LMFDB - Embedded newform 8034.2.a.ba.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8034, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8034 = 2 \cdot 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8034.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$64.1518129839$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - x^{13} - 44 x^{12} + 36 x^{11} + 722 x^{10} - 451 x^{9} - 5438 x^{8} + 2268 x^{7} + 18441 x^{6} + \cdots - 1492 $ x^14 - x^13 - 44x^12 + 36x^11 + 722x^10 - 451x^9 - 5438x^8 + 2268x^7 + 18441x^6 - 4126x^5 - 22759x^4 + 2997x^3 + 10504x^2 - 506x - 1492
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$3.09495$ of defining polynomial
Character	$\chi$	$=$	8034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.09495 q^{5} +1.00000 q^{6} +3.97310 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.09495 q^{5} +1.00000 q^{6} +3.97310 q^{7} -1.00000 q^{8} +1.00000 q^{9} +3.09495 q^{10} -2.08878 q^{11} -1.00000 q^{12} -1.00000 q^{13} -3.97310 q^{14} +3.09495 q^{15} +1.00000 q^{16} +3.07102 q^{17} -1.00000 q^{18} -6.35933 q^{19} -3.09495 q^{20} -3.97310 q^{21} +2.08878 q^{22} +0.753374 q^{23} +1.00000 q^{24} +4.57874 q^{25} +1.00000 q^{26} -1.00000 q^{27} +3.97310 q^{28} -7.73052 q^{29} -3.09495 q^{30} +5.41795 q^{31} -1.00000 q^{32} +2.08878 q^{33} -3.07102 q^{34} -12.2966 q^{35} +1.00000 q^{36} +6.26162 q^{37} +6.35933 q^{38} +1.00000 q^{39} +3.09495 q^{40} -3.19603 q^{41} +3.97310 q^{42} +4.21307 q^{43} -2.08878 q^{44} -3.09495 q^{45} -0.753374 q^{46} -9.09805 q^{47} -1.00000 q^{48} +8.78553 q^{49} -4.57874 q^{50} -3.07102 q^{51} -1.00000 q^{52} +1.78997 q^{53} +1.00000 q^{54} +6.46468 q^{55} -3.97310 q^{56} +6.35933 q^{57} +7.73052 q^{58} +3.06235 q^{59} +3.09495 q^{60} -7.26725 q^{61} -5.41795 q^{62} +3.97310 q^{63} +1.00000 q^{64} +3.09495 q^{65} -2.08878 q^{66} -4.59049 q^{67} +3.07102 q^{68} -0.753374 q^{69} +12.2966 q^{70} +6.81056 q^{71} -1.00000 q^{72} -1.90860 q^{73} -6.26162 q^{74} -4.57874 q^{75} -6.35933 q^{76} -8.29894 q^{77} -1.00000 q^{78} +3.61660 q^{79} -3.09495 q^{80} +1.00000 q^{81} +3.19603 q^{82} +11.1151 q^{83} -3.97310 q^{84} -9.50467 q^{85} -4.21307 q^{86} +7.73052 q^{87} +2.08878 q^{88} -10.2078 q^{89} +3.09495 q^{90} -3.97310 q^{91} +0.753374 q^{92} -5.41795 q^{93} +9.09805 q^{94} +19.6818 q^{95} +1.00000 q^{96} +14.6236 q^{97} -8.78553 q^{98} -2.08878 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 14 q^{2} - 14 q^{3} + 14 q^{4} - q^{5} + 14 q^{6} + 5 q^{7} - 14 q^{8} + 14 q^{9}+O(q^{10}) $ 14 * q - 14 * q^2 - 14 * q^3 + 14 * q^4 - q^5 + 14 * q^6 + 5 * q^7 - 14 * q^8 + 14 * q^9	\( 14 q - 14 q^{2} - 14 q^{3} + 14 q^{4} - q^{5} + 14 q^{6} + 5 q^{7} - 14 q^{8} + 14 q^{9} + q^{10} - q^{11} - 14 q^{12} - 14 q^{13} - 5 q^{14} + q^{15} + 14 q^{16} - 12 q^{17} - 14 q^{18} + 10 q^{19} - q^{20} - 5 q^{21} + q^{22} - q^{23} + 14 q^{24} + 19 q^{25} + 14 q^{26} - 14 q^{27} + 5 q^{28} + 6 q^{29} - q^{30} + 20 q^{31} - 14 q^{32} + q^{33} + 12 q^{34} - 16 q^{35} + 14 q^{36} - 3 q^{37} - 10 q^{38} + 14 q^{39} + q^{40} + q^{41} + 5 q^{42} + 6 q^{43} - q^{44} - q^{45} + q^{46} - 13 q^{47} - 14 q^{48} + 9 q^{49} - 19 q^{50} + 12 q^{51} - 14 q^{52} - 27 q^{53} + 14 q^{54} + 10 q^{55} - 5 q^{56} - 10 q^{57} - 6 q^{58} - 6 q^{59} + q^{60} - 4 q^{61} - 20 q^{62} + 5 q^{63} + 14 q^{64} + q^{65} - q^{66} + 13 q^{67} - 12 q^{68} + q^{69} + 16 q^{70} + 18 q^{71} - 14 q^{72} + 11 q^{73} + 3 q^{74} - 19 q^{75} + 10 q^{76} - 15 q^{77} - 14 q^{78} + 33 q^{79} - q^{80} + 14 q^{81} - q^{82} - 25 q^{83} - 5 q^{84} + 25 q^{85} - 6 q^{86} - 6 q^{87} + q^{88} + 3 q^{89} + q^{90} - 5 q^{91} - q^{92} - 20 q^{93} + 13 q^{94} + 30 q^{95} + 14 q^{96} + 11 q^{97} - 9 q^{98} - q^{99}+O(q^{100}) \) 14 * q - 14 * q^2 - 14 * q^3 + 14 * q^4 - q^5 + 14 * q^6 + 5 * q^7 - 14 * q^8 + 14 * q^9 + q^10 - q^11 - 14 * q^12 - 14 * q^13 - 5 * q^14 + q^15 + 14 * q^16 - 12 * q^17 - 14 * q^18 + 10 * q^19 - q^20 - 5 * q^21 + q^22 - q^23 + 14 * q^24 + 19 * q^25 + 14 * q^26 - 14 * q^27 + 5 * q^28 + 6 * q^29 - q^30 + 20 * q^31 - 14 * q^32 + q^33 + 12 * q^34 - 16 * q^35 + 14 * q^36 - 3 * q^37 - 10 * q^38 + 14 * q^39 + q^40 + q^41 + 5 * q^42 + 6 * q^43 - q^44 - q^45 + q^46 - 13 * q^47 - 14 * q^48 + 9 * q^49 - 19 * q^50 + 12 * q^51 - 14 * q^52 - 27 * q^53 + 14 * q^54 + 10 * q^55 - 5 * q^56 - 10 * q^57 - 6 * q^58 - 6 * q^59 + q^60 - 4 * q^61 - 20 * q^62 + 5 * q^63 + 14 * q^64 + q^65 - q^66 + 13 * q^67 - 12 * q^68 + q^69 + 16 * q^70 + 18 * q^71 - 14 * q^72 + 11 * q^73 + 3 * q^74 - 19 * q^75 + 10 * q^76 - 15 * q^77 - 14 * q^78 + 33 * q^79 - q^80 + 14 * q^81 - q^82 - 25 * q^83 - 5 * q^84 + 25 * q^85 - 6 * q^86 - 6 * q^87 + q^88 + 3 * q^89 + q^90 - 5 * q^91 - q^92 - 20 * q^93 + 13 * q^94 + 30 * q^95 + 14 * q^96 + 11 * q^97 - 9 * q^98 - q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	−3.09495	−1.38411	−0.692053	−	0.721847i	$-0.743293\pi$
$5$	−3.09495	−1.38411	−0.692053	+	0.721847i	$0.743293\pi$
$6$	1.00000	0.408248
$7$	3.97310	1.50169	0.750846	−	0.660478i	$-0.229646\pi$
$7$	3.97310	1.50169	0.750846	+	0.660478i	$0.229646\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	3.09495	0.978710
$11$	−2.08878	−0.629791	−0.314896	−	0.949126i	$-0.601969\pi$
$11$	−2.08878	−0.629791	−0.314896	+	0.949126i	$0.601969\pi$
$12$	−1.00000	−0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−3.97310	−1.06186
$15$	3.09495	0.799114
$16$	1.00000	0.250000
$17$	3.07102	0.744832	0.372416	−	0.928066i	$-0.378529\pi$
$17$	3.07102	0.744832	0.372416	+	0.928066i	$0.378529\pi$
$18$	−1.00000	−0.235702
$19$	−6.35933	−1.45893	−0.729465	−	0.684018i	$-0.760231\pi$
$19$	−6.35933	−1.45893	−0.729465	+	0.684018i	$0.760231\pi$
$20$	−3.09495	−0.692053
$21$	−3.97310	−0.867002
$22$	2.08878	0.445329
$23$	0.753374	0.157089	0.0785447	−	0.996911i	$-0.474973\pi$
$23$	0.753374	0.157089	0.0785447	+	0.996911i	$0.474973\pi$
$24$	1.00000	0.204124
$25$	4.57874	0.915748
$26$	1.00000	0.196116
$27$	−1.00000	−0.192450
$28$	3.97310	0.750846
$29$	−7.73052	−1.43552	−0.717761	−	0.696290i	$-0.754833\pi$
$29$	−7.73052	−1.43552	−0.717761	+	0.696290i	$0.754833\pi$
$30$	−3.09495	−0.565059
