LMFDB - Embedded newform 1849.4.a.c.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1849,4,Mod(1,1849)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1849, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("1849.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1849 = 43^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1849.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:	$109.094531601$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 32x^{4} - 16x^{3} + 251x^{2} + 276x + 60 $ x^6 - 32x^4 - 16x^3 + 251x^2 + 276x + 60
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 43)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-0.847740$ of defining polynomial
Character	$\chi$	$=$	1849.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.84774 q^{2} -9.49653 q^{3} -4.58586 q^{4} -2.98245 q^{5} +17.5471 q^{6} +26.0720 q^{7} +23.2554 q^{8} +63.1842 q^{9} +O(q^{10})$	\(q-1.84774 q^{2} -9.49653 q^{3} -4.58586 q^{4} -2.98245 q^{5} +17.5471 q^{6} +26.0720 q^{7} +23.2554 q^{8} +63.1842 q^{9} +5.51080 q^{10} -36.8506 q^{11} +43.5497 q^{12} +89.5430 q^{13} -48.1743 q^{14} +28.3230 q^{15} -6.28309 q^{16} -28.8042 q^{17} -116.748 q^{18} +58.8677 q^{19} +13.6771 q^{20} -247.594 q^{21} +68.0904 q^{22} +2.63139 q^{23} -220.846 q^{24} -116.105 q^{25} -165.452 q^{26} -343.624 q^{27} -119.563 q^{28} -173.812 q^{29} -52.3335 q^{30} +57.9476 q^{31} -174.434 q^{32} +349.953 q^{33} +53.2227 q^{34} -77.7586 q^{35} -289.753 q^{36} -52.0754 q^{37} -108.772 q^{38} -850.348 q^{39} -69.3581 q^{40} +142.704 q^{41} +457.489 q^{42} +168.992 q^{44} -188.444 q^{45} -4.86213 q^{46} -106.853 q^{47} +59.6676 q^{48} +336.750 q^{49} +214.532 q^{50} +273.540 q^{51} -410.631 q^{52} +244.652 q^{53} +634.928 q^{54} +109.905 q^{55} +606.315 q^{56} -559.039 q^{57} +321.160 q^{58} -127.799 q^{59} -129.885 q^{60} +443.613 q^{61} -107.072 q^{62} +1647.34 q^{63} +372.573 q^{64} -267.058 q^{65} -646.622 q^{66} -117.896 q^{67} +132.092 q^{68} -24.9891 q^{69} +143.678 q^{70} -816.799 q^{71} +1469.37 q^{72} +620.953 q^{73} +96.2217 q^{74} +1102.59 q^{75} -269.959 q^{76} -960.770 q^{77} +1571.22 q^{78} +377.771 q^{79} +18.7390 q^{80} +1557.27 q^{81} -263.680 q^{82} -1453.23 q^{83} +1135.43 q^{84} +85.9072 q^{85} +1650.62 q^{87} -856.975 q^{88} -627.993 q^{89} +348.195 q^{90} +2334.57 q^{91} -12.0672 q^{92} -550.302 q^{93} +197.436 q^{94} -175.570 q^{95} +1656.52 q^{96} -817.163 q^{97} -622.227 q^{98} -2328.38 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} - 7 q^{3} + 22 q^{4} - 43 q^{5} - 3 q^{6} - 8 q^{7} - 54 q^{8} + 81 q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 - 7 * q^3 + 22 * q^4 - 43 * q^5 - 3 * q^6 - 8 * q^7 - 54 * q^8 + 81 * q^9	\( 6 q - 6 q^{2} - 7 q^{3} + 22 q^{4} - 43 q^{5} - 3 q^{6} - 8 q^{7} - 54 q^{8} + 81 q^{9} + 57 q^{10} - 28 q^{11} + 157 q^{12} + 56 q^{13} - 184 q^{14} - 124 q^{15} - 54 q^{16} + 19 q^{17} + 81 q^{18} + 75 q^{19} - 135 q^{20} - 18 q^{21} + 504 q^{22} + 131 q^{23} - 567 q^{24} + 105 q^{25} - 44 q^{26} - 238 q^{27} + 404 q^{28} - 515 q^{29} + 396 q^{30} + 237 q^{31} - 558 q^{32} - 540 q^{33} + 107 q^{34} + 198 q^{35} + 73 q^{36} - 269 q^{37} + 527 q^{38} - 290 q^{39} + 613 q^{40} + 471 q^{41} - 362 q^{42} - 428 q^{44} - 334 q^{45} + 67 q^{46} + 415 q^{47} + 989 q^{48} + 350 q^{49} - 1335 q^{50} + 1241 q^{51} - 8 q^{52} + 450 q^{53} + 402 q^{54} + 1732 q^{55} - 780 q^{56} - 1000 q^{57} - 1055 q^{58} + 356 q^{59} - 2732 q^{60} + 1328 q^{61} - 1603 q^{62} + 2290 q^{63} + 466 q^{64} + 62 q^{65} + 156 q^{66} - 632 q^{67} + 571 q^{68} + 1130 q^{69} + 1902 q^{70} + 144 q^{71} - 567 q^{72} - 864 q^{73} + 1207 q^{74} + 2494 q^{75} - 1005 q^{76} - 2660 q^{77} + 2222 q^{78} - 1613 q^{79} - 2399 q^{80} - 102 q^{81} - 1673 q^{82} - 682 q^{83} + 3758 q^{84} - 84 q^{85} + 449 q^{87} + 608 q^{88} - 3378 q^{89} + 930 q^{90} + 3900 q^{91} + 3491 q^{92} - 1879 q^{93} - 3197 q^{94} - 79 q^{95} - 591 q^{96} - 55 q^{97} - 2398 q^{98} - 1612 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 - 7 * q^3 + 22 * q^4 - 43 * q^5 - 3 * q^6 - 8 * q^7 - 54 * q^8 + 81 * q^9 + 57 * q^10 - 28 * q^11 + 157 * q^12 + 56 * q^13 - 184 * q^14 - 124 * q^15 - 54 * q^16 + 19 * q^17 + 81 * q^18 + 75 * q^19 - 135 * q^20 - 18 * q^21 + 504 * q^22 + 131 * q^23 - 567 * q^24 + 105 * q^25 - 44 * q^26 - 238 * q^27 + 404 * q^28 - 515 * q^29 + 396 * q^30 + 237 * q^31 - 558 * q^32 - 540 * q^33 + 107 * q^34 + 198 * q^35 + 73 * q^36 - 269 * q^37 + 527 * q^38 - 290 * q^39 + 613 * q^40 + 471 * q^41 - 362 * q^42 - 428 * q^44 - 334 * q^45 + 67 * q^46 + 415 * q^47 + 989 * q^48 + 350 * q^49 - 1335 * q^50 + 1241 * q^51 - 8 * q^52 + 450 * q^53 + 402 * q^54 + 1732 * q^55 - 780 * q^56 - 1000 * q^57 - 1055 * q^58 + 356 * q^59 - 2732 * q^60 + 1328 * q^61 - 1603 * q^62 + 2290 * q^63 + 466 * q^64 + 62 * q^65 + 156 * q^66 - 632 * q^67 + 571 * q^68 + 1130 * q^69 + 1902 * q^70 + 144 * q^71 - 567 * q^72 - 864 * q^73 + 1207 * q^74 + 2494 * q^75 - 1005 * q^76 - 2660 * q^77 + 2222 * q^78 - 1613 * q^79 - 2399 * q^80 - 102 * q^81 - 1673 * q^82 - 682 * q^83 + 3758 * q^84 - 84 * q^85 + 449 * q^87 + 608 * q^88 - 3378 * q^89 + 930 * q^90 + 3900 * q^91 + 3491 * q^92 - 1879 * q^93 - 3197 * q^94 - 79 * q^95 - 591 * q^96 - 55 * q^97 - 2398 * q^98 - 1612 * 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 $

$2$	−1.84774	−0.653275	−0.326637	−	0.945150i	$-0.605916\pi$
$2$	−1.84774	−0.653275	−0.326637	+	0.945150i	$0.605916\pi$
$3$	−9.49653	−1.82761	−0.913804	−	0.406154i	$-0.866870\pi$
$3$	−9.49653	−1.82761	−0.913804	+	0.406154i	$0.866870\pi$
$4$	−4.58586	−0.573232
$5$	−2.98245	−0.266759	−0.133379	−	0.991065i	$-0.542583\pi$
$5$	−2.98245	−0.266759	−0.133379	+	0.991065i	$0.542583\pi$
$6$	17.5471	1.19393
$7$	26.0720	1.40776	0.703878	−	0.710321i	$-0.251450\pi$
$7$	26.0720	1.40776	0.703878	+	0.710321i	$0.251450\pi$
$8$	23.2554	1.02775
$9$	63.1842	2.34015
$10$	5.51080	0.174267
$11$	−36.8506	−1.01008	−0.505040	−	0.863096i	$-0.668522\pi$
$11$	−36.8506	−1.01008	−0.505040	+	0.863096i	$0.668522\pi$
$12$	43.5497	1.04764
$13$	89.5430	1.91037	0.955183	−	0.296016i	$-0.0956581\pi$
$13$	89.5430	1.91037	0.955183	+	0.296016i	$0.0956581\pi$
$14$	−48.1743	−0.919652
$15$	28.3230	0.487531
$16$	−6.28309	−0.0981733
$17$	−28.8042	−0.410944	−0.205472	−	0.978663i	$-0.565873\pi$
