LMFDB - Embedded newform 4034.2.a.d.1.3

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:	$52$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
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)

$f(q)$	$=$	$q+1.00000 q^{2} -3.09514 q^{3} +1.00000 q^{4} +3.37243 q^{5} -3.09514 q^{6} +1.17193 q^{7} +1.00000 q^{8} +6.57990 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -3.09514 q^{3} +1.00000 q^{4} +3.37243 q^{5} -3.09514 q^{6} +1.17193 q^{7} +1.00000 q^{8} +6.57990 q^{9} +3.37243 q^{10} -1.16179 q^{11} -3.09514 q^{12} +7.15502 q^{13} +1.17193 q^{14} -10.4381 q^{15} +1.00000 q^{16} +5.64765 q^{17} +6.57990 q^{18} +0.667721 q^{19} +3.37243 q^{20} -3.62727 q^{21} -1.16179 q^{22} +2.74436 q^{23} -3.09514 q^{24} +6.37325 q^{25} +7.15502 q^{26} -11.0803 q^{27} +1.17193 q^{28} -1.38111 q^{29} -10.4381 q^{30} -0.606427 q^{31} +1.00000 q^{32} +3.59590 q^{33} +5.64765 q^{34} +3.95223 q^{35} +6.57990 q^{36} +10.1198 q^{37} +0.667721 q^{38} -22.1458 q^{39} +3.37243 q^{40} -2.86718 q^{41} -3.62727 q^{42} +2.19997 q^{43} -1.16179 q^{44} +22.1902 q^{45} +2.74436 q^{46} -3.44861 q^{47} -3.09514 q^{48} -5.62659 q^{49} +6.37325 q^{50} -17.4803 q^{51} +7.15502 q^{52} -10.4093 q^{53} -11.0803 q^{54} -3.91805 q^{55} +1.17193 q^{56} -2.06669 q^{57} -1.38111 q^{58} +8.31170 q^{59} -10.4381 q^{60} -8.17995 q^{61} -0.606427 q^{62} +7.71115 q^{63} +1.00000 q^{64} +24.1298 q^{65} +3.59590 q^{66} -1.41052 q^{67} +5.64765 q^{68} -8.49417 q^{69} +3.95223 q^{70} +2.93219 q^{71} +6.57990 q^{72} +0.186200 q^{73} +10.1198 q^{74} -19.7261 q^{75} +0.667721 q^{76} -1.36153 q^{77} -22.1458 q^{78} -7.87285 q^{79} +3.37243 q^{80} +14.5553 q^{81} -2.86718 q^{82} -12.1226 q^{83} -3.62727 q^{84} +19.0463 q^{85} +2.19997 q^{86} +4.27472 q^{87} -1.16179 q^{88} -10.9044 q^{89} +22.1902 q^{90} +8.38515 q^{91} +2.74436 q^{92} +1.87698 q^{93} -3.44861 q^{94} +2.25184 q^{95} -3.09514 q^{96} +12.0786 q^{97} -5.62659 q^{98} -7.64445 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q + 52 q^{2} + 16 q^{3} + 52 q^{4} + 24 q^{5} + 16 q^{6} + 12 q^{7} + 52 q^{8} + 70 q^{9}+O(q^{10}) $ 52 * q + 52 * q^2 + 16 * q^3 + 52 * q^4 + 24 * q^5 + 16 * q^6 + 12 * q^7 + 52 * q^8 + 70 * q^9	\( 52 q + 52 q^{2} + 16 q^{3} + 52 q^{4} + 24 q^{5} + 16 q^{6} + 12 q^{7} + 52 q^{8} + 70 q^{9} + 24 q^{10} + 19 q^{11} + 16 q^{12} + 27 q^{13} + 12 q^{14} + 5 q^{15} + 52 q^{16} + 43 q^{17} + 70 q^{18} + 35 q^{19} + 24 q^{20} + 29 q^{21} + 19 q^{22} + 2 q^{23} + 16 q^{24} + 88 q^{25} + 27 q^{26} + 49 q^{27} + 12 q^{28} + 31 q^{29} + 5 q^{30} + 59 q^{31} + 52 q^{32} + 45 q^{33} + 43 q^{34} + 18 q^{35} + 70 q^{36} + 60 q^{37} + 35 q^{38} + 6 q^{39} + 24 q^{40} + 56 q^{41} + 29 q^{42} + 34 q^{43} + 19 q^{44} + 61 q^{45} + 2 q^{46} - 4 q^{47} + 16 q^{48} + 102 q^{49} + 88 q^{50} + 23 q^{51} + 27 q^{52} + 30 q^{53} + 49 q^{54} + 24 q^{55} + 12 q^{56} + 32 q^{57} + 31 q^{58} + 27 q^{59} + 5 q^{60} + 107 q^{61} + 59 q^{62} - 4 q^{63} + 52 q^{64} + 46 q^{65} + 45 q^{66} + 22 q^{67} + 43 q^{68} + 36 q^{69} + 18 q^{70} + 8 q^{71} + 70 q^{72} + 66 q^{73} + 60 q^{74} + 53 q^{75} + 35 q^{76} + 26 q^{77} + 6 q^{78} + 50 q^{79} + 24 q^{80} + 108 q^{81} + 56 q^{82} + 52 q^{83} + 29 q^{84} + 19 q^{85} + 34 q^{86} - 32 q^{87} + 19 q^{88} + 62 q^{89} + 61 q^{90} + 69 q^{91} + 2 q^{92} + 21 q^{93} - 4 q^{94} - 44 q^{95} + 16 q^{96} + 82 q^{97} + 102 q^{98} + 16 q^{99}+O(q^{100}) \) 52 * q + 52 * q^2 + 16 * q^3 + 52 * q^4 + 24 * q^5 + 16 * q^6 + 12 * q^7 + 52 * q^8 + 70 * q^9 + 24 * q^10 + 19 * q^11 + 16 * q^12 + 27 * q^13 + 12 * q^14 + 5 * q^15 + 52 * q^16 + 43 * q^17 + 70 * q^18 + 35 * q^19 + 24 * q^20 + 29 * q^21 + 19 * q^22 + 2 * q^23 + 16 * q^24 + 88 * q^25 + 27 * q^26 + 49 * q^27 + 12 * q^28 + 31 * q^29 + 5 * q^30 + 59 * q^31 + 52 * q^32 + 45 * q^33 + 43 * q^34 + 18 * q^35 + 70 * q^36 + 60 * q^37 + 35 * q^38 + 6 * q^39 + 24 * q^40 + 56 * q^41 + 29 * q^42 + 34 * q^43 + 19 * q^44 + 61 * q^45 + 2 * q^46 - 4 * q^47 + 16 * q^48 + 102 * q^49 + 88 * q^50 + 23 * q^51 + 27 * q^52 + 30 * q^53 + 49 * q^54 + 24 * q^55 + 12 * q^56 + 32 * q^57 + 31 * q^58 + 27 * q^59 + 5 * q^60 + 107 * q^61 + 59 * q^62 - 4 * q^63 + 52 * q^64 + 46 * q^65 + 45 * q^66 + 22 * q^67 + 43 * q^68 + 36 * q^69 + 18 * q^70 + 8 * q^71 + 70 * q^72 + 66 * q^73 + 60 * q^74 + 53 * q^75 + 35 * q^76 + 26 * q^77 + 6 * q^78 + 50 * q^79 + 24 * q^80 + 108 * q^81 + 56 * q^82 + 52 * q^83 + 29 * q^84 + 19 * q^85 + 34 * q^86 - 32 * q^87 + 19 * q^88 + 62 * q^89 + 61 * q^90 + 69 * q^91 + 2 * q^92 + 21 * q^93 - 4 * q^94 - 44 * q^95 + 16 * q^96 + 82 * q^97 + 102 * q^98 + 16 * 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
$3$	−3.09514	−1.78698	−0.893490	−	0.449083i	$-0.851751\pi$
$3$	−3.09514	−1.78698	−0.893490	+	0.449083i	$0.851751\pi$
$4$	1.00000	0.500000
$5$	3.37243	1.50819	0.754097	−	0.656763i	$-0.228075\pi$
$5$	3.37243	1.50819	0.754097	+	0.656763i	$0.228075\pi$
$6$	−3.09514	−1.26359
$7$	1.17193	0.442946	0.221473	−	0.975166i	$-0.428913\pi$
$7$	1.17193	0.442946	0.221473	+	0.975166i	$0.428913\pi$
$8$	1.00000	0.353553
$9$	6.57990	2.19330
$10$	3.37243	1.06645
$11$	−1.16179	−0.350292	−0.175146	−	0.984542i	$-0.556040\pi$
$11$	−1.16179	−0.350292	−0.175146	+	0.984542i	$0.556040\pi$
$12$	−3.09514	−0.893490
$13$	7.15502	1.98445	0.992223	−	0.124474i	$-0.0397243\pi$
$13$	7.15502	1.98445	0.992223	+	0.124474i	$0.0397243\pi$
$14$	1.17193	0.313210
$15$	−10.4381	−2.69511
$16$	1.00000	0.250000
$17$	5.64765	1.36976	0.684878	−	0.728657i	$-0.259855\pi$
$17$	5.64765	1.36976	0.684878	+	0.728657i	$0.259855\pi$
$18$	6.57990	1.55090
$19$	0.667721	0.153186	0.0765929	−	0.997062i	$-0.475596\pi$
$19$	0.667721	0.153186	0.0765929	+	0.997062i	$0.475596\pi$
$20$	3.37243	0.754097
$21$	−3.62727	−0.791536
$22$	−1.16179	−0.247694
$23$	2.74436	0.572238	0.286119	−	0.958194i	$-0.407635\pi$
$23$	2.74436	0.572238	0.286119	+	0.958194i	$0.407635\pi$
$24$	−3.09514	−0.631793
$25$	6.37325	1.27465
$26$	7.15502	1.40322
$27$	−11.0803	−2.13240
$28$	1.17193	0.221473
$29$	−1.38111	−0.256465	−0.128233	−	0.991744i	$-0.540930\pi$
$29$	−1.38111	−0.256465	−0.128233	+	0.991744i	$0.540930\pi$
$30$	−10.4381	−1.90573
$31$	−0.606427	−0.108917	−0.0544587	−	0.998516i	$-0.517343\pi$
