LMFDB - Embedded newform 2400.2.w.h.607.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2400,2,Mod(607,2400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2400, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 0, 1]))

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

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

chi := DirichletCharacter("2400.607");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2400 = 2^{5} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2400.w (of order $4$, 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:	$19.1640964851$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			607.4
Root			$-0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	2400.607
Dual form			2400.2.w.h.2143.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{3} +(1.43916 - 1.43916i) q^{7} +1.00000i q^{9} +O(q^{10})$	$q+(0.707107 + 0.707107i) q^{3} +(1.43916 - 1.43916i) q^{7} +1.00000i q^{9} +5.86370i q^{11} +(0.189469 - 0.189469i) q^{13} +(1.31784 + 1.31784i) q^{17} +3.59575 q^{19} +2.03528 q^{21} +(-1.71744 - 1.71744i) q^{23} +(-0.707107 + 0.707107i) q^{27} -4.49938i q^{29} +0.0611001i q^{31} +(-4.14626 + 4.14626i) q^{33} +(8.29253 + 8.29253i) q^{37} +0.267949 q^{39} -10.0857 q^{41} +(5.06022 + 5.06022i) q^{43} +(0.0498881 - 0.0498881i) q^{47} +2.85765i q^{49} +1.86370i q^{51} +(-3.16088 + 3.16088i) q^{53} +(2.54258 + 2.54258i) q^{57} -3.46410 q^{59} -12.9202 q^{61} +(1.43916 + 1.43916i) q^{63} +(4.45377 - 4.45377i) q^{67} -2.42883i q^{69} +6.98466i q^{71} +(2.53590 - 2.53590i) q^{73} +(8.43879 + 8.43879i) q^{77} +15.1915 q^{79} -1.00000 q^{81} +(7.77729 + 7.77729i) q^{83} +(3.18154 - 3.18154i) q^{87} +8.99876i q^{89} -0.545351i q^{91} +(-0.0432043 + 0.0432043i) q^{93} +(-6.40289 - 6.40289i) q^{97} -5.86370 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{7}+O(q^{10}) $ 8 * q - 8 * q^7	$ 8 q - 8 q^{7} + 8 q^{17} - 16 q^{19} + 8 q^{21} - 8 q^{23} - 8 q^{33} + 16 q^{37} + 16 q^{39} - 16 q^{41} + 24 q^{43} - 16 q^{47} + 8 q^{53} + 8 q^{57} - 24 q^{61} - 8 q^{63} + 8 q^{67} + 48 q^{73} - 8 q^{77} + 32 q^{79} - 8 q^{81} - 16 q^{83} - 8 q^{87} - 24 q^{93} - 32 q^{97} - 16 q^{99}+O(q^{100}) $ 8 * q - 8 * q^7 + 8 * q^17 - 16 * q^19 + 8 * q^21 - 8 * q^23 - 8 * q^33 + 16 * q^37 + 16 * q^39 - 16 * q^41 + 24 * q^43 - 16 * q^47 + 8 * q^53 + 8 * q^57 - 24 * q^61 - 8 * q^63 + 8 * q^67 + 48 * q^73 - 8 * q^77 + 32 * q^79 - 8 * q^81 - 16 * q^83 - 8 * q^87 - 24 * q^93 - 32 * q^97 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2400\mathbb{Z}\right)^\times$.

$n$	$577$	$901$	$1601$	$1951$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$	$-1$

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
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	1.43916	−	1.43916i	0.543950	−	0.543950i	−0.380734	−	0.924685i	$-0.624329\pi$
$7$	1.43916	−	1.43916i	0.543950	−	0.543950i	0.924685	+	0.380734i	$0.124329\pi$
$8$		0			0
$9$			1.00000i			0.333333i
$10$		0			0
$11$			5.86370i			1.76797i	0.467512	+	0.883987i	$0.345150\pi$
$11$			5.86370i			1.76797i	−0.467512	+	0.883987i	$0.654850\pi$
$12$		0			0
$13$	0.189469	−	0.189469i	0.0525492	−	0.0525492i	−0.680344	−	0.732893i	$-0.738170\pi$
$13$	0.189469	−	0.189469i	0.0525492	−	0.0525492i	0.732893	+	0.680344i	$0.238170\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.31784	+	1.31784i	0.319622	+	0.319622i	0.848622	−	0.529000i	$-0.177433\pi$
$17$	1.31784	+	1.31784i	0.319622	+	0.319622i	−0.529000	+	0.848622i	$0.677433\pi$
$18$		0			0
$19$	3.59575			0.824923			0.412461	−	0.910975i	$-0.364669\pi$
$19$	3.59575			0.824923			0.412461	+	0.910975i	$0.364669\pi$
$20$		0			0
$21$	2.03528			0.444134
$22$		0			0
$23$	−1.71744	−	1.71744i	−0.358111	−	0.358111i	0.505005	−	0.863116i	$-0.331490\pi$
$23$	−1.71744	−	1.71744i	−0.358111	−	0.358111i	−0.863116	+	0.505005i	$0.831490\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$		0			0
$29$		−	4.49938i		−	0.835513i	−0.908559	−	0.417757i	$-0.862816\pi$
$29$		−	4.49938i		−	0.835513i	0.908559	−	0.417757i	$-0.137184\pi$
$30$		0			0
$31$			0.0611001i			0.0109739i	0.999985	+	0.00548695i	$0.00174656\pi$
$31$			0.0611001i			0.0109739i	−0.999985	+	0.00548695i	$0.998253\pi$
$32$		0			0
$33$	−4.14626	+	4.14626i	−0.721772	+	0.721772i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	8.29253	+	8.29253i	1.36328	+	1.36328i	0.869697	+	0.493587i	$0.164314\pi$
$37$	8.29253	+	8.29253i	1.36328	+	1.36328i	0.493587	+	0.869697i	$0.335686\pi$
$38$		0			0
$39$	0.267949			0.0429062
$40$		0			0
$41$	−10.0857			−1.57512			−0.787559	−	0.616239i	$-0.788656\pi$
$41$	−10.0857			−1.57512			−0.787559	+	0.616239i	$0.788656\pi$
$42$		0			0
$43$	5.06022	+	5.06022i	0.771676	+	0.771676i	0.978399	−	0.206723i	$-0.0662799\pi$
$43$	5.06022	+	5.06022i	0.771676	+	0.771676i	−0.206723	+	0.978399i	$0.566280\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	0.0498881	−	0.0498881i	0.00727692	−	0.00727692i	−0.703459	−	0.710736i	$-0.748362\pi$
$47$	0.0498881	−	0.0498881i	0.00727692	−	0.00727692i	0.710736	+	0.703459i	$0.248362\pi$
$48$		0			0
$49$			2.85765i			0.408236i
$50$		0			0
$51$			1.86370i			0.260971i
$52$		0			0
$53$	−3.16088	+	3.16088i	−0.434180	+	0.434180i	−0.890048	−	0.455868i	$-0.849329\pi$
$53$	−3.16088	+	3.16088i	−0.434180	+	0.434180i	0.455868	+	0.890048i	$0.349329\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	2.54258	+	2.54258i	0.336773	+	0.336773i
$58$		0			0
$59$	−3.46410			−0.450988			−0.225494	−	0.974245i	$-0.572400\pi$
$59$	−3.46410			−0.450988			−0.225494	+	0.974245i	$0.572400\pi$
$60$		0			0
$61$	−12.9202			−1.65426			−0.827128	−	0.562013i	$-0.810027\pi$
$61$	−12.9202			−1.65426			−0.827128	+	0.562013i	$0.810027\pi$
$62$		0			0
$63$	1.43916	+	1.43916i	0.181317	+	0.181317i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	4.45377	−	4.45377i	0.544115	−	0.544115i	−0.380618	−	0.924732i	$-0.624289\pi$
$67$	4.45377	−	4.45377i	0.544115	−	0.544115i	0.924732	+	0.380618i	$0.124289\pi$
