LMFDB - Embedded newform 4006.2.a.h.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("4006.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4006 = 2 \cdot 2003 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4006.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$31.9880710497$
Analytic rank:	$0$
Dimension:	$42$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	4006.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.67728 q^{3} +1.00000 q^{4} +1.83767 q^{5} +1.67728 q^{6} +4.34649 q^{7} -1.00000 q^{8} -0.186728 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.67728 q^{3} +1.00000 q^{4} +1.83767 q^{5} +1.67728 q^{6} +4.34649 q^{7} -1.00000 q^{8} -0.186728 q^{9} -1.83767 q^{10} -3.12207 q^{11} -1.67728 q^{12} -1.45926 q^{13} -4.34649 q^{14} -3.08229 q^{15} +1.00000 q^{16} +7.19635 q^{17} +0.186728 q^{18} -1.42373 q^{19} +1.83767 q^{20} -7.29028 q^{21} +3.12207 q^{22} -3.84407 q^{23} +1.67728 q^{24} -1.62297 q^{25} +1.45926 q^{26} +5.34504 q^{27} +4.34649 q^{28} -2.37377 q^{29} +3.08229 q^{30} -9.37454 q^{31} -1.00000 q^{32} +5.23659 q^{33} -7.19635 q^{34} +7.98741 q^{35} -0.186728 q^{36} +3.02156 q^{37} +1.42373 q^{38} +2.44758 q^{39} -1.83767 q^{40} +4.86747 q^{41} +7.29028 q^{42} +0.736530 q^{43} -3.12207 q^{44} -0.343143 q^{45} +3.84407 q^{46} +6.51698 q^{47} -1.67728 q^{48} +11.8920 q^{49} +1.62297 q^{50} -12.0703 q^{51} -1.45926 q^{52} +10.3671 q^{53} -5.34504 q^{54} -5.73734 q^{55} -4.34649 q^{56} +2.38799 q^{57} +2.37377 q^{58} -1.43766 q^{59} -3.08229 q^{60} +11.7254 q^{61} +9.37454 q^{62} -0.811609 q^{63} +1.00000 q^{64} -2.68163 q^{65} -5.23659 q^{66} +13.3564 q^{67} +7.19635 q^{68} +6.44759 q^{69} -7.98741 q^{70} -4.30326 q^{71} +0.186728 q^{72} -0.705872 q^{73} -3.02156 q^{74} +2.72218 q^{75} -1.42373 q^{76} -13.5701 q^{77} -2.44758 q^{78} +2.30224 q^{79} +1.83767 q^{80} -8.40495 q^{81} -4.86747 q^{82} +3.07087 q^{83} -7.29028 q^{84} +13.2245 q^{85} -0.736530 q^{86} +3.98147 q^{87} +3.12207 q^{88} +1.00500 q^{89} +0.343143 q^{90} -6.34264 q^{91} -3.84407 q^{92} +15.7237 q^{93} -6.51698 q^{94} -2.61634 q^{95} +1.67728 q^{96} +2.04288 q^{97} -11.8920 q^{98} +0.582977 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q - 42 q^{2} + 42 q^{4} + 27 q^{5} - 10 q^{7} - 42 q^{8} + 56 q^{9}+O(q^{10}) $ 42 * q - 42 * q^2 + 42 * q^4 + 27 * q^5 - 10 * q^7 - 42 * q^8 + 56 * q^9	\( 42 q - 42 q^{2} + 42 q^{4} + 27 q^{5} - 10 q^{7} - 42 q^{8} + 56 q^{9} - 27 q^{10} + 23 q^{11} + 15 q^{13} + 10 q^{14} + 6 q^{15} + 42 q^{16} + 14 q^{17} - 56 q^{18} - 4 q^{19} + 27 q^{20} + 26 q^{21} - 23 q^{22} + 12 q^{23} + 45 q^{25} - 15 q^{26} - 3 q^{27} - 10 q^{28} + 41 q^{29} - 6 q^{30} + 18 q^{31} - 42 q^{32} + 25 q^{33} - 14 q^{34} + 8 q^{35} + 56 q^{36} + 33 q^{37} + 4 q^{38} + 10 q^{39} - 27 q^{40} + 84 q^{41} - 26 q^{42} - 36 q^{43} + 23 q^{44} + 66 q^{45} - 12 q^{46} + 28 q^{47} + 58 q^{49} - 45 q^{50} + 17 q^{51} + 15 q^{52} + 68 q^{53} + 3 q^{54} - 28 q^{55} + 10 q^{56} - 9 q^{57} - 41 q^{58} + 59 q^{59} + 6 q^{60} + 41 q^{61} - 18 q^{62} - 28 q^{63} + 42 q^{64} + 44 q^{65} - 25 q^{66} + 14 q^{68} + 67 q^{69} - 8 q^{70} + 69 q^{71} - 56 q^{72} - 27 q^{73} - 33 q^{74} + 14 q^{75} - 4 q^{76} + 43 q^{77} - 10 q^{78} - 19 q^{79} + 27 q^{80} + 74 q^{81} - 84 q^{82} + 20 q^{83} + 26 q^{84} + 16 q^{85} + 36 q^{86} - 28 q^{87} - 23 q^{88} + 123 q^{89} - 66 q^{90} - 9 q^{91} + 12 q^{92} + 48 q^{93} - 28 q^{94} + 28 q^{95} + 10 q^{97} - 58 q^{98} + 75 q^{99}+O(q^{100}) \) 42 * q - 42 * q^2 + 42 * q^4 + 27 * q^5 - 10 * q^7 - 42 * q^8 + 56 * q^9 - 27 * q^10 + 23 * q^11 + 15 * q^13 + 10 * q^14 + 6 * q^15 + 42 * q^16 + 14 * q^17 - 56 * q^18 - 4 * q^19 + 27 * q^20 + 26 * q^21 - 23 * q^22 + 12 * q^23 + 45 * q^25 - 15 * q^26 - 3 * q^27 - 10 * q^28 + 41 * q^29 - 6 * q^30 + 18 * q^31 - 42 * q^32 + 25 * q^33 - 14 * q^34 + 8 * q^35 + 56 * q^36 + 33 * q^37 + 4 * q^38 + 10 * q^39 - 27 * q^40 + 84 * q^41 - 26 * q^42 - 36 * q^43 + 23 * q^44 + 66 * q^45 - 12 * q^46 + 28 * q^47 + 58 * q^49 - 45 * q^50 + 17 * q^51 + 15 * q^52 + 68 * q^53 + 3 * q^54 - 28 * q^55 + 10 * q^56 - 9 * q^57 - 41 * q^58 + 59 * q^59 + 6 * q^60 + 41 * q^61 - 18 * q^62 - 28 * q^63 + 42 * q^64 + 44 * q^65 - 25 * q^66 + 14 * q^68 + 67 * q^69 - 8 * q^70 + 69 * q^71 - 56 * q^72 - 27 * q^73 - 33 * q^74 + 14 * q^75 - 4 * q^76 + 43 * q^77 - 10 * q^78 - 19 * q^79 + 27 * q^80 + 74 * q^81 - 84 * q^82 + 20 * q^83 + 26 * q^84 + 16 * q^85 + 36 * q^86 - 28 * q^87 - 23 * q^88 + 123 * q^89 - 66 * q^90 - 9 * q^91 + 12 * q^92 + 48 * q^93 - 28 * q^94 + 28 * q^95 + 10 * q^97 - 58 * q^98 + 75 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.67728	−0.968379	−0.484189	−	0.874963i	$-0.660885\pi$
$3$	−1.67728	−0.968379	−0.484189	+	0.874963i	$0.660885\pi$
$4$	1.00000	0.500000
$5$	1.83767	0.821831	0.410915	−	0.911673i	$-0.365209\pi$
$5$	1.83767	0.821831	0.410915	+	0.911673i	$0.365209\pi$
$6$	1.67728	0.684747
$7$	4.34649	1.64282	0.821409	−	0.570340i	$-0.193188\pi$
$7$	4.34649	1.64282	0.821409	+	0.570340i	$0.193188\pi$
$8$	−1.00000	−0.353553
$9$	−0.186728	−0.0622425
$10$	−1.83767	−0.581122
$11$	−3.12207	−0.941340	−0.470670	−	0.882309i	$-0.655988\pi$
$11$	−3.12207	−0.941340	−0.470670	+	0.882309i	$0.655988\pi$
$12$	−1.67728	−0.484189
$13$	−1.45926	−0.404725	−0.202362	−	0.979311i	$-0.564862\pi$
$13$	−1.45926	−0.404725	−0.202362	+	0.979311i	$0.564862\pi$
$14$	−4.34649	−1.16165
$15$	−3.08229	−0.795843
$16$	1.00000	0.250000
$17$	7.19635	1.74537	0.872686	−	0.488282i	$-0.162376\pi$
$17$	7.19635	1.74537	0.872686	+	0.488282i	$0.162376\pi$
$18$	0.186728	0.0440121
$19$	−1.42373	−0.326625	−0.163313	−	0.986574i	$-0.552218\pi$
$19$	−1.42373	−0.326625	−0.163313	+	0.986574i	$0.552218\pi$
$20$	1.83767	0.410915
$21$	−7.29028	−1.59087
$22$	3.12207	0.665628
$23$	−3.84407	−0.801545	−0.400772	−	0.916178i	$-0.631258\pi$
$23$	−3.84407	−0.801545	−0.400772	+	0.916178i	$0.631258\pi$
$24$	1.67728	0.342374
$25$	−1.62297	−0.324594
$26$	1.45926	0.286184
$27$	5.34504	1.02865
$28$	4.34649	0.821409
$29$	−2.37377	−0.440797	−0.220399	−	0.975410i	$-0.570736\pi$
$29$	−2.37377	−0.440797	−0.220399	+	0.975410i	$0.570736\pi$
$30$	3.08229	0.562746
$31$	−9.37454	−1.68372	−0.841858	−	0.539699i	$-0.818538\pi$
