LMFDB - Embedded newform 1849.4.a.g.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1849.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$109.094531601$
Analytic rank:	$1$
Dimension:	$30$
Twist minimal:	no (minimal twist has level 43)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
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)

$f(q)$	$=$	$q-1.77522 q^{2} -4.21024 q^{3} -4.84859 q^{4} -5.54921 q^{5} +7.47410 q^{6} -24.8990 q^{7} +22.8091 q^{8} -9.27388 q^{9} +O(q^{10})$	\(q-1.77522 q^{2} -4.21024 q^{3} -4.84859 q^{4} -5.54921 q^{5} +7.47410 q^{6} -24.8990 q^{7} +22.8091 q^{8} -9.27388 q^{9} +9.85108 q^{10} +11.4079 q^{11} +20.4137 q^{12} -15.2247 q^{13} +44.2013 q^{14} +23.3635 q^{15} -1.70241 q^{16} -76.3993 q^{17} +16.4632 q^{18} -86.9425 q^{19} +26.9059 q^{20} +104.831 q^{21} -20.2515 q^{22} +31.6433 q^{23} -96.0317 q^{24} -94.2062 q^{25} +27.0272 q^{26} +152.722 q^{27} +120.725 q^{28} -148.429 q^{29} -41.4754 q^{30} +203.374 q^{31} -179.451 q^{32} -48.0299 q^{33} +135.626 q^{34} +138.170 q^{35} +44.9653 q^{36} -229.660 q^{37} +154.342 q^{38} +64.0996 q^{39} -126.572 q^{40} -21.6070 q^{41} -186.098 q^{42} -55.3122 q^{44} +51.4628 q^{45} -56.1738 q^{46} +605.261 q^{47} +7.16757 q^{48} +276.962 q^{49} +167.237 q^{50} +321.659 q^{51} +73.8183 q^{52} +230.915 q^{53} -271.115 q^{54} -63.3048 q^{55} -567.924 q^{56} +366.049 q^{57} +263.494 q^{58} -199.451 q^{59} -113.280 q^{60} +31.3311 q^{61} -361.034 q^{62} +230.911 q^{63} +332.184 q^{64} +84.4850 q^{65} +85.2637 q^{66} +600.409 q^{67} +370.429 q^{68} -133.226 q^{69} -245.282 q^{70} +753.209 q^{71} -211.529 q^{72} -443.263 q^{73} +407.698 q^{74} +396.631 q^{75} +421.549 q^{76} -284.045 q^{77} -113.791 q^{78} +305.769 q^{79} +9.44706 q^{80} -392.600 q^{81} +38.3572 q^{82} +714.201 q^{83} -508.282 q^{84} +423.956 q^{85} +624.922 q^{87} +260.203 q^{88} +1024.60 q^{89} -91.3578 q^{90} +379.080 q^{91} -153.425 q^{92} -856.254 q^{93} -1074.47 q^{94} +482.463 q^{95} +755.530 q^{96} -1413.22 q^{97} -491.668 q^{98} -105.795 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.77522	−0.627635	−0.313818	−	0.949483i	$-0.601608\pi$
$2$	−1.77522	−0.627635	−0.313818	+	0.949483i	$0.601608\pi$
$3$	−4.21024	−0.810261	−0.405130	−	0.914259i	$-0.632774\pi$
$3$	−4.21024	−0.810261	−0.405130	+	0.914259i	$0.632774\pi$
$4$	−4.84859	−0.606074
$5$	−5.54921	−0.496337	−0.248168	−	0.968717i	$-0.579829\pi$
$5$	−5.54921	−0.496337	−0.248168	+	0.968717i	$0.579829\pi$
$6$	7.47410	0.508548
$7$	−24.8990	−1.34442	−0.672211	−	0.740360i	$-0.734655\pi$
$7$	−24.8990	−1.34442	−0.672211	+	0.740360i	$0.734655\pi$
$8$	22.8091	1.00803
$9$	−9.27388	−0.343477
$10$	9.85108	0.311518
$11$	11.4079	0.312691	0.156346	−	0.987702i	$-0.450029\pi$
$11$	11.4079	0.312691	0.156346	+	0.987702i	$0.450029\pi$
$12$	20.4137	0.491078
$13$	−15.2247	−0.324813	−0.162406	−	0.986724i	$-0.551926\pi$
$13$	−15.2247	−0.324813	−0.162406	+	0.986724i	$0.551926\pi$
$14$	44.2013	0.843806
$15$	23.3635	0.402162
$16$	−1.70241	−0.0266002
$17$	−76.3993	−1.08997	−0.544987	−	0.838445i	$-0.683465\pi$
$17$	−76.3993	−1.08997	−0.544987	+	0.838445i	$0.683465\pi$
$18$	16.4632	0.215578
$19$	−86.9425	−1.04979	−0.524894	−	0.851167i	$-0.675895\pi$
$19$	−86.9425	−1.04979	−0.524894	+	0.851167i	$0.675895\pi$
$20$	26.9059	0.300817
$21$	104.831	1.08933
$22$	−20.2515	−0.196256
$23$	31.6433	0.286873	0.143437	−	0.989660i	$-0.454185\pi$
$23$	31.6433	0.286873	0.143437	+	0.989660i	$0.454185\pi$
$24$	−96.0317	−0.816766
$25$	−94.2062	−0.753650
$26$	27.0272	0.203864
$27$	152.722	1.08857
$28$	120.725	0.814819
$29$	−148.429	−0.950434	−0.475217	−	0.879869i	$-0.657631\pi$
$29$	−148.429	−0.950434	−0.475217	+	0.879869i	$0.657631\pi$
$30$	−41.4754	−0.252411
$31$	203.374	1.17829	0.589146	−	0.808026i	$-0.299464\pi$
$31$	203.374	1.17829	0.589146	+	0.808026i	$0.299464\pi$
$32$	−179.451	−0.991333
$33$	−48.0299	−0.253362
$34$	135.626	0.684106
$35$	138.170	0.667286
$36$	44.9653	0.208173
$37$	−229.660	−1.02043	−0.510215	−	0.860047i	$-0.670434\pi$
$37$	−229.660	−1.02043	−0.510215	+	0.860047i	$0.670434\pi$
$38$	154.342	0.658884
$39$	64.0996	0.263183
$40$	−126.572	−0.500322
$41$	−21.6070	−0.0823036	−0.0411518	−	0.999153i	$-0.513103\pi$
$41$	−21.6070	−0.0823036	−0.0411518	+	0.999153i	$0.513103\pi$
$42$	−186.098	−0.683703
$43$	0	0
$43$	0	0
$44$	−55.3122	−0.189514
$45$	51.4628	0.170480
$46$	−56.1738	−0.180052
$47$	605.261	1.87843	0.939216	−	0.343326i	$-0.111554\pi$
$47$	605.261	1.87843	0.939216	+	0.343326i	$0.111554\pi$
$48$	7.16757	0.0215531
$49$	276.962	0.807468
$50$	167.237	0.473017
$51$	321.659	0.883163
$52$	73.8183	0.196861
$53$	230.915	0.598464	0.299232	−	0.954180i	$-0.403270\pi$
$53$	230.915	0.598464	0.299232	+	0.954180i	$0.403270\pi$
$54$	−271.115	−0.683223
$55$	−63.3048	−0.155200
$56$	−567.924	−1.35521
$57$	366.049	0.850603
$58$	263.494	0.596526
$59$	−199.451	−0.440108	−0.220054	−	0.975488i	$-0.570623\pi$
$59$	−199.451	−0.440108	−0.220054	+	0.975488i	$0.570623\pi$
$60$	−113.280	−0.243740
$61$	31.3311	0.0657628	0.0328814	−	0.999459i	$-0.489532\pi$
$61$	31.3311	0.0657628	0.0328814	+	0.999459i	$0.489532\pi$
$62$	−361.034	−0.739538
$63$	230.911	0.461778
$64$	332.184	0.648796
$65$	84.4850	0.161217
$66$	85.2637	0.159019
$67$	600.409	1.09480	0.547400	−	0.836871i	$-0.315618\pi$
$67$	600.409	1.09480	0.547400	+	0.836871i	$0.315618\pi$
$68$	370.429	0.660604
$69$	−133.226	−0.232442
$70$	−245.282	−0.418812
$71$	753.209	1.25901	0.629503	−	0.776998i	$-0.283258\pi$
$71$	753.209	1.25901	0.629503	+	0.776998i	$0.283258\pi$
$72$	−211.529	−0.346235
