LMFDB - Embedded newform 2520.2.bi.r.361.4

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			361.4
Root			$-4.17259i$ of defining polynomial
Character	$\chi$	$=$	2520.361
Dual form			2520.2.bi.r.1801.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{5} +(0.835066 - 2.51051i) q^{7} +O(q^{10})$	$q+(-0.500000 - 0.866025i) q^{5} +(0.835066 - 2.51051i) q^{7} +(3.11357 - 5.39287i) q^{11} -3.77007 q^{13} +(0.313192 - 0.542464i) q^{17} +(-0.206663 - 0.357951i) q^{19} +(2.04173 + 3.53638i) q^{23} +(-0.500000 + 0.866025i) q^{25} -4.12720 q^{29} +(4.32848 - 7.49714i) q^{31} +(-2.59170 + 0.532067i) q^{35} +(-3.59170 - 6.22101i) q^{37} +4.88688 q^{41} -10.6236 q^{43} +(5.49861 + 9.52387i) q^{47} +(-5.60533 - 4.19288i) q^{49} +(-0.271463 + 0.470188i) q^{53} -6.22715 q^{55} +(-4.16354 + 7.21147i) q^{59} +(0.963468 + 1.66878i) q^{61} +(1.88504 + 3.26498i) q^{65} +(-3.50520 + 6.07118i) q^{67} -12.3271 q^{71} +(-2.58548 + 4.47818i) q^{73} +(-10.9388 - 12.3201i) q^{77} +(-3.57807 - 6.19739i) q^{79} +10.0541 q^{83} -0.626384 q^{85} +(-1.60653 - 2.78259i) q^{89} +(-3.14826 + 9.46481i) q^{91} +(-0.206663 + 0.357951i) q^{95} +13.7007 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2520\mathbb{Z}\right)^\times$.

$n$	$281$	$631$	$1081$	$1261$	$2017$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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
$7$	0.835066	−	2.51051i	0.315625	−	0.948884i
$7$	0.835066	−	2.51051i	0.315625	−	0.948884i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	3.11357	−	5.39287i	0.938777	−	1.62601i	0.171022	−	0.985267i	$-0.445293\pi$
$11$	3.11357	−	5.39287i	0.938777	−	1.62601i	0.767755	−	0.640743i	$-0.221374\pi$
$12$		0			0
$13$	−3.77007			−1.04563			−0.522815	−	0.852446i	$-0.675118\pi$
$13$	−3.77007			−1.04563			−0.522815	+	0.852446i	$0.675118\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.313192	−	0.542464i	0.0759602	−	0.131567i	−0.825543	−	0.564339i	$-0.809131\pi$
$17$	0.313192	−	0.542464i	0.0759602	−	0.131567i	0.901503	+	0.432772i	$0.142464\pi$
$18$		0			0
$19$	−0.206663	−	0.357951i	−0.0474117	−	0.0821196i	0.841346	−	0.540497i	$-0.181764\pi$
$19$	−0.206663	−	0.357951i	−0.0474117	−	0.0821196i	−0.888757	+	0.458378i	$0.848431\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.04173	+	3.53638i	0.425730	+	0.737386i	0.996488	−	0.0837323i	$-0.0266841\pi$
$23$	2.04173	+	3.53638i	0.425730	+	0.737386i	−0.570758	+	0.821118i	$0.693351\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−4.12720			−0.766403			−0.383201	−	0.923665i	$-0.625178\pi$
$29$	−4.12720			−0.766403			−0.383201	+	0.923665i	$0.625178\pi$
$30$		0			0
$31$	4.32848	−	7.49714i	0.777418	−	1.34653i	−0.156008	−	0.987756i	$-0.549863\pi$
$31$	4.32848	−	7.49714i	0.777418	−	1.34653i	0.933426	−	0.358771i	$-0.116804\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−2.59170	+	0.532067i	−0.438077	+	0.0899358i
$36$		0			0
$37$	−3.59170	−	6.22101i	−0.590472	−	1.02273i	−0.994169	−	0.107834i	$-0.965608\pi$
$37$	−3.59170	−	6.22101i	−0.590472	−	1.02273i	0.403697	−	0.914893i	$-0.367725\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	4.88688			0.763203			0.381601	−	0.924327i	$-0.375373\pi$
$41$	4.88688			0.763203			0.381601	+	0.924327i	$0.375373\pi$
$42$		0			0
$43$	−10.6236			−1.62008			−0.810042	−	0.586372i	$-0.800556\pi$
$43$	−10.6236			−1.62008			−0.810042	+	0.586372i	$0.800556\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	5.49861	+	9.52387i	0.802055	+	1.38920i	0.918262	+	0.395974i	$0.129593\pi$
$47$	5.49861	+	9.52387i	0.802055	+	1.38920i	−0.116207	+	0.993225i	$0.537074\pi$
$48$		0			0
$49$	−5.60533	−	4.19288i	−0.800762	−	0.598983i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−0.271463	+	0.470188i	−0.0372884	+	0.0645853i	−0.884067	−	0.467360i	$-0.845205\pi$
$53$	−0.271463	+	0.470188i	−0.0372884	+	0.0645853i	0.846779	+	0.531945i	$0.178539\pi$
$54$		0			0
$55$	−6.22715			−0.839668
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−4.16354	+	7.21147i	−0.542047	+	0.938853i	0.456739	+	0.889601i	$0.349017\pi$
$59$	−4.16354	+	7.21147i	−0.542047	+	0.938853i	−0.998786	+	0.0492526i	$0.984316\pi$
$60$		0			0
$61$	0.963468	+	1.66878i	0.123359	+	0.213665i	0.921090	−	0.389349i	$-0.127300\pi$
$61$	0.963468	+	1.66878i	0.123359	+	0.213665i	−0.797731	+	0.603013i	$0.793967\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	1.88504	+	3.26498i	0.233810	+	0.404971i
$66$		0			0
$67$	−3.50520	+	6.07118i	−0.428228	+	0.741713i	−0.996716	−	0.0809791i	$-0.974195\pi$
$67$	−3.50520	+	6.07118i	−0.428228	+	0.741713i	0.568488	+	0.822692i	$0.307529\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−12.3271			−1.46296			−0.731478	−	0.681865i	$-0.761169\pi$
$71$	−12.3271			−1.46296			−0.731478	+	0.681865i	$0.761169\pi$
$72$		0			0
$73$	−2.58548	+	4.47818i	−0.302607	+	0.524131i	−0.976726	−	0.214492i	$-0.931190\pi$
$73$	−2.58548	+	4.47818i	−0.302607	+	0.524131i	0.674119	+	0.738623i	$0.264524\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−10.9388	−	12.3201i	−1.24659	−	1.40400i
$78$		0			0
$79$	−3.57807	−	6.19739i	−0.402564	−	0.697261i	0.591471	−	0.806327i	$-0.298548\pi$
$79$	−3.57807	−	6.19739i	−0.402564	−	0.697261i	−0.994035	+	0.109065i	$0.965214\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	10.0541			1.10359			0.551793	−	0.833981i	$-0.313944\pi$
$83$	10.0541			1.10359			0.551793	+	0.833981i	$0.313944\pi$
$84$		0			0
$85$	−0.626384			−0.0679409
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−1.60653	−	2.78259i	−0.170292	−	0.294954i	0.768230	−	0.640174i	$-0.221138\pi$
$89$	−1.60653	−	2.78259i	−0.170292	−	0.294954i	−0.938522	+	0.345220i	$0.887804\pi$
$90$		0			0