$31$	−9.37454	−1.68372	−0.841858	+	0.539699i	$0.818538\pi$
$32$	−1.00000	−0.176777
$33$	5.23659	0.911574
$34$	−7.19635	−1.23416
$35$	7.98741	1.35012
$36$	−0.186728	−0.0311213
$37$	3.02156	0.496741	0.248370	−	0.968665i	$-0.420105\pi$
$37$	3.02156	0.496741	0.248370	+	0.968665i	$0.420105\pi$
$38$	1.42373	0.230959
$39$	2.44758	0.391927
$40$	−1.83767	−0.290561
$41$	4.86747	0.760171	0.380086	−	0.924951i	$-0.375894\pi$
$41$	4.86747	0.760171	0.380086	+	0.924951i	$0.375894\pi$
$42$	7.29028	1.12492
$43$	0.736530	0.112320	0.0561599	−	0.998422i	$-0.482114\pi$
$43$	0.736530	0.112320	0.0561599	+	0.998422i	$0.482114\pi$
$44$	−3.12207	−0.470670
$45$	−0.343143	−0.0511528
$46$	3.84407	0.566778
$47$	6.51698	0.950599	0.475300	−	0.879824i	$-0.342340\pi$
$47$	6.51698	0.950599	0.475300	+	0.879824i	$0.342340\pi$
$48$	−1.67728	−0.242095
$49$	11.8920	1.69885
$50$	1.62297	0.229523
$51$	−12.0703	−1.69018
$52$	−1.45926	−0.202362
$53$	10.3671	1.42403	0.712017	−	0.702162i	$-0.247782\pi$
$53$	10.3671	1.42403	0.712017	+	0.702162i	$0.247782\pi$
$54$	−5.34504	−0.727368
$55$	−5.73734	−0.773622
$56$	−4.34649	−0.580824
$57$	2.38799	0.316297
$58$	2.37377	0.311691
$59$	−1.43766	−0.187168	−0.0935839	−	0.995611i	$-0.529832\pi$
$59$	−1.43766	−0.187168	−0.0935839	+	0.995611i	$0.529832\pi$
$60$	−3.08229	−0.397922
$61$	11.7254	1.50129	0.750643	−	0.660708i	$-0.229744\pi$
$61$	11.7254	1.50129	0.750643	+	0.660708i	$0.229744\pi$
$62$	9.37454	1.19057
$63$	−0.811609	−0.102253
$64$	1.00000	0.125000
$65$	−2.68163	−0.332615
$66$	−5.23659	−0.644580
$67$	13.3564	1.63174	0.815871	−	0.578235i	$-0.196258\pi$
$67$	13.3564	1.63174	0.815871	+	0.578235i	$0.196258\pi$
$68$	7.19635	0.872686
$69$	6.44759	0.776199
$70$	−7.98741	−0.954678
$71$	−4.30326	−0.510703	−0.255352	−	0.966848i	$-0.582191\pi$
$71$	−4.30326	−0.510703	−0.255352	+	0.966848i	$0.582191\pi$
$72$	0.186728	0.0220061
$73$	−0.705872	−0.0826161	−0.0413080	−	0.999146i	$-0.513152\pi$
$73$	−0.705872	−0.0826161	−0.0413080	+	0.999146i	$0.513152\pi$
$74$	−3.02156	−0.351249
$75$	2.72218	0.314330
$76$	−1.42373	−0.163313
$77$	−13.5701	−1.54645
$78$	−2.44758	−0.277134
$79$	2.30224	0.259022	0.129511	−	0.991578i	$-0.458659\pi$
$79$	2.30224	0.259022	0.129511	+	0.991578i	$0.458659\pi$
$80$	1.83767	0.205458
$81$	−8.40495	−0.933883
$82$	−4.86747	−0.537522
$83$	3.07087	0.337072	0.168536	−	0.985696i	$-0.446096\pi$
$83$	3.07087	0.337072	0.168536	+	0.985696i	$0.446096\pi$
$84$	−7.29028	−0.795435
$85$	13.2245	1.43440
$86$	−0.736530	−0.0794221
$87$	3.98147	0.426859
$88$	3.12207	0.332814
$89$	1.00500	0.106530	0.0532650	−	0.998580i	$-0.483037\pi$
$89$	1.00500	0.106530	0.0532650	+	0.998580i	$0.483037\pi$
$90$	0.343143	0.0361705
$91$	−6.34264	−0.664889
$92$	−3.84407	−0.400772
$93$	15.7237	1.63048
$94$	−6.51698	−0.672175
$95$	−2.61634	−0.268431
$96$	1.67728	0.171187
$97$	2.04288	0.207423	0.103711	−	0.994607i	$-0.466928\pi$
$97$	2.04288	0.207423	0.103711	+	0.994607i	$0.466928\pi$
$98$	−11.8920	−1.20127
$99$	0.582977	0.0585914
$100$	−1.62297	−0.162297
$101$	1.31398	0.130746	0.0653729	−	0.997861i	$-0.479176\pi$
$101$	1.31398	0.130746	0.0653729	+	0.997861i	$0.479176\pi$
$102$	12.0703	1.19514
$103$	−10.6517	−1.04955	−0.524773	−	0.851242i	$-0.675850\pi$
$103$	−10.6517	−1.04955	−0.524773	+	0.851242i	$0.675850\pi$
$104$	1.45926	0.143092
$105$	−13.3971	−1.30743
$106$	−10.3671	−1.00694
$107$	13.8864	1.34245	0.671226	−	0.741253i	$-0.265768\pi$
$107$	13.8864	1.34245	0.671226	+	0.741253i	$0.265768\pi$
$108$	5.34504	0.514327
$109$	−8.73711	−0.836863	−0.418432	−	0.908248i	$-0.637420\pi$
$109$	−8.73711	−0.836863	−0.418432	+	0.908248i	$0.637420\pi$
$110$	5.73734	0.547034
$111$	−5.06800	−0.481033
$112$	4.34649	0.410705
$113$	4.24731	0.399553	0.199776	−	0.979841i	$-0.435978\pi$
$113$	4.24731	0.399553	0.199776	+	0.979841i	$0.435978\pi$
$114$	−2.38799	−0.223656
$115$	−7.06414	−0.658734
$116$	−2.37377	−0.220399
$117$	0.272483	0.0251911
$118$	1.43766	0.132348
$119$	31.2788	2.86733
$120$	3.08229	0.281373
$121$	−1.25266	−0.113879
$122$	−11.7254	−1.06157
$123$	−8.16412	−0.736134
$124$	−9.37454	−0.841858
$125$	−12.1708	−1.08859
$126$	0.811609	0.0723039
$127$	12.3152	1.09280	0.546401	−	0.837524i	$-0.315998\pi$
$127$	12.3152	1.09280	0.546401	+	0.837524i	$0.315998\pi$
$128$	−1.00000	−0.0883883
$129$	−1.23537	−0.108768
$130$	2.68163	0.235195
$131$	−3.54201	−0.309467	−0.154733	−	0.987956i	$-0.549452\pi$
$131$	−3.54201	−0.309467	−0.154733	+	0.987956i	$0.549452\pi$
$132$	5.23659	0.455787
$133$	−6.18821	−0.536586
$134$	−13.3564	−1.15382
$135$	9.82241	0.845379
$136$	−7.19635	−0.617082
$137$	−15.8198	−1.35158	−0.675788	−	0.737096i	$-0.736197\pi$
$137$	−15.8198	−1.35158	−0.675788	+	0.737096i	$0.736197\pi$
$138$	−6.44759	−0.548856
$139$	−7.38172	−0.626110	−0.313055	−	0.949735i	$-0.601352\pi$
$139$	−7.38172	−0.626110	−0.313055	+	0.949735i	$0.601352\pi$
$140$	7.98741	0.675059
$141$	−10.9308	−0.920540
$142$	4.30326	0.361122
$143$	4.55590	0.380984
$144$	−0.186728	−0.0155606
$145$	−4.36220	−0.362261
$146$	0.705872	0.0584184
$147$	−19.9462	−1.64513
$148$	3.02156	0.248370
$149$	12.4129	1.01690	0.508451	−	0.861091i	$-0.330218\pi$
$149$	12.4129	1.01690	0.508451	+	0.861091i	$0.330218\pi$
$150$	−2.72218	−0.222265
$151$	12.7569	1.03814	0.519072	−	0.854731i	$-0.326278\pi$
$151$	12.7569	1.03814	0.519072	+	0.854731i	$0.326278\pi$
$152$	1.42373	0.115480
$153$	−1.34376	−0.108636
$154$	13.5701	1.09351
$155$	−17.2273	−1.38373
$156$	2.44758	0.195963
$157$	3.67743	0.293491	0.146746	−	0.989174i	$-0.453120\pi$
$157$	3.67743	0.293491	0.146746	+	0.989174i	$0.453120\pi$
$158$	−2.30224	−0.183156
$159$	−17.3886	−1.37900
$160$	−1.83767	−0.145281
$161$	−16.7082	−1.31679
$162$	8.40495	0.660355
$163$	−16.4579	−1.28909	−0.644543	−	0.764568i	$-0.722952\pi$
$163$	−16.4579	−1.28909	−0.644543	+	0.764568i	$0.722952\pi$
$164$	4.86747	0.380086
$165$	9.62313	0.749159
$166$	−3.07087	−0.238346
$167$	15.8349	1.22534	0.612672	−	0.790337i	$-0.290095\pi$
$167$	15.8349	1.22534	0.612672	+	0.790337i	$0.290095\pi$
$168$	7.29028	0.562458
$169$	−10.8706	−0.836198
$170$	−13.2245	−1.01427
$171$	0.265849	0.0203300
$172$	0.736530	0.0561599
$173$	23.6349	1.79692	0.898462	−	0.439050i	$-0.144685\pi$
