LMFDB - Embedded newform 8034.2.a.bd.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8034,2,Mod(1,8034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8034, 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("8034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8034 = 2 \cdot 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8034.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:	$64.1518129839$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 5 x^{15} - 36 x^{14} + 196 x^{13} + 498 x^{12} - 3101 x^{11} - 3150 x^{10} + 25368 x^{9} + \cdots - 66432 $ x^16 - 5x^15 - 36x^14 + 196x^13 + 498x^12 - 3101x^11 - 3150x^10 + 25368x^9 + 6763x^8 - 113788x^7 + 19731x^6 + 270913x^5 - 122680x^4 - 296326x^3 + 185524x^2 + 94528*x - 66432
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Root			$2.32411$ of defining polynomial
Character	$\chi$	$=$	8034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.32411 q^{5} +1.00000 q^{6} -3.70744 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.32411 q^{5} +1.00000 q^{6} -3.70744 q^{7} +1.00000 q^{8} +1.00000 q^{9} +2.32411 q^{10} +6.03187 q^{11} +1.00000 q^{12} -1.00000 q^{13} -3.70744 q^{14} +2.32411 q^{15} +1.00000 q^{16} +7.20115 q^{17} +1.00000 q^{18} +0.841202 q^{19} +2.32411 q^{20} -3.70744 q^{21} +6.03187 q^{22} +2.94538 q^{23} +1.00000 q^{24} +0.401498 q^{25} -1.00000 q^{26} +1.00000 q^{27} -3.70744 q^{28} -1.46685 q^{29} +2.32411 q^{30} +3.49975 q^{31} +1.00000 q^{32} +6.03187 q^{33} +7.20115 q^{34} -8.61651 q^{35} +1.00000 q^{36} -1.44780 q^{37} +0.841202 q^{38} -1.00000 q^{39} +2.32411 q^{40} +11.7351 q^{41} -3.70744 q^{42} -9.92938 q^{43} +6.03187 q^{44} +2.32411 q^{45} +2.94538 q^{46} -10.3301 q^{47} +1.00000 q^{48} +6.74512 q^{49} +0.401498 q^{50} +7.20115 q^{51} -1.00000 q^{52} -9.19838 q^{53} +1.00000 q^{54} +14.0187 q^{55} -3.70744 q^{56} +0.841202 q^{57} -1.46685 q^{58} -0.782122 q^{59} +2.32411 q^{60} +5.91826 q^{61} +3.49975 q^{62} -3.70744 q^{63} +1.00000 q^{64} -2.32411 q^{65} +6.03187 q^{66} +4.71378 q^{67} +7.20115 q^{68} +2.94538 q^{69} -8.61651 q^{70} -4.98753 q^{71} +1.00000 q^{72} -4.01235 q^{73} -1.44780 q^{74} +0.401498 q^{75} +0.841202 q^{76} -22.3628 q^{77} -1.00000 q^{78} +7.92716 q^{79} +2.32411 q^{80} +1.00000 q^{81} +11.7351 q^{82} -8.29536 q^{83} -3.70744 q^{84} +16.7363 q^{85} -9.92938 q^{86} -1.46685 q^{87} +6.03187 q^{88} +2.41377 q^{89} +2.32411 q^{90} +3.70744 q^{91} +2.94538 q^{92} +3.49975 q^{93} -10.3301 q^{94} +1.95505 q^{95} +1.00000 q^{96} +2.64651 q^{97} +6.74512 q^{98} +6.03187 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{2} + 16 q^{3} + 16 q^{4} + 5 q^{5} + 16 q^{6} + 4 q^{7} + 16 q^{8} + 16 q^{9}+O(q^{10}) $ 16 * q + 16 * q^2 + 16 * q^3 + 16 * q^4 + 5 * q^5 + 16 * q^6 + 4 * q^7 + 16 * q^8 + 16 * q^9	\( 16 q + 16 q^{2} + 16 q^{3} + 16 q^{4} + 5 q^{5} + 16 q^{6} + 4 q^{7} + 16 q^{8} + 16 q^{9} + 5 q^{10} + 18 q^{11} + 16 q^{12} - 16 q^{13} + 4 q^{14} + 5 q^{15} + 16 q^{16} + 17 q^{17} + 16 q^{18} + 8 q^{19} + 5 q^{20} + 4 q^{21} + 18 q^{22} + 9 q^{23} + 16 q^{24} + 17 q^{25} - 16 q^{26} + 16 q^{27} + 4 q^{28} + 14 q^{29} + 5 q^{30} + 12 q^{31} + 16 q^{32} + 18 q^{33} + 17 q^{34} + 16 q^{35} + 16 q^{36} + 31 q^{37} + 8 q^{38} - 16 q^{39} + 5 q^{40} + 29 q^{41} + 4 q^{42} + 30 q^{43} + 18 q^{44} + 5 q^{45} + 9 q^{46} - q^{47} + 16 q^{48} + 36 q^{49} + 17 q^{50} + 17 q^{51} - 16 q^{52} + 12 q^{53} + 16 q^{54} + 30 q^{55} + 4 q^{56} + 8 q^{57} + 14 q^{58} + 38 q^{59} + 5 q^{60} + 12 q^{62} + 4 q^{63} + 16 q^{64} - 5 q^{65} + 18 q^{66} + 28 q^{67} + 17 q^{68} + 9 q^{69} + 16 q^{70} + 32 q^{71} + 16 q^{72} + 20 q^{73} + 31 q^{74} + 17 q^{75} + 8 q^{76} + 26 q^{77} - 16 q^{78} + 13 q^{79} + 5 q^{80} + 16 q^{81} + 29 q^{82} + 39 q^{83} + 4 q^{84} + 31 q^{85} + 30 q^{86} + 14 q^{87} + 18 q^{88} + 9 q^{89} + 5 q^{90} - 4 q^{91} + 9 q^{92} + 12 q^{93} - q^{94} - 20 q^{95} + 16 q^{96} + 35 q^{97} + 36 q^{98} + 18 q^{99}+O(q^{100}) \) 16 * q + 16 * q^2 + 16 * q^3 + 16 * q^4 + 5 * q^5 + 16 * q^6 + 4 * q^7 + 16 * q^8 + 16 * q^9 + 5 * q^10 + 18 * q^11 + 16 * q^12 - 16 * q^13 + 4 * q^14 + 5 * q^15 + 16 * q^16 + 17 * q^17 + 16 * q^18 + 8 * q^19 + 5 * q^20 + 4 * q^21 + 18 * q^22 + 9 * q^23 + 16 * q^24 + 17 * q^25 - 16 * q^26 + 16 * q^27 + 4 * q^28 + 14 * q^29 + 5 * q^30 + 12 * q^31 + 16 * q^32 + 18 * q^33 + 17 * q^34 + 16 * q^35 + 16 * q^36 + 31 * q^37 + 8 * q^38 - 16 * q^39 + 5 * q^40 + 29 * q^41 + 4 * q^42 + 30 * q^43 + 18 * q^44 + 5 * q^45 + 9 * q^46 - q^47 + 16 * q^48 + 36 * q^49 + 17 * q^50 + 17 * q^51 - 16 * q^52 + 12 * q^53 + 16 * q^54 + 30 * q^55 + 4 * q^56 + 8 * q^57 + 14 * q^58 + 38 * q^59 + 5 * q^60 + 12 * q^62 + 4 * q^63 + 16 * q^64 - 5 * q^65 + 18 * q^66 + 28 * q^67 + 17 * q^68 + 9 * q^69 + 16 * q^70 + 32 * q^71 + 16 * q^72 + 20 * q^73 + 31 * q^74 + 17 * q^75 + 8 * q^76 + 26 * q^77 - 16 * q^78 + 13 * q^79 + 5 * q^80 + 16 * q^81 + 29 * q^82 + 39 * q^83 + 4 * q^84 + 31 * q^85 + 30 * q^86 + 14 * q^87 + 18 * q^88 + 9 * q^89 + 5 * q^90 - 4 * q^91 + 9 * q^92 + 12 * q^93 - q^94 - 20 * q^95 + 16 * q^96 + 35 * q^97 + 36 * q^98 + 18 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	2.32411	1.03937	0.519687	−	0.854357i	$-0.326048\pi$
$5$	2.32411	1.03937	0.519687	+	0.854357i	$0.326048\pi$
$6$	1.00000	0.408248
$7$	−3.70744	−1.40128	−0.700640	−	0.713515i	$-0.747102\pi$
$7$	−3.70744	−1.40128	−0.700640	+	0.713515i	$0.747102\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	2.32411	0.734949
$11$	6.03187	1.81868	0.909338	−	0.416057i	$-0.136588\pi$
$11$	6.03187	1.81868	0.909338	+	0.416057i	$0.136588\pi$
$12$	1.00000	0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−3.70744	−0.990855
$15$	2.32411	0.600083
$16$	1.00000	0.250000
$17$	7.20115	1.74653	0.873267	−	0.487241i	$-0.161997\pi$
$17$	7.20115	1.74653	0.873267	+	0.487241i	$0.161997\pi$
$18$	1.00000	0.235702
$19$	0.841202	0.192985	0.0964925	−	0.995334i	$-0.469238\pi$
$19$	0.841202	0.192985	0.0964925	+	0.995334i	$0.469238\pi$
$20$	2.32411	0.519687
$21$	−3.70744	−0.809030
$22$	6.03187	1.28600
$23$	2.94538	0.614154	0.307077	−	0.951685i	$-0.400649\pi$
$23$	2.94538	0.614154	0.307077	+	0.951685i	$0.400649\pi$
$24$	1.00000	0.204124
$25$	0.401498	0.0802995
