LMFDB - Embedded newform 900.3.ba.a.161.16

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			161.16
Character	$\chi$	$=$	900.161
Dual form			900.3.ba.a.341.16

$q$-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	0.998828	−	0.0484105i	$-0.0154156\pi$
$11$	7.08545	+	9.75228i	0.644132	+	0.886571i	−0.354696	+	0.934982i	$0.615416\pi$
$12$		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	−0.760576	−	0.649249i	$-0.775083\pi$
$17$	−16.9027	+	5.49202i	−0.994276	+	0.323060i	−0.233700	+	0.972309i	$0.575083\pi$
$18$		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	$-0.912759\pi$
$23$	−21.2199	−	29.2067i	−0.922603	−	1.26985i	0.0400721	−	0.999197i	$-0.487241\pi$
$24$		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	0.208764	−	0.977966i	$-0.433056\pi$
$29$	−5.71813	−	1.85793i	−0.197177	−	0.0640667i	−0.405941	+	0.913899i	$0.633056\pi$
$30$		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	$-0.513555\pi$
$41$	37.7519	−	51.9611i	0.920779	−	1.26734i	0.963349	−	0.268250i	$-0.0864452\pi$
$42$		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	0.0117617	−	0.999931i	$-0.496256\pi$
$47$	−26.6240	−	8.65065i	−0.566467	−	0.184056i	−0.578229	+	0.815874i	$0.696256\pi$
$48$		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	0.0262277	−	0.999656i	$-0.491651\pi$
$53$	−28.6272	−	9.30156i	−0.540137	−	0.175501i	−0.566364	+	0.824155i	$0.691651\pi$
$54$		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	−0.923415	−	0.383803i	$-0.874614\pi$
$59$	−16.1097	+	22.1731i	−0.273046	+	0.375815i	0.650369	+	0.759618i	$0.274614\pi$
$60$		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	−0.203500	−	0.979075i	$-0.565232\pi$
$71$	−66.9971	−	21.7687i	−0.943621	−	0.306601i	−0.740121	+	0.672474i	$0.765232\pi$
$72$		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	−0.264420	−	0.964408i	$-0.585180\pi$
$83$	7.34754	−	2.38736i	0.0885246	−	0.0287634i	0.352944	+	0.935644i	$0.385180\pi$
$84$		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	0.820521	−	0.571616i	$-0.193683\pi$
$89$	2.07613	+	2.85755i	0.0233273	+	0.0321073i	−0.797194	+	0.603723i	$0.793683\pi$
$90$		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	$-0.742328\pi$
$101$		−	146.236i		−	1.44788i	0.689860	−	0.723942i	$-0.257672\pi$
$102$		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	$0.0983424\pi$
$107$			65.0689i			0.608120i	−0.952653	+	0.304060i	$0.901658\pi$
$108$		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	−0.951952	−	0.306247i	$-0.900927\pi$
$113$	−41.4172	+	57.0059i	−0.366524	+	0.504477i	0.585428	+	0.810725i	$0.300927\pi$
$114$		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	−0.854782	−	0.518987i	$-0.826309\pi$
$131$	−162.605	+	52.8337i	−1.24126	+	0.403311i	−0.386480	+	0.922298i	$0.626309\pi$
$132$		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	−0.574208	−	0.818710i	$-0.694690\pi$
$137$	52.3164	−	72.0073i	0.381871	−	0.525601i	0.956079	+	0.293109i	$0.0946898\pi$
$138$		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	$-0.962053\pi$
$149$		−	35.4421i		−	0.237866i	0.992902	−	0.118933i	$-0.0379474\pi$
$150$		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	−0.737066	−	0.675821i	$-0.763789\pi$
$167$	−156.333	+	50.7957i	−0.936126	+	0.304166i	−0.199061	+	0.979987i	$0.563789\pi$
$168$		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	0.626879	−	0.779116i	$-0.284332\pi$
$173$	−53.2530	−	73.2965i	−0.307821	−	0.423679i	−0.934700	+	0.355437i	$0.884332\pi$
$174$		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	−0.0521447	−	0.998640i	$-0.516606\pi$
$179$	−121.956	−	39.6258i	−0.681316	−	0.221373i	−0.629172	+	0.777266i	$0.716606\pi$
$180$		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	−0.341292	−	0.939957i	$-0.610864\pi$
$191$	125.702	−	173.014i	0.658126	−	0.905833i	0.999418	+	0.0341248i	$0.0108644\pi$
