LMFDB - Embedded newform 7595.2.a.u.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7595,2,Mod(1,7595)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7595, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("7595.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7595 = 5 \cdot 7^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7595.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:	$60.6463803352$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 3x^{6} - 9x^{5} + 29x^{4} + 18x^{3} - 70x^{2} - 10x + 48 $ x^7 - 3x^6 - 9x^5 + 29x^4 + 18x^3 - 70x^2 - 10x + 48
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1085)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.53671$ of defining polynomial
Character	$\chi$	$=$	7595.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.53671 q^{2} -2.16264 q^{3} +4.43491 q^{4} +1.00000 q^{5} +5.48599 q^{6} -6.17668 q^{8} +1.67701 q^{9} +O(q^{10})$	\(q-2.53671 q^{2} -2.16264 q^{3} +4.43491 q^{4} +1.00000 q^{5} +5.48599 q^{6} -6.17668 q^{8} +1.67701 q^{9} -2.53671 q^{10} -2.85565 q^{11} -9.59111 q^{12} -3.87576 q^{13} -2.16264 q^{15} +6.79863 q^{16} +7.42848 q^{17} -4.25408 q^{18} -4.55277 q^{19} +4.43491 q^{20} +7.24395 q^{22} +8.00368 q^{23} +13.3579 q^{24} +1.00000 q^{25} +9.83169 q^{26} +2.86116 q^{27} +4.12792 q^{29} +5.48599 q^{30} +1.00000 q^{31} -4.89282 q^{32} +6.17573 q^{33} -18.8439 q^{34} +7.43737 q^{36} +9.54114 q^{37} +11.5491 q^{38} +8.38187 q^{39} -6.17668 q^{40} -8.59414 q^{41} +1.97569 q^{43} -12.6645 q^{44} +1.67701 q^{45} -20.3030 q^{46} -10.4620 q^{47} -14.7030 q^{48} -2.53671 q^{50} -16.0651 q^{51} -17.1887 q^{52} +9.32098 q^{53} -7.25794 q^{54} -2.85565 q^{55} +9.84599 q^{57} -10.4714 q^{58} +3.59331 q^{59} -9.59111 q^{60} +12.5997 q^{61} -2.53671 q^{62} -1.18557 q^{64} -3.87576 q^{65} -15.6661 q^{66} +0.455398 q^{67} +32.9447 q^{68} -17.3091 q^{69} -8.42898 q^{71} -10.3583 q^{72} +5.78299 q^{73} -24.2031 q^{74} -2.16264 q^{75} -20.1911 q^{76} -21.2624 q^{78} -1.32975 q^{79} +6.79863 q^{80} -11.2187 q^{81} +21.8009 q^{82} -10.1287 q^{83} +7.42848 q^{85} -5.01176 q^{86} -8.92720 q^{87} +17.6384 q^{88} +2.76868 q^{89} -4.25408 q^{90} +35.4956 q^{92} -2.16264 q^{93} +26.5392 q^{94} -4.55277 q^{95} +10.5814 q^{96} -16.6690 q^{97} -4.78893 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 3 q^{2} - 2 q^{3} + 13 q^{4} + 7 q^{5} + 12 q^{6} + 9 q^{8} + 11 q^{9}+O(q^{10}) $ 7 * q + 3 * q^2 - 2 * q^3 + 13 * q^4 + 7 * q^5 + 12 * q^6 + 9 * q^8 + 11 * q^9	$ 7 q + 3 q^{2} - 2 q^{3} + 13 q^{4} + 7 q^{5} + 12 q^{6} + 9 q^{8} + 11 q^{9} + 3 q^{10} + 5 q^{11} - 4 q^{12} - 9 q^{13} - 2 q^{15} + 13 q^{16} + 2 q^{17} - 5 q^{18} - 13 q^{19} + 13 q^{20} + 20 q^{22} + 8 q^{23} + 8 q^{24} + 7 q^{25} - 4 q^{26} - 8 q^{27} - q^{29} + 12 q^{30} + 7 q^{31} + 11 q^{32} + 13 q^{33} - 20 q^{34} - 3 q^{36} + 37 q^{37} + 4 q^{38} + 21 q^{39} + 9 q^{40} - 9 q^{41} + 19 q^{43} + 16 q^{44} + 11 q^{45} + 8 q^{46} + q^{47} - 8 q^{48} + 3 q^{50} - 4 q^{51} - 26 q^{52} + 25 q^{53} + 32 q^{54} + 5 q^{55} + 33 q^{57} + 4 q^{58} - 7 q^{59} - 4 q^{60} + 34 q^{61} + 3 q^{62} + 49 q^{64} - 9 q^{65} - 32 q^{66} + 20 q^{68} - 4 q^{69} - 23 q^{71} - 17 q^{72} + 3 q^{73} - 18 q^{74} - 2 q^{75} - 10 q^{76} + 14 q^{78} + 13 q^{79} + 13 q^{80} - 5 q^{81} + 78 q^{82} + 13 q^{83} + 2 q^{85} + 10 q^{86} + 17 q^{87} + 52 q^{88} + 10 q^{89} - 5 q^{90} + 60 q^{92} - 2 q^{93} + 38 q^{94} - 13 q^{95} + 26 q^{96} - 3 q^{97} - 36 q^{99}+O(q^{100}) $ 7 * q + 3 * q^2 - 2 * q^3 + 13 * q^4 + 7 * q^5 + 12 * q^6 + 9 * q^8 + 11 * q^9 + 3 * q^10 + 5 * q^11 - 4 * q^12 - 9 * q^13 - 2 * q^15 + 13 * q^16 + 2 * q^17 - 5 * q^18 - 13 * q^19 + 13 * q^20 + 20 * q^22 + 8 * q^23 + 8 * q^24 + 7 * q^25 - 4 * q^26 - 8 * q^27 - q^29 + 12 * q^30 + 7 * q^31 + 11 * q^32 + 13 * q^33 - 20 * q^34 - 3 * q^36 + 37 * q^37 + 4 * q^38 + 21 * q^39 + 9 * q^40 - 9 * q^41 + 19 * q^43 + 16 * q^44 + 11 * q^45 + 8 * q^46 + q^47 - 8 * q^48 + 3 * q^50 - 4 * q^51 - 26 * q^52 + 25 * q^53 + 32 * q^54 + 5 * q^55 + 33 * q^57 + 4 * q^58 - 7 * q^59 - 4 * q^60 + 34 * q^61 + 3 * q^62 + 49 * q^64 - 9 * q^65 - 32 * q^66 + 20 * q^68 - 4 * q^69 - 23 * q^71 - 17 * q^72 + 3 * q^73 - 18 * q^74 - 2 * q^75 - 10 * q^76 + 14 * q^78 + 13 * q^79 + 13 * q^80 - 5 * q^81 + 78 * q^82 + 13 * q^83 + 2 * q^85 + 10 * q^86 + 17 * q^87 + 52 * q^88 + 10 * q^89 - 5 * q^90 + 60 * q^92 - 2 * q^93 + 38 * q^94 - 13 * q^95 + 26 * q^96 - 3 * q^97 - 36 * 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 $

$2$	−2.53671	−1.79373	−0.896864	−	0.442307i	$-0.854160\pi$
$2$	−2.53671	−1.79373	−0.896864	+	0.442307i	$0.854160\pi$
$3$	−2.16264	−1.24860	−0.624300	−	0.781185i	$-0.714616\pi$
$3$	−2.16264	−1.24860	−0.624300	+	0.781185i	$0.714616\pi$
$4$	4.43491	2.21746
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	5.48599	2.23965
$7$	0	0
$7$	0	0
$8$	−6.17668	−2.18379
$9$	1.67701	0.559002
$10$	−2.53671	−0.802179
$11$	−2.85565	−0.861010	−0.430505	−	0.902588i	$-0.641664\pi$
$11$	−2.85565	−0.861010	−0.430505	+	0.902588i	$0.641664\pi$
$12$	−9.59111	−2.76872
$13$	−3.87576	−1.07494	−0.537471	−	0.843282i	$-0.680620\pi$
$13$	−3.87576	−1.07494	−0.537471	+	0.843282i	$0.680620\pi$
$14$	0	0
$15$	−2.16264	−0.558391
$16$	6.79863	1.69966
$17$	7.42848	1.80167	0.900835	−	0.434161i	$-0.142955\pi$
$17$	7.42848	1.80167	0.900835	+	0.434161i	$0.142955\pi$
$18$	−4.25408	−1.00270
$19$	−4.55277	−1.04448	−0.522238	−	0.852800i	$-0.674903\pi$
$19$	−4.55277	−1.04448	−0.522238	+	0.852800i	$0.674903\pi$
$20$	4.43491	0.991677
$21$	0	0
$22$	7.24395	1.54442
$23$	8.00368	1.66888	0.834442	−	0.551096i	$-0.185790\pi$
$23$	8.00368	1.66888	0.834442	+	0.551096i	$0.185790\pi$
$24$	13.3579	2.72667
$25$	1.00000	0.200000
$26$	9.83169	1.92815
$27$	2.86116	0.550630
$28$	0	0
$29$	4.12792	0.766536	0.383268	−	0.923637i	$-0.374799\pi$