$73$	−443.263	−0.710685	−0.355343	−	0.934736i	$-0.615636\pi$
$73$	−443.263	−0.710685	−0.355343	+	0.934736i	$0.615636\pi$
$74$	407.698	0.640458
$75$	396.631	0.610653
$76$	421.549	0.636250
$77$	−284.045	−0.420389
$78$	−113.791	−0.165183
$79$	305.769	0.435465	0.217732	−	0.976009i	$-0.430134\pi$
$79$	305.769	0.435465	0.217732	+	0.976009i	$0.430134\pi$
$80$	9.44706	0.0132027
$81$	−392.600	−0.538546
$82$	38.3572	0.0516566
$83$	714.201	0.944503	0.472252	−	0.881464i	$-0.343441\pi$
$83$	714.201	0.944503	0.472252	+	0.881464i	$0.343441\pi$
$84$	−508.282	−0.660216
$85$	423.956	0.540994
$86$	0	0
$87$	624.922	0.770100
$88$	260.203	0.315202
$89$	1024.60	1.22031	0.610154	−	0.792283i	$-0.291108\pi$
$89$	1024.60	1.22031	0.610154	+	0.792283i	$0.291108\pi$
$90$	−91.3578	−0.106999
$91$	379.080	0.436685
$92$	−153.425	−0.173866
$93$	−856.254	−0.954725
$94$	−1074.47	−1.17897
$95$	482.463	0.521049
$96$	755.530	0.803239
$97$	−1413.22	−1.47929	−0.739645	−	0.672997i	$-0.765007\pi$
$97$	−1413.22	−1.47929	−0.739645	+	0.672997i	$0.765007\pi$
$98$	−491.668	−0.506795
$99$	−105.795	−0.107402
$100$	456.768	0.456768
$101$	359.416	0.354092	0.177046	−	0.984203i	$-0.443346\pi$
$101$	359.416	0.354092	0.177046	+	0.984203i	$0.443346\pi$
$102$	−571.016	−0.554304
$103$	1903.13	1.82059	0.910297	−	0.413955i	$-0.135853\pi$
$103$	1903.13	1.82059	0.910297	+	0.413955i	$0.135853\pi$
$104$	−347.261	−0.327421
$105$	−581.729	−0.540675
$106$	−409.925	−0.375617
$107$	1087.03	0.982126	0.491063	−	0.871124i	$-0.336609\pi$
$107$	1087.03	0.982126	0.491063	+	0.871124i	$0.336609\pi$
$108$	−740.485	−0.659752
$109$	1536.48	1.35017	0.675084	−	0.737741i	$-0.264107\pi$
$109$	1536.48	1.35017	0.675084	+	0.737741i	$0.264107\pi$
$110$	112.380	0.0974091
$111$	966.925	0.826815
$112$	42.3885	0.0357619
$113$	−1732.78	−1.44254	−0.721268	−	0.692656i	$-0.756440\pi$
$113$	−1732.78	−1.44254	−0.721268	+	0.692656i	$0.756440\pi$
$114$	−649.817	−0.533868
$115$	−175.595	−0.142386
$116$	719.672	0.576034
$117$	141.192	0.111566
$118$	354.070	0.276227
$119$	1902.27	1.46538
$120$	532.900	0.405391
$121$	−1200.86	−0.902224
$122$	−55.6196	−0.0412751
$123$	90.9707	0.0666874
$124$	−986.078	−0.714133
$125$	1216.42	0.870401
$126$	−409.917	−0.289828
$127$	−2169.63	−1.51593	−0.757967	−	0.652293i	$-0.773807\pi$
$127$	−2169.63	−1.51593	−0.757967	+	0.652293i	$0.773807\pi$
$128$	845.905	0.584126
$129$	0	0
$130$	−149.980	−0.101185
$131$	−555.547	−0.370522	−0.185261	−	0.982689i	$-0.559313\pi$
$131$	−555.547	−0.370522	−0.185261	+	0.982689i	$0.559313\pi$
$132$	232.877	0.153556
$133$	2164.78	1.41136
$134$	−1065.86	−0.687135
$135$	−847.486	−0.540296
$136$	−1742.60	−1.09872
$137$	−892.173	−0.556376	−0.278188	−	0.960527i	$-0.589734\pi$
$137$	−892.173	−0.556376	−0.278188	+	0.960527i	$0.589734\pi$
$138$	236.505	0.145889
$139$	−1890.50	−1.15360	−0.576799	−	0.816886i	$-0.695698\pi$
$139$	−1890.50	−1.15360	−0.576799	+	0.816886i	$0.695698\pi$
$140$	−669.930	−0.404424
$141$	−2548.29	−1.52202
$142$	−1337.11	−0.790197
$143$	−173.681	−0.101566
$144$	15.7880	0.00913657
$145$	823.665	0.471736
$146$	786.890	0.446051
$147$	−1166.07	−0.654260
$148$	1113.53	0.618457
$149$	2631.07	1.44661	0.723307	−	0.690527i	$-0.242621\pi$
$149$	2631.07	1.44661	0.723307	+	0.690527i	$0.242621\pi$
$150$	−704.107	−0.383267
$151$	−100.623	−0.0542291	−0.0271145	−	0.999632i	$-0.508632\pi$
$151$	−100.623	−0.0542291	−0.0271145	+	0.999632i	$0.508632\pi$
$152$	−1983.08	−1.05822
$153$	708.518	0.374381
$154$	504.243	0.263851
$155$	−1128.57	−0.584830
$156$	−310.793	−0.159509
$157$	360.939	0.183478	0.0917391	−	0.995783i	$-0.470757\pi$
$157$	360.939	0.183478	0.0917391	+	0.995783i	$0.470757\pi$
$158$	−542.808	−0.273313
$159$	−972.206	−0.484912
$160$	995.809	0.492035
$161$	−787.887	−0.385678
$162$	696.952	0.338011
$163$	−3922.65	−1.88494	−0.942471	−	0.334289i	$-0.891504\pi$
$163$	−3922.65	−1.88494	−0.942471	+	0.334289i	$0.891504\pi$
$164$	104.764	0.0498821
$165$	266.528	0.125753
$166$	−1267.86	−0.592803
$167$	1858.89	0.861348	0.430674	−	0.902508i	$-0.358276\pi$
$167$	1858.89	0.861348	0.430674	+	0.902508i	$0.358276\pi$
$168$	2391.10	1.09808
$169$	−1965.21	−0.894497
$170$	−752.615	−0.339547
$171$	806.295	0.360578
$172$	0	0
$173$	3426.98	1.50606	0.753030	−	0.657986i	$-0.228591\pi$
$173$	3426.98	1.50606	0.753030	+	0.657986i	$0.228591\pi$
$174$	−1109.37	−0.483342
$175$	2345.64	1.01322
$176$	−19.4209	−0.00831766
$177$	839.738	0.356602
$178$	−1818.89	−0.765908
$179$	−1169.35	−0.488275	−0.244138	−	0.969741i	$-0.578505\pi$
$179$	−1169.35	−0.488275	−0.244138	+	0.969741i	$0.578505\pi$
$180$	−249.522	−0.103324
$181$	−192.200	−0.0789286	−0.0394643	−	0.999221i	$-0.512565\pi$
$181$	−192.200	−0.0789286	−0.0394643	+	0.999221i	$0.512565\pi$
$182$	−672.950	−0.274079
$183$	−131.911	−0.0532851
$184$	721.755	0.289176
$185$	1274.43	0.506477
$186$	1520.04	0.599219
$187$	−871.554	−0.340825
$188$	−2934.66	−1.13847
$189$	−3802.62	−1.46349
$190$	−856.478	−0.327028
$191$	−655.104	−0.248176	−0.124088	−	0.992271i	$-0.539601\pi$
$191$	−655.104	−0.248176	−0.124088	+	0.992271i	$0.539601\pi$
$192$	−1398.57	−0.525694
$193$	4653.46	1.73556	0.867781	−	0.496946i	$-0.165545\pi$
$193$	4653.46	1.73556	0.867781	+	0.496946i	$0.165545\pi$
$194$	2508.78	0.928455
$195$	−355.702	−0.130628
$196$	−1342.87	−0.489385
$197$	3087.56	1.11665	0.558324	−	0.829623i	$-0.311445\pi$
$197$	3087.56	1.11665	0.558324	+	0.829623i	$0.311445\pi$
$198$	187.810	0.0674095
$199$	2241.55	0.798488	0.399244	−	0.916845i	$-0.369273\pi$
$199$	2241.55	0.798488	0.399244	+	0.916845i	$0.369273\pi$
$200$	−2148.76	−0.759701