$31$	5.41795	0.973092	0.486546	−	0.873655i	$-0.338257\pi$
$31$	5.41795	0.973092	0.486546	+	0.873655i	$0.338257\pi$
$32$	−1.00000	−0.176777
$33$	2.08878	0.363610
$34$	−3.07102	−0.526676
$35$	−12.2966	−2.07850
$36$	1.00000	0.166667
$37$	6.26162	1.02940	0.514702	−	0.857369i	$-0.327903\pi$
$37$	6.26162	1.02940	0.514702	+	0.857369i	$0.327903\pi$
$38$	6.35933	1.03162
$39$	1.00000	0.160128
$40$	3.09495	0.489355
$41$	−3.19603	−0.499136	−0.249568	−	0.968357i	$-0.580289\pi$
$41$	−3.19603	−0.499136	−0.249568	+	0.968357i	$0.580289\pi$
$42$	3.97310	0.613063
$43$	4.21307	0.642486	0.321243	−	0.946997i	$-0.395899\pi$
$43$	4.21307	0.642486	0.321243	+	0.946997i	$0.395899\pi$
$44$	−2.08878	−0.314896
$45$	−3.09495	−0.461368
$46$	−0.753374	−0.111079
$47$	−9.09805	−1.32709	−0.663544	−	0.748138i	$-0.730948\pi$
$47$	−9.09805	−1.32709	−0.663544	+	0.748138i	$0.730948\pi$
$48$	−1.00000	−0.144338
$49$	8.78553	1.25508
$50$	−4.57874	−0.647532
$51$	−3.07102	−0.430029
$52$	−1.00000	−0.138675
$53$	1.78997	0.245872	0.122936	−	0.992415i	$-0.460769\pi$
$53$	1.78997	0.245872	0.122936	+	0.992415i	$0.460769\pi$
$54$	1.00000	0.136083
$55$	6.46468	0.871697
$56$	−3.97310	−0.530928
$57$	6.35933	0.842314
$58$	7.73052	1.01507
$59$	3.06235	0.398684	0.199342	−	0.979930i	$-0.436120\pi$
$59$	3.06235	0.398684	0.199342	+	0.979930i	$0.436120\pi$
$60$	3.09495	0.399557
$61$	−7.26725	−0.930476	−0.465238	−	0.885186i	$-0.654031\pi$
$61$	−7.26725	−0.930476	−0.465238	+	0.885186i	$0.654031\pi$
$62$	−5.41795	−0.688080
$63$	3.97310	0.500564
$64$	1.00000	0.125000
$65$	3.09495	0.383882
$66$	−2.08878	−0.257111
$67$	−4.59049	−0.560818	−0.280409	−	0.959881i	$-0.590470\pi$
$67$	−4.59049	−0.560818	−0.280409	+	0.959881i	$0.590470\pi$
$68$	3.07102	0.372416
$69$	−0.753374	−0.0906956
$70$	12.2966	1.46972
$71$	6.81056	0.808265	0.404133	−	0.914700i	$-0.367573\pi$
$71$	6.81056	0.808265	0.404133	+	0.914700i	$0.367573\pi$
$72$	−1.00000	−0.117851
$73$	−1.90860	−0.223385	−0.111693	−	0.993743i	$-0.535627\pi$
$73$	−1.90860	−0.223385	−0.111693	+	0.993743i	$0.535627\pi$
$74$	−6.26162	−0.727898
$75$	−4.57874	−0.528707
$76$	−6.35933	−0.729465
$77$	−8.29894	−0.945752
$78$	−1.00000	−0.113228
$79$	3.61660	0.406899	0.203450	−	0.979085i	$-0.434785\pi$
$79$	3.61660	0.406899	0.203450	+	0.979085i	$0.434785\pi$
$80$	−3.09495	−0.346026
$81$	1.00000	0.111111
$82$	3.19603	0.352942
$83$	11.1151	1.22004	0.610021	−	0.792385i	$-0.291161\pi$
$83$	11.1151	1.22004	0.610021	+	0.792385i	$0.291161\pi$
$84$	−3.97310	−0.433501
$85$	−9.50467	−1.03093
$86$	−4.21307	−0.454306
$87$	7.73052	0.828799
$88$	2.08878	0.222665
$89$	−10.2078	−1.08202	−0.541011	−	0.841015i	$-0.681958\pi$
$89$	−10.2078	−1.08202	−0.541011	+	0.841015i	$0.681958\pi$
$90$	3.09495	0.326237
$91$	−3.97310	−0.416494
$92$	0.753374	0.0785447
$93$	−5.41795	−0.561815
$94$	9.09805	0.938392
$95$	19.6818	2.01931
$96$	1.00000	0.102062
$97$	14.6236	1.48480	0.742402	−	0.669955i	$-0.233686\pi$
$97$	14.6236	1.48480	0.742402	+	0.669955i	$0.233686\pi$
$98$	−8.78553	−0.887473
$99$	−2.08878	−0.209930
$100$	4.57874	0.457874
$101$	−2.52140	−0.250888	−0.125444	−	0.992101i	$-0.540036\pi$
$101$	−2.52140	−0.250888	−0.125444	+	0.992101i	$0.540036\pi$
$102$	3.07102	0.304076
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	1.00000	0.0980581
$105$	12.2966	1.20002
$106$	−1.78997	−0.173858
$107$	−11.8799	−1.14847	−0.574236	−	0.818690i	$-0.694701\pi$
$107$	−11.8799	−1.14847	−0.574236	+	0.818690i	$0.694701\pi$
$108$	−1.00000	−0.0962250
$109$	1.43249	0.137207	0.0686036	−	0.997644i	$-0.478146\pi$
$109$	1.43249	0.137207	0.0686036	+	0.997644i	$0.478146\pi$
$110$	−6.46468	−0.616383
$111$	−6.26162	−0.594326
$112$	3.97310	0.375423
$113$	14.4197	1.35649	0.678244	−	0.734836i	$-0.262741\pi$
$113$	14.4197	1.35649	0.678244	+	0.734836i	$0.262741\pi$
$114$	−6.35933	−0.595606
$115$	−2.33166	−0.217428
$116$	−7.73052	−0.717761
$117$	−1.00000	−0.0924500
$118$	−3.06235	−0.281912
$119$	12.2015	1.11851
$120$	−3.09495	−0.282529
$121$	−6.63700	−0.603363
$122$	7.26725	0.657946
$123$	3.19603	0.288176
$124$	5.41795	0.486546
$125$	1.30378	0.116614
$126$	−3.97310	−0.353952
$127$	−12.9427	−1.14848	−0.574238	−	0.818688i	$-0.694702\pi$
$127$	−12.9427	−1.14848	−0.574238	+	0.818688i	$0.694702\pi$
$128$	−1.00000	−0.0883883
$129$	−4.21307	−0.370940
$130$	−3.09495	−0.271445
$131$	−10.3348	−0.902953	−0.451476	−	0.892283i	$-0.649102\pi$
$131$	−10.3348	−0.902953	−0.451476	+	0.892283i	$0.649102\pi$
$132$	2.08878	0.181805
$133$	−25.2663	−2.19086
$134$	4.59049	0.396558
$135$	3.09495	0.266371
$136$	−3.07102	−0.263338
$137$	8.59513	0.734331	0.367166	−	0.930156i	$-0.380328\pi$
$137$	8.59513	0.734331	0.367166	+	0.930156i	$0.380328\pi$
$138$	0.753374	0.0641315
$139$	−8.32306	−0.705952	−0.352976	−	0.935632i	$-0.614830\pi$
$139$	−8.32306	−0.705952	−0.352976	+	0.935632i	$0.614830\pi$
$140$	−12.2966	−1.03925
$141$	9.09805	0.766194
$142$	−6.81056	−0.571530
$143$	2.08878	0.174673
$144$	1.00000	0.0833333
$145$	23.9256	1.98691
$146$	1.90860	0.157957
$147$	−8.78553	−0.724619
$148$	6.26162	0.514702
$149$	2.51358	0.205921	0.102960	−	0.994685i	$-0.467169\pi$
$149$	2.51358	0.205921	0.102960	+	0.994685i	$0.467169\pi$
$150$	4.57874	0.373853
$151$	14.7689	1.20188	0.600939	−	0.799295i	$-0.294794\pi$
$151$	14.7689	1.20188	0.600939	+	0.799295i	$0.294794\pi$
$152$	6.35933	0.515810
$153$	3.07102	0.248277
$154$	8.29894	0.668747
$155$	−16.7683	−1.34686
$156$	1.00000	0.0800641
$157$	1.41185	0.112678	0.0563389	−	0.998412i	$-0.482057\pi$
$157$	1.41185	0.112678	0.0563389	+	0.998412i	$0.482057\pi$
$158$	−3.61660	−0.287721
$159$	−1.78997	−0.141954
$160$	3.09495	0.244678
$161$	2.99323	0.235900
$162$	−1.00000	−0.0785674
$163$	12.2897	0.962607	0.481303	−	0.876554i	$-0.340164\pi$
$163$	12.2897	0.962607	0.481303	+	0.876554i	$0.340164\pi$
$164$	−3.19603	−0.249568
$165$	−6.46468	−0.503275
$166$	−11.1151	−0.862700
$167$	−2.97526	−0.230233	−0.115116	−	0.993352i	$-0.536724\pi$
$167$	−2.97526	−0.230233	−0.115116	+	0.993352i	$0.536724\pi$
$168$	3.97310	0.306531
$169$	1.00000	0.0769231
$170$	9.50467	0.728975
$171$	−6.35933	−0.486310
$172$	4.21307	0.321243
$173$	−23.4486	−1.78276	−0.891382	−	0.453253i	$-0.850263\pi$
