LMFDB - Embedded newform 900.3.y.a.89.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(900, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 3]))

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

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

chi := DirichletCharacter("900.89");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	900.y (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$24.5232237924$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			89.7
Character	$\chi$	$=$	900.89
Dual form			900.3.y.a.809.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.55393 + 4.29854i) q^{5} -5.96546i q^{7} +O(q^{10})$	$q+(-2.55393 + 4.29854i) q^{5} -5.96546i q^{7} +(5.17267 + 7.11956i) q^{11} +(2.69444 - 3.70858i) q^{13} +(0.512675 + 1.57785i) q^{17} +(2.22259 + 6.84044i) q^{19} +(-12.5179 + 9.09477i) q^{23} +(-11.9549 - 21.9564i) q^{25} +(33.4616 + 10.8723i) q^{29} +(-5.11966 - 15.7567i) q^{31} +(25.6427 + 15.2354i) q^{35} +(-42.0702 + 57.9047i) q^{37} +(13.6373 - 18.7701i) q^{41} +44.5186i q^{43} +(-15.3388 + 47.2080i) q^{47} +13.4133 q^{49} +(-1.28209 + 3.94585i) q^{53} +(-43.8144 + 4.05202i) q^{55} +(-58.3097 + 80.2565i) q^{59} +(-28.4310 + 20.6564i) q^{61} +(9.06005 + 21.0536i) q^{65} +(-37.6924 + 12.2470i) q^{67} +(23.5958 + 7.66676i) q^{71} +(-37.8321 - 52.0715i) q^{73} +(42.4714 - 30.8573i) q^{77} +(-22.6483 + 69.7042i) q^{79} +(19.1411 + 58.9102i) q^{83} +(-8.09179 - 1.82597i) q^{85} +(17.9309 + 24.6798i) q^{89} +(-22.1234 - 16.0736i) q^{91} +(-35.0803 - 7.91612i) q^{95} +(-44.4221 - 14.4336i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q+O(q^{10}) $ 80 * q	$ 80 q + 60 q^{19} + 56 q^{25} - 120 q^{31} + 20 q^{37} - 680 q^{49} - 56 q^{55} - 80 q^{61} - 280 q^{67} - 360 q^{73} + 40 q^{79} + 192 q^{85} + 140 q^{91} - 40 q^{97}+O(q^{100}) $ 80 * q + 60 * q^19 + 56 * q^25 - 120 * q^31 + 20 * q^37 - 680 * q^49 - 56 * q^55 - 80 * q^61 - 280 * q^67 - 360 * q^73 + 40 * q^79 + 192 * q^85 + 140 * q^91 - 40 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−2.55393	+	4.29854i	−0.510786	+	0.859708i
$5$	−2.55393	+	4.29854i	−0.510786	+	0.859708i
$6$		0			0
$7$		−	5.96546i		−	0.852208i	−0.904674	−	0.426104i	$-0.859886\pi$
$7$		−	5.96546i		−	0.852208i	0.904674	−	0.426104i	$-0.140114\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	5.17267	+	7.11956i	0.470242	+	0.647233i	0.976593	−	0.215094i	$-0.0690059\pi$
$11$	5.17267	+	7.11956i	0.470242	+	0.647233i	−0.506351	+	0.862328i	$0.669006\pi$
$12$		0			0
$13$	2.69444	−	3.70858i	0.207265	−	0.285275i	−0.692711	−	0.721215i	$-0.743584\pi$
$13$	2.69444	−	3.70858i	0.207265	−	0.285275i	0.899976	+	0.435940i	$0.143584\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.512675	+	1.57785i	0.0301574	+	0.0928148i	0.965002	−	0.262241i	$-0.0844617\pi$
$17$	0.512675	+	1.57785i	0.0301574	+	0.0928148i	−0.934845	+	0.355056i	$0.884462\pi$
$18$		0			0
$19$	2.22259	+	6.84044i	0.116979	+	0.360023i	0.992355	−	0.123420i	$-0.0393861\pi$
$19$	2.22259	+	6.84044i	0.116979	+	0.360023i	−0.875376	+	0.483443i	$0.839386\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−12.5179	+	9.09477i	−0.544256	+	0.395425i	−0.825663	−	0.564163i	$-0.809199\pi$
$23$	−12.5179	+	9.09477i	−0.544256	+	0.395425i	0.281407	+	0.959588i	$0.409199\pi$
$24$		0			0
$25$	−11.9549	−	21.9564i	−0.478194	−	0.878254i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	33.4616	+	10.8723i	1.15385	+	0.374908i	0.822591	−	0.568633i	$-0.192528\pi$
$29$	33.4616	+	10.8723i	1.15385	+	0.374908i	0.331256	+	0.943541i	$0.392528\pi$
$30$		0			0
$31$	−5.11966	−	15.7567i	−0.165150	−	0.508280i	0.833897	−	0.551920i	$-0.186105\pi$
$31$	−5.11966	−	15.7567i	−0.165150	−	0.508280i	−0.999047	+	0.0436398i	$0.986105\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	25.6427	+	15.2354i	0.732650	+	0.435296i
$36$		0			0
$37$	−42.0702	+	57.9047i	−1.13703	+	1.56499i	−0.363068	+	0.931763i	$0.618271\pi$
$37$	−42.0702	+	57.9047i	−1.13703	+	1.56499i	−0.773965	+	0.633228i	$0.781729\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	13.6373	−	18.7701i	0.332617	−	0.457808i	−0.609650	−	0.792671i	$-0.708690\pi$
$41$	13.6373	−	18.7701i	0.332617	−	0.457808i	0.942267	+	0.334863i	$0.108690\pi$
$42$		0			0
$43$			44.5186i			1.03532i	0.855588	+	0.517658i	$0.173196\pi$
$43$			44.5186i			1.03532i	−0.855588	+	0.517658i	$0.826804\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−15.3388	+	47.2080i	−0.326358	+	1.00443i	0.644466	+	0.764633i	$0.277080\pi$
$47$	−15.3388	+	47.2080i	−0.326358	+	1.00443i	−0.970824	+	0.239793i	$0.922920\pi$
$48$		0			0
$49$	13.4133			0.273742
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−1.28209	+	3.94585i	−0.0241903	+	0.0744500i	−0.962423	−	0.271555i	$-0.912462\pi$
$53$	−1.28209	+	3.94585i	−0.0241903	+	0.0744500i	0.938233	+	0.346005i	$0.112462\pi$
$54$		0			0
$55$	−43.8144	+	4.05202i	−0.796625	+	0.0736730i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−58.3097	+	80.2565i	−0.988301	+	1.36028i	−0.0560650	+	0.998427i	$0.517855\pi$
$59$	−58.3097	+	80.2565i	−0.988301	+	1.36028i	−0.932236	+	0.361852i	$0.882145\pi$
$60$		0			0
$61$	−28.4310	+	20.6564i	−0.466083	+	0.338629i	−0.795913	−	0.605411i	$-0.793009\pi$
$61$	−28.4310	+	20.6564i	−0.466083	+	0.338629i	0.329830	+	0.944040i	$0.393009\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	9.06005	+	21.0536i	0.139385	+	0.323902i
$66$		0			0
$67$	−37.6924	+	12.2470i	−0.562574	+	0.182791i	−0.576479	−	0.817112i	$-0.695574\pi$
$67$	−37.6924	+	12.2470i	−0.562574	+	0.182791i	0.0139052	+	0.999903i	$0.495574\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	23.5958	+	7.66676i	0.332336	+	0.107982i	0.470432	−	0.882436i	$-0.344098\pi$
$71$	23.5958	+	7.66676i	0.332336	+	0.107982i	−0.138096	+	0.990419i	$0.544098\pi$
$72$		0			0
$73$	−37.8321	−	52.0715i	−0.518248	−	0.713308i	0.467035	−	0.884239i	$-0.345322\pi$
$73$	−37.8321	−	52.0715i	−0.518248	−	0.713308i	−0.985283	+	0.170931i	$0.945322\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	42.4714	−	30.8573i	0.551577	−	0.400744i
