LMFDB - Embedded newform 4030.2.a.m.1.8

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:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} - 15x^{6} + 31x^{5} + 79x^{4} - 85x^{3} - 162x^{2} + 45x + 81 $ x^8 - 3x^7 - 15x^6 + 31x^5 + 79x^4 - 85x^3 - 162x^2 + 45*x + 81
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			1.8
Root			$-2.44665$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +3.44665 q^{3} +1.00000 q^{4} +1.00000 q^{5} -3.44665 q^{6} +4.56226 q^{7} -1.00000 q^{8} +8.87940 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +3.44665 q^{3} +1.00000 q^{4} +1.00000 q^{5} -3.44665 q^{6} +4.56226 q^{7} -1.00000 q^{8} +8.87940 q^{9} -1.00000 q^{10} -3.59443 q^{11} +3.44665 q^{12} +1.00000 q^{13} -4.56226 q^{14} +3.44665 q^{15} +1.00000 q^{16} +6.24352 q^{17} -8.87940 q^{18} -4.80126 q^{19} +1.00000 q^{20} +15.7245 q^{21} +3.59443 q^{22} +4.70242 q^{23} -3.44665 q^{24} +1.00000 q^{25} -1.00000 q^{26} +20.2642 q^{27} +4.56226 q^{28} -0.684608 q^{29} -3.44665 q^{30} +1.00000 q^{31} -1.00000 q^{32} -12.3887 q^{33} -6.24352 q^{34} +4.56226 q^{35} +8.87940 q^{36} -11.4165 q^{37} +4.80126 q^{38} +3.44665 q^{39} -1.00000 q^{40} +0.472683 q^{41} -15.7245 q^{42} -8.13009 q^{43} -3.59443 q^{44} +8.87940 q^{45} -4.70242 q^{46} -9.97952 q^{47} +3.44665 q^{48} +13.8142 q^{49} -1.00000 q^{50} +21.5192 q^{51} +1.00000 q^{52} -4.20774 q^{53} -20.2642 q^{54} -3.59443 q^{55} -4.56226 q^{56} -16.5483 q^{57} +0.684608 q^{58} -4.91100 q^{59} +3.44665 q^{60} -7.61448 q^{61} -1.00000 q^{62} +40.5101 q^{63} +1.00000 q^{64} +1.00000 q^{65} +12.3887 q^{66} -11.3533 q^{67} +6.24352 q^{68} +16.2076 q^{69} -4.56226 q^{70} +7.42752 q^{71} -8.87940 q^{72} -1.88322 q^{73} +11.4165 q^{74} +3.44665 q^{75} -4.80126 q^{76} -16.3987 q^{77} -3.44665 q^{78} -7.82565 q^{79} +1.00000 q^{80} +43.2055 q^{81} -0.472683 q^{82} +13.1851 q^{83} +15.7245 q^{84} +6.24352 q^{85} +8.13009 q^{86} -2.35961 q^{87} +3.59443 q^{88} -7.29907 q^{89} -8.87940 q^{90} +4.56226 q^{91} +4.70242 q^{92} +3.44665 q^{93} +9.97952 q^{94} -4.80126 q^{95} -3.44665 q^{96} +13.5364 q^{97} -13.8142 q^{98} -31.9164 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} + 5 q^{3} + 8 q^{4} + 8 q^{5} - 5 q^{6} + 5 q^{7} - 8 q^{8} + 17 q^{9}+O(q^{10}) $ 8 * q - 8 * q^2 + 5 * q^3 + 8 * q^4 + 8 * q^5 - 5 * q^6 + 5 * q^7 - 8 * q^8 + 17 * q^9	\( 8 q - 8 q^{2} + 5 q^{3} + 8 q^{4} + 8 q^{5} - 5 q^{6} + 5 q^{7} - 8 q^{8} + 17 q^{9} - 8 q^{10} + 4 q^{11} + 5 q^{12} + 8 q^{13} - 5 q^{14} + 5 q^{15} + 8 q^{16} + 19 q^{17} - 17 q^{18} - 14 q^{19} + 8 q^{20} + 3 q^{21} - 4 q^{22} + 8 q^{23} - 5 q^{24} + 8 q^{25} - 8 q^{26} + 17 q^{27} + 5 q^{28} + 21 q^{29} - 5 q^{30} + 8 q^{31} - 8 q^{32} + 4 q^{33} - 19 q^{34} + 5 q^{35} + 17 q^{36} - 3 q^{37} + 14 q^{38} + 5 q^{39} - 8 q^{40} - 8 q^{41} - 3 q^{42} + 25 q^{43} + 4 q^{44} + 17 q^{45} - 8 q^{46} + 11 q^{47} + 5 q^{48} + 15 q^{49} - 8 q^{50} + 7 q^{51} + 8 q^{52} + 2 q^{53} - 17 q^{54} + 4 q^{55} - 5 q^{56} + 9 q^{57} - 21 q^{58} - 22 q^{59} + 5 q^{60} - 2 q^{61} - 8 q^{62} + 30 q^{63} + 8 q^{64} + 8 q^{65} - 4 q^{66} - 14 q^{67} + 19 q^{68} + 36 q^{69} - 5 q^{70} + 4 q^{71} - 17 q^{72} + 17 q^{73} + 3 q^{74} + 5 q^{75} - 14 q^{76} + 17 q^{77} - 5 q^{78} - 12 q^{79} + 8 q^{80} + 40 q^{81} + 8 q^{82} + 21 q^{83} + 3 q^{84} + 19 q^{85} - 25 q^{86} + 25 q^{87} - 4 q^{88} - 25 q^{89} - 17 q^{90} + 5 q^{91} + 8 q^{92} + 5 q^{93} - 11 q^{94} - 14 q^{95} - 5 q^{96} + 8 q^{97} - 15 q^{98} - 57 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 + 5 * q^3 + 8 * q^4 + 8 * q^5 - 5 * q^6 + 5 * q^7 - 8 * q^8 + 17 * q^9 - 8 * q^10 + 4 * q^11 + 5 * q^12 + 8 * q^13 - 5 * q^14 + 5 * q^15 + 8 * q^16 + 19 * q^17 - 17 * q^18 - 14 * q^19 + 8 * q^20 + 3 * q^21 - 4 * q^22 + 8 * q^23 - 5 * q^24 + 8 * q^25 - 8 * q^26 + 17 * q^27 + 5 * q^28 + 21 * q^29 - 5 * q^30 + 8 * q^31 - 8 * q^32 + 4 * q^33 - 19 * q^34 + 5 * q^35 + 17 * q^36 - 3 * q^37 + 14 * q^38 + 5 * q^39 - 8 * q^40 - 8 * q^41 - 3 * q^42 + 25 * q^43 + 4 * q^44 + 17 * q^45 - 8 * q^46 + 11 * q^47 + 5 * q^48 + 15 * q^49 - 8 * q^50 + 7 * q^51 + 8 * q^52 + 2 * q^53 - 17 * q^54 + 4 * q^55 - 5 * q^56 + 9 * q^57 - 21 * q^58 - 22 * q^59 + 5 * q^60 - 2 * q^61 - 8 * q^62 + 30 * q^63 + 8 * q^64 + 8 * q^65 - 4 * q^66 - 14 * q^67 + 19 * q^68 + 36 * q^69 - 5 * q^70 + 4 * q^71 - 17 * q^72 + 17 * q^73 + 3 * q^74 + 5 * q^75 - 14 * q^76 + 17 * q^77 - 5 * q^78 - 12 * q^79 + 8 * q^80 + 40 * q^81 + 8 * q^82 + 21 * q^83 + 3 * q^84 + 19 * q^85 - 25 * q^86 + 25 * q^87 - 4 * q^88 - 25 * q^89 - 17 * q^90 + 5 * q^91 + 8 * q^92 + 5 * q^93 - 11 * q^94 - 14 * q^95 - 5 * q^96 + 8 * q^97 - 15 * q^98 - 57 * 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
$3$	3.44665	1.98992	0.994962	−	0.100251i	$-0.0319646\pi$
$3$	3.44665	1.98992	0.994962	+	0.100251i	$0.0319646\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−3.44665	−1.40709
$7$	4.56226	1.72437	0.862186	−	0.506591i	$-0.169095\pi$
$7$	4.56226	1.72437	0.862186	+	0.506591i	$0.169095\pi$
$8$	−1.00000	−0.353553
$9$	8.87940	2.95980
$10$	−1.00000	−0.316228
$11$	−3.59443	−1.08376	−0.541881	−	0.840455i	$-0.682288\pi$
$11$	−3.59443	−1.08376	−0.541881	+	0.840455i	$0.682288\pi$
$12$	3.44665	0.994962
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−4.56226	−1.21932
$15$	3.44665	0.889921
$16$	1.00000	0.250000
$17$	6.24352	1.51428	0.757139	−	0.653254i	$-0.226597\pi$
$17$	6.24352	1.51428	0.757139	+	0.653254i	$0.226597\pi$
$18$	−8.87940	−2.09289
$19$	−4.80126	−1.10148	−0.550742	−	0.834676i	$-0.685655\pi$
$19$	−4.80126	−1.10148	−0.550742	+	0.834676i	$0.685655\pi$
$20$	1.00000	0.223607
$21$	15.7245	3.43137
$22$	3.59443	0.766335
$23$	4.70242	0.980523	0.490262	−	0.871575i	$-0.336901\pi$
$23$	4.70242	0.980523	0.490262	+	0.871575i	$0.336901\pi$
$24$	−3.44665	−0.703545
$25$	1.00000	0.200000
$26$	−1.00000	−0.196116
$27$	20.2642	3.89985
$28$	4.56226	0.862186
$29$	−0.684608	−0.127129	−0.0635643	−	0.997978i	$-0.520247\pi$
$29$	−0.684608	−0.127129	−0.0635643	+	0.997978i	$0.520247\pi$
$30$	−3.44665	−0.629269
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	−1.00000	−0.176777
$33$	−12.3887	−2.15660
$34$	−6.24352	−1.07076
