LMFDB - Embedded newform 1045.4.a.e.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1045,4,Mod(1,1045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1045, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("1045.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1045 = 5 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1045.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:	$61.6569959560$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	1045.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.0230482 q^{2} +4.90691 q^{3} -7.99947 q^{4} +5.00000 q^{5} +0.113095 q^{6} +35.2639 q^{7} -0.368758 q^{8} -2.92227 q^{9} +O(q^{10})$	\(q+0.0230482 q^{2} +4.90691 q^{3} -7.99947 q^{4} +5.00000 q^{5} +0.113095 q^{6} +35.2639 q^{7} -0.368758 q^{8} -2.92227 q^{9} +0.115241 q^{10} +11.0000 q^{11} -39.2526 q^{12} +77.7559 q^{13} +0.812769 q^{14} +24.5345 q^{15} +63.9873 q^{16} +87.2633 q^{17} -0.0673529 q^{18} -19.0000 q^{19} -39.9973 q^{20} +173.037 q^{21} +0.253530 q^{22} +43.6378 q^{23} -1.80946 q^{24} +25.0000 q^{25} +1.79213 q^{26} -146.826 q^{27} -282.093 q^{28} -134.680 q^{29} +0.565476 q^{30} -228.521 q^{31} +4.42485 q^{32} +53.9760 q^{33} +2.01126 q^{34} +176.320 q^{35} +23.3766 q^{36} +11.7847 q^{37} -0.437915 q^{38} +381.541 q^{39} -1.84379 q^{40} -434.190 q^{41} +3.98818 q^{42} +474.577 q^{43} -87.9942 q^{44} -14.6114 q^{45} +1.00577 q^{46} -375.478 q^{47} +313.979 q^{48} +900.546 q^{49} +0.576204 q^{50} +428.193 q^{51} -622.006 q^{52} +692.604 q^{53} -3.38406 q^{54} +55.0000 q^{55} -13.0039 q^{56} -93.2312 q^{57} -3.10413 q^{58} +831.332 q^{59} -196.263 q^{60} -598.071 q^{61} -5.26698 q^{62} -103.051 q^{63} -511.796 q^{64} +388.779 q^{65} +1.24405 q^{66} +8.05544 q^{67} -698.060 q^{68} +214.127 q^{69} +4.06384 q^{70} +245.504 q^{71} +1.07761 q^{72} -477.025 q^{73} +0.271617 q^{74} +122.673 q^{75} +151.990 q^{76} +387.903 q^{77} +8.79381 q^{78} -321.821 q^{79} +319.936 q^{80} -641.559 q^{81} -10.0073 q^{82} -171.578 q^{83} -1384.20 q^{84} +436.317 q^{85} +10.9381 q^{86} -660.864 q^{87} -4.05634 q^{88} +632.359 q^{89} -0.336765 q^{90} +2741.98 q^{91} -349.080 q^{92} -1121.33 q^{93} -8.65407 q^{94} -95.0000 q^{95} +21.7123 q^{96} -378.323 q^{97} +20.7559 q^{98} -32.1450 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 12 q^{2} + 21 q^{3} + 96 q^{4} + 110 q^{5} + 27 q^{6} + 93 q^{7} + 114 q^{8} + 209 q^{9}+O(q^{10}) $ 22 * q + 12 * q^2 + 21 * q^3 + 96 * q^4 + 110 * q^5 + 27 * q^6 + 93 * q^7 + 114 * q^8 + 209 * q^9	\( 22 q + 12 q^{2} + 21 q^{3} + 96 q^{4} + 110 q^{5} + 27 q^{6} + 93 q^{7} + 114 q^{8} + 209 q^{9} + 60 q^{10} + 242 q^{11} + 164 q^{12} + 207 q^{13} + 129 q^{14} + 105 q^{15} + 604 q^{16} + 209 q^{17} + 869 q^{18} - 418 q^{19} + 480 q^{20} + 45 q^{21} + 132 q^{22} + 191 q^{23} + 458 q^{24} + 550 q^{25} + 363 q^{26} + 45 q^{27} + 577 q^{28} + 389 q^{29} + 135 q^{30} + 198 q^{31} + 1149 q^{32} + 231 q^{33} + 467 q^{34} + 465 q^{35} + 1315 q^{36} + 312 q^{37} - 228 q^{38} + 137 q^{39} + 570 q^{40} + 632 q^{41} - 1794 q^{42} + 1584 q^{43} + 1056 q^{44} + 1045 q^{45} + 681 q^{46} - 54 q^{47} + 2491 q^{48} + 1063 q^{49} + 300 q^{50} + 37 q^{51} + 1246 q^{52} + 343 q^{53} + 1078 q^{54} + 1210 q^{55} - 87 q^{56} - 399 q^{57} - 1424 q^{58} + 2787 q^{59} + 820 q^{60} + 2070 q^{61} - 446 q^{62} + 1696 q^{63} + 1758 q^{64} + 1035 q^{65} + 297 q^{66} + 2423 q^{67} - 524 q^{68} - 997 q^{69} + 645 q^{70} + 2538 q^{71} + 6010 q^{72} + 1397 q^{73} - 1977 q^{74} + 525 q^{75} - 1824 q^{76} + 1023 q^{77} + 202 q^{78} + 878 q^{79} + 3020 q^{80} + 2030 q^{81} - 190 q^{82} + 4932 q^{83} - 4580 q^{84} + 1045 q^{85} - 3394 q^{86} + 6009 q^{87} + 1254 q^{88} + 1812 q^{89} + 4345 q^{90} + 4349 q^{91} - 788 q^{92} - 4848 q^{93} - 2152 q^{94} - 2090 q^{95} + 4032 q^{96} + 988 q^{97} + 1366 q^{98} + 2299 q^{99}+O(q^{100}) \) 22 * q + 12 * q^2 + 21 * q^3 + 96 * q^4 + 110 * q^5 + 27 * q^6 + 93 * q^7 + 114 * q^8 + 209 * q^9 + 60 * q^10 + 242 * q^11 + 164 * q^12 + 207 * q^13 + 129 * q^14 + 105 * q^15 + 604 * q^16 + 209 * q^17 + 869 * q^18 - 418 * q^19 + 480 * q^20 + 45 * q^21 + 132 * q^22 + 191 * q^23 + 458 * q^24 + 550 * q^25 + 363 * q^26 + 45 * q^27 + 577 * q^28 + 389 * q^29 + 135 * q^30 + 198 * q^31 + 1149 * q^32 + 231 * q^33 + 467 * q^34 + 465 * q^35 + 1315 * q^36 + 312 * q^37 - 228 * q^38 + 137 * q^39 + 570 * q^40 + 632 * q^41 - 1794 * q^42 + 1584 * q^43 + 1056 * q^44 + 1045 * q^45 + 681 * q^46 - 54 * q^47 + 2491 * q^48 + 1063 * q^49 + 300 * q^50 + 37 * q^51 + 1246 * q^52 + 343 * q^53 + 1078 * q^54 + 1210 * q^55 - 87 * q^56 - 399 * q^57 - 1424 * q^58 + 2787 * q^59 + 820 * q^60 + 2070 * q^61 - 446 * q^62 + 1696 * q^63 + 1758 * q^64 + 1035 * q^65 + 297 * q^66 + 2423 * q^67 - 524 * q^68 - 997 * q^69 + 645 * q^70 + 2538 * q^71 + 6010 * q^72 + 1397 * q^73 - 1977 * q^74 + 525 * q^75 - 1824 * q^76 + 1023 * q^77 + 202 * q^78 + 878 * q^79 + 3020 * q^80 + 2030 * q^81 - 190 * q^82 + 4932 * q^83 - 4580 * q^84 + 1045 * q^85 - 3394 * q^86 + 6009 * q^87 + 1254 * q^88 + 1812 * q^89 + 4345 * q^90 + 4349 * q^91 - 788 * q^92 - 4848 * q^93 - 2152 * q^94 - 2090 * q^95 + 4032 * q^96 + 988 * q^97 + 1366 * q^98 + 2299 * 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 $

$2$	0.0230482	0.00814875	0.00407438	−	0.999992i	$-0.498703\pi$
$2$	0.0230482	0.00814875	0.00407438	+	0.999992i	$0.498703\pi$
$3$	4.90691	0.944335	0.472167	−	0.881509i	$-0.343472\pi$
$3$	4.90691	0.944335	0.472167	+	0.881509i	$0.343472\pi$
$4$	−7.99947	−0.999934
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	0.113095	0.00769515
$7$	35.2639	1.90407	0.952037	−	0.305983i	$-0.0989851\pi$
$7$	35.2639	1.90407	0.952037	+	0.305983i	$0.0989851\pi$
$8$	−0.368758	−0.0162970
$9$	−2.92227	−0.108232
$10$	0.115241	0.00364423
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	−39.2526	−0.944272
$13$	77.7559	1.65889	0.829446	−	0.558587i	$-0.188656\pi$
$13$	77.7559	1.65889	0.829446	+	0.558587i	$0.188656\pi$
$14$	0.812769	0.0155158
$15$	24.5345	0.422319
$16$	63.9873	0.999801
$17$	87.2633	1.24497	0.622484	−	0.782632i	$-0.286124\pi$
$17$	87.2633	1.24497	0.622484	+	0.782632i	$0.286124\pi$
$18$	−0.0673529	−0.000881958 0
$19$	−19.0000	−0.229416
$19$	−19.0000	−0.229416
$20$	−39.9973	−0.447184
$21$	173.037	1.79808
$22$	0.253530	0.00245694
$23$	43.6378	0.395614	0.197807	−	0.980241i	$-0.436618\pi$
$23$	43.6378	0.395614	0.197807	+	0.980241i	$0.436618\pi$