$17$	−28.8042	−0.410944	−0.205472	+	0.978663i	$0.565873\pi$
$18$	−116.748	−1.52876
$19$	58.8677	0.710799	0.355400	−	0.934714i	$-0.384345\pi$
$19$	58.8677	0.710799	0.355400	+	0.934714i	$0.384345\pi$
$20$	13.6771	0.152915
$21$	−247.594	−2.57283
$22$	68.0904	0.659860
$23$	2.63139	0.0238558	0.0119279	−	0.999929i	$-0.496203\pi$
$23$	2.63139	0.0238558	0.0119279	+	0.999929i	$0.496203\pi$
$24$	−220.846	−1.87833
$25$	−116.105	−0.928840
$26$	−165.452	−1.24799
$27$	−343.624	−2.44928
$28$	−119.563	−0.806971
$29$	−173.812	−1.11297	−0.556486	−	0.830857i	$-0.687851\pi$
$29$	−173.812	−1.11297	−0.556486	+	0.830857i	$0.687851\pi$
$30$	−52.3335	−0.318492
$31$	57.9476	0.335732	0.167866	−	0.985810i	$-0.446312\pi$
$31$	57.9476	0.335732	0.167866	+	0.985810i	$0.446312\pi$
$32$	−174.434	−0.963619
$33$	349.953	1.84603
$34$	53.2227	0.268459
$35$	−77.7586	−0.375531
$36$	−289.753	−1.34145
$37$	−52.0754	−0.231382	−0.115691	−	0.993285i	$-0.536908\pi$
$37$	−52.0754	−0.231382	−0.115691	+	0.993285i	$0.536908\pi$
$38$	−108.772	−0.464347
$39$	−850.348	−3.49140
$40$	−69.3581	−0.274162
$41$	142.704	0.543577	0.271788	−	0.962357i	$-0.412385\pi$
$41$	142.704	0.543577	0.271788	+	0.962357i	$0.412385\pi$
$42$	457.489	1.68076
$43$	0	0
$43$	0	0
$44$	168.992	0.579010
$45$	−188.444	−0.624257
$46$	−4.86213	−0.0155844
$47$	−106.853	−0.331618	−0.165809	−	0.986158i	$-0.553024\pi$
$47$	−106.853	−0.331618	−0.165809	+	0.986158i	$0.553024\pi$
$48$	59.6676	0.179422
$49$	336.750	0.981779
$50$	214.532	0.606788
$51$	273.540	0.751045
$52$	−410.631	−1.09508
$53$	244.652	0.634067	0.317033	−	0.948414i	$-0.397313\pi$
$53$	244.652	0.634067	0.317033	+	0.948414i	$0.397313\pi$
$54$	634.928	1.60005
$55$	109.905	0.269448
$56$	606.315	1.44683
$57$	−559.039	−1.29906
$58$	321.160	0.727076
$59$	−127.799	−0.281999	−0.141000	−	0.990010i	$-0.545032\pi$
$59$	−127.799	−0.281999	−0.141000	+	0.990010i	$0.545032\pi$
$60$	−129.885	−0.279468
$61$	443.613	0.931128	0.465564	−	0.885014i	$-0.345851\pi$
$61$	443.613	0.931128	0.465564	+	0.885014i	$0.345851\pi$
$62$	−107.072	−0.219325
$63$	1647.34	3.29437
$64$	372.573	0.727681
$65$	−267.058	−0.509607
$66$	−646.622	−1.20597
$67$	−117.896	−0.214975	−0.107487	−	0.994206i	$-0.534280\pi$
$67$	−117.896	−0.214975	−0.107487	+	0.994206i	$0.534280\pi$
$68$	132.092	0.235566
$69$	−24.9891	−0.0435991
$70$	143.678	0.245325
$71$	−816.799	−1.36530	−0.682650	−	0.730746i	$-0.739173\pi$
$71$	−816.799	−1.36530	−0.682650	+	0.730746i	$0.739173\pi$
$72$	1469.37	2.40510
$73$	620.953	0.995576	0.497788	−	0.867299i	$-0.334146\pi$
$73$	620.953	0.995576	0.497788	+	0.867299i	$0.334146\pi$
$74$	96.2217	0.151156
$75$	1102.59	1.69756
$76$	−269.959	−0.407453
$77$	−960.770	−1.42195
$78$	1571.22	2.28085
$79$	377.771	0.538007	0.269003	−	0.963139i	$-0.413306\pi$
$79$	377.771	0.538007	0.269003	+	0.963139i	$0.413306\pi$
$80$	18.7390	0.0261886
$81$	1557.27	2.13617
$82$	−263.680	−0.355105
$83$	−1453.23	−1.92184	−0.960919	−	0.276829i	$-0.910716\pi$
$83$	−1453.23	−1.92184	−0.960919	+	0.276829i	$0.910716\pi$
$84$	1135.43	1.47483
$85$	85.9072	0.109623
$86$	0	0
$87$	1650.62	2.03408
$88$	−856.975	−1.03811
$89$	−627.993	−0.747945	−0.373973	−	0.927440i	$-0.622005\pi$
$89$	−627.993	−0.747945	−0.373973	+	0.927440i	$0.622005\pi$
$90$	348.195	0.407811
$91$	2334.57	2.68933
$92$	−12.0672	−0.0136749
$93$	−550.302	−0.613587
$94$	197.436	0.216638
$95$	−175.570	−0.189612
$96$	1656.52	1.76112
$97$	−817.163	−0.855365	−0.427682	−	0.903929i	$-0.640670\pi$
$97$	−817.163	−0.855365	−0.427682	+	0.903929i	$0.640670\pi$
$98$	−622.227	−0.641372
$99$	−2328.38	−2.36374
$100$	532.441	0.532441
$101$	513.438	0.505832	0.252916	−	0.967488i	$-0.418610\pi$
$101$	513.438	0.505832	0.252916	+	0.967488i	$0.418610\pi$
$102$	−505.431	−0.490639
$103$	689.788	0.659872	0.329936	−	0.944003i	$-0.392973\pi$
$103$	689.788	0.659872	0.329936	+	0.944003i	$0.392973\pi$
$104$	2082.36	1.96338
$105$	738.437	0.686325
$106$	−452.053	−0.414220
$107$	320.710	0.289759	0.144879	−	0.989449i	$-0.453721\pi$
$107$	320.710	0.289759	0.144879	+	0.989449i	$0.453721\pi$
$108$	1575.81	1.40400
$109$	−1691.51	−1.48640	−0.743200	−	0.669069i	$-0.766693\pi$
$109$	−1691.51	−1.48640	−0.743200	+	0.669069i	$0.766693\pi$
$110$	−203.076	−0.176023
$111$	494.535	0.422876
$112$	−163.813	−0.138204
$113$	−856.360	−0.712916	−0.356458	−	0.934311i	$-0.616016\pi$
$113$	−856.360	−0.712916	−0.356458	+	0.934311i	$0.616016\pi$
$114$	1032.96	0.848645
$115$	−7.84801	−0.00636374
$116$	797.079	0.637990
$117$	5657.70	4.47055
$118$	236.139	0.184223
$119$	−750.984	−0.578509
$120$	658.662	0.501061
$121$	26.9674	0.0202610
$122$	−819.682	−0.608283
$123$	−1355.19	−0.993445
$124$	−265.739	−0.192452
$125$	719.084	0.514535
$126$	−3043.85	−2.15213
$127$	−2233.72	−1.56071	−0.780357	−	0.625335i	$-0.784962\pi$
$127$	−2233.72	−1.56071	−0.780357	+	0.625335i	$0.784962\pi$
$128$	707.051	0.488243
$129$	0	0
$130$	493.454	0.332913
$131$	2051.51	1.36825	0.684126	−	0.729364i	$-0.260184\pi$
$131$	2051.51	1.36825	0.684126	+	0.729364i	$0.260184\pi$
$132$	−1604.83	−1.05820
$133$	1534.80	1.00063
$134$	217.841	0.140437
$135$	1024.84	0.653367
$136$	−669.853	−0.422349
$137$	−2594.49	−1.61797	−0.808986	−	0.587827i	$-0.799983\pi$
$137$	−2594.49	−1.61797	−0.808986	+	0.587827i	$0.799983\pi$
$138$	46.1734	0.0284822
$139$	1140.44	0.695905	0.347953	−	0.937512i	$-0.386877\pi$
$139$	1140.44	0.695905	0.347953	+	0.937512i	$0.386877\pi$
$140$	356.590	0.215267
$141$	1014.73	0.606068
$142$	1509.23	0.891916
$143$	−3299.71	−1.92962
$144$	−396.992	−0.229741
$145$	518.388	0.296895
$146$	−1147.36	−0.650385
$147$	−3197.96	−1.79431
$148$	238.810	0.132636
$149$	2112.03	1.16124	0.580618	−	0.814176i	$-0.302811\pi$
$149$	2112.03	1.16124	0.580618	+	0.814176i	$0.302811\pi$
$150$	−2037.31	−1.10897
$151$	1351.31	0.728265	0.364132	−	0.931347i	$-0.381366\pi$
$151$	1351.31	0.728265	0.364132	+	0.931347i	$0.381366\pi$
$152$	1368.99	0.730526
$153$	−1819.97	−0.961672
$154$	1775.25	0.928922
$155$	−172.826	−0.0895595
$156$	3899.57	2.00138
$157$	1506.02	0.765562	0.382781	−	0.923839i	$-0.374966\pi$
$157$	1506.02	0.765562	0.382781	+	0.923839i	$0.374966\pi$
$158$	−698.022	−0.351466
$159$	−2323.35	−1.15883
$160$	520.240	0.257054
$161$	68.6057	0.0335832
$162$	−2877.43	−1.39551
$163$	1258.30	0.604647	0.302323	−	0.953205i	$-0.402238\pi$
$163$	1258.30	0.604647	0.302323	+	0.953205i	$0.402238\pi$
