\pi$
$788$	10.9634	0.390555
$789$	6.82263	0.242892
$790$	2.62986	0.0935661
$791$	45.4100	1.61459
$792$	−33.3400	−1.18469
$793$	5.83469	0.207196
$794$	21.4716	0.761998
$795$	−2.79668	−0.0991879
$796$	−28.6019	−1.01377
$797$	−32.7716	−1.16083	−0.580415	−	0.814321i	$-0.697110\pi$
$797$	−32.7716	−1.16083	−0.580415	+	0.814321i	$0.697110\pi$
$798$	1.61299	0.0570991
$799$	1.00000	0.0353775
$800$	−19.9423	−0.705068
$801$	4.63902	0.163912
$802$	−1.18833	−0.0419614
$803$	−33.1457	−1.16969
$804$	−2.43388	−0.0858363
$805$	26.5612	0.936160
$806$	−2.59482	−0.0913985
$807$	4.40136	0.154935
$808$	−39.4416	−1.38755
$809$	34.9693	1.22946	0.614728	−	0.788740i	$-0.289266\pi$
$809$	34.9693	1.22946	0.614728	+	0.788740i	$0.289266\pi$
$810$	−8.62152	−0.302929
$811$	−55.3301	−1.94290	−0.971451	−	0.237242i	$-0.923757\pi$
$811$	−55.3301	−1.94290	−0.971451	+	0.237242i	$0.923757\pi$
$812$	19.0393	0.668149
$813$	−0.320749	−0.0112492
$814$	−15.4438	−0.541305
$815$	20.0249	0.701441
$816$	0.0939930	0.00329041
$817$	5.83830	0.204256
$818$	−7.99371	−0.279494
$819$	−7.51864	−0.262723
$820$	−20.4351	−0.713625
$821$	−44.6451	−1.55812	−0.779062	−	0.626946i	$-0.784305\pi$
$821$	−44.6451	−1.55812	−0.779062	+	0.626946i	$0.784305\pi$
$822$	−3.98976	−0.139159
$823$	−47.4308	−1.65333	−0.826666	−	0.562693i	$-0.809765\pi$
$823$	−47.4308	−1.65333	−0.826666	+	0.562693i	$0.809765\pi$
$824$	−27.6710	−0.963965
$825$	−3.85685	−0.134278
$826$	29.4518	1.02476
$827$	−13.3702	−0.464927	−0.232463	−	0.972605i	$-0.574679\pi$
$827$	−13.3702	−0.464927	−0.232463	+	0.972605i	$0.574679\pi$
$828$	−16.5428	−0.574903
$829$	36.8046	1.27828	0.639139	−	0.769092i	$-0.279291\pi$
$829$	36.8046	1.27828	0.639139	+	0.769092i	$0.279291\pi$
$830$	−0.624616	−0.0216807
$831$	1.11569	0.0387028
$832$	2.12341	0.0736161
$833$	−17.5469	−0.607964
$834$	−4.54040	−0.157221
$835$	9.40551	0.325491
$836$	−7.92876	−0.274222
$837$	−9.64905	−0.333520
$838$	−1.92198	−0.0663937
$839$	−8.87780	−0.306496	−0.153248	−	0.988188i	$-0.548973\pi$
$839$	−8.87780	−0.306496	−0.153248	+	0.988188i	$0.548973\pi$
$840$	−4.56871	−0.157636
$841$	−20.4302	−0.704489
$842$	−28.6682	−0.987972
$843$	−0.926293	−0.0319032
$844$	10.3326	0.355662
$845$	15.8542	0.545402
$846$	2.42683	0.0834361
$847$	30.7100	1.05521
$848$	−2.90356	−0.0997085
$849$	−4.84437	−0.166258
$850$	2.85952	0.0980808
$851$	−19.3381	−0.662901
$852$	−3.88488	−0.133094
$853$	−5.87690	−0.201221	−0.100611	−	0.994926i	$-0.532080\pi$
$853$	−5.87690	−0.201221	−0.100611	+	0.994926i	$0.532080\pi$
$854$	46.2289	1.58192