$24$	−1.80946	−0.0153898
$25$	25.0000	0.200000
$26$	1.79213	0.0135179
$27$	−146.826	−1.04654
$28$	−282.093	−1.90395
$29$	−134.680	−0.862397	−0.431199	−	0.902257i	$-0.641909\pi$
$29$	−134.680	−0.862397	−0.431199	+	0.902257i	$0.641909\pi$
$30$	0.565476	0.00344138
$31$	−228.521	−1.32398	−0.661992	−	0.749511i	$-0.730289\pi$
$31$	−228.521	−1.32398	−0.661992	+	0.749511i	$0.730289\pi$
$32$	4.42485	0.0244441
$33$	53.9760	0.284728
$34$	2.01126	0.0101449
$35$	176.320	0.851528
$36$	23.3766	0.108225
$37$	11.7847	0.0523622	0.0261811	−	0.999657i	$-0.491665\pi$
$37$	11.7847	0.0523622	0.0261811	+	0.999657i	$0.491665\pi$
$38$	−0.437915	−0.00186945
$39$	381.541	1.56655
$40$	−1.84379	−0.00728822
$41$	−434.190	−1.65388	−0.826940	−	0.562290i	$-0.809920\pi$
$41$	−434.190	−1.65388	−0.826940	+	0.562290i	$0.809920\pi$
$42$	3.98818	0.0146521
$43$	474.577	1.68308	0.841538	−	0.540198i	$-0.181651\pi$
$43$	474.577	1.68308	0.841538	+	0.540198i	$0.181651\pi$
$44$	−87.9942	−0.301491
$45$	−14.6114	−0.0484029
$46$	1.00577	0.00322376
$47$	−375.478	−1.16530	−0.582650	−	0.812723i	$-0.697984\pi$
$47$	−375.478	−1.16530	−0.582650	+	0.812723i	$0.697984\pi$
$48$	313.979	0.944146
$49$	900.546	2.62550
$50$	0.576204	0.00162975
$51$	428.193	1.17567
$52$	−622.006	−1.65878
$53$	692.604	1.79503	0.897514	−	0.440986i	$-0.145371\pi$
$53$	692.604	1.79503	0.897514	+	0.440986i	$0.145371\pi$
$54$	−3.38406	−0.00852801
$55$	55.0000	0.134840
$56$	−13.0039	−0.0310306
$57$	−93.2312	−0.216645
$58$	−3.10413	−0.00702746
$59$	831.332	1.83441	0.917205	−	0.398416i	$-0.130440\pi$
$59$	831.332	1.83441	0.917205	+	0.398416i	$0.130440\pi$
$60$	−196.263	−0.422291
$61$	−598.071	−1.25533	−0.627665	−	0.778483i	$-0.715989\pi$
$61$	−598.071	−1.25533	−0.627665	+	0.778483i	$0.715989\pi$
$62$	−5.26698	−0.0107888
$63$	−103.051	−0.206082
$64$	−511.796	−0.999602
$65$	388.779	0.741879
$66$	1.24405	0.00232017
$67$	8.05544	0.0146885	0.00734425	−	0.999973i	$-0.497662\pi$
$67$	8.05544	0.0146885	0.00734425	+	0.999973i	$0.497662\pi$
$68$	−698.060	−1.24489
$69$	214.127	0.373592
$70$	4.06384	0.00693889
$71$	245.504	0.410366	0.205183	−	0.978724i	$-0.434221\pi$
$71$	245.504	0.410366	0.205183	+	0.978724i	$0.434221\pi$
$72$	1.07761	0.00176386
$73$	−477.025	−0.764817	−0.382408	−	0.923993i	$-0.624905\pi$
$73$	−477.025	−0.764817	−0.382408	+	0.923993i	$0.624905\pi$
$74$	0.271617	0.000426686 0
$75$	122.673	0.188867
$76$	151.990	0.229401
$77$	387.903	0.574100
$78$	8.79381	0.0127654
$79$	−321.821	−0.458326	−0.229163	−	0.973388i	$-0.573599\pi$
$79$	−321.821	−0.458326	−0.229163	+	0.973388i	$0.573599\pi$
$80$	319.936	0.447125
$81$	−641.559	−0.880054
$82$	−10.0073	−0.0134771
$83$	−171.578	−0.226905	−0.113453	−	0.993543i	$-0.536191\pi$
$83$	−171.578	−0.226905	−0.113453	+	0.993543i	$0.536191\pi$
$84$	−1384.20	−1.79796
$85$	436.317	0.556767
$86$	10.9381	0.0137150
$87$	−660.864	−0.814392
$88$	−4.05634	−0.00491372
$89$	632.359	0.753145	0.376572	−	0.926387i	$-0.377103\pi$
$89$	632.359	0.753145	0.376572	+	0.926387i	$0.377103\pi$
$90$	−0.336765	−0.000394424 0
$91$	2741.98	3.15865
$92$	−349.080	−0.395588
$93$	−1121.33	−1.25028
$94$	−8.65407	−0.00949574
$95$	−95.0000	−0.102598
$96$	21.7123	0.0230834
$97$	−378.323	−0.396009	−0.198004	−	0.980201i	$-0.563446\pi$
$97$	−378.323	−0.396009	−0.198004	+	0.980201i	$0.563446\pi$
$98$	20.7559	0.0213945
$99$	−32.1450	−0.0326332
$100$	−199.987	−0.199987
$101$	1637.65	1.61338	0.806692	−	0.590972i	$-0.201256\pi$
$101$	1637.65	1.61338	0.806692	+	0.590972i	$0.201256\pi$
$102$	9.86906	0.00958022
$103$	853.458	0.816444	0.408222	−	0.912883i	$-0.366149\pi$
$103$	853.458	0.816444	0.408222	+	0.912883i	$0.366149\pi$
$104$	−28.6731	−0.0270349
$105$	865.184	0.804127
$106$	15.9632	0.0146272
$107$	−1061.49	−0.959051	−0.479526	−	0.877528i	$-0.659191\pi$
$107$	−1061.49	−0.959051	−0.479526	+	0.877528i	$0.659191\pi$
$108$	1174.53	1.04647
$109$	−1296.30	−1.13911	−0.569555	−	0.821953i	$-0.692885\pi$
$109$	−1296.30	−1.13911	−0.569555	+	0.821953i	$0.692885\pi$
$110$	1.26765	0.00109878
$111$	57.8266	0.0494474
$112$	2256.44	1.90369
$113$	682.590	0.568254	0.284127	−	0.958787i	$-0.408296\pi$
$113$	682.590	0.568254	0.284127	+	0.958787i	$0.408296\pi$
$114$	−2.14881	−0.00176539
$115$	218.189	0.176924
$116$	1077.37	0.862340
$117$	−227.224	−0.179546
$118$	19.1607	0.0149482
$119$	3077.25	2.37051
$120$	−9.04731	−0.00688252
$121$	121.000	0.0909091
$122$	−13.7844	−0.0102294
$123$	−2130.53	−1.56182
$124$	1828.04	1.32390
$125$	125.000	0.0894427
$126$	−2.37513	−0.00167931
$127$	−371.592	−0.259633	−0.129817	−	0.991538i	$-0.541439\pi$
$127$	−371.592	−0.259633	−0.129817	+	0.991538i	$0.541439\pi$
$128$	−47.1948	−0.0325896
$129$	2328.70	1.58939
$130$	8.96065	0.00604539
$131$	464.668	0.309910	0.154955	−	0.987922i	$-0.450477\pi$
$131$	464.668	0.309910	0.154955	+	0.987922i	$0.450477\pi$
$132$	−431.779	−0.284709
$133$	−670.015	−0.436825
$134$	0.185663	0.000119693 0
$135$	−734.129	−0.468028
$136$	−32.1791	−0.0202892
$137$	−159.290	−0.0993363	−0.0496681	−	0.998766i	$-0.515816\pi$
$137$	−159.290	−0.0993363	−0.0496681	+	0.998766i	$0.515816\pi$
$138$	4.93523	0.00304431
$139$	1880.04	1.14721	0.573606	−	0.819131i	$-0.305544\pi$
$139$	1880.04	1.14721	0.573606	+	0.819131i	$0.305544\pi$
$140$	−1410.46	−0.851471
$141$	−1842.44	−1.10043
$142$	5.65842	0.00334397
$143$	855.315	0.500175
$144$	−186.988	−0.108211
$145$	−673.402	−0.385676
$146$	−10.9946	−0.00623230
$147$	4418.89	2.47935
$148$	−94.2717	−0.0523587
$149$	−1450.10	−0.797292	−0.398646	−	0.917105i	$-0.630520\pi$
$149$	−1450.10	−0.797292	−0.398646	+	0.917105i	$0.630520\pi$
$150$	2.82738	0.00153903
$151$	1503.19	0.810116	0.405058	−	0.914291i	$-0.367251\pi$
$151$	1503.19	0.810116	0.405058	+	0.914291i	$0.367251\pi$
$152$	7.00641	0.00373878
$153$	−255.007	−0.134746
$154$	8.94046	0.00467820
$155$	−1142.60	−0.592104
$156$	−3052.12	−1.56645
$157$	−2787.03	−1.41675	−0.708373	−	0.705838i	$-0.750570\pi$
$157$	−2787.03	−1.41675	−0.708373	+	0.705838i	$0.750570\pi$
$158$	−7.41739	−0.00373478
$159$	3398.54	1.69511
$160$	22.1243	0.0109317
$161$	1538.84	0.753278
$162$	−14.7868	−0.00717134
$163$	−3061.28	−1.47103	−0.735515	−	0.677508i	$-0.763060\pi$
$163$	−3061.28	−1.47103	−0.735515	+	0.677508i	$0.763060\pi$
$164$	3473.29	1.65377
$165$	269.880	0.127334
$166$	−3.95456	−0.00184899
$167$	2366.91	1.09675	0.548375	−	0.836233i	$-0.315247\pi$
