LMFDB - Embedded newform 375.2.g.e.151.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [375,2,Mod(76,375)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(375, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("375.76");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 375 = 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	375.g (of order $5$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.99439007580$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
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} + 20x^{14} + 156x^{12} + 610x^{10} + 1286x^{8} + 1440x^{6} + 761x^{4} + 130x^{2} + 1 $ x^16 + 20x^14 + 156x^12 + 610x^10 + 1286x^8 + 1440x^6 + 761x^4 + 130*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	no (minimal twist has level 75)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			151.2
Root			$-1.53655i$ of defining polynomial
Character	$\chi$	$=$	375.151
Dual form			375.2.g.e.226.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.474819 - 1.46134i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-0.292036 + 0.212177i) q^{4} +(1.24309 + 0.903160i) q^{6} -1.49550 q^{7} +(-2.03746 - 1.48030i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.474819 - 1.46134i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-0.292036 + 0.212177i) q^{4} +(1.24309 + 0.903160i) q^{6} -1.49550 q^{7} +(-2.03746 - 1.48030i) q^{8} +(0.309017 - 0.951057i) q^{9} +(-0.728123 - 2.24093i) q^{11} +(0.111548 - 0.343309i) q^{12} +(-0.417020 + 1.28346i) q^{13} +(0.710090 + 2.18543i) q^{14} +(-1.41890 + 4.36692i) q^{16} +(-1.77502 - 1.28963i) q^{17} -1.53655 q^{18} +(-4.62004 - 3.35666i) q^{19} +(1.20988 - 0.879031i) q^{21} +(-2.92904 + 2.12807i) q^{22} +(-2.71781 - 8.36455i) q^{23} +2.51844 q^{24} +2.07358 q^{26} +(0.309017 + 0.951057i) q^{27} +(0.436739 - 0.317309i) q^{28} +(-6.39137 + 4.64360i) q^{29} +(2.99107 + 2.17314i) q^{31} +2.01841 q^{32} +(1.90625 + 1.38497i) q^{33} +(-1.04178 + 3.20626i) q^{34} +(0.111548 + 0.343309i) q^{36} +(-3.01321 + 9.27372i) q^{37} +(-2.71154 + 8.34527i) q^{38} +(-0.417020 - 1.28346i) q^{39} +(0.573380 - 1.76468i) q^{41} +(-1.85904 - 1.35067i) q^{42} +8.01874 q^{43} +(0.688111 + 0.499942i) q^{44} +(-10.9330 + 7.94330i) q^{46} +(5.39046 - 3.91640i) q^{47} +(-1.41890 - 4.36692i) q^{48} -4.76349 q^{49} +2.19405 q^{51} +(-0.150535 - 0.463298i) q^{52} +(3.37484 - 2.45196i) q^{53} +(1.24309 - 0.903160i) q^{54} +(3.04701 + 2.21378i) q^{56} +5.71069 q^{57} +(9.82064 + 7.13511i) q^{58} +(3.41917 - 10.5231i) q^{59} +(-3.78151 - 11.6383i) q^{61} +(1.75549 - 5.40283i) q^{62} +(-0.462134 + 1.42230i) q^{63} +(1.87942 + 5.78425i) q^{64} +(1.11879 - 3.44330i) q^{66} +(3.48976 + 2.53546i) q^{67} +0.792000 q^{68} +(7.11531 + 5.16958i) q^{69} +(-4.67410 + 3.39593i) q^{71} +(-2.03746 + 1.48030i) q^{72} +(-2.14051 - 6.58781i) q^{73} +14.9828 q^{74} +2.06142 q^{76} +(1.08890 + 3.35130i) q^{77} +(-1.67756 + 1.21882i) q^{78} +(8.63118 - 6.27092i) q^{79} +(-0.809017 - 0.587785i) q^{81} -2.85106 q^{82} +(0.181222 + 0.131666i) q^{83} +(-0.166819 + 0.513417i) q^{84} +(-3.80745 - 11.7181i) q^{86} +(2.44129 - 7.51351i) q^{87} +(-1.83373 + 5.64364i) q^{88} +(0.132620 + 0.408162i) q^{89} +(0.623652 - 1.91940i) q^{91} +(2.56846 + 1.86610i) q^{92} -3.69717 q^{93} +(-8.28270 - 6.01773i) q^{94} +(-1.63293 + 1.18639i) q^{96} +(10.1083 - 7.34411i) q^{97} +(2.26180 + 6.96109i) q^{98} -2.35626 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{2} - 4 q^{3} - 2 q^{4} + 2 q^{6} - 16 q^{7} + 6 q^{8} - 4 q^{9}+O(q^{10}) $ 16 * q + 2 * q^2 - 4 * q^3 - 2 * q^4 + 2 * q^6 - 16 * q^7 + 6 * q^8 - 4 * q^9	$ 16 q + 2 q^{2} - 4 q^{3} - 2 q^{4} + 2 q^{6} - 16 q^{7} + 6 q^{8} - 4 q^{9} - 6 q^{11} - 2 q^{12} + 8 q^{13} + 12 q^{14} - 10 q^{16} + 8 q^{17} - 8 q^{18} + 2 q^{19} + 4 q^{21} - 4 q^{22} + 2 q^{23} - 24 q^{24} + 12 q^{26} - 4 q^{27} + 28 q^{28} - 16 q^{29} + 6 q^{31} + 4 q^{32} + 4 q^{33} + 36 q^{34} - 2 q^{36} + 24 q^{37} - 38 q^{38} + 8 q^{39} - 14 q^{41} - 18 q^{42} - 40 q^{43} - 26 q^{44} + 16 q^{46} - 10 q^{47} - 10 q^{48} - 32 q^{51} + 48 q^{52} + 12 q^{53} + 2 q^{54} - 28 q^{57} + 44 q^{58} - 12 q^{59} + 28 q^{62} + 4 q^{63} - 8 q^{64} + 16 q^{66} - 12 q^{67} + 4 q^{68} + 12 q^{69} - 8 q^{71} + 6 q^{72} - 8 q^{73} + 52 q^{74} - 32 q^{76} + 18 q^{77} + 32 q^{78} + 20 q^{79} - 4 q^{81} - 32 q^{82} + 6 q^{83} - 12 q^{84} - 36 q^{86} + 14 q^{87} + 16 q^{88} - 18 q^{89} + 26 q^{91} - 36 q^{92} - 44 q^{93} + 38 q^{94} - 26 q^{96} + 8 q^{97} - 18 q^{98} + 4 q^{99}+O(q^{100}) $ 16 * q + 2 * q^2 - 4 * q^3 - 2 * q^4 + 2 * q^6 - 16 * q^7 + 6 * q^8 - 4 * q^9 - 6 * q^11 - 2 * q^12 + 8 * q^13 + 12 * q^14 - 10 * q^16 + 8 * q^17 - 8 * q^18 + 2 * q^19 + 4 * q^21 - 4 * q^22 + 2 * q^23 - 24 * q^24 + 12 * q^26 - 4 * q^27 + 28 * q^28 - 16 * q^29 + 6 * q^31 + 4 * q^32 + 4 * q^33 + 36 * q^34 - 2 * q^36 + 24 * q^37 - 38 * q^38 + 8 * q^39 - 14 * q^41 - 18 * q^42 - 40 * q^43 - 26 * q^44 + 16 * q^46 - 10 * q^47 - 10 * q^48 - 32 * q^51 + 48 * q^52 + 12 * q^53 + 2 * q^54 - 28 * q^57 + 44 * q^58 - 12 * q^59 + 28 * q^62 + 4 * q^63 - 8 * q^64 + 16 * q^66 - 12 * q^67 + 4 * q^68 + 12 * q^69 - 8 * q^71 + 6 * q^72 - 8 * q^73 + 52 * q^74 - 32 * q^76 + 18 * q^77 + 32 * q^78 + 20 * q^79 - 4 * q^81 - 32 * q^82 + 6 * q^83 - 12 * q^84 - 36 * q^86 + 14 * q^87 + 16 * q^88 - 18 * q^89 + 26 * q^91 - 36 * q^92 - 44 * q^93 + 38 * q^94 - 26 * q^96 + 8 * q^97 - 18 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/375\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$

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 $

$2$	−0.474819	−	1.46134i	−0.335748	−	1.03333i	−0.966353	−	0.257221i	$-0.917193\pi$
$2$	−0.474819	−	1.46134i	−0.335748	−	1.03333i	0.630605	−	0.776104i	$-0.282807\pi$
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$4$	−0.292036	+	0.212177i	−0.146018	+	0.106088i
$5$		0			0
$5$		0			0
$6$	1.24309	+	0.903160i	0.507490	+	0.368713i
$7$	−1.49550			−0.565244			−0.282622	−	0.959231i	$-0.591204\pi$
$7$	−1.49550			−0.565244			−0.282622	+	0.959231i	$0.591204\pi$
$8$	−2.03746	−	1.48030i	−0.720350	−	0.523365i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$		0			0
$11$	−0.728123	−	2.24093i	−0.219537	−	0.675666i	−0.998800	−	0.0489693i	$-0.984406\pi$
$11$	−0.728123	−	2.24093i	−0.219537	−	0.675666i	0.779263	−	0.626697i	$-0.215594\pi$
$12$	0.111548	−	0.343309i	0.0322011	−	0.0991048i
$13$	−0.417020	+	1.28346i	−0.115661	+	0.355967i	−0.992084	−	0.125574i	$-0.959923\pi$
$13$	−0.417020	+	1.28346i	−0.115661	+	0.355967i	0.876424	+	0.481541i	$0.159923\pi$
$14$	0.710090	+	2.18543i	0.189780	+	0.584081i
$15$		0			0
$16$	−1.41890	+	4.36692i	−0.354724	+	1.09173i
$17$	−1.77502	−	1.28963i	−0.430507	−	0.312781i	0.351345	−	0.936246i	$-0.385724\pi$
$17$	−1.77502	−	1.28963i	−0.430507	−	0.312781i	−0.781851	+	0.623465i	$0.785724\pi$
$18$	−1.53655			−0.362168
$19$	−4.62004	−	3.35666i	−1.05991	−	0.770070i	−0.0858386	−	0.996309i	$-0.527357\pi$
$19$	−4.62004	−	3.35666i	−1.05991	−	0.770070i	−0.974072	+	0.226239i	$0.927357\pi$
$20$		0			0
$21$	1.20988	−	0.879031i	0.264018	−	0.191820i
$22$	−2.92904	+	2.12807i	−0.624474	+	0.453707i
$23$	−2.71781	−	8.36455i	−0.566702	−	1.74413i	−0.662840	−	0.748762i	$-0.730649\pi$
$23$	−2.71781	−	8.36455i	−0.566702	−	1.74413i	0.0961375	−	0.995368i	$-0.469351\pi$
$24$	2.51844			0.514074
$25$		0			0
$26$	2.07358			0.406662
$27$	0.309017	+	0.951057i	0.0594703	+	0.183031i
$28$	0.436739	−	0.317309i	0.0825359	−	0.0599658i
$29$	−6.39137	+	4.64360i	−1.18685	+	0.862296i	−0.992928	−	0.118722i	$-0.962120\pi$
$29$	−6.39137	+	4.64360i	−1.18685	+	0.862296i	−0.193920	+	0.981017i	$0.562120\pi$
$30$		0			0
$31$	2.99107	+	2.17314i	0.537213	+	0.390308i	0.823049	−	0.567971i	$-0.192271\pi$
$31$	2.99107	+	2.17314i	0.537213	+	0.390308i	−0.285836	+	0.958279i	$0.592271\pi$
$32$	2.01841			0.356808
$33$	1.90625	+	1.38497i	0.331836	+	0.241093i
$34$	−1.04178	+	3.20626i	−0.178663	+	0.549869i
$35$		0			0
$36$	0.111548	+	0.343309i	0.0185913	+	0.0572182i
$37$	−3.01321	+	9.27372i	−0.495369	+	1.52459i	0.321011	+	0.947076i	$0.395977\pi$
$37$	−3.01321	+	9.27372i	−0.495369	+	1.52459i	−0.816380	+	0.577515i	$0.804023\pi$
$38$	−2.71154	+	8.34527i	−0.439870	+	1.35378i
$39$	−0.417020	−	1.28346i	−0.0667767	−	0.205518i
$40$		0			0
$41$	0.573380	−	1.76468i	0.0895468	−	0.275597i	−0.896247	−	0.443555i	$-0.853717\pi$
$41$	0.573380	−	1.76468i	0.0895468	−	0.275597i	0.985794	+	0.167958i	$0.0537172\pi$
$42$	−1.85904	−	1.35067i	−0.286856	−	0.208413i
$43$	8.01874			1.22285			0.611423	−	0.791304i	$-0.290597\pi$
$43$	8.01874			1.22285			0.611423	+	0.791304i	$0.290597\pi$
