LMFDB - Embedded newform 2695.2.a.k.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2695,2,Mod(1,2695)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2695, 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("2695.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2695 = 5 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2695.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:	$21.5196833447$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.1957.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 4x^{2} - x + 1 $ x^4 - 4*x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 385)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.06150$ of defining polynomial
Character	$\chi$	$=$	2695.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.57641 q^{2} +0.514916 q^{3} +4.63791 q^{4} -1.00000 q^{5} -1.32664 q^{6} -6.79636 q^{8} -2.73486 q^{9} +O(q^{10})$	\(q-2.57641 q^{2} +0.514916 q^{3} +4.63791 q^{4} -1.00000 q^{5} -1.32664 q^{6} -6.79636 q^{8} -2.73486 q^{9} +2.57641 q^{10} +1.00000 q^{11} +2.38814 q^{12} +1.97017 q^{13} -0.514916 q^{15} +8.23442 q^{16} +2.38814 q^{17} +7.04614 q^{18} -4.54097 q^{19} -4.63791 q^{20} -2.57641 q^{22} -2.71477 q^{23} -3.49956 q^{24} +1.00000 q^{25} -5.07597 q^{26} -2.95297 q^{27} +1.93472 q^{29} +1.32664 q^{30} +3.59089 q^{31} -7.62255 q^{32} +0.514916 q^{33} -6.15283 q^{34} -12.6841 q^{36} +6.13747 q^{37} +11.6994 q^{38} +1.01447 q^{39} +6.79636 q^{40} -8.20275 q^{41} +9.15756 q^{43} +4.63791 q^{44} +2.73486 q^{45} +6.99438 q^{46} +7.44964 q^{47} +4.24003 q^{48} -2.57641 q^{50} +1.22969 q^{51} +9.13747 q^{52} -12.2814 q^{53} +7.60808 q^{54} -1.00000 q^{55} -2.33822 q^{57} -4.98464 q^{58} -1.85981 q^{59} -2.38814 q^{60} +0.932884 q^{61} -9.25161 q^{62} +3.17003 q^{64} -1.97017 q^{65} -1.32664 q^{66} -11.5569 q^{67} +11.0760 q^{68} -1.39788 q^{69} -12.4842 q^{71} +18.5871 q^{72} +7.16730 q^{73} -15.8127 q^{74} +0.514916 q^{75} -21.0606 q^{76} -2.61370 q^{78} -0.820230 q^{79} -8.23442 q^{80} +6.68405 q^{81} +21.1337 q^{82} +9.83688 q^{83} -2.38814 q^{85} -23.5937 q^{86} +0.996218 q^{87} -6.79636 q^{88} -10.5996 q^{89} -7.04614 q^{90} -12.5909 q^{92} +1.84900 q^{93} -19.1934 q^{94} +4.54097 q^{95} -3.92497 q^{96} +7.02009 q^{97} -2.73486 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 4 q^{5} - 7 q^{6} - 9 q^{8} - q^{9}+O(q^{10}) $ 4 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 - 4 * q^5 - 7 * q^6 - 9 * q^8 - q^9	$ 4 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 4 q^{5} - 7 q^{6} - 9 q^{8} - q^{9} + 3 q^{10} + 4 q^{11} + 3 q^{12} + 6 q^{13} - 3 q^{15} + 5 q^{16} + 3 q^{17} + q^{18} + 3 q^{19} - 3 q^{20} - 3 q^{22} - 6 q^{23} + 4 q^{24} + 4 q^{25} + 5 q^{26} - 3 q^{27} - 8 q^{29} + 7 q^{30} - 10 q^{31} + 4 q^{32} + 3 q^{33} - 10 q^{34} - 8 q^{36} - 9 q^{37} + 23 q^{38} - 13 q^{39} + 9 q^{40} - 15 q^{41} - 2 q^{43} + 3 q^{44} + q^{45} + 16 q^{46} + 15 q^{47} + q^{48} - 3 q^{50} + q^{51} + 3 q^{52} - 30 q^{53} + 13 q^{54} - 4 q^{55} - 6 q^{57} - q^{58} - 17 q^{59} - 3 q^{60} - 16 q^{62} + 5 q^{64} - 6 q^{65} - 7 q^{66} - 25 q^{67} + 19 q^{68} - 6 q^{69} - 13 q^{71} + 26 q^{72} - 3 q^{73} - 16 q^{74} + 3 q^{75} - 40 q^{76} - 5 q^{78} - 4 q^{79} - 5 q^{80} - 16 q^{81} + 27 q^{82} - 18 q^{83} - 3 q^{85} - 10 q^{86} - 20 q^{87} - 9 q^{88} - 25 q^{89} - q^{90} - 26 q^{92} + 10 q^{93} - 23 q^{94} - 3 q^{95} + 7 q^{96} + 23 q^{97} - q^{99}+O(q^{100}) $ 4 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 - 4 * q^5 - 7 * q^6 - 9 * q^8 - q^9 + 3 * q^10 + 4 * q^11 + 3 * q^12 + 6 * q^13 - 3 * q^15 + 5 * q^16 + 3 * q^17 + q^18 + 3 * q^19 - 3 * q^20 - 3 * q^22 - 6 * q^23 + 4 * q^24 + 4 * q^25 + 5 * q^26 - 3 * q^27 - 8 * q^29 + 7 * q^30 - 10 * q^31 + 4 * q^32 + 3 * q^33 - 10 * q^34 - 8 * q^36 - 9 * q^37 + 23 * q^38 - 13 * q^39 + 9 * q^40 - 15 * q^41 - 2 * q^43 + 3 * q^44 + q^45 + 16 * q^46 + 15 * q^47 + q^48 - 3 * q^50 + q^51 + 3 * q^52 - 30 * q^53 + 13 * q^54 - 4 * q^55 - 6 * q^57 - q^58 - 17 * q^59 - 3 * q^60 - 16 * q^62 + 5 * q^64 - 6 * q^65 - 7 * q^66 - 25 * q^67 + 19 * q^68 - 6 * q^69 - 13 * q^71 + 26 * q^72 - 3 * q^73 - 16 * q^74 + 3 * q^75 - 40 * q^76 - 5 * q^78 - 4 * q^79 - 5 * q^80 - 16 * q^81 + 27 * q^82 - 18 * q^83 - 3 * q^85 - 10 * q^86 - 20 * q^87 - 9 * q^88 - 25 * q^89 - q^90 - 26 * q^92 + 10 * q^93 - 23 * q^94 - 3 * q^95 + 7 * q^96 + 23 * q^97 - 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 $

$2$	−2.57641	−1.82180	−0.910900	−	0.412627i	$-0.864611\pi$
$2$	−2.57641	−1.82180	−0.910900	+	0.412627i	$0.864611\pi$
$3$	0.514916	0.297287	0.148643	−	0.988891i	$-0.452509\pi$
$3$	0.514916	0.297287	0.148643	+	0.988891i	$0.452509\pi$
$4$	4.63791	2.31896
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.32664	−0.541597
$7$	0	0
$7$	0	0
$8$	−6.79636	−2.40288
$9$	−2.73486	−0.911620
$10$	2.57641	0.814734
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	2.38814	0.689396
$13$	1.97017	0.546426	0.273213	−	0.961954i	$-0.411914\pi$
$13$	1.97017	0.546426	0.273213	+	0.961954i	$0.411914\pi$
$14$	0	0
$15$	−0.514916	−0.132951
$16$	8.23442	2.05860
$17$	2.38814	0.579208	0.289604	−	0.957147i	$-0.406476\pi$
$17$	2.38814	0.579208	0.289604	+	0.957147i	$0.406476\pi$
$18$	7.04614	1.66079
$19$	−4.54097	−1.04177	−0.520885	−	0.853627i	$-0.674398\pi$
$19$	−4.54097	−1.04177	−0.520885	+	0.853627i	$0.674398\pi$
$20$	−4.63791	−1.03707
$21$	0	0
$22$	−2.57641	−0.549294
$23$	−2.71477	−0.566069	−0.283035	−	0.959110i	$-0.591341\pi$
$23$	−2.71477	−0.566069	−0.283035	+	0.959110i	$0.591341\pi$
$24$	−3.49956	−0.714344
$25$	1.00000	0.200000
$26$	−5.07597	−0.995480
$27$	−2.95297	−0.568300
$28$	0	0
$29$	1.93472	0.359268	0.179634	−	0.983733i	$-0.442509\pi$
$29$	1.93472	0.359268	0.179634	+	0.983733i	$0.442509\pi$
$30$	1.32664	0.242210
$31$	3.59089	0.644942	0.322471	−	0.946579i	$-0.395486\pi$