$167$	2366.91	1.09675	0.548375	+	0.836233i	$0.315247\pi$
$168$	−63.8088	−0.0293033
$169$	3848.98	1.75192
$170$	10.0563	0.00453695
$171$	55.5231	0.0248302
$172$	−3796.36	−1.68296
$173$	4136.64	1.81794	0.908968	−	0.416865i	$-0.136871\pi$
$173$	4136.64	1.81794	0.908968	+	0.416865i	$0.136871\pi$
$174$	−15.2317	−0.00663628
$175$	881.599	0.380815
$176$	703.860	0.301451
$177$	4079.27	1.73230
$178$	14.5747	0.00613719
$179$	854.285	0.356717	0.178358	−	0.983966i	$-0.442921\pi$
$179$	854.285	0.356717	0.178358	+	0.983966i	$0.442921\pi$
$180$	116.883	0.0483997
$181$	−587.603	−0.241305	−0.120653	−	0.992695i	$-0.538499\pi$
$181$	−587.603	−0.241305	−0.120653	+	0.992695i	$0.538499\pi$
$182$	63.1976	0.0257391
$183$	−2934.68	−1.18545
$184$	−16.0918	−0.00644731
$185$	58.9237	0.0234171
$186$	−25.8446	−0.0101883
$187$	959.896	0.375372
$188$	3003.62	1.16522
$189$	−5177.66	−1.99269
$190$	−2.18957	−0.000836044 0
$191$	2016.65	0.763977	0.381989	−	0.924167i	$-0.375239\pi$
$191$	2016.65	0.763977	0.381989	+	0.924167i	$0.375239\pi$
$192$	−2511.34	−0.943958
$193$	4120.34	1.53673	0.768364	−	0.640013i	$-0.221071\pi$
$193$	4120.34	1.53673	0.768364	+	0.640013i	$0.221071\pi$
$194$	−8.71964	−0.00322698
$195$	1907.70	0.700582
$196$	−7203.89	−2.62532
$197$	−2712.00	−0.980823	−0.490411	−	0.871491i	$-0.663153\pi$
$197$	−2712.00	−0.980823	−0.490411	+	0.871491i	$0.663153\pi$
$198$	−0.740882	−0.000265920 0
$199$	−446.987	−0.159226	−0.0796132	−	0.996826i	$-0.525369\pi$
$199$	−446.987	−0.159226	−0.0796132	+	0.996826i	$0.525369\pi$
$200$	−9.21896	−0.00325939
$201$	39.5273	0.0138708
$202$	37.7447	0.0131471
$203$	−4749.36	−1.64207
$204$	−3425.32	−1.17559
$205$	−2170.95	−0.739637
$206$	19.6706	0.00665300
$207$	−127.522	−0.0428182
$208$	4975.38	1.65856
$209$	−209.000	−0.0691714
$210$	19.9409	0.00655263
$211$	−4078.25	−1.33061	−0.665303	−	0.746573i	$-0.731698\pi$
$211$	−4078.25	−1.33061	−0.665303	+	0.746573i	$0.731698\pi$
$212$	−5540.46	−1.79491
$213$	1204.67	0.387523
$214$	−24.4655	−0.00781507
$215$	2372.88	0.752694
$216$	54.1432	0.0170555
$217$	−8058.54	−2.52096
$218$	−29.8773	−0.00928233
$219$	−2340.72	−0.722243
$220$	−439.971	−0.134831
$221$	6785.24	2.06527
$222$	1.33280	0.000402935 0
$223$	3478.62	1.04460	0.522299	−	0.852762i	$-0.325074\pi$
$223$	3478.62	1.04460	0.522299	+	0.852762i	$0.325074\pi$
$224$	156.038	0.0465434
$225$	−73.0568	−0.0216464
$226$	15.7324	0.00463056
$227$	−921.712	−0.269499	−0.134749	−	0.990880i	$-0.543023\pi$
$227$	−921.712	−0.269499	−0.134749	+	0.990880i	$0.543023\pi$
$228$	745.800	0.216631
$229$	−5985.51	−1.72722	−0.863611	−	0.504159i	$-0.831803\pi$
$229$	−5985.51	−1.72722	−0.863611	+	0.504159i	$0.831803\pi$
$230$	5.02886	0.00144171
$231$	1903.41	0.542142
$232$	49.6645	0.0140545
$233$	−2698.32	−0.758682	−0.379341	−	0.925257i	$-0.623849\pi$
$233$	−2698.32	−0.758682	−0.379341	+	0.925257i	$0.623849\pi$
$234$	−5.23709	−0.00146307
$235$	−1877.39	−0.521138
$236$	−6650.21	−1.83429
$237$	−1579.15	−0.432813
$238$	70.9249	0.0193167
$239$	1866.95	0.505285	0.252643	−	0.967560i	$-0.418700\pi$
$239$	1866.95	0.505285	0.252643	+	0.967560i	$0.418700\pi$
$240$	1569.90	0.422235
$241$	1146.71	0.306499	0.153250	−	0.988188i	$-0.451026\pi$
$241$	1146.71	0.306499	0.153250	+	0.988188i	$0.451026\pi$
$242$	2.78883	0.000740796 0
$243$	816.226	0.215477
$244$	4784.25	1.25525
$245$	4502.73	1.17416
$246$	−49.1048	−0.0127269
$247$	−1477.36	−0.380576
$248$	84.2688	0.0215769
$249$	−841.917	−0.214274
$250$	2.88102	0.000728847 0
$251$	1730.54	0.435183	0.217592	−	0.976040i	$-0.430180\pi$
$251$	1730.54	0.435183	0.217592	+	0.976040i	$0.430180\pi$
$252$	824.351	0.206068
$253$	480.016	0.119282
$254$	−8.56450	−0.00211569
$255$	2140.96	0.525774
$256$	4093.28	0.999336
$257$	1888.20	0.458297	0.229149	−	0.973391i	$-0.426406\pi$
$257$	1888.20	0.458297	0.229149	+	0.973391i	$0.426406\pi$
$258$	53.6723	0.0129515
$259$	415.577	0.0997014
$260$	−3110.03	−0.741830
$261$	393.573	0.0933392
$262$	10.7097	0.00252538
$263$	−6433.46	−1.50838	−0.754191	−	0.656656i	$-0.771971\pi$
$263$	−6433.46	−1.50838	−0.754191	+	0.656656i	$0.771971\pi$
$264$	−19.9041	−0.00464020
$265$	3463.02	0.802761
$266$	−15.4426	−0.00355958
$267$	3102.93	0.711221
$268$	−64.4393	−0.0146875
$269$	1943.24	0.440451	0.220226	−	0.975449i	$-0.429321\pi$
$269$	1943.24	0.440451	0.220226	+	0.975449i	$0.429321\pi$
$270$	−16.9203	−0.00381384
$271$	163.542	0.0366585	0.0183292	−	0.999832i	$-0.494165\pi$
$271$	163.542	0.0366585	0.0183292	+	0.999832i	$0.494165\pi$
$272$	5583.74	1.24472
$273$	13454.6	2.98283
$274$	−3.67134	−0.000809467 0
$275$	275.000	0.0603023
$276$	−1712.90	−0.373567
$277$	998.259	0.216533	0.108266	−	0.994122i	$-0.465470\pi$
$277$	998.259	0.216533	0.108266	+	0.994122i	$0.465470\pi$
$278$	43.3314	0.00934835
$279$	667.799	0.143298
$280$	−65.0193	−0.0138773
$281$	5617.04	1.19247	0.596236	−	0.802809i	$-0.296662\pi$
$281$	5617.04	1.19247	0.596236	+	0.802809i	$0.296662\pi$
$282$	−42.4647	−0.00896716
$283$	202.791	0.0425959	0.0212980	−	0.999773i	$-0.493220\pi$
$283$	202.791	0.0425959	0.0212980	+	0.999773i	$0.493220\pi$
$284$	−1963.90	−0.410339
$285$	−466.156	−0.0968867
$286$	19.7134	0.00407580
$287$	−15311.2	−3.14911
$288$	−12.9306	−0.00264564
$289$	2701.88	0.549946
$290$	−15.5207	−0.00314278
$291$	−1856.39	−0.373965
$292$	3815.95	0.764766
$293$	−4788.33	−0.954735	−0.477367	−	0.878704i	$-0.658409\pi$
$293$	−4788.33	−0.954735	−0.477367	+	0.878704i	$0.658409\pi$
$294$	101.847	0.0202036
$295$	4156.66	0.820373
$296$	−4.34572	−0.000853344 0
$297$	−1615.08	−0.315544
$298$	−33.4221	−0.00649694
$299$	3393.10	0.656281
$300$	−981.316	−0.188854
$301$	16735.4	3.20470
$302$	34.6457	0.00660144
$303$	8035.77	1.52357
$304$	−1215.76	−0.229370
$305$	−2990.36	−0.561401
$306$	−5.87744	−0.00109801
$307$	−3837.55	−0.713421	−0.356711	−	0.934215i	$-0.616102\pi$
$307$	−3837.55	−0.713421	−0.356711	+	0.934215i	$0.616102\pi$
$308$	−3103.02	−0.574062
$309$	4187.84	0.770996
$310$	−26.3349	−0.00482491
$311$	−7178.17	−1.30880	−0.654400	−	0.756149i	$-0.727079\pi$
$311$	−7178.17	−1.30880	−0.654400	+	0.756149i	$0.727079\pi$
$312$	−140.696	−0.0255300
$313$	−6538.13	−1.18069	−0.590346	−	0.807150i	$-0.701009\pi$
$313$	−6538.13	−1.18069	−0.590346	+	0.807150i	$0.701009\pi$
$314$	−64.2359	−0.0115447
$315$	−515.254	−0.0921627
$316$	2574.40	0.458295
$317$	−1655.85	−0.293382	−0.146691	−	0.989182i	$-0.546862\pi$
$317$	−1655.85	−0.293382	−0.146691	+	0.989182i	$0.546862\pi$
