LMFDB - Embedded newform 4029.2.a.k.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4029,2,Mod(1,4029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4029, 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("4029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4029 = 3 \cdot 17 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4029.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:	$32.1717269744$
Analytic rank:	$0$
Dimension:	$31$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	4029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.73268 q^{2} +1.00000 q^{3} +1.00217 q^{4} +2.89501 q^{5} -1.73268 q^{6} +3.30216 q^{7} +1.72891 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.73268 q^{2} +1.00000 q^{3} +1.00217 q^{4} +2.89501 q^{5} -1.73268 q^{6} +3.30216 q^{7} +1.72891 q^{8} +1.00000 q^{9} -5.01613 q^{10} +3.25201 q^{11} +1.00217 q^{12} -1.42446 q^{13} -5.72157 q^{14} +2.89501 q^{15} -5.00000 q^{16} +1.00000 q^{17} -1.73268 q^{18} +2.32004 q^{19} +2.90131 q^{20} +3.30216 q^{21} -5.63469 q^{22} -8.40319 q^{23} +1.72891 q^{24} +3.38110 q^{25} +2.46812 q^{26} +1.00000 q^{27} +3.30933 q^{28} -0.650361 q^{29} -5.01613 q^{30} -0.747325 q^{31} +5.20556 q^{32} +3.25201 q^{33} -1.73268 q^{34} +9.55979 q^{35} +1.00217 q^{36} +5.76664 q^{37} -4.01988 q^{38} -1.42446 q^{39} +5.00522 q^{40} -9.70082 q^{41} -5.72157 q^{42} +10.5114 q^{43} +3.25908 q^{44} +2.89501 q^{45} +14.5600 q^{46} +6.77674 q^{47} -5.00000 q^{48} +3.90424 q^{49} -5.85836 q^{50} +1.00000 q^{51} -1.42755 q^{52} +13.2002 q^{53} -1.73268 q^{54} +9.41461 q^{55} +5.70914 q^{56} +2.32004 q^{57} +1.12687 q^{58} -7.73933 q^{59} +2.90131 q^{60} -2.72918 q^{61} +1.29487 q^{62} +3.30216 q^{63} +0.980433 q^{64} -4.12382 q^{65} -5.63469 q^{66} -2.41577 q^{67} +1.00217 q^{68} -8.40319 q^{69} -16.5640 q^{70} +13.6953 q^{71} +1.72891 q^{72} -5.37321 q^{73} -9.99174 q^{74} +3.38110 q^{75} +2.32508 q^{76} +10.7386 q^{77} +2.46812 q^{78} +1.00000 q^{79} -14.4751 q^{80} +1.00000 q^{81} +16.8084 q^{82} -4.72563 q^{83} +3.30933 q^{84} +2.89501 q^{85} -18.2128 q^{86} -0.650361 q^{87} +5.62244 q^{88} +11.4989 q^{89} -5.01613 q^{90} -4.70378 q^{91} -8.42145 q^{92} -0.747325 q^{93} -11.7419 q^{94} +6.71653 q^{95} +5.20556 q^{96} -2.34223 q^{97} -6.76479 q^{98} +3.25201 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q + 4 q^{2} + 31 q^{3} + 34 q^{4} + 11 q^{5} + 4 q^{6} + 4 q^{7} + 12 q^{8} + 31 q^{9}+O(q^{10}) $ 31 * q + 4 * q^2 + 31 * q^3 + 34 * q^4 + 11 * q^5 + 4 * q^6 + 4 * q^7 + 12 * q^8 + 31 * q^9	\( 31 q + 4 q^{2} + 31 q^{3} + 34 q^{4} + 11 q^{5} + 4 q^{6} + 4 q^{7} + 12 q^{8} + 31 q^{9} + 5 q^{10} + 26 q^{11} + 34 q^{12} + 7 q^{13} + 19 q^{14} + 11 q^{15} + 40 q^{16} + 31 q^{17} + 4 q^{18} + 32 q^{19} + 23 q^{20} + 4 q^{21} + 2 q^{22} + 29 q^{23} + 12 q^{24} + 32 q^{25} + 13 q^{26} + 31 q^{27} - 13 q^{28} + 25 q^{29} + 5 q^{30} + 22 q^{31} + 28 q^{32} + 26 q^{33} + 4 q^{34} + 20 q^{35} + 34 q^{36} - 4 q^{37} + 19 q^{38} + 7 q^{39} - 3 q^{40} + 33 q^{41} + 19 q^{42} + 6 q^{43} + 30 q^{44} + 11 q^{45} - 11 q^{46} + 23 q^{47} + 40 q^{48} + 31 q^{49} + 6 q^{50} + 31 q^{51} - 7 q^{52} + 12 q^{53} + 4 q^{54} + 40 q^{56} + 32 q^{57} + 9 q^{58} + 27 q^{59} + 23 q^{60} - 4 q^{61} + 25 q^{62} + 4 q^{63} + 10 q^{64} + 54 q^{65} + 2 q^{66} + 34 q^{68} + 29 q^{69} - 59 q^{70} + 35 q^{71} + 12 q^{72} + 5 q^{73} + 48 q^{74} + 32 q^{75} + 32 q^{76} + 42 q^{77} + 13 q^{78} + 31 q^{79} + 24 q^{80} + 31 q^{81} + 5 q^{82} + 67 q^{83} - 13 q^{84} + 11 q^{85} - 20 q^{86} + 25 q^{87} - 7 q^{88} + 22 q^{89} + 5 q^{90} + 16 q^{91} + 57 q^{92} + 22 q^{93} + 45 q^{94} + 73 q^{95} + 28 q^{96} - 13 q^{97} - 19 q^{98} + 26 q^{99}+O(q^{100}) \) 31 * q + 4 * q^2 + 31 * q^3 + 34 * q^4 + 11 * q^5 + 4 * q^6 + 4 * q^7 + 12 * q^8 + 31 * q^9 + 5 * q^10 + 26 * q^11 + 34 * q^12 + 7 * q^13 + 19 * q^14 + 11 * q^15 + 40 * q^16 + 31 * q^17 + 4 * q^18 + 32 * q^19 + 23 * q^20 + 4 * q^21 + 2 * q^22 + 29 * q^23 + 12 * q^24 + 32 * q^25 + 13 * q^26 + 31 * q^27 - 13 * q^28 + 25 * q^29 + 5 * q^30 + 22 * q^31 + 28 * q^32 + 26 * q^33 + 4 * q^34 + 20 * q^35 + 34 * q^36 - 4 * q^37 + 19 * q^38 + 7 * q^39 - 3 * q^40 + 33 * q^41 + 19 * q^42 + 6 * q^43 + 30 * q^44 + 11 * q^45 - 11 * q^46 + 23 * q^47 + 40 * q^48 + 31 * q^49 + 6 * q^50 + 31 * q^51 - 7 * q^52 + 12 * q^53 + 4 * q^54 + 40 * q^56 + 32 * q^57 + 9 * q^58 + 27 * q^59 + 23 * q^60 - 4 * q^61 + 25 * q^62 + 4 * q^63 + 10 * q^64 + 54 * q^65 + 2 * q^66 + 34 * q^68 + 29 * q^69 - 59 * q^70 + 35 * q^71 + 12 * q^72 + 5 * q^73 + 48 * q^74 + 32 * q^75 + 32 * q^76 + 42 * q^77 + 13 * q^78 + 31 * q^79 + 24 * q^80 + 31 * q^81 + 5 * q^82 + 67 * q^83 - 13 * q^84 + 11 * q^85 - 20 * q^86 + 25 * q^87 - 7 * q^88 + 22 * q^89 + 5 * q^90 + 16 * q^91 + 57 * q^92 + 22 * q^93 + 45 * q^94 + 73 * q^95 + 28 * q^96 - 13 * q^97 - 19 * q^98 + 26 * 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 $

$2$	−1.73268	−1.22519	−0.612594	−	0.790398i	$-0.709874\pi$
$2$	−1.73268	−1.22519	−0.612594	+	0.790398i	$0.709874\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00217	0.501087
$5$	2.89501	1.29469	0.647345	−	0.762197i	$-0.275879\pi$
$5$	2.89501	1.29469	0.647345	+	0.762197i	$0.275879\pi$
$6$	−1.73268	−0.707363
$7$	3.30216	1.24810	0.624049	−	0.781385i	$-0.285487\pi$
$7$	3.30216	1.24810	0.624049	+	0.781385i	$0.285487\pi$
$8$	1.72891	0.611263
$9$	1.00000	0.333333
$10$	−5.01613	−1.58624
$11$	3.25201	0.980518	0.490259	−	0.871577i	$-0.336902\pi$
$11$	3.25201	0.980518	0.490259	+	0.871577i	$0.336902\pi$
$12$	1.00217	0.289303
$13$	−1.42446	−0.395073	−0.197536	−	0.980296i	$-0.563294\pi$
$13$	−1.42446	−0.395073	−0.197536	+	0.980296i	$0.563294\pi$
$14$	−5.72157	−1.52916
$15$	2.89501	0.747489
$16$	−5.00000	−1.25000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.73268	−0.408396
$19$	2.32004	0.532253	0.266126	−	0.963938i	$-0.414256\pi$
$19$	2.32004	0.532253	0.266126	+	0.963938i	$0.414256\pi$
$20$	2.90131	0.648752
$21$	3.30216	0.720590
$22$	−5.63469	−1.20132
$23$	−8.40319	−1.75219	−0.876093	−	0.482142i	$-0.839859\pi$
$23$	−8.40319	−1.75219	−0.876093	+	0.482142i	$0.839859\pi$
$24$	1.72891	0.352913
$25$	3.38110	0.676220
$26$	2.46812	0.484039
$27$	1.00000	0.192450
$28$	3.30933	0.625405
