LMFDB - Embedded newform 1849.4.a.h.1.9

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:	$0$
Dimension:	$30$
Twist minimal:	no (minimal twist has level 43)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
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)

$f(q)$	$=$	$q-1.99192 q^{2} +10.2076 q^{3} -4.03226 q^{4} -6.84373 q^{5} -20.3326 q^{6} -3.06785 q^{7} +23.9673 q^{8} +77.1944 q^{9} +O(q^{10})$	\(q-1.99192 q^{2} +10.2076 q^{3} -4.03226 q^{4} -6.84373 q^{5} -20.3326 q^{6} -3.06785 q^{7} +23.9673 q^{8} +77.1944 q^{9} +13.6322 q^{10} -55.5509 q^{11} -41.1596 q^{12} +26.7334 q^{13} +6.11091 q^{14} -69.8578 q^{15} -15.4828 q^{16} +40.1392 q^{17} -153.765 q^{18} +64.0680 q^{19} +27.5957 q^{20} -31.3153 q^{21} +110.653 q^{22} -111.100 q^{23} +244.648 q^{24} -78.1633 q^{25} -53.2507 q^{26} +512.362 q^{27} +12.3704 q^{28} -126.560 q^{29} +139.151 q^{30} +203.345 q^{31} -160.898 q^{32} -567.039 q^{33} -79.9540 q^{34} +20.9955 q^{35} -311.268 q^{36} -46.2282 q^{37} -127.618 q^{38} +272.883 q^{39} -164.026 q^{40} +200.645 q^{41} +62.3775 q^{42} +223.996 q^{44} -528.298 q^{45} +221.303 q^{46} +376.759 q^{47} -158.041 q^{48} -333.588 q^{49} +155.695 q^{50} +409.724 q^{51} -107.796 q^{52} +612.239 q^{53} -1020.58 q^{54} +380.175 q^{55} -73.5280 q^{56} +653.978 q^{57} +252.097 q^{58} +270.064 q^{59} +281.685 q^{60} +292.472 q^{61} -405.047 q^{62} -236.821 q^{63} +444.357 q^{64} -182.956 q^{65} +1129.50 q^{66} -270.489 q^{67} -161.852 q^{68} -1134.07 q^{69} -41.8214 q^{70} -340.360 q^{71} +1850.14 q^{72} -56.5822 q^{73} +92.0828 q^{74} -797.857 q^{75} -258.339 q^{76} +170.422 q^{77} -543.560 q^{78} -746.369 q^{79} +105.960 q^{80} +3145.72 q^{81} -399.669 q^{82} +1009.86 q^{83} +126.271 q^{84} -274.702 q^{85} -1291.87 q^{87} -1331.40 q^{88} -493.858 q^{89} +1052.33 q^{90} -82.0141 q^{91} +447.986 q^{92} +2075.66 q^{93} -750.472 q^{94} -438.464 q^{95} -1642.38 q^{96} -233.566 q^{97} +664.481 q^{98} -4288.22 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 6 q^{2} + 2 q^{3} + 114 q^{4} + 27 q^{5} + 8 q^{6} + 48 q^{7} + 90 q^{8} + 216 q^{9}+O(q^{10}) $ 30 * q + 6 * q^2 + 2 * q^3 + 114 * q^4 + 27 * q^5 + 8 * q^6 + 48 * q^7 + 90 * q^8 + 216 * q^9	\( 30 q + 6 q^{2} + 2 q^{3} + 114 q^{4} + 27 q^{5} + 8 q^{6} + 48 q^{7} + 90 q^{8} + 216 q^{9} - 27 q^{10} + 80 q^{11} - 36 q^{12} - 13 q^{13} + 36 q^{14} + 16 q^{15} + 318 q^{16} + 66 q^{17} + 80 q^{18} + 254 q^{19} + 312 q^{20} - 548 q^{21} + 305 q^{22} - 105 q^{23} + 123 q^{24} + 523 q^{25} + 549 q^{26} - 10 q^{27} + 578 q^{28} + 793 q^{29} + 1560 q^{30} - 359 q^{31} + 676 q^{32} + 208 q^{33} + 1007 q^{34} - 514 q^{35} + 776 q^{36} + 510 q^{37} - 2066 q^{38} + 898 q^{39} - 1248 q^{40} - 270 q^{41} - 915 q^{42} + 3256 q^{44} + 807 q^{45} + 1960 q^{46} + 1421 q^{47} - 632 q^{48} + 386 q^{49} - 141 q^{50} + 209 q^{51} + 2825 q^{52} - 21 q^{53} + 2368 q^{54} + 2258 q^{55} + 2521 q^{56} - 1723 q^{57} - 347 q^{58} + 1752 q^{59} + 2711 q^{60} + 1759 q^{61} + 395 q^{62} + 2204 q^{63} + 222 q^{64} + 1151 q^{65} + 160 q^{66} - 3001 q^{67} + 1921 q^{68} + 1660 q^{69} + 1597 q^{70} + 727 q^{71} + 9100 q^{72} + 4623 q^{73} - 2649 q^{74} + 1027 q^{75} + 874 q^{76} + 3556 q^{77} - 4979 q^{78} + 546 q^{79} + 5809 q^{80} - 410 q^{81} - 4397 q^{82} - 492 q^{83} - 10611 q^{84} - 1723 q^{85} + 5937 q^{87} + 3974 q^{88} + 5218 q^{89} + 10492 q^{90} + 1104 q^{91} + 1060 q^{92} + 1997 q^{93} - 2134 q^{94} + 6346 q^{95} - 11984 q^{96} + 2590 q^{97} + 6270 q^{98} - 2693 q^{99}+O(q^{100}) \) 30 * q + 6 * q^2 + 2 * q^3 + 114 * q^4 + 27 * q^5 + 8 * q^6 + 48 * q^7 + 90 * q^8 + 216 * q^9 - 27 * q^10 + 80 * q^11 - 36 * q^12 - 13 * q^13 + 36 * q^14 + 16 * q^15 + 318 * q^16 + 66 * q^17 + 80 * q^18 + 254 * q^19 + 312 * q^20 - 548 * q^21 + 305 * q^22 - 105 * q^23 + 123 * q^24 + 523 * q^25 + 549 * q^26 - 10 * q^27 + 578 * q^28 + 793 * q^29 + 1560 * q^30 - 359 * q^31 + 676 * q^32 + 208 * q^33 + 1007 * q^34 - 514 * q^35 + 776 * q^36 + 510 * q^37 - 2066 * q^38 + 898 * q^39 - 1248 * q^40 - 270 * q^41 - 915 * q^42 + 3256 * q^44 + 807 * q^45 + 1960 * q^46 + 1421 * q^47 - 632 * q^48 + 386 * q^49 - 141 * q^50 + 209 * q^51 + 2825 * q^52 - 21 * q^53 + 2368 * q^54 + 2258 * q^55 + 2521 * q^56 - 1723 * q^57 - 347 * q^58 + 1752 * q^59 + 2711 * q^60 + 1759 * q^61 + 395 * q^62 + 2204 * q^63 + 222 * q^64 + 1151 * q^65 + 160 * q^66 - 3001 * q^67 + 1921 * q^68 + 1660 * q^69 + 1597 * q^70 + 727 * q^71 + 9100 * q^72 + 4623 * q^73 - 2649 * q^74 + 1027 * q^75 + 874 * q^76 + 3556 * q^77 - 4979 * q^78 + 546 * q^79 + 5809 * q^80 - 410 * q^81 - 4397 * q^82 - 492 * q^83 - 10611 * q^84 - 1723 * q^85 + 5937 * q^87 + 3974 * q^88 + 5218 * q^89 + 10492 * q^90 + 1104 * q^91 + 1060 * q^92 + 1997 * q^93 - 2134 * q^94 + 6346 * q^95 - 11984 * q^96 + 2590 * q^97 + 6270 * q^98 - 2693 * 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 $

$2$	−1.99192	−0.704249	−0.352125	−	0.935953i	$-0.614541\pi$
$2$	−1.99192	−0.704249	−0.352125	+	0.935953i	$0.614541\pi$
$3$	10.2076	1.96445	0.982223	−	0.187716i	$-0.0601084\pi$
$3$	10.2076	1.96445	0.982223	+	0.187716i	$0.0601084\pi$
$4$	−4.03226	−0.504033
$5$	−6.84373	−0.612122	−0.306061	−	0.952012i	$-0.599011\pi$
$5$	−6.84373	−0.612122	−0.306061	+	0.952012i	$0.599011\pi$
$6$	−20.3326	−1.38346
$7$	−3.06785	−0.165648	−0.0828242	−	0.996564i	$-0.526394\pi$
$7$	−3.06785	−0.165648	−0.0828242	+	0.996564i	$0.526394\pi$
$8$	23.9673	1.05921
$9$	77.1944	2.85905
$10$	13.6322	0.431087
$11$	−55.5509	−1.52266	−0.761328	−	0.648366i	$-0.775452\pi$
$11$	−55.5509	−1.52266	−0.761328	+	0.648366i	$0.775452\pi$
$12$	−41.1596	−0.990146
$13$	26.7334	0.570347	0.285173	−	0.958476i	$-0.407949\pi$
$13$	26.7334	0.570347	0.285173	+	0.958476i	$0.407949\pi$
$14$	6.11091	0.116658
$15$	−69.8578	−1.20248
$16$	−15.4828	−0.241918
$17$	40.1392	0.572658	0.286329	−	0.958131i	$-0.407565\pi$
$17$	40.1392	0.572658	0.286329	+	0.958131i	$0.407565\pi$
$18$	−153.765	−2.01349
$19$	64.0680	0.773590	0.386795	−	0.922166i	$-0.373582\pi$
$19$	64.0680	0.773590	0.386795	+	0.922166i	$0.373582\pi$
$20$	27.5957	0.308530
$21$	−31.3153	−0.325407
$22$	110.653	1.07233
$23$	−111.100	−1.00722	−0.503610	−	0.863931i	$-0.667995\pi$
$23$	−111.100	−1.00722	−0.503610	+	0.863931i	$0.667995\pi$
