LMFDB - Embedded newform 7595.2.a.s.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:	$1$
Dimension:	$4$
Coefficient field:	4.4.8468.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 5x^{2} + 3x + 4 $ x^4 - x^3 - 5x^2 + 3x + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 155)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.27841$ 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)

$f(q)$	$=$	$q-2.19117 q^{2} -2.27841 q^{3} +2.80122 q^{4} -1.00000 q^{5} +4.99239 q^{6} -1.75561 q^{8} +2.19117 q^{9} +O(q^{10})$	\(q-2.19117 q^{2} -2.27841 q^{3} +2.80122 q^{4} -1.00000 q^{5} +4.99239 q^{6} -1.75561 q^{8} +2.19117 q^{9} +2.19117 q^{10} -4.99239 q^{11} -6.38234 q^{12} -2.43556 q^{13} +2.27841 q^{15} -1.75561 q^{16} -4.71397 q^{17} -4.80122 q^{18} -5.74800 q^{19} -2.80122 q^{20} +10.9392 q^{22} -1.38995 q^{23} +4.00000 q^{24} +1.00000 q^{25} +5.33672 q^{26} +1.84285 q^{27} -5.16688 q^{29} -4.99239 q^{30} +1.00000 q^{31} +7.35805 q^{32} +11.3747 q^{33} +10.3291 q^{34} +6.13794 q^{36} -4.31641 q^{37} +12.5948 q^{38} +5.54922 q^{39} +1.75561 q^{40} +10.0091 q^{41} +2.15715 q^{43} -13.9848 q^{44} -2.19117 q^{45} +3.04561 q^{46} +8.20785 q^{47} +4.00000 q^{48} -2.19117 q^{50} +10.7404 q^{51} -6.82254 q^{52} +13.3921 q^{53} -4.03800 q^{54} +4.99239 q^{55} +13.0963 q^{57} +11.3215 q^{58} -0.672342 q^{59} +6.38234 q^{60} -1.44317 q^{61} -2.19117 q^{62} -12.6115 q^{64} +2.43556 q^{65} -24.9239 q^{66} -14.9772 q^{67} -13.2049 q^{68} +3.16688 q^{69} -2.80883 q^{71} -3.84683 q^{72} -2.85046 q^{73} +9.45799 q^{74} -2.27841 q^{75} -16.1014 q^{76} -12.1593 q^{78} +6.85258 q^{79} +1.75561 q^{80} -10.7723 q^{81} -21.9316 q^{82} +14.5243 q^{83} +4.71397 q^{85} -4.72667 q^{86} +11.7723 q^{87} +8.76467 q^{88} -8.15462 q^{89} +4.80122 q^{90} -3.89355 q^{92} -2.27841 q^{93} -17.9848 q^{94} +5.74800 q^{95} -16.7647 q^{96} +15.7951 q^{97} -10.9392 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} - q^{3} + 5 q^{4} - 4 q^{5} + 4 q^{6} + 3 q^{8} - q^{9}+O(q^{10}) $ 4 * q + q^2 - q^3 + 5 * q^4 - 4 * q^5 + 4 * q^6 + 3 * q^8 - q^9	$ 4 q + q^{2} - q^{3} + 5 q^{4} - 4 q^{5} + 4 q^{6} + 3 q^{8} - q^{9} - q^{10} - 4 q^{11} - 6 q^{12} - 10 q^{13} + q^{15} + 3 q^{16} - 11 q^{17} - 13 q^{18} + 3 q^{19} - 5 q^{20} + 8 q^{22} - 2 q^{23} + 16 q^{24} + 4 q^{25} - 2 q^{26} - q^{27} - 8 q^{29} - 4 q^{30} + 4 q^{31} + 7 q^{32} + 10 q^{33} + 2 q^{34} - 5 q^{36} + 3 q^{37} + 22 q^{38} - 10 q^{39} - 3 q^{40} + 11 q^{41} + 17 q^{43} - 24 q^{44} + q^{45} + 16 q^{46} + 10 q^{47} + 16 q^{48} + q^{50} + q^{51} - 22 q^{52} + 13 q^{53} - 4 q^{54} + 4 q^{55} + 25 q^{57} - 10 q^{58} + 3 q^{59} + 6 q^{60} - 22 q^{61} + q^{62} - 9 q^{64} + 10 q^{65} - 32 q^{66} - 12 q^{67} - 28 q^{68} - 21 q^{71} - 13 q^{72} - 19 q^{73} - 2 q^{74} - q^{75} - 2 q^{76} - 20 q^{78} - 2 q^{79} - 3 q^{80} - 20 q^{81} - 36 q^{82} + 15 q^{83} + 11 q^{85} + 8 q^{86} + 24 q^{87} - 4 q^{88} + 10 q^{89} + 13 q^{90} + 24 q^{92} - q^{93} - 40 q^{94} - 3 q^{95} - 28 q^{96} - 4 q^{97} - 8 q^{99}+O(q^{100}) $ 4 * q + q^2 - q^3 + 5 * q^4 - 4 * q^5 + 4 * q^6 + 3 * q^8 - q^9 - q^10 - 4 * q^11 - 6 * q^12 - 10 * q^13 + q^15 + 3 * q^16 - 11 * q^17 - 13 * q^18 + 3 * q^19 - 5 * q^20 + 8 * q^22 - 2 * q^23 + 16 * q^24 + 4 * q^25 - 2 * q^26 - q^27 - 8 * q^29 - 4 * q^30 + 4 * q^31 + 7 * q^32 + 10 * q^33 + 2 * q^34 - 5 * q^36 + 3 * q^37 + 22 * q^38 - 10 * q^39 - 3 * q^40 + 11 * q^41 + 17 * q^43 - 24 * q^44 + q^45 + 16 * q^46 + 10 * q^47 + 16 * q^48 + q^50 + q^51 - 22 * q^52 + 13 * q^53 - 4 * q^54 + 4 * q^55 + 25 * q^57 - 10 * q^58 + 3 * q^59 + 6 * q^60 - 22 * q^61 + q^62 - 9 * q^64 + 10 * q^65 - 32 * q^66 - 12 * q^67 - 28 * q^68 - 21 * q^71 - 13 * q^72 - 19 * q^73 - 2 * q^74 - q^75 - 2 * q^76 - 20 * q^78 - 2 * q^79 - 3 * q^80 - 20 * q^81 - 36 * q^82 + 15 * q^83 + 11 * q^85 + 8 * q^86 + 24 * q^87 - 4 * q^88 + 10 * q^89 + 13 * q^90 + 24 * q^92 - q^93 - 40 * q^94 - 3 * q^95 - 28 * q^96 - 4 * q^97 - 8 * 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 $

$2$	−2.19117	−1.54939	−0.774695	−	0.632335i	$-0.782097\pi$
$2$	−2.19117	−1.54939	−0.774695	+	0.632335i	$0.782097\pi$
$3$	−2.27841	−1.31544	−0.657721	−	0.753261i	$-0.728480\pi$
$3$	−2.27841	−1.31544	−0.657721	+	0.753261i	$0.728480\pi$
$4$	2.80122	1.40061
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	4.99239	2.03813
$7$	0	0
$7$	0	0
$8$	−1.75561	−0.620701
$9$	2.19117	0.730390
$10$	2.19117	0.692908
$11$	−4.99239	−1.50526	−0.752631	−	0.658443i	$-0.771215\pi$
$11$	−4.99239	−1.50526	−0.752631	+	0.658443i	$0.771215\pi$
$12$	−6.38234	−1.84242
$13$	−2.43556	−0.675503	−0.337752	−	0.941235i	$-0.609666\pi$
$13$	−2.43556	−0.675503	−0.337752	+	0.941235i	$0.609666\pi$
$14$	0	0
$15$	2.27841	0.588284
$16$	−1.75561	−0.438902
$17$	−4.71397	−1.14331	−0.571653	−	0.820495i	$-0.693698\pi$
$17$	−4.71397	−1.14331	−0.571653	+	0.820495i	$0.693698\pi$
$18$	−4.80122	−1.13166
$19$	−5.74800	−1.31868	−0.659340	−	0.751845i	$-0.729164\pi$
$19$	−5.74800	−1.31868	−0.659340	+	0.751845i	$0.729164\pi$
$20$	−2.80122	−0.626372
$21$	0	0
$22$	10.9392	2.33224
$23$	−1.38995	−0.289824	−0.144912	−	0.989445i	$-0.546290\pi$
$23$	−1.38995	−0.289824	−0.144912	+	0.989445i	$0.546290\pi$
$24$	4.00000	0.816497
$25$	1.00000	0.200000
$26$	5.33672	1.04662
$27$	1.84285	0.354657
$28$	0	0
$29$	−5.16688	−0.959465	−0.479733	−	0.877415i	$-0.659266\pi$
$29$	−5.16688	−0.959465	−0.479733	+	0.877415i	$0.659266\pi$
$30$	−4.99239	−0.911481
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	7.35805	1.30073
$33$	11.3747	1.98009
$34$	10.3291	1.77143
$35$	0	0
$36$	6.13794	1.02299
$37$	−4.31641	−0.709614	−0.354807	−	0.934940i	$-0.615453\pi$
$37$	−4.31641	−0.709614	−0.354807	+	0.934940i	$0.615453\pi$
$38$	12.5948	2.04315
$39$	5.54922	0.888586
$40$	1.75561	0.277586
$41$	10.0091	1.56315	0.781577	−	0.623809i	$-0.214416\pi$
