LMFDB - Embedded newform 8026.2.a.c.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8026,2,Mod(1,8026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8026, 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("8026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8026 = 2 \cdot 4013 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8026.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:	$64.0879326623$
Analytic rank:	$0$
Dimension:	$86$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	8026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -3.04565 q^{3} +1.00000 q^{4} -0.405483 q^{5} +3.04565 q^{6} -0.211812 q^{7} -1.00000 q^{8} +6.27596 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -3.04565 q^{3} +1.00000 q^{4} -0.405483 q^{5} +3.04565 q^{6} -0.211812 q^{7} -1.00000 q^{8} +6.27596 q^{9} +0.405483 q^{10} -2.15871 q^{11} -3.04565 q^{12} -2.88228 q^{13} +0.211812 q^{14} +1.23496 q^{15} +1.00000 q^{16} +2.39963 q^{17} -6.27596 q^{18} +6.94396 q^{19} -0.405483 q^{20} +0.645104 q^{21} +2.15871 q^{22} -0.181212 q^{23} +3.04565 q^{24} -4.83558 q^{25} +2.88228 q^{26} -9.97742 q^{27} -0.211812 q^{28} +7.82275 q^{29} -1.23496 q^{30} +11.0829 q^{31} -1.00000 q^{32} +6.57466 q^{33} -2.39963 q^{34} +0.0858861 q^{35} +6.27596 q^{36} +5.12941 q^{37} -6.94396 q^{38} +8.77841 q^{39} +0.405483 q^{40} +2.72196 q^{41} -0.645104 q^{42} -7.70126 q^{43} -2.15871 q^{44} -2.54480 q^{45} +0.181212 q^{46} -9.50182 q^{47} -3.04565 q^{48} -6.95514 q^{49} +4.83558 q^{50} -7.30842 q^{51} -2.88228 q^{52} -2.68607 q^{53} +9.97742 q^{54} +0.875319 q^{55} +0.211812 q^{56} -21.1489 q^{57} -7.82275 q^{58} +0.249098 q^{59} +1.23496 q^{60} +4.49812 q^{61} -11.0829 q^{62} -1.32932 q^{63} +1.00000 q^{64} +1.16872 q^{65} -6.57466 q^{66} +10.1429 q^{67} +2.39963 q^{68} +0.551909 q^{69} -0.0858861 q^{70} +14.7762 q^{71} -6.27596 q^{72} -3.87466 q^{73} -5.12941 q^{74} +14.7275 q^{75} +6.94396 q^{76} +0.457240 q^{77} -8.77841 q^{78} +1.73578 q^{79} -0.405483 q^{80} +11.5598 q^{81} -2.72196 q^{82} +10.4177 q^{83} +0.645104 q^{84} -0.973009 q^{85} +7.70126 q^{86} -23.8253 q^{87} +2.15871 q^{88} +11.7778 q^{89} +2.54480 q^{90} +0.610502 q^{91} -0.181212 q^{92} -33.7547 q^{93} +9.50182 q^{94} -2.81566 q^{95} +3.04565 q^{96} -14.0830 q^{97} +6.95514 q^{98} -13.5480 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 86 q - 86 q^{2} + 11 q^{3} + 86 q^{4} + 25 q^{5} - 11 q^{6} - 3 q^{7} - 86 q^{8} + 105 q^{9}+O(q^{10}) $ 86 * q - 86 * q^2 + 11 * q^3 + 86 * q^4 + 25 * q^5 - 11 * q^6 - 3 * q^7 - 86 * q^8 + 105 * q^9	\( 86 q - 86 q^{2} + 11 q^{3} + 86 q^{4} + 25 q^{5} - 11 q^{6} - 3 q^{7} - 86 q^{8} + 105 q^{9} - 25 q^{10} + 44 q^{11} + 11 q^{12} - 36 q^{13} + 3 q^{14} + 19 q^{15} + 86 q^{16} + 21 q^{17} - 105 q^{18} + 35 q^{19} + 25 q^{20} + 23 q^{21} - 44 q^{22} + 38 q^{23} - 11 q^{24} + 85 q^{25} + 36 q^{26} + 47 q^{27} - 3 q^{28} + 30 q^{29} - 19 q^{30} + 23 q^{31} - 86 q^{32} + 5 q^{33} - 21 q^{34} + 59 q^{35} + 105 q^{36} - 20 q^{37} - 35 q^{38} + 4 q^{39} - 25 q^{40} + 64 q^{41} - 23 q^{42} + 23 q^{43} + 44 q^{44} + 60 q^{45} - 38 q^{46} + 77 q^{47} + 11 q^{48} + 109 q^{49} - 85 q^{50} + 47 q^{51} - 36 q^{52} + 22 q^{53} - 47 q^{54} + 6 q^{55} + 3 q^{56} - 9 q^{57} - 30 q^{58} + 145 q^{59} + 19 q^{60} - 24 q^{61} - 23 q^{62} + 6 q^{63} + 86 q^{64} + 37 q^{65} - 5 q^{66} + 44 q^{67} + 21 q^{68} + 25 q^{69} - 59 q^{70} + 107 q^{71} - 105 q^{72} - 55 q^{73} + 20 q^{74} + 86 q^{75} + 35 q^{76} + 25 q^{77} - 4 q^{78} + 2 q^{79} + 25 q^{80} + 170 q^{81} - 64 q^{82} + 109 q^{83} + 23 q^{84} - 13 q^{85} - 23 q^{86} + 3 q^{87} - 44 q^{88} + 121 q^{89} - 60 q^{90} + 81 q^{91} + 38 q^{92} + 27 q^{93} - 77 q^{94} + 49 q^{95} - 11 q^{96} - 56 q^{97} - 109 q^{98} + 158 q^{99}+O(q^{100}) \) 86 * q - 86 * q^2 + 11 * q^3 + 86 * q^4 + 25 * q^5 - 11 * q^6 - 3 * q^7 - 86 * q^8 + 105 * q^9 - 25 * q^10 + 44 * q^11 + 11 * q^12 - 36 * q^13 + 3 * q^14 + 19 * q^15 + 86 * q^16 + 21 * q^17 - 105 * q^18 + 35 * q^19 + 25 * q^20 + 23 * q^21 - 44 * q^22 + 38 * q^23 - 11 * q^24 + 85 * q^25 + 36 * q^26 + 47 * q^27 - 3 * q^28 + 30 * q^29 - 19 * q^30 + 23 * q^31 - 86 * q^32 + 5 * q^33 - 21 * q^34 + 59 * q^35 + 105 * q^36 - 20 * q^37 - 35 * q^38 + 4 * q^39 - 25 * q^40 + 64 * q^41 - 23 * q^42 + 23 * q^43 + 44 * q^44 + 60 * q^45 - 38 * q^46 + 77 * q^47 + 11 * q^48 + 109 * q^49 - 85 * q^50 + 47 * q^51 - 36 * q^52 + 22 * q^53 - 47 * q^54 + 6 * q^55 + 3 * q^56 - 9 * q^57 - 30 * q^58 + 145 * q^59 + 19 * q^60 - 24 * q^61 - 23 * q^62 + 6 * q^63 + 86 * q^64 + 37 * q^65 - 5 * q^66 + 44 * q^67 + 21 * q^68 + 25 * q^69 - 59 * q^70 + 107 * q^71 - 105 * q^72 - 55 * q^73 + 20 * q^74 + 86 * q^75 + 35 * q^76 + 25 * q^77 - 4 * q^78 + 2 * q^79 + 25 * q^80 + 170 * q^81 - 64 * q^82 + 109 * q^83 + 23 * q^84 - 13 * q^85 - 23 * q^86 + 3 * q^87 - 44 * q^88 + 121 * q^89 - 60 * q^90 + 81 * q^91 + 38 * q^92 + 27 * q^93 - 77 * q^94 + 49 * q^95 - 11 * q^96 - 56 * q^97 - 109 * q^98 + 158 * 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
$3$	−3.04565	−1.75840	−0.879202	−	0.476449i	$-0.841924\pi$
$3$	−3.04565	−1.75840	−0.879202	+	0.476449i	$0.841924\pi$
$4$	1.00000	0.500000
$5$	−0.405483	−0.181337	−0.0906687	−	0.995881i	$-0.528900\pi$
$5$	−0.405483	−0.181337	−0.0906687	+	0.995881i	$0.528900\pi$
$6$	3.04565	1.24338
$7$	−0.211812	−0.0800574	−0.0400287	−	0.999199i	$-0.512745\pi$
$7$	−0.211812	−0.0800574	−0.0400287	+	0.999199i	$0.512745\pi$
$8$	−1.00000	−0.353553
$9$	6.27596	2.09199
$10$	0.405483	0.128225
$11$	−2.15871	−0.650874	−0.325437	−	0.945564i	$-0.605511\pi$
$11$	−2.15871	−0.650874	−0.325437	+	0.945564i	$0.605511\pi$
$12$	−3.04565	−0.879202
$13$	−2.88228	−0.799401	−0.399701	−	0.916646i	$-0.630886\pi$
$13$	−2.88228	−0.799401	−0.399701	+	0.916646i	$0.630886\pi$
$14$	0.211812	0.0566091
$15$	1.23496	0.318865
$16$	1.00000	0.250000
$17$	2.39963	0.581996	0.290998	−	0.956724i	$-0.406013\pi$
$17$	2.39963	0.581996	0.290998	+	0.956724i	$0.406013\pi$
$18$	−6.27596	−1.47926
$19$	6.94396	1.59305	0.796527	−	0.604603i	$-0.206668\pi$
$19$	6.94396	1.59305	0.796527	+	0.604603i	$0.206668\pi$
$20$	−0.405483	−0.0906687
$21$	0.645104	0.140773
$22$	2.15871	0.460238
$23$	−0.181212	−0.0377854	−0.0188927	−	0.999822i	$-0.506014\pi$
$23$	−0.181212	−0.0377854	−0.0188927	+	0.999822i	$0.506014\pi$
$24$	3.04565	0.621690
