LMFDB - Embedded newform 6009.2.a.c.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6009,2,Mod(1,6009)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6009, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6009.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6009 = 3 \cdot 2003 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6009.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:	$47.9821065746$
Analytic rank:	$0$
Dimension:	$92$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	6009.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.28351 q^{2} +1.00000 q^{3} +3.21443 q^{4} -3.38813 q^{5} -2.28351 q^{6} +0.924728 q^{7} -2.77317 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.28351 q^{2} +1.00000 q^{3} +3.21443 q^{4} -3.38813 q^{5} -2.28351 q^{6} +0.924728 q^{7} -2.77317 q^{8} +1.00000 q^{9} +7.73684 q^{10} +2.68431 q^{11} +3.21443 q^{12} -6.70664 q^{13} -2.11163 q^{14} -3.38813 q^{15} -0.0962944 q^{16} -0.0164547 q^{17} -2.28351 q^{18} -7.70218 q^{19} -10.8909 q^{20} +0.924728 q^{21} -6.12966 q^{22} -3.57269 q^{23} -2.77317 q^{24} +6.47943 q^{25} +15.3147 q^{26} +1.00000 q^{27} +2.97248 q^{28} +5.27171 q^{29} +7.73684 q^{30} -4.70136 q^{31} +5.76623 q^{32} +2.68431 q^{33} +0.0375744 q^{34} -3.13310 q^{35} +3.21443 q^{36} -7.62011 q^{37} +17.5880 q^{38} -6.70664 q^{39} +9.39586 q^{40} -9.02806 q^{41} -2.11163 q^{42} +2.75505 q^{43} +8.62854 q^{44} -3.38813 q^{45} +8.15829 q^{46} -7.79701 q^{47} -0.0962944 q^{48} -6.14488 q^{49} -14.7959 q^{50} -0.0164547 q^{51} -21.5580 q^{52} +3.53242 q^{53} -2.28351 q^{54} -9.09480 q^{55} -2.56443 q^{56} -7.70218 q^{57} -12.0380 q^{58} +12.9231 q^{59} -10.8909 q^{60} +11.1506 q^{61} +10.7356 q^{62} +0.924728 q^{63} -12.9747 q^{64} +22.7230 q^{65} -6.12966 q^{66} -2.86034 q^{67} -0.0528924 q^{68} -3.57269 q^{69} +7.15447 q^{70} +2.73213 q^{71} -2.77317 q^{72} -8.30961 q^{73} +17.4006 q^{74} +6.47943 q^{75} -24.7581 q^{76} +2.48226 q^{77} +15.3147 q^{78} +12.7025 q^{79} +0.326258 q^{80} +1.00000 q^{81} +20.6157 q^{82} -5.36077 q^{83} +2.97248 q^{84} +0.0557506 q^{85} -6.29120 q^{86} +5.27171 q^{87} -7.44406 q^{88} -7.31698 q^{89} +7.73684 q^{90} -6.20182 q^{91} -11.4842 q^{92} -4.70136 q^{93} +17.8046 q^{94} +26.0960 q^{95} +5.76623 q^{96} +1.91774 q^{97} +14.0319 q^{98} +2.68431 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 92 q + 17 q^{2} + 92 q^{3} + 107 q^{4} + 34 q^{5} + 17 q^{6} + 22 q^{7} + 51 q^{8} + 92 q^{9}+O(q^{10}) $ 92 * q + 17 * q^2 + 92 * q^3 + 107 * q^4 + 34 * q^5 + 17 * q^6 + 22 * q^7 + 51 * q^8 + 92 * q^9	\( 92 q + 17 q^{2} + 92 q^{3} + 107 q^{4} + 34 q^{5} + 17 q^{6} + 22 q^{7} + 51 q^{8} + 92 q^{9} + 13 q^{10} + 40 q^{11} + 107 q^{12} + 6 q^{13} + 37 q^{14} + 34 q^{15} + 133 q^{16} + 77 q^{17} + 17 q^{18} + 34 q^{19} + 55 q^{20} + 22 q^{21} + 8 q^{22} + 83 q^{23} + 51 q^{24} + 110 q^{25} + 22 q^{26} + 92 q^{27} + 32 q^{28} + 97 q^{29} + 13 q^{30} + 44 q^{31} + 104 q^{32} + 40 q^{33} + 20 q^{34} + 80 q^{35} + 107 q^{36} + 12 q^{37} + 54 q^{38} + 6 q^{39} + 23 q^{40} + 67 q^{41} + 37 q^{42} + 30 q^{43} + 87 q^{44} + 34 q^{45} + 33 q^{46} + 69 q^{47} + 133 q^{48} + 112 q^{49} + 58 q^{50} + 77 q^{51} - 3 q^{52} + 113 q^{53} + 17 q^{54} + 42 q^{55} + 92 q^{56} + 34 q^{57} - 30 q^{58} + 72 q^{59} + 55 q^{60} + 19 q^{61} + 60 q^{62} + 22 q^{63} + 147 q^{64} + 74 q^{65} + 8 q^{66} + 26 q^{67} + 171 q^{68} + 83 q^{69} - 35 q^{70} + 134 q^{71} + 51 q^{72} - 17 q^{73} + 95 q^{74} + 110 q^{75} + 27 q^{76} + 108 q^{77} + 22 q^{78} + 159 q^{79} + 79 q^{80} + 92 q^{81} - 64 q^{82} + 73 q^{83} + 32 q^{84} - 4 q^{85} + 22 q^{86} + 97 q^{87} - 16 q^{88} + 50 q^{89} + 13 q^{90} + 17 q^{91} + 154 q^{92} + 44 q^{93} + 8 q^{94} + 155 q^{95} + 104 q^{96} - 20 q^{97} + 63 q^{98} + 40 q^{99}+O(q^{100}) \) 92 * q + 17 * q^2 + 92 * q^3 + 107 * q^4 + 34 * q^5 + 17 * q^6 + 22 * q^7 + 51 * q^8 + 92 * q^9 + 13 * q^10 + 40 * q^11 + 107 * q^12 + 6 * q^13 + 37 * q^14 + 34 * q^15 + 133 * q^16 + 77 * q^17 + 17 * q^18 + 34 * q^19 + 55 * q^20 + 22 * q^21 + 8 * q^22 + 83 * q^23 + 51 * q^24 + 110 * q^25 + 22 * q^26 + 92 * q^27 + 32 * q^28 + 97 * q^29 + 13 * q^30 + 44 * q^31 + 104 * q^32 + 40 * q^33 + 20 * q^34 + 80 * q^35 + 107 * q^36 + 12 * q^37 + 54 * q^38 + 6 * q^39 + 23 * q^40 + 67 * q^41 + 37 * q^42 + 30 * q^43 + 87 * q^44 + 34 * q^45 + 33 * q^46 + 69 * q^47 + 133 * q^48 + 112 * q^49 + 58 * q^50 + 77 * q^51 - 3 * q^52 + 113 * q^53 + 17 * q^54 + 42 * q^55 + 92 * q^56 + 34 * q^57 - 30 * q^58 + 72 * q^59 + 55 * q^60 + 19 * q^61 + 60 * q^62 + 22 * q^63 + 147 * q^64 + 74 * q^65 + 8 * q^66 + 26 * q^67 + 171 * q^68 + 83 * q^69 - 35 * q^70 + 134 * q^71 + 51 * q^72 - 17 * q^73 + 95 * q^74 + 110 * q^75 + 27 * q^76 + 108 * q^77 + 22 * q^78 + 159 * q^79 + 79 * q^80 + 92 * q^81 - 64 * q^82 + 73 * q^83 + 32 * q^84 - 4 * q^85 + 22 * q^86 + 97 * q^87 - 16 * q^88 + 50 * q^89 + 13 * q^90 + 17 * q^91 + 154 * q^92 + 44 * q^93 + 8 * q^94 + 155 * q^95 + 104 * q^96 - 20 * q^97 + 63 * q^98 + 40 * 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 $

$2$	−2.28351	−1.61469	−0.807344	−	0.590081i	$-0.799096\pi$
$2$	−2.28351	−1.61469	−0.807344	+	0.590081i	$0.799096\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.21443	1.60722
$5$	−3.38813	−1.51522	−0.757609	−	0.652709i	$-0.773633\pi$
$5$	−3.38813	−1.51522	−0.757609	+	0.652709i	$0.773633\pi$
$6$	−2.28351	−0.932240
$7$	0.924728	0.349514	0.174757	−	0.984612i	$-0.444086\pi$
$7$	0.924728	0.349514	0.174757	+	0.984612i	$0.444086\pi$
$8$	−2.77317	−0.980463
$9$	1.00000	0.333333
$10$	7.73684	2.44660
$11$	2.68431	0.809351	0.404675	−	0.914460i	$-0.367384\pi$
$11$	2.68431	0.809351	0.404675	+	0.914460i	$0.367384\pi$
$12$	3.21443	0.927926
$13$	−6.70664	−1.86009	−0.930043	−	0.367450i	$-0.880231\pi$
$13$	−6.70664	−1.86009	−0.930043	+	0.367450i	$0.880231\pi$
$14$	−2.11163	−0.564357
$15$	−3.38813	−0.874811
$16$	−0.0962944	−0.0240736
$17$	−0.0164547	−0.00399084	−0.00199542	−	0.999998i	$-0.500635\pi$
$17$	−0.0164547	−0.00399084	−0.00199542	+	0.999998i	$0.500635\pi$
$18$	−2.28351	−0.538229
$19$	−7.70218	−1.76700	−0.883501	−	0.468429i	$-0.844820\pi$
$19$	−7.70218	−1.76700	−0.883501	+	0.468429i	$0.844820\pi$
$20$	−10.8909	−2.43528
$21$	0.924728	0.201792
$22$	−6.12966	−1.30685
$23$	−3.57269	−0.744958	−0.372479	−	0.928041i	$-0.621492\pi$
