LMFDB - Embedded newform 900.3.ba.a.161.10

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			161.10
Character	$\chi$	$=$	900.161
Dual form			900.3.ba.a.341.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.709639 + 4.94939i) q^{5} -11.1410 q^{7} +O(q^{10})$	$q+(-0.709639 + 4.94939i) q^{5} -11.1410 q^{7} +(-6.47189 - 8.90780i) q^{11} +(6.61103 + 4.80319i) q^{13} +(7.13313 - 2.31769i) q^{17} +(-8.19242 - 25.2137i) q^{19} +(-9.21280 - 12.6803i) q^{23} +(-23.9928 - 7.02456i) q^{25} +(49.3193 + 16.0248i) q^{29} +(12.5804 + 38.7186i) q^{31} +(7.90609 - 55.1411i) q^{35} +(40.4877 + 29.4161i) q^{37} +(37.3385 - 51.3920i) q^{41} +62.8666 q^{43} +(-60.6521 - 19.7071i) q^{47} +75.1220 q^{49} +(13.0949 + 4.25480i) q^{53} +(48.6808 - 25.7106i) q^{55} +(54.3397 - 74.7922i) q^{59} +(-58.3945 + 42.4261i) q^{61} +(-28.4643 + 29.3120i) q^{65} +(35.8377 + 110.297i) q^{67} +(-55.0578 - 17.8894i) q^{71} +(31.0482 - 22.5579i) q^{73} +(72.1034 + 99.2418i) q^{77} +(2.95530 - 9.09546i) q^{79} +(-4.96634 + 1.61366i) q^{83} +(6.40921 + 36.9493i) q^{85} +(-2.02422 - 2.78610i) q^{89} +(-73.6535 - 53.5124i) q^{91} +(130.606 - 22.6548i) q^{95} +(45.7465 - 140.793i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−0.709639	+	4.94939i	−0.141928	+	0.989877i
$5$	−0.709639	+	4.94939i	−0.141928	+	0.989877i
$6$		0			0
$7$	−11.1410			−1.59157			−0.795786	−	0.605578i	$-0.792942\pi$
$7$	−11.1410			−1.59157			−0.795786	+	0.605578i	$0.792942\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−6.47189	−	8.90780i	−0.588354	−	0.809800i	0.406226	−	0.913773i	$-0.366844\pi$
$11$	−6.47189	−	8.90780i	−0.588354	−	0.809800i	−0.994580	+	0.103973i	$0.966844\pi$
$12$		0			0
$13$	6.61103	+	4.80319i	0.508541	+	0.369476i	0.812270	−	0.583282i	$-0.198232\pi$
$13$	6.61103	+	4.80319i	0.508541	+	0.369476i	−0.303729	+	0.952758i	$0.598232\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	7.13313	−	2.31769i	0.419596	−	0.136335i	−0.0916067	−	0.995795i	$-0.529200\pi$
$17$	7.13313	−	2.31769i	0.419596	−	0.136335i	0.511202	+	0.859460i	$0.329200\pi$
$18$		0			0
$19$	−8.19242	−	25.2137i	−0.431180	−	1.32703i	−0.896951	−	0.442130i	$-0.854223\pi$
$19$	−8.19242	−	25.2137i	−0.431180	−	1.32703i	0.465771	−	0.884905i	$-0.345777\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−9.21280	−	12.6803i	−0.400556	−	0.551319i	0.560327	−	0.828271i	$-0.310675\pi$
$23$	−9.21280	−	12.6803i	−0.400556	−	0.551319i	−0.960884	+	0.276953i	$0.910675\pi$
$24$		0			0
$25$	−23.9928	−	7.02456i	−0.959713	−	0.280982i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	49.3193	+	16.0248i	1.70067	+	0.552580i	0.988736	−	0.149671i	$-0.0478213\pi$
$29$	49.3193	+	16.0248i	1.70067	+	0.552580i	0.711930	+	0.702250i	$0.247821\pi$
$30$		0			0
$31$	12.5804	+	38.7186i	0.405821	+	1.24899i	0.920208	+	0.391429i	$0.128019\pi$
$31$	12.5804	+	38.7186i	0.405821	+	1.24899i	−0.514388	+	0.857558i	$0.671981\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	7.90609	−	55.1411i	0.225888	−	1.57546i
$36$		0			0
$37$	40.4877	+	29.4161i	1.09426	+	0.795029i	0.980114	−	0.198435i	$-0.0635859\pi$
$37$	40.4877	+	29.4161i	1.09426	+	0.795029i	0.114149	+	0.993464i	$0.463586\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	37.3385	−	51.3920i	0.910695	−	1.25346i	−0.0562334	−	0.998418i	$-0.517909\pi$
$41$	37.3385	−	51.3920i	0.910695	−	1.25346i	0.966929	−	0.255047i	$-0.0820909\pi$
$42$		0			0
$43$	62.8666			1.46201			0.731007	−	0.682370i	$-0.239051\pi$
$43$	62.8666			1.46201			0.731007	+	0.682370i	$0.239051\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−60.6521	−	19.7071i	−1.29047	−	0.419299i	−0.418215	−	0.908348i	$-0.637344\pi$
$47$	−60.6521	−	19.7071i	−1.29047	−	0.419299i	−0.872256	+	0.489049i	$0.837344\pi$
$48$		0			0
$49$	75.1220			1.53310
$50$		0			0
$51$		0			0
$52$		0			0
$53$	13.0949	+	4.25480i	0.247074	+	0.0802793i	0.429936	−	0.902859i	$-0.358536\pi$
$53$	13.0949	+	4.25480i	0.247074	+	0.0802793i	−0.182862	+	0.983139i	$0.558536\pi$
$54$		0			0
$55$	48.6808	−	25.7106i	0.885106	−	0.467465i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	54.3397	−	74.7922i	0.921012	−	1.26766i	−0.0422515	−	0.999107i	$-0.513453\pi$
$59$	54.3397	−	74.7922i	0.921012	−	1.26766i	0.963264	−	0.268557i	$-0.0865469\pi$
$60$		0			0
$61$	−58.3945	+	42.4261i	−0.957287	+	0.695510i	−0.952519	−	0.304479i	$-0.901518\pi$
$61$	−58.3945	+	42.4261i	−0.957287	+	0.695510i	−0.00476819	+	0.999989i	$0.501518\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−28.4643	+	29.3120i	−0.437912	+	0.450954i
$66$		0			0
$67$	35.8377	+	110.297i	0.534891	+	1.64623i	0.743884	+	0.668309i	$0.232981\pi$
$67$	35.8377	+	110.297i	0.534891	+	1.64623i	−0.208993	+	0.977917i	$0.567019\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−55.0578	−	17.8894i	−0.775463	−	0.251963i	−0.105561	−	0.994413i	$-0.533664\pi$
$71$	−55.0578	−	17.8894i	−0.775463	−	0.251963i	−0.669902	+	0.742450i	$0.733664\pi$
$72$		0			0
$73$	31.0482	−	22.5579i	0.425318	−	0.309012i	−0.354456	−	0.935073i	$-0.615334\pi$
$73$	31.0482	−	22.5579i	0.425318	−	0.309012i	0.779774	+	0.626061i	$0.215334\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	72.1034	+	99.2418i	0.936408	+	1.28885i
$78$		0			0
$79$	2.95530	−	9.09546i	0.0374088	−	0.115132i	−0.930608	−	0.366017i	$-0.880721\pi$
$79$	2.95530	−	9.09546i	0.0374088	−	0.115132i	0.968017	+	0.250884i	$0.0807213\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−4.96634	+	1.61366i	−0.0598354	+	0.0194417i	−0.338782	−	0.940865i	$-0.610015\pi$
$83$	−4.96634	+	1.61366i	−0.0598354	+	0.0194417i	0.278946	+	0.960307i	$0.410015\pi$
$84$		0			0
$85$	6.40921	+	36.9493i	0.0754025	+	0.434698i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−2.02422	−	2.78610i	−0.0227441	−	0.0313045i	0.797494	−	0.603328i	$-0.206159\pi$
$89$	−2.02422	−	2.78610i	−0.0227441	−	0.0313045i	−0.820238	+	0.572023i	$0.806159\pi$