$201$	−2527.87	−0.887074
$202$	−638.043	−0.222240
$203$	3695.74	1.27778
$204$	−1559.59	−0.535262
$205$	119.902	0.0408503
$206$	−3378.48	−1.14267
$207$	−293.456	−0.0985344
$208$	25.9187	0.00864009
$209$	−991.830	−0.328260
$210$	1032.70	0.339347
$211$	2162.67	0.705612	0.352806	−	0.935696i	$-0.385227\pi$
$211$	2162.67	0.705612	0.352806	+	0.935696i	$0.385227\pi$
$212$	−1119.61	−0.362713
$213$	−3171.19	−1.02012
$214$	−1929.72	−0.616417
$215$	0	0
$216$	3483.44	1.09731
$217$	−5063.82	−1.58412
$218$	−2727.60	−0.847413
$219$	1866.24	0.575840
$220$	306.939	0.0940628
$221$	1163.15	0.354037
$222$	−1716.51	−0.518938
$223$	3117.97	0.936298	0.468149	−	0.883649i	$-0.344921\pi$
$223$	3117.97	0.936298	0.468149	+	0.883649i	$0.344921\pi$
$224$	4468.14	1.33277
$225$	873.658	0.258862
$226$	3076.07	0.905386
$227$	−2881.26	−0.842448	−0.421224	−	0.906957i	$-0.638399\pi$
$227$	−2881.26	−0.842448	−0.421224	+	0.906957i	$0.638399\pi$
$228$	−1774.82	−0.515528
$229$	−4716.93	−1.36115	−0.680575	−	0.732678i	$-0.738270\pi$
$229$	−4716.93	−1.36115	−0.680575	+	0.732678i	$0.738270\pi$
$230$	311.721	0.0893663
$231$	1195.90	0.340625
$232$	−3385.53	−0.958065
$233$	1638.16	0.460599	0.230300	−	0.973120i	$-0.426029\pi$
$233$	1638.16	0.460599	0.230300	+	0.973120i	$0.426029\pi$
$234$	−250.647	−0.0700226
$235$	−3358.72	−0.932335
$236$	967.058	0.266738
$237$	−1287.36	−0.352840
$238$	−3376.94	−0.919726
$239$	−6381.61	−1.72716	−0.863582	−	0.504209i	$-0.831784\pi$
$239$	−6381.61	−1.72716	−0.863582	+	0.504209i	$0.831784\pi$
$240$	−39.7744	−0.0106976
$241$	−1500.42	−0.401040	−0.200520	−	0.979690i	$-0.564263\pi$
$241$	−1500.42	−0.401040	−0.200520	+	0.979690i	$0.564263\pi$
$242$	2131.79	0.566268
$243$	−2470.55	−0.652204
$244$	−151.912	−0.0398571
$245$	−1536.92	−0.400776
$246$	−161.493	−0.0418554
$247$	1323.67	0.340985
$248$	4638.78	1.18775
$249$	−3006.96	−0.765294
$250$	−2159.42	−0.546294
$251$	6318.82	1.58900	0.794502	−	0.607261i	$-0.207732\pi$
$251$	6318.82	1.58900	0.794502	+	0.607261i	$0.207732\pi$
$252$	−1119.59	−0.279872
$253$	360.983	0.0897028
$254$	3851.57	0.951454
$255$	−1784.96	−0.438346
$256$	−4159.14	−1.01541
$257$	−6590.31	−1.59958	−0.799791	−	0.600279i	$-0.795056\pi$
$257$	−6590.31	−1.59958	−0.799791	+	0.600279i	$0.795056\pi$
$258$	0	0
$259$	5718.32	1.37189
$260$	−409.633	−0.0977092
$261$	1376.51	0.326453
$262$	986.219	0.232553
$263$	143.103	0.0335518	0.0167759	−	0.999859i	$-0.494660\pi$
$263$	143.103	0.0335518	0.0167759	+	0.999859i	$0.494660\pi$
$264$	−1095.52	−0.255396
$265$	−1281.40	−0.297040
$266$	−3842.97	−0.885818
$267$	−4313.81	−0.988768
$268$	−2911.14	−0.663530
$269$	6614.71	1.49928	0.749640	−	0.661846i	$-0.230227\pi$
$269$	6614.71	1.49928	0.749640	+	0.661846i	$0.230227\pi$
$270$	1504.47	0.339109
$271$	−2037.90	−0.456803	−0.228401	−	0.973567i	$-0.573350\pi$
$271$	−2037.90	−0.456803	−0.228401	+	0.973567i	$0.573350\pi$
$272$	130.063	0.0289935
$273$	−1596.02	−0.353829
$274$	1583.80	0.349201
$275$	−1074.69	−0.235660
$276$	645.958	0.140877
$277$	−5018.81	−1.08863	−0.544316	−	0.838880i	$-0.683211\pi$
$277$	−5018.81	−1.08863	−0.544316	+	0.838880i	$0.683211\pi$
$278$	3356.05	0.724038
$279$	−1886.07	−0.404717
$280$	3151.53	0.672643
$281$	5987.11	1.27104	0.635518	−	0.772086i	$-0.280787\pi$
$281$	5987.11	1.27104	0.635518	+	0.772086i	$0.280787\pi$
$282$	4523.78	0.955274
$283$	−1342.24	−0.281936	−0.140968	−	0.990014i	$-0.545021\pi$
$283$	−1342.24	−0.281936	−0.140968	+	0.990014i	$0.545021\pi$
$284$	−3652.00	−0.763051
$285$	−2031.28	−0.422185
$286$	308.323	0.0637465
$287$	537.993	0.110651
$288$	1664.20	0.340500
$289$	923.848	0.188042
$290$	−1462.19	−0.296078
$291$	5950.01	1.19861
$292$	2149.20	0.430728
$293$	−5079.54	−1.01280	−0.506399	−	0.862299i	$-0.669024\pi$
$293$	−5079.54	−1.01280	−0.506399	+	0.862299i	$0.669024\pi$
$294$	2070.04	0.410636
$295$	1106.80	0.218442
$296$	−5238.34	−1.02862
$297$	1742.23	0.340386
$298$	−4670.72	−0.907945
$299$	−481.759	−0.0931801
$300$	−1923.10	−0.370101
$301$	0	0
$302$	178.628	0.0340361
$303$	−1513.23	−0.286907
$304$	148.012	0.0279246
$305$	−173.863	−0.0326405
$306$	−1257.78	−0.234975
$307$	−8346.68	−1.55169	−0.775847	−	0.630921i	$-0.782677\pi$
$307$	−8346.68	−1.55169	−0.775847	+	0.630921i	$0.782677\pi$
$308$	1377.22	0.254787
$309$	−8012.65	−1.47516
$310$	2003.45	0.367060
$311$	−1200.09	−0.218813	−0.109407	−	0.993997i	$-0.534895\pi$
$311$	−1200.09	−0.218813	−0.109407	+	0.993997i	$0.534895\pi$
$312$	1462.05	0.265296
$313$	−1326.15	−0.239484	−0.119742	−	0.992805i	$-0.538207\pi$
$313$	−1326.15	−0.239484	−0.119742	+	0.992805i	$0.538207\pi$
$314$	−640.746	−0.115157
$315$	−1281.37	−0.229197
$316$	−1482.55	−0.263924
$317$	−6175.51	−1.09417	−0.547084	−	0.837078i	$-0.684262\pi$
$317$	−6175.51	−1.09417	−0.547084	+	0.837078i	$0.684262\pi$
$318$	1725.88	0.304348
$319$	−1693.26	−0.297193
$320$	−1843.36	−0.322021
$321$	−4576.67	−0.795778
$322$	1398.67	0.242065
$323$	6642.34	1.14424
$324$	1903.56	0.326399
$325$	1434.26	0.244795
$326$	6963.56	1.18306
$327$	−6468.96	−1.09399
$328$	−492.836	−0.0829644
$329$	−15070.4	−2.52540
$330$	−473.146	−0.0789268
$331$	−10083.0	−1.67436	−0.837178	−	0.546931i	$-0.815796\pi$
$331$	−10083.0	−1.67436	−0.837178	+	0.546931i	$0.815796\pi$
$332$	−3462.87	−0.572439
$333$	2129.84	0.350495
$334$	−3299.94	−0.540612
$335$	−3331.80	−0.543390
$336$	−178.466	−0.0289765
$337$	3339.63	0.539825	0.269913	−	0.962885i	$-0.413005\pi$
$337$	3339.63	0.539825	0.269913	+	0.962885i	$0.413005\pi$
$338$	3488.68	0.561418
$339$	7295.43	1.16883
$340$	−2055.59	−0.327882
$341$	2320.07	0.368442