$68$		0			0
$69$		−	2.42883i		−	0.292396i
$70$		0			0
$71$			6.98466i			0.828927i	0.910066	+	0.414463i	$0.136031\pi$
$71$			6.98466i			0.828927i	−0.910066	+	0.414463i	$0.863969\pi$
$72$		0			0
$73$	2.53590	−	2.53590i	0.296804	−	0.296804i	−0.542956	−	0.839761i	$-0.682695\pi$
$73$	2.53590	−	2.53590i	0.296804	−	0.296804i	0.839761	+	0.542956i	$0.182695\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	8.43879	+	8.43879i	0.961690	+	0.961690i
$78$		0			0
$79$	15.1915			1.70918			0.854589	−	0.519305i	$-0.173809\pi$
$79$	15.1915			1.70918			0.854589	+	0.519305i	$0.173809\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	7.77729	+	7.77729i	0.853669	+	0.853669i	0.990583	−	0.136914i	$-0.0437184\pi$
$83$	7.77729	+	7.77729i	0.853669	+	0.853669i	−0.136914	+	0.990583i	$0.543718\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	3.18154	−	3.18154i	0.341097	−	0.341097i
$88$		0			0
$89$			8.99876i			0.953866i	0.878940	+	0.476933i	$0.158252\pi$
$89$			8.99876i			0.953866i	−0.878940	+	0.476933i	$0.841748\pi$
$90$		0			0
$91$		−	0.545351i		−	0.0571683i
$92$		0			0
$93$	−0.0432043	+	0.0432043i	−0.00448008	+	0.00448008i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−6.40289	−	6.40289i	−0.650115	−	0.650115i	0.302906	−	0.953020i	$-0.402043\pi$
$97$	−6.40289	−	6.40289i	−0.650115	−	0.650115i	−0.953020	+	0.302906i	$0.902043\pi$
$98$		0			0
$99$	−5.86370			−0.589324
$100$		0			0
$101$	13.4276			1.33609			0.668047	−	0.744119i	$-0.267130\pi$
$101$	13.4276			1.33609			0.668047	+	0.744119i	$0.267130\pi$
$102$		0			0
$103$	6.63567	+	6.63567i	0.653832	+	0.653832i	0.953914	−	0.300081i	$-0.0970138\pi$
$103$	6.63567	+	6.63567i	0.653832	+	0.653832i	−0.300081	+	0.953914i	$0.597014\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	11.5240	−	11.5240i	1.11406	−	1.11406i	0.121468	−	0.992595i	$-0.461240\pi$
$107$	11.5240	−	11.5240i	1.11406	−	1.11406i	0.992595	−	0.121468i	$-0.0387601\pi$
$108$		0			0
$109$		−	13.4629i		−	1.28951i	−0.764390	−	0.644754i	$-0.776960\pi$
$109$		−	13.4629i		−	1.28951i	0.764390	−	0.644754i	$-0.223040\pi$
$110$		0			0
$111$			11.7274i			1.11312i
$112$		0			0
$113$	−8.00000	+	8.00000i	−0.752577	+	0.752577i	−0.974959	−	0.222383i	$-0.928617\pi$
$113$	−8.00000	+	8.00000i	−0.752577	+	0.752577i	0.222383	+	0.974959i	$0.428617\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	0.189469	+	0.189469i	0.0175164	+	0.0175164i
$118$		0			0
$119$	3.79315			0.347718
$120$		0			0
$121$	−23.3830			−2.12573
$122$		0			0
$123$	−7.13165	−	7.13165i	−0.643039	−	0.643039i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	14.3631	−	14.3631i	1.27452	−	1.27452i	0.330825	−	0.943692i	$-0.392673\pi$
$127$	14.3631	−	14.3631i	1.27452	−	1.27452i	0.943692	−	0.330825i	$-0.107327\pi$
$128$		0			0
$129$			7.15623i			0.630071i
$130$		0			0
$131$			9.98590i			0.872472i	0.899832	+	0.436236i	$0.143689\pi$
$131$			9.98590i			0.872472i	−0.899832	+	0.436236i	$0.856311\pi$
$132$		0			0
$133$	5.17486	−	5.17486i	0.448717	−	0.448717i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−0.571690	−	0.571690i	−0.0488428	−	0.0488428i	0.682264	−	0.731106i	$-0.260996\pi$
$137$	−0.571690	−	0.571690i	−0.0488428	−	0.0488428i	−0.731106	+	0.682264i	$0.760996\pi$
$138$		0			0
$139$	−7.46410			−0.633097			−0.316548	−	0.948576i	$-0.602524\pi$
$139$	−7.46410			−0.633097			−0.316548	+	0.948576i	$0.602524\pi$
$140$		0			0
$141$	0.0705524			0.00594158
$142$		0			0
$143$	1.11099	+	1.11099i	0.0929055	+	0.0929055i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−2.02066	+	2.02066i	−0.166662	+	0.166662i
$148$		0			0
$149$			10.5266i			0.862373i	0.902263	+	0.431187i	$0.141905\pi$
$149$			10.5266i			0.862373i	−0.902263	+	0.431187i	$0.858095\pi$
$150$		0			0
$151$			7.26190i			0.590965i	0.955348	+	0.295482i	$0.0954804\pi$
$151$			7.26190i			0.590965i	−0.955348	+	0.295482i	$0.904520\pi$
$152$		0			0
$153$	−1.31784	+	1.31784i	−0.106541	+	0.106541i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	8.20940	+	8.20940i	0.655182	+	0.655182i	0.954236	−	0.299054i	$-0.0966712\pi$
$157$	8.20940	+	8.20940i	0.655182	+	0.655182i	−0.299054	+	0.954236i	$0.596671\pi$
$158$		0			0
$159$	−4.47015			−0.354506
$160$		0			0
$161$	−4.94333			−0.389589
$162$		0			0
$163$	3.74754	+	3.74754i	0.293530	+	0.293530i	0.838473	−	0.544943i	$-0.183449\pi$
$163$	3.74754	+	3.74754i	0.293530	+	0.293530i	−0.544943	+	0.838473i	$0.683449\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	2.79780	−	2.79780i	0.216500	−	0.216500i	−0.590522	−	0.807022i	$-0.701078\pi$
$167$	2.79780	−	2.79780i	0.216500	−	0.216500i	0.807022	+	0.590522i	$0.201078\pi$
$168$		0			0
$169$			12.9282i			0.994477i
$170$		0			0
$171$			3.59575i			0.274974i
$172$		0			0
$173$	−12.2874	+	12.2874i	−0.934191	+	0.934191i	−0.997964	−	0.0637731i	$-0.979687\pi$
$173$	−12.2874	+	12.2874i	−0.934191	+	0.934191i	0.0637731	+	0.997964i	$0.479687\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−2.44949	−	2.44949i	−0.184115	−	0.184115i
$178$		0			0
$179$	6.25120			0.467237			0.233618	−	0.972328i	$-0.424943\pi$
$179$	6.25120			0.467237			0.233618	+	0.972328i	$0.424943\pi$
$180$		0			0
$181$	−4.99071			−0.370957			−0.185478	−	0.982648i	$-0.559383\pi$
$181$	−4.99071			−0.370957			−0.185478	+	0.982648i	$0.559383\pi$
$182$		0			0
$183$	−9.13593	−	9.13593i	−0.675348	−	0.675348i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−7.72741	+	7.72741i	−0.565084	+	0.565084i
$188$		0			0
$189$			2.03528i			0.148045i
$190$		0			0
$191$		−	13.9222i		−	1.00737i	−0.863887	−	0.503686i	$-0.831977\pi$
$191$		−	13.9222i		−	1.00737i	0.863887	−	0.503686i	$-0.168023\pi$
$192$		0			0
$193$	−1.89621	+	1.89621i	−0.136492	+	0.136492i	−0.772052	−	0.635560i	$-0.780769\pi$
$193$	−1.89621	+	1.89621i	−0.136492	+	0.136492i	0.635560	+	0.772052i	$0.280769\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	14.3283	+	14.3283i	1.02085	+	1.02085i	0.999778	+	0.0210726i	$0.00670812\pi$