$26$	−1.00000	−0.196116
$27$	1.00000	0.192450
$28$	−3.70744	−0.700640
$29$	−1.46685	−0.272387	−0.136193	−	0.990682i	$-0.543487\pi$
$29$	−1.46685	−0.272387	−0.136193	+	0.990682i	$0.543487\pi$
$30$	2.32411	0.424323
$31$	3.49975	0.628574	0.314287	−	0.949328i	$-0.398234\pi$
$31$	3.49975	0.628574	0.314287	+	0.949328i	$0.398234\pi$
$32$	1.00000	0.176777
$33$	6.03187	1.05001
$34$	7.20115	1.23499
$35$	−8.61651	−1.45646
$36$	1.00000	0.166667
$37$	−1.44780	−0.238017	−0.119008	−	0.992893i	$-0.537972\pi$
$37$	−1.44780	−0.238017	−0.119008	+	0.992893i	$0.537972\pi$
$38$	0.841202	0.136461
$39$	−1.00000	−0.160128
$40$	2.32411	0.367474
$41$	11.7351	1.83271	0.916357	−	0.400363i	$-0.131116\pi$
$41$	11.7351	1.83271	0.916357	+	0.400363i	$0.131116\pi$
$42$	−3.70744	−0.572071
$43$	−9.92938	−1.51422	−0.757108	−	0.653289i	$-0.773388\pi$
$43$	−9.92938	−1.51422	−0.757108	+	0.653289i	$0.773388\pi$
$44$	6.03187	0.909338
$45$	2.32411	0.346458
$46$	2.94538	0.434273
$47$	−10.3301	−1.50679	−0.753397	−	0.657566i	$-0.771586\pi$
$47$	−10.3301	−1.50679	−0.753397	+	0.657566i	$0.771586\pi$
$48$	1.00000	0.144338
$49$	6.74512	0.963588
$50$	0.401498	0.0567803
$51$	7.20115	1.00836
$52$	−1.00000	−0.138675
$53$	−9.19838	−1.26349	−0.631747	−	0.775174i	$-0.717662\pi$
$53$	−9.19838	−1.26349	−0.631747	+	0.775174i	$0.717662\pi$
$54$	1.00000	0.136083
$55$	14.0187	1.89029
$56$	−3.70744	−0.495428
$57$	0.841202	0.111420
$58$	−1.46685	−0.192607
$59$	−0.782122	−0.101824	−0.0509118	−	0.998703i	$-0.516213\pi$
$59$	−0.782122	−0.101824	−0.0509118	+	0.998703i	$0.516213\pi$
$60$	2.32411	0.300042
$61$	5.91826	0.757755	0.378878	−	0.925447i	$-0.376310\pi$
$61$	5.91826	0.757755	0.378878	+	0.925447i	$0.376310\pi$
$62$	3.49975	0.444469
$63$	−3.70744	−0.467094
$64$	1.00000	0.125000
$65$	−2.32411	−0.288271
$66$	6.03187	0.742472
$67$	4.71378	0.575880	0.287940	−	0.957648i	$-0.407030\pi$
$67$	4.71378	0.575880	0.287940	+	0.957648i	$0.407030\pi$
$68$	7.20115	0.873267
$69$	2.94538	0.354582
$70$	−8.61651	−1.02987
$71$	−4.98753	−0.591911	−0.295956	−	0.955202i	$-0.595638\pi$
$71$	−4.98753	−0.591911	−0.295956	+	0.955202i	$0.595638\pi$
$72$	1.00000	0.117851
$73$	−4.01235	−0.469610	−0.234805	−	0.972042i	$-0.575445\pi$
$73$	−4.01235	−0.469610	−0.234805	+	0.972042i	$0.575445\pi$
$74$	−1.44780	−0.168303
$75$	0.401498	0.0463610
$76$	0.841202	0.0964925
$77$	−22.3628	−2.54848
$78$	−1.00000	−0.113228
$79$	7.92716	0.891876	0.445938	−	0.895064i	$-0.352870\pi$
$79$	7.92716	0.891876	0.445938	+	0.895064i	$0.352870\pi$
$80$	2.32411	0.259844
$81$	1.00000	0.111111
$82$	11.7351	1.29592
$83$	−8.29536	−0.910534	−0.455267	−	0.890355i	$-0.650456\pi$
$83$	−8.29536	−0.910534	−0.455267	+	0.890355i	$0.650456\pi$
$84$	−3.70744	−0.404515
$85$	16.7363	1.81530
$86$	−9.92938	−1.07071
$87$	−1.46685	−0.157263
$88$	6.03187	0.642999
$89$	2.41377	0.255859	0.127930	−	0.991783i	$-0.459167\pi$
$89$	2.41377	0.255859	0.127930	+	0.991783i	$0.459167\pi$
$90$	2.32411	0.244983
$91$	3.70744	0.388645
$92$	2.94538	0.307077
$93$	3.49975	0.362908
$94$	−10.3301	−1.06546
$95$	1.95505	0.200584
$96$	1.00000	0.102062
$97$	2.64651	0.268713	0.134356	−	0.990933i	$-0.457103\pi$
$97$	2.64651	0.268713	0.134356	+	0.990933i	$0.457103\pi$
$98$	6.74512	0.681360
$99$	6.03187	0.606226
$100$	0.401498	0.0401498
$101$	−11.2571	−1.12012	−0.560059	−	0.828452i	$-0.689222\pi$
$101$	−11.2571	−1.12012	−0.560059	+	0.828452i	$0.689222\pi$
$102$	7.20115	0.713020
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	−1.00000	−0.0980581
$105$	−8.61651	−0.840885
$106$	−9.19838	−0.893426
$107$	−6.14170	−0.593740	−0.296870	−	0.954918i	$-0.595943\pi$
$107$	−6.14170	−0.593740	−0.296870	+	0.954918i	$0.595943\pi$
$108$	1.00000	0.0962250
$109$	9.92960	0.951083	0.475541	−	0.879693i	$-0.342252\pi$
$109$	9.92960	0.951083	0.475541	+	0.879693i	$0.342252\pi$
$110$	14.0187	1.33663
$111$	−1.44780	−0.137419
$112$	−3.70744	−0.350320
$113$	14.7366	1.38630	0.693152	−	0.720791i	$-0.256221\pi$
$113$	14.7366	1.38630	0.693152	+	0.720791i	$0.256221\pi$
$114$	0.841202	0.0787858
$115$	6.84539	0.638336
$116$	−1.46685	−0.136193
$117$	−1.00000	−0.0924500
$118$	−0.782122	−0.0720002
$119$	−26.6978	−2.44739
$120$	2.32411	0.212161
$121$	25.3834	2.30759
$122$	5.91826	0.535814
$123$	11.7351	1.05812
$124$	3.49975	0.314287
$125$	−10.6874	−0.955913
$126$	−3.70744	−0.330285
$127$	−12.1254	−1.07595	−0.537976	−	0.842960i	$-0.680811\pi$
$127$	−12.1254	−1.07595	−0.537976	+	0.842960i	$0.680811\pi$
$128$	1.00000	0.0883883
$129$	−9.92938	−0.874233
$130$	−2.32411	−0.203838
$131$	16.1038	1.40699	0.703496	−	0.710699i	$-0.251621\pi$
$131$	16.1038	1.40699	0.703496	+	0.710699i	$0.251621\pi$
$132$	6.03187	0.525007
$133$	−3.11871	−0.270426
$134$	4.71378	0.407209
$135$	2.32411	0.200028
$136$	7.20115	0.617493
$137$	9.39811	0.802935	0.401467	−	0.915873i	$-0.368500\pi$
$137$	9.39811	0.802935	0.401467	+	0.915873i	$0.368500\pi$
$138$	2.94538	0.250727
$139$	2.52169	0.213887	0.106943	−	0.994265i	$-0.465894\pi$
$139$	2.52169	0.213887	0.106943	+	0.994265i	$0.465894\pi$
$140$	−8.61651	−0.728228
$141$	−10.3301	−0.869948
$142$	−4.98753	−0.418545
$143$	−6.03187	−0.504410
$144$	1.00000	0.0833333
$145$	−3.40912	−0.283112
$146$	−4.01235	−0.332065
$147$	6.74512	0.556328
$148$	−1.44780	−0.119008
$149$	14.9136	1.22177	0.610885	−	0.791719i	$-0.290814\pi$
$149$	14.9136	1.22177	0.610885	+	0.791719i	$0.290814\pi$
$150$	0.401498	0.0327821
$151$	−4.64018	−0.377613	−0.188806	−	0.982014i	$-0.560462\pi$
$151$	−4.64018	−0.377613	−0.188806	+	0.982014i	$0.560462\pi$
$152$	0.841202	0.0682305
$153$	7.20115	0.582178
$154$	−22.3628	−1.80205
$155$	8.13382	0.653324
$156$	−1.00000	−0.0800641
$157$	4.55047	0.363167	0.181583	−	0.983376i	$-0.441878\pi$
$157$	4.55047	0.363167	0.181583	+	0.983376i	$0.441878\pi$
$158$	7.92716	0.630651
$159$	−9.19838	−0.729479
$160$	2.32411	0.183737
$161$	−10.9198	−0.860603
$162$	1.00000	0.0785674
$163$	−18.8878	−1.47940	−0.739702	−	0.672934i	$-0.765034\pi$
$163$	−18.8878	−1.47940	−0.739702	+	0.672934i	$0.765034\pi$
$164$	11.7351	0.916357
$165$	14.0187	1.09136
$166$	−8.29536	−0.643845
$167$	−11.4799	−0.888342	−0.444171	−	0.895942i	$-0.646502\pi$
$167$	−11.4799	−0.888342	−0.444171	+	0.895942i	$0.646502\pi$
$168$	−3.70744	−0.286035
$169$	1.00000	0.0769231
