LMFDB - Embedded newform 8006.2.a.b.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8006,2,Mod(1,8006)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8006, 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("8006.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8006 = 2 \cdot 4003 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8006.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:	$63.9282318582$
Analytic rank:	$1$
Dimension:	$75$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	8006.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.43887 q^{3} +1.00000 q^{4} +2.67337 q^{5} +2.43887 q^{6} +3.98930 q^{7} -1.00000 q^{8} +2.94808 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.43887 q^{3} +1.00000 q^{4} +2.67337 q^{5} +2.43887 q^{6} +3.98930 q^{7} -1.00000 q^{8} +2.94808 q^{9} -2.67337 q^{10} -1.14354 q^{11} -2.43887 q^{12} -3.98522 q^{13} -3.98930 q^{14} -6.51999 q^{15} +1.00000 q^{16} +1.24784 q^{17} -2.94808 q^{18} +2.66615 q^{19} +2.67337 q^{20} -9.72938 q^{21} +1.14354 q^{22} -3.35887 q^{23} +2.43887 q^{24} +2.14689 q^{25} +3.98522 q^{26} +0.126621 q^{27} +3.98930 q^{28} -3.36291 q^{29} +6.51999 q^{30} -2.46371 q^{31} -1.00000 q^{32} +2.78894 q^{33} -1.24784 q^{34} +10.6649 q^{35} +2.94808 q^{36} -5.33589 q^{37} -2.66615 q^{38} +9.71942 q^{39} -2.67337 q^{40} +0.914017 q^{41} +9.72938 q^{42} -0.524364 q^{43} -1.14354 q^{44} +7.88131 q^{45} +3.35887 q^{46} +6.62269 q^{47} -2.43887 q^{48} +8.91453 q^{49} -2.14689 q^{50} -3.04332 q^{51} -3.98522 q^{52} +10.3536 q^{53} -0.126621 q^{54} -3.05710 q^{55} -3.98930 q^{56} -6.50239 q^{57} +3.36291 q^{58} -6.08696 q^{59} -6.51999 q^{60} +2.32055 q^{61} +2.46371 q^{62} +11.7608 q^{63} +1.00000 q^{64} -10.6539 q^{65} -2.78894 q^{66} -15.6073 q^{67} +1.24784 q^{68} +8.19183 q^{69} -10.6649 q^{70} -4.75242 q^{71} -2.94808 q^{72} +12.8439 q^{73} +5.33589 q^{74} -5.23599 q^{75} +2.66615 q^{76} -4.56192 q^{77} -9.71942 q^{78} -7.75542 q^{79} +2.67337 q^{80} -9.15306 q^{81} -0.914017 q^{82} -11.5504 q^{83} -9.72938 q^{84} +3.33594 q^{85} +0.524364 q^{86} +8.20170 q^{87} +1.14354 q^{88} -8.30924 q^{89} -7.88131 q^{90} -15.8982 q^{91} -3.35887 q^{92} +6.00866 q^{93} -6.62269 q^{94} +7.12760 q^{95} +2.43887 q^{96} -19.2779 q^{97} -8.91453 q^{98} -3.37124 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 75 q - 75 q^{2} + q^{3} + 75 q^{4} - 9 q^{5} - q^{6} - 8 q^{7} - 75 q^{8} + 66 q^{9}+O(q^{10}) $ 75 * q - 75 * q^2 + q^3 + 75 * q^4 - 9 * q^5 - q^6 - 8 * q^7 - 75 * q^8 + 66 * q^9	\( 75 q - 75 q^{2} + q^{3} + 75 q^{4} - 9 q^{5} - q^{6} - 8 q^{7} - 75 q^{8} + 66 q^{9} + 9 q^{10} - 5 q^{11} + q^{12} - 35 q^{13} + 8 q^{14} - 21 q^{15} + 75 q^{16} + 4 q^{17} - 66 q^{18} - 59 q^{19} - 9 q^{20} - 62 q^{21} + 5 q^{22} + 43 q^{23} - q^{24} + 44 q^{25} + 35 q^{26} + 4 q^{27} - 8 q^{28} - 38 q^{29} + 21 q^{30} - 51 q^{31} - 75 q^{32} - 19 q^{33} - 4 q^{34} + 14 q^{35} + 66 q^{36} - 63 q^{37} + 59 q^{38} - 34 q^{39} + 9 q^{40} - 27 q^{41} + 62 q^{42} - 39 q^{43} - 5 q^{44} - 52 q^{45} - 43 q^{46} + 40 q^{47} + q^{48} + 29 q^{49} - 44 q^{50} - 34 q^{51} - 35 q^{52} - 39 q^{53} - 4 q^{54} - 48 q^{55} + 8 q^{56} - 28 q^{57} + 38 q^{58} + 5 q^{59} - 21 q^{60} - 98 q^{61} + 51 q^{62} + 2 q^{63} + 75 q^{64} - q^{65} + 19 q^{66} - 59 q^{67} + 4 q^{68} - 69 q^{69} - 14 q^{70} - 9 q^{71} - 66 q^{72} - 51 q^{73} + 63 q^{74} - q^{75} - 59 q^{76} - 25 q^{77} + 34 q^{78} - 139 q^{79} - 9 q^{80} + 23 q^{81} + 27 q^{82} + 31 q^{83} - 62 q^{84} - 149 q^{85} + 39 q^{86} + q^{87} + 5 q^{88} - 39 q^{89} + 52 q^{90} - 93 q^{91} + 43 q^{92} - 83 q^{93} - 40 q^{94} + 2 q^{95} - q^{96} - 70 q^{97} - 29 q^{98} - 61 q^{99}+O(q^{100}) \) 75 * q - 75 * q^2 + q^3 + 75 * q^4 - 9 * q^5 - q^6 - 8 * q^7 - 75 * q^8 + 66 * q^9 + 9 * q^10 - 5 * q^11 + q^12 - 35 * q^13 + 8 * q^14 - 21 * q^15 + 75 * q^16 + 4 * q^17 - 66 * q^18 - 59 * q^19 - 9 * q^20 - 62 * q^21 + 5 * q^22 + 43 * q^23 - q^24 + 44 * q^25 + 35 * q^26 + 4 * q^27 - 8 * q^28 - 38 * q^29 + 21 * q^30 - 51 * q^31 - 75 * q^32 - 19 * q^33 - 4 * q^34 + 14 * q^35 + 66 * q^36 - 63 * q^37 + 59 * q^38 - 34 * q^39 + 9 * q^40 - 27 * q^41 + 62 * q^42 - 39 * q^43 - 5 * q^44 - 52 * q^45 - 43 * q^46 + 40 * q^47 + q^48 + 29 * q^49 - 44 * q^50 - 34 * q^51 - 35 * q^52 - 39 * q^53 - 4 * q^54 - 48 * q^55 + 8 * q^56 - 28 * q^57 + 38 * q^58 + 5 * q^59 - 21 * q^60 - 98 * q^61 + 51 * q^62 + 2 * q^63 + 75 * q^64 - q^65 + 19 * q^66 - 59 * q^67 + 4 * q^68 - 69 * q^69 - 14 * q^70 - 9 * q^71 - 66 * q^72 - 51 * q^73 + 63 * q^74 - q^75 - 59 * q^76 - 25 * q^77 + 34 * q^78 - 139 * q^79 - 9 * q^80 + 23 * q^81 + 27 * q^82 + 31 * q^83 - 62 * q^84 - 149 * q^85 + 39 * q^86 + q^87 + 5 * q^88 - 39 * q^89 + 52 * q^90 - 93 * q^91 + 43 * q^92 - 83 * q^93 - 40 * q^94 + 2 * q^95 - q^96 - 70 * q^97 - 29 * 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
$3$	−2.43887	−1.40808	−0.704041	−	0.710159i	$-0.748623\pi$
$3$	−2.43887	−1.40808	−0.704041	+	0.710159i	$0.748623\pi$
$4$	1.00000	0.500000
$5$	2.67337	1.19557	0.597783	−	0.801658i	$-0.296048\pi$
$5$	2.67337	1.19557	0.597783	+	0.801658i	$0.296048\pi$
$6$	2.43887	0.995664
$7$	3.98930	1.50781	0.753907	−	0.656981i	$-0.228167\pi$
$7$	3.98930	1.50781	0.753907	+	0.656981i	$0.228167\pi$
$8$	−1.00000	−0.353553
$9$	2.94808	0.982694
$10$	−2.67337	−0.845393
$11$	−1.14354	−0.344790	−0.172395	−	0.985028i	$-0.555151\pi$
$11$	−1.14354	−0.344790	−0.172395	+	0.985028i	$0.555151\pi$
$12$	−2.43887	−0.704041
$13$	−3.98522	−1.10530	−0.552650	−	0.833413i	$-0.686383\pi$
$13$	−3.98522	−1.10530	−0.552650	+	0.833413i	$0.686383\pi$
$14$	−3.98930	−1.06619
$15$	−6.51999	−1.68346
$16$	1.00000	0.250000
$17$	1.24784	0.302646	0.151323	−	0.988484i	$-0.451647\pi$
$17$	1.24784	0.302646	0.151323	+	0.988484i	$0.451647\pi$
$18$	−2.94808	−0.694870
$19$	2.66615	0.611657	0.305828	−	0.952087i	$-0.401067\pi$
$19$	2.66615	0.611657	0.305828	+	0.952087i	$0.401067\pi$
$20$	2.67337	0.597783
$21$	−9.72938	−2.12313
$22$	1.14354	0.243803
$23$	−3.35887	−0.700372	−0.350186	−	0.936680i	$-0.613882\pi$
$23$	−3.35887	−0.700372	−0.350186	+	0.936680i	$0.613882\pi$
$24$	2.43887	0.497832
$25$	2.14689	0.429379
$26$	3.98522	0.781565
$27$	0.126621	0.0243682
$28$	3.98930	0.753907
