LMFDB - Embedded newform 4006.2.a.i.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4006,2,Mod(1,4006)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4006, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4006.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4006 = 2 \cdot 2003 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4006.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:	$31.9880710497$
Analytic rank:	$0$
Dimension:	$46$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	4006.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.75438 q^{3} +1.00000 q^{4} +1.48781 q^{5} -1.75438 q^{6} +4.69044 q^{7} +1.00000 q^{8} +0.0778341 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.75438 q^{3} +1.00000 q^{4} +1.48781 q^{5} -1.75438 q^{6} +4.69044 q^{7} +1.00000 q^{8} +0.0778341 q^{9} +1.48781 q^{10} -3.31484 q^{11} -1.75438 q^{12} +5.09947 q^{13} +4.69044 q^{14} -2.61017 q^{15} +1.00000 q^{16} -2.48617 q^{17} +0.0778341 q^{18} -0.550373 q^{19} +1.48781 q^{20} -8.22879 q^{21} -3.31484 q^{22} +5.58398 q^{23} -1.75438 q^{24} -2.78643 q^{25} +5.09947 q^{26} +5.12658 q^{27} +4.69044 q^{28} +8.67580 q^{29} -2.61017 q^{30} -2.43588 q^{31} +1.00000 q^{32} +5.81548 q^{33} -2.48617 q^{34} +6.97846 q^{35} +0.0778341 q^{36} -6.90608 q^{37} -0.550373 q^{38} -8.94638 q^{39} +1.48781 q^{40} +5.15857 q^{41} -8.22879 q^{42} +5.66380 q^{43} -3.31484 q^{44} +0.115802 q^{45} +5.58398 q^{46} -0.641823 q^{47} -1.75438 q^{48} +15.0002 q^{49} -2.78643 q^{50} +4.36167 q^{51} +5.09947 q^{52} -2.92217 q^{53} +5.12658 q^{54} -4.93184 q^{55} +4.69044 q^{56} +0.965561 q^{57} +8.67580 q^{58} -2.52347 q^{59} -2.61017 q^{60} -0.801735 q^{61} -2.43588 q^{62} +0.365076 q^{63} +1.00000 q^{64} +7.58702 q^{65} +5.81548 q^{66} +0.653229 q^{67} -2.48617 q^{68} -9.79639 q^{69} +6.97846 q^{70} +3.08721 q^{71} +0.0778341 q^{72} +1.58769 q^{73} -6.90608 q^{74} +4.88845 q^{75} -0.550373 q^{76} -15.5481 q^{77} -8.94638 q^{78} -5.97248 q^{79} +1.48781 q^{80} -9.22744 q^{81} +5.15857 q^{82} +5.53378 q^{83} -8.22879 q^{84} -3.69893 q^{85} +5.66380 q^{86} -15.2206 q^{87} -3.31484 q^{88} +1.48788 q^{89} +0.115802 q^{90} +23.9187 q^{91} +5.58398 q^{92} +4.27346 q^{93} -0.641823 q^{94} -0.818848 q^{95} -1.75438 q^{96} -4.11729 q^{97} +15.0002 q^{98} -0.258008 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q + 46 q^{2} + 21 q^{3} + 46 q^{4} + 23 q^{5} + 21 q^{6} + 26 q^{7} + 46 q^{8} + 59 q^{9}+O(q^{10}) $ 46 * q + 46 * q^2 + 21 * q^3 + 46 * q^4 + 23 * q^5 + 21 * q^6 + 26 * q^7 + 46 * q^8 + 59 * q^9	\( 46 q + 46 q^{2} + 21 q^{3} + 46 q^{4} + 23 q^{5} + 21 q^{6} + 26 q^{7} + 46 q^{8} + 59 q^{9} + 23 q^{10} + 39 q^{11} + 21 q^{12} + 8 q^{13} + 26 q^{14} + 14 q^{15} + 46 q^{16} + 36 q^{17} + 59 q^{18} + 37 q^{19} + 23 q^{20} + 20 q^{21} + 39 q^{22} + 38 q^{23} + 21 q^{24} + 57 q^{25} + 8 q^{26} + 63 q^{27} + 26 q^{28} + 23 q^{29} + 14 q^{30} + 44 q^{31} + 46 q^{32} + 25 q^{33} + 36 q^{34} + 26 q^{35} + 59 q^{36} + 9 q^{37} + 37 q^{38} - 2 q^{39} + 23 q^{40} + 50 q^{41} + 20 q^{42} + 46 q^{43} + 39 q^{44} + 30 q^{45} + 38 q^{46} + 57 q^{47} + 21 q^{48} + 62 q^{49} + 57 q^{50} + 5 q^{51} + 8 q^{52} + 21 q^{53} + 63 q^{54} + 40 q^{55} + 26 q^{56} + 3 q^{57} + 23 q^{58} + 68 q^{59} + 14 q^{60} - q^{61} + 44 q^{62} + 40 q^{63} + 46 q^{64} + 18 q^{65} + 25 q^{66} + 42 q^{67} + 36 q^{68} - 7 q^{69} + 26 q^{70} + 67 q^{71} + 59 q^{72} + 48 q^{73} + 9 q^{74} + 71 q^{75} + 37 q^{76} - 5 q^{77} - 2 q^{78} + 40 q^{79} + 23 q^{80} + 82 q^{81} + 50 q^{82} + 48 q^{83} + 20 q^{84} - 68 q^{85} + 46 q^{86} + 18 q^{87} + 39 q^{88} + 90 q^{89} + 30 q^{90} + 9 q^{91} + 38 q^{92} - 42 q^{93} + 57 q^{94} + 6 q^{95} + 21 q^{96} + 46 q^{97} + 62 q^{98} + 61 q^{99}+O(q^{100}) \) 46 * q + 46 * q^2 + 21 * q^3 + 46 * q^4 + 23 * q^5 + 21 * q^6 + 26 * q^7 + 46 * q^8 + 59 * q^9 + 23 * q^10 + 39 * q^11 + 21 * q^12 + 8 * q^13 + 26 * q^14 + 14 * q^15 + 46 * q^16 + 36 * q^17 + 59 * q^18 + 37 * q^19 + 23 * q^20 + 20 * q^21 + 39 * q^22 + 38 * q^23 + 21 * q^24 + 57 * q^25 + 8 * q^26 + 63 * q^27 + 26 * q^28 + 23 * q^29 + 14 * q^30 + 44 * q^31 + 46 * q^32 + 25 * q^33 + 36 * q^34 + 26 * q^35 + 59 * q^36 + 9 * q^37 + 37 * q^38 - 2 * q^39 + 23 * q^40 + 50 * q^41 + 20 * q^42 + 46 * q^43 + 39 * q^44 + 30 * q^45 + 38 * q^46 + 57 * q^47 + 21 * q^48 + 62 * q^49 + 57 * q^50 + 5 * q^51 + 8 * q^52 + 21 * q^53 + 63 * q^54 + 40 * q^55 + 26 * q^56 + 3 * q^57 + 23 * q^58 + 68 * q^59 + 14 * q^60 - q^61 + 44 * q^62 + 40 * q^63 + 46 * q^64 + 18 * q^65 + 25 * q^66 + 42 * q^67 + 36 * q^68 - 7 * q^69 + 26 * q^70 + 67 * q^71 + 59 * q^72 + 48 * q^73 + 9 * q^74 + 71 * q^75 + 37 * q^76 - 5 * q^77 - 2 * q^78 + 40 * q^79 + 23 * q^80 + 82 * q^81 + 50 * q^82 + 48 * q^83 + 20 * q^84 - 68 * q^85 + 46 * q^86 + 18 * q^87 + 39 * q^88 + 90 * q^89 + 30 * q^90 + 9 * q^91 + 38 * q^92 - 42 * q^93 + 57 * q^94 + 6 * q^95 + 21 * q^96 + 46 * q^97 + 62 * q^98 + 61 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.75438	−1.01289	−0.506445	−	0.862272i	$-0.669041\pi$
$3$	−1.75438	−1.01289	−0.506445	+	0.862272i	$0.669041\pi$
$4$	1.00000	0.500000
$5$	1.48781	0.665367	0.332684	−	0.943039i	$-0.392046\pi$
$5$	1.48781	0.665367	0.332684	+	0.943039i	$0.392046\pi$
$6$	−1.75438	−0.716221
$7$	4.69044	1.77282	0.886409	−	0.462902i	$-0.153192\pi$
$7$	4.69044	1.77282	0.886409	+	0.462902i	$0.153192\pi$
$8$	1.00000	0.353553
$9$	0.0778341	0.0259447
$10$	1.48781	0.470486
$11$	−3.31484	−0.999462	−0.499731	−	0.866181i	$-0.666568\pi$
$11$	−3.31484	−0.999462	−0.499731	+	0.866181i	$0.666568\pi$
$12$	−1.75438	−0.506445
$13$	5.09947	1.41434	0.707169	−	0.707045i	$-0.249972\pi$
$13$	5.09947	1.41434	0.707169	+	0.707045i	$0.249972\pi$
$14$	4.69044	1.25357
$15$	−2.61017	−0.673943
$16$	1.00000	0.250000
$17$	−2.48617	−0.602984	−0.301492	−	0.953469i	$-0.597485\pi$
$17$	−2.48617	−0.602984	−0.301492	+	0.953469i	$0.597485\pi$
$18$	0.0778341	0.0183457
$19$	−0.550373	−0.126264	−0.0631321	−	0.998005i	$-0.520109\pi$
$19$	−0.550373	−0.126264	−0.0631321	+	0.998005i	$0.520109\pi$
$20$	1.48781	0.332684
$21$	−8.22879	−1.79567
$22$	−3.31484	−0.706727
$23$	5.58398	1.16434	0.582170	−	0.813067i	$-0.302204\pi$
$23$	5.58398	1.16434	0.582170	+	0.813067i	$0.302204\pi$
$24$	−1.75438	−0.358110
$25$	−2.78643	−0.557287
$26$	5.09947	1.00009
