LMFDB - Embedded newform 375.2.g.c.226.1

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:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
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} + 3x^{10} - 2x^{9} + 34x^{8} - 22x^{7} + 236x^{6} - 179x^{5} + 877x^{4} - 409x^{3} + 96x^{2} - 11x + 1 $ x^12 + 3x^10 - 2x^9 + 34x^8 - 22x^7 + 236x^6 - 179x^5 + 877x^4 - 409x^3 + 96x^2 - 11x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5 $
Twist minimal:	no (minimal twist has level 75)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			226.1
Root			$1.97423 + 1.43436i$ of defining polynomial
Character	$\chi$	$=$	375.226
Dual form			375.2.g.c.151.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.754089 + 2.32085i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-3.19965 - 2.32468i) q^{4} +(1.97423 - 1.43436i) q^{6} +3.44028 q^{7} +(3.85959 - 2.80415i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.754089 + 2.32085i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-3.19965 - 2.32468i) q^{4} +(1.97423 - 1.43436i) q^{6} +3.44028 q^{7} +(3.85959 - 2.80415i) q^{8} +(0.309017 + 0.951057i) q^{9} +(-1.00942 + 3.10669i) q^{11} +(1.22216 + 3.76141i) q^{12} +(0.998755 + 3.07385i) q^{13} +(-2.59428 + 7.98437i) q^{14} +(1.15323 + 3.54927i) q^{16} +(-4.08826 + 2.97030i) q^{17} -2.44028 q^{18} +(2.49274 - 1.81108i) q^{19} +(-2.78325 - 2.02215i) q^{21} +(-6.44895 - 4.68544i) q^{22} +(-0.478250 + 1.47190i) q^{23} -4.77071 q^{24} -7.88709 q^{26} +(0.309017 - 0.951057i) q^{27} +(-11.0077 - 7.99756i) q^{28} +(2.52590 + 1.83517i) q^{29} +(-6.02080 + 4.37437i) q^{31} +0.434479 q^{32} +(2.64270 - 1.92004i) q^{33} +(-3.81069 - 11.7281i) q^{34} +(1.22216 - 3.76141i) q^{36} +(1.77944 + 5.47655i) q^{37} +(2.32349 + 7.15098i) q^{38} +(0.998755 - 3.07385i) q^{39} +(1.67476 + 5.15437i) q^{41} +(6.79191 - 4.93461i) q^{42} -2.53106 q^{43} +(10.4519 - 7.59371i) q^{44} +(-3.05541 - 2.21989i) q^{46} +(5.72106 + 4.15659i) q^{47} +(1.15323 - 3.54927i) q^{48} +4.83555 q^{49} +5.05337 q^{51} +(3.95006 - 12.1570i) q^{52} +(-8.21277 - 5.96693i) q^{53} +(1.97423 + 1.43436i) q^{54} +(13.2781 - 9.64708i) q^{56} -3.08119 q^{57} +(-6.16391 + 4.47834i) q^{58} +(0.534773 + 1.64586i) q^{59} +(2.42149 - 7.45259i) q^{61} +(-5.61202 - 17.2720i) q^{62} +(1.06311 + 3.27190i) q^{63} +(-2.63409 + 8.10689i) q^{64} +(2.46328 + 7.58119i) q^{66} +(-1.49595 + 1.08687i) q^{67} +19.9860 q^{68} +(1.25207 - 0.909685i) q^{69} +(0.577613 + 0.419660i) q^{71} +(3.85959 + 2.80415i) q^{72} +(0.581036 - 1.78825i) q^{73} -14.0521 q^{74} -12.1861 q^{76} +(-3.47270 + 10.6879i) q^{77} +(6.38079 + 4.63591i) q^{78} +(10.7868 + 7.83708i) q^{79} +(-0.809017 + 0.587785i) q^{81} -13.2254 q^{82} +(3.20166 - 2.32614i) q^{83} +(4.20457 + 12.9403i) q^{84} +(1.90864 - 5.87419i) q^{86} +(-0.964807 - 2.96937i) q^{87} +(4.81567 + 14.8211i) q^{88} +(2.63713 - 8.11624i) q^{89} +(3.43600 + 10.5749i) q^{91} +(4.95193 - 3.59779i) q^{92} +7.44212 q^{93} +(-13.9610 + 10.1433i) q^{94} +(-0.351501 - 0.255380i) q^{96} +(-8.61831 - 6.26157i) q^{97} +(-3.64643 + 11.2226i) q^{98} -3.26656 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{3} - 10 q^{4} + 12 q^{7} - 9 q^{8} - 3 q^{9}+O(q^{10}) $ 12 * q - 3 * q^3 - 10 * q^4 + 12 * q^7 - 9 * q^8 - 3 * q^9	$ 12 q - 3 q^{3} - 10 q^{4} + 12 q^{7} - 9 q^{8} - 3 q^{9} - 4 q^{11} + 2 q^{13} + 6 q^{14} + 16 q^{16} + q^{17} + 7 q^{19} - 3 q^{21} - 13 q^{22} - 19 q^{23} + 6 q^{24} - 56 q^{26} - 3 q^{27} - q^{28} - q^{29} + 13 q^{31} + 32 q^{32} + q^{33} - 25 q^{34} - 8 q^{37} + 22 q^{38} + 2 q^{39} + 8 q^{41} + 16 q^{42} + 4 q^{43} + 33 q^{44} - 22 q^{46} + 13 q^{47} + 16 q^{48} - 28 q^{49} + 26 q^{51} - 44 q^{52} - 44 q^{53} + 45 q^{56} + 22 q^{57} - 41 q^{58} - 22 q^{59} - 8 q^{61} - 41 q^{62} - 3 q^{63} + 49 q^{64} - 3 q^{66} + 6 q^{67} + 100 q^{68} + 6 q^{69} - 21 q^{71} - 9 q^{72} + 16 q^{73} - 44 q^{74} - 52 q^{76} - q^{77} + 19 q^{78} + 10 q^{79} - 3 q^{81} - 26 q^{82} + 10 q^{83} - 6 q^{84} + 56 q^{86} + 4 q^{87} + 16 q^{88} + 57 q^{89} - 7 q^{91} - 3 q^{92} - 22 q^{93} - 23 q^{94} - 23 q^{96} - 4 q^{97} + 18 q^{98} + 6 q^{99}+O(q^{100}) $ 12 * q - 3 * q^3 - 10 * q^4 + 12 * q^7 - 9 * q^8 - 3 * q^9 - 4 * q^11 + 2 * q^13 + 6 * q^14 + 16 * q^16 + q^17 + 7 * q^19 - 3 * q^21 - 13 * q^22 - 19 * q^23 + 6 * q^24 - 56 * q^26 - 3 * q^27 - q^28 - q^29 + 13 * q^31 + 32 * q^32 + q^33 - 25 * q^34 - 8 * q^37 + 22 * q^38 + 2 * q^39 + 8 * q^41 + 16 * q^42 + 4 * q^43 + 33 * q^44 - 22 * q^46 + 13 * q^47 + 16 * q^48 - 28 * q^49 + 26 * q^51 - 44 * q^52 - 44 * q^53 + 45 * q^56 + 22 * q^57 - 41 * q^58 - 22 * q^59 - 8 * q^61 - 41 * q^62 - 3 * q^63 + 49 * q^64 - 3 * q^66 + 6 * q^67 + 100 * q^68 + 6 * q^69 - 21 * q^71 - 9 * q^72 + 16 * q^73 - 44 * q^74 - 52 * q^76 - q^77 + 19 * q^78 + 10 * q^79 - 3 * q^81 - 26 * q^82 + 10 * q^83 - 6 * q^84 + 56 * q^86 + 4 * q^87 + 16 * q^88 + 57 * q^89 - 7 * q^91 - 3 * q^92 - 22 * q^93 - 23 * q^94 - 23 * q^96 - 4 * q^97 + 18 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$

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 $

$2$	−0.754089	+	2.32085i	−0.533221	+	1.64109i	0.214240	+	0.976781i	$0.431273\pi$
$2$	−0.754089	+	2.32085i	−0.533221	+	1.64109i	−0.747461	+	0.664306i	$0.768727\pi$
$3$	−0.809017	−	0.587785i	−0.467086	−	0.339358i
$3$	−0.809017	−	0.587785i	−0.467086	−	0.339358i
$4$	−3.19965	−	2.32468i	−1.59982	−	1.16234i
$5$		0			0
$5$		0			0
$6$	1.97423	−	1.43436i	0.805976	−	0.585576i
$7$	3.44028			1.30030			0.650152	−	0.759804i	$-0.274705\pi$
$7$	3.44028			1.30030			0.650152	+	0.759804i	$0.274705\pi$
$8$	3.85959	−	2.80415i	1.36457	−	0.991418i
$9$	0.309017	+	0.951057i	0.103006	+	0.317019i
$10$		0			0
$11$	−1.00942	+	3.10669i	−0.304353	+	0.936701i	0.675565	+	0.737300i	$0.263900\pi$
$11$	−1.00942	+	3.10669i	−0.304353	+	0.936701i	−0.979918	+	0.199401i	$0.936100\pi$
$12$	1.22216	+	3.76141i	0.352806	+	1.08583i
$13$	0.998755	+	3.07385i	0.277005	+	0.852533i	0.988682	+	0.150026i	$0.0479358\pi$
$13$	0.998755	+	3.07385i	0.277005	+	0.852533i	−0.711677	+	0.702506i	$0.752064\pi$
$14$	−2.59428	+	7.98437i	−0.693350	+	2.13391i
$15$		0			0
$16$	1.15323	+	3.54927i	0.288307	+	0.887317i
$17$	−4.08826	+	2.97030i	−0.991550	+	0.720403i	−0.960260	−	0.279107i	$-0.909961\pi$
$17$	−4.08826	+	2.97030i	−0.991550	+	0.720403i	−0.0312897	+	0.999510i	$0.509961\pi$
$18$	−2.44028			−0.575180
$19$	2.49274	−	1.81108i	0.571873	−	0.415490i	−0.263912	−	0.964547i	$-0.585013\pi$
$19$	2.49274	−	1.81108i	0.571873	−	0.415490i	0.835785	+	0.549056i	$0.185013\pi$
$20$		0			0
$21$	−2.78325	−	2.02215i	−0.607354	−	0.441269i
$22$	−6.44895	−	4.68544i	−1.37492	−	0.998938i
$23$	−0.478250	+	1.47190i	−0.0997219	+	0.306913i	−0.988455	−	0.151512i	$-0.951586\pi$
$23$	−0.478250	+	1.47190i	−0.0997219	+	0.306913i	0.888734	+	0.458424i	$0.151586\pi$
$24$	−4.77071			−0.973817
$25$		0			0
$26$	−7.88709			−1.54679
$27$	0.309017	−	0.951057i	0.0594703	−	0.183031i
$28$	−11.0077	−	7.99756i	−2.08026	−	1.51140i
$29$	2.52590	+	1.83517i	0.469047	+	0.340783i	0.797070	−	0.603887i	$-0.206382\pi$
$29$	2.52590	+	1.83517i	0.469047	+	0.340783i	−0.328022	+	0.944670i	$0.606382\pi$
$30$		0			0
$31$	−6.02080	+	4.37437i	−1.08137	+	0.785659i	−0.977921	−	0.208976i	$-0.932987\pi$
$31$	−6.02080	+	4.37437i	−1.08137	+	0.785659i	−0.103446	+	0.994635i	$0.532987\pi$
$32$	0.434479			0.0768057
$33$	2.64270	−	1.92004i	0.460036	−	0.334236i
$34$	−3.81069	−	11.7281i	−0.653528	−	2.01135i
$35$		0			0
$36$	1.22216	−	3.76141i	0.203693	−	0.626902i
$37$	1.77944	+	5.47655i	0.292538	+	0.900339i	0.984037	+	0.177962i	$0.0569505\pi$
$37$	1.77944	+	5.47655i	0.292538	+	0.900339i	−0.691499	+	0.722377i	$0.743050\pi$
$38$	2.32349	+	7.15098i	0.376921	+	1.16004i
$39$	0.998755	−	3.07385i	0.159929	−	0.492210i
$40$		0			0
$41$	1.67476	+	5.15437i	0.261553	+	0.804977i	0.992468	+	0.122508i	$0.0390938\pi$
$41$	1.67476	+	5.15437i	0.261553	+	0.804977i	−0.730915	+	0.682469i	$0.760906\pi$
$42$	6.79191	−	4.93461i	1.04801	−	0.761427i
$43$	−2.53106			−0.385982			−0.192991	−	0.981201i	$-0.561819\pi$
$43$	−2.53106			−0.385982			−0.192991	+	0.981201i	$0.561819\pi$
$44$	10.4519	−	7.59371i	1.57568	−	1.14480i
$45$		0			0
$46$	−3.05541	−	2.21989i	−0.450496	−	0.327305i
$47$	5.72106	+	4.15659i	0.834502	+	0.606301i	0.920829	−	0.389966i	$-0.127513\pi$
$47$	5.72106	+	4.15659i	0.834502	+	0.606301i	−0.0863273	+	0.996267i	$0.527513\pi$
$48$	1.15323	−	3.54927i	0.166454	−	0.512293i
$49$	4.83555			0.690793
