LMFDB - Embedded newform 2001.2.a.i.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2001,2,Mod(1,2001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2001, 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("2001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2001 = 3 \cdot 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2001.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:	$15.9780654445$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 3x^{6} - 5x^{5} + 18x^{4} + 4x^{3} - 26x^{2} + x + 8 $ x^7 - 3x^6 - 5x^5 + 18x^4 + 4x^3 - 26*x^2 + x + 8
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-0.586186$ of defining polynomial
Character	$\chi$	$=$	2001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.586186 q^{2} +1.00000 q^{3} -1.65639 q^{4} -0.842866 q^{5} +0.586186 q^{6} +1.23837 q^{7} -2.14332 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.586186 q^{2} +1.00000 q^{3} -1.65639 q^{4} -0.842866 q^{5} +0.586186 q^{6} +1.23837 q^{7} -2.14332 q^{8} +1.00000 q^{9} -0.494076 q^{10} +1.47020 q^{11} -1.65639 q^{12} -3.26028 q^{13} +0.725912 q^{14} -0.842866 q^{15} +2.05639 q^{16} -4.93493 q^{17} +0.586186 q^{18} +0.260886 q^{19} +1.39611 q^{20} +1.23837 q^{21} +0.861812 q^{22} +1.00000 q^{23} -2.14332 q^{24} -4.28958 q^{25} -1.91113 q^{26} +1.00000 q^{27} -2.05121 q^{28} -1.00000 q^{29} -0.494076 q^{30} -0.101716 q^{31} +5.49207 q^{32} +1.47020 q^{33} -2.89279 q^{34} -1.04378 q^{35} -1.65639 q^{36} -3.33423 q^{37} +0.152928 q^{38} -3.26028 q^{39} +1.80653 q^{40} -0.732484 q^{41} +0.725912 q^{42} -5.01063 q^{43} -2.43522 q^{44} -0.842866 q^{45} +0.586186 q^{46} -8.71377 q^{47} +2.05639 q^{48} -5.46645 q^{49} -2.51449 q^{50} -4.93493 q^{51} +5.40027 q^{52} -4.24097 q^{53} +0.586186 q^{54} -1.23918 q^{55} -2.65422 q^{56} +0.260886 q^{57} -0.586186 q^{58} +8.76778 q^{59} +1.39611 q^{60} -1.88602 q^{61} -0.0596245 q^{62} +1.23837 q^{63} -0.893403 q^{64} +2.74797 q^{65} +0.861812 q^{66} -3.21685 q^{67} +8.17415 q^{68} +1.00000 q^{69} -0.611847 q^{70} -1.72395 q^{71} -2.14332 q^{72} -2.64612 q^{73} -1.95448 q^{74} -4.28958 q^{75} -0.432129 q^{76} +1.82065 q^{77} -1.91113 q^{78} +0.465342 q^{79} -1.73326 q^{80} +1.00000 q^{81} -0.429372 q^{82} -8.34128 q^{83} -2.05121 q^{84} +4.15949 q^{85} -2.93716 q^{86} -1.00000 q^{87} -3.15112 q^{88} -5.13593 q^{89} -0.494076 q^{90} -4.03741 q^{91} -1.65639 q^{92} -0.101716 q^{93} -5.10789 q^{94} -0.219892 q^{95} +5.49207 q^{96} -6.87730 q^{97} -3.20436 q^{98} +1.47020 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 3 q^{2} + 7 q^{3} + 5 q^{4} - 3 q^{5} - 3 q^{6} - 5 q^{7} - 6 q^{8} + 7 q^{9}+O(q^{10}) $ 7 * q - 3 * q^2 + 7 * q^3 + 5 * q^4 - 3 * q^5 - 3 * q^6 - 5 * q^7 - 6 * q^8 + 7 * q^9	\( 7 q - 3 q^{2} + 7 q^{3} + 5 q^{4} - 3 q^{5} - 3 q^{6} - 5 q^{7} - 6 q^{8} + 7 q^{9} + 3 q^{10} - 4 q^{11} + 5 q^{12} - 18 q^{13} - 2 q^{14} - 3 q^{15} - 7 q^{16} - 3 q^{17} - 3 q^{18} - 4 q^{19} - 2 q^{20} - 5 q^{21} - 26 q^{22} + 7 q^{23} - 6 q^{24} - 8 q^{25} - 7 q^{26} + 7 q^{27} - 6 q^{28} - 7 q^{29} + 3 q^{30} - 22 q^{31} + 5 q^{32} - 4 q^{33} + 9 q^{34} + 3 q^{35} + 5 q^{36} - 25 q^{37} + 14 q^{38} - 18 q^{39} - 10 q^{40} - 13 q^{41} - 2 q^{42} - 2 q^{43} + 4 q^{44} - 3 q^{45} - 3 q^{46} - 25 q^{47} - 7 q^{48} - 8 q^{49} + 19 q^{50} - 3 q^{51} - 12 q^{52} - 5 q^{53} - 3 q^{54} - 15 q^{55} + 18 q^{56} - 4 q^{57} + 3 q^{58} + 11 q^{59} - 2 q^{60} - 33 q^{61} + 28 q^{62} - 5 q^{63} - 14 q^{64} - 2 q^{65} - 26 q^{66} + 8 q^{67} + 12 q^{68} + 7 q^{69} - 22 q^{70} - 6 q^{71} - 6 q^{72} + 15 q^{73} + 34 q^{74} - 8 q^{75} - 28 q^{76} - q^{77} - 7 q^{78} - 15 q^{79} - 12 q^{80} + 7 q^{81} - 14 q^{82} + 21 q^{83} - 6 q^{84} - 28 q^{85} - 12 q^{86} - 7 q^{87} - 13 q^{88} + 8 q^{89} + 3 q^{90} + 6 q^{91} + 5 q^{92} - 22 q^{93} - 35 q^{94} - 25 q^{95} + 5 q^{96} + 13 q^{97} + q^{98} - 4 q^{99}+O(q^{100}) \) 7 * q - 3 * q^2 + 7 * q^3 + 5 * q^4 - 3 * q^5 - 3 * q^6 - 5 * q^7 - 6 * q^8 + 7 * q^9 + 3 * q^10 - 4 * q^11 + 5 * q^12 - 18 * q^13 - 2 * q^14 - 3 * q^15 - 7 * q^16 - 3 * q^17 - 3 * q^18 - 4 * q^19 - 2 * q^20 - 5 * q^21 - 26 * q^22 + 7 * q^23 - 6 * q^24 - 8 * q^25 - 7 * q^26 + 7 * q^27 - 6 * q^28 - 7 * q^29 + 3 * q^30 - 22 * q^31 + 5 * q^32 - 4 * q^33 + 9 * q^34 + 3 * q^35 + 5 * q^36 - 25 * q^37 + 14 * q^38 - 18 * q^39 - 10 * q^40 - 13 * q^41 - 2 * q^42 - 2 * q^43 + 4 * q^44 - 3 * q^45 - 3 * q^46 - 25 * q^47 - 7 * q^48 - 8 * q^49 + 19 * q^50 - 3 * q^51 - 12 * q^52 - 5 * q^53 - 3 * q^54 - 15 * q^55 + 18 * q^56 - 4 * q^57 + 3 * q^58 + 11 * q^59 - 2 * q^60 - 33 * q^61 + 28 * q^62 - 5 * q^63 - 14 * q^64 - 2 * q^65 - 26 * q^66 + 8 * q^67 + 12 * q^68 + 7 * q^69 - 22 * q^70 - 6 * q^71 - 6 * q^72 + 15 * q^73 + 34 * q^74 - 8 * q^75 - 28 * q^76 - q^77 - 7 * q^78 - 15 * q^79 - 12 * q^80 + 7 * q^81 - 14 * q^82 + 21 * q^83 - 6 * q^84 - 28 * q^85 - 12 * q^86 - 7 * q^87 - 13 * q^88 + 8 * q^89 + 3 * q^90 + 6 * q^91 + 5 * q^92 - 22 * q^93 - 35 * q^94 - 25 * q^95 + 5 * q^96 + 13 * q^97 + q^98 - 4 * 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 $

$2$	0.586186	0.414496	0.207248	−	0.978288i	$-0.433549\pi$
$2$	0.586186	0.414496	0.207248	+	0.978288i	$0.433549\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.65639	−0.828193
$5$	−0.842866	−0.376941	−0.188471	−	0.982079i	$-0.560353\pi$
$5$	−0.842866	−0.376941	−0.188471	+	0.982079i	$0.560353\pi$
$6$	0.586186	0.239309
$7$	1.23837	0.468058	0.234029	−	0.972230i	$-0.424809\pi$
$7$	1.23837	0.468058	0.234029	+	0.972230i	$0.424809\pi$
$8$	−2.14332	−0.757779
$9$	1.00000	0.333333
$10$	−0.494076	−0.156241
$11$	1.47020	0.443283	0.221641	−	0.975128i	$-0.428859\pi$
$11$	1.47020	0.443283	0.221641	+	0.975128i	$0.428859\pi$
$12$	−1.65639	−0.478158
$13$	−3.26028	−0.904238	−0.452119	−	0.891958i	$-0.649332\pi$
$13$	−3.26028	−0.904238	−0.452119	+	0.891958i	$0.649332\pi$
$14$	0.725912	0.194008
$15$	−0.842866	−0.217627
$16$	2.05639	0.514097
$17$	−4.93493	−1.19690	−0.598448	−	0.801161i	$-0.704216\pi$
$17$	−4.93493	−1.19690	−0.598448	+	0.801161i	$0.704216\pi$
$18$	0.586186	0.138165
$19$	0.260886	0.0598514	0.0299257	−	0.999552i	$-0.490473\pi$
$19$	0.260886	0.0598514	0.0299257	+	0.999552i	$0.490473\pi$
$20$	1.39611	0.312180
$21$	1.23837	0.270234
$22$	0.861812	0.183739
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−2.14332	−0.437504