$29$	−3.36291	−0.624477	−0.312239	−	0.950004i	$-0.601079\pi$
$29$	−3.36291	−0.624477	−0.312239	+	0.950004i	$0.601079\pi$
$30$	6.51999	1.19038
$31$	−2.46371	−0.442495	−0.221247	−	0.975218i	$-0.571013\pi$
$31$	−2.46371	−0.442495	−0.221247	+	0.975218i	$0.571013\pi$
$32$	−1.00000	−0.176777
$33$	2.78894	0.485492
$34$	−1.24784	−0.214003
$35$	10.6649	1.80269
$36$	2.94808	0.491347
$37$	−5.33589	−0.877216	−0.438608	−	0.898679i	$-0.644528\pi$
$37$	−5.33589	−0.877216	−0.438608	+	0.898679i	$0.644528\pi$
$38$	−2.66615	−0.432507
$39$	9.71942	1.55635
$40$	−2.67337	−0.422697
$41$	0.914017	0.142745	0.0713727	−	0.997450i	$-0.477262\pi$
$41$	0.914017	0.142745	0.0713727	+	0.997450i	$0.477262\pi$
$42$	9.72938	1.50128
$43$	−0.524364	−0.0799647	−0.0399824	−	0.999200i	$-0.512730\pi$
$43$	−0.524364	−0.0799647	−0.0399824	+	0.999200i	$0.512730\pi$
$44$	−1.14354	−0.172395
$45$	7.88131	1.17488
$46$	3.35887	0.495238
$47$	6.62269	0.966018	0.483009	−	0.875615i	$-0.339544\pi$
$47$	6.62269	0.966018	0.483009	+	0.875615i	$0.339544\pi$
$48$	−2.43887	−0.352020
$49$	8.91453	1.27350
$50$	−2.14689	−0.303617
$51$	−3.04332	−0.426151
$52$	−3.98522	−0.552650
$53$	10.3536	1.42218	0.711088	−	0.703103i	$-0.248203\pi$
$53$	10.3536	1.42218	0.711088	+	0.703103i	$0.248203\pi$
$54$	−0.126621	−0.0172309
$55$	−3.05710	−0.412219
$56$	−3.98930	−0.533093
$57$	−6.50239	−0.861263
$58$	3.36291	0.441572
$59$	−6.08696	−0.792455	−0.396228	−	0.918152i	$-0.629681\pi$
$59$	−6.08696	−0.792455	−0.396228	+	0.918152i	$0.629681\pi$
$60$	−6.51999	−0.841728
$61$	2.32055	0.297115	0.148558	−	0.988904i	$-0.452537\pi$
$61$	2.32055	0.297115	0.148558	+	0.988904i	$0.452537\pi$
$62$	2.46371	0.312891
$63$	11.7608	1.48172
$64$	1.00000	0.125000
$65$	−10.6539	−1.32146
$66$	−2.78894	−0.343295
$67$	−15.6073	−1.90674	−0.953370	−	0.301804i	$-0.902411\pi$
$67$	−15.6073	−1.90674	−0.953370	+	0.301804i	$0.902411\pi$
$68$	1.24784	0.151323
$69$	8.19183	0.986181
$70$	−10.6649	−1.27470
$71$	−4.75242	−0.564008	−0.282004	−	0.959413i	$-0.590999\pi$
$71$	−4.75242	−0.564008	−0.282004	+	0.959413i	$0.590999\pi$
$72$	−2.94808	−0.347435
$73$	12.8439	1.50327	0.751634	−	0.659581i	$-0.229266\pi$
$73$	12.8439	1.50327	0.751634	+	0.659581i	$0.229266\pi$
$74$	5.33589	0.620285
$75$	−5.23599	−0.604600
$76$	2.66615	0.305828
$77$	−4.56192	−0.519879
$78$	−9.71942	−1.10051
$79$	−7.75542	−0.872553	−0.436276	−	0.899813i	$-0.643703\pi$
$79$	−7.75542	−0.872553	−0.436276	+	0.899813i	$0.643703\pi$
$80$	2.67337	0.298892
$81$	−9.15306	−1.01701
$82$	−0.914017	−0.100936
$83$	−11.5504	−1.26782	−0.633912	−	0.773405i	$-0.718552\pi$
$83$	−11.5504	−1.26782	−0.633912	+	0.773405i	$0.718552\pi$
$84$	−9.72938	−1.06156
$85$	3.33594	0.361834
$86$	0.524364	0.0565436
$87$	8.20170	0.879315
$88$	1.14354	0.121902
$89$	−8.30924	−0.880778	−0.440389	−	0.897807i	$-0.645159\pi$
$89$	−8.30924	−0.880778	−0.440389	+	0.897807i	$0.645159\pi$
$90$	−7.88131	−0.830763
$91$	−15.8982	−1.66659
$92$	−3.35887	−0.350186
$93$	6.00866	0.623069
$94$	−6.62269	−0.683078
$95$	7.12760	0.731276
$96$	2.43887	0.248916
$97$	−19.2779	−1.95738	−0.978688	−	0.205352i	$-0.934166\pi$
$97$	−19.2779	−1.95738	−0.978688	+	0.205352i	$0.934166\pi$
$98$	−8.91453	−0.900503
$99$	−3.37124	−0.338823
$100$	2.14689	0.214689
$101$	−11.2708	−1.12149	−0.560744	−	0.827989i	$-0.689485\pi$
$101$	−11.2708	−1.12149	−0.560744	+	0.827989i	$0.689485\pi$
$102$	3.04332	0.301334
$103$	2.68504	0.264565	0.132283	−	0.991212i	$-0.457769\pi$
$103$	2.68504	0.264565	0.132283	+	0.991212i	$0.457769\pi$
$104$	3.98522	0.390783
$105$	−26.0102	−2.53834
$106$	−10.3536	−1.00563
$107$	2.17939	0.210689	0.105345	−	0.994436i	$-0.466405\pi$
$107$	2.17939	0.210689	0.105345	+	0.994436i	$0.466405\pi$
$108$	0.126621	0.0121841
$109$	13.6444	1.30690	0.653449	−	0.756971i	$-0.273321\pi$
$109$	13.6444	1.30690	0.653449	+	0.756971i	$0.273321\pi$
$110$	3.05710	0.291483
$111$	13.0135	1.23519
$112$	3.98930	0.376954
$113$	−10.6458	−1.00147	−0.500734	−	0.865601i	$-0.666937\pi$
$113$	−10.6458	−1.00147	−0.500734	+	0.865601i	$0.666937\pi$
$114$	6.50239	0.609005
$115$	−8.97948	−0.837341
$116$	−3.36291	−0.312239
$117$	−11.7487	−1.08617
$118$	6.08696	0.560350
$119$	4.97802	0.456334
$120$	6.51999	0.595191
$121$	−9.69232	−0.881120
$122$	−2.32055	−0.210092
$123$	−2.22917	−0.200997
$124$	−2.46371	−0.221247
$125$	−7.62740	−0.682216
$126$	−11.7608	−1.04773
$127$	−8.63798	−0.766497	−0.383249	−	0.923645i	$-0.625195\pi$
$127$	−8.63798	−0.766497	−0.383249	+	0.923645i	$0.625195\pi$
$128$	−1.00000	−0.0883883
$129$	1.27885	0.112597
$130$	10.6539	0.934413
$131$	11.2982	0.987125	0.493563	−	0.869710i	$-0.335694\pi$
$131$	11.2982	0.987125	0.493563	+	0.869710i	$0.335694\pi$
$132$	2.78894	0.242746
$133$	10.6361	0.922265
$134$	15.6073	1.34827
$135$	0.338504	0.0291338
$136$	−1.24784	−0.107002
$137$	−14.8069	−1.26504	−0.632521	−	0.774543i	$-0.717980\pi$
$137$	−14.8069	−1.26504	−0.632521	+	0.774543i	$0.717980\pi$
$138$	−8.19183	−0.697335
$139$	0.591438	0.0501651	0.0250826	−	0.999685i	$-0.492015\pi$
$139$	0.591438	0.0501651	0.0250826	+	0.999685i	$0.492015\pi$
$140$	10.6649	0.901346
$141$	−16.1519	−1.36023
$142$	4.75242	0.398814
$143$	4.55725	0.381096
$144$	2.94808	0.245674
$145$	−8.99030	−0.746604
$146$	−12.8439	−1.06297
$147$	−21.7414	−1.79320
$148$	−5.33589	−0.438608
$149$	9.36652	0.767335	0.383668	−	0.923471i	$-0.374661\pi$
$149$	9.36652	0.767335	0.383668	+	0.923471i	$0.374661\pi$
$150$	5.23599	0.427517
$151$	23.4176	1.90569	0.952847	−	0.303450i	$-0.0981385\pi$
$151$	23.4176	1.90569	0.952847	+	0.303450i	$0.0981385\pi$
$152$	−2.66615	−0.216253
$153$	3.67874	0.297409
$154$	4.56192	0.367610
$155$	−6.58639	−0.529032
$156$	9.71942	0.778176
$157$	−12.0478	−0.961520	−0.480760	−	0.876852i	$-0.659639\pi$
$157$	−12.0478	−0.961520	−0.480760	+	0.876852i	$0.659639\pi$
$158$	7.75542	0.616988
$159$	−25.2511	−2.00254
$160$	−2.67337	−0.211348
$161$	−13.3995	−1.05603
$162$	9.15306	0.719132
$163$	10.6004	0.830291	0.415146	−	0.909755i	$-0.363731\pi$
$163$	10.6004	0.830291	0.415146	+	0.909755i	$0.363731\pi$
$164$	0.914017	0.0713727
$165$	7.45586	0.580438
$166$	11.5504	0.896487
$167$	16.0081	1.23874	0.619370	−	0.785099i	$-0.287388\pi$
$167$	16.0081	1.23874	0.619370	+	0.785099i	$0.287388\pi$
$168$	9.72938	0.750638
$169$	2.88194	0.221688