$342$	−1431.35	−0.226312
$343$	1644.29	0.258844
$344$	0	0
$345$	739.299	0.115370
$346$	−6083.64	−0.945256
$347$	7019.93	1.08602	0.543011	−	0.839726i	$-0.317284\pi$
$347$	7019.93	1.08602	0.543011	+	0.839726i	$0.317284\pi$
$348$	−3029.99	−0.466738
$349$	−9937.81	−1.52424	−0.762119	−	0.647437i	$-0.775841\pi$
$349$	−9937.81	−1.52424	−0.762119	+	0.647437i	$0.775841\pi$
$350$	−4164.03	−0.635934
$351$	−2325.14	−0.353581
$352$	−2047.15	−0.309981
$353$	6375.65	0.961308	0.480654	−	0.876910i	$-0.340399\pi$
$353$	6375.65	0.961308	0.480654	+	0.876910i	$0.340399\pi$
$354$	−1490.72	−0.223816
$355$	−4179.72	−0.624891
$356$	−4967.87	−0.739597
$357$	−8009.00	−1.18734
$358$	2075.85	0.306459
$359$	−2809.35	−0.413013	−0.206506	−	0.978445i	$-0.566209\pi$
$359$	−2809.35	−0.413013	−0.206506	+	0.978445i	$0.566209\pi$
$360$	1173.82	0.171849
$361$	700.002	0.102056
$362$	341.197	0.0495384
$363$	5055.91	0.731037
$364$	−1838.00	−0.264664
$365$	2459.76	0.352739
$366$	234.172	0.0334436
$367$	5061.20	0.719871	0.359936	−	0.932977i	$-0.382799\pi$
$367$	5061.20	0.719871	0.359936	+	0.932977i	$0.382799\pi$
$368$	−53.8700	−0.00763089
$369$	200.381	0.0282694
$370$	−2262.40	−0.317883
$371$	−5749.55	−0.804587
$372$	4151.63	0.578634
$373$	6461.72	0.896984	0.448492	−	0.893787i	$-0.351961\pi$
$373$	6461.72	0.896984	0.448492	+	0.893787i	$0.351961\pi$
$374$	1547.20	0.213914
$375$	−5121.43	−0.705252
$376$	13805.4	1.89351
$377$	2259.79	0.308713
$378$	6750.49	0.918539
$379$	−10001.9	−1.35557	−0.677786	−	0.735259i	$-0.737060\pi$
$379$	−10001.9	−1.35557	−0.677786	+	0.735259i	$0.737060\pi$
$380$	−2339.26	−0.315794
$381$	9134.67	1.22830
$382$	1162.95	0.155764
$383$	6544.30	0.873103	0.436551	−	0.899679i	$-0.356200\pi$
$383$	6544.30	0.873103	0.436551	+	0.899679i	$0.356200\pi$
$384$	−3561.46	−0.473295
$385$	1576.23	0.208654
$386$	−8260.92	−1.08930
$387$	0	0
$388$	6852.15	0.896560
$389$	13565.1	1.76806	0.884031	−	0.467429i	$-0.154820\pi$
$389$	13565.1	1.76806	0.884031	+	0.467429i	$0.154820\pi$
$390$	631.450	0.0819864
$391$	−2417.53	−0.312684
$392$	6317.24	0.813951
$393$	2338.99	0.300220
$394$	−5481.10	−0.700848
$395$	−1696.78	−0.216137
$396$	512.959	0.0650938
$397$	4894.48	0.618757	0.309379	−	0.950939i	$-0.399879\pi$
$397$	4894.48	0.618757	0.309379	+	0.950939i	$0.399879\pi$
$398$	−3979.24	−0.501159
$399$	−9114.26	−1.14357
$400$	160.378	0.0200473
$401$	−5540.84	−0.690016	−0.345008	−	0.938600i	$-0.612124\pi$
$401$	−5540.84	−0.690016	−0.345008	+	0.938600i	$0.612124\pi$
$402$	4487.52	0.556759
$403$	−3096.31	−0.382725
$404$	−1742.66	−0.214606
$405$	2178.62	0.267300
$406$	−6560.76	−0.801982
$407$	−2619.94	−0.319080
$408$	7336.75	0.890253
$409$	8166.09	0.987254	0.493627	−	0.869674i	$-0.335671\pi$
$409$	8166.09	0.987254	0.493627	+	0.869674i	$0.335671\pi$
$410$	−212.852	−0.0256391
$411$	3756.26	0.450810
$412$	−9227.52	−1.10342
$413$	4966.15	0.591690
$414$	520.950	0.0618437
$415$	−3963.25	−0.468792
$416$	2732.08	0.321998
$417$	7959.45	0.934715
$418$	1760.72	0.206027
$419$	−800.484	−0.0933323	−0.0466661	−	0.998911i	$-0.514860\pi$
$419$	−800.484	−0.0933323	−0.0466661	+	0.998911i	$0.514860\pi$
$420$	2820.57	0.327689
$421$	−4233.24	−0.490060	−0.245030	−	0.969515i	$-0.578798\pi$
$421$	−4233.24	−0.490060	−0.245030	+	0.969515i	$0.578798\pi$
$422$	−3839.21	−0.442867
$423$	−5613.12	−0.645199
$424$	5266.95	0.603269
$425$	7197.29	0.821458
$426$	5629.56	0.640266
$427$	−780.113	−0.0884129
$428$	−5270.58	−0.595241
$429$	731.240	0.0822951
$430$	0	0
$431$	−16282.8	−1.81975	−0.909877	−	0.414879i	$-0.863824\pi$
$431$	−16282.8	−1.81975	−0.909877	+	0.414879i	$0.863824\pi$
$432$	−259.996	−0.0289561
$433$	5381.42	0.597262	0.298631	−	0.954369i	$-0.403470\pi$
$433$	5381.42	0.597262	0.298631	+	0.954369i	$0.403470\pi$
$434$	8989.40	0.994251
$435$	−3467.83	−0.382229
$436$	−7449.78	−0.818302
$437$	−2751.15	−0.301156
$438$	−3312.99	−0.361418
$439$	−9823.99	−1.06805	−0.534024	−	0.845469i	$-0.679321\pi$
$439$	−9823.99	−1.06805	−0.534024	+	0.845469i	$0.679321\pi$
$440$	−1443.92	−0.156446
$441$	−2568.51	−0.277347
$442$	−2064.86	−0.222206
$443$	−4521.95	−0.484976	−0.242488	−	0.970154i	$-0.577963\pi$
$443$	−4521.95	−0.484976	−0.242488	+	0.970154i	$0.577963\pi$
$444$	−4688.23	−0.501111
$445$	−5685.73	−0.605684
$446$	−5535.08	−0.587654
$447$	−11077.4	−1.17213
$448$	−8271.05	−0.872255
$449$	9698.43	1.01937	0.509685	−	0.860361i	$-0.329762\pi$
$449$	9698.43	1.01937	0.509685	+	0.860361i	$0.329762\pi$
$450$	−1550.93	−0.162471
$451$	−246.490	−0.0257356
$452$	8401.56	0.874283
$453$	423.647	0.0439397
$454$	5114.86	0.528750
$455$	−2103.59	−0.216743
$456$	8349.24	0.857432
$457$	−1549.54	−0.158609	−0.0793047	−	0.996850i	$-0.525270\pi$
$457$	−1549.54	−0.158609	−0.0793047	+	0.996850i	$0.525270\pi$
$458$	8373.59	0.854306
$459$	−11667.8	−1.18651
$460$	851.391	0.0862963
$461$	11280.5	1.13966	0.569831	−	0.821762i	$-0.307009\pi$
$461$	11280.5	1.13966	0.569831	+	0.821762i	$0.307009\pi$
$462$	−2122.98	−0.213788
$463$	7144.05	0.717089	0.358545	−	0.933513i	$-0.383273\pi$
$463$	7144.05	0.717089	0.358545	+	0.933513i	$0.383273\pi$
$464$	252.688	0.0252818
$465$	4751.54	0.473865
$466$	−2908.10	−0.289088
$467$	−12175.9	−1.20649	−0.603246	−	0.797555i	$-0.706126\pi$
$467$	−12175.9	−1.20649	−0.603246	+	0.797555i	$0.706126\pi$
$468$	−684.582	−0.0676171
$469$	−14949.6	−1.47187
$470$	5962.47	0.585166
$471$	−1519.64	−0.148665
$472$	−4549.30	−0.443641
$473$	0	0
$474$	2285.35	0.221455
$475$	8190.53	0.791173
$476$	−9223.32	−0.888131
$477$	−2141.48	−0.205559
$478$	11328.8	1.08403
$479$	−5198.23	−0.495852	−0.247926	−	0.968779i	$-0.579749\pi$