$31$	3.59089	0.644942	0.322471	+	0.946579i	$0.395486\pi$
$32$	−7.62255	−1.34749
$33$	0.514916	0.0896354
$34$	−6.15283	−1.05520
$35$	0	0
$36$	−12.6841	−2.11401
$37$	6.13747	1.00899	0.504497	−	0.863414i	$-0.331678\pi$
$37$	6.13747	1.00899	0.504497	+	0.863414i	$0.331678\pi$
$38$	11.6994	1.89790
$39$	1.01447	0.162445
$40$	6.79636	1.07460
$41$	−8.20275	−1.28105	−0.640527	−	0.767936i	$-0.721284\pi$
$41$	−8.20275	−1.28105	−0.640527	+	0.767936i	$0.721284\pi$
$42$	0	0
$43$	9.15756	1.39651	0.698257	−	0.715847i	$-0.253959\pi$
$43$	9.15756	1.39651	0.698257	+	0.715847i	$0.253959\pi$
$44$	4.63791	0.699192
$45$	2.73486	0.407689
$46$	6.99438	1.03127
$47$	7.44964	1.08664	0.543320	−	0.839525i	$-0.317167\pi$
$47$	7.44964	1.08664	0.543320	+	0.839525i	$0.317167\pi$
$48$	4.24003	0.611996
$49$	0	0
$50$	−2.57641	−0.364360
$51$	1.22969	0.172191
$52$	9.13747	1.26714
$53$	−12.2814	−1.68699	−0.843493	−	0.537140i	$-0.819505\pi$
$53$	−12.2814	−1.68699	−0.843493	+	0.537140i	$0.819505\pi$
$54$	7.60808	1.03533
$55$	−1.00000	−0.134840
$56$	0	0
$57$	−2.33822	−0.309704
$58$	−4.98464	−0.654515
$59$	−1.85981	−0.242126	−0.121063	−	0.992645i	$-0.538630\pi$
$59$	−1.85981	−0.242126	−0.121063	+	0.992645i	$0.538630\pi$
$60$	−2.38814	−0.308307
$61$	0.932884	0.119444	0.0597218	−	0.998215i	$-0.480979\pi$
$61$	0.932884	0.119444	0.0597218	+	0.998215i	$0.480979\pi$
$62$	−9.25161	−1.17496
$63$	0	0
$64$	3.17003	0.396253
$65$	−1.97017	−0.244369
$66$	−1.32664	−0.163298
$67$	−11.5569	−1.41190	−0.705952	−	0.708260i	$-0.749480\pi$
$67$	−11.5569	−1.41190	−0.705952	+	0.708260i	$0.749480\pi$
$68$	11.0760	1.34316
$69$	−1.39788	−0.168285
$70$	0	0
$71$	−12.4842	−1.48160	−0.740801	−	0.671725i	$-0.765554\pi$
$71$	−12.4842	−1.48160	−0.740801	+	0.671725i	$0.765554\pi$
$72$	18.5871	2.19051
$73$	7.16730	0.838869	0.419435	−	0.907786i	$-0.362228\pi$
$73$	7.16730	0.838869	0.419435	+	0.907786i	$0.362228\pi$
$74$	−15.8127	−1.83819
$75$	0.514916	0.0594574
$76$	−21.0606	−2.41582
$77$	0	0
$78$	−2.61370	−0.295943
$79$	−0.820230	−0.0922831	−0.0461416	−	0.998935i	$-0.514693\pi$
$79$	−0.820230	−0.0922831	−0.0461416	+	0.998935i	$0.514693\pi$
$80$	−8.23442	−0.920636
$81$	6.68405	0.742672
$82$	21.1337	2.33383
$83$	9.83688	1.07974	0.539869	−	0.841749i	$-0.318474\pi$
$83$	9.83688	1.07974	0.539869	+	0.841749i	$0.318474\pi$
$84$	0	0
$85$	−2.38814	−0.259030
$86$	−23.5937	−2.54417
$87$	0.996218	0.106806
$88$	−6.79636	−0.724494
$89$	−10.5996	−1.12355	−0.561776	−	0.827289i	$-0.689882\pi$
$89$	−10.5996	−1.12355	−0.561776	+	0.827289i	$0.689882\pi$
$90$	−7.04614	−0.742728
$91$	0	0
$92$	−12.5909	−1.31269
$93$	1.84900	0.191733
$94$	−19.1934	−1.97964
$95$	4.54097	0.465893
$96$	−3.92497	−0.400591
$97$	7.02009	0.712782	0.356391	−	0.934337i	$-0.384007\pi$
$97$	7.02009	0.712782	0.356391	+	0.934337i	$0.384007\pi$
$98$	0	0
$99$	−2.73486	−0.274864
$100$	4.63791	0.463791
$101$	−16.5946	−1.65122	−0.825610	−	0.564241i	$-0.809169\pi$
$101$	−16.5946	−1.65122	−0.825610	+	0.564241i	$0.809169\pi$
$102$	−3.16819	−0.313698
$103$	−16.0494	−1.58139	−0.790696	−	0.612209i	$-0.790281\pi$
$103$	−16.0494	−1.58139	−0.790696	+	0.612209i	$0.790281\pi$
$104$	−13.3900	−1.31299
$105$	0	0
$106$	31.6421	3.07335
$107$	−5.42086	−0.524054	−0.262027	−	0.965060i	$-0.584391\pi$
$107$	−5.42086	−0.524054	−0.262027	+	0.965060i	$0.584391\pi$
$108$	−13.6956	−1.31786
$109$	−2.59774	−0.248818	−0.124409	−	0.992231i	$-0.539704\pi$
$109$	−2.59774	−0.248818	−0.124409	+	0.992231i	$0.539704\pi$
$110$	2.57641	0.245652
$111$	3.16028	0.299961
$112$	0	0
$113$	−12.9031	−1.21382	−0.606909	−	0.794772i	$-0.707591\pi$
$113$	−12.9031	−1.21382	−0.606909	+	0.794772i	$0.707591\pi$
$114$	6.02422	0.564219
$115$	2.71477	0.253154
$116$	8.97306	0.833128
$117$	−5.38814	−0.498133
$118$	4.79163	0.441106
$119$	0	0
$120$	3.49956	0.319464
$121$	1.00000	0.0909091
$122$	−2.40350	−0.217602
$123$	−4.22373	−0.380841
$124$	16.6542	1.49559
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	14.3787	1.27591	0.637953	−	0.770075i	$-0.279781\pi$
$127$	14.3787	1.27591	0.637953	+	0.770075i	$0.279781\pi$
$128$	7.07780	0.625595
$129$	4.71537	0.415165
$130$	5.07597	0.445192
$131$	21.7647	1.90159	0.950797	−	0.309813i	$-0.100267\pi$
$131$	21.7647	1.90159	0.950797	+	0.309813i	$0.100267\pi$
$132$	2.38814	0.207861
$133$	0	0
$134$	29.7754	2.57221
$135$	2.95297	0.254151
$136$	−16.2306	−1.39177
$137$	12.1854	1.04107	0.520536	−	0.853840i	$-0.325732\pi$
$137$	12.1854	1.04107	0.520536	+	0.853840i	$0.325732\pi$
$138$	3.60152	0.306582
$139$	−12.6389	−1.07201	−0.536007	−	0.844214i	$-0.680068\pi$
$139$	−12.6389	−1.07201	−0.536007	+	0.844214i	$0.680068\pi$
$140$	0	0
$141$	3.83594	0.323044
$142$	32.1645	2.69918
$143$	1.97017	0.164754
$144$	−22.5200	−1.87667
$145$	−1.93472	−0.160670
$146$	−18.4659	−1.52825
$147$	0	0
$148$	28.4651	2.33981
$149$	−4.17186	−0.341772	−0.170886	−	0.985291i	$-0.554663\pi$
$149$	−4.17186	−0.341772	−0.170886	+	0.985291i	$0.554663\pi$
$150$	−1.32664	−0.108319
$151$	4.75618	0.387053	0.193526	−	0.981095i	$-0.438007\pi$
$151$	4.75618	0.387053	0.193526	+	0.981095i	$0.438007\pi$
$152$	30.8620	2.50324
$153$	−6.53122	−0.528018
$154$	0	0
$155$	−3.59089	−0.288427
$156$	4.70503	0.376704
$157$	16.2344	1.29565	0.647824	−	0.761790i	$-0.275679\pi$
$157$	16.2344	1.29565	0.647824	+	0.761790i	$0.275679\pi$
$158$	2.11325	0.168121
$159$	−6.32391	−0.501519
$160$	7.62255	0.602616
$161$	0	0
$162$	−17.2209	−1.35300
$163$	2.81934	0.220828	0.110414	−	0.993886i	$-0.464782\pi$
$163$	2.81934	0.220828	0.110414	+	0.993886i	$0.464782\pi$
$164$	−38.0436	−2.97071
$165$	−0.514916	−0.0400862
$166$	−25.3439	−1.96707
$167$	10.5853	0.819113	0.409556	−	0.912285i	$-0.365684\pi$
$167$	10.5853	0.819113	0.409556	+	0.912285i	$0.365684\pi$
$168$	0	0
$169$	−9.11844	−0.701418
$170$	6.15283	0.471901
$171$	12.4189	0.949698
$172$	42.4720	3.23846
$173$	−16.1999	−1.23166	−0.615828	−	0.787880i	$-0.711178\pi$