$164$	−654.420	−0.311595
$165$	−1043.72	−0.492445
$166$	2685.19	1.25549
$167$	2764.50	1.28098	0.640489	−	0.767967i	$-0.278732\pi$
$167$	2764.50	1.28098	0.640489	+	0.767967i	$0.278732\pi$
$168$	−5757.89	−2.64423
$169$	5820.95	2.64950
$170$	−158.734	−0.0716139
$171$	3719.51	1.66338
$172$	0	0
$173$	1004.21	0.441322	0.220661	−	0.975351i	$-0.429179\pi$
$173$	1004.21	0.441322	0.220661	+	0.975351i	$0.429179\pi$
$174$	−3049.91	−1.32881
$175$	−3027.09	−1.30758
$176$	231.536	0.0991628
$177$	1213.64	0.515384
$178$	1160.37	0.488614
$179$	−2666.39	−1.11338	−0.556692	−	0.830719i	$-0.687930\pi$
$179$	−2666.39	−1.11338	−0.556692	+	0.830719i	$0.687930\pi$
$180$	864.176	0.357844
$181$	3016.21	1.23863	0.619317	−	0.785141i	$-0.287409\pi$
$181$	3016.21	1.23863	0.619317	+	0.785141i	$0.287409\pi$
$182$	−4313.67	−1.75687
$183$	−4212.79	−1.70174
$184$	61.1941	0.0245179
$185$	155.312	0.0617232
$186$	1016.81	0.400841
$187$	1061.45	0.415086
$188$	490.010	0.190094
$189$	−8958.98	−3.44799
$190$	324.408	0.123869
$191$	−1413.15	−0.535352	−0.267676	−	0.963509i	$-0.586256\pi$
$191$	−1413.15	−0.535352	−0.267676	+	0.963509i	$0.586256\pi$
$192$	−3538.15	−1.32992
$193$	−1246.60	−0.464934	−0.232467	−	0.972604i	$-0.574680\pi$
$193$	−1246.60	−0.464934	−0.232467	+	0.972604i	$0.574680\pi$
$194$	1509.91	0.558788
$195$	2536.12	0.931362
$196$	−1544.29	−0.562787
$197$	−4931.17	−1.78341	−0.891704	−	0.452619i	$-0.850490\pi$
$197$	−4931.17	−1.78341	−0.891704	+	0.452619i	$0.850490\pi$
$198$	4302.23	1.54417
$199$	−552.461	−0.196799	−0.0983993	−	0.995147i	$-0.531372\pi$
$199$	−552.461	−0.196799	−0.0983993	+	0.995147i	$0.531372\pi$
$200$	−2700.07	−0.954618
$201$	1119.60	0.392889
$202$	−948.700	−0.330447
$203$	−4531.64	−1.56679
$204$	−1254.42	−0.430523
$205$	−425.609	−0.145004
$206$	−1274.55	−0.431078
$207$	166.262	0.0558263
$208$	−562.607	−0.187547
$209$	−2169.31	−0.717964
$210$	−1364.44	−0.448359
$211$	−2302.22	−0.751145	−0.375572	−	0.926793i	$-0.622554\pi$
$211$	−2302.22	−0.751145	−0.375572	+	0.926793i	$0.622554\pi$
$212$	−1121.94	−0.363467
$213$	7756.76	2.49523
$214$	−592.588	−0.189292
$215$	0	0
$216$	−7991.12	−2.51725
$217$	1510.81	0.472629
$218$	3125.48	0.971028
$219$	−5896.90	−1.81952
$220$	−504.010	−0.154456
$221$	−2579.21	−0.785053
$222$	−913.773	−0.276254
$223$	−2558.41	−0.768269	−0.384135	−	0.923277i	$-0.625500\pi$
$223$	−2558.41	−0.768269	−0.384135	+	0.923277i	$0.625500\pi$
$224$	−4547.84	−1.35654
$225$	−7336.00	−2.17363
$226$	1582.33	0.465730
$227$	−3622.76	−1.05926	−0.529628	−	0.848230i	$-0.677669\pi$
$227$	−3622.76	−1.05926	−0.529628	+	0.848230i	$0.677669\pi$
$228$	2563.67	0.744664
$229$	1155.46	0.333428	0.166714	−	0.986005i	$-0.446684\pi$
$229$	1155.46	0.333428	0.166714	+	0.986005i	$0.446684\pi$
$230$	14.5011	0.00415727
$231$	9123.98	2.59876
$232$	−4042.08	−1.14386
$233$	−527.800	−0.148401	−0.0742003	−	0.997243i	$-0.523640\pi$
$233$	−527.800	−0.148401	−0.0742003	+	0.997243i	$0.523640\pi$
$234$	−10454.0	−2.92050
$235$	318.683	0.0884620
$236$	586.066	0.161651
$237$	−3587.51	−0.983266
$238$	1387.62	0.377925
$239$	−1341.41	−0.363048	−0.181524	−	0.983387i	$-0.558103\pi$
$239$	−1341.41	−0.363048	−0.181524	+	0.983387i	$0.558103\pi$
$240$	−177.956	−0.0478625
$241$	3738.93	0.999361	0.499680	−	0.866210i	$-0.333451\pi$
$241$	3738.93	0.999361	0.499680	+	0.866210i	$0.333451\pi$
$242$	−49.8287	−0.0132360
$243$	−5510.79	−1.45480
$244$	−2034.34	−0.533752
$245$	−1004.34	−0.261898
$246$	2504.05	0.648993
$247$	5271.19	1.35789
$248$	1347.59	0.345050
$249$	13800.6	3.51237
$250$	−1328.68	−0.336133
$251$	−1741.62	−0.437969	−0.218985	−	0.975728i	$-0.570274\pi$
$251$	−1741.62	−0.437969	−0.218985	+	0.975728i	$0.570274\pi$
$252$	−7554.46	−1.88844
$253$	−96.9684	−0.0240963
$254$	4127.33	1.01957
$255$	−815.821	−0.200348
$256$	−4287.03	−1.04664
$257$	−4121.68	−1.00040	−0.500200	−	0.865910i	$-0.666740\pi$
$257$	−4121.68	−1.00040	−0.500200	+	0.865910i	$0.666740\pi$
$258$	0	0
$259$	−1357.71	−0.325730
$260$	1224.69	0.292123
$261$	−10982.2	−2.60452
$262$	−3790.65	−0.893844
$263$	−4315.46	−1.01180	−0.505898	−	0.862593i	$-0.668839\pi$
$263$	−4315.46	−1.01180	−0.505898	+	0.862593i	$0.668839\pi$
$264$	8138.30	1.89726
$265$	−729.663	−0.169143
$266$	−2835.91	−0.653688
$267$	5963.76	1.36695
$268$	540.654	0.123230
$269$	5195.44	1.17759	0.588794	−	0.808283i	$-0.299603\pi$
$269$	5195.44	1.17759	0.588794	+	0.808283i	$0.299603\pi$
$270$	−1893.64	−0.426828
$271$	−7874.15	−1.76502	−0.882510	−	0.470294i	$-0.844148\pi$
$271$	−7874.15	−1.76502	−0.882510	+	0.470294i	$0.844148\pi$
$272$	180.979	0.0403437
$273$	−22170.3	−4.91504
$274$	4793.94	1.05698
$275$	4278.54	0.938202
$276$	114.596	0.0249924
$277$	175.471	0.0380615	0.0190307	−	0.999819i	$-0.493942\pi$
$277$	175.471	0.0380615	0.0190307	+	0.999819i	$0.493942\pi$
$278$	−2107.24	−0.454617
$279$	3661.37	0.785665
$280$	−1808.31	−0.385954
$281$	7263.01	1.54190	0.770951	−	0.636894i	$-0.219781\pi$
$281$	7263.01	1.54190	0.770951	+	0.636894i	$0.219781\pi$
$282$	−1874.96	−0.395929
$283$	2314.68	0.486196	0.243098	−	0.970002i	$-0.421836\pi$
$283$	2314.68	0.486196	0.243098	+	0.970002i	$0.421836\pi$
$284$	3745.72	0.782633
$285$	1667.31	0.346536
$286$	6097.01	1.26057
$287$	3720.58	0.765224
$288$	−11021.4	−2.25502
$289$	−4083.32	−0.831125
$290$	−957.846	−0.193954
$291$	7760.22	1.56327
$292$	−2847.60	−0.570696
$293$	8723.52	1.73936	0.869681	−	0.493614i	$-0.164324\pi$
$293$	8723.52	1.73936	0.869681	+	0.493614i	$0.164324\pi$
$294$	5909.00	1.17218
$295$	381.153	0.0752258
$296$	−1211.03	−0.237804
$297$	12662.8	2.47397
$298$	−3902.48	−0.758607
$299$	235.623	0.0455733
$300$	−5056.34	−0.973093
$301$	0	0
$302$	−2496.87	−0.475757
$303$	−4875.88	−0.924462
$304$	−369.871	−0.0697815
$305$	−1323.06	−0.248387
$306$	3362.83	0.628236
$307$	1579.68	0.293672	0.146836	−	0.989161i	$-0.453091\pi$
$307$	1579.68	0.293672	0.146836	+	0.989161i	$0.453091\pi$
$308$	4405.95	0.815105
$309$	−6550.59	−1.20599
$310$	319.338	0.0585070
$311$	−5604.24	−1.02182	−0.510912	−	0.859633i	$-0.670692\pi$
$311$	−5604.24	−1.02182	−0.510912	+	0.859633i	$0.670692\pi$
$312$	−19775.2	−3.58830
$313$	−3429.86	−0.619384	−0.309692	−	0.950837i	$-0.600226\pi$
$313$	−3429.86	−0.619384	−0.309692	+	0.950837i	$0.600226\pi$
$314$	−2782.73	−0.500123
$315$	−4913.11	−0.878802
$316$	−1732.40	−0.308403
