LMFDB - Embedded newform 6023.2.a.a.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6023,2,Mod(1,6023)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6023, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6023.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6023 = 19 \cdot 317 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6023.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:	$48.0938971374$
Analytic rank:	$1$
Dimension:	$98$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	6023.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.23585 q^{2} +2.07159 q^{3} +2.99900 q^{4} +2.91944 q^{5} -4.63176 q^{6} -1.89696 q^{7} -2.23362 q^{8} +1.29150 q^{9} +O(q^{10})$	\(q-2.23585 q^{2} +2.07159 q^{3} +2.99900 q^{4} +2.91944 q^{5} -4.63176 q^{6} -1.89696 q^{7} -2.23362 q^{8} +1.29150 q^{9} -6.52741 q^{10} +2.98335 q^{11} +6.21272 q^{12} -4.56878 q^{13} +4.24131 q^{14} +6.04789 q^{15} -1.00398 q^{16} +1.25601 q^{17} -2.88760 q^{18} +1.00000 q^{19} +8.75541 q^{20} -3.92973 q^{21} -6.67031 q^{22} -6.85861 q^{23} -4.62715 q^{24} +3.52312 q^{25} +10.2151 q^{26} -3.53931 q^{27} -5.68899 q^{28} -1.57601 q^{29} -13.5221 q^{30} -0.531034 q^{31} +6.71198 q^{32} +6.18029 q^{33} -2.80824 q^{34} -5.53806 q^{35} +3.87322 q^{36} +3.07543 q^{37} -2.23585 q^{38} -9.46465 q^{39} -6.52092 q^{40} -12.4614 q^{41} +8.78627 q^{42} +1.69221 q^{43} +8.94708 q^{44} +3.77046 q^{45} +15.3348 q^{46} +5.70748 q^{47} -2.07984 q^{48} -3.40154 q^{49} -7.87715 q^{50} +2.60194 q^{51} -13.7018 q^{52} -10.8940 q^{53} +7.91336 q^{54} +8.70971 q^{55} +4.23709 q^{56} +2.07159 q^{57} +3.52371 q^{58} -14.4948 q^{59} +18.1377 q^{60} +13.5609 q^{61} +1.18731 q^{62} -2.44993 q^{63} -12.9990 q^{64} -13.3383 q^{65} -13.8182 q^{66} -10.4131 q^{67} +3.76677 q^{68} -14.2083 q^{69} +12.3822 q^{70} -6.64663 q^{71} -2.88473 q^{72} -2.87518 q^{73} -6.87618 q^{74} +7.29847 q^{75} +2.99900 q^{76} -5.65930 q^{77} +21.1615 q^{78} +3.46304 q^{79} -2.93106 q^{80} -11.2065 q^{81} +27.8618 q^{82} +6.27586 q^{83} -11.7853 q^{84} +3.66683 q^{85} -3.78351 q^{86} -3.26484 q^{87} -6.66367 q^{88} +11.5389 q^{89} -8.43017 q^{90} +8.66679 q^{91} -20.5690 q^{92} -1.10009 q^{93} -12.7610 q^{94} +2.91944 q^{95} +13.9045 q^{96} +8.32391 q^{97} +7.60532 q^{98} +3.85300 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 98 q - 8 q^{2} - 25 q^{3} + 82 q^{4} - 10 q^{5} - 4 q^{6} - 18 q^{7} - 18 q^{8} + 61 q^{9}+O(q^{10}) $ 98 * q - 8 * q^2 - 25 * q^3 + 82 * q^4 - 10 * q^5 - 4 * q^6 - 18 * q^7 - 18 * q^8 + 61 * q^9	\( 98 q - 8 q^{2} - 25 q^{3} + 82 q^{4} - 10 q^{5} - 4 q^{6} - 18 q^{7} - 18 q^{8} + 61 q^{9} - 24 q^{10} - 12 q^{11} - 51 q^{12} - 58 q^{13} - 15 q^{14} - 18 q^{15} + 58 q^{16} - 25 q^{17} - 40 q^{18} + 98 q^{19} - 12 q^{20} - 24 q^{21} - 59 q^{22} - 38 q^{23} - 9 q^{24} - 12 q^{25} - 3 q^{26} - 85 q^{27} - 33 q^{28} - 24 q^{29} - 22 q^{30} - 56 q^{31} - 29 q^{32} - 51 q^{33} - 38 q^{34} - 10 q^{35} + 50 q^{36} - 124 q^{37} - 8 q^{38} - 4 q^{39} - 80 q^{40} - 28 q^{41} - 37 q^{42} - 63 q^{43} - 7 q^{44} - 32 q^{45} - 47 q^{46} - 10 q^{47} - 88 q^{48} + 6 q^{49} - 17 q^{50} - 22 q^{51} - 119 q^{52} - 65 q^{53} + 24 q^{54} - 30 q^{55} - 39 q^{56} - 25 q^{57} - 91 q^{58} - 26 q^{59} - 60 q^{60} - 60 q^{61} + 6 q^{62} - 26 q^{63} + 50 q^{64} - 40 q^{65} + 57 q^{66} - 108 q^{67} - 41 q^{68} - 15 q^{69} - 36 q^{70} - 19 q^{71} - 47 q^{72} - 136 q^{73} + 22 q^{74} - 48 q^{75} + 82 q^{76} - 35 q^{77} - 56 q^{78} - 98 q^{79} - 42 q^{80} + 6 q^{81} - 37 q^{82} - 31 q^{83} - 24 q^{84} - 71 q^{85} - 24 q^{86} + 7 q^{87} - 166 q^{88} - 38 q^{89} + 26 q^{90} - 100 q^{91} - 59 q^{92} - 21 q^{93} - 48 q^{94} - 10 q^{95} - 16 q^{96} - 190 q^{97} - 80 q^{98} - 17 q^{99}+O(q^{100}) \) 98 * q - 8 * q^2 - 25 * q^3 + 82 * q^4 - 10 * q^5 - 4 * q^6 - 18 * q^7 - 18 * q^8 + 61 * q^9 - 24 * q^10 - 12 * q^11 - 51 * q^12 - 58 * q^13 - 15 * q^14 - 18 * q^15 + 58 * q^16 - 25 * q^17 - 40 * q^18 + 98 * q^19 - 12 * q^20 - 24 * q^21 - 59 * q^22 - 38 * q^23 - 9 * q^24 - 12 * q^25 - 3 * q^26 - 85 * q^27 - 33 * q^28 - 24 * q^29 - 22 * q^30 - 56 * q^31 - 29 * q^32 - 51 * q^33 - 38 * q^34 - 10 * q^35 + 50 * q^36 - 124 * q^37 - 8 * q^38 - 4 * q^39 - 80 * q^40 - 28 * q^41 - 37 * q^42 - 63 * q^43 - 7 * q^44 - 32 * q^45 - 47 * q^46 - 10 * q^47 - 88 * q^48 + 6 * q^49 - 17 * q^50 - 22 * q^51 - 119 * q^52 - 65 * q^53 + 24 * q^54 - 30 * q^55 - 39 * q^56 - 25 * q^57 - 91 * q^58 - 26 * q^59 - 60 * q^60 - 60 * q^61 + 6 * q^62 - 26 * q^63 + 50 * q^64 - 40 * q^65 + 57 * q^66 - 108 * q^67 - 41 * q^68 - 15 * q^69 - 36 * q^70 - 19 * q^71 - 47 * q^72 - 136 * q^73 + 22 * q^74 - 48 * q^75 + 82 * q^76 - 35 * q^77 - 56 * q^78 - 98 * q^79 - 42 * q^80 + 6 * q^81 - 37 * q^82 - 31 * q^83 - 24 * q^84 - 71 * q^85 - 24 * q^86 + 7 * q^87 - 166 * q^88 - 38 * q^89 + 26 * q^90 - 100 * q^91 - 59 * q^92 - 21 * q^93 - 48 * q^94 - 10 * q^95 - 16 * q^96 - 190 * q^97 - 80 * q^98 - 17 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.23585	−1.58098	−0.790491	−	0.612474i	$-0.790174\pi$
$2$	−2.23585	−1.58098	−0.790491	+	0.612474i	$0.790174\pi$
$3$	2.07159	1.19604	0.598018	−	0.801483i	$-0.295955\pi$
$3$	2.07159	1.19604	0.598018	+	0.801483i	$0.295955\pi$
$4$	2.99900	1.49950
$5$	2.91944	1.30561	0.652806	−	0.757525i	$-0.273592\pi$
$5$	2.91944	1.30561	0.652806	+	0.757525i	$0.273592\pi$
$6$	−4.63176	−1.89091
$7$	−1.89696	−0.716984	−0.358492	−	0.933533i	$-0.616709\pi$
$7$	−1.89696	−0.716984	−0.358492	+	0.933533i	$0.616709\pi$
$8$	−2.23362	−0.789704
$9$	1.29150	0.430501
$10$	−6.52741	−2.06415
$11$	2.98335	0.899514	0.449757	−	0.893151i	$-0.351511\pi$
$11$	2.98335	0.899514	0.449757	+	0.893151i	$0.351511\pi$
$12$	6.21272	1.79346
$13$	−4.56878	−1.26715	−0.633575	−	0.773681i	$-0.718413\pi$
$13$	−4.56878	−1.26715	−0.633575	+	0.773681i	$0.718413\pi$
$14$	4.24131	1.13354
$15$	6.04789	1.56156
$16$	−1.00398	−0.250995
$17$	1.25601	0.304626	0.152313	−	0.988332i	$-0.451328\pi$
$17$	1.25601	0.304626	0.152313	+	0.988332i	$0.451328\pi$
$18$	−2.88760	−0.680614
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	8.75541	1.95777
$21$	−3.92973	−0.857538
$22$	−6.67031	−1.42212
$23$	−6.85861	−1.43012	−0.715060	−	0.699063i	$-0.753600\pi$
$23$	−6.85861	−1.43012	−0.715060	+	0.699063i	$0.753600\pi$