$41$	10.0091	1.56315	0.781577	+	0.623809i	$0.214416\pi$
$42$	0	0
$43$	2.15715	0.328962	0.164481	−	0.986380i	$-0.447405\pi$
$43$	2.15715	0.328962	0.164481	+	0.986380i	$0.447405\pi$
$44$	−13.9848	−2.10828
$45$	−2.19117	−0.326640
$46$	3.04561	0.449051
$47$	8.20785	1.19724	0.598619	−	0.801034i	$-0.295716\pi$
$47$	8.20785	1.19724	0.598619	+	0.801034i	$0.295716\pi$
$48$	4.00000	0.577350
$49$	0	0
$50$	−2.19117	−0.309878
$51$	10.7404	1.50395
$52$	−6.82254	−0.946116
$53$	13.3921	1.83954	0.919771	−	0.392455i	$-0.128374\pi$
$53$	13.3921	1.83954	0.919771	+	0.392455i	$0.128374\pi$
$54$	−4.03800	−0.549502
$55$	4.99239	0.673174
$56$	0	0
$57$	13.0963	1.73465
$58$	11.3215	1.48659
$59$	−0.672342	−0.0875315	−0.0437657	−	0.999042i	$-0.513936\pi$
$59$	−0.672342	−0.0875315	−0.0437657	+	0.999042i	$0.513936\pi$
$60$	6.38234	0.823956
$61$	−1.44317	−0.184779	−0.0923897	−	0.995723i	$-0.529451\pi$
$61$	−1.44317	−0.184779	−0.0923897	+	0.995723i	$0.529451\pi$
$62$	−2.19117	−0.278279
$63$	0	0
$64$	−12.6115	−1.57644
$65$	2.43556	0.302094
$66$	−24.9239	−3.06793
$67$	−14.9772	−1.82975	−0.914876	−	0.403735i	$-0.867712\pi$
$67$	−14.9772	−1.82975	−0.914876	+	0.403735i	$0.867712\pi$
$68$	−13.2049	−1.60133
$69$	3.16688	0.381247
$70$	0	0
$71$	−2.80883	−0.333347	−0.166673	−	0.986012i	$-0.553303\pi$
$71$	−2.80883	−0.333347	−0.166673	+	0.986012i	$0.553303\pi$
$72$	−3.84683	−0.453353
$73$	−2.85046	−0.333622	−0.166811	−	0.985989i	$-0.553347\pi$
$73$	−2.85046	−0.333622	−0.166811	+	0.985989i	$0.553347\pi$
$74$	9.45799	1.09947
$75$	−2.27841	−0.263089
$76$	−16.1014	−1.84696
$77$	0	0
$78$	−12.1593	−1.37677
$79$	6.85258	0.770976	0.385488	−	0.922713i	$-0.374033\pi$
$79$	6.85258	0.770976	0.385488	+	0.922713i	$0.374033\pi$
$80$	1.75561	0.196283
$81$	−10.7723	−1.19692
$82$	−21.9316	−2.42193
$83$	14.5243	1.59424	0.797122	−	0.603818i	$-0.206355\pi$
$83$	14.5243	1.59424	0.797122	+	0.603818i	$0.206355\pi$
$84$	0	0
$85$	4.71397	0.511302
$86$	−4.72667	−0.509690
$87$	11.7723	1.26212
$88$	8.76467	0.934317
$89$	−8.15462	−0.864388	−0.432194	−	0.901781i	$-0.642260\pi$
$89$	−8.15462	−0.864388	−0.432194	+	0.901781i	$0.642260\pi$
$90$	4.80122	0.506093
$91$	0	0
$92$	−3.89355	−0.405931
$93$	−2.27841	−0.236260
$94$	−17.9848	−1.85499
$95$	5.74800	0.589732
$96$	−16.7647	−1.71104
$97$	15.7951	1.60375	0.801873	−	0.597495i	$-0.203837\pi$
$97$	15.7951	1.60375	0.801873	+	0.597495i	$0.203837\pi$
$98$	0	0
$99$	−10.9392	−1.09943
$100$	2.80122	0.280122
$101$	−16.4294	−1.63479	−0.817393	−	0.576080i	$-0.804582\pi$
$101$	−16.4294	−1.63479	−0.817393	+	0.576080i	$0.804582\pi$
$102$	−23.5340	−2.33021
$103$	−3.04561	−0.300093	−0.150047	−	0.988679i	$-0.547942\pi$
$103$	−3.04561	−0.300093	−0.150047	+	0.988679i	$0.547942\pi$
$104$	4.27589	0.419285
$105$	0	0
$106$	−29.3443	−2.85017
$107$	12.5264	1.21097	0.605485	−	0.795856i	$-0.292979\pi$
$107$	12.5264	1.21097	0.605485	+	0.795856i	$0.292979\pi$
$108$	5.16223	0.496736
$109$	−8.27014	−0.792136	−0.396068	−	0.918221i	$-0.629625\pi$
$109$	−8.27014	−0.792136	−0.396068	+	0.918221i	$0.629625\pi$
$110$	−10.9392	−1.04301
$111$	9.83458	0.933457
$112$	0	0
$113$	1.61302	0.151740	0.0758700	−	0.997118i	$-0.475827\pi$
$113$	1.61302	0.151740	0.0758700	+	0.997118i	$0.475827\pi$
$114$	−28.6962	−2.68765
$115$	1.38995	0.129613
$116$	−14.4736	−1.34384
$117$	−5.33672	−0.493380
$118$	1.47321	0.135620
$119$	0	0
$120$	−4.00000	−0.365148
$121$	13.9239	1.26581
$122$	3.16223	0.286295
$123$	−22.8048	−2.05624
$124$	2.80122	0.251557
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	3.64044	0.323037	0.161518	−	0.986870i	$-0.448361\pi$
$127$	3.64044	0.323037	0.161518	+	0.986870i	$0.448361\pi$
$128$	12.9178	1.14179
$129$	−4.91487	−0.432731
$130$	−5.33672	−0.468062
$131$	8.32005	0.726926	0.363463	−	0.931609i	$-0.381594\pi$
$131$	8.32005	0.726926	0.363463	+	0.931609i	$0.381594\pi$
$132$	31.8631	2.77333
$133$	0	0
$134$	32.8175	2.83500
$135$	−1.84285	−0.158607
$136$	8.27589	0.709652
$137$	22.6303	1.93344	0.966719	−	0.255842i	$-0.0823526\pi$
$137$	22.6303	1.93344	0.966719	+	0.255842i	$0.0823526\pi$
$138$	−6.93916	−0.590701
$139$	17.3595	1.47241	0.736207	−	0.676757i	$-0.236615\pi$
$139$	17.3595	1.47241	0.736207	+	0.676757i	$0.236615\pi$
$140$	0	0
$141$	−18.7009	−1.57490
$142$	6.15462	0.516485
$143$	12.1593	1.01681
$144$	−3.84683	−0.320569
$145$	5.16688	0.429086
$146$	6.24585	0.516910
$147$	0	0
$148$	−12.0912	−0.993893
$149$	12.8997	1.05678	0.528390	−	0.849002i	$-0.322796\pi$
$149$	12.8997	1.05678	0.528390	+	0.849002i	$0.322796\pi$
$150$	4.99239	0.407627
$151$	−6.34434	−0.516295	−0.258147	−	0.966106i	$-0.583112\pi$
$151$	−6.34434	−0.516295	−0.258147	+	0.966106i	$0.583112\pi$
$152$	10.0912	0.818506
$153$	−10.3291	−0.835059
$154$	0	0
$155$	−1.00000	−0.0803219
$156$	15.5446	1.24456
$157$	−12.0228	−0.959522	−0.479761	−	0.877399i	$-0.659277\pi$
$157$	−12.0228	−0.959522	−0.479761	+	0.877399i	$0.659277\pi$
$158$	−15.0152	−1.19454
$159$	−30.5127	−2.41981
$160$	−7.35805	−0.581705
$161$	0	0
$162$	23.6039	1.85450
$163$	0.256427	0.0200850	0.0100425	−	0.999950i	$-0.496803\pi$
$163$	0.256427	0.0200850	0.0100425	+	0.999950i	$0.496803\pi$
$164$	28.0376	2.18937
$165$	−11.3747	−0.885521
$166$	−31.8251	−2.47011
$167$	−5.70172	−0.441212	−0.220606	−	0.975363i	$-0.570804\pi$
$167$	−5.70172	−0.441212	−0.220606	+	0.975363i	$0.570804\pi$
$168$	0	0
$169$	−7.06804	−0.543696
$170$	−10.3291	−0.792207
$171$	−12.5948	−0.963151
$172$	6.04264	0.460747
$173$	−13.8556	−1.05342	−0.526709	−	0.850046i	$-0.676574\pi$
$173$	−13.8556	−1.05342	−0.526709	+	0.850046i	$0.676574\pi$
$174$	−25.7951	−1.95552
$175$	0	0
$176$	8.76467	0.660662
$177$	1.53187	0.115143
$178$	17.8682	1.33927
$179$	10.8939	0.814248	0.407124	−	0.913373i	$-0.366532\pi$
$179$	10.8939	0.814248	0.407124	+	0.913373i	$0.366532\pi$
$180$	−6.13794	−0.457495
