LMFDB - Embedded newform 425.2.k.b.86.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [425,2,Mod(86,425)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("425.86"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(425, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.k (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [76] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$19$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			86.18
Character	$\chi$	$=$	425.86
Dual form			425.2.k.b.341.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.71096 - 1.24309i) q^{2} +(0.882251 - 2.71529i) q^{3} +(0.764097 - 2.35165i) q^{4} +(1.52540 + 1.63498i) q^{5} +(-1.86584 - 5.74248i) q^{6} -1.34454 q^{7} +(-0.308905 - 0.950711i) q^{8} +(-4.16738 - 3.02778i) q^{9} +(4.64233 + 0.901189i) q^{10} +(-1.07914 + 0.784042i) q^{11} +(-5.71128 - 4.14949i) q^{12} +(-2.37863 - 1.72817i) q^{13} +(-2.30047 + 1.67139i) q^{14} +(5.78523 - 2.69943i) q^{15} +(2.29052 + 1.66416i) q^{16} +(0.309017 + 0.951057i) q^{17} -10.8940 q^{18} +(0.638585 + 1.96536i) q^{19} +(5.01045 - 2.33792i) q^{20} +(-1.18622 + 3.65082i) q^{21} +(-0.871740 + 2.68294i) q^{22} +(5.93794 - 4.31416i) q^{23} -2.85399 q^{24} +(-0.346321 + 4.98799i) q^{25} -6.21802 q^{26} +(-4.96867 + 3.60995i) q^{27} +(-1.02736 + 3.16189i) q^{28} +(-1.67146 + 5.14423i) q^{29} +(6.54269 - 11.8102i) q^{30} +(1.06901 + 3.29007i) q^{31} +7.98698 q^{32} +(1.17683 + 3.62190i) q^{33} +(1.71096 + 1.24309i) q^{34} +(-2.05096 - 2.19830i) q^{35} +(-10.3045 + 7.48669i) q^{36} +(-9.29700 - 6.75467i) q^{37} +(3.53572 + 2.56885i) q^{38} +(-6.79104 + 4.93398i) q^{39} +(1.08319 - 1.95527i) q^{40} +(6.79284 + 4.93529i) q^{41} +(2.50871 + 7.72101i) q^{42} +0.615947 q^{43} +(1.01922 + 3.13685i) q^{44} +(-1.40655 - 11.4321i) q^{45} +(4.79671 - 14.7628i) q^{46} +(-0.224579 + 0.691184i) q^{47} +(6.53949 - 4.75122i) q^{48} -5.19220 q^{49} +(5.60797 + 8.96479i) q^{50} +2.85502 q^{51} +(-5.88156 + 4.27321i) q^{52} +(-1.90499 + 5.86296i) q^{53} +(-4.01373 + 12.3530i) q^{54} +(-2.92802 - 0.568399i) q^{55} +(0.415336 + 1.27827i) q^{56} +5.89992 q^{57} +(3.53492 + 10.8794i) q^{58} +(-10.5415 - 7.65888i) q^{59} +(-1.92765 - 15.6675i) q^{60} +(-2.77474 + 2.01596i) q^{61} +(5.91889 + 4.30033i) q^{62} +(5.60322 + 4.07097i) q^{63} +(9.08439 - 6.60020i) q^{64} +(-0.802823 - 6.52516i) q^{65} +(6.51586 + 4.73405i) q^{66} +(1.08516 + 3.33978i) q^{67} +2.47267 q^{68} +(-6.47545 - 19.9294i) q^{69} +(-6.24181 - 1.21169i) q^{70} +(1.85211 - 5.70021i) q^{71} +(-1.59122 + 4.89726i) q^{72} +(6.13543 - 4.45765i) q^{73} -24.3035 q^{74} +(13.2383 + 5.34102i) q^{75} +5.10978 