$479$	−5198.23	−0.495852	−0.247926	+	0.968779i	$0.579749\pi$
$480$	−4192.60	−0.398677
$481$	3496.51	0.331449
$482$	2663.58	0.251707
$483$	3317.19	0.312500
$484$	5822.48	0.546815
$485$	7842.28	0.734226
$486$	4385.76	0.409346
$487$	12928.0	1.20292	0.601462	−	0.798901i	$-0.294585\pi$
$487$	12928.0	1.20292	0.601462	+	0.798901i	$0.294585\pi$
$488$	714.633	0.0662908
$489$	16515.3	1.52729
$490$	2728.37	0.251541
$491$	3655.61	0.335999	0.167999	−	0.985787i	$-0.446269\pi$
$491$	3655.61	0.335999	0.167999	+	0.985787i	$0.446269\pi$
$492$	−441.080	−0.0404175
$493$	11339.9	1.03595
$494$	−2349.81	−0.214014
$495$	587.081	0.0533077
$496$	−346.227	−0.0313429
$497$	−18754.2	−1.69264
$498$	5338.01	0.480325
$499$	8225.98	0.737967	0.368983	−	0.929436i	$-0.379706\pi$
$499$	8225.98	0.737967	0.368983	+	0.929436i	$0.379706\pi$
$500$	−5897.94	−0.527527
$501$	−7826.37	−0.697917
$502$	−11217.3	−0.997315
$503$	−4117.12	−0.364957	−0.182478	−	0.983210i	$-0.558412\pi$
$503$	−4117.12	−0.364957	−0.182478	+	0.983210i	$0.558412\pi$
$504$	5266.86	0.465485
$505$	−1994.48	−0.175749
$506$	−640.824	−0.0563006
$507$	8274.00	0.724776
$508$	10519.7	0.918768
$509$	−3069.68	−0.267311	−0.133655	−	0.991028i	$-0.542672\pi$
$509$	−3069.68	−0.267311	−0.133655	+	0.991028i	$0.542672\pi$
$510$	3168.69	0.275121
$511$	11036.8	0.955460
$512$	616.143	0.0531835
$513$	−13278.0	−1.14277
$514$	11699.3	1.00395
$515$	−10560.9	−0.903628
$516$	0	0
$517$	6904.74	0.587370
$518$	−10151.3	−0.861046
$519$	−14428.4	−1.22030
$520$	1927.03	0.162511
$521$	−13269.8	−1.11586	−0.557928	−	0.829889i	$-0.688403\pi$
$521$	−13269.8	−1.11586	−0.557928	+	0.829889i	$0.688403\pi$
$522$	−2443.62	−0.204893
$523$	6010.79	0.502550	0.251275	−	0.967916i	$-0.419150\pi$
$523$	6010.79	0.502550	0.251275	+	0.967916i	$0.419150\pi$
$524$	2693.62	0.224564
$525$	−9875.72	−0.820975
$526$	−254.040	−0.0210583
$527$	−15537.6	−1.28431
$528$	81.7668	0.00673948
$529$	−11165.7	−0.917704
$530$	2274.76	0.186432
$531$	1849.69	0.151167
$532$	−10496.2	−0.855387
$533$	328.960	0.0267333
$534$	7657.97	0.620585
$535$	−6032.18	−0.487465
$536$	13694.8	1.10359
$537$	4923.24	0.395630
$538$	−11742.6	−0.941000
$539$	3159.54	0.252488
$540$	4109.11	0.327459
$541$	−6799.14	−0.540329	−0.270164	−	0.962814i	$-0.587078\pi$
$541$	−6799.14	−0.540329	−0.270164	+	0.962814i	$0.587078\pi$
$542$	3617.72	0.286705
$543$	809.206	0.0639528
$544$	13709.9	1.08053
$545$	−8526.27	−0.670138
$546$	2833.28	0.222076
$547$	1969.09	0.153916	0.0769580	−	0.997034i	$-0.475479\pi$
$547$	1969.09	0.153916	0.0769580	+	0.997034i	$0.475479\pi$
$548$	4325.78	0.337205
$549$	−290.561	−0.0225880
$550$	1907.82	0.147908
$551$	12904.8	0.997755
$552$	−3038.76	−0.234308
$553$	−7613.35	−0.585448
$554$	8909.50	0.683264
$555$	−5365.67	−0.410379
$556$	9166.26	0.699165
$557$	16068.7	1.22236	0.611180	−	0.791492i	$-0.290695\pi$
$557$	16068.7	1.22236	0.611180	+	0.791492i	$0.290695\pi$
$558$	3348.19	0.254014
$559$	0	0
$560$	−235.223	−0.0177499
$561$	3669.45	0.276157
$562$	−10628.4	−0.797747
$563$	4498.28	0.336732	0.168366	−	0.985725i	$-0.446151\pi$
$563$	4498.28	0.336732	0.168366	+	0.985725i	$0.446151\pi$
$564$	12355.6	0.922457
$565$	9615.58	0.715983
$566$	2382.77	0.176953
$567$	9775.36	0.724033
$568$	17180.0	1.26911
$569$	−3589.95	−0.264497	−0.132248	−	0.991217i	$-0.542220\pi$
$569$	−3589.95	−0.264497	−0.132248	+	0.991217i	$0.542220\pi$
$570$	3605.98	0.264978
$571$	1838.63	0.134753	0.0673766	−	0.997728i	$-0.478537\pi$
$571$	1838.63	0.134753	0.0673766	+	0.997728i	$0.478537\pi$
$572$	842.110	0.0615566
$573$	2758.15	0.201088
$574$	−955.057	−0.0694483
$575$	−2981.00	−0.216202
$576$	−3080.63	−0.222847
$577$	10404.4	0.750679	0.375339	−	0.926887i	$-0.377526\pi$
$577$	10404.4	0.750679	0.375339	+	0.926887i	$0.377526\pi$
$578$	−1640.03	−0.118021
$579$	−19592.2	−1.40626
$580$	−3993.62	−0.285907
$581$	−17782.9	−1.26981
$582$	−10562.6	−0.752291
$583$	2634.25	0.187134
$584$	−10110.4	−0.716391
$585$	−783.504	−0.0553742
$586$	9017.30	0.635667
$587$	2692.40	0.189314	0.0946570	−	0.995510i	$-0.469825\pi$
$587$	2692.40	0.189314	0.0946570	+	0.995510i	$0.469825\pi$
$588$	5653.82	0.396530
$589$	−17681.9	−1.23696
$590$	−1964.81	−0.137102
$591$	−12999.4	−0.904776
$592$	390.977	0.0271437
$593$	−23499.4	−1.62732	−0.813662	−	0.581338i	$-0.802529\pi$
$593$	−23499.4	−1.62732	−0.813662	+	0.581338i	$0.802529\pi$
$594$	−3092.84	−0.213638
$595$	−10556.1	−0.727323
$596$	−12757.0	−0.876755
$597$	−9437.45	−0.646984
$598$	855.229	0.0584831
$599$	6713.51	0.457941	0.228970	−	0.973433i	$-0.426464\pi$
$599$	6713.51	0.457941	0.228970	+	0.973433i	$0.426464\pi$
$600$	9046.78	0.615556
$601$	27329.6	1.85490	0.927452	−	0.373943i	$-0.121995\pi$
$601$	27329.6	1.85490	0.927452	+	0.373943i	$0.121995\pi$
$602$	0	0
$603$	−5568.12	−0.376039
$604$	487.881	0.0328668
$605$	6663.83	0.447807
$606$	2686.31	0.180073
$607$	4099.54	0.274127	0.137064	−	0.990562i	$-0.456234\pi$
$607$	4099.54	0.274127	0.137064	+	0.990562i	$0.456234\pi$
$608$	15601.9	1.04069
$609$	−15560.0	−1.03534
$610$	308.645	0.0204863
$611$	−9214.90	−0.610139
$612$	−3435.31	−0.226903
$613$	8654.09	0.570205	0.285102	−	0.958497i	$-0.407972\pi$
$613$	8654.09	0.570205	0.285102	+	0.958497i	$0.407972\pi$
$614$	14817.2	0.973898
$615$	−504.816	−0.0330994
$616$	−6478.81	−0.423764
$617$	9705.03	0.633241	0.316621	−	0.948552i	$-0.397452\pi$
$617$	9705.03	0.633241	0.316621	+	0.948552i	$0.397452\pi$
$618$	14224.2	0.925860
$619$	1056.50	0.0686018	0.0343009	−	0.999412i	$-0.489080\pi$
$619$	1056.50	0.0686018	0.0343009	+	0.999412i	$0.489080\pi$