$170$	−3.33594	−0.255855
$171$	7.86003	0.601071
$172$	−0.524364	−0.0399824
$173$	5.95403	0.452676	0.226338	−	0.974049i	$-0.427325\pi$
$173$	5.95403	0.452676	0.226338	+	0.974049i	$0.427325\pi$
$174$	−8.20170	−0.621769
$175$	8.56461	0.647423
$176$	−1.14354	−0.0861974
$177$	14.8453	1.11584
$178$	8.30924	0.622804
$179$	−10.2288	−0.764538	−0.382269	−	0.924051i	$-0.624857\pi$
$179$	−10.2288	−0.764538	−0.382269	+	0.924051i	$0.624857\pi$
$180$	7.88131	0.587438
$181$	−26.8038	−1.99231	−0.996156	−	0.0875969i	$-0.972081\pi$
$181$	−26.8038	−1.99231	−0.996156	+	0.0875969i	$0.972081\pi$
$182$	15.8982	1.17846
$183$	−5.65951	−0.418363
$184$	3.35887	0.247619
$185$	−14.2648	−1.04877
$186$	−6.00866	−0.440576
$187$	−1.42696	−0.104349
$188$	6.62269	0.483009
$189$	0.505129	0.0367427
$190$	−7.12760	−0.517090
$191$	20.0092	1.44782	0.723909	−	0.689896i	$-0.242344\pi$
$191$	20.0092	1.44782	0.723909	+	0.689896i	$0.242344\pi$
$192$	−2.43887	−0.176010
$193$	4.72279	0.339954	0.169977	−	0.985448i	$-0.445631\pi$
$193$	4.72279	0.339954	0.169977	+	0.985448i	$0.445631\pi$
$194$	19.2779	1.38407
$195$	25.9836	1.86072
$196$	8.91453	0.636752
$197$	14.7863	1.05348	0.526739	−	0.850027i	$-0.323414\pi$
$197$	14.7863	1.05348	0.526739	+	0.850027i	$0.323414\pi$
$198$	3.37124	0.239584
$199$	−25.5361	−1.81021	−0.905103	−	0.425192i	$-0.860207\pi$
$199$	−25.5361	−1.81021	−0.905103	+	0.425192i	$0.860207\pi$
$200$	−2.14689	−0.151808
$201$	38.0643	2.68485
$202$	11.2708	0.793011
$203$	−13.4157	−0.941596
$204$	−3.04332	−0.213075
$205$	2.44350	0.170662
$206$	−2.68504	−0.187076
$207$	−9.90221	−0.688251
$208$	−3.98522	−0.276325
$209$	−3.04884	−0.210893
$210$	26.0102	1.79488
$211$	−27.2832	−1.87825	−0.939126	−	0.343573i	$-0.888363\pi$
$211$	−27.2832	−1.87825	−0.939126	+	0.343573i	$0.888363\pi$
$212$	10.3536	0.711088
$213$	11.5905	0.794170
$214$	−2.17939	−0.148980
$215$	−1.40182	−0.0956031
$216$	−0.126621	−0.00861545
$217$	−9.82847	−0.667200
$218$	−13.6444	−0.924116
$219$	−31.3247	−2.11672
$220$	−3.05710	−0.206109
$221$	−4.97292	−0.334515
$222$	−13.0135	−0.873412
$223$	2.34314	0.156908	0.0784541	−	0.996918i	$-0.475002\pi$
$223$	2.34314	0.156908	0.0784541	+	0.996918i	$0.475002\pi$
$224$	−3.98930	−0.266546
$225$	6.32922	0.421948
$226$	10.6458	0.708145
$227$	7.80687	0.518160	0.259080	−	0.965856i	$-0.416581\pi$
$227$	7.80687	0.518160	0.259080	+	0.965856i	$0.416581\pi$
$228$	−6.50239	−0.430631
$229$	1.01713	0.0672137	0.0336069	−	0.999435i	$-0.489301\pi$
$229$	1.01713	0.0672137	0.0336069	+	0.999435i	$0.489301\pi$
$230$	8.97948	0.592089
$231$	11.1259	0.732032
$232$	3.36291	0.220786
$233$	−7.41651	−0.485872	−0.242936	−	0.970042i	$-0.578111\pi$
$233$	−7.41651	−0.485872	−0.242936	+	0.970042i	$0.578111\pi$
$234$	11.7487	0.768039
$235$	17.7049	1.15494
$236$	−6.08696	−0.396228
$237$	18.9144	1.22863
$238$	−4.97802	−0.322677
$239$	9.82879	0.635772	0.317886	−	0.948129i	$-0.397027\pi$
$239$	9.82879	0.635772	0.317886	+	0.948129i	$0.397027\pi$
$240$	−6.51999	−0.420864
$241$	2.62178	0.168884	0.0844419	−	0.996428i	$-0.473089\pi$
$241$	2.62178	0.168884	0.0844419	+	0.996428i	$0.473089\pi$
$242$	9.69232	0.623046
$243$	21.9432	1.40766
$244$	2.32055	0.148558
$245$	23.8318	1.52256
$246$	2.22917	0.142127
$247$	−10.6252	−0.676064
$248$	2.46371	0.156446
$249$	28.1700	1.78520
$250$	7.62740	0.482399
$251$	−20.9147	−1.32012	−0.660062	−	0.751211i	$-0.729470\pi$
$251$	−20.9147	−1.32012	−0.660062	+	0.751211i	$0.729470\pi$
$252$	11.7608	0.740860
$253$	3.84099	0.241481
$254$	8.63798	0.541995
$255$	−8.13592	−0.509491
$256$	1.00000	0.0625000
$257$	6.28390	0.391979	0.195989	−	0.980606i	$-0.437208\pi$
$257$	6.28390	0.391979	0.195989	+	0.980606i	$0.437208\pi$
$258$	−1.27885	−0.0796180
$259$	−21.2865	−1.32268
$260$	−10.6539	−0.660730
$261$	−9.91414	−0.613670
$262$	−11.2982	−0.698003
$263$	18.6289	1.14871	0.574353	−	0.818608i	$-0.305254\pi$
$263$	18.6289	1.14871	0.574353	+	0.818608i	$0.305254\pi$
$264$	−2.78894	−0.171647
$265$	27.6790	1.70031
$266$	−10.6361	−0.652140
$267$	20.2652	1.24021
$268$	−15.6073	−0.953370
$269$	−18.5404	−1.13043	−0.565214	−	0.824944i	$-0.691206\pi$
$269$	−18.5404	−1.13043	−0.565214	+	0.824944i	$0.691206\pi$
$270$	−0.338504	−0.0206007
$271$	10.3966	0.631551	0.315775	−	0.948834i	$-0.397735\pi$
$271$	10.3966	0.631551	0.315775	+	0.948834i	$0.397735\pi$
$272$	1.24784	0.0756616
$273$	38.7737	2.34669
$274$	14.8069	0.894519
$275$	−2.45506	−0.148045
$276$	8.19183	0.493090
$277$	15.6426	0.939870	0.469935	−	0.882701i	$-0.344277\pi$
$277$	15.6426	0.939870	0.469935	+	0.882701i	$0.344277\pi$
$278$	−0.591438	−0.0354721
$279$	−7.26321	−0.434837
$280$	−10.6649	−0.637348
$281$	22.5010	1.34230	0.671149	−	0.741322i	$-0.265801\pi$
$281$	22.5010	1.34230	0.671149	+	0.741322i	$0.265801\pi$
$282$	16.1519	0.961830
$283$	0.627318	0.0372902	0.0186451	−	0.999826i	$-0.494065\pi$
$283$	0.627318	0.0372902	0.0186451	+	0.999826i	$0.494065\pi$
$284$	−4.75242	−0.282004
$285$	−17.3833	−1.02970
$286$	−4.55725	−0.269476
$287$	3.64629	0.215234
$288$	−2.94808	−0.173717
$289$	−15.4429	−0.908405
$290$	8.99030	0.527929
$291$	47.0163	2.75615
$292$	12.8439	0.751634
$293$	−25.1967	−1.47201	−0.736004	−	0.676977i	$-0.763290\pi$
$293$	−25.1967	−1.47201	−0.736004	+	0.676977i	$0.763290\pi$
$294$	21.7414	1.26798
$295$	−16.2727	−0.947433
$296$	5.33589	0.310143
$297$	−0.144796	−0.00840190
$298$	−9.36652	−0.542588
$299$	13.3858	0.774121
$300$	−5.23599	−0.302300
$301$	−2.09185	−0.120572
$302$	−23.4176	−1.34753
$303$	27.4880	1.57915
$304$	2.66615	0.152914
$305$	6.20367	0.355221
$306$	−3.67874	−0.210300
$307$	−9.10969	−0.519918	−0.259959	−	0.965620i	$-0.583709\pi$
$307$	−9.10969	−0.519918	−0.259959	+	0.965620i	$0.583709\pi$
$308$	−4.56192	−0.259939
$309$	−6.54847	−0.372529
$310$	6.58639	0.374082
$311$	−3.02506	−0.171536	−0.0857678	−	0.996315i	$-0.527334\pi$
$311$	−3.02506	−0.171536	−0.0857678	+	0.996315i	$0.527334\pi$
$312$	−9.71942	−0.550254
$313$	−20.0113	−1.13111	−0.565554	−	0.824711i	$-0.691338\pi$
$313$	−20.0113	−1.13111	−0.565554	+	0.824711i	$0.691338\pi$
$314$	12.0478	0.679897
$315$	31.4409	1.77149
$316$	−7.75542	−0.436276
$317$	−13.3866	−0.751865	−0.375932	−	0.926647i	$-0.622678\pi$
$317$	−13.3866	−0.751865	−0.375932	+	0.926647i	$0.622678\pi$