$44$	0.688111	+	0.499942i	0.103737	+	0.0753691i
$45$		0			0
$46$	−10.9330	+	7.94330i	−1.61198	+	1.17118i
$47$	5.39046	−	3.91640i	0.786280	−	0.571266i	−0.120577	−	0.992704i	$-0.538475\pi$
$47$	5.39046	−	3.91640i	0.786280	−	0.571266i	0.906857	+	0.421438i	$0.138475\pi$
$48$	−1.41890	−	4.36692i	−0.204800	−	0.630310i
$49$	−4.76349			−0.680499
$50$		0			0
$51$	2.19405			0.307228
$52$	−0.150535	−	0.463298i	−0.0208754	−	0.0642478i
$53$	3.37484	−	2.45196i	0.463569	−	0.336803i	−0.331360	−	0.943504i	$-0.607508\pi$
$53$	3.37484	−	2.45196i	0.463569	−	0.336803i	0.794930	+	0.606701i	$0.207508\pi$
$54$	1.24309	−	0.903160i	0.169163	−	0.122904i
$55$		0			0
$56$	3.04701	+	2.21378i	0.407174	+	0.295829i
$57$	5.71069			0.756399
$58$	9.82064	+	7.13511i	1.28951	+	0.936886i
$59$	3.41917	−	10.5231i	0.445138	−	1.36999i	−0.437195	−	0.899367i	$-0.644028\pi$
$59$	3.41917	−	10.5231i	0.445138	−	1.36999i	0.882332	−	0.470627i	$-0.155972\pi$
$60$		0			0
$61$	−3.78151	−	11.6383i	−0.484173	−	1.49013i	−0.833175	−	0.553009i	$-0.813480\pi$
$61$	−3.78151	−	11.6383i	−0.484173	−	1.49013i	0.349003	−	0.937122i	$-0.386520\pi$
$62$	1.75549	−	5.40283i	0.222947	−	0.686161i
$63$	−0.462134	+	1.42230i	−0.0582234	+	0.179193i
$64$	1.87942	+	5.78425i	0.234927	+	0.723031i
$65$		0			0
$66$	1.11879	−	3.44330i	0.137714	−	0.423841i
$67$	3.48976	+	2.53546i	0.426342	+	0.309756i	0.780185	−	0.625549i	$-0.215125\pi$
$67$	3.48976	+	2.53546i	0.426342	+	0.309756i	−0.353842	+	0.935305i	$0.615125\pi$
$68$	0.792000			0.0960442
$69$	7.11531	+	5.16958i	0.856583	+	0.622344i
$70$		0			0
$71$	−4.67410	+	3.39593i	−0.554713	+	0.403023i	−0.829520	−	0.558477i	$-0.811386\pi$
$71$	−4.67410	+	3.39593i	−0.554713	+	0.403023i	0.274807	+	0.961499i	$0.411386\pi$
$72$	−2.03746	+	1.48030i	−0.240117	+	0.174455i
$73$	−2.14051	−	6.58781i	−0.250528	−	0.771045i	−0.994678	−	0.103033i	$-0.967145\pi$
$73$	−2.14051	−	6.58781i	−0.250528	−	0.771045i	0.744150	−	0.668012i	$-0.232855\pi$
$74$	14.9828			1.74172
$75$		0			0
$76$	2.06142			0.236461
$77$	1.08890	+	3.35130i	0.124092	+	0.381917i
$78$	−1.67756	+	1.21882i	−0.189946	+	0.138004i
$79$	8.63118	−	6.27092i	0.971084	−	0.705534i	0.0153858	−	0.999882i	$-0.495102\pi$
$79$	8.63118	−	6.27092i	0.971084	−	0.705534i	0.955698	+	0.294348i	$0.0951024\pi$
$80$		0			0
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	−2.85106			−0.314846
$83$	0.181222	+	0.131666i	0.0198917	+	0.0144522i	0.597687	−	0.801730i	$-0.296087\pi$
$83$	0.181222	+	0.131666i	0.0198917	+	0.0144522i	−0.577795	+	0.816182i	$0.696087\pi$
$84$	−0.166819	+	0.513417i	−0.0182015	+	0.0560184i
$85$		0			0
$86$	−3.80745	−	11.7181i	−0.410568	−	1.26360i
$87$	2.44129	−	7.51351i	0.261733	−	0.805533i
$88$	−1.83373	+	5.64364i	−0.195476	+	0.601615i
$89$	0.132620	+	0.408162i	0.0140577	+	0.0432651i	0.957839	−	0.287304i	$-0.0927592\pi$
$89$	0.132620	+	0.408162i	0.0140577	+	0.0432651i	−0.943782	+	0.330570i	$0.892759\pi$
$90$		0			0
$91$	0.623652	−	1.91940i	0.0653765	−	0.201208i
$92$	2.56846	+	1.86610i	0.267780	+	0.194554i
$93$	−3.69717			−0.383379
$94$	−8.28270	−	6.01773i	−0.854295	−	0.620682i
$95$		0			0
$96$	−1.63293	+	1.18639i	−0.166660	+	0.121086i
$97$	10.1083	−	7.34411i	1.02634	−	0.745682i	0.0587692	−	0.998272i	$-0.481282\pi$
$97$	10.1083	−	7.34411i	1.02634	−	0.745682i	0.967573	+	0.252590i	$0.0812824\pi$
$98$	2.26180	+	6.96109i	0.228476	+	0.703177i
$99$	−2.35626			−0.236813
$100$		0			0
$101$	8.19767			0.815698			0.407849	−	0.913049i	$-0.366279\pi$
$101$	8.19767			0.815698			0.407849	+	0.913049i	$0.366279\pi$
$102$	−1.04178	−	3.20626i	−0.103151	−	0.317467i
$103$	2.02258	−	1.46949i	0.199291	−	0.144794i	−0.483664	−	0.875254i	$-0.660694\pi$
$103$	2.02258	−	1.46949i	0.199291	−	0.144794i	0.682955	+	0.730460i	$0.260694\pi$
$104$	2.74956	−	1.99767i	0.269617	−	0.195888i
$105$		0			0
$106$	−5.18559	−	3.76755i	−0.503669	−	0.365937i
$107$	1.81004			0.174983			0.0874914	−	0.996165i	$-0.472115\pi$
$107$	1.81004			0.174983			0.0874914	+	0.996165i	$0.472115\pi$
$108$	−0.292036	−	0.212177i	−0.0281012	−	0.0204167i
$109$	−0.910913	+	2.80350i	−0.0872496	+	0.268527i	−0.985156	−	0.171659i	$-0.945087\pi$
$109$	−0.910913	+	2.80350i	−0.0872496	+	0.268527i	0.897907	+	0.440186i	$0.145087\pi$
$110$		0			0
$111$	−3.01321	−	9.27372i	−0.286002	−	0.880223i
$112$	2.12196	−	6.53071i	0.200506	−	0.617094i
$113$	−4.27571	+	13.1593i	−0.402225	+	1.23792i	0.520966	+	0.853577i	$0.325572\pi$
$113$	−4.27571	+	13.1593i	−0.402225	+	1.23792i	−0.923191	+	0.384342i	$0.874428\pi$
$114$	−2.71154	−	8.34527i	−0.253959	−	0.781606i
$115$		0			0
$116$	0.881247	−	2.71220i	0.0818217	−	0.251821i
$117$	1.09177	+	0.793220i	0.100934	+	0.0733332i
$118$	−17.0014			−1.56510
$119$	2.65454	+	1.92864i	0.243341	+	0.176798i
$120$		0			0
$121$	4.40757	−	3.20229i	0.400689	−	0.291117i
$122$	−15.2120	+	11.0522i	−1.37723	+	1.00062i
$123$	0.573380	+	1.76468i	0.0516999	+	0.159116i
$124$	−1.33459			−0.119850
$125$		0			0
$126$	2.29790			0.204713
$127$	−1.77374	−	5.45902i	−0.157394	−	0.484410i	0.841001	−	0.541033i	$-0.181967\pi$
$127$	−1.77374	−	5.45902i	−0.157394	−	0.484410i	−0.998396	+	0.0566233i	$0.981967\pi$
$128$	10.8262	−	7.86572i	0.956914	−	0.695238i
$129$	−6.48730	+	4.71330i	−0.571175	+	0.414983i
$130$		0			0
$131$	3.52534	+	2.56131i	0.308010	+	0.223783i	0.731042	−	0.682332i	$-0.239034\pi$
$131$	3.52534	+	2.56131i	0.308010	+	0.223783i	−0.423032	+	0.906115i	$0.639034\pi$
$132$	−0.850553			−0.0740311
$133$	6.90926	+	5.01987i	0.599108	+	0.435278i
$134$	2.04817	−	6.30363i	0.176935	−	0.544550i
$135$		0			0
$136$	1.70750	+	5.25514i	0.146417	+	0.450624i
$137$	−0.610187	+	1.87796i	−0.0521318	+	0.160445i	−0.973733	−	0.227693i	$-0.926882\pi$
$137$	−0.610187	+	1.87796i	−0.0521318	+	0.160445i	0.921601	+	0.388138i	$0.126882\pi$
$138$	4.17604	−	12.8525i	0.355488	−	1.09408i
$139$	0.518869	+	1.59692i	0.0440099	+	0.135449i	0.970647	−	0.240508i	$-0.0773141\pi$
$139$	0.518869	+	1.59692i	0.0440099	+	0.135449i	−0.926637	+	0.375957i	$0.877314\pi$
$140$		0			0
$141$	−2.05897	+	6.33687i	−0.173397	+	0.533661i
$142$	7.18197	+	5.21801i	0.602698	+	0.437885i
$143$	3.17978			0.265907
$144$	3.71472	+	2.69890i	0.309560	+	0.224909i
$145$		0			0
$146$	−8.61070	+	6.25604i	−0.712627	+	0.517754i
$147$	3.85375	−	2.79991i	0.317852	−	0.230933i
$148$	−1.08770	−	3.34759i	−0.0894083	−	0.275171i
$149$	−7.38524			−0.605023			−0.302511	−	0.953146i	$-0.597825\pi$
$149$	−7.38524			−0.605023			−0.302511	+	0.953146i	$0.597825\pi$
$150$		0			0
$151$	−4.26137			−0.346785			−0.173393	−	0.984853i	$-0.555473\pi$
$151$	−4.26137			−0.346785			−0.173393	+	0.984853i	$0.555473\pi$
$152$	4.44428	+	13.6781i	0.360479	+	1.10944i
$153$	−1.77502	+	1.28963i	−0.143502	+	0.104260i
$154$	4.38037	−	3.18253i	0.352980	−	0.256455i
$155$		0			0
$156$	0.394104	+	0.286334i	0.0315536	+	0.0229250i
$157$	−16.0573			−1.28152			−0.640758	−	0.767743i	$-0.721380\pi$
$157$	−16.0573			−1.28152			−0.640758	+	0.767743i	$0.721380\pi$
$158$	−13.2622	−	9.63557i	−1.05509	−	0.766565i
$159$	−1.28907	+	3.96736i	−0.102230	+	0.314632i
$160$		0			0
$161$	4.06447	+	12.5092i	0.320325	+	0.985859i
$162$	−0.474819	+	1.46134i	−0.0373053	+	0.114814i
$163$	6.88916	−	21.2026i	0.539600	−	1.66072i	−0.193893	−	0.981023i	$-0.562111\pi$
$163$	6.88916	−	21.2026i	0.539600	−	1.66072i	0.733493	−	0.679697i	$-0.237889\pi$
$164$	0.206976	+	0.637008i	0.0161621	+	0.0497420i
$165$		0			0
$166$	0.106361	−	0.327345i	0.00825520	−	0.0254069i
$167$	−5.23111	−	3.80062i	−0.404795	−	0.294101i	0.366696	−	0.930341i	$-0.380489\pi$
$167$	−5.23111	−	3.80062i	−0.404795	−	0.294101i	−0.771491	+	0.636240i	$0.780489\pi$
$168$	−3.76631			−0.290577
$169$	9.04387	+	6.57075i	0.695682	+	0.505443i
$170$		0			0
$171$	−4.62004	+	3.35666i	−0.353303	+	0.256690i
$172$	−2.34176	+	1.70139i	−0.178558	+	0.129730i
$173$	3.65198	+	11.2396i	0.277655	+	0.854533i	0.988505	+	0.151190i	$0.0483104\pi$
$173$	3.65198	+	11.2396i	0.277655	+	0.854533i	−0.710850	+	0.703344i	$0.751690\pi$
$174$	−12.1390			−0.920254
$175$		0			0
$176$	10.8191			0.815520
$177$	3.41917	+	10.5231i	0.257000	+	0.790966i
$178$	0.533494	−	0.387606i	0.0399871	−	0.0290523i
$179$	−12.6001	+	9.15450i	−0.941775	+	0.684240i	−0.948847	−	0.315735i	$-0.897749\pi$
$179$	−12.6001	+	9.15450i	−0.941775	+	0.684240i	0.00707213	+	0.999975i	$0.497749\pi$
$180$		0			0
$181$	11.7952	+	8.56974i	0.876733	+	0.636984i	0.932385	−	0.361466i	$-0.117724\pi$
$181$	11.7952	+	8.56974i	0.876733	+	0.636984i	−0.0556522	+	0.998450i	$0.517724\pi$
$182$	−3.10103			−0.229864
$183$	9.90012	+	7.19286i	0.731838	+	0.531711i
$184$	−6.84463	+	21.0656i	−0.504593	+	1.55298i
$185$		0			0