$23$	−3.57269	−0.744958	−0.372479	+	0.928041i	$0.621492\pi$
$24$	−2.77317	−0.566071
$25$	6.47943	1.29589
$26$	15.3147	3.00346
$27$	1.00000	0.192450
$28$	2.97248	0.561745
$29$	5.27171	0.978932	0.489466	−	0.872022i	$-0.337192\pi$
$29$	5.27171	0.978932	0.489466	+	0.872022i	$0.337192\pi$
$30$	7.73684	1.41255
$31$	−4.70136	−0.844389	−0.422195	−	0.906505i	$-0.638740\pi$
$31$	−4.70136	−0.844389	−0.422195	+	0.906505i	$0.638740\pi$
$32$	5.76623	1.01933
$33$	2.68431	0.467279
$34$	0.0375744	0.00644396
$35$	−3.13310	−0.529590
$36$	3.21443	0.535739
$37$	−7.62011	−1.25274	−0.626369	−	0.779527i	$-0.715460\pi$
$37$	−7.62011	−1.25274	−0.626369	+	0.779527i	$0.715460\pi$
$38$	17.5880	2.85316
$39$	−6.70664	−1.07392
$40$	9.39586	1.48562
$41$	−9.02806	−1.40995	−0.704973	−	0.709234i	$-0.749041\pi$
$41$	−9.02806	−1.40995	−0.704973	+	0.709234i	$0.749041\pi$
$42$	−2.11163	−0.325831
$43$	2.75505	0.420142	0.210071	−	0.977686i	$-0.432631\pi$
$43$	2.75505	0.420142	0.210071	+	0.977686i	$0.432631\pi$
$44$	8.62854	1.30080
$45$	−3.38813	−0.505073
$46$	8.15829	1.20287
$47$	−7.79701	−1.13731	−0.568656	−	0.822576i	$-0.692536\pi$
$47$	−7.79701	−1.13731	−0.568656	+	0.822576i	$0.692536\pi$
$48$	−0.0962944	−0.0138989
$49$	−6.14488	−0.877840
$50$	−14.7959	−2.09245
$51$	−0.0164547	−0.00230411
$52$	−21.5580	−2.98956
$53$	3.53242	0.485215	0.242607	−	0.970125i	$-0.421997\pi$
$53$	3.53242	0.485215	0.242607	+	0.970125i	$0.421997\pi$
$54$	−2.28351	−0.310747
$55$	−9.09480	−1.22634
$56$	−2.56443	−0.342686
$57$	−7.70218	−1.02018
$58$	−12.0380	−1.58067
$59$	12.9231	1.68245	0.841223	−	0.540689i	$-0.181836\pi$
$59$	12.9231	1.68245	0.841223	+	0.540689i	$0.181836\pi$
$60$	−10.8909	−1.40601
$61$	11.1506	1.42769	0.713844	−	0.700305i	$-0.246953\pi$
$61$	11.1506	1.42769	0.713844	+	0.700305i	$0.246953\pi$
$62$	10.7356	1.36342
$63$	0.924728	0.116505
$64$	−12.9747	−1.62183
$65$	22.7230	2.81844
$66$	−6.12966	−0.754510
$67$	−2.86034	−0.349446	−0.174723	−	0.984618i	$-0.555903\pi$
$67$	−2.86034	−0.349446	−0.174723	+	0.984618i	$0.555903\pi$
$68$	−0.0528924	−0.00641414
$69$	−3.57269	−0.430102
$70$	7.15447	0.855123
$71$	2.73213	0.324244	0.162122	−	0.986771i	$-0.448166\pi$
$71$	2.73213	0.324244	0.162122	+	0.986771i	$0.448166\pi$
$72$	−2.77317	−0.326821
$73$	−8.30961	−0.972567	−0.486283	−	0.873801i	$-0.661648\pi$
$73$	−8.30961	−0.972567	−0.486283	+	0.873801i	$0.661648\pi$
$74$	17.4006	2.02278
$75$	6.47943	0.748180
$76$	−24.7581	−2.83995
$77$	2.48226	0.282880
$78$	15.3147	1.73405
$79$	12.7025	1.42914	0.714570	−	0.699564i	$-0.246622\pi$
$79$	12.7025	1.42914	0.714570	+	0.699564i	$0.246622\pi$
$80$	0.326258	0.0364767
$81$	1.00000	0.111111
$82$	20.6157	2.27662
$83$	−5.36077	−0.588421	−0.294210	−	0.955741i	$-0.595057\pi$
$83$	−5.36077	−0.588421	−0.294210	+	0.955741i	$0.595057\pi$
$84$	2.97248	0.324324
$85$	0.0557506	0.00604700
$86$	−6.29120	−0.678398
$87$	5.27171	0.565186
$88$	−7.44406	−0.793539
$89$	−7.31698	−0.775598	−0.387799	−	0.921744i	$-0.626765\pi$
$89$	−7.31698	−0.775598	−0.387799	+	0.921744i	$0.626765\pi$
$90$	7.73684	0.815534
$91$	−6.20182	−0.650127
$92$	−11.4842	−1.19731
$93$	−4.70136	−0.487508
$94$	17.8046	1.83640
$95$	26.0960	2.67739
$96$	5.76623	0.588513
$97$	1.91774	0.194717	0.0973583	−	0.995249i	$-0.468961\pi$
$97$	1.91774	0.194717	0.0973583	+	0.995249i	$0.468961\pi$
$98$	14.0319	1.41744
$99$	2.68431	0.269784
$100$	20.8277	2.08277
$101$	7.28177	0.724563	0.362282	−	0.932069i	$-0.381998\pi$
$101$	7.28177	0.724563	0.362282	+	0.932069i	$0.381998\pi$
$102$	0.0375744	0.00372042
$103$	11.9968	1.18208	0.591041	−	0.806642i	$-0.298717\pi$
$103$	11.9968	1.18208	0.591041	+	0.806642i	$0.298717\pi$
$104$	18.5986	1.82375
$105$	−3.13310	−0.305759
$106$	−8.06632	−0.783470
$107$	8.05728	0.778927	0.389463	−	0.921042i	$-0.372660\pi$
$107$	8.05728	0.778927	0.389463	+	0.921042i	$0.372660\pi$
$108$	3.21443	0.309309
$109$	−6.30838	−0.604233	−0.302117	−	0.953271i	$-0.597693\pi$
$109$	−6.30838	−0.604233	−0.302117	+	0.953271i	$0.597693\pi$
$110$	20.7681	1.98016
$111$	−7.62011	−0.723269
$112$	−0.0890461	−0.00841407
$113$	2.26207	0.212798	0.106399	−	0.994324i	$-0.466068\pi$
$113$	2.26207	0.212798	0.106399	+	0.994324i	$0.466068\pi$
$114$	17.5880	1.64727
$115$	12.1048	1.12877
$116$	16.9455	1.57335
$117$	−6.70664	−0.620029
$118$	−29.5101	−2.71662
$119$	−0.0152161	−0.00139486
$120$	9.39586	0.857721
$121$	−3.79446	−0.344951
$122$	−25.4625	−2.30527
$123$	−9.02806	−0.814033
$124$	−15.1122	−1.35712
$125$	−5.01249	−0.448330
$126$	−2.11163	−0.188119
$127$	0.616641	0.0547180	0.0273590	−	0.999626i	$-0.491290\pi$
$127$	0.616641	0.0547180	0.0273590	+	0.999626i	$0.491290\pi$
$128$	18.0954	1.59942
$129$	2.75505	0.242569
$130$	−51.8882	−4.55089
$131$	−17.8824	−1.56239	−0.781194	−	0.624288i	$-0.785389\pi$
$131$	−17.8824	−1.56239	−0.781194	+	0.624288i	$0.785389\pi$
$132$	8.62854	0.751018
$133$	−7.12243	−0.617593
$134$	6.53162	0.564246
$135$	−3.38813	−0.291604
$136$	0.0456316	0.00391288
$137$	−10.1048	−0.863309	−0.431654	−	0.902039i	$-0.642070\pi$
$137$	−10.1048	−0.863309	−0.431654	+	0.902039i	$0.642070\pi$
$138$	8.15829	0.694480
$139$	−18.9205	−1.60481	−0.802406	−	0.596779i	$-0.796447\pi$
$139$	−18.9205	−1.60481	−0.802406	+	0.596779i	$0.796447\pi$
$140$	−10.0711	−0.851166
$141$	−7.79701	−0.656627
$142$	−6.23885	−0.523553
$143$	−18.0027	−1.50546
$144$	−0.0962944	−0.00802453
$145$	−17.8612	−1.48329
$146$	18.9751	1.57039
$147$	−6.14488	−0.506821
$148$	−24.4943	−2.01342
$149$	19.9941	1.63798	0.818989	−	0.573810i	$-0.194535\pi$
$149$	19.9941	1.63798	0.818989	+	0.573810i	$0.194535\pi$
$150$	−14.7959	−1.20808
$151$	2.78728	0.226825	0.113413	−	0.993548i	$-0.463822\pi$
$151$	2.78728	0.226825	0.113413	+	0.993548i	$0.463822\pi$
$152$	21.3595	1.73248
$153$	−0.0164547	−0.00133028
$154$	−5.66827	−0.456763
$155$	15.9288	1.27943
$156$	−21.5580	−1.72602
$157$	8.10958	0.647215	0.323607	−	0.946191i	$-0.395104\pi$
$157$	8.10958	0.647215	0.323607	+	0.946191i	$0.395104\pi$
$158$	−29.0063	−2.30762
$159$	3.53242	0.280139
$160$	−19.5367	−1.54451
$161$	−3.30377	−0.260374
$162$	−2.28351	−0.179410
$163$	−4.83872	−0.378998	−0.189499	−	0.981881i	$-0.560686\pi$
$163$	−4.83872	−0.378998	−0.189499	+	0.981881i	$0.560686\pi$
$164$	−29.0201	−2.26609
$165$	−9.09480	−0.708029
$166$	12.2414	0.950116
