LMFDB - Embedded newform 4030.2.a.i.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4030,2,Mod(1,4030)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4030, 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("4030.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4030 = 2 \cdot 5 \cdot 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4030.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:	$32.1797120146$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 3x^{6} - 8x^{5} + 24x^{4} + 18x^{3} - 48x^{2} - 9x + 4 $ x^7 - 3x^6 - 8x^5 + 24x^4 + 18x^3 - 48x^2 - 9x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.80718$ of defining polynomial
Character	$\chi$	$=$	4030.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.80718 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.80718 q^{6} -3.36542 q^{7} -1.00000 q^{8} +0.265910 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.80718 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.80718 q^{6} -3.36542 q^{7} -1.00000 q^{8} +0.265910 q^{9} +1.00000 q^{10} -2.02178 q^{11} -1.80718 q^{12} -1.00000 q^{13} +3.36542 q^{14} +1.80718 q^{15} +1.00000 q^{16} +2.23160 q^{17} -0.265910 q^{18} -5.56078 q^{19} -1.00000 q^{20} +6.08193 q^{21} +2.02178 q^{22} +8.30642 q^{23} +1.80718 q^{24} +1.00000 q^{25} +1.00000 q^{26} +4.94100 q^{27} -3.36542 q^{28} +0.369356 q^{29} -1.80718 q^{30} -1.00000 q^{31} -1.00000 q^{32} +3.65372 q^{33} -2.23160 q^{34} +3.36542 q^{35} +0.265910 q^{36} +3.78229 q^{37} +5.56078 q^{38} +1.80718 q^{39} +1.00000 q^{40} -0.244950 q^{41} -6.08193 q^{42} +6.47052 q^{43} -2.02178 q^{44} -0.265910 q^{45} -8.30642 q^{46} +8.05247 q^{47} -1.80718 q^{48} +4.32606 q^{49} -1.00000 q^{50} -4.03292 q^{51} -1.00000 q^{52} -10.8620 q^{53} -4.94100 q^{54} +2.02178 q^{55} +3.36542 q^{56} +10.0494 q^{57} -0.369356 q^{58} +12.1826 q^{59} +1.80718 q^{60} -5.85311 q^{61} +1.00000 q^{62} -0.894899 q^{63} +1.00000 q^{64} +1.00000 q^{65} -3.65372 q^{66} +15.6668 q^{67} +2.23160 q^{68} -15.0112 q^{69} -3.36542 q^{70} -10.7952 q^{71} -0.265910 q^{72} +2.09951 q^{73} -3.78229 q^{74} -1.80718 q^{75} -5.56078 q^{76} +6.80414 q^{77} -1.80718 q^{78} +2.60644 q^{79} -1.00000 q^{80} -9.72702 q^{81} +0.244950 q^{82} -5.51556 q^{83} +6.08193 q^{84} -2.23160 q^{85} -6.47052 q^{86} -0.667494 q^{87} +2.02178 q^{88} -10.2794 q^{89} +0.265910 q^{90} +3.36542 q^{91} +8.30642 q^{92} +1.80718 q^{93} -8.05247 q^{94} +5.56078 q^{95} +1.80718 q^{96} -15.5452 q^{97} -4.32606 q^{98} -0.537611 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 7 q^{2} + 3 q^{3} + 7 q^{4} - 7 q^{5} - 3 q^{6} + 2 q^{7} - 7 q^{8} + 4 q^{9}+O(q^{10}) $ 7 * q - 7 * q^2 + 3 * q^3 + 7 * q^4 - 7 * q^5 - 3 * q^6 + 2 * q^7 - 7 * q^8 + 4 * q^9	$ 7 q - 7 q^{2} + 3 q^{3} + 7 q^{4} - 7 q^{5} - 3 q^{6} + 2 q^{7} - 7 q^{8} + 4 q^{9} + 7 q^{10} - 6 q^{11} + 3 q^{12} - 7 q^{13} - 2 q^{14} - 3 q^{15} + 7 q^{16} - 4 q^{18} - 9 q^{19} - 7 q^{20} + q^{21} + 6 q^{22} + 7 q^{23} - 3 q^{24} + 7 q^{25} + 7 q^{26} + 9 q^{27} + 2 q^{28} - 4 q^{29} + 3 q^{30} - 7 q^{31} - 7 q^{32} - 2 q^{35} + 4 q^{36} + 2 q^{37} + 9 q^{38} - 3 q^{39} + 7 q^{40} - 14 q^{41} - q^{42} + 9 q^{43} - 6 q^{44} - 4 q^{45} - 7 q^{46} - 8 q^{47} + 3 q^{48} - q^{49} - 7 q^{50} - 7 q^{51} - 7 q^{52} - 6 q^{53} - 9 q^{54} + 6 q^{55} - 2 q^{56} - 11 q^{57} + 4 q^{58} - 15 q^{59} - 3 q^{60} + q^{61} + 7 q^{62} - 17 q^{63} + 7 q^{64} + 7 q^{65} + 14 q^{67} - 14 q^{69} + 2 q^{70} - 16 q^{71} - 4 q^{72} - 13 q^{73} - 2 q^{74} + 3 q^{75} - 9 q^{76} - 5 q^{77} + 3 q^{78} - 14 q^{79} - 7 q^{80} - 25 q^{81} + 14 q^{82} - 10 q^{83} + q^{84} - 9 q^{86} - 9 q^{87} + 6 q^{88} - 26 q^{89} + 4 q^{90} - 2 q^{91} + 7 q^{92} - 3 q^{93} + 8 q^{94} + 9 q^{95} - 3 q^{96} - 5 q^{97} + q^{98} - 37 q^{99}+O(q^{100}) $ 7 * q - 7 * q^2 + 3 * q^3 + 7 * q^4 - 7 * q^5 - 3 * q^6 + 2 * q^7 - 7 * q^8 + 4 * q^9 + 7 * q^10 - 6 * q^11 + 3 * q^12 - 7 * q^13 - 2 * q^14 - 3 * q^15 + 7 * q^16 - 4 * q^18 - 9 * q^19 - 7 * q^20 + q^21 + 6 * q^22 + 7 * q^23 - 3 * q^24 + 7 * q^25 + 7 * q^26 + 9 * q^27 + 2 * q^28 - 4 * q^29 + 3 * q^30 - 7 * q^31 - 7 * q^32 - 2 * q^35 + 4 * q^36 + 2 * q^37 + 9 * q^38 - 3 * q^39 + 7 * q^40 - 14 * q^41 - q^42 + 9 * q^43 - 6 * q^44 - 4 * q^45 - 7 * q^46 - 8 * q^47 + 3 * q^48 - q^49 - 7 * q^50 - 7 * q^51 - 7 * q^52 - 6 * q^53 - 9 * q^54 + 6 * q^55 - 2 * q^56 - 11 * q^57 + 4 * q^58 - 15 * q^59 - 3 * q^60 + q^61 + 7 * q^62 - 17 * q^63 + 7 * q^64 + 7 * q^65 + 14 * q^67 - 14 * q^69 + 2 * q^70 - 16 * q^71 - 4 * q^72 - 13 * q^73 - 2 * q^74 + 3 * q^75 - 9 * q^76 - 5 * q^77 + 3 * q^78 - 14 * q^79 - 7 * q^80 - 25 * q^81 + 14 * q^82 - 10 * q^83 + q^84 - 9 * q^86 - 9 * q^87 + 6 * q^88 - 26 * q^89 + 4 * q^90 - 2 * q^91 + 7 * q^92 - 3 * q^93 + 8 * q^94 + 9 * q^95 - 3 * q^96 - 5 * q^97 + q^98 - 37 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.80718	−1.04338	−0.521689	−	0.853136i	$-0.674698\pi$
$3$	−1.80718	−1.04338	−0.521689	+	0.853136i	$0.674698\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.80718	0.737779
$7$	−3.36542	−1.27201	−0.636005	−	0.771685i	$-0.719414\pi$
$7$	−3.36542	−1.27201	−0.636005	+	0.771685i	$0.719414\pi$
$8$	−1.00000	−0.353553
$9$	0.265910	0.0886366
$10$	1.00000	0.316228
$11$	−2.02178	−0.609589	−0.304795	−	0.952418i	$-0.598588\pi$
$11$	−2.02178	−0.609589	−0.304795	+	0.952418i	$0.598588\pi$
$12$	−1.80718	−0.521689
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	3.36542	0.899447
$15$	1.80718	0.466613
$16$	1.00000	0.250000
$17$	2.23160	0.541243	0.270622	−	0.962686i	$-0.412771\pi$
$17$	2.23160	0.541243	0.270622	+	0.962686i	$0.412771\pi$
$18$	−0.265910	−0.0626756
$19$	−5.56078	−1.27573	−0.637866	−	0.770148i	$-0.720182\pi$
$19$	−5.56078	−1.27573	−0.637866	+	0.770148i	$0.720182\pi$
$20$	−1.00000	−0.223607
$21$	6.08193	1.32719
$22$	2.02178	0.431045
$23$	8.30642	1.73201	0.866004	−	0.500036i	$-0.166680\pi$
$23$	8.30642	1.73201	0.866004	+	0.500036i	$0.166680\pi$
$24$	1.80718	0.368890
$25$	1.00000	0.200000
$26$	1.00000	0.196116
$27$	4.94100	0.950896
$28$	−3.36542	−0.636005
$29$	0.369356	0.0685877	0.0342939	−	0.999412i	$-0.489082\pi$
$29$	0.369356	0.0685877	0.0342939	+	0.999412i	$0.489082\pi$
$30$	−1.80718	−0.329945