$173$	−23.4486	−1.78276	−0.891382	+	0.453253i	$0.850263\pi$
$174$	−7.73052	−0.586049
$175$	18.1918	1.37517
$176$	−2.08878	−0.157448
$177$	−3.06235	−0.230180
$178$	10.2078	0.765105
$179$	−13.5864	−1.01549	−0.507747	−	0.861506i	$-0.669521\pi$
$179$	−13.5864	−1.01549	−0.507747	+	0.861506i	$0.669521\pi$
$180$	−3.09495	−0.230684
$181$	−11.7992	−0.877030	−0.438515	−	0.898724i	$-0.644495\pi$
$181$	−11.7992	−0.877030	−0.438515	+	0.898724i	$0.644495\pi$
$182$	3.97310	0.294506
$183$	7.26725	0.537210
$184$	−0.753374	−0.0555395
$185$	−19.3794	−1.42480
$186$	5.41795	0.397263
$187$	−6.41469	−0.469088
$188$	−9.09805	−0.663544
$189$	−3.97310	−0.289001
$190$	−19.6818	−1.42787
$191$	12.0182	0.869604	0.434802	−	0.900526i	$-0.356818\pi$
$191$	12.0182	0.869604	0.434802	+	0.900526i	$0.356818\pi$
$192$	−1.00000	−0.0721688
$193$	2.88551	0.207703	0.103852	−	0.994593i	$-0.466883\pi$
$193$	2.88551	0.207703	0.103852	+	0.994593i	$0.466883\pi$
$194$	−14.6236	−1.04991
$195$	−3.09495	−0.221634
$196$	8.78553	0.627538
$197$	15.7583	1.12273	0.561367	−	0.827567i	$-0.310275\pi$
$197$	15.7583	1.12273	0.561367	+	0.827567i	$0.310275\pi$
$198$	2.08878	0.148443
$199$	−0.965819	−0.0684651	−0.0342326	−	0.999414i	$-0.510899\pi$
$199$	−0.965819	−0.0684651	−0.0342326	+	0.999414i	$0.510899\pi$
$200$	−4.57874	−0.323766
$201$	4.59049	0.323789
$202$	2.52140	0.177405
$203$	−30.7141	−2.15571
$204$	−3.07102	−0.215014
$205$	9.89156	0.690856
$206$	−1.00000	−0.0696733
$207$	0.753374	0.0523631
$208$	−1.00000	−0.0693375
$209$	13.2832	0.918821
$210$	−12.2966	−0.848544
$211$	7.71356	0.531023	0.265512	−	0.964108i	$-0.414459\pi$
$211$	7.71356	0.531023	0.265512	+	0.964108i	$0.414459\pi$
$212$	1.78997	0.122936
$213$	−6.81056	−0.466652
$214$	11.8799	0.812092
$215$	−13.0392	−0.889269
$216$	1.00000	0.0680414
$217$	21.5261	1.46128
$218$	−1.43249	−0.0970202
$219$	1.90860	0.128972
$220$	6.46468	0.435849
$221$	−3.07102	−0.206579
$222$	6.26162	0.420252
$223$	11.7910	0.789583	0.394791	−	0.918771i	$-0.370817\pi$
$223$	11.7910	0.789583	0.394791	+	0.918771i	$0.370817\pi$
$224$	−3.97310	−0.265464
$225$	4.57874	0.305249
$226$	−14.4197	−0.959182
$227$	2.29930	0.152610	0.0763048	−	0.997085i	$-0.475688\pi$
$227$	2.29930	0.152610	0.0763048	+	0.997085i	$0.475688\pi$
$228$	6.35933	0.421157
$229$	−14.0302	−0.927139	−0.463569	−	0.886061i	$-0.653432\pi$
$229$	−14.0302	−0.927139	−0.463569	+	0.886061i	$0.653432\pi$
$230$	2.33166	0.153745
$231$	8.29894	0.546030
$232$	7.73052	0.507534
$233$	−7.93621	−0.519918	−0.259959	−	0.965620i	$-0.583709\pi$
$233$	−7.93621	−0.519918	−0.259959	+	0.965620i	$0.583709\pi$
$234$	1.00000	0.0653720
$235$	28.1581	1.83683
$236$	3.06235	0.199342
$237$	−3.61660	−0.234923
$238$	−12.2015	−0.790904
$239$	−14.3211	−0.926354	−0.463177	−	0.886266i	$-0.653291\pi$
$239$	−14.3211	−0.926354	−0.463177	+	0.886266i	$0.653291\pi$
$240$	3.09495	0.199778
$241$	−14.4962	−0.933784	−0.466892	−	0.884314i	$-0.654626\pi$
$241$	−14.4962	−0.933784	−0.466892	+	0.884314i	$0.654626\pi$
$242$	6.63700	0.426642
$243$	−1.00000	−0.0641500
$244$	−7.26725	−0.465238
$245$	−27.1908	−1.73716
$246$	−3.19603	−0.203771
$247$	6.35933	0.404634
$248$	−5.41795	−0.344040
$249$	−11.1151	−0.704392
$250$	−1.30378	−0.0824584
$251$	−9.08432	−0.573397	−0.286699	−	0.958021i	$-0.592558\pi$
$251$	−9.08432	−0.573397	−0.286699	+	0.958021i	$0.592558\pi$
$252$	3.97310	0.250282
$253$	−1.57363	−0.0989335
$254$	12.9427	0.812095
$255$	9.50467	0.595205
$256$	1.00000	0.0625000
$257$	17.0807	1.06547	0.532733	−	0.846283i	$-0.321165\pi$
$257$	17.0807	1.06547	0.532733	+	0.846283i	$0.321165\pi$
$258$	4.21307	0.262294
$259$	24.8780	1.54585
$260$	3.09495	0.191941
$261$	−7.73052	−0.478507
$262$	10.3348	0.638484
$263$	3.31151	0.204196	0.102098	−	0.994774i	$-0.467444\pi$
$263$	3.31151	0.204196	0.102098	+	0.994774i	$0.467444\pi$
$264$	−2.08878	−0.128556
$265$	−5.53989	−0.340313
$266$	25.2663	1.54917
$267$	10.2078	0.624706
$268$	−4.59049	−0.280409
$269$	7.49680	0.457088	0.228544	−	0.973534i	$-0.426603\pi$
$269$	7.49680	0.457088	0.228544	+	0.973534i	$0.426603\pi$
$270$	−3.09495	−0.188353
$271$	−4.30922	−0.261766	−0.130883	−	0.991398i	$-0.541781\pi$
$271$	−4.30922	−0.261766	−0.130883	+	0.991398i	$0.541781\pi$
$272$	3.07102	0.186208
$273$	3.97310	0.240463
$274$	−8.59513	−0.519251
$275$	−9.56398	−0.576730
$276$	−0.753374	−0.0453478
$277$	7.46649	0.448618	0.224309	−	0.974518i	$-0.427987\pi$
$277$	7.46649	0.448618	0.224309	+	0.974518i	$0.427987\pi$
$278$	8.32306	0.499184
$279$	5.41795	0.324364
$280$	12.2966	0.734860
$281$	−24.4370	−1.45779	−0.728895	−	0.684626i	$-0.759966\pi$
$281$	−24.4370	−1.45779	−0.728895	+	0.684626i	$0.759966\pi$
$282$	−9.09805	−0.541781
$283$	5.72108	0.340083	0.170042	−	0.985437i	$-0.445610\pi$
$283$	5.72108	0.340083	0.170042	+	0.985437i	$0.445610\pi$
$284$	6.81056	0.404133
$285$	−19.6818	−1.16585
$286$	−2.08878	−0.123512
$287$	−12.6981	−0.749547
$288$	−1.00000	−0.0589256
$289$	−7.56883	−0.445225
$290$	−23.9256	−1.40496
$291$	−14.6236	−0.857252
$292$	−1.90860	−0.111693
$293$	21.1961	1.23829	0.619145	−	0.785276i	$-0.287479\pi$
$293$	21.1961	1.23829	0.619145	+	0.785276i	$0.287479\pi$
$294$	8.78553	0.512383
$295$	−9.47783	−0.551821
$296$	−6.26162	−0.363949
$297$	2.08878	0.121203
$298$	−2.51358	−0.145608
$299$	−0.753374	−0.0435688
$300$	−4.57874	−0.264354
$301$	16.7389	0.964816
$302$	−14.7689	−0.849856
$303$	2.52140	0.144850
$304$	−6.35933	−0.364733
$305$	22.4918	1.28788
$306$	−3.07102	−0.175559
$307$	1.23481	0.0704743	0.0352371	−	0.999379i	$-0.488781\pi$
$307$	1.23481	0.0704743	0.0352371	+	0.999379i	$0.488781\pi$
$308$	−8.29894	−0.472876
$309$	−1.00000	−0.0568880
$310$	16.7683	0.952375
$311$	−19.4195	−1.10118	−0.550589	−	0.834777i	$-0.685597\pi$
$311$	−19.4195	−1.10118	−0.550589	+	0.834777i	$0.685597\pi$
$312$	−1.00000	−0.0566139
$313$	8.68698	0.491017	0.245508	−	0.969394i	$-0.421045\pi$
$313$	8.68698	0.491017	0.245508	+	0.969394i	$0.421045\pi$
$314$	−1.41185	−0.0796753
$315$	−12.2966	−0.692833
$316$	3.61660	0.203450
$317$	10.3957	0.583878	0.291939	−	0.956437i	$-0.405700\pi$
$317$	10.3957	0.583878	0.291939	+	0.956437i	$0.405700\pi$
$318$	1.78997	0.100377
