LMFDB - Embedded newform 4730.2.a.l.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4730,2,Mod(1,4730)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4730, 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("4730.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4730 = 2 \cdot 5 \cdot 11 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4730.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:	$37.7692401561$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{17}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 4 $ x^2 - x - 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.56155$ of defining polynomial
Character	$\chi$	$=$	4730.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.56155 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.56155 q^{6} -3.00000 q^{7} -1.00000 q^{8} -0.561553 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.56155 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.56155 q^{6} -3.00000 q^{7} -1.00000 q^{8} -0.561553 q^{9} -1.00000 q^{10} -1.00000 q^{11} +1.56155 q^{12} -0.561553 q^{13} +3.00000 q^{14} +1.56155 q^{15} +1.00000 q^{16} +5.56155 q^{17} +0.561553 q^{18} -1.00000 q^{19} +1.00000 q^{20} -4.68466 q^{21} +1.00000 q^{22} -0.876894 q^{23} -1.56155 q^{24} +1.00000 q^{25} +0.561553 q^{26} -5.56155 q^{27} -3.00000 q^{28} -2.12311 q^{29} -1.56155 q^{30} +6.12311 q^{31} -1.00000 q^{32} -1.56155 q^{33} -5.56155 q^{34} -3.00000 q^{35} -0.561553 q^{36} +1.56155 q^{37} +1.00000 q^{38} -0.876894 q^{39} -1.00000 q^{40} -4.56155 q^{41} +4.68466 q^{42} +1.00000 q^{43} -1.00000 q^{44} -0.561553 q^{45} +0.876894 q^{46} -2.00000 q^{47} +1.56155 q^{48} +2.00000 q^{49} -1.00000 q^{50} +8.68466 q^{51} -0.561553 q^{52} -3.56155 q^{53} +5.56155 q^{54} -1.00000 q^{55} +3.00000 q^{56} -1.56155 q^{57} +2.12311 q^{58} +0.876894 q^{59} +1.56155 q^{60} -14.3693 q^{61} -6.12311 q^{62} +1.68466 q^{63} +1.00000 q^{64} -0.561553 q^{65} +1.56155 q^{66} -1.43845 q^{67} +5.56155 q^{68} -1.36932 q^{69} +3.00000 q^{70} +8.43845 q^{71} +0.561553 q^{72} +0.561553 q^{73} -1.56155 q^{74} +1.56155 q^{75} -1.00000 q^{76} +3.00000 q^{77} +0.876894 q^{78} -0.561553 q^{79} +1.00000 q^{80} -7.00000 q^{81} +4.56155 q^{82} -17.3693 q^{83} -4.68466 q^{84} +5.56155 q^{85} -1.00000 q^{86} -3.31534 q^{87} +1.00000 q^{88} +0.684658 q^{89} +0.561553 q^{90} +1.68466 q^{91} -0.876894 q^{92} +9.56155 q^{93} +2.00000 q^{94} -1.00000 q^{95} -1.56155 q^{96} +13.1231 q^{97} -2.00000 q^{98} +0.561553 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - q^{3} + 2 q^{4} + 2 q^{5} + q^{6} - 6 q^{7} - 2 q^{8} + 3 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 - q^3 + 2 * q^4 + 2 * q^5 + q^6 - 6 * q^7 - 2 * q^8 + 3 * q^9	\( 2 q - 2 q^{2} - q^{3} + 2 q^{4} + 2 q^{5} + q^{6} - 6 q^{7} - 2 q^{8} + 3 q^{9} - 2 q^{10} - 2 q^{11} - q^{12} + 3 q^{13} + 6 q^{14} - q^{15} + 2 q^{16} + 7 q^{17} - 3 q^{18} - 2 q^{19} + 2 q^{20} + 3 q^{21} + 2 q^{22} - 10 q^{23} + q^{24} + 2 q^{25} - 3 q^{26} - 7 q^{27} - 6 q^{28} + 4 q^{29} + q^{30} + 4 q^{31} - 2 q^{32} + q^{33} - 7 q^{34} - 6 q^{35} + 3 q^{36} - q^{37} + 2 q^{38} - 10 q^{39} - 2 q^{40} - 5 q^{41} - 3 q^{42} + 2 q^{43} - 2 q^{44} + 3 q^{45} + 10 q^{46} - 4 q^{47} - q^{48} + 4 q^{49} - 2 q^{50} + 5 q^{51} + 3 q^{52} - 3 q^{53} + 7 q^{54} - 2 q^{55} + 6 q^{56} + q^{57} - 4 q^{58} + 10 q^{59} - q^{60} - 4 q^{61} - 4 q^{62} - 9 q^{63} + 2 q^{64} + 3 q^{65} - q^{66} - 7 q^{67} + 7 q^{68} + 22 q^{69} + 6 q^{70} + 21 q^{71} - 3 q^{72} - 3 q^{73} + q^{74} - q^{75} - 2 q^{76} + 6 q^{77} + 10 q^{78} + 3 q^{79} + 2 q^{80} - 14 q^{81} + 5 q^{82} - 10 q^{83} + 3 q^{84} + 7 q^{85} - 2 q^{86} - 19 q^{87} + 2 q^{88} - 11 q^{89} - 3 q^{90} - 9 q^{91} - 10 q^{92} + 15 q^{93} + 4 q^{94} - 2 q^{95} + q^{96} + 18 q^{97} - 4 q^{98} - 3 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - q^3 + 2 * q^4 + 2 * q^5 + q^6 - 6 * q^7 - 2 * q^8 + 3 * q^9 - 2 * q^10 - 2 * q^11 - q^12 + 3 * q^13 + 6 * q^14 - q^15 + 2 * q^16 + 7 * q^17 - 3 * q^18 - 2 * q^19 + 2 * q^20 + 3 * q^21 + 2 * q^22 - 10 * q^23 + q^24 + 2 * q^25 - 3 * q^26 - 7 * q^27 - 6 * q^28 + 4 * q^29 + q^30 + 4 * q^31 - 2 * q^32 + q^33 - 7 * q^34 - 6 * q^35 + 3 * q^36 - q^37 + 2 * q^38 - 10 * q^39 - 2 * q^40 - 5 * q^41 - 3 * q^42 + 2 * q^43 - 2 * q^44 + 3 * q^45 + 10 * q^46 - 4 * q^47 - q^48 + 4 * q^49 - 2 * q^50 + 5 * q^51 + 3 * q^52 - 3 * q^53 + 7 * q^54 - 2 * q^55 + 6 * q^56 + q^57 - 4 * q^58 + 10 * q^59 - q^60 - 4 * q^61 - 4 * q^62 - 9 * q^63 + 2 * q^64 + 3 * q^65 - q^66 - 7 * q^67 + 7 * q^68 + 22 * q^69 + 6 * q^70 + 21 * q^71 - 3 * q^72 - 3 * q^73 + q^74 - q^75 - 2 * q^76 + 6 * q^77 + 10 * q^78 + 3 * q^79 + 2 * q^80 - 14 * q^81 + 5 * q^82 - 10 * q^83 + 3 * q^84 + 7 * q^85 - 2 * q^86 - 19 * q^87 + 2 * q^88 - 11 * q^89 - 3 * q^90 - 9 * q^91 - 10 * q^92 + 15 * q^93 + 4 * q^94 - 2 * q^95 + q^96 + 18 * q^97 - 4 * q^98 - 3 * 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
$3$	1.56155	0.901563	0.450781	−	0.892634i	$-0.351145\pi$
$3$	1.56155	0.901563	0.450781	+	0.892634i	$0.351145\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.56155	−0.637501
$7$	−3.00000	−1.13389	−0.566947	−	0.823754i	$-0.691875\pi$
$7$	−3.00000	−1.13389	−0.566947	+	0.823754i	$0.691875\pi$
$8$	−1.00000	−0.353553
$9$	−0.561553	−0.187184
$10$	−1.00000	−0.316228
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	1.56155	0.450781
$13$	−0.561553	−0.155747	−0.0778734	−	0.996963i	$-0.524813\pi$
$13$	−0.561553	−0.155747	−0.0778734	+	0.996963i	$0.524813\pi$
$14$	3.00000	0.801784
$15$	1.56155	0.403191
$16$	1.00000	0.250000
$17$	5.56155	1.34887	0.674437	−	0.738332i	$-0.264386\pi$
$17$	5.56155	1.34887	0.674437	+	0.738332i	$0.264386\pi$
$18$	0.561553	0.132359
$19$	−1.00000	−0.229416	−0.114708	−	0.993399i	$-0.536593\pi$
$19$	−1.00000	−0.229416	−0.114708	+	0.993399i	$0.536593\pi$
$20$	1.00000	0.223607
$21$	−4.68466	−1.02228
$22$	1.00000	0.213201
$23$	−0.876894	−0.182845	−0.0914226	−	0.995812i	$-0.529141\pi$
$23$	−0.876894	−0.182845	−0.0914226	+	0.995812i	$0.529141\pi$
$24$	−1.56155	−0.318751
$25$	1.00000	0.200000
$26$	0.561553	0.110130
$27$	−5.56155	−1.07032
$28$	−3.00000	−0.566947
$29$	−2.12311	−0.394251	−0.197125	−	0.980378i	$-0.563161\pi$
$29$	−2.12311	−0.394251	−0.197125	+	0.980378i	$0.563161\pi$
