LMFDB - Embedded newform 1502.2.a.g.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1502,2,Mod(1,1502)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1502, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1502.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1502 = 2 \cdot 751 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1502.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:	$11.9935303836$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} - 25 x^{14} + 59 x^{13} + 273 x^{12} - 443 x^{11} - 1620 x^{10} + 1595 x^{9} + \cdots + 864 $ x^16 - 3x^15 - 25x^14 + 59x^13 + 273x^12 - 443x^11 - 1620x^10 + 1595x^9 + 5490x^8 - 2787x^7 - 10540x^6 + 1919x^5 + 10822x^4 + 132x^3 - 5202x^2 - 408*x + 864
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$-1.04534$ of defining polynomial
Character	$\chi$	$=$	1502.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +2.04534 q^{3} +1.00000 q^{4} +3.81409 q^{5} +2.04534 q^{6} +0.856873 q^{7} +1.00000 q^{8} +1.18340 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.04534 q^{3} +1.00000 q^{4} +3.81409 q^{5} +2.04534 q^{6} +0.856873 q^{7} +1.00000 q^{8} +1.18340 q^{9} +3.81409 q^{10} -0.287962 q^{11} +2.04534 q^{12} -2.99256 q^{13} +0.856873 q^{14} +7.80109 q^{15} +1.00000 q^{16} +0.234175 q^{17} +1.18340 q^{18} -6.00213 q^{19} +3.81409 q^{20} +1.75259 q^{21} -0.287962 q^{22} +0.503796 q^{23} +2.04534 q^{24} +9.54725 q^{25} -2.99256 q^{26} -3.71555 q^{27} +0.856873 q^{28} -5.92614 q^{29} +7.80109 q^{30} +8.72095 q^{31} +1.00000 q^{32} -0.588979 q^{33} +0.234175 q^{34} +3.26819 q^{35} +1.18340 q^{36} -8.74641 q^{37} -6.00213 q^{38} -6.12080 q^{39} +3.81409 q^{40} +4.43713 q^{41} +1.75259 q^{42} +0.190690 q^{43} -0.287962 q^{44} +4.51360 q^{45} +0.503796 q^{46} -7.85188 q^{47} +2.04534 q^{48} -6.26577 q^{49} +9.54725 q^{50} +0.478966 q^{51} -2.99256 q^{52} +8.87554 q^{53} -3.71555 q^{54} -1.09831 q^{55} +0.856873 q^{56} -12.2764 q^{57} -5.92614 q^{58} -5.29486 q^{59} +7.80109 q^{60} -2.70503 q^{61} +8.72095 q^{62} +1.01403 q^{63} +1.00000 q^{64} -11.4139 q^{65} -0.588979 q^{66} +7.01908 q^{67} +0.234175 q^{68} +1.03043 q^{69} +3.26819 q^{70} +4.28687 q^{71} +1.18340 q^{72} -10.1158 q^{73} -8.74641 q^{74} +19.5273 q^{75} -6.00213 q^{76} -0.246747 q^{77} -6.12080 q^{78} -2.45995 q^{79} +3.81409 q^{80} -11.1498 q^{81} +4.43713 q^{82} +9.82731 q^{83} +1.75259 q^{84} +0.893162 q^{85} +0.190690 q^{86} -12.1210 q^{87} -0.287962 q^{88} +1.69696 q^{89} +4.51360 q^{90} -2.56425 q^{91} +0.503796 q^{92} +17.8373 q^{93} -7.85188 q^{94} -22.8926 q^{95} +2.04534 q^{96} +14.9225 q^{97} -6.26577 q^{98} -0.340775 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{2} + 13 q^{3} + 16 q^{4} + 4 q^{5} + 13 q^{6} + 7 q^{7} + 16 q^{8} + 21 q^{9}+O(q^{10}) $ 16 * q + 16 * q^2 + 13 * q^3 + 16 * q^4 + 4 * q^5 + 13 * q^6 + 7 * q^7 + 16 * q^8 + 21 * q^9	\( 16 q + 16 q^{2} + 13 q^{3} + 16 q^{4} + 4 q^{5} + 13 q^{6} + 7 q^{7} + 16 q^{8} + 21 q^{9} + 4 q^{10} + 4 q^{11} + 13 q^{12} + 17 q^{13} + 7 q^{14} + 8 q^{15} + 16 q^{16} - q^{17} + 21 q^{18} + 23 q^{19} + 4 q^{20} + 9 q^{21} + 4 q^{22} + 15 q^{23} + 13 q^{24} + 24 q^{25} + 17 q^{26} + 31 q^{27} + 7 q^{28} + 4 q^{29} + 8 q^{30} + 42 q^{31} + 16 q^{32} + 3 q^{33} - q^{34} - 13 q^{35} + 21 q^{36} + 31 q^{37} + 23 q^{38} - 2 q^{39} + 4 q^{40} - 9 q^{41} + 9 q^{42} + 13 q^{43} + 4 q^{44} - 2 q^{45} + 15 q^{46} + 18 q^{47} + 13 q^{48} - 9 q^{49} + 24 q^{50} - 2 q^{51} + 17 q^{52} - 14 q^{53} + 31 q^{54} - 2 q^{55} + 7 q^{56} - 18 q^{57} + 4 q^{58} + 4 q^{59} + 8 q^{60} + q^{61} + 42 q^{62} + 17 q^{63} + 16 q^{64} - 32 q^{65} + 3 q^{66} + 5 q^{67} - q^{68} + 6 q^{69} - 13 q^{70} + 9 q^{71} + 21 q^{72} + 28 q^{73} + 31 q^{74} + 16 q^{75} + 23 q^{76} - 30 q^{77} - 2 q^{78} + 10 q^{79} + 4 q^{80} + 12 q^{81} - 9 q^{82} + 3 q^{83} + 9 q^{84} - 7 q^{85} + 13 q^{86} - 22 q^{87} + 4 q^{88} - 17 q^{89} - 2 q^{90} + 12 q^{91} + 15 q^{92} - q^{93} + 18 q^{94} - 4 q^{95} + 13 q^{96} - 17 q^{97} - 9 q^{98} - 10 q^{99}+O(q^{100}) \) 16 * q + 16 * q^2 + 13 * q^3 + 16 * q^4 + 4 * q^5 + 13 * q^6 + 7 * q^7 + 16 * q^8 + 21 * q^9 + 4 * q^10 + 4 * q^11 + 13 * q^12 + 17 * q^13 + 7 * q^14 + 8 * q^15 + 16 * q^16 - q^17 + 21 * q^18 + 23 * q^19 + 4 * q^20 + 9 * q^21 + 4 * q^22 + 15 * q^23 + 13 * q^24 + 24 * q^25 + 17 * q^26 + 31 * q^27 + 7 * q^28 + 4 * q^29 + 8 * q^30 + 42 * q^31 + 16 * q^32 + 3 * q^33 - q^34 - 13 * q^35 + 21 * q^36 + 31 * q^37 + 23 * q^38 - 2 * q^39 + 4 * q^40 - 9 * q^41 + 9 * q^42 + 13 * q^43 + 4 * q^44 - 2 * q^45 + 15 * q^46 + 18 * q^47 + 13 * q^48 - 9 * q^49 + 24 * q^50 - 2 * q^51 + 17 * q^52 - 14 * q^53 + 31 * q^54 - 2 * q^55 + 7 * q^56 - 18 * q^57 + 4 * q^58 + 4 * q^59 + 8 * q^60 + q^61 + 42 * q^62 + 17 * q^63 + 16 * q^64 - 32 * q^65 + 3 * q^66 + 5 * q^67 - q^68 + 6 * q^69 - 13 * q^70 + 9 * q^71 + 21 * q^72 + 28 * q^73 + 31 * q^74 + 16 * q^75 + 23 * q^76 - 30 * q^77 - 2 * q^78 + 10 * q^79 + 4 * q^80 + 12 * q^81 - 9 * q^82 + 3 * q^83 + 9 * q^84 - 7 * q^85 + 13 * q^86 - 22 * q^87 + 4 * q^88 - 17 * q^89 - 2 * q^90 + 12 * q^91 + 15 * q^92 - q^93 + 18 * q^94 - 4 * q^95 + 13 * q^96 - 17 * q^97 - 9 * q^98 - 10 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	2.04534	1.18088	0.590438	−	0.807083i	$-0.298955\pi$
$3$	2.04534	1.18088	0.590438	+	0.807083i	$0.298955\pi$
$4$	1.00000	0.500000
$5$	3.81409	1.70571	0.852855	−	0.522147i	$-0.174869\pi$
$5$	3.81409	1.70571	0.852855	+	0.522147i	$0.174869\pi$
$6$	2.04534	0.835005
$7$	0.856873	0.323868	0.161934	−	0.986802i	$-0.448227\pi$
$7$	0.856873	0.323868	0.161934	+	0.986802i	$0.448227\pi$
$8$	1.00000	0.353553
$9$	1.18340	0.394467
$10$	3.81409	1.20612
$11$	−0.287962	−0.0868237	−0.0434119	−	0.999057i	$-0.513823\pi$
$11$	−0.287962	−0.0868237	−0.0434119	+	0.999057i	$0.513823\pi$
$12$	2.04534	0.590438
$13$	−2.99256	−0.829988	−0.414994	−	0.909824i	$-0.636216\pi$
$13$	−2.99256	−0.829988	−0.414994	+	0.909824i	$0.636216\pi$
$14$	0.856873	0.229009
$15$	7.80109	2.01423
$16$	1.00000	0.250000
$17$	0.234175	0.0567957	0.0283978	−	0.999597i	$-0.490959\pi$
$17$	0.234175	0.0567957	0.0283978	+	0.999597i	$0.490959\pi$
$18$	1.18340	0.278931
$19$	−6.00213	−1.37698	−0.688491	−	0.725245i	$-0.741727\pi$
$19$	−6.00213	−1.37698	−0.688491	+	0.725245i	$0.741727\pi$
$20$	3.81409	0.852855