q^{76} +(1.45095 - 1.05418i) q^{77} +(-5.48586 + 16.8837i) q^{78} +(0.174749 - 0.537821i) q^{79} +(0.773086 + 6.28347i) q^{80} +(0.643053 + 1.97911i) q^{81} +17.7573 q^{82} +(1.71901 + 5.29058i) q^{83} +(7.67906 + 5.57917i) q^{84} +(-1.08358 + 1.95598i) q^{85} +(1.05386 - 0.765677i) q^{86} +(12.4934 + 9.07699i) q^{87} +(1.07875 + 0.783757i) q^{88} +(-3.38650 + 2.46044i) q^{89} +(-16.6177 - 17.8115i) q^{90} +(3.19817 + 2.32360i) q^{91} +(-5.60824 - 17.2604i) q^{92} +9.87664 q^{93} +(0.474955 + 1.46176i) q^{94} +(-2.23923 + 4.04203i) q^{95} +(7.04652 - 21.6869i) q^{96} +(5.28373 - 16.2616i) q^{97} +(-8.88368 + 6.45437i) q^{98} +6.87109 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q - 6 q^{2} - 7 q^{3} - 26 q^{4} + 13 q^{5} + 12 q^{6} + 22 q^{7} + 10 q^{8} - 24 q^{9} - 6 q^{10} - 16 q^{11} - 15 q^{12} - q^{13} - 19 q^{14} - 3 q^{15} + 30 q^{16} - 19 q^{17} + 6 q^{18} + 18 q^{19}+ \cdots - 64 q^{99}+O(q^{100}) $ 76 * q - 6 * q^2 - 7 * q^3 - 26 * q^4 + 13 * q^5 + 12 * q^6 + 22 * q^7 + 10 * q^8 - 24 * q^9 - 6 * q^10 - 16 * q^11 - 15 * q^12 - q^13 - 19 * q^14 - 3 * q^15 + 30 * q^16 - 19 * q^17 + 6 * q^18 + 18 * q^19 - 23 * q^20 - 22 * q^21 - 15 * q^22 - 8 * q^23 - 22 * q^24 + 35 * q^25 - 14 * q^26 - 10 * q^27 - 29 * q^28 - 25 * q^29 + 57 * q^30 + 22 * q^31 + 54 * q^32 - 22 * q^33 - 6 * q^34 - 19 * q^35 - 91 * q^36 - 49 * q^37 + 15 * q^38 + 25 * q^39 - 2 * q^40 + 16 * q^41 - 28 * q^42 + 104 * q^43 + 18 * q^44 + 10 * q^45 - 55 * q^46 - 26 * q^47 - 86 * q^48 + 2 * q^49 - 17 * q^50 + 18 * q^51 + 53 * q^52 - 41 * q^53 - 6 * q^54 + 67 * q^55 + 115 * q^56 + 84 * q^57 - 12 * q^58 - 7 * q^59 - 32 * q^60 - 21 * q^61 - 23 * q^62 - 21 * q^63 + 6 * q^64 - 72 * q^65 + 102 * q^66 - 15 * q^67 + 74 * q^68 + 48 * q^69 - 60 * q^70 - 8 * q^71 + 9 * q^72 - 25 * q^73 - 60 * q^74 + 68 * q^75 - 76 * q^76 - 36 * q^77 - 51 * q^78 + 2 * q^79 + 217 * q^80 + 20 * q^81 - 12 * q^82 - 41 * q^83 - 48 * q^84 - 7 * q^85 - 87 * q^86 - 54 * q^87 - 4 * q^88 + 77 * q^89 - 93 * q^90 + 79 * q^91 - 19 * q^92 + 72 * q^93 + 15 * q^94 + 57 * q^95 + 28 * q^96 + 13 * q^97 - 62 * q^98 - 64 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

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 $

$2$	1.71096	−	1.24309i	1.20983	−	0.878997i	0.214619	−	0.976698i	$-0.431149\pi$
$2$	1.71096	−	1.24309i	1.20983	−	0.878997i	0.995216	+	0.0977013i	$0.0311490\pi$
$3$	0.882251	−	2.71529i	0.509368	−	1.56767i	−0.283934	−	0.958844i	$-0.591640\pi$
$3$	0.882251	−	2.71529i	0.509368	−	1.56767i	0.793302	−	0.608829i	$-0.208360\pi$
$4$	0.764097	−	2.35165i	0.382049	−	1.17582i
$5$	1.52540	+	1.63498i	0.682179	+	0.731185i