$192$		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	0.900727	−	0.434386i	$-0.143035\pi$
$197$	270.698	+	87.9553i	1.37410	+	0.446473i	0.473377	+	0.880860i	$0.343035\pi$
$198$		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	0.971011	−	0.239034i	$-0.0768307\pi$
$227$	100.701	+	138.603i	0.443618	+	0.610587i	−0.527394	+	0.849621i	$0.676831\pi$
$228$		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	0.165672	−	0.986181i	$-0.447021\pi$
$233$	204.892	−	66.5735i	0.879365	−	0.285723i	0.713694	+	0.700458i	$0.247021\pi$
$234$		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	$0.0305745\pi$
$239$	186.183	+	256.259i	0.779009	+	1.07221i	−0.216382	+	0.976309i	$0.569426\pi$
$240$		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	$0.0412479\pi$
$251$			64.8693i			0.258443i	−0.991616	+	0.129222i	$0.958752\pi$
$252$		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	$0.447610\pi$
$257$			507.054i			1.97297i	−0.163846	+	0.986486i	$0.552390\pi$
$258$		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	−0.973557	−	0.228445i	$-0.926636\pi$
$263$	−119.783	+	164.867i	−0.455447	+	0.626869i	0.518110	+	0.855314i	$0.326636\pi$
$264$		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	0.755184	−	0.655513i	$-0.227547\pi$
$269$	471.138	−	153.082i	1.75144	−	0.569078i	0.996257	+	0.0864349i	$0.0275475\pi$
$270$		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	0.659360	−	0.751827i	$-0.270827\pi$
$281$	459.353	−	149.253i	1.63471	−	0.531148i	0.975347	+	0.220679i	$0.0708272\pi$
$282$		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	$-0.732836\pi$
$293$		−	436.096i		−	1.48838i	0.667968	−	0.744190i	$-0.267164\pi$
$294$		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	0.734692	−	0.678401i	$-0.237327\pi$
$311$	−42.7745	−	58.8740i	−0.137538	−	0.189305i	−0.872230	+	0.489096i	$0.837327\pi$
$312$		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	−0.559935	−	0.828536i	$-0.689174\pi$
$317$	−166.720	+	54.1706i	−0.525931	+	0.170885i	0.0340044	+	0.999422i	$0.489174\pi$
$318$		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	0.0241964	−	0.999707i	$-0.492297\pi$
$347$	−188.713	−	61.3166i	−0.543841	−	0.176705i	−0.568038	+	0.823002i	$0.692297\pi$
$348$		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	0.562836	−	0.826569i	$-0.309710\pi$
$353$	187.914	+	61.0569i	0.532334	+	0.172966i	−0.0305015	+	0.999535i	$0.509710\pi$
$354$		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	−0.569057	−	0.822298i	$-0.692692\pi$
$359$	139.595	−	192.135i	0.388843	−	0.535196i	0.957900	+	0.287102i	$0.0926917\pi$
$360$		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	−0.463406	−	0.886146i	$-0.653373\pi$
$383$	−121.582	+	39.5043i	−0.317446	+	0.103145i	0.145960	+	0.989290i	$0.453373\pi$
$384$		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	$0.0667212\pi$
$389$	339.890	+	467.819i	0.873754	+	1.20262i	−0.104358	+	0.994540i	$0.533279\pi$
$390$		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	$-0.950867\pi$
$401$		−	123.302i		−	0.307487i	0.988111	−	0.153743i	$-0.0491329\pi$
$402$		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	−0.167920	−	0.985801i	$-0.553705\pi$
$419$	115.506	−	37.5300i	0.275669	−	0.0895704i	0.443589	+	0.896230i	$0.353705\pi$
$420$		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	0.219928	−	0.975516i	$-0.429418\pi$
$431$	418.607	−	136.014i	0.971247	−	0.315577i	0.751319	+	0.659939i	$0.229418\pi$
$432$		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	$0.0413698\pi$
$443$			114.827i			0.259203i	−0.991566	+	0.129601i	$0.958630\pi$
$444$		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	$0.102006\pi$
$449$			282.874i			0.630009i	−0.949090	+	0.315005i	$0.897994\pi$
$450$		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	$-0.829158\pi$
$461$	−497.934	−	685.347i	−1.08012	−	1.48665i	−0.220724	−	0.975336i	$-0.570842\pi$