$24$	−4.62715	−0.944514
$25$	3.52312	0.704624
$26$	10.2151	2.00334
$27$	−3.53931	−0.681141
$28$	−5.68899	−1.07512
$29$	−1.57601	−0.292657	−0.146328	−	0.989236i	$-0.546746\pi$
$29$	−1.57601	−0.292657	−0.146328	+	0.989236i	$0.546746\pi$
$30$	−13.5221	−2.46880
$31$	−0.531034	−0.0953765	−0.0476882	−	0.998862i	$-0.515185\pi$
$31$	−0.531034	−0.0953765	−0.0476882	+	0.998862i	$0.515185\pi$
$32$	6.71198	1.18652
$33$	6.18029	1.07585
$34$	−2.80824	−0.481609
$35$	−5.53806	−0.936103
$36$	3.87322	0.645537
$37$	3.07543	0.505597	0.252799	−	0.967519i	$-0.418649\pi$
$37$	3.07543	0.505597	0.252799	+	0.967519i	$0.418649\pi$
$38$	−2.23585	−0.362702
$39$	−9.46465	−1.51556
$40$	−6.52092	−1.03105
$41$	−12.4614	−1.94614	−0.973072	−	0.230499i	$-0.925964\pi$
$41$	−12.4614	−1.94614	−0.973072	+	0.230499i	$0.925964\pi$
$42$	8.78627	1.35575
$43$	1.69221	0.258059	0.129029	−	0.991641i	$-0.458814\pi$
$43$	1.69221	0.258059	0.129029	+	0.991641i	$0.458814\pi$
$44$	8.94708	1.34882
$45$	3.77046	0.562067
$46$	15.3348	2.26099
$47$	5.70748	0.832521	0.416260	−	0.909245i	$-0.363340\pi$
$47$	5.70748	0.832521	0.416260	+	0.909245i	$0.363340\pi$
$48$	−2.07984	−0.300199
$49$	−3.40154	−0.485935
$50$	−7.87715	−1.11400
$51$	2.60194	0.364344
$52$	−13.7018	−1.90010
$53$	−10.8940	−1.49641	−0.748203	−	0.663470i	$-0.769083\pi$
$53$	−10.8940	−1.49641	−0.748203	+	0.663470i	$0.769083\pi$
$54$	7.91336	1.07687
$55$	8.70971	1.17442
$56$	4.23709	0.566205
$57$	2.07159	0.274389
$58$	3.52371	0.462685
$59$	−14.4948	−1.88706	−0.943528	−	0.331292i	$-0.892516\pi$
$59$	−14.4948	−1.88706	−0.943528	+	0.331292i	$0.892516\pi$
$60$	18.1377	2.34156
$61$	13.5609	1.73629	0.868145	−	0.496311i	$-0.165313\pi$
$61$	13.5609	1.73629	0.868145	+	0.496311i	$0.165313\pi$
$62$	1.18731	0.150788
$63$	−2.44993	−0.308662
$64$	−12.9990	−1.62487
$65$	−13.3383	−1.65441
$66$	−13.8182	−1.70090
$67$	−10.4131	−1.27216	−0.636080	−	0.771623i	$-0.719445\pi$
$67$	−10.4131	−1.27216	−0.636080	+	0.771623i	$0.719445\pi$
$68$	3.76677	0.456788
$69$	−14.2083	−1.71047
$70$	12.3822	1.47996
$71$	−6.64663	−0.788810	−0.394405	−	0.918937i	$-0.629049\pi$
$71$	−6.64663	−0.788810	−0.394405	+	0.918937i	$0.629049\pi$
$72$	−2.88473	−0.339968
$73$	−2.87518	−0.336514	−0.168257	−	0.985743i	$-0.553814\pi$
$73$	−2.87518	−0.336514	−0.168257	+	0.985743i	$0.553814\pi$
$74$	−6.87618	−0.799340
$75$	7.29847	0.842755
$76$	2.99900	0.344009
$77$	−5.65930	−0.644937
$78$	21.1615	2.39607
$79$	3.46304	0.389622	0.194811	−	0.980841i	$-0.437591\pi$
$79$	3.46304	0.389622	0.194811	+	0.980841i	$0.437591\pi$
$80$	−2.93106	−0.327702
$81$	−11.2065	−1.24517
$82$	27.8618	3.07682
$83$	6.27586	0.688865	0.344433	−	0.938811i	$-0.388071\pi$
$83$	6.27586	0.688865	0.344433	+	0.938811i	$0.388071\pi$
$84$	−11.7853	−1.28588
$85$	3.66683	0.397724
$86$	−3.78351	−0.407986
$87$	−3.26484	−0.350028
$88$	−6.66367	−0.710350
$89$	11.5389	1.22312	0.611560	−	0.791198i	$-0.290542\pi$
$89$	11.5389	1.22312	0.611560	+	0.791198i	$0.290542\pi$
$90$	−8.43017	−0.888618
$91$	8.66679	0.908526
$92$	−20.5690	−2.14447
$93$	−1.10009	−0.114074
$94$	−12.7610	−1.31620
$95$	2.91944	0.299528
$96$	13.9045	1.41912
$97$	8.32391	0.845165	0.422583	−	0.906324i	$-0.361124\pi$
$97$	8.32391	0.845165	0.422583	+	0.906324i	$0.361124\pi$
$98$	7.60532	0.768253
$99$	3.85300	0.387242
$100$	10.5658	1.05658
$101$	3.23569	0.321963	0.160982	−	0.986957i	$-0.448534\pi$
$101$	3.23569	0.321963	0.160982	+	0.986957i	$0.448534\pi$
$102$	−5.81753	−0.576021
$103$	6.37257	0.627908	0.313954	−	0.949438i	$-0.398346\pi$
$103$	6.37257	0.627908	0.313954	+	0.949438i	$0.398346\pi$
$104$	10.2049	1.00067
$105$	−11.4726	−1.11961
$106$	24.3573	2.36579
$107$	1.47458	0.142553	0.0712763	−	0.997457i	$-0.477293\pi$
$107$	1.47458	0.142553	0.0712763	+	0.997457i	$0.477293\pi$
$108$	−10.6144	−1.02137
$109$	−4.87861	−0.467286	−0.233643	−	0.972322i	$-0.575065\pi$
$109$	−4.87861	−0.467286	−0.233643	+	0.972322i	$0.575065\pi$
$110$	−19.4736	−1.85673
$111$	6.37104	0.604712
$112$	1.90451	0.179959
$113$	−1.51460	−0.142482	−0.0712409	−	0.997459i	$-0.522696\pi$
$113$	−1.51460	−0.142482	−0.0712409	+	0.997459i	$0.522696\pi$
$114$	−4.63176	−0.433804
$115$	−20.0233	−1.86718
$116$	−4.72645	−0.438840
$117$	−5.90059	−0.545509
$118$	32.4080	2.98340
$119$	−2.38260	−0.218412
$120$	−13.5087	−1.23317
$121$	−2.09962	−0.190874
$122$	−30.3200	−2.74504
$123$	−25.8150	−2.32766
$124$	−1.59257	−0.143017
$125$	−4.31166	−0.385647
$126$	5.47766	0.487989
$127$	−0.475668	−0.0422087	−0.0211044	−	0.999777i	$-0.506718\pi$
$127$	−0.475668	−0.0422087	−0.0211044	+	0.999777i	$0.506718\pi$
$128$	15.6398	1.38237
$129$	3.50556	0.308648
$130$	29.8223	2.61559
$131$	1.52547	0.133281	0.0666404	−	0.997777i	$-0.478772\pi$
$131$	1.52547	0.133281	0.0666404	+	0.997777i	$0.478772\pi$
$132$	18.5347	1.61324
$133$	−1.89696	−0.164487
$134$	23.2820	2.01126
$135$	−10.3328	−0.889306
$136$	−2.80544	−0.240565
$137$	−12.1533	−1.03833	−0.519165	−	0.854674i	$-0.673757\pi$
$137$	−12.1533	−1.03833	−0.519165	+	0.854674i	$0.673757\pi$
$138$	31.7675	2.70423
$139$	−8.30089	−0.704073	−0.352036	−	0.935986i	$-0.614511\pi$
$139$	−8.30089	−0.704073	−0.352036	+	0.935986i	$0.614511\pi$
$140$	−16.6087	−1.40369
$141$	11.8236	0.995724
$142$	14.8608	1.24709
$143$	−13.6303	−1.13982
$144$	−1.29664	−0.108054
$145$	−4.60105	−0.382097
$146$	6.42845	0.532022
$147$	−7.04661	−0.581195
$148$	9.22322	0.758144
$149$	5.60138	0.458883	0.229441	−	0.973323i	$-0.426310\pi$
$149$	5.60138	0.458883	0.229441	+	0.973323i	$0.426310\pi$
$150$	−16.3183	−1.33238
$151$	−14.6785	−1.19452	−0.597260	−	0.802048i	$-0.703744\pi$
$151$	−14.6785	−1.19452	−0.597260	+	0.802048i	$0.703744\pi$
$152$	−2.23362	−0.181171
$153$	1.62214	0.131142
$154$	12.6533	1.01963
$155$	−1.55032	−0.124525
$156$	−28.3845	−2.27258
$157$	−4.38467	−0.349935	−0.174967	−	0.984574i	$-0.555982\pi$
$157$	−4.38467	−0.349935	−0.174967	+	0.984574i	$0.555982\pi$
$158$	−7.74282	−0.615986
$159$	−22.5680	−1.78976
$160$	19.5952	1.54914
$161$	13.0105	1.02537
$162$	25.0561	1.96859
$163$	−4.81840	−0.377406	−0.188703	−	0.982034i	$-0.560428\pi$
$163$	−4.81840	−0.377406	−0.188703	+	0.982034i	$0.560428\pi$
$164$	−37.3718	−2.91825
$165$	18.0430	1.40464
$166$	−14.0319	−1.08908
