LMFDB - Embedded newform 1200.3.bg.q.1057.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1200,3,Mod(193,1200)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1200, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1200.193");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1200 = 2^{4} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1200.bg (of order $4$, degree $2$, not 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:	$32.6976317232$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 8x^{6} + 269x^{4} - 1116x^{3} + 2312x^{2} + 680x + 100 $ x^8 - 4x^7 + 8x^6 + 269x^4 - 1116x^3 + 2312x^2 + 680x + 100
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2}\cdot 5^{2} $
Twist minimal:	no (minimal twist has level 120)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1057.4
Root			$-0.137883 - 0.137883i$ of defining polynomial
Character	$\chi$	$=$	1200.1057
Dual form			1200.3.bg.q.193.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22474 - 1.22474i) q^{3} +(7.33876 + 7.33876i) q^{7} -3.00000i q^{9} +O(q^{10})$	$q+(1.22474 - 1.22474i) q^{3} +(7.33876 + 7.33876i) q^{7} -3.00000i q^{9} -6.49926 q^{11} +(-11.2377 + 11.2377i) q^{13} +(10.1367 + 10.1367i) q^{17} -6.67753i q^{19} +17.9762 q^{21} +(-21.0772 + 21.0772i) q^{23} +(-3.67423 - 3.67423i) q^{27} +12.2171i q^{29} -46.1933 q^{31} +(-7.95994 + 7.95994i) q^{33} +(48.6316 + 48.6316i) q^{37} +27.5267i q^{39} -60.0326 q^{41} +(22.1739 - 22.1739i) q^{43} +(-51.3507 - 51.3507i) q^{47} +58.7149i q^{49} +24.8298 q^{51} +(-42.4339 + 42.4339i) q^{53} +(-8.17826 - 8.17826i) q^{57} +0.297219i q^{59} +46.8766 q^{61} +(22.0163 - 22.0163i) q^{63} +(-13.4220 - 13.4220i) q^{67} +51.6285i q^{69} -46.3448 q^{71} +(42.4381 - 42.4381i) q^{73} +(-47.6965 - 47.6965i) q^{77} +27.7474i q^{79} -9.00000 q^{81} +(71.7548 - 71.7548i) q^{83} +(14.9628 + 14.9628i) q^{87} +69.5780i q^{89} -164.942 q^{91} +(-56.5750 + 56.5750i) q^{93} +(110.825 + 110.825i) q^{97} +19.4978i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{7}+O(q^{10}) $ 8 * q + 4 * q^7	$ 8 q + 4 q^{7} - 32 q^{11} + 4 q^{13} - 52 q^{17} - 24 q^{21} - 40 q^{23} - 96 q^{31} - 60 q^{33} + 60 q^{37} - 152 q^{41} - 88 q^{43} - 16 q^{47} + 168 q^{51} - 108 q^{53} + 24 q^{57} + 264 q^{61} + 12 q^{63} - 216 q^{67} + 240 q^{71} + 208 q^{73} - 168 q^{77} - 72 q^{81} + 336 q^{83} + 252 q^{87} - 592 q^{91} - 264 q^{93} + 208 q^{97}+O(q^{100}) $ 8 * q + 4 * q^7 - 32 * q^11 + 4 * q^13 - 52 * q^17 - 24 * q^21 - 40 * q^23 - 96 * q^31 - 60 * q^33 + 60 * q^37 - 152 * q^41 - 88 * q^43 - 16 * q^47 + 168 * q^51 - 108 * q^53 + 24 * q^57 + 264 * q^61 + 12 * q^63 - 216 * q^67 + 240 * q^71 + 208 * q^73 - 168 * q^77 - 72 * q^81 + 336 * q^83 + 252 * q^87 - 592 * q^91 - 264 * q^93 + 208 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1200\mathbb{Z}\right)^\times$.

$n$	$401$	$577$	$751$	$901$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$1$	$1$

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
$3$	1.22474	−	1.22474i	0.408248	−	0.408248i
$3$	1.22474	−	1.22474i	0.408248	−	0.408248i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	7.33876	+	7.33876i	1.04839	+	1.04839i	0.998768	+	0.0496268i	$0.0158032\pi$
$7$	7.33876	+	7.33876i	1.04839	+	1.04839i	0.0496268	+	0.998768i	$0.484197\pi$
$8$		0			0
$9$		−	3.00000i		−	0.333333i
$10$		0			0
$11$	−6.49926			−0.590842			−0.295421	−	0.955367i	$-0.595460\pi$
$11$	−6.49926			−0.590842			−0.295421	+	0.955367i	$0.595460\pi$
$12$		0			0
$13$	−11.2377	+	11.2377i	−0.864442	+	0.864442i	−0.991850	−	0.127409i	$-0.959334\pi$
$13$	−11.2377	+	11.2377i	−0.864442	+	0.864442i	0.127409	+	0.991850i	$0.459334\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	10.1367	+	10.1367i	0.596278	+	0.596278i	0.939320	−	0.343042i	$-0.111457\pi$
$17$	10.1367	+	10.1367i	0.596278	+	0.596278i	−0.343042	+	0.939320i	$0.611457\pi$
$18$		0			0
$19$		−	6.67753i		−	0.351449i	−0.984439	−	0.175724i	$-0.943773\pi$
$19$		−	6.67753i		−	0.351449i	0.984439	−	0.175724i	$-0.0562267\pi$
$20$		0			0
$21$	17.9762			0.856011
$22$		0			0
$23$	−21.0772	+	21.0772i	−0.916402	+	0.916402i	−0.996766	−	0.0803637i	$-0.974392\pi$
$23$	−21.0772	+	21.0772i	−0.916402	+	0.916402i	0.0803637	+	0.996766i	$0.474392\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−3.67423	−	3.67423i	−0.136083	−	0.136083i
$28$		0			0
$29$			12.2171i			0.421279i	0.977564	+	0.210640i	$0.0675546\pi$
$29$			12.2171i			0.421279i	−0.977564	+	0.210640i	$0.932445\pi$
$30$		0			0
$31$	−46.1933			−1.49011			−0.745053	−	0.667005i	$-0.767576\pi$
$31$	−46.1933			−1.49011			−0.745053	+	0.667005i	$0.767576\pi$
$32$		0			0
$33$	−7.95994	+	7.95994i	−0.241210	+	0.241210i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	48.6316	+	48.6316i	1.31437	+	1.31437i	0.918161	+	0.396207i	$0.129674\pi$
$37$	48.6316	+	48.6316i	1.31437	+	1.31437i	0.396207	+	0.918161i	$0.370326\pi$
$38$		0			0
$39$			27.5267i			0.705814i
$40$		0			0
$41$	−60.0326			−1.46421			−0.732105	−	0.681192i	$-0.761462\pi$
$41$	−60.0326			−1.46421			−0.732105	+	0.681192i	$0.761462\pi$
$42$		0			0
$43$	22.1739	−	22.1739i	0.515672	−	0.515672i	−0.400587	−	0.916259i	$-0.631194\pi$
$43$	22.1739	−	22.1739i	0.515672	−	0.515672i	0.916259	+	0.400587i	$0.131194\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−51.3507	−	51.3507i	−1.09257	−	1.09257i	−0.995254	−	0.0973141i	$-0.968975\pi$
$47$	−51.3507	−	51.3507i	−1.09257	−	1.09257i	−0.0973141	−	0.995254i	$-0.531025\pi$
$48$		0			0
$49$			58.7149i			1.19826i
$50$		0			0
$51$	24.8298			0.486859
$52$		0			0
$53$	−42.4339	+	42.4339i	−0.800640	+	0.800640i	−0.983196	−	0.182555i	$-0.941563\pi$
$53$	−42.4339	+	42.4339i	−0.800640	+	0.800640i	0.182555	+	0.983196i	$0.441563\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−8.17826	−	8.17826i	−0.143478	−	0.143478i
$58$		0			0
$59$			0.297219i			0.00503762i	0.999997	+	0.00251881i	$0.000801763\pi$
$59$			0.297219i			0.00503762i	−0.999997	+	0.00251881i	$0.999198\pi$
$60$		0			0
$61$	46.8766			0.768469			0.384234	−	0.923236i	$-0.374465\pi$
$61$	46.8766			0.768469			0.384234	+	0.923236i	$0.374465\pi$