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	−1.00000	−0.176777
$33$	3.65372	0.636032
$34$	−2.23160	−0.382717
$35$	3.36542	0.568860
$36$	0.265910	0.0443183
$37$	3.78229	0.621804	0.310902	−	0.950442i	$-0.399369\pi$
$37$	3.78229	0.621804	0.310902	+	0.950442i	$0.399369\pi$
$38$	5.56078	0.902078
$39$	1.80718	0.289381
$40$	1.00000	0.158114
$41$	−0.244950	−0.0382547	−0.0191273	−	0.999817i	$-0.506089\pi$
$41$	−0.244950	−0.0382547	−0.0191273	+	0.999817i	$0.506089\pi$
$42$	−6.08193	−0.938463
$43$	6.47052	0.986745	0.493373	−	0.869818i	$-0.335764\pi$
$43$	6.47052	0.986745	0.493373	+	0.869818i	$0.335764\pi$
$44$	−2.02178	−0.304795
$45$	−0.265910	−0.0396395
$46$	−8.30642	−1.22472
$47$	8.05247	1.17457	0.587287	−	0.809379i	$-0.300196\pi$
$47$	8.05247	1.17457	0.587287	+	0.809379i	$0.300196\pi$
$48$	−1.80718	−0.260844
$49$	4.32606	0.618009
$50$	−1.00000	−0.141421
$51$	−4.03292	−0.564721
$52$	−1.00000	−0.138675
$53$	−10.8620	−1.49200	−0.746002	−	0.665944i	$-0.768029\pi$
$53$	−10.8620	−1.49200	−0.746002	+	0.665944i	$0.768029\pi$
$54$	−4.94100	−0.672385
$55$	2.02178	0.272617
$56$	3.36542	0.449723
$57$	10.0494	1.33107
$58$	−0.369356	−0.0484989
$59$	12.1826	1.58603	0.793017	−	0.609199i	$-0.208509\pi$
$59$	12.1826	1.58603	0.793017	+	0.609199i	$0.208509\pi$
$60$	1.80718	0.233306
$61$	−5.85311	−0.749414	−0.374707	−	0.927143i	$-0.622257\pi$
$61$	−5.85311	−0.749414	−0.374707	+	0.927143i	$0.622257\pi$
$62$	1.00000	0.127000
$63$	−0.894899	−0.112747
$64$	1.00000	0.125000
$65$	1.00000	0.124035
$66$	−3.65372	−0.449742
$67$	15.6668	1.91401	0.957004	−	0.290074i	$-0.0936799\pi$
$67$	15.6668	1.91401	0.957004	+	0.290074i	$0.0936799\pi$
$68$	2.23160	0.270622
$69$	−15.0112	−1.80714
$70$	−3.36542	−0.402245
$71$	−10.7952	−1.28115	−0.640574	−	0.767896i	$-0.721304\pi$
$71$	−10.7952	−1.28115	−0.640574	+	0.767896i	$0.721304\pi$
$72$	−0.265910	−0.0313378
$73$	2.09951	0.245729	0.122865	−	0.992423i	$-0.460792\pi$
$73$	2.09951	0.245729	0.122865	+	0.992423i	$0.460792\pi$
$74$	−3.78229	−0.439682
$75$	−1.80718	−0.208676
$76$	−5.56078	−0.637866
$77$	6.80414	0.775404
$78$	−1.80718	−0.204623
$79$	2.60644	0.293247	0.146624	−	0.989192i	$-0.453159\pi$
$79$	2.60644	0.293247	0.146624	+	0.989192i	$0.453159\pi$
$80$	−1.00000	−0.111803
$81$	−9.72702	−1.08078
$82$	0.244950	0.0270502
$83$	−5.51556	−0.605411	−0.302706	−	0.953084i	$-0.597890\pi$
$83$	−5.51556	−0.605411	−0.302706	+	0.953084i	$0.597890\pi$
$84$	6.08193	0.663593
$85$	−2.23160	−0.242051
$86$	−6.47052	−0.697734
$87$	−0.667494	−0.0715629
$88$	2.02178	0.215522
$89$	−10.2794	−1.08961	−0.544807	−	0.838562i	$-0.683397\pi$
$89$	−10.2794	−1.08961	−0.544807	+	0.838562i	$0.683397\pi$
$90$	0.265910	0.0280294
$91$	3.36542	0.352792
$92$	8.30642	0.866004
$93$	1.80718	0.187396
$94$	−8.05247	−0.830549
$95$	5.56078	0.570524
$96$	1.80718	0.184445
$97$	−15.5452	−1.57838	−0.789190	−	0.614150i	$-0.789499\pi$
$97$	−15.5452	−1.57838	−0.789190	+	0.614150i	$0.789499\pi$
$98$	−4.32606	−0.436998
$99$	−0.537611	−0.0540319
$100$	1.00000	0.100000
$101$	18.4703	1.83786	0.918931	−	0.394418i	$-0.129054\pi$
$101$	18.4703	1.83786	0.918931	+	0.394418i	$0.129054\pi$
$102$	4.03292	0.399318
$103$	−3.98185	−0.392343	−0.196172	−	0.980570i	$-0.562851\pi$
$103$	−3.98185	−0.392343	−0.196172	+	0.980570i	$0.562851\pi$
$104$	1.00000	0.0980581
$105$	−6.08193	−0.593536
$106$	10.8620	1.05501
$107$	2.44563	0.236428	0.118214	−	0.992988i	$-0.462283\pi$
$107$	2.44563	0.236428	0.118214	+	0.992988i	$0.462283\pi$
$108$	4.94100	0.475448
$109$	−12.2395	−1.17233	−0.586164	−	0.810192i	$-0.699363\pi$
$109$	−12.2395	−1.17233	−0.586164	+	0.810192i	$0.699363\pi$
$110$	−2.02178	−0.192769
$111$	−6.83529	−0.648777
$112$	−3.36542	−0.318002
$113$	8.38581	0.788871	0.394435	−	0.918924i	$-0.370940\pi$
$113$	8.38581	0.788871	0.394435	+	0.918924i	$0.370940\pi$
$114$	−10.0494	−0.941208
$115$	−8.30642	−0.774578
$116$	0.369356	0.0342939
$117$	−0.265910	−0.0245834
$118$	−12.1826	−1.12150
$119$	−7.51029	−0.688467
$120$	−1.80718	−0.164972
$121$	−6.91241	−0.628401
$122$	5.85311	0.529916
$123$	0.442669	0.0399141
$124$	−1.00000	−0.0898027
$125$	−1.00000	−0.0894427
$126$	0.894899	0.0797239
$127$	17.7093	1.57145	0.785724	−	0.618577i	$-0.212290\pi$
$127$	17.7093	1.57145	0.785724	+	0.618577i	$0.212290\pi$
$128$	−1.00000	−0.0883883
$129$	−11.6934	−1.02955
$130$	−1.00000	−0.0877058
$131$	−4.86878	−0.425387	−0.212694	−	0.977119i	$-0.568224\pi$
$131$	−4.86878	−0.425387	−0.212694	+	0.977119i	$0.568224\pi$
$132$	3.65372	0.318016
$133$	18.7144	1.62274
$134$	−15.6668	−1.35341
$135$	−4.94100	−0.425254
$136$	−2.23160	−0.191358
$137$	−13.8923	−1.18690	−0.593450	−	0.804871i	$-0.702234\pi$
$137$	−13.8923	−1.18690	−0.593450	+	0.804871i	$0.702234\pi$
$138$	15.0112	1.27784
$139$	16.6972	1.41623	0.708117	−	0.706095i	$-0.249545\pi$
$139$	16.6972	1.41623	0.708117	+	0.706095i	$0.249545\pi$
$140$	3.36542	0.284430
$141$	−14.5523	−1.22552
$142$	10.7952	0.905909
$143$	2.02178	0.169070
$144$	0.265910	0.0221592
$145$	−0.369356	−0.0306734
$146$	−2.09951	−0.173757
$147$	−7.81799	−0.644817
$148$	3.78229	0.310902
$149$	6.48257	0.531073	0.265536	−	0.964101i	$-0.414451\pi$
$149$	6.48257	0.531073	0.265536	+	0.964101i	$0.414451\pi$
$150$	1.80718	0.147556
$151$	−8.47323	−0.689541	−0.344771	−	0.938687i	$-0.612043\pi$
$151$	−8.47323	−0.689541	−0.344771	+	0.938687i	$0.612043\pi$
$152$	5.56078	0.451039
$153$	0.593405	0.0479740
$154$	−6.80414	−0.548293
$155$	1.00000	0.0803219
$156$	1.80718	0.144690
$157$	−2.40897	−0.192257	−0.0961285	−	0.995369i	$-0.530646\pi$
$157$	−2.40897	−0.192257	−0.0961285	+	0.995369i	$0.530646\pi$
$158$	−2.60644	−0.207357
$159$	19.6295	1.55672
$160$	1.00000	0.0790569
$161$	−27.9546	−2.20313
$162$	9.72702	0.764227
$163$	17.2947	1.35463	0.677315	−	0.735694i	$-0.263144\pi$
$163$	17.2947	1.35463	0.677315	+	0.735694i	$0.263144\pi$
$164$	−0.244950	−0.0191273
$165$	−3.65372	−0.284442
$166$	5.51556	0.428090
$167$	6.54091	0.506151	0.253075	−	0.967447i	$-0.418558\pi$
$167$	6.54091	0.506151	0.253075	+	0.967447i	$0.418558\pi$
$168$	−6.08193	−0.469231
$169$	1.00000	0.0769231
$170$	2.23160	0.171156
$171$	−1.47867	−0.113077
$172$	6.47052	0.493373
$173$	7.81780	0.594377	0.297188	−	0.954819i	$-0.403951\pi$
