LMFDB - Embedded newform 1859.4.a.e.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1859,4,Mod(1,1859)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1859, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1859.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1859 = 11 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1859.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:	$109.684550701$
Analytic rank:	$0$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 5 x^{10} - 64 x^{9} + 268 x^{8} + 1564 x^{7} - 4963 x^{6} - 16942 x^{5} + 37082 x^{4} + \cdots + 16256 $ x^11 - 5x^10 - 64x^9 + 268x^8 + 1564x^7 - 4963x^6 - 16942x^5 + 37082x^4 + 68209x^3 - 90926x^2 - 1672x + 16256
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 143)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$0.636678$ of defining polynomial
Character	$\chi$	$=$	1859.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.363322 q^{2} -3.74669 q^{3} -7.86800 q^{4} +11.8947 q^{5} +1.36126 q^{6} -28.3874 q^{7} +5.76520 q^{8} -12.9623 q^{9} +O(q^{10})$	\(q-0.363322 q^{2} -3.74669 q^{3} -7.86800 q^{4} +11.8947 q^{5} +1.36126 q^{6} -28.3874 q^{7} +5.76520 q^{8} -12.9623 q^{9} -4.32160 q^{10} -11.0000 q^{11} +29.4790 q^{12} +10.3138 q^{14} -44.5657 q^{15} +60.8493 q^{16} +31.9666 q^{17} +4.70949 q^{18} -154.215 q^{19} -93.5873 q^{20} +106.359 q^{21} +3.99655 q^{22} +4.80697 q^{23} -21.6004 q^{24} +16.4834 q^{25} +149.726 q^{27} +223.352 q^{28} -274.030 q^{29} +16.1917 q^{30} -175.091 q^{31} -68.2295 q^{32} +41.2136 q^{33} -11.6142 q^{34} -337.659 q^{35} +101.987 q^{36} +64.1558 q^{37} +56.0299 q^{38} +68.5752 q^{40} -382.900 q^{41} -38.6426 q^{42} -37.7710 q^{43} +86.5480 q^{44} -154.182 q^{45} -1.74648 q^{46} -43.7152 q^{47} -227.984 q^{48} +462.847 q^{49} -5.98878 q^{50} -119.769 q^{51} -92.8216 q^{53} -54.3990 q^{54} -130.841 q^{55} -163.659 q^{56} +577.798 q^{57} +99.5614 q^{58} -64.9423 q^{59} +350.643 q^{60} -404.578 q^{61} +63.6144 q^{62} +367.967 q^{63} -462.005 q^{64} -14.9738 q^{66} -965.646 q^{67} -251.513 q^{68} -18.0102 q^{69} +122.679 q^{70} -901.051 q^{71} -74.7302 q^{72} -152.959 q^{73} -23.3093 q^{74} -61.7582 q^{75} +1213.37 q^{76} +312.262 q^{77} +682.974 q^{79} +723.783 q^{80} -210.997 q^{81} +139.116 q^{82} +481.122 q^{83} -836.832 q^{84} +380.232 q^{85} +13.7230 q^{86} +1026.71 q^{87} -63.4172 q^{88} -1139.40 q^{89} +56.0179 q^{90} -37.8212 q^{92} +656.011 q^{93} +15.8827 q^{94} -1834.34 q^{95} +255.635 q^{96} +744.462 q^{97} -168.163 q^{98} +142.585 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - 6 q^{2} + 6 q^{3} + 66 q^{4} + 4 q^{5} + 14 q^{6} - 45 q^{7} - 78 q^{8} + 135 q^{9}+O(q^{10}) $ 11 * q - 6 * q^2 + 6 * q^3 + 66 * q^4 + 4 * q^5 + 14 * q^6 - 45 * q^7 - 78 * q^8 + 135 * q^9	\( 11 q - 6 q^{2} + 6 q^{3} + 66 q^{4} + 4 q^{5} + 14 q^{6} - 45 q^{7} - 78 q^{8} + 135 q^{9} + 48 q^{10} - 121 q^{11} + 105 q^{12} - 48 q^{14} + 125 q^{15} + 394 q^{16} + 265 q^{17} - 405 q^{18} - 127 q^{19} + 46 q^{20} + 287 q^{21} + 66 q^{22} + 42 q^{23} + 83 q^{24} + 737 q^{25} + 69 q^{27} - 675 q^{28} + 435 q^{29} + 785 q^{30} + 174 q^{31} - 315 q^{32} - 66 q^{33} - 497 q^{34} + 844 q^{35} + 1572 q^{36} - 187 q^{37} - 1813 q^{38} - 1470 q^{40} - 128 q^{41} - 2630 q^{42} + 696 q^{43} - 726 q^{44} + 1537 q^{45} - 785 q^{46} + 355 q^{47} - 516 q^{48} + 1758 q^{49} + 3414 q^{50} - 25 q^{51} - 693 q^{53} + 4150 q^{54} - 44 q^{55} - 3123 q^{56} - 99 q^{57} + 287 q^{58} + 609 q^{59} + 5013 q^{60} + 1625 q^{61} - 882 q^{62} - 1365 q^{63} - 914 q^{64} - 154 q^{66} - 633 q^{67} + 2873 q^{68} - 2192 q^{69} + 2054 q^{70} + 1937 q^{71} - 3242 q^{72} - 404 q^{73} - 447 q^{74} + 1781 q^{75} + 1814 q^{76} + 495 q^{77} + 1670 q^{79} + 1568 q^{80} + 2619 q^{81} + 1283 q^{82} - 785 q^{83} + 11750 q^{84} - 3189 q^{85} + 5950 q^{86} + 46 q^{87} + 858 q^{88} - 1464 q^{89} + 401 q^{90} - 3786 q^{92} - 1826 q^{93} - 2597 q^{94} - 2356 q^{95} - 4513 q^{96} - 1184 q^{97} - 2823 q^{98} - 1485 q^{99}+O(q^{100}) \) 11 * q - 6 * q^2 + 6 * q^3 + 66 * q^4 + 4 * q^5 + 14 * q^6 - 45 * q^7 - 78 * q^8 + 135 * q^9 + 48 * q^10 - 121 * q^11 + 105 * q^12 - 48 * q^14 + 125 * q^15 + 394 * q^16 + 265 * q^17 - 405 * q^18 - 127 * q^19 + 46 * q^20 + 287 * q^21 + 66 * q^22 + 42 * q^23 + 83 * q^24 + 737 * q^25 + 69 * q^27 - 675 * q^28 + 435 * q^29 + 785 * q^30 + 174 * q^31 - 315 * q^32 - 66 * q^33 - 497 * q^34 + 844 * q^35 + 1572 * q^36 - 187 * q^37 - 1813 * q^38 - 1470 * q^40 - 128 * q^41 - 2630 * q^42 + 696 * q^43 - 726 * q^44 + 1537 * q^45 - 785 * q^46 + 355 * q^47 - 516 * q^48 + 1758 * q^49 + 3414 * q^50 - 25 * q^51 - 693 * q^53 + 4150 * q^54 - 44 * q^55 - 3123 * q^56 - 99 * q^57 + 287 * q^58 + 609 * q^59 + 5013 * q^60 + 1625 * q^61 - 882 * q^62 - 1365 * q^63 - 914 * q^64 - 154 * q^66 - 633 * q^67 + 2873 * q^68 - 2192 * q^69 + 2054 * q^70 + 1937 * q^71 - 3242 * q^72 - 404 * q^73 - 447 * q^74 + 1781 * q^75 + 1814 * q^76 + 495 * q^77 + 1670 * q^79 + 1568 * q^80 + 2619 * q^81 + 1283 * q^82 - 785 * q^83 + 11750 * q^84 - 3189 * q^85 + 5950 * q^86 + 46 * q^87 + 858 * q^88 - 1464 * q^89 + 401 * q^90 - 3786 * q^92 - 1826 * q^93 - 2597 * q^94 - 2356 * q^95 - 4513 * q^96 - 1184 * q^97 - 2823 * q^98 - 1485 * 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 $

$2$	−0.363322	−0.128454	−0.0642269	−	0.997935i	$-0.520458\pi$
$2$	−0.363322	−0.128454	−0.0642269	+	0.997935i	$0.520458\pi$
$3$	−3.74669	−0.721051	−0.360526	−	0.932749i	$-0.617403\pi$
$3$	−3.74669	−0.721051	−0.360526	+	0.932749i	$0.617403\pi$
$4$	−7.86800	−0.983500
$5$	11.8947	1.06389	0.531946	−	0.846778i	$-0.321461\pi$
$5$	11.8947	1.06389	0.531946	+	0.846778i	$0.321461\pi$
$6$	1.36126	0.0926218
$7$	−28.3874	−1.53278	−0.766389	−	0.642377i	$-0.777948\pi$
$7$	−28.3874	−1.53278	−0.766389	+	0.642377i	$0.777948\pi$
$8$	5.76520	0.254788
$9$	−12.9623	−0.480085
$10$	−4.32160	−0.136661
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	29.4790	0.709154
$13$	0	0
$13$	0	0
$14$	10.3138	0.196891
$15$	−44.5657	−0.767121
$16$	60.8493	0.950771
$17$	31.9666	0.456061	0.228030	−	0.973654i	$-0.426771\pi$
$17$	31.9666	0.456061	0.228030	+	0.973654i	$0.426771\pi$
$18$	4.70949	0.0616688
$19$	−154.215	−1.86208	−0.931038	−	0.364922i	$-0.881096\pi$