$27$	5.12658	0.986610
$28$	4.69044	0.886409
$29$	8.67580	1.61106	0.805528	−	0.592558i	$-0.201882\pi$
$29$	8.67580	1.61106	0.805528	+	0.592558i	$0.201882\pi$
$30$	−2.61017	−0.476550
$31$	−2.43588	−0.437498	−0.218749	−	0.975781i	$-0.570198\pi$
$31$	−2.43588	−0.437498	−0.218749	+	0.975781i	$0.570198\pi$
$32$	1.00000	0.176777
$33$	5.81548	1.01234
$34$	−2.48617	−0.426374
$35$	6.97846	1.17958
$36$	0.0778341	0.0129724
$37$	−6.90608	−1.13535	−0.567676	−	0.823252i	$-0.692158\pi$
$37$	−6.90608	−1.13535	−0.567676	+	0.823252i	$0.692158\pi$
$38$	−0.550373	−0.0892823
$39$	−8.94638	−1.43257
$40$	1.48781	0.235243
$41$	5.15857	0.805633	0.402816	−	0.915281i	$-0.368031\pi$
$41$	5.15857	0.805633	0.402816	+	0.915281i	$0.368031\pi$
$42$	−8.22879	−1.26973
$43$	5.66380	0.863722	0.431861	−	0.901940i	$-0.357857\pi$
$43$	5.66380	0.863722	0.431861	+	0.901940i	$0.357857\pi$
$44$	−3.31484	−0.499731
$45$	0.115802	0.0172628
$46$	5.58398	0.823312
$47$	−0.641823	−0.0936196	−0.0468098	−	0.998904i	$-0.514905\pi$
$47$	−0.641823	−0.0936196	−0.0468098	+	0.998904i	$0.514905\pi$
$48$	−1.75438	−0.253222
$49$	15.0002	2.14289
$50$	−2.78643	−0.394061
$51$	4.36167	0.610756
$52$	5.09947	0.707169
$53$	−2.92217	−0.401391	−0.200696	−	0.979654i	$-0.564320\pi$
$53$	−2.92217	−0.401391	−0.200696	+	0.979654i	$0.564320\pi$
$54$	5.12658	0.697639
$55$	−4.93184	−0.665009
$56$	4.69044	0.626786
$57$	0.965561	0.127892
$58$	8.67580	1.13919
$59$	−2.52347	−0.328527	−0.164264	−	0.986416i	$-0.552525\pi$
$59$	−2.52347	−0.328527	−0.164264	+	0.986416i	$0.552525\pi$
$60$	−2.61017	−0.336972
$61$	−0.801735	−0.102652	−0.0513258	−	0.998682i	$-0.516345\pi$
$61$	−0.801735	−0.102652	−0.0513258	+	0.998682i	$0.516345\pi$
$62$	−2.43588	−0.309358
$63$	0.365076	0.0459953
$64$	1.00000	0.125000
$65$	7.58702	0.941053
$66$	5.81548	0.715836
$67$	0.653229	0.0798046	0.0399023	−	0.999204i	$-0.487295\pi$
$67$	0.653229	0.0798046	0.0399023	+	0.999204i	$0.487295\pi$
$68$	−2.48617	−0.301492
$69$	−9.79639	−1.17935
$70$	6.97846	0.834086
$71$	3.08721	0.366385	0.183192	−	0.983077i	$-0.441357\pi$
$71$	3.08721	0.366385	0.183192	+	0.983077i	$0.441357\pi$
$72$	0.0778341	0.00917284
$73$	1.58769	0.185825	0.0929125	−	0.995674i	$-0.470382\pi$
$73$	1.58769	0.185825	0.0929125	+	0.995674i	$0.470382\pi$
$74$	−6.90608	−0.802816
$75$	4.88845	0.564470
$76$	−0.550373	−0.0631321
$77$	−15.5481	−1.77187
$78$	−8.94638	−1.01298
$79$	−5.97248	−0.671957	−0.335979	−	0.941870i	$-0.609067\pi$
$79$	−5.97248	−0.671957	−0.335979	+	0.941870i	$0.609067\pi$
$80$	1.48781	0.166342
$81$	−9.22744	−1.02527
$82$	5.15857	0.569668
$83$	5.53378	0.607411	0.303706	−	0.952766i	$-0.401776\pi$
$83$	5.53378	0.607411	0.303706	+	0.952766i	$0.401776\pi$
$84$	−8.22879	−0.897835
$85$	−3.69893	−0.401205
$86$	5.66380	0.610743
$87$	−15.2206	−1.63182
$88$	−3.31484	−0.353363
$89$	1.48788	0.157715	0.0788576	−	0.996886i	$-0.474873\pi$
$89$	1.48788	0.157715	0.0788576	+	0.996886i	$0.474873\pi$
$90$	0.115802	0.0122066
$91$	23.9187	2.50736
$92$	5.58398	0.582170
$93$	4.27346	0.443137
$94$	−0.641823	−0.0661990
$95$	−0.818848	−0.0840121
$96$	−1.75438	−0.179055
$97$	−4.11729	−0.418047	−0.209024	−	0.977911i	$-0.567029\pi$
$97$	−4.11729	−0.418047	−0.209024	+	0.977911i	$0.567029\pi$
$98$	15.0002	1.51525
$99$	−0.258008	−0.0259308
$100$	−2.78643	−0.278643
$101$	−6.81372	−0.677990	−0.338995	−	0.940788i	$-0.610087\pi$
$101$	−6.81372	−0.677990	−0.338995	+	0.940788i	$0.610087\pi$
$102$	4.36167	0.431869
$103$	1.58470	0.156145	0.0780724	−	0.996948i	$-0.475123\pi$
$103$	1.58470	0.156145	0.0780724	+	0.996948i	$0.475123\pi$
$104$	5.09947	0.500044
$105$	−12.2428	−1.19478
$106$	−2.92217	−0.283826
$107$	17.1013	1.65325	0.826623	−	0.562756i	$-0.190259\pi$
$107$	17.1013	1.65325	0.826623	+	0.562756i	$0.190259\pi$
$108$	5.12658	0.493305
$109$	−14.2033	−1.36043	−0.680217	−	0.733011i	$-0.738114\pi$
$109$	−14.2033	−1.36043	−0.680217	+	0.733011i	$0.738114\pi$
$110$	−4.93184	−0.470233
$111$	12.1159	1.14999
$112$	4.69044	0.443205
$113$	10.6914	1.00576	0.502882	−	0.864355i	$-0.332273\pi$
$113$	10.6914	1.00576	0.502882	+	0.864355i	$0.332273\pi$
$114$	0.965561	0.0904331
$115$	8.30787	0.774713
$116$	8.67580	0.805528
$117$	0.396913	0.0366946
$118$	−2.52347	−0.232304
$119$	−11.6612	−1.06898
$120$	−2.61017	−0.238275
$121$	−0.0118263	−0.00107512
$122$	−0.801735	−0.0725856
$123$	−9.05006	−0.816017
$124$	−2.43588	−0.218749
$125$	−11.5847	−1.03617
$126$	0.365076	0.0325236
$127$	10.3012	0.914082	0.457041	−	0.889446i	$-0.348909\pi$
$127$	10.3012	0.914082	0.457041	+	0.889446i	$0.348909\pi$
$128$	1.00000	0.0883883
$129$	−9.93644	−0.874854
$130$	7.58702	0.665425
$131$	−7.38261	−0.645022	−0.322511	−	0.946566i	$-0.604527\pi$
$131$	−7.38261	−0.645022	−0.322511	+	0.946566i	$0.604527\pi$
$132$	5.81548	0.506172
$133$	−2.58149	−0.223844
$134$	0.653229	0.0564304
$135$	7.62735	0.656458
$136$	−2.48617	−0.213187
$137$	7.86025	0.671546	0.335773	−	0.941943i	$-0.391002\pi$
$137$	7.86025	0.671546	0.335773	+	0.941943i	$0.391002\pi$
$138$	−9.79639	−0.833924
$139$	−13.1174	−1.11260	−0.556300	−	0.830981i	$-0.687780\pi$
$139$	−13.1174	−1.11260	−0.556300	+	0.830981i	$0.687780\pi$
$140$	6.97846	0.589788
$141$	1.12600	0.0948263
$142$	3.08721	0.259073
$143$	−16.9039	−1.41358
$144$	0.0778341	0.00648618
$145$	12.9079	1.07194
$146$	1.58769	0.131398
$147$	−26.3160	−2.17051
$148$	−6.90608	−0.567676
$149$	−10.8553	−0.889298	−0.444649	−	0.895705i	$-0.646671\pi$
$149$	−10.8553	−0.889298	−0.444649	+	0.895705i	$0.646671\pi$
$150$	4.88845	0.399140
$151$	−6.40294	−0.521064	−0.260532	−	0.965465i	$-0.583898\pi$
$151$	−6.40294	−0.521064	−0.260532	+	0.965465i	$0.583898\pi$
$152$	−0.550373	−0.0446412
$153$	−0.193509	−0.0156442
$154$	−15.5481	−1.25290
$155$	−3.62412	−0.291097
$156$	−8.94638	−0.716284
$157$	17.1535	1.36900	0.684498	−	0.729015i	$-0.260021\pi$
$157$	17.1535	1.36900	0.684498	+	0.729015i	$0.260021\pi$
$158$	−5.97248	−0.475145
$159$	5.12659	0.406565
$160$	1.48781	0.117621
$161$	26.1913	2.06416
$162$	−9.22744	−0.724976
$163$	1.31185	0.102752	0.0513759	−	0.998679i	$-0.483639\pi$
$163$	1.31185	0.102752	0.0513759	+	0.998679i	$0.483639\pi$
$164$	5.15857	0.402816
$165$	8.65230	0.673581
$166$	5.53378	0.429505
$167$	7.26484	0.562170	0.281085	−	0.959683i	$-0.409306\pi$
$167$	7.26484	0.562170	0.281085	+	0.959683i	$0.409306\pi$