$62$		0			0
$63$	22.0163	−	22.0163i	0.349465	−	0.349465i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−13.4220	−	13.4220i	−0.200329	−	0.200329i	0.599812	−	0.800141i	$-0.295242\pi$
$67$	−13.4220	−	13.4220i	−0.200329	−	0.200329i	−0.800141	+	0.599812i	$0.795242\pi$
$68$		0			0
$69$			51.6285i			0.748239i
$70$		0			0
$71$	−46.3448			−0.652744			−0.326372	−	0.945241i	$-0.605826\pi$
$71$	−46.3448			−0.652744			−0.326372	+	0.945241i	$0.605826\pi$
$72$		0			0
$73$	42.4381	−	42.4381i	0.581344	−	0.581344i	−0.353928	−	0.935273i	$-0.615154\pi$
$73$	42.4381	−	42.4381i	0.581344	−	0.581344i	0.935273	+	0.353928i	$0.115154\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−47.6965	−	47.6965i	−0.619435	−	0.619435i
$78$		0			0
$79$			27.7474i			0.351234i	0.984459	+	0.175617i	$0.0561920\pi$
$79$			27.7474i			0.351234i	−0.984459	+	0.175617i	$0.943808\pi$
$80$		0			0
$81$	−9.00000			−0.111111
$82$		0			0
$83$	71.7548	−	71.7548i	0.864515	−	0.864515i	−0.127343	−	0.991859i	$-0.540645\pi$
$83$	71.7548	−	71.7548i	0.864515	−	0.864515i	0.991859	+	0.127343i	$0.0406450\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	14.9628	+	14.9628i	0.171986	+	0.171986i
$88$		0			0
$89$			69.5780i			0.781775i	0.920438	+	0.390888i	$0.127832\pi$
$89$			69.5780i			0.781775i	−0.920438	+	0.390888i	$0.872168\pi$
$90$		0			0
$91$	−164.942			−1.81255
$92$		0			0
$93$	−56.5750	+	56.5750i	−0.608334	+	0.608334i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	110.825	+	110.825i	1.14252	+	1.14252i	0.987987	+	0.154536i	$0.0493883\pi$
$97$	110.825	+	110.825i	1.14252	+	1.14252i	0.154536	+	0.987987i	$0.450612\pi$
$98$		0			0
$99$			19.4978i			0.196947i
$100$		0			0
$101$	100.912			0.999131			0.499565	−	0.866276i	$-0.333493\pi$
$101$	100.912			0.999131			0.499565	+	0.866276i	$0.333493\pi$
$102$		0			0
$103$	−133.042	+	133.042i	−1.29167	+	1.29167i	−0.357910	+	0.933756i	$0.616511\pi$
$103$	−133.042	+	133.042i	−1.29167	+	1.29167i	−0.933756	+	0.357910i	$0.883489\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	34.9466	+	34.9466i	0.326604	+	0.326604i	0.851294	−	0.524690i	$-0.175819\pi$
$107$	34.9466	+	34.9466i	0.326604	+	0.326604i	−0.524690	+	0.851294i	$0.675819\pi$
$108$		0			0
$109$			128.984i			1.18334i	0.806180	+	0.591670i	$0.201531\pi$
$109$			128.984i			1.18334i	−0.806180	+	0.591670i	$0.798469\pi$
$110$		0			0
$111$	119.123			1.07318
$112$		0			0
$113$	−43.9289	+	43.9289i	−0.388751	+	0.388751i	−0.874242	−	0.485491i	$-0.838641\pi$
$113$	−43.9289	+	43.9289i	−0.388751	+	0.388751i	0.485491	+	0.874242i	$0.338641\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	33.7132	+	33.7132i	0.288147	+	0.288147i
$118$		0			0
$119$			148.782i			1.25027i
$120$		0			0
$121$	−78.7596			−0.650906
$122$		0			0
$123$	−73.5246	+	73.5246i	−0.597761	+	0.597761i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	108.168	+	108.168i	0.851719	+	0.851719i	0.990345	−	0.138626i	$-0.0442686\pi$
$127$	108.168	+	108.168i	0.851719	+	0.851719i	−0.138626	+	0.990345i	$0.544269\pi$
$128$		0			0
$129$		−	54.3147i		−	0.421045i
$130$		0			0
$131$	47.9670			0.366160			0.183080	−	0.983098i	$-0.441393\pi$
$131$	47.9670			0.366160			0.183080	+	0.983098i	$0.441393\pi$
$132$		0			0
$133$	49.0048	−	49.0048i	0.368457	−	0.368457i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	22.0086	+	22.0086i	0.160646	+	0.160646i	0.782853	−	0.622207i	$-0.213764\pi$
$137$	22.0086	+	22.0086i	0.160646	+	0.160646i	−0.622207	+	0.782853i	$0.713764\pi$
$138$		0			0
$139$			12.3065i			0.0885360i	0.999020	+	0.0442680i	$0.0140955\pi$
$139$			12.3065i			0.0885360i	−0.999020	+	0.0442680i	$0.985904\pi$
$140$		0			0
$141$	−125.783			−0.892078
$142$		0			0
$143$	73.0370	−	73.0370i	0.510748	−	0.510748i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	71.9107	+	71.9107i	0.489189	+	0.489189i
$148$		0			0
$149$		−	214.529i		−	1.43979i	−0.694084	−	0.719894i	$-0.744190\pi$
$149$		−	214.529i		−	1.43979i	0.694084	−	0.719894i	$-0.255810\pi$
$150$		0			0
$151$	76.5767			0.507130			0.253565	−	0.967318i	$-0.418397\pi$
$151$	76.5767			0.507130			0.253565	+	0.967318i	$0.418397\pi$
$152$		0			0
$153$	30.4102	−	30.4102i	0.198759	−	0.198759i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	29.8885	+	29.8885i	0.190372	+	0.190372i	0.795857	−	0.605485i	$-0.207021\pi$
$157$	29.8885	+	29.8885i	0.190372	+	0.190372i	−0.605485	+	0.795857i	$0.707021\pi$
$158$		0			0
$159$			103.942i			0.653720i
$160$		0			0
$161$	−309.362			−1.92150
$162$		0			0
$163$	−52.5813	+	52.5813i	−0.322585	+	0.322585i	−0.849758	−	0.527173i	$-0.823252\pi$
$163$	−52.5813	+	52.5813i	−0.322585	+	0.322585i	0.527173	+	0.849758i	$0.323252\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	192.121	+	192.121i	1.15042	+	1.15042i	0.986468	+	0.163954i	$0.0524249\pi$
$167$	192.121	+	192.121i	1.15042	+	1.15042i	0.163954	+	0.986468i	$0.447575\pi$
$168$		0			0
$169$		−	83.5737i		−	0.494519i
$170$		0			0
$171$	−20.0326			−0.117150
$172$		0			0
$173$	182.829	−	182.829i	1.05682	−	1.05682i	0.0585316	−	0.998286i	$-0.481358\pi$
$173$	182.829	−	182.829i	1.05682	−	1.05682i	0.998286	−	0.0585316i	$-0.0186418\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	0.364018	+	0.364018i	0.00205660	+	0.00205660i
$178$		0			0
$179$			23.4356i			0.130925i	0.997855	+	0.0654625i	$0.0208523\pi$
$179$			23.4356i			0.130925i	−0.997855	+	0.0654625i	$0.979148\pi$
$180$		0			0
$181$	228.033			1.25985			0.629926	−	0.776656i	$-0.283085\pi$
$181$	228.033			1.25985			0.629926	+	0.776656i	$0.283085\pi$
$182$		0			0
$183$	57.4119	−	57.4119i	0.313726	−	0.313726i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−65.8812	−	65.8812i	−0.352306	−	0.352306i
$188$		0			0
$189$		−	53.9287i		−	0.285337i
$190$		0			0
$191$	−45.6728			−0.239124			−0.119562	−	0.992827i	$-0.538149\pi$
$191$	−45.6728			−0.239124			−0.119562	+	0.992827i	$0.538149\pi$
$192$		0			0
$193$	−120.902	+	120.902i	−0.626435	+	0.626435i	−0.947169	−	0.320734i	$-0.896070\pi$
$193$	−120.902	+	120.902i	−0.626435	+	0.626435i	0.320734	+	0.947169i	$0.396070\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−79.9229	−	79.9229i	−0.405700	−	0.405700i	0.474536	−	0.880236i	$-0.342616\pi$
