LMFDB - Embedded newform 6034.2.a.k.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6034,2,Mod(1,6034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6034, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6034 = 2 \cdot 7 \cdot 431 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6034.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:	$48.1817325796$
Analytic rank:	$1$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 3 x^{19} - 32 x^{18} + 106 x^{17} + 382 x^{16} - 1495 x^{15} - 1963 x^{14} + 10784 x^{13} + \cdots - 44 $ x^20 - 3x^19 - 32x^18 + 106x^17 + 382x^16 - 1495x^15 - 1963x^14 + 10784x^13 + 2170x^12 - 42069x^11 + 19553x^10 + 84697x^9 - 82713x^8 - 68589x^7 + 118845x^6 - 10051x^5 - 53572x^4 + 25598x^3 - 557x^2 - 1040*x - 44
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			1.5
Root			$-1.69612$ of defining polynomial
Character	$\chi$	$=$	6034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.69612 q^{3} +1.00000 q^{4} -1.00716 q^{5} +1.69612 q^{6} +1.00000 q^{7} -1.00000 q^{8} -0.123166 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.69612 q^{3} +1.00000 q^{4} -1.00716 q^{5} +1.69612 q^{6} +1.00000 q^{7} -1.00000 q^{8} -0.123166 q^{9} +1.00716 q^{10} -0.765021 q^{11} -1.69612 q^{12} -3.78326 q^{13} -1.00000 q^{14} +1.70827 q^{15} +1.00000 q^{16} +0.262983 q^{17} +0.123166 q^{18} +0.488369 q^{19} -1.00716 q^{20} -1.69612 q^{21} +0.765021 q^{22} -1.03090 q^{23} +1.69612 q^{24} -3.98563 q^{25} +3.78326 q^{26} +5.29727 q^{27} +1.00000 q^{28} +3.23318 q^{29} -1.70827 q^{30} +0.713407 q^{31} -1.00000 q^{32} +1.29757 q^{33} -0.262983 q^{34} -1.00716 q^{35} -0.123166 q^{36} +9.33354 q^{37} -0.488369 q^{38} +6.41687 q^{39} +1.00716 q^{40} +5.45437 q^{41} +1.69612 q^{42} -0.179634 q^{43} -0.765021 q^{44} +0.124048 q^{45} +1.03090 q^{46} +2.62744 q^{47} -1.69612 q^{48} +1.00000 q^{49} +3.98563 q^{50} -0.446052 q^{51} -3.78326 q^{52} -3.83076 q^{53} -5.29727 q^{54} +0.770499 q^{55} -1.00000 q^{56} -0.828335 q^{57} -3.23318 q^{58} +7.63020 q^{59} +1.70827 q^{60} -10.2499 q^{61} -0.713407 q^{62} -0.123166 q^{63} +1.00000 q^{64} +3.81035 q^{65} -1.29757 q^{66} +8.43254 q^{67} +0.262983 q^{68} +1.74853 q^{69} +1.00716 q^{70} -8.36834 q^{71} +0.123166 q^{72} -9.11165 q^{73} -9.33354 q^{74} +6.76012 q^{75} +0.488369 q^{76} -0.765021 q^{77} -6.41687 q^{78} -5.23176 q^{79} -1.00716 q^{80} -8.61533 q^{81} -5.45437 q^{82} -9.15873 q^{83} -1.69612 q^{84} -0.264866 q^{85} +0.179634 q^{86} -5.48387 q^{87} +0.765021 q^{88} +13.2023 q^{89} -0.124048 q^{90} -3.78326 q^{91} -1.03090 q^{92} -1.21003 q^{93} -2.62744 q^{94} -0.491866 q^{95} +1.69612 q^{96} +13.7320 q^{97} -1.00000 q^{98} +0.0942245 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 20 q^{2} + 3 q^{3} + 20 q^{4} - 3 q^{5} - 3 q^{6} + 20 q^{7} - 20 q^{8} + 13 q^{9}+O(q^{10}) $ 20 * q - 20 * q^2 + 3 * q^3 + 20 * q^4 - 3 * q^5 - 3 * q^6 + 20 * q^7 - 20 * q^8 + 13 * q^9	\( 20 q - 20 q^{2} + 3 q^{3} + 20 q^{4} - 3 q^{5} - 3 q^{6} + 20 q^{7} - 20 q^{8} + 13 q^{9} + 3 q^{10} - 8 q^{11} + 3 q^{12} - 4 q^{13} - 20 q^{14} - 25 q^{15} + 20 q^{16} + 9 q^{17} - 13 q^{18} - 14 q^{19} - 3 q^{20} + 3 q^{21} + 8 q^{22} - 23 q^{23} - 3 q^{24} + 31 q^{25} + 4 q^{26} - 21 q^{27} + 20 q^{28} - 48 q^{29} + 25 q^{30} - q^{31} - 20 q^{32} - 29 q^{33} - 9 q^{34} - 3 q^{35} + 13 q^{36} - q^{37} + 14 q^{38} - q^{39} + 3 q^{40} - 27 q^{41} - 3 q^{42} - 3 q^{43} - 8 q^{44} - 12 q^{45} + 23 q^{46} - 26 q^{47} + 3 q^{48} + 20 q^{49} - 31 q^{50} - 17 q^{51} - 4 q^{52} - 43 q^{53} + 21 q^{54} - 16 q^{55} - 20 q^{56} - 25 q^{57} + 48 q^{58} - 19 q^{59} - 25 q^{60} + 9 q^{61} + q^{62} + 13 q^{63} + 20 q^{64} - 87 q^{65} + 29 q^{66} + 32 q^{67} + 9 q^{68} - 23 q^{69} + 3 q^{70} - 63 q^{71} - 13 q^{72} + 2 q^{73} + q^{74} - 8 q^{75} - 14 q^{76} - 8 q^{77} + q^{78} - 51 q^{79} - 3 q^{80} + 4 q^{81} + 27 q^{82} - 24 q^{83} + 3 q^{84} + 31 q^{85} + 3 q^{86} - 33 q^{87} + 8 q^{88} - 35 q^{89} + 12 q^{90} - 4 q^{91} - 23 q^{92} + 17 q^{93} + 26 q^{94} - 30 q^{95} - 3 q^{96} + 5 q^{97} - 20 q^{98} - 31 q^{99}+O(q^{100}) \) 20 * q - 20 * q^2 + 3 * q^3 + 20 * q^4 - 3 * q^5 - 3 * q^6 + 20 * q^7 - 20 * q^8 + 13 * q^9 + 3 * q^10 - 8 * q^11 + 3 * q^12 - 4 * q^13 - 20 * q^14 - 25 * q^15 + 20 * q^16 + 9 * q^17 - 13 * q^18 - 14 * q^19 - 3 * q^20 + 3 * q^21 + 8 * q^22 - 23 * q^23 - 3 * q^24 + 31 * q^25 + 4 * q^26 - 21 * q^27 + 20 * q^28 - 48 * q^29 + 25 * q^30 - q^31 - 20 * q^32 - 29 * q^33 - 9 * q^34 - 3 * q^35 + 13 * q^36 - q^37 + 14 * q^38 - q^39 + 3 * q^40 - 27 * q^41 - 3 * q^42 - 3 * q^43 - 8 * q^44 - 12 * q^45 + 23 * q^46 - 26 * q^47 + 3 * q^48 + 20 * q^49 - 31 * q^50 - 17 * q^51 - 4 * q^52 - 43 * q^53 + 21 * q^54 - 16 * q^55 - 20 * q^56 - 25 * q^57 + 48 * q^58 - 19 * q^59 - 25 * q^60 + 9 * q^61 + q^62 + 13 * q^63 + 20 * q^64 - 87 * q^65 + 29 * q^66 + 32 * q^67 + 9 * q^68 - 23 * q^69 + 3 * q^70 - 63 * q^71 - 13 * q^72 + 2 * q^73 + q^74 - 8 * q^75 - 14 * q^76 - 8 * q^77 + q^78 - 51 * q^79 - 3 * q^80 + 4 * q^81 + 27 * q^82 - 24 * q^83 + 3 * q^84 + 31 * q^85 + 3 * q^86 - 33 * q^87 + 8 * q^88 - 35 * q^89 + 12 * q^90 - 4 * q^91 - 23 * q^92 + 17 * q^93 + 26 * q^94 - 30 * q^95 - 3 * q^96 + 5 * q^97 - 20 * q^98 - 31 * 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
$3$	−1.69612	−0.979257	−0.489629	−	0.871931i	$-0.662868\pi$
$3$	−1.69612	−0.979257	−0.489629	+	0.871931i	$0.662868\pi$
$4$	1.00000	0.500000
$5$	−1.00716	−0.450416	−0.225208	−	0.974311i	$-0.572306\pi$
$5$	−1.00716	−0.450416	−0.225208	+	0.974311i	$0.572306\pi$
$6$	1.69612	0.692439
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	−0.123166	−0.0410553
$10$	1.00716	0.318492
$11$	−0.765021	−0.230663	−0.115331	−	0.993327i	$-0.536793\pi$
$11$	−0.765021	−0.230663	−0.115331	+	0.993327i	$0.536793\pi$
$12$	−1.69612	−0.489629
$13$	−3.78326	−1.04929	−0.524644	−	0.851322i	$-0.675801\pi$
$13$	−3.78326	−1.04929	−0.524644	+	0.851322i	$0.675801\pi$
$14$	−1.00000	−0.267261
$15$	1.70827	0.441073
$16$	1.00000	0.250000
$17$	0.262983	0.0637828	0.0318914	−	0.999491i	$-0.489847\pi$
$17$	0.262983	0.0637828	0.0318914	+	0.999491i	$0.489847\pi$
$18$	0.123166	0.0290305
$19$	0.488369	0.112040	0.0560198	−	0.998430i	$-0.482159\pi$
$19$	0.488369	0.112040	0.0560198	+	0.998430i	$0.482159\pi$
$20$	−1.00716	−0.225208
$21$	−1.69612	−0.370124
$22$	0.765021	0.163103