$318$	78.3302	0.0138130
$319$	−1481.48	−0.260023
$320$	−2558.98	−0.447035
$321$	−5208.65	−0.905665
$322$	35.4675	0.00613828
$323$	−1658.00	−0.285615
$324$	5132.13	0.879995
$325$	1943.90	0.331778
$326$	−70.5569	−0.0119871
$327$	−6360.82	−1.07570
$328$	160.111	0.0269532
$329$	−13240.8	−2.21882
$330$	6.22023	0.00103761
$331$	3362.92	0.558438	0.279219	−	0.960227i	$-0.409924\pi$
$331$	3362.92	0.558438	0.279219	+	0.960227i	$0.409924\pi$
$332$	1372.53	0.226890
$333$	−34.4382	−0.00566727
$334$	54.5530	0.00893714
$335$	40.2772	0.00656889
$336$	11072.2	1.79772
$337$	8073.42	1.30501	0.652504	−	0.757786i	$-0.273719\pi$
$337$	8073.42	1.30501	0.652504	+	0.757786i	$0.273719\pi$
$338$	88.7118	0.0142760
$339$	3349.41	0.536622
$340$	−3490.30	−0.556730
$341$	−2513.73	−0.399196
$342$	1.27971	0.000202335 0
$343$	19661.3	3.09507
$344$	−175.004	−0.0274290
$345$	1070.63	0.167075
$346$	95.3420	0.0148139
$347$	−5720.54	−0.884999	−0.442499	−	0.896769i	$-0.645908\pi$
$347$	−5720.54	−0.884999	−0.442499	+	0.896769i	$0.645908\pi$
$348$	5286.56	0.814338
$349$	2432.14	0.373036	0.186518	−	0.982452i	$-0.440280\pi$
$349$	2432.14	0.373036	0.186518	+	0.982452i	$0.440280\pi$
$350$	20.3192	0.00310317
$351$	−11416.6	−1.73610
$352$	48.6734	0.00737017
$353$	2955.62	0.445643	0.222821	−	0.974859i	$-0.428473\pi$
$353$	2955.62	0.445643	0.222821	+	0.974859i	$0.428473\pi$
$354$	94.0196	0.0141161
$355$	1227.52	0.183521
$356$	−5058.53	−0.753095
$357$	15099.8	2.23856
$358$	19.6897	0.00290680
$359$	−11579.5	−1.70235	−0.851175	−	0.524882i	$-0.824109\pi$
$359$	−11579.5	−1.70235	−0.851175	+	0.524882i	$0.824109\pi$
$360$	5.38806	0.000788821 0
$361$	361.000	0.0526316
$362$	−13.5432	−0.00196634
$363$	593.736	0.0858486
$364$	−21934.4	−3.15844
$365$	−2385.13	−0.342036
$366$	−67.6389	−0.00965996
$367$	−6502.40	−0.924857	−0.462429	−	0.886657i	$-0.653022\pi$
$367$	−6502.40	−0.924857	−0.462429	+	0.886657i	$0.653022\pi$
$368$	2792.27	0.395535
$369$	1268.82	0.179003
$370$	1.35808	0.000190820 0
$371$	24424.0	3.41787
$372$	8970.04	1.25020
$373$	−300.018	−0.0416470	−0.0208235	−	0.999783i	$-0.506629\pi$
$373$	−300.018	−0.0416470	−0.0208235	+	0.999783i	$0.506629\pi$
$374$	22.1238	0.00305881
$375$	613.363	0.0844639
$376$	138.461	0.0189909
$377$	−10472.2	−1.43062
$378$	−119.335	−0.0162380
$379$	−12731.0	−1.72545	−0.862725	−	0.505673i	$-0.831244\pi$
$379$	−12731.0	−1.72545	−0.862725	+	0.505673i	$0.831244\pi$
$380$	759.950	0.102591
$381$	−1823.37	−0.245181
$382$	46.4801	0.00622546
$383$	5727.05	0.764069	0.382034	−	0.924148i	$-0.375224\pi$
$383$	5727.05	0.764069	0.382034	+	0.924148i	$0.375224\pi$
$384$	−231.580	−0.0307755
$385$	1939.52	0.256745
$386$	94.9662	0.0125224
$387$	−1386.84	−0.182163
$388$	3026.38	0.395982
$389$	3480.77	0.453681	0.226841	−	0.973932i	$-0.427160\pi$
$389$	3480.77	0.453681	0.226841	+	0.973932i	$0.427160\pi$
$390$	43.9691	0.00570887
$391$	3807.98	0.492527
$392$	−332.084	−0.0427876
$393$	2280.08	0.292659
$394$	−62.5066	−0.00799248
$395$	−1609.11	−0.204969
$396$	257.143	0.0326311
$397$	3535.63	0.446973	0.223487	−	0.974707i	$-0.428256\pi$
$397$	3535.63	0.446973	0.223487	+	0.974707i	$0.428256\pi$
$398$	−10.3022	−0.00129750
$399$	−3287.70	−0.412508
$400$	1599.68	0.199960
$401$	−5826.63	−0.725606	−0.362803	−	0.931866i	$-0.618180\pi$
$401$	−5826.63	−0.725606	−0.362803	+	0.931866i	$0.618180\pi$
$402$	0.911031	0.000113030 0
$403$	−17768.8	−2.19635
$404$	−13100.3	−1.61328
$405$	−3207.80	−0.393572
$406$	−109.464	−0.0133808
$407$	129.632	0.0157878
$408$	−157.900	−0.0191598
$409$	11285.9	1.36443	0.682217	−	0.731150i	$-0.261016\pi$
$409$	11285.9	1.36443	0.682217	+	0.731150i	$0.261016\pi$
$410$	−50.0364	−0.00602712
$411$	−781.622	−0.0938067
$412$	−6827.21	−0.816389
$413$	29316.0	3.49285
$414$	−2.93914	−0.000348915 0
$415$	−857.890	−0.101475
$416$	344.058	0.0405501
$417$	9225.16	1.08335
$418$	−4.81706	−0.000563661 0
$419$	−7270.08	−0.847654	−0.423827	−	0.905743i	$-0.639313\pi$
$419$	−7270.08	−0.847654	−0.423827	+	0.905743i	$0.639313\pi$
$420$	−6921.01	−0.804074
$421$	1397.47	0.161778	0.0808890	−	0.996723i	$-0.474224\pi$
$421$	1397.47	0.161778	0.0808890	+	0.996723i	$0.474224\pi$
$422$	−93.9960	−0.0108428
$423$	1097.25	0.126123
$424$	−255.403	−0.0292535
$425$	2181.58	0.248994
$426$	27.7653	0.00315783
$427$	−21090.3	−2.39024
$428$	8491.39	0.958988
$429$	4196.95	0.472332
$430$	54.6906	0.00613352
$431$	−2590.85	−0.289552	−0.144776	−	0.989464i	$-0.546246\pi$
$431$	−2590.85	−0.289552	−0.144776	+	0.989464i	$0.546246\pi$
$432$	−9394.98	−1.04633
$433$	−10076.1	−1.11830	−0.559150	−	0.829066i	$-0.688873\pi$
$433$	−10076.1	−1.11830	−0.559150	+	0.829066i	$0.688873\pi$
$434$	−185.734	−0.0205427
$435$	−3304.32	−0.364207
$436$	10369.7	1.13903
$437$	−829.119	−0.0907600
$438$	−53.9493	−0.00588538
$439$	−16560.7	−1.80045	−0.900226	−	0.435422i	$-0.856599\pi$
$439$	−16560.7	−1.80045	−0.900226	+	0.435422i	$0.856599\pi$
$440$	−20.2817	−0.00219748
$441$	−2631.64	−0.284163
$442$	156.387	0.0168294
$443$	−7267.63	−0.779449	−0.389724	−	0.920932i	$-0.627430\pi$
$443$	−7267.63	−0.779449	−0.389724	+	0.920932i	$0.627430\pi$
$444$	−462.582	−0.0494441
$445$	3161.79	0.336817
$446$	80.1757	0.00851218
$447$	−7115.49	−0.752911
$448$	−18047.9	−1.90332
$449$	12900.8	1.35596	0.677982	−	0.735078i	$-0.262855\pi$
$449$	12900.8	1.35596	0.677982	+	0.735078i	$0.262855\pi$
$450$	−1.68382	−0.000176392 0
$451$	−4776.09	−0.498663
$452$	−5460.36	−0.568216
$453$	7375.99	0.765021
$454$	−21.2438	−0.00219608
$455$	13709.9	1.41259
$456$	34.3798	0.00353066
$457$	−7486.05	−0.766264	−0.383132	−	0.923694i	$-0.625155\pi$
$457$	−7486.05	−0.766264	−0.383132	+	0.923694i	$0.625155\pi$
$458$	−137.955	−0.0140747
$459$	−12812.5	−1.30291
$460$	−1745.40	−0.176912
$461$	−6748.23	−0.681770	−0.340885	−	0.940105i	$-0.610727\pi$
$461$	−6748.23	−0.681770	−0.340885	+	0.940105i	$0.610727\pi$
$462$	43.8700	0.00441778
$463$	3723.67	0.373766	0.186883	−	0.982382i	$-0.440161\pi$
$463$	3723.67	0.373766	0.186883	+	0.982382i	$0.440161\pi$
$464$	−8617.83	−0.862226
$465$	−5606.65	−0.559144
$466$	−62.1914	−0.00618232
$467$	4350.01	0.431038	0.215519	−	0.976500i	$-0.430856\pi$
$467$	4350.01	0.431038	0.215519	+	0.976500i	$0.430856\pi$
$468$	1817.67	0.179534
$469$	284.067	0.0279680
$470$	−43.2704	−0.00424662
$471$	−13675.7	−1.33788
$472$	−306.560	−0.0298953
$473$	5220.34	0.507466
$474$	−36.3964	−0.00352688
$475$	−475.000	−0.0458831