$30$	−1.56155	−0.285099
$31$	6.12311	1.09974	0.549871	−	0.835250i	$-0.314677\pi$
$31$	6.12311	1.09974	0.549871	+	0.835250i	$0.314677\pi$
$32$	−1.00000	−0.176777
$33$	−1.56155	−0.271831
$34$	−5.56155	−0.953798
$35$	−3.00000	−0.507093
$36$	−0.561553	−0.0935921
$37$	1.56155	0.256718	0.128359	−	0.991728i	$-0.459029\pi$
$37$	1.56155	0.256718	0.128359	+	0.991728i	$0.459029\pi$
$38$	1.00000	0.162221
$39$	−0.876894	−0.140415
$40$	−1.00000	−0.158114
$41$	−4.56155	−0.712395	−0.356197	−	0.934411i	$-0.615927\pi$
$41$	−4.56155	−0.712395	−0.356197	+	0.934411i	$0.615927\pi$
$42$	4.68466	0.722858
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	−1.00000	−0.150756
$45$	−0.561553	−0.0837114
$46$	0.876894	0.129291
$47$	−2.00000	−0.291730	−0.145865	−	0.989305i	$-0.546597\pi$
$47$	−2.00000	−0.291730	−0.145865	+	0.989305i	$0.546597\pi$
$48$	1.56155	0.225391
$49$	2.00000	0.285714
$50$	−1.00000	−0.141421
$51$	8.68466	1.21610
$52$	−0.561553	−0.0778734
$53$	−3.56155	−0.489217	−0.244608	−	0.969622i	$-0.578659\pi$
$53$	−3.56155	−0.489217	−0.244608	+	0.969622i	$0.578659\pi$
$54$	5.56155	0.756831
$55$	−1.00000	−0.134840
$56$	3.00000	0.400892
$57$	−1.56155	−0.206833
$58$	2.12311	0.278777
$59$	0.876894	0.114162	0.0570810	−	0.998370i	$-0.481821\pi$
$59$	0.876894	0.114162	0.0570810	+	0.998370i	$0.481821\pi$
$60$	1.56155	0.201596
$61$	−14.3693	−1.83980	−0.919901	−	0.392150i	$-0.871731\pi$
$61$	−14.3693	−1.83980	−0.919901	+	0.392150i	$0.871731\pi$
$62$	−6.12311	−0.777635
$63$	1.68466	0.212247
$64$	1.00000	0.125000
$65$	−0.561553	−0.0696521
$66$	1.56155	0.192214
$67$	−1.43845	−0.175734	−0.0878671	−	0.996132i	$-0.528005\pi$
$67$	−1.43845	−0.175734	−0.0878671	+	0.996132i	$0.528005\pi$
$68$	5.56155	0.674437
$69$	−1.36932	−0.164846
$70$	3.00000	0.358569
$71$	8.43845	1.00146	0.500730	−	0.865604i	$-0.333065\pi$
$71$	8.43845	1.00146	0.500730	+	0.865604i	$0.333065\pi$
$72$	0.561553	0.0661796
$73$	0.561553	0.0657248	0.0328624	−	0.999460i	$-0.489538\pi$
$73$	0.561553	0.0657248	0.0328624	+	0.999460i	$0.489538\pi$
$74$	−1.56155	−0.181527
$75$	1.56155	0.180313
$76$	−1.00000	−0.114708
$77$	3.00000	0.341882
$78$	0.876894	0.0992887
$79$	−0.561553	−0.0631796	−0.0315898	−	0.999501i	$-0.510057\pi$
$79$	−0.561553	−0.0631796	−0.0315898	+	0.999501i	$0.510057\pi$
$80$	1.00000	0.111803
$81$	−7.00000	−0.777778
$82$	4.56155	0.503739
$83$	−17.3693	−1.90653	−0.953265	−	0.302135i	$-0.902301\pi$
$83$	−17.3693	−1.90653	−0.953265	+	0.302135i	$0.902301\pi$
$84$	−4.68466	−0.511138
$85$	5.56155	0.603235
$86$	−1.00000	−0.107833
$87$	−3.31534	−0.355442
$88$	1.00000	0.106600
$89$	0.684658	0.0725736	0.0362868	−	0.999341i	$-0.488447\pi$
$89$	0.684658	0.0725736	0.0362868	+	0.999341i	$0.488447\pi$
$90$	0.561553	0.0591929
$91$	1.68466	0.176600
$92$	−0.876894	−0.0914226
$93$	9.56155	0.991487
$94$	2.00000	0.206284
$95$	−1.00000	−0.102598
$96$	−1.56155	−0.159375
$97$	13.1231	1.33245	0.666225	−	0.745751i	$-0.267909\pi$
$97$	13.1231	1.33245	0.666225	+	0.745751i	$0.267909\pi$
$98$	−2.00000	−0.202031
$99$	0.561553	0.0564382
$100$	1.00000	0.100000
$101$	3.12311	0.310761	0.155380	−	0.987855i	$-0.450340\pi$
$101$	3.12311	0.310761	0.155380	+	0.987855i	$0.450340\pi$
$102$	−8.68466	−0.859909
$103$	−10.8769	−1.07173	−0.535866	−	0.844303i	$-0.680015\pi$
$103$	−10.8769	−1.07173	−0.535866	+	0.844303i	$0.680015\pi$
$104$	0.561553	0.0550648
$105$	−4.68466	−0.457176
$106$	3.56155	0.345929
$107$	−7.68466	−0.742904	−0.371452	−	0.928452i	$-0.621140\pi$
$107$	−7.68466	−0.742904	−0.371452	+	0.928452i	$0.621140\pi$
$108$	−5.56155	−0.535161
$109$	−11.1231	−1.06540	−0.532700	−	0.846304i	$-0.678823\pi$
$109$	−11.1231	−1.06540	−0.532700	+	0.846304i	$0.678823\pi$
$110$	1.00000	0.0953463
$111$	2.43845	0.231447
$112$	−3.00000	−0.283473
$113$	−3.68466	−0.346624	−0.173312	−	0.984867i	$-0.555447\pi$
$113$	−3.68466	−0.346624	−0.173312	+	0.984867i	$0.555447\pi$
$114$	1.56155	0.146253
$115$	−0.876894	−0.0817708
$116$	−2.12311	−0.197125
$117$	0.315342	0.0291533
$118$	−0.876894	−0.0807247
$119$	−16.6847	−1.52948
$120$	−1.56155	−0.142550
$121$	1.00000	0.0909091
$122$	14.3693	1.30094
$123$	−7.12311	−0.642269
$124$	6.12311	0.549871
$125$	1.00000	0.0894427
$126$	−1.68466	−0.150081
$127$	−8.00000	−0.709885	−0.354943	−	0.934888i	$-0.615500\pi$
$127$	−8.00000	−0.709885	−0.354943	+	0.934888i	$0.615500\pi$
$128$	−1.00000	−0.0883883
$129$	1.56155	0.137487
$130$	0.561553	0.0492514
$131$	−8.68466	−0.758782	−0.379391	−	0.925236i	$-0.623866\pi$
$131$	−8.68466	−0.758782	−0.379391	+	0.925236i	$0.623866\pi$
$132$	−1.56155	−0.135916
$133$	3.00000	0.260133
$134$	1.43845	0.124263
$135$	−5.56155	−0.478662
$136$	−5.56155	−0.476899
$137$	−13.9309	−1.19019	−0.595097	−	0.803654i	$-0.702886\pi$
$137$	−13.9309	−1.19019	−0.595097	+	0.803654i	$0.702886\pi$
$138$	1.36932	0.116564
$139$	−14.2462	−1.20835	−0.604174	−	0.796852i	$-0.706497\pi$
$139$	−14.2462	−1.20835	−0.604174	+	0.796852i	$0.706497\pi$
$140$	−3.00000	−0.253546
$141$	−3.12311	−0.263013
$142$	−8.43845	−0.708139
$143$	0.561553	0.0469594
$144$	−0.561553	−0.0467961
$145$	−2.12311	−0.176314
$146$	−0.561553	−0.0464744
$147$	3.12311	0.257589
$148$	1.56155	0.128359
$149$	−4.12311	−0.337778	−0.168889	−	0.985635i	$-0.554018\pi$
$149$	−4.12311	−0.337778	−0.168889	+	0.985635i	$0.554018\pi$
$150$	−1.56155	−0.127500
$151$	3.75379	0.305479	0.152739	−	0.988266i	$-0.451190\pi$
$151$	3.75379	0.305479	0.152739	+	0.988266i	$0.451190\pi$
$152$	1.00000	0.0811107
$153$	−3.12311	−0.252488
$154$	−3.00000	−0.241747
$155$	6.12311	0.491820
$156$	−0.876894	−0.0702077
$157$	−8.68466	−0.693111	−0.346556	−	0.938029i	$-0.612649\pi$
$157$	−8.68466	−0.693111	−0.346556	+	0.938029i	$0.612649\pi$
$158$	0.561553	0.0446747
$159$	−5.56155	−0.441060
$160$	−1.00000	−0.0790569
$161$	2.63068	0.207327
$162$	7.00000	0.549972
$163$	−25.1771	−1.97202	−0.986011	−	0.166683i	$-0.946694\pi$
$163$	−25.1771	−1.97202	−0.986011	+	0.166683i	$0.946694\pi$
$164$	−4.56155	−0.356197
$165$	−1.56155	−0.121567
$166$	17.3693	1.34812
$167$	−3.31534	−0.256549	−0.128274	−	0.991739i	$-0.540944\pi$
$167$	−3.31534	−0.256549	−0.128274	+	0.991739i	$0.540944\pi$
$168$	4.68466	0.361429
$169$	−12.6847	−0.975743
$170$	−5.56155	−0.426552
$171$	0.561553	0.0429430
$172$	1.00000	0.0762493
