LMFDB - Embedded newform 2900.2.j.c.2593.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2900,2,Mod(1757,2900)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2900, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2900.1757"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 2900 = 2^{2} \cdot 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2900.j (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$23.1566165862$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 36x^{14} + 468x^{12} + 2844x^{10} + 8574x^{8} + 12524x^{6} + 8404x^{4} + 2324x^{2} + 169 $ x^16 + 36x^14 + 468x^12 + 2844x^10 + 8574x^8 + 12524x^6 + 8404x^4 + 2324*x^2 + 169
Coefficient ring:	$\Z[a_1, \ldots, a_{29}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			2593.5
Root			$1.27711i$ of defining polynomial
Character	$\chi$	$=$	2900.2593
Dual form			2900.2.j.c.1757.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+0.277113i q^{3} +(3.60863 - 3.60863i) q^{7} +2.92321 q^{9} +(-2.44164 - 2.44164i) q^{11} +(-2.78793 + 2.78793i) q^{13} +3.19850 q^{17} +(-1.44164 + 1.44164i) q^{19} +(1.00000 + 1.00000i) q^{21} +(4.00813 + 4.00813i) q^{23} +1.64140i q^{27} +(5.17735 - 1.48157i) q^{29} +(6.13742 + 6.13742i) q^{31} +(0.676611 - 0.676611i) q^{33} -2.11132i q^{37} +(-0.772573 - 0.772573i) q^{39} +(4.61899 - 4.61899i) q^{41} -0.0110648i q^{43} +6.65198i q^{47} -19.0445i q^{49} +0.886345i q^{51} +(-6.26354 - 6.26354i) q^{53} +(-0.399497 - 0.399497i) q^{57} -9.31477i q^{59} +(0.963137 + 0.963137i) q^{61} +(10.5488 - 10.5488i) q^{63} +(0.532522 + 0.532522i) q^{67} +(-1.11071 + 1.11071i) q^{69} +5.92321i q^{71} -6.67410 q^{73} -17.6220 q^{77} +(0.521498 - 0.521498i) q^{79} +8.31477 q^{81} +(1.78549 + 1.78549i) q^{83} +(0.410562 + 1.43471i) q^{87} +(2.73571 - 2.73571i) q^{89} +20.1213i q^{91} +(-1.70076 + 1.70076i) q^{93} -13.8692i q^{97} +(-7.13742 - 7.13742i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{9} - 4 q^{11} + 12 q^{19} + 16 q^{21} + 28 q^{29} + 28 q^{31} - 32 q^{39} - 16 q^{41} - 24 q^{61} + 72 q^{69} + 4 q^{79} + 8 q^{81} + 24 q^{89} - 44 q^{99}+O(q^{100}) $ 16 * q - 8 * q^9 - 4 * q^11 + 12 * q^19 + 16 * q^21 + 28 * q^29 + 28 * q^31 - 32 * q^39 - 16 * q^41 - 24 * q^61 + 72 * q^69 + 4 * q^79 + 8 * q^81 + 24 * q^89 - 44 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2900\mathbb{Z}\right)^\times$.

$n$	$901$	$1277$	$1451$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{4}\right)$	$1$

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
$3$			0.277113i			0.159991i	0.996795	+	0.0799957i	$0.0254907\pi$
$3$			0.277113i			0.159991i	−0.996795	+	0.0799957i	$0.974509\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	3.60863	−	3.60863i	1.36394	−	1.36394i	0.495098	−	0.868837i	$-0.335132\pi$
$7$	3.60863	−	3.60863i	1.36394	−	1.36394i	0.868837	−	0.495098i	$-0.164868\pi$
$8$		0			0
$9$	2.92321			0.974403
$10$		0			0
$11$	−2.44164	−	2.44164i	−0.736182	−	0.736182i	0.235655	−	0.971837i	$-0.424277\pi$
$11$	−2.44164	−	2.44164i	−0.736182	−	0.736182i	−0.971837	+	0.235655i	$0.924277\pi$
$12$		0			0
$13$	−2.78793	+	2.78793i	−0.773234	+	0.773234i	−0.978670	−	0.205437i	$-0.934139\pi$
$13$	−2.78793	+	2.78793i	−0.773234	+	0.773234i	0.205437	+	0.978670i	$0.434139\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	3.19850			0.775749			0.387875	−	0.921712i	$-0.373209\pi$
$17$	3.19850			0.775749			0.387875	+	0.921712i	$0.373209\pi$
$18$		0			0
$19$	−1.44164	+	1.44164i	−0.330735	+	0.330735i	−0.852865	−	0.522131i	$-0.825137\pi$
$19$	−1.44164	+	1.44164i	−0.330735	+	0.330735i	0.522131	+	0.852865i	$0.325137\pi$
$20$		0			0
$21$	1.00000	+	1.00000i	0.218218	+	0.218218i
$22$		0			0
$23$	4.00813	+	4.00813i	0.835753	+	0.835753i	0.988297	−	0.152544i	$-0.0487465\pi$
$23$	4.00813	+	4.00813i	0.835753	+	0.835753i	−0.152544	+	0.988297i	$0.548746\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$			1.64140i			0.315887i
$28$		0			0
$29$	5.17735	−	1.48157i	0.961410	−	0.275120i
$29$	5.17735	−	1.48157i	0.961410	−	0.275120i
$30$		0			0
$31$	6.13742	+	6.13742i	1.10231	+	1.10231i	0.994131	+	0.108182i	$0.0345030\pi$
$31$	6.13742	+	6.13742i	1.10231	+	1.10231i	0.108182	+	0.994131i	$0.465497\pi$
$32$		0			0
$33$	0.676611	−	0.676611i	0.117783	−	0.117783i
$34$		0			0
$35$		0			0
$36$		0			0
$37$		−	2.11132i		−	0.347099i	−0.984825	−	0.173550i	$-0.944476\pi$
$37$		−	2.11132i		−	0.347099i	0.984825	−	0.173550i	$-0.0555237\pi$
$38$		0			0
$39$	−0.772573	−	0.772573i	−0.123711	−	0.123711i
$40$		0			0
$41$	4.61899	−	4.61899i	0.721365	−	0.721365i	−0.247518	−	0.968883i	$-0.579615\pi$
$41$	4.61899	−	4.61899i	0.721365	−	0.721365i	0.968883	+	0.247518i	$0.0796150\pi$
$42$		0			0
$43$		−	0.0110648i		−	0.00168737i	−1.00000		0.000843687i	$-0.999731\pi$
$43$		−	0.0110648i		−	0.00168737i	1.00000		0.000843687i	$-0.000268554\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$			6.65198i			0.970290i	0.874434	+	0.485145i	$0.161233\pi$
$47$			6.65198i			0.970290i	−0.874434	+	0.485145i	$0.838767\pi$
$48$		0			0
$49$		−	19.0445i		−	2.72064i
$50$		0			0
$51$			0.886345i			0.124113i
$52$		0			0
$53$	−6.26354	−	6.26354i	−0.860364	−	0.860364i	0.131016	−	0.991380i	$-0.458176\pi$
$53$	−6.26354	−	6.26354i	−0.860364	−	0.860364i	−0.991380	+	0.131016i	$0.958176\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−0.399497	−	0.399497i	−0.0529147	−	0.0529147i
$58$		0			0
$59$		−	9.31477i		−	1.21268i	−0.795206	−	0.606340i	$-0.792637\pi$
$59$		−	9.31477i		−	1.21268i	0.795206	−	0.606340i	$-0.207363\pi$
$60$		0			0
$61$	0.963137	+	0.963137i	0.123317	+	0.123317i	0.766072	−	0.642755i	$-0.222209\pi$
$61$	0.963137	+	0.963137i	0.123317	+	0.123317i	−0.642755	+	0.766072i	$0.722209\pi$
$62$		0			0
$63$	10.5488	−	10.5488i	1.32902	−	1.32902i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	0.532522	+	0.532522i	0.0650579	+	0.0650579i	0.738887	−	0.673829i	$-0.235352\pi$