$24$	244.648	2.08077
$25$	−78.1633	−0.625307
$26$	−53.2507	−0.401666
$27$	512.362	3.65201
$28$	12.3704	0.0834922
$29$	−126.560	−0.810399	−0.405199	−	0.914228i	$-0.632798\pi$
$29$	−126.560	−0.810399	−0.405199	+	0.914228i	$0.632798\pi$
$30$	139.151	0.846847
$31$	203.345	1.17812	0.589062	−	0.808088i	$-0.299497\pi$
$31$	203.345	1.17812	0.589062	+	0.808088i	$0.299497\pi$
$32$	−160.898	−0.888844
$33$	−567.039	−2.99118
$34$	−79.9540	−0.403294
$35$	20.9955	0.101397
$36$	−311.268	−1.44106
$37$	−46.2282	−0.205402	−0.102701	−	0.994712i	$-0.532748\pi$
$37$	−46.2282	−0.205402	−0.102701	+	0.994712i	$0.532748\pi$
$38$	−127.618	−0.544800
$39$	272.883	1.12042
$40$	−164.026	−0.648368
$41$	200.645	0.764282	0.382141	−	0.924104i	$-0.375187\pi$
$41$	200.645	0.764282	0.382141	+	0.924104i	$0.375187\pi$
$42$	62.3775	0.229168
$43$	0	0
$43$	0	0
$44$	223.996	0.767469
$45$	−528.298	−1.75009
$46$	221.303	0.709334
$47$	376.759	1.16927	0.584637	−	0.811295i	$-0.301237\pi$
$47$	376.759	1.16927	0.584637	+	0.811295i	$0.301237\pi$
$48$	−158.041	−0.475235
$49$	−333.588	−0.972561
$50$	155.695	0.440372
$51$	409.724	1.12496
$52$	−107.796	−0.287474
$53$	612.239	1.58674	0.793372	−	0.608737i	$-0.208323\pi$
$53$	612.239	1.58674	0.793372	+	0.608737i	$0.208323\pi$
$54$	−1020.58	−2.57192
$55$	380.175	0.932052
$56$	−73.5280	−0.175457
$57$	653.978	1.51968
$58$	252.097	0.570723
$59$	270.064	0.595922	0.297961	−	0.954578i	$-0.403693\pi$
$59$	270.064	0.595922	0.297961	+	0.954578i	$0.403693\pi$
$60$	281.685	0.606090
$61$	292.472	0.613889	0.306945	−	0.951727i	$-0.400693\pi$
$61$	292.472	0.613889	0.306945	+	0.951727i	$0.400693\pi$
$62$	−405.047	−0.829693
$63$	−236.821	−0.473597
$64$	444.357	0.867886
$65$	−182.956	−0.349122
$66$	1129.50	2.10654
$67$	−270.489	−0.493216	−0.246608	−	0.969115i	$-0.579316\pi$
$67$	−270.489	−0.493216	−0.246608	+	0.969115i	$0.579316\pi$
$68$	−161.852	−0.288639
$69$	−1134.07	−1.97863
$70$	−41.8214	−0.0714088
$71$	−340.360	−0.568919	−0.284460	−	0.958688i	$-0.591814\pi$
$71$	−340.360	−0.568919	−0.284460	+	0.958688i	$0.591814\pi$
$72$	1850.14	3.02835
$73$	−56.5822	−0.0907185	−0.0453592	−	0.998971i	$-0.514443\pi$
$73$	−56.5822	−0.0907185	−0.0453592	+	0.998971i	$0.514443\pi$
$74$	92.0828	0.144654
$75$	−797.857	−1.22838
$76$	−258.339	−0.389915
$77$	170.422	0.252226
$78$	−543.560	−0.789052
$79$	−746.369	−1.06295	−0.531475	−	0.847074i	$-0.678362\pi$
$79$	−746.369	−1.06295	−0.531475	+	0.847074i	$0.678362\pi$
$80$	105.960	0.148083
$81$	3145.72	4.31512
$82$	−399.669	−0.538245
$83$	1009.86	1.33550	0.667751	−	0.744385i	$-0.267257\pi$
$83$	1009.86	1.33550	0.667751	+	0.744385i	$0.267257\pi$
$84$	126.271	0.164016
$85$	−274.702	−0.350537
$86$	0	0
$87$	−1291.87	−1.59199
$88$	−1331.40	−1.61282
$89$	−493.858	−0.588190	−0.294095	−	0.955776i	$-0.595018\pi$
$89$	−493.858	−0.588190	−0.294095	+	0.955776i	$0.595018\pi$
$90$	1052.33	1.23250
$91$	−82.0141	−0.0944770
$92$	447.986	0.507672
$93$	2075.66	2.31436
$94$	−750.472	−0.823460
$95$	−438.464	−0.473531
$96$	−1642.38	−1.74609
$97$	−233.566	−0.244485	−0.122243	−	0.992500i	$-0.539009\pi$
$97$	−233.566	−0.244485	−0.122243	+	0.992500i	$0.539009\pi$
$98$	664.481	0.684925
$99$	−4288.22	−4.35335
$100$	315.175	0.315175
$101$	1110.83	1.09437	0.547185	−	0.837012i	$-0.315700\pi$
$101$	1110.83	1.09437	0.547185	+	0.837012i	$0.315700\pi$
$102$	−816.136	−0.792250
$103$	−774.289	−0.740708	−0.370354	−	0.928891i	$-0.620764\pi$
$103$	−774.289	−0.740708	−0.370354	+	0.928891i	$0.620764\pi$
$104$	640.727	0.604120
$105$	214.313	0.199189
$106$	−1219.53	−1.11746
$107$	121.406	0.109689	0.0548445	−	0.998495i	$-0.482534\pi$
$107$	121.406	0.109689	0.0548445	+	0.998495i	$0.482534\pi$
$108$	−2065.98	−1.84073
$109$	195.148	0.171485	0.0857423	−	0.996317i	$-0.472674\pi$
$109$	195.148	0.171485	0.0857423	+	0.996317i	$0.472674\pi$
$110$	−757.278	−0.656397
$111$	−471.877	−0.403501
$112$	47.4988	0.0400733
$113$	−329.250	−0.274100	−0.137050	−	0.990564i	$-0.543762\pi$
$113$	−329.250	−0.274100	−0.137050	+	0.990564i	$0.543762\pi$
$114$	−1302.67	−1.07023
$115$	760.342	0.616541
$116$	510.322	0.408468
$117$	2063.67	1.63065
$118$	−537.946	−0.419678
$119$	−123.141	−0.0948599
$120$	−1674.30	−1.27369
$121$	1754.90	1.31848
$122$	−582.581	−0.432331
$123$	2048.10	1.50139
$124$	−819.941	−0.593813
$125$	1390.40	0.994886
$126$	471.728	0.333530
$127$	−882.109	−0.616335	−0.308168	−	0.951332i	$-0.599716\pi$
$127$	−882.109	−0.616335	−0.308168	+	0.951332i	$0.599716\pi$
$128$	402.059	0.277636
$129$	0	0
$130$	364.434	0.245869
$131$	825.938	0.550859	0.275429	−	0.961321i	$-0.411180\pi$
$131$	825.938	0.550859	0.275429	+	0.961321i	$0.411180\pi$
$132$	2286.45	1.50765
$133$	−196.551	−0.128144
$134$	538.791	0.347347
$135$	−3506.47	−2.23547
$136$	962.028	0.606568
$137$	1326.25	0.827076	0.413538	−	0.910487i	$-0.364293\pi$
$137$	1326.25	0.827076	0.413538	+	0.910487i	$0.364293\pi$
$138$	2258.96	1.39345
$139$	2692.27	1.64284	0.821422	−	0.570321i	$-0.193181\pi$
$139$	2692.27	1.64284	0.821422	+	0.570321i	$0.193181\pi$
$140$	−84.6596	−0.0511074
$141$	3845.79	2.29698
$142$	677.968	0.400661
$143$	−1485.06	−0.868443
$144$	−1195.18	−0.691656
$145$	866.141	0.496063
$146$	112.707	0.0638884
$147$	−3405.12	−1.91054
$148$	186.404	0.103529
$149$	2564.07	1.40978	0.704888	−	0.709318i	$-0.250997\pi$
$149$	2564.07	1.40978	0.704888	+	0.709318i	$0.250997\pi$
$150$	1589.27	0.865087
$151$	126.823	0.0683489	0.0341744	−	0.999416i	$-0.489120\pi$
$151$	126.823	0.0683489	0.0341744	+	0.999416i	$0.489120\pi$
$152$	1535.54	0.819397
$153$	3098.52	1.63726
$154$	−339.466	−0.177630
$155$	−1391.64	−0.721156
$156$	−1100.34	−0.564727
$157$	2290.52	1.16435	0.582175	−	0.813063i	$-0.302202\pi$
$157$	2290.52	1.16435	0.582175	+	0.813063i	$0.302202\pi$
$158$	1486.71	0.748582
$159$	6249.47	3.11708
$160$	1101.14	0.544081
$161$	340.840	0.166844
$162$	−6266.03	−3.03892
$163$	998.489	0.479802	0.239901	−	0.970797i	$-0.422885\pi$
$163$	998.489	0.479802	0.239901	+	0.970797i	$0.422885\pi$
$164$	−809.055	−0.385223
$165$	3880.67	1.83097
$166$	−2011.56	−0.940526
$167$	−488.023	−0.226134	−0.113067	−	0.993587i	$-0.536067\pi$
$167$	−488.023	−0.226134	−0.113067	+	0.993587i	$0.536067\pi$
$168$	−750.542	−0.344676
$169$	−1482.33	−0.674704
$170$	547.184	0.246865