$197$	−79.9229	−	79.9229i	−0.405700	−	0.405700i	−0.880236	+	0.474536i	$0.842616\pi$
$198$		0			0
$199$		−	352.912i		−	1.77343i	−0.462319	−	0.886713i	$-0.652983\pi$
$199$		−	352.912i		−	1.77343i	0.462319	−	0.886713i	$-0.347017\pi$
$200$		0			0
$201$	−32.8771			−0.163568
$202$		0			0
$203$	−89.6583	+	89.6583i	−0.441667	+	0.441667i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	63.2317	+	63.2317i	0.305467	+	0.305467i
$208$		0			0
$209$			43.3990i			0.207651i
$210$		0			0
$211$	−95.8685			−0.454353			−0.227177	−	0.973854i	$-0.572949\pi$
$211$	−95.8685			−0.454353			−0.227177	+	0.973854i	$0.572949\pi$
$212$		0			0
$213$	−56.7606	+	56.7606i	−0.266482	+	0.266482i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−339.002	−	339.002i	−1.56222	−	1.56222i
$218$		0			0
$219$		−	103.952i		−	0.474666i
$220$		0			0
$221$	−227.828			−1.03089
$222$		0			0
$223$	−134.418	+	134.418i	−0.602771	+	0.602771i	−0.941047	−	0.338276i	$-0.890156\pi$
$223$	−134.418	+	134.418i	−0.602771	+	0.602771i	0.338276	+	0.941047i	$0.390156\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−138.328	−	138.328i	−0.609374	−	0.609374i	0.333408	−	0.942782i	$-0.391801\pi$
$227$	−138.328	−	138.328i	−0.609374	−	0.609374i	−0.942782	+	0.333408i	$0.891801\pi$
$228$		0			0
$229$			314.959i			1.37537i	0.726010	+	0.687684i	$0.241373\pi$
$229$			314.959i			1.37537i	−0.726010	+	0.687684i	$0.758627\pi$
$230$		0			0
$231$	−116.832			−0.505767
$232$		0			0
$233$	21.9824	−	21.9824i	0.0943450	−	0.0943450i	−0.658359	−	0.752704i	$-0.728749\pi$
$233$	21.9824	−	21.9824i	0.0943450	−	0.0943450i	0.752704	+	0.658359i	$0.228749\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	33.9835	+	33.9835i	0.143390	+	0.143390i
$238$		0			0
$239$			2.72755i			0.0114124i	0.999984	+	0.00570618i	$0.00181634\pi$
$239$			2.72755i			0.0114124i	−0.999984	+	0.00570618i	$0.998184\pi$
$240$		0			0
$241$	208.053			0.863289			0.431645	−	0.902044i	$-0.357934\pi$
$241$	208.053			0.863289			0.431645	+	0.902044i	$0.357934\pi$
$242$		0			0
$243$	−11.0227	+	11.0227i	−0.0453609	+	0.0453609i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	75.0403	+	75.0403i	0.303807	+	0.303807i
$248$		0			0
$249$		−	175.763i		−	0.705874i
$250$		0			0
$251$	103.551			0.412555			0.206278	−	0.978493i	$-0.433865\pi$
$251$	103.551			0.412555			0.206278	+	0.978493i	$0.433865\pi$
$252$		0			0
$253$	136.986	−	136.986i	0.541449	−	0.541449i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−243.679	−	243.679i	−0.948168	−	0.948168i	0.0505534	−	0.998721i	$-0.483901\pi$
$257$	−243.679	−	243.679i	−0.948168	−	0.948168i	−0.998721	+	0.0505534i	$0.983901\pi$
$258$		0			0
$259$			713.792i			2.75595i
$260$		0			0
$261$	36.6513			0.140426
$262$		0			0
$263$	154.845	−	154.845i	0.588765	−	0.588765i	−0.348532	−	0.937297i	$-0.613320\pi$
$263$	154.845	−	154.845i	0.588765	−	0.588765i	0.937297	+	0.348532i	$0.113320\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	85.2153	+	85.2153i	0.319158	+	0.319158i
$268$		0			0
$269$			161.614i			0.600797i	0.953814	+	0.300398i	$0.0971196\pi$
$269$			161.614i			0.600797i	−0.953814	+	0.300398i	$0.902880\pi$
$270$		0			0
$271$	372.838			1.37579			0.687893	−	0.725812i	$-0.258536\pi$
$271$	372.838			1.37579			0.687893	+	0.725812i	$0.258536\pi$
$272$		0			0
$273$	−202.012	+	202.012i	−0.739971	+	0.739971i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	288.524	+	288.524i	1.04160	+	1.04160i	0.999096	+	0.0425086i	$0.0135350\pi$
$277$	288.524	+	288.524i	1.04160	+	1.04160i	0.0425086	+	0.999096i	$0.486465\pi$
$278$		0			0
$279$			138.580i			0.496702i
$280$		0			0
$281$	−410.779			−1.46185			−0.730923	−	0.682460i	$-0.760910\pi$
$281$	−410.779			−1.46185			−0.730923	+	0.682460i	$0.760910\pi$
$282$		0			0
$283$	−65.5910	+	65.5910i	−0.231770	+	0.231770i	−0.813431	−	0.581661i	$-0.802403\pi$
$283$	−65.5910	+	65.5910i	−0.231770	+	0.231770i	0.581661	+	0.813431i	$0.302403\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−440.565	−	440.565i	−1.53507	−	1.53507i
$288$		0			0
$289$		−	83.4938i		−	0.288906i
$290$		0			0
$291$	271.464			0.932866
$292$		0			0
$293$	248.012	−	248.012i	0.846458	−	0.846458i	−0.143231	−	0.989689i	$-0.545749\pi$
$293$	248.012	−	248.012i	0.846458	−	0.846458i	0.989689	+	0.143231i	$0.0457492\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	23.8798	+	23.8798i	0.0804034	+	0.0804034i
$298$		0			0
$299$		−	473.721i		−	1.58435i
$300$		0			0
$301$	325.458			1.08126
$302$		0			0
$303$	123.592	−	123.592i	0.407893	−	0.407893i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−201.473	−	201.473i	−0.656262	−	0.656262i	0.298231	−	0.954494i	$-0.403603\pi$
$307$	−201.473	−	201.473i	−0.656262	−	0.656262i	−0.954494	+	0.298231i	$0.903603\pi$
$308$		0			0
$309$			325.884i			1.05464i
$310$		0			0
$311$	21.6670			0.0696688			0.0348344	−	0.999393i	$-0.488910\pi$
$311$	21.6670			0.0696688			0.0348344	+	0.999393i	$0.488910\pi$
$312$		0			0
$313$	−141.247	+	141.247i	−0.451269	+	0.451269i	−0.895776	−	0.444506i	$-0.853379\pi$
$313$	−141.247	+	141.247i	−0.451269	+	0.451269i	0.444506	+	0.895776i	$0.353379\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−140.389	−	140.389i	−0.442868	−	0.442868i	0.450107	−	0.892975i	$-0.351386\pi$
$317$	−140.389	−	140.389i	−0.442868	−	0.442868i	−0.892975	+	0.450107i	$0.851386\pi$
$318$		0			0
$319$		−	79.4021i		−	0.248909i
$320$		0			0
$321$	85.6014			0.266671
$322$		0			0
$323$	67.6882	−	67.6882i	0.209561	−	0.209561i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	157.973	+	157.973i	0.483096	+	0.483096i
$328$		0			0
$329$		−	753.701i		−	2.29088i
$330$		0			0
$331$	148.494			0.448622			0.224311	−	0.974518i	$-0.427987\pi$
$331$	148.494			0.448622			0.224311	+	0.974518i	$0.427987\pi$
$332$		0			0
$333$	145.895	−	145.895i	0.438123	−	0.438123i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	105.576	+	105.576i	0.313282	+	0.313282i	0.846180	−	0.532897i	$-0.178897\pi$
$337$	105.576	+	105.576i	0.313282	+	0.313282i	−0.532897	+	0.846180i	$0.678897\pi$
