LMFDB - Embedded newform 4010.2.a.j.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4010,2,Mod(1,4010)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4010, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("4010.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4010 = 2 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4010.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:	$32.0200112105$
Analytic rank:	$1$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} - 16 x^{10} + 30 x^{9} + 93 x^{8} - 162 x^{7} - 238 x^{6} + 391 x^{5} + 240 x^{4} + \cdots - 8 $ x^12 - 2x^11 - 16x^10 + 30x^9 + 93x^8 - 162x^7 - 238x^6 + 391x^5 + 240x^4 - 408x^3 - 42x^2 + 120*x - 8
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.34926$ of defining polynomial
Character	$\chi$	$=$	4010.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.34926 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.34926 q^{6} -0.317129 q^{7} +1.00000 q^{8} +2.51901 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.34926 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.34926 q^{6} -0.317129 q^{7} +1.00000 q^{8} +2.51901 q^{9} -1.00000 q^{10} +0.699084 q^{11} -2.34926 q^{12} -1.60293 q^{13} -0.317129 q^{14} +2.34926 q^{15} +1.00000 q^{16} +0.615957 q^{17} +2.51901 q^{18} +1.67851 q^{19} -1.00000 q^{20} +0.745018 q^{21} +0.699084 q^{22} -4.91046 q^{23} -2.34926 q^{24} +1.00000 q^{25} -1.60293 q^{26} +1.12998 q^{27} -0.317129 q^{28} -1.51475 q^{29} +2.34926 q^{30} +9.27567 q^{31} +1.00000 q^{32} -1.64233 q^{33} +0.615957 q^{34} +0.317129 q^{35} +2.51901 q^{36} -2.30832 q^{37} +1.67851 q^{38} +3.76568 q^{39} -1.00000 q^{40} +2.64441 q^{41} +0.745018 q^{42} -2.37532 q^{43} +0.699084 q^{44} -2.51901 q^{45} -4.91046 q^{46} -8.32367 q^{47} -2.34926 q^{48} -6.89943 q^{49} +1.00000 q^{50} -1.44704 q^{51} -1.60293 q^{52} +11.5899 q^{53} +1.12998 q^{54} -0.699084 q^{55} -0.317129 q^{56} -3.94326 q^{57} -1.51475 q^{58} -3.35667 q^{59} +2.34926 q^{60} +0.448975 q^{61} +9.27567 q^{62} -0.798851 q^{63} +1.00000 q^{64} +1.60293 q^{65} -1.64233 q^{66} +0.654392 q^{67} +0.615957 q^{68} +11.5359 q^{69} +0.317129 q^{70} +5.61093 q^{71} +2.51901 q^{72} -8.44197 q^{73} -2.30832 q^{74} -2.34926 q^{75} +1.67851 q^{76} -0.221700 q^{77} +3.76568 q^{78} -8.36616 q^{79} -1.00000 q^{80} -10.2116 q^{81} +2.64441 q^{82} -12.6378 q^{83} +0.745018 q^{84} -0.615957 q^{85} -2.37532 q^{86} +3.55853 q^{87} +0.699084 q^{88} -0.0408450 q^{89} -2.51901 q^{90} +0.508335 q^{91} -4.91046 q^{92} -21.7909 q^{93} -8.32367 q^{94} -1.67851 q^{95} -2.34926 q^{96} -10.6359 q^{97} -6.89943 q^{98} +1.76100 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{2} - 2 q^{3} + 12 q^{4} - 12 q^{5} - 2 q^{6} - 9 q^{7} + 12 q^{8}+O(q^{10}) $ 12 * q + 12 * q^2 - 2 * q^3 + 12 * q^4 - 12 * q^5 - 2 * q^6 - 9 * q^7 + 12 * q^8	\( 12 q + 12 q^{2} - 2 q^{3} + 12 q^{4} - 12 q^{5} - 2 q^{6} - 9 q^{7} + 12 q^{8} - 12 q^{10} + q^{11} - 2 q^{12} - 6 q^{13} - 9 q^{14} + 2 q^{15} + 12 q^{16} - 11 q^{17} - 13 q^{19} - 12 q^{20} - 14 q^{21} + q^{22} - 21 q^{23} - 2 q^{24} + 12 q^{25} - 6 q^{26} - 2 q^{27} - 9 q^{28} - 10 q^{29} + 2 q^{30} - 11 q^{31} + 12 q^{32} - 22 q^{33} - 11 q^{34} + 9 q^{35} - 29 q^{37} - 13 q^{38} - 2 q^{39} - 12 q^{40} - q^{41} - 14 q^{42} - 23 q^{43} + q^{44} - 21 q^{46} - 17 q^{47} - 2 q^{48} - 3 q^{49} + 12 q^{50} - 19 q^{51} - 6 q^{52} - 47 q^{53} - 2 q^{54} - q^{55} - 9 q^{56} - 11 q^{57} - 10 q^{58} + 14 q^{59} + 2 q^{60} - 22 q^{61} - 11 q^{62} - 28 q^{63} + 12 q^{64} + 6 q^{65} - 22 q^{66} - 28 q^{67} - 11 q^{68} - q^{69} + 9 q^{70} - 18 q^{71} - 2 q^{73} - 29 q^{74} - 2 q^{75} - 13 q^{76} - 11 q^{77} - 2 q^{78} - 39 q^{79} - 12 q^{80} - 44 q^{81} - q^{82} - 5 q^{83} - 14 q^{84} + 11 q^{85} - 23 q^{86} - 6 q^{87} + q^{88} - 8 q^{89} - 12 q^{91} - 21 q^{92} - 30 q^{93} - 17 q^{94} + 13 q^{95} - 2 q^{96} - 32 q^{97} - 3 q^{98} - 13 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 - 2 * q^3 + 12 * q^4 - 12 * q^5 - 2 * q^6 - 9 * q^7 + 12 * q^8 - 12 * q^10 + q^11 - 2 * q^12 - 6 * q^13 - 9 * q^14 + 2 * q^15 + 12 * q^16 - 11 * q^17 - 13 * q^19 - 12 * q^20 - 14 * q^21 + q^22 - 21 * q^23 - 2 * q^24 + 12 * q^25 - 6 * q^26 - 2 * q^27 - 9 * q^28 - 10 * q^29 + 2 * q^30 - 11 * q^31 + 12 * q^32 - 22 * q^33 - 11 * q^34 + 9 * q^35 - 29 * q^37 - 13 * q^38 - 2 * q^39 - 12 * q^40 - q^41 - 14 * q^42 - 23 * q^43 + q^44 - 21 * q^46 - 17 * q^47 - 2 * q^48 - 3 * q^49 + 12 * q^50 - 19 * q^51 - 6 * q^52 - 47 * q^53 - 2 * q^54 - q^55 - 9 * q^56 - 11 * q^57 - 10 * q^58 + 14 * q^59 + 2 * q^60 - 22 * q^61 - 11 * q^62 - 28 * q^63 + 12 * q^64 + 6 * q^65 - 22 * q^66 - 28 * q^67 - 11 * q^68 - q^69 + 9 * q^70 - 18 * q^71 - 2 * q^73 - 29 * q^74 - 2 * q^75 - 13 * q^76 - 11 * q^77 - 2 * q^78 - 39 * q^79 - 12 * q^80 - 44 * q^81 - q^82 - 5 * q^83 - 14 * q^84 + 11 * q^85 - 23 * q^86 - 6 * q^87 + q^88 - 8 * q^89 - 12 * q^91 - 21 * q^92 - 30 * q^93 - 17 * q^94 + 13 * q^95 - 2 * q^96 - 32 * q^97 - 3 * q^98 - 13 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.34926	−1.35634	−0.678172	−	0.734903i	$-0.737228\pi$
$3$	−2.34926	−1.35634	−0.678172	+	0.734903i	$0.737228\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−2.34926	−0.959080
$7$	−0.317129	−0.119864	−0.0599318	−	0.998202i	$-0.519088\pi$
$7$	−0.317129	−0.119864	−0.0599318	+	0.998202i	$0.519088\pi$
$8$	1.00000	0.353553
$9$	2.51901	0.839669
$10$	−1.00000	−0.316228
$11$	0.699084	0.210782	0.105391	−	0.994431i	$-0.466391\pi$
$11$	0.699084	0.210782	0.105391	+	0.994431i	$0.466391\pi$
$12$	−2.34926	−0.678172
$13$	−1.60293	−0.444572	−0.222286	−	0.974982i	$-0.571352\pi$
$13$	−1.60293	−0.444572	−0.222286	+	0.974982i	$0.571352\pi$
$14$	−0.317129	−0.0847563
$15$	2.34926	0.606575
$16$	1.00000	0.250000
$17$	0.615957	0.149392	0.0746958	−	0.997206i	$-0.476201\pi$
$17$	0.615957	0.149392	0.0746958	+	0.997206i	$0.476201\pi$
$18$	2.51901	0.593736
$19$	1.67851	0.385077	0.192539	−	0.981289i	$-0.438328\pi$
$19$	1.67851	0.385077	0.192539	+	0.981289i	$0.438328\pi$
$20$	−1.00000	−0.223607
$21$	0.745018	0.162576
$22$	0.699084	0.149045
$23$	−4.91046	−1.02390	−0.511951	−	0.859015i	$-0.671077\pi$
$23$	−4.91046	−1.02390	−0.511951	+	0.859015i	$0.671077\pi$
$24$	−2.34926	−0.479540
$25$	1.00000	0.200000
$26$	−1.60293	−0.314360