$319$	16.1474	0.904079
$320$	−3.09495	−0.173013
$321$	11.8799	0.663071
$322$	−2.99323	−0.166806
$323$	−19.5296	−1.08666
$324$	1.00000	0.0555556
$325$	−4.57874	−0.253983
$326$	−12.2897	−0.680666
$327$	−1.43249	−0.0792167
$328$	3.19603	0.176471
$329$	−36.1475	−1.99288
$330$	6.46468	0.355869
$331$	−29.7538	−1.63542	−0.817709	−	0.575632i	$-0.804756\pi$
$331$	−29.7538	−1.63542	−0.817709	+	0.575632i	$0.804756\pi$
$332$	11.1151	0.610021
$333$	6.26162	0.343135
$334$	2.97526	0.162799
$335$	14.2074	0.776231
$336$	−3.97310	−0.216750
$337$	16.0791	0.875887	0.437943	−	0.899003i	$-0.355707\pi$
$337$	16.0791	0.875887	0.437943	+	0.899003i	$0.355707\pi$
$338$	−1.00000	−0.0543928
$339$	−14.4197	−0.783169
$340$	−9.50467	−0.515463
$341$	−11.3169	−0.612845
$342$	6.35933	0.343873
$343$	7.09411	0.383046
$344$	−4.21307	−0.227153
$345$	2.33166	0.125532
$346$	23.4486	1.26060
$347$	18.2402	0.979187	0.489594	−	0.871951i	$-0.337145\pi$
$347$	18.2402	0.979187	0.489594	+	0.871951i	$0.337145\pi$
$348$	7.73052	0.414399
$349$	21.2293	1.13638	0.568190	−	0.822897i	$-0.307644\pi$
$349$	21.2293	1.13638	0.568190	+	0.822897i	$0.307644\pi$
$350$	−18.1918	−0.972392
$351$	1.00000	0.0533761
$352$	2.08878	0.111332
$353$	−12.0968	−0.643847	−0.321923	−	0.946766i	$-0.604329\pi$
$353$	−12.0968	−0.643847	−0.321923	+	0.946766i	$0.604329\pi$
$354$	3.06235	0.162762
$355$	−21.0784	−1.11872
$356$	−10.2078	−0.541011
$357$	−12.2015	−0.645771
$358$	13.5864	0.718062
$359$	−10.2784	−0.542474	−0.271237	−	0.962513i	$-0.587433\pi$
$359$	−10.2784	−0.542474	−0.271237	+	0.962513i	$0.587433\pi$
$360$	3.09495	0.163118
$361$	21.4411	1.12848
$362$	11.7992	0.620154
$363$	6.63700	0.348352
$364$	−3.97310	−0.208247
$365$	5.90704	0.309189
$366$	−7.26725	−0.379865
$367$	−9.96267	−0.520047	−0.260024	−	0.965602i	$-0.583730\pi$
$367$	−9.96267	−0.520047	−0.260024	+	0.965602i	$0.583730\pi$
$368$	0.753374	0.0392723
$369$	−3.19603	−0.166379
$370$	19.3794	1.00749
$371$	7.11175	0.369224
$372$	−5.41795	−0.280908
$373$	14.6558	0.758848	0.379424	−	0.925223i	$-0.376122\pi$
$373$	14.6558	0.758848	0.379424	+	0.925223i	$0.376122\pi$
$374$	6.41469	0.331696
$375$	−1.30378	−0.0673270
$376$	9.09805	0.469196
$377$	7.73052	0.398142
$378$	3.97310	0.204354
$379$	35.2468	1.81051	0.905253	−	0.424874i	$-0.139682\pi$
$379$	35.2468	1.81051	0.905253	+	0.424874i	$0.139682\pi$
$380$	19.6818	1.00966
$381$	12.9427	0.663073
$382$	−12.0182	−0.614903
$383$	7.70592	0.393754	0.196877	−	0.980428i	$-0.436920\pi$
$383$	7.70592	0.393754	0.196877	+	0.980428i	$0.436920\pi$
$384$	1.00000	0.0510310
$385$	25.6848	1.30902
$386$	−2.88551	−0.146868
$387$	4.21307	0.214162
$388$	14.6236	0.742402
$389$	4.86896	0.246866	0.123433	−	0.992353i	$-0.460610\pi$
$389$	4.86896	0.246866	0.123433	+	0.992353i	$0.460610\pi$
$390$	3.09495	0.156719
$391$	2.31363	0.117005
$392$	−8.78553	−0.443736
$393$	10.3348	0.521320
$394$	−15.7583	−0.793893
$395$	−11.1932	−0.563192
$396$	−2.08878	−0.104965
$397$	29.0682	1.45889	0.729446	−	0.684039i	$-0.239778\pi$
$397$	29.0682	1.45889	0.729446	+	0.684039i	$0.239778\pi$
$398$	0.965819	0.0484121
$399$	25.2663	1.26490
$400$	4.57874	0.228937
$401$	33.5973	1.67777	0.838884	−	0.544311i	$-0.183209\pi$
$401$	33.5973	1.67777	0.838884	+	0.544311i	$0.183209\pi$
$402$	−4.59049	−0.228953
$403$	−5.41795	−0.269887
$404$	−2.52140	−0.125444
$405$	−3.09495	−0.153789
$406$	30.7141	1.52432
$407$	−13.0791	−0.648309
$408$	3.07102	0.152038
$409$	32.1938	1.59188	0.795941	−	0.605375i	$-0.206977\pi$
$409$	32.1938	1.59188	0.795941	+	0.605375i	$0.206977\pi$
$410$	−9.89156	−0.488509
$411$	−8.59513	−0.423966
$412$	1.00000	0.0492665
$413$	12.1670	0.598700
$414$	−0.753374	−0.0370263
$415$	−34.4008	−1.68867
$416$	1.00000	0.0490290
$417$	8.32306	0.407582
$418$	−13.2832	−0.649705
$419$	10.2866	0.502534	0.251267	−	0.967918i	$-0.419153\pi$
$419$	10.2866	0.502534	0.251267	+	0.967918i	$0.419153\pi$
$420$	12.2966	0.600011
$421$	3.55842	0.173427	0.0867135	−	0.996233i	$-0.472364\pi$
$421$	3.55842	0.173427	0.0867135	+	0.996233i	$0.472364\pi$
$422$	−7.71356	−0.375490
$423$	−9.09805	−0.442362
$424$	−1.78997	−0.0869288
$425$	14.0614	0.682078
$426$	6.81056	0.329973
$427$	−28.8735	−1.39729
$428$	−11.8799	−0.574236
$429$	−2.08878	−0.100847
$430$	13.0392	0.628808
$431$	34.3904	1.65653	0.828264	−	0.560339i	$-0.189329\pi$
$431$	34.3904	1.65653	0.828264	+	0.560339i	$0.189329\pi$
$432$	−1.00000	−0.0481125
$433$	28.3588	1.36284	0.681418	−	0.731894i	$-0.261364\pi$
$433$	28.3588	1.36284	0.681418	+	0.731894i	$0.261364\pi$
$434$	−21.5261	−1.03328
$435$	−23.9256	−1.14715
$436$	1.43249	0.0686036
$437$	−4.79096	−0.229182
$438$	−1.90860	−0.0911966
$439$	−9.92285	−0.473592	−0.236796	−	0.971559i	$-0.576097\pi$
$439$	−9.92285	−0.473592	−0.236796	+	0.971559i	$0.576097\pi$
$440$	−6.46468	−0.308191
$441$	8.78553	0.418359
$442$	3.07102	0.146074
$443$	23.5320	1.11804	0.559020	−	0.829154i	$-0.311177\pi$
$443$	23.5320	1.11804	0.559020	+	0.829154i	$0.311177\pi$
$444$	−6.26162	−0.297163
$445$	31.5926	1.49763
$446$	−11.7910	−0.558319
$447$	−2.51358	−0.118888
$448$	3.97310	0.187711
$449$	−26.6482	−1.25761	−0.628804	−	0.777564i	$-0.716455\pi$
$449$	−26.6482	−1.25761	−0.628804	+	0.777564i	$0.716455\pi$
$450$	−4.57874	−0.215844
$451$	6.67580	0.314351
$452$	14.4197	0.678244
$453$	−14.7689	−0.693904
$454$	−2.29930	−0.107911
$455$	12.2966	0.576472
$456$	−6.35933	−0.297803
$457$	−3.70020	−0.173088	−0.0865440	−	0.996248i	$-0.527582\pi$
$457$	−3.70020	−0.173088	−0.0865440	+	0.996248i	$0.527582\pi$
$458$	14.0302	0.655586
$459$	−3.07102	−0.143343
$460$	−2.33166	−0.108714
$461$	35.5552	1.65597	0.827985	−	0.560750i	$-0.189487\pi$
$461$	35.5552	1.65597	0.827985	+	0.560750i	$0.189487\pi$
$462$	−8.29894	−0.386101
$463$	−13.5000	−0.627398	−0.313699	−	0.949523i	$-0.601568\pi$
$463$	−13.5000	−0.627398	−0.313699	+	0.949523i	$0.601568\pi$
$464$	−7.73052	−0.358880
$465$	16.7683	0.777611
$466$	7.93621	0.367638
$467$	22.0480	1.02026	0.510129	−	0.860098i	$-0.329598\pi$
$467$	22.0480	1.02026	0.510129	+	0.860098i	$0.329598\pi$
$468$	−1.00000	−0.0462250
$469$	−18.2385	−0.842176
$470$	−28.1581	−1.29883
$471$	−1.41185	−0.0650546
$472$	−3.06235	−0.140956