$168$	−8.22879	−0.634865
$169$	13.0046	1.00035
$170$	−3.69893	−0.283695
$171$	−0.0428378	−0.00327589
$172$	5.66380	0.431861
$173$	15.7088	1.19432	0.597160	−	0.802122i	$-0.296296\pi$
$173$	15.7088	1.19432	0.597160	+	0.802122i	$0.296296\pi$
$174$	−15.2206	−1.15387
$175$	−13.0696	−0.987968
$176$	−3.31484	−0.249866
$177$	4.42711	0.332762
$178$	1.48788	0.111521
$179$	1.51350	0.113125	0.0565623	−	0.998399i	$-0.481986\pi$
$179$	1.51350	0.113125	0.0565623	+	0.998399i	$0.481986\pi$
$180$	0.115802	0.00863138
$181$	−7.19721	−0.534964	−0.267482	−	0.963563i	$-0.586192\pi$
$181$	−7.19721	−0.534964	−0.267482	+	0.963563i	$0.586192\pi$
$182$	23.9187	1.77297
$183$	1.40654	0.103975
$184$	5.58398	0.411656
$185$	−10.2749	−0.755426
$186$	4.27346	0.313345
$187$	8.24124	0.602659
$188$	−0.641823	−0.0468098
$189$	24.0459	1.74908
$190$	−0.818848	−0.0594055
$191$	23.3413	1.68892	0.844460	−	0.535618i	$-0.179921\pi$
$191$	23.3413	1.68892	0.844460	+	0.535618i	$0.179921\pi$
$192$	−1.75438	−0.126611
$193$	−9.38620	−0.675633	−0.337817	−	0.941212i	$-0.609688\pi$
$193$	−9.38620	−0.675633	−0.337817	+	0.941212i	$0.609688\pi$
$194$	−4.11729	−0.295604
$195$	−13.3105	−0.953183
$196$	15.0002	1.07144
$197$	15.9001	1.13283	0.566417	−	0.824118i	$-0.308329\pi$
$197$	15.9001	1.13283	0.566417	+	0.824118i	$0.308329\pi$
$198$	−0.258008	−0.0183358
$199$	7.42897	0.526626	0.263313	−	0.964710i	$-0.415185\pi$
$199$	7.42897	0.526626	0.263313	+	0.964710i	$0.415185\pi$
$200$	−2.78643	−0.197031
$201$	−1.14601	−0.0808332
$202$	−6.81372	−0.479412
$203$	40.6933	2.85611
$204$	4.36167	0.305378
$205$	7.67494	0.536041
$206$	1.58470	0.110411
$207$	0.434624	0.0302085
$208$	5.09947	0.353584
$209$	1.82440	0.126196
$210$	−12.2428	−0.844836
$211$	1.46730	0.101013	0.0505067	−	0.998724i	$-0.483916\pi$
$211$	1.46730	0.101013	0.0505067	+	0.998724i	$0.483916\pi$
$212$	−2.92217	−0.200696
$213$	−5.41613	−0.371107
$214$	17.1013	1.16902
$215$	8.42664	0.574692
$216$	5.12658	0.348819
$217$	−11.4254	−0.775604
$218$	−14.2033	−0.961972
$219$	−2.78540	−0.188220
$220$	−4.93184	−0.332505
$221$	−12.6781	−0.852822
$222$	12.1159	0.813163
$223$	1.72542	0.115542	0.0577712	−	0.998330i	$-0.481601\pi$
$223$	1.72542	0.115542	0.0577712	+	0.998330i	$0.481601\pi$
$224$	4.69044	0.313393
$225$	−0.216880	−0.0144586
$226$	10.6914	0.711182
$227$	−0.166423	−0.0110459	−0.00552293	−	0.999985i	$-0.501758\pi$
$227$	−0.166423	−0.0110459	−0.00552293	+	0.999985i	$0.501758\pi$
$228$	0.965561	0.0639459
$229$	−2.31655	−0.153082	−0.0765409	−	0.997066i	$-0.524388\pi$
$229$	−2.31655	−0.153082	−0.0765409	+	0.997066i	$0.524388\pi$
$230$	8.30787	0.547805
$231$	27.2771	1.79470
$232$	8.67580	0.569594
$233$	13.2682	0.869227	0.434614	−	0.900617i	$-0.356885\pi$
$233$	13.2682	0.869227	0.434614	+	0.900617i	$0.356885\pi$
$234$	0.396913	0.0259470
$235$	−0.954909	−0.0622914
$236$	−2.52347	−0.164264
$237$	10.4780	0.680618
$238$	−11.6612	−0.755884
$239$	3.20086	0.207047	0.103523	−	0.994627i	$-0.466988\pi$
$239$	3.20086	0.207047	0.103523	+	0.994627i	$0.466988\pi$
$240$	−2.61017	−0.168486
$241$	−2.20392	−0.141967	−0.0709835	−	0.997477i	$-0.522614\pi$
$241$	−2.20392	−0.141967	−0.0709835	+	0.997477i	$0.522614\pi$
$242$	−0.0118263	−0.000760226 0
$243$	0.808674	0.0518764
$244$	−0.801735	−0.0513258
$245$	22.3174	1.42581
$246$	−9.05006	−0.577011
$247$	−2.80661	−0.178580
$248$	−2.43588	−0.154679
$249$	−9.70833	−0.615240
$250$	−11.5847	−0.732681
$251$	12.2366	0.772365	0.386183	−	0.922422i	$-0.373793\pi$
$251$	12.2366	0.772365	0.386183	+	0.922422i	$0.373793\pi$
$252$	0.365076	0.0229976
$253$	−18.5100	−1.16371
$254$	10.3012	0.646353
$255$	6.48931	0.406377
$256$	1.00000	0.0625000
$257$	17.7509	1.10727	0.553634	−	0.832760i	$-0.313241\pi$
$257$	17.7509	1.10727	0.553634	+	0.832760i	$0.313241\pi$
$258$	−9.93644	−0.618615
$259$	−32.3925	−2.01278
$260$	7.58702	0.470527
$261$	0.675274	0.0417984
$262$	−7.38261	−0.456099
$263$	6.95305	0.428744	0.214372	−	0.976752i	$-0.431230\pi$
$263$	6.95305	0.428744	0.214372	+	0.976752i	$0.431230\pi$
$264$	5.81548	0.357918
$265$	−4.34762	−0.267072
$266$	−2.58149	−0.158281
$267$	−2.61030	−0.159748
$268$	0.653229	0.0399023
$269$	−20.5502	−1.25296	−0.626482	−	0.779436i	$-0.715506\pi$
$269$	−20.5502	−1.25296	−0.626482	+	0.779436i	$0.715506\pi$
$270$	7.62735	0.464186
$271$	−13.0387	−0.792044	−0.396022	−	0.918241i	$-0.629610\pi$
$271$	−13.0387	−0.792044	−0.396022	+	0.918241i	$0.629610\pi$
$272$	−2.48617	−0.150746
$273$	−41.9624	−2.53968
$274$	7.86025	0.474855
$275$	9.23659	0.556987
$276$	−9.79639	−0.589674
$277$	21.1032	1.26797	0.633984	−	0.773346i	$-0.281418\pi$
$277$	21.1032	1.26797	0.633984	+	0.773346i	$0.281418\pi$
$278$	−13.1174	−0.786728
$279$	−0.189595	−0.0113508
$280$	6.97846	0.417043
$281$	−19.0497	−1.13641	−0.568205	−	0.822887i	$-0.692362\pi$
$281$	−19.0497	−1.13641	−0.568205	+	0.822887i	$0.692362\pi$
$282$	1.12600	0.0670523
$283$	22.7387	1.35167	0.675837	−	0.737052i	$-0.263783\pi$
$283$	22.7387	1.35167	0.675837	+	0.737052i	$0.263783\pi$
$284$	3.08721	0.183192
$285$	1.43657	0.0850949
$286$	−16.9039	−0.999550
$287$	24.1959	1.42824
$288$	0.0778341	0.00458642
$289$	−10.8190	−0.636411
$290$	12.9079	0.757979
$291$	7.22327	0.423436
$292$	1.58769	0.0929125
$293$	−4.26836	−0.249360	−0.124680	−	0.992197i	$-0.539790\pi$
$293$	−4.26836	−0.249360	−0.124680	+	0.992197i	$0.539790\pi$
$294$	−26.3160	−1.53478
$295$	−3.75443	−0.218591
$296$	−6.90608	−0.401408
$297$	−16.9938	−0.986080
$298$	−10.8553	−0.628828
$299$	28.4753	1.64677
$300$	4.88845	0.282235
$301$	26.5657	1.53122
$302$	−6.40294	−0.368448
$303$	11.9538	0.686729
$304$	−0.550373	−0.0315661
$305$	−1.19283	−0.0683010
$306$	−0.193509	−0.0110621
$307$	4.07602	0.232631	0.116315	−	0.993212i	$-0.462892\pi$
$307$	4.07602	0.232631	0.116315	+	0.993212i	$0.462892\pi$
$308$	−15.5481	−0.885933
$309$	−2.78015	−0.158157
$310$	−3.62412	−0.205836
$311$	29.9620	1.69899	0.849494	−	0.527598i	$-0.176907\pi$
$311$	29.9620	1.69899	0.849494	+	0.527598i	$0.176907\pi$
$312$	−8.94638	−0.506489
$313$	−29.9397	−1.69229	−0.846147	−	0.532949i	$-0.821084\pi$
$313$	−29.9397	−1.69229	−0.846147	+	0.532949i	$0.821084\pi$
$314$	17.1535	0.968026
$315$	0.543163	0.0306037
$316$	−5.97248	−0.335979
$317$	12.4009	0.696505	0.348252	−	0.937401i	$-0.386775\pi$
$317$	12.4009	0.696505	0.348252	+	0.937401i	$0.386775\pi$