$91$	−3.14826	+	9.46481i	−0.330027	+	0.992181i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−0.206663	+	0.357951i	−0.0212032	+	0.0367250i
$96$		0			0
$97$	13.7007			1.39110			0.695548	−	0.718480i	$-0.255162\pi$
$97$	13.7007			1.39110			0.695548	+	0.718480i	$0.255162\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	7.67681	−	13.2966i	0.763871	−	1.32306i	−0.176970	−	0.984216i	$-0.556630\pi$
$101$	7.67681	−	13.2966i	0.763871	−	1.32306i	0.940841	−	0.338847i	$-0.110037\pi$
$102$		0			0
$103$	−5.72513	−	9.91621i	−0.564114	−	0.977073i	−0.997132	−	0.0756880i	$-0.975885\pi$
$103$	−5.72513	−	9.91621i	−0.564114	−	0.977073i	0.433018	−	0.901385i	$-0.357449\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1.31319	+	2.27452i	0.126951	+	0.219886i	0.922494	−	0.386012i	$-0.126148\pi$
$107$	1.31319	+	2.27452i	0.126951	+	0.219886i	−0.795543	+	0.605897i	$0.792814\pi$
$108$		0			0
$109$	−2.19200	+	3.79666i	−0.209956	+	0.363654i	−0.951700	−	0.307028i	$-0.900665\pi$
$109$	−2.19200	+	3.79666i	−0.209956	+	0.363654i	0.741744	+	0.670683i	$0.233999\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	5.34026			0.502370			0.251185	−	0.967939i	$-0.419180\pi$
$113$	5.34026			0.502370			0.251185	+	0.967939i	$0.419180\pi$
$114$		0			0
$115$	2.04173	−	3.53638i	0.190392	−	0.329769i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−1.10033	−	1.23927i	−0.100867	−	0.113603i
$120$		0			0
$121$	−13.8887	−	24.0559i	−1.26261	−	2.18690i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	−21.0510			−1.86798			−0.933988	−	0.357305i	$-0.883696\pi$
$127$	−21.0510			−1.86798			−0.933988	+	0.357305i	$0.883696\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−1.04997	−	1.81860i	−0.0917363	−	0.158892i	0.816505	−	0.577338i	$-0.195908\pi$
$131$	−1.04997	−	1.81860i	−0.0917363	−	0.158892i	−0.908242	+	0.418446i	$0.862575\pi$
$132$		0			0
$133$	−1.07122	+	0.219917i	−0.0928863	+	0.0190693i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	5.64028	−	9.76925i	0.481882	−	0.834643i	−0.517902	−	0.855440i	$-0.673287\pi$
$137$	5.64028	−	9.76925i	0.481882	−	0.834643i	0.999784	+	0.0207966i	$0.00662023\pi$
$138$		0			0
$139$	3.70348			0.314125			0.157063	−	0.987589i	$-0.449798\pi$
$139$	3.70348			0.314125			0.157063	+	0.987589i	$0.449798\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−11.7384	+	20.3315i	−0.981614	+	1.70020i
$144$		0			0
$145$	2.06360	+	3.57426i	0.171373	+	0.296826i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−7.26686	−	12.5866i	−0.595324	−	1.03113i	−0.993501	−	0.113823i	$-0.963690\pi$
$149$	−7.26686	−	12.5866i	−0.595324	−	1.03113i	0.398177	−	0.917309i	$-0.369643\pi$
$150$		0			0
$151$	2.93381	−	5.08151i	0.238750	−	0.413527i	−0.721606	−	0.692304i	$-0.756596\pi$
$151$	2.93381	−	5.08151i	0.238750	−	0.413527i	0.960356	+	0.278777i	$0.0899290\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−8.65696			−0.695343
$156$		0			0
$157$	4.46330	−	7.73066i	0.356210	−	0.616974i	−0.631114	−	0.775690i	$-0.717402\pi$
$157$	4.46330	−	7.73066i	0.356210	−	0.616974i	0.987324	+	0.158716i	$0.0507355\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	10.5831	−	2.17267i	0.834065	−	0.171231i
$162$		0			0
$163$	−4.78694	−	8.29123i	−0.374942	−	0.649419i	0.615376	−	0.788234i	$-0.289004\pi$
$163$	−4.78694	−	8.29123i	−0.374942	−	0.649419i	−0.990318	+	0.138815i	$0.955671\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−2.08346			−0.161223			−0.0806114	−	0.996746i	$-0.525687\pi$
$167$	−2.08346			−0.161223			−0.0806114	+	0.996746i	$0.525687\pi$
$168$		0			0
$169$	1.21344			0.0933419
$170$		0			0
$171$		0			0
$172$		0			0
$173$	1.39867	+	2.42256i	0.106339	+	0.184184i	0.914284	−	0.405073i	$-0.132754\pi$
$173$	1.39867	+	2.42256i	0.106339	+	0.184184i	−0.807946	+	0.589257i	$0.799421\pi$
$174$		0			0
$175$	1.75663	+	1.97844i	0.132789	+	0.149556i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−6.23337	+	10.7965i	−0.465904	+	0.806969i	−0.999242	−	0.0389331i	$-0.987604\pi$
$179$	−6.23337	+	10.7965i	−0.465904	+	0.806969i	0.533338	+	0.845902i	$0.320937\pi$
$180$		0			0
$181$	−26.2316			−1.94978			−0.974891	−	0.222683i	$-0.928518\pi$
$181$	−26.2316			−1.94978			−0.974891	+	0.222683i	$0.928518\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−3.59170	+	6.22101i	−0.264067	+	0.457377i
$186$		0			0
$187$	−1.95029	−	3.37801i	−0.142619	−	0.247024i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−3.29652	−	5.70973i	−0.238527	−	0.413142i	0.721764	−	0.692139i	$-0.243331\pi$
$191$	−3.29652	−	5.70973i	−0.238527	−	0.413142i	−0.960292	+	0.278997i	$0.909998\pi$
$192$		0			0
$193$	2.05500	−	3.55936i	0.147922	−	0.256208i	−0.782537	−	0.622604i	$-0.786075\pi$
$193$	2.05500	−	3.55936i	0.147922	−	0.256208i	0.930459	+	0.366395i	$0.119408\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	10.5170			0.749302			0.374651	−	0.927166i	$-0.377762\pi$
$197$	10.5170			0.749302			0.374651	+	0.927166i	$0.377762\pi$
$198$		0			0
$199$	2.08028	−	3.60315i	0.147467	−	0.255420i	−0.782824	−	0.622244i	$-0.786221\pi$
$199$	2.08028	−	3.60315i	0.147467	−	0.255420i	0.930291	+	0.366823i	$0.119555\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−3.44649	+	10.3614i	−0.241896	+	0.727227i
$204$		0			0
$205$	−2.44344	−	4.23216i	−0.170657	−	0.295587i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−2.57384			−0.178036
$210$		0			0
$211$	10.3230			0.710668			0.355334	−	0.934739i	$-0.384367\pi$
$211$	10.3230			0.710668			0.355334	+	0.934739i	$0.384367\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	5.31180	+	9.20031i	0.362262	+	0.627456i
$216$		0			0
$217$	−15.2071	−	17.1273i	−1.03233	−	1.16268i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−1.18076	+	2.04513i	−0.0794263	+	0.137570i