$476$	−24616.4	−2.37035
$477$	−2023.98	−0.194280
$478$	43.0298	0.00411745
$479$	−19303.7	−1.84136	−0.920678	−	0.390324i	$-0.872363\pi$
$479$	−19303.7	−1.84136	−0.920678	+	0.390324i	$0.872363\pi$
$480$	108.562	0.0103232
$481$	916.333	0.0868632
$482$	26.4296	0.00249759
$483$	7550.95	0.711346
$484$	−967.936	−0.0909031
$485$	−1891.61	−0.177100
$486$	18.8125	0.00175587
$487$	10043.7	0.934542	0.467271	−	0.884114i	$-0.345237\pi$
$487$	10043.7	0.934542	0.467271	+	0.884114i	$0.345237\pi$
$488$	220.544	0.0204581
$489$	−15021.4	−1.38914
$490$	103.780	0.00956793
$491$	−7766.49	−0.713842	−0.356921	−	0.934135i	$-0.616174\pi$
$491$	−7766.49	−0.713842	−0.356921	+	0.934135i	$0.616174\pi$
$492$	17043.1	1.56171
$493$	−11752.7	−1.07366
$494$	−34.0505	−0.00310122
$495$	−160.725	−0.0145940
$496$	−14622.4	−1.32372
$497$	8657.44	0.781367
$498$	−19.4046	−0.00174607
$499$	13443.7	1.20606	0.603028	−	0.797720i	$-0.293961\pi$
$499$	13443.7	1.20606	0.603028	+	0.797720i	$0.293961\pi$
$500$	−999.934	−0.0894368
$501$	11614.2	1.03570
$502$	39.8859	0.00354620
$503$	3682.11	0.326396	0.163198	−	0.986593i	$-0.447819\pi$
$503$	3682.11	0.326396	0.163198	+	0.986593i	$0.447819\pi$
$504$	38.0008	0.00335851
$505$	8188.23	0.721527
$506$	11.0635	0.000972000 0
$507$	18886.6	1.65440
$508$	2972.54	0.259616
$509$	−12488.7	−1.08753	−0.543763	−	0.839239i	$-0.683001\pi$
$509$	−12488.7	−1.08753	−0.543763	+	0.839239i	$0.683001\pi$
$510$	49.3453	0.00428440
$511$	−16821.8	−1.45627
$512$	471.901	0.0407329
$513$	2789.69	0.240093
$514$	43.5194	0.00373455
$515$	4267.29	0.365125
$516$	−18628.4	−1.58928
$517$	−4130.26	−0.351351
$518$	9.57827	0.000812442 0
$519$	20298.1	1.71674
$520$	−143.366	−0.0120904
$521$	−7528.69	−0.633086	−0.316543	−	0.948578i	$-0.602522\pi$
$521$	−7528.69	−0.633086	−0.316543	+	0.948578i	$0.602522\pi$
$522$	9.07112	0.000760598 0
$523$	−7799.52	−0.652101	−0.326051	−	0.945352i	$-0.605718\pi$
$523$	−7799.52	−0.652101	−0.326051	+	0.945352i	$0.605718\pi$
$524$	−3717.09	−0.309889
$525$	4325.92	0.359617
$526$	−148.279	−0.0122914
$527$	−19941.5	−1.64832
$528$	3453.77	0.284671
$529$	−10262.7	−0.843490
$530$	79.8162	0.00654150
$531$	−2429.38	−0.198542
$532$	5359.76	0.436796
$533$	−33760.8	−2.74361
$534$	71.5167	0.00579556
$535$	−5307.47	−0.428901
$536$	−2.97051	−0.000239378 0
$537$	4191.90	0.336860
$538$	44.7881	0.00358913
$539$	9906.00	0.791617
$540$	5872.64	0.467997
$541$	18059.4	1.43519	0.717593	−	0.696463i	$-0.245244\pi$
$541$	18059.4	1.43519	0.717593	+	0.696463i	$0.245244\pi$
$542$	3.76934	0.000298721 0
$543$	−2883.31	−0.227873
$544$	386.127	0.0304321
$545$	−6481.50	−0.509426
$546$	310.104	0.0243063
$547$	−18374.5	−1.43627	−0.718134	−	0.695905i	$-0.755003\pi$
$547$	−18374.5	−1.43627	−0.718134	+	0.695905i	$0.755003\pi$
$548$	1274.24	0.0993297
$549$	1747.73	0.135867
$550$	6.33824	0.000491388 0
$551$	2558.93	0.197848
$552$	−78.9610	−0.00608841
$553$	−11348.7	−0.872686
$554$	23.0080	0.00176447
$555$	289.133	0.0221135
$556$	−15039.3	−1.14714
$557$	16772.8	1.27592	0.637959	−	0.770071i	$-0.279779\pi$
$557$	16772.8	1.27592	0.637959	+	0.770071i	$0.279779\pi$
$558$	15.3915	0.00116770
$559$	36901.1	2.79204
$560$	11282.2	0.851358
$561$	4710.12	0.354477
$562$	129.462	0.00971716
$563$	12607.5	0.943772	0.471886	−	0.881660i	$-0.343573\pi$
$563$	12607.5	0.943772	0.471886	+	0.881660i	$0.343573\pi$
$564$	14738.5	1.10036
$565$	3412.95	0.254131
$566$	4.67395	0.000347104 0
$567$	−22623.9	−1.67569
$568$	−90.5316	−0.00668772
$569$	−13802.7	−1.01694	−0.508469	−	0.861080i	$-0.669788\pi$
$569$	−13802.7	−1.01694	−0.508469	+	0.861080i	$0.669788\pi$
$570$	−10.7440	−0.000789506 0
$571$	−12205.7	−0.894558	−0.447279	−	0.894394i	$-0.647607\pi$
$571$	−12205.7	−0.894558	−0.447279	+	0.894394i	$0.647607\pi$
$572$	−6842.06	−0.500142
$573$	9895.51	0.721450
$574$	−352.896	−0.0256613
$575$	1090.95	0.0791228
$576$	1495.61	0.108189
$577$	−8781.31	−0.633572	−0.316786	−	0.948497i	$-0.602604\pi$
$577$	−8781.31	−0.633572	−0.316786	+	0.948497i	$0.602604\pi$
$578$	62.2735	0.00448137
$579$	20218.1	1.45118
$580$	5386.86	0.385650
$581$	−6050.52	−0.432044
$582$	−42.7864	−0.00304735
$583$	7618.64	0.541221
$584$	175.907	0.0124642
$585$	−1136.12	−0.0802952
$586$	−110.362	−0.00777990
$587$	−16797.7	−1.18112	−0.590560	−	0.806994i	$-0.701093\pi$
$587$	−16797.7	−1.18112	−0.590560	+	0.806994i	$0.701093\pi$
$588$	−35348.8	−2.47918
$589$	4341.89	0.303743
$590$	95.8033	0.00668502
$591$	−13307.5	−0.926225
$592$	754.073	0.0523517
$593$	14603.3	1.01127	0.505637	−	0.862746i	$-0.331257\pi$
$593$	14603.3	1.01127	0.505637	+	0.862746i	$0.331257\pi$
$594$	−37.2247	−0.00257129
$595$	15386.2	1.06013
$596$	11600.0	0.797239
$597$	−2193.32	−0.150363
$598$	78.2047	0.00534787
$599$	18317.9	1.24950	0.624750	−	0.780824i	$-0.285201\pi$
$599$	18317.9	1.24950	0.624750	+	0.780824i	$0.285201\pi$
$600$	−45.2366	−0.00307796
$601$	−24809.3	−1.68385	−0.841924	−	0.539596i	$-0.818577\pi$
$601$	−24809.3	−1.68385	−0.841924	+	0.539596i	$0.818577\pi$
$602$	385.721	0.0261143
$603$	−23.5402	−0.00158977
$604$	−12024.7	−0.810062
$605$	605.000	0.0406558
$606$	185.210	0.0124152
$607$	27606.2	1.84597	0.922983	−	0.384840i	$-0.125743\pi$
$607$	27606.2	1.84597	0.922983	+	0.384840i	$0.125743\pi$
$608$	−84.0722	−0.00560786
$609$	−23304.7	−1.55066
$610$	−68.9222	−0.00457472
$611$	−29195.6	−1.93311
$612$	2039.92	0.134737
$613$	−20134.1	−1.32660	−0.663301	−	0.748353i	$-0.730845\pi$
$613$	−20134.1	−1.32660	−0.663301	+	0.748353i	$0.730845\pi$
$614$	−88.4484	−0.00581349
$615$	−10652.6	−0.698465
$616$	−143.043	−0.00935609
$617$	−23793.5	−1.55250	−0.776249	−	0.630426i	$-0.782880\pi$
$617$	−23793.5	−1.55250	−0.776249	+	0.630426i	$0.782880\pi$
$618$	96.5219	0.00628266
$619$	−20515.2	−1.33211	−0.666055	−	0.745903i	$-0.732018\pi$
$619$	−20515.2	−1.33211	−0.666055	+	0.745903i	$0.732018\pi$
$620$	9140.22	0.592064
$621$	−6407.16	−0.414026
$622$	−165.444	−0.0106651
$623$	22299.5	1.43404
$624$	24413.7	1.56624
$625$	625.000	0.0400000
$626$	−150.692	−0.00962117
$627$	−1025.54	−0.0653210
$628$	22294.7	1.41665
$629$	1028.38	0.0651892
$630$	−11.8757	−0.000751012 0
$631$	27625.6	1.74288	0.871441	−	0.490501i	$-0.163186\pi$
$631$	27625.6	1.74288	0.871441	+	0.490501i	$0.163186\pi$
$632$	118.674	0.00746932
$633$	−20011.6	−1.25654
$634$	−38.1643	−0.00239069
$635$	−1857.96	−0.116112
$636$	−27186.5	−1.69499
$637$	70022.7	4.35542
$638$	−34.1455	−0.00211886
