LMFDB - Embedded newform 8034.2.a.q.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:	$1$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 11x^{6} + 21x^{5} + 23x^{4} - 29x^{3} - 27x^{2} + x + 3 $ x^8 - 2x^7 - 11x^6 + 21x^5 + 23x^4 - 29x^3 - 27x^2 + x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-0.749852$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.74985 q^{5} +1.00000 q^{6} -2.02962 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.74985 q^{5} +1.00000 q^{6} -2.02962 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.74985 q^{10} +0.779471 q^{11} +1.00000 q^{12} -1.00000 q^{13} -2.02962 q^{14} -1.74985 q^{15} +1.00000 q^{16} +0.263542 q^{17} +1.00000 q^{18} -1.92707 q^{19} -1.74985 q^{20} -2.02962 q^{21} +0.779471 q^{22} +3.18731 q^{23} +1.00000 q^{24} -1.93802 q^{25} -1.00000 q^{26} +1.00000 q^{27} -2.02962 q^{28} +7.21481 q^{29} -1.74985 q^{30} -3.56795 q^{31} +1.00000 q^{32} +0.779471 q^{33} +0.263542 q^{34} +3.55153 q^{35} +1.00000 q^{36} -1.19794 q^{37} -1.92707 q^{38} -1.00000 q^{39} -1.74985 q^{40} -0.877550 q^{41} -2.02962 q^{42} -8.40643 q^{43} +0.779471 q^{44} -1.74985 q^{45} +3.18731 q^{46} -6.32932 q^{47} +1.00000 q^{48} -2.88065 q^{49} -1.93802 q^{50} +0.263542 q^{51} -1.00000 q^{52} -1.51593 q^{53} +1.00000 q^{54} -1.36396 q^{55} -2.02962 q^{56} -1.92707 q^{57} +7.21481 q^{58} +2.19411 q^{59} -1.74985 q^{60} -1.90493 q^{61} -3.56795 q^{62} -2.02962 q^{63} +1.00000 q^{64} +1.74985 q^{65} +0.779471 q^{66} -5.24292 q^{67} +0.263542 q^{68} +3.18731 q^{69} +3.55153 q^{70} -2.35927 q^{71} +1.00000 q^{72} -4.12695 q^{73} -1.19794 q^{74} -1.93802 q^{75} -1.92707 q^{76} -1.58203 q^{77} -1.00000 q^{78} +1.45048 q^{79} -1.74985 q^{80} +1.00000 q^{81} -0.877550 q^{82} +15.5905 q^{83} -2.02962 q^{84} -0.461159 q^{85} -8.40643 q^{86} +7.21481 q^{87} +0.779471 q^{88} -8.32385 q^{89} -1.74985 q^{90} +2.02962 q^{91} +3.18731 q^{92} -3.56795 q^{93} -6.32932 q^{94} +3.37208 q^{95} +1.00000 q^{96} +5.22522 q^{97} -2.88065 q^{98} +0.779471 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 6 q^{5} + 8 q^{6} - 3 q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 6 * q^5 + 8 * q^6 - 3 * q^7 + 8 * q^8 + 8 * q^9	\( 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 6 q^{5} + 8 q^{6} - 3 q^{7} + 8 q^{8} + 8 q^{9} - 6 q^{10} - 15 q^{11} + 8 q^{12} - 8 q^{13} - 3 q^{14} - 6 q^{15} + 8 q^{16} - 11 q^{17} + 8 q^{18} - 15 q^{19} - 6 q^{20} - 3 q^{21} - 15 q^{22} + q^{23} + 8 q^{24} - 10 q^{25} - 8 q^{26} + 8 q^{27} - 3 q^{28} - 10 q^{29} - 6 q^{30} - 3 q^{31} + 8 q^{32} - 15 q^{33} - 11 q^{34} - 12 q^{35} + 8 q^{36} - 26 q^{37} - 15 q^{38} - 8 q^{39} - 6 q^{40} - 12 q^{41} - 3 q^{42} - 4 q^{43} - 15 q^{44} - 6 q^{45} + q^{46} - 6 q^{47} + 8 q^{48} - 5 q^{49} - 10 q^{50} - 11 q^{51} - 8 q^{52} - 4 q^{53} + 8 q^{54} - 3 q^{56} - 15 q^{57} - 10 q^{58} - 19 q^{59} - 6 q^{60} - 14 q^{61} - 3 q^{62} - 3 q^{63} + 8 q^{64} + 6 q^{65} - 15 q^{66} - 13 q^{67} - 11 q^{68} + q^{69} - 12 q^{70} - 31 q^{71} + 8 q^{72} - 27 q^{73} - 26 q^{74} - 10 q^{75} - 15 q^{76} - 30 q^{77} - 8 q^{78} - 13 q^{79} - 6 q^{80} + 8 q^{81} - 12 q^{82} - 28 q^{83} - 3 q^{84} + 15 q^{85} - 4 q^{86} - 10 q^{87} - 15 q^{88} - 2 q^{89} - 6 q^{90} + 3 q^{91} + q^{92} - 3 q^{93} - 6 q^{94} - 18 q^{95} + 8 q^{96} - 30 q^{97} - 5 q^{98} - 15 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 6 * q^5 + 8 * q^6 - 3 * q^7 + 8 * q^8 + 8 * q^9 - 6 * q^10 - 15 * q^11 + 8 * q^12 - 8 * q^13 - 3 * q^14 - 6 * q^15 + 8 * q^16 - 11 * q^17 + 8 * q^18 - 15 * q^19 - 6 * q^20 - 3 * q^21 - 15 * q^22 + q^23 + 8 * q^24 - 10 * q^25 - 8 * q^26 + 8 * q^27 - 3 * q^28 - 10 * q^29 - 6 * q^30 - 3 * q^31 + 8 * q^32 - 15 * q^33 - 11 * q^34 - 12 * q^35 + 8 * q^36 - 26 * q^37 - 15 * q^38 - 8 * q^39 - 6 * q^40 - 12 * q^41 - 3 * q^42 - 4 * q^43 - 15 * q^44 - 6 * q^45 + q^46 - 6 * q^47 + 8 * q^48 - 5 * q^49 - 10 * q^50 - 11 * q^51 - 8 * q^52 - 4 * q^53 + 8 * q^54 - 3 * q^56 - 15 * q^57 - 10 * q^58 - 19 * q^59 - 6 * q^60 - 14 * q^61 - 3 * q^62 - 3 * q^63 + 8 * q^64 + 6 * q^65 - 15 * q^66 - 13 * q^67 - 11 * q^68 + q^69 - 12 * q^70 - 31 * q^71 + 8 * q^72 - 27 * q^73 - 26 * q^74 - 10 * q^75 - 15 * q^76 - 30 * q^77 - 8 * q^78 - 13 * q^79 - 6 * q^80 + 8 * q^81 - 12 * q^82 - 28 * q^83 - 3 * q^84 + 15 * q^85 - 4 * q^86 - 10 * q^87 - 15 * q^88 - 2 * q^89 - 6 * q^90 + 3 * q^91 + q^92 - 3 * q^93 - 6 * q^94 - 18 * q^95 + 8 * q^96 - 30 * q^97 - 5 * q^98 - 15 * 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
$5$	−1.74985	−0.782557	−0.391279	−	0.920272i	$-0.627967\pi$
$5$	−1.74985	−0.782557	−0.391279	+	0.920272i	$0.627967\pi$
$6$	1.00000	0.408248
$7$	−2.02962	−0.767124	−0.383562	−	0.923515i	$-0.625303\pi$
$7$	−2.02962	−0.767124	−0.383562	+	0.923515i	$0.625303\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−1.74985	−0.553352
$11$	0.779471	0.235019	0.117510	−	0.993072i	$-0.462509\pi$
$11$	0.779471	0.235019	0.117510	+	0.993072i	$0.462509\pi$
$12$	1.00000	0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−2.02962	−0.542438
$15$	−1.74985	−0.451810
$16$	1.00000	0.250000
$17$	0.263542	0.0639182	0.0319591	−	0.999489i	$-0.489825\pi$
$17$	0.263542	0.0639182	0.0319591	+	0.999489i	$0.489825\pi$
$18$	1.00000	0.235702
$19$	−1.92707	−0.442099	−0.221050	−	0.975263i	$-0.570948\pi$
$19$	−1.92707	−0.442099	−0.221050	+	0.975263i	$0.570948\pi$
$20$	−1.74985	−0.391279
$21$	−2.02962	−0.442899
$22$	0.779471	0.166184
$23$	3.18731	0.664601	0.332300	−	0.943174i	$-0.392175\pi$
$23$	3.18731	0.664601	0.332300	+	0.943174i	$0.392175\pi$
$24$	1.00000	0.204124
$25$	−1.93802	−0.387604
$26$	−1.00000	−0.196116
$27$	1.00000	0.192450
$28$	−2.02962	−0.383562
$29$	7.21481	1.33976	0.669879	−	0.742471i	$-0.266346\pi$
$29$	7.21481	1.33976	0.669879	+	0.742471i	$0.266346\pi$
$30$	−1.74985	−0.319478
$31$	−3.56795	−0.640823	−0.320412	−	0.947278i	$-0.603821\pi$
$31$	−3.56795	−0.640823	−0.320412	+	0.947278i	$0.603821\pi$
$32$	1.00000	0.176777
$33$	0.779471	0.135688
$34$	0.263542	0.0451970
$35$	3.55153	0.600319
$36$	1.00000	0.166667
$37$	−1.19794	−0.196940	−0.0984702	−	0.995140i	$-0.531395\pi$
$37$	−1.19794	−0.196940	−0.0984702	+	0.995140i	$0.531395\pi$