$173$	−16.1999	−1.23166	−0.615828	+	0.787880i	$0.711178\pi$
$174$	−2.56667	−0.194579
$175$	0	0
$176$	8.23442	0.620692
$177$	−0.957644	−0.0719810
$178$	27.3089	2.04689
$179$	−25.2791	−1.88945	−0.944723	−	0.327870i	$-0.893669\pi$
$179$	−25.2791	−1.88945	−0.944723	+	0.327870i	$0.893669\pi$
$180$	12.6841	0.945413
$181$	23.8993	1.77642	0.888211	−	0.459435i	$-0.151948\pi$
$181$	23.8993	1.77642	0.888211	+	0.459435i	$0.151948\pi$
$182$	0	0
$183$	0.480357	0.0355090
$184$	18.4506	1.36019
$185$	−6.13747	−0.451236
$186$	−4.76380	−0.349299
$187$	2.38814	0.174638
$188$	34.5508	2.51987
$189$	0	0
$190$	−11.6994	−0.848765
$191$	−20.8060	−1.50547	−0.752734	−	0.658324i	$-0.771266\pi$
$191$	−20.8060	−1.50547	−0.752734	+	0.658324i	$0.771266\pi$
$192$	1.63230	0.117801
$193$	−5.23135	−0.376561	−0.188280	−	0.982115i	$-0.560291\pi$
$193$	−5.23135	−0.376561	−0.188280	+	0.982115i	$0.560291\pi$
$194$	−18.0867	−1.29855
$195$	−1.01447	−0.0726478
$196$	0	0
$197$	−26.8975	−1.91637	−0.958183	−	0.286155i	$-0.907623\pi$
$197$	−26.8975	−1.91637	−0.958183	+	0.286155i	$0.907623\pi$
$198$	7.04614	0.500747
$199$	−27.4413	−1.94526	−0.972631	−	0.232356i	$-0.925357\pi$
$199$	−27.4413	−1.94526	−0.972631	+	0.232356i	$0.925357\pi$
$200$	−6.79636	−0.480575
$201$	−5.95085	−0.419740
$202$	42.7545	3.00819
$203$	0	0
$204$	5.70319	0.399303
$205$	8.20275	0.572905
$206$	41.3498	2.88098
$207$	7.42453	0.516040
$208$	16.2232	1.12488
$209$	−4.54097	−0.314105
$210$	0	0
$211$	−11.1901	−0.770359	−0.385180	−	0.922842i	$-0.625860\pi$
$211$	−11.1901	−0.770359	−0.385180	+	0.922842i	$0.625860\pi$
$212$	−56.9603	−3.91205
$213$	−6.42831	−0.440461
$214$	13.9664	0.954722
$215$	−9.15756	−0.624540
$216$	20.0695	1.36555
$217$	0	0
$218$	6.69285	0.453297
$219$	3.69056	0.249385
$220$	−4.63791	−0.312688
$221$	4.70503	0.316495
$222$	−8.14220	−0.546468
$223$	−17.0992	−1.14505	−0.572523	−	0.819889i	$-0.694035\pi$
$223$	−17.0992	−1.14505	−0.572523	+	0.819889i	$0.694035\pi$
$224$	0	0
$225$	−2.73486	−0.182324
$226$	33.2436	2.21133
$227$	3.52833	0.234183	0.117092	−	0.993121i	$-0.462643\pi$
$227$	3.52833	0.234183	0.117092	+	0.993121i	$0.462643\pi$
$228$	−10.8444	−0.718191
$229$	−13.2451	−0.875261	−0.437631	−	0.899155i	$-0.644182\pi$
$229$	−13.2451	−0.875261	−0.437631	+	0.899155i	$0.644182\pi$
$230$	−6.99438	−0.461196
$231$	0	0
$232$	−13.1490	−0.863277
$233$	−12.3210	−0.807177	−0.403588	−	0.914941i	$-0.632237\pi$
$233$	−12.3210	−0.807177	−0.403588	+	0.914941i	$0.632237\pi$
$234$	13.8821	0.907500
$235$	−7.44964	−0.485961
$236$	−8.62562	−0.561480
$237$	−0.422350	−0.0274346
$238$	0	0
$239$	15.7503	1.01880	0.509400	−	0.860530i	$-0.329867\pi$
$239$	15.7503	1.01880	0.509400	+	0.860530i	$0.329867\pi$
$240$	−4.24003	−0.273693
$241$	16.0942	1.03672	0.518360	−	0.855162i	$-0.326543\pi$
$241$	16.0942	1.03672	0.518360	+	0.855162i	$0.326543\pi$
$242$	−2.57641	−0.165618
$243$	12.3006	0.789087
$244$	4.32664	0.276985
$245$	0	0
$246$	10.8821	0.693816
$247$	−8.94647	−0.569250
$248$	−24.4050	−1.54972
$249$	5.06517	0.320992
$250$	2.57641	0.162947
$251$	21.2232	1.33960	0.669798	−	0.742544i	$-0.266381\pi$
$251$	21.2232	1.33960	0.669798	+	0.742544i	$0.266381\pi$
$252$	0	0
$253$	−2.71477	−0.170676
$254$	−37.0456	−2.32445
$255$	−1.22969	−0.0770062
$256$	−24.5754	−1.53596
$257$	0.592721	0.0369729	0.0184864	−	0.999829i	$-0.494115\pi$
$257$	0.592721	0.0369729	0.0184864	+	0.999829i	$0.494115\pi$
$258$	−12.1488	−0.756349
$259$	0	0
$260$	−9.13747	−0.566682
$261$	−5.29119	−0.327516
$262$	−56.0750	−3.46433
$263$	−11.2384	−0.692988	−0.346494	−	0.938052i	$-0.612628\pi$
$263$	−11.2384	−0.692988	−0.346494	+	0.938052i	$0.612628\pi$
$264$	−3.49956	−0.215383
$265$	12.2814	0.754443
$266$	0	0
$267$	−5.45789	−0.334017
$268$	−53.6000	−3.27414
$269$	−3.85497	−0.235041	−0.117521	−	0.993070i	$-0.537495\pi$
$269$	−3.85497	−0.235041	−0.117521	+	0.993070i	$0.537495\pi$
$270$	−7.60808	−0.463013
$271$	11.5830	0.703616	0.351808	−	0.936072i	$-0.385567\pi$
$271$	11.5830	0.703616	0.351808	+	0.936072i	$0.385567\pi$
$272$	19.6649	1.19236
$273$	0	0
$274$	−31.3948	−1.89663
$275$	1.00000	0.0603023
$276$	−6.48325	−0.390246
$277$	3.93377	0.236358	0.118179	−	0.992992i	$-0.462294\pi$
$277$	3.93377	0.236358	0.118179	+	0.992992i	$0.462294\pi$
$278$	32.5629	1.95300
$279$	−9.82058	−0.587942
$280$	0	0
$281$	−22.6119	−1.34891	−0.674455	−	0.738316i	$-0.735621\pi$
$281$	−22.6119	−1.34891	−0.674455	+	0.738316i	$0.735621\pi$
$282$	−9.88296	−0.588522
$283$	12.9123	0.767554	0.383777	−	0.923426i	$-0.374623\pi$
$283$	12.9123	0.767554	0.383777	+	0.923426i	$0.374623\pi$
$284$	−57.9006	−3.43577
$285$	2.33822	0.138504
$286$	−5.07597	−0.300148
$287$	0	0
$288$	20.8466	1.22840
$289$	−11.2968	−0.664518
$290$	4.98464	0.292708
$291$	3.61476	0.211901
$292$	33.2413	1.94530
$293$	9.52755	0.556606	0.278303	−	0.960493i	$-0.410228\pi$
$293$	9.52755	0.556606	0.278303	+	0.960493i	$0.410228\pi$
$294$	0	0
$295$	1.85981	0.108282
$296$	−41.7124	−2.42449
$297$	−2.95297	−0.171349
$298$	10.7484	0.622641
$299$	−5.34856	−0.309315
$300$	2.38814	0.137879
$301$	0	0
$302$	−12.2539	−0.705133
$303$	−8.54480	−0.490886
$304$	−37.3922	−2.14459
$305$	−0.932884	−0.0534168
$306$	16.8271	0.961943
$307$	−26.4909	−1.51192	−0.755959	−	0.654619i	$-0.772829\pi$
$307$	−26.4909	−1.51192	−0.755959	+	0.654619i	$0.772829\pi$
$308$	0	0
$309$	−8.26408	−0.470127
$310$	9.25161	0.525456
$311$	−23.1515	−1.31280	−0.656400	−	0.754413i	$-0.727922\pi$
$311$	−23.1515	−1.31280	−0.656400	+	0.754413i	$0.727922\pi$
$312$	−6.89471	−0.390336
$313$	−26.3339	−1.48848	−0.744240	−	0.667913i	$-0.767188\pi$
$313$	−26.3339	−1.48848	−0.744240	+	0.667913i	$0.767188\pi$
$314$	−41.8266	−2.36041
$315$	0	0
$316$	−3.80416	−0.214001
$317$	−18.1903	−1.02167	−0.510834	−	0.859679i	$-0.670663\pi$
$317$	−18.1903	−1.02167	−0.510834	+	0.859679i	$0.670663\pi$
$318$	16.2930	0.913667
