LMFDB - Embedded newform 2520.2.bi.s.1801.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2520,2,Mod(361,2520)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2520, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 4]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("2520.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2520 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2520.bi (of order $3$, degree $2$, 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:	$20.1223013094$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 29x^{8} + 247x^{6} + 855x^{4} + 1212x^{2} + 588 $ x^10 + 29x^8 + 247x^6 + 855x^4 + 1212x^2 + 588
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1801.5
Root			$-1.22977i$ of defining polynomial
Character	$\chi$	$=$	2520.1801
Dual form			2520.2.bi.s.361.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{5} +(1.87518 - 1.86646i) q^{7} +O(q^{10})$	$q+(0.500000 - 0.866025i) q^{5} +(1.87518 - 1.86646i) q^{7} +(1.56501 + 2.71069i) q^{11} -3.53916 q^{13} +(-2.76138 - 4.78286i) q^{17} +(2.94839 - 5.10677i) q^{19} +(0.0732100 - 0.126804i) q^{23} +(-0.500000 - 0.866025i) q^{25} -2.91882 q^{29} +(-2.54580 - 4.40946i) q^{31} +(-0.678814 - 2.55719i) q^{35} +(-0.321186 + 0.556310i) q^{37} +8.63076 q^{41} -5.93189 q^{43} +(-0.704564 + 1.22034i) q^{47} +(0.0326205 - 6.99992i) q^{49} +(4.83459 + 8.37376i) q^{53} +3.13003 q^{55} +(-1.67062 - 2.89360i) q^{59} +(6.19876 - 10.7366i) q^{61} +(-1.76958 + 3.06500i) q^{65} +(-6.62555 - 11.4758i) q^{67} +0.658762 q^{71} +(2.34561 + 4.06272i) q^{73} +(7.99409 + 2.16199i) q^{77} +(-2.67499 + 4.63322i) q^{79} -13.4787 q^{83} -5.52277 q^{85} +(7.20978 - 12.4877i) q^{89} +(-6.63657 + 6.60571i) q^{91} +(-2.94839 - 5.10677i) q^{95} -2.86400 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 5 q^{5} - q^{7}+O(q^{10}) $ 10 * q + 5 * q^5 - q^7	$ 10 q + 5 q^{5} - q^{7} + 2 q^{11} + 6 q^{13} - 2 q^{17} + q^{19} - 8 q^{23} - 5 q^{25} + 7 q^{31} + q^{35} - 11 q^{37} - 20 q^{41} + 6 q^{43} - 23 q^{49} + 14 q^{53} + 4 q^{55} - 4 q^{59} - 6 q^{61} + 3 q^{65} - 7 q^{67} + 32 q^{71} + 3 q^{73} - 8 q^{77} - 19 q^{79} - 28 q^{83} - 4 q^{85} + 18 q^{89} - 21 q^{91} - q^{95} + 48 q^{97}+O(q^{100}) $ 10 * q + 5 * q^5 - q^7 + 2 * q^11 + 6 * q^13 - 2 * q^17 + q^19 - 8 * q^23 - 5 * q^25 + 7 * q^31 + q^35 - 11 * q^37 - 20 * q^41 + 6 * q^43 - 23 * q^49 + 14 * q^53 + 4 * q^55 - 4 * q^59 - 6 * q^61 + 3 * q^65 - 7 * q^67 + 32 * q^71 + 3 * q^73 - 8 * q^77 - 19 * q^79 - 28 * q^83 - 4 * q^85 + 18 * q^89 - 21 * q^91 - q^95 + 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2520\mathbb{Z}\right)^\times$.

$n$	$281$	$631$	$1081$	$1261$	$2017$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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
$3$		0			0
$3$		0			0
$4$		0			0
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$		0			0
$7$	1.87518	−	1.86646i	0.708752	−	0.705457i
$7$	1.87518	−	1.86646i	0.708752	−	0.705457i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.56501	+	2.71069i	0.471870	+	0.817302i	0.999482	−	0.0321830i	$-0.0102459\pi$
$11$	1.56501	+	2.71069i	0.471870	+	0.817302i	−0.527612	+	0.849485i	$0.676913\pi$
$12$		0			0
$13$	−3.53916			−0.981586			−0.490793	−	0.871276i	$-0.663293\pi$
$13$	−3.53916			−0.981586			−0.490793	+	0.871276i	$0.663293\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.76138	−	4.78286i	−0.669734	−	1.16001i	−0.977978	−	0.208706i	$-0.933075\pi$
$17$	−2.76138	−	4.78286i	−0.669734	−	1.16001i	0.308245	−	0.951307i	$-0.400258\pi$
$18$		0			0
$19$	2.94839	−	5.10677i	0.676408	−	1.17157i	−0.299648	−	0.954050i	$-0.596869\pi$
$19$	2.94839	−	5.10677i	0.676408	−	1.17157i	0.976055	−	0.217523i	$-0.0697976\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.0732100	−	0.126804i	0.0152653	−	0.0264404i	−0.858292	−	0.513162i	$-0.828474\pi$
$23$	0.0732100	−	0.126804i	0.0152653	−	0.0264404i	0.873557	+	0.486722i	$0.161807\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−2.91882			−0.542011			−0.271006	−	0.962578i	$-0.587356\pi$
$29$	−2.91882			−0.542011			−0.271006	+	0.962578i	$0.587356\pi$
$30$		0			0
$31$	−2.54580	−	4.40946i	−0.457239	−	0.791962i	0.541574	−	0.840653i	$-0.317828\pi$
$31$	−2.54580	−	4.40946i	−0.457239	−	0.791962i	−0.998814	+	0.0486908i	$0.984495\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−0.678814	−	2.55719i	−0.114741	−	0.432244i
$36$		0			0
$37$	−0.321186	+	0.556310i	−0.0528026	+	0.0914568i	−0.891219	−	0.453574i	$-0.850149\pi$
$37$	−0.321186	+	0.556310i	−0.0528026	+	0.0914568i	0.838416	+	0.545031i	$0.183482\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	8.63076			1.34790			0.673949	−	0.738778i	$-0.264597\pi$
$41$	8.63076			1.34790			0.673949	+	0.738778i	$0.264597\pi$
$42$		0			0
$43$	−5.93189			−0.904605			−0.452303	−	0.891865i	$-0.649397\pi$
$43$	−5.93189			−0.904605			−0.452303	+	0.891865i	$0.649397\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−0.704564	+	1.22034i	−0.102771	+	0.178005i	−0.912825	−	0.408350i	$-0.866104\pi$
$47$	−0.704564	+	1.22034i	−0.102771	+	0.178005i	0.810054	+	0.586355i	$0.199438\pi$
$48$		0			0
$49$	0.0326205	−	6.99992i	0.00466007	−	0.999989i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	4.83459	+	8.37376i	0.664082	+	1.15022i	0.979533	+	0.201283i	$0.0645110\pi$
$53$	4.83459	+	8.37376i	0.664082	+	1.15022i	−0.315451	+	0.948942i	$0.602156\pi$
$54$		0			0
$55$	3.13003			0.422053
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−1.67062	−	2.89360i	−0.217496	−	0.376714i	0.736546	−	0.676388i	$-0.236456\pi$
$59$	−1.67062	−	2.89360i	−0.217496	−	0.376714i	−0.954042	+	0.299673i	$0.903122\pi$
$60$		0			0
$61$	6.19876	−	10.7366i	0.793670	−	1.37468i	−0.130011	−	0.991513i	$-0.541501\pi$
$61$	6.19876	−	10.7366i	0.793670	−	1.37468i	0.923680	−	0.383164i	$-0.125165\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−1.76958	+	3.06500i	−0.219489	+	0.380166i
$66$		0			0