$21$	1.75259	0.382447
$22$	−0.287962	−0.0613937
$23$	0.503796	0.105049	0.0525244	−	0.998620i	$-0.483273\pi$
$23$	0.503796	0.105049	0.0525244	+	0.998620i	$0.483273\pi$
$24$	2.04534	0.417503
$25$	9.54725	1.90945
$26$	−2.99256	−0.586890
$27$	−3.71555	−0.715059
$28$	0.856873	0.161934
$29$	−5.92614	−1.10046	−0.550229	−	0.835014i	$-0.685459\pi$
$29$	−5.92614	−1.10046	−0.550229	+	0.835014i	$0.685459\pi$
$30$	7.80109	1.42428
$31$	8.72095	1.56633	0.783164	−	0.621815i	$-0.213604\pi$
$31$	8.72095	1.56633	0.783164	+	0.621815i	$0.213604\pi$
$32$	1.00000	0.176777
$33$	−0.588979	−0.102528
$34$	0.234175	0.0401606
$35$	3.26819	0.552424
$36$	1.18340	0.197234
$37$	−8.74641	−1.43790	−0.718951	−	0.695061i	$-0.755377\pi$
$37$	−8.74641	−1.43790	−0.718951	+	0.695061i	$0.755377\pi$
$38$	−6.00213	−0.973673
$39$	−6.12080	−0.980112
$40$	3.81409	0.603060
$41$	4.43713	0.692963	0.346481	−	0.938057i	$-0.387376\pi$
$41$	4.43713	0.692963	0.346481	+	0.938057i	$0.387376\pi$
$42$	1.75259	0.270431
$43$	0.190690	0.0290800	0.0145400	−	0.999894i	$-0.495372\pi$
$43$	0.190690	0.0290800	0.0145400	+	0.999894i	$0.495372\pi$
$44$	−0.287962	−0.0434119
$45$	4.51360	0.672847
$46$	0.503796	0.0742807
$47$	−7.85188	−1.14531	−0.572657	−	0.819795i	$-0.694087\pi$
$47$	−7.85188	−1.14531	−0.572657	+	0.819795i	$0.694087\pi$
$48$	2.04534	0.295219
$49$	−6.26577	−0.895110
$50$	9.54725	1.35019
$51$	0.478966	0.0670686
$52$	−2.99256	−0.414994
$53$	8.87554	1.21915	0.609574	−	0.792729i	$-0.291340\pi$
$53$	8.87554	1.21915	0.609574	+	0.792729i	$0.291340\pi$
$54$	−3.71555	−0.505623
$55$	−1.09831	−0.148096
$56$	0.856873	0.114504
$57$	−12.2764	−1.62604
$58$	−5.92614	−0.778141
$59$	−5.29486	−0.689333	−0.344666	−	0.938725i	$-0.612008\pi$
$59$	−5.29486	−0.689333	−0.344666	+	0.938725i	$0.612008\pi$
$60$	7.80109	1.00712
$61$	−2.70503	−0.346344	−0.173172	−	0.984892i	$-0.555402\pi$
$61$	−2.70503	−0.346344	−0.173172	+	0.984892i	$0.555402\pi$
$62$	8.72095	1.10756
$63$	1.01403	0.127755
$64$	1.00000	0.125000
$65$	−11.4139	−1.41572
$66$	−0.588979	−0.0724983
$67$	7.01908	0.857517	0.428759	−	0.903419i	$-0.358951\pi$
$67$	7.01908	0.857517	0.428759	+	0.903419i	$0.358951\pi$
$68$	0.234175	0.0283978
$69$	1.03043	0.124050
$70$	3.26819	0.390623
$71$	4.28687	0.508757	0.254379	−	0.967105i	$-0.418129\pi$
$71$	4.28687	0.508757	0.254379	+	0.967105i	$0.418129\pi$
$72$	1.18340	0.139465
$73$	−10.1158	−1.18397	−0.591984	−	0.805950i	$-0.701655\pi$
$73$	−10.1158	−1.18397	−0.591984	+	0.805950i	$0.701655\pi$
$74$	−8.74641	−1.01675
$75$	19.5273	2.25482
$76$	−6.00213	−0.688491
$77$	−0.246747	−0.0281194
$78$	−6.12080	−0.693044
$79$	−2.45995	−0.276766	−0.138383	−	0.990379i	$-0.544190\pi$
$79$	−2.45995	−0.276766	−0.138383	+	0.990379i	$0.544190\pi$
$80$	3.81409	0.426428
$81$	−11.1498	−1.23886
$82$	4.43713	0.489998
$83$	9.82731	1.07869	0.539344	−	0.842086i	$-0.318672\pi$
$83$	9.82731	1.07869	0.539344	+	0.842086i	$0.318672\pi$
$84$	1.75259	0.191224
$85$	0.893162	0.0968770
$86$	0.190690	0.0205627
$87$	−12.1210	−1.29950
$88$	−0.287962	−0.0306968
$89$	1.69696	0.179877	0.0899387	−	0.995947i	$-0.471333\pi$
$89$	1.69696	0.179877	0.0899387	+	0.995947i	$0.471333\pi$
$90$	4.51360	0.475775
$91$	−2.56425	−0.268806
$92$	0.503796	0.0525244
$93$	17.8373	1.84964
$94$	−7.85188	−0.809860
$95$	−22.8926	−2.34873
$96$	2.04534	0.208751
$97$	14.9225	1.51515	0.757574	−	0.652749i	$-0.226385\pi$
$97$	14.9225	1.51515	0.757574	+	0.652749i	$0.226385\pi$
$98$	−6.26577	−0.632938
$99$	−0.340775	−0.0342491
$100$	9.54725	0.954725
$101$	9.28889	0.924279	0.462140	−	0.886807i	$-0.347082\pi$
$101$	9.28889	0.924279	0.462140	+	0.886807i	$0.347082\pi$
$102$	0.478966	0.0474247
$103$	−13.6136	−1.34139	−0.670693	−	0.741735i	$-0.734003\pi$
$103$	−13.6136	−1.34139	−0.670693	+	0.741735i	$0.734003\pi$
$104$	−2.99256	−0.293445
$105$	6.68454	0.652344
$106$	8.87554	0.862068
$107$	2.28722	0.221114	0.110557	−	0.993870i	$-0.464736\pi$
$107$	2.28722	0.221114	0.110557	+	0.993870i	$0.464736\pi$
$108$	−3.71555	−0.357529
$109$	−13.5320	−1.29613	−0.648065	−	0.761585i	$-0.724421\pi$
$109$	−13.5320	−1.29613	−0.648065	+	0.761585i	$0.724421\pi$
$110$	−1.09831	−0.104720
$111$	−17.8894	−1.69798
$112$	0.856873	0.0809669
$113$	14.9632	1.40762	0.703809	−	0.710390i	$-0.251481\pi$
$113$	14.9632	1.40762	0.703809	+	0.710390i	$0.251481\pi$
$114$	−12.2764	−1.14979
$115$	1.92152	0.179183
$116$	−5.92614	−0.550229
$117$	−3.54141	−0.327403
$118$	−5.29486	−0.487432
$119$	0.200658	0.0183943
$120$	7.80109	0.712139
$121$	−10.9171	−0.992462
$122$	−2.70503	−0.244902
$123$	9.07541	0.818303
$124$	8.72095	0.783164
$125$	17.3436	1.55126
$126$	1.01403	0.0903365
$127$	3.03153	0.269005	0.134502	−	0.990913i	$-0.457056\pi$
$127$	3.03153	0.269005	0.134502	+	0.990913i	$0.457056\pi$
$128$	1.00000	0.0883883
$129$	0.390026	0.0343398
$130$	−11.4139	−1.00106
$131$	12.4265	1.08571	0.542853	−	0.839828i	$-0.317344\pi$
$131$	12.4265	1.08571	0.542853	+	0.839828i	$0.317344\pi$
$132$	−0.588979	−0.0512640
$133$	−5.14306	−0.445960
$134$	7.01908	0.606356
$135$	−14.1714	−1.21968
$136$	0.234175	0.0200803
$137$	−6.44378	−0.550529	−0.275265	−	0.961368i	$-0.588766\pi$
$137$	−6.44378	−0.550529	−0.275265	+	0.961368i	$0.588766\pi$
$138$	1.03043	0.0877163
$139$	19.8126	1.68048	0.840242	−	0.542212i	$-0.182413\pi$
$139$	19.8126	1.68048	0.840242	+	0.542212i	$0.182413\pi$
$140$	3.26819	0.276212
$141$	−16.0597	−1.35247
$142$	4.28687	0.359746
$143$	0.861744	0.0720626
$144$	1.18340	0.0986168
$145$	−22.6028	−1.87706
$146$	−10.1158	−0.837191
$147$	−12.8156	−1.05701
$148$	−8.74641	−0.718951
$149$	13.4204	1.09945	0.549723	−	0.835347i	$-0.314733\pi$
$149$	13.4204	1.09945	0.549723	+	0.835347i	$0.314733\pi$
$150$	19.5273	1.59440
$151$	0.378394	0.0307933	0.0153966	−	0.999881i	$-0.495099\pi$
$151$	0.378394	0.0307933	0.0153966	+	0.999881i	$0.495099\pi$
$152$	−6.00213	−0.486837
$153$	0.277123	0.0224040
$154$	−0.246747	−0.0198834
$155$	33.2624	2.67170
$156$	−6.12080	−0.490056
$157$	7.41338	0.591652	0.295826	−	0.955242i	$-0.404405\pi$
$157$	7.41338	0.591652	0.295826	+	0.955242i	$0.404405\pi$
$158$	−2.45995	−0.195703
$159$	18.1535	1.43966
$160$	3.81409	0.301530
$161$	0.431690	0.0340219
$162$	−11.1498	−0.876008
$163$	20.9672	1.64228	0.821139	−	0.570729i	$-0.193339\pi$
$163$	20.9672	1.64228	0.821139	+	0.570729i	$0.193339\pi$
