LMFDB - Embedded newform 1450.2.j.h.1293.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1450,2,Mod(157,1450)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1450, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1450.157"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1450 = 2 \cdot 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1450.j (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,-12,0,0,4,0,28,0,10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$11.5783082931$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 18x^{10} + 119x^{8} + 346x^{6} + 397x^{4} + 80x^{2} + 4 $ x^12 + 18x^10 + 119x^8 + 346x^6 + 397x^4 + 80*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 290)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1293.5
Root			$-2.31763i$ of defining polynomial
Character	$\chi$	$=$	1450.1293
Dual form			1450.2.j.h.157.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000i q^{2} +2.37143 q^{3} -1.00000 q^{4} +2.37143i q^{6} +(-1.54761 + 1.54761i) q^{7} -1.00000i q^{8} +2.62368 q^{9} +(-1.74911 + 1.74911i) q^{11} -2.37143 q^{12} +(-4.70293 + 4.70293i) q^{13} +(-1.54761 - 1.54761i) q^{14} +1.00000 q^{16} +5.49611i q^{17} +2.62368i q^{18} +(-4.80216 - 4.80216i) q^{19} +(-3.67005 + 3.67005i) q^{21} +(-1.74911 - 1.74911i) q^{22} +(-1.90213 - 1.90213i) q^{23} -2.37143i q^{24} +(-4.70293 - 4.70293i) q^{26} -0.892408 q^{27} +(1.54761 - 1.54761i) q^{28} +(2.50843 - 4.76527i) q^{29} +(1.34066 - 1.34066i) q^{31} +1.00000i q^{32} +(-4.14789 + 4.14789i) q^{33} -5.49611 q^{34} -2.62368 q^{36} +9.27054 q^{37} +(4.80216 - 4.80216i) q^{38} +(-11.1527 + 11.1527i) q^{39} +(6.23227 + 6.23227i) q^{41} +(-3.67005 - 3.67005i) q^{42} -8.13887 q^{43} +(1.74911 - 1.74911i) q^{44} +(1.90213 - 1.90213i) q^{46} -3.34747 q^{47} +2.37143 q^{48} +2.20981i q^{49} +13.0336i q^{51} +(4.70293 - 4.70293i) q^{52} +(1.34066 + 1.34066i) q^{53} -0.892408i q^{54} +(1.54761 + 1.54761i) q^{56} +(-11.3880 - 11.3880i) q^{57} +(4.76527 + 2.50843i) q^{58} +8.03932i q^{59} +(-1.90213 + 1.90213i) q^{61} +(1.34066 + 1.34066i) q^{62} +(-4.06044 + 4.06044i) q^{63} -1.00000 q^{64} +(-4.14789 - 4.14789i) q^{66} +(7.71402 + 7.71402i) q^{67} -5.49611i q^{68} +(-4.51078 - 4.51078i) q^{69} -3.31237i q^{71} -2.62368i q^{72} -2.80389i q^{73} +9.27054i q^{74} +(4.80216 + 4.80216i) q^{76} -5.41388i q^{77} +(-11.1527 - 11.1527i) q^{78} +(-1.05529 - 1.05529i) q^{79} -9.98733 q^{81} +(-6.23227 + 6.23227i) q^{82} +(1.00000 + 1.00000i) q^{83} +(3.67005 - 3.67005i) q^{84} -8.13887i q^{86} +(5.94856 - 11.3005i) q^{87} +(1.74911 + 1.74911i) q^{88} +(7.44059 + 7.44059i) q^{89} -14.5566i q^{91} +(1.90213 + 1.90213i) q^{92} +(3.17928 - 3.17928i) q^{93} -3.34747i q^{94} +2.37143i q^{96} -6.98037 q^{97} -2.20981 q^{98} +(-4.58911 + 4.58911i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{4} + 4 q^{7} + 28 q^{9} + 10 q^{11} - 2 q^{13} + 4 q^{14} + 12 q^{16} - 16 q^{19} - 16 q^{21} + 10 q^{22} - 4 q^{23} - 2 q^{26} - 12 q^{27} - 4 q^{28} + 20 q^{29} + 18 q^{31} + 6 q^{33} - 28 q^{36}+ \cdots + 36 q^{99}+O(q^{100}) $ 12 * q - 12 * q^4 + 4 * q^7 + 28 * q^9 + 10 * q^11 - 2 * q^13 + 4 * q^14 + 12 * q^16 - 16 * q^19 - 16 * q^21 + 10 * q^22 - 4 * q^23 - 2 * q^26 - 12 * q^27 - 4 * q^28 + 20 * q^29 + 18 * q^31 + 6 * q^33 - 28 * q^36 + 16 * q^38 - 38 * q^39 + 36 * q^41 - 16 * q^42 + 12 * q^43 - 10 * q^44 + 4 * q^46 - 20 * q^47 + 2 * q^52 + 18 * q^53 - 4 * q^56 + 32 * q^57 - 16 * q^58 - 4 * q^61 + 18 * q^62 + 24 * q^63 - 12 * q^64 + 6 * q^66 + 12 * q^67 + 12 * q^69 + 16 * q^76 - 38 * q^78 + 30 * q^79 + 44 * q^81 - 36 * q^82 + 12 * q^83 + 16 * q^84 + 16 * q^87 - 10 * q^88 + 20 * q^89 + 4 * q^92 - 2 * q^93 - 76 * q^97 - 16 * q^98 + 36 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1450\mathbb{Z}\right)^\times$.

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

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	2.37143			1.36915			0.684573	−	0.728944i	$-0.259989\pi$
$3$	2.37143			1.36915			0.684573	+	0.728944i	$0.259989\pi$
$4$	−1.00000			−0.500000
$5$		0			0
$5$		0			0
$6$			2.37143i			0.968133i
$7$	−1.54761	+	1.54761i	−0.584942	+	0.584942i	−0.936257	−	0.351315i	$-0.885734\pi$
$7$	−1.54761	+	1.54761i	−0.584942	+	0.584942i	0.351315	+	0.936257i	$0.385734\pi$
$8$		−	1.00000i		−	0.353553i
$9$	2.62368			0.874561
$10$		0			0
$11$	−1.74911	+	1.74911i	−0.527376	+	0.527376i	−0.919789	−	0.392413i	$-0.871640\pi$
$11$	−1.74911	+	1.74911i	−0.527376	+	0.527376i	0.392413	+	0.919789i	$0.371640\pi$
$12$	−2.37143			−0.684573
$13$	−4.70293	+	4.70293i	−1.30436	+	1.30436i	−0.378935	+	0.925423i	$0.623710\pi$
$13$	−4.70293	+	4.70293i	−1.30436	+	1.30436i	−0.925423	+	0.378935i	$0.876290\pi$
$14$	−1.54761	−	1.54761i	−0.413616	−	0.413616i
$15$		0			0
$16$	1.00000			0.250000
$17$			5.49611i			1.33300i	0.745504	+	0.666501i	$0.232209\pi$
$17$			5.49611i			1.33300i	−0.745504	+	0.666501i	$0.767791\pi$
$18$			2.62368i			0.618408i
$19$	−4.80216	−	4.80216i	−1.10169	−	1.10169i	−0.994207	−	0.107484i	$-0.965721\pi$
$19$	−4.80216	−	4.80216i	−1.10169	−	1.10169i	−0.107484	−	0.994207i	$-0.534279\pi$
$20$		0			0
$21$	−3.67005	+	3.67005i	−0.800871	+	0.800871i
$22$	−1.74911	−	1.74911i	−0.372911	−	0.372911i
$23$	−1.90213	−	1.90213i	−0.396622	−	0.396622i	0.480418	−	0.877040i	$-0.340485\pi$
$23$	−1.90213	−	1.90213i	−0.396622	−	0.396622i	−0.877040	+	0.480418i	$0.840485\pi$
$24$		−	2.37143i		−	0.484066i
$25$		0			0
$26$	−4.70293	−	4.70293i	−0.922321	−	0.922321i
$27$	−0.892408			−0.171744
$28$	1.54761	−	1.54761i	0.292471	−	0.292471i
$29$	2.50843	−	4.76527i	0.465803	−	0.884889i
$29$	2.50843	−	4.76527i	0.465803	−	0.884889i
$30$		0			0
$31$	1.34066	−	1.34066i	0.240789	−	0.240789i	−0.576387	−	0.817177i	$-0.695538\pi$
$31$	1.34066	−	1.34066i	0.240789	−	0.240789i	0.817177	+	0.576387i	$0.195538\pi$
$32$			1.00000i			0.176777i
$33$	−4.14789	+	4.14789i	−0.722055	+	0.722055i
$34$	−5.49611			−0.942575
$35$		0			0
$36$	−2.62368			−0.437281
$37$	9.27054			1.52407			0.762034	−	0.647537i	$-0.224201\pi$
$37$	9.27054			1.52407			0.762034	+	0.647537i	$0.224201\pi$
$38$	4.80216	−	4.80216i	0.779013	−	0.779013i
$39$	−11.1527	+	11.1527i	−1.78586	+	1.78586i
$40$		0			0
$41$	6.23227	+	6.23227i	0.973317	+	0.973317i	0.999653	−	0.0263359i	$-0.00838394\pi$
$41$	6.23227	+	6.23227i	0.973317	+	0.973317i	−0.0263359	+	0.999653i	$0.508384\pi$
$42$	−3.67005	−	3.67005i	−0.566301	−	0.566301i
$43$	−8.13887			−1.24117			−0.620583	−	0.784141i	$-0.713104\pi$
$43$	−8.13887			−1.24117			−0.620583	+	0.784141i	$0.713104\pi$
$44$	1.74911	−	1.74911i	0.263688	−	0.263688i
$45$		0			0
$46$	1.90213	−	1.90213i	0.280454	−	0.280454i
$47$	−3.34747			−0.488279			−0.244140	−	0.969740i	$-0.578506\pi$
$47$	−3.34747			−0.488279			−0.244140	+	0.969740i	$0.578506\pi$
$48$	2.37143			0.342287
$49$			2.20981i			0.315687i
$50$		0			0
$51$			13.0336i			1.82508i
$52$	4.70293	−	4.70293i	0.652179	−	0.652179i
$53$	1.34066	+	1.34066i	0.184154	+	0.184154i	0.793163	−	0.609009i	$-0.208433\pi$
$53$	1.34066	+	1.34066i	0.184154	+	0.184154i	−0.609009	+	0.793163i	$0.708433\pi$
$54$		−	0.892408i		−	0.121441i
$55$		0			0
$56$	1.54761	+	1.54761i	0.206808	+	0.206808i
$57$	−11.3880	−	11.3880i	−1.50838	−	1.50838i
$58$	4.76527	+	2.50843i	0.625711	+	0.329372i
$59$			8.03932i			1.04663i	0.852139	+	0.523315i	$0.175305\pi$
$59$			8.03932i			1.04663i	−0.852139	+	0.523315i	$0.824695\pi$
$60$		0			0
$61$	−1.90213	+	1.90213i	−0.243543	+	0.243543i	−0.818314	−	0.574771i	$-0.805091\pi$