$19$	−154.215	−1.86208	−0.931038	+	0.364922i	$0.881096\pi$
$20$	−93.5873	−1.04634
$21$	106.359	1.10521
$22$	3.99655	0.0387303
$23$	4.80697	0.0435792	0.0217896	−	0.999763i	$-0.493064\pi$
$23$	4.80697	0.0435792	0.0217896	+	0.999763i	$0.493064\pi$
$24$	−21.6004	−0.183715
$25$	16.4834	0.131867
$26$	0	0
$27$	149.726	1.06722
$28$	223.352	1.50749
$29$	−274.030	−1.75470	−0.877348	−	0.479855i	$-0.840689\pi$
$29$	−274.030	−1.75470	−0.877348	+	0.479855i	$0.840689\pi$
$30$	16.1917	0.0985396
$31$	−175.091	−1.01443	−0.507213	−	0.861821i	$-0.669324\pi$
$31$	−175.091	−1.01443	−0.507213	+	0.861821i	$0.669324\pi$
$32$	−68.2295	−0.376918
$33$	41.2136	0.217405
$34$	−11.6142	−0.0585827
$35$	−337.659	−1.63071
$36$	101.987	0.472164
$37$	64.1558	0.285058	0.142529	−	0.989791i	$-0.454477\pi$
$37$	64.1558	0.285058	0.142529	+	0.989791i	$0.454477\pi$
$38$	56.0299	0.239191
$39$	0	0
$40$	68.5752	0.271067
$41$	−382.900	−1.45851	−0.729256	−	0.684241i	$-0.760134\pi$
$41$	−382.900	−1.45851	−0.729256	+	0.684241i	$0.760134\pi$
$42$	−38.6426	−0.141969
$43$	−37.7710	−0.133954	−0.0669770	−	0.997755i	$-0.521335\pi$
$43$	−37.7710	−0.133954	−0.0669770	+	0.997755i	$0.521335\pi$
$44$	86.5480	0.296536
$45$	−154.182	−0.510759
$46$	−1.74648	−0.00559792
$47$	−43.7152	−0.135671	−0.0678353	−	0.997697i	$-0.521609\pi$
$47$	−43.7152	−0.135671	−0.0678353	+	0.997697i	$0.521609\pi$
$48$	−227.984	−0.685555
$49$	462.847	1.34941
$50$	−5.98878	−0.0169388
$51$	−119.769	−0.328843
$52$	0	0
$53$	−92.8216	−0.240567	−0.120283	−	0.992740i	$-0.538380\pi$
$53$	−92.8216	−0.240567	−0.120283	+	0.992740i	$0.538380\pi$
$54$	−54.3990	−0.137088
$55$	−130.841	−0.320776
$56$	−163.659	−0.390534
$57$	577.798	1.34265
$58$	99.5614	0.225397
$59$	−64.9423	−0.143301	−0.0716505	−	0.997430i	$-0.522827\pi$
$59$	−64.9423	−0.143301	−0.0716505	+	0.997430i	$0.522827\pi$
$60$	350.643	0.754463
$61$	−404.578	−0.849195	−0.424597	−	0.905382i	$-0.639584\pi$
$61$	−404.578	−0.849195	−0.424597	+	0.905382i	$0.639584\pi$
$62$	63.6144	0.130307
$63$	367.967	0.735864
$64$	−462.005	−0.902354
$65$	0	0
$66$	−14.9738	−0.0279265
$67$	−965.646	−1.76078	−0.880392	−	0.474247i	$-0.842720\pi$
$67$	−965.646	−1.76078	−0.880392	+	0.474247i	$0.842720\pi$
$68$	−251.513	−0.448535
$69$	−18.0102	−0.0314228
$70$	122.679	0.209471
$71$	−901.051	−1.50613	−0.753064	−	0.657947i	$-0.771425\pi$
$71$	−901.051	−1.50613	−0.753064	+	0.657947i	$0.771425\pi$
$72$	−74.7302	−0.122320
$73$	−152.959	−0.245240	−0.122620	−	0.992454i	$-0.539130\pi$
$73$	−152.959	−0.245240	−0.122620	+	0.992454i	$0.539130\pi$
$74$	−23.3093	−0.0366168
$75$	−61.7582	−0.0950829
$76$	1213.37	1.83135
$77$	312.262	0.462150
$78$	0	0
$79$	682.974	0.972666	0.486333	−	0.873774i	$-0.338334\pi$
$79$	682.974	0.972666	0.486333	+	0.873774i	$0.338334\pi$
$80$	723.783	1.01152
$81$	−210.997	−0.289433
$82$	139.116	0.187351
$83$	481.122	0.636265	0.318132	−	0.948046i	$-0.396944\pi$
$83$	481.122	0.636265	0.318132	+	0.948046i	$0.396944\pi$
$84$	−836.832	−1.08697
$85$	380.232	0.485199
$86$	13.7230	0.0172069
$87$	1026.71	1.26523
$88$	−63.4172	−0.0768215
$89$	−1139.40	−1.35703	−0.678517	−	0.734585i	$-0.737377\pi$
$89$	−1139.40	−1.35703	−0.678517	+	0.734585i	$0.737377\pi$
$90$	56.0179	0.0656090
$91$	0	0
$92$	−37.8212	−0.0428601
$93$	656.011	0.731453
$94$	15.8827	0.0174274
$95$	−1834.34	−1.98105
$96$	255.635	0.271777
$97$	744.462	0.779265	0.389633	−	0.920970i	$-0.372602\pi$
$97$	744.462	0.779265	0.389633	+	0.920970i	$0.372602\pi$
$98$	−168.163	−0.173337
$99$	142.585	0.144751
$100$	−129.691	−0.129691
$101$	409.268	0.403205	0.201602	−	0.979467i	$-0.435385\pi$
$101$	409.268	0.403205	0.201602	+	0.979467i	$0.435385\pi$
$102$	43.5147	0.0422412
$103$	−2080.38	−1.99015	−0.995075	−	0.0991217i	$-0.968397\pi$
$103$	−2080.38	−1.99015	−0.995075	+	0.0991217i	$0.968397\pi$
$104$	0	0
$105$	1265.11	1.17583
$106$	33.7242	0.0309017
$107$	588.280	0.531506	0.265753	−	0.964041i	$-0.414379\pi$
$107$	588.280	0.531506	0.265753	+	0.964041i	$0.414379\pi$
$108$	−1178.05	−1.04961
$109$	−1850.42	−1.62604	−0.813020	−	0.582236i	$-0.802178\pi$
$109$	−1850.42	−1.62604	−0.813020	+	0.582236i	$0.802178\pi$
$110$	47.5376	0.0412049
$111$	−240.372	−0.205542
$112$	−1727.36	−1.45732
$113$	292.249	0.243297	0.121648	−	0.992573i	$-0.461182\pi$
$113$	292.249	0.243297	0.121648	+	0.992573i	$0.461182\pi$
$114$	−209.927	−0.172469
$115$	57.1773	0.0463636
$116$	2156.07	1.72574
$117$	0	0
$118$	23.5950	0.0184076
$119$	−907.449	−0.699040
$120$	−256.930	−0.195453
$121$	121.000	0.0909091
$122$	146.992	0.109082
$123$	1434.61	1.05166
$124$	1377.61	0.997688
$125$	−1290.77	−0.923600
$126$	−133.690	−0.0945246
$127$	2311.94	1.61537	0.807684	−	0.589616i	$-0.200721\pi$
$127$	2311.94	1.61537	0.807684	+	0.589616i	$0.200721\pi$
$128$	713.693	0.492829
$129$	141.516	0.0965876
$130$	0	0
$131$	−1197.49	−0.798667	−0.399333	−	0.916806i	$-0.630758\pi$
$131$	−1197.49	−0.798667	−0.399333	+	0.916806i	$0.630758\pi$
$132$	−324.269	−0.213818
$133$	4377.78	2.85415
$134$	350.841	0.226179
$135$	1780.95	1.13540
$136$	184.294	0.116199
$137$	783.478	0.488592	0.244296	−	0.969701i	$-0.421443\pi$
$137$	783.478	0.488592	0.244296	+	0.969701i	$0.421443\pi$
$138$	6.54352	0.00403639
$139$	−186.597	−0.113863	−0.0569315	−	0.998378i	$-0.518132\pi$
$139$	−186.597	−0.113863	−0.0569315	+	0.998378i	$0.518132\pi$
$140$	2656.70	1.60380
$141$	163.787	0.0978254
$142$	327.372	0.193468
$143$	0	0
$144$	−788.748	−0.456451
$145$	−3259.50	−1.86681
$146$	55.5736	0.0315021
$147$	−1734.14	−0.972992
$148$	−504.778	−0.280355
$149$	2766.82	1.52126	0.760628	−	0.649188i	$-0.224891\pi$
$149$	2766.82	1.52126	0.760628	+	0.649188i	$0.224891\pi$
$150$	22.4381	0.0122138
$151$	−1911.61	−1.03023	−0.515114	−	0.857122i	$-0.672250\pi$
$151$	−1911.61	−1.03023	−0.515114	+	0.857122i	$0.672250\pi$
$152$	−889.083	−0.474435
$153$	−414.360	−0.218948
$154$	−113.452	−0.0593649
$155$	−2082.65	−1.07924
$156$	0	0
$157$	1556.40	0.791173	0.395587	−	0.918429i	$-0.370541\pi$
$157$	1556.40	0.791173	0.395587	+	0.918429i	$0.370541\pi$
$158$	−248.140	−0.124943
$159$	347.774	0.173461
$160$	−811.568	−0.401001
$161$	−136.457	−0.0667972
$162$	76.6598	0.0371788
$163$	−1815.39	−0.872347	−0.436173	−	0.899863i	$-0.643667\pi$
