LMFDB - Embedded newform 900.3.ba.a.161.3

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			161.3
Character	$\chi$	$=$	900.161
Dual form			900.3.ba.a.341.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.19489 + 2.72083i) q^{5} +5.95985 q^{7} +O(q^{10})$	$q+(-4.19489 + 2.72083i) q^{5} +5.95985 q^{7} +(3.13762 + 4.31857i) q^{11} +(-18.6558 - 13.5542i) q^{13} +(17.4015 - 5.65410i) q^{17} +(-8.22996 - 25.3292i) q^{19} +(13.1397 + 18.0852i) q^{23} +(10.1942 - 22.8271i) q^{25} +(4.93210 + 1.60254i) q^{29} +(10.9715 + 33.7667i) q^{31} +(-25.0009 + 16.2157i) q^{35} +(21.7516 + 15.8035i) q^{37} +(23.6617 - 32.5675i) q^{41} +6.06656 q^{43} +(59.7503 + 19.4141i) q^{47} -13.4802 q^{49} +(-43.5239 - 14.1418i) q^{53} +(-24.9121 - 9.57898i) q^{55} +(0.839566 - 1.15556i) q^{59} +(69.8175 - 50.7254i) q^{61} +(115.138 + 6.09931i) q^{65} +(7.41805 + 22.8304i) q^{67} +(78.7513 + 25.5878i) q^{71} +(84.3867 - 61.3105i) q^{73} +(18.6997 + 25.7380i) q^{77} +(33.0948 - 101.855i) q^{79} +(89.7031 - 29.1463i) q^{83} +(-57.6137 + 71.0649i) q^{85} +(45.6555 + 62.8394i) q^{89} +(-111.186 - 80.7812i) q^{91} +(103.440 + 83.8609i) q^{95} +(25.2304 - 77.6511i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−4.19489	+	2.72083i	−0.838978	+	0.544165i
$5$	−4.19489	+	2.72083i	−0.838978	+	0.544165i
$6$		0			0
$7$	5.95985			0.851407			0.425703	−	0.904863i	$-0.360027\pi$
$7$	5.95985			0.851407			0.425703	+	0.904863i	$0.360027\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	3.13762	+	4.31857i	0.285238	+	0.392597i	0.927460	−	0.373922i	$-0.121987\pi$
$11$	3.13762	+	4.31857i	0.285238	+	0.392597i	−0.642222	+	0.766519i	$0.721987\pi$
$12$		0			0
$13$	−18.6558	−	13.5542i	−1.43506	−	1.04263i	−0.989046	−	0.147609i	$-0.952842\pi$
$13$	−18.6558	−	13.5542i	−1.43506	−	1.04263i	−0.446017	−	0.895025i	$-0.647158\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	17.4015	−	5.65410i	1.02362	−	0.332594i	0.251355	−	0.967895i	$-0.419124\pi$
$17$	17.4015	−	5.65410i	1.02362	−	0.332594i	0.772265	+	0.635301i	$0.219124\pi$
$18$		0			0
$19$	−8.22996	−	25.3292i	−0.433156	−	1.33312i	−0.894965	−	0.446137i	$-0.852799\pi$
$19$	−8.22996	−	25.3292i	−0.433156	−	1.33312i	0.461809	−	0.886979i	$-0.347201\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	13.1397	+	18.0852i	0.571291	+	0.786315i	0.992707	−	0.120553i	$-0.0384667\pi$
$23$	13.1397	+	18.0852i	0.571291	+	0.786315i	−0.421416	+	0.906868i	$0.638467\pi$
$24$		0			0
$25$	10.1942	−	22.8271i	0.407768	−	0.913086i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	4.93210	+	1.60254i	0.170072	+	0.0552599i	0.392816	−	0.919617i	$-0.371501\pi$
$29$	4.93210	+	1.60254i	0.170072	+	0.0552599i	−0.222743	+	0.974877i	$0.571501\pi$
$30$		0			0
$31$	10.9715	+	33.7667i	0.353918	+	1.08925i	0.956634	+	0.291292i	$0.0940851\pi$
$31$	10.9715	+	33.7667i	0.353918	+	1.08925i	−0.602716	+	0.797956i	$0.705915\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−25.0009	+	16.2157i	−0.714311	+	0.463306i
$36$		0			0
$37$	21.7516	+	15.8035i	0.587882	+	0.427121i	0.841557	−	0.540168i	$-0.181639\pi$
$37$	21.7516	+	15.8035i	0.587882	+	0.427121i	−0.253675	+	0.967290i	$0.581639\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	23.6617	−	32.5675i	0.577114	−	0.794329i	−0.416261	−	0.909245i	$-0.636660\pi$
$41$	23.6617	−	32.5675i	0.577114	−	0.794329i	0.993375	+	0.114916i	$0.0366598\pi$
$42$		0			0
$43$	6.06656			0.141083			0.0705414	−	0.997509i	$-0.477527\pi$
$43$	6.06656			0.141083			0.0705414	+	0.997509i	$0.477527\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	59.7503	+	19.4141i	1.27128	+	0.413065i	0.865502	−	0.500905i	$-0.166999\pi$
$47$	59.7503	+	19.4141i	1.27128	+	0.413065i	0.405782	+	0.913970i	$0.366999\pi$
$48$		0			0
$49$	−13.4802			−0.275107
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−43.5239	−	14.1418i	−0.821205	−	0.266826i	−0.131869	−	0.991267i	$-0.542098\pi$
$53$	−43.5239	−	14.1418i	−0.821205	−	0.266826i	−0.689336	+	0.724441i	$0.742098\pi$
$54$		0			0
$55$	−24.9121	−	9.57898i	−0.452946	−	0.174163i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	0.839566	−	1.15556i	0.0142299	−	0.0195858i	−0.801843	−	0.597535i	$-0.796147\pi$
$59$	0.839566	−	1.15556i	0.0142299	−	0.0195858i	0.816073	+	0.577949i	$0.196147\pi$
$60$		0			0
$61$	69.8175	−	50.7254i	1.14455	−	0.831564i	0.156803	−	0.987630i	$-0.449881\pi$
$61$	69.8175	−	50.7254i	1.14455	−	0.831564i	0.987747	+	0.156066i	$0.0498813\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	115.138	+	6.09931i	1.77135	+	0.0938356i
$66$		0			0
$67$	7.41805	+	22.8304i	0.110717	+	0.340753i	0.991030	−	0.133642i	$-0.0426671\pi$
$67$	7.41805	+	22.8304i	0.110717	+	0.340753i	−0.880312	+	0.474394i	$0.842667\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	78.7513	+	25.5878i	1.10917	+	0.360392i	0.805626	−	0.592424i	$-0.201829\pi$
$71$	78.7513	+	25.5878i	1.10917	+	0.360392i	0.303547	+	0.952817i	$0.401829\pi$
$72$		0			0
$73$	84.3867	−	61.3105i	1.15598	−	0.839870i	0.166717	−	0.986005i	$-0.446683\pi$
$73$	84.3867	−	61.3105i	1.15598	−	0.839870i	0.989265	+	0.146135i	$0.0466833\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	18.6997	+	25.7380i	0.242854	+	0.334260i
$78$		0			0
$79$	33.0948	−	101.855i	0.418921	−	1.28931i	−0.489775	−	0.871849i	$-0.662921\pi$
$79$	33.0948	−	101.855i	0.418921	−	1.28931i	0.908696	−	0.417458i	$-0.137079\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	89.7031	−	29.1463i	1.08076	−	0.351160i	0.286091	−	0.958202i	$-0.407644\pi$
$83$	89.7031	−	29.1463i	1.08076	−	0.351160i	0.794670	+	0.607042i	$0.207644\pi$
$84$		0			0
$85$	−57.6137	+	71.0649i	−0.677808	+	0.836058i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	45.6555	+	62.8394i	0.512984	+	0.706061i	0.984419	−	0.175839i	$-0.0562639\pi$
$89$	45.6555	+	62.8394i	0.512984	+	0.706061i	−0.471435	+	0.881901i	$0.656264\pi$
$90$		0			0
