LMFDB - Embedded newform 8034.2.a.w.1.10

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:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} - 8 x^{10} + 94 x^{9} - 7 x^{8} - 580 x^{7} + 180 x^{6} + 1787 x^{5} - 308 x^{4} + \cdots + 768 $ x^12 - 6x^11 - 8x^10 + 94x^9 - 7x^8 - 580x^7 + 180x^6 + 1787x^5 - 308x^4 - 2790x^3 - 352x^2 + 1768*x + 768
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$-2.20360$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.09722 q^{5} -1.00000 q^{6} -0.0373018 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.09722 q^{5} -1.00000 q^{6} -0.0373018 q^{7} -1.00000 q^{8} +1.00000 q^{9} -2.09722 q^{10} -3.17762 q^{11} +1.00000 q^{12} +1.00000 q^{13} +0.0373018 q^{14} +2.09722 q^{15} +1.00000 q^{16} -2.38289 q^{17} -1.00000 q^{18} +2.91209 q^{19} +2.09722 q^{20} -0.0373018 q^{21} +3.17762 q^{22} +3.99261 q^{23} -1.00000 q^{24} -0.601670 q^{25} -1.00000 q^{26} +1.00000 q^{27} -0.0373018 q^{28} -2.46598 q^{29} -2.09722 q^{30} +0.760072 q^{31} -1.00000 q^{32} -3.17762 q^{33} +2.38289 q^{34} -0.0782300 q^{35} +1.00000 q^{36} -8.84213 q^{37} -2.91209 q^{38} +1.00000 q^{39} -2.09722 q^{40} -9.70721 q^{41} +0.0373018 q^{42} -10.8256 q^{43} -3.17762 q^{44} +2.09722 q^{45} -3.99261 q^{46} -5.29982 q^{47} +1.00000 q^{48} -6.99861 q^{49} +0.601670 q^{50} -2.38289 q^{51} +1.00000 q^{52} -10.7397 q^{53} -1.00000 q^{54} -6.66417 q^{55} +0.0373018 q^{56} +2.91209 q^{57} +2.46598 q^{58} +4.58591 q^{59} +2.09722 q^{60} -1.68161 q^{61} -0.760072 q^{62} -0.0373018 q^{63} +1.00000 q^{64} +2.09722 q^{65} +3.17762 q^{66} +7.20145 q^{67} -2.38289 q^{68} +3.99261 q^{69} +0.0782300 q^{70} -14.3856 q^{71} -1.00000 q^{72} +15.2846 q^{73} +8.84213 q^{74} -0.601670 q^{75} +2.91209 q^{76} +0.118531 q^{77} -1.00000 q^{78} +6.39400 q^{79} +2.09722 q^{80} +1.00000 q^{81} +9.70721 q^{82} -5.88671 q^{83} -0.0373018 q^{84} -4.99743 q^{85} +10.8256 q^{86} -2.46598 q^{87} +3.17762 q^{88} +2.63980 q^{89} -2.09722 q^{90} -0.0373018 q^{91} +3.99261 q^{92} +0.760072 q^{93} +5.29982 q^{94} +6.10728 q^{95} -1.00000 q^{96} -2.73678 q^{97} +6.99861 q^{98} -3.17762 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{2} + 12 q^{3} + 12 q^{4} - 4 q^{5} - 12 q^{6} - 12 q^{8} + 12 q^{9}+O(q^{10}) $ 12 * q - 12 * q^2 + 12 * q^3 + 12 * q^4 - 4 * q^5 - 12 * q^6 - 12 * q^8 + 12 * q^9	\( 12 q - 12 q^{2} + 12 q^{3} + 12 q^{4} - 4 q^{5} - 12 q^{6} - 12 q^{8} + 12 q^{9} + 4 q^{10} - 9 q^{11} + 12 q^{12} + 12 q^{13} - 4 q^{15} + 12 q^{16} - 20 q^{17} - 12 q^{18} + 4 q^{19} - 4 q^{20} + 9 q^{22} - 30 q^{23} - 12 q^{24} + 14 q^{25} - 12 q^{26} + 12 q^{27} - 29 q^{29} + 4 q^{30} + 6 q^{31} - 12 q^{32} - 9 q^{33} + 20 q^{34} - 22 q^{35} + 12 q^{36} + 7 q^{37} - 4 q^{38} + 12 q^{39} + 4 q^{40} - 8 q^{41} - 8 q^{43} - 9 q^{44} - 4 q^{45} + 30 q^{46} - 16 q^{47} + 12 q^{48} + 10 q^{49} - 14 q^{50} - 20 q^{51} + 12 q^{52} - 9 q^{53} - 12 q^{54} - 20 q^{55} + 4 q^{57} + 29 q^{58} - 29 q^{59} - 4 q^{60} - 26 q^{61} - 6 q^{62} + 12 q^{64} - 4 q^{65} + 9 q^{66} + 12 q^{67} - 20 q^{68} - 30 q^{69} + 22 q^{70} - 35 q^{71} - 12 q^{72} + 18 q^{73} - 7 q^{74} + 14 q^{75} + 4 q^{76} - 25 q^{77} - 12 q^{78} - 37 q^{79} - 4 q^{80} + 12 q^{81} + 8 q^{82} - 24 q^{83} - 17 q^{85} + 8 q^{86} - 29 q^{87} + 9 q^{88} + 15 q^{89} + 4 q^{90} - 30 q^{92} + 6 q^{93} + 16 q^{94} - 54 q^{95} - 12 q^{96} - 11 q^{97} - 10 q^{98} - 9 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 + 12 * q^3 + 12 * q^4 - 4 * q^5 - 12 * q^6 - 12 * q^8 + 12 * q^9 + 4 * q^10 - 9 * q^11 + 12 * q^12 + 12 * q^13 - 4 * q^15 + 12 * q^16 - 20 * q^17 - 12 * q^18 + 4 * q^19 - 4 * q^20 + 9 * q^22 - 30 * q^23 - 12 * q^24 + 14 * q^25 - 12 * q^26 + 12 * q^27 - 29 * q^29 + 4 * q^30 + 6 * q^31 - 12 * q^32 - 9 * q^33 + 20 * q^34 - 22 * q^35 + 12 * q^36 + 7 * q^37 - 4 * q^38 + 12 * q^39 + 4 * q^40 - 8 * q^41 - 8 * q^43 - 9 * q^44 - 4 * q^45 + 30 * q^46 - 16 * q^47 + 12 * q^48 + 10 * q^49 - 14 * q^50 - 20 * q^51 + 12 * q^52 - 9 * q^53 - 12 * q^54 - 20 * q^55 + 4 * q^57 + 29 * q^58 - 29 * q^59 - 4 * q^60 - 26 * q^61 - 6 * q^62 + 12 * q^64 - 4 * q^65 + 9 * q^66 + 12 * q^67 - 20 * q^68 - 30 * q^69 + 22 * q^70 - 35 * q^71 - 12 * q^72 + 18 * q^73 - 7 * q^74 + 14 * q^75 + 4 * q^76 - 25 * q^77 - 12 * q^78 - 37 * q^79 - 4 * q^80 + 12 * q^81 + 8 * q^82 - 24 * q^83 - 17 * q^85 + 8 * q^86 - 29 * q^87 + 9 * q^88 + 15 * q^89 + 4 * q^90 - 30 * q^92 + 6 * q^93 + 16 * q^94 - 54 * q^95 - 12 * q^96 - 11 * q^97 - 10 * q^98 - 9 * 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
$5$	2.09722	0.937905	0.468953	−	0.883223i	$-0.344632\pi$
$5$	2.09722	0.937905	0.468953	+	0.883223i	$0.344632\pi$
$6$	−1.00000	−0.408248
$7$	−0.0373018	−0.0140987	−0.00704937	−	0.999975i	$-0.502244\pi$
$7$	−0.0373018	−0.0140987	−0.00704937	+	0.999975i	$0.502244\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−2.09722	−0.663199
$11$	−3.17762	−0.958090	−0.479045	−	0.877790i	$-0.659017\pi$
$11$	−3.17762	−0.958090	−0.479045	+	0.877790i	$0.659017\pi$
$12$	1.00000	0.288675
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	0.0373018	0.00996931
$15$	2.09722	0.541500
$16$	1.00000	0.250000
$17$	−2.38289	−0.577935	−0.288967	−	0.957339i	$-0.593312\pi$
$17$	−2.38289	−0.577935	−0.288967	+	0.957339i	$0.593312\pi$
$18$	−1.00000	−0.235702
$19$	2.91209	0.668078	0.334039	−	0.942559i	$-0.391588\pi$
$19$	2.91209	0.668078	0.334039	+	0.942559i	$0.391588\pi$
$20$	2.09722	0.468953
$21$	−0.0373018	−0.00813991
$22$	3.17762	0.677472
$23$	3.99261	0.832518	0.416259	−	0.909246i	$-0.363341\pi$
$23$	3.99261	0.832518	0.416259	+	0.909246i	$0.363341\pi$
$24$	−1.00000	−0.204124
$25$	−0.601670	−0.120334
$26$	−1.00000	−0.196116
$27$	1.00000	0.192450
$28$	−0.0373018	−0.00704937
$29$	−2.46598	−0.457921	−0.228960	−	0.973436i	$-0.573533\pi$
$29$	−2.46598	−0.457921	−0.228960	+	0.973436i	$0.573533\pi$
$30$	−2.09722	−0.382898
$31$	0.760072	0.136513	0.0682564	−	0.997668i	$-0.478256\pi$
$31$	0.760072	0.136513	0.0682564	+	0.997668i	$0.478256\pi$
$32$	−1.00000	−0.176777
$33$	−3.17762	−0.553153
$34$	2.38289	0.408661
$35$	−0.0782300	−0.0132233
$36$	1.00000	0.166667
$37$	−8.84213	−1.45364	−0.726818	−	0.686830i	$-0.759002\pi$