$197$	14.3283	+	14.3283i	1.02085	+	1.02085i	0.0210726	+	0.999778i	$0.493292\pi$
$198$		0			0
$199$	−17.9175			−1.27014			−0.635069	−	0.772455i	$-0.719028\pi$
$199$	−17.9175			−1.27014			−0.635069	+	0.772455i	$0.719028\pi$
$200$		0			0
$201$	6.29858			0.444268
$202$		0			0
$203$	−6.47531	−	6.47531i	−0.454478	−	0.454478i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	1.71744	−	1.71744i	0.119370	−	0.119370i
$208$		0			0
$209$			21.0844i			1.45844i
$210$		0			0
$211$		−	22.6651i		−	1.56033i	−0.625576	−	0.780164i	$-0.715136\pi$
$211$		−	22.6651i		−	1.56033i	0.625576	−	0.780164i	$-0.284864\pi$
$212$		0			0
$213$	−4.93890	+	4.93890i	−0.338408	+	0.338408i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	0.0879327	+	0.0879327i	0.00596926	+	0.00596926i
$218$		0			0
$219$	3.58630			0.242340
$220$		0			0
$221$	0.499378			0.0335918
$222$		0			0
$223$	17.9244	+	17.9244i	1.20031	+	1.20031i	0.974072	+	0.226237i	$0.0726424\pi$
$223$	17.9244	+	17.9244i	1.20031	+	1.20031i	0.226237	+	0.974072i	$0.427358\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	1.80866	−	1.80866i	0.120045	−	0.120045i	−0.644532	−	0.764577i	$-0.722948\pi$
$227$	1.80866	−	1.80866i	0.120045	−	0.120045i	0.764577	+	0.644532i	$0.222948\pi$
$228$		0			0
$229$		−	29.7048i		−	1.96295i	−0.191600	−	0.981473i	$-0.561367\pi$
$229$		−	29.7048i		−	1.96295i	0.191600	−	0.981473i	$-0.438633\pi$
$230$		0			0
$231$			11.9343i			0.785216i
$232$		0			0
$233$	−9.42418	+	9.42418i	−0.617399	+	0.617399i	−0.944863	−	0.327465i	$-0.893806\pi$
$233$	−9.42418	+	9.42418i	−0.617399	+	0.617399i	0.327465	+	0.944863i	$0.393806\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	10.7420	+	10.7420i	0.697769	+	0.697769i
$238$		0			0
$239$	−19.7839			−1.27971			−0.639856	−	0.768495i	$-0.721006\pi$
$239$	−19.7839			−1.27971			−0.639856	+	0.768495i	$0.721006\pi$
$240$		0			0
$241$	−27.5241			−1.77298			−0.886492	−	0.462743i	$-0.846865\pi$
$241$	−27.5241			−1.77298			−0.886492	+	0.462743i	$0.846865\pi$
$242$		0			0
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	0.681283	−	0.681283i	0.0433490	−	0.0433490i
$248$		0			0
$249$			10.9988i			0.697018i
$250$		0			0
$251$			25.9975i			1.64095i	0.571684	+	0.820474i	$0.306290\pi$
$251$			25.9975i			1.64095i	−0.571684	+	0.820474i	$0.693710\pi$
$252$		0			0
$253$	10.0706	−	10.0706i	0.633130	−	0.633130i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−18.5558	−	18.5558i	−1.15748	−	1.15748i	−0.985016	−	0.172466i	$-0.944827\pi$
$257$	−18.5558	−	18.5558i	−1.15748	−	1.15748i	−0.172466	−	0.985016i	$-0.555173\pi$
$258$		0			0
$259$	23.8685			1.48312
$260$		0			0
$261$	4.49938			0.278504
$262$		0			0
$263$	−21.0810	−	21.0810i	−1.29991	−	1.29991i	−0.928447	−	0.371466i	$-0.878855\pi$
$263$	−21.0810	−	21.0810i	−1.29991	−	1.29991i	−0.371466	−	0.928447i	$-0.621145\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−6.36308	+	6.36308i	−0.389414	+	0.389414i
$268$		0			0
$269$		−	17.3570i		−	1.05828i	−0.848536	−	0.529138i	$-0.822515\pi$
$269$		−	17.3570i		−	1.05828i	0.848536	−	0.529138i	$-0.177485\pi$
$270$		0			0
$271$		−	23.0600i		−	1.40080i	−0.713752	−	0.700398i	$-0.753006\pi$
$271$		−	23.0600i		−	1.40080i	0.713752	−	0.700398i	$-0.246994\pi$
$272$		0			0
$273$	0.385621	−	0.385621i	0.0233389	−	0.0233389i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−18.0872	−	18.0872i	−1.08675	−	1.08675i	−0.995861	−	0.0908942i	$-0.971027\pi$
$277$	−18.0872	−	18.0872i	−1.08675	−	1.08675i	−0.0908942	−	0.995861i	$-0.528973\pi$
$278$		0			0
$279$	−0.0611001			−0.00365797
$280$		0			0
$281$	11.5405			0.688448			0.344224	−	0.938888i	$-0.388142\pi$
$281$	11.5405			0.688448			0.344224	+	0.938888i	$0.388142\pi$
$282$		0			0
$283$	6.74703	+	6.74703i	0.401069	+	0.401069i	0.878610	−	0.477541i	$-0.158472\pi$
$283$	6.74703	+	6.74703i	0.401069	+	0.401069i	−0.477541	+	0.878610i	$0.658472\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−14.5149	+	14.5149i	−0.856786	+	0.856786i
$288$		0			0
$289$		−	13.5266i		−	0.795683i
$290$		0			0
$291$		−	9.05505i		−	0.530816i
$292$		0			0
$293$	18.0041	−	18.0041i	1.05181	−	1.05181i	0.0532271	−	0.998582i	$-0.483049\pi$
$293$	18.0041	−	18.0041i	1.05181	−	1.05181i	0.998582	−	0.0532271i	$-0.0169507\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−4.14626	−	4.14626i	−0.240591	−	0.240591i
$298$		0			0
$299$	−0.650802			−0.0376368
$300$		0			0
$301$	14.5649			0.839507
$302$		0			0
$303$	9.49473	+	9.49473i	0.545458	+	0.545458i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	9.25297	−	9.25297i	0.528095	−	0.528095i	−0.391909	−	0.920004i	$-0.628185\pi$
$307$	9.25297	−	9.25297i	0.528095	−	0.528095i	0.920004	+	0.391909i	$0.128185\pi$
$308$		0			0
$309$			9.38426i			0.533852i
$310$		0			0
$311$			5.32051i			0.301698i	0.988557	+	0.150849i	$0.0482008\pi$
$311$			5.32051i			0.301698i	−0.988557	+	0.150849i	$0.951799\pi$
$312$		0			0
$313$	1.41093	−	1.41093i	0.0797505	−	0.0797505i	−0.666106	−	0.745857i	$-0.732040\pi$
$313$	1.41093	−	1.41093i	0.0797505	−	0.0797505i	0.745857	+	0.666106i	$0.232040\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	1.97078	+	1.97078i	0.110690	+	0.110690i	0.760282	−	0.649593i	$-0.225061\pi$
$317$	1.97078	+	1.97078i	0.110690	+	0.110690i	−0.649593	+	0.760282i	$0.725061\pi$
$318$		0			0
$319$	26.3830			1.47717
$320$		0			0
$321$	16.2973			0.909629
$322$		0			0
$323$	4.73862	+	4.73862i	0.263664	+	0.263664i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	9.51968	−	9.51968i	0.526439	−	0.526439i
$328$		0			0
$329$		−	0.143594i		−	0.00791657i
$330$		0			0
$331$		−	6.13431i		−	0.337172i	−0.985687	−	0.168586i	$-0.946080\pi$
$331$		−	6.13431i		−	0.337172i	0.985687	−	0.168586i	$-0.0539201\pi$
$332$		0			0
$333$	−8.29253	+	8.29253i	−0.454428	+	0.454428i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−7.27390	−	7.27390i	−0.396235	−	0.396235i	0.480668	−	0.876903i	$-0.340394\pi$
$337$	−7.27390	−	7.27390i	−0.396235	−	0.396235i	−0.876903	+	0.480668i	$0.840394\pi$