$173$	7.81780	0.594377	0.297188	+	0.954819i	$0.403951\pi$
$174$	0.667494	0.0506026
$175$	−3.36542	−0.254402
$176$	−2.02178	−0.152397
$177$	−22.0161	−1.65483
$178$	10.2794	0.770473
$179$	−21.9456	−1.64029	−0.820147	−	0.572152i	$-0.806109\pi$
$179$	−21.9456	−1.64029	−0.820147	+	0.572152i	$0.806109\pi$
$180$	−0.265910	−0.0198198
$181$	17.8646	1.32786	0.663931	−	0.747794i	$-0.268887\pi$
$181$	17.8646	1.32786	0.663931	+	0.747794i	$0.268887\pi$
$182$	−3.36542	−0.249462
$183$	10.5776	0.781922
$184$	−8.30642	−0.612358
$185$	−3.78229	−0.278079
$186$	−1.80718	−0.132509
$187$	−4.51181	−0.329936
$188$	8.05247	0.587287
$189$	−16.6286	−1.20955
$190$	−5.56078	−0.403422
$191$	18.3221	1.32574	0.662870	−	0.748734i	$-0.269338\pi$
$191$	18.3221	1.32574	0.662870	+	0.748734i	$0.269338\pi$
$192$	−1.80718	−0.130422
$193$	−22.4881	−1.61873	−0.809363	−	0.587309i	$-0.800187\pi$
$193$	−22.4881	−1.61873	−0.809363	+	0.587309i	$0.800187\pi$
$194$	15.5452	1.11608
$195$	−1.80718	−0.129415
$196$	4.32606	0.309005
$197$	−14.9499	−1.06514	−0.532569	−	0.846386i	$-0.678773\pi$
$197$	−14.9499	−1.06514	−0.532569	+	0.846386i	$0.678773\pi$
$198$	0.537611	0.0382063
$199$	5.40305	0.383012	0.191506	−	0.981491i	$-0.438663\pi$
$199$	5.40305	0.383012	0.191506	+	0.981491i	$0.438663\pi$
$200$	−1.00000	−0.0707107
$201$	−28.3128	−1.99703
$202$	−18.4703	−1.29956
$203$	−1.24304	−0.0872443
$204$	−4.03292	−0.282361
$205$	0.244950	0.0171080
$206$	3.98185	0.277429
$207$	2.20876	0.153519
$208$	−1.00000	−0.0693375
$209$	11.2427	0.777672
$210$	6.08193	0.419693
$211$	−11.0354	−0.759708	−0.379854	−	0.925046i	$-0.624026\pi$
$211$	−11.0354	−0.759708	−0.379854	+	0.925046i	$0.624026\pi$
$212$	−10.8620	−0.746002
$213$	19.5088	1.33672
$214$	−2.44563	−0.167180
$215$	−6.47052	−0.441286
$216$	−4.94100	−0.336193
$217$	3.36542	0.228460
$218$	12.2395	0.828961
$219$	−3.79420	−0.256388
$220$	2.02178	0.136308
$221$	−2.23160	−0.150114
$222$	6.83529	0.458754
$223$	−7.43159	−0.497656	−0.248828	−	0.968548i	$-0.580045\pi$
$223$	−7.43159	−0.497656	−0.248828	+	0.968548i	$0.580045\pi$
$224$	3.36542	0.224862
$225$	0.265910	0.0177273
$226$	−8.38581	−0.557816
$227$	21.8537	1.45048	0.725241	−	0.688496i	$-0.241729\pi$
$227$	21.8537	1.45048	0.725241	+	0.688496i	$0.241729\pi$
$228$	10.0494	0.665535
$229$	14.0253	0.926821	0.463410	−	0.886144i	$-0.346626\pi$
$229$	14.0253	0.926821	0.463410	+	0.886144i	$0.346626\pi$
$230$	8.30642	0.547709
$231$	−12.2963	−0.809039
$232$	−0.369356	−0.0242494
$233$	−27.0340	−1.77106	−0.885528	−	0.464587i	$-0.846203\pi$
$233$	−27.0340	−1.77106	−0.885528	+	0.464587i	$0.846203\pi$
$234$	0.265910	0.0173831
$235$	−8.05247	−0.525285
$236$	12.1826	0.793017
$237$	−4.71031	−0.305967
$238$	7.51029	0.486820
$239$	−30.5325	−1.97498	−0.987491	−	0.157678i	$-0.949599\pi$
$239$	−30.5325	−1.97498	−0.987491	+	0.157678i	$0.949599\pi$
$240$	1.80718	0.116653
$241$	19.8457	1.27838	0.639188	−	0.769050i	$-0.279271\pi$
$241$	19.8457	1.27838	0.639188	+	0.769050i	$0.279271\pi$
$242$	6.91241	0.444347
$243$	2.75550	0.176766
$244$	−5.85311	−0.374707
$245$	−4.32606	−0.276382
$246$	−0.442669	−0.0282235
$247$	5.56078	0.353824
$248$	1.00000	0.0635001
$249$	9.96762	0.631673
$250$	1.00000	0.0632456
$251$	−13.0217	−0.821921	−0.410960	−	0.911653i	$-0.634807\pi$
$251$	−13.0217	−0.821921	−0.410960	+	0.911653i	$0.634807\pi$
$252$	−0.894899	−0.0563733
$253$	−16.7937	−1.05581
$254$	−17.7093	−1.11118
$255$	4.03292	0.252551
$256$	1.00000	0.0625000
$257$	20.7648	1.29527	0.647636	−	0.761950i	$-0.275758\pi$
$257$	20.7648	1.29527	0.647636	+	0.761950i	$0.275758\pi$
$258$	11.6934	0.728000
$259$	−12.7290	−0.790941
$260$	1.00000	0.0620174
$261$	0.0982155	0.00607939
$262$	4.86878	0.300794
$263$	−15.4310	−0.951518	−0.475759	−	0.879576i	$-0.657827\pi$
$263$	−15.4310	−0.951518	−0.475759	+	0.879576i	$0.657827\pi$
$264$	−3.65372	−0.224871
$265$	10.8620	0.667244
$266$	−18.7144	−1.14745
$267$	18.5767	1.13688
$268$	15.6668	0.957004
$269$	−0.581098	−0.0354302	−0.0177151	−	0.999843i	$-0.505639\pi$
$269$	−0.581098	−0.0354302	−0.0177151	+	0.999843i	$0.505639\pi$
$270$	4.94100	0.300700
$271$	−1.72460	−0.104762	−0.0523810	−	0.998627i	$-0.516681\pi$
$271$	−1.72460	−0.104762	−0.0523810	+	0.998627i	$0.516681\pi$
$272$	2.23160	0.135311
$273$	−6.08193	−0.368095
$274$	13.8923	0.839265
$275$	−2.02178	−0.121918
$276$	−15.0112	−0.903570
$277$	−6.01833	−0.361606	−0.180803	−	0.983519i	$-0.557870\pi$
$277$	−6.01833	−0.361606	−0.180803	+	0.983519i	$0.557870\pi$
$278$	−16.6972	−1.00143
$279$	−0.265910	−0.0159196
$280$	−3.36542	−0.201122
$281$	−5.33991	−0.318552	−0.159276	−	0.987234i	$-0.550916\pi$
$281$	−5.33991	−0.318552	−0.159276	+	0.987234i	$0.550916\pi$
$282$	14.5523	0.866576
$283$	8.01104	0.476207	0.238104	−	0.971240i	$-0.423474\pi$
$283$	8.01104	0.476207	0.238104	+	0.971240i	$0.423474\pi$
$284$	−10.7952	−0.640574
$285$	−10.0494	−0.595272
$286$	−2.02178	−0.119550
$287$	0.824359	0.0486604
$288$	−0.265910	−0.0156689
$289$	−12.0199	−0.707056
$290$	0.369356	0.0216893
$291$	28.0931	1.64685
$292$	2.09951	0.122865
$293$	3.33386	0.194766	0.0973830	−	0.995247i	$-0.468953\pi$
$293$	3.33386	0.194766	0.0973830	+	0.995247i	$0.468953\pi$
$294$	7.81799	0.455954
$295$	−12.1826	−0.709296
$296$	−3.78229	−0.219841
$297$	−9.98961	−0.579656
$298$	−6.48257	−0.375525
$299$	−8.30642	−0.480373
$300$	−1.80718	−0.104338
$301$	−21.7760	−1.25515
$302$	8.47323	0.487579
$303$	−33.3792	−1.91758
$304$	−5.56078	−0.318933
$305$	5.85311	0.335148
$306$	−0.593405	−0.0339227
$307$	15.6555	0.893508	0.446754	−	0.894657i	$-0.352580\pi$
$307$	15.6555	0.893508	0.446754	+	0.894657i	$0.352580\pi$
$308$	6.80414	0.387702
$309$	7.19593	0.409362
$310$	−1.00000	−0.0567962
$311$	−26.4898	−1.50210	−0.751049	−	0.660246i	$-0.770452\pi$
$311$	−26.4898	−1.50210	−0.751049	+	0.660246i	$0.770452\pi$
$312$	−1.80718	−0.102312
$313$	−15.4214	−0.871671	−0.435836	−	0.900026i	$-0.643547\pi$
$313$	−15.4214	−0.871671	−0.435836	+	0.900026i	$0.643547\pi$
$314$	2.40897	0.135946
$315$	0.894899	0.0504218
$316$	2.60644	0.146624
$317$	−22.3806	−1.25702	−0.628510	−	0.777801i	$-0.716335\pi$
$317$	−22.3806	−1.25702	−0.628510	+	0.777801i	$0.716335\pi$
$318$	−19.6295	−1.10077
$319$	−0.746757	−0.0418103
$320$	−1.00000	−0.0559017