$31$	−0.606427	−0.108917	−0.0544587	+	0.998516i	$0.517343\pi$
$32$	1.00000	0.176777
$33$	3.59590	0.625966
$34$	5.64765	0.968564
$35$	3.95223	0.668049
$36$	6.57990	1.09665
$37$	10.1198	1.66369	0.831843	−	0.555011i	$-0.187286\pi$
$37$	10.1198	1.66369	0.831843	+	0.555011i	$0.187286\pi$
$38$	0.667721	0.108319
$39$	−22.1458	−3.54617
$40$	3.37243	0.533227
$41$	−2.86718	−0.447778	−0.223889	−	0.974615i	$-0.571875\pi$
$41$	−2.86718	−0.447778	−0.223889	+	0.974615i	$0.571875\pi$
$42$	−3.62727	−0.559701
$43$	2.19997	0.335493	0.167746	−	0.985830i	$-0.446351\pi$
$43$	2.19997	0.335493	0.167746	+	0.985830i	$0.446351\pi$
$44$	−1.16179	−0.175146
$45$	22.1902	3.30792
$46$	2.74436	0.404633
$47$	−3.44861	−0.503032	−0.251516	−	0.967853i	$-0.580929\pi$
$47$	−3.44861	−0.503032	−0.251516	+	0.967853i	$0.580929\pi$
$48$	−3.09514	−0.446745
$49$	−5.62659	−0.803799
$50$	6.37325	0.901314
$51$	−17.4803	−2.44773
$52$	7.15502	0.992223
$53$	−10.4093	−1.42983	−0.714916	−	0.699210i	$-0.753535\pi$
$53$	−10.4093	−1.42983	−0.714916	+	0.699210i	$0.753535\pi$
$54$	−11.0803	−1.50784
$55$	−3.91805	−0.528309
$56$	1.17193	0.156605
$57$	−2.06669	−0.273740
$58$	−1.38111	−0.181348
$59$	8.31170	1.08209	0.541046	−	0.840993i	$-0.318029\pi$
$59$	8.31170	1.08209	0.541046	+	0.840993i	$0.318029\pi$
$60$	−10.4381	−1.34756
$61$	−8.17995	−1.04733	−0.523667	−	0.851923i	$-0.675437\pi$
$61$	−8.17995	−1.04733	−0.523667	+	0.851923i	$0.675437\pi$
$62$	−0.606427	−0.0770163
$63$	7.71115	0.971513
$64$	1.00000	0.125000
$65$	24.1298	2.99293
$66$	3.59590	0.442625
$67$	−1.41052	−0.172322	−0.0861611	−	0.996281i	$-0.527460\pi$
$67$	−1.41052	−0.172322	−0.0861611	+	0.996281i	$0.527460\pi$
$68$	5.64765	0.684878
$69$	−8.49417	−1.02258
$70$	3.95223	0.472382
$71$	2.93219	0.347987	0.173994	−	0.984747i	$-0.444333\pi$
$71$	2.93219	0.347987	0.173994	+	0.984747i	$0.444333\pi$
$72$	6.57990	0.775448
$73$	0.186200	0.0217931	0.0108965	−	0.999941i	$-0.496531\pi$
$73$	0.186200	0.0217931	0.0108965	+	0.999941i	$0.496531\pi$
$74$	10.1198	1.17640
$75$	−19.7261	−2.27778
$76$	0.667721	0.0765929
$77$	−1.36153	−0.155161
$78$	−22.1458	−2.50752
$79$	−7.87285	−0.885765	−0.442883	−	0.896580i	$-0.646044\pi$
$79$	−7.87285	−0.885765	−0.442883	+	0.896580i	$0.646044\pi$
$80$	3.37243	0.377049
$81$	14.5553	1.61726
$82$	−2.86718	−0.316627
$83$	−12.1226	−1.33063	−0.665314	−	0.746563i	$-0.731702\pi$
$83$	−12.1226	−1.33063	−0.665314	+	0.746563i	$0.731702\pi$
$84$	−3.62727	−0.395768
$85$	19.0463	2.06586
$86$	2.19997	0.237229
$87$	4.27472	0.458298
$88$	−1.16179	−0.123847
$89$	−10.9044	−1.15587	−0.577934	−	0.816084i	$-0.696141\pi$
$89$	−10.9044	−1.15587	−0.577934	+	0.816084i	$0.696141\pi$
$90$	22.1902	2.33905
$91$	8.38515	0.879003
$92$	2.74436	0.286119
$93$	1.87698	0.194633
$94$	−3.44861	−0.355697
$95$	2.25184	0.231034
$96$	−3.09514	−0.315896
$97$	12.0786	1.22640	0.613200	−	0.789928i	$-0.289882\pi$
$97$	12.0786	1.22640	0.613200	+	0.789928i	$0.289882\pi$
$98$	−5.62659	−0.568371
$99$	−7.64445	−0.768296
$100$	6.37325	0.637325
$101$	−2.77146	−0.275771	−0.137885	−	0.990448i	$-0.544031\pi$
$101$	−2.77146	−0.275771	−0.137885	+	0.990448i	$0.544031\pi$
$102$	−17.4803	−1.73081
$103$	−12.0754	−1.18983	−0.594913	−	0.803790i	$-0.702814\pi$
$103$	−12.0754	−1.18983	−0.594913	+	0.803790i	$0.702814\pi$
$104$	7.15502	0.701608
$105$	−12.2327	−1.19379
$106$	−10.4093	−1.01104
$107$	−1.25914	−0.121726	−0.0608628	−	0.998146i	$-0.519385\pi$
$107$	−1.25914	−0.121726	−0.0608628	+	0.998146i	$0.519385\pi$
$108$	−11.0803	−1.06620
$109$	−7.66963	−0.734617	−0.367309	−	0.930099i	$-0.619721\pi$
$109$	−7.66963	−0.734617	−0.367309	+	0.930099i	$0.619721\pi$
$110$	−3.91805	−0.373571
$111$	−31.3222	−2.97297
$112$	1.17193	0.110737
$113$	6.88774	0.647944	0.323972	−	0.946067i	$-0.394982\pi$
$113$	6.88774	0.647944	0.323972	+	0.946067i	$0.394982\pi$
$114$	−2.06669	−0.193563
$115$	9.25514	0.863046
$116$	−1.38111	−0.128233
$117$	47.0793	4.35248
$118$	8.31170	0.765154
$119$	6.61863	0.606729
$120$	−10.4381	−0.952867
$121$	−9.65025	−0.877295
$122$	−8.17995	−0.740577
$123$	8.87433	0.800171
$124$	−0.606427	−0.0544587
$125$	4.63119	0.414227
$126$	7.71115	0.686964
$127$	19.8666	1.76288	0.881438	−	0.472300i	$-0.156576\pi$
$127$	19.8666	1.76288	0.881438	+	0.472300i	$0.156576\pi$
$128$	1.00000	0.0883883
$129$	−6.80923	−0.599519
$130$	24.1298	2.11632
$131$	−10.9687	−0.958344	−0.479172	−	0.877721i	$-0.659063\pi$
$131$	−10.9687	−0.958344	−0.479172	+	0.877721i	$0.659063\pi$
$132$	3.59590	0.312983
$133$	0.782520	0.0678531
$134$	−1.41052	−0.121850
$135$	−37.3674	−3.21608
$136$	5.64765	0.484282
$137$	−1.02417	−0.0875009	−0.0437504	−	0.999042i	$-0.513931\pi$
$137$	−1.02417	−0.0875009	−0.0437504	+	0.999042i	$0.513931\pi$
$138$	−8.49417	−0.723072
$139$	6.63619	0.562875	0.281437	−	0.959580i	$-0.409189\pi$
$139$	6.63619	0.562875	0.281437	+	0.959580i	$0.409189\pi$
$140$	3.95223	0.334025
$141$	10.6739	0.898909
$142$	2.93219	0.246064
$143$	−8.31262	−0.695136
$144$	6.57990	0.548325
$145$	−4.65768	−0.386800
$146$	0.186200	0.0154100
$147$	17.4151	1.43637
$148$	10.1198	0.831843
$149$	−18.2122	−1.49200	−0.746001	−	0.665945i	$-0.768029\pi$
$149$	−18.2122	−1.49200	−0.746001	+	0.665945i	$0.768029\pi$
$150$	−19.7261	−1.61063
$151$	−4.39046	−0.357291	−0.178645	−	0.983914i	$-0.557171\pi$
$151$	−4.39046	−0.357291	−0.178645	+	0.983914i	$0.557171\pi$
$152$	0.667721	0.0541593
$153$	37.1610	3.00429
$154$	−1.36153	−0.109715
$155$	−2.04513	−0.164269
$156$	−22.1458	−1.77308
$157$	−10.6060	−0.846448	−0.423224	−	0.906025i	$-0.639102\pi$
$157$	−10.6060	−0.846448	−0.423224	+	0.906025i	$0.639102\pi$
$158$	−7.87285	−0.626331
$159$	32.2184	2.55508
$160$	3.37243	0.266614
$161$	3.21618	0.253471
$162$	14.5553	1.14358
$163$	9.28058	0.726911	0.363456	−	0.931611i	$-0.381597\pi$
$163$	9.28058	0.726911	0.363456	+	0.931611i	$0.381597\pi$
$164$	−2.86718	−0.223889
$165$	12.1269	0.944078
$166$	−12.1226	−0.940897
$167$	−25.5066	−1.97376	−0.986880	−	0.161456i	$-0.948381\pi$
$167$	−25.5066	−1.97376	−0.986880	+	0.161456i	$0.948381\pi$
$168$	−3.62727	−0.279850
$169$	38.1943	2.93802
$170$	19.0463	1.46078
$171$	4.39354	0.335982
$172$	2.19997	0.167746
$173$	9.08870	0.691001	0.345500	−	0.938419i	$-0.387709\pi$
