LMFDB - Embedded newform 900.3.ba.a.161.5

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			161.5
Character	$\chi$	$=$	900.161
Dual form			900.3.ba.a.341.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.66894 - 3.39689i) q^{5} -6.21282 q^{7} +O(q^{10})$	$q+(-3.66894 - 3.39689i) q^{5} -6.21282 q^{7} +(-7.08545 - 9.75228i) q^{11} +(-13.8120 - 10.0350i) q^{13} +(16.9027 - 5.49202i) q^{17} +(1.29840 + 3.99607i) q^{19} +(21.2199 + 29.2067i) q^{23} +(1.92229 + 24.9260i) q^{25} +(5.71813 + 1.85793i) q^{29} +(5.34325 + 16.4448i) q^{31} +(22.7945 + 21.1043i) q^{35} +(-7.05040 - 5.12242i) q^{37} +(-37.7519 + 51.9611i) q^{41} -39.0095 q^{43} +(26.6240 + 8.65065i) q^{47} -10.4008 q^{49} +(28.6272 + 9.30156i) q^{53} +(-7.13131 + 59.8491i) q^{55} +(16.1097 - 22.1731i) q^{59} +(-22.4493 + 16.3104i) q^{61} +(16.5877 + 83.7359i) q^{65} +(-6.25254 - 19.2433i) q^{67} +(66.9971 + 21.7687i) q^{71} +(101.702 - 73.8909i) q^{73} +(44.0206 + 60.5892i) q^{77} +(-44.6751 + 137.496i) q^{79} +(-7.34754 + 2.38736i) q^{83} +(-80.6708 - 37.2666i) q^{85} +(-2.07613 - 2.85755i) q^{89} +(85.8117 + 62.3458i) q^{91} +(8.81045 - 19.0719i) q^{95} +(-11.4651 + 35.2859i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−3.66894	−	3.39689i	−0.733789	−	0.679378i
$5$	−3.66894	−	3.39689i	−0.733789	−	0.679378i
$6$		0			0
$7$	−6.21282			−0.887546			−0.443773	−	0.896139i	$-0.646360\pi$
$7$	−6.21282			−0.887546			−0.443773	+	0.896139i	$0.646360\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−7.08545	−	9.75228i	−0.644132	−	0.886571i	0.354696	−	0.934982i	$-0.384584\pi$
$11$	−7.08545	−	9.75228i	−0.644132	−	0.886571i	−0.998828	+	0.0484105i	$0.984584\pi$
$12$		0			0
$13$	−13.8120	−	10.0350i	−1.06246	−	0.771925i	−0.0879211	−	0.996127i	$-0.528022\pi$
$13$	−13.8120	−	10.0350i	−1.06246	−	0.771925i	−0.974543	+	0.224202i	$0.928022\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	16.9027	−	5.49202i	0.994276	−	0.323060i	0.233700	−	0.972309i	$-0.424917\pi$
$17$	16.9027	−	5.49202i	0.994276	−	0.323060i	0.760576	+	0.649249i	$0.224917\pi$
$18$		0			0
$19$	1.29840	+	3.99607i	0.0683370	+	0.210320i	0.979393	−	0.201962i	$-0.0647318\pi$
$19$	1.29840	+	3.99607i	0.0683370	+	0.210320i	−0.911056	+	0.412282i	$0.864732\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	21.2199	+	29.2067i	0.922603	+	1.26985i	0.962676	+	0.270658i	$0.0872412\pi$
$23$	21.2199	+	29.2067i	0.922603	+	1.26985i	−0.0400721	+	0.999197i	$0.512759\pi$
$24$		0			0
$25$	1.92229	+	24.9260i	0.0768918	+	0.997039i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	5.71813	+	1.85793i	0.197177	+	0.0640667i	0.405941	−	0.913899i	$-0.366944\pi$
$29$	5.71813	+	1.85793i	0.197177	+	0.0640667i	−0.208764	+	0.977966i	$0.566944\pi$
$30$		0			0
$31$	5.34325	+	16.4448i	0.172363	+	0.530478i	0.999503	−	0.0315172i	$-0.0100339\pi$
$31$	5.34325	+	16.4448i	0.172363	+	0.530478i	−0.827140	+	0.561995i	$0.810034\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	22.7945	+	21.1043i	0.651271	+	0.602979i
$36$		0			0
$37$	−7.05040	−	5.12242i	−0.190551	−	0.138444i	0.488419	−	0.872609i	$-0.337574\pi$
$37$	−7.05040	−	5.12242i	−0.190551	−	0.138444i	−0.678971	+	0.734165i	$0.737574\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−37.7519	+	51.9611i	−0.920779	+	1.26734i	0.0425707	+	0.999093i	$0.486445\pi$
$41$	−37.7519	+	51.9611i	−0.920779	+	1.26734i	−0.963349	+	0.268250i	$0.913555\pi$
$42$		0			0
$43$	−39.0095			−0.907197			−0.453599	−	0.891206i	$-0.649860\pi$
$43$	−39.0095			−0.907197			−0.453599	+	0.891206i	$0.649860\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	26.6240	+	8.65065i	0.566467	+	0.184056i	0.578229	−	0.815874i	$-0.303744\pi$
$47$	26.6240	+	8.65065i	0.566467	+	0.184056i	−0.0117617	+	0.999931i	$0.503744\pi$
$48$		0			0
$49$	−10.4008			−0.212262
$50$		0			0
$51$		0			0
$52$		0			0
$53$	28.6272	+	9.30156i	0.540137	+	0.175501i	0.566364	−	0.824155i	$-0.308349\pi$
$53$	28.6272	+	9.30156i	0.540137	+	0.175501i	−0.0262277	+	0.999656i	$0.508349\pi$
$54$		0			0
$55$	−7.13131	+	59.8491i	−0.129660	+	1.08816i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	16.1097	−	22.1731i	0.273046	−	0.375815i	−0.650369	−	0.759618i	$-0.725386\pi$
$59$	16.1097	−	22.1731i	0.273046	−	0.375815i	0.923415	+	0.383803i	$0.125386\pi$
$60$		0			0
$61$	−22.4493	+	16.3104i	−0.368022	+	0.267383i	−0.756390	−	0.654121i	$-0.773039\pi$
$61$	−22.4493	+	16.3104i	−0.368022	+	0.267383i	0.388369	+	0.921504i	$0.373039\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	16.5877	+	83.7359i	0.255195	+	1.28824i
$66$		0			0
$67$	−6.25254	−	19.2433i	−0.0933215	−	0.287214i	0.893491	−	0.449081i	$-0.148248\pi$
$67$	−6.25254	−	19.2433i	−0.0933215	−	0.287214i	−0.986813	+	0.161867i	$0.948248\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	66.9971	+	21.7687i	0.943621	+	0.306601i	0.740121	−	0.672474i	$-0.234768\pi$
$71$	66.9971	+	21.7687i	0.943621	+	0.306601i	0.203500	+	0.979075i	$0.434768\pi$
$72$		0			0
$73$	101.702	−	73.8909i	1.39318	−	1.01220i	0.397671	−	0.917528i	$-0.369819\pi$
$73$	101.702	−	73.8909i	1.39318	−	1.01220i	0.995508	−	0.0946757i	$-0.0301814\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	44.0206	+	60.5892i	0.571697	+	0.786873i
$78$		0			0
$79$	−44.6751	+	137.496i	−0.565508	+	1.74045i	0.100931	+	0.994893i	$0.467818\pi$
$79$	−44.6751	+	137.496i	−0.565508	+	1.74045i	−0.666438	+	0.745560i	$0.732182\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−7.34754	+	2.38736i	−0.0885246	+	0.0287634i	−0.352944	−	0.935644i	$-0.614820\pi$
$83$	−7.34754	+	2.38736i	−0.0885246	+	0.0287634i	0.264420	+	0.964408i	$0.414820\pi$
$84$		0			0
$85$	−80.6708	−	37.2666i	−0.949068	−	0.438431i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−2.07613	−	2.85755i	−0.0233273	−	0.0321073i	0.797194	−	0.603723i	$-0.206317\pi$
$89$	−2.07613	−	2.85755i	−0.0233273	−	0.0321073i	−0.820521	+	0.571616i	$0.806317\pi$