$163$	−1815.39	−0.872347	−0.436173	+	0.899863i	$0.643667\pi$
$164$	3012.66	1.43445
$165$	490.223	0.231296
$166$	−174.802	−0.0817307
$167$	2276.24	1.05473	0.527367	−	0.849637i	$-0.323179\pi$
$167$	2276.24	1.05473	0.527367	+	0.849637i	$0.323179\pi$
$168$	613.181	0.281595
$169$	0	0
$170$	−138.147	−0.0623257
$171$	1998.99	0.893955
$172$	297.182	0.131744
$173$	40.8719	0.0179620	0.00898102	−	0.999960i	$-0.497141\pi$
$173$	40.8719	0.0179620	0.00898102	+	0.999960i	$0.497141\pi$
$174$	−373.026	−0.162523
$175$	−467.921	−0.202123
$176$	−669.343	−0.286668
$177$	243.319	0.103327
$178$	413.969	0.174316
$179$	−2065.38	−0.862423	−0.431212	−	0.902251i	$-0.641914\pi$
$179$	−2065.38	−0.862423	−0.431212	+	0.902251i	$0.641914\pi$
$180$	1213.11	0.502331
$181$	−121.589	−0.0499318	−0.0249659	−	0.999688i	$-0.507948\pi$
$181$	−121.589	−0.0499318	−0.0249659	+	0.999688i	$0.507948\pi$
$182$	0	0
$183$	1515.83	0.612313
$184$	27.7131	0.0111035
$185$	763.113	0.303271
$186$	−238.343	−0.0939580
$187$	−351.632	−0.137507
$188$	343.951	0.133432
$189$	−4250.35	−1.63581
$190$	666.458	0.254473
$191$	−3003.61	−1.13787	−0.568937	−	0.822381i	$-0.692645\pi$
$191$	−3003.61	−1.13787	−0.568937	+	0.822381i	$0.692645\pi$
$192$	1730.99	0.650644
$193$	−1185.54	−0.442162	−0.221081	−	0.975255i	$-0.570959\pi$
$193$	−1185.54	−0.442162	−0.221081	+	0.975255i	$0.570959\pi$
$194$	−270.480	−0.100100
$195$	0	0
$196$	−3641.68	−1.32714
$197$	−543.263	−0.196477	−0.0982383	−	0.995163i	$-0.531321\pi$
$197$	−543.263	−0.196477	−0.0982383	+	0.995163i	$0.531321\pi$
$198$	−51.8044	−0.0185938
$199$	−2260.62	−0.805282	−0.402641	−	0.915358i	$-0.631908\pi$
$199$	−2260.62	−0.805282	−0.402641	+	0.915358i	$0.631908\pi$
$200$	95.0300	0.0335982
$201$	3617.98	1.26961
$202$	−148.696	−0.0517932
$203$	7779.02	2.68956
$204$	942.341	0.323417
$205$	−4554.48	−1.55170
$206$	755.847	0.255643
$207$	−62.3093	−0.0209217
$208$	0	0
$209$	1696.37	0.561437
$210$	−459.641	−0.151039
$211$	−3690.46	−1.20408	−0.602041	−	0.798465i	$-0.705646\pi$
$211$	−3690.46	−1.20408	−0.602041	+	0.798465i	$0.705646\pi$
$212$	730.320	0.236597
$213$	3375.96	1.08600
$214$	−213.735	−0.0682740
$215$	−449.273	−0.142513
$216$	863.203	0.271914
$217$	4970.38	1.55489
$218$	672.300	0.208871
$219$	573.092	0.176831
$220$	1029.46	0.315483
$221$	0	0
$222$	87.3326	0.0264026
$223$	−5221.05	−1.56783	−0.783917	−	0.620865i	$-0.786781\pi$
$223$	−5221.05	−1.56783	−0.783917	+	0.620865i	$0.786781\pi$
$224$	1936.86	0.577732
$225$	−213.663	−0.0633074
$226$	−106.181	−0.0312524
$227$	4888.47	1.42933	0.714667	−	0.699464i	$-0.246578\pi$
$227$	4888.47	1.42933	0.714667	+	0.699464i	$0.246578\pi$
$228$	−4546.11	−1.32050
$229$	2721.14	0.785230	0.392615	−	0.919703i	$-0.371570\pi$
$229$	2721.14	0.785230	0.392615	+	0.919703i	$0.371570\pi$
$230$	−20.7738	−0.00595558
$231$	−1169.95	−0.333234
$232$	−1579.84	−0.447076
$233$	−877.453	−0.246712	−0.123356	−	0.992362i	$-0.539366\pi$
$233$	−877.453	−0.246712	−0.123356	+	0.992362i	$0.539366\pi$
$234$	0	0
$235$	−519.978	−0.144339
$236$	510.966	0.140937
$237$	−2558.89	−0.701342
$238$	329.696	0.0897943
$239$	−2625.13	−0.710482	−0.355241	−	0.934775i	$-0.615601\pi$
$239$	−2625.13	−0.710482	−0.355241	+	0.934775i	$0.615601\pi$
$240$	−2711.79	−0.729356
$241$	2905.59	0.776619	0.388310	−	0.921529i	$-0.373059\pi$
$241$	2905.59	0.776619	0.388310	+	0.921529i	$0.373059\pi$
$242$	−43.9620	−0.0116776
$243$	−3252.07	−0.858521
$244$	3183.22	0.835183
$245$	5505.41	1.43562
$246$	−521.226	−0.135090
$247$	0	0
$248$	−1009.43	−0.258464
$249$	−1802.61	−0.458779
$250$	468.966	0.118640
$251$	−2349.12	−0.590738	−0.295369	−	0.955383i	$-0.595443\pi$
$251$	−2349.12	−0.590738	−0.295369	+	0.955383i	$0.595443\pi$
$252$	−2895.16	−0.723722
$253$	−52.8766	−0.0131396
$254$	−839.980	−0.207500
$255$	−1424.61	−0.349854
$256$	3436.74	0.839049
$257$	7392.13	1.79420	0.897099	−	0.441831i	$-0.145671\pi$
$257$	7392.13	1.79420	0.897099	+	0.441831i	$0.145671\pi$
$258$	−51.4160	−0.0124071
$259$	−1821.22	−0.436931
$260$	0	0
$261$	3552.06	0.842403
$262$	435.076	0.102592
$263$	6920.85	1.62265	0.811326	−	0.584594i	$-0.198746\pi$
$263$	6920.85	1.62265	0.811326	+	0.584594i	$0.198746\pi$
$264$	237.605	0.0553923
$265$	−1104.08	−0.255937
$266$	−1590.55	−0.366626
$267$	4268.97	0.978490
$268$	7597.70	1.73173
$269$	2656.19	0.602046	0.301023	−	0.953617i	$-0.402672\pi$
$269$	2656.19	0.602046	0.301023	+	0.953617i	$0.402672\pi$
$270$	−647.058	−0.145847
$271$	3661.35	0.820706	0.410353	−	0.911927i	$-0.365405\pi$
$271$	3661.35	0.820706	0.410353	+	0.911927i	$0.365405\pi$
$272$	1945.14	0.433609
$273$	0	0
$274$	−284.655	−0.0627615
$275$	−181.317	−0.0397594
$276$	141.704	0.0309043
$277$	−788.170	−0.170962	−0.0854812	−	0.996340i	$-0.527243\pi$
$277$	−788.170	−0.170962	−0.0854812	+	0.996340i	$0.527243\pi$
$278$	67.7949	0.0146261
$279$	2269.58	0.487011
$280$	−1946.67	−0.415486
$281$	7145.01	1.51685	0.758427	−	0.651759i	$-0.225968\pi$
$281$	7145.01	1.51685	0.758427	+	0.651759i	$0.225968\pi$
$282$	−59.5076	−0.0125660
$283$	5950.42	1.24988	0.624939	−	0.780673i	$-0.285124\pi$
$283$	5950.42	1.24988	0.624939	+	0.780673i	$0.285124\pi$
$284$	7089.47	1.48128
$285$	6872.72	1.42844
$286$	0	0
$287$	10869.6	2.23557
$288$	884.412	0.180953
$289$	−3891.14	−0.792009
$290$	1184.25	0.239799
$291$	−2789.27	−0.561890
$292$	1203.48	0.241194
$293$	6835.96	1.36301	0.681504	−	0.731815i	$-0.261326\pi$
$293$	6835.96	1.36301	0.681504	+	0.731815i	$0.261326\pi$
$294$	630.053	0.124985
$295$	−772.467	−0.152457
$296$	369.871	0.0726295
$297$	−1646.99	−0.321778
$298$	−1005.25	−0.195411
$299$	0	0
$300$	485.913	0.0935140
$301$	1072.22	0.205322
$302$	694.530	0.132337
$303$	−1533.40	−0.290731
$304$	−9383.91	−1.77041
$305$	−4812.32	−0.903452
$306$	150.546	0.0281247
$307$	−865.787	−0.160955	−0.0804773	−	0.996756i	$-0.525644\pi$
$307$	−865.787	−0.160955	−0.0804773	+	0.996756i	$0.525644\pi$
$308$	−2456.88	−0.454524
$309$	7794.53	1.43500
$310$	756.673	0.138633
$311$	3802.36	0.693287	0.346643	−	0.937997i	$-0.387321\pi$
$311$	3802.36	0.693287	0.346643	+	0.937997i	$0.387321\pi$
$312$	0	0
$313$	3257.28	0.588219	0.294109	−	0.955772i	$-0.404977\pi$
$313$	3257.28	0.588219	0.294109	+	0.955772i	$0.404977\pi$
$314$	−565.475	−0.101629
