LMFDB - Embedded newform 4970.2.a.z.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4970,2,Mod(1,4970)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4970, 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("4970.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4970 = 2 \cdot 5 \cdot 7 \cdot 71 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4970.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:	$39.6856498046$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 4x^{8} - 9x^{7} + 47x^{6} + 6x^{5} - 151x^{4} + 80x^{3} + 79x^{2} - 54x + 8 $ x^9 - 4x^8 - 9x^7 + 47x^6 + 6x^5 - 151x^4 + 80x^3 + 79x^2 - 54x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-2.22106$ of defining polynomial
Character	$\chi$	$=$	4970.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.22106 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.22106 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.93311 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.22106 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.22106 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.93311 q^{9} -1.00000 q^{10} -4.95986 q^{11} -2.22106 q^{12} +1.45443 q^{13} +1.00000 q^{14} +2.22106 q^{15} +1.00000 q^{16} +6.89822 q^{17} +1.93311 q^{18} -5.33473 q^{19} -1.00000 q^{20} -2.22106 q^{21} -4.95986 q^{22} +3.91342 q^{23} -2.22106 q^{24} +1.00000 q^{25} +1.45443 q^{26} +2.36962 q^{27} +1.00000 q^{28} -4.17269 q^{29} +2.22106 q^{30} -6.25953 q^{31} +1.00000 q^{32} +11.0161 q^{33} +6.89822 q^{34} -1.00000 q^{35} +1.93311 q^{36} -1.10774 q^{37} -5.33473 q^{38} -3.23038 q^{39} -1.00000 q^{40} +0.822714 q^{41} -2.22106 q^{42} -2.90442 q^{43} -4.95986 q^{44} -1.93311 q^{45} +3.91342 q^{46} -7.06452 q^{47} -2.22106 q^{48} +1.00000 q^{49} +1.00000 q^{50} -15.3214 q^{51} +1.45443 q^{52} +0.682742 q^{53} +2.36962 q^{54} +4.95986 q^{55} +1.00000 q^{56} +11.8488 q^{57} -4.17269 q^{58} +5.17530 q^{59} +2.22106 q^{60} +5.42131 q^{61} -6.25953 q^{62} +1.93311 q^{63} +1.00000 q^{64} -1.45443 q^{65} +11.0161 q^{66} -3.44964 q^{67} +6.89822 q^{68} -8.69195 q^{69} -1.00000 q^{70} +1.00000 q^{71} +1.93311 q^{72} +6.66332 q^{73} -1.10774 q^{74} -2.22106 q^{75} -5.33473 q^{76} -4.95986 q^{77} -3.23038 q^{78} +5.91342 q^{79} -1.00000 q^{80} -11.0624 q^{81} +0.822714 q^{82} +1.97733 q^{83} -2.22106 q^{84} -6.89822 q^{85} -2.90442 q^{86} +9.26780 q^{87} -4.95986 q^{88} +8.58584 q^{89} -1.93311 q^{90} +1.45443 q^{91} +3.91342 q^{92} +13.9028 q^{93} -7.06452 q^{94} +5.33473 q^{95} -2.22106 q^{96} +6.42703 q^{97} +1.00000 q^{98} -9.58797 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 9 q^{2} + 4 q^{3} + 9 q^{4} - 9 q^{5} + 4 q^{6} + 9 q^{7} + 9 q^{8} + 7 q^{9}+O(q^{10}) $ 9 * q + 9 * q^2 + 4 * q^3 + 9 * q^4 - 9 * q^5 + 4 * q^6 + 9 * q^7 + 9 * q^8 + 7 * q^9	\( 9 q + 9 q^{2} + 4 q^{3} + 9 q^{4} - 9 q^{5} + 4 q^{6} + 9 q^{7} + 9 q^{8} + 7 q^{9} - 9 q^{10} - 2 q^{11} + 4 q^{12} + 11 q^{13} + 9 q^{14} - 4 q^{15} + 9 q^{16} + 9 q^{17} + 7 q^{18} + 9 q^{19} - 9 q^{20} + 4 q^{21} - 2 q^{22} + 2 q^{23} + 4 q^{24} + 9 q^{25} + 11 q^{26} + 7 q^{27} + 9 q^{28} + 2 q^{29} - 4 q^{30} + 18 q^{31} + 9 q^{32} + 8 q^{33} + 9 q^{34} - 9 q^{35} + 7 q^{36} + 15 q^{37} + 9 q^{38} - 7 q^{39} - 9 q^{40} + 15 q^{41} + 4 q^{42} + 7 q^{43} - 2 q^{44} - 7 q^{45} + 2 q^{46} + 12 q^{47} + 4 q^{48} + 9 q^{49} + 9 q^{50} + 4 q^{51} + 11 q^{52} + 3 q^{53} + 7 q^{54} + 2 q^{55} + 9 q^{56} + 9 q^{57} + 2 q^{58} + 24 q^{59} - 4 q^{60} + 25 q^{61} + 18 q^{62} + 7 q^{63} + 9 q^{64} - 11 q^{65} + 8 q^{66} - 4 q^{67} + 9 q^{68} + 3 q^{69} - 9 q^{70} + 9 q^{71} + 7 q^{72} + 32 q^{73} + 15 q^{74} + 4 q^{75} + 9 q^{76} - 2 q^{77} - 7 q^{78} + 20 q^{79} - 9 q^{80} - 7 q^{81} + 15 q^{82} + 11 q^{83} + 4 q^{84} - 9 q^{85} + 7 q^{86} + 26 q^{87} - 2 q^{88} + 10 q^{89} - 7 q^{90} + 11 q^{91} + 2 q^{92} + 32 q^{93} + 12 q^{94} - 9 q^{95} + 4 q^{96} + 19 q^{97} + 9 q^{98} - 7 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 + 4 * q^3 + 9 * q^4 - 9 * q^5 + 4 * q^6 + 9 * q^7 + 9 * q^8 + 7 * q^9 - 9 * q^10 - 2 * q^11 + 4 * q^12 + 11 * q^13 + 9 * q^14 - 4 * q^15 + 9 * q^16 + 9 * q^17 + 7 * q^18 + 9 * q^19 - 9 * q^20 + 4 * q^21 - 2 * q^22 + 2 * q^23 + 4 * q^24 + 9 * q^25 + 11 * q^26 + 7 * q^27 + 9 * q^28 + 2 * q^29 - 4 * q^30 + 18 * q^31 + 9 * q^32 + 8 * q^33 + 9 * q^34 - 9 * q^35 + 7 * q^36 + 15 * q^37 + 9 * q^38 - 7 * q^39 - 9 * q^40 + 15 * q^41 + 4 * q^42 + 7 * q^43 - 2 * q^44 - 7 * q^45 + 2 * q^46 + 12 * q^47 + 4 * q^48 + 9 * q^49 + 9 * q^50 + 4 * q^51 + 11 * q^52 + 3 * q^53 + 7 * q^54 + 2 * q^55 + 9 * q^56 + 9 * q^57 + 2 * q^58 + 24 * q^59 - 4 * q^60 + 25 * q^61 + 18 * q^62 + 7 * q^63 + 9 * q^64 - 11 * q^65 + 8 * q^66 - 4 * q^67 + 9 * q^68 + 3 * q^69 - 9 * q^70 + 9 * q^71 + 7 * q^72 + 32 * q^73 + 15 * q^74 + 4 * q^75 + 9 * q^76 - 2 * q^77 - 7 * q^78 + 20 * q^79 - 9 * q^80 - 7 * q^81 + 15 * q^82 + 11 * q^83 + 4 * q^84 - 9 * q^85 + 7 * q^86 + 26 * q^87 - 2 * q^88 + 10 * q^89 - 7 * q^90 + 11 * q^91 + 2 * q^92 + 32 * q^93 + 12 * q^94 - 9 * q^95 + 4 * q^96 + 19 * q^97 + 9 * q^98 - 7 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.22106	−1.28233	−0.641165	−	0.767403i	$-0.721549\pi$
$3$	−2.22106	−1.28233	−0.641165	+	0.767403i	$0.721549\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−2.22106	−0.906745
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	1.93311	0.644371
$10$	−1.00000	−0.316228
$11$	−4.95986	−1.49545	−0.747727	−	0.664007i	$-0.768855\pi$
$11$	−4.95986	−1.49545	−0.747727	+	0.664007i	$0.768855\pi$
$12$	−2.22106	−0.641165
$13$	1.45443	0.403387	0.201693	−	0.979449i	$-0.435356\pi$
$13$	1.45443	0.403387	0.201693	+	0.979449i	$0.435356\pi$
$14$	1.00000	0.267261
$15$	2.22106	0.573476
$16$	1.00000	0.250000
$17$	6.89822	1.67306	0.836532	−	0.547918i	$-0.184579\pi$
$17$	6.89822	1.67306	0.836532	+	0.547918i	$0.184579\pi$
$18$	1.93311	0.455639
$19$	−5.33473	−1.22387	−0.611935	−	0.790908i	$-0.709609\pi$
$19$	−5.33473	−1.22387	−0.611935	+	0.790908i	$0.709609\pi$
$20$	−1.00000	−0.223607
$21$	−2.22106	−0.484675
$22$	−4.95986	−1.05745
$23$	3.91342	0.816005	0.408002	−	0.912981i	$-0.366225\pi$
$23$	3.91342	0.816005	0.408002	+	0.912981i	$0.366225\pi$
$24$	−2.22106	−0.453372
$25$	1.00000	0.200000
$26$	1.45443	0.285238