$181$	−14.5082	−1.07839	−0.539195	−	0.842181i	$-0.681271\pi$
$181$	−14.5082	−1.07839	−0.539195	+	0.842181i	$0.681271\pi$
$182$	0	0
$183$	3.28814	0.243067
$184$	2.44020	0.179894
$185$	4.31641	0.317349
$186$	4.99239	0.366060
$187$	23.5340	1.72098
$188$	22.9920	1.67686
$189$	0	0
$190$	−12.5948	−0.913725
$191$	−17.6219	−1.27508	−0.637538	−	0.770419i	$-0.720047\pi$
$191$	−17.6219	−1.27508	−0.637538	+	0.770419i	$0.720047\pi$
$192$	28.7342	2.07371
$193$	19.1897	1.38130	0.690651	−	0.723188i	$-0.257324\pi$
$193$	19.1897	1.38130	0.690651	+	0.723188i	$0.257324\pi$
$194$	−34.6096	−2.48483
$195$	−5.54922	−0.397388
$196$	0	0
$197$	3.13352	0.223254	0.111627	−	0.993750i	$-0.464394\pi$
$197$	3.13352	0.223254	0.111627	+	0.993750i	$0.464394\pi$
$198$	23.9696	1.70344
$199$	4.03800	0.286246	0.143123	−	0.989705i	$-0.454286\pi$
$199$	4.03800	0.286246	0.143123	+	0.989705i	$0.454286\pi$
$200$	−1.75561	−0.124140
$201$	34.1242	2.40693
$202$	35.9996	2.53292
$203$	0	0
$204$	30.0862	2.10645
$205$	−10.0091	−0.699064
$206$	6.67345	0.464961
$207$	−3.04561	−0.211685
$208$	4.27589	0.296480
$209$	28.6962	1.98496
$210$	0	0
$211$	1.82551	0.125673	0.0628366	−	0.998024i	$-0.479985\pi$
$211$	1.82551	0.125673	0.0628366	+	0.998024i	$0.479985\pi$
$212$	37.5141	2.57648
$213$	6.39968	0.438499
$214$	−27.4474	−1.87627
$215$	−2.15715	−0.147116
$216$	−3.23533	−0.220136
$217$	0	0
$218$	18.1213	1.22733
$219$	6.49454	0.438860
$220$	13.9848	0.942853
$221$	11.4812	0.772307
$222$	−21.5492	−1.44629
$223$	−24.7714	−1.65882	−0.829409	−	0.558642i	$-0.811323\pi$
$223$	−24.7714	−1.65882	−0.829409	+	0.558642i	$0.811323\pi$
$224$	0	0
$225$	2.19117	0.146078
$226$	−3.53440	−0.235105
$227$	3.51586	0.233356	0.116678	−	0.993170i	$-0.462775\pi$
$227$	3.51586	0.233356	0.116678	+	0.993170i	$0.462775\pi$
$228$	36.6856	2.42957
$229$	−23.5978	−1.55939	−0.779693	−	0.626162i	$-0.784625\pi$
$229$	−23.5978	−1.55939	−0.779693	+	0.626162i	$0.784625\pi$
$230$	−3.04561	−0.200822
$231$	0	0
$232$	9.07101	0.595541
$233$	1.87873	0.123080	0.0615400	−	0.998105i	$-0.480399\pi$
$233$	1.87873	0.123080	0.0615400	+	0.998105i	$0.480399\pi$
$234$	11.6937	0.764439
$235$	−8.20785	−0.535421
$236$	−1.88338	−0.122597
$237$	−15.6130	−1.01417
$238$	0	0
$239$	2.30634	0.149184	0.0745922	−	0.997214i	$-0.476234\pi$
$239$	2.30634	0.149184	0.0745922	+	0.997214i	$0.476234\pi$
$240$	−4.00000	−0.258199
$241$	6.35230	0.409187	0.204594	−	0.978847i	$-0.434413\pi$
$241$	6.35230	0.409187	0.204594	+	0.978847i	$0.434413\pi$
$242$	−30.5097	−1.96124
$243$	19.0152	1.21982
$244$	−4.04264	−0.258804
$245$	0	0
$246$	49.9691	3.18592
$247$	13.9996	0.890773
$248$	−1.75561	−0.111481
$249$	−33.0923	−2.09714
$250$	2.19117	0.138582
$251$	20.8893	1.31852	0.659259	−	0.751916i	$-0.270870\pi$
$251$	20.8893	1.31852	0.659259	+	0.751916i	$0.270870\pi$
$252$	0	0
$253$	6.93916	0.436262
$254$	−7.97682	−0.500510
$255$	−10.7404	−0.672589
$256$	−3.08216	−0.192635
$257$	8.52679	0.531886	0.265943	−	0.963989i	$-0.414317\pi$
$257$	8.52679	0.531886	0.265943	+	0.963989i	$0.414317\pi$
$258$	10.7693	0.670468
$259$	0	0
$260$	6.82254	0.423116
$261$	−11.3215	−0.700783
$262$	−18.2306	−1.12629
$263$	28.4225	1.75260	0.876302	−	0.481762i	$-0.160003\pi$
$263$	28.4225	1.75260	0.876302	+	0.481762i	$0.160003\pi$
$264$	−19.9696	−1.22904
$265$	−13.3921	−0.822668
$266$	0	0
$267$	18.5796	1.13705
$268$	−41.9543	−2.56277
$269$	19.2349	1.17277	0.586387	−	0.810031i	$-0.300550\pi$
$269$	19.2349	1.17277	0.586387	+	0.810031i	$0.300550\pi$
$270$	4.03800	0.245745
$271$	13.7917	0.837789	0.418895	−	0.908035i	$-0.362418\pi$
$271$	13.7917	0.837789	0.418895	+	0.908035i	$0.362418\pi$
$272$	8.27589	0.501799
$273$	0	0
$274$	−49.5868	−2.99565
$275$	−4.99239	−0.301052
$276$	8.87112	0.533979
$277$	13.3392	0.801478	0.400739	−	0.916192i	$-0.368753\pi$
$277$	13.3392	0.801478	0.400739	+	0.916192i	$0.368753\pi$
$278$	−38.0376	−2.28134
$279$	2.19117	0.131182
$280$	0	0
$281$	17.2288	1.02778	0.513891	−	0.857856i	$-0.328204\pi$
$281$	17.2288	1.02778	0.513891	+	0.857856i	$0.328204\pi$
$282$	40.9768	2.44013
$283$	0.556827	0.0330999	0.0165500	−	0.999863i	$-0.494732\pi$
$283$	0.556827	0.0330999	0.0165500	+	0.999863i	$0.494732\pi$
$284$	−7.86815	−0.466889
$285$	−13.0963	−0.775759
$286$	−26.6430	−1.57543
$287$	0	0
$288$	16.1227	0.950040
$289$	5.22156	0.307150
$290$	−11.3215	−0.664821
$291$	−35.9877	−2.10964
$292$	−7.98478	−0.467274
$293$	−10.6781	−0.623821	−0.311910	−	0.950112i	$-0.600969\pi$
$293$	−10.6781	−0.623821	−0.311910	+	0.950112i	$0.600969\pi$
$294$	0	0
$295$	0.672342	0.0391453
$296$	7.57793	0.440458
$297$	−9.20024	−0.533852
$298$	−28.2653	−1.63737
$299$	3.38531	0.195777
$300$	−6.38234	−0.368484
$301$	0	0
$302$	13.9015	0.799942
$303$	37.4330	2.15047
$304$	10.0912	0.578771
$305$	1.44317	0.0826358
$306$	22.6328	1.29383
$307$	8.41238	0.480120	0.240060	−	0.970758i	$-0.422833\pi$
$307$	8.41238	0.480120	0.240060	+	0.970758i	$0.422833\pi$
$308$	0	0
$309$	6.93916	0.394755
$310$	2.19117	0.124450
$311$	−23.9026	−1.35539	−0.677697	−	0.735342i	$-0.737022\pi$
$311$	−23.9026	−1.35539	−0.677697	+	0.735342i	$0.737022\pi$
$312$	−9.74224	−0.551546
$313$	−4.17197	−0.235813	−0.117907	−	0.993025i	$-0.537618\pi$
$313$	−4.17197	−0.235813	−0.117907	+	0.993025i	$0.537618\pi$
$314$	26.3439	1.48667
$315$	0	0
$316$	19.1956	1.07984
$317$	−16.9573	−0.952417	−0.476208	−	0.879332i	$-0.657989\pi$
$317$	−16.9573	−0.952417	−0.476208	+	0.879332i	$0.657989\pi$
$318$	66.8584	3.74923
$319$	25.7951	1.44425
$320$	12.6115	0.705005
$321$	−28.5403	−1.59296
$322$	0	0
$323$	27.0959	1.50766
$324$	−30.1755	−1.67642
$325$	−2.43556	−0.135101
$326$	−0.561876	−0.0311194
$327$	18.8428	1.04201
$328$	−17.5720	−0.970251
$329$	0	0
$330$	24.9239	1.37202
$331$	21.8711	1.20214	0.601071	−	0.799195i	$-0.294741\pi$
$331$	21.8711	1.20214	0.601071	+	0.799195i	$0.294741\pi$
$332$	40.6856	2.23291
$333$	−9.45799	−0.518295
