LMFDB - Embedded newform 900.3.y.a.89.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,3,Mod(89,900)]

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, 3]))

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

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

chi := DirichletCharacter("900.89");

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.y (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			89.8
Character	$\chi$	$=$	900.89
Dual form			900.3.y.a.809.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41055 + 4.79691i) q^{5} +7.51506i q^{7} +O(q^{10})$	$q+(-1.41055 + 4.79691i) q^{5} +7.51506i q^{7} +(-10.9458 - 15.0655i) q^{11} +(-15.0602 + 20.7287i) q^{13} +(3.67897 + 11.3227i) q^{17} +(-9.49503 - 29.2227i) q^{19} +(16.9519 - 12.3163i) q^{23} +(-21.0207 - 13.5326i) q^{25} +(22.6333 + 7.35402i) q^{29} +(-14.7603 - 45.4276i) q^{31} +(-36.0491 - 10.6004i) q^{35} +(-2.42426 + 3.33671i) q^{37} +(30.2868 - 41.6862i) q^{41} +68.8607i q^{43} +(0.519185 - 1.59789i) q^{47} -7.47609 q^{49} +(18.4044 - 56.6429i) q^{53} +(87.7076 - 31.2551i) q^{55} +(33.8383 - 46.5744i) q^{59} +(-52.6841 + 38.2772i) q^{61} +(-78.1902 - 101.481i) q^{65} +(22.2611 - 7.23306i) q^{67} +(-18.4768 - 6.00346i) q^{71} +(-20.2672 - 27.8954i) q^{73} +(113.218 - 82.2580i) q^{77} +(-2.79194 + 8.59272i) q^{79} +(12.4280 + 38.2496i) q^{83} +(-59.5034 + 1.67643i) q^{85} +(-92.1910 - 126.890i) q^{89} +(-155.777 - 113.179i) q^{91} +(153.572 - 4.32669i) q^{95} +(-99.1280 - 32.2086i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q+O(q^{10}) $ 80 * q	$ 80 q + 60 q^{19} + 56 q^{25} - 120 q^{31} + 20 q^{37} - 680 q^{49} - 56 q^{55} - 80 q^{61} - 280 q^{67} - 360 q^{73} + 40 q^{79} + 192 q^{85} + 140 q^{91} - 40 q^{97}+O(q^{100}) $ 80 * q + 60 * q^19 + 56 * q^25 - 120 * q^31 + 20 * q^37 - 680 * q^49 - 56 * q^55 - 80 * q^61 - 280 * q^67 - 360 * q^73 + 40 * q^79 + 192 * q^85 + 140 * q^91 - 40 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$451$	$577$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{10}\right)$

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
$5$	−1.41055	+	4.79691i	−0.282110	+	0.959382i
$5$	−1.41055	+	4.79691i	−0.282110	+	0.959382i
$6$		0			0
$7$			7.51506i			1.07358i	0.843716	+	0.536790i	$0.180363\pi$
$7$			7.51506i			1.07358i	−0.843716	+	0.536790i	$0.819637\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−10.9458	−	15.0655i	−0.995069	−	1.36959i	−0.928302	−	0.371826i	$-0.878732\pi$
$11$	−10.9458	−	15.0655i	−0.995069	−	1.36959i	−0.0667666	−	0.997769i	$-0.521268\pi$
$12$		0			0
$13$	−15.0602	+	20.7287i	−1.15848	+	1.59451i	−0.441794	+	0.897117i	$0.645658\pi$
$13$	−15.0602	+	20.7287i	−1.15848	+	1.59451i	−0.716687	+	0.697395i	$0.754342\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	3.67897	+	11.3227i	0.216410	+	0.666042i	0.999050	+	0.0435678i	$0.0138725\pi$
$17$	3.67897	+	11.3227i	0.216410	+	0.666042i	−0.782640	+	0.622474i	$0.786128\pi$
$18$		0			0
$19$	−9.49503	−	29.2227i	−0.499739	−	1.53804i	−0.809440	−	0.587203i	$-0.800229\pi$
$19$	−9.49503	−	29.2227i	−0.499739	−	1.53804i	0.309701	−	0.950834i	$-0.399771\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	16.9519	−	12.3163i	0.737040	−	0.535491i	−0.154742	−	0.987955i	$-0.549455\pi$
$23$	16.9519	−	12.3163i	0.737040	−	0.535491i	0.891783	+	0.452464i	$0.149455\pi$
$24$		0			0
$25$	−21.0207	−	13.5326i	−0.840828	−	0.541303i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	22.6333	+	7.35402i	0.780460	+	0.253587i	0.672037	−	0.740518i	$-0.265420\pi$
$29$	22.6333	+	7.35402i	0.780460	+	0.253587i	0.108423	+	0.994105i	$0.465420\pi$
$30$		0			0
$31$	−14.7603	−	45.4276i	−0.476140	−	1.46541i	−0.844414	−	0.535690i	$-0.820051\pi$
$31$	−14.7603	−	45.4276i	−0.476140	−	1.46541i	0.368275	−	0.929717i	$-0.379949\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−36.0491	−	10.6004i	−1.02997	−	0.302868i
$36$		0			0
$37$	−2.42426	+	3.33671i	−0.0655205	+	0.0901812i	−0.840520	−	0.541781i	$-0.817750\pi$
$37$	−2.42426	+	3.33671i	−0.0655205	+	0.0901812i	0.774999	+	0.631962i	$0.217750\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	30.2868	−	41.6862i	0.738703	−	1.01674i	−0.259989	−	0.965612i	$-0.583719\pi$
$41$	30.2868	−	41.6862i	0.738703	−	1.01674i	0.998692	−	0.0511260i	$-0.0162810\pi$
$42$		0			0
$43$			68.8607i			1.60141i	0.599058	+	0.800705i	$0.295542\pi$
$43$			68.8607i			1.60141i	−0.599058	+	0.800705i	$0.704458\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	0.519185	−	1.59789i	0.0110465	−	0.0339976i	−0.945381	−	0.325966i	$-0.894310\pi$
$47$	0.519185	−	1.59789i	0.0110465	−	0.0339976i	0.956428	+	0.291969i	$0.0943104\pi$
$48$		0			0
$49$	−7.47609			−0.152573
$50$		0			0
$51$		0			0
$52$		0			0
$53$	18.4044	−	56.6429i	0.347253	−	1.06873i	−0.613114	−	0.789995i	$-0.710083\pi$
$53$	18.4044	−	56.6429i	0.347253	−	1.06873i	0.960367	−	0.278740i	$-0.0899167\pi$
$54$		0			0
$55$	87.7076	−	31.2551i	1.59468	−	0.568274i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	33.8383	−	46.5744i	0.573531	−	0.789397i	−0.419437	−	0.907785i	$-0.637772\pi$
$59$	33.8383	−	46.5744i	0.573531	−	0.789397i	0.992968	+	0.118387i	$0.0377724\pi$
$60$		0			0
$61$	−52.6841	+	38.2772i	−0.863673	+	0.627495i	−0.928882	−	0.370376i	$-0.879229\pi$
$61$	−52.6841	+	38.2772i	−0.863673	+	0.627495i	0.0652084	+	0.997872i	$0.479229\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−78.1902	−	101.481i	−1.20293	−	1.56125i
$66$		0			0
$67$	22.2611	−	7.23306i	0.332255	−	0.107956i	−0.138139	−	0.990413i	$-0.544112\pi$
$67$	22.2611	−	7.23306i	0.332255	−	0.107956i	0.470394	+	0.882457i	$0.344112\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−18.4768	−	6.00346i	−0.260236	−	0.0845558i	0.175993	−	0.984391i	$-0.443686\pi$
$71$	−18.4768	−	6.00346i	−0.260236	−	0.0845558i	−0.436229	+	0.899836i	$0.643686\pi$
$72$		0			0
$73$	−20.2672	−	27.8954i	−0.277633	−	0.382129i	0.647315	−	0.762222i	$-0.275892\pi$
$73$	−20.2672	−	27.8954i	−0.277633	−	0.382129i	−0.924948	+	0.380094i	$0.875892\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	113.218	−	82.2580i	1.47037	−	1.06829i