$61$	−1.90213	+	1.90213i	−0.243543	+	0.243543i	0.574771	+	0.818314i	$0.305091\pi$
$62$	1.34066	+	1.34066i	0.170264	+	0.170264i
$63$	−4.06044	+	4.06044i	−0.511567	+	0.511567i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−4.14789	−	4.14789i	−0.510570	−	0.510570i
$67$	7.71402	+	7.71402i	0.942417	+	0.942417i	0.998430	−	0.0560127i	$-0.0178387\pi$
$67$	7.71402	+	7.71402i	0.942417	+	0.942417i	−0.0560127	+	0.998430i	$0.517839\pi$
$68$		−	5.49611i		−	0.666501i
$69$	−4.51078	−	4.51078i	−0.543034	−	0.543034i
$70$		0			0
$71$		−	3.31237i		−	0.393106i	−0.980493	−	0.196553i	$-0.937025\pi$
$71$		−	3.31237i		−	0.393106i	0.980493	−	0.196553i	$-0.0629748\pi$
$72$		−	2.62368i		−	0.309204i
$73$		−	2.80389i		−	0.328170i	−0.986446	−	0.164085i	$-0.947533\pi$
$73$		−	2.80389i		−	0.328170i	0.986446	−	0.164085i	$-0.0524672\pi$
$74$			9.27054i			1.07768i
$75$		0			0
$76$	4.80216	+	4.80216i	0.550845	+	0.550845i
$77$		−	5.41388i		−	0.616969i
$78$	−11.1527	−	11.1527i	−1.26279	−	1.26279i
$79$	−1.05529	−	1.05529i	−0.118729	−	0.118729i	0.645246	−	0.763975i	$-0.276755\pi$
$79$	−1.05529	−	1.05529i	−0.118729	−	0.118729i	−0.763975	+	0.645246i	$0.776755\pi$
$80$		0			0
$81$	−9.98733			−1.10970
$82$	−6.23227	+	6.23227i	−0.688239	+	0.688239i
$83$	1.00000	+	1.00000i	0.109764	+	0.109764i	0.759856	−	0.650092i	$-0.225269\pi$
$83$	1.00000	+	1.00000i	0.109764	+	0.109764i	−0.650092	+	0.759856i	$0.725269\pi$
$84$	3.67005	−	3.67005i	0.400435	−	0.400435i
$85$		0			0
$86$		−	8.13887i		−	0.877636i
$87$	5.94856	−	11.3005i	0.637752	−	1.21154i
$88$	1.74911	+	1.74911i	0.186456	+	0.186456i
$89$	7.44059	+	7.44059i	0.788700	+	0.788700i	0.981281	−	0.192581i	$-0.0616857\pi$
$89$	7.44059	+	7.44059i	0.788700	+	0.788700i	−0.192581	+	0.981281i	$0.561686\pi$
$90$		0			0
$91$		−	14.5566i		−	1.52595i
$92$	1.90213	+	1.90213i	0.198311	+	0.198311i
$93$	3.17928	−	3.17928i	0.329676	−	0.329676i
$94$		−	3.34747i		−	0.345266i
$95$		0			0
$96$			2.37143i			0.242033i
$97$	−6.98037			−0.708749			−0.354375	−	0.935104i	$-0.615306\pi$
$97$	−6.98037			−0.708749			−0.354375	+	0.935104i	$0.615306\pi$
$98$	−2.20981			−0.223224
$99$	−4.58911	+	4.58911i	−0.461223	+	0.461223i
$100$		0			0
$101$	−8.86530	+	8.86530i	−0.882130	+	0.882130i	−0.993751	−	0.111620i	$-0.964396\pi$
$101$	−8.86530	+	8.86530i	−0.882130	+	0.882130i	0.111620	+	0.993751i	$0.464396\pi$
$102$	−13.0336			−1.29052
$103$	8.53083	+	8.53083i	0.840568	+	0.840568i	0.988933	−	0.148365i	$-0.0474009\pi$
$103$	8.53083	+	8.53083i	0.840568	+	0.840568i	−0.148365	+	0.988933i	$0.547401\pi$
$104$	4.70293	+	4.70293i	0.461160	+	0.461160i
$105$		0			0
$106$	−1.34066	+	1.34066i	−0.130216	+	0.130216i
$107$	10.3819	−	10.3819i	1.00366	−	1.00366i	0.00366325	−	0.999993i	$-0.498834\pi$
$107$	10.3819	−	10.3819i	1.00366	−	1.00366i	0.999993	−	0.00366325i	$-0.00116605\pi$
$108$	0.892408			0.0858720
$109$	2.50284			0.239729			0.119864	−	0.992790i	$-0.461754\pi$
$109$	2.50284			0.239729			0.119864	+	0.992790i	$0.461754\pi$
$110$		0			0
$111$	21.9844			2.08667
$112$	−1.54761	+	1.54761i	−0.146235	+	0.146235i
$113$			4.50808i			0.424084i	0.977261	+	0.212042i	$0.0680114\pi$
$113$			4.50808i			0.424084i	−0.977261	+	0.212042i	$0.931989\pi$
$114$	11.3880	−	11.3880i	1.06658	−	1.06658i
$115$		0			0
$116$	−2.50843	+	4.76527i	−0.232901	+	0.442444i
$117$	−12.3390	+	12.3390i	−1.14074	+	1.14074i
$118$	−8.03932			−0.740079
$119$	−8.50584	−	8.50584i	−0.779729	−	0.779729i
$120$		0			0
$121$			4.88123i			0.443749i
$122$	−1.90213	−	1.90213i	−0.172211	−	0.172211i
$123$	14.7794	+	14.7794i	1.33261	+	1.33261i
$124$	−1.34066	+	1.34066i	−0.120395	+	0.120395i
$125$		0			0
$126$	−4.06044	−	4.06044i	−0.361733	−	0.361733i
$127$		−	5.40735i		−	0.479825i	−0.970795	−	0.239913i	$-0.922881\pi$
$127$		−	5.40735i		−	0.479825i	0.970795	−	0.239913i	$-0.0771188\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−19.3008			−1.69934
$130$		0			0
$131$	10.5711	+	10.5711i	0.923600	+	0.923600i	0.997282	−	0.0736817i	$-0.0234749\pi$
$131$	10.5711	+	10.5711i	0.923600	+	0.923600i	−0.0736817	+	0.997282i	$0.523475\pi$
$132$	4.14789	−	4.14789i	0.361028	−	0.361028i
$133$	14.8637			1.28885
$134$	−7.71402	+	7.71402i	−0.666390	+	0.666390i
$135$		0			0
$136$	5.49611			0.471288
$137$		−	5.27765i		−	0.450900i	−0.974255	−	0.225450i	$-0.927615\pi$
$137$		−	5.27765i		−	0.450900i	0.974255	−	0.225450i	$-0.0723852\pi$
$138$	4.51078	−	4.51078i	0.383983	−	0.383983i
$139$			5.16233i			0.437863i	0.975740	+	0.218932i	$0.0702572\pi$
$139$			5.16233i			0.437863i	−0.975740	+	0.218932i	$0.929743\pi$
$140$		0			0
$141$	−7.93830			−0.668526
$142$	3.31237			0.277968
$143$		−	16.4519i		−	1.37578i
$144$	2.62368			0.218640
$145$		0			0
$146$	2.80389			0.232051
$147$			5.24040i			0.432221i
$148$	−9.27054			−0.762034
$149$	−9.75656			−0.799288			−0.399644	−	0.916670i	$-0.630866\pi$
$149$	−9.75656			−0.799288			−0.399644	+	0.916670i	$0.630866\pi$
$150$		0			0
$151$		−	6.29344i		−	0.512153i	−0.966657	−	0.256076i	$-0.917570\pi$
$151$		−	6.29344i		−	0.512153i	0.966657	−	0.256076i	$-0.0824299\pi$
$152$	−4.80216	+	4.80216i	−0.389507	+	0.389507i
$153$			14.4201i			1.16579i
$154$	5.41388			0.436263
$155$		0			0
$156$	11.1527	−	11.1527i	0.892929	−	0.892929i
$157$	23.4621			1.87248			0.936240	−	0.351360i	$-0.114281\pi$
$157$	23.4621			1.87248			0.936240	+	0.351360i	$0.114281\pi$
$158$	1.05529	−	1.05529i	0.0839543	−	0.0839543i
$159$	3.17928	+	3.17928i	0.252133	+	0.252133i
$160$		0			0
$161$	5.88752			0.464002
$162$		−	9.98733i		−	0.784679i
$163$			5.60923i			0.439349i	0.975573	+	0.219674i	$0.0704995\pi$
$163$			5.60923i			0.439349i	−0.975573	+	0.219674i	$0.929501\pi$
$164$	−6.23227	−	6.23227i	−0.486659	−	0.486659i
$165$		0			0
$166$	−1.00000	+	1.00000i	−0.0776151	+	0.0776151i
$167$	−10.7430	−	10.7430i	−0.831322	−	0.831322i	0.156376	−	0.987698i	$-0.450019\pi$
$167$	−10.7430	−	10.7430i	−0.831322	−	0.831322i	−0.987698	+	0.156376i	$0.950019\pi$
$168$	3.67005	+	3.67005i	0.283151	+	0.283151i
$169$		−	31.2351i		−	2.40270i
$170$		0			0
$171$	−12.5993	−	12.5993i	−0.963496	−	0.963496i
$172$	8.13887			0.620583
$173$	2.54018	−	2.54018i	0.193126	−	0.193126i	−0.603919	−	0.797046i	$-0.706395\pi$
$173$	2.54018	−	2.54018i	0.193126	−	0.193126i	0.797046	+	0.603919i	$0.206395\pi$
$174$	11.3005	+	5.94856i	0.856689	+	0.450959i
$175$		0			0
$176$	−1.74911	+	1.74911i	−0.131844	+	0.131844i
$177$			19.0647i			1.43299i
$178$	−7.44059	+	7.44059i	−0.557695	+	0.557695i
$179$	13.1139			0.980176			0.490088	−	0.871673i	$-0.336965\pi$
$179$	13.1139			0.980176			0.490088	+	0.871673i	$0.336965\pi$
$180$		0			0
$181$	6.48628			0.482121			0.241061	−	0.970510i	$-0.422505\pi$
$181$	6.48628			0.482121			0.241061	+	0.970510i	$0.422505\pi$
$182$	14.5566			1.07901
$183$	−4.51078	+	4.51078i	−0.333446	+	0.333446i
$184$	−1.90213	+	1.90213i	−0.140227	+	0.140227i
$185$		0			0
$186$	3.17928	+	3.17928i	0.233116	+	0.233116i
$187$	−9.61330	−	9.61330i	−0.702994	−	0.702994i
$188$	3.34747			0.244140
$189$	1.38110	−	1.38110i	0.100460	−	0.100460i
$190$		0			0
$191$	15.2545	−	15.2545i	1.10378	−	1.10378i	0.109828	−	0.993951i	$-0.464970\pi$
$191$	15.2545	−	15.2545i	1.10378	−	1.10378i	0.993951	−	0.109828i	$-0.0350299\pi$
$192$	−2.37143			−0.171143
$193$	−10.2509			−0.737877			−0.368938	−	0.929454i	$-0.620279\pi$
$193$	−10.2509			−0.737877			−0.368938	+	0.929454i	$0.620279\pi$
$194$		−	6.98037i		−	0.501161i
$195$		0			0
$196$		−	2.20981i		−	0.157843i