$38$	−1.92707	−0.312611
$39$	−1.00000	−0.160128
$40$	−1.74985	−0.276676
$41$	−0.877550	−0.137050	−0.0685251	−	0.997649i	$-0.521829\pi$
$41$	−0.877550	−0.137050	−0.0685251	+	0.997649i	$0.521829\pi$
$42$	−2.02962	−0.313177
$43$	−8.40643	−1.28197	−0.640984	−	0.767554i	$-0.721474\pi$
$43$	−8.40643	−1.28197	−0.640984	+	0.767554i	$0.721474\pi$
$44$	0.779471	0.117510
$45$	−1.74985	−0.260852
$46$	3.18731	0.469944
$47$	−6.32932	−0.923227	−0.461613	−	0.887081i	$-0.652729\pi$
$47$	−6.32932	−0.923227	−0.461613	+	0.887081i	$0.652729\pi$
$48$	1.00000	0.144338
$49$	−2.88065	−0.411521
$50$	−1.93802	−0.274077
$51$	0.263542	0.0369032
$52$	−1.00000	−0.138675
$53$	−1.51593	−0.208229	−0.104114	−	0.994565i	$-0.533201\pi$
$53$	−1.51593	−0.208229	−0.104114	+	0.994565i	$0.533201\pi$
$54$	1.00000	0.136083
$55$	−1.36396	−0.183916
$56$	−2.02962	−0.271219
$57$	−1.92707	−0.255246
$58$	7.21481	0.947351
$59$	2.19411	0.285649	0.142825	−	0.989748i	$-0.454382\pi$
$59$	2.19411	0.285649	0.142825	+	0.989748i	$0.454382\pi$
$60$	−1.74985	−0.225905
$61$	−1.90493	−0.243901	−0.121950	−	0.992536i	$-0.538915\pi$
$61$	−1.90493	−0.243901	−0.121950	+	0.992536i	$0.538915\pi$
$62$	−3.56795	−0.453131
$63$	−2.02962	−0.255708
$64$	1.00000	0.125000
$65$	1.74985	0.217042
$66$	0.779471	0.0959462
$67$	−5.24292	−0.640524	−0.320262	−	0.947329i	$-0.603771\pi$
$67$	−5.24292	−0.640524	−0.320262	+	0.947329i	$0.603771\pi$
$68$	0.263542	0.0319591
$69$	3.18731	0.383708
$70$	3.55153	0.424489
$71$	−2.35927	−0.279994	−0.139997	−	0.990152i	$-0.544709\pi$
$71$	−2.35927	−0.279994	−0.139997	+	0.990152i	$0.544709\pi$
$72$	1.00000	0.117851
$73$	−4.12695	−0.483023	−0.241511	−	0.970398i	$-0.577643\pi$
$73$	−4.12695	−0.483023	−0.241511	+	0.970398i	$0.577643\pi$
$74$	−1.19794	−0.139258
$75$	−1.93802	−0.223783
$76$	−1.92707	−0.221050
$77$	−1.58203	−0.180289
$78$	−1.00000	−0.113228
$79$	1.45048	0.163192	0.0815960	−	0.996665i	$-0.473998\pi$
$79$	1.45048	0.163192	0.0815960	+	0.996665i	$0.473998\pi$
$80$	−1.74985	−0.195639
$81$	1.00000	0.111111
$82$	−0.877550	−0.0969092
$83$	15.5905	1.71128	0.855639	−	0.517572i	$-0.173164\pi$
$83$	15.5905	1.71128	0.855639	+	0.517572i	$0.173164\pi$
$84$	−2.02962	−0.221450
$85$	−0.461159	−0.0500197
$86$	−8.40643	−0.906488
$87$	7.21481	0.773509
$88$	0.779471	0.0830919
$89$	−8.32385	−0.882327	−0.441163	−	0.897427i	$-0.645434\pi$
$89$	−8.32385	−0.882327	−0.441163	+	0.897427i	$0.645434\pi$
$90$	−1.74985	−0.184451
$91$	2.02962	0.212762
$92$	3.18731	0.332300
$93$	−3.56795	−0.369980
$94$	−6.32932	−0.652820
$95$	3.37208	0.345968
$96$	1.00000	0.102062
$97$	5.22522	0.530541	0.265270	−	0.964174i	$-0.414539\pi$
$97$	5.22522	0.530541	0.265270	+	0.964174i	$0.414539\pi$
$98$	−2.88065	−0.290989
$99$	0.779471	0.0783398
$100$	−1.93802	−0.193802
$101$	−5.89867	−0.586940	−0.293470	−	0.955968i	$-0.594810\pi$
$101$	−5.89867	−0.586940	−0.293470	+	0.955968i	$0.594810\pi$
$102$	0.263542	0.0260945
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	−1.00000	−0.0980581
$105$	3.55153	0.346594
$106$	−1.51593	−0.147240
$107$	−9.50943	−0.919312	−0.459656	−	0.888097i	$-0.652027\pi$
$107$	−9.50943	−0.919312	−0.459656	+	0.888097i	$0.652027\pi$
$108$	1.00000	0.0962250
$109$	−7.23333	−0.692827	−0.346413	−	0.938082i	$-0.612601\pi$
$109$	−7.23333	−0.692827	−0.346413	+	0.938082i	$0.612601\pi$
$110$	−1.36396	−0.130048
$111$	−1.19794	−0.113704
$112$	−2.02962	−0.191781
$113$	−2.08276	−0.195929	−0.0979647	−	0.995190i	$-0.531233\pi$
$113$	−2.08276	−0.195929	−0.0979647	+	0.995190i	$0.531233\pi$
$114$	−1.92707	−0.180486
$115$	−5.57733	−0.520088
$116$	7.21481	0.669879
$117$	−1.00000	−0.0924500
$118$	2.19411	0.201984
$119$	−0.534889	−0.0490332
$120$	−1.74985	−0.159739
$121$	−10.3924	−0.944766
$122$	−1.90493	−0.172464
$123$	−0.877550	−0.0791260
$124$	−3.56795	−0.320412
$125$	12.1405	1.08588
$126$	−2.02962	−0.180813
$127$	1.65344	0.146719	0.0733595	−	0.997306i	$-0.476628\pi$
$127$	1.65344	0.146719	0.0733595	+	0.997306i	$0.476628\pi$
$128$	1.00000	0.0883883
$129$	−8.40643	−0.740145
$130$	1.74985	0.153472
$131$	−0.394299	−0.0344500	−0.0172250	−	0.999852i	$-0.505483\pi$
$131$	−0.394299	−0.0344500	−0.0172250	+	0.999852i	$0.505483\pi$
$132$	0.779471	0.0678442
$133$	3.91121	0.339145
$134$	−5.24292	−0.452919
$135$	−1.74985	−0.150603
$136$	0.263542	0.0225985
$137$	−21.2164	−1.81264	−0.906322	−	0.422589i	$-0.861122\pi$
$137$	−21.2164	−1.81264	−0.906322	+	0.422589i	$0.861122\pi$
$138$	3.18731	0.271322
$139$	3.29987	0.279891	0.139945	−	0.990159i	$-0.455307\pi$
$139$	3.29987	0.279891	0.139945	+	0.990159i	$0.455307\pi$
$140$	3.55153	0.300159
$141$	−6.32932	−0.533025
$142$	−2.35927	−0.197985
$143$	−0.779471	−0.0651826
$144$	1.00000	0.0833333
$145$	−12.6249	−1.04844
$146$	−4.12695	−0.341549
$147$	−2.88065	−0.237592
$148$	−1.19794	−0.0984702
$149$	−18.1059	−1.48329	−0.741645	−	0.670792i	$-0.765954\pi$
$149$	−18.1059	−1.48329	−0.741645	+	0.670792i	$0.765954\pi$
$150$	−1.93802	−0.158239
$151$	1.07701	0.0876458	0.0438229	−	0.999039i	$-0.486046\pi$
$151$	1.07701	0.0876458	0.0438229	+	0.999039i	$0.486046\pi$
$152$	−1.92707	−0.156306
$153$	0.263542	0.0213061
$154$	−1.58203	−0.127483
$155$	6.24339	0.501481
$156$	−1.00000	−0.0800641
$157$	1.77321	0.141517	0.0707586	−	0.997493i	$-0.477458\pi$
$157$	1.77321	0.141517	0.0707586	+	0.997493i	$0.477458\pi$
$158$	1.45048	0.115394
$159$	−1.51593	−0.120221
$160$	−1.74985	−0.138338
$161$	−6.46903	−0.509831
$162$	1.00000	0.0785674
$163$	−12.9529	−1.01455	−0.507273	−	0.861785i	$-0.669347\pi$
$163$	−12.9529	−1.01455	−0.507273	+	0.861785i	$0.669347\pi$
$164$	−0.877550	−0.0685251
$165$	−1.36396	−0.106184
$166$	15.5905	1.21006
$167$	−3.77237	−0.291915	−0.145957	−	0.989291i	$-0.546626\pi$
$167$	−3.77237	−0.291915	−0.145957	+	0.989291i	$0.546626\pi$
$168$	−2.02962	−0.156589
$169$	1.00000	0.0769231
$170$	−0.461159	−0.0353693
$171$	−1.92707	−0.147366
$172$	−8.40643	−0.640984
$173$	−20.0657	−1.52557	−0.762783	−	0.646654i	$-0.776168\pi$
$173$	−20.0657	−1.52557	−0.762783	+	0.646654i	$0.776168\pi$
$174$	7.21481	0.546954
$175$	3.93344	0.297340
$176$	0.779471	0.0587548
$177$	2.19411	0.164920
$178$	−8.32385	−0.623899
$179$	−16.8786	−1.26157	−0.630783	−	0.775960i	$-0.717266\pi$