$27$	1.12998	0.217464
$28$	−0.317129	−0.0599318
$29$	−1.51475	−0.281281	−0.140641	−	0.990061i	$-0.544916\pi$
$29$	−1.51475	−0.281281	−0.140641	+	0.990061i	$0.544916\pi$
$30$	2.34926	0.428914
$31$	9.27567	1.66596	0.832980	−	0.553304i	$-0.186633\pi$
$31$	9.27567	1.66596	0.832980	+	0.553304i	$0.186633\pi$
$32$	1.00000	0.176777
$33$	−1.64233	−0.285893
$34$	0.615957	0.105636
$35$	0.317129	0.0536046
$36$	2.51901	0.419834
$37$	−2.30832	−0.379485	−0.189743	−	0.981834i	$-0.560765\pi$
$37$	−2.30832	−0.379485	−0.189743	+	0.981834i	$0.560765\pi$
$38$	1.67851	0.272291
$39$	3.76568	0.602992
$40$	−1.00000	−0.158114
$41$	2.64441	0.412987	0.206493	−	0.978448i	$-0.433795\pi$
$41$	2.64441	0.412987	0.206493	+	0.978448i	$0.433795\pi$
$42$	0.745018	0.114959
$43$	−2.37532	−0.362233	−0.181116	−	0.983462i	$-0.557971\pi$
$43$	−2.37532	−0.362233	−0.181116	+	0.983462i	$0.557971\pi$
$44$	0.699084	0.105391
$45$	−2.51901	−0.375511
$46$	−4.91046	−0.724008
$47$	−8.32367	−1.21413	−0.607066	−	0.794652i	$-0.707654\pi$
$47$	−8.32367	−1.21413	−0.607066	+	0.794652i	$0.707654\pi$
$48$	−2.34926	−0.339086
$49$	−6.89943	−0.985633
$50$	1.00000	0.141421
$51$	−1.44704	−0.202626
$52$	−1.60293	−0.222286
$53$	11.5899	1.59199	0.795995	−	0.605303i	$-0.206948\pi$
$53$	11.5899	1.59199	0.795995	+	0.605303i	$0.206948\pi$
$54$	1.12998	0.153770
$55$	−0.699084	−0.0942645
$56$	−0.317129	−0.0423782
$57$	−3.94326	−0.522297
$58$	−1.51475	−0.198896
$59$	−3.35667	−0.437001	−0.218500	−	0.975837i	$-0.570117\pi$
$59$	−3.35667	−0.437001	−0.218500	+	0.975837i	$0.570117\pi$
$60$	2.34926	0.303288
$61$	0.448975	0.0574854	0.0287427	−	0.999587i	$-0.490850\pi$
$61$	0.448975	0.0574854	0.0287427	+	0.999587i	$0.490850\pi$
$62$	9.27567	1.17801
$63$	−0.798851	−0.100646
$64$	1.00000	0.125000
$65$	1.60293	0.198818
$66$	−1.64233	−0.202157
$67$	0.654392	0.0799467	0.0399734	−	0.999201i	$-0.487273\pi$
$67$	0.654392	0.0799467	0.0399734	+	0.999201i	$0.487273\pi$
$68$	0.615957	0.0746958
$69$	11.5359	1.38876
$70$	0.317129	0.0379042
$71$	5.61093	0.665895	0.332948	−	0.942945i	$-0.391957\pi$
$71$	5.61093	0.665895	0.332948	+	0.942945i	$0.391957\pi$
$72$	2.51901	0.296868
$73$	−8.44197	−0.988058	−0.494029	−	0.869445i	$-0.664476\pi$
$73$	−8.44197	−0.988058	−0.494029	+	0.869445i	$0.664476\pi$
$74$	−2.30832	−0.268337
$75$	−2.34926	−0.271269
$76$	1.67851	0.192539
$77$	−0.221700	−0.0252651
$78$	3.76568	0.426380
$79$	−8.36616	−0.941266	−0.470633	−	0.882329i	$-0.655974\pi$
$79$	−8.36616	−0.941266	−0.470633	+	0.882329i	$0.655974\pi$
$80$	−1.00000	−0.111803
$81$	−10.2116	−1.13462
$82$	2.64441	0.292026
$83$	−12.6378	−1.38718	−0.693590	−	0.720370i	$-0.743972\pi$
$83$	−12.6378	−1.38718	−0.693590	+	0.720370i	$0.743972\pi$
$84$	0.745018	0.0812881
$85$	−0.615957	−0.0668100
$86$	−2.37532	−0.256137
$87$	3.55853	0.381514
$88$	0.699084	0.0745226
$89$	−0.0408450	−0.00432956	−0.00216478	−	0.999998i	$-0.500689\pi$
$89$	−0.0408450	−0.00432956	−0.00216478	+	0.999998i	$0.500689\pi$
$90$	−2.51901	−0.265527
$91$	0.508335	0.0532879
$92$	−4.91046	−0.511951
$93$	−21.7909	−2.25961
$94$	−8.32367	−0.858521
$95$	−1.67851	−0.172212
$96$	−2.34926	−0.239770
$97$	−10.6359	−1.07991	−0.539955	−	0.841694i	$-0.681559\pi$
$97$	−10.6359	−1.07991	−0.539955	+	0.841694i	$0.681559\pi$
$98$	−6.89943	−0.696948
$99$	1.76100	0.176987
$100$	1.00000	0.100000
$101$	17.7645	1.76764	0.883818	−	0.467830i	$-0.154964\pi$
$101$	17.7645	1.76764	0.883818	+	0.467830i	$0.154964\pi$
$102$	−1.44704	−0.143279
$103$	14.2790	1.40695	0.703474	−	0.710721i	$-0.251631\pi$
$103$	14.2790	1.40695	0.703474	+	0.710721i	$0.251631\pi$
$104$	−1.60293	−0.157180
$105$	−0.745018	−0.0727063
$106$	11.5899	1.12571
$107$	−0.957762	−0.0925904	−0.0462952	−	0.998928i	$-0.514741\pi$
$107$	−0.957762	−0.0925904	−0.0462952	+	0.998928i	$0.514741\pi$
$108$	1.12998	0.108732
$109$	−3.70356	−0.354736	−0.177368	−	0.984145i	$-0.556758\pi$
$109$	−3.70356	−0.354736	−0.177368	+	0.984145i	$0.556758\pi$
$110$	−0.699084	−0.0666551
$111$	5.42283	0.514713
$112$	−0.317129	−0.0299659
$113$	−3.85027	−0.362203	−0.181101	−	0.983464i	$-0.557966\pi$
$113$	−3.85027	−0.362203	−0.181101	+	0.983464i	$0.557966\pi$
$114$	−3.94326	−0.369320
$115$	4.91046	0.457903
$116$	−1.51475	−0.140641
$117$	−4.03778	−0.373293
$118$	−3.35667	−0.309006
$119$	−0.195338	−0.0179066
$120$	2.34926	0.214457
$121$	−10.5113	−0.955571
$122$	0.448975	0.0406483
$123$	−6.21239	−0.560152
$124$	9.27567	0.832980
$125$	−1.00000	−0.0894427
$126$	−0.798851	−0.0711673
$127$	−9.92043	−0.880296	−0.440148	−	0.897925i	$-0.645074\pi$
$127$	−9.92043	−0.880296	−0.440148	+	0.897925i	$0.645074\pi$
$128$	1.00000	0.0883883
$129$	5.58024	0.491312
$130$	1.60293	0.140586
$131$	9.30634	0.813098	0.406549	−	0.913629i	$-0.366732\pi$
$131$	9.30634	0.813098	0.406549	+	0.913629i	$0.366732\pi$
$132$	−1.64233	−0.142946
$133$	−0.532305	−0.0461567
$134$	0.654392	0.0565309
$135$	−1.12998	−0.0972529
$136$	0.615957	0.0528179
$137$	−2.16987	−0.185384	−0.0926920	−	0.995695i	$-0.529547\pi$
$137$	−2.16987	−0.185384	−0.0926920	+	0.995695i	$0.529547\pi$
$138$	11.5359	0.982004
$139$	−20.4417	−1.73384	−0.866922	−	0.498443i	$-0.833905\pi$
$139$	−20.4417	−1.73384	−0.866922	+	0.498443i	$0.833905\pi$
$140$	0.317129	0.0268023
$141$	19.5544	1.64678
$142$	5.61093	0.470859
$143$	−1.12058	−0.0937076
$144$	2.51901	0.209917
$145$	1.51475	0.125793
$146$	−8.44197	−0.698662
$147$	16.2085	1.33686
$148$	−2.30832	−0.189743
$149$	−18.1133	−1.48390	−0.741949	−	0.670456i	$-0.766098\pi$
$149$	−18.1133	−1.48390	−0.741949	+	0.670456i	$0.766098\pi$
$150$	−2.34926	−0.191816
$151$	−2.86959	−0.233524	−0.116762	−	0.993160i	$-0.537251\pi$
$151$	−2.86959	−0.233524	−0.116762	+	0.993160i	$0.537251\pi$
$152$	1.67851	0.136145
$153$	1.55160	0.125439
$154$	−0.221700	−0.0178651
$155$	−9.27567	−0.745040
$156$	3.76568	0.301496
$157$	−13.2510	−1.05755	−0.528773	−	0.848763i	$-0.677348\pi$
$157$	−13.2510	−1.05755	−0.528773	+	0.848763i	$0.677348\pi$
$158$	−8.36616	−0.665576
$159$	−27.2276	−2.15929
$160$	−1.00000	−0.0790569
$161$	1.55725	0.122729
$162$	−10.2116	−0.802301
$163$	−12.0535	−0.944100	−0.472050	−	0.881572i	$-0.656486\pi$
$163$	−12.0535	−0.944100	−0.472050	+	0.881572i	$0.656486\pi$
$164$	2.64441	0.206493
$165$	1.64233	0.127855
$166$	−12.6378	−0.980885
$167$	3.67539	0.284410	0.142205	−	0.989837i	$-0.454581\pi$
