LMFDB - Embedded newform 2520.2.bi.r.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.r.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	0.527612	−	0.849485i	$-0.323087\pi$
$11$	−1.56501	−	2.71069i	−0.471870	−	0.817302i	−0.999482	+	0.0321830i	$0.989754\pi$
$12$		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	$0.0669251\pi$
$17$	2.76138	+	4.78286i	0.669734	+	1.16001i	−0.308245	+	0.951307i	$0.599742\pi$
$18$		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	−0.873557	−	0.486722i	$-0.838193\pi$
$23$	−0.0732100	+	0.126804i	−0.0152653	+	0.0264404i	0.858292	+	0.513162i	$0.171526\pi$
$24$		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	$-0.412644\pi$
$29$	2.91882			0.542011			0.271006	+	0.962578i	$0.412644\pi$
$30$		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	$-0.735403\pi$
$41$	−8.63076			−1.34790			−0.673949	+	0.738778i	$0.735403\pi$
$42$		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	−0.810054	−	0.586355i	$-0.800562\pi$
$47$	0.704564	−	1.22034i	0.102771	−	0.178005i	0.912825	+	0.408350i	$0.133896\pi$
$48$		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	$-0.935489\pi$
$53$	−4.83459	−	8.37376i	−0.664082	−	1.15022i	0.315451	−	0.948942i	$-0.397844\pi$
$54$		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	0.954042	−	0.299673i	$-0.0968777\pi$
$59$	1.67062	+	2.89360i	0.217496	+	0.376714i	−0.736546	+	0.676388i	$0.763544\pi$
$60$		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	$-0.512446\pi$
$71$	−0.658762			−0.0781807			−0.0390903	+	0.999236i	$0.512446\pi$
$72$		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	$-0.234949\pi$
$83$	13.4787			1.47948			0.739740	+	0.672893i	$0.234949\pi$
$84$		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	$0.443550\pi$
$89$	−7.20978	+	12.4877i	−0.764235	+	1.32369i	−0.940650	+	0.339378i	$0.889784\pi$
$90$		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	$-0.931027\pi$
$101$	−6.77861	−	11.7409i	−0.674497	−	1.16826i	0.302118	−	0.953270i	$-0.402306\pi$
$102$		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	−0.624928	−	0.780682i	$-0.714872\pi$
$107$	3.76138	−	6.51491i	0.363627	−	0.629820i	0.988555	+	0.150862i	$0.0482051\pi$
$108$		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	$-0.352536\pi$
$113$	9.50073			0.893754			0.446877	+	0.894596i	$0.352536\pi$
$114$		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	−0.861375	−	0.507969i	$-0.830396\pi$
$131$	0.105604	−	0.182912i	0.00922669	−	0.0159811i	0.870602	+	0.491988i	$0.163730\pi$
$132$		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	0.671602	−	0.740912i	$-0.265606\pi$
$137$	−3.57985	−	6.20049i	−0.305848	−	0.529744i	−0.977450	+	0.211168i	$0.932273\pi$
$138$		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	−0.686044	−	0.727560i	$-0.740654\pi$
$149$	3.50405	−	6.06919i	0.287063	−	0.497207i	0.973107	+	0.230352i	$0.0739878\pi$
$150$		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	$-0.473535\pi$
$167$	2.14642			0.166095			0.0830475	+	0.996546i	$0.473535\pi$
$168$		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	−0.904294	−	0.426910i	$-0.859602\pi$
$173$	−1.08423	+	1.87794i	−0.0824323	+	0.142777i	0.821862	+	0.569687i	$0.192935\pi$
$174$		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	0.915514	−	0.402286i	$-0.131784\pi$
$179$	1.46323	+	2.53439i	0.109367	+	0.189429i	−0.806147	+	0.591715i	$0.798451\pi$
$180$		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	$0.433425\pi$
$191$	−10.2731	+	17.7936i	−0.743338	+	1.28750i	−0.950967	+	0.309291i	$0.899908\pi$
$192$		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	$-0.847446\pi$
$197$	−24.9087			−1.77467			−0.887335	+	0.461126i	$0.847446\pi$