$5$	1.52540	+	1.63498i	0.682179	+	0.731185i
$6$	−1.86584	−	5.74248i	−0.761728	−	2.34436i
$7$	−1.34454			−0.508190			−0.254095	−	0.967179i	$-0.581778\pi$
$7$	−1.34454			−0.508190			−0.254095	+	0.967179i	$0.581778\pi$
$8$	−0.308905	−	0.950711i	−0.109214	−	0.336127i
$9$	−4.16738	−	3.02778i	−1.38913	−	1.00926i
$10$	4.64233	+	0.901189i	1.46803	+	0.284981i
$11$	−1.07914	+	0.784042i	−0.325374	+	0.236398i	−0.738465	−	0.674292i	$-0.764449\pi$
$11$	−1.07914	+	0.784042i	−0.325374	+	0.236398i	0.413091	+	0.910690i	$0.364449\pi$
$12$	−5.71128	−	4.14949i	−1.64871	−	1.19785i
$13$	−2.37863	−	1.72817i	−0.659713	−	0.479309i	0.206853	−	0.978372i	$-0.433678\pi$
$13$	−2.37863	−	1.72817i	−0.659713	−	0.479309i	−0.866566	+	0.499063i	$0.833678\pi$
$14$	−2.30047	+	1.67139i	−0.614825	+	0.446697i
$15$	5.78523	−	2.69943i	1.49374	−	0.696991i
$16$	2.29052	+	1.66416i	0.572631	+	0.416040i
$17$	0.309017	+	0.951057i	0.0749476	+	0.230665i
$17$	0.309017	+	0.951057i	0.0749476	+	0.230665i
$18$	−10.8940			−2.56775
$19$	0.638585	+	1.96536i	0.146501	+	0.450885i	0.997201	−	0.0747671i	$-0.0238213\pi$
$19$	0.638585	+	1.96536i	0.146501	+	0.450885i	−0.850700	+	0.525652i	$0.823821\pi$
$20$	5.01045	−	2.33792i	1.12037	−	0.522774i
$21$	−1.18622	+	3.65082i	−0.258855	+	0.796675i
$22$	−0.871740	+	2.68294i	−0.185855	+	0.572004i
$23$	5.93794	−	4.31416i	1.23815	−	0.899565i	0.240672	−	0.970607i	$-0.422632\pi$
$23$	5.93794	−	4.31416i	1.23815	−	0.899565i	0.997473	+	0.0710414i	$0.0226322\pi$
$24$	−2.85399			−0.582567
$25$	−0.346321	+	4.98799i	−0.0692643	+	0.997598i
$26$	−6.21802			−1.21945
$27$	−4.96867	+	3.60995i	−0.956220	+	0.694735i
$28$	−1.02736	+	3.16189i	−0.194153	+	0.597542i
$29$	−1.67146	+	5.14423i	−0.310382	+	0.955259i	0.667231	+	0.744851i	$0.267479\pi$
$29$	−1.67146	+	5.14423i	−0.310382	+	0.955259i	−0.977614	+	0.210408i	$0.932521\pi$
$30$	6.54269	−	11.8102i	1.19453	−	2.15624i
$31$	1.06901	+	3.29007i	0.192000	+	0.590915i	0.999999	+	0.00173043i	$0.000550814\pi$
$31$	1.06901	+	3.29007i	0.192000	+	0.590915i	−0.807999	+	0.589184i	$0.799449\pi$
$32$	7.98698			1.41191
$33$	1.17683	+	3.62190i	0.204859	+	0.630493i
$34$	1.71096	+	1.24309i	0.293428	+	0.213188i
$35$	−2.05096	−	2.19830i	−0.346676	−	0.371581i
$36$	−10.3045	+	7.48669i	−1.71742	+	1.24778i
$37$	−9.29700	−	6.75467i	−1.52842	−	1.11046i	−0.957110	−	0.289724i	$-0.906437\pi$
$37$	−9.29700	−	6.75467i	−1.52842	−	1.11046i	−0.571307	−	0.820737i	$-0.693563\pi$
$38$	3.53572	+	2.56885i	0.573569	+	0.416722i
$39$	−6.79104	+	4.93398i	−1.08744	+	0.790069i
$40$	1.08319	−	1.95527i	0.171268	−	0.309155i
$41$	6.79284	+	4.93529i	1.06086	+	0.770763i	0.974248	−	0.225479i	$-0.0723948\pi$