$167$	−18.6984	−1.44692	−0.723462	−	0.690364i	$-0.757450\pi$
$167$	−18.6984	−1.44692	−0.723462	+	0.690364i	$0.757450\pi$
$168$	8.77753	0.677201
$169$	7.87372	0.605670
$170$	−8.19848	−0.628794
$171$	1.29150	0.0987637
$172$	5.07493	0.386960
$173$	9.86773	0.750230	0.375115	−	0.926978i	$-0.377603\pi$
$173$	9.86773	0.750230	0.375115	+	0.926978i	$0.377603\pi$
$174$	7.29969	0.553388
$175$	−6.68322	−0.505204
$176$	−2.99523	−0.225774
$177$	−30.0273	−2.25699
$178$	−25.7992	−1.93373
$179$	9.54052	0.713092	0.356546	−	0.934278i	$-0.383954\pi$
$179$	9.54052	0.713092	0.356546	+	0.934278i	$0.383954\pi$
$180$	11.3076	0.842821
$181$	−14.1351	−1.05066	−0.525329	−	0.850899i	$-0.676058\pi$
$181$	−14.1351	−1.05066	−0.525329	+	0.850899i	$0.676058\pi$
$182$	−19.3776	−1.43636
$183$	28.0926	2.07666
$184$	15.3195	1.12937
$185$	8.97852	0.660114
$186$	2.45962	0.180348
$187$	3.74711	0.274016
$188$	17.1167	1.24837
$189$	6.71394	0.488367
$190$	−6.52741	−0.473548
$191$	−0.618677	−0.0447659	−0.0223829	−	0.999749i	$-0.507125\pi$
$191$	−0.618677	−0.0447659	−0.0223829	+	0.999749i	$0.507125\pi$
$192$	−26.9287	−1.94341
$193$	−14.5114	−1.04455	−0.522276	−	0.852777i	$-0.674917\pi$
$193$	−14.5114	−1.04455	−0.522276	+	0.852777i	$0.674917\pi$
$194$	−18.6110	−1.33619
$195$	−27.6315	−1.97873
$196$	−10.2012	−0.728660
$197$	−18.0285	−1.28448	−0.642240	−	0.766503i	$-0.721995\pi$
$197$	−18.0285	−1.28448	−0.642240	+	0.766503i	$0.721995\pi$
$198$	−8.61472	−0.612222
$199$	0.464852	0.0329525	0.0164762	−	0.999864i	$-0.494755\pi$
$199$	0.464852	0.0329525	0.0164762	+	0.999864i	$0.494755\pi$
$200$	−7.86931	−0.556444
$201$	−21.5717	−1.52155
$202$	−7.23450	−0.509018
$203$	2.98962	0.209830
$204$	7.80322	0.546335
$205$	−36.3803	−2.54091
$206$	−14.2481	−0.992710
$207$	−8.85791	−0.615668
$208$	4.58696	0.318049
$209$	2.98335	0.206363
$210$	25.6510	1.77009
$211$	9.50961	0.654668	0.327334	−	0.944909i	$-0.393850\pi$
$211$	9.50961	0.654668	0.327334	+	0.944909i	$0.393850\pi$
$212$	−32.6712	−2.24386
$213$	−13.7691	−0.943445
$214$	−3.29692	−0.225373
$215$	4.94029	0.336925
$216$	7.90548	0.537900
$217$	1.00735	0.0683834
$218$	10.9078	0.738771
$219$	−5.95620	−0.402483
$220$	26.1205	1.76104
$221$	−5.73842	−0.386008
$222$	−14.2447	−0.956039
$223$	−10.3336	−0.691990	−0.345995	−	0.938236i	$-0.612459\pi$
$223$	−10.3336	−0.691990	−0.345995	+	0.938236i	$0.612459\pi$
$224$	−12.7324	−0.850717
$225$	4.55012	0.303341
$226$	3.38642	0.225261
$227$	5.65931	0.375622	0.187811	−	0.982205i	$-0.439861\pi$
$227$	5.65931	0.375622	0.187811	+	0.982205i	$0.439861\pi$
$228$	6.21272	0.411447
$229$	2.40142	0.158690	0.0793451	−	0.996847i	$-0.474717\pi$
$229$	2.40142	0.158690	0.0793451	+	0.996847i	$0.474717\pi$
$230$	44.7690	2.95198
$231$	−11.7238	−0.771367
$232$	3.52020	0.231112
$233$	−4.67437	−0.306228	−0.153114	−	0.988209i	$-0.548930\pi$
$233$	−4.67437	−0.306228	−0.153114	+	0.988209i	$0.548930\pi$
$234$	13.1928	0.862440
$235$	16.6626	1.08695
$236$	−43.4698	−2.82965
$237$	7.17401	0.466002
$238$	5.32712	0.345306
$239$	17.9346	1.16009	0.580047	−	0.814583i	$-0.303034\pi$
$239$	17.9346	1.16009	0.580047	+	0.814583i	$0.303034\pi$
$240$	−6.07196	−0.391944
$241$	19.5073	1.25658	0.628288	−	0.777981i	$-0.283756\pi$
$241$	19.5073	1.25658	0.628288	+	0.777981i	$0.283756\pi$
$242$	4.69442	0.301769
$243$	−12.5974	−0.808126
$244$	40.6691	2.60357
$245$	−9.93059	−0.634442
$246$	57.7183	3.67998
$247$	−4.56878	−0.290704
$248$	1.18613	0.0753192
$249$	13.0010	0.823907
$250$	9.64021	0.609701
$251$	−13.3060	−0.839870	−0.419935	−	0.907554i	$-0.637947\pi$
$251$	−13.3060	−0.839870	−0.419935	+	0.907554i	$0.637947\pi$
$252$	−7.34735	−0.462839
$253$	−20.4616	−1.28641
$254$	1.06352	0.0667312
$255$	7.59619	0.475692
$256$	−8.97014	−0.560634
$257$	−0.272904	−0.0170233	−0.00851164	−	0.999964i	$-0.502709\pi$
$257$	−0.272904	−0.0170233	−0.00851164	+	0.999964i	$0.502709\pi$
$258$	−7.83790	−0.487966
$259$	−5.83396	−0.362505
$260$	−40.0015	−2.48079
$261$	−2.03542	−0.125989
$262$	−3.41071	−0.210714
$263$	−2.31403	−0.142689	−0.0713445	−	0.997452i	$-0.522729\pi$
$263$	−2.31403	−0.142689	−0.0713445	+	0.997452i	$0.522729\pi$
$264$	−13.8044	−0.849604
$265$	−31.8044	−1.95373
$266$	4.24131	0.260051
$267$	23.9039	1.46289
$268$	−31.2289	−1.90761
$269$	17.2020	1.04883	0.524413	−	0.851464i	$-0.324285\pi$
$269$	17.2020	1.04883	0.524413	+	0.851464i	$0.324285\pi$
$270$	23.1026	1.40598
$271$	8.19780	0.497981	0.248990	−	0.968506i	$-0.419901\pi$
$271$	8.19780	0.497981	0.248990	+	0.968506i	$0.419901\pi$
$272$	−1.26101	−0.0764597
$273$	17.9541	1.08663
$274$	27.1730	1.64158
$275$	10.5107	0.633819
$276$	−42.6106	−2.56486
$277$	−4.04078	−0.242787	−0.121393	−	0.992604i	$-0.538736\pi$
$277$	−4.04078	−0.242787	−0.121393	+	0.992604i	$0.538736\pi$
$278$	18.5595	1.11313
$279$	−0.685831	−0.0410597
$280$	12.3699	0.739244
$281$	15.3299	0.914508	0.457254	−	0.889336i	$-0.348833\pi$
$281$	15.3299	0.914508	0.457254	+	0.889336i	$0.348833\pi$
$282$	−26.4357	−1.57422
$283$	25.1592	1.49556	0.747780	−	0.663946i	$-0.231120\pi$
$283$	25.1592	1.49556	0.747780	+	0.663946i	$0.231120\pi$
$284$	−19.9333	−1.18282
$285$	6.04789	0.358246
$286$	30.4752	1.80203
$287$	23.6388	1.39535
$288$	8.66854	0.510799
$289$	−15.4224	−0.907203
$290$	10.2872	0.604088
$291$	17.2438	1.01085
$292$	−8.62267	−0.504603
$293$	7.69321	0.449442	0.224721	−	0.974423i	$-0.427853\pi$
$293$	7.69321	0.449442	0.224721	+	0.974423i	$0.427853\pi$
$294$	15.7551	0.918858
$295$	−42.3165	−2.46376
$296$	−6.86934	−0.399272
$297$	−10.5590	−0.612696
$298$	−12.5238	−0.725485
$299$	31.3355	1.81218
$300$	21.8882	1.26371
$301$	−3.21005	−0.185024
$302$	32.8188	1.88851
$303$	6.70303	0.385079
$304$	−1.00398	−0.0575822
$305$	39.5901	2.26692
$306$	−3.62685	−0.207333
$307$	−14.0045	−0.799277	−0.399638	−	0.916673i	$-0.630864\pi$
$307$	−14.0045	−0.799277	−0.399638	+	0.916673i	$0.630864\pi$
$308$	−16.9723	−0.967084
$309$	13.2014	0.751000
$310$	3.46628	0.196871
$311$	−5.91588	−0.335459	−0.167729	−	0.985833i	$-0.553643\pi$
$311$	−5.91588	−0.335459	−0.167729	+	0.985833i	$0.553643\pi$
$312$	21.1404	1.19684
$313$	−4.50155	−0.254443	−0.127221	−	0.991874i	$-0.540606\pi$
$313$	−4.50155	−0.254443	−0.127221	+	0.991874i	$0.540606\pi$
$314$	9.80345	0.553240
$315$	−7.15242	−0.402993
$316$	10.3857	0.584240