$473$	−8.80017	−0.404632
$474$	3.61660	0.166116
$475$	−29.1177	−1.33601
$476$	12.2015	0.559254
$477$	1.78997	0.0819573
$478$	14.3211	0.655031
$479$	−8.97508	−0.410082	−0.205041	−	0.978753i	$-0.565733\pi$
$479$	−8.97508	−0.410082	−0.205041	+	0.978753i	$0.565733\pi$
$480$	−3.09495	−0.141265
$481$	−6.26162	−0.285505
$482$	14.4962	0.660285
$483$	−2.99323	−0.136197
$484$	−6.63700	−0.301682
$485$	−45.2594	−2.05513
$486$	1.00000	0.0453609
$487$	−4.81808	−0.218328	−0.109164	−	0.994024i	$-0.534817\pi$
$487$	−4.81808	−0.218328	−0.109164	+	0.994024i	$0.534817\pi$
$488$	7.26725	0.328973
$489$	−12.2897	−0.555761
$490$	27.1908	1.22836
$491$	36.5073	1.64755	0.823775	−	0.566917i	$-0.191864\pi$
$491$	36.5073	1.64755	0.823775	+	0.566917i	$0.191864\pi$
$492$	3.19603	0.144088
$493$	−23.7406	−1.06922
$494$	−6.35933	−0.286120
$495$	6.46468	0.290566
$496$	5.41795	0.243273
$497$	27.0591	1.21376
$498$	11.1151	0.498080
$499$	2.73918	0.122622	0.0613112	−	0.998119i	$-0.480472\pi$
$499$	2.73918	0.122622	0.0613112	+	0.998119i	$0.480472\pi$
$500$	1.30378	0.0583069
$501$	2.97526	0.132925
$502$	9.08432	0.405453
$503$	11.9691	0.533678	0.266839	−	0.963741i	$-0.414021\pi$
$503$	11.9691	0.533678	0.266839	+	0.963741i	$0.414021\pi$
$504$	−3.97310	−0.176976
$505$	7.80361	0.347256
$506$	1.57363	0.0699565
$507$	−1.00000	−0.0444116
$508$	−12.9427	−0.574238
$509$	−14.3296	−0.635150	−0.317575	−	0.948233i	$-0.602869\pi$
$509$	−14.3296	−0.635150	−0.317575	+	0.948233i	$0.602869\pi$
$510$	−9.50467	−0.420874
$511$	−7.58308	−0.335456
$512$	−1.00000	−0.0441942
$513$	6.35933	0.280771
$514$	−17.0807	−0.753399
$515$	−3.09495	−0.136380
$516$	−4.21307	−0.185470
$517$	19.0038	0.835788
$518$	−24.8780	−1.09308
$519$	23.4486	1.02928
$520$	−3.09495	−0.135723
$521$	24.2921	1.06426	0.532128	−	0.846664i	$-0.321392\pi$
$521$	24.2921	1.06426	0.532128	+	0.846664i	$0.321392\pi$
$522$	7.73052	0.338356
$523$	21.3771	0.934754	0.467377	−	0.884058i	$-0.345199\pi$
$523$	21.3771	0.934754	0.467377	+	0.884058i	$0.345199\pi$
$524$	−10.3348	−0.451476
$525$	−18.1918	−0.793955
$526$	−3.31151	−0.144388
$527$	16.6386	0.724790
$528$	2.08878	0.0909025
$529$	−22.4324	−0.975323
$530$	5.53989	0.240637
$531$	3.06235	0.132895
$532$	−25.2663	−1.09543
$533$	3.19603	0.138435
$534$	−10.2078	−0.441734
$535$	36.7677	1.58961
$536$	4.59049	0.198279
$537$	13.5864	0.586295
$538$	−7.49680	−0.323210
$539$	−18.3511	−0.790436
$540$	3.09495	0.133186
$541$	32.1472	1.38212	0.691059	−	0.722799i	$-0.257145\pi$
$541$	32.1472	1.38212	0.691059	+	0.722799i	$0.257145\pi$
$542$	4.30922	0.185097
$543$	11.7992	0.506354
$544$	−3.07102	−0.131669
$545$	−4.43348	−0.189909
$546$	−3.97310	−0.170033
$547$	−4.02482	−0.172089	−0.0860445	−	0.996291i	$-0.527423\pi$
$547$	−4.02482	−0.172089	−0.0860445	+	0.996291i	$0.527423\pi$
$548$	8.59513	0.367166
$549$	−7.26725	−0.310159
$550$	9.56398	0.407810
$551$	49.1609	2.09433
$552$	0.753374	0.0320657
$553$	14.3691	0.611037
$554$	−7.46649	−0.317221
$555$	19.3794	0.822611
$556$	−8.32306	−0.352976
$557$	34.5232	1.46279	0.731397	−	0.681952i	$-0.238869\pi$
$557$	34.5232	1.46279	0.731397	+	0.681952i	$0.238869\pi$
$558$	−5.41795	−0.229360
$559$	−4.21307	−0.178194
$560$	−12.2966	−0.519625
$561$	6.41469	0.270828
$562$	24.4370	1.03081
$563$	43.5433	1.83513	0.917566	−	0.397582i	$-0.130151\pi$
$563$	43.5433	1.83513	0.917566	+	0.397582i	$0.130151\pi$
$564$	9.09805	0.383097
$565$	−44.6282	−1.87752
$566$	−5.72108	−0.240475
$567$	3.97310	0.166855
$568$	−6.81056	−0.285765
$569$	22.9529	0.962234	0.481117	−	0.876657i	$-0.340231\pi$
$569$	22.9529	0.962234	0.481117	+	0.876657i	$0.340231\pi$
$570$	19.6818	0.824381
$571$	10.0139	0.419070	0.209535	−	0.977801i	$-0.432805\pi$
$571$	10.0139	0.419070	0.209535	+	0.977801i	$0.432805\pi$
$572$	2.08878	0.0873363
$573$	−12.0182	−0.502066
$574$	12.6981	0.530010
$575$	3.44950	0.143854
$576$	1.00000	0.0416667
$577$	−4.63353	−0.192896	−0.0964481	−	0.995338i	$-0.530748\pi$
$577$	−4.63353	−0.192896	−0.0964481	+	0.995338i	$0.530748\pi$
$578$	7.56883	0.314822
$579$	−2.88551	−0.119918
$580$	23.9256	0.993457
$581$	44.1615	1.83213
$582$	14.6236	0.606169
$583$	−3.73886	−0.154848
$584$	1.90860	0.0789786
$585$	3.09495	0.127961
$586$	−21.1961	−0.875604
$587$	8.19409	0.338206	0.169103	−	0.985598i	$-0.445913\pi$
$587$	8.19409	0.338206	0.169103	+	0.985598i	$0.445913\pi$
$588$	−8.78553	−0.362309
$589$	−34.4545	−1.41967
$590$	9.47783	0.390196
$591$	−15.7583	−0.648211
$592$	6.26162	0.257351
$593$	−24.9784	−1.02574	−0.512871	−	0.858466i	$-0.671418\pi$
$593$	−24.9784	−1.02574	−0.512871	+	0.858466i	$0.671418\pi$
$594$	−2.08878	−0.0857037
$595$	−37.7630	−1.54813
$596$	2.51358	0.102960
$597$	0.965819	0.0395283
$598$	0.753374	0.0308078
$599$	−34.4558	−1.40782	−0.703912	−	0.710287i	$-0.748565\pi$
$599$	−34.4558	−1.40782	−0.703912	+	0.710287i	$0.748565\pi$
$600$	4.57874	0.186926
$601$	−15.7186	−0.641177	−0.320588	−	0.947219i	$-0.603881\pi$
$601$	−15.7186	−0.641177	−0.320588	+	0.947219i	$0.603881\pi$
$602$	−16.7389	−0.682228
$603$	−4.59049	−0.186939
$604$	14.7689	0.600939
$605$	20.5412	0.835118
$606$	−2.52140	−0.102425
$607$	−21.8966	−0.888754	−0.444377	−	0.895840i	$-0.646575\pi$
$607$	−21.8966	−0.888754	−0.444377	+	0.895840i	$0.646575\pi$
$608$	6.35933	0.257905
$609$	30.7141	1.24460
$610$	−22.4918	−0.910666
$611$	9.09805	0.368068
$612$	3.07102	0.124139
$613$	29.8462	1.20548	0.602738	−	0.797939i	$-0.294077\pi$
$613$	29.8462	1.20548	0.602738	+	0.797939i	$0.294077\pi$
$614$	−1.23481	−0.0498328
$615$	−9.89156	−0.398866
$616$	8.29894	0.334374
$617$	41.6456	1.67659	0.838293	−	0.545219i	$-0.183554\pi$
$617$	41.6456	1.67659	0.838293	+	0.545219i	$0.183554\pi$
$618$	1.00000	0.0402259
$619$	−13.6457	−0.548468	−0.274234	−	0.961663i	$-0.588424\pi$
$619$	−13.6457	−0.548468	−0.274234	+	0.961663i	$0.588424\pi$
$620$	−16.7683	−0.673431
$621$	−0.753374	−0.0302319
$622$	19.4195	0.778650
$623$	−40.5565	−1.62486
$624$	1.00000	0.0400320
$625$	−26.9288	−1.07715
$626$	−8.68698	−0.347201
$627$	−13.2832	−0.530482
$628$	1.41185	0.0563389
$629$	19.2296	0.766733
$630$	12.2966	0.489907
$631$	39.0625	1.55506	0.777528	−	0.628849i	$-0.216474\pi$