$67$	0.532522	+	0.532522i	0.0650579	+	0.0650579i	−0.673829	+	0.738887i	$0.735352\pi$
$68$		0			0
$69$	−1.11071	+	1.11071i	−0.133713	+	0.133713i
$70$		0			0
$71$			5.92321i			0.702955i	0.936196	+	0.351478i	$0.114321\pi$
$71$			5.92321i			0.702955i	−0.936196	+	0.351478i	$0.885679\pi$
$72$		0			0
$73$	−6.67410			−0.781145			−0.390572	−	0.920572i	$-0.627723\pi$
$73$	−6.67410			−0.781145			−0.390572	+	0.920572i	$0.627723\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−17.6220			−2.00821
$78$		0			0
$79$	0.521498	−	0.521498i	0.0586731	−	0.0586731i	−0.677161	−	0.735834i	$-0.736790\pi$
$79$	0.521498	−	0.521498i	0.0586731	−	0.0586731i	0.735834	+	0.677161i	$0.236790\pi$
$80$		0			0
$81$	8.31477			0.923863
$82$		0			0
$83$	1.78549	+	1.78549i	0.195983	+	0.195983i	0.798275	−	0.602293i	$-0.205746\pi$
$83$	1.78549	+	1.78549i	0.195983	+	0.195983i	−0.602293	+	0.798275i	$0.705746\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	0.410562	+	1.43471i	0.0440169	+	0.153817i
$88$		0			0
$89$	2.73571	−	2.73571i	0.289985	−	0.289985i	−0.547089	−	0.837074i	$-0.684264\pi$
$89$	2.73571	−	2.73571i	0.289985	−	0.289985i	0.837074	+	0.547089i	$0.184264\pi$
$90$		0			0
$91$			20.1213i			2.10928i
$92$		0			0
$93$	−1.70076	+	1.70076i	−0.176361	+	0.176361i
$94$		0			0
$95$		0			0
$96$		0			0
$97$		−	13.8692i		−	1.40821i	−0.710097	−	0.704104i	$-0.751349\pi$
$97$		−	13.8692i		−	1.40821i	0.710097	−	0.704104i	$-0.248651\pi$
$98$		0			0
$99$	−7.13742	−	7.13742i	−0.717338	−	0.717338i
$100$		0			0
$101$	−4.57906	−	4.57906i	−0.455634	−	0.455634i	0.441586	−	0.897219i	$-0.354416\pi$
$101$	−4.57906	−	4.57906i	−0.455634	−	0.455634i	−0.897219	+	0.441586i	$0.854416\pi$
$102$		0			0
$103$	−5.84234	−	5.84234i	−0.575663	−	0.575663i	0.358042	−	0.933705i	$-0.383444\pi$
$103$	−5.84234	−	5.84234i	−0.575663	−	0.575663i	−0.933705	+	0.358042i	$0.883444\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−5.99707	+	5.99707i	−0.579759	+	0.579759i	−0.934837	−	0.355078i	$-0.884454\pi$
$107$	−5.99707	+	5.99707i	−0.579759	+	0.579759i	0.355078	+	0.934837i	$0.384454\pi$
$108$		0			0
$109$	16.6529			1.59506			0.797529	−	0.603280i	$-0.206140\pi$
$109$	16.6529			1.59506			0.797529	+	0.603280i	$0.206140\pi$
$110$		0			0
$111$	0.585075			0.0555329
$112$		0			0
$113$	−11.0432			−1.03886			−0.519430	−	0.854513i	$-0.673856\pi$
$113$	−11.0432			−1.03886			−0.519430	+	0.854513i	$0.673856\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−8.14971	+	8.14971i	−0.753441	+	0.753441i
$118$		0			0
$119$	11.5422	−	11.5422i	1.05807	−	1.05807i
$120$		0			0
$121$			0.923208i			0.0839280i
$122$		0			0
$123$	1.27998	+	1.27998i	0.115412	+	0.115412i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−10.6086			−0.941359			−0.470679	−	0.882304i	$-0.655991\pi$
$127$	−10.6086			−0.941359			−0.470679	+	0.882304i	$0.655991\pi$
$128$		0			0
$129$	0.00306622			0.000269965
$130$		0			0
$131$	11.0207	−	11.0207i	0.962883	−	0.962883i	−0.0364523	−	0.999335i	$-0.511606\pi$
$131$	11.0207	−	11.0207i	0.962883	−	0.962883i	0.999335	+	0.0364523i	$0.0116057\pi$
$132$		0			0
$133$			10.4047i			0.902202i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	15.7035			1.34164			0.670818	−	0.741622i	$-0.265943\pi$
$137$	15.7035			1.34164			0.670818	+	0.741622i	$0.265943\pi$
$138$		0			0
$139$			3.76656i			0.319475i	0.987160	+	0.159738i	$0.0510648\pi$
$139$			3.76656i			0.319475i	−0.987160	+	0.159738i	$0.948935\pi$
$140$		0			0
$141$	−1.84335			−0.155238
$142$		0			0
$143$	13.6143			1.13848
$144$		0			0
$145$		0			0
$146$		0			0
$147$	5.27747			0.435279
$148$		0			0
$149$	1.92627			0.157807			0.0789033	−	0.996882i	$-0.474858\pi$
$149$	1.92627			0.157807			0.0789033	+	0.996882i	$0.474858\pi$
$150$		0			0
$151$		−	5.33507i		−	0.434162i	−0.976154	−	0.217081i	$-0.930346\pi$
$151$		−	5.33507i		−	0.434162i	0.976154	−	0.217081i	$-0.0696535\pi$
$152$		0			0
$153$	9.34987			0.755892
$154$		0			0
$155$		0			0
$156$		0			0
$157$		−	3.55991i		−	0.284112i	−0.989859	−	0.142056i	$-0.954629\pi$
$157$		−	3.55991i		−	0.284112i	0.989859	−	0.142056i	$-0.0453713\pi$
$158$		0			0
$159$	1.73571	−	1.73571i	0.137651	−	0.137651i
$160$		0			0
$161$	28.9277			2.27983
$162$		0			0
$163$	−24.0811			−1.88618			−0.943090	−	0.332538i	$-0.892095\pi$
$163$	−24.0811			−1.88618			−0.943090	+	0.332538i	$0.892095\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	5.11658	+	5.11658i	0.395933	+	0.395933i	0.876796	−	0.480863i	$-0.159676\pi$
$167$	5.11658	+	5.11658i	0.395933	+	0.395933i	−0.480863	+	0.876796i	$0.659676\pi$
$168$		0			0
$169$		−	2.54515i		−	0.195781i
$170$		0			0
$171$	−4.21421	+	4.21421i	−0.322269	+	0.322269i
$172$		0			0
$173$	9.99414	−	9.99414i	0.759840	−	0.759840i	−0.216453	−	0.976293i	$-0.569449\pi$
$173$	9.99414	−	9.99414i	0.759840	−	0.759840i	0.976293	+	0.216453i	$0.0694488\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	2.58125			0.194018
$178$		0			0
$179$	10.7297			0.801975			0.400988	−	0.916083i	$-0.368667\pi$
$179$	10.7297			0.801975			0.400988	+	0.916083i	$0.368667\pi$
$180$		0			0
$181$	11.3148			0.841020			0.420510	−	0.907288i	$-0.361851\pi$
$181$	11.3148			0.841020			0.420510	+	0.907288i	$0.361851\pi$
$182$		0			0
$183$	−0.266898	+	0.266898i	−0.0197297	+	0.0197297i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−7.80957	−	7.80957i	−0.571093	−	0.571093i
$188$		0			0
$189$	5.92321	+	5.92321i	0.430850	+	0.430850i
$190$		0			0
$191$	−5.24813	−	5.24813i	−0.379741	−	0.379741i	0.491268	−	0.871009i	$-0.336534\pi$
$191$	−5.24813	−	5.24813i	−0.379741	−	0.379741i	−0.871009	+	0.491268i	$0.836534\pi$
$192$		0			0
$193$			26.2256i			1.88776i	0.330284	+	0.943882i	$0.392856\pi$
$193$			26.2256i			1.88776i	−0.330284	+	0.943882i	$0.607144\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	2.89925	−	2.89925i	0.206563	−	0.206563i	−0.596242	−	0.802805i	$-0.703340\pi$
$197$	2.89925	−	2.89925i	0.206563	−	0.206563i	0.802805	+	0.596242i	$0.203340\pi$
$198$		0			0