$222$		0			0
$223$	22.8804			1.53219			0.766093	−	0.642730i	$-0.222198\pi$
$223$	22.8804			1.53219			0.766093	+	0.642730i	$0.222198\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	4.14388	−	7.17741i	0.275039	−	0.476382i	−0.695106	−	0.718907i	$-0.744643\pi$
$227$	4.14388	−	7.17741i	0.275039	−	0.476382i	0.970145	+	0.242526i	$0.0779759\pi$
$228$		0			0
$229$	−11.8521	−	20.5285i	−0.783211	−	1.35656i	−0.930062	−	0.367403i	$-0.880247\pi$
$229$	−11.8521	−	20.5285i	−0.783211	−	1.35656i	0.146850	−	0.989159i	$-0.453086\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	6.59672	+	11.4259i	0.432166	+	0.748533i	0.997060	−	0.0766306i	$-0.0244162\pi$
$233$	6.59672	+	11.4259i	0.432166	+	0.748533i	−0.564894	+	0.825164i	$0.691083\pi$
$234$		0			0
$235$	5.49861	−	9.52387i	0.358690	−	0.621269i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	22.9086			1.48183			0.740916	−	0.671597i	$-0.234391\pi$
$239$	22.9086			1.48183			0.740916	+	0.671597i	$0.234391\pi$
$240$		0			0
$241$	−9.60173	+	16.6307i	−0.618502	+	1.07128i	0.371258	+	0.928530i	$0.378927\pi$
$241$	−9.60173	+	16.6307i	−0.618502	+	1.07128i	−0.989759	+	0.142746i	$0.954407\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−0.828478	+	6.95080i	−0.0529295	+	0.444070i
$246$		0			0
$247$	0.779134	+	1.34950i	0.0495751	+	0.0858667i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	11.2255			0.708548			0.354274	−	0.935142i	$-0.384728\pi$
$251$	11.2255			0.708548			0.354274	+	0.935142i	$0.384728\pi$
$252$		0			0
$253$	25.4283			1.59866
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−8.89747	−	15.4109i	−0.555009	−	0.961304i	−0.997903	−	0.0647296i	$-0.979382\pi$
$257$	−8.89747	−	15.4109i	−0.555009	−	0.961304i	0.442894	−	0.896574i	$-0.353952\pi$
$258$		0			0
$259$	−18.6172	+	3.82205i	−1.15682	+	0.237491i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−15.0238	+	26.0219i	−0.926404	+	1.60458i	−0.137117	+	0.990555i	$0.543784\pi$
$263$	−15.0238	+	26.0219i	−0.926404	+	1.60458i	−0.789287	+	0.614024i	$0.789550\pi$
$264$		0			0
$265$	0.542927			0.0333517
$266$		0			0
$267$		0			0
$268$		0			0
$269$	12.8404	−	22.2401i	0.782890	−	1.35601i	−0.147361	−	0.989083i	$-0.547078\pi$
$269$	12.8404	−	22.2401i	0.782890	−	1.35601i	0.930251	−	0.366923i	$-0.119589\pi$
$270$		0			0
$271$	9.67700	+	16.7611i	0.587836	+	1.01816i	0.994515	+	0.104591i	$0.0333533\pi$
$271$	9.67700	+	16.7611i	0.587836	+	1.01816i	−0.406679	+	0.913571i	$0.633313\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	3.11357	+	5.39287i	0.187755	+	0.325202i
$276$		0			0
$277$	−15.6558	+	27.1166i	−0.940663	+	1.62928i	−0.176453	+	0.984309i	$0.556462\pi$
$277$	−15.6558	+	27.1166i	−0.940663	+	1.62928i	−0.764210	+	0.644968i	$0.776871\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	3.78621			0.225866			0.112933	−	0.993603i	$-0.463975\pi$
$281$	3.78621			0.225866			0.112933	+	0.993603i	$0.463975\pi$
$282$		0			0
$283$	9.26805	−	16.0527i	0.550929	−	0.954236i	−0.447279	−	0.894394i	$-0.647607\pi$
$283$	9.26805	−	16.0527i	0.550929	−	0.954236i	0.998208	−	0.0598420i	$-0.0190597\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	4.08087	−	12.2686i	0.240886	−	0.724191i
$288$		0			0
$289$	8.30382	+	14.3826i	0.488460	+	0.846038i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−29.1048			−1.70032			−0.850161	−	0.526523i	$-0.823495\pi$
$293$	−29.1048			−1.70032			−0.850161	+	0.526523i	$0.823495\pi$
$294$		0			0
$295$	8.32709			0.484822
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−7.69746	−	13.3324i	−0.445156	−	0.771033i
$300$		0			0
$301$	−8.87140	+	26.6707i	−0.511339	+	1.53727i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	0.963468	−	1.66878i	0.0551680	−	0.0955538i
$306$		0			0
$307$	14.0120			0.799709			0.399855	−	0.916579i	$-0.369061\pi$
$307$	14.0120			0.799709			0.399855	+	0.916579i	$0.369061\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−3.88020	+	6.72071i	−0.220026	+	0.381097i	−0.954816	−	0.297199i	$-0.903948\pi$
$311$	−3.88020	+	6.72071i	−0.220026	+	0.381097i	0.734789	+	0.678295i	$0.237281\pi$
$312$		0			0
$313$	6.09874	+	10.5633i	0.344721	+	0.597075i	0.985303	−	0.170815i	$-0.0546401\pi$
$313$	6.09874	+	10.5633i	0.344721	+	0.597075i	−0.640582	+	0.767890i	$0.721307\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−2.45284	−	4.24845i	−0.137765	−	0.238617i	0.788885	−	0.614541i	$-0.210659\pi$
$317$	−2.45284	−	4.24845i	−0.137765	−	0.238617i	−0.926650	+	0.375924i	$0.877325\pi$
$318$		0			0
$319$	−12.8504	+	22.2575i	−0.719482	+	1.24618i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−0.258901			−0.0144056
$324$		0			0
$325$	1.88504	−	3.26498i	0.104563	−	0.181108i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	28.5015	−	5.85126i	1.57134	−	0.322590i
$330$		0			0
$331$	−5.65686	−	9.79798i	−0.310929	−	0.538545i	0.667634	−	0.744489i	$-0.267307\pi$
$331$	−5.65686	−	9.79798i	−0.310929	−	0.538545i	−0.978564	+	0.205944i	$0.933974\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	7.01039			0.383019
$336$		0			0
$337$	16.8091			0.915647			0.457824	−	0.889043i	$-0.348629\pi$
$337$	16.8091			0.915647			0.457824	+	0.889043i	$0.348629\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−26.9541	−	46.6858i	−1.45964	−	2.52818i
$342$		0			0
$343$	−15.2071	+	10.5709i	−0.821106	+	0.570776i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	3.93938	−	6.82321i	0.211477	−	0.366289i	−0.740700	−	0.671836i	$-0.765506\pi$
$347$	3.93938	−	6.82321i	0.211477	−	0.366289i	0.952177	+	0.305547i	$0.0988393\pi$
$348$		0			0
$349$	29.2472			1.56557			0.782783	−	0.622294i	$-0.213799\pi$