$173$	9.08870	0.691001	0.345500	+	0.938419i	$0.387709\pi$
$174$	4.27472	0.324066
$175$	7.46898	0.564602
$176$	−1.16179	−0.0875731
$177$	−25.7259	−1.93368
$178$	−10.9044	−0.817321
$179$	12.9207	0.965737	0.482868	−	0.875693i	$-0.339595\pi$
$179$	12.9207	0.965737	0.482868	+	0.875693i	$0.339595\pi$
$180$	22.1902	1.65396
$181$	4.46300	0.331732	0.165866	−	0.986148i	$-0.446958\pi$
$181$	4.46300	0.331732	0.165866	+	0.986148i	$0.446958\pi$
$182$	8.38515	0.621549
$183$	25.3181	1.87157
$184$	2.74436	0.202317
$185$	34.1283	2.50916
$186$	1.87698	0.137627
$187$	−6.56138	−0.479815
$188$	−3.44861	−0.251516
$189$	−12.9853	−0.944539
$190$	2.25184	0.163366
$191$	7.39196	0.534863	0.267432	−	0.963577i	$-0.413825\pi$
$191$	7.39196	0.534863	0.267432	+	0.963577i	$0.413825\pi$
$192$	−3.09514	−0.223373
$193$	−1.96179	−0.141212	−0.0706062	−	0.997504i	$-0.522493\pi$
$193$	−1.96179	−0.141212	−0.0706062	+	0.997504i	$0.522493\pi$
$194$	12.0786	0.867196
$195$	−74.6850	−5.34831
$196$	−5.62659	−0.401899
$197$	−16.3156	−1.16244	−0.581219	−	0.813747i	$-0.697424\pi$
$197$	−16.3156	−1.16244	−0.581219	+	0.813747i	$0.697424\pi$
$198$	−7.64445	−0.543267
$199$	−1.67899	−0.119021	−0.0595103	−	0.998228i	$-0.518954\pi$
$199$	−1.67899	−0.119021	−0.0595103	+	0.998228i	$0.518954\pi$
$200$	6.37325	0.450657
$201$	4.36575	0.307937
$202$	−2.77146	−0.194999
$203$	−1.61856	−0.113600
$204$	−17.4803	−1.22386
$205$	−9.66935	−0.675337
$206$	−12.0754	−0.841334
$207$	18.0576	1.25509
$208$	7.15502	0.496111
$209$	−0.775751	−0.0536598
$210$	−12.2327	−0.844137
$211$	8.78900	0.605060	0.302530	−	0.953140i	$-0.402169\pi$
$211$	8.78900	0.605060	0.302530	+	0.953140i	$0.402169\pi$
$212$	−10.4093	−0.714916
$213$	−9.07555	−0.621847
$214$	−1.25914	−0.0860730
$215$	7.41925	0.505988
$216$	−11.0803	−0.753918
$217$	−0.710687	−0.0482446
$218$	−7.66963	−0.519453
$219$	−0.576315	−0.0389438
$220$	−3.91805	−0.264155
$221$	40.4091	2.71821
$222$	−31.3222	−2.10221
$223$	0.320562	0.0214664	0.0107332	−	0.999942i	$-0.496583\pi$
$223$	0.320562	0.0214664	0.0107332	+	0.999942i	$0.496583\pi$
$224$	1.17193	0.0783026
$225$	41.9353	2.79569
$226$	6.88774	0.458165
$227$	−1.84108	−0.122197	−0.0610984	−	0.998132i	$-0.519460\pi$
$227$	−1.84108	−0.122197	−0.0610984	+	0.998132i	$0.519460\pi$
$228$	−2.06669	−0.136870
$229$	13.7556	0.908994	0.454497	−	0.890748i	$-0.349819\pi$
$229$	13.7556	0.908994	0.454497	+	0.890748i	$0.349819\pi$
$230$	9.25514	0.610266
$231$	4.21413	0.277269
$232$	−1.38111	−0.0906742
$233$	16.9457	1.11015	0.555076	−	0.831800i	$-0.312689\pi$
$233$	16.9457	1.11015	0.555076	+	0.831800i	$0.312689\pi$
$234$	47.0793	3.07767
$235$	−11.6302	−0.758670
$236$	8.31170	0.541046
$237$	24.3676	1.58285
$238$	6.61863	0.429022
$239$	22.2326	1.43810	0.719052	−	0.694956i	$-0.244576\pi$
$239$	22.2326	1.43810	0.719052	+	0.694956i	$0.244576\pi$
$240$	−10.4381	−0.673778
$241$	−27.1467	−1.74867	−0.874336	−	0.485322i	$-0.838702\pi$
$241$	−27.1467	−1.74867	−0.874336	+	0.485322i	$0.838702\pi$
$242$	−9.65025	−0.620341
$243$	−11.8100	−0.757611
$244$	−8.17995	−0.523667
$245$	−18.9753	−1.21228
$246$	8.87433	0.565806
$247$	4.77756	0.303989
$248$	−0.606427	−0.0385081
$249$	37.5212	2.37781
$250$	4.63119	0.292902
$251$	17.8201	1.12480	0.562398	−	0.826866i	$-0.309879\pi$
$251$	17.8201	1.12480	0.562398	+	0.826866i	$0.309879\pi$
$252$	7.71115	0.485757
$253$	−3.18836	−0.200451
$254$	19.8666	1.24654
$255$	−58.9509	−3.69165
$256$	1.00000	0.0625000
$257$	3.92176	0.244632	0.122316	−	0.992491i	$-0.460968\pi$
$257$	3.92176	0.244632	0.122316	+	0.992491i	$0.460968\pi$
$258$	−6.80923	−0.423924
$259$	11.8597	0.736924
$260$	24.1298	1.49647
$261$	−9.08755	−0.562505
$262$	−10.9687	−0.677652
$263$	3.73202	0.230126	0.115063	−	0.993358i	$-0.463293\pi$
$263$	3.73202	0.230126	0.115063	+	0.993358i	$0.463293\pi$
$264$	3.59590	0.221312
$265$	−35.1047	−2.15647
$266$	0.782520	0.0479794
$267$	33.7507	2.06551
$268$	−1.41052	−0.0861611
$269$	21.3147	1.29958	0.649789	−	0.760115i	$-0.274857\pi$
$269$	21.3147	1.29958	0.649789	+	0.760115i	$0.274857\pi$
$270$	−37.3674	−2.27411
$271$	−9.22422	−0.560332	−0.280166	−	0.959952i	$-0.590389\pi$
$271$	−9.22422	−0.560332	−0.280166	+	0.959952i	$0.590389\pi$
$272$	5.64765	0.342439
$273$	−25.9532	−1.57076
$274$	−1.02417	−0.0618724
$275$	−7.40437	−0.446500
$276$	−8.49417	−0.511289
$277$	12.6430	0.759645	0.379823	−	0.925059i	$-0.375985\pi$
$277$	12.6430	0.759645	0.379823	+	0.925059i	$0.375985\pi$
$278$	6.63619	0.398012
$279$	−3.99023	−0.238889
$280$	3.95223	0.236191
$281$	9.42829	0.562444	0.281222	−	0.959643i	$-0.409260\pi$
$281$	9.42829	0.562444	0.281222	+	0.959643i	$0.409260\pi$
$282$	10.6739	0.635624
$283$	29.5589	1.75709	0.878547	−	0.477656i	$-0.158514\pi$
$283$	29.5589	1.75709	0.878547	+	0.477656i	$0.158514\pi$
$284$	2.93219	0.173994
$285$	−6.96976	−0.412853
$286$	−8.31262	−0.491536
$287$	−3.36012	−0.198342
$288$	6.57990	0.387724
$289$	14.8960	0.876233
$290$	−4.65768	−0.273509
$291$	−37.3851	−2.19155
$292$	0.186200	0.0108965
$293$	−15.8714	−0.927216	−0.463608	−	0.886040i	$-0.653445\pi$
$293$	−15.8714	−0.927216	−0.463608	+	0.886040i	$0.653445\pi$
$294$	17.4151	1.01567
$295$	28.0306	1.63200
$296$	10.1198	0.588202
$297$	12.8729	0.746964
$298$	−18.2122	−1.05501
$299$	19.6359	1.13558
$300$	−19.7261	−1.13889
$301$	2.57821	0.148605
$302$	−4.39046	−0.252643
$303$	8.57807	0.492797
$304$	0.667721	0.0382964
$305$	−27.5863	−1.57958
$306$	37.1610	2.12435
$307$	30.9033	1.76375	0.881873	−	0.471488i	$-0.156283\pi$
$307$	30.9033	1.76375	0.881873	+	0.471488i	$0.156283\pi$
$308$	−1.36153	−0.0775804
$309$	37.3751	2.12620
$310$	−2.04513	−0.116156
$311$	12.3858	0.702337	0.351168	−	0.936312i	$-0.385784\pi$
$311$	12.3858	0.702337	0.351168	+	0.936312i	$0.385784\pi$
$312$	−22.1458	−1.25376
$313$	1.52608	0.0862594	0.0431297	−	0.999069i	$-0.486267\pi$
$313$	1.52608	0.0862594	0.0431297	+	0.999069i	$0.486267\pi$
$314$	−10.6060	−0.598529
$315$	26.0053	1.46523
$316$	−7.87285	−0.442883
$317$	−3.61250	−0.202898	−0.101449	−	0.994841i	$-0.532348\pi$
$317$	−3.61250	−0.202898	−0.101449	+	0.994841i	$0.532348\pi$
$318$	32.2184	1.80672
$319$	1.60456	0.0898378
$320$	3.37243	0.188524
$321$	3.89722	0.217521
$322$	3.21618	0.179231
$323$	3.77106	0.209827