$317$	4493.00	0.796064	0.398032	−	0.917372i	$-0.369693\pi$
$317$	4493.00	0.796064	0.398032	+	0.917372i	$0.369693\pi$
$318$	4292.94	0.757032
$319$	6405.09	1.12419
$320$	−1111.18	−0.194115
$321$	−3045.63	−0.529566
$322$	−126.766	−0.0219390
$323$	−1695.64	−0.292098
$324$	−7141.40	−1.22452
$325$	−10396.4	−1.77442
$326$	−2325.01	−0.395001
$327$	16063.5	2.71656
$328$	3318.64	0.558662
$329$	−2785.86	−0.466837
$330$	1928.52	0.321702
$331$	−4433.87	−0.736277	−0.368139	−	0.929771i	$-0.620005\pi$
$331$	−4433.87	−0.736277	−0.368139	+	0.929771i	$0.620005\pi$
$332$	6664.30	1.10166
$333$	−3290.34	−0.541470
$334$	−5108.07	−0.836831
$335$	351.620	0.0573463
$336$	1555.65	0.252583
$337$	6498.33	1.05040	0.525202	−	0.850977i	$-0.323990\pi$
$337$	6498.33	1.05040	0.525202	+	0.850977i	$0.323990\pi$
$338$	−10755.6	−1.73085
$339$	8132.45	1.30293
$340$	−393.958	−0.0628393
$341$	−2135.41	−0.339116
$342$	−6872.69	−1.08664
$343$	−162.945	−0.0256507
$344$	0	0
$345$	74.5289	0.0116304
$346$	−1855.52	−0.288305
$347$	11973.6	1.85237	0.926187	−	0.377064i	$-0.123066\pi$
$347$	11973.6	1.85237	0.926187	+	0.377064i	$0.123066\pi$
$348$	−7569.49	−1.16600
$349$	−5611.30	−0.860648	−0.430324	−	0.902674i	$-0.641601\pi$
$349$	−5611.30	−0.860648	−0.430324	+	0.902674i	$0.641601\pi$
$350$	5593.28	0.854209
$351$	−30769.1	−4.67902
$352$	6427.99	0.973332
$353$	−2022.00	−0.304874	−0.152437	−	0.988313i	$-0.548712\pi$
$353$	−2022.00	−0.304874	−0.152437	+	0.988313i	$0.548712\pi$
$354$	−2242.50	−0.336688
$355$	2436.07	0.364206
$356$	2879.88	0.428746
$357$	7131.74	1.05729
$358$	4926.81	0.727346
$359$	10135.3	1.49003	0.745014	−	0.667049i	$-0.232443\pi$
$359$	10135.3	1.49003	0.745014	+	0.667049i	$0.232443\pi$
$360$	−4382.34	−0.641582
$361$	−3393.59	−0.494765
$362$	−5573.17	−0.809169
$363$	−256.097	−0.0370292
$364$	−10706.0	−1.54161
$365$	−1851.96	−0.265579
$366$	7784.13	1.11170
$367$	−4379.58	−0.622922	−0.311461	−	0.950259i	$-0.600818\pi$
$367$	−4379.58	−0.622922	−0.311461	+	0.950259i	$0.600818\pi$
$368$	−16.5333	−0.00234200
$369$	9016.64	1.27205
$370$	−286.977	−0.0403222
$371$	6378.57	0.892612
$372$	2523.60	0.351728
$373$	−4392.98	−0.609813	−0.304906	−	0.952382i	$-0.598625\pi$
$373$	−4392.98	−0.609813	−0.304906	+	0.952382i	$0.598625\pi$
$374$	−1961.29	−0.271165
$375$	−6828.81	−0.940369
$376$	−2484.90	−0.340821
$377$	−15563.7	−2.12618
$378$	16553.9	2.25248
$379$	−878.629	−0.119082	−0.0595411	−	0.998226i	$-0.518964\pi$
$379$	−878.629	−0.119082	−0.0595411	+	0.998226i	$0.518964\pi$
$380$	805.140	0.108692
$381$	21212.6	2.85237
$382$	2611.14	0.349732
$383$	−5061.60	−0.675289	−0.337644	−	0.941274i	$-0.609630\pi$
$383$	−5061.60	−0.675289	−0.337644	+	0.941274i	$0.609630\pi$
$384$	−6714.54	−0.892317
$385$	2865.45	0.379317
$386$	2303.39	0.303730
$387$	0	0
$388$	3747.39	0.490322
$389$	3417.17	0.445392	0.222696	−	0.974888i	$-0.428514\pi$
$389$	3417.17	0.445392	0.222696	+	0.974888i	$0.428514\pi$
$390$	−4686.10	−0.608436
$391$	−75.7952	−0.00980339
$392$	7831.26	1.00903
$393$	−19482.2	−2.50063
$394$	9111.52	1.16506
$395$	−1126.68	−0.143518
$396$	10677.6	1.35497
$397$	7634.34	0.965130	0.482565	−	0.875860i	$-0.339705\pi$
$397$	7634.34	0.965130	0.482565	+	0.875860i	$0.339705\pi$
$398$	1020.80	0.128564
$399$	−14575.3	−1.82876
$400$	729.498	0.0911872
$401$	−8402.74	−1.04642	−0.523208	−	0.852205i	$-0.675265\pi$
$401$	−8402.74	−1.04642	−0.523208	+	0.852205i	$0.675265\pi$
$402$	−2068.74	−0.256665
$403$	5188.80	0.641372
$404$	−2354.55	−0.289959
$405$	−4644.48	−0.569842
$406$	8373.30	1.02355
$407$	1919.01	0.233714
$408$	6361.28	0.771888
$409$	11792.8	1.42571	0.712857	−	0.701310i	$-0.247401\pi$
$409$	11792.8	1.42571	0.712857	+	0.701310i	$0.247401\pi$
$410$	786.414	0.0947274
$411$	24638.7	2.95702
$412$	−3163.27	−0.378260
$413$	−3331.97	−0.396986
$414$	−307.210	−0.0364699
$415$	4334.19	0.512667
$416$	−15619.3	−1.84086
$417$	−10830.2	−1.27184
$418$	4008.32	0.469028
$419$	10631.9	1.23962	0.619811	−	0.784751i	$-0.287209\pi$
$419$	10631.9	1.23962	0.619811	+	0.784751i	$0.287209\pi$
$420$	−3386.37	−0.393423
$421$	3136.52	0.363099	0.181550	−	0.983382i	$-0.441889\pi$
$421$	3136.52	0.363099	0.181550	+	0.983382i	$0.441889\pi$
$422$	4253.91	0.490704
$423$	−6751.39	−0.776037
$424$	5689.48	0.651664
$425$	3344.31	0.381701
$426$	−14332.5	−1.63007
$427$	11565.9	1.31080
$428$	−1470.73	−0.166099
$429$	31335.8	3.52659
$430$	0	0
$431$	−170.380	−0.0190416	−0.00952080	−	0.999955i	$-0.503031\pi$
$431$	−170.380	−0.0190416	−0.00952080	+	0.999955i	$0.503031\pi$
$432$	2159.02	0.240454
$433$	−2093.65	−0.232365	−0.116183	−	0.993228i	$-0.537066\pi$
$433$	−2093.65	−0.232365	−0.116183	+	0.993228i	$0.537066\pi$
$434$	−2791.59	−0.308757
$435$	−4922.89	−0.542608
$436$	7757.04	0.852052
$437$	154.904	0.0169567
$438$	10895.9	1.18865
$439$	−10860.1	−1.18070	−0.590348	−	0.807149i	$-0.701010\pi$
$439$	−10860.1	−1.18070	−0.590348	+	0.807149i	$0.701010\pi$
$440$	2555.89	0.276926
$441$	21277.3	2.29751
$442$	4765.72	0.512855
$443$	8256.28	0.885480	0.442740	−	0.896650i	$-0.354006\pi$
$443$	8256.28	0.885480	0.442740	+	0.896650i	$0.354006\pi$
$444$	−2267.87	−0.242406
$445$	1872.96	0.199521
$446$	4727.29	0.501891
$447$	−20057.0	−2.12229
$448$	9713.73	1.02440
$449$	6792.03	0.713888	0.356944	−	0.934126i	$-0.383819\pi$
$449$	6792.03	0.713888	0.356944	+	0.934126i	$0.383819\pi$
$450$	13555.0	1.41998
$451$	−5258.73	−0.549056
$452$	3927.14	0.408666
$453$	−12832.8	−1.33098
$454$	6693.93	0.691986
$455$	−6962.74	−0.717403
$456$	−13000.7	−1.33512
$457$	−4004.62	−0.409908	−0.204954	−	0.978772i	$-0.565705\pi$
$457$	−4004.62	−0.409908	−0.204954	+	0.978772i	$0.565705\pi$
$458$	−2134.99	−0.217820
$459$	9897.82	1.00652
$460$	35.9898	0.00364790
$461$	1164.36	0.117635	0.0588175	−	0.998269i	$-0.481267\pi$
$461$	1164.36	0.117635	0.0588175	+	0.998269i	$0.481267\pi$
$462$	−16858.8	−1.69771
$463$	−2566.99	−0.257664	−0.128832	−	0.991666i	$-0.541123\pi$
$463$	−2566.99	−0.257664	−0.128832	+	0.991666i	$0.541123\pi$
$464$	1092.08	0.109264
$465$	1641.25	0.163680
$466$	975.237	0.0969463
$467$	7654.43	0.758469	0.379234	−	0.925301i	$-0.376187\pi$
$467$	7654.43	0.758469	0.379234	+	0.925301i	$0.376187\pi$
$468$	−25945.4	−2.56266
$469$	−3073.79	−0.302632
$470$	−588.843	−0.0577900
$471$	−14301.9	−1.39915
$472$	−2972.01	−0.289826
$473$	0	0
$474$	6628.79	0.642343