$25$	−4.83558	−0.967117
$26$	2.88228	0.565262
$27$	−9.97742	−1.92016
$28$	−0.211812	−0.0400287
$29$	7.82275	1.45265	0.726324	−	0.687353i	$-0.241227\pi$
$29$	7.82275	1.45265	0.726324	+	0.687353i	$0.241227\pi$
$30$	−1.23496	−0.225471
$31$	11.0829	1.99055	0.995276	−	0.0970811i	$-0.0309506\pi$
$31$	11.0829	1.99055	0.995276	+	0.0970811i	$0.0309506\pi$
$32$	−1.00000	−0.176777
$33$	6.57466	1.14450
$34$	−2.39963	−0.411533
$35$	0.0858861	0.0145174
$36$	6.27596	1.04599
$37$	5.12941	0.843270	0.421635	−	0.906766i	$-0.361456\pi$
$37$	5.12941	0.843270	0.421635	+	0.906766i	$0.361456\pi$
$38$	−6.94396	−1.12646
$39$	8.77841	1.40567
$40$	0.405483	0.0641125
$41$	2.72196	0.425099	0.212549	−	0.977150i	$-0.431823\pi$
$41$	2.72196	0.425099	0.212549	+	0.977150i	$0.431823\pi$
$42$	−0.645104	−0.0995417
$43$	−7.70126	−1.17443	−0.587216	−	0.809430i	$-0.699776\pi$
$43$	−7.70126	−1.17443	−0.587216	+	0.809430i	$0.699776\pi$
$44$	−2.15871	−0.325437
$45$	−2.54480	−0.379356
$46$	0.181212	0.0267183
$47$	−9.50182	−1.38598	−0.692992	−	0.720946i	$-0.743708\pi$
$47$	−9.50182	−1.38598	−0.692992	+	0.720946i	$0.743708\pi$
$48$	−3.04565	−0.439601
$49$	−6.95514	−0.993591
$50$	4.83558	0.683855
$51$	−7.30842	−1.02338
$52$	−2.88228	−0.399701
$53$	−2.68607	−0.368960	−0.184480	−	0.982836i	$-0.559060\pi$
$53$	−2.68607	−0.368960	−0.184480	+	0.982836i	$0.559060\pi$
$54$	9.97742	1.35776
$55$	0.875319	0.118028
$56$	0.211812	0.0283046
$57$	−21.1489	−2.80123
$58$	−7.82275	−1.02718
$59$	0.249098	0.0324298	0.0162149	−	0.999869i	$-0.494838\pi$
$59$	0.249098	0.0324298	0.0162149	+	0.999869i	$0.494838\pi$
$60$	1.23496	0.159432
$61$	4.49812	0.575925	0.287963	−	0.957642i	$-0.407022\pi$
$61$	4.49812	0.575925	0.287963	+	0.957642i	$0.407022\pi$
$62$	−11.0829	−1.40753
$63$	−1.32932	−0.167479
$64$	1.00000	0.125000
$65$	1.16872	0.144961
$66$	−6.57466	−0.809284
$67$	10.1429	1.23915	0.619577	−	0.784936i	$-0.287304\pi$
$67$	10.1429	1.23915	0.619577	+	0.784936i	$0.287304\pi$
$68$	2.39963	0.290998
$69$	0.551909	0.0664420
$70$	−0.0858861	−0.0102654
$71$	14.7762	1.75361	0.876807	−	0.480843i	$-0.159669\pi$
$71$	14.7762	1.75361	0.876807	+	0.480843i	$0.159669\pi$
$72$	−6.27596	−0.739629
$73$	−3.87466	−0.453495	−0.226748	−	0.973954i	$-0.572809\pi$
$73$	−3.87466	−0.453495	−0.226748	+	0.973954i	$0.572809\pi$
$74$	−5.12941	−0.596282
$75$	14.7275	1.70058
$76$	6.94396	0.796527
$77$	0.457240	0.0521073
$78$	−8.77841	−0.993960
$79$	1.73578	0.195291	0.0976453	−	0.995221i	$-0.468869\pi$
$79$	1.73578	0.195291	0.0976453	+	0.995221i	$0.468869\pi$
$80$	−0.405483	−0.0453344
$81$	11.5598	1.28442
$82$	−2.72196	−0.300590
$83$	10.4177	1.14350	0.571748	−	0.820429i	$-0.306265\pi$
$83$	10.4177	1.14350	0.571748	+	0.820429i	$0.306265\pi$
$84$	0.645104	0.0703866
$85$	−0.973009	−0.105538
$86$	7.70126	0.830448
$87$	−23.8253	−2.55434
$88$	2.15871	0.230119
$89$	11.7778	1.24844	0.624222	−	0.781247i	$-0.285416\pi$
$89$	11.7778	1.24844	0.624222	+	0.781247i	$0.285416\pi$
$90$	2.54480	0.268245
$91$	0.610502	0.0639980
$92$	−0.181212	−0.0188927
$93$	−33.7547	−3.50020
$94$	9.50182	0.980038
$95$	−2.81566	−0.288881
$96$	3.04565	0.310845
$97$	−14.0830	−1.42991	−0.714954	−	0.699171i	$-0.753552\pi$
$97$	−14.0830	−1.42991	−0.714954	+	0.699171i	$0.753552\pi$
$98$	6.95514	0.702575
$99$	−13.5480	−1.36162
$100$	−4.83558	−0.483558
$101$	−15.0700	−1.49952	−0.749761	−	0.661709i	$-0.769832\pi$
$101$	−15.0700	−1.49952	−0.749761	+	0.661709i	$0.769832\pi$
$102$	7.30842	0.723642
$103$	−4.31820	−0.425484	−0.212742	−	0.977108i	$-0.568239\pi$
$103$	−4.31820	−0.425484	−0.212742	+	0.977108i	$0.568239\pi$
$104$	2.88228	0.282631
$105$	−0.261579	−0.0255275
$106$	2.68607	0.260894
$107$	17.7947	1.72028	0.860141	−	0.510057i	$-0.170376\pi$
$107$	17.7947	1.72028	0.860141	+	0.510057i	$0.170376\pi$
$108$	−9.97742	−0.960078
$109$	−4.42592	−0.423926	−0.211963	−	0.977278i	$-0.567986\pi$
$109$	−4.42592	−0.423926	−0.211963	+	0.977278i	$0.567986\pi$
$110$	−0.875319	−0.0834584
$111$	−15.6224	−1.48281
$112$	−0.211812	−0.0200143
$113$	7.38207	0.694447	0.347223	−	0.937782i	$-0.387125\pi$
$113$	7.38207	0.694447	0.347223	+	0.937782i	$0.387125\pi$
$114$	21.1489	1.98077
$115$	0.0734785	0.00685191
$116$	7.82275	0.726324
$117$	−18.0891	−1.67234
$118$	−0.249098	−0.0229313
$119$	−0.508270	−0.0465931
$120$	−1.23496	−0.112736
$121$	−6.33999	−0.576362
$122$	−4.49812	−0.407241
$123$	−8.29013	−0.747496
$124$	11.0829	0.995276
$125$	3.98816	0.356712
$126$	1.32932	0.118426
$127$	1.02675	0.0911095	0.0455547	−	0.998962i	$-0.485494\pi$
$127$	1.02675	0.0911095	0.0455547	+	0.998962i	$0.485494\pi$
$128$	−1.00000	−0.0883883
$129$	23.4553	2.06513
$130$	−1.16872	−0.102503
$131$	18.8233	1.64460	0.822302	−	0.569052i	$-0.192690\pi$
$131$	18.8233	1.64460	0.822302	+	0.569052i	$0.192690\pi$
$132$	6.57466	0.572250
$133$	−1.47081	−0.127536
$134$	−10.1429	−0.876214
$135$	4.04567	0.348196
$136$	−2.39963	−0.205767
$137$	5.14314	0.439408	0.219704	−	0.975567i	$-0.429491\pi$
$137$	5.14314	0.439408	0.219704	+	0.975567i	$0.429491\pi$
$138$	−0.551909	−0.0469816
$139$	−7.52067	−0.637895	−0.318947	−	0.947772i	$-0.603329\pi$
$139$	−7.52067	−0.637895	−0.318947	+	0.947772i	$0.603329\pi$
$140$	0.0858861	0.00725870
$141$	28.9392	2.43712
$142$	−14.7762	−1.23999
$143$	6.22200	0.520310
$144$	6.27596	0.522997
$145$	−3.17199	−0.263419
$146$	3.87466	0.320669
$147$	21.1829	1.74713
$148$	5.12941	0.421635
$149$	−11.5223	−0.943943	−0.471972	−	0.881614i	$-0.656458\pi$
$149$	−11.5223	−0.943943	−0.471972	+	0.881614i	$0.656458\pi$
$150$	−14.7275	−1.20249
$151$	0.170707	0.0138919	0.00694595	−	0.999976i	$-0.497789\pi$
$151$	0.170707	0.0138919	0.00694595	+	0.999976i	$0.497789\pi$
$152$	−6.94396	−0.563230
$153$	15.0600	1.21753
$154$	−0.457240	−0.0368454
$155$	−4.49394	−0.360962
$156$	8.77841	0.702836
$157$	1.48141	0.118229	0.0591147	−	0.998251i	$-0.481172\pi$
$157$	1.48141	0.118229	0.0591147	+	0.998251i	$0.481172\pi$
$158$	−1.73578	−0.138091
$159$	8.18083	0.648782
$160$	0.405483	0.0320562
$161$	0.0383829	0.00302500
$162$	−11.5598	−0.908225
$163$	−13.3355	−1.04452	−0.522258	−	0.852787i	$-0.674910\pi$
$163$	−13.3355	−1.04452	−0.522258	+	0.852787i	$0.674910\pi$
$164$	2.72196	0.212549
$165$	−2.66591	−0.207541
$166$	−10.4177	−0.808574
$167$	−9.22602	−0.713931	−0.356966	−	0.934118i	$-0.616189\pi$