$199$		−	18.1243i		−	1.28480i	−0.766370	−	0.642400i	$-0.777939\pi$
$199$		−	18.1243i		−	1.28480i	0.766370	−	0.642400i	$-0.222061\pi$
$200$		0			0
$201$	−0.147569	+	0.147569i	−0.0104087	+	0.0104087i
$202$		0			0
$203$	13.3367	−	24.0296i	0.936054	−	1.68655i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	11.7166	+	11.7166i	0.814360	+	0.814360i
$208$		0			0
$209$	7.03993			0.486962
$210$		0			0
$211$	−13.4048	+	13.4048i	−0.922823	+	0.922823i	−0.997228	−	0.0744052i	$-0.976294\pi$
$211$	−13.4048	+	13.4048i	−0.922823	+	0.922823i	0.0744052	+	0.997228i	$0.476294\pi$
$212$		0			0
$213$	−1.64140			−0.112467
$214$		0			0
$215$		0			0
$216$		0			0
$217$	44.2954			3.00697
$218$		0			0
$219$		−	1.84948i		−	0.124976i
$220$		0			0
$221$	−8.91719	+	8.91719i	−0.599835	+	0.599835i
$222$		0			0
$223$	10.9483	+	10.9483i	0.733151	+	0.733151i	0.971243	−	0.238091i	$-0.0765218\pi$
$223$	10.9483	+	10.9483i	0.733151	+	0.733151i	−0.238091	+	0.971243i	$0.576522\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	9.95648	−	9.95648i	0.660835	−	0.660835i	−0.294742	−	0.955577i	$-0.595234\pi$
$227$	9.95648	−	9.95648i	0.660835	−	0.660835i	0.955577	+	0.294742i	$0.0952337\pi$
$228$		0			0
$229$	−14.4255	−	14.4255i	−0.953262	−	0.953262i	0.0456931	−	0.998956i	$-0.485450\pi$
$229$	−14.4255	−	14.4255i	−0.953262	−	0.953262i	−0.998956	+	0.0456931i	$0.985450\pi$
$230$		0			0
$231$		−	4.88328i		−	0.321296i
$232$		0			0
$233$	18.6682	+	18.6682i	1.22300	+	1.22300i	0.966561	+	0.256436i	$0.0825483\pi$
$233$	18.6682	+	18.6682i	1.22300	+	1.22300i	0.256436	+	0.966561i	$0.417452\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	0.144514	+	0.144514i	0.00938719	+	0.00938719i
$238$		0			0
$239$		−	20.9277i		−	1.35370i	−0.736119	−	0.676852i	$-0.763344\pi$
$239$		−	20.9277i		−	1.35370i	0.736119	−	0.676852i	$-0.236656\pi$
$240$		0			0
$241$		−	15.6130i		−	1.00572i	−0.864368	−	0.502860i	$-0.832281\pi$
$241$		−	15.6130i		−	1.00572i	0.864368	−	0.502860i	$-0.167719\pi$
$242$		0			0
$243$			7.22833i			0.463698i
$244$		0			0
$245$		0			0
$246$		0			0
$247$		−	8.03839i		−	0.511471i
$248$		0			0
$249$	−0.494782	+	0.494782i	−0.0313556	+	0.0313556i
$250$		0			0
$251$	18.8272	+	18.8272i	1.18836	+	1.18836i	0.977520	+	0.210841i	$0.0676203\pi$
$251$	18.8272	+	18.8272i	1.18836	+	1.18836i	0.210841	+	0.977520i	$0.432380\pi$
$252$		0			0
$253$		−	19.5728i		−	1.23053i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−10.4538	+	10.4538i	−0.652093	+	0.652093i	−0.953497	−	0.301404i	$-0.902545\pi$
$257$	−10.4538	+	10.4538i	−0.652093	+	0.652093i	0.301404	+	0.953497i	$0.402545\pi$
$258$		0			0
$259$	−7.61899	−	7.61899i	−0.473421	−	0.473421i
$260$		0			0
$261$	15.1345	−	4.33093i	0.936800	−	0.268078i
$262$		0			0
$263$			27.1953i			1.67694i	0.544951	+	0.838468i	$0.316548\pi$
$263$			27.1953i			1.67694i	−0.544951	+	0.838468i	$0.683452\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	0.758102	+	0.758102i	0.0463951	+	0.0463951i
$268$		0			0
$269$	−5.99693	−	5.99693i	−0.365640	−	0.365640i	0.500245	−	0.865884i	$-0.333243\pi$
$269$	−5.99693	−	5.99693i	−0.365640	−	0.365640i	−0.865884	+	0.500245i	$0.833243\pi$
$270$		0			0
$271$	2.62607	−	2.62607i	0.159522	−	0.159522i	−0.622833	−	0.782355i	$-0.714018\pi$
$271$	2.62607	−	2.62607i	0.159522	−	0.159522i	0.782355	+	0.622833i	$0.214018\pi$
$272$		0			0
$273$	−5.57587			−0.337467
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−15.8258	+	15.8258i	−0.950882	+	0.950882i	−0.998849	−	0.0479667i	$-0.984726\pi$
$277$	−15.8258	+	15.8258i	−0.950882	+	0.950882i	0.0479667	+	0.998849i	$0.484726\pi$
$278$		0			0
$279$	17.9410	+	17.9410i	1.07410	+	1.07410i
$280$		0			0
$281$	−14.8004			−0.882915			−0.441458	−	0.897282i	$-0.645538\pi$
$281$	−14.8004			−0.882915			−0.441458	+	0.897282i	$0.645538\pi$
$282$		0			0
$283$	−12.3338	+	12.3338i	−0.733171	+	0.733171i	−0.971247	−	0.238075i	$-0.923483\pi$
$283$	−12.3338	+	12.3338i	−0.733171	+	0.733171i	0.238075	+	0.971247i	$0.423483\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		−	33.3365i		−	1.96779i
$288$		0			0
$289$	−6.76962			−0.398213
$290$		0			0
$291$	3.84335			0.225301
$292$		0			0
$293$		−	12.7829i		−	0.746786i	−0.927673	−	0.373393i	$-0.878194\pi$
$293$		−	12.7829i		−	0.746786i	0.927673	−	0.373393i	$-0.121806\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	4.00771	−	4.00771i	0.232551	−	0.232551i
$298$		0			0
$299$	−22.3488			−1.29246
$300$		0			0
$301$	−0.0399290	−	0.0399290i	−0.00230147	−	0.00230147i
$302$		0			0
$303$	1.26892	−	1.26892i	0.0728975	−	0.0728975i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−29.7438			−1.69757			−0.848785	−	0.528739i	$-0.822665\pi$
$307$	−29.7438			−1.69757			−0.848785	+	0.528739i	$0.822665\pi$
$308$		0			0
$309$	1.61899	−	1.61899i	0.0921011	−	0.0921011i
$310$		0			0
$311$	13.8303	+	13.8303i	0.784242	+	0.784242i	0.980544	−	0.196302i	$-0.0628932\pi$
$311$	13.8303	+	13.8303i	0.784242	+	0.784242i	−0.196302	+	0.980544i	$0.562893\pi$
$312$		0			0
$313$	2.25584	+	2.25584i	0.127507	+	0.127507i	0.767981	−	0.640473i	$-0.221262\pi$
$313$	2.25584	+	2.25584i	0.127507	+	0.127507i	−0.640473	+	0.767981i	$0.721262\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$			9.51848i			0.534611i	0.963612	+	0.267305i	$0.0861333\pi$
$317$			9.51848i			0.534611i	−0.963612	+	0.267305i	$0.913867\pi$
$318$		0			0
$319$	−16.2587	−	9.02377i	−0.910311	−	0.505234i
$320$		0			0
$321$	−1.66187	−	1.66187i	−0.0927564	−	0.0927564i
$322$		0			0
$323$	−4.61108	+	4.61108i	−0.256567	+	0.256567i
$324$		0			0
$325$		0			0
$326$		0			0
$327$			4.61474i			0.255196i
$328$		0			0
$329$	24.0045	+	24.0045i	1.32341	+	1.32341i
$330$		0			0
$331$	−21.5660	+	21.5660i	−1.18537	+	1.18537i	−0.207040	+	0.978332i	$0.566383\pi$
$331$	−21.5660	+	21.5660i	−1.18537	+	1.18537i	−0.978332	+	0.207040i	$0.933617\pi$
$332$		0			0
$333$		−	6.17184i		−	0.338215i
$334$		0			0
$335$		0			0
$336$		0			0
$337$		−	3.82596i		−	0.208413i	−0.994556	−	0.104207i	$-0.966770\pi$