$631$	39.0625	1.55506	0.777528	+	0.628849i	$0.216474\pi$
$632$	−3.61660	−0.143861
$633$	−7.71356	−0.306587
$634$	−10.3957	−0.412864
$635$	40.0570	1.58961
$636$	−1.78997	−0.0709771
$637$	−8.78553	−0.348096
$638$	−16.1474	−0.639280
$639$	6.81056	0.269422
$640$	3.09495	0.122339
$641$	1.74733	0.0690153	0.0345076	−	0.999404i	$-0.489014\pi$
$641$	1.74733	0.0690153	0.0345076	+	0.999404i	$0.489014\pi$
$642$	−11.8799	−0.468862
$643$	−14.0947	−0.555842	−0.277921	−	0.960604i	$-0.589645\pi$
$643$	−14.0947	−0.555842	−0.277921	+	0.960604i	$0.589645\pi$
$644$	2.99323	0.117950
$645$	13.0392	0.513420
$646$	19.5296	0.768383
$647$	−28.2107	−1.10908	−0.554538	−	0.832158i	$-0.687105\pi$
$647$	−28.2107	−1.10908	−0.554538	+	0.832158i	$0.687105\pi$
$648$	−1.00000	−0.0392837
$649$	−6.39658	−0.251088
$650$	4.57874	0.179593
$651$	−21.5261	−0.843673
$652$	12.2897	0.481303
$653$	−42.2473	−1.65326	−0.826632	−	0.562743i	$-0.809746\pi$
$653$	−42.2473	−1.65326	−0.826632	+	0.562743i	$0.809746\pi$
$654$	1.43249	0.0560146
$655$	31.9856	1.24978
$656$	−3.19603	−0.124784
$657$	−1.90860	−0.0744617
$658$	36.1475	1.40918
$659$	27.3069	1.06372	0.531862	−	0.846831i	$-0.321492\pi$
$659$	27.3069	1.06372	0.531862	+	0.846831i	$0.321492\pi$
$660$	−6.46468	−0.251637
$661$	45.6838	1.77689	0.888447	−	0.458980i	$-0.151785\pi$
$661$	45.6838	1.77689	0.888447	+	0.458980i	$0.151785\pi$
$662$	29.7538	1.15642
$663$	3.07102	0.119269
$664$	−11.1151	−0.431350
$665$	78.1979	3.03239
$666$	−6.26162	−0.242633
$667$	−5.82398	−0.225505
$668$	−2.97526	−0.115116
$669$	−11.7910	−0.455866
$670$	−14.2074	−0.548879
$671$	15.1797	0.586005
$672$	3.97310	0.153266
$673$	−34.7742	−1.34045	−0.670224	−	0.742159i	$-0.733802\pi$
$673$	−34.7742	−1.34045	−0.670224	+	0.742159i	$0.733802\pi$
$674$	−16.0791	−0.619346
$675$	−4.57874	−0.176236
$676$	1.00000	0.0384615
$677$	3.69503	0.142012	0.0710059	−	0.997476i	$-0.477379\pi$
$677$	3.69503	0.142012	0.0710059	+	0.997476i	$0.477379\pi$
$678$	14.4197	0.553784
$679$	58.1011	2.22972
$680$	9.50467	0.364487
$681$	−2.29930	−0.0881092
$682$	11.3169	0.433347
$683$	−19.4471	−0.744125	−0.372062	−	0.928208i	$-0.621349\pi$
$683$	−19.4471	−0.744125	−0.372062	+	0.928208i	$0.621349\pi$
$684$	−6.35933	−0.243155
$685$	−26.6015	−1.01639
$686$	−7.09411	−0.270854
$687$	14.0302	0.535284
$688$	4.21307	0.160622
$689$	−1.78997	−0.0681926
$690$	−2.33166	−0.0887647
$691$	−10.0287	−0.381508	−0.190754	−	0.981638i	$-0.561093\pi$
$691$	−10.0287	−0.381508	−0.190754	+	0.981638i	$0.561093\pi$
$692$	−23.4486	−0.891382
$693$	−8.29894	−0.315251
$694$	−18.2402	−0.692390
$695$	25.7595	0.977113
$696$	−7.73052	−0.293025
$697$	−9.81506	−0.371772
$698$	−21.2293	−0.803542
$699$	7.93621	0.300175
$700$	18.1918	0.687585
$701$	31.8042	1.20123	0.600613	−	0.799540i	$-0.294923\pi$
$701$	31.8042	1.20123	0.600613	+	0.799540i	$0.294923\pi$
$702$	−1.00000	−0.0377426
$703$	−39.8197	−1.50183
$704$	−2.08878	−0.0787239
$705$	−28.1581	−1.06049
$706$	12.0968	0.455269
$707$	−10.0178	−0.376757
$708$	−3.06235	−0.115090
$709$	−23.5901	−0.885943	−0.442972	−	0.896536i	$-0.646076\pi$
$709$	−23.5901	−0.885943	−0.442972	+	0.896536i	$0.646076\pi$
$710$	21.0784	0.791057
$711$	3.61660	0.135633
$712$	10.2078	0.382553
$713$	4.08174	0.152862
$714$	12.2015	0.456629
$715$	−6.46468	−0.241765
$716$	−13.5864	−0.507747
$717$	14.3211	0.534831
$718$	10.2784	0.383587
$719$	28.8301	1.07518	0.537590	−	0.843206i	$-0.319335\pi$
$719$	28.8301	1.07518	0.537590	+	0.843206i	$0.319335\pi$
$720$	−3.09495	−0.115342
$721$	3.97310	0.147966
$722$	−21.4411	−0.797954
$723$	14.4962	0.539121
$724$	−11.7992	−0.438515
$725$	−35.3960	−1.31458
$726$	−6.63700	−0.246322
$727$	51.5821	1.91308	0.956538	−	0.291608i	$-0.0941904\pi$
$727$	51.5821	1.91308	0.956538	+	0.291608i	$0.0941904\pi$
$728$	3.97310	0.147253
$729$	1.00000	0.0370370
$730$	−5.90704	−0.218629
$731$	12.9384	0.478544
$732$	7.26725	0.268605
$733$	−3.58288	−0.132337	−0.0661683	−	0.997808i	$-0.521077\pi$
$733$	−3.58288	−0.132337	−0.0661683	+	0.997808i	$0.521077\pi$
$734$	9.96267	0.367729
$735$	27.1908	1.00295
$736$	−0.753374	−0.0277697
$737$	9.58853	0.353198
$738$	3.19603	0.117647
$739$	14.7686	0.543272	0.271636	−	0.962400i	$-0.412435\pi$
$739$	14.7686	0.543272	0.271636	+	0.962400i	$0.412435\pi$
$740$	−19.3794	−0.712402
$741$	−6.35933	−0.233616
$742$	−7.11175	−0.261081
$743$	−1.95971	−0.0718946	−0.0359473	−	0.999354i	$-0.511445\pi$
$743$	−1.95971	−0.0718946	−0.0359473	+	0.999354i	$0.511445\pi$
$744$	5.41795	0.198632
$745$	−7.77943	−0.285016
$746$	−14.6558	−0.536586
$747$	11.1151	0.406681
$748$	−6.41469	−0.234544
$749$	−47.2000	−1.72465
$750$	1.30378	0.0476074
$751$	−22.9151	−0.836185	−0.418092	−	0.908405i	$-0.637301\pi$
$751$	−22.9151	−0.836185	−0.418092	+	0.908405i	$0.637301\pi$
$752$	−9.09805	−0.331772
$753$	9.08432	0.331051
$754$	−7.73052	−0.281529
$755$	−45.7091	−1.66353
$756$	−3.97310	−0.144500
$757$	−36.3906	−1.32264	−0.661319	−	0.750105i	$-0.730003\pi$
$757$	−36.3906	−1.32264	−0.661319	+	0.750105i	$0.730003\pi$
$758$	−35.2468	−1.28022
$759$	1.57363	0.0571193
$760$	−19.6818	−0.713935
$761$	39.0269	1.41473	0.707363	−	0.706851i	$-0.249885\pi$
$761$	39.0269	1.41473	0.707363	+	0.706851i	$0.249885\pi$
$762$	−12.9427	−0.468863
$763$	5.69141	0.206043
$764$	12.0182	0.434802
$765$	−9.50467	−0.343642
$766$	−7.70592	−0.278426
$767$	−3.06235	−0.110575
$768$	−1.00000	−0.0360844
$769$	36.6546	1.32180	0.660900	−	0.750474i	$-0.270175\pi$
$769$	36.6546	1.32180	0.660900	+	0.750474i	$0.270175\pi$
$770$	−25.6848	−0.925617
$771$	−17.0807	−0.615147
$772$	2.88551	0.103852
$773$	−21.9360	−0.788984	−0.394492	−	0.918899i	$-0.629079\pi$
$773$	−21.9360	−0.788984	−0.394492	+	0.918899i	$0.629079\pi$
$774$	−4.21307	−0.151435
$775$	24.8074	0.891107
$776$	−14.6236	−0.524957
$777$	−24.8780	−0.892495
$778$	−4.86896	−0.174561
$779$	20.3246	0.728204
$780$	−3.09495	−0.110817
$781$	−14.2258	−0.509038
$782$	−2.31363	−0.0827352
$783$	7.73052	0.276266
$784$	8.78553	0.313769
$785$	−4.36961	−0.155958
$786$	−10.3348	−0.368629
$787$	50.9715	1.81694	0.908469	−	0.417953i	$-0.137252\pi$
$787$	50.9715	1.81694	0.908469	+	0.417953i	$0.137252\pi$
$788$	15.7583	0.561367
$789$	−3.31151	−0.117893