$78$		0			0
$79$	−2.79194	+	8.59272i	−0.0353410	+	0.108769i	−0.967171	−	0.254127i	$-0.918212\pi$
$79$	−2.79194	+	8.59272i	−0.0353410	+	0.108769i	0.931830	+	0.362896i	$0.118212\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	12.4280	+	38.2496i	0.149735	+	0.460838i	0.997590	−	0.0693913i	$-0.0221057\pi$
$83$	12.4280	+	38.2496i	0.149735	+	0.460838i	−0.847854	+	0.530230i	$0.822106\pi$
$84$		0			0
$85$	−59.5034	+	1.67643i	−0.700040	+	0.0197227i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−92.1910	−	126.890i	−1.03585	−	1.42573i	−0.900460	−	0.434939i	$-0.856770\pi$
$89$	−92.1910	−	126.890i	−1.03585	−	1.42573i	−0.135394	−	0.990792i	$-0.543230\pi$
$90$		0			0
$91$	−155.777	−	113.179i	−1.71184	−	1.24372i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	153.572	−	4.32669i	1.61655	−	0.0455441i
$96$		0			0
$97$	−99.1280	−	32.2086i	−1.02194	−	0.332048i	−0.250340	−	0.968158i	$-0.580542\pi$
$97$	−99.1280	−	32.2086i	−1.02194	−	0.332048i	−0.771598	+	0.636110i	$0.780542\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$			180.060i			1.78277i	0.453244	+	0.891386i	$0.350267\pi$
$101$			180.060i			1.78277i	−0.453244	+	0.891386i	$0.649733\pi$
$102$		0			0
$103$	−131.815	−	42.8292i	−1.27975	−	0.415817i	−0.411261	−	0.911518i	$-0.634911\pi$
$103$	−131.815	−	42.8292i	−1.27975	−	0.415817i	−0.868494	+	0.495700i	$0.834911\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−173.031			−1.61711			−0.808554	−	0.588422i	$-0.799749\pi$
$107$	−173.031			−1.61711			−0.808554	+	0.588422i	$0.799749\pi$
$108$		0			0
$109$	69.1112	+	50.2122i	0.634048	+	0.460663i	0.857800	−	0.513983i	$-0.171831\pi$
$109$	69.1112	+	50.2122i	0.634048	+	0.460663i	−0.223752	+	0.974646i	$0.571831\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−125.199	−	90.9626i	−1.10796	−	0.804979i	−0.125617	−	0.992079i	$-0.540091\pi$
$113$	−125.199	−	90.9626i	−1.10796	−	0.804979i	−0.982341	+	0.187100i	$0.940091\pi$
$114$		0			0
$115$	35.1686	+	98.6896i	0.305814	+	0.858171i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−85.0909	+	27.6477i	−0.715049	+	0.232334i
$120$		0			0
$121$	−69.7699	+	214.730i	−0.576611	+	1.77463i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	94.5653	−	81.7460i	0.756522	−	0.653968i
$126$		0			0
$127$	−87.2084	−	120.032i	−0.686680	−	0.945134i	0.313310	−	0.949651i	$-0.398562\pi$
$127$	−87.2084	−	120.032i	−0.686680	−	0.945134i	−0.999990	+	0.00451681i	$0.998562\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−51.8346	+	16.8421i	−0.395684	+	0.128566i	−0.500099	−	0.865968i	$-0.666703\pi$
$131$	−51.8346	+	16.8421i	−0.395684	+	0.128566i	0.104415	+	0.994534i	$0.466703\pi$
$132$		0			0
$133$	219.610	−	71.3557i	1.65121	−	0.536509i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−97.2268	−	70.6394i	−0.709685	−	0.515616i	0.173387	−	0.984854i	$-0.444529\pi$
$137$	−97.2268	−	70.6394i	−0.709685	−	0.515616i	−0.883072	+	0.469237i	$0.844529\pi$
$138$		0			0
$139$	−52.6013	+	38.2171i	−0.378427	+	0.274943i	−0.760697	−	0.649108i	$-0.775142\pi$
$139$	−52.6013	+	38.2171i	−0.378427	+	0.274943i	0.382270	+	0.924051i	$0.375142\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	477.134			3.33660
$144$		0			0
$145$	−67.2021	+	98.1969i	−0.463462	+	0.677220i
$146$		0			0
$147$		0			0
$148$		0			0
$149$			37.3773i			0.250855i	0.992103	+	0.125427i	$0.0400302\pi$
$149$			37.3773i			0.250855i	−0.992103	+	0.125427i	$0.959970\pi$
$150$		0			0
$151$	151.315			1.00209			0.501043	−	0.865423i	$-0.332950\pi$
$151$	151.315			1.00209			0.501043	+	0.865423i	$0.332950\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	238.732	−	6.72598i	1.54021	−	0.0433934i
$156$		0			0
$157$			14.8625i			0.0946654i	0.998879	+	0.0473327i	$0.0150721\pi$
$157$			14.8625i			0.0946654i	−0.998879	+	0.0473327i	$0.984928\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	92.5577	+	127.395i	0.574892	+	0.791272i
$162$		0			0
$163$	−43.3315	+	59.6407i	−0.265838	+	0.365894i	−0.920979	−	0.389612i	$-0.872609\pi$
$163$	−43.3315	+	59.6407i	−0.265838	+	0.365894i	0.655141	+	0.755506i	$0.272609\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−51.4978	−	158.494i	−0.308370	−	0.949066i	−0.978398	−	0.206730i	$-0.933718\pi$
$167$	−51.4978	−	158.494i	−0.308370	−	0.949066i	0.670028	−	0.742336i	$-0.266282\pi$
$168$		0			0
$169$	−150.642	−	463.629i	−0.891373	−	2.74337i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−181.872	+	132.138i	−1.05129	+	0.763804i	−0.972457	−	0.233084i	$-0.925118\pi$
$173$	−181.872	+	132.138i	−1.05129	+	0.763804i	−0.0788292	+	0.996888i	$0.525118\pi$
$174$		0			0
$175$	101.698	−	157.972i	0.581132	−	0.902695i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	0.922531	+	0.299749i	0.00515381	+	0.00167457i	0.311593	−	0.950216i	$-0.399138\pi$
$179$	0.922531	+	0.299749i	0.00515381	+	0.00167457i	−0.306439	+	0.951890i	$0.599138\pi$
$180$		0			0
$181$	21.1661	+	65.1427i	0.116940	+	0.359904i	0.992347	−	0.123483i	$-0.0394064\pi$
$181$	21.1661	+	65.1427i	0.116940	+	0.359904i	−0.875407	+	0.483387i	$0.839406\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−12.5863	−	16.3355i	−0.0680343	−	0.0883002i
$186$		0			0
$187$	130.314	−	179.361i	0.696865	−	0.959152i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	161.622	−	222.453i	0.846187	−	1.16468i	−0.138503	−	0.990362i	$-0.544229\pi$
$191$	161.622	−	222.453i	0.846187	−	1.16468i	0.984690	−	0.174315i	$-0.0557709\pi$
$192$		0			0
$193$			315.808i			1.63631i	0.574998	+	0.818155i	$0.305003\pi$
$193$			315.808i			1.63631i	−0.574998	+	0.818155i	$0.694997\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	6.43638	−	19.8091i	0.0326720	−	0.100554i	−0.933391	−	0.358862i	$-0.883165\pi$
$197$	6.43638	−	19.8091i	0.0326720	−	0.100554i	0.966063	+	0.258308i	$0.0831649\pi$
$198$		0			0
$199$	−246.929			−1.24085			−0.620424	−	0.784267i	$-0.713039\pi$
$199$	−246.929			−1.24085			−0.620424	+	0.784267i	$0.713039\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−55.2659	+	170.091i	−0.272246	+	0.837886i