$319$	1.93472	0.108323
$320$	−3.17003	−0.177210
$321$	−2.79129	−0.155795
$322$	0	0
$323$	−10.8444	−0.603401
$324$	31.0001	1.72223
$325$	1.97017	0.109285
$326$	−7.26379	−0.402304
$327$	−1.33762	−0.0739704
$328$	55.7488	3.07821
$329$	0	0
$330$	1.32664	0.0730290
$331$	−16.1641	−0.888457	−0.444229	−	0.895913i	$-0.646522\pi$
$331$	−16.1641	−0.888457	−0.444229	+	0.895913i	$0.646522\pi$
$332$	45.6226	2.50387
$333$	−16.7851	−0.919819
$334$	−27.2720	−1.49226
$335$	11.5569	0.631422
$336$	0	0
$337$	11.0763	0.603365	0.301683	−	0.953408i	$-0.402452\pi$
$337$	11.0763	0.603365	0.301683	+	0.953408i	$0.402452\pi$
$338$	23.4929	1.27784
$339$	−6.64399	−0.360852
$340$	−11.0760	−0.600679
$341$	3.59089	0.194457
$342$	−31.9963	−1.73016
$343$	0	0
$344$	−62.2381	−3.35565
$345$	1.39788	0.0752594
$346$	41.7377	2.24383
$347$	−14.8517	−0.797281	−0.398640	−	0.917107i	$-0.630518\pi$
$347$	−14.8517	−0.797281	−0.398640	+	0.917107i	$0.630518\pi$
$348$	4.62037	0.247678
$349$	0.178880	0.00957522	0.00478761	−	0.999989i	$-0.498476\pi$
$349$	0.178880	0.00957522	0.00478761	+	0.999989i	$0.498476\pi$
$350$	0	0
$351$	−5.81785	−0.310534
$352$	−7.62255	−0.406283
$353$	27.5891	1.46842	0.734210	−	0.678922i	$-0.237553\pi$
$353$	27.5891	1.46842	0.734210	+	0.678922i	$0.237553\pi$
$354$	2.46729	0.131135
$355$	12.4842	0.662592
$356$	−49.1599	−2.60547
$357$	0	0
$358$	65.1294	3.44219
$359$	8.18177	0.431817	0.215909	−	0.976414i	$-0.430729\pi$
$359$	8.18177	0.431817	0.215909	+	0.976414i	$0.430729\pi$
$360$	−18.5871	−0.979626
$361$	1.62037	0.0852828
$362$	−61.5746	−3.23629
$363$	0.514916	0.0270261
$364$	0	0
$365$	−7.16730	−0.375154
$366$	−1.23760	−0.0646904
$367$	8.05666	0.420554	0.210277	−	0.977642i	$-0.432563\pi$
$367$	8.05666	0.420554	0.210277	+	0.977642i	$0.432563\pi$
$368$	−22.3546	−1.16531
$369$	22.4334	1.16784
$370$	15.8127	0.822061
$371$	0	0
$372$	8.57552	0.444620
$373$	−25.8700	−1.33950	−0.669748	−	0.742589i	$-0.733598\pi$
$373$	−25.8700	−1.33950	−0.669748	+	0.742589i	$0.733598\pi$
$374$	−6.15283	−0.318155
$375$	−0.514916	−0.0265902
$376$	−50.6304	−2.61106
$377$	3.81172	0.196314
$378$	0	0
$379$	−14.7314	−0.756702	−0.378351	−	0.925662i	$-0.623509\pi$
$379$	−14.7314	−0.756702	−0.378351	+	0.925662i	$0.623509\pi$
$380$	21.0606	1.08039
$381$	7.40384	0.379310
$382$	53.6049	2.74266
$383$	11.2644	0.575585	0.287793	−	0.957693i	$-0.407079\pi$
$383$	11.2644	0.575585	0.287793	+	0.957693i	$0.407079\pi$
$384$	3.64448	0.185981
$385$	0	0
$386$	13.4781	0.686018
$387$	−25.0446	−1.27309
$388$	32.5586	1.65291
$389$	8.73521	0.442893	0.221446	−	0.975173i	$-0.428922\pi$
$389$	8.73521	0.442893	0.221446	+	0.975173i	$0.428922\pi$
$390$	2.61370	0.132350
$391$	−6.48325	−0.327872
$392$	0	0
$393$	11.2070	0.565319
$394$	69.2991	3.49124
$395$	0.820230	0.0412703
$396$	−12.6841	−0.637398
$397$	−30.6716	−1.53936	−0.769681	−	0.638428i	$-0.779585\pi$
$397$	−30.6716	−1.53936	−0.769681	+	0.638428i	$0.779585\pi$
$398$	70.7002	3.54388
$399$	0	0
$400$	8.23442	0.411721
$401$	−3.35770	−0.167676	−0.0838379	−	0.996479i	$-0.526718\pi$
$401$	−3.35770	−0.167676	−0.0838379	+	0.996479i	$0.526718\pi$
$402$	15.3319	0.764683
$403$	7.07465	0.352413
$404$	−76.9641	−3.82911
$405$	−6.68405	−0.332133
$406$	0	0
$407$	6.13747	0.304223
$408$	−8.35741	−0.413754
$409$	0.881907	0.0436075	0.0218037	−	0.999762i	$-0.493059\pi$
$409$	0.881907	0.0436075	0.0218037	+	0.999762i	$0.493059\pi$
$410$	−21.1337	−1.04372
$411$	6.27448	0.309497
$412$	−74.4356	−3.66718
$413$	0	0
$414$	−19.1287	−0.940123
$415$	−9.83688	−0.482874
$416$	−15.0177	−0.736304
$417$	−6.50795	−0.318696
$418$	11.6994	0.572237
$419$	−16.8636	−0.823843	−0.411921	−	0.911219i	$-0.635142\pi$
$419$	−16.8636	−0.823843	−0.411921	+	0.911219i	$0.635142\pi$
$420$	0	0
$421$	−38.1275	−1.85822	−0.929111	−	0.369801i	$-0.879426\pi$
$421$	−38.1275	−1.85822	−0.929111	+	0.369801i	$0.879426\pi$
$422$	28.8304	1.40344
$423$	−20.3737	−0.990604
$424$	83.4691	4.05362
$425$	2.38814	0.115842
$426$	16.5620	0.802431
$427$	0	0
$428$	−25.1415	−1.21526
$429$	1.01447	0.0489791
$430$	23.5937	1.13779
$431$	−0.392264	−0.0188947	−0.00944734	−	0.999955i	$-0.503007\pi$
$431$	−0.392264	−0.0188947	−0.00944734	+	0.999955i	$0.503007\pi$
$432$	−24.3160	−1.16990
$433$	6.86253	0.329792	0.164896	−	0.986311i	$-0.447271\pi$
$433$	6.86253	0.329792	0.164896	+	0.986311i	$0.447271\pi$
$434$	0	0
$435$	−0.996218	−0.0477650
$436$	−12.0481	−0.576999
$437$	12.3277	0.589714
$438$	−9.50841	−0.454329
$439$	1.53306	0.0731688	0.0365844	−	0.999331i	$-0.488352\pi$
$439$	1.53306	0.0731688	0.0365844	+	0.999331i	$0.488352\pi$
$440$	6.79636	0.324004
$441$	0	0
$442$	−12.1221	−0.576590
$443$	−16.7484	−0.795743	−0.397871	−	0.917441i	$-0.630251\pi$
$443$	−16.7484	−0.795743	−0.397871	+	0.917441i	$0.630251\pi$
$444$	14.6571	0.695596
$445$	10.5996	0.502468
$446$	44.0546	2.08605
$447$	−2.14816	−0.101604
$448$	0	0
$449$	11.8164	0.557653	0.278826	−	0.960342i	$-0.410055\pi$
$449$	11.8164	0.557653	0.278826	+	0.960342i	$0.410055\pi$
$450$	7.04614	0.332158
$451$	−8.20275	−0.386252
$452$	−59.8432	−2.81479
$453$	2.44904	0.115066
$454$	−9.09044	−0.426636
$455$	0	0
$456$	15.8914	0.744181
$457$	−17.8451	−0.834759	−0.417380	−	0.908732i	$-0.637051\pi$
$457$	−17.8451	−0.834759	−0.417380	+	0.908732i	$0.637051\pi$
$458$	34.1249	1.59455
$459$	−7.05210	−0.329164
$460$	12.5909	0.587053
$461$	15.5475	0.724121	0.362060	−	0.932155i	$-0.382073\pi$
$461$	15.5475	0.724121	0.362060	+	0.932155i	$0.382073\pi$
$462$	0	0
$463$	−10.2066	−0.474340	−0.237170	−	0.971468i	$-0.576220\pi$
$463$	−10.2066	−0.474340	−0.237170	+	0.971468i	$0.576220\pi$
$464$	15.9313	0.739591
$465$	−1.84900	−0.0857455
$466$	31.7441	1.47052
$467$	−3.69434	−0.170954	−0.0854768	−	0.996340i	$-0.527241\pi$
$467$	−3.69434	−0.170954	−0.0854768	+	0.996340i	$0.527241\pi$
$468$	−24.9897	−1.15515
$469$	0	0
$470$	19.1934	0.885323
