LMFDB - Embedded newform 8018.2.a.f.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8018,2,Mod(1,8018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8018, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8018 = 2 \cdot 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8018.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.0240523407$
Analytic rank:	$1$
Dimension:	$34$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	8018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.04582 q^{3} +1.00000 q^{4} -4.09434 q^{5} +2.04582 q^{6} +1.49846 q^{7} -1.00000 q^{8} +1.18539 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.04582 q^{3} +1.00000 q^{4} -4.09434 q^{5} +2.04582 q^{6} +1.49846 q^{7} -1.00000 q^{8} +1.18539 q^{9} +4.09434 q^{10} +4.36668 q^{11} -2.04582 q^{12} -2.07746 q^{13} -1.49846 q^{14} +8.37630 q^{15} +1.00000 q^{16} +2.71655 q^{17} -1.18539 q^{18} -1.00000 q^{19} -4.09434 q^{20} -3.06558 q^{21} -4.36668 q^{22} -8.72662 q^{23} +2.04582 q^{24} +11.7636 q^{25} +2.07746 q^{26} +3.71237 q^{27} +1.49846 q^{28} +1.76891 q^{29} -8.37630 q^{30} -3.93079 q^{31} -1.00000 q^{32} -8.93345 q^{33} -2.71655 q^{34} -6.13520 q^{35} +1.18539 q^{36} -9.86688 q^{37} +1.00000 q^{38} +4.25010 q^{39} +4.09434 q^{40} +5.20665 q^{41} +3.06558 q^{42} +4.35112 q^{43} +4.36668 q^{44} -4.85339 q^{45} +8.72662 q^{46} -5.27226 q^{47} -2.04582 q^{48} -4.75463 q^{49} -11.7636 q^{50} -5.55758 q^{51} -2.07746 q^{52} -2.90552 q^{53} -3.71237 q^{54} -17.8787 q^{55} -1.49846 q^{56} +2.04582 q^{57} -1.76891 q^{58} +7.50249 q^{59} +8.37630 q^{60} -4.68551 q^{61} +3.93079 q^{62} +1.77626 q^{63} +1.00000 q^{64} +8.50581 q^{65} +8.93345 q^{66} -8.57101 q^{67} +2.71655 q^{68} +17.8531 q^{69} +6.13520 q^{70} +1.09328 q^{71} -1.18539 q^{72} +11.3584 q^{73} +9.86688 q^{74} -24.0663 q^{75} -1.00000 q^{76} +6.54328 q^{77} -4.25010 q^{78} +7.46127 q^{79} -4.09434 q^{80} -11.1510 q^{81} -5.20665 q^{82} +15.3359 q^{83} -3.06558 q^{84} -11.1225 q^{85} -4.35112 q^{86} -3.61887 q^{87} -4.36668 q^{88} +7.24142 q^{89} +4.85339 q^{90} -3.11298 q^{91} -8.72662 q^{92} +8.04171 q^{93} +5.27226 q^{94} +4.09434 q^{95} +2.04582 q^{96} -16.3302 q^{97} +4.75463 q^{98} +5.17622 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9}+O(q^{10}) $ 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9	\( 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9} - 7 q^{10} + 4 q^{11} - 10 q^{12} - 5 q^{13} + 6 q^{14} - 17 q^{15} + 34 q^{16} + 8 q^{17} - 38 q^{18} - 34 q^{19} + 7 q^{20} - 4 q^{22} - 24 q^{23} + 10 q^{24} + 5 q^{25} + 5 q^{26} - 31 q^{27} - 6 q^{28} + 24 q^{29} + 17 q^{30} - 28 q^{31} - 34 q^{32} - 16 q^{33} - 8 q^{34} + 2 q^{35} + 38 q^{36} - 36 q^{37} + 34 q^{38} - 9 q^{39} - 7 q^{40} + 9 q^{41} - 24 q^{43} + 4 q^{44} + 22 q^{45} + 24 q^{46} - 29 q^{47} - 10 q^{48} + 22 q^{49} - 5 q^{50} - 21 q^{51} - 5 q^{52} - 9 q^{53} + 31 q^{54} - 28 q^{55} + 6 q^{56} + 10 q^{57} - 24 q^{58} - 28 q^{59} - 17 q^{60} + 23 q^{61} + 28 q^{62} - 27 q^{63} + 34 q^{64} - 6 q^{65} + 16 q^{66} - 51 q^{67} + 8 q^{68} - 17 q^{69} - 2 q^{70} - 31 q^{71} - 38 q^{72} - 26 q^{73} + 36 q^{74} - 109 q^{75} - 34 q^{76} - 28 q^{77} + 9 q^{78} - 36 q^{79} + 7 q^{80} + 6 q^{81} - 9 q^{82} - 10 q^{83} - 32 q^{85} + 24 q^{86} - 8 q^{87} - 4 q^{88} - 34 q^{89} - 22 q^{90} - 41 q^{91} - 24 q^{92} - 33 q^{93} + 29 q^{94} - 7 q^{95} + 10 q^{96} - 56 q^{97} - 22 q^{98} - 28 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9 - 7 * q^10 + 4 * q^11 - 10 * q^12 - 5 * q^13 + 6 * q^14 - 17 * q^15 + 34 * q^16 + 8 * q^17 - 38 * q^18 - 34 * q^19 + 7 * q^20 - 4 * q^22 - 24 * q^23 + 10 * q^24 + 5 * q^25 + 5 * q^26 - 31 * q^27 - 6 * q^28 + 24 * q^29 + 17 * q^30 - 28 * q^31 - 34 * q^32 - 16 * q^33 - 8 * q^34 + 2 * q^35 + 38 * q^36 - 36 * q^37 + 34 * q^38 - 9 * q^39 - 7 * q^40 + 9 * q^41 - 24 * q^43 + 4 * q^44 + 22 * q^45 + 24 * q^46 - 29 * q^47 - 10 * q^48 + 22 * q^49 - 5 * q^50 - 21 * q^51 - 5 * q^52 - 9 * q^53 + 31 * q^54 - 28 * q^55 + 6 * q^56 + 10 * q^57 - 24 * q^58 - 28 * q^59 - 17 * q^60 + 23 * q^61 + 28 * q^62 - 27 * q^63 + 34 * q^64 - 6 * q^65 + 16 * q^66 - 51 * q^67 + 8 * q^68 - 17 * q^69 - 2 * q^70 - 31 * q^71 - 38 * q^72 - 26 * q^73 + 36 * q^74 - 109 * q^75 - 34 * q^76 - 28 * q^77 + 9 * q^78 - 36 * q^79 + 7 * q^80 + 6 * q^81 - 9 * q^82 - 10 * q^83 - 32 * q^85 + 24 * q^86 - 8 * q^87 - 4 * q^88 - 34 * q^89 - 22 * q^90 - 41 * q^91 - 24 * q^92 - 33 * q^93 + 29 * q^94 - 7 * q^95 + 10 * q^96 - 56 * q^97 - 22 * q^98 - 28 * 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
$3$	−2.04582	−1.18116	−0.590578	−	0.806980i	$-0.701100\pi$
$3$	−2.04582	−1.18116	−0.590578	+	0.806980i	$0.701100\pi$
$4$	1.00000	0.500000
$5$	−4.09434	−1.83105	−0.915523	−	0.402266i	$-0.868223\pi$
$5$	−4.09434	−1.83105	−0.915523	+	0.402266i	$0.868223\pi$
$6$	2.04582	0.835204
$7$	1.49846	0.566363	0.283182	−	0.959066i	$-0.408610\pi$
$7$	1.49846	0.566363	0.283182	+	0.959066i	$0.408610\pi$
$8$	−1.00000	−0.353553
$9$	1.18539	0.395130
$10$	4.09434	1.29474
$11$	4.36668	1.31660	0.658302	−	0.752754i	$-0.271275\pi$
$11$	4.36668	1.31660	0.658302	+	0.752754i	$0.271275\pi$
$12$	−2.04582	−0.590578
$13$	−2.07746	−0.576182	−0.288091	−	0.957603i	$-0.593021\pi$
$13$	−2.07746	−0.576182	−0.288091	+	0.957603i	$0.593021\pi$
$14$	−1.49846	−0.400479
$15$	8.37630	2.16275
$16$	1.00000	0.250000
$17$	2.71655	0.658861	0.329430	−	0.944180i	$-0.393143\pi$
$17$	2.71655	0.658861	0.329430	+	0.944180i	$0.393143\pi$
$18$	−1.18539	−0.279399
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−4.09434	−0.915523
$21$	−3.06558	−0.668964
$22$	−4.36668	−0.930979
$23$	−8.72662	−1.81963	−0.909813	−	0.415017i	$-0.863776\pi$
$23$	−8.72662	−1.81963	−0.909813	+	0.415017i	$0.863776\pi$
$24$	2.04582	0.417602
$25$	11.7636	2.35273
$26$	2.07746	0.407422
$27$	3.71237	0.714446
$28$	1.49846	0.283182
$29$	1.76891	0.328478	0.164239	−	0.986421i	$-0.447483\pi$
$29$	1.76891	0.328478	0.164239	+	0.986421i	$0.447483\pi$
$30$	−8.37630	−1.52930
$31$	−3.93079	−0.705991	−0.352996	−	0.935625i	$-0.614837\pi$
$31$	−3.93079	−0.705991	−0.352996	+	0.935625i	$0.614837\pi$
$32$	−1.00000	−0.176777
