LMFDB - Embedded newform 900.3.ba.a.161.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,3,Mod(161,900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(900, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 8]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("900.161");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	900.ba (of order $10$, degree $4$, minimal)

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:	no
Analytic conductor:	$24.5232237924$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			161.7
Character	$\chi$	$=$	900.161
Dual form			900.3.ba.a.341.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.65177 - 4.23888i) q^{5} +6.40455 q^{7} +O(q^{10})$	$q+(-2.65177 - 4.23888i) q^{5} +6.40455 q^{7} +(-7.63768 - 10.5124i) q^{11} +(-2.47722 - 1.79980i) q^{13} +(-27.0399 + 8.78580i) q^{17} +(-1.60900 - 4.95199i) q^{19} +(1.08886 + 1.49868i) q^{23} +(-10.9363 + 22.4811i) q^{25} +(18.8359 + 6.12014i) q^{29} +(1.41047 + 4.34098i) q^{31} +(-16.9834 - 27.1481i) q^{35} +(27.4084 + 19.9134i) q^{37} +(5.14508 - 7.08160i) q^{41} -29.6940 q^{43} +(-13.2827 - 4.31580i) q^{47} -7.98180 q^{49} +(-36.9022 - 11.9903i) q^{53} +(-24.3074 + 60.2516i) q^{55} +(-42.2369 + 58.1341i) q^{59} +(6.46094 - 4.69414i) q^{61} +(-1.06016 + 15.2733i) q^{65} +(-13.6107 - 41.8895i) q^{67} +(-40.2562 - 13.0800i) q^{71} +(-88.0786 + 63.9928i) q^{73} +(-48.9159 - 67.3270i) q^{77} +(-35.0562 + 107.892i) q^{79} +(-68.7223 + 22.3292i) q^{83} +(108.946 + 91.3212i) q^{85} +(-76.6686 - 105.525i) q^{89} +(-15.8654 - 11.5269i) q^{91} +(-16.7242 + 19.9519i) q^{95} +(-24.5643 + 75.6012i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 16 q^{7}+O(q^{10}) $ 80 * q + 16 * q^7	$ 80 q + 16 q^{7} - 8 q^{13} + 60 q^{19} - 120 q^{25} + 120 q^{31} + 116 q^{37} - 80 q^{43} + 440 q^{49} + 120 q^{55} + 80 q^{61} + 24 q^{67} + 128 q^{73} + 40 q^{79} + 40 q^{85} - 140 q^{91} + 384 q^{97}+O(q^{100}) $ 80 * q + 16 * q^7 - 8 * q^13 + 60 * q^19 - 120 * q^25 + 120 * q^31 + 116 * q^37 - 80 * q^43 + 440 * q^49 + 120 * q^55 + 80 * q^61 + 24 * q^67 + 128 * q^73 + 40 * q^79 + 40 * q^85 - 140 * q^91 + 384 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$-1$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−2.65177	−	4.23888i	−0.530353	−	0.847777i
$5$	−2.65177	−	4.23888i	−0.530353	−	0.847777i
$6$		0			0
$7$	6.40455			0.914935			0.457468	−	0.889226i	$-0.348757\pi$
$7$	6.40455			0.914935			0.457468	+	0.889226i	$0.348757\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−7.63768	−	10.5124i	−0.694335	−	0.955670i	−0.999994	−	0.00352896i	$-0.998877\pi$
$11$	−7.63768	−	10.5124i	−0.694335	−	0.955670i	0.305659	−	0.952141i	$-0.401123\pi$
$12$		0			0
$13$	−2.47722	−	1.79980i	−0.190555	−	0.138446i	0.488417	−	0.872610i	$-0.337574\pi$
$13$	−2.47722	−	1.79980i	−0.190555	−	0.138446i	−0.678972	+	0.734164i	$0.737574\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−27.0399	+	8.78580i	−1.59058	+	0.516812i	−0.964755	−	0.263149i	$-0.915239\pi$
$17$	−27.0399	+	8.78580i	−1.59058	+	0.516812i	−0.625828	+	0.779961i	$0.715239\pi$
$18$		0			0
$19$	−1.60900	−	4.95199i	−0.0846842	−	0.260631i	0.899744	−	0.436418i	$-0.143753\pi$
$19$	−1.60900	−	4.95199i	−0.0846842	−	0.260631i	−0.984428	+	0.175787i	$0.943753\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	1.08886	+	1.49868i	0.0473416	+	0.0651601i	0.832031	−	0.554728i	$-0.187178\pi$
$23$	1.08886	+	1.49868i	0.0473416	+	0.0651601i	−0.784690	+	0.619888i	$0.787178\pi$
$24$		0			0
$25$	−10.9363	+	22.4811i	−0.437451	+	0.899242i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	18.8359	+	6.12014i	0.649512	+	0.211039i	0.615199	−	0.788372i	$-0.289076\pi$
$29$	18.8359	+	6.12014i	0.649512	+	0.211039i	0.0343133	+	0.999411i	$0.489076\pi$
$30$		0			0
$31$	1.41047	+	4.34098i	0.0454991	+	0.140032i	0.971225	−	0.238163i	$-0.0765451\pi$
$31$	1.41047	+	4.34098i	0.0454991	+	0.140032i	−0.925726	+	0.378194i	$0.876545\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−16.9834	−	27.1481i	−0.485239	−	0.775661i
$36$		0			0
$37$	27.4084	+	19.9134i	0.740767	+	0.538199i	0.892951	−	0.450153i	$-0.148631\pi$
$37$	27.4084	+	19.9134i	0.740767	+	0.538199i	−0.152184	+	0.988352i	$0.548631\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	5.14508	−	7.08160i	0.125490	−	0.172722i	−0.741649	−	0.670788i	$-0.765956\pi$
$41$	5.14508	−	7.08160i	0.125490	−	0.172722i	0.867139	+	0.498066i	$0.165956\pi$
$42$		0			0
$43$	−29.6940			−0.690559			−0.345279	−	0.938500i	$-0.612216\pi$
$43$	−29.6940			−0.690559			−0.345279	+	0.938500i	$0.612216\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−13.2827	−	4.31580i	−0.282610	−	0.0918256i	0.164282	−	0.986413i	$-0.447469\pi$
$47$	−13.2827	−	4.31580i	−0.282610	−	0.0918256i	−0.446892	+	0.894588i	$0.647469\pi$
$48$		0			0
$49$	−7.98180			−0.162894
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−36.9022	−	11.9903i	−0.696268	−	0.226231i	−0.0605645	−	0.998164i	$-0.519290\pi$
$53$	−36.9022	−	11.9903i	−0.696268	−	0.226231i	−0.635704	+	0.771933i	$0.719290\pi$
$54$		0			0
$55$	−24.3074	+	60.2516i	−0.441952	+	1.09548i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−42.2369	+	58.1341i	−0.715879	+	0.985323i	0.283771	+	0.958892i	$0.408414\pi$
$59$	−42.2369	+	58.1341i	−0.715879	+	0.985323i	−0.999651	+	0.0264314i	$0.991586\pi$
$60$		0			0
$61$	6.46094	−	4.69414i	0.105917	−	0.0769532i	−0.533566	−	0.845758i	$-0.679148\pi$
$61$	6.46094	−	4.69414i	0.105917	−	0.0769532i	0.639483	+	0.768805i	$0.279148\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−1.06016	+	15.2733i	−0.0163101	+	0.234974i
$66$		0			0
$67$	−13.6107	−	41.8895i	−0.203145	−	0.625217i	−0.999784	−	0.0207616i	$-0.993391\pi$
$67$	−13.6107	−	41.8895i	−0.203145	−	0.625217i	0.796639	−	0.604455i	$-0.206609\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−40.2562	−	13.0800i	−0.566989	−	0.184226i	0.0114744	−	0.999934i	$-0.496348\pi$
$71$	−40.2562	−	13.0800i	−0.566989	−	0.184226i	−0.578464	+	0.815708i	$0.696348\pi$
$72$		0			0
$73$	−88.0786	+	63.9928i	−1.20656	+	0.876614i	−0.994913	−	0.100733i	$-0.967881\pi$
