LMFDB - Embedded newform 361.2.e.i.234.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [361,2,Mod(28,361)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(361, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("361.28");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 361 = 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	361.e (of order $9$, degree $6$, 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:	$2.88259951297$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	12.0.6053445140625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4x^{9} + 17x^{6} + 4x^{3} + 1 $ x^12 - 4x^9 + 17x^6 + 4*x^3 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			234.2
Root			$-0.580762 - 0.211380i$ of defining polynomial
Character	$\chi$	$=$	361.234
Dual form			361.2.e.i.54.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.473442 - 0.397265i) q^{2} +(2.46015 + 0.895420i) q^{3} +(-0.280969 + 1.59345i) q^{4} +(-0.214641 - 1.21729i) q^{5} +(1.52045 - 0.553400i) q^{6} +(-1.50000 + 2.59808i) q^{7} +(1.11803 + 1.93649i) q^{8} +(2.95241 + 2.47737i) q^{9} +O(q^{10})$	\(q+(0.473442 - 0.397265i) q^{2} +(2.46015 + 0.895420i) q^{3} +(-0.280969 + 1.59345i) q^{4} +(-0.214641 - 1.21729i) q^{5} +(1.52045 - 0.553400i) q^{6} +(-1.50000 + 2.59808i) q^{7} +(1.11803 + 1.93649i) q^{8} +(2.95241 + 2.47737i) q^{9} +(-0.585206 - 0.491046i) q^{10} +(-0.309017 - 0.535233i) q^{11} +(-2.11803 + 3.66854i) q^{12} +(-0.939693 + 0.342020i) q^{13} +(0.321961 + 1.82593i) q^{14} +(0.561937 - 3.18690i) q^{15} +(-1.74229 - 0.634140i) q^{16} +(4.01106 - 3.36568i) q^{17} +2.38197 q^{18} +2.00000 q^{20} +(-6.01659 + 5.04852i) q^{21} +(-0.358931 - 0.130640i) q^{22} +(1.32286 - 7.50230i) q^{23} +(1.01655 + 5.76517i) q^{24} +(3.26274 - 1.18754i) q^{25} +(-0.309017 + 0.535233i) q^{26} +(1.11803 + 1.93649i) q^{27} +(-3.71846 - 3.12016i) q^{28} +(1.05865 + 0.888311i) q^{29} +(-1.00000 - 1.73205i) q^{30} +(-1.07295 + 1.85840i) q^{31} +(-5.27923 + 1.92148i) q^{32} +(-0.280969 - 1.59345i) q^{33} +(0.561937 - 3.18690i) q^{34} +(3.48457 + 1.26828i) q^{35} +(-4.77711 + 4.00847i) q^{36} -2.14590 q^{37} -2.61803 q^{39} +(2.11729 - 1.77662i) q^{40} +(-2.81908 - 1.02606i) q^{41} +(-0.842906 + 4.78036i) q^{42} +(-1.19020 - 6.74997i) q^{43} +(0.939693 - 0.342020i) q^{44} +(2.38197 - 4.12569i) q^{45} +(-2.35410 - 4.07742i) q^{46} +(2.29813 + 1.92836i) q^{47} +(-3.71846 - 3.12016i) q^{48} +(-1.00000 - 1.73205i) q^{49} +(1.07295 - 1.85840i) q^{50} +(12.8815 - 4.68848i) q^{51} +(-0.280969 - 1.59345i) q^{52} +(-1.61948 + 9.18455i) q^{53} +(1.29862 + 0.472660i) q^{54} +(-0.585206 + 0.491046i) q^{55} -6.70820 q^{56} +0.854102 q^{58} +(11.7406 - 9.85152i) q^{59} +(4.92029 + 1.79084i) q^{60} +(-1.00090 + 5.67636i) q^{61} +(0.230299 + 1.30609i) q^{62} +(-10.8650 + 3.95454i) q^{63} +(0.118034 - 0.204441i) q^{64} +(0.618034 + 1.07047i) q^{65} +(-0.766044 - 0.642788i) q^{66} +(5.36231 + 4.49951i) q^{67} +(4.23607 + 7.33708i) q^{68} +(9.97214 - 17.2722i) q^{69} +(2.15358 - 0.783840i) q^{70} +(-0.255634 - 1.44977i) q^{71} +(-1.49651 + 8.48711i) q^{72} +(-10.0624 - 3.66242i) q^{73} +(-1.01596 + 0.852489i) q^{74} +9.09017 q^{75} +1.85410 q^{77} +(-1.23949 + 1.04005i) q^{78} +(-12.6073 - 4.58868i) q^{79} +(-0.397966 + 2.25698i) q^{80} +(-0.991219 - 5.62148i) q^{81} +(-1.74229 + 0.634140i) q^{82} +(0.236068 - 0.408882i) q^{83} +(-6.35410 - 11.0056i) q^{84} +(-4.95794 - 4.16021i) q^{85} +(-3.24502 - 2.72289i) q^{86} +(1.80902 + 3.13331i) q^{87} +(0.690983 - 1.19682i) q^{88} +(-11.4981 + 4.18498i) q^{89} +(-0.511267 - 2.89954i) q^{90} +(0.520945 - 2.95442i) q^{91} +(11.5829 + 4.21582i) q^{92} +(-4.30366 + 3.61120i) q^{93} +1.85410 q^{94} -14.7082 q^{96} +(-5.47408 + 4.59329i) q^{97} +(-1.16152 - 0.422760i) q^{98} +(0.413624 - 2.34578i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 18 q^{7}+O(q^{10}) $ 12 * q - 18 * q^7	$ 12 q - 18 q^{7} + 3 q^{11} - 12 q^{12} + 42 q^{18} + 24 q^{20} + 3 q^{26} - 12 q^{30} - 33 q^{31} - 66 q^{37} - 18 q^{39} + 42 q^{45} + 12 q^{46} - 12 q^{49} + 33 q^{50} - 30 q^{58} - 12 q^{64} - 6 q^{65} + 24 q^{68} + 66 q^{69} + 42 q^{75} - 18 q^{77} - 24 q^{83} - 36 q^{84} + 15 q^{87} + 15 q^{88} - 18 q^{94} - 96 q^{96}+O(q^{100}) $ 12 * q - 18 * q^7 + 3 * q^11 - 12 * q^12 + 42 * q^18 + 24 * q^20 + 3 * q^26 - 12 * q^30 - 33 * q^31 - 66 * q^37 - 18 * q^39 + 42 * q^45 + 12 * q^46 - 12 * q^49 + 33 * q^50 - 30 * q^58 - 12 * q^64 - 6 * q^65 + 24 * q^68 + 66 * q^69 + 42 * q^75 - 18 * q^77 - 24 * q^83 - 36 * q^84 + 15 * q^87 + 15 * q^88 - 18 * q^94 - 96 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/361\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{9}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.473442	−	0.397265i	0.334774	−	0.280908i	−0.459868	−	0.887987i	$-0.652103\pi$
$2$	0.473442	−	0.397265i	0.334774	−	0.280908i	0.794642	+	0.607079i	$0.207659\pi$
$3$	2.46015	+	0.895420i	1.42037	+	0.516971i	0.934154	−	0.356869i	$-0.116156\pi$
$3$	2.46015	+	0.895420i	1.42037	+	0.516971i	0.486212	+	0.873841i	$0.338378\pi$
$4$	−0.280969	+	1.59345i	−0.140484	+	0.796726i
$5$	−0.214641	−	1.21729i	−0.0959904	−	0.544388i	−0.994439	−	0.105311i	$-0.966416\pi$
$5$	−0.214641	−	1.21729i	−0.0959904	−	0.544388i	0.898449	−	0.439078i	$-0.144695\pi$
$6$	1.52045	−	0.553400i	0.620723	−	0.225925i
$7$	−1.50000	+	2.59808i	−0.566947	+	0.981981i	0.429919	+	0.902867i	$0.358542\pi$
$7$	−1.50000	+	2.59808i	−0.566947	+	0.981981i	−0.996866	+	0.0791130i	$0.974791\pi$
$8$	1.11803	+	1.93649i	0.395285	+	0.684653i
$9$	2.95241	+	2.47737i	0.984138	+	0.825790i
$10$	−0.585206	−	0.491046i	−0.185058	−	0.155282i
$11$	−0.309017	−	0.535233i	−0.0931721	−	0.161379i	0.815672	−	0.578514i	$-0.196367\pi$
$11$	−0.309017	−	0.535233i	−0.0931721	−	0.161379i	−0.908844	+	0.417136i	$0.863034\pi$
$12$	−2.11803	+	3.66854i	−0.611424	+	1.05902i
$13$	−0.939693	+	0.342020i	−0.260624	+	0.0948593i	−0.469027	−	0.883184i	$-0.655395\pi$
$13$	−0.939693	+	0.342020i	−0.260624	+	0.0948593i	0.208404	+	0.978043i	$0.433173\pi$
$14$	0.321961	+	1.82593i	0.0860478	+	0.488001i
$15$	0.561937	−	3.18690i	0.145092	−	0.822855i
$16$	−1.74229	−	0.634140i	−0.435571	−	0.158535i
$17$	4.01106	−	3.36568i	0.972825	−	0.816297i	−0.0101664	−	0.999948i	$-0.503236\pi$
$17$	4.01106	−	3.36568i	0.972825	−	0.816297i	0.982991	+	0.183651i	$0.0587917\pi$
$18$	2.38197			0.561435
$19$		0			0
$19$		0			0
$20$	2.00000			0.447214
$21$	−6.01659	+	5.04852i	−1.31293	+	1.10168i
$22$	−0.358931	−	0.130640i	−0.0765243	−	0.0278526i
$23$	1.32286	−	7.50230i	0.275835	−	1.56434i	−0.460462	−	0.887679i	$-0.652316\pi$
$23$	1.32286	−	7.50230i	0.275835	−	1.56434i	0.736297	−	0.676658i	$-0.236573\pi$
$24$	1.01655	+	5.76517i	0.207503	+	1.17681i
$25$	3.26274	−	1.18754i	0.652548	−	0.237508i
$26$	−0.309017	+	0.535233i	−0.0606032	+	0.104968i
$27$	1.11803	+	1.93649i	0.215166	+	0.372678i
$28$	−3.71846	−	3.12016i	−0.702722	−	0.589654i
$29$	1.05865	+	0.888311i	0.196586	+	0.164955i	0.735767	−	0.677235i	$-0.236822\pi$
$29$	1.05865	+	0.888311i	0.196586	+	0.164955i	−0.539181	+	0.842190i	$0.681266\pi$
$30$	−1.00000	−	1.73205i	−0.182574	−	0.316228i
$31$	−1.07295	+	1.85840i	−0.192707	+	0.333779i	−0.946147	−	0.323739i	$-0.895060\pi$
$31$	−1.07295	+	1.85840i	−0.192707	+	0.333779i	0.753439	+	0.657518i	$0.228393\pi$
$32$	−5.27923	+	1.92148i	−0.933244	+	0.339673i
$33$	−0.280969	−	1.59345i	−0.0489104	−	0.277384i
$34$	0.561937	−	3.18690i	0.0963715	−	0.546550i
$35$	3.48457	+	1.26828i	0.589000	+	0.214379i
$36$	−4.77711	+	4.00847i	−0.796184	+	0.668078i
$37$	−2.14590			−0.352783			−0.176392	−	0.984320i	$-0.556443\pi$
$37$	−2.14590			−0.352783			−0.176392	+	0.984320i	$0.556443\pi$
$38$		0			0
$39$	−2.61803			−0.419221
$40$	2.11729	−	1.77662i	0.334774	−	0.280908i
$41$	−2.81908	−	1.02606i	−0.440266	−	0.160244i	0.112370	−	0.993666i	$-0.464156\pi$
$41$	−2.81908	−	1.02606i	−0.440266	−	0.160244i	−0.552636	+	0.833423i	$0.686378\pi$
$42$	−0.842906	+	4.78036i	−0.130063	+	0.737625i
$43$	−1.19020	−	6.74997i	−0.181504	−	1.02936i	−0.930365	−	0.366634i	$-0.880510\pi$
$43$	−1.19020	−	6.74997i	−0.181504	−	1.02936i	0.748861	−	0.662727i	$-0.230601\pi$
$44$	0.939693	−	0.342020i	0.141664	−	0.0515615i
$45$	2.38197	−	4.12569i	0.355083	−	0.615021i
$46$	−2.35410	−	4.07742i	−0.347093	−	0.601183i
$47$	2.29813	+	1.92836i	0.335217	+	0.281281i	0.794822	−	0.606843i	$-0.207564\pi$
$47$	2.29813	+	1.92836i	0.335217	+	0.281281i	−0.459604	+	0.888124i	$0.652009\pi$
$48$	−3.71846	−	3.12016i	−0.536713	−	0.450356i
$49$	−1.00000	−	1.73205i	−0.142857	−	0.247436i
$50$	1.07295	−	1.85840i	0.151738	−	0.262818i
$51$	12.8815	−	4.68848i	1.80377	−	0.656519i
$52$	−0.280969	−	1.59345i	−0.0389633	−	0.220972i
$53$	−1.61948	+	9.18455i	−0.222453	+	1.26160i	0.645041	+	0.764148i	$0.276840\pi$
$53$	−1.61948	+	9.18455i	−0.222453	+	1.26160i	−0.867494	+	0.497447i	$0.834271\pi$
$54$	1.29862	+	0.472660i	0.176720	+	0.0643209i
$55$	−0.585206	+	0.491046i	−0.0789091	+	0.0662126i
$56$	−6.70820			−0.896421
$57$		0			0
$58$	0.854102			0.112149
$59$	11.7406	−	9.85152i	1.52849	−	1.28256i	0.720234	−	0.693731i	$-0.244034\pi$
$59$	11.7406	−	9.85152i	1.52849	−	1.28256i	0.808259	−	0.588827i	$-0.200410\pi$
$60$	4.92029	+	1.79084i	0.635207	+	0.231197i
$61$	−1.00090	+	5.67636i	−0.128152	+	0.726784i	0.851234	+	0.524786i	$0.175855\pi$
