LMFDB - Embedded newform 4034.2.a.c.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4034,2,Mod(1,4034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4034, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4034 = 2 \cdot 2017 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4034.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:	$32.2116521754$
Analytic rank:	$0$
Dimension:	$49$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	4034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.80221 q^{3} +1.00000 q^{4} +1.91358 q^{5} +2.80221 q^{6} -1.55673 q^{7} -1.00000 q^{8} +4.85238 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.80221 q^{3} +1.00000 q^{4} +1.91358 q^{5} +2.80221 q^{6} -1.55673 q^{7} -1.00000 q^{8} +4.85238 q^{9} -1.91358 q^{10} +5.66362 q^{11} -2.80221 q^{12} -3.83536 q^{13} +1.55673 q^{14} -5.36226 q^{15} +1.00000 q^{16} +0.620210 q^{17} -4.85238 q^{18} +6.54668 q^{19} +1.91358 q^{20} +4.36229 q^{21} -5.66362 q^{22} -2.62274 q^{23} +2.80221 q^{24} -1.33819 q^{25} +3.83536 q^{26} -5.19074 q^{27} -1.55673 q^{28} +5.69371 q^{29} +5.36226 q^{30} +1.75112 q^{31} -1.00000 q^{32} -15.8706 q^{33} -0.620210 q^{34} -2.97894 q^{35} +4.85238 q^{36} +6.65561 q^{37} -6.54668 q^{38} +10.7475 q^{39} -1.91358 q^{40} -2.29010 q^{41} -4.36229 q^{42} +1.78345 q^{43} +5.66362 q^{44} +9.28543 q^{45} +2.62274 q^{46} +2.47394 q^{47} -2.80221 q^{48} -4.57659 q^{49} +1.33819 q^{50} -1.73796 q^{51} -3.83536 q^{52} +12.7452 q^{53} +5.19074 q^{54} +10.8378 q^{55} +1.55673 q^{56} -18.3452 q^{57} -5.69371 q^{58} +11.0235 q^{59} -5.36226 q^{60} -2.74708 q^{61} -1.75112 q^{62} -7.55384 q^{63} +1.00000 q^{64} -7.33928 q^{65} +15.8706 q^{66} -3.94472 q^{67} +0.620210 q^{68} +7.34947 q^{69} +2.97894 q^{70} -1.03577 q^{71} -4.85238 q^{72} -7.63003 q^{73} -6.65561 q^{74} +3.74990 q^{75} +6.54668 q^{76} -8.81673 q^{77} -10.7475 q^{78} -15.5419 q^{79} +1.91358 q^{80} -0.0115795 q^{81} +2.29010 q^{82} +3.95552 q^{83} +4.36229 q^{84} +1.18682 q^{85} -1.78345 q^{86} -15.9550 q^{87} -5.66362 q^{88} -6.66256 q^{89} -9.28543 q^{90} +5.97062 q^{91} -2.62274 q^{92} -4.90700 q^{93} -2.47394 q^{94} +12.5276 q^{95} +2.80221 q^{96} -10.0627 q^{97} +4.57659 q^{98} +27.4820 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 49 q - 49 q^{2} + 8 q^{3} + 49 q^{4} - 8 q^{5} - 8 q^{6} + 18 q^{7} - 49 q^{8} + 59 q^{9}+O(q^{10}) $ 49 * q - 49 * q^2 + 8 * q^3 + 49 * q^4 - 8 * q^5 - 8 * q^6 + 18 * q^7 - 49 * q^8 + 59 * q^9	\( 49 q - 49 q^{2} + 8 q^{3} + 49 q^{4} - 8 q^{5} - 8 q^{6} + 18 q^{7} - 49 q^{8} + 59 q^{9} + 8 q^{10} + q^{11} + 8 q^{12} + 9 q^{13} - 18 q^{14} + 15 q^{15} + 49 q^{16} - 27 q^{17} - 59 q^{18} + 27 q^{19} - 8 q^{20} + 13 q^{21} - q^{22} + 16 q^{23} - 8 q^{24} + 71 q^{25} - 9 q^{26} + 29 q^{27} + 18 q^{28} - 7 q^{29} - 15 q^{30} + 75 q^{31} - 49 q^{32} - 3 q^{33} + 27 q^{34} - 16 q^{35} + 59 q^{36} + 36 q^{37} - 27 q^{38} + 24 q^{39} + 8 q^{40} - 12 q^{41} - 13 q^{42} + 22 q^{43} + q^{44} + 5 q^{45} - 16 q^{46} + 26 q^{47} + 8 q^{48} + 107 q^{49} - 71 q^{50} + 35 q^{51} + 9 q^{52} - 10 q^{53} - 29 q^{54} + 76 q^{55} - 18 q^{56} - 10 q^{57} + 7 q^{58} + 9 q^{59} + 15 q^{60} + 87 q^{61} - 75 q^{62} + 68 q^{63} + 49 q^{64} - 6 q^{65} + 3 q^{66} + 46 q^{67} - 27 q^{68} + 70 q^{69} + 16 q^{70} + 40 q^{71} - 59 q^{72} + 6 q^{73} - 36 q^{74} + 69 q^{75} + 27 q^{76} - 12 q^{77} - 24 q^{78} + 76 q^{79} - 8 q^{80} + 77 q^{81} + 12 q^{82} - 32 q^{83} + 13 q^{84} + 19 q^{85} - 22 q^{86} + 36 q^{87} - q^{88} + 34 q^{89} - 5 q^{90} + 119 q^{91} + 16 q^{92} - 5 q^{93} - 26 q^{94} - 2 q^{95} - 8 q^{96} + 52 q^{97} - 107 q^{98} + 26 q^{99}+O(q^{100}) \) 49 * q - 49 * q^2 + 8 * q^3 + 49 * q^4 - 8 * q^5 - 8 * q^6 + 18 * q^7 - 49 * q^8 + 59 * q^9 + 8 * q^10 + q^11 + 8 * q^12 + 9 * q^13 - 18 * q^14 + 15 * q^15 + 49 * q^16 - 27 * q^17 - 59 * q^18 + 27 * q^19 - 8 * q^20 + 13 * q^21 - q^22 + 16 * q^23 - 8 * q^24 + 71 * q^25 - 9 * q^26 + 29 * q^27 + 18 * q^28 - 7 * q^29 - 15 * q^30 + 75 * q^31 - 49 * q^32 - 3 * q^33 + 27 * q^34 - 16 * q^35 + 59 * q^36 + 36 * q^37 - 27 * q^38 + 24 * q^39 + 8 * q^40 - 12 * q^41 - 13 * q^42 + 22 * q^43 + q^44 + 5 * q^45 - 16 * q^46 + 26 * q^47 + 8 * q^48 + 107 * q^49 - 71 * q^50 + 35 * q^51 + 9 * q^52 - 10 * q^53 - 29 * q^54 + 76 * q^55 - 18 * q^56 - 10 * q^57 + 7 * q^58 + 9 * q^59 + 15 * q^60 + 87 * q^61 - 75 * q^62 + 68 * q^63 + 49 * q^64 - 6 * q^65 + 3 * q^66 + 46 * q^67 - 27 * q^68 + 70 * q^69 + 16 * q^70 + 40 * q^71 - 59 * q^72 + 6 * q^73 - 36 * q^74 + 69 * q^75 + 27 * q^76 - 12 * q^77 - 24 * q^78 + 76 * q^79 - 8 * q^80 + 77 * q^81 + 12 * q^82 - 32 * q^83 + 13 * q^84 + 19 * q^85 - 22 * q^86 + 36 * q^87 - q^88 + 34 * q^89 - 5 * q^90 + 119 * q^91 + 16 * q^92 - 5 * q^93 - 26 * q^94 - 2 * q^95 - 8 * q^96 + 52 * q^97 - 107 * q^98 + 26 * 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
$3$	−2.80221	−1.61786	−0.808928	−	0.587908i	$-0.799952\pi$
$3$	−2.80221	−1.61786	−0.808928	+	0.587908i	$0.799952\pi$
$4$	1.00000	0.500000
$5$	1.91358	0.855781	0.427891	−	0.903831i	$-0.359257\pi$
$5$	1.91358	0.855781	0.427891	+	0.903831i	$0.359257\pi$
$6$	2.80221	1.14400
$7$	−1.55673	−0.588389	−0.294195	−	0.955746i	$-0.595051\pi$
$7$	−1.55673	−0.588389	−0.294195	+	0.955746i	$0.595051\pi$
$8$	−1.00000	−0.353553
$9$	4.85238	1.61746
$10$	−1.91358	−0.605129
$11$	5.66362	1.70765	0.853823	−	0.520564i	$-0.174278\pi$
$11$	5.66362	1.70765	0.853823	+	0.520564i	$0.174278\pi$
$12$	−2.80221	−0.808928
$13$	−3.83536	−1.06374	−0.531869	−	0.846827i	$-0.678510\pi$
$13$	−3.83536	−1.06374	−0.531869	+	0.846827i	$0.678510\pi$
$14$	1.55673	0.416054
$15$	−5.36226	−1.38453
$16$	1.00000	0.250000
$17$	0.620210	0.150423	0.0752115	−	0.997168i	$-0.476037\pi$
$17$	0.620210	0.150423	0.0752115	+	0.997168i	$0.476037\pi$
$18$	−4.85238	−1.14372
$19$	6.54668	1.50191	0.750956	−	0.660352i	$-0.229593\pi$
$19$	6.54668	1.50191	0.750956	+	0.660352i	$0.229593\pi$
$20$	1.91358	0.427891
$21$	4.36229	0.951929
$22$	−5.66362	−1.20749
$23$	−2.62274	−0.546880	−0.273440	−	0.961889i	$-0.588161\pi$
$23$	−2.62274	−0.546880	−0.273440	+	0.961889i	$0.588161\pi$
$24$	2.80221	0.571999
$25$	−1.33819	−0.267639
$26$	3.83536	0.752176
$27$	−5.19074	−0.998959
$28$	−1.55673	−0.294195