$29$	−0.650361	−0.120769	−0.0603845	−	0.998175i	$-0.519233\pi$
$29$	−0.650361	−0.120769	−0.0603845	+	0.998175i	$0.519233\pi$
$30$	−5.01613	−0.915815
$31$	−0.747325	−0.134224	−0.0671118	−	0.997745i	$-0.521378\pi$
$31$	−0.747325	−0.134224	−0.0671118	+	0.997745i	$0.521378\pi$
$32$	5.20556	0.920221
$33$	3.25201	0.566102
$34$	−1.73268	−0.297152
$35$	9.55979	1.61590
$36$	1.00217	0.167029
$37$	5.76664	0.948030	0.474015	−	0.880517i	$-0.342804\pi$
$37$	5.76664	0.948030	0.474015	+	0.880517i	$0.342804\pi$
$38$	−4.01988	−0.652110
$39$	−1.42446	−0.228095
$40$	5.00522	0.791395
$41$	−9.70082	−1.51501	−0.757507	−	0.652828i	$-0.773583\pi$
$41$	−9.70082	−1.51501	−0.757507	+	0.652828i	$0.773583\pi$
$42$	−5.72157	−0.882858
$43$	10.5114	1.60297	0.801483	−	0.598017i	$-0.204044\pi$
$43$	10.5114	1.60297	0.801483	+	0.598017i	$0.204044\pi$
$44$	3.25908	0.491325
$45$	2.89501	0.431563
$46$	14.5600	2.14676
$47$	6.77674	0.988488	0.494244	−	0.869323i	$-0.335445\pi$
$47$	6.77674	0.988488	0.494244	+	0.869323i	$0.335445\pi$
$48$	−5.00000	−0.721687
$49$	3.90424	0.557748
$50$	−5.85836	−0.828497
$51$	1.00000	0.140028
$52$	−1.42755	−0.197966
$53$	13.2002	1.81318	0.906591	−	0.422011i	$-0.138676\pi$
$53$	13.2002	1.81318	0.906591	+	0.422011i	$0.138676\pi$
$54$	−1.73268	−0.235788
$55$	9.41461	1.26947
$56$	5.70914	0.762916
$57$	2.32004	0.307296
$58$	1.12687	0.147965
$59$	−7.73933	−1.00757	−0.503787	−	0.863828i	$-0.668060\pi$
$59$	−7.73933	−1.00757	−0.503787	+	0.863828i	$0.668060\pi$
$60$	2.90131	0.374557
$61$	−2.72918	−0.349436	−0.174718	−	0.984619i	$-0.555901\pi$
$61$	−2.72918	−0.349436	−0.174718	+	0.984619i	$0.555901\pi$
$62$	1.29487	0.164449
$63$	3.30216	0.416033
$64$	0.980433	0.122554
$65$	−4.12382	−0.511497
$66$	−5.63469	−0.693582
$67$	−2.41577	−0.295133	−0.147567	−	0.989052i	$-0.547144\pi$
$67$	−2.41577	−0.295133	−0.147567	+	0.989052i	$0.547144\pi$
$68$	1.00217	0.121531
$69$	−8.40319	−1.01162
$70$	−16.5640	−1.97978
$71$	13.6953	1.62534	0.812668	−	0.582728i	$-0.198015\pi$
$71$	13.6953	1.62534	0.812668	+	0.582728i	$0.198015\pi$
$72$	1.72891	0.203754
$73$	−5.37321	−0.628887	−0.314443	−	0.949276i	$-0.601818\pi$
$73$	−5.37321	−0.628887	−0.314443	+	0.949276i	$0.601818\pi$
$74$	−9.99174	−1.16152
$75$	3.38110	0.390416
$76$	2.32508	0.266705
$77$	10.7386	1.22378
$78$	2.46812	0.279460
$79$	1.00000	0.112509
$79$	1.00000	0.112509
$80$	−14.4751	−1.61836
$81$	1.00000	0.111111
$82$	16.8084	1.85618
$83$	−4.72563	−0.518706	−0.259353	−	0.965783i	$-0.583509\pi$
$83$	−4.72563	−0.518706	−0.259353	+	0.965783i	$0.583509\pi$
$84$	3.30933	0.361078
$85$	2.89501	0.314008
$86$	−18.2128	−1.96394
$87$	−0.650361	−0.0697260
$88$	5.62244	0.599354
$89$	11.4989	1.21888	0.609441	−	0.792832i	$-0.291394\pi$
$89$	11.4989	1.21888	0.609441	+	0.792832i	$0.291394\pi$
$90$	−5.01613	−0.528746
$91$	−4.70378	−0.493090
$92$	−8.42145	−0.877997
$93$	−0.747325	−0.0774940
$94$	−11.7419	−1.21108
$95$	6.71653	0.689102
$96$	5.20556	0.531290
$97$	−2.34223	−0.237818	−0.118909	−	0.992905i	$-0.537940\pi$
$97$	−2.34223	−0.237818	−0.118909	+	0.992905i	$0.537940\pi$
$98$	−6.76479	−0.683347
$99$	3.25201	0.326839
$100$	3.38845	0.338845
$101$	13.3969	1.33304	0.666522	−	0.745486i	$-0.267782\pi$
$101$	13.3969	1.33304	0.666522	+	0.745486i	$0.267782\pi$
$102$	−1.73268	−0.171561
$103$	−15.5382	−1.53102	−0.765511	−	0.643423i	$-0.777514\pi$
$103$	−15.5382	−1.53102	−0.765511	+	0.643423i	$0.777514\pi$
$104$	−2.46276	−0.241493
$105$	9.55979	0.932940
$106$	−22.8716	−2.22149
$107$	12.7561	1.23318	0.616591	−	0.787283i	$-0.288513\pi$
$107$	12.7561	1.23318	0.616591	+	0.787283i	$0.288513\pi$
$108$	1.00217	0.0964342
$109$	13.4313	1.28648	0.643242	−	0.765663i	$-0.277589\pi$
$109$	13.4313	1.28648	0.643242	+	0.765663i	$0.277589\pi$
$110$	−16.3125	−1.55534
$111$	5.76664	0.547346
$112$	−16.5108	−1.56012
$113$	8.28805	0.779674	0.389837	−	0.920884i	$-0.372531\pi$
$113$	8.28805	0.779674	0.389837	+	0.920884i	$0.372531\pi$
$114$	−4.01988	−0.376496
$115$	−24.3273	−2.26854
$116$	−0.651774	−0.0605157
$117$	−1.42446	−0.131691
$118$	13.4098	1.23447
$119$	3.30216	0.302708
$120$	5.00522	0.456912
$121$	−0.424426	−0.0385842
$122$	4.72880	0.428125
$123$	−9.70082	−0.874693
$124$	−0.748950	−0.0672577
$125$	−4.68674	−0.419194
$126$	−5.72157	−0.509718
$127$	−7.61952	−0.676123	−0.338061	−	0.941124i	$-0.609771\pi$
$127$	−7.61952	−0.676123	−0.338061	+	0.941124i	$0.609771\pi$
$128$	−12.1099	−1.07037
$129$	10.5114	0.925473
$130$	7.14525	0.626680
$131$	4.38327	0.382968	0.191484	−	0.981496i	$-0.438670\pi$
$131$	4.38327	0.382968	0.191484	+	0.981496i	$0.438670\pi$
$132$	3.25908	0.283666
$133$	7.66112	0.664304
$134$	4.18575	0.361594
$135$	2.89501	0.249163
$136$	1.72891	0.148253
$137$	10.3736	0.886275	0.443137	−	0.896454i	$-0.353865\pi$
$137$	10.3736	0.886275	0.443137	+	0.896454i	$0.353865\pi$
$138$	14.5600	1.23943
$139$	−13.2343	−1.12252	−0.561259	−	0.827640i	$-0.689683\pi$
$139$	−13.2343	−1.12252	−0.561259	+	0.827640i	$0.689683\pi$
$140$	9.58057	0.809706
$141$	6.77674	0.570704
$142$	−23.7296	−1.99134
$143$	−4.63235	−0.387376
$144$	−5.00000	−0.416666
$145$	−1.88280	−0.156358
$146$	9.31005	0.770505
$147$	3.90424	0.322016
$148$	5.77918	0.475046
$149$	−3.90568	−0.319966	−0.159983	−	0.987120i	$-0.551144\pi$
$149$	−3.90568	−0.319966	−0.159983	+	0.987120i	$0.551144\pi$
$150$	−5.85836	−0.478333
$151$	−4.99932	−0.406839	−0.203419	−	0.979092i	$-0.565206\pi$
$151$	−4.99932	−0.406839	−0.203419	+	0.979092i	$0.565206\pi$
$152$	4.01114	0.325346
$153$	1.00000	0.0808452
$154$	−18.6066	−1.49936
$155$	−2.16352	−0.173778
$156$	−1.42755	−0.114296
$157$	−19.1845	−1.53109	−0.765543	−	0.643385i	$-0.777530\pi$
$157$	−19.1845	−1.53109	−0.765543	+	0.643385i	$0.777530\pi$
$158$	−1.73268	−0.137844
$159$	13.2002	1.04684
$160$	15.0702	1.19140
$161$	−27.7486	−2.18690
$162$	−1.73268	−0.136132
$163$	−10.4382	−0.817585	−0.408792	−	0.912627i	$-0.634050\pi$
$163$	−10.4382	−0.817585	−0.408792	+	0.912627i	$0.634050\pi$
$164$	−9.72190	−0.759153
$165$	9.41461	0.732927
$166$	8.18800	0.635512
$167$	8.18465	0.633347	0.316673	−	0.948535i	$-0.397434\pi$
$167$	8.18465	0.633347	0.316673	+	0.948535i	$0.397434\pi$
$168$	5.70914	0.440470
$169$	−10.9709	−0.843917
$170$	−5.01613	−0.384719
$171$	2.32004	0.177418