$334$	12.4934	0.683610
$335$	14.9772	0.818290
$336$	0	0
$337$	−7.78499	−0.424075	−0.212038	−	0.977262i	$-0.568010\pi$
$337$	−7.78499	−0.424075	−0.212038	+	0.977262i	$0.568010\pi$
$338$	15.4873	0.842397
$339$	−3.67513	−0.199605
$340$	13.2049	0.716135
$341$	−4.99239	−0.270353
$342$	27.5974	1.49230
$343$	0	0
$344$	−3.78710	−0.204187
$345$	−3.16688	−0.170499
$346$	30.3598	1.63216
$347$	−11.2683	−0.604913	−0.302456	−	0.953163i	$-0.597807\pi$
$347$	−11.2683	−0.604913	−0.302456	+	0.953163i	$0.597807\pi$
$348$	32.9768	1.76774
$349$	0.943993	0.0505308	0.0252654	−	0.999681i	$-0.491957\pi$
$349$	0.943993	0.0505308	0.0252654	+	0.999681i	$0.491957\pi$
$350$	0	0
$351$	−4.48838	−0.239572
$352$	−36.7342	−1.95794
$353$	25.4275	1.35337	0.676686	−	0.736272i	$-0.263416\pi$
$353$	25.4275	1.35337	0.676686	+	0.736272i	$0.263416\pi$
$354$	−3.35659	−0.178401
$355$	2.80883	0.149077
$356$	−22.8429	−1.21067
$357$	0	0
$358$	−23.8704	−1.26159
$359$	−2.08194	−0.109880	−0.0549402	−	0.998490i	$-0.517497\pi$
$359$	−2.08194	−0.109880	−0.0549402	+	0.998490i	$0.517497\pi$
$360$	3.84683	0.202746
$361$	14.0395	0.738919
$362$	31.7900	1.67085
$363$	−31.7245	−1.66510
$364$	0	0
$365$	2.85046	0.149200
$366$	−7.20488	−0.376605
$367$	−6.58939	−0.343964	−0.171982	−	0.985100i	$-0.555017\pi$
$367$	−6.58939	−0.343964	−0.171982	+	0.985100i	$0.555017\pi$
$368$	2.44020	0.127204
$369$	21.9316	1.14171
$370$	−9.45799	−0.491698
$371$	0	0
$372$	−6.38234	−0.330909
$373$	−13.6404	−0.706275	−0.353138	−	0.935571i	$-0.614885\pi$
$373$	−13.6404	−0.706275	−0.353138	+	0.935571i	$0.614885\pi$
$374$	−51.5669	−2.66646
$375$	2.27841	0.117657
$376$	−14.4098	−0.743127
$377$	12.5842	0.648122
$378$	0	0
$379$	−30.5160	−1.56750	−0.783750	−	0.621076i	$-0.786696\pi$
$379$	−30.5160	−1.56750	−0.783750	+	0.621076i	$0.786696\pi$
$380$	16.1014	0.825984
$381$	−8.29443	−0.424936
$382$	38.6126	1.97559
$383$	31.9366	1.63188	0.815942	−	0.578134i	$-0.196219\pi$
$383$	31.9366	1.63188	0.815942	+	0.578134i	$0.196219\pi$
$384$	−29.4322	−1.50196
$385$	0	0
$386$	−42.0478	−2.14018
$387$	4.72667	0.240270
$388$	44.2454	2.24622
$389$	−2.52941	−0.128246	−0.0641230	−	0.997942i	$-0.520425\pi$
$389$	−2.52941	−0.128246	−0.0641230	+	0.997942i	$0.520425\pi$
$390$	12.1593	0.615708
$391$	6.55218	0.331358
$392$	0	0
$393$	−18.9565	−0.956229
$394$	−6.86607	−0.345908
$395$	−6.85258	−0.344791
$396$	−30.6430	−1.53987
$397$	−9.47786	−0.475680	−0.237840	−	0.971304i	$-0.576439\pi$
$397$	−9.47786	−0.475680	−0.237840	+	0.971304i	$0.576439\pi$
$398$	−8.84794	−0.443507
$399$	0	0
$400$	−1.75561	−0.0877804
$401$	−18.6781	−0.932739	−0.466370	−	0.884590i	$-0.654438\pi$
$401$	−18.6781	−0.932739	−0.466370	+	0.884590i	$0.654438\pi$
$402$	−74.7718	−3.72928
$403$	−2.43556	−0.121324
$404$	−46.0224	−2.28970
$405$	10.7723	0.535279
$406$	0	0
$407$	21.5492	1.06815
$408$	−18.8559	−0.933506
$409$	−19.1424	−0.946529	−0.473265	−	0.880920i	$-0.656925\pi$
$409$	−19.1424	−0.946529	−0.473265	+	0.880920i	$0.656925\pi$
$410$	21.9316	1.08312
$411$	−51.5612	−2.54333
$412$	−8.53143	−0.420313
$413$	0	0
$414$	6.67345	0.327982
$415$	−14.5243	−0.712968
$416$	−17.9210	−0.878648
$417$	−39.5521	−1.93688
$418$	−62.8783	−3.07548
$419$	−26.3733	−1.28842	−0.644209	−	0.764849i	$-0.722813\pi$
$419$	−26.3733	−1.28842	−0.644209	+	0.764849i	$0.722813\pi$
$420$	0	0
$421$	19.5550	0.953051	0.476525	−	0.879161i	$-0.341896\pi$
$421$	19.5550	0.953051	0.476525	+	0.879161i	$0.341896\pi$
$422$	−4.00000	−0.194717
$423$	17.9848	0.874450
$424$	−23.5112	−1.14181
$425$	−4.71397	−0.228661
$426$	−14.0228	−0.679406
$427$	0	0
$428$	35.0891	1.69610
$429$	−27.7038	−1.33755
$430$	4.72667	0.227940
$431$	−28.5460	−1.37501	−0.687507	−	0.726178i	$-0.741295\pi$
$431$	−28.5460	−1.37501	−0.687507	+	0.726178i	$0.741295\pi$
$432$	−3.23533	−0.155660
$433$	4.79976	0.230662	0.115331	−	0.993327i	$-0.463207\pi$
$433$	4.79976	0.230662	0.115331	+	0.993327i	$0.463207\pi$
$434$	0	0
$435$	−11.7723	−0.564438
$436$	−23.1665	−1.10947
$437$	7.98942	0.382186
$438$	−14.2306	−0.679966
$439$	34.5275	1.64791	0.823954	−	0.566657i	$-0.191764\pi$
$439$	34.5275	1.64791	0.823954	+	0.566657i	$0.191764\pi$
$440$	−8.76467	−0.417839
$441$	0	0
$442$	−25.1572	−1.19661
$443$	31.5488	1.49893	0.749465	−	0.662044i	$-0.230311\pi$
$443$	31.5488	1.49893	0.749465	+	0.662044i	$0.230311\pi$
$444$	27.5488	1.30741
$445$	8.15462	0.386566
$446$	54.2784	2.57016
$447$	−29.3907	−1.39013
$448$	0	0
$449$	−24.1513	−1.13977	−0.569885	−	0.821724i	$-0.693012\pi$
$449$	−24.1513	−1.13977	−0.569885	+	0.821724i	$0.693012\pi$
$450$	−4.80122	−0.226332
$451$	−49.9691	−2.35296
$452$	4.51842	0.212529
$453$	14.4550	0.679156
$454$	−7.70384	−0.361559
$455$	0	0
$456$	−22.9920	−1.07670
$457$	12.8665	0.601868	0.300934	−	0.953645i	$-0.402702\pi$
$457$	12.8665	0.601868	0.300934	+	0.953645i	$0.402702\pi$
$458$	51.7067	2.41610
$459$	−8.68716	−0.405482
$460$	3.89355	0.181538
$461$	−30.5716	−1.42386	−0.711932	−	0.702249i	$-0.752179\pi$
$461$	−30.5716	−1.42386	−0.711932	+	0.702249i	$0.752179\pi$
$462$	0	0
$463$	11.3747	0.528628	0.264314	−	0.964437i	$-0.414854\pi$
$463$	11.3747	0.528628	0.264314	+	0.964437i	$0.414854\pi$
$464$	9.07101	0.421111
$465$	2.27841	0.105659
$466$	−4.11662	−0.190699
$467$	−17.8090	−0.824100	−0.412050	−	0.911161i	$-0.635187\pi$
$467$	−17.8090	−0.824100	−0.412050	+	0.911161i	$0.635187\pi$
$468$	−14.9493	−0.691033
$469$	0	0
$470$	17.9848	0.829576
$471$	27.3929	1.26220
$472$	1.18037	0.0543309
$473$	−10.7693	−0.495174
$474$	34.2108	1.57135
$475$	−5.74800	−0.263736
$476$	0	0
$477$	29.3443	1.34358
$478$	−5.05357	−0.231145
$479$	5.72835	0.261735	0.130867	−	0.991400i	$-0.458224\pi$
$479$	5.72835	0.261735	0.130867	+	0.991400i	$0.458224\pi$
$480$	16.7647	0.765199
$481$	10.5129	0.479347
$482$	−13.9190	−0.633991
$483$	0	0
$484$	39.0040	1.77291
$485$	−15.7951	−0.717217