$338$		0			0
$339$			107.603i			0.317414i
$340$		0			0
$341$	300.222			0.880418
$342$		0			0
$343$	−71.2951	+	71.2951i	−0.207858	+	0.207858i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	50.1997	+	50.1997i	0.144668	+	0.144668i	0.775731	−	0.631063i	$-0.217381\pi$
$347$	50.1997	+	50.1997i	0.144668	+	0.144668i	−0.631063	+	0.775731i	$0.717381\pi$
$348$		0			0
$349$		−	19.8453i		−	0.0568634i	−0.999596	−	0.0284317i	$-0.990949\pi$
$349$		−	19.8453i		−	0.0568634i	0.999596	−	0.0284317i	$-0.00905131\pi$
$350$		0			0
$351$	82.5802			0.235271
$352$		0			0
$353$	−284.128	+	284.128i	−0.804895	+	0.804895i	−0.983856	−	0.178961i	$-0.942726\pi$
$353$	−284.128	+	284.128i	−0.804895	+	0.804895i	0.178961	+	0.983856i	$0.442726\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	182.220	+	182.220i	0.510420	+	0.510420i
$358$		0			0
$359$		−	100.273i		−	0.279312i	−0.990200	−	0.139656i	$-0.955400\pi$
$359$		−	100.273i		−	0.279312i	0.990200	−	0.139656i	$-0.0445997\pi$
$360$		0			0
$361$	316.411			0.876484
$362$		0			0
$363$	−96.4604	+	96.4604i	−0.265731	+	0.265731i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−183.908	−	183.908i	−0.501110	−	0.501110i	0.410673	−	0.911783i	$-0.365294\pi$
$367$	−183.908	−	183.908i	−0.501110	−	0.501110i	−0.911783	+	0.410673i	$0.865294\pi$
$368$		0			0
$369$			180.098i			0.488070i
$370$		0			0
$371$	−622.825			−1.67877
$372$		0			0
$373$	120.787	−	120.787i	0.323825	−	0.323825i	−0.526408	−	0.850232i	$-0.676461\pi$
$373$	120.787	−	120.787i	0.323825	−	0.323825i	0.850232	+	0.526408i	$0.176461\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−137.293	−	137.293i	−0.364171	−	0.364171i
$378$		0			0
$379$		−	512.657i		−	1.35266i	−0.736601	−	0.676328i	$-0.763570\pi$
$379$		−	512.657i		−	1.35266i	0.736601	−	0.676328i	$-0.236430\pi$
$380$		0			0
$381$	264.957			0.695426
$382$		0			0
$383$	−35.5753	+	35.5753i	−0.0928858	+	0.0928858i	−0.752023	−	0.659137i	$-0.770922\pi$
$383$	−35.5753	+	35.5753i	−0.0928858	+	0.0928858i	0.659137	+	0.752023i	$0.270922\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−66.5217	−	66.5217i	−0.171891	−	0.171891i
$388$		0			0
$389$		−	61.9756i		−	0.159320i	−0.996822	−	0.0796601i	$-0.974616\pi$
$389$		−	61.9756i		−	0.159320i	0.996822	−	0.0796601i	$-0.0253835\pi$
$390$		0			0
$391$	−427.308			−1.09286
$392$		0			0
$393$	58.7474	−	58.7474i	0.149484	−	0.149484i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−216.266	−	216.266i	−0.544749	−	0.544749i	0.380168	−	0.924917i	$-0.375866\pi$
$397$	−216.266	−	216.266i	−0.544749	−	0.544749i	−0.924917	+	0.380168i	$0.875866\pi$
$398$		0			0
$399$		−	120.037i		−	0.300844i
$400$		0			0
$401$	552.383			1.37751			0.688757	−	0.724992i	$-0.258157\pi$
$401$	552.383			1.37751			0.688757	+	0.724992i	$0.258157\pi$
$402$		0			0
$403$	519.109	−	519.109i	1.28811	−	1.28811i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−316.070	−	316.070i	−0.776584	−	0.776584i
$408$		0			0
$409$		−	403.333i		−	0.986144i	−0.869989	−	0.493072i	$-0.835874\pi$
$409$		−	403.333i		−	0.986144i	0.869989	−	0.493072i	$-0.164126\pi$
$410$		0			0
$411$	53.9097			0.131167
$412$		0			0
$413$	−2.18122	+	2.18122i	−0.00528141	+	0.00528141i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	15.0723	+	15.0723i	0.0361447	+	0.0361447i
$418$		0			0
$419$		−	683.424i		−	1.63108i	−0.578698	−	0.815542i	$-0.696439\pi$
$419$		−	683.424i		−	1.63108i	0.578698	−	0.815542i	$-0.303561\pi$
$420$		0			0
$421$	−458.400			−1.08884			−0.544418	−	0.838814i	$-0.683250\pi$
$421$	−458.400			−1.08884			−0.544418	+	0.838814i	$0.683250\pi$
$422$		0			0
$423$	−154.052	+	154.052i	−0.364189	+	0.364189i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	344.016	+	344.016i	0.805659	+	0.805659i
$428$		0			0
$429$		−	178.903i		−	0.417024i
$430$		0			0
$431$	−541.756			−1.25697			−0.628487	−	0.777820i	$-0.716325\pi$
$431$	−541.756			−1.25697			−0.628487	+	0.777820i	$0.716325\pi$
$432$		0			0
$433$	−100.400	+	100.400i	−0.231870	+	0.231870i	−0.813473	−	0.581603i	$-0.802426\pi$
$433$	−100.400	+	100.400i	−0.231870	+	0.231870i	0.581603	+	0.813473i	$0.302426\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	140.744	+	140.744i	0.322068	+	0.322068i
$438$		0			0
$439$		−	662.148i		−	1.50831i	−0.656696	−	0.754155i	$-0.728047\pi$
$439$		−	662.148i		−	1.50831i	0.656696	−	0.754155i	$-0.271953\pi$
$440$		0			0
$441$	176.145			0.399421
$442$		0			0
$443$	610.219	−	610.219i	1.37747	−	1.37747i	0.528598	−	0.848873i	$-0.322718\pi$
$443$	610.219	−	610.219i	1.37747	−	1.37747i	0.848873	−	0.528598i	$-0.177282\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−262.743	−	262.743i	−0.587791	−	0.587791i
$448$		0			0
$449$		−	127.980i		−	0.285033i	−0.989792	−	0.142516i	$-0.954481\pi$
$449$		−	127.980i		−	0.285033i	0.989792	−	0.142516i	$-0.0455194\pi$
$450$		0			0
$451$	390.167			0.865116
$452$		0			0
$453$	93.7869	−	93.7869i	0.207035	−	0.207035i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	353.895	+	353.895i	0.774387	+	0.774387i	0.978870	−	0.204483i	$-0.0655514\pi$
$457$	353.895	+	353.895i	0.774387	+	0.774387i	−0.204483	+	0.978870i	$0.565551\pi$
$458$		0			0
$459$		−	74.4894i		−	0.162286i
$460$		0			0
$461$	195.452			0.423974			0.211987	−	0.977272i	$-0.432007\pi$
$461$	195.452			0.423974			0.211987	+	0.977272i	$0.432007\pi$
$462$		0			0
$463$	276.549	−	276.549i	0.597297	−	0.597297i	−0.342295	−	0.939592i	$-0.611204\pi$
$463$	276.549	−	276.549i	0.597297	−	0.597297i	0.939592	+	0.342295i	$0.111204\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−276.245	−	276.245i	−0.591532	−	0.591532i	0.346513	−	0.938045i	$-0.387366\pi$
$467$	−276.245	−	276.245i	−0.591532	−	0.591532i	−0.938045	+	0.346513i	$0.887366\pi$
$468$		0			0
$469$		−	197.002i		−	0.420047i
$470$		0			0
$471$	73.2115			0.155438
$472$		0			0
$473$	−144.114	+	144.114i	−0.304681	+	0.304681i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	127.302	+	127.302i	0.266880	+	0.266880i
$478$		0			0
$479$			438.003i			0.914410i	0.889361	+	0.457205i	$0.151150\pi$
$479$			438.003i			0.914410i	−0.889361	+	0.457205i	$0.848850\pi$