$315$	4376.84	0.782880
$316$	−5373.64	−0.956616
$317$	10989.0	1.94702	0.973508	−	0.228654i	$-0.0734325\pi$
$317$	10989.0	1.94702	0.973508	+	0.228654i	$0.0734325\pi$
$318$	−126.354	−0.0222817
$319$	3014.33	0.529061
$320$	−5495.41	−0.960008
$321$	−2204.10	−0.383243
$322$	49.5781	0.00858036
$323$	−4929.74	−0.849220
$324$	1660.12	0.284657
$325$	0	0
$326$	659.573	0.112056
$327$	6932.96	1.17246
$328$	−2207.50	−0.371612
$329$	1240.96	0.207953
$330$	−178.109	−0.0297108
$331$	−4409.82	−0.732283	−0.366141	−	0.930559i	$-0.619321\pi$
$331$	−4409.82	−0.732283	−0.366141	+	0.930559i	$0.619321\pi$
$332$	−3785.46	−0.625766
$333$	−831.607	−0.136852
$334$	−827.009	−0.135485
$335$	−11486.1	−1.87328
$336$	6471.87	1.05080
$337$	6490.56	1.04915	0.524575	−	0.851364i	$-0.324224\pi$
$337$	6490.56	1.04915	0.524575	+	0.851364i	$0.324224\pi$
$338$	0	0
$339$	−1094.97	−0.175429
$340$	−2991.66	−0.477193
$341$	1926.00	0.305861
$342$	−726.277	−0.114832
$343$	−3402.14	−0.535564
$344$	−217.757	−0.0341299
$345$	−214.226	−0.0334305
$346$	−14.8497	−0.00230729
$347$	11489.4	1.77747	0.888735	−	0.458422i	$-0.151585\pi$
$347$	11489.4	1.77747	0.888735	+	0.458422i	$0.151585\pi$
$348$	−8078.13	−1.24435
$349$	1432.81	0.219760	0.109880	−	0.993945i	$-0.464953\pi$
$349$	1432.81	0.219760	0.109880	+	0.993945i	$0.464953\pi$
$350$	170.006	0.0259635
$351$	0	0
$352$	750.525	0.113645
$353$	−11381.9	−1.71614	−0.858069	−	0.513534i	$-0.828336\pi$
$353$	−11381.9	−1.71614	−0.858069	+	0.513534i	$0.828336\pi$
$354$	−88.4031	−0.0132728
$355$	−10717.7	−1.60236
$356$	8964.78	1.33464
$357$	3399.93	0.504043
$358$	750.399	0.110782
$359$	5527.86	0.812673	0.406336	−	0.913724i	$-0.366806\pi$
$359$	5527.86	0.812673	0.406336	+	0.913724i	$0.366806\pi$
$360$	−888.892	−0.130135
$361$	16923.4	2.46733
$362$	44.1761	0.00641393
$363$	−453.350	−0.0655501
$364$	0	0
$365$	−1819.40	−0.260909
$366$	−550.734	−0.0786539
$367$	−4858.50	−0.691040	−0.345520	−	0.938411i	$-0.612297\pi$
$367$	−4858.50	−0.691040	−0.345520	+	0.938411i	$0.612297\pi$
$368$	292.501	0.0414339
$369$	4963.27	0.700210
$370$	−277.256	−0.0389564
$371$	2634.97	0.368735
$372$	−5161.49	−0.719384
$373$	14.8247	0.00205790	0.00102895	−	0.999999i	$-0.499672\pi$
$373$	14.8247	0.00205790	0.00102895	+	0.999999i	$0.499672\pi$
$374$	127.756	0.0176634
$375$	4836.12	0.665963
$376$	−252.027	−0.0345672
$377$	0	0
$378$	1544.25	0.210126
$379$	−2333.53	−0.316267	−0.158134	−	0.987418i	$-0.550548\pi$
$379$	−2333.53	−0.316267	−0.158134	+	0.987418i	$0.550548\pi$
$380$	14432.6	1.94836
$381$	−8662.13	−1.16476
$382$	1091.28	0.146164
$383$	−8445.99	−1.12681	−0.563407	−	0.826179i	$-0.690510\pi$
$383$	−8445.99	−1.12681	−0.563407	+	0.826179i	$0.690510\pi$
$384$	−2673.99	−0.355355
$385$	3714.25	0.491678
$386$	430.734	0.0567974
$387$	489.599	0.0643093
$388$	−5857.43	−0.766407
$389$	−961.088	−0.125268	−0.0626338	−	0.998037i	$-0.519950\pi$
$389$	−961.088	−0.125268	−0.0626338	+	0.998037i	$0.519950\pi$
$390$	0	0
$391$	153.662	0.0198748
$392$	2668.40	0.343813
$393$	4486.63	0.575880
$394$	197.380	0.0252382
$395$	8123.76	1.03481
$396$	−1121.86	−0.142363
$397$	12076.9	1.52675	0.763377	−	0.645954i	$-0.223540\pi$
$397$	12076.9	1.52675	0.763377	+	0.645954i	$0.223540\pi$
$398$	821.334	0.103442
$399$	−16402.2	−2.05799
$400$	1003.00	0.125375
$401$	3461.76	0.431102	0.215551	−	0.976493i	$-0.430845\pi$
$401$	3461.76	0.431102	0.215551	+	0.976493i	$0.430845\pi$
$402$	−1314.49	−0.163087
$403$	0	0
$404$	−3220.12	−0.396552
$405$	−2509.74	−0.307926
$406$	−2826.29	−0.345484
$407$	−705.714	−0.0859483
$408$	−690.491	−0.0837853
$409$	−7321.11	−0.885100	−0.442550	−	0.896744i	$-0.645926\pi$
$409$	−7321.11	−0.885100	−0.442550	+	0.896744i	$0.645926\pi$
$410$	1654.74	0.199322
$411$	−2935.45	−0.352300
$412$	16368.4	1.95731
$413$	1843.54	0.219649
$414$	22.6384	0.00268748
$415$	5722.79	0.676917
$416$	0	0
$417$	699.121	0.0821010
$418$	−616.329	−0.0721188
$419$	−9015.87	−1.05120	−0.525602	−	0.850731i	$-0.676160\pi$
$419$	−9015.87	−1.05120	−0.525602	+	0.850731i	$0.676160\pi$
$420$	−9953.85	−1.15642
$421$	−4037.04	−0.467348	−0.233674	−	0.972315i	$-0.575075\pi$
$421$	−4037.04	−0.467348	−0.233674	+	0.972315i	$0.575075\pi$
$422$	1340.82	0.154669
$423$	566.649	0.0651334
$424$	−535.135	−0.0612935
$425$	526.917	0.0601394
$426$	−1226.56	−0.139500
$427$	11484.9	1.30163
$428$	−4628.58	−0.522736
$429$	0	0
$430$	163.231	0.0183063
$431$	−4821.98	−0.538901	−0.269451	−	0.963014i	$-0.586842\pi$
$431$	−4821.98	−0.538901	−0.269451	+	0.963014i	$0.586842\pi$
$432$	9110.76	1.01468
$433$	−14200.8	−1.57609	−0.788045	−	0.615617i	$-0.788907\pi$
$433$	−14200.8	−1.57609	−0.788045	+	0.615617i	$0.788907\pi$
$434$	−1805.85	−0.199732
$435$	12212.4	1.34606
$436$	14559.1	1.59921
$437$	−741.308	−0.0811478
$438$	−208.217	−0.0227146
$439$	−8526.25	−0.926960	−0.463480	−	0.886107i	$-0.653399\pi$
$439$	−8526.25	−0.926960	−0.463480	+	0.886107i	$0.653399\pi$
$440$	−754.327	−0.0817298
$441$	−5999.56	−0.647830
$442$	0	0
$443$	−5671.37	−0.608250	−0.304125	−	0.952632i	$-0.598364\pi$
$443$	−5671.37	−0.608250	−0.304125	+	0.952632i	$0.598364\pi$
$444$	1891.25	0.202150
$445$	−13552.8	−1.44374
$446$	1896.92	0.201394
$447$	−10366.4	−1.09690
$448$	13115.2	1.38311
$449$	−8451.15	−0.888273	−0.444136	−	0.895959i	$-0.646489\pi$
$449$	−8451.15	−0.888273	−0.444136	+	0.895959i	$0.646489\pi$
$450$	77.6284	0.00813208
$451$	4211.90	0.439758
$452$	−2299.42	−0.239282
$453$	7162.20	0.742847
$454$	−1776.09	−0.183604
$455$	0	0
$456$	3331.12	0.342092
$457$	554.568	0.0567649	0.0283825	−	0.999597i	$-0.490964\pi$
$457$	554.568	0.0567649	0.0283825	+	0.999597i	$0.490964\pi$
$458$	−988.650	−0.100866
$459$	4786.24	0.486716
$460$	−449.871	−0.0455986
$461$	15113.5	1.52691	0.763457	−	0.645859i	$-0.223501\pi$
$461$	15113.5	1.52691	0.763457	+	0.645859i	$0.223501\pi$
$462$	425.069	0.0428052
$463$	−7804.27	−0.783359	−0.391679	−	0.920102i	$-0.628106\pi$
$463$	−7804.27	−0.783359	−0.391679	+	0.920102i	$0.628106\pi$
$464$	−16674.6	−1.66831
$465$	7803.04	0.778188
$466$	318.798	0.0316911
$467$	15715.2	1.55720	0.778598	−	0.627523i	$-0.215931\pi$
$467$	15715.2	1.55720	0.778598	+	0.627523i	$0.215931\pi$
$468$	0	0
$469$	27412.2	2.69889
$470$	188.920	0.0185409
$471$	−5831.35	−0.570477