$50$		0			0
$51$	5.05337			0.707614
$52$	3.95006	−	12.1570i	0.547774	−	1.68588i
$53$	−8.21277	−	5.96693i	−1.12811	−	0.819621i	−0.142692	−	0.989767i	$-0.545576\pi$
$53$	−8.21277	−	5.96693i	−1.12811	−	0.819621i	−0.985419	+	0.170147i	$0.945576\pi$
$54$	1.97423	+	1.43436i	0.268659	+	0.195192i
$55$		0			0
$56$	13.2781	−	9.64708i	1.77436	−	1.28915i
$57$	−3.08119			−0.408114
$58$	−6.16391	+	4.47834i	−0.809361	+	0.588035i
$59$	0.534773	+	1.64586i	0.0696215	+	0.214273i	0.979814	−	0.199913i	$-0.0640661\pi$
$59$	0.534773	+	1.64586i	0.0696215	+	0.214273i	−0.910192	+	0.414187i	$0.864066\pi$
$60$		0			0
$61$	2.42149	−	7.45259i	0.310040	−	0.954206i	−0.667708	−	0.744424i	$-0.732724\pi$
$61$	2.42149	−	7.45259i	0.310040	−	0.954206i	0.977748	−	0.209783i	$-0.0672756\pi$
$62$	−5.61202	−	17.2720i	−0.712727	−	2.19355i
$63$	1.06311	+	3.27190i	0.133939	+	0.412221i
$64$	−2.63409	+	8.10689i	−0.329261	+	1.01336i
$65$		0			0
$66$	2.46328	+	7.58119i	0.303209	+	0.933180i
$67$	−1.49595	+	1.08687i	−0.182760	+	0.132783i	−0.675404	−	0.737448i	$-0.736031\pi$
$67$	−1.49595	+	1.08687i	−0.182760	+	0.132783i	0.492644	+	0.870231i	$0.336031\pi$
$68$	19.9860			2.42366
$69$	1.25207	−	0.909685i	0.150732	−	0.109513i
$70$		0			0
$71$	0.577613	+	0.419660i	0.0685500	+	0.0498045i	0.621533	−	0.783388i	$-0.286510\pi$
$71$	0.577613	+	0.419660i	0.0685500	+	0.0498045i	−0.552982	+	0.833193i	$0.686510\pi$
$72$	3.85959	+	2.80415i	0.454857	+	0.330473i
$73$	0.581036	−	1.78825i	0.0680052	−	0.209298i	−0.911279	−	0.411790i	$-0.864904\pi$
$73$	0.581036	−	1.78825i	0.0680052	−	0.209298i	0.979284	+	0.202491i	$0.0649038\pi$
$74$	−14.0521			−1.63352
$75$		0			0
$76$	−12.1861			−1.39784
$77$	−3.47270	+	10.6879i	−0.395751	+	1.21800i
$78$	6.38079	+	4.63591i	0.722482	+	0.524914i
$79$	10.7868	+	7.83708i	1.21361	+	0.881740i	0.995554	−	0.0941957i	$-0.0300279\pi$
$79$	10.7868	+	7.83708i	1.21361	+	0.881740i	0.218058	+	0.975936i	$0.430028\pi$
$80$		0			0
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	−13.2254			−1.46050
$83$	3.20166	−	2.32614i	0.351428	−	0.255328i	−0.398040	−	0.917368i	$-0.630309\pi$
$83$	3.20166	−	2.32614i	0.351428	−	0.255328i	0.749468	+	0.662041i	$0.230309\pi$
$84$	4.20457	+	12.9403i	0.458756	+	1.41190i
$85$		0			0
$86$	1.90864	−	5.87419i	0.205814	−	0.633430i
$87$	−0.964807	−	2.96937i	−0.103438	−	0.318350i
$88$	4.81567	+	14.8211i	0.513352	+	1.57993i
$89$	2.63713	−	8.11624i	0.279535	−	0.860320i	−0.708449	−	0.705762i	$-0.750605\pi$
$89$	2.63713	−	8.11624i	0.279535	−	0.860320i	0.987984	−	0.154558i	$-0.0493952\pi$
$90$		0			0
$91$	3.43600	+	10.5749i	0.360191	+	1.10855i
$92$	4.95193	−	3.59779i	0.516274	−	0.375095i
$93$	7.44212			0.771712
$94$	−13.9610	+	10.1433i	−1.43997	+	1.04620i
$95$		0			0
$96$	−0.351501	−	0.255380i	−0.0358749	−	0.0260646i
$97$	−8.61831	−	6.26157i	−0.875057	−	0.635766i	0.0568823	−	0.998381i	$-0.481884\pi$
$97$	−8.61831	−	6.26157i	−0.875057	−	0.635766i	−0.931939	+	0.362615i	$0.881884\pi$
$98$	−3.64643	+	11.2226i	−0.368345	+	1.13365i
$99$	−3.26656			−0.328302
$100$		0			0
$101$	1.76173			0.175299			0.0876496	−	0.996151i	$-0.472064\pi$
$101$	1.76173			0.175299			0.0876496	+	0.996151i	$0.472064\pi$
$102$	−3.81069	+	11.7281i	−0.377315	+	1.16126i
$103$	12.8749	+	9.35416i	1.26860	+	0.921693i	0.999146	−	0.0413198i	$-0.0131562\pi$
$103$	12.8749	+	9.35416i	1.26860	+	0.921693i	0.269456	+	0.963013i	$0.413156\pi$
$104$	12.4743	+	9.06313i	1.22321	+	0.888713i
$105$		0			0
$106$	20.0415	−	14.5610i	1.94660	−	1.41429i
$107$	15.7807			1.52558			0.762788	−	0.646649i	$-0.223830\pi$
$107$	15.7807			1.52558			0.762788	+	0.646649i	$0.223830\pi$
$108$	−3.19965	+	2.32468i	−0.307886	+	0.223692i
$109$	−3.06539	−	9.43429i	−0.293611	−	0.903641i	−0.983685	−	0.179902i	$-0.942422\pi$
$109$	−3.06539	−	9.43429i	−0.293611	−	0.903641i	0.690074	−	0.723739i	$-0.257578\pi$
$110$		0			0
$111$	1.77944	−	5.47655i	0.168897	−	0.519811i
$112$	3.96743	+	12.2105i	0.374887	+	1.15378i
$113$	−1.70388	−	5.24399i	−0.160287	−	0.493313i	0.838371	−	0.545100i	$-0.183508\pi$
$113$	−1.70388	−	5.24399i	−0.160287	−	0.493313i	−0.998658	+	0.0517868i	$0.983508\pi$
$114$	2.32349	−	7.15098i	0.217615	−	0.669751i
$115$		0			0
$116$	−3.81580	−	11.7438i	−0.354288	−	1.09039i
$117$	−2.61477	+	1.89974i	−0.241736	+	0.175631i
$118$	−4.22306			−0.388764
$119$	−14.0648	+	10.2187i	−1.28932	+	0.936743i
$120$		0			0
$121$	0.266626	+	0.193715i	0.0242387	+	0.0176105i
$122$	15.4703	+	11.2398i	1.40061	+	1.01761i
$123$	1.67476	−	5.15437i	0.151008	−	0.464754i
$124$	29.4334			2.64320
$125$		0			0
$126$	−8.39527			−0.747910
$127$	0.306572	−	0.943532i	0.0272039	−	0.0837250i	−0.936533	−	0.350580i	$-0.885984\pi$
$127$	0.306572	−	0.943532i	0.0272039	−	0.0837250i	0.963737	+	0.266855i	$0.0859845\pi$
$128$	−16.1255	−	11.7159i	−1.42531	−	1.03555i
$129$	2.04767	+	1.48772i	0.180287	+	0.130986i
$130$		0			0
$131$	10.2029	−	7.41286i	0.891434	−	0.647665i	−0.0448175	−	0.998995i	$-0.514271\pi$
$131$	10.2029	−	7.41286i	0.891434	−	0.647665i	0.936252	+	0.351330i	$0.114271\pi$
$132$	−12.9192			−1.12447
$133$	8.57573	−	6.23063i	0.743610	−	0.540264i
$134$	−1.39438	−	4.29147i	−0.120456	−	0.370727i
$135$		0			0
$136$	−7.44984	+	22.9282i	−0.638818	+	1.96608i
$137$	−2.54650	−	7.83732i	−0.217562	−	0.669588i	−0.998962	−	0.0455566i	$-0.985494\pi$
$137$	−2.54650	−	7.83732i	−0.217562	−	0.669588i	0.781400	−	0.624031i	$-0.214506\pi$
$138$	1.16706	+	3.59186i	0.0993471	+	0.305759i
$139$	2.49182	−	7.66904i	0.211354	−	0.650479i	−0.788039	−	0.615626i	$-0.788903\pi$
$139$	2.49182	−	7.66904i	0.211354	−	0.650479i	0.999392	−	0.0348539i	$-0.0110966\pi$
$140$		0			0
$141$	−2.18525	−	6.72551i	−0.184031	−	0.566390i
$142$	−1.40954	+	1.02409i	−0.118286	+	0.0859397i
$143$	−10.5577			−0.882875
$144$	−3.01919	+	2.19357i	−0.251599	+	0.182797i
$145$		0			0
$146$	3.71209	+	2.69699i	0.307215	+	0.223205i
$147$	−3.91204	−	2.84226i	−0.322660	−	0.234426i
$148$	7.03765	−	21.6597i	0.578491	−	1.78041i
$149$	−19.1101			−1.56556			−0.782781	−	0.622298i	$-0.786199\pi$
$149$	−19.1101			−1.56556			−0.782781	+	0.622298i	$0.786199\pi$
$150$		0			0
$151$	1.58550			0.129026			0.0645132	−	0.997917i	$-0.479451\pi$
$151$	1.58550			0.129026			0.0645132	+	0.997917i	$0.479451\pi$
$152$	4.54239	−	13.9800i	0.368437	−	1.13393i
$153$	−4.08826	−	2.97030i	−0.330517	−	0.240134i
$154$	−22.1862	−	16.1192i	−1.78782	−	1.29892i
$155$		0			0
$156$	−10.3414	+	7.51345i	−0.827973	+	0.601558i
$157$	21.8510			1.74390			0.871948	−	0.489599i	$-0.162857\pi$
$157$	21.8510			1.74390			0.871948	+	0.489599i	$0.162857\pi$
$158$	−26.3229	+	19.1247i	−2.09414	+	1.52148i
$159$	3.13700	+	9.65469i	0.248780	+	0.765667i
$160$		0			0
$161$	−1.64531	+	5.06376i	−0.129669	+	0.399080i
$162$	−0.754089	−	2.32085i	−0.0592468	−	0.182343i
$163$	−3.13153	−	9.63786i	−0.245280	−	0.754896i	−0.995590	−	0.0938092i	$-0.970096\pi$
$163$	−3.13153	−	9.63786i	−0.245280	−	0.754896i	0.750310	−	0.661087i	$-0.229904\pi$
$164$	6.62363	−	20.3854i	0.517219	−	1.59184i
$165$		0			0
$166$	2.98429	+	9.18469i	0.231626	+	0.712870i
$167$	−1.22250	+	0.888195i	−0.0945996	+	0.0687306i	−0.634080	−	0.773268i	$-0.718621\pi$
$167$	−1.22250	+	0.888195i	−0.0945996	+	0.0687306i	0.539480	+	0.841998i	$0.318621\pi$
$168$	−16.4126			−1.26626
$169$	2.06617	−	1.50116i	0.158936	−	0.115474i
$170$		0			0
$171$	2.49274	+	1.81108i	0.190624	+	0.138497i
$172$	8.09848	+	5.88389i	0.617504	+	0.448643i
$173$	4.28153	−	13.1772i	0.325518	−	1.00184i	−0.645688	−	0.763602i	$-0.723429\pi$
$173$	4.28153	−	13.1772i	0.325518	−	1.00184i	0.971206	−	0.238241i	$-0.0765709\pi$
$174$	7.61901			0.577595
$175$		0			0
$176$	−12.1906			−0.918897
$177$	0.534773	−	1.64586i	0.0401960	−	0.123711i
$178$	16.8479	+	12.2407i	1.26281	+	0.917482i
$179$	−11.6949	−	8.49685i	−0.874119	−	0.635085i	0.0575701	−	0.998341i	$-0.481665\pi$
$179$	−11.6949	−	8.49685i	−0.874119	−	0.635085i	−0.931689	+	0.363257i	$0.881665\pi$
$180$		0			0
$181$	−13.9068	+	10.1039i	−1.03369	+	0.751017i	−0.969043	−	0.246891i	$-0.920591\pi$
$181$	−13.9068	+	10.1039i	−1.03369	+	0.751017i	−0.0646435	+	0.997908i	$0.520591\pi$
$182$	−27.1338			−2.01129
$183$	−6.33955	+	4.60595i	−0.468633	+	0.340482i
$184$	2.28159	+	7.02201i	0.168201	+	0.517670i
$185$		0			0
$186$	−5.61202	+	17.2720i	−0.411493	+	1.26645i
$187$	−5.10099	−	15.6992i	−0.373021	−	1.14804i
$188$	−8.64262	−	26.5993i	−0.630328	−	1.93995i
$189$	1.06311	−	3.27190i	0.0773296	−	0.237996i
$190$		0			0
$191$	3.25778	+	10.0264i	0.235725	+	0.725486i	0.997024	+	0.0770858i	$0.0245615\pi$