$73$	−88.0786	+	63.9928i	−1.20656	+	0.876614i	−0.211642	+	0.977347i	$0.567881\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−48.9159	−	67.3270i	−0.635271	−	0.874376i
$78$		0			0
$79$	−35.0562	+	107.892i	−0.443750	+	1.36572i	0.440099	+	0.897949i	$0.354943\pi$
$79$	−35.0562	+	107.892i	−0.443750	+	1.36572i	−0.883849	+	0.467772i	$0.845057\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−68.7223	+	22.3292i	−0.827980	+	0.269027i	−0.692194	−	0.721711i	$-0.743356\pi$
$83$	−68.7223	+	22.3292i	−0.827980	+	0.269027i	−0.135786	+	0.990738i	$0.543356\pi$
$84$		0			0
$85$	108.946	+	91.3212i	1.28171	+	1.07437i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−76.6686	−	105.525i	−0.861445	−	1.18568i	−0.981223	−	0.192877i	$-0.938218\pi$
$89$	−76.6686	−	105.525i	−0.861445	−	1.18568i	0.119778	−	0.992801i	$-0.461782\pi$
$90$		0			0
$91$	−15.8654	−	11.5269i	−0.174346	−	0.126669i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−16.7242	+	19.9519i	−0.176045	+	0.210020i
$96$		0			0
$97$	−24.5643	+	75.6012i	−0.253240	+	0.779394i	0.740931	+	0.671581i	$0.234385\pi$
$97$	−24.5643	+	75.6012i	−0.253240	+	0.779394i	−0.994171	+	0.107813i	$0.965615\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$			15.1877i			0.150374i	0.997169	+	0.0751869i	$0.0239553\pi$
$101$			15.1877i			0.150374i	−0.997169	+	0.0751869i	$0.976045\pi$
$102$		0			0
$103$	−2.88425	+	8.87682i	−0.0280025	+	0.0861827i	−0.964081	−	0.265608i	$-0.914427\pi$
$103$	−2.88425	+	8.87682i	−0.0280025	+	0.0861827i	0.936079	+	0.351791i	$0.114427\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	82.2087i		−	0.768306i	−0.923269	−	0.384153i	$-0.874494\pi$
$107$		−	82.2087i		−	0.768306i	0.923269	−	0.384153i	$-0.125506\pi$
$108$		0			0
$109$	−43.0799	−	31.2994i	−0.395228	−	0.287150i	0.372366	−	0.928086i	$-0.378546\pi$
$109$	−43.0799	−	31.2994i	−0.395228	−	0.287150i	−0.767595	+	0.640936i	$0.778546\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	2.54996	−	3.50973i	0.0225661	−	0.0310595i	−0.797585	−	0.603207i	$-0.793889\pi$
$113$	2.54996	−	3.50973i	0.0225661	−	0.0310595i	0.820151	+	0.572147i	$0.193889\pi$
$114$		0			0
$115$	3.46535	−	8.58969i	0.0301334	−	0.0746929i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−173.178	+	56.2691i	−1.45528	+	0.472849i
$120$		0			0
$121$	−14.7847	+	45.5025i	−0.122187	+	0.376054i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	124.295	−	13.2569i	0.994360	−	0.106055i
$126$		0			0
$127$	121.599	−	88.3467i	0.957471	−	0.695644i	0.00490920	−	0.999988i	$-0.498437\pi$
$127$	121.599	−	88.3467i	0.957471	−	0.695644i	0.952562	+	0.304344i	$0.0984373\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−185.356	+	60.2260i	−1.41493	+	0.459740i	−0.913989	−	0.405739i	$-0.867014\pi$
$131$	−185.356	+	60.2260i	−1.41493	+	0.459740i	−0.500946	+	0.865479i	$0.667014\pi$
$132$		0			0
$133$	−10.3049	−	31.7153i	−0.0774806	−	0.238461i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	20.9414	−	28.8233i	0.152857	−	0.210389i	−0.725720	−	0.687990i	$-0.758493\pi$
$137$	20.9414	−	28.8233i	0.152857	−	0.210389i	0.878577	+	0.477601i	$0.158493\pi$
$138$		0			0
$139$	201.595	−	146.467i	1.45032	−	1.05372i	0.464570	−	0.885537i	$-0.346209\pi$
$139$	201.595	−	146.467i	1.45032	−	1.05372i	0.985755	−	0.168186i	$-0.0537909\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$			39.7878i			0.278236i
$144$		0			0
$145$	−24.0057	−	96.0722i	−0.165557	−	0.662567i
$146$		0			0
$147$		0			0
$148$		0			0
$149$		−	269.977i		−	1.81193i	−0.423357	−	0.905963i	$-0.639148\pi$
$149$		−	269.977i		−	1.81193i	0.423357	−	0.905963i	$-0.360852\pi$
$150$		0			0
$151$	−138.115			−0.914667			−0.457333	−	0.889295i	$-0.651195\pi$
$151$	−138.115			−0.914667			−0.457333	+	0.889295i	$0.651195\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	14.6607	−	17.4901i	0.0945851	−	0.112839i
$156$		0			0
$157$	−92.5578			−0.589540			−0.294770	−	0.955568i	$-0.595243\pi$
$157$	−92.5578			−0.589540			−0.294770	+	0.955568i	$0.595243\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	6.97363	+	9.59837i	0.0433144	+	0.0596172i
$162$		0			0
$163$	210.578	+	152.994i	1.29189	+	0.938615i	0.999842	−	0.0177879i	$-0.00566236\pi$
$163$	210.578	+	152.994i	1.29189	+	0.938615i	0.292051	+	0.956403i	$0.405662\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	78.7484	−	25.5869i	0.471547	−	0.153215i	−0.0635972	−	0.997976i	$-0.520257\pi$
$167$	78.7484	−	25.5869i	0.471547	−	0.153215i	0.535144	+	0.844761i	$0.320257\pi$
$168$		0			0
$169$	−49.3266	−	151.812i	−0.291873	−	0.898293i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	183.908	+	253.128i	1.06305	+	1.46317i	0.876917	+	0.480641i	$0.159596\pi$
$173$	183.908	+	253.128i	1.06305	+	1.46317i	0.186135	+	0.982524i	$0.440404\pi$
$174$		0			0
$175$	−70.0418	+	143.981i	−0.400239	+	0.822748i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	155.165	+	50.4161i	0.866842	+	0.281654i	0.708483	−	0.705727i	$-0.249380\pi$
$179$	155.165	+	50.4161i	0.866842	+	0.281654i	0.158359	+	0.987382i	$0.449380\pi$
$180$		0			0
$181$	−33.3697	−	102.702i	−0.184363	−	0.567412i	0.815574	−	0.578653i	$-0.196422\pi$
$181$	−33.3697	−	102.702i	−0.184363	−	0.567412i	−0.999937	+	0.0112417i	$0.996422\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	11.7298	−	168.987i	0.0634042	−	0.913441i
$186$		0			0
$187$	298.882	+	217.150i	1.59830	+	1.16123i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−127.267	+	175.168i	−0.666318	+	0.917108i	−0.999670	−	0.0256942i	$-0.991820\pi$
$191$	−127.267	+	175.168i	−0.666318	+	0.917108i	0.333352	+	0.942803i	$0.391820\pi$
$192$		0			0
$193$	−188.553			−0.976959			−0.488480	−	0.872575i	$-0.662448\pi$
$193$	−188.553			−0.976959			−0.488480	+	0.872575i	$0.662448\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−6.70553	−	2.17876i	−0.0340382	−	0.0110597i	0.291948	−	0.956434i	$-0.405696\pi$
$197$	−6.70553	−	2.17876i	−0.0340382	−	0.0110597i	−0.325987	+	0.945374i	$0.605696\pi$
$198$		0			0
$199$	−57.3828			−0.288356			−0.144178	−	0.989552i	$-0.546054\pi$