$78$		0			0
$79$	−22.6483	+	69.7042i	−0.286687	+	0.882331i	0.699201	+	0.714925i	$0.253539\pi$
$79$	−22.6483	+	69.7042i	−0.286687	+	0.882331i	−0.985888	+	0.167406i	$0.946461\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	19.1411	+	58.9102i	0.230615	+	0.709761i	0.997673	+	0.0681828i	$0.0217201\pi$
$83$	19.1411	+	58.9102i	0.230615	+	0.709761i	−0.767057	+	0.641578i	$0.778280\pi$
$84$		0			0
$85$	−8.09179	−	1.82597i	−0.0951976	−	0.0214820i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	17.9309	+	24.6798i	0.201471	+	0.277301i	0.897783	−	0.440438i	$-0.145177\pi$
$89$	17.9309	+	24.6798i	0.201471	+	0.277301i	−0.696312	+	0.717739i	$0.745177\pi$
$90$		0			0
$91$	−22.1234	−	16.0736i	−0.243114	−	0.176633i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−35.0803	−	7.91612i	−0.369266	−	0.0833276i
$96$		0			0
$97$	−44.4221	−	14.4336i	−0.457960	−	0.148800i	0.0709468	−	0.997480i	$-0.477398\pi$
$97$	−44.4221	−	14.4336i	−0.457960	−	0.148800i	−0.528907	+	0.848680i	$0.677398\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$			174.247i			1.72522i	0.505869	+	0.862610i	$0.331172\pi$
$101$			174.247i			1.72522i	−0.505869	+	0.862610i	$0.668828\pi$
$102$		0			0
$103$	−64.3521	−	20.9093i	−0.624777	−	0.203002i	−0.0205171	−	0.999790i	$-0.506531\pi$
$103$	−64.3521	−	20.9093i	−0.624777	−	0.203002i	−0.604260	+	0.796787i	$0.706531\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−104.337			−0.975116			−0.487558	−	0.873091i	$-0.662112\pi$
$107$	−104.337			−0.975116			−0.487558	+	0.873091i	$0.662112\pi$
$108$		0			0
$109$	18.3986	+	13.3673i	0.168794	+	0.122636i	0.668975	−	0.743285i	$-0.266733\pi$
$109$	18.3986	+	13.3673i	0.168794	+	0.122636i	−0.500181	+	0.865921i	$0.666733\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	106.869	+	77.6447i	0.945741	+	0.687121i	0.949796	−	0.312871i	$-0.101291\pi$
$113$	106.869	+	77.6447i	0.945741	+	0.687121i	−0.00405495	+	0.999992i	$0.501291\pi$
$114$		0			0
$115$	−7.12441	−	77.0360i	−0.0619514	−	0.669878i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	9.41260	−	3.05834i	0.0790975	−	0.0257003i
$120$		0			0
$121$	13.4593	−	41.4236i	0.111234	−	0.342344i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	124.912	+	4.68662i	0.999297	+	0.0374930i
$126$		0			0
$127$	25.1814	+	34.6593i	0.198279	+	0.272908i	0.896566	−	0.442910i	$-0.146054\pi$
$127$	25.1814	+	34.6593i	0.198279	+	0.272908i	−0.698287	+	0.715818i	$0.746054\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	17.7445	−	5.76555i	0.135455	−	0.0440118i	−0.240505	−	0.970648i	$-0.577313\pi$
$131$	17.7445	−	5.76555i	0.135455	−	0.0440118i	0.375960	+	0.926636i	$0.377313\pi$
$132$		0			0
$133$	40.8064	−	13.2588i	0.306815	−	0.0996901i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−9.33368	−	6.78131i	−0.0681290	−	0.0494986i	0.553199	−	0.833049i	$-0.313407\pi$
$137$	−9.33368	−	6.78131i	−0.0681290	−	0.0494986i	−0.621328	+	0.783550i	$0.713407\pi$
$138$		0			0
$139$	117.969	−	85.7096i	0.848699	−	0.616616i	−0.0760878	−	0.997101i	$-0.524243\pi$
$139$	117.969	−	85.7096i	0.848699	−	0.616616i	0.924787	+	0.380485i	$0.124243\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	40.3409			0.282104
$144$		0			0
$145$	−132.194	+	116.069i	−0.911681	+	0.800473i
$146$		0			0
$147$		0			0
$148$		0			0
$149$			125.323i			0.841094i	0.907271	+	0.420547i	$0.138162\pi$
$149$			125.323i			0.841094i	−0.907271	+	0.420547i	$0.861838\pi$
$150$		0			0
$151$	99.0919			0.656238			0.328119	−	0.944636i	$-0.393585\pi$
$151$	99.0919			0.656238			0.328119	+	0.944636i	$0.393585\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	80.8060	+	18.2345i	0.521329	+	0.117642i
$156$		0			0
$157$			108.209i			0.689231i	0.938744	+	0.344615i	$0.111991\pi$
$157$			108.209i			0.689231i	−0.938744	+	0.344615i	$0.888009\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	54.2545	+	74.6749i	0.336984	+	0.463819i
$162$		0			0
$163$	62.0102	−	85.3498i	0.380431	−	0.523618i	−0.575268	−	0.817965i	$-0.695102\pi$
$163$	62.0102	−	85.3498i	0.380431	−	0.523618i	0.955699	+	0.294347i	$0.0951022\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−19.1036	−	58.7948i	−0.114393	−	0.352065i	0.877427	−	0.479710i	$-0.159258\pi$
$167$	−19.1036	−	58.7948i	−0.114393	−	0.352065i	−0.991820	+	0.127645i	$0.959258\pi$
$168$		0			0
$169$	45.7303	+	140.743i	0.270594	+	0.832802i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	120.072	−	87.2375i	0.694058	−	0.504263i	−0.183934	−	0.982939i	$-0.558883\pi$
$173$	120.072	−	87.2375i	0.694058	−	0.504263i	0.877992	+	0.478676i	$0.158883\pi$
$174$		0			0
$175$	−130.980	+	71.3162i	−0.748455	+	0.407521i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−198.796	−	64.5929i	−1.11059	−	0.360854i	−0.304424	−	0.952537i	$-0.598464\pi$
$179$	−198.796	−	64.5929i	−1.11059	−	0.360854i	−0.806171	+	0.591683i	$0.798464\pi$
$180$		0			0
$181$	14.4448	+	44.4564i	0.0798053	+	0.245615i	0.982997	−	0.183622i	$-0.0587823\pi$
$181$	14.4448	+	44.4564i	0.0798053	+	0.245615i	−0.903192	+	0.429238i	$0.858782\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−141.461	−	328.725i	−0.764654	−	1.77689i
$186$		0			0
$187$	−8.58172	+	11.8117i	−0.0458916	+	0.0631643i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−90.8129	+	124.993i	−0.475460	+	0.654415i	−0.977625	−	0.210357i	$-0.932537\pi$
$191$	−90.8129	+	124.993i	−0.475460	+	0.654415i	0.502164	+	0.864772i	$0.332537\pi$
$192$		0			0
$193$		−	133.860i		−	0.693577i	−0.937943	−	0.346788i	$-0.887272\pi$
$193$		−	133.860i		−	0.693577i	0.937943	−	0.346788i	$-0.112728\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	27.5129	−	84.6759i	0.139659	−	0.429827i	−0.856626	−	0.515937i	$-0.827444\pi$
$197$	27.5129	−	84.6759i	0.139659	−	0.429827i	0.996286	+	0.0861103i	$0.0274437\pi$
$198$		0			0
$199$	−194.479			−0.977283			−0.488642	−	0.872485i	$-0.662507\pi$
$199$	−194.479			−0.977283			−0.488642	+	0.872485i	$0.662507\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	64.8584	−	199.613i	0.319499	−	0.983318i