$33$	−8.93345	−1.55511
$34$	−2.71655	−0.465885
$35$	−6.13520	−1.03704
$36$	1.18539	0.197565
$37$	−9.86688	−1.62210	−0.811052	−	0.584973i	$-0.801105\pi$
$37$	−9.86688	−1.62210	−0.811052	+	0.584973i	$0.801105\pi$
$38$	1.00000	0.162221
$39$	4.25010	0.680561
$40$	4.09434	0.647372
$41$	5.20665	0.813142	0.406571	−	0.913619i	$-0.366724\pi$
$41$	5.20665	0.813142	0.406571	+	0.913619i	$0.366724\pi$
$42$	3.06558	0.473029
$43$	4.35112	0.663539	0.331769	−	0.943361i	$-0.392354\pi$
$43$	4.35112	0.663539	0.331769	+	0.943361i	$0.392354\pi$
$44$	4.36668	0.658302
$45$	−4.85339	−0.723501
$46$	8.72662	1.28667
$47$	−5.27226	−0.769039	−0.384519	−	0.923117i	$-0.625633\pi$
$47$	−5.27226	−0.769039	−0.384519	+	0.923117i	$0.625633\pi$
$48$	−2.04582	−0.295289
$49$	−4.75463	−0.679232
$50$	−11.7636	−1.66363
$51$	−5.55758	−0.778218
$52$	−2.07746	−0.288091
$53$	−2.90552	−0.399104	−0.199552	−	0.979887i	$-0.563949\pi$
$53$	−2.90552	−0.399104	−0.199552	+	0.979887i	$0.563949\pi$
$54$	−3.71237	−0.505190
$55$	−17.8787	−2.41076
$56$	−1.49846	−0.200240
$57$	2.04582	0.270976
$58$	−1.76891	−0.232269
$59$	7.50249	0.976741	0.488371	−	0.872636i	$-0.337591\pi$
$59$	7.50249	0.976741	0.488371	+	0.872636i	$0.337591\pi$
$60$	8.37630	1.08138
$61$	−4.68551	−0.599918	−0.299959	−	0.953952i	$-0.596973\pi$
$61$	−4.68551	−0.599918	−0.299959	+	0.953952i	$0.596973\pi$
$62$	3.93079	0.499211
$63$	1.77626	0.223787
$64$	1.00000	0.125000
$65$	8.50581	1.05502
$66$	8.93345	1.09963
$67$	−8.57101	−1.04712	−0.523558	−	0.851990i	$-0.675396\pi$
$67$	−8.57101	−1.04712	−0.523558	+	0.851990i	$0.675396\pi$
$68$	2.71655	0.329430
$69$	17.8531	2.14926
$70$	6.13520	0.733296
$71$	1.09328	0.129748	0.0648741	−	0.997893i	$-0.479335\pi$
$71$	1.09328	0.129748	0.0648741	+	0.997893i	$0.479335\pi$
$72$	−1.18539	−0.139700
$73$	11.3584	1.32940	0.664700	−	0.747111i	$-0.268560\pi$
$73$	11.3584	1.32940	0.664700	+	0.747111i	$0.268560\pi$
$74$	9.86688	1.14700
$75$	−24.0663	−2.77894
$76$	−1.00000	−0.114708
$77$	6.54328	0.745676
$78$	−4.25010	−0.481230
$79$	7.46127	0.839458	0.419729	−	0.907649i	$-0.362125\pi$
$79$	7.46127	0.839458	0.419729	+	0.907649i	$0.362125\pi$
$80$	−4.09434	−0.457761
$81$	−11.1510	−1.23900
$82$	−5.20665	−0.574978
$83$	15.3359	1.68333	0.841666	−	0.539999i	$-0.181575\pi$
$83$	15.3359	1.68333	0.841666	+	0.539999i	$0.181575\pi$
$84$	−3.06558	−0.334482
$85$	−11.1225	−1.20640
$86$	−4.35112	−0.469193
$87$	−3.61887	−0.387983
$88$	−4.36668	−0.465490
$89$	7.24142	0.767589	0.383795	−	0.923418i	$-0.374617\pi$
$89$	7.24142	0.767589	0.383795	+	0.923418i	$0.374617\pi$
$90$	4.85339	0.511593
$91$	−3.11298	−0.326329
$92$	−8.72662	−0.909813
$93$	8.04171	0.833886
$94$	5.27226	0.543792
$95$	4.09434	0.420071
$96$	2.04582	0.208801
$97$	−16.3302	−1.65808	−0.829042	−	0.559186i	$-0.811114\pi$
$97$	−16.3302	−1.65808	−0.829042	+	0.559186i	$0.811114\pi$
$98$	4.75463	0.480290
$99$	5.17622	0.520230
$100$	11.7636	1.17636
$101$	1.31063	0.130413	0.0652063	−	0.997872i	$-0.479229\pi$
$101$	1.31063	0.130413	0.0652063	+	0.997872i	$0.479229\pi$
$102$	5.55758	0.550283
$103$	−0.646222	−0.0636742	−0.0318371	−	0.999493i	$-0.510136\pi$
$103$	−0.646222	−0.0636742	−0.0318371	+	0.999493i	$0.510136\pi$
$104$	2.07746	0.203711
$105$	12.5515	1.22490
$106$	2.90552	0.282209
$107$	17.4634	1.68825	0.844125	−	0.536147i	$-0.180121\pi$
$107$	17.4634	1.68825	0.844125	+	0.536147i	$0.180121\pi$
$108$	3.71237	0.357223
$109$	13.5424	1.29713	0.648565	−	0.761160i	$-0.275370\pi$
$109$	13.5424	1.29713	0.648565	+	0.761160i	$0.275370\pi$
$110$	17.8787	1.70467
$111$	20.1859	1.91596
$112$	1.49846	0.141591
$113$	−10.1385	−0.953747	−0.476874	−	0.878972i	$-0.658230\pi$
$113$	−10.1385	−0.953747	−0.476874	+	0.878972i	$0.658230\pi$
$114$	−2.04582	−0.191609
$115$	35.7298	3.33182
$116$	1.76891	0.164239
$117$	−2.46259	−0.227667
$118$	−7.50249	−0.690660
$119$	4.07064	0.373155
$120$	−8.37630	−0.764648
$121$	8.06789	0.733445
$122$	4.68551	0.424206
$123$	−10.6519	−0.960447
$124$	−3.93079	−0.352996
$125$	−27.6927	−2.47691
$126$	−1.77626	−0.158241
$127$	−11.5486	−1.02477	−0.512385	−	0.858756i	$-0.671238\pi$
$127$	−11.5486	−1.02477	−0.512385	+	0.858756i	$0.671238\pi$
$128$	−1.00000	−0.0883883
$129$	−8.90161	−0.783743
$130$	−8.50581	−0.746009
$131$	−2.24440	−0.196094	−0.0980469	−	0.995182i	$-0.531260\pi$
$131$	−2.24440	−0.196094	−0.0980469	+	0.995182i	$0.531260\pi$
$132$	−8.93345	−0.777557
$133$	−1.49846	−0.129933
$134$	8.57101	0.740423
$135$	−15.1997	−1.30818
$136$	−2.71655	−0.232942
$137$	0.788239	0.0673438	0.0336719	−	0.999433i	$-0.489280\pi$
$137$	0.788239	0.0673438	0.0336719	+	0.999433i	$0.489280\pi$
$138$	−17.8531	−1.51976
$139$	0.0659961	0.00559771	0.00279886	−	0.999996i	$-0.499109\pi$
$139$	0.0659961	0.00559771	0.00279886	+	0.999996i	$0.499109\pi$
$140$	−6.13520	−0.518519
$141$	10.7861	0.908355
$142$	−1.09328	−0.0917458
$143$	−9.07158	−0.758604
$144$	1.18539	0.0987825
$145$	−7.24251	−0.601458
$146$	−11.3584	−0.940027
$147$	9.72712	0.802280
$148$	−9.86688	−0.811052
$149$	21.7928	1.78533	0.892666	−	0.450718i	$-0.148832\pi$
$149$	21.7928	1.78533	0.892666	+	0.450718i	$0.148832\pi$
$150$	24.0663	1.96501
$151$	3.76642	0.306507	0.153254	−	0.988187i	$-0.451025\pi$
$151$	3.76642	0.306507	0.153254	+	0.988187i	$0.451025\pi$
$152$	1.00000	0.0811107
$153$	3.22017	0.260336
$154$	−6.54328	−0.527273
$155$	16.0940	1.29270
$156$	4.25010	0.340281
$157$	1.35547	0.108178	0.0540892	−	0.998536i	$-0.482774\pi$
$157$	1.35547	0.108178	0.0540892	+	0.998536i	$0.482774\pi$
$158$	−7.46127	−0.593586
$159$	5.94419	0.471405
$160$	4.09434	0.323686
$161$	−13.0765	−1.03057
$162$	11.1510	0.876107
$163$	−3.10546	−0.243238	−0.121619	−	0.992577i	$-0.538809\pi$
$163$	−3.10546	−0.243238	−0.121619	+	0.992577i	$0.538809\pi$
$164$	5.20665	0.406571
$165$	36.5766	2.84749
$166$	−15.3359	−1.19029
$167$	20.7368	1.60466	0.802331	−	0.596879i	$-0.203593\pi$
$167$	20.7368	1.60466	0.802331	+	0.596879i	$0.203593\pi$
$168$	3.06558	0.236514
$169$	−8.68418	−0.668014
$170$	11.1225	0.853057
$171$	−1.18539	−0.0906490
$172$	4.35112	0.331769
$173$	15.9654	1.21382	0.606912	−	0.794769i	$-0.292408\pi$
$173$	15.9654	1.21382	0.606912	+	0.794769i	$0.292408\pi$