$324$	14.5553	0.808630
$325$	45.6008	2.52948
$326$	9.28058	0.514004
$327$	23.7386	1.31275
$328$	−2.86718	−0.158314
$329$	−4.04152	−0.222816
$330$	12.1269	0.667564
$331$	−1.39092	−0.0764521	−0.0382260	−	0.999269i	$-0.512171\pi$
$331$	−1.39092	−0.0764521	−0.0382260	+	0.999269i	$0.512171\pi$
$332$	−12.1226	−0.665314
$333$	66.5873	3.64896
$334$	−25.5066	−1.39566
$335$	−4.75687	−0.259896
$336$	−3.62727	−0.197884
$337$	−10.5385	−0.574068	−0.287034	−	0.957920i	$-0.592669\pi$
$337$	−10.5385	−0.574068	−0.287034	+	0.957920i	$0.592669\pi$
$338$	38.1943	2.07750
$339$	−21.3185	−1.15786
$340$	19.0463	1.03293
$341$	0.704540	0.0381530
$342$	4.39354	0.237575
$343$	−14.7974	−0.798986
$344$	2.19997	0.118615
$345$	−28.6460	−1.54225
$346$	9.08870	0.488611
$347$	−24.8164	−1.33221	−0.666107	−	0.745856i	$-0.732040\pi$
$347$	−24.8164	−1.33221	−0.666107	+	0.745856i	$0.732040\pi$
$348$	4.27472	0.229149
$349$	2.03598	0.108983	0.0544917	−	0.998514i	$-0.482646\pi$
$349$	2.03598	0.108983	0.0544917	+	0.998514i	$0.482646\pi$
$350$	7.46898	0.399234
$351$	−79.2797	−4.23163
$352$	−1.16179	−0.0619235
$353$	3.04380	0.162005	0.0810027	−	0.996714i	$-0.474188\pi$
$353$	3.04380	0.162005	0.0810027	+	0.996714i	$0.474188\pi$
$354$	−25.7259	−1.36732
$355$	9.88861	0.524833
$356$	−10.9044	−0.577934
$357$	−20.4856	−1.08421
$358$	12.9207	0.682879
$359$	−28.6668	−1.51297	−0.756487	−	0.654008i	$-0.773086\pi$
$359$	−28.6668	−1.51297	−0.756487	+	0.654008i	$0.773086\pi$
$360$	22.1902	1.16953
$361$	−18.5541	−0.976534
$362$	4.46300	0.234570
$363$	29.8689	1.56771
$364$	8.38515	0.439501
$365$	0.627946	0.0328682
$366$	25.3181	1.32340
$367$	−24.9528	−1.30253	−0.651263	−	0.758852i	$-0.725760\pi$
$367$	−24.9528	−1.30253	−0.651263	+	0.758852i	$0.725760\pi$
$368$	2.74436	0.143060
$369$	−18.8658	−0.982112
$370$	34.1283	1.77425
$371$	−12.1990	−0.633339
$372$	1.87698	0.0973167
$373$	−37.7095	−1.95252	−0.976262	−	0.216594i	$-0.930505\pi$
$373$	−37.7095	−1.95252	−0.976262	+	0.216594i	$0.930505\pi$
$374$	−6.56138	−0.339281
$375$	−14.3342	−0.740215
$376$	−3.44861	−0.177849
$377$	−9.88185	−0.508941
$378$	−12.9853	−0.667890
$379$	16.6962	0.857624	0.428812	−	0.903394i	$-0.358932\pi$
$379$	16.6962	0.857624	0.428812	+	0.903394i	$0.358932\pi$
$380$	2.25184	0.115517
$381$	−61.4899	−3.15022
$382$	7.39196	0.378205
$383$	−21.8061	−1.11424	−0.557119	−	0.830433i	$-0.688093\pi$
$383$	−21.8061	−1.11424	−0.557119	+	0.830433i	$0.688093\pi$
$384$	−3.09514	−0.157948
$385$	−4.59166	−0.234013
$386$	−1.96179	−0.0998523
$387$	14.4756	0.735836
$388$	12.0786	0.613200
$389$	−3.95997	−0.200778	−0.100389	−	0.994948i	$-0.532009\pi$
$389$	−3.95997	−0.200778	−0.100389	+	0.994948i	$0.532009\pi$
$390$	−74.6850	−3.78182
$391$	15.4992	0.783827
$392$	−5.62659	−0.284186
$393$	33.9498	1.71254
$394$	−16.3156	−0.821968
$395$	−26.5506	−1.33591
$396$	−7.64445	−0.384148
$397$	−27.5576	−1.38308	−0.691538	−	0.722340i	$-0.743066\pi$
$397$	−27.5576	−1.38308	−0.691538	+	0.722340i	$0.743066\pi$
$398$	−1.67899	−0.0841602
$399$	−2.42201	−0.121252
$400$	6.37325	0.318663
$401$	−23.8418	−1.19060	−0.595301	−	0.803503i	$-0.702967\pi$
$401$	−23.8418	−1.19060	−0.595301	+	0.803503i	$0.702967\pi$
$402$	4.36575	0.217744
$403$	−4.33900	−0.216141
$404$	−2.77146	−0.137885
$405$	49.0868	2.43914
$406$	−1.61856	−0.0803276
$407$	−11.7571	−0.582777
$408$	−17.4803	−0.865403
$409$	33.6154	1.66217	0.831087	−	0.556142i	$-0.187719\pi$
$409$	33.6154	1.66217	0.831087	+	0.556142i	$0.187719\pi$
$410$	−9.66935	−0.477535
$411$	3.16995	0.156362
$412$	−12.0754	−0.594913
$413$	9.74070	0.479308
$414$	18.0576	0.887482
$415$	−40.8826	−2.00685
$416$	7.15502	0.350804
$417$	−20.5400	−1.00585
$418$	−0.775751	−0.0379432
$419$	30.4159	1.48591	0.742956	−	0.669340i	$-0.233423\pi$
$419$	30.4159	1.48591	0.742956	+	0.669340i	$0.233423\pi$
$420$	−12.2327	−0.596895
$421$	−6.73706	−0.328344	−0.164172	−	0.986432i	$-0.552495\pi$
$421$	−6.73706	−0.328344	−0.164172	+	0.986432i	$0.552495\pi$
$422$	8.78900	0.427842
$423$	−22.6915	−1.10330
$424$	−10.4093	−0.505522
$425$	35.9939	1.74596
$426$	−9.07555	−0.439712
$427$	−9.58629	−0.463913
$428$	−1.25914	−0.0608628
$429$	25.7287	1.24219
$430$	7.41925	0.357788
$431$	−30.7365	−1.48052	−0.740262	−	0.672319i	$-0.765298\pi$
$431$	−30.7365	−1.48052	−0.740262	+	0.672319i	$0.765298\pi$
$432$	−11.0803	−0.533100
$433$	30.2304	1.45278	0.726390	−	0.687283i	$-0.241197\pi$
$433$	30.2304	1.45278	0.726390	+	0.687283i	$0.241197\pi$
$434$	−0.710687	−0.0341141
$435$	14.4162	0.691203
$436$	−7.66963	−0.367309
$437$	1.83247	0.0876587
$438$	−0.576315	−0.0275374
$439$	−30.0192	−1.43274	−0.716370	−	0.697720i	$-0.754198\pi$
$439$	−30.0192	−1.43274	−0.716370	+	0.697720i	$0.754198\pi$
$440$	−3.91805	−0.186785
$441$	−37.0224	−1.76297
$442$	40.4091	1.92206
$443$	−23.7170	−1.12683	−0.563415	−	0.826174i	$-0.690513\pi$
$443$	−23.7170	−1.12683	−0.563415	+	0.826174i	$0.690513\pi$
$444$	−31.3222	−1.48649
$445$	−36.7744	−1.74327
$446$	0.320562	0.0151790
$447$	56.3694	2.66618
$448$	1.17193	0.0553683
$449$	−0.516878	−0.0243930	−0.0121965	−	0.999926i	$-0.503882\pi$
$449$	−0.516878	−0.0243930	−0.0121965	+	0.999926i	$0.503882\pi$
$450$	41.9353	1.97685
$451$	3.33106	0.156853
$452$	6.88774	0.323972
$453$	13.5891	0.638471
$454$	−1.84108	−0.0864062
$455$	28.2783	1.32571
$456$	−2.06669	−0.0967817
$457$	−25.0503	−1.17180	−0.585902	−	0.810382i	$-0.699260\pi$
$457$	−25.0503	−1.17180	−0.585902	+	0.810382i	$0.699260\pi$
$458$	13.7556	0.642756
$459$	−62.5776	−2.92087
$460$	9.25514	0.431523
$461$	15.4363	0.718939	0.359469	−	0.933157i	$-0.382958\pi$
$461$	15.4363	0.718939	0.359469	+	0.933157i	$0.382958\pi$
$462$	4.21413	0.196059
$463$	−7.55311	−0.351023	−0.175511	−	0.984477i	$-0.556158\pi$
$463$	−7.55311	−0.351023	−0.175511	+	0.984477i	$0.556158\pi$
$464$	−1.38111	−0.0641163
$465$	6.32996	0.293545
$466$	16.9457	0.784996
$467$	6.52998	0.302172	0.151086	−	0.988521i	$-0.451723\pi$
$467$	6.52998	0.302172	0.151086	+	0.988521i	$0.451723\pi$
$468$	47.0793	2.17624
$469$	−1.65302	−0.0763295
$470$	−11.6302	−0.536461
$471$	32.8270	1.51259
$472$	8.31170	0.382577
$473$	−2.55590	−0.117521
$474$	24.3676	1.11924
$475$	4.25556	0.195258
$476$	6.61863	0.303364
$477$	−68.4924	−3.13605