$475$	−6834.84	−0.660218
$476$	3443.90	0.331620
$477$	15458.1	1.48381
$478$	2478.57	0.237170
$479$	−8754.20	−0.835051	−0.417526	−	0.908665i	$-0.637103\pi$
$479$	−8754.20	−0.835051	−0.417526	+	0.908665i	$0.637103\pi$
$480$	−4940.48	−0.469794
$481$	−4662.98	−0.442024
$482$	−6908.58	−0.652857
$483$	−651.517	−0.0613769
$484$	−123.668	−0.0116142
$485$	2437.15	0.228176
$486$	10182.5	0.950386
$487$	−9406.39	−0.875245	−0.437623	−	0.899159i	$-0.644179\pi$
$487$	−9406.39	−0.875245	−0.437623	+	0.899159i	$0.644179\pi$
$488$	10316.4	0.956970
$489$	−11949.5	−1.10506
$490$	1855.76	0.171092
$491$	−6362.18	−0.584768	−0.292384	−	0.956301i	$-0.594449\pi$
$491$	−6362.18	−0.584768	−0.292384	+	0.956301i	$0.594449\pi$
$492$	6214.73	0.569475
$493$	5006.53	0.457369
$494$	−9739.80	−0.887073
$495$	6944.27	0.630549
$496$	−364.090	−0.0329599
$497$	−21295.6	−1.92201
$498$	−25500.0	−2.29454
$499$	−11574.8	−1.03840	−0.519198	−	0.854654i	$-0.673769\pi$
$499$	−11574.8	−1.03840	−0.519198	+	0.854654i	$0.673769\pi$
$500$	−3297.62	−0.294948
$501$	−26253.2	−2.34113
$502$	3218.07	0.286114
$503$	−11443.5	−1.01439	−0.507196	−	0.861831i	$-0.669318\pi$
$503$	−11443.5	−1.01439	−0.507196	+	0.861831i	$0.669318\pi$
$504$	38309.5	3.38580
$505$	−1531.31	−0.134935
$506$	179.172	0.0157415
$507$	−55278.8	−4.84225
$508$	10243.5	0.894651
$509$	−17397.9	−1.51502	−0.757511	−	0.652822i	$-0.773585\pi$
$509$	−17397.9	−1.51502	−0.757511	+	0.652822i	$0.773585\pi$
$510$	1507.42	0.130882
$511$	16189.5	1.40153
$512$	2264.91	0.195499
$513$	−20228.4	−1.74095
$514$	7615.79	0.653537
$515$	−2057.26	−0.176027
$516$	0	0
$517$	3937.58	0.334961
$518$	2508.70	0.212791
$519$	−9536.53	−0.806565
$520$	−6210.54	−0.523750
$521$	23236.4	1.95394	0.976972	−	0.213369i	$-0.0684437\pi$
$521$	23236.4	1.95394	0.976972	+	0.213369i	$0.0684437\pi$
$522$	20292.2	1.70147
$523$	6523.69	0.545432	0.272716	−	0.962095i	$-0.412078\pi$
$523$	6523.69	0.545432	0.272716	+	0.962095i	$0.412078\pi$
$524$	−9407.91	−0.784325
$525$	28746.9	2.38975
$526$	7973.85	0.660981
$527$	−1669.13	−0.137967
$528$	−2198.79	−0.181231
$529$	−12160.1	−0.999431
$530$	1348.23	0.110497
$531$	−8074.85	−0.659922
$532$	−7038.37	−0.573594
$533$	12778.2	1.03843
$534$	−11019.5	−0.892995
$535$	−956.502	−0.0772957
$536$	−2741.72	−0.220941
$537$	25321.5	2.03483
$538$	−9599.82	−0.769289
$539$	−12409.5	−0.991675
$540$	−4699.78	−0.374531
$541$	−13311.4	−1.05786	−0.528930	−	0.848666i	$-0.677406\pi$
$541$	−13311.4	−1.05786	−0.528930	+	0.848666i	$0.677406\pi$
$542$	14549.4	1.15304
$543$	−28643.5	−2.26374
$544$	5024.42	0.395993
$545$	5044.86	0.396510
$546$	40964.9	3.21088
$547$	−24529.8	−1.91740	−0.958700	−	0.284420i	$-0.908199\pi$
$547$	−24529.8	−1.91740	−0.958700	+	0.284420i	$0.908199\pi$
$548$	11898.0	0.927474
$549$	28029.3	2.17898
$550$	−7905.63	−0.612904
$551$	−10231.9	−0.791099
$552$	−581.132	−0.0448091
$553$	9849.25	0.757383
$554$	−324.225	−0.0248646
$555$	−1474.93	−0.112806
$556$	−5229.89	−0.398915
$557$	−1732.87	−0.131821	−0.0659104	−	0.997826i	$-0.520995\pi$
$557$	−1732.87	−0.131821	−0.0659104	+	0.997826i	$0.520995\pi$
$558$	−6765.27	−0.513255
$559$	0	0
$560$	488.564	0.0368672
$561$	−10080.1	−0.758615
$562$	−13420.1	−1.00729
$563$	13482.0	1.00924	0.504618	−	0.863343i	$-0.331634\pi$
$563$	13482.0	1.00924	0.504618	+	0.863343i	$0.331634\pi$
$564$	−4653.40	−0.347417
$565$	2554.05	0.190177
$566$	−4276.92	−0.317619
$567$	40601.1	3.00721
$568$	−18995.0	−1.40319
$569$	23053.6	1.69852	0.849261	−	0.527973i	$-0.177048\pi$
$569$	23053.6	1.69852	0.849261	+	0.527973i	$0.177048\pi$
$570$	−3080.76	−0.226384
$571$	−8791.94	−0.644363	−0.322181	−	0.946678i	$-0.604416\pi$
$571$	−8791.94	−0.644363	−0.322181	+	0.946678i	$0.604416\pi$
$572$	15132.0	1.10612
$573$	13420.1	0.978414
$574$	−6874.68	−0.499901
$575$	−305.518	−0.0221582
$576$	23540.7	1.70289
$577$	12464.3	0.899302	0.449651	−	0.893204i	$-0.351548\pi$
$577$	12464.3	0.899302	0.449651	+	0.893204i	$0.351548\pi$
$578$	7544.91	0.542953
$579$	11838.4	0.849718
$580$	−2377.25	−0.170190
$581$	−37888.6	−2.70548
$582$	−14338.9	−1.02125
$583$	−9015.58	−0.640458
$584$	14440.5	1.02321
$585$	−16873.8	−1.19256
$586$	−16118.8	−1.13628
$587$	24395.5	1.71535	0.857674	−	0.514193i	$-0.171909\pi$
$587$	24395.5	1.71535	0.857674	+	0.514193i	$0.171909\pi$
$588$	14665.4	1.02855
$589$	3411.24	0.238638
$590$	−704.273	−0.0491431
$591$	46829.0	3.25937
$592$	327.194	0.0227155
$593$	8779.99	0.608012	0.304006	−	0.952670i	$-0.401676\pi$
$593$	8779.99	0.608012	0.304006	+	0.952670i	$0.401676\pi$
$594$	−23397.5	−1.61618
$595$	2239.77	0.154322
$596$	−9685.46	−0.665658
$597$	5246.46	0.359671
$598$	−435.370	−0.0297719
$599$	−14440.3	−0.985001	−0.492501	−	0.870312i	$-0.663917\pi$
$599$	−14440.3	−0.985001	−0.492501	+	0.870312i	$0.663917\pi$
$600$	25641.3	1.74467
$601$	−7456.08	−0.506056	−0.253028	−	0.967459i	$-0.581427\pi$
$601$	−7456.08	−0.506056	−0.253028	+	0.967459i	$0.581427\pi$
$602$	0	0
$603$	−7449.16	−0.503074
$604$	−6196.91	−0.417464
$605$	−80.4290	−0.00540480
$606$	9009.37	0.603928
$607$	6832.01	0.456842	0.228421	−	0.973563i	$-0.426644\pi$
$607$	6832.01	0.456842	0.228421	+	0.973563i	$0.426644\pi$
$608$	−10268.5	−0.684939
$609$	43034.9	2.86348
$610$	2444.66	0.162265
$611$	−9567.89	−0.633512
$612$	8346.12	0.551261
$613$	12239.8	0.806460	0.403230	−	0.915099i	$-0.367887\pi$
$613$	12239.8	0.806460	0.403230	+	0.915099i	$0.367887\pi$
$614$	−2918.84	−0.191849
$615$	4041.81	0.265010
$616$	−22343.1	−1.46141
$617$	4307.99	0.281091	0.140546	−	0.990074i	$-0.455114\pi$
$617$	4307.99	0.281091	0.140546	+	0.990074i	$0.455114\pi$
$618$	12103.8	0.787842
$619$	21923.8	1.42357	0.711786	−	0.702396i	$-0.247887\pi$
$619$	21923.8	1.42357	0.711786	+	0.702396i	$0.247887\pi$
$620$	792.556	0.0513384
$621$	−904.210	−0.0584295
$622$	10355.2	0.667531
$623$	−16373.0	−1.05292
$624$	5342.81	0.342762
$625$	12368.5	0.791583
$626$	6337.49	0.404628
$627$	20600.9	1.31216
$628$	−6906.38	−0.438845
$629$	1499.99	0.0950850
$630$	9078.16	0.574099
$631$	−13249.3	−0.835891	−0.417945	−	0.908472i	$-0.637250\pi$
$631$	−13249.3	−0.835891	−0.417945	+	0.908472i	$0.637250\pi$
$632$	8785.21	0.552938
$633$	21863.1	1.37280
$634$	−8301.91	−0.520049
$635$	6661.97	0.416334
$636$	10654.5	0.664276
$637$	30153.6	1.87556
$638$	−11835.0	−0.734405
$639$	−51608.8	−3.19501
$640$	−2108.75	−0.130243