$61$	−1.00090	+	5.67636i	−0.128152	+	0.726784i	−0.979386	+	0.201998i	$0.935256\pi$
$62$	0.230299	+	1.30609i	0.0292480	+	0.165874i
$63$	−10.8650	+	3.95454i	−1.36886	+	0.498225i
$64$	0.118034	−	0.204441i	0.0147542	−	0.0255551i
$65$	0.618034	+	1.07047i	0.0766577	+	0.132775i
$66$	−0.766044	−	0.642788i	−0.0942936	−	0.0791217i
$67$	5.36231	+	4.49951i	0.655111	+	0.549703i	0.908617	−	0.417631i	$-0.137139\pi$
$67$	5.36231	+	4.49951i	0.655111	+	0.549703i	−0.253506	+	0.967334i	$0.581584\pi$
$68$	4.23607	+	7.33708i	0.513699	+	0.889752i
$69$	9.97214	−	17.2722i	1.20050	−	2.07933i
$70$	2.15358	−	0.783840i	0.257403	−	0.0936868i
$71$	−0.255634	−	1.44977i	−0.0303381	−	0.172056i	0.965874	−	0.259012i	$-0.0833971\pi$
$71$	−0.255634	−	1.44977i	−0.0303381	−	0.172056i	−0.996212	+	0.0869563i	$0.972286\pi$
$72$	−1.49651	+	8.48711i	−0.176365	+	1.00022i
$73$	−10.0624	−	3.66242i	−1.17772	−	0.428654i	−0.322322	−	0.946630i	$-0.604463\pi$
$73$	−10.0624	−	3.66242i	−1.17772	−	0.428654i	−0.855395	+	0.517976i	$0.826686\pi$
$74$	−1.01596	+	0.852489i	−0.118103	+	0.0990999i
$75$	9.09017			1.04964
$76$		0			0
$77$	1.85410			0.211295
$78$	−1.23949	+	1.04005i	−0.140344	+	0.117763i
$79$	−12.6073	−	4.58868i	−1.41843	−	0.516267i	−0.484839	−	0.874603i	$-0.661122\pi$
$79$	−12.6073	−	4.58868i	−1.41843	−	0.516267i	−0.933593	+	0.358336i	$0.883344\pi$
$80$	−0.397966	+	2.25698i	−0.0444940	+	0.252338i
$81$	−0.991219	−	5.62148i	−0.110135	−	0.624609i
$82$	−1.74229	+	0.634140i	−0.192403	+	0.0700291i
$83$	0.236068	−	0.408882i	0.0259118	−	0.0448806i	−0.852779	−	0.522272i	$-0.825084\pi$
$83$	0.236068	−	0.408882i	0.0259118	−	0.0448806i	0.878691	+	0.477392i	$0.158418\pi$
$84$	−6.35410	−	11.0056i	−0.693289	−	1.20081i
$85$	−4.95794	−	4.16021i	−0.537765	−	0.451238i
$86$	−3.24502	−	2.72289i	−0.349919	−	0.293617i
$87$	1.80902	+	3.13331i	0.193947	+	0.335926i
$88$	0.690983	−	1.19682i	0.0736590	−	0.127581i
$89$	−11.4981	+	4.18498i	−1.21880	+	0.443607i	−0.869748	−	0.493496i	$-0.835719\pi$
$89$	−11.4981	+	4.18498i	−1.21880	+	0.443607i	−0.349053	+	0.937103i	$0.613497\pi$
$90$	−0.511267	−	2.89954i	−0.0538923	−	0.305639i
$91$	0.520945	−	2.95442i	0.0546098	−	0.309708i
$92$	11.5829	+	4.21582i	1.20760	+	0.439530i
$93$	−4.30366	+	3.61120i	−0.446269	+	0.374464i
$94$	1.85410			0.191236
$95$		0			0
$96$	−14.7082			−1.50115
$97$	−5.47408	+	4.59329i	−0.555808	+	0.466378i	−0.876902	−	0.480669i	$-0.840394\pi$
$97$	−5.47408	+	4.59329i	−0.555808	+	0.466378i	0.321094	+	0.947047i	$0.395949\pi$
$98$	−1.16152	−	0.422760i	−0.117332	−	0.0427052i
$99$	0.413624	−	2.34578i	0.0415708	−	0.235760i
$100$	0.975561	+	5.53268i	0.0975561	+	0.553268i
$101$	−12.3855	+	4.50794i	−1.23240	+	0.448557i	−0.874419	−	0.485172i	$-0.838757\pi$
$101$	−12.3855	+	4.50794i	−1.23240	+	0.448557i	−0.357981	+	0.933729i	$0.616535\pi$
$102$	4.23607	−	7.33708i	0.419433	−	0.726480i
$103$	−0.663119	−	1.14856i	−0.0653391	−	0.113171i	0.831505	−	0.555517i	$-0.187480\pi$
$103$	−0.663119	−	1.14856i	−0.0653391	−	0.113171i	−0.896844	+	0.442346i	$0.854146\pi$
$104$	−1.71293	−	1.43732i	−0.167966	−	0.140941i
$105$	7.43692	+	6.24031i	0.725769	+	0.608992i
$106$	2.88197	+	4.99171i	0.279921	+	0.484838i
$107$	−5.20820	+	9.02087i	−0.503496	+	0.872081i	0.496496	+	0.868039i	$0.334620\pi$
$107$	−5.20820	+	9.02087i	−0.503496	+	0.872081i	−0.999992	+	0.00404164i	$0.998714\pi$
$108$	−3.39984	+	1.23744i	−0.327150	+	0.119073i
$109$	2.90135	+	16.4544i	0.277899	+	1.57604i	0.729600	+	0.683874i	$0.239706\pi$
$109$	2.90135	+	16.4544i	0.277899	+	1.57604i	−0.451702	+	0.892169i	$0.649183\pi$
$110$	−0.0819855	+	0.464963i	−0.00781702	+	0.0443325i
$111$	−5.27923	−	1.92148i	−0.501082	−	0.182379i
$112$	4.26097	−	3.57538i	0.402624	−	0.337842i
$113$	−11.2361			−1.05700			−0.528500	−	0.848933i	$-0.677245\pi$
$113$	−11.2361			−1.05700			−0.528500	+	0.848933i	$0.677245\pi$
$114$		0			0
$115$	−9.41641			−0.878085
$116$	−1.71293	+	1.43732i	−0.159041	+	0.133452i
$117$	−3.62167	−	1.31818i	−0.334824	−	0.121866i
$118$	1.64482	−	9.32823i	0.151418	−	0.858733i
$119$	2.72770	+	15.4696i	0.250048	+	1.41809i
$120$	6.79968	−	2.47488i	0.620723	−	0.225925i
$121$	5.30902	−	9.19549i	0.482638	−	0.835953i
$122$	1.78115	+	3.08505i	0.161258	+	0.279307i
$123$	−6.01659	−	5.04852i	−0.542498	−	0.455210i
$124$	−2.65981	−	2.23185i	−0.238858	−	0.200426i
$125$	−5.23607	−	9.06914i	−0.468328	−	0.811168i
$126$	−3.57295	+	6.18853i	−0.318304	+	0.551318i
$127$	9.61876	−	3.50094i	0.853527	−	0.310658i	0.122049	−	0.992524i	$-0.461053\pi$
$127$	9.61876	−	3.50094i	0.853527	−	0.310658i	0.731477	+	0.681866i	$0.238831\pi$
$128$	−1.97646	−	11.2090i	−0.174696	−	0.990749i
$129$	3.11599	−	17.6717i	0.274348	−	1.55590i
$130$	0.717861	+	0.261280i	0.0629606	+	0.0229158i
$131$	2.99510	−	2.51319i	0.261683	−	0.219578i	−0.502500	−	0.864577i	$-0.667586\pi$
$131$	2.99510	−	2.51319i	0.261683	−	0.219578i	0.764184	+	0.644999i	$0.223142\pi$
$132$	2.61803			0.227871
$133$		0			0
$134$	4.32624			0.373730
$135$	2.11729	−	1.77662i	0.182228	−	0.152907i
$136$	11.0021	+	4.00444i	0.943423	+	0.343378i
$137$	−0.255634	+	1.44977i	−0.0218403	+	0.123862i	−0.993779	−	0.111373i	$-0.964475\pi$
$137$	−0.255634	+	1.44977i	−0.0218403	+	0.123862i	0.971938	+	0.235236i	$0.0755862\pi$
$138$	−2.14043	−	12.1390i	−0.182205	−	1.03334i
$139$	9.20746	−	3.35124i	0.780967	−	0.284249i	0.0793909	−	0.996844i	$-0.474702\pi$
$139$	9.20746	−	3.35124i	0.780967	−	0.284249i	0.701576	+	0.712595i	$0.252480\pi$
$140$	−3.00000	+	5.19615i	−0.253546	+	0.439155i
$141$	3.92705	+	6.80185i	0.330717	+	0.572819i
$142$	−0.696970	−	0.584827i	−0.0584884	−	0.0490776i
$143$	0.473442	+	0.397265i	0.0395912	+	0.0332209i
$144$	−3.57295	−	6.18853i	−0.297746	−	0.515711i
$145$	0.854102	−	1.47935i	0.0709293	−	0.122853i
$146$	−6.21892	+	2.26350i	−0.514681	+	0.187329i
$147$	−0.909234	−	5.15652i	−0.0749923	−	0.425303i
$148$	0.602930	−	3.41939i	0.0495605	−	0.281072i
$149$	12.3007	+	4.47710i	1.00772	+	0.366778i	0.792555	−	0.609800i	$-0.208750\pi$
$149$	12.3007	+	4.47710i	1.00772	+	0.366778i	0.215160	+	0.976579i	$0.430973\pi$
$150$	4.30366	−	3.61120i	0.351393	−	0.294853i
$151$	9.90983			0.806451			0.403225	−	0.915101i	$-0.367889\pi$
$151$	9.90983			0.806451			0.403225	+	0.915101i	$0.367889\pi$
$152$		0			0
$153$	20.1803			1.63148
$154$	0.877809	−	0.736569i	0.0707359	−	0.0593544i
$155$	2.49251	+	0.907200i	0.200203	+	0.0728681i
$156$	0.735585	−	4.17171i	0.0588940	−	0.334004i
$157$	−1.93546	−	10.9766i	−0.154467	−	0.876025i	−0.959272	−	0.282486i	$-0.908841\pi$
$157$	−1.93546	−	10.9766i	−0.154467	−	0.876025i	0.804805	−	0.593540i	$-0.202270\pi$
$158$	−7.79174	+	2.83596i	−0.619878	+	0.225617i
$159$	−12.2082	+	21.1452i	−0.968174	+	1.67693i
$160$	3.47214	+	6.01392i	0.274496	+	0.475442i
$161$	17.5073	+	14.6903i	1.37977	+	1.15776i
$162$	−2.70250	−	2.26767i	−0.212329	−	0.178165i
$163$	−3.11803	−	5.40059i	−0.244223	−	0.423007i	0.717690	−	0.696363i	$-0.245200\pi$
$163$	−3.11803	−	5.40059i	−0.244223	−	0.423007i	−0.961913	+	0.273356i	$0.911866\pi$
$164$	2.42705	−	4.20378i	0.189521	−	0.328260i
$165$	−1.87939	+	0.684040i	−0.146310	+	0.0532525i
$166$	−0.0506699	−	0.287363i	−0.00393274	−	0.0223037i
$167$	−2.73738	+	15.5244i	−0.211825	+	1.20132i	0.674508	+	0.738268i	$0.264356\pi$
$167$	−2.73738	+	15.5244i	−0.211825	+	1.20132i	−0.886332	+	0.463050i	$0.846755\pi$
$168$	−16.5032	−	6.00666i	−1.27325	−	0.463424i
$169$	−9.19253	+	7.71345i	−0.707118	+	0.593342i
$170$	−4.00000			−0.306786
$171$		0			0
$172$	11.0902			0.845618
$173$	−6.49003	+	5.44578i	−0.493428	+	0.414035i	−0.855253	−	0.518211i	$-0.826598\pi$
$173$	−6.49003	+	5.44578i	−0.493428	+	0.414035i	0.361825	+	0.932246i	$0.382154\pi$
$174$	2.10122	+	0.764780i	0.159293	+	0.0579778i
$175$	−1.80879	+	10.2582i	−0.136732	+	0.775444i
$176$	0.198983	+	1.12849i	0.0149989	+	0.0850631i
$177$	37.7048	−	13.7234i	2.83407	−	1.03152i
$178$	−3.78115	+	6.54915i	−0.283409	+	0.490879i
$179$	3.88197	+	6.72376i	0.290152	+	0.502558i	0.973845	−	0.227212i	$-0.0729609\pi$
$179$	3.88197	+	6.72376i	0.290152	+	0.502558i	−0.683694	+	0.729769i	$0.739628\pi$
$180$	5.90483	+	4.95474i	0.440120	+	0.369304i
$181$	−9.19253	−	7.71345i	−0.683276	−	0.573336i	0.233686	−	0.972312i	$-0.424921\pi$
$181$	−9.19253	−	7.71345i	−0.683276	−	0.573336i	−0.916961	+	0.398976i	$0.869366\pi$
$182$	−0.927051	−	1.60570i	−0.0687176	−	0.119022i
$183$	−7.54508	+	13.0685i	−0.557749	+	0.966049i
$184$	16.0071	−	5.82612i	1.18006	−	0.429507i
$185$	0.460598	+	2.61218i	0.0338638	+	0.192051i
$186$	−0.602930	+	3.41939i	−0.0442090	+	0.250722i
$187$	−3.04091	−	1.10680i	−0.222373	−	0.0809373i
$188$	−3.71846	+	3.12016i	−0.271196	+	0.227561i
$189$	−6.70820			−0.487950
$190$		0			0
$191$	9.76393			0.706493			0.353247	−	0.935530i	$-0.385078\pi$
$191$	9.76393			0.706493			0.353247	+	0.935530i	$0.385078\pi$
$192$	0.473442	−	0.397265i	0.0341677	−	0.0286701i
$193$	21.5606	+	7.84740i	1.55196	+	0.564868i	0.968877	−	0.247542i	$-0.0796228\pi$
$193$	21.5606	+	7.84740i	1.55196	+	0.564868i	0.583086	+	0.812410i	$0.301845\pi$
$194$	−0.766901	+	4.34931i	−0.0550603	+	0.312262i
$195$	0.561937	+	3.18690i	0.0402412	+	0.228219i
$196$	3.04091	−	1.10680i	0.217208	−	0.0790572i
$197$	−1.50000	+	2.59808i	−0.106871	+	0.185105i	−0.914501	−	0.404584i	$-0.867416\pi$
$197$	−1.50000	+	2.59808i	−0.106871	+	0.185105i	0.807630	+	0.589689i	$0.200750\pi$