$67$	−6.62555	−	11.4758i	−0.809440	−	1.40199i	−0.913253	−	0.407394i	$-0.866438\pi$
$67$	−6.62555	−	11.4758i	−0.809440	−	1.40199i	0.103813	−	0.994597i	$-0.466896\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	0.658762			0.0781807			0.0390903	−	0.999236i	$-0.487554\pi$
$71$	0.658762			0.0781807			0.0390903	+	0.999236i	$0.487554\pi$
$72$		0			0
$73$	2.34561	+	4.06272i	0.274533	+	0.475505i	0.970017	−	0.243036i	$-0.0781434\pi$
$73$	2.34561	+	4.06272i	0.274533	+	0.475505i	−0.695484	+	0.718541i	$0.744810\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	7.99409	+	2.16199i	0.911011	+	0.246381i
$78$		0			0
$79$	−2.67499	+	4.63322i	−0.300960	+	0.521278i	−0.976354	−	0.216179i	$-0.930640\pi$
$79$	−2.67499	+	4.63322i	−0.300960	+	0.521278i	0.675394	+	0.737457i	$0.263974\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−13.4787			−1.47948			−0.739740	−	0.672893i	$-0.765051\pi$
$83$	−13.4787			−1.47948			−0.739740	+	0.672893i	$0.765051\pi$
$84$		0			0
$85$	−5.52277			−0.599028
$86$		0			0
$87$		0			0
$88$		0			0
$89$	7.20978	−	12.4877i	0.764235	−	1.32369i	−0.176416	−	0.984316i	$-0.556450\pi$
$89$	7.20978	−	12.4877i	0.764235	−	1.32369i	0.940650	−	0.339378i	$-0.110216\pi$
$90$		0			0
$91$	−6.63657	+	6.60571i	−0.695701	+	0.692467i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−2.94839	−	5.10677i	−0.302499	−	0.523943i
$96$		0			0
$97$	−2.86400			−0.290796			−0.145398	−	0.989373i	$-0.546446\pi$
$97$	−2.86400			−0.290796			−0.145398	+	0.989373i	$0.546446\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	6.77861	+	11.7409i	0.674497	+	1.16826i	0.976616	+	0.214993i	$0.0689729\pi$
$101$	6.77861	+	11.7409i	0.674497	+	1.16826i	−0.302118	+	0.953270i	$0.597694\pi$
$102$		0			0
$103$	2.93084	−	5.07636i	0.288784	−	0.500189i	−0.684736	−	0.728792i	$-0.740082\pi$
$103$	2.93084	−	5.07636i	0.288784	−	0.500189i	0.973520	+	0.228603i	$0.0734157\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−3.76138	+	6.51491i	−0.363627	+	0.629820i	−0.988555	−	0.150862i	$-0.951795\pi$
$107$	−3.76138	+	6.51491i	−0.363627	+	0.629820i	0.624928	+	0.780682i	$0.285128\pi$
$108$		0			0
$109$	−2.86417	−	4.96088i	−0.274337	−	0.475166i	0.695630	−	0.718400i	$-0.255125\pi$
$109$	−2.86417	−	4.96088i	−0.274337	−	0.475166i	−0.969968	+	0.243234i	$0.921792\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−9.50073			−0.893754			−0.446877	−	0.894596i	$-0.647464\pi$
$113$	−9.50073			−0.893754			−0.446877	+	0.894596i	$0.647464\pi$
$114$		0			0
$115$	−0.0732100	−	0.126804i	−0.00682687	−	0.0118245i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−14.1051	−	3.81471i	−1.29302	−	0.349693i
$120$		0			0
$121$	0.601458	−	1.04176i	0.0546780	−	0.0947050i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	10.5145			0.933009			0.466504	−	0.884519i	$-0.345513\pi$
$127$	10.5145			0.933009			0.466504	+	0.884519i	$0.345513\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−0.105604	+	0.182912i	−0.00922669	+	0.0159811i	−0.870602	−	0.491988i	$-0.836270\pi$
$131$	−0.105604	+	0.182912i	−0.00922669	+	0.0159811i	0.861375	+	0.507969i	$0.169604\pi$
$132$		0			0
$133$	−4.00282	−	15.0792i	−0.347089	−	1.30753i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	3.57985	+	6.20049i	0.305848	+	0.529744i	0.977450	−	0.211168i	$-0.0677268\pi$
$137$	3.57985	+	6.20049i	0.305848	+	0.529744i	−0.671602	+	0.740912i	$0.734394\pi$
$138$		0			0
$139$	−3.27313			−0.277623			−0.138812	−	0.990319i	$-0.544328\pi$
$139$	−3.27313			−0.277623			−0.138812	+	0.990319i	$0.544328\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−5.53883	−	9.59354i	−0.463180	−	0.802252i
$144$		0			0
$145$	−1.45941	+	2.52777i	−0.121197	+	0.209920i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−3.50405	+	6.06919i	−0.287063	+	0.497207i	−0.973107	−	0.230352i	$-0.926012\pi$
$149$	−3.50405	+	6.06919i	−0.287063	+	0.497207i	0.686044	+	0.727560i	$0.259346\pi$
$150$		0			0
$151$	−9.57842	−	16.5903i	−0.779481	−	1.35010i	−0.932241	−	0.361837i	$-0.882150\pi$
$151$	−9.57842	−	16.5903i	−0.779481	−	1.35010i	0.152760	−	0.988263i	$-0.451184\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−5.09160			−0.408967
$156$		0			0
$157$	−3.00239	−	5.20029i	−0.239617	−	0.415028i	0.720988	−	0.692948i	$-0.243688\pi$
$157$	−3.00239	−	5.20029i	−0.239617	−	0.415028i	−0.960604	+	0.277920i	$0.910355\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−0.0993920	−	0.374424i	−0.00783319	−	0.0295087i
$162$		0			0
$163$	6.41955	−	11.1190i	0.502818	−	0.870907i	−0.497177	−	0.867649i	$-0.665630\pi$
$163$	6.41955	−	11.1190i	0.502818	−	0.870907i	0.999995	−	0.00325713i	$-0.00103678\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−2.14642			−0.166095			−0.0830475	−	0.996546i	$-0.526465\pi$
$167$	−2.14642			−0.166095			−0.0830475	+	0.996546i	$0.526465\pi$
$168$		0			0
$169$	−0.474368			−0.0364899
$170$		0			0
$171$		0			0
$172$		0			0
$173$	1.08423	−	1.87794i	0.0824323	−	0.142777i	−0.821862	−	0.569687i	$-0.807065\pi$
$173$	1.08423	−	1.87794i	0.0824323	−	0.142777i	0.904294	+	0.426910i	$0.140398\pi$
$174$		0			0
$175$	−2.55400	−	0.690724i	−0.193064	−	0.0522138i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−1.46323	−	2.53439i	−0.109367	−	0.189429i	0.806147	−	0.591715i	$-0.201549\pi$
$179$	−1.46323	−	2.53439i	−0.109367	−	0.189429i	−0.915514	+	0.402286i	$0.868216\pi$
$180$		0			0
$181$	21.4630			1.59533			0.797665	−	0.603101i	$-0.206068\pi$
$181$	21.4630			1.59533			0.797665	+	0.603101i	$0.206068\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	0.321186	+	0.556310i	0.0236140	+	0.0409007i
$186$		0			0
$187$	8.64321	−	14.9705i	0.632054	−	1.09475i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	10.2731	−	17.7936i	0.743338	−	1.28750i	−0.207630	−	0.978208i	$-0.566575\pi$
$191$	10.2731	−	17.7936i	0.743338	−	1.28750i	0.950967	−	0.309291i	$-0.100092\pi$
$192$		0			0
$193$	−8.68120	−	15.0363i	−0.624887	−	1.08234i	−0.988563	−	0.150810i	$-0.951812\pi$