$27$	2.36962	0.456034
$28$	1.00000	0.188982
$29$	−4.17269	−0.774849	−0.387424	−	0.921901i	$-0.626635\pi$
$29$	−4.17269	−0.774849	−0.387424	+	0.921901i	$0.626635\pi$
$30$	2.22106	0.405508
$31$	−6.25953	−1.12425	−0.562123	−	0.827054i	$-0.690015\pi$
$31$	−6.25953	−1.12425	−0.562123	+	0.827054i	$0.690015\pi$
$32$	1.00000	0.176777
$33$	11.0161	1.91767
$34$	6.89822	1.18304
$35$	−1.00000	−0.169031
$36$	1.93311	0.322186
$37$	−1.10774	−0.182111	−0.0910557	−	0.995846i	$-0.529024\pi$
$37$	−1.10774	−0.182111	−0.0910557	+	0.995846i	$0.529024\pi$
$38$	−5.33473	−0.865407
$39$	−3.23038	−0.517275
$40$	−1.00000	−0.158114
$41$	0.822714	0.128486	0.0642432	−	0.997934i	$-0.479537\pi$
$41$	0.822714	0.128486	0.0642432	+	0.997934i	$0.479537\pi$
$42$	−2.22106	−0.342717
$43$	−2.90442	−0.442920	−0.221460	−	0.975169i	$-0.571082\pi$
$43$	−2.90442	−0.442920	−0.221460	+	0.975169i	$0.571082\pi$
$44$	−4.95986	−0.747727
$45$	−1.93311	−0.288172
$46$	3.91342	0.577003
$47$	−7.06452	−1.03047	−0.515233	−	0.857050i	$-0.672295\pi$
$47$	−7.06452	−1.03047	−0.515233	+	0.857050i	$0.672295\pi$
$48$	−2.22106	−0.320583
$49$	1.00000	0.142857
$50$	1.00000	0.141421
$51$	−15.3214	−2.14542
$52$	1.45443	0.201693
$53$	0.682742	0.0937819	0.0468909	−	0.998900i	$-0.485069\pi$
$53$	0.682742	0.0937819	0.0468909	+	0.998900i	$0.485069\pi$
$54$	2.36962	0.322464
$55$	4.95986	0.668787
$56$	1.00000	0.133631
$57$	11.8488	1.56941
$58$	−4.17269	−0.547901
$59$	5.17530	0.673767	0.336883	−	0.941546i	$-0.390627\pi$
$59$	5.17530	0.673767	0.336883	+	0.941546i	$0.390627\pi$
$60$	2.22106	0.286738
$61$	5.42131	0.694127	0.347064	−	0.937842i	$-0.387179\pi$
$61$	5.42131	0.694127	0.347064	+	0.937842i	$0.387179\pi$
$62$	−6.25953	−0.794962
$63$	1.93311	0.243549
$64$	1.00000	0.125000
$65$	−1.45443	−0.180400
$66$	11.0161	1.35599
$67$	−3.44964	−0.421441	−0.210721	−	0.977546i	$-0.567581\pi$
$67$	−3.44964	−0.421441	−0.210721	+	0.977546i	$0.567581\pi$
$68$	6.89822	0.836532
$69$	−8.69195	−1.04639
$70$	−1.00000	−0.119523
$71$	1.00000	0.118678
$71$	1.00000	0.118678
$72$	1.93311	0.227820
$73$	6.66332	0.779883	0.389942	−	0.920840i	$-0.372495\pi$
$73$	6.66332	0.779883	0.389942	+	0.920840i	$0.372495\pi$
$74$	−1.10774	−0.128772
$75$	−2.22106	−0.256466
$76$	−5.33473	−0.611935
$77$	−4.95986	−0.565228
$78$	−3.23038	−0.365769
$79$	5.91342	0.665312	0.332656	−	0.943048i	$-0.392055\pi$
$79$	5.91342	0.665312	0.332656	+	0.943048i	$0.392055\pi$
$80$	−1.00000	−0.111803
$81$	−11.0624	−1.22916
$82$	0.822714	0.0908536
$83$	1.97733	0.217040	0.108520	−	0.994094i	$-0.465389\pi$
$83$	1.97733	0.217040	0.108520	+	0.994094i	$0.465389\pi$
$84$	−2.22106	−0.242338
$85$	−6.89822	−0.748217
$86$	−2.90442	−0.313192
$87$	9.26780	0.993612
$88$	−4.95986	−0.528723
$89$	8.58584	0.910097	0.455049	−	0.890467i	$-0.349622\pi$
$89$	8.58584	0.910097	0.455049	+	0.890467i	$0.349622\pi$
$90$	−1.93311	−0.203768
$91$	1.45443	0.152466
$92$	3.91342	0.408002
$93$	13.9028	1.44165
$94$	−7.06452	−0.728650
$95$	5.33473	0.547332
$96$	−2.22106	−0.226686
$97$	6.42703	0.652566	0.326283	−	0.945272i	$-0.394204\pi$
$97$	6.42703	0.652566	0.326283	+	0.945272i	$0.394204\pi$
$98$	1.00000	0.101015
$99$	−9.58797	−0.963627
$100$	1.00000	0.100000
$101$	10.0060	0.995630	0.497815	−	0.867283i	$-0.334136\pi$
$101$	10.0060	0.995630	0.497815	+	0.867283i	$0.334136\pi$
$102$	−15.3214	−1.51704
$103$	10.1564	1.00074	0.500369	−	0.865812i	$-0.333198\pi$
$103$	10.1564	1.00074	0.500369	+	0.865812i	$0.333198\pi$
$104$	1.45443	0.142619
$105$	2.22106	0.216753
$106$	0.682742	0.0663138
$107$	−7.20101	−0.696148	−0.348074	−	0.937467i	$-0.613164\pi$
$107$	−7.20101	−0.696148	−0.348074	+	0.937467i	$0.613164\pi$
$108$	2.36962	0.228017
$109$	−3.72861	−0.357137	−0.178568	−	0.983928i	$-0.557147\pi$
$109$	−3.72861	−0.357137	−0.178568	+	0.983928i	$0.557147\pi$
$110$	4.95986	0.472904
$111$	2.46036	0.233527
$112$	1.00000	0.0944911
$113$	17.1452	1.61289	0.806443	−	0.591312i	$-0.201390\pi$
$113$	17.1452	1.61289	0.806443	+	0.591312i	$0.201390\pi$
$114$	11.8488	1.10974
$115$	−3.91342	−0.364929
$116$	−4.17269	−0.387424
$117$	2.81158	0.259931
$118$	5.17530	0.476425
$119$	6.89822	0.632359
$120$	2.22106	0.202754
$121$	13.6002	1.23638
$122$	5.42131	0.490822
$123$	−1.82730	−0.164762
$124$	−6.25953	−0.562123
$125$	−1.00000	−0.0894427
$126$	1.93311	0.172215
$127$	1.39007	0.123349	0.0616744	−	0.998096i	$-0.480356\pi$
$127$	1.39007	0.123349	0.0616744	+	0.998096i	$0.480356\pi$
$128$	1.00000	0.0883883
$129$	6.45089	0.567970
$130$	−1.45443	−0.127562
$131$	−6.41955	−0.560878	−0.280439	−	0.959872i	$-0.590480\pi$
$131$	−6.41955	−0.560878	−0.280439	+	0.959872i	$0.590480\pi$
$132$	11.0161	0.958833
$133$	−5.33473	−0.462580
$134$	−3.44964	−0.298004
$135$	−2.36962	−0.203944
$136$	6.89822	0.591518
$137$	−18.7483	−1.60177	−0.800886	−	0.598817i	$-0.795638\pi$
$137$	−18.7483	−1.60177	−0.800886	+	0.598817i	$0.795638\pi$
$138$	−8.69195	−0.739908
$139$	5.31650	0.450940	0.225470	−	0.974250i	$-0.427608\pi$
$139$	5.31650	0.450940	0.225470	+	0.974250i	$0.427608\pi$
$140$	−1.00000	−0.0845154
$141$	15.6907	1.32140
$142$	1.00000	0.0839181
$143$	−7.21377	−0.603246
$144$	1.93311	0.161093
$145$	4.17269	0.346523
$146$	6.66332	0.551461
$147$	−2.22106	−0.183190
$148$	−1.10774	−0.0910557
$149$	6.02481	0.493571	0.246786	−	0.969070i	$-0.420626\pi$
$149$	6.02481	0.493571	0.246786	+	0.969070i	$0.420626\pi$
$150$	−2.22106	−0.181349
$151$	−17.5577	−1.42883	−0.714413	−	0.699724i	$-0.753306\pi$
$151$	−17.5577	−1.42883	−0.714413	+	0.699724i	$0.753306\pi$
$152$	−5.33473	−0.432704
$153$	13.3350	1.07807
$154$	−4.95986	−0.399677
$155$	6.25953	0.502778
$156$	−3.23038	−0.258638
$157$	19.0927	1.52376	0.761882	−	0.647716i	$-0.224276\pi$
$157$	19.0927	1.52376	0.761882	+	0.647716i	$0.224276\pi$
$158$	5.91342	0.470447
$159$	−1.51641	−0.120259
$160$	−1.00000	−0.0790569
$161$	3.91342	0.308421
$162$	−11.0624	−0.869145
$163$	17.0291	1.33382	0.666911	−	0.745137i	$-0.267616\pi$
$163$	17.0291	1.33382	0.666911	+	0.745137i	$0.267616\pi$
$164$	0.822714	0.0642432
$165$	−11.0161	−0.857606
$166$	1.97733	0.153471
$167$	14.9636	1.15792	0.578960	−	0.815356i	$-0.303459\pi$
$167$	14.9636	1.15792	0.578960	+	0.815356i	$0.303459\pi$
$168$	−2.22106	−0.171359
$169$	−10.8846	−0.837279
$170$	−6.89822	−0.529069