$25$	−4.28958	−0.857915
$26$	−1.91113	−0.374803
$27$	1.00000	0.192450
$28$	−2.05121	−0.387643
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	−0.494076	−0.0902055
$31$	−0.101716	−0.0182688	−0.00913438	−	0.999958i	$-0.502908\pi$
$31$	−0.101716	−0.0182688	−0.00913438	+	0.999958i	$0.502908\pi$
$32$	5.49207	0.970870
$33$	1.47020	0.255929
$34$	−2.89279	−0.496109
$35$	−1.04378	−0.176430
$36$	−1.65639	−0.276064
$37$	−3.33423	−0.548144	−0.274072	−	0.961709i	$-0.588371\pi$
$37$	−3.33423	−0.548144	−0.274072	+	0.961709i	$0.588371\pi$
$38$	0.152928	0.0248082
$39$	−3.26028	−0.522062
$40$	1.80653	0.285638
$41$	−0.732484	−0.114395	−0.0571974	−	0.998363i	$-0.518216\pi$
$41$	−0.732484	−0.114395	−0.0571974	+	0.998363i	$0.518216\pi$
$42$	0.725912	0.112011
$43$	−5.01063	−0.764114	−0.382057	−	0.924139i	$-0.624784\pi$
$43$	−5.01063	−0.764114	−0.382057	+	0.924139i	$0.624784\pi$
$44$	−2.43522	−0.367124
$45$	−0.842866	−0.125647
$46$	0.586186	0.0864284
$47$	−8.71377	−1.27103	−0.635517	−	0.772087i	$-0.719213\pi$
$47$	−8.71377	−1.27103	−0.635517	+	0.772087i	$0.719213\pi$
$48$	2.05639	0.296814
$49$	−5.46645	−0.780922
$50$	−2.51449	−0.355602
$51$	−4.93493	−0.691029
$52$	5.40027	0.748883
$53$	−4.24097	−0.582541	−0.291271	−	0.956641i	$-0.594078\pi$
$53$	−4.24097	−0.582541	−0.291271	+	0.956641i	$0.594078\pi$
$54$	0.586186	0.0797698
$55$	−1.23918	−0.167091
$56$	−2.65422	−0.354685
$57$	0.260886	0.0345552
$58$	−0.586186	−0.0769700
$59$	8.76778	1.14147	0.570734	−	0.821135i	$-0.306659\pi$
$59$	8.76778	1.14147	0.570734	+	0.821135i	$0.306659\pi$
$60$	1.39611	0.180237
$61$	−1.88602	−0.241481	−0.120740	−	0.992684i	$-0.538527\pi$
$61$	−1.88602	−0.241481	−0.120740	+	0.992684i	$0.538527\pi$
$62$	−0.0596245	−0.00757232
$63$	1.23837	0.156019
$64$	−0.893403	−0.111675
$65$	2.74797	0.340844
$66$	0.861812	0.106082
$67$	−3.21685	−0.393001	−0.196500	−	0.980504i	$-0.562958\pi$
$67$	−3.21685	−0.393001	−0.196500	+	0.980504i	$0.562958\pi$
$68$	8.17415	0.991262
$69$	1.00000	0.120386
$70$	−0.611847	−0.0731297
$71$	−1.72395	−0.204595	−0.102297	−	0.994754i	$-0.532619\pi$
$71$	−1.72395	−0.204595	−0.102297	+	0.994754i	$0.532619\pi$
$72$	−2.14332	−0.252593
$73$	−2.64612	−0.309705	−0.154852	−	0.987938i	$-0.549490\pi$
$73$	−2.64612	−0.309705	−0.154852	+	0.987938i	$0.549490\pi$
$74$	−1.95448	−0.227203
$75$	−4.28958	−0.495318
$76$	−0.432129	−0.0495685
$77$	1.82065	0.207482
$78$	−1.91113	−0.216393
$79$	0.465342	0.0523551	0.0261775	−	0.999657i	$-0.491666\pi$
$79$	0.465342	0.0523551	0.0261775	+	0.999657i	$0.491666\pi$
$80$	−1.73326	−0.193784
$81$	1.00000	0.111111
$82$	−0.429372	−0.0474162
$83$	−8.34128	−0.915575	−0.457787	−	0.889062i	$-0.651358\pi$
$83$	−8.34128	−0.915575	−0.457787	+	0.889062i	$0.651358\pi$
$84$	−2.05121	−0.223806
$85$	4.15949	0.451160
$86$	−2.93716	−0.316722
$87$	−1.00000	−0.107211
$88$	−3.15112	−0.335910
$89$	−5.13593	−0.544408	−0.272204	−	0.962240i	$-0.587753\pi$
$89$	−5.13593	−0.544408	−0.272204	+	0.962240i	$0.587753\pi$
$90$	−0.494076	−0.0520802
$91$	−4.03741	−0.423236
$92$	−1.65639	−0.172690
$93$	−0.101716	−0.0105475
$94$	−5.10789	−0.526838
$95$	−0.219892	−0.0225605
$96$	5.49207	0.560532
$97$	−6.87730	−0.698284	−0.349142	−	0.937070i	$-0.613527\pi$
$97$	−6.87730	−0.698284	−0.349142	+	0.937070i	$0.613527\pi$
$98$	−3.20436	−0.323689
$99$	1.47020	0.147761
$100$	7.10520	0.710520
$101$	−15.4552	−1.53785	−0.768923	−	0.639342i	$-0.779207\pi$
$101$	−15.4552	−1.53785	−0.768923	+	0.639342i	$0.779207\pi$
$102$	−2.89279	−0.286429
$103$	9.59885	0.945803	0.472901	−	0.881115i	$-0.343207\pi$
$103$	9.59885	0.945803	0.472901	+	0.881115i	$0.343207\pi$
$104$	6.98782	0.685212
$105$	−1.04378	−0.101862
$106$	−2.48599	−0.241461
$107$	18.4638	1.78496	0.892480	−	0.451088i	$-0.148964\pi$
$107$	18.4638	1.78496	0.892480	+	0.451088i	$0.148964\pi$
$108$	−1.65639	−0.159386
$109$	−13.6145	−1.30403	−0.652017	−	0.758204i	$-0.726077\pi$
$109$	−13.6145	−1.30403	−0.652017	+	0.758204i	$0.726077\pi$
$110$	−0.726391	−0.0692587
$111$	−3.33423	−0.316471
$112$	2.54656	0.240627
$113$	−9.49007	−0.892750	−0.446375	−	0.894846i	$-0.647285\pi$
$113$	−9.49007	−0.892750	−0.446375	+	0.894846i	$0.647285\pi$
$114$	0.152928	0.0143230
$115$	−0.842866	−0.0785976
$116$	1.65639	0.153792
$117$	−3.26028	−0.301413
$118$	5.13955	0.473134
$119$	−6.11125	−0.560217
$120$	1.80653	0.164913
$121$	−8.83851	−0.803501
$122$	−1.10556	−0.100093
$123$	−0.732484	−0.0660459
$124$	0.168481	0.0151301
$125$	7.82987	0.700325
$126$	0.725912	0.0646694
$127$	19.1350	1.69796	0.848980	−	0.528426i	$-0.177217\pi$
$127$	19.1350	1.69796	0.848980	+	0.528426i	$0.177217\pi$
$128$	−11.5078	−1.01716
$129$	−5.01063	−0.441161
$130$	1.61082	0.141279
$131$	14.4038	1.25846	0.629232	−	0.777218i	$-0.283370\pi$
$131$	14.4038	1.25846	0.629232	+	0.777218i	$0.283370\pi$
$132$	−2.43522	−0.211959
$133$	0.323073	0.0280140
$134$	−1.88567	−0.162897
$135$	−0.842866	−0.0725423
$136$	10.5771	0.906983
$137$	10.9664	0.936922	0.468461	−	0.883484i	$-0.344809\pi$
$137$	10.9664	0.936922	0.468461	+	0.883484i	$0.344809\pi$
$138$	0.586186	0.0498994
$139$	−10.7820	−0.914519	−0.457259	−	0.889333i	$-0.651169\pi$
$139$	−10.7820	−0.914519	−0.457259	+	0.889333i	$0.651169\pi$
$140$	1.72890	0.146118
$141$	−8.71377	−0.733832
$142$	−1.01055	−0.0848038
$143$	−4.79326	−0.400833
$144$	2.05639	0.171366
$145$	0.842866	0.0699962
$146$	−1.55112	−0.128371
$147$	−5.46645	−0.450865
$148$	5.52277	0.453969
$149$	−14.9598	−1.22555	−0.612776	−	0.790257i	$-0.709947\pi$
$149$	−14.9598	−1.22555	−0.612776	+	0.790257i	$0.709947\pi$
$150$	−2.51449	−0.205307
$151$	−4.51476	−0.367406	−0.183703	−	0.982982i	$-0.558808\pi$
$151$	−4.51476	−0.367406	−0.183703	+	0.982982i	$0.558808\pi$
$152$	−0.559163	−0.0453541
$153$	−4.93493	−0.398966
$154$	1.06724	0.0860005
$155$	0.0857330	0.00688624
$156$	5.40027	0.432368
$157$	−16.2289	−1.29521	−0.647604	−	0.761977i	$-0.724229\pi$
$157$	−16.2289	−1.29521	−0.647604	+	0.761977i	$0.724229\pi$
$158$	0.272777	0.0217010
$159$	−4.24097	−0.336330
$160$	−4.62908	−0.365961
$161$	1.23837	0.0975969
$162$	0.586186	0.0460551
$163$	−2.54577	−0.199400	−0.0997001	−	0.995018i	$-0.531788\pi$
$163$	−2.54577	−0.199400	−0.0997001	+	0.995018i	$0.531788\pi$
$164$	1.21328	0.0947410
$165$	−1.23918	−0.0964703
$166$	−4.88954	−0.379502
$167$	19.0688	1.47559	0.737794	−	0.675026i	$-0.235868\pi$