$321$	−4.41970	−0.246683
$322$	27.9546	1.55785
$323$	−12.4095	−0.690481
$324$	−9.72702	−0.540390
$325$	−1.00000	−0.0554700
$326$	−17.2947	−0.957867
$327$	22.1190	1.22318
$328$	0.244950	0.0135251
$329$	−27.1000	−1.49407
$330$	3.65372	0.201131
$331$	−1.09311	−0.0600826	−0.0300413	−	0.999549i	$-0.509564\pi$
$331$	−1.09311	−0.0600826	−0.0300413	+	0.999549i	$0.509564\pi$
$332$	−5.51556	−0.302706
$333$	1.00575	0.0551146
$334$	−6.54091	−0.357902
$335$	−15.6668	−0.855971
$336$	6.08193	0.331797
$337$	21.5186	1.17219	0.586097	−	0.810241i	$-0.300664\pi$
$337$	21.5186	1.17219	0.586097	+	0.810241i	$0.300664\pi$
$338$	−1.00000	−0.0543928
$339$	−15.1547	−0.823090
$340$	−2.23160	−0.121026
$341$	2.02178	0.109485
$342$	1.47867	0.0799572
$343$	8.99892	0.485896
$344$	−6.47052	−0.348867
$345$	15.0112	0.808177
$346$	−7.81780	−0.420288
$347$	−18.2339	−0.978849	−0.489424	−	0.872046i	$-0.662793\pi$
$347$	−18.2339	−0.978849	−0.489424	+	0.872046i	$0.662793\pi$
$348$	−0.667494	−0.0357815
$349$	25.5217	1.36614	0.683072	−	0.730351i	$-0.260643\pi$
$349$	25.5217	1.36614	0.683072	+	0.730351i	$0.260643\pi$
$350$	3.36542	0.179889
$351$	−4.94100	−0.263731
$352$	2.02178	0.107761
$353$	−22.5893	−1.20230	−0.601152	−	0.799134i	$-0.705291\pi$
$353$	−22.5893	−1.20230	−0.601152	+	0.799134i	$0.705291\pi$
$354$	22.0161	1.17014
$355$	10.7952	0.572947
$356$	−10.2794	−0.544807
$357$	13.5725	0.718331
$358$	21.9456	1.15986
$359$	−35.1780	−1.85662	−0.928311	−	0.371804i	$-0.878739\pi$
$359$	−35.1780	−1.85662	−0.928311	+	0.371804i	$0.878739\pi$
$360$	0.265910	0.0140147
$361$	11.9223	0.627490
$362$	−17.8646	−0.938940
$363$	12.4920	0.655659
$364$	3.36542	0.176396
$365$	−2.09951	−0.109893
$366$	−10.5776	−0.552902
$367$	8.43783	0.440451	0.220225	−	0.975449i	$-0.429321\pi$
$367$	8.43783	0.440451	0.220225	+	0.975449i	$0.429321\pi$
$368$	8.30642	0.433002
$369$	−0.0651345	−0.00339077
$370$	3.78229	0.196632
$371$	36.5551	1.89784
$372$	1.80718	0.0936981
$373$	26.4828	1.37123	0.685614	−	0.727965i	$-0.259534\pi$
$373$	26.4828	1.37123	0.685614	+	0.727965i	$0.259534\pi$
$374$	4.51181	0.233300
$375$	1.80718	0.0933225
$376$	−8.05247	−0.415274
$377$	−0.369356	−0.0190228
$378$	16.6286	0.855280
$379$	2.87288	0.147570	0.0737851	−	0.997274i	$-0.476492\pi$
$379$	2.87288	0.147570	0.0737851	+	0.997274i	$0.476492\pi$
$380$	5.56078	0.285262
$381$	−32.0040	−1.63961
$382$	−18.3221	−0.937440
$383$	−21.5537	−1.10134	−0.550670	−	0.834723i	$-0.685628\pi$
$383$	−21.5537	−1.10134	−0.550670	+	0.834723i	$0.685628\pi$
$384$	1.80718	0.0922224
$385$	−6.80414	−0.346771
$386$	22.4881	1.14461
$387$	1.72058	0.0874618
$388$	−15.5452	−0.789190
$389$	−26.2029	−1.32854	−0.664269	−	0.747494i	$-0.731257\pi$
$389$	−26.2029	−1.32854	−0.664269	+	0.747494i	$0.731257\pi$
$390$	1.80718	0.0915103
$391$	18.5366	0.937438
$392$	−4.32606	−0.218499
$393$	8.79878	0.443840
$394$	14.9499	0.753167
$395$	−2.60644	−0.131144
$396$	−0.537611	−0.0270160
$397$	−28.9441	−1.45266	−0.726332	−	0.687344i	$-0.758777\pi$
$397$	−28.9441	−1.45266	−0.726332	+	0.687344i	$0.758777\pi$
$398$	−5.40305	−0.270830
$399$	−33.8203	−1.69313
$400$	1.00000	0.0500000
$401$	22.5877	1.12798	0.563989	−	0.825782i	$-0.309266\pi$
$401$	22.5877	1.12798	0.563989	+	0.825782i	$0.309266\pi$
$402$	28.3128	1.41212
$403$	1.00000	0.0498135
$404$	18.4703	0.918931
$405$	9.72702	0.483340
$406$	1.24304	0.0616910
$407$	−7.64695	−0.379045
$408$	4.03292	0.199659
$409$	5.89672	0.291574	0.145787	−	0.989316i	$-0.453429\pi$
$409$	5.89672	0.291574	0.145787	+	0.989316i	$0.453429\pi$
$410$	−0.244950	−0.0120972
$411$	25.1059	1.23838
$412$	−3.98185	−0.196172
$413$	−40.9995	−2.01745
$414$	−2.20876	−0.108555
$415$	5.51556	0.270748
$416$	1.00000	0.0490290
$417$	−30.1748	−1.47767
$418$	−11.2427	−0.549897
$419$	20.3831	0.995780	0.497890	−	0.867240i	$-0.334108\pi$
$419$	20.3831	0.995780	0.497890	+	0.867240i	$0.334108\pi$
$420$	−6.08193	−0.296768
$421$	1.44447	0.0703993	0.0351996	−	0.999380i	$-0.488793\pi$
$421$	1.44447	0.0703993	0.0351996	+	0.999380i	$0.488793\pi$
$422$	11.0354	0.537195
$423$	2.14123	0.104110
$424$	10.8620	0.527503
$425$	2.23160	0.108249
$426$	−19.5088	−0.945205
$427$	19.6982	0.953262
$428$	2.44563	0.118214
$429$	−3.65372	−0.176403
$430$	6.47052	0.312036
$431$	16.2471	0.782596	0.391298	−	0.920264i	$-0.372026\pi$
$431$	16.2471	0.782596	0.391298	+	0.920264i	$0.372026\pi$
$432$	4.94100	0.237724
$433$	−39.5362	−1.89999	−0.949994	−	0.312267i	$-0.898912\pi$
$433$	−39.5362	−1.89999	−0.949994	+	0.312267i	$0.898912\pi$
$434$	−3.36542	−0.161545
$435$	0.667494	0.0320039
$436$	−12.2395	−0.586164
$437$	−46.1902	−2.20958
$438$	3.79420	0.181294
$439$	16.3272	0.779255	0.389627	−	0.920973i	$-0.372604\pi$
$439$	16.3272	0.779255	0.389627	+	0.920973i	$0.372604\pi$
$440$	−2.02178	−0.0963845
$441$	1.15034	0.0547782
$442$	2.23160	0.106147
$443$	−21.9067	−1.04082	−0.520410	−	0.853917i	$-0.674221\pi$
$443$	−21.9067	−1.04082	−0.520410	+	0.853917i	$0.674221\pi$
$444$	−6.83529	−0.324388
$445$	10.2794	0.487290
$446$	7.43159	0.351896
$447$	−11.7152	−0.554110
$448$	−3.36542	−0.159001
$449$	40.4002	1.90661	0.953303	−	0.302017i	$-0.0976599\pi$
$449$	40.4002	1.90661	0.953303	+	0.302017i	$0.0976599\pi$
$450$	−0.265910	−0.0125351
$451$	0.495234	0.0233197
$452$	8.38581	0.394435
$453$	15.3127	0.719452
$454$	−21.8537	−1.02564
$455$	−3.36542	−0.157773
$456$	−10.0494	−0.470604
$457$	−19.1008	−0.893499	−0.446749	−	0.894659i	$-0.647418\pi$
$457$	−19.1008	−0.893499	−0.446749	+	0.894659i	$0.647418\pi$
$458$	−14.0253	−0.655361
$459$	11.0264	0.514666
$460$	−8.30642	−0.387289
$461$	15.6154	0.727279	0.363640	−	0.931540i	$-0.381534\pi$
$461$	15.6154	0.727279	0.363640	+	0.931540i	$0.381534\pi$
$462$	12.2963	0.572077
$463$	15.2046	0.706619	0.353310	−	0.935506i	$-0.385056\pi$
$463$	15.2046	0.706619	0.353310	+	0.935506i	$0.385056\pi$
$464$	0.369356	0.0171469
$465$	−1.80718	−0.0838061
$466$	27.0340	1.25233
$467$	4.39921	0.203571	0.101786	−	0.994806i	$-0.467544\pi$
$467$	4.39921	0.203571	0.101786	+	0.994806i	$0.467544\pi$
$468$	−0.265910	−0.0122917
$469$	−52.7255	−2.43464
$470$	8.05247	0.371433
$471$	4.35346	0.200597
$472$	−12.1826	−0.560748
$473$	−13.0820	−0.601509
$474$	4.71031	0.216352
$475$	−5.56078	−0.255146