$35$	4.56226	0.771163
$36$	8.87940	1.47990
$37$	−11.4165	−1.87687	−0.938433	−	0.345462i	$-0.887722\pi$
$37$	−11.4165	−1.87687	−0.938433	+	0.345462i	$0.887722\pi$
$38$	4.80126	0.778867
$39$	3.44665	0.551906
$40$	−1.00000	−0.158114
$41$	0.472683	0.0738207	0.0369104	−	0.999319i	$-0.488248\pi$
$41$	0.472683	0.0738207	0.0369104	+	0.999319i	$0.488248\pi$
$42$	−15.7245	−2.42635
$43$	−8.13009	−1.23983	−0.619913	−	0.784670i	$-0.712832\pi$
$43$	−8.13009	−1.23983	−0.619913	+	0.784670i	$0.712832\pi$
$44$	−3.59443	−0.541881
$45$	8.87940	1.32366
$46$	−4.70242	−0.693335
$47$	−9.97952	−1.45566	−0.727832	−	0.685756i	$-0.759472\pi$
$47$	−9.97952	−1.45566	−0.727832	+	0.685756i	$0.759472\pi$
$48$	3.44665	0.497481
$49$	13.8142	1.97346
$50$	−1.00000	−0.141421
$51$	21.5192	3.01330
$52$	1.00000	0.138675
$53$	−4.20774	−0.577978	−0.288989	−	0.957332i	$-0.593319\pi$
$53$	−4.20774	−0.577978	−0.288989	+	0.957332i	$0.593319\pi$
$54$	−20.2642	−2.75761
$55$	−3.59443	−0.484673
$56$	−4.56226	−0.609658
$57$	−16.5483	−2.19187
$58$	0.684608	0.0898935
$59$	−4.91100	−0.639358	−0.319679	−	0.947526i	$-0.603575\pi$
$59$	−4.91100	−0.639358	−0.319679	+	0.947526i	$0.603575\pi$
$60$	3.44665	0.444961
$61$	−7.61448	−0.974934	−0.487467	−	0.873141i	$-0.662079\pi$
$61$	−7.61448	−0.974934	−0.487467	+	0.873141i	$0.662079\pi$
$62$	−1.00000	−0.127000
$63$	40.5101	5.10380
$64$	1.00000	0.125000
$65$	1.00000	0.124035
$66$	12.3887	1.52495
$67$	−11.3533	−1.38702	−0.693511	−	0.720446i	$-0.743937\pi$
$67$	−11.3533	−1.38702	−0.693511	+	0.720446i	$0.743937\pi$
$68$	6.24352	0.757139
$69$	16.2076	1.95117
$70$	−4.56226	−0.545295
$71$	7.42752	0.881484	0.440742	−	0.897634i	$-0.354715\pi$
$71$	7.42752	0.881484	0.440742	+	0.897634i	$0.354715\pi$
$72$	−8.87940	−1.04645
$73$	−1.88322	−0.220414	−0.110207	−	0.993909i	$-0.535151\pi$
$73$	−1.88322	−0.220414	−0.110207	+	0.993909i	$0.535151\pi$
$74$	11.4165	1.32714
$75$	3.44665	0.397985
$76$	−4.80126	−0.550742
$77$	−16.3987	−1.86881
$78$	−3.44665	−0.390256
$79$	−7.82565	−0.880455	−0.440227	−	0.897886i	$-0.645102\pi$
$79$	−7.82565	−0.880455	−0.440227	+	0.897886i	$0.645102\pi$
$80$	1.00000	0.111803
$81$	43.2055	4.80061
$82$	−0.472683	−0.0521991
$83$	13.1851	1.44725	0.723624	−	0.690194i	$-0.242475\pi$
$83$	13.1851	1.44725	0.723624	+	0.690194i	$0.242475\pi$
$84$	15.7245	1.71569
$85$	6.24352	0.677205
$86$	8.13009	0.876690
$87$	−2.35961	−0.252976
$88$	3.59443	0.383167
$89$	−7.29907	−0.773700	−0.386850	−	0.922143i	$-0.626437\pi$
$89$	−7.29907	−0.773700	−0.386850	+	0.922143i	$0.626437\pi$
$90$	−8.87940	−0.935971
$91$	4.56226	0.478255
$92$	4.70242	0.490262
$93$	3.44665	0.357401
$94$	9.97952	1.02931
$95$	−4.80126	−0.492599
$96$	−3.44665	−0.351772
$97$	13.5364	1.37441	0.687205	−	0.726464i	$-0.258837\pi$
$97$	13.5364	1.37441	0.687205	+	0.726464i	$0.258837\pi$
$98$	−13.8142	−1.39545
$99$	−31.9164	−3.20772
$100$	1.00000	0.100000
$101$	15.1235	1.50485	0.752424	−	0.658679i	$-0.228884\pi$
$101$	15.1235	1.50485	0.752424	+	0.658679i	$0.228884\pi$
$102$	−21.5192	−2.13072
$103$	−15.0324	−1.48118	−0.740592	−	0.671955i	$-0.765455\pi$
$103$	−15.0324	−1.48118	−0.740592	+	0.671955i	$0.765455\pi$
$104$	−1.00000	−0.0980581
$105$	15.7245	1.53456
$106$	4.20774	0.408692
$107$	−14.8484	−1.43545	−0.717723	−	0.696329i	$-0.754816\pi$
$107$	−14.8484	−1.43545	−0.717723	+	0.696329i	$0.754816\pi$
$108$	20.2642	1.94993
$109$	8.94746	0.857011	0.428505	−	0.903539i	$-0.359040\pi$
$109$	8.94746	0.857011	0.428505	+	0.903539i	$0.359040\pi$
$110$	3.59443	0.342715
$111$	−39.3488	−3.73482
$112$	4.56226	0.431093
$113$	−5.90854	−0.555828	−0.277914	−	0.960606i	$-0.589643\pi$
$113$	−5.90854	−0.555828	−0.277914	+	0.960606i	$0.589643\pi$
$114$	16.5483	1.54989
$115$	4.70242	0.438503
$116$	−0.684608	−0.0635643
$117$	8.87940	0.820901
$118$	4.91100	0.452095
$119$	28.4846	2.61118
$120$	−3.44665	−0.314635
$121$	1.91992	0.174538
$122$	7.61448	0.689383
$123$	1.62917	0.146898
$124$	1.00000	0.0898027
$125$	1.00000	0.0894427
$126$	−40.5101	−3.60893
$127$	2.27616	0.201977	0.100988	−	0.994888i	$-0.467800\pi$
$127$	2.27616	0.201977	0.100988	+	0.994888i	$0.467800\pi$
$128$	−1.00000	−0.0883883
$129$	−28.0216	−2.46716
$130$	−1.00000	−0.0877058
$131$	−12.3982	−1.08324	−0.541619	−	0.840624i	$-0.682188\pi$
$131$	−12.3982	−1.08324	−0.541619	+	0.840624i	$0.682188\pi$
$132$	−12.3887	−1.07830
$133$	−21.9046	−1.89937
$134$	11.3533	0.980773
$135$	20.2642	1.74407
$136$	−6.24352	−0.535378
$137$	−3.51678	−0.300458	−0.150229	−	0.988651i	$-0.548001\pi$
$137$	−3.51678	−0.300458	−0.150229	+	0.988651i	$0.548001\pi$
$138$	−16.2076	−1.37968
$139$	−5.98485	−0.507628	−0.253814	−	0.967253i	$-0.581685\pi$
$139$	−5.98485	−0.507628	−0.253814	+	0.967253i	$0.581685\pi$
$140$	4.56226	0.385581
$141$	−34.3959	−2.89666
$142$	−7.42752	−0.623303
$143$	−3.59443	−0.300581
$144$	8.87940	0.739950
$145$	−0.684608	−0.0568536
$146$	1.88322	0.155856
$147$	47.6128	3.92704
$148$	−11.4165	−0.938433
$149$	5.22642	0.428165	0.214082	−	0.976816i	$-0.431324\pi$
$149$	5.22642	0.428165	0.214082	+	0.976816i	$0.431324\pi$
$150$	−3.44665	−0.281418
$151$	−12.4218	−1.01087	−0.505434	−	0.862865i	$-0.668668\pi$
$151$	−12.4218	−1.01087	−0.505434	+	0.862865i	$0.668668\pi$
$152$	4.80126	0.389433
$153$	55.4387	4.48196
$154$	16.3987	1.32145
$155$	1.00000	0.0803219
$156$	3.44665	0.275953
$157$	2.75507	0.219879	0.109939	−	0.993938i	$-0.464934\pi$
$157$	2.75507	0.219879	0.109939	+	0.993938i	$0.464934\pi$
$158$	7.82565	0.622575
$159$	−14.5026	−1.15013
$160$	−1.00000	−0.0790569
$161$	21.4537	1.69079
$162$	−43.2055	−3.39454
$163$	−4.91159	−0.384705	−0.192353	−	0.981326i	$-0.561612\pi$
$163$	−4.91159	−0.384705	−0.192353	+	0.981326i	$0.561612\pi$
$164$	0.472683	0.0369104
$165$	−12.3887	−0.964462
$166$	−13.1851	−1.02336
$167$	19.3310	1.49588	0.747938	−	0.663768i	$-0.231044\pi$
$167$	19.3310	1.49588	0.747938	+	0.663768i	$0.231044\pi$
$168$	−15.7245	−1.21317
$169$	1.00000	0.0769231
$170$	−6.24352	−0.478856
$171$	−42.6323	−3.26017
$172$	−8.13009	−0.619913
$173$	14.5303	1.10472	0.552360	−	0.833606i	$-0.313727\pi$
$173$	14.5303	1.10472	0.552360	+	0.833606i	$0.313727\pi$
$174$	2.35961	0.178881
$175$	4.56226	0.344875
