LMFDB - Embedded newform 4034.2.a.c.1.7

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			1.7
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)

$f(q)$	$=$	$q-1.00000 q^{2} -2.70268 q^{3} +1.00000 q^{4} +1.64140 q^{5} +2.70268 q^{6} +4.14098 q^{7} -1.00000 q^{8} +4.30446 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.70268 q^{3} +1.00000 q^{4} +1.64140 q^{5} +2.70268 q^{6} +4.14098 q^{7} -1.00000 q^{8} +4.30446 q^{9} -1.64140 q^{10} +3.17535 q^{11} -2.70268 q^{12} +4.18079 q^{13} -4.14098 q^{14} -4.43617 q^{15} +1.00000 q^{16} -3.80323 q^{17} -4.30446 q^{18} -5.05080 q^{19} +1.64140 q^{20} -11.1917 q^{21} -3.17535 q^{22} +7.73254 q^{23} +2.70268 q^{24} -2.30581 q^{25} -4.18079 q^{26} -3.52553 q^{27} +4.14098 q^{28} +7.09006 q^{29} +4.43617 q^{30} +9.44135 q^{31} -1.00000 q^{32} -8.58195 q^{33} +3.80323 q^{34} +6.79700 q^{35} +4.30446 q^{36} +10.2615 q^{37} +5.05080 q^{38} -11.2993 q^{39} -1.64140 q^{40} +9.50741 q^{41} +11.1917 q^{42} -7.93060 q^{43} +3.17535 q^{44} +7.06533 q^{45} -7.73254 q^{46} +13.5932 q^{47} -2.70268 q^{48} +10.1477 q^{49} +2.30581 q^{50} +10.2789 q^{51} +4.18079 q^{52} -9.93192 q^{53} +3.52553 q^{54} +5.21201 q^{55} -4.14098 q^{56} +13.6507 q^{57} -7.09006 q^{58} -12.7576 q^{59} -4.43617 q^{60} +3.33274 q^{61} -9.44135 q^{62} +17.8247 q^{63} +1.00000 q^{64} +6.86234 q^{65} +8.58195 q^{66} +0.893201 q^{67} -3.80323 q^{68} -20.8985 q^{69} -6.79700 q^{70} -1.57638 q^{71} -4.30446 q^{72} -5.46876 q^{73} -10.2615 q^{74} +6.23187 q^{75} -5.05080 q^{76} +13.1491 q^{77} +11.2993 q^{78} -0.681247 q^{79} +1.64140 q^{80} -3.38500 q^{81} -9.50741 q^{82} -3.45940 q^{83} -11.1917 q^{84} -6.24261 q^{85} +7.93060 q^{86} -19.1621 q^{87} -3.17535 q^{88} -13.8379 q^{89} -7.06533 q^{90} +17.3126 q^{91} +7.73254 q^{92} -25.5169 q^{93} -13.5932 q^{94} -8.29037 q^{95} +2.70268 q^{96} -6.17063 q^{97} -10.1477 q^{98} +13.6682 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−2.70268	−1.56039	−0.780196	−	0.625536i	$-0.784880\pi$
$3$	−2.70268	−1.56039	−0.780196	+	0.625536i	$0.784880\pi$
$4$	1.00000	0.500000
$5$	1.64140	0.734055	0.367028	−	0.930210i	$-0.380375\pi$
$5$	1.64140	0.734055	0.367028	+	0.930210i	$0.380375\pi$
$6$	2.70268	1.10336
$7$	4.14098	1.56514	0.782572	−	0.622560i	$-0.213907\pi$
$7$	4.14098	1.56514	0.782572	+	0.622560i	$0.213907\pi$
$8$	−1.00000	−0.353553
$9$	4.30446	1.43482
$10$	−1.64140	−0.519055
$11$	3.17535	0.957404	0.478702	−	0.877977i	$-0.341107\pi$
$11$	3.17535	0.957404	0.478702	+	0.877977i	$0.341107\pi$
$12$	−2.70268	−0.780196
$13$	4.18079	1.15954	0.579771	−	0.814779i	$-0.303142\pi$
$13$	4.18079	1.15954	0.579771	+	0.814779i	$0.303142\pi$
$14$	−4.14098	−1.10672
$15$	−4.43617	−1.14541
$16$	1.00000	0.250000
$17$	−3.80323	−0.922419	−0.461209	−	0.887291i	$-0.652584\pi$
$17$	−3.80323	−0.922419	−0.461209	+	0.887291i	$0.652584\pi$
$18$	−4.30446	−1.01457
$19$	−5.05080	−1.15873	−0.579367	−	0.815067i	$-0.696700\pi$
$19$	−5.05080	−1.15873	−0.579367	+	0.815067i	$0.696700\pi$
$20$	1.64140	0.367028
$21$	−11.1917	−2.44224
$22$	−3.17535	−0.676987
$23$	7.73254	1.61235	0.806173	−	0.591681i	$-0.201535\pi$
$23$	7.73254	1.61235	0.806173	+	0.591681i	$0.201535\pi$
$24$	2.70268	0.551682
$25$	−2.30581	−0.461163
$26$	−4.18079	−0.819920
$27$	−3.52553	−0.678490
$28$	4.14098	0.782572
$29$	7.09006	1.31659	0.658295	−	0.752760i	$-0.271278\pi$
$29$	7.09006	1.31659	0.658295	+	0.752760i	$0.271278\pi$
$30$	4.43617	0.809929
$31$	9.44135	1.69572	0.847858	−	0.530223i	$-0.177892\pi$
$31$	9.44135	1.69572	0.847858	+	0.530223i	$0.177892\pi$
$32$	−1.00000	−0.176777
$33$	−8.58195	−1.49393
$34$	3.80323	0.652248
$35$	6.79700	1.14890
$36$	4.30446	0.717410
$37$	10.2615	1.68697	0.843486	−	0.537151i	$-0.180499\pi$
$37$	10.2615	1.68697	0.843486	+	0.537151i	$0.180499\pi$
$38$	5.05080	0.819348
$39$	−11.2993	−1.80934
$40$	−1.64140	−0.259528
$41$	9.50741	1.48481	0.742404	−	0.669952i	$-0.233686\pi$
$41$	9.50741	1.48481	0.742404	+	0.669952i	$0.233686\pi$
$42$	11.1917	1.72692
$43$	−7.93060	−1.20941	−0.604703	−	0.796451i	$-0.706708\pi$
$43$	−7.93060	−1.20941	−0.604703	+	0.796451i	$0.706708\pi$
$44$	3.17535	0.478702
$45$	7.06533	1.05324
$46$	−7.73254	−1.14010
$47$	13.5932	1.98278	0.991388	−	0.130954i	$-0.0418039\pi$
$47$	13.5932	1.98278	0.991388	+	0.130954i	$0.0418039\pi$
$48$	−2.70268	−0.390098
$49$	10.1477	1.44968
$50$	2.30581	0.326091
$51$	10.2789	1.43933
$52$	4.18079	0.579771
$53$	−9.93192	−1.36425	−0.682127	−	0.731234i	$-0.738945\pi$
$53$	−9.93192	−1.36425	−0.682127	+	0.731234i	$0.738945\pi$
$54$	3.52553	0.479765
$55$	5.21201	0.702788
$56$	−4.14098	−0.553362
$57$	13.6507	1.80808
$58$	−7.09006	−0.930970
$59$	−12.7576	−1.66089	−0.830446	−	0.557099i	$-0.811915\pi$
$59$	−12.7576	−1.66089	−0.830446	+	0.557099i	$0.811915\pi$
$60$	−4.43617	−0.572707
$61$	3.33274	0.426713	0.213356	−	0.976974i	$-0.431560\pi$
$61$	3.33274	0.426713	0.213356	+	0.976974i	$0.431560\pi$
$62$	−9.44135	−1.19905
$63$	17.8247	2.24570
$64$	1.00000	0.125000
$65$	6.86234	0.851168
$66$	8.58195	1.05636
$67$	0.893201	0.109122	0.0545609	−	0.998510i	$-0.482624\pi$
$67$	0.893201	0.109122	0.0545609	+	0.998510i	$0.482624\pi$
$68$	−3.80323	−0.461209
$69$	−20.8985	−2.51589
$70$	−6.79700	−0.812396
$71$	−1.57638	−0.187082	−0.0935410	−	0.995615i	$-0.529819\pi$
$71$	−1.57638	−0.187082	−0.0935410	+	0.995615i	$0.529819\pi$
$72$	−4.30446	−0.507286
$73$	−5.46876	−0.640070	−0.320035	−	0.947406i	$-0.603695\pi$
$73$	−5.46876	−0.640070	−0.320035	+	0.947406i	$0.603695\pi$
$74$	−10.2615	−1.19287
$75$	6.23187	0.719594
$76$	−5.05080	−0.579367