$167$	19.0688	1.47559	0.737794	+	0.675026i	$0.235868\pi$
$168$	−2.65422	−0.204777
$169$	−2.37061	−0.182354
$170$	2.43823	0.187004
$171$	0.260886	0.0199505
$172$	8.29954	0.632834
$173$	−9.37891	−0.713065	−0.356533	−	0.934283i	$-0.616041\pi$
$173$	−9.37891	−0.713065	−0.356533	+	0.934283i	$0.616041\pi$
$174$	−0.586186	−0.0444386
$175$	−5.31207	−0.401554
$176$	3.02331	0.227890
$177$	8.76778	0.659026
$178$	−3.01061	−0.225655
$179$	4.33101	0.323715	0.161857	−	0.986814i	$-0.448252\pi$
$179$	4.33101	0.323715	0.161857	+	0.986814i	$0.448252\pi$
$180$	1.39611	0.104060
$181$	20.4714	1.52163	0.760813	−	0.648971i	$-0.224801\pi$
$181$	20.4714	1.52163	0.760813	+	0.648971i	$0.224801\pi$
$182$	−2.36667	−0.175430
$183$	−1.88602	−0.139419
$184$	−2.14332	−0.158008
$185$	2.81031	0.206618
$186$	−0.0596245	−0.00437188
$187$	−7.25535	−0.530564
$188$	14.4334	1.05266
$189$	1.23837	0.0900778
$190$	−0.128898	−0.00935122
$191$	7.10652	0.514210	0.257105	−	0.966383i	$-0.417231\pi$
$191$	7.10652	0.514210	0.257105	+	0.966383i	$0.417231\pi$
$192$	−0.893403	−0.0644758
$193$	2.37896	0.171242	0.0856208	−	0.996328i	$-0.472713\pi$
$193$	2.37896	0.171242	0.0856208	+	0.996328i	$0.472713\pi$
$194$	−4.03138	−0.289436
$195$	2.74797	0.196787
$196$	9.05455	0.646754
$197$	4.61033	0.328472	0.164236	−	0.986421i	$-0.447484\pi$
$197$	4.61033	0.328472	0.164236	+	0.986421i	$0.447484\pi$
$198$	0.861812	0.0612463
$199$	−12.7702	−0.905254	−0.452627	−	0.891700i	$-0.649513\pi$
$199$	−12.7702	−0.905254	−0.452627	+	0.891700i	$0.649513\pi$
$200$	9.19394	0.650110
$201$	−3.21685	−0.226899
$202$	−9.05959	−0.637431
$203$	−1.23837	−0.0869162
$204$	8.17415	0.572305
$205$	0.617386	0.0431201
$206$	5.62671	0.392031
$207$	1.00000	0.0695048
$208$	−6.70439	−0.464866
$209$	0.383556	0.0265311
$210$	−0.611847	−0.0422214
$211$	−8.75135	−0.602468	−0.301234	−	0.953550i	$-0.597398\pi$
$211$	−8.75135	−0.602468	−0.301234	+	0.953550i	$0.597398\pi$
$212$	7.02468	0.482457
$213$	−1.72395	−0.118123
$214$	10.8232	0.739858
$215$	4.22329	0.288026
$216$	−2.14332	−0.145835
$217$	−0.125962	−0.00855084
$218$	−7.98064	−0.540517
$219$	−2.64612	−0.178808
$220$	2.05257	0.138384
$221$	16.0892	1.08228
$222$	−1.95448	−0.131176
$223$	29.3753	1.96712	0.983559	−	0.180586i	$-0.0577993\pi$
$223$	29.3753	1.96712	0.983559	+	0.180586i	$0.0577993\pi$
$224$	6.80119	0.454424
$225$	−4.28958	−0.285972
$226$	−5.56294	−0.370041
$227$	21.4702	1.42503	0.712514	−	0.701658i	$-0.247557\pi$
$227$	21.4702	1.42503	0.712514	+	0.701658i	$0.247557\pi$
$228$	−0.432129	−0.0286184
$229$	6.14700	0.406205	0.203103	−	0.979157i	$-0.434898\pi$
$229$	6.14700	0.406205	0.203103	+	0.979157i	$0.434898\pi$
$230$	−0.494076	−0.0325784
$231$	1.82065	0.119790
$232$	2.14332	0.140716
$233$	21.0310	1.37778	0.688892	−	0.724864i	$-0.258097\pi$
$233$	21.0310	1.37778	0.688892	+	0.724864i	$0.258097\pi$
$234$	−1.91113	−0.124934
$235$	7.34454	0.479105
$236$	−14.5228	−0.945355
$237$	0.465342	0.0302272
$238$	−3.58233	−0.232208
$239$	−22.6235	−1.46339	−0.731697	−	0.681630i	$-0.761271\pi$
$239$	−22.6235	−1.46339	−0.731697	+	0.681630i	$0.761271\pi$
$240$	−1.73326	−0.111881
$241$	16.1684	1.04150	0.520749	−	0.853710i	$-0.325653\pi$
$241$	16.1684	1.04150	0.520749	+	0.853710i	$0.325653\pi$
$242$	−5.18101	−0.333048
$243$	1.00000	0.0641500
$244$	3.12398	0.199993
$245$	4.60748	0.294361
$246$	−0.429372	−0.0273758
$247$	−0.850561	−0.0541199
$248$	0.218010	0.0138437
$249$	−8.34128	−0.528607
$250$	4.58976	0.290282
$251$	4.88555	0.308373	0.154186	−	0.988042i	$-0.450724\pi$
$251$	4.88555	0.308373	0.154186	+	0.988042i	$0.450724\pi$
$252$	−2.05121	−0.129214
$253$	1.47020	0.0924308
$254$	11.2167	0.703797
$255$	4.15949	0.260477
$256$	−4.95892	−0.309933
$257$	14.0680	0.877539	0.438770	−	0.898600i	$-0.355414\pi$
$257$	14.0680	0.877539	0.438770	+	0.898600i	$0.355414\pi$
$258$	−2.93716	−0.182860
$259$	−4.12899	−0.256563
$260$	−4.55171	−0.282285
$261$	−1.00000	−0.0618984
$262$	8.44329	0.521628
$263$	−15.7419	−0.970687	−0.485344	−	0.874323i	$-0.661306\pi$
$263$	−15.7419	−0.970687	−0.485344	+	0.874323i	$0.661306\pi$
$264$	−3.15112	−0.193938
$265$	3.57456	0.219584
$266$	0.189381	0.0116117
$267$	−5.13593	−0.314314
$268$	5.32834	0.325480
$269$	5.80954	0.354214	0.177107	−	0.984192i	$-0.443326\pi$
$269$	5.80954	0.354214	0.177107	+	0.984192i	$0.443326\pi$
$270$	−0.494076	−0.0300685
$271$	13.5144	0.820944	0.410472	−	0.911873i	$-0.365364\pi$
$271$	13.5144	0.820944	0.410472	+	0.911873i	$0.365364\pi$
$272$	−10.1481	−0.615321
$273$	−4.03741	−0.244355
$274$	6.42834	0.388350
$275$	−6.30655	−0.380299
$276$	−1.65639	−0.0997027
$277$	−14.1794	−0.851956	−0.425978	−	0.904733i	$-0.640070\pi$
$277$	−14.1794	−0.851956	−0.425978	+	0.904733i	$0.640070\pi$
$278$	−6.32027	−0.379064
$279$	−0.101716	−0.00608958
$280$	2.23715	0.133695
$281$	−0.303631	−0.0181131	−0.00905656	−	0.999959i	$-0.502883\pi$
$281$	−0.303631	−0.0181131	−0.00905656	+	0.999959i	$0.502883\pi$
$282$	−5.10789	−0.304170
$283$	17.4684	1.03839	0.519195	−	0.854656i	$-0.326232\pi$
$283$	17.4684	1.03839	0.519195	+	0.854656i	$0.326232\pi$
$284$	2.85552	0.169444
$285$	−0.219892	−0.0130253
$286$	−2.80974	−0.166144
$287$	−0.907084	−0.0535434
$288$	5.49207	0.323623
$289$	7.35356	0.432562
$290$	0.494076	0.0290131
$291$	−6.87730	−0.403155
$292$	4.38300	0.256495
$293$	18.0182	1.05263	0.526317	−	0.850289i	$-0.323573\pi$
$293$	18.0182	1.05263	0.526317	+	0.850289i	$0.323573\pi$
$294$	−3.20436	−0.186882
$295$	−7.39006	−0.430266
$296$	7.14632	0.415371
$297$	1.47020	0.0853098
$298$	−8.76920	−0.507986
$299$	−3.26028	−0.188547
$300$	7.10520	0.410219
$301$	−6.20499	−0.357650
$302$	−2.64649	−0.152288
$303$	−15.4552	−0.887875
$304$	0.536484	0.0307694
$305$	1.58966	0.0910239
$306$	−2.89279	−0.165370
$307$	14.8992	0.850340	0.425170	−	0.905113i	$-0.360214\pi$
$307$	14.8992	0.850340	0.425170	+	0.905113i	$0.360214\pi$
$308$	−3.01570	−0.171835
$309$	9.59885	0.546060
$310$	0.0502555	0.00285432
$311$	−1.83728	−0.104183	−0.0520914	−	0.998642i	$-0.516589\pi$
$311$	−1.83728	−0.104183	−0.0520914	+	0.998642i	$0.516589\pi$
$312$	6.98782	0.395607
$313$	4.46857	0.252579	0.126289	−	0.991993i	$-0.459693\pi$
$313$	4.46857	0.252579	0.126289	+	0.991993i	$0.459693\pi$
$314$	−9.51315	−0.536858
$315$	−1.04378	−0.0588101
$316$	−0.770786	−0.0433601
$317$	15.9563	0.896194	0.448097	−	0.893985i	$-0.352102\pi$