$349$	29.2472			1.56557			0.782783	+	0.622294i	$0.213799\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	4.51380	−	7.81814i	0.240246	−	0.416117i	−0.720539	−	0.693415i	$-0.756105\pi$
$353$	4.51380	−	7.81814i	0.240246	−	0.416117i	0.960784	+	0.277297i	$0.0894387\pi$
$354$		0			0
$355$	6.16354	+	10.6756i	0.327127	+	0.566600i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	12.0302	+	20.8370i	0.634932	+	1.09973i	0.986529	+	0.163584i	$0.0523053\pi$
$359$	12.0302	+	20.8370i	0.634932	+	1.09973i	−0.351597	+	0.936151i	$0.614361\pi$
$360$		0			0
$361$	9.41458	−	16.3065i	0.495504	−	0.858239i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	5.17095			0.270660
$366$		0			0
$367$	−7.25183	+	12.5605i	−0.378543	+	0.655655i	−0.990850	−	0.134964i	$-0.956908\pi$
$367$	−7.25183	+	12.5605i	−0.378543	+	0.655655i	0.612308	+	0.790619i	$0.290241\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	0.953723	+	1.07415i	0.0495148	+	0.0557671i
$372$		0			0
$373$	−10.5654	−	18.2999i	−0.547057	−	0.947531i	−0.998474	−	0.0552177i	$-0.982415\pi$
$373$	−10.5654	−	18.2999i	−0.547057	−	0.947531i	0.451417	−	0.892313i	$-0.350919\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	15.5599			0.801373
$378$		0			0
$379$	4.96626			0.255100			0.127550	−	0.991832i	$-0.459289\pi$
$379$	4.96626			0.255100			0.127550	+	0.991832i	$0.459289\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	7.08125	+	12.2651i	0.361835	+	0.626716i	0.988263	−	0.152763i	$-0.0488171\pi$
$383$	7.08125	+	12.2651i	0.361835	+	0.626716i	−0.626428	+	0.779479i	$0.715484\pi$
$384$		0			0
$385$	−5.20007	+	15.6333i	−0.265020	+	0.796748i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−12.0905	+	20.9413i	−0.613012	+	1.06177i	0.377718	+	0.925921i	$0.376709\pi$
$389$	−12.0905	+	20.9413i	−0.613012	+	1.06177i	−0.990730	+	0.135847i	$0.956625\pi$
$390$		0			0
$391$	2.55781			0.129354
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−3.57807	+	6.19739i	−0.180032	+	0.311825i
$396$		0			0
$397$	−4.29935	−	7.44670i	−0.215778	−	0.373739i	0.737735	−	0.675091i	$-0.235896\pi$
$397$	−4.29935	−	7.44670i	−0.215778	−	0.373739i	−0.953513	+	0.301352i	$0.902562\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−19.0909	−	33.0665i	−0.953356	−	1.65126i	−0.738087	−	0.674706i	$-0.764270\pi$
$401$	−19.0909	−	33.0665i	−0.953356	−	1.65126i	−0.215269	−	0.976555i	$-0.569063\pi$
$402$		0			0
$403$	−16.3187	+	28.2648i	−0.812891	+	1.40797i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−44.7321			−2.21729
$408$		0			0
$409$	7.21167	−	12.4910i	0.356594	−	0.617639i	−0.630795	−	0.775949i	$-0.717271\pi$
$409$	7.21167	−	12.4910i	0.356594	−	0.617639i	0.987389	+	0.158310i	$0.0506046\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	14.6276	+	16.4747i	0.719779	+	0.810666i
$414$		0			0
$415$	−5.02707	−	8.70714i	−0.246769	−	0.427417i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−10.8929			−0.532151			−0.266075	−	0.963952i	$-0.585727\pi$
$419$	−10.8929			−0.532151			−0.266075	+	0.963952i	$0.585727\pi$
$420$		0			0
$421$	3.95051			0.192536			0.0962679	−	0.995355i	$-0.469309\pi$
$421$	3.95051			0.192536			0.0962679	+	0.995355i	$0.469309\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	0.313192	+	0.542464i	0.0151920	+	0.0263134i
$426$		0			0
$427$	4.99404	−	1.02526i	0.241679	−	0.0496158i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	15.3002	−	26.5007i	0.736985	−	1.27650i	−0.216862	−	0.976202i	$-0.569582\pi$
$431$	15.3002	−	26.5007i	0.736985	−	1.27650i	0.953847	−	0.300293i	$-0.0970846\pi$
$432$		0			0
$433$	26.8636			1.29098			0.645491	−	0.763768i	$-0.276653\pi$
$433$	26.8636			1.29098			0.645491	+	0.763768i	$0.276653\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	0.843900	−	1.46168i	0.0403692	−	0.0699215i
$438$		0			0
$439$	8.10312	+	14.0350i	0.386741	+	0.669855i	0.992009	−	0.126167i	$-0.0402675\pi$
$439$	8.10312	+	14.0350i	0.386741	+	0.669855i	−0.605268	+	0.796022i	$0.706934\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	12.8070	+	22.1824i	0.608479	+	1.05392i	0.991491	+	0.130173i	$0.0415533\pi$
$443$	12.8070	+	22.1824i	0.608479	+	1.05392i	−0.383012	+	0.923743i	$0.625113\pi$
$444$		0			0
$445$	−1.60653	+	2.78259i	−0.0761568	+	0.131907i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	13.3527			0.630153			0.315077	−	0.949066i	$-0.397970\pi$
$449$	13.3527			0.630153			0.315077	+	0.949066i	$0.397970\pi$
$450$		0			0
$451$	15.2157	−	26.3543i	0.716478	−	1.24098i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	9.77089	−	2.00593i	0.458067	−	0.0940396i
$456$		0			0
$457$	2.94506	+	5.10099i	0.137764	+	0.238614i	0.926650	−	0.375925i	$-0.122675\pi$
$457$	2.94506	+	5.10099i	0.137764	+	0.238614i	−0.788886	+	0.614540i	$0.789342\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−7.14635			−0.332839			−0.166419	−	0.986055i	$-0.553221\pi$
$461$	−7.14635			−0.332839			−0.166419	+	0.986055i	$0.553221\pi$
$462$		0			0
$463$	1.97073			0.0915874			0.0457937	−	0.998951i	$-0.485418\pi$
$463$	1.97073			0.0915874			0.0457937	+	0.998951i	$0.485418\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	12.2709	+	21.2538i	0.567829	+	0.983509i	0.996780	+	0.0801813i	$0.0255499\pi$
$467$	12.2709	+	21.2538i	0.567829	+	0.983509i	−0.428951	+	0.903328i	$0.641117\pi$
$468$		0			0
$469$	12.3147	+	13.8697i	0.568640	+	0.640442i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−33.0774	+	57.2917i	−1.52090	+	2.63427i
$474$		0			0
$475$	0.413326			0.0189647
$476$		0			0
$477$		0			0
$478$		0			0
$479$	14.7071	−	25.4734i	0.671983	−	1.16391i	−0.305358	−	0.952237i	$-0.598776\pi$
$479$	14.7071	−	25.4734i	0.671983	−	1.16391i	0.977341	−	0.211671i	$-0.0678904\pi$
$480$		0			0
