LMFDB - Embedded newform 165.4.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [165,4,Mod(1,165)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(165, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("165.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 165 = 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	165.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:	$9.73531515095$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{17}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 4 $ x^2 - x - 4
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.56155$ of defining polynomial
Character	$\chi$	$=$	165.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.56155 q^{2} +3.00000 q^{3} -1.43845 q^{4} -5.00000 q^{5} -7.68466 q^{6} +6.24621 q^{7} +24.1771 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-2.56155 q^{2} +3.00000 q^{3} -1.43845 q^{4} -5.00000 q^{5} -7.68466 q^{6} +6.24621 q^{7} +24.1771 q^{8} +9.00000 q^{9} +12.8078 q^{10} -11.0000 q^{11} -4.31534 q^{12} -49.1231 q^{13} -16.0000 q^{14} -15.0000 q^{15} -50.4233 q^{16} +82.7083 q^{17} -23.0540 q^{18} -130.354 q^{19} +7.19224 q^{20} +18.7386 q^{21} +28.1771 q^{22} -185.693 q^{23} +72.5312 q^{24} +25.0000 q^{25} +125.831 q^{26} +27.0000 q^{27} -8.98485 q^{28} -8.90720 q^{29} +38.4233 q^{30} +5.26137 q^{31} -64.2547 q^{32} -33.0000 q^{33} -211.862 q^{34} -31.2311 q^{35} -12.9460 q^{36} -416.894 q^{37} +333.909 q^{38} -147.369 q^{39} -120.885 q^{40} -298.479 q^{41} -48.0000 q^{42} -513.633 q^{43} +15.8229 q^{44} -45.0000 q^{45} +475.663 q^{46} +557.295 q^{47} -151.270 q^{48} -303.985 q^{49} -64.0388 q^{50} +248.125 q^{51} +70.6610 q^{52} -168.064 q^{53} -69.1619 q^{54} +55.0000 q^{55} +151.015 q^{56} -391.062 q^{57} +22.8163 q^{58} +618.773 q^{59} +21.5767 q^{60} +786.405 q^{61} -13.4773 q^{62} +56.2159 q^{63} +567.978 q^{64} +245.616 q^{65} +84.5312 q^{66} -339.015 q^{67} -118.972 q^{68} -557.080 q^{69} +80.0000 q^{70} +1120.71 q^{71} +217.594 q^{72} -123.430 q^{73} +1067.90 q^{74} +75.0000 q^{75} +187.508 q^{76} -68.7083 q^{77} +377.494 q^{78} -309.835 q^{79} +252.116 q^{80} +81.0000 q^{81} +764.570 q^{82} -1021.22 q^{83} -26.9545 q^{84} -413.542 q^{85} +1315.70 q^{86} -26.7216 q^{87} -265.948 q^{88} -141.879 q^{89} +115.270 q^{90} -306.833 q^{91} +267.110 q^{92} +15.7841 q^{93} -1427.54 q^{94} +651.771 q^{95} -192.764 q^{96} +798.345 q^{97} +778.673 q^{98} -99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} + 6 q^{3} - 7 q^{4} - 10 q^{5} - 3 q^{6} - 4 q^{7} + 3 q^{8} + 18 q^{9}+O(q^{10}) $ 2 * q - q^2 + 6 * q^3 - 7 * q^4 - 10 * q^5 - 3 * q^6 - 4 * q^7 + 3 * q^8 + 18 * q^9	\( 2 q - q^{2} + 6 q^{3} - 7 q^{4} - 10 q^{5} - 3 q^{6} - 4 q^{7} + 3 q^{8} + 18 q^{9} + 5 q^{10} - 22 q^{11} - 21 q^{12} - 90 q^{13} - 32 q^{14} - 30 q^{15} - 39 q^{16} - 16 q^{17} - 9 q^{18} - 170 q^{19} + 35 q^{20} - 12 q^{21} + 11 q^{22} - 124 q^{23} + 9 q^{24} + 50 q^{25} + 62 q^{26} + 54 q^{27} + 48 q^{28} - 158 q^{29} + 15 q^{30} + 60 q^{31} + 123 q^{32} - 66 q^{33} - 366 q^{34} + 20 q^{35} - 63 q^{36} - 372 q^{37} + 272 q^{38} - 270 q^{39} - 15 q^{40} + 38 q^{41} - 96 q^{42} - 516 q^{43} + 77 q^{44} - 90 q^{45} + 572 q^{46} + 224 q^{47} - 117 q^{48} - 542 q^{49} - 25 q^{50} - 48 q^{51} + 298 q^{52} + 472 q^{53} - 27 q^{54} + 110 q^{55} + 368 q^{56} - 510 q^{57} - 210 q^{58} + 248 q^{59} + 105 q^{60} + 72 q^{61} + 72 q^{62} - 36 q^{63} + 769 q^{64} + 450 q^{65} + 33 q^{66} - 744 q^{67} + 430 q^{68} - 372 q^{69} + 160 q^{70} + 2060 q^{71} + 27 q^{72} - 486 q^{73} + 1138 q^{74} + 150 q^{75} + 408 q^{76} + 44 q^{77} + 186 q^{78} + 642 q^{79} + 195 q^{80} + 162 q^{81} + 1290 q^{82} - 286 q^{83} + 144 q^{84} + 80 q^{85} + 1312 q^{86} - 474 q^{87} - 33 q^{88} + 244 q^{89} + 45 q^{90} + 112 q^{91} - 76 q^{92} + 180 q^{93} - 1948 q^{94} + 850 q^{95} + 369 q^{96} - 168 q^{97} + 407 q^{98} - 198 q^{99}+O(q^{100}) \) 2 * q - q^2 + 6 * q^3 - 7 * q^4 - 10 * q^5 - 3 * q^6 - 4 * q^7 + 3 * q^8 + 18 * q^9 + 5 * q^10 - 22 * q^11 - 21 * q^12 - 90 * q^13 - 32 * q^14 - 30 * q^15 - 39 * q^16 - 16 * q^17 - 9 * q^18 - 170 * q^19 + 35 * q^20 - 12 * q^21 + 11 * q^22 - 124 * q^23 + 9 * q^24 + 50 * q^25 + 62 * q^26 + 54 * q^27 + 48 * q^28 - 158 * q^29 + 15 * q^30 + 60 * q^31 + 123 * q^32 - 66 * q^33 - 366 * q^34 + 20 * q^35 - 63 * q^36 - 372 * q^37 + 272 * q^38 - 270 * q^39 - 15 * q^40 + 38 * q^41 - 96 * q^42 - 516 * q^43 + 77 * q^44 - 90 * q^45 + 572 * q^46 + 224 * q^47 - 117 * q^48 - 542 * q^49 - 25 * q^50 - 48 * q^51 + 298 * q^52 + 472 * q^53 - 27 * q^54 + 110 * q^55 + 368 * q^56 - 510 * q^57 - 210 * q^58 + 248 * q^59 + 105 * q^60 + 72 * q^61 + 72 * q^62 - 36 * q^63 + 769 * q^64 + 450 * q^65 + 33 * q^66 - 744 * q^67 + 430 * q^68 - 372 * q^69 + 160 * q^70 + 2060 * q^71 + 27 * q^72 - 486 * q^73 + 1138 * q^74 + 150 * q^75 + 408 * q^76 + 44 * q^77 + 186 * q^78 + 642 * q^79 + 195 * q^80 + 162 * q^81 + 1290 * q^82 - 286 * q^83 + 144 * q^84 + 80 * q^85 + 1312 * q^86 - 474 * q^87 - 33 * q^88 + 244 * q^89 + 45 * q^90 + 112 * q^91 - 76 * q^92 + 180 * q^93 - 1948 * q^94 + 850 * q^95 + 369 * q^96 - 168 * q^97 + 407 * q^98 - 198 * 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 $

$2$	−2.56155	−0.905646	−0.452823	−	0.891601i	$-0.649583\pi$
$2$	−2.56155	−0.905646	−0.452823	+	0.891601i	$0.649583\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	−1.43845	−0.179806
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	−7.68466	−0.522875
$7$	6.24621	0.337264	0.168632	−	0.985679i	$-0.446065\pi$
$7$	6.24621	0.337264	0.168632	+	0.985679i	$0.446065\pi$
$8$	24.1771	1.06849
$9$	9.00000	0.333333
$10$	12.8078	0.405017
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	−4.31534	−0.103811
$13$	−49.1231	−1.04802	−0.524011	−	0.851711i	$-0.675565\pi$
$13$	−49.1231	−1.04802	−0.524011	+	0.851711i	$0.675565\pi$
$14$	−16.0000	−0.305441
$15$	−15.0000	−0.258199
$16$	−50.4233	−0.787864
$17$	82.7083	1.17998	0.589992	−	0.807409i	$-0.299131\pi$
$17$	82.7083	1.17998	0.589992	+	0.807409i	$0.299131\pi$
$18$	−23.0540	−0.301882
$19$	−130.354	−1.57396	−0.786981	−	0.616977i	$-0.788357\pi$
$19$	−130.354	−1.57396	−0.786981	+	0.616977i	$0.788357\pi$
$20$	7.19224	0.0804116
$21$	18.7386	0.194719
$22$	28.1771	0.273062
$23$	−185.693	−1.68347	−0.841733	−	0.539895i	$-0.818464\pi$
$23$	−185.693	−1.68347	−0.841733	+	0.539895i	$0.818464\pi$