$197$	3.43016	−	3.43016i	0.244389	−	0.244389i	−0.574274	−	0.818663i	$-0.694716\pi$
$197$	3.43016	−	3.43016i	0.244389	−	0.244389i	0.818663	+	0.574274i	$0.194716\pi$
$198$	−4.58911	−	4.58911i	−0.326134	−	0.326134i
$199$			5.28540i			0.374672i	0.982296	+	0.187336i	$0.0599853\pi$
$199$			5.28540i			0.374672i	−0.982296	+	0.187336i	$0.940015\pi$
$200$		0			0
$201$	18.2933	+	18.2933i	1.29031	+	1.29031i
$202$	−8.86530	−	8.86530i	−0.623760	−	0.623760i
$203$	3.49272	+	11.2568i	0.245141	+	0.790076i
$204$		−	13.0336i		−	0.912538i
$205$		0			0
$206$	−8.53083	+	8.53083i	−0.594371	+	0.594371i
$207$	−4.99060	−	4.99060i	−0.346870	−	0.346870i
$208$	−4.70293	+	4.70293i	−0.326090	+	0.326090i
$209$	16.7990			1.16201
$210$		0			0
$211$	−0.597369	−	0.597369i	−0.0411246	−	0.0411246i	0.686245	−	0.727370i	$-0.259258\pi$
$211$	−0.597369	−	0.597369i	−0.0411246	−	0.0411246i	−0.727370	+	0.686245i	$0.759258\pi$
$212$	−1.34066	−	1.34066i	−0.0920768	−	0.0920768i
$213$		−	7.85506i		−	0.538220i
$214$	10.3819	+	10.3819i	0.709692	+	0.709692i
$215$		0			0
$216$			0.892408i			0.0607207i
$217$			4.14963i			0.281695i
$218$			2.50284i			0.169514i
$219$		−	6.64923i		−	0.449313i
$220$		0			0
$221$	−25.8478	−	25.8478i	−1.73871	−	1.73871i
$222$			21.9844i			1.47550i
$223$	−9.30527	−	9.30527i	−0.623127	−	0.623127i	0.323203	−	0.946330i	$-0.395240\pi$
$223$	−9.30527	−	9.30527i	−0.623127	−	0.623127i	−0.946330	+	0.323203i	$0.895240\pi$
$224$	−1.54761	−	1.54761i	−0.103404	−	0.103404i
$225$		0			0
$226$	−4.50808			−0.299873
$227$	−13.1820	+	13.1820i	−0.874921	+	0.874921i	−0.993004	−	0.118082i	$-0.962325\pi$
$227$	−13.1820	+	13.1820i	−0.874921	+	0.874921i	0.118082	+	0.993004i	$0.462325\pi$
$228$	11.3880	+	11.3880i	0.754188	+	0.754188i
$229$	−3.41240	+	3.41240i	−0.225498	+	0.225498i	−0.810809	−	0.585311i	$-0.800972\pi$
$229$	−3.41240	+	3.41240i	−0.225498	+	0.225498i	0.585311	+	0.810809i	$0.300972\pi$
$230$		0			0
$231$		−	12.8386i		−	0.844720i
$232$	−4.76527	−	2.50843i	−0.312855	−	0.164686i
$233$	−19.7859	−	19.7859i	−1.29622	−	1.29622i	−0.930872	−	0.365347i	$-0.880951\pi$
$233$	−19.7859	−	19.7859i	−1.29622	−	1.29622i	−0.365347	−	0.930872i	$-0.619049\pi$
$234$	−12.3390	−	12.3390i	−0.806626	−	0.806626i
$235$		0			0
$236$		−	8.03932i		−	0.523315i
$237$	−2.50255	−	2.50255i	−0.162558	−	0.162558i
$238$	8.50584	−	8.50584i	0.551351	−	0.551351i
$239$		−	1.78183i		−	0.115257i	−0.998338	−	0.0576285i	$-0.981646\pi$
$239$		−	1.78183i		−	0.115257i	0.998338	−	0.0576285i	$-0.0183539\pi$
$240$		0			0
$241$			2.56743i			0.165382i	0.996575	+	0.0826912i	$0.0263515\pi$
$241$			2.56743i			0.165382i	−0.996575	+	0.0826912i	$0.973648\pi$
$242$	−4.88123			−0.313778
$243$	−21.0070			−1.34760
$244$	1.90213	−	1.90213i	0.121772	−	0.121772i
$245$		0			0
$246$	−14.7794	+	14.7794i	−0.942300	+	0.942300i
$247$	45.1684			2.87400
$248$	−1.34066	−	1.34066i	−0.0851319	−	0.0851319i
$249$	2.37143	+	2.37143i	0.150283	+	0.150283i
$250$		0			0
$251$	−19.3334	+	19.3334i	−1.22032	+	1.22032i	−0.252797	+	0.967519i	$0.581350\pi$
$251$	−19.3334	+	19.3334i	−1.22032	+	1.22032i	−0.967519	+	0.252797i	$0.918650\pi$
$252$	4.06044	−	4.06044i	0.255784	−	0.255784i
$253$	6.65408			0.418338
$254$	5.40735			0.339288
$255$		0			0
$256$	1.00000			0.0625000
$257$	−0.598364	+	0.598364i	−0.0373249	+	0.0373249i	−0.725523	−	0.688198i	$-0.758402\pi$
$257$	−0.598364	+	0.598364i	−0.0373249	+	0.0373249i	0.688198	+	0.725523i	$0.258402\pi$
$258$		−	19.3008i		−	1.20161i
$259$	−14.3472	+	14.3472i	−0.891490	+	0.891490i
$260$		0			0
$261$	6.58131	−	12.5026i	0.407373	−	0.773889i
$262$	−10.5711	+	10.5711i	−0.653084	+	0.653084i
$263$	−7.05120			−0.434795			−0.217398	−	0.976083i	$-0.569757\pi$
$263$	−7.05120			−0.434795			−0.217398	+	0.976083i	$0.569757\pi$
$264$	4.14789	+	4.14789i	0.255285	+	0.255285i
$265$		0			0
$266$			14.8637i			0.911354i
$267$	17.6448	+	17.6448i	1.07985	+	1.07985i
$268$	−7.71402	−	7.71402i	−0.471209	−	0.471209i
$269$	−0.0364640	+	0.0364640i	−0.00222325	+	0.00222325i	−0.708218	−	0.705994i	$-0.750500\pi$
$269$	−0.0364640	+	0.0364640i	−0.00222325	+	0.00222325i	0.705994	+	0.708218i	$0.250500\pi$
$270$		0			0
$271$	0.0290926	+	0.0290926i	0.00176725	+	0.00176725i	0.707990	−	0.706223i	$-0.249602\pi$
$271$	0.0290926	+	0.0290926i	0.00176725	+	0.00176725i	−0.706223	+	0.707990i	$0.749602\pi$
$272$			5.49611i			0.333251i
$273$		−	34.5200i		−	2.08924i
$274$	5.27765			0.318834
$275$		0			0
$276$	4.51078	+	4.51078i	0.271517	+	0.271517i
$277$	−0.330886	+	0.330886i	−0.0198810	+	0.0198810i	−0.716977	−	0.697096i	$-0.754475\pi$
$277$	−0.330886	+	0.330886i	−0.0198810	+	0.0198810i	0.697096	+	0.716977i	$0.254475\pi$
$278$	−5.16233			−0.309616
$279$	3.51746	−	3.51746i	0.210585	−	0.210585i
$280$		0			0
$281$	−23.3321			−1.39187			−0.695937	−	0.718103i	$-0.745011\pi$
$281$	−23.3321			−1.39187			−0.695937	+	0.718103i	$0.745011\pi$
$282$		−	7.93830i		−	0.472719i
$283$	5.67142	−	5.67142i	0.337131	−	0.337131i	−0.518155	−	0.855286i	$-0.673381\pi$
$283$	5.67142	−	5.67142i	0.337131	−	0.337131i	0.855286	+	0.518155i	$0.173381\pi$
$284$			3.31237i			0.196553i
$285$		0			0
$286$	16.4519			0.972820
$287$	−19.2903			−1.13867
$288$			2.62368i			0.154602i
$289$	−13.2072			−0.776896
$290$		0			0
$291$	−16.5535			−0.970382
$292$			2.80389i			0.164085i
$293$	−17.8844			−1.04482			−0.522409	−	0.852695i	$-0.674966\pi$
$293$	−17.8844			−1.04482			−0.522409	+	0.852695i	$0.674966\pi$
$294$	−5.24040			−0.305626
$295$		0			0
$296$		−	9.27054i		−	0.538839i
$297$	1.56092	−	1.56092i	0.0905737	−	0.0905737i
$298$		−	9.75656i		−	0.565182i
$299$	17.8912			1.03468
$300$		0			0
$301$	12.5958	−	12.5958i	0.726009	−	0.726009i
$302$	6.29344			0.362147
$303$	−21.0234	+	21.0234i	−1.20777	+	1.20777i
$304$	−4.80216	−	4.80216i	−0.275423	−	0.275423i
$305$		0			0
$306$	−14.4201			−0.824340
$307$			28.2201i			1.61061i	0.592862	+	0.805304i	$0.297998\pi$
$307$			28.2201i			1.61061i	−0.592862	+	0.805304i	$0.702002\pi$
$308$			5.41388i			0.308484i
$309$	20.2303	+	20.2303i	1.15086	+	1.15086i
$310$		0			0
$311$	8.09360	−	8.09360i	0.458946	−	0.458946i	−0.439364	−	0.898309i	$-0.644796\pi$
$311$	8.09360	−	8.09360i	0.458946	−	0.458946i	0.898309	+	0.439364i	$0.144796\pi$
$312$	11.1527	+	11.1527i	0.631396	+	0.631396i
$313$	23.7823	+	23.7823i	1.34425	+	1.34425i	0.891777	+	0.452475i	$0.149459\pi$
$313$	23.7823	+	23.7823i	1.34425	+	1.34425i	0.452475	+	0.891777i	$0.350541\pi$
$314$			23.4621i			1.32404i
$315$		0			0
$316$	1.05529	+	1.05529i	0.0593647	+	0.0593647i
$317$	16.1923			0.909451			0.454725	−	0.890632i	$-0.349737\pi$
$317$	16.1923			0.909451			0.454725	+	0.890632i	$0.349737\pi$
$318$	−3.17928	+	3.17928i	−0.178285	+	0.178285i
$319$	3.94747	+	12.7225i	0.221016	+	0.712323i
$320$		0			0
$321$	24.6200	−	24.6200i	1.37415	−	1.37415i
$322$			5.88752i			0.328099i
$323$	26.3932	−	26.3932i	1.46856	−	1.46856i
$324$	9.98733			0.554852
$325$		0			0
$326$	−5.60923			−0.310667
$327$	5.93531			0.328224
$328$	6.23227	−	6.23227i	0.344120	−	0.344120i
$329$	5.18058	−	5.18058i	0.285615	−	0.285615i
$330$		0			0
$331$	23.0465	+	23.0465i	1.26675	+	1.26675i	0.947758	+	0.318991i	$0.103344\pi$
$331$	23.0465	+	23.0465i	1.26675	+	1.26675i	0.318991	+	0.947758i	$0.396656\pi$
$332$	−1.00000	−	1.00000i	−0.0548821	−	0.0548821i
$333$	24.3230			1.33289
$334$	10.7430	−	10.7430i	0.587834	−	0.587834i
$335$		0			0
$336$	−3.67005	+	3.67005i	−0.200218	+	0.200218i
$337$	24.5220			1.33580			0.667900	−	0.744251i	$-0.267193\pi$