$186$	1.75549	+	5.40283i	0.128719	+	0.396155i
$187$	−1.59754	+	4.91672i	−0.116824	+	0.359546i
$188$	−0.743241	+	2.28746i	−0.0542064	+	0.166830i
$189$	−0.462134	−	1.42230i	−0.0336153	−	0.103457i
$190$		0			0
$191$	−6.48577	+	19.9611i	−0.469294	+	1.44434i	0.384207	+	0.923247i	$0.374475\pi$
$191$	−6.48577	+	19.9611i	−0.469294	+	1.44434i	−0.853501	+	0.521091i	$0.825525\pi$
$192$	−4.92037	−	3.57486i	−0.355097	−	0.257993i
$193$	−22.7094			−1.63466			−0.817328	−	0.576173i	$-0.804546\pi$
$193$	−22.7094			−1.63466			−0.817328	+	0.576173i	$0.804546\pi$
$194$	−15.5319	−	11.2846i	−1.11512	−	0.810185i
$195$		0			0
$196$	1.39111	−	1.01070i	0.0993651	−	0.0721930i
$197$	1.09494	−	0.795517i	0.0780109	−	0.0566782i	−0.548096	−	0.836415i	$-0.684647\pi$
$197$	1.09494	−	0.795517i	0.0780109	−	0.0566782i	0.626107	+	0.779737i	$0.284647\pi$
$198$	1.11879	+	3.44330i	0.0795093	+	0.244704i
$199$	−8.96061			−0.635201			−0.317600	−	0.948225i	$-0.602877\pi$
$199$	−8.96061			−0.635201			−0.317600	+	0.948225i	$0.602877\pi$
$200$		0			0
$201$	−4.31358			−0.304257
$202$	−3.89241	−	11.9796i	−0.273869	−	0.842882i
$203$	9.55827	−	6.94449i	0.670859	−	0.487408i
$204$	−0.640742	+	0.465526i	−0.0448609	+	0.0325933i
$205$		0			0
$206$	−3.10780	−	2.25795i	−0.216530	−	0.157319i
$207$	−8.79501			−0.611295
$208$	−5.01304	−	3.64219i	−0.347592	−	0.252540i
$209$	−4.15808	+	12.7973i	−0.287621	+	0.885205i
$210$		0			0
$211$	1.80461	+	5.55401i	0.124234	+	0.382354i	0.993761	−	0.111532i	$-0.0355759\pi$
$211$	1.80461	+	5.55401i	0.124234	+	0.382354i	−0.869527	+	0.493886i	$0.835576\pi$
$212$	−0.465325	+	1.43212i	−0.0319586	+	0.0983586i
$213$	1.78535	−	5.49473i	0.122330	−	0.376493i
$214$	−0.859440	−	2.64508i	−0.0587501	−	0.180814i
$215$		0			0
$216$	0.778240	−	2.39518i	0.0529525	−	0.162971i
$217$	−4.47314	−	3.24993i	−0.303656	−	0.220619i
$218$	4.52939			0.306769
$219$	5.60393	+	4.07149i	0.378678	+	0.275126i
$220$		0			0
$221$	2.39541	−	1.74036i	0.161132	−	0.117070i
$222$	−12.1214	+	8.80668i	−0.813532	+	0.591066i
$223$	2.41681	+	7.43818i	0.161842	+	0.498098i	0.998790	−	0.0491848i	$-0.0156623\pi$
$223$	2.41681	+	7.43818i	0.161842	+	0.498098i	−0.836948	+	0.547283i	$0.815662\pi$
$224$	−3.01853			−0.201684
$225$		0			0
$226$	21.2604			1.41422
$227$	−5.03975	−	15.5107i	−0.334500	−	1.02948i	−0.966968	−	0.254898i	$-0.917958\pi$
$227$	−5.03975	−	15.5107i	−0.334500	−	1.02948i	0.632468	−	0.774586i	$-0.282042\pi$
$228$	−1.66773	+	1.21167i	−0.110448	+	0.0802451i
$229$	17.5628	−	12.7601i	1.16058	−	0.843211i	0.170729	−	0.985318i	$-0.445388\pi$
$229$	17.5628	−	12.7601i	1.16058	−	0.843211i	0.989851	+	0.142107i	$0.0453877\pi$
$230$		0			0
$231$	−2.85079	−	2.07122i	−0.187568	−	0.136276i
$232$	19.8961			1.30624
$233$	−10.9493	−	7.95512i	−0.717312	−	0.521157i	0.168213	−	0.985751i	$-0.446201\pi$
$233$	−10.9493	−	7.95512i	−0.717312	−	0.521157i	−0.885524	+	0.464593i	$0.846201\pi$
$234$	0.640771	−	1.97209i	0.0418885	−	0.128920i
$235$		0			0
$236$	1.23424	+	3.79860i	0.0803421	+	0.247268i
$237$	−3.29682	+	10.1466i	−0.214151	+	0.659090i
$238$	1.55797	−	4.79495i	0.100988	−	0.310810i
$239$	−3.25514	−	10.0183i	−0.210557	−	0.648028i	−0.999439	−	0.0334838i	$-0.989340\pi$
$239$	−3.25514	−	10.0183i	−0.210557	−	0.648028i	0.788882	−	0.614545i	$-0.210660\pi$
$240$		0			0
$241$	6.02082	−	18.5302i	0.387835	−	1.19363i	−0.546567	−	0.837415i	$-0.684066\pi$
$241$	6.02082	−	18.5302i	0.387835	−	1.19363i	0.934403	−	0.356219i	$-0.115934\pi$
$242$	−6.77244	−	4.92047i	−0.435349	−	0.316300i
$243$	1.00000			0.0641500
$244$	3.57371	+	2.59645i	0.228783	+	0.166221i
$245$		0			0
$246$	2.30655	−	1.67581i	0.147060	−	0.106846i
$247$	6.23478	−	4.52983i	0.396709	−	0.288226i
$248$	−2.87728	−	8.85537i	−0.182708	−	0.562317i
$249$	−0.224003			−0.0141956
$250$		0			0
$251$	−20.9446			−1.32201			−0.661007	−	0.750380i	$-0.729871\pi$
$251$	−20.9446			−1.32201			−0.661007	+	0.750380i	$0.729871\pi$
$252$	−0.166819	−	0.513417i	−0.0105086	−	0.0323422i
$253$	−16.7655	+	12.1808i	−1.05404	+	0.765803i
$254$	−7.13529	+	5.18409i	−0.447708	+	0.325279i
$255$		0			0
$256$	−6.79428	−	4.93633i	−0.424643	−	0.308521i
$257$	1.67121			0.104247			0.0521237	−	0.998641i	$-0.483401\pi$
$257$	1.67121			0.104247			0.0521237	+	0.998641i	$0.483401\pi$
$258$	9.96804	+	7.24220i	0.620583	+	0.450880i
$259$	4.50625	−	13.8688i	0.280005	−	0.861766i
$260$		0			0
$261$	2.44129	+	7.51351i	0.151112	+	0.465074i
$262$	2.06905	−	6.36789i	0.127826	−	0.393409i
$263$	−2.33514	+	7.18682i	−0.143991	+	0.443158i	−0.996880	−	0.0789341i	$-0.974848\pi$
$263$	−2.33514	+	7.18682i	−0.143991	+	0.443158i	0.852889	+	0.522092i	$0.174848\pi$
$264$	−1.83373	−	5.64364i	−0.112858	−	0.347342i
$265$		0			0
$266$	4.05510	−	12.4803i	0.248634	−	0.765218i
$267$	−0.347203	−	0.252258i	−0.0212485	−	0.0154379i
$268$	−1.55710			−0.0951151
$269$	9.12904	+	6.63264i	0.556608	+	0.404399i	0.830216	−	0.557442i	$-0.188217\pi$
$269$	9.12904	+	6.63264i	0.556608	+	0.404399i	−0.273608	+	0.961841i	$0.588217\pi$
$270$		0			0
$271$	8.87912	−	6.45106i	0.539368	−	0.391874i	−0.284482	−	0.958681i	$-0.591822\pi$
$271$	8.87912	−	6.45106i	0.539368	−	0.391874i	0.823850	+	0.566808i	$0.191822\pi$
$272$	8.15029	−	5.92153i	0.494184	−	0.359045i
$273$	0.623652	+	1.91940i	0.0377452	+	0.116168i
$274$	3.03407			0.183295
$275$		0			0
$276$	−3.17479			−0.191100
$277$	1.77719	+	5.46964i	0.106781	+	0.328639i	0.990144	−	0.140050i	$-0.0447265\pi$
$277$	1.77719	+	5.46964i	0.106781	+	0.328639i	−0.883363	+	0.468689i	$0.844726\pi$
$278$	2.08727	−	1.51649i	0.125186	−	0.0909531i
$279$	2.99107	−	2.17314i	0.179071	−	0.130103i
$280$		0			0
$281$	−6.87633	−	4.99595i	−0.410208	−	0.298033i	0.363478	−	0.931603i	$-0.381589\pi$
$281$	−6.87633	−	4.99595i	−0.410208	−	0.298033i	−0.773686	+	0.633569i	$0.781589\pi$
$282$	10.2380			0.609663
$283$	−13.9352	−	10.1245i	−0.828360	−	0.601839i	0.0907350	−	0.995875i	$-0.471078\pi$
$283$	−13.9352	−	10.1245i	−0.828360	−	0.601839i	−0.919095	+	0.394036i	$0.871078\pi$
$284$	0.644468	−	1.98347i	0.0382421	−	0.117697i
$285$		0			0
$286$	−1.50982	−	4.64675i	−0.0892776	−	0.274768i
$287$	−0.857487	+	2.63907i	−0.0506158	+	0.155780i
$288$	0.623723	−	1.91962i	0.0367532	−	0.113115i
$289$	−3.76573	−	11.5897i	−0.221513	−	0.681748i
$290$		0			0
$291$	−3.86103	+	11.8830i	−0.226337	+	0.696595i
$292$	2.02289	+	1.46971i	0.118380	+	0.0860084i
$293$	−9.38764			−0.548432			−0.274216	−	0.961668i	$-0.588418\pi$
$293$	−9.38764			−0.548432			−0.274216	+	0.961668i	$0.588418\pi$
$294$	−5.92146	−	4.30219i	−0.345347	−	0.250909i
$295$		0			0
$296$	19.8672	−	14.4344i	1.15476	−	0.838980i
$297$	1.90625	−	1.38497i	0.110612	−	0.0803642i
$298$	3.50665	+	10.7924i	0.203135	+	0.625185i
$299$	11.8689			0.686397
$300$		0			0
$301$	−11.9920			−0.691207
$302$	2.02338	+	6.22732i	0.116432	+	0.358342i
$303$	−6.63205	+	4.81847i	−0.381001	+	0.276814i
$304$	21.2136	−	15.4126i	1.21668	−	0.883973i
$305$		0			0
$306$	2.72741	+	1.98158i	0.155916	+	0.113279i
$307$	−10.6465			−0.607627			−0.303814	−	0.952731i	$-0.598260\pi$
$307$	−10.6465			−0.607627			−0.303814	+	0.952731i	$0.598260\pi$
$308$	−1.02907	−	0.747662i	−0.0586366	−	0.0426020i
$309$	−0.772559	+	2.37769i	−0.0439493	+	0.135262i
$310$		0			0
$311$	−8.45383	−	26.0182i	−0.479373	−	1.47536i	−0.839969	−	0.542635i	$-0.817427\pi$
$311$	−8.45383	−	26.0182i	−0.479373	−	1.47536i	0.360596	−	0.932722i	$-0.382573\pi$
$312$	−1.05024	+	3.23230i	−0.0594581	+	0.182993i
$313$	0.616517	−	1.89744i	0.0348476	−	0.107250i	−0.932120	−	0.362150i	$-0.882043\pi$
$313$	0.616517	−	1.89744i	0.0348476	−	0.107250i	0.966967	+	0.254900i	$0.0820427\pi$
$314$	7.62433	+	23.4653i	0.430266	+	1.32422i
$315$		0			0
$316$	−1.19007	+	3.66267i	−0.0669469	+	0.206041i
$317$	6.99699	+	5.08361i	0.392990	+	0.285524i	0.766680	−	0.642030i	$-0.221907\pi$
$317$	6.99699	+	5.08361i	0.392990	+	0.285524i	−0.373690	+	0.927554i	$0.621907\pi$
$318$	6.40975			0.359441
$319$	15.0597	+	10.9415i	0.843182	+	0.612607i
$320$		0			0
$321$	−1.46435	+	1.06391i	−0.0817321	+	0.0593818i
$322$	16.3503	−	11.8792i	0.911165	−	0.662000i
$323$	3.87184	+	11.9163i	0.215435	+	0.663040i
$324$	0.360976			0.0200542
$325$		0			0
$326$	−34.2554			−1.89723
$327$	−0.910913	−	2.80350i	−0.0503736	−	0.155034i
$328$	−3.78049	+	2.74669i	−0.208743	+	0.151661i
$329$	−8.06141	+	5.85696i	−0.444440	+	0.322905i
$330$		0			0
$331$	3.19020	+	2.31782i	0.175349	+	0.127399i	0.671998	−	0.740553i	$-0.265436\pi$
$331$	3.19020	+	2.31782i	0.175349	+	0.127399i	−0.496649	+	0.867952i	$0.665436\pi$
$332$	−0.0808598			−0.00443776
$333$	7.88870	+	5.73148i	0.432298	+	0.314083i
$334$	−3.07018	+	9.44905i	−0.167993	+	0.517029i