$172$	10.5342	0.803226
$173$	5.56881	0.423389	0.211694	−	0.977336i	$-0.432102\pi$
$173$	5.56881	0.423389	0.211694	+	0.977336i	$0.432102\pi$
$174$	1.12687	0.0854275
$175$	11.1649	0.843989
$176$	−16.2600	−1.22565
$177$	−7.73933	−0.581723
$178$	−19.9239	−1.49336
$179$	−24.2661	−1.81373	−0.906867	−	0.421417i	$-0.861533\pi$
$179$	−24.2661	−1.81373	−0.906867	+	0.421417i	$0.861533\pi$
$180$	2.90131	0.216251
$181$	11.3517	0.843767	0.421884	−	0.906650i	$-0.361369\pi$
$181$	11.3517	0.843767	0.421884	+	0.906650i	$0.361369\pi$
$182$	8.15013	0.604128
$183$	−2.72918	−0.201747
$184$	−14.5284	−1.07105
$185$	16.6945	1.22740
$186$	1.29487	0.0949448
$187$	3.25201	0.237811
$188$	6.79147	0.495319
$189$	3.30216	0.240197
$190$	−11.6376	−0.844280
$191$	7.93371	0.574063	0.287032	−	0.957921i	$-0.407332\pi$
$191$	7.93371	0.574063	0.287032	+	0.957921i	$0.407332\pi$
$192$	0.980433	0.0707566
$193$	−18.0603	−1.30001	−0.650006	−	0.759929i	$-0.725233\pi$
$193$	−18.0603	−1.30001	−0.650006	+	0.759929i	$0.725233\pi$
$194$	4.05834	0.291371
$195$	−4.12382	−0.295313
$196$	3.91273	0.279480
$197$	1.90395	0.135651	0.0678254	−	0.997697i	$-0.478394\pi$
$197$	1.90395	0.135651	0.0678254	+	0.997697i	$0.478394\pi$
$198$	−5.63469	−0.400440
$199$	25.0531	1.77597	0.887984	−	0.459875i	$-0.152106\pi$
$199$	25.0531	1.77597	0.887984	+	0.459875i	$0.152106\pi$
$200$	5.84562	0.413348
$201$	−2.41577	−0.170395
$202$	−23.2125	−1.63323
$203$	−2.14759	−0.150731
$204$	1.00217	0.0701662
$205$	−28.0840	−1.96147
$206$	26.9227	1.87579
$207$	−8.40319	−0.584062
$208$	7.12227	0.493841
$209$	7.54478	0.521884
$210$	−16.5640	−1.14303
$211$	−3.98468	−0.274317	−0.137158	−	0.990549i	$-0.543797\pi$
$211$	−3.98468	−0.274317	−0.137158	+	0.990549i	$0.543797\pi$
$212$	13.2289	0.908561
$213$	13.6953	0.938388
$214$	−22.1023	−1.51088
$215$	30.4305	2.07534
$216$	1.72891	0.117638
$217$	−2.46779	−0.167524
$218$	−23.2721	−1.57619
$219$	−5.37321	−0.363088
$220$	9.43508	0.636113
$221$	−1.42446	−0.0958193
$222$	−9.99174	−0.670602
$223$	20.0652	1.34366	0.671832	−	0.740703i	$-0.265508\pi$
$223$	20.0652	1.34366	0.671832	+	0.740703i	$0.265508\pi$
$224$	17.1896	1.14853
$225$	3.38110	0.225407
$226$	−14.3605	−0.955247
$227$	10.9646	0.727748	0.363874	−	0.931448i	$-0.381454\pi$
$227$	10.9646	0.727748	0.363874	+	0.931448i	$0.381454\pi$
$228$	2.32508	0.153982
$229$	22.5916	1.49290	0.746448	−	0.665444i	$-0.231758\pi$
$229$	22.5916	1.49290	0.746448	+	0.665444i	$0.231758\pi$
$230$	42.1514	2.77938
$231$	10.7386	0.706551
$232$	−1.12442	−0.0738216
$233$	−0.530463	−0.0347518	−0.0173759	−	0.999849i	$-0.505531\pi$
$233$	−0.530463	−0.0347518	−0.0173759	+	0.999849i	$0.505531\pi$
$234$	2.46812	0.161346
$235$	19.6187	1.27979
$236$	−7.75615	−0.504882
$237$	1.00000	0.0649570
$238$	−5.72157	−0.370875
$239$	0.0514535	0.00332825	0.00166412	−	0.999999i	$-0.499470\pi$
$239$	0.0514535	0.00332825	0.00166412	+	0.999999i	$0.499470\pi$
$240$	−14.4751	−0.934361
$241$	−7.69075	−0.495405	−0.247702	−	0.968836i	$-0.579676\pi$
$241$	−7.69075	−0.495405	−0.247702	+	0.968836i	$0.579676\pi$
$242$	0.735393	0.0472729
$243$	1.00000	0.0641500
$244$	−2.73512	−0.175098
$245$	11.3028	0.722111
$246$	16.8084	1.07166
$247$	−3.30479	−0.210279
$248$	−1.29206	−0.0820459
$249$	−4.72563	−0.299475
$250$	8.12061	0.513592
$251$	−20.1716	−1.27322	−0.636611	−	0.771185i	$-0.719664\pi$
$251$	−20.1716	−1.27322	−0.636611	+	0.771185i	$0.719664\pi$
$252$	3.30933	0.208468
$253$	−27.3273	−1.71805
$254$	13.2022	0.828378
$255$	2.89501	0.181293
$256$	19.0217	1.18885
$257$	15.7169	0.980394	0.490197	−	0.871612i	$-0.336925\pi$
$257$	15.7169	0.980394	0.490197	+	0.871612i	$0.336925\pi$
$258$	−18.2128	−1.13388
$259$	19.0424	1.18323
$260$	−4.13278	−0.256304
$261$	−0.650361	−0.0402563
$262$	−7.59480	−0.469208
$263$	−7.62885	−0.470415	−0.235208	−	0.971945i	$-0.575577\pi$
$263$	−7.62885	−0.470415	−0.235208	+	0.971945i	$0.575577\pi$
$264$	5.62244	0.346037
$265$	38.2146	2.34751
$266$	−13.2743	−0.813897
$267$	11.4989	0.703721
$268$	−2.42102	−0.147887
$269$	−31.3153	−1.90932	−0.954662	−	0.297691i	$-0.903784\pi$
$269$	−31.3153	−1.90932	−0.954662	+	0.297691i	$0.903784\pi$
$270$	−5.01613	−0.305272
$271$	−15.9376	−0.968139	−0.484069	−	0.875030i	$-0.660842\pi$
$271$	−15.9376	−0.968139	−0.484069	+	0.875030i	$0.660842\pi$
$272$	−5.00000	−0.303169
$273$	−4.70378	−0.284685
$274$	−17.9741	−1.08585
$275$	10.9954	0.663046
$276$	−8.42145	−0.506912
$277$	−19.8080	−1.19015	−0.595073	−	0.803672i	$-0.702877\pi$
$277$	−19.8080	−1.19015	−0.595073	+	0.803672i	$0.702877\pi$
$278$	22.9308	1.37530
$279$	−0.747325	−0.0447412
$280$	16.5280	0.987739
$281$	9.35604	0.558134	0.279067	−	0.960272i	$-0.409975\pi$
$281$	9.35604	0.558134	0.279067	+	0.960272i	$0.409975\pi$
$282$	−11.7419	−0.699220
$283$	5.57589	0.331452	0.165726	−	0.986172i	$-0.447003\pi$
$283$	5.57589	0.331452	0.165726	+	0.986172i	$0.447003\pi$
$284$	13.7251	0.814434
$285$	6.71653	0.397853
$286$	8.02636	0.474609
$287$	−32.0336	−1.89088
$288$	5.20556	0.306740
$289$	1.00000	0.0588235
$290$	3.26229	0.191568
$291$	−2.34223	−0.137304
$292$	−5.38489	−0.315127
$293$	−4.63022	−0.270500	−0.135250	−	0.990811i	$-0.543184\pi$
$293$	−4.63022	−0.270500	−0.135250	+	0.990811i	$0.543184\pi$
$294$	−6.76479	−0.394531
$295$	−22.4055	−1.30450
$296$	9.97002	0.579496
$297$	3.25201	0.188701
$298$	6.76729	0.392018
$299$	11.9700	0.692241
$300$	3.38845	0.195632
$301$	34.7101	2.00066
$302$	8.66221	0.498454
$303$	13.3969	0.769633
$304$	−11.6002	−0.665315
$305$	−7.90102	−0.452411
$306$	−1.73268	−0.0990506
$307$	11.0056	0.628124	0.314062	−	0.949402i	$-0.398310\pi$
$307$	11.0056	0.628124	0.314062	+	0.949402i	$0.398310\pi$
$308$	10.7620	0.613221
$309$	−15.5382	−0.883936
$310$	3.74868	0.212911
$311$	−18.3578	−1.04098	−0.520489	−	0.853868i	$-0.674250\pi$
$311$	−18.3578	−1.04098	−0.520489	+	0.853868i	$0.674250\pi$
$312$	−2.46276	−0.139426
$313$	10.3244	0.583568	0.291784	−	0.956484i	$-0.405751\pi$
$313$	10.3244	0.583568	0.291784	+	0.956484i	$0.405751\pi$
$314$	33.2405	1.87587
$315$	9.55979	0.538633
$316$	1.00217	0.0563767
$317$	−18.7935	−1.05555	−0.527775	−	0.849384i	$-0.676974\pi$
$317$	−18.7935	−1.05555	−0.527775	+	0.849384i	$0.676974\pi$
$318$	−22.8716	−1.28258
$319$	−2.11498	−0.118416