$337$	24.5220			1.33580			0.667900	+	0.744251i	$0.267193\pi$
$338$	31.2351			1.69897
$339$			10.6906i			0.580633i
$340$		0			0
$341$			4.68991i			0.253973i
$342$	12.5993	−	12.5993i	0.681295	−	0.681295i
$343$	−14.2532	−	14.2532i	−0.769600	−	0.769600i
$344$			8.13887i			0.438818i
$345$		0			0
$346$	2.54018	+	2.54018i	0.136561	+	0.136561i
$347$	−3.63621	−	3.63621i	−0.195202	−	0.195202i	0.602738	−	0.797939i	$-0.294077\pi$
$347$	−3.63621	−	3.63621i	−0.195202	−	0.195202i	−0.797939	+	0.602738i	$0.794077\pi$
$348$	−5.94856	+	11.3005i	−0.318876	+	0.605771i
$349$			12.2722i			0.656917i	0.944518	+	0.328459i	$0.106529\pi$
$349$			12.2722i			0.656917i	−0.944518	+	0.328459i	$0.893471\pi$
$350$		0			0
$351$	4.19693	−	4.19693i	0.224016	−	0.224016i
$352$	−1.74911	−	1.74911i	−0.0932278	−	0.0932278i
$353$	2.84358	−	2.84358i	0.151349	−	0.151349i	−0.627371	−	0.778720i	$-0.715869\pi$
$353$	2.84358	−	2.84358i	0.151349	−	0.151349i	0.778720	+	0.627371i	$0.215869\pi$
$354$	−19.0647			−1.01328
$355$		0			0
$356$	−7.44059	−	7.44059i	−0.394350	−	0.394350i
$357$	−20.1710	−	20.1710i	−1.06756	−	1.06756i
$358$			13.1139i			0.693089i
$359$	−13.5590	−	13.5590i	−0.715619	−	0.715619i	0.252086	−	0.967705i	$-0.418883\pi$
$359$	−13.5590	−	13.5590i	−0.715619	−	0.715619i	−0.967705	+	0.252086i	$0.918883\pi$
$360$		0			0
$361$			27.1215i			1.42745i
$362$			6.48628i			0.340911i
$363$			11.5755i			0.607557i
$364$			14.5566i			0.762973i
$365$		0			0
$366$	−4.51078	−	4.51078i	−0.235782	−	0.235782i
$367$		−	18.8151i		−	0.982138i	−0.871121	−	0.491069i	$-0.836606\pi$
$367$		−	18.8151i		−	0.982138i	0.871121	−	0.491069i	$-0.163394\pi$
$368$	−1.90213	−	1.90213i	−0.0991556	−	0.0991556i
$369$	16.3515	+	16.3515i	0.851226	+	0.851226i
$370$		0			0
$371$	−4.14963			−0.215438
$372$	−3.17928	+	3.17928i	−0.164838	+	0.164838i
$373$	16.4337	+	16.4337i	0.850904	+	0.850904i	0.990245	−	0.139340i	$-0.0444983\pi$
$373$	16.4337	+	16.4337i	0.850904	+	0.850904i	−0.139340	+	0.990245i	$0.544498\pi$
$374$	9.61330	−	9.61330i	0.497092	−	0.497092i
$375$		0			0
$376$			3.34747i			0.172633i
$377$	10.6138	+	34.2077i	0.546638	+	1.76179i
$378$	1.38110	+	1.38110i	0.0710361	+	0.0710361i
$379$	−8.61569	−	8.61569i	−0.442559	−	0.442559i	0.450313	−	0.892871i	$-0.351313\pi$
$379$	−8.61569	−	8.61569i	−0.442559	−	0.442559i	−0.892871	+	0.450313i	$0.851313\pi$
$380$		0			0
$381$		−	12.8232i		−	0.656951i
$382$	15.2545	+	15.2545i	0.780489	+	0.780489i
$383$	7.13804	−	7.13804i	0.364737	−	0.364737i	−0.500817	−	0.865553i	$-0.666967\pi$
$383$	7.13804	−	7.13804i	0.364737	−	0.364737i	0.865553	+	0.500817i	$0.166967\pi$
$384$		−	2.37143i		−	0.121017i
$385$		0			0
$386$		−	10.2509i		−	0.521758i
$387$	−21.3538			−1.08548
$388$	6.98037			0.354375
$389$	21.8568	−	21.8568i	1.10818	−	1.10818i	0.114793	−	0.993389i	$-0.463380\pi$
$389$	21.8568	−	21.8568i	1.10818	−	1.10818i	0.993389	−	0.114793i	$-0.0366205\pi$
$390$		0			0
$391$	10.4543	−	10.4543i	0.528698	−	0.528698i
$392$	2.20981			0.111612
$393$	25.0686	+	25.0686i	1.26454	+	1.26454i
$394$	3.43016	+	3.43016i	0.172809	+	0.172809i
$395$		0			0
$396$	4.58911	−	4.58911i	0.230611	−	0.230611i
$397$	−16.9123	+	16.9123i	−0.848806	+	0.848806i	−0.989984	−	0.141179i	$-0.954911\pi$
$397$	−16.9123	+	16.9123i	−0.848806	+	0.848806i	0.141179	+	0.989984i	$0.454911\pi$
$398$	−5.28540			−0.264933
$399$	35.2483			1.76462
$400$		0			0
$401$	−11.4001			−0.569293			−0.284646	−	0.958633i	$-0.591876\pi$
$401$	−11.4001			−0.569293			−0.284646	+	0.958633i	$0.591876\pi$
$402$	−18.2933	+	18.2933i	−0.912385	+	0.912385i
$403$			12.6100i			0.628151i
$404$	8.86530	−	8.86530i	0.441065	−	0.441065i
$405$		0			0
$406$	−11.2568	+	3.49272i	−0.558668	+	0.173341i
$407$	−16.2152	+	16.2152i	−0.803757	+	0.803757i
$408$	13.0336			0.645262
$409$	23.5498	+	23.5498i	1.16446	+	1.16446i	0.983487	+	0.180976i	$0.0579257\pi$
$409$	23.5498	+	23.5498i	1.16446	+	1.16446i	0.180976	+	0.983487i	$0.442074\pi$
$410$		0			0
$411$		−	12.5156i		−	0.617348i
$412$	−8.53083	−	8.53083i	−0.420284	−	0.420284i
$413$	−12.4417	−	12.4417i	−0.612217	−	0.612217i
$414$	4.99060	−	4.99060i	0.245274	−	0.245274i
$415$		0			0
$416$	−4.70293	−	4.70293i	−0.230580	−	0.230580i
$417$			12.2421i			0.599499i
$418$			16.7990i			0.821666i
$419$	−29.7205			−1.45194			−0.725970	−	0.687726i	$-0.758609\pi$
$419$	−29.7205			−1.45194			−0.725970	+	0.687726i	$0.758609\pi$
$420$		0			0
$421$	2.73660	+	2.73660i	0.133374	+	0.133374i	0.770642	−	0.637268i	$-0.219936\pi$
$421$	2.73660	+	2.73660i	0.133374	+	0.133374i	−0.637268	+	0.770642i	$0.719936\pi$
$422$	0.597369	−	0.597369i	0.0290795	−	0.0290795i
$423$	−8.78271			−0.427030
$424$	1.34066	−	1.34066i	0.0651081	−	0.0651081i
$425$		0			0
$426$	7.85506			0.380579
$427$		−	5.88752i		−	0.284917i
$428$	−10.3819	+	10.3819i	−0.501828	+	0.501828i
$429$		−	39.0145i		−	1.88364i
$430$		0			0
$431$	−22.6167			−1.08941			−0.544705	−	0.838628i	$-0.683358\pi$
$431$	−22.6167			−1.08941			−0.544705	+	0.838628i	$0.683358\pi$
$432$	−0.892408			−0.0429360
$433$			12.4997i			0.600697i	0.953829	+	0.300349i	$0.0971030\pi$
$433$			12.4997i			0.600697i	−0.953829	+	0.300349i	$0.902897\pi$
$434$	−4.14963			−0.199189
$435$		0			0
$436$	−2.50284			−0.119864
$437$			18.2687i			0.873910i
$438$	6.64923			0.317712
$439$	27.0095			1.28909			0.644546	−	0.764565i	$-0.277046\pi$
$439$	27.0095			1.28909			0.644546	+	0.764565i	$0.277046\pi$
$440$		0			0
$441$			5.79783i			0.276087i
$442$	25.8478	−	25.8478i	1.22946	−	1.22946i
$443$		−	22.9835i		−	1.09198i	−0.837792	−	0.545990i	$-0.816154\pi$
$443$		−	22.9835i		−	1.09198i	0.837792	−	0.545990i	$-0.183846\pi$
$444$	−21.9844			−1.04334
$445$		0			0
$446$	9.30527	−	9.30527i	0.440617	−	0.440617i
$447$	−23.1370			−1.09434
$448$	1.54761	−	1.54761i	0.0731177	−	0.0731177i
$449$	17.9733	+	17.9733i	0.848212	+	0.848212i	0.989910	−	0.141698i	$-0.0452561\pi$
$449$	17.9733	+	17.9733i	0.848212	+	0.848212i	−0.141698	+	0.989910i	$0.545256\pi$
$450$		0			0
$451$	−21.8018			−1.02661
$452$		−	4.50808i		−	0.212042i
$453$		−	14.9245i		−	0.701212i
$454$	−13.1820	−	13.1820i	−0.618663	−	0.618663i
$455$		0			0
$456$	−11.3880	+	11.3880i	−0.533291	+	0.533291i
$457$	−13.3089	−	13.3089i	−0.622565	−	0.622565i	0.323622	−	0.946187i	$-0.395100\pi$
$457$	−13.3089	−	13.3089i	−0.622565	−	0.622565i	−0.946187	+	0.323622i	$0.895100\pi$
$458$	−3.41240	−	3.41240i	−0.159451	−	0.159451i
$459$		−	4.90477i		−	0.228935i
$460$		0			0
$461$	−3.57923	−	3.57923i	−0.166701	−	0.166701i	0.618826	−	0.785528i	$-0.287608\pi$
$461$	−3.57923	−	3.57923i	−0.166701	−	0.166701i	−0.785528	+	0.618826i	$0.787608\pi$
$462$	12.8386			0.597307
$463$	0.290546	−	0.290546i	0.0135028	−	0.0135028i	−0.700323	−	0.713826i	$-0.746961\pi$
$463$	0.290546	−	0.290546i	0.0135028	−	0.0135028i	0.713826	+	0.700323i	$0.246961\pi$
$464$	2.50843	−	4.76527i	0.116451	−	0.221222i
$465$		0			0
$466$	19.7859	−	19.7859i	0.916565	−	0.916565i
$467$		−	15.5971i		−	0.721749i	−0.932614	−	0.360874i	$-0.882478\pi$
$467$		−	15.5971i		−	0.721749i	0.932614	−	0.360874i	$-0.117522\pi$
$468$	12.3390	−	12.3390i	0.570371	−	0.570371i
$469$	−23.8766			−1.10252
$470$		0			0
$471$	55.6388			2.56370
$472$	8.03932			0.370040
$473$	14.2358	−	14.2358i	0.654561	−	0.654561i
$474$	2.50255	−	2.50255i	0.114946	−	0.114946i
$475$		0			0
$476$	8.50584	+	8.50584i	0.389864	+	0.389864i
$477$	3.51746	+	3.51746i	0.161054	+	0.161054i
$478$	1.78183			0.0814990
$479$	−3.19653	+	3.19653i	−0.146053	+	0.146053i	−0.776352	−	0.630299i	$-0.782932\pi$