$167$	3.67539	0.284410	0.142205	+	0.989837i	$0.454581\pi$
$168$	0.745018	0.0574794
$169$	−10.4306	−0.802356
$170$	−0.615957	−0.0472418
$171$	4.22818	0.323337
$172$	−2.37532	−0.181116
$173$	11.1518	0.847852	0.423926	−	0.905697i	$-0.360652\pi$
$173$	11.1518	0.847852	0.423926	+	0.905697i	$0.360652\pi$
$174$	3.55853	0.269771
$175$	−0.317129	−0.0239727
$176$	0.699084	0.0526954
$177$	7.88567	0.592723
$178$	−0.0408450	−0.00306146
$179$	−3.59878	−0.268986	−0.134493	−	0.990915i	$-0.542941\pi$
$179$	−3.59878	−0.268986	−0.134493	+	0.990915i	$0.542941\pi$
$180$	−2.51901	−0.187756
$181$	−21.7168	−1.61420	−0.807098	−	0.590417i	$-0.798963\pi$
$181$	−21.7168	−1.61420	−0.807098	+	0.590417i	$0.798963\pi$
$182$	0.508335	0.0376803
$183$	−1.05476	−0.0779700
$184$	−4.91046	−0.362004
$185$	2.30832	0.169711
$186$	−21.7909	−1.59779
$187$	0.430606	0.0314890
$188$	−8.32367	−0.607066
$189$	−0.358348	−0.0260660
$190$	−1.67851	−0.121772
$191$	6.30200	0.455997	0.227998	−	0.973662i	$-0.426782\pi$
$191$	6.30200	0.455997	0.227998	+	0.973662i	$0.426782\pi$
$192$	−2.34926	−0.169543
$193$	−23.3289	−1.67925	−0.839627	−	0.543163i	$-0.817226\pi$
$193$	−23.3289	−1.67925	−0.839627	+	0.543163i	$0.817226\pi$
$194$	−10.6359	−0.763612
$195$	−3.76568	−0.269666
$196$	−6.89943	−0.492816
$197$	−21.7662	−1.55078	−0.775388	−	0.631485i	$-0.782446\pi$
$197$	−21.7662	−1.55078	−0.775388	+	0.631485i	$0.782446\pi$
$198$	1.76100	0.125149
$199$	4.18518	0.296679	0.148340	−	0.988936i	$-0.452607\pi$
$199$	4.18518	0.296679	0.148340	+	0.988936i	$0.452607\pi$
$200$	1.00000	0.0707107
$201$	−1.53734	−0.108435
$202$	17.7645	1.24991
$203$	0.480371	0.0337154
$204$	−1.44704	−0.101313
$205$	−2.64441	−0.184693
$206$	14.2790	0.994863
$207$	−12.3695	−0.859739
$208$	−1.60293	−0.111143
$209$	1.17342	0.0811672
$210$	−0.745018	−0.0514111
$211$	16.3211	1.12359	0.561796	−	0.827276i	$-0.310111\pi$
$211$	16.3211	1.12359	0.561796	+	0.827276i	$0.310111\pi$
$212$	11.5899	0.795995
$213$	−13.1815	−0.903183
$214$	−0.957762	−0.0654713
$215$	2.37532	0.161995
$216$	1.12998	0.0768851
$217$	−2.94159	−0.199688
$218$	−3.70356	−0.250837
$219$	19.8324	1.34015
$220$	−0.699084	−0.0471322
$221$	−0.987334	−0.0664153
$222$	5.42283	0.363957
$223$	24.8429	1.66360	0.831801	−	0.555074i	$-0.187310\pi$
$223$	24.8429	1.66360	0.831801	+	0.555074i	$0.187310\pi$
$224$	−0.317129	−0.0211891
$225$	2.51901	0.167934
$226$	−3.85027	−0.256116
$227$	−20.1112	−1.33483	−0.667414	−	0.744687i	$-0.732599\pi$
$227$	−20.1112	−1.33483	−0.667414	+	0.744687i	$0.732599\pi$
$228$	−3.94326	−0.261148
$229$	−8.74074	−0.577604	−0.288802	−	0.957389i	$-0.593257\pi$
$229$	−8.74074	−0.577604	−0.288802	+	0.957389i	$0.593257\pi$
$230$	4.91046	0.323786
$231$	0.520830	0.0342681
$232$	−1.51475	−0.0994480
$233$	−8.06555	−0.528392	−0.264196	−	0.964469i	$-0.585107\pi$
$233$	−8.06555	−0.528392	−0.264196	+	0.964469i	$0.585107\pi$
$234$	−4.03778	−0.263958
$235$	8.32367	0.542976
$236$	−3.35667	−0.218500
$237$	19.6542	1.27668
$238$	−0.195338	−0.0126619
$239$	−0.707428	−0.0457597	−0.0228799	−	0.999738i	$-0.507284\pi$
$239$	−0.707428	−0.0457597	−0.0228799	+	0.999738i	$0.507284\pi$
$240$	2.34926	0.151644
$241$	26.4541	1.70406	0.852028	−	0.523496i	$-0.175372\pi$
$241$	26.4541	1.70406	0.852028	+	0.523496i	$0.175372\pi$
$242$	−10.5113	−0.675691
$243$	20.5998	1.32148
$244$	0.448975	0.0287427
$245$	6.89943	0.440788
$246$	−6.21239	−0.396087
$247$	−2.69053	−0.171194
$248$	9.27567	0.589006
$249$	29.6895	1.88149
$250$	−1.00000	−0.0632456
$251$	−8.63358	−0.544947	−0.272473	−	0.962163i	$-0.587842\pi$
$251$	−8.63358	−0.544947	−0.272473	+	0.962163i	$0.587842\pi$
$252$	−0.798851	−0.0503229
$253$	−3.43283	−0.215820
$254$	−9.92043	−0.622463
$255$	1.44704	0.0906173
$256$	1.00000	0.0625000
$257$	−28.3042	−1.76557	−0.882783	−	0.469780i	$-0.844333\pi$
$257$	−28.3042	−1.76557	−0.882783	+	0.469780i	$0.844333\pi$
$258$	5.58024	0.347410
$259$	0.732035	0.0454865
$260$	1.60293	0.0994092
$261$	−3.81566	−0.236183
$262$	9.30634	0.574947
$263$	−8.76160	−0.540264	−0.270132	−	0.962823i	$-0.587067\pi$
$263$	−8.76160	−0.540264	−0.270132	+	0.962823i	$0.587067\pi$
$264$	−1.64233	−0.101078
$265$	−11.5899	−0.711960
$266$	−0.532305	−0.0326377
$267$	0.0959553	0.00587237
$268$	0.654392	0.0399734
$269$	16.7340	1.02029	0.510144	−	0.860089i	$-0.329592\pi$
$269$	16.7340	1.02029	0.510144	+	0.860089i	$0.329592\pi$
$270$	−1.12998	−0.0687682
$271$	−29.2339	−1.77583	−0.887917	−	0.460003i	$-0.847848\pi$
$271$	−29.2339	−1.77583	−0.887917	+	0.460003i	$0.847848\pi$
$272$	0.615957	0.0373479
$273$	−1.19421	−0.0722768
$274$	−2.16987	−0.131086
$275$	0.699084	0.0421564
$276$	11.5359	0.694382
$277$	−17.0902	−1.02685	−0.513425	−	0.858135i	$-0.671623\pi$
$277$	−17.0902	−1.02685	−0.513425	+	0.858135i	$0.671623\pi$
$278$	−20.4417	−1.22601
$279$	23.3655	1.39885
$280$	0.317129	0.0189521
$281$	−6.73926	−0.402031	−0.201015	−	0.979588i	$-0.564424\pi$
$281$	−6.73926	−0.402031	−0.201015	+	0.979588i	$0.564424\pi$
$282$	19.5544	1.16445
$283$	7.86286	0.467399	0.233699	−	0.972309i	$-0.424917\pi$
$283$	7.86286	0.467399	0.233699	+	0.972309i	$0.424917\pi$
$284$	5.61093	0.332948
$285$	3.94326	0.233578
$286$	−1.12058	−0.0662613
$287$	−0.838618	−0.0495021
$288$	2.51901	0.148434
$289$	−16.6206	−0.977682
$290$	1.51475	0.0889490
$291$	24.9864	1.46473
$292$	−8.44197	−0.494029
$293$	−26.8374	−1.56786	−0.783928	−	0.620851i	$-0.786787\pi$
$293$	−26.8374	−1.56786	−0.783928	+	0.620851i	$0.786787\pi$
$294$	16.2085	0.945301
$295$	3.35667	0.195433
$296$	−2.30832	−0.134168
$297$	0.789948	0.0458375
$298$	−18.1133	−1.04927
$299$	7.87110	0.455198
$300$	−2.34926	−0.135634
$301$	0.753283	0.0434185
$302$	−2.86959	−0.165127
$303$	−41.7334	−2.39752
$304$	1.67851	0.0962693
$305$	−0.448975	−0.0257083
$306$	1.55160	0.0886991
$307$	28.1223	1.60503	0.802513	−	0.596635i	$-0.203496\pi$
$307$	28.1223	1.60503	0.802513	+	0.596635i	$0.203496\pi$
$308$	−0.221700	−0.0126325
$309$	−33.5450	−1.90831
$310$	−9.27567	−0.526823
$311$	3.48354	0.197533	0.0987666	−	0.995111i	$-0.468510\pi$
$311$	3.48354	0.197533	0.0987666	+	0.995111i	$0.468510\pi$
$312$	3.76568	0.213190
$313$	−30.8586	−1.74423	−0.872115	−	0.489300i	$-0.837252\pi$
$313$	−30.8586	−1.74423	−0.872115	+	0.489300i	$0.837252\pi$
$314$	−13.2510	−0.747798