$478$	22.2326	1.01689
$479$	32.4328	1.48189	0.740946	−	0.671565i	$-0.234377\pi$
$479$	32.4328	1.48189	0.740946	+	0.671565i	$0.234377\pi$
$480$	−10.4381	−0.476433
$481$	72.4074	3.30150
$482$	−27.1467	−1.23650
$483$	−9.95454	−0.452947
$484$	−9.65025	−0.438648
$485$	40.7343	1.84965
$486$	−11.8100	−0.535712
$487$	8.89083	0.402882	0.201441	−	0.979501i	$-0.435438\pi$
$487$	8.89083	0.402882	0.201441	+	0.979501i	$0.435438\pi$
$488$	−8.17995	−0.370289
$489$	−28.7247	−1.29898
$490$	−18.9753	−0.857215
$491$	−22.8834	−1.03271	−0.516357	−	0.856374i	$-0.672712\pi$
$491$	−22.8834	−1.03271	−0.516357	+	0.856374i	$0.672712\pi$
$492$	8.87433	0.400086
$493$	−7.80002	−0.351295
$494$	4.77756	0.214953
$495$	−25.7803	−1.15874
$496$	−0.606427	−0.0272294
$497$	3.43631	0.154140
$498$	37.5212	1.68136
$499$	−31.6203	−1.41552	−0.707760	−	0.706453i	$-0.750294\pi$
$499$	−31.6203	−1.41552	−0.707760	+	0.706453i	$0.750294\pi$
$500$	4.63119	0.207113
$501$	78.9465	3.52707
$502$	17.8201	0.795351
$503$	2.41795	0.107811	0.0539055	−	0.998546i	$-0.482833\pi$
$503$	2.41795	0.107811	0.0539055	+	0.998546i	$0.482833\pi$
$504$	7.71115	0.343482
$505$	−9.34655	−0.415916
$506$	−3.18836	−0.141740
$507$	−118.217	−5.25019
$508$	19.8666	0.881438
$509$	−24.9486	−1.10583	−0.552914	−	0.833238i	$-0.686484\pi$
$509$	−24.9486	−1.10583	−0.552914	+	0.833238i	$0.686484\pi$
$510$	−58.9509	−2.61039
$511$	0.218213	0.00965316
$512$	1.00000	0.0441942
$513$	−7.39854	−0.326654
$514$	3.92176	0.172981
$515$	−40.7234	−1.79449
$516$	−6.80923	−0.299760
$517$	4.00656	0.176208
$518$	11.8597	0.521084
$519$	−28.1308	−1.23480
$520$	24.1298	1.05816
$521$	−7.88696	−0.345534	−0.172767	−	0.984963i	$-0.555271\pi$
$521$	−7.88696	−0.345534	−0.172767	+	0.984963i	$0.555271\pi$
$522$	−9.08755	−0.397751
$523$	12.9709	0.567178	0.283589	−	0.958946i	$-0.408475\pi$
$523$	12.9709	0.567178	0.283589	+	0.958946i	$0.408475\pi$
$524$	−10.9687	−0.479172
$525$	−23.1175	−1.00893
$526$	3.73202	0.162724
$527$	−3.42489	−0.149190
$528$	3.59590	0.156491
$529$	−15.4685	−0.672544
$530$	−35.1047	−1.52485
$531$	54.6901	2.37335
$532$	0.782520	0.0339265
$533$	−20.5147	−0.888592
$534$	33.7507	1.46054
$535$	−4.24636	−0.183586
$536$	−1.41052	−0.0609251
$537$	−39.9913	−1.72575
$538$	21.3147	0.918940
$539$	6.53691	0.281565
$540$	−37.3674	−1.60804
$541$	−20.8661	−0.897103	−0.448551	−	0.893757i	$-0.648060\pi$
$541$	−20.8661	−0.897103	−0.448551	+	0.893757i	$0.648060\pi$
$542$	−9.22422	−0.396214
$543$	−13.8136	−0.592799
$544$	5.64765	0.242141
$545$	−25.8653	−1.10795
$546$	−25.9532	−1.11070
$547$	16.8095	0.718723	0.359362	−	0.933198i	$-0.382994\pi$
$547$	16.8095	0.718723	0.359362	+	0.933198i	$0.382994\pi$
$548$	−1.02417	−0.0437504
$549$	−53.8232	−2.29712
$550$	−7.40437	−0.315723
$551$	−0.922195	−0.0392868
$552$	−8.49417	−0.361536
$553$	−9.22640	−0.392346
$554$	12.6430	0.537150
$555$	−105.632	−4.48382
$556$	6.63619	0.281437
$557$	−36.0122	−1.52588	−0.762942	−	0.646467i	$-0.776246\pi$
$557$	−36.0122	−1.52588	−0.762942	+	0.646467i	$0.776246\pi$
$558$	−3.99023	−0.168920
$559$	15.7409	0.665767
$560$	3.95223	0.167012
$561$	20.3084	0.857421
$562$	9.42829	0.397708
$563$	37.2911	1.57163	0.785817	−	0.618459i	$-0.212243\pi$
$563$	37.2911	1.57163	0.785817	+	0.618459i	$0.212243\pi$
$564$	10.6739	0.449454
$565$	23.2284	0.977225
$566$	29.5589	1.24245
$567$	17.0578	0.716360
$568$	2.93219	0.123032
$569$	34.1456	1.43146	0.715730	−	0.698377i	$-0.246094\pi$
$569$	34.1456	1.43146	0.715730	+	0.698377i	$0.246094\pi$
$570$	−6.96976	−0.291931
$571$	16.5738	0.693592	0.346796	−	0.937941i	$-0.387270\pi$
$571$	16.5738	0.693592	0.346796	+	0.937941i	$0.387270\pi$
$572$	−8.31262	−0.347568
$573$	−22.8791	−0.955790
$574$	−3.36012	−0.140249
$575$	17.4905	0.729404
$576$	6.57990	0.274162
$577$	−33.8131	−1.40766	−0.703830	−	0.710369i	$-0.748528\pi$
$577$	−33.8131	−1.40766	−0.703830	+	0.710369i	$0.748528\pi$
$578$	14.8960	0.619590
$579$	6.07200	0.252344
$580$	−4.65768	−0.193400
$581$	−14.2068	−0.589397
$582$	−37.3851	−1.54966
$583$	12.0935	0.500860
$584$	0.186200	0.00770501
$585$	158.771	6.56439
$586$	−15.8714	−0.655641
$587$	23.6026	0.974182	0.487091	−	0.873351i	$-0.338058\pi$
$587$	23.6026	0.974182	0.487091	+	0.873351i	$0.338058\pi$
$588$	17.4151	0.718186
$589$	−0.404924	−0.0166846
$590$	28.0306	1.15400
$591$	50.4990	2.07725
$592$	10.1198	0.415922
$593$	−0.551759	−0.0226580	−0.0113290	−	0.999936i	$-0.503606\pi$
$593$	−0.551759	−0.0226580	−0.0113290	+	0.999936i	$0.503606\pi$
$594$	12.8729	0.528183
$595$	22.3208	0.915065
$596$	−18.2122	−0.746001
$597$	5.19671	0.212687
$598$	19.6359	0.802973
$599$	8.91389	0.364212	0.182106	−	0.983279i	$-0.441709\pi$
$599$	8.91389	0.364212	0.182106	+	0.983279i	$0.441709\pi$
$600$	−19.7261	−0.805315
$601$	7.12005	0.290433	0.145217	−	0.989400i	$-0.453612\pi$
$601$	7.12005	0.290433	0.145217	+	0.989400i	$0.453612\pi$
$602$	2.57821	0.105080
$603$	−9.28107	−0.377954
$604$	−4.39046	−0.178645
$605$	−32.5447	−1.32313
$606$	8.57807	0.348460
$607$	−17.0202	−0.690830	−0.345415	−	0.938450i	$-0.612262\pi$
$607$	−17.0202	−0.690830	−0.345415	+	0.938450i	$0.612262\pi$
$608$	0.667721	0.0270797
$609$	5.00966	0.203002
$610$	−27.5863	−1.11693
$611$	−24.6749	−0.998240
$612$	37.1610	1.50214
$613$	−28.4716	−1.14996	−0.574978	−	0.818169i	$-0.694990\pi$
$613$	−28.4716	−1.14996	−0.574978	+	0.818169i	$0.694990\pi$
$614$	30.9033	1.24716
$615$	29.9280	1.20681
$616$	−1.36153	−0.0548576
$617$	−6.04550	−0.243383	−0.121691	−	0.992568i	$-0.538832\pi$
$617$	−6.04550	−0.243383	−0.121691	+	0.992568i	$0.538832\pi$
$618$	37.3751	1.50345
$619$	30.5467	1.22777	0.613887	−	0.789394i	$-0.289605\pi$
$619$	30.5467	1.22777	0.613887	+	0.789394i	$0.289605\pi$
$620$	−2.04513	−0.0821344
$621$	−30.4083	−1.22024
$622$	12.3858	0.496627
$623$	−12.7792	−0.511987
$624$	−22.1458	−0.886541
$625$	−16.2479	−0.649916
$626$	1.52608	0.0609946
$627$	2.40106	0.0958890
$628$	−10.6060	−0.423224
$629$	57.1532	2.27885
$630$	26.0053	1.03607
$631$	−36.0509	−1.43516	−0.717581	−	0.696475i	$-0.754751\pi$
$631$	−36.0509	−1.43516	−0.717581	+	0.696475i	$0.754751\pi$
$632$	−7.87285	−0.313165
$633$	−27.2032	−1.08123
$634$	−3.61250	−0.143471
$635$	66.9986	2.65876
$636$	32.2184	1.27754
$637$	−40.2584	−1.59509
