LMFDB - Embedded newform 900.3.ba.a.161.6

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			161.6
Character	$\chi$	$=$	900.161
Dual form			900.3.ba.a.341.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.45827 + 3.61115i) q^{5} +7.44862 q^{7} +O(q^{10})$	$q+(-3.45827 + 3.61115i) q^{5} +7.44862 q^{7} +(-9.51036 - 13.0899i) q^{11} +(-5.04897 - 3.66829i) q^{13} +(0.115893 - 0.0376558i) q^{17} +(10.4370 + 32.1216i) q^{19} +(-17.1222 - 23.5666i) q^{23} +(-1.08077 - 24.9766i) q^{25} +(-15.2626 - 4.95911i) q^{29} +(-4.31562 - 13.2821i) q^{31} +(-25.7593 + 26.8980i) q^{35} +(-27.2068 - 19.7669i) q^{37} +(26.1164 - 35.9462i) q^{41} +13.1487 q^{43} +(53.2611 + 17.3056i) q^{47} +6.48187 q^{49} +(-57.1303 - 18.5628i) q^{53} +(80.1589 + 10.9250i) q^{55} +(19.5991 - 26.9759i) q^{59} +(80.8416 - 58.7348i) q^{61} +(30.7074 - 5.54664i) q^{65} +(-25.6732 - 79.0139i) q^{67} +(-27.7823 - 9.02700i) q^{71} +(18.2308 - 13.2454i) q^{73} +(-70.8390 - 97.5016i) q^{77} +(30.3925 - 93.5385i) q^{79} +(-102.169 + 33.1969i) q^{83} +(-0.264807 + 0.548729i) q^{85} +(-75.5745 - 104.019i) q^{89} +(-37.6078 - 27.3237i) q^{91} +(-152.090 - 73.3959i) q^{95} +(-10.7785 + 33.1729i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−3.45827	+	3.61115i	−0.691654	+	0.722229i
$5$	−3.45827	+	3.61115i	−0.691654	+	0.722229i
$6$		0			0
$7$	7.44862			1.06409			0.532044	−	0.846717i	$-0.321424\pi$
$7$	7.44862			1.06409			0.532044	+	0.846717i	$0.321424\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−9.51036	−	13.0899i	−0.864578	−	1.18999i	−0.980458	−	0.196727i	$-0.936969\pi$
$11$	−9.51036	−	13.0899i	−0.864578	−	1.18999i	0.115880	−	0.993263i	$-0.463031\pi$
$12$		0			0
$13$	−5.04897	−	3.66829i	−0.388382	−	0.282176i	0.376410	−	0.926453i	$-0.377158\pi$
$13$	−5.04897	−	3.66829i	−0.388382	−	0.282176i	−0.764792	+	0.644277i	$0.777158\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.115893	−	0.0376558i	0.00681721	−	0.00221504i	−0.305606	−	0.952158i	$-0.598859\pi$
$17$	0.115893	−	0.0376558i	0.00681721	−	0.00221504i	0.312424	+	0.949943i	$0.398859\pi$
$18$		0			0
$19$	10.4370	+	32.1216i	0.549313	+	1.69061i	0.710507	+	0.703690i	$0.248466\pi$
$19$	10.4370	+	32.1216i	0.549313	+	1.69061i	−0.161194	+	0.986923i	$0.551534\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−17.1222	−	23.5666i	−0.744442	−	1.02464i	−0.998351	−	0.0574079i	$-0.981716\pi$
$23$	−17.1222	−	23.5666i	−0.744442	−	1.02464i	0.253909	−	0.967228i	$-0.418284\pi$
$24$		0			0
$25$	−1.08077	−	24.9766i	−0.0432308	−	0.999065i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−15.2626	−	4.95911i	−0.526296	−	0.171004i	0.0338050	−	0.999428i	$-0.489237\pi$
$29$	−15.2626	−	4.95911i	−0.526296	−	0.171004i	−0.560101	+	0.828425i	$0.689237\pi$
$30$		0			0
$31$	−4.31562	−	13.2821i	−0.139214	−	0.428455i	0.857008	−	0.515303i	$-0.172321\pi$
$31$	−4.31562	−	13.2821i	−0.139214	−	0.428455i	−0.996222	+	0.0868478i	$0.972321\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−25.7593	+	26.8980i	−0.735980	+	0.768516i
$36$		0			0
$37$	−27.2068	−	19.7669i	−0.735320	−	0.534241i	0.155922	−	0.987769i	$-0.450165\pi$
$37$	−27.2068	−	19.7669i	−0.735320	−	0.534241i	−0.891242	+	0.453528i	$0.850165\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	26.1164	−	35.9462i	0.636986	−	0.876736i	−0.361464	−	0.932386i	$-0.617723\pi$
$41$	26.1164	−	35.9462i	0.636986	−	0.876736i	0.998450	+	0.0556498i	$0.0177230\pi$
$42$		0			0
$43$	13.1487			0.305783			0.152891	−	0.988243i	$-0.451142\pi$
$43$	13.1487			0.305783			0.152891	+	0.988243i	$0.451142\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	53.2611	+	17.3056i	1.13322	+	0.368204i	0.814797	−	0.579746i	$-0.196848\pi$
$47$	53.2611	+	17.3056i	1.13322	+	0.368204i	0.318419	+	0.947950i	$0.396848\pi$
$48$		0			0
$49$	6.48187			0.132283
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−57.1303	−	18.5628i	−1.07793	−	0.350241i	−0.284359	−	0.958718i	$-0.591781\pi$
$53$	−57.1303	−	18.5628i	−1.07793	−	0.350241i	−0.793571	+	0.608477i	$0.791781\pi$
$54$		0			0
$55$	80.1589	+	10.9250i	1.45743	+	0.198637i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	19.5991	−	26.9759i	0.332188	−	0.457218i	−0.609951	−	0.792439i	$-0.708811\pi$
$59$	19.5991	−	26.9759i	0.332188	−	0.457218i	0.942140	+	0.335221i	$0.108811\pi$
$60$		0			0
$61$	80.8416	−	58.7348i	1.32527	−	0.962866i	0.325421	−	0.945569i	$-0.394494\pi$
$61$	80.8416	−	58.7348i	1.32527	−	0.962866i	0.999850	−	0.0172968i	$-0.00550603\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	30.7074	−	5.54664i	0.472422	−	0.0853329i
$66$		0			0
$67$	−25.6732	−	79.0139i	−0.383182	−	1.17931i	−0.937791	−	0.347201i	$-0.887132\pi$
$67$	−25.6732	−	79.0139i	−0.383182	−	1.17931i	0.554609	−	0.832111i	$-0.312868\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−27.7823	−	9.02700i	−0.391299	−	0.127141i	0.106758	−	0.994285i	$-0.465953\pi$
$71$	−27.7823	−	9.02700i	−0.391299	−	0.127141i	−0.498057	+	0.867144i	$0.665953\pi$
$72$		0			0
$73$	18.2308	−	13.2454i	0.249737	−	0.181444i	−0.455873	−	0.890045i	$-0.650673\pi$
$73$	18.2308	−	13.2454i	0.249737	−	0.181444i	0.705610	+	0.708600i	$0.250673\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−70.8390	−	97.5016i	−0.919987	−	1.26625i
$78$		0			0
$79$	30.3925	−	93.5385i	0.384715	−	1.18403i	−0.551971	−	0.833863i	$-0.686124\pi$
$79$	30.3925	−	93.5385i	0.384715	−	1.18403i	0.936687	−	0.350169i	$-0.113876\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−102.169	+	33.1969i	−1.23096	+	0.399962i	−0.851061	−	0.525067i	$-0.824040\pi$
$83$	−102.169	+	33.1969i	−1.23096	+	0.399962i	−0.379896	+	0.925029i	$0.624040\pi$
$84$		0			0
$85$	−0.264807	+	0.548729i	−0.00311537	+	0.00645563i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−75.5745	−	104.019i	−0.849152	−	1.16876i	−0.984049	−	0.177898i	$-0.943070\pi$
$89$	−75.5745	−	104.019i	−0.849152	−	1.16876i	0.134897	−	0.990860i	$-0.456930\pi$