$171$	4945.69	2.21173
$172$	0	0
$173$	−209.092	−0.0918901	−0.0459450	−	0.998944i	$-0.514630\pi$
$173$	−209.092	−0.0918901	−0.0459450	+	0.998944i	$0.514630\pi$
$174$	2573.29	1.12115
$175$	239.793	0.103581
$176$	860.081	0.368358
$177$	2756.70	1.17066
$178$	983.725	0.414232
$179$	966.219	0.403456	0.201728	−	0.979442i	$-0.435344\pi$
$179$	966.219	0.403456	0.201728	+	0.979442i	$0.435344\pi$
$180$	2130.24	0.882102
$181$	1351.58	0.555040	0.277520	−	0.960720i	$-0.410488\pi$
$181$	1351.58	0.555040	0.277520	+	0.960720i	$0.410488\pi$
$182$	163.365	0.0665354
$183$	2985.43	1.20595
$184$	−2662.78	−1.06686
$185$	316.373	0.125731
$186$	−4134.54	−1.62989
$187$	−2229.77	−0.871962
$188$	−1519.19	−0.589352
$189$	−1571.85	−0.604949
$190$	873.385	0.333484
$191$	3993.07	1.51271	0.756356	−	0.654160i	$-0.226978\pi$
$191$	3993.07	1.51271	0.756356	+	0.654160i	$0.226978\pi$
$192$	4535.81	1.70492
$193$	−3665.74	−1.36718	−0.683590	−	0.729867i	$-0.739582\pi$
$193$	−3665.74	−1.36718	−0.683590	+	0.729867i	$0.739582\pi$
$194$	465.245	0.172179
$195$	−1867.54	−0.685831
$196$	1345.12	0.490202
$197$	1532.53	0.554255	0.277128	−	0.960833i	$-0.410618\pi$
$197$	1532.53	0.554255	0.277128	+	0.960833i	$0.410618\pi$
$198$	8541.78	3.06585
$199$	5273.73	1.87862	0.939309	−	0.343073i	$-0.111468\pi$
$199$	5273.73	1.87862	0.939309	+	0.343073i	$0.111468\pi$
$200$	−1873.36	−0.662334
$201$	−2761.03	−0.968896
$202$	−2212.67	−0.770709
$203$	388.267	0.134241
$204$	−1652.11	−0.567015
$205$	−1373.16	−0.467834
$206$	1542.32	0.521643
$207$	−8576.33	−2.87969
$208$	−413.907	−0.137977
$209$	−3559.03	−1.17791
$210$	−426.895	−0.140279
$211$	−2077.53	−0.677835	−0.338918	−	0.940816i	$-0.610061\pi$
$211$	−2077.53	−0.677835	−0.338918	+	0.940816i	$0.610061\pi$
$212$	−2468.71	−0.799771
$213$	−3474.24	−1.11761
$214$	−241.830	−0.0772485
$215$	0	0
$216$	12279.9	3.86826
$217$	−623.832	−0.195154
$218$	−388.719	−0.120768
$219$	−577.567	−0.178212
$220$	−1532.97	−0.469785
$221$	1073.06	0.326614
$222$	939.941	0.284165
$223$	3843.45	1.15416	0.577078	−	0.816689i	$-0.304193\pi$
$223$	3843.45	1.15416	0.577078	+	0.816689i	$0.304193\pi$
$224$	493.611	0.147235
$225$	−6033.77	−1.78778
$226$	655.839	0.193034
$227$	−2874.84	−0.840572	−0.420286	−	0.907392i	$-0.638070\pi$
$227$	−2874.84	−0.840572	−0.420286	+	0.907392i	$0.638070\pi$
$228$	−2637.01	−0.765966
$229$	2231.07	0.643813	0.321906	−	0.946772i	$-0.395676\pi$
$229$	2231.07	0.643813	0.321906	+	0.946772i	$0.395676\pi$
$230$	−1514.54	−0.434199
$231$	1739.59	0.495484
$232$	−3033.29	−0.858386
$233$	1568.24	0.440939	0.220469	−	0.975394i	$-0.429241\pi$
$233$	1568.24	0.440939	0.220469	+	0.975394i	$0.429241\pi$
$234$	−4110.66	−1.14839
$235$	−2578.43	−0.715738
$236$	−1088.97	−0.300364
$237$	−7618.61	−2.08811
$238$	245.287	0.0668050
$239$	−5449.26	−1.47483	−0.737413	−	0.675443i	$-0.763953\pi$
$239$	−5449.26	−1.47483	−0.737413	+	0.675443i	$0.763953\pi$
$240$	1081.59	0.290902
$241$	−1105.43	−0.295464	−0.147732	−	0.989027i	$-0.547197\pi$
$241$	−1105.43	−0.295464	−0.147732	+	0.989027i	$0.547197\pi$
$242$	−3495.62	−0.928541
$243$	18276.4	4.82482
$244$	−1179.32	−0.309420
$245$	2282.99	0.595326
$246$	−4079.65	−1.05735
$247$	1712.75	0.441214
$248$	4873.63	1.24789
$249$	10308.2	2.62352
$250$	−2769.55	−0.700648
$251$	2228.59	0.560426	0.280213	−	0.959938i	$-0.409595\pi$
$251$	2228.59	0.560426	0.280213	+	0.959938i	$0.409595\pi$
$252$	954.924	0.238709
$253$	6171.73	1.53365
$254$	1757.09	0.434054
$255$	−2804.04	−0.688611
$256$	−4355.73	−1.06341
$257$	262.409	0.0636910	0.0318455	−	0.999493i	$-0.489862\pi$
$257$	262.409	0.0636910	0.0318455	+	0.999493i	$0.489862\pi$
$258$	0	0
$259$	141.821	0.0340245
$260$	737.728	0.175969
$261$	−9769.71	−2.31697
$262$	−1645.20	−0.387942
$263$	1511.24	0.354324	0.177162	−	0.984182i	$-0.443308\pi$
$263$	1511.24	0.354324	0.177162	+	0.984182i	$0.443308\pi$
$264$	−13590.4	−3.16830
$265$	−4190.00	−0.971281
$266$	391.513	0.0902452
$267$	−5041.09	−1.15547
$268$	1090.68	0.248597
$269$	5064.78	1.14797	0.573987	−	0.818864i	$-0.305396\pi$
$269$	5064.78	1.14797	0.573987	+	0.818864i	$0.305396\pi$
$270$	6984.60	1.57433
$271$	8268.05	1.85331	0.926657	−	0.375908i	$-0.122669\pi$
$271$	8268.05	1.85331	0.926657	+	0.375908i	$0.122669\pi$
$272$	−621.466	−0.138536
$273$	−837.164	−0.185595
$274$	−2641.79	−0.582468
$275$	4342.04	0.952127
$276$	4572.85	0.997294
$277$	−2561.08	−0.555524	−0.277762	−	0.960650i	$-0.589593\pi$
$277$	−2561.08	−0.555524	−0.277762	+	0.960650i	$0.589593\pi$
$278$	−5362.78	−1.15697
$279$	15697.1	3.36832
$280$	503.206	0.107401
$281$	3062.56	0.650168	0.325084	−	0.945685i	$-0.394607\pi$
$281$	3062.56	0.650168	0.325084	+	0.945685i	$0.394607\pi$
$282$	−7660.49	−1.61764
$283$	3529.03	0.741268	0.370634	−	0.928779i	$-0.379140\pi$
$283$	3529.03	0.741268	0.370634	+	0.928779i	$0.379140\pi$
$284$	1372.42	0.286754
$285$	−4475.65	−0.930227
$286$	2958.13	0.611600
$287$	−615.550	−0.126602
$288$	−12420.4	−2.54125
$289$	−3301.84	−0.672063
$290$	−1725.28	−0.349352
$291$	−2384.15	−0.480279
$292$	228.154	0.0457251
$293$	2408.24	0.480174	0.240087	−	0.970751i	$-0.422824\pi$
$293$	2408.24	0.480174	0.240087	+	0.970751i	$0.422824\pi$
$294$	6782.73	1.34550
$295$	−1848.25	−0.364777
$296$	−1107.96	−0.217565
$297$	−28462.2	−5.56075
$298$	−5107.41	−0.992834
$299$	−2970.09	−0.574465
$300$	3217.17	0.619145
$301$	0	0
$302$	−252.620	−0.0481346
$303$	11338.8	2.14983
$304$	−991.949	−0.187145
$305$	−2001.60	−0.375775
$306$	−6172.00	−1.15304
$307$	1074.69	0.199791	0.0998955	−	0.994998i	$-0.468149\pi$
$307$	1074.69	0.199791	0.0998955	+	0.994998i	$0.468149\pi$
$308$	−687.186	−0.127130
$309$	−7903.60	−1.45508
$310$	2772.03	0.507873
$311$	−5909.36	−1.07746	−0.538728	−	0.842480i	$-0.681095\pi$
$311$	−5909.36	−1.07746	−0.538728	+	0.842480i	$0.681095\pi$
$312$	6540.26	1.18676
$313$	3241.10	0.585296	0.292648	−	0.956220i	$-0.405464\pi$
$313$	3241.10	0.585296	0.292648	+	0.956220i	$0.405464\pi$
$314$	−4562.52	−0.819993
$315$	1620.74	0.289899
$316$	3009.56	0.535762
$317$	−6.02888	−0.00106819	−0.000534094	−	1.00000i	$-0.500170\pi$
$317$	−6.02888	−0.00106819	−0.000534094		1.00000i	$0.500170\pi$
$318$	−12448.4	−2.19520
$319$	7030.51	1.23396
$320$	−3041.06	−0.531252
$321$	1239.26	0.215478
$322$	−678.925	−0.117500
$323$	2571.64	0.443002