$638$	1.60456	0.0635249
$639$	19.2935	0.763240
$640$	3.37243	0.133307
$641$	33.7479	1.33296	0.666482	−	0.745521i	$-0.267799\pi$
$641$	33.7479	1.33296	0.666482	+	0.745521i	$0.267799\pi$
$642$	3.89722	0.153811
$643$	42.4192	1.67285	0.836424	−	0.548083i	$-0.184642\pi$
$643$	42.4192	1.67285	0.836424	+	0.548083i	$0.184642\pi$
$644$	3.21618	0.126735
$645$	−22.9636	−0.904191
$646$	3.77106	0.148370
$647$	14.2000	0.558260	0.279130	−	0.960253i	$-0.409954\pi$
$647$	14.2000	0.558260	0.279130	+	0.960253i	$0.409954\pi$
$648$	14.5553	0.571788
$649$	−9.65644	−0.379048
$650$	45.6008	1.78861
$651$	2.19968	0.0862121
$652$	9.28058	0.363456
$653$	−0.454310	−0.0177785	−0.00888927	−	0.999960i	$-0.502830\pi$
$653$	−0.454310	−0.0177785	−0.00888927	+	0.999960i	$0.502830\pi$
$654$	23.7386	0.928252
$655$	−36.9913	−1.44537
$656$	−2.86718	−0.111945
$657$	1.22518	0.0477987
$658$	−4.04152	−0.157555
$659$	−47.9828	−1.86915	−0.934573	−	0.355771i	$-0.884218\pi$
$659$	−47.9828	−1.86915	−0.934573	+	0.355771i	$0.884218\pi$
$660$	12.1269	0.472039
$661$	41.5059	1.61439	0.807196	−	0.590283i	$-0.200984\pi$
$661$	41.5059	1.61439	0.807196	+	0.590283i	$0.200984\pi$
$662$	−1.39092	−0.0540598
$663$	−125.072	−4.85738
$664$	−12.1226	−0.470448
$665$	2.63899	0.102336
$666$	66.5873	2.58021
$667$	−3.79025	−0.146759
$668$	−25.5066	−0.986880
$669$	−0.992184	−0.0383600
$670$	−4.75687	−0.183774
$671$	9.50337	0.366873
$672$	−3.62727	−0.139925
$673$	−5.87453	−0.226447	−0.113223	−	0.993570i	$-0.536118\pi$
$673$	−5.87453	−0.226447	−0.113223	+	0.993570i	$0.536118\pi$
$674$	−10.5385	−0.405927
$675$	−70.6174	−2.71807
$676$	38.1943	1.46901
$677$	−20.5059	−0.788107	−0.394053	−	0.919088i	$-0.628927\pi$
$677$	−20.5059	−0.788107	−0.394053	+	0.919088i	$0.628927\pi$
$678$	−21.3185	−0.818732
$679$	14.1553	0.543230
$680$	19.0463	0.730392
$681$	5.69840	0.218363
$682$	0.704540	0.0269782
$683$	−23.4471	−0.897177	−0.448588	−	0.893738i	$-0.648073\pi$
$683$	−23.4471	−0.897177	−0.448588	+	0.893738i	$0.648073\pi$
$684$	4.39354	0.167991
$685$	−3.45394	−0.131968
$686$	−14.7974	−0.564968
$687$	−42.5754	−1.62435
$688$	2.19997	0.0838732
$689$	−74.4790	−2.83743
$690$	−28.6460	−1.09053
$691$	7.75353	0.294958	0.147479	−	0.989065i	$-0.452884\pi$
$691$	7.75353	0.294958	0.147479	+	0.989065i	$0.452884\pi$
$692$	9.08870	0.345500
$693$	−8.95872	−0.340314
$694$	−24.8164	−0.942017
$695$	22.3801	0.848924
$696$	4.27472	0.162033
$697$	−16.1928	−0.613347
$698$	2.03598	0.0770629
$699$	−52.4494	−1.98382
$700$	7.46898	0.282301
$701$	35.7356	1.34972	0.674858	−	0.737948i	$-0.264205\pi$
$701$	35.7356	1.34972	0.674858	+	0.737948i	$0.264205\pi$
$702$	−79.2797	−2.99222
$703$	6.75721	0.254853
$704$	−1.16179	−0.0437866
$705$	35.9971	1.35573
$706$	3.04380	0.114555
$707$	−3.24795	−0.122152
$708$	−25.7259	−0.966838
$709$	34.4470	1.29368	0.646842	−	0.762624i	$-0.276089\pi$
$709$	34.4470	1.29368	0.646842	+	0.762624i	$0.276089\pi$
$710$	9.88861	0.371113
$711$	−51.8026	−1.94275
$712$	−10.9044	−0.408661
$713$	−1.66425	−0.0623267
$714$	−20.4856	−0.766654
$715$	−28.0337	−1.04840
$716$	12.9207	0.482868
$717$	−68.8129	−2.56986
$718$	−28.6668	−1.06983
$719$	−15.9311	−0.594129	−0.297064	−	0.954857i	$-0.596008\pi$
$719$	−15.9311	−0.594129	−0.297064	+	0.954857i	$0.596008\pi$
$720$	22.1902	0.826980
$721$	−14.1515	−0.527029
$722$	−18.5541	−0.690514
$723$	84.0228	3.12484
$724$	4.46300	0.165866
$725$	−8.80215	−0.326904
$726$	29.8689	1.10854
$727$	16.6532	0.617633	0.308816	−	0.951122i	$-0.400067\pi$
$727$	16.6532	0.617633	0.308816	+	0.951122i	$0.400067\pi$
$728$	8.38515	0.310774
$729$	−7.11244	−0.263424
$730$	0.627946	0.0232413
$731$	12.4247	0.459544
$732$	25.3181	0.935783
$733$	47.0999	1.73967	0.869837	−	0.493339i	$-0.164224\pi$
$733$	47.0999	1.73967	0.869837	+	0.493339i	$0.164224\pi$
$734$	−24.9528	−0.921025
$735$	58.7311	2.16633
$736$	2.74436	0.101158
$737$	1.63872	0.0603632
$738$	−18.8658	−0.694458
$739$	15.5047	0.570350	0.285175	−	0.958475i	$-0.407948\pi$
$739$	15.5047	0.570350	0.285175	+	0.958475i	$0.407948\pi$
$740$	34.1283	1.25458
$741$	−14.7872	−0.543222
$742$	−12.1990	−0.447838
$743$	−5.29716	−0.194334	−0.0971669	−	0.995268i	$-0.530978\pi$
$743$	−5.29716	−0.194334	−0.0971669	+	0.995268i	$0.530978\pi$
$744$	1.87698	0.0688133
$745$	−61.4193	−2.25023
$746$	−37.7095	−1.38064
$747$	−79.7655	−2.91847
$748$	−6.56138	−0.239908
$749$	−1.47562	−0.0539179
$750$	−14.3342	−0.523411
$751$	44.1613	1.61147	0.805735	−	0.592277i	$-0.201771\pi$
$751$	44.1613	1.61147	0.805735	+	0.592277i	$0.201771\pi$
$752$	−3.44861	−0.125758
$753$	−55.1558	−2.00999
$754$	−9.88185	−0.359876
$755$	−14.8065	−0.538864
$756$	−12.9853	−0.472270
$757$	−5.45753	−0.198357	−0.0991787	−	0.995070i	$-0.531622\pi$
$757$	−5.45753	−0.198357	−0.0991787	+	0.995070i	$0.531622\pi$
$758$	16.6962	0.606432
$759$	9.86843	0.358201
$760$	2.25184	0.0816828
$761$	−15.5976	−0.565412	−0.282706	−	0.959207i	$-0.591232\pi$
$761$	−15.5976	−0.565412	−0.282706	+	0.959207i	$0.591232\pi$
$762$	−61.4899	−2.22754
$763$	−8.98824	−0.325396
$764$	7.39196	0.267432
$765$	125.323	4.53105
$766$	−21.8061	−0.787886
$767$	59.4704	2.14735
$768$	−3.09514	−0.111686
$769$	−41.1744	−1.48479	−0.742393	−	0.669965i	$-0.766309\pi$
$769$	−41.1744	−1.48479	−0.742393	+	0.669965i	$0.766309\pi$
$770$	−4.59166	−0.165472
$771$	−12.1384	−0.437153
$772$	−1.96179	−0.0706062
$773$	−37.5374	−1.35013	−0.675063	−	0.737760i	$-0.735883\pi$
$773$	−37.5374	−1.35013	−0.675063	+	0.737760i	$0.735883\pi$
$774$	14.4756	0.520315
$775$	−3.86491	−0.138832
$776$	12.0786	0.433598
$777$	−36.7073	−1.31687
$778$	−3.95997	−0.141972
$779$	−1.91448	−0.0685933
$780$	−74.6850	−2.67415
$781$	−3.40659	−0.121897
$782$	15.4992	0.554249
$783$	15.3031	0.546887
$784$	−5.62659	−0.200950
$785$	−35.7678	−1.27661
$786$	33.9498	1.21095
$787$	13.8501	0.493702	0.246851	−	0.969053i	$-0.420604\pi$
$787$	13.8501	0.493702	0.246851	+	0.969053i	$0.420604\pi$
$788$	−16.3156	−0.581219
$789$	−11.5511	−0.411230
$790$	−26.5506	−0.944628
$791$	8.07191	0.287004
$792$	−7.64445	−0.271634
$793$	−58.5277	−2.07838
$794$	−27.5576	−0.977982
$795$	108.654	3.85356
$796$	−1.67899	−0.0595103
$797$	52.4957	1.85949	0.929746	−	0.368201i	$-0.120026\pi$