$164$	4.43713	0.346481
$165$	−2.24642	−0.174883
$166$	9.82731	0.762747
$167$	11.5239	0.891745	0.445872	−	0.895097i	$-0.352894\pi$
$167$	11.5239	0.891745	0.445872	+	0.895097i	$0.352894\pi$
$168$	1.75259	0.135216
$169$	−4.04457	−0.311120
$170$	0.893162	0.0685024
$171$	−7.10293	−0.543174
$172$	0.190690	0.0145400
$173$	−17.5478	−1.33414	−0.667068	−	0.744997i	$-0.732451\pi$
$173$	−17.5478	−1.33414	−0.667068	+	0.744997i	$0.732451\pi$
$174$	−12.1210	−0.918888
$175$	8.18078	0.618409
$176$	−0.287962	−0.0217059
$177$	−10.8298	−0.814016
$178$	1.69696	0.127193
$179$	−3.91713	−0.292780	−0.146390	−	0.989227i	$-0.546765\pi$
$179$	−3.91713	−0.292780	−0.146390	+	0.989227i	$0.546765\pi$
$180$	4.51360	0.336424
$181$	10.1368	0.753460	0.376730	−	0.926323i	$-0.377048\pi$
$181$	10.1368	0.753460	0.376730	+	0.926323i	$0.377048\pi$
$182$	−2.56425	−0.190075
$183$	−5.53271	−0.408989
$184$	0.503796	0.0371404
$185$	−33.3596	−2.45264
$186$	17.8373	1.30789
$187$	−0.0674333	−0.00493121
$188$	−7.85188	−0.572657
$189$	−3.18376	−0.231584
$190$	−22.8926	−1.66081
$191$	11.4483	0.828371	0.414185	−	0.910193i	$-0.364066\pi$
$191$	11.4483	0.828371	0.414185	+	0.910193i	$0.364066\pi$
$192$	2.04534	0.147609
$193$	−6.95327	−0.500507	−0.250254	−	0.968180i	$-0.580514\pi$
$193$	−6.95327	−0.500507	−0.250254	+	0.968180i	$0.580514\pi$
$194$	14.9225	1.07137
$195$	−23.3453	−1.67179
$196$	−6.26577	−0.447555
$197$	−24.5358	−1.74810	−0.874052	−	0.485833i	$-0.838516\pi$
$197$	−24.5358	−1.74810	−0.874052	+	0.485833i	$0.838516\pi$
$198$	−0.340775	−0.0242178
$199$	1.33551	0.0946718	0.0473359	−	0.998879i	$-0.484927\pi$
$199$	1.33551	0.0946718	0.0473359	+	0.998879i	$0.484927\pi$
$200$	9.54725	0.675093
$201$	14.3564	1.01262
$202$	9.28889	0.653564
$203$	−5.07795	−0.356402
$204$	0.478966	0.0335343
$205$	16.9236	1.18199
$206$	−13.6136	−0.948503
$207$	0.596194	0.0414383
$208$	−2.99256	−0.207497
$209$	1.72838	0.119555
$210$	6.68454	0.461277
$211$	−1.48284	−0.102083	−0.0510414	−	0.998697i	$-0.516254\pi$
$211$	−1.48284	−0.102083	−0.0510414	+	0.998697i	$0.516254\pi$
$212$	8.87554	0.609574
$213$	8.76808	0.600779
$214$	2.28722	0.156351
$215$	0.727309	0.0496020
$216$	−3.71555	−0.252811
$217$	7.47274	0.507283
$218$	−13.5320	−0.916502
$219$	−20.6903	−1.39812
$220$	−1.09831	−0.0740481
$221$	−0.700782	−0.0471397
$222$	−17.8894	−1.20066
$223$	17.9362	1.20110	0.600550	−	0.799587i	$-0.294948\pi$
$223$	17.9362	1.20110	0.600550	+	0.799587i	$0.294948\pi$
$224$	0.856873	0.0572522
$225$	11.2982	0.753216
$226$	14.9632	0.995336
$227$	−7.78319	−0.516588	−0.258294	−	0.966066i	$-0.583160\pi$
$227$	−7.78319	−0.516588	−0.258294	+	0.966066i	$0.583160\pi$
$228$	−12.2764	−0.813022
$229$	19.4060	1.28238	0.641191	−	0.767381i	$-0.278440\pi$
$229$	19.4060	1.28238	0.641191	+	0.767381i	$0.278440\pi$
$230$	1.92152	0.126701
$231$	−0.504680	−0.0332055
$232$	−5.92614	−0.389070
$233$	7.24426	0.474587	0.237294	−	0.971438i	$-0.423740\pi$
$233$	7.24426	0.474587	0.237294	+	0.971438i	$0.423740\pi$
$234$	−3.54141	−0.231509
$235$	−29.9478	−1.95358
$236$	−5.29486	−0.344666
$237$	−5.03142	−0.326826
$238$	0.200658	0.0130067
$239$	13.3031	0.860503	0.430251	−	0.902709i	$-0.358425\pi$
$239$	13.3031	0.860503	0.430251	+	0.902709i	$0.358425\pi$
$240$	7.80109	0.503558
$241$	−12.4927	−0.804728	−0.402364	−	0.915480i	$-0.631811\pi$
$241$	−12.4927	−0.804728	−0.402364	+	0.915480i	$0.631811\pi$
$242$	−10.9171	−0.701776
$243$	−11.6584	−0.747884
$244$	−2.70503	−0.173172
$245$	−23.8982	−1.52680
$246$	9.07541	0.578627
$247$	17.9617	1.14288
$248$	8.72095	0.553781
$249$	20.1002	1.27380
$250$	17.3436	1.09691
$251$	−7.97505	−0.503381	−0.251690	−	0.967808i	$-0.580986\pi$
$251$	−7.97505	−0.503381	−0.251690	+	0.967808i	$0.580986\pi$
$252$	1.01403	0.0638776
$253$	−0.145074	−0.00912073
$254$	3.03153	0.190215
$255$	1.82682	0.114400
$256$	1.00000	0.0625000
$257$	−10.2033	−0.636467	−0.318233	−	0.948012i	$-0.603090\pi$
$257$	−10.2033	−0.636467	−0.318233	+	0.948012i	$0.603090\pi$
$258$	0.390026	0.0242819
$259$	−7.49456	−0.465690
$260$	−11.4139	−0.707860
$261$	−7.01301	−0.434095
$262$	12.4265	0.767710
$263$	−17.3082	−1.06727	−0.533635	−	0.845715i	$-0.679174\pi$
$263$	−17.3082	−1.06727	−0.533635	+	0.845715i	$0.679174\pi$
$264$	−0.588979	−0.0362491
$265$	33.8521	2.07952
$266$	−5.14306	−0.315341
$267$	3.47086	0.212413
$268$	7.01908	0.428759
$269$	17.4845	1.06605	0.533024	−	0.846100i	$-0.321056\pi$
$269$	17.4845	1.06605	0.533024	+	0.846100i	$0.321056\pi$
$270$	−14.1714	−0.862447
$271$	−24.9671	−1.51665	−0.758323	−	0.651879i	$-0.773981\pi$
$271$	−24.9671	−1.51665	−0.758323	+	0.651879i	$0.773981\pi$
$272$	0.234175	0.0141989
$273$	−5.24475	−0.317427
$274$	−6.44378	−0.389283
$275$	−2.74924	−0.165786
$276$	1.03043	0.0620248
$277$	−1.41798	−0.0851982	−0.0425991	−	0.999092i	$-0.513564\pi$
$277$	−1.41798	−0.0851982	−0.0425991	+	0.999092i	$0.513564\pi$
$278$	19.8126	1.18828
$279$	10.3204	0.617865
$280$	3.26819	0.195312
$281$	−5.56619	−0.332051	−0.166026	−	0.986121i	$-0.553093\pi$
$281$	−5.56619	−0.332051	−0.166026	+	0.986121i	$0.553093\pi$
$282$	−16.0597	−0.956344
$283$	−16.7192	−0.993852	−0.496926	−	0.867793i	$-0.665538\pi$
$283$	−16.7192	−0.993852	−0.496926	+	0.867793i	$0.665538\pi$
$284$	4.28687	0.254379
$285$	−46.8231	−2.77356
$286$	0.861744	0.0509560
$287$	3.80205	0.224428
$288$	1.18340	0.0697326
$289$	−16.9452	−0.996774
$290$	−22.6028	−1.32728
$291$	30.5215	1.78920
$292$	−10.1158	−0.591984
$293$	19.5832	1.14406	0.572031	−	0.820232i	$-0.306156\pi$
$293$	19.5832	1.14406	0.572031	+	0.820232i	$0.306156\pi$
$294$	−12.8156	−0.747421
$295$	−20.1951	−1.17580
$296$	−8.74641	−0.508375
$297$	1.06994	0.0620841
$298$	13.4204	0.777426
$299$	−1.50764	−0.0871892
$300$	19.5273	1.12741
$301$	0.163397	0.00941806
$302$	0.378394	0.0217741
$303$	18.9989	1.09146
$304$	−6.00213	−0.344246
$305$	−10.3172	−0.590763
$306$	0.277123	0.0158421
$307$	−2.07927	−0.118670	−0.0593351	−	0.998238i	$-0.518898\pi$
$307$	−2.07927	−0.118670	−0.0593351	+	0.998238i	$0.518898\pi$
$308$	−0.246747	−0.0140597
$309$	−27.8444	−1.58401
$310$	33.2624	1.88918
$311$	−9.70383	−0.550254	−0.275127	−	0.961408i	$-0.588720\pi$
$311$	−9.70383	−0.550254	−0.275127	+	0.961408i	$0.588720\pi$
$312$	−6.12080	−0.346522
$313$	3.70851	0.209617	0.104809	−	0.994492i	$-0.466577\pi$