$167$	16.5608	1.28152	0.640758	−	0.767743i	$-0.278620\pi$
$167$	16.5608	1.28152	0.640758	+	0.767743i	$0.278620\pi$
$168$	−2.56443	−0.197850
$169$	31.9790	2.45992
$170$	−0.127307	−0.00976401
$171$	−7.70218	−0.589001
$172$	8.85593	0.675258
$173$	−16.0031	−1.21669	−0.608345	−	0.793673i	$-0.708166\pi$
$173$	−16.0031	−1.21669	−0.608345	+	0.793673i	$0.708166\pi$
$174$	−12.0380	−0.912599
$175$	5.99171	0.452931
$176$	−0.258484	−0.0194840
$177$	12.9231	0.971360
$178$	16.7084	1.25235
$179$	11.3952	0.851715	0.425857	−	0.904790i	$-0.359973\pi$
$179$	11.3952	0.851715	0.425857	+	0.904790i	$0.359973\pi$
$180$	−10.8909	−0.811761
$181$	−4.30334	−0.319865	−0.159932	−	0.987128i	$-0.551128\pi$
$181$	−4.30334	−0.319865	−0.159932	+	0.987128i	$0.551128\pi$
$182$	14.1619	1.04975
$183$	11.1506	0.824276
$184$	9.90769	0.730404
$185$	25.8179	1.89817
$186$	10.7356	0.787173
$187$	−0.0441695	−0.00322999
$188$	−25.0630	−1.82790
$189$	0.924728	0.0672641
$190$	−59.5905	−4.32315
$191$	19.2979	1.39635	0.698173	−	0.715929i	$-0.253997\pi$
$191$	19.2979	1.39635	0.698173	+	0.715929i	$0.253997\pi$
$192$	−12.9747	−0.936366
$193$	−0.487481	−0.0350897	−0.0175448	−	0.999846i	$-0.505585\pi$
$193$	−0.487481	−0.0350897	−0.0175448	+	0.999846i	$0.505585\pi$
$194$	−4.37918	−0.314407
$195$	22.7230	1.62722
$196$	−19.7523	−1.41088
$197$	−7.65039	−0.545068	−0.272534	−	0.962146i	$-0.587862\pi$
$197$	−7.65039	−0.545068	−0.272534	+	0.962146i	$0.587862\pi$
$198$	−6.12966	−0.435616
$199$	−7.95111	−0.563639	−0.281820	−	0.959467i	$-0.590938\pi$
$199$	−7.95111	−0.563639	−0.281820	+	0.959467i	$0.590938\pi$
$200$	−17.9685	−1.27057
$201$	−2.86034	−0.201753
$202$	−16.6280	−1.16994
$203$	4.87490	0.342151
$204$	−0.0528924	−0.00370321
$205$	30.5882	2.13638
$206$	−27.3949	−1.90869
$207$	−3.57269	−0.248319
$208$	0.645811	0.0447790
$209$	−20.6751	−1.43012
$210$	7.15447	0.493706
$211$	−21.4667	−1.47783	−0.738916	−	0.673798i	$-0.764662\pi$
$211$	−21.4667	−1.47783	−0.738916	+	0.673798i	$0.764662\pi$
$212$	11.3547	0.779845
$213$	2.73213	0.187202
$214$	−18.3989	−1.25772
$215$	−9.33448	−0.636606
$216$	−2.77317	−0.188690
$217$	−4.34748	−0.295126
$218$	14.4053	0.975648
$219$	−8.30961	−0.561512
$220$	−29.2346	−1.97100
$221$	0.110355	0.00742331
$222$	17.4006	1.16785
$223$	9.12558	0.611094	0.305547	−	0.952177i	$-0.401161\pi$
$223$	9.12558	0.611094	0.305547	+	0.952177i	$0.401161\pi$
$224$	5.33219	0.356272
$225$	6.47943	0.431962
$226$	−5.16548	−0.343602
$227$	−20.6179	−1.36846	−0.684230	−	0.729266i	$-0.739862\pi$
$227$	−20.6179	−1.36846	−0.684230	+	0.729266i	$0.739862\pi$
$228$	−24.7581	−1.63965
$229$	−10.7022	−0.707223	−0.353612	−	0.935392i	$-0.615047\pi$
$229$	−10.7022	−0.707223	−0.353612	+	0.935392i	$0.615047\pi$
$230$	−27.6414	−1.82262
$231$	2.48226	0.163321
$232$	−14.6193	−0.959807
$233$	19.6666	1.28840	0.644202	−	0.764856i	$-0.277190\pi$
$233$	19.6666	1.28840	0.644202	+	0.764856i	$0.277190\pi$
$234$	15.3147	1.00115
$235$	26.4173	1.72327
$236$	41.5405	2.70405
$237$	12.7025	0.825115
$238$	0.0347461	0.00225226
$239$	13.5199	0.874532	0.437266	−	0.899332i	$-0.355947\pi$
$239$	13.5199	0.874532	0.437266	+	0.899332i	$0.355947\pi$
$240$	0.326258	0.0210599
$241$	−12.8890	−0.830252	−0.415126	−	0.909764i	$-0.636262\pi$
$241$	−12.8890	−0.830252	−0.415126	+	0.909764i	$0.636262\pi$
$242$	8.66470	0.556988
$243$	1.00000	0.0641500
$244$	35.8428	2.29460
$245$	20.8196	1.33012
$246$	20.6157	1.31441
$247$	51.6557	3.28678
$248$	13.0377	0.827893
$249$	−5.36077	−0.339725
$250$	11.4461	0.723913
$251$	26.3229	1.66149	0.830743	−	0.556657i	$-0.187916\pi$
$251$	26.3229	1.66149	0.830743	+	0.556657i	$0.187916\pi$
$252$	2.97248	0.187248
$253$	−9.59023	−0.602933
$254$	−1.40811	−0.0883525
$255$	0.0557506	0.00349123
$256$	−15.3717	−0.960729
$257$	0.554695	0.0346009	0.0173005	−	0.999850i	$-0.494493\pi$
$257$	0.554695	0.0346009	0.0173005	+	0.999850i	$0.494493\pi$
$258$	−6.29120	−0.391673
$259$	−7.04653	−0.437850
$260$	73.0414	4.52983
$261$	5.27171	0.326311
$262$	40.8346	2.52277
$263$	−20.9667	−1.29286	−0.646431	−	0.762973i	$-0.723739\pi$
$263$	−20.9667	−1.29286	−0.646431	+	0.762973i	$0.723739\pi$
$264$	−7.44406	−0.458150
$265$	−11.9683	−0.735206
$266$	16.2642	0.997219
$267$	−7.31698	−0.447792
$268$	−9.19437	−0.561635
$269$	5.75879	0.351120	0.175560	−	0.984469i	$-0.443826\pi$
$269$	5.75879	0.351120	0.175560	+	0.984469i	$0.443826\pi$
$270$	7.73684	0.470849
$271$	6.82227	0.414424	0.207212	−	0.978296i	$-0.433561\pi$
$271$	6.82227	0.414424	0.207212	+	0.978296i	$0.433561\pi$
$272$	0.00158449	9.60739e−5 0
$273$	−6.20182	−0.375351
$274$	23.0744	1.39397
$275$	17.3928	1.04883
$276$	−11.4842	−0.691266
$277$	1.88260	0.113115	0.0565574	−	0.998399i	$-0.481988\pi$
$277$	1.88260	0.113115	0.0565574	+	0.998399i	$0.481988\pi$
$278$	43.2051	2.59127
$279$	−4.70136	−0.281463
$280$	8.68862	0.519244
$281$	7.82787	0.466971	0.233486	−	0.972360i	$-0.424987\pi$
$281$	7.82787	0.466971	0.233486	+	0.972360i	$0.424987\pi$
$282$	17.8046	1.06025
$283$	−26.0515	−1.54860	−0.774301	−	0.632817i	$-0.781898\pi$
$283$	−26.0515	−1.54860	−0.774301	+	0.632817i	$0.781898\pi$
$284$	8.78224	0.521130
$285$	26.0960	1.54579
$286$	41.1094	2.43085
$287$	−8.34850	−0.492797
$288$	5.76623	0.339778
$289$	−16.9997	−0.999984
$290$	40.7864	2.39506
$291$	1.91774	0.112420
$292$	−26.7107	−1.56312
$293$	−13.7967	−0.806011	−0.403006	−	0.915197i	$-0.632034\pi$
$293$	−13.7967	−0.806011	−0.403006	+	0.915197i	$0.632034\pi$
$294$	14.0319	0.818357
$295$	−43.7852	−2.54927
$296$	21.1319	1.22826
$297$	2.68431	0.155760
$298$	−45.6567	−2.64482
$299$	23.9608	1.38569
$300$	20.8277	1.20249
$301$	2.54768	0.146846
$302$	−6.36479	−0.366252
$303$	7.28177	0.418327
$304$	0.741677	0.0425381
$305$	−37.7797	−2.16326
$306$	0.0375744	0.00214799
$307$	13.2712	0.757428	0.378714	−	0.925514i	$-0.376366\pi$
$307$	13.2712	0.757428	0.378714	+	0.925514i	$0.376366\pi$
$308$	7.97906	0.454649
$309$	11.9968	0.682475
$310$	−36.3737	−2.06588
$311$	23.0199	1.30534	0.652669	−	0.757643i	$-0.273649\pi$
$311$	23.0199	1.30534	0.652669	+	0.757643i	$0.273649\pi$
$312$	18.5986	1.05294
$313$	11.2123	0.633759	0.316880	−	0.948466i	$-0.397365\pi$
$313$	11.2123	0.633759	0.316880	+	0.948466i	$0.397365\pi$
$314$	−18.5183	−1.04505
$315$	−3.13310	−0.176530
$316$	40.8313	2.29694
$317$	−9.14005	−0.513357	−0.256678	−	0.966497i	$-0.582628\pi$