$90$		0			0
$91$	−73.6535	−	53.5124i	−0.809379	−	0.588048i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	130.606	−	22.6548i	1.37480	−	0.238472i
$96$		0			0
$97$	45.7465	−	140.793i	0.471614	−	1.45148i	−0.378857	−	0.925455i	$-0.623683\pi$
$97$	45.7465	−	140.793i	0.471614	−	1.45148i	0.850471	−	0.526022i	$-0.176317\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$		−	150.865i		−	1.49371i	−0.664986	−	0.746855i	$-0.731563\pi$
$101$		−	150.865i		−	1.49371i	0.664986	−	0.746855i	$-0.268437\pi$
$102$		0			0
$103$	−30.1592	+	92.8206i	−0.292808	+	0.901170i	0.691141	+	0.722720i	$0.257108\pi$
$103$	−30.1592	+	92.8206i	−0.292808	+	0.901170i	−0.983949	+	0.178450i	$0.942892\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	91.6119i		−	0.856186i	−0.903735	−	0.428093i	$-0.859186\pi$
$107$		−	91.6119i		−	0.856186i	0.903735	−	0.428093i	$-0.140814\pi$
$108$		0			0
$109$	−105.879	−	76.9253i	−0.971364	−	0.705737i	−0.0156018	−	0.999878i	$-0.504966\pi$
$109$	−105.879	−	76.9253i	−0.971364	−	0.705737i	−0.955762	+	0.294141i	$0.904966\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	13.3769	−	18.4117i	0.118380	−	0.162936i	−0.745715	−	0.666265i	$-0.767892\pi$
$113$	13.3769	−	18.4117i	0.118380	−	0.162936i	0.864094	+	0.503330i	$0.167892\pi$
$114$		0			0
$115$	69.2976	−	36.5992i	0.602588	−	0.318254i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−79.4702	+	25.8214i	−0.667817	+	0.216987i
$120$		0			0
$121$	−0.0723782	+	0.222757i	−0.000598167	+	0.00184097i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	51.7935	−	113.765i	0.414348	−	0.910119i
$126$		0			0
$127$	65.0611	−	47.2697i	0.512293	−	0.372202i	−0.301400	−	0.953498i	$-0.597454\pi$
$127$	65.0611	−	47.2697i	0.512293	−	0.372202i	0.813693	+	0.581295i	$0.197454\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	16.0378	−	5.21100i	0.122426	−	0.0397786i	−0.247163	−	0.968974i	$-0.579498\pi$
$131$	16.0378	−	5.21100i	0.122426	−	0.0397786i	0.369589	+	0.929195i	$0.379498\pi$
$132$		0			0
$133$	91.2717	+	280.906i	0.686254	+	2.11207i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	38.2753	−	52.6814i	0.279382	−	0.384536i	−0.646147	−	0.763213i	$-0.723621\pi$
$137$	38.2753	−	52.6814i	0.279382	−	0.384536i	0.925529	+	0.378677i	$0.123621\pi$
$138$		0			0
$139$	44.2412	−	32.1431i	0.318282	−	0.231246i	−0.417160	−	0.908833i	$-0.636975\pi$
$139$	44.2412	−	32.1431i	0.318282	−	0.231246i	0.735442	+	0.677588i	$0.236975\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		−	89.9755i		−	0.629199i
$144$		0			0
$145$	−114.312	+	232.728i	−0.788358	+	1.60502i
$146$		0			0
$147$		0			0
$148$		0			0
$149$		−	238.625i		−	1.60151i	−0.598992	−	0.800755i	$-0.704432\pi$
$149$		−	238.625i		−	1.60151i	0.598992	−	0.800755i	$-0.295568\pi$
$150$		0			0
$151$	47.8063			0.316598			0.158299	−	0.987391i	$-0.449399\pi$
$151$	47.8063			0.316598			0.158299	+	0.987391i	$0.449399\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−200.561	+	34.7892i	−1.29394	+	0.224446i
$156$		0			0
$157$	166.738			1.06203			0.531014	−	0.847363i	$-0.321811\pi$
$157$	166.738			1.06203			0.531014	+	0.847363i	$0.321811\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	102.640	+	141.272i	0.637514	+	0.877463i
$162$		0			0
$163$	−186.285	−	135.344i	−1.14285	−	0.830332i	−0.155340	−	0.987861i	$-0.549647\pi$
$163$	−186.285	−	135.344i	−1.14285	−	0.830332i	−0.987514	+	0.157529i	$0.949647\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	164.079	−	53.3126i	0.982511	−	0.319237i	0.226655	−	0.973975i	$-0.427221\pi$
$167$	164.079	−	53.3126i	0.982511	−	0.319237i	0.755856	+	0.654738i	$0.227221\pi$
$168$		0			0
$169$	−31.5888	−	97.2204i	−0.186916	−	0.575269i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	82.4581	+	113.494i	0.476636	+	0.656034i	0.977854	−	0.209287i	$-0.0671144\pi$
$173$	82.4581	+	113.494i	0.476636	+	0.656034i	−0.501218	+	0.865321i	$0.667114\pi$
$174$		0			0
$175$	267.304	+	78.2606i	1.52745	+	0.447203i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	305.832	+	99.3709i	1.70856	+	0.555145i	0.990093	−	0.140417i	$-0.0448442\pi$
$179$	305.832	+	99.3709i	1.70856	+	0.555145i	0.718467	+	0.695561i	$0.244844\pi$
$180$		0			0
$181$	−53.5606	−	164.842i	−0.295915	−	0.910732i	−0.982913	−	0.184072i	$-0.941072\pi$
$181$	−53.5606	−	164.842i	−0.295915	−	0.910732i	0.686998	−	0.726659i	$-0.258928\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−174.323	+	179.515i	−0.942287	+	0.970349i
$186$		0			0
$187$	−66.8104	−	48.5406i	−0.357275	−	0.259575i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−45.2710	+	62.3101i	−0.237021	+	0.326231i	−0.910913	−	0.412599i	$-0.864621\pi$
$191$	−45.2710	+	62.3101i	−0.237021	+	0.326231i	0.673892	+	0.738830i	$0.264621\pi$
$192$		0			0
$193$	−261.605			−1.35546			−0.677732	−	0.735309i	$-0.737037\pi$
$193$	−261.605			−1.35546			−0.677732	+	0.735309i	$0.737037\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	25.8281	+	8.39204i	0.131107	+	0.0425992i	0.373835	−	0.927495i	$-0.378042\pi$
$197$	25.8281	+	8.39204i	0.131107	+	0.0425992i	−0.242729	+	0.970094i	$0.578042\pi$
$198$		0			0
$199$	76.1285			0.382555			0.191278	−	0.981536i	$-0.438737\pi$
$199$	76.1285			0.382555			0.191278	+	0.981536i	$0.438737\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−549.467	−	178.533i	−2.70673	−	0.879471i
$204$		0			0
$205$	227.862	+	221.272i	1.11152	+	1.07938i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−171.578	+	236.156i	−0.820946	+	1.12994i
$210$		0			0
$211$	−67.8323	+	49.2831i	−0.321480	+	0.233569i	−0.736807	−	0.676103i	$-0.763667\pi$
$211$	−67.8323	+	49.2831i	−0.321480	+	0.233569i	0.415327	+	0.909672i	$0.363667\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−44.6126	+	311.151i	−0.207500	+	1.44721i
$216$		0			0
$217$	−140.159	−	431.364i	−0.645893	−	1.98785i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	58.2896	+	18.9395i	0.263754	+	0.0856989i