$174$	3.61887	0.274346
$175$	17.6273	1.33250
$176$	4.36668	0.329151
$177$	−15.3488	−1.15368
$178$	−7.24142	−0.542768
$179$	6.73294	0.503244	0.251622	−	0.967826i	$-0.419036\pi$
$179$	6.73294	0.503244	0.251622	+	0.967826i	$0.419036\pi$
$180$	−4.85339	−0.361751
$181$	−11.4281	−0.849445	−0.424723	−	0.905323i	$-0.639628\pi$
$181$	−11.4281	−0.849445	−0.424723	+	0.905323i	$0.639628\pi$
$182$	3.11298	0.230749
$183$	9.58572	0.708596
$184$	8.72662	0.643335
$185$	40.3984	2.97015
$186$	−8.04171	−0.589646
$187$	11.8623	0.867458
$188$	−5.27226	−0.384519
$189$	5.56283	0.404636
$190$	−4.09434	−0.297035
$191$	22.8164	1.65093	0.825467	−	0.564450i	$-0.190912\pi$
$191$	22.8164	1.65093	0.825467	+	0.564450i	$0.190912\pi$
$192$	−2.04582	−0.147645
$193$	−3.66905	−0.264104	−0.132052	−	0.991243i	$-0.542157\pi$
$193$	−3.66905	−0.264104	−0.132052	+	0.991243i	$0.542157\pi$
$194$	16.3302	1.17244
$195$	−17.4014	−1.24614
$196$	−4.75463	−0.339616
$197$	−2.93118	−0.208838	−0.104419	−	0.994533i	$-0.533298\pi$
$197$	−2.93118	−0.208838	−0.104419	+	0.994533i	$0.533298\pi$
$198$	−5.17622	−0.367858
$199$	12.3039	0.872201	0.436100	−	0.899898i	$-0.356359\pi$
$199$	12.3039	0.872201	0.436100	+	0.899898i	$0.356359\pi$
$200$	−11.7636	−0.831815
$201$	17.5348	1.23681
$202$	−1.31063	−0.0922157
$203$	2.65063	0.186038
$204$	−5.55758	−0.389109
$205$	−21.3178	−1.48890
$206$	0.646222	0.0450244
$207$	−10.3445	−0.718989
$208$	−2.07746	−0.144046
$209$	−4.36668	−0.302050
$210$	−12.5515	−0.866137
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	−2.90552	−0.199552
$213$	−2.23665	−0.153253
$214$	−17.4634	−1.19377
$215$	−17.8150	−1.21497
$216$	−3.71237	−0.252595
$217$	−5.89012	−0.399848
$218$	−13.5424	−0.917209
$219$	−23.2373	−1.57023
$220$	−17.8787	−1.20538
$221$	−5.64352	−0.379624
$222$	−20.1859	−1.35479
$223$	−15.1165	−1.01228	−0.506138	−	0.862453i	$-0.668927\pi$
$223$	−15.1165	−1.01228	−0.506138	+	0.862453i	$0.668927\pi$
$224$	−1.49846	−0.100120
$225$	13.9445	0.929634
$226$	10.1385	0.674401
$227$	5.52236	0.366532	0.183266	−	0.983063i	$-0.441333\pi$
$227$	5.52236	0.366532	0.183266	+	0.983063i	$0.441333\pi$
$228$	2.04582	0.135488
$229$	8.47458	0.560016	0.280008	−	0.959998i	$-0.409663\pi$
$229$	8.47458	0.560016	0.280008	+	0.959998i	$0.409663\pi$
$230$	−35.7298	−2.35595
$231$	−13.3864	−0.880760
$232$	−1.76891	−0.116134
$233$	11.7599	0.770415	0.385208	−	0.922830i	$-0.374130\pi$
$233$	11.7599	0.770415	0.385208	+	0.922830i	$0.374130\pi$
$234$	2.46259	0.160985
$235$	21.5865	1.40814
$236$	7.50249	0.488371
$237$	−15.2644	−0.991531
$238$	−4.07064	−0.263860
$239$	−2.68897	−0.173935	−0.0869676	−	0.996211i	$-0.527718\pi$
$239$	−2.68897	−0.173935	−0.0869676	+	0.996211i	$0.527718\pi$
$240$	8.37630	0.540688
$241$	0.0708398	0.00456319	0.00228160	−	0.999997i	$-0.499274\pi$
$241$	0.0708398	0.00456319	0.00228160	+	0.999997i	$0.499274\pi$
$242$	−8.06789	−0.518624
$243$	11.6759	0.749009
$244$	−4.68551	−0.299959
$245$	19.4671	1.24371
$246$	10.6519	0.679139
$247$	2.07746	0.132185
$248$	3.93079	0.249606
$249$	−31.3745	−1.98828
$250$	27.6927	1.75144
$251$	28.0554	1.77084	0.885420	−	0.464792i	$-0.153871\pi$
$251$	28.0554	1.77084	0.885420	+	0.464792i	$0.153871\pi$
$252$	1.77626	0.111894
$253$	−38.1064	−2.39573
$254$	11.5486	0.724621
$255$	22.7547	1.42495
$256$	1.00000	0.0625000
$257$	−11.4019	−0.711230	−0.355615	−	0.934633i	$-0.615729\pi$
$257$	−11.4019	−0.711230	−0.355615	+	0.934633i	$0.615729\pi$
$258$	8.90161	0.554190
$259$	−14.7851	−0.918701
$260$	8.50581	0.527508
$261$	2.09684	0.129791
$262$	2.24440	0.138659
$263$	−32.2678	−1.98972	−0.994859	−	0.101272i	$-0.967709\pi$
$263$	−32.2678	−1.98972	−0.994859	+	0.101272i	$0.967709\pi$
$264$	8.93345	0.549816
$265$	11.8962	0.730779
$266$	1.49846	0.0918763
$267$	−14.8147	−0.906643
$268$	−8.57101	−0.523558
$269$	−25.3155	−1.54351	−0.771756	−	0.635918i	$-0.780621\pi$
$269$	−25.3155	−1.54351	−0.771756	+	0.635918i	$0.780621\pi$
$270$	15.1997	0.925025
$271$	−7.88294	−0.478855	−0.239427	−	0.970914i	$-0.576960\pi$
$271$	−7.88294	−0.478855	−0.239427	+	0.970914i	$0.576960\pi$
$272$	2.71655	0.164715
$273$	6.36860	0.385445
$274$	−0.788239	−0.0476193
$275$	51.3681	3.09761
$276$	17.8531	1.07463
$277$	6.05207	0.363634	0.181817	−	0.983332i	$-0.441802\pi$
$277$	6.05207	0.363634	0.181817	+	0.983332i	$0.441802\pi$
$278$	−0.0659961	−0.00395818
$279$	−4.65952	−0.278958
$280$	6.13520	0.366648
$281$	−23.4655	−1.39984	−0.699918	−	0.714223i	$-0.746780\pi$
$281$	−23.4655	−1.39984	−0.699918	+	0.714223i	$0.746780\pi$
$282$	−10.7861	−0.642304
$283$	31.9526	1.89938	0.949691	−	0.313188i	$-0.101397\pi$
$283$	31.9526	1.89938	0.949691	+	0.313188i	$0.101397\pi$
$284$	1.09328	0.0648741
$285$	−8.37630	−0.496169
$286$	9.07158	0.536414
$287$	7.80193	0.460534
$288$	−1.18539	−0.0698498
$289$	−9.62034	−0.565902
$290$	7.24251	0.425295
$291$	33.4088	1.95846
$292$	11.3584	0.664700
$293$	−0.530799	−0.0310096	−0.0155048	−	0.999880i	$-0.504936\pi$
$293$	−0.530799	−0.0310096	−0.0155048	+	0.999880i	$0.504936\pi$
$294$	−9.72712	−0.567297
$295$	−30.7178	−1.78846
$296$	9.86688	0.573501
$297$	16.2107	0.940642
$298$	−21.7928	−1.26242
$299$	18.1292	1.04844
$300$	−24.0663	−1.38947
$301$	6.51996	0.375804
$302$	−3.76642	−0.216733
$303$	−2.68132	−0.154038
$304$	−1.00000	−0.0573539
$305$	19.1841	1.09848
$306$	−3.22017	−0.184085
$307$	12.2045	0.696546	0.348273	−	0.937393i	$-0.386768\pi$
$307$	12.2045	0.696546	0.348273	+	0.937393i	$0.386768\pi$
$308$	6.54328	0.372838
$309$	1.32206	0.0752092
$310$	−16.0940	−0.914079
$311$	20.4475	1.15947	0.579736	−	0.814804i	$-0.303156\pi$
$311$	20.4475	1.15947	0.579736	+	0.814804i	$0.303156\pi$
$312$	−4.25010	−0.240615
$313$	32.5985	1.84258	0.921288	−	0.388881i	$-0.127138\pi$
$313$	32.5985	1.84258	0.921288	+	0.388881i	$0.127138\pi$
$314$	−1.35547	−0.0764937
$315$	−7.27260	−0.409765
$316$	7.46127	0.419729
$317$	−26.8916	−1.51038	−0.755190	−	0.655505i	$-0.772456\pi$
$317$	−26.8916	−1.51038	−0.755190	+	0.655505i	$0.772456\pi$
$318$	−5.94419	−0.333333
$319$	7.72425	0.432475
$320$	−4.09434	−0.228881
$321$	−35.7270	−1.99409
$322$	13.0765	0.728723
$323$	−2.71655	−0.151153
$324$	−11.1510	−0.619501
$325$	−24.4384	−1.35560