$335$		0			0
$336$	2.12196	+	6.53071i	0.115762	+	0.356279i
$337$	−1.22207	+	3.76115i	−0.0665706	+	0.204883i	−0.978809	−	0.204778i	$-0.934353\pi$
$337$	−1.22207	+	3.76115i	−0.0665706	+	0.204883i	0.912238	+	0.409661i	$0.134353\pi$
$338$	5.30792	−	16.3361i	0.288713	−	0.888567i
$339$	−4.27571	−	13.1593i	−0.232224	−	0.714713i
$340$		0			0
$341$	2.69199	−	8.28511i	0.145780	−	0.448664i
$342$	7.09891	+	5.15766i	0.383865	+	0.278894i
$343$	17.5923			0.949893
$344$	−16.3379	−	11.8701i	−0.880878	−	0.639995i
$345$		0			0
$346$	14.6909	−	10.6736i	0.789789	−	0.573815i
$347$	−8.08690	+	5.87548i	−0.434127	+	0.315412i	−0.783297	−	0.621647i	$-0.786464\pi$
$347$	−8.08690	+	5.87548i	−0.434127	+	0.315412i	0.349170	+	0.937060i	$0.386464\pi$
$348$	0.881247	+	2.71220i	0.0472398	+	0.145389i
$349$	18.4534			0.987789			0.493895	−	0.869522i	$-0.335573\pi$
$349$	18.4534			0.987789			0.493895	+	0.869522i	$0.335573\pi$
$350$		0			0
$351$	−1.34951			−0.0720313
$352$	−1.46965	−	4.52312i	−0.0783327	−	0.241083i
$353$	7.54326	−	5.48050i	0.401487	−	0.291697i	−0.368659	−	0.929565i	$-0.620183\pi$
$353$	7.54326	−	5.48050i	0.401487	−	0.291697i	0.770146	+	0.637867i	$0.220183\pi$
$354$	13.7544	−	9.99316i	0.731038	−	0.531130i
$355$		0			0
$356$	−0.125332	−	0.0910592i	−0.00664260	−	0.00482613i
$357$	−3.28119			−0.173659
$358$	19.3606	+	14.0663i	1.02324	+	0.743428i
$359$	8.94412	−	27.5272i	0.472052	−	1.45283i	−0.377839	−	0.925871i	$-0.623333\pi$
$359$	8.94412	−	27.5272i	0.472052	−	1.45283i	0.849892	−	0.526957i	$-0.176667\pi$
$360$		0			0
$361$	4.20632	+	12.9457i	0.221385	+	0.681354i
$362$	6.92273	−	21.3060i	0.363850	−	1.11982i
$363$	−1.68354	+	5.18141i	−0.0883631	+	0.271954i
$364$	0.225124	+	0.692860i	0.0117997	+	0.0363157i
$365$		0			0
$366$	5.81047	−	17.8828i	0.303718	−	0.934748i
$367$	−3.23501	−	2.35037i	−0.168866	−	0.122688i	0.500142	−	0.865943i	$-0.333281\pi$
$367$	−3.23501	−	2.35037i	−0.168866	−	0.122688i	−0.669008	+	0.743255i	$0.733281\pi$
$368$	40.3836			2.10514
$369$	−1.50113	−	1.09063i	−0.0781456	−	0.0567761i
$370$		0			0
$371$	−5.04705	+	3.66690i	−0.262030	+	0.190376i
$372$	1.07971	−	0.784453i	0.0559802	−	0.0406720i
$373$	0.980386	+	3.01732i	0.0507625	+	0.156231i	0.973224	−	0.229857i	$-0.0738260\pi$
$373$	0.980386	+	3.01732i	0.0507625	+	0.156231i	−0.922462	+	0.386088i	$0.873826\pi$
$374$	7.94355			0.410751
$375$		0			0
$376$	−16.7803			−0.865377
$377$	−3.29453	−	10.1395i	−0.169677	−	0.522212i
$378$	−1.85904	+	1.35067i	−0.0956187	+	0.0694711i
$379$	−23.0736	+	16.7640i	−1.18521	+	0.861107i	−0.992750	−	0.120198i	$-0.961647\pi$
$379$	−23.0736	+	16.7640i	−1.18521	+	0.861107i	−0.192462	+	0.981304i	$0.561647\pi$
$380$		0			0
$381$	4.64372	+	3.37386i	0.237905	+	0.172848i
$382$	32.2497			1.65004
$383$	−9.27224	−	6.73667i	−0.473789	−	0.344228i	0.325127	−	0.945670i	$-0.394593\pi$
$383$	−9.27224	−	6.73667i	−0.473789	−	0.344228i	−0.798916	+	0.601442i	$0.794593\pi$
$384$	−4.13526	+	12.7270i	−0.211026	+	0.649472i
$385$		0			0
$386$	10.7828	+	33.1862i	0.548832	+	1.68913i
$387$	2.47793	−	7.62628i	0.125960	−	0.387665i
$388$	−1.39374	+	4.28949i	−0.0707564	+	0.217766i
$389$	10.5827	+	32.5702i	0.536564	+	1.65137i	0.740245	+	0.672337i	$0.234709\pi$
$389$	10.5827	+	32.5702i	0.536564	+	1.65137i	−0.203681	+	0.979037i	$0.565291\pi$
$390$		0			0
$391$	−5.96301	+	18.3522i	−0.301562	+	0.928113i
$392$	9.70541	+	7.05140i	0.490197	+	0.356149i
$393$	−4.35756			−0.219810
$394$	−1.68242	−	1.22235i	−0.0847591	−	0.0615811i
$395$		0			0
$396$	0.688111	−	0.499942i	0.0345789	−	0.0251230i
$397$	−16.2073	+	11.7753i	−0.813422	+	0.590986i	−0.914821	−	0.403860i	$-0.867668\pi$
$397$	−16.2073	+	11.7753i	−0.813422	+	0.590986i	0.101399	+	0.994846i	$0.467668\pi$
$398$	4.25467	+	13.0945i	0.213267	+	0.656369i
$399$	−8.54031			−0.427550
$400$		0			0
$401$	4.98200			0.248789			0.124395	−	0.992233i	$-0.460301\pi$
$401$	4.98200			0.248789			0.124395	+	0.992233i	$0.460301\pi$
$402$	2.04817	+	6.30363i	0.102154	+	0.314396i
$403$	−4.03647	+	2.93267i	−0.201071	+	0.146087i
$404$	−2.39401	+	1.73935i	−0.119107	+	0.0865361i
$405$		0			0
$406$	−14.6867	−	10.6705i	−0.728890	−	0.529570i
$407$	22.9758			1.13887
$408$	−4.47029	−	3.24785i	−0.221312	−	0.160793i
$409$	7.37286	−	22.6913i	0.364565	−	1.12201i	−0.585689	−	0.810536i	$-0.699176\pi$
$409$	7.37286	−	22.6913i	0.364565	−	1.12201i	0.950253	−	0.311478i	$-0.100824\pi$
$410$		0			0
$411$	−0.610187	−	1.87796i	−0.0300983	−	0.0926330i
$412$	−0.278875	+	0.858290i	−0.0137392	+	0.0422849i
$413$	−5.11335	+	15.7373i	−0.251612	+	0.774381i
$414$	4.17604	+	12.8525i	0.205241	+	0.631667i
$415$		0			0
$416$	−0.841718	+	2.59054i	−0.0412686	+	0.127012i
$417$	−1.35842	−	0.986948i	−0.0665220	−	0.0483311i
$418$	20.6755			1.01127
$419$	−0.390391	−	0.283636i	−0.0190719	−	0.0138565i	0.578208	−	0.815889i	$-0.303752\pi$
$419$	−0.390391	−	0.283636i	−0.0190719	−	0.0138565i	−0.597280	+	0.802033i	$0.703752\pi$
$420$		0			0
$421$	14.3344	−	10.4146i	0.698616	−	0.507575i	−0.180865	−	0.983508i	$-0.557890\pi$
$421$	14.3344	−	10.4146i	0.698616	−	0.507575i	0.879481	+	0.475933i	$0.157890\pi$
$422$	7.25945	−	5.27430i	0.353385	−	0.256749i
$423$	−2.05897	−	6.33687i	−0.100111	−	0.308109i
$424$	−10.5057			−0.510203
$425$		0			0
$426$	−8.87740			−0.430112
$427$	5.65523	+	17.4050i	0.273676	+	0.842288i
$428$	−0.528596	+	0.384047i	−0.0255506	+	0.0185636i
$429$	−2.57250	+	1.86903i	−0.124201	+	0.0902375i
$430$		0			0
$431$	−21.6866	−	15.7562i	−1.04461	−	0.758952i	−0.0734279	−	0.997301i	$-0.523394\pi$
$431$	−21.6866	−	15.7562i	−1.04461	−	0.758952i	−0.971180	+	0.238349i	$0.923394\pi$
$432$	−4.59165			−0.220916
$433$	−7.46816	−	5.42593i	−0.358897	−	0.260754i	0.393695	−	0.919241i	$-0.371197\pi$
$433$	−7.46816	−	5.42593i	−0.358897	−	0.260754i	−0.752592	+	0.658487i	$0.771197\pi$
$434$	−2.62532	+	8.07992i	−0.126020	+	0.387848i
$435$		0			0
$436$	−0.328818	−	1.01200i	−0.0157475	−	0.0484659i
$437$	−15.5205	+	47.7673i	−0.742448	+	2.28502i
$438$	3.28899	−	10.1225i	0.157154	−	0.483671i
$439$	0.309760	+	0.953343i	0.0147840	+	0.0455006i	0.958176	−	0.286178i	$-0.0923850\pi$
$439$	0.309760	+	0.953343i	0.0147840	+	0.0455006i	−0.943392	+	0.331679i	$0.892385\pi$
$440$		0			0
$441$	−1.47200	+	4.53035i	−0.0700952	+	0.215731i
$442$	−3.68065	−	2.67415i	−0.175071	−	0.127196i
$443$	26.2872			1.24894			0.624471	−	0.781048i	$-0.285315\pi$
$443$	26.2872			1.24894			0.624471	+	0.781048i	$0.285315\pi$
$444$	2.84763	+	2.06893i	0.135143	+	0.0981869i
$445$		0			0
$446$	9.72219	−	7.06358i	0.460359	−	0.334470i
$447$	5.97479	−	4.34094i	0.282598	−	0.205319i
$448$	−2.81066	−	8.65032i	−0.132791	−	0.408689i
$449$	4.75449			0.224378			0.112189	−	0.993687i	$-0.464214\pi$
$449$	4.75449			0.224378			0.112189	+	0.993687i	$0.464214\pi$
$450$		0			0
$451$	−4.37202			−0.205870
$452$	−1.54343	−	4.75019i	−0.0725968	−	0.223430i
$453$	3.44752	−	2.50477i	0.161979	−	0.117684i
$454$	−20.2736	+	14.7296i	−0.951485	+	0.691294i
$455$		0			0
$456$	−11.6353	−	8.45353i	−0.544872	−	0.395873i
$457$	−15.9703			−0.747059			−0.373529	−	0.927618i	$-0.621852\pi$
$457$	−15.9703			−0.747059			−0.373529	+	0.927618i	$0.621852\pi$
$458$	−26.9860	−	19.6065i	−1.26097	−	0.916151i
$459$	0.677999	−	2.08667i	0.0316463	−	0.0973972i
$460$		0			0
$461$	12.2852	+	37.8100i	0.572180	+	1.76099i	0.645588	+	0.763686i	$0.276613\pi$
$461$	12.2852	+	37.8100i	0.572180	+	1.76099i	−0.0734077	+	0.997302i	$0.523387\pi$
$462$	−1.67315	+	5.14944i	−0.0778421	+	0.239573i
$463$	8.07181	−	24.8425i	0.375129	−	1.15453i	−0.568263	−	0.822847i	$-0.692384\pi$
$463$	8.07181	−	24.8425i	0.375129	−	1.15453i	0.943392	−	0.331681i	$-0.107616\pi$
$464$	−11.2095	−	34.4994i	−0.520389	−	1.60159i
$465$		0			0
$466$	−6.42623	+	19.7779i	−0.297689	+	0.916194i
$467$	3.11637	+	2.26417i	0.144208	+	0.104773i	0.657550	−	0.753411i	$-0.271593\pi$
$467$	3.11637	+	2.26417i	0.144208	+	0.104773i	−0.513342	+	0.858184i	$0.671593\pi$
$468$	−0.487140			−0.0225181
$469$	−5.21893	−	3.79177i	−0.240988	−	0.175088i
$470$		0			0
$471$	12.9907	−	9.43827i	0.598578	−	0.434893i
$472$	−22.5438	+	16.3790i	−1.03766	+	0.753906i
$473$	−5.83863	−	17.9695i	−0.268460	−	0.826236i
$474$	16.3930			0.752956
$475$		0			0
$476$	−1.18443			−0.0542884
$477$	−1.28907	−	3.96736i	−0.0590226	−	0.181653i
$478$	−13.0945	+	9.51374i	−0.598930	+	0.435148i
$479$	11.5445	−	8.38758i	0.527483	−	0.383239i	−0.291933	−	0.956439i	$-0.594298\pi$
$479$	11.5445	−	8.38758i	0.527483	−	0.383239i	0.819415	+	0.573200i	$0.194298\pi$
$480$		0			0
$481$	−10.6458	−	7.73466i	−0.485409	−	0.352670i
$482$	−29.9377			−1.36363
$483$	−10.6409	−	7.73108i	−0.484179	−	0.351776i