$199$	−57.3828			−0.288356			−0.144178	+	0.989552i	$0.546054\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	120.635	+	39.1967i	0.594262	+	0.193087i
$204$		0			0
$205$	−43.6616	−	3.03066i	−0.212984	−	0.0147837i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−39.7682	+	54.7362i	−0.190278	+	0.261896i
$210$		0			0
$211$	−129.694	+	94.2282i	−0.614663	+	0.446579i	−0.851053	−	0.525079i	$-0.824036\pi$
$211$	−129.694	+	94.2282i	−0.614663	+	0.446579i	0.236390	+	0.971658i	$0.424036\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	78.7416	+	125.870i	0.366240	+	0.585440i
$216$		0			0
$217$	9.03343	+	27.8020i	0.0416287	+	0.128120i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	82.7965	+	26.9022i	0.374645	+	0.121729i
$222$		0			0
$223$	−245.569	+	178.417i	−1.10121	+	0.800074i	−0.981257	−	0.192706i	$-0.938274\pi$
$223$	−245.569	+	178.417i	−1.10121	+	0.800074i	−0.119951	+	0.992780i	$0.538274\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	88.9964	+	122.493i	0.392055	+	0.539617i	0.958728	−	0.284326i	$-0.0917697\pi$
$227$	88.9964	+	122.493i	0.392055	+	0.539617i	−0.566673	+	0.823943i	$0.691770\pi$
$228$		0			0
$229$	135.756	−	417.815i	0.592822	−	1.82452i	0.0275404	−	0.999621i	$-0.491233\pi$
$229$	135.756	−	417.815i	0.592822	−	1.82452i	0.565282	−	0.824898i	$-0.308767\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	145.800	−	47.3732i	0.625749	−	0.203318i	0.0210581	−	0.999778i	$-0.493297\pi$
$233$	145.800	−	47.3732i	0.625749	−	0.203318i	0.604691	+	0.796460i	$0.293297\pi$
$234$		0			0
$235$	16.9284	+	67.7482i	0.0720356	+	0.288290i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	2.24102	+	3.08449i	0.00937664	+	0.0129058i	0.813680	−	0.581314i	$-0.197461\pi$
$239$	2.24102	+	3.08449i	0.00937664	+	0.0129058i	−0.804303	+	0.594219i	$0.797461\pi$
$240$		0			0
$241$	−376.999	−	273.906i	−1.56431	−	1.13654i	−0.932360	−	0.361531i	$-0.882254\pi$
$241$	−376.999	−	273.906i	−1.56431	−	1.13654i	−0.631951	−	0.775008i	$-0.717746\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	21.1659	+	33.8339i	0.0863913	+	0.138098i
$246$		0			0
$247$	−4.92677	+	15.1630i	−0.0199464	+	0.0613888i
$248$		0			0
$249$		0			0
$250$		0			0
$251$			170.159i			0.677926i	0.940800	+	0.338963i	$0.110076\pi$
$251$			170.159i			0.677926i	−0.940800	+	0.338963i	$0.889924\pi$
$252$		0			0
$253$	7.43836	−	22.8929i	0.0294006	−	0.0904858i
$254$		0			0
$255$		0			0
$256$		0			0
$257$		−	192.347i		−	0.748431i	−0.927342	−	0.374215i	$-0.877912\pi$
$257$		−	192.347i		−	0.748431i	0.927342	−	0.374215i	$-0.122088\pi$
$258$		0			0
$259$	175.538	+	127.536i	0.677754	+	0.492417i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	78.2994	−	107.770i	0.297716	−	0.409772i	−0.633785	−	0.773509i	$-0.718500\pi$
$263$	78.2994	−	107.770i	0.297716	−	0.409772i	0.931501	+	0.363738i	$0.118500\pi$
$264$		0			0
$265$	47.0308	+	188.220i	0.177475	+	0.710263i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−211.418	+	68.6939i	−0.785941	+	0.255368i	−0.674375	−	0.738389i	$-0.735587\pi$
$269$	−211.418	+	68.6939i	−0.785941	+	0.255368i	−0.111566	+	0.993757i	$0.535587\pi$
$270$		0			0
$271$	154.476	−	475.427i	0.570020	−	1.75434i	−0.0825210	−	0.996589i	$-0.526297\pi$
$271$	154.476	−	475.427i	0.570020	−	1.75434i	0.652541	−	0.757753i	$-0.273703\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	319.857	−	56.7371i	1.16312	−	0.206317i
$276$		0			0
$277$	277.946	−	201.940i	1.00342	−	0.729024i	0.0405977	−	0.999176i	$-0.487074\pi$
$277$	277.946	−	201.940i	1.00342	−	0.729024i	0.962818	+	0.270151i	$0.0870738\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	252.490	−	82.0390i	0.898542	−	0.291954i	0.176907	−	0.984228i	$-0.443391\pi$
$281$	252.490	−	82.0390i	0.898542	−	0.291954i	0.721635	+	0.692274i	$0.243391\pi$
$282$		0			0
$283$	10.6616	+	32.8131i	0.0376736	+	0.115947i	0.968125	−	0.250469i	$-0.0805847\pi$
$283$	10.6616	+	32.8131i	0.0376736	+	0.115947i	−0.930451	+	0.366416i	$0.880585\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	32.9519	−	45.3544i	0.114815	−	0.158029i
$288$		0			0
$289$	420.161	−	305.265i	1.45384	−	1.05628i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		−	118.927i		−	0.405893i	−0.979190	−	0.202946i	$-0.934948\pi$
$293$		−	118.927i		−	0.405893i	0.979190	−	0.202946i	$-0.0650517\pi$
$294$		0			0
$295$	358.426	+	24.8792i	1.21500	+	0.0843364i
$296$		0			0
$297$		0			0
$298$		0			0
$299$		−	5.67229i		−	0.0189709i
$300$		0			0
$301$	−190.177			−0.631816
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−37.0308	−	14.9394i	−0.121413	−	0.0489816i
$306$		0			0
$307$	559.101			1.82118			0.910589	−	0.413314i	$-0.135629\pi$
$307$	559.101			1.82118			0.910589	+	0.413314i	$0.135629\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	287.409	+	395.585i	0.924146	+	1.27198i	0.962100	+	0.272698i	$0.0879160\pi$
$311$	287.409	+	395.585i	0.924146	+	1.27198i	−0.0379540	+	0.999279i	$0.512084\pi$
$312$		0			0
$313$	−206.023	−	149.685i	−0.658221	−	0.478226i	0.207840	−	0.978163i	$-0.433357\pi$
$313$	−206.023	−	149.685i	−0.658221	−	0.478226i	−0.866062	+	0.499937i	$0.833357\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	550.719	−	178.939i	1.73728	−	0.564478i	0.742813	−	0.669499i	$-0.233491\pi$
$317$	550.719	−	178.939i	1.73728	−	0.564478i	0.994470	+	0.105021i	$0.0334911\pi$
$318$		0			0
$319$	−79.5252	−	244.753i	−0.249295	−	0.767252i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	87.0145	+	119.765i	0.269395	+	0.370790i
$324$		0			0
$325$	67.5530	−	36.0073i	0.207855	−	0.110792i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−85.0695	−	27.6408i	−0.258570	−	0.0840145i
$330$		0			0
$331$	−136.030	−	418.657i	−0.410966	−	1.26482i	−0.915809	−	0.401613i	$-0.868450\pi$
$331$	−136.030	−	418.657i	−0.410966	−	1.26482i	0.504843	−	0.863211i	$-0.331550\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−141.472	+	168.775i	−0.422305	+	0.503807i
$336$		0			0
$337$	−95.4850	−	69.3739i	−0.283338	−	0.205857i	0.437034	−	0.899445i	$-0.356029\pi$
$337$	−95.4850	−	69.3739i	−0.283338	−	0.205857i	−0.720372	+	0.693588i	$0.756029\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	34.8613	−	47.9825i	0.102233	−	0.140711i