$222$		0			0
$223$	−165.909	+	120.540i	−0.743989	+	0.540539i	−0.893958	−	0.448151i	$-0.852083\pi$
$223$	−165.909	+	120.540i	−0.743989	+	0.540539i	0.149969	+	0.988691i	$0.452083\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	130.508	+	179.629i	0.574927	+	0.791319i	0.993128	−	0.117036i	$-0.0373393\pi$
$227$	130.508	+	179.629i	0.574927	+	0.791319i	−0.418201	+	0.908354i	$0.637339\pi$
$228$		0			0
$229$	−65.2222	+	200.733i	−0.284813	+	0.876565i	0.701641	+	0.712530i	$0.252451\pi$
$229$	−65.2222	+	200.733i	−0.284813	+	0.876565i	−0.986455	+	0.164035i	$0.947549\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−138.020	+	44.8456i	−0.592363	+	0.192470i	−0.589831	−	0.807527i	$-0.700806\pi$
$233$	−138.020	+	44.8456i	−0.592363	+	0.192470i	−0.00253134	+	0.999997i	$0.500806\pi$
$234$		0			0
$235$	140.579	−	286.206i	0.598209	−	1.21790i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−85.8660	−	118.184i	−0.359272	−	0.494495i	0.590674	−	0.806910i	$-0.298862\pi$
$239$	−85.8660	−	118.184i	−0.359272	−	0.494495i	−0.949946	+	0.312415i	$0.898862\pi$
$240$		0			0
$241$	−9.81448	−	7.13064i	−0.0407240	−	0.0295877i	0.567237	−	0.823555i	$-0.308012\pi$
$241$	−9.81448	−	7.13064i	−0.0407240	−	0.0295877i	−0.607961	+	0.793967i	$0.708012\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−53.3095	+	371.808i	−0.217590	+	1.51758i
$246$		0			0
$247$	66.9458	−	206.038i	0.271036	−	0.834162i
$248$		0			0
$249$		0			0
$250$		0			0
$251$		−	120.180i		−	0.478803i	−0.970921	−	0.239401i	$-0.923049\pi$
$251$		−	120.180i		−	0.478803i	0.970921	−	0.239401i	$-0.0769512\pi$
$252$		0			0
$253$	−53.3295	+	164.131i	−0.210789	+	0.648741i
$254$		0			0
$255$		0			0
$256$		0			0
$257$			392.216i			1.52613i	0.646321	+	0.763065i	$0.276307\pi$
$257$			392.216i			1.52613i	−0.646321	+	0.763065i	$0.723693\pi$
$258$		0			0
$259$	−451.074	−	327.724i	−1.74160	−	1.26535i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	202.860	−	279.212i	0.771330	−	1.06164i	−0.224857	−	0.974392i	$-0.572191\pi$
$263$	202.860	−	279.212i	0.771330	−	1.06164i	0.996186	−	0.0872522i	$-0.0278086\pi$
$264$		0			0
$265$	−30.3513	+	61.7925i	−0.114533	+	0.233179i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−69.0619	+	22.4396i	−0.256736	+	0.0834184i	−0.434557	−	0.900644i	$-0.643095\pi$
$269$	−69.0619	+	22.4396i	−0.256736	+	0.0834184i	0.177821	+	0.984063i	$0.443095\pi$
$270$		0			0
$271$	−33.5669	+	103.308i	−0.123863	+	0.381212i	−0.993692	−	0.112142i	$-0.964229\pi$
$271$	−33.5669	+	103.308i	−0.123863	+	0.381212i	0.869829	+	0.493353i	$0.164229\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	92.7057	+	259.185i	0.337112	+	0.942492i
$276$		0			0
$277$	−130.198	+	94.5940i	−0.470027	+	0.341495i	−0.797452	−	0.603383i	$-0.793819\pi$
$277$	−130.198	+	94.5940i	−0.470027	+	0.341495i	0.327425	+	0.944877i	$0.393819\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−69.8657	+	22.7007i	−0.248632	+	0.0807855i	−0.430682	−	0.902504i	$-0.641727\pi$
$281$	−69.8657	+	22.7007i	−0.248632	+	0.0807855i	0.182050	+	0.983289i	$0.441727\pi$
$282$		0			0
$283$	−15.8914	−	48.9088i	−0.0561535	−	0.172823i	0.919046	−	0.394150i	$-0.128961\pi$
$283$	−15.8914	−	48.9088i	−0.0561535	−	0.172823i	−0.975200	+	0.221328i	$0.928961\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−415.988	+	572.559i	−1.44944	+	1.99498i
$288$		0			0
$289$	−188.296	+	136.805i	−0.651544	+	0.473374i
$290$		0			0
$291$		0			0
$292$		0			0
$293$			230.227i			0.785758i	0.919590	+	0.392879i	$0.128521\pi$
$293$			230.227i			0.785758i	−0.919590	+	0.392879i	$0.871479\pi$
$294$		0			0
$295$	331.614	+	322.024i	1.12411	+	1.09161i
$296$		0			0
$297$		0			0
$298$		0			0
$299$		−	128.081i		−	0.428364i
$300$		0			0
$301$	−700.397			−2.32690
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−168.544	−	319.124i	−0.552604	−	1.04631i
$306$		0			0
$307$	480.502			1.56515			0.782577	−	0.622554i	$-0.213905\pi$
$307$	480.502			1.56515			0.782577	+	0.622554i	$0.213905\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−287.524	−	395.743i	−0.924515	−	1.27249i	−0.961961	−	0.273187i	$-0.911922\pi$
$311$	−287.524	−	395.743i	−0.924515	−	1.27249i	0.0374465	−	0.999299i	$-0.488078\pi$
$312$		0			0
$313$	225.551	+	163.872i	0.720609	+	0.523553i	0.886579	−	0.462578i	$-0.153075\pi$
$313$	225.551	+	163.872i	0.720609	+	0.523553i	−0.165969	+	0.986131i	$0.553075\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	474.795	−	154.270i	1.49778	−	0.486657i	0.558407	−	0.829567i	$-0.311413\pi$
$317$	474.795	−	154.270i	1.49778	−	0.486657i	0.939368	+	0.342910i	$0.111413\pi$
$318$		0			0
$319$	−176.443	−	543.037i	−0.553114	−	1.70231i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−116.875	−	160.865i	−0.361842	−	0.498033i
$324$		0			0
$325$	−124.877	−	161.682i	−0.384237	−	0.497482i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	675.726	+	219.557i	2.05388	+	0.667345i
$330$		0			0
$331$	−107.484	−	330.801i	−0.324725	−	0.999400i	−0.971565	−	0.236774i	$-0.923910\pi$
$331$	−107.484	−	330.801i	−0.324725	−	0.999400i	0.646840	−	0.762626i	$-0.276090\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−571.335	+	99.1035i	−1.70548	+	0.295831i
$336$		0			0
$337$	−233.399	−	169.574i	−0.692577	−	0.503187i	0.184929	−	0.982752i	$-0.440794\pi$
$337$	−233.399	−	169.574i	−0.692577	−	0.503187i	−0.877506	+	0.479565i	$0.840794\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	263.478	−	362.647i	0.772663	−	1.06348i
$342$		0			0
$343$	−291.025			−0.848469
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−96.1049	−	31.2264i	−0.276959	−	0.0899895i	0.167244	−	0.985916i	$-0.446513\pi$
$347$	−96.1049	−	31.2264i	−0.276959	−	0.0899895i	−0.444203	+	0.895926i	$0.646513\pi$
$348$		0			0
$349$	305.586			0.875605			0.437803	−	0.899071i	$-0.355757\pi$
