LMFDB - Embedded newform 6015.2.a.d.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6015,2,Mod(1,6015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6015, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("6015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6015 = 3 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6015.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:	$48.0300168158$
Analytic rank:	$1$
Dimension:	$29$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	6015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.0716495 q^{2} -1.00000 q^{3} -1.99487 q^{4} +1.00000 q^{5} +0.0716495 q^{6} +4.62140 q^{7} +0.286230 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.0716495 q^{2} -1.00000 q^{3} -1.99487 q^{4} +1.00000 q^{5} +0.0716495 q^{6} +4.62140 q^{7} +0.286230 q^{8} +1.00000 q^{9} -0.0716495 q^{10} +2.89881 q^{11} +1.99487 q^{12} +1.52681 q^{13} -0.331121 q^{14} -1.00000 q^{15} +3.96922 q^{16} -0.0951221 q^{17} -0.0716495 q^{18} -1.55937 q^{19} -1.99487 q^{20} -4.62140 q^{21} -0.207699 q^{22} -2.96330 q^{23} -0.286230 q^{24} +1.00000 q^{25} -0.109395 q^{26} -1.00000 q^{27} -9.21907 q^{28} -10.5800 q^{29} +0.0716495 q^{30} -7.83632 q^{31} -0.856853 q^{32} -2.89881 q^{33} +0.00681545 q^{34} +4.62140 q^{35} -1.99487 q^{36} -8.07372 q^{37} +0.111728 q^{38} -1.52681 q^{39} +0.286230 q^{40} -7.05677 q^{41} +0.331121 q^{42} -8.61827 q^{43} -5.78275 q^{44} +1.00000 q^{45} +0.212319 q^{46} +1.46262 q^{47} -3.96922 q^{48} +14.3573 q^{49} -0.0716495 q^{50} +0.0951221 q^{51} -3.04579 q^{52} -10.8212 q^{53} +0.0716495 q^{54} +2.89881 q^{55} +1.32278 q^{56} +1.55937 q^{57} +0.758054 q^{58} +0.411730 q^{59} +1.99487 q^{60} +6.82849 q^{61} +0.561468 q^{62} +4.62140 q^{63} -7.87706 q^{64} +1.52681 q^{65} +0.207699 q^{66} -4.00504 q^{67} +0.189756 q^{68} +2.96330 q^{69} -0.331121 q^{70} -15.9839 q^{71} +0.286230 q^{72} +3.79724 q^{73} +0.578478 q^{74} -1.00000 q^{75} +3.11074 q^{76} +13.3966 q^{77} +0.109395 q^{78} +2.51144 q^{79} +3.96922 q^{80} +1.00000 q^{81} +0.505614 q^{82} -0.973947 q^{83} +9.21907 q^{84} -0.0951221 q^{85} +0.617494 q^{86} +10.5800 q^{87} +0.829728 q^{88} +13.2138 q^{89} -0.0716495 q^{90} +7.05601 q^{91} +5.91138 q^{92} +7.83632 q^{93} -0.104796 q^{94} -1.55937 q^{95} +0.856853 q^{96} +0.566932 q^{97} -1.02869 q^{98} +2.89881 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 29 q - q^{2} - 29 q^{3} + 27 q^{4} + 29 q^{5} + q^{6} + 2 q^{7} - 6 q^{8} + 29 q^{9}+O(q^{10}) $ 29 * q - q^2 - 29 * q^3 + 27 * q^4 + 29 * q^5 + q^6 + 2 * q^7 - 6 * q^8 + 29 * q^9	\( 29 q - q^{2} - 29 q^{3} + 27 q^{4} + 29 q^{5} + q^{6} + 2 q^{7} - 6 q^{8} + 29 q^{9} - q^{10} - 21 q^{11} - 27 q^{12} - 8 q^{13} - 30 q^{14} - 29 q^{15} + 23 q^{16} - 28 q^{17} - q^{18} - 9 q^{19} + 27 q^{20} - 2 q^{21} - 9 q^{22} + 6 q^{24} + 29 q^{25} - 34 q^{26} - 29 q^{27} + 6 q^{28} - 61 q^{29} + q^{30} - 19 q^{31} - 8 q^{32} + 21 q^{33} - 16 q^{34} + 2 q^{35} + 27 q^{36} - 4 q^{37} + 4 q^{38} + 8 q^{39} - 6 q^{40} - 85 q^{41} + 30 q^{42} + 29 q^{43} - 69 q^{44} + 29 q^{45} - 35 q^{46} - 2 q^{47} - 23 q^{48} + q^{49} - q^{50} + 28 q^{51} - 28 q^{52} - 5 q^{53} + q^{54} - 21 q^{55} - 97 q^{56} + 9 q^{57} + 6 q^{58} - 43 q^{59} - 27 q^{60} - 59 q^{61} - 17 q^{62} + 2 q^{63} - 6 q^{64} - 8 q^{65} + 9 q^{66} + 28 q^{67} - 44 q^{68} - 30 q^{70} - 44 q^{71} - 6 q^{72} - 41 q^{73} - 50 q^{74} - 29 q^{75} - 62 q^{76} - 20 q^{77} + 34 q^{78} - 25 q^{79} + 23 q^{80} + 29 q^{81} - 29 q^{82} - 7 q^{83} - 6 q^{84} - 28 q^{85} - 43 q^{86} + 61 q^{87} - 3 q^{88} - 109 q^{89} - q^{90} - q^{91} - 11 q^{92} + 19 q^{93} - 20 q^{94} - 9 q^{95} + 8 q^{96} - 51 q^{97} - 12 q^{98} - 21 q^{99}+O(q^{100}) \) 29 * q - q^2 - 29 * q^3 + 27 * q^4 + 29 * q^5 + q^6 + 2 * q^7 - 6 * q^8 + 29 * q^9 - q^10 - 21 * q^11 - 27 * q^12 - 8 * q^13 - 30 * q^14 - 29 * q^15 + 23 * q^16 - 28 * q^17 - q^18 - 9 * q^19 + 27 * q^20 - 2 * q^21 - 9 * q^22 + 6 * q^24 + 29 * q^25 - 34 * q^26 - 29 * q^27 + 6 * q^28 - 61 * q^29 + q^30 - 19 * q^31 - 8 * q^32 + 21 * q^33 - 16 * q^34 + 2 * q^35 + 27 * q^36 - 4 * q^37 + 4 * q^38 + 8 * q^39 - 6 * q^40 - 85 * q^41 + 30 * q^42 + 29 * q^43 - 69 * q^44 + 29 * q^45 - 35 * q^46 - 2 * q^47 - 23 * q^48 + q^49 - q^50 + 28 * q^51 - 28 * q^52 - 5 * q^53 + q^54 - 21 * q^55 - 97 * q^56 + 9 * q^57 + 6 * q^58 - 43 * q^59 - 27 * q^60 - 59 * q^61 - 17 * q^62 + 2 * q^63 - 6 * q^64 - 8 * q^65 + 9 * q^66 + 28 * q^67 - 44 * q^68 - 30 * q^70 - 44 * q^71 - 6 * q^72 - 41 * q^73 - 50 * q^74 - 29 * q^75 - 62 * q^76 - 20 * q^77 + 34 * q^78 - 25 * q^79 + 23 * q^80 + 29 * q^81 - 29 * q^82 - 7 * q^83 - 6 * q^84 - 28 * q^85 - 43 * q^86 + 61 * q^87 - 3 * q^88 - 109 * q^89 - q^90 - q^91 - 11 * q^92 + 19 * q^93 - 20 * q^94 - 9 * q^95 + 8 * q^96 - 51 * q^97 - 12 * q^98 - 21 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−0.0716495	−0.0506638	−0.0253319	−	0.999679i	$-0.508064\pi$
$2$	−0.0716495	−0.0506638	−0.0253319	+	0.999679i	$0.508064\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.99487	−0.997433
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.0716495	0.0292508
$7$	4.62140	1.74672	0.873362	−	0.487072i	$-0.161935\pi$
$7$	4.62140	1.74672	0.873362	+	0.487072i	$0.161935\pi$
$8$	0.286230	0.101198
$9$	1.00000	0.333333
$10$	−0.0716495	−0.0226576
$11$	2.89881	0.874026	0.437013	−	0.899455i	$-0.356036\pi$
$11$	2.89881	0.874026	0.437013	+	0.899455i	$0.356036\pi$
$12$	1.99487	0.575868
$13$	1.52681	0.423462	0.211731	−	0.977328i	$-0.432090\pi$
$13$	1.52681	0.423462	0.211731	+	0.977328i	$0.432090\pi$
$14$	−0.331121	−0.0884957
$15$	−1.00000	−0.258199
$16$	3.96922	0.992306
$17$	−0.0951221	−0.0230705	−0.0115352	−	0.999933i	$-0.503672\pi$
$17$	−0.0951221	−0.0230705	−0.0115352	+	0.999933i	$0.503672\pi$
$18$	−0.0716495	−0.0168879
$19$	−1.55937	−0.357745	−0.178873	−	0.983872i	$-0.557245\pi$
$19$	−1.55937	−0.357745	−0.178873	+	0.983872i	$0.557245\pi$
$20$	−1.99487	−0.446066
$21$	−4.62140	−1.00847
$22$	−0.207699	−0.0442815
$23$	−2.96330	−0.617890	−0.308945	−	0.951080i	$-0.599976\pi$
$23$	−2.96330	−0.617890	−0.308945	+	0.951080i	$0.599976\pi$
$24$	−0.286230	−0.0584265
$25$	1.00000	0.200000
$26$	−0.109395	−0.0214542
$27$	−1.00000	−0.192450
$28$	−9.21907	−1.74224
$29$	−10.5800	−1.96466	−0.982331	−	0.187151i	$-0.940075\pi$
$29$	−10.5800	−1.96466	−0.982331	+	0.187151i	$0.940075\pi$