$29$	4.12792	0.766536	0.383268	+	0.923637i	$0.374799\pi$
$30$	5.48599	1.00160
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	−4.89282	−0.864937
$33$	6.17573	1.07506
$34$	−18.8439	−3.23170
$35$	0	0
$36$	7.43737	1.23956
$37$	9.54114	1.56855	0.784277	−	0.620411i	$-0.213034\pi$
$37$	9.54114	1.56855	0.784277	+	0.620411i	$0.213034\pi$
$38$	11.5491	1.87351
$39$	8.38187	1.34217
$40$	−6.17668	−0.976618
$41$	−8.59414	−1.34218	−0.671089	−	0.741376i	$-0.734173\pi$
$41$	−8.59414	−1.34218	−0.671089	+	0.741376i	$0.734173\pi$
$42$	0	0
$43$	1.97569	0.301290	0.150645	−	0.988588i	$-0.451865\pi$
$43$	1.97569	0.301290	0.150645	+	0.988588i	$0.451865\pi$
$44$	−12.6645	−1.90925
$45$	1.67701	0.249993
$46$	−20.3030	−2.99352
$47$	−10.4620	−1.52605	−0.763023	−	0.646371i	$-0.776286\pi$
$47$	−10.4620	−1.52605	−0.763023	+	0.646371i	$0.776286\pi$
$48$	−14.7030	−2.12219
$49$	0	0
$50$	−2.53671	−0.358745
$51$	−16.0651	−2.24957
$52$	−17.1887	−2.38364
$53$	9.32098	1.28034	0.640168	−	0.768235i	$-0.278865\pi$
$53$	9.32098	1.28034	0.640168	+	0.768235i	$0.278865\pi$
$54$	−7.25794	−0.987681
$55$	−2.85565	−0.385055
$56$	0	0
$57$	9.84599	1.30413
$58$	−10.4714	−1.37496
$59$	3.59331	0.467809	0.233904	−	0.972260i	$-0.424850\pi$
$59$	3.59331	0.467809	0.233904	+	0.972260i	$0.424850\pi$
$60$	−9.59111	−1.23821
$61$	12.5997	1.61322	0.806610	−	0.591084i	$-0.201300\pi$
$61$	12.5997	1.61322	0.806610	+	0.591084i	$0.201300\pi$
$62$	−2.53671	−0.322163
$63$	0	0
$64$	−1.18557	−0.148197
$65$	−3.87576	−0.480729
$66$	−15.6661	−1.92836
$67$	0.455398	0.0556357	0.0278179	−	0.999613i	$-0.491144\pi$
$67$	0.455398	0.0556357	0.0278179	+	0.999613i	$0.491144\pi$
$68$	32.9447	3.99513
$69$	−17.3091	−2.08377
$70$	0	0
$71$	−8.42898	−1.00034	−0.500168	−	0.865928i	$-0.666728\pi$
$71$	−8.42898	−1.00034	−0.500168	+	0.865928i	$0.666728\pi$
$72$	−10.3583	−1.22074
$73$	5.78299	0.676848	0.338424	−	0.940994i	$-0.390106\pi$
$73$	5.78299	0.676848	0.338424	+	0.940994i	$0.390106\pi$
$74$	−24.2031	−2.81356
$75$	−2.16264	−0.249720
$76$	−20.1911	−2.31608
$77$	0	0
$78$	−21.2624	−2.40749
$79$	−1.32975	−0.149609	−0.0748044	−	0.997198i	$-0.523833\pi$
$79$	−1.32975	−0.149609	−0.0748044	+	0.997198i	$0.523833\pi$
$80$	6.79863	0.760110
$81$	−11.2187	−1.24652
$82$	21.8009	2.40750
$83$	−10.1287	−1.11177	−0.555884	−	0.831260i	$-0.687620\pi$
$83$	−10.1287	−1.11177	−0.555884	+	0.831260i	$0.687620\pi$
$84$	0	0
$85$	7.42848	0.805731
$86$	−5.01176	−0.540432
$87$	−8.92720	−0.957096
$88$	17.6384	1.88026
$89$	2.76868	0.293479	0.146740	−	0.989175i	$-0.453122\pi$
$89$	2.76868	0.293479	0.146740	+	0.989175i	$0.453122\pi$
$90$	−4.25408	−0.448420
$91$	0	0
$92$	35.4956	3.70068
$93$	−2.16264	−0.224255
$94$	26.5392	2.73731
$95$	−4.55277	−0.467104
$96$	10.5814	1.07996
$97$	−16.6690	−1.69248	−0.846238	−	0.532804i	$-0.821138\pi$
$97$	−16.6690	−1.69248	−0.846238	+	0.532804i	$0.821138\pi$
$98$	0	0
$99$	−4.78893	−0.481306
$100$	4.43491	0.443491
$101$	1.40664	0.139966	0.0699830	−	0.997548i	$-0.477705\pi$
$101$	1.40664	0.139966	0.0699830	+	0.997548i	$0.477705\pi$
$102$	40.7526	4.03511
$103$	−0.114119	−0.0112445	−0.00562226	−	0.999984i	$-0.501790\pi$
$103$	−0.114119	−0.0112445	−0.00562226	+	0.999984i	$0.501790\pi$
$104$	23.9393	2.34744
$105$	0	0
$106$	−23.6447	−2.29657
$107$	−7.30334	−0.706041	−0.353020	−	0.935616i	$-0.614845\pi$
$107$	−7.30334	−0.706041	−0.353020	+	0.935616i	$0.614845\pi$
$108$	12.6890	1.22100
$109$	1.26052	0.120736	0.0603679	−	0.998176i	$-0.480773\pi$
$109$	1.26052	0.120736	0.0603679	+	0.998176i	$0.480773\pi$
$110$	7.24395	0.690684
$111$	−20.6340	−1.95850
$112$	0	0
$113$	5.57702	0.524642	0.262321	−	0.964981i	$-0.415512\pi$
$113$	5.57702	0.524642	0.262321	+	0.964981i	$0.415512\pi$
$114$	−24.9764	−2.33926
$115$	8.00368	0.746347
$116$	18.3070	1.69976
$117$	−6.49967	−0.600895
$118$	−9.11519	−0.839121
$119$	0	0
$120$	13.3579	1.21941
$121$	−2.84529	−0.258663
$122$	−31.9617	−2.89368
$123$	18.5860	1.67584
$124$	4.43491	0.398267
$125$	1.00000	0.0894427
$126$	0	0
$127$	2.17920	0.193373	0.0966865	−	0.995315i	$-0.469176\pi$
$127$	2.17920	0.193373	0.0966865	+	0.995315i	$0.469176\pi$
$128$	12.7931	1.13076
$129$	−4.27270	−0.376191
$130$	9.83169	0.862297
$131$	−18.1509	−1.58585	−0.792926	−	0.609318i	$-0.791443\pi$
$131$	−18.1509	−1.58585	−0.792926	+	0.609318i	$0.791443\pi$
$132$	27.3888	2.38389
$133$	0	0
$134$	−1.15521	−0.0997953
$135$	2.86116	0.246249
$136$	−45.8833	−3.93446
$137$	12.1625	1.03911	0.519556	−	0.854437i	$-0.326098\pi$
$137$	12.1625	1.03911	0.519556	+	0.854437i	$0.326098\pi$
$138$	43.9081	3.73771
$139$	15.4408	1.30967	0.654837	−	0.755770i	$-0.272737\pi$
$139$	15.4408	1.30967	0.654837	+	0.755770i	$0.272737\pi$
$140$	0	0
$141$	22.6256	1.90542
$142$	21.3819	1.79433
$143$	11.0678	0.925536
$144$	11.4013	0.950112
$145$	4.12792	0.342805
$146$	−14.6698	−1.21408
$147$	0	0
$148$	42.3141	3.47820
$149$	16.1031	1.31922	0.659609	−	0.751609i	$-0.270722\pi$
$149$	16.1031	1.31922	0.659609	+	0.751609i	$0.270722\pi$
$150$	5.48599	0.447929
$151$	18.6991	1.52172	0.760858	−	0.648919i	$-0.224779\pi$
$151$	18.6991	1.52172	0.760858	+	0.648919i	$0.224779\pi$
$152$	28.1210	2.28091
$153$	12.4576	1.00714
$154$	0	0
$155$	1.00000	0.0803219
$156$	37.1729	2.97621
$157$	15.0897	1.20429	0.602146	−	0.798386i	$-0.294312\pi$
$157$	15.0897	1.20429	0.602146	+	0.798386i	$0.294312\pi$
$158$	3.37320	0.268357
$159$	−20.1579	−1.59863
$160$	−4.89282	−0.386812
$161$	0	0
$162$	28.4585	2.23591
$163$	11.2420	0.880544	0.440272	−	0.897865i	$-0.354882\pi$
$163$	11.2420	0.880544	0.440272	+	0.897865i	$0.354882\pi$
$164$	−38.1143	−2.97622
$165$	6.17573	0.480780
$166$	25.6936	1.99421
$167$	0.318111	0.0246162	0.0123081	−	0.999924i	$-0.496082\pi$
$167$	0.318111	0.0246162	0.0123081	+	0.999924i	$0.496082\pi$
$168$	0	0
$169$	2.02153	0.155502
$170$	−18.8439	−1.44526
$171$	−7.63501	−0.583864
$172$	8.76202	0.668098