$37$	−8.84213	−1.45364	−0.726818	+	0.686830i	$0.759002\pi$
$38$	−2.91209	−0.472403
$39$	1.00000	0.160128
$40$	−2.09722	−0.331600
$41$	−9.70721	−1.51601	−0.758006	−	0.652248i	$-0.773826\pi$
$41$	−9.70721	−1.51601	−0.758006	+	0.652248i	$0.773826\pi$
$42$	0.0373018	0.00575579
$43$	−10.8256	−1.65089	−0.825447	−	0.564480i	$-0.809077\pi$
$43$	−10.8256	−1.65089	−0.825447	+	0.564480i	$0.809077\pi$
$44$	−3.17762	−0.479045
$45$	2.09722	0.312635
$46$	−3.99261	−0.588679
$47$	−5.29982	−0.773058	−0.386529	−	0.922277i	$-0.626326\pi$
$47$	−5.29982	−0.773058	−0.386529	+	0.922277i	$0.626326\pi$
$48$	1.00000	0.144338
$49$	−6.99861	−0.999801
$50$	0.601670	0.0850890
$51$	−2.38289	−0.333671
$52$	1.00000	0.138675
$53$	−10.7397	−1.47521	−0.737604	−	0.675234i	$-0.764043\pi$
$53$	−10.7397	−1.47521	−0.737604	+	0.675234i	$0.764043\pi$
$54$	−1.00000	−0.136083
$55$	−6.66417	−0.898597
$56$	0.0373018	0.00498466
$57$	2.91209	0.385715
$58$	2.46598	0.323799
$59$	4.58591	0.597034	0.298517	−	0.954404i	$-0.403508\pi$
$59$	4.58591	0.597034	0.298517	+	0.954404i	$0.403508\pi$
$60$	2.09722	0.270750
$61$	−1.68161	−0.215308	−0.107654	−	0.994188i	$-0.534334\pi$
$61$	−1.68161	−0.215308	−0.107654	+	0.994188i	$0.534334\pi$
$62$	−0.760072	−0.0965292
$63$	−0.0373018	−0.00469958
$64$	1.00000	0.125000
$65$	2.09722	0.260128
$66$	3.17762	0.391138
$67$	7.20145	0.879797	0.439899	−	0.898047i	$-0.355014\pi$
$67$	7.20145	0.879797	0.439899	+	0.898047i	$0.355014\pi$
$68$	−2.38289	−0.288967
$69$	3.99261	0.480654
$70$	0.0782300	0.00935027
$71$	−14.3856	−1.70726	−0.853628	−	0.520882i	$-0.825603\pi$
$71$	−14.3856	−1.70726	−0.853628	+	0.520882i	$0.825603\pi$
$72$	−1.00000	−0.117851
$73$	15.2846	1.78893	0.894463	−	0.447141i	$-0.147558\pi$
$73$	15.2846	1.78893	0.894463	+	0.447141i	$0.147558\pi$
$74$	8.84213	1.02788
$75$	−0.601670	−0.0694749
$76$	2.91209	0.334039
$77$	0.118531	0.0135079
$78$	−1.00000	−0.113228
$79$	6.39400	0.719381	0.359691	−	0.933072i	$-0.382882\pi$
$79$	6.39400	0.719381	0.359691	+	0.933072i	$0.382882\pi$
$80$	2.09722	0.234476
$81$	1.00000	0.111111
$82$	9.70721	1.07198
$83$	−5.88671	−0.646151	−0.323075	−	0.946373i	$-0.604717\pi$
$83$	−5.88671	−0.646151	−0.323075	+	0.946373i	$0.604717\pi$
$84$	−0.0373018	−0.00406996
$85$	−4.99743	−0.542048
$86$	10.8256	1.16736
$87$	−2.46598	−0.264381
$88$	3.17762	0.338736
$89$	2.63980	0.279818	0.139909	−	0.990164i	$-0.455319\pi$
$89$	2.63980	0.279818	0.139909	+	0.990164i	$0.455319\pi$
$90$	−2.09722	−0.221066
$91$	−0.0373018	−0.00391029
$92$	3.99261	0.416259
$93$	0.760072	0.0788158
$94$	5.29982	0.546635
$95$	6.10728	0.626594
$96$	−1.00000	−0.102062
$97$	−2.73678	−0.277878	−0.138939	−	0.990301i	$-0.544369\pi$
$97$	−2.73678	−0.277878	−0.138939	+	0.990301i	$0.544369\pi$
$98$	6.99861	0.706966
$99$	−3.17762	−0.319363
$100$	−0.601670	−0.0601670
$101$	17.7613	1.76731	0.883656	−	0.468137i	$-0.155075\pi$
$101$	17.7613	1.76731	0.883656	+	0.468137i	$0.155075\pi$
$102$	2.38289	0.235941
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	−1.00000	−0.0980581
$105$	−0.0782300	−0.00763446
$106$	10.7397	1.04313
$107$	7.44643	0.719873	0.359937	−	0.932977i	$-0.382798\pi$
$107$	7.44643	0.719873	0.359937	+	0.932977i	$0.382798\pi$
$108$	1.00000	0.0962250
$109$	−3.30101	−0.316180	−0.158090	−	0.987425i	$-0.550534\pi$
$109$	−3.30101	−0.316180	−0.158090	+	0.987425i	$0.550534\pi$
$110$	6.66417	0.635404
$111$	−8.84213	−0.839257
$112$	−0.0373018	−0.00352468
$113$	−6.21481	−0.584640	−0.292320	−	0.956321i	$-0.594427\pi$
$113$	−6.21481	−0.584640	−0.292320	+	0.956321i	$0.594427\pi$
$114$	−2.91209	−0.272742
$115$	8.37339	0.780823
$116$	−2.46598	−0.228960
$117$	1.00000	0.0924500
$118$	−4.58591	−0.422167
$119$	0.0888858	0.00814815
$120$	−2.09722	−0.191449
$121$	−0.902708	−0.0820644
$122$	1.68161	0.152246
$123$	−9.70721	−0.875270
$124$	0.760072	0.0682564
$125$	−11.7479	−1.05077
$126$	0.0373018	0.00332310
$127$	4.59734	0.407948	0.203974	−	0.978976i	$-0.434614\pi$
$127$	4.59734	0.407948	0.203974	+	0.978976i	$0.434614\pi$
$128$	−1.00000	−0.0883883
$129$	−10.8256	−0.953144
$130$	−2.09722	−0.183938
$131$	−17.3267	−1.51385	−0.756923	−	0.653505i	$-0.773298\pi$
$131$	−17.3267	−1.51385	−0.756923	+	0.653505i	$0.773298\pi$
$132$	−3.17762	−0.276577
$133$	−0.108626	−0.00941906
$134$	−7.20145	−0.622111
$135$	2.09722	0.180500
$136$	2.38289	0.204331
$137$	−14.5720	−1.24497	−0.622485	−	0.782632i	$-0.713877\pi$
$137$	−14.5720	−1.24497	−0.622485	+	0.782632i	$0.713877\pi$
$138$	−3.99261	−0.339874
$139$	−15.9341	−1.35152	−0.675758	−	0.737124i	$-0.736183\pi$
$139$	−15.9341	−1.35152	−0.675758	+	0.737124i	$0.736183\pi$
$140$	−0.0782300	−0.00661164
$141$	−5.29982	−0.446325
$142$	14.3856	1.20721
$143$	−3.17762	−0.265726
$144$	1.00000	0.0833333
$145$	−5.17170	−0.429486
$146$	−15.2846	−1.26496
$147$	−6.99861	−0.577236
$148$	−8.84213	−0.726818
$149$	−12.4885	−1.02310	−0.511548	−	0.859255i	$-0.670928\pi$
$149$	−12.4885	−1.02310	−0.511548	+	0.859255i	$0.670928\pi$
$150$	0.601670	0.0491262
$151$	11.6943	0.951669	0.475834	−	0.879535i	$-0.342146\pi$
$151$	11.6943	0.951669	0.475834	+	0.879535i	$0.342146\pi$
$152$	−2.91209	−0.236201
$153$	−2.38289	−0.192645
$154$	−0.118531	−0.00955150
$155$	1.59404	0.128036
$156$	1.00000	0.0800641
$157$	−11.0964	−0.885592	−0.442796	−	0.896622i	$-0.646013\pi$
$157$	−11.0964	−0.885592	−0.442796	+	0.896622i	$0.646013\pi$
$158$	−6.39400	−0.508680
$159$	−10.7397	−0.851712
$160$	−2.09722	−0.165800
$161$	−0.148932	−0.0117374
$162$	−1.00000	−0.0785674
$163$	5.69850	0.446341	0.223170	−	0.974779i	$-0.428359\pi$
$163$	5.69850	0.446341	0.223170	+	0.974779i	$0.428359\pi$
$164$	−9.70721	−0.758006
$165$	−6.66417	−0.518805
$166$	5.88671	0.456898
$167$	19.9987	1.54755	0.773773	−	0.633464i	$-0.218367\pi$
$167$	19.9987	1.54755	0.773773	+	0.633464i	$0.218367\pi$
$168$	0.0373018	0.00287789
$169$	1.00000	0.0769231
$170$	4.99743	0.383286
$171$	2.91209	0.222693
$172$	−10.8256	−0.825447
$173$	7.43256	0.565087	0.282544	−	0.959254i	$-0.408822\pi$
$173$	7.43256	0.565087	0.282544	+	0.959254i	$0.408822\pi$
$174$	2.46598	0.186945
$175$	0.0224434	0.00169656
$176$	−3.17762	−0.239522
$177$	4.58591	0.344698
$178$	−2.63980	−0.197861
$179$	24.5685	1.83634	0.918170	−	0.396188i	$-0.129667\pi$