$313$	3.70851	0.209617	0.104809	+	0.994492i	$0.466577\pi$
$314$	7.41338	0.418361
$315$	3.86758	0.217913
$316$	−2.45995	−0.138383
$317$	20.1258	1.13038	0.565188	−	0.824962i	$-0.308803\pi$
$317$	20.1258	1.13038	0.565188	+	0.824962i	$0.308803\pi$
$318$	18.1535	1.01800
$319$	1.70650	0.0955458
$320$	3.81409	0.213214
$321$	4.67814	0.261108
$322$	0.431690	0.0240571
$323$	−1.40555	−0.0782066
$324$	−11.1498	−0.619431
$325$	−28.5707	−1.58482
$326$	20.9672	1.16127
$327$	−27.6775	−1.53057
$328$	4.43713	0.244999
$329$	−6.72807	−0.370930
$330$	−2.24642	−0.123661
$331$	4.97605	0.273508	0.136754	−	0.990605i	$-0.456333\pi$
$331$	4.97605	0.273508	0.136754	+	0.990605i	$0.456333\pi$
$332$	9.82731	0.539344
$333$	−10.3505	−0.567205
$334$	11.5239	0.630559
$335$	26.7714	1.46268
$336$	1.75259	0.0956118
$337$	−5.41663	−0.295063	−0.147531	−	0.989057i	$-0.547133\pi$
$337$	−5.41663	−0.295063	−0.147531	+	0.989057i	$0.547133\pi$
$338$	−4.04457	−0.219995
$339$	30.6047	1.66222
$340$	0.893162	0.0484385
$341$	−2.51130	−0.135995
$342$	−7.10293	−0.384082
$343$	−11.3671	−0.613764
$344$	0.190690	0.0102813
$345$	3.93016	0.211593
$346$	−17.5478	−0.943376
$347$	13.0784	0.702087	0.351044	−	0.936359i	$-0.385827\pi$
$347$	13.0784	0.702087	0.351044	+	0.936359i	$0.385827\pi$
$348$	−12.1210	−0.649752
$349$	−29.8118	−1.59579	−0.797893	−	0.602799i	$-0.794052\pi$
$349$	−29.8118	−1.59579	−0.797893	+	0.602799i	$0.794052\pi$
$350$	8.18078	0.437281
$351$	11.1190	0.593490
$352$	−0.287962	−0.0153484
$353$	−26.1432	−1.39146	−0.695731	−	0.718303i	$-0.744919\pi$
$353$	−26.1432	−1.39146	−0.695731	+	0.718303i	$0.744919\pi$
$354$	−10.8298	−0.575596
$355$	16.3505	0.867793
$356$	1.69696	0.0899387
$357$	0.410413	0.0217214
$358$	−3.91713	−0.207027
$359$	−23.9509	−1.26408	−0.632039	−	0.774936i	$-0.717782\pi$
$359$	−23.9509	−1.26408	−0.632039	+	0.774936i	$0.717782\pi$
$360$	4.51360	0.237887
$361$	17.0255	0.896080
$362$	10.1368	0.532777
$363$	−22.3291	−1.17197
$364$	−2.56425	−0.134403
$365$	−38.5826	−2.01951
$366$	−5.53271	−0.289199
$367$	23.7626	1.24040	0.620198	−	0.784446i	$-0.287052\pi$
$367$	23.7626	1.24040	0.620198	+	0.784446i	$0.287052\pi$
$368$	0.503796	0.0262622
$369$	5.25090	0.273351
$370$	−33.3596	−1.73428
$371$	7.60521	0.394843
$372$	17.8373	0.924820
$373$	−0.0463181	−0.00239826	−0.00119913	−	0.999999i	$-0.500382\pi$
$373$	−0.0463181	−0.00239826	−0.00119913	+	0.999999i	$0.500382\pi$
$374$	−0.0674333	−0.00348690
$375$	35.4735	1.83184
$376$	−7.85188	−0.404930
$377$	17.7344	0.913366
$378$	−3.18376	−0.163755
$379$	0.636668	0.0327034	0.0163517	−	0.999866i	$-0.494795\pi$
$379$	0.636668	0.0327034	0.0163517	+	0.999866i	$0.494795\pi$
$380$	−22.8926	−1.17437
$381$	6.20050	0.317661
$382$	11.4483	0.585747
$383$	−11.3668	−0.580815	−0.290408	−	0.956903i	$-0.593791\pi$
$383$	−11.3668	−0.580815	−0.290408	+	0.956903i	$0.593791\pi$
$384$	2.04534	0.104376
$385$	−0.941113	−0.0479636
$386$	−6.95327	−0.353912
$387$	0.225663	0.0114711
$388$	14.9225	0.757574
$389$	14.6047	0.740488	0.370244	−	0.928934i	$-0.379274\pi$
$389$	14.6047	0.740488	0.370244	+	0.928934i	$0.379274\pi$
$390$	−23.3453	−1.18213
$391$	0.117976	0.00596632
$392$	−6.26577	−0.316469
$393$	25.4163	1.28208
$394$	−24.5358	−1.23610
$395$	−9.38245	−0.472082
$396$	−0.340775	−0.0171246
$397$	−30.3206	−1.52175	−0.760873	−	0.648901i	$-0.775229\pi$
$397$	−30.3206	−1.52175	−0.760873	+	0.648901i	$0.775229\pi$
$398$	1.33551	0.0669431
$399$	−10.5193	−0.526623
$400$	9.54725	0.477362
$401$	−13.9574	−0.696997	−0.348499	−	0.937309i	$-0.613308\pi$
$401$	−13.9574	−0.696997	−0.348499	+	0.937309i	$0.613308\pi$
$402$	14.3564	0.716031
$403$	−26.0980	−1.30003
$404$	9.28889	0.462140
$405$	−42.5262	−2.11314
$406$	−5.07795	−0.252015
$407$	2.51863	0.124844
$408$	0.478966	0.0237123
$409$	24.8109	1.22682	0.613410	−	0.789765i	$-0.289798\pi$
$409$	24.8109	1.22682	0.613410	+	0.789765i	$0.289798\pi$
$410$	16.9236	0.835796
$411$	−13.1797	−0.650107
$412$	−13.6136	−0.670693
$413$	−4.53703	−0.223252
$414$	0.596194	0.0293013
$415$	37.4822	1.83993
$416$	−2.99256	−0.146722
$417$	40.5235	1.98444
$418$	1.72838	0.0845380
$419$	−3.05098	−0.149050	−0.0745252	−	0.997219i	$-0.523744\pi$
$419$	−3.05098	−0.149050	−0.0745252	+	0.997219i	$0.523744\pi$
$420$	6.68454	0.326172
$421$	−23.8546	−1.16260	−0.581302	−	0.813688i	$-0.697456\pi$
$421$	−23.8546	−1.16260	−0.581302	+	0.813688i	$0.697456\pi$
$422$	−1.48284	−0.0721834
$423$	−9.29193	−0.451789
$424$	8.87554	0.431034
$425$	2.23572	0.108449
$426$	8.76808	0.424815
$427$	−2.31787	−0.112170
$428$	2.28722	0.110557
$429$	1.76256	0.0850970
$430$	0.727309	0.0350739
$431$	1.73748	0.0836912	0.0418456	−	0.999124i	$-0.486676\pi$
$431$	1.73748	0.0836912	0.0418456	+	0.999124i	$0.486676\pi$
$432$	−3.71555	−0.178765
$433$	−10.3220	−0.496042	−0.248021	−	0.968755i	$-0.579780\pi$
$433$	−10.3220	−0.496042	−0.248021	+	0.968755i	$0.579780\pi$
$434$	7.47274	0.358703
$435$	−46.2304	−2.21658
$436$	−13.5320	−0.648065
$437$	−3.02385	−0.144650
$438$	−20.6903	−0.988619
$439$	8.17082	0.389972	0.194986	−	0.980806i	$-0.437534\pi$
$439$	8.17082	0.389972	0.194986	+	0.980806i	$0.437534\pi$
$440$	−1.09831	−0.0523599
$441$	−7.41492	−0.353092
$442$	−0.700782	−0.0333328
$443$	12.7213	0.604407	0.302204	−	0.953243i	$-0.402278\pi$
$443$	12.7213	0.604407	0.302204	+	0.953243i	$0.402278\pi$
$444$	−17.8894	−0.848991
$445$	6.47235	0.306819
$446$	17.9362	0.849306
$447$	27.4493	1.29831
$448$	0.856873	0.0404834
$449$	−0.422435	−0.0199359	−0.00996797	−	0.999950i	$-0.503173\pi$
$449$	−0.422435	−0.0199359	−0.00996797	+	0.999950i	$0.503173\pi$
$450$	11.2982	0.532604
$451$	−1.27772	−0.0601656
$452$	14.9632	0.703809
$453$	0.773943	0.0363630
$454$	−7.78319	−0.365283
$455$	−9.78025	−0.458505
$456$	−12.2764	−0.574894
$457$	13.3771	0.625754	0.312877	−	0.949794i	$-0.398707\pi$
$457$	13.3771	0.625754	0.312877	+	0.949794i	$0.398707\pi$
$458$	19.4060	0.906782
$459$	−0.870088	−0.0406123
$460$	1.92152	0.0895915
$461$	41.4089	1.92860	0.964302	−	0.264805i	$-0.0853077\pi$
$461$	41.4089	1.92860	0.964302	+	0.264805i	$0.0853077\pi$
$462$	−0.504680	−0.0234798
$463$	11.7080	0.544116	0.272058	−	0.962281i	$-0.412296\pi$
$463$	11.7080	0.544116	0.272058	+	0.962281i	$0.412296\pi$
$464$	−5.92614	−0.275114
$465$	68.0329	3.15495
$466$	7.24426	0.335584
$467$	−28.7723	−1.33142	−0.665712	−	0.746209i	$-0.731872\pi$