$472$	−374.405	−0.0365114
$473$	415.481	0.0403886
$474$	929.703	0.0900901
$475$	−2541.99	−0.245547
$476$	7139.80	0.687505
$477$	1203.18	0.115492
$478$	953.767	0.0912642
$479$	−17676.6	−1.68615	−0.843076	−	0.537795i	$-0.819257\pi$
$479$	−17676.6	−1.68615	−0.843076	+	0.537795i	$0.819257\pi$
$480$	3040.70	0.289142
$481$	0	0
$482$	−1055.66	−0.0997597
$483$	511.264	0.0481642
$484$	−952.028	−0.0894091
$485$	8855.14	0.829054
$486$	1181.55	0.110280
$487$	−12278.0	−1.14244	−0.571221	−	0.820796i	$-0.693530\pi$
$487$	−12278.0	−1.14244	−0.571221	+	0.820796i	$0.693530\pi$
$488$	−2332.47	−0.216365
$489$	6801.72	0.629007
$490$	−2000.24	−0.184411
$491$	−12937.6	−1.18914	−0.594569	−	0.804044i	$-0.702677\pi$
$491$	−12937.6	−1.18914	−0.594569	+	0.804044i	$0.702677\pi$
$492$	−11287.5	−1.03431
$493$	−8759.81	−0.800247
$494$	0	0
$495$	1696.01	0.154000
$496$	−10654.2	−0.964487
$497$	25578.5	2.30856
$498$	654.930	0.0589320
$499$	−9424.87	−0.845521	−0.422760	−	0.906241i	$-0.638939\pi$
$499$	−9424.87	−0.845521	−0.422760	+	0.906241i	$0.638939\pi$
$500$	10155.8	0.908360
$501$	−8528.37	−0.760517
$502$	853.489	0.0758826
$503$	−1643.64	−0.145699	−0.0728494	−	0.997343i	$-0.523209\pi$
$503$	−1643.64	−0.145699	−0.0728494	+	0.997343i	$0.523209\pi$
$504$	2121.40	0.187489
$505$	4868.11	0.428967
$506$	19.2113	0.00168784
$507$	0	0
$508$	−18190.3	−1.58871
$509$	−8285.67	−0.721524	−0.360762	−	0.932658i	$-0.617483\pi$
$509$	−8285.67	−0.721524	−0.360762	+	0.932658i	$0.617483\pi$
$510$	517.593	0.0449400
$511$	4342.13	0.375899
$512$	−6958.19	−0.600608
$513$	−23090.1	−1.98724
$514$	−2685.73	−0.230472
$515$	−24745.4	−2.11731
$516$	−1113.45	−0.0949939
$517$	480.867	0.0409062
$518$	661.690	0.0561255
$519$	−153.134	−0.0129515
$520$	0	0
$521$	19652.0	1.65253	0.826265	−	0.563282i	$-0.190461\pi$
$521$	19652.0	1.65253	0.826265	+	0.563282i	$0.190461\pi$
$522$	−1290.54	−0.108210
$523$	−2113.30	−0.176689	−0.0883445	−	0.996090i	$-0.528158\pi$
$523$	−2113.30	−0.176689	−0.0883445	+	0.996090i	$0.528158\pi$
$524$	9421.86	0.785489
$525$	1753.16	0.145741
$526$	−2514.50	−0.208436
$527$	−5597.05	−0.462640
$528$	2507.82	0.206702
$529$	−12143.9	−0.998101
$530$	401.138	0.0328761
$531$	841.801	0.0687967
$532$	−34444.4	−2.80705
$533$	0	0
$534$	−1551.01	−0.125691
$535$	6997.40	0.565465
$536$	−5567.14	−0.448627
$537$	7738.34	0.621851
$538$	−965.052	−0.0773352
$539$	−5091.31	−0.406862
$540$	−14012.5	−1.11667
$541$	−12558.9	−0.998057	−0.499028	−	0.866586i	$-0.666310\pi$
$541$	−12558.9	−0.998057	−0.499028	+	0.866586i	$0.666310\pi$
$542$	−1330.25	−0.105423
$543$	455.557	0.0360034
$544$	−2181.06	−0.171898
$545$	−22010.2	−1.72993
$546$	0	0
$547$	−15262.6	−1.19302	−0.596510	−	0.802605i	$-0.703447\pi$
$547$	−15262.6	−1.19302	−0.596510	+	0.802605i	$0.703447\pi$
$548$	−6164.40	−0.480530
$549$	5244.26	0.407686
$550$	65.8766	0.00510725
$551$	42259.7	3.26738
$552$	−103.833	−0.00800617
$553$	−19387.9	−1.49088
$554$	286.360	0.0219608
$555$	−2859.15	−0.218674
$556$	1468.14	0.111984
$557$	11345.1	0.863033	0.431516	−	0.902105i	$-0.357979\pi$
$557$	11345.1	0.863033	0.431516	+	0.902105i	$0.357979\pi$
$558$	−824.589	−0.0625585
$559$	0	0
$560$	−20546.4	−1.55043
$561$	1317.46	0.0991499
$562$	−2595.94	−0.194846
$563$	−4421.81	−0.331007	−0.165503	−	0.986209i	$-0.552925\pi$
$563$	−4421.81	−0.331007	−0.165503	+	0.986209i	$0.552925\pi$
$564$	−1288.68	−0.0962112
$565$	3476.21	0.258841
$566$	−2161.92	−0.160552
$567$	5989.65	0.443636
$568$	−5194.74	−0.383744
$569$	11969.6	0.881886	0.440943	−	0.897535i	$-0.354644\pi$
$569$	11969.6	0.881886	0.440943	+	0.897535i	$0.354644\pi$
$570$	−2497.01	−0.183488
$571$	738.958	0.0541584	0.0270792	−	0.999633i	$-0.491379\pi$
$571$	738.958	0.0541584	0.0270792	+	0.999633i	$0.491379\pi$
$572$	0	0
$573$	11253.6	0.820465
$574$	−3949.15	−0.287168
$575$	79.2351	0.00574666
$576$	5988.65	0.433207
$577$	5212.28	0.376066	0.188033	−	0.982163i	$-0.439789\pi$
$577$	5212.28	0.376066	0.188033	+	0.982163i	$0.439789\pi$
$578$	1413.74	0.101737
$579$	4441.86	0.318821
$580$	25645.8	1.83600
$581$	−13657.8	−0.975252
$582$	1013.40	0.0721769
$583$	1021.04	0.0725336
$584$	−881.841	−0.0624843
$585$	0	0
$586$	−2483.66	−0.175084
$587$	−23250.5	−1.63484	−0.817418	−	0.576044i	$-0.804596\pi$
$587$	−23250.5	−1.63484	−0.817418	+	0.576044i	$0.804596\pi$
$588$	13644.2	0.956937
$589$	27001.7	1.88894
$590$	280.655	0.0195837
$591$	2035.44	0.141670
$592$	3903.84	0.271025
$593$	−5544.75	−0.383972	−0.191986	−	0.981398i	$-0.561493\pi$
$593$	−5544.75	−0.383972	−0.191986	+	0.981398i	$0.561493\pi$
$594$	598.389	0.0413336
$595$	−10793.8	−0.743703
$596$	−21769.4	−1.49615
$597$	8469.85	0.580649
$598$	0	0
$599$	−13816.4	−0.942442	−0.471221	−	0.882015i	$-0.656187\pi$
$599$	−13816.4	−0.942442	−0.471221	+	0.882015i	$0.656187\pi$
$600$	−356.048	−0.0242260
$601$	−19890.6	−1.35001	−0.675003	−	0.737815i	$-0.735858\pi$
$601$	−19890.6	−1.35001	−0.675003	+	0.737815i	$0.735858\pi$
$602$	−389.562	−0.0263743
$603$	12517.0	0.845326
$604$	15040.5	1.01323
$605$	1439.26	0.0967175
$606$	557.119	0.0373456
$607$	−6946.06	−0.464468	−0.232234	−	0.972660i	$-0.574604\pi$
$607$	−6946.06	−0.464468	−0.232234	+	0.972660i	$0.574604\pi$
$608$	10522.0	0.701851
$609$	−29145.6	−1.93931
$610$	1748.42	0.116052
$611$	0	0
$612$	3260.18	0.215335
$613$	−6777.01	−0.446527	−0.223263	−	0.974758i	$-0.571671\pi$
$613$	−6777.01	−0.446527	−0.223263	+	0.974758i	$0.571671\pi$
$614$	314.560	0.0206752
$615$	17064.2	1.11885
$616$	1800.25	0.117750
$617$	24.6709	0.00160975	0.000804874	−	1.00000i	$-0.499744\pi$
$617$	24.6709	0.00160975	0.000804874		1.00000i	$0.499744\pi$
$618$	−2831.93	−0.184331
$619$	−15327.2	−0.995237	−0.497619	−	0.867396i	$-0.665792\pi$
$619$	−15327.2	−0.995237	−0.497619	+	0.867396i	$0.665792\pi$
$620$	16386.3	1.06143
$621$	719.730	0.0465085
$622$	−1381.48	−0.0890553
$623$	32344.6	2.08003
$624$	0	0
$625$	−17413.7	−1.11448
$626$	−1183.44	−0.0755590
$627$	−6355.77	−0.404825
$628$	−12245.7	−0.778119
$629$	2050.84	0.130004
$630$	−1590.21	−0.100564
$631$	−16336.6	−1.03066	−0.515331	−	0.856991i	$-0.672331\pi$
$631$	−16336.6	−1.03066	−0.515331	+	0.856991i	$0.672331\pi$
$632$	3937.48	0.247824
$633$	13827.0	0.868205
$634$	−3992.55	−0.250102
$635$	27499.8	1.71858