$30$	0.0716495	0.0130813
$31$	−7.83632	−1.40744	−0.703722	−	0.710475i	$-0.748480\pi$
$31$	−7.83632	−1.40744	−0.703722	+	0.710475i	$0.748480\pi$
$32$	−0.856853	−0.151472
$33$	−2.89881	−0.504619
$34$	0.00681545	0.00116884
$35$	4.62140	0.781158
$36$	−1.99487	−0.332478
$37$	−8.07372	−1.32731	−0.663656	−	0.748038i	$-0.730996\pi$
$37$	−8.07372	−1.32731	−0.663656	+	0.748038i	$0.730996\pi$
$38$	0.111728	0.0181247
$39$	−1.52681	−0.244486
$40$	0.286230	0.0452570
$41$	−7.05677	−1.10208	−0.551041	−	0.834478i	$-0.685769\pi$
$41$	−7.05677	−1.10208	−0.551041	+	0.834478i	$0.685769\pi$
$42$	0.331121	0.0510930
$43$	−8.61827	−1.31427	−0.657137	−	0.753771i	$-0.728233\pi$
$43$	−8.61827	−1.31427	−0.657137	+	0.753771i	$0.728233\pi$
$44$	−5.78275	−0.871782
$45$	1.00000	0.149071
$46$	0.212319	0.0313047
$47$	1.46262	0.213345	0.106673	−	0.994294i	$-0.465980\pi$
$47$	1.46262	0.213345	0.106673	+	0.994294i	$0.465980\pi$
$48$	−3.96922	−0.572908
$49$	14.3573	2.05104
$50$	−0.0716495	−0.0101328
$51$	0.0951221	0.0133198
$52$	−3.04579	−0.422375
$53$	−10.8212	−1.48641	−0.743205	−	0.669064i	$-0.766695\pi$
$53$	−10.8212	−1.48641	−0.743205	+	0.669064i	$0.766695\pi$
$54$	0.0716495	0.00975026
$55$	2.89881	0.390876
$56$	1.32278	0.176764
$57$	1.55937	0.206544
$58$	0.758054	0.0995373
$59$	0.411730	0.0536027	0.0268013	−	0.999641i	$-0.491468\pi$
$59$	0.411730	0.0536027	0.0268013	+	0.999641i	$0.491468\pi$
$60$	1.99487	0.257536
$61$	6.82849	0.874299	0.437150	−	0.899389i	$-0.355988\pi$
$61$	6.82849	0.874299	0.437150	+	0.899389i	$0.355988\pi$
$62$	0.561468	0.0713066
$63$	4.62140	0.582241
$64$	−7.87706	−0.984632
$65$	1.52681	0.189378
$66$	0.207699	0.0255659
$67$	−4.00504	−0.489293	−0.244647	−	0.969612i	$-0.578672\pi$
$67$	−4.00504	−0.489293	−0.244647	+	0.969612i	$0.578672\pi$
$68$	0.189756	0.0230113
$69$	2.96330	0.356739
$70$	−0.331121	−0.0395765
$71$	−15.9839	−1.89694	−0.948470	−	0.316865i	$-0.897370\pi$
$71$	−15.9839	−1.89694	−0.948470	+	0.316865i	$0.897370\pi$
$72$	0.286230	0.0337325
$73$	3.79724	0.444434	0.222217	−	0.974997i	$-0.428671\pi$
$73$	3.79724	0.444434	0.222217	+	0.974997i	$0.428671\pi$
$74$	0.578478	0.0672467
$75$	−1.00000	−0.115470
$76$	3.11074	0.356827
$77$	13.3966	1.52668
$78$	0.109395	0.0123866
$79$	2.51144	0.282559	0.141279	−	0.989970i	$-0.454878\pi$
$79$	2.51144	0.282559	0.141279	+	0.989970i	$0.454878\pi$
$80$	3.96922	0.443773
$81$	1.00000	0.111111
$82$	0.505614	0.0558357
$83$	−0.973947	−0.106905	−0.0534523	−	0.998570i	$-0.517022\pi$
$83$	−0.973947	−0.106905	−0.0534523	+	0.998570i	$0.517022\pi$
$84$	9.21907	1.00588
$85$	−0.0951221	−0.0103174
$86$	0.617494	0.0665861
$87$	10.5800	1.13430
$88$	0.829728	0.0884493
$89$	13.2138	1.40066	0.700330	−	0.713820i	$-0.253036\pi$
$89$	13.2138	1.40066	0.700330	+	0.713820i	$0.253036\pi$
$90$	−0.0716495	−0.00755252
$91$	7.05601	0.739670
$92$	5.91138	0.616304
$93$	7.83632	0.812589
$94$	−0.104796	−0.0108089
$95$	−1.55937	−0.159988
$96$	0.856853	0.0874522
$97$	0.566932	0.0575632	0.0287816	−	0.999586i	$-0.490837\pi$
$97$	0.566932	0.0575632	0.0287816	+	0.999586i	$0.490837\pi$
$98$	−1.02869	−0.103914
$99$	2.89881	0.291342
$100$	−1.99487	−0.199487
$101$	−2.70902	−0.269557	−0.134779	−	0.990876i	$-0.543032\pi$
$101$	−2.70902	−0.269557	−0.134779	+	0.990876i	$0.543032\pi$
$102$	−0.00681545	−0.000674830 0
$103$	−14.3149	−1.41049	−0.705243	−	0.708966i	$-0.749162\pi$
$103$	−14.3149	−1.41049	−0.705243	+	0.708966i	$0.749162\pi$
$104$	0.437020	0.0428533
$105$	−4.62140	−0.451002
$106$	0.775335	0.0753072
$107$	1.80759	0.174746	0.0873731	−	0.996176i	$-0.472153\pi$
$107$	1.80759	0.174746	0.0873731	+	0.996176i	$0.472153\pi$
$108$	1.99487	0.191956
$109$	−11.5938	−1.11048	−0.555240	−	0.831690i	$-0.687374\pi$
$109$	−11.5938	−1.11048	−0.555240	+	0.831690i	$0.687374\pi$
$110$	−0.207699	−0.0198033
$111$	8.07372	0.766324
$112$	18.3434	1.73328
$113$	−7.30472	−0.687170	−0.343585	−	0.939122i	$-0.611641\pi$
$113$	−7.30472	−0.687170	−0.343585	+	0.939122i	$0.611641\pi$
$114$	−0.111728	−0.0104643
$115$	−2.96330	−0.276329
$116$	21.1057	1.95962
$117$	1.52681	0.141154
$118$	−0.0295002	−0.00271572
$119$	−0.439597	−0.0402978
$120$	−0.286230	−0.0261291
$121$	−2.59687	−0.236079
$122$	−0.489258	−0.0442954
$123$	7.05677	0.636288
$124$	15.6324	1.40383
$125$	1.00000	0.0894427
$126$	−0.331121	−0.0294986
$127$	0.737705	0.0654607	0.0327304	−	0.999464i	$-0.489580\pi$
$127$	0.737705	0.0654607	0.0327304	+	0.999464i	$0.489580\pi$
$128$	2.27809	0.201357
$129$	8.61827	0.758796
$130$	−0.109395	−0.00959461
$131$	−2.15335	−0.188139	−0.0940694	−	0.995566i	$-0.529988\pi$
$131$	−2.15335	−0.188139	−0.0940694	+	0.995566i	$0.529988\pi$
$132$	5.78275	0.503324
$133$	−7.20649	−0.624882
$134$	0.286959	0.0247895
$135$	−1.00000	−0.0860663
$136$	−0.0272268	−0.00233468
$137$	−15.9953	−1.36657	−0.683286	−	0.730151i	$-0.739450\pi$
$137$	−15.9953	−1.36657	−0.683286	+	0.730151i	$0.739450\pi$
$138$	−0.212319	−0.0180738
$139$	21.1097	1.79051	0.895253	−	0.445559i	$-0.146995\pi$
$139$	21.1097	1.79051	0.895253	+	0.445559i	$0.146995\pi$
$140$	−9.21907	−0.779153
$141$	−1.46262	−0.123175
$142$	1.14524	0.0961063
$143$	4.42595	0.370116
$144$	3.96922	0.330769
$145$	−10.5800	−0.878624
$146$	−0.272070	−0.0225167
$147$	−14.3573	−1.18417
$148$	16.1060	1.32390
$149$	−3.29079	−0.269592	−0.134796	−	0.990873i	$-0.543038\pi$
$149$	−3.29079	−0.269592	−0.134796	+	0.990873i	$0.543038\pi$
$150$	0.0716495	0.00585016
$151$	−7.23692	−0.588932	−0.294466	−	0.955662i	$-0.595142\pi$
$151$	−7.23692	−0.588932	−0.294466	+	0.955662i	$0.595142\pi$
$152$	−0.446340	−0.0362030
$153$	−0.0951221	−0.00769017
$154$	−0.959857	−0.0773475
$155$	−7.83632	−0.629428
$156$	3.04579	0.243858
$157$	11.8338	0.944444	0.472222	−	0.881480i	$-0.343452\pi$
$157$	11.8338	0.944444	0.472222	+	0.881480i	$0.343452\pi$
$158$	−0.179943	−0.0143155
$159$	10.8212	0.858179
$160$	−0.856853	−0.0677402
$161$	−13.6946	−1.07928
$162$	−0.0716495	−0.00562932
$163$	−5.71243	−0.447432	−0.223716	−	0.974654i	$-0.571819\pi$
$163$	−5.71243	−0.447432	−0.223716	+	0.974654i	$0.571819\pi$
$164$	14.0773	1.09925
$165$	−2.89881	−0.225672
$166$	0.0697828	0.00541619
$167$	3.99478	0.309125	0.154563	−	0.987983i	$-0.450603\pi$
$167$	3.99478	0.309125	0.154563	+	0.987983i	$0.450603\pi$
$168$	−1.32278	−0.102055
$169$	−10.6688	−0.820680
$170$	0.00681545	0.000522721 0