$173$	−12.5616	−0.955037	−0.477519	−	0.878622i	$-0.658464\pi$
$173$	−12.5616	−0.955037	−0.477519	+	0.878622i	$0.658464\pi$
$174$	3.31534	0.251335
$175$	−3.00000	−0.226779
$176$	−1.00000	−0.0753778
$177$	1.36932	0.102924
$178$	−0.684658	−0.0513173
$179$	−23.6847	−1.77027	−0.885137	−	0.465330i	$-0.845936\pi$
$179$	−23.6847	−1.77027	−0.885137	+	0.465330i	$0.845936\pi$
$180$	−0.561553	−0.0418557
$181$	11.1231	0.826774	0.413387	−	0.910555i	$-0.364346\pi$
$181$	11.1231	0.826774	0.413387	+	0.910555i	$0.364346\pi$
$182$	−1.68466	−0.124875
$183$	−22.4384	−1.65870
$184$	0.876894	0.0646455
$185$	1.56155	0.114808
$186$	−9.56155	−0.701087
$187$	−5.56155	−0.406701
$188$	−2.00000	−0.145865
$189$	16.6847	1.21363
$190$	1.00000	0.0725476
$191$	19.3693	1.40151	0.700757	−	0.713400i	$-0.252846\pi$
$191$	19.3693	1.40151	0.700757	+	0.713400i	$0.252846\pi$
$192$	1.56155	0.112695
$193$	19.8078	1.42579	0.712897	−	0.701269i	$-0.247383\pi$
$193$	19.8078	1.42579	0.712897	+	0.701269i	$0.247383\pi$
$194$	−13.1231	−0.942184
$195$	−0.876894	−0.0627957
$196$	2.00000	0.142857
$197$	−3.68466	−0.262521	−0.131261	−	0.991348i	$-0.541902\pi$
$197$	−3.68466	−0.262521	−0.131261	+	0.991348i	$0.541902\pi$
$198$	−0.561553	−0.0399078
$199$	8.43845	0.598186	0.299093	−	0.954224i	$-0.403316\pi$
$199$	8.43845	0.598186	0.299093	+	0.954224i	$0.403316\pi$
$200$	−1.00000	−0.0707107
$201$	−2.24621	−0.158436
$202$	−3.12311	−0.219741
$203$	6.36932	0.447038
$204$	8.68466	0.608048
$205$	−4.56155	−0.318593
$206$	10.8769	0.757829
$207$	0.492423	0.0342257
$208$	−0.561553	−0.0389367
$209$	1.00000	0.0691714
$210$	4.68466	0.323272
$211$	9.56155	0.658244	0.329122	−	0.944287i	$-0.393247\pi$
$211$	9.56155	0.658244	0.329122	+	0.944287i	$0.393247\pi$
$212$	−3.56155	−0.244608
$213$	13.1771	0.902879
$214$	7.68466	0.525312
$215$	1.00000	0.0681994
$216$	5.56155	0.378416
$217$	−18.3693	−1.24699
$218$	11.1231	0.753352
$219$	0.876894	0.0592550
$220$	−1.00000	−0.0674200
$221$	−3.12311	−0.210083
$222$	−2.43845	−0.163658
$223$	−9.36932	−0.627416	−0.313708	−	0.949520i	$-0.601571\pi$
$223$	−9.36932	−0.627416	−0.313708	+	0.949520i	$0.601571\pi$
$224$	3.00000	0.200446
$225$	−0.561553	−0.0374369
$226$	3.68466	0.245100
$227$	−19.1231	−1.26925	−0.634623	−	0.772822i	$-0.718844\pi$
$227$	−19.1231	−1.26925	−0.634623	+	0.772822i	$0.718844\pi$
$228$	−1.56155	−0.103416
$229$	6.00000	0.396491	0.198246	−	0.980152i	$-0.436476\pi$
$229$	6.00000	0.396491	0.198246	+	0.980152i	$0.436476\pi$
$230$	0.876894	0.0578207
$231$	4.68466	0.308228
$232$	2.12311	0.139389
$233$	8.93087	0.585081	0.292540	−	0.956253i	$-0.405499\pi$
$233$	8.93087	0.585081	0.292540	+	0.956253i	$0.405499\pi$
$234$	−0.315342	−0.0206145
$235$	−2.00000	−0.130466
$236$	0.876894	0.0570810
$237$	−0.876894	−0.0569604
$238$	16.6847	1.08151
$239$	−10.8078	−0.699096	−0.349548	−	0.936918i	$-0.613665\pi$
$239$	−10.8078	−0.699096	−0.349548	+	0.936918i	$0.613665\pi$
$240$	1.56155	0.100798
$241$	20.7386	1.33589	0.667946	−	0.744209i	$-0.267174\pi$
$241$	20.7386	1.33589	0.667946	+	0.744209i	$0.267174\pi$
$242$	−1.00000	−0.0642824
$243$	5.75379	0.369106
$244$	−14.3693	−0.919901
$245$	2.00000	0.127775
$246$	7.12311	0.454153
$247$	0.561553	0.0357307
$248$	−6.12311	−0.388818
$249$	−27.1231	−1.71886
$250$	−1.00000	−0.0632456
$251$	−6.00000	−0.378717	−0.189358	−	0.981908i	$-0.560641\pi$
$251$	−6.00000	−0.378717	−0.189358	+	0.981908i	$0.560641\pi$
$252$	1.68466	0.106124
$253$	0.876894	0.0551299
$254$	8.00000	0.501965
$255$	8.68466	0.543854
$256$	1.00000	0.0625000
$257$	26.1771	1.63288	0.816441	−	0.577429i	$-0.195944\pi$
$257$	26.1771	1.63288	0.816441	+	0.577429i	$0.195944\pi$
$258$	−1.56155	−0.0972180
$259$	−4.68466	−0.291091
$260$	−0.561553	−0.0348260
$261$	1.19224	0.0737976
$262$	8.68466	0.536540
$263$	9.24621	0.570146	0.285073	−	0.958506i	$-0.407982\pi$
$263$	9.24621	0.570146	0.285073	+	0.958506i	$0.407982\pi$
$264$	1.56155	0.0961069
$265$	−3.56155	−0.218784
$266$	−3.00000	−0.183942
$267$	1.06913	0.0654297
$268$	−1.43845	−0.0878671
$269$	13.7538	0.838583	0.419292	−	0.907852i	$-0.362278\pi$
$269$	13.7538	0.838583	0.419292	+	0.907852i	$0.362278\pi$
$270$	5.56155	0.338465
$271$	12.8078	0.778016	0.389008	−	0.921234i	$-0.372818\pi$
$271$	12.8078	0.778016	0.389008	+	0.921234i	$0.372818\pi$
$272$	5.56155	0.337219
$273$	2.63068	0.159216
$274$	13.9309	0.841595
$275$	−1.00000	−0.0603023
$276$	−1.36932	−0.0824232
$277$	−9.75379	−0.586048	−0.293024	−	0.956105i	$-0.594662\pi$
$277$	−9.75379	−0.586048	−0.293024	+	0.956105i	$0.594662\pi$
$278$	14.2462	0.854431
$279$	−3.43845	−0.205854
$280$	3.00000	0.179284
$281$	−6.31534	−0.376742	−0.188371	−	0.982098i	$-0.560321\pi$
$281$	−6.31534	−0.376742	−0.188371	+	0.982098i	$0.560321\pi$
$282$	3.12311	0.185978
$283$	−27.9309	−1.66032	−0.830159	−	0.557527i	$-0.811750\pi$
$283$	−27.9309	−1.66032	−0.830159	+	0.557527i	$0.811750\pi$
$284$	8.43845	0.500730
$285$	−1.56155	−0.0924984
$286$	−0.561553	−0.0332053
$287$	13.6847	0.807780
$288$	0.561553	0.0330898
$289$	13.9309	0.819463
$290$	2.12311	0.124673
$291$	20.4924	1.20129
$292$	0.561553	0.0328624
$293$	−3.75379	−0.219299	−0.109649	−	0.993970i	$-0.534973\pi$
$293$	−3.75379	−0.219299	−0.109649	+	0.993970i	$0.534973\pi$
$294$	−3.12311	−0.182143
$295$	0.876894	0.0510548
$296$	−1.56155	−0.0907634
$297$	5.56155	0.322714
$298$	4.12311	0.238845
$299$	0.492423	0.0284775
$300$	1.56155	0.0901563
$301$	−3.00000	−0.172917
$302$	−3.75379	−0.216006
$303$	4.87689	0.280170
$304$	−1.00000	−0.0573539
$305$	−14.3693	−0.822785
$306$	3.12311	0.178536
$307$	−23.4384	−1.33770	−0.668851	−	0.743396i	$-0.733214\pi$
$307$	−23.4384	−1.33770	−0.668851	+	0.743396i	$0.733214\pi$
$308$	3.00000	0.170941
$309$	−16.9848	−0.966234
$310$	−6.12311	−0.347769
$311$	28.8617	1.63660	0.818300	−	0.574792i	$-0.194917\pi$
$311$	28.8617	1.63660	0.818300	+	0.574792i	$0.194917\pi$
$312$	0.876894	0.0496444
$313$	30.4924	1.72353	0.861767	−	0.507305i	$-0.169358\pi$
$313$	30.4924	1.72353	0.861767	+	0.507305i	$0.169358\pi$
$314$	8.68466	0.490104
$315$	1.68466	0.0949197
$316$	−0.561553	−0.0315898
$317$	−11.0000	−0.617822	−0.308911	−	0.951091i	$-0.599964\pi$
$317$	−11.0000	−0.617822	−0.308911	+	0.951091i	$0.599964\pi$
$318$	5.56155	0.311876
$319$	2.12311	0.118871
$320$	1.00000	0.0559017