$318$	5.12659	0.287485
$319$	−28.7589	−1.61019
$320$	1.48781	0.0831709
$321$	−30.0021	−1.67456
$322$	26.1913	1.45958
$323$	1.36832	0.0761353
$324$	−9.22744	−0.512636
$325$	−14.2093	−0.788191
$326$	1.31185	0.0726565
$327$	24.9180	1.37797
$328$	5.15857	0.284834
$329$	−3.01043	−0.165971
$330$	8.65230	0.476294
$331$	−22.0692	−1.21303	−0.606517	−	0.795071i	$-0.707434\pi$
$331$	−22.0692	−1.21303	−0.606517	+	0.795071i	$0.707434\pi$
$332$	5.53378	0.303706
$333$	−0.537529	−0.0294564
$334$	7.26484	0.397514
$335$	0.971877	0.0530993
$336$	−8.22879	−0.448917
$337$	−20.0825	−1.09396	−0.546981	−	0.837145i	$-0.684223\pi$
$337$	−20.0825	−1.09396	−0.546981	+	0.837145i	$0.684223\pi$
$338$	13.0046	0.707355
$339$	−18.7568	−1.01873
$340$	−3.69893	−0.200603
$341$	8.07457	0.437262
$342$	−0.0428378	−0.00231640
$343$	37.5245	2.02613
$344$	5.66380	0.305372
$345$	−14.5751	−0.784699
$346$	15.7088	0.844512
$347$	12.0905	0.649053	0.324527	−	0.945877i	$-0.394795\pi$
$347$	12.0905	0.649053	0.324527	+	0.945877i	$0.394795\pi$
$348$	−15.2206	−0.815911
$349$	−14.1327	−0.756504	−0.378252	−	0.925703i	$-0.623475\pi$
$349$	−14.1327	−0.756504	−0.378252	+	0.925703i	$0.623475\pi$
$350$	−13.0696	−0.698599
$351$	26.1428	1.39540
$352$	−3.31484	−0.176682
$353$	−18.7177	−0.996240	−0.498120	−	0.867108i	$-0.665976\pi$
$353$	−18.7177	−0.996240	−0.498120	+	0.867108i	$0.665976\pi$
$354$	4.42711	0.235298
$355$	4.59317	0.243780
$356$	1.48788	0.0788576
$357$	20.4581	1.08276
$358$	1.51350	0.0799912
$359$	5.17655	0.273208	0.136604	−	0.990626i	$-0.456381\pi$
$359$	5.17655	0.273208	0.136604	+	0.990626i	$0.456381\pi$
$360$	0.115802	0.00610331
$361$	−18.6971	−0.984057
$362$	−7.19721	−0.378277
$363$	0.0207479	0.00108898
$364$	23.9187	1.25368
$365$	2.36217	0.123642
$366$	1.40654	0.0735212
$367$	−12.3587	−0.645118	−0.322559	−	0.946549i	$-0.604543\pi$
$367$	−12.3587	−0.645118	−0.322559	+	0.946549i	$0.604543\pi$
$368$	5.58398	0.291085
$369$	0.401513	0.0209019
$370$	−10.2749	−0.534167
$371$	−13.7063	−0.711594
$372$	4.27346	0.221568
$373$	−12.8531	−0.665509	−0.332755	−	0.943013i	$-0.607978\pi$
$373$	−12.8531	−0.665509	−0.332755	+	0.943013i	$0.607978\pi$
$374$	8.24124	0.426145
$375$	20.3239	1.04952
$376$	−0.641823	−0.0330995
$377$	44.2420	2.27858
$378$	24.0459	1.23679
$379$	−13.0756	−0.671646	−0.335823	−	0.941925i	$-0.609014\pi$
$379$	−13.0756	−0.671646	−0.335823	+	0.941925i	$0.609014\pi$
$380$	−0.818848	−0.0420060
$381$	−18.0721	−0.925863
$382$	23.3413	1.19425
$383$	15.1733	0.775318	0.387659	−	0.921803i	$-0.373284\pi$
$383$	15.1733	0.775318	0.387659	+	0.921803i	$0.373284\pi$
$384$	−1.75438	−0.0895276
$385$	−23.1325	−1.17894
$386$	−9.38620	−0.477745
$387$	0.440837	0.0224090
$388$	−4.11729	−0.209024
$389$	5.75790	0.291937	0.145969	−	0.989289i	$-0.453370\pi$
$389$	5.75790	0.291937	0.145969	+	0.989289i	$0.453370\pi$
$390$	−13.3105	−0.674002
$391$	−13.8827	−0.702078
$392$	15.0002	0.757625
$393$	12.9519	0.653336
$394$	15.9001	0.801035
$395$	−8.88590	−0.447098
$396$	−0.258008	−0.0129654
$397$	−23.8242	−1.19570	−0.597850	−	0.801608i	$-0.703978\pi$
$397$	−23.8242	−1.19570	−0.597850	+	0.801608i	$0.703978\pi$
$398$	7.42897	0.372381
$399$	4.52891	0.226729
$400$	−2.78643	−0.139322
$401$	35.8663	1.79108	0.895539	−	0.444984i	$-0.146790\pi$
$401$	35.8663	1.79108	0.895539	+	0.444984i	$0.146790\pi$
$402$	−1.14601	−0.0571577
$403$	−12.4217	−0.618769
$404$	−6.81372	−0.338995
$405$	−13.7286	−0.682182
$406$	40.6933	2.01958
$407$	22.8926	1.13474
$408$	4.36167	0.215935
$409$	2.15567	0.106591	0.0532955	−	0.998579i	$-0.483027\pi$
$409$	2.15567	0.106591	0.0532955	+	0.998579i	$0.483027\pi$
$410$	7.67494	0.379038
$411$	−13.7898	−0.680202
$412$	1.58470	0.0780724
$413$	−11.8362	−0.582420
$414$	0.434624	0.0213606
$415$	8.23319	0.404151
$416$	5.09947	0.250022
$417$	23.0128	1.12694
$418$	1.82440	0.0892343
$419$	3.03056	0.148052	0.0740262	−	0.997256i	$-0.476415\pi$
$419$	3.03056	0.148052	0.0740262	+	0.997256i	$0.476415\pi$
$420$	−12.2428	−0.597390
$421$	−7.59709	−0.370259	−0.185130	−	0.982714i	$-0.559271\pi$
$421$	−7.59709	−0.370259	−0.185130	+	0.982714i	$0.559271\pi$
$422$	1.46730	0.0714272
$423$	−0.0499558	−0.00242893
$424$	−2.92217	−0.141913
$425$	6.92753	0.336035
$426$	−5.41613	−0.262412
$427$	−3.76049	−0.181983
$428$	17.1013	0.826623
$429$	29.6558	1.43180
$430$	8.42664	0.406369
$431$	−27.1060	−1.30565	−0.652826	−	0.757508i	$-0.726417\pi$
$431$	−27.1060	−1.30565	−0.652826	+	0.757508i	$0.726417\pi$
$432$	5.12658	0.246653
$433$	25.4182	1.22152	0.610760	−	0.791816i	$-0.290864\pi$
$433$	25.4182	1.22152	0.610760	+	0.791816i	$0.290864\pi$
$434$	−11.4254	−0.548435
$435$	−22.6453	−1.08576
$436$	−14.2033	−0.680217
$437$	−3.07327	−0.147014
$438$	−2.78540	−0.133092
$439$	32.8543	1.56805	0.784024	−	0.620730i	$-0.213164\pi$
$439$	32.8543	1.56805	0.784024	+	0.620730i	$0.213164\pi$
$440$	−4.93184	−0.235116
$441$	1.16753	0.0555966
$442$	−12.6781	−0.603036
$443$	10.1178	0.480710	0.240355	−	0.970685i	$-0.422736\pi$
$443$	10.1178	0.480710	0.240355	+	0.970685i	$0.422736\pi$
$444$	12.1159	0.574993
$445$	2.21368	0.104939
$446$	1.72542	0.0817009
$447$	19.0442	0.900760
$448$	4.69044	0.221602
$449$	−34.9607	−1.64990	−0.824949	−	0.565207i	$-0.808796\pi$
$449$	−34.9607	−1.64990	−0.824949	+	0.565207i	$0.808796\pi$
$450$	−0.216880	−0.0102238
$451$	−17.0998	−0.805199
$452$	10.6914	0.502882
$453$	11.2332	0.527780
$454$	−0.166423	−0.00781060
$455$	35.5864	1.66832
$456$	0.965561	0.0452166
$457$	33.0306	1.54511	0.772553	−	0.634950i	$-0.218979\pi$
$457$	33.0306	1.54511	0.772553	+	0.634950i	$0.218979\pi$
$458$	−2.31655	−0.108245
$459$	−12.7455	−0.594910
$460$	8.30787	0.387357
$461$	−13.6623	−0.636318	−0.318159	−	0.948037i	$-0.603065\pi$
$461$	−13.6623	−0.636318	−0.318159	+	0.948037i	$0.603065\pi$
$462$	27.2771	1.26905
$463$	39.9026	1.85443	0.927215	−	0.374529i	$-0.122196\pi$
$463$	39.9026	1.85443	0.927215	+	0.374529i	$0.122196\pi$
$464$	8.67580	0.402764
$465$	6.35807	0.294849
$466$	13.2682	0.614636
$467$	−41.8142	−1.93493	−0.967466	−	0.253001i	$-0.918582\pi$
$467$	−41.8142	−1.93493	−0.967466	+	0.253001i	$0.918582\pi$
$468$	0.396913	0.0183473
$469$	3.06393	0.141479
$470$	−0.954909	−0.0440467
$471$	−30.0936	−1.38664
$472$	−2.52347	−0.116152
$473$	−18.7746	−0.863257
$474$	10.4780	0.481270
$475$	1.53358	0.0703654