$480$		0			0
$481$	−1093.02			−2.27239
$482$		0			0
$483$	−378.889	+	378.889i	−0.784450	+	0.784450i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	236.626	+	236.626i	0.485885	+	0.485885i	0.907005	−	0.421120i	$-0.138363\pi$
$487$	236.626	+	236.626i	0.485885	+	0.485885i	−0.421120	+	0.907005i	$0.638363\pi$
$488$		0			0
$489$			128.797i			0.263389i
$490$		0			0
$491$	152.293			0.310169			0.155084	−	0.987901i	$-0.450435\pi$
$491$	152.293			0.310169			0.155084	+	0.987901i	$0.450435\pi$
$492$		0			0
$493$	−123.841	+	123.841i	−0.251199	+	0.251199i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−340.114	−	340.114i	−0.684334	−	0.684334i
$498$		0			0
$499$			229.494i			0.459908i	0.973201	+	0.229954i	$0.0738576\pi$
$499$			229.494i			0.459908i	−0.973201	+	0.229954i	$0.926142\pi$
$500$		0			0
$501$	470.597			0.939316
$502$		0			0
$503$	−64.9436	+	64.9436i	−0.129113	+	0.129113i	−0.768710	−	0.639597i	$-0.779101\pi$
$503$	−64.9436	+	64.9436i	−0.129113	+	0.129113i	0.639597	+	0.768710i	$0.279101\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−102.356	−	102.356i	−0.201886	−	0.201886i
$508$		0			0
$509$			29.1487i			0.0572666i	0.999590	+	0.0286333i	$0.00911550\pi$
$509$			29.1487i			0.0572666i	−0.999590	+	0.0286333i	$0.990884\pi$
$510$		0			0
$511$	622.887			1.21896
$512$		0			0
$513$	−24.5348	+	24.5348i	−0.0478261	+	0.0478261i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	333.741	+	333.741i	0.645535	+	0.645535i
$518$		0			0
$519$		−	447.839i		−	0.862888i
$520$		0			0
$521$	−457.336			−0.877805			−0.438903	−	0.898535i	$-0.644633\pi$
$521$	−457.336			−0.877805			−0.438903	+	0.898535i	$0.644633\pi$
$522$		0			0
$523$	−17.5997	+	17.5997i	−0.0336515	+	0.0336515i	−0.723732	−	0.690081i	$-0.757575\pi$
$523$	−17.5997	+	17.5997i	−0.0336515	+	0.0336515i	0.690081	+	0.723732i	$0.257575\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−468.249	−	468.249i	−0.888518	−	0.888518i
$528$		0			0
$529$		−	359.500i		−	0.679585i
$530$		0			0
$531$	0.891658			0.00167921
$532$		0			0
$533$	674.631	−	674.631i	1.26572	−	1.26572i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	28.7026	+	28.7026i	0.0534499	+	0.0534499i
$538$		0			0
$539$		−	381.603i		−	0.707984i
$540$		0			0
$541$	611.683			1.13065			0.565326	−	0.824867i	$-0.308750\pi$
$541$	611.683			1.13065			0.565326	+	0.824867i	$0.308750\pi$
$542$		0			0
$543$	279.282	−	279.282i	0.514332	−	0.514332i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	190.249	+	190.249i	0.347804	+	0.347804i	0.859291	−	0.511487i	$-0.170905\pi$
$547$	190.249	+	190.249i	0.347804	+	0.347804i	−0.511487	+	0.859291i	$0.670905\pi$
$548$		0			0
$549$		−	140.630i		−	0.256156i
$550$		0			0
$551$	81.5799			0.148058
$552$		0			0
$553$	−203.632	+	203.632i	−0.368231	+	0.368231i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	459.747	+	459.747i	0.825399	+	0.825399i	0.986876	−	0.161478i	$-0.0516260\pi$
$557$	459.747	+	459.747i	0.825399	+	0.825399i	−0.161478	+	0.986876i	$0.551626\pi$
$558$		0			0
$559$			498.369i			0.891537i
$560$		0			0
$561$	−161.375			−0.287657
$562$		0			0
$563$	−433.620	+	433.620i	−0.770195	+	0.770195i	−0.978140	−	0.207945i	$-0.933322\pi$
$563$	−433.620	+	433.620i	−0.770195	+	0.770195i	0.207945	+	0.978140i	$0.433322\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−66.0489	−	66.0489i	−0.116488	−	0.116488i
$568$		0			0
$569$			651.255i			1.14456i	0.820058	+	0.572281i	$0.193941\pi$
$569$			651.255i			1.14456i	−0.820058	+	0.572281i	$0.806059\pi$
$570$		0			0
$571$	254.843			0.446310			0.223155	−	0.974783i	$-0.428364\pi$
$571$	254.843			0.446310			0.223155	+	0.974783i	$0.428364\pi$
$572$		0			0
$573$	−55.9375	+	55.9375i	−0.0976221	+	0.0976221i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−94.7924	−	94.7924i	−0.164285	−	0.164285i	0.620177	−	0.784462i	$-0.287061\pi$
$577$	−94.7924	−	94.7924i	−0.164285	−	0.164285i	−0.784462	+	0.620177i	$0.787061\pi$
$578$		0			0
$579$			296.148i			0.511482i
$580$		0			0
$581$	1053.18			1.81271
$582$		0			0
$583$	275.789	−	275.789i	0.473052	−	0.473052i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	351.941	+	351.941i	0.599560	+	0.599560i	0.940195	−	0.340636i	$-0.110642\pi$
$587$	351.941	+	351.941i	0.599560	+	0.599560i	−0.340636	+	0.940195i	$0.610642\pi$
$588$		0			0
$589$			308.457i			0.523696i
$590$		0			0
$591$	−195.770			−0.331253
$592$		0			0
$593$	439.108	−	439.108i	0.740485	−	0.740485i	−0.232186	−	0.972671i	$-0.574588\pi$
$593$	439.108	−	439.108i	0.740485	−	0.740485i	0.972671	+	0.232186i	$0.0745879\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−432.227	−	432.227i	−0.723999	−	0.723999i
$598$		0			0
$599$			147.821i			0.246779i	0.992358	+	0.123390i	$0.0393765\pi$
$599$			147.821i			0.246779i	−0.992358	+	0.123390i	$0.960623\pi$
$600$		0			0
$601$	−385.979			−0.642228			−0.321114	−	0.947041i	$-0.604057\pi$
$601$	−385.979			−0.642228			−0.321114	+	0.947041i	$0.604057\pi$
$602$		0			0
$603$	−40.2660	+	40.2660i	−0.0667762	+	0.0667762i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	180.038	+	180.038i	0.296603	+	0.296603i	0.839682	−	0.543079i	$-0.182742\pi$
$607$	180.038	+	180.038i	0.296603	+	0.296603i	−0.543079	+	0.839682i	$0.682742\pi$
$608$		0			0
$609$			219.617i			0.360619i
$610$		0			0
$611$	1154.13			1.88892
$612$		0			0
$613$	−219.954	+	219.954i	−0.358816	+	0.358816i	−0.863376	−	0.504561i	$-0.831654\pi$
$613$	−219.954	+	219.954i	−0.358816	+	0.358816i	0.504561	+	0.863376i	$0.331654\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−101.157	−	101.157i	−0.163949	−	0.163949i	0.620365	−	0.784314i	$-0.286985\pi$
$617$	−101.157	−	101.157i	−0.163949	−	0.163949i	−0.784314	+	0.620365i	$0.786985\pi$
$618$		0			0
$619$			262.439i			0.423972i	0.977273	+	0.211986i	$0.0679931\pi$
$619$			262.439i			0.423972i	−0.977273	+	0.211986i	$0.932007\pi$
$620$		0			0
$621$	154.885			0.249413
$622$		0			0
$623$	−510.616	+	510.616i	−0.819609	+	0.819609i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	53.1527	+	53.1527i	0.0847730	+	0.0847730i
$628$		0			0
$629$			985.930i			1.56746i