$176$	−3.59443	−0.270940
$177$	−16.9265	−1.27227
$178$	7.29907	0.547089
$179$	10.7316	0.802120	0.401060	−	0.916052i	$-0.368642\pi$
$179$	10.7316	0.802120	0.401060	+	0.916052i	$0.368642\pi$
$180$	8.87940	0.661831
$181$	−13.6050	−1.01125	−0.505625	−	0.862754i	$-0.668738\pi$
$181$	−13.6050	−1.01125	−0.505625	+	0.862754i	$0.668738\pi$
$182$	−4.56226	−0.338177
$183$	−26.2444	−1.94005
$184$	−4.70242	−0.346667
$185$	−11.4165	−0.839360
$186$	−3.44665	−0.252721
$187$	−22.4419	−1.64111
$188$	−9.97952	−0.727832
$189$	92.4507	6.72480
$190$	4.80126	0.348320
$191$	−2.16358	−0.156551	−0.0782755	−	0.996932i	$-0.524941\pi$
$191$	−2.16358	−0.156551	−0.0782755	+	0.996932i	$0.524941\pi$
$192$	3.44665	0.248741
$193$	−4.90880	−0.353343	−0.176672	−	0.984270i	$-0.556533\pi$
$193$	−4.90880	−0.353343	−0.176672	+	0.984270i	$0.556533\pi$
$194$	−13.5364	−0.971854
$195$	3.44665	0.246820
$196$	13.8142	0.986731
$197$	12.6326	0.900033	0.450017	−	0.893020i	$-0.351418\pi$
$197$	12.6326	0.900033	0.450017	+	0.893020i	$0.351418\pi$
$198$	31.9164	2.26820
$199$	−3.18546	−0.225811	−0.112905	−	0.993606i	$-0.536016\pi$
$199$	−3.18546	−0.225811	−0.112905	+	0.993606i	$0.536016\pi$
$200$	−1.00000	−0.0707107
$201$	−39.1307	−2.76007
$202$	−15.1235	−1.06409
$203$	−3.12336	−0.219217
$204$	21.5192	1.50665
$205$	0.472683	0.0330136
$206$	15.0324	1.04736
$207$	41.7547	2.90215
$208$	1.00000	0.0693375
$209$	17.2578	1.19375
$210$	−15.7245	−1.08509
$211$	−0.785593	−0.0540825	−0.0270412	−	0.999634i	$-0.508609\pi$
$211$	−0.785593	−0.0540825	−0.0270412	+	0.999634i	$0.508609\pi$
$212$	−4.20774	−0.288989
$213$	25.6001	1.75409
$214$	14.8484	1.01501
$215$	−8.13009	−0.554467
$216$	−20.2642	−1.37881
$217$	4.56226	0.309706
$218$	−8.94746	−0.605998
$219$	−6.49080	−0.438608
$220$	−3.59443	−0.242336
$221$	6.24352	0.419985
$222$	39.3488	2.64092
$223$	−13.9089	−0.931410	−0.465705	−	0.884940i	$-0.654199\pi$
$223$	−13.9089	−0.931410	−0.465705	+	0.884940i	$0.654199\pi$
$224$	−4.56226	−0.304829
$225$	8.87940	0.591960
$226$	5.90854	0.393030
$227$	−16.7407	−1.11112	−0.555559	−	0.831477i	$-0.687496\pi$
$227$	−16.7407	−1.11112	−0.555559	+	0.831477i	$0.687496\pi$
$228$	−16.5483	−1.09593
$229$	2.19452	0.145018	0.0725090	−	0.997368i	$-0.476899\pi$
$229$	2.19452	0.145018	0.0725090	+	0.997368i	$0.476899\pi$
$230$	−4.70242	−0.310069
$231$	−56.5207	−3.71879
$232$	0.684608	0.0449467
$233$	−1.32650	−0.0869021	−0.0434511	−	0.999056i	$-0.513835\pi$
$233$	−1.32650	−0.0869021	−0.0434511	+	0.999056i	$0.513835\pi$
$234$	−8.87940	−0.580464
$235$	−9.97952	−0.650992
$236$	−4.91100	−0.319679
$237$	−26.9723	−1.75204
$238$	−28.4846	−1.84638
$239$	15.2874	0.988862	0.494431	−	0.869217i	$-0.335376\pi$
$239$	15.2874	0.988862	0.494431	+	0.869217i	$0.335376\pi$
$240$	3.44665	0.222480
$241$	25.6782	1.65408	0.827038	−	0.562146i	$-0.190024\pi$
$241$	25.6782	1.65408	0.827038	+	0.562146i	$0.190024\pi$
$242$	−1.91992	−0.123417
$243$	88.1216	5.65300
$244$	−7.61448	−0.487467
$245$	13.8142	0.882559
$246$	−1.62917	−0.103872
$247$	−4.80126	−0.305497
$248$	−1.00000	−0.0635001
$249$	45.4443	2.87991
$250$	−1.00000	−0.0632456
$251$	25.5083	1.61007	0.805035	−	0.593227i	$-0.202146\pi$
$251$	25.5083	1.61007	0.805035	+	0.593227i	$0.202146\pi$
$252$	40.5101	2.55190
$253$	−16.9025	−1.06265
$254$	−2.27616	−0.142819
$255$	21.5192	1.34759
$256$	1.00000	0.0625000
$257$	−7.92138	−0.494122	−0.247061	−	0.969000i	$-0.579465\pi$
$257$	−7.92138	−0.494122	−0.247061	+	0.969000i	$0.579465\pi$
$258$	28.0216	1.74455
$259$	−52.0852	−3.23642
$260$	1.00000	0.0620174
$261$	−6.07891	−0.376275
$262$	12.3982	0.765965
$263$	−11.8712	−0.732012	−0.366006	−	0.930612i	$-0.619275\pi$
$263$	−11.8712	−0.732012	−0.366006	+	0.930612i	$0.619275\pi$
$264$	12.3887	0.762474
$265$	−4.20774	−0.258480
$266$	21.9046	1.34306
$267$	−25.1574	−1.53960
$268$	−11.3533	−0.693511
$269$	26.9700	1.64439	0.822195	−	0.569206i	$-0.192749\pi$
$269$	26.9700	1.64439	0.822195	+	0.569206i	$0.192749\pi$
$270$	−20.2642	−1.23324
$271$	6.75448	0.410306	0.205153	−	0.978730i	$-0.434231\pi$
$271$	6.75448	0.410306	0.205153	+	0.978730i	$0.434231\pi$
$272$	6.24352	0.378569
$273$	15.7245	0.951691
$274$	3.51678	0.212456
$275$	−3.59443	−0.216752
$276$	16.2076	0.975584
$277$	1.82534	0.109674	0.0548371	−	0.998495i	$-0.482536\pi$
$277$	1.82534	0.109674	0.0548371	+	0.998495i	$0.482536\pi$
$278$	5.98485	0.358947
$279$	8.87940	0.531596
$280$	−4.56226	−0.272647
$281$	−2.22622	−0.132805	−0.0664027	−	0.997793i	$-0.521152\pi$
$281$	−2.22622	−0.132805	−0.0664027	+	0.997793i	$0.521152\pi$
$282$	34.3959	2.04825
$283$	16.9067	1.00500	0.502499	−	0.864578i	$-0.332414\pi$
$283$	16.9067	1.00500	0.502499	+	0.864578i	$0.332414\pi$
$284$	7.42752	0.440742
$285$	−16.5483	−0.980234
$286$	3.59443	0.212543
$287$	2.15650	0.127294
$288$	−8.87940	−0.523223
$289$	21.9816	1.29304
$290$	0.684608	0.0402016
$291$	46.6551	2.73497
$292$	−1.88322	−0.110207
$293$	−3.90086	−0.227890	−0.113945	−	0.993487i	$-0.536349\pi$
$293$	−3.90086	−0.227890	−0.113945	+	0.993487i	$0.536349\pi$
$294$	−47.6128	−2.77684
$295$	−4.91100	−0.285930
$296$	11.4165	0.663572
$297$	−72.8383	−4.22651
$298$	−5.22642	−0.302758
$299$	4.70242	0.271948
$300$	3.44665	0.198992
$301$	−37.0916	−2.13792
$302$	12.4218	0.714792
$303$	52.1256	2.99454
$304$	−4.80126	−0.275371
$305$	−7.61448	−0.436004
$306$	−55.4387	−3.16922
$307$	19.0558	1.08757	0.543787	−	0.839223i	$-0.316990\pi$
$307$	19.0558	1.08757	0.543787	+	0.839223i	$0.316990\pi$
$308$	−16.3987	−0.934404
$309$	−51.8113	−2.94744
$310$	−1.00000	−0.0567962
$311$	−13.4574	−0.763101	−0.381551	−	0.924348i	$-0.624610\pi$
$311$	−13.4574	−0.763101	−0.381551	+	0.924348i	$0.624610\pi$
$312$	−3.44665	−0.195128
$313$	−26.8986	−1.52040	−0.760199	−	0.649690i	$-0.774899\pi$
$313$	−26.8986	−1.52040	−0.760199	+	0.649690i	$0.774899\pi$
$314$	−2.75507	−0.155478
$315$	40.5101	2.28249
$316$	−7.82565	−0.440227
$317$	−3.61226	−0.202884	−0.101442	−	0.994841i	$-0.532346\pi$
$317$	−3.61226	−0.202884	−0.101442	+	0.994841i	$0.532346\pi$
$318$	14.5026	0.813266
$319$	2.46078	0.137777
$320$	1.00000	0.0559017
$321$	−51.1771	−2.85643
$322$	−21.4537	−1.19557
$323$	−29.9768	−1.66795