$320$	2.83837	0.158669
$321$	12.7561	0.711979
$322$	48.0795	2.67936
$323$	2.32004	0.129090
$324$	1.00217	0.0556763
$325$	−4.81623	−0.267156
$326$	18.0861	1.00170
$327$	13.4313	0.742752
$328$	−16.7719	−0.926071
$329$	22.3778	1.23373
$330$	−16.3125	−0.897973
$331$	−24.7950	−1.36286	−0.681428	−	0.731885i	$-0.738641\pi$
$331$	−24.7950	−1.36286	−0.681428	+	0.731885i	$0.738641\pi$
$332$	−4.73591	−0.259917
$333$	5.76664	0.316010
$334$	−14.1814	−0.775969
$335$	−6.99369	−0.382106
$336$	−16.5108	−0.900736
$337$	−6.81474	−0.371223	−0.185611	−	0.982623i	$-0.559427\pi$
$337$	−6.81474	−0.371223	−0.185611	+	0.982623i	$0.559427\pi$
$338$	19.0091	1.03396
$339$	8.28805	0.450145
$340$	2.90131	0.157345
$341$	−2.43031	−0.131609
$342$	−4.01988	−0.217370
$343$	−10.2227	−0.551973
$344$	18.1732	0.979834
$345$	−24.3273	−1.30974
$346$	−9.64895	−0.518731
$347$	25.4044	1.36378	0.681889	−	0.731455i	$-0.261159\pi$
$347$	25.4044	1.36378	0.681889	+	0.731455i	$0.261159\pi$
$348$	−0.651774	−0.0349388
$349$	−31.5518	−1.68893	−0.844464	−	0.535613i	$-0.820081\pi$
$349$	−31.5518	−1.68893	−0.844464	+	0.535613i	$0.820081\pi$
$350$	−19.3452	−1.03405
$351$	−1.42446	−0.0760318
$352$	16.9285	0.902294
$353$	−9.54881	−0.508232	−0.254116	−	0.967174i	$-0.581785\pi$
$353$	−9.54881	−0.508232	−0.254116	+	0.967174i	$0.581785\pi$
$354$	13.4098	0.712721
$355$	39.6481	2.10430
$356$	11.5239	0.610765
$357$	3.30216	0.174769
$358$	42.0454	2.22217
$359$	35.3269	1.86448	0.932242	−	0.361835i	$-0.117850\pi$
$359$	35.3269	1.86448	0.932242	+	0.361835i	$0.117850\pi$
$360$	5.00522	0.263798
$361$	−13.6174	−0.716707
$362$	−19.6689	−1.03377
$363$	−0.424426	−0.0222766
$364$	−4.71400	−0.247081
$365$	−15.5555	−0.814213
$366$	4.72880	0.247178
$367$	−6.91799	−0.361116	−0.180558	−	0.983564i	$-0.557790\pi$
$367$	−6.91799	−0.361116	−0.180558	+	0.983564i	$0.557790\pi$
$368$	42.0159	2.19023
$369$	−9.70082	−0.505004
$370$	−28.9262	−1.50380
$371$	43.5890	2.26303
$372$	−0.748950	−0.0388312
$373$	−4.97404	−0.257546	−0.128773	−	0.991674i	$-0.541104\pi$
$373$	−4.97404	−0.257546	−0.128773	+	0.991674i	$0.541104\pi$
$374$	−5.63469	−0.291363
$375$	−4.68674	−0.242022
$376$	11.7164	0.604226
$377$	0.926410	0.0477125
$378$	−5.72157	−0.294286
$379$	−17.1110	−0.878934	−0.439467	−	0.898259i	$-0.644833\pi$
$379$	−17.1110	−0.878934	−0.439467	+	0.898259i	$0.644833\pi$
$380$	6.73113	0.345300
$381$	−7.61952	−0.390360
$382$	−13.7466	−0.703336
$383$	18.6188	0.951377	0.475688	−	0.879614i	$-0.342199\pi$
$383$	18.6188	0.951377	0.475688	+	0.879614i	$0.342199\pi$
$384$	−12.1099	−0.617980
$385$	31.0885	1.58442
$386$	31.2927	1.59276
$387$	10.5114	0.534322
$388$	−2.34732	−0.119167
$389$	−18.4109	−0.933470	−0.466735	−	0.884397i	$-0.654570\pi$
$389$	−18.4109	−0.933470	−0.466735	+	0.884397i	$0.654570\pi$
$390$	7.14525	0.361814
$391$	−8.40319	−0.424967
$392$	6.75008	0.340931
$393$	4.38327	0.221107
$394$	−3.29893	−0.166198
$395$	2.89501	0.145664
$396$	3.25908	0.163775
$397$	5.48451	0.275260	0.137630	−	0.990484i	$-0.456052\pi$
$397$	5.48451	0.275260	0.137630	+	0.990484i	$0.456052\pi$
$398$	−43.4090	−2.17590
$399$	7.66112	0.383536
$400$	−16.9055	−0.845274
$401$	21.9988	1.09857	0.549283	−	0.835636i	$-0.314901\pi$
$401$	21.9988	1.09857	0.549283	+	0.835636i	$0.314901\pi$
$402$	4.18575	0.208766
$403$	1.06453	0.0530281
$404$	13.4260	0.667970
$405$	2.89501	0.143854
$406$	3.72109	0.184674
$407$	18.7532	0.929561
$408$	1.72891	0.0855939
$409$	20.8864	1.03277	0.516384	−	0.856357i	$-0.327278\pi$
$409$	20.8864	1.03277	0.516384	+	0.856357i	$0.327278\pi$
$410$	48.6605	2.40317
$411$	10.3736	0.511691
$412$	−15.5719	−0.767175
$413$	−25.5565	−1.25755
$414$	14.5600	0.715586
$415$	−13.6808	−0.671563
$416$	−7.41509	−0.363555
$417$	−13.2343	−0.648086
$418$	−13.0727	−0.639406
$419$	−3.09533	−0.151217	−0.0756083	−	0.997138i	$-0.524090\pi$
$419$	−3.09533	−0.151217	−0.0756083	+	0.997138i	$0.524090\pi$
$420$	9.58057	0.467484
$421$	7.34024	0.357742	0.178871	−	0.983873i	$-0.442756\pi$
$421$	7.34024	0.357742	0.178871	+	0.983873i	$0.442756\pi$
$422$	6.90417	0.336090
$423$	6.77674	0.329496
$424$	22.8219	1.10833
$425$	3.38110	0.164007
$426$	−23.7296	−1.14970
$427$	−9.01219	−0.436130
$428$	12.7839	0.617932
$429$	−4.63235	−0.223652
$430$	−52.7263	−2.54269
$431$	−24.5569	−1.18286	−0.591432	−	0.806355i	$-0.701437\pi$
$431$	−24.5569	−1.18286	−0.591432	+	0.806355i	$0.701437\pi$
$432$	−5.00000	−0.240562
$433$	28.8618	1.38701	0.693505	−	0.720451i	$-0.256065\pi$
$433$	28.8618	1.38701	0.693505	+	0.720451i	$0.256065\pi$
$434$	4.27588	0.205249
$435$	−1.88280	−0.0902735
$436$	13.4605	0.644640
$437$	−19.4957	−0.932606
$438$	9.31005	0.444851
$439$	−10.2511	−0.489259	−0.244630	−	0.969617i	$-0.578666\pi$
$439$	−10.2511	−0.489259	−0.244630	+	0.969617i	$0.578666\pi$
$440$	16.2770	0.775977
$441$	3.90424	0.185916
$442$	2.46812	0.117397
$443$	14.3162	0.680184	0.340092	−	0.940392i	$-0.389542\pi$
$443$	14.3162	0.680184	0.340092	+	0.940392i	$0.389542\pi$
$444$	5.77918	0.274268
$445$	33.2895	1.57807
$446$	−34.7665	−1.64624
$447$	−3.90568	−0.184732
$448$	3.23754	0.152959
$449$	34.8130	1.64293	0.821463	−	0.570262i	$-0.193158\pi$
$449$	34.8130	1.64293	0.821463	+	0.570262i	$0.193158\pi$
$450$	−5.85836	−0.276166
$451$	−31.5472	−1.48550
$452$	8.30606	0.390684
$453$	−4.99932	−0.234889
$454$	−18.9982	−0.891628
$455$	−13.6175	−0.638398
$456$	4.01114	0.187839
$457$	14.8635	0.695286	0.347643	−	0.937627i	$-0.386982\pi$
$457$	14.8635	0.695286	0.347643	+	0.937627i	$0.386982\pi$
$458$	−39.1440	−1.82908
$459$	1.00000	0.0466760
$460$	−24.3802	−1.13673
$461$	0.316575	0.0147444	0.00737219	−	0.999973i	$-0.497653\pi$
$461$	0.316575	0.0147444	0.00737219	+	0.999973i	$0.497653\pi$
$462$	−18.6066	−0.865658
$463$	−5.22500	−0.242826	−0.121413	−	0.992602i	$-0.538743\pi$
$463$	−5.22500	−0.242826	−0.121413	+	0.992602i	$0.538743\pi$
$464$	3.25180	0.150961
$465$	−2.16352	−0.100331
$466$	0.919122	0.0425775
$467$	−16.2752	−0.753126	−0.376563	−	0.926391i	$-0.622894\pi$
$467$	−16.2752	−0.753126	−0.376563	+	0.926391i	$0.622894\pi$
$468$	−1.42755	−0.0659886
$469$	−7.97726	−0.368355
$470$	−33.9930	−1.56798
$471$	−19.1845	−0.883973
$472$	−13.3806	−0.615893
$473$	34.1830	1.57174
$474$	−1.73268	−0.0795845
$475$	7.84427	0.359920