$204$		0			0
$205$	157.244	+	204.084i	0.767044	+	0.995530i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−336.326	+	462.913i	−1.60921	+	2.21489i
$210$		0			0
$211$	11.8491	−	8.60890i	0.0561571	−	0.0408005i	−0.559353	−	0.828930i	$-0.688950\pi$
$211$	11.8491	−	8.60890i	0.0561571	−	0.0408005i	0.615510	+	0.788129i	$0.288950\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−330.318	−	97.1315i	−1.53636	−	0.451774i
$216$		0			0
$217$	341.391	−	110.925i	1.57323	−	0.511174i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−290.111	−	94.2627i	−1.31272	−	0.426528i
$222$		0			0
$223$	153.991	+	211.951i	0.690543	+	0.950451i	1.00000		0.000462324i	$-0.000147162\pi$
$223$	153.991	+	211.951i	0.690543	+	0.950451i	−0.309457	+	0.950914i	$0.600147\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	6.98989	−	5.07845i	0.0307924	−	0.0223720i	−0.572283	−	0.820056i	$-0.693942\pi$
$227$	6.98989	−	5.07845i	0.0307924	−	0.0223720i	0.603075	+	0.797684i	$0.293942\pi$
$228$		0			0
$229$	−7.01084	+	21.5771i	−0.0306150	+	0.0942233i	−0.965196	−	0.261526i	$-0.915774\pi$
$229$	−7.01084	+	21.5771i	−0.0306150	+	0.0942233i	0.934581	+	0.355749i	$0.115774\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	2.13074	+	6.55775i	0.00914482	+	0.0281449i	0.955525	−	0.294911i	$-0.0952899\pi$
$233$	2.13074	+	6.55775i	0.00914482	+	0.0281449i	−0.946380	+	0.323056i	$0.895290\pi$
$234$		0			0
$235$	6.93259	+	4.74439i	0.0295004	+	0.0201889i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	34.6929	+	47.7507i	0.145159	+	0.199794i	0.875405	−	0.483390i	$-0.160595\pi$
$239$	34.6929	+	47.7507i	0.145159	+	0.199794i	−0.730246	+	0.683184i	$0.760595\pi$
$240$		0			0
$241$	−95.3814	−	69.2986i	−0.395773	−	0.287546i	0.372044	−	0.928215i	$-0.378657\pi$
$241$	−95.3814	−	69.2986i	−0.395773	−	0.287546i	−0.767817	+	0.640669i	$0.778657\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	10.5454	−	35.8621i	0.0430425	−	0.146376i
$246$		0			0
$247$	748.745	+	243.282i	3.03136	+	0.984947i
$248$		0			0
$249$		0			0
$250$		0			0
$251$			324.122i			1.29132i	0.763624	+	0.645661i	$0.223418\pi$
$251$			324.122i			1.29132i	−0.763624	+	0.645661i	$0.776582\pi$
$252$		0			0
$253$	−371.103	−	120.579i	−1.46681	−	0.476596i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−208.548			−0.811470			−0.405735	−	0.913991i	$-0.632984\pi$
$257$	−208.548			−0.811470			−0.405735	+	0.913991i	$0.632984\pi$
$258$		0			0
$259$	−25.0755	−	18.2184i	−0.0968167	−	0.0703415i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	104.010	+	75.5676i	0.395475	+	0.287329i	0.767695	−	0.640815i	$-0.221403\pi$
$263$	104.010	+	75.5676i	0.395475	+	0.287329i	−0.372220	+	0.928144i	$0.621403\pi$
$264$		0			0
$265$	245.751	+	168.182i	0.927361	+	0.634649i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	163.854	−	53.2394i	0.609123	−	0.197916i	0.0118177	−	0.999930i	$-0.496238\pi$
$269$	163.854	−	53.2394i	0.609123	−	0.197916i	0.597305	+	0.802014i	$0.296238\pi$
$270$		0			0
$271$	2.67046	−	8.21883i	0.00985409	−	0.0303278i	−0.946009	−	0.324142i	$-0.894925\pi$
$271$	2.67046	−	8.21883i	0.00985409	−	0.0303278i	0.955863	+	0.293814i	$0.0949246\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	26.2118	+	464.812i	0.0953156	+	1.69023i
$276$		0			0
$277$	100.857	+	138.818i	0.364105	+	0.501148i	0.951287	−	0.308307i	$-0.0997625\pi$
$277$	100.857	+	138.818i	0.364105	+	0.501148i	−0.587181	+	0.809455i	$0.699763\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	352.995	−	114.695i	1.25621	−	0.408168i	0.396068	−	0.918221i	$-0.370374\pi$
$281$	352.995	−	114.695i	1.25621	−	0.408168i	0.860143	+	0.510054i	$0.170374\pi$
$282$		0			0
$283$	32.1814	−	10.4564i	0.113715	−	0.0369483i	−0.251607	−	0.967830i	$-0.580959\pi$
$283$	32.1814	−	10.4564i	0.113715	−	0.0369483i	0.365322	+	0.930881i	$0.380959\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	313.274	+	227.607i	1.09155	+	0.793057i
$288$		0			0
$289$	119.137	−	86.5580i	0.412238	−	0.299509i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−64.6023			−0.220486			−0.110243	−	0.993905i	$-0.535163\pi$
$293$	−64.6023			−0.220486			−0.110243	+	0.993905i	$0.535163\pi$
$294$		0			0
$295$	175.683	+	228.015i	0.595535	+	0.772932i
$296$		0			0
$297$		0			0
$298$		0			0
$299$			536.877i			1.79558i
$300$		0			0
$301$	−517.492			−1.71924
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−109.299	−	306.713i	−0.358357	−	1.00562i
$306$		0			0
$307$		−	437.444i		−	1.42490i	−0.701723	−	0.712450i	$-0.747586\pi$
$307$		−	437.444i		−	1.42490i	0.701723	−	0.712450i	$-0.252414\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	183.318	+	252.315i	0.589446	+	0.811302i	0.994691	−	0.102906i	$-0.0328140\pi$
$311$	183.318	+	252.315i	0.589446	+	0.811302i	−0.405246	+	0.914208i	$0.632814\pi$
$312$		0			0
$313$	−306.601	+	422.000i	−0.979555	+	1.34824i	−0.0424864	+	0.999097i	$0.513528\pi$
$313$	−306.601	+	422.000i	−0.979555	+	1.34824i	−0.937069	+	0.349145i	$0.886472\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−104.983	−	323.103i	−0.331175	−	1.01925i	−0.968576	−	0.248719i	$-0.919990\pi$
$317$	−104.983	−	323.103i	−0.331175	−	1.01925i	0.637400	−	0.770533i	$-0.280010\pi$
$318$		0			0
$319$	−136.947	−	421.479i	−0.429300	−	1.32125i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	295.948	−	215.019i	0.916249	−	0.665694i
$324$		0			0
$325$	597.089	−	231.927i	1.83720	−	0.713621i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	12.0082	+	3.90171i	0.0364991	+	0.0118593i
$330$		0			0
$331$	−36.0430	−	110.929i	−0.108891	−	0.335133i	0.881733	−	0.471749i	$-0.156377\pi$
$331$	−36.0430	−	110.929i	−0.108891	−	0.335133i	−0.990624	+	0.136616i	$0.956377\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	3.29596	+	116.987i	0.00983868	+	0.349215i
$336$		0			0
$337$	326.934	−	449.986i	0.970131	−	1.33527i	0.0281496	−	0.999604i	$-0.491039\pi$
$337$	326.934	−	449.986i	0.970131	−	1.33527i	0.941981	−	0.335666i	$-0.108961\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−522.829	+	719.612i	−1.53322	+	2.11030i