$315$	0.798851	0.0450101
$316$	−8.36616	−0.470633
$317$	−1.65336	−0.0928620	−0.0464310	−	0.998921i	$-0.514785\pi$
$317$	−1.65336	−0.0928620	−0.0464310	+	0.998921i	$0.514785\pi$
$318$	−27.2276	−1.52685
$319$	−1.05894	−0.0592890
$320$	−1.00000	−0.0559017
$321$	2.25003	0.125584
$322$	1.55725	0.0867822
$323$	1.03389	0.0575273
$324$	−10.2116	−0.567312
$325$	−1.60293	−0.0889143
$326$	−12.0535	−0.667580
$327$	8.70061	0.481145
$328$	2.64441	0.146013
$329$	2.63968	0.145530
$330$	1.64233	0.0904072
$331$	29.5741	1.62554	0.812770	−	0.582585i	$-0.197959\pi$
$331$	29.5741	1.62554	0.812770	+	0.582585i	$0.197959\pi$
$332$	−12.6378	−0.693590
$333$	−5.81467	−0.318642
$334$	3.67539	0.201108
$335$	−0.654392	−0.0357533
$336$	0.745018	0.0406441
$337$	34.6851	1.88942	0.944709	−	0.327911i	$-0.106345\pi$
$337$	34.6851	1.88942	0.944709	+	0.327911i	$0.106345\pi$
$338$	−10.4306	−0.567351
$339$	9.04527	0.491272
$340$	−0.615957	−0.0334050
$341$	6.48447	0.351154
$342$	4.22818	0.228634
$343$	4.40792	0.238005
$344$	−2.37532	−0.128069
$345$	−11.5359	−0.621074
$346$	11.1518	0.599522
$347$	35.0526	1.88172	0.940860	−	0.338796i	$-0.110020\pi$
$347$	35.0526	1.88172	0.940860	+	0.338796i	$0.110020\pi$
$348$	3.55853	0.190757
$349$	24.0734	1.28862	0.644310	−	0.764765i	$-0.277145\pi$
$349$	24.0734	1.28862	0.644310	+	0.764765i	$0.277145\pi$
$350$	−0.317129	−0.0169513
$351$	−1.81127	−0.0966783
$352$	0.699084	0.0372613
$353$	−22.8144	−1.21429	−0.607145	−	0.794591i	$-0.707685\pi$
$353$	−22.8144	−1.21429	−0.607145	+	0.794591i	$0.707685\pi$
$354$	7.88567	0.419119
$355$	−5.61093	−0.297797
$356$	−0.0408450	−0.00216478
$357$	0.458899	0.0242875
$358$	−3.59878	−0.190202
$359$	−34.0131	−1.79514	−0.897571	−	0.440870i	$-0.854670\pi$
$359$	−34.0131	−1.79514	−0.897571	+	0.440870i	$0.854670\pi$
$360$	−2.51901	−0.132763
$361$	−16.1826	−0.851716
$362$	−21.7168	−1.14141
$363$	24.6937	1.29608
$364$	0.508335	0.0266440
$365$	8.44197	0.441873
$366$	−1.05476	−0.0551331
$367$	30.4876	1.59144	0.795719	−	0.605666i	$-0.207093\pi$
$367$	30.4876	1.59144	0.795719	+	0.605666i	$0.207093\pi$
$368$	−4.91046	−0.255975
$369$	6.66128	0.346772
$370$	2.30832	0.120004
$371$	−3.67549	−0.190822
$372$	−21.7909	−1.12981
$373$	9.72113	0.503341	0.251670	−	0.967813i	$-0.419020\pi$
$373$	9.72113	0.503341	0.251670	+	0.967813i	$0.419020\pi$
$374$	0.430606	0.0222661
$375$	2.34926	0.121315
$376$	−8.32367	−0.429260
$377$	2.42803	0.125050
$378$	−0.358348	−0.0184315
$379$	13.3062	0.683494	0.341747	−	0.939792i	$-0.388981\pi$
$379$	13.3062	0.683494	0.341747	+	0.939792i	$0.388981\pi$
$380$	−1.67851	−0.0861058
$381$	23.3056	1.19398
$382$	6.30200	0.322438
$383$	6.18967	0.316277	0.158139	−	0.987417i	$-0.449451\pi$
$383$	6.18967	0.316277	0.158139	+	0.987417i	$0.449451\pi$
$384$	−2.34926	−0.119885
$385$	0.221700	0.0112989
$386$	−23.3289	−1.18741
$387$	−5.98345	−0.304156
$388$	−10.6359	−0.539955
$389$	−24.8519	−1.26004	−0.630021	−	0.776578i	$-0.716954\pi$
$389$	−24.8519	−1.26004	−0.630021	+	0.776578i	$0.716954\pi$
$390$	−3.76568	−0.190683
$391$	−3.02463	−0.152962
$392$	−6.89943	−0.348474
$393$	−21.8630	−1.10284
$394$	−21.7662	−1.09656
$395$	8.36616	0.420947
$396$	1.76100	0.0884935
$397$	0.254479	0.0127719	0.00638597	−	0.999980i	$-0.497967\pi$
$397$	0.254479	0.0127719	0.00638597	+	0.999980i	$0.497967\pi$
$398$	4.18518	0.209784
$399$	1.25052	0.0626044
$400$	1.00000	0.0500000
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	−1.53734	−0.0766753
$403$	−14.8682	−0.740638
$404$	17.7645	0.883818
$405$	10.2116	0.507420
$406$	0.480371	0.0238404
$407$	−1.61371	−0.0799886
$408$	−1.44704	−0.0716393
$409$	2.54678	0.125930	0.0629651	−	0.998016i	$-0.479944\pi$
$409$	2.54678	0.125930	0.0629651	+	0.998016i	$0.479944\pi$
$410$	−2.64441	−0.130598
$411$	5.09757	0.251445
$412$	14.2790	0.703474
$413$	1.06450	0.0523805
$414$	−12.3695	−0.607927
$415$	12.6378	0.620366
$416$	−1.60293	−0.0785899
$417$	48.0229	2.35169
$418$	1.17342	0.0573939
$419$	18.6998	0.913543	0.456772	−	0.889584i	$-0.349006\pi$
$419$	18.6998	0.913543	0.456772	+	0.889584i	$0.349006\pi$
$420$	−0.745018	−0.0363532
$421$	1.18205	0.0576094	0.0288047	−	0.999585i	$-0.490830\pi$
$421$	1.18205	0.0576094	0.0288047	+	0.999585i	$0.490830\pi$
$422$	16.3211	0.794499
$423$	−20.9674	−1.01947
$424$	11.5899	0.562854
$425$	0.615957	0.0298783
$426$	−13.1815	−0.638647
$427$	−0.142383	−0.00689041
$428$	−0.957762	−0.0462952
$429$	2.63253	0.127100
$430$	2.37532	0.114548
$431$	−13.8332	−0.666322	−0.333161	−	0.942870i	$-0.608115\pi$
$431$	−13.8332	−0.666322	−0.333161	+	0.942870i	$0.608115\pi$
$432$	1.12998	0.0543660
$433$	−1.71563	−0.0824479	−0.0412239	−	0.999150i	$-0.513126\pi$
$433$	−1.71563	−0.0824479	−0.0412239	+	0.999150i	$0.513126\pi$
$434$	−2.94159	−0.141201
$435$	−3.55853	−0.170618
$436$	−3.70356	−0.177368
$437$	−8.24227	−0.394281
$438$	19.8324	0.947627
$439$	18.3289	0.874789	0.437394	−	0.899270i	$-0.355901\pi$
$439$	18.3289	0.874789	0.437394	+	0.899270i	$0.355901\pi$
$440$	−0.699084	−0.0333275
$441$	−17.3797	−0.827605
$442$	−0.987334	−0.0469627
$443$	17.6701	0.839530	0.419765	−	0.907633i	$-0.362113\pi$
$443$	17.6701	0.839530	0.419765	+	0.907633i	$0.362113\pi$
$444$	5.42283	0.257356
$445$	0.0408450	0.00193624
$446$	24.8429	1.17634
$447$	42.5527	2.01268
$448$	−0.317129	−0.0149829
$449$	26.5397	1.25249	0.626244	−	0.779627i	$-0.284591\pi$
$449$	26.5397	1.25249	0.626244	+	0.779627i	$0.284591\pi$
$450$	2.51901	0.118747
$451$	1.84866	0.0870501
$452$	−3.85027	−0.181101
$453$	6.74141	0.316739
$454$	−20.1112	−0.943866
$455$	−0.508335	−0.0238311
$456$	−3.94326	−0.184660
$457$	−1.78862	−0.0836681	−0.0418340	−	0.999125i	$-0.513320\pi$
$457$	−1.78862	−0.0836681	−0.0418340	+	0.999125i	$0.513320\pi$
$458$	−8.74074	−0.408428
$459$	0.696017	0.0324873
$460$	4.91046	0.228951
$461$	41.0777	1.91318	0.956590	−	0.291436i	$-0.0941330\pi$
$461$	41.0777	1.91318	0.956590	+	0.291436i	$0.0941330\pi$
$462$	0.520830	0.0242312
$463$	−35.2966	−1.64037	−0.820186	−	0.572097i	$-0.806130\pi$
$463$	−35.2966	−1.64037	−0.820186	+	0.572097i	$0.806130\pi$
$464$	−1.51475	−0.0703204
$465$	21.7909	1.01053
$466$	−8.06555	−0.373629
$467$	32.2393	1.49186	0.745928	−	0.666027i	$-0.232006\pi$
$467$	32.2393	1.49186	0.745928	+	0.666027i	$0.232006\pi$
$468$	−4.03778	−0.186647
$469$	−0.207527	−0.00958270