$321$	−12.0000	−0.669775
$322$	−2.63068	−0.146602
$323$	−5.56155	−0.309453
$324$	−7.00000	−0.388889
$325$	−0.561553	−0.0311493
$326$	25.1771	1.39443
$327$	−17.3693	−0.960525
$328$	4.56155	0.251870
$329$	6.00000	0.330791
$330$	1.56155	0.0859607
$331$	16.4924	0.906506	0.453253	−	0.891382i	$-0.350263\pi$
$331$	16.4924	0.906506	0.453253	+	0.891382i	$0.350263\pi$
$332$	−17.3693	−0.953265
$333$	−0.876894	−0.0480535
$334$	3.31534	0.181407
$335$	−1.43845	−0.0785908
$336$	−4.68466	−0.255569
$337$	−26.6847	−1.45361	−0.726803	−	0.686846i	$-0.758995\pi$
$337$	−26.6847	−1.45361	−0.726803	+	0.686846i	$0.758995\pi$
$338$	12.6847	0.689954
$339$	−5.75379	−0.312503
$340$	5.56155	0.301618
$341$	−6.12311	−0.331585
$342$	−0.561553	−0.0303653
$343$	15.0000	0.809924
$344$	−1.00000	−0.0539164
$345$	−1.36932	−0.0737215
$346$	12.5616	0.675313
$347$	14.0000	0.751559	0.375780	−	0.926709i	$-0.377375\pi$
$347$	14.0000	0.751559	0.375780	+	0.926709i	$0.377375\pi$
$348$	−3.31534	−0.177721
$349$	−3.75379	−0.200936	−0.100468	−	0.994940i	$-0.532034\pi$
$349$	−3.75379	−0.200936	−0.100468	+	0.994940i	$0.532034\pi$
$350$	3.00000	0.160357
$351$	3.12311	0.166699
$352$	1.00000	0.0533002
$353$	−2.49242	−0.132658	−0.0663291	−	0.997798i	$-0.521129\pi$
$353$	−2.49242	−0.132658	−0.0663291	+	0.997798i	$0.521129\pi$
$354$	−1.36932	−0.0727784
$355$	8.43845	0.447866
$356$	0.684658	0.0362868
$357$	−26.0540	−1.37892
$358$	23.6847	1.25177
$359$	13.9309	0.735243	0.367622	−	0.929975i	$-0.380172\pi$
$359$	13.9309	0.735243	0.367622	+	0.929975i	$0.380172\pi$
$360$	0.561553	0.0295964
$361$	−18.0000	−0.947368
$362$	−11.1231	−0.584617
$363$	1.56155	0.0819603
$364$	1.68466	0.0883001
$365$	0.561553	0.0293930
$366$	22.4384	1.17288
$367$	4.49242	0.234503	0.117251	−	0.993102i	$-0.462592\pi$
$367$	4.49242	0.234503	0.117251	+	0.993102i	$0.462592\pi$
$368$	−0.876894	−0.0457113
$369$	2.56155	0.133349
$370$	−1.56155	−0.0811813
$371$	10.6847	0.554720
$372$	9.56155	0.495743
$373$	11.6155	0.601429	0.300715	−	0.953714i	$-0.402775\pi$
$373$	11.6155	0.601429	0.300715	+	0.953714i	$0.402775\pi$
$374$	5.56155	0.287581
$375$	1.56155	0.0806382
$376$	2.00000	0.103142
$377$	1.19224	0.0614033
$378$	−16.6847	−0.858166
$379$	−18.4924	−0.949892	−0.474946	−	0.880015i	$-0.657532\pi$
$379$	−18.4924	−0.949892	−0.474946	+	0.880015i	$0.657532\pi$
$380$	−1.00000	−0.0512989
$381$	−12.4924	−0.640006
$382$	−19.3693	−0.991020
$383$	−2.80776	−0.143470	−0.0717350	−	0.997424i	$-0.522854\pi$
$383$	−2.80776	−0.143470	−0.0717350	+	0.997424i	$0.522854\pi$
$384$	−1.56155	−0.0796877
$385$	3.00000	0.152894
$386$	−19.8078	−1.00819
$387$	−0.561553	−0.0285453
$388$	13.1231	0.666225
$389$	14.4924	0.734795	0.367397	−	0.930064i	$-0.380249\pi$
$389$	14.4924	0.734795	0.367397	+	0.930064i	$0.380249\pi$
$390$	0.876894	0.0444033
$391$	−4.87689	−0.246635
$392$	−2.00000	−0.101015
$393$	−13.5616	−0.684090
$394$	3.68466	0.185630
$395$	−0.561553	−0.0282548
$396$	0.561553	0.0282191
$397$	8.24621	0.413865	0.206933	−	0.978355i	$-0.433652\pi$
$397$	8.24621	0.413865	0.206933	+	0.978355i	$0.433652\pi$
$398$	−8.43845	−0.422981
$399$	4.68466	0.234526
$400$	1.00000	0.0500000
$401$	31.4924	1.57266	0.786328	−	0.617809i	$-0.211979\pi$
$401$	31.4924	1.57266	0.786328	+	0.617809i	$0.211979\pi$
$402$	2.24621	0.112031
$403$	−3.43845	−0.171281
$404$	3.12311	0.155380
$405$	−7.00000	−0.347833
$406$	−6.36932	−0.316104
$407$	−1.56155	−0.0774033
$408$	−8.68466	−0.429955
$409$	12.4924	0.617711	0.308855	−	0.951109i	$-0.400054\pi$
$409$	12.4924	0.617711	0.308855	+	0.951109i	$0.400054\pi$
$410$	4.56155	0.225279
$411$	−21.7538	−1.07304
$412$	−10.8769	−0.535866
$413$	−2.63068	−0.129447
$414$	−0.492423	−0.0242012
$415$	−17.3693	−0.852626
$416$	0.561553	0.0275324
$417$	−22.2462	−1.08940
$418$	−1.00000	−0.0489116
$419$	17.4384	0.851924	0.425962	−	0.904741i	$-0.359936\pi$
$419$	17.4384	0.851924	0.425962	+	0.904741i	$0.359936\pi$
$420$	−4.68466	−0.228588
$421$	−25.9309	−1.26379	−0.631897	−	0.775053i	$-0.717723\pi$
$421$	−25.9309	−1.26379	−0.631897	+	0.775053i	$0.717723\pi$
$422$	−9.56155	−0.465449
$423$	1.12311	0.0546073
$424$	3.56155	0.172964
$425$	5.56155	0.269775
$426$	−13.1771	−0.638432
$427$	43.1080	2.08614
$428$	−7.68466	−0.371452
$429$	0.876894	0.0423369
$430$	−1.00000	−0.0482243
$431$	−22.2462	−1.07156	−0.535781	−	0.844357i	$-0.679983\pi$
$431$	−22.2462	−1.07156	−0.535781	+	0.844357i	$0.679983\pi$
$432$	−5.56155	−0.267580
$433$	15.6847	0.753757	0.376878	−	0.926263i	$-0.376997\pi$
$433$	15.6847	0.753757	0.376878	+	0.926263i	$0.376997\pi$
$434$	18.3693	0.881755
$435$	−3.31534	−0.158958
$436$	−11.1231	−0.532700
$437$	0.876894	0.0419475
$438$	−0.876894	−0.0418996
$439$	−17.7538	−0.847342	−0.423671	−	0.905816i	$-0.639259\pi$
$439$	−17.7538	−0.847342	−0.423671	+	0.905816i	$0.639259\pi$
$440$	1.00000	0.0476731
$441$	−1.12311	−0.0534812
$442$	3.12311	0.148551
$443$	−4.80776	−0.228424	−0.114212	−	0.993456i	$-0.536434\pi$
$443$	−4.80776	−0.228424	−0.114212	+	0.993456i	$0.536434\pi$
$444$	2.43845	0.115724
$445$	0.684658	0.0324559
$446$	9.36932	0.443650
$447$	−6.43845	−0.304528
$448$	−3.00000	−0.141737
$449$	−24.8769	−1.17401	−0.587007	−	0.809582i	$-0.699694\pi$
$449$	−24.8769	−1.17401	−0.587007	+	0.809582i	$0.699694\pi$
$450$	0.561553	0.0264719
$451$	4.56155	0.214795
$452$	−3.68466	−0.173312
$453$	5.86174	0.275409
$454$	19.1231	0.897492
$455$	1.68466	0.0789780
$456$	1.56155	0.0731264
$457$	−8.43845	−0.394734	−0.197367	−	0.980330i	$-0.563239\pi$
$457$	−8.43845	−0.394734	−0.197367	+	0.980330i	$0.563239\pi$
$458$	−6.00000	−0.280362
$459$	−30.9309	−1.44373
$460$	−0.876894	−0.0408854
$461$	25.1771	1.17261	0.586307	−	0.810089i	$-0.300581\pi$
$461$	25.1771	1.17261	0.586307	+	0.810089i	$0.300581\pi$
$462$	−4.68466	−0.217950
$463$	8.06913	0.375004	0.187502	−	0.982264i	$-0.439961\pi$
$463$	8.06913	0.375004	0.187502	+	0.982264i	$0.439961\pi$
$464$	−2.12311	−0.0985627
$465$	9.56155	0.443406
$466$	−8.93087	−0.413715
$467$	1.56155	0.0722600	0.0361300	−	0.999347i	$-0.488497\pi$
$467$	1.56155	0.0722600	0.0361300	+	0.999347i	$0.488497\pi$
$468$	0.315342	0.0145767
$469$	4.31534	0.199264
$470$	2.00000	0.0922531
$471$	−13.5616	−0.624883
$472$	−0.876894	−0.0403623
$473$	−1.00000	−0.0459800
$474$	0.876894	0.0402771
$475$	−1.00000	−0.0458831