$342$		0			0
$343$			312.055i			0.909780i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−111.598	+	343.463i	−0.321607	+	0.989806i	0.651341	+	0.758785i	$0.274207\pi$
$347$	−111.598	+	343.463i	−0.321607	+	0.989806i	−0.972949	+	0.231021i	$0.925793\pi$
$348$		0			0
$349$	−245.436			−0.703255			−0.351627	−	0.936140i	$-0.614372\pi$
$349$	−245.436			−0.703255			−0.351627	+	0.936140i	$0.614372\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−53.4679	+	164.557i	−0.151467	+	0.466168i	−0.997786	−	0.0665089i	$-0.978814\pi$
$353$	−53.4679	+	164.557i	−0.151467	+	0.466168i	0.846319	+	0.532677i	$0.178814\pi$
$354$		0			0
$355$	54.8605	−	80.1632i	0.154537	−	0.225812i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−110.726	+	152.402i	−0.308430	+	0.424517i	−0.934891	−	0.354936i	$-0.884503\pi$
$359$	−110.726	+	152.402i	−0.308430	+	0.424517i	0.626461	+	0.779453i	$0.284503\pi$
$360$		0			0
$361$	−471.756	+	342.751i	−1.30680	+	0.949448i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	162.400	−	57.8720i	0.444930	−	0.158553i
$366$		0			0
$367$	−361.537	+	117.471i	−0.985115	+	0.320083i	−0.756902	−	0.653528i	$-0.773288\pi$
$367$	−361.537	+	117.471i	−0.985115	+	0.320083i	−0.228213	+	0.973611i	$0.573288\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	425.675	+	138.310i	1.14737	+	0.372804i
$372$		0			0
$373$	2.32723	+	3.20315i	0.00623922	+	0.00858754i	0.812125	−	0.583483i	$-0.198311\pi$
$373$	2.32723	+	3.20315i	0.00623922	+	0.00858754i	−0.805886	+	0.592071i	$0.798311\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−493.303	+	358.405i	−1.30850	+	0.950677i
$378$		0			0
$379$	176.054	−	541.837i	0.464521	−	1.42965i	−0.395062	−	0.918654i	$-0.629277\pi$
$379$	176.054	−	541.837i	0.464521	−	1.42965i	0.859584	−	0.510995i	$-0.170723\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	16.5424	+	50.9124i	0.0431917	+	0.132930i	0.970327	−	0.241796i	$-0.0777366\pi$
$383$	16.5424	+	50.9124i	0.0431917	+	0.132930i	−0.927135	+	0.374727i	$0.877737\pi$
$384$		0			0
$385$	234.884	+	659.128i	0.610088	+	1.71202i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−420.514	−	578.788i	−1.08101	−	1.48789i	−0.858401	−	0.512978i	$-0.828542\pi$
$389$	−420.514	−	578.788i	−1.08101	−	1.48789i	−0.222611	−	0.974907i	$-0.571458\pi$
$390$		0			0
$391$	201.820	+	146.631i	0.516163	+	0.375014i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−37.2803	−	25.5132i	−0.0943805	−	0.0645903i
$396$		0			0
$397$	−425.638	−	138.298i	−1.07214	−	0.348358i	−0.280818	−	0.959761i	$-0.590606\pi$
$397$	−425.638	−	138.298i	−1.07214	−	0.348358i	−0.791320	+	0.611403i	$0.790606\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$			72.6503i			0.181173i	0.995889	+	0.0905865i	$0.0288741\pi$
$401$			72.6503i			0.181173i	−0.995889	+	0.0905865i	$0.971126\pi$
$402$		0			0
$403$	1163.95	+	378.190i	2.88821	+	0.938436i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	76.8046			0.188709
$408$		0			0
$409$	358.554	+	260.505i	0.876661	+	0.636932i	0.932366	−	0.361516i	$-0.117741\pi$
$409$	358.554	+	260.505i	0.876661	+	0.636932i	−0.0557048	+	0.998447i	$0.517741\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	350.010	+	254.297i	0.847481	+	0.615731i
$414$		0			0
$415$	−201.010	+	5.66321i	−0.484362	+	0.0136463i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−109.399	+	35.5460i	−0.261097	+	0.0848354i	−0.436640	−	0.899636i	$-0.643832\pi$
$419$	−109.399	+	35.5460i	−0.261097	+	0.0848354i	0.175544	+	0.984472i	$0.443832\pi$
$420$		0			0
$421$	27.7506	−	85.4076i	0.0659159	−	0.202868i	−0.912674	−	0.408689i	$-0.865986\pi$
$421$	27.7506	−	85.4076i	0.0659159	−	0.202868i	0.978590	+	0.205820i	$0.0659862\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	75.8909	−	287.797i	0.178567	−	0.677170i
$426$		0			0
$427$	−287.656	−	395.924i	−0.673666	−	0.927222i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−377.555	+	122.675i	−0.875998	+	0.284629i	−0.712295	−	0.701881i	$-0.752344\pi$
$431$	−377.555	+	122.675i	−0.875998	+	0.284629i	−0.163703	+	0.986510i	$0.552344\pi$
$432$		0			0
$433$	−64.2860	+	20.8878i	−0.148467	+	0.0482397i	−0.382308	−	0.924035i	$-0.624871\pi$
$433$	−64.2860	+	20.8878i	−0.148467	+	0.0482397i	0.233841	+	0.972275i	$0.424871\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−520.875	−	378.438i	−1.19193	−	0.865990i
$438$		0			0
$439$	359.799	−	261.409i	0.819588	−	0.595466i	−0.0970063	−	0.995284i	$-0.530927\pi$
$439$	359.799	−	261.409i	0.819588	−	0.595466i	0.916595	+	0.399818i	$0.130927\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−40.8374			−0.0921838			−0.0460919	−	0.998937i	$-0.514677\pi$
$443$	−40.8374			−0.0921838			−0.0460919	+	0.998937i	$0.514677\pi$
$444$		0			0
$445$	738.720	−	263.247i	1.66005	−	0.591566i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	555.176i		−	1.23647i	−0.785992	−	0.618236i	$-0.787848\pi$
$449$		−	555.176i		−	1.23647i	0.785992	−	0.618236i	$-0.212152\pi$
$450$		0			0
$451$	−959.538			−2.12758
$452$		0			0
$453$		0			0
$454$		0			0
$455$	762.639	−	587.604i	1.67613	−	1.29144i
$456$		0			0
$457$			255.088i			0.558179i	0.960265	+	0.279090i	$0.0900326\pi$
$457$			255.088i			0.558179i	−0.960265	+	0.279090i	$0.909967\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	43.0082	+	59.1958i	0.0932933	+	0.128407i	0.853112	−	0.521728i	$-0.174712\pi$
$461$	43.0082	+	59.1958i	0.0932933	+	0.128407i	−0.759819	+	0.650135i	$0.774712\pi$
$462$		0			0
$463$	−158.404	+	218.024i	−0.342125	+	0.470894i	−0.945061	−	0.326895i	$-0.893998\pi$
$463$	−158.404	+	218.024i	−0.342125	+	0.470894i	0.602936	+	0.797790i	$0.293998\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−193.744	−	596.283i	−0.414869	−	1.27684i	−0.912368	−	0.409372i	$-0.865748\pi$
$467$	−193.744	−	596.283i	−0.414869	−	1.27684i	0.497498	−	0.867465i	$-0.334252\pi$
$468$		0			0
$469$	54.3569	+	167.293i	0.115899	+	0.356702i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	1037.42	−	753.732i	2.19328	−	1.59351i
$474$		0			0