$476$	3.30933	0.151683
$477$	13.2002	0.604394
$478$	−0.0891523	−0.00407773
$479$	30.6770	1.40167	0.700833	−	0.713325i	$-0.252812\pi$
$479$	30.6770	1.40167	0.700833	+	0.713325i	$0.252812\pi$
$480$	15.0702	0.687856
$481$	−8.21433	−0.374541
$482$	13.3256	0.606964
$483$	−27.7486	−1.26261
$484$	−0.425348	−0.0193340
$485$	−6.78079	−0.307900
$486$	−1.73268	−0.0785959
$487$	−4.28298	−0.194080	−0.0970401	−	0.995280i	$-0.530938\pi$
$487$	−4.28298	−0.194080	−0.0970401	+	0.995280i	$0.530938\pi$
$488$	−4.71852	−0.213597
$489$	−10.4382	−0.472033
$490$	−19.5842	−0.884722
$491$	−5.59334	−0.252424	−0.126212	−	0.992003i	$-0.540282\pi$
$491$	−5.59334	−0.252424	−0.126212	+	0.992003i	$0.540282\pi$
$492$	−9.72190	−0.438297
$493$	−0.650361	−0.0292908
$494$	5.72614	0.257631
$495$	9.41461	0.423155
$496$	3.73662	0.167779
$497$	45.2241	2.02858
$498$	8.18800	0.366913
$499$	−6.05647	−0.271125	−0.135562	−	0.990769i	$-0.543284\pi$
$499$	−6.05647	−0.271125	−0.135562	+	0.990769i	$0.543284\pi$
$500$	−4.69692	−0.210053
$501$	8.18465	0.365663
$502$	34.9510	1.55994
$503$	22.6653	1.01059	0.505297	−	0.862945i	$-0.331383\pi$
$503$	22.6653	1.01059	0.505297	+	0.862945i	$0.331383\pi$
$504$	5.70914	0.254305
$505$	38.7843	1.72588
$506$	47.3493	2.10493
$507$	−10.9709	−0.487236
$508$	−7.63608	−0.338796
$509$	−24.1078	−1.06856	−0.534280	−	0.845308i	$-0.679417\pi$
$509$	−24.1078	−1.06856	−0.534280	+	0.845308i	$0.679417\pi$
$510$	−5.01613	−0.222118
$511$	−17.7432	−0.784912
$512$	−8.73867	−0.386198
$513$	2.32004	0.102432
$514$	−27.2323	−1.20117
$515$	−44.9832	−1.98220
$516$	10.5342	0.463742
$517$	22.0380	0.969231
$518$	−32.9943	−1.44969
$519$	5.56881	0.244443
$520$	−7.12972	−0.312659
$521$	26.6737	1.16860	0.584298	−	0.811539i	$-0.301370\pi$
$521$	26.6737	1.16860	0.584298	+	0.811539i	$0.301370\pi$
$522$	1.12687	0.0493216
$523$	−41.1586	−1.79974	−0.899870	−	0.436158i	$-0.856339\pi$
$523$	−41.1586	−1.79974	−0.899870	+	0.436158i	$0.856339\pi$
$524$	4.39280	0.191900
$525$	11.1649	0.487277
$526$	13.2183	0.576347
$527$	−0.747325	−0.0325540
$528$	−16.2600	−0.707627
$529$	47.6136	2.07015
$530$	−66.2137	−2.87614
$531$	−7.73933	−0.335858
$532$	7.67778	0.332874
$533$	13.8184	0.598541
$534$	−19.9239	−0.862191
$535$	36.9292	1.59659
$536$	−4.17666	−0.180404
$537$	−24.2661	−1.04716
$538$	54.2593	2.33928
$539$	12.6966	0.546882
$540$	2.90131	0.124852
$541$	−12.9681	−0.557544	−0.278772	−	0.960357i	$-0.589927\pi$
$541$	−12.9681	−0.557544	−0.278772	+	0.960357i	$0.589927\pi$
$542$	27.6147	1.18615
$543$	11.3517	0.487149
$544$	5.20556	0.223186
$545$	38.8837	1.66560
$546$	8.15013	0.348793
$547$	−11.8639	−0.507262	−0.253631	−	0.967301i	$-0.581625\pi$
$547$	−11.8639	−0.507262	−0.253631	+	0.967301i	$0.581625\pi$
$548$	10.3961	0.444100
$549$	−2.72918	−0.116479
$550$	−19.0514	−0.812356
$551$	−1.50886	−0.0642796
$552$	−14.5284	−0.618369
$553$	3.30216	0.140422
$554$	34.3208	1.45815
$555$	16.6945	0.708642
$556$	−13.2631	−0.562479
$557$	−15.3175	−0.649024	−0.324512	−	0.945882i	$-0.605200\pi$
$557$	−15.3175	−0.649024	−0.324512	+	0.945882i	$0.605200\pi$
$558$	1.29487	0.0548164
$559$	−14.9730	−0.633289
$560$	−47.7989	−2.01987
$561$	3.25201	0.137300
$562$	−16.2110	−0.683820
$563$	8.49218	0.357903	0.178951	−	0.983858i	$-0.442730\pi$
$563$	8.49218	0.357903	0.178951	+	0.983858i	$0.442730\pi$
$564$	6.79147	0.285972
$565$	23.9940	1.00944
$566$	−9.66123	−0.406092
$567$	3.30216	0.138678
$568$	23.6780	0.993507
$569$	−35.3929	−1.48375	−0.741873	−	0.670540i	$-0.766062\pi$
$569$	−35.3929	−1.48375	−0.741873	+	0.670540i	$0.766062\pi$
$570$	−11.6376	−0.487445
$571$	20.4482	0.855731	0.427866	−	0.903842i	$-0.359266\pi$
$571$	20.4482	0.855731	0.427866	+	0.903842i	$0.359266\pi$
$572$	−4.64241	−0.194109
$573$	7.93371	0.331435
$574$	55.5040	2.31669
$575$	−28.4120	−1.18486
$576$	0.980433	0.0408514
$577$	13.4627	0.560459	0.280229	−	0.959933i	$-0.409589\pi$
$577$	13.4627	0.560459	0.280229	+	0.959933i	$0.409589\pi$
$578$	−1.73268	−0.0720699
$579$	−18.0603	−0.750562
$580$	−1.88690	−0.0783491
$581$	−15.6048	−0.647396
$582$	4.05834	0.168223
$583$	42.9271	1.77786
$584$	−9.28981	−0.384415
$585$	−4.12382	−0.170499
$586$	8.02268	0.331414
$587$	−14.9574	−0.617359	−0.308679	−	0.951166i	$-0.599887\pi$
$587$	−14.9574	−0.617359	−0.308679	+	0.951166i	$0.599887\pi$
$588$	3.91273	0.161358
$589$	−1.73382	−0.0714409
$590$	38.8214	1.59825
$591$	1.90395	0.0783181
$592$	−28.8332	−1.18504
$593$	22.7972	0.936167	0.468084	−	0.883684i	$-0.344945\pi$
$593$	22.7972	0.936167	0.468084	+	0.883684i	$0.344945\pi$
$594$	−5.63469	−0.231194
$595$	9.55979	0.391913
$596$	−3.91417	−0.160331
$597$	25.0531	1.02536
$598$	−20.7401	−0.848126
$599$	0.906214	0.0370269	0.0185134	−	0.999829i	$-0.494107\pi$
$599$	0.906214	0.0370269	0.0185134	+	0.999829i	$0.494107\pi$
$600$	5.84562	0.238647
$601$	7.70721	0.314384	0.157192	−	0.987568i	$-0.449756\pi$
$601$	7.70721	0.314384	0.157192	+	0.987568i	$0.449756\pi$
$602$	−60.1415	−2.45119
$603$	−2.41577	−0.0983778
$604$	−5.01019	−0.203862
$605$	−1.22872	−0.0499545
$606$	−23.2125	−0.942945
$607$	−30.5002	−1.23796	−0.618982	−	0.785405i	$-0.712455\pi$
$607$	−30.5002	−1.23796	−0.618982	+	0.785405i	$0.712455\pi$
$608$	12.0771	0.489790
$609$	−2.14759	−0.0870249
$610$	13.6899	0.554289
$611$	−9.65316	−0.390525
$612$	1.00217	0.0405105
$613$	−9.01178	−0.363982	−0.181991	−	0.983300i	$-0.558254\pi$
$613$	−9.01178	−0.363982	−0.181991	+	0.983300i	$0.558254\pi$
$614$	−19.0692	−0.769571
$615$	−28.0840	−1.13246
$616$	18.5662	0.748053
$617$	−14.8958	−0.599682	−0.299841	−	0.953989i	$-0.596934\pi$
$617$	−14.8958	−0.599682	−0.299841	+	0.953989i	$0.596934\pi$
$618$	26.9227	1.08299
$619$	16.7953	0.675060	0.337530	−	0.941315i	$-0.390409\pi$
$619$	16.7953	0.675060	0.337530	+	0.941315i	$0.390409\pi$
$620$	−2.16822	−0.0870778
$621$	−8.40319	−0.337208
$622$	31.8082	1.27539
$623$	37.9712	1.52128
$624$	7.12227	0.285119
$625$	−30.4737	−1.21895
$626$	−17.8888	−0.714980
$627$	7.54478	0.301310
$628$	−19.2262	−0.767207
$629$	5.76664	0.229931
$630$	−16.5640	−0.659927
$631$	37.6810	1.50006	0.750029	−	0.661405i	$-0.230040\pi$
$631$	37.6810	1.50006	0.750029	+	0.661405i	$0.230040\pi$
$632$	1.72891	0.0687724
$633$	−3.98468	−0.158377
$634$	32.5631	1.29325
$635$	−22.0586	−0.875369