$198$		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	0.506785	−	0.862073i	$-0.330834\pi$
$227$	−7.43057	−	12.8701i	−0.493184	−	0.854220i	−0.999969	+	0.00785238i	$0.997500\pi$
$228$		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	−0.994860	−	0.101256i	$-0.967714\pi$
$233$	−6.25441	+	10.8330i	−0.409740	+	0.709691i	0.585120	+	0.810947i	$0.301047\pi$
$234$		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	$-0.655607\pi$
$239$	−14.5201			−0.939228			−0.469614	+	0.882872i	$0.655607\pi$
$240$		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	$-0.197963\pi$
$251$	25.7531			1.62552			0.812762	+	0.582596i	$0.197963\pi$
$252$		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	−0.675304	−	0.737540i	$-0.735987\pi$
$257$	4.82662	−	8.35996i	0.301077	−	0.521480i	0.976380	+	0.216060i	$0.0693207\pi$
$258$		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	$0.0929029\pi$
$263$	11.8069	+	20.4501i	0.728042	+	1.26101i	−0.229667	+	0.973269i	$0.573764\pi$
$264$		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	0.544453	−	0.838791i	$-0.316737\pi$
$269$	−7.44923	−	12.9024i	−0.454188	−	0.786676i	−0.998641	+	0.0521149i	$0.983404\pi$
$270$		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	$-0.702610\pi$
$281$	−19.9279			−1.18880			−0.594400	+	0.804169i	$0.702610\pi$
$282$		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	$-0.246953\pi$
$293$	24.4381			1.42769			0.713844	+	0.700305i	$0.246953\pi$
$294$		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	0.601441	−	0.798917i	$-0.294593\pi$
$311$	−6.89822	−	11.9481i	−0.391162	−	0.677513i	−0.992603	+	0.121405i	$0.961260\pi$
$312$		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	−0.897163	−	0.441699i	$-0.854376\pi$
$317$	−1.17616	+	2.03716i	−0.0660595	+	0.114418i	0.831104	+	0.556117i	$0.187709\pi$
$318$		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	$0.234160\pi$
$347$	17.7311	+	30.7112i	0.951856	+	1.64866i	0.210451	+	0.977604i	$0.432507\pi$
$348$		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	$0.123380\pi$
$353$	14.8473	+	25.7164i	0.790244	+	1.36874i	−0.135571	+	0.990768i	$0.543287\pi$
$354$		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	$-0.455714\pi$
$359$	17.5641	−	30.4219i	0.926997	−	1.60561i	0.788317	−	0.615269i	$-0.210952\pi$
$360$		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	$-0.662622\pi$
$383$	9.99973	−	17.3200i	0.510962	−	0.885013i	0.999919	−	0.0127049i	$-0.00404419\pi$
$384$		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	$-0.844421\pi$
$389$	−16.7269	−	28.9718i	−0.848087	−	1.46893i	0.0348254	−	0.999393i	$-0.488912\pi$
$390$		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	−0.970440	−	0.241343i	$-0.922412\pi$
$401$	−5.53112	+	9.58018i	−0.276211	+	0.478412i	0.694229	+	0.719754i	$0.255746\pi$
$402$		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	$-0.644152\pi$
$419$	−17.9126			−0.875090			−0.437545	+	0.899197i	$0.644152\pi$
$420$		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	0.736138	−	0.676831i	$-0.236647\pi$
$431$	−4.52755	−	7.84194i	−0.218084	−	0.377733i	−0.954222	+	0.299099i	$0.903314\pi$
$432$		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	−0.826202	−	0.563374i	$-0.809503\pi$
$443$	1.57427	−	2.72671i	0.0747956	−	0.129550i	0.900997	+	0.433825i	$0.142836\pi$
$444$		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	$-0.336406\pi$
$449$	20.8343			0.983233			0.491616	+	0.870812i	$0.336406\pi$
$450$		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	$-0.822920\pi$
$461$	−36.4665			−1.69842			−0.849208	+	0.528058i	$0.822920\pi$
$462$		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	−0.863759	−	0.503905i	$-0.831896\pi$