$171$	−1.55937	−0.119248
$172$	17.1923	1.31090
$173$	0.541735	0.0411874	0.0205937	−	0.999788i	$-0.493444\pi$
$173$	0.541735	0.0411874	0.0205937	+	0.999788i	$0.493444\pi$
$174$	−0.758054	−0.0574679
$175$	4.62140	0.349345
$176$	11.5060	0.867301
$177$	−0.411730	−0.0309475
$178$	−0.946762	−0.0709628
$179$	−11.0220	−0.823824	−0.411912	−	0.911224i	$-0.635139\pi$
$179$	−11.0220	−0.823824	−0.411912	+	0.911224i	$0.635139\pi$
$180$	−1.99487	−0.148689
$181$	−0.0856108	−0.00636340	−0.00318170	−	0.999995i	$-0.501013\pi$
$181$	−0.0856108	−0.00636340	−0.00318170	+	0.999995i	$0.501013\pi$
$182$	−0.505559	−0.0374745
$183$	−6.82849	−0.504777
$184$	−0.848185	−0.0625290
$185$	−8.07372	−0.593592
$186$	−0.561468	−0.0411689
$187$	−0.275741	−0.0201642
$188$	−2.91773	−0.212798
$189$	−4.62140	−0.336157
$190$	0.111728	0.00810563
$191$	−12.2243	−0.884517	−0.442258	−	0.896888i	$-0.645823\pi$
$191$	−12.2243	−0.884517	−0.442258	+	0.896888i	$0.645823\pi$
$192$	7.87706	0.568478
$193$	−24.1680	−1.73965	−0.869826	−	0.493359i	$-0.835769\pi$
$193$	−24.1680	−1.73965	−0.869826	+	0.493359i	$0.835769\pi$
$194$	−0.0406204	−0.00291637
$195$	−1.52681	−0.109337
$196$	−28.6409	−2.04578
$197$	6.21716	0.442954	0.221477	−	0.975166i	$-0.428912\pi$
$197$	6.21716	0.442954	0.221477	+	0.975166i	$0.428912\pi$
$198$	−0.207699	−0.0147605
$199$	14.0514	0.996081	0.498040	−	0.867154i	$-0.334053\pi$
$199$	14.0514	0.996081	0.498040	+	0.867154i	$0.334053\pi$
$200$	0.286230	0.0202395
$201$	4.00504	0.282494
$202$	0.194100	0.0136568
$203$	−48.8945	−3.43172
$204$	−0.189756	−0.0132856
$205$	−7.05677	−0.492866
$206$	1.02565	0.0714606
$207$	−2.96330	−0.205963
$208$	6.06026	0.420204
$209$	−4.52034	−0.312678
$210$	0.331121	0.0228495
$211$	23.4883	1.61700	0.808501	−	0.588495i	$-0.200279\pi$
$211$	23.4883	1.61700	0.808501	+	0.588495i	$0.200279\pi$
$212$	21.5869	1.48259
$213$	15.9839	1.09520
$214$	−0.129513	−0.00885332
$215$	−8.61827	−0.587761
$216$	−0.286230	−0.0194755
$217$	−36.2147	−2.45842
$218$	0.830687	0.0562612
$219$	−3.79724	−0.256594
$220$	−5.78275	−0.389873
$221$	−0.145234	−0.00976947
$222$	−0.578478	−0.0388249
$223$	−11.0254	−0.738314	−0.369157	−	0.929367i	$-0.620353\pi$
$223$	−11.0254	−0.738314	−0.369157	+	0.929367i	$0.620353\pi$
$224$	−3.95986	−0.264579
$225$	1.00000	0.0666667
$226$	0.523380	0.0348147
$227$	17.6223	1.16963	0.584816	−	0.811166i	$-0.301167\pi$
$227$	17.6223	1.16963	0.584816	+	0.811166i	$0.301167\pi$
$228$	−3.11074	−0.206014
$229$	19.8208	1.30980	0.654898	−	0.755717i	$-0.272712\pi$
$229$	19.8208	1.30980	0.654898	+	0.755717i	$0.272712\pi$
$230$	0.212319	0.0139999
$231$	−13.3966	−0.881430
$232$	−3.02832	−0.198819
$233$	9.01257	0.590433	0.295217	−	0.955430i	$-0.404608\pi$
$233$	9.01257	0.590433	0.295217	+	0.955430i	$0.404608\pi$
$234$	−0.109395	−0.00715140
$235$	1.46262	0.0954109
$236$	−0.821346	−0.0534651
$237$	−2.51144	−0.163135
$238$	0.0314969	0.00204164
$239$	−10.4772	−0.677711	−0.338856	−	0.940838i	$-0.610040\pi$
$239$	−10.4772	−0.677711	−0.338856	+	0.940838i	$0.610040\pi$
$240$	−3.96922	−0.256212
$241$	10.2822	0.662337	0.331169	−	0.943572i	$-0.392557\pi$
$241$	10.2822	0.662337	0.331169	+	0.943572i	$0.392557\pi$
$242$	0.186065	0.0119607
$243$	−1.00000	−0.0641500
$244$	−13.6219	−0.872055
$245$	14.3573	0.917254
$246$	−0.505614	−0.0322368
$247$	−2.38087	−0.151491
$248$	−2.24299	−0.142430
$249$	0.973947	0.0617214
$250$	−0.0716495	−0.00453151
$251$	−19.0777	−1.20417	−0.602086	−	0.798432i	$-0.705663\pi$
$251$	−19.0777	−1.20417	−0.602086	+	0.798432i	$0.705663\pi$
$252$	−9.21907	−0.580747
$253$	−8.59005	−0.540052
$254$	−0.0528562	−0.00331649
$255$	0.0951221	0.00595678
$256$	15.5909	0.974430
$257$	13.0623	0.814803	0.407401	−	0.913249i	$-0.366435\pi$
$257$	13.0623	0.814803	0.407401	+	0.913249i	$0.366435\pi$
$258$	−0.617494	−0.0384435
$259$	−37.3119	−2.31845
$260$	−3.04579	−0.188892
$261$	−10.5800	−0.654887
$262$	0.154286	0.00953184
$263$	−7.85456	−0.484333	−0.242166	−	0.970235i	$-0.577858\pi$
$263$	−7.85456	−0.484333	−0.242166	+	0.970235i	$0.577858\pi$
$264$	−0.829728	−0.0510662
$265$	−10.8212	−0.664743
$266$	0.516341	0.0316589
$267$	−13.2138	−0.808671
$268$	7.98951	0.488037
$269$	17.3708	1.05912	0.529559	−	0.848273i	$-0.322358\pi$
$269$	17.3708	1.05912	0.529559	+	0.848273i	$0.322358\pi$
$270$	0.0716495	0.00436045
$271$	10.1317	0.615456	0.307728	−	0.951474i	$-0.400431\pi$
$271$	10.1317	0.615456	0.307728	+	0.951474i	$0.400431\pi$
$272$	−0.377561	−0.0228930
$273$	−7.05601	−0.427049
$274$	1.14606	0.0692358
$275$	2.89881	0.174805
$276$	−5.91138	−0.355823
$277$	1.41375	0.0849442	0.0424721	−	0.999098i	$-0.486477\pi$
$277$	1.41375	0.0849442	0.0424721	+	0.999098i	$0.486477\pi$
$278$	−1.51250	−0.0907139
$279$	−7.83632	−0.469148
$280$	1.32278	0.0790514
$281$	27.1525	1.61978	0.809890	−	0.586581i	$-0.199527\pi$
$281$	27.1525	1.61978	0.809890	+	0.586581i	$0.199527\pi$
$282$	0.104796	0.00624051
$283$	31.3539	1.86380	0.931899	−	0.362719i	$-0.118152\pi$
$283$	31.3539	1.86380	0.931899	+	0.362719i	$0.118152\pi$
$284$	31.8858	1.89207
$285$	1.55937	0.0923694
$286$	−0.317117	−0.0187515
$287$	−32.6121	−1.92503
$288$	−0.856853	−0.0504906
$289$	−16.9910	−0.999468
$290$	0.758054	0.0445144
$291$	−0.566932	−0.0332341
$292$	−7.57499	−0.443293
$293$	7.90554	0.461846	0.230923	−	0.972972i	$-0.425825\pi$
$293$	7.90554	0.461846	0.230923	+	0.972972i	$0.425825\pi$
$294$	1.02869	0.0599946
$295$	0.411730	0.0239718
$296$	−2.31094	−0.134321
$297$	−2.89881	−0.168206
$298$	0.235783	0.0136586
$299$	−4.52440	−0.261653
$300$	1.99487	0.115174
$301$	−39.8284	−2.29567
$302$	0.518522	0.0298376
$303$	2.70902	0.155629
$304$	−6.18951	−0.354993
$305$	6.82849	0.390998
$306$	0.00681545	0.000389613 0
$307$	0.307230	0.0175346	0.00876728	−	0.999962i	$-0.497209\pi$
$307$	0.307230	0.0175346	0.00876728	+	0.999962i	$0.497209\pi$
$308$	−26.7244	−1.52276
$309$	14.3149	0.814344
$310$	0.561468	0.0318893
$311$	20.6044	1.16837	0.584186	−	0.811620i	$-0.301414\pi$
$311$	20.6044	1.16837	0.584186	+	0.811620i	$0.301414\pi$
$312$	−0.437020	−0.0247414
$313$	−12.2320	−0.691393	−0.345697	−	0.938346i	$-0.612357\pi$
$313$	−12.2320	−0.691393	−0.345697	+	0.938346i	$0.612357\pi$
$314$	−0.847889	−0.0478492
$315$	4.62140	0.260386
$316$	−5.00999	−0.281834
$317$	11.3707	0.638644	0.319322	−	0.947646i	$-0.396545\pi$