$23$	−1.03090	−0.214957	−0.107478	−	0.994207i	$-0.534278\pi$
$23$	−1.03090	−0.214957	−0.107478	+	0.994207i	$0.534278\pi$
$24$	1.69612	0.346220
$25$	−3.98563	−0.797126
$26$	3.78326	0.741958
$27$	5.29727	1.01946
$28$	1.00000	0.188982
$29$	3.23318	0.600386	0.300193	−	0.953879i	$-0.402949\pi$
$29$	3.23318	0.600386	0.300193	+	0.953879i	$0.402949\pi$
$30$	−1.70827	−0.311886
$31$	0.713407	0.128132	0.0640659	−	0.997946i	$-0.479593\pi$
$31$	0.713407	0.128132	0.0640659	+	0.997946i	$0.479593\pi$
$32$	−1.00000	−0.176777
$33$	1.29757	0.225878
$34$	−0.262983	−0.0451012
$35$	−1.00716	−0.170241
$36$	−0.123166	−0.0205276
$37$	9.33354	1.53442	0.767212	−	0.641393i	$-0.221643\pi$
$37$	9.33354	1.53442	0.767212	+	0.641393i	$0.221643\pi$
$38$	−0.488369	−0.0792240
$39$	6.41687	1.02752
$40$	1.00716	0.159246
$41$	5.45437	0.851830	0.425915	−	0.904763i	$-0.359952\pi$
$41$	5.45437	0.851830	0.425915	+	0.904763i	$0.359952\pi$
$42$	1.69612	0.261718
$43$	−0.179634	−0.0273939	−0.0136970	−	0.999906i	$-0.504360\pi$
$43$	−0.179634	−0.0273939	−0.0136970	+	0.999906i	$0.504360\pi$
$44$	−0.765021	−0.115331
$45$	0.124048	0.0184919
$46$	1.03090	0.151997
$47$	2.62744	0.383252	0.191626	−	0.981468i	$-0.438624\pi$
$47$	2.62744	0.383252	0.191626	+	0.981468i	$0.438624\pi$
$48$	−1.69612	−0.244814
$49$	1.00000	0.142857
$50$	3.98563	0.563653
$51$	−0.446052	−0.0624598
$52$	−3.78326	−0.524644
$53$	−3.83076	−0.526196	−0.263098	−	0.964769i	$-0.584744\pi$
$53$	−3.83076	−0.526196	−0.263098	+	0.964769i	$0.584744\pi$
$54$	−5.29727	−0.720868
$55$	0.770499	0.103894
$56$	−1.00000	−0.133631
$57$	−0.828335	−0.109716
$58$	−3.23318	−0.424537
$59$	7.63020	0.993367	0.496684	−	0.867932i	$-0.334551\pi$
$59$	7.63020	0.993367	0.496684	+	0.867932i	$0.334551\pi$
$60$	1.70827	0.220536
$61$	−10.2499	−1.31236	−0.656180	−	0.754605i	$-0.727829\pi$
$61$	−10.2499	−1.31236	−0.656180	+	0.754605i	$0.727829\pi$
$62$	−0.713407	−0.0906028
$63$	−0.123166	−0.0155174
$64$	1.00000	0.125000
$65$	3.81035	0.472616
$66$	−1.29757	−0.159720
$67$	8.43254	1.03020	0.515099	−	0.857131i	$-0.327755\pi$
$67$	8.43254	1.03020	0.515099	+	0.857131i	$0.327755\pi$
$68$	0.262983	0.0318914
$69$	1.74853	0.210498
$70$	1.00716	0.120379
$71$	−8.36834	−0.993140	−0.496570	−	0.867997i	$-0.665407\pi$
$71$	−8.36834	−0.993140	−0.496570	+	0.867997i	$0.665407\pi$
$72$	0.123166	0.0145152
$73$	−9.11165	−1.06644	−0.533219	−	0.845977i	$-0.679018\pi$
$73$	−9.11165	−1.06644	−0.533219	+	0.845977i	$0.679018\pi$
$74$	−9.33354	−1.08500
$75$	6.76012	0.780591
$76$	0.488369	0.0560198
$77$	−0.765021	−0.0871823
$78$	−6.41687	−0.726568
$79$	−5.23176	−0.588619	−0.294310	−	0.955710i	$-0.595090\pi$
$79$	−5.23176	−0.588619	−0.294310	+	0.955710i	$0.595090\pi$
$80$	−1.00716	−0.112604
$81$	−8.61533	−0.957259
$82$	−5.45437	−0.602335
$83$	−9.15873	−1.00530	−0.502651	−	0.864490i	$-0.667642\pi$
$83$	−9.15873	−1.00530	−0.502651	+	0.864490i	$0.667642\pi$
$84$	−1.69612	−0.185062
$85$	−0.264866	−0.0287288
$86$	0.179634	0.0193704
$87$	−5.48387	−0.587932
$88$	0.765021	0.0815515
$89$	13.2023	1.39944	0.699722	−	0.714415i	$-0.253307\pi$
$89$	13.2023	1.39944	0.699722	+	0.714415i	$0.253307\pi$
$90$	−0.124048	−0.0130758
$91$	−3.78326	−0.396593
$92$	−1.03090	−0.107478
$93$	−1.21003	−0.125474
$94$	−2.62744	−0.271000
$95$	−0.491866	−0.0504644
$96$	1.69612	0.173110
$97$	13.7320	1.39428	0.697139	−	0.716936i	$-0.254456\pi$
$97$	13.7320	1.39428	0.697139	+	0.716936i	$0.254456\pi$
$98$	−1.00000	−0.101015
$99$	0.0942245	0.00946992
$100$	−3.98563	−0.398563
$101$	−4.22353	−0.420256	−0.210128	−	0.977674i	$-0.567388\pi$
$101$	−4.22353	−0.420256	−0.210128	+	0.977674i	$0.567388\pi$
$102$	0.446052	0.0441657
$103$	17.5557	1.72982	0.864910	−	0.501928i	$-0.167376\pi$
$103$	17.5557	1.72982	0.864910	+	0.501928i	$0.167376\pi$
$104$	3.78326	0.370979
$105$	1.70827	0.166710
$106$	3.83076	0.372077
$107$	−2.46352	−0.238158	−0.119079	−	0.992885i	$-0.537994\pi$
$107$	−2.46352	−0.238158	−0.119079	+	0.992885i	$0.537994\pi$
$108$	5.29727	0.509730
$109$	3.41702	0.327291	0.163646	−	0.986519i	$-0.447675\pi$
$109$	3.41702	0.327291	0.163646	+	0.986519i	$0.447675\pi$
$110$	−0.770499	−0.0734642
$111$	−15.8308	−1.50260
$112$	1.00000	0.0944911
$113$	−13.9521	−1.31250	−0.656250	−	0.754544i	$-0.727858\pi$
$113$	−13.9521	−1.31250	−0.656250	+	0.754544i	$0.727858\pi$
$114$	0.828335	0.0775806
$115$	1.03828	0.0968200
$116$	3.23318	0.300193
$117$	0.465968	0.0430788
$118$	−7.63020	−0.702417
$119$	0.262983	0.0241076
$120$	−1.70827	−0.155943
$121$	−10.4147	−0.946795
$122$	10.2499	0.927978
$123$	−9.25129	−0.834161
$124$	0.713407	0.0640659
$125$	9.04997	0.809454
$126$	0.123166	0.0109725
$127$	21.5814	1.91504	0.957518	−	0.288373i	$-0.0931143\pi$
$127$	21.5814	1.91504	0.957518	+	0.288373i	$0.0931143\pi$
$128$	−1.00000	−0.0883883
$129$	0.304682	0.0268257
$130$	−3.81035	−0.334190
$131$	−2.26728	−0.198093	−0.0990464	−	0.995083i	$-0.531579\pi$
$131$	−2.26728	−0.198093	−0.0990464	+	0.995083i	$0.531579\pi$
$132$	1.29757	0.112939
$133$	0.488369	0.0423470
$134$	−8.43254	−0.728460
$135$	−5.33520	−0.459181
$136$	−0.262983	−0.0225506
$137$	−3.66942	−0.313500	−0.156750	−	0.987638i	$-0.550102\pi$
$137$	−3.66942	−0.313500	−0.156750	+	0.987638i	$0.550102\pi$
$138$	−1.74853	−0.148845
$139$	6.09438	0.516918	0.258459	−	0.966022i	$-0.416785\pi$
$139$	6.09438	0.516918	0.258459	+	0.966022i	$0.416785\pi$
$140$	−1.00716	−0.0851206
$141$	−4.45646	−0.375302
$142$	8.36834	0.702256
$143$	2.89427	0.242031
$144$	−0.123166	−0.0102638
$145$	−3.25633	−0.270423
$146$	9.11165	0.754085
$147$	−1.69612	−0.139894
$148$	9.33354	0.767212
$149$	10.8494	0.888814	0.444407	−	0.895825i	$-0.353414\pi$
$149$	10.8494	0.888814	0.444407	+	0.895825i	$0.353414\pi$
$150$	−6.76012	−0.551961
$151$	−4.00942	−0.326282	−0.163141	−	0.986603i	$-0.552163\pi$
$151$	−4.00942	−0.326282	−0.163141	+	0.986603i	$0.552163\pi$
$152$	−0.488369	−0.0396120
$153$	−0.0323905	−0.00261862
$154$	0.765021	0.0616472
$155$	−0.718516	−0.0577126
$156$	6.41687	0.513761
$157$	0.416446	0.0332360	0.0166180	−	0.999862i	$-0.494710\pi$
$157$	0.416446	0.0332360	0.0166180	+	0.999862i	$0.494710\pi$
$158$	5.23176	0.416217
$159$	6.49745	0.515281
$160$	1.00716	0.0796230
$161$	−1.03090	−0.0812461
$162$	8.61533	0.676884
$163$	10.3971	0.814365	0.407183	−	0.913347i	$-0.366511\pi$
$163$	10.3971	0.814365	0.407183	+	0.913347i	$0.366511\pi$