$171$	−10.3126	−0.788627
$172$	−2.90442	−0.221460
$173$	11.2451	0.854952	0.427476	−	0.904027i	$-0.359403\pi$
$173$	11.2451	0.854952	0.427476	+	0.904027i	$0.359403\pi$
$174$	9.26780	0.702590
$175$	1.00000	0.0755929
$176$	−4.95986	−0.373863
$177$	−11.4947	−0.863992
$178$	8.58584	0.643536
$179$	−10.3091	−0.770539	−0.385270	−	0.922804i	$-0.625892\pi$
$179$	−10.3091	−0.770539	−0.385270	+	0.922804i	$0.625892\pi$
$180$	−1.93311	−0.144086
$181$	3.37663	0.250983	0.125491	−	0.992095i	$-0.459949\pi$
$181$	3.37663	0.250983	0.125491	+	0.992095i	$0.459949\pi$
$182$	1.45443	0.107810
$183$	−12.0411	−0.890100
$184$	3.91342	0.288501
$185$	1.10774	0.0814427
$186$	13.9028	1.01940
$187$	−34.2142	−2.50199
$188$	−7.06452	−0.515233
$189$	2.36962	0.172364
$190$	5.33473	0.387022
$191$	13.3422	0.965408	0.482704	−	0.875784i	$-0.339655\pi$
$191$	13.3422	0.965408	0.482704	+	0.875784i	$0.339655\pi$
$192$	−2.22106	−0.160291
$193$	2.06596	0.148711	0.0743555	−	0.997232i	$-0.476310\pi$
$193$	2.06596	0.148711	0.0743555	+	0.997232i	$0.476310\pi$
$194$	6.42703	0.461434
$195$	3.23038	0.231332
$196$	1.00000	0.0714286
$197$	−6.59787	−0.470079	−0.235039	−	0.971986i	$-0.575522\pi$
$197$	−6.59787	−0.470079	−0.235039	+	0.971986i	$0.575522\pi$
$198$	−9.58797	−0.681387
$199$	12.7062	0.900717	0.450359	−	0.892848i	$-0.351296\pi$
$199$	12.7062	0.900717	0.450359	+	0.892848i	$0.351296\pi$
$200$	1.00000	0.0707107
$201$	7.66187	0.540427
$202$	10.0060	0.704017
$203$	−4.17269	−0.292865
$204$	−15.3214	−1.07271
$205$	−0.822714	−0.0574608
$206$	10.1564	0.707629
$207$	7.56509	0.525810
$208$	1.45443	0.100847
$209$	26.4595	1.83024
$210$	2.22106	0.153268
$211$	22.5895	1.55512	0.777562	−	0.628806i	$-0.216456\pi$
$211$	22.5895	1.55512	0.777562	+	0.628806i	$0.216456\pi$
$212$	0.682742	0.0468909
$213$	−2.22106	−0.152185
$214$	−7.20101	−0.492251
$215$	2.90442	0.198080
$216$	2.36962	0.161232
$217$	−6.25953	−0.424925
$218$	−3.72861	−0.252534
$219$	−14.7997	−1.00007
$220$	4.95986	0.334394
$221$	10.0330	0.674892
$222$	2.46036	0.165128
$223$	23.6538	1.58397	0.791987	−	0.610538i	$-0.209047\pi$
$223$	23.6538	1.58397	0.791987	+	0.610538i	$0.209047\pi$
$224$	1.00000	0.0668153
$225$	1.93311	0.128874
$226$	17.1452	1.14048
$227$	−11.3442	−0.752943	−0.376471	−	0.926428i	$-0.622863\pi$
$227$	−11.3442	−0.752943	−0.376471	+	0.926428i	$0.622863\pi$
$228$	11.8488	0.784703
$229$	1.21116	0.0800360	0.0400180	−	0.999199i	$-0.487258\pi$
$229$	1.21116	0.0800360	0.0400180	+	0.999199i	$0.487258\pi$
$230$	−3.91342	−0.258043
$231$	11.0161	0.724809
$232$	−4.17269	−0.273950
$233$	1.60040	0.104846	0.0524228	−	0.998625i	$-0.483306\pi$
$233$	1.60040	0.104846	0.0524228	+	0.998625i	$0.483306\pi$
$234$	2.81158	0.183799
$235$	7.06452	0.460839
$236$	5.17530	0.336883
$237$	−13.1341	−0.853150
$238$	6.89822	0.447145
$239$	16.3645	1.05853	0.529267	−	0.848455i	$-0.322467\pi$
$239$	16.3645	1.05853	0.529267	+	0.848455i	$0.322467\pi$
$240$	2.22106	0.143369
$241$	11.7331	0.755794	0.377897	−	0.925848i	$-0.376647\pi$
$241$	11.7331	0.755794	0.377897	+	0.925848i	$0.376647\pi$
$242$	13.6002	0.874253
$243$	17.4614	1.12015
$244$	5.42131	0.347064
$245$	−1.00000	−0.0638877
$246$	−1.82730	−0.116504
$247$	−7.75900	−0.493693
$248$	−6.25953	−0.397481
$249$	−4.39177	−0.278317
$250$	−1.00000	−0.0632456
$251$	20.1129	1.26952	0.634759	−	0.772710i	$-0.281099\pi$
$251$	20.1129	1.26952	0.634759	+	0.772710i	$0.281099\pi$
$252$	1.93311	0.121775
$253$	−19.4100	−1.22030
$254$	1.39007	0.0872208
$255$	15.3214	0.959462
$256$	1.00000	0.0625000
$257$	−2.88190	−0.179768	−0.0898839	−	0.995952i	$-0.528650\pi$
$257$	−2.88190	−0.179768	−0.0898839	+	0.995952i	$0.528650\pi$
$258$	6.45089	0.401615
$259$	−1.10774	−0.0688316
$260$	−1.45443	−0.0902000
$261$	−8.06628	−0.499290
$262$	−6.41955	−0.396601
$263$	16.4635	1.01518	0.507591	−	0.861598i	$-0.330536\pi$
$263$	16.4635	1.01518	0.507591	+	0.861598i	$0.330536\pi$
$264$	11.0161	0.677997
$265$	−0.682742	−0.0419405
$266$	−5.33473	−0.327093
$267$	−19.0697	−1.16705
$268$	−3.44964	−0.210721
$269$	−8.05895	−0.491363	−0.245681	−	0.969351i	$-0.579012\pi$
$269$	−8.05895	−0.491363	−0.245681	+	0.969351i	$0.579012\pi$
$270$	−2.36962	−0.144210
$271$	−4.28373	−0.260218	−0.130109	−	0.991500i	$-0.541533\pi$
$271$	−4.28373	−0.260218	−0.130109	+	0.991500i	$0.541533\pi$
$272$	6.89822	0.418266
$273$	−3.23038	−0.195512
$274$	−18.7483	−1.13262
$275$	−4.95986	−0.299091
$276$	−8.69195	−0.523194
$277$	−10.8497	−0.651896	−0.325948	−	0.945388i	$-0.605683\pi$
$277$	−10.8497	−0.651896	−0.325948	+	0.945388i	$0.605683\pi$
$278$	5.31650	0.318863
$279$	−12.1004	−0.724431
$280$	−1.00000	−0.0597614
$281$	26.3022	1.56906	0.784529	−	0.620092i	$-0.212905\pi$
$281$	26.3022	1.56906	0.784529	+	0.620092i	$0.212905\pi$
$282$	15.6907	0.934370
$283$	16.7857	0.997808	0.498904	−	0.866657i	$-0.333736\pi$
$283$	16.7857	0.997808	0.498904	+	0.866657i	$0.333736\pi$
$284$	1.00000	0.0593391
$285$	−11.8488	−0.701860
$286$	−7.21377	−0.426559
$287$	0.822714	0.0485633
$288$	1.93311	0.113910
$289$	30.5855	1.79915
$290$	4.17269	0.245029
$291$	−14.2748	−0.836805
$292$	6.66332	0.389942
$293$	−13.1554	−0.768549	−0.384274	−	0.923219i	$-0.625548\pi$
$293$	−13.1554	−0.768549	−0.384274	+	0.923219i	$0.625548\pi$
$294$	−2.22106	−0.129535
$295$	−5.17530	−0.301318
$296$	−1.10774	−0.0643861
$297$	−11.7530	−0.681977
$298$	6.02481	0.349008
$299$	5.69181	0.329166
$300$	−2.22106	−0.128233
$301$	−2.90442	−0.167408
$302$	−17.5577	−1.01033
$303$	−22.2239	−1.27673
$304$	−5.33473	−0.305968
$305$	−5.42131	−0.310423
$306$	13.3350	0.762314
$307$	−8.49210	−0.484670	−0.242335	−	0.970193i	$-0.577913\pi$
$307$	−8.49210	−0.484670	−0.242335	+	0.970193i	$0.577913\pi$
$308$	−4.95986	−0.282614
$309$	−22.5580	−1.28328
$310$	6.25953	0.355518
$311$	−3.25021	−0.184303	−0.0921513	−	0.995745i	$-0.529374\pi$
$311$	−3.25021	−0.184303	−0.0921513	+	0.995745i	$0.529374\pi$
$312$	−3.23038	−0.182884
$313$	−10.2954	−0.581930	−0.290965	−	0.956734i	$-0.593976\pi$
$313$	−10.2954	−0.581930	−0.290965	+	0.956734i	$0.593976\pi$
$314$	19.0927	1.07746
$315$	−1.93311	−0.108919
$316$	5.91342	0.332656
$317$	−4.53247	−0.254569	−0.127284	−	0.991866i	$-0.540626\pi$
$317$	−4.53247	−0.254569	−0.127284	+	0.991866i	$0.540626\pi$
$318$	−1.51641	−0.0850362