$170$	16.7363	1.28361
$171$	0.841202	0.0643283
$172$	−9.92938	−0.757108
$173$	−12.8620	−0.977883	−0.488941	−	0.872317i	$-0.662617\pi$
$173$	−12.8620	−0.977883	−0.488941	+	0.872317i	$0.662617\pi$
$174$	−1.46685	−0.111202
$175$	−1.48853	−0.112522
$176$	6.03187	0.454669
$177$	−0.782122	−0.0587879
$178$	2.41377	0.180920
$179$	−0.940655	−0.0703079	−0.0351539	−	0.999382i	$-0.511192\pi$
$179$	−0.940655	−0.0703079	−0.0351539	+	0.999382i	$0.511192\pi$
$180$	2.32411	0.173229
$181$	15.1128	1.12333	0.561664	−	0.827365i	$-0.310161\pi$
$181$	15.1128	1.12333	0.561664	+	0.827365i	$0.310161\pi$
$182$	3.70744	0.274814
$183$	5.91826	0.437490
$184$	2.94538	0.217136
$185$	−3.36485	−0.247389
$186$	3.49975	0.256614
$187$	43.4364	3.17638
$188$	−10.3301	−0.753397
$189$	−3.70744	−0.269677
$190$	1.95505	0.141834
$191$	10.9366	0.791344	0.395672	−	0.918392i	$-0.370512\pi$
$191$	10.9366	0.791344	0.395672	+	0.918392i	$0.370512\pi$
$192$	1.00000	0.0721688
$193$	−21.5581	−1.55179	−0.775893	−	0.630864i	$-0.782700\pi$
$193$	−21.5581	−1.55179	−0.775893	+	0.630864i	$0.782700\pi$
$194$	2.64651	0.190009
$195$	−2.32411	−0.166433
$196$	6.74512	0.481794
$197$	0.833763	0.0594031	0.0297016	−	0.999559i	$-0.490544\pi$
$197$	0.833763	0.0594031	0.0297016	+	0.999559i	$0.490544\pi$
$198$	6.03187	0.428666
$199$	18.1586	1.28723	0.643615	−	0.765350i	$-0.277434\pi$
$199$	18.1586	1.28723	0.643615	+	0.765350i	$0.277434\pi$
$200$	0.401498	0.0283902
$201$	4.71378	0.332485
$202$	−11.2571	−0.792044
$203$	5.43825	0.381691
$204$	7.20115	0.504181
$205$	27.2737	1.90488
$206$	1.00000	0.0696733
$207$	2.94538	0.204718
$208$	−1.00000	−0.0693375
$209$	5.07402	0.350977
$210$	−8.61651	−0.594596
$211$	28.4693	1.95991	0.979955	−	0.199221i	$-0.0638412\pi$
$211$	28.4693	1.95991	0.979955	+	0.199221i	$0.0638412\pi$
$212$	−9.19838	−0.631747
$213$	−4.98753	−0.341740
$214$	−6.14170	−0.419838
$215$	−23.0770	−1.57384
$216$	1.00000	0.0680414
$217$	−12.9751	−0.880809
$218$	9.92960	0.672517
$219$	−4.01235	−0.271130
$220$	14.0187	0.945143
$221$	−7.20115	−0.484402
$222$	−1.44780	−0.0971700
$223$	−8.30446	−0.556108	−0.278054	−	0.960566i	$-0.589689\pi$
$223$	−8.30446	−0.556108	−0.278054	+	0.960566i	$0.589689\pi$
$224$	−3.70744	−0.247714
$225$	0.401498	0.0267665
$226$	14.7366	0.980265
$227$	22.0374	1.46267	0.731336	−	0.682017i	$-0.238897\pi$
$227$	22.0374	1.46267	0.731336	+	0.682017i	$0.238897\pi$
$228$	0.841202	0.0557100
$229$	21.8771	1.44568	0.722839	−	0.691017i	$-0.242837\pi$
$229$	21.8771	1.44568	0.722839	+	0.691017i	$0.242837\pi$
$230$	6.84539	0.451372
$231$	−22.3628	−1.47136
$232$	−1.46685	−0.0963033
$233$	−25.2568	−1.65463	−0.827313	−	0.561741i	$-0.810132\pi$
$233$	−25.2568	−1.65463	−0.827313	+	0.561741i	$0.810132\pi$
$234$	−1.00000	−0.0653720
$235$	−24.0082	−1.56612
$236$	−0.782122	−0.0509118
$237$	7.92716	0.514925
$238$	−26.6978	−1.73056
$239$	19.9522	1.29060	0.645301	−	0.763928i	$-0.276732\pi$
$239$	19.9522	1.29060	0.645301	+	0.763928i	$0.276732\pi$
$240$	2.32411	0.150021
$241$	9.65207	0.621745	0.310872	−	0.950452i	$-0.399379\pi$
$241$	9.65207	0.621745	0.310872	+	0.950452i	$0.399379\pi$
$242$	25.3834	1.63171
$243$	1.00000	0.0641500
$244$	5.91826	0.378878
$245$	15.6764	1.00153
$246$	11.7351	0.748202
$247$	−0.841202	−0.0535244
$248$	3.49975	0.222235
$249$	−8.29536	−0.525697
$250$	−10.6874	−0.675933
$251$	10.5259	0.664391	0.332195	−	0.943211i	$-0.392211\pi$
$251$	10.5259	0.664391	0.332195	+	0.943211i	$0.392211\pi$
$252$	−3.70744	−0.233547
$253$	17.7661	1.11695
$254$	−12.1254	−0.760814
$255$	16.7363	1.04807
$256$	1.00000	0.0625000
$257$	−4.46927	−0.278785	−0.139393	−	0.990237i	$-0.544515\pi$
$257$	−4.46927	−0.278785	−0.139393	+	0.990237i	$0.544515\pi$
$258$	−9.92938	−0.618176
$259$	5.36763	0.333528
$260$	−2.32411	−0.144135
$261$	−1.46685	−0.0907957
$262$	16.1038	0.994893
$263$	9.78847	0.603583	0.301791	−	0.953374i	$-0.402415\pi$
$263$	9.78847	0.603583	0.301791	+	0.953374i	$0.402415\pi$
$264$	6.03187	0.371236
$265$	−21.3781	−1.31324
$266$	−3.11871	−0.191220
$267$	2.41377	0.147720
$268$	4.71378	0.287940
$269$	−19.5484	−1.19189	−0.595944	−	0.803026i	$-0.703222\pi$
$269$	−19.5484	−1.19189	−0.595944	+	0.803026i	$0.703222\pi$
$270$	2.32411	0.141441
$271$	−32.7032	−1.98658	−0.993288	−	0.115668i	$-0.963099\pi$
$271$	−32.7032	−1.98658	−0.993288	+	0.115668i	$0.963099\pi$
$272$	7.20115	0.436634
$273$	3.70744	0.224385
$274$	9.39811	0.567761
$275$	2.42178	0.146039
$276$	2.94538	0.177291
$277$	−0.514016	−0.0308843	−0.0154421	−	0.999881i	$-0.504916\pi$
$277$	−0.514016	−0.0308843	−0.0154421	+	0.999881i	$0.504916\pi$
$278$	2.52169	0.151241
$279$	3.49975	0.209525
$280$	−8.61651	−0.514935
$281$	−6.88904	−0.410966	−0.205483	−	0.978661i	$-0.565876\pi$
$281$	−6.88904	−0.410966	−0.205483	+	0.978661i	$0.565876\pi$
$282$	−10.3301	−0.615146
$283$	5.41359	0.321804	0.160902	−	0.986970i	$-0.448560\pi$
$283$	5.41359	0.321804	0.160902	+	0.986970i	$0.448560\pi$
$284$	−4.98753	−0.295956
$285$	1.95505	0.115807
$286$	−6.03187	−0.356672
$287$	−43.5072	−2.56815
$288$	1.00000	0.0589256
$289$	34.8565	2.05038
$290$	−3.40912	−0.200190
$291$	2.64651	0.155141
$292$	−4.01235	−0.234805
$293$	22.3703	1.30689	0.653443	−	0.756975i	$-0.273324\pi$
$293$	22.3703	1.30689	0.653443	+	0.756975i	$0.273324\pi$
$294$	6.74512	0.393383
$295$	−1.81774	−0.105833
$296$	−1.44780	−0.0841516
$297$	6.03187	0.350005
$298$	14.9136	0.863922
$299$	−2.94538	−0.170336
$300$	0.401498	0.0231805
$301$	36.8126	2.12184
$302$	−4.64018	−0.267012
$303$	−11.2571	−0.646701
$304$	0.841202	0.0482462
$305$	13.7547	0.787591
$306$	7.20115	0.411662
$307$	6.51875	0.372044	0.186022	−	0.982546i	$-0.440440\pi$
$307$	6.51875	0.372044	0.186022	+	0.982546i	$0.440440\pi$
$308$	−22.3628	−1.27424
$309$	1.00000	0.0568880
$310$	8.13382	0.461970
$311$	7.28059	0.412845	0.206422	−	0.978463i	$-0.433818\pi$
$311$	7.28059	0.412845	0.206422	+	0.978463i	$0.433818\pi$
$312$	−1.00000	−0.0566139
$313$	−7.68846	−0.434578	−0.217289	−	0.976107i	$-0.569721\pi$
$313$	−7.68846	−0.434578	−0.217289	+	0.976107i	$0.569721\pi$
$314$	4.55047	0.256798
$315$	−8.61651	−0.485485
$316$	7.92716	0.445938
$317$	−18.5462	−1.04166	−0.520829	−	0.853661i	$-0.674377\pi$
$317$	−18.5462	−1.04166	−0.520829	+	0.853661i	$0.674377\pi$