$317$	1.00000	0.0561656
$317$	1.00000	0.0561656
$318$	50.4585	2.82957
$319$	−4.70178	−0.263249
$320$	−37.9498	−2.12146
$321$	3.05472	0.170498
$322$	−29.0895	−1.62109
$323$	1.25601	0.0698861
$324$	−33.6084	−1.86714
$325$	−16.0963	−0.892864
$326$	10.7732	0.596672
$327$	−10.1065	−0.558891
$328$	27.8340	1.53688
$329$	−10.8269	−0.596904
$330$	−40.3413	−2.22072
$331$	14.6231	0.803759	0.401880	−	0.915693i	$-0.368357\pi$
$331$	14.6231	0.803759	0.401880	+	0.915693i	$0.368357\pi$
$332$	18.8213	1.03296
$333$	3.97192	0.217660
$334$	41.8067	2.28756
$335$	−30.4004	−1.66095
$336$	3.94537	0.215238
$337$	19.2941	1.05102	0.525509	−	0.850788i	$-0.323875\pi$
$337$	19.2941	1.05102	0.525509	+	0.850788i	$0.323875\pi$
$338$	−17.6044	−0.957554
$339$	−3.13764	−0.170413
$340$	10.9969	0.596388
$341$	−1.58426	−0.0857925
$342$	−2.88760	−0.156144
$343$	19.7313	1.06539
$344$	−3.77974	−0.203790
$345$	−41.4801	−2.23322
$346$	−22.0627	−1.18610
$347$	−7.84312	−0.421041	−0.210520	−	0.977589i	$-0.567516\pi$
$347$	−7.84312	−0.421041	−0.210520	+	0.977589i	$0.567516\pi$
$348$	−9.79128	−0.524868
$349$	7.74270	0.414457	0.207229	−	0.978293i	$-0.433556\pi$
$349$	7.74270	0.414457	0.207229	+	0.978293i	$0.433556\pi$
$350$	14.9426	0.798718
$351$	16.1703	0.863108
$352$	20.0242	1.06729
$353$	−27.4227	−1.45956	−0.729781	−	0.683681i	$-0.760378\pi$
$353$	−27.4227	−1.45956	−0.729781	+	0.683681i	$0.760378\pi$
$354$	67.1363	3.56825
$355$	−19.4044	−1.02988
$356$	34.6052	1.83407
$357$	−4.93577	−0.261229
$358$	−21.3311	−1.12738
$359$	18.8969	0.997343	0.498671	−	0.866791i	$-0.333821\pi$
$359$	18.8969	0.997343	0.498671	+	0.866791i	$0.333821\pi$
$360$	−8.42178	−0.443867
$361$	1.00000	0.0526316
$362$	31.6040	1.66107
$363$	−4.34956	−0.228293
$364$	25.9917	1.36234
$365$	−8.39390	−0.439357
$366$	−62.8107	−3.28317
$367$	−11.7181	−0.611678	−0.305839	−	0.952083i	$-0.598937\pi$
$367$	−11.7181	−0.611678	−0.305839	+	0.952083i	$0.598937\pi$
$368$	6.88591	0.358953
$369$	−16.0939	−0.837817
$370$	−20.0746	−1.04363
$371$	20.6655	1.07290
$372$	−3.29916	−0.171054
$373$	−27.0002	−1.39802	−0.699008	−	0.715114i	$-0.746375\pi$
$373$	−27.0002	−1.39802	−0.699008	+	0.715114i	$0.746375\pi$
$374$	−8.37796	−0.433214
$375$	−8.93202	−0.461247
$376$	−12.7483	−0.657445
$377$	7.20042	0.370840
$378$	−15.0113	−0.772099
$379$	−9.21897	−0.473547	−0.236773	−	0.971565i	$-0.576090\pi$
$379$	−9.21897	−0.473547	−0.236773	+	0.971565i	$0.576090\pi$
$380$	8.75541	0.449143
$381$	−0.985391	−0.0504831
$382$	1.38327	0.0707740
$383$	10.6281	0.543073	0.271537	−	0.962428i	$-0.412468\pi$
$383$	10.6281	0.543073	0.271537	+	0.962428i	$0.412468\pi$
$384$	32.3993	1.65337
$385$	−16.5220	−0.842038
$386$	32.4452	1.65142
$387$	2.18549	0.111095
$388$	24.9635	1.26733
$389$	27.3884	1.38865	0.694323	−	0.719664i	$-0.255704\pi$
$389$	27.3884	1.38865	0.694323	+	0.719664i	$0.255704\pi$
$390$	61.7797	3.12834
$391$	−8.61446	−0.435652
$392$	7.59775	0.383744
$393$	3.16015	0.159408
$394$	40.3090	2.03074
$395$	10.1101	0.508696
$396$	11.5552	0.580670
$397$	−1.93064	−0.0968958	−0.0484479	−	0.998826i	$-0.515427\pi$
$397$	−1.93064	−0.0968958	−0.0484479	+	0.998826i	$0.515427\pi$
$398$	−1.03934	−0.0520973
$399$	−3.92973	−0.196733
$400$	−3.53714	−0.176857
$401$	22.5103	1.12411	0.562056	−	0.827099i	$-0.310011\pi$
$401$	22.5103	1.12411	0.562056	+	0.827099i	$0.310011\pi$
$402$	48.2310	2.40554
$403$	2.42617	0.120856
$404$	9.70384	0.482784
$405$	−32.7168	−1.62571
$406$	−6.68433	−0.331738
$407$	9.17508	0.454792
$408$	−5.81174	−0.287724
$409$	−1.51312	−0.0748190	−0.0374095	−	0.999300i	$-0.511911\pi$
$409$	−1.51312	−0.0748190	−0.0374095	+	0.999300i	$0.511911\pi$
$410$	81.3407	4.01713
$411$	−25.1768	−1.24188
$412$	19.1114	0.941549
$413$	27.4960	1.35299
$414$	19.8049	0.973359
$415$	18.3220	0.899391
$416$	−30.6656	−1.50350
$417$	−17.1961	−0.842096
$418$	−6.67031	−0.326256
$419$	19.3056	0.943139	0.471569	−	0.881829i	$-0.343688\pi$
$419$	19.3056	0.943139	0.471569	+	0.881829i	$0.343688\pi$
$420$	−34.4064	−1.67886
$421$	4.63034	0.225669	0.112834	−	0.993614i	$-0.464007\pi$
$421$	4.63034	0.225669	0.112834	+	0.993614i	$0.464007\pi$
$422$	−21.2620	−1.03502
$423$	7.37122	0.358401
$424$	24.3331	1.18172
$425$	4.42506	0.214647
$426$	30.7856	1.49157
$427$	−25.7244	−1.24489
$428$	4.42226	0.213758
$429$	−28.2364	−1.36326
$430$	−11.0457	−0.532672
$431$	1.57549	0.0758887	0.0379444	−	0.999280i	$-0.487919\pi$
$431$	1.57549	0.0758887	0.0379444	+	0.999280i	$0.487919\pi$
$432$	3.55340	0.170963
$433$	−8.69111	−0.417668	−0.208834	−	0.977951i	$-0.566967\pi$
$433$	−8.69111	−0.417668	−0.208834	+	0.977951i	$0.566967\pi$
$434$	−2.25228	−0.108113
$435$	−9.53151	−0.457001
$436$	−14.6310	−0.700697
$437$	−6.85861	−0.328092
$438$	13.3171	0.636317
$439$	8.17207	0.390032	0.195016	−	0.980800i	$-0.437524\pi$
$439$	8.17207	0.390032	0.195016	+	0.980800i	$0.437524\pi$
$440$	−19.4542	−0.927441
$441$	−4.39310	−0.209195
$442$	12.8302	0.610271
$443$	−17.6090	−0.836629	−0.418315	−	0.908302i	$-0.637379\pi$
$443$	−17.6090	−0.836629	−0.418315	+	0.908302i	$0.637379\pi$
$444$	19.1068	0.906767
$445$	33.6871	1.59692
$446$	23.1044	1.09402
$447$	11.6038	0.548840
$448$	24.6586	1.16501
$449$	−6.22673	−0.293858	−0.146929	−	0.989147i	$-0.546939\pi$
$449$	−6.22673	−0.293858	−0.146929	+	0.989147i	$0.546939\pi$
$450$	−10.1734	−0.479577
$451$	−37.1767	−1.75058
$452$	−4.54230	−0.213652
$453$	−30.4079	−1.42869
$454$	−12.6534	−0.593851
$455$	25.3021	1.18618
$456$	−4.62715	−0.216686
$457$	29.4704	1.37857	0.689283	−	0.724492i	$-0.257926\pi$
$457$	29.4704	1.37857	0.689283	+	0.724492i	$0.257926\pi$
$458$	−5.36920	−0.250886
$459$	−4.44540	−0.207494
$460$	−60.0499	−2.79984
$461$	−1.03262	−0.0480939	−0.0240469	−	0.999711i	$-0.507655\pi$
$461$	−1.03262	−0.0480939	−0.0240469	+	0.999711i	$0.507655\pi$
$462$	26.2125	1.21952
$463$	−23.8414	−1.10800	−0.554002	−	0.832515i	$-0.686900\pi$
$463$	−23.8414	−1.10800	−0.554002	+	0.832515i	$0.686900\pi$
$464$	1.58228	0.0734555
$465$	−3.21163	−0.148936
$466$	10.4512	0.484141
$467$	3.63895	0.168390	0.0841952	−	0.996449i	$-0.473168\pi$
$467$	3.63895	0.168390	0.0841952	+	0.996449i	$0.473168\pi$
$468$	−17.6959	−0.817992
$469$	19.7532	0.912118
$470$	−37.2550	−1.71845
$471$	−9.08326	−0.418534
$472$	32.3758	1.49022
$473$	5.04844	0.232128