$319$	20.6959	1.15875
$320$	−1.00000	−0.0559017
$321$	15.9939	0.892691
$322$	3.91342	0.218086
$323$	−36.8001	−2.04761
$324$	−11.0624	−0.614578
$325$	1.45443	0.0806774
$326$	17.0291	0.943155
$327$	8.28148	0.457967
$328$	0.822714	0.0454268
$329$	−7.06452	−0.389480
$330$	−11.0161	−0.606419
$331$	−6.61111	−0.363380	−0.181690	−	0.983356i	$-0.558157\pi$
$331$	−6.61111	−0.363380	−0.181690	+	0.983356i	$0.558157\pi$
$332$	1.97733	0.108520
$333$	−2.14139	−0.117347
$334$	14.9636	0.818773
$335$	3.44964	0.188474
$336$	−2.22106	−0.121169
$337$	17.6421	0.961026	0.480513	−	0.876988i	$-0.340451\pi$
$337$	17.6421	0.961026	0.480513	+	0.876988i	$0.340451\pi$
$338$	−10.8846	−0.592046
$339$	−38.0806	−2.06825
$340$	−6.89822	−0.374109
$341$	31.0464	1.68126
$342$	−10.3126	−0.557644
$343$	1.00000	0.0539949
$344$	−2.90442	−0.156596
$345$	8.69195	0.467959
$346$	11.2451	0.604542
$347$	−28.5288	−1.53151	−0.765754	−	0.643134i	$-0.777634\pi$
$347$	−28.5288	−1.53151	−0.765754	+	0.643134i	$0.777634\pi$
$348$	9.26780	0.496806
$349$	16.4297	0.879460	0.439730	−	0.898130i	$-0.355074\pi$
$349$	16.4297	0.879460	0.439730	+	0.898130i	$0.355074\pi$
$350$	1.00000	0.0534522
$351$	3.44645	0.183958
$352$	−4.95986	−0.264361
$353$	5.40018	0.287423	0.143711	−	0.989620i	$-0.454096\pi$
$353$	5.40018	0.287423	0.143711	+	0.989620i	$0.454096\pi$
$354$	−11.4947	−0.610934
$355$	−1.00000	−0.0530745
$356$	8.58584	0.455049
$357$	−15.3214	−0.810893
$358$	−10.3091	−0.544853
$359$	6.88943	0.363610	0.181805	−	0.983335i	$-0.441806\pi$
$359$	6.88943	0.363610	0.181805	+	0.983335i	$0.441806\pi$
$360$	−1.93311	−0.101884
$361$	9.45932	0.497859
$362$	3.37663	0.177472
$363$	−30.2068	−1.58545
$364$	1.45443	0.0762329
$365$	−6.66332	−0.348774
$366$	−12.0411	−0.629396
$367$	17.6574	0.921707	0.460854	−	0.887476i	$-0.347543\pi$
$367$	17.6574	0.921707	0.460854	+	0.887476i	$0.347543\pi$
$368$	3.91342	0.204001
$369$	1.59040	0.0827929
$370$	1.10774	0.0575887
$371$	0.682742	0.0354462
$372$	13.9028	0.720827
$373$	21.5354	1.11506	0.557530	−	0.830157i	$-0.311749\pi$
$373$	21.5354	1.11506	0.557530	+	0.830157i	$0.311749\pi$
$374$	−34.2142	−1.76917
$375$	2.22106	0.114695
$376$	−7.06452	−0.364325
$377$	−6.06889	−0.312564
$378$	2.36962	0.121880
$379$	10.1569	0.521726	0.260863	−	0.965376i	$-0.415993\pi$
$379$	10.1569	0.521726	0.260863	+	0.965376i	$0.415993\pi$
$380$	5.33473	0.273666
$381$	−3.08743	−0.158174
$382$	13.3422	0.682646
$383$	−16.8556	−0.861279	−0.430640	−	0.902524i	$-0.641712\pi$
$383$	−16.8556	−0.861279	−0.430640	+	0.902524i	$0.641712\pi$
$384$	−2.22106	−0.113343
$385$	4.95986	0.252778
$386$	2.06596	0.105155
$387$	−5.61457	−0.285405
$388$	6.42703	0.326283
$389$	1.77970	0.0902346	0.0451173	−	0.998982i	$-0.485634\pi$
$389$	1.77970	0.0902346	0.0451173	+	0.998982i	$0.485634\pi$
$390$	3.23038	0.163577
$391$	26.9957	1.36523
$392$	1.00000	0.0505076
$393$	14.2582	0.719232
$394$	−6.59787	−0.332396
$395$	−5.91342	−0.297537
$396$	−9.58797	−0.481814
$397$	37.6626	1.89023	0.945115	−	0.326738i	$-0.105949\pi$
$397$	37.6626	1.89023	0.945115	+	0.326738i	$0.105949\pi$
$398$	12.7062	0.636903
$399$	11.8488	0.593180
$400$	1.00000	0.0500000
$401$	−28.7436	−1.43539	−0.717694	−	0.696358i	$-0.754803\pi$
$401$	−28.7436	−1.43539	−0.717694	+	0.696358i	$0.754803\pi$
$402$	7.66187	0.382139
$403$	−9.10406	−0.453506
$404$	10.0060	0.497815
$405$	11.0624	0.549696
$406$	−4.17269	−0.207087
$407$	5.49423	0.272339
$408$	−15.3214	−0.758521
$409$	12.0460	0.595637	0.297819	−	0.954622i	$-0.403741\pi$
$409$	12.0460	0.595637	0.297819	+	0.954622i	$0.403741\pi$
$410$	−0.822714	−0.0406309
$411$	41.6410	2.05400
$412$	10.1564	0.500369
$413$	5.17530	0.254660
$414$	7.56509	0.371804
$415$	−1.97733	−0.0970633
$416$	1.45443	0.0713094
$417$	−11.8083	−0.578254
$418$	26.4595	1.29418
$419$	−0.115852	−0.00565975	−0.00282988	−	0.999996i	$-0.500901\pi$
$419$	−0.115852	−0.00565975	−0.00282988	+	0.999996i	$0.500901\pi$
$420$	2.22106	0.108377
$421$	−3.43245	−0.167287	−0.0836437	−	0.996496i	$-0.526656\pi$
$421$	−3.43245	−0.167287	−0.0836437	+	0.996496i	$0.526656\pi$
$422$	22.5895	1.09964
$423$	−13.6565	−0.664003
$424$	0.682742	0.0331569
$425$	6.89822	0.334613
$426$	−2.22106	−0.107611
$427$	5.42131	0.262355
$428$	−7.20101	−0.348074
$429$	16.0222	0.773561
$430$	2.90442	0.140064
$431$	−4.73502	−0.228078	−0.114039	−	0.993476i	$-0.536379\pi$
$431$	−4.73502	−0.228078	−0.114039	+	0.993476i	$0.536379\pi$
$432$	2.36962	0.114008
$433$	22.1844	1.06612	0.533058	−	0.846079i	$-0.321043\pi$
$433$	22.1844	1.06612	0.533058	+	0.846079i	$0.321043\pi$
$434$	−6.25953	−0.300467
$435$	−9.26780	−0.444357
$436$	−3.72861	−0.178568
$437$	−20.8770	−0.998684
$438$	−14.7997	−0.707155
$439$	30.6211	1.46146	0.730732	−	0.682664i	$-0.239179\pi$
$439$	30.6211	1.46146	0.730732	+	0.682664i	$0.239179\pi$
$440$	4.95986	0.236452
$441$	1.93311	0.0920530
$442$	10.0330	0.477221
$443$	13.4199	0.637599	0.318800	−	0.947822i	$-0.396720\pi$
$443$	13.4199	0.637599	0.318800	+	0.947822i	$0.396720\pi$
$444$	2.46036	0.116763
$445$	−8.58584	−0.407008
$446$	23.6538	1.12004
$447$	−13.3815	−0.632921
$448$	1.00000	0.0472456
$449$	−15.7124	−0.741515	−0.370758	−	0.928730i	$-0.620902\pi$
$449$	−15.7124	−0.741515	−0.370758	+	0.928730i	$0.620902\pi$
$450$	1.93311	0.0911279
$451$	−4.08054	−0.192145
$452$	17.1452	0.806443
$453$	38.9967	1.83223
$454$	−11.3442	−0.532411
$455$	−1.45443	−0.0681848
$456$	11.8488	0.554869
$457$	11.2295	0.525294	0.262647	−	0.964892i	$-0.415405\pi$
$457$	11.2295	0.525294	0.262647	+	0.964892i	$0.415405\pi$
$458$	1.21116	0.0565940
$459$	16.3462	0.762974
$460$	−3.91342	−0.182464
$461$	20.5689	0.957989	0.478994	−	0.877818i	$-0.341001\pi$
$461$	20.5689	0.957989	0.478994	+	0.877818i	$0.341001\pi$
$462$	11.0161	0.512518
$463$	2.58909	0.120325	0.0601627	−	0.998189i	$-0.480838\pi$
$463$	2.58909	0.120325	0.0601627	+	0.998189i	$0.480838\pi$
$464$	−4.17269	−0.193712
$465$	−13.9028	−0.644727
$466$	1.60040	0.0741370
$467$	−22.5175	−1.04199	−0.520993	−	0.853561i	$-0.674438\pi$
$467$	−22.5175	−1.04199	−0.520993	+	0.853561i	$0.674438\pi$
$468$	2.81158	0.129965
$469$	−3.44964	−0.159290
$470$	7.06452	0.325862
$471$	−42.4061	−1.95397
$472$	5.17530	0.238213
$473$	14.4055	0.662366
$474$	−13.1341	−0.603268
$475$	−5.33473	−0.244774
$476$	6.89822	0.316179