$179$	−16.8786	−1.26157	−0.630783	+	0.775960i	$0.717266\pi$
$180$	−1.74985	−0.130426
$181$	17.7642	1.32040	0.660200	−	0.751090i	$-0.270472\pi$
$181$	17.7642	1.32040	0.660200	+	0.751090i	$0.270472\pi$
$182$	2.02962	0.150445
$183$	−1.90493	−0.140816
$184$	3.18731	0.234972
$185$	2.09622	0.154117
$186$	−3.56795	−0.261615
$187$	0.205423	0.0150220
$188$	−6.32932	−0.461613
$189$	−2.02962	−0.147633
$190$	3.37208	0.244636
$191$	−9.31466	−0.673985	−0.336993	−	0.941507i	$-0.609410\pi$
$191$	−9.31466	−0.673985	−0.336993	+	0.941507i	$0.609410\pi$
$192$	1.00000	0.0721688
$193$	5.65689	0.407192	0.203596	−	0.979055i	$-0.434737\pi$
$193$	5.65689	0.407192	0.203596	+	0.979055i	$0.434737\pi$
$194$	5.22522	0.375149
$195$	1.74985	0.125309
$196$	−2.88065	−0.205760
$197$	18.3383	1.30655	0.653276	−	0.757120i	$-0.273394\pi$
$197$	18.3383	1.30655	0.653276	+	0.757120i	$0.273394\pi$
$198$	0.779471	0.0553946
$199$	−13.6687	−0.968949	−0.484474	−	0.874805i	$-0.660989\pi$
$199$	−13.6687	−0.968949	−0.484474	+	0.874805i	$0.660989\pi$
$200$	−1.93802	−0.137039
$201$	−5.24292	−0.369807
$202$	−5.89867	−0.415029
$203$	−14.6433	−1.02776
$204$	0.263542	0.0184516
$205$	1.53558	0.107250
$206$	−1.00000	−0.0696733
$207$	3.18731	0.221534
$208$	−1.00000	−0.0693375
$209$	−1.50209	−0.103902
$210$	3.55153	0.245079
$211$	20.5331	1.41356	0.706779	−	0.707434i	$-0.250147\pi$
$211$	20.5331	1.41356	0.706779	+	0.707434i	$0.250147\pi$
$212$	−1.51593	−0.104114
$213$	−2.35927	−0.161654
$214$	−9.50943	−0.650052
$215$	14.7100	1.00321
$216$	1.00000	0.0680414
$217$	7.24159	0.491591
$218$	−7.23333	−0.489903
$219$	−4.12695	−0.278873
$220$	−1.36396	−0.0919580
$221$	−0.263542	−0.0177277
$222$	−1.19794	−0.0804006
$223$	−9.24309	−0.618963	−0.309482	−	0.950905i	$-0.600156\pi$
$223$	−9.24309	−0.618963	−0.309482	+	0.950905i	$0.600156\pi$
$224$	−2.02962	−0.135610
$225$	−1.93802	−0.129201
$226$	−2.08276	−0.138543
$227$	−18.7660	−1.24554	−0.622772	−	0.782403i	$-0.713994\pi$
$227$	−18.7660	−1.24554	−0.622772	+	0.782403i	$0.713994\pi$
$228$	−1.92707	−0.127623
$229$	−21.6151	−1.42837	−0.714184	−	0.699958i	$-0.753202\pi$
$229$	−21.6151	−1.42837	−0.714184	+	0.699958i	$0.753202\pi$
$230$	−5.57733	−0.367758
$231$	−1.58203	−0.104090
$232$	7.21481	0.473676
$233$	−22.3608	−1.46491	−0.732453	−	0.680817i	$-0.761625\pi$
$233$	−22.3608	−1.46491	−0.732453	+	0.680817i	$0.761625\pi$
$234$	−1.00000	−0.0653720
$235$	11.0754	0.722478
$236$	2.19411	0.142825
$237$	1.45048	0.0942189
$238$	−0.534889	−0.0346717
$239$	−2.12760	−0.137623	−0.0688114	−	0.997630i	$-0.521921\pi$
$239$	−2.12760	−0.137623	−0.0688114	+	0.997630i	$0.521921\pi$
$240$	−1.74985	−0.112952
$241$	12.2326	0.787973	0.393986	−	0.919116i	$-0.371096\pi$
$241$	12.2326	0.787973	0.393986	+	0.919116i	$0.371096\pi$
$242$	−10.3924	−0.668050
$243$	1.00000	0.0641500
$244$	−1.90493	−0.121950
$245$	5.04070	0.322039
$246$	−0.877550	−0.0559505
$247$	1.92707	0.122616
$248$	−3.56795	−0.226565
$249$	15.5905	0.988007
$250$	12.1405	0.767833
$251$	24.2180	1.52863	0.764314	−	0.644844i	$-0.223078\pi$
$251$	24.2180	1.52863	0.764314	+	0.644844i	$0.223078\pi$
$252$	−2.02962	−0.127854
$253$	2.48442	0.156194
$254$	1.65344	0.103746
$255$	−0.461159	−0.0288789
$256$	1.00000	0.0625000
$257$	30.4142	1.89719	0.948594	−	0.316496i	$-0.102506\pi$
$257$	30.4142	1.89719	0.948594	+	0.316496i	$0.102506\pi$
$258$	−8.40643	−0.523361
$259$	2.43136	0.151078
$260$	1.74985	0.108521
$261$	7.21481	0.446586
$262$	−0.394299	−0.0243599
$263$	−2.28933	−0.141166	−0.0705831	−	0.997506i	$-0.522486\pi$
$263$	−2.28933	−0.141166	−0.0705831	+	0.997506i	$0.522486\pi$
$264$	0.779471	0.0479731
$265$	2.65265	0.162951
$266$	3.91121	0.239812
$267$	−8.32385	−0.509412
$268$	−5.24292	−0.320262
$269$	−10.9247	−0.666092	−0.333046	−	0.942911i	$-0.608076\pi$
$269$	−10.9247	−0.666092	−0.333046	+	0.942911i	$0.608076\pi$
$270$	−1.74985	−0.106493
$271$	−13.4837	−0.819077	−0.409538	−	0.912293i	$-0.634310\pi$
$271$	−13.4837	−0.819077	−0.409538	+	0.912293i	$0.634310\pi$
$272$	0.263542	0.0159796
$273$	2.02962	0.122838
$274$	−21.2164	−1.28173
$275$	−1.51063	−0.0910944
$276$	3.18731	0.191854
$277$	9.60543	0.577134	0.288567	−	0.957460i	$-0.406821\pi$
$277$	9.60543	0.577134	0.288567	+	0.957460i	$0.406821\pi$
$278$	3.29987	0.197913
$279$	−3.56795	−0.213608
$280$	3.55153	0.212245
$281$	9.27069	0.553043	0.276522	−	0.961008i	$-0.410818\pi$
$281$	9.27069	0.553043	0.276522	+	0.961008i	$0.410818\pi$
$282$	−6.32932	−0.376906
$283$	28.8002	1.71199	0.855997	−	0.516981i	$-0.172944\pi$
$283$	28.8002	1.71199	0.855997	+	0.516981i	$0.172944\pi$
$284$	−2.35927	−0.139997
$285$	3.37208	0.199745
$286$	−0.779471	−0.0460911
$287$	1.78109	0.105135
$288$	1.00000	0.0589256
$289$	−16.9305	−0.995914
$290$	−12.6249	−0.741357
$291$	5.22522	0.306308
$292$	−4.12695	−0.241511
$293$	−31.4445	−1.83701	−0.918504	−	0.395411i	$-0.870602\pi$
$293$	−31.4445	−1.83701	−0.918504	+	0.395411i	$0.870602\pi$
$294$	−2.88065	−0.168003
$295$	−3.83937	−0.223537
$296$	−1.19794	−0.0696289
$297$	0.779471	0.0452295
$298$	−18.1059	−1.04884
$299$	−3.18731	−0.184327
$300$	−1.93802	−0.111892
$301$	17.0618	0.983428
$302$	1.07701	0.0619749
$303$	−5.89867	−0.338870
$304$	−1.92707	−0.110525
$305$	3.33334	0.190866
$306$	0.263542	0.0150657
$307$	−14.2698	−0.814420	−0.407210	−	0.913334i	$-0.633498\pi$
$307$	−14.2698	−0.814420	−0.407210	+	0.913334i	$0.633498\pi$
$308$	−1.58203	−0.0901444
$309$	−1.00000	−0.0568880
$310$	6.24339	0.354601
$311$	−3.46080	−0.196244	−0.0981221	−	0.995174i	$-0.531284\pi$
$311$	−3.46080	−0.196244	−0.0981221	+	0.995174i	$0.531284\pi$
$312$	−1.00000	−0.0566139
$313$	26.6877	1.50848	0.754238	−	0.656601i	$-0.228006\pi$
$313$	26.6877	1.50848	0.754238	+	0.656601i	$0.228006\pi$
$314$	1.77321	0.100068
$315$	3.55153	0.200106
$316$	1.45048	0.0815960
$317$	19.5559	1.09837	0.549185	−	0.835701i	$-0.314938\pi$
$317$	19.5559	1.09837	0.549185	+	0.835701i	$0.314938\pi$
$318$	−1.51593	−0.0850091
$319$	5.62373	0.314869
$320$	−1.74985	−0.0978197
$321$	−9.50943	−0.530765
$322$	−6.46903	−0.360505
$323$	−0.507862	−0.0282582
$324$	1.00000	0.0555556
$325$	1.93802	0.107502
$326$	−12.9529	−0.717393
$327$	−7.23333	−0.400004
$328$	−0.877550	−0.0484546