$167$	−9.22602	−0.713931	−0.356966	+	0.934118i	$0.616189\pi$
$168$	−0.645104	−0.0497709
$169$	−4.69245	−0.360957
$170$	0.973009	0.0746264
$171$	43.5801	3.33265
$172$	−7.70126	−0.587216
$173$	−3.11029	−0.236471	−0.118235	−	0.992986i	$-0.537724\pi$
$173$	−3.11029	−0.236471	−0.118235	+	0.992986i	$0.537724\pi$
$174$	23.8253	1.80619
$175$	1.02423	0.0774248
$176$	−2.15871	−0.162719
$177$	−0.758664	−0.0570246
$178$	−11.7778	−0.882783
$179$	6.17553	0.461581	0.230790	−	0.973003i	$-0.425869\pi$
$179$	6.17553	0.461581	0.230790	+	0.973003i	$0.425869\pi$
$180$	−2.54480	−0.189678
$181$	−9.22557	−0.685731	−0.342866	−	0.939384i	$-0.611398\pi$
$181$	−9.22557	−0.685731	−0.342866	+	0.939384i	$0.611398\pi$
$182$	−0.610502	−0.0452534
$183$	−13.6997	−1.01271
$184$	0.181212	0.0133592
$185$	−2.07989	−0.152916
$186$	33.7547	2.47501
$187$	−5.18010	−0.378806
$188$	−9.50182	−0.692992
$189$	2.11334	0.153723
$190$	2.81566	0.204269
$191$	−8.77932	−0.635249	−0.317625	−	0.948217i	$-0.602885\pi$
$191$	−8.77932	−0.635249	−0.317625	+	0.948217i	$0.602885\pi$
$192$	−3.04565	−0.219801
$193$	−3.66944	−0.264132	−0.132066	−	0.991241i	$-0.542161\pi$
$193$	−3.66944	−0.264132	−0.132066	+	0.991241i	$0.542161\pi$
$194$	14.0830	1.01110
$195$	−3.55950	−0.254901
$196$	−6.95514	−0.496795
$197$	−7.65204	−0.545185	−0.272593	−	0.962130i	$-0.587881\pi$
$197$	−7.65204	−0.545185	−0.272593	+	0.962130i	$0.587881\pi$
$198$	13.5480	0.962811
$199$	−1.46863	−0.104108	−0.0520542	−	0.998644i	$-0.516577\pi$
$199$	−1.46863	−0.104108	−0.0520542	+	0.998644i	$0.516577\pi$
$200$	4.83558	0.341927
$201$	−30.8917	−2.17893
$202$	15.0700	1.06032
$203$	−1.65695	−0.116295
$204$	−7.30842	−0.511692
$205$	−1.10371	−0.0770864
$206$	4.31820	0.300863
$207$	−1.13728	−0.0790466
$208$	−2.88228	−0.199850
$209$	−14.9900	−1.03688
$210$	0.261579	0.0180507
$211$	16.6578	1.14677	0.573385	−	0.819286i	$-0.305630\pi$
$211$	16.6578	1.14677	0.573385	+	0.819286i	$0.305630\pi$
$212$	−2.68607	−0.184480
$213$	−45.0031	−3.08356
$214$	−17.7947	−1.21642
$215$	3.12273	0.212968
$216$	9.97742	0.678878
$217$	−2.34750	−0.159358
$218$	4.42592	0.299761
$219$	11.8009	0.797428
$220$	0.875319	0.0590140
$221$	−6.91641	−0.465248
$222$	15.6224	1.04850
$223$	−23.5772	−1.57884	−0.789422	−	0.613850i	$-0.789620\pi$
$223$	−23.5772	−1.57884	−0.789422	+	0.613850i	$0.789620\pi$
$224$	0.211812	0.0141523
$225$	−30.3479	−2.02320
$226$	−7.38207	−0.491048
$227$	−0.245607	−0.0163015	−0.00815076	−	0.999967i	$-0.502594\pi$
$227$	−0.245607	−0.0163015	−0.00815076	+	0.999967i	$0.502594\pi$
$228$	−21.1489	−1.40062
$229$	18.9554	1.25261	0.626303	−	0.779580i	$-0.284567\pi$
$229$	18.9554	1.25261	0.626303	+	0.779580i	$0.284567\pi$
$230$	−0.0734785	−0.00484503
$231$	−1.39259	−0.0916257
$232$	−7.82275	−0.513589
$233$	−22.2179	−1.45554	−0.727770	−	0.685821i	$-0.759443\pi$
$233$	−22.2179	−1.45554	−0.727770	+	0.685821i	$0.759443\pi$
$234$	18.0891	1.18252
$235$	3.85283	0.251331
$236$	0.249098	0.0162149
$237$	−5.28657	−0.343400
$238$	0.508270	0.0329463
$239$	−20.7334	−1.34113	−0.670566	−	0.741850i	$-0.733949\pi$
$239$	−20.7334	−1.34113	−0.670566	+	0.741850i	$0.733949\pi$
$240$	1.23496	0.0797162
$241$	−21.3774	−1.37704	−0.688520	−	0.725217i	$-0.741739\pi$
$241$	−21.3774	−1.37704	−0.688520	+	0.725217i	$0.741739\pi$
$242$	6.33999	0.407550
$243$	−5.27483	−0.338381
$244$	4.49812	0.287963
$245$	2.82019	0.180175
$246$	8.29013	0.528559
$247$	−20.0145	−1.27349
$248$	−11.0829	−0.703767
$249$	−31.7288	−2.01073
$250$	−3.98816	−0.252233
$251$	−24.3815	−1.53895	−0.769474	−	0.638678i	$-0.779482\pi$
$251$	−24.3815	−1.53895	−0.769474	+	0.638678i	$0.779482\pi$
$252$	−1.32932	−0.0837395
$253$	0.391184	0.0245935
$254$	−1.02675	−0.0644241
$255$	2.96344	0.185578
$256$	1.00000	0.0625000
$257$	−4.25406	−0.265361	−0.132681	−	0.991159i	$-0.542358\pi$
$257$	−4.25406	−0.265361	−0.132681	+	0.991159i	$0.542358\pi$
$258$	−23.4553	−1.46026
$259$	−1.08647	−0.0675100
$260$	1.16872	0.0724807
$261$	49.0953	3.03892
$262$	−18.8233	−1.16291
$263$	5.39480	0.332658	0.166329	−	0.986070i	$-0.446809\pi$
$263$	5.39480	0.332658	0.166329	+	0.986070i	$0.446809\pi$
$264$	−6.57466	−0.404642
$265$	1.08916	0.0669063
$266$	1.47081	0.0901814
$267$	−35.8710	−2.19527
$268$	10.1429	0.619577
$269$	−16.9318	−1.03235	−0.516174	−	0.856484i	$-0.672644\pi$
$269$	−16.9318	−1.03235	−0.516174	+	0.856484i	$0.672644\pi$
$270$	−4.04567	−0.246212
$271$	−0.0320321	−0.00194581	−0.000972906	−	1.00000i	$-0.500310\pi$
$271$	−0.0320321	−0.00194581	−0.000972906		1.00000i	$0.500310\pi$
$272$	2.39963	0.145499
$273$	−1.85937	−0.112534
$274$	−5.14314	−0.310708
$275$	10.4386	0.629472
$276$	0.551909	0.0332210
$277$	26.5870	1.59746	0.798730	−	0.601690i	$-0.205506\pi$
$277$	26.5870	1.59746	0.798730	+	0.601690i	$0.205506\pi$
$278$	7.52067	0.451060
$279$	69.5560	4.16421
$280$	−0.0858861	−0.00513268
$281$	−9.21630	−0.549798	−0.274899	−	0.961473i	$-0.588644\pi$
$281$	−9.21630	−0.549798	−0.274899	+	0.961473i	$0.588644\pi$
$282$	−28.9392	−1.72330
$283$	−1.96246	−0.116656	−0.0583281	−	0.998297i	$-0.518577\pi$
$283$	−1.96246	−0.116656	−0.0583281	+	0.998297i	$0.518577\pi$
$284$	14.7762	0.876807
$285$	8.57550	0.507969
$286$	−6.22200	−0.367915
$287$	−0.576544	−0.0340323
$288$	−6.27596	−0.369815
$289$	−11.2418	−0.661281
$290$	3.17199	0.186266
$291$	42.8917	2.51436
$292$	−3.87466	−0.226748
$293$	19.6595	1.14852	0.574260	−	0.818673i	$-0.305290\pi$
$293$	19.6595	1.14852	0.574260	+	0.818673i	$0.305290\pi$
$294$	−21.1829	−1.23541
$295$	−0.101005	−0.00588073
$296$	−5.12941	−0.298141
$297$	21.5383	1.24978
$298$	11.5223	0.667469
$299$	0.522305	0.0302057
$300$	14.7275	0.850291
$301$	1.63122	0.0940219
$302$	−0.170707	−0.00982306
$303$	45.8979	2.63677
$304$	6.94396	0.398264
$305$	−1.82391	−0.104437
$306$	−15.0600	−0.860922
$307$	8.37016	0.477710	0.238855	−	0.971055i	$-0.423228\pi$
$307$	8.37016	0.477710	0.238855	+	0.971055i	$0.423228\pi$
$308$	0.457240	0.0260537
$309$	13.1517	0.748174
$310$	4.49394	0.255239
$311$	9.03469	0.512310	0.256155	−	0.966636i	$-0.417544\pi$
$311$	9.03469	0.512310	0.256155	+	0.966636i	$0.417544\pi$
$312$	−8.77841	−0.496980
$313$	8.14134	0.460176	0.230088	−	0.973170i	$-0.426099\pi$
$313$	8.14134	0.460176	0.230088	+	0.973170i	$0.426099\pi$
$314$	−1.48141	−0.0836008
$315$	0.539018	0.0303702
$316$	1.73578	0.0976453
$317$	24.4337	1.37233	0.686167	−	0.727444i	$-0.259292\pi$