$476$	−16.6847	−0.764740
$477$	2.00000	0.0915737
$478$	10.8078	0.494336
$479$	7.50758	0.343030	0.171515	−	0.985182i	$-0.445134\pi$
$479$	7.50758	0.343030	0.171515	+	0.985182i	$0.445134\pi$
$480$	−1.56155	−0.0712748
$481$	−0.876894	−0.0399829
$482$	−20.7386	−0.944619
$483$	4.10795	0.186918
$484$	1.00000	0.0454545
$485$	13.1231	0.595890
$486$	−5.75379	−0.260997
$487$	−39.3693	−1.78399	−0.891997	−	0.452041i	$-0.850696\pi$
$487$	−39.3693	−1.78399	−0.891997	+	0.452041i	$0.850696\pi$
$488$	14.3693	0.650468
$489$	−39.3153	−1.77790
$490$	−2.00000	−0.0903508
$491$	18.0540	0.814765	0.407382	−	0.913258i	$-0.366442\pi$
$491$	18.0540	0.814765	0.407382	+	0.913258i	$0.366442\pi$
$492$	−7.12311	−0.321134
$493$	−11.8078	−0.531795
$494$	−0.561553	−0.0252655
$495$	0.561553	0.0252399
$496$	6.12311	0.274936
$497$	−25.3153	−1.13555
$498$	27.1231	1.21542
$499$	−15.0540	−0.673908	−0.336954	−	0.941521i	$-0.609397\pi$
$499$	−15.0540	−0.673908	−0.336954	+	0.941521i	$0.609397\pi$
$500$	1.00000	0.0447214
$501$	−5.17708	−0.231295
$502$	6.00000	0.267793
$503$	−16.0000	−0.713405	−0.356702	−	0.934218i	$-0.616099\pi$
$503$	−16.0000	−0.713405	−0.356702	+	0.934218i	$0.616099\pi$
$504$	−1.68466	−0.0750407
$505$	3.12311	0.138976
$506$	−0.876894	−0.0389827
$507$	−19.8078	−0.879694
$508$	−8.00000	−0.354943
$509$	−18.2462	−0.808749	−0.404375	−	0.914593i	$-0.632511\pi$
$509$	−18.2462	−0.808749	−0.404375	+	0.914593i	$0.632511\pi$
$510$	−8.68466	−0.384563
$511$	−1.68466	−0.0745249
$512$	−1.00000	−0.0441942
$513$	5.56155	0.245549
$514$	−26.1771	−1.15462
$515$	−10.8769	−0.479293
$516$	1.56155	0.0687435
$517$	2.00000	0.0879599
$518$	4.68466	0.205832
$519$	−19.6155	−0.861026
$520$	0.561553	0.0246257
$521$	36.7386	1.60955	0.804774	−	0.593581i	$-0.202286\pi$
$521$	36.7386	1.60955	0.804774	+	0.593581i	$0.202286\pi$
$522$	−1.19224	−0.0521827
$523$	7.36932	0.322238	0.161119	−	0.986935i	$-0.448490\pi$
$523$	7.36932	0.322238	0.161119	+	0.986935i	$0.448490\pi$
$524$	−8.68466	−0.379391
$525$	−4.68466	−0.204455
$526$	−9.24621	−0.403154
$527$	34.0540	1.48341
$528$	−1.56155	−0.0679579
$529$	−22.2311	−0.966568
$530$	3.56155	0.154704
$531$	−0.492423	−0.0213693
$532$	3.00000	0.130066
$533$	2.56155	0.110953
$534$	−1.06913	−0.0462658
$535$	−7.68466	−0.332237
$536$	1.43845	0.0621315
$537$	−36.9848	−1.59601
$538$	−13.7538	−0.592968
$539$	−2.00000	−0.0861461
$540$	−5.56155	−0.239331
$541$	11.1771	0.480540	0.240270	−	0.970706i	$-0.422764\pi$
$541$	11.1771	0.480540	0.240270	+	0.970706i	$0.422764\pi$
$542$	−12.8078	−0.550141
$543$	17.3693	0.745389
$544$	−5.56155	−0.238450
$545$	−11.1231	−0.476461
$546$	−2.63068	−0.112583
$547$	−36.0000	−1.53925	−0.769624	−	0.638497i	$-0.779557\pi$
$547$	−36.0000	−1.53925	−0.769624	+	0.638497i	$0.779557\pi$
$548$	−13.9309	−0.595097
$549$	8.06913	0.344382
$550$	1.00000	0.0426401
$551$	2.12311	0.0904473
$552$	1.36932	0.0582820
$553$	1.68466	0.0716390
$554$	9.75379	0.414399
$555$	2.43845	0.103506
$556$	−14.2462	−0.604174
$557$	14.3153	0.606560	0.303280	−	0.952901i	$-0.401918\pi$
$557$	14.3153	0.606560	0.303280	+	0.952901i	$0.401918\pi$
$558$	3.43845	0.145561
$559$	−0.561553	−0.0237512
$560$	−3.00000	−0.126773
$561$	−8.68466	−0.366667
$562$	6.31534	0.266397
$563$	−36.5616	−1.54089	−0.770443	−	0.637509i	$-0.779965\pi$
$563$	−36.5616	−1.54089	−0.770443	+	0.637509i	$0.779965\pi$
$564$	−3.12311	−0.131506
$565$	−3.68466	−0.155015
$566$	27.9309	1.17402
$567$	21.0000	0.881917
$568$	−8.43845	−0.354069
$569$	20.3153	0.851663	0.425832	−	0.904802i	$-0.359982\pi$
$569$	20.3153	0.851663	0.425832	+	0.904802i	$0.359982\pi$
$570$	1.56155	0.0654062
$571$	32.3693	1.35461	0.677307	−	0.735701i	$-0.263147\pi$
$571$	32.3693	1.35461	0.677307	+	0.735701i	$0.263147\pi$
$572$	0.561553	0.0234797
$573$	30.2462	1.26355
$574$	−13.6847	−0.571187
$575$	−0.876894	−0.0365690
$576$	−0.561553	−0.0233980
$577$	2.17708	0.0906331	0.0453165	−	0.998973i	$-0.485570\pi$
$577$	2.17708	0.0906331	0.0453165	+	0.998973i	$0.485570\pi$
$578$	−13.9309	−0.579448
$579$	30.9309	1.28544
$580$	−2.12311	−0.0881572
$581$	52.1080	2.16180
$582$	−20.4924	−0.849438
$583$	3.56155	0.147504
$584$	−0.561553	−0.0232372
$585$	0.315342	0.0130378
$586$	3.75379	0.155068
$587$	20.6847	0.853747	0.426874	−	0.904311i	$-0.359615\pi$
$587$	20.6847	0.853747	0.426874	+	0.904311i	$0.359615\pi$
$588$	3.12311	0.128795
$589$	−6.12311	−0.252298
$590$	−0.876894	−0.0361012
$591$	−5.75379	−0.236679
$592$	1.56155	0.0641794
$593$	−25.0540	−1.02884	−0.514422	−	0.857537i	$-0.671993\pi$
$593$	−25.0540	−1.02884	−0.514422	+	0.857537i	$0.671993\pi$
$594$	−5.56155	−0.228193
$595$	−16.6847	−0.684004
$596$	−4.12311	−0.168889
$597$	13.1771	0.539302
$598$	−0.492423	−0.0201367
$599$	34.4384	1.40712	0.703558	−	0.710637i	$-0.251593\pi$
$599$	34.4384	1.40712	0.703558	+	0.710637i	$0.251593\pi$
$600$	−1.56155	−0.0637501
$601$	−0.876894	−0.0357693	−0.0178846	−	0.999840i	$-0.505693\pi$
$601$	−0.876894	−0.0357693	−0.0178846	+	0.999840i	$0.505693\pi$
$602$	3.00000	0.122271
$603$	0.807764	0.0328947
$604$	3.75379	0.152739
$605$	1.00000	0.0406558
$606$	−4.87689	−0.198110
$607$	−0.192236	−0.00780262	−0.00390131	−	0.999992i	$-0.501242\pi$
$607$	−0.192236	−0.00780262	−0.00390131	+	0.999992i	$0.501242\pi$
$608$	1.00000	0.0405554
$609$	9.94602	0.403033
$610$	14.3693	0.581797
$611$	1.12311	0.0454360
$612$	−3.12311	−0.126244
$613$	13.6847	0.552718	0.276359	−	0.961054i	$-0.410872\pi$
$613$	13.6847	0.552718	0.276359	+	0.961054i	$0.410872\pi$
$614$	23.4384	0.945899
$615$	−7.12311	−0.287231
$616$	−3.00000	−0.120873
$617$	28.4924	1.14706	0.573531	−	0.819184i	$-0.305573\pi$
$617$	28.4924	1.14706	0.573531	+	0.819184i	$0.305573\pi$
$618$	16.9848	0.683231
$619$	−20.0000	−0.803868	−0.401934	−	0.915669i	$-0.631662\pi$
$619$	−20.0000	−0.803868	−0.401934	+	0.915669i	$0.631662\pi$
$620$	6.12311	0.245910
$621$	4.87689	0.195703
$622$	−28.8617	−1.15725
$623$	−2.05398	−0.0822908
$624$	−0.876894	−0.0351039
$625$	1.00000	0.0400000
$626$	−30.4924	−1.21872
$627$	1.56155	0.0623624
$628$	−8.68466	−0.346556
$629$	8.68466	0.346280
$630$	−1.68466	−0.0671184
$631$	−20.6847	−0.823443	−0.411722	−	0.911310i	$-0.635072\pi$
$631$	−20.6847	−0.823443	−0.411722	+	0.911310i	$0.635072\pi$
$632$	0.561553	0.0223374
$633$	14.9309	0.593449