$29$	5.69371	1.05729	0.528647	−	0.848842i	$-0.322699\pi$
$29$	5.69371	1.05729	0.528647	+	0.848842i	$0.322699\pi$
$30$	5.36226	0.979011
$31$	1.75112	0.314510	0.157255	−	0.987558i	$-0.449735\pi$
$31$	1.75112	0.314510	0.157255	+	0.987558i	$0.449735\pi$
$32$	−1.00000	−0.176777
$33$	−15.8706	−2.76272
$34$	−0.620210	−0.106365
$35$	−2.97894	−0.503532
$36$	4.85238	0.808729
$37$	6.65561	1.09417	0.547087	−	0.837075i	$-0.315737\pi$
$37$	6.65561	1.09417	0.547087	+	0.837075i	$0.315737\pi$
$38$	−6.54668	−1.06201
$39$	10.7475	1.72097
$40$	−1.91358	−0.302564
$41$	−2.29010	−0.357653	−0.178827	−	0.983881i	$-0.557230\pi$
$41$	−2.29010	−0.357653	−0.178827	+	0.983881i	$0.557230\pi$
$42$	−4.36229	−0.673115
$43$	1.78345	0.271974	0.135987	−	0.990711i	$-0.456579\pi$
$43$	1.78345	0.271974	0.135987	+	0.990711i	$0.456579\pi$
$44$	5.66362	0.853823
$45$	9.28543	1.38419
$46$	2.62274	0.386702
$47$	2.47394	0.360862	0.180431	−	0.983588i	$-0.442251\pi$
$47$	2.47394	0.360862	0.180431	+	0.983588i	$0.442251\pi$
$48$	−2.80221	−0.404464
$49$	−4.57659	−0.653798
$50$	1.33819	0.189249
$51$	−1.73796	−0.243363
$52$	−3.83536	−0.531869
$53$	12.7452	1.75069	0.875345	−	0.483499i	$-0.160634\pi$
$53$	12.7452	1.75069	0.875345	+	0.483499i	$0.160634\pi$
$54$	5.19074	0.706371
$55$	10.8378	1.46137
$56$	1.55673	0.208027
$57$	−18.3452	−2.42988
$58$	−5.69371	−0.747620
$59$	11.0235	1.43513	0.717567	−	0.696489i	$-0.245256\pi$
$59$	11.0235	1.43513	0.717567	+	0.696489i	$0.245256\pi$
$60$	−5.36226	−0.692265
$61$	−2.74708	−0.351727	−0.175864	−	0.984415i	$-0.556272\pi$
$61$	−2.74708	−0.351727	−0.175864	+	0.984415i	$0.556272\pi$
$62$	−1.75112	−0.222392
$63$	−7.55384	−0.951695
$64$	1.00000	0.125000
$65$	−7.33928	−0.910326
$66$	15.8706	1.95354
$67$	−3.94472	−0.481925	−0.240962	−	0.970534i	$-0.577463\pi$
$67$	−3.94472	−0.481925	−0.240962	+	0.970534i	$0.577463\pi$
$68$	0.620210	0.0752115
$69$	7.34947	0.884773
$70$	2.97894	0.356051
$71$	−1.03577	−0.122924	−0.0614618	−	0.998109i	$-0.519576\pi$
$71$	−1.03577	−0.122924	−0.0614618	+	0.998109i	$0.519576\pi$
$72$	−4.85238	−0.571858
$73$	−7.63003	−0.893027	−0.446514	−	0.894777i	$-0.647335\pi$
$73$	−7.63003	−0.893027	−0.446514	+	0.894777i	$0.647335\pi$
$74$	−6.65561	−0.773698
$75$	3.74990	0.433001
$76$	6.54668	0.750956
$77$	−8.81673	−1.00476
$78$	−10.7475	−1.21691
$79$	−15.5419	−1.74859	−0.874297	−	0.485391i	$-0.838677\pi$
$79$	−15.5419	−1.74859	−0.874297	+	0.485391i	$0.838677\pi$
$80$	1.91358	0.213945
$81$	−0.0115795	−0.00128662
$82$	2.29010	0.252899
$83$	3.95552	0.434175	0.217087	−	0.976152i	$-0.430344\pi$
$83$	3.95552	0.434175	0.217087	+	0.976152i	$0.430344\pi$
$84$	4.36229	0.475964
$85$	1.18682	0.128729
$86$	−1.78345	−0.192315
$87$	−15.9550	−1.71055
$88$	−5.66362	−0.603744
$89$	−6.66256	−0.706230	−0.353115	−	0.935580i	$-0.614878\pi$
$89$	−6.66256	−0.706230	−0.353115	+	0.935580i	$0.614878\pi$
$90$	−9.28543	−0.978770
$91$	5.97062	0.625891
$92$	−2.62274	−0.273440
$93$	−4.90700	−0.508832
$94$	−2.47394	−0.255168
$95$	12.5276	1.28531
$96$	2.80221	0.285999
$97$	−10.0627	−1.02171	−0.510856	−	0.859666i	$-0.670672\pi$
$97$	−10.0627	−1.02171	−0.510856	+	0.859666i	$0.670672\pi$
$98$	4.57659	0.462305
$99$	27.4820	2.76205
$100$	−1.33819	−0.133819
$101$	5.44879	0.542174	0.271087	−	0.962555i	$-0.412617\pi$
$101$	5.44879	0.542174	0.271087	+	0.962555i	$0.412617\pi$
$102$	1.73796	0.172083
$103$	7.38923	0.728083	0.364041	−	0.931383i	$-0.381397\pi$
$103$	7.38923	0.728083	0.364041	+	0.931383i	$0.381397\pi$
$104$	3.83536	0.376088
$105$	8.34760	0.814643
$106$	−12.7452	−1.23792
$107$	−2.57946	−0.249366	−0.124683	−	0.992197i	$-0.539791\pi$
$107$	−2.57946	−0.249366	−0.124683	+	0.992197i	$0.539791\pi$
$108$	−5.19074	−0.499479
$109$	−1.74070	−0.166729	−0.0833646	−	0.996519i	$-0.526567\pi$
$109$	−1.74070	−0.166729	−0.0833646	+	0.996519i	$0.526567\pi$
$110$	−10.8378	−1.03334
$111$	−18.6504	−1.77022
$112$	−1.55673	−0.147097
$113$	14.9518	1.40654	0.703271	−	0.710921i	$-0.251722\pi$
$113$	14.9518	1.40654	0.703271	+	0.710921i	$0.251722\pi$
$114$	18.3452	1.71818
$115$	−5.01884	−0.468009
$116$	5.69371	0.528647
$117$	−18.6106	−1.72055
$118$	−11.0235	−1.01479
$119$	−0.965500	−0.0885073
$120$	5.36226	0.489505
$121$	21.0766	1.91605
$122$	2.74708	0.248709
$123$	6.41734	0.578632
$124$	1.75112	0.157255
$125$	−12.1287	−1.08482
$126$	7.55384	0.672950
$127$	7.46853	0.662725	0.331363	−	0.943503i	$-0.392492\pi$
$127$	7.46853	0.662725	0.331363	+	0.943503i	$0.392492\pi$
$128$	−1.00000	−0.0883883
$129$	−4.99761	−0.440015
$130$	7.33928	0.643698
$131$	20.3142	1.77486	0.887432	−	0.460939i	$-0.152487\pi$
$131$	20.3142	1.77486	0.887432	+	0.460939i	$0.152487\pi$
$132$	−15.8706	−1.38136
$133$	−10.1914	−0.883709
$134$	3.94472	0.340772
$135$	−9.93293	−0.854890
$136$	−0.620210	−0.0531826
$137$	−23.3224	−1.99257	−0.996283	−	0.0861430i	$-0.972546\pi$
$137$	−23.3224	−1.99257	−0.996283	+	0.0861430i	$0.972546\pi$
$138$	−7.34947	−0.625629
$139$	9.65317	0.818771	0.409386	−	0.912361i	$-0.365743\pi$
$139$	9.65317	0.818771	0.409386	+	0.912361i	$0.365743\pi$
$140$	−2.97894	−0.251766
$141$	−6.93250	−0.583822
$142$	1.03577	0.0869201
$143$	−21.7220	−1.81649
$144$	4.85238	0.404365
$145$	10.8954	0.904813
$146$	7.63003	0.631465
$147$	12.8246	1.05775
$148$	6.65561	0.547087
$149$	−16.2465	−1.33097	−0.665483	−	0.746413i	$-0.731775\pi$
$149$	−16.2465	−1.33097	−0.665483	+	0.746413i	$0.731775\pi$
$150$	−3.74990	−0.306178
$151$	−9.53244	−0.775739	−0.387869	−	0.921714i	$-0.626789\pi$
$151$	−9.53244	−0.775739	−0.387869	+	0.921714i	$0.626789\pi$
$152$	−6.54668	−0.531006
$153$	3.00949	0.243303
$154$	8.81673	0.710473
$155$	3.35092	0.269152
$156$	10.7475	0.860487
$157$	−3.18404	−0.254114	−0.127057	−	0.991895i	$-0.540553\pi$
$157$	−3.18404	−0.254114	−0.127057	+	0.991895i	$0.540553\pi$
$158$	15.5419	1.23644
$159$	−35.7147	−2.83236
$160$	−1.91358	−0.151282
$161$	4.08291	0.321778
$162$	0.0115795	0.000909775 0
$163$	−7.37195	−0.577416	−0.288708	−	0.957417i	$-0.593226\pi$
$163$	−7.37195	−0.577416	−0.288708	+	0.957417i	$0.593226\pi$
$164$	−2.29010	−0.178827
$165$	−30.3698	−2.36429
$166$	−3.95552	−0.307008
$167$	12.4348	0.962230	0.481115	−	0.876657i	$-0.340232\pi$
$167$	12.4348	0.962230	0.481115	+	0.876657i	$0.340232\pi$
$168$	−4.36229	−0.336558