$338$		0			0
$339$	−11.3137			−0.614476
$340$		0			0
$341$	−0.358273			−0.0194016
$342$		0			0
$343$	14.1867	+	14.1867i	0.766011	+	0.766011i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	14.6471	−	14.6471i	0.786295	−	0.786295i	−0.194590	−	0.980885i	$-0.562338\pi$
$347$	14.6471	−	14.6471i	0.786295	−	0.786295i	0.980885	+	0.194590i	$0.0623376\pi$
$348$		0			0
$349$			5.85890i			0.313619i	0.987629	+	0.156810i	$0.0501209\pi$
$349$			5.85890i			0.313619i	−0.987629	+	0.156810i	$0.949879\pi$
$350$		0			0
$351$			0.267949i			0.0143021i
$352$		0			0
$353$	24.7727	−	24.7727i	1.31852	−	1.31852i	0.403564	−	0.914952i	$-0.367771\pi$
$353$	24.7727	−	24.7727i	1.31852	−	1.31852i	0.914952	−	0.403564i	$-0.132229\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	2.68216	+	2.68216i	0.141955	+	0.141955i
$358$		0			0
$359$	−7.28545			−0.384511			−0.192256	−	0.981345i	$-0.561580\pi$
$359$	−7.28545			−0.384511			−0.192256	+	0.981345i	$0.561580\pi$
$360$		0			0
$361$	−6.07055			−0.319503
$362$		0			0
$363$	−16.5343	−	16.5343i	−0.867825	−	0.867825i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−10.9531	+	10.9531i	−0.571750	+	0.571750i	−0.932617	−	0.360867i	$-0.882481\pi$
$367$	−10.9531	+	10.9531i	−0.571750	+	0.571750i	0.360867	+	0.932617i	$0.382481\pi$
$368$		0			0
$369$		−	10.0857i		−	0.525040i
$370$		0			0
$371$			9.09800i			0.472345i
$372$		0			0
$373$	16.6682	−	16.6682i	0.863046	−	0.863046i	−0.128645	−	0.991691i	$-0.541063\pi$
$373$	16.6682	−	16.6682i	0.863046	−	0.863046i	0.991691	+	0.128645i	$0.0410628\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−0.852491	−	0.852491i	−0.0439055	−	0.0439055i
$378$		0			0
$379$	0.667551			0.0342898			0.0171449	−	0.999853i	$-0.494542\pi$
$379$	0.667551			0.0342898			0.0171449	+	0.999853i	$0.494542\pi$
$380$		0			0
$381$	20.3125			1.04064
$382$		0			0
$383$	−5.87780	−	5.87780i	−0.300342	−	0.300342i	0.540806	−	0.841147i	$-0.318119\pi$
$383$	−5.87780	−	5.87780i	−0.300342	−	0.300342i	−0.841147	+	0.540806i	$0.818119\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−5.06022	+	5.06022i	−0.257225	+	0.257225i
$388$		0			0
$389$		−	32.1961i		−	1.63241i	−0.577764	−	0.816204i	$-0.696075\pi$
$389$		−	32.1961i		−	1.63241i	0.577764	−	0.816204i	$-0.303925\pi$
$390$		0			0
$391$		−	4.52661i		−	0.228921i
$392$		0			0
$393$	−7.06110	+	7.06110i	−0.356185	+	0.356185i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	5.36761	+	5.36761i	0.269393	+	0.269393i	0.828855	−	0.559463i	$-0.188993\pi$
$397$	5.36761	+	5.36761i	0.269393	+	0.269393i	−0.559463	+	0.828855i	$0.688993\pi$
$398$		0			0
$399$	7.31835			0.366376
$400$		0			0
$401$	16.4006			0.819009			0.409504	−	0.912308i	$-0.365702\pi$
$401$	16.4006			0.819009			0.409504	+	0.912308i	$0.365702\pi$
$402$		0			0
$403$	0.0115766	+	0.0115766i	0.000576670	+	0.000576670i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−48.6249	+	48.6249i	−2.41025	+	2.41025i
$408$		0			0
$409$			3.71655i			0.183771i	0.995770	+	0.0918857i	$0.0292894\pi$
$409$			3.71655i			0.183771i	−0.995770	+	0.0918857i	$0.970711\pi$
$410$		0			0
$411$		−	0.808492i		−	0.0398800i
$412$		0			0
$413$	−4.98539	+	4.98539i	−0.245315	+	0.245315i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−5.27792	−	5.27792i	−0.258461	−	0.258461i
$418$		0			0
$419$	1.45929			0.0712912			0.0356456	−	0.999364i	$-0.488651\pi$
$419$	1.45929			0.0712912			0.0356456	+	0.999364i	$0.488651\pi$
$420$		0			0
$421$	11.2432			0.547958			0.273979	−	0.961736i	$-0.411660\pi$
$421$	11.2432			0.547958			0.273979	+	0.961736i	$0.411660\pi$
$422$		0			0
$423$	0.0498881	+	0.0498881i	0.00242564	+	0.00242564i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−18.5941	+	18.5941i	−0.899834	+	0.899834i
$428$		0			0
$429$			1.57117i			0.0758570i
$430$		0			0
$431$		−	22.5802i		−	1.08765i	−0.839198	−	0.543826i	$-0.816975\pi$
$431$		−	22.5802i		−	1.08765i	0.839198	−	0.543826i	$-0.183025\pi$
$432$		0			0
$433$	18.3749	−	18.3749i	0.883043	−	0.883043i	−0.110800	−	0.993843i	$-0.535341\pi$
$433$	18.3749	−	18.3749i	0.883043	−	0.883043i	0.993843	+	0.110800i	$0.0353414\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−6.17549	−	6.17549i	−0.295414	−	0.295414i
$438$		0			0
$439$	7.00821			0.334484			0.167242	−	0.985916i	$-0.446514\pi$
$439$	7.00821			0.334484			0.167242	+	0.985916i	$0.446514\pi$
$440$		0			0
$441$	−2.85765			−0.136079
$442$		0			0
$443$	−18.8070	−	18.8070i	−0.893549	−	0.893549i	0.101306	−	0.994855i	$-0.467698\pi$
$443$	−18.8070	−	18.8070i	−0.893549	−	0.893549i	−0.994855	+	0.101306i	$0.967698\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−7.44344	+	7.44344i	−0.352063	+	0.352063i
$448$		0			0
$449$			12.0000i			0.566315i	0.959073	+	0.283158i	$0.0913819\pi$
$449$			12.0000i			0.566315i	−0.959073	+	0.283158i	$0.908618\pi$
$450$		0			0
$451$		−	59.1394i		−	2.78477i
$452$		0			0
$453$	−5.13494	+	5.13494i	−0.241260	+	0.241260i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−5.17157	−	5.17157i	−0.241916	−	0.241916i	0.575726	−	0.817642i	$-0.304719\pi$
$457$	−5.17157	−	5.17157i	−0.241916	−	0.241916i	−0.817642	+	0.575726i	$0.804719\pi$
$458$		0			0
$459$	−1.86370			−0.0869902
$460$		0			0
$461$	16.0247			0.746347			0.373173	−	0.927762i	$-0.378270\pi$
$461$	16.0247			0.746347			0.373173	+	0.927762i	$0.378270\pi$
$462$		0			0
$463$	−6.73545	−	6.73545i	−0.313023	−	0.313023i	0.533057	−	0.846080i	$-0.321043\pi$
$463$	−6.73545	−	6.73545i	−0.313023	−	0.313023i	−0.846080	+	0.533057i	$0.821043\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	5.34507	−	5.34507i	0.247340	−	0.247340i	−0.572538	−	0.819878i	$-0.694041\pi$
$467$	5.34507	−	5.34507i	0.247340	−	0.247340i	0.819878	+	0.572538i	$0.194041\pi$
$468$		0			0
$469$		−	12.8194i		−	0.591943i
$470$		0			0
$471$			11.6099i			0.534954i
$472$		0			0
$473$	−29.6716	+	29.6716i	−1.36430	+	1.36430i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−3.16088	−	3.16088i	−0.144727	−	0.144727i
$478$		0			0