$77$	13.1491	1.49848
$78$	11.2993	1.27940
$79$	−0.681247	−0.0766463	−0.0383231	−	0.999265i	$-0.512202\pi$
$79$	−0.681247	−0.0766463	−0.0383231	+	0.999265i	$0.512202\pi$
$80$	1.64140	0.183514
$81$	−3.38500	−0.376111
$82$	−9.50741	−1.04992
$83$	−3.45940	−0.379719	−0.189859	−	0.981811i	$-0.560803\pi$
$83$	−3.45940	−0.379719	−0.189859	+	0.981811i	$0.560803\pi$
$84$	−11.1917	−1.22112
$85$	−6.24261	−0.677106
$86$	7.93060	0.855179
$87$	−19.1621	−2.05440
$88$	−3.17535	−0.338494
$89$	−13.8379	−1.46681	−0.733407	−	0.679790i	$-0.762071\pi$
$89$	−13.8379	−1.46681	−0.733407	+	0.679790i	$0.762071\pi$
$90$	−7.06533	−0.744751
$91$	17.3126	1.81485
$92$	7.73254	0.806173
$93$	−25.5169	−2.64598
$94$	−13.5932	−1.40204
$95$	−8.29037	−0.850574
$96$	2.70268	0.275841
$97$	−6.17063	−0.626532	−0.313266	−	0.949665i	$-0.601423\pi$
$97$	−6.17063	−0.626532	−0.313266	+	0.949665i	$0.601423\pi$
$98$	−10.1477	−1.02508
$99$	13.6682	1.37370
$100$	−2.30581	−0.230581
$101$	9.99446	0.994486	0.497243	−	0.867611i	$-0.334346\pi$
$101$	9.99446	0.994486	0.497243	+	0.867611i	$0.334346\pi$
$102$	−10.2789	−1.01776
$103$	15.5794	1.53509	0.767544	−	0.640997i	$-0.221479\pi$
$103$	15.5794	1.53509	0.767544	+	0.640997i	$0.221479\pi$
$104$	−4.18079	−0.409960
$105$	−18.3701	−1.79274
$106$	9.93192	0.964673
$107$	−6.83697	−0.660955	−0.330478	−	0.943814i	$-0.607210\pi$
$107$	−6.83697	−0.660955	−0.330478	+	0.943814i	$0.607210\pi$
$108$	−3.52553	−0.339245
$109$	1.25995	0.120681	0.0603405	−	0.998178i	$-0.480781\pi$
$109$	1.25995	0.120681	0.0603405	+	0.998178i	$0.480781\pi$
$110$	−5.21201	−0.496946
$111$	−27.7334	−2.63234
$112$	4.14098	0.391286
$113$	−1.76526	−0.166062	−0.0830310	−	0.996547i	$-0.526460\pi$
$113$	−1.76526	−0.166062	−0.0830310	+	0.996547i	$0.526460\pi$
$114$	−13.6507	−1.27850
$115$	12.6922	1.18355
$116$	7.09006	0.658295
$117$	17.9960	1.66373
$118$	12.7576	1.17443
$119$	−15.7491	−1.44372
$120$	4.43617	0.404965
$121$	−0.917146	−0.0833769
$122$	−3.33274	−0.301732
$123$	−25.6955	−2.31688
$124$	9.44135	0.847858
$125$	−11.9917	−1.07257
$126$	−17.8247	−1.58795
$127$	7.38044	0.654908	0.327454	−	0.944867i	$-0.393809\pi$
$127$	7.38044	0.654908	0.327454	+	0.944867i	$0.393809\pi$
$128$	−1.00000	−0.0883883
$129$	21.4339	1.88715
$130$	−6.86234	−0.601867
$131$	4.91415	0.429351	0.214676	−	0.976685i	$-0.431131\pi$
$131$	4.91415	0.429351	0.214676	+	0.976685i	$0.431131\pi$
$132$	−8.58195	−0.746963
$133$	−20.9153	−1.81358
$134$	−0.893201	−0.0771608
$135$	−5.78680	−0.498049
$136$	3.80323	0.326124
$137$	−15.5631	−1.32965	−0.664823	−	0.747001i	$-0.731493\pi$
$137$	−15.5631	−1.32965	−0.664823	+	0.747001i	$0.731493\pi$
$138$	20.8985	1.77900
$139$	−8.50109	−0.721053	−0.360527	−	0.932749i	$-0.617403\pi$
$139$	−8.50109	−0.721053	−0.360527	+	0.932749i	$0.617403\pi$
$140$	6.79700	0.574451
$141$	−36.7381	−3.09391
$142$	1.57638	0.132287
$143$	13.2755	1.11015
$144$	4.30446	0.358705
$145$	11.6376	0.966450
$146$	5.46876	0.452598
$147$	−27.4260	−2.26206
$148$	10.2615	0.843486
$149$	−0.118245	−0.00968697	−0.00484349	−	0.999988i	$-0.501542\pi$
$149$	−0.118245	−0.00968697	−0.00484349	+	0.999988i	$0.501542\pi$
$150$	−6.23187	−0.508830
$151$	0.482007	0.0392251	0.0196126	−	0.999808i	$-0.493757\pi$
$151$	0.482007	0.0392251	0.0196126	+	0.999808i	$0.493757\pi$
$152$	5.05080	0.409674
$153$	−16.3709	−1.32350
$154$	−13.1491	−1.05958
$155$	15.4970	1.24475
$156$	−11.2993	−0.904670
$157$	−8.01657	−0.639792	−0.319896	−	0.947453i	$-0.603648\pi$
$157$	−8.01657	−0.639792	−0.319896	+	0.947453i	$0.603648\pi$
$158$	0.681247	0.0541971
$159$	26.8428	2.12877
$160$	−1.64140	−0.129764
$161$	32.0203	2.52355
$162$	3.38500	0.265951
$163$	12.9079	1.01102	0.505512	−	0.862820i	$-0.331304\pi$
$163$	12.9079	1.01102	0.505512	+	0.862820i	$0.331304\pi$
$164$	9.50741	0.742404
$165$	−14.0864	−1.09662
$166$	3.45940	0.268502
$167$	−13.2917	−1.02854	−0.514271	−	0.857628i	$-0.671937\pi$
$167$	−13.2917	−1.02854	−0.514271	+	0.857628i	$0.671937\pi$
$168$	11.1917	0.863461
$169$	4.47900	0.344539
$170$	6.24261	0.478786
$171$	−21.7410	−1.66257
$172$	−7.93060	−0.604703
$173$	−8.73222	−0.663899	−0.331949	−	0.943297i	$-0.607706\pi$
$173$	−8.73222	−0.663899	−0.331949	+	0.943297i	$0.607706\pi$
$174$	19.1621	1.45268
$175$	−9.54833	−0.721786
$176$	3.17535	0.239351
$177$	34.4796	2.59164
$178$	13.8379	1.03719
$179$	3.87770	0.289833	0.144916	−	0.989444i	$-0.453709\pi$
$179$	3.87770	0.289833	0.144916	+	0.989444i	$0.453709\pi$
$180$	7.06533	0.526619
$181$	24.2346	1.80135	0.900673	−	0.434498i	$-0.143074\pi$
$181$	24.2346	1.80135	0.900673	+	0.434498i	$0.143074\pi$
$182$	−17.3126	−1.28329
$183$	−9.00730	−0.665839
$184$	−7.73254	−0.570050
$185$	16.8431	1.23833
$186$	25.5169	1.87099
$187$	−12.0766	−0.883128
$188$	13.5932	0.991388
$189$	−14.5992	−1.06193
$190$	8.29037	0.601447
$191$	−1.54877	−0.112065	−0.0560324	−	0.998429i	$-0.517845\pi$
$191$	−1.54877	−0.112065	−0.0560324	+	0.998429i	$0.517845\pi$
$192$	−2.70268	−0.195049
$193$	−5.42572	−0.390552	−0.195276	−	0.980748i	$-0.562560\pi$
$193$	−5.42572	−0.390552	−0.195276	+	0.980748i	$0.562560\pi$
$194$	6.17063	0.443025
$195$	−18.5467	−1.32816
$196$	10.1477	0.724838
$197$	−15.7883	−1.12487	−0.562434	−	0.826843i	$-0.690135\pi$
$197$	−15.7883	−1.12487	−0.562434	+	0.826843i	$0.690135\pi$
$198$	−13.6682	−0.971355
$199$	−0.610108	−0.0432494	−0.0216247	−	0.999766i	$-0.506884\pi$
$199$	−0.610108	−0.0432494	−0.0216247	+	0.999766i	$0.506884\pi$
$200$	2.30581	0.163046
$201$	−2.41403	−0.170273
$202$	−9.99446	−0.703208
$203$	29.3598	2.06065
$204$	10.2789	0.719667