$193$	−8.68120	−	15.0363i	−0.624887	−	1.08234i	0.363676	−	0.931526i	$-0.381522\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	24.9087			1.77467			0.887335	−	0.461126i	$-0.152554\pi$
$197$	24.9087			1.77467			0.887335	+	0.461126i	$0.152554\pi$
$198$		0			0
$199$	−5.97116	−	10.3424i	−0.423284	−	0.733150i	0.572974	−	0.819573i	$-0.305789\pi$
$199$	−5.97116	−	10.3424i	−0.423284	−	0.733150i	−0.996258	+	0.0864236i	$0.972456\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−5.47332	+	5.44788i	−0.384152	+	0.382366i
$204$		0			0
$205$	4.31538	−	7.47446i	0.301399	−	0.522039i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	18.4571			1.27671
$210$		0			0
$211$	0.0571436			0.00393393			0.00196696	−	0.999998i	$-0.499374\pi$
$211$	0.0571436			0.00393393			0.00196696	+	0.999998i	$0.499374\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−2.96595	+	5.13717i	−0.202276	+	0.350352i
$216$		0			0
$217$	−13.0039	−	3.51689i	−0.882765	−	0.238742i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	9.77297	+	16.9273i	0.657401	+	1.13865i
$222$		0			0
$223$	26.5790			1.77986			0.889932	−	0.456093i	$-0.150751\pi$
$223$	26.5790			1.77986			0.889932	+	0.456093i	$0.150751\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	7.43057	+	12.8701i	0.493184	+	0.854220i	0.999969	−	0.00785238i	$-0.00249952\pi$
$227$	7.43057	+	12.8701i	0.493184	+	0.854220i	−0.506785	+	0.862073i	$0.669166\pi$
$228$		0			0
$229$	−2.59730	+	4.49866i	−0.171634	+	0.297280i	−0.938991	−	0.343941i	$-0.888238\pi$
$229$	−2.59730	+	4.49866i	−0.171634	+	0.297280i	0.767357	+	0.641220i	$0.221571\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	6.25441	−	10.8330i	0.409740	−	0.709691i	−0.585120	−	0.810947i	$-0.698953\pi$
$233$	6.25441	−	10.8330i	0.409740	−	0.709691i	0.994860	+	0.101256i	$0.0322860\pi$
$234$		0			0
$235$	0.704564	+	1.22034i	0.0459607	+	0.0796062i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	14.5201			0.939228			0.469614	−	0.882872i	$-0.344393\pi$
$239$	14.5201			0.939228			0.469614	+	0.882872i	$0.344393\pi$
$240$		0			0
$241$	−6.31809	−	10.9433i	−0.406984	−	0.704917i	0.587566	−	0.809176i	$-0.300086\pi$
$241$	−6.31809	−	10.9433i	−0.406984	−	0.704917i	−0.994550	+	0.104259i	$0.966753\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−6.04580	−	3.52821i	−0.386252	−	0.225409i
$246$		0			0
$247$	−10.4348	+	18.0736i	−0.663952	+	1.15000i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−25.7531			−1.62552			−0.812762	−	0.582596i	$-0.802037\pi$
$251$	−25.7531			−1.62552			−0.812762	+	0.582596i	$0.802037\pi$
$252$		0			0
$253$	0.458299			0.0288130
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−4.82662	+	8.35996i	−0.301077	+	0.521480i	−0.976380	−	0.216060i	$-0.930679\pi$
$257$	−4.82662	+	8.35996i	−0.301077	+	0.521480i	0.675304	+	0.737540i	$0.264013\pi$
$258$		0			0
$259$	0.436051	+	1.64266i	0.0270949	+	0.102070i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−11.8069	−	20.4501i	−0.728042	−	1.26101i	−0.957709	−	0.287737i	$-0.907097\pi$
$263$	−11.8069	−	20.4501i	−0.728042	−	1.26101i	0.229667	−	0.973269i	$-0.426236\pi$
$264$		0			0
$265$	9.66919			0.593973
$266$		0			0
$267$		0			0
$268$		0			0
$269$	7.44923	+	12.9024i	0.454188	+	0.786676i	0.998641	−	0.0521149i	$-0.0165962\pi$
$269$	7.44923	+	12.9024i	0.454188	+	0.786676i	−0.544453	+	0.838791i	$0.683263\pi$
$270$		0			0
$271$	−11.2256	+	19.4433i	−0.681905	+	1.18109i	0.292494	+	0.956267i	$0.405515\pi$
$271$	−11.2256	+	19.4433i	−0.681905	+	1.18109i	−0.974399	+	0.224827i	$0.927818\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	1.56501	−	2.71069i	0.0943739	−	0.163460i
$276$		0			0
$277$	9.33400	+	16.1670i	0.560826	+	0.971379i	0.997425	+	0.0717224i	$0.0228496\pi$
$277$	9.33400	+	16.1670i	0.560826	+	0.971379i	−0.436599	+	0.899656i	$0.643817\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	19.9279			1.18880			0.594400	−	0.804169i	$-0.297390\pi$
$281$	19.9279			1.18880			0.594400	+	0.804169i	$0.297390\pi$
$282$		0			0
$283$	9.73835	+	16.8673i	0.578885	+	1.00266i	0.995608	+	0.0936241i	$0.0298452\pi$
$283$	9.73835	+	16.8673i	0.578885	+	1.00266i	−0.416723	+	0.909034i	$0.636821\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	16.1843	−	16.1090i	0.955326	−	0.950885i
$288$		0			0
$289$	−6.75047	+	11.6922i	−0.397087	+	0.687774i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−24.4381			−1.42769			−0.713844	−	0.700305i	$-0.753047\pi$
$293$	−24.4381			−1.42769			−0.713844	+	0.700305i	$0.753047\pi$
$294$		0			0
$295$	−3.34124			−0.194534
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−0.259102	+	0.448778i	−0.0149842	+	0.0259535i
$300$		0			0
$301$	−11.1234	+	11.0717i	−0.641141	+	0.638160i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−6.19876	−	10.7366i	−0.354940	−	0.614774i
$306$		0			0
$307$	−3.63208			−0.207294			−0.103647	−	0.994614i	$-0.533051\pi$
$307$	−3.63208			−0.207294			−0.103647	+	0.994614i	$0.533051\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	6.89822	+	11.9481i	0.391162	+	0.677513i	0.992603	−	0.121405i	$-0.0387399\pi$
$311$	6.89822	+	11.9481i	0.391162	+	0.677513i	−0.601441	+	0.798917i	$0.705407\pi$
$312$		0			0
$313$	−7.45360	+	12.9100i	−0.421303	+	0.729718i	−0.996067	−	0.0886012i	$-0.971760\pi$
$313$	−7.45360	+	12.9100i	−0.421303	+	0.729718i	0.574765	+	0.818319i	$0.305094\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	1.17616	−	2.03716i	0.0660595	−	0.114418i	−0.831104	−	0.556117i	$-0.812291\pi$
$317$	1.17616	−	2.03716i	0.0660595	−	0.114418i	0.897163	+	0.441699i	$0.145624\pi$
$318$		0			0
$319$	−4.56800	−	7.91200i	−0.255759	−	0.442987i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−32.5666			−1.81205
$324$		0			0
$325$	1.76958	+	3.06500i	0.0981586	+	0.170016i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	0.956536	+	3.60340i	0.0527355	+	0.198662i
$330$		0			0
$331$	−16.3584	+	28.3335i	−0.899137	+	1.55735i	−0.0705370	+	0.997509i	$0.522471\pi$