$479$	−3.98110			−0.181901			−0.0909504	−	0.995855i	$-0.528990\pi$
$479$	−3.98110			−0.181901			−0.0909504	+	0.995855i	$0.528990\pi$
$480$		0			0
$481$	3.14235			0.143279
$482$		0			0
$483$	−3.49546	−	3.49546i	−0.159049	−	0.159049i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−3.88208	+	3.88208i	−0.175914	+	0.175914i	−0.789572	−	0.613658i	$-0.789697\pi$
$487$	−3.88208	+	3.88208i	−0.175914	+	0.175914i	0.613658	+	0.789572i	$0.289697\pi$
$488$		0			0
$489$			5.29983i			0.239666i
$490$		0			0
$491$			11.6145i			0.524155i	0.965047	+	0.262077i	$0.0844076\pi$
$491$			11.6145i			0.524155i	−0.965047	+	0.262077i	$0.915592\pi$
$492$		0			0
$493$	5.92945	−	5.92945i	0.267049	−	0.267049i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	10.0520	+	10.0520i	0.450895	+	0.450895i
$498$		0			0
$499$	6.12916			0.274379			0.137190	−	0.990545i	$-0.456193\pi$
$499$	6.12916			0.274379			0.137190	+	0.990545i	$0.456193\pi$
$500$		0			0
$501$	3.95668			0.176771
$502$		0			0
$503$	−14.3937	−	14.3937i	−0.641784	−	0.641784i	0.309210	−	0.950994i	$-0.399935\pi$
$503$	−14.3937	−	14.3937i	−0.641784	−	0.641784i	−0.950994	+	0.309210i	$0.899935\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−9.14162	+	9.14162i	−0.405994	+	0.405994i
$508$		0			0
$509$			27.6665i			1.22629i	0.789969	+	0.613147i	$0.210097\pi$
$509$			27.6665i			1.22629i	−0.789969	+	0.613147i	$0.789903\pi$
$510$		0			0
$511$		−	7.29911i		−	0.322894i
$512$		0			0
$513$	−2.54258	+	2.54258i	−0.112258	+	0.112258i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	0.292529	+	0.292529i	0.0128654	+	0.0128654i
$518$		0			0
$519$	−17.3770			−0.762764
$520$		0			0
$521$	18.5417			0.812328			0.406164	−	0.913800i	$-0.366866\pi$
$521$	18.5417			0.812328			0.406164	+	0.913800i	$0.366866\pi$
$522$		0			0
$523$	−23.8786	−	23.8786i	−1.04414	−	1.04414i	−0.998980	−	0.0451598i	$-0.985620\pi$
$523$	−23.8786	−	23.8786i	−1.04414	−	1.04414i	−0.0451598	−	0.998980i	$-0.514380\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−0.0805200	+	0.0805200i	−0.00350751	+	0.00350751i
$528$		0			0
$529$		−	17.1008i		−	0.743513i
$530$		0			0
$531$		−	3.46410i		−	0.150329i
$532$		0			0
$533$	−1.91092	+	1.91092i	−0.0827712	+	0.0827712i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	4.42027	+	4.42027i	0.190749	+	0.190749i
$538$		0			0
$539$	−16.7564			−0.721750
$540$		0			0
$541$	−6.60521			−0.283980			−0.141990	−	0.989868i	$-0.545350\pi$
$541$	−6.60521			−0.283980			−0.141990	+	0.989868i	$0.545350\pi$
$542$		0			0
$543$	−3.52897	−	3.52897i	−0.151442	−	0.151442i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−16.4336	+	16.4336i	−0.702651	+	0.702651i	−0.964979	−	0.262327i	$-0.915510\pi$
$547$	−16.4336	+	16.4336i	−0.702651	+	0.702651i	0.262327	+	0.964979i	$0.415510\pi$
$548$		0			0
$549$		−	12.9202i		−	0.551419i
$550$		0			0
$551$		−	16.1787i		−	0.689234i
$552$		0			0
$553$	21.8630	−	21.8630i	0.929708	−	0.929708i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−20.6398	−	20.6398i	−0.874534	−	0.874534i	0.118428	−	0.992963i	$-0.462214\pi$
$557$	−20.6398	−	20.6398i	−0.874534	−	0.874534i	−0.992963	+	0.118428i	$0.962214\pi$
$558$		0			0
$559$	1.91751			0.0811019
$560$		0			0
$561$	−10.9282			−0.461389
$562$		0			0
$563$	22.5152	+	22.5152i	0.948902	+	0.948902i	0.998756	−	0.0498546i	$-0.0158758\pi$
$563$	22.5152	+	22.5152i	0.948902	+	0.948902i	−0.0498546	+	0.998756i	$0.515876\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−1.43916	+	1.43916i	−0.0604389	+	0.0604389i
$568$		0			0
$569$		−	14.7695i		−	0.619169i	−0.950872	−	0.309584i	$-0.899810\pi$
$569$		−	14.7695i		−	0.619169i	0.950872	−	0.309584i	$-0.100190\pi$
$570$		0			0
$571$			1.87515i			0.0784725i	0.999230	+	0.0392362i	$0.0124925\pi$
$571$			1.87515i			0.0784725i	−0.999230	+	0.0392362i	$0.987508\pi$
$572$		0			0
$573$	9.84445	−	9.84445i	0.411258	−	0.411258i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−16.1877	−	16.1877i	−0.673903	−	0.673903i	0.284710	−	0.958614i	$-0.408103\pi$
$577$	−16.1877	−	16.1877i	−0.673903	−	0.673903i	−0.958614	+	0.284710i	$0.908103\pi$
$578$		0			0
$579$	−2.68165			−0.111445
$580$		0			0
$581$	22.3855			0.928707
$582$		0			0
$583$	−18.5344	−	18.5344i	−0.767618	−	0.767618i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−17.0198	+	17.0198i	−0.702481	+	0.702481i	−0.964943	−	0.262461i	$-0.915466\pi$
$587$	−17.0198	+	17.0198i	−0.702481	+	0.702481i	0.262461	+	0.964943i	$0.415466\pi$
$588$		0			0
$589$			0.219701i			0.00905262i
$590$		0			0
$591$			20.2633i			0.833521i
$592$		0			0
$593$	−0.384097	+	0.384097i	−0.0157730	+	0.0157730i	−0.714949	−	0.699176i	$-0.753550\pi$
$593$	−0.384097	+	0.384097i	−0.0157730	+	0.0157730i	0.699176	+	0.714949i	$0.253550\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−12.6696	−	12.6696i	−0.518532	−	0.518532i
$598$		0			0
$599$	−16.3951			−0.669886			−0.334943	−	0.942238i	$-0.608717\pi$
$599$	−16.3951			−0.669886			−0.334943	+	0.942238i	$0.608717\pi$
$600$		0			0
$601$	24.4851			0.998767			0.499383	−	0.866381i	$-0.333560\pi$
$601$	24.4851			0.998767			0.499383	+	0.866381i	$0.333560\pi$
$602$		0			0
$603$	4.45377	+	4.45377i	0.181372	+	0.181372i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	28.2540	−	28.2540i	1.14680	−	1.14680i	0.159616	−	0.987179i	$-0.448974\pi$
$607$	28.2540	−	28.2540i	1.14680	−	1.14680i	0.987179	−	0.159616i	$-0.0510256\pi$
$608$		0			0
$609$		−	9.15748i		−	0.371080i
$610$		0			0
$611$		−	0.0189044i		−	0.000764792i
$612$		0			0
$613$	−7.24213	+	7.24213i	−0.292507	+	0.292507i	−0.838070	−	0.545563i	$-0.816316\pi$
$613$	−7.24213	+	7.24213i	−0.292507	+	0.292507i	0.545563	+	0.838070i	$0.316316\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−22.4030	−	22.4030i	−0.901911	−	0.901911i	0.0936905	−	0.995601i	$-0.470134\pi$
$617$	−22.4030	−	22.4030i	−0.901911	−	0.901911i	−0.995601	+	0.0936905i	$0.970134\pi$
$618$		0			0
$619$	−8.28205			−0.332884			−0.166442	−	0.986051i	$-0.553228\pi$