$467$	−28.7723	−1.33142	−0.665712	+	0.746209i	$0.731872\pi$
$468$	−3.54141	−0.163702
$469$	6.01446	0.277722
$470$	−29.9478	−1.38139
$471$	15.1629	0.698668
$472$	−5.29486	−0.243716
$473$	−0.0549115	−0.00252483
$474$	−5.03142	−0.231101
$475$	−57.3038	−2.62928
$476$	0.200658	0.00919714
$477$	10.5033	0.480914
$478$	13.3031	0.608467
$479$	−11.9851	−0.547612	−0.273806	−	0.961785i	$-0.588283\pi$
$479$	−11.9851	−0.547612	−0.273806	+	0.961785i	$0.588283\pi$
$480$	7.80109	0.356069
$481$	26.1742	1.19344
$482$	−12.4927	−0.569029
$483$	0.882950	0.0401756
$484$	−10.9171	−0.496231
$485$	56.9156	2.58440
$486$	−11.6584	−0.528834
$487$	31.2805	1.41746	0.708728	−	0.705482i	$-0.249269\pi$
$487$	31.2805	1.41746	0.708728	+	0.705482i	$0.249269\pi$
$488$	−2.70503	−0.122451
$489$	42.8850	1.93933
$490$	−23.8982	−1.07961
$491$	34.1995	1.54340	0.771701	−	0.635985i	$-0.219406\pi$
$491$	34.1995	1.54340	0.771701	+	0.635985i	$0.219406\pi$
$492$	9.07541	0.409151
$493$	−1.38775	−0.0625012
$494$	17.9617	0.808137
$495$	−1.29974	−0.0584191
$496$	8.72095	0.391582
$497$	3.67330	0.164770
$498$	20.1002	0.900710
$499$	19.8989	0.890798	0.445399	−	0.895332i	$-0.353062\pi$
$499$	19.8989	0.890798	0.445399	+	0.895332i	$0.353062\pi$
$500$	17.3436	0.775629
$501$	23.5702	1.05304
$502$	−7.97505	−0.355944
$503$	−25.9600	−1.15750	−0.578751	−	0.815505i	$-0.696460\pi$
$503$	−25.9600	−1.15750	−0.578751	+	0.815505i	$0.696460\pi$
$504$	1.01403	0.0451683
$505$	35.4286	1.57655
$506$	−0.145074	−0.00644933
$507$	−8.27250	−0.367395
$508$	3.03153	0.134502
$509$	−41.7538	−1.85071	−0.925353	−	0.379107i	$-0.876231\pi$
$509$	−41.7538	−1.85071	−0.925353	+	0.379107i	$0.876231\pi$
$510$	1.82682	0.0808928
$511$	−8.66797	−0.383448
$512$	1.00000	0.0441942
$513$	22.3012	0.984623
$514$	−10.2033	−0.450050
$515$	−51.9234	−2.28802
$516$	0.390026	0.0171699
$517$	2.26104	0.0994405
$518$	−7.49456	−0.329292
$519$	−35.8912	−1.57545
$520$	−11.4139	−0.500532
$521$	11.3445	0.497011	0.248505	−	0.968631i	$-0.420061\pi$
$521$	11.3445	0.497011	0.248505	+	0.968631i	$0.420061\pi$
$522$	−7.01301	−0.306951
$523$	19.6137	0.857648	0.428824	−	0.903388i	$-0.358928\pi$
$523$	19.6137	0.857648	0.428824	+	0.903388i	$0.358928\pi$
$524$	12.4265	0.542853
$525$	16.7324	0.730264
$526$	−17.3082	−0.754674
$527$	2.04222	0.0889607
$528$	−0.588979	−0.0256320
$529$	−22.7462	−0.988965
$530$	33.8521	1.47044
$531$	−6.26595	−0.271919
$532$	−5.14306	−0.222980
$533$	−13.2784	−0.575150
$534$	3.47086	0.150199
$535$	8.72366	0.377157
$536$	7.01908	0.303178
$537$	−8.01184	−0.345737
$538$	17.4845	0.753809
$539$	1.80430	0.0777168
$540$	−14.1714	−0.609842
$541$	−35.1123	−1.50959	−0.754797	−	0.655958i	$-0.772265\pi$
$541$	−35.1123	−1.50959	−0.754797	+	0.655958i	$0.772265\pi$
$542$	−24.9671	−1.07243
$543$	20.7331	0.889743
$544$	0.234175	0.0100402
$545$	−51.6122	−2.21082
$546$	−5.24475	−0.224454
$547$	−28.7864	−1.23082	−0.615409	−	0.788208i	$-0.711009\pi$
$547$	−28.7864	−1.23082	−0.615409	+	0.788208i	$0.711009\pi$
$548$	−6.44378	−0.275265
$549$	−3.20114	−0.136621
$550$	−2.74924	−0.117228
$551$	35.5695	1.51531
$552$	1.03043	0.0438582
$553$	−2.10786	−0.0896354
$554$	−1.41798	−0.0602442
$555$	−68.2316	−2.89627
$556$	19.8126	0.840242
$557$	9.03618	0.382875	0.191438	−	0.981505i	$-0.438685\pi$
$557$	9.03618	0.382875	0.191438	+	0.981505i	$0.438685\pi$
$558$	10.3204	0.436897
$559$	−0.570652	−0.0241360
$560$	3.26819	0.138106
$561$	−0.137924	−0.00582315
$562$	−5.56619	−0.234796
$563$	−20.8688	−0.879516	−0.439758	−	0.898116i	$-0.644936\pi$
$563$	−20.8688	−0.879516	−0.439758	+	0.898116i	$0.644936\pi$
$564$	−16.0597	−0.676237
$565$	57.0708	2.40099
$566$	−16.7192	−0.702759
$567$	−9.55393	−0.401227
$568$	4.28687	0.179873
$569$	−41.8642	−1.75504	−0.877520	−	0.479540i	$-0.840804\pi$
$569$	−41.8642	−1.75504	−0.877520	+	0.479540i	$0.840804\pi$
$570$	−46.8231	−1.96120
$571$	39.7306	1.66268	0.831338	−	0.555768i	$-0.187576\pi$
$571$	39.7306	1.66268	0.831338	+	0.555768i	$0.187576\pi$
$572$	0.861744	0.0360313
$573$	23.4157	0.978203
$574$	3.80205	0.158695
$575$	4.80987	0.200585
$576$	1.18340	0.0493084
$577$	−4.02148	−0.167416	−0.0837082	−	0.996490i	$-0.526676\pi$
$577$	−4.02148	−0.167416	−0.0837082	+	0.996490i	$0.526676\pi$
$578$	−16.9452	−0.704826
$579$	−14.2218	−0.591037
$580$	−22.6028	−0.938531
$581$	8.42076	0.349352
$582$	30.5215	1.26516
$583$	−2.55582	−0.105851
$584$	−10.1158	−0.418596
$585$	−13.5072	−0.558455
$586$	19.5832	0.808974
$587$	−7.94056	−0.327742	−0.163871	−	0.986482i	$-0.552398\pi$
$587$	−7.94056	−0.327742	−0.163871	+	0.986482i	$0.552398\pi$
$588$	−12.8156	−0.528507
$589$	−52.3442	−2.15681
$590$	−20.1951	−0.831418
$591$	−50.1840	−2.06429
$592$	−8.74641	−0.359475
$593$	−18.3366	−0.752993	−0.376496	−	0.926418i	$-0.622871\pi$
$593$	−18.3366	−0.752993	−0.376496	+	0.926418i	$0.622871\pi$
$594$	1.06994	0.0439001
$595$	0.765326	0.0313753
$596$	13.4204	0.549723
$597$	2.73157	0.111796
$598$	−1.50764	−0.0616521
$599$	−38.1311	−1.55799	−0.778997	−	0.627028i	$-0.784271\pi$
$599$	−38.1311	−1.55799	−0.778997	+	0.627028i	$0.784271\pi$
$600$	19.5273	0.797200
$601$	−41.2656	−1.68326	−0.841630	−	0.540054i	$-0.818404\pi$
$601$	−41.2656	−1.68326	−0.841630	+	0.540054i	$0.818404\pi$
$602$	0.163397	0.00665957
$603$	8.30640	0.338263
$604$	0.378394	0.0153966
$605$	−41.6387	−1.69285
$606$	18.9989	0.771778
$607$	43.0091	1.74569	0.872844	−	0.488000i	$-0.162273\pi$
$607$	43.0091	1.74569	0.872844	+	0.488000i	$0.162273\pi$
$608$	−6.00213	−0.243418
$609$	−10.3861	−0.420867
$610$	−10.3172	−0.417733
$611$	23.4973	0.950597
$612$	0.277123	0.0112020
$613$	7.57451	0.305932	0.152966	−	0.988231i	$-0.451118\pi$
$613$	7.57451	0.305932	0.152966	+	0.988231i	$0.451118\pi$
$614$	−2.07927	−0.0839126
$615$	34.6144	1.39579
$616$	−0.246747	−0.00994171
$617$	−29.5596	−1.19002	−0.595011	−	0.803717i	$-0.702852\pi$
$617$	−29.5596	−1.19002	−0.595011	+	0.803717i	$0.702852\pi$
$618$	−27.8444	−1.12006
$619$	31.8753	1.28118	0.640588	−	0.767885i	$-0.278691\pi$
$619$	31.8753	1.28118	0.640588	+	0.767885i	$0.278691\pi$
$620$	33.2624	1.33585
$621$	−1.87188	−0.0751161
$622$	−9.70383	−0.389088
$623$	1.45408	0.0582565
$624$	−6.12080	−0.245028
$625$	18.4137	0.736549
$626$	3.70851	0.148222
$627$	3.53512	0.141179
$628$	7.41338	0.295826
$629$	−2.04819	−0.0816666