$41$	6.79284	+	4.93529i	1.06086	+	0.770763i	0.0866157	+	0.996242i	$0.472395\pi$
$42$	2.50871	+	7.72101i	0.387102	+	1.19138i
$43$	0.615947			0.0939310			0.0469655	−	0.998897i	$-0.485045\pi$
$43$	0.615947			0.0939310			0.0469655	+	0.998897i	$0.485045\pi$
$44$	1.01922	+	3.13685i	0.153654	+	0.472898i
$45$	−1.40655	−	11.4321i	−0.209677	−	1.70420i
$46$	4.79671	−	14.7628i	0.707237	−	2.17665i
$47$	−0.224579	+	0.691184i	−0.0327582	+	0.100819i	−0.966099	−	0.258173i	$-0.916880\pi$
$47$	−0.224579	+	0.691184i	−0.0327582	+	0.100819i	0.933341	+	0.358992i	$0.116880\pi$
$48$	6.53949	−	4.75122i	0.943895	−	0.685780i
$49$	−5.19220			−0.741743
$50$	5.60797	+	8.96479i	0.793087	+	1.26781i
$51$	2.85502			0.399783
$52$	−5.88156	+	4.27321i	−0.815626	+	0.592587i
$53$	−1.90499	+	5.86296i	−0.261671	+	0.805339i	0.730771	+	0.682623i	$0.239161\pi$
$53$	−1.90499	+	5.86296i	−0.261671	+	0.805339i	−0.992442	+	0.122717i	$0.960839\pi$
$54$	−4.01373	+	12.3530i	−0.546199	+	1.68103i
$55$	−2.92802	−	0.568399i	−0.394813	−	0.0766429i
$56$	0.415336	+	1.27827i	0.0555016	+	0.170816i
$57$	5.89992			0.781463
$58$	3.53492	+	10.8794i	0.464158	+	1.42853i
$59$	−10.5415	−	7.65888i	−1.37239	−	0.997101i	−0.997546	−	0.0700135i	$-0.977696\pi$
$59$	−10.5415	−	7.65888i	−1.37239	−	0.997101i	−0.374845	−	0.927087i	$-0.622304\pi$
$60$	−1.92765	−	15.6675i	−0.248858	−	2.02266i
$61$	−2.77474	+	2.01596i	−0.355269	+	0.258118i	−0.751076	−	0.660216i	$-0.770465\pi$
$61$	−2.77474	+	2.01596i	−0.355269	+	0.258118i	0.395807	+	0.918334i	$0.370465\pi$
$62$	5.91889	+	4.30033i	0.751700	+	0.546142i
$63$	5.60322	+	4.07097i	0.705939	+	0.512895i
$64$	9.08439	−	6.60020i	1.13555	−	0.825025i
$65$	−0.802823	−	6.52516i	−0.0995780	−	0.809347i
$66$	6.51586	+	4.73405i	0.802047	+	0.582721i
$67$	1.08516	+	3.33978i	0.132574	+	0.408020i	0.995205	−	0.0978139i	$-0.0311850\pi$
$67$	1.08516	+	3.33978i	0.132574	+	0.408020i	−0.862631	+	0.505834i	$0.831185\pi$
$68$	2.47267			0.299855
$69$	−6.47545	−	19.9294i	−0.779552	−	2.39922i
$70$	−6.24181	−	1.21169i	−0.746039	−	0.144824i
$71$	1.85211	−	5.70021i	0.219805	−	0.676491i	−0.778972	−	0.627058i	$-0.784259\pi$
$71$	1.85211	−	5.70021i	0.219805	−	0.676491i	0.998777	−	0.0494325i	$-0.0157413\pi$
$72$	−1.59122	+	4.89726i	−0.187527	+	0.577148i
$73$	6.13543	−	4.45765i	0.718098	−	0.521729i	−0.167678	−	0.985842i	$-0.553627\pi$
$73$	6.13543	−	4.45765i	0.718098	−	0.521729i	0.885776	+	0.464113i	$0.153627\pi$
$74$	−24.3035			−2.82522
$75$	13.2383	+	5.34102i	1.52863	+	0.616728i
$76$	5.10978			0.586133
$77$	1.45095	−	1.05418i	0.165351	−	0.120135i
$78$	−5.48586	+	16.8837i	−0.621151	+	1.91171i