$349$	305.586			0.875605			0.437803	+	0.899071i	$0.355757\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−139.371	−	45.2845i	−0.394820	−	0.128285i	0.104877	−	0.994485i	$-0.466555\pi$
$353$	−139.371	−	45.2845i	−0.394820	−	0.128285i	−0.499697	+	0.866201i	$0.666555\pi$
$354$		0			0
$355$	127.613	−	259.807i	0.359472	−	0.731852i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	231.584	−	318.748i	0.645080	−	0.887877i	−0.353793	−	0.935324i	$-0.615108\pi$
$359$	231.584	−	318.748i	0.645080	−	0.887877i	0.998874	+	0.0474467i	$0.0151084\pi$
$360$		0			0
$361$	−276.558	+	200.931i	−0.766089	+	0.556596i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	89.6145	+	169.678i	0.245519	+	0.464870i
$366$		0			0
$367$	150.058	+	461.830i	0.408876	+	1.25839i	0.917615	+	0.397471i	$0.130112\pi$
$367$	150.058	+	461.830i	0.408876	+	1.25839i	−0.508739	+	0.860921i	$0.669888\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−145.891	−	47.4028i	−0.393237	−	0.127770i
$372$		0			0
$373$	−105.391	+	76.5707i	−0.282548	+	0.205283i	−0.720028	−	0.693945i	$-0.755871\pi$
$373$	−105.391	+	76.5707i	−0.282548	+	0.205283i	0.437480	+	0.899228i	$0.355871\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	249.081	+	342.831i	0.660693	+	0.909365i
$378$		0			0
$379$	133.822	−	411.861i	0.353092	−	1.08670i	−0.604016	−	0.796972i	$-0.706434\pi$
$379$	133.822	−	411.861i	0.353092	−	1.08670i	0.957108	−	0.289732i	$-0.0935662\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−199.473	+	64.8127i	−0.520817	+	0.169224i	−0.557616	−	0.830099i	$-0.688284\pi$
$383$	−199.473	+	64.8127i	−0.520817	+	0.169224i	0.0367989	+	0.999323i	$0.488284\pi$
$384$		0			0
$385$	−542.353	+	286.442i	−1.40871	+	0.744004i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	315.948	+	434.865i	0.812206	+	1.11791i	0.990979	+	0.134015i	$0.0427871\pi$
$389$	315.948	+	434.865i	0.812206	+	1.11791i	−0.178773	+	0.983890i	$0.557213\pi$
$390$		0			0
$391$	−95.1052	−	69.0980i	−0.243236	−	0.176721i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	42.9198	+	21.0814i	0.108658	+	0.0533706i
$396$		0			0
$397$	93.3072	−	287.170i	0.235031	−	0.723350i	−0.762087	−	0.647475i	$-0.775825\pi$
$397$	93.3072	−	287.170i	0.235031	−	0.723350i	0.997117	−	0.0758752i	$-0.0241751\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$			429.830i			1.07190i	0.844251	+	0.535948i	$0.180046\pi$
$401$			429.830i			1.07190i	−0.844251	+	0.535948i	$0.819954\pi$
$402$		0			0
$403$	−102.803	+	316.396i	−0.255095	+	0.785102i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	551.034i		−	1.35389i
$408$		0			0
$409$	−71.6936	−	52.0884i	−0.175290	−	0.127356i	0.496681	−	0.867933i	$-0.334552\pi$
$409$	−71.6936	−	52.0884i	−0.175290	−	0.127356i	−0.671971	+	0.740578i	$0.734552\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−605.399	+	833.260i	−1.46586	+	2.01758i
$414$		0			0
$415$	−4.46232	−	25.7254i	−0.0107526	−	0.0619890i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−434.535	+	141.189i	−1.03708	+	0.336966i	−0.777584	−	0.628779i	$-0.783555\pi$
$419$	−434.535	+	141.189i	−1.03708	+	0.336966i	−0.259492	+	0.965745i	$0.583555\pi$
$420$		0			0
$421$	−45.8357	+	141.068i	−0.108873	+	0.335078i	−0.990620	−	0.136646i	$-0.956368\pi$
$421$	−45.8357	+	141.068i	−0.108873	+	0.335078i	0.881747	+	0.471723i	$0.156368\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−187.425	+	5.50096i	−0.440999	+	0.0129434i
$426$		0			0
$427$	650.574	−	472.669i	1.52359	−	1.10695i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	150.076	−	48.7627i	0.348204	−	0.113138i	−0.129693	−	0.991554i	$-0.541399\pi$
$431$	150.076	−	48.7627i	0.348204	−	0.113138i	0.477897	+	0.878416i	$0.341399\pi$
$432$		0			0
$433$	201.805	+	621.091i	0.466062	+	1.43439i	0.857642	+	0.514247i	$0.171929\pi$
$433$	201.805	+	621.091i	0.466062	+	1.43439i	−0.391580	+	0.920144i	$0.628071\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−244.242	+	336.171i	−0.558907	+	0.769270i
$438$		0			0
$439$	285.709	−	207.580i	0.650818	−	0.472847i	−0.212732	−	0.977111i	$-0.568236\pi$
$439$	285.709	−	207.580i	0.650818	−	0.472847i	0.863550	+	0.504264i	$0.168236\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$			557.306i			1.25803i	0.777395	+	0.629013i	$0.216541\pi$
$443$			557.306i			1.25803i	−0.777395	+	0.629013i	$0.783459\pi$
$444$		0			0
$445$	15.2260	−	8.04153i	0.0342157	−	0.0180709i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	326.153i		−	0.726400i	−0.931711	−	0.363200i	$-0.881684\pi$
$449$		−	326.153i		−	0.726400i	0.931711	−	0.363200i	$-0.118316\pi$
$450$		0			0
$451$	−699.441			−1.55087
$452$		0			0
$453$		0			0
$454$		0			0
$455$	317.121	−	326.565i	0.696969	−	0.717725i
$456$		0			0
$457$	500.536			1.09526			0.547632	−	0.836719i	$-0.315529\pi$
$457$	500.536			1.09526			0.547632	+	0.836719i	$0.315529\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−286.888	−	394.868i	−0.622317	−	0.856546i	0.375202	−	0.926943i	$-0.377573\pi$
$461$	−286.888	−	394.868i	−0.622317	−	0.856546i	−0.997519	+	0.0703968i	$0.977573\pi$
$462$		0			0
$463$	655.472	+	476.229i	1.41571	+	1.02857i	0.992462	+	0.122556i	$0.0391092\pi$
$463$	655.472	+	476.229i	1.41571	+	1.02857i	0.423246	+	0.906015i	$0.360891\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−579.503	+	188.292i	−1.24090	+	0.403194i	−0.854653	−	0.519199i	$-0.826230\pi$
$467$	−579.503	+	188.292i	−1.24090	+	0.403194i	−0.386251	+	0.922394i	$0.626230\pi$
$468$		0			0
$469$	−399.268	−	1228.82i	−0.851318	−	2.62009i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−406.866	−	560.003i	−0.860181	−	1.18394i
$474$		0			0
$475$	19.4444	+	662.495i	0.0409356	+	1.39473i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	584.038	+	189.766i	1.21929	+	0.396170i	0.846822	−	0.531876i	$-0.178513\pi$
$479$	584.038	+	189.766i	1.21929	+	0.396170i	0.372465	+	0.928046i	$0.378513\pi$
$480$		0			0