$24$	72.5312	0.616891
$25$	25.0000	0.200000
$26$	125.831	0.949137
$27$	27.0000	0.192450
$28$	−8.98485	−0.0606420
$29$	−8.90720	−0.0570354	−0.0285177	−	0.999593i	$-0.509079\pi$
$29$	−8.90720	−0.0570354	−0.0285177	+	0.999593i	$0.509079\pi$
$30$	38.4233	0.233837
$31$	5.26137	0.0304829	0.0152414	−	0.999884i	$-0.495148\pi$
$31$	5.26137	0.0304829	0.0152414	+	0.999884i	$0.495148\pi$
$32$	−64.2547	−0.354961
$33$	−33.0000	−0.174078
$34$	−211.862	−1.06865
$35$	−31.2311	−0.150829
$36$	−12.9460	−0.0599353
$37$	−416.894	−1.85235	−0.926175	−	0.377094i	$-0.876923\pi$
$37$	−416.894	−1.85235	−0.926175	+	0.377094i	$0.876923\pi$
$38$	333.909	1.42545
$39$	−147.369	−0.605076
$40$	−120.885	−0.477842
$41$	−298.479	−1.13694	−0.568471	−	0.822703i	$-0.692465\pi$
$41$	−298.479	−1.13694	−0.568471	+	0.822703i	$0.692465\pi$
$42$	−48.0000	−0.176347
$43$	−513.633	−1.82159	−0.910793	−	0.412863i	$-0.864529\pi$
$43$	−513.633	−1.82159	−0.910793	+	0.412863i	$0.864529\pi$
$44$	15.8229	0.0542135
$45$	−45.0000	−0.149071
$46$	475.663	1.52462
$47$	557.295	1.72957	0.864786	−	0.502140i	$-0.167454\pi$
$47$	557.295	1.72957	0.864786	+	0.502140i	$0.167454\pi$
$48$	−151.270	−0.454873
$49$	−303.985	−0.886253
$50$	−64.0388	−0.181129
$51$	248.125	0.681264
$52$	70.6610	0.188441
$53$	−168.064	−0.435574	−0.217787	−	0.975996i	$-0.569884\pi$
$53$	−168.064	−0.435574	−0.217787	+	0.975996i	$0.569884\pi$
$54$	−69.1619	−0.174292
$55$	55.0000	0.134840
$56$	151.015	0.360362
$57$	−391.062	−0.908728
$58$	22.8163	0.0516539
$59$	618.773	1.36538	0.682689	−	0.730709i	$-0.260810\pi$
$59$	618.773	1.36538	0.682689	+	0.730709i	$0.260810\pi$
$60$	21.5767	0.0464257
$61$	786.405	1.65064	0.825319	−	0.564667i	$-0.190996\pi$
$61$	786.405	1.65064	0.825319	+	0.564667i	$0.190996\pi$
$62$	−13.4773	−0.0276067
$63$	56.2159	0.112421
$64$	567.978	1.10933
$65$	245.616	0.468690
$66$	84.5312	0.157653
$67$	−339.015	−0.618169	−0.309084	−	0.951035i	$-0.600023\pi$
$67$	−339.015	−0.618169	−0.309084	+	0.951035i	$0.600023\pi$
$68$	−118.972	−0.212168
$69$	−557.080	−0.971949
$70$	80.0000	0.136598
$71$	1120.71	1.87329	0.936645	−	0.350280i	$-0.113913\pi$
$71$	1120.71	1.87329	0.936645	+	0.350280i	$0.113913\pi$
$72$	217.594	0.356162
$73$	−123.430	−0.197896	−0.0989478	−	0.995093i	$-0.531548\pi$
$73$	−123.430	−0.197896	−0.0989478	+	0.995093i	$0.531548\pi$
$74$	1067.90	1.67757
$75$	75.0000	0.115470
$76$	187.508	0.283008
$77$	−68.7083	−0.101689
$78$	377.494	0.547985
$79$	−309.835	−0.441255	−0.220628	−	0.975358i	$-0.570811\pi$
$79$	−309.835	−0.441255	−0.220628	+	0.975358i	$0.570811\pi$
$80$	252.116	0.352343
$81$	81.0000	0.111111
$82$	764.570	1.02967
$83$	−1021.22	−1.35053	−0.675263	−	0.737577i	$-0.735970\pi$
$83$	−1021.22	−1.35053	−0.675263	+	0.737577i	$0.735970\pi$
$84$	−26.9545	−0.0350117
$85$	−413.542	−0.527705
$86$	1315.70	1.64971
$87$	−26.7216	−0.0329294
$88$	−265.948	−0.322161
$89$	−141.879	−0.168979	−0.0844894	−	0.996424i	$-0.526926\pi$
$89$	−141.879	−0.168979	−0.0844894	+	0.996424i	$0.526926\pi$
$90$	115.270	0.135006
$91$	−306.833	−0.353460
$92$	267.110	0.302697
$93$	15.7841	0.0175993
$94$	−1427.54	−1.56638
$95$	651.771	0.703898
$96$	−192.764	−0.204937
$97$	798.345	0.835666	0.417833	−	0.908524i	$-0.362790\pi$
$97$	798.345	0.835666	0.417833	+	0.908524i	$0.362790\pi$
$98$	778.673	0.802631
$99$	−99.0000	−0.100504
$100$	−35.9612	−0.0359612
$101$	241.400	0.237823	0.118912	−	0.992905i	$-0.462059\pi$
$101$	241.400	0.237823	0.118912	+	0.992905i	$0.462059\pi$
$102$	−635.585	−0.616983
$103$	1168.38	1.11771	0.558853	−	0.829267i	$-0.311242\pi$
$103$	1168.38	1.11771	0.558853	+	0.829267i	$0.311242\pi$
$104$	−1187.65	−1.11980
$105$	−93.6932	−0.0870811
$106$	430.506	0.394476
$107$	−2106.82	−1.90350	−0.951748	−	0.306882i	$-0.900714\pi$
$107$	−2106.82	−1.90350	−0.951748	+	0.306882i	$0.900714\pi$
$108$	−38.8381	−0.0346037
$109$	493.792	0.433914	0.216957	−	0.976181i	$-0.430387\pi$
$109$	493.792	0.433914	0.216957	+	0.976181i	$0.430387\pi$
$110$	−140.885	−0.122117
$111$	−1250.68	−1.06945
$112$	−314.955	−0.265718
$113$	170.000	0.141524	0.0707622	−	0.997493i	$-0.477457\pi$
$113$	170.000	0.141524	0.0707622	+	0.997493i	$0.477457\pi$
$114$	1001.73	0.822986
$115$	928.466	0.752869
$116$	12.8125	0.0102553
$117$	−442.108	−0.349341
$118$	−1585.02	−1.23655
$119$	516.614	0.397966
$120$	−362.656	−0.275882
$121$	121.000	0.0909091
$122$	−2014.42	−1.49489
$123$	−895.437	−0.656414
$124$	−7.56820	−0.00548100
$125$	−125.000	−0.0894427
$126$	−144.000	−0.101814
$127$	−948.182	−0.662500	−0.331250	−	0.943543i	$-0.607470\pi$
$127$	−948.182	−0.662500	−0.331250	+	0.943543i	$0.607470\pi$
$128$	−940.868	−0.649702
$129$	−1540.90	−1.05169
$130$	−629.157	−0.424467
$131$	−1484.84	−0.990312	−0.495156	−	0.868804i	$-0.664889\pi$
$131$	−1484.84	−0.990312	−0.495156	+	0.868804i	$0.664889\pi$
$132$	47.4688	0.0313002
$133$	−814.220	−0.530841
$134$	868.405	0.559842
$135$	−135.000	−0.0860663
$136$	1999.65	1.26080
$137$	684.928	0.427134	0.213567	−	0.976928i	$-0.431492\pi$
$137$	684.928	0.427134	0.213567	+	0.976928i	$0.431492\pi$
$138$	1426.99	0.880242
$139$	830.483	0.506767	0.253384	−	0.967366i	$-0.418457\pi$
$139$	830.483	0.506767	0.253384	+	0.967366i	$0.418457\pi$
$140$	44.9242	0.0271199
$141$	1671.89	0.998569
$142$	−2870.75	−1.69654
$143$	540.354	0.315991
$144$	−453.810	−0.262621
$145$	44.5360	0.0255070
$146$	316.172	0.179223
$147$	−911.955	−0.511679
$148$	599.680	0.333063
$149$	−1213.64	−0.667285	−0.333642	−	0.942700i	$-0.608278\pi$
$149$	−1213.64	−0.667285	−0.333642	+	0.942700i	$0.608278\pi$
$150$	−192.116	−0.104575
$151$	30.8466	0.0166242	0.00831212	−	0.999965i	$-0.497354\pi$
$151$	30.8466	0.0166242	0.00831212	+	0.999965i	$0.497354\pi$
$152$	−3151.58	−1.68176
$153$	744.375	0.393328
$154$	176.000	0.0920941
$155$	−26.3068	−0.0136324
$156$	211.983	0.108796
$157$	345.239	0.175497	0.0877485	−	0.996143i	$-0.472033\pi$
$157$	345.239	0.175497	0.0877485	+	0.996143i	$0.472033\pi$
$158$	793.659	0.399621
$159$	−504.193	−0.251479
$160$	321.274	0.158743
$161$	−1159.88	−0.567772
$162$	−207.486	−0.100627
$163$	1921.49	0.923331	0.461665	−	0.887054i	$-0.347252\pi$
$163$	1921.49	0.923331	0.461665	+	0.887054i	$0.347252\pi$
$164$	429.346	0.204429
$165$	165.000	0.0778499
$166$	2615.91	1.22310
$167$	172.297	0.0798369	0.0399185	−	0.999203i	$-0.487290\pi$
$167$	172.297	0.0798369	0.0399185	+	0.999203i	$0.487290\pi$
$168$	453.045	0.208055