$324$	−12684.4	−2.17496
$325$	−2089.57	−0.356642
$326$	−1988.91	−0.337900
$327$	1991.99	0.336872
$328$	4808.92	0.809538
$329$	−1155.84	−0.193688
$330$	−7729.97	−1.28946
$331$	−8455.13	−1.40404	−0.702018	−	0.712159i	$-0.747718\pi$
$331$	−8455.13	−1.40404	−0.702018	+	0.712159i	$0.747718\pi$
$332$	−4072.02	−0.673137
$333$	−3568.56	−0.587255
$334$	972.102	0.159255
$335$	1851.15	0.301908
$336$	484.847	0.0787219
$337$	−11343.1	−1.83352	−0.916762	−	0.399433i	$-0.869207\pi$
$337$	−11343.1	−1.83352	−0.916762	+	0.399433i	$0.869207\pi$
$338$	2952.67	0.475160
$339$	−3360.84	−0.538454
$340$	1107.67	0.176682
$341$	−11296.0	−1.79388
$342$	−9851.40	−1.55761
$343$	2075.67	0.326751
$344$	0	0
$345$	7761.24	1.21116
$346$	416.494	0.0647135
$347$	−2180.25	−0.337297	−0.168648	−	0.985676i	$-0.553940\pi$
$347$	−2180.25	−0.337297	−0.168648	+	0.985676i	$0.553940\pi$
$348$	5209.15	0.802413
$349$	6626.04	1.01629	0.508143	−	0.861273i	$-0.330332\pi$
$349$	6626.04	1.01629	0.508143	+	0.861273i	$0.330332\pi$
$350$	−477.649	−0.0729469
$351$	13697.2	2.08291
$352$	8938.02	1.35340
$353$	−5639.16	−0.850261	−0.425131	−	0.905132i	$-0.639772\pi$
$353$	−5639.16	−0.850261	−0.425131	+	0.905132i	$0.639772\pi$
$354$	−5491.12	−0.824435
$355$	2329.33	0.348248
$356$	1991.37	0.296467
$357$	−1256.97	−0.186347
$358$	−1924.63	−0.284133
$359$	−8966.46	−1.31819	−0.659097	−	0.752058i	$-0.729061\pi$
$359$	−8966.46	−1.31819	−0.659097	+	0.752058i	$0.729061\pi$
$360$	−12661.9	−1.85372
$361$	−2754.29	−0.401559
$362$	−2692.24	−0.390886
$363$	17913.3	2.59009
$364$	330.702	0.0476195
$365$	387.234	0.0555308
$366$	−5946.73	−0.849291
$367$	7348.77	1.04524	0.522620	−	0.852566i	$-0.324955\pi$
$367$	7348.77	1.04524	0.522620	+	0.852566i	$0.324955\pi$
$368$	1720.14	0.243665
$369$	15488.7	2.18512
$370$	−630.190	−0.0885460
$371$	−1878.26	−0.262842
$372$	−8369.60	−1.16651
$373$	9025.83	1.25292	0.626460	−	0.779453i	$-0.284503\pi$
$373$	9025.83	1.25292	0.626460	+	0.779453i	$0.284503\pi$
$374$	4441.52	0.614079
$375$	14192.6	1.95440
$376$	9029.88	1.23851
$377$	−3383.37	−0.462208
$378$	3131.00	0.426035
$379$	−1109.88	−0.150424	−0.0752121	−	0.997168i	$-0.523963\pi$
$379$	−1109.88	−0.150424	−0.0752121	+	0.997168i	$0.523963\pi$
$380$	1768.00	0.238675
$381$	−9004.19	−1.21076
$382$	−7953.86	−1.06533
$383$	5623.99	0.750320	0.375160	−	0.926960i	$-0.377588\pi$
$383$	5623.99	0.750320	0.375160	+	0.926960i	$0.377588\pi$
$384$	4104.05	0.545400
$385$	−1166.32	−0.154393
$386$	7301.85	0.962835
$387$	0	0
$388$	941.801	0.123229
$389$	9720.63	1.26698	0.633490	−	0.773750i	$-0.281622\pi$
$389$	9720.63	1.26698	0.633490	+	0.773750i	$0.281622\pi$
$390$	3719.98	0.482996
$391$	−4459.48	−0.576792
$392$	−7995.20	−1.03015
$393$	8430.81	1.08213
$394$	−3052.68	−0.390334
$395$	5107.95	0.650656
$396$	17291.2	2.19423
$397$	7028.01	0.888478	0.444239	−	0.895908i	$-0.353474\pi$
$397$	7028.01	0.888478	0.444239	+	0.895908i	$0.353474\pi$
$398$	−10504.8	−1.32302
$399$	−2006.31	−0.251732
$400$	1210.18	0.151273
$401$	−1825.44	−0.227327	−0.113663	−	0.993519i	$-0.536259\pi$
$401$	−1825.44	−0.227327	−0.113663	+	0.993519i	$0.536259\pi$
$402$	5499.75	0.682345
$403$	5436.10	0.671939
$404$	−4479.14	−0.551598
$405$	−21528.5	−2.64138
$406$	−773.395	−0.0945393
$407$	2568.02	0.312757
$408$	9819.96	1.19157
$409$	−964.011	−0.116546	−0.0582730	−	0.998301i	$-0.518559\pi$
$409$	−964.011	−0.116546	−0.0582730	+	0.998301i	$0.518559\pi$
$410$	2735.23	0.329472
$411$	13537.8	1.62475
$412$	3122.14	0.373341
$413$	−828.518	−0.0987135
$414$	17083.3	2.02802
$415$	−6911.22	−0.817490
$416$	−4301.35	−0.506949
$417$	27481.5	3.22728
$418$	7089.30	0.829543
$419$	3567.90	0.415998	0.207999	−	0.978129i	$-0.433305\pi$
$419$	3567.90	0.415998	0.207999	+	0.978129i	$0.433305\pi$
$420$	−864.168	−0.100398
$421$	1564.20	0.181080	0.0905400	−	0.995893i	$-0.471141\pi$
$421$	1564.20	0.181080	0.0905400	+	0.995893i	$0.471141\pi$
$422$	4138.27	0.477365
$423$	29083.6	3.34301
$424$	14673.7	1.68070
$425$	−3137.41	−0.358087
$426$	6920.41	0.787077
$427$	−897.261	−0.101690
$428$	−489.540	−0.0552869
$429$	−15158.9	−1.70601
$430$	0	0
$431$	−3359.76	−0.375485	−0.187743	−	0.982218i	$-0.560117\pi$
$431$	−3359.76	−0.375485	−0.187743	+	0.982218i	$0.560117\pi$
$432$	−7932.78	−0.883487
$433$	−4767.12	−0.529083	−0.264542	−	0.964374i	$-0.585221\pi$
$433$	−4767.12	−0.529083	−0.264542	+	0.964374i	$0.585221\pi$
$434$	1242.62	0.137437
$435$	8841.19	0.974489
$436$	−786.889	−0.0864338
$437$	−7117.98	−0.779174
$438$	1150.47	0.125505
$439$	−6133.96	−0.666875	−0.333437	−	0.942772i	$-0.608209\pi$
$439$	−6133.96	−0.666875	−0.333437	+	0.942772i	$0.608209\pi$
$440$	9111.77	0.987243
$441$	−25751.1	−2.78060
$442$	−2137.44	−0.230018
$443$	8236.67	0.883377	0.441689	−	0.897168i	$-0.354380\pi$
$443$	8236.67	0.883377	0.441689	+	0.897168i	$0.354380\pi$
$444$	1902.73	0.203378
$445$	3379.83	0.360044
$446$	−7655.84	−0.812813
$447$	26172.9	2.76943
$448$	−1363.22	−0.143764
$449$	13107.1	1.37765	0.688823	−	0.724930i	$-0.258128\pi$
$449$	13107.1	1.37765	0.688823	+	0.724930i	$0.258128\pi$
$450$	12018.8	1.25905
$451$	−11146.0	−1.16374
$452$	1327.62	0.138155
$453$	1294.55	0.134268
$454$	5726.44	0.591972
$455$	561.282	0.0578315
$456$	15674.1	1.60966
$457$	−14371.3	−1.47104	−0.735518	−	0.677505i	$-0.763061\pi$
$457$	−14371.3	−1.47104	−0.735518	+	0.677505i	$0.763061\pi$
$458$	−4444.10	−0.453405
$459$	20565.8	2.09135
$460$	−3065.90	−0.310757
$461$	4672.44	0.472055	0.236027	−	0.971746i	$-0.424154\pi$
$461$	4672.44	0.472055	0.236027	+	0.971746i	$0.424154\pi$
$462$	−3465.12	−0.348944
$463$	−17951.5	−1.80190	−0.900948	−	0.433928i	$-0.857127\pi$
$463$	−17951.5	−1.80190	−0.900948	+	0.433928i	$0.857127\pi$
$464$	1959.49	0.196050
$465$	−14205.2	−1.41667
$466$	−3123.80	−0.310531
$467$	10912.5	1.08130	0.540652	−	0.841246i	$-0.318178\pi$
$467$	10912.5	1.08130	0.540652	+	0.841246i	$0.318178\pi$
$468$	−8321.25	−0.821902
$469$	829.819	0.0817004
$470$	5136.03	0.504058
$471$	23380.6	2.28730
$472$	6472.71	0.631209
$473$	0	0
$474$	15175.7	1.47055
$475$	−5007.77	−0.483731
$476$	496.537	0.0478125
$477$	47261.4	4.53658
$478$	10854.5	1.03864
$479$	−3565.14	−0.340073	−0.170037	−	0.985438i	$-0.554389\pi$
$479$	−3565.14	−0.340073	−0.170037	+	0.985438i	$0.554389\pi$