$484$	−0.607720	+	1.87037i	−0.0276236	+	0.0850167i
$485$		0			0
$486$	−0.474819	−	1.46134i	−0.0215382	−	0.0662879i
$487$	7.67049	−	23.6073i	0.347583	−	1.06975i	−0.612604	−	0.790390i	$-0.709878\pi$
$487$	7.67049	−	23.6073i	0.347583	−	1.06975i	0.960186	−	0.279360i	$-0.0901223\pi$
$488$	−9.52349	+	29.3103i	−0.431108	+	1.32681i
$489$	6.88916	+	21.2026i	0.311538	+	0.958817i
$490$		0			0
$491$	3.55040	−	10.9270i	0.160227	−	0.493129i	−0.838426	−	0.545016i	$-0.816524\pi$
$491$	3.55040	−	10.9270i	0.160227	−	0.493129i	0.998653	+	0.0518868i	$0.0165235\pi$
$492$	−0.541871	−	0.393693i	−0.0244295	−	0.0177490i
$493$	17.3334			0.780656
$494$	−9.58003	−	6.96030i	−0.431026	−	0.313159i
$495$		0			0
$496$	−13.7340	+	9.97831i	−0.616673	+	0.448039i
$497$	6.99010	−	5.07860i	0.313549	−	0.227806i
$498$	0.106361	+	0.327345i	0.00476614	+	0.0146687i
$499$	−4.17487			−0.186893			−0.0934465	−	0.995624i	$-0.529788\pi$
$499$	−4.17487			−0.186893			−0.0934465	+	0.995624i	$0.529788\pi$
$500$		0			0
$501$	6.46601			0.288880
$502$	9.94491	+	30.6073i	0.443863	+	1.36607i
$503$	−31.3221	+	22.7569i	−1.39658	+	1.01468i	−0.401478	+	0.915869i	$0.631503\pi$
$503$	−31.3221	+	22.7569i	−1.39658	+	1.01468i	−0.995106	+	0.0988094i	$0.968497\pi$
$504$	3.04701	−	2.21378i	0.135725	−	0.0986097i
$505$		0			0
$506$	25.7610	+	18.7164i	1.14521	+	0.832047i
$507$	−11.1788			−0.496469
$508$	1.67627	+	1.21788i	0.0743726	+	0.0540349i
$509$	9.32603	−	28.7026i	0.413369	−	1.27222i	−0.500333	−	0.865833i	$-0.666789\pi$
$509$	9.32603	−	28.7026i	0.413369	−	1.27222i	0.913702	−	0.406385i	$-0.133211\pi$
$510$		0			0
$511$	3.20112	+	9.85205i	0.141609	+	0.435829i
$512$	4.28289	−	13.1814i	0.189279	−	0.582540i
$513$	1.76470	−	5.43119i	0.0779134	−	0.239793i
$514$	−0.793523	−	2.44221i	−0.0350008	−	0.107721i
$515$		0			0
$516$	0.894473	−	2.75291i	0.0393770	−	0.121190i
$517$	−12.7013	−	9.22804i	−0.558603	−	0.405849i
$518$	−22.4067			−0.984496
$519$	−9.56100	−	6.94647i	−0.419681	−	0.304916i
$520$		0			0
$521$	20.6183	−	14.9801i	0.903304	−	0.656288i	−0.0360088	−	0.999351i	$-0.511464\pi$
$521$	20.6183	−	14.9801i	0.903304	−	0.656288i	0.939312	+	0.343063i	$0.111464\pi$
$522$	9.82064	−	7.13511i	0.429838	−	0.312295i
$523$	−1.20263	−	3.70132i	−0.0525874	−	0.161847i	0.921314	−	0.388820i	$-0.127117\pi$
$523$	−1.20263	−	3.70132i	−0.0525874	−	0.161847i	−0.973901	+	0.226973i	$0.927117\pi$
$524$	−1.57298			−0.0687158
$525$		0			0
$526$	11.6112			0.506271
$527$	−2.50668	−	7.71476i	−0.109193	−	0.336060i
$528$	−8.75283	+	6.35931i	−0.380918	+	0.276753i
$529$	−43.9719	+	31.9474i	−1.91182	+	1.38902i
$530$		0			0
$531$	−8.95150	−	6.50365i	−0.388462	−	0.282234i
$532$	−3.08285			−0.133659
$533$	2.02578	+	1.47182i	0.0877463	+	0.0637514i
$534$	−0.203777	+	0.627160i	−0.00881828	+	0.0271399i
$535$		0			0
$536$	−3.35700	−	10.3318i	−0.145000	−	0.446265i
$537$	4.81281	−	14.8123i	0.207688	−	0.639198i
$538$	5.35792	−	16.4900i	0.230996	−	0.710933i
$539$	3.46841	+	10.6747i	0.149395	+	0.459790i
$540$		0			0
$541$	12.4270	−	38.2465i	0.534280	−	1.64435i	−0.210919	−	0.977504i	$-0.567646\pi$
$541$	12.4270	−	38.2465i	0.534280	−	1.64435i	0.745199	−	0.666842i	$-0.232354\pi$
$542$	−13.6432	−	9.91235i	−0.586025	−	0.425772i
$543$	−14.5797			−0.625675
$544$	−3.58273	−	2.60300i	−0.153608	−	0.111603i
$545$		0			0
$546$	2.50879	−	1.82274i	0.107366	−	0.0780061i
$547$	5.96992	−	4.33740i	0.255255	−	0.185454i	−0.452797	−	0.891613i	$-0.649574\pi$
$547$	5.96992	−	4.33740i	0.255255	−	0.185454i	0.708053	+	0.706160i	$0.249574\pi$
$548$	−0.220263	−	0.677900i	−0.00940917	−	0.0289584i
$549$	−12.2372			−0.522272
$550$		0			0
$551$	45.1154			1.92198
$552$	−6.84463	−	21.0656i	−0.291327	−	0.896611i
$553$	−12.9079	+	9.37814i	−0.548900	+	0.398799i
$554$	7.14917	−	5.19418i	0.303739	−	0.220679i
$555$		0			0
$556$	−0.490357	−	0.356265i	−0.0207958	−	0.0151090i
$557$	−1.52499			−0.0646160			−0.0323080	−	0.999478i	$-0.510286\pi$
$557$	−1.52499			−0.0646160			−0.0323080	+	0.999478i	$0.510286\pi$
$558$	−4.59592	−	3.33913i	−0.194561	−	0.141357i
$559$	−3.34398	+	10.2917i	−0.141435	+	0.435293i
$560$		0			0
$561$	−1.59754	−	4.91672i	−0.0674481	−	0.207584i
$562$	−4.03578	+	12.4209i	−0.170239	+	0.523942i
$563$	−4.26305	+	13.1203i	−0.179666	+	0.552955i	−0.999816	−	0.0191938i	$-0.993890\pi$
$563$	−4.26305	+	13.1203i	−0.179666	+	0.552955i	0.820150	+	0.572149i	$0.193890\pi$
$564$	−0.743241	−	2.28746i	−0.0312961	−	0.0963194i
$565$		0			0
$566$	−8.17867	+	25.1714i	−0.343775	+	1.05803i
$567$	1.20988	+	0.879031i	0.0508103	+	0.0369158i
$568$	14.5503			0.610516
$569$	6.87586	+	4.99561i	0.288251	+	0.209427i	0.722508	−	0.691362i	$-0.242989\pi$
$569$	6.87586	+	4.99561i	0.288251	+	0.209427i	−0.434257	+	0.900789i	$0.642989\pi$
$570$		0			0
$571$	−31.8130	+	23.1135i	−1.33133	+	0.967269i	−0.331617	+	0.943414i	$0.607594\pi$
$571$	−31.8130	+	23.1135i	−1.33133	+	0.967269i	−0.999715	+	0.0238553i	$0.992406\pi$
$572$	−0.928611	+	0.674675i	−0.0388272	+	0.0282096i
$573$	−6.48577	−	19.9611i	−0.270947	−	0.833889i
$574$	4.26374			0.177965
$575$		0			0
$576$	6.08192			0.253413
$577$	−7.59664	−	23.3800i	−0.316252	−	0.973324i	−0.975236	−	0.221167i	$-0.929013\pi$
$577$	−7.59664	−	23.3800i	−0.316252	−	0.973324i	0.658984	−	0.752157i	$-0.270987\pi$
$578$	−15.1485	+	11.0060i	−0.630095	+	0.457791i
$579$	18.3723	−	13.3482i	0.763525	−	0.554734i
$580$		0			0
$581$	−0.271017	−	0.196905i	−0.0112437	−	0.00816901i
$582$	19.1985			0.795802
$583$	−7.95197	−	5.77745i	−0.329337	−	0.239277i
$584$	−5.39074	+	16.5910i	−0.223070	+	0.686540i
$585$		0			0
$586$	4.45743	+	13.7186i	0.184135	+	0.566708i
$587$	2.85615	−	8.79033i	0.117886	−	0.362816i	−0.874652	−	0.484751i	$-0.838910\pi$
$587$	2.85615	−	8.79033i	0.117886	−	0.362816i	0.992538	+	0.121936i	$0.0389101\pi$
$588$	−0.531357	+	1.63535i	−0.0219128	+	0.0674407i
$589$	−6.52439	−	20.0800i	−0.268833	−	0.827383i
$590$		0			0
$591$	−0.418228	+	1.28717i	−0.0172036	+	0.0529472i
$592$	−36.2221	−	26.3169i	−1.48872	−	1.08162i
$593$	6.07888			0.249630			0.124815	−	0.992180i	$-0.460166\pi$
$593$	6.07888			0.249630			0.124815	+	0.992180i	$0.460166\pi$
$594$	−2.92904	−	2.12807i	−0.120180	−	0.0873160i
$595$		0			0
$596$	2.15676	−	1.56698i	0.0883442	−	0.0641858i
$597$	7.24929	−	5.26692i	0.296694	−	0.215560i
$598$	−5.63559	−	17.3446i	−0.230456	−	0.709272i
$599$	6.40129			0.261550			0.130775	−	0.991412i	$-0.458254\pi$
$599$	6.40129			0.261550			0.130775	+	0.991412i	$0.458254\pi$
$600$		0			0
$601$	−38.4675			−1.56912			−0.784560	−	0.620052i	$-0.787111\pi$
$601$	−38.4675			−1.56912			−0.784560	+	0.620052i	$0.787111\pi$
$602$	5.69403	+	17.5244i	0.232071	+	0.714242i
$603$	3.48976	−	2.53546i	0.142114	−	0.103252i
$604$	1.24447	−	0.904162i	0.0506369	−	0.0367898i
$605$		0			0
$606$	10.1905	+	7.40380i	0.413959	+	0.300759i
$607$	−5.22464			−0.212062			−0.106031	−	0.994363i	$-0.533814\pi$
$607$	−5.22464			−0.212062			−0.106031	+	0.994363i	$0.533814\pi$
$608$	−9.32514	−	6.77511i	−0.378184	−	0.274767i
$609$	−3.65093	+	11.2364i	−0.147943	+	0.455323i
$610$		0			0
$611$	2.77860	+	8.55164i	0.112410	+	0.345962i
$612$	0.244742	−	0.753237i	0.00989309	−	0.0304478i
$613$	−9.21343	+	28.3560i	−0.372127	+	1.14529i	0.573270	+	0.819367i	$0.305675\pi$
$613$	−9.21343	+	28.3560i	−0.372127	+	1.14529i	−0.945397	+	0.325922i	$0.894325\pi$
$614$	5.05516	+	15.5582i	0.204010	+	0.627877i
$615$		0			0
$616$	2.74234	−	8.44005i	0.110492	−	0.340059i
$617$	18.8521	+	13.6969i	0.758958	+	0.551415i	0.898591	−	0.438788i	$-0.144592\pi$
$617$	18.8521	+	13.6969i	0.758958	+	0.551415i	−0.139633	+	0.990203i	$0.544592\pi$
$618$	3.84145			0.154526
$619$	0.191326	+	0.139007i	0.00769006	+	0.00558715i	0.591624	−	0.806214i	$-0.298487\pi$
$619$	0.191326	+	0.139007i	0.00769006	+	0.00558715i	−0.583934	+	0.811801i	$0.698487\pi$
$620$		0			0
$621$	7.11531	−	5.16958i	0.285528	−	0.207448i
$622$	−34.0075	+	24.7079i	−1.36358	+	0.990696i
$623$	−0.198333	−	0.610405i	−0.00794603	−	0.0244554i
$624$	6.19646			0.248057
$625$		0			0
$626$	−3.06555			−0.122524
$627$	−4.15808	−	12.7973i	−0.166058	−	0.511073i
$628$	4.68932	−	3.40699i	0.187124	−	0.135954i
$629$	17.3082	−	12.5751i	0.690123	−	0.501404i
$630$		0			0
$631$	14.4643	+	10.5090i	0.575816	+	0.418355i	0.837213	−	0.546876i	$-0.184183\pi$
$631$	14.4643	+	10.5090i	0.575816	+	0.418355i	−0.261397	+	0.965231i	$0.584183\pi$
$632$	−26.8685			−1.06877
$633$	−4.72452	−	3.43257i	−0.187783	−	0.136432i
$634$	4.10659	−	12.6388i	0.163094	−	0.501951i
$635$		0			0
$636$	−0.465325	−	1.43212i	−0.0184513	−	0.0567873i
$637$	1.98647	−	6.11374i	0.0787069	−	0.242235i
$638$	8.83867	−	27.2026i	0.349926	−	1.07696i