$79$	0.174749	−	0.537821i	0.0196607	−	0.0605095i	−0.940745	−	0.339115i	$-0.889872\pi$
$79$	0.174749	−	0.537821i	0.0196607	−	0.0605095i	0.960406	+	0.278606i	$0.0898723\pi$
$80$	0.773086	+	6.28347i	0.0864337	+	0.702513i
$81$	0.643053	+	1.97911i	0.0714503	+	0.219901i
$82$	17.7573			1.96097
$83$	1.71901	+	5.29058i	0.188686	+	0.580717i	0.999992	−	0.00390481i	$-0.00124294\pi$
$83$	1.71901	+	5.29058i	0.188686	+	0.580717i	−0.811306	+	0.584622i	$0.801243\pi$
$84$	7.67906	+	5.57917i	0.837855	+	0.608737i
$85$	−1.08358	+	1.95598i	−0.117531	+	0.212155i
$86$	1.05386	−	0.765677i	0.113641	−	0.0825650i
$87$	12.4934	+	9.07699i	1.33943	+	0.973156i
$88$	1.07875	+	0.783757i	0.114995	+	0.0835488i
$89$	−3.38650	+	2.46044i	−0.358968	+	0.260806i	−0.752622	−	0.658453i	$-0.771211\pi$
$89$	−3.38650	+	2.46044i	−0.358968	+	0.260806i	0.393653	+	0.919259i	$0.371211\pi$
$90$	−16.6177	−	17.8115i	−1.75166	−	1.87750i
$91$	3.19817	+	2.32360i	0.335259	+	0.243580i
$92$	−5.60824	−	17.2604i	−0.584699	−	1.79952i
$93$	9.87664			1.02416
$94$	0.474955	+	1.46176i	0.0489879	+	0.150769i
$95$	−2.23923	+	4.04203i	−0.229740	+	0.414704i
$96$	7.04652	−	21.6869i	0.719182	−	2.21341i
$97$	5.28373	−	16.2616i	0.536481	−	1.65112i	−0.203946	−	0.978982i	$-0.565377\pi$
$97$	5.28373	−	16.2616i	0.536481	−	1.65112i	0.740427	−	0.672137i	$-0.234623\pi$
$98$	−8.88368	+	6.45437i	−0.897387	+	0.651990i
$99$	6.87109			0.690571
$100$	11.4654	+	4.62574i	1.14654	+	0.462574i
$101$	9.11000			0.906479			0.453239	−	0.891389i	$-0.350268\pi$
$101$	9.11000			0.906479			0.453239	+	0.891389i	$0.350268\pi$
$102$	4.88484	−	3.54905i	0.483672	−	0.351408i
$103$	−0.443006	+	1.36343i	−0.0436506	+	0.134343i	−0.970507	−	0.241074i	$-0.922500\pi$
$103$	−0.443006	+	1.36343i	−0.0436506	+	0.134343i	0.926856	+	0.375417i	$0.122500\pi$
$104$	−0.908225	+	2.79523i	−0.0890588	+	0.274095i
$105$	−7.77849	+	3.62950i	−0.759103	+	0.354203i
$106$	4.02881	+	12.3994i	0.391312	+	1.20434i
$107$	11.5741			1.11891			0.559456	−	0.828860i	$-0.311010\pi$
$107$	11.5741			1.11891			0.559456	+	0.828860i	$0.311010\pi$
$108$	4.69279	+	14.4429i	0.451564	+	1.38977i
$109$	−13.2669	−	9.63895i	−1.27074	−	0.923244i	−0.271504	−	0.962437i	$-0.587521\pi$
$109$	−13.2669	−	9.63895i	−1.27074	−	0.923244i	−0.999232	+	0.0391935i	$0.987521\pi$
$110$	−5.71630	+	2.66727i	−0.545028	+	0.254314i
$111$	−26.5432	+	19.2847i	−2.51936	+	1.83043i
$112$	−3.07971	−	2.23754i	−0.291005	−	0.211427i
$113$	−10.3035	−	7.48594i	−0.969273	−	0.704218i	−0.0139872	−	0.999902i	$-0.504452\pi$
$113$	−10.3035	−	7.48594i	−0.969273	−	0.704218i	−0.955286	+	0.295684i	$0.904452\pi$
$114$	10.0946	−	7.33412i	0.945442	−	0.686904i
$115$	16.1113	+	3.12759i	1.50239	+	0.291650i