$474$	−16.0400	−0.736741
$475$	3.52312	0.161652
$476$	−7.14542	−0.327510
$477$	−14.0696	−0.644204
$478$	−40.0990	−1.83409
$479$	−13.0468	−0.596122	−0.298061	−	0.954547i	$-0.596340\pi$
$479$	−13.0468	−0.596122	−0.298061	+	0.954547i	$0.596340\pi$
$480$	40.5934	1.85282
$481$	−14.0509	−0.640668
$482$	−43.6153	−1.98662
$483$	26.9525	1.22638
$484$	−6.29677	−0.286217
$485$	24.3012	1.10346
$486$	28.1659	1.27763
$487$	−11.2790	−0.511101	−0.255550	−	0.966796i	$-0.582257\pi$
$487$	−11.2790	−0.511101	−0.255550	+	0.966796i	$0.582257\pi$
$488$	−30.2898	−1.37115
$489$	−9.98177	−0.451391
$490$	22.2033	1.00304
$491$	−3.74227	−0.168886	−0.0844432	−	0.996428i	$-0.526911\pi$
$491$	−3.74227	−0.168886	−0.0844432	+	0.996428i	$0.526911\pi$
$492$	−77.4192	−3.49033
$493$	−1.97947	−0.0891511
$494$	10.2151	0.459598
$495$	11.2486	0.505587
$496$	0.533148	0.0239390
$497$	12.6084	0.565564
$498$	−29.0683	−1.30258
$499$	41.0668	1.83840	0.919201	−	0.393789i	$-0.128836\pi$
$499$	41.0668	1.83840	0.919201	+	0.393789i	$0.128836\pi$
$500$	−12.9307	−0.578279
$501$	−38.7354	−1.73057
$502$	29.7503	1.32782
$503$	17.8332	0.795143	0.397572	−	0.917571i	$-0.369853\pi$
$503$	17.8332	0.795143	0.397572	+	0.917571i	$0.369853\pi$
$504$	5.47221	0.243752
$505$	9.44639	0.420359
$506$	45.7491	2.03379
$507$	16.3111	0.724403
$508$	−1.42653	−0.0632921
$509$	−0.795572	−0.0352631	−0.0176316	−	0.999845i	$-0.505613\pi$
$509$	−0.795572	−0.0352631	−0.0176316	+	0.999845i	$0.505613\pi$
$510$	−16.9839	−0.752060
$511$	5.45409	0.241275
$512$	−11.2237	−0.496023
$513$	−3.53931	−0.156265
$514$	0.610171	0.0269135
$515$	18.6043	0.819804
$516$	10.5132	0.462818
$517$	17.0274	0.748864
$518$	13.0438	0.573113
$519$	20.4419	0.897302
$520$	29.7926	1.30649
$521$	33.4798	1.46678	0.733388	−	0.679811i	$-0.237938\pi$
$521$	33.4798	1.46678	0.733388	+	0.679811i	$0.237938\pi$
$522$	4.55087	0.199186
$523$	−39.5028	−1.72733	−0.863667	−	0.504062i	$-0.831838\pi$
$523$	−39.5028	−1.72733	−0.863667	+	0.504062i	$0.831838\pi$
$524$	4.57488	0.199855
$525$	−13.8449	−0.604241
$526$	5.17381	0.225589
$527$	−0.666982	−0.0290542
$528$	−6.20489	−0.270033
$529$	24.0406	1.04524
$530$	71.1096	3.08881
$531$	−18.7200	−0.812379
$532$	−5.68899	−0.246649
$533$	56.9334	2.46606
$534$	−53.4454	−2.31281
$535$	4.30493	0.186118
$536$	23.2589	1.00463
$537$	19.7641	0.852883
$538$	−38.4610	−1.65817
$539$	−10.1480	−0.437105
$540$	−30.9881	−1.33352
$541$	12.3390	0.530497	0.265249	−	0.964180i	$-0.414546\pi$
$541$	12.3390	0.530497	0.265249	+	0.964180i	$0.414546\pi$
$542$	−18.3290	−0.787298
$543$	−29.2823	−1.25662
$544$	8.43030	0.361446
$545$	−14.2428	−0.610095
$546$	−40.1425	−1.71794
$547$	−25.6831	−1.09813	−0.549065	−	0.835780i	$-0.685016\pi$
$547$	−25.6831	−1.09813	−0.549065	+	0.835780i	$0.685016\pi$
$548$	−36.4479	−1.55698
$549$	17.5139	0.747474
$550$	−23.5003	−1.00206
$551$	−1.57601	−0.0671401
$552$	31.7359	1.35077
$553$	−6.56925	−0.279353
$554$	9.03455	0.383841
$555$	18.5998	0.789520
$556$	−24.8944	−1.05576
$557$	18.6467	0.790085	0.395042	−	0.918663i	$-0.370730\pi$
$557$	18.6467	0.790085	0.395042	+	0.918663i	$0.370730\pi$
$558$	1.53341	0.0649146
$559$	−7.73131	−0.327000
$560$	5.56010	0.234957
$561$	7.76249	0.327733
$562$	−34.2754	−1.44582
$563$	24.6091	1.03715	0.518576	−	0.855032i	$-0.326463\pi$
$563$	24.6091	1.03715	0.518576	+	0.855032i	$0.326463\pi$
$564$	35.4590	1.49309
$565$	−4.42179	−0.186026
$566$	−56.2521	−2.36445
$567$	21.2583	0.892766
$568$	14.8461	0.622927
$569$	10.7209	0.449444	0.224722	−	0.974423i	$-0.427853\pi$
$569$	10.7209	0.449444	0.224722	+	0.974423i	$0.427853\pi$
$570$	−13.5221	−0.566380
$571$	−3.63241	−0.152011	−0.0760057	−	0.997107i	$-0.524217\pi$
$571$	−3.63241	−0.152011	−0.0760057	+	0.997107i	$0.524217\pi$
$572$	−40.8772	−1.70916
$573$	−1.28165	−0.0535416
$574$	−52.8527	−2.20603
$575$	−24.1637	−1.00770
$576$	−16.7882	−0.699510
$577$	−34.0408	−1.41714	−0.708569	−	0.705641i	$-0.750659\pi$
$577$	−34.0408	−1.41714	−0.708569	+	0.705641i	$0.750659\pi$
$578$	34.4822	1.43427
$579$	−30.0617	−1.24932
$580$	−13.7986	−0.572955
$581$	−11.9051	−0.493905
$582$	−38.5544	−1.59813
$583$	−32.5006	−1.34604
$584$	6.42205	0.265746
$585$	−17.2264	−0.712224
$586$	−17.2008	−0.710559
$587$	−9.07997	−0.374770	−0.187385	−	0.982287i	$-0.560001\pi$
$587$	−9.07997	−0.374770	−0.187385	+	0.982287i	$0.560001\pi$
$588$	−21.1328	−0.871503
$589$	−0.531034	−0.0218809
$590$	94.6133	3.89517
$591$	−37.3478	−1.53628
$592$	−3.08767	−0.126902
$593$	−8.08920	−0.332184	−0.166092	−	0.986110i	$-0.553115\pi$
$593$	−8.08920	−0.332184	−0.166092	+	0.986110i	$0.553115\pi$
$594$	23.6083	0.968661
$595$	−6.95584	−0.285162
$596$	16.7986	0.688095
$597$	0.962985	0.0394123
$598$	−70.0612	−2.86502
$599$	15.2754	0.624134	0.312067	−	0.950060i	$-0.398979\pi$
$599$	15.2754	0.624134	0.312067	+	0.950060i	$0.398979\pi$
$600$	−16.3020	−0.665527
$601$	−11.0004	−0.448716	−0.224358	−	0.974507i	$-0.572028\pi$
$601$	−11.0004	−0.448716	−0.224358	+	0.974507i	$0.572028\pi$
$602$	7.17717	0.292520
$603$	−13.4485	−0.547666
$604$	−44.0209	−1.79118
$605$	−6.12971	−0.249208
$606$	−14.9869	−0.608803
$607$	17.0025	0.690111	0.345056	−	0.938582i	$-0.387860\pi$
$607$	17.0025	0.690111	0.345056	+	0.938582i	$0.387860\pi$
$608$	6.71198	0.272207
$609$	6.19328	0.250964
$610$	−88.5173	−3.58396
$611$	−26.0762	−1.05493
$612$	4.86479	0.196648
$613$	28.2846	1.14240	0.571201	−	0.820810i	$-0.306478\pi$
$613$	28.2846	1.14240	0.571201	+	0.820810i	$0.306478\pi$
$614$	31.3118	1.26364
$615$	−75.3652	−3.03902
$616$	12.6407	0.509309
$617$	−17.3845	−0.699875	−0.349938	−	0.936773i	$-0.613797\pi$
$617$	−17.3845	−0.699875	−0.349938	+	0.936773i	$0.613797\pi$
$618$	−29.5162	−1.18732
$619$	5.64340	0.226828	0.113414	−	0.993548i	$-0.463821\pi$
$619$	5.64340	0.226828	0.113414	+	0.993548i	$0.463821\pi$
$620$	−4.64942	−0.186725
$621$	24.2748	0.974113
$622$	13.2270	0.530354
$623$	−21.8888	−0.876957
$624$	9.50232	0.380397
$625$	−30.2032	−1.20813
$626$	10.0648	0.402269
$627$	6.18029	0.246817
$628$	−13.1496	−0.524728
$629$	3.86276	0.154018
$630$	15.9917	0.637124
$631$	−24.0657	−0.958040	−0.479020	−	0.877804i	$-0.659008\pi$
$631$	−24.0657	−0.958040	−0.479020	+	0.877804i	$0.659008\pi$
$632$	−7.73511	−0.307686
$633$	19.7000	0.783006