$317$	−9.14005	−0.513357	−0.256678	+	0.966497i	$0.582628\pi$
$318$	−8.06632	−0.452337
$319$	14.1509	0.792299
$320$	43.9599	2.45743
$321$	8.05728	0.449714
$322$	7.54420	0.420422
$323$	0.126737	0.00705183
$324$	3.21443	0.178580
$325$	−43.4552	−2.41046
$326$	11.0493	0.611963
$327$	−6.30838	−0.348854
$328$	25.0363	1.38240
$329$	−7.21012	−0.397507
$330$	20.7681	1.14325
$331$	21.6462	1.18978	0.594890	−	0.803807i	$-0.297196\pi$
$331$	21.6462	1.18978	0.594890	+	0.803807i	$0.297196\pi$
$332$	−17.2318	−0.945719
$333$	−7.62011	−0.417579
$334$	−37.8169	−2.06925
$335$	9.69120	0.529487
$336$	−0.0890461	−0.00485786
$337$	−1.65451	−0.0901267	−0.0450634	−	0.998984i	$-0.514349\pi$
$337$	−1.65451	−0.0901267	−0.0450634	+	0.998984i	$0.514349\pi$
$338$	−73.0244	−3.97200
$339$	2.26207	0.122859
$340$	0.179206	0.00971883
$341$	−12.6199	−0.683407
$342$	17.5880	0.951052
$343$	−12.1554	−0.656332
$344$	−7.64023	−0.411934
$345$	12.1048	0.651698
$346$	36.5432	1.96457
$347$	7.05444	0.378702	0.189351	−	0.981909i	$-0.439362\pi$
$347$	7.05444	0.378702	0.189351	+	0.981909i	$0.439362\pi$
$348$	16.9455	0.908376
$349$	20.5258	1.09872	0.549361	−	0.835585i	$-0.314871\pi$
$349$	20.5258	1.09872	0.549361	+	0.835585i	$0.314871\pi$
$350$	−13.6821	−0.731341
$351$	−6.70664	−0.357974
$352$	15.4784	0.825000
$353$	15.3407	0.816504	0.408252	−	0.912869i	$-0.366138\pi$
$353$	15.3407	0.816504	0.408252	+	0.912869i	$0.366138\pi$
$354$	−29.5101	−1.56844
$355$	−9.25680	−0.491300
$356$	−23.5199	−1.24655
$357$	−0.0152161	−0.000805321 0
$358$	−26.0210	−1.37525
$359$	11.4595	0.604809	0.302405	−	0.953180i	$-0.402211\pi$
$359$	11.4595	0.604809	0.302405	+	0.953180i	$0.402211\pi$
$360$	9.39586	0.495205
$361$	40.3236	2.12230
$362$	9.82674	0.516482
$363$	−3.79446	−0.199158
$364$	−19.9353	−1.04489
$365$	28.1541	1.47365
$366$	−25.4625	−1.33095
$367$	4.98333	0.260128	0.130064	−	0.991506i	$-0.458482\pi$
$367$	4.98333	0.260128	0.130064	+	0.991506i	$0.458482\pi$
$368$	0.344030	0.0179338
$369$	−9.02806	−0.469982
$370$	−58.9556	−3.06495
$371$	3.26653	0.169590
$372$	−15.1122	−0.783531
$373$	34.8113	1.80246	0.901231	−	0.433339i	$-0.142665\pi$
$373$	34.8113	1.80246	0.901231	+	0.433339i	$0.142665\pi$
$374$	0.100862	0.00521543
$375$	−5.01249	−0.258844
$376$	21.6224	1.11509
$377$	−35.3554	−1.82090
$378$	−2.11163	−0.108610
$379$	−9.57716	−0.491946	−0.245973	−	0.969277i	$-0.579107\pi$
$379$	−9.57716	−0.491946	−0.245973	+	0.969277i	$0.579107\pi$
$380$	83.8838	4.30315
$381$	0.616641	0.0315915
$382$	−44.0670	−2.25466
$383$	−32.7650	−1.67421	−0.837107	−	0.547039i	$-0.815755\pi$
$383$	−32.7650	−1.67421	−0.837107	+	0.547039i	$0.815755\pi$
$384$	18.0954	0.923425
$385$	−8.41022	−0.428625
$386$	1.11317	0.0566589
$387$	2.75505	0.140047
$388$	6.16443	0.312952
$389$	7.80943	0.395954	0.197977	−	0.980207i	$-0.436563\pi$
$389$	7.80943	0.395954	0.197977	+	0.980207i	$0.436563\pi$
$390$	−51.8882	−2.62746
$391$	0.0587875	0.00297301
$392$	17.0408	0.860690
$393$	−17.8824	−0.902045
$394$	17.4698	0.880114
$395$	−43.0377	−2.16546
$396$	8.62854	0.433601
$397$	−2.15694	−0.108254	−0.0541269	−	0.998534i	$-0.517238\pi$
$397$	−2.15694	−0.108254	−0.0541269	+	0.998534i	$0.517238\pi$
$398$	18.1565	0.910101
$399$	−7.12243	−0.356567
$400$	−0.623932	−0.0311966
$401$	1.49085	0.0744497	0.0372248	−	0.999307i	$-0.488148\pi$
$401$	1.49085	0.0744497	0.0372248	+	0.999307i	$0.488148\pi$
$402$	6.53162	0.325768
$403$	31.5303	1.57064
$404$	23.4068	1.16453
$405$	−3.38813	−0.168358
$406$	−11.1319	−0.552466
$407$	−20.4548	−1.01391
$408$	0.0456316	0.00225910
$409$	1.04883	0.0518611	0.0259306	−	0.999664i	$-0.491745\pi$
$409$	1.04883	0.0518611	0.0259306	+	0.999664i	$0.491745\pi$
$410$	−69.8487	−3.44958
$411$	−10.1048	−0.498432
$412$	38.5629	1.89986
$413$	11.9504	0.588039
$414$	8.15829	0.400958
$415$	18.1630	0.891586
$416$	−38.6720	−1.89605
$417$	−18.9205	−0.926539
$418$	47.2118	2.30920
$419$	−40.1965	−1.96373	−0.981864	−	0.189588i	$-0.939285\pi$
$419$	−40.1965	−1.96373	−0.981864	+	0.189588i	$0.939285\pi$
$420$	−10.0711	−0.491421
$421$	17.5464	0.855159	0.427579	−	0.903978i	$-0.359366\pi$
$421$	17.5464	0.855159	0.427579	+	0.903978i	$0.359366\pi$
$422$	49.0196	2.38624
$423$	−7.79701	−0.379104
$424$	−9.79599	−0.475735
$425$	−0.106617	−0.00517167
$426$	−6.23885	−0.302273
$427$	10.3113	0.498998
$428$	25.8996	1.25190
$429$	−18.0027	−0.869179
$430$	21.3154	1.02792
$431$	−22.6981	−1.09333	−0.546664	−	0.837352i	$-0.684102\pi$
$431$	−22.6981	−1.09333	−0.546664	+	0.837352i	$0.684102\pi$
$432$	−0.0962944	−0.00463297
$433$	−4.68427	−0.225112	−0.112556	−	0.993645i	$-0.535904\pi$
$433$	−4.68427	−0.225112	−0.112556	+	0.993645i	$0.535904\pi$
$434$	9.92753	0.476536
$435$	−17.8612	−0.856381
$436$	−20.2779	−0.971133
$437$	27.5175	1.31634
$438$	18.9751	0.906666
$439$	30.2553	1.44401	0.722003	−	0.691890i	$-0.243222\pi$
$439$	30.2553	1.44401	0.722003	+	0.691890i	$0.243222\pi$
$440$	25.2214	1.20238
$441$	−6.14488	−0.292613
$442$	−0.251998	−0.0119863
$443$	−31.5273	−1.49791	−0.748954	−	0.662622i	$-0.769444\pi$
$443$	−31.5273	−1.49791	−0.748954	+	0.662622i	$0.769444\pi$
$444$	−24.4943	−1.16245
$445$	24.7909	1.17520
$446$	−20.8384	−0.986726
$447$	19.9941	0.945687
$448$	−11.9980	−0.566854
$449$	−11.4499	−0.540352	−0.270176	−	0.962811i	$-0.587082\pi$
$449$	−11.4499	−0.540352	−0.270176	+	0.962811i	$0.587082\pi$
$450$	−14.7959	−0.697483
$451$	−24.2341	−1.14114
$452$	7.27128	0.342012
$453$	2.78728	0.130958
$454$	47.0813	2.20964
$455$	21.0126	0.985084
$456$	21.3595	1.00025
$457$	28.7503	1.34488	0.672442	−	0.740150i	$-0.265246\pi$
$457$	28.7503	1.34488	0.672442	+	0.740150i	$0.265246\pi$
$458$	24.4387	1.14194
$459$	−0.0164547	−0.000768038 0
$460$	38.9099	1.81418
$461$	−10.8444	−0.505076	−0.252538	−	0.967587i	$-0.581265\pi$
$461$	−10.8444	−0.505076	−0.252538	+	0.967587i	$0.581265\pi$
$462$	−5.66827	−0.263712
$463$	0.339703	0.0157874	0.00789368	−	0.999969i	$-0.497487\pi$
$463$	0.339703	0.0157874	0.00789368	+	0.999969i	$0.497487\pi$
$464$	−0.507636	−0.0235664
$465$	15.9288	0.738681
$466$	−44.9090	−2.08037
$467$	−11.6938	−0.541122	−0.270561	−	0.962703i	$-0.587209\pi$
$467$	−11.6938	−0.541122	−0.270561	+	0.962703i	$0.587209\pi$
$468$	−21.5580	−0.996520
$469$	−2.64504	−0.122136
$470$	−60.3242	−2.78255
$471$	8.10958	0.373670