$91$	−111.186	−	80.7812i	−1.22182	−	0.887705i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	103.440	+	83.8609i	1.08884	+	0.882747i
$96$		0			0
$97$	25.2304	−	77.6511i	0.260107	−	0.800526i	−0.732674	−	0.680580i	$-0.761728\pi$
$97$	25.2304	−	77.6511i	0.260107	−	0.800526i	0.992780	−	0.119946i	$-0.0382722\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$		−	27.1385i		−	0.268698i	−0.990934	−	0.134349i	$-0.957106\pi$
$101$		−	27.1385i		−	0.268698i	0.990934	−	0.134349i	$-0.0428943\pi$
$102$		0			0
$103$	12.1723	−	37.4624i	0.118177	−	0.363713i	−0.874419	−	0.485171i	$-0.838757\pi$
$103$	12.1723	−	37.4624i	0.118177	−	0.363713i	0.992596	+	0.121459i	$0.0387572\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	132.970i		−	1.24271i	−0.783527	−	0.621357i	$-0.786582\pi$
$107$		−	132.970i		−	1.24271i	0.783527	−	0.621357i	$-0.213418\pi$
$108$		0			0
$109$	140.955	+	102.410i	1.29317	+	0.939541i	0.999864	−	0.0164784i	$-0.00524549\pi$
$109$	140.955	+	102.410i	1.29317	+	0.939541i	0.293303	+	0.956019i	$0.405245\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−90.4236	+	124.457i	−0.800208	+	1.10139i	0.192553	+	0.981287i	$0.438323\pi$
$113$	−90.4236	+	124.457i	−0.800208	+	1.10139i	−0.992761	+	0.120106i	$0.961677\pi$
$114$		0			0
$115$	−104.326	−	40.1147i	−0.907186	−	0.348824i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	103.711	−	33.6976i	0.871517	−	0.283173i
$120$		0			0
$121$	28.5857	−	87.9778i	0.236246	−	0.727089i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	19.3451	+	123.494i	0.154761	+	0.987952i
$126$		0			0
$127$	−79.0775	+	57.4532i	−0.622658	+	0.452387i	−0.853849	−	0.520521i	$-0.825738\pi$
$127$	−79.0775	+	57.4532i	−0.622658	+	0.452387i	0.231191	+	0.972908i	$0.425738\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−232.600	+	75.5762i	−1.77557	+	0.576918i	−0.998614	−	0.0526372i	$-0.983237\pi$
$131$	−232.600	+	75.5762i	−1.77557	+	0.576918i	−0.776956	+	0.629555i	$0.783237\pi$
$132$		0			0
$133$	−49.0493	−	150.958i	−0.368792	−	1.13502i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−110.057	+	151.480i	−0.803335	+	1.10570i	0.188982	+	0.981980i	$0.439481\pi$
$137$	−110.057	+	151.480i	−0.803335	+	1.10570i	−0.992318	+	0.123716i	$0.960519\pi$
$138$		0			0
$139$	23.7294	−	17.2404i	0.170715	−	0.124032i	−0.499147	−	0.866517i	$-0.666353\pi$
$139$	23.7294	−	17.2404i	0.170715	−	0.124032i	0.669862	+	0.742485i	$0.266353\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		−	123.094i		−	0.860800i
$144$		0			0
$145$	−25.0498	+	6.69693i	−0.172758	+	0.0461857i
$146$		0			0
$147$		0			0
$148$		0			0
$149$		−	194.177i		−	1.30320i	−0.758561	−	0.651602i	$-0.774097\pi$
$149$		−	194.177i		−	1.30320i	0.758561	−	0.651602i	$-0.225903\pi$
$150$		0			0
$151$	59.3545			0.393076			0.196538	−	0.980496i	$-0.437030\pi$
$151$	59.3545			0.393076			0.196538	+	0.980496i	$0.437030\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−137.897	−	111.796i	−0.889660	−	0.721265i
$156$		0			0
$157$	−42.6457			−0.271629			−0.135814	−	0.990734i	$-0.543365\pi$
$157$	−42.6457			−0.271629			−0.135814	+	0.990734i	$0.543365\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	78.3106	+	107.785i	0.486401	+	0.669474i
$162$		0			0
$163$	−61.5916	−	44.7489i	−0.377862	−	0.274533i	0.382601	−	0.923914i	$-0.375028\pi$
$163$	−61.5916	−	44.7489i	−0.377862	−	0.274533i	−0.760464	+	0.649380i	$0.775028\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	234.832	−	76.3017i	1.40618	−	0.456896i	0.494998	−	0.868894i	$-0.335169\pi$
$167$	234.832	−	76.3017i	1.40618	−	0.456896i	0.911185	+	0.411998i	$0.135169\pi$
$168$		0			0
$169$	112.098	+	345.002i	0.663302	+	2.04143i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	82.5270	+	113.589i	0.477035	+	0.656582i	0.977932	−	0.208925i	$-0.0669965\pi$
$173$	82.5270	+	113.589i	0.477035	+	0.656582i	−0.500897	+	0.865507i	$0.666996\pi$
$174$		0			0
$175$	60.7559	−	136.046i	0.347176	−	0.777407i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	0.421706	+	0.137021i	0.00235590	+	0.000765478i	0.310195	−	0.950673i	$-0.399606\pi$
$179$	0.421706	+	0.137021i	0.00235590	+	0.000765478i	−0.307839	+	0.951439i	$0.599606\pi$
$180$		0			0
$181$	23.7864	+	73.2071i	0.131417	+	0.404459i	0.995015	−	0.0997205i	$-0.0317949\pi$
$181$	23.7864	+	73.2071i	0.131417	+	0.404459i	−0.863599	+	0.504180i	$0.831795\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−134.244	−	7.11146i	−0.725645	−	0.0384403i
$186$		0			0
$187$	79.0171	+	57.4093i	0.422551	+	0.307002i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	119.156	−	164.004i	0.623854	−	0.858662i	−0.373772	−	0.927521i	$-0.621936\pi$
$191$	119.156	−	164.004i	0.623854	−	0.858662i	0.997626	+	0.0688586i	$0.0219357\pi$
$192$		0			0
$193$	−293.183			−1.51908			−0.759541	−	0.650459i	$-0.774577\pi$
$193$	−293.183			−1.51908			−0.759541	+	0.650459i	$0.774577\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	5.55566	+	1.80514i	0.0282013	+	0.00916316i	0.323084	−	0.946370i	$-0.395280\pi$
$197$	5.55566	+	1.80514i	0.0282013	+	0.00916316i	−0.294882	+	0.955534i	$0.595280\pi$
$198$		0			0
$199$	11.4223			0.0573983			0.0286991	−	0.999588i	$-0.490864\pi$
$199$	11.4223			0.0573983			0.0286991	+	0.999588i	$0.490864\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	29.3946	+	9.55087i	0.144801	+	0.0470486i
$204$		0			0
$205$	−10.6476	+	200.996i	−0.0519395	+	0.980470i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	83.5634	−	115.015i	0.399825	−	0.550312i
$210$		0			0
$211$	336.606	−	244.558i	1.59529	−	1.15905i	0.699435	−	0.714697i	$-0.253435\pi$
$211$	336.606	−	244.558i	1.59529	−	1.15905i	0.895854	−	0.444348i	$-0.146565\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−25.4485	+	16.5061i	−0.118365	+	0.0767724i
$216$		0			0
$217$	65.3882	+	201.244i	0.301328	+	0.927393i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−401.277	−	130.383i	−1.81573	−	0.589967i
