LMFDB - Embedded newform 1849.4.a.h.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1849.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$109.094531601$
Analytic rank:	$0$
Dimension:	$30$
Twist minimal:	no (minimal twist has level 43)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
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	$-0.398392\pi$
$2$	1.77522	0.627635	0.313818	+	0.949483i	$0.398392\pi$
$3$	4.21024	0.810261	0.405130	−	0.914259i	$-0.367226\pi$
$3$	4.21024	0.810261	0.405130	+	0.914259i	$0.367226\pi$
$4$	−4.84859	−0.606074
$5$	5.54921	0.496337	0.248168	−	0.968717i	$-0.420171\pi$
$5$	5.54921	0.496337	0.248168	+	0.968717i	$0.420171\pi$
$6$	7.47410	0.508548
$7$	24.8990	1.34442	0.672211	−	0.740360i	$-0.265345\pi$
$7$	24.8990	1.34442	0.672211	+	0.740360i	$0.265345\pi$
$8$	−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	$-0.324105\pi$
$19$	86.9425	1.04979	0.524894	+	0.851167i	$0.324105\pi$
$20$	−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	$-0.342369\pi$
$29$	148.429	0.950434	0.475217	+	0.879869i	$0.342369\pi$
$30$	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	$-0.329566\pi$
$37$	229.660	1.02043	0.510215	+	0.860047i	$0.329566\pi$
$38$	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	$-0.510468\pi$
$61$	−31.3311	−0.0657628	−0.0328814	+	0.999459i	$0.510468\pi$
$62$	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	$-0.716742\pi$
$71$	−753.209	−1.25901	−0.629503	+	0.776998i	$0.716742\pi$
$72$	211.529	0.346235
$73$	443.263	0.710685	0.355343	−	0.934736i	$-0.384364\pi$
$73$	443.263	0.710685	0.355343	+	0.934736i	$0.384364\pi$
$74$	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	$-0.708892\pi$
$89$	−1024.60	−1.22031	−0.610154	+	0.792283i	$0.708892\pi$
$90$	−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	$-0.243560\pi$
$113$	1732.78	1.44254	0.721268	+	0.692656i	$0.243560\pi$
$114$	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	$-0.440687\pi$
$131$	555.547	0.370522	0.185261	+	0.982689i	$0.440687\pi$
$132$	−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	$-0.410266\pi$
$137$	892.173	0.556376	0.278188	+	0.960527i	$0.410266\pi$
$138$	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	$-0.757379\pi$
$149$	−2631.07	−1.44661	−0.723307	+	0.690527i	$0.757379\pi$
$150$	−704.107	−0.383267
$151$	100.623	0.0542291	0.0271145	−	0.999632i	$-0.491368\pi$
$151$	100.623	0.0542291	0.0271145	+	0.999632i	$0.491368\pi$
$152$	−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	$-0.529243\pi$
$157$	−360.939	−0.183478	−0.0917391	+	0.995783i	$0.529243\pi$
$158$	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	$-0.108496\pi$
$163$	3922.65	1.88494	0.942471	+	0.334289i	$0.108496\pi$
$164$	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	$-0.421495\pi$
$179$	1169.35	0.488275	0.244138	+	0.969741i	$0.421495\pi$
$180$	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	$-0.460399\pi$
$191$	655.104	0.248176	0.124088	+	0.992271i	$0.460399\pi$
$192$	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	$-0.630727\pi$
$199$	−2241.55	−0.798488	−0.399244	+	0.916845i	$0.630727\pi$
$200$	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	$-0.614773\pi$
$211$	−2162.67	−0.705612	−0.352806	+	0.935696i	$0.614773\pi$
$212$	−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	$-0.655079\pi$
$223$	−3117.97	−0.936298	−0.468149	+	0.883649i	$0.655079\pi$
$224$	4468.14	1.33277
$225$	873.658	0.258862
$226$	3076.07	0.905386
$227$	2881.26	0.842448	0.421224	−	0.906957i	$-0.361601\pi$
$227$	2881.26	0.842448	0.421224	+	0.906957i	$0.361601\pi$
$228$	−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	$-0.573971\pi$
$233$	−1638.16	−0.460599	−0.230300	+	0.973120i	$0.573971\pi$
$234$	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	$-0.435737\pi$
$241$	1500.42	0.401040	0.200520	+	0.979690i	$0.435737\pi$
$242$	−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	$-0.204944\pi$
$257$	6590.31	1.59958	0.799791	+	0.600279i	$0.204944\pi$
$258$	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	$-0.505340\pi$
$263$	−143.103	−0.0335518	−0.0167759	+	0.999859i	$0.505340\pi$