$326$	3.10546	0.171996
$327$	−27.7054	−1.53211
$328$	−5.20665	−0.287489
$329$	−7.90026	−0.435555
$330$	−36.5766	−2.01348
$331$	−28.2584	−1.55322	−0.776610	−	0.629982i	$-0.783062\pi$
$331$	−28.2584	−1.55322	−0.776610	+	0.629982i	$0.783062\pi$
$332$	15.3359	0.841666
$333$	−11.6961	−0.640942
$334$	−20.7368	−1.13467
$335$	35.0927	1.91732
$336$	−3.06558	−0.167241
$337$	−19.2134	−1.04662	−0.523310	−	0.852142i	$-0.675303\pi$
$337$	−19.2134	−1.04662	−0.523310	+	0.852142i	$0.675303\pi$
$338$	8.68418	0.472357
$339$	20.7415	1.12652
$340$	−11.1225	−0.603202
$341$	−17.1645	−0.929511
$342$	1.18539	0.0640986
$343$	−17.6138	−0.951056
$344$	−4.35112	−0.234596
$345$	−73.0968	−3.93540
$346$	−15.9654	−0.858303
$347$	−16.9938	−0.912277	−0.456139	−	0.889909i	$-0.650768\pi$
$347$	−16.9938	−0.912277	−0.456139	+	0.889909i	$0.650768\pi$
$348$	−3.61887	−0.193992
$349$	−11.9704	−0.640761	−0.320381	−	0.947289i	$-0.603811\pi$
$349$	−11.9704	−0.640761	−0.320381	+	0.947289i	$0.603811\pi$
$350$	−17.6273	−0.942220
$351$	−7.71228	−0.411651
$352$	−4.36668	−0.232745
$353$	30.9605	1.64786	0.823931	−	0.566691i	$-0.191777\pi$
$353$	30.9605	1.64786	0.823931	+	0.566691i	$0.191777\pi$
$354$	15.3488	0.815778
$355$	−4.47625	−0.237575
$356$	7.24142	0.383795
$357$	−8.32780	−0.440754
$358$	−6.73294	−0.355847
$359$	−30.9264	−1.63223	−0.816117	−	0.577887i	$-0.803877\pi$
$359$	−30.9264	−1.63223	−0.816117	+	0.577887i	$0.803877\pi$
$360$	4.85339	0.255796
$361$	1.00000	0.0526316
$362$	11.4281	0.600649
$363$	−16.5055	−0.866313
$364$	−3.11298	−0.163164
$365$	−46.5052	−2.43419
$366$	−9.58572	−0.501053
$367$	−36.5323	−1.90697	−0.953484	−	0.301443i	$-0.902532\pi$
$367$	−36.5323	−1.90697	−0.953484	+	0.301443i	$0.902532\pi$
$368$	−8.72662	−0.454907
$369$	6.17191	0.321297
$370$	−40.3984	−2.10021
$371$	−4.35380	−0.226038
$372$	8.04171	0.416943
$373$	14.1511	0.732718	0.366359	−	0.930474i	$-0.380604\pi$
$373$	14.1511	0.732718	0.366359	+	0.930474i	$0.380604\pi$
$374$	−11.8623	−0.613386
$375$	56.6543	2.92562
$376$	5.27226	0.271896
$377$	−3.67482	−0.189263
$378$	−5.56283	−0.286121
$379$	7.71892	0.396495	0.198247	−	0.980152i	$-0.436475\pi$
$379$	7.71892	0.396495	0.198247	+	0.980152i	$0.436475\pi$
$380$	4.09434	0.210035
$381$	23.6263	1.21041
$382$	−22.8164	−1.16739
$383$	12.3725	0.632207	0.316104	−	0.948725i	$-0.397625\pi$
$383$	12.3725	0.632207	0.316104	+	0.948725i	$0.397625\pi$
$384$	2.04582	0.104400
$385$	−26.7904	−1.36537
$386$	3.66905	0.186750
$387$	5.15777	0.262184
$388$	−16.3302	−0.829042
$389$	−25.4546	−1.29060	−0.645299	−	0.763930i	$-0.723267\pi$
$389$	−25.4546	−1.29060	−0.645299	+	0.763930i	$0.723267\pi$
$390$	17.4014	0.881153
$391$	−23.7063	−1.19888
$392$	4.75463	0.240145
$393$	4.59163	0.231617
$394$	2.93118	0.147671
$395$	−30.5490	−1.53709
$396$	5.17622	0.260115
$397$	12.6444	0.634605	0.317302	−	0.948324i	$-0.397223\pi$
$397$	12.6444	0.634605	0.317302	+	0.948324i	$0.397223\pi$
$398$	−12.3039	−0.616739
$399$	3.06558	0.153471
$400$	11.7636	0.588182
$401$	−14.7905	−0.738605	−0.369302	−	0.929309i	$-0.620403\pi$
$401$	−14.7905	−0.738605	−0.369302	+	0.929309i	$0.620403\pi$
$402$	−17.5348	−0.874555
$403$	8.16605	0.406780
$404$	1.31063	0.0652063
$405$	45.6561	2.26867
$406$	−2.65063	−0.131548
$407$	−43.0855	−2.13567
$408$	5.55758	0.275141
$409$	−7.91564	−0.391403	−0.195702	−	0.980663i	$-0.562698\pi$
$409$	−7.91564	−0.391403	−0.195702	+	0.980663i	$0.562698\pi$
$410$	21.3178	1.05281
$411$	−1.61260	−0.0795436
$412$	−0.646222	−0.0318371
$413$	11.2422	0.553191
$414$	10.3445	0.508402
$415$	−62.7903	−3.08226
$416$	2.07746	0.101856
$417$	−0.135016	−0.00661177
$418$	4.36668	0.213581
$419$	3.22411	0.157508	0.0787540	−	0.996894i	$-0.474906\pi$
$419$	3.22411	0.157508	0.0787540	+	0.996894i	$0.474906\pi$
$420$	12.5515	0.612452
$421$	26.3204	1.28278	0.641389	−	0.767216i	$-0.278358\pi$
$421$	26.3204	1.28278	0.641389	+	0.767216i	$0.278358\pi$
$422$	1.00000	0.0486792
$423$	−6.24969	−0.303870
$424$	2.90552	0.141105
$425$	31.9566	1.55012
$426$	2.23665	0.108366
$427$	−7.02103	−0.339771
$428$	17.4634	0.844125
$429$	18.5588	0.896030
$430$	17.8150	0.859114
$431$	−2.92758	−0.141016	−0.0705082	−	0.997511i	$-0.522462\pi$
$431$	−2.92758	−0.141016	−0.0705082	+	0.997511i	$0.522462\pi$
$432$	3.71237	0.178611
$433$	−15.5142	−0.745567	−0.372784	−	0.927918i	$-0.621597\pi$
$433$	−15.5142	−0.745567	−0.372784	+	0.927918i	$0.621597\pi$
$434$	5.89012	0.282735
$435$	14.8169	0.710415
$436$	13.5424	0.648565
$437$	8.72662	0.417451
$438$	23.2373	1.11032
$439$	25.6971	1.22645	0.613227	−	0.789906i	$-0.289871\pi$
$439$	25.6971	1.22645	0.613227	+	0.789906i	$0.289871\pi$
$440$	17.8787	0.852333
$441$	−5.63609	−0.268385
$442$	5.64352	0.268435
$443$	−4.35774	−0.207042	−0.103521	−	0.994627i	$-0.533011\pi$
$443$	−4.35774	−0.207042	−0.103521	+	0.994627i	$0.533011\pi$
$444$	20.1859	0.957980
$445$	−29.6489	−1.40549
$446$	15.1165	0.715787
$447$	−44.5841	−2.10876
$448$	1.49846	0.0707954
$449$	−13.8264	−0.652509	−0.326254	−	0.945282i	$-0.605787\pi$
$449$	−13.8264	−0.652509	−0.326254	+	0.945282i	$0.605787\pi$
$450$	−13.9445	−0.657350
$451$	22.7358	1.07059
$452$	−10.1385	−0.476874
$453$	−7.70544	−0.362033
$454$	−5.52236	−0.259177
$455$	12.7456	0.597523
$456$	−2.04582	−0.0958044
$457$	11.6026	0.542748	0.271374	−	0.962474i	$-0.412522\pi$
$457$	11.6026	0.542748	0.271374	+	0.962474i	$0.412522\pi$
$458$	−8.47458	−0.395991
$459$	10.0848	0.470720
$460$	35.7298	1.66591
$461$	19.3868	0.902934	0.451467	−	0.892288i	$-0.350901\pi$
$461$	19.3868	0.902934	0.451467	+	0.892288i	$0.350901\pi$
$462$	13.3864	0.622791
$463$	30.5402	1.41932	0.709662	−	0.704543i	$-0.248848\pi$
$463$	30.5402	1.41932	0.709662	+	0.704543i	$0.248848\pi$
$464$	1.76891	0.0821194
$465$	−32.9255	−1.52688
$466$	−11.7599	−0.544766
$467$	−23.8146	−1.10201	−0.551003	−	0.834503i	$-0.685755\pi$
$467$	−23.8146	−1.10201	−0.551003	+	0.834503i	$0.685755\pi$
$468$	−2.46259	−0.113833
$469$	−12.8433	−0.593048
$470$	−21.5865	−0.995709
$471$	−2.77306	−0.127776
$472$	−7.50249	−0.345330
$473$	18.9999	0.873618
$474$	15.2644	0.701118
$475$	−11.7636	−0.539753
$476$	4.07064	0.186577
$477$	−3.44418	−0.157698
$478$	2.68897	0.122991