$462$		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	−0.144882	−	0.989449i	$-0.546280\pi$
$467$	149.202	−	48.4787i	0.319490	−	0.103809i	0.464372	+	0.885640i	$0.346280\pi$
$468$		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	−0.301908	−	0.953337i	$-0.597623\pi$
$479$	−530.020	−	172.214i	−1.10651	−	0.359528i	−0.804606	+	0.593809i	$0.797623\pi$
$480$		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	$-0.564273\pi$
$491$	389.441	−	536.019i	0.793159	−	1.09169i	0.993708	−	0.112005i	$-0.0357274\pi$
$492$		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	0.180382	−	0.983597i	$-0.442267\pi$
$503$	−126.670	−	41.1577i	−0.251830	−	0.0818244i	−0.432212	+	0.901772i	$0.642267\pi$
$504$		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	−0.786304	−	0.617840i	$-0.788008\pi$
$509$	22.5373	−	31.0200i	0.0442776	−	0.0609429i	0.830582	+	0.556897i	$0.188008\pi$
$510$		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	0.235074	−	0.971977i	$-0.424467\pi$
$521$	−76.0979	−	24.7257i	−0.146061	−	0.0474582i	−0.381135	+	0.924519i	$0.624467\pi$
$522$		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	$-0.974802\pi$
$557$		−	88.0940i		−	0.158158i	0.996868	−	0.0790790i	$-0.0251979\pi$
$558$		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	−0.349576	−	0.936908i	$-0.613674\pi$
$563$	365.670	−	503.301i	0.649502	−	0.893963i	0.999077	+	0.0429456i	$0.0136742\pi$
$564$		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	−0.285786	−	0.958293i	$-0.592255\pi$
$569$	26.3326	−	8.55599i	0.0462788	−	0.0150369i	0.332065	+	0.943257i	$0.392255\pi$
$570$		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	−0.996671	−	0.0815250i	$-0.974021\pi$
$587$	−358.744	+	493.769i	−0.611148	+	0.841173i	0.385523	+	0.922698i	$0.374021\pi$
$588$		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	$-0.821949\pi$
$593$		−	629.346i		−	1.06129i	0.847594	−	0.530646i	$-0.178051\pi$
$594$		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	$-0.737099\pi$
$599$		−	880.743i		−	1.47036i	0.677874	−	0.735178i	$-0.262901\pi$
$600$		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	−0.856020	−	0.516943i	$-0.827070\pi$
$617$	−767.982	+	249.532i	−1.24470	+	0.404429i	−0.388683	+	0.921371i	$0.627070\pi$
$618$		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	−0.986170	−	0.165738i	$-0.946999\pi$
$641$	−335.756	+	462.129i	−0.523801	+	0.720950i	0.462369	+	0.886688i	$0.346999\pi$
$642$		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	−0.668141	−	0.744035i	$-0.732910\pi$
$647$	−1064.97	−	346.029i	−1.64601	−	0.534821i	−0.977870	+	0.209214i	$0.932910\pi$
$648$		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	0.446667	−	0.894700i	$-0.352611\pi$
$653$	184.235	+	59.8616i	0.282136	+	0.0916716i	−0.164531	+	0.986372i	$0.552611\pi$
$654$		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	−0.945979	−	0.324228i	$-0.894895\pi$
$659$	−227.550	+	313.196i	−0.345296	+	0.475259i	0.600683	+	0.799487i	$0.294895\pi$
$660$		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	0.966237	−	0.257653i	$-0.0829492\pi$
$677$	286.108	+	393.793i	0.422611	+	0.581674i	−0.543627	+	0.839327i	$0.682949\pi$
$678$		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	−0.827475	−	0.561503i	$-0.810223\pi$
$683$	−796.974	+	258.953i	−1.16687	+	0.379140i	−0.339398	+	0.940643i	$0.610223\pi$
$684$		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	$-0.941434\pi$
$701$		−	256.502i		−	0.365909i	0.983121	−	0.182955i	$-0.0585661\pi$
$702$		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	0.340089	−	0.940393i	$-0.389543\pi$
$719$	839.775	−	272.859i	1.16798	−	0.379498i	0.827887	+	0.560895i	$0.189543\pi$
$720$		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	$-0.636576\pi$
$743$		−	1351.30i		−	1.81871i	0.416021	−	0.909355i	$-0.363424\pi$
$744$		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	0.680112	−	0.733108i	$-0.261931\pi$