$90$		0			0
$91$	85.8117	+	62.3458i	0.942986	+	0.685119i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	8.81045	−	19.0719i	0.0927416	−	0.200757i
$96$		0			0
$97$	−11.4651	+	35.2859i	−0.118197	+	0.363772i	−0.992600	−	0.121427i	$-0.961253\pi$
$97$	−11.4651	+	35.2859i	−0.118197	+	0.363772i	0.874404	+	0.485199i	$0.161253\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$			146.236i			1.44788i	0.689860	+	0.723942i	$0.257672\pi$
$101$			146.236i			1.44788i	−0.689860	+	0.723942i	$0.742328\pi$
$102$		0			0
$103$	−47.8583	+	147.293i	−0.464643	+	1.43003i	0.394787	+	0.918773i	$0.370818\pi$
$103$	−47.8583	+	147.293i	−0.464643	+	1.43003i	−0.859430	+	0.511253i	$0.829182\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	65.0689i		−	0.608120i	−0.952653	−	0.304060i	$-0.901658\pi$
$107$		−	65.0689i		−	0.608120i	0.952653	−	0.304060i	$-0.0983424\pi$
$108$		0			0
$109$	−145.757	−	105.899i	−1.33722	−	0.971549i	−0.999541	−	0.0302887i	$-0.990357\pi$
$109$	−145.757	−	105.899i	−1.33722	−	0.971549i	−0.337682	−	0.941260i	$-0.609643\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	41.4172	−	57.0059i	0.366524	−	0.504477i	−0.585428	−	0.810725i	$-0.699073\pi$
$113$	41.4172	−	57.0059i	0.366524	−	0.504477i	0.951952	+	0.306247i	$0.0990734\pi$
$114$		0			0
$115$	21.3572	−	179.239i	0.185715	−	1.55860i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−105.013	+	34.1209i	−0.882465	+	0.286730i
$120$		0			0
$121$	−7.51239	+	23.1208i	−0.0620859	+	0.191081i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	77.6180	−	97.9819i	0.620944	−	0.783855i
$126$		0			0
$127$	−25.9092	+	18.8242i	−0.204010	+	0.148222i	−0.685099	−	0.728450i	$-0.740241\pi$
$127$	−25.9092	+	18.8242i	−0.204010	+	0.148222i	0.481090	+	0.876671i	$0.340241\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	162.605	−	52.8337i	1.24126	−	0.403311i	0.386480	−	0.922298i	$-0.373691\pi$
$131$	162.605	−	52.8337i	1.24126	−	0.403311i	0.854782	+	0.518987i	$0.173691\pi$
$132$		0			0
$133$	−8.06675	−	24.8269i	−0.0606523	−	0.186668i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−52.3164	+	72.0073i	−0.381871	+	0.525601i	−0.956079	−	0.293109i	$-0.905310\pi$
$137$	−52.3164	+	72.0073i	−0.381871	+	0.525601i	0.574208	+	0.818710i	$0.305310\pi$
$138$		0			0
$139$	−161.663	+	117.455i	−1.16304	+	0.844999i	−0.990160	−	0.139943i	$-0.955308\pi$
$139$	−161.663	+	117.455i	−1.16304	+	0.844999i	−0.172882	+	0.984942i	$0.555308\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$			205.801i			1.43917i
$144$		0			0
$145$	−14.6683	−	26.2405i	−0.101161	−	0.180969i
$146$		0			0
$147$		0			0
$148$		0			0
$149$			35.4421i			0.237866i	0.992902	+	0.118933i	$0.0379474\pi$
$149$			35.4421i			0.237866i	−0.992902	+	0.118933i	$0.962053\pi$
$150$		0			0
$151$	−49.2061			−0.325868			−0.162934	−	0.986637i	$-0.552096\pi$
$151$	−49.2061			−0.325868			−0.162934	+	0.986637i	$0.552096\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	36.2572	−	78.4855i	0.233917	−	0.506358i
$156$		0			0
$157$	−191.115			−1.21729			−0.608646	−	0.793442i	$-0.708287\pi$
$157$	−191.115			−1.21729			−0.608646	+	0.793442i	$0.708287\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−131.835	−	181.456i	−0.818853	−	1.12705i
$162$		0			0
$163$	127.542	+	92.6644i	0.782464	+	0.568493i	0.905717	−	0.423882i	$-0.139333\pi$
$163$	127.542	+	92.6644i	0.782464	+	0.568493i	−0.123254	+	0.992375i	$0.539333\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	156.333	−	50.7957i	0.936126	−	0.304166i	0.199061	−	0.979987i	$-0.436211\pi$
$167$	156.333	−	50.7957i	0.936126	−	0.304166i	0.737066	+	0.675821i	$0.236211\pi$
$168$		0			0
$169$	37.8465	+	116.480i	0.223944	+	0.689228i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	53.2530	+	73.2965i	0.307821	+	0.423679i	0.934700	−	0.355437i	$-0.115668\pi$
$173$	53.2530	+	73.2965i	0.307821	+	0.423679i	−0.626879	+	0.779116i	$0.715668\pi$
$174$		0			0
$175$	−11.9429	−	154.861i	−0.0682450	−	0.884919i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	121.956	+	39.6258i	0.681316	+	0.221373i	0.629172	−	0.777266i	$-0.283394\pi$
$179$	121.956	+	39.6258i	0.681316	+	0.221373i	0.0521447	+	0.998640i	$0.483394\pi$
$180$		0			0
$181$	84.7223	+	260.748i	0.468079	+	1.44060i	0.855069	+	0.518515i	$0.173515\pi$
$181$	84.7223	+	260.748i	0.468079	+	1.44060i	−0.386990	+	0.922084i	$0.626485\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	8.46725	+	42.7433i	0.0457689	+	0.231045i
$186$		0			0
$187$	−173.323	−	125.926i	−0.926860	−	0.673403i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−125.702	+	173.014i	−0.658126	+	0.905833i	−0.999418	−	0.0341248i	$-0.989136\pi$
$191$	−125.702	+	173.014i	−0.658126	+	0.905833i	0.341292	+	0.939957i	$0.389136\pi$
$192$		0			0
$193$	160.937			0.833873			0.416937	−	0.908936i	$-0.363104\pi$
$193$	160.937			0.833873			0.416937	+	0.908936i	$0.363104\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−270.698	−	87.9553i	−1.37410	−	0.446473i	−0.473377	−	0.880860i	$-0.656965\pi$
$197$	−270.698	−	87.9553i	−1.37410	−	0.446473i	−0.900727	+	0.434386i	$0.856965\pi$
$198$		0			0
$199$	379.429			1.90668			0.953339	−	0.301902i	$-0.0976216\pi$
$199$	379.429			1.90668			0.953339	+	0.301902i	$0.0976216\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−35.5257	−	11.5430i	−0.175004	−	0.0568621i
$204$		0			0
$205$	315.016	−	62.4031i	1.53666	−	0.304406i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	29.7711	−	40.9764i	0.142445	−	0.196059i
$210$		0			0
$211$	149.890	−	108.901i	0.710379	−	0.516120i	−0.172917	−	0.984936i	$-0.555319\pi$
$211$	149.890	−	108.901i	0.710379	−	0.516120i	0.883296	+	0.468816i	$0.155319\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	143.124	+	132.511i	0.665691	+	0.616330i
$216$		0			0
$217$	−33.1966	−	102.169i	−0.152980	−	0.470824i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−288.573	−	93.7630i	−1.30576	−	0.424267i