$317$	24.4337	1.37233	0.686167	+	0.727444i	$0.259292\pi$
$318$	−8.18083	−0.458758
$319$	−16.8870	−0.945491
$320$	−0.405483	−0.0226672
$321$	−54.1965	−3.02495
$322$	−0.0383829	−0.00213900
$323$	16.6629	0.927151
$324$	11.5598	0.642212
$325$	13.9375	0.773114
$326$	13.3355	0.738585
$327$	13.4798	0.745433
$328$	−2.72196	−0.150295
$329$	2.01260	0.110958
$330$	2.66591	0.146754
$331$	−12.9307	−0.710736	−0.355368	−	0.934726i	$-0.615644\pi$
$331$	−12.9307	−0.710736	−0.355368	+	0.934726i	$0.615644\pi$
$332$	10.4177	0.571748
$333$	32.1920	1.76411
$334$	9.22602	0.504825
$335$	−4.11278	−0.224705
$336$	0.645104	0.0351933
$337$	−0.0929043	−0.00506082	−0.00253041	−	0.999997i	$-0.500805\pi$
$337$	−0.0929043	−0.00506082	−0.00253041	+	0.999997i	$0.500805\pi$
$338$	4.69245	0.255235
$339$	−22.4832	−1.22112
$340$	−0.973009	−0.0527688
$341$	−23.9248	−1.29560
$342$	−43.5801	−2.35654
$343$	2.95586	0.159602
$344$	7.70126	0.415224
$345$	−0.223790	−0.0120484
$346$	3.11029	0.167210
$347$	28.3306	1.52086	0.760432	−	0.649417i	$-0.224987\pi$
$347$	28.3306	1.52086	0.760432	+	0.649417i	$0.224987\pi$
$348$	−23.8253	−1.27717
$349$	2.98608	0.159841	0.0799207	−	0.996801i	$-0.474533\pi$
$349$	2.98608	0.159841	0.0799207	+	0.996801i	$0.474533\pi$
$350$	−1.02423	−0.0547476
$351$	28.7578	1.53498
$352$	2.15871	0.115059
$353$	−11.3130	−0.602129	−0.301065	−	0.953604i	$-0.597342\pi$
$353$	−11.3130	−0.602129	−0.301065	+	0.953604i	$0.597342\pi$
$354$	0.758664	0.0403225
$355$	−5.99150	−0.317996
$356$	11.7778	0.624222
$357$	1.54801	0.0819295
$358$	−6.17553	−0.326387
$359$	−20.9159	−1.10390	−0.551949	−	0.833878i	$-0.686116\pi$
$359$	−20.9159	−1.10390	−0.551949	+	0.833878i	$0.686116\pi$
$360$	2.54480	0.134122
$361$	29.2186	1.53782
$362$	9.22557	0.484885
$363$	19.3094	1.01348
$364$	0.610502	0.0319990
$365$	1.57111	0.0822357
$366$	13.6997	0.716094
$367$	31.6784	1.65360	0.826799	−	0.562497i	$-0.190159\pi$
$367$	31.6784	1.65360	0.826799	+	0.562497i	$0.190159\pi$
$368$	−0.181212	−0.00944635
$369$	17.0829	0.889301
$370$	2.07989	0.108128
$371$	0.568942	0.0295380
$372$	−33.7547	−1.75010
$373$	10.8472	0.561647	0.280823	−	0.959759i	$-0.409392\pi$
$373$	10.8472	0.561647	0.280823	+	0.959759i	$0.409392\pi$
$374$	5.18010	0.267856
$375$	−12.1465	−0.627244
$376$	9.50182	0.490019
$377$	−22.5474	−1.16125
$378$	−2.11334	−0.108698
$379$	17.5604	0.902018	0.451009	−	0.892519i	$-0.351064\pi$
$379$	17.5604	0.902018	0.451009	+	0.892519i	$0.351064\pi$
$380$	−2.81566	−0.144440
$381$	−3.12712	−0.160207
$382$	8.77932	0.449189
$383$	18.2116	0.930568	0.465284	−	0.885161i	$-0.345952\pi$
$383$	18.2116	0.930568	0.465284	+	0.885161i	$0.345952\pi$
$384$	3.04565	0.155422
$385$	−0.185403	−0.00944901
$386$	3.66944	0.186769
$387$	−48.3328	−2.45690
$388$	−14.0830	−0.714954
$389$	21.9359	1.11220	0.556098	−	0.831117i	$-0.312298\pi$
$389$	21.9359	1.11220	0.556098	+	0.831117i	$0.312298\pi$
$390$	3.55950	0.180242
$391$	−0.434843	−0.0219909
$392$	6.95514	0.351287
$393$	−57.3292	−2.89188
$394$	7.65204	0.385504
$395$	−0.703829	−0.0354135
$396$	−13.5480	−0.680811
$397$	29.5759	1.48437	0.742186	−	0.670194i	$-0.233789\pi$
$397$	29.5759	1.48437	0.742186	+	0.670194i	$0.233789\pi$
$398$	1.46863	0.0736158
$399$	4.47958	0.224260
$400$	−4.83558	−0.241779
$401$	−7.76169	−0.387600	−0.193800	−	0.981041i	$-0.562081\pi$
$401$	−7.76169	−0.387600	−0.193800	+	0.981041i	$0.562081\pi$
$402$	30.8917	1.54074
$403$	−31.9441	−1.59125
$404$	−15.0700	−0.749761
$405$	−4.68731	−0.232914
$406$	1.65695	0.0822331
$407$	−11.0729	−0.548863
$408$	7.30842	0.361821
$409$	35.4119	1.75100	0.875502	−	0.483214i	$-0.160531\pi$
$409$	35.4119	1.75100	0.875502	+	0.483214i	$0.160531\pi$
$410$	1.10371	0.0545083
$411$	−15.6642	−0.772657
$412$	−4.31820	−0.212742
$413$	−0.0527619	−0.00259624
$414$	1.13728	0.0558944
$415$	−4.22422	−0.207359
$416$	2.88228	0.141316
$417$	22.9053	1.12168
$418$	14.9900	0.733184
$419$	34.4826	1.68458	0.842292	−	0.539021i	$-0.181206\pi$
$419$	34.4826	1.68458	0.842292	+	0.539021i	$0.181206\pi$
$420$	−0.261579	−0.0127637
$421$	−28.3409	−1.38125	−0.690624	−	0.723214i	$-0.742664\pi$
$421$	−28.3409	−1.38125	−0.690624	+	0.723214i	$0.742664\pi$
$422$	−16.6578	−0.810889
$423$	−59.6331	−2.89946
$424$	2.68607	0.130447
$425$	−11.6036	−0.562858
$426$	45.0031	2.18041
$427$	−0.952755	−0.0461071
$428$	17.7947	0.860141
$429$	−18.9500	−0.914916
$430$	−3.12273	−0.150591
$431$	35.8299	1.72586	0.862932	−	0.505320i	$-0.168626\pi$
$431$	35.8299	1.72586	0.862932	+	0.505320i	$0.168626\pi$
$432$	−9.97742	−0.480039
$433$	−8.53995	−0.410404	−0.205202	−	0.978720i	$-0.565785\pi$
$433$	−8.53995	−0.410404	−0.205202	+	0.978720i	$0.565785\pi$
$434$	2.34750	0.112683
$435$	9.66076	0.463198
$436$	−4.42592	−0.211963
$437$	−1.25833	−0.0601942
$438$	−11.8009	−0.563867
$439$	−6.09663	−0.290976	−0.145488	−	0.989360i	$-0.546475\pi$
$439$	−6.09663	−0.290976	−0.145488	+	0.989360i	$0.546475\pi$
$440$	−0.875319	−0.0417292
$441$	−43.6502	−2.07858
$442$	6.91641	0.328980
$443$	−0.257793	−0.0122481	−0.00612406	−	0.999981i	$-0.501949\pi$
$443$	−0.257793	−0.0122481	−0.00612406	+	0.999981i	$0.501949\pi$
$444$	−15.6224	−0.741405
$445$	−4.77569	−0.226390
$446$	23.5772	1.11641
$447$	35.0928	1.65983
$448$	−0.211812	−0.0100072
$449$	−12.0636	−0.569316	−0.284658	−	0.958629i	$-0.591880\pi$
$449$	−12.0636	−0.569316	−0.284658	+	0.958629i	$0.591880\pi$
$450$	30.3479	1.43062
$451$	−5.87591	−0.276686
$452$	7.38207	0.347223
$453$	−0.519912	−0.0244276
$454$	0.245607	0.0115269
$455$	−0.247548	−0.0116052
$456$	21.1489	0.990386
$457$	27.5677	1.28956	0.644781	−	0.764367i	$-0.276949\pi$
$457$	27.5677	1.28956	0.644781	+	0.764367i	$0.276949\pi$
$458$	−18.9554	−0.885726
$459$	−23.9421	−1.11752
$460$	0.0734785	0.00342595
$461$	−18.1940	−0.847381	−0.423690	−	0.905807i	$-0.639266\pi$
$461$	−18.1940	−0.847381	−0.423690	+	0.905807i	$0.639266\pi$
$462$	1.39259	0.0647892
$463$	3.80413	0.176793	0.0883965	−	0.996085i	$-0.471826\pi$
$463$	3.80413	0.176793	0.0883965	+	0.996085i	$0.471826\pi$
$464$	7.82275	0.363162
$465$	13.6869	0.634717
$466$	22.2179	1.02922
$467$	−7.99283	−0.369864	−0.184932	−	0.982751i	$-0.559207\pi$
$467$	−7.99283	−0.369864	−0.184932	+	0.982751i	$0.559207\pi$
$468$	−18.0891	−0.836169
$469$	−2.14839	−0.0992034
$470$	−3.85283	−0.177718
$471$	−4.51185	−0.207895
$472$	−0.249098	−0.0114657