$164$	5.45437	0.425915
$165$	−1.30686	−0.101739
$166$	9.15873	0.710856
$167$	−6.08017	−0.470498	−0.235249	−	0.971935i	$-0.575591\pi$
$167$	−6.08017	−0.470498	−0.235249	+	0.971935i	$0.575591\pi$
$168$	1.69612	0.130859
$169$	1.31305	0.101004
$170$	0.264866	0.0203143
$171$	−0.0601504	−0.00459982
$172$	−0.179634	−0.0136970
$173$	1.11500	0.0847719	0.0423860	−	0.999101i	$-0.486504\pi$
$173$	1.11500	0.0847719	0.0423860	+	0.999101i	$0.486504\pi$
$174$	5.48387	0.415731
$175$	−3.98563	−0.301285
$176$	−0.765021	−0.0576656
$177$	−12.9418	−0.972762
$178$	−13.2023	−0.989557
$179$	−15.6154	−1.16715	−0.583574	−	0.812060i	$-0.698346\pi$
$179$	−15.6154	−1.16715	−0.583574	+	0.812060i	$0.698346\pi$
$180$	0.124048	0.00924597
$181$	−16.6028	−1.23407	−0.617037	−	0.786934i	$-0.711667\pi$
$181$	−16.6028	−1.23407	−0.617037	+	0.786934i	$0.711667\pi$
$182$	3.78326	0.280434
$183$	17.3850	1.28514
$184$	1.03090	0.0759987
$185$	−9.40037	−0.691129
$186$	1.21003	0.0887235
$187$	−0.201188	−0.0147123
$188$	2.62744	0.191626
$189$	5.29727	0.385320
$190$	0.491866	0.0356837
$191$	−13.8828	−1.00452	−0.502262	−	0.864716i	$-0.667499\pi$
$191$	−13.8828	−1.00452	−0.502262	+	0.864716i	$0.667499\pi$
$192$	−1.69612	−0.122407
$193$	12.5178	0.901050	0.450525	−	0.892764i	$-0.351237\pi$
$193$	12.5178	0.901050	0.450525	+	0.892764i	$0.351237\pi$
$194$	−13.7320	−0.985903
$195$	−6.46282	−0.462812
$196$	1.00000	0.0714286
$197$	−8.54669	−0.608927	−0.304463	−	0.952524i	$-0.598477\pi$
$197$	−8.54669	−0.608927	−0.304463	+	0.952524i	$0.598477\pi$
$198$	−0.0942245	−0.00669624
$199$	−0.823227	−0.0583570	−0.0291785	−	0.999574i	$-0.509289\pi$
$199$	−0.823227	−0.0583570	−0.0291785	+	0.999574i	$0.509289\pi$
$200$	3.98563	0.281826
$201$	−14.3026	−1.00883
$202$	4.22353	0.297166
$203$	3.23318	0.226925
$204$	−0.446052	−0.0312299
$205$	−5.49343	−0.383678
$206$	−17.5557	−1.22317
$207$	0.126971	0.00882511
$208$	−3.78326	−0.262322
$209$	−0.373613	−0.0258433
$210$	−1.70827	−0.117882
$211$	14.4294	0.993360	0.496680	−	0.867934i	$-0.334552\pi$
$211$	14.4294	0.993360	0.496680	+	0.867934i	$0.334552\pi$
$212$	−3.83076	−0.263098
$213$	14.1937	0.972539
$214$	2.46352	0.168403
$215$	0.180920	0.0123387
$216$	−5.29727	−0.360434
$217$	0.713407	0.0484293
$218$	−3.41702	−0.231430
$219$	15.4545	1.04432
$220$	0.770499	0.0519470
$221$	−0.994933	−0.0669265
$222$	15.8308	1.06250
$223$	−1.61659	−0.108255	−0.0541273	−	0.998534i	$-0.517238\pi$
$223$	−1.61659	−0.108255	−0.0541273	+	0.998534i	$0.517238\pi$
$224$	−1.00000	−0.0668153
$225$	0.490893	0.0327262
$226$	13.9521	0.928077
$227$	18.7450	1.24415	0.622073	−	0.782959i	$-0.286291\pi$
$227$	18.7450	1.24415	0.622073	+	0.782959i	$0.286291\pi$
$228$	−0.828335	−0.0548578
$229$	11.6712	0.771257	0.385628	−	0.922654i	$-0.373985\pi$
$229$	11.6712	0.771257	0.385628	+	0.922654i	$0.373985\pi$
$230$	−1.03828	−0.0684621
$231$	1.29757	0.0853739
$232$	−3.23318	−0.212268
$233$	9.99235	0.654621	0.327310	−	0.944917i	$-0.393858\pi$
$233$	9.99235	0.654621	0.327310	+	0.944917i	$0.393858\pi$
$234$	−0.465968	−0.0304613
$235$	−2.64625	−0.172623
$236$	7.63020	0.496684
$237$	8.87372	0.576410
$238$	−0.262983	−0.0170467
$239$	−18.1837	−1.17621	−0.588104	−	0.808785i	$-0.700125\pi$
$239$	−18.1837	−1.17621	−0.588104	+	0.808785i	$0.700125\pi$
$240$	1.70827	0.110268
$241$	8.38467	0.540104	0.270052	−	0.962846i	$-0.412959\pi$
$241$	8.38467	0.540104	0.270052	+	0.962846i	$0.412959\pi$
$242$	10.4147	0.669485
$243$	−1.27916	−0.0820579
$244$	−10.2499	−0.656180
$245$	−1.00716	−0.0643451
$246$	9.25129	0.589841
$247$	−1.84763	−0.117562
$248$	−0.713407	−0.0453014
$249$	15.5343	0.984449
$250$	−9.04997	−0.572370
$251$	−27.6588	−1.74581	−0.872905	−	0.487890i	$-0.837767\pi$
$251$	−27.6588	−1.74581	−0.872905	+	0.487890i	$0.837767\pi$
$252$	−0.123166	−0.00775872
$253$	0.788658	0.0495825
$254$	−21.5814	−1.35414
$255$	0.449246	0.0281329
$256$	1.00000	0.0625000
$257$	−3.87250	−0.241560	−0.120780	−	0.992679i	$-0.538540\pi$
$257$	−3.87250	−0.241560	−0.120780	+	0.992679i	$0.538540\pi$
$258$	−0.304682	−0.0189686
$259$	9.33354	0.579958
$260$	3.81035	0.236308
$261$	−0.398217	−0.0246490
$262$	2.26728	0.140073
$263$	−27.0269	−1.66655	−0.833276	−	0.552857i	$-0.813537\pi$
$263$	−27.0269	−1.66655	−0.833276	+	0.552857i	$0.813537\pi$
$264$	−1.29757	−0.0798599
$265$	3.85819	0.237007
$266$	−0.488369	−0.0299438
$267$	−22.3928	−1.37042
$268$	8.43254	0.515099
$269$	−3.15264	−0.192220	−0.0961099	−	0.995371i	$-0.530640\pi$
$269$	−3.15264	−0.192220	−0.0961099	+	0.995371i	$0.530640\pi$
$270$	5.33520	0.324690
$271$	−7.44017	−0.451958	−0.225979	−	0.974132i	$-0.572558\pi$
$271$	−7.44017	−0.451958	−0.225979	+	0.974132i	$0.572558\pi$
$272$	0.262983	0.0159457
$273$	6.41687	0.388367
$274$	3.66942	0.221678
$275$	3.04909	0.183867
$276$	1.74853	0.105249
$277$	−27.0486	−1.62519	−0.812596	−	0.582827i	$-0.801947\pi$
$277$	−27.0486	−1.62519	−0.812596	+	0.582827i	$0.801947\pi$
$278$	−6.09438	−0.365516
$279$	−0.0878674	−0.00526049
$280$	1.00716	0.0601893
$281$	3.64810	0.217627	0.108814	−	0.994062i	$-0.465295\pi$
$281$	3.64810	0.217627	0.108814	+	0.994062i	$0.465295\pi$
$282$	4.45646	0.265379
$283$	4.01869	0.238886	0.119443	−	0.992841i	$-0.461889\pi$
$283$	4.01869	0.238886	0.119443	+	0.992841i	$0.461889\pi$
$284$	−8.36834	−0.496570
$285$	0.834266	0.0494176
$286$	−2.89427	−0.171142
$287$	5.45437	0.321961
$288$	0.123166	0.00725762
$289$	−16.9308	−0.995932
$290$	3.25633	0.191218
$291$	−23.2912	−1.36536
$292$	−9.11165	−0.533219
$293$	9.68235	0.565649	0.282824	−	0.959172i	$-0.408729\pi$
$293$	9.68235	0.565649	0.282824	+	0.959172i	$0.408729\pi$
$294$	1.69612	0.0989199
$295$	−7.68483	−0.447428
$296$	−9.33354	−0.542501
$297$	−4.05253	−0.235152
$298$	−10.8494	−0.628486
$299$	3.90015	0.225551
$300$	6.76012	0.390296
$301$	−0.179634	−0.0103539
$302$	4.00942	0.230716
$303$	7.16362	0.411539
$304$	0.488369	0.0280099
$305$	10.3232	0.591108
$306$	0.0323905	0.00185164
$307$	−9.16379	−0.523005	−0.261503	−	0.965203i	$-0.584218\pi$
$307$	−9.16379	−0.523005	−0.261503	+	0.965203i	$0.584218\pi$
$308$	−0.765021	−0.0435911
$309$	−29.7767	−1.69394
$310$	0.718516	0.0408089
$311$	7.43371	0.421527	0.210764	−	0.977537i	$-0.432405\pi$
$311$	7.43371	0.421527	0.210764	+	0.977537i	$0.432405\pi$
$312$	−6.41687	−0.363284
$313$	20.6097	1.16493	0.582465	−	0.812856i	$-0.302088\pi$