$337$		−	3.82596i		−	0.208413i	0.994556	−	0.104207i	$-0.0332303\pi$
$338$		0			0
$339$		−	3.06022i		−	0.166209i
$340$		0			0
$341$		−	29.9707i		−	1.62301i
$342$		0			0
$343$	−43.4641	−	43.4641i	−2.34684	−	2.34684i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−2.51125	−	2.51125i	−0.134811	−	0.134811i	0.636481	−	0.771292i	$-0.280389\pi$
$347$	−2.51125	−	2.51125i	−0.134811	−	0.134811i	−0.771292	+	0.636481i	$0.780389\pi$
$348$		0			0
$349$			29.3592i			1.57156i	0.618504	+	0.785782i	$0.287739\pi$
$349$			29.3592i			1.57156i	−0.618504	+	0.785782i	$0.712261\pi$
$350$		0			0
$351$	−4.57611	−	4.57611i	−0.244255	−	0.244255i
$352$		0			0
$353$	21.8065	−	21.8065i	1.16064	−	1.16064i	0.176310	−	0.984335i	$-0.443584\pi$
$353$	21.8065	−	21.8065i	1.16064	−	1.16064i	0.984335	−	0.176310i	$-0.0564160\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	3.19850	+	3.19850i	0.169282	+	0.169282i
$358$		0			0
$359$	−0.291005	+	0.291005i	−0.0153586	+	0.0153586i	−0.714744	−	0.699386i	$-0.753457\pi$
$359$	−0.291005	+	0.291005i	−0.0153586	+	0.0153586i	0.699386	+	0.714744i	$0.253457\pi$
$360$		0			0
$361$			14.8434i			0.781229i
$362$		0			0
$363$	−0.255833			−0.0134278
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−21.6841			−1.13190			−0.565952	−	0.824439i	$-0.691491\pi$
$367$	−21.6841			−1.13190			−0.565952	+	0.824439i	$0.691491\pi$
$368$		0			0
$369$	13.5023	−	13.5023i	0.702900	−	0.702900i
$370$		0			0
$371$	−45.2057			−2.34696
$372$		0			0
$373$	3.53778	+	3.53778i	0.183179	+	0.183179i	0.792740	−	0.609560i	$-0.208654\pi$
$373$	3.53778	+	3.53778i	0.183179	+	0.183179i	−0.609560	+	0.792740i	$0.708654\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−10.3036	+	18.5646i	−0.530662	+	0.956127i
$378$		0			0
$379$	−11.4921	+	11.4921i	−0.590311	+	0.590311i	−0.937715	−	0.347405i	$-0.887063\pi$
$379$	−11.4921	+	11.4921i	−0.590311	+	0.590311i	0.347405	+	0.937715i	$0.387063\pi$
$380$		0			0
$381$		−	2.93978i		−	0.150609i
$382$		0			0
$383$	−12.1791	+	12.1791i	−0.622324	+	0.622324i	−0.946125	−	0.323801i	$-0.895039\pi$
$383$	−12.1791	+	12.1791i	−0.622324	+	0.622324i	0.323801	+	0.946125i	$0.395039\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		−	0.0323449i		−	0.00164418i
$388$		0			0
$389$	24.4729	+	24.4729i	1.24082	+	1.24082i	0.959659	+	0.281166i	$0.0907210\pi$
$389$	24.4729	+	24.4729i	1.24082	+	1.24082i	0.281166	+	0.959659i	$0.409279\pi$
$390$		0			0
$391$	12.8200	+	12.8200i	0.648335	+	0.648335i
$392$		0			0
$393$	3.05398	+	3.05398i	0.154053	+	0.154053i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−13.9748	+	13.9748i	−0.701376	+	0.701376i	−0.964706	−	0.263330i	$-0.915179\pi$
$397$	−13.9748	+	13.9748i	−0.701376	+	0.701376i	0.263330	+	0.964706i	$0.415179\pi$
$398$		0			0
$399$	−2.88328			−0.144345
$400$		0			0
$401$	−22.3930			−1.11825			−0.559127	−	0.829082i	$-0.688864\pi$
$401$	−22.3930			−1.11825			−0.559127	+	0.829082i	$0.688864\pi$
$402$		0			0
$403$	−34.2214			−1.70469
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−5.15509	+	5.15509i	−0.255528	+	0.255528i
$408$		0			0
$409$	−15.6559	+	15.6559i	−0.774132	+	0.774132i	−0.978826	−	0.204694i	$-0.934380\pi$
$409$	−15.6559	+	15.6559i	−0.774132	+	0.774132i	0.204694	+	0.978826i	$0.434380\pi$
$410$		0			0
$411$			4.35163i			0.214650i
$412$		0			0
$413$	−33.6136	−	33.6136i	−1.65402	−	1.65402i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−1.04376			−0.0511133
$418$		0			0
$419$	−26.4993			−1.29458			−0.647288	−	0.762245i	$-0.724097\pi$
$419$	−26.4993			−1.29458			−0.647288	+	0.762245i	$0.724097\pi$
$420$		0			0
$421$	−3.05048	+	3.05048i	−0.148671	+	0.148671i	−0.777524	−	0.628853i	$-0.783525\pi$
$421$	−3.05048	+	3.05048i	−0.148671	+	0.148671i	0.628853	+	0.777524i	$0.283525\pi$
$422$		0			0
$423$			19.4451i			0.945454i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	6.95122			0.336393
$428$		0			0
$429$			3.77269i			0.182147i
$430$		0			0
$431$	21.8141			1.05075			0.525374	−	0.850871i	$-0.323925\pi$
$431$	21.8141			1.05075			0.525374	+	0.850871i	$0.323925\pi$
$432$		0			0
$433$	37.4314			1.79884			0.899419	−	0.437087i	$-0.143990\pi$
$433$	37.4314			1.79884			0.899419	+	0.437087i	$0.143990\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−11.5566			−0.552825
$438$		0			0
$439$	−12.4315			−0.593323			−0.296661	−	0.954983i	$-0.595873\pi$
$439$	−12.4315			−0.593323			−0.296661	+	0.954983i	$0.595873\pi$
$440$		0			0
$441$		−	55.6709i		−	2.65100i
$442$		0			0
$443$	31.2763			1.48598			0.742990	−	0.669302i	$-0.233407\pi$
$443$	31.2763			1.48598			0.742990	+	0.669302i	$0.233407\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$			0.533796i			0.0252477i
$448$		0			0
$449$	−14.4685	+	14.4685i	−0.682809	+	0.682809i	−0.960632	−	0.277823i	$-0.910387\pi$
$449$	−14.4685	+	14.4685i	−0.682809	+	0.682809i	0.277823	+	0.960632i	$0.410387\pi$
$450$		0			0
$451$	−22.5558			−1.06211
$452$		0			0
$453$	1.47842			0.0694621
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−13.8971	−	13.8971i	−0.650079	−	0.650079i	0.302933	−	0.953012i	$-0.402034\pi$
$457$	−13.8971	−	13.8971i	−0.650079	−	0.650079i	−0.953012	+	0.302933i	$0.902034\pi$
$458$		0			0
$459$			5.25001i			0.245049i
$460$		0			0
$461$	25.7402	−	25.7402i	1.19884	−	1.19884i	0.224330	−	0.974513i	$-0.427981\pi$
$461$	25.7402	−	25.7402i	1.19884	−	1.19884i	0.974513	−	0.224330i	$-0.0720192\pi$
$462$		0			0
$463$	27.0353	−	27.0353i	1.25644	−	1.25644i	0.303654	−	0.952783i	$-0.401793\pi$
$463$	27.0353	−	27.0353i	1.25644	−	1.25644i	0.952783	−	0.303654i	$-0.0982065\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	19.3698			0.896327			0.448164	−	0.893952i	$-0.352078\pi$
$467$	19.3698			0.896327			0.448164	+	0.893952i	$0.352078\pi$
$468$		0			0
$469$	3.84335			0.177469
$470$		0			0
$471$	0.986499			0.0454555
$472$		0			0
$473$	−0.0270164	+	0.0270164i	−0.00124221	+	0.00124221i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−18.3096	−	18.3096i	−0.838341	−	0.838341i