$636$	13.2289	0.524558
$637$	−5.56141	−0.220351
$638$	3.66458	0.145082
$639$	13.6953	0.541778
$640$	−35.0583	−1.38580
$641$	−46.6921	−1.84423	−0.922113	−	0.386920i	$-0.873539\pi$
$641$	−46.6921	−1.84423	−0.922113	+	0.386920i	$0.873539\pi$
$642$	−22.1023	−0.872308
$643$	2.03218	0.0801413	0.0400707	−	0.999197i	$-0.487242\pi$
$643$	2.03218	0.0801413	0.0400707	+	0.999197i	$0.487242\pi$
$644$	−27.8090	−1.09583
$645$	30.4305	1.19820
$646$	−4.01988	−0.158160
$647$	−7.22391	−0.284001	−0.142001	−	0.989867i	$-0.545353\pi$
$647$	−7.22391	−0.284001	−0.142001	+	0.989867i	$0.545353\pi$
$648$	1.72891	0.0679181
$649$	−25.1684	−0.987945
$650$	8.34497	0.327317
$651$	−2.46779	−0.0967201
$652$	−10.4609	−0.409681
$653$	−17.3032	−0.677128	−0.338564	−	0.940943i	$-0.609941\pi$
$653$	−17.3032	−0.677128	−0.338564	+	0.940943i	$0.609941\pi$
$654$	−23.2721	−0.910011
$655$	12.6896	0.495825
$656$	48.5040	1.89376
$657$	−5.37321	−0.209629
$658$	−38.7736	−1.51155
$659$	25.5753	0.996272	0.498136	−	0.867099i	$-0.334018\pi$
$659$	25.5753	0.996272	0.498136	+	0.867099i	$0.334018\pi$
$660$	9.43508	0.367260
$661$	31.0826	1.20897	0.604486	−	0.796616i	$-0.293379\pi$
$661$	31.0826	1.20897	0.604486	+	0.796616i	$0.293379\pi$
$662$	42.9618	1.66976
$663$	−1.42446	−0.0553213
$664$	−8.17021	−0.317065
$665$	22.1791	0.860067
$666$	−9.99174	−0.387172
$667$	5.46510	0.211610
$668$	8.20244	0.317362
$669$	20.0652	0.775765
$670$	12.1178	0.468152
$671$	−8.87533	−0.342628
$672$	17.1896	0.663102
$673$	−29.0271	−1.11891	−0.559457	−	0.828860i	$-0.688990\pi$
$673$	−29.0271	−1.11891	−0.559457	+	0.828860i	$0.688990\pi$
$674$	11.8078	0.454818
$675$	3.38110	0.130139
$676$	−10.9948	−0.422876
$677$	10.2887	0.395427	0.197714	−	0.980260i	$-0.436648\pi$
$677$	10.2887	0.395427	0.197714	+	0.980260i	$0.436648\pi$
$678$	−14.3605	−0.551512
$679$	−7.73442	−0.296820
$680$	5.00522	0.191942
$681$	10.9646	0.420165
$682$	4.21095	0.161245
$683$	−14.2011	−0.543390	−0.271695	−	0.962383i	$-0.587584\pi$
$683$	−14.2011	−0.543390	−0.271695	+	0.962383i	$0.587584\pi$
$684$	2.32508	0.0889016
$685$	30.0316	1.14745
$686$	17.7126	0.676271
$687$	22.5916	0.861923
$688$	−52.5567	−2.00371
$689$	−18.8030	−0.716339
$690$	42.1514	1.60468
$691$	24.1178	0.917484	0.458742	−	0.888569i	$-0.348300\pi$
$691$	24.1178	0.917484	0.458742	+	0.888569i	$0.348300\pi$
$692$	5.58091	0.212154
$693$	10.7386	0.407928
$694$	−44.0176	−1.67089
$695$	−38.3135	−1.45331
$696$	−1.12442	−0.0426209
$697$	−9.70082	−0.367445
$698$	54.6691	2.06925
$699$	−0.530463	−0.0200640
$700$	11.1892	0.422912
$701$	−7.23044	−0.273090	−0.136545	−	0.990634i	$-0.543600\pi$
$701$	−7.23044	−0.273090	−0.136545	+	0.990634i	$0.543600\pi$
$702$	2.46812	0.0931533
$703$	13.3788	0.504592
$704$	3.18838	0.120167
$705$	19.6187	0.738884
$706$	16.5450	0.622680
$707$	44.2387	1.66377
$708$	−7.75615	−0.291494
$709$	−42.4767	−1.59525	−0.797624	−	0.603155i	$-0.793910\pi$
$709$	−42.4767	−1.59525	−0.797624	+	0.603155i	$0.793910\pi$
$710$	−68.6974	−2.57817
$711$	1.00000	0.0375029
$712$	19.8806	0.745057
$713$	6.27991	0.235185
$714$	−5.72157	−0.214125
$715$	−13.4107	−0.501532
$716$	−24.3189	−0.908838
$717$	0.0514535	0.00192157
$718$	−61.2102	−2.28434
$719$	34.6722	1.29306	0.646528	−	0.762891i	$-0.276221\pi$
$719$	34.6722	1.29306	0.646528	+	0.762891i	$0.276221\pi$
$720$	−14.4751	−0.539453
$721$	−51.3095	−1.91086
$722$	23.5946	0.878101
$723$	−7.69075	−0.286022
$724$	11.3764	0.422801
$725$	−2.19893	−0.0816664
$726$	0.735393	0.0272930
$727$	−21.3405	−0.791476	−0.395738	−	0.918364i	$-0.629511\pi$
$727$	−21.3405	−0.791476	−0.395738	+	0.918364i	$0.629511\pi$
$728$	−8.13241	−0.301407
$729$	1.00000	0.0370370
$730$	26.9527	0.997564
$731$	10.5114	0.388777
$732$	−2.73512	−0.101093
$733$	−33.9813	−1.25513	−0.627564	−	0.778565i	$-0.715948\pi$
$733$	−33.9813	−1.25513	−0.627564	+	0.778565i	$0.715948\pi$
$734$	11.9867	0.442435
$735$	11.3028	0.416911
$736$	−43.7433	−1.61240
$737$	−7.85611	−0.289384
$738$	16.8084	0.618726
$739$	29.7665	1.09498	0.547489	−	0.836813i	$-0.315584\pi$
$739$	29.7665	1.09498	0.547489	+	0.836813i	$0.315584\pi$
$740$	16.7308	0.615036
$741$	−3.30479	−0.121404
$742$	−75.5257	−2.77264
$743$	−30.0331	−1.10181	−0.550904	−	0.834568i	$-0.685717\pi$
$743$	−30.0331	−1.10181	−0.550904	+	0.834568i	$0.685717\pi$
$744$	−1.29206	−0.0473692
$745$	−11.3070	−0.414256
$746$	8.61841	0.315543
$747$	−4.72563	−0.172902
$748$	3.25908	0.119164
$749$	42.1228	1.53913
$750$	8.12061	0.296523
$751$	−39.7193	−1.44938	−0.724689	−	0.689076i	$-0.758017\pi$
$751$	−39.7193	−1.44938	−0.724689	+	0.689076i	$0.758017\pi$
$752$	−33.8836	−1.23561
$753$	−20.1716	−0.735095
$754$	−1.60517	−0.0584569
$755$	−14.4731	−0.526730
$756$	3.30933	0.120359
$757$	4.61255	0.167646	0.0838230	−	0.996481i	$-0.473287\pi$
$757$	4.61255	0.167646	0.0838230	+	0.996481i	$0.473287\pi$
$758$	29.6479	1.07686
$759$	−27.3273	−0.991917
$760$	11.6123	0.421222
$761$	22.4080	0.812288	0.406144	−	0.913809i	$-0.366873\pi$
$761$	22.4080	0.812288	0.406144	+	0.913809i	$0.366873\pi$
$762$	13.2022	0.478264
$763$	44.3522	1.60566
$764$	7.95096	0.287655
$765$	2.89501	0.104669
$766$	−32.2604	−1.16562
$767$	11.0243	0.398065
$768$	19.0217	0.686386
$769$	−32.3445	−1.16637	−0.583185	−	0.812339i	$-0.698194\pi$
$769$	−32.3445	−1.16637	−0.583185	+	0.812339i	$0.698194\pi$
$770$	−53.8664	−1.94121
$771$	15.7169	0.566030
$772$	−18.0996	−0.651418
$773$	−7.69642	−0.276821	−0.138410	−	0.990375i	$-0.544199\pi$
$773$	−7.69642	−0.276821	−0.138410	+	0.990375i	$0.544199\pi$
$774$	−18.2128	−0.654646
$775$	−2.52678	−0.0907647
$776$	−4.04951	−0.145369
$777$	19.0424	0.683141
$778$	31.9002	1.14368
$779$	−22.5062	−0.806370
$780$	−4.13278	−0.147977
$781$	44.5373	1.59367
$782$	14.5600	0.520665
$783$	−0.650361	−0.0232420
$784$	−19.5212	−0.697185
$785$	−55.5392	−1.98228
$786$	−7.59480	−0.270897
$787$	5.50440	0.196211	0.0981053	−	0.995176i	$-0.468722\pi$
$787$	5.50440	0.196211	0.0981053	+	0.995176i	$0.468722\pi$
$788$	1.90809	0.0679729
$789$	−7.62885	−0.271594
$790$	−5.01613	−0.178466
$791$	27.3684	0.973109
$792$	5.62244	0.199785
$793$	3.88760	0.138053
$794$	−9.50289	−0.337245
$795$	38.2146	1.35533
$796$	25.1076	0.889914
$797$	32.4486	1.14939	0.574694	−	0.818368i	$-0.305121\pi$