$619$	−8.28205			−0.332884			−0.166442	+	0.986051i	$0.553228\pi$
$620$		0			0
$621$	2.42883			0.0974654
$622$		0			0
$623$	12.9506	+	12.9506i	0.518856	+	0.518856i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−14.9089	+	14.9089i	−0.595406	+	0.595406i
$628$		0			0
$629$			21.8564i			0.871472i
$630$		0			0
$631$			28.0654i			1.11727i	0.829415	+	0.558633i	$0.188674\pi$
$631$			28.0654i			1.11727i	−0.829415	+	0.558633i	$0.811326\pi$
$632$		0			0
$633$	16.0266	−	16.0266i	0.637001	−	0.637001i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	0.541435	+	0.541435i	0.0214525	+	0.0214525i
$638$		0			0
$639$	−6.98466			−0.276309
$640$		0			0
$641$	38.3100			1.51315			0.756577	−	0.653905i	$-0.226870\pi$
$641$	38.3100			1.51315			0.756577	+	0.653905i	$0.226870\pi$
$642$		0			0
$643$	11.6476	+	11.6476i	0.459335	+	0.459335i	0.898437	−	0.439102i	$-0.144703\pi$
$643$	11.6476	+	11.6476i	0.459335	+	0.459335i	−0.439102	+	0.898437i	$0.644703\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−0.806003	+	0.806003i	−0.0316872	+	0.0316872i	−0.722773	−	0.691086i	$-0.757133\pi$
$647$	−0.806003	+	0.806003i	−0.0316872	+	0.0316872i	0.691086	+	0.722773i	$0.257133\pi$
$648$		0			0
$649$		−	20.3125i		−	0.797334i
$650$		0			0
$651$			0.124356i			0.00487388i
$652$		0			0
$653$	3.09445	−	3.09445i	0.121095	−	0.121095i	−0.643962	−	0.765057i	$-0.722711\pi$
$653$	3.09445	−	3.09445i	0.121095	−	0.121095i	0.765057	+	0.643962i	$0.222711\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	2.53590	+	2.53590i	0.0989348	+	0.0989348i
$658$		0			0
$659$	39.2971			1.53080			0.765399	−	0.643556i	$-0.222542\pi$
$659$	39.2971			1.53080			0.765399	+	0.643556i	$0.222542\pi$
$660$		0			0
$661$	−22.6677			−0.881672			−0.440836	−	0.897588i	$-0.645318\pi$
$661$	−22.6677			−0.881672			−0.440836	+	0.897588i	$0.645318\pi$
$662$		0			0
$663$	0.353113	+	0.353113i	0.0137138	+	0.0137138i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−7.72741	+	7.72741i	−0.299206	+	0.299206i
$668$		0			0
$669$			25.3490i			0.980048i
$670$		0			0
$671$		−	75.7600i		−	2.92468i
$672$		0			0
$673$	19.1210	−	19.1210i	0.737059	−	0.737059i	−0.234949	−	0.972008i	$-0.575492\pi$
$673$	19.1210	−	19.1210i	0.737059	−	0.737059i	0.972008	+	0.234949i	$0.0754923\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−19.7525	−	19.7525i	−0.759150	−	0.759150i	0.217017	−	0.976168i	$-0.430367\pi$
$677$	−19.7525	−	19.7525i	−0.759150	−	0.759150i	−0.976168	+	0.217017i	$0.930367\pi$
$678$		0			0
$679$	−18.4295			−0.707260
$680$		0			0
$681$	2.55783			0.0980161
$682$		0			0
$683$	7.67576	+	7.67576i	0.293705	+	0.293705i	0.838542	−	0.544837i	$-0.183409\pi$
$683$	7.67576	+	7.67576i	0.293705	+	0.293705i	−0.544837	+	0.838542i	$0.683409\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	21.0044	−	21.0044i	0.801370	−	0.801370i
$688$		0			0
$689$			1.19777i			0.0456316i
$690$		0			0
$691$		−	19.2197i		−	0.731152i	−0.930782	−	0.365576i	$-0.880872\pi$
$691$		−	19.2197i		−	0.731152i	0.930782	−	0.365576i	$-0.119128\pi$
$692$		0			0
$693$	−8.43879	+	8.43879i	−0.320563	+	0.320563i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−13.2913	−	13.2913i	−0.503443	−	0.503443i
$698$		0			0
$699$	−13.3278			−0.504104
$700$		0			0
$701$	1.95668			0.0739028			0.0369514	−	0.999317i	$-0.488235\pi$
$701$	1.95668			0.0739028			0.0369514	+	0.999317i	$0.488235\pi$
$702$		0			0
$703$	29.8179	+	29.8179i	1.12460	+	1.12460i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	19.3244	−	19.3244i	0.726769	−	0.726769i
$708$		0			0
$709$			27.9492i			1.04965i	0.851209	+	0.524827i	$0.175870\pi$
$709$			27.9492i			1.04965i	−0.851209	+	0.524827i	$0.824130\pi$
$710$		0			0
$711$			15.1915i			0.569726i
$712$		0			0
$713$	0.104936	−	0.104936i	0.00392987	−	0.00392987i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−13.9893	−	13.9893i	−0.522440	−	0.522440i
$718$		0			0
$719$	29.7907			1.11100			0.555502	−	0.831515i	$-0.312526\pi$
$719$	29.7907			1.11100			0.555502	+	0.831515i	$0.312526\pi$
$720$		0			0
$721$	19.0996			0.711305
$722$		0			0
$723$	−19.4625	−	19.4625i	−0.723818	−	0.723818i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	15.9733	−	15.9733i	0.592417	−	0.592417i	−0.345867	−	0.938284i	$-0.612415\pi$
$727$	15.9733	−	15.9733i	0.592417	−	0.592417i	0.938284	+	0.345867i	$0.112415\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$			13.3371i			0.493290i
$732$		0			0
$733$	11.8685	−	11.8685i	0.438373	−	0.438373i	−0.453091	−	0.891464i	$-0.649679\pi$
$733$	11.8685	−	11.8685i	0.438373	−	0.438373i	0.891464	+	0.453091i	$0.149679\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	26.1156	+	26.1156i	0.961980	+	0.961980i
$738$		0			0
$739$	−1.86171			−0.0684842			−0.0342421	−	0.999414i	$-0.510902\pi$
$739$	−1.86171			−0.0684842			−0.0342421	+	0.999414i	$0.510902\pi$
$740$		0			0
$741$	0.963479			0.0353943
$742$		0			0
$743$	−31.3336	−	31.3336i	−1.14952	−	1.14952i	−0.986647	−	0.162873i	$-0.947924\pi$
$743$	−31.3336	−	31.3336i	−1.14952	−	1.14952i	−0.162873	−	0.986647i	$-0.552076\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−7.77729	+	7.77729i	−0.284556	+	0.284556i
$748$		0			0
$749$		−	33.1696i		−	1.21199i
$750$		0			0
$751$		−	33.1608i		−	1.21006i	−0.796204	−	0.605028i	$-0.793162\pi$
$751$		−	33.1608i		−	1.21006i	0.796204	−	0.605028i	$-0.206838\pi$
$752$		0			0
$753$	−18.3830	+	18.3830i	−0.669914	+	0.669914i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−16.2094	−	16.2094i	−0.589141	−	0.589141i	0.348258	−	0.937399i	$-0.386773\pi$
$757$	−16.2094	−	16.2094i	−0.589141	−	0.589141i	−0.937399	+	0.348258i	$0.886773\pi$
$758$		0			0
$759$	14.2419			0.516949
$760$		0			0
$761$	−41.3657			−1.49950			−0.749752	−	0.661718i	$-0.769827\pi$
$761$	−41.3657			−1.49950			−0.749752	+	0.661718i	$0.769827\pi$
$762$		0			0
$763$	−19.3752	−	19.3752i	−0.701428	−	0.701428i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−0.656339	+	0.656339i	−0.0236990	+	0.0236990i
$768$		0			0