$317$	15.9563	0.896194	0.448097	+	0.893985i	$0.352102\pi$
$318$	−2.48599	−0.139408
$319$	−1.47020	−0.0823155
$320$	0.753019	0.0420950
$321$	18.4638	1.03055
$322$	0.725912	0.0404535
$323$	−1.28746	−0.0716360
$324$	−1.65639	−0.0920215
$325$	13.9852	0.775759
$326$	−1.49230	−0.0826506
$327$	−13.6145	−0.752885
$328$	1.56995	0.0866860
$329$	−10.7908	−0.594918
$330$	−0.726391	−0.0399865
$331$	−35.5195	−1.95233	−0.976164	−	0.217035i	$-0.930362\pi$
$331$	−35.5195	−1.95233	−0.976164	+	0.217035i	$0.930362\pi$
$332$	13.8164	0.758273
$333$	−3.33423	−0.182715
$334$	11.1779	0.611625
$335$	2.71137	0.148138
$336$	2.54656	0.138926
$337$	−20.6824	−1.12664	−0.563322	−	0.826237i	$-0.690477\pi$
$337$	−20.6824	−1.12664	−0.563322	+	0.826237i	$0.690477\pi$
$338$	−1.38962	−0.0755851
$339$	−9.49007	−0.515430
$340$	−6.88971	−0.373647
$341$	−0.149543	−0.00809822
$342$	0.152928	0.00826939
$343$	−15.4380	−0.833575
$344$	10.7394	0.579029
$345$	−0.842866	−0.0453784
$346$	−5.49778	−0.295563
$347$	13.4784	0.723557	0.361779	−	0.932264i	$-0.382170\pi$
$347$	13.4784	0.723557	0.361779	+	0.932264i	$0.382170\pi$
$348$	1.65639	0.0887916
$349$	−32.9095	−1.76160	−0.880801	−	0.473486i	$-0.842995\pi$
$349$	−32.9095	−1.76160	−0.880801	+	0.473486i	$0.842995\pi$
$350$	−3.11386	−0.166443
$351$	−3.26028	−0.174021
$352$	8.07445	0.430370
$353$	23.8249	1.26807	0.634035	−	0.773305i	$-0.281398\pi$
$353$	23.8249	1.26807	0.634035	+	0.773305i	$0.281398\pi$
$354$	5.13955	0.273164
$355$	1.45306	0.0771202
$356$	8.50709	0.450875
$357$	−6.11125	−0.323442
$358$	2.53877	0.134178
$359$	26.2175	1.38370	0.691852	−	0.722039i	$-0.256795\pi$
$359$	26.2175	1.38370	0.691852	+	0.722039i	$0.256795\pi$
$360$	1.80653	0.0952126
$361$	−18.9319	−0.996418
$362$	12.0000	0.630708
$363$	−8.83851	−0.463901
$364$	6.68751	0.350521
$365$	2.23032	0.116740
$366$	−1.10556	−0.0577886
$367$	9.01887	0.470781	0.235391	−	0.971901i	$-0.424363\pi$
$367$	9.01887	0.470781	0.235391	+	0.971901i	$0.424363\pi$
$368$	2.05639	0.107197
$369$	−0.732484	−0.0381316
$370$	1.64736	0.0856422
$371$	−5.25187	−0.272663
$372$	0.168481	0.00873534
$373$	−8.59391	−0.444976	−0.222488	−	0.974935i	$-0.571418\pi$
$373$	−8.59391	−0.444976	−0.222488	+	0.974935i	$0.571418\pi$
$374$	−4.25298	−0.219916
$375$	7.82987	0.404333
$376$	18.6764	0.963162
$377$	3.26028	0.167913
$378$	0.725912	0.0373369
$379$	8.48972	0.436088	0.218044	−	0.975939i	$-0.430032\pi$
$379$	8.48972	0.436088	0.218044	+	0.975939i	$0.430032\pi$
$380$	0.364226	0.0186844
$381$	19.1350	0.980317
$382$	4.16574	0.213138
$383$	10.6436	0.543865	0.271933	−	0.962316i	$-0.412337\pi$
$383$	10.6436	0.543865	0.271933	+	0.962316i	$0.412337\pi$
$384$	−11.5078	−0.587257
$385$	−1.53456	−0.0782085
$386$	1.39451	0.0709789
$387$	−5.01063	−0.254705
$388$	11.3915	0.578314
$389$	−14.6896	−0.744794	−0.372397	−	0.928074i	$-0.621464\pi$
$389$	−14.6896	−0.744794	−0.372397	+	0.928074i	$0.621464\pi$
$390$	1.61082	0.0815672
$391$	−4.93493	−0.249570
$392$	11.7164	0.591766
$393$	14.4038	0.726574
$394$	2.70251	0.136150
$395$	−0.392221	−0.0197348
$396$	−2.43522	−0.122375
$397$	7.75333	0.389128	0.194564	−	0.980890i	$-0.437671\pi$
$397$	7.75333	0.389128	0.194564	+	0.980890i	$0.437671\pi$
$398$	−7.48570	−0.375224
$399$	0.323073	0.0161739
$400$	−8.82103	−0.441052
$401$	−1.17706	−0.0587797	−0.0293899	−	0.999568i	$-0.509356\pi$
$401$	−1.17706	−0.0587797	−0.0293899	+	0.999568i	$0.509356\pi$
$402$	−1.88567	−0.0940487
$403$	0.331623	0.0165193
$404$	25.5997	1.27363
$405$	−0.842866	−0.0418823
$406$	−0.725912	−0.0360264
$407$	−4.90199	−0.242982
$408$	10.5771	0.523647
$409$	−23.6328	−1.16857	−0.584283	−	0.811550i	$-0.698624\pi$
$409$	−23.6328	−1.16857	−0.584283	+	0.811550i	$0.698624\pi$
$410$	0.361903	0.0178731
$411$	10.9664	0.540932
$412$	−15.8994	−0.783307
$413$	10.8577	0.534273
$414$	0.586186	0.0288095
$415$	7.03058	0.345118
$416$	−17.9057	−0.877897
$417$	−10.7820	−0.527998
$418$	0.224835	0.0109970
$419$	18.6252	0.909901	0.454951	−	0.890517i	$-0.349657\pi$
$419$	18.6252	0.909901	0.454951	+	0.890517i	$0.349657\pi$
$420$	1.72890	0.0843615
$421$	−31.0986	−1.51565	−0.757827	−	0.652456i	$-0.773739\pi$
$421$	−31.0986	−1.51565	−0.757827	+	0.652456i	$0.773739\pi$
$422$	−5.12992	−0.249720
$423$	−8.71377	−0.423678
$424$	9.08975	0.441437
$425$	21.1688	1.02684
$426$	−1.01055	−0.0489615
$427$	−2.33559	−0.113027
$428$	−30.5831	−1.47829
$429$	−4.79326	−0.231421
$430$	2.47563	0.119386
$431$	9.88560	0.476173	0.238086	−	0.971244i	$-0.423480\pi$
$431$	9.88560	0.476173	0.238086	+	0.971244i	$0.423480\pi$
$432$	2.05639	0.0989380
$433$	−8.91141	−0.428255	−0.214127	−	0.976806i	$-0.568691\pi$
$433$	−8.91141	−0.428255	−0.214127	+	0.976806i	$0.568691\pi$
$434$	−0.0738370	−0.00354429
$435$	0.842866	0.0404123
$436$	22.5509	1.07999
$437$	0.260886	0.0124799
$438$	−1.55112	−0.0741153
$439$	−31.9814	−1.52639	−0.763193	−	0.646170i	$-0.776370\pi$
$439$	−31.9814	−1.52639	−0.763193	+	0.646170i	$0.776370\pi$
$440$	2.65597	0.126618
$441$	−5.46645	−0.260307
$442$	9.43128	0.448600
$443$	20.8775	0.991921	0.495960	−	0.868345i	$-0.334816\pi$
$443$	20.8775	0.991921	0.495960	+	0.868345i	$0.334816\pi$
$444$	5.52277	0.262099
$445$	4.32890	0.205210
$446$	17.2194	0.815363
$447$	−14.9598	−0.707573
$448$	−1.10636	−0.0522706
$449$	−13.7130	−0.647158	−0.323579	−	0.946201i	$-0.604886\pi$
$449$	−13.7130	−0.647158	−0.323579	+	0.946201i	$0.604886\pi$
$450$	−2.51449	−0.118534
$451$	−1.07690	−0.0507092
$452$	15.7192	0.739370
$453$	−4.51476	−0.212122
$454$	12.5855	0.590668
$455$	3.40300	0.159535
$456$	−0.559163	−0.0261852
$457$	12.8613	0.601627	0.300813	−	0.953683i	$-0.402742\pi$
$457$	12.8613	0.601627	0.300813	+	0.953683i	$0.402742\pi$
$458$	3.60328	0.168370
$459$	−4.93493	−0.230343
$460$	1.39611	0.0650940
$461$	−24.1332	−1.12400	−0.561998	−	0.827139i	$-0.689967\pi$
$461$	−24.1332	−1.12400	−0.561998	+	0.827139i	$0.689967\pi$
$462$	1.06724	0.0496524
$463$	−40.5906	−1.88640	−0.943202	−	0.332219i	$-0.892203\pi$
$463$	−40.5906	−1.88640	−0.943202	+	0.332219i	$0.892203\pi$
$464$	−2.05639	−0.0954654
$465$	0.0857330	0.00397577
$466$	12.3281	0.571086
$467$	−16.4110	−0.759413	−0.379706	−	0.925107i	$-0.623975\pi$
$467$	−16.4110	−0.759413	−0.379706	+	0.925107i	$0.623975\pi$
$468$	5.40027	0.249628
$469$	−3.98363	−0.183947
$470$	4.30526	0.198587
$471$	−16.2289	−0.747788
$472$	−18.7922	−0.864979