$476$	−7.51029	−0.344233
$477$	−2.88830	−0.132246
$478$	30.5325	1.39652
$479$	−30.3270	−1.38567	−0.692837	−	0.721094i	$-0.743639\pi$
$479$	−30.3270	−1.38567	−0.692837	+	0.721094i	$0.743639\pi$
$480$	−1.80718	−0.0824862
$481$	−3.78229	−0.172457
$482$	−19.8457	−0.903948
$483$	50.5191	2.29870
$484$	−6.91241	−0.314200
$485$	15.5452	0.705873
$486$	−2.75550	−0.124992
$487$	5.98853	0.271366	0.135683	−	0.990752i	$-0.456677\pi$
$487$	5.98853	0.271366	0.135683	+	0.990752i	$0.456677\pi$
$488$	5.85311	0.264958
$489$	−31.2548	−1.41339
$490$	4.32606	0.195432
$491$	−30.4924	−1.37610	−0.688052	−	0.725661i	$-0.741534\pi$
$491$	−30.4924	−1.37610	−0.688052	+	0.725661i	$0.741534\pi$
$492$	0.442669	0.0199570
$493$	0.824257	0.0371227
$494$	−5.56078	−0.250191
$495$	0.537611	0.0241638
$496$	−1.00000	−0.0449013
$497$	36.3302	1.62963
$498$	−9.96762	−0.446660
$499$	−31.0594	−1.39041	−0.695205	−	0.718811i	$-0.744686\pi$
$499$	−31.0594	−1.39041	−0.695205	+	0.718811i	$0.744686\pi$
$500$	−1.00000	−0.0447214
$501$	−11.8206	−0.528106
$502$	13.0217	0.581186
$503$	−30.9841	−1.38151	−0.690756	−	0.723088i	$-0.742722\pi$
$503$	−30.9841	−1.38151	−0.690756	+	0.723088i	$0.742722\pi$
$504$	0.894899	0.0398620
$505$	−18.4703	−0.821917
$506$	16.7937	0.746573
$507$	−1.80718	−0.0802598
$508$	17.7093	0.785724
$509$	−35.6966	−1.58222	−0.791111	−	0.611673i	$-0.790497\pi$
$509$	−35.6966	−1.58222	−0.791111	+	0.611673i	$0.790497\pi$
$510$	−4.03292	−0.178581
$511$	−7.06574	−0.312570
$512$	−1.00000	−0.0441942
$513$	−27.4758	−1.21309
$514$	−20.7648	−0.915896
$515$	3.98185	0.175461
$516$	−11.6934	−0.514774
$517$	−16.2803	−0.716007
$518$	12.7290	0.559280
$519$	−14.1282	−0.620159
$520$	−1.00000	−0.0438529
$521$	31.7807	1.39234	0.696169	−	0.717878i	$-0.254886\pi$
$521$	31.7807	1.39234	0.696169	+	0.717878i	$0.254886\pi$
$522$	−0.0982155	−0.00429877
$523$	−29.1525	−1.27475	−0.637374	−	0.770554i	$-0.719979\pi$
$523$	−29.1525	−1.27475	−0.637374	+	0.770554i	$0.719979\pi$
$524$	−4.86878	−0.212694
$525$	6.08193	0.265437
$526$	15.4310	0.672825
$527$	−2.23160	−0.0972102
$528$	3.65372	0.159008
$529$	45.9967	1.99985
$530$	−10.8620	−0.471813
$531$	3.23946	0.140581
$532$	18.7144	0.811371
$533$	0.244950	0.0106099
$534$	−18.5767	−0.803894
$535$	−2.44563	−0.105734
$536$	−15.6668	−0.676704
$537$	39.6598	1.71145
$538$	0.581098	0.0250529
$539$	−8.74634	−0.376732
$540$	−4.94100	−0.212627
$541$	−11.0321	−0.474305	−0.237153	−	0.971472i	$-0.576214\pi$
$541$	−11.0321	−0.474305	−0.237153	+	0.971472i	$0.576214\pi$
$542$	1.72460	0.0740779
$543$	−32.2845	−1.38546
$544$	−2.23160	−0.0956792
$545$	12.2395	0.524281
$546$	6.08193	0.260283
$547$	−0.0649663	−0.00277776	−0.00138888	−	0.999999i	$-0.500442\pi$
$547$	−0.0649663	−0.00277776	−0.00138888	+	0.999999i	$0.500442\pi$
$548$	−13.8923	−0.593450
$549$	−1.55640	−0.0664255
$550$	2.02178	0.0862089
$551$	−2.05391	−0.0874995
$552$	15.0112	0.638920
$553$	−8.77176	−0.373013
$554$	6.01833	0.255694
$555$	6.83529	0.290142
$556$	16.6972	0.708117
$557$	18.1589	0.769419	0.384710	−	0.923038i	$-0.374302\pi$
$557$	18.1589	0.769419	0.384710	+	0.923038i	$0.374302\pi$
$558$	0.265910	0.0112569
$559$	−6.47052	−0.273674
$560$	3.36542	0.142215
$561$	8.15366	0.344248
$562$	5.33991	0.225251
$563$	−19.6600	−0.828569	−0.414285	−	0.910147i	$-0.635968\pi$
$563$	−19.6600	−0.828569	−0.414285	+	0.910147i	$0.635968\pi$
$564$	−14.5523	−0.612762
$565$	−8.38581	−0.352794
$566$	−8.01104	−0.336729
$567$	32.7355	1.37476
$568$	10.7952	0.452954
$569$	−2.42199	−0.101535	−0.0507674	−	0.998711i	$-0.516167\pi$
$569$	−2.42199	−0.101535	−0.0507674	+	0.998711i	$0.516167\pi$
$570$	10.0494	0.420921
$571$	−21.2495	−0.889263	−0.444631	−	0.895714i	$-0.646665\pi$
$571$	−21.2495	−0.889263	−0.444631	+	0.895714i	$0.646665\pi$
$572$	2.02178	0.0845348
$573$	−33.1114	−1.38325
$574$	−0.824359	−0.0344081
$575$	8.30642	0.346402
$576$	0.265910	0.0110796
$577$	2.06776	0.0860820	0.0430410	−	0.999073i	$-0.486295\pi$
$577$	2.06776	0.0860820	0.0430410	+	0.999073i	$0.486295\pi$
$578$	12.0199	0.499964
$579$	40.6400	1.68894
$580$	−0.369356	−0.0153367
$581$	18.5622	0.770089
$582$	−28.0931	−1.16450
$583$	21.9605	0.909509
$584$	−2.09951	−0.0868784
$585$	0.265910	0.0109940
$586$	−3.33386	−0.137720
$587$	28.3649	1.17074	0.585372	−	0.810765i	$-0.300948\pi$
$587$	28.3649	1.17074	0.585372	+	0.810765i	$0.300948\pi$
$588$	−7.81799	−0.322408
$589$	5.56078	0.229128
$590$	12.1826	0.501548
$591$	27.0173	1.11134
$592$	3.78229	0.155451
$593$	−8.20018	−0.336741	−0.168370	−	0.985724i	$-0.553850\pi$
$593$	−8.20018	−0.336741	−0.168370	+	0.985724i	$0.553850\pi$
$594$	9.98961	0.409879
$595$	7.51029	0.307892
$596$	6.48257	0.265536
$597$	−9.76430	−0.399626
$598$	8.30642	0.339675
$599$	−10.4559	−0.427218	−0.213609	−	0.976919i	$-0.568522\pi$
$599$	−10.4559	−0.427218	−0.213609	+	0.976919i	$0.568522\pi$
$600$	1.80718	0.0737779
$601$	−32.8039	−1.33810	−0.669050	−	0.743217i	$-0.733299\pi$
$601$	−32.8039	−1.33810	−0.669050	+	0.743217i	$0.733299\pi$
$602$	21.7760	0.887525
$603$	4.16597	0.169651
$604$	−8.47323	−0.344771
$605$	6.91241	0.281029
$606$	33.3792	1.35594
$607$	−11.3305	−0.459891	−0.229945	−	0.973204i	$-0.573855\pi$
$607$	−11.3305	−0.459891	−0.229945	+	0.973204i	$0.573855\pi$
$608$	5.56078	0.225520
$609$	2.24640	0.0910287
$610$	−5.85311	−0.236986
$611$	−8.05247	−0.325768
$612$	0.593405	0.0239870
$613$	25.2918	1.02153	0.510763	−	0.859722i	$-0.329363\pi$
$613$	25.2918	1.02153	0.510763	+	0.859722i	$0.329363\pi$
$614$	−15.6555	−0.631806
$615$	−0.442669	−0.0178501
$616$	−6.80414	−0.274147
$617$	41.2522	1.66075	0.830375	−	0.557204i	$-0.188126\pi$
$617$	41.2522	1.66075	0.830375	+	0.557204i	$0.188126\pi$
$618$	−7.19593	−0.289463
$619$	24.1056	0.968886	0.484443	−	0.874823i	$-0.339022\pi$
$619$	24.1056	0.968886	0.484443	+	0.874823i	$0.339022\pi$
$620$	1.00000	0.0401610
$621$	41.0420	1.64696
$622$	26.4898	1.06214
$623$	34.5945	1.38600
$624$	1.80718	0.0723452
$625$	1.00000	0.0400000
$626$	15.4214	0.616365
$627$	−20.3176	−0.811405
$628$	−2.40897	−0.0961285
$629$	8.44057	0.336548
$630$	−0.894899	−0.0356536
$631$	17.7217	0.705488	0.352744	−	0.935720i	$-0.385249\pi$
$631$	17.7217	0.705488	0.352744	+	0.935720i	$0.385249\pi$
$632$	−2.60644	−0.103678