$317$	11.3707	0.638644	0.319322	+	0.947646i	$0.396545\pi$
$318$	−0.775335	−0.0434786
$319$	−30.6695	−1.71716
$320$	−7.87706	−0.440341
$321$	−1.80759	−0.100890
$322$	0.981208	0.0546806
$323$	0.148331	0.00825336
$324$	−1.99487	−0.110826
$325$	1.52681	0.0846923
$326$	0.409293	0.0226686
$327$	11.5938	0.641136
$328$	−2.01986	−0.111528
$329$	6.75935	0.372655
$330$	0.207699	0.0114334
$331$	−15.1886	−0.834841	−0.417421	−	0.908713i	$-0.637066\pi$
$331$	−15.1886	−0.834841	−0.417421	+	0.908713i	$0.637066\pi$
$332$	1.94289	0.106630
$333$	−8.07372	−0.442437
$334$	−0.286224	−0.0156615
$335$	−4.00504	−0.218819
$336$	−18.3434	−1.00071
$337$	19.7829	1.07765	0.538823	−	0.842419i	$-0.318869\pi$
$337$	19.7829	1.07765	0.538823	+	0.842419i	$0.318869\pi$
$338$	0.764417	0.0415788
$339$	7.30472	0.396738
$340$	0.189756	0.0102910
$341$	−22.7160	−1.23014
$342$	0.111728	0.00604158
$343$	34.0010	1.83588
$344$	−2.46681	−0.133001
$345$	2.96330	0.159538
$346$	−0.0388151	−0.00208671
$347$	−1.50635	−0.0808649	−0.0404325	−	0.999182i	$-0.512874\pi$
$347$	−1.50635	−0.0808649	−0.0404325	+	0.999182i	$0.512874\pi$
$348$	−21.1057	−1.13139
$349$	−21.4722	−1.14938	−0.574691	−	0.818371i	$-0.694878\pi$
$349$	−21.4722	−1.14938	−0.574691	+	0.818371i	$0.694878\pi$
$350$	−0.331121	−0.0176991
$351$	−1.52681	−0.0814952
$352$	−2.48386	−0.132390
$353$	−4.66436	−0.248259	−0.124129	−	0.992266i	$-0.539614\pi$
$353$	−4.66436	−0.248259	−0.124129	+	0.992266i	$0.539614\pi$
$354$	0.0295002	0.00156792
$355$	−15.9839	−0.848338
$356$	−26.3598	−1.39706
$357$	0.439597	0.0232659
$358$	0.789721	0.0417381
$359$	−4.19927	−0.221629	−0.110815	−	0.993841i	$-0.535346\pi$
$359$	−4.19927	−0.221629	−0.110815	+	0.993841i	$0.535346\pi$
$360$	0.286230	0.0150857
$361$	−16.5683	−0.872018
$362$	0.00613397	0.000322394 0
$363$	2.59687	0.136300
$364$	−14.0758	−0.737772
$365$	3.79724	0.198757
$366$	0.489258	0.0255739
$367$	1.66859	0.0870999	0.0435499	−	0.999051i	$-0.486133\pi$
$367$	1.66859	0.0870999	0.0435499	+	0.999051i	$0.486133\pi$
$368$	−11.7620	−0.613136
$369$	−7.05677	−0.367361
$370$	0.578478	0.0300736
$371$	−50.0092	−2.59635
$372$	−15.6324	−0.810503
$373$	33.7758	1.74884	0.874422	−	0.485166i	$-0.161241\pi$
$373$	33.7758	1.74884	0.874422	+	0.485166i	$0.161241\pi$
$374$	0.0197567	0.00102160
$375$	−1.00000	−0.0516398
$376$	0.418646	0.0215900
$377$	−16.1537	−0.831959
$378$	0.331121	0.0170310
$379$	−18.1426	−0.931923	−0.465961	−	0.884805i	$-0.654291\pi$
$379$	−18.1426	−0.931923	−0.465961	+	0.884805i	$0.654291\pi$
$380$	3.11074	0.159578
$381$	−0.737705	−0.0377938
$382$	0.875862	0.0448130
$383$	−37.3463	−1.90831	−0.954155	−	0.299314i	$-0.903242\pi$
$383$	−37.3463	−1.90831	−0.954155	+	0.299314i	$0.903242\pi$
$384$	−2.27809	−0.116253
$385$	13.3966	0.682752
$386$	1.73163	0.0881374
$387$	−8.61827	−0.438091
$388$	−1.13095	−0.0574155
$389$	27.6331	1.40105	0.700526	−	0.713627i	$-0.252949\pi$
$389$	27.6331	1.40105	0.700526	+	0.713627i	$0.252949\pi$
$390$	0.109395	0.00553945
$391$	0.281875	0.0142550
$392$	4.10949	0.207561
$393$	2.15335	0.108622
$394$	−0.445456	−0.0224418
$395$	2.51144	0.126364
$396$	−5.78275	−0.290594
$397$	22.2501	1.11670	0.558351	−	0.829605i	$-0.311434\pi$
$397$	22.2501	1.11670	0.558351	+	0.829605i	$0.311434\pi$
$398$	−1.00678	−0.0504653
$399$	7.20649	0.360776
$400$	3.96922	0.198461
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	−0.286959	−0.0143122
$403$	−11.9646	−0.595999
$404$	5.40413	0.268865
$405$	1.00000	0.0496904
$406$	3.50327	0.173864
$407$	−23.4042	−1.16010
$408$	0.0272268	0.00134793
$409$	−25.1225	−1.24223	−0.621114	−	0.783720i	$-0.713320\pi$
$409$	−25.1225	−1.24223	−0.621114	+	0.783720i	$0.713320\pi$
$410$	0.505614	0.0249705
$411$	15.9953	0.788991
$412$	28.5562	1.40686
$413$	1.90277	0.0936290
$414$	0.212319	0.0104349
$415$	−0.973947	−0.0478092
$416$	−1.30825	−0.0641425
$417$	−21.1097	−1.03375
$418$	0.323880	0.0158415
$419$	15.7664	0.770241	0.385121	−	0.922866i	$-0.374160\pi$
$419$	15.7664	0.770241	0.385121	+	0.922866i	$0.374160\pi$
$420$	9.21907	0.449844
$421$	18.8951	0.920893	0.460446	−	0.887687i	$-0.347689\pi$
$421$	18.8951	0.920893	0.460446	+	0.887687i	$0.347689\pi$
$422$	−1.68293	−0.0819235
$423$	1.46262	0.0711151
$424$	−3.09736	−0.150421
$425$	−0.0951221	−0.00461410
$426$	−1.14524	−0.0554870
$427$	31.5572	1.52716
$428$	−3.60590	−0.174298
$429$	−4.42595	−0.213687
$430$	0.617494	0.0297782
$431$	35.8146	1.72513	0.862565	−	0.505946i	$-0.168856\pi$
$431$	35.8146	1.72513	0.862565	+	0.505946i	$0.168856\pi$
$432$	−3.96922	−0.190969
$433$	−20.1077	−0.966313	−0.483156	−	0.875534i	$-0.660510\pi$
$433$	−20.1077	−0.966313	−0.483156	+	0.875534i	$0.660510\pi$
$434$	2.59477	0.124553
$435$	10.5800	0.507274
$436$	23.1280	1.10763
$437$	4.62089	0.221047
$438$	0.272070	0.0130000
$439$	5.24401	0.250283	0.125141	−	0.992139i	$-0.460062\pi$
$439$	5.24401	0.250283	0.125141	+	0.992139i	$0.460062\pi$
$440$	0.829728	0.0395557
$441$	14.3573	0.683681
$442$	0.0104059	0.000494959 0
$443$	−9.86894	−0.468888	−0.234444	−	0.972130i	$-0.575327\pi$
$443$	−9.86894	−0.468888	−0.234444	+	0.972130i	$0.575327\pi$
$444$	−16.1060	−0.764357
$445$	13.2138	0.626394
$446$	0.789962	0.0374058
$447$	3.29079	0.155649
$448$	−36.4030	−1.71988
$449$	18.8938	0.891651	0.445826	−	0.895120i	$-0.352910\pi$
$449$	18.8938	0.891651	0.445826	+	0.895120i	$0.352910\pi$
$450$	−0.0716495	−0.00337759
$451$	−20.4563	−0.963248
$452$	14.5719	0.685406
$453$	7.23692	0.340020
$454$	−1.26263	−0.0592580
$455$	7.05601	0.330791
$456$	0.446340	0.0209018
$457$	28.9597	1.35468	0.677339	−	0.735671i	$-0.263133\pi$
$457$	28.9597	1.35468	0.677339	+	0.735671i	$0.263133\pi$
$458$	−1.42015	−0.0663593
$459$	0.0951221	0.00443992
$460$	5.91138	0.275619
$461$	0.617183	0.0287451	0.0143725	−	0.999897i	$-0.495425\pi$
$461$	0.617183	0.0287451	0.0143725	+	0.999897i	$0.495425\pi$
$462$	0.959857	0.0446566
$463$	−29.0733	−1.35115	−0.675575	−	0.737291i	$-0.736105\pi$
$463$	−29.0733	−1.35115	−0.675575	+	0.737291i	$0.736105\pi$
$464$	−41.9945	−1.94955
$465$	7.83632	0.363401
$466$	−0.645746	−0.0299136
$467$	0.354924	0.0164239	0.00821196	−	0.999966i	$-0.497386\pi$
$467$	0.354924	0.0164239	0.00821196	+	0.999966i	$0.497386\pi$
$468$	−3.04579	−0.140792
$469$	−18.5089	−0.854660
$470$	−0.104796	−0.00483388
$471$	−11.8338	−0.545275
$472$	0.117849	0.00542446
$473$	−24.9828	−1.14871
$474$	0.179943	0.00826507