$471$	8.35936	0.385179
$472$	12.6399	0.581799
$473$	9.15756	0.421065
$474$	1.08815	0.0499803
$475$	−4.54097	−0.208354
$476$	0	0
$477$	33.5880	1.53789
$478$	−40.5792	−1.85605
$479$	−12.7795	−0.583911	−0.291955	−	0.956432i	$-0.594306\pi$
$479$	−12.7795	−0.583911	−0.291955	+	0.956432i	$0.594306\pi$
$480$	3.92497	0.179150
$481$	12.0918	0.551341
$482$	−41.4654	−1.88870
$483$	0	0
$484$	4.63791	0.210814
$485$	−7.02009	−0.318766
$486$	−31.6916	−1.43756
$487$	−19.2129	−0.870619	−0.435310	−	0.900281i	$-0.643361\pi$
$487$	−19.2129	−0.870619	−0.435310	+	0.900281i	$0.643361\pi$
$488$	−6.34022	−0.287008
$489$	1.45172	0.0656492
$490$	0	0
$491$	13.0183	0.587508	0.293754	−	0.955881i	$-0.405095\pi$
$491$	13.0183	0.587508	0.293754	+	0.955881i	$0.405095\pi$
$492$	−19.5893	−0.883153
$493$	4.62037	0.208091
$494$	23.0498	1.03706
$495$	2.73486	0.122923
$496$	29.5689	1.32768
$497$	0	0
$498$	−13.0500	−0.584783
$499$	−20.2863	−0.908141	−0.454071	−	0.890966i	$-0.650029\pi$
$499$	−20.2863	−0.908141	−0.454071	+	0.890966i	$0.650029\pi$
$500$	−4.63791	−0.207414
$501$	5.45053	0.243512
$502$	−54.6797	−2.44048
$503$	−20.6614	−0.921247	−0.460624	−	0.887596i	$-0.652374\pi$
$503$	−20.6614	−0.921247	−0.460624	+	0.887596i	$0.652374\pi$
$504$	0	0
$505$	16.5946	0.738448
$506$	6.99438	0.310938
$507$	−4.69523	−0.208523
$508$	66.6873	2.95877
$509$	11.7884	0.522510	0.261255	−	0.965270i	$-0.415864\pi$
$509$	11.7884	0.522510	0.261255	+	0.965270i	$0.415864\pi$
$510$	3.16819	0.140290
$511$	0	0
$512$	49.1608	2.17262
$513$	13.4093	0.592037
$514$	−1.52709	−0.0673572
$515$	16.0494	0.707220
$516$	21.8695	0.962751
$517$	7.44964	0.327635
$518$	0	0
$519$	−8.34159	−0.366155
$520$	13.3900	0.587189
$521$	27.6989	1.21351	0.606755	−	0.794889i	$-0.292471\pi$
$521$	27.6989	1.21351	0.606755	+	0.794889i	$0.292471\pi$
$522$	13.6323	0.596669
$523$	−21.6669	−0.947425	−0.473713	−	0.880679i	$-0.657086\pi$
$523$	−21.6669	−0.947425	−0.473713	+	0.880679i	$0.657086\pi$
$524$	100.943	4.40972
$525$	0	0
$526$	28.9547	1.26249
$527$	8.57552	0.373556
$528$	4.24003	0.184524
$529$	−15.6300	−0.679565
$530$	−31.6421	−1.37444
$531$	5.08631	0.220727
$532$	0	0
$533$	−16.1608	−0.700002
$534$	14.0618	0.608513
$535$	5.42086	0.234364
$536$	78.5450	3.39263
$537$	−13.0166	−0.561708
$538$	9.93199	0.428199
$539$	0	0
$540$	13.6956	0.589366
$541$	33.2488	1.42948	0.714738	−	0.699392i	$-0.246546\pi$
$541$	33.2488	1.42948	0.714738	+	0.699392i	$0.246546\pi$
$542$	−29.8426	−1.28185
$543$	12.3061	0.528107
$544$	−18.2037	−0.780477
$545$	2.59774	0.111275
$546$	0	0
$547$	8.82697	0.377414	0.188707	−	0.982033i	$-0.439570\pi$
$547$	8.82697	0.377414	0.188707	+	0.982033i	$0.439570\pi$
$548$	56.5150	2.41420
$549$	−2.55131	−0.108887
$550$	−2.57641	−0.109859
$551$	−8.78549	−0.374275
$552$	9.50050	0.404368
$553$	0	0
$554$	−10.1350	−0.430596
$555$	−3.16028	−0.134146
$556$	−58.6179	−2.48595
$557$	−3.96042	−0.167809	−0.0839043	−	0.996474i	$-0.526739\pi$
$557$	−3.96042	−0.167809	−0.0839043	+	0.996474i	$0.526739\pi$
$558$	25.3019	1.07111
$559$	18.0419	0.763092
$560$	0	0
$561$	1.22969	0.0519175
$562$	58.2575	2.45745
$563$	−28.6872	−1.20902	−0.604510	−	0.796597i	$-0.706631\pi$
$563$	−28.6872	−1.20902	−0.604510	+	0.796597i	$0.706631\pi$
$564$	17.7907	0.749125
$565$	12.9031	0.542835
$566$	−33.2673	−1.39833
$567$	0	0
$568$	84.8471	3.56010
$569$	5.35724	0.224587	0.112294	−	0.993675i	$-0.464180\pi$
$569$	5.35724	0.224587	0.112294	+	0.993675i	$0.464180\pi$
$570$	−6.02422	−0.252327
$571$	12.0942	0.506125	0.253063	−	0.967450i	$-0.418562\pi$
$571$	12.0942	0.506125	0.253063	+	0.967450i	$0.418562\pi$
$572$	9.13747	0.382057
$573$	−10.7133	−0.447556
$574$	0	0
$575$	−2.71477	−0.113214
$576$	−8.66958	−0.361233
$577$	−13.3430	−0.555476	−0.277738	−	0.960657i	$-0.589585\pi$
$577$	−13.3430	−0.555476	−0.277738	+	0.960657i	$0.589585\pi$
$578$	29.1053	1.21062
$579$	−2.69370	−0.111947
$580$	−8.97306	−0.372586
$581$	0	0
$582$	−9.31311	−0.386041
$583$	−12.2814	−0.508645
$584$	−48.7116	−2.01570
$585$	5.38814	0.222772
$586$	−24.5469	−1.01402
$587$	2.31418	0.0955164	0.0477582	−	0.998859i	$-0.484792\pi$
$587$	2.31418	0.0955164	0.0477582	+	0.998859i	$0.484792\pi$
$588$	0	0
$589$	−16.3061	−0.671881
$590$	−4.79163	−0.197268
$591$	−13.8499	−0.569711
$592$	50.5385	2.07712
$593$	32.4544	1.33274	0.666370	−	0.745621i	$-0.267847\pi$
$593$	32.4544	1.33274	0.666370	+	0.745621i	$0.267847\pi$
$594$	7.60808	0.312163
$595$	0	0
$596$	−19.3487	−0.792555
$597$	−14.1300	−0.578301
$598$	13.7801	0.563511
$599$	−6.45447	−0.263723	−0.131861	−	0.991268i	$-0.542095\pi$
$599$	−6.45447	−0.263723	−0.131861	+	0.991268i	$0.542095\pi$
$600$	−3.49956	−0.142869
$601$	10.1597	0.414422	0.207211	−	0.978296i	$-0.433561\pi$
$601$	10.1597	0.414422	0.207211	+	0.978296i	$0.433561\pi$
$602$	0	0
$603$	31.6066	1.28712
$604$	22.0588	0.897559
$605$	−1.00000	−0.0406558
$606$	22.0150	0.894297
$607$	−23.6158	−0.958535	−0.479268	−	0.877669i	$-0.659098\pi$
$607$	−23.6158	−0.958535	−0.479268	+	0.877669i	$0.659098\pi$
$608$	34.6138	1.40377
$609$	0	0
$610$	2.40350	0.0973148
$611$	14.6770	0.593769
$612$	−30.2912	−1.22445
$613$	−5.50182	−0.222216	−0.111108	−	0.993808i	$-0.535440\pi$
$613$	−5.50182	−0.222216	−0.111108	+	0.993808i	$0.535440\pi$
$614$	68.2516	2.75441
$615$	4.22373	0.170317
$616$	0	0
$617$	32.6648	1.31504	0.657518	−	0.753439i	$-0.271606\pi$
$617$	32.6648	1.31504	0.657518	+	0.753439i	$0.271606\pi$
$618$	21.2917	0.856478
$619$	23.3985	0.940467	0.470233	−	0.882542i	$-0.344170\pi$
$619$	23.3985	0.940467	0.470233	+	0.882542i	$0.344170\pi$
$620$	−16.6542	−0.668850
$621$	8.01665	0.321697
$622$	59.6478	2.39166
$623$	0	0
$624$	8.35358	0.334411
$625$	1.00000	0.0400000
$626$	67.8470	2.71171
$627$	−2.33822	−0.0933794
$628$	75.2938	3.00455
$629$	14.6571	0.584417
$630$	0	0
$631$	−5.72328	−0.227840	−0.113920	−	0.993490i	$-0.536341\pi$