$198$	−0.736068	−	1.27491i	−0.0523101	−	0.0906037i
$199$	10.2776	+	8.62390i	0.728557	+	0.611332i	0.929738	−	0.368222i	$-0.120033\pi$
$199$	10.2776	+	8.62390i	0.728557	+	0.611332i	−0.201181	+	0.979554i	$0.564478\pi$
$200$	5.94752	+	4.99056i	0.420553	+	0.352886i
$201$	9.16312	+	15.8710i	0.646317	+	1.11945i
$202$	−4.07295	+	7.05455i	−0.286572	+	0.496357i
$203$	−3.89587	+	1.41798i	−0.273436	+	0.0995227i
$204$	3.85158	+	21.8434i	0.269664	+	1.52934i
$205$	−0.643923	+	3.65187i	−0.0449735	+	0.255058i
$206$	−0.770229	−	0.280340i	−0.0536644	−	0.0195322i
$207$	22.4916	−	18.8727i	1.56327	−	1.31174i
$208$	1.85410			0.128559
$209$		0			0
$210$	6.00000			0.414039
$211$	−2.18637	+	1.83458i	−0.150516	+	0.126298i	−0.714936	−	0.699190i	$-0.753544\pi$
$211$	−2.18637	+	1.83458i	−0.150516	+	0.126298i	0.564420	+	0.825488i	$0.309100\pi$
$212$	−14.1801	−	5.16114i	−0.973895	−	0.354469i
$213$	0.669258	−	3.79555i	0.0458568	−	0.260067i
$214$	1.11789	+	6.33989i	0.0764177	+	0.433386i
$215$	−7.96120	+	2.89764i	−0.542950	+	0.197617i
$216$	−2.50000	+	4.33013i	−0.170103	+	0.294628i
$217$	−3.21885	−	5.57521i	−0.218510	−	0.378470i
$218$	7.91036	+	6.63758i	0.535757	+	0.449553i
$219$	−21.4756	−	18.0202i	−1.45119	−	1.21769i
$220$	−0.618034	−	1.07047i	−0.0416678	−	0.0721708i
$221$	−2.61803	+	4.53457i	−0.176108	+	0.305028i
$222$	−3.26274	+	1.18754i	−0.218981	+	0.0797025i
$223$	−3.41262	−	19.3539i	−0.228526	−	1.29603i	−0.855829	−	0.517259i	$-0.826952\pi$
$223$	−3.41262	−	19.3539i	−0.228526	−	1.29603i	0.627303	−	0.778775i	$-0.284159\pi$
$224$	2.92668	−	16.5981i	0.195547	−	1.10900i
$225$	12.5749	+	4.57690i	0.838329	+	0.305127i
$226$	−5.31962	+	4.46369i	−0.353856	+	0.296920i
$227$	10.4164			0.691361			0.345681	−	0.938352i	$-0.387648\pi$
$227$	10.4164			0.691361			0.345681	+	0.938352i	$0.387648\pi$
$228$		0			0
$229$	−11.3820			−0.752141			−0.376071	−	0.926591i	$-0.622725\pi$
$229$	−11.3820			−0.752141			−0.376071	+	0.926591i	$0.622725\pi$
$230$	−4.45812	+	3.74081i	−0.293960	+	0.246661i
$231$	4.56136	+	1.66020i	0.300116	+	0.109233i
$232$	−0.536602	+	3.04322i	−0.0352297	+	0.199797i
$233$	2.33941	+	13.2675i	0.153260	+	0.869180i	0.960359	+	0.278765i	$0.0899250\pi$
$233$	2.33941	+	13.2675i	0.153260	+	0.869180i	−0.807099	+	0.590416i	$0.798964\pi$
$234$	−2.23832	+	0.814680i	−0.146323	+	0.0532573i
$235$	1.85410	−	3.21140i	0.120948	−	0.209489i
$236$	12.3992	+	21.4760i	0.807118	+	1.39797i
$237$	−26.9070	−	22.5777i	−1.74780	−	1.46658i
$238$	7.43692	+	6.24031i	0.482064	+	0.404499i
$239$	−7.66312	−	13.2729i	−0.495686	−	0.858553i	0.504302	−	0.863528i	$-0.331750\pi$
$239$	−7.66312	−	13.2729i	−0.495686	−	0.858553i	−0.999988	+	0.00497428i	$0.998417\pi$
$240$	−3.00000	+	5.19615i	−0.193649	+	0.335410i
$241$	−18.0236	+	6.56006i	−1.16100	+	0.422571i	−0.849456	−	0.527660i	$-0.823070\pi$
$241$	−18.0236	+	6.56006i	−1.16100	+	0.422571i	−0.311548	+	0.950230i	$0.600847\pi$
$242$	−1.13953	−	6.46261i	−0.0732519	−	0.415432i
$243$	3.75991	−	21.3235i	0.241199	−	1.36790i
$244$	−8.76380	−	3.18976i	−0.561045	−	0.204204i
$245$	−1.89377	+	1.58906i	−0.120988	+	0.101521i
$246$	−4.85410			−0.309486
$247$		0			0
$248$	−4.79837			−0.304697
$249$	0.946883	−	0.794529i	0.0600063	−	0.0503512i
$250$	−6.08182	−	2.21360i	−0.384648	−	0.140000i
$251$	3.36195	−	19.0665i	0.212204	−	1.20347i	−0.673488	−	0.739198i	$-0.735205\pi$
$251$	3.36195	−	19.0665i	0.212204	−	1.20347i	0.885693	−	0.464272i	$-0.153684\pi$
$252$	−3.24865	−	18.4240i	−0.204645	−	1.16060i
$253$	−4.42426	+	1.61030i	−0.278151	+	0.101239i
$254$	3.16312	−	5.47868i	0.198472	−	0.343763i
$255$	−8.47214	−	14.6742i	−0.530546	−	0.918932i
$256$	−5.02702	−	4.21817i	−0.314189	−	0.263636i
$257$	18.6614	+	15.6587i	1.16406	+	0.976766i	0.999953	−	0.00967637i	$-0.00308013\pi$
$257$	18.6614	+	15.6587i	1.16406	+	0.976766i	0.164111	+	0.986442i	$0.447525\pi$
$258$	−5.54508	−	9.60437i	−0.345222	−	0.597942i
$259$	3.21885	−	5.57521i	0.200009	−	0.346426i
$260$	−1.87939	+	0.684040i	−0.116555	+	0.0424224i
$261$	0.924892	+	5.24532i	0.0572493	+	0.324677i
$262$	0.419605	−	2.37970i	0.0259233	−	0.147018i
$263$	−2.76671	−	1.00700i	−0.170603	−	0.0620943i	0.255307	−	0.966860i	$-0.417824\pi$
$263$	−2.76671	−	1.00700i	−0.170603	−	0.0620943i	−0.425909	+	0.904766i	$0.640046\pi$
$264$	2.77157	−	2.32563i	0.170579	−	0.143132i
$265$	11.5279			0.708151
$266$		0			0
$267$	−32.0344			−1.96048
$268$	−8.67640	+	7.28037i	−0.529996	+	0.444719i
$269$	13.7888	+	5.01872i	0.840720	+	0.305997i	0.726251	−	0.687430i	$-0.241261\pi$
$269$	13.7888	+	5.01872i	0.840720	+	0.305997i	0.114469	+	0.993427i	$0.463483\pi$
$270$	0.296626	−	1.68225i	0.0180521	−	0.102379i
$271$	1.36385	+	7.73478i	0.0828480	+	0.469854i	0.997800	+	0.0662923i	$0.0211170\pi$
$271$	1.36385	+	7.73478i	0.0828480	+	0.469854i	−0.914952	+	0.403562i	$0.867772\pi$
$272$	−9.12273	+	3.32040i	−0.553147	+	0.201329i
$273$	3.92705	−	6.80185i	0.237676	−	0.411667i
$274$	0.454915	+	0.787936i	0.0274824	+	0.0476010i
$275$	−1.64385	−	1.37936i	−0.0991281	−	0.0831783i
$276$	24.7206	+	20.7431i	1.48801	+	1.24859i
$277$	7.70820	+	13.3510i	0.463141	+	0.802184i	0.999115	−	0.0420503i	$-0.0133890\pi$
$277$	7.70820	+	13.3510i	0.463141	+	0.802184i	−0.535974	+	0.844234i	$0.680056\pi$
$278$	3.02786	−	5.24441i	0.181599	−	0.314539i
$279$	−7.77174	+	2.82868i	−0.465282	+	0.169349i
$280$	1.43986	+	8.16583i	0.0860478	+	0.488001i
$281$	−1.47715	+	8.37734i	−0.0881195	+	0.499750i	0.908520	+	0.417841i	$0.137213\pi$
$281$	−1.47715	+	8.37734i	−0.0881195	+	0.499750i	−0.996640	+	0.0819097i	$0.973898\pi$
$282$	4.56136	+	1.66020i	0.271625	+	0.0988635i
$283$	−2.32452	+	1.95050i	−0.138178	+	0.115945i	−0.709257	−	0.704950i	$-0.750969\pi$
$283$	−2.32452	+	1.95050i	−0.138178	+	0.115945i	0.571079	+	0.820895i	$0.306525\pi$
$284$	2.38197			0.141344
$285$		0			0
$286$	0.381966			0.0225861
$287$	6.89440	−	5.78509i	0.406964	−	0.341483i
$288$	−20.3467	−	7.40558i	−1.19894	−	0.436378i
$289$	1.80879	−	10.2582i	0.106399	−	0.603421i
$290$	−0.183325	−	1.03969i	−0.0107652	−	0.0610527i
$291$	−17.5800	+	6.39858i	−1.03056	+	0.375092i
$292$	8.66312	−	15.0050i	0.506971	−	0.878099i
$293$	−8.42705	−	14.5961i	−0.492314	−	0.852712i	0.507647	−	0.861565i	$-0.330515\pi$
$293$	−8.42705	−	14.5961i	−0.492314	−	0.852712i	−0.999961	+	0.00885289i	$0.997182\pi$
$294$	−2.47897	−	2.08010i	−0.144577	−	0.121314i
$295$	−14.5122	−	12.1771i	−0.844930	−	0.708981i
$296$	−2.39919	−	4.15551i	−0.139450	−	0.241534i
$297$	0.690983	−	1.19682i	0.0400949	−	0.0694464i
$298$	7.60227	−	2.76700i	0.440388	−	0.160288i
$299$	1.32286	+	7.50230i	0.0765028	+	0.433869i
$300$	−2.55405	+	14.4848i	−0.147458	+	0.836278i
$301$	19.3222	+	7.03272i	1.11372	+	0.405359i
$302$	4.69172	−	3.93682i	0.269978	−	0.226539i
$303$	−34.5066			−1.98235
$304$		0			0
$305$	7.12461			0.407954
$306$	9.55421	−	8.01693i	0.546178	−	0.458298i
$307$	−1.57282	−	0.572460i	−0.0897657	−	0.0326720i	0.296747	−	0.954956i	$-0.404098\pi$
$307$	−1.57282	−	0.572460i	−0.0897657	−	0.0326720i	−0.386513	+	0.922284i	$0.626320\pi$
$308$	−0.520945	+	2.95442i	−0.0296836	+	0.168344i
$309$	−0.602930	−	3.41939i	−0.0342995	−	0.194522i
$310$	1.54046	−	0.560681i	0.0874921	−	0.0318445i
$311$	9.32624	−	16.1535i	0.528842	−	0.915982i	−0.470592	−	0.882351i	$-0.655960\pi$
$311$	9.32624	−	16.1535i	0.528842	−	0.915982i	0.999434	−	0.0336310i	$-0.0107071\pi$
$312$	−2.92705	−	5.06980i	−0.165712	−	0.287021i
$313$	3.31409	+	2.78085i	0.187323	+	0.157183i	0.731627	−	0.681705i	$-0.238761\pi$
$313$	3.31409	+	2.78085i	0.187323	+	0.157183i	−0.544303	+	0.838889i	$0.683206\pi$
$314$	−5.27693	−	4.42787i	−0.297794	−	0.249879i
$315$	7.14590	+	12.3771i	0.402626	+	0.697368i
$316$	10.8541	−	18.7999i	0.610591	−	1.05757i
$317$	16.9145	−	6.15636i	0.950011	−	0.345776i	0.179900	−	0.983685i	$-0.442423\pi$
$317$	16.9145	−	6.15636i	0.950011	−	0.345776i	0.770112	+	0.637909i	$0.220201\pi$
$318$	2.62038	+	14.8609i	0.146944	+	0.833359i
$319$	0.148313	−	0.841126i	0.00830395	−	0.0470940i
$320$	−0.274199	−	0.0998001i	−0.0153282	−	0.00557900i
$321$	−20.8904	+	17.5291i	−1.16599	+	0.978382i
$322$	14.1246			0.787134
$323$		0			0
$324$	9.23607			0.513115
$325$	−2.65981	+	2.23185i	−0.147540	+	0.123801i
$326$	−3.62167	−	1.31818i	−0.200586	−	0.0730073i
$327$	−7.59583	+	43.0781i	−0.420050	+	2.38222i
$328$	−1.16487	−	6.60629i	−0.0643190	−	0.364771i
$329$	−8.45723	+	3.07818i	−0.466262	+	0.169706i
$330$	−0.618034	+	1.07047i	−0.0340217	+	0.0589272i
$331$	−3.47214	−	6.01392i	−0.190846	−	0.330555i	0.754685	−	0.656087i	$-0.227790\pi$
$331$	−3.47214	−	6.01392i	−0.190846	−	0.330555i	−0.945531	+	0.325533i	$0.894456\pi$
$332$	0.585206	+	0.491046i	0.0321173	+	0.0269497i
$333$	−6.33558	−	5.31618i	−0.347188	−	0.291325i
$334$	4.87132	+	8.43738i	0.266547	+	0.461673i
$335$	4.32624	−	7.49326i	0.236368	−	0.409401i
$336$	13.6841	−	4.98060i	0.746528	−	0.271714i
$337$	−4.01555	−	22.7733i	−0.218741	−	1.24054i	−0.874296	−	0.485393i	$-0.838676\pi$
$337$	−4.01555	−	22.7733i	−0.218741	−	1.24054i	0.655555	−	0.755147i	$-0.272435\pi$
$338$	−1.28785	+	7.30374i	−0.0700496	+	0.397271i
$339$	−27.6424	−	10.0610i	−1.50133	−	0.546439i
$340$	8.02212	−	6.73136i	0.435061	−	0.365059i
$341$	1.32624			0.0718198
$342$		0			0
$343$	−15.0000			−0.809924
$344$	11.7406	−	9.85152i	0.633010	−	0.531158i
$345$	−23.1657	−	8.43164i	−1.24720	−	0.453944i
$346$	−0.909234	+	5.15652i	−0.0488807	+	0.277216i