$173$	23.6349	1.79692	0.898462	+	0.439050i	$0.144685\pi$
$174$	−3.98147	−0.301835
$175$	−7.05422	−0.533249
$176$	−3.12207	−0.235335
$177$	2.41136	0.181249
$178$	−1.00500	−0.0753281
$179$	22.0369	1.64712	0.823558	−	0.567233i	$-0.191986\pi$
$179$	22.0369	1.64712	0.823558	+	0.567233i	$0.191986\pi$
$180$	−0.343143	−0.0255764
$181$	−17.3531	−1.28984	−0.644921	−	0.764249i	$-0.723110\pi$
$181$	−17.3531	−1.28984	−0.644921	+	0.764249i	$0.723110\pi$
$182$	6.34264	0.470148
$183$	−19.6668	−1.45381
$184$	3.84407	0.283389
$185$	5.55262	0.408237
$186$	−15.7237	−1.15292
$187$	−22.4675	−1.64299
$188$	6.51698	0.475300
$189$	23.2321	1.68989
$190$	2.61634	0.189809
$191$	−9.73826	−0.704636	−0.352318	−	0.935880i	$-0.614606\pi$
$191$	−9.73826	−0.704636	−0.352318	+	0.935880i	$0.614606\pi$
$192$	−1.67728	−0.121047
$193$	4.54525	0.327174	0.163587	−	0.986529i	$-0.447694\pi$
$193$	4.54525	0.327174	0.163587	+	0.986529i	$0.447694\pi$
$194$	−2.04288	−0.146670
$195$	4.49785	0.322098
$196$	11.8920	0.849426
$197$	5.21493	0.371548	0.185774	−	0.982592i	$-0.440521\pi$
$197$	5.21493	0.371548	0.185774	+	0.982592i	$0.440521\pi$
$198$	−0.582977	−0.0414304
$199$	−4.15238	−0.294355	−0.147177	−	0.989110i	$-0.547019\pi$
$199$	−4.15238	−0.294355	−0.147177	+	0.989110i	$0.547019\pi$
$200$	1.62297	0.114761
$201$	−22.4024	−1.58014
$202$	−1.31398	−0.0924513
$203$	−10.3175	−0.724150
$204$	−12.0703	−0.845090
$205$	8.94480	0.624732
$206$	10.6517	0.742141
$207$	0.717794	0.0498902
$208$	−1.45926	−0.101181
$209$	4.44498	0.307466
$210$	13.3971	0.924490
$211$	3.90589	0.268893	0.134446	−	0.990921i	$-0.457074\pi$
$211$	3.90589	0.268893	0.134446	+	0.990921i	$0.457074\pi$
$212$	10.3671	0.712017
$213$	7.21778	0.494554
$214$	−13.8864	−0.949257
$215$	1.35350	0.0923079
$216$	−5.34504	−0.363684
$217$	−40.7463	−2.76604
$218$	8.73711	0.591752
$219$	1.18395	0.0800036
$220$	−5.73734	−0.386811
$221$	−10.5013	−0.706395
$222$	5.06800	0.340142
$223$	13.2702	0.888639	0.444320	−	0.895868i	$-0.353446\pi$
$223$	13.2702	0.888639	0.444320	+	0.895868i	$0.353446\pi$
$224$	−4.34649	−0.290412
$225$	0.303053	0.0202036
$226$	−4.24731	−0.282527
$227$	18.2184	1.20920	0.604599	−	0.796530i	$-0.293333\pi$
$227$	18.2184	1.20920	0.604599	+	0.796530i	$0.293333\pi$
$228$	2.38799	0.158149
$229$	5.36759	0.354701	0.177350	−	0.984148i	$-0.443247\pi$
$229$	5.36759	0.354701	0.177350	+	0.984148i	$0.443247\pi$
$230$	7.06414	0.465795
$231$	22.7608	1.49755
$232$	2.37377	0.155845
$233$	3.10684	0.203536	0.101768	−	0.994808i	$-0.467550\pi$
$233$	3.10684	0.203536	0.101768	+	0.994808i	$0.467550\pi$
$234$	−0.272483	−0.0178128
$235$	11.9761	0.781232
$236$	−1.43766	−0.0935839
$237$	−3.86150	−0.250831
$238$	−31.2788	−2.02751
$239$	−25.1587	−1.62738	−0.813691	−	0.581298i	$-0.802545\pi$
$239$	−25.1587	−1.62738	−0.813691	+	0.581298i	$0.802545\pi$
$240$	−3.08229	−0.198961
$241$	−3.12108	−0.201046	−0.100523	−	0.994935i	$-0.532052\pi$
$241$	−3.12108	−0.201046	−0.100523	+	0.994935i	$0.532052\pi$
$242$	1.25266	0.0805243
$243$	−1.93765	−0.124300
$244$	11.7254	0.750643
$245$	21.8535	1.39617
$246$	8.16412	0.520525
$247$	2.07758	0.132193
$248$	9.37454	0.595284
$249$	−5.15071	−0.326413
$250$	12.1708	0.769751
$251$	10.5090	0.663324	0.331662	−	0.943398i	$-0.392391\pi$
$251$	10.5090	0.663324	0.331662	+	0.943398i	$0.392391\pi$
$252$	−0.811609	−0.0511266
$253$	12.0015	0.754526
$254$	−12.3152	−0.772727
$255$	−22.1812	−1.38904
$256$	1.00000	0.0625000
$257$	9.06010	0.565154	0.282577	−	0.959245i	$-0.408811\pi$
$257$	9.06010	0.565154	0.282577	+	0.959245i	$0.408811\pi$
$258$	1.23537	0.0769107
$259$	13.1332	0.816055
$260$	−2.68163	−0.166308
$261$	0.443247	0.0274363
$262$	3.54201	0.218826
$263$	5.18207	0.319540	0.159770	−	0.987154i	$-0.448925\pi$
$263$	5.18207	0.319540	0.159770	+	0.987154i	$0.448925\pi$
$264$	−5.23659	−0.322290
$265$	19.0513	1.17031
$266$	6.18821	0.379424
$267$	−1.68567	−0.103161
$268$	13.3564	0.815871
$269$	28.2615	1.72313	0.861567	−	0.507644i	$-0.169483\pi$
$269$	28.2615	1.72313	0.861567	+	0.507644i	$0.169483\pi$
$270$	−9.82241	−0.597773
$271$	−14.5932	−0.886474	−0.443237	−	0.896404i	$-0.646170\pi$
$271$	−14.5932	−0.886474	−0.443237	+	0.896404i	$0.646170\pi$
$272$	7.19635	0.436343
$273$	10.6384	0.643865
$274$	15.8198	0.955709
$275$	5.06703	0.305554
$276$	6.44759	0.388099
$277$	−2.58668	−0.155418	−0.0777092	−	0.996976i	$-0.524761\pi$
$277$	−2.58668	−0.155418	−0.0777092	+	0.996976i	$0.524761\pi$
$278$	7.38172	0.442726
$279$	1.75048	0.104799
$280$	−7.98741	−0.477339
$281$	26.4215	1.57617	0.788086	−	0.615565i	$-0.211072\pi$
$281$	26.4215	1.57617	0.788086	+	0.615565i	$0.211072\pi$
$282$	10.9308	0.650920
$283$	−31.4457	−1.86925	−0.934626	−	0.355633i	$-0.884265\pi$
$283$	−31.4457	−1.86925	−0.934626	+	0.355633i	$0.884265\pi$
$284$	−4.30326	−0.255352
$285$	4.38834	0.259943
$286$	−4.55590	−0.269396
$287$	21.1564	1.24882
$288$	0.186728	0.0110030
$289$	34.7875	2.04632
$290$	4.36220	0.256157
$291$	−3.42648	−0.200864
$292$	−0.705872	−0.0413080
$293$	11.6519	0.680710	0.340355	−	0.940297i	$-0.389453\pi$
$293$	11.6519	0.680710	0.340355	+	0.940297i	$0.389453\pi$
$294$	19.9462	1.16328
$295$	−2.64195	−0.153820
$296$	−3.02156	−0.175624
$297$	−16.6876	−0.968313
$298$	−12.4129	−0.719059
$299$	5.60949	0.324405
$300$	2.72218	0.157165
$301$	3.20132	0.184521
$302$	−12.7569	−0.734079
$303$	−2.20391	−0.126612
$304$	−1.42373	−0.0816563
$305$	21.5474	1.23380
$306$	1.34376	0.0768175
$307$	4.32158	0.246646	0.123323	−	0.992367i	$-0.460645\pi$
$307$	4.32158	0.246646	0.123323	+	0.992367i	$0.460645\pi$
$308$	−13.5701	−0.773225
$309$	17.8659	1.01636
$310$	17.2273	0.978445
$311$	7.17597	0.406912	0.203456	−	0.979084i	$-0.434783\pi$
$311$	7.17597	0.406912	0.203456	+	0.979084i	$0.434783\pi$
$312$	−2.44758	−0.138567
$313$	30.1467	1.70399	0.851997	−	0.523547i	$-0.175392\pi$
$313$	30.1467	1.70399	0.851997	+	0.523547i	$0.175392\pi$
$314$	−3.67743	−0.207530
$315$	−1.49147	−0.0840348
$316$	2.30224	0.129511
$317$	19.4532	1.09260	0.546301	−	0.837589i	$-0.316036\pi$
$317$	19.4532	1.09260	0.546301	+	0.837589i	$0.316036\pi$
$318$	17.3886	0.975103
$319$	7.41107	0.414940
$320$	1.83767	0.102729
$321$	−23.2915	−1.30000
$322$	16.7082	0.931113
$323$	−10.2456	−0.570083
$324$	−8.40495	−0.466942