$475$	−195.866	+	742.774i	−0.412350	+	1.56373i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−704.115	−	228.781i	−1.46997	−	0.477622i	−0.538870	−	0.842389i	$-0.681149\pi$
$479$	−704.115	−	228.781i	−1.46997	−	0.477622i	−0.931099	+	0.364767i	$0.881149\pi$
$480$		0			0
$481$	−32.6555	−	100.503i	−0.0678908	−	0.208946i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	294.327	−	430.076i	0.606860	−	0.886755i
$486$		0			0
$487$	226.780	−	312.136i	0.465668	−	0.640937i	−0.510004	−	0.860172i	$-0.670356\pi$
$487$	226.780	−	312.136i	0.465668	−	0.640937i	0.975672	+	0.219235i	$0.0703562\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−437.566	+	602.258i	−0.891173	+	1.22659i	0.0820267	+	0.996630i	$0.473861\pi$
$491$	−437.566	+	602.258i	−0.891173	+	1.22659i	−0.973199	+	0.229964i	$0.926139\pi$
$492$		0			0
$493$			283.326i			0.574698i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	45.1164	−	138.854i	0.0907774	−	0.279384i
$498$		0			0
$499$	520.538			1.04316			0.521581	−	0.853202i	$-0.325342\pi$
$499$	520.538			1.04316			0.521581	+	0.853202i	$0.325342\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−23.4380	+	72.1347i	−0.0465964	+	0.143409i	−0.971648	−	0.236433i	$-0.924022\pi$
$503$	−23.4380	+	72.1347i	−0.0465964	+	0.143409i	0.925051	+	0.379842i	$0.124022\pi$
$504$		0			0
$505$	−863.732	−	253.984i	−1.71036	−	0.502938i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−420.199	+	578.354i	−0.825538	+	1.13626i	0.163200	+	0.986593i	$0.447819\pi$
$509$	−420.199	+	578.354i	−0.825538	+	1.13626i	−0.988737	+	0.149662i	$0.952181\pi$
$510$		0			0
$511$	209.635	−	152.309i	0.410245	−	0.298061i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	391.379	−	571.890i	0.759959	−	1.11047i
$516$		0			0
$517$	−29.7559	+	9.66829i	−0.0575550	+	0.0187007i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	346.096	+	112.453i	0.664292	+	0.215842i	0.621705	−	0.783251i	$-0.286440\pi$
$521$	346.096	+	112.453i	0.664292	+	0.215842i	0.0425866	+	0.999093i	$0.486440\pi$
$522$		0			0
$523$	−157.381	−	216.616i	−0.300920	−	0.414180i	0.631603	−	0.775292i	$-0.282397\pi$
$523$	−157.381	−	216.616i	−0.300920	−	0.414180i	−0.932523	+	0.361112i	$0.882397\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	460.061	−	334.254i	0.872982	−	0.634258i
$528$		0			0
$529$	−27.7933	+	85.5389i	−0.0525393	+	0.161699i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	407.972	+	1255.61i	0.765427	+	2.35574i
$534$		0			0
$535$	244.068	−	830.012i	0.456203	−	1.55142i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	81.8314	+	112.631i	0.151821	+	0.208963i
$540$		0			0
$541$	−475.003	−	345.110i	−0.878010	−	0.637911i	0.0547145	−	0.998502i	$-0.482575\pi$
$541$	−475.003	−	345.110i	−0.878010	−	0.637911i	−0.932724	+	0.360591i	$0.882575\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−338.348	+	260.693i	−0.620823	+	0.478336i
$546$		0			0
$547$	220.911	+	71.7784i	0.403860	+	0.131222i	0.503901	−	0.863761i	$-0.331898\pi$
$547$	220.911	+	71.7784i	0.403860	+	0.131222i	−0.100041	+	0.994983i	$0.531898\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		−	731.234i		−	1.32710i
$552$		0			0
$553$	−64.5748	−	20.9816i	−0.116772	−	0.0379414i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	295.524			0.530565			0.265282	−	0.964171i	$-0.414535\pi$
$557$	295.524			0.530565			0.265282	+	0.964171i	$0.414535\pi$
$558$		0			0
$559$	−1427.39	−	1037.06i	−2.55347	−	1.85520i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−26.5744	−	19.3075i	−0.0472015	−	0.0342939i	0.563934	−	0.825820i	$-0.309287\pi$
$563$	−26.5744	−	19.3075i	−0.0472015	−	0.0342939i	−0.611136	+	0.791526i	$0.709287\pi$
$564$		0			0
$565$	612.939	−	472.262i	1.08485	−	0.835862i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	328.187	−	106.634i	0.576778	−	0.187407i	−0.00607855	−	0.999982i	$-0.501935\pi$
$569$	328.187	−	106.634i	0.576778	−	0.187407i	0.582857	+	0.812575i	$0.301935\pi$
$570$		0			0
$571$	−109.377	+	336.627i	−0.191553	+	0.589539i	0.808447	+	0.588569i	$0.200309\pi$
$571$	−109.377	+	336.627i	−0.191553	+	0.589539i	−1.00000		0.000969583i	$0.999691\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−523.012	+	29.4938i	−0.909587	+	0.0512936i
$576$		0			0
$577$	341.462	+	469.982i	0.591788	+	0.814527i	0.994926	−	0.100613i	$-0.0320803\pi$
$577$	341.462	+	469.982i	0.591788	+	0.814527i	−0.403137	+	0.915140i	$0.632080\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−287.448	+	93.3975i	−0.494747	+	0.160753i
$582$		0			0
$583$	−1054.81	+	342.727i	−1.80927	+	0.587869i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−135.447	−	98.4083i	−0.230745	−	0.167646i	0.466405	−	0.884571i	$-0.345549\pi$
$587$	−135.447	−	98.4083i	−0.230745	−	0.167646i	−0.697150	+	0.716925i	$0.745549\pi$
$588$		0			0
$589$	−1187.37	+	862.674i	−2.01591	+	1.46464i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−745.902			−1.25785			−0.628923	−	0.777468i	$-0.716504\pi$
$593$	−745.902			−1.25785			−0.628923	+	0.777468i	$0.716504\pi$
$594$		0			0
$595$	−12.5985	−	447.172i	−0.0211739	−	0.751549i
$596$		0			0
$597$		0			0
$598$		0			0
$599$			70.8547i			0.118288i	0.998249	+	0.0591442i	$0.0188372\pi$
$599$			70.8547i			0.118288i	−0.998249	+	0.0591442i	$0.981163\pi$
$600$		0			0
$601$	−184.883			−0.307625			−0.153813	−	0.988100i	$-0.549155\pi$
$601$	−184.883			−0.307625			−0.153813	+	0.988100i	$0.549155\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−931.625	−	637.567i	−1.53988	−	1.05383i
$606$		0			0
$607$		−	355.592i		−	0.585819i	−0.956140	−	0.292910i	$-0.905376\pi$
$607$		−	355.592i		−	0.585819i	0.956140	−	0.292910i	$-0.0946235\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	25.3030	+	34.8266i	0.0414124	+	0.0569993i
$612$		0			0
$613$	−263.222	+	362.294i	−0.429400	+	0.591018i	−0.967815	−	0.251661i	$-0.919023\pi$
$613$	−263.222	+	362.294i	−0.429400	+	0.591018i	0.538415	+	0.842680i	$0.319023\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−43.3668	−	133.469i	−0.0702865	−	0.216320i	0.909743	−	0.415172i	$-0.136279\pi$