$639$	−717.429	−0.0444148
$640$	−235.974	−0.0145745
$641$	11134.3	0.686079	0.343040	−	0.939321i	$-0.388543\pi$
$641$	11134.3	0.686079	0.343040	+	0.939321i	$0.388543\pi$
$642$	−120.050	−0.00738004
$643$	9636.46	0.591018	0.295509	−	0.955340i	$-0.404511\pi$
$643$	9636.46	0.591018	0.295509	+	0.955340i	$0.404511\pi$
$644$	−12309.9	−0.753228
$645$	11643.5	0.710795
$646$	−38.2139	−0.00232741
$647$	16915.1	1.02783	0.513913	−	0.857842i	$-0.328196\pi$
$647$	16915.1	1.02783	0.513913	+	0.857842i	$0.328196\pi$
$648$	236.580	0.0143422
$649$	9144.65	0.553095
$650$	44.8032	0.00270358
$651$	−39542.5	−2.38063
$652$	24488.6	1.47093
$653$	3790.53	0.227159	0.113580	−	0.993529i	$-0.463768\pi$
$653$	3790.53	0.227159	0.113580	+	0.993529i	$0.463768\pi$
$654$	−146.605	−0.00876563
$655$	2323.34	0.138596
$656$	−27782.6	−1.65355
$657$	1394.00	0.0827778
$658$	−305.177	−0.0180806
$659$	1212.49	0.0716723	0.0358362	−	0.999358i	$-0.488591\pi$
$659$	1212.49	0.0716723	0.0358362	+	0.999358i	$0.488591\pi$
$660$	−2158.90	−0.127326
$661$	8814.62	0.518682	0.259341	−	0.965786i	$-0.416495\pi$
$661$	8814.62	0.518682	0.259341	+	0.965786i	$0.416495\pi$
$662$	77.5091	0.00455057
$663$	33294.5	1.95030
$664$	63.2708	0.00369787
$665$	−3350.07	−0.195354
$666$	−0.793737	−4.61812e−5 0
$667$	−5877.16	−0.341176
$668$	−18934.0	−1.09668
$669$	17069.3	0.986451
$670$	0.928315	5.35283e−5 0
$671$	−6578.78	−0.378496
$672$	765.663	0.0439525
$673$	−9147.01	−0.523910	−0.261955	−	0.965080i	$-0.584367\pi$
$673$	−9147.01	−0.523910	−0.261955	+	0.965080i	$0.584367\pi$
$674$	186.078	0.0106342
$675$	−3670.64	−0.209308
$676$	−30789.8	−1.75181
$677$	12992.4	0.737574	0.368787	−	0.929514i	$-0.379773\pi$
$677$	12992.4	0.737574	0.368787	+	0.929514i	$0.379773\pi$
$678$	77.1976	0.00437280
$679$	−13341.1	−0.754030
$680$	−160.895	−0.00907361
$681$	−4522.76	−0.254497
$682$	−57.9368	−0.00325295
$683$	−9931.64	−0.556403	−0.278202	−	0.960523i	$-0.589738\pi$
$683$	−9931.64	−0.556403	−0.278202	+	0.960523i	$0.589738\pi$
$684$	−444.156	−0.0248285
$685$	−796.451	−0.0444245
$686$	453.156	0.0252209
$687$	−29370.3	−1.63108
$688$	30366.9	1.68274
$689$	53854.0	2.97776
$690$	24.6761	0.00136146
$691$	−4781.02	−0.263211	−0.131605	−	0.991302i	$-0.542013\pi$
$691$	−4781.02	−0.263211	−0.131605	+	0.991302i	$0.542013\pi$
$692$	−33090.9	−1.81782
$693$	−1133.56	−0.0621361
$694$	−131.848	−0.00721164
$695$	9400.18	0.513049
$696$	243.699	0.0132721
$697$	−37888.8	−2.05903
$698$	56.0564	0.00303978
$699$	−13240.4	−0.716450
$700$	−7052.32	−0.380789
$701$	−30853.2	−1.66235	−0.831175	−	0.556011i	$-0.812331\pi$
$701$	−30853.2	−1.66235	−0.831175	+	0.556011i	$0.812331\pi$
$702$	−263.131	−0.0141471
$703$	−223.910	−0.0120127
$704$	−5629.76	−0.301391
$705$	−9212.18	−0.492129
$706$	68.1217	0.00363143
$707$	57749.8	3.07200
$708$	−32632.0	−1.73218
$709$	27671.3	1.46575	0.732877	−	0.680362i	$-0.238177\pi$
$709$	27671.3	1.46575	0.732877	+	0.680362i	$0.238177\pi$
$710$	28.2921	0.00149547
$711$	940.449	0.0496056
$712$	−233.188	−0.0122740
$713$	−9972.14	−0.523786
$714$	348.022	0.0182414
$715$	4276.57	0.223685
$716$	−6833.83	−0.356693
$717$	9160.97	0.477158
$718$	−266.887	−0.0138720
$719$	32751.0	1.69876	0.849379	−	0.527784i	$-0.176977\pi$
$719$	32751.0	1.69876	0.849379	+	0.527784i	$0.176977\pi$
$720$	−934.940	−0.0483933
$721$	30096.3	1.55457
$722$	8.32038	0.000428882 0
$723$	5626.81	0.289438
$724$	4700.51	0.241289
$725$	−3367.01	−0.172479
$726$	13.6845	0.000699559 0
$727$	−17060.8	−0.870356	−0.435178	−	0.900344i	$-0.643315\pi$
$727$	−17060.8	−0.870356	−0.435178	+	0.900344i	$0.643315\pi$
$728$	−1011.13	−0.0514765
$729$	21327.2	1.08354
$730$	−54.9728	−0.00278717
$731$	41413.1	2.09538
$732$	23475.9	1.18537
$733$	3075.26	0.154962	0.0774812	−	0.996994i	$-0.475312\pi$
$733$	3075.26	0.154962	0.0774812	+	0.996994i	$0.475312\pi$
$734$	−149.868	−0.00753643
$735$	22094.5	1.10880
$736$	193.091	0.00967042
$737$	88.6099	0.00442875
$738$	29.2440	0.00145865
$739$	19419.3	0.966644	0.483322	−	0.875443i	$-0.339430\pi$
$739$	19419.3	0.966644	0.483322	+	0.875443i	$0.339430\pi$
$740$	−471.358	−0.0234155
$741$	−7249.28	−0.359391
$742$	562.927	0.0278513
$743$	20818.6	1.02794	0.513971	−	0.857807i	$-0.328174\pi$
$743$	20818.6	1.02794	0.513971	+	0.857807i	$0.328174\pi$
$744$	413.499	0.0203758
$745$	−7250.48	−0.356560
$746$	−6.91486	−0.000339372 0
$747$	501.397	0.0245585
$748$	−7678.66	−0.375347
$749$	−37432.5	−1.82610
$750$	14.1369	0.000688275 0
$751$	−27483.8	−1.33542	−0.667709	−	0.744422i	$-0.732725\pi$
$751$	−27483.8	−1.33542	−0.667709	+	0.744422i	$0.732725\pi$
$752$	−24025.8	−1.16507
$753$	8491.62	0.410959
$754$	−241.365	−0.0116578
$755$	7515.93	0.362295
$756$	41418.5	1.99256
$757$	15222.4	0.730867	0.365434	−	0.930837i	$-0.380921\pi$
$757$	15222.4	0.730867	0.365434	+	0.930837i	$0.380921\pi$
$758$	−293.425	−0.0140603
$759$	2355.39	0.112642
$760$	35.0320	0.00167203
$761$	16062.3	0.765121	0.382560	−	0.923930i	$-0.375042\pi$
$761$	16062.3	0.765121	0.382560	+	0.923930i	$0.375042\pi$
$762$	−42.0252	−0.00199792
$763$	−45712.7	−2.16895
$764$	−16132.1	−0.763927
$765$	−1275.03	−0.0602601
$766$	131.998	0.00622621
$767$	64640.9	3.04309
$768$	20085.3	0.943708
$769$	10130.3	0.475044	0.237522	−	0.971382i	$-0.423665\pi$
$769$	10130.3	0.475044	0.237522	+	0.971382i	$0.423665\pi$
$770$	44.7023	0.00209215
$771$	9265.20	0.432786
$772$	−32960.5	−1.53663
$773$	19498.6	0.907266	0.453633	−	0.891189i	$-0.350128\pi$
$773$	19498.6	0.907266	0.453633	+	0.891189i	$0.350128\pi$
$774$	−31.9641	−0.00148440
$775$	−5713.01	−0.264797
$776$	139.510	0.00645374
$777$	2039.19	0.0941515
$778$	80.2253	0.00369694
$779$	8249.61	0.379426
$780$	−15260.6	−0.700536
$781$	2700.54	0.123730
$782$	87.7670	0.00401348
$783$	19774.6	0.902535
$784$	57623.4	2.62497
$785$	−13935.1	−0.633588
$786$	52.5517	0.00238480
$787$	−8345.38	−0.377993	−0.188997	−	0.981978i	$-0.560524\pi$
$787$	−8345.38	−0.377993	−0.188997	+	0.981978i	$0.560524\pi$
$788$	21694.6	0.980758
$789$	−31568.4	−1.42442
$790$	−37.0869	−0.00167025
$791$	24070.8	1.08200
$792$	11.8537	0.000531823 0
$793$	−46503.5	−2.08246
$794$	81.4898	0.00364227
$795$	16992.7	0.758075
$796$	3575.66	0.159216
$797$	−17410.0	−0.773768	−0.386884	−	0.922128i	$-0.626449\pi$
$797$	−17410.0	−0.773768	−0.386884	+	0.922128i	$0.626449\pi$
$798$	−75.7754	−0.00336143
$799$	−32765.4	−1.45076
$800$	110.621	0.00488882
$801$	−1847.92	−0.0815146