$634$	11.0000	0.436866
$635$	−8.00000	−0.317470
$636$	−5.56155	−0.220530
$637$	−1.12311	−0.0444991
$638$	−2.12311	−0.0840546
$639$	−4.73863	−0.187457
$640$	−1.00000	−0.0395285
$641$	27.1771	1.07343	0.536715	−	0.843764i	$-0.319665\pi$
$641$	27.1771	1.07343	0.536715	+	0.843764i	$0.319665\pi$
$642$	12.0000	0.473602
$643$	−47.2462	−1.86321	−0.931604	−	0.363474i	$-0.881591\pi$
$643$	−47.2462	−1.86321	−0.931604	+	0.363474i	$0.881591\pi$
$644$	2.63068	0.103663
$645$	1.56155	0.0614861
$646$	5.56155	0.218816
$647$	33.0540	1.29949	0.649743	−	0.760154i	$-0.274877\pi$
$647$	33.0540	1.29949	0.649743	+	0.760154i	$0.274877\pi$
$648$	7.00000	0.274986
$649$	−0.876894	−0.0344211
$650$	0.561553	0.0220259
$651$	−28.6847	−1.12424
$652$	−25.1771	−0.986011
$653$	11.0691	0.433169	0.216584	−	0.976264i	$-0.430508\pi$
$653$	11.0691	0.433169	0.216584	+	0.976264i	$0.430508\pi$
$654$	17.3693	0.679194
$655$	−8.68466	−0.339338
$656$	−4.56155	−0.178099
$657$	−0.315342	−0.0123026
$658$	−6.00000	−0.233904
$659$	2.43845	0.0949884	0.0474942	−	0.998872i	$-0.484876\pi$
$659$	2.43845	0.0949884	0.0474942	+	0.998872i	$0.484876\pi$
$660$	−1.56155	−0.0607834
$661$	−30.0000	−1.16686	−0.583432	−	0.812162i	$-0.698291\pi$
$661$	−30.0000	−1.16686	−0.583432	+	0.812162i	$0.698291\pi$
$662$	−16.4924	−0.640996
$663$	−4.87689	−0.189403
$664$	17.3693	0.674060
$665$	3.00000	0.116335
$666$	0.876894	0.0339790
$667$	1.86174	0.0720868
$668$	−3.31534	−0.128274
$669$	−14.6307	−0.565655
$670$	1.43845	0.0555721
$671$	14.3693	0.554721
$672$	4.68466	0.180715
$673$	−5.49242	−0.211717	−0.105859	−	0.994381i	$-0.533759\pi$
$673$	−5.49242	−0.211717	−0.105859	+	0.994381i	$0.533759\pi$
$674$	26.6847	1.02785
$675$	−5.56155	−0.214064
$676$	−12.6847	−0.487871
$677$	−42.1080	−1.61834	−0.809170	−	0.587575i	$-0.800083\pi$
$677$	−42.1080	−1.61834	−0.809170	+	0.587575i	$0.800083\pi$
$678$	5.75379	0.220973
$679$	−39.3693	−1.51086
$680$	−5.56155	−0.213276
$681$	−29.8617	−1.14430
$682$	6.12311	0.234466
$683$	2.43845	0.0933046	0.0466523	−	0.998911i	$-0.485145\pi$
$683$	2.43845	0.0933046	0.0466523	+	0.998911i	$0.485145\pi$
$684$	0.561553	0.0214715
$685$	−13.9309	−0.532271
$686$	−15.0000	−0.572703
$687$	9.36932	0.357462
$688$	1.00000	0.0381246
$689$	2.00000	0.0761939
$690$	1.36932	0.0521290
$691$	−39.1231	−1.48831	−0.744157	−	0.668005i	$-0.767148\pi$
$691$	−39.1231	−1.48831	−0.744157	+	0.668005i	$0.767148\pi$
$692$	−12.5616	−0.477519
$693$	−1.68466	−0.0639949
$694$	−14.0000	−0.531433
$695$	−14.2462	−0.540390
$696$	3.31534	0.125668
$697$	−25.3693	−0.960931
$698$	3.75379	0.142083
$699$	13.9460	0.527487
$700$	−3.00000	−0.113389
$701$	25.6695	0.969524	0.484762	−	0.874646i	$-0.338906\pi$
$701$	25.6695	0.969524	0.484762	+	0.874646i	$0.338906\pi$
$702$	−3.12311	−0.117874
$703$	−1.56155	−0.0588951
$704$	−1.00000	−0.0376889
$705$	−3.12311	−0.117623
$706$	2.49242	0.0938036
$707$	−9.36932	−0.352369
$708$	1.36932	0.0514621
$709$	−1.50758	−0.0566183	−0.0283091	−	0.999599i	$-0.509012\pi$
$709$	−1.50758	−0.0566183	−0.0283091	+	0.999599i	$0.509012\pi$
$710$	−8.43845	−0.316689
$711$	0.315342	0.0118262
$712$	−0.684658	−0.0256587
$713$	−5.36932	−0.201082
$714$	26.0540	0.975046
$715$	0.561553	0.0210009
$716$	−23.6847	−0.885137
$717$	−16.8769	−0.630279
$718$	−13.9309	−0.519895
$719$	−14.0540	−0.524125	−0.262062	−	0.965051i	$-0.584403\pi$
$719$	−14.0540	−0.524125	−0.262062	+	0.965051i	$0.584403\pi$
$720$	−0.561553	−0.0209278
$721$	32.6307	1.21523
$722$	18.0000	0.669891
$723$	32.3845	1.20439
$724$	11.1231	0.413387
$725$	−2.12311	−0.0788502
$726$	−1.56155	−0.0579547
$727$	35.1231	1.30264	0.651322	−	0.758802i	$-0.274215\pi$
$727$	35.1231	1.30264	0.651322	+	0.758802i	$0.274215\pi$
$728$	−1.68466	−0.0624376
$729$	29.9848	1.11055
$730$	−0.561553	−0.0207840
$731$	5.56155	0.205701
$732$	−22.4384	−0.829349
$733$	6.87689	0.254004	0.127002	−	0.991902i	$-0.459465\pi$
$733$	6.87689	0.254004	0.127002	+	0.991902i	$0.459465\pi$
$734$	−4.49242	−0.165818
$735$	3.12311	0.115197
$736$	0.876894	0.0323228
$737$	1.43845	0.0529859
$738$	−2.56155	−0.0942921
$739$	−2.06913	−0.0761142	−0.0380571	−	0.999276i	$-0.512117\pi$
$739$	−2.06913	−0.0761142	−0.0380571	+	0.999276i	$0.512117\pi$
$740$	1.56155	0.0574038
$741$	0.876894	0.0322135
$742$	−10.6847	−0.392246
$743$	18.1231	0.664872	0.332436	−	0.943126i	$-0.392129\pi$
$743$	18.1231	0.664872	0.332436	+	0.943126i	$0.392129\pi$
$744$	−9.56155	−0.350544
$745$	−4.12311	−0.151059
$746$	−11.6155	−0.425275
$747$	9.75379	0.356872
$748$	−5.56155	−0.203351
$749$	23.0540	0.842374
$750$	−1.56155	−0.0570198
$751$	−39.8078	−1.45261	−0.726303	−	0.687375i	$-0.758763\pi$
$751$	−39.8078	−1.45261	−0.726303	+	0.687375i	$0.758763\pi$
$752$	−2.00000	−0.0729325
$753$	−9.36932	−0.341437
$754$	−1.19224	−0.0434187
$755$	3.75379	0.136614
$756$	16.6847	0.606815
$757$	6.00000	0.218074	0.109037	−	0.994038i	$-0.465223\pi$
$757$	6.00000	0.218074	0.109037	+	0.994038i	$0.465223\pi$
$758$	18.4924	0.671675
$759$	1.36932	0.0497031
$760$	1.00000	0.0362738
$761$	9.50758	0.344649	0.172325	−	0.985040i	$-0.444872\pi$
$761$	9.50758	0.344649	0.172325	+	0.985040i	$0.444872\pi$
$762$	12.4924	0.452553
$763$	33.3693	1.20805
$764$	19.3693	0.700757
$765$	−3.12311	−0.112916
$766$	2.80776	0.101449
$767$	−0.492423	−0.0177803
$768$	1.56155	0.0563477
$769$	−9.68466	−0.349238	−0.174619	−	0.984636i	$-0.555869\pi$
$769$	−9.68466	−0.349238	−0.174619	+	0.984636i	$0.555869\pi$
$770$	−3.00000	−0.108112
$771$	40.8769	1.47215
$772$	19.8078	0.712897
$773$	−14.4384	−0.519315	−0.259657	−	0.965701i	$-0.583610\pi$
$773$	−14.4384	−0.519315	−0.259657	+	0.965701i	$0.583610\pi$
$774$	0.561553	0.0201846
$775$	6.12311	0.219948
$776$	−13.1231	−0.471092
$777$	−7.31534	−0.262436
$778$	−14.4924	−0.519579
$779$	4.56155	0.163435
$780$	−0.876894	−0.0313979
$781$	−8.43845	−0.301951
$782$	4.87689	0.174397
$783$	11.8078	0.421975
$784$	2.00000	0.0714286
$785$	−8.68466	−0.309969
$786$	13.5616	0.483725
$787$	−11.6847	−0.416513	−0.208257	−	0.978074i	$-0.566779\pi$
$787$	−11.6847	−0.416513	−0.208257	+	0.978074i	$0.566779\pi$
$788$	−3.68466	−0.131261
$789$	14.4384	0.514022
$790$	0.561553	0.0199792
$791$	11.0540	0.393034
$792$	−0.561553	−0.0199539
$793$	8.06913	0.286543
$794$	−8.24621	−0.292647
$795$	−5.56155	−0.197248