$222$		0			0
$223$	308.190	−	223.913i	1.38202	−	1.00409i	0.385328	−	0.922780i	$-0.374088\pi$
$223$	308.190	−	223.913i	1.38202	−	1.00409i	0.996689	−	0.0813144i	$-0.0259118\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−100.701	−	138.603i	−0.443618	−	0.610587i	0.527394	−	0.849621i	$-0.323169\pi$
$227$	−100.701	−	138.603i	−0.443618	−	0.610587i	−0.971011	+	0.239034i	$0.923169\pi$
$228$		0			0
$229$	−24.7904	+	76.2970i	−0.108255	+	0.333175i	−0.990481	−	0.137652i	$-0.956044\pi$
$229$	−24.7904	+	76.2970i	−0.108255	+	0.333175i	0.882226	+	0.470827i	$0.156044\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−204.892	+	66.5735i	−0.879365	+	0.285723i	−0.713694	−	0.700458i	$-0.752979\pi$
$233$	−204.892	+	66.5735i	−0.879365	+	0.285723i	−0.165672	+	0.986181i	$0.552979\pi$
$234$		0			0
$235$	−68.2965	−	122.177i	−0.290624	−	0.519904i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−186.183	−	256.259i	−0.779009	−	1.07221i	−0.995390	−	0.0959049i	$-0.969426\pi$
$239$	−186.183	−	256.259i	−0.779009	−	1.07221i	0.216382	−	0.976309i	$-0.430574\pi$
$240$		0			0
$241$	−122.879	−	89.2769i	−0.509872	−	0.370444i	0.302903	−	0.953021i	$-0.402044\pi$
$241$	−122.879	−	89.2769i	−0.509872	−	0.370444i	−0.812775	+	0.582578i	$0.802044\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	38.1600	+	35.3304i	0.155755	+	0.144206i
$246$		0			0
$247$	22.1671	−	68.2234i	0.0897454	−	0.276208i
$248$		0			0
$249$		0			0
$250$		0			0
$251$		−	64.8693i		−	0.258443i	−0.991616	−	0.129222i	$-0.958752\pi$
$251$		−	64.8693i		−	0.258443i	0.991616	−	0.129222i	$-0.0412479\pi$
$252$		0			0
$253$	134.479	−	413.885i	0.531539	−	1.63591i
$254$		0			0
$255$		0			0
$256$		0			0
$257$		−	507.054i		−	1.97297i	−0.163846	−	0.986486i	$-0.552390\pi$
$257$		−	507.054i		−	1.97297i	0.163846	−	0.986486i	$-0.447610\pi$
$258$		0			0
$259$	43.8029	+	31.8247i	0.169123	+	0.122875i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	119.783	−	164.867i	0.455447	−	0.626869i	−0.518110	−	0.855314i	$-0.673364\pi$
$263$	119.783	−	164.867i	0.455447	−	0.626869i	0.973557	+	0.228445i	$0.0733641\pi$
$264$		0			0
$265$	−73.4354	−	131.370i	−0.277115	−	0.495738i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−471.138	+	153.082i	−1.75144	+	0.569078i	−0.996257	−	0.0864349i	$-0.972453\pi$
$269$	−471.138	+	153.082i	−1.75144	+	0.569078i	−0.755184	+	0.655513i	$0.772453\pi$
$270$		0			0
$271$	−82.2074	+	253.008i	−0.303348	+	0.933610i	0.676940	+	0.736038i	$0.263306\pi$
$271$	−82.2074	+	253.008i	−0.303348	+	0.933610i	−0.980288	+	0.197572i	$0.936694\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	229.465	−	195.359i	0.834418	−	0.710395i
$276$		0			0
$277$	−342.543	+	248.872i	−1.23662	+	0.898456i	−0.997368	−	0.0725022i	$-0.976902\pi$
$277$	−342.543	+	248.872i	−1.23662	+	0.898456i	−0.239250	+	0.970958i	$0.576902\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−459.353	+	149.253i	−1.63471	+	0.531148i	−0.975347	−	0.220679i	$-0.929173\pi$
$281$	−459.353	+	149.253i	−1.63471	+	0.531148i	−0.659360	+	0.751827i	$0.729173\pi$
$282$		0			0
$283$	82.7131	+	254.565i	0.292272	+	0.899522i	0.984124	+	0.177482i	$0.0567952\pi$
$283$	82.7131	+	254.565i	0.292272	+	0.899522i	−0.691852	+	0.722040i	$0.743205\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	234.546	−	322.825i	0.817234	−	1.12483i
$288$		0			0
$289$	21.7326	−	15.7897i	0.0751993	−	0.0546355i
$290$		0			0
$291$		0			0
$292$		0			0
$293$			436.096i			1.48838i	0.667968	+	0.744190i	$0.267164\pi$
$293$			436.096i			1.48838i	−0.667968	+	0.744190i	$0.732836\pi$
$294$		0			0
$295$	−134.425	+	26.6290i	−0.455679	+	0.0902678i
$296$		0			0
$297$		0			0
$298$		0			0
$299$		−	616.345i		−	2.06136i
$300$		0			0
$301$	242.359			0.805180
$302$		0			0
$303$		0			0
$304$		0			0
$305$	137.770	+	16.4160i	0.451704	+	0.0538228i
$306$		0			0
$307$	114.620			0.373355			0.186678	−	0.982421i	$-0.440228\pi$
$307$	114.620			0.373355			0.186678	+	0.982421i	$0.440228\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	42.7745	+	58.8740i	0.137538	+	0.189305i	0.872230	−	0.489096i	$-0.162673\pi$
$311$	42.7745	+	58.8740i	0.137538	+	0.189305i	−0.734692	+	0.678401i	$0.762673\pi$
$312$		0			0
$313$	−149.177	−	108.384i	−0.476604	−	0.346273i	0.323405	−	0.946261i	$-0.395172\pi$
$313$	−149.177	−	108.384i	−0.476604	−	0.346273i	−0.800010	+	0.599987i	$0.795172\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	166.720	−	54.1706i	0.525931	−	0.170885i	−0.0340044	−	0.999422i	$-0.510826\pi$
$317$	166.720	−	54.1706i	0.525931	−	0.170885i	0.559935	+	0.828536i	$0.310826\pi$
$318$		0			0
$319$	−22.3964	−	68.9291i	−0.0702083	−	0.216079i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	43.8930	+	60.4135i	0.135892	+	0.187039i
$324$		0			0
$325$	223.582	−	363.569i	0.687945	−	1.11867i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−165.410	−	53.7450i	−0.502766	−	0.163359i
$330$		0			0
$331$	89.8890	+	276.650i	0.271568	+	0.835800i	0.990107	+	0.140314i	$0.0448111\pi$
$331$	89.8890	+	276.650i	0.271568	+	0.835800i	−0.718539	+	0.695486i	$0.755189\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−42.4272	+	91.8419i	−0.126649	+	0.274155i
$336$		0			0
$337$	−278.740	−	202.516i	−0.827121	−	0.600939i	0.0916220	−	0.995794i	$-0.470795\pi$
$337$	−278.740	−	202.516i	−0.827121	−	0.600939i	−0.918743	+	0.394855i	$0.870795\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	122.515	−	168.628i	0.359282	−	0.494510i
$342$		0			0
$343$	369.047			1.07594
$344$		0			0
$345$		0			0
$346$		0			0
$347$	188.713	+	61.3166i	0.543841	+	0.176705i	0.568038	−	0.823002i	$-0.307703\pi$
$347$	188.713	+	61.3166i	0.543841	+	0.176705i	−0.0241964	+	0.999707i	$0.507703\pi$
$348$		0			0
$349$	−659.198			−1.88882			−0.944410	−	0.328771i	$-0.893366\pi$