$470$	8.32367	0.383942
$471$	31.1300	1.43440
$472$	−3.35667	−0.154503
$473$	−1.66055	−0.0763521
$474$	19.6542	0.902749
$475$	1.67851	0.0770154
$476$	−0.195338	−0.00895331
$477$	29.1950	1.33675
$478$	−0.707428	−0.0323570
$479$	7.85356	0.358838	0.179419	−	0.983773i	$-0.442578\pi$
$479$	7.85356	0.358838	0.179419	+	0.983773i	$0.442578\pi$
$480$	2.34926	0.107228
$481$	3.70006	0.168708
$482$	26.4541	1.20495
$483$	−3.65838	−0.166462
$484$	−10.5113	−0.477786
$485$	10.6359	0.482951
$486$	20.5998	0.934426
$487$	−40.5056	−1.83549	−0.917743	−	0.397175i	$-0.869991\pi$
$487$	−40.5056	−1.83549	−0.917743	+	0.397175i	$0.869991\pi$
$488$	0.448975	0.0203242
$489$	28.3167	1.28052
$490$	6.89943	0.311684
$491$	−7.39540	−0.333750	−0.166875	−	0.985978i	$-0.553368\pi$
$491$	−7.39540	−0.333750	−0.166875	+	0.985978i	$0.553368\pi$
$492$	−6.21239	−0.280076
$493$	−0.933020	−0.0420211
$494$	−2.69053	−0.121053
$495$	−1.76100	−0.0791510
$496$	9.27567	0.416490
$497$	−1.77939	−0.0798166
$498$	29.6895	1.33042
$499$	4.71139	0.210911	0.105455	−	0.994424i	$-0.466370\pi$
$499$	4.71139	0.210911	0.105455	+	0.994424i	$0.466370\pi$
$500$	−1.00000	−0.0447214
$501$	−8.63442	−0.385758
$502$	−8.63358	−0.385336
$503$	−38.0703	−1.69747	−0.848735	−	0.528818i	$-0.822636\pi$
$503$	−38.0703	−1.69747	−0.848735	+	0.528818i	$0.822636\pi$
$504$	−0.798851	−0.0355836
$505$	−17.7645	−0.790511
$506$	−3.43283	−0.152608
$507$	24.5042	1.08827
$508$	−9.92043	−0.440148
$509$	29.6045	1.31220	0.656098	−	0.754676i	$-0.272206\pi$
$509$	29.6045	1.31220	0.656098	+	0.754676i	$0.272206\pi$
$510$	1.44704	0.0640761
$511$	2.67720	0.118432
$512$	1.00000	0.0441942
$513$	1.89668	0.0837404
$514$	−28.3042	−1.24844
$515$	−14.2790	−0.629206
$516$	5.58024	0.245656
$517$	−5.81894	−0.255917
$518$	0.732035	0.0321638
$519$	−26.1983	−1.14998
$520$	1.60293	0.0702929
$521$	5.19498	0.227596	0.113798	−	0.993504i	$-0.463698\pi$
$521$	5.19498	0.227596	0.113798	+	0.993504i	$0.463698\pi$
$522$	−3.81566	−0.167007
$523$	−6.93942	−0.303439	−0.151720	−	0.988424i	$-0.548481\pi$
$523$	−6.93942	−0.303439	−0.151720	+	0.988424i	$0.548481\pi$
$524$	9.30634	0.406549
$525$	0.745018	0.0325152
$526$	−8.76160	−0.382024
$527$	5.71342	0.248880
$528$	−1.64233	−0.0714732
$529$	1.11263	0.0483751
$530$	−11.5899	−0.503432
$531$	−8.45547	−0.366936
$532$	−0.532305	−0.0230784
$533$	−4.23879	−0.183602
$534$	0.0959553	0.00415239
$535$	0.957762	0.0414077
$536$	0.654392	0.0282654
$537$	8.45446	0.364837
$538$	16.7340	0.721452
$539$	−4.82328	−0.207753
$540$	−1.12998	−0.0486264
$541$	−27.9516	−1.20173	−0.600867	−	0.799349i	$-0.705178\pi$
$541$	−27.9516	−1.20173	−0.600867	+	0.799349i	$0.705178\pi$
$542$	−29.2339	−1.25570
$543$	51.0183	2.18941
$544$	0.615957	0.0264090
$545$	3.70356	0.158643
$546$	−1.19421	−0.0511074
$547$	−13.1035	−0.560264	−0.280132	−	0.959961i	$-0.590378\pi$
$547$	−13.1035	−0.560264	−0.280132	+	0.959961i	$0.590378\pi$
$548$	−2.16987	−0.0926920
$549$	1.13097	0.0482687
$550$	0.699084	0.0298090
$551$	−2.54252	−0.108315
$552$	11.5359	0.491002
$553$	2.65315	0.112824
$554$	−17.0902	−0.726092
$555$	−5.42283	−0.230186
$556$	−20.4417	−0.866922
$557$	−1.14811	−0.0486472	−0.0243236	−	0.999704i	$-0.507743\pi$
$557$	−1.14811	−0.0486472	−0.0243236	+	0.999704i	$0.507743\pi$
$558$	23.3655	0.989139
$559$	3.80746	0.161038
$560$	0.317129	0.0134012
$561$	−1.01160	−0.0427100
$562$	−6.73926	−0.284279
$563$	7.41109	0.312340	0.156170	−	0.987730i	$-0.450085\pi$
$563$	7.41109	0.312340	0.156170	+	0.987730i	$0.450085\pi$
$564$	19.5544	0.823390
$565$	3.85027	0.161982
$566$	7.86286	0.330501
$567$	3.23840	0.136000
$568$	5.61093	0.235430
$569$	28.5435	1.19661	0.598303	−	0.801270i	$-0.295842\pi$
$569$	28.5435	1.19661	0.598303	+	0.801270i	$0.295842\pi$
$570$	3.94326	0.165165
$571$	42.4799	1.77773	0.888865	−	0.458169i	$-0.151495\pi$
$571$	42.4799	1.77773	0.888865	+	0.458169i	$0.151495\pi$
$572$	−1.12058	−0.0468538
$573$	−14.8050	−0.618488
$574$	−0.838618	−0.0350033
$575$	−4.91046	−0.204780
$576$	2.51901	0.104959
$577$	10.7160	0.446114	0.223057	−	0.974805i	$-0.428396\pi$
$577$	10.7160	0.446114	0.223057	+	0.974805i	$0.428396\pi$
$578$	−16.6206	−0.691326
$579$	54.8057	2.27765
$580$	1.51475	0.0628965
$581$	4.00782	0.166272
$582$	24.9864	1.03572
$583$	8.10229	0.335563
$584$	−8.44197	−0.349331
$585$	4.03778	0.166942
$586$	−26.8374	−1.10864
$587$	7.01674	0.289612	0.144806	−	0.989460i	$-0.453744\pi$
$587$	7.01674	0.289612	0.144806	+	0.989460i	$0.453744\pi$
$588$	16.2085	0.668428
$589$	15.5693	0.641523
$590$	3.35667	0.138192
$591$	51.1343	2.10339
$592$	−2.30832	−0.0948713
$593$	−8.78573	−0.360787	−0.180393	−	0.983595i	$-0.557737\pi$
$593$	−8.78573	−0.360787	−0.180393	+	0.983595i	$0.557737\pi$
$594$	0.789948	0.0324120
$595$	0.195338	0.00800808
$596$	−18.1133	−0.741949
$597$	−9.83206	−0.402399
$598$	7.87110	0.321873
$599$	−6.77353	−0.276759	−0.138379	−	0.990379i	$-0.544189\pi$
$599$	−6.77353	−0.276759	−0.138379	+	0.990379i	$0.544189\pi$
$600$	−2.34926	−0.0959080
$601$	−19.4014	−0.791398	−0.395699	−	0.918380i	$-0.629498\pi$
$601$	−19.4014	−0.791398	−0.395699	+	0.918380i	$0.629498\pi$
$602$	0.753283	0.0307015
$603$	1.64842	0.0671288
$604$	−2.86959	−0.116762
$605$	10.5113	0.427344
$606$	−41.7334	−1.69530
$607$	−10.4265	−0.423198	−0.211599	−	0.977357i	$-0.567867\pi$
$607$	−10.4265	−0.423198	−0.211599	+	0.977357i	$0.567867\pi$
$608$	1.67851	0.0680726
$609$	−1.12851	−0.0457297
$610$	−0.448975	−0.0181785
$611$	13.3422	0.539768
$612$	1.55160	0.0627197
$613$	22.5251	0.909778	0.454889	−	0.890548i	$-0.349679\pi$
$613$	22.5251	0.909778	0.454889	+	0.890548i	$0.349679\pi$
$614$	28.1223	1.13492
$615$	6.21239	0.250508
$616$	−0.221700	−0.00893255
$617$	−22.1704	−0.892547	−0.446273	−	0.894897i	$-0.647249\pi$
$617$	−22.1704	−0.892547	−0.446273	+	0.894897i	$0.647249\pi$
$618$	−33.5450	−1.34938
$619$	−24.9146	−1.00140	−0.500701	−	0.865620i	$-0.666924\pi$
$619$	−24.9146	−1.00140	−0.500701	+	0.865620i	$0.666924\pi$
$620$	−9.27567	−0.372520
$621$	−5.54870	−0.222662
$622$	3.48354	0.139677
$623$	0.0129531	0.000518956 0
$624$	3.76568	0.150748
$625$	1.00000	0.0400000
$626$	−30.8586	−1.23336
$627$	−2.75667	−0.110091
$628$	−13.2510	−0.528773
$629$	−1.42183	−0.0566919
$630$	0.798851	0.0318270
$631$	−13.5305	−0.538639	−0.269320	−	0.963051i	$-0.586799\pi$