$179$	24.5685	1.83634	0.918170	+	0.396188i	$0.129667\pi$
$180$	2.09722	0.156318
$181$	−6.64229	−0.493718	−0.246859	−	0.969051i	$-0.579398\pi$
$181$	−6.64229	−0.493718	−0.246859	+	0.969051i	$0.579398\pi$
$182$	0.0373018	0.00276499
$183$	−1.68161	−0.124308
$184$	−3.99261	−0.294339
$185$	−18.5439	−1.36337
$186$	−0.760072	−0.0557312
$187$	7.57191	0.553713
$188$	−5.29982	−0.386529
$189$	−0.0373018	−0.00271330
$190$	−6.10728	−0.443069
$191$	−12.5288	−0.906550	−0.453275	−	0.891371i	$-0.649745\pi$
$191$	−12.5288	−0.906550	−0.453275	+	0.891371i	$0.649745\pi$
$192$	1.00000	0.0721688
$193$	4.59720	0.330914	0.165457	−	0.986217i	$-0.447090\pi$
$193$	4.59720	0.330914	0.165457	+	0.986217i	$0.447090\pi$
$194$	2.73678	0.196489
$195$	2.09722	0.150185
$196$	−6.99861	−0.499901
$197$	15.5509	1.10796	0.553978	−	0.832532i	$-0.313109\pi$
$197$	15.5509	1.10796	0.553978	+	0.832532i	$0.313109\pi$
$198$	3.17762	0.225824
$199$	−9.66523	−0.685150	−0.342575	−	0.939491i	$-0.611299\pi$
$199$	−9.66523	−0.685150	−0.342575	+	0.939491i	$0.611299\pi$
$200$	0.601670	0.0425445
$201$	7.20145	0.507951
$202$	−17.7613	−1.24968
$203$	0.0919853	0.00645610
$204$	−2.38289	−0.166835
$205$	−20.3582	−1.42188
$206$	1.00000	0.0696733
$207$	3.99261	0.277506
$208$	1.00000	0.0693375
$209$	−9.25351	−0.640079
$210$	0.0782300	0.00539838
$211$	−3.17494	−0.218572	−0.109286	−	0.994010i	$-0.534856\pi$
$211$	−3.17494	−0.218572	−0.109286	+	0.994010i	$0.534856\pi$
$212$	−10.7397	−0.737604
$213$	−14.3856	−0.985685
$214$	−7.44643	−0.509027
$215$	−22.7037	−1.54838
$216$	−1.00000	−0.0680414
$217$	−0.0283520	−0.00192466
$218$	3.30101	0.223573
$219$	15.2846	1.03284
$220$	−6.66417	−0.449299
$221$	−2.38289	−0.160290
$222$	8.84213	0.593445
$223$	−1.36542	−0.0914350	−0.0457175	−	0.998954i	$-0.514557\pi$
$223$	−1.36542	−0.0914350	−0.0457175	+	0.998954i	$0.514557\pi$
$224$	0.0373018	0.00249233
$225$	−0.601670	−0.0401114
$226$	6.21481	0.413403
$227$	−10.1984	−0.676892	−0.338446	−	0.940986i	$-0.609901\pi$
$227$	−10.1984	−0.676892	−0.338446	+	0.940986i	$0.609901\pi$
$228$	2.91209	0.192858
$229$	20.1236	1.32980	0.664902	−	0.746931i	$-0.268473\pi$
$229$	20.1236	1.32980	0.664902	+	0.746931i	$0.268473\pi$
$230$	−8.37339	−0.552125
$231$	0.118531	0.00779876
$232$	2.46598	0.161899
$233$	−20.9544	−1.37277	−0.686383	−	0.727240i	$-0.740803\pi$
$233$	−20.9544	−1.37277	−0.686383	+	0.727240i	$0.740803\pi$
$234$	−1.00000	−0.0653720
$235$	−11.1149	−0.725055
$236$	4.58591	0.298517
$237$	6.39400	0.415335
$238$	−0.0888858	−0.00576161
$239$	−22.3195	−1.44373	−0.721865	−	0.692034i	$-0.756715\pi$
$239$	−22.3195	−1.44373	−0.721865	+	0.692034i	$0.756715\pi$
$240$	2.09722	0.135375
$241$	26.3016	1.69424	0.847118	−	0.531405i	$-0.178336\pi$
$241$	26.3016	1.69424	0.847118	+	0.531405i	$0.178336\pi$
$242$	0.902708	0.0580283
$243$	1.00000	0.0641500
$244$	−1.68161	−0.107654
$245$	−14.6776	−0.937719
$246$	9.70721	0.618909
$247$	2.91209	0.185292
$248$	−0.760072	−0.0482646
$249$	−5.88671	−0.373055
$250$	11.7479	0.743004
$251$	14.0004	0.883696	0.441848	−	0.897090i	$-0.354323\pi$
$251$	14.0004	0.883696	0.441848	+	0.897090i	$0.354323\pi$
$252$	−0.0373018	−0.00234979
$253$	−12.6870	−0.797627
$254$	−4.59734	−0.288463
$255$	−4.99743	−0.312951
$256$	1.00000	0.0625000
$257$	11.7882	0.735330	0.367665	−	0.929958i	$-0.380157\pi$
$257$	11.7882	0.735330	0.367665	+	0.929958i	$0.380157\pi$
$258$	10.8256	0.673974
$259$	0.329827	0.0204944
$260$	2.09722	0.130064
$261$	−2.46598	−0.152640
$262$	17.3267	1.07045
$263$	−3.34403	−0.206201	−0.103101	−	0.994671i	$-0.532876\pi$
$263$	−3.34403	−0.206201	−0.103101	+	0.994671i	$0.532876\pi$
$264$	3.17762	0.195569
$265$	−22.5235	−1.38361
$266$	0.108626	0.00666028
$267$	2.63980	0.161553
$268$	7.20145	0.439899
$269$	16.1066	0.982037	0.491019	−	0.871149i	$-0.336625\pi$
$269$	16.1066	0.982037	0.491019	+	0.871149i	$0.336625\pi$
$270$	−2.09722	−0.127633
$271$	−9.09091	−0.552234	−0.276117	−	0.961124i	$-0.589048\pi$
$271$	−9.09091	−0.552234	−0.276117	+	0.961124i	$0.589048\pi$
$272$	−2.38289	−0.144484
$273$	−0.0373018	−0.00225760
$274$	14.5720	0.880327
$275$	1.91188	0.115291
$276$	3.99261	0.240327
$277$	20.2183	1.21480	0.607401	−	0.794396i	$-0.292212\pi$
$277$	20.2183	1.21480	0.607401	+	0.794396i	$0.292212\pi$
$278$	15.9341	0.955666
$279$	0.760072	0.0455043
$280$	0.0782300	0.00467513
$281$	10.4908	0.625827	0.312913	−	0.949782i	$-0.398695\pi$
$281$	10.4908	0.625827	0.312913	+	0.949782i	$0.398695\pi$
$282$	5.29982	0.315600
$283$	−20.5499	−1.22157	−0.610783	−	0.791798i	$-0.709145\pi$
$283$	−20.5499	−1.22157	−0.610783	+	0.791798i	$0.709145\pi$
$284$	−14.3856	−0.853628
$285$	6.10728	0.361764
$286$	3.17762	0.187897
$287$	0.362096	0.0213739
$288$	−1.00000	−0.0589256
$289$	−11.3219	−0.665992
$290$	5.17170	0.303693
$291$	−2.73678	−0.160433
$292$	15.2846	0.894463
$293$	−2.35918	−0.137825	−0.0689124	−	0.997623i	$-0.521953\pi$
$293$	−2.35918	−0.137825	−0.0689124	+	0.997623i	$0.521953\pi$
$294$	6.99861	0.408167
$295$	9.61765	0.559961
$296$	8.84213	0.513938
$297$	−3.17762	−0.184384
$298$	12.4885	0.723438
$299$	3.99261	0.230899
$300$	−0.601670	−0.0347375
$301$	0.403815	0.0232755
$302$	−11.6943	−0.672931
$303$	17.7613	1.02036
$304$	2.91209	0.167020
$305$	−3.52671	−0.201939
$306$	2.38289	0.136220
$307$	−23.9915	−1.36927	−0.684633	−	0.728888i	$-0.740038\pi$
$307$	−23.9915	−1.36927	−0.684633	+	0.728888i	$0.740038\pi$
$308$	0.118531	0.00675393
$309$	−1.00000	−0.0568880
$310$	−1.59404	−0.0905352
$311$	−9.06740	−0.514165	−0.257083	−	0.966389i	$-0.582761\pi$
$311$	−9.06740	−0.514165	−0.257083	+	0.966389i	$0.582761\pi$
$312$	−1.00000	−0.0566139
$313$	27.0568	1.52934	0.764670	−	0.644422i	$-0.222902\pi$
$313$	27.0568	1.52934	0.764670	+	0.644422i	$0.222902\pi$
$314$	11.0964	0.626208
$315$	−0.0782300	−0.00440776
$316$	6.39400	0.359691
$317$	25.3558	1.42412	0.712062	−	0.702116i	$-0.247761\pi$
$317$	25.3558	1.42412	0.712062	+	0.702116i	$0.247761\pi$
$318$	10.7397	0.602251
$319$	7.83595	0.438729
$320$	2.09722	0.117238
$321$	7.44643	0.415619
$322$	0.148932	0.00829963
$323$	−6.93916	−0.386105
$324$	1.00000	0.0555556
$325$	−0.601670	−0.0333747
$326$	−5.69850	−0.315610
$327$	−3.30101	−0.182546