$639$	1.78535	+	5.49473i	0.0706272	+	0.217368i
$640$		0			0
$641$	3.35839	−	10.3361i	0.132648	−	0.408250i	−0.862568	−	0.505940i	$-0.831146\pi$
$641$	3.35839	−	10.3361i	0.132648	−	0.408250i	0.995217	+	0.0976905i	$0.0311455\pi$
$642$	2.25004	+	1.63475i	0.0888021	+	0.0645185i
$643$	−3.09039			−0.121873			−0.0609366	−	0.998142i	$-0.519409\pi$
$643$	−3.09039			−0.121873			−0.0609366	+	0.998142i	$0.519409\pi$
$644$	−3.84112	−	2.79074i	−0.151361	−	0.109970i
$645$		0			0
$646$	15.5754	−	11.3162i	0.612805	−	0.445229i
$647$	−4.47957	+	3.25460i	−0.176110	+	0.127951i	−0.672348	−	0.740235i	$-0.734714\pi$
$647$	−4.47957	+	3.25460i	−0.176110	+	0.127951i	0.496238	+	0.868186i	$0.334714\pi$
$648$	0.778240	+	2.39518i	0.0305721	+	0.0940914i
$649$	−26.0712			−1.02338
$650$		0			0
$651$	5.52910			0.216703
$652$	2.48682	+	7.65366i	0.0973915	+	0.299740i
$653$	31.4509	−	22.8504i	1.23077	−	0.894206i	0.233821	−	0.972280i	$-0.424877\pi$
$653$	31.4509	−	22.8504i	1.23077	−	0.894206i	0.996948	+	0.0780738i	$0.0248770\pi$
$654$	−3.66436	+	2.66231i	−0.143288	+	0.104105i
$655$		0			0
$656$	6.89265	+	5.00780i	0.269113	+	0.195522i
$657$	−6.92684			−0.270242
$658$	12.3867	+	8.99949i	0.482885	+	0.350837i
$659$	−6.34687	+	19.5337i	−0.247239	+	0.760923i	0.748021	+	0.663675i	$0.231004\pi$
$659$	−6.34687	+	19.5337i	−0.247239	+	0.760923i	−0.995260	+	0.0972484i	$0.968996\pi$
$660$		0			0
$661$	11.8741	+	36.5447i	0.461848	+	1.42142i	0.862903	+	0.505369i	$0.168644\pi$
$661$	11.8741	+	36.5447i	0.461848	+	1.42142i	−0.401055	+	0.916054i	$0.631356\pi$
$662$	1.87236	−	5.76252i	0.0727712	−	0.223967i
$663$	−0.914964	+	2.81597i	−0.0355342	+	0.109363i
$664$	−0.174328	−	0.536526i	−0.00676524	−	0.0208213i
$665$		0			0
$666$	4.62995	−	14.2495i	0.179407	−	0.552157i
$667$	56.2122	+	40.8405i	2.17654	+	1.58135i
$668$	2.33408			0.0903081
$669$	−6.32730	−	4.59705i	−0.244627	−	0.177732i
$670$		0			0
$671$	−23.3272	+	16.9482i	−0.900537	+	0.654278i
$672$	2.44204	−	1.77424i	0.0942037	−	0.0684430i
$673$	4.01164	+	12.3466i	0.154637	+	0.475925i	0.998124	−	0.0612254i	$-0.0195009\pi$
$673$	4.01164	+	12.3466i	0.154637	+	0.475925i	−0.843487	+	0.537150i	$0.819501\pi$
$674$	6.07660			0.234062
$675$		0			0
$676$	−4.03529			−0.155204
$677$	−2.23715	−	6.88524i	−0.0859807	−	0.264621i	0.898818	−	0.438323i	$-0.144427\pi$
$677$	−2.23715	−	6.88524i	−0.0859807	−	0.264621i	−0.984798	+	0.173701i	$0.944427\pi$
$678$	−17.2000	+	12.4965i	−0.660563	+	0.479927i
$679$	−15.1169	+	10.9831i	−0.580134	+	0.421492i
$680$		0			0
$681$	13.1942	+	9.58617i	0.505604	+	0.367343i
$682$	−13.3856			−0.512561
$683$	20.1283	+	14.6241i	0.770188	+	0.559575i	0.902018	−	0.431698i	$-0.142085\pi$
$683$	20.1283	+	14.6241i	0.770188	+	0.559575i	−0.131830	+	0.991272i	$0.542085\pi$
$684$	0.637015	−	1.96053i	0.0243569	−	0.0749627i
$685$		0			0
$686$	−8.35314	−	25.7083i	−0.318924	−	0.981548i
$687$	−6.70838	+	20.6463i	−0.255941	+	0.787704i
$688$	−11.3778	+	35.0172i	−0.433774	+	1.33502i
$689$	1.73961	+	5.35397i	0.0662739	+	0.203970i
$690$		0			0
$691$	−10.2812	+	31.6422i	−0.391114	+	1.20373i	0.540832	+	0.841130i	$0.318109\pi$
$691$	−10.2812	+	31.6422i	−0.391114	+	1.20373i	−0.931947	+	0.362595i	$0.881891\pi$
$692$	−3.45130	−	2.50751i	−0.131199	−	0.0953213i
$693$	3.52377			0.133857
$694$	12.4259	+	9.02794i	0.471681	+	0.342696i
$695$		0			0
$696$	−16.0963	+	11.6946i	−0.610127	+	0.443283i
$697$	−3.29355	+	2.39290i	−0.124752	+	0.0906377i
$698$	−8.76204	−	26.9668i	−0.331648	−	1.02071i
$699$	13.5341			0.511905
$700$		0			0
$701$	−13.2163			−0.499173			−0.249586	−	0.968353i	$-0.580295\pi$
$701$	−13.2163			−0.499173			−0.249586	+	0.968353i	$0.580295\pi$
$702$	0.640771	+	1.97209i	0.0241844	+	0.0744318i
$703$	45.0499	−	32.7307i	1.69909	−	1.23446i
$704$	11.5937	−	8.42328i	0.436952	−	0.317464i
$705$		0			0
$706$	−11.5906	−	8.42104i	−0.436217	−	0.316930i
$707$	−12.2596			−0.461069
$708$	−3.23128	−	2.34766i	−0.121439	−	0.0882306i
$709$	1.93157	−	5.94475i	0.0725415	−	0.223260i	−0.908212	−	0.418511i	$-0.862552\pi$
$709$	1.93157	−	5.94475i	0.0725415	−	0.223260i	0.980753	+	0.195251i	$0.0625522\pi$
$710$		0			0
$711$	−3.29682	−	10.1466i	−0.123640	−	0.380526i
$712$	0.333995	−	1.02793i	0.0125170	−	0.0385233i
$713$	10.0482	−	30.9252i	0.376308	−	1.15816i
$714$	1.55797	+	4.79495i	0.0583057	+	0.179446i
$715$		0			0
$716$	1.73731	−	5.34689i	0.0649263	−	0.199823i
$717$	8.52206	+	6.19164i	0.318262	+	0.231231i
$718$	−44.4735			−1.65973
$719$	−22.2492	−	16.1650i	−0.829757	−	0.602854i	0.0897336	−	0.995966i	$-0.471398\pi$
$719$	−22.2492	−	16.1650i	−0.829757	−	0.602854i	−0.919491	+	0.393112i	$0.871398\pi$
$720$		0			0
$721$	−3.02477	+	2.19762i	−0.112648	+	0.0818437i
$722$	16.9209	−	12.2938i	0.629731	−	0.457526i
$723$	6.02082	+	18.5302i	0.223917	+	0.689145i
$724$	−5.26293			−0.195595
$725$		0			0
$726$	8.37120			0.310684
$727$	6.81063	+	20.9610i	0.252592	+	0.777399i	0.994295	+	0.106670i	$0.0340188\pi$
$727$	6.81063	+	20.9610i	0.252592	+	0.777399i	−0.741702	+	0.670729i	$0.765981\pi$
$728$	−4.11196	+	2.98751i	−0.152399	+	0.110725i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$		0			0
$731$	−14.2335	−	10.3412i	−0.526443	−	0.382484i
$732$	−4.41735			−0.163270
$733$	28.0838	+	20.4041i	1.03730	+	0.753641i	0.969756	−	0.244076i	$-0.0784845\pi$
$733$	28.0838	+	20.4041i	1.03730	+	0.753641i	0.0675414	+	0.997716i	$0.478485\pi$
$734$	−1.89865	+	5.84345i	−0.0700806	+	0.215686i
$735$		0			0
$736$	−5.48565	−	16.8831i	−0.202204	−	0.622319i
$737$	3.14082	−	9.66645i	0.115694	−	0.356068i
$738$	−0.881025	+	2.71151i	−0.0324310	+	0.0998122i
$739$	−2.34418	−	7.21465i	−0.0862321	−	0.265395i	0.898638	−	0.438692i	$-0.144558\pi$
$739$	−2.34418	−	7.21465i	−0.0862321	−	0.265395i	−0.984870	+	0.173297i	$0.944558\pi$
$740$		0			0
$741$	−2.38147	+	7.32942i	−0.0874856	+	0.269253i
$742$	7.75503	+	5.63436i	0.284696	+	0.206844i
$743$	−27.5328			−1.01008			−0.505040	−	0.863096i	$-0.668522\pi$
$743$	−27.5328			−1.01008			−0.505040	+	0.863096i	$0.668522\pi$
$744$	7.53283	+	5.47292i	0.276167	+	0.200647i
$745$		0			0
$746$	3.94383	−	2.86536i	0.144394	−	0.104908i
$747$	0.181222	−	0.131666i	0.00663057	−	0.00481739i
$748$	−0.576674	−	1.77482i	−0.0210853	−	0.0648938i
$749$	−2.70690			−0.0989081
$750$		0			0
$751$	4.24930			0.155059			0.0775296	−	0.996990i	$-0.475297\pi$
$751$	4.24930			0.155059			0.0775296	+	0.996990i	$0.475297\pi$
$752$	9.45408	+	29.0967i	0.344755	+	1.06105i
$753$	16.9446	−	12.3109i	0.617494	−	0.448636i
$754$	−13.2530	+	9.62888i	−0.482646	+	0.350663i
$755$		0			0
$756$	0.436739	+	0.317309i	0.0158840	+	0.0115404i
$757$	45.6609			1.65957			0.829787	−	0.558081i	$-0.188462\pi$
$757$	45.6609			1.65957			0.829787	+	0.558081i	$0.188462\pi$
$758$	35.4537	+	25.7586i	1.28774	+	0.935595i
$759$	6.40385	−	19.7090i	0.232445	−	0.715392i
$760$		0			0
$761$	−12.3999	−	38.1628i	−0.449495	−	1.38340i	−0.877479	−	0.479616i	$-0.840776\pi$
$761$	−12.3999	−	38.1628i	−0.449495	−	1.38340i	0.427984	−	0.903786i	$-0.359224\pi$
$762$	2.72544	−	8.38804i	0.0987323	−	0.303867i
$763$	1.36227	−	4.19262i	0.0493173	−	0.151783i
$764$	−2.34121	−	7.20550i	−0.0847020	−	0.260686i
$765$		0			0
$766$	−5.44196	+	16.7486i	−0.196626	+	0.605152i
$767$	12.0801	+	8.77671i	0.436187	+	0.316909i
$768$	8.39819			0.303044
$769$	30.6092	+	22.2389i	1.10380	+	0.801954i	0.981675	−	0.190561i	$-0.0610307\pi$
$769$	30.6092	+	22.2389i	1.10380	+	0.801954i	0.122120	+	0.992515i	$0.461031\pi$
$770$		0			0
$771$	−1.35204	+	0.982314i	−0.0486925	+	0.0353772i
$772$	6.63195	−	4.81840i	0.238689	−	0.173418i
$773$	8.10082	+	24.9318i	0.291366	+	0.896733i	0.984418	+	0.175845i	$0.0562658\pi$
$773$	8.10082	+	24.9318i	0.291366	+	0.896733i	−0.693052	+	0.720888i	$0.743734\pi$
$774$	−12.3212			−0.442875
$775$		0			0
$776$	−31.4667			−1.12959
$777$	4.50625	+	13.8688i	0.161661	+	0.497541i
$778$	42.5713	−	30.9299i	1.52626	−	1.10889i
$779$	−8.57247	+	6.22826i	−0.307140	+	0.223151i
$780$		0			0
$781$	11.0134	+	8.00168i	0.394089	+	0.286323i
$782$	29.6503			1.06029
$783$	−6.39137	−	4.64360i	−0.228409	−	0.165949i
$784$	6.75891	−	20.8018i	0.241390	−	0.742921i
$785$		0			0
$786$	2.06905	+	6.36789i	0.0738007	+	0.227135i
$787$	0.745515	−	2.29446i	0.0265747	−	0.0817887i	−0.936890	−	0.349626i	$-0.886309\pi$
$787$	0.745515	−	2.29446i	0.0265747	−	0.0817887i	0.963464	+	0.267837i	$0.0863088\pi$
$788$	−0.150970	+	0.464639i	−0.00537810	+	0.0165521i
$789$	−2.33514	−	7.18682i	−0.0831331	−	0.255858i
$790$		0			0
$791$	6.39430	−	19.6796i	0.227355	−	0.699727i
$792$	4.80077	+	3.48796i	0.170588	+	0.123939i
$793$	16.5142			0.586437
$794$	24.9033	+	18.0933i	0.883785	+	0.642108i
$795$		0			0