$313$	20.6097	1.16493	0.582465	+	0.812856i	$0.302088\pi$
$314$	−0.416446	−0.0235014
$315$	0.124048	0.00698930
$316$	−5.23176	−0.294310
$317$	0.398491	0.0223815	0.0111908	−	0.999937i	$-0.496438\pi$
$317$	0.398491	0.0223815	0.0111908	+	0.999937i	$0.496438\pi$
$318$	−6.49745	−0.364359
$319$	−2.47345	−0.138487
$320$	−1.00716	−0.0563020
$321$	4.17844	0.233218
$322$	1.03090	0.0574496
$323$	0.128433	0.00714620
$324$	−8.61533	−0.478630
$325$	15.0787	0.836414
$326$	−10.3971	−0.575843
$327$	−5.79569	−0.320503
$328$	−5.45437	−0.301167
$329$	2.62744	0.144855
$330$	1.30686	0.0719404
$331$	32.1961	1.76966	0.884829	−	0.465917i	$-0.154275\pi$
$331$	32.1961	1.76966	0.884829	+	0.465917i	$0.154275\pi$
$332$	−9.15873	−0.502651
$333$	−1.14957	−0.0629962
$334$	6.08017	0.332692
$335$	−8.49292	−0.464018
$336$	−1.69612	−0.0925311
$337$	18.5565	1.01084	0.505419	−	0.862874i	$-0.331338\pi$
$337$	18.5565	1.01084	0.505419	+	0.862874i	$0.331338\pi$
$338$	−1.31305	−0.0714205
$339$	23.6644	1.28527
$340$	−0.264866	−0.0143644
$341$	−0.545772	−0.0295552
$342$	0.0601504	0.00325256
$343$	1.00000	0.0539949
$344$	0.179634	0.00968522
$345$	−1.76105	−0.0948116
$346$	−1.11500	−0.0599428
$347$	−18.9346	−1.01646	−0.508230	−	0.861221i	$-0.669700\pi$
$347$	−18.9346	−1.01646	−0.508230	+	0.861221i	$0.669700\pi$
$348$	−5.48387	−0.293966
$349$	17.8225	0.954017	0.477009	−	0.878899i	$-0.341721\pi$
$349$	17.8225	0.954017	0.477009	+	0.878899i	$0.341721\pi$
$350$	3.98563	0.213041
$351$	−20.0410	−1.06971
$352$	0.765021	0.0407758
$353$	−20.5658	−1.09460	−0.547302	−	0.836935i	$-0.684345\pi$
$353$	−20.5658	−1.09460	−0.547302	+	0.836935i	$0.684345\pi$
$354$	12.9418	0.687847
$355$	8.42827	0.447326
$356$	13.2023	0.699722
$357$	−0.446052	−0.0236076
$358$	15.6154	0.825298
$359$	16.2767	0.859054	0.429527	−	0.903054i	$-0.358680\pi$
$359$	16.2767	0.859054	0.429527	+	0.903054i	$0.358680\pi$
$360$	−0.124048	−0.00653789
$361$	−18.7615	−0.987447
$362$	16.6028	0.872622
$363$	17.6647	0.927156
$364$	−3.78326	−0.198297
$365$	9.17689	0.480340
$366$	−17.3850	−0.908730
$367$	−4.33761	−0.226422	−0.113211	−	0.993571i	$-0.536114\pi$
$367$	−4.33761	−0.226422	−0.113211	+	0.993571i	$0.536114\pi$
$368$	−1.03090	−0.0537392
$369$	−0.671793	−0.0349721
$370$	9.40037	0.488702
$371$	−3.83076	−0.198883
$372$	−1.21003	−0.0627370
$373$	8.02193	0.415360	0.207680	−	0.978197i	$-0.433409\pi$
$373$	8.02193	0.415360	0.207680	+	0.978197i	$0.433409\pi$
$374$	0.201188	0.0104032
$375$	−15.3499	−0.792663
$376$	−2.62744	−0.135500
$377$	−12.2319	−0.629977
$378$	−5.29727	−0.272462
$379$	−27.2428	−1.39937	−0.699685	−	0.714452i	$-0.746676\pi$
$379$	−27.2428	−1.39937	−0.699685	+	0.714452i	$0.746676\pi$
$380$	−0.491866	−0.0252322
$381$	−36.6047	−1.87531
$382$	13.8828	0.710306
$383$	−10.5865	−0.540943	−0.270472	−	0.962728i	$-0.587180\pi$
$383$	−10.5865	−0.540943	−0.270472	+	0.962728i	$0.587180\pi$
$384$	1.69612	0.0865549
$385$	0.770499	0.0392683
$386$	−12.5178	−0.637139
$387$	0.0221248	0.00112467
$388$	13.7320	0.697139
$389$	−37.6594	−1.90941	−0.954704	−	0.297559i	$-0.903828\pi$
$389$	−37.6594	−1.90941	−0.954704	+	0.297559i	$0.903828\pi$
$390$	6.46282	0.327258
$391$	−0.271109	−0.0137105
$392$	−1.00000	−0.0505076
$393$	3.84558	0.193984
$394$	8.54669	0.430576
$395$	5.26922	0.265123
$396$	0.0942245	0.00473496
$397$	−9.68994	−0.486324	−0.243162	−	0.969986i	$-0.578185\pi$
$397$	−9.68994	−0.486324	−0.243162	+	0.969986i	$0.578185\pi$
$398$	0.823227	0.0412646
$399$	−0.828335	−0.0414686
$400$	−3.98563	−0.199281
$401$	−25.1086	−1.25386	−0.626931	−	0.779075i	$-0.715689\pi$
$401$	−25.1086	−1.25386	−0.626931	+	0.779075i	$0.715689\pi$
$402$	14.3026	0.713350
$403$	−2.69901	−0.134447
$404$	−4.22353	−0.210128
$405$	8.67702	0.431165
$406$	−3.23318	−0.160460
$407$	−7.14036	−0.353934
$408$	0.446052	0.0220829
$409$	−25.1004	−1.24113	−0.620567	−	0.784153i	$-0.713097\pi$
$409$	−25.1004	−1.24113	−0.620567	+	0.784153i	$0.713097\pi$
$410$	5.49343	0.271301
$411$	6.22380	0.306997
$412$	17.5557	0.864910
$413$	7.63020	0.375458
$414$	−0.126971	−0.00624030
$415$	9.22431	0.452804
$416$	3.78326	0.185490
$417$	−10.3368	−0.506196
$418$	0.373613	0.0182740
$419$	−3.34872	−0.163596	−0.0817979	−	0.996649i	$-0.526066\pi$
$419$	−3.34872	−0.163596	−0.0817979	+	0.996649i	$0.526066\pi$
$420$	1.70827	0.0833549
$421$	−0.691299	−0.0336919	−0.0168459	−	0.999858i	$-0.505362\pi$
$421$	−0.691299	−0.0336919	−0.0168459	+	0.999858i	$0.505362\pi$
$422$	−14.4294	−0.702411
$423$	−0.323611	−0.0157345
$424$	3.83076	0.186038
$425$	−1.04815	−0.0508429
$426$	−14.1937	−0.687689
$427$	−10.2499	−0.496025
$428$	−2.46352	−0.119079
$429$	−4.90905	−0.237011
$430$	−0.180920	−0.00872475
$431$	1.00000	0.0481683
$431$	1.00000	0.0481683
$432$	5.29727	0.254865
$433$	−2.95272	−0.141898	−0.0709492	−	0.997480i	$-0.522603\pi$
$433$	−2.95272	−0.141898	−0.0709492	+	0.997480i	$0.522603\pi$
$434$	−0.713407	−0.0342447
$435$	5.52313	0.264814
$436$	3.41702	0.163646
$437$	−0.503458	−0.0240837
$438$	−15.4545	−0.738444
$439$	1.90523	0.0909317	0.0454659	−	0.998966i	$-0.485523\pi$
$439$	1.90523	0.0909317	0.0454659	+	0.998966i	$0.485523\pi$
$440$	−0.770499	−0.0367321
$441$	−0.123166	−0.00586504
$442$	0.994933	0.0473242
$443$	−5.54518	−0.263459	−0.131730	−	0.991286i	$-0.542053\pi$
$443$	−5.54518	−0.263459	−0.131730	+	0.991286i	$0.542053\pi$
$444$	−15.8308	−0.751298
$445$	−13.2969	−0.630332
$446$	1.61659	0.0765475
$447$	−18.4018	−0.870377
$448$	1.00000	0.0472456
$449$	−15.5505	−0.733874	−0.366937	−	0.930246i	$-0.619594\pi$
$449$	−15.5505	−0.733874	−0.366937	+	0.930246i	$0.619594\pi$
$450$	−0.490893	−0.0231409
$451$	−4.17271	−0.196485
$452$	−13.9521	−0.656250
$453$	6.80047	0.319514
$454$	−18.7450	−0.879744
$455$	3.81035	0.178632
$456$	0.828335	0.0387903
$457$	8.95655	0.418970	0.209485	−	0.977812i	$-0.432821\pi$
$457$	8.95655	0.418970	0.209485	+	0.977812i	$0.432821\pi$
$458$	−11.6712	−0.545361
$459$	1.39309	0.0650241
$460$	1.03828	0.0484100
$461$	21.6395	1.00785	0.503926	−	0.863747i	$-0.331888\pi$
$461$	21.6395	1.00785	0.503926	+	0.863747i	$0.331888\pi$
$462$	−1.29757	−0.0603684
$463$	−37.0190	−1.72042	−0.860210	−	0.509940i	$-0.829668\pi$
$463$	−37.0190	−1.72042	−0.860210	+	0.509940i	$0.829668\pi$
$464$	3.23318	0.150096
$465$	1.21869	0.0565155
$466$	−9.99235	−0.462887
$467$	−36.1285	−1.67183	−0.835913	−	0.548862i	$-0.815061\pi$
$467$	−36.1285	−1.67183	−0.835913	+	0.548862i	$0.815061\pi$