$324$	43.2055	2.40031
$325$	1.00000	0.0554700
$326$	4.91159	0.272028
$327$	30.8388	1.70539
$328$	−0.472683	−0.0260996
$329$	−45.5292	−2.51011
$330$	12.3887	0.681978
$331$	−23.4815	−1.29066	−0.645330	−	0.763904i	$-0.723280\pi$
$331$	−23.4815	−1.29066	−0.645330	+	0.763904i	$0.723280\pi$
$332$	13.1851	0.723624
$333$	−101.372	−5.55514
$334$	−19.3310	−1.05774
$335$	−11.3533	−0.620295
$336$	15.7245	0.857843
$337$	−13.5308	−0.737072	−0.368536	−	0.929613i	$-0.620141\pi$
$337$	−13.5308	−0.737072	−0.368536	+	0.929613i	$0.620141\pi$
$338$	−1.00000	−0.0543928
$339$	−20.3647	−1.10606
$340$	6.24352	0.338603
$341$	−3.59443	−0.194649
$342$	42.6323	2.30529
$343$	31.0883	1.67861
$344$	8.13009	0.438345
$345$	16.2076	0.872589
$346$	−14.5303	−0.781155
$347$	21.1982	1.13798	0.568991	−	0.822344i	$-0.307334\pi$
$347$	21.1982	1.13798	0.568991	+	0.822344i	$0.307334\pi$
$348$	−2.35961	−0.126488
$349$	−4.29748	−0.230039	−0.115019	−	0.993363i	$-0.536693\pi$
$349$	−4.29748	−0.230039	−0.115019	+	0.993363i	$0.536693\pi$
$350$	−4.56226	−0.243863
$351$	20.2642	1.08162
$352$	3.59443	0.191584
$353$	−36.8655	−1.96215	−0.981075	−	0.193626i	$-0.937975\pi$
$353$	−36.8655	−1.96215	−0.981075	+	0.193626i	$0.937975\pi$
$354$	16.9265	0.899634
$355$	7.42752	0.394212
$356$	−7.29907	−0.386850
$357$	98.1764	5.19605
$358$	−10.7316	−0.567184
$359$	−11.2928	−0.596009	−0.298004	−	0.954565i	$-0.596321\pi$
$359$	−11.2928	−0.596009	−0.298004	+	0.954565i	$0.596321\pi$
$360$	−8.87940	−0.467985
$361$	4.05207	0.213267
$362$	13.6050	0.715061
$363$	6.61730	0.347318
$364$	4.56226	0.239127
$365$	−1.88322	−0.0985722
$366$	26.2444	1.37182
$367$	2.06836	0.107968	0.0539839	−	0.998542i	$-0.482808\pi$
$367$	2.06836	0.107968	0.0539839	+	0.998542i	$0.482808\pi$
$368$	4.70242	0.245131
$369$	4.19714	0.218494
$370$	11.4165	0.593517
$371$	−19.1968	−0.996649
$372$	3.44665	0.178700
$373$	13.0858	0.677559	0.338779	−	0.940866i	$-0.389986\pi$
$373$	13.0858	0.677559	0.338779	+	0.940866i	$0.389986\pi$
$374$	22.4419	1.16044
$375$	3.44665	0.177984
$376$	9.97952	0.514655
$377$	−0.684608	−0.0352591
$378$	−92.4507	−4.75515
$379$	3.18127	0.163411	0.0817054	−	0.996657i	$-0.473963\pi$
$379$	3.18127	0.163411	0.0817054	+	0.996657i	$0.473963\pi$
$380$	−4.80126	−0.246299
$381$	7.84513	0.401918
$382$	2.16358	0.110698
$383$	28.2983	1.44597	0.722987	−	0.690862i	$-0.242769\pi$
$383$	28.2983	1.44597	0.722987	+	0.690862i	$0.242769\pi$
$384$	−3.44665	−0.175886
$385$	−16.3987	−0.835756
$386$	4.90880	0.249851
$387$	−72.1903	−3.66964
$388$	13.5364	0.687205
$389$	−3.90955	−0.198222	−0.0991110	−	0.995076i	$-0.531600\pi$
$389$	−3.90955	−0.198222	−0.0991110	+	0.995076i	$0.531600\pi$
$390$	−3.44665	−0.174528
$391$	29.3597	1.48478
$392$	−13.8142	−0.697724
$393$	−42.7323	−2.15556
$394$	−12.6326	−0.636420
$395$	−7.82565	−0.393751
$396$	−31.9164	−1.60386
$397$	−6.68160	−0.335340	−0.167670	−	0.985843i	$-0.553624\pi$
$397$	−6.68160	−0.335340	−0.167670	+	0.985843i	$0.553624\pi$
$398$	3.18546	0.159672
$399$	−75.4975	−3.77960
$400$	1.00000	0.0500000
$401$	2.05434	0.102589	0.0512945	−	0.998684i	$-0.483665\pi$
$401$	2.05434	0.102589	0.0512945	+	0.998684i	$0.483665\pi$
$402$	39.1307	1.95166
$403$	1.00000	0.0498135
$404$	15.1235	0.752424
$405$	43.2055	2.14690
$406$	3.12336	0.155010
$407$	41.0359	2.03407
$408$	−21.5192	−1.06536
$409$	15.1375	0.748499	0.374249	−	0.927328i	$-0.377900\pi$
$409$	15.1375	0.748499	0.374249	+	0.927328i	$0.377900\pi$
$410$	−0.472683	−0.0233442
$411$	−12.1211	−0.597890
$412$	−15.0324	−0.740592
$413$	−22.4053	−1.10249
$414$	−41.7547	−2.05213
$415$	13.1851	0.647229
$416$	−1.00000	−0.0490290
$417$	−20.6277	−1.01014
$418$	−17.2578	−0.844106
$419$	25.6806	1.25458	0.627289	−	0.778786i	$-0.284164\pi$
$419$	25.6806	1.25458	0.627289	+	0.778786i	$0.284164\pi$
$420$	15.7245	0.767278
$421$	−28.7406	−1.40073	−0.700365	−	0.713785i	$-0.746980\pi$
$421$	−28.7406	−1.40073	−0.700365	+	0.713785i	$0.746980\pi$
$422$	0.785593	0.0382421
$423$	−88.6122	−4.30847
$424$	4.20774	0.204346
$425$	6.24352	0.302855
$426$	−25.6001	−1.24033
$427$	−34.7392	−1.68115
$428$	−14.8484	−0.717723
$429$	−12.3887	−0.598134
$430$	8.13009	0.392068
$431$	−26.5435	−1.27856	−0.639279	−	0.768975i	$-0.720767\pi$
$431$	−26.5435	−1.27856	−0.639279	+	0.768975i	$0.720767\pi$
$432$	20.2642	0.974963
$433$	25.2466	1.21328	0.606638	−	0.794978i	$-0.292518\pi$
$433$	25.2466	1.21328	0.606638	+	0.794978i	$0.292518\pi$
$434$	−4.56226	−0.218996
$435$	−2.35961	−0.113134
$436$	8.94746	0.428505
$437$	−22.5776	−1.08003
$438$	6.49080	0.310142
$439$	8.34352	0.398214	0.199107	−	0.979978i	$-0.436196\pi$
$439$	8.34352	0.398214	0.199107	+	0.979978i	$0.436196\pi$
$440$	3.59443	0.171358
$441$	122.662	5.84105
$442$	−6.24352	−0.296974
$443$	26.5456	1.26122	0.630610	−	0.776100i	$-0.282805\pi$
$443$	26.5456	1.26122	0.630610	+	0.776100i	$0.282805\pi$
$444$	−39.3488	−1.86741
$445$	−7.29907	−0.346009
$446$	13.9089	0.658606
$447$	18.0136	0.852016
$448$	4.56226	0.215547
$449$	19.6784	0.928682	0.464341	−	0.885656i	$-0.346291\pi$
$449$	19.6784	0.928682	0.464341	+	0.885656i	$0.346291\pi$
$450$	−8.87940	−0.418579
$451$	−1.69903	−0.0800040
$452$	−5.90854	−0.277914
$453$	−42.8134	−2.01155
$454$	16.7407	0.785679
$455$	4.56226	0.213882
$456$	16.5483	0.774943
$457$	33.5535	1.56956	0.784782	−	0.619771i	$-0.212775\pi$
$457$	33.5535	1.56956	0.784782	+	0.619771i	$0.212775\pi$
$458$	−2.19452	−0.102543
$459$	126.520	5.90546
$460$	4.70242	0.219252
$461$	26.5823	1.23806	0.619031	−	0.785367i	$-0.287526\pi$
$461$	26.5823	1.23806	0.619031	+	0.785367i	$0.287526\pi$
$462$	56.5207	2.62958
$463$	2.40039	0.111556	0.0557778	−	0.998443i	$-0.482236\pi$
$463$	2.40039	0.111556	0.0557778	+	0.998443i	$0.482236\pi$
$464$	−0.684608	−0.0317821
$465$	3.44665	0.159835
$466$	1.32650	0.0614491
$467$	6.49132	0.300382	0.150191	−	0.988657i	$-0.452011\pi$
$467$	6.49132	0.300382	0.150191	+	0.988657i	$0.452011\pi$
$468$	8.87940	0.410450
$469$	−51.7966	−2.39174
$470$	9.97952	0.460321
$471$	9.49578	0.437542
$472$	4.91100	0.226047
$473$	29.2230	1.34368
$474$	26.9723	1.23888
$475$	−4.80126	−0.220297
$476$	28.4846	1.30559
$477$	−37.3622	−1.71070
$478$	−15.2874	−0.699231