$204$		0			0
$205$	45.8553	+	106.558i	0.223685	+	0.519795i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−37.2042	+	51.2072i	−0.178011	+	0.245011i
$210$		0			0
$211$	332.381	−	241.489i	1.57526	−	1.14450i	0.653379	−	0.757031i	$-0.273351\pi$
$211$	332.381	−	241.489i	1.57526	−	1.14450i	0.921885	−	0.387464i	$-0.126649\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−191.365	−	113.697i	−0.890069	−	0.528825i
$216$		0			0
$217$	−93.9958	+	30.5411i	−0.433160	+	0.140742i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	7.23296	+	2.35013i	0.0327283	+	0.0106341i
$222$		0			0
$223$	−220.676	−	303.735i	−0.989579	−	1.36204i	−0.931506	−	0.363727i	$-0.881504\pi$
$223$	−220.676	−	303.735i	−0.989579	−	1.36204i	−0.0580737	−	0.998312i	$-0.518496\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−103.589	+	75.2615i	−0.456337	+	0.331548i	−0.792093	−	0.610401i	$-0.791008\pi$
$227$	−103.589	+	75.2615i	−0.456337	+	0.331548i	0.335756	+	0.941949i	$0.391008\pi$
$228$		0			0
$229$	−64.1317	+	197.377i	−0.280051	+	0.861908i	0.707788	+	0.706425i	$0.249693\pi$
$229$	−64.1317	+	197.377i	−0.280051	+	0.861908i	−0.987839	+	0.155483i	$0.950307\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−1.06502	−	3.27778i	−0.00457088	−	0.0140677i	0.948745	−	0.316042i	$-0.102354\pi$
$233$	−1.06502	−	3.27778i	−0.00457088	−	0.0140677i	−0.953316	+	0.301975i	$0.902354\pi$
$234$		0			0
$235$	−163.751	−	186.501i	−0.696813	−	0.793619i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−227.224	−	312.747i	−0.950727	−	1.30856i	−0.951204	−	0.308564i	$-0.900152\pi$
$239$	−227.224	−	312.747i	−0.950727	−	1.30856i	0.000476106	−	1.00000i	$-0.499848\pi$
$240$		0			0
$241$	350.498	+	254.652i	1.45435	+	1.05665i	0.984791	+	0.173744i	$0.0555867\pi$
$241$	350.498	+	254.652i	1.45435	+	1.05665i	0.469558	+	0.882902i	$0.344413\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−34.2568	+	57.6578i	−0.139824	+	0.235338i
$246$		0			0
$247$	31.3570	+	10.1885i	0.126951	+	0.0412490i
$248$		0			0
$249$		0			0
$250$		0			0
$251$		−	142.770i		−	0.568803i	−0.958705	−	0.284402i	$-0.908205\pi$
$251$		−	142.770i		−	0.568803i	0.958705	−	0.284402i	$-0.0917949\pi$
$252$		0			0
$253$	−129.502	−	42.0776i	−0.511864	−	0.166315i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−119.380			−0.464514			−0.232257	−	0.972654i	$-0.574611\pi$
$257$	−119.380			−0.464514			−0.232257	+	0.972654i	$0.574611\pi$
$258$		0			0
$259$	345.428	+	250.968i	1.33370	+	0.968988i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−42.8985	−	31.1676i	−0.163112	−	0.118508i	0.503235	−	0.864150i	$-0.332143\pi$
$263$	−42.8985	−	31.1676i	−0.163112	−	0.118508i	−0.666347	+	0.745642i	$0.732143\pi$
$264$		0			0
$265$	−13.6870	−	15.5885i	−0.0516492	−	0.0588247i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	98.7891	−	32.0985i	0.367246	−	0.119325i	−0.119580	−	0.992825i	$-0.538155\pi$
$269$	98.7891	−	32.0985i	0.367246	−	0.119325i	0.486825	+	0.873499i	$0.338155\pi$
$270$		0			0
$271$	65.7369	−	202.317i	0.242572	−	0.746559i	−0.753455	−	0.657500i	$-0.771614\pi$
$271$	65.7369	−	202.317i	0.242572	−	0.746559i	0.996026	−	0.0890589i	$-0.0283859\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	94.4812	−	198.686i	0.343568	−	0.722495i
$276$		0			0
$277$	180.765	+	248.802i	0.652582	+	0.898202i	0.999208	−	0.0398013i	$-0.0126725\pi$
$277$	180.765	+	248.802i	0.652582	+	0.898202i	−0.346625	+	0.938004i	$0.612672\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	65.5515	−	21.2990i	0.233279	−	0.0757970i	−0.190045	−	0.981775i	$-0.560863\pi$
$281$	65.5515	−	21.2990i	0.233279	−	0.0757970i	0.423324	+	0.905978i	$0.360863\pi$
$282$		0			0
$283$	410.296	−	133.313i	1.44981	−	0.471072i	0.524869	−	0.851183i	$-0.324114\pi$
$283$	410.296	−	133.313i	1.44981	−	0.471072i	0.924941	+	0.380111i	$0.124114\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−111.972	−	81.3526i	−0.390147	−	0.283459i
$288$		0			0
$289$	231.579	−	168.252i	0.801312	−	0.582187i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	173.323			0.591544			0.295772	−	0.955258i	$-0.404423\pi$
$293$	173.323			0.591544			0.295772	+	0.955258i	$0.404423\pi$
$294$		0			0
$295$	−196.066	−	455.616i	−0.664632	−	1.54446i
$296$		0			0
$297$		0			0
$298$		0			0
$299$			70.9289i			0.237220i
$300$		0			0
$301$	265.574			0.882304
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−16.1812	−	174.967i	−0.0530531	−	0.573662i
$306$		0			0
$307$			74.3533i			0.242193i	0.992641	+	0.121097i	$0.0386411\pi$
$307$			74.3533i			0.242193i	−0.992641	+	0.121097i	$0.961359\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	112.755	+	155.193i	0.362555	+	0.499014i	0.950858	−	0.309626i	$-0.100204\pi$
$311$	112.755	+	155.193i	0.362555	+	0.499014i	−0.588303	+	0.808640i	$0.700204\pi$
$312$		0			0
$313$	191.016	−	262.911i	0.610274	−	0.839970i	−0.386326	−	0.922362i	$-0.626256\pi$
$313$	191.016	−	262.911i	0.610274	−	0.839970i	0.996600	+	0.0823923i	$0.0262560\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−168.174	−	517.587i	−0.530518	−	1.63277i	−0.753139	−	0.657861i	$-0.771461\pi$
$317$	−168.174	−	517.587i	−0.530518	−	1.63277i	0.222622	−	0.974905i	$-0.428539\pi$
$318$		0			0
$319$	95.6793	+	294.471i	0.299935	+	0.923106i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−9.65374	+	7.01385i	−0.0298877	+	0.0217147i
$324$		0			0
$325$	−113.638	−	14.8245i	−0.349657	−	0.0456140i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	281.617	+	91.5030i	0.855980	+	0.278125i
$330$		0			0
$331$	−48.0936	−	148.017i	−0.145298	−	0.447181i	0.851751	−	0.523946i	$-0.175541\pi$
$331$	−48.0936	−	148.017i	−0.145298	−	0.447181i	−0.997049	+	0.0767652i	$0.975541\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	43.6197	−	193.300i	0.130208	−	0.577016i
$336$		0			0
$337$	−280.823	+	386.520i	−0.833302	+	1.14694i	0.153997	+	0.988071i	$0.450785\pi$
$337$	−280.823	+	386.520i	−0.833302	+	1.14694i	−0.987299	+	0.158871i	$0.949215\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	85.6984	−	117.954i	0.251315	−	0.345906i