$169$	1.70997	0.131536
$170$	−1.18682	−0.0910253
$171$	31.7670	2.42928
$172$	1.78345	0.135987
$173$	0.341752	0.0259829	0.0129915	−	0.999916i	$-0.495865\pi$
$173$	0.341752	0.0259829	0.0129915	+	0.999916i	$0.495865\pi$
$174$	15.9550	1.20954
$175$	2.08321	0.157476
$176$	5.66362	0.426911
$177$	−30.8901	−2.32184
$178$	6.66256	0.499380
$179$	−14.6189	−1.09267	−0.546333	−	0.837568i	$-0.683977\pi$
$179$	−14.6189	−1.09267	−0.546333	+	0.837568i	$0.683977\pi$
$180$	9.28543	0.692095
$181$	9.62758	0.715613	0.357806	−	0.933796i	$-0.383525\pi$
$181$	9.62758	0.715613	0.357806	+	0.933796i	$0.383525\pi$
$182$	−5.97062	−0.442572
$183$	7.69789	0.569044
$184$	2.62274	0.193351
$185$	12.7361	0.936374
$186$	4.90700	0.359799
$187$	3.51263	0.256869
$188$	2.47394	0.180431
$189$	8.08059	0.587777
$190$	−12.5276	−0.908850
$191$	9.57871	0.693091	0.346546	−	0.938033i	$-0.387355\pi$
$191$	9.57871	0.693091	0.346546	+	0.938033i	$0.387355\pi$
$192$	−2.80221	−0.202232
$193$	−15.8685	−1.14224	−0.571120	−	0.820867i	$-0.693491\pi$
$193$	−15.8685	−1.14224	−0.571120	+	0.820867i	$0.693491\pi$
$194$	10.0627	0.722460
$195$	20.5662	1.47278
$196$	−4.57659	−0.326899
$197$	−14.8708	−1.05950	−0.529749	−	0.848155i	$-0.677714\pi$
$197$	−14.8708	−1.05950	−0.529749	+	0.848155i	$0.677714\pi$
$198$	−27.4820	−1.95306
$199$	−3.19643	−0.226589	−0.113295	−	0.993561i	$-0.536140\pi$
$199$	−3.19643	−0.226589	−0.113295	+	0.993561i	$0.536140\pi$
$200$	1.33819	0.0946246
$201$	11.0539	0.779685
$202$	−5.44879	−0.383375
$203$	−8.86357	−0.622101
$204$	−1.73796	−0.121681
$205$	−4.38230	−0.306073
$206$	−7.38923	−0.514832
$207$	−12.7265	−0.884555
$208$	−3.83536	−0.265934
$209$	37.0779	2.56473
$210$	−8.34760	−0.576039
$211$	13.2518	0.912289	0.456145	−	0.889906i	$-0.349230\pi$
$211$	13.2518	0.912289	0.456145	+	0.889906i	$0.349230\pi$
$212$	12.7452	0.875345
$213$	2.90245	0.198873
$214$	2.57946	0.176328
$215$	3.41279	0.232750
$216$	5.19074	0.353185
$217$	−2.72602	−0.185054
$218$	1.74070	0.117895
$219$	21.3809	1.44479
$220$	10.8378	0.730685
$221$	−2.37873	−0.160011
$222$	18.6504	1.25173
$223$	16.5831	1.11049	0.555243	−	0.831688i	$-0.312625\pi$
$223$	16.5831	1.11049	0.555243	+	0.831688i	$0.312625\pi$
$224$	1.55673	0.104013
$225$	−6.49342	−0.432895
$226$	−14.9518	−0.994576
$227$	−9.87639	−0.655519	−0.327759	−	0.944761i	$-0.606294\pi$
$227$	−9.87639	−0.655519	−0.327759	+	0.944761i	$0.606294\pi$
$228$	−18.3452	−1.21494
$229$	−24.9163	−1.64652	−0.823258	−	0.567667i	$-0.807846\pi$
$229$	−24.9163	−1.64652	−0.823258	+	0.567667i	$0.807846\pi$
$230$	5.01884	0.330933
$231$	24.7063	1.62556
$232$	−5.69371	−0.373810
$233$	−1.94097	−0.127157	−0.0635784	−	0.997977i	$-0.520251\pi$
$233$	−1.94097	−0.127157	−0.0635784	+	0.997977i	$0.520251\pi$
$234$	18.6106	1.21661
$235$	4.73410	0.308819
$236$	11.0235	0.717567
$237$	43.5515	2.82897
$238$	0.965500	0.0625841
$239$	9.51977	0.615783	0.307891	−	0.951422i	$-0.400377\pi$
$239$	9.51977	0.615783	0.307891	+	0.951422i	$0.400377\pi$
$240$	−5.36226	−0.346133
$241$	6.58295	0.424045	0.212022	−	0.977265i	$-0.431995\pi$
$241$	6.58295	0.424045	0.212022	+	0.977265i	$0.431995\pi$
$242$	−21.0766	−1.35485
$243$	15.6047	1.00104
$244$	−2.74708	−0.175864
$245$	−8.75769	−0.559508
$246$	−6.41734	−0.409155
$247$	−25.1089	−1.59764
$248$	−1.75112	−0.111196
$249$	−11.0842	−0.702432
$250$	12.1287	0.767084
$251$	23.5399	1.48583	0.742913	−	0.669387i	$-0.233443\pi$
$251$	23.5399	1.48583	0.742913	+	0.669387i	$0.233443\pi$
$252$	−7.55384	−0.475847
$253$	−14.8542	−0.933876
$254$	−7.46853	−0.468618
$255$	−3.32573	−0.208265
$256$	1.00000	0.0625000
$257$	28.5969	1.78383	0.891913	−	0.452208i	$-0.149363\pi$
$257$	28.5969	1.78383	0.891913	+	0.452208i	$0.149363\pi$
$258$	4.99761	0.311138
$259$	−10.3610	−0.643801
$260$	−7.33928	−0.455163
$261$	27.6280	1.71013
$262$	−20.3142	−1.25502
$263$	15.0770	0.929690	0.464845	−	0.885392i	$-0.346110\pi$
$263$	15.0770	0.929690	0.464845	+	0.885392i	$0.346110\pi$
$264$	15.8706	0.976770
$265$	24.3890	1.49821
$266$	10.1914	0.624876
$267$	18.6699	1.14258
$268$	−3.94472	−0.240962
$269$	26.9618	1.64389	0.821945	−	0.569567i	$-0.192889\pi$
$269$	26.9618	1.64389	0.821945	+	0.569567i	$0.192889\pi$
$270$	9.93293	0.604499
$271$	−5.50356	−0.334317	−0.167159	−	0.985930i	$-0.553459\pi$
$271$	−5.50356	−0.334317	−0.167159	+	0.985930i	$0.553459\pi$
$272$	0.620210	0.0376058
$273$	−16.7309	−1.01260
$274$	23.3224	1.40896
$275$	−7.57902	−0.457032
$276$	7.34947	0.442386
$277$	25.2940	1.51977	0.759886	−	0.650056i	$-0.225255\pi$
$277$	25.2940	1.51977	0.759886	+	0.650056i	$0.225255\pi$
$278$	−9.65317	−0.578959
$279$	8.49709	0.508707
$280$	2.97894	0.178026
$281$	2.97676	0.177579	0.0887894	−	0.996050i	$-0.471700\pi$
$281$	2.97676	0.177579	0.0887894	+	0.996050i	$0.471700\pi$
$282$	6.93250	0.412825
$283$	8.82823	0.524784	0.262392	−	0.964961i	$-0.415489\pi$
$283$	8.82823	0.524784	0.262392	+	0.964961i	$0.415489\pi$
$284$	−1.03577	−0.0614618
$285$	−35.1050	−2.07944
$286$	21.7220	1.28445
$287$	3.56507	0.210439
$288$	−4.85238	−0.285929
$289$	−16.6153	−0.977373
$290$	−10.8954	−0.639799
$291$	28.1978	1.65298
$292$	−7.63003	−0.446514
$293$	10.2785	0.600476	0.300238	−	0.953864i	$-0.402934\pi$
$293$	10.2785	0.600476	0.300238	+	0.953864i	$0.402934\pi$
$294$	−12.8246	−0.747943
$295$	21.0944	1.22816
$296$	−6.65561	−0.386849
$297$	−29.3984	−1.70587
$298$	16.2465	0.941136
$299$	10.0592	0.581736
$300$	3.74990	0.216501
$301$	−2.77636	−0.160027
$302$	9.53244	0.548530
$303$	−15.2686	−0.877160
$304$	6.54668	0.375478
$305$	−5.25677	−0.301002
$306$	−3.00949	−0.172041
$307$	15.8478	0.904481	0.452240	−	0.891896i	$-0.350625\pi$
$307$	15.8478	0.904481	0.452240	+	0.891896i	$0.350625\pi$
$308$	−8.81673	−0.502380
$309$	−20.7062	−1.17793
$310$	−3.35092	−0.190319
$311$	20.0382	1.13626	0.568132	−	0.822937i	$-0.307666\pi$
$311$	20.0382	1.13626	0.568132	+	0.822937i	$0.307666\pi$
$312$	−10.7475	−0.608456
$313$	33.4970	1.89336	0.946680	−	0.322175i	$-0.104414\pi$
$313$	33.4970	1.89336	0.946680	+	0.322175i	$0.104414\pi$
$314$	3.18404	0.179686
$315$	−14.4549	−0.814443
$316$	−15.5419	−0.874297
$317$	3.27051	0.183690	0.0918450	−	0.995773i	$-0.470724\pi$
$317$	3.27051	0.183690	0.0918450	+	0.995773i	$0.470724\pi$
$318$	35.7147	2.00278