$769$			22.0835i			0.796350i	0.917309	+	0.398175i	$0.130356\pi$
$769$			22.0835i			0.796350i	−0.917309	+	0.398175i	$0.869644\pi$
$770$		0			0
$771$		−	26.2419i		−	0.945079i
$772$		0			0
$773$	9.27276	−	9.27276i	0.333518	−	0.333518i	−0.520403	−	0.853921i	$-0.674218\pi$
$773$	9.27276	−	9.27276i	0.333518	−	0.333518i	0.853921	+	0.520403i	$0.174218\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	16.8776	+	16.8776i	0.605480	+	0.605480i
$778$		0			0
$779$	−36.2656			−1.29935
$780$		0			0
$781$	−40.9560			−1.46552
$782$		0			0
$783$	3.18154	+	3.18154i	0.113699	+	0.113699i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−14.8582	+	14.8582i	−0.529637	+	0.529637i	−0.920464	−	0.390827i	$-0.872189\pi$
$787$	−14.8582	+	14.8582i	−0.529637	+	0.529637i	0.390827	+	0.920464i	$0.372189\pi$
$788$		0			0
$789$		−	29.8131i		−	1.06137i
$790$		0			0
$791$			23.0265i			0.818729i
$792$		0			0
$793$	−2.44797	+	2.44797i	−0.0869298	+	0.0869298i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−5.07180	−	5.07180i	−0.179652	−	0.179652i	0.611552	−	0.791204i	$-0.290546\pi$
$797$	−5.07180	−	5.07180i	−0.179652	−	0.179652i	−0.791204	+	0.611552i	$0.790546\pi$
$798$		0			0
$799$	0.131489			0.00465173
$800$		0			0
$801$	−8.99876			−0.317955
$802$		0			0
$803$	14.8698	+	14.8698i	0.524742	+	0.524742i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	12.2733	−	12.2733i	0.432040	−	0.432040i
$808$		0			0
$809$		−	27.7707i		−	0.976367i	−0.872741	−	0.488183i	$-0.837660\pi$
$809$		−	27.7707i		−	0.976367i	0.872741	−	0.488183i	$-0.162340\pi$
$810$		0			0
$811$			21.4240i			0.752297i	0.926559	+	0.376149i	$0.122752\pi$
$811$			21.4240i			0.752297i	−0.926559	+	0.376149i	$0.877248\pi$
$812$		0			0
$813$	16.3059	−	16.3059i	0.571873	−	0.571873i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	18.1953	+	18.1953i	0.636573	+	0.636573i
$818$		0			0
$819$	0.545351			0.0190561
$820$		0			0
$821$	−9.61449			−0.335548			−0.167774	−	0.985825i	$-0.553658\pi$
$821$	−9.61449			−0.335548			−0.167774	+	0.985825i	$0.553658\pi$
$822$		0			0
$823$	−16.0363	−	16.0363i	−0.558991	−	0.558991i	0.370029	−	0.929020i	$-0.379348\pi$
$823$	−16.0363	−	16.0363i	−0.558991	−	0.558991i	−0.929020	+	0.370029i	$0.879348\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	9.30198	−	9.30198i	0.323462	−	0.323462i	−0.526632	−	0.850093i	$-0.676545\pi$
$827$	9.30198	−	9.30198i	0.323462	−	0.323462i	0.850093	+	0.526632i	$0.176545\pi$
$828$		0			0
$829$			29.7556i			1.03345i	0.856150	+	0.516727i	$0.172850\pi$
$829$			29.7556i			1.03345i	−0.856150	+	0.516727i	$0.827150\pi$
$830$		0			0
$831$		−	25.5792i		−	0.887332i
$832$		0			0
$833$	−3.76592	+	3.76592i	−0.130481	+	0.130481i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−0.0432043	−	0.0432043i	−0.00149336	−	0.00149336i
$838$		0			0
$839$	−23.6375			−0.816055			−0.408028	−	0.912970i	$-0.633783\pi$
$839$	−23.6375			−0.816055			−0.408028	+	0.912970i	$0.633783\pi$
$840$		0			0
$841$	8.75560			0.301917
$842$		0			0
$843$	8.16036	+	8.16036i	0.281058	+	0.281058i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−33.6518	+	33.6518i	−1.15629	+	1.15629i
$848$		0			0
$849$			9.54174i			0.327472i
$850$		0			0
$851$		−	28.4838i		−	0.976413i
$852$		0			0
$853$	−35.0444	+	35.0444i	−1.19990	+	1.19990i	−0.225701	+	0.974197i	$0.572467\pi$
$853$	−35.0444	+	35.0444i	−1.19990	+	1.19990i	−0.974197	+	0.225701i	$0.927533\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	12.1514	+	12.1514i	0.415085	+	0.415085i	0.883506	−	0.468421i	$-0.155177\pi$
$857$	12.1514	+	12.1514i	0.415085	+	0.415085i	−0.468421	+	0.883506i	$0.655177\pi$
$858$		0			0
$859$	−17.3205			−0.590968			−0.295484	−	0.955348i	$-0.595481\pi$
$859$	−17.3205			−0.590968			−0.295484	+	0.955348i	$0.595481\pi$
$860$		0			0
$861$	−20.5271			−0.699563
$862$		0			0
$863$	−15.6758	−	15.6758i	−0.533609	−	0.533609i	0.388035	−	0.921644i	$-0.373154\pi$
$863$	−15.6758	−	15.6758i	−0.533609	−	0.533609i	−0.921644	+	0.388035i	$0.873154\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	9.56476	−	9.56476i	0.324836	−	0.324836i
$868$		0			0
$869$			89.0785i			3.02178i
$870$		0			0
$871$		−	1.68770i		−	0.0571855i
$872$		0			0
$873$	6.40289	−	6.40289i	0.216705	−	0.216705i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−13.5669	−	13.5669i	−0.458123	−	0.458123i	0.439916	−	0.898039i	$-0.355008\pi$
$877$	−13.5669	−	13.5669i	−0.458123	−	0.458123i	−0.898039	+	0.439916i	$0.855008\pi$
$878$		0			0
$879$	25.4616			0.858799
$880$		0			0
$881$	−18.4561			−0.621800			−0.310900	−	0.950443i	$-0.600630\pi$
$881$	−18.4561			−0.621800			−0.310900	+	0.950443i	$0.600630\pi$
$882$		0			0
$883$	12.9907	+	12.9907i	0.437172	+	0.437172i	0.891059	−	0.453887i	$-0.149963\pi$
$883$	12.9907	+	12.9907i	0.437172	+	0.437172i	−0.453887	+	0.891059i	$0.649963\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−16.4967	+	16.4967i	−0.553904	+	0.553904i	−0.927565	−	0.373662i	$-0.878102\pi$
$887$	−16.4967	+	16.4967i	−0.553904	+	0.553904i	0.373662	+	0.927565i	$0.378102\pi$
$888$		0			0
$889$		−	41.3415i		−	1.38655i
$890$		0			0
$891$		−	5.86370i		−	0.196441i
$892$		0			0
$893$	0.179385	−	0.179385i	0.00600290	−	0.00600290i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−0.460186	−	0.460186i	−0.0153652	−	0.0153652i
$898$		0			0
$899$	0.274913			0.00916885
$900$		0			0
$901$	−8.33104			−0.277547
$902$		0			0
$903$	10.2989	+	10.2989i	0.342727	+	0.342727i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	16.0998	−	16.0998i	0.534584	−	0.534584i	−0.387349	−	0.921933i	$-0.626609\pi$
$907$	16.0998	−	16.0998i	0.534584	−	0.534584i	0.921933	+	0.387349i	$0.126609\pi$
$908$		0			0
$909$			13.4276i			0.445365i
$910$		0			0
$911$			35.8310i			1.18713i	0.804784	+	0.593567i	$0.202281\pi$
$911$			35.8310i			1.18713i	−0.804784	+	0.593567i	$0.797719\pi$
$912$		0			0
$913$	−45.6037	+	45.6037i	−1.50926	+	1.50926i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	14.3713	+	14.3713i	0.474582	+	0.474582i