$90$		0			0
$91$	−37.6078	−	27.3237i	−0.413273	−	0.300260i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−152.090	−	73.3959i	−1.60094	−	0.772588i
$96$		0			0
$97$	−10.7785	+	33.1729i	−0.111119	+	0.341988i	−0.991118	−	0.132987i	$-0.957543\pi$
$97$	−10.7785	+	33.1729i	−0.111119	+	0.341988i	0.879999	+	0.474975i	$0.157543\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$			21.6240i			0.214099i	0.994254	+	0.107050i	$0.0341403\pi$
$101$			21.6240i			0.214099i	−0.994254	+	0.107050i	$0.965860\pi$
$102$		0			0
$103$	−19.8096	+	60.9678i	−0.192326	+	0.591920i	0.807671	+	0.589633i	$0.200728\pi$
$103$	−19.8096	+	60.9678i	−0.192326	+	0.591920i	−0.999997	+	0.00228645i	$0.999272\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	74.0043i		−	0.691629i	−0.938303	−	0.345814i	$-0.887603\pi$
$107$		−	74.0043i		−	0.691629i	0.938303	−	0.345814i	$-0.112397\pi$
$108$		0			0
$109$	−74.6303	−	54.2221i	−0.684682	−	0.497450i	0.190226	−	0.981740i	$-0.439078\pi$
$109$	−74.6303	−	54.2221i	−0.684682	−	0.497450i	−0.874908	+	0.484290i	$0.839078\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	104.460	−	143.776i	0.924422	−	1.27236i	−0.0375736	−	0.999294i	$-0.511963\pi$
$113$	104.460	−	143.776i	0.924422	−	1.27236i	0.961996	−	0.273064i	$-0.0880371\pi$
$114$		0			0
$115$	144.316	+	19.6691i	1.25492	+	0.171035i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	0.863239	−	0.280483i	0.00725411	−	0.00235700i
$120$		0			0
$121$	−43.5072	+	133.901i	−0.359564	+	1.10662i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	93.9319	+	82.4730i	0.751455	+	0.659784i
$126$		0			0
$127$	199.068	−	144.631i	1.56746	−	1.13883i	0.637926	−	0.770098i	$-0.279793\pi$
$127$	199.068	−	144.631i	1.56746	−	1.13883i	0.929537	−	0.368730i	$-0.120207\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−118.573	+	38.5266i	−0.905136	+	0.294097i	−0.724355	−	0.689427i	$-0.757862\pi$
$131$	−118.573	+	38.5266i	−0.905136	+	0.294097i	−0.180781	+	0.983523i	$0.557862\pi$
$132$		0			0
$133$	77.7409	+	239.262i	0.584518	+	1.79896i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−34.3553	+	47.2860i	−0.250769	+	0.345153i	−0.915780	−	0.401680i	$-0.868427\pi$
$137$	−34.3553	+	47.2860i	−0.250769	+	0.345153i	0.665012	+	0.746833i	$0.268427\pi$
$138$		0			0
$139$	−63.1276	+	45.8649i	−0.454155	+	0.329963i	−0.791234	−	0.611513i	$-0.790561\pi$
$139$	−63.1276	+	45.8649i	−0.454155	+	0.329963i	0.337079	+	0.941476i	$0.390561\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$			100.977i			0.706135i
$144$		0			0
$145$	70.6901	−	37.9655i	0.487518	−	0.261831i
$146$		0			0
$147$		0			0
$148$		0			0
$149$			161.733i			1.08546i	0.839909	+	0.542728i	$0.182608\pi$
$149$			161.733i			1.08546i	−0.839909	+	0.542728i	$0.817392\pi$
$150$		0			0
$151$	−231.090			−1.53039			−0.765197	−	0.643796i	$-0.777359\pi$
$151$	−231.090			−1.53039			−0.765197	+	0.643796i	$0.777359\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	62.8882	+	30.3488i	0.405731	+	0.195798i
$156$		0			0
$157$	116.838			0.744191			0.372096	−	0.928194i	$-0.378639\pi$
$157$	116.838			0.744191			0.372096	+	0.928194i	$0.378639\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−127.536	−	175.539i	−0.792151	−	1.09030i
$162$		0			0
$163$	−117.888	−	85.6508i	−0.723240	−	0.525465i	0.164178	−	0.986431i	$-0.447503\pi$
$163$	−117.888	−	85.6508i	−0.723240	−	0.525465i	−0.887418	+	0.460966i	$0.847503\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−56.3230	+	18.3004i	−0.337263	+	0.109583i	−0.472752	−	0.881195i	$-0.656739\pi$
$167$	−56.3230	+	18.3004i	−0.337263	+	0.109583i	0.135489	+	0.990779i	$0.456739\pi$
$168$		0			0
$169$	−40.1881	−	123.686i	−0.237800	−	0.731872i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	103.584	+	142.572i	0.598753	+	0.824113i	0.995593	−	0.0937748i	$-0.0298934\pi$
$173$	103.584	+	142.572i	0.598753	+	0.824113i	−0.396840	+	0.917888i	$0.629893\pi$
$174$		0			0
$175$	−8.05023	−	186.041i	−0.0460013	−	1.06309i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−79.2331	−	25.7444i	−0.442643	−	0.143823i	0.0792117	−	0.996858i	$-0.474760\pi$
$179$	−79.2331	−	25.7444i	−0.442643	−	0.143823i	−0.521855	+	0.853034i	$0.674760\pi$
$180$		0			0
$181$	50.7444	+	156.175i	0.280356	+	0.862847i	0.987752	+	0.156030i	$0.0498695\pi$
$181$	50.7444	+	156.175i	0.280356	+	0.862847i	−0.707397	+	0.706817i	$0.750130\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	165.470	−	29.8886i	0.894431	−	0.161560i
$186$		0			0
$187$	−1.59509	−	1.15890i	−0.00852989	−	0.00619733i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	4.11049	−	5.65760i	0.0215209	−	0.0296210i	−0.798121	−	0.602497i	$-0.794172\pi$
$191$	4.11049	−	5.65760i	0.0215209	−	0.0296210i	0.819642	+	0.572876i	$0.194172\pi$
$192$		0			0
$193$	67.6133			0.350328			0.175164	−	0.984539i	$-0.443954\pi$
$193$	67.6133			0.350328			0.175164	+	0.984539i	$0.443954\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	292.205	+	94.9433i	1.48328	+	0.481946i	0.935090	−	0.354411i	$-0.115319\pi$
$197$	292.205	+	94.9433i	1.48328	+	0.481946i	0.548186	+	0.836356i	$0.315319\pi$
$198$		0			0
$199$	−229.790			−1.15472			−0.577362	−	0.816489i	$-0.695918\pi$
$199$	−229.790			−1.15472			−0.577362	+	0.816489i	$0.695918\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−113.685	−	36.9385i	−0.560025	−	0.181963i
$204$		0			0
$205$	39.4893	+	218.622i	0.192631	+	1.06645i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	321.210	−	442.107i	1.53689	−	2.11535i
$210$		0			0
$211$	−297.243	+	215.960i	−1.40873	+	1.02351i	−0.415229	+	0.909717i	$0.636298\pi$
$211$	−297.243	+	215.960i	−1.40873	+	1.02351i	−0.993505	+	0.113788i	$0.963702\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−45.4716	+	47.4817i	−0.211496	+	0.220845i
$216$		0			0