$328$	9.70721	0.535991
$329$	0.197693	0.0108991
$330$	6.66417	0.366851
$331$	−13.8421	−0.760829	−0.380414	−	0.924816i	$-0.624219\pi$
$331$	−13.8421	−0.760829	−0.380414	+	0.924816i	$0.624219\pi$
$332$	−5.88671	−0.323075
$333$	−8.84213	−0.484545
$334$	−19.9987	−1.09428
$335$	15.1030	0.825166
$336$	−0.0373018	−0.00203498
$337$	−0.107575	−0.00585998	−0.00292999	−	0.999996i	$-0.500933\pi$
$337$	−0.107575	−0.00585998	−0.00292999	+	0.999996i	$0.500933\pi$
$338$	−1.00000	−0.0543928
$339$	−6.21481	−0.337542
$340$	−4.99743	−0.271024
$341$	−2.41522	−0.130792
$342$	−2.91209	−0.157468
$343$	0.522173	0.0281947
$344$	10.8256	0.583679
$345$	8.37339	0.450808
$346$	−7.43256	−0.399577
$347$	−33.6802	−1.80805	−0.904025	−	0.427481i	$-0.859401\pi$
$347$	−33.6802	−1.80805	−0.904025	+	0.427481i	$0.859401\pi$
$348$	−2.46598	−0.132190
$349$	−14.2268	−0.761543	−0.380771	−	0.924669i	$-0.624342\pi$
$349$	−14.2268	−0.761543	−0.380771	+	0.924669i	$0.624342\pi$
$350$	−0.0224434	−0.00119965
$351$	1.00000	0.0533761
$352$	3.17762	0.169368
$353$	2.62388	0.139655	0.0698274	−	0.997559i	$-0.477755\pi$
$353$	2.62388	0.139655	0.0698274	+	0.997559i	$0.477755\pi$
$354$	−4.58591	−0.243738
$355$	−30.1698	−1.60124
$356$	2.63980	0.139909
$357$	0.0888858	0.00470434
$358$	−24.5685	−1.29849
$359$	−15.8065	−0.834234	−0.417117	−	0.908853i	$-0.636959\pi$
$359$	−15.8065	−0.834234	−0.417117	+	0.908853i	$0.636959\pi$
$360$	−2.09722	−0.110533
$361$	−10.5198	−0.553672
$362$	6.64229	0.349111
$363$	−0.902708	−0.0473799
$364$	−0.0373018	−0.00195514
$365$	32.0552	1.67784
$366$	1.68161	0.0878993
$367$	11.4273	0.596500	0.298250	−	0.954488i	$-0.403597\pi$
$367$	11.4273	0.596500	0.298250	+	0.954488i	$0.403597\pi$
$368$	3.99261	0.208129
$369$	−9.70721	−0.505337
$370$	18.5439	0.964050
$371$	0.400609	0.0207986
$372$	0.760072	0.0394079
$373$	−5.05968	−0.261980	−0.130990	−	0.991384i	$-0.541816\pi$
$373$	−5.05968	−0.261980	−0.130990	+	0.991384i	$0.541816\pi$
$374$	−7.57191	−0.391534
$375$	−11.7479	−0.606661
$376$	5.29982	0.273317
$377$	−2.46598	−0.127004
$378$	0.0373018	0.00191860
$379$	12.8369	0.659389	0.329695	−	0.944088i	$-0.393054\pi$
$379$	12.8369	0.659389	0.329695	+	0.944088i	$0.393054\pi$
$380$	6.10728	0.313297
$381$	4.59734	0.235529
$382$	12.5288	0.641028
$383$	−19.1538	−0.978715	−0.489357	−	0.872083i	$-0.662769\pi$
$383$	−19.1538	−0.978715	−0.489357	+	0.872083i	$0.662769\pi$
$384$	−1.00000	−0.0510310
$385$	0.248585	0.0126691
$386$	−4.59720	−0.233991
$387$	−10.8256	−0.550298
$388$	−2.73678	−0.138939
$389$	11.7164	0.594045	0.297022	−	0.954870i	$-0.404006\pi$
$389$	11.7164	0.594045	0.297022	+	0.954870i	$0.404006\pi$
$390$	−2.09722	−0.106197
$391$	−9.51394	−0.481141
$392$	6.99861	0.353483
$393$	−17.3267	−0.874019
$394$	−15.5509	−0.783443
$395$	13.4096	0.674712
$396$	−3.17762	−0.159682
$397$	23.4133	1.17508	0.587540	−	0.809195i	$-0.300097\pi$
$397$	23.4133	1.17508	0.587540	+	0.809195i	$0.300097\pi$
$398$	9.66523	0.484474
$399$	−0.108626	−0.00543810
$400$	−0.601670	−0.0300835
$401$	28.4310	1.41978	0.709889	−	0.704314i	$-0.248745\pi$
$401$	28.4310	1.41978	0.709889	+	0.704314i	$0.248745\pi$
$402$	−7.20145	−0.359176
$403$	0.760072	0.0378619
$404$	17.7613	0.883656
$405$	2.09722	0.104212
$406$	−0.0919853	−0.00456515
$407$	28.0969	1.39271
$408$	2.38289	0.117970
$409$	−5.14846	−0.254575	−0.127287	−	0.991866i	$-0.540627\pi$
$409$	−5.14846	−0.254575	−0.127287	+	0.991866i	$0.540627\pi$
$410$	20.3582	1.00542
$411$	−14.5720	−0.718784
$412$	−1.00000	−0.0492665
$413$	−0.171062	−0.00841743
$414$	−3.99261	−0.196226
$415$	−12.3457	−0.606028
$416$	−1.00000	−0.0490290
$417$	−15.9341	−0.780298
$418$	9.25351	0.452604
$419$	−15.5597	−0.760143	−0.380072	−	0.924957i	$-0.624101\pi$
$419$	−15.5597	−0.760143	−0.380072	+	0.924957i	$0.624101\pi$
$420$	−0.0782300	−0.00381723
$421$	19.2163	0.936547	0.468274	−	0.883584i	$-0.344876\pi$
$421$	19.2163	0.936547	0.468274	+	0.883584i	$0.344876\pi$
$422$	3.17494	0.154554
$423$	−5.29982	−0.257686
$424$	10.7397	0.521565
$425$	1.43371	0.0695452
$426$	14.3856	0.696985
$427$	0.0627271	0.00303558
$428$	7.44643	0.359937
$429$	−3.17762	−0.153417
$430$	22.7037	1.09487
$431$	−24.8965	−1.19922	−0.599611	−	0.800292i	$-0.704678\pi$
$431$	−24.8965	−1.19922	−0.599611	+	0.800292i	$0.704678\pi$
$432$	1.00000	0.0481125
$433$	29.0280	1.39500	0.697498	−	0.716586i	$-0.254296\pi$
$433$	29.0280	1.39500	0.697498	+	0.716586i	$0.254296\pi$
$434$	0.0283520	0.00136094
$435$	−5.17170	−0.247964
$436$	−3.30101	−0.158090
$437$	11.6268	0.556187
$438$	−15.2846	−0.730326
$439$	−12.1657	−0.580636	−0.290318	−	0.956930i	$-0.593761\pi$
$439$	−12.1657	−0.580636	−0.290318	+	0.956930i	$0.593761\pi$
$440$	6.66417	0.317702
$441$	−6.99861	−0.333267
$442$	2.38289	0.113342
$443$	−26.0682	−1.23854	−0.619269	−	0.785179i	$-0.712571\pi$
$443$	−26.0682	−1.23854	−0.619269	+	0.785179i	$0.712571\pi$
$444$	−8.84213	−0.419629
$445$	5.53623	0.262443
$446$	1.36542	0.0646543
$447$	−12.4885	−0.590685
$448$	−0.0373018	−0.00176234
$449$	−17.1631	−0.809977	−0.404988	−	0.914322i	$-0.632724\pi$
$449$	−17.1631	−0.809977	−0.404988	+	0.914322i	$0.632724\pi$
$450$	0.601670	0.0283630
$451$	30.8459	1.45248
$452$	−6.21481	−0.292320
$453$	11.6943	0.549446
$454$	10.1984	0.478635
$455$	−0.0782300	−0.00366748
$456$	−2.91209	−0.136371
$457$	1.04913	0.0490760	0.0245380	−	0.999699i	$-0.492189\pi$
$457$	1.04913	0.0490760	0.0245380	+	0.999699i	$0.492189\pi$
$458$	−20.1236	−0.940313
$459$	−2.38289	−0.111224
$460$	8.37339	0.390411
$461$	1.36203	0.0634362	0.0317181	−	0.999497i	$-0.489902\pi$
$461$	1.36203	0.0634362	0.0317181	+	0.999497i	$0.489902\pi$
$462$	−0.118531	−0.00551456
$463$	−17.9663	−0.834963	−0.417482	−	0.908685i	$-0.637087\pi$
$463$	−17.9663	−0.834963	−0.417482	+	0.908685i	$0.637087\pi$
$464$	−2.46598	−0.114480
$465$	1.59404	0.0739217
$466$	20.9544	0.970692
$467$	−12.2355	−0.566194	−0.283097	−	0.959091i	$-0.591362\pi$
$467$	−12.2355	−0.566194	−0.283097	+	0.959091i	$0.591362\pi$
$468$	1.00000	0.0462250
$469$	−0.268627	−0.0124040
$470$	11.1149	0.512691
$471$	−11.0964	−0.511297
$472$	−4.58591	−0.211083
$473$	34.3998	1.58170
$474$	−6.39400	−0.293686
$475$	−1.75212	−0.0803926
$476$	0.0888858	0.00407407