$480$	11240.0	1.06882
$481$	−1235.84	−0.117150
$482$	2201.92	0.208081
$483$	3479.14	0.327757
$484$	−7076.23	−0.664559
$485$	1598.47	0.149655
$486$	−36405.1	−3.39788
$487$	−5292.58	−0.492463	−0.246232	−	0.969211i	$-0.579192\pi$
$487$	−5292.58	−0.492463	−0.246232	+	0.969211i	$0.579192\pi$
$488$	7009.76	0.650240
$489$	10192.1	0.942545
$490$	−4547.53	−0.419258
$491$	16858.3	1.54950	0.774749	−	0.632268i	$-0.217876\pi$
$491$	16858.3	1.54950	0.774749	+	0.632268i	$0.217876\pi$
$492$	−8258.48	−0.756750
$493$	−5080.01	−0.464081
$494$	−3411.67	−0.310725
$495$	29347.4	2.66478
$496$	−3148.34	−0.285009
$497$	1044.17	0.0942405
$498$	−20533.1	−1.84761
$499$	−1336.95	−0.119940	−0.0599700	−	0.998200i	$-0.519100\pi$
$499$	−1336.95	−0.119940	−0.0599700	+	0.998200i	$0.519100\pi$
$500$	−5606.44	−0.501455
$501$	−4981.53	−0.444228
$502$	−4439.16	−0.394680
$503$	−588.399	−0.0521579	−0.0260789	−	0.999660i	$-0.508302\pi$
$503$	−588.399	−0.0521579	−0.0260789	+	0.999660i	$0.508302\pi$
$504$	−5675.95	−0.501641
$505$	−7602.20	−0.669888
$506$	−12293.6	−1.08007
$507$	−15130.9	−1.32542
$508$	3556.90	0.310653
$509$	−4470.26	−0.389275	−0.194637	−	0.980875i	$-0.562353\pi$
$509$	−4470.26	−0.389275	−0.194637	+	0.980875i	$0.562353\pi$
$510$	5585.42	0.484954
$511$	173.586	0.0150274
$512$	5459.78	0.471270
$513$	32826.0	2.82515
$514$	−522.696	−0.0448544
$515$	5299.03	0.453404
$516$	0	0
$517$	−20929.3	−1.78040
$518$	−282.496	−0.0239617
$519$	−2134.32	−0.180513
$520$	−4384.96	−0.369795
$521$	−2004.94	−0.168595	−0.0842973	−	0.996441i	$-0.526865\pi$
$521$	−2004.94	−0.168595	−0.0842973	+	0.996441i	$0.526865\pi$
$522$	19460.5	1.63173
$523$	15088.9	1.26155	0.630775	−	0.775966i	$-0.282737\pi$
$523$	15088.9	1.26155	0.630775	+	0.775966i	$0.282737\pi$
$524$	−3330.40	−0.277651
$525$	2447.71	0.203479
$526$	−3010.27	−0.249532
$527$	8162.11	0.674662
$528$	8779.33	0.723620
$529$	176.312	0.0144910
$530$	8346.13	0.684024
$531$	20847.5	1.70377
$532$	792.545	0.0645887
$533$	5363.93	0.435906
$534$	10041.4	0.813737
$535$	−830.868	−0.0671431
$536$	−6482.88	−0.522421
$537$	9862.74	0.792567
$538$	−10088.6	−0.808460
$539$	18531.1	1.48088
$540$	14139.0	1.12675
$541$	22064.9	1.75351	0.876753	−	0.480942i	$-0.159705\pi$
$541$	22064.9	1.75351	0.876753	+	0.480942i	$0.159705\pi$
$542$	−16469.3	−1.30520
$543$	13796.3	1.09035
$544$	−6458.31	−0.509003
$545$	−1335.54	−0.104969
$546$	1667.56	0.130705
$547$	14252.1	1.11403	0.557015	−	0.830503i	$-0.311947\pi$
$547$	14252.1	1.11403	0.557015	+	0.830503i	$0.311947\pi$
$548$	−5347.80	−0.416874
$549$	22577.2	1.75514
$550$	−8648.99	−0.670535
$551$	−8108.43	−0.626916
$552$	−27180.5	−2.09579
$553$	2289.75	0.176076
$554$	5101.46	0.391228
$555$	3229.40	0.246992
$556$	−10855.9	−0.828047
$557$	−25835.0	−1.96529	−0.982644	−	0.185501i	$-0.940609\pi$
$557$	−25835.0	−1.96529	−0.982644	+	0.185501i	$0.940609\pi$
$558$	−31267.3	−2.37214
$559$	0	0
$560$	−325.069	−0.0245298
$561$	−22760.5	−1.71292
$562$	−6100.37	−0.457880
$563$	−8682.88	−0.649982	−0.324991	−	0.945717i	$-0.605361\pi$
$563$	−8682.88	−0.649982	−0.324991	+	0.945717i	$0.605361\pi$
$564$	−15507.2	−1.15775
$565$	2253.30	0.167782
$566$	−7029.53	−0.522038
$567$	−9650.61	−0.714793
$568$	−8157.49	−0.602607
$569$	19555.3	1.44077	0.720386	−	0.693573i	$-0.243965\pi$
$569$	19555.3	1.44077	0.720386	+	0.693573i	$0.243965\pi$
$570$	8915.13	0.655112
$571$	6344.93	0.465021	0.232511	−	0.972594i	$-0.425306\pi$
$571$	6344.93	0.465021	0.232511	+	0.972594i	$0.425306\pi$
$572$	5988.17	0.437724
$573$	40759.5	2.97164
$574$	1226.13	0.0891594
$575$	8683.98	0.629821
$576$	34301.9	2.48133
$577$	−4453.16	−0.321295	−0.160648	−	0.987012i	$-0.551358\pi$
$577$	−4453.16	−0.321295	−0.160648	+	0.987012i	$0.551358\pi$
$578$	6577.00	0.473300
$579$	−37418.3	−2.68575
$580$	−3492.51	−0.250032
$581$	−3098.10	−0.221224
$582$	4749.02	0.338236
$583$	−34010.4	−2.41607
$584$	−1356.12	−0.0960903
$585$	−14123.2	−0.998158
$586$	−4797.02	−0.338162
$587$	−7983.41	−0.561347	−0.280673	−	0.959803i	$-0.590558\pi$
$587$	−7983.41	−0.561347	−0.280673	+	0.959803i	$0.590558\pi$
$588$	13730.4	0.962977
$589$	13027.9	0.911384
$590$	3681.56	0.256894
$591$	15643.4	1.08880
$592$	715.740	0.0496904
$593$	14816.9	1.02606	0.513032	−	0.858369i	$-0.328522\pi$
$593$	14816.9	1.02606	0.513032	+	0.858369i	$0.328522\pi$
$594$	56694.4	3.91616
$595$	842.745	0.0580658
$596$	−10339.0	−0.710574
$597$	53831.9	3.69044
$598$	5916.18	0.404566
$599$	17405.1	1.18723	0.593617	−	0.804748i	$-0.297700\pi$
$599$	17405.1	1.18723	0.593617	+	0.804748i	$0.297700\pi$
$600$	−19122.5	−1.30112
$601$	−22919.3	−1.55557	−0.777785	−	0.628531i	$-0.783657\pi$
$601$	−22919.3	−1.55557	−0.777785	+	0.628531i	$0.783657\pi$
$602$	0	0
$603$	−20880.2	−1.41013
$604$	−511.382	−0.0344501
$605$	−12010.1	−0.807073
$606$	−22586.0	−1.51402
$607$	−24432.6	−1.63375	−0.816877	−	0.576812i	$-0.804297\pi$
$607$	−24432.6	−1.63375	−0.816877	+	0.576812i	$0.804297\pi$
$608$	−10308.4	−0.687600
$609$	3963.26	0.263710
$610$	3987.03	0.264639
$611$	10072.0	0.666892
$612$	−12494.1	−0.825232
$613$	−12618.6	−0.831420	−0.415710	−	0.909497i	$-0.636467\pi$
$613$	−12618.6	−0.831420	−0.415710	+	0.909497i	$0.636467\pi$
$614$	−2140.70	−0.140703
$615$	−14016.7	−0.919034
$616$	4084.55	0.267161
$617$	−13727.0	−0.895669	−0.447835	−	0.894116i	$-0.647805\pi$
$617$	−13727.0	−0.895669	−0.447835	+	0.894116i	$0.647805\pi$
$618$	15743.3	1.02474
$619$	−23560.4	−1.52984	−0.764920	−	0.644126i	$-0.777221\pi$
$619$	−23560.4	−1.52984	−0.764920	+	0.644126i	$0.777221\pi$
$620$	5611.45	0.363486
$621$	−56923.7	−3.67837
$622$	11771.0	0.758798
$623$	1515.08	0.0974326
$624$	−4224.98	−0.271049
$625$	254.920	0.0163149
$626$	−6456.00	−0.412195
$627$	−36329.1	−2.31394
$628$	−9235.96	−0.586871
$629$	−1855.56	−0.117625
$630$	−3228.38	−0.204161
$631$	9127.67	0.575858	0.287929	−	0.957652i	$-0.407033\pi$
$631$	9127.67	0.575858	0.287929	+	0.957652i	$0.407033\pi$
$632$	−17888.4	−1.12589
$633$	−21206.5	−1.33157
$634$	12.0090	0.000752271 0
$635$	6036.92	0.377272
$636$	−25199.5	−1.57111
$637$	−8917.95	−0.554697
$638$	−14004.2	−0.869015
$639$	−26273.9	−1.62657
$640$	−2751.59	−0.169947
$641$	1386.22	0.0854174	0.0427087	−	0.999088i	$-0.486401\pi$
$641$	1386.22	0.0854174	0.0427087	+	0.999088i	$0.486401\pi$