$479$	−3.19653	+	3.19653i	−0.146053	+	0.146053i	0.630299	+	0.776352i	$0.282932\pi$
$480$		0			0
$481$	−43.5987	+	43.5987i	−1.98793	+	1.98793i
$482$	−2.56743			−0.116943
$483$	13.9619			0.635286
$484$		−	4.88123i		−	0.221874i
$485$		0			0
$486$		−	21.0070i		−	0.952899i
$487$	−25.6678	+	25.6678i	−1.16312	+	1.16312i	−0.179328	+	0.983789i	$0.557392\pi$
$487$	−25.6678	+	25.6678i	−1.16312	+	1.16312i	−0.983789	+	0.179328i	$0.942608\pi$
$488$	1.90213	+	1.90213i	0.0861055	+	0.0861055i
$489$			13.3019i			0.601533i
$490$		0			0
$491$	11.1994	+	11.1994i	0.505420	+	0.505420i	0.913117	−	0.407697i	$-0.133668\pi$
$491$	11.1994	+	11.1994i	0.505420	+	0.505420i	−0.407697	+	0.913117i	$0.633668\pi$
$492$	−14.7794	−	14.7794i	−0.666307	−	0.666307i
$493$	26.1905	+	13.7866i	1.17956	+	0.620916i
$494$			45.1684i			2.03222i
$495$		0			0
$496$	1.34066	−	1.34066i	0.0601973	−	0.0601973i
$497$	5.12626	+	5.12626i	0.229944	+	0.229944i
$498$	−2.37143	+	2.37143i	−0.106266	+	0.106266i
$499$	−6.43997			−0.288293			−0.144146	−	0.989556i	$-0.546044\pi$
$499$	−6.43997			−0.288293			−0.144146	+	0.989556i	$0.546044\pi$
$500$		0			0
$501$	−25.4764	−	25.4764i	−1.13820	−	1.13820i
$502$	−19.3334	−	19.3334i	−0.862894	−	0.862894i
$503$		−	10.1538i		−	0.452736i	−0.974042	−	0.226368i	$-0.927315\pi$
$503$		−	10.1538i		−	0.452736i	0.974042	−	0.226368i	$-0.0726852\pi$
$504$	4.06044	+	4.06044i	0.180866	+	0.180866i
$505$		0			0
$506$			6.65408i			0.295810i
$507$		−	74.0719i		−	3.28965i
$508$			5.40735i			0.239913i
$509$		−	17.5592i		−	0.778299i	−0.921175	−	0.389150i	$-0.872769\pi$
$509$		−	17.5592i		−	0.778299i	0.921175	−	0.389150i	$-0.127231\pi$
$510$		0			0
$511$	4.33933	+	4.33933i	0.191960	+	0.191960i
$512$			1.00000i			0.0441942i
$513$	4.28549	+	4.28549i	0.189209	+	0.189209i
$514$	−0.598364	−	0.598364i	−0.0263927	−	0.0263927i
$515$		0			0
$516$	19.3008			0.849668
$517$	5.85510	−	5.85510i	0.257507	−	0.257507i
$518$	−14.3472	−	14.3472i	−0.630379	−	0.630379i
$519$	6.02386	−	6.02386i	0.264418	−	0.264418i
$520$		0			0
$521$		−	0.989319i		−	0.0433429i	−0.999765	−	0.0216714i	$-0.993101\pi$
$521$		−	0.989319i		−	0.0433429i	0.999765	−	0.0216714i	$-0.00689877\pi$
$522$	12.5026	+	6.58131i	0.547222	+	0.288056i
$523$	1.04327	+	1.04327i	0.0456189	+	0.0456189i	0.729548	−	0.683929i	$-0.239730\pi$
$523$	1.04327	+	1.04327i	0.0456189	+	0.0456189i	−0.683929	+	0.729548i	$0.739730\pi$
$524$	−10.5711	−	10.5711i	−0.461800	−	0.461800i
$525$		0			0
$526$		−	7.05120i		−	0.307447i
$527$	7.36841	+	7.36841i	0.320973	+	0.320973i
$528$	−4.14789	+	4.14789i	−0.180514	+	0.180514i
$529$		−	15.7638i		−	0.685382i
$530$		0			0
$531$			21.0926i			0.915342i
$532$	−14.8637			−0.644425
$533$	−58.6199			−2.53911
$534$	−17.6448	+	17.6448i	−0.763567	+	0.763567i
$535$		0			0
$536$	7.71402	−	7.71402i	0.333195	−	0.333195i
$537$	31.0986			1.34200
$538$	−0.0364640	−	0.0364640i	−0.00157207	−	0.00157207i
$539$	−3.86519	−	3.86519i	−0.166486	−	0.166486i
$540$		0			0
$541$	−10.1475	+	10.1475i	−0.436274	+	0.436274i	−0.890756	−	0.454482i	$-0.849824\pi$
$541$	−10.1475	+	10.1475i	−0.436274	+	0.436274i	0.454482	+	0.890756i	$0.349824\pi$
$542$	−0.0290926	+	0.0290926i	−0.00124963	+	0.00124963i
$543$	15.3818			0.660095
$544$	−5.49611			−0.235644
$545$		0			0
$546$	34.5200			1.47732
$547$	4.95983	−	4.95983i	0.212067	−	0.212067i	−0.593078	−	0.805145i	$-0.702087\pi$
$547$	4.95983	−	4.95983i	0.212067	−	0.212067i	0.805145	+	0.593078i	$0.202087\pi$
$548$			5.27765i			0.225450i
$549$	−4.99060	+	4.99060i	−0.212993	+	0.212993i
$550$		0			0
$551$	−34.9294	+	10.8377i	−1.48804	+	0.461703i
$552$	−4.51078	+	4.51078i	−0.191991	+	0.191991i
$553$	3.26635			0.138899
$554$	−0.330886	−	0.330886i	−0.0140580	−	0.0140580i
$555$		0			0
$556$		−	5.16233i		−	0.218932i
$557$	18.4793	+	18.4793i	0.782992	+	0.782992i	0.980335	−	0.197342i	$-0.0632311\pi$
$557$	18.4793	+	18.4793i	0.782992	+	0.782992i	−0.197342	+	0.980335i	$0.563231\pi$
$558$	3.51746	+	3.51746i	0.148906	+	0.148906i
$559$	38.2765	−	38.2765i	1.61892	−	1.61892i
$560$		0			0
$561$	−22.7973	−	22.7973i	−0.962501	−	0.962501i
$562$		−	23.3321i		−	0.984203i
$563$			28.4102i			1.19735i	0.800993	+	0.598674i	$0.204305\pi$
$563$			28.4102i			1.19735i	−0.800993	+	0.598674i	$0.795695\pi$
$564$	7.93830			0.334263
$565$		0			0
$566$	5.67142	+	5.67142i	0.238388	+	0.238388i
$567$	15.4565	−	15.4565i	0.649112	−	0.649112i
$568$	−3.31237			−0.138984
$569$	−6.58267	+	6.58267i	−0.275960	+	0.275960i	−0.831494	−	0.555534i	$-0.812514\pi$
$569$	−6.58267	+	6.58267i	−0.275960	+	0.275960i	0.555534	+	0.831494i	$0.312514\pi$
$570$		0			0
$571$	38.4563			1.60934			0.804672	−	0.593719i	$-0.202341\pi$
$571$	38.4563			1.60934			0.804672	+	0.593719i	$0.202341\pi$
$572$			16.4519i			0.687888i
$573$	36.1750	−	36.1750i	1.51123	−	1.51123i
$574$		−	19.2903i		−	0.805160i
$575$		0			0
$576$	−2.62368			−0.109320
$577$	30.8367			1.28375			0.641875	−	0.766809i	$-0.278157\pi$
$577$	30.8367			1.28375			0.641875	+	0.766809i	$0.278157\pi$
$578$		−	13.2072i		−	0.549348i
$579$	−24.3093			−1.01026
$580$		0			0
$581$	−3.09522			−0.128411
$582$		−	16.5535i		−	0.686163i
$583$	−4.68991			−0.194236
$584$	−2.80389			−0.116026
$585$		0			0
$586$		−	17.8844i		−	0.738797i
$587$	29.1768	−	29.1768i	1.20425	−	1.20425i	0.231394	−	0.972860i	$-0.425671\pi$
$587$	29.1768	−	29.1768i	1.20425	−	1.20425i	0.972860	−	0.231394i	$-0.0743288\pi$
$588$		−	5.24040i		−	0.216111i
$589$	−12.8761			−0.530551
$590$		0			0
$591$	8.13439	−	8.13439i	0.334604	−	0.334604i
$592$	9.27054			0.381017
$593$	−24.1758	+	24.1758i	−0.992782	+	0.992782i	−0.999974	−	0.00719201i	$-0.997711\pi$
$593$	−24.1758	+	24.1758i	−0.992782	+	0.992782i	0.00719201	+	0.999974i	$0.497711\pi$
$594$	1.56092	+	1.56092i	0.0640453	+	0.0640453i
$595$		0			0
$596$	9.75656			0.399644
$597$			12.5340i			0.512981i
$598$			17.8912i			0.731626i
$599$	3.24477	+	3.24477i	0.132578	+	0.132578i	0.770282	−	0.637704i	$-0.220116\pi$
$599$	3.24477	+	3.24477i	0.132578	+	0.132578i	−0.637704	+	0.770282i	$0.720116\pi$
$600$		0			0
$601$	12.8663	−	12.8663i	0.524825	−	0.524825i	−0.394199	−	0.919025i	$-0.628978\pi$
$601$	12.8663	−	12.8663i	0.524825	−	0.524825i	0.919025	+	0.394199i	$0.128978\pi$
$602$	12.5958	+	12.5958i	0.513366	+	0.513366i
$603$	20.2391	+	20.2391i	0.824202	+	0.824202i
$604$			6.29344i			0.256076i
$605$		0			0
$606$	−21.0234	−	21.0234i	−0.854019	−	0.854019i
$607$	−19.8274			−0.804769			−0.402385	−	0.915471i	$-0.631819\pi$
$607$	−19.8274			−0.804769			−0.402385	+	0.915471i	$0.631819\pi$
$608$	4.80216	−	4.80216i	0.194753	−	0.194753i
$609$	8.28274	+	26.6948i	0.335633	+	1.08173i
$610$		0			0
$611$	15.7429	−	15.7429i	0.636891	−	0.636891i
$612$		−	14.4201i		−	0.582896i
$613$	1.95319	−	1.95319i	0.0788886	−	0.0788886i	−0.666561	−	0.745450i	$-0.732235\pi$
$613$	1.95319	−	1.95319i	0.0788886	−	0.0788886i	0.745450	+	0.666561i	$0.232235\pi$
$614$	−28.2201			−1.13887
$615$		0			0
$616$	−5.41388			−0.218131
$617$	−36.4561			−1.46767			−0.733833	−	0.679330i	$-0.762271\pi$
$617$	−36.4561			−1.46767			−0.733833	+	0.679330i	$0.762271\pi$
$618$	−20.2303	+	20.2303i	−0.813781	+	0.813781i
$619$	14.0991	−	14.0991i	0.566692	−	0.566692i	−0.364508	−	0.931200i	$-0.618763\pi$
$619$	14.0991	−	14.0991i	0.566692	−	0.566692i	0.931200	+	0.364508i	$0.118763\pi$
$620$		0			0
$621$	1.69748	+	1.69748i	0.0681175	+	0.0681175i
$622$	8.09360	+	8.09360i	0.324524	+	0.324524i
$623$	−23.0303			−0.922688