$217$	−32.1454	−	98.9333i	−0.148135	−	0.455914i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−0.723270	−	0.235005i	−0.00327272	−	0.00106337i
$222$		0			0
$223$	360.189	−	261.693i	1.61520	−	1.17351i	0.772810	−	0.634637i	$-0.218850\pi$
$223$	360.189	−	261.693i	1.61520	−	1.17351i	0.842387	−	0.538873i	$-0.181150\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	175.926	+	242.141i	0.775003	+	1.06670i	0.995816	+	0.0913845i	$0.0291292\pi$
$227$	175.926	+	242.141i	0.775003	+	1.06670i	−0.220812	+	0.975316i	$0.570871\pi$
$228$		0			0
$229$	93.3409	−	287.274i	0.407602	−	1.25447i	−0.511100	−	0.859521i	$-0.670762\pi$
$229$	93.3409	−	287.274i	0.407602	−	1.25447i	0.918703	−	0.394950i	$-0.129238\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−169.895	+	55.2023i	−0.729164	+	0.236920i	−0.649992	−	0.759941i	$-0.725228\pi$
$233$	−169.895	+	55.2023i	−0.729164	+	0.236920i	−0.0791723	+	0.996861i	$0.525228\pi$
$234$		0			0
$235$	−246.684	+	132.486i	−1.04972	+	0.563772i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	79.0375	+	108.786i	0.330701	+	0.455171i	0.941697	−	0.336463i	$-0.109231\pi$
$239$	79.0375	+	108.786i	0.330701	+	0.455171i	−0.610996	+	0.791634i	$0.709231\pi$
$240$		0			0
$241$	−11.7015	−	8.50163i	−0.0485539	−	0.0352765i	0.563244	−	0.826291i	$-0.309553\pi$
$241$	−11.7015	−	8.50163i	−0.0485539	−	0.0352765i	−0.611797	+	0.791014i	$0.709553\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−22.4160	+	23.4070i	−0.0914940	+	0.0955387i
$246$		0			0
$247$	65.1357	−	200.467i	0.263707	−	0.811608i
$248$		0			0
$249$		0			0
$250$		0			0
$251$		−	139.417i		−	0.555447i	−0.960661	−	0.277724i	$-0.910420\pi$
$251$		−	139.417i		−	0.555447i	0.960661	−	0.277724i	$-0.0895800\pi$
$252$		0			0
$253$	−145.647	+	448.254i	−0.575679	+	1.77176i
$254$		0			0
$255$		0			0
$256$		0			0
$257$			437.670i			1.70300i	0.524357	+	0.851499i	$0.324306\pi$
$257$			437.670i			1.70300i	−0.524357	+	0.851499i	$0.675694\pi$
$258$		0			0
$259$	−202.653	−	147.236i	−0.782445	−	0.568479i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−198.769	+	273.583i	−0.755778	+	1.04024i	0.241776	+	0.970332i	$0.422270\pi$
$263$	−198.769	+	273.583i	−0.755778	+	1.04024i	−0.997554	+	0.0699065i	$0.977730\pi$
$264$		0			0
$265$	264.605	−	142.111i	0.998508	−	0.536268i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	422.236	−	137.193i	1.56965	−	0.510010i	0.610285	−	0.792182i	$-0.291055\pi$
$269$	422.236	−	137.193i	1.56965	−	0.510010i	0.959364	+	0.282172i	$0.0910548\pi$
$270$		0			0
$271$	−61.0199	+	187.800i	−0.225166	+	0.692989i	0.773109	+	0.634273i	$0.218701\pi$
$271$	−61.0199	+	187.800i	−0.225166	+	0.692989i	−0.998275	+	0.0587157i	$0.981299\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−316.663	+	251.684i	−1.15150	+	0.915214i
$276$		0			0
$277$	−76.7511	+	55.7630i	−0.277080	+	0.201310i	−0.717643	−	0.696411i	$-0.754779\pi$
$277$	−76.7511	+	55.7630i	−0.277080	+	0.201310i	0.440563	+	0.897722i	$0.354779\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	298.679	−	97.0467i	1.06291	−	0.345362i	0.275190	−	0.961390i	$-0.411259\pi$
$281$	298.679	−	97.0467i	1.06291	−	0.345362i	0.787724	+	0.616028i	$0.211259\pi$
$282$		0			0
$283$	80.5309	+	247.849i	0.284561	+	0.875790i	0.986530	+	0.163582i	$0.0523048\pi$
$283$	80.5309	+	247.849i	0.284561	+	0.875790i	−0.701968	+	0.712208i	$0.747695\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	194.531	−	267.749i	0.677809	−	0.932924i
$288$		0			0
$289$	−233.794	+	169.861i	−0.808975	+	0.587755i
$290$		0			0
$291$		0			0
$292$		0			0
$293$			232.694i			0.794178i	0.917780	+	0.397089i	$0.129980\pi$
$293$			232.694i			0.794178i	−0.917780	+	0.397089i	$0.870020\pi$
$294$		0			0
$295$	29.6349	+	164.065i	0.100457	+	0.556153i
$296$		0			0
$297$		0			0
$298$		0			0
$299$			181.796i			0.608014i
$300$		0			0
$301$	97.9393			0.325380
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−67.4716	+	495.052i	−0.221218	+	1.62312i
$306$		0			0
$307$	−438.991			−1.42994			−0.714969	−	0.699157i	$-0.753559\pi$
$307$	−438.991			−1.42994			−0.714969	+	0.699157i	$0.753559\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−91.5892	−	126.062i	−0.294499	−	0.405343i	0.635970	−	0.771714i	$-0.280600\pi$
$311$	−91.5892	−	126.062i	−0.294499	−	0.405343i	−0.930469	+	0.366371i	$0.880600\pi$
$312$		0			0
$313$	422.103	+	306.676i	1.34857	+	0.979795i	0.999081	+	0.0428548i	$0.0136453\pi$
$313$	422.103	+	306.676i	1.34857	+	0.979795i	0.349490	+	0.936940i	$0.386355\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	274.095	−	89.0589i	0.864653	−	0.280943i	0.157082	−	0.987586i	$-0.449791\pi$
$317$	274.095	−	89.0589i	0.864653	−	0.280943i	0.707570	+	0.706643i	$0.249791\pi$
$318$		0			0
$319$	80.2384	+	246.948i	0.251531	+	0.774133i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	2.41913	+	3.32965i	0.00748957	+	0.0103085i
$324$		0			0
$325$	−86.1648	+	130.071i	−0.265122	+	0.400218i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	396.722	+	128.903i	1.20584	+	0.391802i
$330$		0			0
$331$	−4.47261	−	13.7653i	−0.0135124	−	0.0415869i	0.944073	−	0.329737i	$-0.106960\pi$
$331$	−4.47261	−	13.7653i	−0.0135124	−	0.0415869i	−0.957585	+	0.288150i	$0.906960\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	374.116	+	180.542i	1.11676	+	0.538930i
$336$		0			0
$337$	198.742	+	144.394i	0.589738	+	0.428469i	0.842221	−	0.539132i	$-0.181247\pi$
$337$	198.742	+	144.394i	0.589738	+	0.428469i	−0.252484	+	0.967601i	$0.581247\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−132.818	+	182.809i	−0.389497	+	0.536096i
$342$		0			0
$343$	−316.701			−0.923327
$344$		0			0
$345$		0			0
$346$		0			0
$347$	195.006	+	63.3614i	0.561978	+	0.182598i	0.576211	−	0.817301i	$-0.304531\pi$
$347$	195.006	+	63.3614i	0.561978	+	0.182598i	−0.0142329	+	0.999899i	$0.504531\pi$
$348$		0			0
$349$	−687.361			−1.96952			−0.984758	−	0.173933i	$-0.944352\pi$