$797$	52.4957	1.85949	0.929746	+	0.368201i	$0.120026\pi$
$798$	−2.42201	−0.0857382
$799$	−19.4766	−0.689032
$800$	6.37325	0.225329
$801$	−71.7500	−2.53516
$802$	−23.8418	−0.841882
$803$	−0.216325	−0.00763395
$804$	4.36575	0.153968
$805$	10.8463	0.382283
$806$	−4.33900	−0.152835
$807$	−65.9719	−2.32232
$808$	−2.77146	−0.0974997
$809$	29.0869	1.02264	0.511320	−	0.859390i	$-0.329157\pi$
$809$	29.0869	1.02264	0.511320	+	0.859390i	$0.329157\pi$
$810$	49.0868	1.72473
$811$	−46.5542	−1.63474	−0.817370	−	0.576113i	$-0.804569\pi$
$811$	−46.5542	−1.63474	−0.817370	+	0.576113i	$0.804569\pi$
$812$	−1.61856	−0.0568002
$813$	28.5503	1.00130
$814$	−11.7571	−0.412085
$815$	31.2981	1.09632
$816$	−17.4803	−0.611932
$817$	1.46897	0.0513927
$818$	33.6154	1.17533
$819$	55.1734	1.92792
$820$	−9.66935	−0.337668
$821$	−27.7167	−0.967318	−0.483659	−	0.875256i	$-0.660693\pi$
$821$	−27.7167	−0.967318	−0.483659	+	0.875256i	$0.660693\pi$
$822$	3.16995	0.110565
$823$	−21.1696	−0.737925	−0.368963	−	0.929444i	$-0.620287\pi$
$823$	−21.1696	−0.737925	−0.368963	+	0.929444i	$0.620287\pi$
$824$	−12.0754	−0.420667
$825$	22.9176	0.797888
$826$	9.74070	0.338922
$827$	41.8849	1.45648	0.728240	−	0.685322i	$-0.240339\pi$
$827$	41.8849	1.45648	0.728240	+	0.685322i	$0.240339\pi$
$828$	18.0576	0.627544
$829$	40.3873	1.40271	0.701354	−	0.712813i	$-0.252579\pi$
$829$	40.3873	1.40271	0.701354	+	0.712813i	$0.252579\pi$
$830$	−40.8826	−1.41905
$831$	−39.1319	−1.35747
$832$	7.15502	0.248056
$833$	−31.7770	−1.10101
$834$	−20.5400	−0.711240
$835$	−86.0191	−2.97681
$836$	−0.775751	−0.0268299
$837$	6.71938	0.232256
$838$	30.4159	1.05070
$839$	18.2820	0.631163	0.315582	−	0.948898i	$-0.397800\pi$
$839$	18.2820	0.631163	0.315582	+	0.948898i	$0.397800\pi$
$840$	−12.2327	−0.422069
$841$	−27.0925	−0.934226
$842$	−6.73706	−0.232174
$843$	−29.1819	−1.00508
$844$	8.78900	0.302530
$845$	128.808	4.43111
$846$	−22.6915	−0.780151
$847$	−11.3094	−0.388595
$848$	−10.4093	−0.357458
$849$	−91.4889	−3.13989
$850$	35.9939	1.23458
$851$	27.7724	0.952025
$852$	−9.07555	−0.310923
$853$	−12.6294	−0.432421	−0.216211	−	0.976347i	$-0.569370\pi$
$853$	−12.6294	−0.432421	−0.216211	+	0.976347i	$0.569370\pi$
$854$	−9.58629	−0.328036
$855$	14.8169	0.506726
$856$	−1.25914	−0.0430365
$857$	−6.89281	−0.235454	−0.117727	−	0.993046i	$-0.537561\pi$
$857$	−6.89281	−0.235454	−0.117727	+	0.993046i	$0.537561\pi$
$858$	25.7287	0.878364
$859$	−4.77038	−0.162763	−0.0813817	−	0.996683i	$-0.525933\pi$
$859$	−4.77038	−0.162763	−0.0813817	+	0.996683i	$0.525933\pi$
$860$	7.41925	0.252994
$861$	10.4001	0.354433
$862$	−30.7365	−1.04689
$863$	−22.4496	−0.764194	−0.382097	−	0.924122i	$-0.624798\pi$
$863$	−22.4496	−0.764194	−0.382097	+	0.924122i	$0.624798\pi$
$864$	−11.0803	−0.376959
$865$	30.6510	1.04216
$866$	30.2304	1.02727
$867$	−46.1051	−1.56581
$868$	−0.710687	−0.0241223
$869$	9.14659	0.310277
$870$	14.4162	0.488754
$871$	−10.0923	−0.341964
$872$	−7.66963	−0.259726
$873$	79.4762	2.68986
$874$	1.83247	0.0619841
$875$	5.42741	0.183480
$876$	−0.576315	−0.0194719
$877$	23.0906	0.779713	0.389856	−	0.920876i	$-0.372525\pi$
$877$	23.0906	0.779713	0.389856	+	0.920876i	$0.372525\pi$
$878$	−30.0192	−1.01310
$879$	49.1241	1.65692
$880$	−3.91805	−0.132077
$881$	−17.3678	−0.585136	−0.292568	−	0.956245i	$-0.594510\pi$
$881$	−17.3678	−0.585136	−0.292568	+	0.956245i	$0.594510\pi$
$882$	−37.0224	−1.24661
$883$	13.1839	0.443672	0.221836	−	0.975084i	$-0.428795\pi$
$883$	13.1839	0.443672	0.221836	+	0.975084i	$0.428795\pi$
$884$	40.4091	1.35910
$885$	−86.7586	−2.91636
$886$	−23.7170	−0.796789
$887$	−36.6399	−1.23025	−0.615124	−	0.788430i	$-0.710894\pi$
$887$	−36.6399	−1.23025	−0.615124	+	0.788430i	$0.710894\pi$
$888$	−31.3222	−1.05111
$889$	23.2822	0.780859
$890$	−36.7744	−1.23268
$891$	−16.9102	−0.566514
$892$	0.320562	0.0107332
$893$	−2.30271	−0.0770574
$894$	56.3694	1.88527
$895$	43.5740	1.45652
$896$	1.17193	0.0391513
$897$	−60.7760	−2.02925
$898$	−0.516878	−0.0172485
$899$	0.837541	0.0279336
$900$	41.9353	1.39784
$901$	−58.7883	−1.95852
$902$	3.33106	0.110912
$903$	−7.97991	−0.265555
$904$	6.88774	0.229083
$905$	15.0511	0.500317
$906$	13.5891	0.451467
$907$	−23.7389	−0.788238	−0.394119	−	0.919059i	$-0.628950\pi$
$907$	−23.7389	−0.788238	−0.394119	+	0.919059i	$0.628950\pi$
$908$	−1.84108	−0.0610984
$909$	−18.2359	−0.604848
$910$	28.2783	0.937417
$911$	53.1573	1.76118	0.880591	−	0.473878i	$-0.157146\pi$
$911$	53.1573	1.76118	0.880591	+	0.473878i	$0.157146\pi$
$912$	−2.06669	−0.0684350
$913$	14.0839	0.466109
$914$	−25.0503	−0.828590
$915$	85.3833	2.82269
$916$	13.7556	0.454497
$917$	−12.8546	−0.424495
$918$	−62.5776	−2.06537
$919$	−47.5739	−1.56932	−0.784659	−	0.619928i	$-0.787162\pi$
$919$	−47.5739	−1.56932	−0.784659	+	0.619928i	$0.787162\pi$
$920$	9.25514	0.305133
$921$	−95.6501	−3.15178
$922$	15.4363	0.508367
$923$	20.9799	0.690562
$924$	4.21413	0.138635
$925$	64.4961	2.12062
$926$	−7.55311	−0.248211
$927$	−79.4550	−2.60964
$928$	−1.38111	−0.0453371
$929$	−2.58507	−0.0848133	−0.0424067	−	0.999100i	$-0.513503\pi$
$929$	−2.58507	−0.0848133	−0.0424067	+	0.999100i	$0.513503\pi$
$930$	6.32996	0.207568
$931$	−3.75699	−0.123131
$932$	16.9457	0.555076
$933$	−38.3359	−1.25506
$934$	6.52998	0.213668
$935$	−22.1278	−0.723655
$936$	47.0793	1.53883
$937$	33.6028	1.09775	0.548877	−	0.835903i	$-0.315055\pi$
$937$	33.6028	1.09775	0.548877	+	0.835903i	$0.315055\pi$
$938$	−1.65302	−0.0539731
$939$	−4.72345	−0.154144
$940$	−11.6302	−0.379335
$941$	13.2256	0.431141	0.215571	−	0.976488i	$-0.430839\pi$
$941$	13.2256	0.431141	0.215571	+	0.976488i	$0.430839\pi$
$942$	32.8270	1.06956
$943$	−7.86857	−0.256236
$944$	8.31170	0.270523
$945$	−43.7918	−1.42455
$946$	−2.55590	−0.0830996
$947$	15.2233	0.494692	0.247346	−	0.968927i	$-0.420442\pi$
$947$	15.2233	0.494692	0.247346	+	0.968927i	$0.420442\pi$
$948$	24.3676	0.791423
$949$	1.33227	0.0432472
$950$	4.25556	0.138068
$951$	11.1812	0.362575
$952$	6.61863	0.214511
$953$	33.4859	1.08471	0.542357	−	0.840148i	$-0.317532\pi$
$953$	33.4859	1.08471	0.542357	+	0.840148i	$0.317532\pi$
$954$	−68.4924	−2.21752
$955$	24.9288	0.806678
$956$	22.2326	0.719052
$957$	−4.96632	−0.160538
$958$	32.4328	1.04786