$473$	−7.36664	−0.338718
$474$	0.272777	0.0125291
$475$	−1.11909	−0.0513475
$476$	10.1226	0.463968
$477$	−4.24097	−0.194180
$478$	−13.2616	−0.606571
$479$	−11.5781	−0.529017	−0.264508	−	0.964383i	$-0.585210\pi$
$479$	−11.5781	−0.529017	−0.264508	+	0.964383i	$0.585210\pi$
$480$	−4.62908	−0.211287
$481$	10.8705	0.495652
$482$	9.47768	0.431697
$483$	1.23837	0.0563476
$484$	14.6400	0.665454
$485$	5.79664	0.263212
$486$	0.586186	0.0265899
$487$	−5.57197	−0.252490	−0.126245	−	0.991999i	$-0.540293\pi$
$487$	−5.57197	−0.252490	−0.126245	+	0.991999i	$0.540293\pi$
$488$	4.04236	0.182989
$489$	−2.54577	−0.115124
$490$	2.70084	0.122012
$491$	20.4086	0.921028	0.460514	−	0.887653i	$-0.347665\pi$
$491$	20.4086	0.921028	0.460514	+	0.887653i	$0.347665\pi$
$492$	1.21328	0.0546988
$493$	4.93493	0.222258
$494$	−0.498587	−0.0224325
$495$	−1.23918	−0.0556971
$496$	−0.209168	−0.00939191
$497$	−2.13488	−0.0957624
$498$	−4.88954	−0.219106
$499$	−32.6022	−1.45947	−0.729737	−	0.683728i	$-0.760357\pi$
$499$	−32.6022	−1.45947	−0.729737	+	0.683728i	$0.760357\pi$
$500$	−12.9693	−0.580004
$501$	19.0688	0.851931
$502$	2.86384	0.127819
$503$	6.33199	0.282330	0.141165	−	0.989986i	$-0.454915\pi$
$503$	6.33199	0.282330	0.141165	+	0.989986i	$0.454915\pi$
$504$	−2.65422	−0.118228
$505$	13.0266	0.579677
$506$	0.861812	0.0383122
$507$	−2.37061	−0.105282
$508$	−31.6950	−1.40624
$509$	27.0573	1.19929	0.599646	−	0.800265i	$-0.295308\pi$
$509$	27.0573	1.19929	0.599646	+	0.800265i	$0.295308\pi$
$510$	2.43823	0.107967
$511$	−3.27686	−0.144960
$512$	20.1088	0.888693
$513$	0.260886	0.0115184
$514$	8.24647	0.363736
$515$	−8.09054	−0.356512
$516$	8.29954	0.365367
$517$	−12.8110	−0.563427
$518$	−2.42036	−0.106344
$519$	−9.37891	−0.411688
$520$	−5.88979	−0.258284
$521$	−5.85670	−0.256587	−0.128293	−	0.991736i	$-0.540950\pi$
$521$	−5.85670	−0.256587	−0.128293	+	0.991736i	$0.540950\pi$
$522$	−0.586186	−0.0256567
$523$	8.29727	0.362814	0.181407	−	0.983408i	$-0.441935\pi$
$523$	8.29727	0.362814	0.181407	+	0.983408i	$0.441935\pi$
$524$	−23.8582	−1.04225
$525$	−5.31207	−0.231838
$526$	−9.22768	−0.402346
$527$	0.501962	0.0218658
$528$	3.02331	0.131572
$529$	1.00000	0.0434783
$530$	2.09536	0.0910166
$531$	8.76778	0.380489
$532$	−0.535133	−0.0232010
$533$	2.38810	0.103440
$534$	−3.01061	−0.130282
$535$	−15.5625	−0.672824
$536$	6.89474	0.297807
$537$	4.33101	0.186897
$538$	3.40547	0.146820
$539$	−8.03679	−0.346169
$540$	1.39611	0.0600791
$541$	11.0825	0.476473	0.238237	−	0.971207i	$-0.423431\pi$
$541$	11.0825	0.476473	0.238237	+	0.971207i	$0.423431\pi$
$542$	7.92197	0.340278
$543$	20.4714	0.878511
$544$	−27.1030	−1.16203
$545$	11.4752	0.491544
$546$	−2.36667	−0.101284
$547$	21.4790	0.918375	0.459187	−	0.888339i	$-0.348141\pi$
$547$	21.4790	0.918375	0.459187	+	0.888339i	$0.348141\pi$
$548$	−18.1646	−0.775952
$549$	−1.88602	−0.0804935
$550$	−3.69681	−0.157632
$551$	−0.260886	−0.0111141
$552$	−2.14332	−0.0912258
$553$	0.576264	0.0245052
$554$	−8.31175	−0.353132
$555$	2.81031	0.119291
$556$	17.8592	0.757398
$557$	38.2929	1.62252	0.811262	−	0.584683i	$-0.198781\pi$
$557$	38.2929	1.62252	0.811262	+	0.584683i	$0.198781\pi$
$558$	−0.0596245	−0.00252411
$559$	16.3360	0.690940
$560$	−2.14641	−0.0907023
$561$	−7.25535	−0.306321
$562$	−0.177984	−0.00750781
$563$	−4.52231	−0.190592	−0.0952962	−	0.995449i	$-0.530380\pi$
$563$	−4.52231	−0.190592	−0.0952962	+	0.995449i	$0.530380\pi$
$564$	14.4334	0.607754
$565$	7.99885	0.336514
$566$	10.2397	0.430409
$567$	1.23837	0.0520065
$568$	3.69497	0.155038
$569$	44.8603	1.88064	0.940321	−	0.340289i	$-0.110525\pi$
$569$	44.8603	1.88064	0.940321	+	0.340289i	$0.110525\pi$
$570$	−0.128898	−0.00539893
$571$	0.417218	0.0174600	0.00873001	−	0.999962i	$-0.497221\pi$
$571$	0.417218	0.0174600	0.00873001	+	0.999962i	$0.497221\pi$
$572$	7.93949	0.331967
$573$	7.10652	0.296879
$574$	−0.531719	−0.0221935
$575$	−4.28958	−0.178888
$576$	−0.893403	−0.0372251
$577$	−11.8343	−0.492670	−0.246335	−	0.969185i	$-0.579226\pi$
$577$	−11.8343	−0.492670	−0.246335	+	0.969185i	$0.579226\pi$
$578$	4.31055	0.179295
$579$	2.37896	0.0988663
$580$	−1.39611	−0.0579704
$581$	−10.3296	−0.428542
$582$	−4.03138	−0.167106
$583$	−6.23508	−0.258230
$584$	5.67148	0.234688
$585$	2.74797	0.113615
$586$	10.5620	0.436312
$587$	−18.5466	−0.765501	−0.382750	−	0.923852i	$-0.625023\pi$
$587$	−18.5466	−0.765501	−0.382750	+	0.923852i	$0.625023\pi$
$588$	9.05455	0.373403
$589$	−0.0265363	−0.00109341
$590$	−4.33195	−0.178343
$591$	4.61033	0.189643
$592$	−6.85646	−0.281799
$593$	−29.0821	−1.19426	−0.597129	−	0.802145i	$-0.703692\pi$
$593$	−29.0821	−1.19426	−0.597129	+	0.802145i	$0.703692\pi$
$594$	0.861812	0.0353606
$595$	5.15096	0.211169
$596$	24.7792	1.01499
$597$	−12.7702	−0.522649
$598$	−1.91113	−0.0781518
$599$	29.5204	1.20617	0.603085	−	0.797677i	$-0.293938\pi$
$599$	29.5204	1.20617	0.603085	+	0.797677i	$0.293938\pi$
$600$	9.19394	0.375341
$601$	3.49768	0.142673	0.0713367	−	0.997452i	$-0.477274\pi$
$601$	3.49768	0.142673	0.0713367	+	0.997452i	$0.477274\pi$
$602$	−3.63728	−0.148244
$603$	−3.21685	−0.131000
$604$	7.47819	0.304283
$605$	7.44967	0.302872
$606$	−9.05959	−0.368021
$607$	7.88945	0.320223	0.160111	−	0.987099i	$-0.448815\pi$
$607$	7.88945	0.320223	0.160111	+	0.987099i	$0.448815\pi$
$608$	1.43281	0.0581079
$609$	−1.23837	−0.0501811
$610$	0.931839	0.0377291
$611$	28.4093	1.14932
$612$	8.17415	0.330421
$613$	−33.4560	−1.35127	−0.675637	−	0.737235i	$-0.736131\pi$
$613$	−33.4560	−1.35127	−0.675637	+	0.737235i	$0.736131\pi$
$614$	8.73368	0.352463
$615$	0.617386	0.0248954
$616$	−3.90223	−0.157225
$617$	−33.2433	−1.33832	−0.669162	−	0.743117i	$-0.733347\pi$
$617$	−33.2433	−1.33832	−0.669162	+	0.743117i	$0.733347\pi$
$618$	5.62671	0.226339
$619$	−23.1547	−0.930668	−0.465334	−	0.885135i	$-0.654066\pi$
$619$	−23.1547	−0.930668	−0.465334	+	0.885135i	$0.654066\pi$
$620$	−0.142007	−0.00570314
$621$	1.00000	0.0401286
$622$	−1.07699	−0.0431834
$623$	−6.36016	−0.254815
$624$	−6.70439	−0.268390
$625$	14.8484	0.593934
$626$	2.61941	0.104693
$627$	0.383556	0.0153177
$628$	26.8813	1.07268
$629$	16.4542	0.656071
$630$	−0.611847	−0.0243766
$631$	−17.7854	−0.708027	−0.354014	−	0.935240i	$-0.615183\pi$
$631$	−17.7854	−0.708027	−0.354014	+	0.935240i	$0.615183\pi$
$632$	−0.997378	−0.0396735
$633$	−8.75135	−0.347835
$634$	9.35334	0.371469