$342$		0			0
$343$	−364.943			−1.06397
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−326.505	−	106.088i	−0.940935	−	0.305728i	−0.201908	−	0.979404i	$-0.564714\pi$
$347$	−326.505	−	106.088i	−0.940935	−	0.305728i	−0.739027	+	0.673676i	$0.764714\pi$
$348$		0			0
$349$	−293.247			−0.840249			−0.420125	−	0.907466i	$-0.638014\pi$
$349$	−293.247			−0.840249			−0.420125	+	0.907466i	$0.638014\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	499.906	+	162.429i	1.41616	+	0.460139i	0.914381	−	0.404855i	$-0.132678\pi$
$353$	499.906	+	162.429i	1.41616	+	0.460139i	0.501782	+	0.864994i	$0.332678\pi$
$354$		0			0
$355$	51.3053	+	205.327i	0.144522	+	0.578385i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−84.2923	+	116.018i	−0.234797	+	0.323171i	−0.910115	−	0.414356i	$-0.864007\pi$
$359$	−84.2923	+	116.018i	−0.234797	+	0.323171i	0.675317	+	0.737527i	$0.264007\pi$
$360$		0			0
$361$	270.122	−	196.255i	0.748260	−	0.543643i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	504.822	+	203.661i	1.38307	+	0.557975i
$366$		0			0
$367$	46.5084	+	143.138i	0.126726	+	0.390022i	0.994212	−	0.107440i	$-0.0342654\pi$
$367$	46.5084	+	143.138i	0.126726	+	0.390022i	−0.867486	+	0.497462i	$0.834265\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−236.342	−	76.7922i	−0.637040	−	0.206987i
$372$		0			0
$373$	−353.068	+	256.519i	−0.946563	+	0.687718i	−0.949991	−	0.312276i	$-0.898909\pi$
$373$	−353.068	+	256.519i	−0.946563	+	0.687718i	0.00342873	+	0.999994i	$0.498909\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−35.6455	−	49.0618i	−0.0945503	−	0.130137i
$378$		0			0
$379$	202.259	−	622.489i	0.533665	−	1.64245i	−0.212852	−	0.977084i	$-0.568275\pi$
$379$	202.259	−	622.489i	0.533665	−	1.64245i	0.746517	−	0.665367i	$-0.231725\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−298.099	+	96.8583i	−0.778327	+	0.252894i	−0.671126	−	0.741344i	$-0.734189\pi$
$383$	−298.099	+	96.8583i	−0.778327	+	0.252894i	−0.107201	+	0.994237i	$0.534189\pi$
$384$		0			0
$385$	−155.678	+	385.884i	−0.404357	+	1.00230i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	23.3414	+	32.1267i	0.0600037	+	0.0825880i	0.837964	−	0.545725i	$-0.183746\pi$
$389$	23.3414	+	32.1267i	0.0600037	+	0.0825880i	−0.777961	+	0.628313i	$0.783746\pi$
$390$		0			0
$391$	−42.6097	−	30.9577i	−0.108976	−	0.0791758i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	550.302	−	137.505i	1.39317	−	0.348114i
$396$		0			0
$397$	181.148	−	557.515i	0.456291	−	1.40432i	−0.413322	−	0.910585i	$-0.635632\pi$
$397$	181.148	−	557.515i	0.456291	−	1.40432i	0.869613	−	0.493734i	$-0.164368\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$			240.627i			0.600067i	0.953929	+	0.300034i	$0.0969979\pi$
$401$			240.627i			0.600067i	−0.953929	+	0.300034i	$0.903002\pi$
$402$		0			0
$403$	4.31887	−	13.2921i	0.0107168	−	0.0329829i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	440.219i		−	1.08162i
$408$		0			0
$409$	278.080	+	202.037i	0.679902	+	0.493977i	0.873325	−	0.487138i	$-0.161959\pi$
$409$	278.080	+	202.037i	0.679902	+	0.493977i	−0.193423	+	0.981115i	$0.561959\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−270.508	+	372.322i	−0.654983	+	0.901507i
$414$		0			0
$415$	276.887	+	232.094i	0.667197	+	0.559263i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	181.855	−	59.0884i	0.434023	−	0.141023i	−0.0838535	−	0.996478i	$-0.526723\pi$
$419$	181.855	−	59.0884i	0.434023	−	0.141023i	0.517876	+	0.855456i	$0.326723\pi$
$420$		0			0
$421$	−170.176	+	523.749i	−0.404219	+	1.24406i	0.517326	+	0.855788i	$0.326927\pi$
$421$	−170.176	+	523.749i	−0.404219	+	1.24406i	−0.921545	+	0.388270i	$0.873073\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	98.2017	−	703.970i	0.231063	−	1.65640i
$426$		0			0
$427$	41.3794	−	30.0639i	0.0969072	−	0.0704072i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−523.416	+	170.068i	−1.21442	+	0.394589i	−0.845047	−	0.534691i	$-0.820428\pi$
$431$	−523.416	+	170.068i	−1.21442	+	0.394589i	−0.369374	+	0.929281i	$0.620428\pi$
$432$		0			0
$433$	69.2362	+	213.087i	0.159899	+	0.492118i	0.998624	−	0.0524365i	$-0.0166987\pi$
$433$	69.2362	+	213.087i	0.159899	+	0.492118i	−0.838725	+	0.544555i	$0.816699\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	5.66949	−	7.80338i	0.0129737	−	0.0178567i
$438$		0			0
$439$	−381.341	+	277.061i	−0.868659	+	0.631118i	−0.930227	−	0.366985i	$-0.880390\pi$
$439$	−381.341	+	277.061i	−0.868659	+	0.631118i	0.0615676	+	0.998103i	$0.480390\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$			627.722i			1.41698i	0.705721	+	0.708490i	$0.250623\pi$
$443$			627.722i			1.41698i	−0.705721	+	0.708490i	$0.749377\pi$
$444$		0			0
$445$	−244.002	+	604.818i	−0.548320	+	1.35914i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	361.286i		−	0.804646i	−0.915498	−	0.402323i	$-0.868203\pi$
$449$		−	361.286i		−	0.804646i	0.915498	−	0.402323i	$-0.131797\pi$
$450$		0			0
$451$	−113.741			−0.252197
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−6.78982	+	97.8185i	−0.0149227	+	0.214986i
$456$		0			0
$457$	346.134			0.757404			0.378702	−	0.925519i	$-0.376370\pi$
$457$	346.134			0.757404			0.378702	+	0.925519i	$0.376370\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−434.514	−	598.058i	−0.942547	−	1.29730i	−0.954759	−	0.297379i	$-0.903887\pi$
$461$	−434.514	−	598.058i	−0.942547	−	1.29730i	0.0122123	−	0.999925i	$-0.496113\pi$
$462$		0			0
$463$	−139.715	−	101.509i	−0.301761	−	0.219242i	0.426592	−	0.904444i	$-0.359714\pi$
$463$	−139.715	−	101.509i	−0.301761	−	0.219242i	−0.728353	+	0.685202i	$0.759714\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−256.382	+	83.3037i	−0.548999	+	0.178381i	−0.570365	−	0.821391i	$-0.693198\pi$
$467$	−256.382	+	83.3037i	−0.548999	+	0.178381i	0.0213664	+	0.999772i	$0.493198\pi$
$468$		0			0
$469$	−87.1705	−	268.283i	−0.185865	−	0.572033i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	226.794	+	312.155i	0.479479	+	0.659946i
$474$		0			0