$797$	32.4486	1.14939	0.574694	+	0.818368i	$0.305121\pi$
$798$	−13.2743	−0.469904
$799$	6.77674	0.239744
$800$	17.6005	0.622272
$801$	11.4989	0.406294
$802$	−38.1168	−1.34595
$803$	−17.4737	−0.616635
$804$	−2.42102	−0.0853829
$805$	−80.3327	−2.83135
$806$	−1.84449	−0.0649694
$807$	−31.3153	−1.10235
$808$	23.1621	0.814840
$809$	−44.6435	−1.56958	−0.784791	−	0.619761i	$-0.787229\pi$
$809$	−44.6435	−1.56958	−0.784791	+	0.619761i	$0.787229\pi$
$810$	−5.01613	−0.176249
$811$	−38.5940	−1.35522	−0.677610	−	0.735421i	$-0.736984\pi$
$811$	−38.5940	−1.35522	−0.677610	+	0.735421i	$0.736984\pi$
$812$	−2.15226	−0.0755296
$813$	−15.9376	−0.558955
$814$	−32.4932	−1.13889
$815$	−30.2188	−1.05852
$816$	−5.00000	−0.175035
$817$	24.3867	0.853184
$818$	−36.1895	−1.26534
$819$	−4.70378	−0.164363
$820$	−28.1450	−0.982867
$821$	11.6148	0.405358	0.202679	−	0.979245i	$-0.435035\pi$
$821$	11.6148	0.405358	0.202679	+	0.979245i	$0.435035\pi$
$822$	−17.9741	−0.626918
$823$	45.7841	1.59593	0.797967	−	0.602702i	$-0.205909\pi$
$823$	45.7841	1.59593	0.797967	+	0.602702i	$0.205909\pi$
$824$	−26.8641	−0.935856
$825$	10.9954	0.382810
$826$	44.2811	1.54074
$827$	18.8140	0.654226	0.327113	−	0.944985i	$-0.393924\pi$
$827$	18.8140	0.654226	0.327113	+	0.944985i	$0.393924\pi$
$828$	−8.42145	−0.292666
$829$	18.8467	0.654573	0.327287	−	0.944925i	$-0.393866\pi$
$829$	18.8467	0.654573	0.327287	+	0.944925i	$0.393866\pi$
$830$	23.7044	0.822791
$831$	−19.8080	−0.687131
$832$	−1.39658	−0.0484178
$833$	3.90424	0.135274
$834$	22.9308	0.794028
$835$	23.6947	0.819987
$836$	7.56118	0.261509
$837$	−0.747325	−0.0258313
$838$	5.36321	0.185269
$839$	12.2399	0.422567	0.211284	−	0.977425i	$-0.432236\pi$
$839$	12.2399	0.422567	0.211284	+	0.977425i	$0.432236\pi$
$840$	16.5280	0.570271
$841$	−28.5770	−0.985415
$842$	−12.7183	−0.438301
$843$	9.35604	0.322239
$844$	−3.99334	−0.137456
$845$	−31.7610	−1.09261
$846$	−11.7419	−0.403695
$847$	−1.40152	−0.0481568
$848$	−66.0008	−2.26648
$849$	5.57589	0.191364
$850$	−5.85836	−0.200940
$851$	−48.4582	−1.66113
$852$	13.7251	0.470214
$853$	−19.3697	−0.663205	−0.331603	−	0.943419i	$-0.607589\pi$
$853$	−19.3697	−0.663205	−0.331603	+	0.943419i	$0.607589\pi$
$854$	15.6152	0.534342
$855$	6.71653	0.229701
$856$	22.0543	0.753799
$857$	−6.39647	−0.218499	−0.109250	−	0.994014i	$-0.534845\pi$
$857$	−6.39647	−0.218499	−0.109250	+	0.994014i	$0.534845\pi$
$858$	8.02636	0.274016
$859$	−15.0393	−0.513134	−0.256567	−	0.966526i	$-0.582591\pi$
$859$	−15.0393	−0.513134	−0.256567	+	0.966526i	$0.582591\pi$
$860$	30.4967	1.03993
$861$	−32.0336	−1.09170
$862$	42.5492	1.44923
$863$	−34.9273	−1.18894	−0.594469	−	0.804118i	$-0.702638\pi$
$863$	−34.9273	−1.18894	−0.594469	+	0.804118i	$0.702638\pi$
$864$	5.20556	0.177097
$865$	16.1218	0.548157
$866$	−50.0083	−1.69935
$867$	1.00000	0.0339618
$868$	−2.47315	−0.0839442
$869$	3.25201	0.110317
$870$	3.26229	0.110602
$871$	3.44116	0.116599
$872$	23.2215	0.786380
$873$	−2.34223	−0.0792726
$874$	33.7798	1.14262
$875$	−15.4763	−0.523196
$876$	−5.38489	−0.181939
$877$	48.8667	1.65011	0.825056	−	0.565050i	$-0.191143\pi$
$877$	48.8667	1.65011	0.825056	+	0.565050i	$0.191143\pi$
$878$	17.7619	0.599435
$879$	−4.63022	−0.156174
$880$	−47.0730	−1.58683
$881$	−21.5267	−0.725254	−0.362627	−	0.931934i	$-0.618120\pi$
$881$	−21.5267	−0.725254	−0.362627	+	0.931934i	$0.618120\pi$
$882$	−6.76479	−0.227782
$883$	−48.4105	−1.62914	−0.814572	−	0.580062i	$-0.803028\pi$
$883$	−48.4105	−1.62914	−0.814572	+	0.580062i	$0.803028\pi$
$884$	−1.42755	−0.0480138
$885$	−22.4055	−0.753151
$886$	−24.8054	−0.833354
$887$	52.3777	1.75867	0.879335	−	0.476204i	$-0.157988\pi$
$887$	52.3777	1.75867	0.879335	+	0.476204i	$0.157988\pi$
$888$	9.97002	0.334572
$889$	−25.1608	−0.843868
$890$	−57.6799	−1.93344
$891$	3.25201	0.108946
$892$	20.1088	0.673293
$893$	15.7223	0.526126
$894$	6.76729	0.226332
$895$	−70.2507	−2.34822
$896$	−39.9888	−1.33593
$897$	11.9700	0.399666
$898$	−60.3197	−2.01289
$899$	0.486031	0.0162100
$900$	3.38845	0.112948
$901$	13.2002	0.439761
$902$	54.6611	1.82001
$903$	34.7101	1.15508
$904$	14.3293	0.476586
$905$	32.8634	1.09242
$906$	8.66221	0.287783
$907$	6.98423	0.231908	0.115954	−	0.993255i	$-0.463008\pi$
$907$	6.98423	0.231908	0.115954	+	0.993255i	$0.463008\pi$
$908$	10.9885	0.364665
$909$	13.3969	0.444348
$910$	23.5947	0.782158
$911$	−54.4137	−1.80281	−0.901403	−	0.432981i	$-0.857462\pi$
$911$	−54.4137	−1.80281	−0.901403	+	0.432981i	$0.857462\pi$
$912$	−11.6002	−0.384120
$913$	−15.3678	−0.508600
$914$	−25.7537	−0.851857
$915$	−7.90102	−0.261200
$916$	22.6407	0.748070
$917$	14.4742	0.477982
$918$	−1.73268	−0.0571869
$919$	−11.7468	−0.387491	−0.193746	−	0.981052i	$-0.562064\pi$
$919$	−11.7468	−0.387491	−0.193746	+	0.981052i	$0.562064\pi$
$920$	−42.0598	−1.38667
$921$	11.0056	0.362648
$922$	−0.548523	−0.0180647
$923$	−19.5084	−0.642126
$924$	10.7620	0.354044
$925$	19.4976	0.641077
$926$	9.05324	0.297508
$927$	−15.5382	−0.510341
$928$	−3.38549	−0.111134
$929$	−0.356652	−0.0117014	−0.00585069	−	0.999983i	$-0.501862\pi$
$929$	−0.356652	−0.0117014	−0.00585069	+	0.999983i	$0.501862\pi$
$930$	3.74868	0.122924
$931$	9.05798	0.296863
$932$	−0.531616	−0.0174137
$933$	−18.3578	−0.601009
$934$	28.1997	0.922721
$935$	9.41461	0.307891
$936$	−2.46276	−0.0804978
$937$	5.46143	0.178417	0.0892085	−	0.996013i	$-0.471566\pi$
$937$	5.46143	0.178417	0.0892085	+	0.996013i	$0.471566\pi$
$938$	13.8220	0.451305
$939$	10.3244	0.336923
$940$	19.6614	0.641284
$941$	32.0106	1.04352	0.521758	−	0.853094i	$-0.325276\pi$
$941$	32.0106	1.04352	0.521758	+	0.853094i	$0.325276\pi$
$942$	33.2405	1.08303
$943$	81.5178	2.65458
$944$	38.6966	1.25947
$945$	9.55979	0.310980
$946$	−59.2282	−1.92568
$947$	−3.22143	−0.104683	−0.0523413	−	0.998629i	$-0.516668\pi$
$947$	−3.22143	−0.104683	−0.0523413	+	0.998629i	$0.516668\pi$
$948$	1.00217	0.0325491
$949$	7.65390	0.248456
$950$	−13.5916	−0.440970
$951$	−18.7935	−0.609422
$952$	5.70914	0.185034
$953$	−18.1062	−0.586519	−0.293259	−	0.956033i	$-0.594740\pi$
$953$	−18.1062	−0.586519	−0.293259	+	0.956033i	$0.594740\pi$
$954$	−22.8716	−0.740496
$955$	22.9682	0.743233
$956$	0.0515653	0.00166774
$957$	−2.11498	−0.0683676
$958$	−53.1533	−1.71730