$475$	−1.55937	−0.0715490
$476$	0.876937	0.0401943
$477$	−10.8212	−0.495470
$478$	0.750683	0.0343354
$479$	−4.37875	−0.200070	−0.100035	−	0.994984i	$-0.531896\pi$
$479$	−4.37875	−0.200070	−0.100035	+	0.994984i	$0.531896\pi$
$480$	0.856853	0.0391098
$481$	−12.3271	−0.562066
$482$	−0.736717	−0.0335566
$483$	13.6946	0.623124
$484$	5.18041	0.235473
$485$	0.566932	0.0257430
$486$	0.0716495	0.00325009
$487$	35.6764	1.61665	0.808326	−	0.588735i	$-0.200374\pi$
$487$	35.6764	1.61665	0.808326	+	0.588735i	$0.200374\pi$
$488$	1.95452	0.0884770
$489$	5.71243	0.258325
$490$	−1.02869	−0.0464716
$491$	−43.0429	−1.94250	−0.971249	−	0.238064i	$-0.923487\pi$
$491$	−43.0429	−1.94250	−0.971249	+	0.238064i	$0.923487\pi$
$492$	−14.0773	−0.634654
$493$	1.00639	0.0453257
$494$	0.170588	0.00767513
$495$	2.89881	0.130292
$496$	−31.1041	−1.39662
$497$	−73.8680	−3.31343
$498$	−0.0697828	−0.00312704
$499$	10.4367	0.467213	0.233606	−	0.972331i	$-0.424947\pi$
$499$	10.4367	0.467213	0.233606	+	0.972331i	$0.424947\pi$
$500$	−1.99487	−0.0892131
$501$	−3.99478	−0.178474
$502$	1.36690	0.0610079
$503$	−39.3065	−1.75259	−0.876295	−	0.481775i	$-0.839992\pi$
$503$	−39.3065	−1.75259	−0.876295	+	0.481775i	$0.839992\pi$
$504$	1.32278	0.0589214
$505$	−2.70902	−0.120550
$506$	0.615472	0.0273611
$507$	10.6688	0.473820
$508$	−1.47162	−0.0652927
$509$	−18.7958	−0.833109	−0.416554	−	0.909111i	$-0.636762\pi$
$509$	−18.7958	−0.833109	−0.416554	+	0.909111i	$0.636762\pi$
$510$	−0.00681545	−0.000301793 0
$511$	17.5486	0.776302
$512$	−5.67327	−0.250725
$513$	1.55937	0.0688481
$514$	−0.935906	−0.0412810
$515$	−14.3149	−0.630788
$516$	−17.1923	−0.756848
$517$	4.23987	0.186469
$518$	2.67338	0.117461
$519$	−0.541735	−0.0237795
$520$	0.437020	0.0191646
$521$	−11.0244	−0.482986	−0.241493	−	0.970403i	$-0.577637\pi$
$521$	−11.0244	−0.482986	−0.241493	+	0.970403i	$0.577637\pi$
$522$	0.758054	0.0331791
$523$	−7.26362	−0.317616	−0.158808	−	0.987309i	$-0.550765\pi$
$523$	−7.26362	−0.317616	−0.158808	+	0.987309i	$0.550765\pi$
$524$	4.29564	0.187656
$525$	−4.62140	−0.201694
$526$	0.562775	0.0245382
$527$	0.745407	0.0324705
$528$	−11.5060	−0.500736
$529$	−14.2189	−0.618212
$530$	0.775335	0.0336784
$531$	0.411730	0.0178676
$532$	14.3760	0.623278
$533$	−10.7744	−0.466690
$534$	0.946762	0.0409704
$535$	1.80759	0.0781489
$536$	−1.14636	−0.0495153
$537$	11.0220	0.475635
$538$	−1.24461	−0.0536590
$539$	41.6191	1.79266
$540$	1.99487	0.0858454
$541$	34.7846	1.49551	0.747753	−	0.663977i	$-0.231133\pi$
$541$	34.7846	1.49551	0.747753	+	0.663977i	$0.231133\pi$
$542$	−0.725930	−0.0311814
$543$	0.0856108	0.00367391
$544$	0.0815057	0.00349453
$545$	−11.5938	−0.496622
$546$	0.505559	0.0216359
$547$	−13.5601	−0.579789	−0.289895	−	0.957059i	$-0.593620\pi$
$547$	−13.5601	−0.579789	−0.289895	+	0.957059i	$0.593620\pi$
$548$	31.9085	1.36306
$549$	6.82849	0.291433
$550$	−0.207699	−0.00885630
$551$	16.4982	0.702848
$552$	0.848185	0.0361011
$553$	11.6064	0.493552
$554$	−0.101295	−0.00430360
$555$	8.07372	0.342710
$556$	−42.1111	−1.78591
$557$	−4.84632	−0.205345	−0.102672	−	0.994715i	$-0.532739\pi$
$557$	−4.84632	−0.205345	−0.102672	+	0.994715i	$0.532739\pi$
$558$	0.561468	0.0237689
$559$	−13.1585	−0.556544
$560$	18.3434	0.775148
$561$	0.275741	0.0116418
$562$	−1.94546	−0.0820643
$563$	15.9045	0.670296	0.335148	−	0.942166i	$-0.391214\pi$
$563$	15.9045	0.670296	0.335148	+	0.942166i	$0.391214\pi$
$564$	2.91773	0.122859
$565$	−7.30472	−0.307312
$566$	−2.24649	−0.0944271
$567$	4.62140	0.194080
$568$	−4.57508	−0.191966
$569$	−37.8320	−1.58600	−0.792999	−	0.609223i	$-0.791481\pi$
$569$	−37.8320	−1.58600	−0.792999	+	0.609223i	$0.791481\pi$
$570$	−0.111728	−0.00467979
$571$	34.2388	1.43285	0.716424	−	0.697665i	$-0.245778\pi$
$571$	34.2388	1.43285	0.716424	+	0.697665i	$0.245778\pi$
$572$	−8.82917	−0.369166
$573$	12.2243	0.510676
$574$	2.33664	0.0975296
$575$	−2.96330	−0.123578
$576$	−7.87706	−0.328211
$577$	−35.0605	−1.45959	−0.729793	−	0.683668i	$-0.760384\pi$
$577$	−35.0605	−1.45959	−0.729793	+	0.683668i	$0.760384\pi$
$578$	1.21739	0.0506369
$579$	24.1680	1.00439
$580$	21.1057	0.876368
$581$	−4.50099	−0.186733
$582$	0.0406204	0.00168377
$583$	−31.3687	−1.29916
$584$	1.08688	0.0449756
$585$	1.52681	0.0631259
$586$	−0.566428	−0.0233989
$587$	−40.6902	−1.67946	−0.839732	−	0.543002i	$-0.817288\pi$
$587$	−40.6902	−1.67946	−0.839732	+	0.543002i	$0.817288\pi$
$588$	28.6409	1.18113
$589$	12.2198	0.503507
$590$	−0.0295002	−0.00121451
$591$	−6.21716	−0.255740
$592$	−32.0464	−1.31710
$593$	29.0580	1.19327	0.596635	−	0.802513i	$-0.296504\pi$
$593$	29.0580	1.19327	0.596635	+	0.802513i	$0.296504\pi$
$594$	0.207699	0.00852198
$595$	−0.439597	−0.0180217
$596$	6.56469	0.268900
$597$	−14.0514	−0.575087
$598$	0.324171	0.0132563
$599$	−10.4027	−0.425042	−0.212521	−	0.977156i	$-0.568167\pi$
$599$	−10.4027	−0.425042	−0.212521	+	0.977156i	$0.568167\pi$
$600$	−0.286230	−0.0116853
$601$	−3.87626	−0.158116	−0.0790579	−	0.996870i	$-0.525191\pi$
$601$	−3.87626	−0.158116	−0.0790579	+	0.996870i	$0.525191\pi$
$602$	2.85369	0.116308
$603$	−4.00504	−0.163098
$604$	14.4367	0.587421
$605$	−2.59687	−0.105578
$606$	−0.194100	−0.00788476
$607$	48.0378	1.94979	0.974897	−	0.222657i	$-0.0714731\pi$
$607$	48.0378	1.94979	0.974897	+	0.222657i	$0.0714731\pi$
$608$	1.33616	0.0541883
$609$	48.8945	1.98131
$610$	−0.489258	−0.0198095
$611$	2.23315	0.0903435
$612$	0.189756	0.00767043
$613$	24.1709	0.976254	0.488127	−	0.872773i	$-0.337680\pi$
$613$	24.1709	0.976254	0.488127	+	0.872773i	$0.337680\pi$
$614$	−0.0220129	−0.000888368 0
$615$	7.05677	0.284556
$616$	3.83450	0.154496
$617$	−35.9338	−1.44664	−0.723320	−	0.690513i	$-0.757385\pi$
$617$	−35.9338	−1.44664	−0.723320	+	0.690513i	$0.757385\pi$
$618$	−1.02565	−0.0412578
$619$	13.9803	0.561915	0.280957	−	0.959720i	$-0.409348\pi$
$619$	13.9803	0.561915	0.280957	+	0.959720i	$0.409348\pi$
$620$	15.6324	0.627813
$621$	2.96330	0.118913
$622$	−1.47630	−0.0591942
$623$	61.0662	2.44656
$624$	−6.06026	−0.242605
$625$	1.00000	0.0400000
$626$	0.876417	0.0350286
$627$	4.52034	0.180525
$628$	−23.6069	−0.942020
$629$	0.767989	0.0306217
$630$	−0.331121	−0.0131922
$631$	41.4613	1.65055	0.825274	−	0.564733i	$-0.191021\pi$
$631$	41.4613	1.65055	0.825274	+	0.564733i	$0.191021\pi$
$632$	0.718850	0.0285943
$633$	−23.4883	−0.933576