$481$	126.375	+	388.941i	0.262733	+	0.808609i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	664.377	+	326.330i	1.36985	+	0.672845i
$486$		0			0
$487$	6.36309	+	4.62306i	0.0130659	+	0.00949293i	0.594299	−	0.804244i	$-0.297430\pi$
$487$	6.36309	+	4.62306i	0.0130659	+	0.00949293i	−0.581233	+	0.813737i	$0.697430\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−63.4138	+	87.2816i	−0.129152	+	0.177763i	−0.868696	−	0.495346i	$-0.835041\pi$
$491$	−63.4138	+	87.2816i	−0.129152	+	0.177763i	0.739544	+	0.673109i	$0.235041\pi$
$492$		0			0
$493$	388.941			0.788928
$494$		0			0
$495$		0			0
$496$		0			0
$497$	613.400	+	199.306i	1.23420	+	0.401017i
$498$		0			0
$499$	−452.531			−0.906877			−0.453438	−	0.891288i	$-0.649803\pi$
$499$	−452.531			−0.906877			−0.453438	+	0.891288i	$0.649803\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	157.514	+	51.1795i	0.313150	+	0.101748i	0.461375	−	0.887205i	$-0.347356\pi$
$503$	157.514	+	51.1795i	0.313150	+	0.101748i	−0.148226	+	0.988954i	$0.547356\pi$
$504$		0			0
$505$	746.688	+	107.060i	1.47859	+	0.211999i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	173.837	−	239.266i	0.341526	−	0.470070i	−0.603360	−	0.797469i	$-0.706172\pi$
$509$	173.837	−	239.266i	0.341526	−	0.470070i	0.944886	+	0.327398i	$0.106172\pi$
$510$		0			0
$511$	−345.908	+	251.317i	−0.676924	+	0.491814i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−438.003	−	215.139i	−0.850490	−	0.417745i
$516$		0			0
$517$	216.988	+	667.819i	0.419705	+	1.29172i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−86.1604	−	27.9952i	−0.165375	−	0.0537336i	0.225159	−	0.974322i	$-0.427710\pi$
$521$	−86.1604	−	27.9952i	−0.165375	−	0.0537336i	−0.390534	+	0.920588i	$0.627710\pi$
$522$		0			0
$523$	−21.0242	+	15.2750i	−0.0401993	+	0.0292065i	−0.607703	−	0.794164i	$-0.707909\pi$
$523$	−21.0242	+	15.2750i	−0.0401993	+	0.0292065i	0.567504	+	0.823371i	$0.307909\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	179.476	+	247.027i	0.340561	+	0.468742i
$528$		0			0
$529$	87.5549	−	269.466i	0.165510	−	0.509388i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	493.692	−	160.410i	0.926251	−	0.300957i
$534$		0			0
$535$	453.423	+	65.0114i	0.847519	+	0.121517i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−486.181	−	669.171i	−0.902006	−	1.24150i
$540$		0			0
$541$	−775.657	−	563.548i	−1.43375	−	1.04168i	−0.989304	−	0.145871i	$-0.953402\pi$
$541$	−775.657	−	563.548i	−1.43375	−	1.04168i	−0.444443	−	0.895807i	$-0.646598\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	455.869	−	469.445i	0.836457	−	0.861367i
$546$		0			0
$547$	48.6952	−	149.868i	0.0890223	−	0.273983i	−0.896627	−	0.442786i	$-0.853990\pi$
$547$	48.6952	−	149.868i	0.0890223	−	0.273983i	0.985650	+	0.168803i	$0.0539902\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		−	1374.80i		−	2.49510i
$552$		0			0
$553$	−32.9250	+	101.333i	−0.0595388	+	0.183242i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	556.266i		−	0.998683i	−0.866405	−	0.499341i	$-0.833575\pi$
$557$		−	556.266i		−	0.998683i	0.866405	−	0.499341i	$-0.166425\pi$
$558$		0			0
$559$	415.613	+	301.960i	0.743493	+	0.540180i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	567.941	−	781.704i	1.00878	−	1.38846i	0.0889937	−	0.996032i	$-0.471635\pi$
$563$	567.941	−	781.704i	1.00878	−	1.38846i	0.919782	−	0.392429i	$-0.128365\pi$
$564$		0			0
$565$	81.6340	+	79.2732i	0.144485	+	0.140306i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	584.311	−	189.854i	1.02691	−	0.333663i	0.253341	−	0.967377i	$-0.418470\pi$
$569$	584.311	−	189.854i	1.02691	−	0.333663i	0.773567	+	0.633714i	$0.218470\pi$
$570$		0			0
$571$	−152.231	+	468.520i	−0.266605	+	0.820525i	0.724715	+	0.689049i	$0.241972\pi$
$571$	−152.231	+	468.520i	−0.266605	+	0.820525i	−0.991319	+	0.131476i	$0.958028\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	131.967	+	368.953i	0.229509	+	0.641657i
$576$		0			0
$577$	59.2811	−	43.0702i	0.102740	−	0.0746451i	−0.535229	−	0.844707i	$-0.679775\pi$
$577$	59.2811	−	43.0702i	0.102740	−	0.0746451i	0.637969	+	0.770062i	$0.279775\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	55.3300	−	17.9778i	0.0952324	−	0.0309429i
$582$		0			0
$583$	−46.8481	−	144.184i	−0.0803570	−	0.247313i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	300.258	−	413.270i	0.511513	−	0.704038i	−0.472660	−	0.881245i	$-0.656706\pi$
$587$	300.258	−	413.270i	0.511513	−	0.704038i	0.984174	+	0.177207i	$0.0567062\pi$
$588$		0			0
$589$	873.174	−	634.398i	1.48247	−	1.07708i
$590$		0			0
$591$		0			0
$592$		0			0
$593$		−	496.166i		−	0.836705i	−0.908285	−	0.418353i	$-0.862608\pi$
$593$		−	496.166i		−	0.836705i	0.908285	−	0.418353i	$-0.137392\pi$
$594$		0			0
$595$	−71.4050	−	411.652i	−0.120008	−	0.691853i
$596$		0			0
$597$		0			0
$598$		0			0
$599$		−	316.573i		−	0.528503i	−0.964454	−	0.264251i	$-0.914875\pi$
$599$		−	316.573i		−	0.528503i	0.964454	−	0.264251i	$-0.0851248\pi$
$600$		0			0
$601$	1038.58			1.72808			0.864041	−	0.503421i	$-0.167925\pi$
$601$	1038.58			1.72808			0.864041	+	0.503421i	$0.167925\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−1.05115	−	0.516305i	−0.00173744	−	0.000853396i
$606$		0			0
$607$	154.496			0.254525			0.127262	−	0.991869i	$-0.459381\pi$
$607$	154.496			0.254525			0.127262	+	0.991869i	$0.459381\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−306.316	−	421.608i	−0.501336	−	0.690030i
$612$		0			0
$613$	−304.392	−	221.154i	−0.496562	−	0.360773i	0.311140	−	0.950364i	$-0.399289\pi$
$613$	−304.392	−	221.154i	−0.496562	−	0.360773i	−0.807702	+	0.589591i	$0.799289\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	77.2420	−	25.0974i	0.125190	−	0.0406766i	−0.245752	−	0.969333i	$-0.579035\pi$
$617$	77.2420	−	25.0974i	0.125190	−	0.0406766i	0.370942	+	0.928656i	$0.379035\pi$
$618$		0			0