$222$		0			0
$223$	−105.177	+	76.4157i	−0.471647	+	0.342672i	−0.798083	−	0.602548i	$-0.794152\pi$
$223$	−105.177	+	76.4157i	−0.471647	+	0.342672i	0.326436	+	0.945219i	$0.394152\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	167.617	+	230.705i	0.738402	+	1.01632i	0.998709	+	0.0507974i	$0.0161763\pi$
$227$	167.617	+	230.705i	0.738402	+	1.01632i	−0.260307	+	0.965526i	$0.583824\pi$
$228$		0			0
$229$	52.1240	−	160.421i	0.227616	−	0.700529i	−0.770400	−	0.637561i	$-0.779943\pi$
$229$	52.1240	−	160.421i	0.227616	−	0.700529i	0.998016	−	0.0629680i	$-0.0200566\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−305.952	+	99.4098i	−1.31310	+	0.426651i	−0.880119	−	0.474753i	$-0.842538\pi$
$233$	−305.952	+	99.4098i	−1.31310	+	0.426651i	−0.432979	+	0.901404i	$0.642538\pi$
$234$		0			0
$235$	−303.468	+	81.1305i	−1.29136	+	0.345236i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−96.2005	−	132.409i	−0.402513	−	0.554011i	0.558860	−	0.829262i	$-0.311239\pi$
$239$	−96.2005	−	132.409i	−0.402513	−	0.554011i	−0.961372	+	0.275251i	$0.911239\pi$
$240$		0			0
$241$	65.5899	+	47.6538i	0.272157	+	0.197734i	0.715489	−	0.698624i	$-0.246204\pi$
$241$	65.5899	+	47.6538i	0.272157	+	0.197734i	−0.443332	+	0.896357i	$0.646204\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	56.5481	−	36.6774i	0.230808	−	0.149704i
$246$		0			0
$247$	−189.782	+	584.088i	−0.768347	+	2.36473i
$248$		0			0
$249$		0			0
$250$		0			0
$251$		−	407.683i		−	1.62424i	−0.583493	−	0.812118i	$-0.698314\pi$
$251$		−	407.683i		−	1.62424i	0.583493	−	0.812118i	$-0.301686\pi$
$252$		0			0
$253$	−36.8749	+	113.489i	−0.145751	+	0.448574i
$254$		0			0
$255$		0			0
$256$		0			0
$257$			54.3628i			0.211528i	0.994391	+	0.105764i	$0.0337289\pi$
$257$			54.3628i			0.211528i	−0.994391	+	0.105764i	$0.966271\pi$
$258$		0			0
$259$	129.636	+	94.1864i	0.500527	+	0.363654i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−278.593	+	383.450i	−1.05929	+	1.45799i	−0.178820	+	0.983882i	$0.557228\pi$
$263$	−278.593	+	383.450i	−1.05929	+	1.45799i	−0.880469	+	0.474104i	$0.842772\pi$
$264$		0			0
$265$	221.055	−	59.0978i	0.834171	−	0.223011i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−343.439	+	111.590i	−1.27672	+	0.414833i	−0.867425	−	0.497568i	$-0.834227\pi$
$269$	−343.439	+	111.590i	−1.27672	+	0.414833i	−0.409299	+	0.912400i	$0.634227\pi$
$270$		0			0
$271$	91.6660	−	282.119i	0.338251	−	1.04103i	−0.626847	−	0.779142i	$-0.715655\pi$
$271$	91.6660	−	282.119i	0.338251	−	1.04103i	0.965098	−	0.261888i	$-0.0843449\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	130.566	−	27.5986i	0.474786	−	0.100359i
$276$		0			0
$277$	−123.946	+	90.0522i	−0.447460	+	0.325098i	−0.788592	−	0.614917i	$-0.789190\pi$
$277$	−123.946	+	90.0522i	−0.447460	+	0.325098i	0.341132	+	0.940015i	$0.389190\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−247.658	+	80.4691i	−0.881346	+	0.286367i	−0.714516	−	0.699619i	$-0.753353\pi$
$281$	−247.658	+	80.4691i	−0.881346	+	0.286367i	−0.166830	+	0.985986i	$0.553353\pi$
$282$		0			0
$283$	−19.4615	−	59.8963i	−0.0687685	−	0.211648i	0.910766	−	0.412922i	$-0.135492\pi$
$283$	−19.4615	−	59.8963i	−0.0687685	−	0.211648i	−0.979535	+	0.201274i	$0.935492\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	141.020	−	194.097i	0.491359	−	0.676297i
$288$		0			0
$289$	37.0389	−	26.9104i	0.128162	−	0.0931154i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		−	5.73958i		−	0.0195890i	−0.999952	−	0.00979450i	$-0.996882\pi$
$293$		−	5.73958i		−	0.0195890i	0.999952	−	0.00979450i	$-0.00311774\pi$
$294$		0			0
$295$	−0.377799	+	7.13177i	−0.00128067	+	0.0241755i
$296$		0			0
$297$		0			0
$298$		0			0
$299$		−	515.493i		−	1.72406i
$300$		0			0
$301$	36.1558			0.120119
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−154.862	+	402.749i	−0.507743	+	1.32049i
$306$		0			0
$307$	−334.303			−1.08894			−0.544468	−	0.838782i	$-0.683268\pi$
$307$	−334.303			−1.08894			−0.544468	+	0.838782i	$0.683268\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−271.686	−	373.944i	−0.873590	−	1.20239i	−0.978155	−	0.207875i	$-0.933345\pi$
$311$	−271.686	−	373.944i	−0.873590	−	1.20239i	0.104566	−	0.994518i	$-0.466655\pi$
$312$		0			0
$313$	−113.188	−	82.2361i	−0.361624	−	0.262735i	0.392105	−	0.919920i	$-0.371747\pi$
$313$	−113.188	−	82.2361i	−0.361624	−	0.262735i	−0.753729	+	0.657185i	$0.771747\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−22.1339	+	7.19175i	−0.0698232	+	0.0226869i	−0.343720	−	0.939072i	$-0.611687\pi$
$317$	−22.1339	+	7.19175i	−0.0698232	+	0.0226869i	0.273897	+	0.961759i	$0.411687\pi$
$318$		0			0
$319$	8.55441	+	26.3278i	0.0268163	+	0.0825322i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−286.428	−	394.234i	−0.886774	−	1.22054i
$324$		0			0
$325$	−499.586	+	287.684i	−1.53719	+	0.885182i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	356.103	+	115.705i	1.08238	+	0.351686i
$330$		0			0
$331$	−102.364	−	315.044i	−0.309257	−	0.951795i	−0.978054	−	0.208350i	$-0.933191\pi$
$331$	−102.364	−	315.044i	−0.309257	−	0.951795i	0.668797	−	0.743445i	$-0.266809\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−93.2355	−	75.5879i	−0.278315	−	0.225635i
$336$		0			0
$337$	245.043	+	178.034i	0.727129	+	0.528290i	0.888654	−	0.458578i	$-0.151641\pi$
$337$	245.043	+	178.034i	0.727129	+	0.528290i	−0.161525	+	0.986869i	$0.551641\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−111.399	+	153.328i	−0.326684	+	0.449642i
$342$		0			0
$343$	−372.373			−1.08563
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−261.742	−	85.0450i	−0.754299	−	0.245087i	−0.0934688	−	0.995622i	$-0.529796\pi$
$347$	−261.742	−	85.0450i	−0.754299	−	0.245087i	−0.660830	+	0.750536i	$0.729796\pi$
$348$		0			0
$349$	472.032			1.35253			0.676263	−	0.736660i	$-0.263598\pi$