$173$	13.8381	1.05209	0.526046	−	0.850456i	$-0.323674\pi$
$173$	13.8381	1.05209	0.526046	+	0.850456i	$0.323674\pi$
$174$	22.6457	1.71677
$175$	0	0
$176$	−19.4145	−1.46342
$177$	−7.77102	−0.584106
$178$	−7.02334	−0.526422
$179$	−18.0534	−1.34937	−0.674685	−	0.738105i	$-0.735721\pi$
$179$	−18.0534	−1.34937	−0.674685	+	0.738105i	$0.735721\pi$
$180$	7.43737	0.554349
$181$	−17.5700	−1.30597	−0.652984	−	0.757371i	$-0.726483\pi$
$181$	−17.5700	−1.30597	−0.652984	+	0.757371i	$0.726483\pi$
$182$	0	0
$183$	−27.2485	−2.01427
$184$	−49.4362	−3.64448
$185$	9.54114	0.701478
$186$	5.48599	0.402253
$187$	−21.2131	−1.55126
$188$	−46.3983	−3.38394
$189$	0	0
$190$	11.5491	0.837857
$191$	−7.66998	−0.554980	−0.277490	−	0.960728i	$-0.589503\pi$
$191$	−7.66998	−0.554980	−0.277490	+	0.960728i	$0.589503\pi$
$192$	2.56397	0.185038
$193$	−14.8552	−1.06930	−0.534650	−	0.845073i	$-0.679557\pi$
$193$	−14.8552	−1.06930	−0.534650	+	0.845073i	$0.679557\pi$
$194$	42.2844	3.03584
$195$	8.38187	0.600238
$196$	0	0
$197$	−23.2115	−1.65375	−0.826875	−	0.562385i	$-0.809884\pi$
$197$	−23.2115	−1.65375	−0.826875	+	0.562385i	$0.809884\pi$
$198$	12.1481	0.863331
$199$	11.2351	0.796432	0.398216	−	0.917292i	$-0.369630\pi$
$199$	11.2351	0.796432	0.398216	+	0.917292i	$0.369630\pi$
$200$	−6.17668	−0.436757
$201$	−0.984861	−0.0694668
$202$	−3.56825	−0.251061
$203$	0	0
$204$	−71.2474	−4.98831
$205$	−8.59414	−0.600241
$206$	0.289488	0.0201696
$207$	13.4222	0.932909
$208$	−26.3499	−1.82703
$209$	13.0011	0.899304
$210$	0	0
$211$	−5.09828	−0.350980	−0.175490	−	0.984481i	$-0.556151\pi$
$211$	−5.09828	−0.350980	−0.175490	+	0.984481i	$0.556151\pi$
$212$	41.3377	2.83909
$213$	18.2288	1.24902
$214$	18.5265	1.26644
$215$	1.97569	0.134741
$216$	−17.6725	−1.20246
$217$	0	0
$218$	−3.19757	−0.216567
$219$	−12.5065	−0.845112
$220$	−12.6645	−0.853843
$221$	−28.7910	−1.93669
$222$	52.3426	3.51301
$223$	−24.7372	−1.65653	−0.828263	−	0.560339i	$-0.810671\pi$
$223$	−24.7372	−1.65653	−0.828263	+	0.560339i	$0.810671\pi$
$224$	0	0
$225$	1.67701	0.111800
$226$	−14.1473	−0.941065
$227$	16.1832	1.07412	0.537060	−	0.843544i	$-0.319535\pi$
$227$	16.1832	1.07412	0.537060	+	0.843544i	$0.319535\pi$
$228$	43.6661	2.89186
$229$	−16.3790	−1.08235	−0.541177	−	0.840909i	$-0.682021\pi$
$229$	−16.3790	−1.08235	−0.541177	+	0.840909i	$0.682021\pi$
$230$	−20.3030	−1.33874
$231$	0	0
$232$	−25.4968	−1.67395
$233$	3.59052	0.235223	0.117611	−	0.993060i	$-0.462476\pi$
$233$	3.59052	0.235223	0.117611	+	0.993060i	$0.462476\pi$
$234$	16.4878	1.07784
$235$	−10.4620	−0.682468
$236$	15.9360	1.03735
$237$	2.87577	0.186801
$238$	0	0
$239$	−14.8118	−0.958094	−0.479047	−	0.877789i	$-0.659018\pi$
$239$	−14.8118	−0.958094	−0.479047	+	0.877789i	$0.659018\pi$
$240$	−14.7030	−0.949073
$241$	−8.91351	−0.574170	−0.287085	−	0.957905i	$-0.592686\pi$
$241$	−8.91351	−0.574170	−0.287085	+	0.957905i	$0.592686\pi$
$242$	7.21768	0.463970
$243$	15.6784	1.00577
$244$	55.8784	3.57725
$245$	0	0
$246$	−47.1474	−3.00601
$247$	17.6454	1.12275
$248$	−6.17668	−0.392219
$249$	21.9047	1.38815
$250$	−2.53671	−0.160436
$251$	12.8931	0.813805	0.406902	−	0.913472i	$-0.366609\pi$
$251$	12.8931	0.813805	0.406902	+	0.913472i	$0.366609\pi$
$252$	0	0
$253$	−22.8557	−1.43692
$254$	−5.52801	−0.346858
$255$	−16.0651	−1.00604
$256$	−30.0813	−1.88008
$257$	−26.9722	−1.68248	−0.841240	−	0.540662i	$-0.818174\pi$
$257$	−26.9722	−1.68248	−0.841240	+	0.540662i	$0.818174\pi$
$258$	10.8386	0.674783
$259$	0	0
$260$	−17.1887	−1.06600
$261$	6.92254	0.428495
$262$	46.0436	2.84459
$263$	0.697659	0.0430195	0.0215098	−	0.999769i	$-0.493153\pi$
$263$	0.697659	0.0430195	0.0215098	+	0.999769i	$0.493153\pi$
$264$	−38.1455	−2.34769
$265$	9.32098	0.572583
$266$	0	0
$267$	−5.98765	−0.366438
$268$	2.01965	0.123370
$269$	−27.9380	−1.70341	−0.851706	−	0.524020i	$-0.824432\pi$
$269$	−27.9380	−1.70341	−0.851706	+	0.524020i	$0.824432\pi$
$270$	−7.25794	−0.441704
$271$	26.6205	1.61708	0.808540	−	0.588441i	$-0.200258\pi$
$271$	26.6205	1.61708	0.808540	+	0.588441i	$0.200258\pi$
$272$	50.5035	3.06222
$273$	0	0
$274$	−30.8527	−1.86388
$275$	−2.85565	−0.172202
$276$	−76.7642	−4.62066
$277$	2.80547	0.168564	0.0842822	−	0.996442i	$-0.473140\pi$
$277$	2.80547	0.168564	0.0842822	+	0.996442i	$0.473140\pi$
$278$	−39.1689	−2.34920
$279$	1.67701	0.100400
$280$	0	0
$281$	−1.87201	−0.111675	−0.0558373	−	0.998440i	$-0.517783\pi$
$281$	−1.87201	−0.111675	−0.0558373	+	0.998440i	$0.517783\pi$
$282$	−57.3947	−3.41780
$283$	25.2962	1.50370	0.751852	−	0.659332i	$-0.229161\pi$
$283$	25.2962	1.50370	0.751852	+	0.659332i	$0.229161\pi$
$284$	−37.3818	−2.21820
$285$	9.84599	0.583226
$286$	−28.0758	−1.66016
$287$	0	0
$288$	−8.20529	−0.483501
$289$	38.1823	2.24602
$290$	−10.4714	−0.614899
$291$	36.0489	2.11323
$292$	25.6471	1.50088
$293$	−3.70705	−0.216568	−0.108284	−	0.994120i	$-0.534536\pi$
$293$	−3.70705	−0.216568	−0.108284	+	0.994120i	$0.534536\pi$
$294$	0	0
$295$	3.59331	0.209210
$296$	−58.9325	−3.42538
$297$	−8.17046	−0.474098
$298$	−40.8489	−2.36632
$299$	−31.0204	−1.79395
$300$	−9.59111	−0.553743
$301$	0	0
$302$	−47.4344	−2.72954
$303$	−3.04206	−0.174762
$304$	−30.9526	−1.77525
$305$	12.5997	0.721454
$306$	−31.6013	−1.80653
$307$	2.08343	0.118908	0.0594539	−	0.998231i	$-0.481064\pi$
$307$	2.08343	0.118908	0.0594539	+	0.998231i	$0.481064\pi$
$308$	0	0
$309$	0.246799	0.0140399
$310$	−2.53671	−0.144076
$311$	3.02488	0.171525	0.0857627	−	0.996316i	$-0.472667\pi$
$311$	3.02488	0.171525	0.0857627	+	0.996316i	$0.472667\pi$
$312$	−51.7721	−2.93102
$313$	19.5854	1.10703	0.553516	−	0.832838i	$-0.313286\pi$
$313$	19.5854	1.10703	0.553516	+	0.832838i	$0.313286\pi$
$314$	−38.2783	−2.16017
$315$	0	0
$316$	−5.89733	−0.331751
$317$	−14.6736	−0.824152	−0.412076	−	0.911149i	$-0.635196\pi$
$317$	−14.6736	−0.824152	−0.412076	+	0.911149i	$0.635196\pi$