$641$	6897.79	0.425033	0.212517	−	0.977157i	$-0.431834\pi$
$641$	6897.79	0.425033	0.212517	+	0.977157i	$0.431834\pi$
$642$	5627.54	0.345952
$643$	−570.068	−0.0349631	−0.0174816	−	0.999847i	$-0.505565\pi$
$643$	−570.068	−0.0349631	−0.0174816	+	0.999847i	$0.505565\pi$
$644$	−314.616	−0.0192509
$645$	0	0
$646$	3133.10	0.190821
$647$	−15788.1	−0.959341	−0.479670	−	0.877449i	$-0.659244\pi$
$647$	−15788.1	−0.959341	−0.479670	+	0.877449i	$0.659244\pi$
$648$	36214.9	2.19545
$649$	4709.46	0.284842
$650$	19209.8	1.15919
$651$	−14347.5	−0.863782
$652$	−5770.37	−0.346603
$653$	−21960.3	−1.31604	−0.658019	−	0.753001i	$-0.728606\pi$
$653$	−21960.3	−1.31604	−0.658019	+	0.753001i	$0.728606\pi$
$654$	−29681.2	−1.77466
$655$	−6118.52	−0.364993
$656$	−896.623	−0.0533647
$657$	39234.4	2.32980
$658$	5147.55	0.304973
$659$	−12142.6	−0.717766	−0.358883	−	0.933383i	$-0.616842\pi$
$659$	−12142.6	−0.717766	−0.358883	+	0.933383i	$0.616842\pi$
$660$	4786.34	0.282285
$661$	3554.01	0.209130	0.104565	−	0.994518i	$-0.466655\pi$
$661$	3554.01	0.209130	0.104565	+	0.994518i	$0.466655\pi$
$662$	8192.65	0.480992
$663$	24493.6	1.43477
$664$	−33795.4	−1.97518
$665$	−4577.47	−0.266927
$666$	6079.69	0.353729
$667$	−457.369	−0.0265508
$668$	−12677.6	−0.734297
$669$	24296.1	1.40410
$670$	−649.702	−0.0374629
$671$	−16347.4	−0.940514
$672$	43188.7	2.47923
$673$	−20271.0	−1.16106	−0.580528	−	0.814240i	$-0.697154\pi$
$673$	−20271.0	−1.16106	−0.580528	+	0.814240i	$0.697154\pi$
$674$	−12007.2	−0.686203
$675$	39896.5	2.27499
$676$	−26694.0	−1.51878
$677$	−26668.2	−1.51395	−0.756973	−	0.653447i	$-0.773322\pi$
$677$	−26668.2	−1.51395	−0.756973	+	0.653447i	$0.773322\pi$
$678$	−15026.7	−0.851173
$679$	−21305.1	−1.20415
$680$	1997.81	0.112665
$681$	34403.7	1.93591
$682$	3945.67	0.221536
$683$	−5584.15	−0.312843	−0.156421	−	0.987690i	$-0.549996\pi$
$683$	−5584.15	−0.312843	−0.156421	+	0.987690i	$0.549996\pi$
$684$	−17057.1	−0.953502
$685$	7737.95	0.431608
$686$	301.079	0.0167569
$687$	−10972.9	−0.609377
$688$	0	0
$689$	21906.9	1.21130
$690$	−137.710	−0.00759787
$691$	2702.39	0.148776	0.0743878	−	0.997229i	$-0.476300\pi$
$691$	2702.39	0.148776	0.0743878	+	0.997229i	$0.476300\pi$
$692$	−4605.17	−0.252980
$693$	−60705.4	−3.32757
$694$	−22124.0	−1.21011
$695$	−3401.31	−0.185639
$696$	38385.7	2.09053
$697$	−4110.48	−0.223379
$698$	10368.2	0.562240
$699$	5012.27	0.271218
$700$	13881.8	0.749547
$701$	−19885.1	−1.07140	−0.535700	−	0.844408i	$-0.679952\pi$
$701$	−19885.1	−1.07140	−0.535700	+	0.844408i	$0.679952\pi$
$702$	56853.4	3.05669
$703$	−3065.56	−0.164466
$704$	−13729.5	−0.735016
$705$	−3026.38	−0.161674
$706$	3736.14	0.199166
$707$	13386.4	0.712088
$708$	−5565.59	−0.295435
$709$	−7798.56	−0.413090	−0.206545	−	0.978437i	$-0.566222\pi$
$709$	−7798.56	−0.413090	−0.206545	+	0.978437i	$0.566222\pi$
$710$	−4501.22	−0.237926
$711$	23869.1	1.25902
$712$	−14604.2	−0.768703
$713$	152.483	0.00800916
$714$	−13177.6	−0.690700
$715$	9841.24	0.514744
$716$	12227.7	0.638227
$717$	12738.7	0.663509
$718$	−18727.4	−0.973398
$719$	1118.09	0.0579939	0.0289970	−	0.999579i	$-0.490769\pi$
$719$	1118.09	0.0579939	0.0289970	+	0.999579i	$0.490769\pi$
$720$	1184.01	0.0612853
$721$	17984.2	0.928939
$722$	6270.47	0.323217
$723$	−35506.9	−1.82644
$724$	−13831.9	−0.710025
$725$	20180.5	1.03377
$726$	473.200	0.0241902
$727$	1741.54	0.0888449	0.0444225	−	0.999013i	$-0.485855\pi$
$727$	1741.54	0.0888449	0.0444225	+	0.999013i	$0.485855\pi$
$728$	54291.3	2.76397
$729$	10287.2	0.522642
$730$	3421.95	0.173496
$731$	0	0
$732$	19319.2	0.975491
$733$	9461.10	0.476744	0.238372	−	0.971174i	$-0.423386\pi$
$733$	9461.10	0.476744	0.238372	+	0.971174i	$0.423386\pi$
$734$	8092.33	0.406939
$735$	9537.77	0.478648
$736$	−459.003	−0.0229879
$737$	4344.54	0.217141
$738$	−16660.4	−0.831000
$739$	−30605.3	−1.52346	−0.761728	−	0.647897i	$-0.775649\pi$
$739$	−30605.3	−1.52346	−0.761728	+	0.647897i	$0.775649\pi$
$740$	−712.240	−0.0353817
$741$	−50058.1	−2.48169
$742$	−11785.9	−0.583121
$743$	−14556.5	−0.718745	−0.359373	−	0.933194i	$-0.617009\pi$
$743$	−14556.5	−0.718745	−0.359373	+	0.933194i	$0.617009\pi$
$744$	−12797.5	−0.630616
$745$	−6299.03	−0.309770
$746$	8117.10	0.398375
$747$	−91821.1	−4.49740
$748$	−4867.67	−0.237941
$749$	8361.55	0.407910
$750$	12617.9	0.614319
$751$	17528.3	0.851685	0.425843	−	0.904797i	$-0.359978\pi$
$751$	17528.3	0.851685	0.425843	+	0.904797i	$0.359978\pi$
$752$	671.364	0.0325560
$753$	16539.4	0.800436
$754$	28757.7	1.38898
$755$	−4030.22	−0.194271
$756$	41084.6	1.97650
$757$	37789.1	1.81436	0.907179	−	0.420744i	$-0.138231\pi$
$757$	37789.1	1.81436	0.907179	+	0.420744i	$0.138231\pi$
$758$	1623.48	0.0777934
$759$	920.864	0.0440385
$760$	−4082.96	−0.194874
$761$	−3292.90	−0.156856	−0.0784281	−	0.996920i	$-0.524990\pi$
$761$	−3292.90	−0.156856	−0.0784281	+	0.996920i	$0.524990\pi$
$762$	−39195.4	−1.86338
$763$	−44101.2	−2.09249
$764$	6480.52	0.306881
$765$	5427.98	0.256534
$766$	9352.52	0.441149
$767$	−11443.5	−0.538722
$768$	40711.9	1.91285
$769$	−28023.9	−1.31413	−0.657065	−	0.753834i	$-0.728202\pi$
$769$	−28023.9	−1.31413	−0.657065	+	0.753834i	$0.728202\pi$
$770$	−5294.61	−0.247798
$771$	39141.6	1.82834
$772$	5716.73	0.266515
$773$	−22131.0	−1.02975	−0.514875	−	0.857265i	$-0.672162\pi$
$773$	−22131.0	−1.02975	−0.514875	+	0.857265i	$0.672162\pi$
$774$	0	0
$775$	−6728.01	−0.311841
$776$	−19003.5	−0.879103
$777$	12893.5	0.595306
$778$	−6314.04	−0.290963
$779$	8400.67	0.386374
$780$	−11630.3	−0.533887
$781$	30099.6	1.37906
$782$	140.050	0.00640431
$783$	59726.2	2.72598
$784$	−2115.83	−0.0963845
$785$	−4491.63	−0.204220
$786$	35998.0	1.63360
$787$	5390.88	0.244173	0.122087	−	0.992519i	$-0.461041\pi$
$787$	5390.88	0.244173	0.122087	+	0.992519i	$0.461041\pi$
$788$	22613.6	1.02231
$789$	40981.9	1.84917
$790$	2081.82	0.0937567
$791$	−22327.0	−1.00361
$792$	−54147.3	−2.42934
$793$	39722.4	1.77880
$794$	−14106.3	−0.630495
$795$	6929.27	0.309127
$796$	2533.51	0.112811
$797$	43815.4	1.94733	0.973664	−	0.227986i	$-0.0732142\pi$
$797$	43815.4	1.94733	0.973664	+	0.227986i	$0.0732142\pi$
$798$	26931.3	1.19469
$799$	3077.80	0.136276
$800$	20252.6	0.895047
$801$	−39679.2	−1.75031
$802$	15526.1	0.683597
$803$	−22882.5	−1.00561
$804$	−5134.34	−0.225217
$805$	−204.613	−0.00895860
$806$	−9587.56	−0.418992