$631$	−5.72328	−0.227840	−0.113920	+	0.993490i	$0.536341\pi$
$632$	5.57458	0.221745
$633$	−5.76197	−0.229018
$634$	46.8657	1.86128
$635$	−14.3787	−0.570603
$636$	−29.3298	−1.16300
$637$	0	0
$638$	−4.98464	−0.197344
$639$	34.1425	1.35066
$640$	−7.07780	−0.279775
$641$	−20.7898	−0.821148	−0.410574	−	0.911827i	$-0.634672\pi$
$641$	−20.7898	−0.821148	−0.410574	+	0.911827i	$0.634672\pi$
$642$	7.19152	0.283827
$643$	29.4788	1.16253	0.581264	−	0.813715i	$-0.302558\pi$
$643$	29.4788	1.16253	0.581264	+	0.813715i	$0.302558\pi$
$644$	0	0
$645$	−4.71537	−0.185668
$646$	27.9398	1.09928
$647$	−25.0059	−0.983084	−0.491542	−	0.870854i	$-0.663566\pi$
$647$	−25.0059	−0.983084	−0.491542	+	0.870854i	$0.663566\pi$
$648$	−45.4272	−1.78455
$649$	−1.85981	−0.0730038
$650$	−5.07597	−0.199096
$651$	0	0
$652$	13.0759	0.512090
$653$	21.9772	0.860036	0.430018	−	0.902820i	$-0.358507\pi$
$653$	21.9772	0.860036	0.430018	+	0.902820i	$0.358507\pi$
$654$	3.44626	0.134759
$655$	−21.7647	−0.850419
$656$	−67.5449	−2.63718
$657$	−19.6016	−0.764730
$658$	0	0
$659$	27.4501	1.06931	0.534653	−	0.845072i	$-0.320442\pi$
$659$	27.4501	1.06931	0.534653	+	0.845072i	$0.320442\pi$
$660$	−2.38814	−0.0929581
$661$	33.1375	1.28890	0.644449	−	0.764647i	$-0.277087\pi$
$661$	33.1375	1.28890	0.644449	+	0.764647i	$0.277087\pi$
$662$	41.6453	1.61859
$663$	2.42270	0.0940897
$664$	−66.8550	−2.59448
$665$	0	0
$666$	43.2455	1.67573
$667$	−5.25232	−0.203371
$668$	49.0936	1.89949
$669$	−8.80464	−0.340407
$670$	−29.7754	−1.15033
$671$	0.932884	0.0360136
$672$	0	0
$673$	−34.7534	−1.33965	−0.669823	−	0.742521i	$-0.733630\pi$
$673$	−34.7534	−1.33965	−0.669823	+	0.742521i	$0.733630\pi$
$674$	−28.5372	−1.09921
$675$	−2.95297	−0.113660
$676$	−42.2905	−1.62656
$677$	11.3280	0.435372	0.217686	−	0.976019i	$-0.430149\pi$
$677$	11.3280	0.435372	0.217686	+	0.976019i	$0.430149\pi$
$678$	17.1177	0.657400
$679$	0	0
$680$	16.2306	0.622416
$681$	1.81679	0.0696197
$682$	−9.25161	−0.354263
$683$	41.9199	1.60402	0.802011	−	0.597309i	$-0.203764\pi$
$683$	41.9199	1.60402	0.802011	+	0.597309i	$0.203764\pi$
$684$	57.5978	2.20231
$685$	−12.1854	−0.465582
$686$	0	0
$687$	−6.82012	−0.260204
$688$	75.4071	2.87487
$689$	−24.1965	−0.921814
$690$	−3.60152	−0.137108
$691$	−8.11709	−0.308789	−0.154394	−	0.988009i	$-0.549343\pi$
$691$	−8.11709	−0.308789	−0.154394	+	0.988009i	$0.549343\pi$
$692$	−75.1338	−2.85616
$693$	0	0
$694$	38.2641	1.45249
$695$	12.6389	0.479419
$696$	−6.77066	−0.256641
$697$	−19.5893	−0.741997
$698$	−0.460869	−0.0174441
$699$	−6.34429	−0.239963
$700$	0	0
$701$	−18.0131	−0.680347	−0.340174	−	0.940363i	$-0.610486\pi$
$701$	−18.0131	−0.680347	−0.340174	+	0.940363i	$0.610486\pi$
$702$	14.9892	0.565731
$703$	−27.8700	−1.05114
$704$	3.17003	0.119475
$705$	−3.83594	−0.144470
$706$	−71.0810	−2.67517
$707$	0	0
$708$	−4.44147	−0.166921
$709$	−7.01147	−0.263321	−0.131661	−	0.991295i	$-0.542031\pi$
$709$	−7.01147	−0.263321	−0.131661	+	0.991295i	$0.542031\pi$
$710$	−32.1645	−1.20711
$711$	2.24322	0.0841272
$712$	72.0385	2.69976
$713$	−9.74844	−0.365082
$714$	0	0
$715$	−1.97017	−0.0736801
$716$	−117.242	−4.38154
$717$	8.11007	0.302876
$718$	−21.0796	−0.786685
$719$	23.0812	0.860782	0.430391	−	0.902643i	$-0.358376\pi$
$719$	23.0812	0.860782	0.430391	+	0.902643i	$0.358376\pi$
$720$	22.5200	0.839270
$721$	0	0
$722$	−4.17475	−0.155368
$723$	8.28717	0.308203
$724$	110.843	4.11945
$725$	1.93472	0.0718537
$726$	−1.32664	−0.0492361
$727$	43.1087	1.59881	0.799407	−	0.600789i	$-0.205147\pi$
$727$	43.1087	1.59881	0.799407	+	0.600789i	$0.205147\pi$
$728$	0	0
$729$	−13.7184	−0.508087
$730$	18.4659	0.683455
$731$	21.8695	0.808872
$732$	2.22786	0.0823439
$733$	12.4279	0.459034	0.229517	−	0.973305i	$-0.426285\pi$
$733$	12.4279	0.459034	0.229517	+	0.973305i	$0.426285\pi$
$734$	−20.7573	−0.766166
$735$	0	0
$736$	20.6935	0.762773
$737$	−11.5569	−0.425705
$738$	−57.7977	−2.12756
$739$	−4.33349	−0.159410	−0.0797050	−	0.996818i	$-0.525398\pi$
$739$	−4.33349	−0.159410	−0.0797050	+	0.996818i	$0.525398\pi$
$740$	−28.4651	−1.04640
$741$	−4.60668	−0.169231
$742$	0	0
$743$	12.0397	0.441695	0.220848	−	0.975308i	$-0.429118\pi$
$743$	12.0397	0.441695	0.220848	+	0.975308i	$0.429118\pi$
$744$	−12.5665	−0.460710
$745$	4.17186	0.152845
$746$	66.6517	2.44029
$747$	−26.9025	−0.984311
$748$	11.0760	0.404978
$749$	0	0
$750$	1.32664	0.0484419
$751$	31.0800	1.13413	0.567063	−	0.823674i	$-0.308079\pi$
$751$	31.0800	1.13413	0.567063	+	0.823674i	$0.308079\pi$
$752$	61.3434	2.23696
$753$	10.9282	0.398244
$754$	−9.82058	−0.357644
$755$	−4.75618	−0.173095
$756$	0	0
$757$	11.6643	0.423947	0.211973	−	0.977275i	$-0.432011\pi$
$757$	11.6643	0.423947	0.211973	+	0.977275i	$0.432011\pi$
$758$	37.9543	1.37856
$759$	−1.39788	−0.0507398
$760$	−30.8620	−1.11948
$761$	29.4234	1.06660	0.533299	−	0.845927i	$-0.320952\pi$
$761$	29.4234	1.06660	0.533299	+	0.845927i	$0.320952\pi$
$762$	−19.0754	−0.691028
$763$	0	0
$764$	−96.4964	−3.49112
$765$	6.53122	0.236137
$766$	−29.0218	−1.04860
$767$	−3.66413	−0.132304
$768$	−12.6543	−0.456622
$769$	14.5119	0.523314	0.261657	−	0.965161i	$-0.415731\pi$
$769$	14.5119	0.523314	0.261657	+	0.965161i	$0.415731\pi$
$770$	0	0
$771$	0.305201	0.0109916
$772$	−24.2625	−0.873228
$773$	−10.6952	−0.384679	−0.192339	−	0.981328i	$-0.561607\pi$
$773$	−10.6952	−0.384679	−0.192339	+	0.981328i	$0.561607\pi$
$774$	64.5254	2.31932
$775$	3.59089	0.128988
$776$	−47.7110	−1.71273
$777$	0	0
$778$	−22.5055	−0.806862
$779$	37.2484	1.33456
$780$	−4.70503	−0.168467
$781$	−12.4842	−0.446720
$782$	16.7035	0.597317
$783$	−5.71317	−0.204172
$784$	0	0
$785$	−16.2344	−0.579431
$786$	−28.8739	−1.02990
$787$	−1.92200	−0.0685118	−0.0342559	−	0.999413i	$-0.510906\pi$
$787$	−1.92200	−0.0685118	−0.0342559	+	0.999413i	$0.510906\pi$
$788$	−124.748	−4.44397
$789$	−5.78682	−0.206016
$790$	−2.11325	−0.0751862
$791$	0	0