$169$	216.080	0.0983521
$170$	1059.31	0.477913
$171$	−1173.19	−0.524654
$172$	738.833	0.327532
$173$	−1025.29	−0.450587	−0.225293	−	0.974291i	$-0.572334\pi$
$173$	−1025.29	−0.450587	−0.225293	+	0.974291i	$0.572334\pi$
$174$	68.4488	0.0298224
$175$	156.155	0.0674527
$176$	554.656	0.237550
$177$	1856.32	0.788302
$178$	363.430	0.153035
$179$	1658.29	0.692437	0.346219	−	0.938154i	$-0.387466\pi$
$179$	1658.29	0.692437	0.346219	+	0.938154i	$0.387466\pi$
$180$	64.7301	0.0268039
$181$	−2021.81	−0.830275	−0.415137	−	0.909759i	$-0.636266\pi$
$181$	−2021.81	−0.830275	−0.415137	+	0.909759i	$0.636266\pi$
$182$	785.970	0.320110
$183$	2359.22	0.952996
$184$	−4489.52	−1.79876
$185$	2084.47	0.828396
$186$	−40.4318	−0.0159387
$187$	−909.792	−0.355778
$188$	−801.640	−0.310987
$189$	168.648	0.0649064
$190$	−1669.55	−0.637482
$191$	1440.22	0.545607	0.272803	−	0.962070i	$-0.412049\pi$
$191$	1440.22	0.545607	0.272803	+	0.962070i	$0.412049\pi$
$192$	1703.93	0.640473
$193$	−2798.05	−1.04356	−0.521782	−	0.853079i	$-0.674733\pi$
$193$	−2798.05	−1.04356	−0.521782	+	0.853079i	$0.674733\pi$
$194$	−2045.00	−0.756817
$195$	736.847	0.270598
$196$	437.266	0.159354
$197$	458.943	0.165982	0.0829908	−	0.996550i	$-0.473553\pi$
$197$	458.943	0.165982	0.0829908	+	0.996550i	$0.473553\pi$
$198$	253.594	0.0910208
$199$	−2371.04	−0.844615	−0.422308	−	0.906453i	$-0.638780\pi$
$199$	−2371.04	−0.844615	−0.422308	+	0.906453i	$0.638780\pi$
$200$	604.427	0.213697
$201$	−1017.05	−0.356900
$202$	−618.358	−0.215384
$203$	−55.6363	−0.0192360
$204$	−356.915	−0.122495
$205$	1492.40	0.508456
$206$	−2992.86	−1.01225
$207$	−1671.24	−0.561155
$208$	2476.95	0.825699
$209$	1433.90	0.474568
$210$	240.000	0.0788646
$211$	4319.87	1.40944	0.704721	−	0.709484i	$-0.251072\pi$
$211$	4319.87	1.40944	0.704721	+	0.709484i	$0.251072\pi$
$212$	241.752	0.0783187
$213$	3362.12	1.08154
$214$	5396.73	1.72389
$215$	2568.16	0.814638
$216$	652.781	0.205630
$217$	32.8636	0.0102808
$218$	−1264.87	−0.392973
$219$	−370.290	−0.114255
$220$	−79.1146	−0.0242450
$221$	−4062.89	−1.23665
$222$	3203.69	0.968547
$223$	−3837.73	−1.15244	−0.576219	−	0.817295i	$-0.695473\pi$
$223$	−3837.73	−1.15244	−0.576219	+	0.817295i	$0.695473\pi$
$224$	−401.349	−0.119715
$225$	225.000	0.0666667
$226$	−435.464	−0.128171
$227$	−5003.71	−1.46303	−0.731515	−	0.681825i	$-0.761187\pi$
$227$	−5003.71	−1.46303	−0.731515	+	0.681825i	$0.761187\pi$
$228$	562.523	0.163395
$229$	−277.375	−0.0800412	−0.0400206	−	0.999199i	$-0.512742\pi$
$229$	−277.375	−0.0800412	−0.0400206	+	0.999199i	$0.512742\pi$
$230$	−2378.31	−0.681832
$231$	−206.125	−0.0587101
$232$	−215.350	−0.0609415
$233$	2269.91	0.638225	0.319113	−	0.947717i	$-0.396615\pi$
$233$	2269.91	0.638225	0.319113	+	0.947717i	$0.396615\pi$
$234$	1132.48	0.316379
$235$	−2786.48	−0.773488
$236$	−890.072	−0.245503
$237$	−929.505	−0.254759
$238$	−1323.33	−0.360416
$239$	−1617.11	−0.437665	−0.218832	−	0.975762i	$-0.570225\pi$
$239$	−1617.11	−0.437665	−0.218832	+	0.975762i	$0.570225\pi$
$240$	756.349	0.203426
$241$	5646.63	1.50926	0.754629	−	0.656151i	$-0.227817\pi$
$241$	5646.63	1.50926	0.754629	+	0.656151i	$0.227817\pi$
$242$	−309.948	−0.0823314
$243$	243.000	0.0641500
$244$	−1131.20	−0.296794
$245$	1519.92	0.396344
$246$	2293.71	0.594478
$247$	6403.40	1.64955
$248$	127.204	0.0325705
$249$	−3063.66	−0.779726
$250$	320.194	0.0810034
$251$	−6217.61	−1.56355	−0.781777	−	0.623558i	$-0.785687\pi$
$251$	−6217.61	−1.56355	−0.781777	+	0.623558i	$0.785687\pi$
$252$	−80.8636	−0.0202140
$253$	2042.62	0.507584
$254$	2428.82	0.599991
$255$	−1240.62	−0.304670
$256$	−2133.74	−0.520933
$257$	7712.75	1.87202	0.936008	−	0.351980i	$-0.114491\pi$
$257$	7712.75	1.87202	0.936008	+	0.351980i	$0.114491\pi$
$258$	3947.09	0.952462
$259$	−2604.01	−0.624730
$260$	−353.305	−0.0842732
$261$	−80.1648	−0.0190118
$262$	3803.49	0.896871
$263$	206.347	0.0483798	0.0241899	−	0.999707i	$-0.492299\pi$
$263$	206.347	0.0483798	0.0241899	+	0.999707i	$0.492299\pi$
$264$	−797.844	−0.186000
$265$	840.322	0.194795
$266$	2085.67	0.480753
$267$	−425.636	−0.0975600
$268$	487.655	0.111150
$269$	1712.47	0.388146	0.194073	−	0.980987i	$-0.437830\pi$
$269$	1712.47	0.388146	0.194073	+	0.980987i	$0.437830\pi$
$270$	345.810	0.0779456
$271$	−477.081	−0.106940	−0.0534698	−	0.998569i	$-0.517028\pi$
$271$	−477.081	−0.106940	−0.0534698	+	0.998569i	$0.517028\pi$
$272$	−4170.43	−0.929666
$273$	−920.500	−0.204070
$274$	−1754.48	−0.386832
$275$	−275.000	−0.0603023
$276$	801.329	0.174762
$277$	4283.48	0.929130	0.464565	−	0.885539i	$-0.346211\pi$
$277$	4283.48	0.929130	0.464565	+	0.885539i	$0.346211\pi$
$278$	−2127.33	−0.458952
$279$	47.3523	0.0101610
$280$	−755.076	−0.161159
$281$	3477.79	0.738319	0.369160	−	0.929366i	$-0.379646\pi$
$281$	3477.79	0.738319	0.369160	+	0.929366i	$0.379646\pi$
$282$	−4282.62	−0.904350
$283$	−6568.27	−1.37966	−0.689829	−	0.723973i	$-0.742314\pi$
$283$	−6568.27	−1.37966	−0.689829	+	0.723973i	$0.742314\pi$
$284$	−1612.08	−0.336829
$285$	1955.31	0.406395
$286$	−1384.15	−0.286176
$287$	−1864.36	−0.383449
$288$	−578.292	−0.118320
$289$	1927.67	0.392360
$290$	−114.081	−0.0231003
$291$	2395.03	0.482472
$292$	177.547	0.0355828
$293$	8352.29	1.66534	0.832672	−	0.553766i	$-0.186810\pi$
$293$	8352.29	1.66534	0.832672	+	0.553766i	$0.186810\pi$
$294$	2336.02	0.463399
$295$	−3093.86	−0.610616
$296$	−10079.3	−1.97921
$297$	−297.000	−0.0580259
$298$	3108.81	0.604324
$299$	9121.83	1.76431
$300$	−107.884	−0.0207622
$301$	−3208.26	−0.614355
$302$	−79.0152	−0.0150557
$303$	724.199	0.137307
$304$	6572.89	1.24007
$305$	−3932.03	−0.738187
$306$	−1906.76	−0.356216
$307$	5383.89	1.00090	0.500448	−	0.865767i	$-0.333169\pi$
$307$	5383.89	1.00090	0.500448	+	0.865767i	$0.333169\pi$
$308$	98.8333	0.0182843
$309$	3505.14	0.645308
$310$	67.3863	0.0123461
$311$	−1790.41	−0.326447	−0.163223	−	0.986589i	$-0.552189\pi$
$311$	−1790.41	−0.326447	−0.163223	+	0.986589i	$0.552189\pi$
$312$	−3562.96	−0.646516
$313$	−809.076	−0.146108	−0.0730538	−	0.997328i	$-0.523274\pi$
$313$	−809.076	−0.146108	−0.0730538	+	0.997328i	$0.523274\pi$
$314$	−884.347	−0.158938
$315$	−281.080	−0.0502763
$316$	445.682	0.0793403
$317$	10744.5	1.90370	0.951849	−	0.306567i	$-0.0991804\pi$
$317$	10744.5	1.90370	0.951849	+	0.306567i	$0.0991804\pi$
$318$	1291.52	0.227751
$319$	97.9792	0.0171968
$320$	−2839.89	−0.496109