$630$	3.86758	0.154088
$631$	47.2595	1.88137	0.940686	−	0.339277i	$-0.110183\pi$
$631$	47.2595	1.88137	0.940686	+	0.339277i	$0.110183\pi$
$632$	−2.45995	−0.0978514
$633$	−3.03290	−0.120547
$634$	20.1258	0.799297
$635$	11.5625	0.458844
$636$	18.1535	0.719832
$637$	18.7507	0.742930
$638$	1.70650	0.0675611
$639$	5.07309	0.200688
$640$	3.81409	0.150765
$641$	19.9752	0.788974	0.394487	−	0.918902i	$-0.370922\pi$
$641$	19.9752	0.788974	0.394487	+	0.918902i	$0.370922\pi$
$642$	4.67814	0.184632
$643$	−21.2907	−0.839623	−0.419812	−	0.907611i	$-0.637904\pi$
$643$	−21.2907	−0.839623	−0.419812	+	0.907611i	$0.637904\pi$
$644$	0.431690	0.0170109
$645$	1.48759	0.0585738
$646$	−1.40555	−0.0553004
$647$	−45.8958	−1.80435	−0.902175	−	0.431371i	$-0.858030\pi$
$647$	−45.8958	−1.80435	−0.902175	+	0.431371i	$0.858030\pi$
$648$	−11.1498	−0.438004
$649$	1.52472	0.0598504
$650$	−28.5707	−1.12064
$651$	15.2843	0.599038
$652$	20.9672	0.821139
$653$	34.3935	1.34592	0.672960	−	0.739679i	$-0.265023\pi$
$653$	34.3935	1.34592	0.672960	+	0.739679i	$0.265023\pi$
$654$	−27.6775	−1.08227
$655$	47.3956	1.85190
$656$	4.43713	0.173241
$657$	−11.9711	−0.467036
$658$	−6.72807	−0.262287
$659$	22.1922	0.864487	0.432243	−	0.901757i	$-0.357722\pi$
$659$	22.1922	0.864487	0.432243	+	0.901757i	$0.357722\pi$
$660$	−2.24642	−0.0874416
$661$	13.0098	0.506023	0.253011	−	0.967463i	$-0.418579\pi$
$661$	13.0098	0.506023	0.253011	+	0.967463i	$0.418579\pi$
$662$	4.97605	0.193400
$663$	−1.43334	−0.0556661
$664$	9.82731	0.381374
$665$	−19.6161	−0.760678
$666$	−10.3505	−0.401075
$667$	−2.98557	−0.115602
$668$	11.5239	0.445872
$669$	36.6857	1.41835
$670$	26.7714	1.03427
$671$	0.778947	0.0300709
$672$	1.75259	0.0676078
$673$	32.1115	1.23781	0.618904	−	0.785467i	$-0.287577\pi$
$673$	32.1115	1.23781	0.618904	+	0.785467i	$0.287577\pi$
$674$	−5.41663	−0.208641
$675$	−35.4733	−1.36537
$676$	−4.04457	−0.155560
$677$	−22.1688	−0.852018	−0.426009	−	0.904719i	$-0.640081\pi$
$677$	−22.1688	−0.852018	−0.426009	+	0.904719i	$0.640081\pi$
$678$	30.6047	1.17537
$679$	12.7867	0.490707
$680$	0.893162	0.0342512
$681$	−15.9192	−0.610027
$682$	−2.51130	−0.0961626
$683$	2.71931	0.104052	0.0520258	−	0.998646i	$-0.483432\pi$
$683$	2.71931	0.104052	0.0520258	+	0.998646i	$0.483432\pi$
$684$	−7.10293	−0.271587
$685$	−24.5771	−0.939044
$686$	−11.3671	−0.433997
$687$	39.6918	1.51433
$688$	0.190690	0.00727000
$689$	−26.5606	−1.01188
$690$	3.93016	0.149619
$691$	20.7633	0.789874	0.394937	−	0.918708i	$-0.370766\pi$
$691$	20.7633	0.789874	0.394937	+	0.918708i	$0.370766\pi$
$692$	−17.5478	−0.667068
$693$	−0.292000	−0.0110922
$694$	13.0784	0.496451
$695$	75.5670	2.86642
$696$	−12.1210	−0.459444
$697$	1.03906	0.0393573
$698$	−29.8118	−1.12839
$699$	14.8170	0.560429
$700$	8.18078	0.309204
$701$	−6.24849	−0.236002	−0.118001	−	0.993013i	$-0.537649\pi$
$701$	−6.24849	−0.236002	−0.118001	+	0.993013i	$0.537649\pi$
$702$	11.1190	0.419661
$703$	52.4971	1.97996
$704$	−0.287962	−0.0108530
$705$	−61.2532	−2.30693
$706$	−26.1432	−0.983912
$707$	7.95940	0.299344
$708$	−10.8298	−0.407008
$709$	24.9076	0.935425	0.467712	−	0.883881i	$-0.345078\pi$
$709$	24.9076	0.935425	0.467712	+	0.883881i	$0.345078\pi$
$710$	16.3505	0.613622
$711$	−2.91111	−0.109175
$712$	1.69696	0.0635963
$713$	4.39358	0.164541
$714$	0.410413	0.0153593
$715$	3.28676	0.122918
$716$	−3.91713	−0.146390
$717$	27.2092	1.01615
$718$	−23.9509	−0.893839
$719$	27.7185	1.03373	0.516863	−	0.856068i	$-0.327100\pi$
$719$	27.7185	1.03373	0.516863	+	0.856068i	$0.327100\pi$
$720$	4.51360	0.168212
$721$	−11.6651	−0.434431
$722$	17.0255	0.633624
$723$	−25.5519	−0.950284
$724$	10.1368	0.376730
$725$	−56.5784	−2.10127
$726$	−22.3291	−0.828711
$727$	−16.2587	−0.603002	−0.301501	−	0.953466i	$-0.597488\pi$
$727$	−16.2587	−0.603002	−0.301501	+	0.953466i	$0.597488\pi$
$728$	−2.56425	−0.0950373
$729$	9.60402	0.355705
$730$	−38.5826	−1.42801
$731$	0.0446548	0.00165162
$732$	−5.53271	−0.204495
$733$	0.848900	0.0313548	0.0156774	−	0.999877i	$-0.495010\pi$
$733$	0.848900	0.0313548	0.0156774	+	0.999877i	$0.495010\pi$
$734$	23.7626	0.877092
$735$	−48.8798	−1.80296
$736$	0.503796	0.0185702
$737$	−2.02123	−0.0744529
$738$	5.25090	0.193288
$739$	41.1987	1.51552	0.757759	−	0.652535i	$-0.226294\pi$
$739$	41.1987	1.51552	0.757759	+	0.652535i	$0.226294\pi$
$740$	−33.3596	−1.22632
$741$	36.7378	1.34960
$742$	7.60521	0.279196
$743$	−5.57726	−0.204610	−0.102305	−	0.994753i	$-0.532622\pi$
$743$	−5.57726	−0.204610	−0.102305	+	0.994753i	$0.532622\pi$
$744$	17.8373	0.653946
$745$	51.1867	1.87534
$746$	−0.0463181	−0.00169583
$747$	11.6297	0.425507
$748$	−0.0674333	−0.00246561
$749$	1.95986	0.0716117
$750$	35.4735	1.29531
$751$	−1.00000	−0.0364905
$751$	−1.00000	−0.0364905
$752$	−7.85188	−0.286329
$753$	−16.3117	−0.594430
$754$	17.7344	0.645847
$755$	1.44323	0.0525244
$756$	−3.18376	−0.115792
$757$	42.1833	1.53318	0.766589	−	0.642138i	$-0.221952\pi$
$757$	42.1833	1.53318	0.766589	+	0.642138i	$0.221952\pi$
$758$	0.636668	0.0231248
$759$	−0.296725	−0.0107705
$760$	−22.8926	−0.830403
$761$	−37.7892	−1.36986	−0.684928	−	0.728611i	$-0.740166\pi$
$761$	−37.7892	−1.36986	−0.684928	+	0.728611i	$0.740166\pi$
$762$	6.20050	0.224620
$763$	−11.5952	−0.419774
$764$	11.4483	0.414185
$765$	1.05697	0.0382148
$766$	−11.3668	−0.410698
$767$	15.8452	0.572138
$768$	2.04534	0.0738047
$769$	18.6390	0.672140	0.336070	−	0.941837i	$-0.390902\pi$
$769$	18.6390	0.672140	0.336070	+	0.941837i	$0.390902\pi$
$770$	−0.941113	−0.0339154
$771$	−20.8693	−0.751588
$772$	−6.95327	−0.250254
$773$	40.6754	1.46299	0.731497	−	0.681845i	$-0.238822\pi$
$773$	40.6754	1.46299	0.731497	+	0.681845i	$0.238822\pi$
$774$	0.225663	0.00811129
$775$	83.2611	2.99083
$776$	14.9225	0.535686
$777$	−15.3289	−0.549921
$778$	14.6047	0.523604
$779$	−26.6322	−0.954197
$780$	−23.3453	−0.835894
$781$	−1.23445	−0.0441722
$782$	0.117976	0.00421883
$783$	22.0189	0.786892
$784$	−6.26577	−0.223777
$785$	28.2753	1.00919
$786$	25.4163	0.906570
$787$	0.256843	0.00915547	0.00457774	−	0.999990i	$-0.498543\pi$
$787$	0.256843	0.00915547	0.00457774	+	0.999990i	$0.498543\pi$
$788$	−24.5358	−0.874052
$789$	−35.4011	−1.26031
$790$	−9.38245	−0.333812
$791$	12.8215	0.455882
$792$	−0.340775	−0.0121089
$793$	8.09499	0.287461
$794$	−30.3206	−1.07604