$478$		0			0
$479$	14.4756	+	14.4756i	0.661405	+	0.661405i	0.955711	−	0.294306i	$-0.0950886\pi$
$479$	14.4756	+	14.4756i	0.661405	+	0.661405i	−0.294306	+	0.955711i	$0.595089\pi$
$480$		0			0
$481$	5.88623	+	5.88623i	0.268389	+	0.268389i
$482$		0			0
$483$			8.01626i			0.364753i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−8.15950	+	8.15950i	−0.369742	+	0.369742i	−0.867383	−	0.497641i	$-0.834200\pi$
$487$	−8.15950	+	8.15950i	−0.369742	+	0.369742i	0.497641	+	0.867383i	$0.334200\pi$
$488$		0			0
$489$		−	6.67320i		−	0.301773i
$490$		0			0
$491$	−3.52898	+	3.52898i	−0.159261	+	0.159261i	−0.782239	−	0.622978i	$-0.785922\pi$
$491$	−3.52898	+	3.52898i	−0.159261	+	0.159261i	0.622978	+	0.782239i	$0.285922\pi$
$492$		0			0
$493$	16.5597	−	4.73879i	0.745813	−	0.213424i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	21.3747	+	21.3747i	0.958786	+	0.958786i
$498$		0			0
$499$	35.0662			1.56978			0.784890	−	0.619635i	$-0.212719\pi$
$499$	35.0662			1.56978			0.784890	+	0.619635i	$0.212719\pi$
$500$		0			0
$501$	−1.41787	+	1.41787i	−0.0633459	+	0.0633459i
$502$		0			0
$503$	−32.0156			−1.42751			−0.713753	−	0.700398i	$-0.753006\pi$
$503$	−32.0156			−1.42751			−0.713753	+	0.700398i	$0.753006\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	0.705294			0.0313232
$508$		0			0
$509$		−	7.30864i		−	0.323950i	−0.986795	−	0.161975i	$-0.948214\pi$
$509$		−	7.30864i		−	0.323950i	0.986795	−	0.161975i	$-0.0517863\pi$
$510$		0			0
$511$	−24.0844	+	24.0844i	−1.06543	+	1.06543i
$512$		0			0
$513$	−2.36631	−	2.36631i	−0.104475	−	0.104475i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	16.2417	−	16.2417i	0.714310	−	0.714310i
$518$		0			0
$519$	2.76951	+	2.76951i	0.121568	+	0.121568i
$520$		0			0
$521$		−	27.1673i		−	1.19022i	−0.803644	−	0.595111i	$-0.797108\pi$
$521$		−	27.1673i		−	1.19022i	0.803644	−	0.595111i	$-0.202892\pi$
$522$		0			0
$523$	25.4884	+	25.4884i	1.11453	+	1.11453i	0.992530	+	0.122000i	$0.0389307\pi$
$523$	25.4884	+	25.4884i	1.11453	+	1.11453i	0.122000	+	0.992530i	$0.461069\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	19.6305	+	19.6305i	0.855119	+	0.855119i
$528$		0			0
$529$			9.13022i			0.396966i
$530$		0			0
$531$		−	27.2290i		−	1.18164i
$532$		0			0
$533$			25.7549i			1.11557i
$534$		0			0
$535$		0			0
$536$		0			0
$537$			2.97334i			0.128309i
$538$		0			0
$539$	−46.4997	+	46.4997i	−2.00288	+	2.00288i
$540$		0			0
$541$	−9.20112	−	9.20112i	−0.395587	−	0.395587i	0.481086	−	0.876673i	$-0.340242\pi$
$541$	−9.20112	−	9.20112i	−0.395587	−	0.395587i	−0.876673	+	0.481086i	$0.840242\pi$
$542$		0			0
$543$			3.13547i			0.134556i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−1.30742	+	1.30742i	−0.0559014	+	0.0559014i	−0.734505	−	0.678603i	$-0.762586\pi$
$547$	−1.30742	+	1.30742i	−0.0559014	+	0.0559014i	0.678603	+	0.734505i	$0.262586\pi$
$548$		0			0
$549$	2.81545	+	2.81545i	0.120161	+	0.120161i
$550$		0			0
$551$	−5.32799	+	9.59976i	−0.226980	+	0.408964i
$552$		0			0
$553$		−	3.76379i		−	0.160053i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−8.07074	−	8.07074i	−0.341968	−	0.341968i	0.515139	−	0.857107i	$-0.327740\pi$
$557$	−8.07074	−	8.07074i	−0.341968	−	0.341968i	−0.857107	+	0.515139i	$0.827740\pi$
$558$		0			0
$559$	0.0308481	+	0.0308481i	0.00130473	+	0.00130473i
$560$		0			0
$561$	2.16414	−	2.16414i	0.0913699	−	0.0913699i
$562$		0			0
$563$	−18.3375			−0.772834			−0.386417	−	0.922324i	$-0.626287\pi$
$563$	−18.3375			−0.772834			−0.386417	+	0.922324i	$0.626287\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	30.0050	−	30.0050i	1.26009	−	1.26009i
$568$		0			0
$569$	−3.84028	−	3.84028i	−0.160993	−	0.160993i	0.622013	−	0.783007i	$-0.286315\pi$
$569$	−3.84028	−	3.84028i	−0.160993	−	0.160993i	−0.783007	+	0.622013i	$0.786315\pi$
$570$		0			0
$571$	−19.1966			−0.803352			−0.401676	−	0.915782i	$-0.631572\pi$
$571$	−19.1966			−0.803352			−0.401676	+	0.915782i	$0.631572\pi$
$572$		0			0
$573$	1.45433	−	1.45433i	0.0607553	−	0.0607553i
$574$		0			0
$575$		0			0
$576$		0			0
$577$		−	12.0899i		−	0.503310i	−0.967817	−	0.251655i	$-0.919025\pi$
$577$		−	12.0899i		−	0.503310i	0.967817	−	0.251655i	$-0.0809748\pi$
$578$		0			0
$579$	−7.26747			−0.302026
$580$		0			0
$581$	12.8863			0.534616
$582$		0			0
$583$			30.5866i			1.26677i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	29.8093	−	29.8093i	1.23036	−	1.23036i	0.266539	−	0.963824i	$-0.414120\pi$
$587$	29.8093	−	29.8093i	1.23036	−	1.23036i	0.963824	−	0.266539i	$-0.0858801\pi$
$588$		0			0
$589$	−17.6959			−0.729147
$590$		0			0
$591$	0.803421	+	0.803421i	0.0330483	+	0.0330483i
$592$		0			0
$593$	−26.4315	+	26.4315i	−1.08541	+	1.08541i	−0.0894166	+	0.995994i	$0.528500\pi$
$593$	−26.4315	+	26.4315i	−1.08541	+	1.08541i	−0.995994	+	0.0894166i	$0.971500\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	5.02249			0.205557
$598$		0			0
$599$	−18.8303	+	18.8303i	−0.769383	+	0.769383i	−0.977998	−	0.208615i	$-0.933105\pi$
$599$	−18.8303	+	18.8303i	−0.769383	+	0.769383i	0.208615	+	0.977998i	$0.433105\pi$
$600$		0			0
$601$	−3.65892	−	3.65892i	−0.149250	−	0.149250i	0.628533	−	0.777783i	$-0.283656\pi$
$601$	−3.65892	−	3.65892i	−0.149250	−	0.149250i	−0.777783	+	0.628533i	$0.783656\pi$
$602$		0			0
$603$	1.55667	+	1.55667i	0.0633926	+	0.0633926i
$604$		0			0
$605$		0			0
$606$		0			0
$607$			18.0591i			0.732998i	0.930419	+	0.366499i	$0.119444\pi$
$607$			18.0591i			0.732998i	−0.930419	+	0.366499i	$0.880556\pi$
$608$		0			0
$609$	6.65892	+	3.69578i	0.269833	+	0.149761i
$610$		0			0
$611$	−18.5453	−	18.5453i	−0.750261	−	0.750261i
$612$		0			0
$613$	23.9236	−	23.9236i	0.966265	−	0.966265i	−0.0331846	−	0.999449i	$-0.510565\pi$
$613$	23.9236	−	23.9236i	0.966265	−	0.966265i	0.999449	+	0.0331846i	$0.0105649\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	27.9182i		−	1.12394i	−0.827157	−	0.561971i	$-0.810043\pi$