$321$	−6320.46	−1.09898
$322$	2971.09	0.514200
$323$	−10781.4	−1.85725
$324$	−116.514	−0.0199784
$325$	−1228.08	−0.209605
$326$	−4922.00	−0.836210
$327$	1481.37	0.250521
$328$	−7216.35	−1.21481
$329$	3480.98	0.583322
$330$	−422.656	−0.0705044
$331$	3399.12	0.564449	0.282224	−	0.959348i	$-0.408928\pi$
$331$	3399.12	0.564449	0.282224	+	0.959348i	$0.408928\pi$
$332$	1468.97	0.242832
$333$	−3752.05	−0.617450
$334$	−441.349	−0.0723039
$335$	1695.08	0.276453
$336$	−944.864	−0.153412
$337$	−11840.0	−1.91384	−0.956919	−	0.290356i	$-0.906226\pi$
$337$	−11840.0	−1.91384	−0.956919	+	0.290356i	$0.906226\pi$
$338$	−553.499	−0.0890721
$339$	510.000	0.0817091
$340$	594.858	0.0948844
$341$	−57.8750	−0.00919093
$342$	3005.18	0.475151
$343$	−4041.20	−0.636165
$344$	−12418.1	−1.94634
$345$	2785.40	0.434669
$346$	2626.34	0.408072
$347$	−2076.67	−0.321272	−0.160636	−	0.987014i	$-0.551355\pi$
$347$	−2076.67	−0.321272	−0.160636	+	0.987014i	$0.551355\pi$
$348$	38.4376	0.00592090
$349$	5837.37	0.895322	0.447661	−	0.894203i	$-0.352257\pi$
$349$	5837.37	0.895322	0.447661	+	0.894203i	$0.352257\pi$
$350$	−400.000	−0.0610883
$351$	−1326.32	−0.201692
$352$	706.802	0.107025
$353$	−2423.64	−0.365431	−0.182715	−	0.983166i	$-0.558489\pi$
$353$	−2423.64	−0.365431	−0.182715	+	0.983166i	$0.558489\pi$
$354$	−4755.06	−0.713922
$355$	−5603.54	−0.837761
$356$	204.085	0.0303834
$357$	1549.84	0.229765
$358$	−4247.79	−0.627103
$359$	−3882.22	−0.570740	−0.285370	−	0.958417i	$-0.592116\pi$
$359$	−3882.22	−0.570740	−0.285370	+	0.958417i	$0.592116\pi$
$360$	−1087.97	−0.159281
$361$	10133.2	1.47736
$362$	5178.96	0.751935
$363$	363.000	0.0524864
$364$	441.363	0.0635542
$365$	617.150	0.0885016
$366$	−6043.26	−0.863077
$367$	5666.65	0.805986	0.402993	−	0.915203i	$-0.367970\pi$
$367$	5666.65	0.805986	0.402993	+	0.915203i	$0.367970\pi$
$368$	9363.26	1.32634
$369$	−2686.31	−0.378981
$370$	−5339.48	−0.750233
$371$	−1049.77	−0.146903
$372$	−22.7046	−0.00316446
$373$	174.771	0.0242608	0.0121304	−	0.999926i	$-0.496139\pi$
$373$	174.771	0.0242608	0.0121304	+	0.999926i	$0.496139\pi$
$374$	2330.48	0.322209
$375$	−375.000	−0.0516398
$376$	13473.8	1.84802
$377$	437.550	0.0597744
$378$	−432.000	−0.0587822
$379$	252.686	0.0342470	0.0171235	−	0.999853i	$-0.494549\pi$
$379$	252.686	0.0342470	0.0171235	+	0.999853i	$0.494549\pi$
$380$	−937.538	−0.126565
$381$	−2844.55	−0.382495
$382$	−3689.21	−0.494126
$383$	−11014.5	−1.46950	−0.734748	−	0.678340i	$-0.762700\pi$
$383$	−11014.5	−1.46950	−0.734748	+	0.678340i	$0.762700\pi$
$384$	−2822.61	−0.375105
$385$	343.542	0.0454766
$386$	7167.35	0.945099
$387$	−4622.69	−0.607196
$388$	−1148.38	−0.150258
$389$	8099.40	1.05567	0.527835	−	0.849347i	$-0.323004\pi$
$389$	8099.40	1.05567	0.527835	+	0.849347i	$0.323004\pi$
$390$	−1887.47	−0.245066
$391$	−15358.4	−1.98646
$392$	−7349.47	−0.946949
$393$	−4454.51	−0.571757
$394$	−1175.61	−0.150320
$395$	1549.18	0.197335
$396$	142.406	0.0180712
$397$	−424.353	−0.0536465	−0.0268232	−	0.999640i	$-0.508539\pi$
$397$	−424.353	−0.0536465	−0.0268232	+	0.999640i	$0.508539\pi$
$398$	6073.54	0.764922
$399$	−2442.66	−0.306481
$400$	−1260.58	−0.157573
$401$	−5904.18	−0.735263	−0.367632	−	0.929972i	$-0.619831\pi$
$401$	−5904.18	−0.735263	−0.367632	+	0.929972i	$0.619831\pi$
$402$	2605.22	0.323225
$403$	−258.455	−0.0319468
$404$	−347.241	−0.0427620
$405$	−405.000	−0.0496904
$406$	142.515	0.0174210
$407$	4585.83	0.558504
$408$	5998.94	0.727921
$409$	1370.47	0.165686	0.0828430	−	0.996563i	$-0.473600\pi$
$409$	1370.47	0.165686	0.0828430	+	0.996563i	$0.473600\pi$
$410$	−3822.85	−0.460481
$411$	2054.78	0.246606
$412$	−1680.65	−0.200970
$413$	3864.98	0.460493
$414$	4280.97	0.508208
$415$	5106.11	0.603973
$416$	3156.39	0.372007
$417$	2491.45	0.292582
$418$	−3673.00	−0.429790
$419$	1268.73	0.147927	0.0739635	−	0.997261i	$-0.476435\pi$
$419$	1268.73	0.147927	0.0739635	+	0.997261i	$0.476435\pi$
$420$	134.773	0.0156577
$421$	−12241.9	−1.41719	−0.708594	−	0.705617i	$-0.750670\pi$
$421$	−12241.9	−1.41719	−0.708594	+	0.705617i	$0.750670\pi$
$422$	−11065.6	−1.27646
$423$	5015.66	0.576524
$424$	−4063.31	−0.465405
$425$	2067.71	0.235997
$426$	−8612.26	−0.979496
$427$	4912.05	0.556700
$428$	3030.55	0.342260
$429$	1621.06	0.182437
$430$	−6578.48	−0.737774
$431$	8050.11	0.899675	0.449838	−	0.893110i	$-0.351482\pi$
$431$	8050.11	0.899675	0.449838	+	0.893110i	$0.351482\pi$
$432$	−1361.43	−0.151624
$433$	−16565.7	−1.83856	−0.919282	−	0.393600i	$-0.871230\pi$
$433$	−16565.7	−1.83856	−0.919282	+	0.393600i	$0.871230\pi$
$434$	−84.1819	−0.00931073
$435$	133.608	0.0147265
$436$	−710.293	−0.0780203
$437$	24205.9	2.64971
$438$	948.517	0.103475
$439$	4705.80	0.511607	0.255804	−	0.966729i	$-0.417660\pi$
$439$	4705.80	0.511607	0.255804	+	0.966729i	$0.417660\pi$
$440$	1329.74	0.144075
$441$	−2735.86	−0.295418
$442$	10407.3	1.11997
$443$	15094.0	1.61882	0.809408	−	0.587246i	$-0.199788\pi$
$443$	15094.0	1.61882	0.809408	+	0.587246i	$0.199788\pi$
$444$	1799.04	0.192294
$445$	709.394	0.0755696
$446$	9830.56	1.04370
$447$	−3640.93	−0.385257
$448$	3547.71	0.374138
$449$	973.478	0.102319	0.0511595	−	0.998690i	$-0.483708\pi$
$449$	973.478	0.102319	0.0511595	+	0.998690i	$0.483708\pi$
$450$	−576.349	−0.0603764
$451$	3283.27	0.342801
$452$	−244.536	−0.0254469
$453$	92.5398	0.00959801
$454$	12817.3	1.32499
$455$	1534.17	0.158072
$456$	−9454.75	−0.970963
$457$	62.6577	0.00641358	0.00320679	−	0.999995i	$-0.498979\pi$
$457$	62.6577	0.00641358	0.00320679	+	0.999995i	$0.498979\pi$
$458$	710.510	0.0724890
$459$	2233.12	0.227088
$460$	−1335.55	−0.135370
$461$	−11866.2	−1.19884	−0.599419	−	0.800436i	$-0.704602\pi$
$461$	−11866.2	−1.19884	−0.599419	+	0.800436i	$0.704602\pi$
$462$	528.000	0.0531705
$463$	−13144.8	−1.31942	−0.659711	−	0.751519i	$-0.729321\pi$
$463$	−13144.8	−1.31942	−0.659711	+	0.751519i	$0.729321\pi$
$464$	449.131	0.0449361
$465$	−78.9205	−0.00787065
$466$	−5814.48	−0.578006
$467$	−10176.8	−1.00840	−0.504201	−	0.863586i	$-0.668213\pi$
$467$	−10176.8	−1.00840	−0.504201	+	0.863586i	$0.668213\pi$
$468$	635.949	0.0628136
$469$	−2117.56	−0.208486
$470$	7137.71	0.700506
$471$	1035.72	0.101323
$472$	14960.1	1.45889
$473$	5649.96	0.549229
$474$	2380.98	0.230721
$475$	−3258.85	−0.314793
$476$	−743.121	−0.0715565
$477$	−1512.58	−0.145191
$478$	4142.30	0.396369
$479$	3431.25	0.327302	0.163651	−	0.986518i	$-0.447673\pi$