$481$	13.5410	+	23.4536i	0.617415	+	1.06939i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−6.85035	−	11.8652i	−0.311058	−	0.538769i
$486$		0			0
$487$	−13.3624	+	23.1444i	−0.605509	+	1.04877i	0.386462	+	0.922305i	$0.373697\pi$
$487$	−13.3624	+	23.1444i	−0.605509	+	1.04877i	−0.991971	+	0.126467i	$0.959636\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	28.9946			1.30851			0.654254	−	0.756275i	$-0.272983\pi$
$491$	28.9946			1.30851			0.654254	+	0.756275i	$0.272983\pi$
$492$		0			0
$493$	−1.29261	+	2.23886i	−0.0582161	+	0.100833i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−10.2939	+	30.9473i	−0.461746	+	1.38818i
$498$		0			0
$499$	−16.0424	−	27.7862i	−0.718154	−	1.24388i	−0.961730	−	0.273998i	$-0.911654\pi$
$499$	−16.0424	−	27.7862i	−0.718154	−	1.24388i	0.243576	−	0.969882i	$-0.421680\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−26.4528			−1.17947			−0.589737	−	0.807596i	$-0.700768\pi$
$503$	−26.4528			−1.17947			−0.589737	+	0.807596i	$0.700768\pi$
$504$		0			0
$505$	−15.3536			−0.683227
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−1.38606	−	2.40073i	−0.0614361	−	0.106411i	0.833671	−	0.552261i	$-0.186235\pi$
$509$	−1.38606	−	2.40073i	−0.0614361	−	0.106411i	−0.895108	+	0.445850i	$0.852901\pi$
$510$		0			0
$511$	9.08347	+	10.2304i	0.401829	+	0.452568i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−5.72513	+	9.91621i	−0.252279	+	0.436960i
$516$		0			0
$517$	68.4813			3.01180
$518$		0			0
$519$		0			0
$520$		0			0
$521$	0.216885	−	0.375656i	0.00950190	−	0.0164578i	−0.861235	−	0.508206i	$-0.830309\pi$
$521$	0.216885	−	0.375656i	0.00950190	−	0.0164578i	0.870737	+	0.491749i	$0.163642\pi$
$522$		0			0
$523$	11.3483	+	19.6559i	0.496228	+	0.859492i	0.999991	−	0.00435014i	$-0.00138470\pi$
$523$	11.3483	+	19.6559i	0.496228	+	0.859492i	−0.503763	+	0.863842i	$0.668051\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−2.71129	−	4.69609i	−0.118106	−	0.204565i
$528$		0			0
$529$	3.16269	−	5.47794i	0.137508	−	0.238171i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−18.4239			−0.798028
$534$		0			0
$535$	1.31319	−	2.27452i	0.0567742	−	0.0983359i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−40.0643	+	17.1740i	−1.72569	+	0.739735i
$540$		0			0
$541$	7.52227	+	13.0290i	0.323408	+	0.560158i	0.981189	−	0.193051i	$-0.0618382\pi$
$541$	7.52227	+	13.0290i	0.323408	+	0.560158i	−0.657781	+	0.753209i	$0.728505\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	4.38401			0.187790
$546$		0			0
$547$	14.5681			0.622889			0.311444	−	0.950264i	$-0.399187\pi$
$547$	14.5681			0.622889			0.311444	+	0.950264i	$0.399187\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	0.852941	+	1.47734i	0.0363365	+	0.0629366i
$552$		0			0
$553$	−18.5465	+	3.80755i	−0.788679	+	0.161913i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	8.66883	−	15.0149i	0.367310	−	0.636200i	−0.621834	−	0.783149i	$-0.713612\pi$
$557$	8.66883	−	15.0149i	0.367310	−	0.636200i	0.989144	+	0.146949i	$0.0469454\pi$
$558$		0			0
$559$	40.0517			1.69401
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−12.6108	+	21.8426i	−0.531482	+	0.920554i	0.467842	+	0.883812i	$0.345031\pi$
$563$	−12.6108	+	21.8426i	−0.531482	+	0.920554i	−0.999325	+	0.0367425i	$0.988302\pi$
$564$		0			0
$565$	−2.67013	−	4.62480i	−0.112333	−	0.194567i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	5.95671	+	10.3173i	0.249718	+	0.432525i	0.963448	−	0.267897i	$-0.0863287\pi$
$569$	5.95671	+	10.3173i	0.249718	+	0.432525i	−0.713729	+	0.700422i	$0.752995\pi$
$570$		0			0
$571$	18.9693	−	32.8559i	0.793842	−	1.37498i	−0.129729	−	0.991549i	$-0.541411\pi$
$571$	18.9693	−	32.8559i	0.793842	−	1.37498i	0.923572	−	0.383426i	$-0.125256\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−4.08346			−0.170292
$576$		0			0
$577$	8.94540	−	15.4939i	0.372402	−	0.645019i	−0.617533	−	0.786545i	$-0.711868\pi$
$577$	8.94540	−	15.4939i	0.372402	−	0.645019i	0.989934	+	0.141526i	$0.0452010\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	8.39587	−	25.2410i	0.348319	−	1.04717i
$582$		0			0
$583$	1.69044	+	2.92793i	0.0700110	+	0.121263i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−3.76676			−0.155471			−0.0777355	−	0.996974i	$-0.524769\pi$
$587$	−3.76676			−0.155471			−0.0777355	+	0.996974i	$0.524769\pi$
$588$		0			0
$589$	−3.57814			−0.147435
$590$		0			0
$591$		0			0
$592$		0			0
$593$	18.0905	+	31.3337i	0.742889	+	1.28672i	0.951175	+	0.308654i	$0.0998784\pi$
$593$	18.0905	+	31.3337i	0.742889	+	1.28672i	−0.208285	+	0.978068i	$0.566788\pi$
$594$		0			0
$595$	−0.523072	+	1.57254i	−0.0214439	+	0.0644680i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	20.7404	−	35.9234i	0.847430	−	1.46779i	−0.0360636	−	0.999349i	$-0.511482\pi$
$599$	20.7404	−	35.9234i	0.847430	−	1.46779i	0.883494	−	0.468443i	$-0.155185\pi$
$600$		0			0
$601$	0.243447			0.00993042			0.00496521	−	0.999988i	$-0.498420\pi$
$601$	0.243447			0.00993042			0.00496521	+	0.999988i	$0.498420\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−13.8887	+	24.0559i	−0.564655	+	0.978011i
$606$		0			0
$607$	−0.985363	−	1.70670i	−0.0399947	−	0.0692728i	0.845335	−	0.534236i	$-0.179401\pi$
$607$	−0.985363	−	1.70670i	−0.0399947	−	0.0692728i	−0.885330	+	0.464964i	$0.846067\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−20.7302	−	35.9057i	−0.838652	−	1.45259i
$612$		0			0
$613$	−15.1837	+	26.2989i	−0.613262	+	1.06220i	0.377424	+	0.926040i	$0.376810\pi$
$613$	−15.1837	+	26.2989i	−0.613262	+	1.06220i	−0.990687	+	0.136161i	$0.956524\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	46.1284			1.85706			0.928529	−	0.371259i	$-0.121074\pi$