$349$	−687.361			−1.96952			−0.984758	+	0.173933i	$0.944352\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−489.971	−	159.201i	−1.38802	−	0.450995i	−0.482723	−	0.875773i	$-0.660352\pi$
$353$	−489.971	−	159.201i	−1.38802	−	0.450995i	−0.905297	+	0.424778i	$0.860352\pi$
$354$		0			0
$355$	128.676	−	69.1080i	0.362468	−	0.194670i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	91.0844	−	125.367i	0.253717	−	0.349212i	−0.663092	−	0.748538i	$-0.730756\pi$
$359$	91.0844	−	125.367i	0.253717	−	0.349212i	0.916809	+	0.399327i	$0.130756\pi$
$360$		0			0
$361$	−630.815	+	458.314i	−1.74741	+	1.26957i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−15.2157	+	111.640i	−0.0416868	+	0.305864i
$366$		0			0
$367$	−99.7959	−	307.140i	−0.271924	−	0.836894i	−0.990017	−	0.140948i	$-0.954985\pi$
$367$	−99.7959	−	307.140i	−0.271924	−	0.836894i	0.718094	−	0.695947i	$-0.245015\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−425.541	−	138.267i	−1.14701	−	0.372687i
$372$		0			0
$373$	−505.496	+	367.264i	−1.35522	+	0.984623i	−0.356484	+	0.934301i	$0.616025\pi$
$373$	−505.496	+	367.264i	−1.35522	+	0.984623i	−0.998733	+	0.0503218i	$0.983975\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	58.8688	+	81.0260i	0.156151	+	0.214923i
$378$		0			0
$379$	18.4153	−	56.6763i	0.0485891	−	0.149542i	−0.923818	−	0.382831i	$-0.874949\pi$
$379$	18.4153	−	56.6763i	0.0485891	−	0.149542i	0.972407	+	0.233290i	$0.0749490\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	242.821	−	78.8973i	0.633997	−	0.205998i	0.0256522	−	0.999671i	$-0.491834\pi$
$383$	242.821	−	78.8973i	0.633997	−	0.205998i	0.608345	+	0.793673i	$0.291834\pi$
$384$		0			0
$385$	597.073	+	81.3763i	1.55084	+	0.211367i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−345.673	−	475.778i	−0.888620	−	1.22308i	−0.973958	−	0.226729i	$-0.927197\pi$
$389$	−345.673	−	475.778i	−0.888620	−	1.22308i	0.0853378	−	0.996352i	$-0.472803\pi$
$390$		0			0
$391$	−2.87175	−	2.08645i	−0.00734463	−	0.00533618i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	232.676	+	433.233i	0.589053	+	1.09679i
$396$		0			0
$397$	149.628	−	460.508i	0.376897	−	1.15997i	−0.565293	−	0.824890i	$-0.691237\pi$
$397$	149.628	−	460.508i	0.376897	−	1.15997i	0.942190	−	0.335079i	$-0.108763\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$		−	289.494i		−	0.721931i	−0.932579	−	0.360966i	$-0.882447\pi$
$401$		−	289.494i		−	0.721931i	0.932579	−	0.360966i	$-0.117553\pi$
$402$		0			0
$403$	−26.9332	+	82.8920i	−0.0668318	+	0.205687i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			544.125i			1.33692i
$408$		0			0
$409$	−42.6533	−	30.9894i	−0.104287	−	0.0757687i	0.534420	−	0.845219i	$-0.320530\pi$
$409$	−42.6533	−	30.9894i	−0.104287	−	0.0757687i	−0.638706	+	0.769450i	$0.720530\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	145.986	−	200.933i	0.353478	−	0.486520i
$414$		0			0
$415$	233.450	−	483.752i	0.562531	−	1.16567i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−189.388	+	61.5360i	−0.452001	+	0.146864i	−0.526166	−	0.850382i	$-0.676371\pi$
$419$	−189.388	+	61.5360i	−0.452001	+	0.146864i	0.0741650	+	0.997246i	$0.476371\pi$
$420$		0			0
$421$	74.1283	−	228.143i	0.176077	−	0.541908i	−0.823604	−	0.567165i	$-0.808040\pi$
$421$	74.1283	−	228.143i	0.176077	−	0.541908i	0.999681	+	0.0252566i	$0.00804029\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−1.06577	−	2.85391i	−0.00250769	−	0.00671508i
$426$		0			0
$427$	602.158	−	437.493i	1.41021	−	1.02457i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−6.12908	+	1.99146i	−0.0142206	+	0.00462056i	−0.316119	−	0.948720i	$-0.602380\pi$
$431$	−6.12908	+	1.99146i	−0.0142206	+	0.00462056i	0.301898	+	0.953340i	$0.402380\pi$
$432$		0			0
$433$	69.0076	+	212.384i	0.159371	+	0.490493i	0.998578	−	0.0533195i	$-0.0169802\pi$
$433$	69.0076	+	212.384i	0.159371	+	0.490493i	−0.839207	+	0.543813i	$0.816980\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	578.296	−	795.956i	1.32333	−	1.82141i
$438$		0			0
$439$	280.148	−	203.539i	0.638150	−	0.463643i	−0.221064	−	0.975259i	$-0.570953\pi$
$439$	280.148	−	203.539i	0.638150	−	0.463643i	0.859214	+	0.511616i	$0.170953\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$			122.641i			0.276842i	0.990373	+	0.138421i	$0.0442027\pi$
$443$			122.641i			0.276842i	−0.990373	+	0.138421i	$0.955797\pi$
$444$		0			0
$445$	636.987	+	86.8163i	1.43143	+	0.195093i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			334.862i			0.745795i	0.927873	+	0.372897i	$0.121636\pi$
$449$			334.862i			0.745795i	−0.927873	+	0.372897i	$0.878364\pi$
$450$		0			0
$451$	−718.908			−1.59403
$452$		0			0
$453$		0			0
$454$		0			0
$455$	228.728	−	41.3148i	0.502699	−	0.0908018i
$456$		0			0
$457$	109.167			0.238878			0.119439	−	0.992842i	$-0.461890\pi$
$457$	109.167			0.238878			0.119439	+	0.992842i	$0.461890\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	231.117	+	318.106i	0.501339	+	0.690034i	0.982429	−	0.186637i	$-0.0597589\pi$
$461$	231.117	+	318.106i	0.501339	+	0.690034i	−0.481090	+	0.876671i	$0.659759\pi$
$462$		0			0
$463$	291.312	+	211.650i	0.629183	+	0.457128i	0.856117	−	0.516782i	$-0.172870\pi$
$463$	291.312	+	211.650i	0.629183	+	0.457128i	−0.226934	+	0.973910i	$0.572870\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−337.415	+	109.633i	−0.722516	+	0.234760i	−0.647114	−	0.762393i	$-0.724024\pi$
$467$	−337.415	+	109.633i	−0.722516	+	0.234760i	−0.0754023	+	0.997153i	$0.524024\pi$
$468$		0			0
$469$	−191.230	−	588.544i	−0.407739	−	1.25489i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−125.048	−	172.114i	−0.264373	−	0.363878i
$474$		0			0
$475$	791.010	−	295.396i	1.66529	−	0.621886i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−740.888	−	240.729i	−1.54674	−	0.502566i	−0.593513	−	0.804824i	$-0.702259\pi$
$479$	−740.888	−	240.729i	−1.54674	−	0.502566i	−0.953226	+	0.302258i	$0.902259\pi$
$480$		0			0