$855$	−5.30928	−0.181574
$856$	−15.6247	−0.534040
$857$	−30.3816	−1.03781	−0.518907	−	0.854831i	$-0.673661\pi$
$857$	−30.3816	−1.03781	−0.518907	+	0.854831i	$0.673661\pi$
$858$	0.480570	0.0164064
$859$	−8.37229	−0.285659	−0.142829	−	0.989747i	$-0.545620\pi$
$859$	−8.37229	−0.285659	−0.142829	+	0.989747i	$0.545620\pi$
$860$	−6.55289	−0.223452
$861$	16.6994	0.569114
$862$	−25.7661	−0.877597
$863$	26.5688	0.904413	0.452207	−	0.891913i	$-0.350637\pi$
$863$	26.5688	0.904413	0.452207	+	0.891913i	$0.350637\pi$
$864$	9.24013	0.314356
$865$	15.6278	0.531360
$866$	−13.0488	−0.443418
$867$	−0.269629	−0.00915708
$868$	39.2668	1.33280
$869$	10.5641	0.358361
$870$	−0.814890	−0.0276273
$871$	−3.56483	−0.120790
$872$	−10.0692	−0.340986
$873$	46.2382	1.56492
$874$	5.19806	0.175827
$875$	52.1302	1.76232
$876$	2.82889	0.0955794
$877$	12.9818	0.438364	0.219182	−	0.975684i	$-0.429661\pi$
$877$	12.9818	0.438364	0.219182	+	0.975684i	$0.429661\pi$
$878$	−9.48428	−0.320079
$879$	6.79565	0.229211
$880$	1.80031	0.0606885
$881$	−11.2729	−0.379793	−0.189896	−	0.981804i	$-0.560815\pi$
$881$	−11.2729	−0.379793	−0.189896	+	0.981804i	$0.560815\pi$
$882$	−42.5833	−1.43385
$883$	20.8034	0.700089	0.350044	−	0.936733i	$-0.386166\pi$
$883$	20.8034	0.700089	0.350044	+	0.936733i	$0.386166\pi$
$884$	0.680520	0.0228884
$885$	2.40759	0.0809302
$886$	24.9977	0.839813
$887$	−2.81003	−0.0943514	−0.0471757	−	0.998887i	$-0.515022\pi$
$887$	−2.81003	−0.0943514	−0.0471757	+	0.998887i	$0.515022\pi$
$888$	3.32628	0.111623
$889$	−28.9417	−0.970675
$890$	1.63608	0.0548415
$891$	−34.6324	−1.16023
$892$	30.3275	1.01544
$893$	1.45645	0.0487381
$894$	0.990236	0.0331184
$895$	17.3912	0.581322
$896$	−40.4665	−1.35189
$897$	0.601750	0.0200919
$898$	−7.72089	−0.257649
$899$	17.6745	0.589477
$900$	−13.2543	−0.441809
$901$	8.32916	0.277484
$902$	42.9786	1.43103
$903$	5.35497	0.178202
$904$	−25.1714	−0.837189
$905$	13.5573	0.450659
$906$	2.40826	0.0800090
$907$	−29.1019	−0.966313	−0.483157	−	0.875534i	$-0.660510\pi$
$907$	−29.1019	−0.966313	−0.483157	+	0.875534i	$0.660510\pi$
$908$	−14.8228	−0.491911
$909$	−42.0405	−1.39439
$910$	−2.65166	−0.0879017
$911$	17.3658	0.575355	0.287678	−	0.957727i	$-0.407117\pi$
$911$	17.3658	0.575355	0.287678	+	0.957727i	$0.407117\pi$
$912$	0.136896	0.00453307
$913$	−2.50906	−0.0830378
$914$	6.83304	0.226017
$915$	3.77907	0.124932
$916$	−2.61682	−0.0864623
$917$	91.4943	3.02141
$918$	−1.32494	−0.0437295
$919$	−19.2437	−0.634792	−0.317396	−	0.948293i	$-0.602808\pi$
$919$	−19.2437	−0.634792	−0.317396	+	0.948293i	$0.602808\pi$