$473$	16.6248	0.764407
$474$	5.28657	0.242820
$475$	−33.5781	−1.54067
$476$	−0.508270	−0.0232965
$477$	−16.8577	−0.771860
$478$	20.7334	0.948323
$479$	−5.95739	−0.272200	−0.136100	−	0.990695i	$-0.543457\pi$
$479$	−5.95739	−0.272200	−0.136100	+	0.990695i	$0.543457\pi$
$480$	−1.23496	−0.0563678
$481$	−14.7844	−0.674111
$482$	21.3774	0.973715
$483$	−0.116901	−0.00531917
$484$	−6.33999	−0.288181
$485$	5.71040	0.259296
$486$	5.27483	0.239271
$487$	−4.23946	−0.192108	−0.0960542	−	0.995376i	$-0.530622\pi$
$487$	−4.23946	−0.192108	−0.0960542	+	0.995376i	$0.530622\pi$
$488$	−4.49812	−0.203620
$489$	40.6152	1.83668
$490$	−2.82019	−0.127403
$491$	42.7437	1.92900	0.964499	−	0.264086i	$-0.0850703\pi$
$491$	42.7437	1.92900	0.964499	+	0.264086i	$0.0850703\pi$
$492$	−8.29013	−0.373748
$493$	18.7717	0.845435
$494$	20.0145	0.900494
$495$	5.49347	0.246913
$496$	11.0829	0.497638
$497$	−3.12978	−0.140390
$498$	31.7288	1.42180
$499$	−25.7959	−1.15478	−0.577392	−	0.816467i	$-0.695930\pi$
$499$	−25.7959	−1.15478	−0.577392	+	0.816467i	$0.695930\pi$
$500$	3.98816	0.178356
$501$	28.0992	1.25538
$502$	24.3815	1.08820
$503$	−18.6434	−0.831268	−0.415634	−	0.909532i	$-0.636440\pi$
$503$	−18.6434	−0.831268	−0.415634	+	0.909532i	$0.636440\pi$
$504$	1.32932	0.0592128
$505$	6.11063	0.271920
$506$	−0.391184	−0.0173903
$507$	14.2915	0.634709
$508$	1.02675	0.0455547
$509$	22.6098	1.00216	0.501080	−	0.865401i	$-0.332936\pi$
$509$	22.6098	1.00216	0.501080	+	0.865401i	$0.332936\pi$
$510$	−2.96344	−0.131223
$511$	0.820700	0.0363056
$512$	−1.00000	−0.0441942
$513$	−69.2829	−3.05891
$514$	4.25406	0.187639
$515$	1.75095	0.0771563
$516$	23.4553	1.03256
$517$	20.5116	0.902101
$518$	1.08647	0.0477368
$519$	9.47284	0.415811
$520$	−1.16872	−0.0512516
$521$	36.1843	1.58526	0.792632	−	0.609701i	$-0.208710\pi$
$521$	36.1843	1.58526	0.792632	+	0.609701i	$0.208710\pi$
$522$	−49.0953	−2.14884
$523$	−31.6133	−1.38235	−0.691177	−	0.722686i	$-0.742907\pi$
$523$	−31.6133	−1.38235	−0.691177	+	0.722686i	$0.742907\pi$
$524$	18.8233	0.822302
$525$	−3.11946	−0.136144
$526$	−5.39480	−0.235225
$527$	26.5949	1.15849
$528$	6.57466	0.286125
$529$	−22.9672	−0.998572
$530$	−1.08916	−0.0473099
$531$	1.56333	0.0678427
$532$	−1.47081	−0.0637679
$533$	−7.84546	−0.339825
$534$	35.8710	1.55229
$535$	−7.21546	−0.311952
$536$	−10.1429	−0.438107
$537$	−18.8085	−0.811646
$538$	16.9318	0.729981
$539$	15.0141	0.646703
$540$	4.04567	0.174098
$541$	−1.37914	−0.0592938	−0.0296469	−	0.999560i	$-0.509438\pi$
$541$	−1.37914	−0.0592938	−0.0296469	+	0.999560i	$0.509438\pi$
$542$	0.0320321	0.00137590
$543$	28.0978	1.20579
$544$	−2.39963	−0.102883
$545$	1.79463	0.0768737
$546$	1.85937	0.0795738
$547$	−11.0275	−0.471501	−0.235750	−	0.971814i	$-0.575755\pi$
$547$	−11.0275	−0.471501	−0.235750	+	0.971814i	$0.575755\pi$
$548$	5.14314	0.219704
$549$	28.2300	1.20483
$550$	−10.4386	−0.445104
$551$	54.3209	2.31415
$552$	−0.551909	−0.0234908
$553$	−0.367659	−0.0156345
$554$	−26.5870	−1.12957
$555$	6.33460	0.268889
$556$	−7.52067	−0.318947
$557$	−1.38562	−0.0587108	−0.0293554	−	0.999569i	$-0.509345\pi$
$557$	−1.38562	−0.0587108	−0.0293554	+	0.999569i	$0.509345\pi$
$558$	−69.5560	−2.94454
$559$	22.1972	0.938842
$560$	0.0858861	0.00362935
$561$	15.7767	0.666095
$562$	9.21630	0.388766
$563$	−38.1257	−1.60680	−0.803402	−	0.595437i	$-0.796979\pi$
$563$	−38.1257	−1.60680	−0.803402	+	0.595437i	$0.796979\pi$
$564$	28.9392	1.21856
$565$	−2.99330	−0.125929
$566$	1.96246	0.0824884
$567$	−2.44851	−0.102828
$568$	−14.7762	−0.619996
$569$	11.7756	0.493660	0.246830	−	0.969059i	$-0.420611\pi$
$569$	11.7756	0.493660	0.246830	+	0.969059i	$0.420611\pi$
$570$	−8.57550	−0.359188
$571$	−10.9107	−0.456597	−0.228299	−	0.973591i	$-0.573316\pi$
$571$	−10.9107	−0.456597	−0.228299	+	0.973591i	$0.573316\pi$
$572$	6.22200	0.260155
$573$	26.7387	1.11703
$574$	0.576544	0.0240645
$575$	0.876267	0.0365429
$576$	6.27596	0.261498
$577$	5.30734	0.220947	0.110474	−	0.993879i	$-0.464763\pi$
$577$	5.30734	0.220947	0.110474	+	0.993879i	$0.464763\pi$
$578$	11.2418	0.467596
$579$	11.1758	0.464451
$580$	−3.17199	−0.131710
$581$	−2.20660	−0.0915453
$582$	−42.8917	−1.77792
$583$	5.79844	0.240147
$584$	3.87466	0.160335
$585$	7.33482	0.303258
$586$	−19.6595	−0.812126
$587$	27.2480	1.12464	0.562322	−	0.826918i	$-0.309908\pi$
$587$	27.2480	1.12464	0.562322	+	0.826918i	$0.309908\pi$
$588$	21.1829	0.873567
$589$	76.9595	3.17106
$590$	0.101005	0.00415831
$591$	23.3054	0.958657
$592$	5.12941	0.210817
$593$	41.0044	1.68385	0.841924	−	0.539597i	$-0.181423\pi$
$593$	41.0044	1.68385	0.841924	+	0.539597i	$0.181423\pi$
$594$	−21.5383	−0.883728
$595$	0.206095	0.00844907
$596$	−11.5223	−0.471972
$597$	4.47293	0.183065
$598$	−0.522305	−0.0213587
$599$	26.0808	1.06563	0.532815	−	0.846232i	$-0.321134\pi$
$599$	26.0808	1.06563	0.532815	+	0.846232i	$0.321134\pi$
$600$	−14.7275	−0.601247
$601$	−5.41987	−0.221081	−0.110541	−	0.993872i	$-0.535258\pi$
$601$	−5.41987	−0.221081	−0.110541	+	0.993872i	$0.535258\pi$
$602$	−1.63122	−0.0664835
$603$	63.6565	2.59229
$604$	0.170707	0.00694595
$605$	2.57076	0.104516
$606$	−45.8979	−1.86448
$607$	45.4881	1.84631	0.923153	−	0.384432i	$-0.125603\pi$
$607$	45.4881	1.84631	0.923153	+	0.384432i	$0.125603\pi$
$608$	−6.94396	−0.281615
$609$	5.04649	0.204494
$610$	1.82391	0.0738480
$611$	27.3869	1.10796
$612$	15.0600	0.608764
$613$	−15.0847	−0.609266	−0.304633	−	0.952470i	$-0.598534\pi$
$613$	−15.0847	−0.609266	−0.304633	+	0.952470i	$0.598534\pi$
$614$	−8.37016	−0.337792
$615$	3.36151	0.135549
$616$	−0.457240	−0.0184227
$617$	−19.1899	−0.772556	−0.386278	−	0.922383i	$-0.626239\pi$
$617$	−19.1899	−0.772556	−0.386278	+	0.922383i	$0.626239\pi$
$618$	−13.1517	−0.529039
$619$	16.4563	0.661433	0.330717	−	0.943730i	$-0.392710\pi$
$619$	16.4563	0.661433	0.330717	+	0.943730i	$0.392710\pi$
$620$	−4.49394	−0.180481
$621$	1.80803	0.0725538
$622$	−9.03469	−0.362258
$623$	−2.49468	−0.0999471
$624$	8.77841	0.351418
$625$	22.5608	0.902431
$626$	−8.14134	−0.325394
$627$	45.6542	1.82325
$628$	1.48141	0.0591147
$629$	12.3087	0.490779
$630$	−0.539018	−0.0214750
$631$	−1.75740	−0.0699609	−0.0349805	−	0.999388i	$-0.511137\pi$
$631$	−1.75740	−0.0699609	−0.0349805	+	0.999388i	$0.511137\pi$
$632$	−1.73578	−0.0690456
$633$	−50.7338	−2.01649
$634$	−24.4337	−0.970386