$479$	−31.5928	−1.44351	−0.721755	−	0.692148i	$-0.756664\pi$
$479$	−31.5928	−1.44351	−0.721755	+	0.692148i	$0.756664\pi$
$480$	−8.37630	−0.382324
$481$	20.4980	0.934628
$482$	−0.0708398	−0.00322667
$483$	26.7521	1.21726
$484$	8.06789	0.366722
$485$	66.8616	3.03603
$486$	−11.6759	−0.529630
$487$	−43.3546	−1.96459	−0.982293	−	0.187351i	$-0.940010\pi$
$487$	−43.3546	−1.96459	−0.982293	+	0.187351i	$0.940010\pi$
$488$	4.68551	0.212103
$489$	6.35322	0.287303
$490$	−19.4671	−0.879433
$491$	11.7792	0.531589	0.265794	−	0.964030i	$-0.414366\pi$
$491$	11.7792	0.531589	0.265794	+	0.964030i	$0.414366\pi$
$492$	−10.6519	−0.480224
$493$	4.80533	0.216421
$494$	−2.07746	−0.0934691
$495$	−21.1932	−0.952564
$496$	−3.93079	−0.176498
$497$	1.63823	0.0734846
$498$	31.3745	1.40592
$499$	−14.9516	−0.669325	−0.334663	−	0.942338i	$-0.608622\pi$
$499$	−14.9516	−0.669325	−0.334663	+	0.942338i	$0.608622\pi$
$500$	−27.6927	−1.23845
$501$	−42.4238	−1.89536
$502$	−28.0554	−1.25217
$503$	−11.3813	−0.507469	−0.253734	−	0.967274i	$-0.581659\pi$
$503$	−11.3813	−0.507469	−0.253734	+	0.967274i	$0.581659\pi$
$504$	−1.77626	−0.0791207
$505$	−5.36617	−0.238792
$506$	38.1064	1.69404
$507$	17.7663	0.789029
$508$	−11.5486	−0.512385
$509$	−8.22872	−0.364732	−0.182366	−	0.983231i	$-0.558376\pi$
$509$	−8.22872	−0.364732	−0.182366	+	0.983231i	$0.558376\pi$
$510$	−22.7547	−1.00759
$511$	17.0201	0.752923
$512$	−1.00000	−0.0441942
$513$	−3.71237	−0.163905
$514$	11.4019	0.502915
$515$	2.64586	0.116590
$516$	−8.90161	−0.391872
$517$	−23.0223	−1.01252
$518$	14.7851	0.649620
$519$	−32.6623	−1.43371
$520$	−8.50581	−0.373005
$521$	14.5267	0.636428	0.318214	−	0.948019i	$-0.396917\pi$
$521$	14.5267	0.636428	0.318214	+	0.948019i	$0.396917\pi$
$522$	−2.09684	−0.0917763
$523$	43.6760	1.90982	0.954909	−	0.296898i	$-0.0959521\pi$
$523$	43.6760	1.90982	0.954909	+	0.296898i	$0.0959521\pi$
$524$	−2.24440	−0.0980469
$525$	−36.0624	−1.57389
$526$	32.2678	1.40694
$527$	−10.6782	−0.465150
$528$	−8.93345	−0.388779
$529$	53.1540	2.31104
$530$	−11.8962	−0.516738
$531$	8.89338	0.385940
$532$	−1.49846	−0.0649663
$533$	−10.8166	−0.468518
$534$	14.8147	0.641093
$535$	−71.5011	−3.09126
$536$	8.57101	0.370211
$537$	−13.7744	−0.594409
$538$	25.3155	1.09143
$539$	−20.7619	−0.894280
$540$	−15.1997	−0.654092
$541$	−24.4618	−1.05170	−0.525848	−	0.850578i	$-0.676252\pi$
$541$	−24.4618	−1.05170	−0.525848	+	0.850578i	$0.676252\pi$
$542$	7.88294	0.338601
$543$	23.3799	1.00333
$544$	−2.71655	−0.116471
$545$	−55.4473	−2.37510
$546$	−6.36860	−0.272551
$547$	−5.66493	−0.242215	−0.121107	−	0.992639i	$-0.538645\pi$
$547$	−5.66493	−0.242215	−0.121107	+	0.992639i	$0.538645\pi$
$548$	0.788239	0.0336719
$549$	−5.55415	−0.237045
$550$	−51.3681	−2.19034
$551$	−1.76891	−0.0753579
$552$	−17.8531	−0.759879
$553$	11.1804	0.475438
$554$	−6.05207	−0.257128
$555$	−82.6479	−3.50821
$556$	0.0659961	0.00279886
$557$	11.5574	0.489703	0.244852	−	0.969561i	$-0.421261\pi$
$557$	11.5574	0.489703	0.244852	+	0.969561i	$0.421261\pi$
$558$	4.65952	0.197253
$559$	−9.03925	−0.382319
$560$	−6.13520	−0.259259
$561$	−24.2682	−1.02460
$562$	23.4655	0.989833
$563$	−10.8222	−0.456100	−0.228050	−	0.973649i	$-0.573235\pi$
$563$	−10.8222	−0.456100	−0.228050	+	0.973649i	$0.573235\pi$
$564$	10.7861	0.454177
$565$	41.5104	1.74635
$566$	−31.9526	−1.34307
$567$	−16.7093	−0.701726
$568$	−1.09328	−0.0458729
$569$	6.77462	0.284007	0.142003	−	0.989866i	$-0.454646\pi$
$569$	6.77462	0.284007	0.142003	+	0.989866i	$0.454646\pi$
$570$	8.37630	0.350845
$571$	2.24551	0.0939718	0.0469859	−	0.998896i	$-0.485038\pi$
$571$	2.24551	0.0939718	0.0469859	+	0.998896i	$0.485038\pi$
$572$	−9.07158	−0.379302
$573$	−46.6782	−1.95001
$574$	−7.80193	−0.325646
$575$	−102.657	−4.28109
$576$	1.18539	0.0493913
$577$	0.473162	0.0196980	0.00984899	−	0.999951i	$-0.496865\pi$
$577$	0.473162	0.0196980	0.00984899	+	0.999951i	$0.496865\pi$
$578$	9.62034	0.400153
$579$	7.50623	0.311948
$580$	−7.24251	−0.300729
$581$	22.9801	0.953377
$582$	−33.4088	−1.38484
$583$	−12.6875	−0.525462
$584$	−11.3584	−0.470014
$585$	10.0827	0.416869
$586$	0.530799	0.0219271
$587$	18.2336	0.752581	0.376291	−	0.926502i	$-0.377199\pi$
$587$	18.2336	0.752581	0.376291	+	0.926502i	$0.377199\pi$
$588$	9.72712	0.401140
$589$	3.93079	0.161966
$590$	30.7178	1.26463
$591$	5.99667	0.246670
$592$	−9.86688	−0.405526
$593$	−32.4418	−1.33223	−0.666113	−	0.745850i	$-0.732043\pi$
$593$	−32.4418	−1.33223	−0.666113	+	0.745850i	$0.732043\pi$
$594$	−16.2107	−0.665134
$595$	−16.6666	−0.683263
$596$	21.7928	0.892666
$597$	−25.1716	−1.03021
$598$	−18.1292	−0.741357
$599$	1.69293	0.0691714	0.0345857	−	0.999402i	$-0.488989\pi$
$599$	1.69293	0.0691714	0.0345857	+	0.999402i	$0.488989\pi$
$600$	24.0663	0.982504
$601$	−36.2204	−1.47746	−0.738731	−	0.674000i	$-0.764575\pi$
$601$	−36.2204	−1.47746	−0.738731	+	0.674000i	$0.764575\pi$
$602$	−6.51996	−0.265734
$603$	−10.1600	−0.413747
$604$	3.76642	0.153254
$605$	−33.0327	−1.34297
$606$	2.68132	0.108921
$607$	22.6619	0.919819	0.459910	−	0.887966i	$-0.347882\pi$
$607$	22.6619	0.919819	0.459910	+	0.887966i	$0.347882\pi$
$608$	1.00000	0.0405554
$609$	−5.42272	−0.219740
$610$	−19.1841	−0.776740
$611$	10.9529	0.443106
$612$	3.22017	0.130168
$613$	−33.5176	−1.35376	−0.676881	−	0.736092i	$-0.736669\pi$
$613$	−33.5176	−1.35376	−0.676881	+	0.736092i	$0.736669\pi$
$614$	−12.2045	−0.492532
$615$	43.6124	1.75862
$616$	−6.54328	−0.263636
$617$	−41.9273	−1.68793	−0.843965	−	0.536399i	$-0.819784\pi$
$617$	−41.9273	−1.68793	−0.843965	+	0.536399i	$0.819784\pi$
$618$	−1.32206	−0.0531809
$619$	15.7090	0.631398	0.315699	−	0.948859i	$-0.397761\pi$
$619$	15.7090	0.631398	0.315699	+	0.948859i	$0.397761\pi$
$620$	16.0940	0.646351
$621$	−32.3965	−1.30003
$622$	−20.4475	−0.819871
$623$	10.8510	0.434734
$624$	4.25010	0.170140
$625$	54.5651	2.18261
$626$	−32.5985	−1.30290
$627$	8.93345	0.356768
$628$	1.35547	0.0540892
$629$	−26.8039	−1.06874
$630$	7.27260	0.289747
$631$	41.4461	1.64994	0.824972	−	0.565174i	$-0.191191\pi$
$631$	41.4461	1.64994	0.824972	+	0.565174i	$0.191191\pi$
$632$	−7.46127	−0.296793
$633$	2.04582	0.0813141
$634$	26.8916	1.06800