$205$	15.6054	1.08993
$206$	−15.5794	−1.08547
$207$	33.2844	2.31343
$208$	4.18079	0.289886
$209$	−16.0381	−1.10938
$210$	18.3701	1.26766
$211$	23.5296	1.61985	0.809923	−	0.586537i	$-0.199509\pi$
$211$	23.5296	1.61985	0.809923	+	0.586537i	$0.199509\pi$
$212$	−9.93192	−0.682127
$213$	4.26045	0.291921
$214$	6.83697	0.467366
$215$	−13.0173	−0.887770
$216$	3.52553	0.239882
$217$	39.0964	2.65404
$218$	−1.25995	−0.0853344
$219$	14.7803	0.998759
$220$	5.21201	0.351394
$221$	−15.9005	−1.06958
$222$	27.7334	1.86134
$223$	14.7075	0.984887	0.492443	−	0.870345i	$-0.336104\pi$
$223$	14.7075	0.984887	0.492443	+	0.870345i	$0.336104\pi$
$224$	−4.14098	−0.276681
$225$	−9.92529	−0.661686
$226$	1.76526	0.117424
$227$	−7.19462	−0.477524	−0.238762	−	0.971078i	$-0.576742\pi$
$227$	−7.19462	−0.477524	−0.238762	+	0.971078i	$0.576742\pi$
$228$	13.6507	0.904038
$229$	−12.5167	−0.827127	−0.413564	−	0.910475i	$-0.635716\pi$
$229$	−12.5167	−0.827127	−0.413564	+	0.910475i	$0.635716\pi$
$230$	−12.6922	−0.836896
$231$	−35.5377	−2.33821
$232$	−7.09006	−0.465485
$233$	−2.59938	−0.170291	−0.0851456	−	0.996369i	$-0.527136\pi$
$233$	−2.59938	−0.170291	−0.0851456	+	0.996369i	$0.527136\pi$
$234$	−17.9960	−1.17644
$235$	22.3119	1.45547
$236$	−12.7576	−0.830446
$237$	1.84119	0.119598
$238$	15.7491	1.02086
$239$	−16.0850	−1.04045	−0.520227	−	0.854028i	$-0.674153\pi$
$239$	−16.0850	−1.04045	−0.520227	+	0.854028i	$0.674153\pi$
$240$	−4.43617	−0.286353
$241$	25.9852	1.67386	0.836928	−	0.547314i	$-0.184350\pi$
$241$	25.9852	1.67386	0.836928	+	0.547314i	$0.184350\pi$
$242$	0.917146	0.0589564
$243$	19.7252	1.26537
$244$	3.33274	0.213356
$245$	16.6565	1.06414
$246$	25.6955	1.63828
$247$	−21.1163	−1.34360
$248$	−9.44135	−0.599526
$249$	9.34965	0.592510
$250$	11.9917	0.758425
$251$	−10.9622	−0.691930	−0.345965	−	0.938247i	$-0.612448\pi$
$251$	−10.9622	−0.691930	−0.345965	+	0.938247i	$0.612448\pi$
$252$	17.8247	1.12285
$253$	24.5535	1.54367
$254$	−7.38044	−0.463090
$255$	16.8718	1.05655
$256$	1.00000	0.0625000
$257$	−29.1646	−1.81924	−0.909618	−	0.415447i	$-0.863625\pi$
$257$	−29.1646	−1.81924	−0.909618	+	0.415447i	$0.863625\pi$
$258$	−21.4339	−1.33441
$259$	42.4925	2.64035
$260$	6.86234	0.425584
$261$	30.5189	1.88907
$262$	−4.91415	−0.303597
$263$	6.88526	0.424563	0.212282	−	0.977209i	$-0.431911\pi$
$263$	6.88526	0.424563	0.212282	+	0.977209i	$0.431911\pi$
$264$	8.58195	0.528182
$265$	−16.3022	−1.00144
$266$	20.9153	1.28240
$267$	37.3993	2.28880
$268$	0.893201	0.0545609
$269$	−9.40413	−0.573380	−0.286690	−	0.958023i	$-0.592555\pi$
$269$	−9.40413	−0.573380	−0.286690	+	0.958023i	$0.592555\pi$
$270$	5.78680	0.352174
$271$	27.7254	1.68420	0.842100	−	0.539322i	$-0.181319\pi$
$271$	27.7254	1.68420	0.842100	+	0.539322i	$0.181319\pi$
$272$	−3.80323	−0.230605
$273$	−46.7903	−2.83188
$274$	15.5631	0.940202
$275$	−7.32177	−0.441519
$276$	−20.8985	−1.25794
$277$	−28.0955	−1.68809	−0.844047	−	0.536269i	$-0.819833\pi$
$277$	−28.0955	−1.68809	−0.844047	+	0.536269i	$0.819833\pi$
$278$	8.50109	0.509862
$279$	40.6399	2.43305
$280$	−6.79700	−0.406198
$281$	−27.7128	−1.65321	−0.826605	−	0.562783i	$-0.809731\pi$
$281$	−27.7128	−1.65321	−0.826605	+	0.562783i	$0.809731\pi$
$282$	36.7381	2.18772
$283$	−21.3185	−1.26725	−0.633627	−	0.773639i	$-0.718435\pi$
$283$	−21.3185	−1.26725	−0.633627	+	0.773639i	$0.718435\pi$
$284$	−1.57638	−0.0935410
$285$	22.4062	1.32723
$286$	−13.2755	−0.784995
$287$	39.3700	2.32394
$288$	−4.30446	−0.253643
$289$	−2.53545	−0.149144
$290$	−11.6376	−0.683383
$291$	16.6772	0.977635
$292$	−5.46876	−0.320035
$293$	−11.6267	−0.679241	−0.339620	−	0.940563i	$-0.610299\pi$
$293$	−11.6267	−0.679241	−0.339620	+	0.940563i	$0.610299\pi$
$294$	27.4260	1.59952
$295$	−20.9402	−1.21919
$296$	−10.2615	−0.596435
$297$	−11.1948	−0.649589
$298$	0.118245	0.00684972
$299$	32.3281	1.86958
$300$	6.23187	0.359797
$301$	−32.8405	−1.89289
$302$	−0.482007	−0.0277364
$303$	−27.0118	−1.55179
$304$	−5.05080	−0.289683
$305$	5.47034	0.313231
$306$	16.3709	0.935859
$307$	−17.7955	−1.01564	−0.507821	−	0.861463i	$-0.669549\pi$
$307$	−17.7955	−1.01564	−0.507821	+	0.861463i	$0.669549\pi$
$308$	13.1491	0.749238
$309$	−42.1062	−2.39534
$310$	−15.4970	−0.880171
$311$	−4.42377	−0.250849	−0.125424	−	0.992103i	$-0.540029\pi$
$311$	−4.42377	−0.250849	−0.125424	+	0.992103i	$0.540029\pi$
$312$	11.2993	0.639698
$313$	−7.78261	−0.439899	−0.219949	−	0.975511i	$-0.570589\pi$
$313$	−7.78261	−0.439899	−0.219949	+	0.975511i	$0.570589\pi$
$314$	8.01657	0.452401
$315$	29.2574	1.64847
$316$	−0.681247	−0.0383231
$317$	−16.5898	−0.931778	−0.465889	−	0.884843i	$-0.654265\pi$
$317$	−16.5898	−0.931778	−0.465889	+	0.884843i	$0.654265\pi$
$318$	−26.8428	−1.50527
$319$	22.5134	1.26051
$320$	1.64140	0.0917569
$321$	18.4781	1.03135
$322$	−32.0203	−1.78442
$323$	19.2094	1.06884
$324$	−3.38500	−0.188056
$325$	−9.64013	−0.534738
$326$	−12.9079	−0.714902
$327$	−3.40523	−0.188310
$328$	−9.50741	−0.524959
$329$	56.2893	3.10333
$330$	14.0864	0.775430
$331$	−3.43510	−0.188810	−0.0944049	−	0.995534i	$-0.530095\pi$
$331$	−3.43510	−0.188810	−0.0944049	+	0.995534i	$0.530095\pi$
$332$	−3.45940	−0.189859
$333$	44.1700	2.42050
$334$	13.2917	0.727289
$335$	1.46610	0.0801015
$336$	−11.1917	−0.610559
$337$	1.27983	0.0697170	0.0348585	−	0.999392i	$-0.488902\pi$
$337$	1.27983	0.0697170	0.0348585	+	0.999392i	$0.488902\pi$
$338$	−4.47900	−0.243626
$339$	4.77094	0.259122
$340$	−6.24261	−0.338553
$341$	29.9796	1.62349
$342$	21.7410	1.17562
$343$	13.0347	0.703806
$344$	7.93060	0.427589