$318$	51.1348	2.86750
$319$	−11.7879	−0.659994
$320$	−1.18557	−0.0662756
$321$	15.7945	0.881562
$322$	0	0
$323$	−33.8201	−1.88180
$324$	−49.7538	−2.76410
$325$	−3.87576	−0.214989
$326$	−28.5178	−1.57946
$327$	−2.72605	−0.150751
$328$	53.0832	2.93103
$329$	0	0
$330$	−15.6661	−0.862388
$331$	9.73992	0.535355	0.267677	−	0.963509i	$-0.413744\pi$
$331$	9.73992	0.535355	0.267677	+	0.963509i	$0.413744\pi$
$332$	−44.9199	−2.46530
$333$	16.0005	0.876824
$334$	−0.806956	−0.0441547
$335$	0.455398	0.0248811
$336$	0	0
$337$	34.2264	1.86443	0.932214	−	0.361907i	$-0.117874\pi$
$337$	34.2264	1.86443	0.932214	+	0.361907i	$0.117874\pi$
$338$	−5.12803	−0.278928
$339$	−12.0611	−0.655068
$340$	32.9447	1.78667
$341$	−2.85565	−0.154642
$342$	19.3678	1.04729
$343$	0	0
$344$	−12.2032	−0.657953
$345$	−17.3091	−0.931889
$346$	−35.1033	−1.88716
$347$	−13.0613	−0.701166	−0.350583	−	0.936532i	$-0.614017\pi$
$347$	−13.0613	−0.701166	−0.350583	+	0.936532i	$0.614017\pi$
$348$	−39.5914	−2.12232
$349$	35.4977	1.90015	0.950073	−	0.312026i	$-0.101008\pi$
$349$	35.4977	1.90015	0.950073	+	0.312026i	$0.101008\pi$
$350$	0	0
$351$	−11.0892	−0.591896
$352$	13.9722	0.744719
$353$	10.4041	0.553757	0.276878	−	0.960905i	$-0.410700\pi$
$353$	10.4041	0.553757	0.276878	+	0.960905i	$0.410700\pi$
$354$	19.7129	1.04773
$355$	−8.42898	−0.447364
$356$	12.2788	0.650777
$357$	0	0
$358$	45.7962	2.42040
$359$	−22.5711	−1.19125	−0.595627	−	0.803261i	$-0.703097\pi$
$359$	−22.5711	−1.19125	−0.595627	+	0.803261i	$0.703097\pi$
$360$	−10.3583	−0.545931
$361$	1.72768	0.0909307
$362$	44.5701	2.34255
$363$	6.15333	0.322966
$364$	0	0
$365$	5.78299	0.302696
$366$	69.1216	3.61304
$367$	−3.42506	−0.178787	−0.0893934	−	0.995996i	$-0.528493\pi$
$367$	−3.42506	−0.178787	−0.0893934	+	0.995996i	$0.528493\pi$
$368$	54.4141	2.83653
$369$	−14.4124	−0.750280
$370$	−24.2031	−1.25826
$371$	0	0
$372$	−9.59111	−0.497276
$373$	−11.7796	−0.609925	−0.304962	−	0.952364i	$-0.598644\pi$
$373$	−11.7796	−0.609925	−0.304962	+	0.952364i	$0.598644\pi$
$374$	53.8115	2.78253
$375$	−2.16264	−0.111678
$376$	64.6207	3.33256
$377$	−15.9988	−0.823982
$378$	0	0
$379$	13.8570	0.711785	0.355892	−	0.934527i	$-0.384177\pi$
$379$	13.8570	0.711785	0.355892	+	0.934527i	$0.384177\pi$
$380$	−20.1911	−1.03578
$381$	−4.71283	−0.241446
$382$	19.4565	0.995483
$383$	6.13007	0.313232	0.156616	−	0.987660i	$-0.449942\pi$
$383$	6.13007	0.313232	0.156616	+	0.987660i	$0.449942\pi$
$384$	−27.6669	−1.41187
$385$	0	0
$386$	37.6834	1.91803
$387$	3.31324	0.168422
$388$	−73.9254	−3.75299
$389$	−11.2712	−0.571470	−0.285735	−	0.958309i	$-0.592238\pi$
$389$	−11.2712	−0.571470	−0.285735	+	0.958309i	$0.592238\pi$
$390$	−21.2624	−1.07666
$391$	59.4552	3.00678
$392$	0	0
$393$	39.2538	1.98009
$394$	58.8809	2.96638
$395$	−1.32975	−0.0669070
$396$	−21.2385	−1.06727
$397$	−0.361012	−0.0181187	−0.00905934	−	0.999959i	$-0.502884\pi$
$397$	−0.361012	−0.0181187	−0.00905934	+	0.999959i	$0.502884\pi$
$398$	−28.5001	−1.42858
$399$	0	0
$400$	6.79863	0.339932
$401$	10.5379	0.526239	0.263119	−	0.964763i	$-0.415249\pi$
$401$	10.5379	0.526239	0.263119	+	0.964763i	$0.415249\pi$
$402$	2.49831	0.124604
$403$	−3.87576	−0.193065
$404$	6.23833	0.310369
$405$	−11.2187	−0.557460
$406$	0	0
$407$	−27.2461	−1.35054
$408$	99.2290	4.91257
$409$	26.8979	1.33002	0.665008	−	0.746836i	$-0.268428\pi$
$409$	26.8979	1.33002	0.665008	+	0.746836i	$0.268428\pi$
$410$	21.8009	1.07667
$411$	−26.3031	−1.29743
$412$	−0.506109	−0.0249342
$413$	0	0
$414$	−34.0483	−1.67338
$415$	−10.1287	−0.497198
$416$	18.9634	0.929758
$417$	−33.3929	−1.63526
$418$	−32.9800	−1.61311
$419$	0.721742	0.0352594	0.0176297	−	0.999845i	$-0.494388\pi$
$419$	0.721742	0.0352594	0.0176297	+	0.999845i	$0.494388\pi$
$420$	0	0
$421$	−4.70586	−0.229350	−0.114675	−	0.993403i	$-0.536583\pi$
$421$	−4.70586	−0.229350	−0.114675	+	0.993403i	$0.536583\pi$
$422$	12.9329	0.629562
$423$	−17.5449	−0.853062
$424$	−57.5727	−2.79598
$425$	7.42848	0.360334
$426$	−46.2413	−2.24040
$427$	0	0
$428$	−32.3897	−1.56561
$429$	−23.9357	−1.15562
$430$	−5.01176	−0.241689
$431$	0.958958	0.0461914	0.0230957	−	0.999733i	$-0.492648\pi$
$431$	0.958958	0.0461914	0.0230957	+	0.999733i	$0.492648\pi$
$432$	19.4520	0.935883
$433$	2.95058	0.141796	0.0708980	−	0.997484i	$-0.477414\pi$
$433$	2.95058	0.141796	0.0708980	+	0.997484i	$0.477414\pi$
$434$	0	0
$435$	−8.92720	−0.428026
$436$	5.59029	0.267726
$437$	−36.4389	−1.74311
$438$	31.7254	1.51590
$439$	−6.81777	−0.325394	−0.162697	−	0.986676i	$-0.552019\pi$
$439$	−6.81777	−0.325394	−0.162697	+	0.986676i	$0.552019\pi$
$440$	17.6384	0.840878
$441$	0	0
$442$	73.0345	3.47390
$443$	−11.4259	−0.542861	−0.271431	−	0.962458i	$-0.587497\pi$
$443$	−11.4259	−0.542861	−0.271431	+	0.962458i	$0.587497\pi$
$444$	−91.5101	−4.34288
$445$	2.76868	0.131248
$446$	62.7512	2.97136
$447$	−34.8252	−1.64717
$448$	0	0
$449$	−5.00379	−0.236144	−0.118072	−	0.993005i	$-0.537671\pi$
$449$	−5.00379	−0.236144	−0.118072	+	0.993005i	$0.537671\pi$
$450$	−4.25408	−0.200539
$451$	24.5418	1.15563
$452$	24.7336	1.16337
$453$	−40.4395	−1.90001
$454$	−41.0523	−1.92668
$455$	0	0
$456$	−60.8155	−2.84795
$457$	−36.0525	−1.68647	−0.843233	−	0.537549i	$-0.819350\pi$
$457$	−36.0525	−1.68647	−0.843233	+	0.537549i	$0.819350\pi$
$458$	41.5488	1.94145
$459$	21.2541	0.992054
$460$	35.4956	1.65499
$461$	18.9459	0.882398	0.441199	−	0.897409i	$-0.354553\pi$
$461$	18.9459	0.882398	0.441199	+	0.897409i	$0.354553\pi$
$462$	0	0
$463$	1.05794	0.0491665	0.0245833	−	0.999698i	$-0.492174\pi$
$463$	1.05794	0.0491665	0.0245833	+	0.999698i	$0.492174\pi$
$464$	28.0642	1.30285
$465$	−2.16264	−0.100290
$466$	−9.10812	−0.421926
$467$	4.71914	0.218376	0.109188	−	0.994021i	$-0.465175\pi$
$467$	4.71914	0.218376	0.109188	+	0.994021i	$0.465175\pi$
$468$	−28.8255	−1.33246
$469$	0	0
$470$	26.5392	1.22416