$796$	2.61682	−	1.90123i	0.0927508	−	0.0673874i
$797$	6.56299	−	4.76829i	0.232473	−	0.168902i	−0.465450	−	0.885074i	$-0.654108\pi$
$797$	6.56299	−	4.76829i	0.232473	−	0.168902i	0.697923	+	0.716172i	$0.254108\pi$
$798$	4.05510	+	12.4803i	0.143549	+	0.441799i
$799$	−14.6189			−0.517180
$800$		0			0
$801$	0.429167			0.0151639
$802$	−2.36555	−	7.28041i	−0.0835304	−	0.257080i
$803$	−13.2043	+	9.59348i	−0.465969	+	0.338546i
$804$	1.25972	−	0.915242i	0.0444270	−	0.0322781i
$805$		0			0
$806$	6.20223	+	4.50618i	0.218464	+	0.158724i
$807$	−11.2841			−0.397220
$808$	−16.7024	−	12.1350i	−0.587589	−	0.426908i
$809$	−12.5798	+	38.7166i	−0.442282	+	1.36120i	0.443155	+	0.896445i	$0.353859\pi$
$809$	−12.5798	+	38.7166i	−0.442282	+	1.36120i	−0.885437	+	0.464759i	$0.846141\pi$
$810$		0			0
$811$	−15.2960	−	47.0763i	−0.537116	−	1.65307i	−0.739032	−	0.673671i	$-0.764717\pi$
$811$	−15.2960	−	47.0763i	−0.537116	−	1.65307i	0.201915	−	0.979403i	$-0.435283\pi$
$812$	−1.31790	+	4.05608i	−0.0462493	+	0.142341i
$813$	−3.39152	+	10.4380i	−0.118946	+	0.366078i
$814$	−10.9093	−	33.5755i	−0.382372	−	1.17682i
$815$		0			0
$816$	−3.11313	+	9.58124i	−0.108981	+	0.335410i
$817$	−37.0469	−	26.9162i	−1.29611	−	0.941678i
$818$	−36.6606			−1.28181
$819$	−1.63274	−	1.18626i	−0.0570527	−	0.0414512i
$820$		0			0
$821$	−34.1498	+	24.8113i	−1.19183	+	0.865919i	−0.993457	−	0.114207i	$-0.963567\pi$
$821$	−34.1498	+	24.8113i	−1.19183	+	0.865919i	−0.198378	+	0.980126i	$0.563567\pi$
$822$	−2.45462	+	1.78338i	−0.0856146	+	0.0622027i
$823$	15.2144	+	46.8252i	0.530342	+	1.63222i	0.753504	+	0.657443i	$0.228362\pi$
$823$	15.2144	+	46.8252i	0.530342	+	1.63222i	−0.223162	+	0.974781i	$0.571638\pi$
$824$	−6.29622			−0.219339
$825$		0			0
$826$	25.4255			0.884666
$827$	−15.7602	−	48.5050i	−0.548036	−	1.68668i	−0.713659	−	0.700493i	$-0.752963\pi$
$827$	−15.7602	−	48.5050i	−0.548036	−	1.68668i	0.165623	−	0.986189i	$-0.447037\pi$
$828$	2.56846	−	1.86610i	0.0892602	−	0.0648513i
$829$	30.9321	−	22.4735i	1.07432	−	0.780537i	0.0976336	−	0.995222i	$-0.468873\pi$
$829$	30.9321	−	22.4735i	1.07432	−	0.780537i	0.976683	+	0.214686i	$0.0688727\pi$
$830$		0			0
$831$	−4.65275	−	3.38042i	−0.161402	−	0.117266i
$832$	−8.20758			−0.284547
$833$	8.45531	+	6.14314i	0.292959	+	0.212847i
$834$	−0.797267	+	2.45374i	−0.0276071	+	0.0849659i
$835$		0			0
$836$	−1.50097	−	4.61951i	−0.0519121	−	0.159769i
$837$	−1.14249	+	3.51622i	−0.0394902	+	0.121538i
$838$	−0.229124	+	0.705171i	−0.00791496	+	0.0243597i
$839$	−5.16324	−	15.8908i	−0.178255	−	0.548612i	0.821512	−	0.570191i	$-0.193131\pi$
$839$	−5.16324	−	15.8908i	−0.178255	−	0.548612i	−0.999767	+	0.0215787i	$0.993131\pi$
$840$		0			0
$841$	10.3251	−	31.7774i	0.356038	−	1.09577i
$842$	−22.0255	−	16.0025i	−0.759049	−	0.551481i
$843$	8.49962			0.292742
$844$	−1.70544	−	1.23908i	−0.0587037	−	0.0426507i
$845$		0			0
$846$	−8.28270	+	6.01773i	−0.284765	+	0.206894i
$847$	−6.59151	+	4.78901i	−0.226487	+	0.164552i
$848$	5.91897	+	18.2167i	0.203258	+	0.625564i
$849$	17.2248			0.591154
$850$		0			0
$851$	85.7599			2.93981
$852$	0.644468	+	1.98347i	0.0220791	+	0.0679525i
$853$	−14.7762	+	10.7355i	−0.505928	+	0.367578i	−0.811277	−	0.584662i	$-0.801227\pi$
$853$	−14.7762	+	10.7355i	−0.505928	+	0.367578i	0.305349	+	0.952241i	$0.401227\pi$
$854$	22.7495	−	16.5285i	0.778471	−	0.565593i
$855$		0			0
$856$	−3.68787	−	2.67940i	−0.126049	−	0.0915799i
$857$	53.4773			1.82675			0.913375	−	0.407119i	$-0.133466\pi$
$857$	53.4773			1.82675			0.913375	+	0.407119i	$0.133466\pi$
$858$	3.95276	+	2.87185i	0.134945	+	0.0980433i
$859$	−5.79639	+	17.8395i	−0.197770	+	0.608674i	0.802163	+	0.597105i	$0.203683\pi$
$859$	−5.79639	+	17.8395i	−0.197770	+	0.608674i	−0.999933	+	0.0115690i	$0.996317\pi$
$860$		0			0
$861$	−0.857487	−	2.63907i	−0.0292231	−	0.0899394i
$862$	−12.7281	+	39.1730i	−0.433520	+	1.33424i
$863$	15.8329	−	48.7286i	0.538957	−	1.65874i	−0.195982	−	0.980607i	$-0.562789\pi$
$863$	15.8329	−	48.7286i	0.538957	−	1.65874i	0.734939	−	0.678133i	$-0.237211\pi$
$864$	0.623723	+	1.91962i	0.0212195	+	0.0653069i
$865$		0			0
$866$	−4.38313	+	13.4899i	−0.148945	+	0.458405i
$867$	9.85880	+	7.16284i	0.334822	+	0.243263i
$868$	1.99588			0.0677444
$869$	−20.3373	−	14.7759i	−0.689895	−	0.501238i
$870$		0			0
$871$	−4.70946	+	3.42162i	−0.159574	+	0.115937i
$872$	6.00597	−	4.36359i	0.203388	−	0.147770i
$873$	−3.86103	−	11.8830i	−0.130676	−	0.402179i
$874$	77.1739			2.61045
$875$		0			0
$876$	−2.50042			−0.0844815
$877$	1.87359	+	5.76631i	0.0632666	+	0.194715i	0.977694	−	0.210036i	$-0.0673582\pi$
$877$	1.87359	+	5.76631i	0.0632666	+	0.194715i	−0.914427	+	0.404751i	$0.867358\pi$
$878$	1.24608	−	0.905331i	0.0420532	−	0.0305534i
$879$	7.59476	−	5.51791i	0.256165	−	0.186115i
$880$		0			0
$881$	−18.3403	−	13.3250i	−0.617899	−	0.448930i	0.234288	−	0.972167i	$-0.424724\pi$
$881$	−18.3403	−	13.3250i	−0.617899	−	0.448930i	−0.852187	+	0.523237i	$0.824724\pi$
$882$	7.31933			0.246455
$883$	−4.48114	−	3.25574i	−0.150802	−	0.109564i	0.509826	−	0.860278i	$-0.329710\pi$
$883$	−4.48114	−	3.25574i	−0.150802	−	0.109564i	−0.660628	+	0.750713i	$0.729710\pi$
$884$	−0.330280	+	1.01650i	−0.0111085	+	0.0341885i
$885$		0			0
$886$	−12.4817	−	38.4146i	−0.419329	−	1.29056i
$887$	3.39041	−	10.4346i	0.113839	−	0.350360i	−0.877864	−	0.478909i	$-0.841032\pi$
$887$	3.39041	−	10.4346i	0.113839	−	0.350360i	0.991703	+	0.128550i	$0.0410322\pi$
$888$	−7.58859	+	23.3553i	−0.254656	+	0.783752i
$889$	2.65263	+	8.16394i	0.0889662	+	0.273810i
$890$		0			0
$891$	−0.728123	+	2.24093i	−0.0243930	+	0.0750740i
$892$	−2.28401	−	1.65943i	−0.0764742	−	0.0555617i
$893$	−38.0502			−1.27330
$894$	−9.18054	−	6.67005i	−0.307043	−	0.223080i
$895$		0			0
$896$	−16.1906	+	11.7632i	−0.540890	+	0.392980i
$897$	−9.60216	+	6.97638i	−0.320607	+	0.232934i
$898$	−2.25752	−	6.94794i	−0.0753345	−	0.231856i
$899$	−29.2083			−0.974151
$900$		0			0
$901$	−9.15254			−0.304915
$902$	2.07592	+	6.38902i	0.0691205	+	0.212731i
$903$	9.70173	−	7.04872i	0.322853	−	0.234567i
$904$	28.1912	−	20.4821i	0.937627	−	0.681226i
$905$		0			0
$906$	−5.29727	−	3.84869i	−0.175990	−	0.127864i
$907$	19.3907			0.643856			0.321928	−	0.946764i	$-0.395669\pi$
$907$	19.3907			0.643856			0.321928	+	0.946764i	$0.395669\pi$
$908$	4.76281	+	3.46038i	0.158059	+	0.114837i
$909$	2.53322	−	7.79645i	0.0840216	−	0.258592i
$910$		0			0
$911$	−4.23940	−	13.0475i	−0.140458	−	0.432284i	0.855941	−	0.517073i	$-0.172978\pi$
$911$	−4.23940	−	13.0475i	−0.140458	−	0.432284i	−0.996399	+	0.0847888i	$0.972978\pi$
$912$	−8.10288	+	24.9381i	−0.268313	+	0.825783i
$913$	0.163102	−	0.501975i	0.00539788	−	0.0166130i
$914$	7.58300	+	23.3381i	0.250823	+	0.771955i
$915$		0			0
$916$	−2.42157	+	7.45282i	−0.0800108	+	0.246248i
$917$	−5.27213	−	3.83043i	−0.174101	−	0.126492i
$918$	−3.37126			−0.111268
$919$	26.2209	+	19.0506i	0.864947	+	0.628421i	0.929226	−	0.369511i	$-0.120475\pi$
$919$	26.2209	+	19.0506i	0.864947	+	0.628421i	−0.0642792	+	0.997932i	$0.520475\pi$
$920$		0			0
$921$	8.61319	−	6.25785i	0.283814	−	0.206203i
$922$	49.4202	−	35.9058i	1.62757	−	1.18250i
$923$	−2.40934	−	7.41518i	−0.0793043	−	0.244073i
$924$	1.27200			0.0418457
$925$		0			0
$926$	−40.1360			−1.31895
$927$	−0.772559	−	2.37769i	−0.0253742	−	0.0780936i
$928$	−12.9004	+	9.37270i	−0.423477	+	0.307674i
$929$	3.50664	−	2.54772i	0.115049	−	0.0835880i	−0.528773	−	0.848763i	$-0.677348\pi$
$929$	3.50664	−	2.54772i	0.115049	−	0.0835880i	0.643822	+	0.765175i	$0.277348\pi$
$930$		0			0
$931$	22.0075	+	15.9894i	0.721268	+	0.524032i
$932$	4.88548			0.160029
$933$	22.1324	+	16.0801i	0.724582	+	0.526440i
$934$	1.82902	−	5.62915i	0.0598474	−	0.184192i
$935$		0			0
$936$	−1.05024	−	3.23230i	−0.0343281	−	0.105651i
$937$	16.8700	−	51.9206i	0.551120	−	1.69617i	−0.154857	−	0.987937i	$-0.549492\pi$
$937$	16.8700	−	51.9206i	0.551120	−	1.69617i	0.705977	−	0.708235i	$-0.250508\pi$
$938$	−3.06303	+	9.42705i	−0.100012	+	0.307804i
$939$	0.616517	+	1.89744i	0.0201193	+	0.0619208i
$940$		0			0
$941$	1.30978	−	4.03108i	0.0426975	−	0.131409i	−0.927435	−	0.373983i	$-0.877992\pi$
$941$	1.30978	−	4.03108i	0.0426975	−	0.131409i	0.970133	+	0.242574i	$0.0779917\pi$
$942$	−19.9608	−	14.5023i	−0.650357	−	0.472512i
$943$	−16.3191			−0.531423
$944$	41.1022	+	29.8625i	1.33776	+	0.971940i
$945$		0			0
$946$	−23.4872	+	17.0645i	−0.763636	+	0.554814i
$947$	−10.1992	+	7.41018i	−0.331431	+	0.240798i	−0.741037	−	0.671464i	$-0.765666\pi$
$947$	−10.1992	+	7.41018i	−0.331431	+	0.240798i	0.409607	+	0.912262i	$0.365666\pi$
$948$	−1.19007	−	3.66267i	−0.0386518	−	0.118958i
$949$	9.34781			0.303443