$472$	−35.8380	−1.64958
$473$	7.39543	0.340042
$474$	−29.0063	−1.33230
$475$	−49.9057	−2.28983
$476$	−0.0489111	−0.00224184
$477$	3.53242	0.161738
$478$	−30.8730	−1.41210
$479$	23.1444	1.05750	0.528748	−	0.848779i	$-0.322662\pi$
$479$	23.1444	1.05750	0.528748	+	0.848779i	$0.322662\pi$
$480$	−19.5367	−0.891726
$481$	51.1053	2.33020
$482$	29.4321	1.34060
$483$	−3.30377	−0.150327
$484$	−12.1970	−0.554411
$485$	−6.49754	−0.295038
$486$	−2.28351	−0.103582
$487$	−10.5182	−0.476626	−0.238313	−	0.971188i	$-0.576594\pi$
$487$	−10.5182	−0.476626	−0.238313	+	0.971188i	$0.576594\pi$
$488$	−30.9225	−1.39980
$489$	−4.83872	−0.218814
$490$	−47.5419	−2.14773
$491$	17.6506	0.796559	0.398279	−	0.917264i	$-0.369607\pi$
$491$	17.6506	0.796559	0.398279	+	0.917264i	$0.369607\pi$
$492$	−29.0201	−1.30833
$493$	−0.0867442	−0.00390676
$494$	−117.957	−5.30712
$495$	−9.09480	−0.408781
$496$	0.452714	0.0203275
$497$	2.52648	0.113328
$498$	12.2414	0.548550
$499$	24.9059	1.11494	0.557470	−	0.830197i	$-0.311772\pi$
$499$	24.9059	1.11494	0.557470	+	0.830197i	$0.311772\pi$
$500$	−16.1123	−0.720563
$501$	16.5608	0.739884
$502$	−60.1086	−2.68278
$503$	1.95981	0.0873834	0.0436917	−	0.999045i	$-0.486088\pi$
$503$	1.95981	0.0873834	0.0436917	+	0.999045i	$0.486088\pi$
$504$	−2.56443	−0.114229
$505$	−24.6716	−1.09787
$506$	21.8994	0.973548
$507$	31.9790	1.42024
$508$	1.98215	0.0879437
$509$	2.55468	0.113234	0.0566172	−	0.998396i	$-0.481969\pi$
$509$	2.55468	0.113234	0.0566172	+	0.998396i	$0.481969\pi$
$510$	−0.127307	−0.00563725
$511$	−7.68413	−0.339926
$512$	−1.08934	−0.0481423
$513$	−7.70218	−0.340060
$514$	−1.26665	−0.0558697
$515$	−40.6468	−1.79111
$516$	8.85593	0.389861
$517$	−20.9296	−0.920484
$518$	16.0908	0.706991
$519$	−16.0031	−0.702456
$520$	−63.0146	−2.76337
$521$	3.63736	0.159356	0.0796778	−	0.996821i	$-0.474611\pi$
$521$	3.63736	0.159356	0.0796778	+	0.996821i	$0.474611\pi$
$522$	−12.0380	−0.526890
$523$	34.2370	1.49708	0.748539	−	0.663091i	$-0.230756\pi$
$523$	34.2370	1.49708	0.748539	+	0.663091i	$0.230756\pi$
$524$	−57.4816	−2.51110
$525$	5.99171	0.261500
$526$	47.8777	2.08757
$527$	0.0773593	0.00336982
$528$	−0.258484	−0.0112491
$529$	−10.2359	−0.445037
$530$	27.3297	1.18713
$531$	12.9231	0.560815
$532$	−22.8945	−0.992604
$533$	60.5479	2.62262
$534$	16.7084	0.723044
$535$	−27.2991	−1.18024
$536$	7.93221	0.342619
$537$	11.3952	0.491738
$538$	−13.1503	−0.566948
$539$	−16.4948	−0.710480
$540$	−10.8909	−0.468670
$541$	11.3288	0.487062	0.243531	−	0.969893i	$-0.421694\pi$
$541$	11.3288	0.487062	0.243531	+	0.969893i	$0.421694\pi$
$542$	−15.5787	−0.669165
$543$	−4.30334	−0.184674
$544$	−0.0948814	−0.00406800
$545$	21.3736	0.915545
$546$	14.1619	0.606075
$547$	−15.9811	−0.683304	−0.341652	−	0.939826i	$-0.610986\pi$
$547$	−15.9811	−0.683304	−0.341652	+	0.939826i	$0.610986\pi$
$548$	−32.4811	−1.38752
$549$	11.1506	0.475896
$550$	−39.7167	−1.69353
$551$	−40.6037	−1.72977
$552$	9.90769	0.421699
$553$	11.7463	0.499505
$554$	−4.29895	−0.182645
$555$	25.8179	1.09591
$556$	−60.8185	−2.57928
$557$	31.1789	1.32109	0.660547	−	0.750785i	$-0.270324\pi$
$557$	31.1789	1.32109	0.660547	+	0.750785i	$0.270324\pi$
$558$	10.7356	0.454475
$559$	−18.4771	−0.781500
$560$	0.301700	0.0127491
$561$	−0.0441695	−0.00186484
$562$	−17.8750	−0.754013
$563$	9.53361	0.401794	0.200897	−	0.979612i	$-0.435614\pi$
$563$	9.53361	0.401794	0.200897	+	0.979612i	$0.435614\pi$
$564$	−25.0630	−1.05534
$565$	−7.66420	−0.322435
$566$	59.4890	2.50051
$567$	0.924728	0.0388349
$568$	−7.57665	−0.317909
$569$	2.04451	0.0857102	0.0428551	−	0.999081i	$-0.486355\pi$
$569$	2.04451	0.0857102	0.0428551	+	0.999081i	$0.486355\pi$
$570$	−59.5905	−2.49597
$571$	−11.5176	−0.481997	−0.240999	−	0.970525i	$-0.577475\pi$
$571$	−11.5176	−0.481997	−0.240999	+	0.970525i	$0.577475\pi$
$572$	−57.8685	−2.41960
$573$	19.2979	0.806180
$574$	19.0639	0.795712
$575$	−23.1490	−0.965380
$576$	−12.9747	−0.540611
$577$	14.1483	0.589003	0.294502	−	0.955651i	$-0.404846\pi$
$577$	14.1483	0.589003	0.294502	+	0.955651i	$0.404846\pi$
$578$	38.8191	1.61466
$579$	−0.487481	−0.0202590
$580$	−57.4137	−2.38397
$581$	−4.95725	−0.205662
$582$	−4.37918	−0.181523
$583$	9.48212	0.392709
$584$	23.0440	0.953566
$585$	22.7230	0.939479
$586$	31.5049	1.30146
$587$	28.5122	1.17682	0.588412	−	0.808562i	$-0.299753\pi$
$587$	28.5122	1.17682	0.588412	+	0.808562i	$0.299753\pi$
$588$	−19.7523	−0.814571
$589$	36.2107	1.49204
$590$	99.9840	4.11628
$591$	−7.65039	−0.314695
$592$	0.733774	0.0301579
$593$	41.4042	1.70027	0.850134	−	0.526567i	$-0.176521\pi$
$593$	41.4042	1.70027	0.850134	+	0.526567i	$0.176521\pi$
$594$	−6.12966	−0.251503
$595$	0.0515541	0.00211351
$596$	64.2695	2.63258
$597$	−7.95111	−0.325417
$598$	−54.7147	−2.23745
$599$	33.2754	1.35960	0.679798	−	0.733400i	$-0.262068\pi$
$599$	33.2754	1.35960	0.679798	+	0.733400i	$0.262068\pi$
$600$	−17.9685	−0.733563
$601$	−19.8196	−0.808458	−0.404229	−	0.914658i	$-0.632460\pi$
$601$	−19.8196	−0.808458	−0.404229	+	0.914658i	$0.632460\pi$
$602$	−5.81765	−0.237110
$603$	−2.86034	−0.116482
$604$	8.95951	0.364557
$605$	12.8561	0.522676
$606$	−16.6280	−0.675467
$607$	26.6505	1.08171	0.540855	−	0.841116i	$-0.318101\pi$
$607$	26.6505	1.08171	0.540855	+	0.841116i	$0.318101\pi$
$608$	−44.4125	−1.80117
$609$	4.87490	0.197541
$610$	86.2704	3.49299
$611$	52.2917	2.11550
$612$	−0.0528924	−0.00213805
$613$	38.2735	1.54585	0.772926	−	0.634496i	$-0.218792\pi$
$613$	38.2735	1.54585	0.772926	+	0.634496i	$0.218792\pi$
$614$	−30.3050	−1.22301
$615$	30.5882	1.23344
$616$	−6.88373	−0.277353
$617$	2.95924	0.119134	0.0595672	−	0.998224i	$-0.481028\pi$
$617$	2.95924	0.119134	0.0595672	+	0.998224i	$0.481028\pi$
$618$	−27.3949	−1.10198
$619$	16.2832	0.654478	0.327239	−	0.944942i	$-0.393882\pi$
$619$	16.2832	0.654478	0.327239	+	0.944942i	$0.393882\pi$
$620$	51.2021	2.05633
$621$	−3.57269	−0.143367
$622$	−52.5662	−2.10771
$623$	−6.76622	−0.271083
$624$	0.645811	0.0258531
$625$	−15.4142	−0.616567
$626$	−25.6035	−1.02332
$627$	−20.6751	−0.825683
$628$	26.0677	1.04021
$629$	0.125386	0.00499948
$630$	7.15447	0.285041
$631$	−1.75286	−0.0697804	−0.0348902	−	0.999391i	$-0.511108\pi$
$631$	−1.75286	−0.0697804	−0.0348902	+	0.999391i	$0.511108\pi$
$632$	−35.2261	−1.40122
$633$	−21.4667	−0.853227
$634$	20.8714	0.828910