$349$	−659.198			−1.88882			−0.944410	+	0.328771i	$0.893366\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−187.914	−	61.0569i	−0.532334	−	0.172966i	0.0305015	−	0.999535i	$-0.490290\pi$
$353$	−187.914	−	61.0569i	−0.532334	−	0.172966i	−0.562836	+	0.826569i	$0.690290\pi$
$354$		0			0
$355$	−171.863	−	307.450i	−0.484121	−	0.866056i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−139.595	+	192.135i	−0.388843	+	0.535196i	−0.957900	−	0.287102i	$-0.907308\pi$
$359$	−139.595	+	192.135i	−0.388843	+	0.535196i	0.569057	+	0.822298i	$0.307308\pi$
$360$		0			0
$361$	277.772	−	201.813i	0.769453	−	0.559040i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−624.138	−	74.3691i	−1.70997	−	0.203751i
$366$		0			0
$367$	15.8100	+	48.6581i	0.0430789	+	0.132583i	0.970283	−	0.241974i	$-0.0777948\pi$
$367$	15.8100	+	48.6581i	0.0430789	+	0.132583i	−0.927204	+	0.374557i	$0.877795\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−177.856	−	57.7889i	−0.479396	−	0.155765i
$372$		0			0
$373$	190.294	−	138.257i	0.510172	−	0.370662i	−0.302717	−	0.953081i	$-0.597894\pi$
$373$	190.294	−	138.257i	0.510172	−	0.370662i	0.812889	+	0.582419i	$0.197894\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−60.3346	−	83.0434i	−0.160039	−	0.220274i
$378$		0			0
$379$	−166.153	+	511.366i	−0.438398	+	1.34925i	0.451166	+	0.892440i	$0.351008\pi$
$379$	−166.153	+	511.366i	−0.438398	+	1.34925i	−0.889564	+	0.456811i	$0.848992\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	121.582	−	39.5043i	0.317446	−	0.103145i	−0.145960	−	0.989290i	$-0.546627\pi$
$383$	121.582	−	39.5043i	0.317446	−	0.103145i	0.463406	+	0.886146i	$0.346627\pi$
$384$		0			0
$385$	44.3056	−	371.832i	0.115079	−	0.965796i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−339.890	−	467.819i	−0.873754	−	1.20262i	−0.978112	−	0.208079i	$-0.933279\pi$
$389$	−339.890	−	467.819i	−0.873754	−	1.20262i	0.104358	−	0.994540i	$-0.466721\pi$
$390$		0			0
$391$	519.076	+	377.131i	1.32756	+	0.964530i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	630.968	−	352.708i	1.59739	−	0.892932i
$396$		0			0
$397$	142.662	−	439.069i	0.359351	−	1.10597i	−0.594093	−	0.804396i	$-0.702489\pi$
$397$	142.662	−	439.069i	0.359351	−	1.10597i	0.953444	−	0.301571i	$-0.0975110\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$			123.302i			0.307487i	0.988111	+	0.153743i	$0.0491329\pi$
$401$			123.302i			0.307487i	−0.988111	+	0.153743i	$0.950867\pi$
$402$		0			0
$403$	91.2231	−	280.756i	0.226360	−	0.696665i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			105.052i			0.258113i
$408$		0			0
$409$	109.912	+	79.8559i	0.268734	+	0.195247i	0.713989	−	0.700157i	$-0.246887\pi$
$409$	109.912	+	79.8559i	0.268734	+	0.195247i	−0.445255	+	0.895404i	$0.646887\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−100.087	+	137.758i	−0.242341	+	0.333554i
$414$		0			0
$415$	35.0673	+	16.1997i	0.0844996	+	0.0390354i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−115.506	+	37.5300i	−0.275669	+	0.0895704i	−0.443589	−	0.896230i	$-0.646295\pi$
$419$	−115.506	+	37.5300i	−0.275669	+	0.0895704i	0.167920	+	0.985801i	$0.446295\pi$
$420$		0			0
$421$	−29.2394	+	89.9895i	−0.0694522	+	0.213752i	−0.979758	−	0.200184i	$-0.935846\pi$
$421$	−29.2394	+	89.9895i	−0.0694522	+	0.213752i	0.910306	+	0.413936i	$0.135846\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	169.386	+	410.759i	0.398555	+	0.966491i
$426$		0			0
$427$	139.474	−	101.334i	0.326636	−	0.237315i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−418.607	+	136.014i	−0.971247	+	0.315577i	−0.751319	−	0.659939i	$-0.770582\pi$
$431$	−418.607	+	136.014i	−0.971247	+	0.315577i	−0.219928	+	0.975516i	$0.570582\pi$
$432$		0			0
$433$	80.4662	+	247.650i	0.185834	+	0.571939i	0.999962	−	0.00874723i	$-0.00278436\pi$
$433$	80.4662	+	247.650i	0.185834	+	0.571939i	−0.814128	+	0.580686i	$0.802784\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−89.1600	+	122.718i	−0.204027	+	0.280820i
$438$		0			0
$439$	−611.091	+	443.983i	−1.39201	+	1.01135i	−0.396364	+	0.918093i	$0.629728\pi$
$439$	−611.091	+	443.983i	−1.39201	+	1.01135i	−0.995642	+	0.0932583i	$0.970272\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$		−	114.827i		−	0.259203i	−0.991566	−	0.129601i	$-0.958630\pi$
$443$		−	114.827i		−	0.259203i	0.991566	−	0.129601i	$-0.0413698\pi$
$444$		0			0
$445$	−2.08957	+	17.5366i	−0.00469567	+	0.0394081i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	282.874i		−	0.630009i	−0.949090	−	0.315005i	$-0.897994\pi$
$449$		−	282.874i		−	0.630009i	0.949090	−	0.315005i	$-0.102006\pi$
$450$		0			0
$451$	774.228			1.71669
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−103.056	−	520.236i	−0.226498	−	1.14338i
$456$		0			0
$457$	−243.767			−0.533407			−0.266703	−	0.963779i	$-0.585934\pi$
$457$	−243.767			−0.533407			−0.266703	+	0.963779i	$0.585934\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	497.934	+	685.347i	1.08012	+	1.48665i	0.859392	+	0.511317i	$0.170842\pi$
$461$	497.934	+	685.347i	1.08012	+	1.48665i	0.220724	+	0.975336i	$0.429158\pi$
$462$		0			0
$463$	322.691	+	234.448i	0.696956	+	0.506368i	0.878939	−	0.476934i	$-0.158252\pi$
$463$	322.691	+	234.448i	0.696956	+	0.506368i	−0.181984	+	0.983302i	$0.558252\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−149.202	+	48.4787i	−0.319490	+	0.103809i	−0.464372	−	0.885640i	$-0.653720\pi$
$467$	−149.202	+	48.4787i	−0.319490	+	0.103809i	0.144882	+	0.989449i	$0.453720\pi$
$468$		0			0
$469$	38.8459	+	119.555i	0.0828271	+	0.254916i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	276.400	+	380.432i	0.584355	+	0.804295i
$474$		0			0
$475$	−97.1102	+	40.0456i	−0.204442	+	0.0843066i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	530.020	+	172.214i	1.10651	+	0.359528i	0.804606	−	0.593809i	$-0.202377\pi$
$479$	530.020	+	172.214i	1.10651	+	0.359528i	0.301908	+	0.953337i	$0.402377\pi$
$480$		0			0