$264$	−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	$-0.316789\pi$
$277$	5018.81	1.08863	0.544316	+	0.838880i	$0.316789\pi$
$278$	−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	$-0.461793\pi$
$313$	1326.15	0.239484	0.119742	+	0.992805i	$0.461793\pi$
$314$	−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	$-0.184204\pi$
$331$	10083.0	1.67436	0.837178	+	0.546931i	$0.184204\pi$
$332$	−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	$-0.682716\pi$
$347$	−7019.93	−1.08602	−0.543011	+	0.839726i	$0.682716\pi$
$348$	−3029.99	−0.466738
$349$	9937.81	1.52424	0.762119	−	0.647437i	$-0.224159\pi$
$349$	9937.81	1.52424	0.762119	+	0.647437i	$0.224159\pi$
$350$	−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	$-0.648039\pi$
$373$	−6461.72	−0.896984	−0.448492	+	0.893787i	$0.648039\pi$
$374$	−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	$-0.643800\pi$
$383$	−6544.30	−0.873103	−0.436551	+	0.899679i	$0.643800\pi$
$384$	−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	$-0.845180\pi$
$389$	−13565.1	−1.76806	−0.884031	+	0.467429i	$0.845180\pi$
$390$	−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	$-0.664329\pi$
$409$	−8166.09	−0.987254	−0.493627	+	0.869674i	$0.664329\pi$
$410$	−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	$-0.485140\pi$
$419$	800.484	0.0933323	0.0466661	+	0.998911i	$0.485140\pi$
$420$	−2820.57	−0.327689
$421$	4233.24	0.490060	0.245030	−	0.969515i	$-0.421202\pi$
$421$	4233.24	0.490060	0.245030	+	0.969515i	$0.421202\pi$
$422$	−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	$-0.596530\pi$
$433$	−5381.42	−0.597262	−0.298631	+	0.954369i	$0.596530\pi$
$434$	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	$-0.670238\pi$
$449$	−9698.43	−1.01937	−0.509685	+	0.860361i	$0.670238\pi$
$450$	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	$-0.474730\pi$
$457$	1549.54	0.158609	0.0793047	+	0.996850i	$0.474730\pi$
$458$	−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	$-0.616727\pi$
$463$	−7144.05	−0.717089	−0.358545	+	0.933513i	$0.616727\pi$
$464$	−252.688	−0.0252818
$465$	4751.54	0.473865
$466$	−2908.10	−0.289088
$467$	12175.9	1.20649	0.603246	−	0.797555i	$-0.293874\pi$
$467$	12175.9	1.20649	0.603246	+	0.797555i	$0.293874\pi$
$468$	−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	$-0.553731\pi$
$491$	−3655.61	−0.335999	−0.167999	+	0.985787i	$0.553731\pi$
$492$	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	$-0.620294\pi$
$499$	−8225.98	−0.737967	−0.368983	+	0.929436i	$0.620294\pi$
$500$	5897.94	0.527527
$501$	7826.37	0.697917
$502$	11217.3	0.997315
$503$	4117.12	0.364957	0.182478	−	0.983210i	$-0.441588\pi$
$503$	4117.12	0.364957	0.182478	+	0.983210i	$0.441588\pi$
$504$	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	$-0.311597\pi$
$521$	13269.8	1.11586	0.557928	+	0.829889i	$0.311597\pi$
$522$	−2443.62	−0.204893
$523$	−6010.79	−0.502550	−0.251275	−	0.967916i	$-0.580850\pi$
$523$	−6010.79	−0.502550	−0.251275	+	0.967916i	$0.580850\pi$
$524$	−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	$-0.521463\pi$
$571$	−1838.63	−0.134753	−0.0673766	+	0.997728i	$0.521463\pi$
$572$	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	$-0.622474\pi$
$577$	−10404.4	−0.750679	−0.375339	+	0.926887i	$0.622474\pi$
$578$	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	$-0.530175\pi$
$587$	−2692.40	−0.189314	−0.0946570	+	0.995510i	$0.530175\pi$
$588$	−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	$-0.197471\pi$
$593$	23499.4	1.62732	0.813662	+	0.581338i	$0.197471\pi$
$594$	−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	$-0.878005\pi$
$601$	−27329.6	−1.85490	−0.927452	+	0.373943i	$0.878005\pi$
$602$	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	$-0.543766\pi$
$607$	−4099.54	−0.274127	−0.137064	+	0.990562i	$0.543766\pi$
$608$	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	$-0.545553\pi$
$631$	−4521.20	−0.285240	−0.142620	+	0.989778i	$0.545553\pi$
$632$	−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	$-0.398247\pi$
$641$	10199.8	0.628500	0.314250	+	0.949340i	$0.398247\pi$
$642$	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	$-0.696804\pi$