$191$	3.25778	+	10.0264i	0.235725	+	0.725486i	−0.761300	+	0.648400i	$0.775438\pi$
$192$	6.89613	−	5.01034i	0.497686	−	0.361590i
$193$	0.682908			0.0491568			0.0245784	−	0.999698i	$-0.492176\pi$
$193$	0.682908			0.0491568			0.0245784	+	0.999698i	$0.492176\pi$
$194$	21.0311	−	15.2800i	1.50995	−	1.09704i
$195$		0			0
$196$	−15.4721	−	11.2411i	−1.10515	−	0.802936i
$197$	−18.8478	−	13.6937i	−1.34285	−	0.975639i	−0.999334	−	0.0364929i	$-0.988381\pi$
$197$	−18.8478	−	13.6937i	−1.34285	−	0.975639i	−0.343518	−	0.939146i	$-0.611619\pi$
$198$	2.46328	−	7.58119i	0.175058	−	0.538772i
$199$	10.1946			0.722679			0.361339	−	0.932434i	$-0.382320\pi$
$199$	10.1946			0.722679			0.361339	+	0.932434i	$0.382320\pi$
$200$		0			0
$201$	1.84910			0.130425
$202$	−1.32850	+	4.08872i	−0.0934733	+	0.287681i
$203$	8.68980	+	6.31351i	0.609905	+	0.443122i
$204$	−16.1690	−	11.7475i	−1.13206	−	0.822488i
$205$		0			0
$206$	−31.4184	+	22.8268i	−2.18902	+	1.59042i
$207$	−1.54765			−0.107569
$208$	−9.75813	+	7.08969i	−0.676604	+	0.491582i
$209$	3.11023	+	9.57230i	0.215139	+	0.662130i
$210$		0			0
$211$	5.64172	−	17.3634i	0.388392	−	1.19535i	−0.545598	−	0.838047i	$-0.683697\pi$
$211$	5.64172	−	17.3634i	0.388392	−	1.19535i	0.933990	−	0.357300i	$-0.116303\pi$
$212$	12.4068	+	38.1841i	0.852101	+	2.62250i
$213$	−0.220629	−	0.679025i	−0.0151172	−	0.0465260i
$214$	−11.9000	+	36.6245i	−0.813470	+	2.50360i
$215$		0			0
$216$	−1.47423	−	4.53722i	−0.100309	−	0.308718i
$217$	−20.7133	+	15.0491i	−1.40611	+	1.02160i
$218$	24.2071			1.63951
$219$	−1.52117	+	1.10520i	−0.102791	+	0.0746823i
$220$		0			0
$221$	−13.2134	−	9.60011i	−0.888831	−	0.645774i
$222$	11.3684	+	8.25961i	0.762996	+	0.554349i
$223$	−5.32262	+	16.3813i	−0.356429	+	1.09698i	0.598748	+	0.800938i	$0.295665\pi$
$223$	−5.32262	+	16.3813i	−0.356429	+	1.09698i	−0.955176	+	0.296037i	$0.904335\pi$
$224$	1.49473			0.0998708
$225$		0			0
$226$	13.4554			0.895039
$227$	1.33767	−	4.11692i	0.0887842	−	0.273250i	−0.896800	−	0.442437i	$-0.854114\pi$
$227$	1.33767	−	4.11692i	0.0887842	−	0.273250i	0.985584	+	0.169187i	$0.0541142\pi$
$228$	9.85874	+	7.16279i	0.652911	+	0.474367i
$229$	−16.4349	−	11.9407i	−1.08605	−	0.789062i	−0.107322	−	0.994224i	$-0.534228\pi$
$229$	−16.4349	−	11.9407i	−1.08605	−	0.789062i	−0.978728	+	0.205163i	$0.934228\pi$
$230$		0			0
$231$	9.09165	−	6.60547i	0.598187	−	0.434608i
$232$	14.8950			0.977906
$233$	−0.275839	+	0.200409i	−0.0180708	+	0.0131292i	−0.596784	−	0.802402i	$-0.703555\pi$
$233$	−0.275839	+	0.200409i	−0.0180708	+	0.0131292i	0.578713	+	0.815531i	$0.303555\pi$
$234$	−2.43724	−	7.50107i	−0.159328	−	0.490360i
$235$		0			0
$236$	2.11502	−	6.50936i	0.137676	−	0.423723i
$237$	−4.12020	−	12.6807i	−0.267635	−	0.823697i
$238$	−13.1099	−	40.3480i	−0.849786	−	2.61537i
$239$	−2.21407	+	6.81421i	−0.143216	+	0.440774i	−0.996777	−	0.0802185i	$-0.974438\pi$
$239$	−2.21407	+	6.81421i	−0.143216	+	0.440774i	0.853561	+	0.520993i	$0.174438\pi$
$240$		0			0
$241$	−3.88194	−	11.9474i	−0.250058	−	0.769599i	−0.994763	−	0.102206i	$-0.967410\pi$
$241$	−3.88194	−	11.9474i	−0.250058	−	0.769599i	0.744705	−	0.667393i	$-0.232590\pi$
$242$	−0.650643	+	0.472720i	−0.0418249	+	0.0303876i
$243$	1.00000			0.0641500
$244$	−25.0728	+	18.2165i	−1.60512	+	1.16619i
$245$		0			0
$246$	10.6996	+	7.77370i	0.682181	+	0.495633i
$247$	8.05662	+	5.85348i	0.512631	+	0.372448i
$248$	−10.9714	+	33.7665i	−0.696684	+	2.14417i
$249$	−3.95747			−0.250795
$250$		0			0
$251$	17.0160			1.07404			0.537022	−	0.843568i	$-0.319549\pi$
$251$	17.0160			1.07404			0.537022	+	0.843568i	$0.319549\pi$
$252$	4.20457	−	12.9403i	0.264863	−	0.815164i
$253$	−4.08998	−	2.97154i	−0.257135	−	0.186819i
$254$	1.95861	+	1.42301i	0.122894	+	0.0892879i
$255$		0			0
$256$	25.5586	−	18.5694i	1.59741	−	1.16059i
$257$	−4.13200			−0.257747			−0.128874	−	0.991661i	$-0.541136\pi$
$257$	−4.13200			−0.257747			−0.128874	+	0.991661i	$0.541136\pi$
$258$	−4.99689	+	3.63045i	−0.311093	+	0.226022i
$259$	6.12177	+	18.8409i	0.380388	+	1.17072i
$260$		0			0
$261$	−0.964807	+	2.96937i	−0.0597201	+	0.183799i
$262$	9.51020	+	29.2694i	0.587542	+	1.80827i
$263$	0.320676	+	0.986940i	0.0197737	+	0.0608573i	0.960456	−	0.278430i	$-0.0898141\pi$
$263$	0.320676	+	0.986940i	0.0197737	+	0.0608573i	−0.940683	+	0.339287i	$0.889814\pi$
$264$	4.81567	−	14.8211i	0.296384	−	0.912176i
$265$		0			0
$266$	7.99348	+	24.6014i	0.490112	+	1.50841i
$267$	−6.90408	+	5.01611i	−0.422523	+	0.306981i
$268$	7.31315			0.446722
$269$	12.7741	−	9.28093i	0.778851	−	0.565869i	−0.125783	−	0.992058i	$-0.540144\pi$
$269$	12.7741	−	9.28093i	0.778851	−	0.565869i	0.904634	+	0.426189i	$0.140144\pi$
$270$		0			0
$271$	11.0838	+	8.05286i	0.673294	+	0.489176i	0.871126	−	0.491059i	$-0.163390\pi$
$271$	11.0838	+	8.05286i	0.673294	+	0.489176i	−0.197832	+	0.980236i	$0.563390\pi$
$272$	−15.2571	−	11.0849i	−0.925096	−	0.672122i
$273$	3.43600	−	10.5749i	0.207956	−	0.640023i
$274$	20.1095			1.21486
$275$		0			0
$276$	−6.12092			−0.368436
$277$	−2.15691	+	6.63827i	−0.129596	+	0.398855i	−0.994710	−	0.102719i	$-0.967246\pi$
$277$	−2.15691	+	6.63827i	−0.129596	+	0.398855i	0.865114	+	0.501574i	$0.167246\pi$
$278$	15.9196	+	11.5663i	0.954795	+	0.693699i
$279$	−6.02080	−	4.37437i	−0.360456	−	0.261886i
$280$		0			0
$281$	−6.43834	+	4.67773i	−0.384079	+	0.279050i	−0.763025	−	0.646369i	$-0.776287\pi$
$281$	−6.43834	+	4.67773i	−0.384079	+	0.279050i	0.378946	+	0.925419i	$0.376287\pi$
$282$	17.2567			1.02762
$283$	−22.4868	+	16.3376i	−1.33670	+	0.971169i	−0.337141	+	0.941454i	$0.609460\pi$
$283$	−22.4868	+	16.3376i	−1.33670	+	0.971169i	−0.999558	+	0.0297149i	$0.990540\pi$
$284$	−0.872582	−	2.68553i	−0.0517782	−	0.159357i
$285$		0			0
$286$	7.96141	−	24.5027i	0.470768	−	1.44888i
$287$	5.76163	+	17.7325i	0.340099	+	1.04672i
$288$	0.134261	+	0.413214i	0.00791142	+	0.0243488i
$289$	2.63794	−	8.11876i	0.155173	−	0.477574i
$290$		0			0
$291$	3.29190	+	10.1314i	0.192975	+	0.593915i
$292$	−6.01621	+	4.37103i	−0.352072	+	0.255795i
$293$	14.2098			0.830146			0.415073	−	0.909788i	$-0.363756\pi$
$293$	14.2098			0.830146			0.415073	+	0.909788i	$0.363756\pi$
$294$	9.54649	−	6.93593i	0.556763	−	0.404512i
$295$		0			0
$296$	22.2250	+	16.1474i	1.29180	+	0.938548i
$297$	2.64270	+	1.92004i	0.153345	+	0.111412i
$298$	14.4107	−	44.3517i	0.834791	−	2.56922i
$299$	−5.00206			−0.289276
$300$		0			0
$301$	−8.70755			−0.501895
$302$	−1.19561	+	3.67971i	−0.0687997	+	0.211744i
$303$	−1.42527	−	1.03552i	−0.0818798	−	0.0594892i
$304$	9.30270	+	6.75881i	0.533547	+	0.387644i
$305$		0			0
$306$	9.97652	−	7.24837i	0.570320	−	0.414362i
$307$	23.2911			1.32930			0.664648	−	0.747157i	$-0.268582\pi$
$307$	23.2911			1.32930			0.664648	+	0.747157i	$0.268582\pi$
$308$	35.9573	−	26.1245i	2.04886	−	1.48858i
$309$	−4.91777	−	15.1354i	−0.279762	−	0.861020i
$310$		0			0
$311$	−2.33284	+	7.17976i	−0.132283	+	0.407127i	−0.995158	−	0.0982923i	$-0.968662\pi$
$311$	−2.33284	+	7.17976i	−0.132283	+	0.407127i	0.862874	+	0.505419i	$0.168662\pi$
$312$	−4.76477	−	14.6645i	−0.269752	−	0.830211i
$313$	9.78241	+	30.1072i	0.552934	+	1.70176i	0.701337	+	0.712830i	$0.252587\pi$
$313$	9.78241	+	30.1072i	0.552934	+	1.70176i	−0.148402	+	0.988927i	$0.547413\pi$
$314$	−16.4776	+	50.7127i	−0.929883	+	2.86188i
$315$		0			0
$316$	−16.2953	−	50.1518i	−0.916682	−	2.82126i
$317$	20.9019	−	15.1861i	1.17397	−	0.852938i	0.182490	−	0.983208i	$-0.441584\pi$
$317$	20.9019	−	15.1861i	1.17397	−	0.852938i	0.991479	+	0.130270i	$0.0415844\pi$
$318$	−24.7726			−1.38918
$319$	−8.25100	+	5.99471i	−0.461968	+	0.335639i
$320$		0			0
$321$	−12.7668	−	9.27565i	−0.712575	−	0.517716i
$322$	−10.5115	−	7.63705i	−0.585783	−	0.425596i
$323$	−4.81152	+	14.8083i	−0.267720	+	0.823959i
$324$	3.95498			0.219721
$325$		0			0
$326$	24.7295			1.36964
$327$	−3.06539	+	9.43429i	−0.169516	+	0.521717i
$328$	20.9175	+	15.1975i	1.15498	+	0.839139i
$329$	19.6821	+	14.2999i	1.08511	+	0.788376i
$330$		0			0
$331$	−16.2679	+	11.8193i	−0.894166	+	0.649650i	−0.936961	−	0.349434i	$-0.886374\pi$
$331$	−16.2679	+	11.8193i	−0.894166	+	0.649650i	0.0427948	+	0.999084i	$0.486374\pi$
$332$	−15.6517			−0.859001
$333$	−4.65863	+	3.38469i	−0.255291	+	0.185480i
$334$	−1.13949	−	3.50700i	−0.0623504	−	0.191895i
$335$		0			0
$336$	3.96743	−	12.2105i	0.216441	−	0.666137i
$337$	−1.04564	−	3.21816i	−0.0569599	−	0.175304i	0.918529	−	0.395354i	$-0.129378\pi$