$481$	45.9768	+	141.502i	0.0955858	+	0.294183i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	161.927	−	90.5163i	0.333870	−	0.186631i
$486$		0			0
$487$	−543.914	−	395.176i	−1.11687	−	0.811451i	−0.133135	−	0.991098i	$-0.542504\pi$
$487$	−543.914	−	395.176i	−1.11687	−	0.811451i	−0.983731	+	0.179647i	$0.942504\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−389.441	+	536.019i	−0.793159	+	1.09169i	0.200549	+	0.979684i	$0.435727\pi$
$491$	−389.441	+	536.019i	−0.793159	+	1.09169i	−0.993708	+	0.112005i	$0.964273\pi$
$492$		0			0
$493$	106.856			0.216746
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−416.241	−	135.245i	−0.837508	−	0.272123i
$498$		0			0
$499$	−562.755			−1.12777			−0.563883	−	0.825855i	$-0.690693\pi$
$499$	−562.755			−1.12777			−0.563883	+	0.825855i	$0.690693\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	126.670	+	41.1577i	0.251830	+	0.0818244i	0.432212	−	0.901772i	$-0.357733\pi$
$503$	126.670	+	41.1577i	0.251830	+	0.0818244i	−0.180382	+	0.983597i	$0.557733\pi$
$504$		0			0
$505$	496.749	−	536.533i	0.983661	−	1.06244i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−22.5373	+	31.0200i	−0.0442776	+	0.0609429i	−0.830582	−	0.556897i	$-0.811992\pi$
$509$	−22.5373	+	31.0200i	−0.0442776	+	0.0609429i	0.786304	+	0.617840i	$0.211992\pi$
$510$		0			0
$511$	−631.857	+	459.071i	−1.23651	+	0.898378i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	675.926	−	377.839i	1.31248	−	0.733668i
$516$		0			0
$517$	−104.279	−	320.938i	−0.201701	−	0.620770i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	76.0979	+	24.7257i	0.146061	+	0.0474582i	0.381135	−	0.924519i	$-0.375533\pi$
$521$	76.0979	+	24.7257i	0.146061	+	0.0474582i	−0.235074	+	0.971977i	$0.575533\pi$
$522$		0			0
$523$	−42.4286	+	30.8262i	−0.0811254	+	0.0589410i	−0.627609	−	0.778529i	$-0.715966\pi$
$523$	−42.4286	+	30.8262i	−0.0811254	+	0.0589410i	0.546483	+	0.837470i	$0.315966\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	180.630	+	248.616i	0.342752	+	0.471758i
$528$		0			0
$529$	−239.276	+	736.415i	−0.452317	+	1.39209i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	1042.86	−	338.846i	1.95659	−	0.635734i
$534$		0			0
$535$	−221.032	+	238.734i	−0.413144	+	0.446232i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	73.6945	+	101.432i	0.136725	+	0.188185i
$540$		0			0
$541$	299.247	+	217.416i	0.553138	+	0.401878i	0.828941	−	0.559336i	$-0.188944\pi$
$541$	299.247	+	217.416i	0.553138	+	0.401878i	−0.275803	+	0.961214i	$0.588944\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	175.049	+	883.658i	0.321190	+	1.62139i
$546$		0			0
$547$	12.2604	−	37.7337i	0.0224139	−	0.0689830i	−0.939224	−	0.343305i	$-0.888453\pi$
$547$	12.2604	−	37.7337i	0.0224139	−	0.0689830i	0.961638	+	0.274322i	$0.0884535\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$			25.2624i			0.0458483i
$552$		0			0
$553$	277.559	−	854.237i	0.501914	−	1.54473i
$554$		0			0
$555$		0			0
$556$		0			0
$557$			88.0940i			0.158158i	0.996868	+	0.0790790i	$0.0251979\pi$
$557$			88.0940i			0.158158i	−0.996868	+	0.0790790i	$0.974802\pi$
$558$		0			0
$559$	538.800	+	391.461i	0.963864	+	0.700288i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−365.670	+	503.301i	−0.649502	+	0.893963i	−0.999077	−	0.0429456i	$-0.986326\pi$
$563$	−365.670	+	503.301i	−0.649502	+	0.893963i	0.349576	+	0.936908i	$0.386326\pi$
$564$		0			0
$565$	−345.600	+	68.4618i	−0.611682	+	0.121171i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−26.3326	+	8.55599i	−0.0462788	+	0.0150369i	−0.332065	−	0.943257i	$-0.607745\pi$
$569$	−26.3326	+	8.55599i	−0.0462788	+	0.0150369i	0.285786	+	0.958293i	$0.407745\pi$
$570$		0			0
$571$	−156.339	+	481.163i	−0.273799	+	0.842667i	0.715736	+	0.698371i	$0.246092\pi$
$571$	−156.339	+	481.163i	−0.273799	+	0.842667i	−0.989535	+	0.144295i	$0.953908\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−687.214	+	585.070i	−1.19515	+	1.01751i
$576$		0			0
$577$	−667.559	+	485.010i	−1.15695	+	0.840572i	−0.989389	−	0.145290i	$-0.953588\pi$
$577$	−667.559	+	485.010i	−1.15695	+	0.840572i	−0.167559	+	0.985862i	$0.553588\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	45.6490	−	14.8323i	0.0785697	−	0.0255288i
$582$		0			0
$583$	−112.125	−	345.087i	−0.192325	−	0.591915i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	358.744	−	493.769i	0.611148	−	0.841173i	−0.385523	−	0.922698i	$-0.625979\pi$
$587$	358.744	−	493.769i	0.611148	−	0.841173i	0.996671	+	0.0815250i	$0.0259791\pi$
$588$		0			0
$589$	−58.7770	+	42.7040i	−0.0997912	+	0.0725026i
$590$		0			0
$591$		0			0
$592$		0			0
$593$			629.346i			1.06129i	0.847594	+	0.530646i	$0.178051\pi$
$593$			629.346i			1.06129i	−0.847594	+	0.530646i	$0.821949\pi$
$594$		0			0
$595$	501.193	+	231.531i	0.842341	+	0.389128i
$596$		0			0
$597$		0			0
$598$		0			0
$599$			880.743i			1.47036i	0.677874	+	0.735178i	$0.262901\pi$
$599$			880.743i			1.47036i	−0.677874	+	0.735178i	$0.737099\pi$
$600$		0			0
$601$	−442.149			−0.735689			−0.367844	−	0.929887i	$-0.619904\pi$
$601$	−442.149			−0.735689			−0.367844	+	0.929887i	$0.619904\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	106.101	−	59.3100i	0.175374	−	0.0980331i
$606$		0			0
$607$	−1098.42			−1.80959			−0.904793	−	0.425852i	$-0.859974\pi$
$607$	−1098.42			−1.80959			−0.904793	+	0.425852i	$0.859974\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−280.922	−	386.655i	−0.459773	−	0.632824i
$612$		0			0
$613$	748.032	+	543.477i	1.22028	+	0.886585i	0.996123	−	0.0879676i	$-0.0280372\pi$
$613$	748.032	+	543.477i	1.22028	+	0.886585i	0.224157	+	0.974553i	$0.428037\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	767.982	−	249.532i	1.24470	−	0.404429i	0.388683	−	0.921371i	$-0.372930\pi$
$617$	767.982	−	249.532i	1.24470	−	0.404429i	0.856020	+	0.516943i	$0.172930\pi$
$618$		0			0