$318$	25.2511	1.41601
$319$	3.84562	0.215313
$320$	2.67337	0.149446
$321$	−5.31524	−0.296668
$322$	13.3995	0.746726
$323$	3.32693	0.185116
$324$	−9.15306	−0.508503
$325$	−8.55583	−0.474592
$326$	−10.6004	−0.587104
$327$	−33.2769	−1.84022
$328$	−0.914017	−0.0504681
$329$	26.4199	1.45658
$330$	−7.45586	−0.410432
$331$	−11.9226	−0.655325	−0.327663	−	0.944795i	$-0.606261\pi$
$331$	−11.9226	−0.655325	−0.327663	+	0.944795i	$0.606261\pi$
$332$	−11.5504	−0.633912
$333$	−15.7307	−0.862035
$334$	−16.0081	−0.875922
$335$	−41.7241	−2.27963
$336$	−9.72938	−0.530781
$337$	20.7474	1.13018	0.565092	−	0.825028i	$-0.308841\pi$
$337$	20.7474	1.13018	0.565092	+	0.825028i	$0.308841\pi$
$338$	−2.88194	−0.156757
$339$	25.9636	1.41015
$340$	3.33594	0.180917
$341$	2.81734	0.152568
$342$	−7.86003	−0.425022
$343$	7.63763	0.412393
$344$	0.524364	0.0282718
$345$	21.8998	1.17904
$346$	−5.95403	−0.320090
$347$	−1.48931	−0.0799503	−0.0399752	−	0.999201i	$-0.512728\pi$
$347$	−1.48931	−0.0799503	−0.0399752	+	0.999201i	$0.512728\pi$
$348$	8.20170	0.439657
$349$	2.44592	0.130927	0.0654635	−	0.997855i	$-0.479147\pi$
$349$	2.44592	0.130927	0.0654635	+	0.997855i	$0.479147\pi$
$350$	−8.56461	−0.457798
$351$	−0.504611	−0.0269341
$352$	1.14354	0.0609508
$353$	−3.29034	−0.175127	−0.0875636	−	0.996159i	$-0.527908\pi$
$353$	−3.29034	−0.175127	−0.0875636	+	0.996159i	$0.527908\pi$
$354$	−14.8453	−0.789019
$355$	−12.7050	−0.674309
$356$	−8.30924	−0.440389
$357$	−12.1407	−0.642556
$358$	10.2288	0.540610
$359$	32.0632	1.69223	0.846116	−	0.532998i	$-0.178935\pi$
$359$	32.0632	1.69223	0.846116	+	0.532998i	$0.178935\pi$
$360$	−7.88131	−0.415381
$361$	−11.8916	−0.625876
$362$	26.8038	1.40878
$363$	23.6383	1.24069
$364$	−15.8982	−0.833294
$365$	34.3365	1.79726
$366$	5.65951	0.295827
$367$	27.4272	1.43169	0.715844	−	0.698260i	$-0.246042\pi$
$367$	27.4272	1.43169	0.715844	+	0.698260i	$0.246042\pi$
$368$	−3.35887	−0.175093
$369$	2.69460	0.140275
$370$	14.2648	0.741592
$371$	41.3036	2.14438
$372$	6.00866	0.311534
$373$	25.0642	1.29778	0.648888	−	0.760884i	$-0.275235\pi$
$373$	25.0642	1.29778	0.648888	+	0.760884i	$0.275235\pi$
$374$	1.42696	0.0737861
$375$	18.6022	0.960615
$376$	−6.62269	−0.341539
$377$	13.4019	0.690234
$378$	−0.505129	−0.0259810
$379$	−4.52362	−0.232363	−0.116181	−	0.993228i	$-0.537065\pi$
$379$	−4.52362	−0.232363	−0.116181	+	0.993228i	$0.537065\pi$
$380$	7.12760	0.365638
$381$	21.0669	1.07929
$382$	−20.0092	−1.02376
$383$	35.4087	1.80930	0.904650	−	0.426156i	$-0.140133\pi$
$383$	35.4087	1.80930	0.904650	+	0.426156i	$0.140133\pi$
$384$	2.43887	0.124458
$385$	−12.1957	−0.621550
$386$	−4.72279	−0.240384
$387$	−1.54587	−0.0785809
$388$	−19.2779	−0.978688
$389$	−21.4506	−1.08759	−0.543796	−	0.839218i	$-0.683013\pi$
$389$	−21.4506	−1.08759	−0.543796	+	0.839218i	$0.683013\pi$
$390$	−25.9836	−1.31573
$391$	−4.19133	−0.211965
$392$	−8.91453	−0.450252
$393$	−27.5548	−1.38995
$394$	−14.7863	−0.744922
$395$	−20.7331	−1.04319
$396$	−3.37124	−0.169411
$397$	−31.2177	−1.56677	−0.783386	−	0.621535i	$-0.786509\pi$
$397$	−31.2177	−1.56677	−0.783386	+	0.621535i	$0.786509\pi$
$398$	25.5361	1.28001
$399$	−25.9400	−1.29862
$400$	2.14689	0.107345
$401$	−17.2817	−0.863009	−0.431505	−	0.902111i	$-0.642017\pi$
$401$	−17.2817	−0.863009	−0.431505	+	0.902111i	$0.642017\pi$
$402$	−38.0643	−1.89847
$403$	9.81840	0.489090
$404$	−11.2708	−0.560744
$405$	−24.4695	−1.21590
$406$	13.4157	0.665809
$407$	6.10180	0.302455
$408$	3.04332	0.150667
$409$	−12.2586	−0.606151	−0.303075	−	0.952967i	$-0.598013\pi$
$409$	−12.2586	−0.606151	−0.303075	+	0.952967i	$0.598013\pi$
$410$	−2.44350	−0.120676
$411$	36.1122	1.78128
$412$	2.68504	0.132283
$413$	−24.2827	−1.19488
$414$	9.90221	0.486667
$415$	−30.8785	−1.51577
$416$	3.98522	0.195391
$417$	−1.44244	−0.0706366
$418$	3.04884	0.149124
$419$	2.40955	0.117714	0.0588571	−	0.998266i	$-0.481254\pi$
$419$	2.40955	0.117714	0.0588571	+	0.998266i	$0.481254\pi$
$420$	−26.0102	−1.26917
$421$	23.1329	1.12743	0.563714	−	0.825970i	$-0.309372\pi$
$421$	23.1329	1.12743	0.563714	+	0.825970i	$0.309372\pi$
$422$	27.2832	1.32812
$423$	19.5242	0.949301
$424$	−10.3536	−0.502815
$425$	2.67899	0.129950
$426$	−11.5905	−0.561563
$427$	9.25735	0.447995
$428$	2.17939	0.105345
$429$	−11.1145	−0.536614
$430$	1.40182	0.0676016
$431$	32.9800	1.58859	0.794295	−	0.607532i	$-0.207840\pi$
$431$	32.9800	1.58859	0.794295	+	0.607532i	$0.207840\pi$
$432$	0.126621	0.00609205
$433$	6.75473	0.324612	0.162306	−	0.986740i	$-0.448107\pi$
$433$	6.75473	0.324612	0.162306	+	0.986740i	$0.448107\pi$
$434$	9.82847	0.471782
$435$	21.9262	1.05128
$436$	13.6444	0.653449
$437$	−8.95524	−0.428387
$438$	31.3247	1.49675
$439$	15.6103	0.745037	0.372519	−	0.928025i	$-0.378494\pi$
$439$	15.6103	0.745037	0.372519	+	0.928025i	$0.378494\pi$
$440$	3.05710	0.145741
$441$	26.2808	1.25146
$442$	4.97292	0.236538
$443$	33.1038	1.57281	0.786403	−	0.617713i	$-0.211941\pi$
$443$	33.1038	1.57281	0.786403	+	0.617713i	$0.211941\pi$
$444$	13.0135	0.617596
$445$	−22.2137	−1.05303
$446$	−2.34314	−0.110951
$447$	−22.8437	−1.08047
$448$	3.98930	0.188477
$449$	−26.2263	−1.23770	−0.618848	−	0.785510i	$-0.712400\pi$
$449$	−26.2263	−1.23770	−0.618848	+	0.785510i	$0.712400\pi$
$450$	−6.32922	−0.298362
$451$	−1.04521	−0.0492172
$452$	−10.6458	−0.500734
$453$	−57.1124	−2.68337
$454$	−7.80687	−0.366395
$455$	−42.5018	−1.99252
$456$	6.50239	0.304502
$457$	−5.18810	−0.242689	−0.121345	−	0.992610i	$-0.538721\pi$
$457$	−5.18810	−0.242689	−0.121345	+	0.992610i	$0.538721\pi$
$458$	−1.01713	−0.0475273
$459$	0.158003	0.00737494
$460$	−8.97948	−0.418670
$461$	−0.439060	−0.0204490	−0.0102245	−	0.999948i	$-0.503255\pi$
$461$	−0.439060	−0.0204490	−0.0102245	+	0.999948i	$0.503255\pi$
$462$	−11.1259	−0.517625
$463$	−12.0161	−0.558436	−0.279218	−	0.960228i	$-0.590075\pi$
$463$	−12.0161	−0.558436	−0.279218	+	0.960228i	$0.590075\pi$
$464$	−3.36291	−0.156119
$465$	16.0634	0.744920
$466$	7.41651	0.343563
$467$	−1.33601	−0.0618231	−0.0309116	−	0.999522i	$-0.509841\pi$
$467$	−1.33601	−0.0618231	−0.0309116	+	0.999522i	$0.509841\pi$
$468$	−11.7487	−0.543086
$469$	−62.2624	−2.87501
$470$	−17.7049	−0.816665
$471$	29.3830	1.35390
$472$	6.08696	0.280175
$473$	0.599630	0.0275710