$635$	−16.1283	−0.640030
$636$	7.02468	0.278547
$637$	17.8221	0.706139
$638$	−0.861812	−0.0341194
$639$	−1.72395	−0.0681983
$640$	9.69956	0.383409
$641$	27.7374	1.09556	0.547782	−	0.836621i	$-0.315472\pi$
$641$	27.7374	1.09556	0.547782	+	0.836621i	$0.315472\pi$
$642$	10.8232	0.427157
$643$	15.3293	0.604528	0.302264	−	0.953224i	$-0.402258\pi$
$643$	15.3293	0.604528	0.302264	+	0.953224i	$0.402258\pi$
$644$	−2.05121	−0.0808291
$645$	4.22329	0.166292
$646$	−0.754689	−0.0296928
$647$	−41.3220	−1.62454	−0.812268	−	0.583284i	$-0.801767\pi$
$647$	−41.3220	−1.62454	−0.812268	+	0.583284i	$0.801767\pi$
$648$	−2.14332	−0.0841976
$649$	12.8904	0.505993
$650$	8.19793	0.321549
$651$	−0.125962	−0.00493683
$652$	4.21678	0.165142
$653$	−31.9364	−1.24977	−0.624883	−	0.780718i	$-0.714854\pi$
$653$	−31.9364	−1.24977	−0.624883	+	0.780718i	$0.714854\pi$
$654$	−7.98064	−0.312068
$655$	−12.1405	−0.474367
$656$	−1.50627	−0.0588100
$657$	−2.64612	−0.103235
$658$	−6.32543	−0.246591
$659$	−39.4143	−1.53536	−0.767681	−	0.640833i	$-0.778589\pi$
$659$	−39.4143	−1.53536	−0.767681	+	0.640833i	$0.778589\pi$
$660$	2.05257	0.0798960
$661$	16.5791	0.644850	0.322425	−	0.946595i	$-0.395502\pi$
$661$	16.5791	0.644850	0.322425	+	0.946595i	$0.395502\pi$
$662$	−20.8210	−0.809232
$663$	16.0892	0.624854
$664$	17.8781	0.693803
$665$	−0.272307	−0.0105596
$666$	−1.95448	−0.0757344
$667$	−1.00000	−0.0387202
$668$	−31.5853	−1.22207
$669$	29.3753	1.13572
$670$	1.58937	0.0614026
$671$	−2.77284	−0.107044
$672$	6.80119	0.262362
$673$	−13.0131	−0.501618	−0.250809	−	0.968037i	$-0.580697\pi$
$673$	−13.0131	−0.501618	−0.250809	+	0.968037i	$0.580697\pi$
$674$	−12.1237	−0.466989
$675$	−4.28958	−0.165106
$676$	3.92664	0.151025
$677$	12.2182	0.469583	0.234792	−	0.972046i	$-0.424559\pi$
$677$	12.2182	0.469583	0.234792	+	0.972046i	$0.424559\pi$
$678$	−5.56294	−0.213644
$679$	−8.51661	−0.326838
$680$	−8.91512	−0.341879
$681$	21.4702	0.822740
$682$	−0.0876601	−0.00335668
$683$	1.56826	0.0600076	0.0300038	−	0.999550i	$-0.490448\pi$
$683$	1.56826	0.0600076	0.0300038	+	0.999550i	$0.490448\pi$
$684$	−0.432129	−0.0165228
$685$	−9.24319	−0.353164
$686$	−9.04955	−0.345513
$687$	6.14700	0.234523
$688$	−10.3038	−0.392829
$689$	13.8267	0.526756
$690$	−0.494076	−0.0188091
$691$	6.57025	0.249944	0.124972	−	0.992160i	$-0.460116\pi$
$691$	6.57025	0.249944	0.124972	+	0.992160i	$0.460116\pi$
$692$	15.5351	0.590556
$693$	1.82065	0.0691607
$694$	7.90084	0.299912
$695$	9.08779	0.344720
$696$	2.14332	0.0812424
$697$	3.61476	0.136919
$698$	−19.2911	−0.730177
$699$	21.0310	0.795464
$700$	8.79883	0.332565
$701$	16.6273	0.628004	0.314002	−	0.949422i	$-0.398330\pi$
$701$	16.6273	0.628004	0.314002	+	0.949422i	$0.398330\pi$
$702$	−1.91113	−0.0721308
$703$	−0.869854	−0.0328072
$704$	−1.31348	−0.0495038
$705$	7.34454	0.276611
$706$	13.9658	0.525610
$707$	−19.1391	−0.719801
$708$	−14.5228	−0.545801
$709$	−9.39341	−0.352777	−0.176389	−	0.984321i	$-0.556442\pi$
$709$	−9.39341	−0.352777	−0.176389	+	0.984321i	$0.556442\pi$
$710$	0.851761	0.0319660
$711$	0.465342	0.0174517
$712$	11.0080	0.412541
$713$	−0.101716	−0.00380930
$714$	−3.58233	−0.134065
$715$	4.04008	0.151090
$716$	−7.17382	−0.268098
$717$	−22.6235	−0.844891
$718$	15.3683	0.573540
$719$	−0.289428	−0.0107939	−0.00539693	−	0.999985i	$-0.501718\pi$
$719$	−0.289428	−0.0107939	−0.00539693	+	0.999985i	$0.501718\pi$
$720$	−1.73326	−0.0645947
$721$	11.8869	0.442691
$722$	−11.0976	−0.413011
$723$	16.1684	0.601309
$724$	−33.9085	−1.26020
$725$	4.28958	0.159311
$726$	−5.18101	−0.192285
$727$	12.8787	0.477644	0.238822	−	0.971063i	$-0.423239\pi$
$727$	12.8787	0.477644	0.238822	+	0.971063i	$0.423239\pi$
$728$	8.65347	0.320719
$729$	1.00000	0.0370370
$730$	1.30738	0.0483884
$731$	24.7271	0.914566
$732$	3.12398	0.115466
$733$	−33.0973	−1.22248	−0.611239	−	0.791446i	$-0.709328\pi$
$733$	−33.0973	−1.22248	−0.611239	+	0.791446i	$0.709328\pi$
$734$	5.28673	0.195137
$735$	4.60748	0.169950
$736$	5.49207	0.202440
$737$	−4.72942	−0.174210
$738$	−0.429372	−0.0158054
$739$	17.1818	0.632043	0.316022	−	0.948752i	$-0.397653\pi$
$739$	17.1818	0.632043	0.316022	+	0.948752i	$0.397653\pi$
$740$	−4.65495	−0.171119
$741$	−0.850561	−0.0312461
$742$	−3.07857	−0.113018
$743$	−21.8990	−0.803395	−0.401697	−	0.915772i	$-0.631580\pi$
$743$	−21.8990	−0.803395	−0.401697	+	0.915772i	$0.631580\pi$
$744$	0.218010	0.00799265
$745$	12.6091	0.461961
$746$	−5.03763	−0.184441
$747$	−8.34128	−0.305192
$748$	12.0177	0.439409
$749$	22.8649	0.835465
$750$	4.58976	0.167594
$751$	50.1136	1.82867	0.914336	−	0.404956i	$-0.132713\pi$
$751$	50.1136	1.82867	0.914336	+	0.404956i	$0.132713\pi$
$752$	−17.9189	−0.653435
$753$	4.88555	0.178039
$754$	1.91113	0.0695991
$755$	3.80534	0.138490
$756$	−2.05121	−0.0746018
$757$	49.4866	1.79862	0.899311	−	0.437309i	$-0.144068\pi$
$757$	49.4866	1.79862	0.899311	+	0.437309i	$0.144068\pi$
$758$	4.97655	0.180757
$759$	1.47020	0.0533650
$760$	0.471300	0.0170958
$761$	−18.5155	−0.671186	−0.335593	−	0.942007i	$-0.608937\pi$
$761$	−18.5155	−0.671186	−0.335593	+	0.942007i	$0.608937\pi$
$762$	11.2167	0.406338
$763$	−16.8598	−0.610364
$764$	−11.7711	−0.425865
$765$	4.15949	0.150387
$766$	6.23916	0.225430
$767$	−28.5854	−1.03216
$768$	−4.95892	−0.178940
$769$	9.36922	0.337863	0.168931	−	0.985628i	$-0.445968\pi$
$769$	9.36922	0.337863	0.168931	+	0.985628i	$0.445968\pi$
$770$	−0.899538	−0.0324171
$771$	14.0680	0.506647
$772$	−3.94048	−0.141821
$773$	3.24015	0.116540	0.0582700	−	0.998301i	$-0.481442\pi$
$773$	3.24015	0.116540	0.0582700	+	0.998301i	$0.481442\pi$
$774$	−2.93716	−0.105574
$775$	0.436319	0.0156730
$776$	14.7403	0.529145
$777$	−4.12899	−0.148127
$778$	−8.61085	−0.308714
$779$	−0.191095	−0.00684670
$780$	−4.55171	−0.162977
$781$	−2.53455	−0.0906934
$782$	−2.89279	−0.103446
$783$	−1.00000	−0.0357371
$784$	−11.2411	−0.401469
$785$	13.6788	0.488217
$786$	8.44329	0.301162
$787$	34.2199	1.21981	0.609905	−	0.792475i	$-0.291208\pi$
$787$	34.2199	1.21981	0.609905	+	0.792475i	$0.291208\pi$
$788$	−7.63648	−0.272038
$789$	−15.7419	−0.560427
$790$	−0.229914	−0.00817998
$791$	−11.7522	−0.417859
$792$	−3.15112	−0.111970
$793$	6.14896	0.218356
$794$	4.54489	0.161292
$795$	3.57456	0.126777
$796$	21.1524	0.749725
$797$	−9.08039	−0.321644	−0.160822	−	0.986983i	$-0.551415\pi$