$647$	−19078.3	−1.15926	−0.579632	+	0.814878i	$0.696804\pi$
$648$	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	$-0.475057\pi$
$653$	2612.47	0.156560	0.0782800	+	0.996931i	$0.475057\pi$
$654$	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	$-0.600174\pi$
$673$	−10808.5	−0.619072	−0.309536	+	0.950888i	$0.600174\pi$
$674$	5928.58	0.338813
$675$	14387.3	0.820398
$676$	9528.50	0.542131
$677$	4460.60	0.253227	0.126614	−	0.991952i	$-0.459589\pi$
$677$	4460.60	0.253227	0.126614	+	0.991952i	$0.459589\pi$
$678$	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	$-0.814022\pi$
$691$	−30302.2	−1.66823	−0.834116	+	0.551589i	$0.814022\pi$
$692$	−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	$-0.327050\pi$
$727$	20268.3	1.03399	0.516995	+	0.855988i	$0.327050\pi$
$728$	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	$-0.446914\pi$
$733$	6588.75	0.332007	0.166004	+	0.986125i	$0.446914\pi$
$734$	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	$-0.467765\pi$
$739$	4061.88	0.202190	0.101095	+	0.994877i	$0.467765\pi$
$740$	−6179.21	−0.306963
$741$	−5572.98	−0.276287
$742$	10206.7	0.504987
$743$	126.183	0.00623043	0.00311522	−	0.999995i	$-0.499008\pi$
$743$	126.183	0.00623043	0.00311522	+	0.999995i	$0.499008\pi$
$744$	−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	$-0.727923\pi$
$751$	−27018.5	−1.31281	−0.656403	+	0.754410i	$0.727923\pi$
$752$	−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	$-0.157670\pi$
$757$	36649.0	1.75962	0.879809	+	0.475327i	$0.157670\pi$
$758$	−17755.5	−0.850805
$759$	1519.82	0.0726827
$760$	−11004.5	−0.525232
$761$	−28092.6	−1.33818	−0.669091	−	0.743180i	$-0.733317\pi$
$761$	−28092.6	−1.33818	−0.669091	+	0.743180i	$0.733317\pi$
$762$	−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	$-0.779010\pi$
$773$	−33033.8	−1.53705	−0.768527	+	0.639818i	$0.779010\pi$
$774$	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	$-0.556412\pi$
$811$	−8143.45	−0.352596	−0.176298	+	0.984337i	$0.556412\pi$
$812$	−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	$-0.802759\pi$
$829$	−38862.4	−1.62816	−0.814082	+	0.580750i	$0.802759\pi$
$830$	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	$-0.398877\pi$
$839$	15182.5	0.624743	0.312371	+	0.949960i	$0.398877\pi$
$840$	−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	$-0.314311\pi$
$859$	27735.6	1.10166	0.550831	+	0.834617i	$0.314311\pi$
$860$	0	0
$861$	−2265.08	−0.0896559
$862$	−28905.5	−1.14214
$863$	−46946.3	−1.85176	−0.925881	−	0.377816i	$-0.876675\pi$
$863$	−46946.3	−1.85176	−0.925881	+	0.377816i	$0.876675\pi$
$864$	−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	$-0.804517\pi$
$887$	−43180.2	−1.63455	−0.817277	+	0.576245i	$0.804517\pi$
$888$	−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	$-0.643304\pi$
$911$	−23930.2	−0.870299	−0.435149	+	0.900358i	$0.643304\pi$
$912$	−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	$-0.730974\pi$
$929$	−37580.6	−1.32721	−0.663605	+	0.748083i	$0.730974\pi$
$930$	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	$-0.559212\pi$
$937$	−10609.4	−0.369899	−0.184950	+	0.982748i	$0.559212\pi$
$938$	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	$-0.629346\pi$
$953$	−23257.1	−0.790524	−0.395262	+	0.918568i	$0.629346\pi$
$954$	−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	$-0.236836\pi$
$983$	45350.6	1.47148	0.735738	+	0.677267i	$0.236836\pi$
$984$	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	$-0.600158\pi$
$991$	−19310.1	−0.618977	−0.309488	+	0.950903i	$0.600158\pi$
$992$	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	$-0.522183\pi$
$997$	−4384.16	−0.139265	−0.0696327	+	0.997573i	$0.522183\pi$
$998$	−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.h.1.18		30
43.4	even	7		43.4.e.a.16.5	✓	60
43.11	even	7		43.4.e.a.35.5	yes	60
43.42	odd	2		1849.4.a.g.1.13		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.4.e.a.16.5	✓	60	43.4	even	7
43.4.e.a.35.5	yes	60	43.11	even	7
1849.4.a.g.1.13		30	43.42	odd	2
1849.4.a.h.1.18		30	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

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