$474$	−18.9144	−0.868769
$475$	5.72394	0.262632
$476$	4.97802	0.228167
$477$	30.5233	1.39756
$478$	−9.82879	−0.449559
$479$	−28.0143	−1.28001	−0.640004	−	0.768371i	$-0.721067\pi$
$479$	−28.0143	−1.28001	−0.640004	+	0.768371i	$0.721067\pi$
$480$	6.51999	0.297596
$481$	21.2647	0.969586
$482$	−2.62178	−0.119419
$483$	32.6797	1.48698
$484$	−9.69232	−0.440560
$485$	−51.5370	−2.34017
$486$	−21.9432	−0.995366
$487$	−21.3477	−0.967357	−0.483678	−	0.875246i	$-0.660700\pi$
$487$	−21.3477	−0.967357	−0.483678	+	0.875246i	$0.660700\pi$
$488$	−2.32055	−0.105046
$489$	−25.8531	−1.16912
$490$	−23.8318	−1.07661
$491$	−22.0934	−0.997063	−0.498531	−	0.866872i	$-0.666127\pi$
$491$	−22.0934	−0.997063	−0.498531	+	0.866872i	$0.666127\pi$
$492$	−2.22917	−0.100499
$493$	−4.19638	−0.188996
$494$	10.6252	0.478050
$495$	−9.01258	−0.405085
$496$	−2.46371	−0.110624
$497$	−18.9588	−0.850420
$498$	−28.1700	−1.26233
$499$	−14.3327	−0.641619	−0.320809	−	0.947144i	$-0.603955\pi$
$499$	−14.3327	−0.641619	−0.320809	+	0.947144i	$0.603955\pi$
$500$	−7.62740	−0.341108
$501$	−39.0416	−1.74425
$502$	20.9147	0.933469
$503$	2.30669	0.102850	0.0514252	−	0.998677i	$-0.483624\pi$
$503$	2.30669	0.102850	0.0514252	+	0.998677i	$0.483624\pi$
$504$	−11.7608	−0.523867
$505$	−30.1310	−1.34081
$506$	−3.84099	−0.170753
$507$	−7.02868	−0.312155
$508$	−8.63798	−0.383249
$509$	−34.4415	−1.52659	−0.763296	−	0.646048i	$-0.776420\pi$
$509$	−34.4415	−1.52659	−0.763296	+	0.646048i	$0.776420\pi$
$510$	8.13592	0.360265
$511$	51.2383	2.26665
$512$	−1.00000	−0.0441942
$513$	0.337590	0.0149050
$514$	−6.28390	−0.277171
$515$	7.17811	0.316305
$516$	1.27885	0.0562984
$517$	−7.57330	−0.333073
$518$	21.2865	0.935275
$519$	−14.5211	−0.637405
$520$	10.6539	0.467206
$521$	28.2141	1.23608	0.618041	−	0.786146i	$-0.287926\pi$
$521$	28.2141	1.23608	0.618041	+	0.786146i	$0.287926\pi$
$522$	9.91414	0.433930
$523$	4.19647	0.183499	0.0917494	−	0.995782i	$-0.470754\pi$
$523$	4.19647	0.183499	0.0917494	+	0.995782i	$0.470754\pi$
$524$	11.2982	0.493563
$525$	−20.8880	−0.911625
$526$	−18.6289	−0.812258
$527$	−3.07432	−0.133919
$528$	2.78894	0.121373
$529$	−11.7180	−0.509479
$530$	−27.6790	−1.20230
$531$	−17.9449	−0.778741
$532$	10.6361	0.461132
$533$	−3.64255	−0.157777
$534$	−20.2652	−0.876959
$535$	5.82631	0.251893
$536$	15.6073	0.674134
$537$	24.9467	1.07653
$538$	18.5404	0.799333
$539$	−10.1941	−0.439091
$540$	0.338504	0.0145669
$541$	12.8466	0.552320	0.276160	−	0.961112i	$-0.410938\pi$
$541$	12.8466	0.552320	0.276160	+	0.961112i	$0.410938\pi$
$542$	−10.3966	−0.446574
$543$	65.3710	2.80534
$544$	−1.24784	−0.0535008
$545$	36.4765	1.56248
$546$	−38.7737	−1.65936
$547$	−36.0404	−1.54098	−0.770489	−	0.637453i	$-0.779988\pi$
$547$	−36.0404	−1.54098	−0.770489	+	0.637453i	$0.779988\pi$
$548$	−14.8069	−0.632521
$549$	6.84116	0.291973
$550$	2.45506	0.104684
$551$	−8.96603	−0.381966
$552$	−8.19183	−0.348668
$553$	−30.9387	−1.31565
$554$	−15.6426	−0.664589
$555$	34.7900	1.47675
$556$	0.591438	0.0250826
$557$	−28.2152	−1.19552	−0.597759	−	0.801676i	$-0.703942\pi$
$557$	−28.2152	−1.19552	−0.597759	+	0.801676i	$0.703942\pi$
$558$	7.26321	0.307476
$559$	2.08970	0.0883850
$560$	10.6649	0.450673
$561$	3.48016	0.146932
$562$	−22.5010	−0.949148
$563$	−0.289451	−0.0121989	−0.00609944	−	0.999981i	$-0.501942\pi$
$563$	−0.289451	−0.0121989	−0.00609944	+	0.999981i	$0.501942\pi$
$564$	−16.1519	−0.680116
$565$	−28.4600	−1.19732
$566$	−0.627318	−0.0263681
$567$	−36.5143	−1.53346
$568$	4.75242	0.199407
$569$	−3.61992	−0.151755	−0.0758775	−	0.997117i	$-0.524176\pi$
$569$	−3.61992	−0.151755	−0.0758775	+	0.997117i	$0.524176\pi$
$570$	17.3833	0.728105
$571$	24.8557	1.04018	0.520089	−	0.854112i	$-0.325899\pi$
$571$	24.8557	1.04018	0.520089	+	0.854112i	$0.325899\pi$
$572$	4.55725	0.190548
$573$	−48.7999	−2.03864
$574$	−3.64629	−0.152193
$575$	−7.21113	−0.300725
$576$	2.94808	0.122837
$577$	−3.99845	−0.166458	−0.0832288	−	0.996530i	$-0.526523\pi$
$577$	−3.99845	−0.166458	−0.0832288	+	0.996530i	$0.526523\pi$
$578$	15.4429	0.642340
$579$	−11.5183	−0.478683
$580$	−8.99030	−0.373302
$581$	−46.0782	−1.91164
$582$	−47.0163	−1.94889
$583$	−11.8397	−0.490352
$584$	−12.8439	−0.531485
$585$	−31.4087	−1.29859
$586$	25.1967	1.04087
$587$	29.0695	1.19983	0.599913	−	0.800065i	$-0.295202\pi$
$587$	29.0695	1.19983	0.599913	+	0.800065i	$0.295202\pi$
$588$	−21.7414	−0.896599
$589$	−6.56861	−0.270655
$590$	16.2727	0.669936
$591$	−36.0618	−1.48338
$592$	−5.33589	−0.219304
$593$	−39.3175	−1.61458	−0.807288	−	0.590158i	$-0.799065\pi$
$593$	−39.3175	−1.61458	−0.807288	+	0.590158i	$0.799065\pi$
$594$	0.144796	0.00594104
$595$	13.3081	0.545578
$596$	9.36652	0.383668
$597$	62.2792	2.54892
$598$	−13.3858	−0.547386
$599$	−14.1308	−0.577367	−0.288684	−	0.957425i	$-0.593218\pi$
$599$	−14.1308	−0.577367	−0.288684	+	0.957425i	$0.593218\pi$
$600$	5.23599	0.213759
$601$	−32.7253	−1.33489	−0.667447	−	0.744657i	$-0.732613\pi$
$601$	−32.7253	−1.33489	−0.667447	+	0.744657i	$0.732613\pi$
$602$	2.09185	0.0852573
$603$	−46.0117	−1.87374
$604$	23.4176	0.952847
$605$	−25.9111	−1.05344
$606$	−27.4880	−1.11662
$607$	−14.3243	−0.581405	−0.290702	−	0.956814i	$-0.593889\pi$
$607$	−14.3243	−0.581405	−0.290702	+	0.956814i	$0.593889\pi$
$608$	−2.66615	−0.108127
$609$	32.7191	1.32584
$610$	−6.20367	−0.251179
$611$	−26.3928	−1.06774
$612$	3.67874	0.148704
$613$	−41.2703	−1.66689	−0.833446	−	0.552601i	$-0.813635\pi$
$613$	−41.2703	−1.66689	−0.833446	+	0.552601i	$0.813635\pi$
$614$	9.10969	0.367637
$615$	−5.95938	−0.240306
$616$	4.56192	0.183805
$617$	45.2227	1.82060	0.910298	−	0.413953i	$-0.135852\pi$
$617$	45.2227	1.82060	0.910298	+	0.413953i	$0.135852\pi$
$618$	6.54847	0.263418
$619$	−29.4615	−1.18416	−0.592078	−	0.805880i	$-0.701692\pi$
$619$	−29.4615	−1.18416	−0.592078	+	0.805880i	$0.701692\pi$
$620$	−6.58639	−0.264516
$621$	−0.425302	−0.0170668
$622$	3.02506	0.121294
$623$	−33.1481	−1.32805
$624$	9.71942	0.389088
$625$	−31.1253	−1.24501
$626$	20.0113	0.799814
$627$	7.43573	0.296954
$628$	−12.0478	−0.480760
$629$	−6.65836	−0.265486
$630$	−31.4409	−1.25264
$631$	16.0615	0.639399	0.319699	−	0.947519i	$-0.396418\pi$
$631$	16.0615	0.639399	0.319699	+	0.947519i	$0.396418\pi$
$632$	7.75542	0.308494
$633$	66.5401	2.64473