$476$	−11.6612	−0.534490
$477$	−0.227445	−0.0104140
$478$	3.20086	0.146404
$479$	−27.4951	−1.25628	−0.628141	−	0.778099i	$-0.716184\pi$
$479$	−27.4951	−1.25628	−0.628141	+	0.778099i	$0.716184\pi$
$480$	−2.61017	−0.119137
$481$	−35.2173	−1.60577
$482$	−2.20392	−0.100386
$483$	−45.9494	−2.09077
$484$	−0.0118263	−0.000537561 0
$485$	−6.12573	−0.278155
$486$	0.808674	0.0366822
$487$	−28.9377	−1.31129	−0.655647	−	0.755067i	$-0.727604\pi$
$487$	−28.9377	−1.31129	−0.655647	+	0.755067i	$0.727604\pi$
$488$	−0.801735	−0.0362928
$489$	−2.30147	−0.104076
$490$	22.3174	1.00820
$491$	−13.0478	−0.588841	−0.294421	−	0.955676i	$-0.595127\pi$
$491$	−13.0478	−0.588841	−0.294421	+	0.955676i	$0.595127\pi$
$492$	−9.05006	−0.408008
$493$	−21.5695	−0.971440
$494$	−2.80661	−0.126275
$495$	−0.383866	−0.0172535
$496$	−2.43588	−0.109374
$497$	14.4804	0.649534
$498$	−9.70833	−0.435041
$499$	−19.9713	−0.894036	−0.447018	−	0.894525i	$-0.647514\pi$
$499$	−19.9713	−0.894036	−0.447018	+	0.894525i	$0.647514\pi$
$500$	−11.5847	−0.518084
$501$	−12.7453	−0.569416
$502$	12.2366	0.546145
$503$	−15.8095	−0.704913	−0.352456	−	0.935828i	$-0.614653\pi$
$503$	−15.8095	−0.704913	−0.352456	+	0.935828i	$0.614653\pi$
$504$	0.365076	0.0162618
$505$	−10.1375	−0.451112
$506$	−18.5100	−0.822870
$507$	−22.8149	−1.01324
$508$	10.3012	0.457041
$509$	−8.47932	−0.375839	−0.187920	−	0.982184i	$-0.560174\pi$
$509$	−8.47932	−0.375839	−0.187920	+	0.982184i	$0.560174\pi$
$510$	6.48931	0.287352
$511$	7.44696	0.329434
$512$	1.00000	0.0441942
$513$	−2.82153	−0.124574
$514$	17.7509	0.782957
$515$	2.35772	0.103894
$516$	−9.93644	−0.437427
$517$	2.12754	0.0935692
$518$	−32.3925	−1.42325
$519$	−27.5592	−1.20971
$520$	7.58702	0.332713
$521$	−14.5254	−0.636370	−0.318185	−	0.948029i	$-0.603073\pi$
$521$	−14.5254	−0.636370	−0.318185	+	0.948029i	$0.603073\pi$
$522$	0.675274	0.0295559
$523$	−33.9869	−1.48614	−0.743072	−	0.669211i	$-0.766632\pi$
$523$	−33.9869	−1.48614	−0.743072	+	0.669211i	$0.766632\pi$
$524$	−7.38261	−0.322511
$525$	22.9290	1.00070
$526$	6.95305	0.303168
$527$	6.05601	0.263804
$528$	5.81548	0.253086
$529$	8.18079	0.355687
$530$	−4.34762	−0.188849
$531$	−0.196412	−0.00852355
$532$	−2.58149	−0.111922
$533$	26.3059	1.13944
$534$	−2.61030	−0.112959
$535$	25.4434	1.10002
$536$	0.653229	0.0282152
$537$	−2.65526	−0.114583
$538$	−20.5502	−0.885980
$539$	−49.7233	−2.14173
$540$	7.62735	0.328229
$541$	−13.8195	−0.594147	−0.297073	−	0.954855i	$-0.596011\pi$
$541$	−13.8195	−0.594147	−0.297073	+	0.954855i	$0.596011\pi$
$542$	−13.0387	−0.560059
$543$	12.6266	0.541859
$544$	−2.48617	−0.106593
$545$	−21.1318	−0.905188
$546$	−41.9624	−1.79583
$547$	−7.63482	−0.326441	−0.163221	−	0.986590i	$-0.552188\pi$
$547$	−7.63482	−0.326441	−0.163221	+	0.986590i	$0.552188\pi$
$548$	7.86025	0.335773
$549$	−0.0624023	−0.00266327
$550$	9.23659	0.393849
$551$	−4.77493	−0.203419
$552$	−9.79639	−0.416962
$553$	−28.0136	−1.19126
$554$	21.1032	0.896589
$555$	18.0261	0.765163
$556$	−13.1174	−0.556300
$557$	−21.2957	−0.902328	−0.451164	−	0.892441i	$-0.648991\pi$
$557$	−21.2957	−0.902328	−0.451164	+	0.892441i	$0.648991\pi$
$558$	−0.189595	−0.00802619
$559$	28.8824	1.22159
$560$	6.97846	0.294894
$561$	−14.4582	−0.610427
$562$	−19.0497	−0.803564
$563$	−17.1462	−0.722627	−0.361313	−	0.932444i	$-0.617672\pi$
$563$	−17.1462	−0.722627	−0.361313	+	0.932444i	$0.617672\pi$
$564$	1.12600	0.0474131
$565$	15.9067	0.669202
$566$	22.7387	0.955777
$567$	−43.2808	−1.81762
$568$	3.08721	0.129537
$569$	−28.6456	−1.20089	−0.600444	−	0.799667i	$-0.705009\pi$
$569$	−28.6456	−1.20089	−0.600444	+	0.799667i	$0.705009\pi$
$570$	1.43657	0.0601712
$571$	22.8346	0.955599	0.477799	−	0.878469i	$-0.341435\pi$
$571$	22.8346	0.955599	0.477799	+	0.878469i	$0.341435\pi$
$572$	−16.9039	−0.706788
$573$	−40.9495	−1.71069
$574$	24.1959	1.00992
$575$	−15.5594	−0.648871
$576$	0.0778341	0.00324309
$577$	7.85253	0.326905	0.163453	−	0.986551i	$-0.447737\pi$
$577$	7.85253	0.326905	0.163453	+	0.986551i	$0.447737\pi$
$578$	−10.8190	−0.450010
$579$	16.4669	0.684342
$580$	12.9079	0.535972
$581$	25.9558	1.07683
$582$	7.22327	0.299414
$583$	9.68653	0.401175
$584$	1.58769	0.0656991
$585$	0.590529	0.0244154
$586$	−4.26836	−0.176324
$587$	−4.45643	−0.183937	−0.0919683	−	0.995762i	$-0.529316\pi$
$587$	−4.45643	−0.183937	−0.0919683	+	0.995762i	$0.529316\pi$
$588$	−26.3160	−1.08525
$589$	1.34065	0.0552403
$590$	−3.75443	−0.154567
$591$	−27.8947	−1.14744
$592$	−6.90608	−0.283838
$593$	13.1282	0.539111	0.269555	−	0.962985i	$-0.413123\pi$
$593$	13.1282	0.539111	0.269555	+	0.962985i	$0.413123\pi$
$594$	−16.9938	−0.697264
$595$	−17.3496	−0.711265
$596$	−10.8553	−0.444649
$597$	−13.0332	−0.533414
$598$	28.4753	1.16444
$599$	39.7757	1.62519	0.812596	−	0.582828i	$-0.198054\pi$
$599$	39.7757	1.62519	0.812596	+	0.582828i	$0.198054\pi$
$600$	4.88845	0.199570
$601$	−16.3400	−0.666523	−0.333262	−	0.942834i	$-0.608149\pi$
$601$	−16.3400	−0.666523	−0.333262	+	0.942834i	$0.608149\pi$
$602$	26.5657	1.08274
$603$	0.0508435	0.00207051
$604$	−6.40294	−0.260532
$605$	−0.0175953	−0.000715351 0
$606$	11.9538	0.485591
$607$	8.49103	0.344640	0.172320	−	0.985041i	$-0.444874\pi$
$607$	8.49103	0.344640	0.172320	+	0.985041i	$0.444874\pi$
$608$	−0.550373	−0.0223206
$609$	−71.3914	−2.89292
$610$	−1.19283	−0.0482961
$611$	−3.27296	−0.132410
$612$	−0.193509	−0.00782212
$613$	−34.1862	−1.38077	−0.690384	−	0.723443i	$-0.742558\pi$
$613$	−34.1862	−1.38077	−0.690384	+	0.723443i	$0.742558\pi$
$614$	4.07602	0.164495
$615$	−13.4647	−0.542951
$616$	−15.5481	−0.626449
$617$	−39.7685	−1.60102	−0.800510	−	0.599319i	$-0.795438\pi$
$617$	−39.7685	−1.60102	−0.800510	+	0.599319i	$0.795438\pi$
$618$	−2.78015	−0.111834
$619$	15.7723	0.633943	0.316971	−	0.948435i	$-0.397334\pi$
$619$	15.7723	0.633943	0.316971	+	0.948435i	$0.397334\pi$
$620$	−3.62412	−0.145548
$621$	28.6267	1.14875
$622$	29.9620	1.20137
$623$	6.97882	0.279601
$624$	−8.94638	−0.358142
$625$	−3.30362	−0.132145
$626$	−29.9397	−1.19663
$627$	−3.20068	−0.127823
$628$	17.1535	0.684498
$629$	17.1697	0.684599
$630$	0.543163	0.0216401
$631$	−13.8712	−0.552203	−0.276101	−	0.961129i	$-0.589043\pi$
$631$	−13.8712	−0.552203	−0.276101	+	0.961129i	$0.589043\pi$
$632$	−5.97248	−0.237573
$633$	−2.57420	−0.102315
$634$	12.4009	0.492503