$792$	18.5871	0.660464
$793$	1.83794	0.0652671
$794$	79.0227	2.80441
$795$	6.32391	0.224286
$796$	−127.270	−4.51098
$797$	41.0591	1.45439	0.727193	−	0.686433i	$-0.240824\pi$
$797$	41.0591	1.45439	0.727193	+	0.686433i	$0.240824\pi$
$798$	0	0
$799$	17.7907	0.629391
$800$	−7.62255	−0.269498
$801$	28.9884	1.02425
$802$	8.65084	0.305472
$803$	7.16730	0.252929
$804$	−27.5995	−0.973360
$805$	0	0
$806$	−18.2272	−0.642027
$807$	−1.98498	−0.0698748
$808$	112.783	3.96768
$809$	−28.1550	−0.989877	−0.494939	−	0.868928i	$-0.664809\pi$
$809$	−28.1550	−0.989877	−0.494939	+	0.868928i	$0.664809\pi$
$810$	17.2209	0.605080
$811$	−11.4271	−0.401261	−0.200631	−	0.979667i	$-0.564299\pi$
$811$	−11.4271	−0.401261	−0.200631	+	0.979667i	$0.564299\pi$
$812$	0	0
$813$	5.96426	0.209176
$814$	−15.8127	−0.554234
$815$	−2.81934	−0.0987572
$816$	10.1258	0.354473
$817$	−41.5842	−1.45485
$818$	−2.27216	−0.0794441
$819$	0	0
$820$	38.0436	1.32854
$821$	−26.9284	−0.939808	−0.469904	−	0.882718i	$-0.655711\pi$
$821$	−26.9284	−0.939808	−0.469904	+	0.882718i	$0.655711\pi$
$822$	−16.1657	−0.563842
$823$	28.9038	1.00752	0.503761	−	0.863843i	$-0.331949\pi$
$823$	28.9038	1.00752	0.503761	+	0.863843i	$0.331949\pi$
$824$	109.077	3.79989
$825$	0.514916	0.0179271
$826$	0	0
$827$	46.7846	1.62686	0.813430	−	0.581663i	$-0.197598\pi$
$827$	46.7846	1.62686	0.813430	+	0.581663i	$0.197598\pi$
$828$	34.4343	1.19668
$829$	19.7505	0.685962	0.342981	−	0.939342i	$-0.388563\pi$
$829$	19.7505	0.685962	0.342981	+	0.939342i	$0.388563\pi$
$830$	25.3439	0.879699
$831$	2.02556	0.0702660
$832$	6.24548	0.216523
$833$	0	0
$834$	16.7672	0.580600
$835$	−10.5853	−0.366318
$836$	−21.0606	−0.728396
$837$	−10.6038	−0.366520
$838$	43.4477	1.50088
$839$	26.0530	0.899449	0.449725	−	0.893167i	$-0.351522\pi$
$839$	26.0530	0.899449	0.449725	+	0.893167i	$0.351522\pi$
$840$	0	0
$841$	−25.2569	−0.870926
$842$	98.2323	3.38531
$843$	−11.6432	−0.401014
$844$	−51.8988	−1.78643
$845$	9.11844	0.313684
$846$	52.4912	1.80468
$847$	0	0
$848$	−101.131	−3.47284
$849$	6.64873	0.228184
$850$	−6.15283	−0.211040
$851$	−16.6618	−0.571160
$852$	−29.8140	−1.02141
$853$	−9.81496	−0.336058	−0.168029	−	0.985782i	$-0.553740\pi$
$853$	−9.81496	−0.336058	−0.168029	+	0.985782i	$0.553740\pi$
$854$	0	0
$855$	−12.4189	−0.424718
$856$	36.8421	1.25924
$857$	−31.6507	−1.08117	−0.540583	−	0.841291i	$-0.681796\pi$
$857$	−31.6507	−1.08117	−0.540583	+	0.841291i	$0.681796\pi$
$858$	−2.61370	−0.0892302
$859$	−12.6556	−0.431804	−0.215902	−	0.976415i	$-0.569269\pi$
$859$	−12.6556	−0.431804	−0.215902	+	0.976415i	$0.569269\pi$
$860$	−42.4720	−1.44828
$861$	0	0
$862$	1.01063	0.0344223
$863$	22.1303	0.753325	0.376663	−	0.926350i	$-0.377072\pi$
$863$	22.1303	0.753325	0.376663	+	0.926350i	$0.377072\pi$
$864$	22.5092	0.765778
$865$	16.1999	0.550814
$866$	−17.6807	−0.600816
$867$	−5.81691	−0.197552
$868$	0	0
$869$	−0.820230	−0.0278244
$870$	2.56667	0.0870183
$871$	−22.7691	−0.771501
$872$	17.6552	0.597879
$873$	−19.1990	−0.649787
$874$	−31.7613	−1.07434
$875$	0	0
$876$	17.1165	0.578313
$877$	−33.7159	−1.13850	−0.569252	−	0.822163i	$-0.692767\pi$
$877$	−33.7159	−1.13850	−0.569252	+	0.822163i	$0.692767\pi$
$878$	−3.94979	−0.133299
$879$	4.90589	0.165472
$880$	−8.23442	−0.277582
$881$	12.1303	0.408679	0.204340	−	0.978900i	$-0.434495\pi$
$881$	12.1303	0.408679	0.204340	+	0.978900i	$0.434495\pi$
$882$	0	0
$883$	57.1051	1.92174	0.960871	−	0.276998i	$-0.0893395\pi$
$883$	57.1051	1.92174	0.960871	+	0.276998i	$0.0893395\pi$
$884$	21.8215	0.733937
$885$	0.957644	0.0321909
$886$	43.1509	1.44968
$887$	4.85384	0.162976	0.0814881	−	0.996674i	$-0.474033\pi$
$887$	4.85384	0.162976	0.0814881	+	0.996674i	$0.474033\pi$
$888$	−21.4784	−0.720768
$889$	0	0
$890$	−27.3089	−0.915396
$891$	6.68405	0.223924
$892$	−79.3045	−2.65531
$893$	−33.8285	−1.13203
$894$	5.53455	0.185103
$895$	25.2791	0.844986
$896$	0	0
$897$	−2.75406	−0.0919554
$898$	−30.4441	−1.01593
$899$	6.94736	0.231707
$900$	−12.6841	−0.422802
$901$	−29.3298	−0.977116
$902$	21.1337	0.703675
$903$	0	0
$904$	87.6938	2.91665
$905$	−23.8993	−0.794440
$906$	−6.30973	−0.209627
$907$	−25.9592	−0.861960	−0.430980	−	0.902361i	$-0.641832\pi$
$907$	−25.9592	−0.861960	−0.430980	+	0.902361i	$0.641832\pi$
$908$	16.3641	0.543061
$909$	45.3838	1.50529
$910$	0	0
$911$	−12.9871	−0.430283	−0.215142	−	0.976583i	$-0.569021\pi$
$911$	−12.9871	−0.430283	−0.215142	+	0.976583i	$0.569021\pi$
$912$	−19.2538	−0.637559
$913$	9.83688	0.325553
$914$	45.9764	1.52076
$915$	−0.480357	−0.0158801
$916$	−61.4297	−2.02969
$917$	0	0
$918$	18.1691	0.599671
$919$	7.29768	0.240728	0.120364	−	0.992730i	$-0.461594\pi$
$919$	7.29768	0.240728	0.120364	+	0.992730i	$0.461594\pi$
$920$	−18.4506	−0.608298
$921$	−13.6406	−0.449473
$922$	−40.0569	−1.31920
$923$	−24.5960	−0.809586
$924$	0	0
$925$	6.13747	0.201799
$926$	26.2964	0.864153
$927$	43.8928	1.44163
$928$	−14.7475	−0.484110
$929$	−36.3960	−1.19411	−0.597057	−	0.802199i	$-0.703663\pi$
$929$	−36.3960	−1.19411	−0.597057	+	0.802199i	$0.703663\pi$
$930$	4.76380	0.156211
$931$	0	0
$932$	−57.1438	−1.87181
$933$	−11.9211	−0.390278
$934$	9.51815	0.311444
$935$	−2.38814	−0.0781004
$936$	36.6197	1.19695
$937$	−47.8115	−1.56193	−0.780966	−	0.624573i	$-0.785273\pi$
$937$	−47.8115	−1.56193	−0.780966	+	0.624573i	$0.785273\pi$
$938$	0	0
$939$	−13.5597	−0.442505
$940$	−34.5508	−1.12692
$941$	−9.99129	−0.325707	−0.162853	−	0.986650i	$-0.552070\pi$
$941$	−9.99129	−0.325707	−0.162853	+	0.986650i	$0.552070\pi$
$942$	−21.5372	−0.701719
$943$	22.2686	0.725166
$944$	−15.3144	−0.498442
$945$	0	0
$946$	−23.5937	−0.767096
$947$	49.2374	1.60000	0.800001	−	0.599999i	$-0.204832\pi$
$947$	49.2374	1.60000	0.800001	+	0.599999i	$0.204832\pi$
$948$	−1.95882	−0.0636196
$949$	14.1208	0.458380
$950$	11.6994	0.379579
$951$	−9.36647	−0.303729
$952$	0	0