$624$	−11.1527	+	11.1527i	−0.446464	+	0.446464i
$625$		0			0
$626$	−23.7823	+	23.7823i	−0.950530	+	0.950530i
$627$	39.8377			1.59096
$628$	−23.4621			−0.936240
$629$			50.9519i			2.03159i
$630$		0			0
$631$			40.5547i			1.61446i	0.590238	+	0.807229i	$0.299034\pi$
$631$			40.5547i			1.61446i	−0.590238	+	0.807229i	$0.700966\pi$
$632$	−1.05529	+	1.05529i	−0.0419772	+	0.0419772i
$633$	−1.41662	−	1.41662i	−0.0563055	−	0.0563055i
$634$			16.1923i			0.643079i
$635$		0			0
$636$	−3.17928	−	3.17928i	−0.126067	−	0.126067i
$637$	−10.3926	−	10.3926i	−0.411768	−	0.411768i
$638$	−12.7225	+	3.94747i	−0.503688	+	0.156282i
$639$		−	8.69061i		−	0.343795i
$640$		0			0
$641$	−17.8429	+	17.8429i	−0.704750	+	0.704750i	−0.965426	−	0.260676i	$-0.916055\pi$
$641$	−17.8429	+	17.8429i	−0.704750	+	0.704750i	0.260676	+	0.965426i	$0.416055\pi$
$642$	24.6200	+	24.6200i	0.971673	+	0.971673i
$643$	−4.14331	+	4.14331i	−0.163396	+	0.163396i	−0.784069	−	0.620673i	$-0.786859\pi$
$643$	−4.14331	+	4.14331i	−0.163396	+	0.163396i	0.620673	+	0.784069i	$0.286859\pi$
$644$	−5.88752			−0.232001
$645$		0			0
$646$	26.3932	+	26.3932i	1.03843	+	1.03843i
$647$	−4.54072	−	4.54072i	−0.178514	−	0.178514i	0.612194	−	0.790708i	$-0.290287\pi$
$647$	−4.54072	−	4.54072i	−0.178514	−	0.178514i	−0.790708	+	0.612194i	$0.790287\pi$
$648$			9.98733i			0.392340i
$649$	−14.0616	−	14.0616i	−0.551968	−	0.551968i
$650$		0			0
$651$			9.84057i			0.385682i
$652$		−	5.60923i		−	0.219674i
$653$		−	15.6069i		−	0.610746i	−0.952233	−	0.305373i	$-0.901219\pi$
$653$		−	15.6069i		−	0.610746i	0.952233	−	0.305373i	$-0.0987812\pi$
$654$			5.93531i			0.232089i
$655$		0			0
$656$	6.23227	+	6.23227i	0.243329	+	0.243329i
$657$		−	7.35652i		−	0.287005i
$658$	5.18058	+	5.18058i	0.201960	+	0.201960i
$659$	−18.0250	−	18.0250i	−0.702154	−	0.702154i	0.262718	−	0.964873i	$-0.415381\pi$
$659$	−18.0250	−	18.0250i	−0.702154	−	0.702154i	−0.964873	+	0.262718i	$0.915381\pi$
$660$		0			0
$661$	32.6370			1.26943			0.634717	−	0.772745i	$-0.281117\pi$
$661$	32.6370			1.26943			0.634717	+	0.772745i	$0.281117\pi$
$662$	−23.0465	+	23.0465i	−0.895726	+	0.895726i
$663$	−61.2963	−	61.2963i	−2.38055	−	2.38055i
$664$	1.00000	−	1.00000i	0.0388075	−	0.0388075i
$665$		0			0
$666$			24.3230i			0.942496i
$667$	−13.8355	+	4.29282i	−0.535714	+	0.166219i
$668$	10.7430	+	10.7430i	0.415661	+	0.415661i
$669$	−22.0668	−	22.0668i	−0.853152	−	0.853152i
$670$		0			0
$671$		−	6.65408i		−	0.256878i
$672$	−3.67005	−	3.67005i	−0.141575	−	0.141575i
$673$	12.4688	−	12.4688i	0.480638	−	0.480638i	−0.424697	−	0.905335i	$-0.639620\pi$
$673$	12.4688	−	12.4688i	0.480638	−	0.480638i	0.905335	+	0.424697i	$0.139620\pi$
$674$			24.5220i			0.944553i
$675$		0			0
$676$			31.2351i			1.20135i
$677$	−43.5075			−1.67213			−0.836064	−	0.548632i	$-0.815149\pi$
$677$	−43.5075			−1.67213			−0.836064	+	0.548632i	$0.815149\pi$
$678$	−10.6906			−0.410570
$679$	10.8029	−	10.8029i	0.414577	−	0.414577i
$680$		0			0
$681$	−31.2602	+	31.2602i	−1.19790	+	1.19790i
$682$	−4.68991			−0.179586
$683$	−1.58682	−	1.58682i	−0.0607181	−	0.0607181i	0.676096	−	0.736814i	$-0.263671\pi$
$683$	−1.58682	−	1.58682i	−0.0607181	−	0.0607181i	−0.736814	+	0.676096i	$0.763671\pi$
$684$	12.5993	+	12.5993i	0.481748	+	0.481748i
$685$		0			0
$686$	14.2532	−	14.2532i	0.544189	−	0.544189i
$687$	−8.09227	+	8.09227i	−0.308739	+	0.308739i
$688$	−8.13887			−0.310291
$689$	−12.6100			−0.480404
$690$		0			0
$691$	−13.6208			−0.518160			−0.259080	−	0.965856i	$-0.583419\pi$
$691$	−13.6208			−0.518160			−0.259080	+	0.965856i	$0.583419\pi$
$692$	−2.54018	+	2.54018i	−0.0965632	+	0.0965632i
$693$		−	14.2043i		−	0.539577i
$694$	3.63621	−	3.63621i	0.138028	−	0.138028i
$695$		0			0
$696$	−11.3005	−	5.94856i	−0.428345	−	0.225479i
$697$	−34.2533	+	34.2533i	−1.29743	+	1.29743i
$698$	−12.2722			−0.464511
$699$	−46.9209	−	46.9209i	−1.77471	−	1.77471i
$700$		0			0
$701$		−	5.99924i		−	0.226588i	−0.993561	−	0.113294i	$-0.963860\pi$
$701$		−	5.99924i		−	0.226588i	0.993561	−	0.113294i	$-0.0361402\pi$
$702$	4.19693	+	4.19693i	0.158403	+	0.158403i
$703$	−44.5186	−	44.5186i	−1.67905	−	1.67905i
$704$	1.74911	−	1.74911i	0.0659220	−	0.0659220i
$705$		0			0
$706$	2.84358	+	2.84358i	0.107020	+	0.107020i
$707$		−	27.4401i		−	1.03199i
$708$		−	19.0647i		−	0.716495i
$709$	−30.8193			−1.15744			−0.578722	−	0.815525i	$-0.696448\pi$
$709$	−30.8193			−1.15744			−0.578722	+	0.815525i	$0.696448\pi$
$710$		0			0
$711$	−2.76875	−	2.76875i	−0.103836	−	0.103836i
$712$	7.44059	−	7.44059i	0.278848	−	0.278848i
$713$	−5.10022			−0.191005
$714$	20.1710	−	20.1710i	0.754881	−	0.754881i
$715$		0			0
$716$	−13.1139			−0.490088
$717$		−	4.22548i		−	0.157804i
$718$	13.5590	−	13.5590i	0.506019	−	0.506019i
$719$			27.3779i			1.02102i	0.859871	+	0.510511i	$0.170544\pi$
$719$			27.3779i			1.02102i	−0.859871	+	0.510511i	$0.829456\pi$
$720$		0			0
$721$	−26.4048			−0.983367
$722$	−27.1215			−1.00936
$723$			6.08847i			0.226433i
$724$	−6.48628			−0.241061
$725$		0			0
$726$	−11.5755			−0.429607
$727$		−	29.8682i		−	1.10775i	−0.832600	−	0.553875i	$-0.813148\pi$
$727$		−	29.8682i		−	1.10775i	0.832600	−	0.553875i	$-0.186852\pi$
$728$	−14.5566			−0.539504
$729$	−19.8548			−0.735361
$730$		0			0
$731$		−	44.7321i		−	1.65448i
$732$	4.51078	−	4.51078i	0.166723	−	0.166723i
$733$		−	16.4291i		−	0.606821i	−0.952860	−	0.303411i	$-0.901875\pi$
$733$		−	16.4291i		−	0.606821i	0.952860	−	0.303411i	$-0.0981254\pi$
$734$	18.8151			0.694477
$735$		0			0
$736$	1.90213	−	1.90213i	0.0701136	−	0.0701136i
$737$	−26.9853			−0.994017
$738$	−16.3515	+	16.3515i	−0.601907	+	0.601907i
$739$	22.3784	+	22.3784i	0.823204	+	0.823204i	0.986566	−	0.163362i	$-0.0522339\pi$
$739$	22.3784	+	22.3784i	0.823204	+	0.823204i	−0.163362	+	0.986566i	$0.552234\pi$
$740$		0			0
$741$	107.114			3.93493
$742$		−	4.14963i		−	0.152338i
$743$			26.2298i			0.962278i	0.876644	+	0.481139i	$0.159777\pi$
$743$			26.2298i			0.962278i	−0.876644	+	0.481139i	$0.840223\pi$
$744$	−3.17928	−	3.17928i	−0.116558	−	0.116558i
$745$		0			0
$746$	−16.4337	+	16.4337i	−0.601680	+	0.601680i
$747$	2.62368	+	2.62368i	0.0959956	+	0.0959956i
$748$	9.61330	+	9.61330i	0.351497	+	0.351497i
$749$			32.1343i			1.17416i
$750$		0			0
$751$	−20.2399	−	20.2399i	−0.738565	−	0.738565i	0.233736	−	0.972300i	$-0.424905\pi$
$751$	−20.2399	−	20.2399i	−0.738565	−	0.738565i	−0.972300	+	0.233736i	$0.924905\pi$
$752$	−3.34747			−0.122070
$753$	−45.8479	+	45.8479i	−1.67079	+	1.67079i
$754$	−34.2077	+	10.6138i	−1.24577	+	0.386531i
$755$		0			0
$756$	−1.38110	+	1.38110i	−0.0502301	+	0.0502301i
$757$		−	31.3115i		−	1.13803i	−0.822326	−	0.569017i	$-0.807324\pi$
$757$		−	31.3115i		−	1.13803i	0.822326	−	0.569017i	$-0.192676\pi$
$758$	8.61569	−	8.61569i	0.312936	−	0.312936i
$759$	15.7797			0.572766
$760$		0			0
$761$	22.1543			0.803093			0.401547	−	0.915839i	$-0.368473\pi$
$761$	22.1543			0.803093			0.401547	+	0.915839i	$0.368473\pi$
$762$	12.8232			0.464534
$763$	−3.87342	+	3.87342i	−0.140227	+	0.140227i
$764$	−15.2545	+	15.2545i	−0.551889	+	0.551889i
$765$		0			0
$766$	7.13804	+	7.13804i	0.257908	+	0.257908i
$767$	−37.8083	−	37.8083i	−1.36518	−	1.36518i
$768$	2.37143			0.0855716
$769$	−7.89384	+	7.89384i	−0.284659	+	0.284659i	−0.834964	−	0.550305i	$-0.814512\pi$
$769$	−7.89384	+	7.89384i	−0.284659	+	0.284659i	0.550305	+	0.834964i	$0.314512\pi$
$770$		0			0
$771$	−1.41898	+	1.41898i	−0.0511033	+	0.0511033i
$772$	10.2509			0.368938