$634$	−0.814708	−0.0323562
$635$	0.737705	0.0292749
$636$	−21.5869	−0.855976
$637$	21.9209	0.868538
$638$	2.19746	0.0869982
$639$	−15.9839	−0.632314
$640$	2.27809	0.0900495
$641$	−39.4800	−1.55936	−0.779682	−	0.626175i	$-0.784619\pi$
$641$	−39.4800	−1.55936	−0.779682	+	0.626175i	$0.784619\pi$
$642$	0.129513	0.00511147
$643$	21.3677	0.842661	0.421331	−	0.906907i	$-0.361563\pi$
$643$	21.3677	0.842661	0.421331	+	0.906907i	$0.361563\pi$
$644$	27.3188	1.07651
$645$	8.61827	0.339344
$646$	−0.0106278	−0.000418147 0
$647$	−11.2712	−0.443116	−0.221558	−	0.975147i	$-0.571114\pi$
$647$	−11.2712	−0.443116	−0.221558	+	0.975147i	$0.571114\pi$
$648$	0.286230	0.0112442
$649$	1.19353	0.0468501
$650$	−0.109395	−0.00429084
$651$	36.2147	1.41937
$652$	11.3955	0.446284
$653$	−26.7790	−1.04794	−0.523972	−	0.851735i	$-0.675551\pi$
$653$	−26.7790	−1.04794	−0.523972	+	0.851735i	$0.675551\pi$
$654$	−0.830687	−0.0324824
$655$	−2.15335	−0.0841383
$656$	−28.0099	−1.09360
$657$	3.79724	0.148145
$658$	−0.484304	−0.0188801
$659$	7.54222	0.293803	0.146902	−	0.989151i	$-0.453070\pi$
$659$	7.54222	0.293803	0.146902	+	0.989151i	$0.453070\pi$
$660$	5.78275	0.225093
$661$	−1.87718	−0.0730138	−0.0365069	−	0.999333i	$-0.511623\pi$
$661$	−1.87718	−0.0730138	−0.0365069	+	0.999333i	$0.511623\pi$
$662$	1.08826	0.0422963
$663$	0.145234	0.00564041
$664$	−0.278773	−0.0108185
$665$	−7.20649	−0.279456
$666$	0.578478	0.0224156
$667$	31.3518	1.21394
$668$	−7.96905	−0.308332
$669$	11.0254	0.426266
$670$	0.286959	0.0110862
$671$	19.7945	0.764160
$672$	3.95986	0.152755
$673$	0.494601	0.0190655	0.00953274	−	0.999955i	$-0.496966\pi$
$673$	0.494601	0.0190655	0.00953274	+	0.999955i	$0.496966\pi$
$674$	−1.41744	−0.0545977
$675$	−1.00000	−0.0384900
$676$	21.2829	0.818574
$677$	22.2204	0.853999	0.426999	−	0.904252i	$-0.359571\pi$
$677$	22.2204	0.853999	0.426999	+	0.904252i	$0.359571\pi$
$678$	−0.523380	−0.0201003
$679$	2.62002	0.100547
$680$	−0.0272268	−0.00104410
$681$	−17.6223	−0.675287
$682$	1.62759	0.0623238
$683$	11.1038	0.424876	0.212438	−	0.977175i	$-0.431860\pi$
$683$	11.1038	0.424876	0.212438	+	0.977175i	$0.431860\pi$
$684$	3.11074	0.118942
$685$	−15.9953	−0.611150
$686$	−2.43615	−0.0930127
$687$	−19.8208	−0.756211
$688$	−34.2078	−1.30416
$689$	−16.5220	−0.629438
$690$	−0.212319	−0.00808283
$691$	−6.59025	−0.250705	−0.125352	−	0.992112i	$-0.540006\pi$
$691$	−6.59025	−0.250705	−0.125352	+	0.992112i	$0.540006\pi$
$692$	−1.08069	−0.0410817
$693$	13.3966	0.508894
$694$	0.107929	0.00409693
$695$	21.1097	0.800738
$696$	3.02832	0.114788
$697$	0.671255	0.0254256
$698$	1.53847	0.0582321
$699$	−9.01257	−0.340887
$700$	−9.21907	−0.348448
$701$	−14.8929	−0.562495	−0.281248	−	0.959635i	$-0.590748\pi$
$701$	−14.8929	−0.562495	−0.281248	+	0.959635i	$0.590748\pi$
$702$	0.109395	0.00412886
$703$	12.5900	0.474839
$704$	−22.8341	−0.860593
$705$	−1.46262	−0.0550855
$706$	0.334199	0.0125777
$707$	−12.5194	−0.470842
$708$	0.821346	0.0308681
$709$	−30.0493	−1.12852	−0.564262	−	0.825596i	$-0.690839\pi$
$709$	−30.0493	−1.12852	−0.564262	+	0.825596i	$0.690839\pi$
$710$	1.14524	0.0429801
$711$	2.51144	0.0941863
$712$	3.78219	0.141743
$713$	23.2213	0.869646
$714$	−0.0314969	−0.00117874
$715$	4.42595	0.165521
$716$	21.9874	0.821709
$717$	10.4772	0.391277
$718$	0.300876	0.0112286
$719$	−8.47901	−0.316214	−0.158107	−	0.987422i	$-0.550539\pi$
$719$	−8.47901	−0.316214	−0.158107	+	0.987422i	$0.550539\pi$
$720$	3.96922	0.147924
$721$	−66.1546	−2.46373
$722$	1.18711	0.0441798
$723$	−10.2822	−0.382401
$724$	0.170782	0.00634707
$725$	−10.5800	−0.392932
$726$	−0.186065	−0.00690551
$727$	17.2394	0.639374	0.319687	−	0.947523i	$-0.396422\pi$
$727$	17.2394	0.639374	0.319687	+	0.947523i	$0.396422\pi$
$728$	2.01964	0.0748529
$729$	1.00000	0.0370370
$730$	−0.272070	−0.0100698
$731$	0.819787	0.0303209
$732$	13.6219	0.503481
$733$	29.8986	1.10433	0.552165	−	0.833735i	$-0.313802\pi$
$733$	29.8986	1.10433	0.552165	+	0.833735i	$0.313802\pi$
$734$	−0.119554	−0.00441281
$735$	−14.3573	−0.529577
$736$	2.53911	0.0935928
$737$	−11.6099	−0.427655
$738$	0.505614	0.0186119
$739$	47.0380	1.73032	0.865160	−	0.501496i	$-0.167217\pi$
$739$	47.0380	1.73032	0.865160	+	0.501496i	$0.167217\pi$
$740$	16.1060	0.592068
$741$	2.38087	0.0874636
$742$	3.58313	0.131541
$743$	45.0716	1.65351	0.826757	−	0.562558i	$-0.190183\pi$
$743$	45.0716	1.65351	0.826757	+	0.562558i	$0.190183\pi$
$744$	2.24299	0.0822321
$745$	−3.29079	−0.120565
$746$	−2.42002	−0.0886031
$747$	−0.973947	−0.0356348
$748$	0.550067	0.0201124
$749$	8.35359	0.305233
$750$	0.0716495	0.00261627
$751$	−40.8841	−1.49188	−0.745941	−	0.666012i	$-0.768000\pi$
$751$	−40.8841	−1.49188	−0.745941	+	0.666012i	$0.768000\pi$
$752$	5.80547	0.211704
$753$	19.0777	0.695229
$754$	1.15741	0.0421503
$755$	−7.23692	−0.263379
$756$	9.21907	0.335294
$757$	20.3633	0.740116	0.370058	−	0.929009i	$-0.379338\pi$
$757$	20.3633	0.740116	0.370058	+	0.929009i	$0.379338\pi$
$758$	1.29991	0.0472148
$759$	8.59005	0.311799
$760$	−0.446340	−0.0161905
$761$	−43.5851	−1.57996	−0.789979	−	0.613133i	$-0.789909\pi$
$761$	−43.5851	−1.57996	−0.789979	+	0.613133i	$0.789909\pi$
$762$	0.0528562	0.00191478
$763$	−53.5793	−1.93970
$764$	24.3858	0.882246
$765$	−0.0951221	−0.00343915
$766$	2.67585	0.0966823
$767$	0.628634	0.0226987
$768$	−15.5909	−0.562588
$769$	−44.4580	−1.60320	−0.801598	−	0.597864i	$-0.796016\pi$
$769$	−44.4580	−1.60320	−0.801598	+	0.597864i	$0.796016\pi$
$770$	−0.959857	−0.0345909
$771$	−13.0623	−0.470427
$772$	48.2120	1.73519
$773$	19.6752	0.707666	0.353833	−	0.935309i	$-0.384878\pi$
$773$	19.6752	0.707666	0.353833	+	0.935309i	$0.384878\pi$
$774$	0.617494	0.0221954
$775$	−7.83632	−0.281489
$776$	0.162273	0.00582526
$777$	37.3119	1.33856
$778$	−1.97989	−0.0709826
$779$	11.0042	0.394265
$780$	3.04579	0.109057
$781$	−46.3344	−1.65797
$782$	−0.0201962	−0.000722214 0
$783$	10.5800	0.378099
$784$	56.9873	2.03526
$785$	11.8338	0.422368
$786$	−0.154286	−0.00550321
$787$	37.7117	1.34428	0.672139	−	0.740425i	$-0.265376\pi$
$787$	37.7117	1.34428	0.672139	+	0.740425i	$0.265376\pi$
$788$	−12.4024	−0.441817
$789$	7.85456	0.279630
$790$	−0.179943	−0.00640210
$791$	−33.7580	−1.20030
$792$	0.829728	0.0294831
$793$	10.4258	0.370232
$794$	−1.59421	−0.0565764
$795$	10.8212	0.383789
$796$	−28.0308	−0.993524