$619$	201.030	+	618.708i	0.324766	+	0.999528i	0.971546	+	0.236851i	$0.0761153\pi$
$619$	201.030	+	618.708i	0.324766	+	0.999528i	−0.646780	+	0.762677i	$0.723885\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	22.5519	+	31.0400i	0.0361988	+	0.0498234i
$624$		0			0
$625$	526.311	+	337.078i	0.842098	+	0.539325i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	356.981	+	115.990i	0.567538	+	0.184404i
$630$		0			0
$631$	72.1860	+	222.166i	0.114399	+	0.352085i	0.991821	−	0.127634i	$-0.0407384\pi$
$631$	72.1860	+	222.166i	0.114399	+	0.352085i	−0.877422	+	0.479719i	$0.840738\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	187.786	+	355.557i	0.295726	+	0.559932i
$636$		0			0
$637$	496.634	+	360.825i	0.779644	+	0.566445i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	352.889	−	485.710i	0.550528	−	0.757737i	−0.439555	−	0.898215i	$-0.644864\pi$
$641$	352.889	−	485.710i	0.550528	−	0.757737i	0.990084	+	0.140478i	$0.0448640\pi$
$642$		0			0
$643$	−1076.63			−1.67438			−0.837191	−	0.546910i	$-0.815804\pi$
$643$	−1076.63			−1.67438			−0.837191	+	0.546910i	$0.815804\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	400.096	+	129.999i	0.618386	+	0.200926i	0.601424	−	0.798930i	$-0.294600\pi$
$647$	400.096	+	129.999i	0.618386	+	0.200926i	0.0169627	+	0.999856i	$0.494600\pi$
$648$		0			0
$649$	−1017.91			−1.56844
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−960.076	−	311.947i	−1.47025	−	0.477714i	−0.539069	−	0.842262i	$-0.681224\pi$
$653$	−960.076	−	311.947i	−1.47025	−	0.477714i	−0.931185	+	0.364547i	$0.881224\pi$
$654$		0			0
$655$	14.4102	+	83.0753i	0.0220003	+	0.126832i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	7.09260	−	9.76213i	0.0107627	−	0.0148135i	−0.803602	−	0.595167i	$-0.797086\pi$
$659$	7.09260	−	9.76213i	0.0107627	−	0.0148135i	0.814364	+	0.580354i	$0.197086\pi$
$660$		0			0
$661$	160.528	−	116.630i	0.242856	−	0.176445i	−0.459699	−	0.888075i	$-0.652043\pi$
$661$	160.528	−	116.630i	0.242856	−	0.176445i	0.702555	+	0.711630i	$0.252043\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−1455.08	+	252.397i	−2.18809	+	0.379545i
$666$		0			0
$667$	−251.169	−	773.019i	−0.376565	−	1.15895i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	755.846	+	245.589i	1.12645	+	0.366005i
$672$		0			0
$673$	−1018.20	+	739.768i	−1.51293	+	1.09921i	−0.548078	+	0.836427i	$0.684640\pi$
$673$	−1018.20	+	739.768i	−1.51293	+	1.09921i	−0.964855	+	0.262783i	$0.915360\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−457.929	−	630.285i	−0.676409	−	0.930997i	0.323475	−	0.946237i	$-0.395149\pi$
$677$	−457.929	−	630.285i	−0.676409	−	0.930997i	−0.999884	+	0.0152400i	$0.995149\pi$
$678$		0			0
$679$	−509.662	+	1568.58i	−0.750607	+	2.31013i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	1.72599	−	0.560810i	0.00252708	−	0.000821098i	−0.307753	−	0.951466i	$-0.599577\pi$
$683$	1.72599	−	0.560810i	0.00252708	−	0.000821098i	0.310280	+	0.950645i	$0.399577\pi$
$684$		0			0
$685$	233.579	+	226.824i	0.340991	+	0.331130i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	66.1344	+	91.0262i	0.0959860	+	0.132113i
$690$		0			0
$691$	−244.625	−	177.730i	−0.354015	−	0.257207i	0.396536	−	0.918019i	$-0.370212\pi$
$691$	−244.625	−	177.730i	−0.354015	−	0.257207i	−0.750552	+	0.660812i	$0.770212\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	127.693	+	241.777i	0.183732	+	0.347880i
$696$		0			0
$697$	147.229	−	453.125i	0.211233	−	0.650108i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			901.231i			1.28564i	0.766019	+	0.642818i	$0.222235\pi$
$701$			901.231i			1.28564i	−0.766019	+	0.642818i	$0.777765\pi$
$702$		0			0
$703$	409.994	−	1261.83i	0.583207	−	1.79493i
$704$		0			0
$705$		0			0
$706$		0			0
$707$			1680.79i			2.37735i
$708$		0			0
$709$	218.539	+	158.778i	0.308235	+	0.223946i	0.731139	−	0.682229i	$-0.238989\pi$
$709$	218.539	+	158.778i	0.308235	+	0.223946i	−0.422904	+	0.906175i	$0.638989\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	375.064	−	516.231i	0.526036	−	0.724026i
$714$		0			0
$715$	445.323	+	63.8501i	0.622830	+	0.0893009i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	569.610	−	185.078i	0.792226	−	0.257410i	0.115174	−	0.993345i	$-0.463257\pi$
$719$	569.610	−	185.078i	0.792226	−	0.257410i	0.677052	+	0.735936i	$0.263257\pi$
$720$		0			0
$721$	336.004	−	1034.11i	0.466025	−	1.43428i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−1070.74	−	730.927i	−1.47689	−	1.00817i
$726$		0			0
$727$	201.778	−	146.600i	0.277549	−	0.201651i	−0.440299	−	0.897851i	$-0.645127\pi$
$727$	201.778	−	146.600i	0.277549	−	0.201651i	0.717848	+	0.696200i	$0.245127\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	448.435	−	145.705i	0.613455	−	0.199323i
$732$		0			0
$733$	388.405	+	1195.39i	0.529884	+	1.63082i	0.754450	+	0.656357i	$0.227904\pi$
$733$	388.405	+	1195.39i	0.529884	+	1.63082i	−0.224566	+	0.974459i	$0.572096\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	750.567	−	1033.07i	1.01841	−	1.40172i
$738$		0			0
$739$	208.791	−	151.695i	0.282531	−	0.205271i	−0.437489	−	0.899224i	$-0.644132\pi$
$739$	208.791	−	151.695i	0.282531	−	0.205271i	0.720021	+	0.693953i	$0.244132\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$			433.800i			0.583850i	0.956441	+	0.291925i	$0.0942957\pi$
$743$			433.800i			0.583850i	−0.956441	+	0.291925i	$0.905704\pi$
$744$		0			0
$745$	1181.05	+	169.338i	1.58530	+	0.227299i
$746$		0			0
$747$		0			0
$748$		0			0
$749$			1020.65i			1.36268i
$750$		0			0
$751$	−176.086			−0.234469			−0.117235	−	0.993104i	$-0.537403\pi$
$751$	−176.086			−0.234469			−0.117235	+	0.993104i	$0.537403\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−33.9252	+	236.612i	−0.0449341	+	0.313393i
$756$		0			0
$757$	−1321.71			−1.74598			−0.872992	−	0.487735i	$-0.837823\pi$