$636$	−2736.29	−0.170599
$637$	0	0
$638$	−1095.18	−0.0679599
$639$	11679.7	0.723070
$640$	8489.15	0.524317
$641$	3057.33	0.188389	0.0941943	−	0.995554i	$-0.469973\pi$
$641$	3057.33	0.188389	0.0941943	+	0.995554i	$0.469973\pi$
$642$	800.800	0.0492290
$643$	−13872.7	−0.850835	−0.425417	−	0.904997i	$-0.639873\pi$
$643$	−13872.7	−0.850835	−0.425417	+	0.904997i	$0.639873\pi$
$644$	1073.65	0.0656951
$645$	1683.29	0.102759
$646$	1791.08	0.109086
$647$	16399.7	0.996506	0.498253	−	0.867032i	$-0.333975\pi$
$647$	16399.7	0.996506	0.498253	+	0.867032i	$0.333975\pi$
$648$	−1216.44	−0.0737441
$649$	714.365	0.0432069
$650$	0	0
$651$	−18622.5	−1.12116
$652$	14283.5	0.857953
$653$	−6673.98	−0.399959	−0.199979	−	0.979800i	$-0.564087\pi$
$653$	−6673.98	−0.399959	−0.199979	+	0.979800i	$0.564087\pi$
$654$	−2518.90	−0.150607
$655$	−14243.8	−0.849696
$656$	−23299.2	−1.38671
$657$	1982.71	0.117736
$658$	−450.869	−0.0267123
$659$	15214.5	0.899352	0.449676	−	0.893192i	$-0.351539\pi$
$659$	15214.5	0.899352	0.449676	+	0.893192i	$0.351539\pi$
$660$	−3857.07	−0.227479
$661$	−8735.91	−0.514051	−0.257025	−	0.966405i	$-0.582742\pi$
$661$	−8735.91	−0.514051	−0.257025	+	0.966405i	$0.582742\pi$
$662$	1602.19	0.0940646
$663$	0	0
$664$	2773.76	0.162113
$665$	52072.3	3.03651
$666$	302.142	0.0175792
$667$	−1317.25	−0.0764682
$668$	−17909.4	−1.03733
$669$	19561.7	1.13049
$670$	4173.14	0.240631
$671$	4450.36	0.256042
$672$	−7256.82	−0.416574
$673$	−24928.8	−1.42784	−0.713920	−	0.700228i	$-0.753082\pi$
$673$	−24928.8	−1.42784	−0.713920	+	0.700228i	$0.753082\pi$
$674$	−2358.17	−0.134767
$675$	2468.00	0.140731
$676$	0	0
$677$	−21582.6	−1.22524	−0.612620	−	0.790378i	$-0.709884\pi$
$677$	−21582.6	−1.22524	−0.612620	+	0.790378i	$0.709884\pi$
$678$	397.827	0.0225346
$679$	−21133.4	−1.19444
$680$	2192.11	0.123623
$681$	−18315.6	−1.03062
$682$	−699.758	−0.0392890
$683$	29852.1	1.67241	0.836207	−	0.548414i	$-0.184768\pi$
$683$	29852.1	1.67241	0.836207	+	0.548414i	$0.184768\pi$
$684$	−15728.0	−0.879205
$685$	9319.22	0.519809
$686$	1236.07	0.0687952
$687$	−10195.3	−0.566191
$688$	−2298.34	−0.127360
$689$	0	0
$690$	77.8330	0.00429428
$691$	27523.9	1.51528	0.757639	−	0.652674i	$-0.226353\pi$
$691$	27523.9	1.51528	0.757639	+	0.652674i	$0.226353\pi$
$692$	−321.580	−0.0176657
$693$	−4047.63	−0.221871
$694$	−4174.35	−0.228323
$695$	−2219.51	−0.121138
$696$	5919.17	0.322364
$697$	−12240.0	−0.665170
$698$	−520.571	−0.0282291
$699$	3287.55	0.177892
$700$	3681.60	0.198788
$701$	−30477.1	−1.64209	−0.821043	−	0.570866i	$-0.806608\pi$
$701$	−30477.1	−1.64209	−0.821043	+	0.570866i	$0.806608\pi$
$702$	0	0
$703$	−9893.82	−0.530800
$704$	5082.06	0.272070
$705$	1948.20	0.104076
$706$	4135.30	0.220445
$707$	−11618.1	−0.618023
$708$	−1914.43	−0.101622
$709$	23865.5	1.26416	0.632079	−	0.774904i	$-0.282202\pi$
$709$	23865.5	1.26416	0.632079	+	0.774904i	$0.282202\pi$
$710$	3893.99	0.205829
$711$	−8852.92	−0.466962
$712$	−6568.86	−0.345756
$713$	−841.655	−0.0442079
$714$	−1235.27	−0.0647463
$715$	0	0
$716$	16250.4	0.848193
$717$	9835.54	0.512294
$718$	−2008.40	−0.104391
$719$	15754.2	0.817151	0.408576	−	0.912724i	$-0.366026\pi$
$719$	15754.2	0.817151	0.408576	+	0.912724i	$0.366026\pi$
$720$	−9381.90	−0.485615
$721$	59056.5	3.05046
$722$	−6148.65	−0.316938
$723$	−10886.3	−0.559982
$724$	956.664	0.0491079
$725$	−4516.95	−0.231387
$726$	164.712	0.00842016
$727$	−18662.9	−0.952089	−0.476044	−	0.879421i	$-0.657930\pi$
$727$	−18662.9	−0.952089	−0.476044	+	0.879421i	$0.657930\pi$
$728$	0	0
$729$	17881.4	0.908471
$730$	661.030	0.0335148
$731$	−1207.41	−0.0610911
$732$	−11926.5	−0.602209
$733$	−5925.54	−0.298588	−0.149294	−	0.988793i	$-0.547700\pi$
$733$	−5925.54	−0.298588	−0.149294	+	0.988793i	$0.547700\pi$
$734$	1765.20	0.0887667
$735$	−20627.1	−1.03516
$736$	−327.977	−0.0164258
$737$	10622.1	0.530896
$738$	−1803.27	−0.0899447
$739$	30341.6	1.51033	0.755166	−	0.655534i	$-0.227556\pi$
$739$	30341.6	1.51033	0.755166	+	0.655534i	$0.227556\pi$
$740$	−6004.17	−0.298267
$741$	0	0
$742$	−957.343	−0.0473655
$743$	4645.86	0.229394	0.114697	−	0.993401i	$-0.463410\pi$
$743$	4645.86	0.229394	0.114697	+	0.993401i	$0.463410\pi$
$744$	3782.03	0.186366
$745$	32910.5	1.61845
$746$	−5.38616	−0.000264345 0
$747$	−6236.44	−0.305461
$748$	2766.64	0.135239
$749$	−16699.8	−0.814681
$750$	−1757.07	−0.0855455
$751$	−33216.9	−1.61398	−0.806992	−	0.590562i	$-0.798906\pi$
$751$	−33216.9	−1.61398	−0.806992	+	0.590562i	$0.798906\pi$
$752$	−2660.04	−0.128992
$753$	8801.44	0.425953
$754$	0	0
$755$	−22738.0	−1.09605
$756$	33441.7	1.60882
$757$	1667.88	0.0800794	0.0400397	−	0.999198i	$-0.487252\pi$
$757$	1667.88	0.0800794	0.0400397	+	0.999198i	$0.487252\pi$
$758$	847.822	0.0406257
$759$	198.112	0.00947434
$760$	−10575.4	−0.504748
$761$	7985.32	0.380378	0.190189	−	0.981747i	$-0.439090\pi$
$761$	7985.32	0.380378	0.190189	+	0.981747i	$0.439090\pi$
$762$	3147.15	0.149618
$763$	52528.7	2.49236
$764$	23632.4	1.11910
$765$	−4928.68	−0.232937
$766$	3068.62	0.144744
$767$	0	0
$768$	−12876.4	−0.604997
$769$	2286.56	0.107224	0.0536121	−	0.998562i	$-0.482927\pi$
$769$	2286.56	0.107224	0.0536121	+	0.998562i	$0.482927\pi$
$770$	−1349.47	−0.0631579
$771$	−27696.0	−1.29371
$772$	9327.85	0.434866
$773$	−9747.38	−0.453543	−0.226772	−	0.973948i	$-0.572817\pi$
$773$	−9747.38	−0.453543	−0.226772	+	0.973948i	$0.572817\pi$
$774$	−177.882	−0.00826078
$775$	−2886.09	−0.133769
$776$	4291.97	0.198548
$777$	6823.55	0.315050
$778$	349.185	0.0160911
$779$	59049.1	2.71586
$780$	0	0
$781$	9911.56	0.454115
$782$	−55.8289	−0.00255299
$783$	−41029.6	−1.87264
$784$	28163.9	1.28298
$785$	18512.9	0.841723
$786$	−1630.09	−0.0739740
$787$	−12699.7	−0.575219	−0.287609	−	0.957748i	$-0.592860\pi$
$787$	−12699.7	−0.575219	−0.287609	+	0.957748i	$0.592860\pi$
$788$	4274.39	0.193235
$789$	−25930.3	−1.17002
$790$	−2951.54	−0.132926
$791$	−8296.21	−0.372920
$792$	822.033	0.0368809
$793$	0	0
$794$	−4387.80	−0.196117
$795$	4136.66	0.184544
$796$	17786.5	0.791994
$797$	3932.19	0.174762	0.0873810	−	0.996175i	$-0.472150\pi$
$797$	3932.19	0.174762	0.0873810	+	0.996175i	$0.472150\pi$
$798$	5959.28	0.264356
$799$	−1397.42	−0.0618740
$800$	−1124.65	−0.0497031
$801$	14769.2	0.651492