$342$		0			0
$343$		−	372.324i		−	1.08549i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−37.6029	+	115.730i	−0.108366	+	0.333515i	−0.990506	−	0.137472i	$-0.956102\pi$
$347$	−37.6029	+	115.730i	−0.108366	+	0.333515i	0.882140	+	0.470987i	$0.156102\pi$
$348$		0			0
$349$	596.578			1.70939			0.854696	−	0.519128i	$-0.173743\pi$
$349$	596.578			1.70939			0.854696	+	0.519128i	$0.173743\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	139.861	−	430.449i	0.396208	−	1.21940i	−0.531810	−	0.846864i	$-0.678488\pi$
$353$	139.861	−	430.449i	0.396208	−	1.21940i	0.928017	−	0.372537i	$-0.121512\pi$
$354$		0			0
$355$	−93.2180	+	81.8473i	−0.262586	+	0.230556i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−313.859	+	431.990i	−0.874258	+	1.20331i	0.103720	+	0.994607i	$0.466925\pi$
$359$	−313.859	+	431.990i	−0.874258	+	1.20331i	−0.977978	+	0.208707i	$0.933075\pi$
$360$		0			0
$361$	250.203	−	181.783i	0.693084	−	0.503555i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	320.452	−	29.6359i	0.877950	−	0.0811942i
$366$		0			0
$367$	92.1398	−	29.9380i	0.251062	−	0.0815750i	−0.180782	−	0.983523i	$-0.557863\pi$
$367$	92.1398	−	29.9380i	0.251062	−	0.0815750i	0.431844	+	0.901948i	$0.357863\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	23.5388	+	7.64822i	0.0634469	+	0.0206152i
$372$		0			0
$373$	−12.1480	−	16.7203i	−0.0325684	−	0.0448266i	0.792422	−	0.609973i	$-0.208820\pi$
$373$	−12.1480	−	16.7203i	−0.0325684	−	0.0448266i	−0.824991	+	0.565146i	$0.808820\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	130.481	−	94.8000i	0.346104	−	0.251459i
$378$		0			0
$379$	−76.6118	+	235.787i	−0.202142	+	0.622129i	0.797677	+	0.603085i	$0.206062\pi$
$379$	−76.6118	+	235.787i	−0.202142	+	0.622129i	−0.999819	+	0.0190437i	$0.993938\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−69.7658	−	214.717i	−0.182156	−	0.560619i	0.817732	−	0.575600i	$-0.195231\pi$
$383$	−69.7658	−	214.717i	−0.182156	−	0.560619i	−0.999888	+	0.0149806i	$0.995231\pi$
$384$		0			0
$385$	24.1721	+	261.373i	0.0627847	+	0.678890i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−175.051	−	240.937i	−0.450003	−	0.619376i	0.522395	−	0.852704i	$-0.325039\pi$
$389$	−175.051	−	240.937i	−0.450003	−	0.619376i	−0.972398	+	0.233327i	$0.925039\pi$
$390$		0			0
$391$	−20.7678	−	15.0887i	−0.0531146	−	0.0385900i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−241.784	−	275.374i	−0.612111	−	0.697150i
$396$		0			0
$397$	−662.979	−	215.415i	−1.66997	−	0.542607i	−0.687048	−	0.726612i	$-0.741094\pi$
$397$	−662.979	−	215.415i	−1.66997	−	0.542607i	−0.982925	+	0.184005i	$0.941094\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$			209.656i			0.522832i	0.965226	+	0.261416i	$0.0841894\pi$
$401$			209.656i			0.522832i	−0.965226	+	0.261416i	$0.915811\pi$
$402$		0			0
$403$	−72.2295	−	23.4688i	−0.179230	−	0.0582352i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−629.871			−1.54759
$408$		0			0
$409$	35.1260	+	25.5205i	0.0858827	+	0.0623974i	0.629898	−	0.776678i	$-0.283097\pi$
$409$	35.1260	+	25.5205i	0.0858827	+	0.0623974i	−0.544015	+	0.839075i	$0.683097\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	478.766	+	347.844i	1.15924	+	0.842238i
$414$		0			0
$415$	−302.113	−	68.1740i	−0.727982	−	0.164275i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−644.010	+	209.252i	−1.53702	+	0.499407i	−0.950552	−	0.310567i	$-0.899481\pi$
$419$	−644.010	+	209.252i	−1.53702	+	0.499407i	−0.586466	+	0.809974i	$0.699481\pi$
$420$		0			0
$421$	163.228	−	502.366i	0.387716	−	1.19327i	−0.546775	−	0.837280i	$-0.684145\pi$
$421$	163.228	−	502.366i	0.387716	−	1.19327i	0.934491	−	0.355988i	$-0.115855\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	28.5149	−	30.1195i	0.0670939	−	0.0708693i
$426$		0			0
$427$	123.225	+	169.604i	0.288582	+	0.397199i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−229.672	+	74.6251i	−0.532883	+	0.173144i	−0.563084	−	0.826400i	$-0.690385\pi$
$431$	−229.672	+	74.6251i	−0.532883	+	0.173144i	0.0302011	+	0.999544i	$0.490385\pi$
$432$		0			0
$433$	−21.7992	+	7.08299i	−0.0503446	+	0.0163580i	−0.334081	−	0.942544i	$-0.608426\pi$
$433$	−21.7992	+	7.08299i	−0.0503446	+	0.0163580i	0.283736	+	0.958902i	$0.408426\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−90.0344	−	65.4139i	−0.206028	−	0.149688i
$438$		0			0
$439$	146.750	−	106.620i	0.334283	−	0.242871i	−0.407963	−	0.912999i	$-0.633761\pi$
$439$	146.750	−	106.620i	0.334283	−	0.242871i	0.742246	+	0.670128i	$0.233761\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	291.063			0.657028			0.328514	−	0.944499i	$-0.393452\pi$
$443$	291.063			0.657028			0.328514	+	0.944499i	$0.393452\pi$
$444$		0			0
$445$	−151.881	+	14.0462i	−0.341306	+	0.0315645i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			215.383i			0.479694i	0.970811	+	0.239847i	$0.0770973\pi$
$449$			215.383i			0.479694i	−0.970811	+	0.239847i	$0.922903\pi$
$450$		0			0
$451$	204.176			0.452719
$452$		0			0
$453$		0			0
$454$		0			0
$455$	125.594	−	54.0473i	0.276032	−	0.118785i
$456$		0			0
$457$			485.536i			1.06244i	0.847233	+	0.531221i	$0.178267\pi$
$457$			485.536i			1.06244i	−0.847233	+	0.531221i	$0.821733\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	153.038	+	210.639i	0.331969	+	0.456917i	0.942074	−	0.335404i	$-0.108873\pi$
$461$	153.038	+	210.639i	0.331969	+	0.456917i	−0.610105	+	0.792320i	$0.708873\pi$
$462$		0			0
$463$	−150.099	+	206.593i	−0.324187	+	0.446205i	−0.939740	−	0.341890i	$-0.888933\pi$
$463$	−150.099	+	206.593i	−0.324187	+	0.446205i	0.615553	+	0.788096i	$0.288933\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−159.775	−	491.737i	−0.342130	−	1.05297i	−0.963102	−	0.269136i	$-0.913262\pi$
$467$	−159.775	−	491.737i	−0.342130	−	1.05297i	0.620972	−	0.783833i	$-0.286738\pi$
$468$		0			0
$469$	73.0590	+	224.853i	0.155776	+	0.479430i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−316.953	+	230.280i	−0.670091	+	0.486849i
$474$		0			0