$631$	−13.5305	−0.538639	−0.269320	+	0.963051i	$0.586799\pi$
$632$	−8.36616	−0.332788
$633$	−38.3425	−1.52398
$634$	−1.65336	−0.0656633
$635$	9.92043	0.393680
$636$	−27.2276	−1.07964
$637$	11.0593	0.438184
$638$	−1.05894	−0.0419237
$639$	14.1340	0.559132
$640$	−1.00000	−0.0395285
$641$	1.56619	0.0618608	0.0309304	−	0.999522i	$-0.490153\pi$
$641$	1.56619	0.0618608	0.0309304	+	0.999522i	$0.490153\pi$
$642$	2.25003	0.0888016
$643$	2.33783	0.0921949	0.0460974	−	0.998937i	$-0.485322\pi$
$643$	2.33783	0.0921949	0.0460974	+	0.998937i	$0.485322\pi$
$644$	1.55725	0.0613643
$645$	−5.58024	−0.219722
$646$	1.03389	0.0406779
$647$	13.9221	0.547333	0.273667	−	0.961825i	$-0.411764\pi$
$647$	13.9221	0.547333	0.273667	+	0.961825i	$0.411764\pi$
$648$	−10.2116	−0.401151
$649$	−2.34659	−0.0921118
$650$	−1.60293	−0.0628719
$651$	6.91054	0.270845
$652$	−12.0535	−0.472050
$653$	−21.0040	−0.821952	−0.410976	−	0.911646i	$-0.634812\pi$
$653$	−21.0040	−0.821952	−0.410976	+	0.911646i	$0.634812\pi$
$654$	8.70061	0.340221
$655$	−9.30634	−0.363629
$656$	2.64441	0.103247
$657$	−21.2654	−0.829642
$658$	2.63968	0.102905
$659$	28.7190	1.11873	0.559367	−	0.828920i	$-0.311044\pi$
$659$	28.7190	1.11873	0.559367	+	0.828920i	$0.311044\pi$
$660$	1.64233	0.0639275
$661$	−42.9365	−1.67004	−0.835018	−	0.550223i	$-0.814543\pi$
$661$	−42.9365	−1.67004	−0.835018	+	0.550223i	$0.814543\pi$
$662$	29.5741	1.14943
$663$	2.31950	0.0900820
$664$	−12.6378	−0.490443
$665$	0.532305	0.0206419
$666$	−5.81467	−0.225314
$667$	7.43811	0.288005
$668$	3.67539	0.142205
$669$	−58.3623	−2.25642
$670$	−0.654392	−0.0252814
$671$	0.313872	0.0121169
$672$	0.745018	0.0287397
$673$	−8.56413	−0.330123	−0.165062	−	0.986283i	$-0.552782\pi$
$673$	−8.56413	−0.330123	−0.165062	+	0.986283i	$0.552782\pi$
$674$	34.6851	1.33602
$675$	1.12998	0.0434928
$676$	−10.4306	−0.401178
$677$	19.4410	0.747178	0.373589	−	0.927594i	$-0.378127\pi$
$677$	19.4410	0.747178	0.373589	+	0.927594i	$0.378127\pi$
$678$	9.04527	0.347382
$679$	3.37295	0.129442
$680$	−0.615957	−0.0236209
$681$	47.2464	1.81049
$682$	6.48447	0.248303
$683$	−0.567183	−0.0217026	−0.0108513	−	0.999941i	$-0.503454\pi$
$683$	−0.567183	−0.0217026	−0.0108513	+	0.999941i	$0.503454\pi$
$684$	4.22818	0.161669
$685$	2.16987	0.0829063
$686$	4.40792	0.168295
$687$	20.5342	0.783430
$688$	−2.37532	−0.0905582
$689$	−18.5777	−0.707754
$690$	−11.5359	−0.439165
$691$	22.2195	0.845268	0.422634	−	0.906300i	$-0.361106\pi$
$691$	22.2195	0.845268	0.422634	+	0.906300i	$0.361106\pi$
$692$	11.1518	0.423926
$693$	−0.558464	−0.0212143
$694$	35.0526	1.33058
$695$	20.4417	0.775399
$696$	3.55853	0.134886
$697$	1.62884	0.0616968
$698$	24.0734	0.911192
$699$	18.9480	0.716681
$700$	−0.317129	−0.0119864
$701$	−5.88413	−0.222241	−0.111120	−	0.993807i	$-0.535444\pi$
$701$	−5.88413	−0.222241	−0.111120	+	0.993807i	$0.535444\pi$
$702$	−1.81127	−0.0683619
$703$	−3.87454	−0.146131
$704$	0.699084	0.0263477
$705$	−19.5544	−0.736462
$706$	−22.8144	−0.858632
$707$	−5.63365	−0.211875
$708$	7.88567	0.296362
$709$	32.3153	1.21363	0.606813	−	0.794844i	$-0.292448\pi$
$709$	32.3153	1.21363	0.606813	+	0.794844i	$0.292448\pi$
$710$	−5.61093	−0.210575
$711$	−21.0744	−0.790352
$712$	−0.0408450	−0.00153073
$713$	−45.5478	−1.70578
$714$	0.458899	0.0171739
$715$	1.12058	0.0419073
$716$	−3.59878	−0.134493
$717$	1.66193	0.0620659
$718$	−34.0131	−1.26936
$719$	45.6133	1.70109	0.850545	−	0.525902i	$-0.176272\pi$
$719$	45.6133	1.70109	0.850545	+	0.525902i	$0.176272\pi$
$720$	−2.51901	−0.0938778
$721$	−4.52828	−0.168642
$722$	−16.1826	−0.602254
$723$	−62.1474	−2.31129
$724$	−21.7168	−0.807098
$725$	−1.51475	−0.0562563
$726$	24.6937	0.916469
$727$	−28.7430	−1.06602	−0.533009	−	0.846110i	$-0.678939\pi$
$727$	−28.7430	−1.06602	−0.533009	+	0.846110i	$0.678939\pi$
$728$	0.508335	0.0188401
$729$	−17.7593	−0.657753
$730$	8.44197	0.312451
$731$	−1.46310	−0.0541146
$732$	−1.05476	−0.0389850
$733$	−20.1337	−0.743654	−0.371827	−	0.928302i	$-0.621269\pi$
$733$	−20.1337	−0.743654	−0.371827	+	0.928302i	$0.621269\pi$
$734$	30.4876	1.12532
$735$	−16.2085	−0.597861
$736$	−4.91046	−0.181002
$737$	0.457475	0.0168513
$738$	6.66128	0.245205
$739$	−2.97993	−0.109618	−0.0548092	−	0.998497i	$-0.517455\pi$
$739$	−2.97993	−0.109618	−0.0548092	+	0.998497i	$0.517455\pi$
$740$	2.30832	0.0848555
$741$	6.32075	0.232198
$742$	−3.67549	−0.134931
$743$	21.8978	0.803352	0.401676	−	0.915782i	$-0.368428\pi$
$743$	21.8978	0.803352	0.401676	+	0.915782i	$0.368428\pi$
$744$	−21.7909	−0.798894
$745$	18.1133	0.663619
$746$	9.72113	0.355916
$747$	−31.8348	−1.16477
$748$	0.430606	0.0157445
$749$	0.303734	0.0110982
$750$	2.34926	0.0857827
$751$	−9.26693	−0.338155	−0.169078	−	0.985603i	$-0.554079\pi$
$751$	−9.26693	−0.338155	−0.169078	+	0.985603i	$0.554079\pi$
$752$	−8.32367	−0.303533
$753$	20.2825	0.739135
$754$	2.42803	0.0884235
$755$	2.86959	0.104435
$756$	−0.358348	−0.0130330
$757$	−11.2205	−0.407816	−0.203908	−	0.978990i	$-0.565364\pi$
$757$	−11.2205	−0.407816	−0.203908	+	0.978990i	$0.565364\pi$
$758$	13.3062	0.483303
$759$	8.06459	0.292726
$760$	−1.67851	−0.0608860
$761$	45.7055	1.65682	0.828411	−	0.560121i	$-0.189245\pi$
$761$	45.7055	1.65682	0.828411	+	0.560121i	$0.189245\pi$
$762$	23.3056	0.844274
$763$	1.17451	0.0425200
$764$	6.30200	0.227998
$765$	−1.55160	−0.0560982
$766$	6.18967	0.223642
$767$	5.38049	0.194278
$768$	−2.34926	−0.0847715
$769$	−27.6720	−0.997877	−0.498939	−	0.866637i	$-0.666277\pi$
$769$	−27.6720	−0.997877	−0.498939	+	0.866637i	$0.666277\pi$
$770$	0.221700	0.00798951
$771$	66.4938	2.39472
$772$	−23.3289	−0.839627
$773$	29.8315	1.07297	0.536483	−	0.843911i	$-0.319753\pi$
$773$	29.8315	1.07297	0.536483	+	0.843911i	$0.319753\pi$
$774$	−5.98345	−0.215071
$775$	9.27567	0.333192
$776$	−10.6359	−0.381806
$777$	−1.71974	−0.0616953
$778$	−24.8519	−0.890984
$779$	4.43867	0.159032
$780$	−3.76568	−0.134833
$781$	3.92251	0.140359
$782$	−3.02463	−0.108161
$783$	−1.71163	−0.0611686
$784$	−6.89943	−0.246408
$785$	13.2510	0.472949
$786$	−21.8630	−0.779827
$787$	22.2097	0.791691	0.395846	−	0.918317i	$-0.370452\pi$
$787$	22.2097	0.791691	0.395846	+	0.918317i	$0.370452\pi$
$788$	−21.7662	−0.775388
$789$	20.5833	0.732783
$790$	8.36616	0.297654
$791$	1.22103	0.0434149
$792$	1.76100	0.0625743