$635$	47.2838	1.87640
$636$	5.94419	0.235702
$637$	9.87753	0.391362
$638$	−7.72425	−0.305806
$639$	1.29596	0.0512674
$640$	4.09434	0.161843
$641$	38.9245	1.53742	0.768712	−	0.639595i	$-0.220898\pi$
$641$	38.9245	1.53742	0.768712	+	0.639595i	$0.220898\pi$
$642$	35.7270	1.41003
$643$	−4.98299	−0.196510	−0.0982550	−	0.995161i	$-0.531326\pi$
$643$	−4.98299	−0.196510	−0.0982550	+	0.995161i	$0.531326\pi$
$644$	−13.0765	−0.515285
$645$	36.4462	1.43507
$646$	2.71655	0.106881
$647$	−12.8205	−0.504024	−0.252012	−	0.967724i	$-0.581092\pi$
$647$	−12.8205	−0.504024	−0.252012	+	0.967724i	$0.581092\pi$
$648$	11.1510	0.438053
$649$	32.7610	1.28598
$650$	24.4384	0.958555
$651$	12.0501	0.472282
$652$	−3.10546	−0.121619
$653$	41.3605	1.61856	0.809281	−	0.587422i	$-0.199857\pi$
$653$	41.3605	1.61856	0.809281	+	0.587422i	$0.199857\pi$
$654$	27.7054	1.08337
$655$	9.18932	0.359057
$656$	5.20665	0.203285
$657$	13.4641	0.525286
$658$	7.90026	0.307984
$659$	−23.9235	−0.931926	−0.465963	−	0.884804i	$-0.654292\pi$
$659$	−23.9235	−0.931926	−0.465963	+	0.884804i	$0.654292\pi$
$660$	36.5766	1.42374
$661$	48.5286	1.88754	0.943771	−	0.330599i	$-0.107251\pi$
$661$	48.5286	1.88754	0.943771	+	0.330599i	$0.107251\pi$
$662$	28.2584	1.09829
$663$	11.5456	0.448395
$664$	−15.3359	−0.595147
$665$	6.13520	0.237913
$666$	11.6961	0.453215
$667$	−15.4366	−0.597707
$668$	20.7368	0.802331
$669$	30.9257	1.19566
$670$	−35.0927	−1.35575
$671$	−20.4601	−0.789854
$672$	3.06558	0.118257
$673$	−41.8990	−1.61509	−0.807545	−	0.589806i	$-0.799204\pi$
$673$	−41.8990	−1.61509	−0.807545	+	0.589806i	$0.799204\pi$
$674$	19.2134	0.740072
$675$	43.6710	1.68090
$676$	−8.68418	−0.334007
$677$	−14.1658	−0.544438	−0.272219	−	0.962235i	$-0.587757\pi$
$677$	−14.1658	−0.544438	−0.272219	+	0.962235i	$0.587757\pi$
$678$	−20.7415	−0.796573
$679$	−24.4701	−0.939078
$680$	11.1225	0.426528
$681$	−11.2978	−0.432931
$682$	17.1645	0.657263
$683$	−1.01076	−0.0386757	−0.0193378	−	0.999813i	$-0.506156\pi$
$683$	−1.01076	−0.0386757	−0.0193378	+	0.999813i	$0.506156\pi$
$684$	−1.18539	−0.0453245
$685$	−3.22732	−0.123310
$686$	17.6138	0.672498
$687$	−17.3375	−0.661467
$688$	4.35112	0.165885
$689$	6.03610	0.229957
$690$	73.0968	2.78275
$691$	0.825563	0.0314059	0.0157030	−	0.999877i	$-0.495001\pi$
$691$	0.825563	0.0314059	0.0157030	+	0.999877i	$0.495001\pi$
$692$	15.9654	0.606912
$693$	7.75634	0.294639
$694$	16.9938	0.645077
$695$	−0.270211	−0.0102497
$696$	3.61887	0.137173
$697$	14.1441	0.535747
$698$	11.9704	0.453087
$699$	−24.0586	−0.909981
$700$	17.6273	0.666250
$701$	−38.0743	−1.43805	−0.719024	−	0.694985i	$-0.755411\pi$
$701$	−38.0743	−1.43805	−0.719024	+	0.694985i	$0.755411\pi$
$702$	7.71228	0.291081
$703$	9.86688	0.372136
$704$	4.36668	0.164575
$705$	−44.1621	−1.66324
$706$	−30.9605	−1.16521
$707$	1.96392	0.0738610
$708$	−15.3488	−0.576842
$709$	−7.04075	−0.264421	−0.132211	−	0.991222i	$-0.542207\pi$
$709$	−7.04075	−0.264421	−0.132211	+	0.991222i	$0.542207\pi$
$710$	4.47625	0.167991
$711$	8.84451	0.331695
$712$	−7.24142	−0.271384
$713$	34.3026	1.28464
$714$	8.32780	0.311660
$715$	37.1422	1.38904
$716$	6.73294	0.251622
$717$	5.50116	0.205445
$718$	30.9264	1.15416
$719$	−47.0755	−1.75562	−0.877810	−	0.479009i	$-0.840996\pi$
$719$	−47.0755	−1.75562	−0.877810	+	0.479009i	$0.840996\pi$
$720$	−4.85339	−0.180875
$721$	−0.968336	−0.0360627
$722$	−1.00000	−0.0372161
$723$	−0.144926	−0.00538985
$724$	−11.4281	−0.424723
$725$	20.8088	0.772819
$726$	16.5055	0.612576
$727$	−38.1337	−1.41430	−0.707151	−	0.707062i	$-0.750020\pi$
$727$	−38.1337	−1.41430	−0.707151	+	0.707062i	$0.750020\pi$
$728$	3.11298	0.115375
$729$	9.56624	0.354305
$730$	46.5052	1.72123
$731$	11.8200	0.437180
$732$	9.58572	0.354298
$733$	−12.9104	−0.476856	−0.238428	−	0.971160i	$-0.576632\pi$
$733$	−12.9104	−0.476856	−0.238428	+	0.971160i	$0.576632\pi$
$734$	36.5323	1.34843
$735$	−39.8262	−1.46901
$736$	8.72662	0.321668
$737$	−37.4269	−1.37864
$738$	−6.17191	−0.227191
$739$	9.26237	0.340722	0.170361	−	0.985382i	$-0.445507\pi$
$739$	9.26237	0.340722	0.170361	+	0.985382i	$0.445507\pi$
$740$	40.3984	1.48507
$741$	−4.25010	−0.156131
$742$	4.35380	0.159833
$743$	−8.65339	−0.317462	−0.158731	−	0.987322i	$-0.550740\pi$
$743$	−8.65339	−0.317462	−0.158731	+	0.987322i	$0.550740\pi$
$744$	−8.04171	−0.294823
$745$	−89.2270	−3.26903
$746$	−14.1511	−0.518110
$747$	18.1790	0.665135
$748$	11.8623	0.433729
$749$	26.1681	0.956162
$750$	−56.6543	−2.06872
$751$	−39.3621	−1.43634	−0.718172	−	0.695865i	$-0.755021\pi$
$751$	−39.3621	−1.43634	−0.718172	+	0.695865i	$0.755021\pi$
$752$	−5.27226	−0.192260
$753$	−57.3963	−2.09164
$754$	3.67482	0.133829
$755$	−15.4210	−0.561229
$756$	5.56283	0.202318
$757$	−30.3091	−1.10160	−0.550802	−	0.834636i	$-0.685678\pi$
$757$	−30.3091	−1.10160	−0.550802	+	0.834636i	$0.685678\pi$
$758$	−7.71892	−0.280364
$759$	77.9589	2.82973
$760$	−4.09434	−0.148517
$761$	16.7137	0.605871	0.302936	−	0.953011i	$-0.402033\pi$
$761$	16.7137	0.605871	0.302936	+	0.953011i	$0.402033\pi$
$762$	−23.6263	−0.855891
$763$	20.2927	0.734647
$764$	22.8164	0.825467
$765$	−13.1845	−0.476687
$766$	−12.3725	−0.447038
$767$	−15.5861	−0.562781
$768$	−2.04582	−0.0738223
$769$	37.2199	1.34218	0.671092	−	0.741374i	$-0.265825\pi$
$769$	37.2199	1.34218	0.671092	+	0.741374i	$0.265825\pi$
$770$	26.7904	0.965460
$771$	23.3262	0.840074
$772$	−3.66905	−0.132052
$773$	−42.1269	−1.51520	−0.757599	−	0.652720i	$-0.773628\pi$
$773$	−42.1269	−1.51520	−0.757599	+	0.652720i	$0.773628\pi$
$774$	−5.15777	−0.185392
$775$	−46.2405	−1.66101
$776$	16.3302	0.586221
$777$	30.2477	1.08513
$778$	25.4546	0.912591
$779$	−5.20665	−0.186547
$780$	−17.4014	−0.623070
$781$	4.77399	0.170827
$782$	23.7063	0.847737
$783$	6.56683	0.234679
$784$	−4.75463	−0.169808
$785$	−5.54977	−0.198080
$786$	−4.59163	−0.163778
$787$	−27.6128	−0.984291	−0.492146	−	0.870513i	$-0.663787\pi$
$787$	−27.6128	−0.984291	−0.492146	+	0.870513i	$0.663787\pi$
$788$	−2.93118	−0.104419
$789$	66.0142	2.35017
$790$	30.5490	1.08688
$791$	−15.1921	−0.540168
$792$	−5.17622	−0.183929
$793$	9.73393	0.345662
$794$	−12.6444	−0.448733
$795$	−24.3375	−0.863164