$325$	2.36833	0.131371
$326$	16.4579	0.911521
$327$	14.6546	0.810401
$328$	−4.86747	−0.268761
$329$	28.3260	1.56166
$330$	−9.62313	−0.529736
$331$	−5.69857	−0.313222	−0.156611	−	0.987660i	$-0.550057\pi$
$331$	−5.69857	−0.313222	−0.156611	+	0.987660i	$0.550057\pi$
$332$	3.07087	0.168536
$333$	−0.564208	−0.0309184
$334$	−15.8349	−0.866450
$335$	24.5446	1.34102
$336$	−7.29028	−0.397718
$337$	19.6853	1.07233	0.536163	−	0.844115i	$-0.319873\pi$
$337$	19.6853	1.07233	0.536163	+	0.844115i	$0.319873\pi$
$338$	10.8706	0.591281
$339$	−7.12393	−0.386919
$340$	13.2245	0.717200
$341$	29.2680	1.58495
$342$	−0.265849	−0.0143755
$343$	21.2628	1.14809
$344$	−0.736530	−0.0397110
$345$	11.8485	0.637904
$346$	−23.6349	−1.27062
$347$	3.33574	0.179072	0.0895360	−	0.995984i	$-0.471462\pi$
$347$	3.33574	0.179072	0.0895360	+	0.995984i	$0.471462\pi$
$348$	3.98147	0.213429
$349$	27.9614	1.49674	0.748370	−	0.663282i	$-0.230837\pi$
$349$	27.9614	1.49674	0.748370	+	0.663282i	$0.230837\pi$
$350$	7.05422	0.377064
$351$	−7.79978	−0.416321
$352$	3.12207	0.166407
$353$	−8.89445	−0.473404	−0.236702	−	0.971582i	$-0.576066\pi$
$353$	−8.89445	−0.473404	−0.236702	+	0.971582i	$0.576066\pi$
$354$	−2.41136	−0.128163
$355$	−7.90797	−0.419712
$356$	1.00500	0.0532650
$357$	−52.4634	−2.77666
$358$	−22.0369	−1.16469
$359$	−3.62239	−0.191182	−0.0955911	−	0.995421i	$-0.530474\pi$
$359$	−3.62239	−0.191182	−0.0955911	+	0.995421i	$0.530474\pi$
$360$	0.343143	0.0180853
$361$	−16.9730	−0.893316
$362$	17.3531	0.912056
$363$	2.10107	0.110278
$364$	−6.34264	−0.332445
$365$	−1.29716	−0.0678964
$366$	19.6668	1.02800
$367$	−15.4468	−0.806318	−0.403159	−	0.915130i	$-0.632088\pi$
$367$	−15.4468	−0.806318	−0.403159	+	0.915130i	$0.632088\pi$
$368$	−3.84407	−0.200386
$369$	−0.908891	−0.0473150
$370$	−5.55262	−0.288667
$371$	45.0606	2.33943
$372$	15.7237	0.815238
$373$	36.8227	1.90661	0.953304	−	0.302012i	$-0.0976583\pi$
$373$	36.8227	1.90661	0.953304	+	0.302012i	$0.0976583\pi$
$374$	22.4675	1.16177
$375$	20.4139	1.05417
$376$	−6.51698	−0.336088
$377$	3.46393	0.178402
$378$	−23.2321	−1.19493
$379$	27.4556	1.41030	0.705149	−	0.709059i	$-0.250880\pi$
$379$	27.4556	1.41030	0.705149	+	0.709059i	$0.250880\pi$
$380$	−2.61634	−0.134215
$381$	−20.6561	−1.05825
$382$	9.73826	0.498253
$383$	−35.4972	−1.81382	−0.906910	−	0.421325i	$-0.861565\pi$
$383$	−35.4972	−1.81382	−0.906910	+	0.421325i	$0.861565\pi$
$384$	1.67728	0.0855934
$385$	−24.9373	−1.27092
$386$	−4.54525	−0.231347
$387$	−0.137530	−0.00699107
$388$	2.04288	0.103711
$389$	18.8076	0.953581	0.476790	−	0.879017i	$-0.341800\pi$
$389$	18.8076	0.953581	0.476790	+	0.879017i	$0.341800\pi$
$390$	−4.49785	−0.227757
$391$	−27.6633	−1.39899
$392$	−11.8920	−0.600635
$393$	5.94095	0.299681
$394$	−5.21493	−0.262724
$395$	4.23075	0.212872
$396$	0.582977	0.0292957
$397$	−3.51960	−0.176644	−0.0883219	−	0.996092i	$-0.528150\pi$
$397$	−3.51960	−0.176644	−0.0883219	+	0.996092i	$0.528150\pi$
$398$	4.15238	0.208140
$399$	10.3794	0.519619
$400$	−1.62297	−0.0811485
$401$	−22.0266	−1.09996	−0.549978	−	0.835179i	$-0.685364\pi$
$401$	−22.0266	−1.09996	−0.549978	+	0.835179i	$0.685364\pi$
$402$	22.4024	1.11733
$403$	13.6798	0.681442
$404$	1.31398	0.0653729
$405$	−15.4455	−0.767494
$406$	10.3175	0.512051
$407$	−9.43352	−0.467602
$408$	12.0703	0.597569
$409$	−10.1073	−0.499774	−0.249887	−	0.968275i	$-0.580393\pi$
$409$	−10.1073	−0.499774	−0.249887	+	0.968275i	$0.580393\pi$
$410$	−8.94480	−0.441752
$411$	26.5342	1.30884
$412$	−10.6517	−0.524773
$413$	−6.24878	−0.307483
$414$	−0.717794	−0.0352777
$415$	5.64325	0.277016
$416$	1.45926	0.0715459
$417$	12.3812	0.606311
$418$	−4.44498	−0.217411
$419$	−21.2937	−1.04026	−0.520132	−	0.854086i	$-0.674117\pi$
$419$	−21.2937	−1.04026	−0.520132	+	0.854086i	$0.674117\pi$
$420$	−13.3971	−0.653713
$421$	21.9547	1.07001	0.535003	−	0.844850i	$-0.320310\pi$
$421$	21.9547	1.07001	0.535003	+	0.844850i	$0.320310\pi$
$422$	−3.90589	−0.190136
$423$	−1.21690	−0.0591677
$424$	−10.3671	−0.503472
$425$	−11.6795	−0.566537
$426$	−7.21778	−0.349703
$427$	50.9644	2.46634
$428$	13.8864	0.671226
$429$	−7.64153	−0.368937
$430$	−1.35350	−0.0652715
$431$	23.0292	1.10928	0.554639	−	0.832091i	$-0.312856\pi$
$431$	23.0292	1.10928	0.554639	+	0.832091i	$0.312856\pi$
$432$	5.34504	0.257163
$433$	−35.0000	−1.68199	−0.840995	−	0.541042i	$-0.818030\pi$
$433$	−35.0000	−1.68199	−0.840995	+	0.541042i	$0.818030\pi$
$434$	40.7463	1.95589
$435$	7.31663	0.350806
$436$	−8.73711	−0.418432
$437$	5.47291	0.261805
$438$	−1.18395	−0.0565711
$439$	2.60724	0.124437	0.0622185	−	0.998063i	$-0.480182\pi$
$439$	2.60724	0.124437	0.0622185	+	0.998063i	$0.480182\pi$
$440$	5.73734	0.273517
$441$	−2.22056	−0.105741
$442$	10.5013	0.499497
$443$	1.00138	0.0475772	0.0237886	−	0.999717i	$-0.492427\pi$
$443$	1.00138	0.0475772	0.0237886	+	0.999717i	$0.492427\pi$
$444$	−5.06800	−0.240517
$445$	1.84686	0.0875497
$446$	−13.2702	−0.628363
$447$	−20.8199	−0.984747
$448$	4.34649	0.205352
$449$	−6.14747	−0.290117	−0.145059	−	0.989423i	$-0.546337\pi$
$449$	−6.14747	−0.290117	−0.145059	+	0.989423i	$0.546337\pi$
$450$	−0.303053	−0.0142861
$451$	−15.1966	−0.715580
$452$	4.24731	0.199776
$453$	−21.3970	−1.00532
$454$	−18.2184	−0.855032
$455$	−11.6557	−0.546426
$456$	−2.38799	−0.111828
$457$	41.1661	1.92567	0.962835	−	0.270090i	$-0.0870535\pi$
$457$	41.1661	1.92567	0.962835	+	0.270090i	$0.0870535\pi$
$458$	−5.36759	−0.250811
$459$	38.4648	1.79538
$460$	−7.06414	−0.329367
$461$	13.8367	0.644438	0.322219	−	0.946665i	$-0.395571\pi$
$461$	13.8367	0.644438	0.322219	+	0.946665i	$0.395571\pi$
$462$	−22.7608	−1.05893
$463$	−29.6863	−1.37964	−0.689820	−	0.723980i	$-0.742311\pi$
$463$	−29.6863	−1.37964	−0.689820	+	0.723980i	$0.742311\pi$
$464$	−2.37377	−0.110199
$465$	28.8950	1.33997
$466$	−3.10684	−0.143922
$467$	3.39795	0.157238	0.0786192	−	0.996905i	$-0.474949\pi$
$467$	3.39795	0.157238	0.0786192	+	0.996905i	$0.474949\pi$
$468$	0.272483	0.0125955
$469$	58.0533	2.68065
$470$	−11.9761	−0.552414
$471$	−6.16809	−0.284211
$472$	1.43766	0.0661738
$473$	−2.29950	−0.105731
$474$	3.86150	0.177365
$475$	2.31067	0.106021
$476$	31.2788	1.43366
$477$	−1.93583	−0.0886354
$478$	25.1587	1.15073