$475$	123.620	−	130.577i	0.260253	−	0.274898i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	194.532	+	63.2072i	0.406121	+	0.131957i	0.504952	−	0.863148i	$-0.331510\pi$
$479$	194.532	+	63.2072i	0.406121	+	0.131957i	−0.0988310	+	0.995104i	$0.531510\pi$
$480$		0			0
$481$	101.388	+	312.041i	0.210787	+	0.648734i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	175.495	−	154.088i	0.361845	−	0.317707i
$486$		0			0
$487$	−486.317	+	669.357i	−0.998597	+	1.37445i	−0.0724143	+	0.997375i	$0.523070\pi$
$487$	−486.317	+	669.357i	−0.998597	+	1.37445i	−0.926182	+	0.377076i	$0.876930\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−193.321	+	266.084i	−0.393730	+	0.541923i	−0.959157	−	0.282876i	$-0.908712\pi$
$491$	−193.321	+	266.084i	−0.393730	+	0.541923i	0.565427	+	0.824799i	$0.308712\pi$
$492$		0			0
$493$			58.3714i			0.118400i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	45.7357	−	140.760i	0.0920235	−	0.283219i
$498$		0			0
$499$	296.150			0.593487			0.296744	−	0.954957i	$-0.404099\pi$
$499$	296.150			0.593487			0.296744	+	0.954957i	$0.404099\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−157.710	+	485.381i	−0.313538	+	0.964972i	0.662813	+	0.748785i	$0.269362\pi$
$503$	−157.710	+	485.381i	−0.313538	+	0.964972i	−0.976352	+	0.216188i	$0.930638\pi$
$504$		0			0
$505$	−749.009	−	445.016i	−1.48319	−	0.881220i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−248.572	+	342.130i	−0.488354	+	0.672161i	−0.980083	−	0.198587i	$-0.936365\pi$
$509$	−248.572	+	342.130i	−0.488354	+	0.672161i	0.491730	+	0.870748i	$0.336365\pi$
$510$		0			0
$511$	−310.630	+	225.686i	−0.607886	+	0.441655i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	254.230	−	223.219i	0.493651	−	0.433435i
$516$		0			0
$517$	−415.443	+	134.986i	−0.803565	+	0.261094i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	829.502	+	269.522i	1.59213	+	0.517316i	0.965146	−	0.261712i	$-0.0842872\pi$
$521$	829.502	+	269.522i	1.59213	+	0.517316i	0.626989	+	0.779028i	$0.284287\pi$
$522$		0			0
$523$	−514.149	−	707.665i	−0.983076	−	1.35309i	−0.935156	−	0.354236i	$-0.884741\pi$
$523$	−514.149	−	707.665i	−0.983076	−	1.35309i	−0.0479198	−	0.998851i	$-0.515259\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	22.2370	−	16.1561i	0.0421954	−	0.0306568i
$528$		0			0
$529$	−89.4875	+	275.414i	−0.169164	+	0.520632i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−32.8656	−	101.150i	−0.0616615	−	0.189775i
$534$		0			0
$535$	266.471	−	448.498i	0.498076	−	0.838315i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	69.3828	+	95.4972i	0.128725	+	0.177175i
$540$		0			0
$541$	−557.864	−	405.312i	−1.03117	−	0.749191i	−0.0626296	−	0.998037i	$-0.519949\pi$
$541$	−557.864	−	405.312i	−1.03117	−	0.749191i	−0.968543	+	0.248846i	$0.919949\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−104.449	+	44.9476i	−0.191649	+	0.0824727i
$546$		0			0
$547$	658.871	+	214.080i	1.20452	+	0.391372i	0.841421	−	0.540380i	$-0.181719\pi$
$547$	658.871	+	214.080i	1.20452	+	0.391372i	0.363097	+	0.931751i	$0.381719\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$			253.057i			0.459268i
$552$		0			0
$553$	415.817	+	135.107i	0.751930	+	0.244317i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−15.5607			−0.0279366			−0.0139683	−	0.999902i	$-0.504446\pi$
$557$	−15.5607			−0.0279366			−0.0139683	+	0.999902i	$0.504446\pi$
$558$		0			0
$559$	165.101	+	119.953i	0.295350	+	0.214584i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	621.159	+	451.298i	1.10330	+	0.801596i	0.981596	−	0.190971i	$-0.0611635\pi$
$563$	621.159	+	451.298i	1.10330	+	0.801596i	0.121706	+	0.992566i	$0.461164\pi$
$564$		0			0
$565$	−606.694	+	261.080i	−1.07379	+	0.462088i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−65.1828	+	21.1792i	−0.114557	+	0.0372218i	−0.365734	−	0.930719i	$-0.619182\pi$
$569$	−65.1828	+	21.1792i	−0.114557	+	0.0372218i	0.251178	+	0.967941i	$0.419182\pi$
$570$		0			0
$571$	−91.0219	+	280.137i	−0.159408	+	0.490607i	−0.998581	−	0.0532577i	$-0.983040\pi$
$571$	−91.0219	+	280.137i	−0.159408	+	0.490607i	0.839173	+	0.543865i	$0.183040\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	349.338	+	166.120i	0.607544	+	0.288905i
$576$		0			0
$577$	−252.293	−	347.251i	−0.437249	−	0.601821i	0.532349	−	0.846525i	$-0.321309\pi$
$577$	−252.293	−	347.251i	−0.437249	−	0.601821i	−0.969598	+	0.244704i	$0.921309\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	351.426	−	114.185i	0.604864	−	0.196532i
$582$		0			0
$583$	−34.7245	+	11.2827i	−0.0595618	+	0.0193528i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−241.216	−	175.254i	−0.410930	−	0.298558i	0.363048	−	0.931770i	$-0.381736\pi$
$587$	−241.216	−	175.254i	−0.410930	−	0.298558i	−0.773978	+	0.633212i	$0.781736\pi$
$588$		0			0
$589$	96.4038	−	70.0414i	0.163674	−	0.118916i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	777.524			1.31117			0.655585	−	0.755121i	$-0.272422\pi$
$593$	777.524			1.31117			0.655585	+	0.755121i	$0.272422\pi$
$594$		0			0
$595$	−10.8928	+	48.2712i	−0.0183072	+	0.0811281i
$596$		0			0
$597$		0			0
$598$		0			0
$599$			1061.22i			1.77165i	0.464016	+	0.885827i	$0.346408\pi$
$599$			1061.22i			1.77165i	−0.464016	+	0.885827i	$0.653592\pi$
$600$		0			0
$601$	738.426			1.22866			0.614331	−	0.789049i	$-0.289426\pi$
$601$	738.426			1.22866			0.614331	+	0.789049i	$0.289426\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	143.687	+	163.648i	0.237499	+	0.270493i
$606$		0			0
$607$			3.70790i			0.00610857i	0.999995	+	0.00305428i	$0.000972211\pi$
$607$			3.70790i			0.00610857i	−0.999995	+	0.00305428i	$0.999028\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	133.745	+	184.084i	0.218895	+	0.301284i
$612$		0			0
$613$	−297.836	+	409.936i	−0.485866	+	0.668737i	−0.979619	−	0.200865i	$-0.935625\pi$
$613$	−297.836	+	409.936i	−0.485866	+	0.668737i	0.493753	+	0.869602i	$0.335625\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	294.352	+	905.922i	0.477070	+	1.46827i	0.843146	+	0.537685i	$0.180701\pi$