$617$	46.1284			1.85706			0.928529	+	0.371259i	$0.121074\pi$
$618$		0			0
$619$	−21.4648	+	37.1781i	−0.862742	+	1.49431i	0.00652956	+	0.999979i	$0.497922\pi$
$619$	−21.4648	+	37.1781i	−0.862742	+	1.49431i	−0.869272	+	0.494335i	$0.835412\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−8.32728	+	1.70956i	−0.333625	+	0.0684922i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−4.49957			−0.179409
$630$		0			0
$631$	44.3019			1.76363			0.881816	−	0.471594i	$-0.156321\pi$
$631$	44.3019			1.76363			0.881816	+	0.471594i	$0.156321\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	10.5255	+	18.2307i	0.417692	+	0.723464i
$636$		0			0
$637$	21.1325	+	15.8075i	0.837300	+	0.626315i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	18.1774	−	31.4841i	0.717963	−	1.24355i	−0.243842	−	0.969815i	$-0.578408\pi$
$641$	18.1774	−	31.4841i	0.717963	−	1.24355i	0.961805	−	0.273734i	$-0.0882588\pi$
$642$		0			0
$643$	−3.17731			−0.125301			−0.0626504	−	0.998036i	$-0.519955\pi$
$643$	−3.17731			−0.125301			−0.0626504	+	0.998036i	$0.519955\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	17.5687	−	30.4299i	0.690697	−	1.19632i	−0.280913	−	0.959733i	$-0.590637\pi$
$647$	17.5687	−	30.4299i	0.690697	−	1.19632i	0.971610	−	0.236589i	$-0.0760294\pi$
$648$		0			0
$649$	25.9270	+	44.9069i	1.01772	+	1.76275i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−1.58835	−	2.75110i	−0.0621569	−	0.107659i	0.833272	−	0.552863i	$-0.186465\pi$
$653$	−1.58835	−	2.75110i	−0.0621569	−	0.107659i	−0.895429	+	0.445204i	$0.853131\pi$
$654$		0			0
$655$	−1.04997	+	1.81860i	−0.0410257	+	0.0710587i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	2.70542			0.105388			0.0526941	−	0.998611i	$-0.483219\pi$
$659$	2.70542			0.105388			0.0526941	+	0.998611i	$0.483219\pi$
$660$		0			0
$661$	13.8490	−	23.9871i	0.538662	−	0.932990i	−0.460314	−	0.887756i	$-0.652263\pi$
$661$	13.8490	−	23.9871i	0.538662	−	0.932990i	0.998976	−	0.0452341i	$-0.0144034\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	0.726062	+	0.817742i	0.0281555	+	0.0317107i
$666$		0			0
$667$	−8.42663	−	14.5954i	−0.326280	−	0.565134i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	11.9993			0.463228
$672$		0			0
$673$	−27.0997			−1.04462			−0.522309	−	0.852757i	$-0.674929\pi$
$673$	−27.0997			−1.04462			−0.522309	+	0.852757i	$0.674929\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−23.5828	−	40.8466i	−0.906360	−	1.56986i	−0.819081	−	0.573678i	$-0.805516\pi$
$677$	−23.5828	−	40.8466i	−0.906360	−	1.56986i	−0.0872789	−	0.996184i	$-0.527817\pi$
$678$		0			0
$679$	11.4410	−	34.3958i	0.439065	−	1.31999i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	12.8742	−	22.2988i	0.492619	−	0.853242i	−0.507345	−	0.861743i	$-0.669373\pi$
$683$	12.8742	−	22.2988i	0.492619	−	0.853242i	0.999964	+	0.00850171i	$0.00270621\pi$
$684$		0			0
$685$	−11.2806			−0.431008
$686$		0			0
$687$		0			0
$688$		0			0
$689$	1.02344	−	1.77264i	0.0389898	−	0.0675324i
$690$		0			0
$691$	23.3085	+	40.3715i	0.886696	+	1.53580i	0.843757	+	0.536726i	$0.180339\pi$
$691$	23.3085	+	40.3715i	0.886696	+	1.53580i	0.0429396	+	0.999078i	$0.486328\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−1.85174	−	3.20731i	−0.0702406	−	0.121660i
$696$		0			0
$697$	1.53053	−	2.65096i	0.0579731	−	0.100412i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−3.52122			−0.132995			−0.0664974	−	0.997787i	$-0.521182\pi$
$701$	−3.52122			−0.132995			−0.0664974	+	0.997787i	$0.521182\pi$
$702$		0			0
$703$	−1.48454	+	2.57130i	−0.0559906	+	0.0969785i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−26.9707	−	30.3763i	−1.01434	−	1.14242i
$708$		0			0
$709$	−13.5337	−	23.4410i	−0.508267	−	0.880345i	−0.999954	−	0.00957261i	$-0.996953\pi$
$709$	−13.5337	−	23.4410i	−0.508267	−	0.880345i	0.491687	−	0.870772i	$-0.336380\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	35.3503			1.32388
$714$		0			0
$715$	23.4768			0.877982
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−2.59672	−	4.49766i	−0.0968415	−	0.167734i	0.813534	−	0.581517i	$-0.197541\pi$
$719$	−2.59672	−	4.49766i	−0.0968415	−	0.167734i	−0.910376	+	0.413783i	$0.864207\pi$
$720$		0			0
$721$	−29.6756	+	6.09231i	−1.10518	+	0.226889i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	2.06360	−	3.57426i	0.0766403	−	0.132745i
$726$		0			0
$727$	−11.9507			−0.443228			−0.221614	−	0.975134i	$-0.571133\pi$
$727$	−11.9507			−0.443228			−0.221614	+	0.975134i	$0.571133\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−3.32723	+	5.76293i	−0.123062	+	0.213150i
$732$		0			0
$733$	3.79754	+	6.57754i	0.140265	+	0.242947i	0.927597	−	0.373584i	$-0.121871\pi$
$733$	3.79754	+	6.57754i	0.140265	+	0.242947i	−0.787331	+	0.616530i	$0.788538\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	21.8274	+	37.8061i	0.804022	+	1.39261i
$738$		0			0
$739$	−24.8275	+	43.0025i	−0.913294	+	1.58187i	−0.103913	+	0.994586i	$0.533136\pi$
$739$	−24.8275	+	43.0025i	−0.913294	+	1.58187i	−0.809380	+	0.587285i	$0.800197\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−18.3163			−0.671960			−0.335980	−	0.941869i	$-0.609067\pi$
$743$	−18.3163			−0.671960			−0.335980	+	0.941869i	$0.609067\pi$
$744$		0			0
$745$	−7.26686	+	12.5866i	−0.266237	+	0.461136i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	6.80680	−	1.39741i	0.248715	−	0.0510604i
$750$		0			0
$751$	−15.2827	−	26.4704i	−0.557673	−	0.965918i	−0.997690	−	0.0679284i	$-0.978361\pi$
$751$	−15.2827	−	26.4704i	−0.557673	−	0.965918i	0.440017	−	0.897989i	$-0.354972\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−5.86762			−0.213544
$756$		0			0
$757$	3.82022			0.138848			0.0694241	−	0.997587i	$-0.477884\pi$