$802$	−134.293	−0.00591278
$803$	−5247.28	−0.230601
$804$	−316.197	−0.0138699
$805$	7694.21	0.336876
$806$	−409.538	−0.0178975
$807$	9535.29	0.415933
$808$	−603.895	−0.0262933
$809$	7675.49	0.333567	0.166784	−	0.985994i	$-0.446662\pi$
$809$	7675.49	0.333567	0.166784	+	0.985994i	$0.446662\pi$
$810$	−73.9338	−0.00320712
$811$	−17206.0	−0.744987	−0.372493	−	0.928035i	$-0.621497\pi$
$811$	−17206.0	−0.744987	−0.372493	+	0.928035i	$0.621497\pi$
$812$	37992.4	1.64196
$813$	802.484	0.0346179
$814$	2.98778	0.000128651 0
$815$	−15306.4	−0.657865
$816$	27398.9	1.17543
$817$	−9016.96	−0.386124
$818$	260.120	0.0111184
$819$	−8012.80	−0.341868
$820$	17366.4	0.739588
$821$	−17712.3	−0.752942	−0.376471	−	0.926429i	$-0.622862\pi$
$821$	−17712.3	−0.752942	−0.376471	+	0.926429i	$0.622862\pi$
$822$	−18.0149	−0.000764408 0
$823$	−28864.0	−1.22252	−0.611261	−	0.791429i	$-0.709338\pi$
$823$	−28864.0	−1.22252	−0.611261	+	0.791429i	$0.709338\pi$
$824$	−314.720	−0.0133056
$825$	1349.40	0.0569455
$826$	675.680	0.0284624
$827$	24313.2	1.02231	0.511157	−	0.859487i	$-0.329217\pi$
$827$	24313.2	1.02231	0.511157	+	0.859487i	$0.329217\pi$
$828$	1020.10	0.0428153
$829$	−37636.8	−1.57682	−0.788409	−	0.615152i	$-0.789095\pi$
$829$	−37636.8	−1.57682	−0.788409	+	0.615152i	$0.789095\pi$
$830$	−19.7728	−0.000826895 0
$831$	4898.36	0.204479
$832$	−39795.2	−1.65823
$833$	78584.6	3.26866
$834$	212.623	0.00882797
$835$	11834.6	0.490481
$836$	1671.89	0.0691669
$837$	33552.7	1.38560
$838$	−167.562	−0.00690732
$839$	−2579.99	−0.106164	−0.0530818	−	0.998590i	$-0.516904\pi$
$839$	−2579.99	−0.106164	−0.0530818	+	0.998590i	$0.516904\pi$
$840$	−319.044	−0.0131048
$841$	−6250.19	−0.256271
$842$	32.2091	0.00131829
$843$	27562.3	1.12609
$844$	32623.8	1.33052
$845$	19244.9	0.783484
$846$	25.2895	0.00102775
$847$	4266.94	0.173098
$848$	44317.8	1.79467
$849$	995.074	0.0402248
$850$	50.2815	0.00202899
$851$	514.261	0.0207152
$852$	−9636.68	−0.387497
$853$	10424.5	0.418438	0.209219	−	0.977869i	$-0.432908\pi$
$853$	10424.5	0.418438	0.209219	+	0.977869i	$0.432908\pi$
$854$	−486.094	−0.0194775
$855$	277.616	0.0111044
$856$	391.435	0.0156296
$857$	17837.4	0.710984	0.355492	−	0.934679i	$-0.384313\pi$
$857$	17837.4	0.710984	0.355492	+	0.934679i	$0.384313\pi$
$858$	96.7319	0.00384892
$859$	−32831.9	−1.30409	−0.652044	−	0.758181i	$-0.726088\pi$
$859$	−32831.9	−1.30409	−0.652044	+	0.758181i	$0.726088\pi$
$860$	−18981.8	−0.752644
$861$	−75130.9	−2.97381
$862$	−59.7143	−0.00235949
$863$	16920.9	0.667434	0.333717	−	0.942673i	$-0.391697\pi$
$863$	16920.9	0.667434	0.333717	+	0.942673i	$0.391697\pi$
$864$	−649.683	−0.0255818
$865$	20683.2	0.813006
$866$	−232.234	−0.00911276
$867$	13257.9	0.519333
$868$	64464.0	2.52080
$869$	−3540.03	−0.138190
$870$	−76.1585	−0.00296783
$871$	626.358	0.0243666
$872$	478.021	0.0185640
$873$	1105.56	0.0428609
$874$	−19.1097	−0.000739581 0
$875$	4407.99	0.170306
$876$	18724.5	0.722195
$877$	−16446.5	−0.633247	−0.316623	−	0.948551i	$-0.602549\pi$
$877$	−16446.5	−0.633247	−0.316623	+	0.948551i	$0.602549\pi$
$878$	−381.693	−0.0146714
$879$	−23495.9	−0.901589
$880$	3519.30	0.134813
$881$	−49681.3	−1.89989	−0.949946	−	0.312415i	$-0.898862\pi$
$881$	−49681.3	−1.89989	−0.949946	+	0.312415i	$0.898862\pi$
$882$	−60.6544	−0.00231558
$883$	−18855.9	−0.718630	−0.359315	−	0.933216i	$-0.616990\pi$
$883$	−18855.9	−0.718630	−0.359315	+	0.933216i	$0.616990\pi$
$884$	−54278.3	−2.06513
$885$	20396.3	0.774707
$886$	−167.506	−0.00635153
$887$	−18561.9	−0.702646	−0.351323	−	0.936254i	$-0.614268\pi$
$887$	−18561.9	−0.702646	−0.351323	+	0.936254i	$0.614268\pi$
$888$	−21.3240	−0.000805843 0
$889$	−13103.8	−0.494361
$890$	72.8735	0.00274464
$891$	−7057.15	−0.265346
$892$	−27827.1	−1.04453
$893$	7134.08	0.267338
$894$	−163.999	−0.00613528
$895$	4271.43	0.159529
$896$	−1664.27	−0.0620530
$897$	16649.6	0.619749
$898$	297.340	0.0110494
$899$	30777.2	1.14180
$900$	584.415	0.0216450
$901$	60438.9	2.23475
$902$	−110.080	−0.00406349
$903$	82119.3	3.02631
$904$	−251.711	−0.00926081
$905$	−2938.02	−0.107915
$906$	170.003	0.00623396
$907$	−7160.89	−0.262154	−0.131077	−	0.991372i	$-0.541843\pi$
$907$	−7160.89	−0.262154	−0.131077	+	0.991372i	$0.541843\pi$
$908$	7373.21	0.269481
$909$	−4785.64	−0.174620
$910$	315.988	0.0115109
$911$	−6979.90	−0.253847	−0.126923	−	0.991913i	$-0.540510\pi$
$911$	−6979.90	−0.253847	−0.126923	+	0.991913i	$0.540510\pi$
$912$	−5965.61	−0.216602
$913$	−1887.36	−0.0684145
$914$	−172.540	−0.00624409
$915$	−14673.4	−0.530150
$916$	47880.9	1.72711
$917$	16386.0	0.590091
$918$	−295.305	−0.0106171
$919$	3456.65	0.124075	0.0620373	−	0.998074i	$-0.480240\pi$
$919$	3456.65	0.124075	0.0620373	+	0.998074i	$0.480240\pi$
$920$	−80.4591	−0.00288332
$921$	−18830.5	−0.673708
$922$	−155.534	−0.00555558
$923$	19089.4	0.680753
$924$	−15226.2	−0.542106
$925$	294.619	0.0104724
$926$	85.8238	0.00304573
$927$	−2494.03	−0.0883655
$928$	−595.941	−0.0210805
$929$	17315.0	0.611504	0.305752	−	0.952111i	$-0.401092\pi$
$929$	17315.0	0.611504	0.305752	+	0.952111i	$0.401092\pi$
$930$	−129.223	−0.00455633
$931$	−17110.4	−0.602330
$932$	21585.2	0.758632
$933$	−35222.6	−1.23594
$934$	100.260	0.00351242
$935$	4799.48	0.167871
$936$	83.7906	0.00292605
$937$	−35326.9	−1.23167	−0.615837	−	0.787873i	$-0.711182\pi$
$937$	−35326.9	−1.23167	−0.615837	+	0.787873i	$0.711182\pi$
$938$	6.54721	0.000227904 0
$939$	−32082.0	−1.11497
$940$	15018.1	0.521103
$941$	5266.40	0.182444	0.0912220	−	0.995831i	$-0.470923\pi$
$941$	5266.40	0.182444	0.0912220	+	0.995831i	$0.470923\pi$
$942$	−315.199	−0.0109021
$943$	−18947.1	−0.654298
$944$	53194.6	1.83404
$945$	−25888.3	−0.891160
$946$	120.319	0.00413522
$947$	18018.9	0.618305	0.309152	−	0.951013i	$-0.399955\pi$
$947$	18018.9	0.618305	0.309152	+	0.951013i	$0.399955\pi$
$948$	12632.3	0.432784
$949$	−37091.5	−1.26875
$950$	−10.9479	−0.000373890 0
$951$	−8125.11	−0.277050
$952$	−1134.76	−0.0386321
$953$	24949.3	0.848046	0.424023	−	0.905651i	$-0.360618\pi$
$953$	24949.3	0.848046	0.424023	+	0.905651i	$0.360618\pi$
$954$	−46.6489	−0.00158314
$955$	10083.3	0.341661
$956$	−14934.6	−0.505252
$957$	−7269.51	−0.245548
$958$	−444.915	−0.0150047
$959$	−5617.20	−0.189144
$960$	−12556.7	−0.422151
$961$	22430.7	0.752934
$962$	21.1198	0.000707827 0
$963$	3101.97	0.103800
$964$	−9173.10	−0.306479
$965$	20601.7	0.687245
$966$	174.036	0.00579659