$345$	−34.3028	−1.84680
$346$	8.73222	0.469447
$347$	−8.99197	−0.482714	−0.241357	−	0.970436i	$-0.577593\pi$
$347$	−8.99197	−0.482714	−0.241357	+	0.970436i	$0.577593\pi$
$348$	−19.1621	−1.02720
$349$	27.8235	1.48936	0.744678	−	0.667424i	$-0.232603\pi$
$349$	27.8235	1.48936	0.744678	+	0.667424i	$0.232603\pi$
$350$	9.54833	0.510380
$351$	−14.7395	−0.786737
$352$	−3.17535	−0.169247
$353$	14.3888	0.765841	0.382920	−	0.923781i	$-0.374918\pi$
$353$	14.3888	0.765841	0.382920	+	0.923781i	$0.374918\pi$
$354$	−34.4796	−1.83257
$355$	−2.58747	−0.137329
$356$	−13.8379	−0.733407
$357$	42.5647	2.25276
$358$	−3.87770	−0.204943
$359$	−0.727095	−0.0383746	−0.0191873	−	0.999816i	$-0.506108\pi$
$359$	−0.727095	−0.0383746	−0.0191873	+	0.999816i	$0.506108\pi$
$360$	−7.06533	−0.372376
$361$	6.51059	0.342662
$362$	−24.2346	−1.27374
$363$	2.47875	0.130101
$364$	17.3126	0.907425
$365$	−8.97641	−0.469847
$366$	9.00730	0.470819
$367$	3.23630	0.168934	0.0844668	−	0.996426i	$-0.473081\pi$
$367$	3.23630	0.168934	0.0844668	+	0.996426i	$0.473081\pi$
$368$	7.73254	0.403086
$369$	40.9243	2.13043
$370$	−16.8431	−0.875632
$371$	−41.1279	−2.13525
$372$	−25.5169	−1.32299
$373$	−25.2213	−1.30591	−0.652955	−	0.757396i	$-0.726471\pi$
$373$	−25.2213	−1.30591	−0.652955	+	0.757396i	$0.726471\pi$
$374$	12.0766	0.624465
$375$	32.4098	1.67364
$376$	−13.5932	−0.701018
$377$	29.6420	1.52664
$378$	14.5992	0.750901
$379$	12.9770	0.666581	0.333291	−	0.942824i	$-0.391841\pi$
$379$	12.9770	0.666581	0.333291	+	0.942824i	$0.391841\pi$
$380$	−8.29037	−0.425287
$381$	−19.9469	−1.02191
$382$	1.54877	0.0792418
$383$	30.6257	1.56490	0.782449	−	0.622714i	$-0.213970\pi$
$383$	30.6257	1.56490	0.782449	+	0.622714i	$0.213970\pi$
$384$	2.70268	0.137920
$385$	21.5828	1.09996
$386$	5.42572	0.276162
$387$	−34.1370	−1.73528
$388$	−6.17063	−0.313266
$389$	−15.1975	−0.770544	−0.385272	−	0.922803i	$-0.625892\pi$
$389$	−15.1975	−0.770544	−0.385272	+	0.922803i	$0.625892\pi$
$390$	18.5467	0.939148
$391$	−29.4086	−1.48726
$392$	−10.1477	−0.512538
$393$	−13.2814	−0.669956
$394$	15.7883	0.795401
$395$	−1.11820	−0.0562626
$396$	13.6682	0.686852
$397$	12.0453	0.604537	0.302269	−	0.953223i	$-0.402256\pi$
$397$	12.0453	0.604537	0.302269	+	0.953223i	$0.402256\pi$
$398$	0.610108	0.0305819
$399$	56.5272	2.82990
$400$	−2.30581	−0.115291
$401$	−0.520654	−0.0260002	−0.0130001	−	0.999915i	$-0.504138\pi$
$401$	−0.520654	−0.0260002	−0.0130001	+	0.999915i	$0.504138\pi$
$402$	2.41403	0.120401
$403$	39.4723	1.96625
$404$	9.99446	0.497243
$405$	−5.55613	−0.276086
$406$	−29.3598	−1.45710
$407$	32.5837	1.61511
$408$	−10.2789	−0.508881
$409$	10.0158	0.495251	0.247626	−	0.968856i	$-0.420350\pi$
$409$	10.0158	0.495251	0.247626	+	0.968856i	$0.420350\pi$
$410$	−15.6054	−0.770698
$411$	42.0621	2.07477
$412$	15.5794	0.767544
$413$	−52.8288	−2.59954
$414$	−33.2844	−1.63584
$415$	−5.67826	−0.278735
$416$	−4.18079	−0.204980
$417$	22.9757	1.12512
$418$	16.0381	0.784447
$419$	20.3266	0.993021	0.496510	−	0.868031i	$-0.334614\pi$
$419$	20.3266	0.993021	0.496510	+	0.868031i	$0.334614\pi$
$420$	−18.3701	−0.896368
$421$	35.6935	1.73960	0.869798	−	0.493408i	$-0.164249\pi$
$421$	35.6935	1.73960	0.869798	+	0.493408i	$0.164249\pi$
$422$	−23.5296	−1.14540
$423$	58.5115	2.84493
$424$	9.93192	0.482337
$425$	8.76954	0.425385
$426$	−4.26045	−0.206419
$427$	13.8008	0.667867
$428$	−6.83697	−0.330478
$429$	−35.8793	−1.73227
$430$	13.0173	0.627748
$431$	8.27596	0.398639	0.199320	−	0.979935i	$-0.436127\pi$
$431$	8.27596	0.398639	0.199320	+	0.979935i	$0.436127\pi$
$432$	−3.52553	−0.169622
$433$	14.5639	0.699896	0.349948	−	0.936769i	$-0.386199\pi$
$433$	14.5639	0.699896	0.349948	+	0.936769i	$0.386199\pi$
$434$	−39.0964	−1.87669
$435$	−31.4527	−1.50804
$436$	1.25995	0.0603405
$437$	−39.0555	−1.86828
$438$	−14.7803	−0.706229
$439$	14.8289	0.707743	0.353872	−	0.935294i	$-0.384865\pi$
$439$	14.8289	0.707743	0.353872	+	0.935294i	$0.384865\pi$
$440$	−5.21201	−0.248473
$441$	43.6805	2.08002
$442$	15.9005	0.756310
$443$	34.0793	1.61916	0.809578	−	0.587012i	$-0.199696\pi$
$443$	34.0793	1.61916	0.809578	+	0.587012i	$0.199696\pi$
$444$	−27.7334	−1.31617
$445$	−22.7135	−1.07672
$446$	−14.7075	−0.696420
$447$	0.319577	0.0151155
$448$	4.14098	0.195643
$449$	−35.9264	−1.69547	−0.847735	−	0.530419i	$-0.822034\pi$
$449$	−35.9264	−1.69547	−0.847735	+	0.530419i	$0.822034\pi$
$450$	9.92529	0.467883
$451$	30.1894	1.42156
$452$	−1.76526	−0.0830310
$453$	−1.30271	−0.0612066
$454$	7.19462	0.337660
$455$	28.4168	1.33220
$456$	−13.6507	−0.639252
$457$	−32.5816	−1.52410	−0.762051	−	0.647517i	$-0.775807\pi$
$457$	−32.5816	−1.52410	−0.762051	+	0.647517i	$0.775807\pi$
$458$	12.5167	0.584867
$459$	13.4084	0.625851
$460$	12.6922	0.591775
$461$	−6.66621	−0.310476	−0.155238	−	0.987877i	$-0.549614\pi$
$461$	−6.66621	−0.310476	−0.155238	+	0.987877i	$0.549614\pi$
$462$	35.5377	1.65336
$463$	−6.84971	−0.318333	−0.159167	−	0.987252i	$-0.550881\pi$
$463$	−6.84971	−0.318333	−0.159167	+	0.987252i	$0.550881\pi$
$464$	7.09006	0.329148
$465$	−41.8834	−1.94230
$466$	2.59938	0.120414
$467$	8.80627	0.407506	0.203753	−	0.979022i	$-0.434686\pi$
$467$	8.80627	0.407506	0.203753	+	0.979022i	$0.434686\pi$
$468$	17.9960	0.831867
$469$	3.69873	0.170791
$470$	−22.3119	−1.02917
$471$	21.6662	0.998326
$472$	12.7576	0.587214
$473$	−25.1824	−1.15789
$474$	−1.84119	−0.0845686
$475$	11.6462	0.534365
$476$	−15.7491	−0.721859
$477$	−42.7516	−1.95746
$478$	16.0850	0.735712
$479$	20.7096	0.946247	0.473123	−	0.880996i	$-0.343126\pi$