$331$	−16.3584	+	28.3335i	−0.899137	+	1.55735i	−0.828600	+	0.559841i	$0.810862\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−13.2511			−0.723985
$336$		0			0
$337$	2.65676			0.144723			0.0723615	−	0.997378i	$-0.476946\pi$
$337$	2.65676			0.144723			0.0723615	+	0.997378i	$0.476946\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	7.96843	−	13.8017i	0.431515	−	0.747406i
$342$		0			0
$343$	−13.0039	−	13.1870i	−0.702147	−	0.712032i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−17.7311	−	30.7112i	−0.951856	−	1.64866i	−0.741405	−	0.671058i	$-0.765840\pi$
$347$	−17.7311	−	30.7112i	−0.951856	−	1.64866i	−0.210451	−	0.977604i	$-0.567493\pi$
$348$		0			0
$349$	19.8638			1.06328			0.531642	−	0.846969i	$-0.321575\pi$
$349$	19.8638			1.06328			0.531642	+	0.846969i	$0.321575\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−14.8473	−	25.7164i	−0.790244	−	1.36874i	−0.925816	−	0.377976i	$-0.876620\pi$
$353$	−14.8473	−	25.7164i	−0.790244	−	1.36874i	0.135571	−	0.990768i	$-0.456713\pi$
$354$		0			0
$355$	0.329381	−	0.570505i	0.0174817	−	0.0302792i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−17.5641	+	30.4219i	−0.926997	+	1.60561i	−0.138680	+	0.990337i	$0.544286\pi$
$359$	−17.5641	+	30.4219i	−0.926997	+	1.60561i	−0.788317	+	0.615269i	$0.789048\pi$
$360$		0			0
$361$	−7.88604	−	13.6590i	−0.415055	−	0.718896i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	4.69122			0.245550
$366$		0			0
$367$	5.94568	+	10.2982i	0.310362	+	0.537563i	0.978441	−	0.206528i	$-0.0662164\pi$
$367$	5.94568	+	10.2982i	0.310362	+	0.537563i	−0.668079	+	0.744091i	$0.732883\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	24.6951	+	6.67874i	1.28210	+	0.346743i
$372$		0			0
$373$	−12.7884	+	22.1501i	−0.662156	+	1.14689i	0.317892	+	0.948127i	$0.397025\pi$
$373$	−12.7884	+	22.1501i	−0.662156	+	1.14689i	−0.980048	+	0.198761i	$0.936308\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	10.3302			0.532031
$378$		0			0
$379$	26.9174			1.38265			0.691327	−	0.722542i	$-0.257026\pi$
$379$	26.9174			1.38265			0.691327	+	0.722542i	$0.257026\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−9.99973	+	17.3200i	−0.510962	+	0.885013i	0.488957	+	0.872308i	$0.337378\pi$
$383$	−9.99973	+	17.3200i	−0.510962	+	0.885013i	−0.999919	+	0.0127049i	$0.995956\pi$
$384$		0			0
$385$	5.86938	−	5.84209i	0.299131	−	0.297740i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	16.7269	+	28.9718i	0.848087	+	1.46893i	0.882913	+	0.469537i	$0.155579\pi$
$389$	16.7269	+	28.9718i	0.848087	+	1.46893i	−0.0348254	+	0.999393i	$0.511088\pi$
$390$		0			0
$391$	−0.808644			−0.0408949
$392$		0			0
$393$		0			0
$394$		0			0
$395$	2.67499	+	4.63322i	0.134593	+	0.233123i
$396$		0			0
$397$	1.36765	−	2.36883i	0.0686402	−	0.118888i	−0.829663	−	0.558265i	$-0.811467\pi$
$397$	1.36765	−	2.36883i	0.0686402	−	0.118888i	0.898303	+	0.439377i	$0.144801\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	5.53112	−	9.58018i	0.276211	−	0.478412i	−0.694229	−	0.719754i	$-0.744254\pi$
$401$	5.53112	−	9.58018i	0.276211	−	0.478412i	0.970440	+	0.241343i	$0.0775878\pi$
$402$		0			0
$403$	9.00999	+	15.6058i	0.448820	+	0.777378i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−2.01064			−0.0996638
$408$		0			0
$409$	13.6241	+	23.5977i	0.673669	+	1.16683i	0.976856	+	0.213898i	$0.0686160\pi$
$409$	13.6241	+	23.5977i	0.673669	+	1.16683i	−0.303187	+	0.952931i	$0.598051\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−8.53351	−	2.30787i	−0.419907	−	0.113563i
$414$		0			0
$415$	−6.73935	+	11.6729i	−0.330822	+	0.573000i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	17.9126			0.875090			0.437545	−	0.899197i	$-0.355848\pi$
$419$	17.9126			0.875090			0.437545	+	0.899197i	$0.355848\pi$
$420$		0			0
$421$	36.4906			1.77844			0.889221	−	0.457478i	$-0.151247\pi$
$421$	36.4906			1.77844			0.889221	+	0.457478i	$0.151247\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−2.76138	+	4.78286i	−0.133947	+	0.232003i
$426$		0			0
$427$	−8.41561	−	31.7028i	−0.407260	−	1.53421i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	4.52755	+	7.84194i	0.218084	+	0.377733i	0.954222	−	0.299099i	$-0.0966859\pi$
$431$	4.52755	+	7.84194i	0.218084	+	0.377733i	−0.736138	+	0.676831i	$0.763353\pi$
$432$		0			0
$433$	3.24154			0.155778			0.0778892	−	0.996962i	$-0.475182\pi$
$433$	3.24154			0.155778			0.0778892	+	0.996962i	$0.475182\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−0.431704	−	0.747733i	−0.0206512	−	0.0357689i
$438$		0			0
$439$	9.61353	−	16.6511i	0.458829	−	0.794715i	−0.540071	−	0.841620i	$-0.681602\pi$
$439$	9.61353	−	16.6511i	0.458829	−	0.794715i	0.998899	+	0.0469050i	$0.0149358\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−1.57427	+	2.72671i	−0.0747956	+	0.129550i	−0.900997	−	0.433825i	$-0.857164\pi$
$443$	−1.57427	+	2.72671i	−0.0747956	+	0.129550i	0.826202	+	0.563374i	$0.190497\pi$
$444$		0			0
$445$	−7.20978	−	12.4877i	−0.341776	−	0.591974i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−20.8343			−0.983233			−0.491616	−	0.870812i	$-0.663594\pi$
$449$	−20.8343			−0.983233			−0.491616	+	0.870812i	$0.663594\pi$
$450$		0			0
$451$	13.5073	+	23.3953i	0.636032	+	1.10164i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	2.40243	+	9.05029i	0.112628	+	0.424284i
$456$		0			0
$457$	−17.4872	+	30.2888i	−0.818018	+	1.41685i	0.0891226	+	0.996021i	$0.471594\pi$
$457$	−17.4872	+	30.2888i	−0.818018	+	1.41685i	−0.907140	+	0.420828i	$0.861740\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	36.4665			1.69842			0.849208	−	0.528058i	$-0.177080\pi$
$461$	36.4665			1.69842			0.849208	+	0.528058i	$0.177080\pi$
$462$		0			0
$463$	−28.6711			−1.33246			−0.666230	−	0.745747i	$-0.732093\pi$
$463$	−28.6711			−1.33246			−0.666230	+	0.745747i	$0.732093\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−0.0975696	+	0.168996i	−0.00451498	+	0.00782018i	−0.868274	−	0.496085i	$-0.834771\pi$
$467$	−0.0975696	+	0.168996i	−0.00451498	+	0.00782018i	0.863759	+	0.503905i	$0.168104\pi$