$617$		−	27.9182i		−	1.12394i	0.827157	−	0.561971i	$-0.189957\pi$
$618$		0			0
$619$	5.79033	+	5.79033i	0.232733	+	0.232733i	0.813832	−	0.581100i	$-0.197377\pi$
$619$	5.79033	+	5.79033i	0.232733	+	0.232733i	−0.581100	+	0.813832i	$0.697377\pi$
$620$		0			0
$621$	−6.57894	+	6.57894i	−0.264004	+	0.264004i
$622$		0			0
$623$		−	19.7444i		−	0.791041i
$624$		0			0
$625$		0			0
$626$		0			0
$627$			1.95086i			0.0779097i
$628$		0			0
$629$		−	6.75306i		−	0.269262i
$630$		0			0
$631$			20.9105i			0.832435i	0.909265	+	0.416217i	$0.136644\pi$
$631$			20.9105i			0.832435i	−0.909265	+	0.416217i	$0.863356\pi$
$632$		0			0
$633$	−3.71464	−	3.71464i	−0.147644	−	0.147644i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	53.0947	+	53.0947i	2.10369	+	2.10369i
$638$		0			0
$639$			17.3148i			0.684962i
$640$		0			0
$641$	27.6469	+	27.6469i	1.09199	+	1.09199i	0.995316	+	0.0966700i	$0.0308191\pi$
$641$	27.6469	+	27.6469i	1.09199	+	1.09199i	0.0966700	+	0.995316i	$0.469181\pi$
$642$		0			0
$643$	21.3853	−	21.3853i	0.843355	−	0.843355i	−0.145939	−	0.989294i	$-0.546620\pi$
$643$	21.3853	−	21.3853i	0.843355	−	0.843355i	0.989294	+	0.145939i	$0.0466202\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−8.24380	−	8.24380i	−0.324097	−	0.324097i	0.526239	−	0.850337i	$-0.323602\pi$
$647$	−8.24380	−	8.24380i	−0.324097	−	0.324097i	−0.850337	+	0.526239i	$0.823602\pi$
$648$		0			0
$649$	−22.7433	+	22.7433i	−0.892753	+	0.892753i
$650$		0			0
$651$			12.2748i			0.481089i
$652$		0			0
$653$	−10.6077			−0.415112			−0.207556	−	0.978223i	$-0.566551\pi$
$653$	−10.6077			−0.415112			−0.207556	+	0.978223i	$0.566551\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−19.5098			−0.761150
$658$		0			0
$659$	−24.6028	+	24.6028i	−0.958390	+	0.958390i	−0.999168	−	0.0407781i	$-0.987016\pi$
$659$	−24.6028	+	24.6028i	−0.958390	+	0.958390i	0.0407781	+	0.999168i	$0.487016\pi$
$660$		0			0
$661$	−33.5482			−1.30487			−0.652437	−	0.757843i	$-0.726253\pi$
$661$	−33.5482			−1.30487			−0.652437	+	0.757843i	$0.726253\pi$
$662$		0			0
$663$	−2.47107	−	2.47107i	−0.0959685	−	0.0959685i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	26.6898	+	14.8132i	1.03343	+	0.573568i
$668$		0			0
$669$	−3.03391	+	3.03391i	−0.117298	+	0.117298i
$670$		0			0
$671$		−	4.70327i		−	0.181568i
$672$		0			0
$673$	−25.9698	+	25.9698i	−1.00106	+	1.00106i	−0.00106328	+	0.999999i	$0.500338\pi$
$673$	−25.9698	+	25.9698i	−1.00106	+	1.00106i	−0.999999	+	0.00106328i	$0.999662\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$		−	29.8421i		−	1.14693i	−0.819232	−	0.573463i	$-0.805600\pi$
$677$		−	29.8421i		−	1.14693i	0.819232	−	0.573463i	$-0.194400\pi$
$678$		0			0
$679$	−50.0490	−	50.0490i	−1.92070	−	1.92070i
$680$		0			0
$681$	2.75907	+	2.75907i	0.105728	+	0.105728i
$682$		0			0
$683$	3.23127	+	3.23127i	0.123641	+	0.123641i	0.766220	−	0.642579i	$-0.222135\pi$
$683$	3.23127	+	3.23127i	0.123641	+	0.123641i	−0.642579	+	0.766220i	$0.722135\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	3.99749	−	3.99749i	0.152514	−	0.152514i
$688$		0			0
$689$	34.9247			1.33052
$690$		0			0
$691$	−7.74933			−0.294798			−0.147399	−	0.989077i	$-0.547090\pi$
$691$	−7.74933			−0.294798			−0.147399	+	0.989077i	$0.547090\pi$
$692$		0			0
$693$	−51.5127			−1.95680
$694$		0			0
$695$		0			0
$696$		0			0
$697$	14.7738	−	14.7738i	0.559598	−	0.559598i
$698$		0			0
$699$	−5.17322	+	5.17322i	−0.195669	+	0.195669i
$700$		0			0
$701$		−	51.8645i		−	1.95889i	−0.201703	−	0.979447i	$-0.564648\pi$
$701$		−	51.8645i		−	1.95889i	0.201703	−	0.979447i	$-0.435352\pi$
$702$		0			0
$703$	3.04377	+	3.04377i	0.114798	+	0.114798i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−33.0483			−1.24291
$708$		0			0
$709$	15.5301			0.583243			0.291622	−	0.956534i	$-0.405805\pi$
$709$	15.5301			0.583243			0.291622	+	0.956534i	$0.405805\pi$
$710$		0			0
$711$	1.52445	−	1.52445i	0.0571712	−	0.0571712i
$712$		0			0
$713$			49.1992i			1.84252i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	5.79936			0.216581
$718$		0			0
$719$		−	34.1182i		−	1.27239i	−0.771527	−	0.636197i	$-0.780507\pi$
$719$		−	34.1182i		−	1.27239i	0.771527	−	0.636197i	$-0.219493\pi$
$720$		0			0
$721$	−42.1657			−1.57033
$722$		0			0
$723$	4.32656			0.160907
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−44.2814			−1.64231			−0.821153	−	0.570708i	$-0.806669\pi$
$727$	−44.2814			−1.64231			−0.821153	+	0.570708i	$0.806669\pi$
$728$		0			0
$729$	22.9412			0.849676
$730$		0			0
$731$		−	0.0353909i		−	0.00130898i
$732$		0			0
$733$	10.2144			0.377278			0.188639	−	0.982047i	$-0.439592\pi$
$733$	10.2144			0.377278			0.188639	+	0.982047i	$0.439592\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	2.60045i		−	0.0957889i
$738$		0			0
$739$	−31.1111	+	31.1111i	−1.14444	+	1.14444i	−0.156812	+	0.987628i	$0.550122\pi$
$739$	−31.1111	+	31.1111i	−1.14444	+	1.14444i	−0.987628	+	0.156812i	$0.949878\pi$
$740$		0			0
$741$	2.22754			0.0818309
$742$		0			0
$743$	−7.80384			−0.286295			−0.143148	−	0.989701i	$-0.545722\pi$
$743$	−7.80384			−0.286295			−0.143148	+	0.989701i	$0.545722\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	5.21935	+	5.21935i	0.190966	+	0.190966i
$748$		0			0
$749$			43.2824i			1.58151i
$750$		0			0
$751$	−24.6059	+	24.6059i	−0.897882	+	0.897882i	−0.995249	−	0.0973668i	$-0.968958\pi$
$751$	−24.6059	+	24.6059i	−0.897882	+	0.897882i	0.0973668	+	0.995249i	$0.468958\pi$
$752$		0			0
$753$	−5.21726	+	5.21726i	−0.190128	+	0.190128i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−5.07696			−0.184525			−0.0922627	−	0.995735i	$-0.529410\pi$
$757$	−5.07696			−0.184525			−0.0922627	+	0.995735i	$0.529410\pi$
$758$		0			0
$759$	5.42389			0.196875
$760$		0			0
$761$	−15.5008			−0.561903			−0.280952	−	0.959722i	$-0.590650\pi$
$761$	−15.5008			−0.561903			−0.280952	+	0.959722i	$0.590650\pi$
$762$		0			0