$329$	12.8461	0.708229
$330$	−1.36396	−0.0750834
$331$	−35.3758	−1.94443	−0.972214	−	0.234094i	$-0.924788\pi$
$331$	−35.3758	−1.94443	−0.972214	+	0.234094i	$0.924788\pi$
$332$	15.5905	0.855639
$333$	−1.19794	−0.0656468
$334$	−3.77237	−0.206415
$335$	9.17433	0.501247
$336$	−2.02962	−0.110725
$337$	−12.1028	−0.659283	−0.329642	−	0.944106i	$-0.606928\pi$
$337$	−12.1028	−0.659283	−0.329642	+	0.944106i	$0.606928\pi$
$338$	1.00000	0.0543928
$339$	−2.08276	−0.113120
$340$	−0.461159	−0.0250098
$341$	−2.78112	−0.150606
$342$	−1.92707	−0.104204
$343$	20.0539	1.08281
$344$	−8.40643	−0.453244
$345$	−5.57733	−0.300273
$346$	−20.0657	−1.07874
$347$	−3.81699	−0.204907	−0.102453	−	0.994738i	$-0.532669\pi$
$347$	−3.81699	−0.204907	−0.102453	+	0.994738i	$0.532669\pi$
$348$	7.21481	0.386755
$349$	1.74938	0.0936421	0.0468210	−	0.998903i	$-0.485091\pi$
$349$	1.74938	0.0936421	0.0468210	+	0.998903i	$0.485091\pi$
$350$	3.93344	0.210251
$351$	−1.00000	−0.0533761
$352$	0.779471	0.0415459
$353$	−24.2812	−1.29236	−0.646178	−	0.763186i	$-0.723634\pi$
$353$	−24.2812	−1.29236	−0.646178	+	0.763186i	$0.723634\pi$
$354$	2.19411	0.116616
$355$	4.12837	0.219111
$356$	−8.32385	−0.441163
$357$	−0.534889	−0.0283093
$358$	−16.8786	−0.892061
$359$	−15.5093	−0.818549	−0.409274	−	0.912411i	$-0.634218\pi$
$359$	−15.5093	−0.818549	−0.409274	+	0.912411i	$0.634218\pi$
$360$	−1.74985	−0.0922253
$361$	−15.2864	−0.804548
$362$	17.7642	0.933664
$363$	−10.3924	−0.545461
$364$	2.02962	0.106381
$365$	7.22155	0.377993
$366$	−1.90493	−0.0995721
$367$	−15.4285	−0.805362	−0.402681	−	0.915340i	$-0.631922\pi$
$367$	−15.4285	−0.805362	−0.402681	+	0.915340i	$0.631922\pi$
$368$	3.18731	0.166150
$369$	−0.877550	−0.0456834
$370$	2.09622	0.108977
$371$	3.07676	0.159737
$372$	−3.56795	−0.184990
$373$	26.0656	1.34962	0.674812	−	0.737989i	$-0.264225\pi$
$373$	26.0656	1.34962	0.674812	+	0.737989i	$0.264225\pi$
$374$	0.205423	0.0106222
$375$	12.1405	0.626933
$376$	−6.32932	−0.326410
$377$	−7.21481	−0.371582
$378$	−2.02962	−0.104392
$379$	26.1847	1.34502	0.672508	−	0.740090i	$-0.265217\pi$
$379$	26.1847	1.34502	0.672508	+	0.740090i	$0.265217\pi$
$380$	3.37208	0.172984
$381$	1.65344	0.0847083
$382$	−9.31466	−0.476580
$383$	18.6214	0.951509	0.475754	−	0.879578i	$-0.342175\pi$
$383$	18.6214	0.951509	0.475754	+	0.879578i	$0.342175\pi$
$384$	1.00000	0.0510310
$385$	2.76832	0.141086
$386$	5.65689	0.287928
$387$	−8.40643	−0.427323
$388$	5.22522	0.265270
$389$	22.7756	1.15477	0.577384	−	0.816472i	$-0.304073\pi$
$389$	22.7756	1.15477	0.577384	+	0.816472i	$0.304073\pi$
$390$	1.74985	0.0886072
$391$	0.839990	0.0424801
$392$	−2.88065	−0.145495
$393$	−0.394299	−0.0198897
$394$	18.3383	0.923871
$395$	−2.53813	−0.127707
$396$	0.779471	0.0391699
$397$	9.54045	0.478822	0.239411	−	0.970918i	$-0.423046\pi$
$397$	9.54045	0.478822	0.239411	+	0.970918i	$0.423046\pi$
$398$	−13.6687	−0.685150
$399$	3.91121	0.195805
$400$	−1.93802	−0.0969009
$401$	−14.4073	−0.719465	−0.359733	−	0.933055i	$-0.617132\pi$
$401$	−14.4073	−0.719465	−0.359733	+	0.933055i	$0.617132\pi$
$402$	−5.24292	−0.261493
$403$	3.56795	0.177732
$404$	−5.89867	−0.293470
$405$	−1.74985	−0.0869508
$406$	−14.6433	−0.726736
$407$	−0.933760	−0.0462848
$408$	0.263542	0.0130473
$409$	−20.6224	−1.01971	−0.509856	−	0.860260i	$-0.670301\pi$
$409$	−20.6224	−1.01971	−0.509856	+	0.860260i	$0.670301\pi$
$410$	1.53558	0.0758370
$411$	−21.2164	−1.04653
$412$	−1.00000	−0.0492665
$413$	−4.45321	−0.219128
$414$	3.18731	0.156648
$415$	−27.2810	−1.33917
$416$	−1.00000	−0.0490290
$417$	3.29987	0.161595
$418$	−1.50209	−0.0734697
$419$	−31.0737	−1.51805	−0.759024	−	0.651063i	$-0.774324\pi$
$419$	−31.0737	−1.51805	−0.759024	+	0.651063i	$0.774324\pi$
$420$	3.55153	0.173297
$421$	−24.8955	−1.21333	−0.606667	−	0.794956i	$-0.707494\pi$
$421$	−24.8955	−1.21333	−0.606667	+	0.794956i	$0.707494\pi$
$422$	20.5331	0.999537
$423$	−6.32932	−0.307742
$424$	−1.51593	−0.0736200
$425$	−0.510749	−0.0247749
$426$	−2.35927	−0.114307
$427$	3.86627	0.187102
$428$	−9.50943	−0.459656
$429$	−0.779471	−0.0376332
$430$	14.7100	0.709379
$431$	−5.09020	−0.245186	−0.122593	−	0.992457i	$-0.539121\pi$
$431$	−5.09020	−0.245186	−0.122593	+	0.992457i	$0.539121\pi$
$432$	1.00000	0.0481125
$433$	39.6738	1.90660	0.953301	−	0.302023i	$-0.0976619\pi$
$433$	39.6738	1.90660	0.953301	+	0.302023i	$0.0976619\pi$
$434$	7.24159	0.347607
$435$	−12.6249	−0.605315
$436$	−7.23333	−0.346413
$437$	−6.14216	−0.293820
$438$	−4.12695	−0.197193
$439$	36.0195	1.71912	0.859559	−	0.511036i	$-0.170738\pi$
$439$	36.0195	1.71912	0.859559	+	0.511036i	$0.170738\pi$
$440$	−1.36396	−0.0650242
$441$	−2.88065	−0.137174
$442$	−0.263542	−0.0125354
$443$	26.6207	1.26479	0.632393	−	0.774648i	$-0.282073\pi$
$443$	26.6207	1.26479	0.632393	+	0.774648i	$0.282073\pi$
$444$	−1.19794	−0.0568518
$445$	14.5655	0.690471
$446$	−9.24309	−0.437673
$447$	−18.1059	−0.856378
$448$	−2.02962	−0.0958905
$449$	−26.7816	−1.26390	−0.631950	−	0.775009i	$-0.717745\pi$
$449$	−26.7816	−1.26390	−0.631950	+	0.775009i	$0.717745\pi$
$450$	−1.93802	−0.0913591
$451$	−0.684024	−0.0322094
$452$	−2.08276	−0.0979647
$453$	1.07701	0.0506023
$454$	−18.7660	−0.880733
$455$	−3.55153	−0.166498
$456$	−1.92707	−0.0902431
$457$	−26.0792	−1.21994	−0.609968	−	0.792426i	$-0.708818\pi$
$457$	−26.0792	−1.21994	−0.609968	+	0.792426i	$0.708818\pi$
$458$	−21.6151	−1.01001
$459$	0.263542	0.0123011
$460$	−5.57733	−0.260044
$461$	−4.81621	−0.224313	−0.112157	−	0.993691i	$-0.535776\pi$
$461$	−4.81621	−0.224313	−0.112157	+	0.993691i	$0.535776\pi$
$462$	−1.58203	−0.0736026
$463$	23.3175	1.08366	0.541829	−	0.840489i	$-0.317732\pi$
$463$	23.3175	1.08366	0.541829	+	0.840489i	$0.317732\pi$
$464$	7.21481	0.334939
$465$	6.24339	0.289530
$466$	−22.3608	−1.03585
$467$	9.57439	0.443050	0.221525	−	0.975155i	$-0.428897\pi$
$467$	9.57439	0.443050	0.221525	+	0.975155i	$0.428897\pi$
$468$	−1.00000	−0.0462250
$469$	10.6411	0.491362
$470$	11.0754	0.510869
$471$	1.77321	0.0817050
$472$	2.19411	0.100992
$473$	−6.55256	−0.301287
$474$	1.45048	0.0666229
$475$	3.73469	0.171359
$476$	−0.534889	−0.0245166
$477$	−1.51593	−0.0694096
$478$	−2.12760	−0.0973139