$477$	−10.7397	−0.491736
$478$	22.3195	1.02087
$479$	18.4397	0.842531	0.421265	−	0.906937i	$-0.361586\pi$
$479$	18.4397	0.842531	0.421265	+	0.906937i	$0.361586\pi$
$480$	−2.09722	−0.0957245
$481$	−8.84213	−0.403166
$482$	−26.3016	−1.19801
$483$	−0.148932	−0.00677662
$484$	−0.902708	−0.0410322
$485$	−5.73963	−0.260623
$486$	−1.00000	−0.0453609
$487$	24.9829	1.13208	0.566041	−	0.824377i	$-0.308474\pi$
$487$	24.9829	1.13208	0.566041	+	0.824377i	$0.308474\pi$
$488$	1.68161	0.0761230
$489$	5.69850	0.257695
$490$	14.6776	0.663067
$491$	−21.6861	−0.978679	−0.489339	−	0.872093i	$-0.662762\pi$
$491$	−21.6861	−0.978679	−0.489339	+	0.872093i	$0.662762\pi$
$492$	−9.70721	−0.437635
$493$	5.87614	0.264648
$494$	−2.91209	−0.131021
$495$	−6.66417	−0.299532
$496$	0.760072	0.0341282
$497$	0.536608	0.0240702
$498$	5.88671	0.263790
$499$	28.2202	1.26331	0.631654	−	0.775250i	$-0.282376\pi$
$499$	28.2202	1.26331	0.631654	+	0.775250i	$0.282376\pi$
$500$	−11.7479	−0.525384
$501$	19.9987	0.893476
$502$	−14.0004	−0.624868
$503$	−15.1995	−0.677713	−0.338856	−	0.940838i	$-0.610040\pi$
$503$	−15.1995	−0.677713	−0.338856	+	0.940838i	$0.610040\pi$
$504$	0.0373018	0.00166155
$505$	37.2493	1.65757
$506$	12.6870	0.564007
$507$	1.00000	0.0444116
$508$	4.59734	0.203974
$509$	−27.6342	−1.22487	−0.612433	−	0.790522i	$-0.709809\pi$
$509$	−27.6342	−1.22487	−0.612433	+	0.790522i	$0.709809\pi$
$510$	4.99743	0.221290
$511$	−0.570142	−0.0252216
$512$	−1.00000	−0.0441942
$513$	2.91209	0.128572
$514$	−11.7882	−0.519957
$515$	−2.09722	−0.0924145
$516$	−10.8256	−0.476572
$517$	16.8408	0.740659
$518$	−0.329827	−0.0144918
$519$	7.43256	0.326253
$520$	−2.09722	−0.0919692
$521$	−40.7700	−1.78616	−0.893082	−	0.449893i	$-0.851462\pi$
$521$	−40.7700	−1.78616	−0.893082	+	0.449893i	$0.851462\pi$
$522$	2.46598	0.107933
$523$	9.57148	0.418532	0.209266	−	0.977859i	$-0.432893\pi$
$523$	9.57148	0.418532	0.209266	+	0.977859i	$0.432893\pi$
$524$	−17.3267	−0.756923
$525$	0.0224434	0.000979509 0
$526$	3.34403	0.145806
$527$	−1.81116	−0.0788955
$528$	−3.17762	−0.138288
$529$	−7.05903	−0.306914
$530$	22.5235	0.978357
$531$	4.58591	0.199011
$532$	−0.108626	−0.00470953
$533$	−9.70721	−0.420466
$534$	−2.63980	−0.114235
$535$	15.6168	0.675173
$536$	−7.20145	−0.311055
$537$	24.5685	1.06021
$538$	−16.1066	−0.694405
$539$	22.2389	0.957899
$540$	2.09722	0.0902500
$541$	41.1381	1.76867	0.884333	−	0.466857i	$-0.154614\pi$
$541$	41.1381	1.76867	0.884333	+	0.466857i	$0.154614\pi$
$542$	9.09091	0.390488
$543$	−6.64229	−0.285048
$544$	2.38289	0.102165
$545$	−6.92295	−0.296547
$546$	0.0373018	0.00159637
$547$	18.1876	0.777644	0.388822	−	0.921313i	$-0.372882\pi$
$547$	18.1876	0.777644	0.388822	+	0.921313i	$0.372882\pi$
$548$	−14.5720	−0.622485
$549$	−1.68161	−0.0717695
$550$	−1.91188	−0.0815229
$551$	−7.18114	−0.305927
$552$	−3.99261	−0.169937
$553$	−0.238508	−0.0101424
$554$	−20.2183	−0.858994
$555$	−18.5439	−0.787144
$556$	−15.9341	−0.675758
$557$	6.12099	0.259355	0.129677	−	0.991556i	$-0.458606\pi$
$557$	6.12099	0.259355	0.129677	+	0.991556i	$0.458606\pi$
$558$	−0.760072	−0.0321764
$559$	−10.8256	−0.457875
$560$	−0.0782300	−0.00330582
$561$	7.57191	0.319686
$562$	−10.4908	−0.442526
$563$	−46.7197	−1.96900	−0.984501	−	0.175382i	$-0.943884\pi$
$563$	−46.7197	−1.96900	−0.984501	+	0.175382i	$0.943884\pi$
$564$	−5.29982	−0.223163
$565$	−13.0338	−0.548337
$566$	20.5499	0.863778
$567$	−0.0373018	−0.00156653
$568$	14.3856	0.603606
$569$	−13.9598	−0.585224	−0.292612	−	0.956231i	$-0.594524\pi$
$569$	−13.9598	−0.585224	−0.292612	+	0.956231i	$0.594524\pi$
$570$	−6.10728	−0.255806
$571$	1.97131	0.0824968	0.0412484	−	0.999149i	$-0.486866\pi$
$571$	1.97131	0.0824968	0.0412484	+	0.999149i	$0.486866\pi$
$572$	−3.17762	−0.132863
$573$	−12.5288	−0.523397
$574$	−0.362096	−0.0151136
$575$	−2.40224	−0.100180
$576$	1.00000	0.0416667
$577$	20.8428	0.867697	0.433849	−	0.900986i	$-0.357155\pi$
$577$	20.8428	0.867697	0.433849	+	0.900986i	$0.357155\pi$
$578$	11.3219	0.470927
$579$	4.59720	0.191053
$580$	−5.17170	−0.214743
$581$	0.219585	0.00910991
$582$	2.73678	0.113443
$583$	34.1267	1.41338
$584$	−15.2846	−0.632481
$585$	2.09722	0.0867094
$586$	2.35918	0.0974569
$587$	−34.8380	−1.43792	−0.718958	−	0.695053i	$-0.755381\pi$
$587$	−34.8380	−1.43792	−0.718958	+	0.695053i	$0.755381\pi$
$588$	−6.99861	−0.288618
$589$	2.21339	0.0912013
$590$	−9.61765	−0.395953
$591$	15.5509	0.639678
$592$	−8.84213	−0.363409
$593$	−2.11731	−0.0869477	−0.0434738	−	0.999055i	$-0.513843\pi$
$593$	−2.11731	−0.0869477	−0.0434738	+	0.999055i	$0.513843\pi$
$594$	3.17762	0.130379
$595$	0.186413	0.00764219
$596$	−12.4885	−0.511548
$597$	−9.66523	−0.395571
$598$	−3.99261	−0.163270
$599$	35.5037	1.45064	0.725320	−	0.688411i	$-0.241692\pi$
$599$	35.5037	1.45064	0.725320	+	0.688411i	$0.241692\pi$
$600$	0.601670	0.0245631
$601$	16.5908	0.676752	0.338376	−	0.941011i	$-0.390123\pi$
$601$	16.5908	0.676752	0.338376	+	0.941011i	$0.390123\pi$
$602$	−0.403815	−0.0164583
$603$	7.20145	0.293266
$604$	11.6943	0.475834
$605$	−1.89318	−0.0769686
$606$	−17.7613	−0.721502
$607$	−40.3761	−1.63882	−0.819408	−	0.573210i	$-0.805698\pi$
$607$	−40.3761	−1.63882	−0.819408	+	0.573210i	$0.805698\pi$
$608$	−2.91209	−0.118101
$609$	0.0919853	0.00372743
$610$	3.52671	0.142792
$611$	−5.29982	−0.214408
$612$	−2.38289	−0.0963224
$613$	−14.6447	−0.591493	−0.295747	−	0.955266i	$-0.595568\pi$
$613$	−14.6447	−0.591493	−0.295747	+	0.955266i	$0.595568\pi$
$614$	23.9915	0.968218
$615$	−20.3582	−0.820920
$616$	−0.118531	−0.00477575
$617$	14.9516	0.601927	0.300963	−	0.953636i	$-0.402692\pi$
$617$	14.9516	0.601927	0.300963	+	0.953636i	$0.402692\pi$
$618$	1.00000	0.0402259
$619$	18.1481	0.729435	0.364717	−	0.931118i	$-0.381166\pi$
$619$	18.1481	0.729435	0.364717	+	0.931118i	$0.381166\pi$
$620$	1.59404	0.0640181
$621$	3.99261	0.160218
$622$	9.06740	0.363570
$623$	−0.0984690	−0.00394508
$624$	1.00000	0.0400320
$625$	−21.6296	−0.865186
$626$	−27.0568	−1.08141
$627$	−9.25351	−0.369550
$628$	−11.0964	−0.442796
$629$	21.0698	0.840107
$630$	0.0782300	0.00311676
$631$	12.3163	0.490305	0.245153	−	0.969485i	$-0.421162\pi$
$631$	12.3163	0.490305	0.245153	+	0.969485i	$0.421162\pi$