$479$	3431.25	0.327302	0.163651	+	0.986518i	$0.447673\pi$
$480$	963.821	0.0916504
$481$	20479.1	1.94130
$482$	−14464.1	−1.36685
$483$	−3479.64	−0.327803
$484$	−174.052	−0.0163460
$485$	−3991.72	−0.373721
$486$	−622.457	−0.0580972
$487$	−2833.20	−0.263624	−0.131812	−	0.991275i	$-0.542079\pi$
$487$	−2833.20	−0.263624	−0.131812	+	0.991275i	$0.542079\pi$
$488$	19013.0	1.76368
$489$	5764.48	0.533085
$490$	−3893.37	−0.358948
$491$	−2667.29	−0.245159	−0.122580	−	0.992459i	$-0.539117\pi$
$491$	−2667.29	−0.245159	−0.122580	+	0.992459i	$0.539117\pi$
$492$	1288.04	0.118027
$493$	−736.700	−0.0673008
$494$	−16402.7	−1.49391
$495$	495.000	0.0449467
$496$	−265.295	−0.0240164
$497$	7000.18	0.631793
$498$	7847.74	0.706156
$499$	−11137.0	−0.999120	−0.499560	−	0.866279i	$-0.666505\pi$
$499$	−11137.0	−0.999120	−0.499560	+	0.866279i	$0.666505\pi$
$500$	179.806	0.0160823
$501$	516.892	0.0460939
$502$	15926.7	1.41603
$503$	8780.30	0.778319	0.389159	−	0.921170i	$-0.372766\pi$
$503$	8780.30	0.778319	0.389159	+	0.921170i	$0.372766\pi$
$504$	1359.14	0.120121
$505$	−1207.00	−0.106358
$506$	−5232.29	−0.459691
$507$	648.239	0.0567836
$508$	1363.91	0.119121
$509$	13597.4	1.18408	0.592039	−	0.805910i	$-0.298323\pi$
$509$	13597.4	1.18408	0.592039	+	0.805910i	$0.298323\pi$
$510$	3177.93	0.275923
$511$	−770.969	−0.0667430
$512$	12992.6	1.12148
$513$	−3519.56	−0.302909
$514$	−19756.6	−1.69538
$515$	−5841.89	−0.499854
$516$	2216.50	0.189101
$517$	−6130.25	−0.521486
$518$	6670.30	0.565784
$519$	−3075.88	−0.260146
$520$	5938.27	0.500789
$521$	14001.3	1.17736	0.588682	−	0.808364i	$-0.299647\pi$
$521$	14001.3	1.17736	0.588682	+	0.808364i	$0.299647\pi$
$522$	205.346	0.0172180
$523$	−14749.8	−1.23320	−0.616602	−	0.787275i	$-0.711491\pi$
$523$	−14749.8	−1.23320	−0.616602	+	0.787275i	$0.711491\pi$
$524$	2135.86	0.178064
$525$	468.466	0.0389439
$526$	−528.568	−0.0438149
$527$	435.159	0.0359693
$528$	1663.97	0.137150
$529$	22315.0	1.83406
$530$	−2152.53	−0.176415
$531$	5568.95	0.455126
$532$	1171.21	0.0954483
$533$	14662.2	1.19154
$534$	1090.29	0.0883548
$535$	10534.1	0.851269
$536$	−8196.40	−0.660505
$537$	4974.86	0.399779
$538$	−4386.59	−0.351523
$539$	3343.83	0.267215
$540$	194.190	0.0154752
$541$	1484.06	0.117939	0.0589694	−	0.998260i	$-0.481219\pi$
$541$	1484.06	0.117939	0.0589694	+	0.998260i	$0.481219\pi$
$542$	1222.07	0.0968493
$543$	−6065.42	−0.479359
$544$	−5314.40	−0.418847
$545$	−2468.96	−0.194052
$546$	2357.91	0.184815
$547$	−16562.2	−1.29460	−0.647302	−	0.762234i	$-0.724103\pi$
$547$	−16562.2	−1.29460	−0.647302	+	0.762234i	$0.724103\pi$
$548$	−985.233	−0.0768012
$549$	7077.65	0.550212
$550$	704.427	0.0546125
$551$	1161.09	0.0897716
$552$	−13468.6	−1.03851
$553$	−1935.30	−0.148819
$554$	−10972.3	−0.841463
$555$	6253.41	0.478275
$556$	−1194.61	−0.0911197
$557$	−8821.52	−0.671059	−0.335529	−	0.942030i	$-0.608915\pi$
$557$	−8821.52	−0.671059	−0.335529	+	0.942030i	$0.608915\pi$
$558$	−121.295	−0.00920223
$559$	25231.2	1.90906
$560$	1574.77	0.118833
$561$	−2729.37	−0.205409
$562$	−8908.55	−0.668656
$563$	−5985.53	−0.448064	−0.224032	−	0.974582i	$-0.571922\pi$
$563$	−5985.53	−0.448064	−0.224032	+	0.974582i	$0.571922\pi$
$564$	−2404.92	−0.179549
$565$	−850.000	−0.0632916
$566$	16825.0	1.24948
$567$	505.943	0.0374737
$568$	27095.5	2.00158
$569$	−3453.08	−0.254413	−0.127206	−	0.991876i	$-0.540601\pi$
$569$	−3453.08	−0.254413	−0.127206	+	0.991876i	$0.540601\pi$
$570$	−5008.64	−0.368050
$571$	−21484.5	−1.57460	−0.787302	−	0.616568i	$-0.788523\pi$
$571$	−21484.5	−1.57460	−0.787302	+	0.616568i	$0.788523\pi$
$572$	−777.271	−0.0568170
$573$	4320.67	0.315006
$574$	4775.67	0.347269
$575$	−4642.33	−0.336693
$576$	5111.80	0.369777
$577$	−13294.4	−0.959189	−0.479594	−	0.877490i	$-0.659216\pi$
$577$	−13294.4	−0.959189	−0.479594	+	0.877490i	$0.659216\pi$
$578$	−4937.82	−0.355340
$579$	−8394.14	−0.602502
$580$	−64.0627	−0.00458631
$581$	−6378.77	−0.455483
$582$	−6135.01	−0.436949
$583$	1848.71	0.131330
$584$	−2984.18	−0.211449
$585$	2210.54	0.156230
$586$	−21394.8	−1.50821
$587$	6695.73	0.470805	0.235402	−	0.971898i	$-0.424359\pi$
$587$	6695.73	0.470805	0.235402	+	0.971898i	$0.424359\pi$
$588$	1311.80	0.0920028
$589$	−685.841	−0.0479789
$590$	7925.09	0.553002
$591$	1376.83	0.0958295
$592$	21021.2	1.45940
$593$	−10239.6	−0.709088	−0.354544	−	0.935039i	$-0.615364\pi$
$593$	−10239.6	−0.709088	−0.354544	+	0.935039i	$0.615364\pi$
$594$	760.781	0.0525509
$595$	−2583.07	−0.177976
$596$	1745.76	0.119982
$597$	−7113.11	−0.487639
$598$	−23366.0	−1.59784
$599$	−23890.8	−1.62963	−0.814817	−	0.579719i	$-0.803162\pi$
$599$	−23890.8	−1.62963	−0.814817	+	0.579719i	$0.803162\pi$
$600$	1813.28	0.123378
$601$	−11343.8	−0.769920	−0.384960	−	0.922933i	$-0.625785\pi$
$601$	−11343.8	−0.769920	−0.384960	+	0.922933i	$0.625785\pi$
$602$	8218.12	0.556388
$603$	−3051.14	−0.206056
$604$	−44.3712	−0.00298914
$605$	−605.000	−0.0406558
$606$	−1855.07	−0.124352
$607$	−26032.5	−1.74074	−0.870369	−	0.492399i	$-0.836120\pi$
$607$	−26032.5	−1.74074	−0.870369	+	0.492399i	$0.836120\pi$
$608$	8375.87	0.558695
$609$	−166.909	−0.0111059
$610$	10072.1	0.668536
$611$	−27376.1	−1.81263
$612$	−1070.74	−0.0707226
$613$	−4568.13	−0.300987	−0.150493	−	0.988611i	$-0.548086\pi$
$613$	−4568.13	−0.300987	−0.150493	+	0.988611i	$0.548086\pi$
$614$	−13791.1	−0.906457
$615$	4477.19	0.293557
$616$	−1661.17	−0.108653
$617$	−12755.9	−0.832308	−0.416154	−	0.909294i	$-0.636622\pi$
$617$	−12755.9	−0.832308	−0.416154	+	0.909294i	$0.636622\pi$
$618$	−8978.59	−0.584421
$619$	−1138.94	−0.0739545	−0.0369772	−	0.999316i	$-0.511773\pi$
$619$	−1138.94	−0.0739545	−0.0369772	+	0.999316i	$0.511773\pi$
$620$	37.8410	0.00245118
$621$	−5013.72	−0.323983
$622$	4586.24	0.295645
$623$	−886.205	−0.0569904
$624$	7430.85	0.476718
$625$	625.000	0.0400000
$626$	2072.49	0.132322
$627$	4301.69	0.273992
$628$	−496.607	−0.0315554
$629$	−34480.6	−2.18574
$630$	720.000	0.0455325
$631$	7997.36	0.504548	0.252274	−	0.967656i	$-0.418822\pi$
$631$	7997.36	0.504548	0.252274	+	0.967656i	$0.418822\pi$
$632$	−7490.91	−0.471475
$633$	12959.6	0.813742
$634$	−27522.7	−1.72408
$635$	4740.91	0.296279
$636$	725.255	0.0452173
$637$	14932.7	0.928814
$638$	−250.979	−0.0155742
$639$	10086.4	0.624430
$640$	4704.34	0.290555
$641$	−573.115	−0.0353146	−0.0176573	−	0.999844i	$-0.505621\pi$