$479$	7.60708	0.347576	0.173788	−	0.984783i	$-0.444399\pi$
$479$	7.60708	0.347576	0.173788	+	0.984783i	$0.444399\pi$
$480$	3.08229	0.140687
$481$	−4.40922	−0.201043
$482$	3.12108	0.142161
$483$	28.0244	1.27515
$484$	−1.25266	−0.0569393
$485$	3.75413	0.170466
$486$	1.93765	0.0878936
$487$	−19.9468	−0.903874	−0.451937	−	0.892050i	$-0.649267\pi$
$487$	−19.9468	−0.903874	−0.451937	+	0.892050i	$0.649267\pi$
$488$	−11.7254	−0.530785
$489$	27.6046	1.24832
$490$	−21.8535	−0.987240
$491$	−30.5819	−1.38014	−0.690072	−	0.723741i	$-0.742421\pi$
$491$	−30.5819	−1.38014	−0.690072	+	0.723741i	$0.742421\pi$
$492$	−8.16412	−0.368067
$493$	−17.0824	−0.769355
$494$	−2.07758	−0.0934748
$495$	1.07132	0.0481522
$496$	−9.37454	−0.420929
$497$	−18.7041	−0.838992
$498$	5.15071	0.230809
$499$	6.35824	0.284634	0.142317	−	0.989821i	$-0.454545\pi$
$499$	6.35824	0.284634	0.142317	+	0.989821i	$0.454545\pi$
$500$	−12.1708	−0.544296
$501$	−26.5597	−1.18660
$502$	−10.5090	−0.469041
$503$	−17.8518	−0.795974	−0.397987	−	0.917391i	$-0.630291\pi$
$503$	−17.8518	−0.795974	−0.397987	+	0.917391i	$0.630291\pi$
$504$	0.811609	0.0361519
$505$	2.41466	0.107451
$506$	−12.0015	−0.533531
$507$	18.2330	0.809756
$508$	12.3152	0.546401
$509$	0.228865	0.0101442	0.00507212	−	0.999987i	$-0.498385\pi$
$509$	0.228865	0.0101442	0.00507212	+	0.999987i	$0.498385\pi$
$510$	22.1812	0.982201
$511$	−3.06806	−0.135723
$512$	−1.00000	−0.0441942
$513$	−7.60988	−0.335984
$514$	−9.06010	−0.399624
$515$	−19.5743	−0.862549
$516$	−1.23537	−0.0543840
$517$	−20.3465	−0.894837
$518$	−13.1332	−0.577038
$519$	−39.6423	−1.74010
$520$	2.68163	0.117597
$521$	9.84109	0.431146	0.215573	−	0.976488i	$-0.430838\pi$
$521$	9.84109	0.431146	0.215573	+	0.976488i	$0.430838\pi$
$522$	−0.443247	−0.0194004
$523$	24.5350	1.07284	0.536421	−	0.843951i	$-0.319776\pi$
$523$	24.5350	1.07284	0.536421	+	0.843951i	$0.319776\pi$
$524$	−3.54201	−0.154733
$525$	11.8319	0.516387
$526$	−5.18207	−0.225949
$527$	−67.4625	−2.93871
$528$	5.23659	0.227893
$529$	−8.22310	−0.357526
$530$	−19.0513	−0.827538
$531$	0.268451	0.0116498
$532$	−6.18821	−0.268293
$533$	−7.10289	−0.307660
$534$	1.68567	0.0729461
$535$	25.5187	1.10327
$536$	−13.3564	−0.576908
$537$	−36.9621	−1.59503
$538$	−28.2615	−1.21844
$539$	−37.1276	−1.59920
$540$	9.82241	0.422689
$541$	−26.6316	−1.14498	−0.572490	−	0.819911i	$-0.694023\pi$
$541$	−26.6316	−1.14498	−0.572490	+	0.819911i	$0.694023\pi$
$542$	14.5932	0.626832
$543$	29.1060	1.24906
$544$	−7.19635	−0.308541
$545$	−16.0559	−0.687760
$546$	−10.6384	−0.455281
$547$	−32.0583	−1.37071	−0.685356	−	0.728208i	$-0.740354\pi$
$547$	−32.0583	−1.37071	−0.685356	+	0.728208i	$0.740354\pi$
$548$	−15.8198	−0.675788
$549$	−2.18946	−0.0934438
$550$	−5.06703	−0.216059
$551$	3.37959	0.143976
$552$	−6.44759	−0.274428
$553$	10.0066	0.425526
$554$	2.58668	0.109897
$555$	−9.31331	−0.395328
$556$	−7.38172	−0.313055
$557$	4.65383	0.197189	0.0985946	−	0.995128i	$-0.468565\pi$
$557$	4.65383	0.197189	0.0985946	+	0.995128i	$0.468565\pi$
$558$	−1.75048	−0.0741039
$559$	−1.07479	−0.0454586
$560$	7.98741	0.337530
$561$	37.6844	1.59103
$562$	−26.4215	−1.11452
$563$	−31.4027	−1.32347	−0.661734	−	0.749739i	$-0.730179\pi$
$563$	−31.4027	−1.32347	−0.661734	+	0.749739i	$0.730179\pi$
$564$	−10.9308	−0.460270
$565$	7.80514	0.328365
$566$	31.4457	1.32176
$567$	−36.5320	−1.53420
$568$	4.30326	0.180561
$569$	−10.8116	−0.453247	−0.226624	−	0.973982i	$-0.572769\pi$
$569$	−10.8116	−0.453247	−0.226624	+	0.973982i	$0.572769\pi$
$570$	−4.38834	−0.183807
$571$	20.3541	0.851793	0.425897	−	0.904772i	$-0.359959\pi$
$571$	20.3541	0.851793	0.425897	+	0.904772i	$0.359959\pi$
$572$	4.55590	0.190492
$573$	16.3338	0.682355
$574$	−21.1564	−0.883051
$575$	6.23882	0.260177
$576$	−0.186728	−0.00778031
$577$	3.85462	0.160470	0.0802350	−	0.996776i	$-0.474433\pi$
$577$	3.85462	0.160470	0.0802350	+	0.996776i	$0.474433\pi$
$578$	−34.7875	−1.44697
$579$	−7.62366	−0.316829
$580$	−4.36220	−0.181130
$581$	13.3475	0.553748
$582$	3.42648	0.142032
$583$	−32.3669	−1.34050
$584$	0.705872	0.0292092
$585$	0.500734	0.0207028
$586$	−11.6519	−0.481334
$587$	−44.6604	−1.84333	−0.921666	−	0.387985i	$-0.873171\pi$
$587$	−44.6604	−1.84333	−0.921666	+	0.387985i	$0.873171\pi$
$588$	−19.9462	−0.822566
$589$	13.3468	0.549945
$590$	2.64195	0.108767
$591$	−8.74690	−0.359799
$592$	3.02156	0.124185
$593$	−14.3581	−0.589616	−0.294808	−	0.955557i	$-0.595256\pi$
$593$	−14.3581	−0.589616	−0.294808	+	0.955557i	$0.595256\pi$
$594$	16.6876	0.684700
$595$	57.4802	2.35646
$596$	12.4129	0.508451
$597$	6.96472	0.285047
$598$	−5.60949	−0.229389
$599$	13.1241	0.536238	0.268119	−	0.963386i	$-0.413598\pi$
$599$	13.1241	0.536238	0.268119	+	0.963386i	$0.413598\pi$
$600$	−2.72218	−0.111132
$601$	−41.0911	−1.67614	−0.838071	−	0.545561i	$-0.816317\pi$
$601$	−41.0911	−1.67614	−0.838071	+	0.545561i	$0.816317\pi$
$602$	−3.20132	−0.130476
$603$	−2.49400	−0.101564
$604$	12.7569	0.519072
$605$	−2.30198	−0.0935889
$606$	2.20391	0.0895279
$607$	−30.1460	−1.22359	−0.611793	−	0.791018i	$-0.709552\pi$
$607$	−30.1460	−1.22359	−0.611793	+	0.791018i	$0.709552\pi$
$608$	1.42373	0.0577398
$609$	17.3054	0.701251
$610$	−21.5474	−0.872430
$611$	−9.50994	−0.384731
$612$	−1.34376	−0.0543181
$613$	21.9736	0.887506	0.443753	−	0.896149i	$-0.353647\pi$
$613$	21.9736	0.887506	0.443753	+	0.896149i	$0.353647\pi$
$614$	−4.32158	−0.174405
$615$	−15.0030	−0.604977
$616$	13.5701	0.546753
$617$	41.8499	1.68481	0.842406	−	0.538843i	$-0.181138\pi$
$617$	41.8499	1.68481	0.842406	+	0.538843i	$0.181138\pi$
$618$	−17.8659	−0.718673
$619$	25.3005	1.01691	0.508457	−	0.861088i	$-0.330216\pi$
$619$	25.3005	1.01691	0.508457	+	0.861088i	$0.330216\pi$
$620$	−17.2273	−0.691865
$621$	−20.5467	−0.824511
$622$	−7.17597	−0.287730
$623$	4.36823	0.175009
$624$	2.44758	0.0979817
$625$	−14.2511	−0.570044
$626$	−30.1467	−1.20491
$627$	−7.45548	−0.297743
$628$	3.67743	0.146746
$629$	21.7442	0.866997
$630$	1.49147	0.0594216
$631$	42.3384	1.68546	0.842732	−	0.538333i	$-0.180946\pi$
$631$	42.3384	1.68546	0.842732	+	0.538333i	$0.180946\pi$
$632$	−2.30224	−0.0915781
$633$	−6.55128	−0.260390
$634$	−19.4532	−0.772586
$635$	22.6314	0.898098
$636$	−17.3886	−0.689502