$337$	−1.04564	−	3.21816i	−0.0569599	−	0.175304i	−0.975489	+	0.220050i	$0.929378\pi$
$338$	1.92589	+	5.92729i	0.104755	+	0.322402i
$339$	−1.70388	+	5.24399i	−0.0925419	+	0.284815i
$340$		0			0
$341$	−7.51225	−	23.1203i	−0.406811	−	1.25204i
$342$	−6.08299	+	4.41955i	−0.328930	+	0.238982i
$343$	−7.44633			−0.402064
$344$	−9.76882	+	7.09747i	−0.526700	+	0.382670i
$345$		0			0
$346$	27.3536	+	19.8735i	1.47054	+	1.06841i
$347$	−23.6204	−	17.1612i	−1.26801	−	0.921262i	−0.268887	−	0.963172i	$-0.586656\pi$
$347$	−23.6204	−	17.1612i	−1.26801	−	0.921262i	−0.999121	+	0.0419100i	$0.986656\pi$
$348$	−3.81580	+	11.7438i	−0.204548	+	0.629534i
$349$	−20.3979			−1.09187			−0.545937	−	0.837826i	$-0.683826\pi$
$349$	−20.3979			−1.09187			−0.545937	+	0.837826i	$0.683826\pi$
$350$		0			0
$351$	3.23204			0.172513
$352$	−0.438573	+	1.34979i	−0.0233760	+	0.0719440i
$353$	−1.50757	−	1.09532i	−0.0802400	−	0.0582978i	0.546942	−	0.837170i	$-0.315792\pi$
$353$	−1.50757	−	1.09532i	−0.0802400	−	0.0582978i	−0.627182	+	0.778873i	$0.715792\pi$
$354$	3.41653	+	2.48225i	0.181586	+	0.131930i
$355$		0			0
$356$	−27.3055	+	19.8386i	−1.44719	+	1.05145i
$357$	17.3850			0.920113
$358$	28.5389	−	20.7347i	1.50833	−	1.09586i
$359$	1.18599	+	3.65011i	0.0625943	+	0.192645i	0.977463	−	0.211105i	$-0.0677063\pi$
$359$	1.18599	+	3.65011i	0.0625943	+	0.192645i	−0.914869	+	0.403751i	$0.867706\pi$
$360$		0			0
$361$	−2.93759	+	9.04097i	−0.154610	+	0.475841i
$362$	−12.9626	−	39.8949i	−0.681301	−	2.09683i
$363$	−0.101842	−	0.313438i	−0.00534532	−	0.0164512i
$364$	13.5893	−	41.8236i	0.712274	−	2.19215i
$365$		0			0
$366$	−5.90913	−	18.1864i	−0.308875	−	0.950620i
$367$	20.7335	−	15.0638i	1.08228	−	0.786324i	0.104203	−	0.994556i	$-0.466771\pi$
$367$	20.7335	−	15.0638i	1.08228	−	0.786324i	0.978079	+	0.208232i	$0.0667709\pi$
$368$	−5.77570			−0.301079
$369$	−4.38457	+	3.18557i	−0.228251	+	0.165834i
$370$		0			0
$371$	−28.2543	−	20.5279i	−1.46689	−	1.06576i
$372$	−23.8122	−	17.3005i	−1.23460	−	0.896991i
$373$	−6.62437	+	20.3877i	−0.342997	+	1.05564i	0.619651	+	0.784878i	$0.287274\pi$
$373$	−6.62437	+	20.3877i	−0.342997	+	1.05564i	−0.962648	+	0.270758i	$0.912726\pi$
$374$	40.2821			2.08294
$375$		0			0
$376$	33.7366			1.73983
$377$	−3.11829	+	9.59712i	−0.160600	+	0.494277i
$378$	6.79191	+	4.93461i	0.349338	+	0.253809i
$379$	20.9304	+	15.2068i	1.07512	+	0.781120i	0.976826	−	0.214037i	$-0.0686613\pi$
$379$	20.9304	+	15.2068i	1.07512	+	0.781120i	0.0982945	+	0.995157i	$0.468661\pi$
$380$		0			0
$381$	−0.802617	+	0.583135i	−0.0411193	+	0.0298749i
$382$	−25.7264			−1.31628
$383$	−11.7579	+	8.54263i	−0.600802	+	0.436508i	−0.846163	−	0.532924i	$-0.821093\pi$
$383$	−11.7579	+	8.54263i	−0.600802	+	0.436508i	0.245362	+	0.969432i	$0.421093\pi$
$384$	6.15940	+	18.9567i	0.314321	+	0.967379i
$385$		0			0
$386$	−0.514974	+	1.58493i	−0.0262115	+	0.0806706i
$387$	−0.782139	−	2.40718i	−0.0397584	−	0.122364i
$388$	13.0194	+	40.0696i	0.660960	+	2.03423i
$389$	7.13973	−	21.9738i	0.361999	−	1.11412i	−0.589840	−	0.807520i	$-0.700809\pi$
$389$	7.13973	−	21.9738i	0.361999	−	1.11412i	0.951839	−	0.306598i	$-0.0991907\pi$
$390$		0			0
$391$	−2.41677	−	7.43806i	−0.122221	−	0.376159i
$392$	18.6632	−	13.5596i	0.942635	−	0.684864i
$393$	−12.6115			−0.636167
$394$	45.9940	−	33.4166i	2.31715	−	1.68350i
$395$		0			0
$396$	10.4519	+	7.59371i	0.525225	+	0.381598i
$397$	11.2733	+	8.19052i	0.565790	+	0.411070i	0.833573	−	0.552409i	$-0.186291\pi$
$397$	11.2733	+	8.19052i	0.565790	+	0.411070i	−0.267784	+	0.963479i	$0.586291\pi$
$398$	−7.68766	+	23.6602i	−0.385348	+	1.18598i
$399$	−10.6002			−0.530673
$400$		0			0
$401$	−27.5822			−1.37739			−0.688694	−	0.725052i	$-0.741816\pi$
$401$	−27.5822			−1.37739			−0.688694	+	0.725052i	$0.741816\pi$
$402$	−1.39438	+	4.29147i	−0.0695456	+	0.214039i
$403$	−19.4594	−	14.1381i	−0.969344	−	0.704270i
$404$	−5.63693	−	4.09547i	−0.280448	−	0.203757i
$405$		0			0
$406$	−21.2056	+	15.4068i	−1.05242	+	0.764625i
$407$	−18.8101			−0.932383
$408$	19.5039	−	14.1704i	0.965588	−	0.701541i
$409$	4.08288	+	12.5658i	0.201886	+	0.621340i	0.999827	+	0.0186048i	$0.00592242\pi$
$409$	4.08288	+	12.5658i	0.201886	+	0.621340i	−0.797941	+	0.602735i	$0.794078\pi$
$410$		0			0
$411$	−2.54650	+	7.83732i	−0.125610	+	0.386587i
$412$	−19.4497	−	59.8601i	−0.958218	−	2.94909i
$413$	1.83977	+	5.66223i	0.0905292	+	0.278620i
$414$	1.16706	−	3.59186i	0.0573581	−	0.176530i
$415$		0			0
$416$	0.433937	+	1.33552i	0.0212755	+	0.0654794i
$417$	−6.52367	+	4.73973i	−0.319466	+	0.232105i
$418$	−24.5612			−1.20133
$419$	7.15797	−	5.20057i	0.349690	−	0.254064i	−0.399049	−	0.916930i	$-0.630660\pi$
$419$	7.15797	−	5.20057i	0.349690	−	0.254064i	0.748739	+	0.662865i	$0.230660\pi$
$420$		0			0
$421$	30.3192	+	22.0282i	1.47767	+	1.07359i	0.978299	+	0.207197i	$0.0664341\pi$
$421$	30.3192	+	22.0282i	1.47767	+	1.07359i	0.499367	+	0.866390i	$0.333566\pi$
$422$	36.0435	+	26.1871i	1.75457	+	1.27477i
$423$	−2.18525	+	6.72551i	−0.106250	+	0.327005i
$424$	−48.4301			−2.35197
$425$		0			0
$426$	1.74229			0.0844140
$427$	8.33062	−	25.6390i	0.403147	−	1.24076i
$428$	−50.4926	−	36.6850i	−2.44065	−	1.77324i
$429$	8.54132	+	6.20563i	0.412379	+	0.299611i
$430$		0			0
$431$	21.5397	−	15.6495i	1.03753	−	0.753809i	0.0677274	−	0.997704i	$-0.478425\pi$
$431$	21.5397	−	15.6495i	1.03753	−	0.753809i	0.969802	+	0.243895i	$0.0784252\pi$
$432$	3.73192			0.179552
$433$	28.3133	−	20.5708i	1.36065	−	0.988571i	0.362248	−	0.932082i	$-0.382010\pi$
$433$	28.3133	−	20.5708i	1.36065	−	0.988571i	0.998403	−	0.0564887i	$-0.0179905\pi$
$434$	−19.3069	−	59.4206i	−0.926762	−	2.85228i
$435$		0			0
$436$	−12.1235	+	37.3124i	−0.580613	+	1.78694i
$437$	1.47358	+	4.53521i	0.0704909	+	0.216949i
$438$	−1.41789	−	4.36383i	−0.0677496	−	0.208512i
$439$	6.19701	−	19.0724i	0.295767	−	0.910277i	−0.687196	−	0.726472i	$-0.741159\pi$
$439$	6.19701	−	19.0724i	0.295767	−	0.910277i	0.982963	−	0.183805i	$-0.0588415\pi$
$440$		0			0
$441$	1.49427	+	4.59888i	0.0711556	+	0.218994i
$442$	32.2445	−	23.4270i	1.53371	−	1.11431i
$443$	−4.14871			−0.197111			−0.0985556	−	0.995132i	$-0.531422\pi$
$443$	−4.14871			−0.197111			−0.0985556	+	0.995132i	$0.531422\pi$
$444$	−18.4248	+	13.3864i	−0.874402	+	0.635291i
$445$		0			0
$446$	−34.0048	−	24.7060i	−1.61018	−	1.16986i
$447$	15.4604	+	11.2326i	0.731252	+	0.531286i
$448$	−9.06201	+	27.8900i	−0.428140	+	1.31768i
$449$	−8.34804			−0.393969			−0.196984	−	0.980407i	$-0.563115\pi$
$449$	−8.34804			−0.393969			−0.196984	+	0.980407i	$0.563115\pi$
$450$		0			0
$451$	−17.7035			−0.833627
$452$	−6.73880	+	20.7399i	−0.316967	+	0.975523i
$453$	−1.28270	−	0.931936i	−0.0602665	−	0.0437862i
$454$	8.54602	+	6.20905i	0.401085	+	0.291405i
$455$		0			0
$456$	−11.8921	+	8.64014i	−0.556900	+	0.404612i
$457$	−20.5774			−0.962571			−0.481285	−	0.876564i	$-0.659830\pi$
$457$	−20.5774			−0.962571			−0.481285	+	0.876564i	$0.659830\pi$
$458$	40.1059	−	29.1386i	1.87402	−	1.36156i
$459$	1.56158	+	4.80604i	0.0728882	+	0.224327i
$460$		0			0
$461$	8.86541	−	27.2849i	0.412903	−	1.27079i	−0.501210	−	0.865326i	$-0.667111\pi$
$461$	8.86541	−	27.2849i	0.412903	−	1.27079i	0.914113	−	0.405460i	$-0.132889\pi$
$462$	8.47438	+	26.0815i	0.394264	+	1.21342i
$463$	−12.3853	−	38.1181i	−0.575594	−	1.77150i	−0.634146	−	0.773213i	$-0.718648\pi$
$463$	−12.3853	−	38.1181i	−0.575594	−	1.77150i	0.0585520	−	0.998284i	$-0.481352\pi$
$464$	−3.60058	+	11.0815i	−0.167153	+	0.514444i
$465$		0			0
$466$	−0.257111	−	0.791307i	−0.0119105	−	0.0366566i
$467$	−6.58694	+	4.78569i	−0.304807	+	0.221456i	−0.729665	−	0.683805i	$-0.760324\pi$
$467$	−6.58694	+	4.78569i	−0.304807	+	0.221456i	0.424858	+	0.905260i	$0.360324\pi$
$468$	12.7827			0.590878
$469$	−5.14650	+	3.73915i	−0.237643	+	0.172658i
$470$		0			0
$471$	−17.6778	−	12.8437i	−0.814550	−	0.591805i
$472$	6.67925	+	4.85276i	0.307438	+	0.223366i
$473$	2.55491	−	7.86319i	0.117475	−	0.361550i
$474$	32.5369			1.49447
$475$		0			0
$476$	68.7575			3.15149
$477$	3.13700	−	9.65469i	0.143633	−	0.442058i
$478$	−14.1451	−	10.2770i	−0.646983	−	0.470061i
$479$	22.7027	+	16.4945i	1.03731	+	0.753652i	0.969759	−	0.244064i	$-0.0784807\pi$
$479$	22.7027	+	16.4945i	1.03731	+	0.753652i	0.0675535	+	0.997716i	$0.478481\pi$
$480$		0			0
$481$	−15.0569	+	10.9395i	−0.686534	+	0.498796i
$482$	30.6554			1.39631
$483$	4.30749	−	3.12957i	0.195998	−	0.142401i
$484$	−0.402784	−	1.23964i	−0.0183084	−	0.0563473i
$485$		0			0
$486$	−0.754089	+	2.32085i	−0.0342062	+	0.105276i