$797$	−9.08039	−0.321644	−0.160822	+	0.986983i	$0.551415\pi$
$798$	0.189381	0.00670400
$799$	43.0019	1.52130
$800$	−23.5587	−0.832924
$801$	−5.13593	−0.181469
$802$	−0.689978	−0.0243640
$803$	−3.89033	−0.137287
$804$	5.32834	0.187916
$805$	−1.04378	−0.0367883
$806$	0.194392	0.00684718
$807$	5.80954	0.204505
$808$	33.1254	1.16535
$809$	−2.55646	−0.0898804	−0.0449402	−	0.998990i	$-0.514310\pi$
$809$	−2.55646	−0.0898804	−0.0449402	+	0.998990i	$0.514310\pi$
$810$	−0.494076	−0.0173601
$811$	1.90277	0.0668153	0.0334077	−	0.999442i	$-0.489364\pi$
$811$	1.90277	0.0668153	0.0334077	+	0.999442i	$0.489364\pi$
$812$	2.05121	0.0719834
$813$	13.5144	0.473972
$814$	−2.87348	−0.100715
$815$	2.14574	0.0751621
$816$	−10.1481	−0.355256
$817$	−1.30720	−0.0457333
$818$	−13.8532	−0.484366
$819$	−4.03741	−0.141079
$820$	−1.02263	−0.0357118
$821$	−13.7415	−0.479581	−0.239790	−	0.970825i	$-0.577079\pi$
$821$	−13.7415	−0.479581	−0.239790	+	0.970825i	$0.577079\pi$
$822$	6.42834	0.224214
$823$	−10.1853	−0.355039	−0.177519	−	0.984117i	$-0.556807\pi$
$823$	−10.1853	−0.355039	−0.177519	+	0.984117i	$0.556807\pi$
$824$	−20.5734	−0.716709
$825$	−6.30655	−0.219566
$826$	6.36464	0.221454
$827$	26.7391	0.929809	0.464905	−	0.885361i	$-0.346089\pi$
$827$	26.7391	0.929809	0.464905	+	0.885361i	$0.346089\pi$
$828$	−1.65639	−0.0575634
$829$	−51.5489	−1.79037	−0.895184	−	0.445697i	$-0.852956\pi$
$829$	−51.5489	−1.79037	−0.895184	+	0.445697i	$0.852956\pi$
$830$	4.12123	0.143050
$831$	−14.1794	−0.491877
$832$	2.91274	0.100981
$833$	26.9766	0.934683
$834$	−6.32027	−0.218853
$835$	−16.0724	−0.556210
$836$	−0.635316	−0.0219729
$837$	−0.101716	−0.00351582
$838$	10.9178	0.377150
$839$	4.54360	0.156862	0.0784312	−	0.996920i	$-0.475009\pi$
$839$	4.54360	0.156862	0.0784312	+	0.996920i	$0.475009\pi$
$840$	2.23715	0.0771889
$841$	1.00000	0.0344828
$842$	−18.2296	−0.628232
$843$	−0.303631	−0.0104576
$844$	14.4956	0.498960
$845$	1.99810	0.0687368
$846$	−5.10789	−0.175613
$847$	−10.9453	−0.376085
$848$	−8.72107	−0.299483
$849$	17.4684	0.599515
$850$	12.4088	0.425620
$851$	−3.33423	−0.114296
$852$	2.85552	0.0978286
$853$	−14.2400	−0.487568	−0.243784	−	0.969830i	$-0.578389\pi$
$853$	−14.2400	−0.487568	−0.243784	+	0.969830i	$0.578389\pi$
$854$	−1.36909	−0.0468492
$855$	−0.219892	−0.00752015
$856$	−39.5738	−1.35260
$857$	−2.90828	−0.0993451	−0.0496726	−	0.998766i	$-0.515818\pi$
$857$	−2.90828	−0.0993451	−0.0496726	+	0.998766i	$0.515818\pi$
$858$	−2.80974	−0.0959230
$859$	0.525329	0.0179240	0.00896200	−	0.999960i	$-0.497147\pi$
$859$	0.525329	0.0179240	0.00896200	+	0.999960i	$0.497147\pi$
$860$	−6.99540	−0.238541
$861$	−0.907084	−0.0309133
$862$	5.79480	0.197372
$863$	−35.2839	−1.20108	−0.600539	−	0.799595i	$-0.705047\pi$
$863$	−35.2839	−1.20108	−0.600539	+	0.799595i	$0.705047\pi$
$864$	5.49207	0.186844
$865$	7.90516	0.268784
$866$	−5.22374	−0.177510
$867$	7.35356	0.249740
$868$	0.208641	0.00708175
$869$	0.684147	0.0232081
$870$	0.494076	0.0167507
$871$	10.4878	0.355366
$872$	29.1803	0.988170
$873$	−6.87730	−0.232761
$874$	0.152928	0.00517286
$875$	9.69624	0.327793
$876$	4.38300	0.148088
$877$	−32.9988	−1.11429	−0.557145	−	0.830415i	$-0.688103\pi$
$877$	−32.9988	−1.11429	−0.557145	+	0.830415i	$0.688103\pi$
$878$	−18.7470	−0.632681
$879$	18.0182	0.607738
$880$	−2.54824	−0.0859012
$881$	−8.43036	−0.284026	−0.142013	−	0.989865i	$-0.545358\pi$
$881$	−8.43036	−0.284026	−0.142013	+	0.989865i	$0.545358\pi$
$882$	−3.20436	−0.107896
$883$	−26.7930	−0.901656	−0.450828	−	0.892611i	$-0.648871\pi$
$883$	−26.7930	−0.901656	−0.450828	+	0.892611i	$0.648871\pi$
$884$	−26.6500	−0.896336
$885$	−7.39006	−0.248414
$886$	12.2381	0.411147
$887$	18.0659	0.606594	0.303297	−	0.952896i	$-0.401913\pi$
$887$	18.0659	0.606594	0.303297	+	0.952896i	$0.401913\pi$
$888$	7.14632	0.239815
$889$	23.6962	0.794744
$890$	2.53754	0.0850585
$891$	1.47020	0.0492536
$892$	−48.6569	−1.62915
$893$	−2.27330	−0.0760732
$894$	−8.76920	−0.293286
$895$	−3.65046	−0.122021
$896$	−14.2509	−0.476089
$897$	−3.26028	−0.108857
$898$	−8.03838	−0.268244
$899$	0.101716	0.00339242
$900$	7.10520	0.236840
$901$	20.9289	0.697242
$902$	−0.631264	−0.0210188
$903$	−6.20499	−0.206489
$904$	20.3403	0.676507
$905$	−17.2546	−0.573563
$906$	−2.64649	−0.0879237
$907$	50.2869	1.66975	0.834874	−	0.550441i	$-0.185540\pi$
$907$	50.2869	1.66975	0.834874	+	0.550441i	$0.185540\pi$
$908$	−35.5630	−1.18020
$909$	−15.4552	−0.512615
$910$	1.99479	0.0661266
$911$	−25.2794	−0.837544	−0.418772	−	0.908091i	$-0.637539\pi$
$911$	−25.2794	−0.837544	−0.418772	+	0.908091i	$0.637539\pi$
$912$	0.536484	0.0177647
$913$	−12.2634	−0.405858
$914$	7.53912	0.249372
$915$	1.58966	0.0525527
$916$	−10.1818	−0.336416
$917$	17.8371	0.589034
$918$	−2.89279	−0.0954762
$919$	−48.0884	−1.58629	−0.793146	−	0.609032i	$-0.791558\pi$
$919$	−48.0884	−1.58629	−0.793146	+	0.609032i	$0.791558\pi$
$920$	1.80653	0.0595596
$921$	14.8992	0.490944
$922$	−14.1465	−0.465891
$923$	5.62054	0.185002
$924$	−3.01570	−0.0992091
$925$	14.3024	0.470261
$926$	−23.7936	−0.781907
$927$	9.59885	0.315268
$928$	−5.49207	−0.180286
$929$	−32.8357	−1.07731	−0.538653	−	0.842528i	$-0.681066\pi$
$929$	−32.8357	−1.07731	−0.538653	+	0.842528i	$0.681066\pi$
$930$	0.0502555	0.00164794
$931$	−1.42612	−0.0467393
$932$	−34.8354	−1.14107
$933$	−1.83728	−0.0601500
$934$	−9.61992	−0.314773
$935$	6.11528	0.199991
$936$	6.98782	0.228404
$937$	−28.5880	−0.933930	−0.466965	−	0.884276i	$-0.654653\pi$
$937$	−28.5880	−0.933930	−0.466965	+	0.884276i	$0.654653\pi$
$938$	−2.33515	−0.0762453
$939$	4.46857	0.145826
$940$	−12.1654	−0.396791
$941$	−13.1403	−0.428361	−0.214181	−	0.976794i	$-0.568708\pi$
$941$	−13.1403	−0.428361	−0.214181	+	0.976794i	$0.568708\pi$
$942$	−9.51315	−0.309955
$943$	−0.732484	−0.0238530
$944$	18.0299	0.586825
$945$	−1.04378	−0.0339540
$946$	−4.31822	−0.140397
$947$	−35.6856	−1.15963	−0.579813	−	0.814750i	$-0.696874\pi$
$947$	−35.6856	−1.15963	−0.579813	+	0.814750i	$0.696874\pi$
$948$	−0.770786	−0.0250340
$949$	8.62708	0.280047
$950$	−0.655996	−0.0212833
$951$	15.9563	0.517418
$952$	13.0984	0.424521
$953$	−14.8964	−0.482541	−0.241270	−	0.970458i	$-0.577564\pi$
$953$	−14.8964	−0.482541	−0.241270	+	0.970458i	$0.577564\pi$
$954$	−2.48599	−0.0804870
$955$	−5.98985	−0.193827
$956$	37.4733	1.21197
$957$	−1.47020	−0.0475249