$920$	−14.7233	−0.485412
$921$	7.06820	0.232905
$922$	−0.0524004	−0.00172571
$923$	−5.69008	−0.187291
$924$	−7.27238	−0.239244
$925$	−15.4939	−0.509435
$926$	14.4771	0.475749
$927$	−29.4943	−0.968719
$928$	−16.9255	−0.555605
$929$	−28.0482	−0.920231	−0.460116	−	0.887859i	$-0.652192\pi$
$929$	−28.0482	−0.920231	−0.460116	+	0.887859i	$0.652192\pi$
$930$	−1.68064	−0.0551102
$931$	−25.5561	−0.837567
$932$	14.0181	0.459179
$933$	−5.68412	−0.186090
$934$	15.9931	0.523309
$935$	−5.16439	−0.168893
$936$	4.16769	0.136225
$937$	−7.17990	−0.234557	−0.117279	−	0.993099i	$-0.537417\pi$
$937$	−7.17990	−0.234557	−0.117279	+	0.993099i	$0.537417\pi$
$938$	−28.2446	−0.922219
$939$	7.21105	0.235324
$940$	−1.63471	−0.0533184
$941$	31.9614	1.04191	0.520956	−	0.853584i	$-0.325576\pi$
$941$	31.9614	1.04191	0.520956	+	0.853584i	$0.325576\pi$
$942$	1.92833	0.0628285
$943$	53.8160	1.75249
$944$	2.49960	0.0813550
$945$	−9.86044	−0.320760
$946$	13.7819	0.448087
$947$	−24.1610	−0.785127	−0.392564	−	0.919725i	$-0.628412\pi$
$947$	−24.1610	−0.785127	−0.392564	+	0.919725i	$0.628412\pi$
$948$	−0.901612	−0.0292830
$949$	4.14340	0.134500
$950$	4.16474	0.135122
$951$	−6.04657	−0.196074
$952$	13.6067	0.440996
$953$	−44.9090	−1.45474	−0.727372	−	0.686243i	$-0.759259\pi$
$953$	−44.9090	−1.45474	−0.727372	+	0.686243i	$0.759259\pi$
$954$	20.2134	0.654434
$955$	15.2148	0.492338
$956$	−35.4783	−1.14745
$957$	−3.27339	−0.105814
$958$	−7.48918	−0.241965
$959$	88.4315	2.85560
$960$	1.37531	0.0443880
$961$	5.45200	0.175871
$962$	1.93056	0.0622438
$963$	−16.6542	−0.536674
$964$	6.47368	0.208503
$965$	−22.1872	−0.714232
$966$	4.76774	0.153400
$967$	16.1092	0.518037	0.259018	−	0.965872i	$-0.416601\pi$
$967$	16.1092	0.518037	0.259018	+	0.965872i	$0.416601\pi$
$968$	−17.0230	−0.547140
$969$	−0.392700	−0.0126153
$970$	16.3072	0.523593
$971$	−10.2053	−0.327502	−0.163751	−	0.986502i	$-0.552359\pi$
$971$	−10.2053	−0.327502	−0.163751	+	0.986502i	$0.552359\pi$
$972$	9.24956	0.296680
$973$	100.636	3.22624
$974$	35.9451	1.15176
$975$	0.482128	0.0154405
$976$	3.92349	0.125588
$977$	3.79238	0.121329	0.0606645	−	0.998158i	$-0.480678\pi$
$977$	3.79238	0.121329	0.0606645	+	0.998158i	$0.480678\pi$
$978$	3.59447	0.114938
$979$	6.57208	0.210045
$980$	28.6841	0.916280
$981$	−10.7327	−0.342668
$982$	0.896768	0.0286170
$983$	−26.3100	−0.839160	−0.419580	−	0.907718i	$-0.637823\pi$
$983$	−26.3100	−0.839160	−0.419580	+	0.907718i	$0.637823\pi$
$984$	−9.25671	−0.295093
$985$	10.4004	0.331386
$986$	2.42693	0.0772893