$487$	4.70239	+	14.4725i	0.213086	+	0.655810i	0.999284	+	0.0378360i	$0.0120464\pi$
$487$	4.70239	+	14.4725i	0.213086	+	0.655810i	−0.786198	+	0.617974i	$0.787954\pi$
$488$	−11.5522	−	35.5541i	−0.522945	−	1.60946i
$489$	−3.13153	+	9.63786i	−0.141613	+	0.435839i
$490$		0			0
$491$	2.56246	+	7.88645i	0.115642	+	0.355910i	0.992080	−	0.125604i	$-0.0400869\pi$
$491$	2.56246	+	7.88645i	0.115642	+	0.355910i	−0.876438	+	0.481514i	$0.840087\pi$
$492$	−17.3409	+	12.5989i	−0.781788	+	0.568002i
$493$	−15.7775			−0.710585
$494$	−19.6604	+	14.2842i	−0.884565	+	0.642674i
$495$		0			0
$496$	−22.4691	−	16.3248i	−1.00889	−	0.733005i
$497$	1.98715	+	1.44375i	0.0891360	+	0.0647611i
$498$	2.98429	−	9.18469i	0.133729	−	0.411576i
$499$	−24.4006			−1.09232			−0.546160	−	0.837681i	$-0.683911\pi$
$499$	−24.4006			−1.09232			−0.546160	+	0.837681i	$0.683911\pi$
$500$		0			0
$501$	1.51109			0.0675104
$502$	−12.8316	+	39.4916i	−0.572703	+	1.76260i
$503$	8.47295	+	6.15596i	0.377790	+	0.274481i	0.760434	−	0.649415i	$-0.224986\pi$
$503$	8.47295	+	6.15596i	0.377790	+	0.274481i	−0.382644	+	0.923896i	$0.624986\pi$
$504$	13.2781	+	9.64708i	0.591452	+	0.429715i
$505$		0			0
$506$	9.98070	−	7.25141i	0.443696	−	0.322364i
$507$	−2.55393			−0.113424
$508$	−3.17433	+	2.30629i	−0.140838	+	0.102325i
$509$	−3.41769	−	10.5186i	−0.151486	−	0.466227i	0.846302	−	0.532704i	$-0.178824\pi$
$509$	−3.41769	−	10.5186i	−0.151486	−	0.466227i	−0.997788	+	0.0664770i	$0.978824\pi$
$510$		0			0
$511$	1.99893	−	6.15207i	0.0884274	−	0.272152i
$512$	11.5045	+	35.4071i	0.508431	+	1.56479i
$513$	−0.952141	−	2.93039i	−0.0420381	−	0.129380i
$514$	3.11590	−	9.58974i	0.137436	−	0.422985i
$515$		0			0
$516$	−3.09335	−	9.52034i	−0.136177	−	0.419110i
$517$	−18.6882	+	13.5778i	−0.821906	+	0.597150i
$518$	−48.3432			−2.12408
$519$	−11.2092	+	8.14395i	−0.492029	+	0.357480i
$520$		0			0
$521$	33.5105	+	24.3468i	1.46812	+	1.06665i	0.981153	+	0.193231i	$0.0618968\pi$
$521$	33.5105	+	24.3468i	1.46812	+	1.06665i	0.486967	+	0.873420i	$0.338103\pi$
$522$	−6.16391	−	4.47834i	−0.269787	−	0.196012i
$523$	−4.21576	+	12.9748i	−0.184342	+	0.567347i	−0.999936	−	0.0112775i	$-0.996410\pi$
$523$	−4.21576	+	12.9748i	−0.184342	+	0.567347i	0.815594	+	0.578624i	$0.196410\pi$
$524$	−49.8783			−2.17894
$525$		0			0
$526$	−2.53235			−0.110416
$527$	11.6214	−	35.7671i	0.506238	−	1.55804i
$528$	9.86236	+	7.16543i	0.429204	+	0.311835i
$529$	16.6696	+	12.1112i	0.724766	+	0.526573i
$530$		0			0
$531$	−1.40005	+	1.01720i	−0.0607572	+	0.0441427i
$532$	−41.9235			−1.81762
$533$	−14.1711	+	10.2959i	−0.613818	+	0.445965i
$534$	−6.43533	−	19.8059i	−0.278484	−	0.857086i
$535$		0			0
$536$	−2.72600	+	8.38976i	−0.117745	+	0.362382i
$537$	4.46706	+	13.7482i	0.192768	+	0.593278i
$538$	11.9068	+	36.6454i	0.513339	+	1.57990i
$539$	−4.88112	+	15.0225i	−0.210245	+	0.647066i
$540$		0			0
$541$	4.53011	+	13.9423i	0.194765	+	0.599424i	0.999979	+	0.00644072i	$0.00205016\pi$
$541$	4.53011	+	13.9423i	0.194765	+	0.599424i	−0.805214	+	0.592984i	$0.797950\pi$
$542$	−27.0476	+	19.6513i	−1.16180	+	0.844094i
$543$	17.1898			0.737685
$544$	−1.77626	+	1.29053i	−0.0761566	+	0.0553310i
$545$		0			0
$546$	21.9517	+	15.9489i	0.939447	+	0.682548i
$547$	21.5298	+	15.6423i	0.920549	+	0.668818i	0.943661	−	0.330915i	$-0.107357\pi$
$547$	21.5298	+	15.6423i	0.920549	+	0.668818i	−0.0231115	+	0.999733i	$0.507357\pi$
$548$	−10.0714	+	30.9965i	−0.430227	+	1.32410i
$549$	7.83611			0.334437
$550$		0			0
$551$	9.62005			0.409828
$552$	2.28159	−	7.02201i	0.0971109	−	0.298877i
$553$	37.1097	+	26.9618i	1.57806	+	1.14653i
$554$	−13.7799	−	10.0117i	−0.585453	−	0.425356i
$555$		0			0
$556$	−25.8010	+	18.7455i	−1.09421	+	0.794988i
$557$	10.3141			0.437020			0.218510	−	0.975835i	$-0.429880\pi$
$557$	10.3141			0.437020			0.218510	+	0.975835i	$0.429880\pi$
$558$	14.6925	−	10.6747i	0.621981	−	0.451896i
$559$	−2.52790	−	7.78008i	−0.106919	−	0.329063i
$560$		0			0
$561$	−5.10099	+	15.6992i	−0.215364	+	0.662822i
$562$	−6.00121	−	18.4698i	−0.253146	−	0.779103i
$563$	10.6311	+	32.7193i	0.448049	+	1.37895i	0.879105	+	0.476628i	$0.158141\pi$
$563$	10.6311	+	32.7193i	0.448049	+	1.37895i	−0.431056	+	0.902325i	$0.641859\pi$
$564$	−8.64262	+	26.5993i	−0.363920	+	1.12003i
$565$		0			0
$566$	−20.9600	−	64.5083i	−0.881016	−	2.71149i
$567$	−2.78325	+	2.02215i	−0.116885	+	0.0849222i
$568$	3.40614			0.142918
$569$	9.87387	−	7.17378i	0.413934	−	0.300741i	−0.361259	−	0.932466i	$-0.617653\pi$
$569$	9.87387	−	7.17378i	0.413934	−	0.300741i	0.775193	+	0.631725i	$0.217653\pi$
$570$		0			0
$571$	−34.0308	−	24.7248i	−1.42415	−	1.03470i	−0.991070	−	0.133345i	$-0.957428\pi$
$571$	−34.0308	−	24.7248i	−1.42415	−	1.03470i	−0.433076	−	0.901357i	$-0.642572\pi$
$572$	33.7808	+	24.5432i	1.41245	+	1.02620i
$573$	3.25778	−	10.0264i	0.136096	−	0.418859i
$574$	−45.4992			−1.89910
$575$		0			0
$576$	−8.52409			−0.355170
$577$	−5.41863	+	16.6768i	−0.225581	+	0.694266i	0.772652	+	0.634830i	$0.218930\pi$
$577$	−5.41863	+	16.6768i	−0.225581	+	0.694266i	−0.998232	+	0.0594353i	$0.981070\pi$
$578$	16.8532	+	12.2445i	0.700999	+	0.509305i
$579$	−0.552485	−	0.401404i	−0.0229605	−	0.0166818i
$580$		0			0
$581$	11.0146	−	8.00260i	0.456964	−	0.332004i
$582$	−25.9959			−1.07756
$583$	26.8275	−	19.4913i	1.11108	−	0.807249i
$584$	−2.77196	−	8.53120i	−0.114704	−	0.353024i
$585$		0			0
$586$	−10.7155	+	32.9788i	−0.442651	+	1.36234i
$587$	6.77115	+	20.8395i	0.279475	+	0.860137i	0.988000	+	0.154451i	$0.0493610\pi$
$587$	6.77115	+	20.8395i	0.279475	+	0.860137i	−0.708525	+	0.705686i	$0.750639\pi$
$588$	5.90980	+	18.1885i	0.243716	+	0.750081i
$589$	−7.08595	+	21.8083i	−0.291971	+	0.898595i
$590$		0			0
$591$	7.19923	+	22.1569i	0.296137	+	0.911415i
$592$	−17.3856	+	12.6314i	−0.714545	+	0.519148i
$593$	38.0061			1.56072			0.780361	−	0.625330i	$-0.215035\pi$
$593$	38.0061			1.56072			0.780361	+	0.625330i	$0.215035\pi$
$594$	−6.44895	+	4.68544i	−0.264604	+	0.192246i
$595$		0			0
$596$	61.1456	+	44.4249i	2.50462	+	1.81971i
$597$	−8.24764	−	5.99226i	−0.337553	−	0.245247i
$598$	3.77200	−	11.6090i	0.154248	−	0.474728i
$599$	16.3154			0.666629			0.333314	−	0.942816i	$-0.391833\pi$
$599$	16.3154			0.666629			0.333314	+	0.942816i	$0.391833\pi$
$600$		0			0
$601$	2.31871			0.0945822			0.0472911	−	0.998881i	$-0.484941\pi$
$601$	2.31871			0.0945822			0.0472911	+	0.998881i	$0.484941\pi$
$602$	6.56626	−	20.2089i	0.267621	−	0.823653i
$603$	−1.49595	−	1.08687i	−0.0609199	−	0.0442609i
$604$	−5.07305	−	3.68579i	−0.206420	−	0.149973i
$605$		0			0
$606$	3.47807	−	2.52697i	0.141287	−	0.102651i
$607$	−32.2134			−1.30750			−0.653752	−	0.756709i	$-0.726806\pi$
$607$	−32.2134			−1.30750			−0.653752	+	0.756709i	$0.726806\pi$
$608$	1.08304	−	0.786876i	0.0439231	−	0.0319120i
$609$	−3.31921	−	10.2155i	−0.134501	−	0.413952i
$610$		0			0
$611$	−7.06281	+	21.7371i	−0.285731	+	0.879389i
$612$	6.17601	+	19.0078i	0.249651	+	0.768345i
$613$	−8.01843	−	24.6782i	−0.323861	−	0.996742i	−0.971952	−	0.235179i	$-0.924432\pi$
$613$	−8.01843	−	24.6782i	−0.323861	−	0.996742i	0.648091	−	0.761563i	$-0.275568\pi$
$614$	−17.5636	+	54.0552i	−0.708809	+	2.18149i
$615$		0			0
$616$	16.5673	+	50.9888i	0.667514	+	2.05440i
$617$	1.54016	−	1.11899i	0.0620043	−	0.0450488i	−0.556351	−	0.830947i	$-0.687799\pi$
$617$	1.54016	−	1.11899i	0.0620043	−	0.0450488i	0.618356	+	0.785898i	$0.287799\pi$
$618$	38.8353			1.56218
$619$	16.0829	−	11.6849i	0.646425	−	0.469655i	−0.215627	−	0.976476i	$-0.569179\pi$
$619$	16.0829	−	11.6849i	0.646425	−	0.469655i	0.862052	+	0.506821i	$0.169179\pi$
$620$		0			0
$621$	1.25207	+	0.909685i	0.0502440	+	0.0365044i
$622$	−14.9039	−	10.8283i	−0.597594	−	0.434177i
$623$	9.07246	−	27.9222i	0.363480	−	1.11868i
$624$	12.0617			0.482855
$625$		0			0
$626$	−77.2509			−3.08757
$627$	3.11023	−	9.57230i	0.124211	−	0.382281i
$628$	−69.9154	−	50.7965i	−2.78993	−	2.02700i
$629$	−23.5418	−	17.1041i	−0.938673	−	0.681986i
$630$		0			0
$631$	26.6152	−	19.3371i	1.05953	−	0.769796i	0.0855315	−	0.996335i	$-0.472741\pi$
$631$	26.6152	−	19.3371i	1.05953	−	0.769796i	0.974002	+	0.226539i	$0.0727412\pi$
$632$	63.6090			2.53023
$633$	−14.7702	+	10.7312i	−0.587063	+	0.426526i
$634$	19.4828	+	59.9618i	0.773760	+	2.38139i
$635$		0			0
$636$	12.4068	−	38.1841i	0.491961	−	1.51410i
$637$	4.82953	+	14.8638i	0.191353	+	0.588923i
$638$	−7.69080	−	23.6699i	−0.304482	−	0.937099i
$639$	−0.220629	+	0.679025i	−0.00872793	+	0.0268618i