$349$	472.032			1.35253			0.676263	+	0.736660i	$0.263598\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−237.024	−	77.0137i	−0.671455	−	0.218169i	−0.0466047	−	0.998913i	$-0.514840\pi$
$353$	−237.024	−	77.0137i	−0.671455	−	0.218169i	−0.624851	+	0.780744i	$0.714840\pi$
$354$		0			0
$355$	−399.973	+	106.930i	−1.12668	+	0.301212i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−192.245	+	264.603i	−0.535501	+	0.737054i	−0.987956	−	0.154733i	$-0.950548\pi$
$359$	−192.245	+	264.603i	−0.535501	+	0.737054i	0.452455	+	0.891787i	$0.350548\pi$
$360$		0			0
$361$	−281.781	+	204.726i	−0.780558	+	0.567109i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−187.178	+	486.792i	−0.512815	+	1.33368i
$366$		0			0
$367$	15.2878	+	47.0510i	0.0416562	+	0.128204i	0.969722	−	0.244212i	$-0.0785293\pi$
$367$	15.2878	+	47.0510i	0.0416562	+	0.128204i	−0.928066	+	0.372417i	$0.878529\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−259.396	−	84.2828i	−0.699180	−	0.227177i
$372$		0			0
$373$	410.064	−	297.929i	1.09937	−	0.798737i	0.118411	−	0.992965i	$-0.462220\pi$
$373$	410.064	−	297.929i	1.09937	−	0.798737i	0.980956	+	0.194228i	$0.0622201\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−70.2912	−	96.7475i	−0.186449	−	0.256625i
$378$		0			0
$379$	−189.863	+	584.339i	−0.500958	+	1.54179i	0.306502	+	0.951870i	$0.400841\pi$
$379$	−189.863	+	584.339i	−0.500958	+	1.54179i	−0.807460	+	0.589922i	$0.799159\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−317.859	+	103.279i	−0.829920	+	0.269657i	−0.693012	−	0.720926i	$-0.743717\pi$
$383$	−317.859	+	103.279i	−0.829920	+	0.269657i	−0.136908	+	0.990584i	$0.543717\pi$
$384$		0			0
$385$	−148.472	−	57.0893i	−0.385642	−	0.148284i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−49.5784	−	68.2389i	−0.127451	−	0.175421i	0.740523	−	0.672031i	$-0.234578\pi$
$389$	−49.5784	−	68.2389i	−0.127451	−	0.175421i	−0.867974	+	0.496610i	$0.834578\pi$
$390$		0			0
$391$	330.907	+	240.418i	0.846309	+	0.614879i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	138.302	+	517.317i	0.350131	+	1.30966i
$396$		0			0
$397$	−163.814	+	504.167i	−0.412629	+	1.26994i	0.501725	+	0.865027i	$0.332699\pi$
$397$	−163.814	+	504.167i	−0.412629	+	1.26994i	−0.914354	+	0.404915i	$0.867301\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$			202.738i			0.505582i	0.967521	+	0.252791i	$0.0813485\pi$
$401$			202.738i			0.505582i	−0.967521	+	0.252791i	$0.918651\pi$
$402$		0			0
$403$	253.000	−	778.655i	0.627792	−	1.93215i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			143.521i			0.352632i
$408$		0			0
$409$	552.316	+	401.281i	1.35041	+	0.981128i	0.998991	+	0.0449081i	$0.0142995\pi$
$409$	552.316	+	401.281i	1.35041	+	0.981128i	0.351415	+	0.936220i	$0.385701\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	5.00368	−	6.88698i	0.0121155	−	0.0166755i
$414$		0			0
$415$	−296.993	+	366.332i	−0.715645	+	0.882728i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	732.273	−	237.930i	1.74767	−	0.567852i	0.751861	−	0.659321i	$-0.229156\pi$
$419$	732.273	−	237.930i	1.74767	−	0.567852i	0.995808	+	0.0914692i	$0.0291563\pi$
$420$		0			0
$421$	6.52893	−	20.0940i	0.0155082	−	0.0477292i	−0.943003	−	0.332784i	$-0.892012\pi$
$421$	6.52893	−	20.0940i	0.0155082	−	0.0477292i	0.958511	+	0.285055i	$0.0920119\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	48.3278	−	454.867i	0.113713	−	1.07027i
$426$		0			0
$427$	416.102	−	302.316i	0.974477	−	0.707999i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	548.846	−	178.331i	1.27343	−	0.413761i	0.407165	−	0.913355i	$-0.366517\pi$
$431$	548.846	−	178.331i	1.27343	−	0.413761i	0.866260	+	0.499594i	$0.166517\pi$
$432$		0			0
$433$	−76.7512	−	236.216i	−0.177254	−	0.545533i	0.822475	−	0.568801i	$-0.192593\pi$
$433$	−76.7512	−	236.216i	−0.177254	−	0.545533i	−0.999729	+	0.0232685i	$0.992593\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	349.946	−	481.659i	0.800791	−	1.10219i
$438$		0			0
$439$	465.486	−	338.196i	1.06033	−	0.770377i	0.0861833	−	0.996279i	$-0.472533\pi$
$439$	465.486	−	338.196i	1.06033	−	0.770377i	0.974150	+	0.225902i	$0.0725329\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$			40.5152i			0.0914564i	0.998954	+	0.0457282i	$0.0145608\pi$
$443$			40.5152i			0.0914564i	−0.998954	+	0.0457282i	$0.985439\pi$
$444$		0			0
$445$	−362.495	−	139.384i	−0.814596	−	0.313222i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	888.961i		−	1.97987i	−0.141528	−	0.989934i	$-0.545202\pi$
$449$		−	888.961i		−	1.97987i	0.141528	−	0.989934i	$-0.454798\pi$
$450$		0			0
$451$	214.886			0.476466
$452$		0			0
$453$		0			0
$454$		0			0
$455$	686.204	+	36.3510i	1.50814	+	0.0798922i
$456$		0			0
$457$	690.467			1.51087			0.755434	−	0.655225i	$-0.227426\pi$
$457$	690.467			1.51087			0.755434	+	0.655225i	$0.227426\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	114.457	+	157.537i	0.248281	+	0.341729i	0.914908	−	0.403662i	$-0.132263\pi$
$461$	114.457	+	157.537i	0.248281	+	0.341729i	−0.666627	+	0.745391i	$0.732263\pi$
$462$		0			0
$463$	−322.953	−	234.639i	−0.697522	−	0.506780i	0.181602	−	0.983372i	$-0.441872\pi$
$463$	−322.953	−	234.639i	−0.697522	−	0.506780i	−0.879124	+	0.476592i	$0.841872\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	415.840	−	135.115i	0.890450	−	0.289325i	0.172160	−	0.985069i	$-0.444925\pi$
$467$	415.840	−	135.115i	0.890450	−	0.289325i	0.718290	+	0.695744i	$0.244925\pi$
$468$		0			0
$469$	44.2105	+	136.066i	0.0942654	+	0.290119i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	19.0346	+	26.1988i	0.0402422	+	0.0553887i
$474$		0			0
$475$	−662.091	−	70.3447i	−1.39388	−	0.148094i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−364.145	−	118.318i	−0.760220	−	0.247011i	−0.0968470	−	0.995299i	$-0.530876\pi$
$479$	−364.145	−	118.318i	−0.760220	−	0.247011i	−0.663373	+	0.748289i	$0.730876\pi$