$967$	−44474.2	−1.47900	−0.739500	−	0.673156i	$-0.764938\pi$
$967$	−44474.2	−1.47900	−0.739500	+	0.673156i	$0.764938\pi$
$968$	−44.6197	−0.00148154
$969$	−8135.66	−0.269716
$970$	−43.5982	−0.00144315
$971$	36141.1	1.19446	0.597232	−	0.802069i	$-0.296267\pi$
$971$	36141.1	1.19446	0.597232	+	0.802069i	$0.296267\pi$
$972$	−6529.37	−0.215463
$973$	66297.5	2.18438
$974$	231.488	0.00761535
$975$	9538.52	0.313310
$976$	−38268.9	−1.25508
$977$	−6612.04	−0.216518	−0.108259	−	0.994123i	$-0.534528\pi$
$977$	−6612.04	−0.216518	−0.108259	+	0.994123i	$0.534528\pi$
$978$	−346.216	−0.0113198
$979$	6955.95	0.227082
$980$	−36019.4	−1.17408
$981$	3788.14	0.123288
$982$	−179.003	−0.00581692
$983$	33006.4	1.07095	0.535473	−	0.844552i	$-0.320133\pi$
$983$	33006.4	1.07095	0.535473	+	0.844552i	$0.320133\pi$
$984$	785.650	0.0254529
$985$	−13560.0	−0.438637
$986$	−270.877	−0.00874897
$987$	−64971.5	−2.09531
$988$	11818.1	0.380551
$989$	20709.5	0.665848
$990$	−3.70441	−0.000118923 0
$991$	5447.68	0.174623	0.0873115	−	0.996181i	$-0.472172\pi$
$991$	5447.68	0.174623	0.0873115	+	0.996181i	$0.472172\pi$
$992$	−1011.17	−0.0323636
$993$	16501.5	0.527352
$994$	199.538	0.00636717
$995$	−2234.93	−0.0712082
$996$	6734.89	0.214260
$997$	51174.5	1.62559	0.812794	−	0.582551i	$-0.197945\pi$
$997$	51174.5	1.62559	0.812794	+	0.582551i	$0.197945\pi$
$998$	309.852	0.00982786
$999$	−1730.30	−0.0547992

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.4.a.e.1.10	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.4.a.e.1.10	✓	22	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:	\( N \)	\(=\)	\( 1045 = 5 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1045.a (trivial)

\(f(q)\)	\(=\)	\(q+0.0230482 q^{2} +4.90691 q^{3} -7.99947 q^{4} +5.00000 q^{5} +0.113095 q^{6} +35.2639 q^{7} -0.368758 q^{8} -2.92227 q^{9} +O(q^{10})\)	\(q+0.0230482 q^{2} +4.90691 q^{3} -7.99947 q^{4} +5.00000 q^{5} +0.113095 q^{6} +35.2639 q^{7} -0.368758 q^{8} -2.92227 q^{9} +0.115241 q^{10} +11.0000 q^{11} -39.2526 q^{12} +77.7559 q^{13} +0.812769 q^{14} +24.5345 q^{15} +63.9873 q^{16} +87.2633 q^{17} -0.0673529 q^{18} -19.0000 q^{19} -39.9973 q^{20} +173.037 q^{21} +0.253530 q^{22} +43.6378 q^{23} -1.80946 q^{24} +25.0000 q^{25} +1.79213 q^{26} -146.826 q^{27} -282.093 q^{28} -134.680 q^{29} +0.565476 q^{30} -228.521 q^{31} +4.42485 q^{32} +53.9760 q^{33} +2.01126 q^{34} +176.320 q^{35} +23.3766 q^{36} +11.7847 q^{37} -0.437915 q^{38} +381.541 q^{39} -1.84379 q^{40} -434.190 q^{41} +3.98818 q^{42} +474.577 q^{43} -87.9942 q^{44} -14.6114 q^{45} +1.00577 q^{46} -375.478 q^{47} +313.979 q^{48} +900.546 q^{49} +0.576204 q^{50} +428.193 q^{51} -622.006 q^{52} +692.604 q^{53} -3.38406 q^{54} +55.0000 q^{55} -13.0039 q^{56} -93.2312 q^{57} -3.10413 q^{58} +831.332 q^{59} -196.263 q^{60} -598.071 q^{61} -5.26698 q^{62} -103.051 q^{63} -511.796 q^{64} +388.779 q^{65} +1.24405 q^{66} +8.05544 q^{67} -698.060 q^{68} +214.127 q^{69} +4.06384 q^{70} +245.504 q^{71} +1.07761 q^{72} -477.025 q^{73} +0.271617 q^{74} +122.673 q^{75} +151.990 q^{76} +387.903 q^{77} +8.79381 q^{78} -321.821 q^{79} +319.936 q^{80} -641.559 q^{81} -10.0073 q^{82} -171.578 q^{83} -1384.20 q^{84} +436.317 q^{85} +10.9381 q^{86} -660.864 q^{87} -4.05634 q^{88} +632.359 q^{89} -0.336765 q^{90} +2741.98 q^{91} -349.080 q^{92} -1121.33 q^{93} -8.65407 q^{94} -95.0000 q^{95} +21.7123 q^{96} -378.323 q^{97} +20.7559 q^{98} -32.1450 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 12 q^{2} + 21 q^{3} + 96 q^{4} + 110 q^{5} + 27 q^{6} + 93 q^{7} + 114 q^{8} + 209 q^{9}+O(q^{10}) \) 22 * q + 12 * q^2 + 21 * q^3 + 96 * q^4 + 110 * q^5 + 27 * q^6 + 93 * q^7 + 114 * q^8 + 209 * q^9	\( 22 q + 12 q^{2} + 21 q^{3} + 96 q^{4} + 110 q^{5} + 27 q^{6} + 93 q^{7} + 114 q^{8} + 209 q^{9} + 60 q^{10} + 242 q^{11} + 164 q^{12} + 207 q^{13} + 129 q^{14} + 105 q^{15} + 604 q^{16} + 209 q^{17} + 869 q^{18} - 418 q^{19} + 480 q^{20} + 45 q^{21} + 132 q^{22} + 191 q^{23} + 458 q^{24} + 550 q^{25} + 363 q^{26} + 45 q^{27} + 577 q^{28} + 389 q^{29} + 135 q^{30} + 198 q^{31} + 1149 q^{32} + 231 q^{33} + 467 q^{34} + 465 q^{35} + 1315 q^{36} + 312 q^{37} - 228 q^{38} + 137 q^{39} + 570 q^{40} + 632 q^{41} - 1794 q^{42} + 1584 q^{43} + 1056 q^{44} + 1045 q^{45} + 681 q^{46} - 54 q^{47} + 2491 q^{48} + 1063 q^{49} + 300 q^{50} + 37 q^{51} + 1246 q^{52} + 343 q^{53} + 1078 q^{54} + 1210 q^{55} - 87 q^{56} - 399 q^{57} - 1424 q^{58} + 2787 q^{59} + 820 q^{60} + 2070 q^{61} - 446 q^{62} + 1696 q^{63} + 1758 q^{64} + 1035 q^{65} + 297 q^{66} + 2423 q^{67} - 524 q^{68} - 997 q^{69} + 645 q^{70} + 2538 q^{71} + 6010 q^{72} + 1397 q^{73} - 1977 q^{74} + 525 q^{75} - 1824 q^{76} + 1023 q^{77} + 202 q^{78} + 878 q^{79} + 3020 q^{80} + 2030 q^{81} - 190 q^{82} + 4932 q^{83} - 4580 q^{84} + 1045 q^{85} - 3394 q^{86} + 6009 q^{87} + 1254 q^{88} + 1812 q^{89} + 4345 q^{90} + 4349 q^{91} - 788 q^{92} - 4848 q^{93} - 2152 q^{94} - 2090 q^{95} + 4032 q^{96} + 988 q^{97} + 1366 q^{98} + 2299 q^{99}+O(q^{100}) \) 22 * q + 12 * q^2 + 21 * q^3 + 96 * q^4 + 110 * q^5 + 27 * q^6 + 93 * q^7 + 114 * q^8 + 209 * q^9 + 60 * q^10 + 242 * q^11 + 164 * q^12 + 207 * q^13 + 129 * q^14 + 105 * q^15 + 604 * q^16 + 209 * q^17 + 869 * q^18 - 418 * q^19 + 480 * q^20 + 45 * q^21 + 132 * q^22 + 191 * q^23 + 458 * q^24 + 550 * q^25 + 363 * q^26 + 45 * q^27 + 577 * q^28 + 389 * q^29 + 135 * q^30 + 198 * q^31 + 1149 * q^32 + 231 * q^33 + 467 * q^34 + 465 * q^35 + 1315 * q^36 + 312 * q^37 - 228 * q^38 + 137 * q^39 + 570 * q^40 + 632 * q^41 - 1794 * q^42 + 1584 * q^43 + 1056 * q^44 + 1045 * q^45 + 681 * q^46 - 54 * q^47 + 2491 * q^48 + 1063 * q^49 + 300 * q^50 + 37 * q^51 + 1246 * q^52 + 343 * q^53 + 1078 * q^54 + 1210 * q^55 - 87 * q^56 - 399 * q^57 - 1424 * q^58 + 2787 * q^59 + 820 * q^60 + 2070 * q^61 - 446 * q^62 + 1696 * q^63 + 1758 * q^64 + 1035 * q^65 + 297 * q^66 + 2423 * q^67 - 524 * q^68 - 997 * q^69 + 645 * q^70 + 2538 * q^71 + 6010 * q^72 + 1397 * q^73 - 1977 * q^74 + 525 * q^75 - 1824 * q^76 + 1023 * q^77 + 202 * q^78 + 878 * q^79 + 3020 * q^80 + 2030 * q^81 - 190 * q^82 + 4932 * q^83 - 4580 * q^84 + 1045 * q^85 - 3394 * q^86 + 6009 * q^87 + 1254 * q^88 + 1812 * q^89 + 4345 * q^90 + 4349 * q^91 - 788 * q^92 - 4848 * q^93 - 2152 * q^94 - 2090 * q^95 + 4032 * q^96 + 988 * q^97 + 1366 * q^98 + 2299 * q^99

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