$347$	0.245957	+	1.39489i	0.0132036	+	0.0748816i	0.990698	−	0.136082i	$-0.0434510\pi$
$347$	0.245957	+	1.39489i	0.0132036	+	0.0748816i	−0.977494	+	0.210963i	$0.932340\pi$
$348$	−5.50106	+	2.00222i	−0.294888	+	0.107330i
$349$	−12.9894	+	22.4982i	−0.695304	+	1.20430i	0.274774	+	0.961509i	$0.411397\pi$
$349$	−12.9894	+	22.4982i	−0.695304	+	1.20430i	−0.970078	+	0.242793i	$0.921936\pi$
$350$	3.21885	+	5.57521i	0.172055	+	0.298007i
$351$	−1.71293	−	1.43732i	−0.0914293	−	0.0767183i
$352$	2.65981	+	2.23185i	0.141768	+	0.118958i
$353$	15.7254	+	27.2372i	0.836980	+	1.44969i	0.892408	+	0.451229i	$0.149014\pi$
$353$	15.7254	+	27.2372i	0.836980	+	1.44969i	−0.0554283	+	0.998463i	$0.517652\pi$
$354$	12.3992	−	21.4760i	0.659009	−	1.14144i
$355$	−1.70992	+	0.622360i	−0.0907532	+	0.0330315i
$356$	−3.43795	−	19.4976i	−0.182211	−	1.03337i
$357$	−7.14121	+	40.4998i	−0.377953	+	2.14348i
$358$	4.50900	+	1.64114i	0.238308	+	0.0867370i
$359$	−16.8794	+	14.1635i	−0.890859	+	0.747519i	−0.968382	−	0.249471i	$-0.919743\pi$
$359$	−16.8794	+	14.1635i	−0.890859	+	0.747519i	0.0775235	+	0.996991i	$0.475299\pi$
$360$	10.6525			0.561435
$361$		0			0
$362$	−7.41641			−0.389798
$363$	21.2948	−	17.8685i	1.11769	−	0.937850i
$364$	4.56136	+	1.66020i	0.239080	+	0.0870182i
$365$	−2.29842	+	13.0350i	−0.120305	+	0.682282i
$366$	1.61948	+	9.18455i	0.0846518	+	0.480084i
$367$	−1.82702	+	0.664980i	−0.0953696	+	0.0347117i	−0.389264	−	0.921126i	$-0.627271\pi$
$367$	−1.82702	+	0.664980i	−0.0953696	+	0.0347117i	0.293895	+	0.955838i	$0.405048\pi$
$368$	−7.06231	+	12.2323i	−0.368148	+	0.637651i
$369$	−5.78115	−	10.0133i	−0.300955	−	0.521269i
$370$	1.25579	+	1.05373i	0.0652855	+	0.0547811i
$371$	−21.4329	−	17.9844i	−1.11274	−	0.933702i
$372$	−4.54508	−	7.87232i	−0.235652	−	0.408161i
$373$	1.73607	−	3.00696i	0.0898902	−	0.155694i	−0.817574	−	0.575823i	$-0.804682\pi$
$373$	1.73607	−	3.00696i	0.0898902	−	0.155694i	0.907465	+	0.420129i	$0.138015\pi$
$374$	−1.87939	+	0.684040i	−0.0971807	+	0.0353709i
$375$	−4.76081	−	26.9999i	−0.245847	−	1.39427i
$376$	−1.16487	+	6.60629i	−0.0600734	+	0.340693i
$377$	−1.29862	−	0.472660i	−0.0668825	−	0.0243432i
$378$	−3.17594	+	2.66493i	−0.163353	+	0.137069i
$379$	−25.1246			−1.29056			−0.645282	−	0.763944i	$-0.723260\pi$
$379$	−25.1246			−1.29056			−0.645282	+	0.763944i	$0.723260\pi$
$380$		0			0
$381$	26.7984			1.37292
$382$	4.62265	−	3.87886i	0.236515	−	0.198460i
$383$	2.46015	+	0.895420i	0.125708	+	0.0457538i	0.404108	−	0.914711i	$-0.367582\pi$
$383$	2.46015	+	0.895420i	0.125708	+	0.0457538i	−0.278400	+	0.960465i	$0.589804\pi$
$384$	5.17443	−	29.3457i	0.264057	−	1.49754i
$385$	−0.397966	−	2.25698i	−0.0202822	−	0.115026i
$386$	13.3252	−	4.84996i	0.678233	−	0.246857i
$387$	13.2082	−	22.8773i	0.671411	−	1.16292i
$388$	−5.78115	−	10.0133i	−0.293494	−	0.508346i
$389$	−18.5923	−	15.6008i	−0.942666	−	0.790991i	0.0353809	−	0.999374i	$-0.488736\pi$
$389$	−18.5923	−	15.6008i	−0.942666	−	0.790991i	−0.978047	+	0.208383i	$0.933180\pi$
$390$	1.53209	+	1.28558i	0.0775803	+	0.0650976i
$391$	−19.9443	−	34.5445i	−1.00863	−	1.74699i
$392$	2.23607	−	3.87298i	0.112938	−	0.195615i
$393$	9.61876	−	3.50094i	0.485202	−	0.176599i
$394$	0.321961	+	1.82593i	0.0162202	+	0.0919892i
$395$	−2.87971	+	16.3317i	−0.144894	+	0.821734i
$396$	3.62167	+	1.31818i	0.181996	+	0.0662411i
$397$	−1.93646	+	1.62488i	−0.0971880	+	0.0815504i	−0.690087	−	0.723726i	$-0.742428\pi$
$397$	−1.93646	+	1.62488i	−0.0971880	+	0.0815504i	0.592899	+	0.805277i	$0.297983\pi$
$398$	8.29180			0.415630
$399$		0			0
$400$	−6.43769			−0.321885
$401$	0.0853804	−	0.0716427i	0.00426369	−	0.00357766i	−0.640653	−	0.767830i	$-0.721336\pi$
$401$	0.0853804	−	0.0716427i	0.00426369	−	0.00357766i	0.644917	+	0.764253i	$0.276892\pi$
$402$	10.6432	+	3.87380i	0.530834	+	0.193208i
$403$	0.372631	−	2.11330i	0.0185621	−	0.105271i
$404$	−3.70326	−	21.0022i	−0.184244	−	1.04490i
$405$	−6.63022	+	2.41320i	−0.329458	+	0.119913i
$406$	−1.28115	+	2.21902i	−0.0635826	+	0.110128i
$407$	0.663119	+	1.14856i	0.0328696	+	0.0569318i
$408$	23.4812	+	19.7030i	1.16249	+	0.975445i
$409$	16.6294	+	13.9538i	0.822273	+	0.689969i	0.953503	−	0.301383i	$-0.0974482\pi$
$409$	16.6294	+	13.9538i	0.822273	+	0.689969i	−0.131230	+	0.991352i	$0.541893\pi$
$410$	1.14590	+	1.98475i	0.0565919	+	0.0980200i
$411$	−1.92705	+	3.33775i	−0.0950544	+	0.164639i
$412$	2.01648	−	0.733940i	0.0993451	−	0.0361586i
$413$	7.98412	+	45.2802i	0.392873	+	2.22809i
$414$	3.15100	−	17.8702i	0.154863	−	0.878273i
$415$	−0.548397	−	0.199600i	−0.0269198	−	0.00979799i
$416$	4.30366	−	3.61120i	0.211004	−	0.177054i
$417$	25.6525			1.25621
$418$		0			0
$419$	8.94427			0.436956			0.218478	−	0.975842i	$-0.429891\pi$
$419$	8.94427			0.436956			0.218478	+	0.975842i	$0.429891\pi$
$420$	−12.0332	+	10.0970i	−0.587159	+	0.492685i
$421$	−17.4105	−	6.33690i	−0.848536	−	0.308842i	−0.119093	−	0.992883i	$-0.537999\pi$
$421$	−17.4105	−	6.33690i	−0.848536	−	0.308842i	−0.729443	+	0.684041i	$0.760221\pi$
$422$	−0.306304	+	1.73713i	−0.0149106	+	0.0845624i
$423$	2.00777	+	11.3866i	0.0976213	+	0.553638i
$424$	−19.5964	+	7.13252i	−0.951688	+	0.346386i
$425$	9.09017	−	15.7446i	0.440938	−	0.763727i
$426$	−1.19098	−	2.06284i	−0.0577033	−	0.0999451i
$427$	−13.2463	−	11.1150i	−0.641033	−	0.537890i
$428$	−12.9110	−	10.8336i	−0.624076	−	0.523662i
$429$	0.809017	+	1.40126i	0.0390597	+	0.0676534i
$430$	−2.61803	+	4.53457i	−0.126253	+	0.218676i
$431$	−3.43220	+	1.24922i	−0.165323	+	0.0601728i	−0.423356	−	0.905963i	$-0.639148\pi$
$431$	−3.43220	+	1.24922i	−0.165323	+	0.0601728i	0.258033	+	0.966136i	$0.416926\pi$
$432$	−0.719928	−	4.08291i	−0.0346375	−	0.196439i
$433$	4.09155	−	23.2043i	0.196627	−	1.11513i	−0.713455	−	0.700701i	$-0.752871\pi$
$433$	4.09155	−	23.2043i	0.196627	−	1.11513i	0.910082	−	0.414428i	$-0.136018\pi$
$434$	−3.73877	−	1.36080i	−0.179467	−	0.0653205i
$435$	3.42585	−	2.87463i	0.164257	−	0.137828i
$436$	−27.0344			−1.29471
$437$		0			0
$438$	−17.3262			−0.827880
$439$	−11.1818	+	9.38261i	−0.533676	+	0.447807i	−0.869369	−	0.494164i	$-0.835474\pi$
$439$	−11.1818	+	9.38261i	−0.533676	+	0.447807i	0.335692	+	0.941972i	$0.391030\pi$
$440$	−1.60519	−	0.584240i	−0.0765243	−	0.0278526i
$441$	1.33852	−	7.59110i	0.0637388	−	0.361481i
$442$	0.561937	+	3.18690i	0.0267286	+	0.151586i
$443$	32.3408	−	11.7711i	1.53656	−	0.559262i	0.571343	−	0.820712i	$-0.306423\pi$
$443$	32.3408	−	11.7711i	1.53656	−	0.559262i	0.965217	+	0.261450i	$0.0842005\pi$
$444$	4.54508	−	7.87232i	0.215700	−	0.373604i
$445$	7.56231	+	13.0983i	0.358488	+	0.620919i
$446$	−9.30430	−	7.80723i	−0.440571	−	0.369683i
$447$	26.2527	+	22.0287i	1.24171	+	1.04192i
$448$	0.354102	+	0.613323i	0.0167297	+	0.0289768i
$449$	−16.4443	+	28.4823i	−0.776053	+	1.34416i	0.158147	+	0.987416i	$0.449448\pi$
$449$	−16.4443	+	28.4823i	−0.776053	+	1.34416i	−0.934201	+	0.356748i	$0.883885\pi$
$450$	7.77174	−	2.82868i	0.366363	−	0.133345i
$451$	0.321961	+	1.82593i	0.0151606	+	0.0859799i
$452$	3.15698	−	17.9041i	0.148492	−	0.842140i
$453$	24.3796	+	8.87346i	1.14546	+	0.416912i
$454$	4.93156	−	4.13807i	0.231450	−	0.194209i
$455$	−3.70820			−0.173843
$456$		0			0
$457$	6.29180			0.294318			0.147159	−	0.989113i	$-0.452987\pi$
$457$	6.29180			0.294318			0.147159	+	0.989113i	$0.452987\pi$
$458$	−5.38870	+	4.52165i	−0.251797	+	0.211283i
$459$	11.0021	+	4.00444i	0.513535	+	0.186911i
$460$	2.64572	−	15.0046i	0.123357	−	0.699593i
$461$	0.530622	+	3.00930i	0.0247135	+	0.140157i	0.994668	−	0.103129i	$-0.0328856\pi$
$461$	0.530622	+	3.00930i	0.0247135	+	0.140157i	−0.969954	+	0.243287i	$0.921774\pi$
$462$	2.81908	−	1.02606i	0.131155	−	0.0477367i
$463$	2.63525	−	4.56440i	0.122471	−	0.212125i	−0.798271	−	0.602299i	$-0.794252\pi$
$463$	2.63525	−	4.56440i	0.122471	−	0.212125i	0.920741	+	0.390173i	$0.127585\pi$
$464$	−1.28115	−	2.21902i	−0.0594760	−	0.103016i
$465$	5.31962	+	4.46369i	0.246692	+	0.206999i
$466$	6.37827	+	5.35200i	0.295468	+	0.247927i
$467$	−0.972136	−	1.68379i	−0.0449851	−	0.0779165i	0.842656	−	0.538452i	$-0.180991\pi$
$467$	−0.972136	−	1.68379i	−0.0449851	−	0.0779165i	−0.887641	+	0.460536i	$0.847657\pi$
$468$	3.11803	−	5.40059i	0.144131	−	0.249643i
$469$	−19.7335	+	7.18242i	−0.911210	+	0.331653i
$470$	−0.397966	−	2.25698i	−0.0183568	−	0.104107i
$471$	5.06711	−	28.7370i	0.233480	−	1.32413i
$472$	32.2037	+	11.7212i	1.48230	+	0.539512i
$473$	−3.24502	+	2.72289i	−0.149206	+	0.125199i
$474$	−21.7082			−0.997091
$475$		0			0
$476$	−25.4164			−1.16496
$477$	−27.5349	+	23.1045i	−1.26074	+	1.05788i
$478$	−8.90090	−	3.23966i	−0.407118	−	0.148179i
$479$	2.06812	−	11.7289i	0.0944948	−	0.535907i	−0.900406	−	0.435050i	$-0.856731\pi$
$479$	2.06812	−	11.7289i	0.0944948	−	0.535907i	0.994901	−	0.100857i	$-0.0321583\pi$
$480$	3.15698	+	17.9041i	0.144096	+	0.817208i
$481$	2.01648	−	0.733940i	0.0919438	−	0.0334648i
$482$	−5.92705	+	10.2660i	−0.269970	+	0.467601i
$483$	29.9164	+	51.8167i	1.36124	+	2.35774i
$484$	13.1609	+	11.0433i	0.598223	+	0.501969i
$485$	6.76633	+	5.67762i	0.307243	+	0.257808i
$486$	−6.69098	−	11.5891i	−0.303509	−	0.525693i
$487$	−9.09017	+	15.7446i	−0.411915	+	0.713458i	−0.995099	−	0.0988824i	$-0.968473\pi$
$487$	−9.09017	+	15.7446i	−0.411915	+	0.713458i	0.583184	+	0.812340i	$0.301807\pi$