$468$	0.465968	0.0215394
$469$	8.43254	0.389378
$470$	2.64625	0.122063
$471$	−0.706343	−0.0325466
$472$	−7.63020	−0.351208
$473$	0.137424	0.00631876
$474$	−8.87372	−0.407583
$475$	−1.94646	−0.0893096
$476$	0.262983	0.0120538
$477$	0.471819	0.0216031
$478$	18.1837	0.831704
$479$	−32.3147	−1.47650	−0.738248	−	0.674530i	$-0.764347\pi$
$479$	−32.3147	−1.47650	−0.738248	+	0.674530i	$0.764347\pi$
$480$	−1.70827	−0.0779714
$481$	−35.3112	−1.61005
$482$	−8.38467	−0.381911
$483$	1.74853	0.0795608
$484$	−10.4147	−0.473397
$485$	−13.8304	−0.628005
$486$	1.27916	0.0580237
$487$	−30.0975	−1.36385	−0.681924	−	0.731423i	$-0.738856\pi$
$487$	−30.0975	−1.36385	−0.681924	+	0.731423i	$0.738856\pi$
$488$	10.2499	0.463989
$489$	−17.6348	−0.797473
$490$	1.00716	0.0454989
$491$	−1.26754	−0.0572031	−0.0286016	−	0.999591i	$-0.509105\pi$
$491$	−1.26754	−0.0572031	−0.0286016	+	0.999591i	$0.509105\pi$
$492$	−9.25129	−0.417080
$493$	0.850271	0.0382943
$494$	1.84763	0.0831287
$495$	−0.0948992	−0.00426540
$496$	0.713407	0.0320329
$497$	−8.36834	−0.375372
$498$	−15.5343	−0.696111
$499$	15.4625	0.692197	0.346099	−	0.938198i	$-0.387506\pi$
$499$	15.4625	0.692197	0.346099	+	0.938198i	$0.387506\pi$
$500$	9.04997	0.404727
$501$	10.3127	0.460738
$502$	27.6588	1.23447
$503$	7.25558	0.323510	0.161755	−	0.986831i	$-0.448284\pi$
$503$	7.25558	0.323510	0.161755	+	0.986831i	$0.448284\pi$
$504$	0.123166	0.00548624
$505$	4.25377	0.189290
$506$	−0.788658	−0.0350601
$507$	−2.22709	−0.0989087
$508$	21.5814	0.957518
$509$	40.1608	1.78010	0.890049	−	0.455866i	$-0.150670\pi$
$509$	40.1608	1.78010	0.890049	+	0.455866i	$0.150670\pi$
$510$	−0.449246	−0.0198929
$511$	−9.11165	−0.403076
$512$	−1.00000	−0.0441942
$513$	2.58703	0.114220
$514$	3.87250	0.170809
$515$	−17.6815	−0.779138
$516$	0.304682	0.0134129
$517$	−2.01005	−0.0884018
$518$	−9.33354	−0.410092
$519$	−1.89118	−0.0830135
$520$	−3.81035	−0.167095
$521$	2.71775	0.119067	0.0595335	−	0.998226i	$-0.481039\pi$
$521$	2.71775	0.119067	0.0595335	+	0.998226i	$0.481039\pi$
$522$	0.398217	0.0174295
$523$	−30.9554	−1.35358	−0.676792	−	0.736174i	$-0.736631\pi$
$523$	−30.9554	−1.35358	−0.676792	+	0.736174i	$0.736631\pi$
$524$	−2.26728	−0.0990464
$525$	6.76012	0.295036
$526$	27.0269	1.17843
$527$	0.187614	0.00817260
$528$	1.29757	0.0564695
$529$	−21.9373	−0.953794
$530$	−3.85819	−0.167589
$531$	−0.939780	−0.0407830
$532$	0.488369	0.0211735
$533$	−20.6353	−0.893814
$534$	22.3928	0.969031
$535$	2.48116	0.107270
$536$	−8.43254	−0.364230
$537$	26.4856	1.14294
$538$	3.15264	0.135920
$539$	−0.765021	−0.0329518
$540$	−5.33520	−0.229591
$541$	1.15075	0.0494747	0.0247373	−	0.999694i	$-0.492125\pi$
$541$	1.15075	0.0494747	0.0247373	+	0.999694i	$0.492125\pi$
$542$	7.44017	0.319583
$543$	28.1603	1.20848
$544$	−0.262983	−0.0112753
$545$	−3.44149	−0.147417
$546$	−6.41687	−0.274617
$547$	21.0778	0.901224	0.450612	−	0.892720i	$-0.351206\pi$
$547$	21.0778	0.901224	0.450612	+	0.892720i	$0.351206\pi$
$548$	−3.66942	−0.156750
$549$	1.26243	0.0538793
$550$	−3.04909	−0.130014
$551$	1.57898	0.0672670
$552$	−1.74853	−0.0744223
$553$	−5.23176	−0.222477
$554$	27.0486	1.14918
$555$	15.9442	0.676793
$556$	6.09438	0.258459
$557$	−16.3971	−0.694768	−0.347384	−	0.937723i	$-0.612930\pi$
$557$	−16.3971	−0.694768	−0.347384	+	0.937723i	$0.612930\pi$
$558$	0.0878674	0.00371973
$559$	0.679602	0.0287441
$560$	−1.00716	−0.0425603
$561$	0.341239	0.0144071
$562$	−3.64810	−0.153886
$563$	−18.3022	−0.771345	−0.385673	−	0.922636i	$-0.626031\pi$
$563$	−18.3022	−0.771345	−0.385673	+	0.922636i	$0.626031\pi$
$564$	−4.45646	−0.187651
$565$	14.0520	0.591170
$566$	−4.01869	−0.168918
$567$	−8.61533	−0.361810
$568$	8.36834	0.351128
$569$	−27.3731	−1.14754	−0.573770	−	0.819016i	$-0.694520\pi$
$569$	−27.3731	−1.14754	−0.573770	+	0.819016i	$0.694520\pi$
$570$	−0.834266	−0.0349435
$571$	−34.8473	−1.45831	−0.729157	−	0.684346i	$-0.760088\pi$
$571$	−34.8473	−1.45831	−0.729157	+	0.684346i	$0.760088\pi$
$572$	2.89427	0.121016
$573$	23.5469	0.983687
$574$	−5.45437	−0.227661
$575$	4.10877	0.171348
$576$	−0.123166	−0.00513191
$577$	45.8735	1.90974	0.954869	−	0.297027i	$-0.0959951\pi$
$577$	45.8735	1.90974	0.954869	+	0.297027i	$0.0959951\pi$
$578$	16.9308	0.704230
$579$	−21.2317	−0.882360
$580$	−3.25633	−0.135212
$581$	−9.15873	−0.379968
$582$	23.2912	0.965453
$583$	2.93062	0.121374
$584$	9.11165	0.377043
$585$	−0.469305	−0.0194034
$586$	−9.68235	−0.399974
$587$	−26.7409	−1.10371	−0.551857	−	0.833939i	$-0.686080\pi$
$587$	−26.7409	−1.10371	−0.551857	+	0.833939i	$0.686080\pi$
$588$	−1.69612	−0.0699469
$589$	0.348406	0.0143558
$590$	7.68483	0.316380
$591$	14.4962	0.596296
$592$	9.33354	0.383606
$593$	19.5211	0.801637	0.400818	−	0.916158i	$-0.368726\pi$
$593$	19.5211	0.801637	0.400818	+	0.916158i	$0.368726\pi$
$594$	4.05253	0.166277
$595$	−0.264866	−0.0108585
$596$	10.8494	0.444407
$597$	1.39629	0.0571465
$598$	−3.90015	−0.159489
$599$	−26.9102	−1.09952	−0.549760	−	0.835323i	$-0.685281\pi$
$599$	−26.9102	−1.09952	−0.549760	+	0.835323i	$0.685281\pi$
$600$	−6.76012	−0.275981
$601$	−10.9074	−0.444921	−0.222461	−	0.974942i	$-0.571409\pi$
$601$	−10.9074	−0.444921	−0.222461	+	0.974942i	$0.571409\pi$
$602$	0.179634	0.00732134
$603$	−1.03860	−0.0422951
$604$	−4.00942	−0.163141
$605$	10.4893	0.426451
$606$	−7.16362	−0.291002
$607$	−27.2333	−1.10537	−0.552683	−	0.833391i	$-0.686396\pi$
$607$	−27.2333	−1.10537	−0.552683	+	0.833391i	$0.686396\pi$
$608$	−0.488369	−0.0198060
$609$	−5.48387	−0.222217
$610$	−10.3232	−0.417976
$611$	−9.94029	−0.402141
$612$	−0.0323905	−0.00130931
$613$	−19.0573	−0.769716	−0.384858	−	0.922976i	$-0.625750\pi$
$613$	−19.0573	−0.769716	−0.384858	+	0.922976i	$0.625750\pi$
$614$	9.16379	0.369820
$615$	9.31753	0.375719
$616$	0.765021	0.0308236
$617$	27.9539	1.12538	0.562692	−	0.826667i	$-0.309766\pi$
$617$	27.9539	1.12538	0.562692	+	0.826667i	$0.309766\pi$
$618$	29.7767	1.19779
$619$	0.277481	0.0111529	0.00557646	−	0.999984i	$-0.498225\pi$
$619$	0.277481	0.0111529	0.00557646	+	0.999984i	$0.498225\pi$
$620$	−0.718516	−0.0288563
$621$	−5.46094	−0.219140
$622$	−7.43371	−0.298065
$623$	13.2023	0.528940
$624$	6.41687	0.256881
$625$	10.8134	0.432535
$626$	−20.6097	−0.823730
$627$	0.633694	0.0253073
$628$	0.416446	0.0166180
$629$	2.45456	0.0978699
$630$	−0.124048	−0.00494218