$640$		0			0
$641$	−12.5963	−	38.7673i	−0.497523	−	1.53122i	−0.812988	−	0.582280i	$-0.802161\pi$
$641$	−12.5963	−	38.7673i	−0.497523	−	1.53122i	0.315465	−	0.948937i	$-0.397839\pi$
$642$	31.1547	−	22.6352i	1.22958	−	0.893341i
$643$	−24.9947			−0.985695			−0.492847	−	0.870116i	$-0.664044\pi$
$643$	−24.9947			−0.985695			−0.492847	+	0.870116i	$0.664044\pi$
$644$	17.0360	−	12.3774i	0.671314	−	0.487738i
$645$		0			0
$646$	−30.7396	−	22.3336i	−1.20943	−	0.878705i
$647$	−25.9073	−	18.8228i	−1.01852	−	0.739999i	−0.0525420	−	0.998619i	$-0.516732\pi$
$647$	−25.9073	−	18.8228i	−1.01852	−	0.739999i	−0.965979	+	0.258620i	$0.916732\pi$
$648$	−1.47423	+	4.53722i	−0.0579132	+	0.178239i
$649$	−5.65299			−0.221899
$650$		0			0
$651$	25.6030			1.00346
$652$	−12.3852	+	38.1176i	−0.485040	+	1.49280i
$653$	−36.1446	−	26.2606i	−1.41445	−	1.02766i	−0.992657	−	0.120964i	$-0.961401\pi$
$653$	−36.1446	−	26.2606i	−1.41445	−	1.02766i	−0.421791	−	0.906693i	$-0.638599\pi$
$654$	−19.5840	−	14.2286i	−0.765794	−	0.556382i
$655$		0			0
$656$	−16.3629	+	11.8883i	−0.638862	+	0.464161i
$657$	1.88027			0.0733564
$658$	−48.0298	+	34.8957i	−1.87240	+	1.36038i
$659$	−7.42307	−	22.8458i	−0.289162	−	0.889948i	−0.985120	−	0.171866i	$-0.945020\pi$
$659$	−7.42307	−	22.8458i	−0.289162	−	0.889948i	0.695959	−	0.718082i	$-0.254980\pi$
$660$		0			0
$661$	11.7095	−	36.0382i	0.455447	−	1.40172i	−0.415163	−	0.909747i	$-0.636275\pi$
$661$	11.7095	−	36.0382i	0.455447	−	1.40172i	0.870610	−	0.491974i	$-0.163725\pi$
$662$	−15.1634	−	46.6682i	−0.589343	−	1.81381i
$663$	5.04708	+	15.5333i	0.196012	+	0.603264i
$664$	5.83423	−	17.9559i	0.226412	−	0.696824i
$665$		0			0
$666$	−4.34233	−	13.3643i	−0.168262	−	0.517857i
$667$	−3.90920	+	2.84020i	−0.151365	+	0.109973i
$668$	5.97633			0.231231
$669$	13.9348	−	10.1242i	0.538750	−	0.391425i
$670$		0			0
$671$	20.7085	+	15.0456i	0.799444	+	0.580830i
$672$	−1.20926	−	0.878580i	−0.0466483	−	0.0338920i
$673$	5.69418	−	17.5249i	0.219494	−	0.675534i	−0.779310	−	0.626639i	$-0.784430\pi$
$673$	5.69418	−	17.5249i	0.219494	−	0.675534i	0.998804	−	0.0488951i	$-0.0155700\pi$
$674$	8.25737			0.318062
$675$		0			0
$676$	−10.1008			−0.388491
$677$	7.05064	−	21.6996i	0.270978	−	0.833985i	−0.719277	−	0.694723i	$-0.755527\pi$
$677$	7.05064	−	21.6996i	0.270978	−	0.833985i	0.990256	−	0.139262i	$-0.0444730\pi$
$678$	−10.8856	−	7.90887i	−0.418060	−	0.303738i
$679$	−29.6494	−	21.5416i	−1.13784	−	0.826690i
$680$		0			0
$681$	−3.50206	+	2.54440i	−0.134199	+	0.0975015i
$682$	59.3236			2.27162
$683$	26.0555	−	18.9304i	0.996987	−	0.724353i	0.0355465	−	0.999368i	$-0.488683\pi$
$683$	26.0555	−	18.9304i	0.996987	−	0.724353i	0.961440	+	0.275015i	$0.0886828\pi$
$684$	−3.76570	−	11.5896i	−0.143985	−	0.443141i
$685$		0			0
$686$	5.61519	−	17.2818i	0.214389	−	0.659822i
$687$	6.27758	+	19.3204i	0.239505	+	0.737120i
$688$	−2.91888	−	8.98339i	−0.111281	−	0.342489i
$689$	10.1389	−	31.2043i	0.386261	−	1.18879i
$690$		0			0
$691$	7.59466	+	23.3740i	0.288915	+	0.889188i	0.985198	+	0.171421i	$0.0548358\pi$
$691$	7.59466	+	23.3740i	0.288915	+	0.889188i	−0.696283	+	0.717767i	$0.745164\pi$
$692$	−44.3321	+	32.2092i	−1.68525	+	1.22441i
$693$	−11.2379			−0.426893
$694$	57.6404	−	41.8782i	2.18800	−	1.58967i
$695$		0			0
$696$	−12.0503	−	8.75508i	−0.456767	−	0.331860i
$697$	−22.1568	−	16.0979i	−0.839251	−	0.609751i
$698$	15.3818	−	47.3404i	0.582211	−	1.79186i
$699$	0.340956			0.0128961
$700$		0			0
$701$	−3.66355			−0.138370			−0.0691852	−	0.997604i	$-0.522040\pi$
$701$	−3.66355			−0.138370			−0.0691852	+	0.997604i	$0.522040\pi$
$702$	−2.43724	+	7.50107i	−0.0919879	+	0.283109i
$703$	14.3541	+	10.4289i	0.541377	+	0.393333i
$704$	−22.5267	−	16.3666i	−0.849005	−	0.616838i
$705$		0			0
$706$	3.67890	−	2.67288i	0.138457	−	0.100595i
$707$	6.06087			0.227942
$708$	−5.53719	+	4.02300i	−0.208100	+	0.151194i
$709$	−8.24980	−	25.3903i	−0.309828	−	0.953552i	−0.977831	−	0.209394i	$-0.932851\pi$
$709$	−8.24980	−	25.3903i	−0.309828	−	0.953552i	0.668003	−	0.744158i	$-0.267149\pi$
$710$		0			0
$711$	−4.12020	+	12.6807i	−0.154519	+	0.475562i
$712$	−12.5810	−	38.7202i	−0.471492	−	1.45110i
$713$	−3.55919	−	10.9541i	−0.133293	−	0.410233i
$714$	−13.1099	+	40.3480i	−0.490624	+	1.50999i
$715$		0			0
$716$	17.6671	+	54.3739i	0.660252	+	2.03205i
$717$	5.79651	−	4.21141i	0.216475	−	0.157278i
$718$	−9.36569			−0.349524
$719$	−14.4570	+	10.5036i	−0.539156	+	0.391720i	−0.823771	−	0.566922i	$-0.808134\pi$
$719$	−14.4570	+	10.5036i	−0.539156	+	0.391720i	0.284616	+	0.958642i	$0.408134\pi$
$720$		0			0
$721$	44.2933	+	32.1810i	1.64957	+	1.19848i
$722$	−18.7675	−	13.6354i	−0.698455	−	0.507457i
$723$	−3.88194	+	11.9474i	−0.144371	+	0.444328i
$724$	67.9853			2.52665
$725$		0			0
$726$	0.804239			0.0298481
$727$	10.5290	−	32.4050i	0.390500	−	1.20184i	−0.541910	−	0.840436i	$-0.682299\pi$
$727$	10.5290	−	32.4050i	0.390500	−	1.20184i	0.932411	−	0.361400i	$-0.117701\pi$
$728$	42.9152	+	31.1797i	1.59054	+	1.15560i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$		0			0
$731$	10.3476	−	7.51799i	0.382721	−	0.278063i
$732$	30.9917			1.14549
$733$	−32.5068	+	23.6176i	−1.20067	+	0.872335i	−0.994350	−	0.106150i	$-0.966147\pi$
$733$	−32.5068	+	23.6176i	−1.20067	+	0.872335i	−0.206316	+	0.978485i	$0.566147\pi$
$734$	19.3258	+	59.4788i	0.713330	+	2.19540i
$735$		0			0
$736$	−0.207789	+	0.639509i	−0.00765921	+	0.0235726i
$737$	−1.86652	−	5.74457i	−0.0687542	−	0.211604i
$738$	−4.08688	−	12.5781i	−0.150440	−	0.463007i
$739$	4.78203	−	14.7176i	0.175910	−	0.541395i	−0.823764	−	0.566933i	$-0.808130\pi$
$739$	4.78203	−	14.7176i	0.175910	−	0.541395i	0.999674	+	0.0255381i	$0.00812990\pi$
$740$		0			0
$741$	−3.07736	−	9.47113i	−0.113050	−	0.347931i
$742$	68.9484	−	50.0939i	2.53118	−	1.83901i
$743$	17.1140			0.627853			0.313926	−	0.949447i	$-0.398355\pi$
$743$	17.1140			0.627853			0.313926	+	0.949447i	$0.398355\pi$
$744$	28.7235	−	20.8688i	1.05305	−	0.765089i
$745$		0			0
$746$	−42.3214	−	30.7483i	−1.54950	−	1.12577i
$747$	3.20166	+	2.32614i	0.117143	+	0.0851092i
$748$	−20.1743	+	62.0902i	−0.737647	+	2.27024i
$749$	54.2900			1.98371
$750$		0			0
$751$	−11.1559			−0.407086			−0.203543	−	0.979066i	$-0.565246\pi$
$751$	−11.1559			−0.407086			−0.203543	+	0.979066i	$0.565246\pi$
$752$	−8.15518	+	25.0991i	−0.297389	+	0.915268i
$753$	−13.7663	−	10.0018i	−0.501671	−	0.364485i
$754$	−19.9220	−	14.4742i	−0.725516	−	0.527118i
$755$		0			0
$756$	−11.0077	+	7.99756i	−0.400346	+	0.290868i
$757$	−24.6773			−0.896911			−0.448456	−	0.893805i	$-0.648026\pi$
$757$	−24.6773			−0.896911			−0.448456	+	0.893805i	$0.648026\pi$
$758$	−51.0760	+	37.1089i	−1.85516	+	1.34786i
$759$	1.56223	+	4.80806i	0.0567054	+	0.174521i
$760$		0			0
$761$	−12.4372	+	38.2779i	−0.450850	+	1.38757i	0.425089	+	0.905151i	$0.360243\pi$
$761$	−12.4372	+	38.2779i	−0.450850	+	1.38757i	−0.875939	+	0.482422i	$0.839757\pi$
$762$	−0.748123	−	2.30249i	−0.0271016	−	0.0834103i
$763$	−10.5458	−	32.4566i	−0.381784	−	1.17501i
$764$	12.8845	−	39.6543i	0.466143	−	1.43464i
$765$		0			0
$766$	−10.9596	−	33.7302i	−0.395987	−	1.21872i
$767$	−4.52503	+	3.28763i	−0.163389	+	0.118709i
$768$	−31.5921			−1.13998
$769$	−17.8801	+	12.9907i	−0.644773	+	0.468455i	−0.861487	−	0.507780i	$-0.830466\pi$
$769$	−17.8801	+	12.9907i	−0.644773	+	0.468455i	0.216714	+	0.976235i	$0.430466\pi$
$770$		0			0
$771$	3.34286	+	2.42873i	0.120390	+	0.0874685i
$772$	−2.18507	−	1.58754i	−0.0786423	−	0.0571370i
$773$	−1.51429	+	4.66049i	−0.0544651	+	0.167626i	−0.974589	−	0.224002i	$-0.928088\pi$
$773$	−1.51429	+	4.66049i	−0.0544651	+	0.167626i	0.920124	+	0.391628i	$0.128088\pi$
$774$	6.17649			0.222009
$775$		0			0
$776$	−50.8215			−1.82439
$777$	6.12177	−	18.8409i	0.219617	−	0.675913i
$778$	45.6139	+	33.1405i	1.63534	+	1.18814i
$779$	13.5097	+	9.81537i	0.484035	+	0.351672i
$780$		0			0
$781$	−1.88681	+	1.37085i	−0.0675153	+	0.0490528i
$782$	19.0851			0.682481
$783$	2.52590	−	1.83517i	0.0902682	−	0.0655837i
$784$	5.57648	+	17.1627i	0.199160	+	0.612952i
$785$		0			0
$786$	9.51020	−	29.2694i	0.339218	−	1.04400i
$787$	1.15411	+	3.55198i	0.0411395	+	0.126614i	0.969517	−	0.245024i	$-0.0787960\pi$
$787$	1.15411	+	3.55198i	0.0411395	+	0.126614i	−0.928377	+	0.371639i	$0.878796\pi$
$788$	28.4728	+	87.6303i	1.01430	+	3.12170i
$789$	0.320676	−	0.986940i	0.0114164	−	0.0351360i
$790$		0			0
$791$	−5.86182	−	18.0408i	−0.208422	−	0.641458i
$792$	−12.6076	+	9.15994i	−0.447991	+	0.325484i