$475$	128.923	+	17.9843i	0.271416	+	0.0378617i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−833.189	−	270.720i	−1.73943	−	0.565177i	−0.744676	−	0.667426i	$-0.767396\pi$
$479$	−833.189	−	270.720i	−1.73943	−	0.565177i	−0.994759	+	0.102250i	$0.967396\pi$
$480$		0			0
$481$	−32.0564	−	98.6594i	−0.0666453	−	0.205113i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	385.604	−	96.3515i	0.795059	−	0.198663i
$486$		0			0
$487$	270.570	+	196.580i	0.555585	+	0.403656i	0.829840	−	0.558001i	$-0.188431\pi$
$487$	270.570	+	196.580i	0.555585	+	0.403656i	−0.274256	+	0.961657i	$0.588431\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−344.800	+	474.576i	−0.702240	+	0.966550i	0.297690	+	0.954663i	$0.403784\pi$
$491$	−344.800	+	474.576i	−0.702240	+	0.966550i	−0.999929	+	0.0118873i	$0.996216\pi$
$492$		0			0
$493$	−563.090			−1.14217
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−257.823	−	83.7717i	−0.518758	−	0.168555i
$498$		0			0
$499$	−459.281			−0.920403			−0.460202	−	0.887814i	$-0.652223\pi$
$499$	−459.281			−0.920403			−0.460202	+	0.887814i	$0.652223\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	526.878	+	171.193i	1.04747	+	0.340344i	0.781675	−	0.623686i	$-0.214365\pi$
$503$	526.878	+	171.193i	1.04747	+	0.340344i	0.265795	+	0.964029i	$0.414365\pi$
$504$		0			0
$505$	64.3791	−	40.2743i	0.127483	−	0.0797512i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−17.7591	+	24.4433i	−0.0348901	+	0.0480221i	−0.826106	−	0.563515i	$-0.809449\pi$
$509$	−17.7591	+	24.4433i	−0.0348901	+	0.0480221i	0.791216	+	0.611537i	$0.209449\pi$
$510$		0			0
$511$	−564.103	+	409.845i	−1.10392	+	0.802045i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	45.2762	−	11.3132i	0.0879149	−	0.0219674i
$516$		0			0
$517$	56.0796	+	172.595i	0.108471	+	0.333840i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−38.6889	−	12.5708i	−0.0742590	−	0.0241282i	0.271652	−	0.962396i	$-0.412430\pi$
$521$	−38.6889	−	12.5708i	−0.0742590	−	0.0241282i	−0.345911	+	0.938267i	$0.612430\pi$
$522$		0			0
$523$	432.450	−	314.193i	0.826864	−	0.600752i	−0.0918065	−	0.995777i	$-0.529264\pi$
$523$	432.450	−	314.193i	0.826864	−	0.600752i	0.918670	+	0.395025i	$0.129264\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−76.2780	−	104.988i	−0.144740	−	0.199218i
$528$		0			0
$529$	162.410	−	499.845i	0.307012	−	0.944887i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−25.4910	+	8.28252i	−0.0478255	+	0.0155394i
$534$		0			0
$535$	−348.473	+	217.998i	−0.651352	+	0.407474i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	60.9624	+	83.9076i	0.113103	+	0.155673i
$540$		0			0
$541$	28.6592	+	20.8221i	0.0529745	+	0.0384882i	0.613957	−	0.789339i	$-0.289577\pi$
$541$	28.6592	+	20.8221i	0.0529745	+	0.0384882i	−0.560983	+	0.827827i	$0.689577\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−18.4366	+	265.609i	−0.0338286	+	0.487356i
$546$		0			0
$547$	−111.187	+	342.199i	−0.203267	+	0.625592i	0.796513	+	0.604622i	$0.206676\pi$
$547$	−111.187	+	342.199i	−0.203267	+	0.625592i	−0.999780	+	0.0209707i	$0.993324\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		−	103.122i		−	0.187155i
$552$		0			0
$553$	−224.519	+	690.999i	−0.406002	+	1.24955i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	581.028i		−	1.04314i	−0.853209	−	0.521569i	$-0.825347\pi$
$557$		−	581.028i		−	1.04314i	0.853209	−	0.521569i	$-0.174653\pi$
$558$		0			0
$559$	73.5585	+	53.4434i	0.131590	+	0.0956054i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−497.947	+	685.366i	−0.884454	+	1.21735i	0.0907139	+	0.995877i	$0.471085\pi$
$563$	−497.947	+	685.366i	−0.884454	+	1.21735i	−0.975167	+	0.221469i	$0.928915\pi$
$564$		0			0
$565$	−21.6392	−	1.50203i	−0.0382995	−	0.00265846i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−195.245	+	63.4390i	−0.343137	+	0.111492i	−0.475516	−	0.879707i	$-0.657739\pi$
$569$	−195.245	+	63.4390i	−0.343137	+	0.111492i	0.132379	+	0.991199i	$0.457739\pi$
$570$		0			0
$571$	154.235	−	474.686i	0.270113	−	0.831323i	−0.720358	−	0.693603i	$-0.756022\pi$
$571$	154.235	−	474.686i	0.270113	−	0.831323i	0.990471	−	0.137721i	$-0.0439776\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−45.6000	+	8.08864i	−0.0793043	+	0.0140672i
$576$		0			0
$577$	281.175	−	204.285i	0.487304	−	0.354047i	−0.316842	−	0.948478i	$-0.602623\pi$
$577$	281.175	−	204.285i	0.487304	−	0.354047i	0.804147	+	0.594431i	$0.202623\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−440.135	+	143.009i	−0.757548	+	0.246142i
$582$		0			0
$583$	155.802	+	479.508i	0.267241	+	0.822483i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	222.988	−	306.916i	0.379877	−	0.522856i	−0.575675	−	0.817679i	$-0.695261\pi$
$587$	222.988	−	306.916i	0.379877	−	0.522856i	0.955552	+	0.294823i	$0.0952606\pi$
$588$		0			0
$589$	19.2271	−	13.9693i	0.0326436	−	0.0237170i
$590$		0			0
$591$		0			0
$592$		0			0
$593$		−	1032.11i		−	1.74049i	−0.492615	−	0.870247i	$-0.663959\pi$
$593$		−	1032.11i		−	1.74049i	0.492615	−	0.870247i	$-0.336041\pi$
$594$		0			0
$595$	697.747	+	584.871i	1.17268	+	0.982976i
$596$		0			0
$597$		0			0
$598$		0			0
$599$		−	473.462i		−	0.790421i	−0.918591	−	0.395210i	$-0.870672\pi$
$599$		−	473.462i		−	0.790421i	0.918591	−	0.395210i	$-0.129328\pi$
$600$		0			0
$601$	−282.810			−0.470566			−0.235283	−	0.971927i	$-0.575602\pi$
$601$	−282.810			−0.470566			−0.235283	+	0.971927i	$0.575602\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	232.085	−	57.9916i	0.383612	−	0.0958538i
$606$		0			0
$607$	426.439			0.702535			0.351268	−	0.936275i	$-0.385751\pi$
$607$	426.439			0.702535			0.351268	+	0.936275i	$0.385751\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	25.1365	+	34.5974i	0.0411399	+	0.0566242i
$612$		0			0
$613$	−141.691	−	102.944i	−0.231143	−	0.167935i	0.466185	−	0.884687i	$-0.345628\pi$
$613$	−141.691	−	102.944i	−0.231143	−	0.167935i	−0.697328	+	0.716752i	$0.745628\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−137.680	+	44.7349i	−0.223144	+	0.0725039i	−0.418455	−	0.908237i	$-0.637428\pi$