$488$	−12.1113	+	4.40814i	−0.548251	+	0.199547i
$489$	−2.83502	−	16.0782i	−0.128204	−	0.727082i
$490$	−0.265311	+	1.50465i	−0.0119855	+	0.0679733i
$491$	−28.3926	−	10.3341i	−1.28134	−	0.466370i	−0.390465	−	0.920618i	$-0.627686\pi$
$491$	−28.3926	−	10.3341i	−1.28134	−	0.466370i	−0.890875	+	0.454248i	$0.849908\pi$
$492$	9.73505	−	8.16868i	0.438890	−	0.368272i
$493$	7.23607			0.325896
$494$		0			0
$495$	−2.94427			−0.132335
$496$	3.04787	−	2.55747i	0.136853	−	0.114834i
$497$	4.15007	+	1.51050i	0.186156	+	0.0677552i
$498$	0.132655	−	0.752326i	0.00594443	−	0.0337125i
$499$	−2.62636	−	14.8948i	−0.117572	−	0.666784i	−0.985445	−	0.169997i	$-0.945624\pi$
$499$	−2.62636	−	14.8948i	−0.117572	−	0.666784i	0.867872	−	0.496787i	$-0.165487\pi$
$500$	15.9224	−	5.79528i	0.712072	−	0.259173i
$501$	−20.6353	+	35.7413i	−0.921915	+	1.59680i
$502$	−5.98278	−	10.3625i	−0.267024	−	0.462500i
$503$	−13.6607	−	11.4627i	−0.609102	−	0.511097i	0.285255	−	0.958452i	$-0.407922\pi$
$503$	−13.6607	−	11.4627i	−0.609102	−	0.511097i	−0.894357	+	0.447355i	$0.852366\pi$
$504$	−19.8054	−	16.6187i	−0.882202	−	0.740256i
$505$	8.14590	+	14.1091i	0.362488	+	0.627847i
$506$	−1.45492	+	2.51999i	−0.0646789	+	0.112027i
$507$	−29.5218	+	10.7450i	−1.31111	+	0.477204i
$508$	2.87601	+	16.3107i	0.127602	+	0.723670i
$509$	4.69448	−	26.6237i	0.208079	−	1.18008i	−0.684441	−	0.729068i	$-0.739954\pi$
$509$	4.69448	−	26.6237i	0.208079	−	1.18008i	0.892520	−	0.451008i	$-0.148935\pi$
$510$	−9.84059	−	3.58168i	−0.435749	−	0.158600i
$511$	24.6089	−	20.6493i	1.08863	−	0.913471i
$512$	18.7082			0.826794
$513$		0			0
$514$	15.0557			0.664080
$515$	−1.25579	+	1.05373i	−0.0553368	+	0.0464331i
$516$	27.2835	+	9.93036i	1.20109	+	0.437160i
$517$	0.321961	−	1.82593i	0.0141598	−	0.0803045i
$518$	−0.690896	−	3.91827i	−0.0303562	−	0.172159i
$519$	−20.8427	+	7.58612i	−0.914893	+	0.332994i
$520$	−1.38197	+	2.39364i	−0.0606032	+	0.104968i
$521$	−13.6353	−	23.6170i	−0.597371	−	1.03468i	−0.993208	−	0.116356i	$-0.962879\pi$
$521$	−13.6353	−	23.6170i	−0.597371	−	1.03468i	0.395836	−	0.918321i	$-0.370455\pi$
$522$	2.52166	+	2.11593i	0.110370	+	0.0926116i
$523$	−17.1720	−	14.4090i	−0.750878	−	0.630061i	0.184857	−	0.982765i	$-0.440818\pi$
$523$	−17.1720	−	14.4090i	−0.750878	−	0.630061i	−0.935735	+	0.352704i	$0.885262\pi$
$524$	3.16312	+	5.47868i	0.138181	+	0.239337i
$525$	−13.6353	+	23.6170i	−0.595091	+	1.03073i
$526$	−1.70992	+	0.622360i	−0.0745561	+	0.0271362i
$527$	1.95112	+	11.0654i	0.0849922	+	0.482015i
$528$	−0.520945	+	2.95442i	−0.0226712	+	0.128575i
$529$	−32.9216	−	11.9825i	−1.43137	−	0.520978i
$530$	5.45777	−	4.57961i	0.237070	−	0.198926i
$531$	59.0689			2.56337
$532$		0			0
$533$	3.00000			0.129944
$534$	−15.1664	+	12.7261i	−0.656316	+	0.550714i
$535$	12.0989	+	4.40364i	0.523081	+	0.190386i
$536$	−2.71802	+	15.4147i	−0.117401	+	0.665813i
$537$	3.52961	+	20.0174i	0.152314	+	0.863816i
$538$	8.52196	−	3.10174i	0.367408	−	0.133726i
$539$	−0.618034	+	1.07047i	−0.0266206	+	0.0461082i
$540$	2.23607	+	3.87298i	0.0962250	+	0.166667i
$541$	18.2570	+	15.3194i	0.784930	+	0.658634i	0.944485	−	0.328555i	$-0.106562\pi$
$541$	18.2570	+	15.3194i	0.784930	+	0.658634i	−0.159555	+	0.987189i	$0.551006\pi$
$542$	3.71846	+	3.12016i	0.159721	+	0.134022i
$543$	−15.7082	−	27.2074i	−0.674104	−	1.16758i
$544$	−14.7082	+	25.4754i	−0.630609	+	1.09225i
$545$	19.4070	−	7.06356i	0.831304	−	0.302570i
$546$	−0.842906	−	4.78036i	−0.0360730	−	0.204580i
$547$	−6.58526	+	37.3469i	−0.281565	+	1.59684i	0.435737	+	0.900074i	$0.356488\pi$
$547$	−6.58526	+	37.3469i	−0.281565	+	1.59684i	−0.717302	+	0.696762i	$0.754623\pi$
$548$	−2.23832	−	0.814680i	−0.0956161	−	0.0348014i
$549$	−17.0175	+	14.2794i	−0.726290	+	0.609429i
$550$	−1.32624			−0.0565510
$551$		0			0
$552$	44.5967			1.89816
$553$	30.8327	−	25.8717i	1.31114	−	1.10018i
$554$	8.95326	+	3.25872i	0.380388	+	0.138450i
$555$	−1.20586	+	6.83877i	−0.0511859	+	0.290290i
$556$	2.75304	+	15.6132i	0.116755	+	0.662149i
$557$	21.7824	−	7.92814i	0.922950	−	0.335926i	0.163538	−	0.986537i	$-0.447709\pi$
$557$	21.7824	−	7.92814i	0.922950	−	0.335926i	0.759411	+	0.650611i	$0.225487\pi$
$558$	−2.55573	+	4.42665i	−0.108193	+	0.187395i
$559$	3.42705	+	5.93583i	0.144949	+	0.251059i
$560$	−5.26685	−	4.41941i	−0.222565	−	0.186754i
$561$	−6.49003	−	5.44578i	−0.274009	−	0.229921i
$562$	2.62868	+	4.55300i	0.110884	+	0.192057i
$563$	10.4164	−	18.0417i	0.438999	−	0.760369i	−0.558613	−	0.829428i	$-0.688666\pi$
$563$	10.4164	−	18.0417i	0.438999	−	0.760369i	0.997613	+	0.0690592i	$0.0219997\pi$
$564$	−11.9418	+	4.34646i	−0.502841	+	0.183019i
$565$	2.41172	+	13.6775i	0.101462	+	0.575419i
$566$	−0.325658	+	1.84690i	−0.0136884	+	0.0776309i
$567$	16.0919	+	5.85696i	0.675795	+	0.245969i
$568$	2.52166	−	2.11593i	0.105807	−	0.0887823i
$569$	−28.0902			−1.17760			−0.588801	−	0.808278i	$-0.700400\pi$
$569$	−28.0902			−1.17760			−0.588801	+	0.808278i	$0.700400\pi$
$570$		0			0
$571$	22.3262			0.934324			0.467162	−	0.884172i	$-0.345276\pi$
$571$	22.3262			0.934324			0.467162	+	0.884172i	$0.345276\pi$
$572$	−0.766044	+	0.642788i	−0.0320299	+	0.0268763i
$573$	24.0207	+	8.74282i	1.00348	+	0.365237i
$574$	0.965884	−	5.47780i	0.0403152	−	0.228639i
$575$	−4.59314	−	26.0490i	−0.191547	−	1.08632i
$576$	0.854961	−	0.311180i	0.0356234	−	0.0129658i
$577$	−14.0623	+	24.3566i	−0.585421	+	1.01398i	0.409401	+	0.912354i	$0.365738\pi$
$577$	−14.0623	+	24.3566i	−0.585421	+	1.01398i	−0.994823	+	0.101625i	$0.967596\pi$
$578$	−3.21885	−	5.57521i	−0.133886	−	0.231898i
$579$	46.0154	+	38.6115i	1.91234	+	1.60464i
$580$	2.11729	+	1.77662i	0.0879159	+	0.0737702i
$581$	0.708204	+	1.22665i	0.0293812	+	0.0508898i
$582$	−5.78115	+	10.0133i	−0.239636	+	0.415063i
$583$	5.41632	−	1.97138i	0.224321	−	0.0816463i
$584$	−4.15788	−	23.5805i	−0.172054	−	0.975768i
$585$	−0.827248	+	4.69156i	−0.0342025	+	0.193972i
$586$	−9.78822	−	3.56262i	−0.404348	−	0.147171i
$587$	29.2051	−	24.5060i	1.20543	−	1.01147i	0.205967	−	0.978559i	$-0.433966\pi$
$587$	29.2051	−	24.5060i	1.20543	−	1.01147i	0.999458	−	0.0329131i	$-0.0104785\pi$
$588$	8.47214			0.349385
$589$		0			0
$590$	−11.7082			−0.482019
$591$	−6.01659	+	5.04852i	−0.247489	+	0.207668i
$592$	3.73877	+	1.36080i	0.153662	+	0.0559285i
$593$	−2.20676	+	12.5151i	−0.0906206	+	0.513935i	0.905381	+	0.424600i	$0.139585\pi$
$593$	−2.20676	+	12.5151i	−0.0906206	+	0.513935i	−0.996002	+	0.0893350i	$0.971526\pi$
$594$	−0.148313	−	0.841126i	−0.00608537	−	0.0345118i
$595$	18.2455	−	6.64080i	0.747991	−	0.272246i
$596$	−10.5902	+	18.3427i	−0.433790	+	0.751347i
$597$	17.5623	+	30.4188i	0.718777	+	1.24496i
$598$	3.60669	+	3.02638i	0.147489	+	0.123758i
$599$	−1.21310	−	1.01791i	−0.0495660	−	0.0415908i	0.617668	−	0.786439i	$-0.288078\pi$
$599$	−1.21310	−	1.01791i	−0.0495660	−	0.0415908i	−0.667234	+	0.744848i	$0.732522\pi$
$600$	10.1631	+	17.6030i	0.414908	+	0.718641i
$601$	16.8541	−	29.1922i	0.687493	−	1.19077i	−0.285153	−	0.958482i	$-0.592044\pi$
$601$	16.8541	−	29.1922i	0.687493	−	1.19077i	0.972646	−	0.232291i	$-0.0746222\pi$
$602$	11.9418	−	4.34646i	0.486712	−	0.177149i
$603$	4.68480	+	26.5688i	0.190780	+	1.08197i
$604$	−2.78435	+	15.7908i	−0.113294	+	0.642520i
$605$	−12.3331	−	4.48888i	−0.501412	−	0.182499i
$606$	−16.3368	+	13.7082i	−0.663639	+	0.556859i
$607$	−27.2705			−1.10688			−0.553438	−	0.832890i	$-0.686684\pi$
$607$	−27.2705			−1.10688			−0.553438	+	0.832890i	$0.686684\pi$
$608$		0			0
$609$	−10.8541			−0.439830
$610$	3.37309	−	2.83036i	0.136572	−	0.114598i
$611$	−2.81908	−	1.02606i	−0.114048	−	0.0415100i
$612$	−5.67004	+	32.1564i	−0.229198	+	1.29985i
$613$	−0.356973	−	2.02450i	−0.0144180	−	0.0817687i	0.976750	−	0.214383i	$-0.0687740\pi$
$613$	−0.356973	−	2.02450i	−0.0144180	−	0.0817687i	−0.991168	+	0.132614i	$0.957663\pi$
$614$	−0.972057	+	0.353800i	−0.0392290	+	0.0142782i
$615$	−4.85410	+	8.40755i	−0.195736	+	0.339025i
$616$	2.07295	+	3.59045i	0.0835215	+	0.144663i
$617$	17.8689	+	14.9938i	0.719376	+	0.603628i	0.927213	−	0.374535i	$-0.122198\pi$
$617$	17.8689	+	14.9938i	0.719376	+	0.603628i	−0.207836	+	0.978164i	$0.566642\pi$
$618$	−1.64385	−	1.37936i	−0.0661255	−	0.0554859i
$619$	15.0623	+	26.0887i	0.605405	+	1.04859i	0.991987	+	0.126338i	$0.0403222\pi$
$619$	15.0623	+	26.0887i	0.605405	+	1.04859i	−0.386582	+	0.922255i	$0.626344\pi$
$620$	−2.14590	+	3.71680i	−0.0861813	+	0.149270i
$621$	16.0071	−	5.82612i	0.642344	−	0.233794i
$622$	−2.00179	−	11.3527i	−0.0802646	−	0.455203i
$623$	6.37431	−	36.1505i	0.255381	−	1.44834i
$624$	4.56136	+	1.66020i	0.182601	+	0.0664612i
$625$	3.38316	−	2.83881i	0.135327	−	0.113552i
$626$	2.67376			0.106865
$627$		0			0
$628$	18.0344			0.719653
$629$	−8.60733	+	7.22241i	−0.343197	+	0.287976i
$630$	8.30013	+	3.02100i	0.330685	+	0.120360i
$631$	−2.66735	+	15.1273i	−0.106186	+	0.602209i	0.884554	+	0.466437i	$0.154463\pi$
$631$	−2.66735	+	15.1273i	−0.106186	+	0.602209i	−0.990740	+	0.135772i	$0.956649\pi$
$632$	−5.20945	−	29.5442i	−0.207221	−	1.17521i
$633$	−7.02151	+	2.55562i	−0.279080	+	0.101577i
$634$	5.56231	−	9.63420i	0.220907	−	0.382623i
$635$	−6.32624	−	10.9574i	−0.251049	−	0.434830i
$636$	−30.2638	−	25.3943i	−1.20004	−	1.00695i
$637$	1.53209	+	1.28558i	0.0607036	+	0.0509363i
$638$	−0.263932	−	0.457144i	−0.0104492	−	0.0180985i
$639$	2.83688	−	4.91362i	0.112225	−	0.194380i