$486$	−41.6654	−1.88998
$487$	2.88806	0.130870	0.0654352	−	0.997857i	$-0.479156\pi$
$487$	2.88806	0.130870	0.0654352	+	0.997857i	$0.479156\pi$
$488$	2.53364	0.114693
$489$	−0.584248	−0.0264206
$490$	0	0
$491$	16.3490	0.737819	0.368910	−	0.929465i	$-0.379731\pi$
$491$	16.3490	0.737819	0.368910	+	0.929465i	$0.379731\pi$
$492$	−63.8812	−2.87999
$493$	24.3565	1.09696
$494$	−30.6755	−1.38015
$495$	10.9392	0.491679
$496$	−1.75561	−0.0788291
$497$	0	0
$498$	72.5108	3.24928
$499$	31.2378	1.39840	0.699199	−	0.714927i	$-0.253540\pi$
$499$	31.2378	1.39840	0.699199	+	0.714927i	$0.253540\pi$
$500$	−2.80122	−0.125274
$501$	12.9909	0.580390
$502$	−45.7719	−2.04290
$503$	12.8099	0.571167	0.285583	−	0.958354i	$-0.407813\pi$
$503$	12.8099	0.571167	0.285583	+	0.958354i	$0.407813\pi$
$504$	0	0
$505$	16.4294	0.731099
$506$	−15.2049	−0.675939
$507$	16.1039	0.715200
$508$	10.1977	0.452449
$509$	−1.01093	−0.0448086	−0.0224043	−	0.999749i	$-0.507132\pi$
$509$	−1.01093	−0.0448086	−0.0224043	+	0.999749i	$0.507132\pi$
$510$	23.5340	1.04210
$511$	0	0
$512$	−19.0822	−0.843320
$513$	−10.5927	−0.467680
$514$	−18.6836	−0.824099
$515$	3.04561	0.134206
$516$	−13.7676	−0.606087
$517$	−40.9768	−1.80216
$518$	0	0
$519$	31.5687	1.38571
$520$	−4.27589	−0.187510
$521$	34.0725	1.49274	0.746371	−	0.665530i	$-0.231795\pi$
$521$	34.0725	1.49274	0.746371	+	0.665530i	$0.231795\pi$
$522$	24.8073	1.08579
$523$	−3.49520	−0.152834	−0.0764172	−	0.997076i	$-0.524348\pi$
$523$	−3.49520	−0.152834	−0.0764172	+	0.997076i	$0.524348\pi$
$524$	23.3063	1.01814
$525$	0	0
$526$	−62.2784	−2.71547
$527$	−4.71397	−0.205344
$528$	−19.9696	−0.869063
$529$	−21.0680	−0.916002
$530$	29.3443	1.27463
$531$	−1.47321	−0.0639321
$532$	0	0
$533$	−24.3777	−1.05592
$534$	−40.7110	−1.76174
$535$	−12.5264	−0.541563
$536$	26.2940	1.13573
$537$	−24.8208	−1.07110
$538$	−42.1470	−1.81708
$539$	0	0
$540$	−5.16223	−0.222147
$541$	18.5915	0.799312	0.399656	−	0.916665i	$-0.369130\pi$
$541$	18.5915	0.799312	0.399656	+	0.916665i	$0.369130\pi$
$542$	−30.2200	−1.29806
$543$	33.0558	1.41856
$544$	−34.6856	−1.48713
$545$	8.27014	0.354254
$546$	0	0
$547$	−37.4262	−1.60023	−0.800115	−	0.599847i	$-0.795228\pi$
$547$	−37.4262	−1.60023	−0.800115	+	0.599847i	$0.795228\pi$
$548$	63.3925	2.70799
$549$	−3.16223	−0.134961
$550$	10.9392	0.466448
$551$	29.6992	1.26523
$552$	−5.55980	−0.236641
$553$	0	0
$554$	−29.2285	−1.24180
$555$	−9.83458	−0.417455
$556$	48.6278	2.06228
$557$	−8.67942	−0.367759	−0.183879	−	0.982949i	$-0.558866\pi$
$557$	−8.67942	−0.367759	−0.183879	+	0.982949i	$0.558866\pi$
$558$	−4.80122	−0.203252
$559$	−5.25386	−0.222215
$560$	0	0
$561$	−53.6202	−2.26385
$562$	−37.7511	−1.59244
$563$	−15.9011	−0.670152	−0.335076	−	0.942191i	$-0.608762\pi$
$563$	−15.9011	−0.670152	−0.335076	+	0.942191i	$0.608762\pi$
$564$	−52.3852	−2.20582
$565$	−1.61302	−0.0678602
$566$	−1.22010	−0.0512847
$567$	0	0
$568$	4.93121	0.206909
$569$	−14.9124	−0.625162	−0.312581	−	0.949891i	$-0.601194\pi$
$569$	−14.9124	−0.625162	−0.312581	+	0.949891i	$0.601194\pi$
$570$	28.6962	1.20195
$571$	13.5565	0.567321	0.283661	−	0.958925i	$-0.408451\pi$
$571$	13.5565	0.567321	0.283661	+	0.958925i	$0.408451\pi$
$572$	34.0608	1.42415
$573$	40.1500	1.67729
$574$	0	0
$575$	−1.38995	−0.0579649
$576$	−27.6339	−1.15141
$577$	5.64770	0.235117	0.117559	−	0.993066i	$-0.462493\pi$
$577$	5.64770	0.235117	0.117559	+	0.993066i	$0.462493\pi$
$578$	−11.4413	−0.475896
$579$	−43.7220	−1.81702
$580$	14.4736	0.600982
$581$	0	0
$582$	78.8551	3.26865
$583$	−66.8584	−2.76899
$584$	5.00430	0.207079
$585$	5.33672	0.220646
$586$	23.3975	0.966542
$587$	1.11697	0.0461023	0.0230511	−	0.999734i	$-0.492662\pi$
$587$	1.11697	0.0461023	0.0230511	+	0.999734i	$0.492662\pi$
$588$	0	0
$589$	−5.74800	−0.236842
$590$	−1.47321	−0.0606513
$591$	−7.13946	−0.293678
$592$	7.57793	0.311451
$593$	−12.6249	−0.518441	−0.259221	−	0.965818i	$-0.583466\pi$
$593$	−12.6249	−0.518441	−0.259221	+	0.965818i	$0.583466\pi$
$594$	20.1593	0.827145
$595$	0	0
$596$	36.1348	1.48014
$597$	−9.20024	−0.376541
$598$	−7.41777	−0.303335
$599$	7.03633	0.287496	0.143748	−	0.989614i	$-0.454084\pi$
$599$	7.03633	0.287496	0.143748	+	0.989614i	$0.454084\pi$
$600$	4.00000	0.163299
$601$	31.6687	1.29180	0.645898	−	0.763424i	$-0.276483\pi$
$601$	31.6687	1.29180	0.645898	+	0.763424i	$0.276483\pi$
$602$	0	0
$603$	−32.8175	−1.33643
$604$	−17.7719	−0.723128
$605$	−13.9239	−0.566089
$606$	−82.0220	−3.33191
$607$	6.56874	0.266617	0.133308	−	0.991075i	$-0.457440\pi$
$607$	6.56874	0.266617	0.133308	+	0.991075i	$0.457440\pi$
$608$	−42.2940	−1.71525
$609$	0	0
$610$	−3.16223	−0.128035
$611$	−19.9907	−0.808738
$612$	−28.9341	−1.16959
$613$	12.5728	0.507812	0.253906	−	0.967229i	$-0.418285\pi$
$613$	12.5728	0.507812	0.253906	+	0.967229i	$0.418285\pi$
$614$	−18.4329	−0.743893
$615$	22.8048	0.919578
$616$	0	0
$617$	−13.4993	−0.543462	−0.271731	−	0.962373i	$-0.587596\pi$
$617$	−13.4993	−0.543462	−0.271731	+	0.962373i	$0.587596\pi$
$618$	−15.2049	−0.611630
$619$	−10.2412	−0.411629	−0.205814	−	0.978591i	$-0.565984\pi$
$619$	−10.2412	−0.411629	−0.205814	+	0.978591i	$0.565984\pi$
$620$	−2.80122	−0.112500
$621$	−2.56147	−0.102788
$622$	52.3747	2.10003
$623$	0	0
$624$	−9.74224	−0.390002
$625$	1.00000	0.0400000
$626$	9.14148	0.365367
$627$	−65.3819	−2.61110
$628$	−33.6784	−1.34392
$629$	20.3475	0.811307
$630$	0	0
$631$	21.2564	0.846203	0.423101	−	0.906082i	$-0.360941\pi$
$631$	21.2564	0.846203	0.423101	+	0.906082i	$0.360941\pi$
$632$	−12.0304	−0.478545
$633$	−4.15927	−0.165316
$634$	37.1563	1.47567
$635$	−3.64044	−0.144466
$636$	−85.4727	−3.38921
$637$	0	0
$638$	−56.5213	−2.23770
$639$	−6.15462	−0.243473
$640$	−12.9178	−0.510623
$641$	32.7676	1.29424	0.647121	−	0.762387i	$-0.275973\pi$
$641$	32.7676	1.29424	0.647121	+	0.762387i	$0.275973\pi$
$642$	62.5366	2.46812