$479$	20.7096	0.946247	0.473123	+	0.880996i	$0.343126\pi$
$480$	4.43617	0.202482
$481$	42.9010	1.95612
$482$	−25.9852	−1.18359
$483$	−86.5405	−3.93773
$484$	−0.917146	−0.0416885
$485$	−10.1284	−0.459909
$486$	−19.7252	−0.894752
$487$	11.6678	0.528718	0.264359	−	0.964424i	$-0.414840\pi$
$487$	11.6678	0.528718	0.264359	+	0.964424i	$0.414840\pi$
$488$	−3.33274	−0.150866
$489$	−34.8858	−1.57759
$490$	−16.6565	−0.752462
$491$	3.47808	0.156964	0.0784818	−	0.996916i	$-0.474993\pi$
$491$	3.47808	0.156964	0.0784818	+	0.996916i	$0.474993\pi$
$492$	−25.6955	−1.15844
$493$	−26.9651	−1.21445
$494$	21.1163	0.950069
$495$	22.4349	1.00837
$496$	9.44135	0.423929
$497$	−6.52777	−0.292810
$498$	−9.34965	−0.418968
$499$	−17.2059	−0.770244	−0.385122	−	0.922866i	$-0.625841\pi$
$499$	−17.2059	−0.770244	−0.385122	+	0.922866i	$0.625841\pi$
$500$	−11.9917	−0.536287
$501$	35.9231	1.60493
$502$	10.9622	0.489269
$503$	34.0954	1.52024	0.760119	−	0.649784i	$-0.225141\pi$
$503$	34.0954	1.52024	0.760119	+	0.649784i	$0.225141\pi$
$504$	−17.8247	−0.793975
$505$	16.4049	0.730008
$506$	−24.5535	−1.09154
$507$	−12.1053	−0.537615
$508$	7.38044	0.327454
$509$	36.7991	1.63109	0.815545	−	0.578694i	$-0.196437\pi$
$509$	36.7991	1.63109	0.815545	+	0.578694i	$0.196437\pi$
$510$	−16.8718	−0.747094
$511$	−22.6460	−1.00180
$512$	−1.00000	−0.0441942
$513$	17.8068	0.786188
$514$	29.1646	1.28639
$515$	25.5720	1.12684
$516$	21.4339	0.943573
$517$	43.1633	1.89832
$518$	−42.4925	−1.86701
$519$	23.6004	1.03594
$520$	−6.86234	−0.300933
$521$	26.3713	1.15535	0.577673	−	0.816268i	$-0.303961\pi$
$521$	26.3713	1.15535	0.577673	+	0.816268i	$0.303961\pi$
$522$	−30.5189	−1.33577
$523$	−2.00700	−0.0877600	−0.0438800	−	0.999037i	$-0.513972\pi$
$523$	−2.00700	−0.0877600	−0.0438800	+	0.999037i	$0.513972\pi$
$524$	4.91415	0.214676
$525$	25.8061	1.12627
$526$	−6.88526	−0.300211
$527$	−35.9076	−1.56416
$528$	−8.58195	−0.373481
$529$	36.7921	1.59966
$530$	16.3022	0.708123
$531$	−54.9144	−2.38308
$532$	−20.9153	−0.906792
$533$	39.7485	1.72170
$534$	−37.3993	−1.61843
$535$	−11.2222	−0.485178
$536$	−0.893201	−0.0385804
$537$	−10.4802	−0.452253
$538$	9.40413	0.405441
$539$	32.2226	1.38793
$540$	−5.78680	−0.249024
$541$	16.6489	0.715792	0.357896	−	0.933762i	$-0.383494\pi$
$541$	16.6489	0.715792	0.357896	+	0.933762i	$0.383494\pi$
$542$	−27.7254	−1.19091
$543$	−65.4984	−2.81080
$544$	3.80323	0.163062
$545$	2.06807	0.0885865
$546$	46.7903	2.00244
$547$	34.3296	1.46783	0.733913	−	0.679243i	$-0.237692\pi$
$547$	34.3296	1.46783	0.733913	+	0.679243i	$0.237692\pi$
$548$	−15.5631	−0.664823
$549$	14.3456	0.612256
$550$	7.32177	0.312201
$551$	−35.8105	−1.52558
$552$	20.8985	0.889501
$553$	−2.82103	−0.119962
$554$	28.0955	1.19366
$555$	−45.5215	−1.93228
$556$	−8.50109	−0.360527
$557$	−17.5178	−0.742254	−0.371127	−	0.928582i	$-0.621029\pi$
$557$	−17.5178	−0.742254	−0.371127	+	0.928582i	$0.621029\pi$
$558$	−40.6399	−1.72042
$559$	−33.1562	−1.40236
$560$	6.79700	0.287226
$561$	32.6391	1.37802
$562$	27.7128	1.16900
$563$	−0.963006	−0.0405858	−0.0202929	−	0.999794i	$-0.506460\pi$
$563$	−0.963006	−0.0405858	−0.0202929	+	0.999794i	$0.506460\pi$
$564$	−36.7381	−1.54695
$565$	−2.89750	−0.121899
$566$	21.3185	0.896084
$567$	−14.0172	−0.588668
$568$	1.57638	0.0661435
$569$	6.33908	0.265748	0.132874	−	0.991133i	$-0.457579\pi$
$569$	6.33908	0.265748	0.132874	+	0.991133i	$0.457579\pi$
$570$	−22.4062	−0.938492
$571$	−26.0070	−1.08836	−0.544180	−	0.838968i	$-0.683159\pi$
$571$	−26.0070	−1.08836	−0.544180	+	0.838968i	$0.683159\pi$
$572$	13.2755	0.555076
$573$	4.18581	0.174865
$574$	−39.3700	−1.64327
$575$	−17.8298	−0.743554
$576$	4.30446	0.179353
$577$	−45.6963	−1.90236	−0.951181	−	0.308633i	$-0.900128\pi$
$577$	−45.6963	−1.90236	−0.951181	+	0.308633i	$0.900128\pi$
$578$	2.53545	0.105461
$579$	14.6640	0.609414
$580$	11.6376	0.483225
$581$	−14.3253	−0.594315
$582$	−16.6772	−0.691292
$583$	−31.5373	−1.30614
$584$	5.46876	0.226299
$585$	29.5387	1.22127
$586$	11.6267	0.480296
$587$	−7.17959	−0.296333	−0.148167	−	0.988962i	$-0.547337\pi$
$587$	−7.17959	−0.296333	−0.148167	+	0.988962i	$0.547337\pi$
$588$	−27.4260	−1.13103
$589$	−47.6864	−1.96488
$590$	20.9402	0.862095
$591$	42.6706	1.75523
$592$	10.2615	0.421743
$593$	14.3585	0.589635	0.294817	−	0.955554i	$-0.404741\pi$
$593$	14.3585	0.589635	0.294817	+	0.955554i	$0.404741\pi$
$594$	11.1948	0.459329
$595$	−25.8505	−1.05977
$596$	−0.118245	−0.00484349
$597$	1.64892	0.0674860
$598$	−32.3281	−1.32199
$599$	14.5067	0.592728	0.296364	−	0.955075i	$-0.404226\pi$
$599$	14.5067	0.592728	0.296364	+	0.955075i	$0.404226\pi$
$600$	−6.23187	−0.254415
$601$	1.97223	0.0804490	0.0402245	−	0.999191i	$-0.487193\pi$
$601$	1.97223	0.0804490	0.0402245	+	0.999191i	$0.487193\pi$
$602$	32.8405	1.33848
$603$	3.84475	0.156570
$604$	0.482007	0.0196126
$605$	−1.50540	−0.0612033
$606$	27.0118	1.09728
$607$	−18.0881	−0.734174	−0.367087	−	0.930187i	$-0.619645\pi$
$607$	−18.0881	−0.734174	−0.367087	+	0.930187i	$0.619645\pi$
$608$	5.05080	0.204837
$609$	−79.3500	−3.21542
$610$	−5.47034	−0.221488
$611$	56.8305	2.29911
$612$	−16.3709	−0.661752
$613$	20.5059	0.828227	0.414114	−	0.910225i	$-0.364092\pi$
$613$	20.5059	0.828227	0.414114	+	0.910225i	$0.364092\pi$
$614$	17.7955	0.718167
$615$	−42.1765	−1.70072
$616$	−13.1491	−0.529791
$617$	18.0173	0.725350	0.362675	−	0.931916i	$-0.381864\pi$
$617$	18.0173	0.725350	0.362675	+	0.931916i	$0.381864\pi$
$618$	42.1062	1.69376
$619$	29.2420	1.17534	0.587668	−	0.809102i	$-0.300046\pi$
$619$	29.2420	1.17534	0.587668	+	0.809102i	$0.300046\pi$