$479$	13.9202	0.636031	0.318016	−	0.948085i	$-0.396984\pi$
$479$	13.9202	0.636031	0.318016	+	0.948085i	$0.396984\pi$
$480$	−3.44665	−0.157317
$481$	−11.4165	−0.520549
$482$	−25.6782	−1.16961
$483$	73.9434	3.36454
$484$	1.91992	0.0872692
$485$	13.5364	0.614655
$486$	−88.1216	−3.99728
$487$	−4.16194	−0.188595	−0.0942977	−	0.995544i	$-0.530061\pi$
$487$	−4.16194	−0.188595	−0.0942977	+	0.995544i	$0.530061\pi$
$488$	7.61448	0.344691
$489$	−16.9285	−0.765534
$490$	−13.8142	−0.624063
$491$	18.1438	0.818818	0.409409	−	0.912351i	$-0.365735\pi$
$491$	18.1438	0.818818	0.409409	+	0.912351i	$0.365735\pi$
$492$	1.62917	0.0734488
$493$	−4.27437	−0.192508
$494$	4.80126	0.216019
$495$	−31.9164	−1.43453
$496$	1.00000	0.0449013
$497$	33.8863	1.52001
$498$	−45.4443	−2.03641
$499$	25.5437	1.14349	0.571746	−	0.820431i	$-0.306266\pi$
$499$	25.5437	1.14349	0.571746	+	0.820431i	$0.306266\pi$
$500$	1.00000	0.0447214
$501$	66.6271	2.97668
$502$	−25.5083	−1.13849
$503$	−2.51167	−0.111990	−0.0559949	−	0.998431i	$-0.517833\pi$
$503$	−2.51167	−0.111990	−0.0559949	+	0.998431i	$0.517833\pi$
$504$	−40.5101	−1.80446
$505$	15.1235	0.672989
$506$	16.9025	0.751409
$507$	3.44665	0.153071
$508$	2.27616	0.100988
$509$	27.6910	1.22738	0.613690	−	0.789547i	$-0.289684\pi$
$509$	27.6910	1.22738	0.613690	+	0.789547i	$0.289684\pi$
$510$	−21.5192	−0.952888
$511$	−8.59174	−0.380076
$512$	−1.00000	−0.0441942
$513$	−97.2937	−4.29562
$514$	7.92138	0.349397
$515$	−15.0324	−0.662406
$516$	−28.0216	−1.23358
$517$	35.8707	1.57759
$518$	52.0852	2.28849
$519$	50.0809	2.19831
$520$	−1.00000	−0.0438529
$521$	2.27260	0.0995646	0.0497823	−	0.998760i	$-0.484147\pi$
$521$	2.27260	0.0995646	0.0497823	+	0.998760i	$0.484147\pi$
$522$	6.07891	0.266067
$523$	38.9408	1.70276	0.851382	−	0.524546i	$-0.175765\pi$
$523$	38.9408	1.70276	0.851382	+	0.524546i	$0.175765\pi$
$524$	−12.3982	−0.541619
$525$	15.7245	0.686274
$526$	11.8712	0.517611
$527$	6.24352	0.271972
$528$	−12.3887	−0.539151
$529$	−0.887200	−0.0385739
$530$	4.20774	0.182773
$531$	−43.6068	−1.89237
$532$	−21.9046	−0.949684
$533$	0.472683	0.0204742
$534$	25.1574	1.08867
$535$	−14.8484	−0.641951
$536$	11.3533	0.490386
$537$	36.9882	1.59616
$538$	−26.9700	−1.16276
$539$	−49.6543	−2.13876
$540$	20.2642	0.872033
$541$	−20.5657	−0.884188	−0.442094	−	0.896969i	$-0.645764\pi$
$541$	−20.5657	−0.884188	−0.442094	+	0.896969i	$0.645764\pi$
$542$	−6.75448	−0.290130
$543$	−46.8916	−2.01231
$544$	−6.24352	−0.267689
$545$	8.94746	0.383267
$546$	−15.7245	−0.672947
$547$	29.3689	1.25572	0.627861	−	0.778326i	$-0.283931\pi$
$547$	29.3689	1.25572	0.627861	+	0.778326i	$0.283931\pi$
$548$	−3.51678	−0.150229
$549$	−67.6120	−2.88561
$550$	3.59443	0.153267
$551$	3.28698	0.140030
$552$	−16.2076	−0.689842
$553$	−35.7027	−1.51823
$554$	−1.82534	−0.0775514
$555$	−39.3488	−1.67026
$556$	−5.98485	−0.253814
$557$	−21.8826	−0.927194	−0.463597	−	0.886046i	$-0.653441\pi$
$557$	−21.8826	−0.927194	−0.463597	+	0.886046i	$0.653441\pi$
$558$	−8.87940	−0.375895
$559$	−8.13009	−0.343866
$560$	4.56226	0.192791
$561$	−77.3494	−3.26569
$562$	2.22622	0.0939076
$563$	−41.0883	−1.73167	−0.865834	−	0.500332i	$-0.833211\pi$
$563$	−41.0883	−1.73167	−0.865834	+	0.500332i	$0.833211\pi$
$564$	−34.3959	−1.44833
$565$	−5.90854	−0.248574
$566$	−16.9067	−0.710641
$567$	197.115	8.27804
$568$	−7.42752	−0.311652
$569$	20.0220	0.839366	0.419683	−	0.907671i	$-0.362141\pi$
$569$	20.0220	0.839366	0.419683	+	0.907671i	$0.362141\pi$
$570$	16.5483	0.693130
$571$	−33.3656	−1.39631	−0.698154	−	0.715947i	$-0.745995\pi$
$571$	−33.3656	−1.39631	−0.698154	+	0.715947i	$0.745995\pi$
$572$	−3.59443	−0.150291
$573$	−7.45710	−0.311525
$574$	−2.15650	−0.0900108
$575$	4.70242	0.196105
$576$	8.87940	0.369975
$577$	35.7469	1.48816	0.744081	−	0.668089i	$-0.232888\pi$
$577$	35.7469	1.48816	0.744081	+	0.668089i	$0.232888\pi$
$578$	−21.9816	−0.914314
$579$	−16.9189	−0.703126
$580$	−0.684608	−0.0284268
$581$	60.1537	2.49560
$582$	−46.6551	−1.93392
$583$	15.1244	0.626390
$584$	1.88322	0.0779282
$585$	8.87940	0.367118
$586$	3.90086	0.161143
$587$	−26.5848	−1.09727	−0.548636	−	0.836061i	$-0.684853\pi$
$587$	−26.5848	−1.09727	−0.548636	+	0.836061i	$0.684853\pi$
$588$	47.6128	1.96352
$589$	−4.80126	−0.197832
$590$	4.91100	0.202183
$591$	43.5400	1.79100
$592$	−11.4165	−0.469216
$593$	39.8166	1.63507	0.817536	−	0.575878i	$-0.195340\pi$
$593$	39.8166	1.63507	0.817536	+	0.575878i	$0.195340\pi$
$594$	72.8383	2.98859
$595$	28.4846	1.16775
$596$	5.22642	0.214082
$597$	−10.9792	−0.449347
$598$	−4.70242	−0.192296
$599$	16.3228	0.666933	0.333466	−	0.942762i	$-0.391782\pi$
$599$	16.3228	0.666933	0.333466	+	0.942762i	$0.391782\pi$
$600$	−3.44665	−0.140709
$601$	36.6738	1.49596	0.747978	−	0.663723i	$-0.231025\pi$
$601$	36.6738	1.49596	0.747978	+	0.663723i	$0.231025\pi$
$602$	37.0916	1.51174
$603$	−100.810	−4.10531
$604$	−12.4218	−0.505434
$605$	1.91992	0.0780559
$606$	−52.1256	−2.11746
$607$	−18.1649	−0.737289	−0.368644	−	0.929570i	$-0.620178\pi$
$607$	−18.1649	−0.737289	−0.368644	+	0.929570i	$0.620178\pi$
$608$	4.80126	0.194717
$609$	−10.7651	−0.436225
$610$	7.61448	0.308301
$611$	−9.97952	−0.403728
$612$	55.4387	2.24098
$613$	34.6228	1.39840	0.699200	−	0.714926i	$-0.253540\pi$
$613$	34.6228	1.39840	0.699200	+	0.714926i	$0.253540\pi$
$614$	−19.0558	−0.769031
$615$	1.62917	0.0656946
$616$	16.3987	0.660723
$617$	44.0368	1.77286	0.886428	−	0.462866i	$-0.153179\pi$
$617$	44.0368	1.77286	0.886428	+	0.462866i	$0.153179\pi$
$618$	51.8113	2.08416
$619$	−19.0864	−0.767149	−0.383574	−	0.923510i	$-0.625307\pi$
$619$	−19.0864	−0.767149	−0.383574	+	0.923510i	$0.625307\pi$
$620$	1.00000	0.0401610
$621$	95.2910	3.82390
$622$	13.4574	0.539594
$623$	−33.3003	−1.33415
$624$	3.44665	0.137976
$625$	1.00000	0.0400000
$626$	26.8986	1.07508
$627$	59.4815	2.37546
$628$	2.75507	0.109939
$629$	−71.2794	−2.84209
$630$	−40.5101	−1.61396
$631$	9.77471	0.389125	0.194563	−	0.980890i	$-0.437671\pi$
$631$	9.77471	0.389125	0.194563	+	0.980890i	$0.437671\pi$
$632$	7.82565	0.311288
$633$	−2.70767	−0.107620
$634$	3.61226	0.143461
$635$	2.27616	0.0903267
$636$	−14.5026	−0.575066
$637$	13.8142	0.547340