$757$	3.82022			0.138848			0.0694241	+	0.997587i	$0.477884\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	19.6217	+	33.9857i	0.711285	+	1.23198i	0.964375	+	0.264539i	$0.0852196\pi$
$761$	19.6217	+	33.9857i	0.711285	+	1.23198i	−0.253090	+	0.967443i	$0.581447\pi$
$762$		0			0
$763$	7.70110	+	8.67352i	0.278798	+	0.314002i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	15.6969	−	27.1878i	0.566781	−	0.981693i
$768$		0			0
$769$	14.4415			0.520774			0.260387	−	0.965504i	$-0.416150\pi$
$769$	14.4415			0.520774			0.260387	+	0.965504i	$0.416150\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−9.63807	+	16.6936i	−0.346657	+	0.600428i	−0.985653	−	0.168782i	$-0.946017\pi$
$773$	−9.63807	+	16.6936i	−0.346657	+	0.600428i	0.638996	+	0.769210i	$0.279350\pi$
$774$		0			0
$775$	4.32848	+	7.49714i	0.155484	+	0.269305i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−1.00994	−	1.74926i	−0.0361848	−	0.0626739i
$780$		0			0
$781$	−38.3813	+	66.4783i	−1.37339	+	2.37878i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−8.92659			−0.318604
$786$		0			0
$787$	1.97274	−	3.41688i	0.0703205	−	0.121799i	−0.828721	−	0.559662i	$-0.810931\pi$
$787$	1.97274	−	3.41688i	0.0703205	−	0.121799i	0.899042	+	0.437863i	$0.144264\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	4.45947	−	13.4068i	0.158560	−	0.476690i
$792$		0			0
$793$	−3.63234	−	6.29141i	−0.128988	−	0.223414i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−34.9932			−1.23952			−0.619761	−	0.784791i	$-0.712770\pi$
$797$	−34.9932			−1.23952			−0.619761	+	0.784791i	$0.712770\pi$
$798$		0			0
$799$	6.88848			0.243697
$800$		0			0
$801$		0			0
$802$		0			0
$803$	16.1001	+	27.8863i	0.568161	+	0.984084i
$804$		0			0
$805$	−7.17314	−	8.07889i	−0.252820	−	0.284743i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−11.8931	+	20.5995i	−0.418139	+	0.724239i	−0.995752	−	0.0920722i	$-0.970651\pi$
$809$	−11.8931	+	20.5995i	−0.418139	+	0.724239i	0.577613	+	0.816311i	$0.303984\pi$
$810$		0			0
$811$	35.9756			1.26327			0.631637	−	0.775264i	$-0.282383\pi$
$811$	35.9756			1.26327			0.631637	+	0.775264i	$0.282383\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−4.78694	+	8.29123i	−0.167679	+	0.290429i
$816$		0			0
$817$	2.19551	+	3.80273i	0.0768110	+	0.133041i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−11.1929	−	19.3866i	−0.390633	−	0.676597i	0.601900	−	0.798572i	$-0.294411\pi$
$821$	−11.1929	−	19.3866i	−0.390633	−	0.676597i	−0.992533	+	0.121975i	$0.961077\pi$
$822$		0			0
$823$	2.23363	−	3.86876i	0.0778595	−	0.134857i	−0.824467	−	0.565910i	$-0.808525\pi$
$823$	2.23363	−	3.86876i	0.0778595	−	0.134857i	0.902326	+	0.431054i	$0.141858\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−10.1083			−0.351499			−0.175750	−	0.984435i	$-0.556235\pi$
$827$	−10.1083			−0.351499			−0.175750	+	0.984435i	$0.556235\pi$
$828$		0			0
$829$	27.9421	−	48.3971i	0.970469	−	1.68090i	0.276325	−	0.961064i	$-0.410883\pi$
$829$	27.9421	−	48.3971i	0.970469	−	1.68090i	0.694143	−	0.719837i	$-0.255783\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−4.03003	+	1.72752i	−0.139632	+	0.0598549i
$834$		0			0
$835$	1.04173	+	1.80433i	0.0360505	+	0.0624413i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	5.81270			0.200677			0.100338	−	0.994953i	$-0.468007\pi$
$839$	5.81270			0.200677			0.100338	+	0.994953i	$0.468007\pi$
$840$		0			0
$841$	−11.9662			−0.412627
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−0.606722	−	1.05087i	−0.0208719	−	0.0361511i
$846$		0			0
$847$	−71.9905	+	14.7794i	−2.47362	+	0.507827i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	14.6665	−	25.4032i	0.502763	−	0.870811i
$852$		0			0
$853$	−7.12408			−0.243924			−0.121962	−	0.992535i	$-0.538919\pi$
$853$	−7.12408			−0.243924			−0.121962	+	0.992535i	$0.538919\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	11.8602	−	20.5424i	0.405135	−	0.701715i	−0.589202	−	0.807986i	$-0.700558\pi$
$857$	11.8602	−	20.5424i	0.405135	−	0.701715i	0.994337	+	0.106271i	$0.0338911\pi$
$858$		0			0
$859$	−8.10312	−	14.0350i	−0.276475	−	0.478869i	0.694031	−	0.719945i	$-0.255833\pi$
$859$	−8.10312	−	14.0350i	−0.276475	−	0.478869i	−0.970506	+	0.241076i	$0.922500\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	16.9160	+	29.2993i	0.575826	+	0.997361i	0.995951	+	0.0898943i	$0.0286529\pi$
$863$	16.9160	+	29.2993i	0.575826	+	0.997361i	−0.420125	+	0.907466i	$0.638014\pi$
$864$		0			0
$865$	1.39867	−	2.42256i	0.0475561	−	0.0823696i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−44.5623			−1.51167
$870$		0			0
$871$	13.2148	−	22.8888i	0.447768	−	0.775557i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	0.835066	−	2.51051i	0.0282304	−	0.0848708i
$876$		0			0
$877$	−3.44312	−	5.96366i	−0.116266	−	0.201378i	0.802019	−	0.597298i	$-0.203759\pi$
$877$	−3.44312	−	5.96366i	−0.116266	−	0.201378i	−0.918285	+	0.395920i	$0.870426\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	7.26521			0.244771			0.122386	−	0.992483i	$-0.460946\pi$
$881$	7.26521			0.244771			0.122386	+	0.992483i	$0.460946\pi$
$882$		0			0
$883$	6.42372			0.216175			0.108088	−	0.994141i	$-0.465527\pi$
$883$	6.42372			0.216175			0.108088	+	0.994141i	$0.465527\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	22.6147	+	39.1697i	0.759326	+	1.31519i	0.943195	+	0.332240i	$0.107804\pi$
$887$	22.6147	+	39.1697i	0.759326	+	1.31519i	−0.183869	+	0.982951i	$0.558862\pi$
$888$		0			0
$889$	−17.5790	+	52.8488i	−0.589580	+	1.77249i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	2.27272	−	3.93646i	0.0760536	−	0.131729i
$894$		0			0
$895$	12.4667			0.416717
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−17.8645	+	30.9422i	−0.595815	+	1.03198i