$471$	−32.6337	−1.50368
$472$	−22.1947	−1.02159
$473$	−5.64187	−0.259414
$474$	−7.29501	−0.335071
$475$	−4.55277	−0.208895
$476$	0	0
$477$	15.6313	0.715710
$478$	37.5732	1.71856
$479$	−23.9142	−1.09267	−0.546334	−	0.837567i	$-0.683977\pi$
$479$	−23.9142	−1.09267	−0.546334	+	0.837567i	$0.683977\pi$
$480$	10.5814	0.482973
$481$	−36.9792	−1.68610
$482$	22.6110	1.02990
$483$	0	0
$484$	−12.6186	−0.573573
$485$	−16.6690	−0.756899
$486$	−39.7717	−1.80408
$487$	−1.57972	−0.0715840	−0.0357920	−	0.999359i	$-0.511395\pi$
$487$	−1.57972	−0.0715840	−0.0357920	+	0.999359i	$0.511395\pi$
$488$	−77.8240	−3.52293
$489$	−24.3124	−1.09945
$490$	0	0
$491$	30.4726	1.37521	0.687604	−	0.726086i	$-0.258663\pi$
$491$	30.4726	1.37521	0.687604	+	0.726086i	$0.258663\pi$
$492$	82.4274	3.71611
$493$	30.6642	1.38104
$494$	−44.7614	−2.01391
$495$	−4.78893	−0.215247
$496$	6.79863	0.305268
$497$	0	0
$498$	−55.5659	−2.48997
$499$	19.9736	0.894139	0.447070	−	0.894499i	$-0.352468\pi$
$499$	19.9736	0.894139	0.447070	+	0.894499i	$0.352468\pi$
$500$	4.43491	0.198335
$501$	−0.687959	−0.0307357
$502$	−32.7061	−1.45974
$503$	14.9635	0.667191	0.333595	−	0.942716i	$-0.391738\pi$
$503$	14.9635	0.667191	0.333595	+	0.942716i	$0.391738\pi$
$504$	0	0
$505$	1.40664	0.0625947
$506$	57.9783	2.57745
$507$	−4.37183	−0.194160
$508$	9.66458	0.428796
$509$	9.68036	0.429074	0.214537	−	0.976716i	$-0.431176\pi$
$509$	9.68036	0.429074	0.214537	+	0.976716i	$0.431176\pi$
$510$	40.7526	1.80455
$511$	0	0
$512$	50.7214	2.24159
$513$	−13.0262	−0.575120
$514$	68.4207	3.01791
$515$	−0.114119	−0.00502870
$516$	−18.9491	−0.834187
$517$	29.8759	1.31394
$518$	0	0
$519$	−29.9268	−1.31364
$520$	23.9393	1.04981
$521$	−7.37736	−0.323208	−0.161604	−	0.986856i	$-0.551667\pi$
$521$	−7.37736	−0.323208	−0.161604	+	0.986856i	$0.551667\pi$
$522$	−17.5605	−0.768603
$523$	−16.8160	−0.735314	−0.367657	−	0.929961i	$-0.619840\pi$
$523$	−16.8160	−0.735314	−0.367657	+	0.929961i	$0.619840\pi$
$524$	−80.4977	−3.51656
$525$	0	0
$526$	−1.76976	−0.0771653
$527$	7.42848	0.323590
$528$	41.9865	1.82723
$529$	41.0589	1.78517
$530$	−23.6447	−1.02706
$531$	6.02599	0.261506
$532$	0	0
$533$	33.3088	1.44277
$534$	15.1889	0.657290
$535$	−7.30334	−0.315751
$536$	−2.81285	−0.121496
$537$	39.0429	1.68482
$538$	70.8708	3.05546
$539$	0	0
$540$	12.6890	0.546047
$541$	−23.4303	−1.00735	−0.503673	−	0.863895i	$-0.668018\pi$
$541$	−23.4303	−1.00735	−0.503673	+	0.863895i	$0.668018\pi$
$542$	−67.5286	−2.90060
$543$	37.9976	1.63063
$544$	−36.3462	−1.55833
$545$	1.26052	0.0539947
$546$	0	0
$547$	26.8113	1.14637	0.573185	−	0.819426i	$-0.305708\pi$
$547$	26.8113	1.14637	0.573185	+	0.819426i	$0.305708\pi$
$548$	53.9396	2.30418
$549$	21.1297	0.901793
$550$	7.24395	0.308883
$551$	−18.7935	−0.800628
$552$	106.913	4.55050
$553$	0	0
$554$	−7.11668	−0.302359
$555$	−20.6340	−0.875866
$556$	68.4787	2.90415
$557$	20.8563	0.883711	0.441855	−	0.897086i	$-0.354320\pi$
$557$	20.8563	0.883711	0.441855	+	0.897086i	$0.354320\pi$
$558$	−4.25408	−0.180090
$559$	−7.65731	−0.323870
$560$	0	0
$561$	45.8763	1.93690
$562$	4.74875	0.200314
$563$	−4.03165	−0.169914	−0.0849569	−	0.996385i	$-0.527075\pi$
$563$	−4.03165	−0.169914	−0.0849569	+	0.996385i	$0.527075\pi$
$564$	100.343	4.22519
$565$	5.57702	0.234627
$566$	−64.1692	−2.69723
$567$	0	0
$568$	52.0631	2.18452
$569$	21.0036	0.880518	0.440259	−	0.897871i	$-0.354887\pi$
$569$	21.0036	0.880518	0.440259	+	0.897871i	$0.354887\pi$
$570$	−24.9764	−1.04615
$571$	−20.6581	−0.864516	−0.432258	−	0.901750i	$-0.642283\pi$
$571$	−20.6581	−0.864516	−0.432258	+	0.901750i	$0.642283\pi$
$572$	49.0847	2.05234
$573$	16.5874	0.692948
$574$	0	0
$575$	8.00368	0.333777
$576$	−1.98821	−0.0828423
$577$	4.84544	0.201718	0.100859	−	0.994901i	$-0.467841\pi$
$577$	4.84544	0.201718	0.100859	+	0.994901i	$0.467841\pi$
$578$	−96.8574	−4.02874
$579$	32.1264	1.33513
$580$	18.3070	0.760156
$581$	0	0
$582$	−91.4458	−3.79055
$583$	−26.6174	−1.10238
$584$	−35.7197	−1.47809
$585$	−6.49967	−0.268728
$586$	9.40373	0.388465
$587$	−4.53503	−0.187181	−0.0935903	−	0.995611i	$-0.529834\pi$
$587$	−4.53503	−0.187181	−0.0935903	+	0.995611i	$0.529834\pi$
$588$	0	0
$589$	−4.55277	−0.187593
$590$	−9.11519	−0.375266
$591$	50.1981	2.06487
$592$	64.8667	2.66600
$593$	26.7833	1.09986	0.549930	−	0.835211i	$-0.314654\pi$
$593$	26.7833	1.09986	0.549930	+	0.835211i	$0.314654\pi$
$594$	20.7261	0.850402
$595$	0	0
$596$	71.4158	2.92531
$597$	−24.2974	−0.994424
$598$	78.6898	3.21786
$599$	−32.7505	−1.33815	−0.669075	−	0.743195i	$-0.733309\pi$
$599$	−32.7505	−1.33815	−0.669075	+	0.743195i	$0.733309\pi$
$600$	13.3579	0.545335
$601$	20.4652	0.834793	0.417396	−	0.908725i	$-0.362943\pi$
$601$	20.4652	0.834793	0.417396	+	0.908725i	$0.362943\pi$
$602$	0	0
$603$	0.763705	0.0311005
$604$	82.9291	3.37434
$605$	−2.84529	−0.115677
$606$	7.71683	0.313475
$607$	31.0326	1.25957	0.629787	−	0.776768i	$-0.283142\pi$
$607$	31.0326	1.25957	0.629787	+	0.776768i	$0.283142\pi$
$608$	22.2759	0.903406
$609$	0	0
$610$	−31.9617	−1.29409
$611$	40.5484	1.64041
$612$	55.2484	2.23328
$613$	−48.6145	−1.96352	−0.981761	−	0.190121i	$-0.939112\pi$
$613$	−48.6145	−1.96352	−0.981761	+	0.190121i	$0.939112\pi$
$614$	−5.28507	−0.213288
$615$	18.5860	0.749460
$616$	0	0
$617$	−22.0425	−0.887399	−0.443700	−	0.896176i	$-0.646334\pi$
$617$	−22.0425	−0.887399	−0.443700	+	0.896176i	$0.646334\pi$
$618$	−0.626058	−0.0251837
$619$	−25.9649	−1.04362	−0.521809	−	0.853062i	$-0.674743\pi$
$619$	−25.9649	−1.04362	−0.521809	+	0.853062i	$0.674743\pi$
$620$	4.43491	0.178110
$621$	22.8998	0.918938
$622$	−7.67326	−0.307670
$623$	0	0
$624$	56.9853	2.28124
$625$	1.00000	0.0400000
$626$	−49.6826	−1.98571
$627$	−28.1167	−1.12287
$628$	66.9217	2.67047
$629$	70.8761	2.82602
$630$	0	0
$631$	−4.83129	−0.192331	−0.0961653	−	0.995365i	$-0.530658\pi$