$641$	−573.115	−0.0353146	−0.0176573	+	0.999844i	$0.505621\pi$
$642$	16190.2	0.995290
$643$	−16027.8	−0.983009	−0.491504	−	0.870875i	$-0.663553\pi$
$643$	−16027.8	−0.983009	−0.491504	+	0.870875i	$0.663553\pi$
$644$	1668.42	0.102089
$645$	7704.49	0.470332
$646$	27617.1	1.68201
$647$	−2622.74	−0.159367	−0.0796837	−	0.996820i	$-0.525391\pi$
$647$	−2622.74	−0.159367	−0.0796837	+	0.996820i	$0.525391\pi$
$648$	1958.34	0.118721
$649$	−6806.50	−0.411677
$650$	3145.79	0.189827
$651$	98.5908	0.00593560
$652$	−2763.97	−0.166020
$653$	3102.00	0.185897	0.0929484	−	0.995671i	$-0.470371\pi$
$653$	3102.00	0.185897	0.0929484	+	0.995671i	$0.470371\pi$
$654$	−3794.62	−0.226883
$655$	7424.19	0.442881
$656$	15050.3	0.895755
$657$	−1110.87	−0.0659652
$658$	−8916.73	−0.528283
$659$	−20840.2	−1.23190	−0.615948	−	0.787787i	$-0.711227\pi$
$659$	−20840.2	−1.23190	−0.615948	+	0.787787i	$0.711227\pi$
$660$	−237.344	−0.0139979
$661$	18242.9	1.07348	0.536738	−	0.843749i	$-0.319657\pi$
$661$	18242.9	1.07348	0.536738	+	0.843749i	$0.319657\pi$
$662$	−8707.03	−0.511191
$663$	−12188.7	−0.713980
$664$	−24690.2	−1.44302
$665$	4071.10	0.237399
$666$	9611.06	0.559191
$667$	1654.01	0.0960171
$668$	−247.841	−0.0143551
$669$	−11513.2	−0.665361
$670$	−4342.03	−0.250369
$671$	−8650.46	−0.497686
$672$	−1204.05	−0.0691177
$673$	−12746.6	−0.730084	−0.365042	−	0.930991i	$-0.618945\pi$
$673$	−12746.6	−0.730084	−0.365042	+	0.930991i	$0.618945\pi$
$674$	30328.7	1.73326
$675$	675.000	0.0384900
$676$	−310.819	−0.0176843
$677$	−7683.11	−0.436168	−0.218084	−	0.975930i	$-0.569981\pi$
$677$	−7683.11	−0.436168	−0.218084	+	0.975930i	$0.569981\pi$
$678$	−1306.39	−0.0739995
$679$	4986.63	0.281840
$680$	−9998.23	−0.563845
$681$	−15011.1	−0.844681
$682$	148.250	0.00832373
$683$	−21397.1	−1.19874	−0.599368	−	0.800473i	$-0.704582\pi$
$683$	−21397.1	−1.19874	−0.599368	+	0.800473i	$0.704582\pi$
$684$	1687.57	0.0943359
$685$	−3424.64	−0.191020
$686$	10351.8	0.576140
$687$	−832.124	−0.0462118
$688$	25899.0	1.43516
$689$	8255.84	0.456491
$690$	−7134.94	−0.393656
$691$	26137.5	1.43895	0.719477	−	0.694516i	$-0.244381\pi$
$691$	26137.5	1.43895	0.719477	+	0.694516i	$0.244381\pi$
$692$	1474.83	0.0810181
$693$	−618.375	−0.0338963
$694$	5319.50	0.290959
$695$	−4152.41	−0.226633
$696$	−646.051	−0.0351846
$697$	−24686.7	−1.34157
$698$	−14952.7	−0.810845
$699$	6809.72	0.368479
$700$	−224.621	−0.0121284
$701$	13382.4	0.721036	0.360518	−	0.932752i	$-0.382600\pi$
$701$	13382.4	0.721036	0.360518	+	0.932752i	$0.382600\pi$
$702$	3397.45	0.182662
$703$	54343.9	2.91553
$704$	−6247.76	−0.334476
$705$	−8359.43	−0.446574
$706$	6208.27	0.330951
$707$	1507.83	0.0802092
$708$	−2670.22	−0.141741
$709$	18164.6	0.962179	0.481090	−	0.876671i	$-0.340241\pi$
$709$	18164.6	0.962179	0.481090	+	0.876671i	$0.340241\pi$
$710$	14353.8	0.758715
$711$	−2788.52	−0.147085
$712$	−3430.21	−0.180552
$713$	−977.000	−0.0513169
$714$	−3970.00	−0.208086
$715$	−2701.77	−0.141315
$716$	−2385.36	−0.124504
$717$	−4851.32	−0.252686
$718$	9944.50	0.516888
$719$	9665.62	0.501344	0.250672	−	0.968072i	$-0.419348\pi$
$719$	9665.62	0.501344	0.250672	+	0.968072i	$0.419348\pi$
$720$	2269.05	0.117448
$721$	7297.94	0.376962
$722$	−25956.7	−1.33796
$723$	16939.9	0.871371
$724$	2908.26	0.149288
$725$	−222.680	−0.0114071
$726$	−929.844	−0.0475341
$727$	−29779.6	−1.51921	−0.759605	−	0.650385i	$-0.774608\pi$
$727$	−29779.6	−1.51921	−0.759605	+	0.650385i	$0.774608\pi$
$728$	−7418.33	−0.377667
$729$	729.000	0.0370370
$730$	−1580.86	−0.0801511
$731$	−42481.7	−2.14944
$732$	−3393.61	−0.171354
$733$	35029.5	1.76513	0.882567	−	0.470187i	$-0.155814\pi$
$733$	35029.5	1.76513	0.882567	+	0.470187i	$0.155814\pi$
$734$	−14515.4	−0.729937
$735$	4559.77	0.228830
$736$	11931.7	0.597564
$737$	3729.17	0.186385
$738$	6881.13	0.343222
$739$	23297.3	1.15968	0.579842	−	0.814729i	$-0.303114\pi$
$739$	23297.3	1.15968	0.579842	+	0.814729i	$0.303114\pi$
$740$	−2998.40	−0.148950
$741$	19210.2	0.952368
$742$	2689.03	0.133042
$743$	21570.4	1.06506	0.532530	−	0.846411i	$-0.321241\pi$
$743$	21570.4	1.06506	0.532530	+	0.846411i	$0.321241\pi$
$744$	381.613	0.0188046
$745$	6068.21	0.298419
$746$	−447.684	−0.0219717
$747$	−9190.99	−0.450175
$748$	1308.69	0.0639710
$749$	−13159.6	−0.641980
$750$	960.582	0.0467673
$751$	28554.8	1.38746	0.693729	−	0.720236i	$-0.255966\pi$
$751$	28554.8	1.38746	0.693729	+	0.720236i	$0.255966\pi$
$752$	−28100.7	−1.36267
$753$	−18652.8	−0.902719
$754$	−1120.81	−0.0541344
$755$	−154.233	−0.00743458
$756$	−242.591	−0.0116706
$757$	7812.81	0.375114	0.187557	−	0.982254i	$-0.439943\pi$
$757$	7812.81	0.375114	0.187557	+	0.982254i	$0.439943\pi$
$758$	−647.268	−0.0310156
$759$	6127.87	0.293054
$760$	15757.9	0.752105
$761$	2875.13	0.136956	0.0684778	−	0.997653i	$-0.478186\pi$
$761$	2875.13	0.136956	0.0684778	+	0.997653i	$0.478186\pi$
$762$	7286.45	0.346405
$763$	3084.33	0.146344
$764$	−2071.69	−0.0981033
$765$	−3721.87	−0.175902
$766$	28214.3	1.33084
$767$	−30396.0	−1.43095
$768$	−6401.22	−0.300761
$769$	−27657.7	−1.29696	−0.648479	−	0.761233i	$-0.724594\pi$
$769$	−27657.7	−1.29696	−0.648479	+	0.761233i	$0.724594\pi$
$770$	−880.000	−0.0411857
$771$	23138.2	1.08081
$772$	4024.84	0.187639
$773$	−3929.35	−0.182832	−0.0914160	−	0.995813i	$-0.529139\pi$
$773$	−3929.35	−0.182832	−0.0914160	+	0.995813i	$0.529139\pi$
$774$	11841.3	0.549904
$775$	131.534	0.00609658
$776$	19301.6	0.892898
$777$	−7812.02	−0.360688
$778$	−20747.0	−0.956064
$779$	38908.0	1.78950
$780$	−1059.91	−0.0486552
$781$	−12327.8	−0.564818
$782$	39341.3	1.79903
$783$	−240.495	−0.0109765
$784$	15327.9	0.698247
$785$	−1726.19	−0.0784847
$786$	11410.5	0.517809
$787$	−21125.7	−0.956860	−0.478430	−	0.878126i	$-0.658794\pi$
$787$	−21125.7	−0.956860	−0.478430	+	0.878126i	$0.658794\pi$
$788$	−660.166	−0.0298445
$789$	619.040	0.0279321
$790$	−3968.30	−0.178716
$791$	1061.86	0.0477310
$792$	−2393.53	−0.107387
$793$	−38630.7	−1.72991
$794$	1087.00	0.0485847
$795$	2520.97	0.112465
$796$	3410.61	0.151867
$797$	11696.3	0.519828	0.259914	−	0.965632i	$-0.416306\pi$
$797$	11696.3	0.519828	0.259914	+	0.965632i	$0.416306\pi$
$798$	6257.00	0.277563
$799$	46093.0	2.04087
$800$	−1606.37	−0.0709921
$801$	−1276.91	−0.0563263
$802$	15123.9	0.665888
$803$	1357.73	0.0596678
$804$	1462.97	0.0641727
$805$	5799.39	0.253915
$806$	662.045	0.0289324
$807$	5137.42	0.224096