$632$	−6.39400	−0.254340
$633$	−3.17494	−0.126193
$634$	−25.3558	−1.00701
$635$	9.64162	0.382616
$636$	−10.7397	−0.425856
$637$	−6.99861	−0.277295
$638$	−7.83595	−0.310228
$639$	−14.3856	−0.569086
$640$	−2.09722	−0.0828999
$641$	9.98898	0.394541	0.197270	−	0.980349i	$-0.436792\pi$
$641$	9.98898	0.394541	0.197270	+	0.980349i	$0.436792\pi$
$642$	−7.44643	−0.293887
$643$	6.16171	0.242994	0.121497	−	0.992592i	$-0.461231\pi$
$643$	6.16171	0.242994	0.121497	+	0.992592i	$0.461231\pi$
$644$	−0.148932	−0.00586872
$645$	−22.7037	−0.893958
$646$	6.93916	0.273018
$647$	27.2248	1.07032	0.535159	−	0.844751i	$-0.320252\pi$
$647$	27.2248	1.07032	0.535159	+	0.844751i	$0.320252\pi$
$648$	−1.00000	−0.0392837
$649$	−14.5723	−0.572012
$650$	0.601670	0.0235995
$651$	−0.0283520	−0.00111120
$652$	5.69850	0.223170
$653$	27.1892	1.06400	0.531998	−	0.846745i	$-0.321441\pi$
$653$	27.1892	1.06400	0.531998	+	0.846745i	$0.321441\pi$
$654$	3.30101	0.129080
$655$	−36.3380	−1.41984
$656$	−9.70721	−0.379003
$657$	15.2846	0.596309
$658$	−0.197693	−0.00770686
$659$	13.5823	0.529093	0.264546	−	0.964373i	$-0.414778\pi$
$659$	13.5823	0.529093	0.264546	+	0.964373i	$0.414778\pi$
$660$	−6.66417	−0.259403
$661$	−31.9323	−1.24202	−0.621010	−	0.783802i	$-0.713278\pi$
$661$	−31.9323	−1.24202	−0.621010	+	0.783802i	$0.713278\pi$
$662$	13.8421	0.537987
$663$	−2.38289	−0.0925436
$664$	5.88671	0.228449
$665$	−0.227812	−0.00883418
$666$	8.84213	0.342625
$667$	−9.84570	−0.381227
$668$	19.9987	0.773773
$669$	−1.36542	−0.0527900
$670$	−15.1030	−0.583481
$671$	5.34353	0.206285
$672$	0.0373018	0.00143895
$673$	23.8672	0.920012	0.460006	−	0.887916i	$-0.347847\pi$
$673$	23.8672	0.920012	0.460006	+	0.887916i	$0.347847\pi$
$674$	0.107575	0.00414363
$675$	−0.601670	−0.0231583
$676$	1.00000	0.0384615
$677$	−51.5593	−1.98158	−0.990792	−	0.135390i	$-0.956771\pi$
$677$	−51.5593	−1.98158	−0.990792	+	0.135390i	$0.956771\pi$
$678$	6.21481	0.238678
$679$	0.102087	0.00391773
$680$	4.99743	0.191643
$681$	−10.1984	−0.390804
$682$	2.41522	0.0924836
$683$	11.2269	0.429586	0.214793	−	0.976660i	$-0.431092\pi$
$683$	11.2269	0.429586	0.214793	+	0.976660i	$0.431092\pi$
$684$	2.91209	0.111346
$685$	−30.5607	−1.16766
$686$	−0.522173	−0.0199366
$687$	20.1236	0.767763
$688$	−10.8256	−0.412723
$689$	−10.7397	−0.409149
$690$	−8.37339	−0.318769
$691$	−34.2987	−1.30478	−0.652392	−	0.757881i	$-0.726235\pi$
$691$	−34.2987	−1.30478	−0.652392	+	0.757881i	$0.726235\pi$
$692$	7.43256	0.282544
$693$	0.118531	0.00450262
$694$	33.6802	1.27848
$695$	−33.4174	−1.26759
$696$	2.46598	0.0934727
$697$	23.1312	0.876156
$698$	14.2268	0.538492
$699$	−20.9544	−0.792567
$700$	0.0224434	0.000848279 0
$701$	−8.77197	−0.331313	−0.165656	−	0.986184i	$-0.552974\pi$
$701$	−8.77197	−0.331313	−0.165656	+	0.986184i	$0.552974\pi$
$702$	−1.00000	−0.0377426
$703$	−25.7490	−0.971143
$704$	−3.17762	−0.119761
$705$	−11.1149	−0.418611
$706$	−2.62388	−0.0987509
$707$	−0.662526	−0.0249169
$708$	4.58591	0.172349
$709$	25.0019	0.938967	0.469484	−	0.882941i	$-0.344440\pi$
$709$	25.0019	0.938967	0.469484	+	0.882941i	$0.344440\pi$
$710$	30.1698	1.13225
$711$	6.39400	0.239794
$712$	−2.63980	−0.0989305
$713$	3.03467	0.113649
$714$	−0.0888858	−0.00332647
$715$	−6.66417	−0.249226
$716$	24.5685	0.918170
$717$	−22.3195	−0.833538
$718$	15.8065	0.589892
$719$	−39.3676	−1.46816	−0.734081	−	0.679061i	$-0.762387\pi$
$719$	−39.3676	−1.46816	−0.734081	+	0.679061i	$0.762387\pi$
$720$	2.09722	0.0781588
$721$	0.0373018	0.00138919
$722$	10.5198	0.391505
$723$	26.3016	0.978168
$724$	−6.64229	−0.246859
$725$	1.48371	0.0551035
$726$	0.902708	0.0335026
$727$	−5.79125	−0.214786	−0.107393	−	0.994217i	$-0.534250\pi$
$727$	−5.79125	−0.214786	−0.107393	+	0.994217i	$0.534250\pi$
$728$	0.0373018	0.00138250
$729$	1.00000	0.0370370
$730$	−32.0552	−1.18641
$731$	25.7962	0.954108
$732$	−1.68161	−0.0621542
$733$	24.9648	0.922098	0.461049	−	0.887375i	$-0.347473\pi$
$733$	24.9648	0.922098	0.461049	+	0.887375i	$0.347473\pi$
$734$	−11.4273	−0.421789
$735$	−14.6776	−0.541392
$736$	−3.99261	−0.147170
$737$	−22.8835	−0.842925
$738$	9.70721	0.357327
$739$	16.6930	0.614061	0.307031	−	0.951700i	$-0.400665\pi$
$739$	16.6930	0.614061	0.307031	+	0.951700i	$0.400665\pi$
$740$	−18.5439	−0.681687
$741$	2.91209	0.106978
$742$	−0.400609	−0.0147068
$743$	−37.9447	−1.39206	−0.696028	−	0.718014i	$-0.745051\pi$
$743$	−37.9447	−1.39206	−0.696028	+	0.718014i	$0.745051\pi$
$744$	−0.760072	−0.0278656
$745$	−26.1911	−0.959567
$746$	5.05968	0.185248
$747$	−5.88671	−0.215384
$748$	7.57191	0.276857
$749$	−0.277765	−0.0101493
$750$	11.7479	0.428974
$751$	29.4524	1.07474	0.537368	−	0.843348i	$-0.319419\pi$
$751$	29.4524	1.07474	0.537368	+	0.843348i	$0.319419\pi$
$752$	−5.29982	−0.193264
$753$	14.0004	0.510202
$754$	2.46598	0.0898056
$755$	24.5255	0.892575
$756$	−0.0373018	−0.00135665
$757$	8.22118	0.298804	0.149402	−	0.988777i	$-0.452265\pi$
$757$	8.22118	0.298804	0.149402	+	0.988777i	$0.452265\pi$
$758$	−12.8369	−0.466259
$759$	−12.6870	−0.460510
$760$	−6.10728	−0.221534
$761$	−28.5972	−1.03665	−0.518324	−	0.855185i	$-0.673444\pi$
$761$	−28.5972	−1.03665	−0.518324	+	0.855185i	$0.673444\pi$
$762$	−4.59734	−0.166544
$763$	0.123134	0.00445773
$764$	−12.5288	−0.453275
$765$	−4.99743	−0.180683
$766$	19.1538	0.692056
$767$	4.58591	0.165588
$768$	1.00000	0.0360844
$769$	38.8323	1.40033	0.700165	−	0.713981i	$-0.253110\pi$
$769$	38.8323	1.40033	0.700165	+	0.713981i	$0.253110\pi$
$770$	−0.248585	−0.00895840
$771$	11.7882	0.424543
$772$	4.59720	0.165457
$773$	−36.2728	−1.30464	−0.652320	−	0.757943i	$-0.726204\pi$
$773$	−36.2728	−1.30464	−0.652320	+	0.757943i	$0.726204\pi$
$774$	10.8256	0.389119
$775$	−0.457313	−0.0164272
$776$	2.73678	0.0982447
$777$	0.329827	0.0118325
$778$	−11.7164	−0.420053
$779$	−28.2682	−1.01281
$780$	2.09722	0.0750925
$781$	45.7120	1.63570
$782$	9.51394	0.340218
$783$	−2.46598	−0.0881269
$784$	−6.99861	−0.249950
$785$	−23.2717	−0.830601
$786$	17.3267	0.618025
$787$	−44.7173	−1.59400	−0.797000	−	0.603979i	$-0.793581\pi$
$787$	−44.7173	−1.59400	−0.797000	+	0.603979i	$0.793581\pi$
$788$	15.5509	0.553978
$789$	−3.34403	−0.119050