$637$	−17.3534	−0.687567
$638$	−7.41107	−0.293407
$639$	0.803537	0.0317874
$640$	−1.83767	−0.0726403
$641$	24.1514	0.953923	0.476962	−	0.878924i	$-0.341738\pi$
$641$	24.1514	0.953923	0.476962	+	0.878924i	$0.341738\pi$
$642$	23.2915	0.919240
$643$	23.3124	0.919350	0.459675	−	0.888087i	$-0.347966\pi$
$643$	23.3124	0.919350	0.459675	+	0.888087i	$0.347966\pi$
$644$	−16.7082	−0.658396
$645$	−2.27020	−0.0893890
$646$	10.2456	0.403109
$647$	−1.24820	−0.0490720	−0.0245360	−	0.999699i	$-0.507811\pi$
$647$	−1.24820	−0.0490720	−0.0245360	+	0.999699i	$0.507811\pi$
$648$	8.40495	0.330178
$649$	4.48849	0.176188
$650$	−2.36833	−0.0928935
$651$	68.3430	2.67857
$652$	−16.4579	−0.644543
$653$	33.6494	1.31680	0.658401	−	0.752668i	$-0.271233\pi$
$653$	33.6494	1.31680	0.658401	+	0.752668i	$0.271233\pi$
$654$	−14.6546	−0.573040
$655$	−6.50904	−0.254329
$656$	4.86747	0.190043
$657$	0.131806	0.00514223
$658$	−28.3260	−1.10426
$659$	48.7758	1.90004	0.950018	−	0.312194i	$-0.101064\pi$
$659$	48.7758	1.90004	0.950018	+	0.312194i	$0.101064\pi$
$660$	9.62313	0.374580
$661$	−26.4182	−1.02755	−0.513774	−	0.857926i	$-0.671753\pi$
$661$	−26.4182	−1.02755	−0.513774	+	0.857926i	$0.671753\pi$
$662$	5.69857	0.221481
$663$	17.6137	0.684058
$664$	−3.07087	−0.119173
$665$	−11.3719	−0.440983
$666$	0.564208	0.0218626
$667$	9.12493	0.353319
$668$	15.8349	0.612672
$669$	−22.2579	−0.860539
$670$	−24.5446	−0.948241
$671$	−36.6076	−1.41322
$672$	7.29028	0.281229
$673$	−28.2232	−1.08793	−0.543963	−	0.839109i	$-0.683077\pi$
$673$	−28.2232	−1.08793	−0.543963	+	0.839109i	$0.683077\pi$
$674$	−19.6853	−0.758249
$675$	−8.67484	−0.333895
$676$	−10.8706	−0.418099
$677$	12.7377	0.489548	0.244774	−	0.969580i	$-0.421286\pi$
$677$	12.7377	0.489548	0.244774	+	0.969580i	$0.421286\pi$
$678$	7.12393	0.273593
$679$	8.87934	0.340758
$680$	−13.2245	−0.507137
$681$	−30.5574	−1.17096
$682$	−29.2680	−1.12073
$683$	23.7035	0.906990	0.453495	−	0.891259i	$-0.350177\pi$
$683$	23.7035	0.906990	0.453495	+	0.891259i	$0.350177\pi$
$684$	0.265849	0.0101650
$685$	−29.0716	−1.11077
$686$	−21.2628	−0.811819
$687$	−9.00297	−0.343485
$688$	0.736530	0.0280799
$689$	−15.1283	−0.576342
$690$	−11.8485	−0.451066
$691$	30.9708	1.17818	0.589092	−	0.808066i	$-0.299486\pi$
$691$	30.9708	1.17818	0.589092	+	0.808066i	$0.299486\pi$
$692$	23.6349	0.898462
$693$	2.53390	0.0962550
$694$	−3.33574	−0.126623
$695$	−13.5652	−0.514556
$696$	−3.98147	−0.150917
$697$	35.0280	1.32678
$698$	−27.9614	−1.05835
$699$	−5.21105	−0.197100
$700$	−7.05422	−0.266625
$701$	−14.6477	−0.553235	−0.276618	−	0.960980i	$-0.589214\pi$
$701$	−14.6477	−0.553235	−0.276618	+	0.960980i	$0.589214\pi$
$702$	7.79978	0.294384
$703$	−4.30187	−0.162248
$704$	−3.12207	−0.117668
$705$	−20.0872	−0.756528
$706$	8.89445	0.334747
$707$	5.71120	0.214792
$708$	2.41136	0.0906246
$709$	−9.08757	−0.341291	−0.170645	−	0.985333i	$-0.554585\pi$
$709$	−9.08757	−0.341291	−0.170645	+	0.985333i	$0.554585\pi$
$710$	7.90797	0.296781
$711$	−0.429891	−0.0161222
$712$	−1.00500	−0.0376641
$713$	36.0364	1.34957
$714$	52.4634	1.96339
$715$	8.37224	0.313104
$716$	22.0369	0.823558
$717$	42.1982	1.57592
$718$	3.62239	0.135186
$719$	0.828510	0.0308982	0.0154491	−	0.999881i	$-0.495082\pi$
$719$	0.828510	0.0308982	0.0154491	+	0.999881i	$0.495082\pi$
$720$	−0.343143	−0.0127882
$721$	−46.2976	−1.72421
$722$	16.9730	0.631670
$723$	5.23493	0.194689
$724$	−17.3531	−0.644921
$725$	3.85255	0.143080
$726$	−2.10107	−0.0779781
$727$	−12.8346	−0.476008	−0.238004	−	0.971264i	$-0.576493\pi$
$727$	−12.8346	−0.476008	−0.238004	+	0.971264i	$0.576493\pi$
$728$	6.34264	0.235074
$729$	28.4648	1.05425
$730$	1.29716	0.0480100
$731$	5.30033	0.196040
$732$	−19.6668	−0.726907
$733$	−0.216462	−0.00799520	−0.00399760	−	0.999992i	$-0.501272\pi$
$733$	−0.216462	−0.00799520	−0.00399760	+	0.999992i	$0.501272\pi$
$734$	15.4468	0.570153
$735$	−36.6544	−1.35202
$736$	3.84407	0.141694
$737$	−41.6996	−1.53602
$738$	0.908891	0.0334567
$739$	−37.4402	−1.37726	−0.688629	−	0.725114i	$-0.741787\pi$
$739$	−37.4402	−1.37726	−0.688629	+	0.725114i	$0.741787\pi$
$740$	5.55262	0.204118
$741$	−3.48469	−0.128013
$742$	−45.0606	−1.65423
$743$	10.2539	0.376180	0.188090	−	0.982152i	$-0.439770\pi$
$743$	10.2539	0.376180	0.188090	+	0.982152i	$0.439770\pi$
$744$	−15.7237	−0.576460
$745$	22.8108	0.835722
$746$	−36.8227	−1.34818
$747$	−0.573416	−0.0209802
$748$	−22.4675	−0.821494
$749$	60.3572	2.20540
$750$	−20.4139	−0.745411
$751$	−12.9672	−0.473182	−0.236591	−	0.971609i	$-0.576030\pi$
$751$	−12.9672	−0.473182	−0.236591	+	0.971609i	$0.576030\pi$
$752$	6.51698	0.237650
$753$	−17.6266	−0.642349
$754$	−3.46393	−0.126149
$755$	23.4430	0.853179
$756$	23.2321	0.844945
$757$	8.66530	0.314946	0.157473	−	0.987523i	$-0.449665\pi$
$757$	8.66530	0.314946	0.157473	+	0.987523i	$0.449665\pi$
$758$	−27.4556	−0.997232
$759$	−20.1298	−0.730667
$760$	2.61634	0.0949046
$761$	29.0039	1.05139	0.525695	−	0.850673i	$-0.323805\pi$
$761$	29.0039	1.05139	0.525695	+	0.850673i	$0.323805\pi$
$762$	20.6561	0.748293
$763$	−37.9757	−1.37481
$764$	−9.73826	−0.352318
$765$	−2.46938	−0.0892806
$766$	35.4972	1.28256
$767$	2.09792	0.0757514
$768$	−1.67728	−0.0605237
$769$	15.6349	0.563809	0.281904	−	0.959443i	$-0.409034\pi$
$769$	15.6349	0.563809	0.281904	+	0.959443i	$0.409034\pi$
$770$	24.9373	0.898677
$771$	−15.1963	−0.547283
$772$	4.54525	0.163587
$773$	−28.8921	−1.03918	−0.519589	−	0.854416i	$-0.673915\pi$
$773$	−28.8921	−1.03918	−0.519589	+	0.854416i	$0.673915\pi$
$774$	0.137530	0.00494343
$775$	15.2146	0.546525
$776$	−2.04288	−0.0733350
$777$	−22.0280	−0.790250
$778$	−18.8076	−0.674283
$779$	−6.92995	−0.248291
$780$	4.49785	0.161049
$781$	13.4351	0.480745
$782$	27.6633	0.989238
$783$	−12.6879	−0.453427
$784$	11.8920	0.424713
$785$	6.75791	0.241200
$786$	−5.94095	−0.211907
$787$	41.8647	1.49231	0.746157	−	0.665769i	$-0.231897\pi$
$787$	41.8647	1.49231	0.746157	+	0.665769i	$0.231897\pi$
$788$	5.21493	0.185774
$789$	−8.69180	−0.309436
$790$	−4.23075	−0.150523
$791$	18.4609	0.656393
$792$	−0.582977	−0.0207152
$793$	−17.1104	−0.607608
$794$	3.51960	0.124906
$795$	−31.9545	−1.13331
$796$	−4.15238	−0.147177
$797$	−6.45030	−0.228481	−0.114241	−	0.993453i	$-0.536444\pi$