$635$	−0.416330	−0.0165216
$636$	8.18083	0.324391
$637$	20.0467	0.794278
$638$	16.8870	0.668563
$639$	92.7349	3.66854
$640$	0.405483	0.0160281
$641$	−2.10686	−0.0832159	−0.0416079	−	0.999134i	$-0.513248\pi$
$641$	−2.10686	−0.0832159	−0.0416079	+	0.999134i	$0.513248\pi$
$642$	54.1965	2.13896
$643$	6.67041	0.263055	0.131528	−	0.991312i	$-0.458012\pi$
$643$	6.67041	0.263055	0.131528	+	0.991312i	$0.458012\pi$
$644$	0.0383829	0.00151250
$645$	−9.51073	−0.374485
$646$	−16.6629	−0.655595
$647$	21.3811	0.840577	0.420289	−	0.907391i	$-0.361929\pi$
$647$	21.3811	0.840577	0.420289	+	0.907391i	$0.361929\pi$
$648$	−11.5598	−0.454112
$649$	−0.537729	−0.0211077
$650$	−13.9375	−0.546675
$651$	7.14965	0.280217
$652$	−13.3355	−0.522258
$653$	36.4789	1.42753	0.713765	−	0.700386i	$-0.246989\pi$
$653$	36.4789	1.42753	0.713765	+	0.700386i	$0.246989\pi$
$654$	−13.4798	−0.527101
$655$	−7.63254	−0.298228
$656$	2.72196	0.106275
$657$	−24.3172	−0.948706
$658$	−2.01260	−0.0784593
$659$	7.72071	0.300756	0.150378	−	0.988629i	$-0.451951\pi$
$659$	7.72071	0.300756	0.150378	+	0.988629i	$0.451951\pi$
$660$	−2.66591	−0.103770
$661$	−48.8504	−1.90006	−0.950030	−	0.312158i	$-0.898948\pi$
$661$	−48.8504	−1.90006	−0.950030	+	0.312158i	$0.898948\pi$
$662$	12.9307	0.502566
$663$	21.0649	0.818095
$664$	−10.4177	−0.404287
$665$	0.596390	0.0231270
$666$	−32.1920	−1.24741
$667$	−1.41758	−0.0548889
$668$	−9.22602	−0.356966
$669$	71.8077	2.77625
$670$	4.11278	0.158890
$671$	−9.71012	−0.374855
$672$	−0.645104	−0.0248854
$673$	−32.5083	−1.25310	−0.626551	−	0.779381i	$-0.715534\pi$
$673$	−32.5083	−1.25310	−0.626551	+	0.779381i	$0.715534\pi$
$674$	0.0929043	0.00357854
$675$	48.2467	1.85701
$676$	−4.69245	−0.180479
$677$	−27.2377	−1.04683	−0.523415	−	0.852078i	$-0.675342\pi$
$677$	−27.2377	−1.04683	−0.523415	+	0.852078i	$0.675342\pi$
$678$	22.4832	0.863461
$679$	2.98294	0.114475
$680$	0.973009	0.0373132
$681$	0.748033	0.0286647
$682$	23.9248	0.916128
$683$	−34.2634	−1.31105	−0.655526	−	0.755173i	$-0.727553\pi$
$683$	−34.2634	−1.31105	−0.655526	+	0.755173i	$0.727553\pi$
$684$	43.5801	1.66633
$685$	−2.08545	−0.0796811
$686$	−2.95586	−0.112855
$687$	−57.7313	−2.20259
$688$	−7.70126	−0.293608
$689$	7.74202	0.294947
$690$	0.223790	0.00851952
$691$	−8.22506	−0.312896	−0.156448	−	0.987686i	$-0.550004\pi$
$691$	−8.22506	−0.312896	−0.156448	+	0.987686i	$0.550004\pi$
$692$	−3.11029	−0.118235
$693$	2.86962	0.109008
$694$	−28.3306	−1.07541
$695$	3.04950	0.115674
$696$	23.8253	0.903097
$697$	6.53170	0.247406
$698$	−2.98608	−0.113025
$699$	67.6677	2.55943
$700$	1.02423	0.0387124
$701$	12.2502	0.462686	0.231343	−	0.972872i	$-0.425688\pi$
$701$	12.2502	0.462686	0.231343	+	0.972872i	$0.425688\pi$
$702$	−28.7578	−1.08539
$703$	35.6184	1.34337
$704$	−2.15871	−0.0813593
$705$	−11.7344	−0.441941
$706$	11.3130	0.425770
$707$	3.19201	0.120048
$708$	−0.758664	−0.0285123
$709$	−26.7304	−1.00388	−0.501941	−	0.864902i	$-0.667380\pi$
$709$	−26.7304	−1.00388	−0.501941	+	0.864902i	$0.667380\pi$
$710$	5.99150	0.224857
$711$	10.8937	0.408545
$712$	−11.7778	−0.441391
$713$	−2.00836	−0.0752138
$714$	−1.54801	−0.0579329
$715$	−2.52292	−0.0943517
$716$	6.17553	0.230790
$717$	63.1466	2.35825
$718$	20.9159	0.780574
$719$	46.8486	1.74716	0.873579	−	0.486683i	$-0.161793\pi$
$719$	46.8486	1.74716	0.873579	+	0.486683i	$0.161793\pi$
$720$	−2.54480	−0.0948389
$721$	0.914645	0.0340632
$722$	−29.2186	−1.08741
$723$	65.1080	2.42139
$724$	−9.22557	−0.342866
$725$	−37.8276	−1.40488
$726$	−19.3094	−0.716637
$727$	47.7791	1.77203	0.886015	−	0.463656i	$-0.153463\pi$
$727$	47.7791	1.77203	0.886015	+	0.463656i	$0.153463\pi$
$728$	−0.610502	−0.0226267
$729$	−18.6142	−0.689413
$730$	−1.57111	−0.0581494
$731$	−18.4802	−0.683514
$732$	−13.6997	−0.506355
$733$	12.6125	0.465854	0.232927	−	0.972494i	$-0.425170\pi$
$733$	12.6125	0.465854	0.232927	+	0.972494i	$0.425170\pi$
$734$	−31.6784	−1.16927
$735$	−8.58930	−0.316821
$736$	0.181212	0.00667958
$737$	−21.8956	−0.806533
$738$	−17.0829	−0.628831
$739$	−9.05852	−0.333223	−0.166612	−	0.986023i	$-0.553283\pi$
$739$	−9.05852	−0.333223	−0.166612	+	0.986023i	$0.553283\pi$
$740$	−2.07989	−0.0764582
$741$	60.9570	2.23931
$742$	−0.568942	−0.0208865
$743$	−15.1078	−0.554252	−0.277126	−	0.960834i	$-0.589382\pi$
$743$	−15.1078	−0.554252	−0.277126	+	0.960834i	$0.589382\pi$
$744$	33.7547	1.23751
$745$	4.67209	0.171172
$746$	−10.8472	−0.397144
$747$	65.3814	2.39218
$748$	−5.18010	−0.189403
$749$	−3.76914	−0.137721
$750$	12.1465	0.443529
$751$	8.03268	0.293117	0.146558	−	0.989202i	$-0.453180\pi$
$751$	8.03268	0.293117	0.146558	+	0.989202i	$0.453180\pi$
$752$	−9.50182	−0.346496
$753$	74.2575	2.70609
$754$	22.5474	0.821127
$755$	−0.0692186	−0.00251912
$756$	2.11334	0.0768613
$757$	−30.2240	−1.09851	−0.549256	−	0.835654i	$-0.685089\pi$
$757$	−30.2240	−1.09851	−0.549256	+	0.835654i	$0.685089\pi$
$758$	−17.5604	−0.637823
$759$	−1.19141	−0.0432454
$760$	2.81566	0.102135
$761$	38.2680	1.38721	0.693607	−	0.720353i	$-0.256020\pi$
$761$	38.2680	1.38721	0.693607	+	0.720353i	$0.256020\pi$
$762$	3.12712	0.113284
$763$	0.937462	0.0339384
$764$	−8.77932	−0.317625
$765$	−6.10657	−0.220783
$766$	−18.2116	−0.658011
$767$	−0.717970	−0.0259244
$768$	−3.04565	−0.109900
$769$	−32.1803	−1.16045	−0.580225	−	0.814456i	$-0.697035\pi$
$769$	−32.1803	−1.16045	−0.580225	+	0.814456i	$0.697035\pi$
$770$	0.185403	0.00668146
$771$	12.9564	0.466612
$772$	−3.66944	−0.132066
$773$	9.01736	0.324332	0.162166	−	0.986763i	$-0.448152\pi$
$773$	9.01736	0.324332	0.162166	+	0.986763i	$0.448152\pi$
$774$	48.3328	1.73729
$775$	−53.5924	−1.92510
$776$	14.0830	0.505549
$777$	3.30900	0.118710
$778$	−21.9359	−0.786442
$779$	18.9012	0.677206
$780$	−3.55950	−0.127450
$781$	−31.8975	−1.14138
$782$	0.434843	0.0155499
$783$	−78.0509	−2.78931
$784$	−6.95514	−0.248398
$785$	−0.600687	−0.0214394
$786$	57.3292	2.04487
$787$	15.4825	0.551893	0.275947	−	0.961173i	$-0.411009\pi$
$787$	15.4825	0.551893	0.275947	+	0.961173i	$0.411009\pi$
$788$	−7.65204	−0.272593
$789$	−16.4307	−0.584947
$790$	0.703829	0.0250411
$791$	−1.56361	−0.0555956
$792$	13.5480	0.481406
$793$	−12.9649	−0.460395
$794$	−29.5759	−1.04961
$795$	−3.31719	−0.117648
$796$	−1.46863	−0.0520542
$797$	13.1164	0.464608	0.232304	−	0.972643i	$-0.425374\pi$
$797$	13.1164	0.464608	0.232304	+	0.972643i	$0.425374\pi$