$319$	32.2470	1.80548
$320$	1.91358	0.106973
$321$	7.22819	0.403438
$322$	−4.08291	−0.227531
$323$	4.06032	0.225922
$324$	−0.0115795	−0.000643308 0
$325$	5.13245	0.284697
$326$	7.37195	0.408294
$327$	4.87782	0.269744
$328$	2.29010	0.126450
$329$	−3.85126	−0.212327
$330$	30.3698	1.67180
$331$	8.63105	0.474406	0.237203	−	0.971460i	$-0.423769\pi$
$331$	8.63105	0.474406	0.237203	+	0.971460i	$0.423769\pi$
$332$	3.95552	0.217087
$333$	32.2955	1.76978
$334$	−12.4348	−0.680400
$335$	−7.54856	−0.412422
$336$	4.36229	0.237982
$337$	−12.2722	−0.668507	−0.334254	−	0.942483i	$-0.608484\pi$
$337$	−12.2722	−0.668507	−0.334254	+	0.942483i	$0.608484\pi$
$338$	−1.70997	−0.0930103
$339$	−41.8979	−2.27558
$340$	1.18682	0.0643646
$341$	9.91767	0.537072
$342$	−31.7670	−1.71776
$343$	18.0216	0.973077
$344$	−1.78345	−0.0961574
$345$	14.0638	0.757172
$346$	−0.341752	−0.0183727
$347$	−5.66054	−0.303874	−0.151937	−	0.988390i	$-0.548551\pi$
$347$	−5.66054	−0.303874	−0.151937	+	0.988390i	$0.548551\pi$
$348$	−15.9550	−0.855275
$349$	5.64704	0.302279	0.151140	−	0.988512i	$-0.451706\pi$
$349$	5.64704	0.302279	0.151140	+	0.988512i	$0.451706\pi$
$350$	−2.08321	−0.111352
$351$	19.9084	1.06263
$352$	−5.66362	−0.301872
$353$	−24.2694	−1.29173	−0.645866	−	0.763451i	$-0.723503\pi$
$353$	−24.2694	−1.29173	−0.645866	+	0.763451i	$0.723503\pi$
$354$	30.8901	1.64179
$355$	−1.98204	−0.105196
$356$	−6.66256	−0.353115
$357$	2.70553	0.143192
$358$	14.6189	0.772632
$359$	−30.3780	−1.60329	−0.801646	−	0.597799i	$-0.796042\pi$
$359$	−30.3780	−1.60329	−0.801646	+	0.597799i	$0.796042\pi$
$360$	−9.28543	−0.489385
$361$	23.8591	1.25574
$362$	−9.62758	−0.506015
$363$	−59.0610	−3.09990
$364$	5.97062	0.312946
$365$	−14.6007	−0.764236
$366$	−7.69789	−0.402375
$367$	12.7103	0.663470	0.331735	−	0.943373i	$-0.392366\pi$
$367$	12.7103	0.663470	0.331735	+	0.943373i	$0.392366\pi$
$368$	−2.62274	−0.136720
$369$	−11.1124	−0.578490
$370$	−12.7361	−0.662116
$371$	−19.8409	−1.03009
$372$	−4.90700	−0.254416
$373$	1.49471	0.0773930	0.0386965	−	0.999251i	$-0.487679\pi$
$373$	1.49471	0.0773930	0.0386965	+	0.999251i	$0.487679\pi$
$374$	−3.51263	−0.181634
$375$	33.9871	1.75508
$376$	−2.47394	−0.127584
$377$	−21.8374	−1.12468
$378$	−8.08059	−0.415621
$379$	31.6410	1.62529	0.812645	−	0.582759i	$-0.198027\pi$
$379$	31.6410	1.62529	0.812645	+	0.582759i	$0.198027\pi$
$380$	12.5276	0.642654
$381$	−20.9284	−1.07219
$382$	−9.57871	−0.490090
$383$	17.9516	0.917285	0.458643	−	0.888621i	$-0.348336\pi$
$383$	17.9516	0.917285	0.458643	+	0.888621i	$0.348336\pi$
$384$	2.80221	0.143000
$385$	−16.8716	−0.859854
$386$	15.8685	0.807685
$387$	8.65399	0.439907
$388$	−10.0627	−0.510856
$389$	23.0482	1.16859	0.584295	−	0.811541i	$-0.301371\pi$
$389$	23.0482	1.16859	0.584295	+	0.811541i	$0.301371\pi$
$390$	−20.5662	−1.04141
$391$	−1.62665	−0.0822633
$392$	4.57659	0.231153
$393$	−56.9247	−2.87147
$394$	14.8708	0.749178
$395$	−29.7406	−1.49641
$396$	27.4820	1.38102
$397$	22.7194	1.14025	0.570126	−	0.821557i	$-0.306894\pi$
$397$	22.7194	1.14025	0.570126	+	0.821557i	$0.306894\pi$
$398$	3.19643	0.160223
$399$	28.5585	1.42971
$400$	−1.33819	−0.0669097
$401$	38.4998	1.92259	0.961293	−	0.275528i	$-0.0888528\pi$
$401$	38.4998	1.92259	0.961293	+	0.275528i	$0.0888528\pi$
$402$	−11.0539	−0.551320
$403$	−6.71617	−0.334556
$404$	5.44879	0.271087
$405$	−0.0221584	−0.00110106
$406$	8.86357	0.439892
$407$	37.6948	1.86846
$408$	1.73796	0.0860417
$409$	37.3668	1.84767	0.923835	−	0.382790i	$-0.125037\pi$
$409$	37.3668	1.84767	0.923835	+	0.382790i	$0.125037\pi$
$410$	4.38230	0.216426
$411$	65.3542	3.22368
$412$	7.38923	0.364041
$413$	−17.1606	−0.844418
$414$	12.7265	0.625475
$415$	7.56922	0.371558
$416$	3.83536	0.188044
$417$	−27.0502	−1.32465
$418$	−37.0779	−1.81354
$419$	−23.9400	−1.16955	−0.584774	−	0.811197i	$-0.698817\pi$
$419$	−23.9400	−1.16955	−0.584774	+	0.811197i	$0.698817\pi$
$420$	8.34760	0.407321
$421$	−20.7564	−1.01160	−0.505802	−	0.862649i	$-0.668803\pi$
$421$	−20.7564	−1.01160	−0.505802	+	0.862649i	$0.668803\pi$
$422$	−13.2518	−0.645086
$423$	12.0045	0.583679
$424$	−12.7452	−0.618962
$425$	−0.829961	−0.0402590
$426$	−2.90245	−0.140624
$427$	4.27646	0.206953
$428$	−2.57946	−0.124683
$429$	60.8696	2.93881
$430$	−3.41279	−0.164579
$431$	−0.515613	−0.0248362	−0.0124181	−	0.999923i	$-0.503953\pi$
$431$	−0.515613	−0.0248362	−0.0124181	+	0.999923i	$0.503953\pi$
$432$	−5.19074	−0.249740
$433$	−2.86435	−0.137652	−0.0688259	−	0.997629i	$-0.521925\pi$
$433$	−2.86435	−0.137652	−0.0688259	+	0.997629i	$0.521925\pi$
$434$	2.72602	0.130853
$435$	−30.5312	−1.46386
$436$	−1.74070	−0.0833646
$437$	−17.1703	−0.821365
$438$	−21.3809	−1.02162
$439$	30.6773	1.46415	0.732073	−	0.681226i	$-0.238553\pi$
$439$	30.6773	1.46415	0.732073	+	0.681226i	$0.238553\pi$
$440$	−10.8378	−0.516672
$441$	−22.2073	−1.05749
$442$	2.37873	0.113145
$443$	9.42756	0.447917	0.223958	−	0.974599i	$-0.428102\pi$
$443$	9.42756	0.447917	0.223958	+	0.974599i	$0.428102\pi$
$444$	−18.6504	−0.885109
$445$	−12.7494	−0.604379
$446$	−16.5831	−0.785232
$447$	45.5261	2.15331
$448$	−1.55673	−0.0735486
$449$	−19.4660	−0.918657	−0.459328	−	0.888267i	$-0.651910\pi$
$449$	−19.4660	−0.918657	−0.459328	+	0.888267i	$0.651910\pi$
$450$	6.49342	0.306103
$451$	−12.9703	−0.610745
$452$	14.9518	0.703271
$453$	26.7119	1.25503
$454$	9.87639	0.463522
$455$	11.4253	0.535626
$456$	18.3452	0.859092
$457$	3.06459	0.143355	0.0716777	−	0.997428i	$-0.477165\pi$
$457$	3.06459	0.143355	0.0716777	+	0.997428i	$0.477165\pi$
$458$	24.9163	1.16426
$459$	−3.21935	−0.150266
$460$	−5.01884	−0.234005
$461$	−0.0686854	−0.00319900	−0.00159950	−	0.999999i	$-0.500509\pi$
$461$	−0.0686854	−0.00319900	−0.00159950	+	0.999999i	$0.500509\pi$
$462$	−24.7063	−1.14944
$463$	25.5176	1.18590	0.592952	−	0.805238i	$-0.297962\pi$
$463$	25.5176	1.18590	0.592952	+	0.805238i	$0.297962\pi$
$464$	5.69371	0.264324
$465$	−9.38996	−0.435449
$466$	1.94097	0.0899135
$467$	−6.78406	−0.313929	−0.156964	−	0.987604i	$-0.550171\pi$
$467$	−6.78406	−0.313929	−0.156964	+	0.987604i	$0.550171\pi$
$468$	−18.6106	−0.860275
$469$	6.14087	0.283559
$470$	−4.73410	−0.218368
$471$	8.92236	0.411121
$472$	−11.0235	−0.507397
$473$	10.1008	0.464435
$474$	−43.5515	−2.00039