$807$	−49338.6	−2.15217
$808$	11940.2	0.519870
$809$	−19752.4	−0.858415	−0.429208	−	0.903206i	$-0.641207\pi$
$809$	−19752.4	−0.858415	−0.429208	+	0.903206i	$0.641207\pi$
$810$	8581.79	0.372263
$811$	−21280.3	−0.921398	−0.460699	−	0.887556i	$-0.652401\pi$
$811$	−21280.3	−0.921398	−0.460699	+	0.887556i	$0.652401\pi$
$812$	20781.5	0.898135
$813$	74777.1	3.22577
$814$	−3545.83	−0.152680
$815$	−3752.81	−0.161295
$816$	−1718.68	−0.0737325
$817$	0	0
$818$	−21790.0	−0.931383
$819$	147508.	6.29345
$820$	1951.78	0.0831208
$821$	−19716.5	−0.838136	−0.419068	−	0.907955i	$-0.637643\pi$
$821$	−19716.5	−0.838136	−0.419068	+	0.907955i	$0.637643\pi$
$822$	−45525.9	−1.93175
$823$	16269.0	0.689065	0.344532	−	0.938774i	$-0.388037\pi$
$823$	16269.0	0.689065	0.344532	+	0.938774i	$0.388037\pi$
$824$	16041.3	0.678185
$825$	−40631.3	−1.71467
$826$	6156.61	0.259341
$827$	−27410.0	−1.15253	−0.576263	−	0.817264i	$-0.695490\pi$
$827$	−27410.0	−1.15253	−0.576263	+	0.817264i	$0.695490\pi$
$828$	−762.455	−0.0320014
$829$	25392.8	1.06385	0.531923	−	0.846792i	$-0.321469\pi$
$829$	25392.8	1.06385	0.531923	+	0.846792i	$0.321469\pi$
$830$	−8008.45	−0.334913
$831$	−1666.37	−0.0695615
$832$	33361.3	1.39014
$833$	−9699.82	−0.403456
$834$	20011.4	0.830863
$835$	−8244.99	−0.341712
$836$	9948.15	0.411560
$837$	−19912.2	−0.822302
$838$	−19645.0	−0.809814
$839$	20579.5	0.846823	0.423412	−	0.905937i	$-0.360832\pi$
$839$	20579.5	0.846823	0.423412	+	0.905937i	$0.360832\pi$
$840$	17172.6	0.705372
$841$	5821.76	0.238704
$842$	−5795.48	−0.237203
$843$	−68973.4	−2.81799
$844$	10557.7	0.430580
$845$	−17360.7	−0.706777
$846$	12474.8	0.506966
$847$	703.094	0.0285225
$848$	−1537.17	−0.0622484
$849$	−21981.4	−0.888575
$850$	−6179.42	−0.249356
$851$	−137.031	−0.00551980
$852$	−35571.4	−1.43035
$853$	6873.98	0.275921	0.137961	−	0.990438i	$-0.455945\pi$
$853$	6873.98	0.275921	0.137961	+	0.990438i	$0.455945\pi$
$854$	−21370.8	−0.856314
$855$	−11093.3	−0.443721
$856$	7458.23	0.297800
$857$	−20623.8	−0.822049	−0.411025	−	0.911624i	$-0.634829\pi$
$857$	−20623.8	−0.822049	−0.411025	+	0.911624i	$0.634829\pi$
$858$	−57900.5	−2.30384
$859$	−40959.1	−1.62690	−0.813450	−	0.581635i	$-0.802413\pi$
$859$	−40959.1	−1.62690	−0.813450	+	0.581635i	$0.802413\pi$
$860$	0	0
$861$	−35332.7	−1.39853
$862$	314.819	0.0124394
$863$	−33784.0	−1.33258	−0.666292	−	0.745691i	$-0.732120\pi$
$863$	−33784.0	−1.33258	−0.666292	+	0.745691i	$0.732120\pi$
$864$	59939.6	2.36017
$865$	−2995.01	−0.117727
$866$	3868.52	0.151799
$867$	38777.4	1.51897
$868$	−6928.36	−0.270926
$869$	−13921.1	−0.543430
$870$	9096.22	0.354472
$871$	−10556.8	−0.410680
$872$	−39336.8	−1.52765
$873$	−51631.8	−2.00169
$874$	−286.223	−0.0110774
$875$	18748.0	0.724340
$876$	27042.3	1.04301
$877$	−37125.7	−1.42947	−0.714736	−	0.699395i	$-0.753453\pi$
$877$	−37125.7	−1.42947	−0.714736	+	0.699395i	$0.753453\pi$
$878$	20066.7	0.771319
$879$	−82843.2	−3.17887
$880$	−690.545	−0.0264526
$881$	−108.651	−0.00415499	−0.00207749	−	0.999998i	$-0.500661\pi$
$881$	−108.651	−0.00415499	−0.00207749	+	0.999998i	$0.500661\pi$
$882$	−39314.9	−1.50091
$883$	−19622.4	−0.747843	−0.373921	−	0.927460i	$-0.621987\pi$
$883$	−19622.4	−0.747843	−0.373921	+	0.927460i	$0.621987\pi$
$884$	11827.9	0.450017
$885$	−3619.64	−0.137483
$886$	−15255.5	−0.578462
$887$	26012.1	0.984668	0.492334	−	0.870406i	$-0.336144\pi$
$887$	26012.1	0.984668	0.492334	+	0.870406i	$0.336144\pi$
$888$	11500.6	0.434612
$889$	−58237.6	−2.19710
$890$	−3460.74	−0.130342
$891$	−57386.2	−2.15770
$892$	11732.5	0.440397
$893$	−6290.17	−0.235714
$894$	37060.1	1.38644
$895$	7952.40	0.297005
$896$	18434.3	0.687327
$897$	−2237.60	−0.0832902
$898$	−12549.9	−0.466365
$899$	−10072.0	−0.373660
$900$	33641.8	1.24599
$901$	−7047.01	−0.260566
$902$	9716.78	0.358684
$903$	0	0
$904$	−19915.0	−0.732702
$905$	−8995.70	−0.330417
$906$	23711.6	0.869498
$907$	−42258.2	−1.54703	−0.773517	−	0.633776i	$-0.781504\pi$
$907$	−42258.2	−1.54703	−0.773517	+	0.633776i	$0.781504\pi$
$908$	16613.5	0.607200
$909$	32441.2	1.18372
$910$	12865.3	0.468661
$911$	−6717.75	−0.244313	−0.122156	−	0.992511i	$-0.538981\pi$
$911$	−6717.75	−0.244313	−0.122156	+	0.992511i	$0.538981\pi$
$912$	3512.50	0.127533
$913$	53552.4	1.94121
$914$	7399.49	0.267783
$915$	12564.4	0.453954
$916$	−5298.78	−0.191132
$917$	53486.9	1.92616
$918$	−18288.6	−0.657532
$919$	46824.2	1.68073	0.840364	−	0.542023i	$-0.182341\pi$
$919$	46824.2	1.68073	0.840364	+	0.542023i	$0.182341\pi$
$920$	−182.509	−0.00654036
$921$	−15001.5	−0.536717
$922$	−2151.44	−0.0768479
$923$	−73138.7	−2.60822
$924$	−41841.3	−1.48969
$925$	6046.21	0.214917
$926$	4743.14	0.168325
$927$	43583.7	1.54420
$928$	30318.7	1.07248
$929$	−14300.0	−0.505025	−0.252513	−	0.967594i	$-0.581257\pi$
$929$	−14300.0	−0.505025	−0.252513	+	0.967594i	$0.581257\pi$
$930$	−3032.60	−0.106928
$931$	19823.7	0.697848
$932$	2420.41	0.0850679
$933$	53220.8	1.86749
$934$	−14143.4	−0.495489
$935$	−3165.73	−0.110728
$936$	131572.	4.59462
$937$	−44630.3	−1.55604	−0.778019	−	0.628241i	$-0.783775\pi$
$937$	−44630.3	−1.55604	−0.778019	+	0.628241i	$0.783775\pi$
$938$	5679.56	0.197702
$939$	32571.8	1.13199
$940$	−1461.43	−0.0507092
$941$	−12069.3	−0.418116	−0.209058	−	0.977903i	$-0.567040\pi$
$941$	−12069.3	−0.418116	−0.209058	+	0.977903i	$0.567040\pi$
$942$	26426.3	0.914028
$943$	375.511	0.0129675
$944$	802.970	0.0276848
$945$	26719.7	0.919781
$946$	0	0
$947$	23634.0	0.810984	0.405492	−	0.914099i	$-0.367100\pi$
$947$	23634.0	0.810984	0.405492	+	0.914099i	$0.367100\pi$
$948$	16451.8	0.563640
$949$	55602.0	1.90192
$950$	12629.0	0.431304
$951$	−42668.0	−1.45489
$952$	−17464.4	−0.594564
$953$	31376.9	1.06652	0.533262	−	0.845950i	$-0.320966\pi$
$953$	31376.9	1.06652	0.533262	+	0.845950i	$0.320966\pi$
$954$	−28562.6	−0.969339
$955$	4214.67	0.142810
$956$	6151.50	0.208110
$957$	−60826.2	−2.05458
$958$	16175.5	0.545518
$959$	−67643.6	−2.27771
$960$	10552.4	0.354767
$961$	−26433.1	−0.887284
$962$	8615.98	0.288763
$963$	20263.8	0.678080
$964$	−17146.2	−0.572865
$965$	3717.93	0.124025
$966$	1203.83	0.0400960
$967$	32665.7	1.08631	0.543154	−	0.839633i	$-0.317230\pi$
$967$	32665.7	1.08631	0.543154	+	0.839633i	$0.317230\pi$
$968$	627.137	0.0208233
$969$	16102.7	0.533842
$970$	−4503.22	−0.149062
$971$	−41567.8	−1.37381	−0.686907	−	0.726745i	$-0.741032\pi$