$480$		0			0
$481$	−191.590	−	589.654i	−0.398316	−	1.22589i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	105.437	+	394.385i	0.217395	+	0.813165i
$486$		0			0
$487$	45.3245	+	32.9302i	0.0930688	+	0.0676184i	0.633346	−	0.773868i	$-0.281681\pi$
$487$	45.3245	+	32.9302i	0.0930688	+	0.0676184i	−0.540278	+	0.841487i	$0.681681\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−362.911	+	499.505i	−0.739127	+	1.01732i	0.259541	+	0.965732i	$0.416429\pi$
$491$	−362.911	+	499.505i	−0.739127	+	1.01732i	−0.998668	+	0.0515892i	$0.983571\pi$
$492$		0			0
$493$	94.8871			0.192469
$494$		0			0
$495$		0			0
$496$		0			0
$497$	469.345	+	152.500i	0.944357	+	0.306840i
$498$		0			0
$499$	−354.096			−0.709611			−0.354806	−	0.934940i	$-0.615453\pi$
$499$	−354.096			−0.709611			−0.354806	+	0.934940i	$0.615453\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	676.136	+	219.690i	1.34421	+	0.436759i	0.890740	−	0.454514i	$-0.150187\pi$
$503$	676.136	+	219.690i	1.34421	+	0.436759i	0.453467	+	0.891273i	$0.350187\pi$
$504$		0			0
$505$	73.8392	+	113.843i	0.146216	+	0.225432i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−103.994	+	143.136i	−0.204311	+	0.281209i	−0.898860	−	0.438235i	$-0.855604\pi$
$509$	−103.994	+	143.136i	−0.204311	+	0.281209i	0.694550	+	0.719445i	$0.255604\pi$
$510$		0			0
$511$	502.932	−	365.401i	0.984211	−	0.715071i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	50.8674	+	190.269i	0.0987716	+	0.369455i
$516$		0			0
$517$	103.633	+	318.950i	0.200451	+	0.616924i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−19.5534	−	6.35328i	−0.0375305	−	0.0121944i	0.290192	−	0.956969i	$-0.406281\pi$
$521$	−19.5534	−	6.35328i	−0.0375305	−	0.0121944i	−0.327722	+	0.944774i	$0.606281\pi$
$522$		0			0
$523$	−369.486	+	268.448i	−0.706475	+	0.513284i	−0.882035	−	0.471185i	$-0.843827\pi$
$523$	−369.486	+	268.448i	−0.706475	+	0.513284i	0.175560	+	0.984469i	$0.443827\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	381.841	+	525.559i	0.724555	+	0.997265i
$528$		0			0
$529$	9.04574	−	27.8399i	0.0170997	−	0.0526275i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−882.856	+	286.857i	−1.65639	+	0.538194i
$534$		0			0
$535$	361.790	+	557.796i	0.676242	+	1.04261i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−42.2959	−	58.2153i	−0.0784710	−	0.108006i
$540$		0			0
$541$	198.849	+	144.472i	0.367558	+	0.267047i	0.756198	−	0.654343i	$-0.227055\pi$
$541$	198.849	+	144.472i	0.367558	+	0.267047i	−0.388640	+	0.921390i	$0.627055\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−869.932	−	46.0838i	−1.59620	−	0.0845574i
$546$		0			0
$547$	−113.124	+	348.159i	−0.206808	+	0.636488i	0.792827	+	0.609447i	$0.208609\pi$
$547$	−113.124	+	348.159i	−0.206808	+	0.636488i	−0.999634	+	0.0270412i	$0.991391\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		−	138.115i		−	0.250662i
$552$		0			0
$553$	197.240	−	607.042i	0.356672	−	1.09773i
$554$		0			0
$555$		0			0
$556$		0			0
$557$			9.33377i			0.0167572i	0.999965	+	0.00837861i	$0.00266702\pi$
$557$			9.33377i			0.0167572i	−0.999965	+	0.00837861i	$0.997333\pi$
$558$		0			0
$559$	−113.177	−	82.2276i	−0.202463	−	0.147098i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	322.556	−	443.961i	0.572925	−	0.788563i	−0.419973	−	0.907537i	$-0.637960\pi$
$563$	322.556	−	443.961i	0.572925	−	0.788563i	0.992897	+	0.118974i	$0.0379604\pi$
$564$		0			0
$565$	40.6900	−	768.112i	0.0720176	−	1.35949i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−74.4264	+	24.1826i	−0.130802	+	0.0425002i	−0.373687	−	0.927555i	$-0.621906\pi$
$569$	−74.4264	+	24.1826i	−0.130802	+	0.0425002i	0.242884	+	0.970055i	$0.421906\pi$
$570$		0			0
$571$	130.532	−	401.738i	0.228603	−	0.703569i	−0.769303	−	0.638885i	$-0.779396\pi$
$571$	130.532	−	401.738i	0.228603	−	0.703569i	0.997906	−	0.0646839i	$-0.0206039\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	546.783	−	115.577i	0.950927	−	0.201004i
$576$		0			0
$577$	−706.452	+	513.268i	−1.22435	+	0.889545i	−0.996454	−	0.0841393i	$-0.973186\pi$
$577$	−706.452	+	513.268i	−1.22435	+	0.889545i	−0.227900	+	0.973685i	$0.573186\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	534.617	−	173.708i	0.920167	−	0.298980i
$582$		0			0
$583$	−75.4894	−	232.332i	−0.129484	−	0.398512i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−165.391	+	227.642i	−0.281757	+	0.387806i	−0.926315	−	0.376750i	$-0.877042\pi$
$587$	−165.391	+	227.642i	−0.281757	+	0.387806i	0.644558	+	0.764556i	$0.277042\pi$
$588$		0			0
$589$	764.989	−	555.797i	1.29879	−	0.943628i
$590$		0			0
$591$		0			0
$592$		0			0
$593$			424.416i			0.715710i	0.933777	+	0.357855i	$0.116492\pi$
$593$			424.416i			0.715710i	−0.933777	+	0.357855i	$0.883508\pi$
$594$		0			0
$595$	−343.369	+	423.536i	−0.577091	+	0.711825i
$596$		0			0
$597$		0			0
$598$		0			0
$599$			745.353i			1.24433i	0.782887	+	0.622164i	$0.213746\pi$
$599$			745.353i			1.24433i	−0.782887	+	0.622164i	$0.786254\pi$
$600$		0			0
$601$	1017.82			1.69354			0.846769	−	0.531961i	$-0.178545\pi$
$601$	1017.82			1.69354			0.846769	+	0.531961i	$0.178545\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	119.458	+	446.834i	0.197452	+	0.738568i
$606$		0			0
$607$	−902.496			−1.48681			−0.743407	−	0.668839i	$-0.766791\pi$
$607$	−902.496			−1.48681			−0.743407	+	0.668839i	$0.766791\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−851.548	−	1172.06i	−1.39370	−	1.91826i
$612$		0			0
$613$	−434.137	−	315.419i	−0.708217	−	0.514549i	0.174381	−	0.984678i	$-0.444207\pi$
$613$	−434.137	−	315.419i	−0.708217	−	0.514549i	−0.882598	+	0.470129i	$0.844207\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	354.478	−	115.177i	0.574519	−	0.186672i	−0.00732484	−	0.999973i	$-0.502332\pi$
$617$	354.478	−	115.177i	0.574519	−	0.186672i	0.581844	+	0.813301i	$0.302332\pi$
$618$		0			0