$790$	−13.4096	−0.477093
$791$	0.231823	0.00824269
$792$	3.17762	0.112912
$793$	−1.68161	−0.0597158
$794$	−23.4133	−0.830907
$795$	−22.5235	−0.798825
$796$	−9.66523	−0.342575
$797$	49.2580	1.74481	0.872403	−	0.488787i	$-0.162560\pi$
$797$	49.2580	1.74481	0.872403	+	0.488787i	$0.162560\pi$
$798$	0.108626	0.00384531
$799$	12.6289	0.446777
$800$	0.601670	0.0212723
$801$	2.63980	0.0932726
$802$	−28.4310	−1.00393
$803$	−48.5687	−1.71395
$804$	7.20145	0.253976
$805$	−0.312342	−0.0110086
$806$	−0.760072	−0.0267724
$807$	16.1066	0.566979
$808$	−17.7613	−0.624839
$809$	−33.0157	−1.16077	−0.580384	−	0.814343i	$-0.697098\pi$
$809$	−33.0157	−1.16077	−0.580384	+	0.814343i	$0.697098\pi$
$810$	−2.09722	−0.0736888
$811$	11.8002	0.414360	0.207180	−	0.978303i	$-0.433571\pi$
$811$	11.8002	0.414360	0.207180	+	0.978303i	$0.433571\pi$
$812$	0.0919853	0.00322805
$813$	−9.09091	−0.318832
$814$	−28.0969	−0.984797
$815$	11.9510	0.418625
$816$	−2.38289	−0.0834177
$817$	−31.5252	−1.10293
$818$	5.14846	0.180012
$819$	−0.0373018	−0.00130343
$820$	−20.3582	−0.710938
$821$	−16.4095	−0.572695	−0.286348	−	0.958126i	$-0.592441\pi$
$821$	−16.4095	−0.572695	−0.286348	+	0.958126i	$0.592441\pi$
$822$	14.5720	0.508257
$823$	−12.2205	−0.425979	−0.212989	−	0.977055i	$-0.568320\pi$
$823$	−12.2205	−0.425979	−0.212989	+	0.977055i	$0.568320\pi$
$824$	1.00000	0.0348367
$825$	1.91188	0.0665632
$826$	0.171062	0.00595202
$827$	−38.8199	−1.34990	−0.674951	−	0.737863i	$-0.735835\pi$
$827$	−38.8199	−1.34990	−0.674951	+	0.737863i	$0.735835\pi$
$828$	3.99261	0.138753
$829$	41.0684	1.42637	0.713183	−	0.700978i	$-0.247253\pi$
$829$	41.0684	1.42637	0.713183	+	0.700978i	$0.247253\pi$
$830$	12.3457	0.428527
$831$	20.2183	0.701366
$832$	1.00000	0.0346688
$833$	16.6769	0.577820
$834$	15.9341	0.551754
$835$	41.9416	1.45145
$836$	−9.25351	−0.320039
$837$	0.760072	0.0262719
$838$	15.5597	0.537502
$839$	38.0471	1.31353	0.656766	−	0.754094i	$-0.271924\pi$
$839$	38.0471	1.31353	0.656766	+	0.754094i	$0.271924\pi$
$840$	0.0782300	0.00269919
$841$	−22.9190	−0.790309
$842$	−19.2163	−0.662239
$843$	10.4908	0.361321
$844$	−3.17494	−0.109286
$845$	2.09722	0.0721465
$846$	5.29982	0.182212
$847$	0.0336726	0.00115700
$848$	−10.7397	−0.368802
$849$	−20.5499	−0.705272
$850$	−1.43371	−0.0491759
$851$	−35.3032	−1.21018
$852$	−14.3856	−0.492843
$853$	−3.25026	−0.111287	−0.0556434	−	0.998451i	$-0.517721\pi$
$853$	−3.25026	−0.111287	−0.0556434	+	0.998451i	$0.517721\pi$
$854$	−0.0627271	−0.00214648
$855$	6.10728	0.208865
$856$	−7.44643	−0.254514
$857$	5.18334	0.177059	0.0885297	−	0.996074i	$-0.471783\pi$
$857$	5.18334	0.177059	0.0885297	+	0.996074i	$0.471783\pi$
$858$	3.17762	0.108482
$859$	−12.7539	−0.435159	−0.217580	−	0.976043i	$-0.569816\pi$
$859$	−12.7539	−0.435159	−0.217580	+	0.976043i	$0.569816\pi$
$860$	−22.7037	−0.774191
$861$	0.362096	0.0123402
$862$	24.8965	0.847977
$863$	23.8338	0.811312	0.405656	−	0.914026i	$-0.367043\pi$
$863$	23.8338	0.811312	0.405656	+	0.914026i	$0.367043\pi$
$864$	−1.00000	−0.0340207
$865$	15.5877	0.529998
$866$	−29.0280	−0.986412
$867$	−11.3219	−0.384510
$868$	−0.0283520	−0.000962330 0
$869$	−20.3177	−0.689232
$870$	5.17170	0.175337
$871$	7.20145	0.244012
$872$	3.30101	0.111786
$873$	−2.73678	−0.0926260
$874$	−11.6268	−0.393284
$875$	0.438219	0.0148145
$876$	15.2846	0.516419
$877$	−38.2283	−1.29088	−0.645438	−	0.763812i	$-0.723325\pi$
$877$	−38.2283	−1.29088	−0.645438	+	0.763812i	$0.723325\pi$
$878$	12.1657	0.410571
$879$	−2.35918	−0.0795732
$880$	−6.66417	−0.224649
$881$	8.71342	0.293562	0.146781	−	0.989169i	$-0.453109\pi$
$881$	8.71342	0.293562	0.146781	+	0.989169i	$0.453109\pi$
$882$	6.99861	0.235655
$883$	31.4124	1.05711	0.528555	−	0.848899i	$-0.322734\pi$
$883$	31.4124	1.05711	0.528555	+	0.848899i	$0.322734\pi$
$884$	−2.38289	−0.0801451
$885$	9.61765	0.323294
$886$	26.0682	0.875779
$887$	−33.5550	−1.12667	−0.563334	−	0.826229i	$-0.690482\pi$
$887$	−33.5550	−1.12667	−0.563334	+	0.826229i	$0.690482\pi$
$888$	8.84213	0.296722
$889$	−0.171489	−0.00575155
$890$	−5.53623	−0.185575
$891$	−3.17762	−0.106454
$892$	−1.36542	−0.0457175
$893$	−15.4335	−0.516463
$894$	12.4885	0.417677
$895$	51.5256	1.72231
$896$	0.0373018	0.00124616
$897$	3.99261	0.133310
$898$	17.1631	0.572740
$899$	−1.87432	−0.0625121
$900$	−0.601670	−0.0200557
$901$	25.5914	0.852574
$902$	−30.8459	−1.02705
$903$	0.403815	0.0134381
$904$	6.21481	0.206701
$905$	−13.9303	−0.463060
$906$	−11.6943	−0.388517
$907$	−8.26058	−0.274288	−0.137144	−	0.990551i	$-0.543792\pi$
$907$	−8.26058	−0.274288	−0.137144	+	0.990551i	$0.543792\pi$
$908$	−10.1984	−0.338446
$909$	17.7613	0.589104
$910$	0.0782300	0.00259330
$911$	18.2362	0.604191	0.302095	−	0.953278i	$-0.402314\pi$
$911$	18.2362	0.604191	0.302095	+	0.953278i	$0.402314\pi$
$912$	2.91209	0.0964288
$913$	18.7058	0.619070
$914$	−1.04913	−0.0347020
$915$	−3.52671	−0.116589
$916$	20.1236	0.664902
$917$	0.646318	0.0213433
$918$	2.38289	0.0786469
$919$	−50.2704	−1.65827	−0.829133	−	0.559051i	$-0.811165\pi$
$919$	−50.2704	−1.65827	−0.829133	+	0.559051i	$0.811165\pi$
$920$	−8.37339	−0.276062
$921$	−23.9915	−0.790547
$922$	−1.36203	−0.0448562
$923$	−14.3856	−0.473508
$924$	0.118531	0.00389938
$925$	5.32004	0.174922
$926$	17.9663	0.590408
$927$	−1.00000	−0.0328443
$928$	2.46598	0.0809497
$929$	−26.0641	−0.855137	−0.427568	−	0.903983i	$-0.640630\pi$
$929$	−26.0641	−0.855137	−0.427568	+	0.903983i	$0.640630\pi$
$930$	−1.59404	−0.0522705
$931$	−20.3805	−0.667945
$932$	−20.9544	−0.686383
$933$	−9.06740	−0.296853
$934$	12.2355	0.400359
$935$	15.8800	0.519330
$936$	−1.00000	−0.0326860
$937$	50.1578	1.63858	0.819292	−	0.573376i	$-0.194367\pi$
$937$	50.1578	1.63858	0.819292	+	0.573376i	$0.194367\pi$
$938$	0.268627	0.00877097
$939$	27.0568	0.882965
$940$	−11.1149	−0.362528
$941$	52.6830	1.71742	0.858708	−	0.512466i	$-0.171268\pi$
$941$	52.6830	1.71742	0.858708	+	0.512466i	$0.171268\pi$
$942$	11.0964	0.361542
$943$	−38.7572	−1.26211
$944$	4.58591	0.149259
$945$	−0.0782300	−0.00254482
$946$	−34.3998	−1.11843
$947$	14.4382	0.469180	0.234590	−	0.972094i	$-0.424625\pi$
$947$	14.4382	0.469180	0.234590	+	0.972094i	$0.424625\pi$
$948$	6.39400	0.207668