$795$	69.2389	2.45565
$796$	1.33551	0.0473359
$797$	29.5068	1.04518	0.522592	−	0.852583i	$-0.324965\pi$
$797$	29.5068	1.04518	0.522592	+	0.852583i	$0.324965\pi$
$798$	−10.5193	−0.372379
$799$	−1.83871	−0.0650489
$800$	9.54725	0.337546
$801$	2.00819	0.0709558
$802$	−13.9574	−0.492851
$803$	2.91297	0.102796
$804$	14.3564	0.506311
$805$	1.64650	0.0580315
$806$	−26.0980	−0.919262
$807$	35.7616	1.25887
$808$	9.28889	0.326782
$809$	−32.6649	−1.14844	−0.574218	−	0.818702i	$-0.694694\pi$
$809$	−32.6649	−1.14844	−0.574218	+	0.818702i	$0.694694\pi$
$810$	−42.5262	−1.49422
$811$	37.4465	1.31493	0.657463	−	0.753487i	$-0.271630\pi$
$811$	37.4465	1.31493	0.657463	+	0.753487i	$0.271630\pi$
$812$	−5.07795	−0.178201
$813$	−51.0662	−1.79097
$814$	2.51863	0.0882780
$815$	79.9707	2.80125
$816$	0.478966	0.0167672
$817$	−1.14455	−0.0400426
$818$	24.8109	0.867492
$819$	−3.03453	−0.106035
$820$	16.9236	0.590997
$821$	34.8199	1.21522	0.607611	−	0.794235i	$-0.292128\pi$
$821$	34.8199	1.21522	0.607611	+	0.794235i	$0.292128\pi$
$822$	−13.1797	−0.459695
$823$	29.9198	1.04294	0.521469	−	0.853270i	$-0.325384\pi$
$823$	29.9198	1.04294	0.521469	+	0.853270i	$0.325384\pi$
$824$	−13.6136	−0.474252
$825$	−5.62313	−0.195772
$826$	−4.53703	−0.157863
$827$	31.5955	1.09868	0.549342	−	0.835598i	$-0.314878\pi$
$827$	31.5955	1.09868	0.549342	+	0.835598i	$0.314878\pi$
$828$	0.596194	0.0207192
$829$	−17.4262	−0.605238	−0.302619	−	0.953112i	$-0.597861\pi$
$829$	−17.4262	−0.605238	−0.302619	+	0.953112i	$0.597861\pi$
$830$	37.4822	1.30103
$831$	−2.90025	−0.100608
$832$	−2.99256	−0.103748
$833$	−1.46728	−0.0508384
$834$	40.5235	1.40321
$835$	43.9531	1.52106
$836$	1.72838	0.0597774
$837$	−32.4032	−1.12002
$838$	−3.05098	−0.105395
$839$	13.7025	0.473064	0.236532	−	0.971624i	$-0.423989\pi$
$839$	13.7025	0.473064	0.236532	+	0.971624i	$0.423989\pi$
$840$	6.68454	0.230639
$841$	6.11919	0.211006
$842$	−23.8546	−0.822085
$843$	−11.3847	−0.392111
$844$	−1.48284	−0.0510414
$845$	−15.4263	−0.530682
$846$	−9.29193	−0.319463
$847$	−9.35455	−0.321426
$848$	8.87554	0.304787
$849$	−34.1963	−1.17362
$850$	2.23572	0.0766847
$851$	−4.40641	−0.151050
$852$	8.76808	0.300390
$853$	17.3319	0.593432	0.296716	−	0.954966i	$-0.404109\pi$
$853$	17.3319	0.593432	0.296716	+	0.954966i	$0.404109\pi$
$854$	−2.31787	−0.0793159
$855$	−27.0912	−0.926499
$856$	2.28722	0.0781757
$857$	−5.98234	−0.204353	−0.102176	−	0.994766i	$-0.532581\pi$
$857$	−5.98234	−0.204353	−0.102176	+	0.994766i	$0.532581\pi$
$858$	1.76256	0.0601727
$859$	30.5655	1.04288	0.521440	−	0.853288i	$-0.325395\pi$
$859$	30.5655	1.04288	0.521440	+	0.853288i	$0.325395\pi$
$860$	0.727309	0.0248010
$861$	7.77648	0.265022
$862$	1.73748	0.0591786
$863$	−12.9548	−0.440988	−0.220494	−	0.975388i	$-0.570767\pi$
$863$	−12.9548	−0.440988	−0.220494	+	0.975388i	$0.570767\pi$
$864$	−3.71555	−0.126406
$865$	−66.9288	−2.27565
$866$	−10.3220	−0.350754
$867$	−34.6586	−1.17707
$868$	7.47274	0.253641
$869$	0.708371	0.0240298
$870$	−46.2304	−1.56736
$871$	−21.0050	−0.711729
$872$	−13.5320	−0.458251
$873$	17.6593	0.597676
$874$	−3.02385	−0.102283
$875$	14.8613	0.502402
$876$	−20.6903	−0.699059
$877$	−7.79625	−0.263261	−0.131630	−	0.991299i	$-0.542021\pi$
$877$	−7.79625	−0.263261	−0.131630	+	0.991299i	$0.542021\pi$
$878$	8.17082	0.275752
$879$	40.0542	1.35099
$880$	−1.09831	−0.0370241
$881$	8.46920	0.285334	0.142667	−	0.989771i	$-0.454432\pi$
$881$	8.46920	0.285334	0.142667	+	0.989771i	$0.454432\pi$
$882$	−7.41492	−0.249673
$883$	−24.2399	−0.815736	−0.407868	−	0.913041i	$-0.633728\pi$
$883$	−24.2399	−0.815736	−0.407868	+	0.913041i	$0.633728\pi$
$884$	−0.700782	−0.0235699
$885$	−41.3057	−1.38848
$886$	12.7213	0.427380
$887$	−16.9201	−0.568123	−0.284061	−	0.958806i	$-0.591682\pi$
$887$	−16.9201	−0.568123	−0.284061	+	0.958806i	$0.591682\pi$
$888$	−17.8894	−0.600328
$889$	2.59763	0.0871219
$890$	6.47235	0.216954
$891$	3.21071	0.107563
$892$	17.9362	0.600550
$893$	47.1280	1.57708
$894$	27.4493	0.918043
$895$	−14.9403	−0.499398
$896$	0.856873	0.0286261
$897$	−3.08364	−0.102960
$898$	−0.422435	−0.0140968
$899$	−51.6816	−1.72368
$900$	11.2982	0.376608
$901$	2.07843	0.0692424
$902$	−1.27772	−0.0425435
$903$	0.334202	0.0111216
$904$	14.9632	0.497668
$905$	38.6625	1.28519
$906$	0.773943	0.0257125
$907$	−19.6353	−0.651979	−0.325989	−	0.945373i	$-0.605697\pi$
$907$	−19.6353	−0.651979	−0.325989	+	0.945373i	$0.605697\pi$
$908$	−7.78319	−0.258294
$909$	10.9925	0.364598
$910$	−9.78025	−0.324212
$911$	37.6366	1.24696	0.623478	−	0.781841i	$-0.285719\pi$
$911$	37.6366	1.24696	0.623478	+	0.781841i	$0.285719\pi$
$912$	−12.2764	−0.406511
$913$	−2.82989	−0.0936557
$914$	13.3771	0.442475
$915$	−21.1022	−0.697618
$916$	19.4060	0.641191
$917$	10.6479	0.351625
$918$	−0.870088	−0.0287172
$919$	18.6425	0.614959	0.307479	−	0.951555i	$-0.400515\pi$
$919$	18.6425	0.614959	0.307479	+	0.951555i	$0.400515\pi$
$920$	1.92152	0.0633507
$921$	−4.25281	−0.140135
$922$	41.4089	1.36373
$923$	−12.8287	−0.422262
$924$	−0.504680	−0.0166028
$925$	−83.5042	−2.74560
$926$	11.7080	0.384748
$927$	−16.1103	−0.529133
$928$	−5.92614	−0.194535
$929$	−55.2361	−1.81224	−0.906119	−	0.423023i	$-0.860969\pi$
$929$	−55.2361	−1.81224	−0.906119	+	0.423023i	$0.860969\pi$
$930$	68.0329	2.23089
$931$	37.6079	1.23255
$932$	7.24426	0.237294
$933$	−19.8476	−0.649781
$934$	−28.7723	−0.941459
$935$	−0.257197	−0.00841123
$936$	−3.54141	−0.115754
$937$	3.47845	0.113636	0.0568179	−	0.998385i	$-0.481905\pi$
$937$	3.47845	0.113636	0.0568179	+	0.998385i	$0.481905\pi$
$938$	6.01446	0.196379
$939$	7.58514	0.247532
$940$	−29.9478	−0.976788
$941$	0.953381	0.0310793	0.0155397	−	0.999879i	$-0.495053\pi$
$941$	0.953381	0.0310793	0.0155397	+	0.999879i	$0.495053\pi$
$942$	15.1629	0.494033
$943$	2.23541	0.0727949
$944$	−5.29486	−0.172333
$945$	−12.1431	−0.395016
$946$	−0.0549115	−0.00178533
$947$	52.3787	1.70208	0.851040	−	0.525101i	$-0.175973\pi$
$947$	52.3787	1.70208	0.851040	+	0.525101i	$0.175973\pi$
$948$	−5.03142	−0.163413
$949$	30.2722	0.982678
$950$	−57.3038	−1.85918
$951$	41.1640	1.33483
$952$	0.200658	0.00650336
$953$	−41.0755	−1.33056	−0.665282	−	0.746592i	$-0.731689\pi$
$953$	−41.0755	−1.33056	−0.665282	+	0.746592i	$0.731689\pi$
$954$	10.5033	0.340058
$955$	43.6648	1.41296
$956$	13.3031	0.430251