$797$	22.6015	0.800585	0.400292	−	0.916387i	$-0.368909\pi$
$797$	22.6015	0.800585	0.400292	+	0.916387i	$0.368909\pi$
$798$	−0.516341	−0.0182783
$799$	−0.139128	−0.00492198
$800$	−0.856853	−0.0302943
$801$	13.2138	0.466886
$802$	−0.0716495	−0.00253003
$803$	11.0075	0.388446
$804$	−7.98951	−0.281768
$805$	−13.6946	−0.482670
$806$	0.857257	0.0301956
$807$	−17.3708	−0.611482
$808$	−0.775402	−0.0272786
$809$	27.1594	0.954873	0.477437	−	0.878666i	$-0.341566\pi$
$809$	27.1594	0.954873	0.477437	+	0.878666i	$0.341566\pi$
$810$	−0.0716495	−0.00251751
$811$	−13.0953	−0.459837	−0.229918	−	0.973210i	$-0.573846\pi$
$811$	−13.0953	−0.459837	−0.229918	+	0.973210i	$0.573846\pi$
$812$	97.5380	3.42291
$813$	−10.1317	−0.355334
$814$	1.67690	0.0587753
$815$	−5.71243	−0.200098
$816$	0.377561	0.0132173
$817$	13.4391	0.470175
$818$	1.80002	0.0629361
$819$	7.05601	0.246557
$820$	14.0773	0.491601
$821$	−26.8929	−0.938568	−0.469284	−	0.883047i	$-0.655488\pi$
$821$	−26.8929	−0.938568	−0.469284	+	0.883047i	$0.655488\pi$
$822$	−1.14606	−0.0399733
$823$	34.4670	1.20145	0.600723	−	0.799457i	$-0.294880\pi$
$823$	34.4670	1.20145	0.600723	+	0.799457i	$0.294880\pi$
$824$	−4.09735	−0.142738
$825$	−2.89881	−0.100924
$826$	−0.136332	−0.00474360
$827$	−42.4508	−1.47616	−0.738080	−	0.674713i	$-0.764267\pi$
$827$	−42.4508	−1.47616	−0.738080	+	0.674713i	$0.764267\pi$
$828$	5.91138	0.205435
$829$	−1.87609	−0.0651594	−0.0325797	−	0.999469i	$-0.510372\pi$
$829$	−1.87609	−0.0651594	−0.0325797	+	0.999469i	$0.510372\pi$
$830$	0.0697828	0.00242220
$831$	−1.41375	−0.0490426
$832$	−12.0268	−0.416954
$833$	−1.36570	−0.0473186
$834$	1.51250	0.0523737
$835$	3.99478	0.138245
$836$	9.01747	0.311876
$837$	7.83632	0.270863
$838$	−1.12966	−0.0390234
$839$	8.41645	0.290568	0.145284	−	0.989390i	$-0.453590\pi$
$839$	8.41645	0.290568	0.145284	+	0.989390i	$0.453590\pi$
$840$	−1.32278	−0.0456403
$841$	82.9370	2.85990
$842$	−1.35383	−0.0466560
$843$	−27.1525	−0.935181
$844$	−46.8560	−1.61285
$845$	−10.6688	−0.367019
$846$	−0.104796	−0.00360296
$847$	−12.0012	−0.412365
$848$	−42.9519	−1.47497
$849$	−31.3539	−1.07606
$850$	0.00681545	0.000233768 0
$851$	23.9248	0.820132
$852$	−31.8858	−1.09239
$853$	−8.11260	−0.277770	−0.138885	−	0.990309i	$-0.544352\pi$
$853$	−8.11260	−0.277770	−0.138885	+	0.990309i	$0.544352\pi$
$854$	−2.26106	−0.0773717
$855$	−1.55937	−0.0533295
$856$	0.517387	0.0176839
$857$	−11.8307	−0.404129	−0.202064	−	0.979372i	$-0.564765\pi$
$857$	−11.8307	−0.404129	−0.202064	+	0.979372i	$0.564765\pi$
$858$	0.317117	0.0108262
$859$	5.36475	0.183043	0.0915214	−	0.995803i	$-0.470827\pi$
$859$	5.36475	0.183043	0.0915214	+	0.995803i	$0.470827\pi$
$860$	17.1923	0.586252
$861$	32.6121	1.11142
$862$	−2.56610	−0.0874017
$863$	24.7016	0.840852	0.420426	−	0.907327i	$-0.361881\pi$
$863$	24.7016	0.840852	0.420426	+	0.907327i	$0.361881\pi$
$864$	0.856853	0.0291507
$865$	0.541735	0.0184196
$866$	1.44070	0.0489571
$867$	16.9910	0.577043
$868$	72.2436	2.45211
$869$	7.28020	0.246964
$870$	−0.758054	−0.0257004
$871$	−6.11494	−0.207197
$872$	−3.31848	−0.112378
$873$	0.566932	0.0191877
$874$	−0.331084	−0.0111991
$875$	4.62140	0.156232
$876$	7.57499	0.255935
$877$	−13.3920	−0.452217	−0.226109	−	0.974102i	$-0.572600\pi$
$877$	−13.3920	−0.452217	−0.226109	+	0.974102i	$0.572600\pi$
$878$	−0.375731	−0.0126803
$879$	−7.90554	−0.266647
$880$	11.5060	0.387869
$881$	33.9517	1.14386	0.571930	−	0.820302i	$-0.306195\pi$
$881$	33.9517	1.14386	0.571930	+	0.820302i	$0.306195\pi$
$882$	−1.02869	−0.0346379
$883$	20.9592	0.705332	0.352666	−	0.935749i	$-0.385275\pi$
$883$	20.9592	0.705332	0.352666	+	0.935749i	$0.385275\pi$
$884$	0.289722	0.00974440
$885$	−0.411730	−0.0138401
$886$	0.707105	0.0237556
$887$	50.2307	1.68658	0.843291	−	0.537457i	$-0.180615\pi$
$887$	50.2307	1.68658	0.843291	+	0.537457i	$0.180615\pi$
$888$	2.31094	0.0775501
$889$	3.40923	0.114342
$890$	−0.946762	−0.0317355
$891$	2.89881	0.0971139
$892$	21.9941	0.736418
$893$	−2.28077	−0.0763232
$894$	−0.235783	−0.00788578
$895$	−11.0220	−0.368425
$896$	10.5280	0.351715
$897$	4.52440	0.151065
$898$	−1.35373	−0.0451745
$899$	82.9085	2.76515
$900$	−1.99487	−0.0664955
$901$	1.02934	0.0342922
$902$	1.46568	0.0488019
$903$	39.8284	1.32541
$904$	−2.09083	−0.0695400
$905$	−0.0856108	−0.00284580
$906$	−0.518522	−0.0172267
$907$	21.6974	0.720450	0.360225	−	0.932866i	$-0.382700\pi$
$907$	21.6974	0.720450	0.360225	+	0.932866i	$0.382700\pi$
$908$	−35.1541	−1.16663
$909$	−2.70902	−0.0898524
$910$	−0.505559	−0.0167591
$911$	−55.4956	−1.83865	−0.919325	−	0.393499i	$-0.871264\pi$
$911$	−55.4956	−1.83865	−0.919325	+	0.393499i	$0.871264\pi$
$912$	6.18951	0.204955
$913$	−2.82329	−0.0934373
$914$	−2.07495	−0.0686332
$915$	−6.82849	−0.225743
$916$	−39.5399	−1.30643
$917$	−9.95147	−0.328627
$918$	−0.00681545	−0.000224943 0
$919$	21.1867	0.698884	0.349442	−	0.936958i	$-0.386371\pi$
$919$	21.1867	0.698884	0.349442	+	0.936958i	$0.386371\pi$
$920$	−0.848185	−0.0279638
$921$	−0.307230	−0.0101236
$922$	−0.0442208	−0.00145634
$923$	−24.4044	−0.803282
$924$	26.7244	0.879167
$925$	−8.07372	−0.265462
$926$	2.08309	0.0684545
$927$	−14.3149	−0.470162
$928$	9.06553	0.297591
$929$	12.3654	0.405695	0.202848	−	0.979210i	$-0.434980\pi$
$929$	12.3654	0.405695	0.202848	+	0.979210i	$0.434980\pi$
$930$	−0.561468	−0.0184113
$931$	−22.3884	−0.733750
$932$	−17.9789	−0.588918
$933$	−20.6044	−0.674559
$934$	−0.0254301	−0.000832098 0
$935$	−0.275741	−0.00901771
$936$	0.437020	0.0142844
$937$	−6.77077	−0.221191	−0.110596	−	0.993865i	$-0.535276\pi$
$937$	−6.77077	−0.221191	−0.110596	+	0.993865i	$0.535276\pi$
$938$	1.32615	0.0433003
$939$	12.2320	0.399176
$940$	−2.91773	−0.0951660
$941$	−46.4126	−1.51301	−0.756503	−	0.653990i	$-0.773094\pi$
$941$	−46.4126	−1.51301	−0.756503	+	0.653990i	$0.773094\pi$
$942$	0.847889	0.0276257
$943$	20.9113	0.680966
$944$	1.63425	0.0531902
$945$	−4.62140	−0.150334
$946$	1.79000	0.0581980
$947$	6.25340	0.203208	0.101604	−	0.994825i	$-0.467602\pi$
$947$	6.25340	0.203208	0.101604	+	0.994825i	$0.467602\pi$
$948$	5.00999	0.162717
$949$	5.79768	0.188201
$950$	0.111728	0.00362495
$951$	−11.3707	−0.368722
$952$	−0.125826	−0.00407804
$953$	−2.49479	−0.0808142	−0.0404071	−	0.999183i	$-0.512865\pi$
$953$	−2.49479	−0.0808142	−0.0404071	+	0.999183i	$0.512865\pi$
$954$	0.775335	0.0251024