$949$	15.2846	0.496159
$950$	1.75212	0.0568461
$951$	25.3558	0.822219
$952$	−0.0888858	−0.00288081
$953$	−54.7392	−1.77318	−0.886588	−	0.462561i	$-0.846931\pi$
$953$	−54.7392	−1.77318	−0.886588	+	0.462561i	$0.846931\pi$
$954$	10.7397	0.347710
$955$	−26.2756	−0.850258
$956$	−22.3195	−0.721865
$957$	7.83595	0.253300
$958$	−18.4397	−0.595759
$959$	0.543561	0.0175525
$960$	2.09722	0.0676875
$961$	−30.4223	−0.981364
$962$	8.84213	0.285082
$963$	7.44643	0.239958
$964$	26.3016	0.847118
$965$	9.64134	0.310366
$966$	0.148932	0.00479179
$967$	1.08880	0.0350135	0.0175068	−	0.999847i	$-0.494427\pi$
$967$	1.08880	0.0350135	0.0175068	+	0.999847i	$0.494427\pi$
$968$	0.902708	0.0290141
$969$	−6.93916	−0.222918
$970$	5.73963	0.184288
$971$	−32.3608	−1.03851	−0.519254	−	0.854620i	$-0.673790\pi$
$971$	−32.3608	−1.03851	−0.519254	+	0.854620i	$0.673790\pi$
$972$	1.00000	0.0320750
$973$	0.594371	0.0190547
$974$	−24.9829	−0.800504
$975$	−0.601670	−0.0192689
$976$	−1.68161	−0.0538271
$977$	32.4148	1.03704	0.518521	−	0.855065i	$-0.326483\pi$
$977$	32.4148	1.03704	0.518521	+	0.855065i	$0.326483\pi$
$978$	−5.69850	−0.182218
$979$	−8.38828	−0.268091
$980$	−14.6776	−0.468859
$981$	−3.30101	−0.105393
$982$	21.6861	0.692030
$983$	52.2186	1.66552	0.832758	−	0.553638i	$-0.186761\pi$
$983$	52.2186	1.66552	0.832758	+	0.553638i	$0.186761\pi$
$984$	9.70721	0.309455
$985$	32.6136	1.03916
$986$	−5.87614	−0.187135
$987$	0.197693	0.00629262
$988$	2.91209	0.0926458
$989$	−43.2226	−1.37440
$990$	6.66417	0.211801
$991$	−26.0290	−0.826838	−0.413419	−	0.910541i	$-0.635665\pi$
$991$	−26.0290	−0.826838	−0.413419	+	0.910541i	$0.635665\pi$
$992$	−0.760072	−0.0241323
$993$	−13.8421	−0.439265
$994$	−0.536608	−0.0170202
$995$	−20.2701	−0.642606
$996$	−5.88671	−0.186528
$997$	26.7927	0.848534	0.424267	−	0.905537i	$-0.360532\pi$
$997$	26.7927	0.848534	0.424267	+	0.905537i	$0.360532\pi$
$998$	−28.2202	−0.893294
$999$	−8.84213	−0.279752

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.w.1.10	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.w.1.10	✓	12	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.09722 q^{5} -1.00000 q^{6} -0.0373018 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.09722 q^{5} -1.00000 q^{6} -0.0373018 q^{7} -1.00000 q^{8} +1.00000 q^{9} -2.09722 q^{10} -3.17762 q^{11} +1.00000 q^{12} +1.00000 q^{13} +0.0373018 q^{14} +2.09722 q^{15} +1.00000 q^{16} -2.38289 q^{17} -1.00000 q^{18} +2.91209 q^{19} +2.09722 q^{20} -0.0373018 q^{21} +3.17762 q^{22} +3.99261 q^{23} -1.00000 q^{24} -0.601670 q^{25} -1.00000 q^{26} +1.00000 q^{27} -0.0373018 q^{28} -2.46598 q^{29} -2.09722 q^{30} +0.760072 q^{31} -1.00000 q^{32} -3.17762 q^{33} +2.38289 q^{34} -0.0782300 q^{35} +1.00000 q^{36} -8.84213 q^{37} -2.91209 q^{38} +1.00000 q^{39} -2.09722 q^{40} -9.70721 q^{41} +0.0373018 q^{42} -10.8256 q^{43} -3.17762 q^{44} +2.09722 q^{45} -3.99261 q^{46} -5.29982 q^{47} +1.00000 q^{48} -6.99861 q^{49} +0.601670 q^{50} -2.38289 q^{51} +1.00000 q^{52} -10.7397 q^{53} -1.00000 q^{54} -6.66417 q^{55} +0.0373018 q^{56} +2.91209 q^{57} +2.46598 q^{58} +4.58591 q^{59} +2.09722 q^{60} -1.68161 q^{61} -0.760072 q^{62} -0.0373018 q^{63} +1.00000 q^{64} +2.09722 q^{65} +3.17762 q^{66} +7.20145 q^{67} -2.38289 q^{68} +3.99261 q^{69} +0.0782300 q^{70} -14.3856 q^{71} -1.00000 q^{72} +15.2846 q^{73} +8.84213 q^{74} -0.601670 q^{75} +2.91209 q^{76} +0.118531 q^{77} -1.00000 q^{78} +6.39400 q^{79} +2.09722 q^{80} +1.00000 q^{81} +9.70721 q^{82} -5.88671 q^{83} -0.0373018 q^{84} -4.99743 q^{85} +10.8256 q^{86} -2.46598 q^{87} +3.17762 q^{88} +2.63980 q^{89} -2.09722 q^{90} -0.0373018 q^{91} +3.99261 q^{92} +0.760072 q^{93} +5.29982 q^{94} +6.10728 q^{95} -1.00000 q^{96} -2.73678 q^{97} +6.99861 q^{98} -3.17762 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{2} + 12 q^{3} + 12 q^{4} - 4 q^{5} - 12 q^{6} - 12 q^{8} + 12 q^{9}+O(q^{10}) \) 12 * q - 12 * q^2 + 12 * q^3 + 12 * q^4 - 4 * q^5 - 12 * q^6 - 12 * q^8 + 12 * q^9	\( 12 q - 12 q^{2} + 12 q^{3} + 12 q^{4} - 4 q^{5} - 12 q^{6} - 12 q^{8} + 12 q^{9} + 4 q^{10} - 9 q^{11} + 12 q^{12} + 12 q^{13} - 4 q^{15} + 12 q^{16} - 20 q^{17} - 12 q^{18} + 4 q^{19} - 4 q^{20} + 9 q^{22} - 30 q^{23} - 12 q^{24} + 14 q^{25} - 12 q^{26} + 12 q^{27} - 29 q^{29} + 4 q^{30} + 6 q^{31} - 12 q^{32} - 9 q^{33} + 20 q^{34} - 22 q^{35} + 12 q^{36} + 7 q^{37} - 4 q^{38} + 12 q^{39} + 4 q^{40} - 8 q^{41} - 8 q^{43} - 9 q^{44} - 4 q^{45} + 30 q^{46} - 16 q^{47} + 12 q^{48} + 10 q^{49} - 14 q^{50} - 20 q^{51} + 12 q^{52} - 9 q^{53} - 12 q^{54} - 20 q^{55} + 4 q^{57} + 29 q^{58} - 29 q^{59} - 4 q^{60} - 26 q^{61} - 6 q^{62} + 12 q^{64} - 4 q^{65} + 9 q^{66} + 12 q^{67} - 20 q^{68} - 30 q^{69} + 22 q^{70} - 35 q^{71} - 12 q^{72} + 18 q^{73} - 7 q^{74} + 14 q^{75} + 4 q^{76} - 25 q^{77} - 12 q^{78} - 37 q^{79} - 4 q^{80} + 12 q^{81} + 8 q^{82} - 24 q^{83} - 17 q^{85} + 8 q^{86} - 29 q^{87} + 9 q^{88} + 15 q^{89} + 4 q^{90} - 30 q^{92} + 6 q^{93} + 16 q^{94} - 54 q^{95} - 12 q^{96} - 11 q^{97} - 10 q^{98} - 9 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 + 12 * q^3 + 12 * q^4 - 4 * q^5 - 12 * q^6 - 12 * q^8 + 12 * q^9 + 4 * q^10 - 9 * q^11 + 12 * q^12 + 12 * q^13 - 4 * q^15 + 12 * q^16 - 20 * q^17 - 12 * q^18 + 4 * q^19 - 4 * q^20 + 9 * q^22 - 30 * q^23 - 12 * q^24 + 14 * q^25 - 12 * q^26 + 12 * q^27 - 29 * q^29 + 4 * q^30 + 6 * q^31 - 12 * q^32 - 9 * q^33 + 20 * q^34 - 22 * q^35 + 12 * q^36 + 7 * q^37 - 4 * q^38 + 12 * q^39 + 4 * q^40 - 8 * q^41 - 8 * q^43 - 9 * q^44 - 4 * q^45 + 30 * q^46 - 16 * q^47 + 12 * q^48 + 10 * q^49 - 14 * q^50 - 20 * q^51 + 12 * q^52 - 9 * q^53 - 12 * q^54 - 20 * q^55 + 4 * q^57 + 29 * q^58 - 29 * q^59 - 4 * q^60 - 26 * q^61 - 6 * q^62 + 12 * q^64 - 4 * q^65 + 9 * q^66 + 12 * q^67 - 20 * q^68 - 30 * q^69 + 22 * q^70 - 35 * q^71 - 12 * q^72 + 18 * q^73 - 7 * q^74 + 14 * q^75 + 4 * q^76 - 25 * q^77 - 12 * q^78 - 37 * q^79 - 4 * q^80 + 12 * q^81 + 8 * q^82 - 24 * q^83 - 17 * q^85 + 8 * q^86 - 29 * q^87 + 9 * q^88 + 15 * q^89 + 4 * q^90 - 30 * q^92 + 6 * q^93 + 16 * q^94 - 54 * q^95 - 12 * q^96 - 11 * q^97 - 10 * q^98 - 9 * q^99

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