$318$	−9.19838	−0.515820
$319$	−8.84784	−0.495384
$320$	2.32411	0.129922
$321$	−6.14170	−0.342796
$322$	−10.9198	−0.608538
$323$	6.05762	0.337055
$324$	1.00000	0.0555556
$325$	−0.401498	−0.0222711
$326$	−18.8878	−1.04610
$327$	9.92960	0.549108
$328$	11.7351	0.647962
$329$	38.2981	2.11144
$330$	14.0187	0.771706
$331$	0.452873	0.0248921	0.0124461	−	0.999923i	$-0.496038\pi$
$331$	0.452873	0.0248921	0.0124461	+	0.999923i	$0.496038\pi$
$332$	−8.29536	−0.455267
$333$	−1.44780	−0.0793389
$334$	−11.4799	−0.628153
$335$	10.9554	0.598555
$336$	−3.70744	−0.202257
$337$	−10.7409	−0.585093	−0.292546	−	0.956251i	$-0.594503\pi$
$337$	−10.7409	−0.585093	−0.292546	+	0.956251i	$0.594503\pi$
$338$	1.00000	0.0543928
$339$	14.7366	0.800383
$340$	16.7363	0.907652
$341$	21.1101	1.14317
$342$	0.841202	0.0454870
$343$	0.944967	0.0510234
$344$	−9.92938	−0.535356
$345$	6.84539	0.368544
$346$	−12.8620	−0.691467
$347$	−15.5969	−0.837285	−0.418642	−	0.908151i	$-0.637494\pi$
$347$	−15.5969	−0.837285	−0.418642	+	0.908151i	$0.637494\pi$
$348$	−1.46685	−0.0786313
$349$	−29.6900	−1.58927	−0.794636	−	0.607086i	$-0.792338\pi$
$349$	−29.6900	−1.58927	−0.794636	+	0.607086i	$0.792338\pi$
$350$	−1.48853	−0.0795652
$351$	−1.00000	−0.0533761
$352$	6.03187	0.321500
$353$	8.91641	0.474573	0.237286	−	0.971440i	$-0.423742\pi$
$353$	8.91641	0.474573	0.237286	+	0.971440i	$0.423742\pi$
$354$	−0.782122	−0.0415693
$355$	−11.5916	−0.615218
$356$	2.41377	0.127930
$357$	−26.6978	−1.41300
$358$	−0.940655	−0.0497152
$359$	−11.3388	−0.598441	−0.299220	−	0.954184i	$-0.596727\pi$
$359$	−11.3388	−0.598441	−0.299220	+	0.954184i	$0.596727\pi$
$360$	2.32411	0.122491
$361$	−18.2924	−0.962757
$362$	15.1128	0.794313
$363$	25.3834	1.33228
$364$	3.70744	0.194323
$365$	−9.32516	−0.488101
$366$	5.91826	0.309352
$367$	−1.06892	−0.0557969	−0.0278985	−	0.999611i	$-0.508882\pi$
$367$	−1.06892	−0.0557969	−0.0278985	+	0.999611i	$0.508882\pi$
$368$	2.94538	0.153539
$369$	11.7351	0.610904
$370$	−3.36485	−0.174930
$371$	34.1025	1.77051
$372$	3.49975	0.181454
$373$	−18.0980	−0.937079	−0.468539	−	0.883443i	$-0.655220\pi$
$373$	−18.0980	−0.937079	−0.468539	+	0.883443i	$0.655220\pi$
$374$	43.4364	2.24604
$375$	−10.6874	−0.551897
$376$	−10.3301	−0.532732
$377$	1.46685	0.0755466
$378$	−3.70744	−0.190690
$379$	−23.3350	−1.19864	−0.599320	−	0.800510i	$-0.704562\pi$
$379$	−23.3350	−1.19864	−0.599320	+	0.800510i	$0.704562\pi$
$380$	1.95505	0.100292
$381$	−12.1254	−0.621202
$382$	10.9366	0.559564
$383$	−5.79309	−0.296013	−0.148007	−	0.988986i	$-0.547286\pi$
$383$	−5.79309	−0.296013	−0.148007	+	0.988986i	$0.547286\pi$
$384$	1.00000	0.0510310
$385$	−51.9736	−2.64882
$386$	−21.5581	−1.09728
$387$	−9.92938	−0.504739
$388$	2.64651	0.134356
$389$	−32.5677	−1.65125	−0.825624	−	0.564221i	$-0.809176\pi$
$389$	−32.5677	−1.65125	−0.825624	+	0.564221i	$0.809176\pi$
$390$	−2.32411	−0.117686
$391$	21.2101	1.07264
$392$	6.74512	0.340680
$393$	16.1038	0.812327
$394$	0.833763	0.0420044
$395$	18.4236	0.926993
$396$	6.03187	0.303113
$397$	26.4230	1.32613	0.663066	−	0.748561i	$-0.269255\pi$
$397$	26.4230	1.32613	0.663066	+	0.748561i	$0.269255\pi$
$398$	18.1586	0.910209
$399$	−3.11871	−0.156131
$400$	0.401498	0.0200749
$401$	13.5667	0.677489	0.338745	−	0.940878i	$-0.389998\pi$
$401$	13.5667	0.677489	0.338745	+	0.940878i	$0.389998\pi$
$402$	4.71378	0.235102
$403$	−3.49975	−0.174335
$404$	−11.2571	−0.560059
$405$	2.32411	0.115486
$406$	5.43825	0.269896
$407$	−8.73294	−0.432876
$408$	7.20115	0.356510
$409$	−26.4123	−1.30601	−0.653003	−	0.757355i	$-0.726491\pi$
$409$	−26.4123	−1.30601	−0.653003	+	0.757355i	$0.726491\pi$
$410$	27.2737	1.34695
$411$	9.39811	0.463575
$412$	1.00000	0.0492665
$413$	2.89967	0.142683
$414$	2.94538	0.144758
$415$	−19.2794	−0.946386
$416$	−1.00000	−0.0490290
$417$	2.52169	0.123488
$418$	5.07402	0.248178
$419$	1.21727	0.0594674	0.0297337	−	0.999558i	$-0.490534\pi$
$419$	1.21727	0.0594674	0.0297337	+	0.999558i	$0.490534\pi$
$420$	−8.61651	−0.420443
$421$	34.5797	1.68531	0.842655	−	0.538454i	$-0.180992\pi$
$421$	34.5797	1.68531	0.842655	+	0.538454i	$0.180992\pi$
$422$	28.4693	1.38587
$423$	−10.3301	−0.502265
$424$	−9.19838	−0.446713
$425$	2.89124	0.140246
$426$	−4.98753	−0.241647
$427$	−21.9416	−1.06183
$428$	−6.14170	−0.296870
$429$	−6.03187	−0.291221
$430$	−23.0770	−1.11287
$431$	−34.2783	−1.65113	−0.825564	−	0.564309i	$-0.809143\pi$
$431$	−34.2783	−1.65113	−0.825564	+	0.564309i	$0.809143\pi$
$432$	1.00000	0.0481125
$433$	−19.3932	−0.931978	−0.465989	−	0.884791i	$-0.654301\pi$
$433$	−19.3932	−0.931978	−0.465989	+	0.884791i	$0.654301\pi$
$434$	−12.9751	−0.622826
$435$	−3.40912	−0.163455
$436$	9.92960	0.475541
$437$	2.47766	0.118523
$438$	−4.01235	−0.191718
$439$	20.8177	0.993574	0.496787	−	0.867872i	$-0.334513\pi$
$439$	20.8177	0.993574	0.496787	+	0.867872i	$0.334513\pi$
$440$	14.0187	0.668317
$441$	6.74512	0.321196
$442$	−7.20115	−0.342524
$443$	4.21146	0.200093	0.100046	−	0.994983i	$-0.468101\pi$
$443$	4.21146	0.200093	0.100046	+	0.994983i	$0.468101\pi$
$444$	−1.44780	−0.0687095
$445$	5.60988	0.265934
$446$	−8.30446	−0.393227
$447$	14.9136	0.705389
$448$	−3.70744	−0.175160
$449$	8.78315	0.414503	0.207251	−	0.978288i	$-0.433548\pi$
$449$	8.78315	0.414503	0.207251	+	0.978288i	$0.433548\pi$
$450$	0.401498	0.0189268
$451$	70.7845	3.33311
$452$	14.7366	0.693152
$453$	−4.64018	−0.218015
$454$	22.0374	1.03427
$455$	8.61651	0.403948
$456$	0.841202	0.0393929
$457$	28.6493	1.34016	0.670078	−	0.742291i	$-0.266261\pi$
$457$	28.6493	1.34016	0.670078	+	0.742291i	$0.266261\pi$
$458$	21.8771	1.02225
$459$	7.20115	0.336121
$460$	6.84539	0.319168
$461$	17.1412	0.798345	0.399173	−	0.916876i	$-0.369297\pi$
$461$	17.1412	0.798345	0.399173	+	0.916876i	$0.369297\pi$
$462$	−22.3628	−1.04041
$463$	−21.8785	−1.01678	−0.508390	−	0.861127i	$-0.669759\pi$
$463$	−21.8785	−1.01678	−0.508390	+	0.861127i	$0.669759\pi$
$464$	−1.46685	−0.0680967
$465$	8.13382	0.377197
$466$	−25.2568	−1.17000
$467$	−15.9695	−0.738982	−0.369491	−	0.929234i	$-0.620468\pi$
$467$	−15.9695	−0.738982	−0.369491	+	0.929234i	$0.620468\pi$
$468$	−1.00000	−0.0462250
$469$	−17.4761	−0.806970
$470$	−24.0082	−1.10742
$471$	4.55047	0.209674
$472$	−0.782122	−0.0360001