$620$	5471.96	0.354450
$621$	4832.62	0.312281
$622$	2130.43	0.137335
$623$	−25511.5	−1.64061
$624$	−109.124	−0.00700073
$625$	5025.59	0.321638
$626$	2354.21	0.150309
$627$	4175.84	0.265976
$628$	−1750.05	−0.111201
$629$	17545.9	1.11224
$630$	2274.72	0.143852
$631$	4521.20	0.285240	0.142620	−	0.989778i	$-0.454447\pi$
$631$	4521.20	0.285240	0.142620	+	0.989778i	$0.454447\pi$
$632$	6974.31	0.438961
$633$	−9105.35	−0.571730
$634$	10962.9	0.686738
$635$	12039.7	0.752414
$636$	4713.83	0.293892
$637$	−4216.65	−0.262276
$638$	3005.91	0.186529
$639$	−6985.17	−0.432440
$640$	−4694.11	−0.289923
$641$	−10199.8	−0.628500	−0.314250	−	0.949340i	$-0.601753\pi$
$641$	−10199.8	−0.628500	−0.314250	+	0.949340i	$0.601753\pi$
$642$	8124.60	0.499458
$643$	−17822.0	−1.09305	−0.546523	−	0.837444i	$-0.684049\pi$
$643$	−17822.0	−1.09305	−0.546523	+	0.837444i	$0.684049\pi$
$644$	3820.14	0.233750
$645$	0	0
$646$	−11791.6	−0.718166
$647$	19078.3	1.15926	0.579632	−	0.814878i	$-0.303196\pi$
$647$	19078.3	1.15926	0.579632	+	0.814878i	$0.303196\pi$
$648$	−8954.85	−0.542870
$649$	−2275.32	−0.137618
$650$	−2546.13	−0.153642
$651$	21319.9	1.28355
$652$	19019.3	1.14241
$653$	−2612.47	−0.156560	−0.0782800	−	0.996931i	$-0.524943\pi$
$653$	−2612.47	−0.156560	−0.0782800	+	0.996931i	$0.524943\pi$
$654$	11483.8	0.686626
$655$	3082.85	0.183904
$656$	36.7841	0.00218929
$657$	4110.77	0.244104
$658$	26753.3	1.58503
$659$	3517.93	0.207950	0.103975	−	0.994580i	$-0.466844\pi$
$659$	3517.93	0.207950	0.103975	+	0.994580i	$0.466844\pi$
$660$	−1292.29	−0.0762154
$661$	14980.0	0.881474	0.440737	−	0.897636i	$-0.354717\pi$
$661$	14980.0	0.881474	0.440737	+	0.897636i	$0.354717\pi$
$662$	17899.5	1.05088
$663$	−4897.16	−0.286863
$664$	16290.3	0.952086
$665$	−12012.9	−0.700509
$666$	−3780.94	−0.219983
$667$	−4696.79	−0.272654
$668$	−9012.99	−0.522041
$669$	−13127.4	−0.758646
$670$	5914.68	0.341051
$671$	357.421	0.0205635
$672$	−18812.0	−1.07989
$673$	10808.5	0.619072	0.309536	−	0.950888i	$-0.399826\pi$
$673$	10808.5	0.619072	0.309536	+	0.950888i	$0.399826\pi$
$674$	−5928.58	−0.338813
$675$	−14387.3	−0.820398
$676$	9528.50	0.542131
$677$	−4460.60	−0.253227	−0.126614	−	0.991952i	$-0.540411\pi$
$677$	−4460.60	−0.253227	−0.126614	+	0.991952i	$0.540411\pi$
$678$	−12951.0	−0.733599
$679$	35187.9	1.98879
$680$	9670.05	0.545337
$681$	12130.8	0.682603
$682$	−4118.63	−0.231247
$683$	−23307.5	−1.30577	−0.652883	−	0.757459i	$-0.726441\pi$
$683$	−23307.5	−1.30577	−0.652883	+	0.757459i	$0.726441\pi$
$684$	−3909.40	−0.218537
$685$	4950.86	0.276150
$686$	−2918.98	−0.162460
$687$	19859.4	1.10289
$688$	0	0
$689$	−3515.60	−0.194389
$690$	−1312.42	−0.0724100
$691$	30302.2	1.66823	0.834116	−	0.551589i	$-0.185978\pi$
$691$	30302.2	1.66823	0.834116	+	0.551589i	$0.185978\pi$
$692$	−16616.0	−0.912784
$693$	2634.20	0.144394
$694$	−12461.9	−0.681626
$695$	10490.8	0.572573
$696$	14253.9	0.776283
$697$	1650.76	0.0897087
$698$	17641.8	0.956665
$699$	−6897.06	−0.373205
$700$	−11373.1	−0.614088
$701$	15302.3	0.824481	0.412241	−	0.911075i	$-0.364746\pi$
$701$	15302.3	0.824481	0.412241	+	0.911075i	$0.364746\pi$
$702$	4127.64	0.221920
$703$	19967.3	1.07124
$704$	3789.51	0.202873
$705$	14141.0	0.755435
$706$	−11318.2	−0.603351
$707$	−8949.11	−0.476048
$708$	−4071.55	−0.216127
$709$	−16048.6	−0.850096	−0.425048	−	0.905171i	$-0.639743\pi$
$709$	−16048.6	−0.850096	−0.425048	+	0.905171i	$0.639743\pi$
$710$	7419.92	0.392204
$711$	−2835.67	−0.149572
$712$	23370.2	1.23011
$713$	6435.43	0.338021
$714$	14217.7	0.745218
$715$	963.795	0.0504110
$716$	5669.70	0.295931
$717$	26868.1	1.39945
$718$	4987.21	0.259221
$719$	−27578.6	−1.43047	−0.715234	−	0.698885i	$-0.753680\pi$
$719$	−27578.6	−1.43047	−0.715234	+	0.698885i	$0.753680\pi$
$720$	−87.6109	−0.00453482
$721$	−47386.2	−2.44765
$722$	−1242.66	−0.0640539
$723$	6317.13	0.324947
$724$	931.897	0.0478366
$725$	13982.9	0.716295
$726$	−8975.35	−0.458825
$727$	−20268.3	−1.03399	−0.516995	−	0.855988i	$-0.672950\pi$
$727$	−20268.3	−1.03399	−0.516995	+	0.855988i	$0.672950\pi$
$728$	8646.46	0.440191
$729$	21001.8	1.06700
$730$	−4366.62	−0.221392
$731$	0	0
$732$	639.584	0.0322947
$733$	−6588.75	−0.332007	−0.166004	−	0.986125i	$-0.553086\pi$
$733$	−6588.75	−0.332007	−0.166004	+	0.986125i	$0.553086\pi$
$734$	−8984.75	−0.451817
$735$	6470.80	0.324733
$736$	−5678.41	−0.284387
$737$	6849.39	0.342335
$738$	−355.720	−0.0177429
$739$	−4061.88	−0.202190	−0.101095	−	0.994877i	$-0.532235\pi$
$739$	−4061.88	−0.202190	−0.101095	+	0.994877i	$0.532235\pi$
$740$	−6179.21	−0.306963
$741$	−5572.98	−0.276287
$742$	10206.7	0.504987
$743$	−126.183	−0.00623043	−0.00311522	−	0.999995i	$-0.500992\pi$
$743$	−126.183	−0.00623043	−0.00311522	+	0.999995i	$0.500992\pi$
$744$	−19530.4	−0.962390
$745$	−14600.4	−0.718007
$746$	−11471.0	−0.562979
$747$	−6623.42	−0.324415
$748$	4225.81	0.206565
$749$	−27066.1	−1.32039
$750$	9091.67	0.442641
$751$	27018.5	1.31281	0.656403	−	0.754410i	$-0.272077\pi$
$751$	27018.5	1.31281	0.656403	+	0.754410i	$0.272077\pi$
$752$	−1030.40	−0.0499667
$753$	−26603.7	−1.28751
$754$	−4011.62	−0.193759
$755$	558.379	0.0269159
$756$	18437.4	0.886985
$757$	−36649.0	−1.75962	−0.879809	−	0.475327i	$-0.842330\pi$
$757$	−36649.0	−1.75962	−0.879809	+	0.475327i	$0.842330\pi$
$758$	17755.5	0.850805
$759$	−1519.82	−0.0726827
$760$	11004.5	0.525232
$761$	28092.6	1.33818	0.669091	−	0.743180i	$-0.266683\pi$
$761$	28092.6	1.33818	0.669091	+	0.743180i	$0.266683\pi$
$762$	−16216.0	−0.770926
$763$	−38256.9	−1.81520
$764$	3176.33	0.150413
$765$	−3931.72	−0.185819
$766$	−11617.6	−0.547990