$808$	5836.34	0.254111
$809$	14310.2	0.621902	0.310951	−	0.950426i	$-0.399352\pi$
$809$	14310.2	0.621902	0.310951	+	0.950426i	$0.399352\pi$
$810$	1037.43	0.0450019
$811$	21697.9	0.939477	0.469739	−	0.882806i	$-0.344348\pi$
$811$	21697.9	0.939477	0.469739	+	0.882806i	$0.344348\pi$
$812$	80.0299	0.00345874
$813$	−1431.24	−0.0617416
$814$	−11746.9	−0.505807
$815$	−9607.46	−0.412926
$816$	−12511.3	−0.536743
$817$	66954.1	2.86711
$818$	−3510.54	−0.150053
$819$	−2761.50	−0.117820
$820$	−2146.73	−0.0914233
$821$	3613.00	0.153587	0.0767934	−	0.997047i	$-0.475532\pi$
$821$	3613.00	0.153587	0.0767934	+	0.997047i	$0.475532\pi$
$822$	−5263.44	−0.223338
$823$	−4763.98	−0.201776	−0.100888	−	0.994898i	$-0.532168\pi$
$823$	−4763.98	−0.201776	−0.100888	+	0.994898i	$0.532168\pi$
$824$	28248.0	1.19425
$825$	−825.000	−0.0348155
$826$	−9900.36	−0.417043
$827$	−33571.7	−1.41161	−0.705806	−	0.708405i	$-0.749415\pi$
$827$	−33571.7	−1.41161	−0.705806	+	0.708405i	$0.749415\pi$
$828$	2403.99	0.100899
$829$	17980.5	0.753303	0.376652	−	0.926355i	$-0.377075\pi$
$829$	17980.5	0.753303	0.376652	+	0.926355i	$0.377075\pi$
$830$	−13079.6	−0.546986
$831$	12850.4	0.536434
$832$	−27900.9	−1.16261
$833$	−25142.1	−1.04576
$834$	−6381.98	−0.264976
$835$	−861.486	−0.0357041
$836$	−2062.58	−0.0853301
$837$	142.057	0.00586643
$838$	−3249.91	−0.133969
$839$	−40139.5	−1.65169	−0.825847	−	0.563895i	$-0.809302\pi$
$839$	−40139.5	−1.65169	−0.825847	+	0.563895i	$0.809302\pi$
$840$	−2265.23	−0.0930450
$841$	−24309.7	−0.996747
$842$	31358.4	1.28347
$843$	10433.4	0.426269
$844$	−6213.91	−0.253426
$845$	−1080.40	−0.0439844
$846$	−12847.9	−0.522127
$847$	755.792	0.0306603
$848$	8474.36	0.343173
$849$	−19704.8	−0.796546
$850$	−5296.54	−0.213729
$851$	77414.4	3.11837
$852$	−4836.24	−0.194468
$853$	−15369.2	−0.616919	−0.308459	−	0.951237i	$-0.599813\pi$
$853$	−15369.2	−0.616919	−0.308459	+	0.951237i	$0.599813\pi$
$854$	−12582.5	−0.504173
$855$	5865.94	0.234633
$856$	−50936.8	−2.03386
$857$	10324.9	0.411541	0.205770	−	0.978600i	$-0.434030\pi$
$857$	10324.9	0.411541	0.205770	+	0.978600i	$0.434030\pi$
$858$	−4152.44	−0.165224
$859$	−27112.5	−1.07691	−0.538455	−	0.842655i	$-0.680992\pi$
$859$	−27112.5	−1.07691	−0.538455	+	0.842655i	$0.680992\pi$
$860$	−3694.17	−0.146477
$861$	−5593.09	−0.221384
$862$	−20620.8	−0.814787
$863$	30463.6	1.20161	0.600807	−	0.799394i	$-0.294846\pi$
$863$	30463.6	1.20161	0.600807	+	0.799394i	$0.294846\pi$
$864$	−1734.88	−0.0683122
$865$	5126.46	0.201508
$866$	42434.0	1.66509
$867$	5783.00	0.226529
$868$	−47.2726	−0.00184854
$869$	3408.19	0.133044
$870$	−342.244	−0.0133370
$871$	16653.5	0.647855
$872$	11938.4	0.463631
$873$	7185.10	0.278555
$874$	−62004.6	−2.39970
$875$	−780.776	−0.0301658
$876$	532.642	0.0205437
$877$	−5086.12	−0.195833	−0.0979167	−	0.995195i	$-0.531218\pi$
$877$	−5086.12	−0.195833	−0.0979167	+	0.995195i	$0.531218\pi$
$878$	−12054.2	−0.463335
$879$	25056.9	0.961487
$880$	−2773.28	−0.106236
$881$	−10625.5	−0.406338	−0.203169	−	0.979144i	$-0.565124\pi$
$881$	−10625.5	−0.406338	−0.203169	+	0.979144i	$0.565124\pi$
$882$	7008.06	0.267544
$883$	13112.2	0.499728	0.249864	−	0.968281i	$-0.419614\pi$
$883$	13112.2	0.499728	0.249864	+	0.968281i	$0.419614\pi$
$884$	5844.25	0.222357
$885$	−9281.59	−0.352539
$886$	−38664.0	−1.46607
$887$	−14442.8	−0.546719	−0.273360	−	0.961912i	$-0.588135\pi$
$887$	−14442.8	−0.546719	−0.273360	+	0.961912i	$0.588135\pi$
$888$	−30237.8	−1.14270
$889$	−5922.54	−0.223437
$890$	−1817.15	−0.0684393
$891$	−891.000	−0.0335013
$892$	5520.38	0.207215
$893$	−72645.8	−2.72228
$894$	9326.43	0.348906
$895$	−8291.44	−0.309667
$896$	−5876.86	−0.219121
$897$	27365.5	1.01863
$898$	−2493.61	−0.0926648
$899$	−46.8641	−0.00173860
$900$	−323.651	−0.0119871
$901$	−13900.3	−0.513970
$902$	−8410.27	−0.310456
$903$	−9624.77	−0.354698
$904$	4110.10	0.151217
$905$	10109.0	0.371310
$906$	−237.045	−0.00869239
$907$	−44981.9	−1.64675	−0.823374	−	0.567499i	$-0.807911\pi$
$907$	−44981.9	−1.64675	−0.823374	+	0.567499i	$0.807911\pi$
$908$	7197.57	0.263062
$909$	2172.60	0.0792745
$910$	−3929.85	−0.143157
$911$	6841.96	0.248830	0.124415	−	0.992230i	$-0.460295\pi$
$911$	6841.96	0.248830	0.124415	+	0.992230i	$0.460295\pi$
$912$	19718.7	0.715954
$913$	11233.4	0.407199
$914$	−160.501	−0.00580843
$915$	−11796.1	−0.426193
$916$	398.989	0.0143919
$917$	−9274.61	−0.333996
$918$	−5720.27	−0.205661
$919$	−4753.54	−0.170625	−0.0853127	−	0.996354i	$-0.527189\pi$
$919$	−4753.54	−0.170625	−0.0853127	+	0.996354i	$0.527189\pi$
$920$	22447.6	0.804430
$921$	16151.7	0.577868
$922$	30395.9	1.08572
$923$	−55052.7	−1.96325
$924$	296.500	0.0105564
$925$	−10422.3	−0.370470
$926$	33671.2	1.19493
$927$	10515.4	0.372569
$928$	572.330	0.0202453
$929$	−7507.93	−0.265153	−0.132576	−	0.991173i	$-0.542325\pi$
$929$	−7507.93	−0.265153	−0.132576	+	0.991173i	$0.542325\pi$
$930$	202.159	0.00712802
$931$	39625.7	1.39493
$932$	−3265.14	−0.114757
$933$	−5371.24	−0.188474
$934$	26068.3	0.913256
$935$	4548.96	0.159109
$936$	−10688.9	−0.373266
$937$	8540.47	0.297764	0.148882	−	0.988855i	$-0.452433\pi$
$937$	8540.47	0.297764	0.148882	+	0.988855i	$0.452433\pi$
$938$	5424.24	0.188814
$939$	−2427.23	−0.0843552
$940$	4008.20	0.139078
$941$	9101.13	0.315290	0.157645	−	0.987496i	$-0.449610\pi$
$941$	9101.13	0.315290	0.157645	+	0.987496i	$0.449610\pi$
$942$	−2653.04	−0.0917630
$943$	55425.5	1.91400
$944$	−31200.6	−1.07573
$945$	−843.239	−0.0290270
$946$	−14472.7	−0.497407
$947$	47540.0	1.63130	0.815650	−	0.578546i	$-0.196380\pi$
$947$	47540.0	1.63130	0.815650	+	0.578546i	$0.196380\pi$
$948$	1337.04	0.0458072
$949$	6063.26	0.207399
$950$	8347.73	0.285091
$951$	32233.6	1.09910
$952$	12490.2	0.425221
$953$	47370.7	1.61016	0.805082	−	0.593164i	$-0.202121\pi$
$953$	47370.7	1.61016	0.805082	+	0.593164i	$0.202121\pi$
$954$	3874.55	0.131492
$955$	−7201.12	−0.244003
$956$	2326.12	0.0786947
$957$	293.938	0.00992859
$958$	−8789.33	−0.296420
$959$	4278.20	0.144057
$960$	−8519.67	−0.286428
$961$	−29763.3	−0.999071
$962$	−52458.4	−1.75813
$963$	−18961.4	−0.634498
$964$	−8122.38	−0.271374
$965$	13990.2	0.466696
$966$	8913.27	0.296874
$967$	−36171.6	−1.20290	−0.601448	−	0.798912i	$-0.705409\pi$
$967$	−36171.6	−1.20290	−0.601448	+	0.798912i	$0.705409\pi$
$968$	2925.43	0.0971351
$969$	−32344.1	−1.07228
$970$	10225.0	0.338459