$473$	−59.8927	−2.75387
$474$	7.92716	0.364107
$475$	0.337741	0.0154966
$476$	−26.6978	−1.22369
$477$	−9.19838	−0.421165
$478$	19.9522	0.912594
$479$	8.07799	0.369093	0.184546	−	0.982824i	$-0.440918\pi$
$479$	8.07799	0.369093	0.184546	+	0.982824i	$0.440918\pi$
$480$	2.32411	0.106081
$481$	1.44780	0.0660140
$482$	9.65207	0.439640
$483$	−10.9198	−0.496869
$484$	25.3834	1.15379
$485$	6.15080	0.279293
$486$	1.00000	0.0453609
$487$	−11.0295	−0.499792	−0.249896	−	0.968273i	$-0.580397\pi$
$487$	−11.0295	−0.499792	−0.249896	+	0.968273i	$0.580397\pi$
$488$	5.91826	0.267907
$489$	−18.8878	−0.854134
$490$	15.6764	0.708188
$491$	−15.2720	−0.689214	−0.344607	−	0.938747i	$-0.611988\pi$
$491$	−15.2720	−0.689214	−0.344607	+	0.938747i	$0.611988\pi$
$492$	11.7351	0.529059
$493$	−10.5630	−0.475733
$494$	−0.841202	−0.0378475
$495$	14.0187	0.630095
$496$	3.49975	0.157144
$497$	18.4910	0.829434
$498$	−8.29536	−0.371724
$499$	−25.9466	−1.16153	−0.580765	−	0.814072i	$-0.697246\pi$
$499$	−25.9466	−1.16153	−0.580765	+	0.814072i	$0.697246\pi$
$500$	−10.6874	−0.477957
$501$	−11.4799	−0.512885
$502$	10.5259	0.469795
$503$	−35.9092	−1.60111	−0.800555	−	0.599259i	$-0.795462\pi$
$503$	−35.9092	−1.60111	−0.800555	+	0.599259i	$0.795462\pi$
$504$	−3.70744	−0.165143
$505$	−26.1627	−1.16422
$506$	17.7661	0.789802
$507$	1.00000	0.0444116
$508$	−12.1254	−0.537976
$509$	−28.4325	−1.26025	−0.630125	−	0.776494i	$-0.716996\pi$
$509$	−28.4325	−1.26025	−0.630125	+	0.776494i	$0.716996\pi$
$510$	16.7363	0.741095
$511$	14.8756	0.658056
$512$	1.00000	0.0441942
$513$	0.841202	0.0371400
$514$	−4.46927	−0.197131
$515$	2.32411	0.102413
$516$	−9.92938	−0.437117
$517$	−62.3096	−2.74037
$518$	5.36763	0.235840
$519$	−12.8620	−0.564581
$520$	−2.32411	−0.101919
$521$	−15.6267	−0.684620	−0.342310	−	0.939587i	$-0.611209\pi$
$521$	−15.6267	−0.684620	−0.342310	+	0.939587i	$0.611209\pi$
$522$	−1.46685	−0.0642022
$523$	35.7297	1.56235	0.781176	−	0.624311i	$-0.214620\pi$
$523$	35.7297	1.56235	0.781176	+	0.624311i	$0.214620\pi$
$524$	16.1038	0.703496
$525$	−1.48853	−0.0649647
$526$	9.78847	0.426798
$527$	25.2022	1.09783
$528$	6.03187	0.262503
$529$	−14.3247	−0.622815
$530$	−21.3781	−0.928604
$531$	−0.782122	−0.0339412
$532$	−3.11871	−0.135213
$533$	−11.7351	−0.508303
$534$	2.41377	0.104454
$535$	−14.2740	−0.617119
$536$	4.71378	0.203604
$537$	−0.940655	−0.0405923
$538$	−19.5484	−0.842792
$539$	40.6857	1.75246
$540$	2.32411	0.100014
$541$	−43.3227	−1.86259	−0.931294	−	0.364269i	$-0.881319\pi$
$541$	−43.3227	−1.86259	−0.931294	+	0.364269i	$0.881319\pi$
$542$	−32.7032	−1.40472
$543$	15.1128	0.648554
$544$	7.20115	0.308747
$545$	23.0775	0.988531
$546$	3.70744	0.158664
$547$	−44.2358	−1.89139	−0.945694	−	0.325060i	$-0.894616\pi$
$547$	−44.2358	−1.89139	−0.945694	+	0.325060i	$0.894616\pi$
$548$	9.39811	0.401467
$549$	5.91826	0.252585
$550$	2.42178	0.103265
$551$	−1.23392	−0.0525666
$552$	2.94538	0.125364
$553$	−29.3895	−1.24977
$554$	−0.514016	−0.0218385
$555$	−3.36485	−0.142830
$556$	2.52169	0.106943
$557$	36.8227	1.56023	0.780113	−	0.625639i	$-0.215161\pi$
$557$	36.8227	1.56023	0.780113	+	0.625639i	$0.215161\pi$
$558$	3.49975	0.148156
$559$	9.92938	0.419968
$560$	−8.61651	−0.364114
$561$	43.4364	1.83389
$562$	−6.88904	−0.290597
$563$	−14.7663	−0.622325	−0.311163	−	0.950357i	$-0.600718\pi$
$563$	−14.7663	−0.622325	−0.311163	+	0.950357i	$0.600718\pi$
$564$	−10.3301	−0.434974
$565$	34.2496	1.44089
$566$	5.41359	0.227550
$567$	−3.70744	−0.155698
$568$	−4.98753	−0.209272
$569$	−22.4169	−0.939763	−0.469882	−	0.882729i	$-0.655703\pi$
$569$	−22.4169	−0.939763	−0.469882	+	0.882729i	$0.655703\pi$
$570$	1.95505	0.0818879
$571$	3.66422	0.153343	0.0766715	−	0.997056i	$-0.475571\pi$
$571$	3.66422	0.153343	0.0766715	+	0.997056i	$0.475571\pi$
$572$	−6.03187	−0.252205
$573$	10.9366	0.456882
$574$	−43.5072	−1.81595
$575$	1.18256	0.0493163
$576$	1.00000	0.0416667
$577$	43.8857	1.82699	0.913493	−	0.406855i	$-0.133375\pi$
$577$	43.8857	1.82699	0.913493	+	0.406855i	$0.133375\pi$
$578$	34.8565	1.44984
$579$	−21.5581	−0.895924
$580$	−3.40912	−0.141556
$581$	30.7546	1.27591
$582$	2.64651	0.109702
$583$	−55.4834	−2.29789
$584$	−4.01235	−0.166032
$585$	−2.32411	−0.0960902
$586$	22.3703	0.924108
$587$	−39.8800	−1.64602	−0.823012	−	0.568023i	$-0.807708\pi$
$587$	−39.8800	−1.64602	−0.823012	+	0.568023i	$0.807708\pi$
$588$	6.74512	0.278164
$589$	2.94400	0.121305
$590$	−1.81774	−0.0748351
$591$	0.833763	0.0342964
$592$	−1.44780	−0.0595042
$593$	28.1128	1.15446	0.577228	−	0.816583i	$-0.304135\pi$
$593$	28.1128	1.15446	0.577228	+	0.816583i	$0.304135\pi$
$594$	6.03187	0.247491
$595$	−62.0487	−2.54375
$596$	14.9136	0.610885
$597$	18.1586	0.743182
$598$	−2.94538	−0.120446
$599$	−23.6619	−0.966797	−0.483399	−	0.875400i	$-0.660598\pi$
$599$	−23.6619	−0.966797	−0.483399	+	0.875400i	$0.660598\pi$
$600$	0.401498	0.0163911
$601$	6.25971	0.255339	0.127670	−	0.991817i	$-0.459250\pi$
$601$	6.25971	0.255339	0.127670	+	0.991817i	$0.459250\pi$
$602$	36.8126	1.50037
$603$	4.71378	0.191960
$604$	−4.64018	−0.188806
$605$	58.9940	2.39845
$606$	−11.2571	−0.457287
$607$	−27.8412	−1.13004	−0.565021	−	0.825077i	$-0.691132\pi$
$607$	−27.8412	−1.13004	−0.565021	+	0.825077i	$0.691132\pi$
$608$	0.841202	0.0341152
$609$	5.43825	0.220369
$610$	13.7547	0.556911
$611$	10.3301	0.417909
$612$	7.20115	0.291089
$613$	43.1396	1.74239	0.871196	−	0.490935i	$-0.163345\pi$
$613$	43.1396	1.74239	0.871196	+	0.490935i	$0.163345\pi$
$614$	6.51875	0.263075
$615$	27.2737	1.09978
$616$	−22.3628	−0.901023
$617$	−29.4645	−1.18619	−0.593097	−	0.805131i	$-0.702095\pi$
$617$	−29.4645	−1.18619	−0.593097	+	0.805131i	$0.702095\pi$
$618$	1.00000	0.0402259
$619$	13.5799	0.545821	0.272911	−	0.962039i	$-0.412014\pi$
$619$	13.5799	0.545821	0.272911	+	0.962039i	$0.412014\pi$
$620$	8.13382	0.326662
$621$	2.94538	0.118194
$622$	7.28059	0.291925
$623$	−8.94891	−0.358531
$624$	−1.00000	−0.0400320
$625$	−26.8463	−1.07385
$626$	−7.68846	−0.307293
$627$	5.07402	0.202637
$628$	4.55047	0.181583
$629$	−10.4258	−0.415705
$630$	−8.61651	−0.343290
$631$	1.44201	0.0574053	0.0287027	−	0.999588i	$-0.490862\pi$
$631$	1.44201	0.0574053	0.0287027	+	0.999588i	$0.490862\pi$
$632$	7.92716	0.315326