$479$	20.7678	0.948905	0.474453	−	0.880281i	$-0.342646\pi$
$479$	20.7678	0.948905	0.474453	+	0.880281i	$0.342646\pi$
$480$	−1.74985	−0.0798694
$481$	1.19794	0.0546214
$482$	12.2326	0.557181
$483$	−6.46903	−0.294351
$484$	−10.3924	−0.472383
$485$	−9.14336	−0.415179
$486$	1.00000	0.0453609
$487$	−10.5599	−0.478513	−0.239256	−	0.970956i	$-0.576904\pi$
$487$	−10.5599	−0.478513	−0.239256	+	0.970956i	$0.576904\pi$
$488$	−1.90493	−0.0862320
$489$	−12.9529	−0.585749
$490$	5.04070	0.227716
$491$	−28.6870	−1.29463	−0.647313	−	0.762225i	$-0.724107\pi$
$491$	−28.6870	−1.29463	−0.647313	+	0.762225i	$0.724107\pi$
$492$	−0.877550	−0.0395630
$493$	1.90140	0.0856349
$494$	1.92707	0.0867028
$495$	−1.36396	−0.0613054
$496$	−3.56795	−0.160206
$497$	4.78842	0.214790
$498$	15.5905	0.698627
$499$	−4.80092	−0.214919	−0.107459	−	0.994209i	$-0.534272\pi$
$499$	−4.80092	−0.214919	−0.107459	+	0.994209i	$0.534272\pi$
$500$	12.1405	0.542940
$501$	−3.77237	−0.168537
$502$	24.2180	1.08090
$503$	41.6508	1.85712	0.928558	−	0.371187i	$-0.121049\pi$
$503$	41.6508	1.85712	0.928558	+	0.371187i	$0.121049\pi$
$504$	−2.02962	−0.0904064
$505$	10.3218	0.459314
$506$	2.48442	0.110446
$507$	1.00000	0.0444116
$508$	1.65344	0.0733595
$509$	23.4251	1.03830	0.519151	−	0.854683i	$-0.326248\pi$
$509$	23.4251	1.03830	0.519151	+	0.854683i	$0.326248\pi$
$510$	−0.461159	−0.0204205
$511$	8.37613	0.370538
$512$	1.00000	0.0441942
$513$	−1.92707	−0.0850820
$514$	30.4142	1.34151
$515$	1.74985	0.0771077
$516$	−8.40643	−0.370072
$517$	−4.93352	−0.216976
$518$	2.43136	0.106828
$519$	−20.0657	−0.880786
$520$	1.74985	0.0767361
$521$	20.8136	0.911861	0.455931	−	0.890015i	$-0.349307\pi$
$521$	20.8136	0.911861	0.455931	+	0.890015i	$0.349307\pi$
$522$	7.21481	0.315784
$523$	1.79791	0.0786172	0.0393086	−	0.999227i	$-0.487484\pi$
$523$	1.79791	0.0786172	0.0393086	+	0.999227i	$0.487484\pi$
$524$	−0.394299	−0.0172250
$525$	3.93344	0.171669
$526$	−2.28933	−0.0998196
$527$	−0.940304	−0.0409603
$528$	0.779471	0.0339221
$529$	−12.8410	−0.558306
$530$	2.65265	0.115224
$531$	2.19411	0.0952164
$532$	3.91121	0.169572
$533$	0.877550	0.0380109
$534$	−8.32385	−0.360208
$535$	16.6401	0.719414
$536$	−5.24292	−0.226460
$537$	−16.8786	−0.728365
$538$	−10.9247	−0.470998
$539$	−2.24538	−0.0967154
$540$	−1.74985	−0.0753016
$541$	16.2010	0.696536	0.348268	−	0.937395i	$-0.386770\pi$
$541$	16.2010	0.696536	0.348268	+	0.937395i	$0.386770\pi$
$542$	−13.4837	−0.579175
$543$	17.7642	0.762333
$544$	0.263542	0.0112993
$545$	12.6572	0.542177
$546$	2.02962	0.0868597
$547$	−3.63169	−0.155280	−0.0776399	−	0.996981i	$-0.524738\pi$
$547$	−3.63169	−0.155280	−0.0776399	+	0.996981i	$0.524738\pi$
$548$	−21.2164	−0.906322
$549$	−1.90493	−0.0813003
$550$	−1.51063	−0.0644134
$551$	−13.9034	−0.592305
$552$	3.18731	0.135661
$553$	−2.94393	−0.125188
$554$	9.60543	0.408096
$555$	2.09622	0.0889796
$556$	3.29987	0.139945
$557$	2.61912	0.110976	0.0554878	−	0.998459i	$-0.482329\pi$
$557$	2.61912	0.110976	0.0554878	+	0.998459i	$0.482329\pi$
$558$	−3.56795	−0.151044
$559$	8.40643	0.355554
$560$	3.55153	0.150080
$561$	0.205423	0.00867297
$562$	9.27069	0.391061
$563$	−10.6238	−0.447739	−0.223870	−	0.974619i	$-0.571869\pi$
$563$	−10.6238	−0.447739	−0.223870	+	0.974619i	$0.571869\pi$
$564$	−6.32932	−0.266513
$565$	3.64452	0.153326
$566$	28.8002	1.21056
$567$	−2.02962	−0.0852360
$568$	−2.35927	−0.0989927
$569$	−18.7159	−0.784610	−0.392305	−	0.919835i	$-0.628322\pi$
$569$	−18.7159	−0.784610	−0.392305	+	0.919835i	$0.628322\pi$
$570$	3.37208	0.141241
$571$	16.3878	0.685809	0.342905	−	0.939370i	$-0.388589\pi$
$571$	16.3878	0.685809	0.342905	+	0.939370i	$0.388589\pi$
$572$	−0.779471	−0.0325913
$573$	−9.31466	−0.389126
$574$	1.78109	0.0743413
$575$	−6.17707	−0.257602
$576$	1.00000	0.0416667
$577$	32.5993	1.35713	0.678563	−	0.734542i	$-0.262603\pi$
$577$	32.5993	1.35713	0.678563	+	0.734542i	$0.262603\pi$
$578$	−16.9305	−0.704218
$579$	5.65689	0.235092
$580$	−12.6249	−0.524218
$581$	−31.6428	−1.31276
$582$	5.22522	0.216592
$583$	−1.18162	−0.0489378
$584$	−4.12695	−0.170774
$585$	1.74985	0.0723475
$586$	−31.4445	−1.29896
$587$	−5.65824	−0.233540	−0.116770	−	0.993159i	$-0.537254\pi$
$587$	−5.65824	−0.233540	−0.116770	+	0.993159i	$0.537254\pi$
$588$	−2.88065	−0.118796
$589$	6.87568	0.283308
$590$	−3.83937	−0.158064
$591$	18.3383	0.754338
$592$	−1.19794	−0.0492351
$593$	16.6793	0.684937	0.342468	−	0.939529i	$-0.388737\pi$
$593$	16.6793	0.684937	0.342468	+	0.939529i	$0.388737\pi$
$594$	0.779471	0.0319821
$595$	0.935977	0.0383713
$596$	−18.1059	−0.741645
$597$	−13.6687	−0.559423
$598$	−3.18731	−0.130339
$599$	45.2656	1.84950	0.924751	−	0.380573i	$-0.124273\pi$
$599$	45.2656	1.84950	0.924751	+	0.380573i	$0.124273\pi$
$600$	−1.93802	−0.0791193
$601$	30.4841	1.24347	0.621735	−	0.783227i	$-0.286428\pi$
$601$	30.4841	1.24347	0.621735	+	0.783227i	$0.286428\pi$
$602$	17.0618	0.695389
$603$	−5.24292	−0.213508
$604$	1.07701	0.0438229
$605$	18.1852	0.739334
$606$	−5.89867	−0.239617
$607$	9.29213	0.377156	0.188578	−	0.982058i	$-0.439612\pi$
$607$	9.29213	0.377156	0.188578	+	0.982058i	$0.439612\pi$
$608$	−1.92707	−0.0781528
$609$	−14.6433	−0.593377
$610$	3.33334	0.134963
$611$	6.32932	0.256057
$612$	0.263542	0.0106530
$613$	31.3178	1.26491	0.632456	−	0.774596i	$-0.282047\pi$
$613$	31.3178	1.26491	0.632456	+	0.774596i	$0.282047\pi$
$614$	−14.2698	−0.575882
$615$	1.53558	0.0619206
$616$	−1.58203	−0.0637417
$617$	−27.8619	−1.12168	−0.560840	−	0.827924i	$-0.689522\pi$
$617$	−27.8619	−1.12168	−0.560840	+	0.827924i	$0.689522\pi$
$618$	−1.00000	−0.0402259
$619$	18.8951	0.759459	0.379729	−	0.925098i	$-0.376017\pi$
$619$	18.8951	0.759459	0.379729	+	0.925098i	$0.376017\pi$
$620$	6.24339	0.250741
$621$	3.18731	0.127903
$622$	−3.46080	−0.138766
$623$	16.8943	0.676854
$624$	−1.00000	−0.0400320
$625$	−11.5540	−0.462160
$626$	26.6877	1.06665
$627$	−1.50209	−0.0599877
$628$	1.77321	0.0707586
$629$	−0.315707	−0.0125881
$630$	3.55153	0.141496
$631$	−5.40195	−0.215048	−0.107524	−	0.994202i	$-0.534292\pi$
$631$	−5.40195	−0.215048	−0.107524	+	0.994202i	$0.534292\pi$
$632$	1.45048	0.0576971
$633$	20.5331	0.816119
$634$	19.5559	0.776664