$475$	−8.76073	−0.401970
$476$	−0.965500	−0.0442536
$477$	61.8446	2.83167
$478$	−9.51977	−0.435424
$479$	−25.6540	−1.17216	−0.586082	−	0.810252i	$-0.699330\pi$
$479$	−25.6540	−1.17216	−0.586082	+	0.810252i	$0.699330\pi$
$480$	5.36226	0.244753
$481$	−25.5266	−1.16391
$482$	−6.58295	−0.299845
$483$	−11.4412	−0.520591
$484$	21.0766	0.958026
$485$	−19.2558	−0.874362
$486$	−15.6047	−0.707843
$487$	6.68135	0.302761	0.151381	−	0.988476i	$-0.451628\pi$
$487$	6.68135	0.302761	0.151381	+	0.988476i	$0.451628\pi$
$488$	2.74708	0.124354
$489$	20.6577	0.934175
$490$	8.75769	0.395632
$491$	−36.5102	−1.64768	−0.823841	−	0.566821i	$-0.808173\pi$
$491$	−36.5102	−1.64768	−0.823841	+	0.566821i	$0.808173\pi$
$492$	6.41734	0.289316
$493$	3.53129	0.159041
$494$	25.1089	1.12970
$495$	52.5891	2.36371
$496$	1.75112	0.0786276
$497$	1.61242	0.0723269
$498$	11.0842	0.496694
$499$	14.4973	0.648988	0.324494	−	0.945888i	$-0.394806\pi$
$499$	14.4973	0.648988	0.324494	+	0.945888i	$0.394806\pi$
$500$	−12.1287	−0.542411
$501$	−34.8448	−1.55675
$502$	−23.5399	−1.05064
$503$	−22.5691	−1.00631	−0.503154	−	0.864197i	$-0.667827\pi$
$503$	−22.5691	−1.00631	−0.503154	+	0.864197i	$0.667827\pi$
$504$	7.55384	0.336475
$505$	10.4267	0.463983
$506$	14.8542	0.660350
$507$	−4.79170	−0.212807
$508$	7.46853	0.331363
$509$	−18.6837	−0.828142	−0.414071	−	0.910245i	$-0.635893\pi$
$509$	−18.6837	−0.828142	−0.414071	+	0.910245i	$0.635893\pi$
$510$	3.32573	0.147266
$511$	11.8779	0.525447
$512$	−1.00000	−0.0441942
$513$	−33.9821	−1.50035
$514$	−28.5969	−1.26135
$515$	14.1399	0.623079
$516$	−4.99761	−0.220007
$517$	14.0115	0.616224
$518$	10.3610	0.455236
$519$	−0.957661	−0.0420367
$520$	7.33928	0.321849
$521$	−28.7983	−1.26168	−0.630838	−	0.775914i	$-0.717289\pi$
$521$	−28.7983	−1.26168	−0.630838	+	0.775914i	$0.717289\pi$
$522$	−27.6280	−1.20924
$523$	3.97574	0.173847	0.0869234	−	0.996215i	$-0.472296\pi$
$523$	3.97574	0.173847	0.0869234	+	0.996215i	$0.472296\pi$
$524$	20.3142	0.887432
$525$	−5.83759	−0.254773
$526$	−15.0770	−0.657390
$527$	1.08606	0.0473096
$528$	−15.8706	−0.690681
$529$	−16.1212	−0.700923
$530$	−24.3890	−1.05939
$531$	53.4900	2.32127
$532$	−10.1914	−0.441854
$533$	8.78335	0.380449
$534$	−18.6699	−0.807925
$535$	−4.93602	−0.213403
$536$	3.94472	0.170386
$537$	40.9651	1.76778
$538$	−26.9618	−1.16241
$539$	−25.9200	−1.11646
$540$	−9.93293	−0.427445
$541$	−7.90132	−0.339704	−0.169852	−	0.985470i	$-0.554329\pi$
$541$	−7.90132	−0.339704	−0.169852	+	0.985470i	$0.554329\pi$
$542$	5.50356	0.236398
$543$	−26.9785	−1.15776
$544$	−0.620210	−0.0265913
$545$	−3.33098	−0.142684
$546$	16.7309	0.716018
$547$	39.6035	1.69332	0.846662	−	0.532130i	$-0.178608\pi$
$547$	39.6035	1.69332	0.846662	+	0.532130i	$0.178608\pi$
$548$	−23.3224	−0.996283
$549$	−13.3299	−0.568905
$550$	7.57902	0.323171
$551$	37.2749	1.58796
$552$	−7.34947	−0.312814
$553$	24.1945	1.02885
$554$	−25.2940	−1.07464
$555$	−35.6891	−1.51492
$556$	9.65317	0.409386
$557$	14.4649	0.612896	0.306448	−	0.951887i	$-0.400859\pi$
$557$	14.4649	0.612896	0.306448	+	0.951887i	$0.400859\pi$
$558$	−8.49709	−0.359710
$559$	−6.84018	−0.289309
$560$	−2.97894	−0.125883
$561$	−9.84313	−0.415577
$562$	−2.97676	−0.125567
$563$	−10.1987	−0.429823	−0.214911	−	0.976634i	$-0.568946\pi$
$563$	−10.1987	−0.429823	−0.214911	+	0.976634i	$0.568946\pi$
$564$	−6.93250	−0.291911
$565$	28.6115	1.20369
$566$	−8.82823	−0.371078
$567$	0.0180262	0.000757031 0
$568$	1.03577	0.0434600
$569$	11.9765	0.502082	0.251041	−	0.967976i	$-0.419227\pi$
$569$	11.9765	0.502082	0.251041	+	0.967976i	$0.419227\pi$
$570$	35.1050	1.47039
$571$	12.2758	0.513725	0.256863	−	0.966448i	$-0.417311\pi$
$571$	12.2758	0.513725	0.256863	+	0.966448i	$0.417311\pi$
$572$	−21.7220	−0.908243
$573$	−26.8416	−1.12132
$574$	−3.56507	−0.148803
$575$	3.50974	0.146366
$576$	4.85238	0.202182
$577$	3.49747	0.145602	0.0728008	−	0.997347i	$-0.476806\pi$
$577$	3.49747	0.145602	0.0728008	+	0.997347i	$0.476806\pi$
$578$	16.6153	0.691107
$579$	44.4669	1.84798
$580$	10.8954	0.452406
$581$	−6.15768	−0.255464
$582$	−28.1978	−1.16884
$583$	72.1840	2.98956
$584$	7.63003	0.315733
$585$	−35.6130	−1.47241
$586$	−10.2785	−0.424601
$587$	3.03512	0.125273	0.0626364	−	0.998036i	$-0.480049\pi$
$587$	3.03512	0.125273	0.0626364	+	0.998036i	$0.480049\pi$
$588$	12.8246	0.528876
$589$	11.4640	0.472367
$590$	−21.0944	−0.868441
$591$	41.6710	1.71411
$592$	6.65561	0.273544
$593$	8.00136	0.328576	0.164288	−	0.986412i	$-0.447467\pi$
$593$	8.00136	0.328576	0.164288	+	0.986412i	$0.447467\pi$
$594$	29.3984	1.20623
$595$	−1.84757	−0.0757428
$596$	−16.2465	−0.665483
$597$	8.95707	0.366589
$598$	−10.0592	−0.411350
$599$	4.52106	0.184725	0.0923627	−	0.995725i	$-0.470558\pi$
$599$	4.52106	0.184725	0.0923627	+	0.995725i	$0.470558\pi$
$600$	−3.74990	−0.153089
$601$	−35.9537	−1.46658	−0.733292	−	0.679914i	$-0.762017\pi$
$601$	−35.9537	−1.46658	−0.733292	+	0.679914i	$0.762017\pi$
$602$	2.77636	0.113156
$603$	−19.1413	−0.779493
$604$	−9.53244	−0.387869
$605$	40.3318	1.63972
$606$	15.2686	0.620246
$607$	23.1880	0.941172	0.470586	−	0.882354i	$-0.344042\pi$
$607$	23.1880	0.941172	0.470586	+	0.882354i	$0.344042\pi$
$608$	−6.54668	−0.265503
$609$	24.8376	1.00647
$610$	5.25677	0.212840
$611$	−9.48846	−0.383862
$612$	3.00949	0.121651
$613$	−6.89631	−0.278539	−0.139270	−	0.990254i	$-0.544475\pi$
$613$	−6.89631	−0.278539	−0.139270	+	0.990254i	$0.544475\pi$
$614$	−15.8478	−0.639565
$615$	12.2801	0.495182
$616$	8.81673	0.355236
$617$	−1.84842	−0.0744145	−0.0372072	−	0.999308i	$-0.511846\pi$
$617$	−1.84842	−0.0744145	−0.0372072	+	0.999308i	$0.511846\pi$
$618$	20.7062	0.832924
$619$	−46.0451	−1.85071	−0.925355	−	0.379102i	$-0.876233\pi$
$619$	−46.0451	−1.85071	−0.925355	+	0.379102i	$0.876233\pi$
$620$	3.35092	0.134576
$621$	13.6140	0.546310
$622$	−20.0382	−0.803460
$623$	10.3718	0.415538
$624$	10.7475	0.430243
$625$	−16.5183	−0.660731
$626$	−33.4970	−1.33881
$627$	−103.900	−4.14937
$628$	−3.18404	−0.127057
$629$	4.12787	0.164589
$630$	14.4549	0.575898
$631$	10.2024	0.406150	0.203075	−	0.979163i	$-0.434907\pi$
$631$	10.2024	0.406150	0.203075	+	0.979163i	$0.434907\pi$
$632$	15.5419	0.618222
$633$	−37.1342	−1.47595
$634$	−3.27051	−0.129888
$635$	14.2917	0.567148