$477$	1.31982	0.0604303
$478$	16.3645	0.748497
$479$	−33.1595	−1.51510	−0.757548	−	0.652779i	$-0.773603\pi$
$479$	−33.1595	−1.51510	−0.757548	+	0.652779i	$0.773603\pi$
$480$	2.22106	0.101377
$481$	−1.61113	−0.0734613
$482$	11.7331	0.534427
$483$	−8.69195	−0.395497
$484$	13.6002	0.618190
$485$	−6.42703	−0.291836
$486$	17.4614	0.792067
$487$	−15.2417	−0.690667	−0.345334	−	0.938480i	$-0.612234\pi$
$487$	−15.2417	−0.690667	−0.345334	+	0.938480i	$0.612234\pi$
$488$	5.42131	0.245411
$489$	−37.8227	−1.71040
$490$	−1.00000	−0.0451754
$491$	41.3596	1.86653	0.933265	−	0.359187i	$-0.116946\pi$
$491$	41.3596	1.86653	0.933265	+	0.359187i	$0.116946\pi$
$492$	−1.82730	−0.0823810
$493$	−28.7841	−1.29637
$494$	−7.75900	−0.349094
$495$	9.58797	0.430947
$496$	−6.25953	−0.281061
$497$	1.00000	0.0448561
$498$	−4.39177	−0.196800
$499$	−15.7416	−0.704693	−0.352346	−	0.935870i	$-0.614616\pi$
$499$	−15.7416	−0.704693	−0.352346	+	0.935870i	$0.614616\pi$
$500$	−1.00000	−0.0447214
$501$	−33.2351	−1.48484
$502$	20.1129	0.897684
$503$	−31.6548	−1.41142	−0.705709	−	0.708501i	$-0.749372\pi$
$503$	−31.6548	−1.41142	−0.705709	+	0.708501i	$0.749372\pi$
$504$	1.93311	0.0861077
$505$	−10.0060	−0.445259
$506$	−19.4100	−0.862880
$507$	24.1754	1.07367
$508$	1.39007	0.0616744
$509$	18.8281	0.834539	0.417270	−	0.908783i	$-0.362987\pi$
$509$	18.8281	0.834539	0.417270	+	0.908783i	$0.362987\pi$
$510$	15.3214	0.678442
$511$	6.66332	0.294768
$512$	1.00000	0.0441942
$513$	−12.6413	−0.558126
$514$	−2.88190	−0.127115
$515$	−10.1564	−0.447544
$516$	6.45089	0.283985
$517$	35.0390	1.54101
$518$	−1.10774	−0.0486713
$519$	−24.9761	−1.09633
$520$	−1.45443	−0.0637811
$521$	−11.4638	−0.502239	−0.251119	−	0.967956i	$-0.580799\pi$
$521$	−11.4638	−0.502239	−0.251119	+	0.967956i	$0.580799\pi$
$522$	−8.06628	−0.353052
$523$	−33.8930	−1.48204	−0.741019	−	0.671484i	$-0.765657\pi$
$523$	−33.8930	−1.48204	−0.741019	+	0.671484i	$0.765657\pi$
$524$	−6.41955	−0.280439
$525$	−2.22106	−0.0969351
$526$	16.4635	0.717842
$527$	−43.1797	−1.88094
$528$	11.0161	0.479416
$529$	−7.68513	−0.334136
$530$	−0.682742	−0.0296564
$531$	10.0044	0.434156
$532$	−5.33473	−0.231290
$533$	1.19658	0.0518297
$534$	−19.0697	−0.825226
$535$	7.20101	0.311327
$536$	−3.44964	−0.149002
$537$	22.8972	0.988086
$538$	−8.05895	−0.347446
$539$	−4.95986	−0.213636
$540$	−2.36962	−0.101972
$541$	−27.1082	−1.16547	−0.582736	−	0.812661i	$-0.698018\pi$
$541$	−27.1082	−1.16547	−0.582736	+	0.812661i	$0.698018\pi$
$542$	−4.28373	−0.184002
$543$	−7.49970	−0.321843
$544$	6.89822	0.295759
$545$	3.72861	0.159716
$546$	−3.23038	−0.138248
$547$	45.6949	1.95377	0.976887	−	0.213756i	$-0.0685698\pi$
$547$	45.6949	1.95377	0.976887	+	0.213756i	$0.0685698\pi$
$548$	−18.7483	−0.800886
$549$	10.4800	0.447276
$550$	−4.95986	−0.211489
$551$	22.2602	0.948315
$552$	−8.69195	−0.369954
$553$	5.91342	0.251464
$554$	−10.8497	−0.460960
$555$	−2.46036	−0.104436
$556$	5.31650	0.225470
$557$	−39.7241	−1.68317	−0.841583	−	0.540128i	$-0.818376\pi$
$557$	−39.7241	−1.68317	−0.841583	+	0.540128i	$0.818376\pi$
$558$	−12.1004	−0.512250
$559$	−4.22428	−0.178668
$560$	−1.00000	−0.0422577
$561$	75.9918	3.20838
$562$	26.3022	1.10949
$563$	−45.0579	−1.89896	−0.949482	−	0.313822i	$-0.898391\pi$
$563$	−45.0579	−1.89896	−0.949482	+	0.313822i	$0.898391\pi$
$564$	15.6907	0.660699
$565$	−17.1452	−0.721304
$566$	16.7857	0.705557
$567$	−11.0624	−0.464578
$568$	1.00000	0.0419591
$569$	4.02858	0.168887	0.0844434	−	0.996428i	$-0.473089\pi$
$569$	4.02858	0.168887	0.0844434	+	0.996428i	$0.473089\pi$
$570$	−11.8488	−0.496290
$571$	25.8944	1.08365	0.541823	−	0.840493i	$-0.317734\pi$
$571$	25.8944	1.08365	0.541823	+	0.840493i	$0.317734\pi$
$572$	−7.21377	−0.301623
$573$	−29.6338	−1.23797
$574$	0.822714	0.0343394
$575$	3.91342	0.163201
$576$	1.93311	0.0805464
$577$	14.8309	0.617420	0.308710	−	0.951156i	$-0.400103\pi$
$577$	14.8309	0.617420	0.308710	+	0.951156i	$0.400103\pi$
$578$	30.5855	1.27219
$579$	−4.58862	−0.190697
$580$	4.17269	0.173261
$581$	1.97733	0.0820335
$582$	−14.2748	−0.591711
$583$	−3.38630	−0.140246
$584$	6.66332	0.275730
$585$	−2.81158	−0.116245
$586$	−13.1554	−0.543446
$587$	4.27648	0.176509	0.0882547	−	0.996098i	$-0.471871\pi$
$587$	4.27648	0.176509	0.0882547	+	0.996098i	$0.471871\pi$
$588$	−2.22106	−0.0915950
$589$	33.3929	1.37593
$590$	−5.17530	−0.213064
$591$	14.6543	0.602797
$592$	−1.10774	−0.0455278
$593$	−41.7196	−1.71322	−0.856609	−	0.515966i	$-0.827433\pi$
$593$	−41.7196	−1.71322	−0.856609	+	0.515966i	$0.827433\pi$
$594$	−11.7530	−0.482230
$595$	−6.89822	−0.282800
$596$	6.02481	0.246786
$597$	−28.2212	−1.15502
$598$	5.69181	0.232755
$599$	−33.0091	−1.34871	−0.674357	−	0.738405i	$-0.735579\pi$
$599$	−33.0091	−1.34871	−0.674357	+	0.738405i	$0.735579\pi$
$600$	−2.22106	−0.0906745
$601$	35.8468	1.46222	0.731111	−	0.682259i	$-0.239002\pi$
$601$	35.8468	1.46222	0.731111	+	0.682259i	$0.239002\pi$
$602$	−2.90442	−0.118375
$603$	−6.66856	−0.271565
$604$	−17.5577	−0.714413
$605$	−13.6002	−0.552926
$606$	−22.2239	−0.902782
$607$	−26.1717	−1.06228	−0.531138	−	0.847286i	$-0.678235\pi$
$607$	−26.1717	−1.06228	−0.531138	+	0.847286i	$0.678235\pi$
$608$	−5.33473	−0.216352
$609$	9.26780	0.375550
$610$	−5.42131	−0.219502
$611$	−10.2749	−0.415677
$612$	13.3350	0.539037
$613$	−34.0090	−1.37361	−0.686805	−	0.726842i	$-0.740987\pi$
$613$	−34.0090	−1.37361	−0.686805	+	0.726842i	$0.740987\pi$
$614$	−8.49210	−0.342713
$615$	1.82730	0.0736838
$616$	−4.95986	−0.199838
$617$	7.70251	0.310091	0.155046	−	0.987907i	$-0.450448\pi$
$617$	7.70251	0.310091	0.155046	+	0.987907i	$0.450448\pi$
$618$	−22.5580	−0.907415
$619$	−10.2642	−0.412554	−0.206277	−	0.978494i	$-0.566135\pi$
$619$	−10.2642	−0.412554	−0.206277	+	0.978494i	$0.566135\pi$
$620$	6.25953	0.251389
$621$	9.27332	0.372126
$622$	−3.25021	−0.130322
$623$	8.58584	0.343984
$624$	−3.23038	−0.129319
$625$	1.00000	0.0400000
$626$	−10.2954	−0.411487
$627$	−58.7682	−2.34697
$628$	19.0927	0.761882
$629$	−7.64144	−0.304684
$630$	−1.93311	−0.0770171
$631$	−1.63492	−0.0650852	−0.0325426	−	0.999470i	$-0.510360\pi$
$631$	−1.63492	−0.0650852	−0.0325426	+	0.999470i	$0.510360\pi$
$632$	5.91342	0.235223
$633$	−50.1726	−1.99418
$634$	−4.53247	−0.180007