$918$		0			0
$919$	40.6860			1.34211			0.671054	−	0.741408i	$-0.265842\pi$
$919$	40.6860			1.34211			0.671054	+	0.741408i	$0.265842\pi$
$920$		0			0
$921$	13.0857			0.431188
$922$		0			0
$923$	1.32337	+	1.32337i	0.0435594	+	0.0435594i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−6.63567	+	6.63567i	−0.217944	+	0.217944i
$928$		0			0
$929$		−	12.5392i		−	0.411399i	−0.978615	−	0.205700i	$-0.934053\pi$
$929$		−	12.5392i		−	0.411399i	0.978615	−	0.205700i	$-0.0659470\pi$
$930$		0			0
$931$			10.2754i			0.336763i
$932$		0			0
$933$	−3.76217	+	3.76217i	−0.123168	+	0.123168i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	28.5518	+	28.5518i	0.932747	+	0.932747i	0.997877	−	0.0651295i	$-0.0207460\pi$
$937$	28.5518	+	28.5518i	0.932747	+	0.932747i	−0.0651295	+	0.997877i	$0.520746\pi$
$938$		0			0
$939$	1.99536			0.0651160
$940$		0			0
$941$	−50.4350			−1.64413			−0.822067	−	0.569391i	$-0.807179\pi$
$941$	−50.4350			−1.64413			−0.822067	+	0.569391i	$0.807179\pi$
$942$		0			0
$943$	17.3215	+	17.3215i	0.564067	+	0.564067i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	22.8359	−	22.8359i	0.742067	−	0.742067i	−0.230908	−	0.972976i	$-0.574170\pi$
$947$	22.8359	−	22.8359i	0.742067	−	0.742067i	0.972976	+	0.230908i	$0.0741697\pi$
$948$		0			0
$949$		−	0.960947i		−	0.0311936i
$950$		0			0
$951$			2.78710i			0.0903779i
$952$		0			0
$953$	32.0502	−	32.0502i	1.03821	−	1.03821i	0.0389670	−	0.999240i	$-0.487593\pi$
$953$	32.0502	−	32.0502i	1.03821	−	1.03821i	0.999240	−	0.0389670i	$-0.0124067\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	18.6556	+	18.6556i	0.603050	+	0.603050i
$958$		0			0
$959$	−1.64550			−0.0531361
$960$		0			0
$961$	30.9963			0.999880
$962$		0			0
$963$	11.5240	+	11.5240i	0.371354	+	0.371354i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	18.1104	−	18.1104i	0.582392	−	0.582392i	−0.353168	−	0.935560i	$-0.614896\pi$
$967$	18.1104	−	18.1104i	0.582392	−	0.582392i	0.935560	+	0.353168i	$0.114896\pi$
$968$		0			0
$969$			6.70142i			0.215281i
$970$		0			0
$971$			57.1890i			1.83528i	0.397409	+	0.917641i	$0.369909\pi$
$971$			57.1890i			1.83528i	−0.397409	+	0.917641i	$0.630091\pi$
$972$		0			0
$973$	−10.7420	+	10.7420i	−0.344373	+	0.344373i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	16.3190	+	16.3190i	0.522092	+	0.522092i	0.918203	−	0.396111i	$-0.129640\pi$
$977$	16.3190	+	16.3190i	0.522092	+	0.522092i	−0.396111	+	0.918203i	$0.629640\pi$
$978$		0			0
$979$	−52.7660			−1.68641
$980$		0			0
$981$	13.4629			0.429836
$982$		0			0
$983$	−7.35504	−	7.35504i	−0.234589	−	0.234589i	0.580016	−	0.814605i	$-0.303046\pi$
$983$	−7.35504	−	7.35504i	−0.234589	−	0.234589i	−0.814605	+	0.580016i	$0.803046\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	0.101536	−	0.101536i	0.00323193	−	0.00323193i
$988$		0			0
$989$		−	17.3812i		−	0.552691i
$990$		0			0
$991$			55.2058i			1.75367i	0.480790	+	0.876836i	$0.340350\pi$
$991$			55.2058i			1.75367i	−0.480790	+	0.876836i	$0.659650\pi$
$992$		0			0
$993$	4.33761	−	4.33761i	0.137650	−	0.137650i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	1.48549	+	1.48549i	0.0470461	+	0.0470461i	0.730238	−	0.683192i	$-0.239409\pi$
$997$	1.48549	+	1.48549i	0.0470461	+	0.0470461i	−0.683192	+	0.730238i	$0.739409\pi$
$998$		0			0
$999$	−11.7274			−0.371039

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2400.2.w.h.607.4	yes	8
4.3	odd	2		2400.2.w.l.607.1	yes	8
5.2	odd	4		2400.2.w.g.2143.4	yes	8
5.3	odd	4		2400.2.w.l.2143.1	yes	8
5.4	even	2		2400.2.w.k.607.1	yes	8
20.3	even	4	inner	2400.2.w.h.2143.4	yes	8
20.7	even	4		2400.2.w.k.2143.1	yes	8
20.19	odd	2		2400.2.w.g.607.4	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2400.2.w.g.607.4	✓	8	20.19	odd	2
2400.2.w.g.2143.4	yes	8	5.2	odd	4
2400.2.w.h.607.4	yes	8	1.1	even	1	trivial
2400.2.w.h.2143.4	yes	8	20.3	even	4	inner
2400.2.w.k.607.1	yes	8	5.4	even	2
2400.2.w.k.2143.1	yes	8	20.7	even	4
2400.2.w.l.607.1	yes	8	4.3	odd	2
2400.2.w.l.2143.1	yes	8	5.3	odd	4

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:	\( N \)	\(=\)	\( 2400 = 2^{5} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2400.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{3} +(1.43916 - 1.43916i) q^{7} +1.00000i q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{3} +(1.43916 - 1.43916i) q^{7} +1.00000i q^{9} +5.86370i q^{11} +(0.189469 - 0.189469i) q^{13} +(1.31784 + 1.31784i) q^{17} +3.59575 q^{19} +2.03528 q^{21} +(-1.71744 - 1.71744i) q^{23} +(-0.707107 + 0.707107i) q^{27} -4.49938i q^{29} +0.0611001i q^{31} +(-4.14626 + 4.14626i) q^{33} +(8.29253 + 8.29253i) q^{37} +0.267949 q^{39} -10.0857 q^{41} +(5.06022 + 5.06022i) q^{43} +(0.0498881 - 0.0498881i) q^{47} +2.85765i q^{49} +1.86370i q^{51} +(-3.16088 + 3.16088i) q^{53} +(2.54258 + 2.54258i) q^{57} -3.46410 q^{59} -12.9202 q^{61} +(1.43916 + 1.43916i) q^{63} +(4.45377 - 4.45377i) q^{67} -2.42883i q^{69} +6.98466i q^{71} +(2.53590 - 2.53590i) q^{73} +(8.43879 + 8.43879i) q^{77} +15.1915 q^{79} -1.00000 q^{81} +(7.77729 + 7.77729i) q^{83} +(3.18154 - 3.18154i) q^{87} +8.99876i q^{89} -0.545351i q^{91} +(-0.0432043 + 0.0432043i) q^{93} +(-6.40289 - 6.40289i) q^{97} -5.86370 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{7}+O(q^{10}) \) 8 * q - 8 * q^7	\( 8 q - 8 q^{7} + 8 q^{17} - 16 q^{19} + 8 q^{21} - 8 q^{23} - 8 q^{33} + 16 q^{37} + 16 q^{39} - 16 q^{41} + 24 q^{43} - 16 q^{47} + 8 q^{53} + 8 q^{57} - 24 q^{61} - 8 q^{63} + 8 q^{67} + 48 q^{73} - 8 q^{77} + 32 q^{79} - 8 q^{81} - 16 q^{83} - 8 q^{87} - 24 q^{93} - 32 q^{97} - 16 q^{99}+O(q^{100}) \) 8 * q - 8 * q^7 + 8 * q^17 - 16 * q^19 + 8 * q^21 - 8 * q^23 - 8 * q^33 + 16 * q^37 + 16 * q^39 - 16 * q^41 + 24 * q^43 - 16 * q^47 + 8 * q^53 + 8 * q^57 - 24 * q^61 - 8 * q^63 + 8 * q^67 + 48 * q^73 - 8 * q^77 + 32 * q^79 - 8 * q^81 - 16 * q^83 - 8 * q^87 - 24 * q^93 - 32 * q^97 - 16 * q^99

Introduction

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