$631$	−4.83129	−0.192331	−0.0961653	+	0.995365i	$0.530658\pi$
$632$	8.21344	0.326713
$633$	11.0257	0.438234
$634$	37.2227	1.47830
$635$	2.17920	0.0864790
$636$	−89.3986	−3.54488
$637$	0	0
$638$	29.9025	1.18385
$639$	−14.1354	−0.559189
$640$	12.7931	0.505692
$641$	−20.8751	−0.824515	−0.412257	−	0.911067i	$-0.635260\pi$
$641$	−20.8751	−0.824515	−0.412257	+	0.911067i	$0.635260\pi$
$642$	−40.0661	−1.58128
$643$	−18.9990	−0.749247	−0.374623	−	0.927177i	$-0.622228\pi$
$643$	−18.9990	−0.749247	−0.374623	+	0.927177i	$0.622228\pi$
$644$	0	0
$645$	−4.27270	−0.168238
$646$	85.7919	3.37544
$647$	0.973240	0.0382620	0.0191310	−	0.999817i	$-0.493910\pi$
$647$	0.973240	0.0382620	0.0191310	+	0.999817i	$0.493910\pi$
$648$	69.2941	2.72213
$649$	−10.2612	−0.402788
$650$	9.83169	0.385631
$651$	0	0
$652$	49.8574	1.95257
$653$	25.8352	1.01101	0.505505	−	0.862824i	$-0.331306\pi$
$653$	25.8352	1.01101	0.505505	+	0.862824i	$0.331306\pi$
$654$	6.91520	0.270406
$655$	−18.1509	−0.709215
$656$	−58.4284	−2.28124
$657$	9.69810	0.378359
$658$	0	0
$659$	−4.29456	−0.167292	−0.0836462	−	0.996496i	$-0.526657\pi$
$659$	−4.29456	−0.167292	−0.0836462	+	0.996496i	$0.526657\pi$
$660$	27.3888	1.06611
$661$	42.1807	1.64064	0.820319	−	0.571906i	$-0.193796\pi$
$661$	42.1807	1.64064	0.820319	+	0.571906i	$0.193796\pi$
$662$	−24.7074	−0.960280
$663$	62.2645	2.41815
$664$	62.5617	2.42786
$665$	0	0
$666$	−40.5888	−1.57278
$667$	33.0386	1.27926
$668$	1.41079	0.0545853
$669$	53.4977	2.06834
$670$	−1.15521	−0.0446298
$671$	−35.9801	−1.38900
$672$	0	0
$673$	16.3798	0.631396	0.315698	−	0.948860i	$-0.397761\pi$
$673$	16.3798	0.631396	0.315698	+	0.948860i	$0.397761\pi$
$674$	−86.8224	−3.34428
$675$	2.86116	0.110126
$676$	8.96529	0.344819
$677$	−16.7249	−0.642789	−0.321395	−	0.946945i	$-0.604152\pi$
$677$	−16.7249	−0.642789	−0.321395	+	0.946945i	$0.604152\pi$
$678$	30.5955	1.17501
$679$	0	0
$680$	−45.8833	−1.75954
$681$	−34.9985	−1.34115
$682$	7.24395	0.277385
$683$	−16.2012	−0.619922	−0.309961	−	0.950749i	$-0.600316\pi$
$683$	−16.2012	−0.619922	−0.309961	+	0.950749i	$0.600316\pi$
$684$	−33.8606	−1.29469
$685$	12.1625	0.464705
$686$	0	0
$687$	35.4218	1.35143
$688$	13.4320	0.512090
$689$	−36.1259	−1.37629
$690$	43.9081	1.67155
$691$	16.3820	0.623200	0.311600	−	0.950213i	$-0.399135\pi$
$691$	16.3820	0.623200	0.311600	+	0.950213i	$0.399135\pi$
$692$	61.3708	2.33297
$693$	0	0
$694$	33.1327	1.25770
$695$	15.4408	0.585704
$696$	55.1404	2.09009
$697$	−63.8413	−2.41816
$698$	−90.0474	−3.40834
$699$	−7.76500	−0.293699
$700$	0	0
$701$	21.0659	0.795647	0.397823	−	0.917462i	$-0.369766\pi$
$701$	21.0659	0.795647	0.397823	+	0.917462i	$0.369766\pi$
$702$	28.1300	1.06170
$703$	−43.4386	−1.63832
$704$	3.38558	0.127599
$705$	22.6256	0.852130
$706$	−26.3923	−0.993288
$707$	0	0
$708$	−34.4638	−1.29523
$709$	−2.56373	−0.0962829	−0.0481415	−	0.998841i	$-0.515330\pi$
$709$	−2.56373	−0.0962829	−0.0481415	+	0.998841i	$0.515330\pi$
$710$	21.3819	0.802449
$711$	−2.23000	−0.0836315
$712$	−17.1012	−0.640896
$713$	8.00368	0.299740
$714$	0	0
$715$	11.0678	0.413912
$716$	−80.0651	−2.99217
$717$	32.0325	1.19628
$718$	57.2563	2.13679
$719$	−28.1518	−1.04988	−0.524942	−	0.851138i	$-0.675913\pi$
$719$	−28.1518	−1.04988	−0.524942	+	0.851138i	$0.675913\pi$
$720$	11.4013	0.424903
$721$	0	0
$722$	−4.38264	−0.163105
$723$	19.2767	0.716908
$724$	−77.9215	−2.89593
$725$	4.12792	0.153307
$726$	−15.6092	−0.579313
$727$	4.51507	0.167455	0.0837274	−	0.996489i	$-0.473318\pi$
$727$	4.51507	0.167455	0.0837274	+	0.996489i	$0.473318\pi$
$728$	0	0
$729$	−0.250806	−0.00928912
$730$	−14.6698	−0.542953
$731$	14.6764	0.542825
$732$	−120.845	−4.46655
$733$	7.61773	0.281367	0.140684	−	0.990055i	$-0.455070\pi$
$733$	7.61773	0.281367	0.140684	+	0.990055i	$0.455070\pi$
$734$	8.68840	0.320695
$735$	0	0
$736$	−39.1606	−1.44348
$737$	−1.30046	−0.0479029
$738$	36.5602	1.34580
$739$	41.9827	1.54436	0.772180	−	0.635404i	$-0.219166\pi$
$739$	41.9827	1.54436	0.772180	+	0.635404i	$0.219166\pi$
$740$	42.3141	1.55550
$741$	−38.1607	−1.40187
$742$	0	0
$743$	41.8957	1.53700	0.768501	−	0.639848i	$-0.221003\pi$
$743$	41.8957	1.53700	0.768501	+	0.639848i	$0.221003\pi$
$744$	13.3579	0.489725
$745$	16.1031	0.589972
$746$	29.8815	1.09404
$747$	−16.9859	−0.621480
$748$	−94.0782	−3.43984
$749$	0	0
$750$	5.48599	0.200320
$751$	12.8671	0.469526	0.234763	−	0.972053i	$-0.424569\pi$
$751$	12.8671	0.469526	0.234763	+	0.972053i	$0.424569\pi$
$752$	−71.1276	−2.59376
$753$	−27.8831	−1.01612
$754$	40.5845	1.47800
$755$	18.6991	0.680532
$756$	0	0
$757$	−5.88386	−0.213853	−0.106926	−	0.994267i	$-0.534101\pi$
$757$	−5.88386	−0.213853	−0.106926	+	0.994267i	$0.534101\pi$
$758$	−35.1512	−1.27675
$759$	49.4286	1.79414
$760$	28.1210	1.02005
$761$	38.0358	1.37880	0.689399	−	0.724382i	$-0.257875\pi$
$761$	38.0358	1.37880	0.689399	+	0.724382i	$0.257875\pi$
$762$	11.9551	0.433087
$763$	0	0
$764$	−34.0157	−1.23064
$765$	12.4576	0.450405
$766$	−15.5502	−0.561853
$767$	−13.9268	−0.502868
$768$	65.0550	2.34747
$769$	−12.2694	−0.442447	−0.221223	−	0.975223i	$-0.571005\pi$
$769$	−12.2694	−0.442447	−0.221223	+	0.975223i	$0.571005\pi$
$770$	0	0
$771$	58.3311	2.10074
$772$	−65.8815	−2.37113
$773$	−16.6237	−0.597912	−0.298956	−	0.954267i	$-0.596638\pi$
$773$	−16.6237	−0.597912	−0.298956	+	0.954267i	$0.596638\pi$
$774$	−8.40475	−0.302102
$775$	1.00000	0.0359211
$776$	102.959	3.69601
$777$	0	0
$778$	28.5917	1.02506
$779$	39.1271	1.40187
$780$	37.1729	1.33100
$781$	24.0702	0.861299
$782$	−150.821	−5.39334
$783$	11.8106	0.422078
$784$	0	0
$785$	15.0897	0.538576
$786$	−99.5758	−3.55175
$787$	17.8491	0.636252	0.318126	−	0.948049i	$-0.396947\pi$
$787$	17.8491	0.636252	0.318126	+	0.948049i	$0.396947\pi$
$788$	−102.941	−3.66712
$789$	−1.50878	−0.0537142
$790$	3.37320	0.120013
$791$	0	0
$792$	29.5797	1.05107
$793$	−48.8332	−1.73412