$617$	−137.680	+	44.7349i	−0.223144	+	0.0725039i	0.195311	+	0.980741i	$0.437428\pi$
$618$		0			0
$619$	81.4074	+	250.546i	0.131514	+	0.404760i	0.995032	−	0.0995598i	$-0.0317434\pi$
$619$	81.4074	+	250.546i	0.131514	+	0.404760i	−0.863517	+	0.504319i	$0.831743\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−491.028	−	675.842i	−0.788167	−	1.08482i
$624$		0			0
$625$	−385.796	−	491.718i	−0.617274	−	0.786749i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−916.075	−	297.651i	−1.45640	−	0.473213i
$630$		0			0
$631$	−119.477	−	367.713i	−0.189346	−	0.582747i	0.810650	−	0.585531i	$-0.199114\pi$
$631$	−119.477	−	367.713i	−0.189346	−	0.582747i	−0.999996	+	0.00278376i	$0.999114\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−696.943	−	281.168i	−1.09755	−	0.442785i
$636$		0			0
$637$	19.7726	+	14.3657i	0.0310403	+	0.0225521i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−126.177	+	173.667i	−0.196843	+	0.270932i	−0.896017	−	0.444021i	$-0.853552\pi$
$641$	−126.177	+	173.667i	−0.196843	+	0.270932i	0.699173	+	0.714952i	$0.253552\pi$
$642$		0			0
$643$	−548.794			−0.853490			−0.426745	−	0.904372i	$-0.640340\pi$
$643$	−548.794			−0.853490			−0.426745	+	0.904372i	$0.640340\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	111.627	+	36.2697i	0.172530	+	0.0560583i	0.394008	−	0.919107i	$-0.371088\pi$
$647$	111.627	+	36.2697i	0.172530	+	0.0560583i	−0.221478	+	0.975165i	$0.571088\pi$
$648$		0			0
$649$	933.719			1.43870
$650$		0			0
$651$		0			0
$652$		0			0
$653$	3.65171	+	1.18651i	0.00559220	+	0.00181702i	0.311812	−	0.950144i	$-0.399064\pi$
$653$	3.65171	+	1.18651i	0.00559220	+	0.00181702i	−0.306220	+	0.951961i	$0.599064\pi$
$654$		0			0
$655$	746.813	+	625.999i	1.14017	+	0.955724i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−575.488	+	792.091i	−0.873274	+	1.20196i	0.104965	+	0.994476i	$0.466527\pi$
$659$	−575.488	+	792.091i	−0.873274	+	1.20196i	−0.978239	+	0.207483i	$0.933473\pi$
$660$		0			0
$661$	345.603	−	251.095i	0.522849	−	0.379872i	−0.294827	−	0.955551i	$-0.595262\pi$
$661$	345.603	−	251.095i	0.522849	−	0.379872i	0.817676	+	0.575679i	$0.195262\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−107.111	+	127.783i	−0.161069	+	0.192155i
$666$		0			0
$667$	11.3374	+	34.8929i	0.0169976	+	0.0523132i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−98.6932	−	32.0674i	−0.147084	−	0.0477904i
$672$		0			0
$673$	−581.966	+	422.823i	−0.864733	+	0.628266i	−0.929169	−	0.369656i	$-0.879475\pi$
$673$	−581.966	+	422.823i	−0.864733	+	0.628266i	0.0644352	+	0.997922i	$0.479475\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−406.648	−	559.703i	−0.600662	−	0.826740i	0.395107	−	0.918635i	$-0.370708\pi$
$677$	−406.648	−	559.703i	−0.600662	−	0.826740i	−0.995769	+	0.0918952i	$0.970708\pi$
$678$		0			0
$679$	−157.323	+	484.191i	−0.231699	+	0.713095i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−412.828	+	134.136i	−0.604434	+	0.196392i	−0.595217	−	0.803565i	$-0.702934\pi$
$683$	−412.828	+	134.136i	−0.604434	+	0.196392i	−0.00921688	+	0.999958i	$0.502934\pi$
$684$		0			0
$685$	−177.710	−	12.3353i	−0.259431	−	0.0180078i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	69.8347	+	96.1192i	0.101357	+	0.139505i
$690$		0			0
$691$	−460.520	−	334.588i	−0.666455	−	0.484208i	0.202382	−	0.979307i	$-0.435132\pi$
$691$	−460.520	−	334.588i	−0.666455	−	0.484208i	−0.868837	+	0.495099i	$0.835132\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−1155.44	−	466.141i	−1.66251	−	0.670706i
$696$		0			0
$697$	−76.9051	+	236.690i	−0.110337	+	0.339583i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			269.426i			0.384345i	0.981361	+	0.192173i	$0.0615534\pi$
$701$			269.426i			0.384345i	−0.981361	+	0.192173i	$0.938447\pi$
$702$		0			0
$703$	54.5107	−	167.767i	0.0775402	−	0.238644i
$704$		0			0
$705$		0			0
$706$		0			0
$707$			97.2706i			0.137582i
$708$		0			0
$709$	−433.936	−	315.273i	−0.612040	−	0.444673i	0.238092	−	0.971243i	$-0.423478\pi$
$709$	−433.936	−	315.273i	−0.612040	−	0.444673i	−0.850132	+	0.526569i	$0.823478\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−4.96995	+	6.84055i	−0.00697048	+	0.00959404i
$714$		0			0
$715$	168.656	−	105.508i	0.235882	−	0.147563i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	90.4529	−	29.3899i	0.125804	−	0.0408761i	−0.245438	−	0.969412i	$-0.578932\pi$
$719$	90.4529	−	29.3899i	0.125804	−	0.0408761i	0.371242	+	0.928536i	$0.378932\pi$
$720$		0			0
$721$	−18.4723	+	56.8520i	−0.0256204	+	0.0788516i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−343.581	+	356.519i	−0.473905	+	0.491750i
$726$		0			0
$727$	−892.381	+	648.353i	−1.22748	+	0.891819i	−0.996699	−	0.0811855i	$-0.974129\pi$
$727$	−892.381	+	648.353i	−1.22748	+	0.891819i	−0.230785	+	0.973005i	$0.574129\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	802.924	−	260.886i	1.09839	−	0.356889i
$732$		0			0
$733$	443.580	+	1365.20i	0.605157	+	1.86248i	0.495705	+	0.868491i	$0.334910\pi$
$733$	443.580	+	1365.20i	0.605157	+	1.86248i	0.109453	+	0.993992i	$0.465090\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−336.404	+	463.020i	−0.456450	+	0.628250i
$738$		0			0
$739$	843.208	−	612.626i	1.14101	−	0.828994i	0.153752	−	0.988109i	$-0.450864\pi$
$739$	843.208	−	612.626i	1.14101	−	0.828994i	0.987260	+	0.159116i	$0.0508643\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		−	1006.03i		−	1.35401i	−0.735977	−	0.677006i	$-0.763277\pi$
$743$		−	1006.03i		−	1.35401i	0.735977	−	0.677006i	$-0.236723\pi$
$744$		0			0
$745$	−1144.40	+	715.916i	−1.53611	+	0.960961i
$746$		0			0
$747$		0			0
$748$		0			0
$749$		−	526.510i		−	0.702950i
$750$		0			0
$751$	−698.284			−0.929806			−0.464903	−	0.885362i	$-0.653911\pi$
$751$	−698.284			−0.929806			−0.464903	+	0.885362i	$0.653911\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	366.248	+	585.452i	0.485097	+	0.775433i
$756$		0			0
$757$	−240.559			−0.317779			−0.158889	−	0.987296i	$-0.550791\pi$
$757$	−240.559			−0.317779			−0.158889	+	0.987296i	$0.550791\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	449.802	+	619.099i	0.591067	+	0.813534i	0.994854	−	0.101319i	$-0.0323063\pi$