$630$		0			0
$631$	−445.266			−0.705651			−0.352826	−	0.935689i	$-0.614779\pi$
$631$	−445.266			−0.705651			−0.352826	+	0.935689i	$0.614779\pi$
$632$		0			0
$633$	−117.415	+	117.415i	−0.185489	+	0.185489i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−659.823	−	659.823i	−1.03583	−	1.03583i
$638$		0			0
$639$			139.035i			0.217581i
$640$		0			0
$641$	−235.326			−0.367123			−0.183562	−	0.983008i	$-0.558763\pi$
$641$	−235.326			−0.367123			−0.183562	+	0.983008i	$0.558763\pi$
$642$		0			0
$643$	−552.893	+	552.893i	−0.859865	+	0.859865i	−0.991322	−	0.131457i	$-0.958035\pi$
$643$	−552.893	+	552.893i	−0.859865	+	0.859865i	0.131457	+	0.991322i	$0.458035\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	221.390	+	221.390i	0.342179	+	0.342179i	0.857186	−	0.515007i	$-0.172211\pi$
$647$	221.390	+	221.390i	0.342179	+	0.342179i	−0.515007	+	0.857186i	$0.672211\pi$
$648$		0			0
$649$		−	1.93171i		−	0.00297644i
$650$		0			0
$651$	−830.381			−1.27555
$652$		0			0
$653$	−570.367	+	570.367i	−0.873456	+	0.873456i	−0.992847	−	0.119391i	$-0.961906\pi$
$653$	−570.367	+	570.367i	−0.873456	+	0.873456i	0.119391	+	0.992847i	$0.461906\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−127.314	−	127.314i	−0.193781	−	0.193781i
$658$		0			0
$659$			1249.81i			1.89653i	0.317486	+	0.948263i	$0.397161\pi$
$659$			1249.81i			1.89653i	−0.317486	+	0.948263i	$0.602839\pi$
$660$		0			0
$661$	172.140			0.260423			0.130211	−	0.991486i	$-0.458434\pi$
$661$	172.140			0.260423			0.130211	+	0.991486i	$0.458434\pi$
$662$		0			0
$663$	−279.031	+	279.031i	−0.420861	+	0.420861i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−257.503	−	257.503i	−0.386061	−	0.386061i
$668$		0			0
$669$			329.255i			0.492160i
$670$		0			0
$671$	−304.663			−0.454044
$672$		0			0
$673$	217.222	−	217.222i	0.322767	−	0.322767i	−0.527061	−	0.849828i	$-0.676706\pi$
$673$	217.222	−	217.222i	0.322767	−	0.322767i	0.849828	+	0.527061i	$0.176706\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−654.178	−	654.178i	−0.966290	−	0.966290i	0.0331601	−	0.999450i	$-0.489443\pi$
$677$	−654.178	−	654.178i	−0.966290	−	0.966290i	−0.999450	+	0.0331601i	$0.989443\pi$
$678$		0			0
$679$			1626.63i			2.39563i
$680$		0			0
$681$	−338.833			−0.497552
$682$		0			0
$683$	603.781	−	603.781i	0.884013	−	0.884013i	−0.109926	−	0.993940i	$-0.535062\pi$
$683$	603.781	−	603.781i	0.884013	−	0.884013i	0.993940	+	0.109926i	$0.0350615\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	385.745	+	385.745i	0.561492	+	0.561492i
$688$		0			0
$689$		−	953.723i		−	1.38421i
$690$		0			0
$691$	−666.747			−0.964902			−0.482451	−	0.875923i	$-0.660253\pi$
$691$	−666.747			−0.964902			−0.482451	+	0.875923i	$0.660253\pi$
$692$		0			0
$693$	−143.090	+	143.090i	−0.206478	+	0.206478i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−608.534	−	608.534i	−0.873075	−	0.873075i
$698$		0			0
$699$		−	53.8456i		−	0.0770324i
$700$		0			0
$701$	−674.096			−0.961621			−0.480810	−	0.876825i	$-0.659657\pi$
$701$	−674.096			−0.961621			−0.480810	+	0.876825i	$0.659657\pi$
$702$		0			0
$703$	324.739	−	324.739i	0.461933	−	0.461933i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	740.571	+	740.571i	1.04748	+	1.04748i
$708$		0			0
$709$		−	1122.78i		−	1.58361i	−0.610773	−	0.791806i	$-0.709141\pi$
$709$		−	1122.78i		−	1.58361i	0.610773	−	0.791806i	$-0.290859\pi$
$710$		0			0
$711$	83.2423			0.117078
$712$		0			0
$713$	973.628	−	973.628i	1.36554	−	1.36554i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	3.34056	+	3.34056i	0.00465907	+	0.00465907i
$718$		0			0
$719$		−	1322.86i		−	1.83986i	−0.392083	−	0.919930i	$-0.628245\pi$
$719$		−	1322.86i		−	1.83986i	0.392083	−	0.919930i	$-0.371755\pi$
$720$		0			0
$721$	−1952.72			−2.70835
$722$		0			0
$723$	254.811	−	254.811i	0.352436	−	0.352436i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	580.977	+	580.977i	0.799144	+	0.799144i	0.982961	−	0.183817i	$-0.0588453\pi$
$727$	580.977	+	580.977i	0.799144	+	0.799144i	−0.183817	+	0.982961i	$0.558845\pi$
$728$		0			0
$729$			27.0000i			0.0370370i
$730$		0			0
$731$	449.541			0.614968
$732$		0			0
$733$	−202.908	+	202.908i	−0.276819	+	0.276819i	−0.831838	−	0.555019i	$-0.812711\pi$
$733$	−202.908	+	202.908i	−0.276819	+	0.276819i	0.555019	+	0.831838i	$0.312711\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	87.2332	+	87.2332i	0.118363	+	0.118363i
$738$		0			0
$739$			204.671i			0.276956i	0.990366	+	0.138478i	$0.0442210\pi$
$739$			204.671i			0.276956i	−0.990366	+	0.138478i	$0.955779\pi$
$740$		0			0
$741$	183.810			0.248057
$742$		0			0
$743$	−670.164	+	670.164i	−0.901970	+	0.901970i	−0.995606	−	0.0936366i	$-0.970151\pi$
$743$	−670.164	+	670.164i	−0.901970	+	0.901970i	0.0936366	+	0.995606i	$0.470151\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−215.264	−	215.264i	−0.288172	−	0.288172i
$748$		0			0
$749$			512.930i			0.684819i
$750$		0			0
$751$	931.441			1.24027			0.620134	−	0.784496i	$-0.287078\pi$
$751$	931.441			1.24027			0.620134	+	0.784496i	$0.287078\pi$
$752$		0			0
$753$	126.824	−	126.824i	0.168425	−	0.168425i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	202.255	+	202.255i	0.267180	+	0.267180i	0.827963	−	0.560783i	$-0.189500\pi$
$757$	202.255	+	202.255i	0.267180	+	0.267180i	−0.560783	+	0.827963i	$0.689500\pi$
$758$		0			0
$759$		−	335.547i		−	0.442091i
$760$		0			0
$761$	−388.957			−0.511113			−0.255557	−	0.966794i	$-0.582259\pi$
$761$	−388.957			−0.511113			−0.255557	+	0.966794i	$0.582259\pi$
$762$		0			0
$763$	−946.583	+	946.583i	−1.24061	+	1.24061i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−3.34008	−	3.34008i	−0.00435473	−	0.00435473i
$768$		0			0
$769$			651.967i			0.847811i	0.905706	+	0.423906i	$0.139341\pi$
$769$			651.967i			0.847811i	−0.905706	+	0.423906i	$0.860659\pi$
$770$		0			0
$771$	−596.890			−0.774176
$772$		0			0
$773$	−440.537	+	440.537i	−0.569906	+	0.569906i	−0.932102	−	0.362196i	$-0.882027\pi$
$773$	−440.537	+	440.537i	−0.569906	+	0.569906i	0.362196	+	0.932102i	$0.382027\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	874.213	+	874.213i	1.12511	+	1.12511i