$794$	0.915784	0.0325000
$795$	−20.1579	−0.714927
$796$	49.8265	1.76605
$797$	45.2973	1.60451	0.802256	−	0.596981i	$-0.203633\pi$
$797$	45.2973	1.60451	0.802256	+	0.596981i	$0.203633\pi$
$798$	0	0
$799$	−77.7170	−2.74943
$800$	−4.89282	−0.172987
$801$	4.64309	0.164055
$802$	−26.7317	−0.943928
$803$	−16.5142	−0.582772
$804$	−4.36778	−0.154040
$805$	0	0
$806$	9.83169	0.346307
$807$	60.4199	2.12688
$808$	−8.68837	−0.305656
$809$	2.78296	0.0978438	0.0489219	−	0.998803i	$-0.484421\pi$
$809$	2.78296	0.0978438	0.0489219	+	0.998803i	$0.484421\pi$
$810$	28.4585	0.999931
$811$	1.79342	0.0629756	0.0314878	−	0.999504i	$-0.489975\pi$
$811$	1.79342	0.0629756	0.0314878	+	0.999504i	$0.489975\pi$
$812$	0	0
$813$	−57.5705	−2.01909
$814$	69.1155	2.42250
$815$	11.2420	0.393791
$816$	−109.221	−3.82349
$817$	−8.99486	−0.314690
$818$	−68.2323	−2.38569
$819$	0	0
$820$	−38.1143	−1.33101
$821$	45.8230	1.59923	0.799617	−	0.600510i	$-0.205036\pi$
$821$	45.8230	1.59923	0.799617	+	0.600510i	$0.205036\pi$
$822$	66.7233	2.32724
$823$	32.6010	1.13640	0.568199	−	0.822891i	$-0.307640\pi$
$823$	32.6010	1.13640	0.568199	+	0.822891i	$0.307640\pi$
$824$	0.704878	0.0245556
$825$	6.17573	0.215011
$826$	0	0
$827$	45.1772	1.57097	0.785483	−	0.618883i	$-0.212415\pi$
$827$	45.1772	1.57097	0.785483	+	0.618883i	$0.212415\pi$
$828$	59.5264	2.06868
$829$	−1.92723	−0.0669354	−0.0334677	−	0.999440i	$-0.510655\pi$
$829$	−1.92723	−0.0669354	−0.0334677	+	0.999440i	$0.510655\pi$
$830$	25.6936	0.891837
$831$	−6.06722	−0.210470
$832$	4.59500	0.159303
$833$	0	0
$834$	84.7083	2.93321
$835$	0.318111	0.0110087
$836$	57.6587	1.99417
$837$	2.86116	0.0988961
$838$	−1.83085	−0.0632457
$839$	−50.6900	−1.75001	−0.875007	−	0.484110i	$-0.839143\pi$
$839$	−50.6900	−1.75001	−0.875007	+	0.484110i	$0.839143\pi$
$840$	0	0
$841$	−11.9603	−0.412423
$842$	11.9374	0.411391
$843$	4.04848	0.139437
$844$	−22.6104	−0.778283
$845$	2.02153	0.0695426
$846$	44.5064	1.53016
$847$	0	0
$848$	63.3699	2.17613
$849$	−54.7065	−1.87752
$850$	−18.8439	−0.646341
$851$	76.3642	2.61773
$852$	80.8433	2.76965
$853$	7.68812	0.263236	0.131618	−	0.991300i	$-0.457983\pi$
$853$	7.68812	0.263236	0.131618	+	0.991300i	$0.457983\pi$
$854$	0	0
$855$	−7.63501	−0.261112
$856$	45.1104	1.54184
$857$	−13.4936	−0.460934	−0.230467	−	0.973080i	$-0.574025\pi$
$857$	−13.4936	−0.460934	−0.230467	+	0.973080i	$0.574025\pi$
$858$	60.7179	2.07287
$859$	−27.5161	−0.938836	−0.469418	−	0.882976i	$-0.655536\pi$
$859$	−27.5161	−0.938836	−0.469418	+	0.882976i	$0.655536\pi$
$860$	8.76202	0.298782
$861$	0	0
$862$	−2.43260	−0.0828548
$863$	−3.30858	−0.112625	−0.0563127	−	0.998413i	$-0.517934\pi$
$863$	−3.30858	−0.112625	−0.0563127	+	0.998413i	$0.517934\pi$
$864$	−13.9991	−0.476261
$865$	13.8381	0.470510
$866$	−7.48478	−0.254343
$867$	−82.5744	−2.80437
$868$	0	0
$869$	3.79730	0.128815
$870$	22.6457	0.767763
$871$	−1.76501	−0.0598052
$872$	−7.78582	−0.263661
$873$	−27.9539	−0.946098
$874$	92.4350	3.12666
$875$	0	0
$876$	−55.4653	−1.87400
$877$	−10.6222	−0.358687	−0.179344	−	0.983786i	$-0.557397\pi$
$877$	−10.6222	−0.358687	−0.179344	+	0.983786i	$0.557397\pi$
$878$	17.2947	0.583669
$879$	8.01702	0.270407
$880$	−19.4145	−0.654462
$881$	11.5314	0.388502	0.194251	−	0.980952i	$-0.437772\pi$
$881$	11.5314	0.388502	0.194251	+	0.980952i	$0.437772\pi$
$882$	0	0
$883$	40.9923	1.37950	0.689751	−	0.724047i	$-0.257720\pi$
$883$	40.9923	1.37950	0.689751	+	0.724047i	$0.257720\pi$
$884$	−127.686	−4.29453
$885$	−7.77102	−0.261220
$886$	28.9842	0.973745
$887$	21.4851	0.721401	0.360700	−	0.932682i	$-0.382538\pi$
$887$	21.4851	0.721401	0.360700	+	0.932682i	$0.382538\pi$
$888$	127.450	4.27693
$889$	0	0
$890$	−7.02334	−0.235423
$891$	32.0365	1.07326
$892$	−109.707	−3.67328
$893$	47.6312	1.59392
$894$	88.3415	2.95458
$895$	−18.0534	−0.603457
$896$	0	0
$897$	67.0858	2.23993
$898$	12.6932	0.423577
$899$	4.12792	0.137674
$900$	7.43737	0.247912
$901$	69.2407	2.30674
$902$	−62.2555	−2.07288
$903$	0	0
$904$	−34.4475	−1.14571
$905$	−17.5700	−0.584047
$906$	102.583	3.40811
$907$	25.0070	0.830345	0.415172	−	0.909743i	$-0.363721\pi$
$907$	25.0070	0.830345	0.415172	+	0.909743i	$0.363721\pi$
$908$	71.7713	2.38181
$909$	2.35894	0.0782413
$910$	0	0
$911$	−59.5710	−1.97368	−0.986838	−	0.161712i	$-0.948299\pi$
$911$	−59.5710	−1.97368	−0.986838	+	0.161712i	$0.948299\pi$
$912$	66.9392	2.21658
$913$	28.9240	0.957243
$914$	91.4549	3.02506
$915$	−27.2485	−0.900807
$916$	−72.6394	−2.40007
$917$	0	0
$918$	−53.9154	−1.77947
$919$	−24.7868	−0.817640	−0.408820	−	0.912615i	$-0.634060\pi$
$919$	−24.7868	−0.817640	−0.408820	+	0.912615i	$0.634060\pi$
$920$	−49.4362	−1.62986
$921$	−4.50571	−0.148468
$922$	−48.0603	−1.58278
$923$	32.6687	1.07530
$924$	0	0
$925$	9.54114	0.313711
$926$	−2.68368	−0.0881913
$927$	−0.191379	−0.00628570
$928$	−20.1972	−0.663005
$929$	42.3399	1.38913	0.694564	−	0.719431i	$-0.255597\pi$
$929$	42.3399	1.38913	0.694564	+	0.719431i	$0.255597\pi$
$930$	5.48599	0.179893
$931$	0	0
$932$	15.9237	0.521597
$933$	−6.54173	−0.214167
$934$	−11.9711	−0.391706
$935$	−21.2131	−0.693742
$936$	40.1464	1.31223
$937$	43.6437	1.42578	0.712888	−	0.701278i	$-0.247387\pi$
$937$	43.6437	1.42578	0.712888	+	0.701278i	$0.247387\pi$
$938$	0	0
$939$	−42.3562	−1.38224
$940$	−46.3983	−1.51334
$941$	39.9829	1.30341	0.651703	−	0.758474i	$-0.274055\pi$
$941$	39.9829	1.30341	0.651703	+	0.758474i	$0.274055\pi$
$942$	82.7822	2.69719
$943$	−68.7847	−2.23994
$944$	24.4296	0.795115
$945$	0	0
$946$	14.3118	0.465317
$947$	−16.4269	−0.533803	−0.266901	−	0.963724i	$-0.586000\pi$
$947$	−16.4269	−0.533803	−0.266901	+	0.963724i	$0.586000\pi$
$948$	12.7538	0.414224
$949$	−22.4135	−0.727573
$950$	11.5491	0.374701
$951$	31.7337	1.02904
$952$	0	0
$953$	−36.1600	−1.17134	−0.585669	−	0.810551i	$-0.699168\pi$
$953$	−36.1600	−1.17134	−0.585669	+	0.810551i	$0.699168\pi$