$767$	3036.58	0.142953
$768$	17511.0	0.822750
$769$	−3936.22	−0.184582	−0.0922910	−	0.995732i	$-0.529419\pi$
$769$	−3936.22	−0.184582	−0.0922910	+	0.995732i	$0.529419\pi$
$770$	−2798.15	−0.130959
$771$	27746.8	1.29608
$772$	−22562.7	−1.05188
$773$	33033.8	1.53705	0.768527	−	0.639818i	$-0.220990\pi$
$773$	33033.8	1.53705	0.768527	+	0.639818i	$0.220990\pi$
$774$	0	0
$775$	−19159.1	−0.888020
$776$	−32234.4	−1.49117
$777$	−24075.5	−1.11159
$778$	−24081.0	−1.10970
$779$	1878.57	0.0864014
$780$	1724.65	0.0791699
$781$	8592.52	0.393681
$782$	4291.64	0.196252
$783$	−22668.4	−1.03461
$784$	−471.503	−0.0214788
$785$	−2002.93	−0.0910669
$786$	−4152.22	−0.188428
$787$	28871.8	1.30771	0.653855	−	0.756620i	$-0.273151\pi$
$787$	28871.8	1.30771	0.653855	+	0.756620i	$0.273151\pi$
$788$	−14970.3	−0.676771
$789$	−602.499	−0.0271857
$790$	3012.16	0.135655
$791$	43144.6	1.93937
$792$	−2413.10	−0.108265
$793$	−477.006	−0.0213606
$794$	−8688.77	−0.388354
$795$	5394.98	0.240680
$796$	−10868.4	−0.483943
$797$	10827.3	0.481210	0.240605	−	0.970623i	$-0.422654\pi$
$797$	10827.3	0.481210	0.240605	+	0.970623i	$0.422654\pi$
$798$	16179.8	0.717744
$799$	−46241.5	−2.04744
$800$	16905.4	0.747118
$801$	−9502.02	−0.419148
$802$	9836.21	0.433078
$803$	−5056.69	−0.222225
$804$	12256.6	0.537633
$805$	4372.16	0.191426
$806$	5496.63	0.240212
$807$	−27849.5	−1.21481
$808$	8197.96	0.356934
$809$	10356.9	0.450098	0.225049	−	0.974347i	$-0.427746\pi$
$809$	10356.9	0.450098	0.225049	+	0.974347i	$0.427746\pi$
$810$	−3867.54	−0.167767
$811$	8143.45	0.352596	0.176298	−	0.984337i	$-0.443588\pi$
$811$	8143.45	0.352596	0.176298	+	0.984337i	$0.443588\pi$
$812$	−17919.1	−0.774432
$813$	8580.04	0.370129
$814$	4650.97	0.200266
$815$	21767.6	0.935566
$816$	−547.597	−0.0234923
$817$	0	0
$818$	−14496.6	−0.619635
$819$	−3515.54	−0.149991
$820$	−581.355	−0.0247583
$821$	−20617.9	−0.876453	−0.438227	−	0.898864i	$-0.644393\pi$
$821$	−20617.9	−0.876453	−0.438227	+	0.898864i	$0.644393\pi$
$822$	−6668.19	−0.282944
$823$	38726.2	1.64023	0.820116	−	0.572197i	$-0.193909\pi$
$823$	38726.2	1.64023	0.820116	+	0.572197i	$0.193909\pi$
$824$	43408.7	1.83521
$825$	4524.72	0.190946
$826$	−8816.00	−0.371366
$827$	−14397.4	−0.605378	−0.302689	−	0.953089i	$-0.597884\pi$
$827$	−14397.4	−0.605378	−0.302689	+	0.953089i	$0.597884\pi$
$828$	1422.85	0.0597192
$829$	38862.4	1.62816	0.814082	−	0.580750i	$-0.197241\pi$
$829$	38862.4	1.62816	0.814082	+	0.580750i	$0.197241\pi$
$830$	7035.65	0.294230
$831$	21130.4	0.882076
$832$	−5057.39	−0.210737
$833$	−21159.7	−0.880118
$834$	−14129.8	−0.586660
$835$	−10315.4	−0.427519
$836$	4808.98	0.198950
$837$	31059.7	1.28265
$838$	1421.04	0.0585786
$839$	−15182.5	−0.624743	−0.312371	−	0.949960i	$-0.601123\pi$
$839$	−15182.5	−0.624743	−0.312371	+	0.949960i	$0.601123\pi$
$840$	−13268.7	−0.545016
$841$	−2357.79	−0.0966744
$842$	7514.93	0.307579
$843$	−25207.2	−1.02987
$844$	−10485.9	−0.427653
$845$	10905.4	0.443972
$846$	9964.52	0.404949
$847$	29900.3	1.21297
$848$	−393.112	−0.0159193
$849$	5651.14	0.228441
$850$	−12776.8	−0.515576
$851$	−7267.21	−0.292734
$852$	15375.8	0.618271
$853$	−3152.25	−0.126531	−0.0632655	−	0.997997i	$-0.520151\pi$
$853$	−3152.25	−0.126531	−0.0632655	+	0.997997i	$0.520151\pi$
$854$	1384.87	0.0554911
$855$	−4474.30	−0.178968
$856$	24794.2	0.990011
$857$	−26695.4	−1.06406	−0.532028	−	0.846727i	$-0.678570\pi$
$857$	−26695.4	−1.06406	−0.532028	+	0.846727i	$0.678570\pi$
$858$	−1298.11	−0.0516513
$859$	−27735.6	−1.10166	−0.550831	−	0.834617i	$-0.685689\pi$
$859$	−27735.6	−1.10166	−0.550831	+	0.834617i	$0.685689\pi$
$860$	0	0
$861$	−2265.08	−0.0896559
$862$	28905.5	1.14214
$863$	46946.3	1.85176	0.925881	−	0.377816i	$-0.123325\pi$
$863$	46946.3	1.85176	0.925881	+	0.377816i	$0.123325\pi$
$864$	−27406.0	−1.07913
$865$	−19017.0	−0.747513
$866$	−9553.21	−0.374863
$867$	−3889.62	−0.152363
$868$	24552.4	0.960095
$869$	3488.18	0.136166
$870$	6156.16	0.239900
$871$	−9141.04	−0.355605
$872$	35045.8	1.36101
$873$	13106.1	0.508103
$874$	4883.90	0.189016
$875$	−30287.7	−1.17019
$876$	−9048.65	−0.349002
$877$	−18299.6	−0.704597	−0.352299	−	0.935888i	$-0.614600\pi$
$877$	−18299.6	−0.704597	−0.352299	+	0.935888i	$0.614600\pi$
$878$	17439.7	0.670345
$879$	21386.1	0.820630
$880$	107.771	0.00412836
$881$	19412.7	0.742373	0.371187	−	0.928558i	$-0.378951\pi$
$881$	19412.7	0.742373	0.371187	+	0.928558i	$0.378951\pi$
$882$	4559.67	0.174073
$883$	−7074.06	−0.269605	−0.134802	−	0.990873i	$-0.543040\pi$
$883$	−7074.06	−0.269605	−0.134802	+	0.990873i	$0.543040\pi$
$884$	−5639.66	−0.214573
$885$	−4659.89	−0.176995
$886$	8027.45	0.304388
$887$	43180.2	1.63455	0.817277	−	0.576245i	$-0.195483\pi$
$887$	43180.2	1.63455	0.817277	+	0.576245i	$0.195483\pi$
$888$	22054.7	0.833453
$889$	54021.7	2.03805
$890$	10093.4	0.380148
$891$	−4478.74	−0.168399
$892$	−15117.8	−0.567466
$893$	−52622.9	−1.97196
$894$	19664.9	0.735673
$895$	6488.97	0.242349
$896$	−21062.2	−0.785312
$897$	2028.32	0.0755002
$898$	−17216.9	−0.639793
$899$	−30186.7	−1.11989
$900$	−4236.01	−0.156889
$901$	−17641.7	−0.652309
$902$	437.574	0.0161526
$903$	0	0
$904$	−39523.2	−1.45412
$905$	1066.56	0.0391752
$906$	−752.068	−0.0275781
$907$	43010.5	1.57458	0.787288	−	0.616586i	$-0.211485\pi$
$907$	43010.5	1.57458	0.787288	+	0.616586i	$0.211485\pi$
$908$	13970.0	0.510586
$909$	−3333.18	−0.121622
$910$	3734.34	0.136036
$911$	23930.2	0.870299	0.435149	−	0.900358i	$-0.356696\pi$
$911$	23930.2	0.870299	0.435149	+	0.900358i	$0.356696\pi$
$912$	−623.167	−0.0226262
$913$	8147.52	0.295338