$958$	−6.78691	−0.219275
$959$	13.5804	0.438534
$960$	0.753019	0.0243036
$961$	−30.9897	−0.999666
$962$	6.37213	0.205446
$963$	18.4638	0.594986
$964$	−26.7811	−0.862561
$965$	−2.00515	−0.0645480
$966$	0.725912	0.0233558
$967$	−15.5500	−0.500053	−0.250026	−	0.968239i	$-0.580439\pi$
$967$	−15.5500	−0.500053	−0.250026	+	0.968239i	$0.580439\pi$
$968$	18.9438	0.608876
$969$	−1.28746	−0.0413591
$970$	3.39791	0.109100
$971$	−40.0985	−1.28682	−0.643410	−	0.765522i	$-0.722481\pi$
$971$	−40.0985	−1.28682	−0.643410	+	0.765522i	$0.722481\pi$
$972$	−1.65639	−0.0531286
$973$	−13.3521	−0.428048
$974$	−3.26621	−0.104656
$975$	13.9852	0.447885
$976$	−3.87840	−0.124144
$977$	−12.6678	−0.405277	−0.202639	−	0.979254i	$-0.564952\pi$
$977$	−12.6678	−0.405277	−0.202639	+	0.979254i	$0.564952\pi$
$978$	−1.49230	−0.0477183
$979$	−7.55086	−0.241326
$980$	−7.63177	−0.243788
$981$	−13.6145	−0.434678
$982$	11.9632	0.381762
$983$	−41.8116	−1.33358	−0.666792	−	0.745244i	$-0.732333\pi$
$983$	−41.8116	−1.33358	−0.666792	+	0.745244i	$0.732333\pi$
$984$	1.56995	0.0500482
$985$	−3.88589	−0.123815
$986$	2.89279	0.0921251
$987$	−10.7908	−0.343476
$988$	1.40886	0.0448217
$989$	−5.01063	−0.159329
$990$	−0.726391	−0.0230862
$991$	6.44884	0.204854	0.102427	−	0.994741i	$-0.467339\pi$
$991$	6.44884	0.204854	0.102427	+	0.994741i	$0.467339\pi$
$992$	−0.558632	−0.0177366
$993$	−35.5195	−1.12718
$994$	−1.25143	−0.0396931
$995$	10.7635	0.341227
$996$	13.8164	0.437789
$997$	28.3269	0.897123	0.448562	−	0.893752i	$-0.351936\pi$
$997$	28.3269	0.897123	0.448562	+	0.893752i	$0.351936\pi$
$998$	−19.1109	−0.604946
$999$	−3.33423	−0.105490

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.2.a.i.1.5	✓	7
3.2	odd	2		6003.2.a.j.1.3		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.2.a.i.1.5	✓	7	1.1	even	1	trivial
6003.2.a.j.1.3		7	3.2	odd	2

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:	\( N \)	\(=\)	\( 2001 = 3 \cdot 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2001.a (trivial)

\(f(q)\)	\(=\)	\(q+0.586186 q^{2} +1.00000 q^{3} -1.65639 q^{4} -0.842866 q^{5} +0.586186 q^{6} +1.23837 q^{7} -2.14332 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.586186 q^{2} +1.00000 q^{3} -1.65639 q^{4} -0.842866 q^{5} +0.586186 q^{6} +1.23837 q^{7} -2.14332 q^{8} +1.00000 q^{9} -0.494076 q^{10} +1.47020 q^{11} -1.65639 q^{12} -3.26028 q^{13} +0.725912 q^{14} -0.842866 q^{15} +2.05639 q^{16} -4.93493 q^{17} +0.586186 q^{18} +0.260886 q^{19} +1.39611 q^{20} +1.23837 q^{21} +0.861812 q^{22} +1.00000 q^{23} -2.14332 q^{24} -4.28958 q^{25} -1.91113 q^{26} +1.00000 q^{27} -2.05121 q^{28} -1.00000 q^{29} -0.494076 q^{30} -0.101716 q^{31} +5.49207 q^{32} +1.47020 q^{33} -2.89279 q^{34} -1.04378 q^{35} -1.65639 q^{36} -3.33423 q^{37} +0.152928 q^{38} -3.26028 q^{39} +1.80653 q^{40} -0.732484 q^{41} +0.725912 q^{42} -5.01063 q^{43} -2.43522 q^{44} -0.842866 q^{45} +0.586186 q^{46} -8.71377 q^{47} +2.05639 q^{48} -5.46645 q^{49} -2.51449 q^{50} -4.93493 q^{51} +5.40027 q^{52} -4.24097 q^{53} +0.586186 q^{54} -1.23918 q^{55} -2.65422 q^{56} +0.260886 q^{57} -0.586186 q^{58} +8.76778 q^{59} +1.39611 q^{60} -1.88602 q^{61} -0.0596245 q^{62} +1.23837 q^{63} -0.893403 q^{64} +2.74797 q^{65} +0.861812 q^{66} -3.21685 q^{67} +8.17415 q^{68} +1.00000 q^{69} -0.611847 q^{70} -1.72395 q^{71} -2.14332 q^{72} -2.64612 q^{73} -1.95448 q^{74} -4.28958 q^{75} -0.432129 q^{76} +1.82065 q^{77} -1.91113 q^{78} +0.465342 q^{79} -1.73326 q^{80} +1.00000 q^{81} -0.429372 q^{82} -8.34128 q^{83} -2.05121 q^{84} +4.15949 q^{85} -2.93716 q^{86} -1.00000 q^{87} -3.15112 q^{88} -5.13593 q^{89} -0.494076 q^{90} -4.03741 q^{91} -1.65639 q^{92} -0.101716 q^{93} -5.10789 q^{94} -0.219892 q^{95} +5.49207 q^{96} -6.87730 q^{97} -3.20436 q^{98} +1.47020 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 3 q^{2} + 7 q^{3} + 5 q^{4} - 3 q^{5} - 3 q^{6} - 5 q^{7} - 6 q^{8} + 7 q^{9}+O(q^{10}) \) 7 * q - 3 * q^2 + 7 * q^3 + 5 * q^4 - 3 * q^5 - 3 * q^6 - 5 * q^7 - 6 * q^8 + 7 * q^9	\( 7 q - 3 q^{2} + 7 q^{3} + 5 q^{4} - 3 q^{5} - 3 q^{6} - 5 q^{7} - 6 q^{8} + 7 q^{9} + 3 q^{10} - 4 q^{11} + 5 q^{12} - 18 q^{13} - 2 q^{14} - 3 q^{15} - 7 q^{16} - 3 q^{17} - 3 q^{18} - 4 q^{19} - 2 q^{20} - 5 q^{21} - 26 q^{22} + 7 q^{23} - 6 q^{24} - 8 q^{25} - 7 q^{26} + 7 q^{27} - 6 q^{28} - 7 q^{29} + 3 q^{30} - 22 q^{31} + 5 q^{32} - 4 q^{33} + 9 q^{34} + 3 q^{35} + 5 q^{36} - 25 q^{37} + 14 q^{38} - 18 q^{39} - 10 q^{40} - 13 q^{41} - 2 q^{42} - 2 q^{43} + 4 q^{44} - 3 q^{45} - 3 q^{46} - 25 q^{47} - 7 q^{48} - 8 q^{49} + 19 q^{50} - 3 q^{51} - 12 q^{52} - 5 q^{53} - 3 q^{54} - 15 q^{55} + 18 q^{56} - 4 q^{57} + 3 q^{58} + 11 q^{59} - 2 q^{60} - 33 q^{61} + 28 q^{62} - 5 q^{63} - 14 q^{64} - 2 q^{65} - 26 q^{66} + 8 q^{67} + 12 q^{68} + 7 q^{69} - 22 q^{70} - 6 q^{71} - 6 q^{72} + 15 q^{73} + 34 q^{74} - 8 q^{75} - 28 q^{76} - q^{77} - 7 q^{78} - 15 q^{79} - 12 q^{80} + 7 q^{81} - 14 q^{82} + 21 q^{83} - 6 q^{84} - 28 q^{85} - 12 q^{86} - 7 q^{87} - 13 q^{88} + 8 q^{89} + 3 q^{90} + 6 q^{91} + 5 q^{92} - 22 q^{93} - 35 q^{94} - 25 q^{95} + 5 q^{96} + 13 q^{97} + q^{98} - 4 q^{99}+O(q^{100}) \) 7 * q - 3 * q^2 + 7 * q^3 + 5 * q^4 - 3 * q^5 - 3 * q^6 - 5 * q^7 - 6 * q^8 + 7 * q^9 + 3 * q^10 - 4 * q^11 + 5 * q^12 - 18 * q^13 - 2 * q^14 - 3 * q^15 - 7 * q^16 - 3 * q^17 - 3 * q^18 - 4 * q^19 - 2 * q^20 - 5 * q^21 - 26 * q^22 + 7 * q^23 - 6 * q^24 - 8 * q^25 - 7 * q^26 + 7 * q^27 - 6 * q^28 - 7 * q^29 + 3 * q^30 - 22 * q^31 + 5 * q^32 - 4 * q^33 + 9 * q^34 + 3 * q^35 + 5 * q^36 - 25 * q^37 + 14 * q^38 - 18 * q^39 - 10 * q^40 - 13 * q^41 - 2 * q^42 - 2 * q^43 + 4 * q^44 - 3 * q^45 - 3 * q^46 - 25 * q^47 - 7 * q^48 - 8 * q^49 + 19 * q^50 - 3 * q^51 - 12 * q^52 - 5 * q^53 - 3 * q^54 - 15 * q^55 + 18 * q^56 - 4 * q^57 + 3 * q^58 + 11 * q^59 - 2 * q^60 - 33 * q^61 + 28 * q^62 - 5 * q^63 - 14 * q^64 - 2 * q^65 - 26 * q^66 + 8 * q^67 + 12 * q^68 + 7 * q^69 - 22 * q^70 - 6 * q^71 - 6 * q^72 + 15 * q^73 + 34 * q^74 - 8 * q^75 - 28 * q^76 - q^77 - 7 * q^78 - 15 * q^79 - 12 * q^80 + 7 * q^81 - 14 * q^82 + 21 * q^83 - 6 * q^84 - 28 * q^85 - 12 * q^86 - 7 * q^87 - 13 * q^88 + 8 * q^89 + 3 * q^90 + 6 * q^91 + 5 * q^92 - 22 * q^93 - 35 * q^94 - 25 * q^95 + 5 * q^96 + 13 * q^97 + q^98 - 4 * q^99

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