$796$	12.3039	0.436100
$797$	−44.7859	−1.58640	−0.793200	−	0.608962i	$-0.791586\pi$
$797$	−44.7859	−1.58640	−0.793200	+	0.608962i	$0.791586\pi$
$798$	−3.06558	−0.108520
$799$	−14.3224	−0.506689
$800$	−11.7636	−0.415908
$801$	8.58391	0.303298
$802$	14.7905	0.522272
$803$	49.5985	1.75029
$804$	17.5348	0.618404
$805$	53.5396	1.88702
$806$	−8.16605	−0.287637
$807$	51.7910	1.82313
$808$	−1.31063	−0.0461078
$809$	37.4511	1.31671	0.658355	−	0.752708i	$-0.271253\pi$
$809$	37.4511	1.31671	0.658355	+	0.752708i	$0.271253\pi$
$810$	−45.6561	−1.60419
$811$	−38.7566	−1.36093	−0.680464	−	0.732782i	$-0.738222\pi$
$811$	−38.7566	−1.36093	−0.680464	+	0.732782i	$0.738222\pi$
$812$	2.65063	0.0930188
$813$	16.1271	0.565602
$814$	43.0855	1.51015
$815$	12.7148	0.445381
$816$	−5.55758	−0.194554
$817$	−4.35112	−0.152226
$818$	7.91564	0.276764
$819$	−3.69009	−0.128942
$820$	−21.3178	−0.744450
$821$	28.0920	0.980417	0.490208	−	0.871605i	$-0.336921\pi$
$821$	28.0920	0.980417	0.490208	+	0.871605i	$0.336921\pi$
$822$	1.61260	0.0562458
$823$	32.8455	1.14492	0.572461	−	0.819932i	$-0.305989\pi$
$823$	32.8455	1.14492	0.572461	+	0.819932i	$0.305989\pi$
$824$	0.646222	0.0225122
$825$	−105.090	−3.65876
$826$	−11.2422	−0.391165
$827$	−7.59414	−0.264074	−0.132037	−	0.991245i	$-0.542152\pi$
$827$	−7.59414	−0.264074	−0.132037	+	0.991245i	$0.542152\pi$
$828$	−10.3445	−0.359495
$829$	−24.7291	−0.858878	−0.429439	−	0.903096i	$-0.641289\pi$
$829$	−24.7291	−0.858878	−0.429439	+	0.903096i	$0.641289\pi$
$830$	62.7903	2.17948
$831$	−12.3815	−0.429508
$832$	−2.07746	−0.0720228
$833$	−12.9162	−0.447520
$834$	0.135016	0.00467523
$835$	−84.9036	−2.93821
$836$	−4.36668	−0.151025
$837$	−14.5926	−0.504393
$838$	−3.22411	−0.111375
$839$	−14.8366	−0.512215	−0.256107	−	0.966648i	$-0.582440\pi$
$839$	−14.8366	−0.512215	−0.256107	+	0.966648i	$0.582440\pi$
$840$	−12.5515	−0.433069
$841$	−25.8710	−0.892102
$842$	−26.3204	−0.907061
$843$	48.0063	1.65342
$844$	−1.00000	−0.0344214
$845$	35.5560	1.22316
$846$	6.24969	0.214869
$847$	12.0894	0.415396
$848$	−2.90552	−0.0997761
$849$	−65.3693	−2.24347
$850$	−31.9566	−1.09610
$851$	86.1045	2.95163
$852$	−2.23665	−0.0766264
$853$	46.3414	1.58670	0.793350	−	0.608766i	$-0.208335\pi$
$853$	46.3414	1.58670	0.793350	+	0.608766i	$0.208335\pi$
$854$	7.02103	0.240255
$855$	4.85339	0.165983
$856$	−17.4634	−0.596886
$857$	38.8509	1.32712	0.663561	−	0.748122i	$-0.269044\pi$
$857$	38.8509	1.32712	0.663561	+	0.748122i	$0.269044\pi$
$858$	−18.5588	−0.633589
$859$	−9.96164	−0.339887	−0.169943	−	0.985454i	$-0.554358\pi$
$859$	−9.96164	−0.339887	−0.169943	+	0.985454i	$0.554358\pi$
$860$	−17.8150	−0.607485
$861$	−15.9614	−0.543962
$862$	2.92758	0.0997136
$863$	−9.72885	−0.331174	−0.165587	−	0.986195i	$-0.552952\pi$
$863$	−9.72885	−0.331174	−0.165587	+	0.986195i	$0.552952\pi$
$864$	−3.71237	−0.126297
$865$	−65.3676	−2.22257
$866$	15.5142	0.527196
$867$	19.6815	0.668419
$868$	−5.89012	−0.199924
$869$	32.5810	1.10523
$870$	−14.8169	−0.502339
$871$	17.8059	0.603330
$872$	−13.5424	−0.458604
$873$	−19.3577	−0.655159
$874$	−8.72662	−0.295182
$875$	−41.4963	−1.40283
$876$	−23.2373	−0.785114
$877$	−41.7847	−1.41097	−0.705484	−	0.708726i	$-0.749270\pi$
$877$	−41.7847	−1.41097	−0.705484	+	0.708726i	$0.749270\pi$
$878$	−25.6971	−0.867234
$879$	1.08592	0.0366272
$880$	−17.8787	−0.602690
$881$	36.0925	1.21599	0.607993	−	0.793942i	$-0.291975\pi$
$881$	36.0925	1.21599	0.607993	+	0.793942i	$0.291975\pi$
$882$	5.63609	0.189777
$883$	11.4951	0.386841	0.193421	−	0.981116i	$-0.438042\pi$
$883$	11.4951	0.386841	0.193421	+	0.981116i	$0.438042\pi$
$884$	−5.64352	−0.189812
$885$	62.8431	2.11245
$886$	4.35774	0.146401
$887$	38.3961	1.28921	0.644607	−	0.764514i	$-0.277021\pi$
$887$	38.3961	1.28921	0.644607	+	0.764514i	$0.277021\pi$
$888$	−20.1859	−0.677394
$889$	−17.3050	−0.580392
$890$	29.6489	0.993832
$891$	−48.6929	−1.63127
$892$	−15.1165	−0.506138
$893$	5.27226	0.176430
$894$	44.5841	1.49112
$895$	−27.5670	−0.921462
$896$	−1.49846	−0.0500599
$897$	−37.0891	−1.23837
$898$	13.8264	0.461393
$899$	−6.95320	−0.231902
$900$	13.9445	0.464817
$901$	−7.89301	−0.262954
$902$	−22.7358	−0.757018
$903$	−13.3387	−0.443883
$904$	10.1385	0.337201
$905$	46.7906	1.55537
$906$	7.70544	0.255996
$907$	−41.2826	−1.37077	−0.685383	−	0.728183i	$-0.740365\pi$
$907$	−41.2826	−1.37077	−0.685383	+	0.728183i	$0.740365\pi$
$908$	5.52236	0.183266
$909$	1.55361	0.0515300
$910$	−12.7456	−0.422512
$911$	22.5764	0.747991	0.373995	−	0.927431i	$-0.377988\pi$
$911$	22.5764	0.747991	0.373995	+	0.927431i	$0.377988\pi$
$912$	2.04582	0.0677440
$913$	66.9669	2.21628
$914$	−11.6026	−0.383781
$915$	−39.2472	−1.29747
$916$	8.47458	0.280008
$917$	−3.36313	−0.111060
$918$	−10.0848	−0.332850
$919$	−5.67769	−0.187290	−0.0936449	−	0.995606i	$-0.529852\pi$
$919$	−5.67769	−0.187290	−0.0936449	+	0.995606i	$0.529852\pi$
$920$	−35.7298	−1.17798
$921$	−24.9682	−0.822729
$922$	−19.3868	−0.638471
$923$	−2.27124	−0.0747586
$924$	−13.3864	−0.440380
$925$	−116.070	−3.81637
$926$	−30.5402	−1.00361
$927$	−0.766026	−0.0251596
$928$	−1.76891	−0.0580672
$929$	−24.6134	−0.807540	−0.403770	−	0.914860i	$-0.632300\pi$
$929$	−24.6134	−0.807540	−0.403770	+	0.914860i	$0.632300\pi$
$930$	32.9255	1.07967
$931$	4.75463	0.155827
$932$	11.7599	0.385208
$933$	−41.8320	−1.36952
$934$	23.8146	0.779236
$935$	−48.5684	−1.58836
$936$	2.46259	0.0804924
$937$	−20.7073	−0.676477	−0.338239	−	0.941060i	$-0.609831\pi$
$937$	−20.7073	−0.676477	−0.338239	+	0.941060i	$0.609831\pi$
$938$	12.8433	0.419348
$939$	−66.6907	−2.17637
$940$	21.5865	0.704072
$941$	7.68290	0.250455	0.125228	−	0.992128i	$-0.460034\pi$
$941$	7.68290	0.250455	0.125228	+	0.992128i	$0.460034\pi$
$942$	2.77306	0.0903510
$943$	−45.4365	−1.47961
$944$	7.50249	0.244185
$945$	−22.7761	−0.740907
$946$	−18.9999	−0.617741
$947$	−30.5206	−0.991787	−0.495894	−	0.868383i	$-0.665159\pi$
$947$	−30.5206	−0.991787	−0.495894	+	0.868383i	$0.665159\pi$
$948$	−15.2644	−0.495766
$949$	−23.5966	−0.765976
$950$	11.7636	0.381663
$951$	55.0154	1.78400
$952$	−4.07064	−0.131930
$953$	−7.70126	−0.249468	−0.124734	−	0.992190i	$-0.539808\pi$