$481$	64.8557	+	199.605i	0.134835	+	0.414980i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−82.5171	−	153.643i	−0.170138	−	0.316791i
$486$		0			0
$487$	−169.591	−	123.215i	−0.348236	−	0.253008i	0.399893	−	0.916562i	$-0.369047\pi$
$487$	−169.591	−	123.215i	−0.348236	−	0.253008i	−0.748129	+	0.663554i	$0.769047\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	42.5959	−	58.6282i	0.0867533	−	0.119406i	−0.763434	−	0.645885i	$-0.776488\pi$
$491$	42.5959	−	58.6282i	0.0867533	−	0.119406i	0.850188	+	0.526480i	$0.176488\pi$
$492$		0			0
$493$	−1.95556			−0.00396665
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−206.939	−	67.2387i	−0.416377	−	0.135289i
$498$		0			0
$499$	−235.125			−0.471193			−0.235596	−	0.971851i	$-0.575704\pi$
$499$	−235.125			−0.471193			−0.235596	+	0.971851i	$0.575704\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−373.254	−	121.278i	−0.742056	−	0.241109i	−0.0864965	−	0.996252i	$-0.527567\pi$
$503$	−373.254	−	121.278i	−0.742056	−	0.241109i	−0.655559	+	0.755144i	$0.727567\pi$
$504$		0			0
$505$	−78.0875	−	74.7816i	−0.154629	−	0.148082i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	176.771	−	243.304i	0.347290	−	0.478004i	−0.599263	−	0.800552i	$-0.704540\pi$
$509$	176.771	−	243.304i	0.347290	−	0.478004i	0.946553	+	0.322549i	$0.104540\pi$
$510$		0			0
$511$	135.794	−	98.6602i	0.265742	−	0.193073i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−151.657	−	282.378i	−0.294479	−	0.548307i
$516$		0			0
$517$	−280.004	−	861.765i	−0.541595	−	1.66686i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	301.221	+	97.8726i	0.578159	+	0.187855i	0.583476	−	0.812131i	$-0.301692\pi$
$521$	301.221	+	97.8726i	0.578159	+	0.187855i	−0.00531676	+	0.999986i	$0.501692\pi$
$522$		0			0
$523$	−736.375	+	535.008i	−1.40798	+	1.02296i	−0.414372	+	0.910108i	$0.635999\pi$
$523$	−736.375	+	535.008i	−1.40798	+	1.02296i	−0.993612	+	0.112852i	$0.964001\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1.00030	−	1.37679i	−0.00189810	−	0.00261250i
$528$		0			0
$529$	−98.7477	+	303.914i	−0.186669	+	0.574507i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−263.722	+	85.6885i	−0.494788	+	0.160766i
$534$		0			0
$535$	267.240	+	255.927i	0.499514	+	0.478367i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−61.6449	−	84.8469i	−0.114369	−	0.157415i
$540$		0			0
$541$	−427.905	−	310.891i	−0.790952	−	0.574660i	0.117294	−	0.993097i	$-0.462578\pi$
$541$	−427.905	−	310.891i	−0.790952	−	0.574660i	−0.908246	+	0.418437i	$0.862578\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	453.896	−	81.9865i	0.832836	−	0.150434i
$546$		0			0
$547$	122.525	−	377.093i	0.223995	−	0.689385i	−0.774397	−	0.632700i	$-0.781947\pi$
$547$	122.525	−	377.093i	0.223995	−	0.689385i	0.998392	−	0.0566853i	$-0.0180532\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		−	542.017i		−	0.983697i
$552$		0			0
$553$	226.382	−	696.733i	0.409371	−	1.25991i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	835.785i		−	1.50051i	−0.661148	−	0.750256i	$-0.729930\pi$
$557$		−	835.785i		−	1.50051i	0.661148	−	0.750256i	$-0.270070\pi$
$558$		0			0
$559$	−66.3872	−	48.2331i	−0.118761	−	0.0862846i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−268.926	+	370.144i	−0.477666	+	0.657450i	−0.978054	−	0.208351i	$-0.933190\pi$
$563$	−268.926	+	370.144i	−0.477666	+	0.657450i	0.500389	+	0.865801i	$0.333190\pi$
$564$		0			0
$565$	157.948	+	874.437i	0.279555	+	1.54768i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	427.337	−	138.850i	0.751031	−	0.244025i	0.0916064	−	0.995795i	$-0.470800\pi$
$569$	427.337	−	138.850i	0.751031	−	0.244025i	0.659425	+	0.751770i	$0.270800\pi$
$570$		0			0
$571$	−189.413	+	582.954i	−0.331722	+	1.02094i	0.636592	+	0.771201i	$0.280344\pi$
$571$	−189.413	+	582.954i	−0.331722	+	1.02094i	−0.968314	+	0.249735i	$0.919656\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−570.110	+	453.124i	−0.991495	+	0.788041i
$576$		0			0
$577$	−330.405	+	240.053i	−0.572626	+	0.416037i	−0.836058	−	0.548641i	$-0.815145\pi$
$577$	−330.405	+	240.053i	−0.572626	+	0.416037i	0.263432	+	0.964678i	$0.415145\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−761.021	+	247.271i	−1.30985	+	0.425595i
$582$		0			0
$583$	300.345	+	924.368i	0.515172	+	1.58554i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−375.707	+	517.116i	−0.640046	+	0.880948i	−0.998618	−	0.0525541i	$-0.983264\pi$
$587$	−375.707	+	517.116i	−0.640046	+	0.880948i	0.358572	+	0.933502i	$0.383264\pi$
$588$		0			0
$589$	381.601	−	277.250i	0.647880	−	0.470712i
$590$		0			0
$591$		0			0
$592$		0			0
$593$			726.902i			1.22580i	0.790159	+	0.612902i	$0.209998\pi$
$593$			726.902i			1.22580i	−0.790159	+	0.612902i	$0.790002\pi$
$594$		0			0
$595$	−1.97244	+	4.08727i	−0.00331503	+	0.00686936i
$596$		0			0
$597$		0			0
$598$		0			0
$599$		−	834.164i		−	1.39259i	−0.717753	−	0.696297i	$-0.754830\pi$
$599$		−	834.164i		−	1.39259i	0.717753	−	0.696297i	$-0.245170\pi$
$600$		0			0
$601$	477.216			0.794037			0.397019	−	0.917811i	$-0.370045\pi$
$601$	477.216			0.794037			0.397019	+	0.917811i	$0.370045\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−333.078	−	620.178i	−0.550542	−	1.02509i
$606$		0			0
$607$	576.654			0.950007			0.475003	−	0.879984i	$-0.342447\pi$
$607$	576.654			0.950007			0.475003	+	0.879984i	$0.342447\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−205.432	−	282.753i	−0.336223	−	0.462771i
$612$		0			0
$613$	984.996	+	715.641i	1.60684	+	1.16744i	0.872430	+	0.488740i	$0.162543\pi$
$613$	984.996	+	715.641i	1.60684	+	1.16744i	0.734415	+	0.678701i	$0.237457\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	914.741	−	297.217i	1.48256	−	0.481713i	0.547685	−	0.836685i	$-0.315509\pi$
$617$	914.741	−	297.217i	1.48256	−	0.481713i	0.934877	+	0.354971i	$0.115509\pi$
$618$		0			0