$620$	15.4970	0.622375
$621$	−27.2613	−1.09396
$622$	4.42377	0.177377
$623$	−57.3024	−2.29577
$624$	−11.2993	−0.452335
$625$	−8.15415	−0.326166
$626$	7.78261	0.311056
$627$	43.3457	1.73106
$628$	−8.01657	−0.319896
$629$	−39.0267	−1.55609
$630$	−29.2574	−1.16564
$631$	8.92482	0.355292	0.177646	−	0.984094i	$-0.443152\pi$
$631$	8.92482	0.355292	0.177646	+	0.984094i	$0.443152\pi$
$632$	0.681247	0.0270985
$633$	−63.5929	−2.52759
$634$	16.5898	0.658866
$635$	12.1142	0.480739
$636$	26.8428	1.06438
$637$	42.4255	1.68096
$638$	−22.5134	−0.891315
$639$	−6.78547	−0.268429
$640$	−1.64140	−0.0648819
$641$	40.7633	1.61005	0.805027	−	0.593238i	$-0.202151\pi$
$641$	40.7633	1.61005	0.805027	+	0.593238i	$0.202151\pi$
$642$	−18.4781	−0.729274
$643$	−10.3749	−0.409145	−0.204573	−	0.978851i	$-0.565580\pi$
$643$	−10.3749	−0.409145	−0.204573	+	0.978851i	$0.565580\pi$
$644$	32.0203	1.26178
$645$	35.1815	1.38527
$646$	−19.2094	−0.755782
$647$	7.99512	0.314321	0.157160	−	0.987573i	$-0.449766\pi$
$647$	7.99512	0.314321	0.157160	+	0.987573i	$0.449766\pi$
$648$	3.38500	0.132975
$649$	−40.5097	−1.59015
$650$	9.64013	0.378117
$651$	−105.665	−4.14134
$652$	12.9079	0.505512
$653$	−32.0268	−1.25331	−0.626653	−	0.779299i	$-0.715575\pi$
$653$	−32.0268	−1.25331	−0.626653	+	0.779299i	$0.715575\pi$
$654$	3.40523	0.133155
$655$	8.06607	0.315167
$656$	9.50741	0.371202
$657$	−23.5401	−0.918385
$658$	−56.2893	−2.19439
$659$	7.29304	0.284096	0.142048	−	0.989860i	$-0.454631\pi$
$659$	7.29304	0.284096	0.142048	+	0.989860i	$0.454631\pi$
$660$	−14.0864	−0.548312
$661$	−15.6017	−0.606835	−0.303417	−	0.952858i	$-0.598128\pi$
$661$	−15.6017	−0.606835	−0.303417	+	0.952858i	$0.598128\pi$
$662$	3.43510	0.133509
$663$	42.9739	1.66897
$664$	3.45940	0.134251
$665$	−34.3303	−1.33127
$666$	−44.1700	−1.71155
$667$	54.8241	2.12280
$668$	−13.2917	−0.514271
$669$	−39.7496	−1.53681
$670$	−1.46610	−0.0566403
$671$	10.5826	0.408537
$672$	11.1917	0.431730
$673$	17.8830	0.689339	0.344669	−	0.938724i	$-0.387991\pi$
$673$	17.8830	0.689339	0.344669	+	0.938724i	$0.387991\pi$
$674$	−1.27983	−0.0492974
$675$	8.12923	0.312894
$676$	4.47900	0.172269
$677$	28.5188	1.09607	0.548034	−	0.836456i	$-0.315376\pi$
$677$	28.5188	1.09607	0.548034	+	0.836456i	$0.315376\pi$
$678$	−4.77094	−0.183227
$679$	−25.5524	−0.980613
$680$	6.24261	0.239393
$681$	19.4447	0.745124
$682$	−29.9796	−1.14798
$683$	−31.0663	−1.18872	−0.594360	−	0.804199i	$-0.702595\pi$
$683$	−31.0663	−1.18872	−0.594360	+	0.804199i	$0.702595\pi$
$684$	−21.7410	−0.831287
$685$	−25.5453	−0.976034
$686$	−13.0347	−0.497666
$687$	33.8286	1.29064
$688$	−7.93060	−0.302351
$689$	−41.5233	−1.58191
$690$	34.3028	1.30589
$691$	−51.0355	−1.94148	−0.970742	−	0.240126i	$-0.922811\pi$
$691$	−51.0355	−1.94148	−0.970742	+	0.240126i	$0.922811\pi$
$692$	−8.73222	−0.331949
$693$	56.5996	2.15004
$694$	8.99197	0.341330
$695$	−13.9537	−0.529293
$696$	19.1621	0.726339
$697$	−36.1589	−1.36961
$698$	−27.8235	−1.05313
$699$	7.02529	0.265721
$700$	−9.54833	−0.360893
$701$	−28.6312	−1.08139	−0.540693	−	0.841220i	$-0.681838\pi$
$701$	−28.6312	−1.08139	−0.540693	+	0.841220i	$0.681838\pi$
$702$	14.7395	0.556307
$703$	−51.8285	−1.95475
$704$	3.17535	0.119676
$705$	−60.3018	−2.27110
$706$	−14.3888	−0.541531
$707$	41.3869	1.55651
$708$	34.4796	1.29582
$709$	10.5833	0.397466	0.198733	−	0.980054i	$-0.436317\pi$
$709$	10.5833	0.397466	0.198733	+	0.980054i	$0.436317\pi$
$710$	2.58747	0.0971060
$711$	−2.93240	−0.109974
$712$	13.8379	0.518597
$713$	73.0055	2.73408
$714$	−42.5647	−1.59294
$715$	21.7903	0.814912
$716$	3.87770	0.144916
$717$	43.4726	1.62351
$718$	0.727095	0.0271349
$719$	−36.9312	−1.37730	−0.688651	−	0.725093i	$-0.741797\pi$
$719$	−36.9312	−1.37730	−0.688651	+	0.725093i	$0.741797\pi$
$720$	7.06533	0.263309
$721$	64.5142	2.40263
$722$	−6.51059	−0.242299
$723$	−70.2296	−2.61187
$724$	24.2346	0.900673
$725$	−16.3484	−0.607163
$726$	−2.47875	−0.0919950
$727$	29.2653	1.08539	0.542695	−	0.839930i	$-0.317404\pi$
$727$	29.2653	1.08539	0.542695	+	0.839930i	$0.317404\pi$
$728$	−17.3126	−0.641647
$729$	−43.1557	−1.59836
$730$	8.97641	0.332232
$731$	30.1619	1.11558
$732$	−9.00730	−0.332920
$733$	32.8149	1.21205	0.606023	−	0.795447i	$-0.292764\pi$
$733$	32.8149	1.21205	0.606023	+	0.795447i	$0.292764\pi$
$734$	−3.23630	−0.119454
$735$	−45.0170	−1.66048
$736$	−7.73254	−0.285025
$737$	2.83623	0.104474
$738$	−40.9243	−1.50644
$739$	1.88010	0.0691606	0.0345803	−	0.999402i	$-0.488991\pi$
$739$	1.88010	0.0691606	0.0345803	+	0.999402i	$0.488991\pi$
$740$	16.8431	0.619165
$741$	57.0706	2.09654
$742$	41.1279	1.50985
$743$	25.8317	0.947673	0.473837	−	0.880613i	$-0.342869\pi$
$743$	25.8317	0.947673	0.473837	+	0.880613i	$0.342869\pi$
$744$	25.5169	0.935495
$745$	−0.194086	−0.00711077
$746$	25.2213	0.923418
$747$	−14.8909	−0.544828
$748$	−12.0766	−0.441564
$749$	−28.3118	−1.03449
$750$	−32.4098	−1.18344
$751$	8.62721	0.314811	0.157406	−	0.987534i	$-0.449687\pi$
$751$	8.62721	0.314811	0.157406	+	0.987534i	$0.449687\pi$
$752$	13.5932	0.495694
$753$	29.6274	1.07968
$754$	−29.6420	−1.07950
$755$	0.791164	0.0287934
$756$	−14.5992	−0.530967
$757$	25.2061	0.916132	0.458066	−	0.888918i	$-0.348542\pi$
$757$	25.2061	0.916132	0.458066	+	0.888918i	$0.348542\pi$
$758$	−12.9770	−0.471344
$759$	−66.3602	−2.40872
$760$	8.29037	0.300723
$761$	−28.2181	−1.02291	−0.511453	−	0.859311i	$-0.670893\pi$
$761$	−28.2181	−1.02291	−0.511453	+	0.859311i	$0.670893\pi$
$762$	19.9469	0.722602
$763$	5.21742	0.188883
$764$	−1.54877	−0.0560324