$635$	−1.39007	−0.0551633
$636$	−1.51641	−0.0601297
$637$	1.45443	0.0576267
$638$	20.6959	0.819360
$639$	1.93311	0.0764728
$640$	−1.00000	−0.0395285
$641$	15.8058	0.624292	0.312146	−	0.950034i	$-0.398952\pi$
$641$	15.8058	0.624292	0.312146	+	0.950034i	$0.398952\pi$
$642$	15.9939	0.631228
$643$	11.1713	0.440554	0.220277	−	0.975437i	$-0.429304\pi$
$643$	11.1713	0.440554	0.220277	+	0.975437i	$0.429304\pi$
$644$	3.91342	0.154210
$645$	−6.45089	−0.254004
$646$	−36.8001	−1.44788
$647$	−22.0344	−0.866261	−0.433131	−	0.901331i	$-0.642591\pi$
$647$	−22.0344	−0.866261	−0.433131	+	0.901331i	$0.642591\pi$
$648$	−11.0624	−0.434573
$649$	−25.6688	−1.00759
$650$	1.45443	0.0570475
$651$	13.9028	0.544894
$652$	17.0291	0.666911
$653$	−1.47130	−0.0575762	−0.0287881	−	0.999586i	$-0.509165\pi$
$653$	−1.47130	−0.0575762	−0.0287881	+	0.999586i	$0.509165\pi$
$654$	8.28148	0.323832
$655$	6.41955	0.250832
$656$	0.822714	0.0321216
$657$	12.8810	0.502534
$658$	−7.06452	−0.275404
$659$	−32.6771	−1.27292	−0.636460	−	0.771309i	$-0.719602\pi$
$659$	−32.6771	−1.27292	−0.636460	+	0.771309i	$0.719602\pi$
$660$	−11.0161	−0.428803
$661$	3.83365	0.149112	0.0745559	−	0.997217i	$-0.476246\pi$
$661$	3.83365	0.149112	0.0745559	+	0.997217i	$0.476246\pi$
$662$	−6.61111	−0.256948
$663$	−22.2839	−0.865435
$664$	1.97733	0.0767353
$665$	5.33473	0.206872
$666$	−2.14139	−0.0829771
$667$	−16.3295	−0.632280
$668$	14.9636	0.578960
$669$	−52.5365	−2.03118
$670$	3.44964	0.133271
$671$	−26.8889	−1.03803
$672$	−2.22106	−0.0856793
$673$	−7.89239	−0.304229	−0.152115	−	0.988363i	$-0.548608\pi$
$673$	−7.89239	−0.304229	−0.152115	+	0.988363i	$0.548608\pi$
$674$	17.6421	0.679548
$675$	2.36962	0.0912067
$676$	−10.8846	−0.418640
$677$	19.7112	0.757563	0.378781	−	0.925486i	$-0.376343\pi$
$677$	19.7112	0.757563	0.378781	+	0.925486i	$0.376343\pi$
$678$	−38.0806	−1.46248
$679$	6.42703	0.246647
$680$	−6.89822	−0.264535
$681$	25.1962	0.965521
$682$	31.0464	1.18883
$683$	41.3158	1.58090	0.790452	−	0.612524i	$-0.209846\pi$
$683$	41.3158	1.58090	0.790452	+	0.612524i	$0.209846\pi$
$684$	−10.3126	−0.394314
$685$	18.7483	0.716334
$686$	1.00000	0.0381802
$687$	−2.69007	−0.102633
$688$	−2.90442	−0.110730
$689$	0.993002	0.0378304
$690$	8.69195	0.330897
$691$	−12.9256	−0.491712	−0.245856	−	0.969306i	$-0.579069\pi$
$691$	−12.9256	−0.491712	−0.245856	+	0.969306i	$0.579069\pi$
$692$	11.2451	0.427476
$693$	−9.58797	−0.364217
$694$	−28.5288	−1.08294
$695$	−5.31650	−0.201666
$696$	9.26780	0.351295
$697$	5.67526	0.214966
$698$	16.4297	0.621872
$699$	−3.55458	−0.134447
$700$	1.00000	0.0377964
$701$	−51.7659	−1.95517	−0.977585	−	0.210540i	$-0.932478\pi$
$701$	−51.7659	−1.95517	−0.977585	+	0.210540i	$0.932478\pi$
$702$	3.44645	0.130078
$703$	5.90949	0.222881
$704$	−4.95986	−0.186932
$705$	−15.6907	−0.590947
$706$	5.40018	0.203238
$707$	10.0060	0.376313
$708$	−11.4947	−0.431996
$709$	−38.0918	−1.43057	−0.715284	−	0.698834i	$-0.753703\pi$
$709$	−38.0918	−1.43057	−0.715284	+	0.698834i	$0.753703\pi$
$710$	−1.00000	−0.0375293
$711$	11.4313	0.428708
$712$	8.58584	0.321768
$713$	−24.4962	−0.917390
$714$	−15.3214	−0.573388
$715$	7.21377	0.269780
$716$	−10.3091	−0.385270
$717$	−36.3467	−1.35739
$718$	6.88943	0.257111
$719$	−5.86631	−0.218776	−0.109388	−	0.993999i	$-0.534889\pi$
$719$	−5.86631	−0.218776	−0.109388	+	0.993999i	$0.534889\pi$
$720$	−1.93311	−0.0720429
$721$	10.1564	0.378244
$722$	9.45932	0.352040
$723$	−26.0599	−0.969177
$724$	3.37663	0.125491
$725$	−4.17269	−0.154970
$726$	−30.2068	−1.12108
$727$	19.1632	0.710723	0.355361	−	0.934729i	$-0.384358\pi$
$727$	19.1632	0.710723	0.355361	+	0.934729i	$0.384358\pi$
$728$	1.45443	0.0539048
$729$	−5.59569	−0.207248
$730$	−6.66332	−0.246621
$731$	−20.0353	−0.741033
$732$	−12.0411	−0.445050
$733$	−11.9935	−0.442991	−0.221495	−	0.975161i	$-0.571094\pi$
$733$	−11.9935	−0.442991	−0.221495	+	0.975161i	$0.571094\pi$
$734$	17.6574	0.651746
$735$	2.22106	0.0819251
$736$	3.91342	0.144251
$737$	17.1097	0.630246
$738$	1.59040	0.0585434
$739$	24.6043	0.905085	0.452543	−	0.891743i	$-0.350517\pi$
$739$	24.6043	0.905085	0.452543	+	0.891743i	$0.350517\pi$
$740$	1.10774	0.0407213
$741$	17.2332	0.633078
$742$	0.682742	0.0250643
$743$	44.0470	1.61593	0.807964	−	0.589231i	$-0.200569\pi$
$743$	44.0470	1.61593	0.807964	+	0.589231i	$0.200569\pi$
$744$	13.9028	0.509702
$745$	−6.02481	−0.220732
$746$	21.5354	0.788467
$747$	3.82241	0.139854
$748$	−34.2142	−1.25100
$749$	−7.20101	−0.263119
$750$	2.22106	0.0811017
$751$	−26.7611	−0.976528	−0.488264	−	0.872696i	$-0.662370\pi$
$751$	−26.7611	−0.976528	−0.488264	+	0.872696i	$0.662370\pi$
$752$	−7.06452	−0.257617
$753$	−44.6721	−1.62794
$754$	−6.06889	−0.221016
$755$	17.5577	0.638990
$756$	2.36962	0.0861822
$757$	−28.0863	−1.02081	−0.510407	−	0.859933i	$-0.670505\pi$
$757$	−28.0863	−1.02081	−0.510407	+	0.859933i	$0.670505\pi$
$758$	10.1569	0.368916
$759$	43.1108	1.56482
$760$	5.33473	0.193511
$761$	41.3379	1.49850	0.749248	−	0.662289i	$-0.230415\pi$
$761$	41.3379	1.49850	0.749248	+	0.662289i	$0.230415\pi$
$762$	−3.08743	−0.111846
$763$	−3.72861	−0.134985
$764$	13.3422	0.482704
$765$	−13.3350	−0.482130
$766$	−16.8556	−0.609016
$767$	7.52712	0.271789
$768$	−2.22106	−0.0801457
$769$	1.74283	0.0628480	0.0314240	−	0.999506i	$-0.489996\pi$
$769$	1.74283	0.0628480	0.0314240	+	0.999506i	$0.489996\pi$
$770$	4.95986	0.178741
$771$	6.40087	0.230522
$772$	2.06596	0.0743555
$773$	−33.6800	−1.21139	−0.605693	−	0.795698i	$-0.707104\pi$
$773$	−33.6800	−1.21139	−0.605693	+	0.795698i	$0.707104\pi$
$774$	−5.61457	−0.201812
$775$	−6.25953	−0.224849
$776$	6.42703	0.230717
$777$	2.46036	0.0882649
$778$	1.77970	0.0638055
$779$	−4.38896	−0.157251
$780$	3.23038	0.115666
$781$	−4.95986	−0.177478
$782$	26.9957	0.965363
$783$	−9.88768	−0.353357
$784$	1.00000	0.0357143
$785$	−19.0927	−0.681448
$786$	14.2582	0.508573
$787$	1.34328	0.0478828	0.0239414	−	0.999713i	$-0.492378\pi$
$787$	1.34328	0.0478828	0.0239414	+	0.999713i	$0.492378\pi$
$788$	−6.59787	−0.235039
$789$	−36.5664	−1.30180
$790$	−5.91342	−0.210390
$791$	17.1452	0.609613
$792$	−9.58797	−0.340694
$793$	7.88492	0.280002
$794$	37.6626	1.33659
$795$	1.51641	0.0537816
$796$	12.7062	0.450359
$797$	1.69691	0.0601076	0.0300538	−	0.999548i	$-0.490432\pi$