$619$	−349.360	−	1075.22i	−0.564395	−	1.73703i	−0.669743	−	0.742593i	$-0.733596\pi$
$619$	−349.360	−	1075.22i	−0.564395	−	1.73703i	0.105348	−	0.994435i	$-0.466404\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−562.926	−	774.801i	−0.903573	−	1.24366i
$624$		0			0
$625$	−622.664	+	53.9879i	−0.996262	+	0.0863807i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−3.89741	−	1.26634i	−0.00619619	−	0.00201327i
$630$		0			0
$631$	−130.582	−	401.889i	−0.206944	−	0.636908i	−0.999628	−	0.0272751i	$-0.991317\pi$
$631$	−130.582	−	401.889i	−0.206944	−	0.636908i	0.792684	−	0.609633i	$-0.208683\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−166.145	+	1219.04i	−0.261646	+	1.91974i
$636$		0			0
$637$	−32.7268	−	23.7774i	−0.0513764	−	0.0373271i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	307.815	−	423.671i	0.480211	−	0.660954i	−0.498334	−	0.866985i	$-0.666055\pi$
$641$	307.815	−	423.671i	0.480211	−	0.660954i	0.978545	+	0.206031i	$0.0660548\pi$
$642$		0			0
$643$	356.838			0.554958			0.277479	−	0.960732i	$-0.410501\pi$
$643$	356.838			0.554958			0.277479	+	0.960732i	$0.410501\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	125.417	+	40.7503i	0.193843	+	0.0629835i	0.404330	−	0.914613i	$-0.367505\pi$
$647$	125.417	+	40.7503i	0.193843	+	0.0629835i	−0.210487	+	0.977597i	$0.567505\pi$
$648$		0			0
$649$	−539.506			−0.831288
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−501.849	−	163.060i	−0.768528	−	0.249710i	−0.101593	−	0.994826i	$-0.532394\pi$
$653$	−501.849	−	163.060i	−0.768528	−	0.249710i	−0.666935	+	0.745116i	$0.732394\pi$
$654$		0			0
$655$	270.931	−	561.419i	0.413635	−	0.857129i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	65.5446	−	90.2144i	0.0994607	−	0.136896i	−0.756386	−	0.654126i	$-0.773037\pi$
$659$	65.5446	−	90.2144i	0.0994607	−	0.136896i	0.855847	+	0.517230i	$0.173037\pi$
$660$		0			0
$661$	421.134	−	305.972i	0.637117	−	0.462892i	−0.221742	−	0.975105i	$-0.571174\pi$
$661$	421.134	−	305.972i	0.637117	−	0.462892i	0.858858	+	0.512213i	$0.171174\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−1132.86	−	546.698i	−1.70355	−	0.822102i
$666$		0			0
$667$	144.459	+	444.598i	0.216580	+	0.666564i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−1537.67	−	499.618i	−2.29160	−	0.744587i
$672$		0			0
$673$	796.458	−	578.661i	1.18344	−	0.859823i	0.190889	−	0.981612i	$-0.438863\pi$
$673$	796.458	−	578.661i	1.18344	−	0.859823i	0.992556	+	0.121789i	$0.0388631\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−195.540	−	269.138i	−0.288833	−	0.397545i	0.639801	−	0.768540i	$-0.279017\pi$
$677$	−195.540	−	269.138i	−0.288833	−	0.397545i	−0.928635	+	0.370995i	$0.879017\pi$
$678$		0			0
$679$	−80.2850	+	247.092i	−0.118240	+	0.363906i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	736.087	−	239.169i	1.07773	−	0.350174i	0.284234	−	0.958755i	$-0.408261\pi$
$683$	736.087	−	239.169i	1.07773	−	0.350174i	0.793492	+	0.608580i	$0.208261\pi$
$684$		0			0
$685$	−51.9469	−	287.590i	−0.0758349	−	0.419839i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	220.356	+	303.293i	0.319819	+	0.440194i
$690$		0			0
$691$	398.402	+	289.456i	0.576558	+	0.418894i	0.837482	−	0.546466i	$-0.184027\pi$
$691$	398.402	+	289.456i	0.576558	+	0.418894i	−0.260924	+	0.965359i	$0.584027\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	52.6873	−	386.576i	0.0758090	−	0.556225i
$696$		0			0
$697$	1.67312	−	5.14933i	0.00240046	−	0.00738784i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	130.840i		−	0.186648i	−0.995636	−	0.0933241i	$-0.970251\pi$
$701$		−	130.840i		−	0.186648i	0.995636	−	0.0933241i	$-0.0297493\pi$
$702$		0			0
$703$	350.989	−	1080.23i	0.499274	−	1.53661i
$704$		0			0
$705$		0			0
$706$		0			0
$707$			161.069i			0.227820i
$708$		0			0
$709$	735.398	+	534.298i	1.03723	+	0.753594i	0.969743	−	0.244126i	$-0.0785012\pi$
$709$	735.398	+	534.298i	1.03723	+	0.753594i	0.0674892	+	0.997720i	$0.478501\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−239.122	+	329.123i	−0.335374	+	0.461603i
$714$		0			0
$715$	−364.644	−	349.206i	−0.509991	−	0.488401i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−52.6919	+	17.1206i	−0.0732850	+	0.0238117i	−0.345430	−	0.938444i	$-0.612267\pi$
$719$	−52.6919	+	17.1206i	−0.0732850	+	0.0238117i	0.272145	+	0.962256i	$0.412267\pi$
$720$		0			0
$721$	−147.554	+	454.125i	−0.204652	+	0.629855i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−107.367	+	386.567i	−0.148092	+	0.533196i
$726$		0			0
$727$	881.940	−	640.767i	1.21312	−	0.881385i	0.217612	−	0.976035i	$-0.430173\pi$
$727$	881.940	−	640.767i	1.21312	−	0.881385i	0.995511	+	0.0946501i	$0.0301732\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	1.52383	−	0.495123i	0.00208458	−	0.000677322i
$732$		0			0
$733$	−117.799	−	362.550i	−0.160709	−	0.494611i	0.837986	−	0.545692i	$-0.183733\pi$
$733$	−117.799	−	362.550i	−0.160709	−	0.494611i	−0.998694	+	0.0510815i	$0.983733\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−790.122	+	1087.51i	−1.07208	+	1.47559i
$738$		0			0
$739$	−170.651	+	123.985i	−0.230921	+	0.167774i	−0.697229	−	0.716849i	$-0.745584\pi$
$739$	−170.651	+	123.985i	−0.230921	+	0.167774i	0.466308	+	0.884622i	$0.345584\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		−	346.514i		−	0.466371i	−0.972432	−	0.233186i	$-0.925085\pi$
$743$		−	346.514i		−	0.466371i	0.972432	−	0.233186i	$-0.0749150\pi$
$744$		0			0
$745$	−584.041	−	559.316i	−0.783948	−	0.750759i
$746$		0			0
$747$		0			0
$748$		0			0
$749$		−	551.229i		−	0.735954i
$750$		0			0
$751$	−176.363			−0.234838			−0.117419	−	0.993082i	$-0.537462\pi$
$751$	−176.363			−0.234838			−0.117419	+	0.993082i	$0.537462\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	799.170	−	834.499i	1.05850	−	1.10530i
$756$		0			0
$757$	180.765			0.238791			0.119395	−	0.992847i	$-0.461904\pi$