$468$		0			0
$469$	−33.8433	−	9.15285i	−1.56274	−	0.422639i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−9.28350	−	16.0795i	−0.426856	−	0.739336i
$474$		0			0
$475$	−5.89679			−0.270563
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−5.78547	−	10.0207i	−0.264345	−	0.457859i	0.703047	−	0.711144i	$-0.251822\pi$
$479$	−5.78547	−	10.0207i	−0.264345	−	0.457859i	−0.967392	+	0.253285i	$0.918489\pi$
$480$		0			0
$481$	1.13673	−	1.96887i	0.0518303	−	0.0897727i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−1.43200	+	2.48030i	−0.0650239	+	0.112625i
$486$		0			0
$487$	14.7824	+	25.6039i	0.669854	+	1.16022i	0.977945	+	0.208864i	$0.0669767\pi$
$487$	14.7824	+	25.6039i	0.669854	+	1.16022i	−0.308090	+	0.951357i	$0.599690\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	39.0817			1.76373			0.881866	−	0.471501i	$-0.156288\pi$
$491$	39.0817			1.76373			0.881866	+	0.471501i	$0.156288\pi$
$492$		0			0
$493$	8.05998	+	13.9603i	0.363003	+	0.628740i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	1.23530	−	1.22956i	0.0554107	−	0.0551531i
$498$		0			0
$499$	−8.43216	+	14.6049i	−0.377475	+	0.653807i	−0.990694	−	0.136106i	$-0.956541\pi$
$499$	−8.43216	+	14.6049i	−0.377475	+	0.653807i	0.613219	+	0.789913i	$0.289874\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−17.2768			−0.770335			−0.385167	−	0.922847i	$-0.625856\pi$
$503$	−17.2768			−0.770335			−0.385167	+	0.922847i	$0.625856\pi$
$504$		0			0
$505$	13.5572			0.603289
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−0.189173	+	0.327657i	−0.00838495	+	0.0145232i	−0.870187	−	0.492721i	$-0.836002\pi$
$509$	−0.189173	+	0.327657i	−0.00838495	+	0.0145232i	0.861802	+	0.507244i	$0.169336\pi$
$510$		0			0
$511$	11.9814	+	3.24034i	0.530024	+	0.143344i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−2.93084	−	5.07636i	−0.129148	−	0.223691i
$516$		0			0
$517$	−4.41061			−0.193978
$518$		0			0
$519$		0			0
$520$		0			0
$521$	9.39844	+	16.2786i	0.411753	+	0.713178i	0.995082	−	0.0990588i	$-0.0315832\pi$
$521$	9.39844	+	16.2786i	0.411753	+	0.713178i	−0.583328	+	0.812237i	$0.698250\pi$
$522$		0			0
$523$	3.76719	−	6.52496i	0.164728	−	0.285317i	−0.771831	−	0.635828i	$-0.780659\pi$
$523$	3.76719	−	6.52496i	0.164728	−	0.285317i	0.936559	+	0.350511i	$0.113992\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−14.0599	+	24.3524i	−0.612457	+	1.06081i
$528$		0			0
$529$	11.4893	+	19.9000i	0.499534	+	0.865218i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−30.5456			−1.32308
$534$		0			0
$535$	3.76138	+	6.51491i	0.162619	+	0.281664i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	19.0256	−	10.8666i	0.819492	−	0.468056i
$540$		0			0
$541$	0.347666	−	0.602175i	0.0149473	−	0.0258895i	−0.858455	−	0.512889i	$-0.828575\pi$
$541$	0.347666	−	0.602175i	0.0149473	−	0.0258895i	0.873402	+	0.486999i	$0.161909\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−5.72833			−0.245375
$546$		0			0
$547$	21.8791			0.935482			0.467741	−	0.883866i	$-0.345068\pi$
$547$	21.8791			0.935482			0.467741	+	0.883866i	$0.345068\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−8.60583	+	14.9057i	−0.366621	+	0.635006i
$552$		0			0
$553$	3.63165	+	13.6809i	0.154433	+	0.581772i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	18.4950	+	32.0343i	0.783660	+	1.35734i	0.929796	+	0.368074i	$0.119983\pi$
$557$	18.4950	+	32.0343i	0.783660	+	1.35734i	−0.146137	+	0.989264i	$0.546684\pi$
$558$		0			0
$559$	20.9939			0.887947
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−20.8040	−	36.0336i	−0.876784	−	1.51863i	−0.854850	−	0.518875i	$-0.826351\pi$
$563$	−20.8040	−	36.0336i	−0.876784	−	1.51863i	−0.0219336	−	0.999759i	$-0.506982\pi$
$564$		0			0
$565$	−4.75037	+	8.22787i	−0.199849	+	0.346149i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	9.42337	−	16.3218i	0.395048	−	0.684244i	−0.598059	−	0.801452i	$-0.704061\pi$
$569$	9.42337	−	16.3218i	0.395048	−	0.684244i	0.993107	+	0.117208i	$0.0373945\pi$
$570$		0			0
$571$	−9.33875	−	16.1752i	−0.390815	−	0.676911i	0.601743	−	0.798690i	$-0.294473\pi$
$571$	−9.33875	−	16.1752i	−0.390815	−	0.676911i	−0.992557	+	0.121779i	$0.961140\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−0.146420			−0.00610614
$576$		0			0
$577$	13.9151	+	24.1016i	0.579292	+	1.00336i	0.995561	+	0.0941215i	$0.0300042\pi$
$577$	13.9151	+	24.1016i	0.579292	+	1.00336i	−0.416269	+	0.909242i	$0.636662\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−25.2750	+	25.1575i	−1.04858	+	1.04371i
$582$		0			0
$583$	−15.1324	+	26.2101i	−0.626721	+	1.08551i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	17.4459			0.720070			0.360035	−	0.932939i	$-0.382765\pi$
$587$	17.4459			0.720070			0.360035	+	0.932939i	$0.382765\pi$
$588$		0			0
$589$	−30.0241			−1.23712
$590$		0			0
$591$		0			0
$592$		0			0
$593$	8.44153	−	14.6212i	0.346652	−	0.600419i	−0.639000	−	0.769206i	$-0.720652\pi$
$593$	8.44153	−	14.6212i	0.346652	−	0.600419i	0.985653	+	0.168787i	$0.0539851\pi$
$594$		0			0
$595$	−10.3562	+	10.3080i	−0.424563	+	0.422589i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−2.76198	−	4.78388i	−0.112851	−	0.195464i	0.804067	−	0.594538i	$-0.202665\pi$
$599$	−2.76198	−	4.78388i	−0.112851	−	0.195464i	−0.916919	+	0.399074i	$0.869332\pi$
$600$		0			0
$601$	41.7051			1.70119			0.850593	−	0.525824i	$-0.176243\pi$
$601$	41.7051			1.70119			0.850593	+	0.525824i	$0.176243\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−0.601458	−	1.04176i	−0.0244527	−	0.0423534i
$606$		0			0
$607$	14.3356	−	24.8299i	0.581862	−	1.00781i	−0.413397	−	0.910551i	$-0.635658\pi$
$607$	14.3356	−	24.8299i	0.581862	−	1.00781i	0.995259	−	0.0972636i	$-0.0310090\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	2.49356	−	4.31898i	0.100879	−	0.174727i
$612$		0			0
$613$	3.10644	+	5.38052i	0.125468	+	0.217317i	0.921916	−	0.387390i	$-0.126623\pi$