$635$	−2.89327	−0.114816
$636$	−1.51593	−0.0601105
$637$	2.88065	0.114135
$638$	5.62373	0.222646
$639$	−2.35927	−0.0933312
$640$	−1.74985	−0.0691690
$641$	−5.10962	−0.201818	−0.100909	−	0.994896i	$-0.532175\pi$
$641$	−5.10962	−0.201818	−0.100909	+	0.994896i	$0.532175\pi$
$642$	−9.50943	−0.375307
$643$	8.19707	0.323261	0.161630	−	0.986851i	$-0.448325\pi$
$643$	8.19707	0.323261	0.161630	+	0.986851i	$0.448325\pi$
$644$	−6.46903	−0.254916
$645$	14.7100	0.579206
$646$	−0.507862	−0.0199816
$647$	2.23503	0.0878682	0.0439341	−	0.999034i	$-0.486011\pi$
$647$	2.23503	0.0878682	0.0439341	+	0.999034i	$0.486011\pi$
$648$	1.00000	0.0392837
$649$	1.71025	0.0671330
$650$	1.93802	0.0760154
$651$	7.24159	0.283820
$652$	−12.9529	−0.507273
$653$	−2.95987	−0.115829	−0.0579143	−	0.998322i	$-0.518445\pi$
$653$	−2.95987	−0.115829	−0.0579143	+	0.998322i	$0.518445\pi$
$654$	−7.23333	−0.282845
$655$	0.689964	0.0269591
$656$	−0.877550	−0.0342626
$657$	−4.12695	−0.161008
$658$	12.8461	0.500794
$659$	8.70192	0.338979	0.169489	−	0.985532i	$-0.445788\pi$
$659$	8.70192	0.338979	0.169489	+	0.985532i	$0.445788\pi$
$660$	−1.36396	−0.0530920
$661$	22.1043	0.859757	0.429879	−	0.902887i	$-0.358556\pi$
$661$	22.1043	0.859757	0.429879	+	0.902887i	$0.358556\pi$
$662$	−35.3758	−1.37492
$663$	−0.263542	−0.0102351
$664$	15.5905	0.605028
$665$	−6.84404	−0.265400
$666$	−1.19794	−0.0464193
$667$	22.9959	0.890404
$668$	−3.77237	−0.145957
$669$	−9.24309	−0.357359
$670$	9.17433	0.354435
$671$	−1.48483	−0.0573214
$672$	−2.02962	−0.0782943
$673$	−43.9137	−1.69275	−0.846375	−	0.532588i	$-0.821220\pi$
$673$	−43.9137	−1.69275	−0.846375	+	0.532588i	$0.821220\pi$
$674$	−12.1028	−0.466184
$675$	−1.93802	−0.0745944
$676$	1.00000	0.0384615
$677$	42.4496	1.63147	0.815736	−	0.578424i	$-0.196332\pi$
$677$	42.4496	1.63147	0.815736	+	0.578424i	$0.196332\pi$
$678$	−2.08276	−0.0799878
$679$	−10.6052	−0.406990
$680$	−0.461159	−0.0176846
$681$	−18.7660	−0.719115
$682$	−2.78112	−0.106494
$683$	−41.3373	−1.58173	−0.790865	−	0.611991i	$-0.790369\pi$
$683$	−41.3373	−1.58173	−0.790865	+	0.611991i	$0.790369\pi$
$684$	−1.92707	−0.0736832
$685$	37.1256	1.41850
$686$	20.0539	0.765663
$687$	−21.6151	−0.824668
$688$	−8.40643	−0.320492
$689$	1.51593	0.0577523
$690$	−5.57733	−0.212325
$691$	−6.67606	−0.253969	−0.126985	−	0.991905i	$-0.540530\pi$
$691$	−6.67606	−0.253969	−0.126985	+	0.991905i	$0.540530\pi$
$692$	−20.0657	−0.762783
$693$	−1.58203	−0.0600963
$694$	−3.81699	−0.144891
$695$	−5.77428	−0.219031
$696$	7.21481	0.273477
$697$	−0.231271	−0.00876001
$698$	1.74938	0.0662149
$699$	−22.3608	−0.845764
$700$	3.93344	0.148670
$701$	−25.4403	−0.960865	−0.480433	−	0.877032i	$-0.659520\pi$
$701$	−25.4403	−0.960865	−0.480433	+	0.877032i	$0.659520\pi$
$702$	−1.00000	−0.0377426
$703$	2.30851	0.0870672
$704$	0.779471	0.0293774
$705$	11.0754	0.417123
$706$	−24.2812	−0.913834
$707$	11.9721	0.450256
$708$	2.19411	0.0824598
$709$	−18.4841	−0.694184	−0.347092	−	0.937831i	$-0.612831\pi$
$709$	−18.4841	−0.694184	−0.347092	+	0.937831i	$0.612831\pi$
$710$	4.12837	0.154935
$711$	1.45048	0.0543973
$712$	−8.32385	−0.311950
$713$	−11.3722	−0.425892
$714$	−0.534889	−0.0200177
$715$	1.36396	0.0510091
$716$	−16.8786	−0.630783
$717$	−2.12760	−0.0794565
$718$	−15.5093	−0.578801
$719$	20.4761	0.763630	0.381815	−	0.924239i	$-0.375299\pi$
$719$	20.4761	0.763630	0.381815	+	0.924239i	$0.375299\pi$
$720$	−1.74985	−0.0652131
$721$	2.02962	0.0755870
$722$	−15.2864	−0.568902
$723$	12.2326	0.454936
$724$	17.7642	0.660200
$725$	−13.9824	−0.519295
$726$	−10.3924	−0.385699
$727$	−0.276765	−0.0102647	−0.00513233	−	0.999987i	$-0.501634\pi$
$727$	−0.276765	−0.0102647	−0.00513233	+	0.999987i	$0.501634\pi$
$728$	2.02962	0.0752227
$729$	1.00000	0.0370370
$730$	7.22155	0.267281
$731$	−2.21544	−0.0819411
$732$	−1.90493	−0.0704081
$733$	17.4312	0.643837	0.321919	−	0.946767i	$-0.395672\pi$
$733$	17.4312	0.643837	0.321919	+	0.946767i	$0.395672\pi$
$734$	−15.4285	−0.569477
$735$	5.04070	0.185929
$736$	3.18731	0.117486
$737$	−4.08670	−0.150536
$738$	−0.877550	−0.0323031
$739$	−31.1430	−1.14562	−0.572808	−	0.819690i	$-0.694146\pi$
$739$	−31.1430	−1.14562	−0.572808	+	0.819690i	$0.694146\pi$
$740$	2.09622	0.0770586
$741$	1.92707	0.0707925
$742$	3.07676	0.112951
$743$	−25.8587	−0.948662	−0.474331	−	0.880347i	$-0.657310\pi$
$743$	−25.8587	−0.948662	−0.474331	+	0.880347i	$0.657310\pi$
$744$	−3.56795	−0.130808
$745$	31.6826	1.16076
$746$	26.0656	0.954329
$747$	15.5905	0.570426
$748$	0.205423	0.00751101
$749$	19.3005	0.705226
$750$	12.1405	0.443309
$751$	47.3584	1.72813	0.864066	−	0.503378i	$-0.167910\pi$
$751$	47.3584	1.72813	0.864066	+	0.503378i	$0.167910\pi$
$752$	−6.32932	−0.230807
$753$	24.2180	0.882554
$754$	−7.21481	−0.262748
$755$	−1.88461	−0.0685879
$756$	−2.02962	−0.0738165
$757$	26.0930	0.948367	0.474183	−	0.880426i	$-0.342743\pi$
$757$	26.0930	0.948367	0.474183	+	0.880426i	$0.342743\pi$
$758$	26.1847	0.951070
$759$	2.48442	0.0901787
$760$	3.37208	0.122318
$761$	11.0905	0.402029	0.201015	−	0.979588i	$-0.435576\pi$
$761$	11.0905	0.402029	0.201015	+	0.979588i	$0.435576\pi$
$762$	1.65344	0.0598978
$763$	14.6809	0.531484
$764$	−9.31466	−0.336993
$765$	−0.461159	−0.0166732
$766$	18.6214	0.672818
$767$	−2.19411	−0.0792248
$768$	1.00000	0.0360844
$769$	27.2959	0.984316	0.492158	−	0.870506i	$-0.336208\pi$
$769$	27.2959	0.984316	0.492158	+	0.870506i	$0.336208\pi$
$770$	2.76832	0.0997632
$771$	30.4142	1.09534
$772$	5.65689	0.203596
$773$	−29.1005	−1.04667	−0.523336	−	0.852126i	$-0.675313\pi$
$773$	−29.1005	−1.04667	−0.523336	+	0.852126i	$0.675313\pi$
$774$	−8.40643	−0.302163
$775$	6.91476	0.248386
$776$	5.22522	0.187574
$777$	2.43136	0.0872247
$778$	22.7756	0.816545
$779$	1.69110	0.0605898
$780$	1.74985	0.0626547
$781$	−1.83898	−0.0658039
$782$	0.839990	0.0300380
$783$	7.21481	0.257836
$784$	−2.88065	−0.102880
$785$	−3.10285	−0.110745
$786$	−0.394299	−0.0140642
$787$	32.7100	1.16599	0.582993	−	0.812477i	$-0.301882\pi$
$787$	32.7100	1.16599	0.582993	+	0.812477i	$0.301882\pi$
$788$	18.3383	0.653276
$789$	−2.28933	−0.0815024
$790$	−2.53813	−0.0903026
$791$	4.22721	0.150302
$792$	0.779471	0.0276973