$633$	19.9430	0.792662
$634$	22.3806	0.888848
$635$	−17.7093	−0.702773
$636$	19.6295	0.778362
$637$	−4.32606	−0.171405
$638$	0.746757	0.0295644
$639$	−2.87054	−0.113557
$640$	1.00000	0.0395285
$641$	−26.0146	−1.02751	−0.513757	−	0.857935i	$-0.671747\pi$
$641$	−26.0146	−1.02751	−0.513757	+	0.857935i	$0.671747\pi$
$642$	4.41970	0.174432
$643$	13.5081	0.532706	0.266353	−	0.963876i	$-0.414181\pi$
$643$	13.5081	0.532706	0.266353	+	0.963876i	$0.414181\pi$
$644$	−27.9546	−1.10157
$645$	11.6934	0.460428
$646$	12.4095	0.488244
$647$	14.6850	0.577328	0.288664	−	0.957430i	$-0.406789\pi$
$647$	14.6850	0.577328	0.288664	+	0.957430i	$0.406789\pi$
$648$	9.72702	0.382113
$649$	−24.6304	−0.966830
$650$	1.00000	0.0392232
$651$	−6.08193	−0.238370
$652$	17.2947	0.677315
$653$	47.8256	1.87156	0.935779	−	0.352586i	$-0.114698\pi$
$653$	47.8256	1.87156	0.935779	+	0.352586i	$0.114698\pi$
$654$	−22.1190	−0.864919
$655$	4.86878	0.190239
$656$	−0.244950	−0.00956367
$657$	0.558281	0.0217806
$658$	27.1000	1.05647
$659$	3.65746	0.142474	0.0712371	−	0.997459i	$-0.477305\pi$
$659$	3.65746	0.142474	0.0712371	+	0.997459i	$0.477305\pi$
$660$	−3.65372	−0.142221
$661$	−48.9931	−1.90561	−0.952805	−	0.303582i	$-0.901817\pi$
$661$	−48.9931	−1.90561	−0.952805	+	0.303582i	$0.901817\pi$
$662$	1.09311	0.0424848
$663$	4.03292	0.156625
$664$	5.51556	0.214045
$665$	−18.7144	−0.725713
$666$	−1.00575	−0.0389719
$667$	3.06803	0.118795
$668$	6.54091	0.253075
$669$	13.4303	0.519243
$670$	15.6668	0.605263
$671$	11.8337	0.456835
$672$	−6.08193	−0.234616
$673$	−1.32916	−0.0512353	−0.0256176	−	0.999672i	$-0.508155\pi$
$673$	−1.32916	−0.0512353	−0.0256176	+	0.999672i	$0.508155\pi$
$674$	−21.5186	−0.828866
$675$	4.94100	0.190179
$676$	1.00000	0.0384615
$677$	−32.4601	−1.24754	−0.623772	−	0.781606i	$-0.714401\pi$
$677$	−32.4601	−1.24754	−0.623772	+	0.781606i	$0.714401\pi$
$678$	15.1547	0.582012
$679$	52.3163	2.00771
$680$	2.23160	0.0855781
$681$	−39.4936	−1.51340
$682$	−2.02178	−0.0774179
$683$	41.5883	1.59133	0.795665	−	0.605736i	$-0.207121\pi$
$683$	41.5883	1.59133	0.795665	+	0.605736i	$0.207121\pi$
$684$	−1.47867	−0.0565383
$685$	13.8923	0.530798
$686$	−8.99892	−0.343581
$687$	−25.3464	−0.967024
$688$	6.47052	0.246686
$689$	10.8620	0.413807
$690$	−15.0112	−0.571468
$691$	26.7295	1.01684	0.508418	−	0.861110i	$-0.330230\pi$
$691$	26.7295	1.01684	0.508418	+	0.861110i	$0.330230\pi$
$692$	7.81780	0.297188
$693$	1.80929	0.0687291
$694$	18.2339	0.692151
$695$	−16.6972	−0.633359
$696$	0.667494	0.0253013
$697$	−0.546630	−0.0207051
$698$	−25.5217	−0.966010
$699$	48.8554	1.84788
$700$	−3.36542	−0.127201
$701$	−15.4769	−0.584556	−0.292278	−	0.956333i	$-0.594413\pi$
$701$	−15.4769	−0.584556	−0.292278	+	0.956333i	$0.594413\pi$
$702$	4.94100	0.186486
$703$	−21.0325	−0.793255
$704$	−2.02178	−0.0761987
$705$	14.5523	0.548071
$706$	22.5893	0.850158
$707$	−62.1603	−2.33778
$708$	−22.0161	−0.827416
$709$	−25.2524	−0.948375	−0.474187	−	0.880424i	$-0.657258\pi$
$709$	−25.2524	−0.948375	−0.474187	+	0.880424i	$0.657258\pi$
$710$	−10.7952	−0.405135
$711$	0.693077	0.0259924
$712$	10.2794	0.385237
$713$	−8.30642	−0.311078
$714$	−13.5725	−0.507937
$715$	−2.02178	−0.0756102
$716$	−21.9456	−0.820147
$717$	55.1778	2.06065
$718$	35.1780	1.31283
$719$	50.7615	1.89309	0.946543	−	0.322577i	$-0.104549\pi$
$719$	50.7615	1.89309	0.946543	+	0.322577i	$0.104549\pi$
$720$	−0.265910	−0.00990988
$721$	13.4006	0.499064
$722$	−11.9223	−0.443703
$723$	−35.8649	−1.33383
$724$	17.8646	0.663931
$725$	0.369356	0.0137175
$726$	−12.4920	−0.463621
$727$	53.1832	1.97246	0.986228	−	0.165389i	$-0.0528881\pi$
$727$	53.1832	1.97246	0.986228	+	0.165389i	$0.0528881\pi$
$728$	−3.36542	−0.124731
$729$	24.2014	0.896347
$730$	2.09951	0.0777064
$731$	14.4396	0.534070
$732$	10.5776	0.390961
$733$	−23.6775	−0.874549	−0.437274	−	0.899328i	$-0.644056\pi$
$733$	−23.6775	−0.874549	−0.437274	+	0.899328i	$0.644056\pi$
$734$	−8.43783	−0.311446
$735$	7.81799	0.288371
$736$	−8.30642	−0.306179
$737$	−31.6749	−1.16676
$738$	0.0651345	0.00239763
$739$	25.2262	0.927959	0.463980	−	0.885846i	$-0.346421\pi$
$739$	25.2262	0.927959	0.463980	+	0.885846i	$0.346421\pi$
$740$	−3.78229	−0.139040
$741$	−10.0494	−0.369172
$742$	−36.5551	−1.34198
$743$	−42.8245	−1.57108	−0.785539	−	0.618812i	$-0.787614\pi$
$743$	−42.8245	−1.57108	−0.785539	+	0.618812i	$0.787614\pi$
$744$	−1.80718	−0.0662545
$745$	−6.48257	−0.237503
$746$	−26.4828	−0.969605
$747$	−1.46664	−0.0536616
$748$	−4.51181	−0.164968
$749$	−8.23057	−0.300738
$750$	−1.80718	−0.0659890
$751$	28.1114	1.02580	0.512899	−	0.858449i	$-0.328571\pi$
$751$	28.1114	1.02580	0.512899	+	0.858449i	$0.328571\pi$
$752$	8.05247	0.293643
$753$	23.5325	0.857574
$754$	0.369356	0.0134512
$755$	8.47323	0.308372
$756$	−16.6286	−0.604775
$757$	50.2893	1.82780	0.913898	−	0.405943i	$-0.133057\pi$
$757$	50.2893	1.82780	0.913898	+	0.405943i	$0.133057\pi$
$758$	−2.87288	−0.104348
$759$	30.3494	1.10161
$760$	−5.56078	−0.201711
$761$	40.4315	1.46564	0.732821	−	0.680422i	$-0.238203\pi$
$761$	40.4315	1.46564	0.732821	+	0.680422i	$0.238203\pi$
$762$	32.0040	1.15938
$763$	41.1910	1.49121
$764$	18.3221	0.662870
$765$	−0.593405	−0.0214546
$766$	21.5537	0.778766
$767$	−12.1826	−0.439887
$768$	−1.80718	−0.0652111
$769$	−22.6387	−0.816371	−0.408186	−	0.912899i	$-0.633838\pi$
$769$	−22.6387	−0.816371	−0.408186	+	0.912899i	$0.633838\pi$
$770$	6.80414	0.245204
$771$	−37.5258	−1.35146
$772$	−22.4881	−0.809363
$773$	−27.4766	−0.988266	−0.494133	−	0.869386i	$-0.664514\pi$
$773$	−27.4766	−0.988266	−0.494133	+	0.869386i	$0.664514\pi$
$774$	−1.72058	−0.0618448
$775$	−1.00000	−0.0359211
$776$	15.5452	0.558041
$777$	23.0036	0.825250
$778$	26.2029	0.939418
$779$	1.36211	0.0488027
$780$	−1.80718	−0.0647075
$781$	21.8254	0.780974
$782$	−18.5366	−0.662869
$783$	1.82499	0.0652198
$784$	4.32606	0.154502
$785$	2.40897	0.0859800
$786$	−8.79878	−0.313842
$787$	−6.27645	−0.223731	−0.111866	−	0.993723i	$-0.535683\pi$
$787$	−6.27645	−0.223731	−0.111866	+	0.993723i	$0.535683\pi$
$788$	−14.9499	−0.532569
$789$	27.8867	0.992793
$790$	2.60644	0.0927329
$791$	−28.2218	−1.00345
$792$	0.537611	0.0191032
$793$	5.85311	0.207850
$794$	28.9441	1.02719