$613$	3.10644	+	5.38052i	0.125468	+	0.217317i	−0.796448	+	0.604707i	$0.793290\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−14.6550			−0.589988			−0.294994	−	0.955499i	$-0.595318\pi$
$617$	−14.6550			−0.589988			−0.294994	+	0.955499i	$0.595318\pi$
$618$		0			0
$619$	15.4589	+	26.7756i	0.621347	+	1.07620i	0.989235	+	0.146334i	$0.0467475\pi$
$619$	15.4589	+	26.7756i	0.621347	+	1.07620i	−0.367889	+	0.929870i	$0.619919\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−9.78820	−	36.8735i	−0.392156	−	1.47731i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	3.54767			0.141455
$630$		0			0
$631$	−23.4514			−0.933584			−0.466792	−	0.884367i	$-0.654590\pi$
$631$	−23.4514			−0.933584			−0.466792	+	0.884367i	$0.654590\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	5.25724	−	9.10580i	0.208627	−	0.361353i
$636$		0			0
$637$	−0.115449	+	24.7738i	−0.00457426	+	0.981575i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−10.6564	−	18.4574i	−0.420903	−	0.729025i	0.575125	−	0.818065i	$-0.304953\pi$
$641$	−10.6564	−	18.4574i	−0.420903	−	0.729025i	−0.996028	+	0.0890406i	$0.971620\pi$
$642$		0			0
$643$	−0.958256			−0.0377899			−0.0188950	−	0.999821i	$-0.506015\pi$
$643$	−0.958256			−0.0377899			−0.0188950	+	0.999821i	$0.506015\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	0.836865	+	1.44949i	0.0329006	+	0.0569855i	0.882007	−	0.471237i	$-0.156192\pi$
$647$	0.836865	+	1.44949i	0.0329006	+	0.0569855i	−0.849106	+	0.528222i	$0.822859\pi$
$648$		0			0
$649$	5.22909	−	9.05704i	0.205260	−	0.355520i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−18.2047	+	31.5315i	−0.712405	+	1.23392i	0.251547	+	0.967845i	$0.419061\pi$
$653$	−18.2047	+	31.5315i	−0.712405	+	1.23392i	−0.963952	+	0.266077i	$0.914273\pi$
$654$		0			0
$655$	0.105604	+	0.182912i	0.00412630	+	0.00714696i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−17.6686			−0.688273			−0.344136	−	0.938920i	$-0.611828\pi$
$659$	−17.6686			−0.688273			−0.344136	+	0.938920i	$0.611828\pi$
$660$		0			0
$661$	0.772562	+	1.33812i	0.0300492	+	0.0520467i	0.880659	−	0.473751i	$-0.157100\pi$
$661$	0.772562	+	1.33812i	0.0300492	+	0.0520467i	−0.850610	+	0.525798i	$0.823767\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−15.0604	−	4.07305i	−0.584016	−	0.157946i
$666$		0			0
$667$	−0.213687	+	0.370117i	−0.00827399	+	0.0143310i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	38.8046			1.49803
$672$		0			0
$673$	45.0768			1.73758			0.868792	−	0.495178i	$-0.164897\pi$
$673$	45.0768			1.73758			0.868792	+	0.495178i	$0.164897\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−15.3864	+	26.6501i	−0.591349	+	1.02425i	0.402702	+	0.915331i	$0.368071\pi$
$677$	−15.3864	+	26.6501i	−0.591349	+	1.02425i	−0.994051	+	0.108916i	$0.965262\pi$
$678$		0			0
$679$	−5.37053	+	5.34556i	−0.206102	+	0.205144i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−2.48261	−	4.30000i	−0.0949943	−	0.164535i	0.814612	−	0.580006i	$-0.196950\pi$
$683$	−2.48261	−	4.30000i	−0.0949943	−	0.164535i	−0.909606	+	0.415471i	$0.863617\pi$
$684$		0			0
$685$	7.15971			0.273558
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−17.1104	−	29.6361i	−0.651854	−	1.12904i
$690$		0			0
$691$	−7.58026	+	13.1294i	−0.288367	+	0.499466i	−0.973420	−	0.229027i	$-0.926446\pi$
$691$	−7.58026	+	13.1294i	−0.288367	+	0.499466i	0.685053	+	0.728493i	$0.259779\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−1.63657	+	2.83462i	−0.0620785	+	0.107523i
$696$		0			0
$697$	−23.8328	−	41.2797i	−0.902733	−	1.56358i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	16.9545			0.640364			0.320182	−	0.947356i	$-0.396256\pi$
$701$	16.9545			0.640364			0.320182	+	0.947356i	$0.396256\pi$
$702$		0			0
$703$	1.89396	+	3.28044i	0.0714322	+	0.123724i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	34.6251	+	9.36430i	1.30221	+	0.352181i
$708$		0			0
$709$	−23.1603	+	40.1149i	−0.869805	+	1.50655i	−0.00760839	+	0.999971i	$0.502422\pi$
$709$	−23.1603	+	40.1149i	−0.869805	+	1.50655i	−0.862196	+	0.506575i	$0.830911\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−0.745513			−0.0279197
$714$		0			0
$715$	−11.0777			−0.414281
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−10.2544	+	17.7612i	−0.382425	+	0.662380i	−0.991408	−	0.130803i	$-0.958244\pi$
$719$	−10.2544	+	17.7612i	−0.382425	+	0.662380i	0.608983	+	0.793183i	$0.291578\pi$
$720$		0			0
$721$	−3.97899	−	14.9894i	−0.148185	−	0.558235i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	1.45941	+	2.52777i	0.0542011	+	0.0938791i
$726$		0			0
$727$	42.7056			1.58386			0.791931	−	0.610611i	$-0.209076\pi$
$727$	42.7056			1.58386			0.791931	+	0.610611i	$0.209076\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	16.3802	+	28.3714i	0.605845	+	1.04935i
$732$		0			0
$733$	9.31438	−	16.1330i	0.344034	−	0.595885i	−0.641143	−	0.767421i	$-0.721540\pi$
$733$	9.31438	−	16.1330i	0.344034	−	0.595885i	0.985178	+	0.171536i	$0.0548730\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	20.7382	−	35.9195i	0.763900	−	1.32311i
$738$		0			0
$739$	−7.39263	−	12.8044i	−0.271942	−	0.471018i	0.697417	−	0.716666i	$-0.254333\pi$
$739$	−7.39263	−	12.8044i	−0.271942	−	0.471018i	−0.969359	+	0.245648i	$0.920999\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	13.3016			0.487988			0.243994	−	0.969777i	$-0.421542\pi$
$743$	13.3016			0.487988			0.243994	+	0.969777i	$0.421542\pi$
$744$		0			0
$745$	3.50405	+	6.06919i	0.128378	+	0.222358i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	5.10656	+	19.2371i	0.186590	+	0.702909i
$750$		0			0
$751$	−14.1441	+	24.4983i	−0.516126	+	0.893956i	0.483699	+	0.875234i	$0.339293\pi$
$751$	−14.1441	+	24.4983i	−0.516126	+	0.893956i	−0.999825	+	0.0187215i	$0.994040\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−19.1568			−0.697189
$756$		0			0
$757$	−29.8800			−1.08601			−0.543003	−	0.839731i	$-0.682713\pi$
$757$	−29.8800			−1.08601			−0.543003	+	0.839731i	$0.682713\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	25.7487	−	44.5980i	0.933389	−	1.61668i	0.155906	−	0.987772i	$-0.450170\pi$