$635$	15.3262	0.608200
$636$	5.12659	0.203282
$637$	76.4930	3.03076
$638$	−28.7589	−1.13858
$639$	0.240291	0.00950575
$640$	1.48781	0.0588107
$641$	−36.7669	−1.45221	−0.726103	−	0.687586i	$-0.758670\pi$
$641$	−36.7669	−1.45221	−0.726103	+	0.687586i	$0.758670\pi$
$642$	−30.0021	−1.18409
$643$	35.3864	1.39550	0.697751	−	0.716340i	$-0.254184\pi$
$643$	35.3864	1.39550	0.697751	+	0.716340i	$0.254184\pi$
$644$	26.1913	1.03208
$645$	−14.7835	−0.582099
$646$	1.36832	0.0538358
$647$	9.49910	0.373448	0.186724	−	0.982412i	$-0.440213\pi$
$647$	9.49910	0.373448	0.186724	+	0.982412i	$0.440213\pi$
$648$	−9.22744	−0.362488
$649$	8.36489	0.328351
$650$	−14.2093	−0.557336
$651$	20.0444	0.785601
$652$	1.31185	0.0513759
$653$	−24.2120	−0.947491	−0.473745	−	0.880662i	$-0.657098\pi$
$653$	−24.2120	−0.947491	−0.473745	+	0.880662i	$0.657098\pi$
$654$	24.9180	0.974371
$655$	−10.9839	−0.429176
$656$	5.15857	0.201408
$657$	0.123576	0.00482118
$658$	−3.01043	−0.117359
$659$	−40.6746	−1.58446	−0.792229	−	0.610224i	$-0.791080\pi$
$659$	−40.6746	−1.58446	−0.792229	+	0.610224i	$0.791080\pi$
$660$	8.65230	0.336790
$661$	38.6378	1.50284	0.751418	−	0.659827i	$-0.229370\pi$
$661$	38.6378	1.50284	0.751418	+	0.659827i	$0.229370\pi$
$662$	−22.0692	−0.857744
$663$	22.2422	0.863815
$664$	5.53378	0.214752
$665$	−3.84076	−0.148938
$666$	−0.537529	−0.0208288
$667$	48.4455	1.87582
$668$	7.26484	0.281085
$669$	−3.02703	−0.117032
$670$	0.971877	0.0375469
$671$	2.65762	0.102596
$672$	−8.22879	−0.317432
$673$	−25.2116	−0.971834	−0.485917	−	0.874005i	$-0.661514\pi$
$673$	−25.2116	−0.971834	−0.485917	+	0.874005i	$0.661514\pi$
$674$	−20.0825	−0.773548
$675$	−14.2849	−0.549825
$676$	13.0046	0.500175
$677$	10.3089	0.396202	0.198101	−	0.980182i	$-0.436523\pi$
$677$	10.3089	0.396202	0.198101	+	0.980182i	$0.436523\pi$
$678$	−18.7568	−0.720349
$679$	−19.3119	−0.741122
$680$	−3.69893	−0.141848
$681$	0.291968	0.0111882
$682$	8.07457	0.309191
$683$	15.4442	0.590955	0.295477	−	0.955350i	$-0.404521\pi$
$683$	15.4442	0.590955	0.295477	+	0.955350i	$0.404521\pi$
$684$	−0.0428378	−0.00163795
$685$	11.6945	0.446825
$686$	37.5245	1.43269
$687$	4.06409	0.155055
$688$	5.66380	0.215930
$689$	−14.9015	−0.567702
$690$	−14.5751	−0.554866
$691$	−10.8127	−0.411334	−0.205667	−	0.978622i	$-0.565936\pi$
$691$	−10.8127	−0.411334	−0.205667	+	0.978622i	$0.565936\pi$
$692$	15.7088	0.597160
$693$	−1.21017	−0.0459705
$694$	12.0905	0.458950
$695$	−19.5161	−0.740288
$696$	−15.2206	−0.576936
$697$	−12.8250	−0.485783
$698$	−14.1327	−0.534929
$699$	−23.2774	−0.880431
$700$	−13.0696	−0.493984
$701$	−32.9947	−1.24619	−0.623096	−	0.782145i	$-0.714126\pi$
$701$	−32.9947	−1.24619	−0.623096	+	0.782145i	$0.714126\pi$
$702$	26.1428	0.986697
$703$	3.80092	0.143354
$704$	−3.31484	−0.124933
$705$	1.67527	0.0630943
$706$	−18.7177	−0.704448
$707$	−31.9593	−1.20195
$708$	4.42711	0.166381
$709$	−34.6321	−1.30063	−0.650317	−	0.759663i	$-0.725364\pi$
$709$	−34.6321	−1.30063	−0.650317	+	0.759663i	$0.725364\pi$
$710$	4.59317	0.172379
$711$	−0.464863	−0.0174337
$712$	1.48788	0.0557607
$713$	−13.6019	−0.509396
$714$	20.4581	0.765626
$715$	−25.1498	−0.940547
$716$	1.51350	0.0565623
$717$	−5.61552	−0.209715
$718$	5.17655	0.193187
$719$	−35.7297	−1.33249	−0.666246	−	0.745732i	$-0.732100\pi$
$719$	−35.7297	−1.33249	−0.666246	+	0.745732i	$0.732100\pi$
$720$	0.115802	0.00431569
$721$	7.43292	0.276817
$722$	−18.6971	−0.695834
$723$	3.86650	0.143797
$724$	−7.19721	−0.267482
$725$	−24.1745	−0.897820
$726$	0.0207479	0.000770025 0
$727$	−16.8194	−0.623799	−0.311899	−	0.950115i	$-0.600965\pi$
$727$	−16.8194	−0.623799	−0.311899	+	0.950115i	$0.600965\pi$
$728$	23.9187	0.886487
$729$	26.2636	0.972726
$730$	2.36217	0.0874280
$731$	−14.0811	−0.520810
$732$	1.40654	0.0519874
$733$	16.2678	0.600864	0.300432	−	0.953803i	$-0.402869\pi$
$733$	16.2678	0.600864	0.300432	+	0.953803i	$0.402869\pi$
$734$	−12.3587	−0.456167
$735$	−39.1531	−1.44418
$736$	5.58398	0.205828
$737$	−2.16535	−0.0797617
$738$	0.401513	0.0147799
$739$	24.2167	0.890827	0.445414	−	0.895325i	$-0.353057\pi$
$739$	24.2167	0.890827	0.445414	+	0.895325i	$0.353057\pi$
$740$	−10.2749	−0.377713
$741$	4.92385	0.180882
$742$	−13.7063	−0.503173
$743$	29.8705	1.09584	0.547921	−	0.836530i	$-0.315420\pi$
$743$	29.8705	1.09584	0.547921	+	0.836530i	$0.315420\pi$
$744$	4.27346	0.156672
$745$	−16.1505	−0.591709
$746$	−12.8531	−0.470586
$747$	0.430717	0.0157591
$748$	8.24124	0.301330
$749$	80.2126	2.93091
$750$	20.3239	0.742125
$751$	−10.3009	−0.375886	−0.187943	−	0.982180i	$-0.560182\pi$
$751$	−10.3009	−0.375886	−0.187943	+	0.982180i	$0.560182\pi$
$752$	−0.641823	−0.0234049
$753$	−21.4675	−0.782320
$754$	44.2420	1.61120
$755$	−9.52634	−0.346699
$756$	24.0459	0.874541
$757$	−42.1771	−1.53295	−0.766476	−	0.642273i	$-0.777991\pi$
$757$	−42.1771	−1.53295	−0.766476	+	0.642273i	$0.777991\pi$
$758$	−13.0756	−0.474926
$759$	32.4735	1.17871
$760$	−0.818848	−0.0297028
$761$	32.9081	1.19292	0.596459	−	0.802643i	$-0.296574\pi$
$761$	32.9081	1.19292	0.596459	+	0.802643i	$0.296574\pi$
$762$	−18.0721	−0.654684
$763$	−66.6199	−2.41180
$764$	23.3413	0.844460
$765$	−0.287903	−0.0104092
$766$	15.1733	0.548233
$767$	−12.8683	−0.464649
$768$	−1.75438	−0.0633056
$769$	9.23212	0.332919	0.166459	−	0.986048i	$-0.446767\pi$
$769$	9.23212	0.332919	0.166459	+	0.986048i	$0.446767\pi$
$770$	−23.1325	−0.833637
$771$	−31.1417	−1.12154
$772$	−9.38620	−0.337817
$773$	−39.7937	−1.43128	−0.715640	−	0.698469i	$-0.753865\pi$
$773$	−39.7937	−1.43128	−0.715640	+	0.698469i	$0.753865\pi$
$774$	0.440837	0.0158456
$775$	6.78743	0.243812
$776$	−4.11729	−0.147802
$777$	56.8287	2.03872
$778$	5.75790	0.206431
$779$	−2.83914	−0.101723
$780$	−13.3105	−0.476592
$781$	−10.2336	−0.366188
$782$	−13.8827	−0.496444
$783$	44.4772	1.58948
$784$	15.0002	0.535722
$785$	25.5210	0.910885
$786$	12.9519	0.461978
$787$	14.2752	0.508855	0.254428	−	0.967092i	$-0.418113\pi$
$787$	14.2752	0.508855	0.254428	+	0.967092i	$0.418113\pi$
$788$	15.9001	0.566417
$789$	−12.1983	−0.434270
$790$	−8.88590	−0.316146
$791$	50.1474	1.78304
$792$	−0.258008	−0.00916791
$793$	−4.08842	−0.145184
$794$	−23.8242	−0.845488
$795$	7.62736	0.270515
$796$	7.42897	0.263313
$797$	35.0727	1.24234	0.621169	−	0.783676i	$-0.286658\pi$