$793$	1.90493	0.0676459
$794$	9.54045	0.338578
$795$	2.65265	0.0940798
$796$	−13.6687	−0.484474
$797$	−36.5294	−1.29394	−0.646968	−	0.762517i	$-0.723963\pi$
$797$	−36.5294	−1.29394	−0.646968	+	0.762517i	$0.723963\pi$
$798$	3.91121	0.138455
$799$	−1.66804	−0.0590110
$800$	−1.93802	−0.0685193
$801$	−8.32385	−0.294109
$802$	−14.4073	−0.508739
$803$	−3.21683	−0.113520
$804$	−5.24292	−0.184903
$805$	11.3198	0.398972
$806$	3.56795	0.125676
$807$	−10.9247	−0.384568
$808$	−5.89867	−0.207515
$809$	19.9144	0.700153	0.350077	−	0.936721i	$-0.386156\pi$
$809$	19.9144	0.700153	0.350077	+	0.936721i	$0.386156\pi$
$810$	−1.74985	−0.0614835
$811$	13.4751	0.473176	0.236588	−	0.971610i	$-0.423971\pi$
$811$	13.4751	0.473176	0.236588	+	0.971610i	$0.423971\pi$
$812$	−14.6433	−0.513880
$813$	−13.4837	−0.472894
$814$	−0.933760	−0.0327283
$815$	22.6656	0.793941
$816$	0.263542	0.00922580
$817$	16.1997	0.566757
$818$	−20.6224	−0.721045
$819$	2.02962	0.0709206
$820$	1.53558	0.0536248
$821$	−0.764423	−0.0266786	−0.0133393	−	0.999911i	$-0.504246\pi$
$821$	−0.764423	−0.0266786	−0.0133393	+	0.999911i	$0.504246\pi$
$822$	−21.2164	−0.740009
$823$	−46.0572	−1.60545	−0.802727	−	0.596346i	$-0.796618\pi$
$823$	−46.0572	−1.60545	−0.802727	+	0.596346i	$0.796618\pi$
$824$	−1.00000	−0.0348367
$825$	−1.51063	−0.0525933
$826$	−4.45321	−0.154947
$827$	27.7940	0.966491	0.483245	−	0.875485i	$-0.339458\pi$
$827$	27.7940	0.966491	0.483245	+	0.875485i	$0.339458\pi$
$828$	3.18731	0.110767
$829$	−26.5172	−0.920980	−0.460490	−	0.887665i	$-0.652326\pi$
$829$	−26.5172	−0.920980	−0.460490	+	0.887665i	$0.652326\pi$
$830$	−27.2810	−0.946939
$831$	9.60543	0.333209
$832$	−1.00000	−0.0346688
$833$	−0.759170	−0.0263037
$834$	3.29987	0.114265
$835$	6.60109	0.228440
$836$	−1.50209	−0.0519509
$837$	−3.56795	−0.123327
$838$	−31.0737	−1.07342
$839$	1.27873	0.0441468	0.0220734	−	0.999756i	$-0.492973\pi$
$839$	1.27873	0.0441468	0.0220734	+	0.999756i	$0.492973\pi$
$840$	3.55153	0.122540
$841$	23.0535	0.794949
$842$	−24.8955	−0.857957
$843$	9.27069	0.319300
$844$	20.5331	0.706779
$845$	−1.74985	−0.0601967
$846$	−6.32932	−0.217607
$847$	21.0927	0.724753
$848$	−1.51593	−0.0520572
$849$	28.8002	0.988420
$850$	−0.510749	−0.0175185
$851$	−3.81822	−0.130887
$852$	−2.35927	−0.0808272
$853$	5.04218	0.172641	0.0863205	−	0.996267i	$-0.472489\pi$
$853$	5.04218	0.172641	0.0863205	+	0.996267i	$0.472489\pi$
$854$	3.86627	0.132301
$855$	3.37208	0.115323
$856$	−9.50943	−0.325026
$857$	−30.9090	−1.05583	−0.527915	−	0.849297i	$-0.677026\pi$
$857$	−30.9090	−1.05583	−0.527915	+	0.849297i	$0.677026\pi$
$858$	−0.779471	−0.0266107
$859$	0.725677	0.0247598	0.0123799	−	0.999923i	$-0.496059\pi$
$859$	0.725677	0.0247598	0.0123799	+	0.999923i	$0.496059\pi$
$860$	14.7100	0.501607
$861$	1.78109	0.0606994
$862$	−5.09020	−0.173373
$863$	33.6854	1.14667	0.573333	−	0.819323i	$-0.305650\pi$
$863$	33.6854	1.14667	0.573333	+	0.819323i	$0.305650\pi$
$864$	1.00000	0.0340207
$865$	35.1120	1.19384
$866$	39.6738	1.34817
$867$	−16.9305	−0.574991
$868$	7.24159	0.245795
$869$	1.13061	0.0383533
$870$	−12.6249	−0.428023
$871$	5.24292	0.177649
$872$	−7.23333	−0.244951
$873$	5.22522	0.176847
$874$	−6.14216	−0.207762
$875$	−24.6406	−0.833004
$876$	−4.12695	−0.139437
$877$	22.2780	0.752276	0.376138	−	0.926564i	$-0.377252\pi$
$877$	22.2780	0.752276	0.376138	+	0.926564i	$0.377252\pi$
$878$	36.0195	1.21560
$879$	−31.4445	−1.06060
$880$	−1.36396	−0.0459790
$881$	42.4758	1.43105	0.715524	−	0.698588i	$-0.246188\pi$
$881$	42.4758	1.43105	0.715524	+	0.698588i	$0.246188\pi$
$882$	−2.88065	−0.0969964
$883$	−55.2786	−1.86027	−0.930136	−	0.367214i	$-0.880312\pi$
$883$	−55.2786	−1.86027	−0.930136	+	0.367214i	$0.880312\pi$
$884$	−0.263542	−0.00886386
$885$	−3.83937	−0.129059
$886$	26.6207	0.894338
$887$	16.2134	0.544394	0.272197	−	0.962241i	$-0.412250\pi$
$887$	16.2134	0.544394	0.272197	+	0.962241i	$0.412250\pi$
$888$	−1.19794	−0.0402003
$889$	−3.35585	−0.112552
$890$	14.5655	0.488237
$891$	0.779471	0.0261133
$892$	−9.24309	−0.309482
$893$	12.1970	0.408158
$894$	−18.1059	−0.605551
$895$	29.5350	0.987247
$896$	−2.02962	−0.0678048
$897$	−3.18731	−0.106421
$898$	−26.7816	−0.893712
$899$	−25.7421	−0.858548
$900$	−1.93802	−0.0646006
$901$	−0.399510	−0.0133096
$902$	−0.684024	−0.0227755
$903$	17.0618	0.567783
$904$	−2.08276	−0.0692715
$905$	−31.0846	−1.03329
$906$	1.07701	0.0357812
$907$	40.9450	1.35956	0.679779	−	0.733417i	$-0.262076\pi$
$907$	40.9450	1.35956	0.679779	+	0.733417i	$0.262076\pi$
$908$	−18.7660	−0.622772
$909$	−5.89867	−0.195647
$910$	−3.55153	−0.117732
$911$	12.0792	0.400203	0.200101	−	0.979775i	$-0.435873\pi$
$911$	12.0792	0.400203	0.200101	+	0.979775i	$0.435873\pi$
$912$	−1.92707	−0.0638115
$913$	12.1523	0.402183
$914$	−26.0792	−0.862625
$915$	3.33334	0.110197
$916$	−21.6151	−0.714184
$917$	0.800276	0.0264274
$918$	0.263542	0.00869817
$919$	4.54816	0.150030	0.0750149	−	0.997182i	$-0.476100\pi$
$919$	4.54816	0.150030	0.0750149	+	0.997182i	$0.476100\pi$
$920$	−5.57733	−0.183879
$921$	−14.2698	−0.470206
$922$	−4.81621	−0.158613
$923$	2.35927	0.0776563
$924$	−1.58203	−0.0520449
$925$	2.32163	0.0763348
$926$	23.3175	0.766261
$927$	−1.00000	−0.0328443
$928$	7.21481	0.236838
$929$	13.7348	0.450623	0.225311	−	0.974287i	$-0.427660\pi$
$929$	13.7348	0.450623	0.225311	+	0.974287i	$0.427660\pi$
$930$	6.24339	0.204729
$931$	5.55120	0.181933
$932$	−22.3608	−0.732453
$933$	−3.46080	−0.113302
$934$	9.57439	0.313284
$935$	−0.359460	−0.0117556
$936$	−1.00000	−0.0326860
$937$	−37.4058	−1.22199	−0.610997	−	0.791633i	$-0.709231\pi$
$937$	−37.4058	−1.22199	−0.610997	+	0.791633i	$0.709231\pi$
$938$	10.6411	0.347445
$939$	26.6877	0.870920
$940$	11.0754	0.361239
$941$	32.3295	1.05391	0.526955	−	0.849893i	$-0.323334\pi$
$941$	32.3295	1.05391	0.526955	+	0.849893i	$0.323334\pi$
$942$	1.77321	0.0577742
$943$	−2.79703	−0.0910837
$944$	2.19411	0.0714123
$945$	3.55153	0.115531
$946$	−6.55256	−0.213042
$947$	48.6984	1.58248	0.791242	−	0.611503i	$-0.209435\pi$
$947$	48.6984	1.58248	0.791242	+	0.611503i	$0.209435\pi$
$948$	1.45048	0.0471095
$949$	4.12695	0.133966
$950$	3.73469	0.121169
$951$	19.5559	0.634144
$952$	−0.534889	−0.0173359