$987$	1.33587	0.0425213
$988$	0.991140	0.0315324
$989$	17.2571	0.548744
$990$	−12.5331	−0.398327
$991$	−40.8803	−1.29861	−0.649303	−	0.760530i	$-0.724939\pi$
$991$	−40.8803	−1.29861	−0.649303	+	0.760530i	$0.724939\pi$
$992$	−34.9072	−1.10830
$993$	−3.28672	−0.104301
$994$	−45.0831	−1.42995
$995$	−27.1332	−0.860181
$996$	0.214141	0.00678533
$997$	29.4998	0.934268	0.467134	−	0.884187i	$-0.345287\pi$
$997$	29.4998	0.934268	0.467134	+	0.884187i	$0.345287\pi$
$998$	26.2380	0.830548
$999$	7.17896	0.227132

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	799.2.a.e.1.9	✓	12
3.2	odd	2		7191.2.a.v.1.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
799.2.a.e.1.9	✓	12	1.1	even	1	trivial
7191.2.a.v.1.4		12	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)

\(f(q)\)	\(=\)	\(q+0.829033 q^{2} -0.269629 q^{3} -1.31270 q^{4} -1.24530 q^{5} -0.223531 q^{6} +4.95448 q^{7} -2.74634 q^{8} -2.92730 q^{9} +O(q^{10})\)	\(q+0.829033 q^{2} -0.269629 q^{3} -1.31270 q^{4} -1.24530 q^{5} -0.223531 q^{6} +4.95448 q^{7} -2.74634 q^{8} -2.92730 q^{9} -1.03240 q^{10} -4.14710 q^{11} +0.353943 q^{12} +0.518411 q^{13} +4.10743 q^{14} +0.335769 q^{15} +0.348601 q^{16} -1.00000 q^{17} -2.42683 q^{18} -1.45645 q^{19} +1.63471 q^{20} -1.33587 q^{21} -3.43808 q^{22} -4.30503 q^{23} +0.740493 q^{24} -3.44923 q^{25} +0.429780 q^{26} +1.59817 q^{27} -6.50377 q^{28} -2.92743 q^{29} +0.278364 q^{30} -6.03755 q^{31} +5.78168 q^{32} +1.11818 q^{33} -0.829033 q^{34} -6.16982 q^{35} +3.84268 q^{36} +4.49198 q^{37} -1.20744 q^{38} -0.139779 q^{39} +3.42002 q^{40} -12.5007 q^{41} -1.10748 q^{42} -4.00859 q^{43} +5.44391 q^{44} +3.64537 q^{45} -3.56901 q^{46} -1.00000 q^{47} -0.0939930 q^{48} +17.5469 q^{49} -2.85952 q^{50} +0.269629 q^{51} -0.680520 q^{52} -8.32916 q^{53} +1.32494 q^{54} +5.16439 q^{55} -13.6067 q^{56} +0.392700 q^{57} -2.42693 q^{58} +7.17036 q^{59} -0.440766 q^{60} +11.2550 q^{61} -5.00533 q^{62} -14.5033 q^{63} +4.09600 q^{64} -0.645577 q^{65} +0.927007 q^{66} -6.87647 q^{67} +1.31270 q^{68} +1.16076 q^{69} -5.11498 q^{70} -10.9760 q^{71} +8.03936 q^{72} +7.99250 q^{73} +3.72400 q^{74} +0.930012 q^{75} +1.91188 q^{76} -20.5467 q^{77} -0.115881 q^{78} -2.54734 q^{79} -0.434113 q^{80} +8.35099 q^{81} -10.3635 q^{82} +0.605016 q^{83} +1.75361 q^{84} +1.24530 q^{85} -3.32326 q^{86} +0.789319 q^{87} +11.3893 q^{88} -1.58474 q^{89} +3.02213 q^{90} +2.56846 q^{91} +5.65123 q^{92} +1.62790 q^{93} -0.829033 q^{94} +1.81371 q^{95} -1.55891 q^{96} -15.7955 q^{97} +14.5470 