$765$	−26.8711	−0.971526
$766$	−30.6257	−1.10655
$767$	−53.3367	−1.92588
$768$	−2.70268	−0.0975244
$769$	−26.8955	−0.969877	−0.484938	−	0.874548i	$-0.661158\pi$
$769$	−26.8955	−0.969877	−0.484938	+	0.874548i	$0.661158\pi$
$770$	−21.5828	−0.777792
$771$	78.8224	2.83872
$772$	−5.42572	−0.195276
$773$	3.84257	0.138207	0.0691037	−	0.997609i	$-0.477986\pi$
$773$	3.84257	0.138207	0.0691037	+	0.997609i	$0.477986\pi$
$774$	34.1370	1.22703
$775$	−21.7700	−0.782001
$776$	6.17063	0.221513
$777$	−114.843	−4.11999
$778$	15.1975	0.544857
$779$	−48.0200	−1.72050
$780$	−18.5467	−0.664078
$781$	−5.00556	−0.179113
$782$	29.4086	1.05165
$783$	−24.9962	−0.893293
$784$	10.1477	0.362419
$785$	−13.1584	−0.469643
$786$	13.2814	0.473730
$787$	−35.4185	−1.26253	−0.631266	−	0.775566i	$-0.717465\pi$
$787$	−35.4185	−1.26253	−0.631266	+	0.775566i	$0.717465\pi$
$788$	−15.7883	−0.562434
$789$	−18.6086	−0.662484
$790$	1.11820	0.0397837
$791$	−7.30993	−0.259911
$792$	−13.6682	−0.485677
$793$	13.9335	0.494792
$794$	−12.0453	−0.427472
$795$	44.0596	1.56263
$796$	−0.610108	−0.0216247
$797$	0.935175	0.0331256	0.0165628	−	0.999863i	$-0.494728\pi$
$797$	0.935175	0.0331256	0.0165628	+	0.999863i	$0.494728\pi$
$798$	−56.5272	−2.00104
$799$	−51.6982	−1.82895
$800$	2.30581	0.0815229
$801$	−59.5646	−2.10461
$802$	0.520654	0.0183849
$803$	−17.3652	−0.612806
$804$	−2.41403	−0.0851364
$805$	52.5580	1.85243
$806$	−39.4723	−1.39035
$807$	25.4163	0.894697
$808$	−9.99446	−0.351604
$809$	27.8481	0.979088	0.489544	−	0.871979i	$-0.337163\pi$
$809$	27.8481	0.979088	0.489544	+	0.871979i	$0.337163\pi$
$810$	5.55613	0.195223
$811$	−10.7672	−0.378087	−0.189044	−	0.981969i	$-0.560539\pi$
$811$	−10.7672	−0.378087	−0.189044	+	0.981969i	$0.560539\pi$
$812$	29.3598	1.03033
$813$	−74.9329	−2.62801
$814$	−32.5837	−1.14206
$815$	21.1870	0.742147
$816$	10.2789	0.359833
$817$	40.0559	1.40138
$818$	−10.0158	−0.350196
$819$	74.5213	2.60398
$820$	15.6054	0.544966
$821$	17.0004	0.593317	0.296658	−	0.954984i	$-0.404128\pi$
$821$	17.0004	0.593317	0.296658	+	0.954984i	$0.404128\pi$
$822$	−42.0621	−1.46708
$823$	7.82072	0.272613	0.136307	−	0.990667i	$-0.456477\pi$
$823$	7.82072	0.272613	0.136307	+	0.990667i	$0.456477\pi$
$824$	−15.5794	−0.542735
$825$	19.7884	0.688943
$826$	52.8288	1.83815
$827$	−56.7903	−1.97479	−0.987396	−	0.158267i	$-0.949409\pi$
$827$	−56.7903	−1.97479	−0.987396	+	0.158267i	$0.949409\pi$
$828$	33.2844	1.15671
$829$	44.4805	1.54487	0.772436	−	0.635093i	$-0.219038\pi$
$829$	44.4805	1.54487	0.772436	+	0.635093i	$0.219038\pi$
$830$	5.67826	0.197095
$831$	75.9330	2.63409
$832$	4.18079	0.144943
$833$	−38.5941	−1.33721
$834$	−22.9757	−0.795583
$835$	−21.8169	−0.755006
$836$	−16.0381	−0.554688
$837$	−33.2858	−1.15053
$838$	−20.3266	−0.702172
$839$	8.15661	0.281597	0.140799	−	0.990038i	$-0.455033\pi$
$839$	8.15661	0.281597	0.140799	+	0.990038i	$0.455033\pi$
$840$	18.3701	0.633828
$841$	21.2689	0.733410
$842$	−35.6935	−1.23008
$843$	74.8988	2.57965
$844$	23.5296	0.809923
$845$	7.35183	0.252911
$846$	−58.5115	−2.01167
$847$	−3.79789	−0.130497
$848$	−9.93192	−0.341063
$849$	57.6170	1.97741
$850$	−8.76954	−0.300793
$851$	79.3470	2.71998
$852$	4.26045	0.145961
$853$	6.40166	0.219189	0.109594	−	0.993976i	$-0.465045\pi$
$853$	6.40166	0.219189	0.109594	+	0.993976i	$0.465045\pi$
$854$	−13.8008	−0.472253
$855$	−35.6856	−1.22042
$856$	6.83697	0.233683
$857$	26.9623	0.921014	0.460507	−	0.887656i	$-0.347668\pi$
$857$	26.9623	0.921014	0.460507	+	0.887656i	$0.347668\pi$
$858$	35.8793	1.22490
$859$	−32.3126	−1.10249	−0.551246	−	0.834343i	$-0.685847\pi$
$859$	−32.3126	−1.10249	−0.551246	+	0.834343i	$0.685847\pi$
$860$	−13.0173	−0.443885
$861$	−106.404	−3.62625
$862$	−8.27596	−0.281880
$863$	21.8527	0.743876	0.371938	−	0.928258i	$-0.378693\pi$
$863$	21.8527	0.743876	0.371938	+	0.928258i	$0.378693\pi$
$864$	3.52553	0.119941
$865$	−14.3330	−0.487338
$866$	−14.5639	−0.494901
$867$	6.85249	0.232723
$868$	39.0964	1.32702
$869$	−2.16320	−0.0733815
$870$	31.4527	1.06635
$871$	3.73428	0.126531
$872$	−1.25995	−0.0426672
$873$	−26.5612	−0.898961
$874$	39.0555	1.32107
$875$	−49.6576	−1.67873
$876$	14.7803	0.499380
$877$	−2.58133	−0.0871653	−0.0435827	−	0.999050i	$-0.513877\pi$
$877$	−2.58133	−0.0871653	−0.0435827	+	0.999050i	$0.513877\pi$
$878$	−14.8289	−0.500450
$879$	31.4233	1.05988
$880$	5.21201	0.175697
$881$	5.35735	0.180494	0.0902468	−	0.995919i	$-0.471234\pi$
$881$	5.35735	0.180494	0.0902468	+	0.995919i	$0.471234\pi$
$882$	−43.6805	−1.47080
$883$	−43.0159	−1.44760	−0.723801	−	0.690009i	$-0.757606\pi$
$883$	−43.0159	−1.44760	−0.723801	+	0.690009i	$0.757606\pi$
$884$	−15.9005	−0.534792
$885$	56.5947	1.90241
$886$	−34.0793	−1.14492
$887$	−21.5379	−0.723171	−0.361586	−	0.932339i	$-0.617764\pi$
$887$	−21.5379	−0.723171	−0.361586	+	0.932339i	$0.617764\pi$
$888$	27.7334	0.930671
$889$	30.5623	1.02503
$890$	22.7135	0.761357
$891$	−10.7486	−0.360091
$892$	14.7075	0.492443
$893$	−68.6567	−2.29751
$894$	−0.319577	−0.0106882
$895$	6.36485	0.212753
$896$	−4.14098	−0.138340
$897$	−87.3724	−2.91728
$898$	35.9264	1.19888
$899$	66.9397	2.23256
$900$	−9.92529	−0.330843
$901$	37.7734	1.25841
$902$	−30.1894	−1.00520
$903$	88.7572	2.95365
$904$	1.76526	0.0587118
$905$	39.7787	1.32229
$906$	1.30271	0.0432796
$907$	−36.8217	−1.22265	−0.611323	−	0.791381i	$-0.709362\pi$
$907$	−36.8217	−1.22265	−0.611323	+	0.791381i	$0.709362\pi$
$908$	−7.19462	−0.238762
$909$	43.0208	1.42691
$910$	−28.4168	−0.942008
$911$	−2.96077	−0.0980947	−0.0490473	−	0.998796i	$-0.515619\pi$