$643$	−12.8052	−0.504988	−0.252494	−	0.967598i	$-0.581251\pi$
$643$	−12.8052	−0.504988	−0.252494	+	0.967598i	$0.581251\pi$
$644$	0	0
$645$	4.91487	0.193523
$646$	−59.3717	−2.33595
$647$	1.36929	0.0538324	0.0269162	−	0.999638i	$-0.491431\pi$
$647$	1.36929	0.0538324	0.0269162	+	0.999638i	$0.491431\pi$
$648$	18.9119	0.742930
$649$	3.35659	0.131758
$650$	5.33672	0.209324
$651$	0	0
$652$	0.718310	0.0281312
$653$	24.6611	0.965065	0.482532	−	0.875878i	$-0.339717\pi$
$653$	24.6611	0.965065	0.482532	+	0.875878i	$0.339717\pi$
$654$	−41.2877	−1.61448
$655$	−8.32005	−0.325091
$656$	−17.5720	−0.686071
$657$	−6.24585	−0.243674
$658$	0	0
$659$	−37.5553	−1.46295	−0.731473	−	0.681871i	$-0.761167\pi$
$659$	−37.5553	−1.46295	−0.731473	+	0.681871i	$0.761167\pi$
$660$	−31.8631	−1.24027
$661$	13.2427	0.515080	0.257540	−	0.966268i	$-0.417088\pi$
$661$	13.2427	0.515080	0.257540	+	0.966268i	$0.417088\pi$
$662$	−47.9232	−1.86259
$663$	−26.1589	−1.01593
$664$	−25.4989	−0.989549
$665$	0	0
$666$	20.7241	0.803041
$667$	7.18170	0.278076
$668$	−15.9718	−0.617966
$669$	56.4396	2.18208
$670$	−32.8175	−1.26785
$671$	7.20488	0.278141
$672$	0	0
$673$	2.67133	0.102972	0.0514861	−	0.998674i	$-0.483604\pi$
$673$	2.67133	0.102972	0.0514861	+	0.998674i	$0.483604\pi$
$674$	17.0582	0.657058
$675$	1.84285	0.0709314
$676$	−19.7991	−0.761505
$677$	−37.0811	−1.42514	−0.712571	−	0.701600i	$-0.752469\pi$
$677$	−37.0811	−1.42514	−0.712571	+	0.701600i	$0.752469\pi$
$678$	8.05282	0.309267
$679$	0	0
$680$	−8.27589	−0.317366
$681$	−8.01058	−0.306966
$682$	10.9392	0.418882
$683$	26.2074	1.00280	0.501400	−	0.865216i	$-0.332819\pi$
$683$	26.2074	1.00280	0.501400	+	0.865216i	$0.332819\pi$
$684$	−35.2809	−1.34900
$685$	−22.6303	−0.864659
$686$	0	0
$687$	53.7655	2.05128
$688$	−3.78710	−0.144382
$689$	−32.6172	−1.24262
$690$	6.93916	0.264169
$691$	−28.7324	−1.09303	−0.546516	−	0.837448i	$-0.684046\pi$
$691$	−28.7324	−1.09303	−0.546516	+	0.837448i	$0.684046\pi$
$692$	−38.8124	−1.47543
$693$	0	0
$694$	24.6907	0.937246
$695$	−17.3595	−0.658483
$696$	−20.6675	−0.783400
$697$	−47.1825	−1.78716
$698$	−2.06845	−0.0782919
$699$	−4.28053	−0.161905
$700$	0	0
$701$	−50.2576	−1.89820	−0.949102	−	0.314968i	$-0.898006\pi$
$701$	−50.2576	−1.89820	−0.949102	+	0.314968i	$0.898006\pi$
$702$	9.83480	0.371190
$703$	24.8107	0.935754
$704$	62.9615	2.37295
$705$	18.7009	0.704316
$706$	−55.7160	−2.09690
$707$	0	0
$708$	4.29111	0.161270
$709$	17.5518	0.659173	0.329587	−	0.944125i	$-0.393091\pi$
$709$	17.5518	0.659173	0.329587	+	0.944125i	$0.393091\pi$
$710$	−6.15462	−0.230979
$711$	15.0152	0.563113
$712$	14.3163	0.536527
$713$	−1.38995	−0.0520540
$714$	0	0
$715$	−12.1593	−0.454731
$716$	30.5162	1.14044
$717$	−5.25479	−0.196244
$718$	4.56188	0.170248
$719$	31.4309	1.17217	0.586087	−	0.810248i	$-0.300668\pi$
$719$	31.4309	1.17217	0.586087	+	0.810248i	$0.300668\pi$
$720$	3.84683	0.143363
$721$	0	0
$722$	−30.7628	−1.14487
$723$	−14.4732	−0.538262
$724$	−40.6408	−1.51040
$725$	−5.16688	−0.191893
$726$	69.5137	2.57990
$727$	33.1665	1.23008	0.615038	−	0.788497i	$-0.289141\pi$
$727$	33.1665	1.23008	0.615038	+	0.788497i	$0.289141\pi$
$728$	0	0
$729$	−11.0076	−0.407687
$730$	−6.24585	−0.231169
$731$	−10.1687	−0.376104
$732$	9.21082	0.340442
$733$	18.4272	0.680624	0.340312	−	0.940313i	$-0.389467\pi$
$733$	18.4272	0.680624	0.340312	+	0.940313i	$0.389467\pi$
$734$	14.4385	0.532934
$735$	0	0
$736$	−10.2273	−0.376984
$737$	74.7718	2.75426
$738$	−48.0557	−1.76896
$739$	43.3750	1.59558	0.797788	−	0.602938i	$-0.206003\pi$
$739$	43.3750	1.59558	0.797788	+	0.602938i	$0.206003\pi$
$740$	12.0912	0.444482
$741$	−31.8969	−1.17176
$742$	0	0
$743$	−17.6531	−0.647631	−0.323815	−	0.946120i	$-0.604966\pi$
$743$	−17.6531	−0.647631	−0.323815	+	0.946120i	$0.604966\pi$
$744$	4.00000	0.146647
$745$	−12.8997	−0.472607
$746$	29.8885	1.09430
$747$	31.8251	1.16442
$748$	65.9239	2.41042
$749$	0	0
$750$	−4.99239	−0.182296
$751$	−28.3786	−1.03555	−0.517775	−	0.855517i	$-0.673240\pi$
$751$	−28.3786	−1.03555	−0.517775	+	0.855517i	$0.673240\pi$
$752$	−14.4098	−0.525470
$753$	−47.5944	−1.73444
$754$	−27.5742	−1.00419
$755$	6.34434	0.230894
$756$	0	0
$757$	−18.9234	−0.687784	−0.343892	−	0.939009i	$-0.611745\pi$
$757$	−18.9234	−0.687784	−0.343892	+	0.939009i	$0.611745\pi$
$758$	66.8657	2.42867
$759$	−15.8103	−0.573877
$760$	−10.0912	−0.366047
$761$	−10.1107	−0.366512	−0.183256	−	0.983065i	$-0.558664\pi$
$761$	−10.1107	−0.366512	−0.183256	+	0.983065i	$0.558664\pi$
$762$	18.1745	0.658392
$763$	0	0
$764$	−49.3628	−1.78588
$765$	10.3291	0.373450
$766$	−69.9784	−2.52842
$767$	1.63753	0.0591278
$768$	7.02243	0.253400
$769$	−4.47770	−0.161470	−0.0807349	−	0.996736i	$-0.525727\pi$
$769$	−4.47770	−0.161470	−0.0807349	+	0.996736i	$0.525727\pi$
$770$	0	0
$771$	−19.4275	−0.699666
$772$	53.7544	1.93466
$773$	21.3747	0.768795	0.384398	−	0.923168i	$-0.374409\pi$
$773$	21.3747	0.768795	0.384398	+	0.923168i	$0.374409\pi$
$774$	−10.3569	−0.372272
$775$	1.00000	0.0359211
$776$	−27.7299	−0.995447
$777$	0	0
$778$	5.54236	0.198703
$779$	−57.5321	−2.06130
$780$	−15.5446	−0.556585
$781$	14.0228	0.501774
$782$	−14.3569	−0.513403
$783$	−9.52179	−0.340281
$784$	0	0
$785$	12.0228	0.429111
$786$	41.5369	1.48157
$787$	36.0634	1.28552	0.642761	−	0.766067i	$-0.277789\pi$
$787$	36.0634	1.28552	0.642761	+	0.766067i	$0.277789\pi$
$788$	8.77768	0.312692
$789$	−64.7581	−2.30545
$790$	15.0152	0.534216
$791$	0	0
$792$	19.2049	0.682416
$793$	3.51494	0.124819
$794$	20.7676	0.737014
$795$	30.5127	1.08217
$796$	11.3113	0.400919
$797$	−16.8981	−0.598563	−0.299281	−	0.954165i	$-0.596747\pi$
$797$	−16.8981	−0.598563	−0.299281	+	0.954165i	$0.596747\pi$
$798$	0	0
$799$	−38.6916	−1.36881
$800$	7.35805	0.260146
$801$	−17.8682	−0.631340
$802$	40.9269	1.44518
$803$	14.2306	0.502188
$804$	95.5893	3.37118