$953$	47.7121	1.54555	0.772774	−	0.634681i	$-0.218869\pi$
$953$	47.7121	1.54555	0.772774	+	0.634681i	$0.218869\pi$
$954$	−1.51593	−0.0490800
$955$	16.2993	0.527432
$956$	−2.12760	−0.0688114
$957$	5.62373	0.181790
$958$	20.7678	0.670977
$959$	43.0613	1.39052
$960$	−1.74985	−0.0564762
$961$	−18.2697	−0.589345
$962$	1.19794	0.0386232
$963$	−9.50943	−0.306437
$964$	12.2326	0.393986
$965$	−9.89871	−0.318651
$966$	−6.46903	−0.208138
$967$	−31.3385	−1.00778	−0.503889	−	0.863768i	$-0.668098\pi$
$967$	−31.3385	−1.00778	−0.503889	+	0.863768i	$0.668098\pi$
$968$	−10.3924	−0.334025
$969$	−0.507862	−0.0163149
$970$	−9.14336	−0.293576
$971$	−23.7554	−0.762346	−0.381173	−	0.924504i	$-0.624480\pi$
$971$	−23.7554	−0.762346	−0.381173	+	0.924504i	$0.624480\pi$
$972$	1.00000	0.0320750
$973$	−6.69747	−0.214711
$974$	−10.5599	−0.338359
$975$	1.93802	0.0620663
$976$	−1.90493	−0.0609752
$977$	−32.1319	−1.02799	−0.513994	−	0.857793i	$-0.671835\pi$
$977$	−32.1319	−1.02799	−0.513994	+	0.857793i	$0.671835\pi$
$978$	−12.9529	−0.414187
$979$	−6.48820	−0.207364
$980$	5.04070	0.161019
$981$	−7.23333	−0.230942
$982$	−28.6870	−0.915438
$983$	−31.7186	−1.01167	−0.505833	−	0.862631i	$-0.668815\pi$
$983$	−31.7186	−1.01167	−0.505833	+	0.862631i	$0.668815\pi$
$984$	−0.877550	−0.0279753
$985$	−32.0893	−1.02245
$986$	1.90140	0.0605530
$987$	12.8461	0.408896
$988$	1.92707	0.0613081
$989$	−26.7939	−0.851997
$990$	−1.36396	−0.0433494
$991$	−28.6616	−0.910464	−0.455232	−	0.890373i	$-0.650444\pi$
$991$	−28.6616	−0.910464	−0.455232	+	0.890373i	$0.650444\pi$
$992$	−3.56795	−0.113283
$993$	−35.3758	−1.12262
$994$	4.78842	0.151879
$995$	23.9182	0.758258
$996$	15.5905	0.494004
$997$	−25.4054	−0.804596	−0.402298	−	0.915509i	$-0.631788\pi$
$997$	−25.4054	−0.804596	−0.402298	+	0.915509i	$0.631788\pi$
$998$	−4.80092	−0.151970
$999$	−1.19794	−0.0379012

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.q.1.3	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.q.1.3	✓	8	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.74985 q^{5} +1.00000 q^{6} -2.02962 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.74985 q^{5} +1.00000 q^{6} -2.02962 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.74985 q^{10} +0.779471 q^{11} +1.00000 q^{12} -1.00000 q^{13} -2.02962 q^{14} -1.74985 q^{15} +1.00000 q^{16} +0.263542 q^{17} +1.00000 q^{18} -1.92707 q^{19} -1.74985 q^{20} -2.02962 q^{21} +0.779471 q^{22} +3.18731 q^{23} +1.00000 q^{24} -1.93802 q^{25} -1.00000 q^{26} +1.00000 q^{27} -2.02962 q^{28} +7.21481 q^{29} -1.74985 q^{30} -3.56795 q^{31} +1.00000 q^{32} +0.779471 q^{33} +0.263542 q^{34} +3.55153 q^{35} +1.00000 q^{36} -1.19794 q^{37} -1.92707 q^{38} -1.00000 q^{39} -1.74985 q^{40} -0.877550 q^{41} -2.02962 q^{42} -8.40643 q^{43} +0.779471 q^{44} -1.74985 q^{45} +3.18731 q^{46} -6.32932 q^{47} +1.00000 q^{48} -2.88065 q^{49} -1.93802 q^{50} +0.263542 q^{51} -1.00000 q^{52} -1.51593 q^{53} +1.00000 q^{54} -1.36396 q^{55} -2.02962 q^{56} -1.92707 q^{57} +7.21481 q^{58} +2.19411 q^{59} -1.74985 q^{60} -1.90493 q^{61} -3.56795 q^{62} -2.02962 q^{63} +1.00000 q^{64} +1.74985 q^{65} +0.779471 q^{66} -5.24292 q^{67} +0.263542 q^{68} +3.18731 q^{69} +3.55153 q^{70} -2.35927 q^{71} +1.00000 q^{72} -4.12695 q^{73} -1.19794 q^{74} -1.93802 q^{75} -1.92707 q^{76} -1.58203 q^{77} -1.00000 q^{78} +1.45048 q^{79} -1.74985 q^{80} +1.00000 q^{81} -0.877550 q^{82} +15.5905 q^{83} -2.02962 q^{84} -0.461159 q^{85} -8.40643 q^{86} +7.21481 q^{87} +0.779471 q^{88} -8.32385 q^{89} -1.74985 q^{90} +2.02962 q^{91} +3.18731 q^{92} -3.56795 q^{93} -6.32932 q^{94} +3.37208 q^{95} +1.00000 q^{96} +5.22522 q^{97} -2.88065 q^{98} +0.779471 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 6 q^{5} + 8 q^{6} - 3 q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 6 * q^5 + 8 * q^6 - 3 * q^7 + 8 * q^8 + 8 * q^9	\( 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 6 q^{5} + 8 q^{6} - 3 q^{7} + 8 q^{8} + 8 q^{9} - 6 q^{10} - 15 q^{11} + 8 q^{12} - 8 q^{13} - 3 q^{14} - 6 q^{15} + 8 q^{16} - 11 q^{17} + 8 q^{18} - 15 q^{19} - 6 q^{20} - 3 q^{21} - 15 q^{22} + q^{23} + 8 q^{24} - 10 q^{25} - 8 q^{26} + 8 q^{27} - 3 q^{28} - 10 q^{29} - 6 q^{30} - 3 q^{31} + 8 q^{32} - 15 q^{33} - 11 q^{34} - 12 q^{35} + 8 q^{36} - 26 q^{37} - 15 q^{38} - 8 q^{39} - 6 q^{40} - 12 q^{41} - 3 q^{42} - 4 q^{43} - 15 q^{44} - 6 q^{45} + q^{46} - 6 q^{47} + 8 q^{48} - 5 q^{49} - 10 q^{50} - 11 q^{51} - 8 q^{52} - 4 q^{53} + 8 q^{54} - 3 q^{56} - 15 q^{57} - 10 q^{58} - 19 q^{59} - 6 q^{60} - 14 q^{61} - 3 q^{62} - 3 q^{63} + 8 q^{64} + 6 q^{65} - 15 q^{66} - 13 q^{67} - 11 q^{68} + q^{69} - 12 q^{70} - 31 q^{71} + 8 q^{72} - 27 q^{73} - 26 q^{74} - 10 q^{75} - 15 q^{76} - 30 q^{77} - 8 q^{78} - 13 q^{79} - 6 q^{80} + 8 q^{81} - 12 q^{82} - 28 q^{83} - 3 q^{84} + 15 q^{85} - 4 q^{86} - 10 q^{87} - 15 q^{88} - 2 q^{89} - 6 q^{90} + 3 q^{91} + q^{92} - 3 q^{93} - 6 q^{94} - 18 q^{95} + 8 q^{96} - 30 q^{97} - 5 q^{98} - 15 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 6 * q^5 + 8 * q^6 - 3 * q^7 + 8 * q^8 + 8 * q^9 - 6 * q^10 - 15 * q^11 + 8 * q^12 - 8 * q^13 - 3 * q^14 - 6 * q^15 + 8 * q^16 - 11 * q^17 + 8 * q^18 - 15 * q^19 - 6 * q^20 - 3 * q^21 - 15 * q^22 + q^23 + 8 * q^24 - 10 * q^25 - 8 * q^26 + 8 * q^27 - 3 * q^28 - 10 * q^29 - 6 * q^30 - 3 * q^31 + 8 * q^32 - 15 * q^33 - 11 * q^34 - 12 * q^35 + 8 * q^36 - 26 * q^37 - 15 * q^38 - 8 * q^39 - 6 * q^40 - 12 * q^41 - 3 * q^42 - 4 * q^43 - 15 * q^44 - 6 * q^45 + q^46 - 6 * q^47 + 8 * q^48 - 5 * q^49 - 10 * q^50 - 11 * q^51 - 8 * q^52 - 4 * q^53 + 8 * q^54 - 3 * q^56 - 15 * q^57 - 10 * q^58 - 19 * q^59 - 6 * q^60 - 14 * q^61 - 3 * q^62 - 3 * q^63 + 8 * q^64 + 6 * q^65 - 15 * q^66 - 13 * q^67 - 11 * q^68 + q^69 - 12 * q^70 - 31 * q^71 + 8 * q^72 - 27 * q^73 - 26 * q^74 - 10 * q^75 - 15 * q^76 - 30 * q^77 - 8 * q^78 - 13 * q^79 - 6 * q^80 + 8 * q^81 - 12 * q^82 - 28 * q^83 - 3 * q^84 + 15 * q^85 - 4 * q^86 - 10 * q^87 - 15 * q^88 - 2 * q^89 - 6 * q^90 + 3 * q^91 + q^92 - 3 * q^93 - 6 * q^94 - 18 * q^95 + 8 * q^96 - 30 * q^97 - 5 * q^98 - 15 * q^99

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