$467$	0.0975696	−	0.168996i	0.00451498	−	0.00782018i	0.868274	+	0.496085i	$0.165229\pi$
$468$		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	0.967392	−	0.253285i	$-0.0815109\pi$
$479$	5.78547	+	10.0207i	0.264345	+	0.457859i	−0.703047	+	0.711144i	$0.748178\pi$
$480$		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	$-0.843712\pi$
$491$	−39.0817			−1.76373			−0.881866	+	0.471501i	$0.843712\pi$
$492$		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	$-0.374144\pi$
$503$	17.2768			0.770335			0.385167	+	0.922847i	$0.374144\pi$
$504$		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	−0.861802	−	0.507244i	$-0.830664\pi$
$509$	0.189173	−	0.327657i	0.00838495	−	0.0145232i	0.870187	+	0.492721i	$0.163998\pi$
$510$		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	0.583328	−	0.812237i	$-0.301750\pi$
$521$	−9.39844	−	16.2786i	−0.411753	−	0.713178i	−0.995082	+	0.0990588i	$0.968417\pi$
$522$		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	$-0.880017\pi$
$557$	−18.4950	−	32.0343i	−0.783660	−	1.35734i	0.146137	−	0.989264i	$-0.453316\pi$
$558$		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	$0.173649\pi$
$563$	20.8040	+	36.0336i	0.876784	+	1.51863i	0.0219336	+	0.999759i	$0.493018\pi$
$564$		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	−0.993107	−	0.117208i	$-0.962606\pi$
$569$	−9.42337	+	16.3218i	−0.395048	+	0.684244i	0.598059	+	0.801452i	$0.295939\pi$
$570$		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	$-0.617235\pi$
$587$	−17.4459			−0.720070			−0.360035	+	0.932939i	$0.617235\pi$
$588$		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	−0.985653	−	0.168787i	$-0.946015\pi$
$593$	−8.44153	+	14.6212i	−0.346652	+	0.600419i	0.639000	+	0.769206i	$0.279348\pi$
$594$		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	0.916919	−	0.399074i	$-0.130668\pi$
$599$	2.76198	+	4.78388i	0.112851	+	0.195464i	−0.804067	+	0.594538i	$0.797335\pi$
$600$		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	$-0.404682\pi$
$617$	14.6550			0.589988			0.294994	+	0.955499i	$0.404682\pi$
$618$		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	0.996028	−	0.0890406i	$-0.0283801\pi$
$641$	10.6564	+	18.4574i	0.420903	+	0.729025i	−0.575125	+	0.818065i	$0.695047\pi$
$642$		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	0.849106	−	0.528222i	$-0.177141\pi$
$647$	−0.836865	−	1.44949i	−0.0329006	−	0.0569855i	−0.882007	+	0.471237i	$0.843808\pi$
$648$		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	$-0.580939\pi$
$653$	18.2047	−	31.5315i	0.712405	−	1.23392i	0.963952	−	0.266077i	$-0.0857274\pi$
$654$		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	$-0.388172\pi$
$659$	17.6686			0.688273			0.344136	+	0.938920i	$0.388172\pi$
$660$		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	$-0.631929\pi$
$677$	15.3864	−	26.6501i	0.591349	−	1.02425i	0.994051	−	0.108916i	$-0.0347378\pi$
$678$		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	0.909606	−	0.415471i	$-0.136383\pi$
$683$	2.48261	+	4.30000i	0.0949943	+	0.164535i	−0.814612	+	0.580006i	$0.803050\pi$
$684$		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	$-0.603744\pi$
$701$	−16.9545			−0.640364			−0.320182	+	0.947356i	$0.603744\pi$
$702$		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	−0.608983	−	0.793183i	$-0.708422\pi$
$719$	10.2544	−	17.7612i	0.382425	−	0.662380i	0.991408	+	0.130803i	$0.0417557\pi$
$720$		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	$-0.578458\pi$
$743$	−13.3016			−0.487988			−0.243994	+	0.969777i	$0.578458\pi$
$744$		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	$0.549830\pi$