$954$	−39.6522	−1.28379
$955$	−7.66998	−0.248195
$956$	−65.6889	−2.12453
$957$	25.4929	0.824069
$958$	60.6635	1.95995
$959$	0	0
$960$	2.56397	0.0827517
$961$	1.00000	0.0322581
$962$	93.8055	3.02441
$963$	−12.2477	−0.394678
$964$	−39.5307	−1.27320
$965$	−14.8552	−0.478206
$966$	0	0
$967$	−37.9891	−1.22165	−0.610824	−	0.791767i	$-0.709162\pi$
$967$	−37.9891	−1.22165	−0.610824	+	0.791767i	$0.709162\pi$
$968$	17.5744	0.564864
$969$	73.1407	2.34962
$970$	42.2844	1.35767
$971$	−52.9782	−1.70015	−0.850076	−	0.526660i	$-0.823444\pi$
$971$	−52.9782	−1.70015	−0.850076	+	0.526660i	$0.823444\pi$
$972$	69.5326	2.23026
$973$	0	0
$974$	4.00730	0.128402
$975$	8.38187	0.268435
$976$	85.6604	2.74192
$977$	−4.10453	−0.131316	−0.0656578	−	0.997842i	$-0.520915\pi$
$977$	−4.10453	−0.131316	−0.0656578	+	0.997842i	$0.520915\pi$
$978$	61.6737	1.97211
$979$	−7.90636	−0.252688
$980$	0	0
$981$	2.11390	0.0674915
$982$	−77.3002	−2.46675
$983$	−24.3254	−0.775861	−0.387930	−	0.921689i	$-0.626810\pi$
$983$	−24.3254	−0.775861	−0.387930	+	0.921689i	$0.626810\pi$
$984$	−114.800	−3.65968
$985$	−23.2115	−0.739580
$986$	−77.7862	−2.47722
$987$	0	0
$988$	78.2560	2.48965
$989$	15.8128	0.502818
$990$	12.1481	0.386093
$991$	35.6227	1.13159	0.565796	−	0.824546i	$-0.308569\pi$
$991$	35.6227	1.13159	0.565796	+	0.824546i	$0.308569\pi$
$992$	−4.89282	−0.155347
$993$	−21.0639	−0.668444
$994$	0	0
$995$	11.2351	0.356175
$996$	97.1454	3.07817
$997$	38.0200	1.20411	0.602053	−	0.798456i	$-0.294350\pi$
$997$	38.0200	1.20411	0.602053	+	0.798456i	$0.294350\pi$
$998$	−50.6672	−1.60384
$999$	27.2987	0.863693

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7595.2.a.u.1.1		7
7.6	odd	2		1085.2.a.p.1.1	✓	7
21.20	even	2		9765.2.a.bc.1.7		7
35.34	odd	2		5425.2.a.ba.1.7		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1085.2.a.p.1.1	✓	7	7.6	odd	2
5425.2.a.ba.1.7		7	35.34	odd	2
7595.2.a.u.1.1		7	1.1	even	1	trivial
9765.2.a.bc.1.7		7	21.20	even	2

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:	\( N \)	\(=\)	\( 7595 = 5 \cdot 7^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7595.a (trivial)

\(f(q)\)	\(=\)	\(q-2.53671 q^{2} -2.16264 q^{3} +4.43491 q^{4} +1.00000 q^{5} +5.48599 q^{6} -6.17668 q^{8} +1.67701 q^{9} +O(q^{10})\)	\(q-2.53671 q^{2} -2.16264 q^{3} +4.43491 q^{4} +1.00000 q^{5} +5.48599 q^{6} -6.17668 q^{8} +1.67701 q^{9} -2.53671 q^{10} -2.85565 q^{11} -9.59111 q^{12} -3.87576 q^{13} -2.16264 q^{15} +6.79863 q^{16} +7.42848 q^{17} -4.25408 q^{18} -4.55277 q^{19} +4.43491 q^{20} +7.24395 q^{22} +8.00368 q^{23} +13.3579 q^{24} +1.00000 q^{25} +9.83169 q^{26} +2.86116 q^{27} +4.12792 q^{29} +5.48599 q^{30} +1.00000 q^{31} -4.89282 q^{32} +6.17573 q^{33} -18.8439 q^{34} +7.43737 q^{36} +9.54114 q^{37} +11.5491 q^{38} +8.38187 q^{39} -6.17668 q^{40} -8.59414 q^{41} +1.97569 q^{43} -12.6645 q^{44} +1.67701 q^{45} -20.3030 q^{46} -10.4620 q^{47} -14.7030 q^{48} -2.53671 q^{50} -16.0651 q^{51} -17.1887 q^{52} +9.32098 q^{53} -7.25794 q^{54} -2.85565 q^{55} +9.84599 q^{57} -10.4714 q^{58} +3.59331 q^{59} -9.59111 q^{60} +12.5997 q^{61} -2.53671 q^{62} -1.18557 q^{64} -3.87576 q^{65} -15.6661 q^{66} +0.455398 q^{67} +32.9447 q^{68} -17.3091 q^{69} -8.42898 q^{71} -10.3583 q^{72} +5.78299 q^{73} -24.2031 q^{74} -2.16264 q^{75} -20.1911 q^{76} -21.2624 q^{78} -1.32975 q^{79} +6.79863 q^{80} -11.2187 q^{81} +21.8009 q^{82} -10.1287 q^{83} +7.42848 q^{85} -5.01176 q^{86} -8.92720 q^{87} +17.6384 q^{88} +2.76868 q^{89} -4.25408 q^{90} +35.4956 q^{92} -2.16264 q^{93} +26.5392 q^{94} -4.55277 q^{95} +10.5814 q^{96} -16.6690 q^{97} -4.78893 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 3 q^{2} - 2 q^{3} + 13 q^{4} + 7 q^{5} + 12 q^{6} + 9 q^{8} + 11 q^{9}+O(q^{10}) \) 7 * q + 3 * q^2 - 2 * q^3 + 13 * q^4 + 7 * q^5 + 12 * q^6 + 9 * q^8 + 11 * q^9	\( 7 q + 3 q^{2} - 2 q^{3} + 13 q^{4} + 7 q^{5} + 12 q^{6} + 9 q^{8} + 11 q^{9} + 3 q^{10} + 5 q^{11} - 4 q^{12} - 9 q^{13} - 2 q^{15} + 13 q^{16} + 2 q^{17} - 5 q^{18} - 13 q^{19} + 13 q^{20} + 20 q^{22} + 8 q^{23} + 8 q^{24} + 7 q^{25} - 4 q^{26} - 8 q^{27} - q^{29} + 12 q^{30} + 7 q^{31} + 11 q^{32} + 13 q^{33} - 20 q^{34} - 3 q^{36} + 37 q^{37} + 4 q^{38} + 21 q^{39} + 9 q^{40} - 9 q^{41} + 19 q^{43} + 16 q^{44} + 11 q^{45} + 8 q^{46} + q^{47} - 8 q^{48} + 3 q^{50} - 4 q^{51} - 26 q^{52} + 25 q^{53} + 32 q^{54} + 5 q^{55} + 33 q^{57} + 4 q^{58} - 7 q^{59} - 4 q^{60} + 34 q^{61} + 3 q^{62} + 49 q^{64} - 9 q^{65} - 32 q^{66} + 20 q^{68} - 4 q^{69} - 23 q^{71} - 17 q^{72} + 3 q^{73} - 18 q^{74} - 2 q^{75} - 10 q^{76} + 14 q^{78} + 13 q^{79} + 13 q^{80} - 5 q^{81} + 78 q^{82} + 13 q^{83} + 2 q^{85} + 10 q^{86} + 17 q^{87} + 52 q^{88} + 10 q^{89} - 5 q^{90} + 60 q^{92} - 2 q^{93} + 38 q^{94} - 13 q^{95} + 26 q^{96} - 3 q^{97} - 36 q^{99}+O(q^{100}) \) 7 * q + 3 * q^2 - 2 * q^3 + 13 * q^4 + 7 * q^5 + 12 * q^6 + 9 * q^8 + 11 * q^9 + 3 * q^10 + 5 * q^11 - 4 * q^12 - 9 * q^13 - 2 * q^15 + 13 * q^16 + 2 * q^17 - 5 * q^18 - 13 * q^19 + 13 * q^20 + 20 * q^22 + 8 * q^23 + 8 * q^24 + 7 * q^25 - 4 * q^26 - 8 * q^27 - q^29 + 12 * q^30 + 7 * q^31 + 11 * q^32 + 13 * q^33 - 20 * q^34 - 3 * q^36 + 37 * q^37 + 4 * q^38 + 21 * q^39 + 9 * q^40 - 9 * q^41 + 19 * q^43 + 16 * q^44 + 11 * q^45 + 8 * q^46 + q^47 - 8 * q^48 + 3 * q^50 - 4 * q^51 - 26 * q^52 + 25 * q^53 + 32 * q^54 + 5 * q^55 + 33 * q^57 + 4 * q^58 - 7 * q^59 - 4 * q^60 + 34 * q^61 + 3 * q^62 + 49 * q^64 - 9 * q^65 - 32 * q^66 + 20 * q^68 - 4 * q^69 - 23 * q^71 - 17 * q^72 + 3 * q^73 - 18 * q^74 - 2 * q^75 - 10 * q^76 + 14 * q^78 + 13 * q^79 + 13 * q^80 - 5 * q^81 + 78 * q^82 + 13 * q^83 + 2 * q^85 + 10 * q^86 + 17 * q^87 + 52 * q^88 + 10 * q^89 - 5 * q^90 + 60 * q^92 - 2 * q^93 + 38 * q^94 - 13 * q^95 + 26 * q^96 - 3 * q^97 - 36 * q^99

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