$798$	−4.47958	−0.158575
$799$	−22.8009	−0.806636
$800$	4.83558	0.170964
$801$	73.9170	2.61173
$802$	7.76169	0.274075
$803$	8.36426	0.295168
$804$	−30.8917	−1.08947
$805$	−0.0155636	−0.000548546 0
$806$	31.9441	1.12518
$807$	51.5682	1.81529
$808$	15.0700	0.530161
$809$	0.221213	0.00777744	0.00388872	−	0.999992i	$-0.498762\pi$
$809$	0.221213	0.00777744	0.00388872	+	0.999992i	$0.498762\pi$
$810$	4.68731	0.164695
$811$	22.2285	0.780549	0.390275	−	0.920698i	$-0.372380\pi$
$811$	22.2285	0.780549	0.390275	+	0.920698i	$0.372380\pi$
$812$	−1.65695	−0.0581476
$813$	0.0975585	0.00342152
$814$	11.0729	0.388105
$815$	5.40732	0.189410
$816$	−7.30842	−0.255846
$817$	−53.4773	−1.87093
$818$	−35.4119	−1.23815
$819$	3.83149	0.133883
$820$	−1.10371	−0.0385432
$821$	2.37900	0.0830276	0.0415138	−	0.999138i	$-0.486782\pi$
$821$	2.37900	0.0830276	0.0415138	+	0.999138i	$0.486782\pi$
$822$	15.6642	0.546351
$823$	22.5710	0.786776	0.393388	−	0.919373i	$-0.371303\pi$
$823$	22.5710	0.786776	0.393388	+	0.919373i	$0.371303\pi$
$824$	4.31820	0.150431
$825$	−31.7923	−1.10687
$826$	0.0527619	0.00183582
$827$	44.6851	1.55385	0.776927	−	0.629591i	$-0.216777\pi$
$827$	44.6851	1.55385	0.776927	+	0.629591i	$0.216777\pi$
$828$	−1.13728	−0.0395233
$829$	−23.8140	−0.827094	−0.413547	−	0.910483i	$-0.635710\pi$
$829$	−23.8140	−0.827094	−0.413547	+	0.910483i	$0.635710\pi$
$830$	4.22422	0.146625
$831$	−80.9747	−2.80898
$832$	−2.88228	−0.0999252
$833$	−16.6898	−0.578266
$834$	−22.9053	−0.793145
$835$	3.74099	0.129462
$836$	−14.9900	−0.518439
$837$	−110.579	−3.82217
$838$	−34.4826	−1.19118
$839$	20.1951	0.697212	0.348606	−	0.937269i	$-0.386655\pi$
$839$	20.1951	0.697212	0.348606	+	0.937269i	$0.386655\pi$
$840$	0.261579	0.00902533
$841$	32.1954	1.11019
$842$	28.3409	0.976690
$843$	28.0696	0.966768
$844$	16.6578	0.573385
$845$	1.90271	0.0654551
$846$	59.6331	2.05023
$847$	1.34288	0.0461421
$848$	−2.68607	−0.0922401
$849$	5.97696	0.205129
$850$	11.6036	0.398001
$851$	−0.929513	−0.0318633
$852$	−45.0031	−1.54178
$853$	−23.1339	−0.792089	−0.396045	−	0.918231i	$-0.629617\pi$
$853$	−23.1339	−0.792089	−0.396045	+	0.918231i	$0.629617\pi$
$854$	0.952755	0.0326026
$855$	−17.6710	−0.604334
$856$	−17.7947	−0.608211
$857$	13.4520	0.459510	0.229755	−	0.973248i	$-0.426207\pi$
$857$	13.4520	0.459510	0.229755	+	0.973248i	$0.426207\pi$
$858$	18.9500	0.646943
$859$	19.5185	0.665963	0.332981	−	0.942933i	$-0.391945\pi$
$859$	19.5185	0.665963	0.332981	+	0.942933i	$0.391945\pi$
$860$	3.12273	0.106484
$861$	1.75595	0.0598426
$862$	−35.8299	−1.22037
$863$	−29.7915	−1.01412	−0.507058	−	0.861912i	$-0.669267\pi$
$863$	−29.7915	−1.01412	−0.507058	+	0.861912i	$0.669267\pi$
$864$	9.97742	0.339439
$865$	1.26117	0.0428810
$866$	8.53995	0.290199
$867$	34.2385	1.16280
$868$	−2.34750	−0.0796792
$869$	−3.74704	−0.127110
$870$	−9.66076	−0.327531
$871$	−29.2347	−0.990581
$872$	4.42592	0.149880
$873$	−88.3841	−2.99135
$874$	1.25833	0.0425637
$875$	−0.844740	−0.0285574
$876$	11.8009	0.398714
$877$	28.5104	0.962728	0.481364	−	0.876521i	$-0.340142\pi$
$877$	28.5104	0.962728	0.481364	+	0.876521i	$0.340142\pi$
$878$	6.09663	0.205751
$879$	−59.8759	−2.01956
$880$	0.875319	0.0295070
$881$	−4.94037	−0.166445	−0.0832226	−	0.996531i	$-0.526521\pi$
$881$	−4.94037	−0.166445	−0.0832226	+	0.996531i	$0.526521\pi$
$882$	43.6502	1.46978
$883$	13.5773	0.456914	0.228457	−	0.973554i	$-0.426632\pi$
$883$	13.5773	0.456914	0.228457	+	0.973554i	$0.426632\pi$
$884$	−6.91641	−0.232624
$885$	0.307625	0.0103407
$886$	0.257793	0.00866073
$887$	12.2066	0.409858	0.204929	−	0.978777i	$-0.434304\pi$
$887$	12.2066	0.409858	0.204929	+	0.978777i	$0.434304\pi$
$888$	15.6224	0.524252
$889$	−0.217478	−0.00729399
$890$	4.77569	0.160082
$891$	−24.9542	−0.835998
$892$	−23.5772	−0.789422
$893$	−65.9803	−2.20795
$894$	−35.0928	−1.17368
$895$	−2.50407	−0.0837019
$896$	0.211812	0.00707614
$897$	−1.59076	−0.0531138
$898$	12.0636	0.402567
$899$	86.6990	2.89157
$900$	−30.3479	−1.01160
$901$	−6.44558	−0.214733
$902$	5.87591	0.195647
$903$	−4.96812	−0.165329
$904$	−7.38207	−0.245524
$905$	3.74081	0.124349
$906$	0.519912	0.0172729
$907$	1.61118	0.0534982	0.0267491	−	0.999642i	$-0.491484\pi$
$907$	1.61118	0.0534982	0.0267491	+	0.999642i	$0.491484\pi$
$908$	−0.245607	−0.00815076
$909$	−94.5788	−3.13698
$910$	0.247548	0.00820614
$911$	−11.6988	−0.387598	−0.193799	−	0.981041i	$-0.562081\pi$
$911$	−11.6988	−0.387598	−0.193799	+	0.981041i	$0.562081\pi$
$912$	−21.1489	−0.700309
$913$	−22.4889	−0.744273
$914$	−27.5677	−0.911858
$915$	5.55499	0.183642
$916$	18.9554	0.626303
$917$	−3.98701	−0.131663
$918$	23.9421	0.790208
$919$	−4.57870	−0.151037	−0.0755187	−	0.997144i	$-0.524061\pi$
$919$	−4.57870	−0.151037	−0.0755187	+	0.997144i	$0.524061\pi$
$920$	−0.0734785	−0.00242251
$921$	−25.4925	−0.840008
$922$	18.1940	0.599189
$923$	−42.5892	−1.40184
$924$	−1.39259	−0.0458129
$925$	−24.8037	−0.815540
$926$	−3.80413	−0.125011
$927$	−27.1008	−0.890108
$928$	−7.82275	−0.256794
$929$	−10.7238	−0.351837	−0.175919	−	0.984405i	$-0.556290\pi$
$929$	−10.7238	−0.351837	−0.175919	+	0.984405i	$0.556290\pi$
$930$	−13.6869	−0.448813
$931$	−48.2962	−1.58284
$932$	−22.2179	−0.727770
$933$	−27.5165	−0.900849
$934$	7.99283	0.261533
$935$	2.10044	0.0686918
$936$	18.0891	0.591261
$937$	11.8516	0.387175	0.193587	−	0.981083i	$-0.437988\pi$
$937$	11.8516	0.387175	0.193587	+	0.981083i	$0.437988\pi$
$938$	2.14839	0.0701474
$939$	−24.7957	−0.809176
$940$	3.85283	0.125665
$941$	0.0541102	0.00176394	0.000881970	−	1.00000i	$-0.499719\pi$
$941$	0.0541102	0.00176394	0.000881970		1.00000i	$0.499719\pi$
$942$	4.51185	0.147004
$943$	−0.493253	−0.0160625
$944$	0.249098	0.00810744
$945$	−0.856922	−0.0278757
$946$	−16.6248	−0.540518
$947$	49.6654	1.61391	0.806954	−	0.590614i	$-0.201115\pi$
$947$	49.6654	1.61391	0.806954	+	0.590614i	$0.201115\pi$
$948$	−5.28657	−0.171700
$949$	11.1679	0.362525
$950$	33.5781	1.08942
$951$	−74.4164	−2.41312
$952$	0.508270	0.0164731
$953$	16.9472	0.548972	0.274486	−	0.961591i	$-0.411492\pi$
$953$	16.9472	0.548972	0.274486	+	0.961591i	$0.411492\pi$
$954$	16.8577	0.545788
$955$	3.55986	0.115195
$956$	−20.7334	−0.670566
$957$	51.4319	1.66256
$958$	5.95739	0.192474
$959$	−1.08938	−0.0351779
$960$	1.23496	0.0398581
$961$	91.8313	2.96230
$962$	14.7844	0.476669