$914$	2750.78	0.0995488
$915$	732.004	0.0264473
$916$	22870.5	0.824958
$917$	13832.6	0.498138
$918$	20713.0	0.744695
$919$	20304.1	0.728804	0.364402	−	0.931242i	$-0.381273\pi$
$919$	20304.1	0.728804	0.364402	+	0.931242i	$0.381273\pi$
$920$	−4005.17	−0.143529
$921$	35141.5	1.25728
$922$	−20025.3	−0.715292
$923$	−11467.4	−0.408942
$924$	−5798.42	−0.206444
$925$	21635.4	0.769047
$926$	−12682.3	−0.450070
$927$	−17649.4	−0.625333
$928$	26635.7	0.942197
$929$	37580.6	1.32721	0.663605	−	0.748083i	$-0.269026\pi$
$929$	37580.6	1.32721	0.663605	+	0.748083i	$0.269026\pi$
$930$	−8435.02	−0.297414
$931$	−24079.7	−0.847671
$932$	−7942.78	−0.279157
$933$	5052.67	0.177296
$934$	21614.8	0.757236
$935$	4836.44	0.169164
$936$	3220.46	0.112462
$937$	10609.4	0.369899	0.184950	−	0.982748i	$-0.440788\pi$
$937$	10609.4	0.369899	0.184950	+	0.982748i	$0.440788\pi$
$938$	26538.8	0.923799
$939$	5583.42	0.194045
$940$	16285.1	0.565064
$941$	−10736.6	−0.371949	−0.185974	−	0.982555i	$-0.559544\pi$
$941$	−10736.6	−0.371949	−0.185974	+	0.982555i	$0.559544\pi$
$942$	2697.70	0.0933075
$943$	−683.717	−0.0236107
$944$	339.549	0.0117070
$945$	21101.6	0.726385
$946$	0	0
$947$	39345.9	1.35013	0.675063	−	0.737760i	$-0.264116\pi$
$947$	39345.9	1.35013	0.675063	+	0.737760i	$0.264116\pi$
$948$	6241.89	0.213847
$949$	6748.54	0.230840
$950$	−14540.0	−0.496568
$951$	26000.4	0.886562
$952$	43389.0	1.47715
$953$	23257.1	0.790524	0.395262	−	0.918568i	$-0.370654\pi$
$953$	23257.1	0.790524	0.395262	+	0.918568i	$0.370654\pi$
$954$	3801.59	0.129016
$955$	3635.31	0.123179
$956$	30941.8	1.04679
$957$	7129.04	0.240804
$958$	9228.00	0.311214
$959$	22214.2	0.748003
$960$	7760.98	0.260921
$961$	11570.1	0.388374
$962$	−6207.07	−0.208029
$963$	−10081.0	−0.337338
$964$	7274.93	0.243060
$965$	−25823.1	−0.861423
$966$	−5888.75	−0.196136
$967$	−18234.7	−0.606399	−0.303199	−	0.952927i	$-0.598055\pi$
$967$	−18234.7	−0.606399	−0.303199	+	0.952927i	$0.598055\pi$
$968$	−27390.5	−0.909468
$969$	−27965.9	−0.927134
$970$	−13921.8	−0.460826
$971$	−29695.2	−0.981426	−0.490713	−	0.871321i	$-0.663264\pi$
$971$	−29695.2	−0.981426	−0.490713	+	0.871321i	$0.663264\pi$
$972$	11978.7	0.395284
$973$	47071.6	1.55092
$974$	−22950.1	−0.754998
$975$	−6038.58	−0.198348
$976$	−53.3385	−0.00174931
$977$	−55703.7	−1.82407	−0.912036	−	0.410109i	$-0.865491\pi$
$977$	−55703.7	−1.82407	−0.912036	+	0.410109i	$0.865491\pi$
$978$	−29318.3	−0.958584
$979$	11688.5	0.381580
$980$	7451.89	0.242900
$981$	−14249.2	−0.463752
$982$	−6489.52	−0.210885
$983$	−45350.6	−1.47148	−0.735738	−	0.677267i	$-0.763164\pi$
$983$	−45350.6	−1.47148	−0.735738	+	0.677267i	$0.763164\pi$
$984$	2074.96	0.0672228
$985$	−17133.5	−0.554233
$986$	−20130.8	−0.650197
$987$	63450.0	2.04624
$988$	−6417.95	−0.206662
$989$	0	0
$990$	−1042.20	−0.0334578
$991$	19310.1	0.618977	0.309488	−	0.950903i	$-0.399842\pi$
$991$	19310.1	0.618977	0.309488	+	0.950903i	$0.399842\pi$
$992$	−36495.6	−1.16808
$993$	42451.8	1.35666
$994$	33292.8	1.06236
$995$	−12438.8	−0.396319
$996$	14579.5	0.463825
$997$	4384.16	0.139265	0.0696327	−	0.997573i	$-0.477817\pi$
$997$	4384.16	0.139265	0.0696327	+	0.997573i	$0.477817\pi$
$998$	−14602.9	−0.463174
$999$	−35074.1	−1.11081

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.4.a.g.1.13		30
43.32	odd	14		43.4.e.a.35.5	yes	60
43.39	odd	14		43.4.e.a.16.5	✓	60
43.42	odd	2		1849.4.a.h.1.18		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.4.e.a.16.5	✓	60	43.39	odd	14
43.4.e.a.35.5	yes	60	43.32	odd	14
1849.4.a.g.1.13		30	1.1	even	1	trivial
1849.4.a.h.1.18		30	43.42	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.77522 q^{2} -4.21024 q^{3} -4.84859 q^{4} -5.54921 q^{5} +7.47410 q^{6} -24.8990 q^{7} +22.8091 q^{8} -9.27388 q^{9} +O(q^{10})\)	\(q-1.77522 q^{2} -4.21024 q^{3} -4.84859 q^{4} -5.54921 q^{5} +7.47410 q^{6} -24.8990 q^{7} +22.8091 q^{8} -9.27388 q^{9} +9.85108 q^{10} +11.4079 q^{11} +20.4137 q^{12} -15.2247 q^{13} +44.2013 q^{14} +23.3635 q^{15} -1.70241 q^{16} -76.3993 q^{17} +16.4632 q^{18} -86.9425 q^{19} +26.9059 q^{20} +104.831 q^{21} -20.2515 q^{22} +31.6433 q^{23} -96.0317 q^{24} -94.2062 q^{25} +27.0272 q^{26} +152.722 q^{27} +120.725 q^{28} -148.429 q^{29} -41.4754 q^{30} +203.374 q^{31} -179.451 q^{32} -48.0299 q^{33} +135.626 q^{34} +138.170 q^{35} +44.9653 q^{36} -229.660 q^{37} +154.342 q^{38} +64.0996 q^{39} -126.572 q^{40} -21.6070 q^{41} -186.098 q^{42} -55.3122 q^{44} +51.4628 q^{45} -56.1738 q^{46} +605.261 q^{47} +7.16757 q^{48} +276.962 q^{49} +167.237 q^{50} +321.659 q^{51} +73.8183 q^{52} +230.915 q^{53} -271.115 q^{54} -63.3048 q^{55} -567.924 q^{56} +366.049 q^{57} +263.494 q^{58} -199.451 q^{59} -113.280 q^{60} +31.3311 q^{61} -361.034 q^{62} +230.911 q^{63} +332.184 q^{64} +84.4850 q^{65} +85.2637 q^{66} +600.409 q^{67} +370.429 q^{68} -133.226 q^{69} -245.282 q^{70} +753.209 q^{71} -211.529 q^{72} -443.263 q^{73} +407.698 q^{74} +396.631 q^{75} +421.549 q^{76} -284.045 q^{77} -113.791 q^{78} +305.769 q^{79} +9.44706 q^{80} -392.600 q^{81} +38.3572 q^{82} +714.201 q^{83} -508.282 q^{84} +423.956 q^{85} +624.922 q^{87} +260.203 q^{88} +1024.60 q^{89} -91.3578 q^{90} +379.080 q^{91} -153.425 q^{92} -856.254 q^{93} -1074.47 q^{94} +482.463 q^{95} +755.530 q^{96} -1413.22 q^{97} -491.668 q^{98} -105.795 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 6 q^{2} - 2 q^{3} + 114 q^{4} - 27 q^{5} + 8 q^{6} - 48 q^{7} - 90 q^{8} + 216 q^{9}+O(q^{10}) \) 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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