$757$	−1321.71			−1.74598			−0.872992	+	0.487735i	$0.837823\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	638.172	+	878.369i	0.838597	+	1.15423i	0.986261	+	0.165192i	$0.0528244\pi$
$761$	638.172	+	878.369i	0.838597	+	1.15423i	−0.147664	+	0.989038i	$0.547176\pi$
$762$		0			0
$763$	1179.59	+	857.026i	1.54600	+	1.12323i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	718.483	−	233.449i	0.936744	−	0.304367i
$768$		0			0
$769$	−38.7659	−	119.309i	−0.0504108	−	0.155149i	0.922682	−	0.385562i	$-0.125992\pi$
$769$	−38.7659	−	119.309i	−0.0504108	−	0.155149i	−0.973093	+	0.230413i	$0.925992\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−495.242	−	681.643i	−0.640676	−	0.881815i	0.357976	−	0.933731i	$-0.383467\pi$
$773$	−495.242	−	681.643i	−0.640676	−	0.881815i	−0.998651	+	0.0519162i	$0.983467\pi$
$774$		0			0
$775$	−29.8592	−	1017.34i	−0.0385280	−	1.31270i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−1601.67	−	520.416i	−2.05606	−	0.668056i
$780$		0			0
$781$	196.974	+	606.222i	0.252207	+	0.776213i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−118.324	+	825.253i	−0.150731	+	1.05128i
$786$		0			0
$787$	297.026	+	215.802i	0.377416	+	0.274209i	0.760279	−	0.649596i	$-0.225062\pi$
$787$	297.026	+	215.802i	0.377416	+	0.274209i	−0.382863	+	0.923805i	$0.625062\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−149.032	+	205.125i	−0.188410	+	0.259324i
$792$		0			0
$793$	−589.829			−0.743794
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−526.700	−	171.135i	−0.660853	−	0.214724i	−0.0406597	−	0.999173i	$-0.512946\pi$
$797$	−526.700	−	171.135i	−0.660853	−	0.214724i	−0.620194	+	0.784449i	$0.712946\pi$
$798$		0			0
$799$	−478.314			−0.598641
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−401.882	−	130.579i	−0.500475	−	0.162614i
$804$		0			0
$805$	−772.045	+	407.752i	−0.959062	+	0.506524i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	893.062	−	1229.19i	1.10391	−	1.51940i	0.273809	−	0.961784i	$-0.411716\pi$
$809$	893.062	−	1229.19i	1.10391	−	1.51940i	0.830099	−	0.557616i	$-0.188284\pi$
$810$		0			0
$811$	1132.53	−	822.833i	1.39646	−	1.01459i	0.401344	−	0.915928i	$-0.368543\pi$
$811$	1132.53	−	822.833i	1.39646	−	1.01459i	0.995121	−	0.0986632i	$-0.0314567\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	802.066	−	825.952i	0.984129	−	1.01344i
$816$		0			0
$817$	−515.029	−	1585.10i	−0.630391	−	1.94014i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−1411.01	−	458.466i	−1.71865	−	0.558424i	−0.726916	−	0.686726i	$-0.759047\pi$
$821$	−1411.01	−	458.466i	−1.71865	−	0.558424i	−0.991735	+	0.128303i	$0.959047\pi$
$822$		0			0
$823$	476.529	−	346.218i	0.579014	−	0.420678i	−0.259355	−	0.965782i	$-0.583510\pi$
$823$	476.529	−	346.218i	0.579014	−	0.420678i	0.838368	+	0.545104i	$0.183510\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	482.490	+	664.091i	0.583422	+	0.803012i	0.994065	−	0.108784i	$-0.0346958\pi$
$827$	482.490	+	664.091i	0.583422	+	0.803012i	−0.410643	+	0.911796i	$0.634696\pi$
$828$		0			0
$829$	268.526	−	826.437i	0.323915	−	0.996908i	−0.648013	−	0.761629i	$-0.724400\pi$
$829$	268.526	−	826.437i	0.323915	−	0.996908i	0.971928	−	0.235279i	$-0.0756002\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	535.854	−	174.110i	0.643283	−	0.209015i
$834$		0			0
$835$	147.427	+	849.924i	0.176560	+	1.01787i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−215.496	−	296.605i	−0.256849	−	0.353523i	0.661046	−	0.750345i	$-0.270113\pi$
$839$	−215.496	−	296.605i	−0.256849	−	0.353523i	−0.917895	+	0.396823i	$0.870113\pi$
$840$		0			0
$841$	1495.22	+	1086.34i	1.77790	+	1.29172i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	503.598	−	87.3539i	0.595974	−	0.103377i
$846$		0			0
$847$	0.806366	−	2.48174i	0.000952026	−	0.00293003i
$848$		0			0
$849$		0			0
$850$		0			0
$851$		−	784.402i		−	0.921741i
$852$		0			0
$853$	123.708	−	380.733i	0.145026	−	0.446345i	−0.851988	−	0.523561i	$-0.824603\pi$
$853$	123.708	−	380.733i	0.145026	−	0.446345i	0.997014	+	0.0772159i	$0.0246031\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$			801.458i			0.935190i	0.883943	+	0.467595i	$0.154879\pi$
$857$			801.458i			0.935190i	−0.883943	+	0.467595i	$0.845121\pi$
$858$		0			0
$859$	732.884	+	532.472i	0.853183	+	0.619874i	0.926022	−	0.377470i	$-0.123206\pi$
$859$	732.884	+	532.472i	0.853183	+	0.619874i	−0.0728386	+	0.997344i	$0.523206\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	167.534	−	230.591i	0.194130	−	0.267197i	−0.700845	−	0.713314i	$-0.747194\pi$
$863$	167.534	−	230.591i	0.194130	−	0.267197i	0.894975	+	0.446117i	$0.147194\pi$
$864$		0			0
$865$	−620.240	+	327.577i	−0.717041	+	0.378702i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−100.147	+	32.5397i	−0.115244	+	0.0374450i
$870$		0			0
$871$	−292.854	+	901.313i	−0.336228	+	1.03480i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−577.031	+	1267.45i	−0.659464	+	1.44852i
$876$		0			0
$877$	−222.757	+	161.842i	−0.253999	+	0.184541i	−0.707497	−	0.706716i	$-0.750176\pi$
$877$	−222.757	+	161.842i	−0.253999	+	0.184541i	0.453498	+	0.891257i	$0.350176\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	530.774	−	172.459i	0.602467	−	0.195753i	0.00812669	−	0.999967i	$-0.497413\pi$
$881$	530.774	−	172.459i	0.602467	−	0.195753i	0.594340	+	0.804214i	$0.297413\pi$
$882$		0			0
$883$	−245.157	−	754.515i	−0.277641	−	0.854491i	−0.988509	−	0.151165i	$-0.951698\pi$
$883$	−245.157	−	754.515i	−0.277641	−	0.854491i	0.710868	−	0.703326i	$-0.248302\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	324.484	−	446.613i	0.365821	−	0.503510i	−0.585938	−	0.810356i	$-0.699274\pi$
$887$	324.484	−	446.613i	0.365821	−	0.503510i	0.951759	+	0.306846i	$0.0992737\pi$
$888$		0			0
$889$	−724.846	+	526.632i	−0.815350	+	0.592387i
$890$		0			0
$891$		0			0
$892$		0			0
$893$			1690.71i			1.89329i
$894$		0			0
$895$	−708.855	+	1443.16i	−0.792017	+	1.61247i