$638$	−2.46078	−0.0974231
$639$	65.9519	2.60902
$640$	−1.00000	−0.0395285
$641$	−46.6882	−1.84407	−0.922036	−	0.387104i	$-0.873475\pi$
$641$	−46.6882	−1.84407	−0.922036	+	0.387104i	$0.873475\pi$
$642$	51.1771	2.01980
$643$	3.03756	0.119789	0.0598947	−	0.998205i	$-0.480923\pi$
$643$	3.03756	0.119789	0.0598947	+	0.998205i	$0.480923\pi$
$644$	21.4537	0.845394
$645$	−28.0216	−1.10335
$646$	29.9768	1.17942
$647$	20.4547	0.804158	0.402079	−	0.915605i	$-0.368288\pi$
$647$	20.4547	0.804158	0.402079	+	0.915605i	$0.368288\pi$
$648$	−43.2055	−1.69727
$649$	17.6523	0.692912
$650$	−1.00000	−0.0392232
$651$	15.7245	0.616292
$652$	−4.91159	−0.192353
$653$	−33.0647	−1.29392	−0.646961	−	0.762523i	$-0.723960\pi$
$653$	−33.0647	−1.29392	−0.646961	+	0.762523i	$0.723960\pi$
$654$	−30.8388	−1.20589
$655$	−12.3982	−0.484439
$656$	0.472683	0.0184552
$657$	−16.7219	−0.652382
$658$	45.5292	1.77491
$659$	−9.71105	−0.378289	−0.189144	−	0.981949i	$-0.560571\pi$
$659$	−9.71105	−0.378289	−0.189144	+	0.981949i	$0.560571\pi$
$660$	−12.3887	−0.482231
$661$	−16.2250	−0.631079	−0.315540	−	0.948912i	$-0.602186\pi$
$661$	−16.2250	−0.631079	−0.315540	+	0.948912i	$0.602186\pi$
$662$	23.4815	0.912635
$663$	21.5192	0.835738
$664$	−13.1851	−0.511679
$665$	−21.9046	−0.849424
$666$	101.372	3.92808
$667$	−3.21932	−0.124653
$668$	19.3310	0.747938
$669$	−47.9391	−1.85343
$670$	11.3533	0.438615
$671$	27.3697	1.05660
$672$	−15.7245	−0.606586
$673$	19.6144	0.756079	0.378039	−	0.925790i	$-0.376598\pi$
$673$	19.6144	0.756079	0.378039	+	0.925790i	$0.376598\pi$
$674$	13.5308	0.521189
$675$	20.2642	0.779970
$676$	1.00000	0.0384615
$677$	−40.0790	−1.54036	−0.770180	−	0.637827i	$-0.779834\pi$
$677$	−40.0790	−1.54036	−0.770180	+	0.637827i	$0.779834\pi$
$678$	20.3647	0.782100
$679$	61.7564	2.36999
$680$	−6.24352	−0.239428
$681$	−57.6993	−2.21104
$682$	3.59443	0.137638
$683$	−13.4820	−0.515876	−0.257938	−	0.966162i	$-0.583043\pi$
$683$	−13.4820	−0.515876	−0.257938	+	0.966162i	$0.583043\pi$
$684$	−42.6323	−1.63009
$685$	−3.51678	−0.134369
$686$	−31.0883	−1.18696
$687$	7.56374	0.288575
$688$	−8.13009	−0.309957
$689$	−4.20774	−0.160302
$690$	−16.2076	−0.617013
$691$	15.0094	0.570983	0.285491	−	0.958381i	$-0.407843\pi$
$691$	15.0094	0.570983	0.285491	+	0.958381i	$0.407843\pi$
$692$	14.5303	0.552360
$693$	−145.611	−5.53130
$694$	−21.1982	−0.804674
$695$	−5.98485	−0.227018
$696$	2.35961	0.0894406
$697$	2.95121	0.111785
$698$	4.29748	0.162662
$699$	−4.57199	−0.172929
$700$	4.56226	0.172437
$701$	−14.5981	−0.551364	−0.275682	−	0.961249i	$-0.588904\pi$
$701$	−14.5981	−0.551364	−0.275682	+	0.961249i	$0.588904\pi$
$702$	−20.2642	−0.764824
$703$	54.8137	2.06734
$704$	−3.59443	−0.135470
$705$	−34.3959	−1.29543
$706$	36.8655	1.38745
$707$	68.9976	2.59492
$708$	−16.9265	−0.636137
$709$	−40.5262	−1.52199	−0.760996	−	0.648757i	$-0.775289\pi$
$709$	−40.5262	−1.52199	−0.760996	+	0.648757i	$0.775289\pi$
$710$	−7.42752	−0.278750
$711$	−69.4871	−2.60597
$712$	7.29907	0.273544
$713$	4.70242	0.176107
$714$	−98.1764	−3.67416
$715$	−3.59443	−0.134424
$716$	10.7316	0.401060
$717$	52.6905	1.96776
$718$	11.2928	0.421442
$719$	−39.8069	−1.48455	−0.742273	−	0.670098i	$-0.766252\pi$
$719$	−39.8069	−1.48455	−0.742273	+	0.670098i	$0.766252\pi$
$720$	8.87940	0.330916
$721$	−68.5816	−2.55411
$722$	−4.05207	−0.150802
$723$	88.5037	3.29149
$724$	−13.6050	−0.505625
$725$	−0.684608	−0.0254257
$726$	−6.61730	−0.245591
$727$	9.38063	0.347908	0.173954	−	0.984754i	$-0.444346\pi$
$727$	9.38063	0.347908	0.173954	+	0.984754i	$0.444346\pi$
$728$	−4.56226	−0.169089
$729$	174.108	6.44843
$730$	1.88322	0.0697011
$731$	−50.7604	−1.87744
$732$	−26.2444	−0.970023
$733$	−8.42086	−0.311031	−0.155516	−	0.987833i	$-0.549704\pi$
$733$	−8.42086	−0.311031	−0.155516	+	0.987833i	$0.549704\pi$
$734$	−2.06836	−0.0763447
$735$	47.6128	1.75623
$736$	−4.70242	−0.173334
$737$	40.8085	1.50320
$738$	−4.19714	−0.154499
$739$	17.5014	0.643800	0.321900	−	0.946774i	$-0.395678\pi$
$739$	17.5014	0.643800	0.321900	+	0.946774i	$0.395678\pi$
$740$	−11.4165	−0.419680
$741$	−16.5483	−0.607915
$742$	19.1968	0.704738
$743$	−12.3370	−0.452600	−0.226300	−	0.974058i	$-0.572663\pi$
$743$	−12.3370	−0.452600	−0.226300	+	0.974058i	$0.572663\pi$
$744$	−3.44665	−0.126360
$745$	5.22642	0.191481
$746$	−13.0858	−0.479107
$747$	117.075	4.28356
$748$	−22.4419	−0.820557
$749$	−67.7422	−2.47524
$750$	−3.44665	−0.125854
$751$	−20.3327	−0.741950	−0.370975	−	0.928643i	$-0.620976\pi$
$751$	−20.3327	−0.741950	−0.370975	+	0.928643i	$0.620976\pi$
$752$	−9.97952	−0.363916
$753$	87.9182	3.20392
$754$	0.684608	0.0249320
$755$	−12.4218	−0.452074
$756$	92.4507	3.36240
$757$	0.530512	0.0192818	0.00964090	−	0.999954i	$-0.496931\pi$
$757$	0.530512	0.0192818	0.00964090	+	0.999954i	$0.496931\pi$
$758$	−3.18127	−0.115549
$759$	−58.2571	−2.11460
$760$	4.80126	0.174160
$761$	−26.8374	−0.972855	−0.486428	−	0.873721i	$-0.661700\pi$
$761$	−26.8374	−0.972855	−0.486428	+	0.873721i	$0.661700\pi$
$762$	−7.84513	−0.284199
$763$	40.8206	1.47781
$764$	−2.16358	−0.0782755
$765$	55.4387	2.00439
$766$	−28.2983	−1.02246
$767$	−4.91100	−0.177326
$768$	3.44665	0.124370
$769$	−15.9148	−0.573902	−0.286951	−	0.957945i	$-0.592642\pi$
$769$	−15.9148	−0.573902	−0.286951	+	0.957945i	$0.592642\pi$
$770$	16.3987	0.590969
$771$	−27.3022	−0.983265
$772$	−4.90880	−0.176672
$773$	−14.6800	−0.528002	−0.264001	−	0.964522i	$-0.585042\pi$
$773$	−14.6800	−0.528002	−0.264001	+	0.964522i	$0.585042\pi$
$774$	72.1903	2.59483
$775$	1.00000	0.0359211
$776$	−13.5364	−0.485927
$777$	−179.519	−6.44022
$778$	3.90955	0.140164
$779$	−2.26947	−0.0813123
$780$	3.44665	0.123410
$781$	−26.6977	−0.955318
$782$	−29.3597	−1.04990
$783$	−13.8731	−0.495783
$784$	13.8142	0.493365
$785$	2.75507	0.0983328
$786$	42.7323	1.52421
$787$	−48.7361	−1.73725	−0.868627	−	0.495467i	$-0.834997\pi$
$787$	−48.7361	−1.73725	−0.868627	+	0.495467i	$0.834997\pi$
$788$	12.6326	0.450017
$789$	−40.9160	−1.45665
$790$	7.82565	0.278424
$791$	−26.9563	−0.958455
$792$	31.9164	1.13410
$793$	−7.61448	−0.270398
$794$	6.68160	0.237121
$795$	−14.5026	−0.514355
$796$	−3.18546	−0.112905