$761$	25.7487	−	44.5980i	0.933389	−	1.61668i	0.777482	−	0.628905i	$-0.216497\pi$
$762$		0			0
$763$	−14.6301	−	3.95669i	−0.529647	−	0.143242i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	5.91258	+	10.2409i	0.213491	+	0.369777i
$768$		0			0
$769$	−32.9959			−1.18986			−0.594932	−	0.803776i	$-0.702821\pi$
$769$	−32.9959			−1.18986			−0.594932	+	0.803776i	$0.702821\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	7.56630	+	13.1052i	0.272141	+	0.471362i	0.969410	−	0.245448i	$-0.0789350\pi$
$773$	7.56630	+	13.1052i	0.272141	+	0.471362i	−0.697269	+	0.716810i	$0.745602\pi$
$774$		0			0
$775$	−2.54580	+	4.40946i	−0.0914479	+	0.158392i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	25.4469	−	44.0753i	0.911729	−	1.57916i
$780$		0			0
$781$	1.03097	+	1.78570i	0.0368911	+	0.0638972i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−6.00478			−0.214320
$786$		0			0
$787$	6.70761	+	11.6179i	0.239101	+	0.414134i	0.960456	−	0.278430i	$-0.0898141\pi$
$787$	6.70761	+	11.6179i	0.239101	+	0.414134i	−0.721356	+	0.692565i	$0.756481\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−17.8156	+	17.7328i	−0.633450	+	0.630505i
$792$		0			0
$793$	−21.9384	+	37.9984i	−0.779055	+	1.34936i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	26.8075			0.949571			0.474785	−	0.880102i	$-0.342526\pi$
$797$	26.8075			0.949571			0.474785	+	0.880102i	$0.342526\pi$
$798$		0			0
$799$	7.78228			0.275317
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−7.34183	+	12.7164i	−0.259088	+	0.448753i
$804$		0			0
$805$	−0.373956	−	0.101136i	−0.0131802	−	0.00356457i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	0.0360362	+	0.0624165i	0.00126697	+	0.00219445i	0.866658	−	0.498902i	$-0.166263\pi$
$809$	0.0360362	+	0.0624165i	0.00126697	+	0.00219445i	−0.865391	+	0.501097i	$0.832930\pi$
$810$		0			0
$811$	26.2578			0.922038			0.461019	−	0.887390i	$-0.347484\pi$
$811$	26.2578			0.922038			0.461019	+	0.887390i	$0.347484\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−6.41955	−	11.1190i	−0.224867	−	0.389481i
$816$		0			0
$817$	−17.4896	+	30.2928i	−0.611882	+	1.05981i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−2.29573	+	3.97633i	−0.0801217	+	0.138775i	−0.903302	−	0.429005i	$-0.858864\pi$
$821$	−2.29573	+	3.97633i	−0.0801217	+	0.138775i	0.823180	+	0.567780i	$0.192198\pi$
$822$		0			0
$823$	−17.2120	−	29.8121i	−0.599974	−	1.03919i	−0.992824	−	0.119583i	$-0.961844\pi$
$823$	−17.2120	−	29.8121i	−0.599974	−	1.03919i	0.392850	−	0.919603i	$-0.371489\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	16.9574			0.589666			0.294833	−	0.955549i	$-0.404736\pi$
$827$	16.9574			0.589666			0.294833	+	0.955549i	$0.404736\pi$
$828$		0			0
$829$	4.36886	+	7.56709i	0.151737	+	0.262816i	0.931866	−	0.362802i	$-0.118180\pi$
$829$	4.36886	+	7.56709i	0.151737	+	0.262816i	−0.780129	+	0.625618i	$0.784847\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−33.5697	+	19.1735i	−1.16312	+	0.664321i
$834$		0			0
$835$	−1.07321	+	1.85885i	−0.0371400	+	0.0643283i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−3.15230			−0.108830			−0.0544148	−	0.998518i	$-0.517329\pi$
$839$	−3.15230			−0.108830			−0.0544148	+	0.998518i	$0.517329\pi$
$840$		0			0
$841$	−20.4805			−0.706224
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−0.237184	+	0.410815i	−0.00815938	+	0.0141325i
$846$		0			0
$847$	−0.816556	−	3.07608i	−0.0280572	−	0.105695i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	0.0470280	+	0.0814549i	0.00161210	+	0.00279224i
$852$		0			0
$853$	34.9120			1.19536			0.597682	−	0.801733i	$-0.296089\pi$
$853$	34.9120			1.19536			0.597682	+	0.801733i	$0.296089\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−22.0322	−	38.1609i	−0.752605	−	1.30355i	−0.946556	−	0.322539i	$-0.895464\pi$
$857$	−22.0322	−	38.1609i	−0.752605	−	1.30355i	0.193951	−	0.981011i	$-0.437870\pi$
$858$		0			0
$859$	−9.61353	+	16.6511i	−0.328009	+	0.568129i	−0.982117	−	0.188273i	$-0.939711\pi$
$859$	−9.61353	+	16.6511i	−0.328009	+	0.568129i	0.654107	+	0.756402i	$0.273044\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−4.40940	+	7.63730i	−0.150098	+	0.259977i	−0.931263	−	0.364347i	$-0.881292\pi$
$863$	−4.40940	+	7.63730i	−0.150098	+	0.259977i	0.781166	+	0.624324i	$0.214625\pi$
$864$		0			0
$865$	−1.08423	−	1.87794i	−0.0368648	−	0.0638518i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−16.7456			−0.568056
$870$		0			0
$871$	23.4489	+	40.6146i	0.794534	+	1.37617i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−1.87518	+	1.86646i	−0.0633927	+	0.0630980i
$876$		0			0
$877$	−20.8631	+	36.1359i	−0.704496	+	1.22022i	0.262377	+	0.964965i	$0.415494\pi$
$877$	−20.8631	+	36.1359i	−0.704496	+	1.22022i	−0.966873	+	0.255257i	$0.917840\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−20.3791			−0.686590			−0.343295	−	0.939228i	$-0.611543\pi$
$881$	−20.3791			−0.686590			−0.343295	+	0.939228i	$0.611543\pi$
$882$		0			0
$883$	6.35431			0.213840			0.106920	−	0.994268i	$-0.465901\pi$
$883$	6.35431			0.213840			0.106920	+	0.994268i	$0.465901\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	5.75542	−	9.96867i	0.193248	−	0.334715i	−0.753077	−	0.657933i	$-0.771431\pi$
$887$	5.75542	−	9.96867i	0.193248	−	0.334715i	0.946325	+	0.323217i	$0.104764\pi$
$888$		0			0
$889$	19.7166	−	19.6249i	0.661272	−	0.658198i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	4.15466	+	7.19608i	0.139030	+	0.240808i
$894$		0			0
$895$	−2.92647			−0.0978210
$896$		0			0
$897$		0			0
$898$		0			0
$899$	7.43074	+	12.8704i	0.247829	+	0.429252i
$900$		0			0
$901$	26.7003	−	46.2463i	0.889517	−	1.54069i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	10.7315	−	18.5875i	0.356727	−	0.617869i
$906$		0			0
$907$	−12.7519	−	22.0869i	−0.423419	−	0.733383i	0.572852	−	0.819659i	$-0.305837\pi$