$795$	−19.6295	−0.696188
$796$	5.40305	0.191506
$797$	32.8314	1.16295	0.581474	−	0.813565i	$-0.302476\pi$
$797$	32.8314	1.16295	0.581474	+	0.813565i	$0.302476\pi$
$798$	33.8203	1.19723
$799$	17.9699	0.635730
$800$	−1.00000	−0.0353553
$801$	−2.73339	−0.0965797
$802$	−22.5877	−0.797601
$803$	−4.24475	−0.149794
$804$	−28.3128	−0.998517
$805$	27.9546	0.985271
$806$	−1.00000	−0.0352235
$807$	1.05015	0.0369670
$808$	−18.4703	−0.649782
$809$	−12.2721	−0.431464	−0.215732	−	0.976453i	$-0.569214\pi$
$809$	−12.2721	−0.431464	−0.215732	+	0.976453i	$0.569214\pi$
$810$	−9.72702	−0.341773
$811$	−41.1083	−1.44351	−0.721754	−	0.692150i	$-0.756664\pi$
$811$	−41.1083	−1.44351	−0.721754	+	0.692150i	$0.756664\pi$
$812$	−1.24304	−0.0436221
$813$	3.11667	0.109306
$814$	7.64695	0.268025
$815$	−17.2947	−0.605809
$816$	−4.03292	−0.141180
$817$	−35.9812	−1.25882
$818$	−5.89672	−0.206174
$819$	0.894899	0.0312703
$820$	0.244950	0.00855401
$821$	39.4743	1.37766	0.688831	−	0.724922i	$-0.258124\pi$
$821$	39.4743	1.37766	0.688831	+	0.724922i	$0.258124\pi$
$822$	−25.1059	−0.875670
$823$	−6.97279	−0.243056	−0.121528	−	0.992588i	$-0.538779\pi$
$823$	−6.97279	−0.243056	−0.121528	+	0.992588i	$0.538779\pi$
$824$	3.98185	0.138714
$825$	3.65372	0.127206
$826$	40.9995	1.42655
$827$	20.4560	0.711325	0.355662	−	0.934614i	$-0.384255\pi$
$827$	20.4560	0.711325	0.355662	+	0.934614i	$0.384255\pi$
$828$	2.20876	0.0767597
$829$	12.6236	0.438436	0.219218	−	0.975676i	$-0.429649\pi$
$829$	12.6236	0.438436	0.219218	+	0.975676i	$0.429649\pi$
$830$	−5.51556	−0.191448
$831$	10.8762	0.377292
$832$	−1.00000	−0.0346688
$833$	9.65406	0.334493
$834$	30.1748	1.04487
$835$	−6.54091	−0.226357
$836$	11.2427	0.388836
$837$	−4.94100	−0.170786
$838$	−20.3831	−0.704123
$839$	−9.86147	−0.340456	−0.170228	−	0.985405i	$-0.554450\pi$
$839$	−9.86147	−0.340456	−0.170228	+	0.985405i	$0.554450\pi$
$840$	6.08193	0.209847
$841$	−28.8636	−0.995296
$842$	−1.44447	−0.0497798
$843$	9.65019	0.332370
$844$	−11.0354	−0.379854
$845$	−1.00000	−0.0344010
$846$	−2.14123	−0.0736170
$847$	23.2632	0.799332
$848$	−10.8620	−0.373001
$849$	−14.4774	−0.496864
$850$	−2.23160	−0.0765434
$851$	31.4173	1.07697
$852$	19.5088	0.668361
$853$	−21.5766	−0.738768	−0.369384	−	0.929277i	$-0.620431\pi$
$853$	−21.5766	−0.738768	−0.369384	+	0.929277i	$0.620431\pi$
$854$	−19.6982	−0.674058
$855$	1.47867	0.0505693
$856$	−2.44563	−0.0835898
$857$	−34.5585	−1.18050	−0.590248	−	0.807222i	$-0.700970\pi$
$857$	−34.5585	−1.18050	−0.590248	+	0.807222i	$0.700970\pi$
$858$	3.65372	0.124736
$859$	−43.5086	−1.48449	−0.742247	−	0.670127i	$-0.766240\pi$
$859$	−43.5086	−1.48449	−0.742247	+	0.670127i	$0.766240\pi$
$860$	−6.47052	−0.220643
$861$	−1.48977	−0.0507711
$862$	−16.2471	−0.553379
$863$	−42.2365	−1.43775	−0.718873	−	0.695141i	$-0.755342\pi$
$863$	−42.2365	−1.43775	−0.718873	+	0.695141i	$0.755342\pi$
$864$	−4.94100	−0.168096
$865$	−7.81780	−0.265813
$866$	39.5362	1.34349
$867$	21.7222	0.737726
$868$	3.36542	0.114230
$869$	−5.26964	−0.178760
$870$	−0.667494	−0.0226302
$871$	−15.6668	−0.530850
$872$	12.2395	0.414481
$873$	−4.13363	−0.139902
$874$	46.1902	1.56241
$875$	3.36542	0.113772
$876$	−3.79420	−0.128194
$877$	25.1255	0.848428	0.424214	−	0.905562i	$-0.360550\pi$
$877$	25.1255	0.848428	0.424214	+	0.905562i	$0.360550\pi$
$878$	−16.3272	−0.551016
$879$	−6.02489	−0.203214
$880$	2.02178	0.0681541
$881$	45.5399	1.53428	0.767140	−	0.641480i	$-0.221679\pi$
$881$	45.5399	1.53428	0.767140	+	0.641480i	$0.221679\pi$
$882$	−1.15034	−0.0387341
$883$	34.1272	1.14847	0.574237	−	0.818689i	$-0.305299\pi$
$883$	34.1272	1.14847	0.574237	+	0.818689i	$0.305299\pi$
$884$	−2.23160	−0.0750570
$885$	22.0161	0.740064
$886$	21.9067	0.735971
$887$	31.8763	1.07030	0.535150	−	0.844757i	$-0.320255\pi$
$887$	31.8763	1.07030	0.535150	+	0.844757i	$0.320255\pi$
$888$	6.83529	0.229377
$889$	−59.5994	−1.99890
$890$	−10.2794	−0.344566
$891$	19.6659	0.658832
$892$	−7.43159	−0.248828
$893$	−44.7780	−1.49844
$894$	11.7152	0.391815
$895$	21.9456	0.733562
$896$	3.36542	0.112431
$897$	15.0112	0.501210
$898$	−40.4002	−1.34817
$899$	−0.369356	−0.0123187
$900$	0.265910	0.00886366
$901$	−24.2396	−0.807537
$902$	−0.495234	−0.0164895
$903$	39.3533	1.30960
$904$	−8.38581	−0.278908
$905$	−17.8646	−0.593838
$906$	−15.3127	−0.508729
$907$	−2.97921	−0.0989232	−0.0494616	−	0.998776i	$-0.515751\pi$
$907$	−2.97921	−0.0989232	−0.0494616	+	0.998776i	$0.515751\pi$
$908$	21.8537	0.725241
$909$	4.91143	0.162902
$910$	3.36542	0.111563
$911$	16.4634	0.545456	0.272728	−	0.962091i	$-0.412074\pi$
$911$	16.4634	0.545456	0.272728	+	0.962091i	$0.412074\pi$
$912$	10.0494	0.332767
$913$	11.1512	0.369052
$914$	19.1008	0.631799
$915$	−10.5776	−0.349686
$916$	14.0253	0.463410
$917$	16.3855	0.541097
$918$	−11.0264	−0.363924
$919$	−27.9494	−0.921965	−0.460982	−	0.887409i	$-0.652503\pi$
$919$	−27.9494	−0.921965	−0.460982	+	0.887409i	$0.652503\pi$
$920$	8.30642	0.273855
$921$	−28.2924	−0.932266
$922$	−15.6154	−0.514264
$923$	10.7952	0.355327
$924$	−12.2963	−0.404519
$925$	3.78229	0.124361
$926$	−15.2046	−0.499655
$927$	−1.05881	−0.0347760
$928$	−0.369356	−0.0121247
$929$	−3.36988	−0.110562	−0.0552811	−	0.998471i	$-0.517606\pi$
$929$	−3.36988	−0.110562	−0.0552811	+	0.998471i	$0.517606\pi$
$930$	1.80718	0.0592599
$931$	−24.0563	−0.788413
$932$	−27.0340	−0.885528
$933$	47.8719	1.56726
$934$	−4.39921	−0.143947
$935$	4.51181	0.147552
$936$	0.265910	0.00869154
$937$	−7.70973	−0.251866	−0.125933	−	0.992039i	$-0.540192\pi$
$937$	−7.70973	−0.251866	−0.125933	+	0.992039i	$0.540192\pi$
$938$	52.7255	1.72155
$939$	27.8694	0.909482
$940$	−8.05247	−0.262643
$941$	2.28762	0.0745743	0.0372871	−	0.999305i	$-0.488128\pi$
$941$	2.28762	0.0745743	0.0372871	+	0.999305i	$0.488128\pi$
$942$	−4.35346	−0.141843
$943$	−2.03465	−0.0662575
$944$	12.1826	0.396509
$945$	16.6286	0.540927
$946$	13.0820	0.425331
$947$	−33.1205	−1.07627	−0.538136	−	0.842858i	$-0.680871\pi$
$947$	−33.1205	−1.07627	−0.538136	+	0.842858i	$0.680871\pi$
$948$	−4.71031	−0.152984
$949$	−2.09951	−0.0681530
$950$	5.56078	0.180416
$951$	40.4459	1.31155
$952$	7.51029	0.243410
$953$	−5.46041	−0.176880	−0.0884400	−	0.996082i	$-0.528188\pi$