$635$	−2.08926	−0.0829097
$636$	11.3547	0.450244
$637$	41.2115	1.63286
$638$	−32.3138	−1.27932
$639$	2.73213	0.108081
$640$	−61.3095	−2.42347
$641$	−19.7274	−0.779184	−0.389592	−	0.920988i	$-0.627384\pi$
$641$	−19.7274	−0.779184	−0.389592	+	0.920988i	$0.627384\pi$
$642$	−18.3989	−0.726147
$643$	−13.0102	−0.513074	−0.256537	−	0.966534i	$-0.582582\pi$
$643$	−13.0102	−0.513074	−0.256537	+	0.966534i	$0.582582\pi$
$644$	−10.6197	−0.418477
$645$	−9.33448	−0.367545
$646$	−0.289405	−0.0113865
$647$	−4.02194	−0.158119	−0.0790594	−	0.996870i	$-0.525192\pi$
$647$	−4.02194	−0.158119	−0.0790594	+	0.996870i	$0.525192\pi$
$648$	−2.77317	−0.108940
$649$	34.6897	1.36169
$650$	99.2304	3.89214
$651$	−4.34748	−0.170391
$652$	−15.5537	−0.609131
$653$	−1.66679	−0.0652265	−0.0326132	−	0.999468i	$-0.510383\pi$
$653$	−1.66679	−0.0652265	−0.0326132	+	0.999468i	$0.510383\pi$
$654$	14.4053	0.563291
$655$	60.5877	2.36736
$656$	0.869351	0.0339425
$657$	−8.30961	−0.324189
$658$	16.4644	0.641849
$659$	−18.7486	−0.730340	−0.365170	−	0.930941i	$-0.618989\pi$
$659$	−18.7486	−0.730340	−0.365170	+	0.930941i	$0.618989\pi$
$660$	−29.2346	−1.13796
$661$	45.2075	1.75837	0.879183	−	0.476484i	$-0.158089\pi$
$661$	45.2075	1.75837	0.879183	+	0.476484i	$0.158089\pi$
$662$	−49.4293	−1.92112
$663$	0.110355	0.00428585
$664$	14.8663	0.576925
$665$	24.1317	0.935787
$666$	17.4006	0.674260
$667$	−18.8342	−0.729263
$668$	53.2337	2.05967
$669$	9.12558	0.352815
$670$	−22.1300	−0.854956
$671$	29.9317	1.15550
$672$	5.33219	0.205694
$673$	16.1325	0.621862	0.310931	−	0.950432i	$-0.399359\pi$
$673$	16.1325	0.621862	0.310931	+	0.950432i	$0.399359\pi$
$674$	3.77809	0.145527
$675$	6.47943	0.249393
$676$	102.794	3.95362
$677$	36.9876	1.42155	0.710775	−	0.703420i	$-0.248345\pi$
$677$	36.9876	1.42155	0.710775	+	0.703420i	$0.248345\pi$
$678$	−5.16548	−0.198379
$679$	1.77339	0.0680563
$680$	−0.154606	−0.00592886
$681$	−20.6179	−0.790081
$682$	28.8178	1.10349
$683$	−47.1797	−1.80528	−0.902641	−	0.430394i	$-0.858375\pi$
$683$	−47.1797	−1.80528	−0.902641	+	0.430394i	$0.858375\pi$
$684$	−24.7581	−0.946651
$685$	34.2363	1.30810
$686$	27.7571	1.05977
$687$	−10.7022	−0.408315
$688$	−0.265296	−0.0101143
$689$	−23.6906	−0.902542
$690$	−27.6414	−1.05229
$691$	−42.4516	−1.61493	−0.807467	−	0.589913i	$-0.799162\pi$
$691$	−42.4516	−1.61493	−0.807467	+	0.589913i	$0.799162\pi$
$692$	−51.4407	−1.95548
$693$	2.48226	0.0942933
$694$	−16.1089	−0.611486
$695$	64.1050	2.43164
$696$	−14.6193	−0.554145
$697$	0.148554	0.00562687
$698$	−46.8709	−1.77409
$699$	19.6666	0.743860
$700$	19.2599	0.727957
$701$	34.4251	1.30022	0.650108	−	0.759841i	$-0.274723\pi$
$701$	34.4251	1.30022	0.650108	+	0.759841i	$0.274723\pi$
$702$	15.3147	0.578016
$703$	58.6915	2.21359
$704$	−34.8281	−1.31263
$705$	26.4173	0.994933
$706$	−35.0307	−1.31840
$707$	6.73366	0.253245
$708$	41.5405	1.56119
$709$	4.56797	0.171554	0.0857769	−	0.996314i	$-0.472663\pi$
$709$	4.56797	0.171554	0.0857769	+	0.996314i	$0.472663\pi$
$710$	21.1380	0.793296
$711$	12.7025	0.476380
$712$	20.2912	0.760446
$713$	16.7965	0.629035
$714$	0.0347461	0.00130034
$715$	60.9955	2.28110
$716$	36.6290	1.36889
$717$	13.5199	0.504911
$718$	−26.1679	−0.976578
$719$	13.7703	0.513546	0.256773	−	0.966472i	$-0.417341\pi$
$719$	13.7703	0.513546	0.256773	+	0.966472i	$0.417341\pi$
$720$	0.326258	0.0121589
$721$	11.0938	0.413154
$722$	−92.0795	−3.42684
$723$	−12.8890	−0.479346
$724$	−13.8328	−0.514092
$725$	34.1576	1.26858
$726$	8.66470	0.321577
$727$	−11.1327	−0.412890	−0.206445	−	0.978458i	$-0.566189\pi$
$727$	−11.1327	−0.412890	−0.206445	+	0.978458i	$0.566189\pi$
$728$	17.1987	0.637426
$729$	1.00000	0.0370370
$730$	−64.2901	−2.37948
$731$	−0.0453335	−0.00167672
$732$	35.8428	1.32479
$733$	−22.8888	−0.845419	−0.422709	−	0.906265i	$-0.638921\pi$
$733$	−22.8888	−0.845419	−0.422709	+	0.906265i	$0.638921\pi$
$734$	−11.3795	−0.420025
$735$	20.8196	0.767944
$736$	−20.6010	−0.759362
$737$	−7.67805	−0.282825
$738$	20.6157	0.758874
$739$	12.9506	0.476396	0.238198	−	0.971217i	$-0.423443\pi$
$739$	12.9506	0.476396	0.238198	+	0.971217i	$0.423443\pi$
$740$	82.9899	3.05077
$741$	51.6557	1.89762
$742$	−7.45916	−0.273834
$743$	−50.8809	−1.86664	−0.933320	−	0.359046i	$-0.883102\pi$
$743$	−50.8809	−1.86664	−0.933320	+	0.359046i	$0.883102\pi$
$744$	13.0377	0.477984
$745$	−67.7425	−2.48189
$746$	−79.4921	−2.91041
$747$	−5.36077	−0.196140
$748$	−0.141980	−0.00519129
$749$	7.45080	0.272246
$750$	11.4461	0.417952
$751$	51.6067	1.88316	0.941578	−	0.336796i	$-0.109343\pi$
$751$	51.6067	1.88316	0.941578	+	0.336796i	$0.109343\pi$
$752$	0.750808	0.0273792
$753$	26.3229	0.959259
$754$	80.7346	2.94018
$755$	−9.44366	−0.343690
$756$	2.97248	0.108108
$757$	17.0575	0.619964	0.309982	−	0.950742i	$-0.399677\pi$
$757$	17.0575	0.619964	0.309982	+	0.950742i	$0.399677\pi$
$758$	21.8696	0.794339
$759$	−9.59023	−0.348103
$760$	−72.3686	−2.62509
$761$	54.3491	1.97015	0.985077	−	0.172117i	$-0.0550607\pi$
$761$	54.3491	1.97015	0.985077	+	0.172117i	$0.0550607\pi$
$762$	−1.40811	−0.0510103
$763$	−5.83354	−0.211188
$764$	62.0317	2.24423
$765$	0.0557506	0.00201567
$766$	74.8194	2.70333
$767$	−86.6706	−3.12949
$768$	−15.3717	−0.554677
$769$	28.1166	1.01391	0.506955	−	0.861973i	$-0.330771\pi$
$769$	28.1166	1.01391	0.506955	+	0.861973i	$0.330771\pi$
$770$	19.2048	0.692095
$771$	0.554695	0.0199768
$772$	−1.56698	−0.0563967
$773$	20.0611	0.721548	0.360774	−	0.932653i	$-0.382513\pi$
$773$	20.0611	0.721548	0.360774	+	0.932653i	$0.382513\pi$
$774$	−6.29120	−0.226133
$775$	−30.4621	−1.09423
$776$	−5.31821	−0.190913
$777$	−7.04653	−0.252793
$778$	−17.8329	−0.639342
$779$	69.5358	2.49138
$780$	73.0414	2.61530
$781$	7.33389	0.262427
$782$	−0.134242	−0.00480048
$783$	5.27171	0.188395
$784$	0.591717	0.0211328
$785$	−27.4763	−0.980671
$786$	40.8346	1.45652
$787$	−15.5957	−0.555925	−0.277962	−	0.960592i	$-0.589659\pi$
$787$	−15.5957	−0.555925	−0.277962	+	0.960592i	$0.589659\pi$
$788$	−24.5917	−0.876042
$789$	−20.9667	−0.746434
$790$	98.2770	3.49654
$791$	2.09180	0.0743760
$792$	−7.44406	−0.264513
$793$	−74.7830	−2.65562
$794$	4.92540	0.174796
$795$	−11.9683	−0.424472
$796$	−25.5583	−0.905890
$797$	−32.7360	−1.15957	−0.579784	−	0.814770i	$-0.696863\pi$
$797$	−32.7360	−1.15957	−0.579784	+	0.814770i	$0.696863\pi$