$634$	−2.23585	−0.0887968
$635$	−1.38868	−0.0551082
$636$	−67.6814	−2.68374
$637$	15.5409	0.615752
$638$	10.5124	0.416192
$639$	−8.58414	−0.339583
$640$	45.6594	1.80485
$641$	−36.8018	−1.45358	−0.726792	−	0.686857i	$-0.758990\pi$
$641$	−36.8018	−1.45358	−0.726792	+	0.686857i	$0.758990\pi$
$642$	−6.82989	−0.269554
$643$	21.7945	0.859491	0.429746	−	0.902950i	$-0.358603\pi$
$643$	21.7945	0.859491	0.429746	+	0.902950i	$0.358603\pi$
$644$	39.0186	1.53755
$645$	10.2343	0.402974
$646$	−2.80824	−0.110489
$647$	21.2662	0.836060	0.418030	−	0.908433i	$-0.362721\pi$
$647$	21.2662	0.836060	0.418030	+	0.908433i	$0.362721\pi$
$648$	25.0311	0.983316
$649$	−43.2429	−1.69743
$650$	35.9889	1.41160
$651$	2.08682	0.0817890
$652$	−14.4504	−0.565922
$653$	40.4310	1.58219	0.791094	−	0.611695i	$-0.209512\pi$
$653$	40.4310	1.58219	0.791094	+	0.611695i	$0.209512\pi$
$654$	22.5966	0.883596
$655$	4.45351	0.174013
$656$	12.5110	0.488473
$657$	−3.71330	−0.144870
$658$	24.2072	0.943694
$659$	−46.1899	−1.79930	−0.899652	−	0.436607i	$-0.856180\pi$
$659$	−46.1899	−1.79930	−0.899652	+	0.436607i	$0.856180\pi$
$660$	54.1110	2.10627
$661$	−36.4509	−1.41778	−0.708888	−	0.705321i	$-0.750803\pi$
$661$	−36.4509	−1.41778	−0.708888	+	0.705321i	$0.750803\pi$
$662$	−32.6950	−1.27073
$663$	−11.8877	−0.461679
$664$	−14.0179	−0.544000
$665$	−5.53806	−0.214757
$666$	−8.88060	−0.344116
$667$	10.8092	0.418534
$668$	−56.0765	−2.16967
$669$	−21.4071	−0.827645
$670$	67.9705	2.62593
$671$	40.4568	1.56182
$672$	−26.3763	−1.01749
$673$	5.69491	0.219523	0.109761	−	0.993958i	$-0.464991\pi$
$673$	5.69491	0.219523	0.109761	+	0.993958i	$0.464991\pi$
$674$	−43.1387	−1.66164
$675$	−12.4694	−0.479948
$676$	23.6133	0.908204
$677$	−47.0562	−1.80852	−0.904258	−	0.426986i	$-0.859575\pi$
$677$	−47.0562	−1.80852	−0.904258	+	0.426986i	$0.859575\pi$
$678$	7.01528	0.269420
$679$	−15.7901	−0.605970
$680$	−8.19032	−0.314084
$681$	11.7238	0.449257
$682$	3.54216	0.135636
$683$	−48.3145	−1.84870	−0.924352	−	0.381542i	$-0.875393\pi$
$683$	−48.3145	−1.84870	−0.924352	+	0.381542i	$0.875393\pi$
$684$	3.87322	0.148096
$685$	−35.4809	−1.35566
$686$	−44.1162	−1.68436
$687$	4.97477	0.189799
$688$	−1.69894	−0.0647715
$689$	49.7723	1.89617
$690$	92.7432	3.53067
$691$	−31.0288	−1.18039	−0.590195	−	0.807260i	$-0.700949\pi$
$691$	−31.0288	−1.18039	−0.590195	+	0.807260i	$0.700949\pi$
$692$	29.5934	1.12497
$693$	−7.30900	−0.277646
$694$	17.5360	0.665657
$695$	−24.2339	−0.919246
$696$	7.29242	0.276419
$697$	−15.6516	−0.592847
$698$	−17.3115	−0.655249
$699$	−9.68339	−0.366259
$700$	−20.0430	−0.757554
$701$	39.2345	1.48187	0.740933	−	0.671579i	$-0.234384\pi$
$701$	39.2345	1.48187	0.740933	+	0.671579i	$0.234384\pi$
$702$	−36.1544	−1.36456
$703$	3.07543	0.115992
$704$	−38.7806	−1.46160
$705$	34.5182	1.30003
$706$	61.3129	2.30754
$707$	−6.13797	−0.230842
$708$	−90.0519	−3.38436
$709$	13.4568	0.505381	0.252690	−	0.967547i	$-0.418685\pi$
$709$	13.4568	0.505381	0.252690	+	0.967547i	$0.418685\pi$
$710$	43.3853	1.62822
$711$	4.47252	0.167733
$712$	−25.7735	−0.965902
$713$	3.64215	0.136400
$714$	11.0356	0.412998
$715$	−39.7927	−1.48816
$716$	28.6121	1.06928
$717$	37.1532	1.38751
$718$	−42.2507	−1.57678
$719$	−25.0124	−0.932805	−0.466402	−	0.884573i	$-0.654450\pi$
$719$	−25.0124	−0.932805	−0.466402	+	0.884573i	$0.654450\pi$
$720$	−3.78547	−0.141076
$721$	−12.0885	−0.450199
$722$	−2.23585	−0.0832095
$723$	40.4112	1.50291
$724$	−42.3914	−1.57546
$725$	−5.55246	−0.206213
$726$	9.72494	0.360926
$727$	−6.30467	−0.233827	−0.116914	−	0.993142i	$-0.537300\pi$
$727$	−6.30467	−0.233827	−0.116914	+	0.993142i	$0.537300\pi$
$728$	−19.3583	−0.717467
$729$	7.52281	0.278622
$730$	18.7675	0.694615
$731$	2.12542	0.0786116
$732$	84.2498	3.11396
$733$	14.2231	0.525344	0.262672	−	0.964885i	$-0.415396\pi$
$733$	14.2231	0.525344	0.262672	+	0.964885i	$0.415396\pi$
$734$	26.1998	0.967052
$735$	−20.5722	−0.758815
$736$	−46.0349	−1.69687
$737$	−31.0659	−1.14433
$738$	35.9836	1.32457
$739$	28.7887	1.05901	0.529505	−	0.848307i	$-0.322378\pi$
$739$	28.7887	1.05901	0.529505	+	0.848307i	$0.322378\pi$
$740$	26.9266	0.989842
$741$	−9.46465	−0.347693
$742$	−46.2048	−1.69623
$743$	−27.5909	−1.01221	−0.506107	−	0.862471i	$-0.668916\pi$
$743$	−27.5909	−1.01221	−0.506107	+	0.862471i	$0.668916\pi$
$744$	2.45718	0.0900844
$745$	16.3529	0.599123
$746$	60.3682	2.21024
$747$	8.10529	0.296557
$748$	11.2376	0.410887
$749$	−2.79721	−0.102208
$750$	19.9706	0.729224
$751$	−22.2787	−0.812963	−0.406482	−	0.913659i	$-0.633244\pi$
$751$	−22.2787	−0.812963	−0.406482	+	0.913659i	$0.633244\pi$
$752$	−5.73019	−0.208959
$753$	−27.5647	−1.00451
$754$	−16.0990	−0.586292
$755$	−42.8530	−1.55958
$756$	20.1351	0.732308
$757$	33.0290	1.20046	0.600229	−	0.799828i	$-0.295076\pi$
$757$	33.0290	1.20046	0.600229	+	0.799828i	$0.295076\pi$
$758$	20.6122	0.748669
$759$	−42.3882	−1.53859
$760$	−6.52092	−0.236538
$761$	−34.4711	−1.24958	−0.624789	−	0.780794i	$-0.714815\pi$
$761$	−34.4711	−1.24958	−0.624789	+	0.780794i	$0.714815\pi$
$762$	2.20318	0.0798129
$763$	9.25453	0.335037
$764$	−1.85541	−0.0671265
$765$	4.73573	0.171221
$766$	−23.7629	−0.858588
$767$	66.2233	2.39118
$768$	−18.5825	−0.670538
$769$	−42.0821	−1.51752	−0.758760	−	0.651370i	$-0.774195\pi$
$769$	−42.0821	−1.51752	−0.758760	+	0.651370i	$0.774195\pi$
$770$	36.9406	1.33125
$771$	−0.565346	−0.0203605
$772$	−43.5197	−1.56631
$773$	−38.6294	−1.38940	−0.694702	−	0.719298i	$-0.744464\pi$
$773$	−38.6294	−1.38940	−0.694702	+	0.719298i	$0.744464\pi$
$774$	−4.88641	−0.175638
$775$	−1.87090	−0.0672045
$776$	−18.5925	−0.667430
$777$	−12.0856	−0.433569
$778$	−61.2362	−2.19542
$779$	−12.4614	−0.446476
$780$	−82.8669	−2.96711
$781$	−19.8292	−0.709546
$782$	19.2606	0.688758
$783$	5.57798	0.199341
$784$	3.41508	0.121967
$785$	−12.8008	−0.456879
$786$	−7.06561	−0.252022
$787$	−28.6928	−1.02279	−0.511393	−	0.859347i	$-0.670870\pi$
$787$	−28.6928	−1.02279	−0.511393	+	0.859347i	$0.670870\pi$
$788$	−54.0677	−1.92608
$789$	−4.79372	−0.170661
$790$	−22.6047	−0.804239
$791$	2.87314	0.102157
$792$	−8.60615	−0.305806
$793$	−61.9565	−2.20014
$794$	4.31660	0.153190
$795$	−65.8857	−2.33673
$796$	1.39409	0.0494123
$797$	5.57585	0.197507	0.0987533	−	0.995112i	$-0.468515\pi$