$959$	34.2552	1.10616
$960$	2.83837	0.0916078
$961$	−30.4415	−0.981984
$962$	14.2328	0.458883
$963$	12.7561	0.411061
$964$	−7.70747	−0.248241
$965$	−52.2849	−1.68311
$966$	48.0795	1.54693
$967$	−12.0886	−0.388742	−0.194371	−	0.980928i	$-0.562267\pi$
$967$	−12.0886	−0.388742	−0.194371	+	0.980928i	$0.562267\pi$
$968$	−0.733795	−0.0235851
$969$	2.32004	0.0745303
$970$	11.7489	0.377236
$971$	−59.8453	−1.92053	−0.960264	−	0.279095i	$-0.909966\pi$
$971$	−59.8453	−1.92053	−0.960264	+	0.279095i	$0.909966\pi$
$972$	1.00217	0.0321447
$973$	−43.7017	−1.40101
$974$	7.42102	0.237785
$975$	−4.81623	−0.154243
$976$	13.6459	0.436795
$977$	−20.9069	−0.668873	−0.334436	−	0.942418i	$-0.608546\pi$
$977$	−20.9069	−0.668873	−0.334436	+	0.942418i	$0.608546\pi$
$978$	18.0861	0.578329
$979$	37.3946	1.19514
$980$	11.3274	0.361840
$981$	13.4313	0.428828
$982$	9.69145	0.309267
$983$	23.4501	0.747943	0.373971	−	0.927440i	$-0.377996\pi$
$983$	23.4501	0.747943	0.373971	+	0.927440i	$0.377996\pi$
$984$	−16.7719	−0.534667
$985$	5.51196	0.175626
$986$	1.12687	0.0358867
$987$	22.3778	0.712295
$988$	−3.31197	−0.105368
$989$	−88.3289	−2.80870
$990$	−16.3125	−0.518445
$991$	−61.3153	−1.94775	−0.973873	−	0.227094i	$-0.927078\pi$
$991$	−61.3153	−1.94775	−0.973873	+	0.227094i	$0.927078\pi$
$992$	−3.89025	−0.123515
$993$	−24.7950	−0.786846
$994$	−78.3588	−2.48539
$995$	72.5291	2.29933
$996$	−4.73591	−0.150063
$997$	−62.0644	−1.96560	−0.982799	−	0.184679i	$-0.940875\pi$
$997$	−62.0644	−1.96560	−0.982799	+	0.184679i	$0.940875\pi$
$998$	10.4939	0.332179
$999$	5.76664	0.182449

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.k.1.7	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.k.1.7	✓	31	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:	\( N \)	\(=\)	\( 4029 = 3 \cdot 17 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4029.a (trivial)

\(f(q)\)	\(=\)	\(q-1.73268 q^{2} +1.00000 q^{3} +1.00217 q^{4} +2.89501 q^{5} -1.73268 q^{6} +3.30216 q^{7} +1.72891 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.73268 q^{2} +1.00000 q^{3} +1.00217 q^{4} +2.89501 q^{5} -1.73268 q^{6} +3.30216 q^{7} +1.72891 q^{8} +1.00000 q^{9} -5.01613 q^{10} +3.25201 q^{11} +1.00217 q^{12} -1.42446 q^{13} -5.72157 q^{14} +2.89501 q^{15} -5.00000 q^{16} +1.00000 q^{17} -1.73268 q^{18} +2.32004 q^{19} +2.90131 q^{20} +3.30216 q^{21} -5.63469 q^{22} -8.40319 q^{23} +1.72891 q^{24} +3.38110 q^{25} +2.46812 q^{26} +1.00000 q^{27} +3.30933 q^{28} -0.650361 q^{29} -5.01613 q^{30} -0.747325 q^{31} +5.20556 q^{32} +3.25201 q^{33} -1.73268 q^{34} +9.55979 q^{35} +1.00217 q^{36} +5.76664 q^{37} -4.01988 q^{38} -1.42446 q^{39} +5.00522 q^{40} -9.70082 q^{41} -5.72157 q^{42} +10.5114 q^{43} +3.25908 q^{44} +2.89501 q^{45} +14.5600 q^{46} +6.77674 q^{47} -5.00000 q^{48} +3.90424 q^{49} -5.85836 q^{50} +1.00000 q^{51} -1.42755 q^{52} +13.2002 q^{53} -1.73268 q^{54} +9.41461 q^{55} +5.70914 q^{56} +2.32004 q^{57} +1.12687 q^{58} -7.73933 q^{59} +2.90131 q^{60} -2.72918 q^{61} +1.29487 q^{62} +3.30216 q^{63} +0.980433 q^{64} -4.12382 q^{65} -5.63469 q^{66} -2.41577 q^{67} +1.00217 q^{68} -8.40319 q^{69} -16.5640 q^{70} +13.6953 q^{71} +1.72891 q^{72} -5.37321 q^{73} -9.99174 q^{74} +3.38110 q^{75} +2.32508 q^{76} +10.7386 q^{77} +2.46812 q^{78} +1.00000 q^{79} -14.4751 q^{80} +1.00000 q^{81} +16.8084 q^{82} -4.72563 q^{83} +3.30933 q^{84} +2.89501 q^{85} -18.2128 q^{86} -0.650361 q^{87} +5.62244 q^{88} +11.4989 q^{89} -5.01613 q^{90} -4.70378 q^{91} -8.42145 q^{92} -0.747325 q^{93} -11.7419 q^{94} +6.71653 q^{95} +5.20556 q^{96} -2.34223 q^{97} -6.76479 q^{98} +3.25201 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 4 q^{2} + 31 q^{3} + 34 q^{4} + 11 q^{5} + 4 q^{6} + 4 q^{7} + 12 q^{8} + 31 q^{9}+O(q^{10}) \) 31 * q + 4 * q^2 + 31 * q^3 + 34 * q^4 + 11 * q^5 + 4 * q^6 + 4 * q^7 + 12 * q^8 + 31 * q^9	\( 31 q + 4 q^{2} + 31 q^{3} + 34 q^{4} + 11 q^{5} + 4 q^{6} + 4 q^{7} + 12 q^{8} + 31 q^{9} + 5 q^{10} + 26 q^{11} + 34 q^{12} + 7 q^{13} + 19 q^{14} + 11 q^{15} + 40 q^{16} + 31 q^{17} + 4 q^{18} + 32 q^{19} + 23 q^{20} + 4 q^{21} + 2 q^{22} + 29 q^{23} + 12 q^{24} + 32 q^{25} + 13 q^{26} + 31 q^{27} - 13 q^{28} + 25 q^{29} + 5 q^{30} + 22 q^{31} + 28 q^{32} + 26 q^{33} + 4 q^{34} + 20 q^{35} + 34 q^{36} - 4 q^{37} + 19 q^{38} + 7 q^{39} - 3 q^{40} + 33 q^{41} + 19 q^{42} + 6 q^{43} + 30 q^{44} + 11 q^{45} - 11 q^{46} + 23 q^{47} + 40 q^{48} + 31 q^{49} + 6 q^{50} + 31 q^{51} - 7 q^{52} + 12 q^{53} + 4 q^{54} + 40 q^{56} + 32 q^{57} + 9 q^{58} + 27 q^{59} + 23 q^{60} - 4 q^{61} + 25 q^{62} + 4 q^{63} + 10 q^{64} + 54 q^{65} + 2 q^{66} + 34 q^{68} + 29 q^{69} - 59 q^{70} + 35 q^{71} + 12 q^{72} + 5 q^{73} + 48 q^{74} + 32 q^{75} + 32 q^{76} + 42 q^{77} + 13 q^{78} + 31 q^{79} + 24 q^{80} + 31 q^{81} + 5 q^{82} + 67 q^{83} - 13 q^{84} + 11 q^{85} - 20 q^{86} + 25 q^{87} - 7 q^{88} + 22 q^{89} + 5 q^{90} + 16 q^{91} + 57 q^{92} + 22 q^{93} + 45 q^{94} + 73 q^{95} + 28 q^{96} - 13 q^{97} - 19 q^{98} + 26 q^{99}+O(q^{100}) \) 31 * q + 4 * q^2 + 31 * q^3 + 34 * q^4 + 11 * q^5 + 4 * q^6 + 4 * q^7 + 12 * q^8 + 31 * q^9 + 5 * q^10 + 26 * q^11 + 34 * q^12 + 7 * q^13 + 19 * q^14 + 11 * q^15 + 40 * q^16 + 31 * q^17 + 4 * q^18 + 32 * q^19 + 23 * q^20 + 4 * q^21 + 2 * q^22 + 29 * q^23 + 12 * q^24 + 32 * q^25 + 13 * q^26 + 31 * q^27 - 13 * q^28 + 25 * q^29 + 5 * q^30 + 22 * q^31 + 28 * q^32 + 26 * q^33 + 4 * q^34 + 20 * q^35 + 34 * q^36 - 4 * q^37 + 19 * q^38 + 7 * q^39 - 3 * q^40 + 33 * q^41 + 19 * q^42 + 6 * q^43 + 30 * q^44 + 11 * q^45 - 11 * q^46 + 23 * q^47 + 40 * q^48 + 31 * q^49 + 6 * q^50 + 31 * q^51 - 7 * q^52 + 12 * q^53 + 4 * q^54 + 40 * q^56 + 32 * q^57 + 9 * q^58 + 27 * q^59 + 23 * q^60 - 4 * q^61 + 25 * q^62 + 4 * q^63 + 10 * q^64 + 54 * q^65 + 2 * q^66 + 34 * q^68 + 29 * q^69 - 59 * q^70 + 35 * q^71 + 12 * q^72 + 5 * q^73 + 48 * q^74 + 32 * q^75 + 32 * q^76 + 42 * q^77 + 13 * q^78 + 31 * q^79 + 24 * q^80 + 31 * q^81 + 5 * q^82 + 67 * q^83 - 13 * q^84 + 11 * q^85 - 20 * q^86 + 25 * q^87 - 7 * q^88 + 22 * q^89 + 5 * q^90 + 16 * q^91 + 57 * q^92 + 22 * q^93 + 45 * q^94 + 73 * q^95 + 28 * q^96 - 13 * q^97 - 19 * q^98 + 26 * q^99

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