$796$	8.43845	0.299093
$797$	21.6847	0.768110	0.384055	−	0.923310i	$-0.374527\pi$
$797$	21.6847	0.768110	0.384055	+	0.923310i	$0.374527\pi$
$798$	−4.68466	−0.165835
$799$	−11.1231	−0.393507
$800$	−1.00000	−0.0353553
$801$	−0.384472	−0.0135846
$802$	−31.4924	−1.11204
$803$	−0.561553	−0.0198168
$804$	−2.24621	−0.0792178
$805$	2.63068	0.0927194
$806$	3.43845	0.121114
$807$	21.4773	0.756036
$808$	−3.12311	−0.109870
$809$	24.4233	0.858677	0.429339	−	0.903144i	$-0.358747\pi$
$809$	24.4233	0.858677	0.429339	+	0.903144i	$0.358747\pi$
$810$	7.00000	0.245955
$811$	5.00000	0.175574	0.0877869	−	0.996139i	$-0.472021\pi$
$811$	5.00000	0.175574	0.0877869	+	0.996139i	$0.472021\pi$
$812$	6.36932	0.223519
$813$	20.0000	0.701431
$814$	1.56155	0.0547324
$815$	−25.1771	−0.881915
$816$	8.68466	0.304024
$817$	−1.00000	−0.0349856
$818$	−12.4924	−0.436787
$819$	−0.946025	−0.0330568
$820$	−4.56155	−0.159296
$821$	10.0000	0.349002	0.174501	−	0.984657i	$-0.444169\pi$
$821$	10.0000	0.349002	0.174501	+	0.984657i	$0.444169\pi$
$822$	21.7538	0.758751
$823$	49.6155	1.72949	0.864744	−	0.502212i	$-0.167480\pi$
$823$	49.6155	1.72949	0.864744	+	0.502212i	$0.167480\pi$
$824$	10.8769	0.378915
$825$	−1.56155	−0.0543663
$826$	2.63068	0.0915332
$827$	12.1771	0.423439	0.211719	−	0.977331i	$-0.432094\pi$
$827$	12.1771	0.423439	0.211719	+	0.977331i	$0.432094\pi$
$828$	0.492423	0.0171129
$829$	−23.5464	−0.817800	−0.408900	−	0.912579i	$-0.634088\pi$
$829$	−23.5464	−0.817800	−0.408900	+	0.912579i	$0.634088\pi$
$830$	17.3693	0.602898
$831$	−15.2311	−0.528359
$832$	−0.561553	−0.0194683
$833$	11.1231	0.385393
$834$	22.2462	0.770323
$835$	−3.31534	−0.114732
$836$	1.00000	0.0345857
$837$	−34.0540	−1.17708
$838$	−17.4384	−0.602401
$839$	25.6155	0.884346	0.442173	−	0.896930i	$-0.354208\pi$
$839$	25.6155	0.884346	0.442173	+	0.896930i	$0.354208\pi$
$840$	4.68466	0.161636
$841$	−24.4924	−0.844566
$842$	25.9309	0.893637
$843$	−9.86174	−0.339656
$844$	9.56155	0.329122
$845$	−12.6847	−0.436366
$846$	−1.12311	−0.0386132
$847$	−3.00000	−0.103081
$848$	−3.56155	−0.122304
$849$	−43.6155	−1.49688
$850$	−5.56155	−0.190760
$851$	−1.36932	−0.0469396
$852$	13.1771	0.451439
$853$	−22.9848	−0.786986	−0.393493	−	0.919328i	$-0.628733\pi$
$853$	−22.9848	−0.786986	−0.393493	+	0.919328i	$0.628733\pi$
$854$	−43.1080	−1.47512
$855$	0.561553	0.0192047
$856$	7.68466	0.262656
$857$	3.31534	0.113250	0.0566250	−	0.998396i	$-0.481966\pi$
$857$	3.31534	0.113250	0.0566250	+	0.998396i	$0.481966\pi$
$858$	−0.876894	−0.0299367
$859$	36.4233	1.24275	0.621373	−	0.783515i	$-0.286575\pi$
$859$	36.4233	1.24275	0.621373	+	0.783515i	$0.286575\pi$
$860$	1.00000	0.0340997
$861$	21.3693	0.728264
$862$	22.2462	0.757709
$863$	−3.12311	−0.106312	−0.0531559	−	0.998586i	$-0.516928\pi$
$863$	−3.12311	−0.106312	−0.0531559	+	0.998586i	$0.516928\pi$
$864$	5.56155	0.189208
$865$	−12.5616	−0.427106
$866$	−15.6847	−0.532986
$867$	21.7538	0.738797
$868$	−18.3693	−0.623495
$869$	0.561553	0.0190494
$870$	3.31534	0.112401
$871$	0.807764	0.0273700
$872$	11.1231	0.376676
$873$	−7.36932	−0.249414
$874$	−0.876894	−0.0296614
$875$	−3.00000	−0.101419
$876$	0.876894	0.0296275
$877$	4.24621	0.143384	0.0716922	−	0.997427i	$-0.477160\pi$
$877$	4.24621	0.143384	0.0716922	+	0.997427i	$0.477160\pi$
$878$	17.7538	0.599161
$879$	−5.86174	−0.197712
$880$	−1.00000	−0.0337100
$881$	−32.4233	−1.09237	−0.546184	−	0.837665i	$-0.683920\pi$
$881$	−32.4233	−1.09237	−0.546184	+	0.837665i	$0.683920\pi$
$882$	1.12311	0.0378169
$883$	−23.9848	−0.807154	−0.403577	−	0.914946i	$-0.632233\pi$
$883$	−23.9848	−0.807154	−0.403577	+	0.914946i	$0.632233\pi$
$884$	−3.12311	−0.105041
$885$	1.36932	0.0460291
$886$	4.80776	0.161520
$887$	−42.4233	−1.42443	−0.712217	−	0.701959i	$-0.752309\pi$
$887$	−42.4233	−1.42443	−0.712217	+	0.701959i	$0.752309\pi$
$888$	−2.43845	−0.0818289
$889$	24.0000	0.804934
$890$	−0.684658	−0.0229498
$891$	7.00000	0.234509
$892$	−9.36932	−0.313708
$893$	2.00000	0.0669274
$894$	6.43845	0.215334
$895$	−23.6847	−0.791691
$896$	3.00000	0.100223
$897$	0.768944	0.0256743
$898$	24.8769	0.830153
$899$	−13.0000	−0.433574
$900$	−0.561553	−0.0187184
$901$	−19.8078	−0.659892
$902$	−4.56155	−0.151883
$903$	−4.68466	−0.155896
$904$	3.68466	0.122550
$905$	11.1231	0.369745
$906$	−5.86174	−0.194743
$907$	−3.24621	−0.107789	−0.0538943	−	0.998547i	$-0.517163\pi$
$907$	−3.24621	−0.107789	−0.0538943	+	0.998547i	$0.517163\pi$
$908$	−19.1231	−0.634623
$909$	−1.75379	−0.0581695
$910$	−1.68466	−0.0558459
$911$	0.930870	0.0308411	0.0154205	−	0.999881i	$-0.495091\pi$
$911$	0.930870	0.0308411	0.0154205	+	0.999881i	$0.495091\pi$
$912$	−1.56155	−0.0517082
$913$	17.3693	0.574840
$914$	8.43845	0.279119
$915$	−22.4384	−0.741792
$916$	6.00000	0.198246
$917$	26.0540	0.860378
$918$	30.9309	1.02087
$919$	13.3002	0.438733	0.219366	−	0.975643i	$-0.429601\pi$
$919$	13.3002	0.438733	0.219366	+	0.975643i	$0.429601\pi$
$920$	0.876894	0.0289104
$921$	−36.6004	−1.20602
$922$	−25.1771	−0.829163
$923$	−4.73863	−0.155974
$924$	4.68466	0.154114
$925$	1.56155	0.0513435
$926$	−8.06913	−0.265168
$927$	6.10795	0.200611
$928$	2.12311	0.0696944
$929$	−23.5616	−0.773029	−0.386515	−	0.922283i	$-0.626321\pi$
$929$	−23.5616	−0.773029	−0.386515	+	0.922283i	$0.626321\pi$
$930$	−9.56155	−0.313536
$931$	−2.00000	−0.0655474
$932$	8.93087	0.292540
$933$	45.0691	1.47550
$934$	−1.56155	−0.0510956
$935$	−5.56155	−0.181882
$936$	−0.315342	−0.0103073
$937$	−36.7386	−1.20020	−0.600099	−	0.799925i	$-0.704872\pi$
$937$	−36.7386	−1.20020	−0.600099	+	0.799925i	$0.704872\pi$
$938$	−4.31534	−0.140901
$939$	47.6155	1.55387
$940$	−2.00000	−0.0652328
$941$	4.43845	0.144689	0.0723446	−	0.997380i	$-0.476952\pi$
$941$	4.43845	0.144689	0.0723446	+	0.997380i	$0.476952\pi$
$942$	13.5616	0.441859
$943$	4.00000	0.130258
$944$	0.876894	0.0285405
$945$	16.6847	0.542752
$946$	1.00000	0.0325128
$947$	4.36932	0.141984	0.0709919	−	0.997477i	$-0.477384\pi$
$947$	4.36932	0.141984	0.0709919	+	0.997477i	$0.477384\pi$
$948$	−0.876894	−0.0284802
$949$	−0.315342	−0.0102364
$950$	1.00000	0.0324443
$951$	−17.1771	−0.557005
$952$	16.6847	0.540753
$953$	−28.6155	−0.926948	−0.463474	−	0.886111i	$-0.653397\pi$
$953$	−28.6155	−0.926948	−0.463474	+	0.886111i	$0.653397\pi$