$797$	1.69691	0.0601076	0.0300538	+	0.999548i	$0.490432\pi$
$798$	11.8488	0.419442
$799$	−48.7326	−1.72404
$800$	1.00000	0.0353553
$801$	16.5974	0.586440
$802$	−28.7436	−1.01497
$803$	−33.0491	−1.16628
$804$	7.66187	0.270213
$805$	−3.91342	−0.137930
$806$	−9.10406	−0.320677
$807$	17.8994	0.630089
$808$	10.0060	0.352009
$809$	−49.0636	−1.72498	−0.862492	−	0.506071i	$-0.831097\pi$
$809$	−49.0636	−1.72498	−0.862492	+	0.506071i	$0.831097\pi$
$810$	11.0624	0.388694
$811$	3.67791	0.129149	0.0645744	−	0.997913i	$-0.479431\pi$
$811$	3.67791	0.129149	0.0645744	+	0.997913i	$0.479431\pi$
$812$	−4.17269	−0.146433
$813$	9.51443	0.333686
$814$	5.49423	0.192573
$815$	−17.0291	−0.596503
$816$	−15.3214	−0.536355
$817$	15.4943	0.542077
$818$	12.0460	0.421179
$819$	2.81158	0.0982446
$820$	−0.822714	−0.0287304
$821$	2.07436	0.0723957	0.0361978	−	0.999345i	$-0.488475\pi$
$821$	2.07436	0.0723957	0.0361978	+	0.999345i	$0.488475\pi$
$822$	41.6410	1.45240
$823$	49.1281	1.71250	0.856248	−	0.516565i	$-0.172789\pi$
$823$	49.1281	1.71250	0.856248	+	0.516565i	$0.172789\pi$
$824$	10.1564	0.353815
$825$	11.0161	0.383533
$826$	5.17530	0.180072
$827$	−33.2686	−1.15686	−0.578432	−	0.815731i	$-0.696335\pi$
$827$	−33.2686	−1.15686	−0.578432	+	0.815731i	$0.696335\pi$
$828$	7.56509	0.262905
$829$	−14.5766	−0.506268	−0.253134	−	0.967431i	$-0.581461\pi$
$829$	−14.5766	−0.506268	−0.253134	+	0.967431i	$0.581461\pi$
$830$	−1.97733	−0.0686342
$831$	24.0979	0.835946
$832$	1.45443	0.0504233
$833$	6.89822	0.239009
$834$	−11.8083	−0.408887
$835$	−14.9636	−0.517838
$836$	26.4595	0.915121
$837$	−14.8327	−0.512694
$838$	−0.115852	−0.00400205
$839$	−16.8156	−0.580537	−0.290269	−	0.956945i	$-0.593745\pi$
$839$	−16.8156	−0.580537	−0.290269	+	0.956945i	$0.593745\pi$
$840$	2.22106	0.0766339
$841$	−11.5887	−0.399609
$842$	−3.43245	−0.118290
$843$	−58.4188	−2.01205
$844$	22.5895	0.777562
$845$	10.8846	0.374443
$846$	−13.6565	−0.469521
$847$	13.6002	0.467308
$848$	0.682742	0.0234455
$849$	−37.2821	−1.27952
$850$	6.89822	0.236607
$851$	−4.33505	−0.148604
$852$	−2.22106	−0.0760923
$853$	19.2784	0.660081	0.330040	−	0.943967i	$-0.392938\pi$
$853$	19.2784	0.660081	0.330040	+	0.943967i	$0.392938\pi$
$854$	5.42131	0.185513
$855$	10.3126	0.352685
$856$	−7.20101	−0.246125
$857$	−3.67557	−0.125555	−0.0627775	−	0.998028i	$-0.519996\pi$
$857$	−3.67557	−0.125555	−0.0627775	+	0.998028i	$0.519996\pi$
$858$	16.0222	0.546990
$859$	−22.8512	−0.779673	−0.389836	−	0.920884i	$-0.627468\pi$
$859$	−22.8512	−0.779673	−0.389836	+	0.920884i	$0.627468\pi$
$860$	2.90442	0.0990399
$861$	−1.82730	−0.0622742
$862$	−4.73502	−0.161276
$863$	−7.62961	−0.259715	−0.129857	−	0.991533i	$-0.541452\pi$
$863$	−7.62961	−0.259715	−0.129857	+	0.991533i	$0.541452\pi$
$864$	2.36962	0.0806161
$865$	−11.2451	−0.382346
$866$	22.1844	0.753858
$867$	−67.9322	−2.30710
$868$	−6.25953	−0.212462
$869$	−29.3297	−0.994943
$870$	−9.26780	−0.314208
$871$	−5.01727	−0.170004
$872$	−3.72861	−0.126267
$873$	12.4242	0.420495
$874$	−20.8770	−0.706177
$875$	−1.00000	−0.0338062
$876$	−14.7997	−0.500034
$877$	0.499454	0.0168654	0.00843268	−	0.999964i	$-0.497316\pi$
$877$	0.499454	0.0168654	0.00843268	+	0.999964i	$0.497316\pi$
$878$	30.6211	1.03341
$879$	29.2190	0.985533
$880$	4.95986	0.167197
$881$	34.3816	1.15835	0.579173	−	0.815204i	$-0.303375\pi$
$881$	34.3816	1.15835	0.579173	+	0.815204i	$0.303375\pi$
$882$	1.93311	0.0650913
$883$	−52.7881	−1.77646	−0.888230	−	0.459398i	$-0.848065\pi$
$883$	−52.7881	−1.77646	−0.888230	+	0.459398i	$0.848065\pi$
$884$	10.0330	0.337446
$885$	11.4947	0.386389
$886$	13.4199	0.450851
$887$	−35.6939	−1.19848	−0.599242	−	0.800568i	$-0.704531\pi$
$887$	−35.6939	−1.19848	−0.599242	+	0.800568i	$0.704531\pi$
$888$	2.46036	0.0825642
$889$	1.39007	0.0466215
$890$	−8.58584	−0.287798
$891$	54.8680	1.83815
$892$	23.6538	0.791987
$893$	37.6873	1.26116
$894$	−13.3815	−0.447543
$895$	10.3091	0.344596
$896$	1.00000	0.0334077
$897$	−12.6418	−0.422099
$898$	−15.7124	−0.524330
$899$	26.1191	0.871120
$900$	1.93311	0.0644371
$901$	4.70971	0.156903
$902$	−4.08054	−0.135867
$903$	6.45089	0.214672
$904$	17.1452	0.570241
$905$	−3.37663	−0.112243
$906$	38.9967	1.29558
$907$	−7.09931	−0.235729	−0.117864	−	0.993030i	$-0.537605\pi$
$907$	−7.09931	−0.235729	−0.117864	+	0.993030i	$0.537605\pi$
$908$	−11.3442	−0.376471
$909$	19.3427	0.641556
$910$	−1.45443	−0.0482139
$911$	−3.38239	−0.112064	−0.0560318	−	0.998429i	$-0.517845\pi$
$911$	−3.38239	−0.112064	−0.0560318	+	0.998429i	$0.517845\pi$
$912$	11.8488	0.392352
$913$	−9.80728	−0.324574
$914$	11.2295	0.371439
$915$	12.0411	0.398065
$916$	1.21116	0.0400180
$917$	−6.41955	−0.211992
$918$	16.3462	0.539504
$919$	6.58445	0.217201	0.108601	−	0.994085i	$-0.465363\pi$
$919$	6.58445	0.217201	0.108601	+	0.994085i	$0.465363\pi$
$920$	−3.91342	−0.129022
$921$	18.8615	0.621507
$922$	20.5689	0.677400
$923$	1.45443	0.0478732
$924$	11.0161	0.362405
$925$	−1.10774	−0.0364223
$926$	2.58909	0.0850828
$927$	19.6335	0.644847
$928$	−4.17269	−0.136975
$929$	12.8346	0.421091	0.210545	−	0.977584i	$-0.432476\pi$
$929$	12.8346	0.421091	0.210545	+	0.977584i	$0.432476\pi$
$930$	−13.9028	−0.455891
$931$	−5.33473	−0.174839
$932$	1.60040	0.0524228
$933$	7.21892	0.236337
$934$	−22.5175	−0.736795
$935$	34.2142	1.11892
$936$	2.81158	0.0918994
$937$	55.3897	1.80950	0.904751	−	0.425941i	$-0.140057\pi$
$937$	55.3897	1.80950	0.904751	+	0.425941i	$0.140057\pi$
$938$	−3.44964	−0.112635
$939$	22.8667	0.746227
$940$	7.06452	0.230419
$941$	−58.3902	−1.90346	−0.951732	−	0.306929i	$-0.900699\pi$
$941$	−58.3902	−1.90346	−0.951732	+	0.306929i	$0.900699\pi$
$942$	−42.4061	−1.38166
$943$	3.21963	0.104845
$944$	5.17530	0.168442
$945$	−2.36962	−0.0770837
$946$	14.4055	0.468363
$947$	39.4021	1.28040	0.640198	−	0.768210i	$-0.278852\pi$
$947$	39.4021	1.28040	0.640198	+	0.768210i	$0.278852\pi$
$948$	−13.1341	−0.426575
$949$	9.69135	0.314594
$950$	−5.33473	−0.173081
$951$	10.0669	0.326441
$952$	6.89822	0.223573
$953$	15.6471	0.506860	0.253430	−	0.967354i	$-0.418441\pi$
$953$	15.6471	0.506860	0.253430	+	0.967354i	$0.418441\pi$
$954$	1.31982	0.0427307
$955$	−13.3422	−0.431744
$956$	16.3645	0.529267
$957$	−45.9669	−1.48590
$958$	−33.1595	−1.07133
$959$	−18.7483	−0.605413