$797$	12.7389	0.451234	0.225617	−	0.974216i	$-0.427560\pi$
$797$	12.7389	0.451234	0.225617	+	0.974216i	$0.427560\pi$
$798$	75.4975	2.67258
$799$	−62.3074	−2.20428
$800$	−1.00000	−0.0353553
$801$	−64.8114	−2.29000
$802$	−2.05434	−0.0725413
$803$	6.76910	0.238876
$804$	−39.1307	−1.38003
$805$	21.4537	0.756143
$806$	−1.00000	−0.0352235
$807$	92.9562	3.27221
$808$	−15.1235	−0.532044
$809$	14.8968	0.523743	0.261872	−	0.965103i	$-0.415660\pi$
$809$	14.8968	0.523743	0.261872	+	0.965103i	$0.415660\pi$
$810$	−43.2055	−1.51809
$811$	9.28005	0.325867	0.162933	−	0.986637i	$-0.447904\pi$
$811$	9.28005	0.325867	0.162933	+	0.986637i	$0.447904\pi$
$812$	−3.12336	−0.109609
$813$	23.2803	0.816477
$814$	−41.0359	−1.43831
$815$	−4.91159	−0.172045
$816$	21.5192	0.753324
$817$	39.0346	1.36565
$818$	−15.1375	−0.529269
$819$	40.5101	1.41554
$820$	0.472683	0.0165068
$821$	−23.2807	−0.812503	−0.406251	−	0.913761i	$-0.633164\pi$
$821$	−23.2807	−0.812503	−0.406251	+	0.913761i	$0.633164\pi$
$822$	12.1211	0.422772
$823$	9.50851	0.331446	0.165723	−	0.986172i	$-0.447004\pi$
$823$	9.50851	0.331446	0.165723	+	0.986172i	$0.447004\pi$
$824$	15.0324	0.523678
$825$	−12.3887	−0.431321
$826$	22.4053	0.779580
$827$	−39.4744	−1.37266	−0.686330	−	0.727290i	$-0.740780\pi$
$827$	−39.4744	−1.37266	−0.686330	+	0.727290i	$0.740780\pi$
$828$	41.7547	1.45108
$829$	16.6840	0.579459	0.289729	−	0.957109i	$-0.406435\pi$
$829$	16.6840	0.579459	0.289729	+	0.957109i	$0.406435\pi$
$830$	−13.1851	−0.457660
$831$	6.29132	0.218244
$832$	1.00000	0.0346688
$833$	86.2495	2.98837
$834$	20.6277	0.714278
$835$	19.3310	0.668976
$836$	17.2578	0.596873
$837$	20.2642	0.700434
$838$	−25.6806	−0.887121
$839$	14.5223	0.501366	0.250683	−	0.968069i	$-0.419345\pi$
$839$	14.5223	0.501366	0.250683	+	0.968069i	$0.419345\pi$
$840$	−15.7245	−0.542547
$841$	−28.5313	−0.983838
$842$	28.7406	0.990466
$843$	−7.67301	−0.264273
$844$	−0.785593	−0.0270412
$845$	1.00000	0.0344010
$846$	88.6122	3.04655
$847$	8.75919	0.300969
$848$	−4.20774	−0.144494
$849$	58.2714	1.99987
$850$	−6.24352	−0.214151
$851$	−53.6854	−1.84031
$852$	25.6001	0.877043
$853$	30.8746	1.05713	0.528564	−	0.848894i	$-0.322731\pi$
$853$	30.8746	1.05713	0.528564	+	0.848894i	$0.322731\pi$
$854$	34.7392	1.18875
$855$	−42.6323	−1.45799
$856$	14.8484	0.507507
$857$	40.7380	1.39158	0.695791	−	0.718244i	$-0.255054\pi$
$857$	40.7380	1.39158	0.695791	+	0.718244i	$0.255054\pi$
$858$	12.3887	0.422945
$859$	37.3406	1.27405	0.637023	−	0.770845i	$-0.280166\pi$
$859$	37.3406	1.27405	0.637023	+	0.770845i	$0.280166\pi$
$860$	−8.13009	−0.277234
$861$	7.43272	0.253306
$862$	26.5435	0.904076
$863$	−9.37322	−0.319068	−0.159534	−	0.987192i	$-0.550999\pi$
$863$	−9.37322	−0.319068	−0.159534	+	0.987192i	$0.550999\pi$
$864$	−20.2642	−0.689403
$865$	14.5303	0.494046
$866$	−25.2466	−0.857916
$867$	75.7629	2.57304
$868$	4.56226	0.154853
$869$	28.1288	0.954203
$870$	2.35961	0.0799981
$871$	−11.3533	−0.384691
$872$	−8.94746	−0.302999
$873$	120.195	4.06798
$874$	22.5776	0.763697
$875$	4.56226	0.154233
$876$	−6.49080	−0.219304
$877$	−50.1033	−1.69187	−0.845933	−	0.533289i	$-0.820956\pi$
$877$	−50.1033	−1.69187	−0.845933	+	0.533289i	$0.820956\pi$
$878$	−8.34352	−0.281580
$879$	−13.4449	−0.453485
$880$	−3.59443	−0.121168
$881$	26.6028	0.896272	0.448136	−	0.893965i	$-0.352088\pi$
$881$	26.6028	0.896272	0.448136	+	0.893965i	$0.352088\pi$
$882$	−122.662	−4.13024
$883$	−1.57554	−0.0530212	−0.0265106	−	0.999649i	$-0.508440\pi$
$883$	−1.57554	−0.0530212	−0.0265106	+	0.999649i	$0.508440\pi$
$884$	6.24352	0.209992
$885$	−16.9265	−0.568979
$886$	−26.5456	−0.891817
$887$	−1.51095	−0.0507327	−0.0253663	−	0.999678i	$-0.508075\pi$
$887$	−1.51095	−0.0507327	−0.0253663	+	0.999678i	$0.508075\pi$
$888$	39.3488	1.32046
$889$	10.3844	0.348283
$890$	7.29907	0.244665
$891$	−155.299	−5.20272
$892$	−13.9089	−0.465705
$893$	47.9143	1.60339
$894$	−18.0136	−0.602466
$895$	10.7316	0.358719
$896$	−4.56226	−0.152414
$897$	16.2076	0.541156
$898$	−19.6784	−0.656677
$899$	−0.684608	−0.0228330
$900$	8.87940	0.295980
$901$	−26.2711	−0.875219
$902$	1.69903	0.0565714
$903$	−127.842	−4.25431
$904$	5.90854	0.196515
$905$	−13.6050	−0.452244
$906$	42.8134	1.42238
$907$	−8.26312	−0.274373	−0.137186	−	0.990545i	$-0.543806\pi$
$907$	−8.26312	−0.274373	−0.137186	+	0.990545i	$0.543806\pi$
$908$	−16.7407	−0.555559
$909$	134.288	4.45405
$910$	−4.56226	−0.151237
$911$	−16.4376	−0.544601	−0.272300	−	0.962212i	$-0.587784\pi$
$911$	−16.4376	−0.544601	−0.272300	+	0.962212i	$0.587784\pi$
$912$	−16.5483	−0.547967
$913$	−47.3928	−1.56847
$914$	−33.5535	−1.10985
$915$	−26.2444	−0.867615
$916$	2.19452	0.0725090
$917$	−56.5639	−1.86791
$918$	−126.520	−4.17579
$919$	53.4344	1.76264	0.881318	−	0.472523i	$-0.156657\pi$
$919$	53.4344	1.76264	0.881318	+	0.472523i	$0.156657\pi$
$920$	−4.70242	−0.155034
$921$	65.6788	2.16419
$922$	−26.5823	−0.875442
$923$	7.42752	0.244480
$924$	−56.5207	−1.85939
$925$	−11.4165	−0.375373
$926$	−2.40039	−0.0788817
$927$	−133.478	−4.38401
$928$	0.684608	0.0224734
$929$	22.1754	0.727553	0.363776	−	0.931486i	$-0.381487\pi$
$929$	22.1754	0.727553	0.363776	+	0.931486i	$0.381487\pi$
$930$	−3.44665	−0.113020
$931$	−66.3257	−2.17374
$932$	−1.32650	−0.0434511
$933$	−46.3831	−1.51851
$934$	−6.49132	−0.212402
$935$	−22.4419	−0.733929
$936$	−8.87940	−0.290232
$937$	−3.36452	−0.109914	−0.0549570	−	0.998489i	$-0.517502\pi$
$937$	−3.36452	−0.109914	−0.0549570	+	0.998489i	$0.517502\pi$
$938$	51.7966	1.69122
$939$	−92.7100	−3.02548
$940$	−9.97952	−0.325496
$941$	30.8832	1.00676	0.503381	−	0.864064i	$-0.332089\pi$
$941$	30.8832	1.00676	0.503381	+	0.864064i	$0.332089\pi$
$942$	−9.49578	−0.309389
$943$	2.22276	0.0723829
$944$	−4.91100	−0.159840
$945$	92.4507	3.00742
$946$	−29.2230	−0.950123
$947$	0.460895	0.0149771	0.00748854	−	0.999972i	$-0.497616\pi$
$947$	0.460895	0.0149771	0.00748854	+	0.999972i	$0.497616\pi$
$948$	−26.9723	−0.876019
$949$	−1.88322	−0.0611319
$950$	4.80126	0.155773
$951$	−12.4502	−0.403725
$952$	−28.4846	−0.923191
$953$	17.0890	0.553566	0.276783	−	0.960933i	$-0.410732\pi$
$953$	17.0890	0.553566	0.276783	+	0.960933i	$0.410732\pi$
$954$	37.3622	1.20965