$953$	−27.0740	−0.877012	−0.438506	−	0.898728i	$-0.644492\pi$
$953$	−27.0740	−0.877012	−0.438506	+	0.898728i	$0.644492\pi$
$954$	−86.5367	−2.80173
$955$	20.8060	0.673266
$956$	73.0484	2.36255
$957$	0.996218	0.0322032
$958$	32.9253	1.06377
$959$	0	0
$960$	−1.63230	−0.0526822
$961$	−18.1055	−0.584050
$962$	−31.1536	−1.00443
$963$	14.8253	0.477739
$964$	74.6436	2.40411
$965$	5.23135	0.168403
$966$	0	0
$967$	43.2201	1.38987	0.694933	−	0.719075i	$-0.255434\pi$
$967$	43.2201	1.38987	0.694933	+	0.719075i	$0.255434\pi$
$968$	−6.79636	−0.218443
$969$	−5.58398	−0.179383
$970$	18.0867	0.580728
$971$	16.4908	0.529214	0.264607	−	0.964356i	$-0.414758\pi$
$971$	16.4908	0.529214	0.264607	+	0.964356i	$0.414758\pi$
$972$	57.0493	1.82986
$973$	0	0
$974$	49.5004	1.58609
$975$	1.01447	0.0324891
$976$	7.68176	0.245887
$977$	30.9590	0.990466	0.495233	−	0.868760i	$-0.335083\pi$
$977$	30.9590	0.990466	0.495233	+	0.868760i	$0.335083\pi$
$978$	−3.74024	−0.119600
$979$	−10.5996	−0.338764
$980$	0	0
$981$	7.10445	0.226828
$982$	−33.5406	−1.07032
$983$	−17.8492	−0.569300	−0.284650	−	0.958632i	$-0.591877\pi$
$983$	−17.8492	−0.569300	−0.284650	+	0.958632i	$0.591877\pi$
$984$	28.7060	0.915113
$985$	26.8975	0.857025
$986$	−11.9040	−0.379100
$987$	0	0
$988$	−41.4929	−1.32007
$989$	−24.8607	−0.790524
$990$	−7.04614	−0.223941
$991$	49.8641	1.58399	0.791993	−	0.610530i	$-0.209044\pi$
$991$	49.8641	1.58399	0.791993	+	0.610530i	$0.209044\pi$
$992$	−27.3717	−0.869053
$993$	−8.32314	−0.264127
$994$	0	0
$995$	27.4413	0.869947
$996$	23.4918	0.744367
$997$	−16.4334	−0.520451	−0.260225	−	0.965548i	$-0.583797\pi$
$997$	−16.4334	−0.520451	−0.260225	+	0.965548i	$0.583797\pi$
$998$	52.2660	1.65445
$999$	−18.1238	−0.573411

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2695.2.a.k.1.1		4
7.3	odd	6		385.2.i.a.331.4	yes	8
7.5	odd	6		385.2.i.a.221.4	✓	8
7.6	odd	2		2695.2.a.j.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.i.a.221.4	✓	8	7.5	odd	6
385.2.i.a.331.4	yes	8	7.3	odd	6
2695.2.a.j.1.1		4	7.6	odd	2
2695.2.a.k.1.1		4	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:	\( N \)	\(=\)	\( 2695 = 5 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2695.a (trivial)

\(f(q)\)	\(=\)	\(q-2.57641 q^{2} +0.514916 q^{3} +4.63791 q^{4} -1.00000 q^{5} -1.32664 q^{6} -6.79636 q^{8} -2.73486 q^{9} +O(q^{10})\)	\(q-2.57641 q^{2} +0.514916 q^{3} +4.63791 q^{4} -1.00000 q^{5} -1.32664 q^{6} -6.79636 q^{8} -2.73486 q^{9} +2.57641 q^{10} +1.00000 q^{11} +2.38814 q^{12} +1.97017 q^{13} -0.514916 q^{15} +8.23442 q^{16} +2.38814 q^{17} +7.04614 q^{18} -4.54097 q^{19} -4.63791 q^{20} -2.57641 q^{22} -2.71477 q^{23} -3.49956 q^{24} +1.00000 q^{25} -5.07597 q^{26} -2.95297 q^{27} +1.93472 q^{29} +1.32664 q^{30} +3.59089 q^{31} -7.62255 q^{32} +0.514916 q^{33} -6.15283 q^{34} -12.6841 q^{36} +6.13747 q^{37} +11.6994 q^{38} +1.01447 q^{39} +6.79636 q^{40} -8.20275 q^{41} +9.15756 q^{43} +4.63791 q^{44} +2.73486 q^{45} +6.99438 q^{46} +7.44964 q^{47} +4.24003 q^{48} -2.57641 q^{50} +1.22969 q^{51} +9.13747 q^{52} -12.2814 q^{53} +7.60808 q^{54} -1.00000 q^{55} -2.33822 q^{57} -4.98464 q^{58} -1.85981 q^{59} -2.38814 q^{60} +0.932884 q^{61} -9.25161 q^{62} +3.17003 q^{64} -1.97017 q^{65} -1.32664 q^{66} -11.5569 q^{67} +11.0760 q^{68} -1.39788 q^{69} -12.4842 q^{71} +18.5871 q^{72} +7.16730 q^{73} -15.8127 q^{74} +0.514916 q^{75} -21.0606 q^{76} -2.61370 q^{78} -0.820230 q^{79} -8.23442 q^{80} +6.68405 q^{81} +21.1337 q^{82} +9.83688 q^{83} -2.38814 q^{85} -23.5937 q^{86} +0.996218 q^{87} -6.79636 q^{88} -10.5996 q^{89} -7.04614 q^{90} -12.5909 q^{92} +1.84900 q^{93} -19.1934 q^{94} +4.54097 q^{95} -3.92497 q^{96} +7.02009 q^{97} -2.73486 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 4 q^{5} - 7 q^{6} - 9 q^{8} - q^{9}+O(q^{10}) \) 4 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 - 4 * q^5 - 7 * q^6 - 9 * q^8 - q^9	\( 4 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 4 q^{5} - 7 q^{6} - 9 q^{8} - q^{9} + 3 q^{10} + 4 q^{11} + 3 q^{12} + 6 q^{13} - 3 q^{15} + 5 q^{16} + 3 q^{17} + q^{18} + 3 q^{19} - 3 q^{20} - 3 q^{22} - 6 q^{23} + 4 q^{24} + 4 q^{25} + 5 q^{26} - 3 q^{27} - 8 q^{29} + 7 q^{30} - 10 q^{31} + 4 q^{32} + 3 q^{33} - 10 q^{34} - 8 q^{36} - 9 q^{37} + 23 q^{38} - 13 q^{39} + 9 q^{40} - 15 q^{41} - 2 q^{43} + 3 q^{44} + q^{45} + 16 q^{46} + 15 q^{47} + q^{48} - 3 q^{50} + q^{51} + 3 q^{52} - 30 q^{53} + 13 q^{54} - 4 q^{55} - 6 q^{57} - q^{58} - 17 q^{59} - 3 q^{60} - 16 q^{62} + 5 q^{64} - 6 q^{65} - 7 q^{66} - 25 q^{67} + 19 q^{68} - 6 q^{69} - 13 q^{71} + 26 q^{72} - 3 q^{73} - 16 q^{74} + 3 q^{75} - 40 q^{76} - 5 q^{78} - 4 q^{79} - 5 q^{80} - 16 q^{81} + 27 q^{82} - 18 q^{83} - 3 q^{85} - 10 q^{86} - 20 q^{87} - 9 q^{88} - 25 q^{89} - q^{90} - 26 q^{92} + 10 q^{93} - 23 q^{94} - 3 q^{95} + 7 q^{96} + 23 q^{97} - q^{99}+O(q^{100}) \) 4 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 - 4 * q^5 - 7 * q^6 - 9 * q^8 - q^9 + 3 * q^10 + 4 * q^11 + 3 * q^12 + 6 * q^13 - 3 * q^15 + 5 * q^16 + 3 * q^17 + q^18 + 3 * q^19 - 3 * q^20 - 3 * q^22 - 6 * q^23 + 4 * q^24 + 4 * q^25 + 5 * q^26 - 3 * q^27 - 8 * q^29 + 7 * q^30 - 10 * q^31 + 4 * q^32 + 3 * q^33 - 10 * q^34 - 8 * q^36 - 9 * q^37 + 23 * q^38 - 13 * q^39 + 9 * q^40 - 15 * q^41 - 2 * q^43 + 3 * q^44 + q^45 + 16 * q^46 + 15 * q^47 + q^48 - 3 * q^50 + q^51 + 3 * q^52 - 30 * q^53 + 13 * q^54 - 4 * q^55 - 6 * q^57 - q^58 - 17 * q^59 - 3 * q^60 - 16 * q^62 + 5 * q^64 - 6 * q^65 - 7 * q^66 - 25 * q^67 + 19 * q^68 - 6 * q^69 - 13 * q^71 + 26 * q^72 - 3 * q^73 - 16 * q^74 + 3 * q^75 - 40 * q^76 - 5 * q^78 - 4 * q^79 - 5 * q^80 - 16 * q^81 + 27 * q^82 - 18 * q^83 - 3 * q^85 - 10 * q^86 - 20 * q^87 - 9 * q^88 - 25 * q^89 - q^90 - 26 * q^92 + 10 * q^93 - 23 * q^94 - 3 * q^95 + 7 * q^96 + 23 * q^97 - q^99

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