$763$	60.0942	−	60.0942i	2.17556	−	2.17556i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	25.9690	+	25.9690i	0.937685	+	0.937685i
$768$		0			0
$769$	7.35163	+	7.35163i	0.265107	+	0.265107i	0.827125	−	0.562018i	$-0.189975\pi$
$769$	7.35163	+	7.35163i	0.265107	+	0.265107i	−0.562018	+	0.827125i	$0.689975\pi$
$770$		0			0
$771$	−2.89690	−	2.89690i	−0.104329	−	0.104329i
$772$		0			0
$773$			42.6208i			1.53296i	0.642266	+	0.766482i	$0.277995\pi$
$773$			42.6208i			1.53296i	−0.642266	+	0.766482i	$0.722005\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	2.11132	−	2.11132i	0.0757433	−	0.0757433i
$778$		0			0
$779$			13.3178i			0.477161i
$780$		0			0
$781$	14.4623	−	14.4623i	0.517503	−	0.517503i
$782$		0			0
$783$	2.43185	+	8.49810i	0.0869071	+	0.303697i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−9.33475	−	9.33475i	−0.332748	−	0.332748i	0.520881	−	0.853629i	$-0.325603\pi$
$787$	−9.33475	−	9.33475i	−0.332748	−	0.332748i	−0.853629	+	0.520881i	$0.825603\pi$
$788$		0			0
$789$	−7.53618			−0.268295
$790$		0			0
$791$	−39.8510	+	39.8510i	−1.41694	+	1.41694i
$792$		0			0
$793$	−5.37033			−0.190706
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−51.1951			−1.81342			−0.906711	−	0.421752i	$-0.861415\pi$
$797$	−51.1951			−1.81342			−0.906711	+	0.421752i	$0.861415\pi$
$798$		0			0
$799$			21.2763i			0.752702i
$800$		0			0
$801$	7.99705	−	7.99705i	0.282562	−	0.282562i
$802$		0			0
$803$	16.2958	+	16.2958i	0.575065	+	0.575065i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	1.66183	−	1.66183i	0.0584992	−	0.0584992i
$808$		0			0
$809$	10.8570	+	10.8570i	0.381711	+	0.381711i	0.871718	−	0.490008i	$-0.163006\pi$
$809$	10.8570	+	10.8570i	0.381711	+	0.381711i	−0.490008	+	0.871718i	$0.663006\pi$
$810$		0			0
$811$		−	1.51201i		−	0.0530939i	−0.999648	−	0.0265470i	$-0.991549\pi$
$811$		−	1.51201i		−	0.0530939i	0.999648	−	0.0265470i	$-0.00845115\pi$
$812$		0			0
$813$	0.727719	+	0.727719i	0.0255222	+	0.0255222i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	0.0159515	+	0.0159515i	0.000558073	+	0.000558073i
$818$		0			0
$819$			58.8186i			2.05529i
$820$		0			0
$821$			37.2198i			1.29898i	0.760370	+	0.649490i	$0.225018\pi$
$821$			37.2198i			1.29898i	−0.760370	+	0.649490i	$0.774982\pi$
$822$		0			0
$823$		−	10.8321i		−	0.377582i	−0.982017	−	0.188791i	$-0.939543\pi$
$823$		−	10.8321i		−	0.377582i	0.982017	−	0.188791i	$-0.0604569\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			31.1953i			1.08477i	0.840131	+	0.542384i	$0.182478\pi$
$827$			31.1953i			1.08477i	−0.840131	+	0.542384i	$0.817522\pi$
$828$		0			0
$829$	−5.11672	+	5.11672i	−0.177711	+	0.177711i	−0.790357	−	0.612646i	$-0.790105\pi$
$829$	−5.11672	+	5.11672i	−0.177711	+	0.177711i	0.612646	+	0.790357i	$0.290105\pi$
$830$		0			0
$831$	−4.38555	−	4.38555i	−0.152133	−	0.152133i
$832$		0			0
$833$		−	60.9136i		−	2.11053i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−10.0740	+	10.0740i	−0.348207	+	0.348207i
$838$		0			0
$839$	3.91306	+	3.91306i	0.135094	+	0.135094i	0.771420	−	0.636326i	$-0.219547\pi$
$839$	3.91306	+	3.91306i	0.135094	+	0.135094i	−0.636326	+	0.771420i	$0.719547\pi$
$840$		0			0
$841$	24.6099	−	15.3412i	0.848618	−	0.529007i
$842$		0			0
$843$		−	4.10137i		−	0.141259i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	3.33152	+	3.33152i	0.114472	+	0.114472i
$848$		0			0
$849$	−3.41787	−	3.41787i	−0.117301	−	0.117301i
$850$		0			0
$851$	8.46246	−	8.46246i	0.290089	−	0.290089i
$852$		0			0
$853$	19.3178			0.661430			0.330715	−	0.943731i	$-0.392710\pi$
$853$	19.3178			0.661430			0.330715	+	0.943731i	$0.392710\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−13.6114	+	13.6114i	−0.464958	+	0.464958i	−0.900277	−	0.435318i	$-0.856636\pi$
$857$	−13.6114	+	13.6114i	−0.464958	+	0.464958i	0.435318	+	0.900277i	$0.356636\pi$
$858$		0			0
$859$	−15.7934	−	15.7934i	−0.538864	−	0.538864i	0.384332	−	0.923195i	$-0.374432\pi$
$859$	−15.7934	−	15.7934i	−0.538864	−	0.538864i	−0.923195	+	0.384332i	$0.874432\pi$
$860$		0			0
$861$	9.23798			0.314830
$862$		0			0
$863$	11.8939	−	11.8939i	0.404872	−	0.404872i	−0.475074	−	0.879946i	$-0.657579\pi$
$863$	11.8939	−	11.8939i	0.404872	−	0.404872i	0.879946	+	0.475074i	$0.157579\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		−	1.87595i		−	0.0637107i
$868$		0			0
$869$	−2.54662			−0.0863881
$870$		0			0
$871$	−2.96927			−0.100610
$872$		0			0
$873$		−	40.5427i		−	1.37216i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−5.15424	+	5.15424i	−0.174046	+	0.174046i	−0.788755	−	0.614708i	$-0.789274\pi$
$877$	−5.15424	+	5.15424i	−0.174046	+	0.174046i	0.614708	+	0.788755i	$0.289274\pi$
$878$		0			0
$879$	3.54232			0.119479
$880$		0			0
$881$	−16.8034	−	16.8034i	−0.566122	−	0.566122i	0.364918	−	0.931040i	$-0.381097\pi$
$881$	−16.8034	−	16.8034i	−0.566122	−	0.566122i	−0.931040	+	0.364918i	$0.881097\pi$
$882$		0			0
$883$	−8.17142	+	8.17142i	−0.274990	+	0.274990i	−0.831105	−	0.556115i	$-0.812291\pi$
$883$	−8.17142	+	8.17142i	−0.274990	+	0.274990i	0.556115	+	0.831105i	$0.312291\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−53.1622			−1.78501			−0.892506	−	0.451035i	$-0.851055\pi$
$887$	−53.1622			−1.78501			−0.892506	+	0.451035i	$0.851055\pi$
$888$		0			0
$889$	−38.2824	+	38.2824i	−1.28395	+	1.28395i
$890$		0			0
$891$	−20.3017	−	20.3017i	−0.680132	−	0.680132i
$892$		0			0
$893$	−9.58975	−	9.58975i	−0.320909	−	0.320909i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		−	6.19315i		−	0.206783i
$898$		0			0
$899$	40.8686	+	22.6826i	1.36304	+	0.756506i
$900$		0			0
$901$	−20.0339	−	20.0339i	−0.667426	−	0.667426i
$902$		0			0
$903$	0.0110648	−	0.0110648i	0.000368215	−	0.000368215i
$904$		0			0
$905$		0			0
$906$		0			0
$907$			46.2177i			1.53463i	0.641268	+	0.767317i	$0.278409\pi$
$907$			46.2177i			1.53463i	−0.641268	+	0.767317i	$0.721591\pi$
$908$		0			0
$909$	−13.3855	−	13.3855i	−0.443971	−	0.443971i
$910$		0			0