$617$	−43.3668	−	133.469i	−0.0702865	−	0.216320i	−0.980029	+	0.198852i	$0.936279\pi$
$618$		0			0
$619$	−61.5912	−	189.558i	−0.0995011	−	0.306233i	0.888899	−	0.458102i	$-0.151471\pi$
$619$	−61.5912	−	189.558i	−0.0995011	−	0.306233i	−0.988401	+	0.151869i	$0.951471\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	953.586	−	692.821i	1.53064	−	1.11207i
$624$		0			0
$625$	258.739	+	568.928i	0.413982	+	0.910285i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−46.6994	−	15.1735i	−0.0742438	−	0.0241233i
$630$		0			0
$631$	−6.48105	−	19.9466i	−0.0102711	−	0.0316111i	0.945790	−	0.324780i	$-0.105290\pi$
$631$	−6.48105	−	19.9466i	−0.0102711	−	0.0316111i	−0.956061	+	0.293169i	$0.905290\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	698.795	−	249.019i	1.10046	−	0.392157i
$636$		0			0
$637$	112.592	−	154.969i	0.176753	−	0.243280i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	340.407	−	468.529i	0.531055	−	0.730935i	−0.456235	−	0.889859i	$-0.650802\pi$
$641$	340.407	−	468.529i	0.531055	−	0.730935i	0.987291	+	0.158924i	$0.0508025\pi$
$642$		0			0
$643$			610.632i			0.949660i	0.880077	+	0.474830i	$0.157491\pi$
$643$			610.632i			0.949660i	−0.880077	+	0.474830i	$0.842509\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	340.671	−	1048.48i	0.526540	−	1.62052i	−0.234710	−	0.972065i	$-0.575414\pi$
$647$	340.671	−	1048.48i	0.526540	−	1.62052i	0.761250	−	0.648458i	$-0.224586\pi$
$648$		0			0
$649$	−1072.06			−1.65186
$650$		0			0
$651$		0			0
$652$		0			0
$653$	269.558	−	829.615i	0.412800	−	1.27047i	−0.501404	−	0.865213i	$-0.667183\pi$
$653$	269.558	−	829.615i	0.412800	−	1.27047i	0.914204	−	0.405254i	$-0.132817\pi$
$654$		0			0
$655$	−7.67460	−	272.403i	−0.0117169	−	0.415882i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	57.0715	−	78.5522i	0.0866032	−	0.119199i	−0.763517	−	0.645788i	$-0.776529\pi$
$659$	57.0715	−	78.5522i	0.0866032	−	0.119199i	0.850120	+	0.526589i	$0.176529\pi$
$660$		0			0
$661$	−693.991	+	504.214i	−1.04991	+	0.762805i	−0.972196	−	0.234171i	$-0.924763\pi$
$661$	−693.991	+	504.214i	−1.04991	+	0.762805i	−0.0777154	+	0.996976i	$0.524763\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	32.5153	+	1154.10i	0.0488953	+	1.73549i
$666$		0			0
$667$	474.253	−	154.094i	0.711024	−	0.231026i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	1153.33	+	374.741i	1.71883	+	0.558481i
$672$		0			0
$673$	−280.385	−	385.917i	−0.416620	−	0.573429i	0.548197	−	0.836349i	$-0.315314\pi$
$673$	−280.385	−	385.917i	−0.416620	−	0.573429i	−0.964817	+	0.262921i	$0.915314\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	511.046	−	371.297i	0.754869	−	0.548444i	−0.142463	−	0.989800i	$-0.545502\pi$
$677$	511.046	−	371.297i	0.754869	−	0.548444i	0.897332	+	0.441356i	$0.145502\pi$
$678$		0			0
$679$	242.050	−	744.953i	0.356480	−	1.09713i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−83.5959	−	257.282i	−0.122395	−	0.376694i	0.871022	−	0.491244i	$-0.163457\pi$
$683$	−83.5959	−	257.282i	−0.122395	−	0.376694i	−0.993418	+	0.114550i	$0.963457\pi$
$684$		0			0
$685$	475.994	−	366.748i	0.694882	−	0.535398i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	896.957	+	1234.55i	1.30182	+	1.79181i
$690$		0			0
$691$	413.211	+	300.216i	0.597991	+	0.434466i	0.845165	−	0.534505i	$-0.179502\pi$
$691$	413.211	+	300.216i	0.597991	+	0.434466i	−0.247174	+	0.968971i	$0.579502\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−109.127	−	306.231i	−0.157017	−	0.440620i
$696$		0			0
$697$	583.426	+	189.567i	0.837053	+	0.271975i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	721.282i		−	1.02893i	−0.857511	−	0.514466i	$-0.827990\pi$
$701$		−	721.282i		−	1.02893i	0.857511	−	0.514466i	$-0.172010\pi$
$702$		0			0
$703$	120.526	+	39.1613i	0.171445	+	0.0557059i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−1353.16			−1.91395
$708$		0			0
$709$	−16.9773	−	12.3347i	−0.0239454	−	0.0173973i	0.575748	−	0.817627i	$-0.304711\pi$
$709$	−16.9773	−	12.3347i	−0.0239454	−	0.0173973i	−0.599694	+	0.800230i	$0.704711\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−809.716	−	588.293i	−1.13565	−	0.825096i
$714$		0			0
$715$	−673.022	+	2288.77i	−0.941290	+	3.20108i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	556.974	−	180.972i	0.774651	−	0.251699i	0.105096	−	0.994462i	$-0.466485\pi$
$719$	556.974	−	180.972i	0.774651	−	0.251699i	0.669555	+	0.742763i	$0.266485\pi$
$720$		0			0
$721$	321.864	−	990.595i	0.446413	−	1.37392i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−376.250	−	460.874i	−0.518965	−	0.635688i
$726$		0			0
$727$	−360.877	−	496.704i	−0.496392	−	0.683225i	0.485159	−	0.874426i	$-0.338762\pi$
$727$	−360.877	−	496.704i	−0.496392	−	0.683225i	−0.981551	+	0.191201i	$0.938762\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−779.690	+	253.337i	−1.06661	+	0.346562i
$732$		0			0
$733$	−213.940	+	69.5134i	−0.291869	+	0.0948341i	−0.451292	−	0.892376i	$-0.649037\pi$
$733$	−213.940	+	69.5134i	−0.291869	+	0.0948341i	0.159423	+	0.987210i	$0.449037\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−352.634	−	256.204i	−0.478473	−	0.347631i
$738$		0			0
$739$	815.069	−	592.182i	1.10293	−	0.801329i	0.121398	−	0.992604i	$-0.461262\pi$
$739$	815.069	−	592.182i	1.10293	−	0.801329i	0.981536	+	0.191275i	$0.0612622\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−534.043			−0.718766			−0.359383	−	0.933190i	$-0.617013\pi$
$743$	−534.043			−0.718766			−0.359383	+	0.933190i	$0.617013\pi$
$744$		0			0
$745$	−179.296	−	52.7226i	−0.240665	−	0.0707687i
$746$		0			0
$747$		0			0
$748$		0			0
$749$		−	1300.33i		−	1.73609i
$750$		0			0
$751$	138.020			0.183781			0.0918907	−	0.995769i	$-0.470709\pi$
$751$	138.020			0.183781			0.0918907	+	0.995769i	$0.470709\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−213.437	+	725.844i	−0.282699	+	0.961383i
$756$		0			0
$757$		−	269.365i		−	0.355832i	−0.984046	−	0.177916i	$-0.943065\pi$