$116$	10.8203	+	7.86138i	1.00464	+	0.729911i
$117$	4.68011	+	14.4039i	0.432676	+	1.33164i
$118$	−27.5569			−2.53682
$119$	−0.415487	−	1.27874i	−0.0380876	−	0.117222i
$120$	−4.35346	−	4.66621i	−0.397415	−	0.425965i
$121$	−2.84936	+	8.76944i	−0.259033	+	0.797221i
$122$	−2.24145	+	6.89849i	−0.202932	+	0.624560i
$123$	19.3937	−	14.0904i	1.74867	−	1.27049i
$124$	8.55393			0.768165
$125$	−8.68355	+	7.04244i	−0.776680	+	0.629895i
$126$	14.6475			1.30490
$127$	−14.0523	+	10.2096i	−1.24694	+	0.905957i	−0.998041	−	0.0625711i	$-0.980070\pi$
$127$	−14.0523	+	10.2096i	−1.24694	+	0.905957i	−0.248903	+	0.968528i	$0.580070\pi$
$128$	2.40222	−	7.39328i	0.212328	−	0.653480i
$129$	0.543420	−	1.67247i	0.0478454	−	0.147253i
$130$	−9.48496	−	10.1663i	−0.831886	−	0.891647i
$131$	−4.89265	−	15.0580i	−0.427473	−	1.31563i	−0.900606	−	0.434636i	$-0.856877\pi$
$131$	−4.89265	−	15.0580i	−0.427473	−	1.31563i	0.473133	−	0.880991i	$-0.343123\pi$
$132$	9.41666			0.819615
$133$	−0.858605	−	2.64251i	−0.0744505	−	0.229135i
$134$	6.00832	+	4.36530i	0.519040	+	0.377105i
$135$	−13.4814	−	2.61706i	−1.16029	−	0.225241i
$136$	0.808723	−	0.587572i	0.0693474	−	0.0503838i
$137$	−13.6381	−	9.90869i	−1.16518	−	0.846556i	−0.174760	−	0.984611i	$-0.555915\pi$
$137$	−13.6381	−	9.90869i	−1.16518	−	0.846556i	−0.990425	+	0.138055i	$0.955915\pi$
$138$	−35.8533	−	26.0489i	−3.05203	−	2.21743i
$139$	−7.71914	+	5.60829i	−0.654729	+	0.475689i	−0.864879	−	0.501981i	$-0.832605\pi$
$139$	−7.71914	+	5.60829i	−0.654729	+	0.475689i	0.210150	+	0.977669i	$0.432605\pi$
$140$	−6.73677	+	3.14343i	−0.569361	+	0.265668i
$141$	1.67863	+	1.21959i	0.141366	+	0.102708i
$142$	−3.91697	−	12.0552i	−0.328705	−	1.01165i
$143$	3.92184			0.327961
$144$	−4.50676	−	13.8704i	−0.375563	−	1.15586i
$145$	−10.9604	+	5.11419i	−0.910208	+	0.424710i
$146$	4.95625	−	15.2538i	0.410182	−	1.26241i
$147$	−4.58083	+	14.0983i	−0.377820	+	1.16281i
$148$	−22.9884	+	16.7021i	−1.88964	+	1.37290i
$149$	−10.7566			−0.881213			−0.440606	−	0.897700i	$-0.645237\pi$
$149$	−10.7566			−0.881213			−0.440606	+	0.897700i	$0.645237\pi$
$150$	29.2896	−	7.31807i	2.39149	−	0.597518i
$151$	10.2626			0.835159			0.417580	−	0.908640i	$-0.362878\pi$
$151$	10.2626			0.835159			0.417580	+	0.908640i	$0.362878\pi$
$152$	1.67123	−	1.21422i	0.135555	−	0.0984862i
$153$	1.59180	−	4.89904i	0.128689	−	0.396064i
$154$	1.17209	−	3.60733i	0.0944498	−	0.290687i
$155$	−3.74854	+	6.76648i	−0.301090	+	0.543497i
$156$	6.41397	+	19.7402i	0.513529	+	1.58048i
$157$	−5.82472			−0.464863			−0.232431	−	0.972613i	$-0.574668\pi$
$157$	−5.82472			−0.464863			−0.232431	+	0.972613i	$0.574668\pi$