$619$	−184.156	−	566.775i	−0.297506	−	0.915630i	−0.982368	−	0.186957i	$-0.940137\pi$
$619$	−184.156	−	566.775i	−0.297506	−	0.915630i	0.684862	−	0.728673i	$-0.259863\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	12.8987	+	17.7535i	0.0207041	+	0.0284967i
$624$		0			0
$625$	−617.610	+	95.8302i	−0.988175	+	0.153328i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−147.303	−	47.8617i	−0.234186	−	0.0760917i
$630$		0			0
$631$	−3.80487	−	11.7102i	−0.00602990	−	0.0185581i	0.947996	−	0.318281i	$-0.103106\pi$
$631$	−3.80487	−	11.7102i	−0.00602990	−	0.0185581i	−0.954026	+	0.299723i	$0.903106\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	159.003	+	18.9460i	0.250399	+	0.0298362i
$636$		0			0
$637$	143.656	+	104.373i	0.225520	+	0.163850i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	335.756	−	462.129i	0.523801	−	0.720950i	−0.462369	−	0.886688i	$-0.653001\pi$
$641$	335.756	−	462.129i	0.523801	−	0.720950i	0.986170	+	0.165738i	$0.0530005\pi$
$642$		0			0
$643$	−754.965			−1.17413			−0.587065	−	0.809540i	$-0.699717\pi$
$643$	−754.965			−1.17413			−0.587065	+	0.809540i	$0.699717\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	1064.97	+	346.029i	1.64601	+	0.534821i	0.977870	−	0.209214i	$-0.0670904\pi$
$647$	1064.97	+	346.029i	1.64601	+	0.534821i	0.668141	+	0.744035i	$0.267090\pi$
$648$		0			0
$649$	−330.383			−0.509065
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−184.235	−	59.8616i	−0.282136	−	0.0916716i	0.164531	−	0.986372i	$-0.447389\pi$
$653$	−184.235	−	59.8616i	−0.282136	−	0.0916716i	−0.446667	+	0.894700i	$0.647389\pi$
$654$		0			0
$655$	−776.060	−	358.509i	−1.18482	−	0.547341i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	227.550	−	313.196i	0.345296	−	0.475259i	−0.600683	−	0.799487i	$-0.705105\pi$
$659$	227.550	−	313.196i	0.345296	−	0.475259i	0.945979	+	0.324228i	$0.105105\pi$
$660$		0			0
$661$	−984.558	+	715.323i	−1.48950	+	1.08218i	−0.515159	+	0.857095i	$0.672267\pi$
$661$	−984.558	+	715.323i	−1.48950	+	1.08218i	−0.974338	+	0.225088i	$0.927733\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−54.7378	+	118.490i	−0.0823124	+	0.178181i
$666$		0			0
$667$	67.0740	+	206.433i	0.100561	+	0.309494i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	318.127	+	103.366i	0.474109	+	0.154047i
$672$		0			0
$673$	−480.808	+	349.328i	−0.714425	+	0.519060i	−0.884598	−	0.466354i	$-0.845567\pi$
$673$	−480.808	+	349.328i	−0.714425	+	0.519060i	0.170173	+	0.985414i	$0.445567\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−286.108	−	393.793i	−0.422611	−	0.581674i	0.543627	−	0.839327i	$-0.317051\pi$
$677$	−286.108	−	393.793i	−0.422611	−	0.581674i	−0.966237	+	0.257653i	$0.917051\pi$
$678$		0			0
$679$	71.2305	−	219.225i	0.104905	−	0.322864i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	796.974	−	258.953i	1.16687	−	0.379140i	0.339398	−	0.940643i	$-0.389777\pi$
$683$	796.974	−	258.953i	1.16687	−	0.379140i	0.827475	+	0.561503i	$0.189777\pi$
$684$		0			0
$685$	436.547	−	86.4779i	0.637294	−	0.126245i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−302.059	−	415.749i	−0.438402	−	0.603409i
$690$		0			0
$691$	840.674	+	610.786i	1.21661	+	0.883915i	0.995814	−	0.0914055i	$-0.0291360\pi$
$691$	840.674	+	610.786i	1.21661	+	0.883915i	0.220792	+	0.975321i	$0.429136\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	992.113	+	118.215i	1.42750	+	0.170094i
$696$		0			0
$697$	−352.738	+	1085.62i	−0.506080	+	1.55755i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			256.502i			0.365909i	0.983121	+	0.182955i	$0.0585661\pi$
$701$			256.502i			0.365909i	−0.983121	+	0.182955i	$0.941434\pi$
$702$		0			0
$703$	11.3153	−	34.8249i	0.0160957	−	0.0495375i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		−	908.541i		−	1.28506i
$708$		0			0
$709$	−130.344	−	94.7004i	−0.183842	−	0.133569i	0.492058	−	0.870562i	$-0.336245\pi$
$709$	−130.344	−	94.7004i	−0.183842	−	0.133569i	−0.675900	+	0.736993i	$0.736245\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−366.915	+	505.016i	−0.514608	+	0.708297i
$714$		0			0
$715$	699.085	−	755.074i	0.977741	−	1.05605i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−839.775	+	272.859i	−1.16798	+	0.379498i	−0.827887	−	0.560895i	$-0.810457\pi$
$719$	−839.775	+	272.859i	−1.16798	+	0.379498i	−0.340089	+	0.940393i	$0.610457\pi$
$720$		0			0
$721$	297.335	−	915.103i	0.412392	−	1.26921i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−35.3189	+	146.102i	−0.0487157	+	0.201519i
$726$		0			0
$727$	72.0289	−	52.3321i	0.0990769	−	0.0719836i	−0.537144	−	0.843491i	$-0.680497\pi$
$727$	72.0289	−	52.3321i	0.0990769	−	0.0719836i	0.636221	+	0.771507i	$0.280497\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−659.365	+	214.241i	−0.902004	+	0.293079i
$732$		0			0
$733$	−88.0257	−	270.915i	−0.120090	−	0.369598i	0.872885	−	0.487926i	$-0.162246\pi$
$733$	−88.0257	−	270.915i	−0.120090	−	0.369598i	−0.992975	+	0.118328i	$0.962246\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−143.364	+	197.324i	−0.194524	+	0.267740i
$738$		0			0
$739$	1051.42	−	763.904i	1.42277	−	1.03370i	0.431458	−	0.902133i	$-0.357999\pi$
$739$	1051.42	−	763.904i	1.42277	−	1.03370i	0.991307	−	0.131566i	$-0.0420006\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$			1351.30i			1.81871i	0.416021	+	0.909355i	$0.363424\pi$
$743$			1351.30i			1.81871i	−0.416021	+	0.909355i	$0.636576\pi$
$744$		0			0
$745$	120.393	−	130.035i	0.161601	−	0.174544i
$746$		0			0
$747$		0			0
$748$		0			0
$749$			404.262i			0.539735i
$750$		0			0
$751$	−441.641			−0.588071			−0.294035	−	0.955795i	$-0.594998\pi$
$751$	−441.641			−0.588071			−0.294035	+	0.955795i	$0.594998\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	180.534	+	167.148i	0.239118	+	0.221388i
$756$		0			0
$757$	1024.28			1.35308			0.676542	−	0.736404i	$-0.263478\pi$