$778$		0			0
$779$			400.869i			0.514594i
$780$		0			0
$781$	301.207			0.385669
$782$		0			0
$783$	44.8885	−	44.8885i	0.0573288	−	0.0573288i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	191.557	+	191.557i	0.243402	+	0.243402i	0.818256	−	0.574854i	$-0.194941\pi$
$787$	191.557	+	191.557i	0.243402	+	0.243402i	−0.574854	+	0.818256i	$0.694941\pi$
$788$		0			0
$789$		−	379.292i		−	0.480725i
$790$		0			0
$791$	−644.768			−0.815130
$792$		0			0
$793$	−526.787	+	526.787i	−0.664297	+	0.664297i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	895.946	+	895.946i	1.12415	+	1.12415i	0.991111	+	0.133036i	$0.0424727\pi$
$797$	895.946	+	895.946i	1.12415	+	1.12415i	0.133036	+	0.991111i	$0.457527\pi$
$798$		0			0
$799$		−	1041.06i		−	1.30295i
$800$		0			0
$801$	208.734			0.260592
$802$		0			0
$803$	−275.817	+	275.817i	−0.343483	+	0.343483i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	197.936	+	197.936i	0.245274	+	0.245274i
$808$		0			0
$809$		−	67.2114i		−	0.0830796i	−0.999137	−	0.0415398i	$-0.986774\pi$
$809$		−	67.2114i		−	0.0830796i	0.999137	−	0.0415398i	$-0.0132263\pi$
$810$		0			0
$811$	581.810			0.717398			0.358699	−	0.933453i	$-0.383221\pi$
$811$	581.810			0.717398			0.358699	+	0.933453i	$0.383221\pi$
$812$		0			0
$813$	456.631	−	456.631i	0.561662	−	0.561662i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−148.067	−	148.067i	−0.181232	−	0.181232i
$818$		0			0
$819$			494.827i			0.604184i
$820$		0			0
$821$	−996.580			−1.21386			−0.606931	−	0.794755i	$-0.707599\pi$
$821$	−996.580			−1.21386			−0.606931	+	0.794755i	$0.707599\pi$
$822$		0			0
$823$	350.797	−	350.797i	0.426241	−	0.426241i	−0.461104	−	0.887346i	$-0.652547\pi$
$823$	350.797	−	350.797i	0.426241	−	0.426241i	0.887346	+	0.461104i	$0.152547\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−297.042	−	297.042i	−0.359180	−	0.359180i	0.504330	−	0.863511i	$-0.331739\pi$
$827$	−297.042	−	297.042i	−0.359180	−	0.359180i	−0.863511	+	0.504330i	$0.831739\pi$
$828$		0			0
$829$			110.932i			0.133814i	0.997759	+	0.0669071i	$0.0213131\pi$
$829$			110.932i			0.133814i	−0.997759	+	0.0669071i	$0.978687\pi$
$830$		0			0
$831$	706.738			0.850467
$832$		0			0
$833$	−595.176	+	595.176i	−0.714497	+	0.714497i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	169.725	+	169.725i	0.202778	+	0.202778i
$838$		0			0
$839$			1476.86i			1.76026i	0.474733	+	0.880130i	$0.342545\pi$
$839$			1476.86i			1.76026i	−0.474733	+	0.880130i	$0.657455\pi$
$840$		0			0
$841$	691.743			0.822524
$842$		0			0
$843$	−503.099	+	503.099i	−0.596796	+	0.596796i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−577.998	−	577.998i	−0.682406	−	0.682406i
$848$		0			0
$849$			160.664i			0.189240i
$850$		0			0
$851$	−2050.04			−2.40898
$852$		0			0
$853$	599.321	−	599.321i	0.702604	−	0.702604i	−0.262365	−	0.964969i	$-0.584502\pi$
$853$	599.321	−	599.321i	0.702604	−	0.702604i	0.964969	+	0.262365i	$0.0845023\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	759.494	+	759.494i	0.886224	+	0.886224i	0.994158	−	0.107934i	$-0.0344235\pi$
$857$	759.494	+	759.494i	0.886224	+	0.886224i	−0.107934	+	0.994158i	$0.534424\pi$
$858$		0			0
$859$		−	166.778i		−	0.194154i	−0.995277	−	0.0970771i	$-0.969051\pi$
$859$		−	166.778i		−	0.194154i	0.995277	−	0.0970771i	$-0.0309493\pi$
$860$		0			0
$861$	−1079.16			−1.25338
$862$		0			0
$863$	−469.970	+	469.970i	−0.544577	+	0.544577i	−0.924867	−	0.380290i	$-0.875824\pi$
$863$	−469.970	+	469.970i	−0.544577	+	0.544577i	0.380290	+	0.924867i	$0.375824\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−102.259	−	102.259i	−0.117945	−	0.117945i
$868$		0			0
$869$		−	180.338i		−	0.207523i
$870$		0			0
$871$	301.666			0.346345
$872$		0			0
$873$	332.474	−	332.474i	0.380841	−	0.380841i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−40.8091	−	40.8091i	−0.0465327	−	0.0465327i	0.683458	−	0.729990i	$-0.260475\pi$
$877$	−40.8091	−	40.8091i	−0.0465327	−	0.0465327i	−0.729990	+	0.683458i	$0.760475\pi$
$878$		0			0
$879$		−	607.503i		−	0.691130i
$880$		0			0
$881$	567.251			0.643871			0.321936	−	0.946762i	$-0.395667\pi$
$881$	567.251			0.643871			0.321936	+	0.946762i	$0.395667\pi$
$882$		0			0
$883$	−281.362	+	281.362i	−0.318643	+	0.318643i	−0.848246	−	0.529603i	$-0.822341\pi$
$883$	−281.362	+	281.362i	−0.318643	+	0.318643i	0.529603	+	0.848246i	$0.322341\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	845.570	+	845.570i	0.953292	+	0.953292i	0.998957	−	0.0456647i	$-0.0145406\pi$
$887$	845.570	+	845.570i	0.953292	+	0.953292i	−0.0456647	+	0.998957i	$0.514541\pi$
$888$		0			0
$889$			1587.64i			1.78588i
$890$		0			0
$891$	58.4933			0.0656491
$892$		0			0
$893$	−342.896	+	342.896i	−0.383982	+	0.383982i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−580.188	−	580.188i	−0.646809	−	0.646809i
$898$		0			0
$899$		−	564.348i		−	0.627751i
$900$		0			0
$901$	−860.282			−0.954808
$902$		0			0
$903$	398.603	−	398.603i	0.441421	−	0.441421i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	11.5422	+	11.5422i	0.0127257	+	0.0127257i	0.713441	−	0.700715i	$-0.247136\pi$
$907$	11.5422	+	11.5422i	0.0127257	+	0.0127257i	−0.700715	+	0.713441i	$0.747136\pi$
$908$		0			0
$909$		−	302.737i		−	0.333044i
$910$		0			0
$911$	−318.836			−0.349984			−0.174992	−	0.984570i	$-0.555990\pi$
$911$	−318.836			−0.349984			−0.174992	+	0.984570i	$0.555990\pi$
$912$		0			0
$913$	−466.353	+	466.353i	−0.510792	+	0.510792i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	352.019	+	352.019i	0.383881	+	0.383881i
$918$		0			0
$919$			1025.89i			1.11631i	0.829735	+	0.558157i	$0.188491\pi$
$919$			1025.89i			1.11631i	−0.829735	+	0.558157i	$0.811509\pi$
$920$		0			0
$921$	−493.505			−0.535836
$922$		0			0
$923$	520.811	−	520.811i	0.564259	−	0.564259i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	399.125	+	399.125i	0.430555	+	0.430555i
$928$		0			0
$929$			124.806i			0.134345i	0.997741	+	0.0671724i	$0.0213978\pi$
$929$			124.806i			0.134345i	−0.997741	+	0.0671724i	$0.978602\pi$
$930$		0			0
$931$	392.070			0.421128
$932$		0			0