$642$	−2468.50	−0.151750
$643$	−1666.60	−0.102215	−0.0511074	−	0.998693i	$-0.516275\pi$
$643$	−1666.60	−0.102215	−0.0511074	+	0.998693i	$0.516275\pi$
$644$	−1374.35	−0.0840950
$645$	0	0
$646$	−5122.49	−0.311984
$647$	−9557.30	−0.580736	−0.290368	−	0.956915i	$-0.593778\pi$
$647$	−9557.30	−0.580736	−0.290368	+	0.956915i	$0.593778\pi$
$648$	75394.5	4.57064
$649$	−15002.3	−0.907385
$650$	4162.25	0.251165
$651$	−6367.81	−0.383370
$652$	−4026.17	−0.241836
$653$	−13618.2	−0.816114	−0.408057	−	0.912956i	$-0.633794\pi$
$653$	−13618.2	−0.816114	−0.408057	+	0.912956i	$0.633794\pi$
$654$	−3967.88	−0.237242
$655$	−5652.50	−0.337193
$656$	−3106.54	−0.184894
$657$	−4367.83	−0.259369
$658$	2302.34	0.136405
$659$	−9970.72	−0.589384	−0.294692	−	0.955592i	$-0.595217\pi$
$659$	−9970.72	−0.589384	−0.294692	+	0.955592i	$0.595217\pi$
$660$	−15647.9	−0.922867
$661$	−24896.2	−1.46498	−0.732489	−	0.680779i	$-0.761641\pi$
$661$	−24896.2	−1.46498	−0.732489	+	0.680779i	$0.761641\pi$
$662$	16841.9	0.988792
$663$	10953.3	0.641615
$664$	24203.6	1.41458
$665$	1345.14	0.0784397
$666$	7108.27	0.413574
$667$	14060.9	0.816249
$668$	1967.84	0.113979
$669$	39232.3	2.26728
$670$	−3687.34	−0.212619
$671$	−16247.1	−0.934742
$672$	5038.56	0.289236
$673$	−17736.0	−1.01586	−0.507928	−	0.861400i	$-0.669588\pi$
$673$	−17736.0	−1.01586	−0.507928	+	0.861400i	$0.669588\pi$
$674$	22594.5	1.29126
$675$	−40048.0	−2.28362
$676$	5977.13	0.340073
$677$	−11989.8	−0.680659	−0.340330	−	0.940306i	$-0.610539\pi$
$677$	−11989.8	−0.680659	−0.340330	+	0.940306i	$0.610539\pi$
$678$	6694.52	0.379206
$679$	716.547	0.0404986
$680$	−6583.86	−0.371293
$681$	−29345.1	−1.65126
$682$	22500.7	1.26334
$683$	2050.49	0.114875	0.0574377	−	0.998349i	$-0.481707\pi$
$683$	2050.49	0.114875	0.0574377	+	0.998349i	$0.481707\pi$
$684$	−19942.3	−1.11479
$685$	−9076.52	−0.506272
$686$	−4134.57	−0.230114
$687$	22773.8	1.26474
$688$	0	0
$689$	16367.2	0.904995
$690$	−15459.8	−0.852960
$691$	−8777.30	−0.483219	−0.241610	−	0.970374i	$-0.577675\pi$
$691$	−8777.30	−0.483219	−0.241610	+	0.970374i	$0.577675\pi$
$692$	843.115	0.0463156
$693$	13155.6	0.721126
$694$	4342.88	0.237541
$695$	−18425.2	−1.00562
$696$	−30962.5	−1.68625
$697$	8053.75	0.437672
$698$	−13198.5	−0.715718
$699$	16007.9	0.866200
$700$	−966.910	−0.0522082
$701$	14868.3	0.801096	0.400548	−	0.916276i	$-0.368820\pi$
$701$	14868.3	0.801096	0.400548	+	0.916276i	$0.368820\pi$
$702$	−27283.7	−1.46689
$703$	−2961.75	−0.158897
$704$	−24684.5	−1.32149
$705$	−26319.5	−1.40603
$706$	11232.7	0.598796
$707$	−3407.85	−0.181280
$708$	−11115.7	−0.590050
$709$	−23185.2	−1.22812	−0.614061	−	0.789258i	$-0.710465\pi$
$709$	−23185.2	−1.22812	−0.614061	+	0.789258i	$0.710465\pi$
$710$	−4639.83	−0.245253
$711$	−57615.5	−3.03903
$712$	−11836.4	−0.623019
$713$	−22591.7	−1.18663
$714$	2503.78	0.131235
$715$	10163.4	0.531593
$716$	−3896.05	−0.203355
$717$	−55623.7	−2.89722
$718$	17860.5	0.928338
$719$	−5797.16	−0.300692	−0.150346	−	0.988633i	$-0.548039\pi$
$719$	−5797.16	−0.300692	−0.150346	+	0.988633i	$0.548039\pi$
$720$	8179.51	0.423378
$721$	2375.40	0.122697
$722$	5486.33	0.282798
$723$	−11283.7	−0.580424
$724$	−5449.93	−0.279758
$725$	9892.33	0.506748
$726$	−35681.8	−1.82407
$727$	29941.3	1.52746	0.763729	−	0.645537i	$-0.223366\pi$
$727$	29941.3	1.52746	0.763729	+	0.645537i	$0.223366\pi$
$728$	−1965.65	−0.100071
$729$	101623.	5.16298
$730$	−771.338	−0.0391075
$731$	0	0
$732$	−12038.0	−0.607840
$733$	30969.4	1.56055	0.780274	−	0.625438i	$-0.215080\pi$
$733$	30969.4	1.56055	0.780274	+	0.625438i	$0.215080\pi$
$734$	−14638.2	−0.736109
$735$	23303.8	1.16949
$736$	17875.8	0.895260
$737$	15025.9	0.750999
$738$	−30852.2	−1.53887
$739$	3888.14	0.193542	0.0967709	−	0.995307i	$-0.469149\pi$
$739$	3888.14	0.193542	0.0967709	+	0.995307i	$0.469149\pi$
$740$	−1275.70	−0.0633726
$741$	17483.1	0.866742
$742$	3741.33	0.185106
$743$	−30332.8	−1.49772	−0.748858	−	0.662730i	$-0.769398\pi$
$743$	−30332.8	−1.49772	−0.748858	+	0.662730i	$0.769398\pi$
$744$	49747.9	2.45140
$745$	−17547.8	−0.862955
$746$	−17978.7	−0.882369
$747$	77955.6	3.81827
$748$	8991.01	0.439497
$749$	−372.455	−0.0181698
$750$	−28270.4	−1.37639
$751$	19928.4	0.968308	0.484154	−	0.874983i	$-0.339127\pi$
$751$	19928.4	0.968308	0.484154	+	0.874983i	$0.339127\pi$
$752$	−5833.26	−0.282869
$753$	22748.4	1.10093
$754$	6739.40	0.325510
$755$	−867.940	−0.0418379
$756$	6338.12	0.304914
$757$	2314.42	0.111122	0.0555608	−	0.998455i	$-0.482305\pi$
$757$	2314.42	0.111122	0.0555608	+	0.998455i	$0.482305\pi$
$758$	2210.79	0.105936
$759$	62998.3	3.01277
$760$	−10508.8	−0.501571
$761$	11104.3	0.528951	0.264476	−	0.964392i	$-0.414801\pi$
$761$	11104.3	0.528951	0.264476	+	0.964392i	$0.414801\pi$
$762$	17935.6	0.852675
$763$	−598.686	−0.0284061
$764$	−16101.1	−0.762457
$765$	−21205.5	−1.00220
$766$	−11202.5	−0.528413
$767$	7219.74	0.339882
$768$	−44461.4	−2.08901
$769$	−7885.30	−0.369768	−0.184884	−	0.982760i	$-0.559191\pi$
$769$	−7885.30	−0.369768	−0.184884	+	0.982760i	$0.559191\pi$
$770$	2323.22	0.108731
$771$	2678.55	0.125118
$772$	14781.2	0.689103
$773$	31845.1	1.48175	0.740873	−	0.671645i	$-0.234412\pi$
$773$	31845.1	1.48175	0.740873	+	0.671645i	$0.234412\pi$
$774$	0	0
$775$	−15894.1	−0.736689
$776$	−5597.95	−0.258962
$777$	1447.65	0.0668393
$778$	−19362.7	−0.892271
$779$	12854.9	0.591240
$780$	7530.40	0.345682
$781$	18907.3	0.866269
$782$	8882.93	0.406206
$783$	−64844.5	−2.95958
$784$	5164.87	0.235280
$785$	−15675.7	−0.712725
$786$	−16793.5	−0.762091
$787$	38505.2	1.74404	0.872022	−	0.489467i	$-0.162808\pi$
$787$	38505.2	1.74404	0.872022	+	0.489467i	$0.162808\pi$
$788$	−6179.57	−0.279363
$789$	15426.1	0.696050
$790$	−10174.6	−0.458224
$791$	1010.09	0.0454041
$792$	−102777.	−4.61113
$793$	7818.78	0.350130
$794$	−13999.2	−0.625710
$795$	−42769.7	−1.90803
$796$	−21265.1	−0.946885
$797$	−11779.5	−0.523529	−0.261765	−	0.965132i	$-0.584304\pi$
$797$	−11779.5	−0.523529	−0.261765	+	0.965132i	$0.584304\pi$
$798$	3996.40	0.177282
$799$	15122.8	0.669594
$800$	12576.3	0.555800
$801$	−38123.1	−1.68166
$802$	3636.12	0.160095
$803$	3143.19	0.138133
$804$	11133.2	0.488356
$805$	−2332.62	−0.102129
$806$	−10828.3	−0.473213
$807$	51699.1	2.25513
$808$	26623.5	1.15917