$761$	−172.962	−	238.061i	−0.227282	−	0.312827i	−0.907394	+	0.420282i	$0.861931\pi$
$762$		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	0.695206	−	0.718811i	$-0.255313\pi$
$773$	−157.116	−	216.251i	−0.203255	−	0.279756i	−0.898460	+	0.439055i	$0.855313\pi$
$774$		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	0.568134	−	0.822936i	$-0.307665\pi$
$797$	433.612	+	140.889i	0.544055	+	0.176774i	−0.0240795	+	0.999710i	$0.507665\pi$
$798$		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	−0.992904	−	0.118919i	$-0.962057\pi$
$809$	−463.541	+	638.010i	−0.572981	+	0.788640i	0.419923	+	0.907560i	$0.362057\pi$
$810$		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	0.478999	−	0.877815i	$-0.341000\pi$
$821$	287.802	+	93.5125i	0.350550	+	0.113901i	−0.128449	+	0.991716i	$0.541000\pi$
$822$		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	0.681778	−	0.731559i	$-0.261207\pi$
$827$	−185.791	−	255.719i	−0.224657	−	0.309213i	−0.906435	+	0.422346i	$0.861207\pi$
$828$		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	$-0.988242\pi$
$839$	−608.808	−	837.952i	−0.725635	−	0.998751i	0.273683	−	0.961820i	$-0.411758\pi$
$840$		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	$-0.759563\pi$
$857$		−	1175.03i		−	1.37110i	0.728027	−	0.685548i	$-0.240437\pi$
$858$		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	$0.413608\pi$
$863$	−630.852	+	868.294i	−0.730999	+	1.00613i	−0.999086	+	0.0427392i	$0.986392\pi$
$864$		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	−0.637186	−	0.770710i	$-0.719902\pi$
$881$	−616.407	+	200.283i	−0.699667	+	0.227336i	−0.0624818	+	0.998046i	$0.519902\pi$
$882$		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	−0.808046	−	0.589119i	$-0.799475\pi$
$887$	1.71980	−	2.36710i	0.00193890	−	0.00266866i	0.809985	+	0.586450i	$0.199475\pi$
$888$		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	0.825399	−	0.564551i	$-0.190950\pi$
$911$	30.4428	+	41.9009i	0.0334169	+	0.0459944i	−0.791982	+	0.610545i	$0.790950\pi$
$912$		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	0.679950	−	0.733258i	$-0.262001\pi$
$929$	742.311	+	241.191i	0.799043	+	0.259625i	0.119093	+	0.992883i	$0.462001\pi$
$930$		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	−0.890168	−	0.455632i	$-0.849413\pi$
$941$	−171.035	+	235.410i	−0.181759	+	0.250170i	0.708409	+	0.705802i	$0.249413\pi$
$942$		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	0.612207	−	0.790697i	$-0.290282\pi$
$947$	608.668	+	197.768i	0.642733	+	0.208837i	0.0305258	+	0.999534i	$0.490282\pi$
$948$		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	0.580453	−	0.814293i	$-0.302875\pi$
$953$	544.564	+	176.940i	0.571421	+	0.185666i	−0.00903291	+	0.999959i	$0.502875\pi$
$954$		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	0.143496	−	0.989651i	$-0.454166\pi$
$971$	−312.774	−	101.626i	−0.322115	−	0.104662i	−0.465611	+	0.884989i	$0.654166\pi$
$972$		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	0.980523	−	0.196406i	$-0.0629272\pi$
$977$	479.444	+	659.898i	0.490731	+	0.675433i	−0.489792	+	0.871839i	$0.662927\pi$
$978$		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	−0.166840	−	0.985984i	$-0.553356\pi$
$983$	273.010	−	88.7062i	0.277731	−	0.0902403i	0.444571	+	0.895744i	$0.353356\pi$
$984$		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.161.16	yes	80
3.2	odd	2	inner	900.3.ba.a.161.5	✓	80
25.16	even	5	inner	900.3.ba.a.341.5	yes	80
75.41	odd	10	inner	900.3.ba.a.341.16	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
900.3.ba.a.161.5	✓	80	3.2	odd	2	inner
900.3.ba.a.161.16	yes	80	1.1	even	1	trivial
900.3.ba.a.341.5	yes	80	25.16	even	5	inner
900.3.ba.a.341.16	yes	80	75.41	odd	10	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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