$633$	28.4693	1.13155
$634$	−18.5462	−0.736563
$635$	−28.1807	−1.11832
$636$	−9.19838	−0.364740
$637$	−6.74512	−0.267251
$638$	−8.84784	−0.350289
$639$	−4.98753	−0.197304
$640$	2.32411	0.0918686
$641$	−33.8008	−1.33505	−0.667526	−	0.744587i	$-0.732647\pi$
$641$	−33.8008	−1.33505	−0.667526	+	0.744587i	$0.732647\pi$
$642$	−6.14170	−0.242393
$643$	−34.3119	−1.35313	−0.676565	−	0.736383i	$-0.736532\pi$
$643$	−34.3119	−1.35313	−0.676565	+	0.736383i	$0.736532\pi$
$644$	−10.9198	−0.430301
$645$	−23.0770	−0.908656
$646$	6.05762	0.238334
$647$	18.9657	0.745619	0.372809	−	0.927908i	$-0.378395\pi$
$647$	18.9657	0.745619	0.372809	+	0.927908i	$0.378395\pi$
$648$	1.00000	0.0392837
$649$	−4.71766	−0.185184
$650$	−0.401498	−0.0157480
$651$	−12.9751	−0.508536
$652$	−18.8878	−0.739702
$653$	3.42901	0.134188	0.0670938	−	0.997747i	$-0.478627\pi$
$653$	3.42901	0.134188	0.0670938	+	0.997747i	$0.478627\pi$
$654$	9.92960	0.388278
$655$	37.4269	1.46239
$656$	11.7351	0.458178
$657$	−4.01235	−0.156537
$658$	38.2981	1.49301
$659$	1.99800	0.0778310	0.0389155	−	0.999243i	$-0.487610\pi$
$659$	1.99800	0.0778310	0.0389155	+	0.999243i	$0.487610\pi$
$660$	14.0187	0.545679
$661$	−33.9422	−1.32020	−0.660100	−	0.751178i	$-0.729486\pi$
$661$	−33.9422	−1.32020	−0.660100	+	0.751178i	$0.729486\pi$
$662$	0.452873	0.0176014
$663$	−7.20115	−0.279669
$664$	−8.29536	−0.321922
$665$	−7.24822	−0.281074
$666$	−1.44780	−0.0561011
$667$	−4.32043	−0.167288
$668$	−11.4799	−0.444171
$669$	−8.30446	−0.321069
$670$	10.9554	0.423242
$671$	35.6981	1.37811
$672$	−3.70744	−0.143018
$673$	9.03168	0.348146	0.174073	−	0.984733i	$-0.444307\pi$
$673$	9.03168	0.348146	0.174073	+	0.984733i	$0.444307\pi$
$674$	−10.7409	−0.413723
$675$	0.401498	0.0154537
$676$	1.00000	0.0384615
$677$	−30.0635	−1.15543	−0.577717	−	0.816237i	$-0.696056\pi$
$677$	−30.0635	−1.15543	−0.577717	+	0.816237i	$0.696056\pi$
$678$	14.7366	0.565956
$679$	−9.81180	−0.376542
$680$	16.7363	0.641807
$681$	22.0374	0.844474
$682$	21.1101	0.808346
$683$	40.5312	1.55088	0.775441	−	0.631420i	$-0.217528\pi$
$683$	40.5312	1.55088	0.775441	+	0.631420i	$0.217528\pi$
$684$	0.841202	0.0321642
$685$	21.8423	0.834550
$686$	0.944967	0.0360790
$687$	21.8771	0.834662
$688$	−9.92938	−0.378554
$689$	9.19838	0.350430
$690$	6.84539	0.260600
$691$	−44.4951	−1.69267	−0.846336	−	0.532650i	$-0.821196\pi$
$691$	−44.4951	−1.69267	−0.846336	+	0.532650i	$0.821196\pi$
$692$	−12.8620	−0.488941
$693$	−22.3628	−0.849492
$694$	−15.5969	−0.592050
$695$	5.86069	0.222309
$696$	−1.46685	−0.0556008
$697$	84.5061	3.20090
$698$	−29.6900	−1.12378
$699$	−25.2568	−0.955299
$700$	−1.48853	−0.0562611
$701$	5.87594	0.221931	0.110966	−	0.993824i	$-0.464606\pi$
$701$	5.87594	0.221931	0.110966	+	0.993824i	$0.464606\pi$
$702$	−1.00000	−0.0377426
$703$	−1.21789	−0.0459337
$704$	6.03187	0.227335
$705$	−24.0082	−0.904202
$706$	8.91641	0.335574
$707$	41.7349	1.56960
$708$	−0.782122	−0.0293939
$709$	9.80404	0.368199	0.184099	−	0.982908i	$-0.441063\pi$
$709$	9.80404	0.368199	0.184099	+	0.982908i	$0.441063\pi$
$710$	−11.5916	−0.435025
$711$	7.92716	0.297292
$712$	2.41377	0.0904599
$713$	10.3081	0.386042
$714$	−26.6978	−0.999141
$715$	−14.0187	−0.524271
$716$	−0.940655	−0.0351539
$717$	19.9522	0.745130
$718$	−11.3388	−0.423162
$719$	−43.8124	−1.63393	−0.816963	−	0.576690i	$-0.804344\pi$
$719$	−43.8124	−1.63393	−0.816963	+	0.576690i	$0.804344\pi$
$720$	2.32411	0.0866145
$721$	−3.70744	−0.138072
$722$	−18.2924	−0.680772
$723$	9.65207	0.358964
$724$	15.1128	0.561664
$725$	−0.588936	−0.0218725
$726$	25.3834	0.942068
$727$	15.0560	0.558397	0.279199	−	0.960233i	$-0.409931\pi$
$727$	15.0560	0.558397	0.279199	+	0.960233i	$0.409931\pi$
$728$	3.70744	0.137407
$729$	1.00000	0.0370370
$730$	−9.32516	−0.345140
$731$	−71.5029	−2.64463
$732$	5.91826	0.218745
$733$	−26.1371	−0.965397	−0.482699	−	0.875787i	$-0.660343\pi$
$733$	−26.1371	−0.965397	−0.482699	+	0.875787i	$0.660343\pi$
$734$	−1.06892	−0.0394544
$735$	15.6764	0.578233
$736$	2.94538	0.108568
$737$	28.4329	1.04734
$738$	11.7351	0.431975
$739$	−32.4206	−1.19261	−0.596305	−	0.802758i	$-0.703365\pi$
$739$	−32.4206	−1.19261	−0.596305	+	0.802758i	$0.703365\pi$
$740$	−3.36485	−0.123694
$741$	−0.841202	−0.0309023
$742$	34.1025	1.25194
$743$	−11.5313	−0.423044	−0.211522	−	0.977373i	$-0.567842\pi$
$743$	−11.5313	−0.423044	−0.211522	+	0.977373i	$0.567842\pi$
$744$	3.49975	0.128307
$745$	34.6609	1.26988
$746$	−18.0980	−0.662615
$747$	−8.29536	−0.303511
$748$	43.4364	1.58819
$749$	22.7700	0.831997
$750$	−10.6874	−0.390250
$751$	−4.96932	−0.181333	−0.0906665	−	0.995881i	$-0.528900\pi$
$751$	−4.96932	−0.181333	−0.0906665	+	0.995881i	$0.528900\pi$
$752$	−10.3301	−0.376699
$753$	10.5259	0.383586
$754$	1.46685	0.0534195
$755$	−10.7843	−0.392481
$756$	−3.70744	−0.134838
$757$	−5.52191	−0.200697	−0.100349	−	0.994952i	$-0.531996\pi$
$757$	−5.52191	−0.200697	−0.100349	+	0.994952i	$0.531996\pi$
$758$	−23.3350	−0.847566
$759$	17.7661	0.644870
$760$	1.95505	0.0709170
$761$	31.8903	1.15602	0.578011	−	0.816029i	$-0.303829\pi$
$761$	31.8903	1.15602	0.578011	+	0.816029i	$0.303829\pi$
$762$	−12.1254	−0.439256
$763$	−36.8134	−1.33273
$764$	10.9366	0.395672
$765$	16.7363	0.605101
$766$	−5.79309	−0.209313
$767$	0.782122	0.0282408
$768$	1.00000	0.0360844
$769$	−0.416475	−0.0150185	−0.00750924	−	0.999972i	$-0.502390\pi$
$769$	−0.416475	−0.0150185	−0.00750924	+	0.999972i	$0.502390\pi$
$770$	−51.9736	−1.87300
$771$	−4.46927	−0.160957
$772$	−21.5581	−0.775893
$773$	−9.29585	−0.334349	−0.167174	−	0.985927i	$-0.553464\pi$
$773$	−9.29585	−0.334349	−0.167174	+	0.985927i	$0.553464\pi$
$774$	−9.92938	−0.356904
$775$	1.40514	0.0504742
$776$	2.64651	0.0950043
$777$	5.36763	0.192563
$778$	−32.5677	−1.16761
$779$	9.87158	0.353686
$780$	−2.32411	−0.0832166
$781$	−30.0842	−1.07650
$782$	21.2101	0.758472
$783$	−1.46685	−0.0524209
$784$	6.74512	0.240897
$785$	10.5758	0.377466
$786$	16.1038	0.574402
$787$	20.7160	0.738446	0.369223	−	0.929341i	$-0.379624\pi$
$787$	20.7160	0.738446	0.369223	+	0.929341i	$0.379624\pi$
$788$	0.833763	0.0297016
$789$	9.78847	0.348479
$790$	18.4236	0.655483
$791$	−54.6351	−1.94260
$792$	6.03187	0.214333
$793$	−5.91826	−0.210163
$794$	26.4230	0.937717
$795$	−21.3781	−0.758202