$757$	1024.28			1.35308			0.676542	+	0.736404i	$0.263478\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	172.962	+	238.061i	0.227282	+	0.312827i	0.907394	−	0.420282i	$-0.138069\pi$
$761$	172.962	+	238.061i	0.227282	+	0.312827i	−0.680112	+	0.733108i	$0.738069\pi$
$762$		0			0
$763$	905.564	+	657.931i	1.18685	+	0.862295i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−445.015	+	144.594i	−0.580203	+	0.188519i
$768$		0			0
$769$	214.742	+	660.909i	0.279249	+	0.859439i	0.988064	+	0.154045i	$0.0492300\pi$
$769$	214.742	+	660.909i	0.279249	+	0.859439i	−0.708815	+	0.705394i	$0.750770\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	157.116	+	216.251i	0.203255	+	0.279756i	0.898460	−	0.439055i	$-0.144687\pi$
$773$	157.116	+	216.251i	0.203255	+	0.279756i	−0.695206	+	0.718811i	$0.744687\pi$
$774$		0			0
$775$	−399.632	+	164.797i	−0.515654	+	0.212642i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−256.658	−	83.3931i	−0.329470	−	0.107051i
$780$		0			0
$781$	−262.410	−	807.616i	−0.335993	−	1.03408i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	701.189	+	649.196i	0.893235	+	0.827001i
$786$		0			0
$787$	−31.0390	−	22.5512i	−0.0394397	−	0.0286546i	0.567891	−	0.823104i	$-0.307760\pi$
$787$	−31.0390	−	22.5512i	−0.0394397	−	0.0286546i	−0.607330	+	0.794449i	$0.707760\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−257.318	+	354.168i	−0.325307	+	0.447747i
$792$		0			0
$793$	473.746			0.597409
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−433.612	−	140.889i	−0.544055	−	0.176774i	0.0240795	−	0.999710i	$-0.492335\pi$
$797$	−433.612	−	140.889i	−0.544055	−	0.176774i	−0.568134	+	0.822936i	$0.692335\pi$
$798$		0			0
$799$	497.526			0.622686
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−1441.21	−	468.277i	−1.79478	−	0.583160i
$804$		0			0
$805$	−132.689	+	1113.58i	−0.164831	+	1.38333i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	463.541	−	638.010i	0.572981	−	0.788640i	−0.419923	−	0.907560i	$-0.637943\pi$
$809$	463.541	−	638.010i	0.572981	−	0.788640i	0.992904	+	0.118919i	$0.0379430\pi$
$810$		0			0
$811$	599.208	−	435.350i	0.738851	−	0.536807i	−0.153500	−	0.988149i	$-0.549054\pi$
$811$	599.208	−	435.350i	0.738851	−	0.536807i	0.892351	+	0.451342i	$0.149054\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−153.172	−	773.225i	−0.187942	−	0.948743i
$816$		0			0
$817$	−50.6500	−	155.885i	−0.0619952	−	0.190801i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−287.802	−	93.5125i	−0.350550	−	0.113901i	0.128449	−	0.991716i	$-0.459000\pi$
$821$	−287.802	−	93.5125i	−0.350550	−	0.113901i	−0.478999	+	0.877815i	$0.659000\pi$
$822$		0			0
$823$	−529.065	+	384.388i	−0.642850	+	0.467058i	−0.860828	−	0.508896i	$-0.830054\pi$
$823$	−529.065	+	384.388i	−0.642850	+	0.467058i	0.217978	+	0.975954i	$0.430054\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	185.791	+	255.719i	0.224657	+	0.309213i	0.906435	−	0.422346i	$-0.138793\pi$
$827$	185.791	+	255.719i	0.224657	+	0.309213i	−0.681778	+	0.731559i	$0.738793\pi$
$828$		0			0
$829$	−273.321	+	841.195i	−0.329699	+	1.01471i	0.639575	+	0.768729i	$0.279110\pi$
$829$	−273.321	+	841.195i	−0.329699	+	1.01471i	−0.969274	+	0.245982i	$0.920890\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−175.802	+	57.1215i	−0.211047	+	0.0685732i
$834$		0			0
$835$	−746.125	−	344.680i	−0.893563	−	0.412790i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	608.808	+	837.952i	0.725635	+	0.998751i	0.999318	+	0.0369309i	$0.0117581\pi$
$839$	608.808	+	837.952i	0.725635	+	0.998751i	−0.273683	+	0.961820i	$0.588242\pi$
$840$		0			0
$841$	−651.138	−	473.080i	−0.774243	−	0.562520i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	256.811	−	555.917i	0.303919	−	0.657890i
$846$		0			0
$847$	46.6732	−	143.645i	0.0551041	−	0.169593i
$848$		0			0
$849$		0			0
$850$		0			0
$851$		−	314.616i		−	0.369701i
$852$		0			0
$853$	167.715	−	516.174i	0.196618	−	0.605128i	−0.803336	−	0.595526i	$-0.796944\pi$
$853$	167.715	−	516.174i	0.196618	−	0.605128i	0.999954	−	0.00960157i	$-0.00305632\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$			1175.03i			1.37110i	0.728027	+	0.685548i	$0.240437\pi$
$857$			1175.03i			1.37110i	−0.728027	+	0.685548i	$0.759563\pi$
$858$		0			0
$859$	540.173	+	392.459i	0.628839	+	0.456879i	0.855998	−	0.516979i	$-0.172944\pi$
$859$	540.173	+	392.459i	0.628839	+	0.456879i	−0.227159	+	0.973858i	$0.572944\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	630.852	−	868.294i	0.730999	−	1.00613i	−0.268087	−	0.963395i	$-0.586392\pi$
$863$	630.852	−	868.294i	0.730999	−	1.00613i	0.999086	−	0.0427392i	$-0.0136085\pi$
$864$		0			0
$865$	53.5977	−	449.815i	0.0619626	−	0.520017i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	1657.44	−	538.535i	1.90730	−	0.619718i
$870$		0			0
$871$	−106.747	+	328.534i	−0.122557	+	0.377192i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−482.227	+	608.744i	−0.551117	+	0.695707i
$876$		0			0
$877$	306.385	−	222.601i	0.349355	−	0.253822i	−0.399243	−	0.916845i	$-0.630727\pi$
$877$	306.385	−	222.601i	0.349355	−	0.253822i	0.748599	+	0.663024i	$0.230727\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	616.407	−	200.283i	0.699667	−	0.227336i	0.0624818	−	0.998046i	$-0.480098\pi$
$881$	616.407	−	200.283i	0.699667	−	0.227336i	0.637186	+	0.770710i	$0.280098\pi$
$882$		0			0
$883$	332.661	+	1023.82i	0.376739	+	1.15948i	0.942298	+	0.334776i	$0.108661\pi$
$883$	332.661	+	1023.82i	0.376739	+	1.15948i	−0.565559	+	0.824708i	$0.691339\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−1.71980	+	2.36710i	−0.00193890	+	0.00266866i	−0.809985	−	0.586450i	$-0.800525\pi$
$887$	−1.71980	+	2.36710i	−0.00193890	+	0.00266866i	0.808046	+	0.589119i	$0.200525\pi$
$888$		0			0
$889$	160.970	−	116.951i	0.181068	−	0.131554i
$890$		0			0
$891$		0			0
$892$		0			0
$893$			117.623i			0.131717i
$894$		0			0
$895$	−312.844	−	559.654i	−0.349546	−	0.625312i