$619$	−206.447	−	635.378i	−0.333517	−	1.02646i	−0.967448	−	0.253069i	$-0.918560\pi$
$619$	−206.447	−	635.378i	−0.333517	−	1.02646i	0.633932	−	0.773389i	$-0.281440\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	272.100	+	374.513i	0.436758	+	0.601145i
$624$		0			0
$625$	−417.156	−	465.409i	−0.667450	−	0.744654i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	467.867	+	152.019i	0.743826	+	0.241684i
$630$		0			0
$631$	−123.668	−	380.612i	−0.195988	−	0.603188i	−0.999964	−	0.00852644i	$-0.997286\pi$
$631$	−123.668	−	380.612i	−0.195988	−	0.603188i	0.803976	−	0.594662i	$-0.202714\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	175.401	−	456.166i	0.276223	−	0.718372i
$636$		0			0
$637$	251.485	+	182.714i	0.394795	+	0.286836i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	321.276	−	442.199i	0.501211	−	0.689858i	−0.481195	−	0.876613i	$-0.659797\pi$
$641$	321.276	−	442.199i	0.501211	−	0.689858i	0.982406	+	0.186756i	$0.0597972\pi$
$642$		0			0
$643$	287.103			0.446505			0.223252	−	0.974761i	$-0.428333\pi$
$643$	287.103			0.446505			0.223252	+	0.974761i	$0.428333\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	550.345	+	178.818i	0.850611	+	0.276380i	0.701702	−	0.712471i	$-0.252424\pi$
$647$	550.345	+	178.818i	0.850611	+	0.276380i	0.148909	+	0.988851i	$0.452424\pi$
$648$		0			0
$649$	7.62462			0.0117483
$650$		0			0
$651$		0			0
$652$		0			0
$653$	475.931	+	154.639i	0.728837	+	0.236814i	0.649850	−	0.760062i	$-0.274832\pi$
$653$	475.931	+	154.639i	0.728837	+	0.236814i	0.0789867	+	0.996876i	$0.474832\pi$
$654$		0			0
$655$	770.100	−	949.897i	1.17573	−	1.45022i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	117.680	−	161.973i	0.178574	−	0.245785i	−0.710342	−	0.703857i	$-0.751460\pi$
$659$	117.680	−	161.973i	0.178574	−	0.245785i	0.888915	+	0.458071i	$0.151460\pi$
$660$		0			0
$661$	157.015	−	114.078i	0.237542	−	0.172584i	−0.462645	−	0.886543i	$-0.653100\pi$
$661$	157.015	−	114.078i	0.237542	−	0.172584i	0.700188	+	0.713959i	$0.253100\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	616.487	+	499.798i	0.927049	+	0.751576i
$666$		0			0
$667$	35.8240	+	110.255i	0.0537092	+	0.165300i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	438.122	+	142.354i	0.652939	+	0.212153i
$672$		0			0
$673$	−821.783	+	597.061i	−1.22107	+	0.887163i	−0.996189	−	0.0872221i	$-0.972201\pi$
$673$	−821.783	+	597.061i	−1.22107	+	0.887163i	−0.224886	+	0.974385i	$0.572201\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	85.5174	+	117.705i	0.126318	+	0.173862i	0.867492	−	0.497451i	$-0.165731\pi$
$677$	85.5174	+	117.705i	0.126318	+	0.173862i	−0.741174	+	0.671313i	$0.765731\pi$
$678$		0			0
$679$	150.369	−	462.788i	0.221457	−	0.681574i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−313.191	+	101.762i	−0.458552	+	0.148993i	−0.529179	−	0.848510i	$-0.677500\pi$
$683$	−313.191	+	101.762i	−0.458552	+	0.148993i	0.0706269	+	0.997503i	$0.477500\pi$
$684$		0			0
$685$	49.5248	−	934.889i	0.0722990	−	1.36480i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	620.293	+	853.759i	0.900279	+	1.23913i
$690$		0			0
$691$	−453.498	−	329.486i	−0.656292	−	0.476824i	0.209117	−	0.977891i	$-0.432941\pi$
$691$	−453.498	−	329.486i	−0.656292	−	0.476824i	−0.865409	+	0.501066i	$0.832941\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−52.6341	+	136.885i	−0.0757325	+	0.196958i
$696$		0			0
$697$	227.610	−	700.511i	0.326556	−	1.00504i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			538.821i			0.768646i	0.923199	+	0.384323i	$0.125565\pi$
$701$			538.821i			0.768646i	−0.923199	+	0.384323i	$0.874435\pi$
$702$		0			0
$703$	221.275	−	681.014i	0.314758	−	0.968725i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		−	161.741i		−	0.228771i
$708$		0			0
$709$	179.215	+	130.207i	0.252771	+	0.183649i	0.706954	−	0.707259i	$-0.250069\pi$
$709$	179.215	+	130.207i	0.252771	+	0.183649i	−0.454183	+	0.890909i	$0.650069\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−466.517	+	642.105i	−0.654301	+	0.900568i
$714$		0			0
$715$	334.919	+	516.368i	0.468418	+	0.722193i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	862.471	−	280.234i	1.19954	−	0.389755i	0.359950	−	0.932972i	$-0.382794\pi$
$719$	862.471	−	280.234i	1.19954	−	0.389755i	0.839593	+	0.543217i	$0.182794\pi$
$720$		0			0
$721$	72.5449	−	223.270i	0.100617	−	0.309667i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	86.8602	−	96.2492i	0.119807	−	0.132757i
$726$		0			0
$727$	−143.129	+	103.989i	−0.196876	+	0.143039i	−0.681856	−	0.731486i	$-0.738827\pi$
$727$	−143.129	+	103.989i	−0.196876	+	0.143039i	0.484980	+	0.874525i	$0.338827\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	105.567	−	34.3010i	0.144415	−	0.0469233i
$732$		0			0
$733$	172.526	+	530.979i	0.235369	+	0.724392i	0.997072	+	0.0764657i	$0.0243636\pi$
$733$	172.526	+	530.979i	0.235369	+	0.724392i	−0.761703	+	0.647926i	$0.775636\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−75.3197	+	103.669i	−0.102198	+	0.140663i
$738$		0			0
$739$	−332.508	+	241.581i	−0.449943	+	0.326903i	−0.789573	−	0.613656i	$-0.789698\pi$
$739$	−332.508	+	241.581i	−0.449943	+	0.326903i	0.339630	+	0.940559i	$0.389698\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		−	1022.43i		−	1.37608i	−0.725674	−	0.688039i	$-0.758472\pi$
$743$		−	1022.43i		−	1.37608i	0.725674	−	0.688039i	$-0.241528\pi$
$744$		0			0
$745$	528.323	+	814.553i	0.709159	+	1.09336i
$746$		0			0
$747$		0			0
$748$		0			0
$749$		−	792.483i		−	1.05806i
$750$		0			0
$751$	−195.085			−0.259766			−0.129883	−	0.991529i	$-0.541460\pi$
$751$	−195.085			−0.259766			−0.129883	+	0.991529i	$0.541460\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−248.986	+	161.493i	−0.329782	+	0.213898i
$756$		0			0
$757$	510.166			0.673932			0.336966	−	0.941517i	$-0.390599\pi$