$971$	−31713.2	−1.04812	−0.524060	−	0.851681i	$-0.675583\pi$
$971$	−31713.2	−1.04812	−0.524060	+	0.851681i	$0.675583\pi$
$972$	−349.543	−0.0115346
$973$	5187.37	0.170914
$974$	7257.40	0.238750
$975$	−3684.23	−0.121015
$976$	−39653.1	−1.30048
$977$	22800.5	0.746626	0.373313	−	0.927706i	$-0.378222\pi$
$977$	22800.5	0.746626	0.373313	+	0.927706i	$0.378222\pi$
$978$	−14766.0	−0.482786
$979$	1560.67	0.0509490
$980$	−2186.33	−0.0712651
$981$	4444.12	0.144638
$982$	6832.41	0.222027
$983$	−44597.4	−1.44704	−0.723518	−	0.690305i	$-0.757476\pi$
$983$	−44597.4	−1.44704	−0.723518	+	0.690305i	$0.757476\pi$
$984$	−21649.1	−0.701369
$985$	−2294.72	−0.0742292
$986$	1887.10	0.0609507
$987$	10443.0	0.336781
$988$	−9210.95	−0.296599
$989$	95378.1	3.06658
$990$	−1267.97	−0.0407057
$991$	−34788.1	−1.11512	−0.557558	−	0.830138i	$-0.688261\pi$
$991$	−34788.1	−1.11512	−0.557558	+	0.830138i	$0.688261\pi$
$992$	−338.068	−0.0108202
$993$	10197.4	0.325885
$994$	−17931.3	−0.572180
$995$	11855.2	0.377723
$996$	4406.92	0.140199
$997$	−20360.5	−0.646765	−0.323383	−	0.946268i	$-0.604820\pi$
$997$	−20360.5	−0.646765	−0.323383	+	0.946268i	$0.604820\pi$
$998$	28528.0	0.904849
$999$	−11256.1	−0.356485

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	165.4.a.c.1.1	✓	2
3.2	odd	2		495.4.a.d.1.2		2
5.2	odd	4		825.4.c.j.199.1		4
5.3	odd	4		825.4.c.j.199.4		4
5.4	even	2		825.4.a.m.1.2		2
11.10	odd	2		1815.4.a.n.1.2		2
15.14	odd	2		2475.4.a.n.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.4.a.c.1.1	✓	2	1.1	even	1	trivial
495.4.a.d.1.2		2	3.2	odd	2
825.4.a.m.1.2		2	5.4	even	2
825.4.c.j.199.1		4	5.2	odd	4
825.4.c.j.199.4		4	5.3	odd	4
1815.4.a.n.1.2		2	11.10	odd	2
2475.4.a.n.1.1		2	15.14	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:	\( N \)	\(=\)	\( 165 = 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	165.a (trivial)

\(f(q)\)	\(=\)	\(q-2.56155 q^{2} +3.00000 q^{3} -1.43845 q^{4} -5.00000 q^{5} -7.68466 q^{6} +6.24621 q^{7} +24.1771 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-2.56155 q^{2} +3.00000 q^{3} -1.43845 q^{4} -5.00000 q^{5} -7.68466 q^{6} +6.24621 q^{7} +24.1771 q^{8} +9.00000 q^{9} +12.8078 q^{10} -11.0000 q^{11} -4.31534 q^{12} -49.1231 q^{13} -16.0000 q^{14} -15.0000 q^{15} -50.4233 q^{16} +82.7083 q^{17} -23.0540 q^{18} -130.354 q^{19} +7.19224 q^{20} +18.7386 q^{21} +28.1771 q^{22} -185.693 q^{23} +72.5312 q^{24} +25.0000 q^{25} +125.831 q^{26} +27.0000 q^{27} -8.98485 q^{28} -8.90720 q^{29} +38.4233 q^{30} +5.26137 q^{31} -64.2547 q^{32} -33.0000 q^{33} -211.862 q^{34} -31.2311 q^{35} -12.9460 q^{36} -416.894 q^{37} +333.909 q^{38} -147.369 q^{39} -120.885 q^{40} -298.479 q^{41} -48.0000 q^{42} -513.633 q^{43} +15.8229 q^{44} -45.0000 q^{45} +475.663 q^{46} +557.295 q^{47} -151.270 q^{48} -303.985 q^{49} -64.0388 q^{50} +248.125 q^{51} +70.6610 q^{52} -168.064 q^{53} -69.1619 q^{54} +55.0000 q^{55} +151.015 q^{56} -391.062 q^{57} +22.8163 q^{58} +618.773 q^{59} +21.5767 q^{60} +786.405 q^{61} -13.4773 q^{62} +56.2159 q^{63} +567.978 q^{64} +245.616 q^{65} +84.5312 q^{66} -339.015 q^{67} -118.972 q^{68} -557.080 q^{69} +80.0000 q^{70} +1120.71 q^{71} +217.594 q^{72} -123.430 q^{73} +1067.90 q^{74} +75.0000 q^{75} +187.508 q^{76} -68.7083 q^{77} +377.494 q^{78} -309.835 q^{79} +252.116 q^{80} +81.0000 q^{81} +764.570 q^{82} -1021.22 q^{83} -26.9545 q^{84} -413.542 q^{85} +1315.70 q^{86} -26.7216 q^{87} -265.948 q^{88} -141.879 q^{89} +115.270 q^{90} -306.833 q^{91} +267.110 q^{92} +15.7841 q^{93} -1427.54 q^{94} +651.771 q^{95} -192.764 q^{96} +798.345 q^{97} +778.673 q^{98} -99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} + 6 q^{3} - 7 q^{4} - 10 q^{5} - 3 q^{6} - 4 q^{7} + 3 q^{8} + 18 q^{9}+O(q^{10}) \) 2 * q - q^2 + 6 * q^3 - 7 * q^4 - 10 * q^5 - 3 * q^6 - 4 * q^7 + 3 * q^8 + 18 * q^9	\( 2 q - q^{2} + 6 q^{3} - 7 q^{4} - 10 q^{5} - 3 q^{6} - 4 q^{7} + 3 q^{8} + 18 q^{9} + 5 q^{10} - 22 q^{11} - 21 q^{12} - 90 q^{13} - 32 q^{14} - 30 q^{15} - 39 q^{16} - 16 q^{17} - 9 q^{18} - 170 q^{19} + 35 q^{20} - 12 q^{21} + 11 q^{22} - 124 q^{23} + 9 q^{24} + 50 q^{25} + 62 q^{26} + 54 q^{27} + 48 q^{28} - 158 q^{29} + 15 q^{30} + 60 q^{31} + 123 q^{32} - 66 q^{33} - 366 q^{34} + 20 q^{35} - 63 q^{36} - 372 q^{37} + 272 q^{38} - 270 q^{39} - 15 q^{40} + 38 q^{41} - 96 q^{42} - 516 q^{43} + 77 q^{44} - 90 q^{45} + 572 q^{46} + 224 q^{47} - 117 q^{48} - 542 q^{49} - 25 q^{50} - 48 q^{51} + 298 q^{52} + 472 q^{53} - 27 q^{54} + 110 q^{55} + 368 q^{56} - 510 q^{57} - 210 q^{58} + 248 q^{59} + 105 q^{60} + 72 q^{61} + 72 q^{62} - 36 q^{63} + 769 q^{64} + 450 q^{65} + 33 q^{66} - 744 q^{67} + 430 q^{68} - 372 q^{69} + 160 q^{70} + 2060 q^{71} + 27 q^{72} - 486 q^{73} + 1138 q^{74} + 150 q^{75} + 408 q^{76} + 44 q^{77} + 186 q^{78} + 642 q^{79} + 195 q^{80} + 162 q^{81} + 1290 q^{82} - 286 q^{83} + 144 q^{84} + 80 q^{85} + 1312 q^{86} - 474 q^{87} - 33 q^{88} + 244 q^{89} + 45 q^{90} + 112 q^{91} - 76 q^{92} + 180 q^{93} - 1948 q^{94} + 850 q^{95} + 369 q^{96} - 168 q^{97} + 407 q^{98} - 198 q^{99}+O(q^{100}) \) 2 * q - q^2 + 6 * q^3 - 7 * q^4 - 10 * q^5 - 3 * q^6 - 4 * q^7 + 3 * q^8 + 18 * q^9 + 5 * q^10 - 22 * q^11 - 21 * q^12 - 90 * q^13 - 32 * q^14 - 30 * q^15 - 39 * q^16 - 16 * q^17 - 9 * q^18 - 170 * q^19 + 35 * q^20 - 12 * q^21 + 11 * q^22 - 124 * q^23 + 9 * q^24 + 50 * q^25 + 62 * q^26 + 54 * q^27 + 48 * q^28 - 158 * q^29 + 15 * q^30 + 60 * q^31 + 123 * q^32 - 66 * q^33 - 366 * q^34 + 20 * q^35 - 63 * q^36 - 372 * q^37 + 272 * q^38 - 270 * q^39 - 15 * q^40 + 38 * q^41 - 96 * q^42 - 516 * q^43 + 77 * q^44 - 90 * q^45 + 572 * q^46 + 224 * q^47 - 117 * q^48 - 542 * q^49 - 25 * q^50 - 48 * q^51 + 298 * q^52 + 472 * q^53 - 27 * q^54 + 110 * q^55 + 368 * q^56 - 510 * q^57 - 210 * q^58 + 248 * q^59 + 105 * q^60 + 72 * q^61 + 72 * q^62 - 36 * q^63 + 769 * q^64 + 450 * q^65 + 33 * q^66 - 744 * q^67 + 430 * q^68 - 372 * q^69 + 160 * q^70 + 2060 * q^71 + 27 * q^72 - 486 * q^73 + 1138 * q^74 + 150 * q^75 + 408 * q^76 + 44 * q^77 + 186 * q^78 + 642 * q^79 + 195 * q^80 + 162 * q^81 + 1290 * q^82 - 286 * q^83 + 144 * q^84 + 80 * q^85 + 1312 * q^86 - 474 * q^87 - 33 * q^88 + 244 * q^89 + 45 * q^90 + 112 * q^91 - 76 * q^92 + 180 * q^93 - 1948 * q^94 + 850 * q^95 + 369 * q^96 - 168 * q^97 + 407 * q^98 - 198 * q^99

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