$809$	16768.1	0.728722	0.364361	−	0.931258i	$-0.381287\pi$
$809$	16768.1	0.728722	0.364361	+	0.931258i	$0.381287\pi$
$810$	42883.0	1.86019
$811$	19311.6	0.836154	0.418077	−	0.908412i	$-0.362704\pi$
$811$	19311.6	0.836154	0.418077	+	0.908412i	$0.362704\pi$
$812$	−1565.59	−0.0676620
$813$	84396.6	3.64074
$814$	−5115.28	−0.220259
$815$	−6833.39	−0.293697
$816$	−6343.65	−0.272147
$817$	0	0
$818$	1920.23	0.0820774
$819$	−6331.03	−0.270115
$820$	5536.96	0.235804
$821$	−17452.2	−0.741884	−0.370942	−	0.928656i	$-0.620965\pi$
$821$	−17452.2	−0.741884	−0.370942	+	0.928656i	$0.620965\pi$
$822$	−26966.2	−1.14423
$823$	−42702.9	−1.80866	−0.904331	−	0.426832i	$-0.859630\pi$
$823$	−42702.9	−1.80866	−0.904331	+	0.426832i	$0.859630\pi$
$824$	−18557.6	−0.784569
$825$	44321.7	1.87040
$826$	1650.34	0.0695189
$827$	18657.6	0.784509	0.392255	−	0.919857i	$-0.371695\pi$
$827$	18657.6	0.784509	0.392255	+	0.919857i	$0.371695\pi$
$828$	34582.0	1.45146
$829$	−37259.1	−1.56099	−0.780497	−	0.625160i	$-0.785034\pi$
$829$	−37259.1	−1.56099	−0.780497	+	0.625160i	$0.785034\pi$
$830$	13766.6	0.575717
$831$	−26142.4	−1.09130
$832$	11879.2	0.494996
$833$	−13390.0	−0.556945
$834$	−54740.9	−2.27281
$835$	3339.90	0.138422
$836$	14351.0	0.593706
$837$	104186.	4.30252
$838$	−7106.96	−0.292966
$839$	−42508.6	−1.74918	−0.874589	−	0.484866i	$-0.838868\pi$
$839$	−42508.6	−1.74918	−0.874589	+	0.484866i	$0.838868\pi$
$840$	5136.51	0.210984
$841$	−8371.62	−0.343254
$842$	−3115.77	−0.127525
$843$	31261.3	1.27722
$844$	8377.16	0.341651
$845$	10144.6	0.413001
$846$	−57932.2	−2.35432
$847$	−5383.78	−0.218405
$848$	−9479.14	−0.383862
$849$	36022.8	1.45618
$850$	6249.47	0.252182
$851$	5135.97	0.206885
$852$	14009.1	0.563313
$853$	8255.22	0.331364	0.165682	−	0.986179i	$-0.447018\pi$
$853$	8255.22	0.331364	0.165682	+	0.986179i	$0.447018\pi$
$854$	1787.27	0.0716149
$855$	−33847.0	−1.35385
$856$	2909.76	0.116184
$857$	−24374.2	−0.971536	−0.485768	−	0.874088i	$-0.661460\pi$
$857$	−24374.2	−0.971536	−0.485768	+	0.874088i	$0.661460\pi$
$858$	30195.3	1.20146
$859$	−6798.94	−0.270055	−0.135027	−	0.990842i	$-0.543112\pi$
$859$	−6798.94	−0.270055	−0.135027	+	0.990842i	$0.543112\pi$
$860$	0	0
$861$	−6283.27	−0.248703
$862$	6692.38	0.264435
$863$	−390.235	−0.0153925	−0.00769627	−	0.999970i	$-0.502450\pi$
$863$	−390.235	−0.0153925	−0.00769627	+	0.999970i	$0.502450\pi$
$864$	−82438.0	−3.24606
$865$	1430.97	0.0562479
$866$	9495.70	0.372606
$867$	−33703.8	−1.32023
$868$	2515.45	0.0983642
$869$	41461.5	1.61851
$870$	−17610.9	−0.686283
$871$	−7231.08	−0.281304
$872$	4677.17	0.181639
$873$	−18030.0	−0.698996
$874$	14178.4	0.548733
$875$	−4265.53	−0.164801
$876$	2328.90	0.0898245
$877$	−15894.3	−0.611987	−0.305994	−	0.952034i	$-0.598989\pi$
$877$	−15894.3	−0.611987	−0.305994	+	0.952034i	$0.598989\pi$
$878$	12218.4	0.469646
$879$	24582.3	0.943276
$880$	−5886.16	−0.225480
$881$	−34652.8	−1.32518	−0.662589	−	0.748983i	$-0.730542\pi$
$881$	−34652.8	−1.32518	−0.662589	+	0.748983i	$0.730542\pi$
$882$	51294.2	1.95824
$883$	−4583.85	−0.174698	−0.0873492	−	0.996178i	$-0.527840\pi$
$883$	−4583.85	−0.174698	−0.0873492	+	0.996178i	$0.527840\pi$
$884$	−4326.85	−0.164624
$885$	−18866.1	−0.716585
$886$	−16406.8	−0.622118
$887$	−38327.0	−1.45084	−0.725420	−	0.688306i	$-0.758355\pi$
$887$	−38327.0	−1.45084	−0.725420	+	0.688306i	$0.758355\pi$
$888$	−11309.6	−0.427394
$889$	2706.18	0.102095
$890$	−6732.35	−0.253561
$891$	−174748.	−6.57045
$892$	−15497.8	−0.581732
$893$	24138.2	0.904538
$894$	−52134.3	−1.95037
$895$	−6612.54	−0.246964
$896$	−1233.46	−0.0459899
$897$	−30317.4	−1.12850
$898$	−26108.3	−0.970206
$899$	−25735.3	−0.954750
$900$	24329.7	0.901102
$901$	24574.8	0.908662
$902$	22202.0	0.819562
$903$	0	0
$904$	−7891.23	−0.290330
$905$	−9249.86	−0.339752
$906$	−2578.64	−0.0945580
$907$	22235.1	0.814008	0.407004	−	0.913426i	$-0.366574\pi$
$907$	22235.1	0.814008	0.407004	+	0.913426i	$0.366574\pi$
$908$	11592.1	0.423676
$909$	85749.5	3.12886
$910$	−1118.03	−0.0407278
$911$	21205.9	0.771220	0.385610	−	0.922662i	$-0.373991\pi$
$911$	21205.9	0.771220	0.385610	+	0.922662i	$0.373991\pi$
$912$	−10125.4	−0.367637
$913$	−56098.7	−2.03351
$914$	28626.5	1.03598
$915$	−20431.5	−0.738190
$916$	−8996.25	−0.324503
$917$	−2533.85	−0.0912489
$918$	−40965.4	−1.47283
$919$	−23740.6	−0.852156	−0.426078	−	0.904686i	$-0.640105\pi$
$919$	−23740.6	−0.852156	−0.426078	+	0.904686i	$0.640105\pi$
$920$	18223.3	0.653049
$921$	10970.0	0.392479
$922$	−9307.12	−0.332444
$923$	−9098.97	−0.324481
$924$	−7014.49	−0.249740
$925$	3613.35	0.128439
$926$	35757.9	1.26898
$927$	−59770.7	−2.11772
$928$	20363.2	0.720318
$929$	43369.3	1.53165	0.765824	−	0.643051i	$-0.222332\pi$
$929$	43369.3	1.53165	0.765824	+	0.643051i	$0.222332\pi$
$930$	28295.7	0.997690
$931$	−21372.3	−0.752363
$932$	−6323.55	−0.222248
$933$	−60320.1	−2.11661
$934$	−21736.7	−0.761508
$935$	15259.9	0.533747
$936$	49460.5	1.72721
$937$	38803.4	1.35288	0.676442	−	0.736496i	$-0.263521\pi$
$937$	38803.4	1.35288	0.676442	+	0.736496i	$0.263521\pi$
$938$	−1652.93	−0.0575375
$939$	33083.7	1.14978
$940$	10396.9	0.360756
$941$	3621.93	0.125474	0.0627372	−	0.998030i	$-0.480017\pi$
$941$	3621.93	0.125474	0.0627372	+	0.998030i	$0.480017\pi$
$942$	−46572.2	−1.61083
$943$	−22291.8	−0.769799
$944$	−4181.34	−0.144164
$945$	10757.3	0.370303
$946$	0	0
$947$	−40963.7	−1.40564	−0.702820	−	0.711367i	$-0.748076\pi$
$947$	−40963.7	−1.40564	−0.702820	+	0.711367i	$0.748076\pi$
$948$	30720.3	1.05248
$949$	−1512.64	−0.0517410
$950$	9975.06	0.340667
$951$	−61.5402	−0.00209840
$952$	−2951.36	−0.100477
$953$	−7398.28	−0.251473	−0.125736	−	0.992064i	$-0.540129\pi$
$953$	−7398.28	−0.251473	−0.125736	+	0.992064i	$0.540129\pi$
$954$	−94140.8	−3.19489
$955$	−27327.5	−0.925965
$956$	21972.8	0.743360
$957$	71764.4	2.42405
$958$	7101.46	0.239497
$959$	−4068.75	−0.137004
$960$	−31041.9	−1.04362
$961$	11558.2	0.387976
$962$	2461.69	0.0825031
$963$	9371.84	0.313607
$964$	4457.38	0.148924
$965$	25087.3	0.836880
$966$	−6930.17	−0.230822
$967$	−25661.7	−0.853388	−0.426694	−	0.904396i	$-0.640322\pi$
$967$	−25661.7	−0.853388	−0.426694	+	0.904396i	$0.640322\pi$
$968$	42060.2	1.39656
$969$	26250.2	0.870255
$970$	−3184.01	−0.105394