$757$	510.166			0.673932			0.336966	+	0.941517i	$0.390599\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−453.523	−	624.220i	−0.595956	−	0.820263i	0.399374	−	0.916788i	$-0.369227\pi$
$761$	−453.523	−	624.220i	−0.595956	−	0.820263i	−0.995331	+	0.0965245i	$0.969227\pi$
$762$		0			0
$763$	840.072	+	610.348i	1.10101	+	0.799932i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−31.3256	+	10.1783i	−0.0408417	+	0.0132703i
$768$		0			0
$769$	282.913	+	870.716i	0.367897	+	1.13227i	0.948147	+	0.317832i	$0.102955\pi$
$769$	282.913	+	870.716i	0.367897	+	1.13227i	−0.580250	+	0.814439i	$0.697045\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	501.059	+	689.649i	0.648201	+	0.892172i	0.999020	−	0.0442715i	$-0.0140967\pi$
$773$	501.059	+	689.649i	0.648201	+	0.892172i	−0.350819	+	0.936443i	$0.614097\pi$
$774$		0			0
$775$	882.642	+	93.7773i	1.13889	+	0.121003i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−1019.64	−	331.302i	−1.30891	−	0.425292i
$780$		0			0
$781$	136.589	+	420.378i	0.174890	+	0.538256i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	178.894	−	116.032i	0.227890	−	0.147811i
$786$		0			0
$787$	−190.617	−	138.492i	−0.242208	−	0.175974i	0.460059	−	0.887889i	$-0.347828\pi$
$787$	−190.617	−	138.492i	−0.242208	−	0.175974i	−0.702266	+	0.711914i	$0.747828\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−538.911	+	741.747i	−0.681303	+	0.937733i
$792$		0			0
$793$	−1990.05			−2.50952
$794$		0			0
$795$		0			0
$796$		0			0
$797$	637.587	+	207.165i	0.799984	+	0.259930i	0.680350	−	0.732888i	$-0.261828\pi$
$797$	637.587	+	207.165i	0.799984	+	0.259930i	0.119634	+	0.992818i	$0.461828\pi$
$798$		0			0
$799$	1149.52			1.43870
$800$		0			0
$801$		0			0
$802$		0			0
$803$	529.547	+	172.060i	0.659461	+	0.214272i
$804$		0			0
$805$	−621.769	−	239.078i	−0.772384	−	0.296991i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	735.814	−	1012.76i	0.909535	−	1.25187i	−0.0577903	−	0.998329i	$-0.518405\pi$
$809$	735.814	−	1012.76i	0.909535	−	1.25187i	0.967325	−	0.253539i	$-0.0815945\pi$
$810$		0			0
$811$	−462.944	+	336.349i	−0.570831	+	0.414733i	−0.835407	−	0.549632i	$-0.814768\pi$
$811$	−462.944	+	336.349i	−0.570831	+	0.414733i	0.264576	+	0.964365i	$0.414768\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	380.124	+	20.1367i	0.466410	+	0.0247076i
$816$		0			0
$817$	−49.9275	−	153.661i	−0.0611108	−	0.188080i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	419.383	+	136.266i	0.510819	+	0.165975i	0.553075	−	0.833132i	$-0.313454\pi$
$821$	419.383	+	136.266i	0.510819	+	0.165975i	−0.0422555	+	0.999107i	$0.513454\pi$
$822$		0			0
$823$	422.900	−	307.255i	0.513852	−	0.373335i	−0.300431	−	0.953804i	$-0.597131\pi$
$823$	422.900	−	307.255i	0.513852	−	0.373335i	0.814283	+	0.580468i	$0.197131\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−439.057	−	604.310i	−0.530903	−	0.730725i	0.456365	−	0.889793i	$-0.349151\pi$
$827$	−439.057	−	604.310i	−0.530903	−	0.730725i	−0.987268	+	0.159068i	$0.949151\pi$
$828$		0			0
$829$	−443.845	+	1366.01i	−0.535398	+	1.64778i	0.207391	+	0.978258i	$0.433503\pi$
$829$	−443.845	+	1366.01i	−0.535398	+	1.64778i	−0.742788	+	0.669526i	$0.766497\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−234.577	+	76.2186i	−0.281605	+	0.0914990i
$834$		0			0
$835$	−777.493	+	959.016i	−0.931129	+	1.14852i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−1.21660	−	1.67450i	−0.00145006	−	0.00199583i	0.808291	−	0.588783i	$-0.200393\pi$
$839$	−1.21660	−	1.67450i	−0.00145006	−	0.00199583i	−0.809741	+	0.586787i	$0.800393\pi$
$840$		0			0
$841$	−658.626	−	478.520i	−0.783146	−	0.568989i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−1408.93	−	1142.25i	−1.66737	−	1.35177i
$846$		0			0
$847$	170.366	−	524.334i	0.201141	−	0.619048i
$848$		0			0
$849$		0			0
$850$		0			0
$851$			601.037i			0.706271i
$852$		0			0
$853$	241.421	−	743.018i	0.283026	−	0.871064i	−0.703957	−	0.710242i	$-0.748585\pi$
$853$	241.421	−	743.018i	0.283026	−	0.871064i	0.986983	−	0.160822i	$-0.0514146\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		−	332.954i		−	0.388511i	−0.980951	−	0.194255i	$-0.937771\pi$
$857$		−	332.954i		−	0.388511i	0.980951	−	0.194255i	$-0.0622290\pi$
$858$		0			0
$859$	1281.68	+	931.198i	1.49207	+	1.08405i	0.973411	+	0.229065i	$0.0735668\pi$
$859$	1281.68	+	931.198i	1.49207	+	1.08405i	0.518654	+	0.854984i	$0.326433\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−417.895	+	575.183i	−0.484235	+	0.666493i	−0.979312	−	0.202356i	$-0.935140\pi$
$863$	−417.895	+	575.183i	−0.484235	+	0.666493i	0.495076	+	0.868849i	$0.335140\pi$
$864$		0			0
$865$	−655.247	−	251.950i	−0.757511	−	0.291272i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	543.708	−	176.661i	0.625671	−	0.203293i
$870$		0			0
$871$	171.059	−	526.466i	0.196394	−	0.604439i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	115.294	+	736.005i	0.131765	+	0.841149i
$876$		0			0
$877$	776.260	−	563.986i	0.885131	−	0.643085i	−0.0494729	−	0.998775i	$-0.515754\pi$
$877$	776.260	−	563.986i	0.885131	−	0.643085i	0.934604	+	0.355690i	$0.115754\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−651.978	+	211.840i	−0.740043	+	0.240455i	−0.654691	−	0.755896i	$-0.727201\pi$
$881$	−651.978	+	211.840i	−0.740043	+	0.240455i	−0.0853516	+	0.996351i	$0.527201\pi$
$882$		0			0
$883$	422.805	+	1301.26i	0.478828	+	1.47368i	0.840725	+	0.541462i	$0.182129\pi$
$883$	422.805	+	1301.26i	0.478828	+	1.47368i	−0.361897	+	0.932218i	$0.617871\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−813.594	+	1119.82i	−0.917242	+	1.26248i	0.0473903	+	0.998876i	$0.484910\pi$
$887$	−813.594	+	1119.82i	−0.917242	+	1.26248i	−0.964632	+	0.263599i	$0.915090\pi$
$888$		0			0
$889$	−471.290	+	342.412i	−0.530135	+	0.385165i
$890$		0			0
$891$		0			0
$892$		0			0
$893$		−	1673.21i		−	1.87369i
$894$		0			0
$895$	−2.14182	+	0.572603i	−0.00239310	+	0.000639780i