$634$	13.3866	0.531649
$635$	−23.0925	−0.916398
$636$	−25.2511	−1.00127
$637$	−35.5263	−1.40760
$638$	−3.84562	−0.152249
$639$	−14.0105	−0.554247
$640$	−2.67337	−0.105674
$641$	−10.0421	−0.396640	−0.198320	−	0.980137i	$-0.563549\pi$
$641$	−10.0421	−0.396640	−0.198320	+	0.980137i	$0.563549\pi$
$642$	5.31524	0.209776
$643$	6.13568	0.241968	0.120984	−	0.992654i	$-0.461395\pi$
$643$	6.13568	0.241968	0.120984	+	0.992654i	$0.461395\pi$
$644$	−13.3995	−0.528015
$645$	3.41885	0.134617
$646$	−3.32693	−0.130896
$647$	12.9385	0.508665	0.254332	−	0.967117i	$-0.418144\pi$
$647$	12.9385	0.508665	0.254332	+	0.967117i	$0.418144\pi$
$648$	9.15306	0.359566
$649$	6.96068	0.273230
$650$	8.55583	0.335587
$651$	23.9704	0.939472
$652$	10.6004	0.415146
$653$	−21.7189	−0.849927	−0.424963	−	0.905210i	$-0.639713\pi$
$653$	−21.7189	−0.849927	−0.424963	+	0.905210i	$0.639713\pi$
$654$	33.2769	1.30123
$655$	30.2042	1.18017
$656$	0.914017	0.0356864
$657$	37.8649	1.47725
$658$	−26.4199	−1.02996
$659$	40.1802	1.56520	0.782599	−	0.622527i	$-0.213894\pi$
$659$	40.1802	1.56520	0.782599	+	0.622527i	$0.213894\pi$
$660$	7.45586	0.290219
$661$	18.8491	0.733147	0.366573	−	0.930389i	$-0.380531\pi$
$661$	18.8491	0.733147	0.366573	+	0.930389i	$0.380531\pi$
$662$	11.9226	0.463385
$663$	12.1283	0.471024
$664$	11.5504	0.448244
$665$	28.4341	1.10263
$666$	15.7307	0.609551
$667$	11.2956	0.437366
$668$	16.0081	0.619370
$669$	−5.71461	−0.220940
$670$	41.7241	1.61194
$671$	−2.65363	−0.102442
$672$	9.72938	0.375319
$673$	−11.8606	−0.457193	−0.228596	−	0.973521i	$-0.573414\pi$
$673$	−11.8606	−0.457193	−0.228596	+	0.973521i	$0.573414\pi$
$674$	−20.7474	−0.799161
$675$	0.271841	0.0104632
$676$	2.88194	0.110844
$677$	−36.4092	−1.39932	−0.699659	−	0.714477i	$-0.746665\pi$
$677$	−36.4092	−1.39932	−0.699659	+	0.714477i	$0.746665\pi$
$678$	−25.9636	−0.997126
$679$	−76.9054	−2.95136
$680$	−3.33594	−0.127928
$681$	−19.0399	−0.729612
$682$	−2.81734	−0.107882
$683$	25.4454	0.973641	0.486821	−	0.873502i	$-0.338157\pi$
$683$	25.4454	0.973641	0.486821	+	0.873502i	$0.338157\pi$
$684$	7.86003	0.300536
$685$	−39.5844	−1.51244
$686$	−7.63763	−0.291606
$687$	−2.48064	−0.0946424
$688$	−0.524364	−0.0199912
$689$	−41.2613	−1.57193
$690$	−21.8998	−0.833710
$691$	29.5371	1.12365	0.561823	−	0.827258i	$-0.310100\pi$
$691$	29.5371	1.12365	0.561823	+	0.827258i	$0.310100\pi$
$692$	5.95403	0.226338
$693$	−13.4489	−0.510882
$694$	1.48931	0.0565334
$695$	1.58113	0.0599757
$696$	−8.20170	−0.310885
$697$	1.14055	0.0432014
$698$	−2.44592	−0.0925794
$699$	18.0879	0.684147
$700$	8.56461	0.323712
$701$	6.18713	0.233685	0.116842	−	0.993150i	$-0.462723\pi$
$701$	6.18713	0.233685	0.116842	+	0.993150i	$0.462723\pi$
$702$	0.504611	0.0190453
$703$	−14.2263	−0.536555
$704$	−1.14354	−0.0430987
$705$	−43.1799	−1.62625
$706$	3.29034	0.123834
$707$	−44.9627	−1.69099
$708$	14.8453	0.557921
$709$	8.47415	0.318254	0.159127	−	0.987258i	$-0.449132\pi$
$709$	8.47415	0.318254	0.159127	+	0.987258i	$0.449132\pi$
$710$	12.7050	0.476809
$711$	−22.8636	−0.857452
$712$	8.30924	0.311402
$713$	8.27526	0.309911
$714$	12.1407	0.454356
$715$	12.1832	0.455626
$716$	−10.2288	−0.382269
$717$	−23.9711	−0.895219
$718$	−32.0632	−1.19659
$719$	−19.8403	−0.739917	−0.369959	−	0.929048i	$-0.620628\pi$
$719$	−19.8403	−0.739917	−0.369959	+	0.929048i	$0.620628\pi$
$720$	7.88131	0.293719
$721$	10.7115	0.398915
$722$	11.8916	0.442561
$723$	−6.39418	−0.237802
$724$	−26.8038	−0.996156
$725$	−7.21982	−0.268137
$726$	−23.6383	−0.877300
$727$	−15.1470	−0.561772	−0.280886	−	0.959741i	$-0.590628\pi$
$727$	−15.1470	−0.561772	−0.280886	+	0.959741i	$0.590628\pi$
$728$	15.8982	0.589228
$729$	−26.0575	−0.965094
$730$	−34.3365	−1.27085
$731$	−0.654323	−0.0242010
$732$	−5.65951	−0.209181
$733$	9.34690	0.345236	0.172618	−	0.984989i	$-0.444777\pi$
$733$	9.34690	0.345236	0.172618	+	0.984989i	$0.444777\pi$
$734$	−27.4272	−1.01236
$735$	−58.1227	−2.14389
$736$	3.35887	0.123809
$737$	17.8476	0.657424
$738$	−2.69460	−0.0991895
$739$	−44.1572	−1.62435	−0.812175	−	0.583414i	$-0.801717\pi$
$739$	−44.1572	−1.62435	−0.812175	+	0.583414i	$0.801717\pi$
$740$	−14.2648	−0.524385
$741$	25.9134	0.951953
$742$	−41.3036	−1.51630
$743$	25.5551	0.937527	0.468764	−	0.883324i	$-0.344700\pi$
$743$	25.5551	0.937527	0.468764	+	0.883324i	$0.344700\pi$
$744$	−6.00866	−0.220288
$745$	25.0401	0.917400
$746$	−25.0642	−0.917666
$747$	−34.0516	−1.24588
$748$	−1.42696	−0.0521747
$749$	8.69424	0.317681
$750$	−18.6022	−0.679257
$751$	22.4676	0.819854	0.409927	−	0.912118i	$-0.365554\pi$
$751$	22.4676	0.819854	0.409927	+	0.912118i	$0.365554\pi$
$752$	6.62269	0.241505
$753$	51.0082	1.85884
$754$	−13.4019	−0.488069
$755$	62.6038	2.27838
$756$	0.505129	0.0183713
$757$	2.03241	0.0738691	0.0369346	−	0.999318i	$-0.488241\pi$
$757$	2.03241	0.0738691	0.0369346	+	0.999318i	$0.488241\pi$
$758$	4.52362	0.164305
$759$	−9.36767	−0.340025
$760$	−7.12760	−0.258545
$761$	48.9683	1.77510	0.887549	−	0.460714i	$-0.152406\pi$
$761$	48.9683	1.77510	0.887549	+	0.460714i	$0.152406\pi$
$762$	−21.0669	−0.763174
$763$	54.4317	1.97056
$764$	20.0092	0.723909
$765$	9.83463	0.355572
$766$	−35.4087	−1.27937
$767$	24.2579	0.875901
$768$	−2.43887	−0.0880051
$769$	−17.8819	−0.644837	−0.322418	−	0.946597i	$-0.604496\pi$
$769$	−17.8819	−0.644837	−0.322418	+	0.946597i	$0.604496\pi$
$770$	12.1957	0.439502
$771$	−15.3256	−0.551938
$772$	4.72279	0.169977
$773$	−54.9037	−1.97475	−0.987374	−	0.158405i	$-0.949365\pi$
$773$	−54.9037	−1.97475	−0.987374	+	0.158405i	$0.949365\pi$
$774$	1.54587	0.0555651
$775$	−5.28932	−0.189998
$776$	19.2779	0.692037
$777$	51.9150	1.86244
$778$	21.4506	0.769043
$779$	2.43691	0.0873112
$780$	25.9836	0.930361
$781$	5.43457	0.194464
$782$	4.19133	0.149882
$783$	−0.425815	−0.0152174
$784$	8.91453	0.318376
$785$	−32.2082	−1.14956
$786$	27.5548	0.982845
$787$	−17.3942	−0.620035	−0.310017	−	0.950731i	$-0.600335\pi$
$787$	−17.3942	−0.620035	−0.310017	+	0.950731i	$0.600335\pi$
$788$	14.7863	0.526739
$789$	−45.4334	−1.61747
$790$	20.7331	0.737650
$791$	−42.4691	−1.51003
$792$	3.37124	0.119792
$793$	−9.24787	−0.328402
$794$	31.2177	1.10788
$795$	−67.5054	−2.39417
$796$	−25.5361	−0.905103
$797$	41.6371	1.47486	0.737432	−	0.675422i	$-0.236038\pi$