$798$	16.2642	0.575745
$799$	0.128297	0.00453883
$800$	37.3618	1.32094
$801$	−7.31698	−0.258533
$802$	−3.40438	−0.120213
$803$	−22.3056	−0.787148
$804$	−9.19437	−0.324260
$805$	11.1936	0.394523
$806$	−71.9999	−2.53609
$807$	5.75879	0.202719
$808$	−20.1936	−0.710408
$809$	−1.25969	−0.0442885	−0.0221442	−	0.999755i	$-0.507049\pi$
$809$	−1.25969	−0.0442885	−0.0221442	+	0.999755i	$0.507049\pi$
$810$	7.73684	0.271845
$811$	−37.6301	−1.32137	−0.660686	−	0.750662i	$-0.729735\pi$
$811$	−37.6301	−1.32137	−0.660686	+	0.750662i	$0.729735\pi$
$812$	15.6700	0.549910
$813$	6.82227	0.239268
$814$	46.7087	1.63714
$815$	16.3942	0.574264
$816$	0.00158449	5.54683e−5 0
$817$	−21.2199	−0.742391
$818$	−2.39501	−0.0837395
$819$	−6.20182	−0.216709
$820$	98.3238	3.43362
$821$	−3.67687	−0.128324	−0.0641618	−	0.997940i	$-0.520437\pi$
$821$	−3.67687	−0.128324	−0.0641618	+	0.997940i	$0.520437\pi$
$822$	23.0744	0.804811
$823$	6.46654	0.225409	0.112705	−	0.993629i	$-0.464049\pi$
$823$	6.46654	0.225409	0.112705	+	0.993629i	$0.464049\pi$
$824$	−33.2692	−1.15899
$825$	17.3928	0.605540
$826$	−27.2888	−0.949499
$827$	−22.5770	−0.785081	−0.392540	−	0.919735i	$-0.628404\pi$
$827$	−22.5770	−0.785081	−0.392540	+	0.919735i	$0.628404\pi$
$828$	−11.4842	−0.399103
$829$	−45.7014	−1.58727	−0.793637	−	0.608391i	$-0.791815\pi$
$829$	−45.7014	−1.58727	−0.793637	+	0.608391i	$0.791815\pi$
$830$	−41.4754	−1.43963
$831$	1.88260	0.0653068
$832$	87.0164	3.01675
$833$	0.101112	0.00350332
$834$	43.2051	1.49607
$835$	−56.1103	−1.94178
$836$	−66.4586	−2.29852
$837$	−4.70136	−0.162503
$838$	91.7892	3.17081
$839$	−25.7005	−0.887281	−0.443640	−	0.896205i	$-0.646313\pi$
$839$	−25.7005	−0.887281	−0.443640	+	0.896205i	$0.646313\pi$
$840$	8.68862	0.299786
$841$	−1.20910	−0.0416929
$842$	−40.0674	−1.38081
$843$	7.82787	0.269606
$844$	−69.0034	−2.37519
$845$	−108.349	−3.72732
$846$	17.8046	0.612134
$847$	−3.50885	−0.120565
$848$	−0.340152	−0.0116809
$849$	−26.0515	−0.894086
$850$	0.243461	0.00835064
$851$	27.2243	0.933238
$852$	8.78224	0.300874
$853$	2.12909	0.0728985	0.0364493	−	0.999336i	$-0.488395\pi$
$853$	2.12909	0.0728985	0.0364493	+	0.999336i	$0.488395\pi$
$854$	−23.5459	−0.805725
$855$	26.0960	0.892464
$856$	−22.3442	−0.763709
$857$	13.2934	0.454092	0.227046	−	0.973884i	$-0.427093\pi$
$857$	13.2934	0.454092	0.227046	+	0.973884i	$0.427093\pi$
$858$	41.1094	1.40345
$859$	8.13194	0.277458	0.138729	−	0.990330i	$-0.455698\pi$
$859$	8.13194	0.277458	0.138729	+	0.990330i	$0.455698\pi$
$860$	−30.0050	−1.02316
$861$	−8.34850	−0.284516
$862$	51.8313	1.76538
$863$	12.3432	0.420169	0.210084	−	0.977683i	$-0.432626\pi$
$863$	12.3432	0.420169	0.210084	+	0.977683i	$0.432626\pi$
$864$	5.76623	0.196171
$865$	54.2204	1.84355
$866$	10.6966	0.363485
$867$	−16.9997	−0.577341
$868$	−13.9747	−0.474331
$869$	34.0974	1.15668
$870$	40.7864	1.38279
$871$	19.1833	0.650000
$872$	17.4942	0.592429
$873$	1.91774	0.0649056
$874$	−62.8367	−2.12548
$875$	−4.63519	−0.156698
$876$	−26.7107	−0.902470
$877$	−21.2829	−0.718673	−0.359337	−	0.933208i	$-0.616997\pi$
$877$	−21.2829	−0.718673	−0.359337	+	0.933208i	$0.616997\pi$
$878$	−69.0883	−2.33162
$879$	−13.7967	−0.465351
$880$	0.875778	0.0295225
$881$	−34.9578	−1.17776	−0.588879	−	0.808221i	$-0.700431\pi$
$881$	−34.9578	−1.17776	−0.588879	+	0.808221i	$0.700431\pi$
$882$	14.0319	0.472479
$883$	26.3228	0.885832	0.442916	−	0.896563i	$-0.353944\pi$
$883$	26.3228	0.885832	0.442916	+	0.896563i	$0.353944\pi$
$884$	0.354730	0.0119309
$885$	−43.7852	−1.47182
$886$	71.9930	2.41865
$887$	−22.7117	−0.762583	−0.381292	−	0.924455i	$-0.624521\pi$
$887$	−22.7117	−0.762583	−0.381292	+	0.924455i	$0.624521\pi$
$888$	21.1319	0.709139
$889$	0.570225	0.0191247
$890$	−56.6103	−1.89758
$891$	2.68431	0.0899279
$892$	29.3335	0.982160
$893$	60.0540	2.00963
$894$	−45.6567	−1.52699
$895$	−38.6083	−1.29053
$896$	16.7333	0.559020
$897$	23.9608	0.800027
$898$	26.1459	0.872500
$899$	−24.7842	−0.826599
$900$	20.8277	0.694256
$901$	−0.0581248	−0.00193642
$902$	55.3390	1.84259
$903$	2.54768	0.0847813
$904$	−6.27312	−0.208641
$905$	14.5803	0.484665
$906$	−6.36479	−0.211456
$907$	−32.7024	−1.08587	−0.542933	−	0.839776i	$-0.682686\pi$
$907$	−32.7024	−1.08587	−0.542933	+	0.839776i	$0.682686\pi$
$908$	−66.2749	−2.19941
$909$	7.28177	0.241521
$910$	−47.9825	−1.59060
$911$	−26.7090	−0.884907	−0.442454	−	0.896791i	$-0.645892\pi$
$911$	−26.7090	−0.884907	−0.442454	+	0.896791i	$0.645892\pi$
$912$	0.741677	0.0245594
$913$	−14.3900	−0.476239
$914$	−65.6517	−2.17157
$915$	−37.7797	−1.24896
$916$	−34.4016	−1.13666
$917$	−16.5363	−0.546077
$918$	0.0375744	0.00124014
$919$	−1.49255	−0.0492348	−0.0246174	−	0.999697i	$-0.507837\pi$
$919$	−1.49255	−0.0492348	−0.0246174	+	0.999697i	$0.507837\pi$
$920$	−33.5685	−1.10672
$921$	13.2712	0.437301
$922$	24.7634	0.815539
$923$	−18.3234	−0.603122
$924$	7.97906	0.262492
$925$	−49.3739	−1.62341
$926$	−0.775717	−0.0254916
$927$	11.9968	0.394027
$928$	30.3979	0.997859
$929$	54.8829	1.80065	0.900325	−	0.435218i	$-0.143329\pi$
$929$	54.8829	1.80065	0.900325	+	0.435218i	$0.143329\pi$
$930$	−36.3737	−1.19274
$931$	47.3290	1.55114
$932$	63.2170	2.07074
$933$	23.0199	0.753637
$934$	26.7028	0.873744
$935$	0.149652	0.00489414
$936$	18.5986	0.607916
$937$	−30.9501	−1.01110	−0.505548	−	0.862798i	$-0.668710\pi$
$937$	−30.9501	−1.01110	−0.505548	+	0.862798i	$0.668710\pi$
$938$	6.03998	0.197212
$939$	11.2123	0.365901
$940$	84.9166	2.76967
$941$	17.5408	0.571813	0.285907	−	0.958257i	$-0.407705\pi$
$941$	17.5408	0.571813	0.285907	+	0.958257i	$0.407705\pi$
$942$	−18.5183	−0.603360
$943$	32.2545	1.05035
$944$	−1.24442	−0.0405025
$945$	−3.13310	−0.101920
$946$	−16.8876	−0.549062
$947$	33.4497	1.08697	0.543484	−	0.839420i	$-0.317105\pi$
$947$	33.4497	1.08697	0.543484	+	0.839420i	$0.317105\pi$
$948$	40.8313	1.32614
$949$	55.7296	1.80906
$950$	113.960	3.69736
$951$	−9.14005	−0.296387
$952$	0.0421968	0.00136761
$953$	58.4061	1.89196	0.945979	−	0.324228i	$-0.105104\pi$
$953$	58.4061	1.89196	0.945979	+	0.324228i	$0.105104\pi$
$954$	−8.06632	−0.261157
$955$	−65.3837	−2.11577
$956$	43.4589	1.40556
$957$	14.1509	0.457434
$958$	−52.8506	−1.70753
$959$	−9.34417	−0.301739
$960$	43.9599	1.41880
$961$	−8.89722	−0.287007
$962$	−116.700	−3.76255
$963$	8.05728	0.259642