$953$	−5.46041	−0.176880	−0.0884400	+	0.996082i	$0.528188\pi$
$954$	2.88830	0.0935122
$955$	−18.3221	−0.592889
$956$	−30.5325	−0.987491
$957$	1.34953	0.0436240
$958$	30.3270	0.979819
$959$	46.7535	1.50975
$960$	1.80718	0.0583266
$961$	1.00000	0.0322581
$962$	3.78229	0.121946
$963$	0.650317	0.0209562
$964$	19.8457	0.639188
$965$	22.4881	0.723916
$966$	−50.5191	−1.62543
$967$	44.9934	1.44689	0.723445	−	0.690382i	$-0.242558\pi$
$967$	44.9934	1.44689	0.723445	+	0.690382i	$0.242558\pi$
$968$	6.91241	0.222173
$969$	22.4262	0.720432
$970$	−15.5452	−0.499127
$971$	2.58018	0.0828020	0.0414010	−	0.999143i	$-0.486818\pi$
$971$	2.58018	0.0828020	0.0414010	+	0.999143i	$0.486818\pi$
$972$	2.75550	0.0883828
$973$	−56.1930	−1.80146
$974$	−5.98853	−0.191885
$975$	1.80718	0.0578762
$976$	−5.85311	−0.187354
$977$	−4.73004	−0.151327	−0.0756637	−	0.997133i	$-0.524108\pi$
$977$	−4.73004	−0.151327	−0.0756637	+	0.997133i	$0.524108\pi$
$978$	31.2548	0.999417
$979$	20.7827	0.664217
$980$	−4.32606	−0.138191
$981$	−3.25459	−0.103911
$982$	30.4924	0.973053
$983$	−29.4836	−0.940379	−0.470190	−	0.882565i	$-0.655814\pi$
$983$	−29.4836	−0.940379	−0.470190	+	0.882565i	$0.655814\pi$
$984$	−0.442669	−0.0141118
$985$	14.9499	0.476344
$986$	−0.824257	−0.0262497
$987$	48.9746	1.55888
$988$	5.56078	0.176912
$989$	53.7469	1.70905
$990$	−0.537611	−0.0170864
$991$	−17.8010	−0.565467	−0.282733	−	0.959199i	$-0.591241\pi$
$991$	−17.8010	−0.565467	−0.282733	+	0.959199i	$0.591241\pi$
$992$	1.00000	0.0317500
$993$	1.97545	0.0626889
$994$	−36.3302	−1.15233
$995$	−5.40305	−0.171288
$996$	9.96762	0.315836
$997$	−10.7553	−0.340623	−0.170311	−	0.985390i	$-0.554477\pi$
$997$	−10.7553	−0.340623	−0.170311	+	0.985390i	$0.554477\pi$
$998$	31.0594	0.983168
$999$	18.6883	0.591271

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4030.2.a.i.1.2	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4030.2.a.i.1.2	✓	7	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:	\( N \)	\(=\)	\( 4030 = 2 \cdot 5 \cdot 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4030.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.80718 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.80718 q^{6} -3.36542 q^{7} -1.00000 q^{8} +0.265910 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.80718 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.80718 q^{6} -3.36542 q^{7} -1.00000 q^{8} +0.265910 q^{9} +1.00000 q^{10} -2.02178 q^{11} -1.80718 q^{12} -1.00000 q^{13} +3.36542 q^{14} +1.80718 q^{15} +1.00000 q^{16} +2.23160 q^{17} -0.265910 q^{18} -5.56078 q^{19} -1.00000 q^{20} +6.08193 q^{21} +2.02178 q^{22} +8.30642 q^{23} +1.80718 q^{24} +1.00000 q^{25} +1.00000 q^{26} +4.94100 q^{27} -3.36542 q^{28} +0.369356 q^{29} -1.80718 q^{30} -1.00000 q^{31} -1.00000 q^{32} +3.65372 q^{33} -2.23160 q^{34} +3.36542 q^{35} +0.265910 q^{36} +3.78229 q^{37} +5.56078 q^{38} +1.80718 q^{39} +1.00000 q^{40} -0.244950 q^{41} -6.08193 q^{42} +6.47052 q^{43} -2.02178 q^{44} -0.265910 q^{45} -8.30642 q^{46} +8.05247 q^{47} -1.80718 q^{48} +4.32606 q^{49} -1.00000 q^{50} -4.03292 q^{51} -1.00000 q^{52} -10.8620 q^{53} -4.94100 q^{54} +2.02178 q^{55} +3.36542 q^{56} +10.0494 q^{57} -0.369356 q^{58} +12.1826 q^{59} +1.80718 q^{60} -5.85311 q^{61} +1.00000 q^{62} -0.894899 q^{63} +1.00000 q^{64} +1.00000 q^{65} -3.65372 q^{66} +15.6668 q^{67} +2.23160 q^{68} -15.0112 q^{69} -3.36542 q^{70} -10.7952 q^{71} -0.265910 q^{72} +2.09951 q^{73} -3.78229 q^{74} -1.80718 q^{75} -5.56078 q^{76} +6.80414 q^{77} -1.80718 q^{78} +2.60644 q^{79} -1.00000 q^{80} -9.72702 q^{81} +0.244950 q^{82} -5.51556 q^{83} +6.08193 q^{84} -2.23160 q^{85} -6.47052 q^{86} -0.667494 q^{87} +2.02178 q^{88} -10.2794 q^{89} +0.265910 q^{90} +3.36542 q^{91} +8.30642 q^{92} +1.80718 q^{93} -8.05247 q^{94} +5.56078 q^{95} +1.80718 q^{96} -15.5452 q^{97} -4.32606 q^{98} -0.537611 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 7 q^{2} + 3 q^{3} + 7 q^{4} - 7 q^{5} - 3 q^{6} + 2 q^{7} - 7 q^{8} + 4 q^{9}+O(q^{10}) \) 7 * q - 7 * q^2 + 3 * q^3 + 7 * q^4 - 7 * q^5 - 3 * q^6 + 2 * q^7 - 7 * q^8 + 4 * q^9	\( 7 q - 7 q^{2} + 3 q^{3} + 7 q^{4} - 7 q^{5} - 3 q^{6} + 2 q^{7} - 7 q^{8} + 4 q^{9} + 7 q^{10} - 6 q^{11} + 3 q^{12} - 7 q^{13} - 2 q^{14} - 3 q^{15} + 7 q^{16} - 4 q^{18} - 9 q^{19} - 7 q^{20} + q^{21} + 6 q^{22} + 7 q^{23} - 3 q^{24} + 7 q^{25} + 7 q^{26} + 9 q^{27} + 2 q^{28} - 4 q^{29} + 3 q^{30} - 7 q^{31} - 7 q^{32} - 2 q^{35} + 4 q^{36} + 2 q^{37} + 9 q^{38} - 3 q^{39} + 7 q^{40} - 14 q^{41} - q^{42} + 9 q^{43} - 6 q^{44} - 4 q^{45} - 7 q^{46} - 8 q^{47} + 3 q^{48} - q^{49} - 7 q^{50} - 7 q^{51} - 7 q^{52} - 6 q^{53} - 9 q^{54} + 6 q^{55} - 2 q^{56} - 11 q^{57} + 4 q^{58} - 15 q^{59} - 3 q^{60} + q^{61} + 7 q^{62} - 17 q^{63} + 7 q^{64} + 7 q^{65} + 14 q^{67} - 14 q^{69} + 2 q^{70} - 16 q^{71} - 4 q^{72} - 13 q^{73} - 2 q^{74} + 3 q^{75} - 9 q^{76} - 5 q^{77} + 3 q^{78} - 14 q^{79} - 7 q^{80} - 25 q^{81} + 14 q^{82} - 10 q^{83} + q^{84} - 9 q^{86} - 9 q^{87} + 6 q^{88} - 26 q^{89} + 4 q^{90} - 2 q^{91} + 7 q^{92} - 3 q^{93} + 8 q^{94} + 9 q^{95} - 3 q^{96} - 5 q^{97} + q^{98} - 37 q^{99}+O(q^{100}) \) 7 * q - 7 * q^2 + 3 * q^3 + 7 * q^4 - 7 * q^5 - 3 * q^6 + 2 * q^7 - 7 * q^8 + 4 * q^9 + 7 * q^10 - 6 * q^11 + 3 * q^12 - 7 * q^13 - 2 * q^14 - 3 * q^15 + 7 * q^16 - 4 * q^18 - 9 * q^19 - 7 * q^20 + q^21 + 6 * q^22 + 7 * q^23 - 3 * q^24 + 7 * q^25 + 7 * q^26 + 9 * q^27 + 2 * q^28 - 4 * q^29 + 3 * q^30 - 7 * q^31 - 7 * q^32 - 2 * q^35 + 4 * q^36 + 2 * q^37 + 9 * q^38 - 3 * q^39 + 7 * q^40 - 14 * q^41 - q^42 + 9 * q^43 - 6 * q^44 - 4 * q^45 - 7 * q^46 - 8 * q^47 + 3 * q^48 - q^49 - 7 * q^50 - 7 * q^51 - 7 * q^52 - 6 * q^53 - 9 * q^54 + 6 * q^55 - 2 * q^56 - 11 * q^57 + 4 * q^58 - 15 * q^59 - 3 * q^60 + q^61 + 7 * q^62 - 17 * q^63 + 7 * q^64 + 7 * q^65 + 14 * q^67 - 14 * q^69 + 2 * q^70 - 16 * q^71 - 4 * q^72 - 13 * q^73 - 2 * q^74 + 3 * q^75 - 9 * q^76 - 5 * q^77 + 3 * q^78 - 14 * q^79 - 7 * q^80 - 25 * q^81 + 14 * q^82 - 10 * q^83 + q^84 - 9 * q^86 - 9 * q^87 + 6 * q^88 - 26 * q^89 + 4 * q^90 - 2 * q^91 + 7 * q^92 - 3 * q^93 + 8 * q^94 + 9 * q^95 - 3 * q^96 - 5 * q^97 + q^98 - 37 * q^99

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