$802$	−1257.73	−0.0553767
$803$	1682.55	0.0739427
$804$	−28466.3	−1.24867
$805$	−1623.12	−0.0710651
$806$	0	0
$807$	−9951.91	−0.434106
$808$	2359.51	0.102732
$809$	−15002.8	−0.652005	−0.326002	−	0.945369i	$-0.605702\pi$
$809$	−15002.8	−0.652005	−0.326002	+	0.945369i	$0.605702\pi$
$810$	911.844	0.0395542
$811$	19867.7	0.860233	0.430117	−	0.902773i	$-0.358472\pi$
$811$	19867.7	0.860233	0.430117	+	0.902773i	$0.358472\pi$
$812$	−61205.3	−2.64518
$813$	−13718.0	−0.591771
$814$	256.402	0.0110404
$815$	−21593.5	−0.928083
$816$	−7287.86	−0.312654
$817$	5824.87	0.249432
$818$	2659.92	0.113694
$819$	0	0
$820$	35834.6	1.52610
$821$	−13380.8	−0.568811	−0.284406	−	0.958704i	$-0.591796\pi$
$821$	−13380.8	−0.568811	−0.284406	+	0.958704i	$0.591796\pi$
$822$	1066.52	0.0452543
$823$	−2114.77	−0.0895700	−0.0447850	−	0.998997i	$-0.514260\pi$
$823$	−2114.77	−0.0895700	−0.0447850	+	0.998997i	$0.514260\pi$
$824$	−11993.8	−0.507067
$825$	679.340	0.0286686
$826$	−669.801	−0.0282147
$827$	−39948.4	−1.67974	−0.839868	−	0.542791i	$-0.817367\pi$
$827$	−39948.4	−1.67974	−0.839868	+	0.542791i	$0.817367\pi$
$828$	490.250	0.0205765
$829$	−4688.10	−0.196411	−0.0982053	−	0.995166i	$-0.531310\pi$
$829$	−4688.10	−0.196411	−0.0982053	+	0.995166i	$0.531310\pi$
$830$	−2079.22	−0.0869526
$831$	2953.03	0.123273
$832$	0	0
$833$	14795.6	0.615412
$834$	−254.006	−0.0105462
$835$	27075.1	1.12212
$836$	−13347.0	−0.552173
$837$	−26215.7	−1.08261
$838$	3275.67	0.135031
$839$	37742.3	1.55305	0.776525	−	0.630087i	$-0.216981\pi$
$839$	37742.3	1.55305	0.776525	+	0.630087i	$0.216981\pi$
$840$	7293.59	0.299586
$841$	50703.6	2.07896
$842$	1466.75	0.0600326
$843$	−26770.2	−1.09373
$844$	29036.5	1.18421
$845$	0	0
$846$	−205.876	−0.00836664
$847$	−3434.88	−0.139343
$848$	−5648.14	−0.228724
$849$	−22294.4	−0.901227
$850$	−191.441	−0.00772514
$851$	308.395	0.0124226
$852$	−26562.1	−1.06808
$853$	11646.3	0.467483	0.233741	−	0.972299i	$-0.424903\pi$
$853$	11646.3	0.467483	0.233741	+	0.972299i	$0.424903\pi$
$854$	−4172.73	−0.167199
$855$	23777.3	0.951072
$856$	3391.55	0.135421
$857$	1089.01	0.0434071	0.0217035	−	0.999764i	$-0.493091\pi$
$857$	1089.01	0.0434071	0.0217035	+	0.999764i	$0.493091\pi$
$858$	0	0
$859$	−12819.9	−0.509208	−0.254604	−	0.967045i	$-0.581945\pi$
$859$	−12819.9	−0.509208	−0.254604	+	0.967045i	$0.581945\pi$
$860$	3534.88	0.140161
$861$	−40724.9	−1.61196
$862$	1751.93	0.0692240
$863$	36664.3	1.44620	0.723098	−	0.690746i	$-0.242718\pi$
$863$	36664.3	1.44620	0.723098	+	0.690746i	$0.242718\pi$
$864$	−10215.8	−0.402254
$865$	486.158	0.0191097
$866$	5159.47	0.202455
$867$	14578.9	0.571079
$868$	−39106.9	−1.52923
$869$	−7512.72	−0.293270
$870$	−4437.02	−0.172907
$871$	0	0
$872$	−10668.0	−0.414296
$873$	−9649.95	−0.374114
$874$	269.334	0.0104237
$875$	36641.7	1.41567
$876$	−4509.08	−0.173913
$877$	−20615.5	−0.793769	−0.396885	−	0.917869i	$-0.629909\pi$
$877$	−20615.5	−0.793769	−0.396885	+	0.917869i	$0.629909\pi$
$878$	3097.78	0.119072
$879$	−25612.2	−0.982798
$880$	−7961.62	−0.304984
$881$	−29537.3	−1.12955	−0.564777	−	0.825244i	$-0.691038\pi$
$881$	−29537.3	−1.12955	−0.564777	+	0.825244i	$0.691038\pi$
$882$	2179.77	0.0832163
$883$	4500.96	0.171539	0.0857697	−	0.996315i	$-0.472665\pi$
$883$	4500.96	0.171539	0.0857697	+	0.996315i	$0.472665\pi$
$884$	0	0
$885$	2894.20	0.109929
$886$	2060.53	0.0781321
$887$	14168.6	0.536343	0.268171	−	0.963371i	$-0.413581\pi$
$887$	14168.6	0.536343	0.268171	+	0.963371i	$0.413581\pi$
$888$	−1385.79	−0.0523696
$889$	−65630.1	−2.47600
$890$	4924.03	0.185454
$891$	2320.96	0.0872673
$892$	41079.2	1.54196
$893$	6741.56	0.252629
$894$	3766.36	0.140901
$895$	−24567.0	−0.917525
$896$	−20259.9	−0.755398
$897$	0	0
$898$	3070.49	0.114102
$899$	47980.2	1.78001
$900$	1681.10	0.0622628
$901$	−2967.19	−0.109713
$902$	−1530.28	−0.0564886
$903$	−4017.28	−0.148047
$904$	1684.88	0.0619891
$905$	−1446.27	−0.0531221
$906$	−2602.19	−0.0954216
$907$	−50952.3	−1.86532	−0.932659	−	0.360758i	$-0.882518\pi$
$907$	−50952.3	−1.86532	−0.932659	+	0.360758i	$0.882518\pi$
$908$	−38462.4	−1.40575
$909$	−5305.06	−0.193573
$910$	0	0
$911$	16945.4	0.616275	0.308138	−	0.951342i	$-0.400294\pi$
$911$	16945.4	0.616275	0.308138	+	0.951342i	$0.400294\pi$
$912$	35158.6	1.27655
$913$	−5292.34	−0.191841
$914$	−201.487	−0.00729167
$915$	18030.3	0.651435
$916$	−21409.9	−0.772274
$917$	33993.7	1.22418
$918$	−1738.95	−0.0625205
$919$	−6233.15	−0.223735	−0.111868	−	0.993723i	$-0.535683\pi$
$919$	−6233.15	−0.223735	−0.111868	+	0.993723i	$0.535683\pi$
$920$	329.639	0.0118129
$921$	3243.84	0.116057
$922$	−5491.08	−0.196138
$923$	0	0
$924$	9205.15	0.327735
$925$	1057.51	0.0375898
$926$	2835.47	0.100625
$927$	26966.5	0.955442
$928$	18697.0	0.661377
$929$	10269.0	0.362664	0.181332	−	0.983422i	$-0.441959\pi$
$929$	10269.0	0.362664	0.181332	+	0.983422i	$0.441959\pi$
$930$	−2835.02	−0.0999612
$931$	−71378.1	−2.51270
$932$	6903.80	0.242641
$933$	−14246.3	−0.499895
$934$	−5709.67	−0.200028
$935$	−4182.55	−0.146293
$936$	0	0
$937$	−53.0084	−0.00184814	−0.000924072	−	1.00000i	$-0.500294\pi$
$937$	−53.0084	−0.00184814	−0.000924072		1.00000i	$0.500294\pi$
$938$	−9959.48	−0.346683
$939$	−12204.0	−0.424136
$940$	4091.19	0.141957
$941$	21534.4	0.746018	0.373009	−	0.927828i	$-0.378326\pi$
$941$	21534.4	0.746018	0.373009	+	0.927828i	$0.378326\pi$
$942$	2118.66	0.0732799
$943$	−1840.59	−0.0635608
$944$	−3951.69	−0.136247
$945$	−50556.5	−1.74032
$946$	−150.953	−0.00518807
$947$	−25140.0	−0.862660	−0.431330	−	0.902194i	$-0.641956\pi$
$947$	−25140.0	−0.862660	−0.431330	+	0.902194i	$0.641956\pi$
$948$	20133.4	0.689769
$949$	0	0
$950$	923.563	0.0315414
$951$	−41172.4	−1.40390
$952$	−5231.62	−0.178107
$953$	28837.6	0.980212	0.490106	−	0.871663i	$-0.336958\pi$
$953$	28837.6	0.980212	0.490106	+	0.871663i	$0.336958\pi$
$954$	−437.143	−0.0148355
$955$	−35727.0	−1.21057
$956$	20654.5	0.698759
$957$	−11293.8	−0.381480
$958$	6422.32	0.216593
$959$	−22240.9	−0.748902
$960$	20589.6	0.692215
$961$	865.761	0.0290611
$962$	0	0
$963$	−7625.46	−0.255168
$964$	−22861.1	−0.763805
$965$	−14101.7	−0.470413
$966$	−185.754	−0.00618688
$967$	−21760.1	−0.723637	−0.361818	−	0.932249i	$-0.617844\pi$