$640$	−13.2204	+	4.81184i	−0.522583	+	0.190205i
$641$	0.259330	+	1.47073i	0.0102429	+	0.0580905i	0.989501	−	0.144527i	$-0.0461662\pi$
$641$	0.259330	+	1.47073i	0.0102429	+	0.0580905i	−0.979258	+	0.202618i	$0.935055\pi$
$642$	−2.92668	+	16.5981i	−0.115507	+	0.655073i
$643$	35.4341	+	12.8970i	1.39739	+	0.508607i	0.927401	−	0.374068i	$-0.122037\pi$
$643$	35.4341	+	12.8970i	1.39739	+	0.508607i	0.469984	+	0.882675i	$0.344260\pi$
$644$	−28.3273	+	23.7695i	−1.11625	+	0.936648i
$645$	−22.1803			−0.873350
$646$		0			0
$647$	−1.47214			−0.0578756			−0.0289378	−	0.999581i	$-0.509212\pi$
$647$	−1.47214			−0.0578756			−0.0289378	+	0.999581i	$0.509212\pi$
$648$	9.77774	−	8.20450i	0.384106	−	0.322303i
$649$	−8.90090	−	3.23966i	−0.349391	−	0.127168i
$650$	−0.372631	+	2.11330i	−0.0146158	+	0.0828903i
$651$	−2.92668	−	16.5981i	−0.114706	−	0.650529i
$652$	9.48166	−	3.45104i	0.371330	−	0.135153i
$653$	1.71885	−	2.97713i	0.0672637	−	0.116504i	−0.830432	−	0.557120i	$-0.811906\pi$
$653$	1.71885	−	2.97713i	0.0672637	−	0.116504i	0.897696	+	0.440616i	$0.145240\pi$
$654$	13.5172	+	23.4125i	0.528565	+	0.915502i
$655$	−3.70215	−	3.10647i	−0.144655	−	0.121380i
$656$	4.26097	+	3.57538i	0.166363	+	0.139595i
$657$	−20.6353	−	35.7413i	−0.805058	−	1.39440i
$658$	−2.78115	+	4.81710i	−0.108421	+	0.187790i
$659$	43.0164	−	15.6567i	1.67568	−	0.609898i	0.682973	−	0.730444i	$-0.260687\pi$
$659$	43.0164	−	15.6567i	1.67568	−	0.609898i	0.992708	+	0.120546i	$0.0384645\pi$
$660$	−0.561937	−	3.18690i	−0.0218734	−	0.124050i
$661$	3.71892	−	21.0910i	0.144649	−	0.820347i	−0.822999	−	0.568043i	$-0.807701\pi$
$661$	3.71892	−	21.0910i	0.144649	−	0.820347i	0.967648	−	0.252304i	$-0.0811882\pi$
$662$	−4.03297	−	1.46788i	−0.156746	−	0.0570508i
$663$	−10.5011	+	8.81146i	−0.407829	+	0.342209i
$664$	1.05573			0.0409702
$665$		0			0
$666$	−5.11146			−0.198065
$667$	8.06481	−	6.76718i	0.312271	−	0.262026i
$668$	−23.9683	−	8.72376i	−0.927363	−	0.337533i
$669$	8.93435	−	50.6692i	0.345422	−	1.95898i
$670$	−0.928588	−	5.26628i	−0.0358745	−	0.203454i
$671$	3.34747	−	1.21838i	0.129228	−	0.0470351i
$672$	22.0623	−	38.2130i	0.851072	−	1.47410i
$673$	−3.06231	−	5.30407i	−0.118043	−	0.204457i	0.800949	−	0.598733i	$-0.204329\pi$
$673$	−3.06231	−	5.30407i	−0.118043	−	0.204457i	−0.918992	+	0.394276i	$0.870995\pi$
$674$	−10.9482	−	9.18659i	−0.421707	−	0.353854i
$675$	5.94752	+	4.99056i	0.228920	+	0.192087i
$676$	−9.70820	−	16.8151i	−0.373392	−	0.646735i
$677$	5.87132	−	10.1694i	0.225653	−	0.390843i	−0.730862	−	0.682525i	$-0.760882\pi$
$677$	5.87132	−	10.1694i	0.225653	−	0.390843i	0.956515	+	0.291682i	$0.0942150\pi$
$678$	−17.0839	+	6.21804i	−0.656104	+	0.238802i
$679$	−3.72262	−	21.1120i	−0.142861	−	0.810204i
$680$	2.51306	−	14.2523i	0.0963715	−	0.546550i
$681$	25.6259	+	9.32706i	0.981987	+	0.357414i
$682$	0.627896	−	0.526867i	0.0240434	−	0.0201748i
$683$	21.6525			0.828509			0.414254	−	0.910161i	$-0.364042\pi$
$683$	21.6525			0.828509			0.414254	+	0.910161i	$0.364042\pi$
$684$		0			0
$685$	1.81966			0.0695256
$686$	−7.10162	+	5.95897i	−0.271141	+	0.227514i
$687$	−28.0013	−	10.1916i	−1.06832	−	0.388835i
$688$	−2.20676	+	12.5151i	−0.0841318	+	0.477135i
$689$	−1.61948	−	9.18455i	−0.0616974	−	0.349904i
$690$	−14.3172	+	5.21104i	−0.545047	+	0.198381i
$691$	8.40983	−	14.5663i	0.319925	−	0.554126i	−0.660547	−	0.750785i	$-0.729676\pi$
$691$	8.40983	−	14.5663i	0.319925	−	0.554126i	0.980472	+	0.196658i	$0.0630089\pi$
$692$	−6.85410	−	11.8717i	−0.260554	−	0.451293i
$693$	5.47408	+	4.59329i	0.207943	+	0.174485i
$694$	0.670586	+	0.562689i	0.0254551	+	0.0213594i
$695$	−6.05573	−	10.4888i	−0.229707	−	0.397864i
$696$	−4.04508	+	7.00629i	−0.153329	+	0.265573i
$697$	−14.7609	+	5.37252i	−0.559108	+	0.203499i
$698$	2.78805	+	15.8118i	0.105529	+	0.598486i
$699$	−6.12466	+	34.7347i	−0.231656	+	1.31379i
$700$	−15.8377	−	5.76444i	−0.598608	−	0.217875i
$701$	29.5932	−	24.8317i	1.11772	−	0.937878i	0.119233	−	0.992866i	$-0.461956\pi$
$701$	29.5932	−	24.8317i	1.11772	−	0.937878i	0.998487	+	0.0549878i	$0.0175120\pi$
$702$	−1.38197			−0.0521589
$703$		0			0
$704$	−0.145898			−0.00549874
$705$	7.43692	−	6.24031i	0.280090	−	0.235024i
$706$	18.2655	+	6.64808i	0.687430	+	0.250204i
$707$	6.86623	−	38.9403i	0.258231	−	1.46450i
$708$	11.2738	+	63.9367i	0.423694	+	2.40289i
$709$	−40.7981	+	14.8493i	−1.53220	+	0.557677i	−0.964160	−	0.265322i	$-0.914522\pi$
$709$	−40.7981	+	14.8493i	−1.53220	+	0.557677i	−0.568044	+	0.822998i	$0.692300\pi$
$710$	−0.562306	+	0.973942i	−0.0211030	+	0.0365514i
$711$	−25.8541	−	44.7806i	−0.969605	−	1.67940i
$712$	−20.9595	−	17.5871i	−0.785490	−	0.659105i
$713$	12.5229	+	10.5080i	0.468987	+	0.393527i
$714$	12.7082	+	22.0113i	0.475593	+	0.823751i
$715$	0.381966	−	0.661585i	0.0142847	−	0.0247419i
$716$	−11.8047	+	4.29656i	−0.441163	+	0.160570i
$717$	−6.96757	−	39.5150i	−0.260209	−	1.47572i
$718$	−2.36475	+	13.4111i	−0.0882516	+	0.500500i
$719$	−16.8821	−	6.14458i	−0.629596	−	0.229154i	0.00745935	−	0.999972i	$-0.497626\pi$
$719$	−16.8821	−	6.14458i	−0.629596	−	0.229154i	−0.637056	+	0.770818i	$0.719848\pi$
$720$	−6.76633	+	5.67762i	−0.252166	+	0.211593i
$721$	3.97871			0.148175
$722$		0			0
$723$	−50.2148			−1.86751
$724$	14.8738	−	12.4806i	0.552782	−	0.463839i
$725$	4.50900	+	1.64114i	0.167460	+	0.0609504i
$726$	2.98333	−	16.9193i	0.110722	−	0.627935i
$727$	7.30518	+	41.4298i	0.270934	+	1.53654i	0.751587	+	0.659634i	$0.229289\pi$
$727$	7.30518	+	41.4298i	0.270934	+	1.53654i	−0.480653	+	0.876911i	$0.659600\pi$
$728$	6.30365	−	2.29434i	0.233629	−	0.0850339i
$729$	19.7812	−	34.2620i	0.732635	−	1.26896i
$730$	4.09017	+	7.08438i	0.151384	+	0.262205i
$731$	−27.4922	−	23.0687i	−1.01684	−	0.853227i
$732$	−18.7041	−	15.6946i	−0.691322	−	0.580088i
$733$	−20.4787	−	35.4702i	−0.756399	−	1.31012i	−0.944676	−	0.328005i	$-0.893624\pi$
$733$	−20.4787	−	35.4702i	−0.756399	−	1.31012i	0.188277	−	0.982116i	$-0.439710\pi$
$734$	−0.600813	+	1.04064i	−0.0221764	+	0.0384107i
$735$	−6.08182	+	2.21360i	−0.224331	+	0.0816499i
$736$	7.43186	+	42.1482i	0.273942	+	1.55360i
$737$	0.751243	−	4.26051i	0.0276724	−	0.156938i
$738$	−6.71495	−	2.44404i	−0.247181	−	0.0899664i
$739$	−19.1511	+	16.0697i	−0.704485	+	0.591133i	−0.923046	−	0.384690i	$-0.874308\pi$
$739$	−19.1511	+	16.0697i	−0.704485	+	0.591133i	0.218561	+	0.975823i	$0.429864\pi$
$740$	−4.29180			−0.157770
$741$		0			0
$742$	−17.2918			−0.634802
$743$	−31.6841	+	26.5861i	−1.16238	+	0.975351i	−0.999935	−	0.0113675i	$-0.996382\pi$
$743$	−31.6841	+	26.5861i	−1.16238	+	0.975351i	−0.162442	+	0.986718i	$0.551937\pi$
$744$	−11.8047	−	4.29656i	−0.432782	−	0.157520i
$745$	2.80969	−	15.9345i	0.102939	−	0.583796i
$746$	−0.372631	−	2.11330i	−0.0136430	−	0.0773733i
$747$	1.70992	−	0.622360i	0.0625627	−	0.0227710i
$748$	2.61803	−	4.53457i	0.0957248	−	0.165800i
$749$	−15.6246	−	27.0626i	−0.570911	−	0.988847i
$750$	−12.9801	−	10.8916i	−0.473965	−	0.397704i
$751$	18.2733	+	15.3331i	0.666802	+	0.559514i	0.912117	−	0.409930i	$-0.134447\pi$
$751$	18.2733	+	15.3331i	0.666802	+	0.559514i	−0.245315	+	0.969443i	$0.578891\pi$
$752$	−2.78115	−	4.81710i	−0.101418	−	0.175661i
$753$	25.3435	−	43.8962i	0.923567	−	1.59966i
$754$	−0.802593	+	0.292120i	−0.0292287	+	0.0106384i
$755$	−2.12706	−	12.0631i	−0.0774115	−	0.439022i
$756$	1.88480	−	10.6892i	0.0685493	−	0.388763i
$757$	14.7932	+	5.38430i	0.537670	+	0.195696i	0.596560	−	0.802569i	$-0.296534\pi$
$757$	14.7932	+	5.38430i	0.537670	+	0.195696i	−0.0588900	+	0.998264i	$0.518756\pi$
$758$	−11.8950	+	9.98112i	−0.432047	+	0.362531i
$759$	−12.3262			−0.447414
$760$		0			0
$761$	−30.8885			−1.11971			−0.559854	−	0.828591i	$-0.689143\pi$
$761$	−30.8885			−1.11971			−0.559854	+	0.828591i	$0.689143\pi$
$762$	12.6875	−	10.6460i	0.459618	−	0.385666i
$763$	−47.1017	−	17.1436i	−1.70520	−	0.620641i
$764$	−2.74336	+	15.5584i	−0.0992512	+	0.562882i
$765$	−4.33153	−	24.5653i	−0.156607	−	0.888161i
$766$	1.52045	−	0.553400i	0.0549363	−	0.0199952i
$767$	−7.66312	+	13.2729i	−0.276699	+	0.479257i
$768$	−8.59017	−	14.8786i	−0.309971	−	0.536886i
$769$	−31.8913	−	26.7600i	−1.15003	−	0.964991i	−0.150311	−	0.988639i	$-0.548027\pi$
$769$	−31.8913	−	26.7600i	−1.15003	−	0.964991i	−0.999720	+	0.0236480i	$0.992472\pi$
$770$	−1.08503	−	0.910449i	−0.0391018	−	0.0328103i
$771$	31.8885	+	55.2326i	1.14844	+	1.98915i
$772$	−18.5623	+	32.1509i	−0.668072	+	1.15713i
$773$	27.1787	−	9.89224i	0.977550	−	0.355799i	0.196663	−	0.980471i	$-0.436989\pi$
$773$	27.1787	−	9.89224i	0.977550	−	0.355799i	0.780887	+	0.624672i	$0.214767\pi$
$774$	−2.83502	−	16.0782i	−0.101903	−	0.577919i
$775$	−1.29383	+	7.33765i	−0.0464756	+	0.263576i
$776$	−15.0151	−	5.46504i	−0.539010	−	0.196184i
$777$	12.9110	−	10.8336i	0.463179	−	0.388654i
$778$	−15.0000			−0.537776
$779$		0			0
$780$	−5.23607			−0.187481
$781$	−0.696970	+	0.584827i	−0.0249396	+	0.0209268i
$782$	−23.1657	−	8.43164i	−0.828406	−	0.301515i
$783$	−0.536602	+	3.04322i	−0.0191766	+	0.108756i
$784$	0.643923	+	3.65187i	0.0229972	+	0.130424i
$785$	−12.9462	+	4.71204i	−0.462071	+	0.168180i
$786$	3.16312	−	5.47868i	0.112825	−	0.195418i
$787$	19.0000	+	32.9090i	0.677277	+	1.17308i	0.975798	+	0.218675i	$0.0701734\pi$
$787$	19.0000	+	32.9090i	0.677277	+	1.17308i	−0.298521	+	0.954403i	$0.596493\pi$
$788$	−3.71846	−	3.12016i	−0.132465	−	0.111151i