$793$	25.3266			0.899375
$794$	−27.5100	+	19.9872i	−0.976294	+	0.709319i
$795$		0			0
$796$	−32.6193	−	23.6993i	−1.15616	−	0.839998i
$797$	2.70538	+	1.96557i	0.0958295	+	0.0696242i	0.634668	−	0.772785i	$-0.281137\pi$
$797$	2.70538	+	1.96557i	0.0958295	+	0.0696242i	−0.538839	+	0.842409i	$0.681137\pi$
$798$	7.99348	−	24.6014i	0.282966	−	0.870880i
$799$	−35.7355			−1.26423
$800$		0			0
$801$	8.53392			0.301531
$802$	20.7994	−	64.0140i	0.734453	−	2.26041i
$803$	4.96901	+	3.61019i	0.175352	+	0.127401i
$804$	−5.91646	−	4.29856i	−0.208658	−	0.151599i
$805$		0			0
$806$	47.4866	−	34.5010i	1.67264	−	1.21525i
$807$	−15.7897			−0.555823
$808$	6.79957	−	4.94017i	0.239208	−	0.173795i
$809$	10.5954	+	32.6094i	0.372516	+	1.14649i	0.945140	+	0.326667i	$0.105926\pi$
$809$	10.5954	+	32.6094i	0.372516	+	1.14649i	−0.572624	+	0.819818i	$0.694074\pi$
$810$		0			0
$811$	−1.07152	+	3.29778i	−0.0376260	+	0.115801i	−0.968105	−	0.250543i	$-0.919391\pi$
$811$	−1.07152	+	3.29778i	−0.0376260	+	0.115801i	0.930479	+	0.366344i	$0.119391\pi$
$812$	−13.1274	−	40.4020i	−0.460682	−	1.41783i
$813$	−4.23364	−	13.0298i	−0.148480	−	0.456975i
$814$	14.1845	−	43.6554i	0.497167	−	1.53012i
$815$		0			0
$816$	5.82768	+	17.9358i	0.204010	+	0.627877i
$817$	−6.30926	+	4.58394i	−0.220733	+	0.160372i
$818$	−32.2422			−1.12732
$819$	−8.99556	+	6.53566i	−0.314330	+	0.228374i
$820$		0			0
$821$	11.8771	+	8.62922i	0.414514	+	0.301162i	0.775427	−	0.631438i	$-0.217535\pi$
$821$	11.8771	+	8.62922i	0.414514	+	0.301162i	−0.360913	+	0.932600i	$0.617535\pi$
$822$	−16.2689	−	11.8201i	−0.567445	−	0.412273i
$823$	6.44912	−	19.8483i	0.224802	−	0.691870i	−0.773510	−	0.633785i	$-0.781501\pi$
$823$	6.44912	−	19.8483i	0.224802	−	0.691870i	0.998312	−	0.0580851i	$-0.0184995\pi$
$824$	75.9223			2.64488
$825$		0			0
$826$	−14.5285			−0.505512
$827$	−13.9946	+	43.0710i	−0.486641	+	1.49773i	0.342950	+	0.939354i	$0.388574\pi$
$827$	−13.9946	+	43.0710i	−0.486641	+	1.49773i	−0.829590	+	0.558372i	$0.811426\pi$
$828$	4.95193	+	3.59779i	0.172091	+	0.125032i
$829$	7.81291	+	5.67641i	0.271354	+	0.197150i	0.715137	−	0.698984i	$-0.246364\pi$
$829$	7.81291	+	5.67641i	0.271354	+	0.197150i	−0.443784	+	0.896134i	$0.646364\pi$
$830$		0			0
$831$	5.64685	−	4.10268i	0.195887	−	0.142320i
$832$	−27.5502			−0.955131
$833$	−19.7690	+	14.3630i	−0.684955	+	0.497649i
$834$	−6.08075	−	18.7146i	−0.210559	−	0.648035i
$835$		0			0
$836$	12.3009	−	37.8583i	0.425436	−	1.30936i
$837$	2.29974	+	7.07787i	0.0794907	+	0.244647i
$838$	6.67198	+	20.5342i	0.230480	+	0.709344i
$839$	−7.77848	+	23.9397i	−0.268543	+	0.826490i	0.722313	+	0.691566i	$0.243079\pi$
$839$	−7.77848	+	23.9397i	−0.268543	+	0.826490i	−0.990856	+	0.134924i	$0.956921\pi$
$840$		0			0
$841$	−5.94919	−	18.3097i	−0.205144	−	0.631370i
$842$	−73.9874	+	53.7550i	−2.54977	+	1.85252i
$843$	7.95823			0.274096
$844$	−58.4159	+	42.4416i	−2.01076	+	1.46090i
$845$		0			0
$846$	−13.9610	−	10.1433i	−0.479989	−	0.348733i
$847$	0.917269	+	0.666435i	0.0315177	+	0.0228990i
$848$	11.7070	−	36.0305i	0.402021	−	1.23729i
$849$	27.7952			0.953928
$850$		0			0
$851$	−8.91196			−0.305498
$852$	−0.872582	+	2.68553i	−0.0298942	+	0.0920048i
$853$	−2.59571	−	1.88589i	−0.0888753	−	0.0645717i	0.542460	−	0.840081i	$-0.317493\pi$
$853$	−2.59571	−	1.88589i	−0.0888753	−	0.0645717i	−0.631336	+	0.775510i	$0.717493\pi$
$854$	53.2222	+	38.6682i	1.82123	+	1.32320i
$855$		0			0
$856$	60.9069	−	44.2514i	2.08175	−	1.51248i
$857$	−19.4569			−0.664634			−0.332317	−	0.943168i	$-0.607830\pi$
$857$	−19.4569			−0.664634			−0.332317	+	0.943168i	$0.607830\pi$
$858$	−20.8432	+	15.1435i	−0.711577	+	0.516991i
$859$	5.20173	+	16.0093i	0.177481	+	0.546230i	0.999738	−	0.0228862i	$-0.00728553\pi$
$859$	5.20173	+	16.0093i	0.177481	+	0.546230i	−0.822257	+	0.569116i	$0.807286\pi$
$860$		0			0
$861$	5.76163	−	17.7325i	0.196356	−	0.604322i
$862$	20.0772	+	61.7914i	0.683833	+	2.10462i
$863$	−1.17803	−	3.62560i	−0.0401006	−	0.123417i	0.929002	−	0.370074i	$-0.120668\pi$
$863$	−1.17803	−	3.62560i	−0.0401006	−	0.123417i	−0.969103	+	0.246657i	$0.920668\pi$
$864$	0.134261	−	0.413214i	0.00456766	−	0.0140578i
$865$		0			0
$866$	26.3910	+	81.2231i	0.896802	+	2.76007i
$867$	−6.90623	+	5.01767i	−0.234548	+	0.170409i
$868$	101.259			3.43697
$869$	−35.2358	+	25.6003i	−1.19529	+	0.868431i
$870$		0			0
$871$	−4.83497	−	3.51281i	−0.163827	−	0.119027i
$872$	−38.2863	−	27.8166i	−1.29654	−	0.941990i
$873$	3.29190	−	10.1314i	0.111414	−	0.342897i
$874$	−11.6367			−0.393619
$875$		0			0
$876$	7.43645			0.251254
$877$	7.95569	−	24.4851i	0.268644	−	0.826803i	−0.722187	−	0.691698i	$-0.756863\pi$
$877$	7.95569	−	24.4851i	0.268644	−	0.826803i	0.990831	−	0.135105i	$-0.0431371\pi$
$878$	39.5911	+	28.7646i	1.33613	+	0.970759i
$879$	−11.4960	−	8.35231i	−0.387749	−	0.281717i
$880$		0			0
$881$	−36.6110	+	26.5995i	−1.23346	+	0.896159i	−0.997144	−	0.0755181i	$-0.975939\pi$
$881$	−36.6110	+	26.5995i	−1.23346	+	0.896159i	−0.236313	+	0.971677i	$0.575939\pi$
$882$	−11.8001			−0.397330
$883$	35.9186	−	26.0964i	1.20876	−	0.878212i	0.213639	−	0.976913i	$-0.431469\pi$
$883$	35.9186	−	26.0964i	1.20876	−	0.878212i	0.995117	+	0.0987003i	$0.0314685\pi$
$884$	19.9611	+	61.4340i	0.671365	+	2.06625i
$885$		0			0
$886$	3.12850	−	9.62853i	0.105104	−	0.323477i
$887$	12.0495	+	37.0844i	0.404581	+	1.24517i	0.921245	+	0.388984i	$0.127174\pi$
$887$	12.0495	+	37.0844i	0.404581	+	1.24517i	−0.516664	+	0.856189i	$0.672826\pi$
$888$	−8.48919	−	26.1270i	−0.284878	−	0.876766i
$889$	1.05470	−	3.24602i	0.0353734	−	0.108868i
$890$		0			0
$891$	−1.00942	−	3.10669i	−0.0338170	−	0.104078i
$892$	55.1119	−	40.0411i	1.84528	−	1.34068i
$893$	21.7890			0.729142
$894$	−37.7278	+	27.4108i	−1.26181	+	0.916755i
$895$		0			0
$896$	−55.4764	−	40.3059i	−1.85334	−	1.34653i
$897$	4.04675	+	2.94014i	0.135117	+	0.0981683i
$898$	6.29517	−	19.3745i	0.210072	−	0.646537i
$899$	−23.2356			−0.774952
$900$		0			0
$901$	51.2995			1.70903
$902$	13.3500	−	41.0872i	0.444508	−	1.36805i
$903$	7.04455	+	5.11817i	0.234428	+	0.170322i
$904$	−21.2812	−	15.4617i	−0.707803	−	0.514249i
$905$		0			0
$906$	3.13015	−	2.27419i	0.103992	−	0.0755548i
$907$	−11.0201			−0.365915			−0.182958	−	0.983121i	$-0.558567\pi$
$907$	−11.0201			−0.365915			−0.182958	+	0.983121i	$0.558567\pi$
$908$	−13.8506	+	10.0630i	−0.459648	+	0.333954i
$909$	0.544406	+	1.67551i	0.0180568	+	0.0555731i
$910$		0			0
$911$	−16.3540	+	50.3325i	−0.541833	+	1.66759i	0.186571	+	0.982441i	$0.440263\pi$
$911$	−16.3540	+	50.3325i	−0.541833	+	1.66759i	−0.728404	+	0.685148i	$0.759737\pi$
$912$	−3.55332	−	10.9360i	−0.117662	−	0.362127i
$913$	3.99477	+	12.2946i	0.132207	+	0.406893i
$914$	15.5172	−	47.7570i	0.513263	−	1.57966i
$915$		0			0
$916$	24.8277	+	76.4119i	0.820331	+	2.52472i
$917$	35.1010	−	25.5023i	1.15914	−	0.842162i
$918$	−12.3317			−0.407005
$919$	38.5129	−	27.9812i	1.27042	−	0.923016i	0.271203	−	0.962522i	$-0.412579\pi$
$919$	38.5129	−	27.9812i	1.27042	−	0.923016i	0.999219	+	0.0395064i	$0.0125786\pi$
$920$		0			0
$921$	−18.8429	−	13.6902i	−0.620896	−	0.451107i
$922$	56.6388	+	41.1505i	1.86530	+	1.35522i
$923$	−0.713080	+	2.19463i	−0.0234713	+	0.0722372i
$924$	−44.4457			−1.46216
$925$		0			0
$926$	97.8059			3.21410
$927$	−4.91777	+	15.1354i	−0.161521	+	0.497110i
$928$	1.09745	+	0.797343i	0.0360255	+	0.0261741i
$929$	−17.5465	−	12.7483i	−0.575682	−	0.418258i	0.261483	−	0.965208i	$-0.415789\pi$
$929$	−17.5465	−	12.7483i	−0.575682	−	0.418258i	−0.837165	+	0.546951i	$0.815789\pi$
$930$		0			0
$931$	12.0538	−	8.75757i	0.395046	−	0.287018i
$932$	1.34848			0.0441708
$933$	6.10746	−	4.43733i	0.199949	−	0.145272i
$934$	−6.13972	−	18.8961i	−0.200898	−	0.618300i
$935$		0			0
$936$	−4.76477	+	14.6645i	−0.155741	+	0.479323i
$937$	−0.680112	−	2.09317i	−0.0222183	−	0.0683809i	0.939333	−	0.343008i	$-0.111446\pi$
$937$	−0.680112	−	2.09317i	−0.0222183	−	0.0683809i	−0.961551	+	0.274627i	$0.911446\pi$
$938$	−4.79708	−	14.7639i	−0.156630	−	0.482058i
$939$	9.78241	−	30.1072i	0.319237	−	0.982510i
$940$		0			0
$941$	−5.18833	−	15.9680i	−0.169135	−	0.520543i	0.830183	−	0.557492i	$-0.188236\pi$
$941$	−5.18833	−	15.9680i	−0.169135	−	0.520543i	−0.999317	+	0.0369489i	$0.988236\pi$
$942$	43.1388	−	31.3422i	1.40554	−	1.02118i
$943$	−8.38767			−0.273140
$944$	−5.22489	+	3.79611i	−0.170056	+	0.123553i
$945$		0			0
$946$	16.3226	+	11.8591i	0.530695	+	0.385572i
$947$	29.6207	+	21.5207i	0.962544	+	0.699329i	0.953740	−	0.300632i	$-0.0971975\pi$