$959$	−1.20025	−0.0387582
$960$	−10.4381	−0.336889
$961$	−30.6322	−0.988137
$962$	72.4074	2.33451
$963$	−8.28501	−0.266981
$964$	−27.1467	−0.874336
$965$	−6.61598	−0.212976
$966$	−9.95454	−0.320282
$967$	−25.4020	−0.816872	−0.408436	−	0.912787i	$-0.633926\pi$
$967$	−25.4020	−0.816872	−0.408436	+	0.912787i	$0.633926\pi$
$968$	−9.65025	−0.310171
$969$	−11.6720	−0.374957
$970$	40.7343	1.30790
$971$	−38.8539	−1.24688	−0.623441	−	0.781871i	$-0.714266\pi$
$971$	−38.8539	−1.24688	−0.623441	+	0.781871i	$0.714266\pi$
$972$	−11.8100	−0.378806
$973$	7.77713	0.249323
$974$	8.89083	0.284880
$975$	−141.141	−4.52012
$976$	−8.17995	−0.261834
$977$	47.1513	1.50850	0.754251	−	0.656586i	$-0.228000\pi$
$977$	47.1513	1.50850	0.754251	+	0.656586i	$0.228000\pi$
$978$	−28.7247	−0.918515
$979$	12.6686	0.404891
$980$	−18.9753	−0.606142
$981$	−50.4654	−1.61124
$982$	−22.8834	−0.730239
$983$	−9.88423	−0.315258	−0.157629	−	0.987498i	$-0.550385\pi$
$983$	−9.88423	−0.315258	−0.157629	+	0.987498i	$0.550385\pi$
$984$	8.87433	0.282903
$985$	−55.0231	−1.75318
$986$	−7.80002	−0.248403
$987$	12.5091	0.398168
$988$	4.77756	0.151994
$989$	6.03751	0.191982
$990$	−25.7803	−0.819353
$991$	−24.5650	−0.780333	−0.390166	−	0.920744i	$-0.627583\pi$
$991$	−24.5650	−0.780333	−0.390166	+	0.920744i	$0.627583\pi$
$992$	−0.606427	−0.0192541
$993$	4.30511	0.136618
$994$	3.43631	0.108993
$995$	−5.66227	−0.179506
$996$	37.5212	1.18890
$997$	−42.6533	−1.35084	−0.675422	−	0.737432i	$-0.736038\pi$
$997$	−42.6533	−1.35084	−0.675422	+	0.737432i	$0.736038\pi$
$998$	−31.6203	−1.00092
$999$	−112.130	−3.54765

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4034.2.a.d.1.3	✓	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4034.2.a.d.1.3	✓	52	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -3.09514 q^{3} +1.00000 q^{4} +3.37243 q^{5} -3.09514 q^{6} +1.17193 q^{7} +1.00000 q^{8} +6.57990 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -3.09514 q^{3} +1.00000 q^{4} +3.37243 q^{5} -3.09514 q^{6} +1.17193 q^{7} +1.00000 q^{8} +6.57990 q^{9} +3.37243 q^{10} -1.16179 q^{11} -3.09514 q^{12} +7.15502 q^{13} +1.17193 q^{14} -10.4381 q^{15} +1.00000 q^{16} +5.64765 q^{17} +6.57990 q^{18} +0.667721 q^{19} +3.37243 q^{20} -3.62727 q^{21} -1.16179 q^{22} +2.74436 q^{23} -3.09514 q^{24} +6.37325 q^{25} +7.15502 q^{26} -11.0803 q^{27} +1.17193 q^{28} -1.38111 q^{29} -10.4381 q^{30} -0.606427 q^{31} +1.00000 q^{32} +3.59590 q^{33} +5.64765 q^{34} +3.95223 q^{35} +6.57990 q^{36} +10.1198 q^{37} +0.667721 q^{38} -22.1458 q^{39} +3.37243 q^{40} -2.86718 q^{41} -3.62727 q^{42} +2.19997 q^{43} -1.16179 q^{44} +22.1902 q^{45} +2.74436 q^{46} -3.44861 q^{47} -3.09514 q^{48} -5.62659 q^{49} +6.37325 q^{50} -17.4803 q^{51} +7.15502 q^{52} -10.4093 q^{53} -11.0803 q^{54} -3.91805 q^{55} +1.17193 q^{56} -2.06669 q^{57} -1.38111 q^{58} +8.31170 q^{59} -10.4381 q^{60} -8.17995 q^{61} -0.606427 q^{62} +7.71115 q^{63} +1.00000 q^{64} +24.1298 q^{65} +3.59590 q^{66} -1.41052 q^{67} +5.64765 q^{68} -8.49417 q^{69} +3.95223 q^{70} +2.93219 q^{71} +6.57990 q^{72} +0.186200 q^{73} +10.1198 q^{74} -19.7261 q^{75} +0.667721 q^{76} -1.36153 q^{77} -22.1458 q^{78} -7.87285 q^{79} +3.37243 q^{80} +14.5553 q^{81} -2.86718 q^{82} -12.1226 q^{83} -3.62727 q^{84} +19.0463 q^{85} +2.19997 q^{86} +4.27472 q^{87} -1.16179 q^{88} -10.9044 q^{89} +22.1902 q^{90} +8.38515 q^{91} +2.74436 q^{92} +1.87698 q^{93} -3.44861 q^{94} +2.25184 q^{95} -3.09514 q^{96} +12.0786 q^{97} -5.62659 q^{98} -7.64445 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 52 q^{2} + 16 q^{3} + 52 q^{4} + 24 q^{5} + 16 q^{6} + 12 q^{7} + 52 q^{8} + 70 q^{9}+O(q^{10}) \) 52 * q + 52 * q^2 + 16 * q^3 + 52 * q^4 + 24 * q^5 + 16 * q^6 + 12 * q^7 + 52 * q^8 + 70 * q^9	\( 52 q + 52 q^{2} + 16 q^{3} + 52 q^{4} + 24 q^{5} + 16 q^{6} + 12 q^{7} + 52 q^{8} + 70 q^{9} + 24 q^{10} + 19 q^{11} + 16 q^{12} + 27 q^{13} + 12 q^{14} + 5 q^{15} + 52 q^{16} + 43 q^{17} + 70 q^{18} + 35 q^{19} + 24 q^{20} + 29 q^{21} + 19 q^{22} + 2 q^{23} + 16 q^{24} + 88 q^{25} + 27 q^{26} + 49 q^{27} + 12 q^{28} + 31 q^{29} + 5 q^{30} + 59 q^{31} + 52 q^{32} + 45 q^{33} + 43 q^{34} + 18 q^{35} + 70 q^{36} + 60 q^{37} + 35 q^{38} + 6 q^{39} + 24 q^{40} + 56 q^{41} + 29 q^{42} + 34 q^{43} + 19 q^{44} + 61 q^{45} + 2 q^{46} - 4 q^{47} + 16 q^{48} + 102 q^{49} + 88 q^{50} + 23 q^{51} + 27 q^{52} + 30 q^{53} + 49 q^{54} + 24 q^{55} + 12 q^{56} + 32 q^{57} + 31 q^{58} + 27 q^{59} + 5 q^{60} + 107 q^{61} + 59 q^{62} - 4 q^{63} + 52 q^{64} + 46 q^{65} + 45 q^{66} + 22 q^{67} + 43 q^{68} + 36 q^{69} + 18 q^{70} + 8 q^{71} + 70 q^{72} + 66 q^{73} + 60 q^{74} + 53 q^{75} + 35 q^{76} + 26 q^{77} + 6 q^{78} + 50 q^{79} + 24 q^{80} + 108 q^{81} + 56 q^{82} + 52 q^{83} + 29 q^{84} + 19 q^{85} + 34 q^{86} - 32 q^{87} + 19 q^{88} + 62 q^{89} + 61 q^{90} + 69 q^{91} + 2 q^{92} + 21 q^{93} - 4 q^{94} - 44 q^{95} + 16 q^{96} + 82 q^{97} + 102 q^{98} + 16 q^{99}+O(q^{100}) \) 52 * q + 52 * q^2 + 16 * q^3 + 52 * q^4 + 24 * q^5 + 16 * q^6 + 12 * q^7 + 52 * q^8 + 70 * q^9 + 24 * q^10 + 19 * q^11 + 16 * q^12 + 27 * q^13 + 12 * q^14 + 5 * q^15 + 52 * q^16 + 43 * q^17 + 70 * q^18 + 35 * q^19 + 24 * q^20 + 29 * q^21 + 19 * q^22 + 2 * q^23 + 16 * q^24 + 88 * q^25 + 27 * q^26 + 49 * q^27 + 12 * q^28 + 31 * q^29 + 5 * q^30 + 59 * q^31 + 52 * q^32 + 45 * q^33 + 43 * q^34 + 18 * q^35 + 70 * q^36 + 60 * q^37 + 35 * q^38 + 6 * q^39 + 24 * q^40 + 56 * q^41 + 29 * q^42 + 34 * q^43 + 19 * q^44 + 61 * q^45 + 2 * q^46 - 4 * q^47 + 16 * q^48 + 102 * q^49 + 88 * q^50 + 23 * q^51 + 27 * q^52 + 30 * q^53 + 49 * q^54 + 24 * q^55 + 12 * q^56 + 32 * q^57 + 31 * q^58 + 27 * q^59 + 5 * q^60 + 107 * q^61 + 59 * q^62 - 4 * q^63 + 52 * q^64 + 46 * q^65 + 45 * q^66 + 22 * q^67 + 43 * q^68 + 36 * q^69 + 18 * q^70 + 8 * q^71 + 70 * q^72 + 66 * q^73 + 60 * q^74 + 53 * q^75 + 35 * q^76 + 26 * q^77 + 6 * q^78 + 50 * q^79 + 24 * q^80 + 108 * q^81 + 56 * q^82 + 52 * q^83 + 29 * q^84 + 19 * q^85 + 34 * q^86 - 32 * q^87 + 19 * q^88 + 62 * q^89 + 61 * q^90 + 69 * q^91 + 2 * q^92 + 21 * q^93 - 4 * q^94 - 44 * q^95 + 16 * q^96 + 82 * q^97 + 102 * q^98 + 16 * q^99

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