$955$	−2.16358	−0.0700118
$956$	15.2874	0.494431
$957$	8.48143	0.274166
$958$	−13.9202	−0.449742
$959$	−16.0444	−0.518102
$960$	3.44665	0.111240
$961$	1.00000	0.0322581
$962$	11.4165	0.368084
$963$	−131.845	−4.24863
$964$	25.6782	0.827038
$965$	−4.90880	−0.158020
$966$	−73.9434	−2.37909
$967$	53.5409	1.72176	0.860880	−	0.508808i	$-0.169914\pi$
$967$	53.5409	1.72176	0.860880	+	0.508808i	$0.169914\pi$
$968$	−1.91992	−0.0617086
$969$	−103.319	−3.31910
$970$	−13.5364	−0.434627
$971$	8.05676	0.258554	0.129277	−	0.991609i	$-0.458734\pi$
$971$	8.05676	0.258554	0.129277	+	0.991609i	$0.458734\pi$
$972$	88.1216	2.82650
$973$	−27.3044	−0.875340
$974$	4.16194	0.133357
$975$	3.44665	0.110381
$976$	−7.61448	−0.243734
$977$	16.3114	0.521847	0.260924	−	0.965359i	$-0.415973\pi$
$977$	16.3114	0.521847	0.260924	+	0.965359i	$0.415973\pi$
$978$	16.9285	0.541315
$979$	26.2360	0.838506
$980$	13.8142	0.441279
$981$	79.4480	2.53658
$982$	−18.1438	−0.578992
$983$	43.6638	1.39266	0.696329	−	0.717723i	$-0.254815\pi$
$983$	43.6638	1.39266	0.696329	+	0.717723i	$0.254815\pi$
$984$	−1.62917	−0.0519362
$985$	12.6326	0.402507
$986$	4.27437	0.136124
$987$	−156.923	−4.99492
$988$	−4.80126	−0.152748
$989$	−38.2311	−1.21568
$990$	31.9164	1.01437
$991$	−51.3834	−1.63225	−0.816124	−	0.577876i	$-0.803882\pi$
$991$	−51.3834	−1.63225	−0.816124	+	0.577876i	$0.803882\pi$
$992$	−1.00000	−0.0317500
$993$	−80.9325	−2.56832
$994$	−33.8863	−1.07481
$995$	−3.18546	−0.100986
$996$	45.4443	1.43996
$997$	−41.1319	−1.30266	−0.651330	−	0.758795i	$-0.725789\pi$
$997$	−41.1319	−1.30266	−0.651330	+	0.758795i	$0.725789\pi$
$998$	−25.5437	−0.808571
$999$	−231.347	−7.31950

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4030.2.a.m.1.8	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4030.2.a.m.1.8	✓	8	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +3.44665 q^{3} +1.00000 q^{4} +1.00000 q^{5} -3.44665 q^{6} +4.56226 q^{7} -1.00000 q^{8} +8.87940 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +3.44665 q^{3} +1.00000 q^{4} +1.00000 q^{5} -3.44665 q^{6} +4.56226 q^{7} -1.00000 q^{8} +8.87940 q^{9} -1.00000 q^{10} -3.59443 q^{11} +3.44665 q^{12} +1.00000 q^{13} -4.56226 q^{14} +3.44665 q^{15} +1.00000 q^{16} +6.24352 q^{17} -8.87940 q^{18} -4.80126 q^{19} +1.00000 q^{20} +15.7245 q^{21} +3.59443 q^{22} +4.70242 q^{23} -3.44665 q^{24} +1.00000 q^{25} -1.00000 q^{26} +20.2642 q^{27} +4.56226 q^{28} -0.684608 q^{29} -3.44665 q^{30} +1.00000 q^{31} -1.00000 q^{32} -12.3887 q^{33} -6.24352 q^{34} +4.56226 q^{35} +8.87940 q^{36} -11.4165 q^{37} +4.80126 q^{38} +3.44665 q^{39} -1.00000 q^{40} +0.472683 q^{41} -15.7245 q^{42} -8.13009 q^{43} -3.59443 q^{44} +8.87940 q^{45} -4.70242 q^{46} -9.97952 q^{47} +3.44665 q^{48} +13.8142 q^{49} -1.00000 q^{50} +21.5192 q^{51} +1.00000 q^{52} -4.20774 q^{53} -20.2642 q^{54} -3.59443 q^{55} -4.56226 q^{56} -16.5483 q^{57} +0.684608 q^{58} -4.91100 q^{59} +3.44665 q^{60} -7.61448 q^{61} -1.00000 q^{62} +40.5101 q^{63} +1.00000 q^{64} +1.00000 q^{65} +12.3887 q^{66} -11.3533 q^{67} +6.24352 q^{68} +16.2076 q^{69} -4.56226 q^{70} +7.42752 q^{71} -8.87940 q^{72} -1.88322 q^{73} +11.4165 q^{74} +3.44665 q^{75} -4.80126 q^{76} -16.3987 q^{77} -3.44665 q^{78} -7.82565 q^{79} +1.00000 q^{80} +43.2055 q^{81} -0.472683 q^{82} +13.1851 q^{83} +15.7245 q^{84} +6.24352 q^{85} +8.13009 q^{86} -2.35961 q^{87} +3.59443 q^{88} -7.29907 q^{89} -8.87940 q^{90} +4.56226 q^{91} +4.70242 q^{92} +3.44665 q^{93} +9.97952 q^{94} -4.80126 q^{95} -3.44665 q^{96} +13.5364 q^{97} -13.8142 q^{98} -31.9164 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 5 q^{3} + 8 q^{4} + 8 q^{5} - 5 q^{6} + 5 q^{7} - 8 q^{8} + 17 q^{9}+O(q^{10}) \) 8 * q - 8 * q^2 + 5 * q^3 + 8 * q^4 + 8 * q^5 - 5 * q^6 + 5 * q^7 - 8 * q^8 + 17 * q^9	\( 8 q - 8 q^{2} + 5 q^{3} + 8 q^{4} + 8 q^{5} - 5 q^{6} + 5 q^{7} - 8 q^{8} + 17 q^{9} - 8 q^{10} + 4 q^{11} + 5 q^{12} + 8 q^{13} - 5 q^{14} + 5 q^{15} + 8 q^{16} + 19 q^{17} - 17 q^{18} - 14 q^{19} + 8 q^{20} + 3 q^{21} - 4 q^{22} + 8 q^{23} - 5 q^{24} + 8 q^{25} - 8 q^{26} + 17 q^{27} + 5 q^{28} + 21 q^{29} - 5 q^{30} + 8 q^{31} - 8 q^{32} + 4 q^{33} - 19 q^{34} + 5 q^{35} + 17 q^{36} - 3 q^{37} + 14 q^{38} + 5 q^{39} - 8 q^{40} - 8 q^{41} - 3 q^{42} + 25 q^{43} + 4 q^{44} + 17 q^{45} - 8 q^{46} + 11 q^{47} + 5 q^{48} + 15 q^{49} - 8 q^{50} + 7 q^{51} + 8 q^{52} + 2 q^{53} - 17 q^{54} + 4 q^{55} - 5 q^{56} + 9 q^{57} - 21 q^{58} - 22 q^{59} + 5 q^{60} - 2 q^{61} - 8 q^{62} + 30 q^{63} + 8 q^{64} + 8 q^{65} - 4 q^{66} - 14 q^{67} + 19 q^{68} + 36 q^{69} - 5 q^{70} + 4 q^{71} - 17 q^{72} + 17 q^{73} + 3 q^{74} + 5 q^{75} - 14 q^{76} + 17 q^{77} - 5 q^{78} - 12 q^{79} + 8 q^{80} + 40 q^{81} + 8 q^{82} + 21 q^{83} + 3 q^{84} + 19 q^{85} - 25 q^{86} + 25 q^{87} - 4 q^{88} - 25 q^{89} - 17 q^{90} + 5 q^{91} + 8 q^{92} + 5 q^{93} - 11 q^{94} - 14 q^{95} - 5 q^{96} + 8 q^{97} - 15 q^{98} - 57 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 + 5 * q^3 + 8 * q^4 + 8 * q^5 - 5 * q^6 + 5 * q^7 - 8 * q^8 + 17 * q^9 - 8 * q^10 + 4 * q^11 + 5 * q^12 + 8 * q^13 - 5 * q^14 + 5 * q^15 + 8 * q^16 + 19 * q^17 - 17 * q^18 - 14 * q^19 + 8 * q^20 + 3 * q^21 - 4 * q^22 + 8 * q^23 - 5 * q^24 + 8 * q^25 - 8 * q^26 + 17 * q^27 + 5 * q^28 + 21 * q^29 - 5 * q^30 + 8 * q^31 - 8 * q^32 + 4 * q^33 - 19 * q^34 + 5 * q^35 + 17 * q^36 - 3 * q^37 + 14 * q^38 + 5 * q^39 - 8 * q^40 - 8 * q^41 - 3 * q^42 + 25 * q^43 + 4 * q^44 + 17 * q^45 - 8 * q^46 + 11 * q^47 + 5 * q^48 + 15 * q^49 - 8 * q^50 + 7 * q^51 + 8 * q^52 + 2 * q^53 - 17 * q^54 + 4 * q^55 - 5 * q^56 + 9 * q^57 - 21 * q^58 - 22 * q^59 + 5 * q^60 - 2 * q^61 - 8 * q^62 + 30 * q^63 + 8 * q^64 + 8 * q^65 - 4 * q^66 - 14 * q^67 + 19 * q^68 + 36 * q^69 - 5 * q^70 + 4 * q^71 - 17 * q^72 + 17 * q^73 + 3 * q^74 + 5 * q^75 - 14 * q^76 + 17 * q^77 - 5 * q^78 - 12 * q^79 + 8 * q^80 + 40 * q^81 + 8 * q^82 + 21 * q^83 + 3 * q^84 + 19 * q^85 - 25 * q^86 + 25 * q^87 - 4 * q^88 - 25 * q^89 - 17 * q^90 + 5 * q^91 + 8 * q^92 + 5 * q^93 - 11 * q^94 - 14 * q^95 - 5 * q^96 + 8 * q^97 - 15 * q^98 - 57 * q^99

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