$761$	−25.7487	+	44.5980i	−0.933389	+	1.61668i	−0.777482	+	0.628905i	$0.783503\pi$
$762$		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	0.697269	−	0.716810i	$-0.254398\pi$
$773$	−7.56630	−	13.1052i	−0.272141	−	0.471362i	−0.969410	+	0.245448i	$0.921065\pi$
$774$		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	$-0.657474\pi$
$797$	−26.8075			−0.949571			−0.474785	+	0.880102i	$0.657474\pi$
$798$		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	0.865391	−	0.501097i	$-0.167070\pi$
$809$	−0.0360362	−	0.0624165i	−0.00126697	−	0.00219445i	−0.866658	+	0.498902i	$0.833737\pi$
$810$		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	−0.823180	−	0.567780i	$-0.807802\pi$
$821$	2.29573	−	3.97633i	0.0801217	−	0.138775i	0.903302	+	0.429005i	$0.141136\pi$
$822$		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	$-0.595264\pi$
$827$	−16.9574			−0.589666			−0.294833	+	0.955549i	$0.595264\pi$
$828$		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	$-0.482671\pi$
$839$	3.15230			0.108830			0.0544148	+	0.998518i	$0.482671\pi$
$840$		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	$0.104536\pi$
$857$	22.0322	+	38.1609i	0.752605	+	1.30355i	−0.193951	+	0.981011i	$0.562130\pi$
$858$		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	−0.781166	−	0.624324i	$-0.785375\pi$
$863$	4.40940	−	7.63730i	0.150098	−	0.259977i	0.931263	+	0.364347i	$0.118708\pi$
$864$		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	$-0.388457\pi$
$881$	20.3791			0.686590			0.343295	+	0.939228i	$0.388457\pi$
$882$		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	−0.946325	−	0.323217i	$-0.895236\pi$
$887$	−5.75542	+	9.96867i	−0.193248	+	0.334715i	0.753077	+	0.657933i	$0.228569\pi$
$888$		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	$-0.713670\pi$
$911$	−37.5459			−1.24395			−0.621976	+	0.783036i	$0.713670\pi$
$912$		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	$0.352421\pi$
$929$	−16.7943	+	29.0886i	−0.551003	+	0.954365i	−0.998203	+	0.0599308i	$0.980912\pi$
$930$		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	$-0.863895\pi$
$941$	−24.9732	−	43.2549i	−0.814104	−	1.41007i	0.0958663	−	0.995394i	$-0.469438\pi$
$942$		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	−0.628499	−	0.777811i	$-0.716330\pi$
$947$	11.0586	−	19.1540i	0.359355	−	0.622420i	0.987853	+	0.155390i	$0.0496635\pi$
$948$		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	$-0.0791898\pi$
$953$	59.8406			1.93843			0.969213	+	0.246224i	$0.0791898\pi$
$954$		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	−0.820157	−	0.572138i	$-0.806114\pi$
$971$	2.66137	−	4.60963i	0.0854074	−	0.147930i	0.905565	+	0.424208i	$0.139447\pi$
$972$		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	$-0.999482\pi$
$977$	−15.6726	−	27.1457i	−0.501410	−	0.868467i	0.498589	−	0.866838i	$-0.333852\pi$
$978$		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	$-0.842597\pi$
$983$	−26.6847	−	46.2193i	−0.851110	−	1.47417i	0.0290970	−	0.999577i	$-0.490737\pi$
$984$		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.r.1801.5	yes	10
3.2	odd	2		2520.2.bi.s.1801.5	yes	10
7.4	even	3	inner	2520.2.bi.r.361.5	✓	10
21.11	odd	6		2520.2.bi.s.361.5	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2520.2.bi.r.361.5	✓	10	7.4	even	3	inner
2520.2.bi.r.1801.5	yes	10	1.1	even	1	trivial
2520.2.bi.s.361.5	yes	10	21.11	odd	6
2520.2.bi.s.1801.5	yes	10	3.2	odd	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:	\( N \)	\(=\)	\( 2520 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \)
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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