$805$	0	0
$806$	5.33672	0.187978
$807$	−43.8251	−1.54272
$808$	28.8436	1.01471
$809$	1.58984	0.0558957	0.0279478	−	0.999609i	$-0.491103\pi$
$809$	1.58984	0.0558957	0.0279478	+	0.999609i	$0.491103\pi$
$810$	−23.6039	−0.829356
$811$	−17.4096	−0.611334	−0.305667	−	0.952139i	$-0.598879\pi$
$811$	−17.4096	−0.611334	−0.305667	+	0.952139i	$0.598879\pi$
$812$	0	0
$813$	−31.4233	−1.10206
$814$	−47.2180	−1.65499
$815$	−0.256427	−0.00898226
$816$	−18.8559	−0.660088
$817$	−12.3993	−0.433796
$818$	41.9442	1.46654
$819$	0	0
$820$	−28.0376	−0.979115
$821$	−4.16391	−0.145321	−0.0726607	−	0.997357i	$-0.523149\pi$
$821$	−4.16391	−0.145321	−0.0726607	+	0.997357i	$0.523149\pi$
$822$	112.979	3.94060
$823$	−14.7701	−0.514854	−0.257427	−	0.966298i	$-0.582875\pi$
$823$	−14.7701	−0.514854	−0.257427	+	0.966298i	$0.582875\pi$
$824$	5.34690	0.186268
$825$	11.3747	0.396017
$826$	0	0
$827$	−2.50439	−0.0870863	−0.0435432	−	0.999052i	$-0.513865\pi$
$827$	−2.50439	−0.0870863	−0.0435432	+	0.999052i	$0.513865\pi$
$828$	−8.53143	−0.296488
$829$	−33.1956	−1.15293	−0.576465	−	0.817122i	$-0.695568\pi$
$829$	−33.1956	−1.15293	−0.576465	+	0.817122i	$0.695568\pi$
$830$	31.8251	1.10467
$831$	−30.3923	−1.05430
$832$	30.7161	1.06489
$833$	0	0
$834$	86.6654	3.00098
$835$	5.70172	0.197316
$836$	80.3844	2.78015
$837$	1.84285	0.0636983
$838$	57.7883	1.99626
$839$	−10.5316	−0.363592	−0.181796	−	0.983336i	$-0.558191\pi$
$839$	−10.5316	−0.363592	−0.181796	+	0.983336i	$0.558191\pi$
$840$	0	0
$841$	−2.30337	−0.0794265
$842$	−42.8482	−1.47665
$843$	−39.2543	−1.35199
$844$	5.11365	0.176019
$845$	7.06804	0.243148
$846$	−39.4077	−1.35486
$847$	0	0
$848$	−23.5112	−0.807378
$849$	−1.26868	−0.0435411
$850$	10.3291	0.354286
$851$	5.99959	0.205663
$852$	17.9269	0.614166
$853$	−38.3367	−1.31262	−0.656311	−	0.754490i	$-0.727884\pi$
$853$	−38.3367	−1.31262	−0.656311	+	0.754490i	$0.727884\pi$
$854$	0	0
$855$	12.5948	0.430734
$856$	−21.9914	−0.751651
$857$	−6.68112	−0.228223	−0.114111	−	0.993468i	$-0.536402\pi$
$857$	−6.68112	−0.228223	−0.114111	+	0.993468i	$0.536402\pi$
$858$	60.7038	2.07239
$859$	−14.0300	−0.478699	−0.239349	−	0.970933i	$-0.576934\pi$
$859$	−14.0300	−0.478699	−0.239349	+	0.970933i	$0.576934\pi$
$860$	−6.04264	−0.206052
$861$	0	0
$862$	62.5492	2.13043
$863$	−6.17370	−0.210155	−0.105078	−	0.994464i	$-0.533509\pi$
$863$	−6.17370	−0.210155	−0.105078	+	0.994464i	$0.533509\pi$
$864$	13.5598	0.461314
$865$	13.8556	0.471103
$866$	−10.5171	−0.357385
$867$	−11.8969	−0.404039
$868$	0	0
$869$	−34.2108	−1.16052
$870$	25.7951	0.874535
$871$	36.4778	1.23600
$872$	14.5191	0.491679
$873$	34.6096	1.17136
$874$	−17.5062	−0.592155
$875$	0	0
$876$	18.1926	0.614672
$877$	−26.8323	−0.906063	−0.453031	−	0.891495i	$-0.649657\pi$
$877$	−26.8323	−0.906063	−0.453031	+	0.891495i	$0.649657\pi$
$878$	−75.6555	−2.55325
$879$	24.3291	0.820601
$880$	−8.76467	−0.295457
$881$	−1.34933	−0.0454600	−0.0227300	−	0.999742i	$-0.507236\pi$
$881$	−1.34933	−0.0454600	−0.0227300	+	0.999742i	$0.507236\pi$
$882$	0	0
$883$	−2.30160	−0.0774549	−0.0387274	−	0.999250i	$-0.512330\pi$
$883$	−2.30160	−0.0774549	−0.0387274	+	0.999250i	$0.512330\pi$
$884$	32.1613	1.08170
$885$	−1.53187	−0.0514933
$886$	−69.1288	−2.32243
$887$	−28.3102	−0.950562	−0.475281	−	0.879834i	$-0.657654\pi$
$887$	−28.3102	−0.950562	−0.475281	+	0.879834i	$0.657654\pi$
$888$	−17.2657	−0.579397
$889$	0	0
$890$	−17.8682	−0.598942
$891$	53.7794	1.80168
$892$	−69.3902	−2.32336
$893$	−47.1787	−1.57877
$894$	64.4001	2.15386
$895$	−10.8939	−0.364143
$896$	0	0
$897$	−7.71313	−0.257534
$898$	52.9196	1.76595
$899$	−5.16688	−0.172325
$900$	6.13794	0.204598
$901$	−63.1299	−2.10316
$902$	109.491	3.64565
$903$	0	0
$904$	−2.83183	−0.0941852
$905$	14.5082	0.482270
$906$	−31.6734	−1.05228
$907$	−34.3106	−1.13926	−0.569632	−	0.821900i	$-0.692914\pi$
$907$	−34.3106	−1.13926	−0.569632	+	0.821900i	$0.692914\pi$
$908$	9.84869	0.326840
$909$	−35.9996	−1.19403
$910$	0	0
$911$	50.9606	1.68840	0.844200	−	0.536028i	$-0.180076\pi$
$911$	50.9606	1.68840	0.844200	+	0.536028i	$0.180076\pi$
$912$	−22.9920	−0.761341
$913$	−72.5108	−2.39976
$914$	−28.1926	−0.932529
$915$	−3.28814	−0.108703
$916$	−66.1026	−2.18409
$917$	0	0
$918$	19.0350	0.628250
$919$	34.8768	1.15048	0.575239	−	0.817985i	$-0.304909\pi$
$919$	34.8768	1.15048	0.575239	+	0.817985i	$0.304909\pi$
$920$	−2.44020	−0.0804512
$921$	−19.1669	−0.631570
$922$	66.9876	2.20612
$923$	6.84108	0.225177
$924$	0	0
$925$	−4.31641	−0.141923
$926$	−24.9239	−0.819052
$927$	−6.67345	−0.219185
$928$	−38.0181	−1.24801
$929$	31.5112	1.03385	0.516925	−	0.856031i	$-0.327077\pi$
$929$	31.5112	1.03385	0.516925	+	0.856031i	$0.327077\pi$
$930$	−4.99239	−0.163707
$931$	0	0
$932$	5.26275	0.172387
$933$	54.4601	1.78294
$934$	39.0224	1.27685
$935$	−23.5340	−0.769644
$936$	9.36919	0.306242
$937$	−32.4318	−1.05950	−0.529751	−	0.848153i	$-0.677715\pi$
$937$	−32.4318	−1.05950	−0.529751	+	0.848153i	$0.677715\pi$
$938$	0	0
$939$	9.50546	0.310199
$940$	−22.9920	−0.749916
$941$	58.2556	1.89908	0.949539	−	0.313648i	$-0.101551\pi$
$941$	58.2556	1.89908	0.949539	+	0.313648i	$0.101551\pi$
$942$	−60.0224	−1.95563
$943$	−13.9121	−0.453040
$944$	1.18037	0.0384177
$945$	0	0
$946$	23.5974	0.767217
$947$	4.71660	0.153269	0.0766344	−	0.997059i	$-0.475583\pi$
$947$	4.71660	0.153269	0.0766344	+	0.997059i	$0.475583\pi$
$948$	−43.7355	−1.42046
$949$	6.94248	0.225362
$950$	12.5948	0.408630
$951$	38.6357	1.25285
$952$	0	0
$953$	45.8332	1.48468	0.742341	−	0.670022i	$-0.233716\pi$
$953$	45.8332	1.48468	0.742341	+	0.670022i	$0.233716\pi$
$954$	−64.2983	−2.08173
$955$	17.6219	0.570231
$956$	6.46055	0.208949
$957$	−58.7718	−1.89982
$958$	−12.5518	−0.405530
$959$	0	0
$960$	−28.7342	−0.927393
$961$	1.00000	0.0322581
$962$	−23.0355	−0.742695
$963$	27.4474	0.884480
$964$	17.7942	0.573112