$793$	−0.719674	−0.0255564
$794$	0.254479	0.00903113
$795$	27.2276	0.965663
$796$	4.18518	0.148340
$797$	12.9287	0.457956	0.228978	−	0.973432i	$-0.426462\pi$
$797$	12.9287	0.457956	0.228978	+	0.973432i	$0.426462\pi$
$798$	1.25052	0.0442680
$799$	−5.12702	−0.181381
$800$	1.00000	0.0353553
$801$	−0.102889	−0.00363540
$802$	1.00000	0.0353112
$803$	−5.90165	−0.208265
$804$	−1.53734	−0.0542176
$805$	−1.55725	−0.0548859
$806$	−14.8682	−0.523710
$807$	−39.3124	−1.38386
$808$	17.7645	0.624954
$809$	−10.6768	−0.375378	−0.187689	−	0.982229i	$-0.560100\pi$
$809$	−10.6768	−0.375378	−0.187689	+	0.982229i	$0.560100\pi$
$810$	10.2116	0.358800
$811$	−9.76595	−0.342929	−0.171464	−	0.985190i	$-0.554850\pi$
$811$	−9.76595	−0.342929	−0.171464	+	0.985190i	$0.554850\pi$
$812$	0.480371	0.0168577
$813$	68.6780	2.40864
$814$	−1.61371	−0.0565605
$815$	12.0535	0.422214
$816$	−1.44704	−0.0506566
$817$	−3.98700	−0.139488
$818$	2.54678	0.0890462
$819$	1.28050	0.0447442
$820$	−2.64441	−0.0923467
$821$	−23.7799	−0.829926	−0.414963	−	0.909838i	$-0.636205\pi$
$821$	−23.7799	−0.829926	−0.414963	+	0.909838i	$0.636205\pi$
$822$	5.09757	0.177798
$823$	−9.48972	−0.330791	−0.165395	−	0.986227i	$-0.552890\pi$
$823$	−9.48972	−0.330791	−0.165395	+	0.986227i	$0.552890\pi$
$824$	14.2790	0.497431
$825$	−1.64233	−0.0571785
$826$	1.06450	0.0370386
$827$	2.32884	0.0809818	0.0404909	−	0.999180i	$-0.487108\pi$
$827$	2.32884	0.0809818	0.0404909	+	0.999180i	$0.487108\pi$
$828$	−12.3695	−0.429869
$829$	10.4688	0.363597	0.181799	−	0.983336i	$-0.441808\pi$
$829$	10.4688	0.363597	0.181799	+	0.983336i	$0.441808\pi$
$830$	12.6378	0.438665
$831$	40.1492	1.39276
$832$	−1.60293	−0.0555715
$833$	−4.24975	−0.147245
$834$	48.0229	1.66290
$835$	−3.67539	−0.127192
$836$	1.17342	0.0405836
$837$	10.4813	0.362286
$838$	18.6998	0.645973
$839$	−36.2350	−1.25097	−0.625485	−	0.780236i	$-0.715099\pi$
$839$	−36.2350	−1.25097	−0.625485	+	0.780236i	$0.715099\pi$
$840$	−0.745018	−0.0257056
$841$	−26.7055	−0.920881
$842$	1.18205	0.0407360
$843$	15.8323	0.545292
$844$	16.3211	0.561796
$845$	10.4306	0.358825
$846$	−20.9674	−0.720873
$847$	3.33343	0.114538
$848$	11.5899	0.397998
$849$	−18.4719	−0.633953
$850$	0.615957	0.0211272
$851$	11.3349	0.388556
$852$	−13.1815	−0.451591
$853$	11.9159	0.407993	0.203996	−	0.978972i	$-0.434607\pi$
$853$	11.9159	0.407993	0.203996	+	0.978972i	$0.434607\pi$
$854$	−0.142383	−0.00487225
$855$	−4.22818	−0.144601
$856$	−0.957762	−0.0327356
$857$	32.0420	1.09453	0.547267	−	0.836958i	$-0.315668\pi$
$857$	32.0420	1.09453	0.547267	+	0.836958i	$0.315668\pi$
$858$	2.63253	0.0898731
$859$	8.38247	0.286006	0.143003	−	0.989722i	$-0.454324\pi$
$859$	8.38247	0.286006	0.143003	+	0.989722i	$0.454324\pi$
$860$	2.37532	0.0809977
$861$	1.97013	0.0671418
$862$	−13.8332	−0.471161
$863$	−53.5179	−1.82177	−0.910885	−	0.412661i	$-0.864599\pi$
$863$	−53.5179	−1.82177	−0.910885	+	0.412661i	$0.864599\pi$
$864$	1.12998	0.0384426
$865$	−11.1518	−0.379171
$866$	−1.71563	−0.0582994
$867$	39.0460	1.32607
$868$	−2.94159	−0.0998439
$869$	−5.84865	−0.198402
$870$	−3.55853	−0.120645
$871$	−1.04894	−0.0355421
$872$	−3.70356	−0.125418
$873$	−26.7919	−0.906768
$874$	−8.24227	−0.278799
$875$	0.317129	0.0107209
$876$	19.8324	0.670073
$877$	−21.8005	−0.736149	−0.368074	−	0.929796i	$-0.619983\pi$
$877$	−21.8005	−0.736149	−0.368074	+	0.929796i	$0.619983\pi$
$878$	18.3289	0.618569
$879$	63.0479	2.12655
$880$	−0.699084	−0.0235661
$881$	15.2902	0.515142	0.257571	−	0.966259i	$-0.417078\pi$
$881$	15.2902	0.515142	0.257571	+	0.966259i	$0.417078\pi$
$882$	−17.3797	−0.585205
$883$	−2.40237	−0.0808461	−0.0404230	−	0.999183i	$-0.512871\pi$
$883$	−2.40237	−0.0808461	−0.0404230	+	0.999183i	$0.512871\pi$
$884$	−0.987334	−0.0332076
$885$	−7.88567	−0.265074
$886$	17.6701	0.593637
$887$	38.9647	1.30831	0.654154	−	0.756362i	$-0.273025\pi$
$887$	38.9647	1.30831	0.654154	+	0.756362i	$0.273025\pi$
$888$	5.42283	0.181978
$889$	3.14606	0.105515
$890$	0.0408450	0.00136913
$891$	−7.13878	−0.239158
$892$	24.8429	0.831801
$893$	−13.9714	−0.467534
$894$	42.5527	1.42318
$895$	3.59878	0.120294
$896$	−0.317129	−0.0105945
$897$	−18.4912	−0.617405
$898$	26.5397	0.885642
$899$	−14.0503	−0.468603
$900$	2.51901	0.0839669
$901$	7.13887	0.237830
$902$	1.84866	0.0615537
$903$	−1.76966	−0.0588905
$904$	−3.85027	−0.128058
$905$	21.7168	0.721891
$906$	6.74141	0.223968
$907$	−29.8334	−0.990600	−0.495300	−	0.868722i	$-0.664942\pi$
$907$	−29.8334	−0.990600	−0.495300	+	0.868722i	$0.664942\pi$
$908$	−20.1112	−0.667414
$909$	44.7490	1.48423
$910$	−0.508335	−0.0168511
$911$	55.6944	1.84524	0.922620	−	0.385711i	$-0.126044\pi$
$911$	55.6944	1.84524	0.922620	+	0.385711i	$0.126044\pi$
$912$	−3.94326	−0.130574
$913$	−8.83490	−0.292392
$914$	−1.78862	−0.0591623
$915$	1.05476	0.0348692
$916$	−8.74074	−0.288802
$917$	−2.95131	−0.0974609
$918$	0.696017	0.0229720
$919$	43.1532	1.42349	0.711746	−	0.702437i	$-0.247905\pi$
$919$	43.1532	1.42349	0.711746	+	0.702437i	$0.247905\pi$
$920$	4.91046	0.161893
$921$	−66.0666	−2.17697
$922$	41.0777	1.35282
$923$	−8.99391	−0.296038
$924$	0.520830	0.0171341
$925$	−2.30832	−0.0758971
$926$	−35.2966	−1.15992
$927$	35.9688	1.18137
$928$	−1.51475	−0.0497240
$929$	16.9717	0.556823	0.278412	−	0.960462i	$-0.410192\pi$
$929$	16.9717	0.556823	0.278412	+	0.960462i	$0.410192\pi$
$930$	21.7909	0.714553
$931$	−11.5808	−0.379545
$932$	−8.06555	−0.264196
$933$	−8.18372	−0.267923
$934$	32.2393	1.05490
$935$	−0.430606	−0.0140823
$936$	−4.03778	−0.131979
$937$	−7.73969	−0.252845	−0.126422	−	0.991977i	$-0.540349\pi$
$937$	−7.73969	−0.252845	−0.126422	+	0.991977i	$0.540349\pi$
$938$	−0.207527	−0.00677599
$939$	72.4947	2.36578
$940$	8.32367	0.271488
$941$	−36.1047	−1.17698	−0.588489	−	0.808505i	$-0.700277\pi$
$941$	−36.1047	−1.17698	−0.588489	+	0.808505i	$0.700277\pi$
$942$	31.1300	1.01427
$943$	−12.9853	−0.422858
$944$	−3.35667	−0.109250
$945$	0.358348	0.0116571
$946$	−1.66055	−0.0539891
$947$	31.8490	1.03495	0.517476	−	0.855697i	$-0.326872\pi$
$947$	31.8490	1.03495	0.517476	+	0.855697i	$0.326872\pi$
$948$	19.6542	0.638340
$949$	13.5319	0.439263
$950$	1.67851	0.0544581
$951$	3.88417	0.125953
$952$	−0.195338	−0.00633094
$953$	3.67313	0.118984	0.0594921	−	0.998229i	$-0.481052\pi$
$953$	3.67313	0.118984	0.0594921	+	0.998229i	$0.481052\pi$