$761$	449.802	+	619.099i	0.591067	+	0.813534i	−0.403787	+	0.914853i	$0.632306\pi$
$762$		0			0
$763$	−275.907	−	200.458i	−0.361608	−	0.262724i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	209.260	−	67.9926i	0.272829	−	0.0886475i
$768$		0			0
$769$	−15.2844	−	47.0405i	−0.0198757	−	0.0611710i	0.940627	−	0.339443i	$-0.110238\pi$
$769$	−15.2844	−	47.0405i	−0.0198757	−	0.0611710i	−0.960502	+	0.278272i	$0.910238\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−65.8162	−	90.5883i	−0.0851439	−	0.117191i	0.764320	−	0.644837i	$-0.223075\pi$
$773$	−65.8162	−	90.5883i	−0.0851439	−	0.117191i	−0.849464	+	0.527646i	$0.823075\pi$
$774$		0			0
$775$	−113.015	−	15.7653i	−0.145826	−	0.0203423i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−43.3465	−	14.0841i	−0.0556438	−	0.0180798i
$780$		0			0
$781$	169.962	+	523.090i	0.217621	+	0.669769i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	245.442	+	392.342i	0.312664	+	0.499798i
$786$		0			0
$787$	815.520	+	592.510i	1.03624	+	0.752872i	0.969548	−	0.244902i	$-0.0787558\pi$
$787$	815.520	+	592.510i	1.03624	+	0.752872i	0.0666911	+	0.997774i	$0.478756\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	16.3314	−	22.4782i	0.0206465	−	0.0284174i
$792$		0			0
$793$	−24.4537			−0.0308369
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−30.3919	−	9.87494i	−0.0381329	−	0.0123901i	0.289888	−	0.957060i	$-0.406382\pi$
$797$	−30.3919	−	9.87494i	−0.0381329	−	0.0123901i	−0.328021	+	0.944670i	$0.606382\pi$
$798$		0			0
$799$	397.080			0.496971
$800$		0			0
$801$		0			0
$802$		0			0
$803$	1345.43	+	437.158i	1.67551	+	0.544405i
$804$		0			0
$805$	22.1940	−	55.0130i	0.0275701	−	0.0683392i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−104.062	+	143.229i	−0.128631	+	0.177045i	−0.868475	−	0.495734i	$-0.834899\pi$
$809$	−104.062	+	143.229i	−0.128631	+	0.177045i	0.739844	+	0.672778i	$0.234899\pi$
$810$		0			0
$811$	−700.534	+	508.968i	−0.863790	+	0.627580i	−0.928913	−	0.370297i	$-0.879256\pi$
$811$	−700.534	+	508.968i	−0.863790	+	0.627580i	0.0651233	+	0.997877i	$0.479256\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	90.1198	−	1298.32i	0.110576	−	1.59303i
$816$		0			0
$817$	47.7777	+	147.045i	0.0584794	+	0.179981i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−168.994	−	54.9095i	−0.205839	−	0.0668813i	0.204283	−	0.978912i	$-0.434514\pi$
$821$	−168.994	−	54.9095i	−0.205839	−	0.0668813i	−0.410122	+	0.912031i	$0.634514\pi$
$822$		0			0
$823$	512.628	−	372.446i	0.622877	−	0.452546i	−0.231048	−	0.972942i	$-0.574216\pi$
$823$	512.628	−	372.446i	0.622877	−	0.452546i	0.853925	+	0.520396i	$0.174216\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	493.072	+	678.656i	0.596218	+	0.820623i	0.995355	−	0.0962675i	$-0.0306904\pi$
$827$	493.072	+	678.656i	0.596218	+	0.820623i	−0.399138	+	0.916891i	$0.630690\pi$
$828$		0			0
$829$	−235.221	+	723.936i	−0.283741	+	0.873264i	0.703032	+	0.711158i	$0.251829\pi$
$829$	−235.221	+	723.936i	−0.283741	+	0.873264i	−0.986773	+	0.162107i	$0.948171\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	215.827	−	70.1265i	0.259096	−	0.0841854i
$834$		0			0
$835$	−317.282	−	265.955i	−0.379979	−	0.318509i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	369.544	+	508.633i	0.440457	+	0.606238i	0.970314	−	0.241850i	$-0.0777541\pi$
$839$	369.544	+	508.633i	0.440457	+	0.606238i	−0.529856	+	0.848087i	$0.677754\pi$
$840$		0			0
$841$	−363.050	−	263.771i	−0.431688	−	0.313640i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−512.709	+	611.658i	−0.606756	+	0.723856i
$846$		0			0
$847$	−94.6890	+	291.423i	−0.111793	+	0.344065i
$848$		0			0
$849$		0			0
$850$		0			0
$851$			62.7592i			0.0737476i
$852$		0			0
$853$	140.866	−	433.541i	0.165142	−	0.508254i	−0.833905	−	0.551908i	$-0.813900\pi$
$853$	140.866	−	433.541i	0.165142	−	0.508254i	0.999047	+	0.0436539i	$0.0138999\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$			1558.32i			1.81834i	0.416423	+	0.909171i	$0.363283\pi$
$857$			1558.32i			1.81834i	−0.416423	+	0.909171i	$0.636717\pi$
$858$		0			0
$859$	−788.279	−	572.718i	−0.917670	−	0.666726i	0.0252728	−	0.999681i	$-0.491955\pi$
$859$	−788.279	−	572.718i	−0.917670	−	0.666726i	−0.942943	+	0.332954i	$0.891955\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−188.167	+	258.990i	−0.218039	+	0.300105i	−0.903999	−	0.427534i	$-0.859382\pi$
$863$	−188.167	+	258.990i	−0.218039	+	0.300105i	0.685960	+	0.727639i	$0.259382\pi$
$864$		0			0
$865$	585.298	−	1450.80i	0.676645	−	1.67723i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	1401.95	−	455.521i	1.61329	−	0.524190i
$870$		0			0
$871$	−41.6762	+	128.266i	−0.0478486	+	0.147263i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	796.053	−	84.9046i	0.909775	−	0.0970339i
$876$		0			0
$877$	957.827	−	695.902i	1.09216	−	0.793503i	0.112400	−	0.993663i	$-0.464146\pi$
$877$	957.827	−	695.902i	1.09216	−	0.793503i	0.979763	+	0.200160i	$0.0641461\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−711.158	+	231.069i	−0.807216	+	0.262281i	−0.683418	−	0.730027i	$-0.739508\pi$
$881$	−711.158	+	231.069i	−0.807216	+	0.262281i	−0.123798	+	0.992307i	$0.539508\pi$
$882$		0			0
$883$	−243.167	−	748.390i	−0.275387	−	0.847554i	−0.989117	−	0.147133i	$-0.952996\pi$
$883$	−243.167	−	748.390i	−0.275387	−	0.847554i	0.713730	−	0.700421i	$-0.247004\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	647.316	−	890.955i	0.729782	−	1.00446i	−0.269360	−	0.963040i	$-0.586812\pi$
$887$	647.316	−	890.955i	0.729782	−	1.00446i	0.999142	−	0.0414189i	$-0.0131878\pi$
$888$		0			0
$889$	778.785	−	565.821i	0.876024	−	0.636469i
$890$		0			0
$891$		0			0
$892$		0			0
$893$			72.7199i			0.0814332i
$894$		0			0
$895$	−197.753	−	791.417i	−0.220953	−	0.884265i
$896$		0			0
$897$		0			0
$898$		0			0
$899$			90.3984i			0.100554i
$900$		0			0
$901$	1103.18			1.22439
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−346.851	+	413.791i	−0.383261	+	0.457228i
$906$		0			0
$907$	−1028.21			−1.13364			−0.566822	−	0.823841i	$-0.691827\pi$