$950$		0			0
$951$	−8.64876			−0.280455
$952$	−2.55356	−	7.85903i	−0.0827612	−	0.254713i
$953$	25.2118	−	18.3174i	0.816690	−	0.593360i	−0.0990725	−	0.995080i	$-0.531588\pi$
$953$	25.2118	−	18.3174i	0.816690	−	0.593360i	0.915762	+	0.401720i	$0.131588\pi$
$954$	−5.18559	+	3.76755i	−0.167890	+	0.121979i
$955$		0			0
$956$	3.07626	+	2.23503i	0.0994934	+	0.0722862i
$957$	−18.6148			−0.601732
$958$	−17.7387	−	12.8879i	−0.573111	−	0.416390i
$959$	0.912532	−	2.80848i	0.0294672	−	0.0906907i
$960$		0			0
$961$	−5.35555	−	16.4827i	−0.172760	−	0.531700i
$962$	−6.24814	+	19.2298i	−0.201448	+	0.619994i
$963$	0.559332	−	1.72145i	0.0180242	−	0.0554729i
$964$	2.17337	+	6.68896i	0.0699997	+	0.215437i
$965$		0			0
$966$	−6.24525	+	19.2209i	−0.200938	+	0.618422i
$967$	−1.25647	−	0.912880i	−0.0404054	−	0.0293562i	0.567399	−	0.823443i	$-0.307950\pi$
$967$	−1.25647	−	0.912880i	−0.0404054	−	0.0293562i	−0.607805	+	0.794087i	$0.707950\pi$
$968$	−13.7206			−0.440997
$969$	−10.1366	−	7.36467i	−0.325635	−	0.236587i
$970$		0			0
$971$	30.9548	−	22.4900i	0.993388	−	0.721739i	0.0327278	−	0.999464i	$-0.489581\pi$
$971$	30.9548	−	22.4900i	0.993388	−	0.721739i	0.960660	+	0.277725i	$0.0895806\pi$
$972$	−0.292036	+	0.212177i	−0.00936706	+	0.00680557i
$973$	−0.775967	−	2.38818i	−0.0248764	−	0.0765616i
$974$	−38.1405			−1.22210
$975$		0			0
$976$	56.1890			1.79857
$977$	−6.29348	−	19.3693i	−0.201346	−	0.619680i	−0.999844	−	0.0176817i	$-0.994371\pi$
$977$	−6.29348	−	19.3693i	−0.201346	−	0.619680i	0.798497	−	0.601998i	$-0.205629\pi$
$978$	27.7132	−	20.1348i	0.886172	−	0.643841i
$979$	0.818100	−	0.594384i	0.0261466	−	0.0189966i
$980$		0			0
$981$	2.38480	+	1.73266i	0.0761408	+	0.0553195i
$982$	−17.6539			−0.563359
$983$	10.7241	+	7.79150i	0.342045	+	0.248510i	0.745524	−	0.666479i	$-0.232199\pi$
$983$	10.7241	+	7.79150i	0.342045	+	0.248510i	−0.403479	+	0.914989i	$0.632199\pi$
$984$	1.44402	−	4.44424i	0.0460337	−	0.141677i
$985$		0			0
$986$	−8.23022	−	25.3300i	−0.262103	−	0.806671i
$987$	3.07919	−	9.47676i	0.0980116	−	0.301649i
$988$	−0.859655	+	2.64575i	−0.0273493	+	0.0841724i
$989$	−21.7934	−	67.0732i	−0.692990	−	2.13280i
$990$		0			0
$991$	−0.692448	+	2.13113i	−0.0219963	+	0.0676977i	−0.961452	−	0.274972i	$-0.911331\pi$
$991$	−0.692448	+	2.13113i	−0.0219963	+	0.0676977i	0.939456	+	0.342670i	$0.111331\pi$
$992$	6.03721	+	4.38629i	0.191682	+	0.139265i
$993$	−3.94331			−0.125137
$994$	−10.7406	−	7.80351i	−0.340671	−	0.247512i
$995$		0			0
$996$	0.0654169	−	0.0475282i	0.00207281	−	0.00150599i
$997$	11.3589	−	8.25272i	0.359740	−	0.261366i	−0.393204	−	0.919451i	$-0.628633\pi$
$997$	11.3589	−	8.25272i	0.359740	−	0.261366i	0.752943	+	0.658085i	$0.228633\pi$
$998$	1.98231	+	6.10092i	0.0627489	+	0.193121i
$999$	−9.75097			−0.308507

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	375.2.g.e.151.2		16
5.2	odd	4		75.2.i.a.19.4	yes	16
5.3	odd	4		375.2.i.c.349.1		16
5.4	even	2		375.2.g.d.151.3		16
15.2	even	4		225.2.m.b.19.1		16
25.2	odd	20		1875.2.b.h.1249.4		16
25.3	odd	20		75.2.i.a.4.4	✓	16
25.4	even	10		375.2.g.d.226.3		16
25.11	even	5		1875.2.a.m.1.3		8
25.14	even	10		1875.2.a.p.1.6		8
25.21	even	5	inner	375.2.g.e.226.2		16
25.22	odd	20		375.2.i.c.274.1		16
25.23	odd	20		1875.2.b.h.1249.13		16
75.11	odd	10		5625.2.a.bd.1.6		8
75.14	odd	10		5625.2.a.t.1.3		8
75.53	even	20		225.2.m.b.154.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.i.a.4.4	✓	16	25.3	odd	20
75.2.i.a.19.4	yes	16	5.2	odd	4
225.2.m.b.19.1		16	15.2	even	4
225.2.m.b.154.1		16	75.53	even	20
375.2.g.d.151.3		16	5.4	even	2
375.2.g.d.226.3		16	25.4	even	10
375.2.g.e.151.2		16	1.1	even	1	trivial
375.2.g.e.226.2		16	25.21	even	5	inner
375.2.i.c.274.1		16	25.22	odd	20
375.2.i.c.349.1		16	5.3	odd	4
1875.2.a.m.1.3		8	25.11	even	5
1875.2.a.p.1.6		8	25.14	even	10
1875.2.b.h.1249.4		16	25.2	odd	20
1875.2.b.h.1249.13		16	25.23	odd	20
5625.2.a.t.1.3		8	75.14	odd	10
5625.2.a.bd.1.6		8	75.11	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 375 = 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	375.g (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.474819 - 1.46134i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-0.292036 + 0.212177i) q^{4} +(1.24309 + 0.903160i) q^{6} -1.49550 q^{7} +(-2.03746 - 1.48030i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.474819 - 1.46134i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-0.292036 + 0.212177i) q^{4} +(1.24309 + 0.903160i) q^{6} -1.49550 q^{7} +(-2.03746 - 1.48030i) q^{8} +(0.309017 - 0.951057i) q^{9} +(-0.728123 - 2.24093i) q^{11} +(0.111548 - 0.343309i) q^{12} +(-0.417020 + 1.28346i) q^{13} +(0.710090 + 2.18543i) q^{14} +(-1.41890 + 4.36692i) q^{16} +(-1.77502 - 1.28963i) q^{17} -1.53655 q^{18} +(-4.62004 - 3.35666i) q^{19} +(1.20988 - 0.879031i) q^{21} +(-2.92904 + 2.12807i) q^{22} +(-2.71781 - 8.36455i) q^{23} +2.51844 q^{24} +2.07358 q^{26} +(0.309017 + 0.951057i) q^{27} +(0.436739 - 0.317309i) q^{28} +(-6.39137 + 4.64360i) q^{29} +(2.99107 + 2.17314i) q^{31} +2.01841 q^{32} +(1.90625 + 1.38497i) q^{33} +(-1.04178 + 3.20626i) q^{34} +(0.111548 + 0.343309i) q^{36} +(-3.01321 + 9.27372i) q^{37} +(-2.71154 + 8.34527i) q^{38} +(-0.417020 - 1.28346i) q^{39} +(0.573380 - 1.76468i) q^{41} +(-1.85904 - 1.35067i) q^{42} +8.01874 q^{43} +(0.688111 + 0.499942i) q^{44} +(-10.9330 + 7.94330i) q^{46} +(5.39046 - 3.91640i) q^{47} +(-1.41890 - 4.36692i) q^{48} -4.76349 q^{49} +2.19405 q^{51} +(-0.150535 - 0.463298i) q^{52} +(3.37484 - 2.45196i) q^{53} +(1.24309 - 0.903160i) q^{54} +(3.04701 + 2.21378i) q^{56} +5.71069 q^{57} +(9.82064 + 7.13511i) q^{58} +(3.41917 - 10.5231i) q^{59} +(-3.78151 - 11.6383i) q^{61} +(1.75549 - 5.40283i) q^{62} +(-0.462134 + 1.42230i) q^{63} +(1.87942 + 5.78425i) q^{64} +(1.11879 - 3.44330i) q^{66} +(3.48976 + 2.53546i) q^{67} +0.792000 q^{68} +(7.11531 + 5.16958i) q^{69} +(-4.67410 + 3.39593i) q^{71} +(-2.03746 + 1.48030i) q^{72} +(-2.14051 - 6.58781i) q^{73} +14.9828 q^{74} +2.06142 q^{76} +(1.08890 + 3.35130i) q^{77} +(-1.67756 + 1.21882i) q^{78} +(8.63118 - 6.27092i) q^{79} +(-0.809017 - 0.587785i) q^{81} -2.85106 q^{82} +(0.181222 + 0.131666i) q^{83} +(-0.166819 + 0.513417i) q^{84} +(-3.80745 - 11.7181i) q^{86} +(2.44129 - 7.51351i) q^{87} +(-1.83373 + 5.64364i) q^{88} +(0.132620 + 0.408162i) q^{89} +(0.623652 - 1.91940i) q^{91} +(2.56846 + 1.86610i) q^{92} -3.69717 q^{93} +(-8.28270 - 6.01773i) q^{94} +(-1.63293 + 1.18639i) q^{96} +(10.1083 - 7.34411i) q^{97} +(2.26180 + 6.96109i) q^{98} -2.35626 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{2} - 4 q^{3} - 2 q^{4} + 2 q^{6} - 16 q^{7} + 6 q^{8} - 4 q^{9}+O(q^{10}) \) 16 * q + 2 * q^2 - 4 * q^3 - 2 * q^4 + 2 * q^6 - 16 * q^7 + 6 * q^8 - 4 * q^9	\( 16 q + 2 q^{2} - 4 q^{3} - 2 q^{4} + 2 q^{6} - 16 q^{7} + 6 q^{8} - 4 q^{9} - 6 q^{11} - 2 q^{12} + 8 q^{13} + 12 q^{14} - 10 q^{16} + 8 q^{17} - 8 q^{18} + 2 q^{19} + 4 q^{21} - 4 q^{22} + 2 q^{23} - 24 q^{24} + 12 q^{26} - 4 q^{27} + 28 q^{28} - 16 q^{29} + 6 q^{31} + 4 q^{32} + 4 q^{33} + 36 q^{34} - 2 q^{36} + 24 q^{37} - 38 q^{38} + 8 q^{39} - 14 q^{41} - 18 q^{42} - 40 q^{43} - 26 q^{44} + 16 q^{46} - 10 q^{47} - 10 q^{48} - 32 q^{51} + 48 q^{52} + 12 q^{53} + 2 q^{54} - 28 q^{57} + 44 q^{58} - 12 q^{59} + 28 q^{62} + 4 q^{63} - 8 q^{64} + 16 q^{66} - 12 q^{67} + 4 q^{68} + 12 q^{69} - 8 q^{71} + 6 q^{72} - 8 q^{73} + 52 q^{74} - 32 q^{76} + 18 q^{77} + 32 q^{78} + 20 q^{79} - 4 q^{81} - 32 q^{82} + 6 q^{83} - 12 q^{84} - 36 q^{86} + 14 q^{87} + 16 q^{88} - 18 q^{89} + 26 q^{91} - 36 q^{92} - 44 q^{93} + 38 q^{94} - 26 q^{96} + 8 q^{97} - 18 q^{98} + 4 q^{99}+O(q^{100}) \) 16 * q + 2 * q^2 - 4 * q^3 - 2 * q^4 + 2 * q^6 - 16 * q^7 + 6 * q^8 - 4 * q^9 - 6 * q^11 - 2 * q^12 + 8 * q^13 + 12 * q^14 - 10 * q^16 + 8 * q^17 - 8 * q^18 + 2 * q^19 + 4 * q^21 - 4 * q^22 + 2 * q^23 - 24 * q^24 + 12 * q^26 - 4 * q^27 + 28 * q^28 - 16 * q^29 + 6 * q^31 + 4 * q^32 + 4 * q^33 + 36 * q^34 - 2 * q^36 + 24 * q^37 - 38 * q^38 + 8 * q^39 - 14 * q^41 - 18 * q^42 - 40 * q^43 - 26 * q^44 + 16 * q^46 - 10 * q^47 - 10 * q^48 - 32 * q^51 + 48 * q^52 + 12 * q^53 + 2 * q^54 - 28 * q^57 + 44 * q^58 - 12 * q^59 + 28 * q^62 + 4 * q^63 - 8 * q^64 + 16 * q^66 - 12 * q^67 + 4 * q^68 + 12 * q^69 - 8 * q^71 + 6 * q^72 - 8 * q^73 + 52 * q^74 - 32 * q^76 + 18 * q^77 + 32 * q^78 + 20 * q^79 - 4 * q^81 - 32 * q^82 + 6 * q^83 - 12 * q^84 - 36 * q^86 + 14 * q^87 + 16 * q^88 - 18 * q^89 + 26 * q^91 - 36 * q^92 - 44 * q^93 + 38 * q^94 - 26 * q^96 + 8 * q^97 - 18 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more