$911$	18.8777	−	18.8777i	0.625445	−	0.625445i	−0.321473	−	0.946919i	$-0.604178\pi$
$911$	18.8777	−	18.8777i	0.625445	−	0.625445i	0.946919	+	0.321473i	$0.104178\pi$
$912$		0			0
$913$		−	8.71904i		−	0.288558i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		−	79.5393i		−	2.62662i
$918$		0			0
$919$		−	47.2683i		−	1.55924i	−0.626255	−	0.779618i	$-0.715413\pi$
$919$		−	47.2683i		−	1.55924i	0.626255	−	0.779618i	$-0.284587\pi$
$920$		0			0
$921$		−	8.24240i		−	0.271596i
$922$		0			0
$923$	−16.5135	−	16.5135i	−0.543549	−	0.543549i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−17.0784	−	17.0784i	−0.560928	−	0.560928i
$928$		0			0
$929$		−	13.2380i		−	0.434324i	−0.976136	−	0.217162i	$-0.930320\pi$
$929$		−	13.2380i		−	0.434324i	0.976136	−	0.217162i	$-0.0696800\pi$
$930$		0			0
$931$	27.4553	+	27.4553i	0.899810	+	0.899810i
$932$		0			0
$933$	−3.83255	+	3.83255i	−0.125472	+	0.125472i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	25.4724	+	25.4724i	0.832148	+	0.832148i	0.987810	−	0.155662i	$-0.0497512\pi$
$937$	25.4724	+	25.4724i	0.832148	+	0.832148i	−0.155662	+	0.987810i	$0.549751\pi$
$938$		0			0
$939$	−0.625122	+	0.625122i	−0.0204001	+	0.0204001i
$940$		0			0
$941$		−	23.8675i		−	0.778059i	−0.921225	−	0.389029i	$-0.872810\pi$
$941$		−	23.8675i		−	0.778059i	0.921225	−	0.389029i	$-0.127190\pi$
$942$		0			0
$943$	37.0270			1.20577
$944$		0			0
$945$		0			0
$946$		0			0
$947$	2.28285			0.0741828			0.0370914	−	0.999312i	$-0.488191\pi$
$947$	2.28285			0.0741828			0.0370914	+	0.999312i	$0.488191\pi$
$948$		0			0
$949$	18.6070	−	18.6070i	0.604007	−	0.604007i
$950$		0			0
$951$	−2.63770			−0.0855331
$952$		0			0
$953$	−8.45384	−	8.45384i	−0.273847	−	0.273847i	0.556800	−	0.830647i	$-0.312029\pi$
$953$	−8.45384	−	8.45384i	−0.273847	−	0.273847i	−0.830647	+	0.556800i	$0.812029\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	2.50061	−	4.50550i	0.0808331	−	0.145642i
$958$		0			0
$959$	56.6680	−	56.6680i	1.82990	−	1.82990i
$960$		0			0
$961$			44.3359i			1.43019i
$962$		0			0
$963$	−17.5307	+	17.5307i	−0.564918	+	0.564918i
$964$		0			0
$965$		0			0
$966$		0			0
$967$			27.3592i			0.879811i	0.898044	+	0.439906i	$0.144988\pi$
$967$			27.3592i			0.879811i	−0.898044	+	0.439906i	$0.855012\pi$
$968$		0			0
$969$	−1.27779	−	1.27779i	−0.0410486	−	0.0410486i
$970$		0			0
$971$	−19.8439	−	19.8439i	−0.636820	−	0.636820i	0.312950	−	0.949770i	$-0.398683\pi$
$971$	−19.8439	−	19.8439i	−0.636820	−	0.636820i	−0.949770	+	0.312950i	$0.898683\pi$
$972$		0			0
$973$	13.5921	+	13.5921i	0.435744	+	0.435744i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−37.7220	+	37.7220i	−1.20683	+	1.20683i	−0.234787	+	0.972047i	$0.575439\pi$
$977$	−37.7220	+	37.7220i	−1.20683	+	1.20683i	−0.972047	+	0.234787i	$0.924561\pi$
$978$		0			0
$979$	−13.3592			−0.426963
$980$		0			0
$981$	48.6799			1.55423
$982$		0			0
$983$	−3.04910			−0.0972510			−0.0486255	−	0.998817i	$-0.515484\pi$
$983$	−3.04910			−0.0972510			−0.0486255	+	0.998817i	$0.515484\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−6.65198	+	6.65198i	−0.211735	+	0.211735i
$988$		0			0
$989$	0.0443494	−	0.0443494i	0.00141023	−	0.00141023i
$990$		0			0
$991$			4.05650i			0.128859i	0.997922	+	0.0644294i	$0.0205227\pi$
$991$			4.05650i			0.128859i	−0.997922	+	0.0644294i	$0.979477\pi$
$992$		0			0
$993$	−5.97621	−	5.97621i	−0.189649	−	0.189649i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	42.1611			1.33526			0.667628	−	0.744495i	$-0.267310\pi$
$997$	42.1611			1.33526			0.667628	+	0.744495i	$0.267310\pi$
$998$		0			0
$999$	3.46552			0.109644

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2900.2.j.c.2593.5	yes	16
5.2	odd	4		2900.2.s.c.157.5	yes	16
5.3	odd	4		2900.2.s.c.157.4	yes	16
5.4	even	2	inner	2900.2.j.c.2593.4	yes	16
29.17	odd	4		2900.2.s.c.1293.5	yes	16
145.17	even	4	inner	2900.2.j.c.1757.4	✓	16
145.104	odd	4		2900.2.s.c.1293.4	yes	16
145.133	even	4	inner	2900.2.j.c.1757.5	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2900.2.j.c.1757.4	✓	16	145.17	even	4	inner
2900.2.j.c.1757.5	yes	16	145.133	even	4	inner
2900.2.j.c.2593.4	yes	16	5.4	even	2	inner
2900.2.j.c.2593.5	yes	16	1.1	even	1	trivial
2900.2.s.c.157.4	yes	16	5.3	odd	4
2900.2.s.c.157.5	yes	16	5.2	odd	4
2900.2.s.c.1293.4	yes	16	145.104	odd	4
2900.2.s.c.1293.5	yes	16	29.17	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 2900 = 2^{2} \cdot 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2900.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+0.277113i q^{3} +(3.60863 - 3.60863i) q^{7} +2.92321 q^{9} +(-2.44164 - 2.44164i) q^{11} +(-2.78793 + 2.78793i) q^{13} +3.19850 q^{17} +(-1.44164 + 1.44164i) q^{19} +(1.00000 + 1.00000i) q^{21} +(4.00813 + 4.00813i) q^{23} +1.64140i q^{27} +(5.17735 - 1.48157i) q^{29} +(6.13742 + 6.13742i) q^{31} +(0.676611 - 0.676611i) q^{33} -2.11132i q^{37} +(-0.772573 - 0.772573i) q^{39} +(4.61899 - 4.61899i) q^{41} -0.0110648i q^{43} +6.65198i q^{47} -19.0445i q^{49} +0.886345i q^{51} +(-6.26354 - 6.26354i) q^{53} +(-0.399497 - 0.399497i) q^{57} -9.31477i q^{59} +(0.963137 + 0.963137i) q^{61} +(10.5488 - 10.5488i) q^{63} +(0.532522 + 0.532522i) q^{67} +(-1.11071 + 1.11071i) q^{69} +5.92321i q^{71} -6.67410 q^{73} -17.6220 q^{77} +(0.521498 - 0.521498i) q^{79} +8.31477 q^{81} +(1.78549 + 1.78549i) q^{83} +(0.410562 + 1.43471i) q^{87} +(2.73571 - 2.73571i) q^{89} +20.1213i q^{91} +(-1.70076 + 1.70076i) q^{93} -13.8692i q^{97} +(-7.13742 - 7.13742i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{9} - 4 q^{11} + 12 q^{19} + 16 q^{21} + 28 q^{29} + 28 q^{31} - 32 q^{39} - 16 q^{41} - 24 q^{61} + 72 q^{69} + 4 q^{79} + 8 q^{81} + 24 q^{89} - 44 q^{99}+O(q^{100}) \) 16 * q - 8 * q^9 - 4 * q^11 + 12 * q^19 + 16 * q^21 + 28 * q^29 + 28 * q^31 - 32 * q^39 - 16 * q^41 - 24 * q^61 + 72 * q^69 + 4 * q^79 + 8 * q^81 + 24 * q^89 - 44 * q^99

Introduction

L-functions

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