$773$	11.6204			0.417957			0.208979	−	0.977920i	$-0.432986\pi$
$773$	11.6204			0.417957			0.208979	+	0.977920i	$0.432986\pi$
$774$		−	21.3538i		−	0.767547i
$775$		0			0
$776$			6.98037i			0.250581i
$777$	−34.0233	+	34.0233i	−1.22058	+	1.22058i
$778$	21.8568	+	21.8568i	0.783603	+	0.783603i
$779$		−	59.8567i		−	2.14459i
$780$		0			0
$781$	5.79370	+	5.79370i	0.207315	+	0.207315i
$782$	10.4543	+	10.4543i	0.373846	+	0.373846i
$783$	−2.23854	+	4.25257i	−0.0799988	+	0.151974i
$784$			2.20981i			0.0789216i
$785$		0			0
$786$	−25.0686	+	25.0686i	−0.894167	+	0.894167i
$787$	−25.0914	−	25.0914i	−0.894412	−	0.894412i	0.100522	−	0.994935i	$-0.467949\pi$
$787$	−25.0914	−	25.0914i	−0.894412	−	0.894412i	−0.994935	+	0.100522i	$0.967949\pi$
$788$	−3.43016	+	3.43016i	−0.122194	+	0.122194i
$789$	−16.7214			−0.595298
$790$		0			0
$791$	−6.97674	−	6.97674i	−0.248064	−	0.248064i
$792$	4.58911	+	4.58911i	0.163067	+	0.163067i
$793$		−	17.8912i		−	0.635335i
$794$	−16.9123	−	16.9123i	−0.600196	−	0.600196i
$795$		0			0
$796$		−	5.28540i		−	0.187336i
$797$			5.24181i			0.185674i	0.995681	+	0.0928372i	$0.0295936\pi$
$797$			5.24181i			0.185674i	−0.995681	+	0.0928372i	$0.970406\pi$
$798$			35.2483i			1.24778i
$799$		−	18.3981i		−	0.650877i
$800$		0			0
$801$	19.5217	+	19.5217i	0.689767	+	0.689767i
$802$		−	11.4001i		−	0.402551i
$803$	4.90431	+	4.90431i	0.173069	+	0.173069i
$804$	−18.2933	−	18.2933i	−0.645154	−	0.645154i
$805$		0			0
$806$	−12.6100			−0.444170
$807$	−0.0864718	+	0.0864718i	−0.00304395	+	0.00304395i
$808$	8.86530	+	8.86530i	0.311880	+	0.311880i
$809$	−31.8511	+	31.8511i	−1.11982	+	1.11982i	−0.128057	+	0.991767i	$0.540874\pi$
$809$	−31.8511	+	31.8511i	−1.11982	+	1.11982i	−0.991767	+	0.128057i	$0.959126\pi$
$810$		0			0
$811$		−	1.13345i		−	0.0398009i	−0.999802	−	0.0199004i	$-0.993665\pi$
$811$		−	1.13345i		−	0.0398009i	0.999802	−	0.0199004i	$-0.00633492\pi$
$812$	−3.49272	−	11.2568i	−0.122570	−	0.395038i
$813$	0.0689911	+	0.0689911i	0.00241962	+	0.00241962i
$814$	−16.2152	−	16.2152i	−0.568342	−	0.568342i
$815$		0			0
$816$			13.0336i			0.456269i
$817$	39.0841	+	39.0841i	1.36738	+	1.36738i
$818$	−23.5498	+	23.5498i	−0.823400	+	0.823400i
$819$		−	38.1919i		−	1.33453i
$820$		0			0
$821$			0.203732i			0.00711030i	0.999994	+	0.00355515i	$0.00113164\pi$
$821$			0.203732i			0.00711030i	−0.999994	+	0.00355515i	$0.998868\pi$
$822$	12.5156			0.436531
$823$	40.6757			1.41787			0.708933	−	0.705276i	$-0.249177\pi$
$823$	40.6757			1.41787			0.708933	+	0.705276i	$0.249177\pi$
$824$	8.53083	−	8.53083i	0.297186	−	0.297186i
$825$		0			0
$826$	12.4417	−	12.4417i	0.432903	−	0.432903i
$827$	42.8178			1.48892			0.744460	−	0.667667i	$-0.232707\pi$
$827$	42.8178			1.48892			0.744460	+	0.667667i	$0.232707\pi$
$828$	4.99060	+	4.99060i	0.173435	+	0.173435i
$829$	17.7392	+	17.7392i	0.616109	+	0.616109i	0.944531	−	0.328422i	$-0.106517\pi$
$829$	17.7392	+	17.7392i	0.616109	+	0.616109i	−0.328422	+	0.944531i	$0.606517\pi$
$830$		0			0
$831$	−0.784672	+	0.784672i	−0.0272200	+	0.0272200i
$832$	4.70293	−	4.70293i	0.163045	−	0.163045i
$833$	−12.1453			−0.420811
$834$	−12.2421			−0.423910
$835$		0			0
$836$	−16.7990			−0.581006
$837$	−1.19641	+	1.19641i	−0.0413541	+	0.0413541i
$838$		−	29.7205i		−	1.02668i
$839$	−19.7783	+	19.7783i	−0.682823	+	0.682823i	−0.960635	−	0.277812i	$-0.910391\pi$
$839$	−19.7783	+	19.7783i	−0.682823	+	0.682823i	0.277812	+	0.960635i	$0.410391\pi$
$840$		0			0
$841$	−16.4156	−	23.9066i	−0.566055	−	0.824367i
$842$	−2.73660	+	2.73660i	−0.0943096	+	0.0943096i
$843$	−55.3304			−1.90568
$844$	0.597369	+	0.597369i	0.0205623	+	0.0205623i
$845$		0			0
$846$		−	8.78271i		−	0.301956i
$847$	−7.55425	−	7.55425i	−0.259567	−	0.259567i
$848$	1.34066	+	1.34066i	0.0460384	+	0.0460384i
$849$	13.4494	−	13.4494i	0.461582	−	0.461582i
$850$		0			0
$851$	−17.6338	−	17.6338i	−0.604479	−	0.604479i
$852$			7.85506i			0.269110i
$853$			42.0722i			1.44053i	0.693701	+	0.720263i	$0.255979\pi$
$853$			42.0722i			1.44053i	−0.693701	+	0.720263i	$0.744021\pi$
$854$	5.88752			0.201467
$855$		0			0
$856$	−10.3819	−	10.3819i	−0.354846	−	0.354846i
$857$	31.3395	−	31.3395i	1.07054	−	1.07054i	0.0732222	−	0.997316i	$-0.476672\pi$
$857$	31.3395	−	31.3395i	1.07054	−	1.07054i	0.997316	−	0.0732222i	$-0.0233282\pi$
$858$	39.0145			1.33193
$859$	23.5554	−	23.5554i	0.803699	−	0.803699i	−0.179973	−	0.983672i	$-0.557601\pi$
$859$	23.5554	−	23.5554i	0.803699	−	0.803699i	0.983672	+	0.179973i	$0.0576010\pi$
$860$		0			0
$861$	−45.7455			−1.55900
$862$		−	22.6167i		−	0.770329i
$863$	−22.3672	+	22.3672i	−0.761389	+	0.761389i	−0.976573	−	0.215185i	$-0.930965\pi$
$863$	−22.3672	+	22.3672i	−0.761389	+	0.761389i	0.215185	+	0.976573i	$0.430965\pi$
$864$		−	0.892408i		−	0.0303603i
$865$		0			0
$866$	−12.4997			−0.424757
$867$	−31.3200			−1.06368
$868$		−	4.14963i		−	0.140848i
$869$	3.69163			0.125230
$870$		0			0
$871$	−72.5570			−2.45850
$872$		−	2.50284i		−	0.0847569i
$873$	−18.3143			−0.619845
$874$	−18.2687			−0.617948
$875$		0			0
$876$			6.64923i			0.224657i
$877$	−40.1211	+	40.1211i	−1.35479	+	1.35479i	−0.474585	+	0.880210i	$0.657402\pi$
$877$	−40.1211	+	40.1211i	−1.35479	+	1.35479i	−0.880210	+	0.474585i	$0.842598\pi$
$878$			27.0095i			0.911526i
$879$	−42.4116			−1.43051
$880$		0			0
$881$	2.72309	−	2.72309i	0.0917433	−	0.0917433i	−0.659746	−	0.751489i	$-0.729336\pi$
$881$	2.72309	−	2.72309i	0.0917433	−	0.0917433i	0.751489	+	0.659746i	$0.229336\pi$
$882$	−5.79783			−0.195223
$883$	18.4641	−	18.4641i	0.621367	−	0.621367i	−0.324514	−	0.945881i	$-0.605201\pi$
$883$	18.4641	−	18.4641i	0.621367	−	0.621367i	0.945881	+	0.324514i	$0.105201\pi$
$884$	25.8478	+	25.8478i	0.869356	+	0.869356i
$885$		0			0
$886$	22.9835			0.772146
$887$			18.2921i			0.614187i	0.951679	+	0.307094i	$0.0993564\pi$
$887$			18.2921i			0.614187i	−0.951679	+	0.307094i	$0.900644\pi$
$888$		−	21.9844i		−	0.737750i
$889$	8.36847	+	8.36847i	0.280670	+	0.280670i
$890$		0			0
$891$	17.4689	−	17.4689i	0.585231	−	0.585231i
$892$	9.30527	+	9.30527i	0.311564	+	0.311564i
$893$	16.0751	+	16.0751i	0.537933	+	0.537933i
$894$		−	23.1370i		−	0.773817i
$895$		0			0
$896$	1.54761	+	1.54761i	0.0517020	+	0.0517020i
$897$	42.4278			1.41662
$898$	−17.9733	+	17.9733i	−0.599777	+	0.599777i
$899$	−3.02566	−	9.75154i	−0.100911	−	0.325232i
$900$		0			0
$901$	−7.36841	+	7.36841i	−0.245477	+	0.245477i
$902$		−	21.8018i		−	0.725922i
$903$	29.8700	−	29.8700i	0.994013	−	0.994013i
$904$	4.50808			0.149936
$905$		0			0
$906$	14.9245			0.495832
$907$	−41.7431			−1.38606			−0.693029	−	0.720910i	$-0.743724\pi$
$907$	−41.7431			−1.38606			−0.693029	+	0.720910i	$0.743724\pi$
$908$	13.1820	−	13.1820i	0.437461	−	0.437461i
$909$	−23.2597	+	23.2597i	−0.771477	+	0.771477i
$910$		0			0
$911$	−18.2115	−	18.2115i	−0.603373	−	0.603373i	0.337833	−	0.941206i	$-0.390306\pi$
$911$	−18.2115	−	18.2115i	−0.603373	−	0.603373i	−0.941206	+	0.337833i	$0.890306\pi$
$912$	−11.3880	−	11.3880i	−0.377094	−	0.377094i
$913$	−3.49822			−0.115774
$914$	13.3089	−	13.3089i	0.440220	−	0.440220i
$915$		0			0
$916$	3.41240	−	3.41240i	0.112749	−	0.112749i
$917$	−32.7198			−1.08050
$918$	4.90477			0.161882
$919$		−	28.2547i		−	0.932037i	−0.884775	−	0.466018i	$-0.845688\pi$
$919$		−	28.2547i		−	0.932037i	0.884775	−	0.466018i	$-0.154312\pi$
$920$		0			0
$921$			66.9221i			2.20516i
$922$	3.57923	−	3.57923i	0.117876	−	0.117876i
$923$	15.5778	+	15.5778i	0.512751	+	0.512751i
$924$			12.8386i			0.422360i
$925$		0			0