$757$	180.765			0.238791			0.119395	+	0.992847i	$0.461904\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−629.043	−	865.804i	−0.826601	−	1.13772i	−0.988546	−	0.150919i	$-0.951777\pi$
$761$	−629.043	−	865.804i	−0.826601	−	1.13772i	0.161946	−	0.986800i	$-0.448223\pi$
$762$		0			0
$763$	−555.893	−	403.880i	−0.728562	−	0.529331i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−197.911	+	64.3051i	−0.258032	+	0.0838398i
$768$		0			0
$769$	−226.526	−	697.177i	−0.294573	−	0.906602i	−0.983365	−	0.181643i	$-0.941859\pi$
$769$	−226.526	−	697.177i	−0.294573	−	0.906602i	0.688792	−	0.724959i	$-0.258141\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−55.1959	−	75.9706i	−0.0714047	−	0.0982802i	0.771821	−	0.635840i	$-0.219346\pi$
$773$	−55.1959	−	75.9706i	−0.0714047	−	0.0982802i	−0.843226	+	0.537560i	$0.819346\pi$
$774$		0			0
$775$	−327.078	+	122.145i	−0.422036	+	0.157606i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	1427.23	+	463.734i	1.83213	+	0.595294i
$780$		0			0
$781$	146.057	+	449.517i	0.187013	+	0.575566i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−404.057	+	421.919i	−0.514723	+	0.537477i
$786$		0			0
$787$	−193.739	−	140.760i	−0.246174	−	0.178856i	0.457855	−	0.889027i	$-0.348618\pi$
$787$	−193.739	−	140.760i	−0.246174	−	0.178856i	−0.704030	+	0.710171i	$0.748618\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	778.080	−	1070.94i	0.983666	−	1.35390i
$792$		0			0
$793$	−623.623			−0.786410
$794$		0			0
$795$		0			0
$796$		0			0
$797$	569.713	+	185.111i	0.714822	+	0.232260i	0.643777	−	0.765213i	$-0.277367\pi$
$797$	569.713	+	185.111i	0.714822	+	0.232260i	0.0710451	+	0.997473i	$0.477367\pi$
$798$		0			0
$799$	6.82422			0.00854096
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−346.763	−	112.670i	−0.431834	−	0.140311i
$804$		0			0
$805$	1074.95	+	146.507i	1.33534	+	0.181997i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	294.655	−	405.558i	0.364222	−	0.501308i	−0.587097	−	0.809516i	$-0.699729\pi$
$809$	294.655	−	405.558i	0.364222	−	0.501308i	0.951319	+	0.308208i	$0.0997294\pi$
$810$		0			0
$811$	−531.207	+	385.945i	−0.655003	+	0.475887i	−0.864972	−	0.501821i	$-0.832664\pi$
$811$	−531.207	+	385.945i	−0.655003	+	0.475887i	0.209969	+	0.977708i	$0.432664\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	716.986	−	129.508i	0.879738	−	0.158906i
$816$		0			0
$817$	137.232	+	422.356i	0.167971	+	0.516960i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	1181.90	+	384.024i	1.43959	+	0.467752i	0.921770	−	0.387737i	$-0.126743\pi$
$821$	1181.90	+	384.024i	1.43959	+	0.467752i	0.517821	+	0.855489i	$0.326743\pi$
$822$		0			0
$823$	−720.182	+	523.243i	−0.875070	+	0.635775i	−0.931943	−	0.362606i	$-0.881887\pi$
$823$	−720.182	+	523.243i	−0.875070	+	0.635775i	0.0568727	+	0.998381i	$0.481887\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	512.214	+	705.001i	0.619363	+	0.852481i	0.997306	−	0.0733483i	$-0.0233685\pi$
$827$	512.214	+	705.001i	0.619363	+	0.852481i	−0.377943	+	0.925829i	$0.623368\pi$
$828$		0			0
$829$	−156.111	+	480.460i	−0.188312	+	0.579565i	−0.999990	−	0.00454049i	$-0.998555\pi$
$829$	−156.111	+	480.460i	−0.188312	+	0.579565i	0.811677	+	0.584106i	$0.198555\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	0.751200	−	0.244080i	0.000901801	−	0.000293013i
$834$		0			0
$835$	128.694	−	266.678i	0.154125	−	0.319375i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−383.532	−	527.886i	−0.457130	−	0.629185i	0.516781	−	0.856118i	$-0.327130\pi$
$839$	−383.532	−	527.886i	−0.457130	−	0.629185i	−0.973910	+	0.226933i	$0.927130\pi$
$840$		0			0
$841$	−472.030	−	342.950i	−0.561272	−	0.407788i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	585.631	+	282.615i	0.693054	+	0.334456i
$846$		0			0
$847$	−324.068	+	997.380i	−0.382607	+	1.17754i
$848$		0			0
$849$		0			0
$850$		0			0
$851$			979.625i			1.15115i
$852$		0			0
$853$	240.348	−	739.714i	0.281768	−	0.867191i	−0.705581	−	0.708629i	$-0.749314\pi$
$853$	240.348	−	739.714i	0.281768	−	0.867191i	0.987349	−	0.158563i	$-0.0506860\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		−	155.078i		−	0.180954i	−0.995899	−	0.0904770i	$-0.971161\pi$
$857$		−	155.078i		−	0.180954i	0.995899	−	0.0904770i	$-0.0288392\pi$
$858$		0			0
$859$	123.408	+	89.6611i	0.143665	+	0.104379i	0.657296	−	0.753632i	$-0.271700\pi$
$859$	123.408	+	89.6611i	0.143665	+	0.104379i	−0.513631	+	0.858011i	$0.671700\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	485.380	−	668.069i	0.562434	−	0.774124i	−0.429200	−	0.903210i	$-0.641204\pi$
$863$	485.380	−	668.069i	0.562434	−	0.774124i	0.991633	+	0.129086i	$0.0412043\pi$
$864$		0			0
$865$	−873.069	−	118.992i	−1.00933	−	0.137564i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−1513.45	+	491.751i	−1.74160	+	0.565881i
$870$		0			0
$871$	−160.223	+	493.116i	−0.183953	+	0.566149i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	699.662	+	614.310i	0.799614	+	0.702069i
$876$		0			0
$877$	−748.479	+	543.802i	−0.853454	+	0.620070i	−0.926096	−	0.377288i	$-0.876857\pi$
$877$	−748.479	+	543.802i	−0.853454	+	0.620070i	0.0726424	+	0.997358i	$0.476857\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−761.572	+	247.450i	−0.864440	+	0.280874i	−0.707482	−	0.706732i	$-0.750169\pi$
$881$	−761.572	+	247.450i	−0.864440	+	0.280874i	−0.156958	+	0.987605i	$0.550169\pi$
$882$		0			0
$883$	−277.463	−	853.943i	−0.314228	−	0.967093i	−0.976071	−	0.217451i	$-0.930226\pi$
$883$	−277.463	−	853.943i	−0.314228	−	0.967093i	0.661844	−	0.749642i	$-0.269774\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−84.5474	+	116.369i	−0.0953184	+	0.131194i	−0.854012	−	0.520253i	$-0.825838\pi$
$887$	−84.5474	+	116.369i	−0.0953184	+	0.131194i	0.758694	+	0.651447i	$0.225838\pi$
$888$		0			0
$889$	1482.78	−	1077.30i	1.66792	−	1.21181i
$890$		0			0
$891$		0			0
$892$		0			0
$893$			1891.45i			2.11809i
$894$		0			0