$953$	−7.70126	−0.249468	−0.124734	+	0.992190i	$0.539808\pi$
$954$	3.44418	0.111509
$955$	−93.4181	−3.02294
$956$	−2.68897	−0.0869676
$957$	−15.8024	−0.510820
$958$	31.5928	1.02072
$959$	1.18114	0.0381411
$960$	8.37630	0.270344
$961$	−15.5489	−0.501576
$962$	−20.4980	−0.660882
$963$	20.7009	0.667078
$964$	0.0708398	0.00228160
$965$	15.0224	0.483587
$966$	−26.7521	−0.860736
$967$	10.0243	0.322358	0.161179	−	0.986925i	$-0.448470\pi$
$967$	10.0243	0.322358	0.161179	+	0.986925i	$0.448470\pi$
$968$	−8.06789	−0.259312
$969$	5.55758	0.178535
$970$	−66.8616	−2.14680
$971$	25.6509	0.823177	0.411589	−	0.911370i	$-0.364974\pi$
$971$	25.6509	0.823177	0.411589	+	0.911370i	$0.364974\pi$
$972$	11.6759	0.374505
$973$	0.0988922	0.00317034
$974$	43.3546	1.38917
$975$	49.9967	1.60118
$976$	−4.68551	−0.149979
$977$	35.3621	1.13133	0.565667	−	0.824634i	$-0.308619\pi$
$977$	35.3621	1.13133	0.565667	+	0.824634i	$0.308619\pi$
$978$	−6.35322	−0.203154
$979$	31.6210	1.01061
$980$	19.4671	0.621853
$981$	16.0531	0.512535
$982$	−11.7792	−0.375890
$983$	−30.7198	−0.979809	−0.489904	−	0.871776i	$-0.662968\pi$
$983$	−30.7198	−0.979809	−0.489904	+	0.871776i	$0.662968\pi$
$984$	10.6519	0.339569
$985$	12.0013	0.382392
$986$	−4.80533	−0.153033
$987$	16.1625	0.514459
$988$	2.07746	0.0660927
$989$	−37.9705	−1.20739
$990$	21.1932	0.673565
$991$	−22.4415	−0.712877	−0.356439	−	0.934319i	$-0.616009\pi$
$991$	−22.4415	−0.712877	−0.356439	+	0.934319i	$0.616009\pi$
$992$	3.93079	0.124803
$993$	57.8116	1.83460
$994$	−1.63823	−0.0519615
$995$	−50.3764	−1.59704
$996$	−31.3745	−0.994139
$997$	−22.9174	−0.725803	−0.362901	−	0.931828i	$-0.618214\pi$
$997$	−22.9174	−0.725803	−0.362901	+	0.931828i	$0.618214\pi$
$998$	14.9516	0.473284
$999$	−36.6295	−1.15891

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.f.1.10	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.f.1.10	✓	34	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:	\( N \)	\(=\)	\( 8018 = 2 \cdot 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8018.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.04582 q^{3} +1.00000 q^{4} -4.09434 q^{5} +2.04582 q^{6} +1.49846 q^{7} -1.00000 q^{8} +1.18539 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.04582 q^{3} +1.00000 q^{4} -4.09434 q^{5} +2.04582 q^{6} +1.49846 q^{7} -1.00000 q^{8} +1.18539 q^{9} +4.09434 q^{10} +4.36668 q^{11} -2.04582 q^{12} -2.07746 q^{13} -1.49846 q^{14} +8.37630 q^{15} +1.00000 q^{16} +2.71655 q^{17} -1.18539 q^{18} -1.00000 q^{19} -4.09434 q^{20} -3.06558 q^{21} -4.36668 q^{22} -8.72662 q^{23} +2.04582 q^{24} +11.7636 q^{25} +2.07746 q^{26} +3.71237 q^{27} +1.49846 q^{28} +1.76891 q^{29} -8.37630 q^{30} -3.93079 q^{31} -1.00000 q^{32} -8.93345 q^{33} -2.71655 q^{34} -6.13520 q^{35} +1.18539 q^{36} -9.86688 q^{37} +1.00000 q^{38} +4.25010 q^{39} +4.09434 q^{40} +5.20665 q^{41} +3.06558 q^{42} +4.35112 q^{43} +4.36668 q^{44} -4.85339 q^{45} +8.72662 q^{46} -5.27226 q^{47} -2.04582 q^{48} -4.75463 q^{49} -11.7636 q^{50} -5.55758 q^{51} -2.07746 q^{52} -2.90552 q^{53} -3.71237 q^{54} -17.8787 q^{55} -1.49846 q^{56} +2.04582 q^{57} -1.76891 q^{58} +7.50249 q^{59} +8.37630 q^{60} -4.68551 q^{61} +3.93079 q^{62} +1.77626 q^{63} +1.00000 q^{64} +8.50581 q^{65} +8.93345 q^{66} -8.57101 q^{67} +2.71655 q^{68} +17.8531 q^{69} +6.13520 q^{70} +1.09328 q^{71} -1.18539 q^{72} +11.3584 q^{73} +9.86688 q^{74} -24.0663 q^{75} -1.00000 q^{76} +6.54328 q^{77} -4.25010 q^{78} +7.46127 q^{79} -4.09434 q^{80} -11.1510 q^{81} -5.20665 q^{82} +15.3359 q^{83} -3.06558 q^{84} -11.1225 q^{85} -4.35112 q^{86} -3.61887 q^{87} -4.36668 q^{88} +7.24142 q^{89} +4.85339 q^{90} -3.11298 q^{91} -8.72662 q^{92} +8.04171 q^{93} +5.27226 q^{94} +4.09434 q^{95} +2.04582 q^{96} -16.3302 q^{97} +4.75463 q^{98} +5.17622 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9}+O(q^{10}) \) 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9	\( 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9} - 7 q^{10} + 4 q^{11} - 10 q^{12} - 5 q^{13} + 6 q^{14} - 17 q^{15} + 34 q^{16} + 8 q^{17} - 38 q^{18} - 34 q^{19} + 7 q^{20} - 4 q^{22} - 24 q^{23} + 10 q^{24} + 5 q^{25} + 5 q^{26} - 31 q^{27} - 6 q^{28} + 24 q^{29} + 17 q^{30} - 28 q^{31} - 34 q^{32} - 16 q^{33} - 8 q^{34} + 2 q^{35} + 38 q^{36} - 36 q^{37} + 34 q^{38} - 9 q^{39} - 7 q^{40} + 9 q^{41} - 24 q^{43} + 4 q^{44} + 22 q^{45} + 24 q^{46} - 29 q^{47} - 10 q^{48} + 22 q^{49} - 5 q^{50} - 21 q^{51} - 5 q^{52} - 9 q^{53} + 31 q^{54} - 28 q^{55} + 6 q^{56} + 10 q^{57} - 24 q^{58} - 28 q^{59} - 17 q^{60} + 23 q^{61} + 28 q^{62} - 27 q^{63} + 34 q^{64} - 6 q^{65} + 16 q^{66} - 51 q^{67} + 8 q^{68} - 17 q^{69} - 2 q^{70} - 31 q^{71} - 38 q^{72} - 26 q^{73} + 36 q^{74} - 109 q^{75} - 34 q^{76} - 28 q^{77} + 9 q^{78} - 36 q^{79} + 7 q^{80} + 6 q^{81} - 9 q^{82} - 10 q^{83} - 32 q^{85} + 24 q^{86} - 8 q^{87} - 4 q^{88} - 34 q^{89} - 22 q^{90} - 41 q^{91} - 24 q^{92} - 33 q^{93} + 29 q^{94} - 7 q^{95} + 10 q^{96} - 56 q^{97} - 22 q^{98} - 28 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9 - 7 * q^10 + 4 * q^11 - 10 * q^12 - 5 * q^13 + 6 * q^14 - 17 * q^15 + 34 * q^16 + 8 * q^17 - 38 * q^18 - 34 * q^19 + 7 * q^20 - 4 * q^22 - 24 * q^23 + 10 * q^24 + 5 * q^25 + 5 * q^26 - 31 * q^27 - 6 * q^28 + 24 * q^29 + 17 * q^30 - 28 * q^31 - 34 * q^32 - 16 * q^33 - 8 * q^34 + 2 * q^35 + 38 * q^36 - 36 * q^37 + 34 * q^38 - 9 * q^39 - 7 * q^40 + 9 * q^41 - 24 * q^43 + 4 * q^44 + 22 * q^45 + 24 * q^46 - 29 * q^47 - 10 * q^48 + 22 * q^49 - 5 * q^50 - 21 * q^51 - 5 * q^52 - 9 * q^53 + 31 * q^54 - 28 * q^55 + 6 * q^56 + 10 * q^57 - 24 * q^58 - 28 * q^59 - 17 * q^60 + 23 * q^61 + 28 * q^62 - 27 * q^63 + 34 * q^64 - 6 * q^65 + 16 * q^66 - 51 * q^67 + 8 * q^68 - 17 * q^69 - 2 * q^70 - 31 * q^71 - 38 * q^72 - 26 * q^73 + 36 * q^74 - 109 * q^75 - 34 * q^76 - 28 * q^77 + 9 * q^78 - 36 * q^79 + 7 * q^80 + 6 * q^81 - 9 * q^82 - 10 * q^83 - 32 * q^85 + 24 * q^86 - 8 * q^87 - 4 * q^88 - 34 * q^89 - 22 * q^90 - 41 * q^91 - 24 * q^92 - 33 * q^93 + 29 * q^94 - 7 * q^95 + 10 * q^96 - 56 * q^97 - 22 * q^98 - 28 * q^99

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