$796$	18.1586	0.643615
$797$	10.4156	0.368938	0.184469	−	0.982838i	$-0.440943\pi$
$797$	10.4156	0.368938	0.184469	+	0.982838i	$0.440943\pi$
$798$	−3.11871	−0.110401
$799$	−74.3883	−2.63167
$800$	0.401498	0.0141951
$801$	2.41377	0.0852864
$802$	13.5667	0.479057
$803$	−24.2020	−0.854070
$804$	4.71378	0.166242
$805$	−25.3789	−0.894488
$806$	−3.49975	−0.123274
$807$	−19.5484	−0.688137
$808$	−11.2571	−0.396022
$809$	3.76084	0.132224	0.0661120	−	0.997812i	$-0.478941\pi$
$809$	3.76084	0.132224	0.0661120	+	0.997812i	$0.478941\pi$
$810$	2.32411	0.0816610
$811$	41.3958	1.45360	0.726802	−	0.686847i	$-0.241006\pi$
$811$	41.3958	1.45360	0.726802	+	0.686847i	$0.241006\pi$
$812$	5.43825	0.190845
$813$	−32.7032	−1.14695
$814$	−8.73294	−0.306089
$815$	−43.8973	−1.53766
$816$	7.20115	0.252091
$817$	−8.35262	−0.292221
$818$	−26.4123	−0.923486
$819$	3.70744	0.129548
$820$	27.2737	0.952438
$821$	22.7409	0.793662	0.396831	−	0.917892i	$-0.370110\pi$
$821$	22.7409	0.793662	0.396831	+	0.917892i	$0.370110\pi$
$822$	9.39811	0.327797
$823$	22.1022	0.770435	0.385218	−	0.922826i	$-0.374126\pi$
$823$	22.1022	0.770435	0.385218	+	0.922826i	$0.374126\pi$
$824$	1.00000	0.0348367
$825$	2.42178	0.0843156
$826$	2.89967	0.100892
$827$	−0.684337	−0.0237967	−0.0118984	−	0.999929i	$-0.503787\pi$
$827$	−0.684337	−0.0237967	−0.0118984	+	0.999929i	$0.503787\pi$
$828$	2.94538	0.102359
$829$	−13.4477	−0.467060	−0.233530	−	0.972350i	$-0.575028\pi$
$829$	−13.4477	−0.467060	−0.233530	+	0.972350i	$0.575028\pi$
$830$	−19.2794	−0.669196
$831$	−0.514016	−0.0178310
$832$	−1.00000	−0.0346688
$833$	48.5726	1.68294
$834$	2.52169	0.0873189
$835$	−26.6806	−0.923320
$836$	5.07402	0.175489
$837$	3.49975	0.120969
$838$	1.21727	0.0420498
$839$	−48.5745	−1.67698	−0.838489	−	0.544919i	$-0.816561\pi$
$839$	−48.5745	−1.67698	−0.838489	+	0.544919i	$0.816561\pi$
$840$	−8.61651	−0.297298
$841$	−26.8484	−0.925805
$842$	34.5797	1.19169
$843$	−6.88904	−0.237271
$844$	28.4693	0.979955
$845$	2.32411	0.0799519
$846$	−10.3301	−0.355155
$847$	−94.1076	−3.23357
$848$	−9.19838	−0.315874
$849$	5.41359	0.185794
$850$	2.89124	0.0991688
$851$	−4.26432	−0.146179
$852$	−4.98753	−0.170870
$853$	−0.315021	−0.0107861	−0.00539305	−	0.999985i	$-0.501717\pi$
$853$	−0.315021	−0.0107861	−0.00539305	+	0.999985i	$0.501717\pi$
$854$	−21.9416	−0.750826
$855$	1.95505	0.0668612
$856$	−6.14170	−0.209919
$857$	56.5799	1.93273	0.966366	−	0.257172i	$-0.0827908\pi$
$857$	56.5799	1.93273	0.966366	+	0.257172i	$0.0827908\pi$
$858$	−6.03187	−0.205925
$859$	−48.8573	−1.66699	−0.833494	−	0.552528i	$-0.813663\pi$
$859$	−48.8573	−1.66699	−0.833494	+	0.552528i	$0.813663\pi$
$860$	−23.0770	−0.786919
$861$	−43.5072	−1.48272
$862$	−34.2783	−1.16752
$863$	17.3896	0.591950	0.295975	−	0.955196i	$-0.404356\pi$
$863$	17.3896	0.591950	0.295975	+	0.955196i	$0.404356\pi$
$864$	1.00000	0.0340207
$865$	−29.8928	−1.01639
$866$	−19.3932	−0.659008
$867$	34.8565	1.18379
$868$	−12.9751	−0.440405
$869$	47.8156	1.62203
$870$	−3.40912	−0.115580
$871$	−4.71378	−0.159720
$872$	9.92960	0.336259
$873$	2.64651	0.0895709
$874$	2.47766	0.0838081
$875$	39.6230	1.33950
$876$	−4.01235	−0.135565
$877$	13.5378	0.457139	0.228570	−	0.973528i	$-0.426595\pi$
$877$	13.5378	0.457139	0.228570	+	0.973528i	$0.426595\pi$
$878$	20.8177	0.702563
$879$	22.3703	0.754531
$880$	14.0187	0.472572
$881$	−22.0276	−0.742128	−0.371064	−	0.928607i	$-0.621007\pi$
$881$	−22.0276	−0.742128	−0.371064	+	0.928607i	$0.621007\pi$
$882$	6.74512	0.227120
$883$	18.5729	0.625027	0.312514	−	0.949913i	$-0.398829\pi$
$883$	18.5729	0.625027	0.312514	+	0.949913i	$0.398829\pi$
$884$	−7.20115	−0.242201
$885$	−1.81774	−0.0611026
$886$	4.21146	0.141487
$887$	−9.25537	−0.310765	−0.155382	−	0.987854i	$-0.549661\pi$
$887$	−9.25537	−0.310765	−0.155382	+	0.987854i	$0.549661\pi$
$888$	−1.44780	−0.0485850
$889$	44.9541	1.50771
$890$	5.60988	0.188043
$891$	6.03187	0.202075
$892$	−8.30446	−0.278054
$893$	−8.68967	−0.290789
$894$	14.9136	0.498786
$895$	−2.18619	−0.0730762
$896$	−3.70744	−0.123857
$897$	−2.94538	−0.0983434
$898$	8.78315	0.293098
$899$	−5.13361	−0.171215
$900$	0.401498	0.0133833
$901$	−66.2389	−2.20674
$902$	70.7845	2.35687
$903$	36.8126	1.22505
$904$	14.7366	0.490133
$905$	35.1239	1.16756
$906$	−4.64018	−0.154160
$907$	42.2448	1.40271	0.701357	−	0.712810i	$-0.252578\pi$
$907$	42.2448	1.40271	0.701357	+	0.712810i	$0.252578\pi$
$908$	22.0374	0.731336
$909$	−11.2571	−0.373373
$910$	8.61651	0.285634
$911$	−46.7660	−1.54943	−0.774713	−	0.632313i	$-0.782106\pi$
$911$	−46.7660	−1.54943	−0.774713	+	0.632313i	$0.782106\pi$
$912$	0.841202	0.0278550
$913$	−50.0365	−1.65597
$914$	28.6493	0.947633
$915$	13.7547	0.454716
$916$	21.8771	0.722839
$917$	−59.7037	−1.97159
$918$	7.20115	0.237673
$919$	−26.8302	−0.885047	−0.442524	−	0.896757i	$-0.645917\pi$
$919$	−26.8302	−0.885047	−0.442524	+	0.896757i	$0.645917\pi$
$920$	6.84539	0.225686
$921$	6.51875	0.214800
$922$	17.1412	0.564515
$923$	4.98753	0.164167
$924$	−22.3628	−0.735682
$925$	−0.581288	−0.0191126
$926$	−21.8785	−0.718972
$927$	1.00000	0.0328443
$928$	−1.46685	−0.0481517
$929$	37.3039	1.22390	0.611951	−	0.790896i	$-0.290385\pi$
$929$	37.3039	1.22390	0.611951	+	0.790896i	$0.290385\pi$
$930$	8.13382	0.266719
$931$	5.67400	0.185958
$932$	−25.2568	−0.827313
$933$	7.28059	0.238356
$934$	−15.9695	−0.522539
$935$	100.951	3.30145
$936$	−1.00000	−0.0326860
$937$	49.1631	1.60609	0.803045	−	0.595919i	$-0.203212\pi$
$937$	49.1631	1.60609	0.803045	+	0.595919i	$0.203212\pi$
$938$	−17.4761	−0.570614
$939$	−7.68846	−0.250904
$940$	−24.0082	−0.783062
$941$	−26.5144	−0.864345	−0.432172	−	0.901791i	$-0.642253\pi$
$941$	−26.5144	−0.864345	−0.432172	+	0.901791i	$0.642253\pi$
$942$	4.55047	0.148262
$943$	34.5643	1.12557
$944$	−0.782122	−0.0254559
$945$	−8.61651	−0.280295
$946$	−59.8927	−1.94728
$947$	10.5776	0.343725	0.171863	−	0.985121i	$-0.445022\pi$
$947$	10.5776	0.343725	0.171863	+	0.985121i	$0.445022\pi$
$948$	7.92716	0.257462
$949$	4.01235	0.130247
$950$	0.337741	0.0109578
$951$	−18.5462	−0.601401
$952$	−26.6978	−0.865281
$953$	27.7249	0.898097	0.449049	−	0.893507i	$-0.351763\pi$
$953$	27.7249	0.898097	0.449049	+	0.893507i	$0.351763\pi$
$954$	−9.19838	−0.297809