$797$	35.0727	1.24234	0.621169	+	0.783676i	$0.286658\pi$
$798$	4.52891	0.160322
$799$	1.59568	0.0564511
$800$	−2.78643	−0.0985153
$801$	0.115808	0.00409188
$802$	35.8663	1.26648
$803$	−5.26294	−0.185725
$804$	−1.14601	−0.0404166
$805$	38.9676	1.37343
$806$	−12.4217	−0.437536
$807$	36.0527	1.26911
$808$	−6.81372	−0.239706
$809$	44.8194	1.57577	0.787883	−	0.615825i	$-0.211177\pi$
$809$	44.8194	1.57577	0.787883	+	0.615825i	$0.211177\pi$
$810$	−13.7286	−0.482375
$811$	−10.4443	−0.366749	−0.183375	−	0.983043i	$-0.558702\pi$
$811$	−10.4443	−0.366749	−0.183375	+	0.983043i	$0.558702\pi$
$812$	40.6933	1.42806
$813$	22.8747	0.802252
$814$	22.8926	0.802384
$815$	1.95178	0.0683677
$816$	4.36167	0.152689
$817$	−3.11720	−0.109057
$818$	2.15567	0.0753712
$819$	1.86169	0.0650528
$820$	7.67494	0.268021
$821$	3.42832	0.119649	0.0598245	−	0.998209i	$-0.480946\pi$
$821$	3.42832	0.119649	0.0598245	+	0.998209i	$0.480946\pi$
$822$	−13.7898	−0.480975
$823$	−22.6130	−0.788240	−0.394120	−	0.919059i	$-0.628951\pi$
$823$	−22.6130	−0.788240	−0.394120	+	0.919059i	$0.628951\pi$
$824$	1.58470	0.0552055
$825$	−16.2044	−0.564166
$826$	−11.8362	−0.411833
$827$	−18.8389	−0.655094	−0.327547	−	0.944835i	$-0.606222\pi$
$827$	−18.8389	−0.655094	−0.327547	+	0.944835i	$0.606222\pi$
$828$	0.434624	0.0151042
$829$	−36.6425	−1.27265	−0.636323	−	0.771423i	$-0.719545\pi$
$829$	−36.6425	−1.27265	−0.636323	+	0.771423i	$0.719545\pi$
$830$	8.23319	0.285778
$831$	−37.0229	−1.28431
$832$	5.09947	0.176792
$833$	−37.2930	−1.29213
$834$	23.0128	0.796868
$835$	10.8087	0.374049
$836$	1.82440	0.0630982
$837$	−12.4877	−0.431640
$838$	3.03056	0.104689
$839$	14.3345	0.494883	0.247441	−	0.968903i	$-0.420410\pi$
$839$	14.3345	0.494883	0.247441	+	0.968903i	$0.420410\pi$
$840$	−12.2428	−0.422418
$841$	46.2696	1.59550
$842$	−7.59709	−0.261813
$843$	33.4204	1.15106
$844$	1.46730	0.0505067
$845$	19.3483	0.665600
$846$	−0.0499558	−0.00171751
$847$	−0.0554707	−0.00190600
$848$	−2.92217	−0.100348
$849$	−39.8922	−1.36910
$850$	6.92753	0.237612
$851$	−38.5634	−1.32194
$852$	−5.41613	−0.185554
$853$	−51.6825	−1.76958	−0.884788	−	0.465994i	$-0.845697\pi$
$853$	−51.6825	−1.76958	−0.884788	+	0.465994i	$0.845697\pi$
$854$	−3.76049	−0.128681
$855$	−0.0637344	−0.00217967
$856$	17.1013	0.584511
$857$	−15.8921	−0.542864	−0.271432	−	0.962458i	$-0.587497\pi$
$857$	−15.8921	−0.542864	−0.271432	+	0.962458i	$0.587497\pi$
$858$	29.6558	1.01243
$859$	−17.1535	−0.585270	−0.292635	−	0.956224i	$-0.594532\pi$
$859$	−17.1535	−0.585270	−0.292635	+	0.956224i	$0.594532\pi$
$860$	8.42664	0.287346
$861$	−42.4488	−1.44665
$862$	−27.1060	−0.923235
$863$	−13.9860	−0.476088	−0.238044	−	0.971254i	$-0.576506\pi$
$863$	−13.9860	−0.476088	−0.238044	+	0.971254i	$0.576506\pi$
$864$	5.12658	0.174410
$865$	23.3717	0.794661
$866$	25.4182	0.863745
$867$	18.9806	0.644614
$868$	−11.4254	−0.387802
$869$	19.7978	0.671596
$870$	−22.6453	−0.767748
$871$	3.33112	0.112871
$872$	−14.2033	−0.480986
$873$	−0.320466	−0.0108461
$874$	−3.07327	−0.103955
$875$	−54.3373	−1.83694
$876$	−2.78540	−0.0941101
$877$	−52.6990	−1.77952	−0.889759	−	0.456431i	$-0.849127\pi$
$877$	−52.6990	−1.77952	−0.889759	+	0.456431i	$0.849127\pi$
$878$	32.8543	1.10878
$879$	7.48831	0.252574
$880$	−4.93184	−0.166252
$881$	−54.5520	−1.83790	−0.918952	−	0.394368i	$-0.870963\pi$
$881$	−54.5520	−1.83790	−0.918952	+	0.394368i	$0.870963\pi$
$882$	1.16753	0.0393127
$883$	−21.2799	−0.716126	−0.358063	−	0.933697i	$-0.616563\pi$
$883$	−21.2799	−0.716126	−0.358063	+	0.933697i	$0.616563\pi$
$884$	−12.6781	−0.426411
$885$	6.58668	0.221409
$886$	10.1178	0.339913
$887$	38.3289	1.28696	0.643480	−	0.765463i	$-0.277490\pi$
$887$	38.3289	1.28696	0.643480	+	0.765463i	$0.277490\pi$
$888$	12.1159	0.406582
$889$	48.3170	1.62050
$890$	2.21368	0.0742027
$891$	30.5875	1.02472
$892$	1.72542	0.0577712
$893$	0.353242	0.0118208
$894$	19.0442	0.636933
$895$	2.25180	0.0752694
$896$	4.69044	0.156697
$897$	−49.9564	−1.66799
$898$	−34.9607	−1.16665
$899$	−21.1333	−0.704833
$900$	−0.216880	−0.00722932
$901$	7.26500	0.242032
$902$	−17.0998	−0.569362
$903$	−46.6062	−1.55096
$904$	10.6914	0.355591
$905$	−10.7080	−0.355947
$906$	11.2332	0.373197
$907$	−31.7621	−1.05464	−0.527321	−	0.849666i	$-0.676804\pi$
$907$	−31.7621	−1.05464	−0.527321	+	0.849666i	$0.676804\pi$
$908$	−0.166423	−0.00552293
$909$	−0.530340	−0.0175903
$910$	35.5864	1.17968
$911$	−25.8014	−0.854837	−0.427419	−	0.904054i	$-0.640577\pi$
$911$	−25.8014	−0.854837	−0.427419	+	0.904054i	$0.640577\pi$
$912$	0.965561	0.0319729
$913$	−18.3436	−0.607085
$914$	33.0306	1.09255
$915$	2.09266	0.0691813
$916$	−2.31655	−0.0765409
$917$	−34.6277	−1.14351
$918$	−12.7455	−0.420665
$919$	22.6020	0.745571	0.372786	−	0.927917i	$-0.378403\pi$
$919$	22.6020	0.745571	0.372786	+	0.927917i	$0.378403\pi$
$920$	8.30787	0.273902
$921$	−7.15087	−0.235629
$922$	−13.6623	−0.449945
$923$	15.7431	0.518192
$924$	27.2771	0.897352
$925$	19.2433	0.632717
$926$	39.9026	1.31128
$927$	0.123344	0.00405113
$928$	8.67580	0.284797
$929$	−16.6626	−0.546683	−0.273342	−	0.961917i	$-0.588129\pi$
$929$	−16.6626	−0.546683	−0.273342	+	0.961917i	$0.588129\pi$
$930$	6.35807	0.208489
$931$	−8.25571	−0.270570
$932$	13.2682	0.434614
$933$	−52.5646	−1.72089
$934$	−41.8142	−1.36820
$935$	12.2614	0.400990
$936$	0.396913	0.0129735
$937$	54.1660	1.76953	0.884763	−	0.466042i	$-0.154320\pi$
$937$	54.1660	1.76953	0.884763	+	0.466042i	$0.154320\pi$
$938$	3.06393	0.100041
$939$	52.5256	1.71411
$940$	−0.954909	−0.0311457
$941$	−32.8874	−1.07210	−0.536049	−	0.844187i	$-0.680084\pi$
$941$	−32.8874	−1.07210	−0.536049	+	0.844187i	$0.680084\pi$
$942$	−30.0936	−0.980504
$943$	28.8053	0.938030
$944$	−2.52347	−0.0821319
$945$	35.7756	1.16378
$946$	−18.7746	−0.610415
$947$	46.6433	1.51571	0.757853	−	0.652426i	$-0.226249\pi$
$947$	46.6433	1.51571	0.757853	+	0.652426i	$0.226249\pi$
$948$	10.4780	0.340309
$949$	8.09637	0.262819
$950$	1.53358	0.0497558
$951$	−21.7559	−0.705482
$952$	−11.6612	−0.377942
$953$	−10.7210	−0.347289	−0.173644	−	0.984808i	$-0.555554\pi$
$953$	−10.7210	−0.347289	−0.173644	+	0.984808i	$0.555554\pi$
$954$	−0.227445	−0.00736379
$955$	34.7274	1.12375
$956$	3.20086	0.103523
$957$	50.4539	1.63094
$958$	−27.4951	−0.888326
$959$	36.8680	1.19053
$960$	−2.61017	−0.0842429
$961$	−25.0665	−0.808596