$896$		0			0
$897$		0			0
$898$		0			0
$899$			184.123i			0.204809i
$900$		0			0
$901$	−837.342			−0.929347
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−298.965	−	242.377i	−0.330349	−	0.267820i
$906$		0			0
$907$	−225.550			−0.248677			−0.124339	−	0.992240i	$-0.539681\pi$
$907$	−225.550			−0.248677			−0.124339	+	0.992240i	$0.539681\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	718.032	+	988.286i	0.788180	+	1.08484i	0.994332	+	0.106317i	$0.0339058\pi$
$911$	718.032	+	988.286i	0.788180	+	1.08484i	−0.206152	+	0.978520i	$0.566094\pi$
$912$		0			0
$913$	407.325	+	295.939i	0.446139	+	0.324139i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−1386.26	+	450.423i	−1.51173	+	0.491191i
$918$		0			0
$919$	−560.477	−	1724.97i	−0.609877	−	1.87701i	−0.458947	−	0.888464i	$-0.651773\pi$
$919$	−560.477	−	1724.97i	−0.609877	−	1.87701i	−0.150930	−	0.988544i	$-0.548227\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−1122.35	−	1544.78i	−1.21598	−	1.67365i
$924$		0			0
$925$	582.489	−	335.424i	0.629718	−	0.362620i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−923.193	−	299.964i	−0.993749	−	0.322889i	−0.233384	−	0.972385i	$-0.574980\pi$
$929$	−923.193	−	299.964i	−0.993749	−	0.322889i	−0.760365	+	0.649496i	$0.774980\pi$
$930$		0			0
$931$	110.942	+	341.444i	0.119164	+	0.366749i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−487.669	−	25.8338i	−0.521571	−	0.0276297i
$936$		0			0
$937$	−380.603	−	276.525i	−0.406194	−	0.295117i	0.365865	−	0.930668i	$-0.380773\pi$
$937$	−380.603	−	276.525i	−0.406194	−	0.295117i	−0.772059	+	0.635551i	$0.780773\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	442.004	−	608.367i	0.469718	−	0.646511i	−0.506771	−	0.862081i	$-0.669161\pi$
$941$	442.004	−	608.367i	0.469718	−	0.646511i	0.976488	+	0.215570i	$0.0691609\pi$
$942$		0			0
$943$	899.898			0.954293
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−496.212	−	161.229i	−0.523983	−	0.170252i	0.0350693	−	0.999385i	$-0.488835\pi$
$947$	−496.212	−	161.229i	−0.523983	−	0.170252i	−0.559052	+	0.829133i	$0.688835\pi$
$948$		0			0
$949$	−2405.32			−2.53458
$950$		0			0
$951$		0			0
$952$		0			0
$953$	1377.51	+	447.581i	1.44545	+	0.469655i	0.923592	−	0.383377i	$-0.125239\pi$
$953$	1377.51	+	447.581i	1.44545	+	0.469655i	0.521858	+	0.853032i	$0.325239\pi$
$954$		0			0
$955$	−53.6194	+	1012.18i	−0.0561460	+	1.05988i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−655.923	+	902.800i	−0.683965	+	0.941397i
$960$		0			0
$961$	−242.350	+	176.078i	−0.252186	+	0.183224i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	1229.87	−	797.700i	1.27448	−	0.826632i
$966$		0			0
$967$	−2.46016	−	7.57160i	−0.00254412	−	0.00782999i	0.949776	−	0.312929i	$-0.101310\pi$
$967$	−2.46016	−	7.57160i	−0.00254412	−	0.00782999i	−0.952321	+	0.305099i	$0.901310\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−850.502	−	276.345i	−0.875904	−	0.284598i	−0.163648	−	0.986519i	$-0.552326\pi$
$971$	−850.502	−	276.345i	−0.875904	−	0.284598i	−0.712255	+	0.701920i	$0.752326\pi$
$972$		0			0
$973$	141.424	−	102.750i	0.145348	−	0.105602i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−658.891	−	906.886i	−0.674403	−	0.928235i	0.325447	−	0.945560i	$-0.394485\pi$
$977$	−658.891	−	906.886i	−0.674403	−	0.928235i	−0.999850	+	0.0173247i	$0.994485\pi$
$978$		0			0
$979$	−128.127	+	394.333i	−0.130875	+	0.402792i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	24.7476	−	8.04099i	0.0251756	−	0.00818005i	−0.296402	−	0.955063i	$-0.595787\pi$
$983$	24.7476	−	8.04099i	0.0251756	−	0.00818005i	0.321578	+	0.946883i	$0.395787\pi$
$984$		0			0
$985$	−28.2169	+	7.54361i	−0.0286466	+	0.00765849i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	79.7127	+	109.715i	0.0805993	+	0.110935i
$990$		0			0
$991$	789.012	+	573.250i	0.796177	+	0.578457i	0.909790	−	0.415069i	$-0.136242\pi$
$991$	789.012	+	573.250i	0.796177	+	0.578457i	−0.113613	+	0.993525i	$0.536242\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−47.9151	+	31.0780i	−0.0481559	+	0.0312341i
$996$		0			0
$997$	396.608	−	1220.63i	0.397801	−	1.22431i	−0.528958	−	0.848648i	$-0.677417\pi$
$997$	396.608	−	1220.63i	0.397801	−	1.22431i	0.926759	−	0.375657i	$-0.122583\pi$
$998$		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.161.3	✓	80
3.2	odd	2	inner	900.3.ba.a.161.18	yes	80
25.16	even	5	inner	900.3.ba.a.341.18	yes	80
75.41	odd	10	inner	900.3.ba.a.341.3	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
900.3.ba.a.161.3	✓	80	1.1	even	1	trivial
900.3.ba.a.161.18	yes	80	3.2	odd	2	inner
900.3.ba.a.341.3	yes	80	75.41	odd	10	inner
900.3.ba.a.341.18	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)

\(f(q)\)	\(=\)	\(q+(-4.19489 + 2.72083i) q^{5} +5.95985 q^{7} +O(q^{10})\)	\(q+(-4.19489 + 2.72083i) q^{5} +5.95985 q^{7} +(3.13762 + 4.31857i) q^{11} +(-18.6558 - 13.5542i) q^{13} +(17.4015 - 5.65410i) q^{17} +(-8.22996 - 25.3292i) q^{19} +(13.1397 + 18.0852i) q^{23} +(10.1942 - 22.8271i) q^{25} +(4.93210 + 1.60254i) q^{29} +(10.9715 + 33.7667i) q^{31} +(-25.0009 + 16.2157i) q^{35} +(21.7516 + 15.8035i) q^{37} +(23.6617 - 32.5675i) q^{41} +6.06656 q^{43} +(59.7503 + 19.4141i) q^{47} -13.4802 q^{49} +(-43.5239 - 14.1418i) q^{53} +(-24.9121 - 9.57898i) q^{55} +(0.839566 - 1.15556i) q^{59} +(69.8175 - 50.7254i) q^{61} +(115.138 + 6.09931i) q^{65} +(7.41805 + 22.8304i) q^{67} +(78.7513 + 25.5878i) q^{71} +(84.3867 - 61.3105i) q^{73} +(18.6997 + 25.7380i) q^{77} +(33.0948 - 101.855i) q^{79} +(89.7031 - 29.1463i) q^{83} +(-57.6137 + 71.0649i) q^{85} +(45.6555 + 62.8394i) q^{89} +(-111.186 - 80.7812i) q^{91} +(103.440 + 83.8609i) q^{95} +(25.2304 - 77.6511i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 16 q^{7}+O(q^{10}) \) 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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