$971$	−41567.8	−1.37381	−0.686907	+	0.726745i	$0.741032\pi$
$972$	25271.7	0.833940
$973$	29733.6	0.979665
$974$	17380.6	0.571776
$975$	98729.6	3.24295
$976$	−2787.26	−0.0914119
$977$	−25363.2	−0.830542	−0.415271	−	0.909698i	$-0.636313\pi$
$977$	−25363.2	−0.830542	−0.415271	+	0.909698i	$0.636313\pi$
$978$	22079.5	0.721907
$979$	23141.9	0.755484
$980$	4605.77	0.150128
$981$	−106877.	−3.47841
$982$	11755.7	0.382014
$983$	3961.23	0.128528	0.0642642	−	0.997933i	$-0.479530\pi$
$983$	3961.23	0.128528	0.0642642	+	0.997933i	$0.479530\pi$
$984$	−31515.6	−1.02102
$985$	14707.0	0.475740
$986$	−9250.76	−0.298787
$987$	26456.0	0.853196
$988$	−24172.9	−0.778384
$989$	0	0
$990$	−12831.2	−0.411922
$991$	−27940.2	−0.895610	−0.447805	−	0.894131i	$-0.647794\pi$
$991$	−27940.2	−0.895610	−0.447805	+	0.894131i	$0.647794\pi$
$992$	−10108.0	−0.323518
$993$	42106.4	1.34563
$994$	39348.8	1.25560
$995$	1647.69	0.0524978
$996$	−63287.7	−2.01340
$997$	15531.3	0.493363	0.246681	−	0.969097i	$-0.420660\pi$
$997$	15531.3	0.493363	0.246681	+	0.969097i	$0.420660\pi$
$998$	21387.2	0.678357
$999$	17894.4	0.566719

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.4.a.c.1.3		6
43.42	odd	2		43.4.a.b.1.4	✓	6
129.128	even	2		387.4.a.h.1.3		6
172.171	even	2		688.4.a.i.1.1		6
215.214	odd	2		1075.4.a.b.1.3		6
301.300	even	2		2107.4.a.c.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.4.a.b.1.4	✓	6	43.42	odd	2
387.4.a.h.1.3		6	129.128	even	2
688.4.a.i.1.1		6	172.171	even	2
1075.4.a.b.1.3		6	215.214	odd	2
1849.4.a.c.1.3		6	1.1	even	1	trivial
2107.4.a.c.1.4		6	301.300	even	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:	\( N \)	\(=\)	\( 1849 = 43^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1849.a (trivial)

\(f(q)\)	\(=\)	\(q-1.84774 q^{2} -9.49653 q^{3} -4.58586 q^{4} -2.98245 q^{5} +17.5471 q^{6} +26.0720 q^{7} +23.2554 q^{8} +63.1842 q^{9} +O(q^{10})\)	\(q-1.84774 q^{2} -9.49653 q^{3} -4.58586 q^{4} -2.98245 q^{5} +17.5471 q^{6} +26.0720 q^{7} +23.2554 q^{8} +63.1842 q^{9} +5.51080 q^{10} -36.8506 q^{11} +43.5497 q^{12} +89.5430 q^{13} -48.1743 q^{14} +28.3230 q^{15} -6.28309 q^{16} -28.8042 q^{17} -116.748 q^{18} +58.8677 q^{19} +13.6771 q^{20} -247.594 q^{21} +68.0904 q^{22} +2.63139 q^{23} -220.846 q^{24} -116.105 q^{25} -165.452 q^{26} -343.624 q^{27} -119.563 q^{28} -173.812 q^{29} -52.3335 q^{30} +57.9476 q^{31} -174.434 q^{32} +349.953 q^{33} +53.2227 q^{34} -77.7586 q^{35} -289.753 q^{36} -52.0754 q^{37} -108.772 q^{38} -850.348 q^{39} -69.3581 q^{40} +142.704 q^{41} +457.489 q^{42} +168.992 q^{44} -188.444 q^{45} -4.86213 q^{46} -106.853 q^{47} +59.6676 q^{48} +336.750 q^{49} +214.532 q^{50} +273.540 q^{51} -410.631 q^{52} +244.652 q^{53} +634.928 q^{54} +109.905 q^{55} +606.315 q^{56} -559.039 q^{57} +321.160 q^{58} -127.799 q^{59} -129.885 q^{60} +443.613 q^{61} -107.072 q^{62} +1647.34 q^{63} +372.573 q^{64} -267.058 q^{65} -646.622 q^{66} -117.896 q^{67} +132.092 q^{68} -24.9891 q^{69} +143.678 q^{70} -816.799 q^{71} +1469.37 q^{72} +620.953 q^{73} +96.2217 q^{74} +1102.59 q^{75} -269.959 q^{76} -960.770 q^{77} +1571.22 q^{78} +377.771 q^{79} +18.7390 q^{80} +1557.27 q^{81} -263.680 q^{82} -1453.23 q^{83} +1135.43 q^{84} +85.9072 q^{85} +1650.62 q^{87} -856.975 q^{88} -627.993 q^{89} +348.195 q^{90} +2334.57 q^{91} -12.0672 q^{92} -550.302 q^{93} +197.436 q^{94} -175.570 q^{95} +1656.52 q^{96} -817.163 q^{97} -622.227 q^{98} -2328.38 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} - 7 q^{3} + 22 q^{4} - 43 q^{5} - 3 q^{6} - 8 q^{7} - 54 q^{8} + 81 q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 - 7 * q^3 + 22 * q^4 - 43 * q^5 - 3 * q^6 - 8 * q^7 - 54 * q^8 + 81 * q^9	\( 6 q - 6 q^{2} - 7 q^{3} + 22 q^{4} - 43 q^{5} - 3 q^{6} - 8 q^{7} - 54 q^{8} + 81 q^{9} + 57 q^{10} - 28 q^{11} + 157 q^{12} + 56 q^{13} - 184 q^{14} - 124 q^{15} - 54 q^{16} + 19 q^{17} + 81 q^{18} + 75 q^{19} - 135 q^{20} - 18 q^{21} + 504 q^{22} + 131 q^{23} - 567 q^{24} + 105 q^{25} - 44 q^{26} - 238 q^{27} + 404 q^{28} - 515 q^{29} + 396 q^{30} + 237 q^{31} - 558 q^{32} - 540 q^{33} + 107 q^{34} + 198 q^{35} + 73 q^{36} - 269 q^{37} + 527 q^{38} - 290 q^{39} + 613 q^{40} + 471 q^{41} - 362 q^{42} - 428 q^{44} - 334 q^{45} + 67 q^{46} + 415 q^{47} + 989 q^{48} + 350 q^{49} - 1335 q^{50} + 1241 q^{51} - 8 q^{52} + 450 q^{53} + 402 q^{54} + 1732 q^{55} - 780 q^{56} - 1000 q^{57} - 1055 q^{58} + 356 q^{59} - 2732 q^{60} + 1328 q^{61} - 1603 q^{62} + 2290 q^{63} + 466 q^{64} + 62 q^{65} + 156 q^{66} - 632 q^{67} + 571 q^{68} + 1130 q^{69} + 1902 q^{70} + 144 q^{71} - 567 q^{72} - 864 q^{73} + 1207 q^{74} + 2494 q^{75} - 1005 q^{76} - 2660 q^{77} + 2222 q^{78} - 1613 q^{79} - 2399 q^{80} - 102 q^{81} - 1673 q^{82} - 682 q^{83} + 3758 q^{84} - 84 q^{85} + 449 q^{87} + 608 q^{88} - 3378 q^{89} + 930 q^{90} + 3900 q^{91} + 3491 q^{92} - 1879 q^{93} - 3197 q^{94} - 79 q^{95} - 591 q^{96} - 55 q^{97} - 2398 q^{98} - 1612 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 - 7 * q^3 + 22 * q^4 - 43 * q^5 - 3 * q^6 - 8 * q^7 - 54 * q^8 + 81 * q^9 + 57 * q^10 - 28 * q^11 + 157 * q^12 + 56 * q^13 - 184 * q^14 - 124 * q^15 - 54 * q^16 + 19 * q^17 + 81 * q^18 + 75 * q^19 - 135 * q^20 - 18 * q^21 + 504 * q^22 + 131 * q^23 - 567 * q^24 + 105 * q^25 - 44 * q^26 - 238 * q^27 + 404 * q^28 - 515 * q^29 + 396 * q^30 + 237 * q^31 - 558 * q^32 - 540 * q^33 + 107 * q^34 + 198 * q^35 + 73 * q^36 - 269 * q^37 + 527 * q^38 - 290 * q^39 + 613 * q^40 + 471 * q^41 - 362 * q^42 - 428 * q^44 - 334 * q^45 + 67 * q^46 + 415 * q^47 + 989 * q^48 + 350 * q^49 - 1335 * q^50 + 1241 * q^51 - 8 * q^52 + 450 * q^53 + 402 * q^54 + 1732 * q^55 - 780 * q^56 - 1000 * q^57 - 1055 * q^58 + 356 * q^59 - 2732 * q^60 + 1328 * q^61 - 1603 * q^62 + 2290 * q^63 + 466 * q^64 + 62 * q^65 + 156 * q^66 - 632 * q^67 + 571 * q^68 + 1130 * q^69 + 1902 * q^70 + 144 * q^71 - 567 * q^72 - 864 * q^73 + 1207 * q^74 + 2494 * q^75 - 1005 * q^76 - 2660 * q^77 + 2222 * q^78 - 1613 * q^79 - 2399 * q^80 - 102 * q^81 - 1673 * q^82 - 682 * q^83 + 3758 * q^84 - 84 * q^85 + 449 * q^87 + 608 * q^88 - 3378 * q^89 + 930 * q^90 + 3900 * q^91 + 3491 * q^92 - 1879 * q^93 - 3197 * q^94 - 79 * q^95 - 591 * q^96 - 55 * q^97 - 2398 * q^98 - 1612 * q^99

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