$790$	11.1932	0.398237
$791$	57.2908	2.03703
$792$	2.08878	0.0742216
$793$	7.26725	0.258068
$794$	−29.0682	−1.03159
$795$	5.53989	0.196480
$796$	−0.965819	−0.0342326
$797$	0.459944	0.0162920	0.00814602	−	0.999967i	$-0.497407\pi$
$797$	0.459944	0.0162920	0.00814602	+	0.999967i	$0.497407\pi$
$798$	−25.2663	−0.894416
$799$	−27.9403	−0.988457
$800$	−4.57874	−0.161883
$801$	−10.2078	−0.360674
$802$	−33.5973	−1.18636
$803$	3.98666	0.140686
$804$	4.59049	0.161894
$805$	−9.26392	−0.326510
$806$	5.41795	0.190839
$807$	−7.49680	−0.263900
$808$	2.52140	0.0887024
$809$	33.4757	1.17694	0.588472	−	0.808518i	$-0.299730\pi$
$809$	33.4757	1.17694	0.588472	+	0.808518i	$0.299730\pi$
$810$	3.09495	0.108746
$811$	11.1170	0.390372	0.195186	−	0.980766i	$-0.437469\pi$
$811$	11.1170	0.390372	0.195186	+	0.980766i	$0.437469\pi$
$812$	−30.7141	−1.07786
$813$	4.30922	0.151131
$814$	13.0791	0.458424
$815$	−38.0362	−1.33235
$816$	−3.07102	−0.107507
$817$	−26.7923	−0.937343
$818$	−32.1938	−1.12563
$819$	−3.97310	−0.138831
$820$	9.89156	0.345428
$821$	7.06169	0.246455	0.123227	−	0.992378i	$-0.460676\pi$
$821$	7.06169	0.246455	0.123227	+	0.992378i	$0.460676\pi$
$822$	8.59513	0.299789
$823$	39.6732	1.38292	0.691460	−	0.722415i	$-0.256968\pi$
$823$	39.6732	1.38292	0.691460	+	0.722415i	$0.256968\pi$
$824$	−1.00000	−0.0348367
$825$	9.56398	0.332975
$826$	−12.1670	−0.423345
$827$	−2.94176	−0.102295	−0.0511476	−	0.998691i	$-0.516288\pi$
$827$	−2.94176	−0.102295	−0.0511476	+	0.998691i	$0.516288\pi$
$828$	0.753374	0.0261816
$829$	4.67196	0.162264	0.0811319	−	0.996703i	$-0.474146\pi$
$829$	4.67196	0.162264	0.0811319	+	0.996703i	$0.474146\pi$
$830$	34.4008	1.19407
$831$	−7.46649	−0.259010
$832$	−1.00000	−0.0346688
$833$	26.9806	0.934821
$834$	−8.32306	−0.288204
$835$	9.20830	0.318666
$836$	13.2832	0.459411
$837$	−5.41795	−0.187272
$838$	−10.2866	−0.355345
$839$	35.8053	1.23614	0.618068	−	0.786124i	$-0.287916\pi$
$839$	35.8053	1.23614	0.618068	+	0.786124i	$0.287916\pi$
$840$	−12.2966	−0.424272
$841$	30.7610	1.06072
$842$	−3.55842	−0.122631
$843$	24.4370	0.841655
$844$	7.71356	0.265512
$845$	−3.09495	−0.106470
$846$	9.09805	0.312797
$847$	−26.3695	−0.906065
$848$	1.78997	0.0614680
$849$	−5.72108	−0.196347
$850$	−14.0614	−0.482302
$851$	4.71734	0.161708
$852$	−6.81056	−0.233326
$853$	−29.8185	−1.02097	−0.510483	−	0.859888i	$-0.670533\pi$
$853$	−29.8185	−1.02097	−0.510483	+	0.859888i	$0.670533\pi$
$854$	28.8735	0.988031
$855$	19.6818	0.673105
$856$	11.8799	0.406046
$857$	−32.8346	−1.12161	−0.560804	−	0.827949i	$-0.689508\pi$
$857$	−32.8346	−1.12161	−0.560804	+	0.827949i	$0.689508\pi$
$858$	2.08878	0.0713098
$859$	−37.4820	−1.27887	−0.639434	−	0.768846i	$-0.720831\pi$
$859$	−37.4820	−1.27887	−0.639434	+	0.768846i	$0.720831\pi$
$860$	−13.0392	−0.444634
$861$	12.6981	0.432751
$862$	−34.3904	−1.17134
$863$	4.29422	0.146177	0.0730884	−	0.997325i	$-0.476714\pi$
$863$	4.29422	0.146177	0.0730884	+	0.997325i	$0.476714\pi$
$864$	1.00000	0.0340207
$865$	72.5723	2.46753
$866$	−28.3588	−0.963671
$867$	7.56883	0.257051
$868$	21.5261	0.730642
$869$	−7.55428	−0.256262
$870$	23.9256	0.811154
$871$	4.59049	0.155543
$872$	−1.43249	−0.0485101
$873$	14.6236	0.494935
$874$	4.79096	0.162056
$875$	5.18006	0.175118
$876$	1.90860	0.0644858
$877$	−48.3566	−1.63289	−0.816444	−	0.577425i	$-0.804058\pi$
$877$	−48.3566	−1.63289	−0.816444	+	0.577425i	$0.804058\pi$
$878$	9.92285	0.334880
$879$	−21.1961	−0.714927
$880$	6.46468	0.217924
$881$	−33.8058	−1.13895	−0.569474	−	0.822010i	$-0.692853\pi$
$881$	−33.8058	−1.13895	−0.569474	+	0.822010i	$0.692853\pi$
$882$	−8.78553	−0.295824
$883$	−13.0623	−0.439581	−0.219790	−	0.975547i	$-0.570537\pi$
$883$	−13.0623	−0.439581	−0.219790	+	0.975547i	$0.570537\pi$
$884$	−3.07102	−0.103290
$885$	9.47783	0.318594
$886$	−23.5320	−0.790574
$887$	−2.15806	−0.0724605	−0.0362302	−	0.999343i	$-0.511535\pi$
$887$	−2.15806	−0.0724605	−0.0362302	+	0.999343i	$0.511535\pi$
$888$	6.26162	0.210126
$889$	−51.4225	−1.72466
$890$	−31.5926	−1.05899
$891$	−2.08878	−0.0699768
$892$	11.7910	0.394791
$893$	57.8575	1.93613
$894$	2.51358	0.0840668
$895$	42.0492	1.40555
$896$	−3.97310	−0.132732
$897$	0.753374	0.0251544
$898$	26.6482	0.889263
$899$	−41.8836	−1.39690
$900$	4.57874	0.152625
$901$	5.49705	0.183133
$902$	−6.67580	−0.222280
$903$	−16.7389	−0.557037
$904$	−14.4197	−0.479591
$905$	36.5181	1.21390
$906$	14.7689	0.490665
$907$	−49.8857	−1.65643	−0.828213	−	0.560413i	$-0.810642\pi$
$907$	−49.8857	−1.65643	−0.828213	+	0.560413i	$0.810642\pi$
$908$	2.29930	0.0763048
$909$	−2.52140	−0.0836295
$910$	−12.2966	−0.407627
$911$	20.7445	0.687297	0.343648	−	0.939098i	$-0.388337\pi$
$911$	20.7445	0.687297	0.343648	+	0.939098i	$0.388337\pi$
$912$	6.35933	0.210578
$913$	−23.2170	−0.768372
$914$	3.70020	0.122392
$915$	−22.4918	−0.743556
$916$	−14.0302	−0.463569
$917$	−41.0611	−1.35596
$918$	3.07102	0.101359
$919$	36.8177	1.21451	0.607253	−	0.794509i	$-0.292272\pi$
$919$	36.8177	1.21451	0.607253	+	0.794509i	$0.292272\pi$
$920$	2.33166	0.0768725
$921$	−1.23481	−0.0406883
$922$	−35.5552	−1.17095
$923$	−6.81056	−0.224172
$924$	8.29894	0.273015
$925$	28.6703	0.942674
$926$	13.5000	0.443637
$927$	1.00000	0.0328443
$928$	7.73052	0.253767
$929$	−7.61626	−0.249881	−0.124941	−	0.992164i	$-0.539874\pi$
$929$	−7.61626	−0.249881	−0.124941	+	0.992164i	$0.539874\pi$
$930$	−16.7683	−0.549854
$931$	−55.8701	−1.83107
$932$	−7.93621	−0.259959
$933$	19.4195	0.635765
$934$	−22.0480	−0.721432
$935$	19.8532	0.649268
$936$	1.00000	0.0326860
$937$	46.9034	1.53227	0.766133	−	0.642682i	$-0.222178\pi$
$937$	46.9034	1.53227	0.766133	+	0.642682i	$0.222178\pi$
$938$	18.2385	0.595508
$939$	−8.68698	−0.283489
$940$	28.1581	0.918414
$941$	41.6504	1.35776	0.678882	−	0.734248i	$-0.262465\pi$
$941$	41.6504	1.35776	0.678882	+	0.734248i	$0.262465\pi$
$942$	1.41185	0.0460006
$943$	−2.40780	−0.0784089
$944$	3.06235	0.0996710
$945$	12.2966	0.400007
$946$	8.80017	0.286118
$947$	51.8176	1.68385	0.841923	−	0.539598i	$-0.181424\pi$
$947$	51.8176	1.68385	0.841923	+	0.539598i	$0.181424\pi$
$948$	−3.61660	−0.117462
$949$	1.90860	0.0619559
$950$	29.1177	0.944703