$789$	−5.90483	−	4.95474i	−0.210217	−	0.176393i
$790$	5.12461	+	8.87609i	0.182326	+	0.315797i
$791$	16.8541	−	29.1922i	0.599263	−	1.03795i
$792$	5.00503	−	1.82168i	0.177846	−	0.0647306i
$793$	−1.00090	−	5.67636i	−0.0355429	−	0.201574i
$794$	−0.271292	+	1.53857i	−0.00962778	+	0.0546018i
$795$	28.3602	+	10.3223i	1.00583	+	0.366094i
$796$	−16.6294	+	13.9538i	−0.589415	+	0.494578i
$797$	33.7082			1.19401			0.597003	−	0.802239i	$-0.296358\pi$
$797$	33.7082			1.19401			0.597003	+	0.802239i	$0.296358\pi$
$798$		0			0
$799$	15.7082			0.555716
$800$	−14.9429	+	12.5386i	−0.528311	+	0.443306i
$801$	−44.3150	−	16.1293i	−1.56579	−	0.569902i
$802$	0.0119615	−	0.0678372i	0.000422376	−	0.00239542i
$803$	1.14921	+	6.51749i	0.0405547	+	0.229997i
$804$	−27.8642	+	10.1417i	−0.982695	+	0.357672i
$805$	14.1246	−	24.4645i	0.497827	−	0.862262i
$806$	−0.663119	−	1.14856i	−0.0233574	−	0.0404562i
$807$	29.4287	+	24.6936i	1.03594	+	0.869256i
$808$	−22.5770	−	18.9443i	−0.794255	−	0.666459i
$809$	0.100813	+	0.174613i	0.00354440	+	0.00613908i	0.867792	−	0.496927i	$-0.165538\pi$
$809$	0.100813	+	0.174613i	0.00354440	+	0.00613908i	−0.864248	+	0.503066i	$0.832205\pi$
$810$	−2.18034	+	3.77646i	−0.0766093	+	0.132691i
$811$	−22.5326	+	8.20120i	−0.791227	+	0.287983i	−0.705846	−	0.708365i	$-0.749433\pi$
$811$	−22.5326	+	8.20120i	−0.791227	+	0.287983i	−0.0853812	+	0.996348i	$0.527211\pi$
$812$	−1.16487	−	6.60629i	−0.0408788	−	0.231835i
$813$	−3.57061	+	20.2499i	−0.125227	+	0.710196i
$814$	0.770229	+	0.280340i	0.0269965	+	0.00982592i
$815$	−5.90483	+	4.95474i	−0.206837	+	0.173557i
$816$	−25.4164			−0.889752
$817$		0			0
$818$	13.4164			0.469094
$819$	8.85724	−	7.43211i	0.309497	−	0.259699i
$820$	−5.63816	−	2.05212i	−0.196893	−	0.0716632i
$821$	−9.21162	+	52.2417i	−0.321488	+	1.82325i	0.211800	+	0.977313i	$0.432068\pi$
$821$	−9.21162	+	52.2417i	−0.321488	+	1.82325i	−0.533287	+	0.845934i	$0.679043\pi$
$822$	0.413624	+	2.34578i	0.0144268	+	0.0818184i
$823$	−22.1737	+	8.07056i	−0.772926	+	0.281322i	−0.698220	−	0.715883i	$-0.746024\pi$
$823$	−22.1737	+	8.07056i	−0.772926	+	0.281322i	−0.0747064	+	0.997206i	$0.523802\pi$
$824$	1.48278	−	2.56825i	0.0516551	−	0.0894692i
$825$	−2.80902	−	4.86536i	−0.0977974	−	0.169390i
$826$	21.7682	+	18.2657i	0.757414	+	0.635546i
$827$	12.7138	+	10.6682i	0.442104	+	0.370969i	0.836496	−	0.547973i	$-0.184600\pi$
$827$	12.7138	+	10.6682i	0.442104	+	0.370969i	−0.394392	+	0.918942i	$0.629045\pi$
$828$	23.7533	+	41.1419i	0.825484	+	1.42978i
$829$	10.1631	−	17.6030i	0.352980	−	0.611379i	−0.633790	−	0.773505i	$-0.718502\pi$
$829$	10.1631	−	17.6030i	0.352980	−	0.611379i	0.986770	+	0.162126i	$0.0518351\pi$
$830$	−0.338928	+	0.123360i	−0.0117644	+	0.00428188i
$831$	7.00856	+	39.7475i	0.243124	+	1.37883i
$832$	−0.0409928	+	0.232482i	−0.00142117	+	0.00805985i
$833$	−9.84059	−	3.58168i	−0.340956	−	0.124098i
$834$	12.1449	−	10.1908i	0.420545	−	0.352879i
$835$	19.4853			0.674316
$836$		0			0
$837$	−4.79837			−0.165856
$838$	4.23459	−	3.55324i	0.146281	−	0.122745i
$839$	37.3982	+	13.6118i	1.29113	+	0.469933i	0.894098	−	0.447871i	$-0.147818\pi$
$839$	37.3982	+	13.6118i	1.29113	+	0.469933i	0.397033	+	0.917805i	$0.370040\pi$
$840$	−3.76959	+	21.3784i	−0.130063	+	0.737625i
$841$	−4.70416	−	26.6786i	−0.162212	−	0.919952i
$842$	−10.7603	+	3.91642i	−0.370824	+	0.134969i
$843$	−11.1353	+	19.2868i	−0.383519	+	0.664274i
$844$	−2.30902	−	3.99933i	−0.0794796	−	0.137663i
$845$	11.3626	+	9.53435i	0.390885	+	0.327992i
$846$	5.47408	+	4.59329i	0.188203	+	0.157921i
$847$	15.9271	+	27.5865i	0.547260	+	0.947882i
$848$	8.64590	−	14.9751i	0.296901	−	0.514248i
$849$	−7.46517	+	2.71710i	−0.256204	+	0.0932507i
$850$	−1.95112	−	11.0654i	−0.0669230	−	0.379539i
$851$	−2.83872	+	16.0992i	−0.0973100	+	0.551872i
$852$	5.85999	+	2.13286i	0.200760	+	0.0730706i
$853$	13.2463	−	11.1150i	0.453544	−	0.380569i	−0.387205	−	0.921994i	$-0.626559\pi$
$853$	13.2463	−	11.1150i	0.453544	−	0.380569i	0.840749	+	0.541425i	$0.182115\pi$
$854$	−10.6869			−0.365699
$855$		0			0
$856$	−23.2918			−0.796097
$857$	6.42096	−	5.38782i	0.219336	−	0.184045i	−0.526499	−	0.850176i	$-0.676495\pi$
$857$	6.42096	−	5.38782i	0.219336	−	0.184045i	0.745834	+	0.666131i	$0.232051\pi$
$858$	0.939693	+	0.342020i	0.0320806	+	0.0116764i
$859$	3.21961	−	18.2593i	0.109852	−	0.623001i	−0.879319	−	0.476233i	$-0.842002\pi$
$859$	3.21961	−	18.2593i	0.109852	−	0.623001i	0.989171	−	0.146768i	$-0.0468870\pi$
$860$	−2.38040	−	13.4999i	−0.0811711	−	0.460344i
$861$	22.1413	−	8.05878i	0.754574	−	0.274643i
$862$	−1.12868	+	1.95493i	−0.0384429	+	0.0665850i
$863$	−22.4721	−	38.9229i	−0.764960	−	1.32495i	−0.940268	−	0.340436i	$-0.889425\pi$
$863$	−22.4721	−	38.9229i	−0.764960	−	1.32495i	0.175307	−	0.984514i	$-0.443908\pi$
$864$	−9.62328	−	8.07489i	−0.327391	−	0.274713i
$865$	8.02212	+	6.73136i	0.272760	+	0.228873i
$866$	−7.28115	−	12.6113i	−0.247424	−	0.428550i
$867$	13.6353	−	23.6170i	0.463078	−	0.802074i
$868$	9.78822	−	3.56262i	0.332234	−	0.120923i
$869$	1.43986	+	8.16583i	0.0488437	+	0.277007i
$870$	0.479952	−	2.72194i	0.0162719	−	0.0922825i
$871$	−6.57785	−	2.39414i	−0.222882	−	0.0811224i
$872$	−28.6199	+	24.0150i	−0.969194	+	0.813250i
$873$	−27.5410			−0.932122
$874$		0			0
$875$	31.4164			1.06207
$876$	34.7483	−	29.1573i	1.17404	−	0.985133i
$877$	32.1190	+	11.6904i	1.08458	+	0.394756i	0.821611	−	0.570048i	$-0.193075\pi$
$877$	32.1190	+	11.6904i	1.08458	+	0.394756i	0.262971	+	0.964804i	$0.415298\pi$
$878$	−1.56653	+	8.88423i	−0.0528678	+	0.299828i
$879$	−7.66216	−	43.4543i	−0.258438	−	1.46568i
$880$	1.33099	−	0.484440i	0.0448676	−	0.0163305i
$881$	11.7254	−	20.3090i	0.395040	−	0.684229i	−0.598067	−	0.801446i	$-0.704064\pi$
$881$	11.7254	−	20.3090i	0.395040	−	0.684229i	0.993106	+	0.117218i	$0.0373975\pi$
$882$	−2.38197	−	4.12569i	−0.0802050	−	0.138919i
$883$	10.6656	+	8.94952i	0.358927	+	0.301175i	0.804363	−	0.594138i	$-0.202507\pi$
$883$	10.6656	+	8.94952i	0.358927	+	0.301175i	−0.445436	+	0.895314i	$0.646951\pi$
$884$	−6.49003	−	5.44578i	−0.218283	−	0.183162i
$885$	−24.7984	−	42.9520i	−0.833588	−	1.44382i
$886$	10.6353	−	18.4208i	0.357298	−	0.618859i
$887$	55.1153	−	20.0603i	1.85059	−	0.673560i	0.865654	−	0.500642i	$-0.166903\pi$
$887$	55.1153	−	20.0603i	1.85059	−	0.673560i	0.984936	−	0.172918i	$-0.0553195\pi$
$888$	−2.18142	−	12.3715i	−0.0732037	−	0.415159i
$889$	−5.33242	+	30.2417i	−0.178844	+	1.01427i
$890$	8.78380	+	3.19704i	0.294434	+	0.107165i
$891$	−2.70250	+	2.26767i	−0.0905372	+	0.0759697i
$892$	31.7984			1.06469
$893$		0			0
$894$	21.1803			0.708377
$895$	7.35154	−	6.16867i	0.245735	−	0.206196i
$896$	32.0866	+	11.6786i	1.07194	+	0.390154i
$897$	−3.46329	+	19.6413i	−0.115636	+	0.655803i
$898$	3.52961	+	20.0174i	0.117785	+	0.667991i
$899$	−2.78671	+	1.01428i	−0.0929421	+	0.0338282i
$900$	−10.8262	+	18.7516i	−0.360875	+	0.625053i
$901$	24.4164	+	42.2905i	0.813428	+	1.40890i
$902$	0.877809	+	0.736569i	0.0292278	+	0.0245251i
$903$	41.2383	+	34.6031i	1.37233	+	1.15152i
$904$	−12.5623	−	21.7586i	−0.417816	−	0.723679i
$905$	−7.41641	+	12.8456i	−0.246530	+	0.427002i
$906$	15.0674	−	5.48410i	0.500582	−	0.182197i
$907$	3.04368	+	17.2616i	0.101064	+	0.573161i	0.992720	+	0.120447i	$0.0384329\pi$
$907$	3.04368	+	17.2616i	0.101064	+	0.573161i	−0.891656	+	0.452714i	$0.850456\pi$
$908$	−2.92668	+	16.5981i	−0.0971254	+	0.550826i
$909$	−47.7349	−	17.3741i	−1.58327	−	0.576261i
$910$	−1.75562	+	1.47314i	−0.0581982	+	0.0488341i
$911$	−5.61803			−0.186134			−0.0930669	−	0.995660i	$-0.529667\pi$
$911$	−5.61803			−0.186134			−0.0930669	+	0.995660i	$0.529667\pi$
$912$		0			0
$913$	−0.291796			−0.00965704
$914$	2.97880	−	2.49951i	0.0985299	−	0.0826764i
$915$	17.5276	+	6.37952i	0.579444	+	0.210901i
$916$	3.19798	−	18.1366i	0.105664	−	0.599251i
$917$	2.03680	+	11.5513i	0.0672612	+	0.381457i
$918$	6.79968	−	2.47488i	0.224423	−	0.0816832i
$919$	−18.3541	+	31.7902i	−0.605446	+	1.04866i	0.386535	+	0.922275i	$0.373672\pi$
$919$	−18.3541	+	31.7902i	−0.605446	+	1.04866i	−0.991981	+	0.126388i	$0.959661\pi$
$920$	−10.5279	−	18.2348i	−0.347093	−	0.601183i
$921$	−3.35678	−	2.81667i	−0.110610	−	0.0928125i
$922$	1.44671	+	1.21393i	0.0476448	+	0.0399787i
$923$	0.736068	+	1.27491i	0.0242280	+	0.0419641i
$924$	−3.92705	+	6.80185i	−0.129190	+	0.223764i
$925$	−7.00151	+	2.54834i	−0.230208	+	0.0837889i
$926$	−0.565634	−	3.20787i	−0.0185879	−	0.105417i
$927$	0.887595	−	5.03380i	0.0291524	−	0.165332i
$928$	−7.29571	−	2.65542i	−0.239493	−	0.0871685i
$929$	14.2622	−	11.9674i	0.467929	−	0.392639i	−0.378110	−	0.925761i	$-0.623426\pi$
$929$	14.2622	−	11.9674i	0.467929	−	0.392639i	0.846038	+	0.533122i	$0.178981\pi$
$930$	4.29180			0.140734
$931$		0			0
$932$	−21.7984			−0.714029
$933$	37.4081	−	31.3891i	1.22469	−	1.02763i
$934$	−1.12916	−	0.410980i	−0.0369472	−	0.0134477i
$935$	−0.694593	+	3.93923i	−0.0227156	+	0.128827i
$936$	−1.49651	−	8.48711i	−0.0489148	−	0.277410i
$937$	−19.2052	+	6.99010i	−0.627405	+	0.228357i	−0.636101	−	0.771605i	$-0.719454\pi$
$937$	−19.2052	+	6.99010i	−0.627405	+	0.228357i	0.00869649	+	0.999962i	$0.497232\pi$
$938$	−6.48936	+	11.2399i	−0.211885	+	0.366996i
$939$	5.66312	+	9.80881i	0.184809	+	0.320098i
$940$	4.59627	+	3.85673i	0.149914	+	0.125793i
$941$	−38.0624	−	31.9381i	−1.24080	−	1.04115i	−0.997461	−	0.0712117i	$-0.977313\pi$