$797$	5.57585	0.197507	0.0987533	+	0.995112i	$0.468515\pi$
$798$	8.78627	0.311031
$799$	7.16863	0.253608
$800$	23.6471	0.836052
$801$	14.9025	0.526554
$802$	−50.3296	−1.77720
$803$	−8.57766	−0.302699
$804$	−64.6936	−2.28157
$805$	37.9834	1.33874
$806$	−5.42455	−0.191072
$807$	35.6356	1.25443
$808$	−7.22730	−0.254255
$809$	23.9684	0.842684	0.421342	−	0.906902i	$-0.361559\pi$
$809$	23.9684	0.842684	0.421342	+	0.906902i	$0.361559\pi$
$810$	73.1496	2.57022
$811$	38.2553	1.34332	0.671662	−	0.740858i	$-0.265581\pi$
$811$	38.2553	1.34332	0.671662	+	0.740858i	$0.265581\pi$
$812$	8.96589	0.314641
$813$	16.9825	0.595603
$814$	−20.5141	−0.719017
$815$	−14.0670	−0.492746
$816$	−2.61229	−0.0914486
$817$	1.69221	0.0592028
$818$	3.38310	0.118287
$819$	11.1932	0.391121
$820$	−109.105	−3.81010
$821$	−3.41541	−0.119199	−0.0595993	−	0.998222i	$-0.518982\pi$
$821$	−3.41541	−0.119199	−0.0595993	+	0.998222i	$0.518982\pi$
$822$	56.2914	1.96339
$823$	9.72199	0.338887	0.169444	−	0.985540i	$-0.445803\pi$
$823$	9.72199	0.338887	0.169444	+	0.985540i	$0.445803\pi$
$824$	−14.2339	−0.495861
$825$	21.7739	0.758070
$826$	−61.4768	−2.13905
$827$	−35.8463	−1.24650	−0.623249	−	0.782024i	$-0.714188\pi$
$827$	−35.8463	−1.24650	−0.623249	+	0.782024i	$0.714188\pi$
$828$	−26.5649	−0.923195
$829$	−8.48040	−0.294536	−0.147268	−	0.989097i	$-0.547048\pi$
$829$	−8.48040	−0.294536	−0.147268	+	0.989097i	$0.547048\pi$
$830$	−40.9651	−1.42192
$831$	−8.37085	−0.290381
$832$	59.3895	2.05896
$833$	−4.27236	−0.148029
$834$	38.4478	1.33134
$835$	−54.5887	−1.88912
$836$	8.94708	0.309441
$837$	1.87950	0.0649649
$838$	−43.1643	−1.49108
$839$	32.1646	1.11045	0.555223	−	0.831702i	$-0.312633\pi$
$839$	32.1646	1.11045	0.555223	+	0.831702i	$0.312633\pi$
$840$	25.6254	0.884162
$841$	−26.5162	−0.914352
$842$	−10.3527	−0.356778
$843$	31.7574	1.09378
$844$	28.5194	0.981677
$845$	22.9868	0.790771
$846$	−16.4809	−0.566625
$847$	3.98289	0.136854
$848$	10.9374	0.375591
$849$	52.1197	1.78874
$850$	−9.89375	−0.339353
$851$	−21.0932	−0.723064
$852$	−41.2937	−1.41470
$853$	−39.3905	−1.34870	−0.674352	−	0.738410i	$-0.735577\pi$
$853$	−39.3905	−1.34870	−0.674352	+	0.738410i	$0.735577\pi$
$854$	57.5158	1.96815
$855$	3.77046	0.128947
$856$	−3.29364	−0.112574
$857$	−28.7588	−0.982381	−0.491191	−	0.871052i	$-0.663438\pi$
$857$	−28.7588	−0.982381	−0.491191	+	0.871052i	$0.663438\pi$
$858$	63.1322	2.15530
$859$	58.0253	1.97980	0.989899	−	0.141776i	$-0.0452812\pi$
$859$	58.0253	1.97980	0.989899	+	0.141776i	$0.0452812\pi$
$860$	14.8160	0.505220
$861$	48.9700	1.66889
$862$	−3.52255	−0.119979
$863$	38.2478	1.30197	0.650985	−	0.759091i	$-0.274356\pi$
$863$	38.2478	1.30197	0.650985	+	0.759091i	$0.274356\pi$
$864$	−23.7558	−0.808189
$865$	28.8082	0.979509
$866$	19.4320	0.660326
$867$	−31.9490	−1.08505
$868$	3.02105	0.102541
$869$	10.3315	0.350471
$870$	21.3110	0.722510
$871$	47.5751	1.61202
$872$	10.8970	0.369018
$873$	10.7504	0.363844
$874$	15.3348	0.518707
$875$	8.17906	0.276503
$876$	−17.8627	−0.603524
$877$	−14.7897	−0.499413	−0.249706	−	0.968322i	$-0.580334\pi$
$877$	−14.7897	−0.499413	−0.249706	+	0.968322i	$0.580334\pi$
$878$	−18.2715	−0.616633
$879$	15.9372	0.537549
$880$	−8.74438	−0.294773
$881$	−17.9038	−0.603193	−0.301597	−	0.953436i	$-0.597520\pi$
$881$	−17.9038	−0.603193	−0.301597	+	0.953436i	$0.597520\pi$
$882$	9.82229	0.330734
$883$	−35.1130	−1.18165	−0.590824	−	0.806801i	$-0.701197\pi$
$883$	−35.1130	−1.18165	−0.590824	+	0.806801i	$0.701197\pi$
$884$	−17.2095	−0.578819
$885$	−87.6627	−2.94675
$886$	39.3710	1.32270
$887$	1.91812	0.0644042	0.0322021	−	0.999481i	$-0.489748\pi$
$887$	1.91812	0.0644042	0.0322021	+	0.999481i	$0.489748\pi$
$888$	−14.2305	−0.477543
$889$	0.902323	0.0302630
$890$	−75.3191	−2.52470
$891$	−33.4330	−1.12005
$892$	−30.9906	−1.03764
$893$	5.70748	0.190993
$894$	−25.9443	−0.867706
$895$	27.8529	0.931021
$896$	−29.6680	−0.991140
$897$	64.9144	2.16743
$898$	13.9220	0.464583
$899$	0.836913	0.0279126
$900$	13.6458	0.454861
$901$	−13.6829	−0.455845
$902$	83.1215	2.76764
$903$	−6.64992	−0.221295
$904$	3.38305	0.112518
$905$	−41.2667	−1.37175
$906$	67.9873	2.25873
$907$	25.3206	0.840758	0.420379	−	0.907349i	$-0.361897\pi$
$907$	25.3206	0.840758	0.420379	+	0.907349i	$0.361897\pi$
$908$	16.9723	0.563246
$909$	4.17890	0.138605
$910$	−56.5717	−1.87533
$911$	28.4465	0.942475	0.471237	−	0.882006i	$-0.343807\pi$
$911$	28.4465	0.942475	0.471237	+	0.882006i	$0.343807\pi$
$912$	−2.07984	−0.0688704
$913$	18.7231	0.619644
$914$	−65.8912	−2.17949
$915$	82.0146	2.71132
$916$	7.20187	0.237956
$917$	−2.89375	−0.0955601
$918$	9.93923	0.328044
$919$	11.4893	0.378996	0.189498	−	0.981881i	$-0.439314\pi$
$919$	11.4893	0.378996	0.189498	+	0.981881i	$0.439314\pi$
$920$	44.7244	1.47452
$921$	−29.0116	−0.955963
$922$	2.30878	0.0760355
$923$	30.3670	0.999541
$924$	−35.1596	−1.15667
$925$	10.8351	0.356256
$926$	53.3057	1.75173
$927$	8.23018	0.270315
$928$	−10.5781	−0.347244
$929$	3.66755	0.120329	0.0601643	−	0.998188i	$-0.480838\pi$
$929$	3.66755	0.120329	0.0601643	+	0.998188i	$0.480838\pi$
$930$	7.18072	0.235465
$931$	−3.40154	−0.111481
$932$	−14.0184	−0.459190
$933$	−12.2553	−0.401220
$934$	−8.13612	−0.266222
$935$	10.9395	0.357758
$936$	13.1797	0.430791
$937$	−49.9638	−1.63225	−0.816123	−	0.577879i	$-0.803881\pi$
$937$	−49.9638	−1.63225	−0.816123	+	0.577879i	$0.803881\pi$
$938$	−44.1651	−1.44204
$939$	−9.32538	−0.304322
$940$	49.9713	1.62988
$941$	−6.77461	−0.220846	−0.110423	−	0.993885i	$-0.535221\pi$
$941$	−6.77461	−0.220846	−0.110423	+	0.993885i	$0.535221\pi$
$942$	20.3088	0.661695
$943$	85.4680	2.78322
$944$	14.5525	0.473642
$945$	19.6009	0.637618
$946$	−11.2875	−0.366990
$947$	−33.5052	−1.08877	−0.544386	−	0.838835i	$-0.683237\pi$
$947$	−33.5052	−1.08877	−0.544386	+	0.838835i	$0.683237\pi$
$948$	21.5149	0.698771
$949$	13.1360	0.426414
$950$	−7.87715	−0.255568
$951$	2.07159	0.0671760
$952$	5.32181	0.172481
$953$	22.1428	0.717277	0.358639	−	0.933477i	$-0.383241\pi$
$953$	22.1428	0.717277	0.358639	+	0.933477i	$0.383241\pi$
$954$	31.4575	1.01847
$955$	−1.80619	−0.0584469
$956$	53.7860	1.73956
$957$	−9.74018	−0.314855
$958$	29.1706	0.942458
$959$	23.0544	0.744465
$960$	−78.6165	−2.53734
$961$	−30.7180	−0.990903
$962$	31.4157	1.01288