$757$		−	269.365i		−	0.355832i	0.984046	−	0.177916i	$-0.0569355\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−378.879	−	521.482i	−0.497870	−	0.685259i	0.483945	−	0.875098i	$-0.339203\pi$
$761$	−378.879	−	521.482i	−0.497870	−	0.685259i	−0.981815	+	0.189839i	$0.939203\pi$
$762$		0			0
$763$	−377.348	+	519.375i	−0.494558	+	0.680701i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	455.812	+	1402.85i	0.594279	+	1.82900i
$768$		0			0
$769$	−136.334	−	419.593i	−0.177287	−	0.545634i	0.822443	−	0.568847i	$-0.192610\pi$
$769$	−136.334	−	419.593i	−0.177287	−	0.545634i	−0.999731	+	0.0232129i	$0.992610\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−204.236	+	148.386i	−0.264213	+	0.191962i	−0.712002	−	0.702177i	$-0.752211\pi$
$773$	−204.236	+	148.386i	−0.264213	+	0.191962i	0.447790	+	0.894139i	$0.352211\pi$
$774$		0			0
$775$	−304.480	+	1154.67i	−0.392878	+	1.48989i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−1505.76	−	489.251i	−1.93294	−	0.628050i
$780$		0			0
$781$	111.797	+	344.075i	0.143146	+	0.440557i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−71.2940	−	20.9643i	−0.0908203	−	0.0267061i
$786$		0			0
$787$	−372.393	+	512.555i	−0.473181	+	0.651277i	−0.977177	−	0.212429i	$-0.931863\pi$
$787$	−372.393	+	512.555i	−0.473181	+	0.651277i	0.503996	+	0.863706i	$0.331863\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	683.589	−	940.880i	0.864209	−	1.18948i
$792$		0			0
$793$		−	1668.53i		−	2.10408i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−116.939	+	359.900i	−0.146724	+	0.451569i	−0.997229	−	0.0743981i	$-0.976296\pi$
$797$	−116.939	+	359.900i	−0.146724	+	0.451569i	0.850505	+	0.525967i	$0.176296\pi$
$798$		0			0
$799$	20.0025			0.0250344
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−198.419	+	610.672i	−0.247098	+	0.760489i
$804$		0			0
$805$	−741.658	+	264.294i	−0.921315	+	0.328316i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−551.959	+	759.706i	−0.682273	+	0.939068i	−0.999958	−	0.00912795i	$-0.997094\pi$
$809$	−551.959	+	759.706i	−0.682273	+	0.939068i	0.317685	+	0.948196i	$0.397094\pi$
$810$		0			0
$811$	69.0580	−	50.1736i	0.0851517	−	0.0618663i	−0.544395	−	0.838829i	$-0.683241\pi$
$811$	69.0580	−	50.1736i	0.0851517	−	0.0618663i	0.629547	+	0.776963i	$0.283241\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−224.970	−	291.984i	−0.276037	−	0.358262i
$816$		0			0
$817$	2012.30	−	653.834i	2.46303	−	0.800287i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	26.4137	+	8.58234i	0.0321726	+	0.0104535i	0.325059	−	0.945694i	$-0.394616\pi$
$821$	26.4137	+	8.58234i	0.0321726	+	0.0104535i	−0.292886	+	0.956147i	$0.594616\pi$
$822$		0			0
$823$	−61.5259	−	84.6832i	−0.0747581	−	0.102896i	0.770000	−	0.638043i	$-0.220256\pi$
$823$	−61.5259	−	84.6832i	−0.0747581	−	0.102896i	−0.844759	+	0.535148i	$0.820256\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−728.148	+	529.030i	−0.880469	+	0.639698i	−0.933376	−	0.358901i	$-0.883151\pi$
$827$	−728.148	+	529.030i	−0.880469	+	0.639698i	0.0529065	+	0.998599i	$0.483151\pi$
$828$		0			0
$829$	−89.0819	+	274.166i	−0.107457	+	0.330719i	−0.990299	−	0.138951i	$-0.955627\pi$
$829$	−89.0819	+	274.166i	−0.107457	+	0.330719i	0.882842	+	0.469670i	$0.155627\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−27.5043	−	84.6496i	−0.0330184	−	0.101620i
$834$		0			0
$835$	832.921	−	23.4665i	0.997511	−	0.0281036i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	645.064	+	887.854i	0.768848	+	1.05823i	0.996426	+	0.0844689i	$0.0269194\pi$
$839$	645.064	+	887.854i	0.768848	+	1.05823i	−0.227578	+	0.973760i	$0.573081\pi$
$840$		0			0
$841$	−222.197	−	161.435i	−0.264205	−	0.191956i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	2436.47	−	68.6445i	2.88340	−	0.0812361i
$846$		0			0
$847$	−1613.71	−	524.325i	−1.90520	−	0.619038i
$848$		0			0
$849$		0			0
$850$		0			0
$851$			86.4215i			0.101553i
$852$		0			0
$853$	1405.81	+	456.775i	1.64808	+	0.535492i	0.978322	−	0.207090i	$-0.0663994\pi$
$853$	1405.81	+	456.775i	1.64808	+	0.535492i	0.669754	+	0.742583i	$0.266399\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	1184.54			1.38220			0.691098	−	0.722761i	$-0.257127\pi$
$857$	1184.54			1.38220			0.691098	+	0.722761i	$0.257127\pi$
$858$		0			0
$859$	711.973	+	517.279i	0.828839	+	0.602187i	0.919231	−	0.393719i	$-0.128812\pi$
$859$	711.973	+	517.279i	0.828839	+	0.602187i	−0.0903913	+	0.995906i	$0.528812\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−256.888	−	186.640i	−0.297668	−	0.216269i	0.428919	−	0.903343i	$-0.358895\pi$
$863$	−256.888	−	186.640i	−0.297668	−	0.216269i	−0.726587	+	0.687074i	$0.758895\pi$
$864$		0			0
$865$	−377.314	−	1058.81i	−0.436201	−	1.22406i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	160.014	−	51.9917i	0.184136	−	0.0598293i
$870$		0			0
$871$	−185.326	+	570.374i	−0.212773	+	0.654849i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	614.326	+	710.664i	0.702086	+	0.812187i
$876$		0			0
$877$	−41.8114	−	57.5484i	−0.0476755	−	0.0656197i	0.784514	−	0.620112i	$-0.212913\pi$
$877$	−41.8114	−	57.5484i	−0.0476755	−	0.0656197i	−0.832189	+	0.554492i	$0.812913\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	1617.38	−	525.518i	1.83584	−	0.596502i	0.837066	−	0.547102i	$-0.184269\pi$
$881$	1617.38	−	525.518i	1.83584	−	0.596502i	0.998779	−	0.0494000i	$-0.0157309\pi$
$882$		0			0
$883$	394.338	−	128.128i	0.446588	−	0.145105i	−0.0770849	−	0.997025i	$-0.524561\pi$
$883$	394.338	−	128.128i	0.446588	−	0.145105i	0.523673	+	0.851919i	$0.324561\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	291.051	+	211.461i	0.328129	+	0.238400i	0.739636	−	0.673007i	$-0.234997\pi$
$887$	291.051	+	211.461i	0.328129	+	0.238400i	−0.411507	+	0.911407i	$0.634997\pi$
$888$		0			0
$889$	902.048	−	655.376i	1.01468	−	0.737206i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−51.6243			−0.0578100
$894$		0			0
$895$	−2.73914	+	4.00249i	−0.00306050	+	0.00447205i
$896$		0			0
$897$		0			0
$898$		0			0
$899$		−	1136.73i		−	1.26443i
$900$		0			0
$901$	709.061			0.786971
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−342.340	+	9.64498i	−0.378276	+	0.0106574i