q^{98} +12.1398 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{2} - q^{3} + 8 q^{4} - 11 q^{5} - q^{6} + q^{7} - 12 q^{8} - 3 q^{9}+O(q^{10}) \) 12 * q - 4 * q^2 - q^3 + 8 * q^4 - 11 * q^5 - q^6 + q^7 - 12 * q^8 - 3 * q^9	\( 12 q - 4 q^{2} - q^{3} + 8 q^{4} - 11 q^{5} - q^{6} + q^{7} - 12 q^{8} - 3 q^{9} - 2 q^{10} - 6 q^{11} - 4 q^{12} - 13 q^{13} - 15 q^{14} - 15 q^{15} + 4 q^{16} - 12 q^{17} - 9 q^{18} - 9 q^{19} - 23 q^{20} - 6 q^{21} + 11 q^{22} - 2 q^{23} - 6 q^{24} + q^{25} - 9 q^{26} + 2 q^{27} + 23 q^{28} - 14 q^{29} + 25 q^{30} - 18 q^{31} - 28 q^{32} - 17 q^{33} + 4 q^{34} - 15 q^{35} - 13 q^{36} + 8 q^{37} - 13 q^{38} - 9 q^{39} + 21 q^{40} - 43 q^{41} - 21 q^{42} - 7 q^{43} + 4 q^{44} - q^{45} - 24 q^{46} - 12 q^{47} - 2 q^{48} - 19 q^{49} + 8 q^{50} + q^{51} - 14 q^{52} + 5 q^{53} - q^{54} - 7 q^{55} - 26 q^{56} + 2 q^{57} + 27 q^{58} - 25 q^{59} - 13 q^{60} - q^{61} + 5 q^{62} - 13 q^{63} + 34 q^{64} - 8 q^{65} + 2 q^{66} - 2 q^{67} - 8 q^{68} - 27 q^{69} + 31 q^{70} - 5 q^{71} + 27 q^{72} + 6 q^{73} + 21 q^{74} + 14 q^{75} - 41 q^{76} - 22 q^{77} + 40 q^{78} - 10 q^{79} - 24 q^{80} - 4 q^{81} + 9 q^{82} - 45 q^{83} + 24 q^{84} + 11 q^{85} - 48 q^{86} + 7 q^{87} + 25 q^{88} - 65 q^{89} + 32 q^{90} + 7 q^{91} - 8 q^{92} - 15 q^{93} + 4 q^{94} + 44 q^{95} + 12 q^{96} - 21 q^{97} + 41 q^{98} - 41 q^{99}+O(q^{100}) \) 12 * q - 4 * q^2 - q^3 + 8 * q^4 - 11 * q^5 - q^6 + q^7 - 12 * q^8 - 3 * q^9 - 2 * q^10 - 6 * q^11 - 4 * q^12 - 13 * q^13 - 15 * q^14 - 15 * q^15 + 4 * q^16 - 12 * q^17 - 9 * q^18 - 9 * q^19 - 23 * q^20 - 6 * q^21 + 11 * q^22 - 2 * q^23 - 6 * q^24 + q^25 - 9 * q^26 + 2 * q^27 + 23 * q^28 - 14 * q^29 + 25 * q^30 - 18 * q^31 - 28 * q^32 - 17 * q^33 + 4 * q^34 - 15 * q^35 - 13 * q^36 + 8 * q^37 - 13 * q^38 - 9 * q^39 + 21 * q^40 - 43 * q^41 - 21 * q^42 - 7 * q^43 + 4 * q^44 - q^45 - 24 * q^46 - 12 * q^47 - 2 * q^48 - 19 * q^49 + 8 * q^50 + q^51 - 14 * q^52 + 5 * q^53 - q^54 - 7 * q^55 - 26 * q^56 + 2 * q^57 + 27 * q^58 - 25 * q^59 - 13 * q^60 - q^61 + 5 * q^62 - 13 * q^63 + 34 * q^64 - 8 * q^65 + 2 * q^66 - 2 * q^67 - 8 * q^68 - 27 * q^69 + 31 * q^70 - 5 * q^71 + 27 * q^72 + 6 * q^73 + 21 * q^74 + 14 * q^75 - 41 * q^76 - 22 * q^77 + 40 * q^78 - 10 * q^79 - 24 * q^80 - 4 * q^81 + 9 * q^82 - 45 * q^83 + 24 * q^84 + 11 * q^85 - 48 * q^86 + 7 * q^87 + 25 * q^88 - 65 * q^89 + 32 * q^90 + 7 * q^91 - 8 * q^92 - 15 * q^93 + 4 * q^94 + 44 * q^95 + 12 * q^96 - 21 * q^97 + 41 * q^98 - 41 * q^99

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