$631$	−28.9385	−1.15202	−0.576012	−	0.817442i	$-0.695392\pi$
$631$	−28.9385	−1.15202	−0.576012	+	0.817442i	$0.695392\pi$
$632$	5.23176	0.208108
$633$	−24.4740	−0.972755
$634$	−0.398491	−0.0158261
$635$	−21.7359	−0.862563
$636$	6.49745	0.257641
$637$	−3.78326	−0.149898
$638$	2.47345	0.0979248
$639$	1.03069	0.0407736
$640$	1.00716	0.0398115
$641$	−26.1801	−1.03405	−0.517025	−	0.855970i	$-0.672961\pi$
$641$	−26.1801	−1.03405	−0.517025	+	0.855970i	$0.672961\pi$
$642$	−4.17844	−0.164910
$643$	−23.9965	−0.946331	−0.473166	−	0.880973i	$-0.656889\pi$
$643$	−23.9965	−0.946331	−0.473166	+	0.880973i	$0.656889\pi$
$644$	−1.03090	−0.0406230
$645$	−0.306863	−0.0120827
$646$	−0.128433	−0.00505313
$647$	−18.7646	−0.737712	−0.368856	−	0.929487i	$-0.620250\pi$
$647$	−18.7646	−0.737712	−0.368856	+	0.929487i	$0.620250\pi$
$648$	8.61533	0.338442
$649$	−5.83727	−0.229133
$650$	−15.0787	−0.591434
$651$	−1.21003	−0.0474247
$652$	10.3971	0.407183
$653$	−1.79515	−0.0702495	−0.0351248	−	0.999383i	$-0.511183\pi$
$653$	−1.79515	−0.0702495	−0.0351248	+	0.999383i	$0.511183\pi$
$654$	5.79569	0.226630
$655$	2.28351	0.0892242
$656$	5.45437	0.212958
$657$	1.12224	0.0437829
$658$	−2.62744	−0.102428
$659$	41.7698	1.62712	0.813561	−	0.581480i	$-0.197526\pi$
$659$	41.7698	1.62712	0.813561	+	0.581480i	$0.197526\pi$
$660$	−1.30686	−0.0508695
$661$	34.1692	1.32903	0.664513	−	0.747277i	$-0.268639\pi$
$661$	34.1692	1.32903	0.664513	+	0.747277i	$0.268639\pi$
$662$	−32.1961	−1.25134
$663$	1.68753	0.0655382
$664$	9.15873	0.355428
$665$	−0.491866	−0.0190738
$666$	1.14957	0.0445451
$667$	−3.33307	−0.129057
$668$	−6.08017	−0.235249
$669$	2.74193	0.106009
$670$	8.49292	0.328110
$671$	7.84136	0.302712
$672$	1.69612	0.0654294
$673$	3.11730	0.120163	0.0600815	−	0.998193i	$-0.480864\pi$
$673$	3.11730	0.120163	0.0600815	+	0.998193i	$0.480864\pi$
$674$	−18.5565	−0.714770
$675$	−21.1130	−0.812638
$676$	1.31305	0.0505019
$677$	−17.9072	−0.688231	−0.344115	−	0.938927i	$-0.611821\pi$
$677$	−17.9072	−0.688231	−0.344115	+	0.938927i	$0.611821\pi$
$678$	−23.6644	−0.908826
$679$	13.7320	0.526988
$680$	0.264866	0.0101572
$681$	−31.7938	−1.21834
$682$	0.545772	0.0208987
$683$	−42.0001	−1.60709	−0.803544	−	0.595245i	$-0.797055\pi$
$683$	−42.0001	−1.60709	−0.803544	+	0.595245i	$0.797055\pi$
$684$	−0.0601504	−0.00229991
$685$	3.69570	0.141205
$686$	−1.00000	−0.0381802
$687$	−19.7958	−0.755259
$688$	−0.179634	−0.00684848
$689$	14.4928	0.552131
$690$	1.76105	0.0670420
$691$	25.2823	0.961783	0.480891	−	0.876780i	$-0.340313\pi$
$691$	25.2823	0.961783	0.480891	+	0.876780i	$0.340313\pi$
$692$	1.11500	0.0423860
$693$	0.0942245	0.00357929
$694$	18.9346	0.718746
$695$	−6.13801	−0.232828
$696$	5.48387	0.207865
$697$	1.43441	0.0543321
$698$	−17.8225	−0.674592
$699$	−16.9483	−0.641042
$700$	−3.98563	−0.150643
$701$	6.78864	0.256403	0.128202	−	0.991748i	$-0.459080\pi$
$701$	6.78864	0.256403	0.128202	+	0.991748i	$0.459080\pi$
$702$	20.0410	0.756397
$703$	4.55822	0.171916
$704$	−0.765021	−0.0288328
$705$	4.48837	0.169042
$706$	20.5658	0.774003
$707$	−4.22353	−0.158842
$708$	−12.9418	−0.486381
$709$	4.20490	0.157918	0.0789591	−	0.996878i	$-0.474840\pi$
$709$	4.20490	0.157918	0.0789591	+	0.996878i	$0.474840\pi$
$710$	−8.42827	−0.316307
$711$	0.644375	0.0241659
$712$	−13.2023	−0.494778
$713$	−0.735450	−0.0275428
$714$	0.446052	0.0166931
$715$	−2.91500	−0.109015
$716$	−15.6154	−0.583574
$717$	30.8418	1.15181
$718$	−16.2767	−0.607443
$719$	−37.2999	−1.39105	−0.695526	−	0.718501i	$-0.744829\pi$
$719$	−37.2999	−1.39105	−0.695526	+	0.718501i	$0.744829\pi$
$720$	0.124048	0.00462299
$721$	17.5557	0.653810
$722$	18.7615	0.698231
$723$	−14.2214	−0.528901
$724$	−16.6028	−0.617037
$725$	−12.8862	−0.478583
$726$	−17.6647	−0.655598
$727$	41.7835	1.54967	0.774833	−	0.632166i	$-0.217834\pi$
$727$	41.7835	1.54967	0.774833	+	0.632166i	$0.217834\pi$
$728$	3.78326	0.140217
$729$	28.0156	1.03762
$730$	−9.17689	−0.339652
$731$	−0.0472407	−0.00174726
$732$	17.3850	0.642569
$733$	47.7701	1.76443	0.882215	−	0.470846i	$-0.156051\pi$
$733$	47.7701	1.76443	0.882215	+	0.470846i	$0.156051\pi$
$734$	4.33761	0.160104
$735$	1.70827	0.0630104
$736$	1.03090	0.0379994
$737$	−6.45107	−0.237628
$738$	0.671793	0.0247290
$739$	−27.8388	−1.02407	−0.512033	−	0.858965i	$-0.671108\pi$
$739$	−27.8388	−1.02407	−0.512033	+	0.858965i	$0.671108\pi$
$740$	−9.40037	−0.345565
$741$	3.13380	0.115123
$742$	3.83076	0.140632
$743$	31.0995	1.14093	0.570464	−	0.821322i	$-0.306763\pi$
$743$	31.0995	1.14093	0.570464	+	0.821322i	$0.306763\pi$
$744$	1.21003	0.0443617
$745$	−10.9270	−0.400336
$746$	−8.02193	−0.293704
$747$	1.12804	0.0412729
$748$	−0.201188	−0.00735615
$749$	−2.46352	−0.0900152
$750$	15.3499	0.560498
$751$	−14.2671	−0.520615	−0.260307	−	0.965526i	$-0.583824\pi$
$751$	−14.2671	−0.520615	−0.260307	+	0.965526i	$0.583824\pi$
$752$	2.62744	0.0958129
$753$	46.9128	1.70960
$754$	12.2319	0.445461
$755$	4.03813	0.146963
$756$	5.29727	0.192660
$757$	37.5275	1.36396	0.681980	−	0.731371i	$-0.261119\pi$
$757$	37.5275	1.36396	0.681980	+	0.731371i	$0.261119\pi$
$758$	27.2428	0.989503
$759$	−1.33766	−0.0485540
$760$	0.491866	0.0178419
$761$	−20.7614	−0.752600	−0.376300	−	0.926498i	$-0.622804\pi$
$761$	−20.7614	−0.752600	−0.376300	+	0.926498i	$0.622804\pi$
$762$	36.6047	1.32605
$763$	3.41702	0.123705
$764$	−13.8828	−0.502262
$765$	0.0326225	0.00117947
$766$	10.5865	0.382505
$767$	−28.8670	−1.04233
$768$	−1.69612	−0.0612036
$769$	−39.9247	−1.43972	−0.719860	−	0.694119i	$-0.755794\pi$
$769$	−39.9247	−1.43972	−0.719860	+	0.694119i	$0.755794\pi$
$770$	−0.770499	−0.0277669
$771$	6.56823	0.236549
$772$	12.5178	0.450525
$773$	−23.6771	−0.851605	−0.425803	−	0.904816i	$-0.640008\pi$
$773$	−23.6771	−0.851605	−0.425803	+	0.904816i	$0.640008\pi$
$774$	−0.0221248	−0.000795259 0
$775$	−2.84338	−0.102137
$776$	−13.7320	−0.492952
$777$	−15.8308	−0.567928
$778$	37.6594	1.35015
$779$	2.66375	0.0954387
$780$	−6.46282	−0.231406
$781$	6.40196	0.229080
$782$	0.271109	0.00969482
$783$	17.1270	0.612070
$784$	1.00000	0.0357143
$785$	−0.419428	−0.0149700
$786$	−3.84558	−0.137167
$787$	6.75904	0.240934	0.120467	−	0.992717i	$-0.461561\pi$
$787$	6.75904	0.240934	0.120467	+	0.992717i	$0.461561\pi$
$788$	−8.54669	−0.304463
$789$	45.8410	1.63198
$790$	−5.26922	−0.187471
$791$	−13.9521	−0.496078