$964$	−41.4307	−1.33439
$965$	1.65165	0.0531685
$966$	7.54420	0.242731
$967$	−4.64415	−0.149346	−0.0746729	−	0.997208i	$-0.523791\pi$
$967$	−4.64415	−0.149346	−0.0746729	+	0.997208i	$0.523791\pi$
$968$	10.5227	0.338212
$969$	0.126737	0.00407137
$970$	14.8372	0.476395
$971$	−6.06223	−0.194546	−0.0972731	−	0.995258i	$-0.531012\pi$
$971$	−6.06223	−0.194546	−0.0972731	+	0.995258i	$0.531012\pi$
$972$	3.21443	0.103103
$973$	−17.4963	−0.560905
$974$	24.0185	0.769603
$975$	−43.4552	−1.39168
$976$	−1.07374	−0.0343696
$977$	−2.18306	−0.0698423	−0.0349212	−	0.999390i	$-0.511118\pi$
$977$	−2.18306	−0.0698423	−0.0349212	+	0.999390i	$0.511118\pi$
$978$	11.0493	0.353317
$979$	−19.6411	−0.627731
$980$	66.9233	2.13779
$981$	−6.30838	−0.201411
$982$	−40.3053	−1.28619
$983$	30.4336	0.970680	0.485340	−	0.874326i	$-0.338696\pi$
$983$	30.4336	0.970680	0.485340	+	0.874326i	$0.338696\pi$
$984$	25.0363	0.798129
$985$	25.9205	0.825897
$986$	0.198081	0.00630820
$987$	−7.21012	−0.229501
$988$	166.044	5.28256
$989$	−9.84296	−0.312988
$990$	20.7681	0.660054
$991$	51.3508	1.63121	0.815606	−	0.578608i	$-0.196404\pi$
$991$	51.3508	1.63121	0.815606	+	0.578608i	$0.196404\pi$
$992$	−27.1091	−0.860715
$993$	21.6462	0.686920
$994$	−5.76924	−0.182989
$995$	26.9394	0.854036
$996$	−17.2318	−0.546011
$997$	−43.6145	−1.38129	−0.690643	−	0.723196i	$-0.742672\pi$
$997$	−43.6145	−1.38129	−0.690643	+	0.723196i	$0.742672\pi$
$998$	−56.8729	−1.80028
$999$	−7.62011	−0.241090

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6009.2.a.c.1.10	✓	92

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6009.2.a.c.1.10	✓	92	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:	\( N \)	\(=\)	\( 6009 = 3 \cdot 2003 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6009.a (trivial)

\(f(q)\)	\(=\)	\(q-2.28351 q^{2} +1.00000 q^{3} +3.21443 q^{4} -3.38813 q^{5} -2.28351 q^{6} +0.924728 q^{7} -2.77317 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.28351 q^{2} +1.00000 q^{3} +3.21443 q^{4} -3.38813 q^{5} -2.28351 q^{6} +0.924728 q^{7} -2.77317 q^{8} +1.00000 q^{9} +7.73684 q^{10} +2.68431 q^{11} +3.21443 q^{12} -6.70664 q^{13} -2.11163 q^{14} -3.38813 q^{15} -0.0962944 q^{16} -0.0164547 q^{17} -2.28351 q^{18} -7.70218 q^{19} -10.8909 q^{20} +0.924728 q^{21} -6.12966 q^{22} -3.57269 q^{23} -2.77317 q^{24} +6.47943 q^{25} +15.3147 q^{26} +1.00000 q^{27} +2.97248 q^{28} +5.27171 q^{29} +7.73684 q^{30} -4.70136 q^{31} +5.76623 q^{32} +2.68431 q^{33} +0.0375744 q^{34} -3.13310 q^{35} +3.21443 q^{36} -7.62011 q^{37} +17.5880 q^{38} -6.70664 q^{39} +9.39586 q^{40} -9.02806 q^{41} -2.11163 q^{42} +2.75505 q^{43} +8.62854 q^{44} -3.38813 q^{45} +8.15829 q^{46} -7.79701 q^{47} -0.0962944 q^{48} -6.14488 q^{49} -14.7959 q^{50} -0.0164547 q^{51} -21.5580 q^{52} +3.53242 q^{53} -2.28351 q^{54} -9.09480 q^{55} -2.56443 q^{56} -7.70218 q^{57} -12.0380 q^{58} +12.9231 q^{59} -10.8909 q^{60} +11.1506 q^{61} +10.7356 q^{62} +0.924728 q^{63} -12.9747 q^{64} +22.7230 q^{65} -6.12966 q^{66} -2.86034 q^{67} -0.0528924 q^{68} -3.57269 q^{69} +7.15447 q^{70} +2.73213 q^{71} -2.77317 q^{72} -8.30961 q^{73} +17.4006 q^{74} +6.47943 q^{75} -24.7581 q^{76} +2.48226 q^{77} +15.3147 q^{78} +12.7025 q^{79} +0.326258 q^{80} +1.00000 q^{81} +20.6157 q^{82} -5.36077 q^{83} +2.97248 q^{84} +0.0557506 q^{85} -6.29120 q^{86} +5.27171 q^{87} -7.44406 q^{88} -7.31698 q^{89} +7.73684 q^{90} -6.20182 q^{91} -11.4842 q^{92} -4.70136 q^{93} +17.8046 q^{94} +26.0960 q^{95} +5.76623 q^{96} +1.91774 q^{97} +14.0319 q^{98} +2.68431 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 92 q + 17 q^{2} + 92 q^{3} + 107 q^{4} + 34 q^{5} + 17 q^{6} + 22 q^{7} + 51 q^{8} + 92 q^{9}+O(q^{10}) \) 92 * q + 17 * q^2 + 92 * q^3 + 107 * q^4 + 34 * q^5 + 17 * q^6 + 22 * q^7 + 51 * q^8 + 92 * q^9	\( 92 q + 17 q^{2} + 92 q^{3} + 107 q^{4} + 34 q^{5} + 17 q^{6} + 22 q^{7} + 51 q^{8} + 92 q^{9} + 13 q^{10} + 40 q^{11} + 107 q^{12} + 6 q^{13} + 37 q^{14} + 34 q^{15} + 133 q^{16} + 77 q^{17} + 17 q^{18} + 34 q^{19} + 55 q^{20} + 22 q^{21} + 8 q^{22} + 83 q^{23} + 51 q^{24} + 110 q^{25} + 22 q^{26} + 92 q^{27} + 32 q^{28} + 97 q^{29} + 13 q^{30} + 44 q^{31} + 104 q^{32} + 40 q^{33} + 20 q^{34} + 80 q^{35} + 107 q^{36} + 12 q^{37} + 54 q^{38} + 6 q^{39} + 23 q^{40} + 67 q^{41} + 37 q^{42} + 30 q^{43} + 87 q^{44} + 34 q^{45} + 33 q^{46} + 69 q^{47} + 133 q^{48} + 112 q^{49} + 58 q^{50} + 77 q^{51} - 3 q^{52} + 113 q^{53} + 17 q^{54} + 42 q^{55} + 92 q^{56} + 34 q^{57} - 30 q^{58} + 72 q^{59} + 55 q^{60} + 19 q^{61} + 60 q^{62} + 22 q^{63} + 147 q^{64} + 74 q^{65} + 8 q^{66} + 26 q^{67} + 171 q^{68} + 83 q^{69} - 35 q^{70} + 134 q^{71} + 51 q^{72} - 17 q^{73} + 95 q^{74} + 110 q^{75} + 27 q^{76} + 108 q^{77} + 22 q^{78} + 159 q^{79} + 79 q^{80} + 92 q^{81} - 64 q^{82} + 73 q^{83} + 32 q^{84} - 4 q^{85} + 22 q^{86} + 97 q^{87} - 16 q^{88} + 50 q^{89} + 13 q^{90} + 17 q^{91} + 154 q^{92} + 44 q^{93} + 8 q^{94} + 155 q^{95} + 104 q^{96} - 20 q^{97} + 63 q^{98} + 40 q^{99}+O(q^{100}) \) 92 * q + 17 * q^2 + 92 * q^3 + 107 * q^4 + 34 * q^5 + 17 * q^6 + 22 * q^7 + 51 * q^8 + 92 * q^9 + 13 * q^10 + 40 * q^11 + 107 * q^12 + 6 * q^13 + 37 * q^14 + 34 * q^15 + 133 * q^16 + 77 * q^17 + 17 * q^18 + 34 * q^19 + 55 * q^20 + 22 * q^21 + 8 * q^22 + 83 * q^23 + 51 * q^24 + 110 * q^25 + 22 * q^26 + 92 * q^27 + 32 * q^28 + 97 * q^29 + 13 * q^30 + 44 * q^31 + 104 * q^32 + 40 * q^33 + 20 * q^34 + 80 * q^35 + 107 * q^36 + 12 * q^37 + 54 * q^38 + 6 * q^39 + 23 * q^40 + 67 * q^41 + 37 * q^42 + 30 * q^43 + 87 * q^44 + 34 * q^45 + 33 * q^46 + 69 * q^47 + 133 * q^48 + 112 * q^49 + 58 * q^50 + 77 * q^51 - 3 * q^52 + 113 * q^53 + 17 * q^54 + 42 * q^55 + 92 * q^56 + 34 * q^57 - 30 * q^58 + 72 * q^59 + 55 * q^60 + 19 * q^61 + 60 * q^62 + 22 * q^63 + 147 * q^64 + 74 * q^65 + 8 * q^66 + 26 * q^67 + 171 * q^68 + 83 * q^69 - 35 * q^70 + 134 * q^71 + 51 * q^72 - 17 * q^73 + 95 * q^74 + 110 * q^75 + 27 * q^76 + 108 * q^77 + 22 * q^78 + 159 * q^79 + 79 * q^80 + 92 * q^81 - 64 * q^82 + 73 * q^83 + 32 * q^84 - 4 * q^85 + 22 * q^86 + 97 * q^87 - 16 * q^88 + 50 * q^89 + 13 * q^90 + 17 * q^91 + 154 * q^92 + 44 * q^93 + 8 * q^94 + 155 * q^95 + 104 * q^96 - 20 * q^97 + 63 * q^98 + 40 * q^99

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