$963$	1.90442	0.0613690
$964$	58.5025	1.88424
$965$	−42.3651	−1.36378
$966$	−60.2616	−1.93889
$967$	41.7204	1.34164	0.670819	−	0.741621i	$-0.265943\pi$
$967$	41.7204	1.34164	0.670819	+	0.741621i	$0.265943\pi$
$968$	4.68975	0.150734
$969$	2.60194	0.0835863
$970$	−54.3336	−1.74455
$971$	1.79932	0.0577429	0.0288715	−	0.999583i	$-0.490809\pi$
$971$	1.79932	0.0577429	0.0288715	+	0.999583i	$0.490809\pi$
$972$	−37.7798	−1.21179
$973$	15.7465	0.504809
$974$	25.2181	0.808040
$975$	−33.3451	−1.06790
$976$	−13.6148	−0.435800
$977$	−7.80046	−0.249559	−0.124779	−	0.992185i	$-0.539822\pi$
$977$	−7.80046	−0.249559	−0.124779	+	0.992185i	$0.539822\pi$
$978$	22.3177	0.713641
$979$	34.4245	1.10021
$980$	−29.7819	−0.951347
$981$	−6.30074	−0.201167
$982$	8.36715	0.267006
$983$	−42.1199	−1.34341	−0.671707	−	0.740817i	$-0.734439\pi$
$983$	−42.1199	−1.34341	−0.671707	+	0.740817i	$0.734439\pi$
$984$	57.6609	1.83816
$985$	−52.6332	−1.67703
$986$	4.42580	0.140946
$987$	−22.4288	−0.713918
$988$	−13.7018	−0.435912
$989$	−11.6062	−0.369055
$990$	−25.1501	−0.799324
$991$	25.0456	0.795598	0.397799	−	0.917473i	$-0.369774\pi$
$991$	25.0456	0.795598	0.397799	+	0.917473i	$0.369774\pi$
$992$	−3.56429	−0.113166
$993$	30.2932	0.961324
$994$	−28.1904	−0.894146
$995$	1.35711	0.0430232
$996$	38.9902	1.23545
$997$	55.1229	1.74576	0.872880	−	0.487935i	$-0.162250\pi$
$997$	55.1229	1.74576	0.872880	+	0.487935i	$0.162250\pi$
$998$	−91.8190	−2.90648
$999$	−10.8849	−0.344383

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6023.2.a.a.1.12	✓	98

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6023.2.a.a.1.12	✓	98	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:	\( N \)	\(=\)	\( 6023 = 19 \cdot 317 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6023.a (trivial)

\(f(q)\)	\(=\)	\(q-2.23585 q^{2} +2.07159 q^{3} +2.99900 q^{4} +2.91944 q^{5} -4.63176 q^{6} -1.89696 q^{7} -2.23362 q^{8} +1.29150 q^{9} +O(q^{10})\)	\(q-2.23585 q^{2} +2.07159 q^{3} +2.99900 q^{4} +2.91944 q^{5} -4.63176 q^{6} -1.89696 q^{7} -2.23362 q^{8} +1.29150 q^{9} -6.52741 q^{10} +2.98335 q^{11} +6.21272 q^{12} -4.56878 q^{13} +4.24131 q^{14} +6.04789 q^{15} -1.00398 q^{16} +1.25601 q^{17} -2.88760 q^{18} +1.00000 q^{19} +8.75541 q^{20} -3.92973 q^{21} -6.67031 q^{22} -6.85861 q^{23} -4.62715 q^{24} +3.52312 q^{25} +10.2151 q^{26} -3.53931 q^{27} -5.68899 q^{28} -1.57601 q^{29} -13.5221 q^{30} -0.531034 q^{31} +6.71198 q^{32} +6.18029 q^{33} -2.80824 q^{34} -5.53806 q^{35} +3.87322 q^{36} +3.07543 q^{37} -2.23585 q^{38} -9.46465 q^{39} -6.52092 q^{40} -12.4614 q^{41} +8.78627 q^{42} +1.69221 q^{43} +8.94708 q^{44} +3.77046 q^{45} +15.3348 q^{46} +5.70748 q^{47} -2.07984 q^{48} -3.40154 q^{49} -7.87715 q^{50} +2.60194 q^{51} -13.7018 q^{52} -10.8940 q^{53} +7.91336 q^{54} +8.70971 q^{55} +4.23709 q^{56} +2.07159 q^{57} +3.52371 q^{58} -14.4948 q^{59} +18.1377 q^{60} +13.5609 q^{61} +1.18731 q^{62} -2.44993 q^{63} -12.9990 q^{64} -13.3383 q^{65} -13.8182 q^{66} -10.4131 q^{67} +3.76677 q^{68} -14.2083 q^{69} +12.3822 q^{70} -6.64663 q^{71} -2.88473 q^{72} -2.87518 q^{73} -6.87618 q^{74} +7.29847 q^{75} +2.99900 q^{76} -5.65930 q^{77} +21.1615 q^{78} +3.46304 q^{79} -2.93106 q^{80} -11.2065 q^{81} +27.8618 q^{82} +6.27586 q^{83} -11.7853 q^{84} +3.66683 q^{85} -3.78351 q^{86} -3.26484 q^{87} -6.66367 q^{88} +11.5389 q^{89} -8.43017 q^{90} +8.66679 q^{91} -20.5690 q^{92} -1.10009 q^{93} -12.7610 q^{94} +2.91944 q^{95} +13.9045 q^{96} +8.32391 q^{97} +7.60532 q^{98} +3.85300 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 98 q - 8 q^{2} - 25 q^{3} + 82 q^{4} - 10 q^{5} - 4 q^{6} - 18 q^{7} - 18 q^{8} + 61 q^{9}+O(q^{10}) \) 98 * q - 8 * q^2 - 25 * q^3 + 82 * q^4 - 10 * q^5 - 4 * q^6 - 18 * q^7 - 18 * q^8 + 61 * q^9	\( 98 q - 8 q^{2} - 25 q^{3} + 82 q^{4} - 10 q^{5} - 4 q^{6} - 18 q^{7} - 18 q^{8} + 61 q^{9} - 24 q^{10} - 12 q^{11} - 51 q^{12} - 58 q^{13} - 15 q^{14} - 18 q^{15} + 58 q^{16} - 25 q^{17} - 40 q^{18} + 98 q^{19} - 12 q^{20} - 24 q^{21} - 59 q^{22} - 38 q^{23} - 9 q^{24} - 12 q^{25} - 3 q^{26} - 85 q^{27} - 33 q^{28} - 24 q^{29} - 22 q^{30} - 56 q^{31} - 29 q^{32} - 51 q^{33} - 38 q^{34} - 10 q^{35} + 50 q^{36} - 124 q^{37} - 8 q^{38} - 4 q^{39} - 80 q^{40} - 28 q^{41} - 37 q^{42} - 63 q^{43} - 7 q^{44} - 32 q^{45} - 47 q^{46} - 10 q^{47} - 88 q^{48} + 6 q^{49} - 17 q^{50} - 22 q^{51} - 119 q^{52} - 65 q^{53} + 24 q^{54} - 30 q^{55} - 39 q^{56} - 25 q^{57} - 91 q^{58} - 26 q^{59} - 60 q^{60} - 60 q^{61} + 6 q^{62} - 26 q^{63} + 50 q^{64} - 40 q^{65} + 57 q^{66} - 108 q^{67} - 41 q^{68} - 15 q^{69} - 36 q^{70} - 19 q^{71} - 47 q^{72} - 136 q^{73} + 22 q^{74} - 48 q^{75} + 82 q^{76} - 35 q^{77} - 56 q^{78} - 98 q^{79} - 42 q^{80} + 6 q^{81} - 37 q^{82} - 31 q^{83} - 24 q^{84} - 71 q^{85} - 24 q^{86} + 7 q^{87} - 166 q^{88} - 38 q^{89} + 26 q^{90} - 100 q^{91} - 59 q^{92} - 21 q^{93} - 48 q^{94} - 10 q^{95} - 16 q^{96} - 190 q^{97} - 80 q^{98} - 17 q^{99}+O(q^{100}) \) 98 * q - 8 * q^2 - 25 * q^3 + 82 * q^4 - 10 * q^5 - 4 * q^6 - 18 * q^7 - 18 * q^8 + 61 * q^9 - 24 * q^10 - 12 * q^11 - 51 * q^12 - 58 * q^13 - 15 * q^14 - 18 * q^15 + 58 * q^16 - 25 * q^17 - 40 * q^18 + 98 * q^19 - 12 * q^20 - 24 * q^21 - 59 * q^22 - 38 * q^23 - 9 * q^24 - 12 * q^25 - 3 * q^26 - 85 * q^27 - 33 * q^28 - 24 * q^29 - 22 * q^30 - 56 * q^31 - 29 * q^32 - 51 * q^33 - 38 * q^34 - 10 * q^35 + 50 * q^36 - 124 * q^37 - 8 * q^38 - 4 * q^39 - 80 * q^40 - 28 * q^41 - 37 * q^42 - 63 * q^43 - 7 * q^44 - 32 * q^45 - 47 * q^46 - 10 * q^47 - 88 * q^48 + 6 * q^49 - 17 * q^50 - 22 * q^51 - 119 * q^52 - 65 * q^53 + 24 * q^54 - 30 * q^55 - 39 * q^56 - 25 * q^57 - 91 * q^58 - 26 * q^59 - 60 * q^60 - 60 * q^61 + 6 * q^62 - 26 * q^63 + 50 * q^64 - 40 * q^65 + 57 * q^66 - 108 * q^67 - 41 * q^68 - 15 * q^69 - 36 * q^70 - 19 * q^71 - 47 * q^72 - 136 * q^73 + 22 * q^74 - 48 * q^75 + 82 * q^76 - 35 * q^77 - 56 * q^78 - 98 * q^79 - 42 * q^80 + 6 * q^81 - 37 * q^82 - 31 * q^83 - 24 * q^84 - 71 * q^85 - 24 * q^86 + 7 * q^87 - 166 * q^88 - 38 * q^89 + 26 * q^90 - 100 * q^91 - 59 * q^92 - 21 * q^93 - 48 * q^94 - 10 * q^95 - 16 * q^96 - 190 * q^97 - 80 * q^98 - 17 * q^99

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