$792$	−0.0942245	−0.00334812
$793$	38.7779	1.37704
$794$	9.68994	0.343883
$795$	−6.54397	−0.232091
$796$	−0.823227	−0.0291785
$797$	34.2611	1.21359	0.606796	−	0.794858i	$-0.292455\pi$
$797$	34.2611	1.21359	0.606796	+	0.794858i	$0.292455\pi$
$798$	0.828335	0.0293227
$799$	0.690973	0.0244449
$800$	3.98563	0.140913
$801$	−1.62608	−0.0574546
$802$	25.1086	0.886614
$803$	6.97061	0.245987
$804$	−14.3026	−0.504415
$805$	1.03828	0.0365945
$806$	2.69901	0.0950684
$807$	5.34727	0.188233
$808$	4.22353	0.148583
$809$	14.2327	0.500396	0.250198	−	0.968195i	$-0.419504\pi$
$809$	14.2327	0.500396	0.250198	+	0.968195i	$0.419504\pi$
$810$	−8.67702	−0.304879
$811$	−0.938876	−0.0329684	−0.0164842	−	0.999864i	$-0.505247\pi$
$811$	−0.938876	−0.0329684	−0.0164842	+	0.999864i	$0.505247\pi$
$812$	3.23318	0.113462
$813$	12.6194	0.442583
$814$	7.14036	0.250269
$815$	−10.4716	−0.366803
$816$	−0.446052	−0.0156149
$817$	−0.0877278	−0.00306921
$818$	25.1004	0.877614
$819$	0.465968	0.0162823
$820$	−5.49343	−0.191839
$821$	7.33490	0.255990	0.127995	−	0.991775i	$-0.459146\pi$
$821$	7.33490	0.255990	0.127995	+	0.991775i	$0.459146\pi$
$822$	−6.22380	−0.217080
$823$	−15.4552	−0.538733	−0.269367	−	0.963038i	$-0.586814\pi$
$823$	−15.4552	−0.538733	−0.269367	+	0.963038i	$0.586814\pi$
$824$	−17.5557	−0.611583
$825$	−5.17163	−0.180053
$826$	−7.63020	−0.265489
$827$	24.0437	0.836081	0.418041	−	0.908428i	$-0.362717\pi$
$827$	24.0437	0.836081	0.418041	+	0.908428i	$0.362717\pi$
$828$	0.126971	0.00441256
$829$	15.7765	0.547939	0.273969	−	0.961738i	$-0.411663\pi$
$829$	15.7765	0.547939	0.273969	+	0.961738i	$0.411663\pi$
$830$	−9.22431	−0.320181
$831$	45.8777	1.59148
$832$	−3.78326	−0.131161
$833$	0.262983	0.00911183
$834$	10.3368	0.357935
$835$	6.12371	0.211920
$836$	−0.373613	−0.0129217
$837$	3.77911	0.130625
$838$	3.34872	0.115680
$839$	−35.4992	−1.22557	−0.612785	−	0.790250i	$-0.709951\pi$
$839$	−35.4992	−1.22557	−0.612785	+	0.790250i	$0.709951\pi$
$840$	−1.70827	−0.0589408
$841$	−18.5466	−0.639537
$842$	0.691299	0.0238238
$843$	−6.18763	−0.213113
$844$	14.4294	0.496680
$845$	−1.32245	−0.0454937
$846$	0.323611	0.0111260
$847$	−10.4147	−0.357855
$848$	−3.83076	−0.131549
$849$	−6.81620	−0.233931
$850$	1.04815	0.0359514
$851$	−9.62192	−0.329835
$852$	14.1937	0.486270
$853$	29.5348	1.01125	0.505626	−	0.862753i	$-0.331262\pi$
$853$	29.5348	1.01125	0.505626	+	0.862753i	$0.331262\pi$
$854$	10.2499	0.350743
$855$	0.0605811	0.00207183
$856$	2.46352	0.0842015
$857$	9.60364	0.328054	0.164027	−	0.986456i	$-0.447552\pi$
$857$	9.60364	0.328054	0.164027	+	0.986456i	$0.447552\pi$
$858$	4.90905	0.167592
$859$	−11.6892	−0.398831	−0.199416	−	0.979915i	$-0.563904\pi$
$859$	−11.6892	−0.398831	−0.199416	+	0.979915i	$0.563904\pi$
$860$	0.180920	0.00616933
$861$	−9.25129	−0.315283
$862$	−1.00000	−0.0340601
$863$	−44.7321	−1.52270	−0.761349	−	0.648342i	$-0.775463\pi$
$863$	−44.7321	−1.52270	−0.761349	+	0.648342i	$0.775463\pi$
$864$	−5.29727	−0.180217
$865$	−1.12298	−0.0381826
$866$	2.95272	0.100337
$867$	28.7168	0.975273
$868$	0.713407	0.0242146
$869$	4.00241	0.135772
$870$	−5.52313	−0.187252
$871$	−31.9025	−1.08097
$872$	−3.41702	−0.115715
$873$	−1.69132	−0.0572425
$874$	0.503458	0.0170297
$875$	9.04997	0.305945
$876$	15.4545	0.522159
$877$	−13.9897	−0.472399	−0.236200	−	0.971705i	$-0.575902\pi$
$877$	−13.9897	−0.472399	−0.236200	+	0.971705i	$0.575902\pi$
$878$	−1.90523	−0.0642984
$879$	−16.4225	−0.553916
$880$	0.770499	0.0259735
$881$	−18.9466	−0.638327	−0.319163	−	0.947700i	$-0.603402\pi$
$881$	−18.9466	−0.638327	−0.319163	+	0.947700i	$0.603402\pi$
$882$	0.123166	0.00414721
$883$	4.25827	0.143302	0.0716510	−	0.997430i	$-0.477173\pi$
$883$	4.25827	0.143302	0.0716510	+	0.997430i	$0.477173\pi$
$884$	−0.994933	−0.0334632
$885$	13.0344	0.438147
$886$	5.54518	0.186294
$887$	−43.6568	−1.46585	−0.732926	−	0.680308i	$-0.761846\pi$
$887$	−43.6568	−1.46585	−0.732926	+	0.680308i	$0.761846\pi$
$888$	15.8308	0.531248
$889$	21.5814	0.723816
$890$	13.2969	0.445712
$891$	6.59091	0.220804
$892$	−1.61659	−0.0541273
$893$	1.28316	0.0429394
$894$	18.4018	0.615450
$895$	15.7272	0.525702
$896$	−1.00000	−0.0334077
$897$	−6.61514	−0.220873
$898$	15.5505	0.518927
$899$	2.30657	0.0769285
$900$	0.490893	0.0163631
$901$	−1.00743	−0.0335622
$902$	4.17271	0.138936
$903$	0.304682	0.0101392
$904$	13.9521	0.464039
$905$	16.7216	0.555846
$906$	−6.80047	−0.225931
$907$	13.6977	0.454826	0.227413	−	0.973798i	$-0.426973\pi$
$907$	13.6977	0.454826	0.227413	+	0.973798i	$0.426973\pi$
$908$	18.7450	0.622073
$909$	0.520194	0.0172537
$910$	−3.81035	−0.126312
$911$	0.740870	0.0245461	0.0122731	−	0.999925i	$-0.496093\pi$
$911$	0.740870	0.0245461	0.0122731	+	0.999925i	$0.496093\pi$
$912$	−0.828335	−0.0274289
$913$	7.00663	0.231886
$914$	−8.95655	−0.296256
$915$	−17.5095	−0.578846
$916$	11.6712	0.385628
$917$	−2.26728	−0.0748721
$918$	−1.39309	−0.0459789
$919$	16.0966	0.530978	0.265489	−	0.964114i	$-0.414467\pi$
$919$	16.0966	0.530978	0.265489	+	0.964114i	$0.414467\pi$
$920$	−1.03828	−0.0342310
$921$	15.5429	0.512157
$922$	−21.6395	−0.712660
$923$	31.6596	1.04209
$924$	1.29757	0.0426869
$925$	−37.2000	−1.22313
$926$	37.0190	1.21652
$927$	−2.16227	−0.0710182
$928$	−3.23318	−0.106134
$929$	43.0627	1.41284	0.706420	−	0.707793i	$-0.250309\pi$
$929$	43.0627	1.41284	0.706420	+	0.707793i	$0.250309\pi$
$930$	−1.21869	−0.0399625
$931$	0.488369	0.0160057
$932$	9.99235	0.327310
$933$	−12.6085	−0.412783
$934$	36.1285	1.18216
$935$	0.202628	0.00662665
$936$	−0.465968	−0.0152307
$937$	−17.2173	−0.562465	−0.281232	−	0.959640i	$-0.590743\pi$
$937$	−17.2173	−0.562465	−0.281232	+	0.959640i	$0.590743\pi$
$938$	−8.43254	−0.275332
$939$	−34.9566	−1.14077
$940$	−2.64625	−0.0863113
$941$	11.6204	0.378814	0.189407	−	0.981899i	$-0.439343\pi$
$941$	11.6204	0.378814	0.189407	+	0.981899i	$0.439343\pi$
$942$	0.706343	0.0230139
$943$	−5.62290	−0.183107
$944$	7.63020	0.248342
$945$	−5.33520	−0.173554
$946$	−0.137424	−0.00446804
$947$	−8.43641	−0.274146	−0.137073	−	0.990561i	$-0.543770\pi$
$947$	−8.43641	−0.274146	−0.137073	+	0.990561i	$0.543770\pi$
$948$	8.87372	0.288205
$949$	34.4717	1.11900
$950$	1.94646	0.0631515
$951$	−0.675891	−0.0219173
$952$	−0.262983	−0.00852333
$953$	14.2269	0.460854	0.230427	−	0.973090i	$-0.425988\pi$
$953$	14.2269	0.460854	0.230427	+	0.973090i	$0.425988\pi$