$636$	−35.7147	−1.41618
$637$	17.5529	0.695469
$638$	−32.2470	−1.27667
$639$	−5.02595	−0.198824
$640$	−1.91358	−0.0756411
$641$	1.57269	0.0621175	0.0310588	−	0.999518i	$-0.490112\pi$
$641$	1.57269	0.0621175	0.0310588	+	0.999518i	$0.490112\pi$
$642$	−7.22819	−0.285274
$643$	−13.0014	−0.512724	−0.256362	−	0.966581i	$-0.582524\pi$
$643$	−13.0014	−0.512724	−0.256362	+	0.966581i	$0.582524\pi$
$644$	4.08291	0.160889
$645$	−9.56335	−0.376556
$646$	−4.06032	−0.159751
$647$	−17.8170	−0.700459	−0.350229	−	0.936664i	$-0.613896\pi$
$647$	−17.8170	−0.700459	−0.350229	+	0.936664i	$0.613896\pi$
$648$	0.0115795	0.000454888 0
$649$	62.4328	2.45070
$650$	−5.13245	−0.201311
$651$	7.63889	0.299392
$652$	−7.37195	−0.288708
$653$	−18.1655	−0.710873	−0.355436	−	0.934700i	$-0.615668\pi$
$653$	−18.1655	−0.710873	−0.355436	+	0.934700i	$0.615668\pi$
$654$	−4.87782	−0.190738
$655$	38.8730	1.51889
$656$	−2.29010	−0.0894134
$657$	−37.0238	−1.44443
$658$	3.85126	0.150138
$659$	−13.5562	−0.528075	−0.264037	−	0.964512i	$-0.585054\pi$
$659$	−13.5562	−0.528075	−0.264037	+	0.964512i	$0.585054\pi$
$660$	−30.3698	−1.18214
$661$	34.4258	1.33901	0.669504	−	0.742808i	$-0.266507\pi$
$661$	34.4258	1.33901	0.669504	+	0.742808i	$0.266507\pi$
$662$	−8.63105	−0.335455
$663$	6.66569	0.258874
$664$	−3.95552	−0.153504
$665$	−19.5022	−0.756261
$666$	−32.2955	−1.25143
$667$	−14.9331	−0.578213
$668$	12.4348	0.481115
$669$	−46.4693	−1.79661
$670$	7.54856	0.291626
$671$	−15.5584	−0.600626
$672$	−4.36229	−0.168279
$673$	−47.7236	−1.83961	−0.919805	−	0.392377i	$-0.871653\pi$
$673$	−47.7236	−1.83961	−0.919805	+	0.392377i	$0.871653\pi$
$674$	12.2722	0.472706
$675$	6.94622	0.267360
$676$	1.70997	0.0657682
$677$	−26.5072	−1.01876	−0.509378	−	0.860543i	$-0.670124\pi$
$677$	−26.5072	−1.01876	−0.509378	+	0.860543i	$0.670124\pi$
$678$	41.8979	1.60908
$679$	15.6649	0.601164
$680$	−1.18682	−0.0455126
$681$	27.6757	1.06054
$682$	−9.91767	−0.379767
$683$	10.4648	0.400423	0.200212	−	0.979753i	$-0.435837\pi$
$683$	10.4648	0.400423	0.200212	+	0.979753i	$0.435837\pi$
$684$	31.7670	1.21464
$685$	−44.6293	−1.70520
$686$	−18.0216	−0.688069
$687$	69.8207	2.66383
$688$	1.78345	0.0679935
$689$	−48.8825	−1.86227
$690$	−14.0638	−0.535401
$691$	16.7240	0.636209	0.318105	−	0.948056i	$-0.396954\pi$
$691$	16.7240	0.636209	0.318105	+	0.948056i	$0.396954\pi$
$692$	0.341752	0.0129915
$693$	−42.7821	−1.62516
$694$	5.66054	0.214871
$695$	18.4722	0.700689
$696$	15.9550	0.604771
$697$	−1.42034	−0.0537993
$698$	−5.64704	−0.213744
$699$	5.43899	0.205722
$700$	2.08321	0.0787379
$701$	44.3792	1.67618	0.838090	−	0.545532i	$-0.183672\pi$
$701$	44.3792	1.67618	0.838090	+	0.545532i	$0.183672\pi$
$702$	−19.9084	−0.751393
$703$	43.5721	1.64335
$704$	5.66362	0.213456
$705$	−13.2659	−0.499624
$706$	24.2694	0.913392
$707$	−8.48230	−0.319010
$708$	−30.8901	−1.16092
$709$	10.7124	0.402313	0.201156	−	0.979559i	$-0.435530\pi$
$709$	10.7124	0.402313	0.201156	+	0.979559i	$0.435530\pi$
$710$	1.98204	0.0743845
$711$	−75.4149	−2.82828
$712$	6.66256	0.249690
$713$	−4.59274	−0.171999
$714$	−2.70553	−0.101252
$715$	−41.5669	−1.55451
$716$	−14.6189	−0.546333
$717$	−26.6764	−0.996248
$718$	30.3780	1.13370
$719$	−37.3595	−1.39328	−0.696638	−	0.717423i	$-0.745322\pi$
$719$	−37.3595	−1.39328	−0.696638	+	0.717423i	$0.745322\pi$
$720$	9.28543	0.346048
$721$	−11.5030	−0.428396
$722$	−23.8591	−0.887942
$723$	−18.4468	−0.686043
$724$	9.62758	0.357806
$725$	−7.61928	−0.282973
$726$	59.0610	2.19196
$727$	23.2189	0.861140	0.430570	−	0.902557i	$-0.358313\pi$
$727$	23.2189	0.861140	0.430570	+	0.902557i	$0.358313\pi$
$728$	−5.97062	−0.221286
$729$	−43.6928	−1.61825
$730$	14.6007	0.540396
$731$	1.10612	0.0409112
$732$	7.69789	0.284522
$733$	−14.6231	−0.540118	−0.270059	−	0.962844i	$-0.587043\pi$
$733$	−14.6231	−0.540118	−0.270059	+	0.962844i	$0.587043\pi$
$734$	−12.7103	−0.469144
$735$	24.5409	0.905204
$736$	2.62274	0.0966756
$737$	−22.3414	−0.822956
$738$	11.1124	0.409054
$739$	29.5236	1.08604	0.543022	−	0.839718i	$-0.317280\pi$
$739$	29.5236	1.08604	0.543022	+	0.839718i	$0.317280\pi$
$740$	12.7361	0.468187
$741$	70.3603	2.58475
$742$	19.8409	0.728381
$743$	34.1979	1.25460	0.627300	−	0.778778i	$-0.284160\pi$
$743$	34.1979	1.25460	0.627300	+	0.778778i	$0.284160\pi$
$744$	4.90700	0.179899
$745$	−31.0891	−1.13902
$746$	−1.49471	−0.0547251
$747$	19.1937	0.702259
$748$	3.51263	0.128435
$749$	4.01553	0.146724
$750$	−33.9871	−1.24103
$751$	−18.2784	−0.666990	−0.333495	−	0.942752i	$-0.608228\pi$
$751$	−18.2784	−0.666990	−0.333495	+	0.942752i	$0.608228\pi$
$752$	2.47394	0.0902154
$753$	−65.9638	−2.40385
$754$	21.8374	0.795271
$755$	−18.2411	−0.663862
$756$	8.08059	0.293888
$757$	30.4172	1.10553	0.552766	−	0.833337i	$-0.313572\pi$
$757$	30.4172	1.10553	0.552766	+	0.833337i	$0.313572\pi$
$758$	−31.6410	−1.14925
$759$	41.6246	1.51088
$760$	−12.5276	−0.454425
$761$	−42.7249	−1.54878	−0.774389	−	0.632710i	$-0.781943\pi$
$761$	−42.7249	−1.54878	−0.774389	+	0.632710i	$0.781943\pi$
$762$	20.9284	0.758156
$763$	2.70981	0.0981017
$764$	9.57871	0.346546
$765$	5.75892	0.208214
$766$	−17.9516	−0.648619
$767$	−42.2790	−1.52661
$768$	−2.80221	−0.101116
$769$	−8.45214	−0.304792	−0.152396	−	0.988320i	$-0.548699\pi$
$769$	−8.45214	−0.304792	−0.152396	+	0.988320i	$0.548699\pi$
$770$	16.8716	0.608009
$771$	−80.1345	−2.88597
$772$	−15.8685	−0.571120
$773$	12.5036	0.449722	0.224861	−	0.974391i	$-0.427807\pi$
$773$	12.5036	0.449722	0.224861	+	0.974391i	$0.427807\pi$
$774$	−8.65399	−0.311061
$775$	−2.34334	−0.0841752
$776$	10.0627	0.361230
$777$	29.0337	1.04158
$778$	−23.0482	−0.826318
$779$	−14.9926	−0.537164
$780$	20.5662	0.736388
$781$	−5.86622	−0.209910
$782$	1.62665	0.0581689
$783$	−29.5546	−1.05619
$784$	−4.57659	−0.163450
$785$	−6.09294	−0.217466
$786$	56.9247	2.03044
$787$	−5.14173	−0.183283	−0.0916414	−	0.995792i	$-0.529211\pi$
$787$	−5.14173	−0.183283	−0.0916414	+	0.995792i	$0.529211\pi$
$788$	−14.8708	−0.529749
$789$	−42.2490	−1.50410
$790$	29.7406	1.05812
$791$	−23.2759	−0.827595
$792$	−27.4820	−0.976530
$793$	10.5360	0.374146
$794$	−22.7194	−0.806280
$795$	−68.3432	−2.42388
$796$	−3.19643	−0.113295
$797$	34.5570	1.22407	0.612035	−	0.790830i	$-0.290351\pi$