$955$	−12.2243	−0.395568
$956$	20.9005	0.675972
$957$	30.6695	0.991406
$958$	0.313735	0.0101363
$959$	−73.9207	−2.38702
$960$	7.87706	0.254231
$961$	30.4079	0.980901
$962$	0.883228	0.0284764
$963$	1.80759	0.0582488
$964$	−20.5117	−0.660637
$965$	−24.1680	−0.777996
$966$	−0.981208	−0.0315699
$967$	51.8919	1.66873	0.834366	−	0.551211i	$-0.185834\pi$
$967$	51.8919	1.66873	0.834366	+	0.551211i	$0.185834\pi$
$968$	−0.743303	−0.0238907
$969$	−0.148331	−0.00476508
$970$	−0.0406204	−0.00130424
$971$	−53.9508	−1.73136	−0.865681	−	0.500595i	$-0.833114\pi$
$971$	−53.9508	−1.73136	−0.865681	+	0.500595i	$0.833114\pi$
$972$	1.99487	0.0639854
$973$	97.5565	3.12752
$974$	−2.55620	−0.0819058
$975$	−1.52681	−0.0488971
$976$	27.1038	0.867572
$977$	38.3682	1.22751	0.613754	−	0.789498i	$-0.289659\pi$
$977$	38.3682	1.22751	0.613754	+	0.789498i	$0.289659\pi$
$978$	−0.409293	−0.0130877
$979$	38.3043	1.22421
$980$	−28.6409	−0.914900
$981$	−11.5938	−0.370160
$982$	3.08400	0.0984144
$983$	29.0085	0.925229	0.462614	−	0.886560i	$-0.346911\pi$
$983$	29.0085	0.925229	0.462614	+	0.886560i	$0.346911\pi$
$984$	2.01986	0.0643908
$985$	6.21716	0.198095
$986$	−0.0721077	−0.00229638
$987$	−6.75935	−0.215152
$988$	4.74952	0.151103
$989$	25.5385	0.812076
$990$	−0.207699	−0.00660109
$991$	−28.0391	−0.890692	−0.445346	−	0.895358i	$-0.646919\pi$
$991$	−28.0391	−0.890692	−0.445346	+	0.895358i	$0.646919\pi$
$992$	6.71458	0.213188
$993$	15.1886	0.481996
$994$	5.29260	0.167871
$995$	14.0514	0.445461
$996$	−1.94289	−0.0615629
$997$	2.61295	0.0827530	0.0413765	−	0.999144i	$-0.486826\pi$
$997$	2.61295	0.0827530	0.0413765	+	0.999144i	$0.486826\pi$
$998$	−0.747787	−0.0236708
$999$	8.07372	0.255441

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6015.2.a.d.1.15	✓	29

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6015.2.a.d.1.15	✓	29	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:	\( N \)	\(=\)	\( 6015 = 3 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6015.a (trivial)

\(f(q)\)	\(=\)	\(q-0.0716495 q^{2} -1.00000 q^{3} -1.99487 q^{4} +1.00000 q^{5} +0.0716495 q^{6} +4.62140 q^{7} +0.286230 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.0716495 q^{2} -1.00000 q^{3} -1.99487 q^{4} +1.00000 q^{5} +0.0716495 q^{6} +4.62140 q^{7} +0.286230 q^{8} +1.00000 q^{9} -0.0716495 q^{10} +2.89881 q^{11} +1.99487 q^{12} +1.52681 q^{13} -0.331121 q^{14} -1.00000 q^{15} +3.96922 q^{16} -0.0951221 q^{17} -0.0716495 q^{18} -1.55937 q^{19} -1.99487 q^{20} -4.62140 q^{21} -0.207699 q^{22} -2.96330 q^{23} -0.286230 q^{24} +1.00000 q^{25} -0.109395 q^{26} -1.00000 q^{27} -9.21907 q^{28} -10.5800 q^{29} +0.0716495 q^{30} -7.83632 q^{31} -0.856853 q^{32} -2.89881 q^{33} +0.00681545 q^{34} +4.62140 q^{35} -1.99487 q^{36} -8.07372 q^{37} +0.111728 q^{38} -1.52681 q^{39} +0.286230 q^{40} -7.05677 q^{41} +0.331121 q^{42} -8.61827 q^{43} -5.78275 q^{44} +1.00000 q^{45} +0.212319 q^{46} +1.46262 q^{47} -3.96922 q^{48} +14.3573 q^{49} -0.0716495 q^{50} +0.0951221 q^{51} -3.04579 q^{52} -10.8212 q^{53} +0.0716495 q^{54} +2.89881 q^{55} +1.32278 q^{56} +1.55937 q^{57} +0.758054 q^{58} +0.411730 q^{59} +1.99487 q^{60} +6.82849 q^{61} +0.561468 q^{62} +4.62140 q^{63} -7.87706 q^{64} +1.52681 q^{65} +0.207699 q^{66} -4.00504 q^{67} +0.189756 q^{68} +2.96330 q^{69} -0.331121 q^{70} -15.9839 q^{71} +0.286230 q^{72} +3.79724 q^{73} +0.578478 q^{74} -1.00000 q^{75} +3.11074 q^{76} +13.3966 q^{77} +0.109395 q^{78} +2.51144 q^{79} +3.96922 q^{80} +1.00000 q^{81} +0.505614 q^{82} -0.973947 q^{83} +9.21907 q^{84} -0.0951221 q^{85} +0.617494 q^{86} +10.5800 q^{87} +0.829728 q^{88} +13.2138 q^{89} -0.0716495 q^{90} +7.05601 q^{91} +5.91138 q^{92} +7.83632 q^{93} -0.104796 q^{94} -1.55937 q^{95} +0.856853 q^{96} +0.566932 q^{97} -1.02869 q^{98} +2.89881 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 29 q - q^{2} - 29 q^{3} + 27 q^{4} + 29 q^{5} + q^{6} + 2 q^{7} - 6 q^{8} + 29 q^{9}+O(q^{10}) \) 29 * q - q^2 - 29 * q^3 + 27 * q^4 + 29 * q^5 + q^6 + 2 * q^7 - 6 * q^8 + 29 * q^9	\( 29 q - q^{2} - 29 q^{3} + 27 q^{4} + 29 q^{5} + q^{6} + 2 q^{7} - 6 q^{8} + 29 q^{9} - q^{10} - 21 q^{11} - 27 q^{12} - 8 q^{13} - 30 q^{14} - 29 q^{15} + 23 q^{16} - 28 q^{17} - q^{18} - 9 q^{19} + 27 q^{20} - 2 q^{21} - 9 q^{22} + 6 q^{24} + 29 q^{25} - 34 q^{26} - 29 q^{27} + 6 q^{28} - 61 q^{29} + q^{30} - 19 q^{31} - 8 q^{32} + 21 q^{33} - 16 q^{34} + 2 q^{35} + 27 q^{36} - 4 q^{37} + 4 q^{38} + 8 q^{39} - 6 q^{40} - 85 q^{41} + 30 q^{42} + 29 q^{43} - 69 q^{44} + 29 q^{45} - 35 q^{46} - 2 q^{47} - 23 q^{48} + q^{49} - q^{50} + 28 q^{51} - 28 q^{52} - 5 q^{53} + q^{54} - 21 q^{55} - 97 q^{56} + 9 q^{57} + 6 q^{58} - 43 q^{59} - 27 q^{60} - 59 q^{61} - 17 q^{62} + 2 q^{63} - 6 q^{64} - 8 q^{65} + 9 q^{66} + 28 q^{67} - 44 q^{68} - 30 q^{70} - 44 q^{71} - 6 q^{72} - 41 q^{73} - 50 q^{74} - 29 q^{75} - 62 q^{76} - 20 q^{77} + 34 q^{78} - 25 q^{79} + 23 q^{80} + 29 q^{81} - 29 q^{82} - 7 q^{83} - 6 q^{84} - 28 q^{85} - 43 q^{86} + 61 q^{87} - 3 q^{88} - 109 q^{89} - q^{90} - q^{91} - 11 q^{92} + 19 q^{93} - 20 q^{94} - 9 q^{95} + 8 q^{96} - 51 q^{97} - 12 q^{98} - 21 q^{99}+O(q^{100}) \) 29 * q - q^2 - 29 * q^3 + 27 * q^4 + 29 * q^5 + q^6 + 2 * q^7 - 6 * q^8 + 29 * q^9 - q^10 - 21 * q^11 - 27 * q^12 - 8 * q^13 - 30 * q^14 - 29 * q^15 + 23 * q^16 - 28 * q^17 - q^18 - 9 * q^19 + 27 * q^20 - 2 * q^21 - 9 * q^22 + 6 * q^24 + 29 * q^25 - 34 * q^26 - 29 * q^27 + 6 * q^28 - 61 * q^29 + q^30 - 19 * q^31 - 8 * q^32 + 21 * q^33 - 16 * q^34 + 2 * q^35 + 27 * q^36 - 4 * q^37 + 4 * q^38 + 8 * q^39 - 6 * q^40 - 85 * q^41 + 30 * q^42 + 29 * q^43 - 69 * q^44 + 29 * q^45 - 35 * q^46 - 2 * q^47 - 23 * q^48 + q^49 - q^50 + 28 * q^51 - 28 * q^52 - 5 * q^53 + q^54 - 21 * q^55 - 97 * q^56 + 9 * q^57 + 6 * q^58 - 43 * q^59 - 27 * q^60 - 59 * q^61 - 17 * q^62 + 2 * q^63 - 6 * q^64 - 8 * q^65 + 9 * q^66 + 28 * q^67 - 44 * q^68 - 30 * q^70 - 44 * q^71 - 6 * q^72 - 41 * q^73 - 50 * q^74 - 29 * q^75 - 62 * q^76 - 20 * q^77 + 34 * q^78 - 25 * q^79 + 23 * q^80 + 29 * q^81 - 29 * q^82 - 7 * q^83 - 6 * q^84 - 28 * q^85 - 43 * q^86 + 61 * q^87 - 3 * q^88 - 109 * q^89 - q^90 - q^91 - 11 * q^92 + 19 * q^93 - 20 * q^94 - 9 * q^95 + 8 * q^96 - 51 * q^97 - 12 * q^98 - 21 * q^99

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