$967$	−21760.1	−0.723637	−0.361818	+	0.932249i	$0.617844\pi$
$968$	697.589	0.0231626
$969$	18470.2	0.612331
$970$	−3217.27	−0.106495
$971$	−27195.8	−0.898820	−0.449410	−	0.893326i	$-0.648366\pi$
$971$	−27195.8	−0.898820	−0.449410	+	0.893326i	$0.648366\pi$
$972$	25587.3	0.844355
$973$	5297.01	0.174527
$974$	4460.88	0.146751
$975$	0	0
$976$	−24618.3	−0.807390
$977$	28694.5	0.939630	0.469815	−	0.882765i	$-0.344321\pi$
$977$	28694.5	0.939630	0.469815	+	0.882765i	$0.344321\pi$
$978$	−2471.22	−0.0807983
$979$	12533.4	0.409161
$980$	−43316.6	−1.41194
$981$	23985.7	0.780637
$982$	4700.53	0.152749
$983$	32358.2	1.04991	0.524957	−	0.851129i	$-0.324081\pi$
$983$	32358.2	1.04991	0.524957	+	0.851129i	$0.324081\pi$
$984$	8270.81	0.267951
$985$	−6461.94	−0.209030
$986$	3182.63	0.102795
$987$	−4649.50	−0.149945
$988$	0	0
$989$	−181.564	−0.00583761
$990$	−616.197	−0.0197818
$991$	33456.0	1.07242	0.536209	−	0.844085i	$-0.319856\pi$
$991$	33456.0	1.07242	0.536209	+	0.844085i	$0.319856\pi$
$992$	11946.4	0.382356
$993$	16522.2	0.528013
$994$	−9293.26	−0.296543
$995$	−26889.3	−0.856733
$996$	14183.0	0.451209
$997$	−53178.3	−1.68924	−0.844620	−	0.535366i	$-0.820174\pi$
$997$	−53178.3	−1.68924	−0.844620	+	0.535366i	$0.820174\pi$
$998$	3424.26	0.108610
$999$	9605.82	0.304219

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.4.a.e.1.6		11
13.12	even	2		143.4.a.d.1.6	✓	11
39.38	odd	2		1287.4.a.m.1.6		11
52.51	odd	2		2288.4.a.u.1.9		11
143.142	odd	2		1573.4.a.f.1.6		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.a.d.1.6	✓	11	13.12	even	2
1287.4.a.m.1.6		11	39.38	odd	2
1573.4.a.f.1.6		11	143.142	odd	2
1859.4.a.e.1.6		11	1.1	even	1	trivial
2288.4.a.u.1.9		11	52.51	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:	\( N \)	\(=\)	\( 1859 = 11 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1859.a (trivial)

\(f(q)\)	\(=\)	\(q-0.363322 q^{2} -3.74669 q^{3} -7.86800 q^{4} +11.8947 q^{5} +1.36126 q^{6} -28.3874 q^{7} +5.76520 q^{8} -12.9623 q^{9} +O(q^{10})\)	\(q-0.363322 q^{2} -3.74669 q^{3} -7.86800 q^{4} +11.8947 q^{5} +1.36126 q^{6} -28.3874 q^{7} +5.76520 q^{8} -12.9623 q^{9} -4.32160 q^{10} -11.0000 q^{11} +29.4790 q^{12} +10.3138 q^{14} -44.5657 q^{15} +60.8493 q^{16} +31.9666 q^{17} +4.70949 q^{18} -154.215 q^{19} -93.5873 q^{20} +106.359 q^{21} +3.99655 q^{22} +4.80697 q^{23} -21.6004 q^{24} +16.4834 q^{25} +149.726 q^{27} +223.352 q^{28} -274.030 q^{29} +16.1917 q^{30} -175.091 q^{31} -68.2295 q^{32} +41.2136 q^{33} -11.6142 q^{34} -337.659 q^{35} +101.987 q^{36} +64.1558 q^{37} +56.0299 q^{38} +68.5752 q^{40} -382.900 q^{41} -38.6426 q^{42} -37.7710 q^{43} +86.5480 q^{44} -154.182 q^{45} -1.74648 q^{46} -43.7152 q^{47} -227.984 q^{48} +462.847 q^{49} -5.98878 q^{50} -119.769 q^{51} -92.8216 q^{53} -54.3990 q^{54} -130.841 q^{55} -163.659 q^{56} +577.798 q^{57} +99.5614 q^{58} -64.9423 q^{59} +350.643 q^{60} -404.578 q^{61} +63.6144 q^{62} +367.967 q^{63} -462.005 q^{64} -14.9738 q^{66} -965.646 q^{67} -251.513 q^{68} -18.0102 q^{69} +122.679 q^{70} -901.051 q^{71} -74.7302 q^{72} -152.959 q^{73} -23.3093 q^{74} -61.7582 q^{75} +1213.37 q^{76} +312.262 q^{77} +682.974 q^{79} +723.783 q^{80} -210.997 q^{81} +139.116 q^{82} +481.122 q^{83} -836.832 q^{84} +380.232 q^{85} +13.7230 q^{86} +1026.71 q^{87} -63.4172 q^{88} -1139.40 q^{89} +56.0179 q^{90} -37.8212 q^{92} +656.011 q^{93} +15.8827 q^{94} -1834.34 q^{95} +255.635 q^{96} +744.462 q^{97} -168.163 q^{98} +142.585 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 6 q^{2} + 6 q^{3} + 66 q^{4} + 4 q^{5} + 14 q^{6} - 45 q^{7} - 78 q^{8} + 135 q^{9}+O(q^{10}) \) 11 * q - 6 * q^2 + 6 * q^3 + 66 * q^4 + 4 * q^5 + 14 * q^6 - 45 * q^7 - 78 * q^8 + 135 * q^9	\( 11 q - 6 q^{2} + 6 q^{3} + 66 q^{4} + 4 q^{5} + 14 q^{6} - 45 q^{7} - 78 q^{8} + 135 q^{9} + 48 q^{10} - 121 q^{11} + 105 q^{12} - 48 q^{14} + 125 q^{15} + 394 q^{16} + 265 q^{17} - 405 q^{18} - 127 q^{19} + 46 q^{20} + 287 q^{21} + 66 q^{22} + 42 q^{23} + 83 q^{24} + 737 q^{25} + 69 q^{27} - 675 q^{28} + 435 q^{29} + 785 q^{30} + 174 q^{31} - 315 q^{32} - 66 q^{33} - 497 q^{34} + 844 q^{35} + 1572 q^{36} - 187 q^{37} - 1813 q^{38} - 1470 q^{40} - 128 q^{41} - 2630 q^{42} + 696 q^{43} - 726 q^{44} + 1537 q^{45} - 785 q^{46} + 355 q^{47} - 516 q^{48} + 1758 q^{49} + 3414 q^{50} - 25 q^{51} - 693 q^{53} + 4150 q^{54} - 44 q^{55} - 3123 q^{56} - 99 q^{57} + 287 q^{58} + 609 q^{59} + 5013 q^{60} + 1625 q^{61} - 882 q^{62} - 1365 q^{63} - 914 q^{64} - 154 q^{66} - 633 q^{67} + 2873 q^{68} - 2192 q^{69} + 2054 q^{70} + 1937 q^{71} - 3242 q^{72} - 404 q^{73} - 447 q^{74} + 1781 q^{75} + 1814 q^{76} + 495 q^{77} + 1670 q^{79} + 1568 q^{80} + 2619 q^{81} + 1283 q^{82} - 785 q^{83} + 11750 q^{84} - 3189 q^{85} + 5950 q^{86} + 46 q^{87} + 858 q^{88} - 1464 q^{89} + 401 q^{90} - 3786 q^{92} - 1826 q^{93} - 2597 q^{94} - 2356 q^{95} - 4513 q^{96} - 1184 q^{97} - 2823 q^{98} - 1485 q^{99}+O(q^{100}) \) 11 * q - 6 * q^2 + 6 * q^3 + 66 * q^4 + 4 * q^5 + 14 * q^6 - 45 * q^7 - 78 * q^8 + 135 * q^9 + 48 * q^10 - 121 * q^11 + 105 * q^12 - 48 * q^14 + 125 * q^15 + 394 * q^16 + 265 * q^17 - 405 * q^18 - 127 * q^19 + 46 * q^20 + 287 * q^21 + 66 * q^22 + 42 * q^23 + 83 * q^24 + 737 * q^25 + 69 * q^27 - 675 * q^28 + 435 * q^29 + 785 * q^30 + 174 * q^31 - 315 * q^32 - 66 * q^33 - 497 * q^34 + 844 * q^35 + 1572 * q^36 - 187 * q^37 - 1813 * q^38 - 1470 * q^40 - 128 * q^41 - 2630 * q^42 + 696 * q^43 - 726 * q^44 + 1537 * q^45 - 785 * q^46 + 355 * q^47 - 516 * q^48 + 1758 * q^49 + 3414 * q^50 - 25 * q^51 - 693 * q^53 + 4150 * q^54 - 44 * q^55 - 3123 * q^56 - 99 * q^57 + 287 * q^58 + 609 * q^59 + 5013 * q^60 + 1625 * q^61 - 882 * q^62 - 1365 * q^63 - 914 * q^64 - 154 * q^66 - 633 * q^67 + 2873 * q^68 - 2192 * q^69 + 2054 * q^70 + 1937 * q^71 - 3242 * q^72 - 404 * q^73 - 447 * q^74 + 1781 * q^75 + 1814 * q^76 + 495 * q^77 + 1670 * q^79 + 1568 * q^80 + 2619 * q^81 + 1283 * q^82 - 785 * q^83 + 11750 * q^84 - 3189 * q^85 + 5950 * q^86 + 46 * q^87 + 858 * q^88 - 1464 * q^89 + 401 * q^90 - 3786 * q^92 - 1826 * q^93 - 2597 * q^94 - 2356 * q^95 - 4513 * q^96 - 1184 * q^97 - 2823 * q^98 - 1485 * q^99

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