$941$	−38.0624	−	31.9381i	−1.24080	−	1.04115i	−0.243337	−	0.969942i	$-0.578242\pi$
$942$	−9.01722	−	15.6183i	−0.293797	−	0.508871i
$943$	−11.4271	+	19.7922i	−0.372116	+	0.644524i
$944$	−26.7027	+	9.71898i	−0.869098	+	0.316326i
$945$	1.43986	+	8.16583i	0.0468385	+	0.265634i
$946$	−0.454617	+	2.57826i	−0.0147809	+	0.0838265i
$947$	1.26626	+	0.460880i	0.0411479	+	0.0149766i	0.362512	−	0.931979i	$-0.381919\pi$
$947$	1.26626	+	0.460880i	0.0411479	+	0.0149766i	−0.321364	+	0.946956i	$0.604141\pi$
$948$	43.5365	−	36.5314i	1.41400	−	1.18649i
$949$	10.7082			0.347603
$950$		0			0
$951$	47.1246			1.52812
$952$	−26.9070	+	22.5777i	−0.872061	+	0.731746i
$953$	28.8563	+	10.5028i	0.934746	+	0.340220i	0.764089	−	0.645111i	$-0.223189\pi$
$953$	28.8563	+	10.5028i	0.934746	+	0.340220i	0.170657	+	0.985330i	$0.445411\pi$
$954$	−3.85756	+	21.8773i	−0.124893	+	0.708303i
$955$	−2.09574	−	11.8855i	−0.0678165	−	0.384607i
$956$	23.3028	−	8.48154i	0.753668	−	0.274313i
$957$	1.11803	−	1.93649i	0.0361409	−	0.0625979i
$958$	−3.68034	−	6.37454i	−0.118906	−	0.205952i
$959$	−3.38316	−	2.83881i	−0.109248	−	0.0916700i
$960$	−0.585206	−	0.491046i	−0.0188874	−	0.0158484i
$961$	13.1976	+	22.8588i	0.425728	+	0.737382i
$962$	0.663119	−	1.14856i	0.0213798	−	0.0370309i
$963$	−37.7248	+	13.7307i	−1.21566	+	0.442466i
$964$	−5.38907	−	30.5630i	−0.173570	−	0.984367i
$965$	4.92478	−	27.9298i	0.158534	−	0.899093i
$966$	34.7486	+	12.6475i	1.11802	+	0.406926i
$967$	−46.3771	+	38.9150i	−1.49139	+	1.25142i	−0.598516	+	0.801111i	$0.704243\pi$
$967$	−46.3771	+	38.9150i	−1.49139	+	1.25142i	−0.892871	+	0.450312i	$0.851313\pi$
$968$	23.7426			0.763118
$969$		0			0
$970$	5.45898			0.175277
$971$	11.1127	−	9.32465i	0.356623	−	0.299242i	−0.446820	−	0.894624i	$-0.647444\pi$
$971$	11.1127	−	9.32465i	0.356623	−	0.299242i	0.803443	+	0.595382i	$0.202999\pi$
$972$	32.9216	+	11.9825i	1.05596	+	0.384338i
$973$	−5.10441	+	28.9485i	−0.163640	+	0.928048i
$974$	1.95112	+	11.0654i	0.0625180	+	0.354557i
$975$	−8.54197	+	3.10902i	−0.273562	+	0.0995684i
$976$	5.34346	−	9.25514i	0.171040	−	0.296250i
$977$	27.6803	+	47.9438i	0.885573	+	1.53386i	0.845056	+	0.534678i	$0.179567\pi$
$977$	27.6803	+	47.9438i	0.885573	+	1.53386i	0.0405165	+	0.999179i	$0.487100\pi$
$978$	−7.72952	−	6.48584i	−0.247163	−	0.207394i
$979$	5.79306	+	4.86096i	0.185147	+	0.155357i
$980$	−2.00000	−	3.46410i	−0.0638877	−	0.110657i
$981$	−32.1976	+	55.7678i	−1.02799	+	1.78053i
$982$	−17.5476	+	6.38680i	−0.559966	+	0.203811i
$983$	−5.27577	−	29.9204i	−0.168271	−	0.954312i	−0.945627	−	0.325252i	$-0.894551\pi$
$983$	−5.27577	−	29.9204i	−0.168271	−	0.954312i	0.777356	−	0.629060i	$-0.216560\pi$
$984$	3.04966	−	17.2955i	0.0972197	−	0.551360i
$985$	3.48457	+	1.26828i	0.111028	+	0.0404108i
$986$	3.42585	−	2.87463i	0.109101	−	0.0915470i
$987$	−23.5623			−0.749996
$988$		0			0
$989$	−52.2148			−1.66033
$990$	−1.39394	+	1.16965i	−0.0443023	+	0.0371741i
$991$	−45.5289	−	16.5712i	−1.44627	−	0.526400i	−0.504726	−	0.863280i	$-0.668406\pi$
$991$	−45.5289	−	16.5712i	−1.44627	−	0.526400i	−0.941548	+	0.336879i	$0.890629\pi$
$992$	2.09346	−	11.8726i	0.0664673	−	0.376955i
$993$	−3.15698	−	17.9041i	−0.100184	−	0.568171i
$994$	2.56488	−	0.933541i	0.0813531	−	0.0296101i
$995$	8.29180	−	14.3618i	0.262868	−	0.455300i
$996$	1.00000	+	1.73205i	0.0316862	+	0.0548821i
$997$	20.1407	+	16.9000i	0.637862	+	0.535230i	0.903361	−	0.428882i	$-0.141092\pi$
$997$	20.1407	+	16.9000i	0.637862	+	0.535230i	−0.265499	+	0.964111i	$0.585537\pi$
$998$	−7.16062	−	6.00847i	−0.226665	−	0.190195i
$999$	−2.39919	−	4.15551i	−0.0759069	−	0.131475i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	361.2.e.i.234.2		12
19.2	odd	18		361.2.e.j.62.2		12
19.3	odd	18		361.2.e.j.54.1		12
19.4	even	9		361.2.a.c.1.2	✓	2
19.5	even	9	inner	361.2.e.i.245.2		12
19.6	even	9		361.2.c.g.292.1		4
19.7	even	3	inner	361.2.e.i.28.2		12
19.8	odd	6		361.2.e.j.99.2		12
19.9	even	9		361.2.c.g.68.1		4
19.10	odd	18		361.2.c.d.68.2		4
19.11	even	3	inner	361.2.e.i.99.1		12
19.12	odd	6		361.2.e.j.28.1		12
19.13	odd	18		361.2.c.d.292.2		4
19.14	odd	18		361.2.e.j.245.1		12
19.15	odd	18		361.2.a.f.1.1	yes	2
19.16	even	9	inner	361.2.e.i.54.2		12
19.17	even	9	inner	361.2.e.i.62.1		12
19.18	odd	2		361.2.e.j.234.1		12
57.23	odd	18		3249.2.a.o.1.1		2
57.53	even	18		3249.2.a.i.1.2		2
76.15	even	18		5776.2.a.s.1.1		2
76.23	odd	18		5776.2.a.bg.1.2		2
95.4	even	18		9025.2.a.s.1.1		2
95.34	odd	18		9025.2.a.n.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
361.2.a.c.1.2	✓	2	19.4	even	9
361.2.a.f.1.1	yes	2	19.15	odd	18
361.2.c.d.68.2		4	19.10	odd	18
361.2.c.d.292.2		4	19.13	odd	18
361.2.c.g.68.1		4	19.9	even	9
361.2.c.g.292.1		4	19.6	even	9
361.2.e.i.28.2		12	19.7	even	3	inner
361.2.e.i.54.2		12	19.16	even	9	inner
361.2.e.i.62.1		12	19.17	even	9	inner
361.2.e.i.99.1		12	19.11	even	3	inner
361.2.e.i.234.2		12	1.1	even	1	trivial
361.2.e.i.245.2		12	19.5	even	9	inner
361.2.e.j.28.1		12	19.12	odd	6
361.2.e.j.54.1		12	19.3	odd	18
361.2.e.j.62.2		12	19.2	odd	18
361.2.e.j.99.2		12	19.8	odd	6
361.2.e.j.234.1		12	19.18	odd	2
361.2.e.j.245.1		12	19.14	odd	18
3249.2.a.i.1.2		2	57.53	even	18
3249.2.a.o.1.1		2	57.23	odd	18
5776.2.a.s.1.1		2	76.15	even	18
5776.2.a.bg.1.2		2	76.23	odd	18
9025.2.a.n.1.2		2	95.34	odd	18
9025.2.a.s.1.1		2	95.4	even	18

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:	\( N \)	\(=\)	\( 361 = 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	361.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.473442 - 0.397265i) q^{2} +(2.46015 + 0.895420i) q^{3} +(-0.280969 + 1.59345i) q^{4} +(-0.214641 - 1.21729i) q^{5} +(1.52045 - 0.553400i) q^{6} +(-1.50000 + 2.59808i) q^{7} +(1.11803 + 1.93649i) q^{8} +(2.95241 + 2.47737i) q^{9} +O(q^{10})\)	\(q+(0.473442 - 0.397265i) q^{2} +(2.46015 + 0.895420i) q^{3} +(-0.280969 + 1.59345i) q^{4} +(-0.214641 - 1.21729i) q^{5} +(1.52045 - 0.553400i) q^{6} +(-1.50000 + 2.59808i) q^{7} +(1.11803 + 1.93649i) q^{8} +(2.95241 + 2.47737i) q^{9} +(-0.585206 - 0.491046i) q^{10} +(-0.309017 - 0.535233i) q^{11} +(-2.11803 + 3.66854i) q^{12} +(-0.939693 + 0.342020i) q^{13} +(0.321961 + 1.82593i) q^{14} +(0.561937 - 3.18690i) q^{15} +(-1.74229 - 0.634140i) q^{16} +(4.01106 - 3.36568i) q^{17} +2.38197 q^{18} +2.00000 q^{20} +(-6.01659 + 5.04852i) q^{21} +(-0.358931 - 0.130640i) q^{22} +(1.32286 - 7.50230i) q^{23} +(1.01655 + 5.76517i) q^{24} +(3.26274 - 1.18754i) q^{25} +(-0.309017 + 0.535233i) q^{26} +(1.11803 + 1.93649i) q^{27} +(-3.71846 - 3.12016i) q^{28} +(1.05865 + 0.888311i) q^{29} +(-1.00000 - 1.73205i) q^{30} +(-1.07295 + 1.85840i) q^{31} +(-5.27923 + 1.92148i) q^{32} +(-0.280969 - 1.59345i) q^{33} +(0.561937 - 3.18690i) q^{34} +(3.48457 + 1.26828i) q^{35} +(-4.77711 + 4.00847i) q^{36} -2.14590 q^{37} -2.61803 q^{39} +(2.11729 - 1.77662i) q^{40} +(-2.81908 - 1.02606i) q^{41} +(-0.842906 + 4.78036i) q^{42} +(-1.19020 - 6.74997i) q^{43} +(0.939693 - 0.342020i) q^{44} +(2.38197 - 4.12569i) q^{45} +(-2.35410 - 4.07742i) q^{46} +(2.29813 + 1.92836i) q^{47} +(-3.71846 - 3.12016i) q^{48} +(-1.00000 - 1.73205i) q^{49} +(1.07295 - 1.85840i) q^{50} +(12.8815 - 4.68848i) q^{51} +(-0.280969 - 1.59345i) q^{52} +(-1.61948 + 9.18455i) q^{53} +(1.29862 + 0.472660i) q^{54} +(-0.585206 + 0.491046i) q^{55} -6.70820 q^{56} +0.854102 q^{58} +(11.7406 - 9.85152i) q^{59} +(4.92029 + 1.79084i) q^{60} +(-1.00090 + 5.67636i) q^{61} +(0.230299 + 1.30609i) q^{62} +(-10.8650 + 3.95454i) q^{63} +(0.118034 - 0.204441i) q^{64} +(0.618034 + 1.07047i) q^{65} +(-0.766044 - 0.642788i) q^{66} +(5.36231 + 4.49951i) q^{67} +(4.23607 + 7.33708i) q^{68} +(9.97214 - 17.2722i) q^{69} +(2.15358 - 0.783840i) q^{70} +(-0.255634 - 1.44977i) q^{71} +(-1.49651 + 8.48711i) q^{72} +(-10.0624 - 3.66242i) q^{73} +(-1.01596 + 0.852489i) q^{74} +9.09017 q^{75} +1.85410 q^{77} +(-1.23949 + 1.04005i) q^{78} +(-12.6073 - 4.58868i) q^{79} +(-0.397966 + 2.25698i) q^{80} +(-0.991219 - 5.62148i) q^{81} +(-1.74229 + 0.634140i) q^{82} +(0.236068 - 0.408882i) q^{83} +(-6.35410 - 11.0056i) q^{84} +(-4.95794 - 4.16021i) q^{85} +(-3.24502 - 2.72289i) q^{86} +(1.80902 + 3.13331i) q^{87} +(0.690983 - 1.19682i) q^{88} +(-11.4981 + 4.18498i) q^{89} +(-0.511267 - 2.89954i) q^{90} +(0.520945 - 2.95442i) q^{91} +(11.5829 + 4.21582i) q^{92} +(-4.30366 + 3.61120i) q^{93} +1.85410 q^{94} -14.7082 q^{96} +(-5.47408 + 4.59329i) q^{97} +(-1.16152 - 0.422760i) q^{98} +(0.413624 - 2.34578i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 18 q^{7}+O(q^{10}) \) 12 * q - 18 * q^7	\( 12 q - 18 q^{7} + 3 q^{11} - 12 q^{12} + 42 q^{18} + 24 q^{20} + 3 q^{26} - 12 q^{30} - 33 q^{31} - 66 q^{37} - 18 q^{39} + 42 q^{45} + 12 q^{46} - 12 q^{49} + 33 q^{50} - 30 q^{58} - 12 q^{64} - 6 q^{65} + 24 q^{68} + 66 q^{69} + 42 q^{75} - 18 q^{77} - 24 q^{83} - 36 q^{84} + 15 q^{87} + 15 q^{88} - 18 q^{94} - 96 q^{96}+O(q^{100}) \) 12 * q - 18 * q^7 + 3 * q^11 - 12 * q^12 + 42 * q^18 + 24 * q^20 + 3 * q^26 - 12 * q^30 - 33 * q^31 - 66 * q^37 - 18 * q^39 + 42 * q^45 + 12 * q^46 - 12 * q^49 + 33 * q^50 - 30 * q^58 - 12 * q^64 - 6 * q^65 + 24 * q^68 + 66 * q^69 + 42 * q^75 - 18 * q^77 - 24 * q^83 - 36 * q^84 + 15 * q^87 + 15 * q^88 - 18 * q^94 - 96 * q^96

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