$896$		0			0
$897$		0			0
$898$		0			0
$899$			103.961i			0.115641i
$900$		0			0
$901$	534.962			0.593742
$902$		0			0
$903$		0			0
$904$		0			0
$905$	574.892	−	1244.46i	0.635240	−	1.37510i
$906$		0			0
$907$	−850.319			−0.937508			−0.468754	−	0.883329i	$-0.655297\pi$
$907$	−850.319			−0.937508			−0.468754	+	0.883329i	$0.655297\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−30.4428	−	41.9009i	−0.0334169	−	0.0459944i	0.791982	−	0.610545i	$-0.209050\pi$
$911$	−30.4428	−	41.9009i	−0.0334169	−	0.0459944i	−0.825399	+	0.564551i	$0.809050\pi$
$912$		0			0
$913$	75.3429	+	54.7398i	0.0825223	+	0.0599560i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−1010.24	+	328.246i	−1.10168	+	0.357957i
$918$		0			0
$919$	−279.372	−	859.818i	−0.303996	−	0.935602i	−0.980050	−	0.198751i	$-0.936312\pi$
$919$	−279.372	−	859.818i	−0.303996	−	0.935602i	0.676055	−	0.736852i	$-0.263688\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−706.917	−	972.987i	−0.765890	−	1.05416i
$924$		0			0
$925$	114.128	−	185.585i	0.123382	−	0.200632i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−742.311	−	241.191i	−0.799043	−	0.259625i	−0.119093	−	0.992883i	$-0.537999\pi$
$929$	−742.311	−	241.191i	−0.799043	−	0.259625i	−0.679950	+	0.733258i	$0.737999\pi$
$930$		0			0
$931$	−13.5045	−	41.5625i	−0.0145053	−	0.0446428i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	208.154	+	1050.78i	0.222624	+	1.12382i
$936$		0			0
$937$	1203.88	+	874.671i	1.28482	+	0.933480i	0.999687	−	0.0250067i	$-0.00796070\pi$
$937$	1203.88	+	874.671i	1.28482	+	0.933480i	0.285138	+	0.958487i	$0.407961\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	171.035	−	235.410i	0.181759	−	0.250170i	−0.708409	−	0.705802i	$-0.750587\pi$
$941$	171.035	−	235.410i	0.181759	−	0.250170i	0.890168	+	0.455632i	$0.150587\pi$
$942$		0			0
$943$	−2318.70			−2.45886
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−608.668	−	197.768i	−0.642733	−	0.208837i	−0.0305258	−	0.999534i	$-0.509718\pi$
$947$	−608.668	−	197.768i	−0.642733	−	0.208837i	−0.612207	+	0.790697i	$0.709718\pi$
$948$		0			0
$949$	−2146.21			−2.26155
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−544.564	−	176.940i	−0.571421	−	0.185666i	0.00903291	−	0.999959i	$-0.497125\pi$
$953$	−544.564	−	176.940i	−0.571421	−	0.185666i	−0.580453	+	0.814293i	$0.697125\pi$
$954$		0			0
$955$	1048.90	−	207.783i	1.09833	−	0.217574i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	325.032	−	447.369i	0.338928	−	0.466495i
$960$		0			0
$961$	535.583	−	389.124i	0.557319	−	0.404916i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−590.471	−	546.687i	−0.611887	−	0.566515i
$966$		0			0
$967$	−293.564	−	903.498i	−0.303583	−	0.934331i	−0.980202	−	0.197999i	$-0.936556\pi$
$967$	−293.564	−	903.498i	−0.303583	−	0.934331i	0.676620	−	0.736333i	$-0.263444\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	312.774	+	101.626i	0.322115	+	0.104662i	0.465611	−	0.884989i	$-0.345834\pi$
$971$	312.774	+	101.626i	0.322115	+	0.104662i	−0.143496	+	0.989651i	$0.545834\pi$
$972$		0			0
$973$	1004.38	−	729.727i	1.03225	−	0.749976i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−479.444	−	659.898i	−0.490731	−	0.675433i	0.489792	−	0.871839i	$-0.337073\pi$
$977$	−479.444	−	659.898i	−0.490731	−	0.675433i	−0.980523	+	0.196406i	$0.937073\pi$
$978$		0			0
$979$	−13.1573	+	40.4941i	−0.0134396	+	0.0413627i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−273.010	+	88.7062i	−0.277731	+	0.0902403i	−0.444571	−	0.895744i	$-0.646644\pi$
$983$	−273.010	+	88.7062i	−0.277731	+	0.0902403i	0.166840	+	0.985984i	$0.446644\pi$
$984$		0			0
$985$	694.403	+	1242.24i	0.704978	+	1.26115i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−827.777	−	1139.34i	−0.836983	−	1.15201i
$990$		0			0
$991$	−893.050	−	648.839i	−0.901160	−	0.654731i	0.0376035	−	0.999293i	$-0.488028\pi$
$991$	−893.050	−	648.839i	−0.901160	−	0.654731i	−0.938764	+	0.344561i	$0.888028\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−1392.10	−	1288.88i	−1.39910	−	1.29535i
$996$		0			0
$997$	−6.83336	+	21.0309i	−0.00685392	+	0.0210942i	−0.954425	−	0.298451i	$-0.903530\pi$
$997$	−6.83336	+	21.0309i	−0.00685392	+	0.0210942i	0.947571	+	0.319545i	$0.103530\pi$
$998$		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.161.5	✓	80
3.2	odd	2	inner	900.3.ba.a.161.16	yes	80
25.16	even	5	inner	900.3.ba.a.341.16	yes	80
75.41	odd	10	inner	900.3.ba.a.341.5	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
900.3.ba.a.161.5	✓	80	1.1	even	1	trivial
900.3.ba.a.161.16	yes	80	3.2	odd	2	inner
900.3.ba.a.341.5	yes	80	75.41	odd	10	inner
900.3.ba.a.341.16	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)

\(f(q)\)	\(=\)	\(q+(-3.66894 - 3.39689i) q^{5} -6.21282 q^{7} +O(q^{10})\)	\(q+(-3.66894 - 3.39689i) q^{5} -6.21282 q^{7} +(-7.08545 - 9.75228i) q^{11} +(-13.8120 - 10.0350i) q^{13} +(16.9027 - 5.49202i) q^{17} +(1.29840 + 3.99607i) q^{19} +(21.2199 + 29.2067i) q^{23} +(1.92229 + 24.9260i) q^{25} +(5.71813 + 1.85793i) q^{29} +(5.34325 + 16.4448i) q^{31} +(22.7945 + 21.1043i) q^{35} +(-7.05040 - 5.12242i) q^{37} +(-37.7519 + 51.9611i) q^{41} -39.0095 q^{43} +(26.6240 + 8.65065i) q^{47} -10.4008 q^{49} +(28.6272 + 9.30156i) q^{53} +(-7.13131 + 59.8491i) q^{55} +(16.1097 - 22.1731i) q^{59} +(-22.4493 + 16.3104i) q^{61} +(16.5877 + 83.7359i) q^{65} +(-6.25254 - 19.2433i) q^{67} +(66.9971 + 21.7687i) q^{71} +(101.702 - 73.8909i) q^{73} +(44.0206 + 60.5892i) q^{77} +(-44.6751 + 137.496i) q^{79} +(-7.34754 + 2.38736i) q^{83} +(-80.6708 - 37.2666i) q^{85} +(-2.07613 - 2.85755i) q^{89} +(85.8117 + 62.3458i) q^{91} +(8.81045 - 19.0719i) q^{95} +(-11.4651 + 35.2859i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 16 q^{7}+O(q^{10}) \) 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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