$926$	0.290546	+	0.290546i	0.00954794	+	0.00954794i
$927$	22.3822	+	22.3822i	0.735128	+	0.735128i
$928$	4.76527	+	2.50843i	0.156428	+	0.0823431i
$929$		−	13.7610i		−	0.451483i	−0.974187	−	0.225741i	$-0.927520\pi$
$929$		−	13.7610i		−	0.451483i	0.974187	−	0.225741i	$-0.0724804\pi$
$930$		0			0
$931$	10.6118	−	10.6118i	0.347789	−	0.347789i
$932$	19.7859	+	19.7859i	0.648109	+	0.648109i
$933$	19.1934	−	19.1934i	0.628364	−	0.628364i
$934$	15.5971			0.510353
$935$		0			0
$936$	12.3390	+	12.3390i	0.403313	+	0.403313i
$937$	−34.2399	−	34.2399i	−1.11857	−	1.11857i	−0.991951	−	0.126619i	$-0.959587\pi$
$937$	−34.2399	−	34.2399i	−1.11857	−	1.11857i	−0.126619	−	0.991951i	$-0.540413\pi$
$938$		−	23.8766i		−	0.779598i
$939$	56.3980	+	56.3980i	1.84048	+	1.84048i
$940$		0			0
$941$		−	34.0332i		−	1.10945i	−0.832034	−	0.554725i	$-0.812824\pi$
$941$		−	34.0332i		−	1.10945i	0.832034	−	0.554725i	$-0.187176\pi$
$942$			55.6388i			1.81281i
$943$		−	23.7092i		−	0.772079i
$944$			8.03932i			0.261657i
$945$		0			0
$946$	14.2358	+	14.2358i	0.462845	+	0.462845i
$947$			27.2465i			0.885391i	0.896672	+	0.442695i	$0.145978\pi$
$947$			27.2465i			0.885391i	−0.896672	+	0.442695i	$0.854022\pi$
$948$	2.50255	+	2.50255i	0.0812789	+	0.0812789i
$949$	13.1865	+	13.1865i	0.428052	+	0.428052i
$950$		0			0
$951$	38.3989			1.24517
$952$	−8.50584	+	8.50584i	−0.275676	+	0.275676i
$953$	21.7888	+	21.7888i	0.705809	+	0.705809i	0.965651	−	0.259842i	$-0.0836706\pi$
$953$	21.7888	+	21.7888i	0.705809	+	0.705809i	−0.259842	+	0.965651i	$0.583671\pi$
$954$	−3.51746	+	3.51746i	−0.113882	+	0.113882i
$955$		0			0
$956$			1.78183i			0.0576285i
$957$	9.36115	+	30.1705i	0.302603	+	0.975274i
$958$	−3.19653	−	3.19653i	−0.103275	−	0.103275i
$959$	8.16774	+	8.16774i	0.263750	+	0.263750i
$960$		0			0
$961$			27.4053i			0.884041i
$962$	−43.5987	−	43.5987i	−1.40568	−	1.40568i
$963$	27.2388	−	27.2388i	0.877759	−	0.877759i
$964$		−	2.56743i		−	0.0826912i
$965$		0			0
$966$			13.9619i			0.449215i
$967$	58.8079			1.89113			0.945567	−	0.325427i	$-0.105508\pi$
$967$	58.8079			1.89113			0.945567	+	0.325427i	$0.105508\pi$
$968$	4.88123			0.156889
$969$	62.5896	−	62.5896i	2.01067	−	2.01067i
$970$		0			0
$971$	−16.5729	+	16.5729i	−0.531849	+	0.531849i	−0.921122	−	0.389273i	$-0.872726\pi$
$971$	−16.5729	+	16.5729i	−0.531849	+	0.531849i	0.389273	+	0.921122i	$0.372726\pi$
$972$	21.0070			0.673801
$973$	−7.98928	−	7.98928i	−0.256124	−	0.256124i
$974$	−25.6678	−	25.6678i	−0.822448	−	0.822448i
$975$		0			0
$976$	−1.90213	+	1.90213i	−0.0608858	+	0.0608858i
$977$	31.7362	−	31.7362i	1.01533	−	1.01533i	0.0154499	−	0.999881i	$-0.495082\pi$
$977$	31.7362	−	31.7362i	1.01533	−	1.01533i	0.999881	−	0.0154499i	$-0.00491806\pi$
$978$	−13.3019			−0.425348
$979$	−26.0288			−0.831884
$980$		0			0
$981$	6.56666			0.209657
$982$	−11.1994	+	11.1994i	−0.357386	+	0.357386i
$983$		−	40.2384i		−	1.28340i	−0.766954	−	0.641702i	$-0.778229\pi$
$983$		−	40.2384i		−	1.28340i	0.766954	−	0.641702i	$-0.221771\pi$
$984$	14.7794	−	14.7794i	0.471150	−	0.471150i
$985$		0			0
$986$	−13.7866	+	26.1905i	−0.439054	+	0.834074i
$987$	12.2854	−	12.2854i	0.391048	−	0.391048i
$988$	−45.1684			−1.43700
$989$	15.4812	+	15.4812i	0.492274	+	0.492274i
$990$		0			0
$991$		−	23.5667i		−	0.748621i	−0.927303	−	0.374310i	$-0.877879\pi$
$991$		−	23.5667i		−	0.748621i	0.927303	−	0.374310i	$-0.122121\pi$
$992$	1.34066	+	1.34066i	0.0425659	+	0.0425659i
$993$	54.6531	+	54.6531i	1.73436	+	1.73436i
$994$	−5.12626	+	5.12626i	−0.162595	+	0.162595i
$995$		0			0
$996$	−2.37143	−	2.37143i	−0.0751417	−	0.0751417i
$997$		−	32.2246i		−	1.02056i	−0.860007	−	0.510282i	$-0.829541\pi$
$997$		−	32.2246i		−	1.02056i	0.860007	−	0.510282i	$-0.170459\pi$
$998$		−	6.43997i		−	0.203854i
$999$	−8.27310			−0.261749

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1450.2.j.h.1293.5		12
5.2	odd	4		1450.2.e.h.307.2		12
5.3	odd	4		290.2.e.f.17.5	✓	12
5.4	even	2		290.2.j.f.133.2	yes	12
29.12	odd	4		1450.2.e.h.1143.5		12
145.12	even	4	inner	1450.2.j.h.157.5		12
145.99	odd	4		290.2.e.f.273.2	yes	12
145.128	even	4		290.2.j.f.157.2	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
290.2.e.f.17.5	✓	12	5.3	odd	4
290.2.e.f.273.2	yes	12	145.99	odd	4
290.2.j.f.133.2	yes	12	5.4	even	2
290.2.j.f.157.2	yes	12	145.128	even	4
1450.2.e.h.307.2		12	5.2	odd	4
1450.2.e.h.1143.5		12	29.12	odd	4
1450.2.j.h.157.5		12	145.12	even	4	inner
1450.2.j.h.1293.5		12	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1450 = 2 \cdot 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1450.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +2.37143 q^{3} -1.00000 q^{4} +2.37143i q^{6} +(-1.54761 + 1.54761i) q^{7} -1.00000i q^{8} +2.62368 q^{9} +(-1.74911 + 1.74911i) q^{11} -2.37143 q^{12} +(-4.70293 + 4.70293i) q^{13} +(-1.54761 - 1.54761i) q^{14} +1.00000 q^{16} +5.49611i q^{17} +2.62368i q^{18} +(-4.80216 - 4.80216i) q^{19} +(-3.67005 + 3.67005i) q^{21} +(-1.74911 - 1.74911i) q^{22} +(-1.90213 - 1.90213i) q^{23} -2.37143i q^{24} +(-4.70293 - 4.70293i) q^{26} -0.892408 q^{27} +(1.54761 - 1.54761i) q^{28} +(2.50843 - 4.76527i) q^{29} +(1.34066 - 1.34066i) q^{31} +1.00000i q^{32} +(-4.14789 + 4.14789i) q^{33} -5.49611 q^{34} -2.62368 q^{36} +9.27054 q^{37} +(4.80216 - 4.80216i) q^{38} +(-11.1527 + 11.1527i) q^{39} +(6.23227 + 6.23227i) q^{41} +(-3.67005 - 3.67005i) q^{42} -8.13887 q^{43} +(1.74911 - 1.74911i) q^{44} +(1.90213 - 1.90213i) q^{46} -3.34747 q^{47} +2.37143 q^{48} +2.20981i q^{49} +13.0336i q^{51} +(4.70293 - 4.70293i) q^{52} +(1.34066 + 1.34066i) q^{53} -0.892408i q^{54} +(1.54761 + 1.54761i) q^{56} +(-11.3880 - 11.3880i) q^{57} +(4.76527 + 2.50843i) q^{58} +8.03932i q^{59} +(-1.90213 + 1.90213i) q^{61} +(1.34066 + 1.34066i) q^{62} +(-4.06044 + 4.06044i) q^{63} -1.00000 q^{64} +(-4.14789 - 4.14789i) q^{66} +(7.71402 + 7.71402i) q^{67} -5.49611i q^{68} +(-4.51078 - 4.51078i) q^{69} -3.31237i q^{71} -2.62368i q^{72} -2.80389i q^{73} +9.27054i q^{74} +(4.80216 + 4.80216i) q^{76} -5.41388i q^{77} +(-11.1527 - 11.1527i) q^{78} +(-1.05529 - 1.05529i) q^{79} -9.98733 q^{81} +(-6.23227 + 6.23227i) q^{82} +(1.00000 + 1.00000i) q^{83} +(3.67005 - 3.67005i) q^{84} -8.13887i q^{86} +(5.94856 - 11.3005i) q^{87} +(1.74911 + 1.74911i) q^{88} +(7.44059 + 7.44059i) q^{89} -14.5566i q^{91} +(1.90213 + 1.90213i) q^{92} +(3.17928 - 3.17928i) q^{93} -3.34747i q^{94} +2.37143i q^{96} -6.98037 q^{97} -2.20981 q^{98} +(-4.58911 + 4.58911i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{4} + 4 q^{7} + 28 q^{9} + 10 q^{11} - 2 q^{13} + 4 q^{14} + 12 q^{16} - 16 q^{19} - 16 q^{21} + 10 q^{22} - 4 q^{23} - 2 q^{26} - 12 q^{27} - 4 q^{28} + 20 q^{29} + 18 q^{31} + 6 q^{33} - 28 q^{36}+ \cdots + 36 q^{99}+O(q^{100}) \) 12 * q - 12 * q^4 + 4 * q^7 + 28 * q^9 + 10 * q^11 - 2 * q^13 + 4 * q^14 + 12 * q^16 - 16 * q^19 - 16 * q^21 + 10 * q^22 - 4 * q^23 - 2 * q^26 - 12 * q^27 - 4 * q^28 + 20 * q^29 + 18 * q^31 + 6 * q^33 - 28 * q^36 + 16 * q^38 - 38 * q^39 + 36 * q^41 - 16 * q^42 + 12 * q^43 - 10 * q^44 + 4 * q^46 - 20 * q^47 + 2 * q^52 + 18 * q^53 - 4 * q^56 + 32 * q^57 - 16 * q^58 - 4 * q^61 + 18 * q^62 + 24 * q^63 - 12 * q^64 + 6 * q^66 + 12 * q^67 + 12 * q^69 + 16 * q^76 - 38 * q^78 + 30 * q^79 + 44 * q^81 - 36 * q^82 + 12 * q^83 + 16 * q^84 + 16 * q^87 - 10 * q^88 + 20 * q^89 + 4 * q^92 - 2 * q^93 - 76 * q^97 - 16 * q^98 + 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more