$951$	−10.3957	−0.337102
$952$	−12.2015	−0.395452
$953$	3.94643	0.127837	0.0639186	−	0.997955i	$-0.479640\pi$
$953$	3.94643	0.127837	0.0639186	+	0.997955i	$0.479640\pi$
$954$	−1.78997	−0.0579526
$955$	−37.1957	−1.20362
$956$	−14.3211	−0.463177
$957$	−16.1474	−0.521970
$958$	8.97508	0.289972
$959$	34.1493	1.10274
$960$	3.09495	0.0998892
$961$	−1.64584	−0.0530916
$962$	6.26162	0.201883
$963$	−11.8799	−0.382824
$964$	−14.4962	−0.466892
$965$	−8.93051	−0.287483
$966$	2.99323	0.0963057
$967$	4.55096	0.146349	0.0731745	−	0.997319i	$-0.476687\pi$
$967$	4.55096	0.146349	0.0731745	+	0.997319i	$0.476687\pi$
$968$	6.63700	0.213321
$969$	19.5296	0.627382
$970$	45.2594	1.45319
$971$	42.2830	1.35693	0.678463	−	0.734634i	$-0.262646\pi$
$971$	42.2830	1.35693	0.678463	+	0.734634i	$0.262646\pi$
$972$	−1.00000	−0.0320750
$973$	−33.0683	−1.06012
$974$	4.81808	0.154381
$975$	4.57874	0.146637
$976$	−7.26725	−0.232619
$977$	42.7941	1.36910	0.684552	−	0.728964i	$-0.259998\pi$
$977$	42.7941	1.36910	0.684552	+	0.728964i	$0.259998\pi$
$978$	12.2897	0.392983
$979$	21.3218	0.681448
$980$	−27.1908	−0.868579
$981$	1.43249	0.0457358
$982$	−36.5073	−1.16499
$983$	−19.0515	−0.607648	−0.303824	−	0.952728i	$-0.598263\pi$
$983$	−19.0515	−0.607648	−0.303824	+	0.952728i	$0.598263\pi$
$984$	−3.19603	−0.101886
$985$	−48.7713	−1.55398
$986$	23.7406	0.756055
$987$	36.1475	1.15059
$988$	6.35933	0.202317
$989$	3.17401	0.100928
$990$	−6.46468	−0.205461
$991$	16.5441	0.525542	0.262771	−	0.964858i	$-0.415364\pi$
$991$	16.5441	0.525542	0.262771	+	0.964858i	$0.415364\pi$
$992$	−5.41795	−0.172020
$993$	29.7538	0.944209
$994$	−27.0591	−0.858261
$995$	2.98917	0.0947629
$996$	−11.1151	−0.352196
$997$	−7.78827	−0.246657	−0.123328	−	0.992366i	$-0.539357\pi$
$997$	−7.78827	−0.246657	−0.123328	+	0.992366i	$0.539357\pi$
$998$	−2.73918	−0.0867071
$999$	−6.26162	−0.198109

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.ba.1.3	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.ba.1.3	✓	14	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.09495 q^{5} +1.00000 q^{6} +3.97310 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.09495 q^{5} +1.00000 q^{6} +3.97310 q^{7} -1.00000 q^{8} +1.00000 q^{9} +3.09495 q^{10} -2.08878 q^{11} -1.00000 q^{12} -1.00000 q^{13} -3.97310 q^{14} +3.09495 q^{15} +1.00000 q^{16} +3.07102 q^{17} -1.00000 q^{18} -6.35933 q^{19} -3.09495 q^{20} -3.97310 q^{21} +2.08878 q^{22} +0.753374 q^{23} +1.00000 q^{24} +4.57874 q^{25} +1.00000 q^{26} -1.00000 q^{27} +3.97310 q^{28} -7.73052 q^{29} -3.09495 q^{30} +5.41795 q^{31} -1.00000 q^{32} +2.08878 q^{33} -3.07102 q^{34} -12.2966 q^{35} +1.00000 q^{36} +6.26162 q^{37} +6.35933 q^{38} +1.00000 q^{39} +3.09495 q^{40} -3.19603 q^{41} +3.97310 q^{42} +4.21307 q^{43} -2.08878 q^{44} -3.09495 q^{45} -0.753374 q^{46} -9.09805 q^{47} -1.00000 q^{48} +8.78553 q^{49} -4.57874 q^{50} -3.07102 q^{51} -1.00000 q^{52} +1.78997 q^{53} +1.00000 q^{54} +6.46468 q^{55} -3.97310 q^{56} +6.35933 q^{57} +7.73052 q^{58} +3.06235 q^{59} +3.09495 q^{60} -7.26725 q^{61} -5.41795 q^{62} +3.97310 q^{63} +1.00000 q^{64} +3.09495 q^{65} -2.08878 q^{66} -4.59049 q^{67} +3.07102 q^{68} -0.753374 q^{69} +12.2966 q^{70} +6.81056 q^{71} -1.00000 q^{72} -1.90860 q^{73} -6.26162 q^{74} -4.57874 q^{75} -6.35933 q^{76} -8.29894 q^{77} -1.00000 q^{78} +3.61660 q^{79} -3.09495 q^{80} +1.00000 q^{81} +3.19603 q^{82} +11.1151 q^{83} -3.97310 q^{84} -9.50467 q^{85} -4.21307 q^{86} +7.73052 q^{87} +2.08878 q^{88} -10.2078 q^{89} +3.09495 q^{90} -3.97310 q^{91} +0.753374 q^{92} -5.41795 q^{93} +9.09805 q^{94} +19.6818 q^{95} +1.00000 q^{96} +14.6236 q^{97} -8.78553 q^{98} -2.08878 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 14 q^{2} - 14 q^{3} + 14 q^{4} - q^{5} + 14 q^{6} + 5 q^{7} - 14 q^{8} + 14 q^{9}+O(q^{10}) \) 14 * q - 14 * q^2 - 14 * q^3 + 14 * q^4 - q^5 + 14 * q^6 + 5 * q^7 - 14 * q^8 + 14 * q^9	\( 14 q - 14 q^{2} - 14 q^{3} + 14 q^{4} - q^{5} + 14 q^{6} + 5 q^{7} - 14 q^{8} + 14 q^{9} + q^{10} - q^{11} - 14 q^{12} - 14 q^{13} - 5 q^{14} + q^{15} + 14 q^{16} - 12 q^{17} - 14 q^{18} + 10 q^{19} - q^{20} - 5 q^{21} + q^{22} - q^{23} + 14 q^{24} + 19 q^{25} + 14 q^{26} - 14 q^{27} + 5 q^{28} + 6 q^{29} - q^{30} + 20 q^{31} - 14 q^{32} + q^{33} + 12 q^{34} - 16 q^{35} + 14 q^{36} - 3 q^{37} - 10 q^{38} + 14 q^{39} + q^{40} + q^{41} + 5 q^{42} + 6 q^{43} - q^{44} - q^{45} + q^{46} - 13 q^{47} - 14 q^{48} + 9 q^{49} - 19 q^{50} + 12 q^{51} - 14 q^{52} - 27 q^{53} + 14 q^{54} + 10 q^{55} - 5 q^{56} - 10 q^{57} - 6 q^{58} - 6 q^{59} + q^{60} - 4 q^{61} - 20 q^{62} + 5 q^{63} + 14 q^{64} + q^{65} - q^{66} + 13 q^{67} - 12 q^{68} + q^{69} + 16 q^{70} + 18 q^{71} - 14 q^{72} + 11 q^{73} + 3 q^{74} - 19 q^{75} + 10 q^{76} - 15 q^{77} - 14 q^{78} + 33 q^{79} - q^{80} + 14 q^{81} - q^{82} - 25 q^{83} - 5 q^{84} + 25 q^{85} - 6 q^{86} - 6 q^{87} + q^{88} + 3 q^{89} + q^{90} - 5 q^{91} - q^{92} - 20 q^{93} + 13 q^{94} + 30 q^{95} + 14 q^{96} + 11 q^{97} - 9 q^{98} - q^{99}+O(q^{100}) \) 14 * q - 14 * q^2 - 14 * q^3 + 14 * q^4 - q^5 + 14 * q^6 + 5 * q^7 - 14 * q^8 + 14 * q^9 + q^10 - q^11 - 14 * q^12 - 14 * q^13 - 5 * q^14 + q^15 + 14 * q^16 - 12 * q^17 - 14 * q^18 + 10 * q^19 - q^20 - 5 * q^21 + q^22 - q^23 + 14 * q^24 + 19 * q^25 + 14 * q^26 - 14 * q^27 + 5 * q^28 + 6 * q^29 - q^30 + 20 * q^31 - 14 * q^32 + q^33 + 12 * q^34 - 16 * q^35 + 14 * q^36 - 3 * q^37 - 10 * q^38 + 14 * q^39 + q^40 + q^41 + 5 * q^42 + 6 * q^43 - q^44 - q^45 + q^46 - 13 * q^47 - 14 * q^48 + 9 * q^49 - 19 * q^50 + 12 * q^51 - 14 * q^52 - 27 * q^53 + 14 * q^54 + 10 * q^55 - 5 * q^56 - 10 * q^57 - 6 * q^58 - 6 * q^59 + q^60 - 4 * q^61 - 20 * q^62 + 5 * q^63 + 14 * q^64 + q^65 - q^66 + 13 * q^67 - 12 * q^68 + q^69 + 16 * q^70 + 18 * q^71 - 14 * q^72 + 11 * q^73 + 3 * q^74 - 19 * q^75 + 10 * q^76 - 15 * q^77 - 14 * q^78 + 33 * q^79 - q^80 + 14 * q^81 - q^82 - 25 * q^83 - 5 * q^84 + 25 * q^85 - 6 * q^86 - 6 * q^87 + q^88 + 3 * q^89 + q^90 - 5 * q^91 - q^92 - 20 * q^93 + 13 * q^94 + 30 * q^95 + 14 * q^96 + 11 * q^97 - 9 * q^98 - q^99

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