$617$	294.352	+	905.922i	0.477070	+	1.46827i	−0.366076	+	0.930585i	$0.619299\pi$
$618$		0			0
$619$	131.430	+	404.501i	0.212327	+	0.653475i	0.999333	+	0.0365291i	$0.0116302\pi$
$619$	131.430	+	404.501i	0.212327	+	0.653475i	−0.787006	+	0.616946i	$0.788370\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	147.226	−	106.966i	0.236318	−	0.171695i
$624$		0			0
$625$	−339.163	+	524.970i	−0.542660	+	0.839952i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−112.933	−	36.6943i	−0.179544	−	0.0583375i
$630$		0			0
$631$	−177.471	−	546.198i	−0.281253	−	0.865607i	−0.987497	−	0.157639i	$-0.949612\pi$
$631$	−177.471	−	546.198i	−0.281253	−	0.865607i	0.706244	−	0.707969i	$-0.250388\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−213.296	+	19.7259i	−0.335899	+	0.0310644i
$636$		0			0
$637$	36.1415	−	49.7444i	0.0567370	−	0.0780917i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−398.368	+	548.306i	−0.621478	+	0.855392i	−0.997460	−	0.0712358i	$-0.977306\pi$
$641$	−398.368	+	548.306i	−0.621478	+	0.855392i	0.375981	+	0.926627i	$0.377306\pi$
$642$		0			0
$643$		−	1101.86i		−	1.71362i	−0.515635	−	0.856809i	$-0.672444\pi$
$643$		−	1101.86i		−	1.71362i	0.515635	−	0.856809i	$-0.327556\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−301.475	+	927.845i	−0.465959	+	1.43407i	0.391814	+	0.920044i	$0.371848\pi$
$647$	−301.475	+	927.845i	−0.465959	+	1.43407i	−0.857773	+	0.514029i	$0.828152\pi$
$648$		0			0
$649$	−873.008			−1.34516
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−83.7287	+	257.690i	−0.128222	+	0.394625i	−0.994474	−	0.104981i	$-0.966522\pi$
$653$	−83.7287	+	257.690i	−0.128222	+	0.394625i	0.866253	+	0.499606i	$0.166522\pi$
$654$		0			0
$655$	−20.5349	+	91.0004i	−0.0313510	+	0.138932i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	662.328	−	911.616i	1.00505	−	1.38333i	0.0828745	−	0.996560i	$-0.473590\pi$
$659$	662.328	−	911.616i	1.00505	−	1.38333i	0.922175	−	0.386772i	$-0.126410\pi$
$660$		0			0
$661$	862.889	−	626.925i	1.30543	−	0.948450i	0.305436	−	0.952213i	$-0.401198\pi$
$661$	862.889	−	626.925i	1.30543	−	0.948450i	0.999993	+	0.00376285i	$0.00119776\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−47.2233	+	209.270i	−0.0710124	+	0.314691i
$666$		0			0
$667$	−517.749	+	168.227i	−0.776236	+	0.252214i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−294.129	−	95.5682i	−0.438344	−	0.142426i
$672$		0			0
$673$	−157.383	−	216.620i	−0.233854	−	0.321872i	0.675921	−	0.736974i	$-0.263746\pi$
$673$	−157.383	−	216.620i	−0.233854	−	0.321872i	−0.909775	+	0.415102i	$0.863746\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−370.162	+	268.938i	−0.546768	+	0.397250i	−0.826593	−	0.562801i	$-0.809724\pi$
$677$	−370.162	+	268.938i	−0.546768	+	0.397250i	0.279824	+	0.960051i	$0.409724\pi$
$678$		0			0
$679$	−86.1031	+	264.998i	−0.126809	+	0.390277i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−376.520	−	1158.81i	−0.551274	−	1.69665i	−0.705585	−	0.708625i	$-0.749316\pi$
$683$	−376.520	−	1158.81i	−0.551274	−	1.69665i	0.154311	−	0.988022i	$-0.450684\pi$
$684$		0			0
$685$	52.9873	−	22.8022i	0.0773538	−	0.0332878i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	11.1790	+	15.3866i	0.0162250	+	0.0223317i
$690$		0			0
$691$	692.641	+	503.233i	1.00237	+	0.728268i	0.962596	−	0.270941i	$-0.0873347\pi$
$691$	692.641	+	503.233i	1.00237	+	0.728268i	0.0397786	+	0.999209i	$0.487335\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	67.1408	+	725.992i	0.0966055	+	1.04459i
$696$		0			0
$697$	36.6080	+	11.8946i	0.0525222	+	0.0170655i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			1015.77i			1.44903i	0.689258	+	0.724516i	$0.257937\pi$
$701$			1015.77i			1.44903i	−0.689258	+	0.724516i	$0.742063\pi$
$702$		0			0
$703$	−489.599	−	159.080i	−0.696442	−	0.226288i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	1039.46			1.47025
$708$		0			0
$709$	217.863	+	158.287i	0.307282	+	0.223253i	0.730729	−	0.682667i	$-0.239180\pi$
$709$	217.863	+	158.287i	0.307282	+	0.223253i	−0.423447	+	0.905921i	$0.639180\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	207.391	+	150.678i	0.290871	+	0.211330i
$714$		0			0
$715$	−103.028	+	173.407i	−0.144095	+	0.242527i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−576.876	+	187.438i	−0.802331	+	0.260693i	−0.681346	−	0.731961i	$-0.738605\pi$
$719$	−576.876	+	187.438i	−0.802331	+	0.260693i	−0.120985	+	0.992654i	$0.538605\pi$
$720$		0			0
$721$	−124.733	+	383.889i	−0.173000	+	0.532440i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−161.312	−	864.671i	−0.222499	−	1.19265i
$726$		0			0
$727$	−1.89515	−	2.60846i	−0.00260681	−	0.00358797i	0.807712	−	0.589578i	$-0.200706\pi$
$727$	−1.89515	−	2.60846i	−0.00260681	−	0.00358797i	−0.810318	+	0.585990i	$0.800706\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−70.2437	+	22.8236i	−0.0960926	+	0.0312224i
$732$		0			0
$733$	89.0130	−	28.9221i	0.121437	−	0.0394571i	−0.247668	−	0.968845i	$-0.579664\pi$
$733$	89.0130	−	28.9221i	0.121437	−	0.0394571i	0.369105	+	0.929388i	$0.379664\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−282.164	−	205.004i	−0.382855	−	0.278160i
$738$		0			0
$739$	−865.121	+	628.547i	−1.17066	+	0.850538i	−0.991088	−	0.133206i	$-0.957473\pi$
$739$	−865.121	+	628.547i	−1.17066	+	0.850538i	−0.179576	+	0.983744i	$0.557473\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	100.915			0.135821			0.0679103	−	0.997691i	$-0.478367\pi$
$743$	100.915			0.135821			0.0679103	+	0.997691i	$0.478367\pi$
$744$		0			0
$745$	−538.706	−	320.067i	−0.723095	−	0.429620i
$746$		0			0
$747$		0			0
$748$		0			0
$749$			622.420i			0.831002i
$750$		0			0
$751$	−380.982			−0.507300			−0.253650	−	0.967296i	$-0.581631\pi$
$751$	−380.982			−0.507300			−0.253650	+	0.967296i	$0.581631\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−253.074	+	425.950i	−0.335197	+	0.564173i
$756$		0			0
$757$			124.692i			0.164719i	0.996603	+	0.0823594i	$0.0262455\pi$
$757$			124.692i			0.164719i	−0.996603	+	0.0823594i	$0.973754\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−233.413	−	321.265i	−0.306719	−	0.422162i	0.627636	−	0.778507i	$-0.284023\pi$