$954$	−0.471819	−0.0152757
$955$	13.9822	0.452453
$956$	−18.1837	−0.588104
$957$	4.19527	0.135614
$958$	32.3147	1.04404
$959$	−3.66942	−0.118492
$960$	1.70827	0.0551341
$961$	−30.4910	−0.983582
$962$	35.3112	1.13848
$963$	0.303422	0.00977763
$964$	8.38467	0.270052
$965$	−12.6074	−0.405847
$966$	−1.74853	−0.0562580
$967$	38.9232	1.25168	0.625842	−	0.779950i	$-0.284755\pi$
$967$	38.9232	1.25168	0.625842	+	0.779950i	$0.284755\pi$
$968$	10.4147	0.334742
$969$	−0.217838	−0.00699797
$970$	13.8304	0.444066
$971$	44.0861	1.41479	0.707394	−	0.706819i	$-0.249871\pi$
$971$	44.0861	1.41479	0.707394	+	0.706819i	$0.249871\pi$
$972$	−1.27916	−0.0410290
$973$	6.09438	0.195377
$974$	30.0975	0.964386
$975$	−25.5753	−0.819064
$976$	−10.2499	−0.328090
$977$	−5.21223	−0.166754	−0.0833770	−	0.996518i	$-0.526571\pi$
$977$	−5.21223	−0.166754	−0.0833770	+	0.996518i	$0.526571\pi$
$978$	17.6348	0.563899
$979$	−10.1001	−0.322800
$980$	−1.00716	−0.0321726
$981$	−0.420861	−0.0134370
$982$	1.26754	0.0404487
$983$	−33.7792	−1.07739	−0.538695	−	0.842501i	$-0.681083\pi$
$983$	−33.7792	−1.07739	−0.538695	+	0.842501i	$0.681083\pi$
$984$	9.25129	0.294920
$985$	8.60789	0.274270
$986$	−0.850271	−0.0270781
$987$	−4.45646	−0.141851
$988$	−1.84763	−0.0587809
$989$	0.185184	0.00588851
$990$	0.0948992	0.00301609
$991$	−33.2855	−1.05735	−0.528675	−	0.848824i	$-0.677311\pi$
$991$	−33.2855	−1.05735	−0.528675	+	0.848824i	$0.677311\pi$
$992$	−0.713407	−0.0226507
$993$	−54.6085	−1.73295
$994$	8.36834	0.265428
$995$	0.829122	0.0262849
$996$	15.5343	0.492224
$997$	7.65919	0.242569	0.121284	−	0.992618i	$-0.461299\pi$
$997$	7.65919	0.242569	0.121284	+	0.992618i	$0.461299\pi$
$998$	−15.4625	−0.489457
$999$	49.4423	1.56429

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.k.1.5	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.k.1.5	✓	20	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:	\( N \)	\(=\)	\( 6034 = 2 \cdot 7 \cdot 431 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.69612 q^{3} +1.00000 q^{4} -1.00716 q^{5} +1.69612 q^{6} +1.00000 q^{7} -1.00000 q^{8} -0.123166 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.69612 q^{3} +1.00000 q^{4} -1.00716 q^{5} +1.69612 q^{6} +1.00000 q^{7} -1.00000 q^{8} -0.123166 q^{9} +1.00716 q^{10} -0.765021 q^{11} -1.69612 q^{12} -3.78326 q^{13} -1.00000 q^{14} +1.70827 q^{15} +1.00000 q^{16} +0.262983 q^{17} +0.123166 q^{18} +0.488369 q^{19} -1.00716 q^{20} -1.69612 q^{21} +0.765021 q^{22} -1.03090 q^{23} +1.69612 q^{24} -3.98563 q^{25} +3.78326 q^{26} +5.29727 q^{27} +1.00000 q^{28} +3.23318 q^{29} -1.70827 q^{30} +0.713407 q^{31} -1.00000 q^{32} +1.29757 q^{33} -0.262983 q^{34} -1.00716 q^{35} -0.123166 q^{36} +9.33354 q^{37} -0.488369 q^{38} +6.41687 q^{39} +1.00716 q^{40} +5.45437 q^{41} +1.69612 q^{42} -0.179634 q^{43} -0.765021 q^{44} +0.124048 q^{45} +1.03090 q^{46} +2.62744 q^{47} -1.69612 q^{48} +1.00000 q^{49} +3.98563 q^{50} -0.446052 q^{51} -3.78326 q^{52} -3.83076 q^{53} -5.29727 q^{54} +0.770499 q^{55} -1.00000 q^{56} -0.828335 q^{57} -3.23318 q^{58} +7.63020 q^{59} +1.70827 q^{60} -10.2499 q^{61} -0.713407 q^{62} -0.123166 q^{63} +1.00000 q^{64} +3.81035 q^{65} -1.29757 q^{66} +8.43254 q^{67} +0.262983 q^{68} +1.74853 q^{69} +1.00716 q^{70} -8.36834 q^{71} +0.123166 q^{72} -9.11165 q^{73} -9.33354 q^{74} +6.76012 q^{75} +0.488369 q^{76} -0.765021 q^{77} -6.41687 q^{78} -5.23176 q^{79} -1.00716 q^{80} -8.61533 q^{81} -5.45437 q^{82} -9.15873 q^{83} -1.69612 q^{84} -0.264866 q^{85} +0.179634 q^{86} -5.48387 q^{87} +0.765021 q^{88} +13.2023 q^{89} -0.124048 q^{90} -3.78326 q^{91} -1.03090 q^{92} -1.21003 q^{93} -2.62744 q^{94} -0.491866 q^{95} +1.69612 q^{96} +13.7320 q^{97} -1.00000 q^{98} +0.0942245 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 20 q^{2} + 3 q^{3} + 20 q^{4} - 3 q^{5} - 3 q^{6} + 20 q^{7} - 20 q^{8} + 13 q^{9}+O(q^{10}) \) 20 * q - 20 * q^2 + 3 * q^3 + 20 * q^4 - 3 * q^5 - 3 * q^6 + 20 * q^7 - 20 * q^8 + 13 * q^9	\( 20 q - 20 q^{2} + 3 q^{3} + 20 q^{4} - 3 q^{5} - 3 q^{6} + 20 q^{7} - 20 q^{8} + 13 q^{9} + 3 q^{10} - 8 q^{11} + 3 q^{12} - 4 q^{13} - 20 q^{14} - 25 q^{15} + 20 q^{16} + 9 q^{17} - 13 q^{18} - 14 q^{19} - 3 q^{20} + 3 q^{21} + 8 q^{22} - 23 q^{23} - 3 q^{24} + 31 q^{25} + 4 q^{26} - 21 q^{27} + 20 q^{28} - 48 q^{29} + 25 q^{30} - q^{31} - 20 q^{32} - 29 q^{33} - 9 q^{34} - 3 q^{35} + 13 q^{36} - q^{37} + 14 q^{38} - q^{39} + 3 q^{40} - 27 q^{41} - 3 q^{42} - 3 q^{43} - 8 q^{44} - 12 q^{45} + 23 q^{46} - 26 q^{47} + 3 q^{48} + 20 q^{49} - 31 q^{50} - 17 q^{51} - 4 q^{52} - 43 q^{53} + 21 q^{54} - 16 q^{55} - 20 q^{56} - 25 q^{57} + 48 q^{58} - 19 q^{59} - 25 q^{60} + 9 q^{61} + q^{62} + 13 q^{63} + 20 q^{64} - 87 q^{65} + 29 q^{66} + 32 q^{67} + 9 q^{68} - 23 q^{69} + 3 q^{70} - 63 q^{71} - 13 q^{72} + 2 q^{73} + q^{74} - 8 q^{75} - 14 q^{76} - 8 q^{77} + q^{78} - 51 q^{79} - 3 q^{80} + 4 q^{81} + 27 q^{82} - 24 q^{83} + 3 q^{84} + 31 q^{85} + 3 q^{86} - 33 q^{87} + 8 q^{88} - 35 q^{89} + 12 q^{90} - 4 q^{91} - 23 q^{92} + 17 q^{93} + 26 q^{94} - 30 q^{95} - 3 q^{96} + 5 q^{97} - 20 q^{98} - 31 q^{99}+O(q^{100}) \) 20 * q - 20 * q^2 + 3 * q^3 + 20 * q^4 - 3 * q^5 - 3 * q^6 + 20 * q^7 - 20 * q^8 + 13 * q^9 + 3 * q^10 - 8 * q^11 + 3 * q^12 - 4 * q^13 - 20 * q^14 - 25 * q^15 + 20 * q^16 + 9 * q^17 - 13 * q^18 - 14 * q^19 - 3 * q^20 + 3 * q^21 + 8 * q^22 - 23 * q^23 - 3 * q^24 + 31 * q^25 + 4 * q^26 - 21 * q^27 + 20 * q^28 - 48 * q^29 + 25 * q^30 - q^31 - 20 * q^32 - 29 * q^33 - 9 * q^34 - 3 * q^35 + 13 * q^36 - q^37 + 14 * q^38 - q^39 + 3 * q^40 - 27 * q^41 - 3 * q^42 - 3 * q^43 - 8 * q^44 - 12 * q^45 + 23 * q^46 - 26 * q^47 + 3 * q^48 + 20 * q^49 - 31 * q^50 - 17 * q^51 - 4 * q^52 - 43 * q^53 + 21 * q^54 - 16 * q^55 - 20 * q^56 - 25 * q^57 + 48 * q^58 - 19 * q^59 - 25 * q^60 + 9 * q^61 + q^62 + 13 * q^63 + 20 * q^64 - 87 * q^65 + 29 * q^66 + 32 * q^67 + 9 * q^68 - 23 * q^69 + 3 * q^70 - 63 * q^71 - 13 * q^72 + 2 * q^73 + q^74 - 8 * q^75 - 14 * q^76 - 8 * q^77 + q^78 - 51 * q^79 - 3 * q^80 + 4 * q^81 + 27 * q^82 - 24 * q^83 + 3 * q^84 + 31 * q^85 + 3 * q^86 - 33 * q^87 + 8 * q^88 - 35 * q^89 + 12 * q^90 - 4 * q^91 - 23 * q^92 + 17 * q^93 + 26 * q^94 - 30 * q^95 - 3 * q^96 + 5 * q^97 - 20 * q^98 - 31 * q^99

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