$797$	41.6371	1.47486	0.737432	+	0.675422i	$0.236038\pi$
$798$	25.9400	0.918266
$799$	8.26407	0.292362
$800$	−2.14689	−0.0759042
$801$	−24.4963	−0.865535
$802$	17.2817	0.610240
$803$	−14.6875	−0.518311
$804$	38.0643	1.34242
$805$	−35.8219	−1.26255
$806$	−9.81840	−0.345839
$807$	45.2176	1.59174
$808$	11.2708	0.396506
$809$	7.23291	0.254296	0.127148	−	0.991884i	$-0.459418\pi$
$809$	7.23291	0.254296	0.127148	+	0.991884i	$0.459418\pi$
$810$	24.4695	0.859770
$811$	−53.0999	−1.86459	−0.932294	−	0.361701i	$-0.882196\pi$
$811$	−53.0999	−1.86459	−0.932294	+	0.361701i	$0.882196\pi$
$812$	−13.4157	−0.470798
$813$	−25.3560	−0.889275
$814$	−6.10180	−0.213868
$815$	28.3389	0.992668
$816$	−3.04332	−0.106538
$817$	−1.39803	−0.0489110
$818$	12.2586	0.428613
$819$	−46.8693	−1.63775
$820$	2.44350	0.0853308
$821$	−38.8679	−1.35650	−0.678250	−	0.734831i	$-0.737262\pi$
$821$	−38.8679	−1.35650	−0.678250	+	0.734831i	$0.737262\pi$
$822$	−36.1122	−1.25956
$823$	55.5839	1.93753	0.968767	−	0.247973i	$-0.0797644\pi$
$823$	55.5839	1.93753	0.968767	+	0.247973i	$0.0797644\pi$
$824$	−2.68504	−0.0935379
$825$	5.98756	0.208460
$826$	24.2827	0.844904
$827$	8.29979	0.288612	0.144306	−	0.989533i	$-0.453905\pi$
$827$	8.29979	0.288612	0.144306	+	0.989533i	$0.453905\pi$
$828$	−9.90221	−0.344126
$829$	−9.10275	−0.316152	−0.158076	−	0.987427i	$-0.550529\pi$
$829$	−9.10275	−0.316152	−0.158076	+	0.987427i	$0.550529\pi$
$830$	30.8785	1.07181
$831$	−38.1501	−1.32341
$832$	−3.98522	−0.138162
$833$	11.1239	0.385421
$834$	1.44244	0.0499476
$835$	42.7954	1.48100
$836$	−3.04884	−0.105446
$837$	−0.311957	−0.0107828
$838$	−2.40955	−0.0832365
$839$	−3.78593	−0.130705	−0.0653525	−	0.997862i	$-0.520817\pi$
$839$	−3.78593	−0.130705	−0.0653525	+	0.997862i	$0.520817\pi$
$840$	26.0102	0.897438
$841$	−17.6908	−0.610028
$842$	−23.1329	−0.797212
$843$	−54.8770	−1.89007
$844$	−27.2832	−0.939126
$845$	7.70449	0.265043
$846$	−19.5242	−0.671257
$847$	−38.6656	−1.32857
$848$	10.3536	0.355544
$849$	−1.52995	−0.0525076
$850$	−2.67899	−0.0918884
$851$	17.9226	0.614377
$852$	11.5905	0.397085
$853$	33.9806	1.16347	0.581736	−	0.813377i	$-0.302373\pi$
$853$	33.9806	1.16347	0.581736	+	0.813377i	$0.302373\pi$
$854$	−9.25735	−0.316780
$855$	21.0127	0.718621
$856$	−2.17939	−0.0744900
$857$	−9.77787	−0.334006	−0.167003	−	0.985956i	$-0.553409\pi$
$857$	−9.77787	−0.334006	−0.167003	+	0.985956i	$0.553409\pi$
$858$	11.1145	0.379444
$859$	−26.4207	−0.901462	−0.450731	−	0.892660i	$-0.648837\pi$
$859$	−26.4207	−0.901462	−0.450731	+	0.892660i	$0.648837\pi$
$860$	−1.40182	−0.0478016
$861$	−8.89282	−0.303067
$862$	−32.9800	−1.12330
$863$	0.351775	0.0119746	0.00598729	−	0.999982i	$-0.498094\pi$
$863$	0.351775	0.0119746	0.00598729	+	0.999982i	$0.498094\pi$
$864$	−0.126621	−0.00430773
$865$	15.9173	0.541204
$866$	−6.75473	−0.229535
$867$	37.6632	1.27911
$868$	−9.82847	−0.333600
$869$	8.86862	0.300847
$870$	−21.9262	−0.743367
$871$	62.1986	2.10752
$872$	−13.6444	−0.462058
$873$	−56.8329	−1.92350
$874$	8.95524	0.302915
$875$	−30.4280	−1.02865
$876$	−31.3247	−1.05836
$877$	32.1011	1.08398	0.541988	−	0.840386i	$-0.317672\pi$
$877$	32.1011	1.08398	0.541988	+	0.840386i	$0.317672\pi$
$878$	−15.6103	−0.526821
$879$	61.4515	2.07271
$880$	−3.05710	−0.103055
$881$	−29.4569	−0.992427	−0.496213	−	0.868201i	$-0.665277\pi$
$881$	−29.4569	−0.992427	−0.496213	+	0.868201i	$0.665277\pi$
$882$	−26.2808	−0.884919
$883$	3.77951	0.127191	0.0635953	−	0.997976i	$-0.479743\pi$
$883$	3.77951	0.127191	0.0635953	+	0.997976i	$0.479743\pi$
$884$	−4.97292	−0.167257
$885$	39.6870	1.33406
$886$	−33.1038	−1.11214
$887$	6.33477	0.212701	0.106350	−	0.994329i	$-0.466083\pi$
$887$	6.33477	0.212701	0.106350	+	0.994329i	$0.466083\pi$
$888$	−13.0135	−0.436706
$889$	−34.4595	−1.15574
$890$	22.2137	0.744604
$891$	10.4669	0.350653
$892$	2.34314	0.0784541
$893$	17.6571	0.590872
$894$	22.8437	0.764008
$895$	−27.3454	−0.914056
$896$	−3.98930	−0.133273
$897$	−32.6462	−1.09003
$898$	26.2263	0.875184
$899$	8.28523	0.276328
$900$	6.32922	0.210974
$901$	12.9197	0.430416
$902$	1.04521	0.0348018
$903$	5.10174	0.169775
$904$	10.6458	0.354073
$905$	−71.6565	−2.38194
$906$	57.1124	1.89743
$907$	16.8834	0.560605	0.280303	−	0.959912i	$-0.409565\pi$
$907$	16.8834	0.560605	0.280303	+	0.959912i	$0.409565\pi$
$908$	7.80687	0.259080
$909$	−33.2273	−1.10208
$910$	42.5018	1.40892
$911$	−36.9445	−1.22403	−0.612014	−	0.790847i	$-0.709640\pi$
$911$	−36.9445	−1.22403	−0.612014	+	0.790847i	$0.709640\pi$
$912$	−6.50239	−0.215316
$913$	13.2084	0.437133
$914$	5.18810	0.171607
$915$	−15.1299	−0.500180
$916$	1.01713	0.0336069
$917$	45.0718	1.48840
$918$	−0.158003	−0.00521487
$919$	−27.6054	−0.910618	−0.455309	−	0.890334i	$-0.650471\pi$
$919$	−27.6054	−0.910618	−0.455309	+	0.890334i	$0.650471\pi$
$920$	8.97948	0.296045
$921$	22.2174	0.732087
$922$	0.439060	0.0144597
$923$	18.9394	0.623398
$924$	11.1259	0.366016
$925$	−11.4556	−0.376658
$926$	12.0161	0.394874
$927$	7.91573	0.259987
$928$	3.36291	0.110393
$929$	4.54038	0.148965	0.0744824	−	0.997222i	$-0.476270\pi$
$929$	4.54038	0.148965	0.0744824	+	0.997222i	$0.476270\pi$
$930$	−16.0634	−0.526738
$931$	23.7675	0.778947
$932$	−7.41651	−0.242936
$933$	7.37773	0.241536
$934$	1.33601	0.0437156
$935$	−3.81478	−0.124757
$936$	11.7487	0.384020
$937$	11.2748	0.368332	0.184166	−	0.982895i	$-0.441042\pi$
$937$	11.2748	0.368332	0.184166	+	0.982895i	$0.441042\pi$
$938$	62.2624	2.03294
$939$	48.8050	1.59269
$940$	17.7049	0.577470
$941$	−17.9005	−0.583540	−0.291770	−	0.956488i	$-0.594244\pi$
$941$	−17.9005	−0.583540	−0.291770	+	0.956488i	$0.594244\pi$
$942$	−29.3830	−0.957351
$943$	−3.07006	−0.0999749
$944$	−6.08696	−0.198114
$945$	1.35039	0.0439283
$946$	−0.599630	−0.0194957
$947$	−53.2792	−1.73134	−0.865671	−	0.500614i	$-0.833108\pi$
$947$	−53.2792	−1.73134	−0.865671	+	0.500614i	$0.833108\pi$
$948$	18.9144	0.614313
$949$	−51.1858	−1.66156
$950$	−5.72394	−0.185709
$951$	32.6481	1.05869
$952$	−4.97802	−0.161339
$953$	−21.0636	−0.682318	−0.341159	−	0.940006i	$-0.610819\pi$
$953$	−21.0636	−0.682318	−0.341159	+	0.940006i	$0.610819\pi$
$954$	−30.5233	−0.988227
$955$	53.4920	1.73096
$956$	9.82879	0.317886
$957$	−9.37896	−0.303179
$958$	28.0143	0.905102