$797$	34.5570	1.22407	0.612035	+	0.790830i	$0.290351\pi$
$798$	−28.5585	−1.01096
$799$	1.53436	0.0542819
$800$	1.33819	0.0473123
$801$	−32.3293	−1.14230
$802$	−38.4998	−1.35947
$803$	−43.2136	−1.52497
$804$	11.0539	0.389842
$805$	7.81299	0.275372
$806$	6.71617	0.236567
$807$	−75.5526	−2.65958
$808$	−5.44879	−0.191688
$809$	−27.4586	−0.965392	−0.482696	−	0.875788i	$-0.660342\pi$
$809$	−27.4586	−0.965392	−0.482696	+	0.875788i	$0.660342\pi$
$810$	0.0221584	0.000778568 0
$811$	39.1128	1.37343	0.686717	−	0.726925i	$-0.259051\pi$
$811$	39.1128	1.37343	0.686717	+	0.726925i	$0.259051\pi$
$812$	−8.86357	−0.311050
$813$	15.4221	0.540877
$814$	−37.6948	−1.32120
$815$	−14.1068	−0.494141
$816$	−1.73796	−0.0608407
$817$	11.6757	0.408481
$818$	−37.3668	−1.30650
$819$	28.9717	1.01235
$820$	−4.38230	−0.153037
$821$	−42.0200	−1.46651	−0.733255	−	0.679954i	$-0.762000\pi$
$821$	−42.0200	−1.46651	−0.733255	+	0.679954i	$0.762000\pi$
$822$	−65.3542	−2.27949
$823$	−52.3387	−1.82441	−0.912207	−	0.409730i	$-0.865623\pi$
$823$	−52.3387	−1.82441	−0.912207	+	0.409730i	$0.865623\pi$
$824$	−7.38923	−0.257416
$825$	21.2380	0.739412
$826$	17.1606	0.597093
$827$	−27.1343	−0.943551	−0.471776	−	0.881719i	$-0.656387\pi$
$827$	−27.1343	−0.943551	−0.471776	+	0.881719i	$0.656387\pi$
$828$	−12.7265	−0.442278
$829$	0.812979	0.0282359	0.0141180	−	0.999900i	$-0.495506\pi$
$829$	0.812979	0.0282359	0.0141180	+	0.999900i	$0.495506\pi$
$830$	−7.56922	−0.262731
$831$	−70.8792	−2.45877
$832$	−3.83536	−0.132967
$833$	−2.83845	−0.0983463
$834$	27.0502	0.936672
$835$	23.7950	0.823459
$836$	37.0779	1.28237
$837$	−9.08961	−0.314183
$838$	23.9400	0.826995
$839$	47.2573	1.63150	0.815752	−	0.578402i	$-0.196323\pi$
$839$	47.2573	1.63150	0.815752	+	0.578402i	$0.196323\pi$
$840$	−8.34760	−0.288020
$841$	3.41828	0.117872
$842$	20.7564	0.715313
$843$	−8.34151	−0.287297
$844$	13.2518	0.456145
$845$	3.27218	0.112566
$846$	−12.0045	−0.412723
$847$	−32.8106	−1.12738
$848$	12.7452	0.437672
$849$	−24.7385	−0.849024
$850$	0.829961	0.0284674
$851$	−17.4559	−0.598382
$852$	2.90245	0.0994363
$853$	9.64984	0.330404	0.165202	−	0.986260i	$-0.447172\pi$
$853$	9.64984	0.330404	0.165202	+	0.986260i	$0.447172\pi$
$854$	−4.27646	−0.146338
$855$	60.7888	2.07893
$856$	2.57946	0.0881642
$857$	33.3547	1.13937	0.569687	−	0.821862i	$-0.307064\pi$
$857$	33.3547	1.13937	0.569687	+	0.821862i	$0.307064\pi$
$858$	−60.8696	−2.07805
$859$	−2.15364	−0.0734811	−0.0367406	−	0.999325i	$-0.511698\pi$
$859$	−2.15364	−0.0734811	−0.0367406	+	0.999325i	$0.511698\pi$
$860$	3.41279	0.116375
$861$	−9.99007	−0.340461
$862$	0.515613	0.0175618
$863$	−44.5190	−1.51544	−0.757722	−	0.652578i	$-0.773688\pi$
$863$	−44.5190	−1.51544	−0.757722	+	0.652578i	$0.773688\pi$
$864$	5.19074	0.176593
$865$	0.653972	0.0222357
$866$	2.86435	0.0973345
$867$	46.5597	1.58125
$868$	−2.72602	−0.0925272
$869$	−88.0231	−2.98598
$870$	30.5312	1.03510
$871$	15.1294	0.512641
$872$	1.74070	0.0589477
$873$	−48.8280	−1.65258
$874$	17.1703	0.580793
$875$	18.8811	0.638297
$876$	21.3809	0.722395
$877$	−30.9670	−1.04568	−0.522840	−	0.852431i	$-0.675128\pi$
$877$	−30.9670	−1.04568	−0.522840	+	0.852431i	$0.675128\pi$
$878$	−30.6773	−1.03531
$879$	−28.8025	−0.971484
$880$	10.8378	0.365343
$881$	56.4583	1.90213	0.951064	−	0.308995i	$-0.0999928\pi$
$881$	56.4583	1.90213	0.951064	+	0.308995i	$0.0999928\pi$
$882$	22.2073	0.747759
$883$	−19.2325	−0.647226	−0.323613	−	0.946190i	$-0.604898\pi$
$883$	−19.2325	−0.647226	−0.323613	+	0.946190i	$0.604898\pi$
$884$	−2.37873	−0.0800053
$885$	−59.1108	−1.98699
$886$	−9.42756	−0.316725
$887$	24.4628	0.821379	0.410690	−	0.911775i	$-0.365288\pi$
$887$	24.4628	0.821379	0.410690	+	0.911775i	$0.365288\pi$
$888$	18.6504	0.625866
$889$	−11.6265	−0.389940
$890$	12.7494	0.427360
$891$	−0.0655821	−0.00219708
$892$	16.5831	0.555243
$893$	16.1961	0.541982
$894$	−45.5261	−1.52262
$895$	−27.9745	−0.935083
$896$	1.55673	0.0520067
$897$	−28.1879	−0.941165
$898$	19.4660	0.649588
$899$	9.97036	0.332530
$900$	−6.49342	−0.216447
$901$	7.90471	0.263344
$902$	12.9703	0.431862
$903$	7.77994	0.258900
$904$	−14.9518	−0.497288
$905$	18.4232	0.612408
$906$	−26.7119	−0.887443
$907$	3.63744	0.120779	0.0603896	−	0.998175i	$-0.480766\pi$
$907$	3.63744	0.120779	0.0603896	+	0.998175i	$0.480766\pi$
$908$	−9.87639	−0.327759
$909$	26.4396	0.876945
$910$	−11.4253	−0.378745
$911$	−45.0778	−1.49349	−0.746747	−	0.665109i	$-0.768385\pi$
$911$	−45.0778	−1.49349	−0.746747	+	0.665109i	$0.768385\pi$
$912$	−18.3452	−0.607469
$913$	22.4025	0.741416
$914$	−3.06459	−0.101368
$915$	14.7306	0.486977
$916$	−24.9163	−0.823258
$917$	−31.6238	−1.04431
$918$	3.21935	0.106254
$919$	34.0668	1.12376	0.561880	−	0.827219i	$-0.310078\pi$
$919$	34.0668	1.12376	0.561880	+	0.827219i	$0.310078\pi$
$920$	5.01884	0.165466
$921$	−44.4088	−1.46332
$922$	0.0686854	0.00226203
$923$	3.97256	0.130758
$924$	24.7063	0.812778
$925$	−8.90649	−0.292844
$926$	−25.5176	−0.838561
$927$	35.8553	1.17764
$928$	−5.69371	−0.186905
$929$	17.4804	0.573514	0.286757	−	0.958003i	$-0.407423\pi$
$929$	17.4804	0.573514	0.286757	+	0.958003i	$0.407423\pi$
$930$	9.38996	0.307909
$931$	−29.9615	−0.981947
$932$	−1.94097	−0.0635784
$933$	−56.1513	−1.83831
$934$	6.78406	0.221981
$935$	6.72172	0.219824
$936$	18.6106	0.608306
$937$	8.90594	0.290944	0.145472	−	0.989362i	$-0.453530\pi$
$937$	8.90594	0.290944	0.145472	+	0.989362i	$0.453530\pi$
$938$	−6.14087	−0.200507
$939$	−93.8655	−3.06318
$940$	4.73410	0.154409
$941$	−26.8945	−0.876737	−0.438368	−	0.898795i	$-0.644443\pi$
$941$	−26.8945	−0.876737	−0.438368	+	0.898795i	$0.644443\pi$
$942$	−8.92236	−0.290706
$943$	6.00634	0.195593
$944$	11.0235	0.358784
$945$	15.4629	0.503008
$946$	−10.1008	−0.328405
$947$	16.4922	0.535925	0.267962	−	0.963429i	$-0.413650\pi$
$947$	16.4922	0.535925	0.267962	+	0.963429i	$0.413650\pi$
$948$	43.5515	1.41449
$949$	29.2639	0.949946
$950$	8.76073	0.284236
$951$	−9.16464	−0.297184
$952$	0.965500	0.0312920
$953$	22.9118	0.742187	0.371093	−	0.928596i	$-0.378983\pi$
$953$	22.9118	0.742187	0.371093	+	0.928596i	$0.378983\pi$
$954$	−61.8446	−2.00229
$955$	18.3297	0.593135
$956$	9.51977	0.307891
$957$	−90.3628	−2.92101
$958$	25.6540	0.828845
$959$	36.3067	1.17240