$957$	3.49037	0.112828
$958$	−11.9851	−0.387220
$959$	−5.52150	−0.178299
$960$	7.80109	0.251779
$961$	45.0549	1.45339
$962$	26.1742	0.843890
$963$	2.70670	0.0872223
$964$	−12.4927	−0.402364
$965$	−26.5204	−0.853721
$966$	0.882950	0.0284085
$967$	−17.2575	−0.554965	−0.277482	−	0.960731i	$-0.589500\pi$
$967$	−17.2575	−0.554965	−0.277482	+	0.960731i	$0.589500\pi$
$968$	−10.9171	−0.350888
$969$	−2.87481	−0.0923523
$970$	56.9156	1.82745
$971$	10.7543	0.345123	0.172562	−	0.984999i	$-0.444796\pi$
$971$	10.7543	0.345123	0.172562	+	0.984999i	$0.444796\pi$
$972$	−11.6584	−0.373942
$973$	16.9769	0.544254
$974$	31.2805	1.00229
$975$	−58.4368	−1.87148
$976$	−2.70503	−0.0865860
$977$	−22.1613	−0.709001	−0.354501	−	0.935056i	$-0.615349\pi$
$977$	−22.1613	−0.709001	−0.354501	+	0.935056i	$0.615349\pi$
$978$	42.8850	1.37131
$979$	−0.488660	−0.0156176
$980$	−23.8982	−0.763399
$981$	−16.0138	−0.511281
$982$	34.1995	1.09135
$983$	−29.3674	−0.936674	−0.468337	−	0.883550i	$-0.655147\pi$
$983$	−29.3674	−0.936674	−0.468337	+	0.883550i	$0.655147\pi$
$984$	9.07541	0.289314
$985$	−93.5816	−2.98176
$986$	−1.38775	−0.0441950
$987$	−13.7612	−0.438023
$988$	17.9617	0.571439
$989$	0.0960690	0.00305482
$990$	−1.29974	−0.0413086
$991$	13.1777	0.418602	0.209301	−	0.977851i	$-0.432881\pi$
$991$	13.1777	0.418602	0.209301	+	0.977851i	$0.432881\pi$
$992$	8.72095	0.276890
$993$	10.1777	0.322979
$994$	3.67330	0.116510
$995$	5.09375	0.161483
$996$	20.1002	0.636898
$997$	−42.1437	−1.33471	−0.667353	−	0.744742i	$-0.732573\pi$
$997$	−42.1437	−1.33471	−0.667353	+	0.744742i	$0.732573\pi$
$998$	19.8989	0.629889
$999$	32.4978	1.02818

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1502.2.a.g.1.10	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1502.2.a.g.1.10	✓	16	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:	\( N \)	\(=\)	\( 1502 = 2 \cdot 751 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1502.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.04534 q^{3} +1.00000 q^{4} +3.81409 q^{5} +2.04534 q^{6} +0.856873 q^{7} +1.00000 q^{8} +1.18340 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.04534 q^{3} +1.00000 q^{4} +3.81409 q^{5} +2.04534 q^{6} +0.856873 q^{7} +1.00000 q^{8} +1.18340 q^{9} +3.81409 q^{10} -0.287962 q^{11} +2.04534 q^{12} -2.99256 q^{13} +0.856873 q^{14} +7.80109 q^{15} +1.00000 q^{16} +0.234175 q^{17} +1.18340 q^{18} -6.00213 q^{19} +3.81409 q^{20} +1.75259 q^{21} -0.287962 q^{22} +0.503796 q^{23} +2.04534 q^{24} +9.54725 q^{25} -2.99256 q^{26} -3.71555 q^{27} +0.856873 q^{28} -5.92614 q^{29} +7.80109 q^{30} +8.72095 q^{31} +1.00000 q^{32} -0.588979 q^{33} +0.234175 q^{34} +3.26819 q^{35} +1.18340 q^{36} -8.74641 q^{37} -6.00213 q^{38} -6.12080 q^{39} +3.81409 q^{40} +4.43713 q^{41} +1.75259 q^{42} +0.190690 q^{43} -0.287962 q^{44} +4.51360 q^{45} +0.503796 q^{46} -7.85188 q^{47} +2.04534 q^{48} -6.26577 q^{49} +9.54725 q^{50} +0.478966 q^{51} -2.99256 q^{52} +8.87554 q^{53} -3.71555 q^{54} -1.09831 q^{55} +0.856873 q^{56} -12.2764 q^{57} -5.92614 q^{58} -5.29486 q^{59} +7.80109 q^{60} -2.70503 q^{61} +8.72095 q^{62} +1.01403 q^{63} +1.00000 q^{64} -11.4139 q^{65} -0.588979 q^{66} +7.01908 q^{67} +0.234175 q^{68} +1.03043 q^{69} +3.26819 q^{70} +4.28687 q^{71} +1.18340 q^{72} -10.1158 q^{73} -8.74641 q^{74} +19.5273 q^{75} -6.00213 q^{76} -0.246747 q^{77} -6.12080 q^{78} -2.45995 q^{79} +3.81409 q^{80} -11.1498 q^{81} +4.43713 q^{82} +9.82731 q^{83} +1.75259 q^{84} +0.893162 q^{85} +0.190690 q^{86} -12.1210 q^{87} -0.287962 q^{88} +1.69696 q^{89} +4.51360 q^{90} -2.56425 q^{91} +0.503796 q^{92} +17.8373 q^{93} -7.85188 q^{94} -22.8926 q^{95} +2.04534 q^{96} +14.9225 q^{97} -6.26577 q^{98} -0.340775 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{2} + 13 q^{3} + 16 q^{4} + 4 q^{5} + 13 q^{6} + 7 q^{7} + 16 q^{8} + 21 q^{9}+O(q^{10}) \) 16 * q + 16 * q^2 + 13 * q^3 + 16 * q^4 + 4 * q^5 + 13 * q^6 + 7 * q^7 + 16 * q^8 + 21 * q^9	\( 16 q + 16 q^{2} + 13 q^{3} + 16 q^{4} + 4 q^{5} + 13 q^{6} + 7 q^{7} + 16 q^{8} + 21 q^{9} + 4 q^{10} + 4 q^{11} + 13 q^{12} + 17 q^{13} + 7 q^{14} + 8 q^{15} + 16 q^{16} - q^{17} + 21 q^{18} + 23 q^{19} + 4 q^{20} + 9 q^{21} + 4 q^{22} + 15 q^{23} + 13 q^{24} + 24 q^{25} + 17 q^{26} + 31 q^{27} + 7 q^{28} + 4 q^{29} + 8 q^{30} + 42 q^{31} + 16 q^{32} + 3 q^{33} - q^{34} - 13 q^{35} + 21 q^{36} + 31 q^{37} + 23 q^{38} - 2 q^{39} + 4 q^{40} - 9 q^{41} + 9 q^{42} + 13 q^{43} + 4 q^{44} - 2 q^{45} + 15 q^{46} + 18 q^{47} + 13 q^{48} - 9 q^{49} + 24 q^{50} - 2 q^{51} + 17 q^{52} - 14 q^{53} + 31 q^{54} - 2 q^{55} + 7 q^{56} - 18 q^{57} + 4 q^{58} + 4 q^{59} + 8 q^{60} + q^{61} + 42 q^{62} + 17 q^{63} + 16 q^{64} - 32 q^{65} + 3 q^{66} + 5 q^{67} - q^{68} + 6 q^{69} - 13 q^{70} + 9 q^{71} + 21 q^{72} + 28 q^{73} + 31 q^{74} + 16 q^{75} + 23 q^{76} - 30 q^{77} - 2 q^{78} + 10 q^{79} + 4 q^{80} + 12 q^{81} - 9 q^{82} + 3 q^{83} + 9 q^{84} - 7 q^{85} + 13 q^{86} - 22 q^{87} + 4 q^{88} - 17 q^{89} - 2 q^{90} + 12 q^{91} + 15 q^{92} - q^{93} + 18 q^{94} - 4 q^{95} + 13 q^{96} - 17 q^{97} - 9 q^{98} - 10 q^{99}+O(q^{100}) \) 16 * q + 16 * q^2 + 13 * q^3 + 16 * q^4 + 4 * q^5 + 13 * q^6 + 7 * q^7 + 16 * q^8 + 21 * q^9 + 4 * q^10 + 4 * q^11 + 13 * q^12 + 17 * q^13 + 7 * q^14 + 8 * q^15 + 16 * q^16 - q^17 + 21 * q^18 + 23 * q^19 + 4 * q^20 + 9 * q^21 + 4 * q^22 + 15 * q^23 + 13 * q^24 + 24 * q^25 + 17 * q^26 + 31 * q^27 + 7 * q^28 + 4 * q^29 + 8 * q^30 + 42 * q^31 + 16 * q^32 + 3 * q^33 - q^34 - 13 * q^35 + 21 * q^36 + 31 * q^37 + 23 * q^38 - 2 * q^39 + 4 * q^40 - 9 * q^41 + 9 * q^42 + 13 * q^43 + 4 * q^44 - 2 * q^45 + 15 * q^46 + 18 * q^47 + 13 * q^48 - 9 * q^49 + 24 * q^50 - 2 * q^51 + 17 * q^52 - 14 * q^53 + 31 * q^54 - 2 * q^55 + 7 * q^56 - 18 * q^57 + 4 * q^58 + 4 * q^59 + 8 * q^60 + q^61 + 42 * q^62 + 17 * q^63 + 16 * q^64 - 32 * q^65 + 3 * q^66 + 5 * q^67 - q^68 + 6 * q^69 - 13 * q^70 + 9 * q^71 + 21 * q^72 + 28 * q^73 + 31 * q^74 + 16 * q^75 + 23 * q^76 - 30 * q^77 - 2 * q^78 + 10 * q^79 + 4 * q^80 + 12 * q^81 - 9 * q^82 + 3 * q^83 + 9 * q^84 - 7 * q^85 + 13 * q^86 - 22 * q^87 + 4 * q^88 - 17 * q^89 - 2 * q^90 + 12 * q^91 + 15 * q^92 - q^93 + 18 * q^94 - 4 * q^95 + 13 * q^96 - 17 * q^97 - 9 * q^98 - 10 * q^99

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