$954$	29.1950	0.945222
$955$	−6.30200	−0.203928
$956$	−0.707428	−0.0228799
$957$	2.48771	0.0804163
$958$	7.85356	0.253737
$959$	0.688128	0.0222208
$960$	2.34926	0.0758219
$961$	55.0380	1.77542
$962$	3.70006	0.119295
$963$	−2.41261	−0.0777453
$964$	26.4541	0.852028
$965$	23.3289	0.750985
$966$	−3.65838	−0.117706
$967$	−43.1856	−1.38875	−0.694377	−	0.719611i	$-0.744320\pi$
$967$	−43.1856	−1.38875	−0.694377	+	0.719611i	$0.744320\pi$
$968$	−10.5113	−0.337845
$969$	−2.42888	−0.0780268
$970$	10.6359	0.341498
$971$	30.9137	0.992067	0.496033	−	0.868303i	$-0.334789\pi$
$971$	30.9137	0.992067	0.496033	+	0.868303i	$0.334789\pi$
$972$	20.5998	0.660739
$973$	6.48267	0.207825
$974$	−40.5056	−1.29788
$975$	3.76568	0.120598
$976$	0.448975	0.0143714
$977$	−52.0601	−1.66555	−0.832775	−	0.553612i	$-0.813249\pi$
$977$	−52.0601	−1.66555	−0.832775	+	0.553612i	$0.813249\pi$
$978$	28.3167	0.905468
$979$	−0.0285541	−0.000912592 0
$980$	6.89943	0.220394
$981$	−9.32929	−0.297861
$982$	−7.39540	−0.235997
$983$	25.0137	0.797813	0.398906	−	0.916992i	$-0.369390\pi$
$983$	25.0137	0.797813	0.398906	+	0.916992i	$0.369390\pi$
$984$	−6.21239	−0.198044
$985$	21.7662	0.693528
$986$	−0.933020	−0.0297134
$987$	−6.20128	−0.197389
$988$	−2.69053	−0.0855972
$989$	11.6639	0.370891
$990$	−1.76100	−0.0559682
$991$	−12.9602	−0.411693	−0.205847	−	0.978584i	$-0.565995\pi$
$991$	−12.9602	−0.411693	−0.205847	+	0.978584i	$0.565995\pi$
$992$	9.27567	0.294503
$993$	−69.4772	−2.20479
$994$	−1.77939	−0.0564388
$995$	−4.18518	−0.132679
$996$	29.6895	0.940747
$997$	−5.52395	−0.174945	−0.0874726	−	0.996167i	$-0.527879\pi$
$997$	−5.52395	−0.174945	−0.0874726	+	0.996167i	$0.527879\pi$
$998$	4.71139	0.149136
$999$	−2.60835	−0.0825244

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4010.2.a.j.1.2	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4010.2.a.j.1.2	✓	12	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:	\( N \)	\(=\)	\( 4010 = 2 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4010.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.34926 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.34926 q^{6} -0.317129 q^{7} +1.00000 q^{8} +2.51901 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.34926 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.34926 q^{6} -0.317129 q^{7} +1.00000 q^{8} +2.51901 q^{9} -1.00000 q^{10} +0.699084 q^{11} -2.34926 q^{12} -1.60293 q^{13} -0.317129 q^{14} +2.34926 q^{15} +1.00000 q^{16} +0.615957 q^{17} +2.51901 q^{18} +1.67851 q^{19} -1.00000 q^{20} +0.745018 q^{21} +0.699084 q^{22} -4.91046 q^{23} -2.34926 q^{24} +1.00000 q^{25} -1.60293 q^{26} +1.12998 q^{27} -0.317129 q^{28} -1.51475 q^{29} +2.34926 q^{30} +9.27567 q^{31} +1.00000 q^{32} -1.64233 q^{33} +0.615957 q^{34} +0.317129 q^{35} +2.51901 q^{36} -2.30832 q^{37} +1.67851 q^{38} +3.76568 q^{39} -1.00000 q^{40} +2.64441 q^{41} +0.745018 q^{42} -2.37532 q^{43} +0.699084 q^{44} -2.51901 q^{45} -4.91046 q^{46} -8.32367 q^{47} -2.34926 q^{48} -6.89943 q^{49} +1.00000 q^{50} -1.44704 q^{51} -1.60293 q^{52} +11.5899 q^{53} +1.12998 q^{54} -0.699084 q^{55} -0.317129 q^{56} -3.94326 q^{57} -1.51475 q^{58} -3.35667 q^{59} +2.34926 q^{60} +0.448975 q^{61} +9.27567 q^{62} -0.798851 q^{63} +1.00000 q^{64} +1.60293 q^{65} -1.64233 q^{66} +0.654392 q^{67} +0.615957 q^{68} +11.5359 q^{69} +0.317129 q^{70} +5.61093 q^{71} +2.51901 q^{72} -8.44197 q^{73} -2.30832 q^{74} -2.34926 q^{75} +1.67851 q^{76} -0.221700 q^{77} +3.76568 q^{78} -8.36616 q^{79} -1.00000 q^{80} -10.2116 q^{81} +2.64441 q^{82} -12.6378 q^{83} +0.745018 q^{84} -0.615957 q^{85} -2.37532 q^{86} +3.55853 q^{87} +0.699084 q^{88} -0.0408450 q^{89} -2.51901 q^{90} +0.508335 q^{91} -4.91046 q^{92} -21.7909 q^{93} -8.32367 q^{94} -1.67851 q^{95} -2.34926 q^{96} -10.6359 q^{97} -6.89943 q^{98} +1.76100 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{2} - 2 q^{3} + 12 q^{4} - 12 q^{5} - 2 q^{6} - 9 q^{7} + 12 q^{8}+O(q^{10}) \) 12 * q + 12 * q^2 - 2 * q^3 + 12 * q^4 - 12 * q^5 - 2 * q^6 - 9 * q^7 + 12 * q^8	\( 12 q + 12 q^{2} - 2 q^{3} + 12 q^{4} - 12 q^{5} - 2 q^{6} - 9 q^{7} + 12 q^{8} - 12 q^{10} + q^{11} - 2 q^{12} - 6 q^{13} - 9 q^{14} + 2 q^{15} + 12 q^{16} - 11 q^{17} - 13 q^{19} - 12 q^{20} - 14 q^{21} + q^{22} - 21 q^{23} - 2 q^{24} + 12 q^{25} - 6 q^{26} - 2 q^{27} - 9 q^{28} - 10 q^{29} + 2 q^{30} - 11 q^{31} + 12 q^{32} - 22 q^{33} - 11 q^{34} + 9 q^{35} - 29 q^{37} - 13 q^{38} - 2 q^{39} - 12 q^{40} - q^{41} - 14 q^{42} - 23 q^{43} + q^{44} - 21 q^{46} - 17 q^{47} - 2 q^{48} - 3 q^{49} + 12 q^{50} - 19 q^{51} - 6 q^{52} - 47 q^{53} - 2 q^{54} - q^{55} - 9 q^{56} - 11 q^{57} - 10 q^{58} + 14 q^{59} + 2 q^{60} - 22 q^{61} - 11 q^{62} - 28 q^{63} + 12 q^{64} + 6 q^{65} - 22 q^{66} - 28 q^{67} - 11 q^{68} - q^{69} + 9 q^{70} - 18 q^{71} - 2 q^{73} - 29 q^{74} - 2 q^{75} - 13 q^{76} - 11 q^{77} - 2 q^{78} - 39 q^{79} - 12 q^{80} - 44 q^{81} - q^{82} - 5 q^{83} - 14 q^{84} + 11 q^{85} - 23 q^{86} - 6 q^{87} + q^{88} - 8 q^{89} - 12 q^{91} - 21 q^{92} - 30 q^{93} - 17 q^{94} + 13 q^{95} - 2 q^{96} - 32 q^{97} - 3 q^{98} - 13 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 - 2 * q^3 + 12 * q^4 - 12 * q^5 - 2 * q^6 - 9 * q^7 + 12 * q^8 - 12 * q^10 + q^11 - 2 * q^12 - 6 * q^13 - 9 * q^14 + 2 * q^15 + 12 * q^16 - 11 * q^17 - 13 * q^19 - 12 * q^20 - 14 * q^21 + q^22 - 21 * q^23 - 2 * q^24 + 12 * q^25 - 6 * q^26 - 2 * q^27 - 9 * q^28 - 10 * q^29 + 2 * q^30 - 11 * q^31 + 12 * q^32 - 22 * q^33 - 11 * q^34 + 9 * q^35 - 29 * q^37 - 13 * q^38 - 2 * q^39 - 12 * q^40 - q^41 - 14 * q^42 - 23 * q^43 + q^44 - 21 * q^46 - 17 * q^47 - 2 * q^48 - 3 * q^49 + 12 * q^50 - 19 * q^51 - 6 * q^52 - 47 * q^53 - 2 * q^54 - q^55 - 9 * q^56 - 11 * q^57 - 10 * q^58 + 14 * q^59 + 2 * q^60 - 22 * q^61 - 11 * q^62 - 28 * q^63 + 12 * q^64 + 6 * q^65 - 22 * q^66 - 28 * q^67 - 11 * q^68 - q^69 + 9 * q^70 - 18 * q^71 - 2 * q^73 - 29 * q^74 - 2 * q^75 - 13 * q^76 - 11 * q^77 - 2 * q^78 - 39 * q^79 - 12 * q^80 - 44 * q^81 - q^82 - 5 * q^83 - 14 * q^84 + 11 * q^85 - 23 * q^86 - 6 * q^87 + q^88 - 8 * q^89 - 12 * q^91 - 21 * q^92 - 30 * q^93 - 17 * q^94 + 13 * q^95 - 2 * q^96 - 32 * q^97 - 3 * q^98 - 13 * q^99

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