$895$	366.976	−	197.091i	0.410029	−	0.220214i
$896$		0			0
$897$		0			0
$898$		0			0
$899$			224.121i			0.249300i
$900$		0			0
$901$	−7.31997			−0.00812427
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−739.459	−	356.850i	−0.817082	−	0.394310i
$906$		0			0
$907$	1024.69			1.12976			0.564879	−	0.825174i	$-0.308923\pi$
$907$	1024.69			1.12976			0.564879	+	0.825174i	$0.308923\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	453.170	+	623.735i	0.497442	+	0.684670i	0.981739	−	0.190233i	$-0.0609245\pi$
$911$	453.170	+	623.735i	0.497442	+	0.684670i	−0.484297	+	0.874904i	$0.660924\pi$
$912$		0			0
$913$	1406.21	+	1021.67i	1.54021	+	1.11903i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−883.203	+	286.970i	−0.963144	+	0.312945i
$918$		0			0
$919$	92.2791	+	284.006i	0.100413	+	0.309038i	0.988626	−	0.150392i	$-0.0480536\pi$
$919$	92.2791	+	284.006i	0.100413	+	0.309038i	−0.888214	+	0.459430i	$0.848054\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	107.158	+	147.490i	0.116098	+	0.159795i
$924$		0			0
$925$	−464.307	+	700.898i	−0.501953	+	0.757728i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	1377.00	+	447.414i	1.48224	+	0.481608i	0.934780	−	0.355227i	$-0.115596\pi$
$929$	1377.00	+	447.414i	1.48224	+	0.481608i	0.547456	+	0.836835i	$0.315596\pi$
$930$		0			0
$931$	67.6510	+	208.208i	0.0726648	+	0.223639i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	9.70121	−	1.75232i	0.0103756	−	0.00187413i
$936$		0			0
$937$	−1094.16	−	794.955i	−1.16773	−	0.848404i	−0.176993	−	0.984212i	$-0.556637\pi$
$937$	−1094.16	−	794.955i	−1.16773	−	0.848404i	−0.990735	+	0.135808i	$0.956637\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−850.556	+	1170.69i	−0.903885	+	1.24409i	0.0653270	+	0.997864i	$0.479191\pi$
$941$	−850.556	+	1170.69i	−0.903885	+	1.24409i	−0.969212	+	0.246227i	$0.920809\pi$
$942$		0			0
$943$	−1294.30			−1.37253
$944$		0			0
$945$		0			0
$946$		0			0
$947$	402.140	+	130.663i	0.424647	+	0.137976i	0.513541	−	0.858065i	$-0.328333\pi$
$947$	402.140	+	130.663i	0.424647	+	0.137976i	−0.0888944	+	0.996041i	$0.528333\pi$
$948$		0			0
$949$	−140.635			−0.148193
$950$		0			0
$951$		0			0
$952$		0			0
$953$	350.518	+	113.890i	0.367805	+	0.119507i	0.487087	−	0.873353i	$-0.338059\pi$
$953$	350.518	+	113.890i	0.367805	+	0.119507i	−0.119282	+	0.992860i	$0.538059\pi$
$954$		0			0
$955$	6.21526	+	34.4091i	0.00650813	+	0.0360305i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−255.899	+	352.215i	−0.266840	+	0.367273i
$960$		0			0
$961$	619.675	−	450.221i	0.644823	−	0.468492i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−233.825	+	244.162i	−0.242306	+	0.253017i
$966$		0			0
$967$	488.896	+	1504.67i	0.505580	+	1.55602i	0.799793	+	0.600276i	$0.204943\pi$
$967$	488.896	+	1504.67i	0.505580	+	1.55602i	−0.294213	+	0.955740i	$0.595057\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	1032.82	+	335.585i	1.06367	+	0.345608i	0.788020	−	0.615650i	$-0.211106\pi$
$971$	1032.82	+	335.585i	1.06367	+	0.345608i	0.275651	+	0.961258i	$0.411106\pi$
$972$		0			0
$973$	−470.213	+	341.630i	−0.483261	+	0.351110i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−393.842	−	542.077i	−0.403113	−	0.554838i	0.558409	−	0.829566i	$-0.311412\pi$
$977$	−393.842	−	542.077i	−0.403113	−	0.554838i	−0.961522	+	0.274728i	$0.911412\pi$
$978$		0			0
$979$	−642.862	+	1978.53i	−0.656652	+	2.02097i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	1761.97	−	572.499i	1.79244	−	0.582400i	0.792810	−	0.609469i	$-0.208617\pi$
$983$	1761.97	−	572.499i	1.79244	−	0.582400i	0.999634	+	0.0270687i	$0.00861727\pi$
$984$		0			0
$985$	−1353.38	+	726.857i	−1.37399	+	0.737926i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−225.133	−	309.869i	−0.227637	−	0.313316i
$990$		0			0
$991$	1374.17	+	998.391i	1.38665	+	1.00746i	0.996224	+	0.0868221i	$0.0276712\pi$
$991$	1374.17	+	998.391i	1.38665	+	1.00746i	0.390423	+	0.920636i	$0.372329\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	794.675	−	829.805i	0.798668	−	0.833975i
$996$		0			0
$997$	152.589	−	469.621i	0.153048	−	0.471034i	−0.844910	−	0.534909i	$-0.820346\pi$
$997$	152.589	−	469.621i	0.153048	−	0.471034i	0.997958	+	0.0638750i	$0.0203459\pi$
$998$		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.161.6	✓	80
3.2	odd	2	inner	900.3.ba.a.161.15	yes	80
25.16	even	5	inner	900.3.ba.a.341.15	yes	80
75.41	odd	10	inner	900.3.ba.a.341.6	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
900.3.ba.a.161.6	✓	80	1.1	even	1	trivial
900.3.ba.a.161.15	yes	80	3.2	odd	2	inner
900.3.ba.a.341.6	yes	80	75.41	odd	10	inner
900.3.ba.a.341.15	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)

\(f(q)\)	\(=\)	\(q+(-3.45827 + 3.61115i) q^{5} +7.44862 q^{7} +O(q^{10})\)	\(q+(-3.45827 + 3.61115i) q^{5} +7.44862 q^{7} +(-9.51036 - 13.0899i) q^{11} +(-5.04897 - 3.66829i) q^{13} +(0.115893 - 0.0376558i) q^{17} +(10.4370 + 32.1216i) q^{19} +(-17.1222 - 23.5666i) q^{23} +(-1.08077 - 24.9766i) q^{25} +(-15.2626 - 4.95911i) q^{29} +(-4.31562 - 13.2821i) q^{31} +(-25.7593 + 26.8980i) q^{35} +(-27.2068 - 19.7669i) q^{37} +(26.1164 - 35.9462i) q^{41} +13.1487 q^{43} +(53.2611 + 17.3056i) q^{47} +6.48187 q^{49} +(-57.1303 - 18.5628i) q^{53} +(80.1589 + 10.9250i) q^{55} +(19.5991 - 26.9759i) q^{59} +(80.8416 - 58.7348i) q^{61} +(30.7074 - 5.54664i) q^{65} +(-25.6732 - 79.0139i) q^{67} +(-27.7823 - 9.02700i) q^{71} +(18.2308 - 13.2454i) q^{73} +(-70.8390 - 97.5016i) q^{77} +(30.3925 - 93.5385i) q^{79} +(-102.169 + 33.1969i) q^{83} +(-0.264807 + 0.548729i) q^{85} +(-75.5745 - 104.019i) q^{89} +(-37.6078 - 27.3237i) q^{91} +(-152.090 - 73.3959i) q^{95} +(-10.7785 + 33.1729i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 16 q^{7}+O(q^{10}) \) 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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