$962$	−35.2173	−1.13545
$963$	1.33107	0.0428930
$964$	−2.20392	−0.0709835
$965$	−13.9648	−0.449544
$966$	−45.9494	−1.47840
$967$	−14.7963	−0.475816	−0.237908	−	0.971288i	$-0.576462\pi$
$967$	−14.7963	−0.475816	−0.237908	+	0.971288i	$0.576462\pi$
$968$	−0.0118263	−0.000380113 0
$969$	−2.40054	−0.0771166
$970$	−6.12573	−0.196685
$971$	−10.2552	−0.329106	−0.164553	−	0.986368i	$-0.552618\pi$
$971$	−10.2552	−0.329106	−0.164553	+	0.986368i	$0.552618\pi$
$972$	0.808674	0.0259382
$973$	−61.5262	−1.97244
$974$	−28.9377	−0.927225
$975$	24.9285	0.798351
$976$	−0.801735	−0.0256629
$977$	4.27364	0.136726	0.0683630	−	0.997661i	$-0.478222\pi$
$977$	4.27364	0.136726	0.0683630	+	0.997661i	$0.478222\pi$
$978$	−2.30147	−0.0735930
$979$	−4.93209	−0.157630
$980$	22.3174	0.712903
$981$	−1.10551	−0.0352961
$982$	−13.0478	−0.416374
$983$	51.5089	1.64288	0.821440	−	0.570295i	$-0.193171\pi$
$983$	51.5089	1.64288	0.821440	+	0.570295i	$0.193171\pi$
$984$	−9.05006	−0.288505
$985$	23.6563	0.753751
$986$	−21.5695	−0.686912
$987$	5.28143	0.168110
$988$	−2.80661	−0.0892901
$989$	31.6265	1.00567
$990$	−0.383866	−0.0122000
$991$	24.2345	0.769836	0.384918	−	0.922951i	$-0.374230\pi$
$991$	24.2345	0.769836	0.384918	+	0.922951i	$0.374230\pi$
$992$	−2.43588	−0.0773394
$993$	38.7177	1.22867
$994$	14.4804	0.459290
$995$	11.0529	0.350399
$996$	−9.70833	−0.307620
$997$	36.4742	1.15515	0.577574	−	0.816338i	$-0.303999\pi$
$997$	36.4742	1.15515	0.577574	+	0.816338i	$0.303999\pi$
$998$	−19.9713	−0.632179
$999$	−35.4046	−1.12015

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4006.2.a.i.1.9	✓	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4006.2.a.i.1.9	✓	46	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:	\( N \)	\(=\)	\( 4006 = 2 \cdot 2003 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4006.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.75438 q^{3} +1.00000 q^{4} +1.48781 q^{5} -1.75438 q^{6} +4.69044 q^{7} +1.00000 q^{8} +0.0778341 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.75438 q^{3} +1.00000 q^{4} +1.48781 q^{5} -1.75438 q^{6} +4.69044 q^{7} +1.00000 q^{8} +0.0778341 q^{9} +1.48781 q^{10} -3.31484 q^{11} -1.75438 q^{12} +5.09947 q^{13} +4.69044 q^{14} -2.61017 q^{15} +1.00000 q^{16} -2.48617 q^{17} +0.0778341 q^{18} -0.550373 q^{19} +1.48781 q^{20} -8.22879 q^{21} -3.31484 q^{22} +5.58398 q^{23} -1.75438 q^{24} -2.78643 q^{25} +5.09947 q^{26} +5.12658 q^{27} +4.69044 q^{28} +8.67580 q^{29} -2.61017 q^{30} -2.43588 q^{31} +1.00000 q^{32} +5.81548 q^{33} -2.48617 q^{34} +6.97846 q^{35} +0.0778341 q^{36} -6.90608 q^{37} -0.550373 q^{38} -8.94638 q^{39} +1.48781 q^{40} +5.15857 q^{41} -8.22879 q^{42} +5.66380 q^{43} -3.31484 q^{44} +0.115802 q^{45} +5.58398 q^{46} -0.641823 q^{47} -1.75438 q^{48} +15.0002 q^{49} -2.78643 q^{50} +4.36167 q^{51} +5.09947 q^{52} -2.92217 q^{53} +5.12658 q^{54} -4.93184 q^{55} +4.69044 q^{56} +0.965561 q^{57} +8.67580 q^{58} -2.52347 q^{59} -2.61017 q^{60} -0.801735 q^{61} -2.43588 q^{62} +0.365076 q^{63} +1.00000 q^{64} +7.58702 q^{65} +5.81548 q^{66} +0.653229 q^{67} -2.48617 q^{68} -9.79639 q^{69} +6.97846 q^{70} +3.08721 q^{71} +0.0778341 q^{72} +1.58769 q^{73} -6.90608 q^{74} +4.88845 q^{75} -0.550373 q^{76} -15.5481 q^{77} -8.94638 q^{78} -5.97248 q^{79} +1.48781 q^{80} -9.22744 q^{81} +5.15857 q^{82} +5.53378 q^{83} -8.22879 q^{84} -3.69893 q^{85} +5.66380 q^{86} -15.2206 q^{87} -3.31484 q^{88} +1.48788 q^{89} +0.115802 q^{90} +23.9187 q^{91} +5.58398 q^{92} +4.27346 q^{93} -0.641823 q^{94} -0.818848 q^{95} -1.75438 q^{96} -4.11729 q^{97} +15.0002 q^{98} -0.258008 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q + 46 q^{2} + 21 q^{3} + 46 q^{4} + 23 q^{5} + 21 q^{6} + 26 q^{7} + 46 q^{8} + 59 q^{9}+O(q^{10}) \) 46 * q + 46 * q^2 + 21 * q^3 + 46 * q^4 + 23 * q^5 + 21 * q^6 + 26 * q^7 + 46 * q^8 + 59 * q^9	\( 46 q + 46 q^{2} + 21 q^{3} + 46 q^{4} + 23 q^{5} + 21 q^{6} + 26 q^{7} + 46 q^{8} + 59 q^{9} + 23 q^{10} + 39 q^{11} + 21 q^{12} + 8 q^{13} + 26 q^{14} + 14 q^{15} + 46 q^{16} + 36 q^{17} + 59 q^{18} + 37 q^{19} + 23 q^{20} + 20 q^{21} + 39 q^{22} + 38 q^{23} + 21 q^{24} + 57 q^{25} + 8 q^{26} + 63 q^{27} + 26 q^{28} + 23 q^{29} + 14 q^{30} + 44 q^{31} + 46 q^{32} + 25 q^{33} + 36 q^{34} + 26 q^{35} + 59 q^{36} + 9 q^{37} + 37 q^{38} - 2 q^{39} + 23 q^{40} + 50 q^{41} + 20 q^{42} + 46 q^{43} + 39 q^{44} + 30 q^{45} + 38 q^{46} + 57 q^{47} + 21 q^{48} + 62 q^{49} + 57 q^{50} + 5 q^{51} + 8 q^{52} + 21 q^{53} + 63 q^{54} + 40 q^{55} + 26 q^{56} + 3 q^{57} + 23 q^{58} + 68 q^{59} + 14 q^{60} - q^{61} + 44 q^{62} + 40 q^{63} + 46 q^{64} + 18 q^{65} + 25 q^{66} + 42 q^{67} + 36 q^{68} - 7 q^{69} + 26 q^{70} + 67 q^{71} + 59 q^{72} + 48 q^{73} + 9 q^{74} + 71 q^{75} + 37 q^{76} - 5 q^{77} - 2 q^{78} + 40 q^{79} + 23 q^{80} + 82 q^{81} + 50 q^{82} + 48 q^{83} + 20 q^{84} - 68 q^{85} + 46 q^{86} + 18 q^{87} + 39 q^{88} + 90 q^{89} + 30 q^{90} + 9 q^{91} + 38 q^{92} - 42 q^{93} + 57 q^{94} + 6 q^{95} + 21 q^{96} + 46 q^{97} + 62 q^{98} + 61 q^{99}+O(q^{100}) \) 46 * q + 46 * q^2 + 21 * q^3 + 46 * q^4 + 23 * q^5 + 21 * q^6 + 26 * q^7 + 46 * q^8 + 59 * q^9 + 23 * q^10 + 39 * q^11 + 21 * q^12 + 8 * q^13 + 26 * q^14 + 14 * q^15 + 46 * q^16 + 36 * q^17 + 59 * q^18 + 37 * q^19 + 23 * q^20 + 20 * q^21 + 39 * q^22 + 38 * q^23 + 21 * q^24 + 57 * q^25 + 8 * q^26 + 63 * q^27 + 26 * q^28 + 23 * q^29 + 14 * q^30 + 44 * q^31 + 46 * q^32 + 25 * q^33 + 36 * q^34 + 26 * q^35 + 59 * q^36 + 9 * q^37 + 37 * q^38 - 2 * q^39 + 23 * q^40 + 50 * q^41 + 20 * q^42 + 46 * q^43 + 39 * q^44 + 30 * q^45 + 38 * q^46 + 57 * q^47 + 21 * q^48 + 62 * q^49 + 57 * q^50 + 5 * q^51 + 8 * q^52 + 21 * q^53 + 63 * q^54 + 40 * q^55 + 26 * q^56 + 3 * q^57 + 23 * q^58 + 68 * q^59 + 14 * q^60 - q^61 + 44 * q^62 + 40 * q^63 + 46 * q^64 + 18 * q^65 + 25 * q^66 + 42 * q^67 + 36 * q^68 - 7 * q^69 + 26 * q^70 + 67 * q^71 + 59 * q^72 + 48 * q^73 + 9 * q^74 + 71 * q^75 + 37 * q^76 - 5 * q^77 - 2 * q^78 + 40 * q^79 + 23 * q^80 + 82 * q^81 + 50 * q^82 + 48 * q^83 + 20 * q^84 - 68 * q^85 + 46 * q^86 + 18 * q^87 + 39 * q^88 + 90 * q^89 + 30 * q^90 + 9 * q^91 + 38 * q^92 - 42 * q^93 + 57 * q^94 + 6 * q^95 + 21 * q^96 + 46 * q^97 + 62 * q^98 + 61 * q^99

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