$933$	26.5365	−	26.5365i	0.0284422	−	0.0284422i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	407.177	+	407.177i	0.434554	+	0.434554i	0.890174	−	0.455620i	$-0.150582\pi$
$937$	407.177	+	407.177i	0.434554	+	0.434554i	−0.455620	+	0.890174i	$0.650582\pi$
$938$		0			0
$939$			345.984i			0.368460i
$940$		0			0
$941$	1098.72			1.16761			0.583805	−	0.811894i	$-0.301563\pi$
$941$	1098.72			1.16761			0.583805	+	0.811894i	$0.301563\pi$
$942$		0			0
$943$	1265.32	−	1265.32i	1.34180	−	1.34180i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	1262.00	+	1262.00i	1.33263	+	1.33263i	0.903014	+	0.429612i	$0.141350\pi$
$947$	1262.00	+	1262.00i	1.33263	+	1.33263i	0.429612	+	0.903014i	$0.358650\pi$
$948$		0			0
$949$			953.818i			1.00508i
$950$		0			0
$951$	−343.882			−0.361601
$952$		0			0
$953$	−1056.17	+	1056.17i	−1.10825	+	1.10825i	−0.114874	+	0.993380i	$0.536646\pi$
$953$	−1056.17	+	1056.17i	−1.10825	+	1.10825i	−0.993380	+	0.114874i	$0.963354\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−97.2473	−	97.2473i	−0.101617	−	0.101617i
$958$		0			0
$959$			323.031i			0.336842i
$960$		0			0
$961$	1172.82			1.22042
$962$		0			0
$963$	104.840	−	104.840i	0.108868	−	0.108868i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−663.854	−	663.854i	−0.686509	−	0.686509i	0.274950	−	0.961459i	$-0.411339\pi$
$967$	−663.854	−	663.854i	−0.686509	−	0.686509i	−0.961459	+	0.274950i	$0.911339\pi$
$968$		0			0
$969$		−	165.802i		−	0.171106i
$970$		0			0
$971$	1455.62			1.49910			0.749549	−	0.661948i	$-0.230270\pi$
$971$	1455.62			1.49910			0.749549	+	0.661948i	$0.230270\pi$
$972$		0			0
$973$	−90.3145	+	90.3145i	−0.0928207	+	0.0928207i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−127.882	−	127.882i	−0.130892	−	0.130892i	0.638626	−	0.769518i	$-0.279503\pi$
$977$	−127.882	−	127.882i	−0.130892	−	0.130892i	−0.769518	+	0.638626i	$0.779503\pi$
$978$		0			0
$979$		−	452.205i		−	0.461905i
$980$		0			0
$981$	386.952			0.394447
$982$		0			0
$983$	−640.848	+	640.848i	−0.651931	+	0.651931i	−0.953458	−	0.301527i	$-0.902504\pi$
$983$	−640.848	+	640.848i	−0.651931	+	0.651931i	0.301527	+	0.953458i	$0.402504\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−923.091	−	923.091i	−0.935250	−	0.935250i
$988$		0			0
$989$			934.729i			0.945126i
$990$		0			0
$991$	−958.240			−0.966943			−0.483471	−	0.875360i	$-0.660624\pi$
$991$	−958.240			−0.966943			−0.483471	+	0.875360i	$0.660624\pi$
$992$		0			0
$993$	181.867	−	181.867i	0.183149	−	0.183149i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−55.5140	−	55.5140i	−0.0556810	−	0.0556810i	0.678718	−	0.734399i	$-0.262536\pi$
$997$	−55.5140	−	55.5140i	−0.0556810	−	0.0556810i	−0.734399	+	0.678718i	$0.762536\pi$
$998$		0			0
$999$		−	357.368i		−	0.357726i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1200.3.bg.q.1057.4		8
4.3	odd	2		600.3.u.h.457.1		8
5.2	odd	4		240.3.bg.e.193.2		8
5.3	odd	4	inner	1200.3.bg.q.193.4		8
5.4	even	2		240.3.bg.e.97.2		8
12.11	even	2		1800.3.v.t.1657.1		8
15.2	even	4		720.3.bh.o.433.2		8
15.14	odd	2		720.3.bh.o.577.2		8
20.3	even	4		600.3.u.h.193.1		8
20.7	even	4		120.3.u.b.73.4	✓	8
20.19	odd	2		120.3.u.b.97.4	yes	8
40.19	odd	2		960.3.bg.l.577.1		8
40.27	even	4		960.3.bg.l.193.1		8
40.29	even	2		960.3.bg.k.577.3		8
40.37	odd	4		960.3.bg.k.193.3		8
60.23	odd	4		1800.3.v.t.793.1		8
60.47	odd	4		360.3.v.f.73.2		8
60.59	even	2		360.3.v.f.217.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.3.u.b.73.4	✓	8	20.7	even	4
120.3.u.b.97.4	yes	8	20.19	odd	2
240.3.bg.e.97.2		8	5.4	even	2
240.3.bg.e.193.2		8	5.2	odd	4
360.3.v.f.73.2		8	60.47	odd	4
360.3.v.f.217.2		8	60.59	even	2
600.3.u.h.193.1		8	20.3	even	4
600.3.u.h.457.1		8	4.3	odd	2
720.3.bh.o.433.2		8	15.2	even	4
720.3.bh.o.577.2		8	15.14	odd	2
960.3.bg.k.193.3		8	40.37	odd	4
960.3.bg.k.577.3		8	40.29	even	2
960.3.bg.l.193.1		8	40.27	even	4
960.3.bg.l.577.1		8	40.19	odd	2
1200.3.bg.q.193.4		8	5.3	odd	4	inner
1200.3.bg.q.1057.4		8	1.1	even	1	trivial
1800.3.v.t.793.1		8	60.23	odd	4
1800.3.v.t.1657.1		8	12.11	even	2

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:	\( N \)	\(=\)	\( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1200.bg (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.22474 - 1.22474i) q^{3} +(7.33876 + 7.33876i) q^{7} -3.00000i q^{9} +O(q^{10})\)	\(q+(1.22474 - 1.22474i) q^{3} +(7.33876 + 7.33876i) q^{7} -3.00000i q^{9} -6.49926 q^{11} +(-11.2377 + 11.2377i) q^{13} +(10.1367 + 10.1367i) q^{17} -6.67753i q^{19} +17.9762 q^{21} +(-21.0772 + 21.0772i) q^{23} +(-3.67423 - 3.67423i) q^{27} +12.2171i q^{29} -46.1933 q^{31} +(-7.95994 + 7.95994i) q^{33} +(48.6316 + 48.6316i) q^{37} +27.5267i q^{39} -60.0326 q^{41} +(22.1739 - 22.1739i) q^{43} +(-51.3507 - 51.3507i) q^{47} +58.7149i q^{49} +24.8298 q^{51} +(-42.4339 + 42.4339i) q^{53} +(-8.17826 - 8.17826i) q^{57} +0.297219i q^{59} +46.8766 q^{61} +(22.0163 - 22.0163i) q^{63} +(-13.4220 - 13.4220i) q^{67} +51.6285i q^{69} -46.3448 q^{71} +(42.4381 - 42.4381i) q^{73} +(-47.6965 - 47.6965i) q^{77} +27.7474i q^{79} -9.00000 q^{81} +(71.7548 - 71.7548i) q^{83} +(14.9628 + 14.9628i) q^{87} +69.5780i q^{89} -164.942 q^{91} +(-56.5750 + 56.5750i) q^{93} +(110.825 + 110.825i) q^{97} +19.4978i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{7}+O(q^{10}) \) 8 * q + 4 * q^7	\( 8 q + 4 q^{7} - 32 q^{11} + 4 q^{13} - 52 q^{17} - 24 q^{21} - 40 q^{23} - 96 q^{31} - 60 q^{33} + 60 q^{37} - 152 q^{41} - 88 q^{43} - 16 q^{47} + 168 q^{51} - 108 q^{53} + 24 q^{57} + 264 q^{61} + 12 q^{63} - 216 q^{67} + 240 q^{71} + 208 q^{73} - 168 q^{77} - 72 q^{81} + 336 q^{83} + 252 q^{87} - 592 q^{91} - 264 q^{93} + 208 q^{97}+O(q^{100}) \) 8 * q + 4 * q^7 - 32 * q^11 + 4 * q^13 - 52 * q^17 - 24 * q^21 - 40 * q^23 - 96 * q^31 - 60 * q^33 + 60 * q^37 - 152 * q^41 - 88 * q^43 - 16 * q^47 + 168 * q^51 - 108 * q^53 + 24 * q^57 + 264 * q^61 + 12 * q^63 - 216 * q^67 + 240 * q^71 + 208 * q^73 - 168 * q^77 - 72 * q^81 + 336 * q^83 + 252 * q^87 - 592 * q^91 - 264 * q^93 + 208 * q^97

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