$797$	−6.45030	−0.228481	−0.114241	+	0.993453i	$0.536444\pi$
$798$	−10.3794	−0.367426
$799$	46.8985	1.65915
$800$	1.62297	0.0573807
$801$	−0.187662	−0.00663070
$802$	22.0266	0.777786
$803$	2.20378	0.0777698
$804$	−22.4024	−0.790072
$805$	−30.7042	−1.08218
$806$	−13.6798	−0.481852
$807$	−47.4025	−1.66865
$808$	−1.31398	−0.0462256
$809$	2.67478	0.0940404	0.0470202	−	0.998894i	$-0.485027\pi$
$809$	2.67478	0.0940404	0.0470202	+	0.998894i	$0.485027\pi$
$810$	15.4455	0.542700
$811$	−4.39196	−0.154222	−0.0771112	−	0.997022i	$-0.524570\pi$
$811$	−4.39196	−0.154222	−0.0771112	+	0.997022i	$0.524570\pi$
$812$	−10.3175	−0.362075
$813$	24.4769	0.858443
$814$	9.43352	0.330645
$815$	−30.2443	−1.05941
$816$	−12.0703	−0.422545
$817$	−1.04862	−0.0366865
$818$	10.1073	0.353393
$819$	1.18435	0.0413844
$820$	8.94480	0.312366
$821$	56.8577	1.98435	0.992174	−	0.124866i	$-0.0398500\pi$
$821$	56.8577	1.98435	0.992174	+	0.124866i	$0.0398500\pi$
$822$	−26.5342	−0.925488
$823$	0.654208	0.0228042	0.0114021	−	0.999935i	$-0.496371\pi$
$823$	0.654208	0.0228042	0.0114021	+	0.999935i	$0.496371\pi$
$824$	10.6517	0.371070
$825$	−8.49884	−0.295892
$826$	6.24878	0.217423
$827$	−43.3740	−1.50826	−0.754131	−	0.656725i	$-0.771941\pi$
$827$	−43.3740	−1.50826	−0.754131	+	0.656725i	$0.771941\pi$
$828$	0.717794	0.0249451
$829$	−53.6506	−1.86336	−0.931682	−	0.363276i	$-0.881658\pi$
$829$	−53.6506	−1.86336	−0.931682	+	0.363276i	$0.881658\pi$
$830$	−5.64325	−0.195880
$831$	4.33859	0.150504
$832$	−1.45926	−0.0505906
$833$	85.5787	2.96513
$834$	−12.3812	−0.428727
$835$	29.0994	1.00703
$836$	4.44498	0.153733
$837$	−50.1073	−1.73196
$838$	21.2937	0.735577
$839$	0.0927105	0.00320072	0.00160036	−	0.999999i	$-0.499491\pi$
$839$	0.0927105	0.00320072	0.00160036	+	0.999999i	$0.499491\pi$
$840$	13.3971	0.462245
$841$	−23.3652	−0.805698
$842$	−21.9547	−0.756609
$843$	−44.3162	−1.52633
$844$	3.90589	0.134446
$845$	−19.9765	−0.687213
$846$	1.21690	0.0418379
$847$	−5.44469	−0.187082
$848$	10.3671	0.356008
$849$	52.7432	1.81014
$850$	11.6795	0.400602
$851$	−11.6151	−0.398160
$852$	7.21778	0.247277
$853$	−6.21319	−0.212736	−0.106368	−	0.994327i	$-0.533922\pi$
$853$	−6.21319	−0.212736	−0.106368	+	0.994327i	$0.533922\pi$
$854$	−50.9644	−1.74397
$855$	0.488543	0.0167078
$856$	−13.8864	−0.474629
$857$	32.6506	1.11532	0.557662	−	0.830068i	$-0.311698\pi$
$857$	32.6506	1.11532	0.557662	+	0.830068i	$0.311698\pi$
$858$	7.64153	0.260878
$859$	−33.1027	−1.12945	−0.564725	−	0.825279i	$-0.691018\pi$
$859$	−33.1027	−1.12945	−0.564725	+	0.825279i	$0.691018\pi$
$860$	1.35350	0.0461539
$861$	−35.4852	−1.20933
$862$	−23.0292	−0.784378
$863$	26.7250	0.909730	0.454865	−	0.890561i	$-0.349688\pi$
$863$	26.7250	0.909730	0.454865	+	0.890561i	$0.349688\pi$
$864$	−5.34504	−0.181842
$865$	43.4331	1.47677
$866$	35.0000	1.18935
$867$	−58.3483	−1.98161
$868$	−40.7463	−1.38302
$869$	−7.18775	−0.243828
$870$	−7.31663	−0.248057
$871$	−19.4904	−0.660406
$872$	8.73711	0.295876
$873$	−0.381461	−0.0129105
$874$	−5.47291	−0.185124
$875$	−52.9004	−1.78836
$876$	1.18395	0.0400018
$877$	−32.1216	−1.08467	−0.542334	−	0.840163i	$-0.682459\pi$
$877$	−32.1216	−1.08467	−0.542334	+	0.840163i	$0.682459\pi$
$878$	−2.60724	−0.0879902
$879$	−19.5435	−0.659185
$880$	−5.73734	−0.193406
$881$	42.1131	1.41883	0.709413	−	0.704793i	$-0.248960\pi$
$881$	42.1131	1.41883	0.709413	+	0.704793i	$0.248960\pi$
$882$	2.22056	0.0747700
$883$	−47.8462	−1.61015	−0.805077	−	0.593171i	$-0.797876\pi$
$883$	−47.8462	−1.61015	−0.805077	+	0.593171i	$0.797876\pi$
$884$	−10.5013	−0.353197
$885$	4.43129	0.148956
$886$	−1.00138	−0.0336421
$887$	2.52223	0.0846881	0.0423440	−	0.999103i	$-0.486517\pi$
$887$	2.52223	0.0846881	0.0423440	+	0.999103i	$0.486517\pi$
$888$	5.06800	0.170071
$889$	53.5281	1.79527
$890$	−1.84686	−0.0619070
$891$	26.2409	0.879102
$892$	13.2702	0.444320
$893$	−9.27840	−0.310490
$894$	20.8199	0.696321
$895$	40.4965	1.35365
$896$	−4.34649	−0.145206
$897$	−9.40869	−0.314147
$898$	6.14747	0.205144
$899$	22.2530	0.742177
$900$	0.303053	0.0101018
$901$	74.6054	2.48547
$902$	15.1966	0.505991
$903$	−5.36951	−0.178686
$904$	−4.24731	−0.141263
$905$	−31.8892	−1.06003
$906$	21.3970	0.710866
$907$	−35.9006	−1.19206	−0.596030	−	0.802962i	$-0.703256\pi$
$907$	−35.9006	−1.19206	−0.596030	+	0.802962i	$0.703256\pi$
$908$	18.2184	0.604599
$909$	−0.245356	−0.00813795
$910$	11.6557	0.386382
$911$	−30.8123	−1.02086	−0.510428	−	0.859921i	$-0.670513\pi$
$911$	−30.8123	−1.02086	−0.510428	+	0.859921i	$0.670513\pi$
$912$	2.38799	0.0790743
$913$	−9.58748	−0.317299
$914$	−41.1661	−1.36165
$915$	−36.1411	−1.19479
$916$	5.36759	0.177350
$917$	−15.3953	−0.508398
$918$	−38.4648	−1.26953
$919$	15.8214	0.521901	0.260951	−	0.965352i	$-0.415964\pi$
$919$	15.8214	0.521901	0.260951	+	0.965352i	$0.415964\pi$
$920$	7.06414	0.232898
$921$	−7.24851	−0.238847
$922$	−13.8367	−0.455687
$923$	6.27956	0.206694
$924$	22.7608	0.748775
$925$	−4.90390	−0.161239
$926$	29.6863	0.975553
$927$	1.98897	0.0653263
$928$	2.37377	0.0779227
$929$	15.3625	0.504028	0.252014	−	0.967724i	$-0.418907\pi$
$929$	15.3625	0.504028	0.252014	+	0.967724i	$0.418907\pi$
$930$	−28.8950	−0.947505
$931$	−16.9309	−0.554888
$932$	3.10684	0.101768
$933$	−12.0361	−0.394045
$934$	−3.39795	−0.111184
$935$	−41.2879	−1.35026
$936$	−0.272483	−0.00890639
$937$	−27.6452	−0.903129	−0.451564	−	0.892239i	$-0.649134\pi$
$937$	−27.6452	−0.903129	−0.451564	+	0.892239i	$0.649134\pi$
$938$	−58.0533	−1.89551
$939$	−50.5645	−1.65011
$940$	11.9761	0.390616
$941$	2.21511	0.0722104	0.0361052	−	0.999348i	$-0.488505\pi$
$941$	2.21511	0.0722104	0.0361052	+	0.999348i	$0.488505\pi$
$942$	6.16809	0.200967
$943$	−18.7109	−0.609311
$944$	−1.43766	−0.0467919
$945$	42.6930	1.38880
$946$	2.29950	0.0747632
$947$	−37.0382	−1.20358	−0.601790	−	0.798655i	$-0.705545\pi$
$947$	−37.0382	−1.20358	−0.601790	+	0.798655i	$0.705545\pi$
$948$	−3.86150	−0.125416
$949$	1.03005	0.0334368
$950$	−2.31067	−0.0749679
$951$	−32.6285	−1.05805
$952$	−31.2788	−1.01375
$953$	7.13854	0.231240	0.115620	−	0.993294i	$-0.463115\pi$
$953$	7.13854	0.231240	0.115620	+	0.993294i	$0.463115\pi$
$954$	1.93583	0.0626747
$955$	−17.8957	−0.579092