$971$	−9447.14	−0.312228	−0.156114	−	0.987739i	$-0.549897\pi$
$971$	−9447.14	−0.312228	−0.156114	+	0.987739i	$0.549897\pi$
$972$	−73695.3	−2.43187
$973$	−8259.48	−0.272134
$974$	10542.4	0.346817
$975$	−21329.4	−0.700604
$976$	−4528.28	−0.148511
$977$	36281.9	1.18809	0.594043	−	0.804433i	$-0.297531\pi$
$977$	36281.9	1.18809	0.594043	+	0.804433i	$0.297531\pi$
$978$	−20301.9	−0.663787
$979$	27434.3	0.895611
$980$	−9205.61	−0.300064
$981$	15064.3	0.490283
$982$	−33580.3	−1.09123
$983$	20667.5	0.670592	0.335296	−	0.942113i	$-0.391164\pi$
$983$	20667.5	0.670592	0.335296	+	0.942113i	$0.391164\pi$
$984$	49087.4	1.59029
$985$	−10488.2	−0.339272
$986$	10119.0	0.326829
$987$	−11798.3	−0.380490
$988$	−6906.28	−0.222387
$989$	0	0
$990$	−58457.6	−1.87667
$991$	9951.71	0.318997	0.159499	−	0.987198i	$-0.449012\pi$
$991$	9951.71	0.318997	0.159499	+	0.987198i	$0.449012\pi$
$992$	−32717.8	−1.04717
$993$	−86306.3	−2.75816
$994$	−2079.91	−0.0663688
$995$	−36092.0	−1.14994
$996$	−41565.5	−1.32234
$997$	5142.09	0.163342	0.0816709	−	0.996659i	$-0.473974\pi$
$997$	5142.09	0.163342	0.0816709	+	0.996659i	$0.473974\pi$
$998$	2663.09	0.0844676
$999$	−23685.6	−0.750129

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.4.a.h.1.9		30
43.4	even	7		43.4.e.a.16.8	✓	60
43.11	even	7		43.4.e.a.35.8	yes	60
43.42	odd	2		1849.4.a.g.1.22		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.4.e.a.16.8	✓	60	43.4	even	7
43.4.e.a.35.8	yes	60	43.11	even	7
1849.4.a.g.1.22		30	43.42	odd	2
1849.4.a.h.1.9		30	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1849 = 43^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1849.a (trivial)

\(f(q)\)	\(=\)	\(q-1.99192 q^{2} +10.2076 q^{3} -4.03226 q^{4} -6.84373 q^{5} -20.3326 q^{6} -3.06785 q^{7} +23.9673 q^{8} +77.1944 q^{9} +O(q^{10})\)	\(q-1.99192 q^{2} +10.2076 q^{3} -4.03226 q^{4} -6.84373 q^{5} -20.3326 q^{6} -3.06785 q^{7} +23.9673 q^{8} +77.1944 q^{9} +13.6322 q^{10} -55.5509 q^{11} -41.1596 q^{12} +26.7334 q^{13} +6.11091 q^{14} -69.8578 q^{15} -15.4828 q^{16} +40.1392 q^{17} -153.765 q^{18} +64.0680 q^{19} +27.5957 q^{20} -31.3153 q^{21} +110.653 q^{22} -111.100 q^{23} +244.648 q^{24} -78.1633 q^{25} -53.2507 q^{26} +512.362 q^{27} +12.3704 q^{28} -126.560 q^{29} +139.151 q^{30} +203.345 q^{31} -160.898 q^{32} -567.039 q^{33} -79.9540 q^{34} +20.9955 q^{35} -311.268 q^{36} -46.2282 q^{37} -127.618 q^{38} +272.883 q^{39} -164.026 q^{40} +200.645 q^{41} +62.3775 q^{42} +223.996 q^{44} -528.298 q^{45} +221.303 q^{46} +376.759 q^{47} -158.041 q^{48} -333.588 q^{49} +155.695 q^{50} +409.724 q^{51} -107.796 q^{52} +612.239 q^{53} -1020.58 q^{54} +380.175 q^{55} -73.5280 q^{56} +653.978 q^{57} +252.097 q^{58} +270.064 q^{59} +281.685 q^{60} +292.472 q^{61} -405.047 q^{62} -236.821 q^{63} +444.357 q^{64} -182.956 q^{65} +1129.50 q^{66} -270.489 q^{67} -161.852 q^{68} -1134.07 q^{69} -41.8214 q^{70} -340.360 q^{71} +1850.14 q^{72} -56.5822 q^{73} +92.0828 q^{74} -797.857 q^{75} -258.339 q^{76} +170.422 q^{77} -543.560 q^{78} -746.369 q^{79} +105.960 q^{80} +3145.72 q^{81} -399.669 q^{82} +1009.86 q^{83} +126.271 q^{84} -274.702 q^{85} -1291.87 q^{87} -1331.40 q^{88} -493.858 q^{89} +1052.33 q^{90} -82.0141 q^{91} +447.986 q^{92} +2075.66 q^{93} -750.472 q^{94} -438.464 q^{95} -1642.38 q^{96} -233.566 q^{97} +664.481 q^{98} -4288.22 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 6 q^{2} + 2 q^{3} + 114 q^{4} + 27 q^{5} + 8 q^{6} + 48 q^{7} + 90 q^{8} + 216 q^{9}+O(q^{10}) \) 30 * q + 6 * q^2 + 2 * q^3 + 114 * q^4 + 27 * q^5 + 8 * q^6 + 48 * q^7 + 90 * q^8 + 216 * q^9	\( 30 q + 6 q^{2} + 2 q^{3} + 114 q^{4} + 27 q^{5} + 8 q^{6} + 48 q^{7} + 90 q^{8} + 216 q^{9} - 27 q^{10} + 80 q^{11} - 36 q^{12} - 13 q^{13} + 36 q^{14} + 16 q^{15} + 318 q^{16} + 66 q^{17} + 80 q^{18} + 254 q^{19} + 312 q^{20} - 548 q^{21} + 305 q^{22} - 105 q^{23} + 123 q^{24} + 523 q^{25} + 549 q^{26} - 10 q^{27} + 578 q^{28} + 793 q^{29} + 1560 q^{30} - 359 q^{31} + 676 q^{32} + 208 q^{33} + 1007 q^{34} - 514 q^{35} + 776 q^{36} + 510 q^{37} - 2066 q^{38} + 898 q^{39} - 1248 q^{40} - 270 q^{41} - 915 q^{42} + 3256 q^{44} + 807 q^{45} + 1960 q^{46} + 1421 q^{47} - 632 q^{48} + 386 q^{49} - 141 q^{50} + 209 q^{51} + 2825 q^{52} - 21 q^{53} + 2368 q^{54} + 2258 q^{55} + 2521 q^{56} - 1723 q^{57} - 347 q^{58} + 1752 q^{59} + 2711 q^{60} + 1759 q^{61} + 395 q^{62} + 2204 q^{63} + 222 q^{64} + 1151 q^{65} + 160 q^{66} - 3001 q^{67} + 1921 q^{68} + 1660 q^{69} + 1597 q^{70} + 727 q^{71} + 9100 q^{72} + 4623 q^{73} - 2649 q^{74} + 1027 q^{75} + 874 q^{76} + 3556 q^{77} - 4979 q^{78} + 546 q^{79} + 5809 q^{80} - 410 q^{81} - 4397 q^{82} - 492 q^{83} - 10611 q^{84} - 1723 q^{85} + 5937 q^{87} + 3974 q^{88} + 5218 q^{89} + 10492 q^{90} + 1104 q^{91} + 1060 q^{92} + 1997 q^{93} - 2134 q^{94} + 6346 q^{95} - 11984 q^{96} + 2590 q^{97} + 6270 q^{98} - 2693 q^{99}+O(q^{100}) \) 30 * q + 6 * q^2 + 2 * q^3 + 114 * q^4 + 27 * q^5 + 8 * q^6 + 48 * q^7 + 90 * q^8 + 216 * q^9 - 27 * q^10 + 80 * q^11 - 36 * q^12 - 13 * q^13 + 36 * q^14 + 16 * q^15 + 318 * q^16 + 66 * q^17 + 80 * q^18 + 254 * q^19 + 312 * q^20 - 548 * q^21 + 305 * q^22 - 105 * q^23 + 123 * q^24 + 523 * q^25 + 549 * q^26 - 10 * q^27 + 578 * q^28 + 793 * q^29 + 1560 * q^30 - 359 * q^31 + 676 * q^32 + 208 * q^33 + 1007 * q^34 - 514 * q^35 + 776 * q^36 + 510 * q^37 - 2066 * q^38 + 898 * q^39 - 1248 * q^40 - 270 * q^41 - 915 * q^42 + 3256 * q^44 + 807 * q^45 + 1960 * q^46 + 1421 * q^47 - 632 * q^48 + 386 * q^49 - 141 * q^50 + 209 * q^51 + 2825 * q^52 - 21 * q^53 + 2368 * q^54 + 2258 * q^55 + 2521 * q^56 - 1723 * q^57 - 347 * q^58 + 1752 * q^59 + 2711 * q^60 + 1759 * q^61 + 395 * q^62 + 2204 * q^63 + 222 * q^64 + 1151 * q^65 + 160 * q^66 - 3001 * q^67 + 1921 * q^68 + 1660 * q^69 + 1597 * q^70 + 727 * q^71 + 9100 * q^72 + 4623 * q^73 - 2649 * q^74 + 1027 * q^75 + 874 * q^76 + 3556 * q^77 - 4979 * q^78 + 546 * q^79 + 5809 * q^80 - 410 * q^81 - 4397 * q^82 - 492 * q^83 - 10611 * q^84 - 1723 * q^85 + 5937 * q^87 + 3974 * q^88 + 5218 * q^89 + 10492 * q^90 + 1104 * q^91 + 1060 * q^92 + 1997 * q^93 - 2134 * q^94 + 6346 * q^95 - 11984 * q^96 + 2590 * q^97 + 6270 * q^98 - 2693 * q^99

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