$959$	−59.0693	−1.90745
$960$	−6.51999	−0.210432
$961$	−24.9301	−0.804198
$962$	−21.2647	−0.685601
$963$	6.42502	0.207043
$964$	2.62178	0.0844419
$965$	12.6258	0.406437
$966$	−32.6797	−1.05145
$967$	−47.9207	−1.54103	−0.770514	−	0.637424i	$-0.780000\pi$
$967$	−47.9207	−1.54103	−0.770514	+	0.637424i	$0.780000\pi$
$968$	9.69232	0.311523
$969$	−8.11396	−0.260658
$970$	51.5370	1.65475
$971$	−24.4045	−0.783179	−0.391590	−	0.920140i	$-0.628075\pi$
$971$	−24.4045	−0.783179	−0.391590	+	0.920140i	$0.628075\pi$
$972$	21.9432	0.703830
$973$	2.35942	0.0756397
$974$	21.3477	0.684025
$975$	20.8666	0.668265
$976$	2.32055	0.0742788
$977$	28.3850	0.908118	0.454059	−	0.890972i	$-0.349976\pi$
$977$	28.3850	0.908118	0.454059	+	0.890972i	$0.349976\pi$
$978$	25.8531	0.826691
$979$	9.50194	0.303683
$980$	23.8318	0.761279
$981$	40.2249	1.28428
$982$	22.0934	0.705030
$983$	3.14340	0.100259	0.0501295	−	0.998743i	$-0.484037\pi$
$983$	3.14340	0.100259	0.0501295	+	0.998743i	$0.484037\pi$
$984$	2.22917	0.0710633
$985$	39.5291	1.25950
$986$	4.19638	0.133640
$987$	−64.4347	−2.05098
$988$	−10.6252	−0.338032
$989$	1.76127	0.0560051
$990$	9.01258	0.286438
$991$	−7.03703	−0.223539	−0.111769	−	0.993734i	$-0.535652\pi$
$991$	−7.03703	−0.223539	−0.111769	+	0.993734i	$0.535652\pi$
$992$	2.46371	0.0782228
$993$	29.0776	0.922751
$994$	18.9588	0.601337
$995$	−68.2674	−2.16422
$996$	28.1700	0.892600
$997$	−17.0091	−0.538684	−0.269342	−	0.963045i	$-0.586806\pi$
$997$	−17.0091	−0.538684	−0.269342	+	0.963045i	$0.586806\pi$
$998$	14.3327	0.453693
$999$	−0.675635	−0.0213762

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8006.2.a.b.1.11	✓	75

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8006.2.a.b.1.11	✓	75	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:	\( N \)	\(=\)	\( 8006 = 2 \cdot 4003 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8006.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.43887 q^{3} +1.00000 q^{4} +2.67337 q^{5} +2.43887 q^{6} +3.98930 q^{7} -1.00000 q^{8} +2.94808 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.43887 q^{3} +1.00000 q^{4} +2.67337 q^{5} +2.43887 q^{6} +3.98930 q^{7} -1.00000 q^{8} +2.94808 q^{9} -2.67337 q^{10} -1.14354 q^{11} -2.43887 q^{12} -3.98522 q^{13} -3.98930 q^{14} -6.51999 q^{15} +1.00000 q^{16} +1.24784 q^{17} -2.94808 q^{18} +2.66615 q^{19} +2.67337 q^{20} -9.72938 q^{21} +1.14354 q^{22} -3.35887 q^{23} +2.43887 q^{24} +2.14689 q^{25} +3.98522 q^{26} +0.126621 q^{27} +3.98930 q^{28} -3.36291 q^{29} +6.51999 q^{30} -2.46371 q^{31} -1.00000 q^{32} +2.78894 q^{33} -1.24784 q^{34} +10.6649 q^{35} +2.94808 q^{36} -5.33589 q^{37} -2.66615 q^{38} +9.71942 q^{39} -2.67337 q^{40} +0.914017 q^{41} +9.72938 q^{42} -0.524364 q^{43} -1.14354 q^{44} +7.88131 q^{45} +3.35887 q^{46} +6.62269 q^{47} -2.43887 q^{48} +8.91453 q^{49} -2.14689 q^{50} -3.04332 q^{51} -3.98522 q^{52} +10.3536 q^{53} -0.126621 q^{54} -3.05710 q^{55} -3.98930 q^{56} -6.50239 q^{57} +3.36291 q^{58} -6.08696 q^{59} -6.51999 q^{60} +2.32055 q^{61} +2.46371 q^{62} +11.7608 q^{63} +1.00000 q^{64} -10.6539 q^{65} -2.78894 q^{66} -15.6073 q^{67} +1.24784 q^{68} +8.19183 q^{69} -10.6649 q^{70} -4.75242 q^{71} -2.94808 q^{72} +12.8439 q^{73} +5.33589 q^{74} -5.23599 q^{75} +2.66615 q^{76} -4.56192 q^{77} -9.71942 q^{78} -7.75542 q^{79} +2.67337 q^{80} -9.15306 q^{81} -0.914017 q^{82} -11.5504 q^{83} -9.72938 q^{84} +3.33594 q^{85} +0.524364 q^{86} +8.20170 q^{87} +1.14354 q^{88} -8.30924 q^{89} -7.88131 q^{90} -15.8982 q^{91} -3.35887 q^{92} +6.00866 q^{93} -6.62269 q^{94} +7.12760 q^{95} +2.43887 q^{96} -19.2779 q^{97} -8.91453 q^{98} -3.37124 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 75 q - 75 q^{2} + q^{3} + 75 q^{4} - 9 q^{5} - q^{6} - 8 q^{7} - 75 q^{8} + 66 q^{9}+O(q^{10}) \) 75 * q - 75 * q^2 + q^3 + 75 * q^4 - 9 * q^5 - q^6 - 8 * q^7 - 75 * q^8 + 66 * q^9	\( 75 q - 75 q^{2} + q^{3} + 75 q^{4} - 9 q^{5} - q^{6} - 8 q^{7} - 75 q^{8} + 66 q^{9} + 9 q^{10} - 5 q^{11} + q^{12} - 35 q^{13} + 8 q^{14} - 21 q^{15} + 75 q^{16} + 4 q^{17} - 66 q^{18} - 59 q^{19} - 9 q^{20} - 62 q^{21} + 5 q^{22} + 43 q^{23} - q^{24} + 44 q^{25} + 35 q^{26} + 4 q^{27} - 8 q^{28} - 38 q^{29} + 21 q^{30} - 51 q^{31} - 75 q^{32} - 19 q^{33} - 4 q^{34} + 14 q^{35} + 66 q^{36} - 63 q^{37} + 59 q^{38} - 34 q^{39} + 9 q^{40} - 27 q^{41} + 62 q^{42} - 39 q^{43} - 5 q^{44} - 52 q^{45} - 43 q^{46} + 40 q^{47} + q^{48} + 29 q^{49} - 44 q^{50} - 34 q^{51} - 35 q^{52} - 39 q^{53} - 4 q^{54} - 48 q^{55} + 8 q^{56} - 28 q^{57} + 38 q^{58} + 5 q^{59} - 21 q^{60} - 98 q^{61} + 51 q^{62} + 2 q^{63} + 75 q^{64} - q^{65} + 19 q^{66} - 59 q^{67} + 4 q^{68} - 69 q^{69} - 14 q^{70} - 9 q^{71} - 66 q^{72} - 51 q^{73} + 63 q^{74} - q^{75} - 59 q^{76} - 25 q^{77} + 34 q^{78} - 139 q^{79} - 9 q^{80} + 23 q^{81} + 27 q^{82} + 31 q^{83} - 62 q^{84} - 149 q^{85} + 39 q^{86} + q^{87} + 5 q^{88} - 39 q^{89} + 52 q^{90} - 93 q^{91} + 43 q^{92} - 83 q^{93} - 40 q^{94} + 2 q^{95} - q^{96} - 70 q^{97} - 29 q^{98} - 61 q^{99}+O(q^{100}) \) 75 * q - 75 * q^2 + q^3 + 75 * q^4 - 9 * q^5 - q^6 - 8 * q^7 - 75 * q^8 + 66 * q^9 + 9 * q^10 - 5 * q^11 + q^12 - 35 * q^13 + 8 * q^14 - 21 * q^15 + 75 * q^16 + 4 * q^17 - 66 * q^18 - 59 * q^19 - 9 * q^20 - 62 * q^21 + 5 * q^22 + 43 * q^23 - q^24 + 44 * q^25 + 35 * q^26 + 4 * q^27 - 8 * q^28 - 38 * q^29 + 21 * q^30 - 51 * q^31 - 75 * q^32 - 19 * q^33 - 4 * q^34 + 14 * q^35 + 66 * q^36 - 63 * q^37 + 59 * q^38 - 34 * q^39 + 9 * q^40 - 27 * q^41 + 62 * q^42 - 39 * q^43 - 5 * q^44 - 52 * q^45 - 43 * q^46 + 40 * q^47 + q^48 + 29 * q^49 - 44 * q^50 - 34 * q^51 - 35 * q^52 - 39 * q^53 - 4 * q^54 - 48 * q^55 + 8 * q^56 - 28 * q^57 + 38 * q^58 + 5 * q^59 - 21 * q^60 - 98 * q^61 + 51 * q^62 + 2 * q^63 + 75 * q^64 - q^65 + 19 * q^66 - 59 * q^67 + 4 * q^68 - 69 * q^69 - 14 * q^70 - 9 * q^71 - 66 * q^72 - 51 * q^73 + 63 * q^74 - q^75 - 59 * q^76 - 25 * q^77 + 34 * q^78 - 139 * q^79 - 9 * q^80 + 23 * q^81 + 27 * q^82 + 31 * q^83 - 62 * q^84 - 149 * q^85 + 39 * q^86 + q^87 + 5 * q^88 - 39 * q^89 + 52 * q^90 - 93 * q^91 + 43 * q^92 - 83 * q^93 - 40 * q^94 + 2 * q^95 - q^96 - 70 * q^97 - 29 * q^98 - 61 * q^99

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