$956$	−25.1587	−0.813691
$957$	−12.4304	−0.401819
$958$	−7.60708	−0.245773
$959$	−68.7606	−2.22039
$960$	−3.08229	−0.0994804
$961$	56.8820	1.83490
$962$	4.40922	0.142159
$963$	−2.59298	−0.0835576
$964$	−3.12108	−0.100523
$965$	8.35267	0.268882
$966$	−28.0244	−0.901670
$967$	45.2291	1.45447	0.727235	−	0.686389i	$-0.240805\pi$
$967$	45.2291	1.45447	0.727235	+	0.686389i	$0.240805\pi$
$968$	1.25266	0.0402622
$969$	17.1848	0.552056
$970$	−3.75413	−0.120538
$971$	−7.45868	−0.239360	−0.119680	−	0.992812i	$-0.538187\pi$
$971$	−7.45868	−0.239360	−0.119680	+	0.992812i	$0.538187\pi$
$972$	−1.93765	−0.0621501
$973$	−32.0846	−1.02858
$974$	19.9468	0.639135
$975$	−3.97236	−0.127217
$976$	11.7254	0.375321
$977$	21.4897	0.687517	0.343759	−	0.939058i	$-0.388300\pi$
$977$	21.4897	0.687517	0.343759	+	0.939058i	$0.388300\pi$
$978$	−27.6046	−0.882698
$979$	−3.13769	−0.100281
$980$	21.8535	0.698084
$981$	1.63146	0.0520885
$982$	30.5819	0.975909
$983$	−31.5013	−1.00474	−0.502368	−	0.864654i	$-0.667538\pi$
$983$	−31.5013	−1.00474	−0.502368	+	0.864654i	$0.667538\pi$
$984$	8.16412	0.260263
$985$	9.58331	0.305350
$986$	17.0824	0.544016
$987$	−47.5106	−1.51228
$988$	2.07758	0.0660967
$989$	−2.83128	−0.0900293
$990$	−1.07132	−0.0340487
$991$	−6.81616	−0.216522	−0.108261	−	0.994122i	$-0.534528\pi$
$991$	−6.81616	−0.216522	−0.108261	+	0.994122i	$0.534528\pi$
$992$	9.37454	0.297642
$993$	9.55810	0.303317
$994$	18.7041	0.593257
$995$	−7.63071	−0.241910
$996$	−5.15071	−0.163207
$997$	−16.4227	−0.520112	−0.260056	−	0.965593i	$-0.583741\pi$
$997$	−16.4227	−0.520112	−0.260056	+	0.965593i	$0.583741\pi$
$998$	−6.35824	−0.201267
$999$	16.1503	0.510974

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4006.2.a.h.1.13	✓	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4006.2.a.h.1.13	✓	42	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 4006 = 2 \cdot 2003 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4006.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.67728 q^{3} +1.00000 q^{4} +1.83767 q^{5} +1.67728 q^{6} +4.34649 q^{7} -1.00000 q^{8} -0.186728 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.67728 q^{3} +1.00000 q^{4} +1.83767 q^{5} +1.67728 q^{6} +4.34649 q^{7} -1.00000 q^{8} -0.186728 q^{9} -1.83767 q^{10} -3.12207 q^{11} -1.67728 q^{12} -1.45926 q^{13} -4.34649 q^{14} -3.08229 q^{15} +1.00000 q^{16} +7.19635 q^{17} +0.186728 q^{18} -1.42373 q^{19} +1.83767 q^{20} -7.29028 q^{21} +3.12207 q^{22} -3.84407 q^{23} +1.67728 q^{24} -1.62297 q^{25} +1.45926 q^{26} +5.34504 q^{27} +4.34649 q^{28} -2.37377 q^{29} +3.08229 q^{30} -9.37454 q^{31} -1.00000 q^{32} +5.23659 q^{33} -7.19635 q^{34} +7.98741 q^{35} -0.186728 q^{36} +3.02156 q^{37} +1.42373 q^{38} +2.44758 q^{39} -1.83767 q^{40} +4.86747 q^{41} +7.29028 q^{42} +0.736530 q^{43} -3.12207 q^{44} -0.343143 q^{45} +3.84407 q^{46} +6.51698 q^{47} -1.67728 q^{48} +11.8920 q^{49} +1.62297 q^{50} -12.0703 q^{51} -1.45926 q^{52} +10.3671 q^{53} -5.34504 q^{54} -5.73734 q^{55} -4.34649 q^{56} +2.38799 q^{57} +2.37377 q^{58} -1.43766 q^{59} -3.08229 q^{60} +11.7254 q^{61} +9.37454 q^{62} -0.811609 q^{63} +1.00000 q^{64} -2.68163 q^{65} -5.23659 q^{66} +13.3564 q^{67} +7.19635 q^{68} +6.44759 q^{69} -7.98741 q^{70} -4.30326 q^{71} +0.186728 q^{72} -0.705872 q^{73} -3.02156 q^{74} +2.72218 q^{75} -1.42373 q^{76} -13.5701 q^{77} -2.44758 q^{78} +2.30224 q^{79} +1.83767 q^{80} -8.40495 q^{81} -4.86747 q^{82} +3.07087 q^{83} -7.29028 q^{84} +13.2245 q^{85} -0.736530 q^{86} +3.98147 q^{87} +3.12207 q^{88} +1.00500 q^{89} +0.343143 q^{90} -6.34264 q^{91} -3.84407 q^{92} +15.7237 q^{93} -6.51698 q^{94} -2.61634 q^{95} +1.67728 q^{96} +2.04288 q^{97} -11.8920 q^{98} +0.582977 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q - 42 q^{2} + 42 q^{4} + 27 q^{5} - 10 q^{7} - 42 q^{8} + 56 q^{9}+O(q^{10}) \) 42 * q - 42 * q^2 + 42 * q^4 + 27 * q^5 - 10 * q^7 - 42 * q^8 + 56 * q^9	\( 42 q - 42 q^{2} + 42 q^{4} + 27 q^{5} - 10 q^{7} - 42 q^{8} + 56 q^{9} - 27 q^{10} + 23 q^{11} + 15 q^{13} + 10 q^{14} + 6 q^{15} + 42 q^{16} + 14 q^{17} - 56 q^{18} - 4 q^{19} + 27 q^{20} + 26 q^{21} - 23 q^{22} + 12 q^{23} + 45 q^{25} - 15 q^{26} - 3 q^{27} - 10 q^{28} + 41 q^{29} - 6 q^{30} + 18 q^{31} - 42 q^{32} + 25 q^{33} - 14 q^{34} + 8 q^{35} + 56 q^{36} + 33 q^{37} + 4 q^{38} + 10 q^{39} - 27 q^{40} + 84 q^{41} - 26 q^{42} - 36 q^{43} + 23 q^{44} + 66 q^{45} - 12 q^{46} + 28 q^{47} + 58 q^{49} - 45 q^{50} + 17 q^{51} + 15 q^{52} + 68 q^{53} + 3 q^{54} - 28 q^{55} + 10 q^{56} - 9 q^{57} - 41 q^{58} + 59 q^{59} + 6 q^{60} + 41 q^{61} - 18 q^{62} - 28 q^{63} + 42 q^{64} + 44 q^{65} - 25 q^{66} + 14 q^{68} + 67 q^{69} - 8 q^{70} + 69 q^{71} - 56 q^{72} - 27 q^{73} - 33 q^{74} + 14 q^{75} - 4 q^{76} + 43 q^{77} - 10 q^{78} - 19 q^{79} + 27 q^{80} + 74 q^{81} - 84 q^{82} + 20 q^{83} + 26 q^{84} + 16 q^{85} + 36 q^{86} - 28 q^{87} - 23 q^{88} + 123 q^{89} - 66 q^{90} - 9 q^{91} + 12 q^{92} + 48 q^{93} - 28 q^{94} + 28 q^{95} + 10 q^{97} - 58 q^{98} + 75 q^{99}+O(q^{100}) \) 42 * q - 42 * q^2 + 42 * q^4 + 27 * q^5 - 10 * q^7 - 42 * q^8 + 56 * q^9 - 27 * q^10 + 23 * q^11 + 15 * q^13 + 10 * q^14 + 6 * q^15 + 42 * q^16 + 14 * q^17 - 56 * q^18 - 4 * q^19 + 27 * q^20 + 26 * q^21 - 23 * q^22 + 12 * q^23 + 45 * q^25 - 15 * q^26 - 3 * q^27 - 10 * q^28 + 41 * q^29 - 6 * q^30 + 18 * q^31 - 42 * q^32 + 25 * q^33 - 14 * q^34 + 8 * q^35 + 56 * q^36 + 33 * q^37 + 4 * q^38 + 10 * q^39 - 27 * q^40 + 84 * q^41 - 26 * q^42 - 36 * q^43 + 23 * q^44 + 66 * q^45 - 12 * q^46 + 28 * q^47 + 58 * q^49 - 45 * q^50 + 17 * q^51 + 15 * q^52 + 68 * q^53 + 3 * q^54 - 28 * q^55 + 10 * q^56 - 9 * q^57 - 41 * q^58 + 59 * q^59 + 6 * q^60 + 41 * q^61 - 18 * q^62 - 28 * q^63 + 42 * q^64 + 44 * q^65 - 25 * q^66 + 14 * q^68 + 67 * q^69 - 8 * q^70 + 69 * q^71 - 56 * q^72 - 27 * q^73 - 33 * q^74 + 14 * q^75 - 4 * q^76 + 43 * q^77 - 10 * q^78 - 19 * q^79 + 27 * q^80 + 74 * q^81 - 84 * q^82 + 20 * q^83 + 26 * q^84 + 16 * q^85 + 36 * q^86 - 28 * q^87 - 23 * q^88 + 123 * q^89 - 66 * q^90 - 9 * q^91 + 12 * q^92 + 48 * q^93 - 28 * q^94 + 28 * q^95 + 10 * q^97 - 58 * q^98 + 75 * q^99

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