$963$	111.679	3.59881
$964$	−21.3774	−0.688520
$965$	1.48789	0.0478970
$966$	0.116901	0.00376122
$967$	−21.9524	−0.705941	−0.352970	−	0.935634i	$-0.614828\pi$
$967$	−21.9524	−0.705941	−0.352970	+	0.935634i	$0.614828\pi$
$968$	6.33999	0.203775
$969$	−50.7494	−1.63031
$970$	−5.71040	−0.183350
$971$	44.8061	1.43790	0.718948	−	0.695064i	$-0.244624\pi$
$971$	44.8061	1.43790	0.718948	+	0.695064i	$0.244624\pi$
$972$	−5.27483	−0.169190
$973$	1.59297	0.0510682
$974$	4.23946	0.135841
$975$	−42.4488	−1.35945
$976$	4.49812	0.143981
$977$	−1.91293	−0.0611999	−0.0306000	−	0.999532i	$-0.509742\pi$
$977$	−1.91293	−0.0611999	−0.0306000	+	0.999532i	$0.509742\pi$
$978$	−40.6152	−1.29873
$979$	−25.4248	−0.812580
$980$	2.82019	0.0900876
$981$	−27.7769	−0.886848
$982$	−42.7437	−1.36401
$983$	−4.94620	−0.157759	−0.0788796	−	0.996884i	$-0.525134\pi$
$983$	−4.94620	−0.157759	−0.0788796	+	0.996884i	$0.525134\pi$
$984$	8.29013	0.264280
$985$	3.10277	0.0988626
$986$	−18.7717	−0.597813
$987$	−6.12967	−0.195109
$988$	−20.0145	−0.636745
$989$	1.39556	0.0443763
$990$	−5.49347	−0.174594
$991$	−9.48534	−0.301312	−0.150656	−	0.988586i	$-0.548139\pi$
$991$	−9.48534	−0.301312	−0.150656	+	0.988586i	$0.548139\pi$
$992$	−11.0829	−0.351883
$993$	39.3824	1.24976
$994$	3.12978	0.0992705
$995$	0.595505	0.0188788
$996$	−31.7288	−1.00536
$997$	51.4378	1.62905	0.814526	−	0.580126i	$-0.196997\pi$
$997$	51.4378	1.62905	0.814526	+	0.580126i	$0.196997\pi$
$998$	25.7959	0.816556
$999$	−51.1783	−1.61921

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8026.2.a.c.1.6	✓	86

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8026.2.a.c.1.6	✓	86	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:	\( N \)	\(=\)	\( 8026 = 2 \cdot 4013 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8026.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.04565 q^{3} +1.00000 q^{4} -0.405483 q^{5} +3.04565 q^{6} -0.211812 q^{7} -1.00000 q^{8} +6.27596 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -3.04565 q^{3} +1.00000 q^{4} -0.405483 q^{5} +3.04565 q^{6} -0.211812 q^{7} -1.00000 q^{8} +6.27596 q^{9} +0.405483 q^{10} -2.15871 q^{11} -3.04565 q^{12} -2.88228 q^{13} +0.211812 q^{14} +1.23496 q^{15} +1.00000 q^{16} +2.39963 q^{17} -6.27596 q^{18} +6.94396 q^{19} -0.405483 q^{20} +0.645104 q^{21} +2.15871 q^{22} -0.181212 q^{23} +3.04565 q^{24} -4.83558 q^{25} +2.88228 q^{26} -9.97742 q^{27} -0.211812 q^{28} +7.82275 q^{29} -1.23496 q^{30} +11.0829 q^{31} -1.00000 q^{32} +6.57466 q^{33} -2.39963 q^{34} +0.0858861 q^{35} +6.27596 q^{36} +5.12941 q^{37} -6.94396 q^{38} +8.77841 q^{39} +0.405483 q^{40} +2.72196 q^{41} -0.645104 q^{42} -7.70126 q^{43} -2.15871 q^{44} -2.54480 q^{45} +0.181212 q^{46} -9.50182 q^{47} -3.04565 q^{48} -6.95514 q^{49} +4.83558 q^{50} -7.30842 q^{51} -2.88228 q^{52} -2.68607 q^{53} +9.97742 q^{54} +0.875319 q^{55} +0.211812 q^{56} -21.1489 q^{57} -7.82275 q^{58} +0.249098 q^{59} +1.23496 q^{60} +4.49812 q^{61} -11.0829 q^{62} -1.32932 q^{63} +1.00000 q^{64} +1.16872 q^{65} -6.57466 q^{66} +10.1429 q^{67} +2.39963 q^{68} +0.551909 q^{69} -0.0858861 q^{70} +14.7762 q^{71} -6.27596 q^{72} -3.87466 q^{73} -5.12941 q^{74} +14.7275 q^{75} +6.94396 q^{76} +0.457240 q^{77} -8.77841 q^{78} +1.73578 q^{79} -0.405483 q^{80} +11.5598 q^{81} -2.72196 q^{82} +10.4177 q^{83} +0.645104 q^{84} -0.973009 q^{85} +7.70126 q^{86} -23.8253 q^{87} +2.15871 q^{88} +11.7778 q^{89} +2.54480 q^{90} +0.610502 q^{91} -0.181212 q^{92} -33.7547 q^{93} +9.50182 q^{94} -2.81566 q^{95} +3.04565 q^{96} -14.0830 q^{97} +6.95514 q^{98} -13.5480 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 86 q - 86 q^{2} + 11 q^{3} + 86 q^{4} + 25 q^{5} - 11 q^{6} - 3 q^{7} - 86 q^{8} + 105 q^{9}+O(q^{10}) \) 86 * q - 86 * q^2 + 11 * q^3 + 86 * q^4 + 25 * q^5 - 11 * q^6 - 3 * q^7 - 86 * q^8 + 105 * q^9	\( 86 q - 86 q^{2} + 11 q^{3} + 86 q^{4} + 25 q^{5} - 11 q^{6} - 3 q^{7} - 86 q^{8} + 105 q^{9} - 25 q^{10} + 44 q^{11} + 11 q^{12} - 36 q^{13} + 3 q^{14} + 19 q^{15} + 86 q^{16} + 21 q^{17} - 105 q^{18} + 35 q^{19} + 25 q^{20} + 23 q^{21} - 44 q^{22} + 38 q^{23} - 11 q^{24} + 85 q^{25} + 36 q^{26} + 47 q^{27} - 3 q^{28} + 30 q^{29} - 19 q^{30} + 23 q^{31} - 86 q^{32} + 5 q^{33} - 21 q^{34} + 59 q^{35} + 105 q^{36} - 20 q^{37} - 35 q^{38} + 4 q^{39} - 25 q^{40} + 64 q^{41} - 23 q^{42} + 23 q^{43} + 44 q^{44} + 60 q^{45} - 38 q^{46} + 77 q^{47} + 11 q^{48} + 109 q^{49} - 85 q^{50} + 47 q^{51} - 36 q^{52} + 22 q^{53} - 47 q^{54} + 6 q^{55} + 3 q^{56} - 9 q^{57} - 30 q^{58} + 145 q^{59} + 19 q^{60} - 24 q^{61} - 23 q^{62} + 6 q^{63} + 86 q^{64} + 37 q^{65} - 5 q^{66} + 44 q^{67} + 21 q^{68} + 25 q^{69} - 59 q^{70} + 107 q^{71} - 105 q^{72} - 55 q^{73} + 20 q^{74} + 86 q^{75} + 35 q^{76} + 25 q^{77} - 4 q^{78} + 2 q^{79} + 25 q^{80} + 170 q^{81} - 64 q^{82} + 109 q^{83} + 23 q^{84} - 13 q^{85} - 23 q^{86} + 3 q^{87} - 44 q^{88} + 121 q^{89} - 60 q^{90} + 81 q^{91} + 38 q^{92} + 27 q^{93} - 77 q^{94} + 49 q^{95} - 11 q^{96} - 56 q^{97} - 109 q^{98} + 158 q^{99}+O(q^{100}) \) 86 * q - 86 * q^2 + 11 * q^3 + 86 * q^4 + 25 * q^5 - 11 * q^6 - 3 * q^7 - 86 * q^8 + 105 * q^9 - 25 * q^10 + 44 * q^11 + 11 * q^12 - 36 * q^13 + 3 * q^14 + 19 * q^15 + 86 * q^16 + 21 * q^17 - 105 * q^18 + 35 * q^19 + 25 * q^20 + 23 * q^21 - 44 * q^22 + 38 * q^23 - 11 * q^24 + 85 * q^25 + 36 * q^26 + 47 * q^27 - 3 * q^28 + 30 * q^29 - 19 * q^30 + 23 * q^31 - 86 * q^32 + 5 * q^33 - 21 * q^34 + 59 * q^35 + 105 * q^36 - 20 * q^37 - 35 * q^38 + 4 * q^39 - 25 * q^40 + 64 * q^41 - 23 * q^42 + 23 * q^43 + 44 * q^44 + 60 * q^45 - 38 * q^46 + 77 * q^47 + 11 * q^48 + 109 * q^49 - 85 * q^50 + 47 * q^51 - 36 * q^52 + 22 * q^53 - 47 * q^54 + 6 * q^55 + 3 * q^56 - 9 * q^57 - 30 * q^58 + 145 * q^59 + 19 * q^60 - 24 * q^61 - 23 * q^62 + 6 * q^63 + 86 * q^64 + 37 * q^65 - 5 * q^66 + 44 * q^67 + 21 * q^68 + 25 * q^69 - 59 * q^70 + 107 * q^71 - 105 * q^72 - 55 * q^73 + 20 * q^74 + 86 * q^75 + 35 * q^76 + 25 * q^77 - 4 * q^78 + 2 * q^79 + 25 * q^80 + 170 * q^81 - 64 * q^82 + 109 * q^83 + 23 * q^84 - 13 * q^85 - 23 * q^86 + 3 * q^87 - 44 * q^88 + 121 * q^89 - 60 * q^90 + 81 * q^91 + 38 * q^92 + 27 * q^93 - 77 * q^94 + 49 * q^95 - 11 * q^96 - 56 * q^97 - 109 * q^98 + 158 * q^99

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