$960$	−5.36226	−0.173066
$961$	−27.9336	−0.901083
$962$	25.5266	0.823012
$963$	−12.5165	−0.403339
$964$	6.58295	0.212022
$965$	−30.3657	−0.977507
$966$	11.4412	0.368113
$967$	−17.4770	−0.562024	−0.281012	−	0.959704i	$-0.590670\pi$
$967$	−17.4770	−0.562024	−0.281012	+	0.959704i	$0.590670\pi$
$968$	−21.0766	−0.677427
$969$	−11.3779	−0.365510
$970$	19.2558	0.618267
$971$	1.07137	0.0343819	0.0171909	−	0.999852i	$-0.494528\pi$
$971$	1.07137	0.0343819	0.0171909	+	0.999852i	$0.494528\pi$
$972$	15.6047	0.500520
$973$	−15.0274	−0.481756
$974$	−6.68135	−0.214084
$975$	−14.3822	−0.460599
$976$	−2.74708	−0.0879319
$977$	25.0866	0.802591	0.401295	−	0.915949i	$-0.368560\pi$
$977$	25.0866	0.802591	0.401295	+	0.915949i	$0.368560\pi$
$978$	−20.6577	−0.660562
$979$	−37.7342	−1.20599
$980$	−8.75769	−0.279754
$981$	−8.44655	−0.269678
$982$	36.5102	1.16509
$983$	−33.8243	−1.07883	−0.539414	−	0.842041i	$-0.681354\pi$
$983$	−33.8243	−1.07883	−0.539414	+	0.842041i	$0.681354\pi$
$984$	−6.41734	−0.204577
$985$	−28.4564	−0.906698
$986$	−3.53129	−0.112459
$987$	10.7920	0.343515
$988$	−25.1089	−0.798820
$989$	−4.67754	−0.148737
$990$	−52.5891	−1.67139
$991$	−2.31109	−0.0734143	−0.0367072	−	0.999326i	$-0.511687\pi$
$991$	−2.31109	−0.0734143	−0.0367072	+	0.999326i	$0.511687\pi$
$992$	−1.75112	−0.0555981
$993$	−24.1860	−0.767520
$994$	−1.61242	−0.0511428
$995$	−6.11664	−0.193911
$996$	−11.0842	−0.351216
$997$	40.8474	1.29365	0.646825	−	0.762639i	$-0.276097\pi$
$997$	40.8474	1.29365	0.646825	+	0.762639i	$0.276097\pi$
$998$	−14.4973	−0.458904
$999$	−34.5475	−1.09304

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4034.2.a.c.1.4	✓	49

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4034.2.a.c.1.4	✓	49	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:	\( N \)	\(=\)	\( 4034 = 2 \cdot 2017 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.80221 q^{3} +1.00000 q^{4} +1.91358 q^{5} +2.80221 q^{6} -1.55673 q^{7} -1.00000 q^{8} +4.85238 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.80221 q^{3} +1.00000 q^{4} +1.91358 q^{5} +2.80221 q^{6} -1.55673 q^{7} -1.00000 q^{8} +4.85238 q^{9} -1.91358 q^{10} +5.66362 q^{11} -2.80221 q^{12} -3.83536 q^{13} +1.55673 q^{14} -5.36226 q^{15} +1.00000 q^{16} +0.620210 q^{17} -4.85238 q^{18} +6.54668 q^{19} +1.91358 q^{20} +4.36229 q^{21} -5.66362 q^{22} -2.62274 q^{23} +2.80221 q^{24} -1.33819 q^{25} +3.83536 q^{26} -5.19074 q^{27} -1.55673 q^{28} +5.69371 q^{29} +5.36226 q^{30} +1.75112 q^{31} -1.00000 q^{32} -15.8706 q^{33} -0.620210 q^{34} -2.97894 q^{35} +4.85238 q^{36} +6.65561 q^{37} -6.54668 q^{38} +10.7475 q^{39} -1.91358 q^{40} -2.29010 q^{41} -4.36229 q^{42} +1.78345 q^{43} +5.66362 q^{44} +9.28543 q^{45} +2.62274 q^{46} +2.47394 q^{47} -2.80221 q^{48} -4.57659 q^{49} +1.33819 q^{50} -1.73796 q^{51} -3.83536 q^{52} +12.7452 q^{53} +5.19074 q^{54} +10.8378 q^{55} +1.55673 q^{56} -18.3452 q^{57} -5.69371 q^{58} +11.0235 q^{59} -5.36226 q^{60} -2.74708 q^{61} -1.75112 q^{62} -7.55384 q^{63} +1.00000 q^{64} -7.33928 q^{65} +15.8706 q^{66} -3.94472 q^{67} +0.620210 q^{68} +7.34947 q^{69} +2.97894 q^{70} -1.03577 q^{71} -4.85238 q^{72} -7.63003 q^{73} -6.65561 q^{74} +3.74990 q^{75} +6.54668 q^{76} -8.81673 q^{77} -10.7475 q^{78} -15.5419 q^{79} +1.91358 q^{80} -0.0115795 q^{81} +2.29010 q^{82} +3.95552 q^{83} +4.36229 q^{84} +1.18682 q^{85} -1.78345 q^{86} -15.9550 q^{87} -5.66362 q^{88} -6.66256 q^{89} -9.28543 q^{90} +5.97062 q^{91} -2.62274 q^{92} -4.90700 q^{93} -2.47394 q^{94} +12.5276 q^{95} +2.80221 q^{96} -10.0627 q^{97} +4.57659 q^{98} +27.4820 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 49 q - 49 q^{2} + 8 q^{3} + 49 q^{4} - 8 q^{5} - 8 q^{6} + 18 q^{7} - 49 q^{8} + 59 q^{9}+O(q^{10}) \) 49 * q - 49 * q^2 + 8 * q^3 + 49 * q^4 - 8 * q^5 - 8 * q^6 + 18 * q^7 - 49 * q^8 + 59 * q^9	\( 49 q - 49 q^{2} + 8 q^{3} + 49 q^{4} - 8 q^{5} - 8 q^{6} + 18 q^{7} - 49 q^{8} + 59 q^{9} + 8 q^{10} + q^{11} + 8 q^{12} + 9 q^{13} - 18 q^{14} + 15 q^{15} + 49 q^{16} - 27 q^{17} - 59 q^{18} + 27 q^{19} - 8 q^{20} + 13 q^{21} - q^{22} + 16 q^{23} - 8 q^{24} + 71 q^{25} - 9 q^{26} + 29 q^{27} + 18 q^{28} - 7 q^{29} - 15 q^{30} + 75 q^{31} - 49 q^{32} - 3 q^{33} + 27 q^{34} - 16 q^{35} + 59 q^{36} + 36 q^{37} - 27 q^{38} + 24 q^{39} + 8 q^{40} - 12 q^{41} - 13 q^{42} + 22 q^{43} + q^{44} + 5 q^{45} - 16 q^{46} + 26 q^{47} + 8 q^{48} + 107 q^{49} - 71 q^{50} + 35 q^{51} + 9 q^{52} - 10 q^{53} - 29 q^{54} + 76 q^{55} - 18 q^{56} - 10 q^{57} + 7 q^{58} + 9 q^{59} + 15 q^{60} + 87 q^{61} - 75 q^{62} + 68 q^{63} + 49 q^{64} - 6 q^{65} + 3 q^{66} + 46 q^{67} - 27 q^{68} + 70 q^{69} + 16 q^{70} + 40 q^{71} - 59 q^{72} + 6 q^{73} - 36 q^{74} + 69 q^{75} + 27 q^{76} - 12 q^{77} - 24 q^{78} + 76 q^{79} - 8 q^{80} + 77 q^{81} + 12 q^{82} - 32 q^{83} + 13 q^{84} + 19 q^{85} - 22 q^{86} + 36 q^{87} - q^{88} + 34 q^{89} - 5 q^{90} + 119 q^{91} + 16 q^{92} - 5 q^{93} - 26 q^{94} - 2 q^{95} - 8 q^{96} + 52 q^{97} - 107 q^{98} + 26 q^{99}+O(q^{100}) \) 49 * q - 49 * q^2 + 8 * q^3 + 49 * q^4 - 8 * q^5 - 8 * q^6 + 18 * q^7 - 49 * q^8 + 59 * q^9 + 8 * q^10 + q^11 + 8 * q^12 + 9 * q^13 - 18 * q^14 + 15 * q^15 + 49 * q^16 - 27 * q^17 - 59 * q^18 + 27 * q^19 - 8 * q^20 + 13 * q^21 - q^22 + 16 * q^23 - 8 * q^24 + 71 * q^25 - 9 * q^26 + 29 * q^27 + 18 * q^28 - 7 * q^29 - 15 * q^30 + 75 * q^31 - 49 * q^32 - 3 * q^33 + 27 * q^34 - 16 * q^35 + 59 * q^36 + 36 * q^37 - 27 * q^38 + 24 * q^39 + 8 * q^40 - 12 * q^41 - 13 * q^42 + 22 * q^43 + q^44 + 5 * q^45 - 16 * q^46 + 26 * q^47 + 8 * q^48 + 107 * q^49 - 71 * q^50 + 35 * q^51 + 9 * q^52 - 10 * q^53 - 29 * q^54 + 76 * q^55 - 18 * q^56 - 10 * q^57 + 7 * q^58 + 9 * q^59 + 15 * q^60 + 87 * q^61 - 75 * q^62 + 68 * q^63 + 49 * q^64 - 6 * q^65 + 3 * q^66 + 46 * q^67 - 27 * q^68 + 70 * q^69 + 16 * q^70 + 40 * q^71 - 59 * q^72 + 6 * q^73 - 36 * q^74 + 69 * q^75 + 27 * q^76 - 12 * q^77 - 24 * q^78 + 76 * q^79 - 8 * q^80 + 77 * q^81 + 12 * q^82 - 32 * q^83 + 13 * q^84 + 19 * q^85 - 22 * q^86 + 36 * q^87 - q^88 + 34 * q^89 - 5 * q^90 + 119 * q^91 + 16 * q^92 - 5 * q^93 - 26 * q^94 - 2 * q^95 - 8 * q^96 + 52 * q^97 - 107 * q^98 + 26 * q^99

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