$954$	−2.00000	−0.0647524
$955$	19.3693	0.626776
$956$	−10.8078	−0.349548
$957$	3.31534	0.107170
$958$	−7.50758	−0.242559
$959$	41.7926	1.34955
$960$	1.56155	0.0503989
$961$	6.49242	0.209433
$962$	0.876894	0.0282722
$963$	4.31534	0.139060
$964$	20.7386	0.667946
$965$	19.8078	0.637634
$966$	−4.10795	−0.132171
$967$	−11.0691	−0.355959	−0.177980	−	0.984034i	$-0.556956\pi$
$967$	−11.0691	−0.355959	−0.177980	+	0.984034i	$0.556956\pi$
$968$	−1.00000	−0.0321412
$969$	−8.68466	−0.278991
$970$	−13.1231	−0.421358
$971$	−20.9848	−0.673436	−0.336718	−	0.941606i	$-0.609317\pi$
$971$	−20.9848	−0.673436	−0.336718	+	0.941606i	$0.609317\pi$
$972$	5.75379	0.184553
$973$	42.7386	1.37014
$974$	39.3693	1.26147
$975$	−0.876894	−0.0280831
$976$	−14.3693	−0.459951
$977$	24.6307	0.788005	0.394003	−	0.919109i	$-0.371090\pi$
$977$	24.6307	0.788005	0.394003	+	0.919109i	$0.371090\pi$
$978$	39.3153	1.25717
$979$	−0.684658	−0.0218818
$980$	2.00000	0.0638877
$981$	6.24621	0.199426
$982$	−18.0540	−0.576126
$983$	−29.6847	−0.946794	−0.473397	−	0.880849i	$-0.656972\pi$
$983$	−29.6847	−0.946794	−0.473397	+	0.880849i	$0.656972\pi$
$984$	7.12311	0.227076
$985$	−3.68466	−0.117403
$986$	11.8078	0.376036
$987$	9.36932	0.298229
$988$	0.561553	0.0178654
$989$	−0.876894	−0.0278836
$990$	−0.561553	−0.0178473
$991$	44.4924	1.41335	0.706674	−	0.707539i	$-0.250195\pi$
$991$	44.4924	1.41335	0.706674	+	0.707539i	$0.250195\pi$
$992$	−6.12311	−0.194409
$993$	25.7538	0.817272
$994$	25.3153	0.802954
$995$	8.43845	0.267517
$996$	−27.1231	−0.859428
$997$	13.7538	0.435587	0.217793	−	0.975995i	$-0.430114\pi$
$997$	13.7538	0.435587	0.217793	+	0.975995i	$0.430114\pi$
$998$	15.0540	0.476525
$999$	−8.68466	−0.274770

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4730.2.a.l.1.2	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4730.2.a.l.1.2	✓	2	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:	\( N \)	\(=\)	\( 4730 = 2 \cdot 5 \cdot 11 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4730.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.56155 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.56155 q^{6} -3.00000 q^{7} -1.00000 q^{8} -0.561553 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.56155 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.56155 q^{6} -3.00000 q^{7} -1.00000 q^{8} -0.561553 q^{9} -1.00000 q^{10} -1.00000 q^{11} +1.56155 q^{12} -0.561553 q^{13} +3.00000 q^{14} +1.56155 q^{15} +1.00000 q^{16} +5.56155 q^{17} +0.561553 q^{18} -1.00000 q^{19} +1.00000 q^{20} -4.68466 q^{21} +1.00000 q^{22} -0.876894 q^{23} -1.56155 q^{24} +1.00000 q^{25} +0.561553 q^{26} -5.56155 q^{27} -3.00000 q^{28} -2.12311 q^{29} -1.56155 q^{30} +6.12311 q^{31} -1.00000 q^{32} -1.56155 q^{33} -5.56155 q^{34} -3.00000 q^{35} -0.561553 q^{36} +1.56155 q^{37} +1.00000 q^{38} -0.876894 q^{39} -1.00000 q^{40} -4.56155 q^{41} +4.68466 q^{42} +1.00000 q^{43} -1.00000 q^{44} -0.561553 q^{45} +0.876894 q^{46} -2.00000 q^{47} +1.56155 q^{48} +2.00000 q^{49} -1.00000 q^{50} +8.68466 q^{51} -0.561553 q^{52} -3.56155 q^{53} +5.56155 q^{54} -1.00000 q^{55} +3.00000 q^{56} -1.56155 q^{57} +2.12311 q^{58} +0.876894 q^{59} +1.56155 q^{60} -14.3693 q^{61} -6.12311 q^{62} +1.68466 q^{63} +1.00000 q^{64} -0.561553 q^{65} +1.56155 q^{66} -1.43845 q^{67} +5.56155 q^{68} -1.36932 q^{69} +3.00000 q^{70} +8.43845 q^{71} +0.561553 q^{72} +0.561553 q^{73} -1.56155 q^{74} +1.56155 q^{75} -1.00000 q^{76} +3.00000 q^{77} +0.876894 q^{78} -0.561553 q^{79} +1.00000 q^{80} -7.00000 q^{81} +4.56155 q^{82} -17.3693 q^{83} -4.68466 q^{84} +5.56155 q^{85} -1.00000 q^{86} -3.31534 q^{87} +1.00000 q^{88} +0.684658 q^{89} +0.561553 q^{90} +1.68466 q^{91} -0.876894 q^{92} +9.56155 q^{93} +2.00000 q^{94} -1.00000 q^{95} -1.56155 q^{96} +13.1231 q^{97} -2.00000 q^{98} +0.561553 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - q^{3} + 2 q^{4} + 2 q^{5} + q^{6} - 6 q^{7} - 2 q^{8} + 3 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - q^3 + 2 * q^4 + 2 * q^5 + q^6 - 6 * q^7 - 2 * q^8 + 3 * q^9	\( 2 q - 2 q^{2} - q^{3} + 2 q^{4} + 2 q^{5} + q^{6} - 6 q^{7} - 2 q^{8} + 3 q^{9} - 2 q^{10} - 2 q^{11} - q^{12} + 3 q^{13} + 6 q^{14} - q^{15} + 2 q^{16} + 7 q^{17} - 3 q^{18} - 2 q^{19} + 2 q^{20} + 3 q^{21} + 2 q^{22} - 10 q^{23} + q^{24} + 2 q^{25} - 3 q^{26} - 7 q^{27} - 6 q^{28} + 4 q^{29} + q^{30} + 4 q^{31} - 2 q^{32} + q^{33} - 7 q^{34} - 6 q^{35} + 3 q^{36} - q^{37} + 2 q^{38} - 10 q^{39} - 2 q^{40} - 5 q^{41} - 3 q^{42} + 2 q^{43} - 2 q^{44} + 3 q^{45} + 10 q^{46} - 4 q^{47} - q^{48} + 4 q^{49} - 2 q^{50} + 5 q^{51} + 3 q^{52} - 3 q^{53} + 7 q^{54} - 2 q^{55} + 6 q^{56} + q^{57} - 4 q^{58} + 10 q^{59} - q^{60} - 4 q^{61} - 4 q^{62} - 9 q^{63} + 2 q^{64} + 3 q^{65} - q^{66} - 7 q^{67} + 7 q^{68} + 22 q^{69} + 6 q^{70} + 21 q^{71} - 3 q^{72} - 3 q^{73} + q^{74} - q^{75} - 2 q^{76} + 6 q^{77} + 10 q^{78} + 3 q^{79} + 2 q^{80} - 14 q^{81} + 5 q^{82} - 10 q^{83} + 3 q^{84} + 7 q^{85} - 2 q^{86} - 19 q^{87} + 2 q^{88} - 11 q^{89} - 3 q^{90} - 9 q^{91} - 10 q^{92} + 15 q^{93} + 4 q^{94} - 2 q^{95} + q^{96} + 18 q^{97} - 4 q^{98} - 3 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - q^3 + 2 * q^4 + 2 * q^5 + q^6 - 6 * q^7 - 2 * q^8 + 3 * q^9 - 2 * q^10 - 2 * q^11 - q^12 + 3 * q^13 + 6 * q^14 - q^15 + 2 * q^16 + 7 * q^17 - 3 * q^18 - 2 * q^19 + 2 * q^20 + 3 * q^21 + 2 * q^22 - 10 * q^23 + q^24 + 2 * q^25 - 3 * q^26 - 7 * q^27 - 6 * q^28 + 4 * q^29 + q^30 + 4 * q^31 - 2 * q^32 + q^33 - 7 * q^34 - 6 * q^35 + 3 * q^36 - q^37 + 2 * q^38 - 10 * q^39 - 2 * q^40 - 5 * q^41 - 3 * q^42 + 2 * q^43 - 2 * q^44 + 3 * q^45 + 10 * q^46 - 4 * q^47 - q^48 + 4 * q^49 - 2 * q^50 + 5 * q^51 + 3 * q^52 - 3 * q^53 + 7 * q^54 - 2 * q^55 + 6 * q^56 + q^57 - 4 * q^58 + 10 * q^59 - q^60 - 4 * q^61 - 4 * q^62 - 9 * q^63 + 2 * q^64 + 3 * q^65 - q^66 - 7 * q^67 + 7 * q^68 + 22 * q^69 + 6 * q^70 + 21 * q^71 - 3 * q^72 - 3 * q^73 + q^74 - q^75 - 2 * q^76 + 6 * q^77 + 10 * q^78 + 3 * q^79 + 2 * q^80 - 14 * q^81 + 5 * q^82 - 10 * q^83 + 3 * q^84 + 7 * q^85 - 2 * q^86 - 19 * q^87 + 2 * q^88 - 11 * q^89 - 3 * q^90 - 9 * q^91 - 10 * q^92 + 15 * q^93 + 4 * q^94 - 2 * q^95 + q^96 + 18 * q^97 - 4 * q^98 - 3 * q^99

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