$900$		0			0
$901$	0.170040	+	0.294518i	0.00566486	+	0.00981183i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	13.1158	+	22.7173i	0.435984	+	0.755147i
$906$		0			0
$907$	−10.8247	+	18.7489i	−0.359428	+	0.622547i	−0.987865	−	0.155313i	$-0.950361\pi$
$907$	−10.8247	+	18.7489i	−0.359428	+	0.622547i	0.628438	+	0.777860i	$0.283695\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−20.3615			−0.674607			−0.337304	−	0.941396i	$-0.609515\pi$
$911$	−20.3615			−0.674607			−0.337304	+	0.941396i	$0.609515\pi$
$912$		0			0
$913$	31.3043	−	54.2206i	1.03602	−	1.79444i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−5.44242	+	1.11731i	−0.179724	+	0.0368968i
$918$		0			0
$919$	−6.41193	−	11.1058i	−0.211510	−	0.366346i	0.740677	−	0.671861i	$-0.234505\pi$
$919$	−6.41193	−	11.1058i	−0.211510	−	0.366346i	−0.952187	+	0.305515i	$0.901171\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	46.4740			1.52971
$924$		0			0
$925$	7.18340			0.236189
$926$		0			0
$927$		0			0
$928$		0			0
$929$	19.3372	+	33.4930i	0.634433	+	1.09887i	0.986635	+	0.162946i	$0.0520998\pi$
$929$	19.3372	+	33.4930i	0.634433	+	1.09887i	−0.352202	+	0.935924i	$0.614567\pi$
$930$		0			0
$931$	−0.342431	+	2.87295i	−0.0112227	+	0.0941570i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−1.95029	+	3.37801i	−0.0637814	+	0.110473i
$936$		0			0
$937$	43.2833			1.41401			0.707003	−	0.707211i	$-0.250047\pi$
$937$	43.2833			1.41401			0.707003	+	0.707211i	$0.250047\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−29.0275	+	50.2770i	−0.946268	+	1.63898i	−0.193077	+	0.981184i	$0.561847\pi$
$941$	−29.0275	+	50.2770i	−0.946268	+	1.63898i	−0.753192	+	0.657801i	$0.771487\pi$
$942$		0			0
$943$	9.97769	+	17.2819i	0.324918	+	0.562775i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−1.58614	−	2.74727i	−0.0515425	−	0.0892743i	0.839103	−	0.543973i	$-0.183080\pi$
$947$	−1.58614	−	2.74727i	−0.0515425	−	0.0892743i	−0.890646	+	0.454698i	$0.849747\pi$
$948$		0			0
$949$	9.74743	−	16.8830i	0.316415	−	0.548047i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	29.1066			0.942857			0.471428	−	0.881904i	$-0.343739\pi$
$953$	29.1066			0.942857			0.471428	+	0.881904i	$0.343739\pi$
$954$		0			0
$955$	−3.29652	+	5.70973i	−0.106673	+	0.184763i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−19.8158	−	22.3179i	−0.639886	−	0.720684i
$960$		0			0
$961$	−21.9714	−	38.0556i	−0.708756	−	1.22760i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−4.10999			−0.132305
$966$		0			0
$967$	−14.5305			−0.467271			−0.233635	−	0.972324i	$-0.575062\pi$
$967$	−14.5305			−0.467271			−0.233635	+	0.972324i	$0.575062\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−19.0841	−	33.0547i	−0.612438	−	1.06077i	−0.990828	−	0.135128i	$-0.956855\pi$
$971$	−19.0841	−	33.0547i	−0.612438	−	1.06077i	0.378390	−	0.925646i	$-0.376478\pi$
$972$		0			0
$973$	3.09265	−	9.29764i	0.0991459	−	0.298069i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−14.5255	+	25.1589i	−0.464713	+	0.804906i	−0.999189	−	0.0402779i	$-0.987176\pi$
$977$	−14.5255	+	25.1589i	−0.464713	+	0.804906i	0.534476	+	0.845184i	$0.320509\pi$
$978$		0			0
$979$	−20.0082			−0.639464
$980$		0			0
$981$		0			0
$982$		0			0
$983$	0.659360	−	1.14204i	0.0210303	−	0.0364256i	−0.855319	−	0.518102i	$-0.826639\pi$
$983$	0.659360	−	1.14204i	0.0210303	−	0.0364256i	0.876349	+	0.481677i	$0.159972\pi$
$984$		0			0
$985$	−5.25848	−	9.10796i	−0.167549	−	0.290204i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−21.6905	−	37.5691i	−0.689718	−	1.19463i
$990$		0			0
$991$	−12.2391	+	21.1987i	−0.388787	+	0.673398i	−0.992287	−	0.123965i	$-0.960439\pi$
$991$	−12.2391	+	21.1987i	−0.388787	+	0.673398i	0.603500	+	0.797363i	$0.293772\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−4.16056			−0.131899
$996$		0			0
$997$	−0.0846554	+	0.146627i	−0.00268106	+	0.00464374i	−0.867363	−	0.497676i	$-0.834187\pi$
$997$	−0.0846554	+	0.146627i	−0.00268106	+	0.00464374i	0.864682	+	0.502320i	$0.167520\pi$
$998$		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.361.4	✓	10
3.2	odd	2		2520.2.bi.s.361.4	yes	10
7.2	even	3	inner	2520.2.bi.r.1801.4	yes	10
21.2	odd	6		2520.2.bi.s.1801.4	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2520.2.bi.r.361.4	✓	10	1.1	even	1	trivial
2520.2.bi.r.1801.4	yes	10	7.2	even	3	inner
2520.2.bi.s.361.4	yes	10	3.2	odd	2
2520.2.bi.s.1801.4	yes	10	21.2	odd	6

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)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{5} +(0.835066 - 2.51051i) q^{7} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{5} +(0.835066 - 2.51051i) q^{7} +(3.11357 - 5.39287i) q^{11} -3.77007 q^{13} +(0.313192 - 0.542464i) q^{17} +(-0.206663 - 0.357951i) q^{19} +(2.04173 + 3.53638i) q^{23} +(-0.500000 + 0.866025i) q^{25} -4.12720 q^{29} +(4.32848 - 7.49714i) q^{31} +(-2.59170 + 0.532067i) q^{35} +(-3.59170 - 6.22101i) q^{37} +4.88688 q^{41} -10.6236 q^{43} +(5.49861 + 9.52387i) q^{47} +(-5.60533 - 4.19288i) q^{49} +(-0.271463 + 0.470188i) q^{53} -6.22715 q^{55} +(-4.16354 + 7.21147i) q^{59} +(0.963468 + 1.66878i) q^{61} +(1.88504 + 3.26498i) q^{65} +(-3.50520 + 6.07118i) q^{67} -12.3271 q^{71} +(-2.58548 + 4.47818i) q^{73} +(-10.9388 - 12.3201i) q^{77} +(-3.57807 - 6.19739i) q^{79} +10.0541 q^{83} -0.626384 q^{85} +(-1.60653 - 2.78259i) q^{89} +(-3.14826 + 9.46481i) q^{91} +(-0.206663 + 0.357951i) q^{95} +13.7007 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 5 q^{5} - q^{7}+O(q^{10}) \) 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

Introduction

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