$947$	29.6207	+	21.5207i	0.962544	+	0.699329i	0.00880418	+	0.999961i	$0.497198\pi$
$948$	−16.2953	+	50.1518i	−0.529247	+	1.62885i
$949$	6.07711			0.197271
$950$		0			0
$951$	−25.8362			−0.837796
$952$	−25.6295	+	78.8796i	−0.830658	+	2.55650i
$953$	35.5383	+	25.8201i	1.15120	+	0.836394i	0.988640	−	0.150305i	$-0.0480256\pi$
$953$	35.5383	+	25.8201i	1.15120	+	0.836394i	0.162558	+	0.986699i	$0.448026\pi$
$954$	20.0415	+	14.5610i	0.648867	+	0.471430i
$955$		0			0
$956$	22.9251	−	16.6561i	0.741450	−	0.538695i
$957$	10.1988			0.329680
$958$	−55.4010	+	40.2512i	−1.78993	+	1.30046i
$959$	−8.76068	−	26.9626i	−0.282897	−	0.870668i
$960$		0			0
$961$	7.53541	−	23.1916i	0.243078	−	0.748116i
$962$	−14.0346	−	43.1940i	−0.452493	−	1.39263i
$963$	4.87650	+	15.0083i	0.157143	+	0.483636i
$964$	−15.3530	+	47.2517i	−0.494487	+	1.52188i
$965$		0			0
$966$	4.01503	+	12.3570i	0.129182	+	0.397580i
$967$	19.8059	−	14.3899i	0.636916	−	0.462747i	−0.221873	−	0.975076i	$-0.571217\pi$
$967$	19.8059	−	14.3899i	0.636916	−	0.462747i	0.858789	+	0.512329i	$0.171217\pi$
$968$	1.57227			0.0505348
$969$	12.5967	−	9.15206i	0.404665	−	0.294007i
$970$		0			0
$971$	15.8773	+	11.5355i	0.509526	+	0.370192i	0.812644	−	0.582761i	$-0.198028\pi$
$971$	15.8773	+	11.5355i	0.509526	+	0.370192i	−0.303118	+	0.952953i	$0.598028\pi$
$972$	−3.19965	−	2.32468i	−0.102629	−	0.0745642i
$973$	8.57257	−	26.3837i	0.274824	−	0.845822i
$974$	−37.1344			−1.18986
$975$		0			0
$976$	29.2438			0.936070
$977$	−9.43236	+	29.0298i	−0.301768	+	0.928746i	0.679096	+	0.734050i	$0.262372\pi$
$977$	−9.43236	+	29.0298i	−0.301768	+	0.928746i	−0.980864	+	0.194696i	$0.937628\pi$
$978$	−20.0066	−	14.5356i	−0.639739	−	0.464798i
$979$	22.5526	+	16.3854i	0.720785	+	0.523681i
$980$		0			0
$981$	8.02529	−	5.83071i	0.256228	−	0.186160i
$982$	−20.2356			−0.645743
$983$	8.38590	−	6.09271i	0.267469	−	0.194327i	−0.445964	−	0.895051i	$-0.647139\pi$
$983$	8.38590	−	6.09271i	0.267469	−	0.194327i	0.713433	+	0.700723i	$0.247139\pi$
$984$	−7.98977	−	24.5900i	−0.254705	−	0.783901i
$985$		0			0
$986$	11.8977	−	36.6173i	0.378899	−	1.16613i
$987$	−7.51788	−	23.1376i	−0.239297	−	0.736479i
$988$	−12.1709	−	37.4582i	−0.387208	−	1.19170i
$989$	1.21048	−	3.72546i	0.0384909	−	0.118463i
$990$		0			0
$991$	−3.12376	−	9.61395i	−0.0992295	−	0.305397i	0.889103	−	0.457707i	$-0.151329\pi$
$991$	−3.12376	−	9.61395i	−0.0992295	−	0.305397i	−0.988333	+	0.152309i	$0.951329\pi$
$992$	−2.61591	+	1.90057i	−0.0830552	+	0.0603431i
$993$	20.1083			0.638116
$994$	−4.84921	+	3.52316i	−0.153808	+	0.111748i
$995$		0			0
$996$	12.6625	+	9.19986i	0.401227	+	0.291509i
$997$	17.2838	+	12.5574i	0.547382	+	0.397697i	0.826819	−	0.562467i	$-0.190148\pi$
$997$	17.2838	+	12.5574i	0.547382	+	0.397697i	−0.279437	+	0.960164i	$0.590148\pi$
$998$	18.4002	−	56.6300i	0.582448	−	1.79259i
$999$	5.75838			0.182187

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	375.2.g.c.226.1		12
5.2	odd	4		375.2.i.d.274.2		24
5.3	odd	4		375.2.i.d.274.5		24
5.4	even	2		75.2.g.c.46.3	yes	12
15.14	odd	2		225.2.h.d.46.1		12
25.6	even	5	inner	375.2.g.c.151.1		12
25.8	odd	20		375.2.i.d.349.2		24
25.9	even	10		1875.2.a.j.1.6		6
25.12	odd	20		1875.2.b.f.1249.2		12
25.13	odd	20		1875.2.b.f.1249.11		12
25.16	even	5		1875.2.a.k.1.1		6
25.17	odd	20		375.2.i.d.349.5		24
25.19	even	10		75.2.g.c.31.3	✓	12
75.41	odd	10		5625.2.a.q.1.6		6
75.44	odd	10		225.2.h.d.181.1		12
75.59	odd	10		5625.2.a.p.1.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.g.c.31.3	✓	12	25.19	even	10
75.2.g.c.46.3	yes	12	5.4	even	2
225.2.h.d.46.1		12	15.14	odd	2
225.2.h.d.181.1		12	75.44	odd	10
375.2.g.c.151.1		12	25.6	even	5	inner
375.2.g.c.226.1		12	1.1	even	1	trivial
375.2.i.d.274.2		24	5.2	odd	4
375.2.i.d.274.5		24	5.3	odd	4
375.2.i.d.349.2		24	25.8	odd	20
375.2.i.d.349.5		24	25.17	odd	20
1875.2.a.j.1.6		6	25.9	even	10
1875.2.a.k.1.1		6	25.16	even	5
1875.2.b.f.1249.2		12	25.12	odd	20
1875.2.b.f.1249.11		12	25.13	odd	20
5625.2.a.p.1.1		6	75.59	odd	10
5625.2.a.q.1.6		6	75.41	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)

\(f(q)\)	\(=\)	\(q+(-0.754089 + 2.32085i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-3.19965 - 2.32468i) q^{4} +(1.97423 - 1.43436i) q^{6} +3.44028 q^{7} +(3.85959 - 2.80415i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.754089 + 2.32085i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-3.19965 - 2.32468i) q^{4} +(1.97423 - 1.43436i) q^{6} +3.44028 q^{7} +(3.85959 - 2.80415i) q^{8} +(0.309017 + 0.951057i) q^{9} +(-1.00942 + 3.10669i) q^{11} +(1.22216 + 3.76141i) q^{12} +(0.998755 + 3.07385i) q^{13} +(-2.59428 + 7.98437i) q^{14} +(1.15323 + 3.54927i) q^{16} +(-4.08826 + 2.97030i) q^{17} -2.44028 q^{18} +(2.49274 - 1.81108i) q^{19} +(-2.78325 - 2.02215i) q^{21} +(-6.44895 - 4.68544i) q^{22} +(-0.478250 + 1.47190i) q^{23} -4.77071 q^{24} -7.88709 q^{26} +(0.309017 - 0.951057i) q^{27} +(-11.0077 - 7.99756i) q^{28} +(2.52590 + 1.83517i) q^{29} +(-6.02080 + 4.37437i) q^{31} +0.434479 q^{32} +(2.64270 - 1.92004i) q^{33} +(-3.81069 - 11.7281i) q^{34} +(1.22216 - 3.76141i) q^{36} +(1.77944 + 5.47655i) q^{37} +(2.32349 + 7.15098i) q^{38} +(0.998755 - 3.07385i) q^{39} +(1.67476 + 5.15437i) q^{41} +(6.79191 - 4.93461i) q^{42} -2.53106 q^{43} +(10.4519 - 7.59371i) q^{44} +(-3.05541 - 2.21989i) q^{46} +(5.72106 + 4.15659i) q^{47} +(1.15323 - 3.54927i) q^{48} +4.83555 q^{49} +5.05337 q^{51} +(3.95006 - 12.1570i) q^{52} +(-8.21277 - 5.96693i) q^{53} +(1.97423 + 1.43436i) q^{54} +(13.2781 - 9.64708i) q^{56} -3.08119 q^{57} +(-6.16391 + 4.47834i) q^{58} +(0.534773 + 1.64586i) q^{59} +(2.42149 - 7.45259i) q^{61} +(-5.61202 - 17.2720i) q^{62} +(1.06311 + 3.27190i) q^{63} +(-2.63409 + 8.10689i) q^{64} +(2.46328 + 7.58119i) q^{66} +(-1.49595 + 1.08687i) q^{67} +19.9860 q^{68} +(1.25207 - 0.909685i) q^{69} +(0.577613 + 0.419660i) q^{71} +(3.85959 + 2.80415i) q^{72} +(0.581036 - 1.78825i) q^{73} -14.0521 q^{74} -12.1861 q^{76} +(-3.47270 + 10.6879i) q^{77} +(6.38079 + 4.63591i) q^{78} +(10.7868 + 7.83708i) q^{79} +(-0.809017 + 0.587785i) q^{81} -13.2254 q^{82} +(3.20166 - 2.32614i) q^{83} +(4.20457 + 12.9403i) q^{84} +(1.90864 - 5.87419i) q^{86} +(-0.964807 - 2.96937i) q^{87} +(4.81567 + 14.8211i) q^{88} +(2.63713 - 8.11624i) q^{89} +(3.43600 + 10.5749i) q^{91} +(4.95193 - 3.59779i) q^{92} +7.44212 q^{93} +(-13.9610 + 10.1433i) q^{94} +(-0.351501 - 0.255380i) q^{96} +(-8.61831 - 6.26157i) q^{97} +(-3.64643 + 11.2226i) q^{98} -3.26656 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{3} - 10 q^{4} + 12 q^{7} - 9 q^{8} - 3 q^{9}+O(q^{10}) \) 12 * q - 3 * q^3 - 10 * q^4 + 12 * q^7 - 9 * q^8 - 3 * q^9	\( 12 q - 3 q^{3} - 10 q^{4} + 12 q^{7} - 9 q^{8} - 3 q^{9} - 4 q^{11} + 2 q^{13} + 6 q^{14} + 16 q^{16} + q^{17} + 7 q^{19} - 3 q^{21} - 13 q^{22} - 19 q^{23} + 6 q^{24} - 56 q^{26} - 3 q^{27} - q^{28} - q^{29} + 13 q^{31} + 32 q^{32} + q^{33} - 25 q^{34} - 8 q^{37} + 22 q^{38} + 2 q^{39} + 8 q^{41} + 16 q^{42} + 4 q^{43} + 33 q^{44} - 22 q^{46} + 13 q^{47} + 16 q^{48} - 28 q^{49} + 26 q^{51} - 44 q^{52} - 44 q^{53} + 45 q^{56} + 22 q^{57} - 41 q^{58} - 22 q^{59} - 8 q^{61} - 41 q^{62} - 3 q^{63} + 49 q^{64} - 3 q^{66} + 6 q^{67} + 100 q^{68} + 6 q^{69} - 21 q^{71} - 9 q^{72} + 16 q^{73} - 44 q^{74} - 52 q^{76} - q^{77} + 19 q^{78} + 10 q^{79} - 3 q^{81} - 26 q^{82} + 10 q^{83} - 6 q^{84} + 56 q^{86} + 4 q^{87} + 16 q^{88} + 57 q^{89} - 7 q^{91} - 3 q^{92} - 22 q^{93} - 23 q^{94} - 23 q^{96} - 4 q^{97} + 18 q^{98} + 6 q^{99}+O(q^{100}) \) 12 * q - 3 * q^3 - 10 * q^4 + 12 * q^7 - 9 * q^8 - 3 * q^9 - 4 * q^11 + 2 * q^13 + 6 * q^14 + 16 * q^16 + q^17 + 7 * q^19 - 3 * q^21 - 13 * q^22 - 19 * q^23 + 6 * q^24 - 56 * q^26 - 3 * q^27 - q^28 - q^29 + 13 * q^31 + 32 * q^32 + q^33 - 25 * q^34 - 8 * q^37 + 22 * q^38 + 2 * q^39 + 8 * q^41 + 16 * q^42 + 4 * q^43 + 33 * q^44 - 22 * q^46 + 13 * q^47 + 16 * q^48 - 28 * q^49 + 26 * q^51 - 44 * q^52 - 44 * q^53 + 45 * q^56 + 22 * q^57 - 41 * q^58 - 22 * q^59 - 8 * q^61 - 41 * q^62 - 3 * q^63 + 49 * q^64 - 3 * q^66 + 6 * q^67 + 100 * q^68 + 6 * q^69 - 21 * q^71 - 9 * q^72 + 16 * q^73 - 44 * q^74 - 52 * q^76 - q^77 + 19 * q^78 + 10 * q^79 - 3 * q^81 - 26 * q^82 + 10 * q^83 - 6 * q^84 + 56 * q^86 + 4 * q^87 + 16 * q^88 + 57 * q^89 - 7 * q^91 - 3 * q^92 - 22 * q^93 - 23 * q^94 - 23 * q^96 - 4 * q^97 + 18 * q^98 + 6 * q^99

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