$761$	−233.413	−	321.265i	−0.306719	−	0.422162i	−0.934354	+	0.356345i	$0.884023\pi$
$762$		0			0
$763$	79.7422	−	109.756i	0.104511	−	0.143848i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	140.525	+	432.492i	0.183214	+	0.563875i
$768$		0			0
$769$	−186.882	−	575.163i	−0.243019	−	0.747936i	−0.995956	−	0.0898433i	$-0.971363\pi$
$769$	−186.882	−	575.163i	−0.243019	−	0.747936i	0.752937	−	0.658093i	$-0.228637\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−1089.85	+	791.822i	−1.40990	+	1.02435i	−0.416558	+	0.909109i	$0.636764\pi$
$773$	−1089.85	+	791.822i	−1.40990	+	1.02435i	−0.993338	+	0.115240i	$0.963236\pi$
$774$		0			0
$775$	−284.754	+	300.778i	−0.367425	+	0.388101i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	158.706	+	51.5667i	0.203730	+	0.0661960i
$780$		0			0
$781$	67.4695	+	207.650i	0.0863886	+	0.265877i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−465.141	−	276.359i	−0.592537	−	0.352050i
$786$		0			0
$787$	168.739	−	232.250i	0.214408	−	0.295108i	−0.688243	−	0.725480i	$-0.741618\pi$
$787$	168.739	−	232.250i	0.214408	−	0.295108i	0.902651	+	0.430372i	$0.141618\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	463.186	−	637.520i	0.585570	−	0.805968i
$792$		0			0
$793$			161.096i			0.203148i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	395.309	−	1216.64i	0.495997	−	1.52652i	−0.319401	−	0.947620i	$-0.603482\pi$
$797$	395.309	−	1216.64i	0.495997	−	1.52652i	0.815397	−	0.578902i	$-0.196518\pi$
$798$		0			0
$799$	−82.3511			−0.103068
$800$		0			0
$801$		0			0
$802$		0			0
$803$	175.033	−	538.697i	0.217974	−	0.670855i
$804$		0			0
$805$	−459.555	+	42.5003i	−0.570876	+	0.0527954i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	792.694	−	1091.05i	0.979845	−	1.34864i	0.0429314	−	0.999078i	$-0.486330\pi$
$809$	792.694	−	1091.05i	0.979845	−	1.34864i	0.936913	−	0.349562i	$-0.113670\pi$
$810$		0			0
$811$	−703.375	+	511.032i	−0.867293	+	0.630125i	−0.929859	−	0.367915i	$-0.880072\pi$
$811$	−703.375	+	511.032i	−0.867293	+	0.630125i	0.0625660	+	0.998041i	$0.480072\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	208.509	+	484.531i	0.255840	+	0.594516i
$816$		0			0
$817$	−304.527	+	98.9467i	−0.372738	+	0.121110i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−77.3630	−	25.1368i	−0.0942302	−	0.0306172i	0.261522	−	0.965197i	$-0.415775\pi$
$821$	−77.3630	−	25.1368i	−0.0942302	−	0.0306172i	−0.355753	+	0.934580i	$0.615775\pi$
$822$		0			0
$823$	−227.247	−	312.779i	−0.276120	−	0.380047i	0.648324	−	0.761365i	$-0.275470\pi$
$823$	−227.247	−	312.779i	−0.276120	−	0.380047i	−0.924444	+	0.381318i	$0.875470\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−150.204	+	109.130i	−0.181625	+	0.131959i	−0.674883	−	0.737925i	$-0.735806\pi$
$827$	−150.204	+	109.130i	−0.181625	+	0.131959i	0.493258	+	0.869883i	$0.335806\pi$
$828$		0			0
$829$	220.332	−	678.111i	0.265780	−	0.817987i	−0.725733	−	0.687977i	$-0.758499\pi$
$829$	220.332	−	678.111i	0.265780	−	0.817987i	0.991513	−	0.130010i	$-0.0415010\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	6.87669	+	21.1643i	0.00825533	+	0.0254073i
$834$		0			0
$835$	301.521	+	68.0404i	0.361103	+	0.0814855i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−146.195	−	201.220i	−0.174249	−	0.239833i	0.712956	−	0.701209i	$-0.247356\pi$
$839$	−146.195	−	201.220i	−0.174249	−	0.239833i	−0.887205	+	0.461376i	$0.847356\pi$
$840$		0			0
$841$	321.086	+	233.283i	0.381791	+	0.277387i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−721.783	−	162.876i	−0.854181	−	0.192752i
$846$		0			0
$847$	−247.111	−	80.2911i	−0.291748	−	0.0947947i
$848$		0			0
$849$		0			0
$850$		0			0
$851$		−	1107.46i		−	1.30137i
$852$		0			0
$853$	1312.01	+	426.297i	1.53811	+	0.499762i	0.950854	−	0.309639i	$-0.100208\pi$
$853$	1312.01	+	426.297i	1.53811	+	0.499762i	0.587256	+	0.809402i	$0.300208\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−625.699			−0.730104			−0.365052	−	0.930987i	$-0.618949\pi$
$857$	−625.699			−0.730104			−0.365052	+	0.930987i	$0.618949\pi$
$858$		0			0
$859$	933.487	+	678.218i	1.08671	+	0.789544i	0.978841	−	0.204621i	$-0.0655961\pi$
$859$	933.487	+	678.218i	1.08671	+	0.789544i	0.107873	+	0.994165i	$0.465596\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	1146.13	+	832.716i	1.32808	+	0.964908i	0.999793	+	0.0203308i	$0.00647195\pi$
$863$	1146.13	+	832.716i	1.32808	+	0.964908i	0.328289	+	0.944577i	$0.393528\pi$
$864$		0			0
$865$	68.3376	+	738.933i	0.0790030	+	0.854258i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−613.415	+	199.311i	−0.705886	+	0.229356i
$870$		0			0
$871$	−56.1410	+	172.784i	−0.0644558	+	0.198374i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	27.9578	−	745.158i	0.0319518	−	0.851609i
$876$		0			0
$877$	173.361	+	238.611i	0.197675	+	0.272076i	0.896335	−	0.443378i	$-0.146220\pi$
$877$	173.361	+	238.611i	0.197675	+	0.272076i	−0.698660	+	0.715454i	$0.746220\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	11.8843	−	3.86145i	0.0134896	−	0.00438303i	−0.302264	−	0.953224i	$-0.597743\pi$
$881$	11.8843	−	3.86145i	0.0134896	−	0.00438303i	0.315754	+	0.948841i	$0.397743\pi$
$882$		0			0
$883$	−293.943	+	95.5078i	−0.332891	+	0.108163i	−0.470693	−	0.882297i	$-0.655996\pi$
$883$	−293.943	+	95.5078i	−0.332891	+	0.108163i	0.137802	+	0.990460i	$0.455996\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	639.699	+	464.769i	0.721194	+	0.523978i	0.886765	−	0.462220i	$-0.152947\pi$
$887$	639.699	+	464.769i	0.721194	+	0.523978i	−0.165571	+	0.986198i	$0.552947\pi$
$888$		0			0
$889$	206.758	−	150.219i	0.232574	−	0.168975i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−357.016			−0.399794
$894$		0			0
$895$	785.368	−	689.568i	0.877506	−	0.770467i
$896$		0			0
$897$		0			0
$898$		0			0
$899$		−	582.906i		−	0.648394i
$900$		0			0
$901$	−6.88326			−0.00763958
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−227.988	−	51.4473i	−0.251921	−	0.0568478i