$907$	−12.7519	−	22.0869i	−0.423419	−	0.733383i	−0.996271	+	0.0862754i	$0.972504\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	37.5459			1.24395			0.621976	−	0.783036i	$-0.286330\pi$
$911$	37.5459			1.24395			0.621976	+	0.783036i	$0.286330\pi$
$912$		0			0
$913$	−21.0944	−	36.5365i	−0.698121	−	1.20918i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	0.143371	+	0.540100i	0.00473454	+	0.0178357i
$918$		0			0
$919$	4.69222	−	8.12717i	0.154782	−	0.268090i	−0.778198	−	0.628020i	$-0.783866\pi$
$919$	4.69222	−	8.12717i	0.154782	−	0.268090i	0.932980	+	0.359929i	$0.117199\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−2.33146			−0.0767410
$924$		0			0
$925$	0.642371			0.0211210
$926$		0			0
$927$		0			0
$928$		0			0
$929$	16.7943	−	29.0886i	0.551003	−	0.954365i	−0.447200	−	0.894434i	$-0.647579\pi$
$929$	16.7943	−	29.0886i	0.551003	−	0.954365i	0.998203	−	0.0599308i	$-0.0190880\pi$
$930$		0			0
$931$	−35.6508	−	20.8051i	−1.16841	−	0.681860i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−8.64321	−	14.9705i	−0.282663	−	0.489587i
$936$		0			0
$937$	34.4312			1.12482			0.562409	−	0.826860i	$-0.309875\pi$
$937$	34.4312			1.12482			0.562409	+	0.826860i	$0.309875\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	24.9732	+	43.2549i	0.814104	+	1.41007i	0.909970	+	0.414674i	$0.136105\pi$
$941$	24.9732	+	43.2549i	0.814104	+	1.41007i	−0.0958663	+	0.995394i	$0.530562\pi$
$942$		0			0
$943$	0.631858	−	1.09441i	0.0205761	−	0.0356389i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−11.0586	+	19.1540i	−0.359355	+	0.622420i	−0.987853	−	0.155390i	$-0.950336\pi$
$947$	−11.0586	+	19.1540i	−0.359355	+	0.622420i	0.628499	+	0.777811i	$0.283670\pi$
$948$		0			0
$949$	−8.30149	−	14.3786i	−0.269478	−	0.466749i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−59.8406			−1.93843			−0.969213	−	0.246224i	$-0.920810\pi$
$953$	−59.8406			−1.93843			−0.969213	+	0.246224i	$0.920810\pi$
$954$		0			0
$955$	−10.2731	−	17.7936i	−0.332431	−	0.575787i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	18.2859	+	4.94538i	0.590482	+	0.159695i
$960$		0			0
$961$	2.53779	−	4.39558i	0.0818641	−	0.141793i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−17.3624			−0.558916
$966$		0			0
$967$	3.70505			0.119146			0.0595732	−	0.998224i	$-0.481026\pi$
$967$	3.70505			0.119146			0.0595732	+	0.998224i	$0.481026\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−2.66137	+	4.60963i	−0.0854074	+	0.147930i	−0.905565	−	0.424208i	$-0.860553\pi$
$971$	−2.66137	+	4.60963i	−0.0854074	+	0.147930i	0.820157	+	0.572138i	$0.193886\pi$
$972$		0			0
$973$	−6.13772	+	6.10918i	−0.196766	+	0.195851i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	15.6726	+	27.1457i	0.501410	+	0.868467i	0.999999	+	0.00162842i	$0.000518343\pi$
$977$	15.6726	+	27.1457i	0.501410	+	0.868467i	−0.498589	+	0.866838i	$0.666148\pi$
$978$		0			0
$979$	45.1336			1.44248
$980$		0			0
$981$		0			0
$982$		0			0
$983$	26.6847	+	46.2193i	0.851110	+	1.47417i	0.880207	+	0.474590i	$0.157403\pi$
$983$	26.6847	+	46.2193i	0.851110	+	1.47417i	−0.0290970	+	0.999577i	$0.509263\pi$
$984$		0			0
$985$	12.4543	−	21.5715i	0.396828	−	0.687326i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−0.434274	+	0.752185i	−0.0138091	+	0.0239181i
$990$		0			0
$991$	3.81499	+	6.60776i	0.121187	+	0.209902i	0.920236	−	0.391364i	$-0.127997\pi$
$991$	3.81499	+	6.60776i	0.121187	+	0.209902i	−0.799049	+	0.601266i	$0.794663\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−11.9423			−0.378597
$996$		0			0
$997$	−7.09598	−	12.2906i	−0.224732	−	0.389247i	0.731507	−	0.681834i	$-0.238817\pi$
$997$	−7.09598	−	12.2906i	−0.224732	−	0.389247i	−0.956239	+	0.292587i	$0.905484\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2520.2.bi.s.1801.5	yes	10
3.2	odd	2		2520.2.bi.r.1801.5	yes	10
7.4	even	3	inner	2520.2.bi.s.361.5	yes	10
21.11	odd	6		2520.2.bi.r.361.5	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2520.2.bi.r.361.5	✓	10	21.11	odd	6
2520.2.bi.r.1801.5	yes	10	3.2	odd	2
2520.2.bi.s.361.5	yes	10	7.4	even	3	inner
2520.2.bi.s.1801.5	yes	10	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 2520 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2520.bi (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{5} +(1.87518 - 1.86646i) q^{7} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{5} +(1.87518 - 1.86646i) q^{7} +(1.56501 + 2.71069i) q^{11} -3.53916 q^{13} +(-2.76138 - 4.78286i) q^{17} +(2.94839 - 5.10677i) q^{19} +(0.0732100 - 0.126804i) q^{23} +(-0.500000 - 0.866025i) q^{25} -2.91882 q^{29} +(-2.54580 - 4.40946i) q^{31} +(-0.678814 - 2.55719i) q^{35} +(-0.321186 + 0.556310i) q^{37} +8.63076 q^{41} -5.93189 q^{43} +(-0.704564 + 1.22034i) q^{47} +(0.0326205 - 6.99992i) q^{49} +(4.83459 + 8.37376i) q^{53} +3.13003 q^{55} +(-1.67062 - 2.89360i) q^{59} +(6.19876 - 10.7366i) q^{61} +(-1.76958 + 3.06500i) q^{65} +(-6.62555 - 11.4758i) q^{67} +0.658762 q^{71} +(2.34561 + 4.06272i) q^{73} +(7.99409 + 2.16199i) q^{77} +(-2.67499 + 4.63322i) q^{79} -13.4787 q^{83} -5.52277 q^{85} +(7.20978 - 12.4877i) q^{89} +(-6.63657 + 6.60571i) q^{91} +(-2.94839 - 5.10677i) q^{95} -2.86400 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 5 q^{5} - q^{7}+O(q^{10}) \) 10 * q + 5 * q^5 - q^7	\( 10 q + 5 q^{5} - q^{7} + 2 q^{11} + 6 q^{13} - 2 q^{17} + q^{19} - 8 q^{23} - 5 q^{25} + 7 q^{31} + q^{35} - 11 q^{37} - 20 q^{41} + 6 q^{43} - 23 q^{49} + 14 q^{53} + 4 q^{55} - 4 q^{59} - 6 q^{61} + 3 q^{65} - 7 q^{67} + 32 q^{71} + 3 q^{73} - 8 q^{77} - 19 q^{79} - 28 q^{83} - 4 q^{85} + 18 q^{89} - 21 q^{91} - q^{95} + 48 q^{97}+O(q^{100}) \) 10 * q + 5 * q^5 - q^7 + 2 * q^11 + 6 * q^13 - 2 * q^17 + q^19 - 8 * q^23 - 5 * q^25 + 7 * q^31 + q^35 - 11 * q^37 - 20 * q^41 + 6 * q^43 - 23 * q^49 + 14 * q^53 + 4 * q^55 - 4 * q^59 - 6 * q^61 + 3 * q^65 - 7 * q^67 + 32 * q^71 + 3 * q^73 - 8 * q^77 - 19 * q^79 - 28 * q^83 - 4 * q^85 + 18 * q^89 - 21 * q^91 - q^95 + 48 * q^97

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