$955$	25.4179	0.822502
$956$	19.9522	0.645301
$957$	−8.84784	−0.286010
$958$	8.07799	0.260988
$959$	−34.8429	−1.12514
$960$	2.32411	0.0750104
$961$	−18.7517	−0.604894
$962$	1.44780	0.0466789
$963$	−6.14170	−0.197913
$964$	9.65207	0.310872
$965$	−50.1035	−1.61289
$966$	−10.9198	−0.351340
$967$	−2.73813	−0.0880524	−0.0440262	−	0.999030i	$-0.514019\pi$
$967$	−2.73813	−0.0880524	−0.0440262	+	0.999030i	$0.514019\pi$
$968$	25.3834	0.815855
$969$	6.05762	0.194599
$970$	6.15080	0.197490
$971$	−41.3339	−1.32647	−0.663234	−	0.748412i	$-0.730817\pi$
$971$	−41.3339	−1.32647	−0.663234	+	0.748412i	$0.730817\pi$
$972$	1.00000	0.0320750
$973$	−9.34901	−0.299716
$974$	−11.0295	−0.353407
$975$	−0.401498	−0.0128582
$976$	5.91826	0.189439
$977$	35.2775	1.12863	0.564313	−	0.825561i	$-0.309141\pi$
$977$	35.2775	1.12863	0.564313	+	0.825561i	$0.309141\pi$
$978$	−18.8878	−0.603964
$979$	14.5596	0.465325
$980$	15.6764	0.500764
$981$	9.92960	0.317028
$982$	−15.2720	−0.487348
$983$	−35.0884	−1.11915	−0.559574	−	0.828781i	$-0.689035\pi$
$983$	−35.0884	−1.11915	−0.559574	+	0.828781i	$0.689035\pi$
$984$	11.7351	0.374101
$985$	1.93776	0.0617421
$986$	−10.5630	−0.336394
$987$	38.2981	1.21904
$988$	−0.841202	−0.0267622
$989$	−29.2458	−0.929962
$990$	14.0187	0.445545
$991$	31.1787	0.990424	0.495212	−	0.868772i	$-0.335090\pi$
$991$	31.1787	0.990424	0.495212	+	0.868772i	$0.335090\pi$
$992$	3.49975	0.111117
$993$	0.452873	0.0143715
$994$	18.4910	0.586499
$995$	42.2026	1.33791
$996$	−8.29536	−0.262849
$997$	−9.49729	−0.300782	−0.150391	−	0.988627i	$-0.548053\pi$
$997$	−9.49729	−0.300782	−0.150391	+	0.988627i	$0.548053\pi$
$998$	−25.9466	−0.821325
$999$	−1.44780	−0.0458064

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.bd.1.13	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.bd.1.13	✓	16	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:	\( N \)	\(=\)	\( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8034.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.32411 q^{5} +1.00000 q^{6} -3.70744 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.32411 q^{5} +1.00000 q^{6} -3.70744 q^{7} +1.00000 q^{8} +1.00000 q^{9} +2.32411 q^{10} +6.03187 q^{11} +1.00000 q^{12} -1.00000 q^{13} -3.70744 q^{14} +2.32411 q^{15} +1.00000 q^{16} +7.20115 q^{17} +1.00000 q^{18} +0.841202 q^{19} +2.32411 q^{20} -3.70744 q^{21} +6.03187 q^{22} +2.94538 q^{23} +1.00000 q^{24} +0.401498 q^{25} -1.00000 q^{26} +1.00000 q^{27} -3.70744 q^{28} -1.46685 q^{29} +2.32411 q^{30} +3.49975 q^{31} +1.00000 q^{32} +6.03187 q^{33} +7.20115 q^{34} -8.61651 q^{35} +1.00000 q^{36} -1.44780 q^{37} +0.841202 q^{38} -1.00000 q^{39} +2.32411 q^{40} +11.7351 q^{41} -3.70744 q^{42} -9.92938 q^{43} +6.03187 q^{44} +2.32411 q^{45} +2.94538 q^{46} -10.3301 q^{47} +1.00000 q^{48} +6.74512 q^{49} +0.401498 q^{50} +7.20115 q^{51} -1.00000 q^{52} -9.19838 q^{53} +1.00000 q^{54} +14.0187 q^{55} -3.70744 q^{56} +0.841202 q^{57} -1.46685 q^{58} -0.782122 q^{59} +2.32411 q^{60} +5.91826 q^{61} +3.49975 q^{62} -3.70744 q^{63} +1.00000 q^{64} -2.32411 q^{65} +6.03187 q^{66} +4.71378 q^{67} +7.20115 q^{68} +2.94538 q^{69} -8.61651 q^{70} -4.98753 q^{71} +1.00000 q^{72} -4.01235 q^{73} -1.44780 q^{74} +0.401498 q^{75} +0.841202 q^{76} -22.3628 q^{77} -1.00000 q^{78} +7.92716 q^{79} +2.32411 q^{80} +1.00000 q^{81} +11.7351 q^{82} -8.29536 q^{83} -3.70744 q^{84} +16.7363 q^{85} -9.92938 q^{86} -1.46685 q^{87} +6.03187 q^{88} +2.41377 q^{89} +2.32411 q^{90} +3.70744 q^{91} +2.94538 q^{92} +3.49975 q^{93} -10.3301 q^{94} +1.95505 q^{95} +1.00000 q^{96} +2.64651 q^{97} +6.74512 q^{98} +6.03187 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{2} + 16 q^{3} + 16 q^{4} + 5 q^{5} + 16 q^{6} + 4 q^{7} + 16 q^{8} + 16 q^{9}+O(q^{10}) \) 16 * q + 16 * q^2 + 16 * q^3 + 16 * q^4 + 5 * q^5 + 16 * q^6 + 4 * q^7 + 16 * q^8 + 16 * q^9	\( 16 q + 16 q^{2} + 16 q^{3} + 16 q^{4} + 5 q^{5} + 16 q^{6} + 4 q^{7} + 16 q^{8} + 16 q^{9} + 5 q^{10} + 18 q^{11} + 16 q^{12} - 16 q^{13} + 4 q^{14} + 5 q^{15} + 16 q^{16} + 17 q^{17} + 16 q^{18} + 8 q^{19} + 5 q^{20} + 4 q^{21} + 18 q^{22} + 9 q^{23} + 16 q^{24} + 17 q^{25} - 16 q^{26} + 16 q^{27} + 4 q^{28} + 14 q^{29} + 5 q^{30} + 12 q^{31} + 16 q^{32} + 18 q^{33} + 17 q^{34} + 16 q^{35} + 16 q^{36} + 31 q^{37} + 8 q^{38} - 16 q^{39} + 5 q^{40} + 29 q^{41} + 4 q^{42} + 30 q^{43} + 18 q^{44} + 5 q^{45} + 9 q^{46} - q^{47} + 16 q^{48} + 36 q^{49} + 17 q^{50} + 17 q^{51} - 16 q^{52} + 12 q^{53} + 16 q^{54} + 30 q^{55} + 4 q^{56} + 8 q^{57} + 14 q^{58} + 38 q^{59} + 5 q^{60} + 12 q^{62} + 4 q^{63} + 16 q^{64} - 5 q^{65} + 18 q^{66} + 28 q^{67} + 17 q^{68} + 9 q^{69} + 16 q^{70} + 32 q^{71} + 16 q^{72} + 20 q^{73} + 31 q^{74} + 17 q^{75} + 8 q^{76} + 26 q^{77} - 16 q^{78} + 13 q^{79} + 5 q^{80} + 16 q^{81} + 29 q^{82} + 39 q^{83} + 4 q^{84} + 31 q^{85} + 30 q^{86} + 14 q^{87} + 18 q^{88} + 9 q^{89} + 5 q^{90} - 4 q^{91} + 9 q^{92} + 12 q^{93} - q^{94} - 20 q^{95} + 16 q^{96} + 35 q^{97} + 36 q^{98} + 18 q^{99}+O(q^{100}) \) 16 * q + 16 * q^2 + 16 * q^3 + 16 * q^4 + 5 * q^5 + 16 * q^6 + 4 * q^7 + 16 * q^8 + 16 * q^9 + 5 * q^10 + 18 * q^11 + 16 * q^12 - 16 * q^13 + 4 * q^14 + 5 * q^15 + 16 * q^16 + 17 * q^17 + 16 * q^18 + 8 * q^19 + 5 * q^20 + 4 * q^21 + 18 * q^22 + 9 * q^23 + 16 * q^24 + 17 * q^25 - 16 * q^26 + 16 * q^27 + 4 * q^28 + 14 * q^29 + 5 * q^30 + 12 * q^31 + 16 * q^32 + 18 * q^33 + 17 * q^34 + 16 * q^35 + 16 * q^36 + 31 * q^37 + 8 * q^38 - 16 * q^39 + 5 * q^40 + 29 * q^41 + 4 * q^42 + 30 * q^43 + 18 * q^44 + 5 * q^45 + 9 * q^46 - q^47 + 16 * q^48 + 36 * q^49 + 17 * q^50 + 17 * q^51 - 16 * q^52 + 12 * q^53 + 16 * q^54 + 30 * q^55 + 4 * q^56 + 8 * q^57 + 14 * q^58 + 38 * q^59 + 5 * q^60 + 12 * q^62 + 4 * q^63 + 16 * q^64 - 5 * q^65 + 18 * q^66 + 28 * q^67 + 17 * q^68 + 9 * q^69 + 16 * q^70 + 32 * q^71 + 16 * q^72 + 20 * q^73 + 31 * q^74 + 17 * q^75 + 8 * q^76 + 26 * q^77 - 16 * q^78 + 13 * q^79 + 5 * q^80 + 16 * q^81 + 29 * q^82 + 39 * q^83 + 4 * q^84 + 31 * q^85 + 30 * q^86 + 14 * q^87 + 18 * q^88 + 9 * q^89 + 5 * q^90 - 4 * q^91 + 9 * q^92 + 12 * q^93 - q^94 - 20 * q^95 + 16 * q^96 + 35 * q^97 + 36 * q^98 + 18 * q^99

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