$911$	−2.96077	−0.0980947	−0.0490473	+	0.998796i	$0.515619\pi$
$912$	13.6507	0.452019
$913$	−10.9848	−0.363544
$914$	32.5816	1.07770
$915$	−14.7846	−0.488763
$916$	−12.5167	−0.413564
$917$	20.3494	0.671996
$918$	−13.4084	−0.442544
$919$	−29.4927	−0.972876	−0.486438	−	0.873715i	$-0.661704\pi$
$919$	−29.4927	−0.972876	−0.486438	+	0.873715i	$0.661704\pi$
$920$	−12.6922	−0.418448
$921$	48.0954	1.58480
$922$	6.66621	0.219540
$923$	−6.59052	−0.216930
$924$	−35.5377	−1.16910
$925$	−23.6610	−0.777969
$926$	6.84971	0.225096
$927$	67.0611	2.20257
$928$	−7.09006	−0.232742
$929$	20.7236	0.679921	0.339960	−	0.940440i	$-0.389586\pi$
$929$	20.7236	0.679921	0.339960	+	0.940440i	$0.389586\pi$
$930$	41.8834	1.37341
$931$	−51.2541	−1.67979
$932$	−2.59938	−0.0851456
$933$	11.9560	0.391422
$934$	−8.80627	−0.288150
$935$	−19.8225	−0.648264
$936$	−17.9960	−0.588219
$937$	−38.9075	−1.27105	−0.635526	−	0.772080i	$-0.719217\pi$
$937$	−38.9075	−1.27105	−0.635526	+	0.772080i	$0.719217\pi$
$938$	−3.69873	−0.120768
$939$	21.0339	0.686414
$940$	22.3119	0.727734
$941$	−24.6031	−0.802037	−0.401018	−	0.916070i	$-0.631344\pi$
$941$	−24.6031	−0.802037	−0.401018	+	0.916070i	$0.631344\pi$
$942$	−21.6662	−0.705923
$943$	73.5164	2.39402
$944$	−12.7576	−0.415223
$945$	−23.9630	−0.779518
$946$	25.1824	0.818752
$947$	−12.5736	−0.408587	−0.204293	−	0.978910i	$-0.565490\pi$
$947$	−12.5736	−0.408587	−0.204293	+	0.978910i	$0.565490\pi$
$948$	1.84119	0.0597991
$949$	−22.8637	−0.742188
$950$	−11.6462	−0.377853
$951$	44.8369	1.45394
$952$	15.7491	0.510431
$953$	−54.0211	−1.74992	−0.874958	−	0.484198i	$-0.839111\pi$
$953$	−54.0211	−1.74992	−0.874958	+	0.484198i	$0.839111\pi$
$954$	42.7516	1.38413
$955$	−2.54214	−0.0822617
$956$	−16.0850	−0.520227
$957$	−60.8465	−1.96689
$958$	−20.7096	−0.669098
$959$	−64.4466	−2.08109
$960$	−4.43617	−0.143177
$961$	58.1390	1.87545
$962$	−42.9010	−1.38318
$963$	−29.4295	−0.948352
$964$	25.9852	0.836928
$965$	−8.90577	−0.286687
$966$	86.5405	2.78439
$967$	30.3300	0.975349	0.487674	−	0.873026i	$-0.337845\pi$
$967$	30.3300	0.975349	0.487674	+	0.873026i	$0.337845\pi$
$968$	0.917146	0.0294782
$969$	−51.9167	−1.66780
$970$	10.1284	0.325205
$971$	24.0492	0.771776	0.385888	−	0.922546i	$-0.373895\pi$
$971$	24.0492	0.771776	0.385888	+	0.922546i	$0.373895\pi$
$972$	19.7252	0.632685
$973$	−35.2029	−1.12855
$974$	−11.6678	−0.373860
$975$	26.0541	0.834400
$976$	3.33274	0.106678
$977$	−46.0912	−1.47459	−0.737295	−	0.675571i	$-0.763897\pi$
$977$	−46.0912	−1.47459	−0.737295	+	0.675571i	$0.763897\pi$
$978$	34.8858	1.11553
$979$	−43.9402	−1.40433
$980$	16.6565	0.532071
$981$	5.42339	0.173156
$982$	−3.47808	−0.110990
$983$	38.9671	1.24286	0.621428	−	0.783471i	$-0.286553\pi$
$983$	38.9671	1.24286	0.621428	+	0.783471i	$0.286553\pi$
$984$	25.6955	0.819141
$985$	−25.9148	−0.825715
$986$	26.9651	0.858744
$987$	−152.132	−4.84241
$988$	−21.1163	−0.671800
$989$	−61.3237	−1.94998
$990$	−22.4349	−0.713028
$991$	54.0184	1.71595	0.857976	−	0.513690i	$-0.171722\pi$
$991$	54.0184	1.71595	0.857976	+	0.513690i	$0.171722\pi$
$992$	−9.44135	−0.299763
$993$	9.28395	0.294617
$994$	6.52777	0.207048
$995$	−1.00143	−0.0317474
$996$	9.34965	0.296255
$997$	24.5561	0.777699	0.388850	−	0.921301i	$-0.372873\pi$
$997$	24.5561	0.777699	0.388850	+	0.921301i	$0.372873\pi$
$998$	17.2059	0.544645
$999$	−36.1771	−1.14459

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4034.2.a.c.1.7	✓	49

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4034.2.a.c.1.7	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.70268 q^{3} +1.00000 q^{4} +1.64140 q^{5} +2.70268 q^{6} +4.14098 q^{7} -1.00000 q^{8} +4.30446 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.70268 q^{3} +1.00000 q^{4} +1.64140 q^{5} +2.70268 q^{6} +4.14098 q^{7} -1.00000 q^{8} +4.30446 q^{9} -1.64140 q^{10} +3.17535 q^{11} -2.70268 q^{12} +4.18079 q^{13} -4.14098 q^{14} -4.43617 q^{15} +1.00000 q^{16} -3.80323 q^{17} -4.30446 q^{18} -5.05080 q^{19} +1.64140 q^{20} -11.1917 q^{21} -3.17535 q^{22} +7.73254 q^{23} +2.70268 q^{24} -2.30581 q^{25} -4.18079 q^{26} -3.52553 q^{27} +4.14098 q^{28} +7.09006 q^{29} +4.43617 q^{30} +9.44135 q^{31} -1.00000 q^{32} -8.58195 q^{33} +3.80323 q^{34} +6.79700 q^{35} +4.30446 q^{36} +10.2615 q^{37} +5.05080 q^{38} -11.2993 q^{39} -1.64140 q^{40} +9.50741 q^{41} +11.1917 q^{42} -7.93060 q^{43} +3.17535 q^{44} +7.06533 q^{45} -7.73254 q^{46} +13.5932 q^{47} -2.70268 q^{48} +10.1477 q^{49} +2.30581 q^{50} +10.2789 q^{51} +4.18079 q^{52} -9.93192 q^{53} +3.52553 q^{54} +5.21201 q^{55} -4.14098 q^{56} +13.6507 q^{57} -7.09006 q^{58} -12.7576 q^{59} -4.43617 q^{60} +3.33274 q^{61} -9.44135 q^{62} +17.8247 q^{63} +1.00000 q^{64} +6.86234 q^{65} +8.58195 q^{66} +0.893201 q^{67} -3.80323 q^{68} -20.8985 q^{69} -6.79700 q^{70} -1.57638 q^{71} -4.30446 q^{72} -5.46876 q^{73} -10.2615 q^{74} +6.23187 q^{75} -5.05080 q^{76} +13.1491 q^{77} +11.2993 q^{78} -0.681247 q^{79} +1.64140 q^{80} -3.38500 q^{81} -9.50741 q^{82} -3.45940 q^{83} -11.1917 q^{84} -6.24261 q^{85} +7.93060 q^{86} -19.1621 q^{87} -3.17535 q^{88} -13.8379 q^{89} -7.06533 q^{90} +17.3126 q^{91} +7.73254 q^{92} -25.5169 q^{93} -13.5932 q^{94} -8.29037 q^{95} +2.70268 q^{96} -6.17063 q^{97} -10.1477 q^{98} +13.6682 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 49 q - 49 q^{2} + 8 q^{3} + 49 q^{4} - 8 q^{5} - 8 q^{6} + 18 q^{7} - 49 q^{8} + 59 q^{9}+O(q^{10}) \) 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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