$906$		0			0
$907$			79.9291i			0.0881247i	0.999029	+	0.0440624i	$0.0140300\pi$
$907$			79.9291i			0.0881247i	−0.999029	+	0.0440624i	$0.985970\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	345.174	+	475.092i	0.378896	+	0.521506i	0.955292	−	0.295665i	$-0.0955413\pi$
$911$	345.174	+	475.092i	0.378896	+	0.521506i	−0.576396	+	0.817171i	$0.695541\pi$
$912$		0			0
$913$	−320.404	+	440.999i	−0.350936	+	0.483022i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−34.3941	−	105.854i	−0.0375072	−	0.115435i
$918$		0			0
$919$	−247.460	−	761.602i	−0.269270	−	0.828729i	−0.990679	−	0.136219i	$-0.956505\pi$
$919$	−247.460	−	761.602i	−0.269270	−	0.828729i	0.721408	−	0.692510i	$-0.243495\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	92.0104	−	66.8494i	0.0996862	−	0.0724263i
$924$		0			0
$925$	1774.32	+	231.466i	1.91818	+	0.250234i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	873.641	+	283.863i	0.940410	+	0.305558i	0.738813	−	0.673911i	$-0.235387\pi$
$929$	873.641	+	283.863i	0.940410	+	0.305558i	0.201597	+	0.979469i	$0.435387\pi$
$930$		0			0
$931$	29.8124	+	91.7532i	0.0320219	+	0.0985534i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−28.8560	−	67.0552i	−0.0308620	−	0.0717168i
$936$		0			0
$937$	1021.63	−	1406.16i	1.09033	−	1.50070i	0.242705	−	0.970100i	$-0.421965\pi$
$937$	1021.63	−	1406.16i	1.09033	−	1.50070i	0.847620	−	0.530604i	$-0.178035\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−177.987	+	244.978i	−0.189147	+	0.260338i	−0.893050	−	0.449958i	$-0.851439\pi$
$941$	−177.987	+	244.978i	−0.189147	+	0.260338i	0.703903	+	0.710296i	$0.251439\pi$
$942$		0			0
$943$			358.990i			0.380689i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	265.853	−	818.210i	0.280731	−	0.864003i	−0.706914	−	0.707299i	$-0.749913\pi$
$947$	265.853	−	818.210i	0.280731	−	0.864003i	0.987646	−	0.156703i	$-0.0500866\pi$
$948$		0			0
$949$	−295.047			−0.310904
$950$		0			0
$951$		0			0
$952$		0			0
$953$	204.813	−	630.350i	0.214914	−	0.661438i	−0.784246	−	0.620451i	$-0.786950\pi$
$953$	204.813	−	630.350i	0.214914	−	0.661438i	0.999160	−	0.0409871i	$-0.0130503\pi$
$954$		0			0
$955$	−305.358	−	709.587i	−0.319747	−	0.743023i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−40.4536	+	55.6796i	−0.0421831	+	0.0580601i
$960$		0			0
$961$	555.403	−	403.524i	0.577943	−	0.419900i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	575.404	+	341.870i	0.596273	+	0.354270i
$966$		0			0
$967$	1480.49	−	481.041i	1.53102	−	0.497457i	0.582135	−	0.813092i	$-0.302217\pi$
$967$	1480.49	−	481.041i	1.53102	−	0.497457i	0.948881	+	0.315635i	$0.102217\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−394.881	−	128.305i	−0.406675	−	0.132137i	0.0985343	−	0.995134i	$-0.468585\pi$
$971$	−394.881	−	128.305i	−0.406675	−	0.132137i	−0.505209	+	0.862997i	$0.668585\pi$
$972$		0			0
$973$	−511.297	−	703.740i	−0.525485	−	0.723268i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	14.0435	−	10.2032i	0.0143741	−	0.0104434i	−0.580575	−	0.814207i	$-0.697172\pi$
$977$	14.0435	−	10.2032i	0.0143741	−	0.0104434i	0.594949	+	0.803763i	$0.297172\pi$
$978$		0			0
$979$	−82.9587	+	255.321i	−0.0847382	+	0.260797i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−224.996	−	692.467i	−0.228887	−	0.704442i	−0.997874	−	0.0651773i	$-0.979239\pi$
$983$	−224.996	−	692.467i	−0.228887	−	0.704442i	0.768987	−	0.639265i	$-0.220761\pi$
$984$		0			0
$985$	293.717	+	334.522i	0.298190	+	0.339616i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−404.886	−	557.278i	−0.409390	−	0.563477i
$990$		0			0
$991$	−397.232	−	288.606i	−0.400839	−	0.291227i	0.369043	−	0.929412i	$-0.379685\pi$
$991$	−397.232	−	288.606i	−0.400839	−	0.291227i	−0.769883	+	0.638185i	$0.779685\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	496.687	−	835.977i	0.499183	−	0.840178i
$996$		0			0
$997$	−370.412	−	120.354i	−0.371526	−	0.120716i	0.117302	−	0.993096i	$-0.462575\pi$
$997$	−370.412	−	120.354i	−0.371526	−	0.120716i	−0.488828	+	0.872380i	$0.662575\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.3.y.a.89.7	✓	80
3.2	odd	2	inner	900.3.y.a.89.14	yes	80
25.9	even	10	inner	900.3.y.a.809.14	yes	80
75.59	odd	10	inner	900.3.y.a.809.7	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
900.3.y.a.89.7	✓	80	1.1	even	1	trivial
900.3.y.a.89.14	yes	80	3.2	odd	2	inner
900.3.y.a.809.7	yes	80	75.59	odd	10	inner
900.3.y.a.809.14	yes	80	25.9	even	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	900.y (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.55393 + 4.29854i) q^{5} -5.96546i q^{7} +O(q^{10})\)	\(q+(-2.55393 + 4.29854i) q^{5} -5.96546i q^{7} +(5.17267 + 7.11956i) q^{11} +(2.69444 - 3.70858i) q^{13} +(0.512675 + 1.57785i) q^{17} +(2.22259 + 6.84044i) q^{19} +(-12.5179 + 9.09477i) q^{23} +(-11.9549 - 21.9564i) q^{25} +(33.4616 + 10.8723i) q^{29} +(-5.11966 - 15.7567i) q^{31} +(25.6427 + 15.2354i) q^{35} +(-42.0702 + 57.9047i) q^{37} +(13.6373 - 18.7701i) q^{41} +44.5186i q^{43} +(-15.3388 + 47.2080i) q^{47} +13.4133 q^{49} +(-1.28209 + 3.94585i) q^{53} +(-43.8144 + 4.05202i) q^{55} +(-58.3097 + 80.2565i) q^{59} +(-28.4310 + 20.6564i) q^{61} +(9.06005 + 21.0536i) q^{65} +(-37.6924 + 12.2470i) q^{67} +(23.5958 + 7.66676i) q^{71} +(-37.8321 - 52.0715i) q^{73} +(42.4714 - 30.8573i) q^{77} +(-22.6483 + 69.7042i) q^{79} +(19.1411 + 58.9102i) q^{83} +(-8.09179 - 1.82597i) q^{85} +(17.9309 + 24.6798i) q^{89} +(-22.1234 - 16.0736i) q^{91} +(-35.0803 - 7.91612i) q^{95} +(-44.4221 - 14.4336i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q+O(q^{10}) \) 80 * q	\( 80 q + 60 q^{19} + 56 q^{25} - 120 q^{31} + 20 q^{37} - 680 q^{49} - 56 q^{55} - 80 q^{61} - 280 q^{67} - 360 q^{73} + 40 q^{79} + 192 q^{85} + 140 q^{91} - 40 q^{97}+O(q^{100}) \) 80 * q + 60 * q^19 + 56 * q^25 - 120 * q^31 + 20 * q^37 - 680 * q^49 - 56 * q^55 - 80 * q^61 - 280 * q^67 - 360 * q^73 + 40 * q^79 + 192 * q^85 + 140 * q^91 - 40 * q^97

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