$965$	−19.1897	−0.617737
$966$	0	0
$967$	0.784541	0.0252291	0.0126146	−	0.999920i	$-0.495985\pi$
$967$	0.784541	0.0252291	0.0126146	+	0.999920i	$0.495985\pi$
$968$	−24.4450	−0.785691
$969$	−61.7357	−1.98324
$970$	34.6096	1.11125
$971$	28.2625	0.906986	0.453493	−	0.891260i	$-0.350178\pi$
$971$	28.2625	0.906986	0.453493	+	0.891260i	$0.350178\pi$
$972$	53.2657	1.70850
$973$	0	0
$974$	−6.32823	−0.202769
$975$	5.54922	0.177717
$976$	2.53364	0.0811000
$977$	−33.6354	−1.07609	−0.538046	−	0.842916i	$-0.680837\pi$
$977$	−33.6354	−1.07609	−0.538046	+	0.842916i	$0.680837\pi$
$978$	1.28019	0.0409358
$979$	40.7110	1.30113
$980$	0	0
$981$	−18.1213	−0.578568
$982$	−35.8234	−1.14317
$983$	32.3523	1.03188	0.515939	−	0.856625i	$-0.327443\pi$
$983$	32.3523	1.03188	0.515939	+	0.856625i	$0.327443\pi$
$984$	40.0363	1.27631
$985$	−3.13352	−0.0998423
$986$	−53.3693	−1.69962
$987$	0	0
$988$	39.2159	1.24763
$989$	−2.99832	−0.0953412
$990$	−23.9696	−0.761802
$991$	−16.2184	−0.515195	−0.257598	−	0.966252i	$-0.582931\pi$
$991$	−16.2184	−0.515195	−0.257598	+	0.966252i	$0.582931\pi$
$992$	7.35805	0.233618
$993$	−49.8313	−1.58135
$994$	0	0
$995$	−4.03800	−0.128013
$996$	−92.6987	−2.93727
$997$	−43.0862	−1.36455	−0.682277	−	0.731093i	$-0.739010\pi$
$997$	−43.0862	−1.36455	−0.682277	+	0.731093i	$0.739010\pi$
$998$	−68.4474	−2.16666
$999$	−7.95451	−0.251670

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7595.2.a.s.1.1		4
7.6	odd	2		155.2.a.e.1.1	✓	4
21.20	even	2		1395.2.a.l.1.4		4
28.27	even	2		2480.2.a.x.1.1		4
35.13	even	4		775.2.b.f.249.7		8
35.27	even	4		775.2.b.f.249.2		8
35.34	odd	2		775.2.a.e.1.4		4
56.13	odd	2		9920.2.a.cb.1.1		4
56.27	even	2		9920.2.a.cg.1.4		4
105.104	even	2		6975.2.a.bn.1.1		4
217.216	even	2		4805.2.a.n.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
155.2.a.e.1.1	✓	4	7.6	odd	2
775.2.a.e.1.4		4	35.34	odd	2
775.2.b.f.249.2		8	35.27	even	4
775.2.b.f.249.7		8	35.13	even	4
1395.2.a.l.1.4		4	21.20	even	2
2480.2.a.x.1.1		4	28.27	even	2
4805.2.a.n.1.1		4	217.216	even	2
6975.2.a.bn.1.1		4	105.104	even	2
7595.2.a.s.1.1		4	1.1	even	1	trivial
9920.2.a.cb.1.1		4	56.13	odd	2
9920.2.a.cg.1.4		4	56.27	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)

\(f(q)\)	\(=\)	\(q-2.19117 q^{2} -2.27841 q^{3} +2.80122 q^{4} -1.00000 q^{5} +4.99239 q^{6} -1.75561 q^{8} +2.19117 q^{9} +O(q^{10})\)	\(q-2.19117 q^{2} -2.27841 q^{3} +2.80122 q^{4} -1.00000 q^{5} +4.99239 q^{6} -1.75561 q^{8} +2.19117 q^{9} +2.19117 q^{10} -4.99239 q^{11} -6.38234 q^{12} -2.43556 q^{13} +2.27841 q^{15} -1.75561 q^{16} -4.71397 q^{17} -4.80122 q^{18} -5.74800 q^{19} -2.80122 q^{20} +10.9392 q^{22} -1.38995 q^{23} +4.00000 q^{24} +1.00000 q^{25} +5.33672 q^{26} +1.84285 q^{27} -5.16688 q^{29} -4.99239 q^{30} +1.00000 q^{31} +7.35805 q^{32} +11.3747 q^{33} +10.3291 q^{34} +6.13794 q^{36} -4.31641 q^{37} +12.5948 q^{38} +5.54922 q^{39} +1.75561 q^{40} +10.0091 q^{41} +2.15715 q^{43} -13.9848 q^{44} -2.19117 q^{45} +3.04561 q^{46} +8.20785 q^{47} +4.00000 q^{48} -2.19117 q^{50} +10.7404 q^{51} -6.82254 q^{52} +13.3921 q^{53} -4.03800 q^{54} +4.99239 q^{55} +13.0963 q^{57} +11.3215 q^{58} -0.672342 q^{59} +6.38234 q^{60} -1.44317 q^{61} -2.19117 q^{62} -12.6115 q^{64} +2.43556 q^{65} -24.9239 q^{66} -14.9772 q^{67} -13.2049 q^{68} +3.16688 q^{69} -2.80883 q^{71} -3.84683 q^{72} -2.85046 q^{73} +9.45799 q^{74} -2.27841 q^{75} -16.1014 q^{76} -12.1593 q^{78} +6.85258 q^{79} +1.75561 q^{80} -10.7723 q^{81} -21.9316 q^{82} +14.5243 q^{83} +4.71397 q^{85} -4.72667 q^{86} +11.7723 q^{87} +8.76467 q^{88} -8.15462 q^{89} +4.80122 q^{90} -3.89355 q^{92} -2.27841 q^{93} -17.9848 q^{94} +5.74800 q^{95} -16.7647 q^{96} +15.7951 q^{97} -10.9392 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} - q^{3} + 5 q^{4} - 4 q^{5} + 4 q^{6} + 3 q^{8} - q^{9}+O(q^{10}) \) 4 * q + q^2 - q^3 + 5 * q^4 - 4 * q^5 + 4 * q^6 + 3 * q^8 - q^9	\( 4 q + q^{2} - q^{3} + 5 q^{4} - 4 q^{5} + 4 q^{6} + 3 q^{8} - q^{9} - q^{10} - 4 q^{11} - 6 q^{12} - 10 q^{13} + q^{15} + 3 q^{16} - 11 q^{17} - 13 q^{18} + 3 q^{19} - 5 q^{20} + 8 q^{22} - 2 q^{23} + 16 q^{24} + 4 q^{25} - 2 q^{26} - q^{27} - 8 q^{29} - 4 q^{30} + 4 q^{31} + 7 q^{32} + 10 q^{33} + 2 q^{34} - 5 q^{36} + 3 q^{37} + 22 q^{38} - 10 q^{39} - 3 q^{40} + 11 q^{41} + 17 q^{43} - 24 q^{44} + q^{45} + 16 q^{46} + 10 q^{47} + 16 q^{48} + q^{50} + q^{51} - 22 q^{52} + 13 q^{53} - 4 q^{54} + 4 q^{55} + 25 q^{57} - 10 q^{58} + 3 q^{59} + 6 q^{60} - 22 q^{61} + q^{62} - 9 q^{64} + 10 q^{65} - 32 q^{66} - 12 q^{67} - 28 q^{68} - 21 q^{71} - 13 q^{72} - 19 q^{73} - 2 q^{74} - q^{75} - 2 q^{76} - 20 q^{78} - 2 q^{79} - 3 q^{80} - 20 q^{81} - 36 q^{82} + 15 q^{83} + 11 q^{85} + 8 q^{86} + 24 q^{87} - 4 q^{88} + 10 q^{89} + 13 q^{90} + 24 q^{92} - q^{93} - 40 q^{94} - 3 q^{95} - 28 q^{96} - 4 q^{97} - 8 q^{99}+O(q^{100}) \) 4 * q + q^2 - q^3 + 5 * q^4 - 4 * q^5 + 4 * q^6 + 3 * q^8 - q^9 - q^10 - 4 * q^11 - 6 * q^12 - 10 * q^13 + q^15 + 3 * q^16 - 11 * q^17 - 13 * q^18 + 3 * q^19 - 5 * q^20 + 8 * q^22 - 2 * q^23 + 16 * q^24 + 4 * q^25 - 2 * q^26 - q^27 - 8 * q^29 - 4 * q^30 + 4 * q^31 + 7 * q^32 + 10 * q^33 + 2 * q^34 - 5 * q^36 + 3 * q^37 + 22 * q^38 - 10 * q^39 - 3 * q^40 + 11 * q^41 + 17 * q^43 - 24 * q^44 + q^45 + 16 * q^46 + 10 * q^47 + 16 * q^48 + q^50 + q^51 - 22 * q^52 + 13 * q^53 - 4 * q^54 + 4 * q^55 + 25 * q^57 - 10 * q^58 + 3 * q^59 + 6 * q^60 - 22 * q^61 + q^62 - 9 * q^64 + 10 * q^65 - 32 * q^66 - 12 * q^67 - 28 * q^68 - 21 * q^71 - 13 * q^72 - 19 * q^73 - 2 * q^74 - q^75 - 2 * q^76 - 20 * q^78 - 2 * q^79 - 3 * q^80 - 20 * q^81 - 36 * q^82 + 15 * q^83 + 11 * q^85 + 8 * q^86 + 24 * q^87 - 4 * q^88 + 10 * q^89 + 13 * q^90 + 24 * q^92 - q^93 - 40 * q^94 - 3 * q^95 - 28 * q^96 - 4 * q^97 - 8 * q^99

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