$906$		0			0
$907$		−	68.2097i		−	0.0752037i	−0.999293	−	0.0376018i	$-0.988028\pi$
$907$		−	68.2097i		−	0.0752037i	0.999293	−	0.0376018i	$-0.0119719\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−215.557	−	296.689i	−0.236616	−	0.325674i	0.674152	−	0.738593i	$-0.264509\pi$
$911$	−215.557	−	296.689i	−0.236616	−	0.325674i	−0.910768	+	0.412919i	$0.864509\pi$
$912$		0			0
$913$	440.217	−	605.906i	0.482165	−	0.663643i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−126.569	−	389.540i	−0.138025	−	0.424799i
$918$		0			0
$919$	−3.29109	−	10.1289i	−0.00358116	−	0.0110217i	0.949250	−	0.314523i	$-0.101844\pi$
$919$	−3.29109	−	10.1289i	−0.00358116	−	0.0110217i	−0.952831	+	0.303501i	$0.901844\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	402.708	−	292.585i	0.436304	−	0.316993i
$924$		0			0
$925$	96.1138	−	37.3334i	0.103907	−	0.0403604i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	500.754	+	162.705i	0.539025	+	0.175140i	0.565862	−	0.824500i	$-0.308544\pi$
$929$	500.754	+	162.705i	0.539025	+	0.175140i	−0.0268372	+	0.999640i	$0.508544\pi$
$930$		0			0
$931$	70.9857	+	218.471i	0.0762467	+	0.234663i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	676.567	+	878.102i	0.723601	+	0.939146i
$936$		0			0
$937$	−258.731	+	356.113i	−0.276127	+	0.380056i	−0.924446	−	0.381312i	$-0.875472\pi$
$937$	−258.731	+	356.113i	−0.276127	+	0.380056i	0.648319	+	0.761369i	$0.275472\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−990.887	+	1363.84i	−1.05301	+	1.44935i	−0.166849	+	0.985982i	$0.553359\pi$
$941$	−990.887	+	1363.84i	−1.05301	+	1.44935i	−0.886166	+	0.463368i	$0.846641\pi$
$942$		0			0
$943$		−	1079.68i		−	1.14495i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−239.032	+	735.664i	−0.252409	+	0.776836i	0.741920	+	0.670489i	$0.233916\pi$
$947$	−239.032	+	735.664i	−0.252409	+	0.776836i	−0.994329	+	0.106347i	$0.966084\pi$
$948$		0			0
$949$	883.463			0.930941
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−463.077	+	1425.20i	−0.485915	+	1.49549i	0.344736	+	0.938700i	$0.387968\pi$
$953$	−463.077	+	1425.20i	−0.485915	+	1.49549i	−0.830651	+	0.556793i	$0.812032\pi$
$954$		0			0
$955$	839.112	+	1089.07i	0.878652	+	1.14038i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	530.859	−	730.665i	0.553555	−	0.761903i
$960$		0			0
$961$	−1068.34	+	776.192i	−1.11169	+	0.807692i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−1514.90	−	445.463i	−1.56985	−	0.461620i
$966$		0			0
$967$	−1413.45	+	459.259i	−1.46169	+	0.474932i	−0.928586	−	0.371117i	$-0.878975\pi$
$967$	−1413.45	+	459.259i	−1.46169	+	0.474932i	−0.533105	+	0.846049i	$0.678975\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−982.973	−	319.387i	−1.01233	−	0.328926i	−0.244548	−	0.969637i	$-0.578640\pi$
$971$	−982.973	−	319.387i	−1.01233	−	0.328926i	−0.767782	+	0.640711i	$0.778640\pi$
$972$		0			0
$973$	−287.204	−	395.302i	−0.295173	−	0.406271i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	230.321	−	167.338i	0.235743	−	0.171277i	−0.463642	−	0.886023i	$-0.653458\pi$
$977$	230.321	−	167.338i	0.235743	−	0.171277i	0.699384	+	0.714746i	$0.253458\pi$
$978$		0			0
$979$	−902.567	+	2777.82i	−0.921927	+	2.83740i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	450.532	+	1386.59i	0.458323	+	1.41057i	0.867189	+	0.497980i	$0.165925\pi$
$983$	450.532	+	1386.59i	0.458323	+	1.41057i	−0.408865	+	0.912595i	$0.634075\pi$
$984$		0			0
$985$	85.9439	+	58.8166i	0.0872526	+	0.0597122i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	848.108	+	1167.32i	0.857541	+	1.18030i
$990$		0			0
$991$	33.7961	+	24.5543i	0.0341031	+	0.0247773i	0.604706	−	0.796449i	$-0.293291\pi$
$991$	33.7961	+	24.5543i	0.0341031	+	0.0247773i	−0.570603	+	0.821226i	$0.693291\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	348.305	−	1184.49i	0.350056	−	1.19045i
$996$		0			0
$997$	393.038	+	127.706i	0.394220	+	0.128090i	0.499418	−	0.866361i	$-0.333547\pi$
$997$	393.038	+	127.706i	0.394220	+	0.128090i	−0.105197	+	0.994451i	$0.533547\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.3.y.a.89.8	✓	80
3.2	odd	2	inner	900.3.y.a.89.13	yes	80
25.9	even	10	inner	900.3.y.a.809.13	yes	80
75.59	odd	10	inner	900.3.y.a.809.8	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
900.3.y.a.89.8	✓	80	1.1	even	1	trivial
900.3.y.a.89.13	yes	80	3.2	odd	2	inner
900.3.y.a.809.8	yes	80	75.59	odd	10	inner
900.3.y.a.809.13	yes	80	25.9	even	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.y (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41055 + 4.79691i) q^{5} +7.51506i q^{7} +O(q^{10})\)	\(q+(-1.41055 + 4.79691i) q^{5} +7.51506i q^{7} +(-10.9458 - 15.0655i) q^{11} +(-15.0602 + 20.7287i) q^{13} +(3.67897 + 11.3227i) q^{17} +(-9.49503 - 29.2227i) q^{19} +(16.9519 - 12.3163i) q^{23} +(-21.0207 - 13.5326i) q^{25} +(22.6333 + 7.35402i) q^{29} +(-14.7603 - 45.4276i) q^{31} +(-36.0491 - 10.6004i) q^{35} +(-2.42426 + 3.33671i) q^{37} +(30.2868 - 41.6862i) q^{41} +68.8607i q^{43} +(0.519185 - 1.59789i) q^{47} -7.47609 q^{49} +(18.4044 - 56.6429i) q^{53} +(87.7076 - 31.2551i) q^{55} +(33.8383 - 46.5744i) q^{59} +(-52.6841 + 38.2772i) q^{61} +(-78.1902 - 101.481i) q^{65} +(22.2611 - 7.23306i) q^{67} +(-18.4768 - 6.00346i) q^{71} +(-20.2672 - 27.8954i) q^{73} +(113.218 - 82.2580i) q^{77} +(-2.79194 + 8.59272i) q^{79} +(12.4280 + 38.2496i) q^{83} +(-59.5034 + 1.67643i) q^{85} +(-92.1910 - 126.890i) q^{89} +(-155.777 - 113.179i) q^{91} +(153.572 - 4.32669i) q^{95} +(-99.1280 - 32.2086i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q+O(q^{10}) \) 80 * q	\( 80 q + 60 q^{19} + 56 q^{25} - 120 q^{31} + 20 q^{37} - 680 q^{49} - 56 q^{55} - 80 q^{61} - 280 q^{67} - 360 q^{73} + 40 q^{79} + 192 q^{85} + 140 q^{91} - 40 q^{97}+O(q^{100}) \) 80 * q + 60 * q^19 + 56 * q^25 - 120 * q^31 + 20 * q^37 - 680 * q^49 - 56 * q^55 - 80 * q^61 - 280 * q^67 - 360 * q^73 + 40 * q^79 + 192 * q^85 + 140 * q^91 - 40 * q^97

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