$896$		0			0
$897$		0			0
$898$		0			0
$899$			2111.17i			2.34836i
$900$		0			0
$901$	103.269			0.114616
$902$		0			0
$903$		0			0
$904$		0			0
$905$	853.877	−	148.113i	0.943511	−	0.163661i
$906$		0			0
$907$	142.171			0.156749			0.0783744	−	0.996924i	$-0.475027\pi$
$907$	142.171			0.156749			0.0783744	+	0.996924i	$0.475027\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	322.232	+	443.515i	0.353713	+	0.486844i	0.948384	−	0.317126i	$-0.102718\pi$
$911$	322.232	+	443.515i	0.353713	+	0.486844i	−0.594671	+	0.803969i	$0.702718\pi$
$912$		0			0
$913$	46.5158	+	33.7957i	0.0509483	+	0.0370161i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−178.677	+	58.0558i	−0.194850	+	0.0633106i
$918$		0			0
$919$	129.403	+	398.260i	0.140808	+	0.433363i	0.996448	−	0.0842085i	$-0.0268362\pi$
$919$	129.403	+	398.260i	0.140808	+	0.433363i	−0.855640	+	0.517571i	$0.826836\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−278.063	−	382.721i	−0.301260	−	0.414649i
$924$		0			0
$925$	−764.780	−	990.183i	−0.826789	−	1.07047i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−944.447	−	306.869i	−1.01663	−	0.330322i	−0.247137	−	0.968981i	$-0.579490\pi$
$929$	−944.447	−	306.869i	−1.01663	−	0.330322i	−0.769490	+	0.638658i	$0.779490\pi$
$930$		0			0
$931$	−615.430	−	1894.10i	−0.661042	−	2.03448i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	287.657	−	296.224i	0.307655	−	0.316817i
$936$		0			0
$937$	151.843	+	110.321i	0.162053	+	0.117738i	0.665856	−	0.746080i	$-0.268066\pi$
$937$	151.843	+	110.321i	0.162053	+	0.117738i	−0.503803	+	0.863818i	$0.668066\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−542.934	+	747.284i	−0.576976	+	0.794139i	−0.993360	−	0.115050i	$-0.963297\pi$
$941$	−542.934	+	747.284i	−0.576976	+	0.794139i	0.416384	+	0.909189i	$0.363297\pi$
$942$		0			0
$943$	−995.660			−1.05584
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−1018.51	−	330.936i	−1.07552	−	0.349457i	−0.282883	−	0.959154i	$-0.591291\pi$
$947$	−1018.51	−	330.936i	−1.07552	−	0.349457i	−0.792634	+	0.609698i	$0.791291\pi$
$948$		0			0
$949$	313.611			0.330464
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−1302.46	−	423.194i	−1.36669	−	0.444065i	−0.468421	−	0.883505i	$-0.655177\pi$
$953$	−1302.46	−	423.194i	−1.36669	−	0.444065i	−0.898272	+	0.439440i	$0.855177\pi$
$954$		0			0
$955$	−276.271	−	268.281i	−0.289289	−	0.280923i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−426.425	+	586.924i	−0.444656	+	0.612017i
$960$		0			0
$961$	−563.398	+	409.332i	−0.586262	+	0.425944i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	185.645	−	1294.78i	0.192378	−	1.34174i
$966$		0			0
$967$	206.867	+	636.670i	0.213926	+	0.658397i	0.999228	+	0.0392842i	$0.0125078\pi$
$967$	206.867	+	636.670i	0.213926	+	0.658397i	−0.785302	+	0.619113i	$0.787492\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	923.133	+	299.944i	0.950704	+	0.308902i	0.743002	−	0.669290i	$-0.233401\pi$
$971$	923.133	+	299.944i	0.950704	+	0.308902i	0.207702	+	0.978192i	$0.433401\pi$
$972$		0			0
$973$	−492.892	+	358.107i	−0.506569	+	0.368044i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−485.079	−	667.654i	−0.496499	−	0.683372i	0.485071	−	0.874475i	$-0.338794\pi$
$977$	−485.079	−	667.654i	−0.496499	−	0.683372i	−0.981570	+	0.191103i	$0.938794\pi$
$978$		0			0
$979$	−11.7175	+	36.0627i	−0.0119688	+	0.0368363i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	1259.12	−	409.111i	1.28089	−	0.416187i	0.411997	−	0.911185i	$-0.364832\pi$
$983$	1259.12	−	409.111i	1.28089	−	0.416187i	0.868894	+	0.494999i	$0.164832\pi$
$984$		0			0
$985$	−59.8641	+	121.878i	−0.0607757	+	0.123734i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−579.177	−	797.169i	−0.585619	−	0.806035i
$990$		0			0
$991$	−1532.66	−	1113.55i	−1.54658	−	1.12366i	−0.946033	−	0.324071i	$-0.894948\pi$
$991$	−1532.66	−	1113.55i	−1.54658	−	1.12366i	−0.600550	−	0.799587i	$-0.705052\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−54.0237	+	376.789i	−0.0542952	+	0.378682i
$996$		0			0
$997$	−450.629	+	1386.89i	−0.451985	+	1.39107i	0.422654	+	0.906291i	$0.361099\pi$
$997$	−450.629	+	1386.89i	−0.451985	+	1.39107i	−0.874639	+	0.484775i	$0.838901\pi$
$998$		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.161.10	✓	80
3.2	odd	2	inner	900.3.ba.a.161.11	yes	80
25.16	even	5	inner	900.3.ba.a.341.11	yes	80
75.41	odd	10	inner	900.3.ba.a.341.10	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
900.3.ba.a.161.10	✓	80	1.1	even	1	trivial
900.3.ba.a.161.11	yes	80	3.2	odd	2	inner
900.3.ba.a.341.10	yes	80	75.41	odd	10	inner
900.3.ba.a.341.11	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)

\(f(q)\)	\(=\)	\(q+(-0.709639 + 4.94939i) q^{5} -11.1410 q^{7} +O(q^{10})\)	\(q+(-0.709639 + 4.94939i) q^{5} -11.1410 q^{7} +(-6.47189 - 8.90780i) q^{11} +(6.61103 + 4.80319i) q^{13} +(7.13313 - 2.31769i) q^{17} +(-8.19242 - 25.2137i) q^{19} +(-9.21280 - 12.6803i) q^{23} +(-23.9928 - 7.02456i) q^{25} +(49.3193 + 16.0248i) q^{29} +(12.5804 + 38.7186i) q^{31} +(7.90609 - 55.1411i) q^{35} +(40.4877 + 29.4161i) q^{37} +(37.3385 - 51.3920i) q^{41} +62.8666 q^{43} +(-60.6521 - 19.7071i) q^{47} +75.1220 q^{49} +(13.0949 + 4.25480i) q^{53} +(48.6808 - 25.7106i) q^{55} +(54.3397 - 74.7922i) q^{59} +(-58.3945 + 42.4261i) q^{61} +(-28.4643 + 29.3120i) q^{65} +(35.8377 + 110.297i) q^{67} +(-55.0578 - 17.8894i) q^{71} +(31.0482 - 22.5579i) q^{73} +(72.1034 + 99.2418i) q^{77} +(2.95530 - 9.09546i) q^{79} +(-4.96634 + 1.61366i) q^{83} +(6.40921 + 36.9493i) q^{85} +(-2.02422 - 2.78610i) q^{89} +(-73.6535 - 53.5124i) q^{91} +(130.606 - 22.6548i) q^{95} +(45.7465 - 140.793i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 16 q^{7}+O(q^{10}) \) 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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