$960$	2.22106	0.0716844
$961$	8.18176	0.263928
$962$	−1.61113	−0.0519450
$963$	−13.9204	−0.448578
$964$	11.7331	0.377897
$965$	−2.06596	−0.0665056
$966$	−8.69195	−0.279659
$967$	−20.8719	−0.671195	−0.335597	−	0.942006i	$-0.608938\pi$
$967$	−20.8719	−0.671195	−0.335597	+	0.942006i	$0.608938\pi$
$968$	13.6002	0.437127
$969$	81.7354	2.62572
$970$	−6.42703	−0.206359
$971$	57.1499	1.83403	0.917014	−	0.398855i	$-0.130592\pi$
$971$	57.1499	1.83403	0.917014	+	0.398855i	$0.130592\pi$
$972$	17.4614	0.560076
$973$	5.31650	0.170439
$974$	−15.2417	−0.488375
$975$	−3.23038	−0.103455
$976$	5.42131	0.173532
$977$	20.2920	0.649198	0.324599	−	0.945852i	$-0.394771\pi$
$977$	20.2920	0.649198	0.324599	+	0.945852i	$0.394771\pi$
$978$	−37.8227	−1.20944
$979$	−42.5845	−1.36101
$980$	−1.00000	−0.0319438
$981$	−7.20784	−0.230129
$982$	41.3596	1.31984
$983$	2.13152	0.0679849	0.0339925	−	0.999422i	$-0.489178\pi$
$983$	2.13152	0.0679849	0.0339925	+	0.999422i	$0.489178\pi$
$984$	−1.82730	−0.0582521
$985$	6.59787	0.210226
$986$	−28.7841	−0.916673
$987$	15.6907	0.499442
$988$	−7.75900	−0.246847
$989$	−11.3662	−0.361425
$990$	9.58797	0.304726
$991$	34.8918	1.10837	0.554187	−	0.832392i	$-0.313029\pi$
$991$	34.8918	1.10837	0.554187	+	0.832392i	$0.313029\pi$
$992$	−6.25953	−0.198740
$993$	14.6837	0.465973
$994$	1.00000	0.0317181
$995$	−12.7062	−0.402813
$996$	−4.39177	−0.139159
$997$	16.6388	0.526956	0.263478	−	0.964665i	$-0.415130\pi$
$997$	16.6388	0.526956	0.263478	+	0.964665i	$0.415130\pi$
$998$	−15.7416	−0.498293
$999$	−2.62492	−0.0830489

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4970.2.a.z.1.2	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4970.2.a.z.1.2	✓	9	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:	\( N \)	\(=\)	\( 4970 = 2 \cdot 5 \cdot 7 \cdot 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4970.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.22106 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.22106 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.93311 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.22106 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.22106 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.93311 q^{9} -1.00000 q^{10} -4.95986 q^{11} -2.22106 q^{12} +1.45443 q^{13} +1.00000 q^{14} +2.22106 q^{15} +1.00000 q^{16} +6.89822 q^{17} +1.93311 q^{18} -5.33473 q^{19} -1.00000 q^{20} -2.22106 q^{21} -4.95986 q^{22} +3.91342 q^{23} -2.22106 q^{24} +1.00000 q^{25} +1.45443 q^{26} +2.36962 q^{27} +1.00000 q^{28} -4.17269 q^{29} +2.22106 q^{30} -6.25953 q^{31} +1.00000 q^{32} +11.0161 q^{33} +6.89822 q^{34} -1.00000 q^{35} +1.93311 q^{36} -1.10774 q^{37} -5.33473 q^{38} -3.23038 q^{39} -1.00000 q^{40} +0.822714 q^{41} -2.22106 q^{42} -2.90442 q^{43} -4.95986 q^{44} -1.93311 q^{45} +3.91342 q^{46} -7.06452 q^{47} -2.22106 q^{48} +1.00000 q^{49} +1.00000 q^{50} -15.3214 q^{51} +1.45443 q^{52} +0.682742 q^{53} +2.36962 q^{54} +4.95986 q^{55} +1.00000 q^{56} +11.8488 q^{57} -4.17269 q^{58} +5.17530 q^{59} +2.22106 q^{60} +5.42131 q^{61} -6.25953 q^{62} +1.93311 q^{63} +1.00000 q^{64} -1.45443 q^{65} +11.0161 q^{66} -3.44964 q^{67} +6.89822 q^{68} -8.69195 q^{69} -1.00000 q^{70} +1.00000 q^{71} +1.93311 q^{72} +6.66332 q^{73} -1.10774 q^{74} -2.22106 q^{75} -5.33473 q^{76} -4.95986 q^{77} -3.23038 q^{78} +5.91342 q^{79} -1.00000 q^{80} -11.0624 q^{81} +0.822714 q^{82} +1.97733 q^{83} -2.22106 q^{84} -6.89822 q^{85} -2.90442 q^{86} +9.26780 q^{87} -4.95986 q^{88} +8.58584 q^{89} -1.93311 q^{90} +1.45443 q^{91} +3.91342 q^{92} +13.9028 q^{93} -7.06452 q^{94} +5.33473 q^{95} -2.22106 q^{96} +6.42703 q^{97} +1.00000 q^{98} -9.58797 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 9 q^{2} + 4 q^{3} + 9 q^{4} - 9 q^{5} + 4 q^{6} + 9 q^{7} + 9 q^{8} + 7 q^{9}+O(q^{10}) \) 9 * q + 9 * q^2 + 4 * q^3 + 9 * q^4 - 9 * q^5 + 4 * q^6 + 9 * q^7 + 9 * q^8 + 7 * q^9	\( 9 q + 9 q^{2} + 4 q^{3} + 9 q^{4} - 9 q^{5} + 4 q^{6} + 9 q^{7} + 9 q^{8} + 7 q^{9} - 9 q^{10} - 2 q^{11} + 4 q^{12} + 11 q^{13} + 9 q^{14} - 4 q^{15} + 9 q^{16} + 9 q^{17} + 7 q^{18} + 9 q^{19} - 9 q^{20} + 4 q^{21} - 2 q^{22} + 2 q^{23} + 4 q^{24} + 9 q^{25} + 11 q^{26} + 7 q^{27} + 9 q^{28} + 2 q^{29} - 4 q^{30} + 18 q^{31} + 9 q^{32} + 8 q^{33} + 9 q^{34} - 9 q^{35} + 7 q^{36} + 15 q^{37} + 9 q^{38} - 7 q^{39} - 9 q^{40} + 15 q^{41} + 4 q^{42} + 7 q^{43} - 2 q^{44} - 7 q^{45} + 2 q^{46} + 12 q^{47} + 4 q^{48} + 9 q^{49} + 9 q^{50} + 4 q^{51} + 11 q^{52} + 3 q^{53} + 7 q^{54} + 2 q^{55} + 9 q^{56} + 9 q^{57} + 2 q^{58} + 24 q^{59} - 4 q^{60} + 25 q^{61} + 18 q^{62} + 7 q^{63} + 9 q^{64} - 11 q^{65} + 8 q^{66} - 4 q^{67} + 9 q^{68} + 3 q^{69} - 9 q^{70} + 9 q^{71} + 7 q^{72} + 32 q^{73} + 15 q^{74} + 4 q^{75} + 9 q^{76} - 2 q^{77} - 7 q^{78} + 20 q^{79} - 9 q^{80} - 7 q^{81} + 15 q^{82} + 11 q^{83} + 4 q^{84} - 9 q^{85} + 7 q^{86} + 26 q^{87} - 2 q^{88} + 10 q^{89} - 7 q^{90} + 11 q^{91} + 2 q^{92} + 32 q^{93} + 12 q^{94} - 9 q^{95} + 4 q^{96} + 19 q^{97} + 9 q^{98} - 7 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 + 4 * q^3 + 9 * q^4 - 9 * q^5 + 4 * q^6 + 9 * q^7 + 9 * q^8 + 7 * q^9 - 9 * q^10 - 2 * q^11 + 4 * q^12 + 11 * q^13 + 9 * q^14 - 4 * q^15 + 9 * q^16 + 9 * q^17 + 7 * q^18 + 9 * q^19 - 9 * q^20 + 4 * q^21 - 2 * q^22 + 2 * q^23 + 4 * q^24 + 9 * q^25 + 11 * q^26 + 7 * q^27 + 9 * q^28 + 2 * q^29 - 4 * q^30 + 18 * q^31 + 9 * q^32 + 8 * q^33 + 9 * q^34 - 9 * q^35 + 7 * q^36 + 15 * q^37 + 9 * q^38 - 7 * q^39 - 9 * q^40 + 15 * q^41 + 4 * q^42 + 7 * q^43 - 2 * q^44 - 7 * q^45 + 2 * q^46 + 12 * q^47 + 4 * q^48 + 9 * q^49 + 9 * q^50 + 4 * q^51 + 11 * q^52 + 3 * q^53 + 7 * q^54 + 2 * q^55 + 9 * q^56 + 9 * q^57 + 2 * q^58 + 24 * q^59 - 4 * q^60 + 25 * q^61 + 18 * q^62 + 7 * q^63 + 9 * q^64 - 11 * q^65 + 8 * q^66 - 4 * q^67 + 9 * q^68 + 3 * q^69 - 9 * q^70 + 9 * q^71 + 7 * q^72 + 32 * q^73 + 15 * q^74 + 4 * q^75 + 9 * q^76 - 2 * q^77 - 7 * q^78 + 20 * q^79 - 9 * q^80 - 7 * q^81 + 15 * q^82 + 11 * q^83 + 4 * q^84 - 9 * q^85 + 7 * q^86 + 26 * q^87 - 2 * q^88 + 10 * q^89 - 7 * q^90 + 11 * q^91 + 2 * q^92 + 32 * q^93 + 12 * q^94 - 9 * q^95 + 4 * q^96 + 19 * q^97 + 9 * q^98 - 7 * q^99

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