$907$	−1028.21			−1.13364			−0.566822	+	0.823841i	$0.691827\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−535.454	−	736.989i	−0.587765	−	0.808989i	0.406755	−	0.913537i	$-0.366660\pi$
$911$	−535.454	−	736.989i	−0.587765	−	0.808989i	−0.994520	+	0.104549i	$0.966660\pi$
$912$		0			0
$913$	759.613	+	551.891i	0.831997	+	0.604481i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−1187.12	+	385.720i	−1.29457	+	0.420632i
$918$		0			0
$919$	−353.826	−	1088.96i	−0.385012	−	1.18494i	−0.936472	−	0.350743i	$-0.885929\pi$
$919$	−353.826	−	1088.96i	−0.385012	−	1.18494i	0.551460	−	0.834201i	$-0.314071\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	76.1819	+	104.855i	0.0825373	+	0.113603i
$924$		0			0
$925$	−747.419	+	398.392i	−0.808021	+	0.430694i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−308.060	−	100.095i	−0.331604	−	0.107745i	0.138483	−	0.990365i	$-0.455777\pi$
$929$	−308.060	−	100.095i	−0.331604	−	0.107745i	−0.470087	+	0.882620i	$0.655777\pi$
$930$		0			0
$931$	12.8427	+	39.5258i	0.0137945	+	0.0424552i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	127.910	−	1842.76i	0.136803	−	1.97086i
$936$		0			0
$937$	−611.800	−	444.498i	−0.652935	−	0.474385i	0.211335	−	0.977414i	$-0.432219\pi$
$937$	−611.800	−	444.498i	−0.652935	−	0.474385i	−0.864270	+	0.503029i	$0.832219\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	720.045	−	991.057i	0.765192	−	1.05320i	−0.231573	−	0.972818i	$-0.574387\pi$
$941$	720.045	−	991.057i	0.765192	−	1.05320i	0.996764	−	0.0803784i	$-0.0256129\pi$
$942$		0			0
$943$	16.2153			0.0171955
$944$		0			0
$945$		0			0
$946$		0			0
$947$	1395.84	+	453.537i	1.47396	+	0.478919i	0.932303	−	0.361678i	$-0.117796\pi$
$947$	1395.84	+	453.537i	1.47396	+	0.478919i	0.541660	+	0.840598i	$0.317796\pi$
$948$		0			0
$949$	333.364			0.351280
$950$		0			0
$951$		0			0
$952$		0			0
$953$	1439.40	+	467.690i	1.51039	+	0.490756i	0.943028	−	0.332713i	$-0.107964\pi$
$953$	1439.40	+	467.690i	1.51039	+	0.490756i	0.567362	+	0.823468i	$0.307964\pi$
$954$		0			0
$955$	1080.00	+	74.9653i	1.13089	+	0.0784977i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	134.120	−	184.600i	0.139854	−	0.192492i
$960$		0			0
$961$	760.611	−	552.616i	0.791478	−	0.575043i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	499.999	+	799.255i	0.518134	+	0.828244i
$966$		0			0
$967$	2.92221	+	8.99364i	0.00302194	+	0.00930056i	0.952556	−	0.304363i	$-0.0984436\pi$
$967$	2.92221	+	8.99364i	0.00302194	+	0.00930056i	−0.949534	+	0.313664i	$0.898444\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	606.110	+	196.937i	0.624212	+	0.202819i	0.604010	−	0.796977i	$-0.293569\pi$
$971$	606.110	+	196.937i	0.624212	+	0.202819i	0.0202027	+	0.999796i	$0.493569\pi$
$972$		0			0
$973$	1291.13	−	938.057i	1.32695	−	0.964088i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−919.151	−	1265.10i	−0.940790	−	1.29489i	−0.955499	−	0.294994i	$-0.904682\pi$
$977$	−919.151	−	1265.10i	−0.940790	−	1.29489i	0.0147096	−	0.999892i	$-0.495318\pi$
$978$		0			0
$979$	−523.750	+	1611.94i	−0.534985	+	1.64651i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−1332.38	+	432.918i	−1.35543	+	0.440405i	−0.894513	−	0.447041i	$-0.852478\pi$
$983$	−1332.38	+	432.918i	−1.35543	+	0.440405i	−0.460912	+	0.887446i	$0.652478\pi$
$984$		0			0
$985$	8.54600	+	34.2015i	0.00867614	+	0.0347224i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−32.3325	−	44.5019i	−0.0326921	−	0.0449968i
$990$		0			0
$991$	791.863	+	575.322i	0.799055	+	0.580547i	0.910637	−	0.413208i	$-0.135592\pi$
$991$	791.863	+	575.322i	0.799055	+	0.580547i	−0.111582	+	0.993755i	$0.535592\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	152.166	+	243.239i	0.152930	+	0.244461i
$996$		0			0
$997$	339.802	−	1045.80i	0.340825	−	1.04895i	−0.622957	−	0.782256i	$-0.714069\pi$
$997$	339.802	−	1045.80i	0.340825	−	1.04895i	0.963781	−	0.266694i	$-0.0859312\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.3.ba.a.161.7	✓	80
3.2	odd	2	inner	900.3.ba.a.161.14	yes	80
25.16	even	5	inner	900.3.ba.a.341.14	yes	80
75.41	odd	10	inner	900.3.ba.a.341.7	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
900.3.ba.a.161.7	✓	80	1.1	even	1	trivial
900.3.ba.a.161.14	yes	80	3.2	odd	2	inner
900.3.ba.a.341.7	yes	80	75.41	odd	10	inner
900.3.ba.a.341.14	yes	80	25.16	even	5	inner

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:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	900.ba (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.65177 - 4.23888i) q^{5} +6.40455 q^{7} +O(q^{10})\)	\(q+(-2.65177 - 4.23888i) q^{5} +6.40455 q^{7} +(-7.63768 - 10.5124i) q^{11} +(-2.47722 - 1.79980i) q^{13} +(-27.0399 + 8.78580i) q^{17} +(-1.60900 - 4.95199i) q^{19} +(1.08886 + 1.49868i) q^{23} +(-10.9363 + 22.4811i) q^{25} +(18.8359 + 6.12014i) q^{29} +(1.41047 + 4.34098i) q^{31} +(-16.9834 - 27.1481i) q^{35} +(27.4084 + 19.9134i) q^{37} +(5.14508 - 7.08160i) q^{41} -29.6940 q^{43} +(-13.2827 - 4.31580i) q^{47} -7.98180 q^{49} +(-36.9022 - 11.9903i) q^{53} +(-24.3074 + 60.2516i) q^{55} +(-42.2369 + 58.1341i) q^{59} +(6.46094 - 4.69414i) q^{61} +(-1.06016 + 15.2733i) q^{65} +(-13.6107 - 41.8895i) q^{67} +(-40.2562 - 13.0800i) q^{71} +(-88.0786 + 63.9928i) q^{73} +(-48.9159 - 67.3270i) q^{77} +(-35.0562 + 107.892i) q^{79} +(-68.7223 + 22.3292i) q^{83} +(108.946 + 91.3212i) q^{85} +(-76.6686 - 105.525i) q^{89} +(-15.8654 - 11.5269i) q^{91} +(-16.7242 + 19.9519i) q^{95} +(-24.5643 + 75.6012i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 16 q^{7}+O(q^{10}) \) 80 * q + 16 * q^7	\( 80 q + 16 q^{7} - 8 q^{13} + 60 q^{19} - 120 q^{25} + 120 q^{31} + 116 q^{37} - 80 q^{43} + 440 q^{49} + 120 q^{55} + 80 q^{61} + 24 q^{67} + 128 q^{73} + 40 q^{79} + 40 q^{85} - 140 q^{91} + 384 q^{97}+O(q^{100}) \) 80 * q + 16 * q^7 - 8 * q^13 + 60 * q^19 - 120 * q^25 + 120 * q^31 + 116 * q^37 - 80 * q^43 + 440 * q^49 + 120 * q^55 + 80 * q^61 + 24 * q^67 + 128 * q^73 + 40 * q^79 + 40 * q^85 - 140 * q^91 + 384 * q^97

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