$158$	−0.369570	−	1.13742i	−0.0294014	−	0.0904883i
$159$	14.2389	+	10.3452i	1.12922	+	0.820428i
$160$	12.1833	+	13.0586i	0.963176	+	1.03237i
$161$	−7.98381	+	5.80058i	−0.629212	+	0.457150i
$162$	3.56045	+	2.58682i	0.279736	+	0.203240i
$163$	19.7186	+	14.3264i	1.54448	+	1.12213i	0.947446	+	0.319915i	$0.103654\pi$
$163$	19.7186	+	14.3264i	1.54448	+	1.12213i	0.597034	+	0.802216i	$0.296346\pi$
$164$	16.7965	−	12.2033i	1.31158	−	0.952921i
$165$	−4.12661	+	7.44894i	−0.321256	+	0.579899i
$166$	9.51784	+	6.91511i	0.738727	+	0.536717i
$167$	2.95793	+	9.10356i	0.228891	+	0.704455i	0.997873	+	0.0651844i	$0.0207635\pi$
$167$	2.95793	+	9.10356i	0.228891	+	0.704455i	−0.768982	+	0.639270i	$0.779236\pi$
$168$	3.83731			0.296055
$169$	−1.34594	−	4.14237i	−0.103534	−	0.318644i
$170$	0.577477	+	4.69360i	0.0442905	+	0.359983i
$171$	3.28945	−	10.1239i	0.251551	−	0.774194i
$172$	0.470643	−	1.44849i	0.0358862	−	0.110446i
$173$	−3.96042	+	2.87741i	−0.301105	+	0.218766i	−0.728070	−	0.685502i	$-0.759583\pi$
$173$	−3.96042	+	2.87741i	−0.301105	+	0.218766i	0.426965	+	0.904268i	$0.359583\pi$
$174$	32.6593			2.47590
$175$	0.465644	−	6.70657i	0.0351994	−	0.506969i
$176$	−3.77657			−0.284670
$177$	−30.0963	+	21.8663i	−2.26218	+	1.64357i
$178$	−2.73564	+	8.41944i	−0.205045	+	0.631064i
$179$	−4.35168	+	13.3931i	−0.325260	+	1.00105i	0.646063	+	0.763284i	$0.276414\pi$
$179$	−4.35168	+	13.3931i	−0.325260	+	1.00105i	−0.971323	+	0.237763i	$0.923586\pi$
$180$	−27.9591	−	5.42755i	−2.08395	−	0.404545i
$181$	4.24557	+	13.0665i	0.315570	+	0.971226i	0.975519	+	0.219915i	$0.0705780\pi$
$181$	4.24557	+	13.0665i	0.315570	+	0.971226i	−0.659949	+	0.751311i	$0.729422\pi$
$182$	8.36040			0.619714
$183$	3.02591	+	9.31280i	0.223682	+	0.688422i
$184$	−5.93578	−	4.31259i	−0.437591	−	0.317929i
$185$	−3.13788	−	25.5040i	−0.230702	−	1.87509i
$186$	16.8986	−	12.2775i	1.23906	−	0.900233i
$187$	−1.07914	−	0.784042i	−0.0789147	−	0.0573349i
$188$	1.45382	+	1.05626i	0.106031	+	0.0770359i
$189$	6.68059	−	4.85373i	0.485941	−	0.353057i
$190$	1.19336	+	9.69934i	0.0865753	+	0.703664i
$191$	−10.2860	−	7.47321i	−0.744268	−	0.540743i	0.149777	−	0.988720i	$-0.452145\pi$
$191$	−10.2860	−	7.47321i	−0.744268	−	0.540743i	−0.894045	+	0.447977i	$0.852145\pi$
$192$	−9.90673	−	30.4898i	−0.714957	−	2.20041i
$193$	14.8329			1.06769			0.533847	−	0.845581i	$-0.320746\pi$
$193$	14.8329			1.06769			0.533847	+	0.845581i	$0.320746\pi$
$194$	−11.1744	−	34.3912i	−0.802274	−	2.46915i
$195$	−18.4260	−	3.57693i	−1.31951	−	0.256150i
$196$	−3.96735	+	12.2102i	−0.283382	+	0.872160i
$197$	0.905479	−	2.78678i	0.0645127	−	0.198550i	−0.913605	−	0.406604i	$-0.866713\pi$
$197$	0.905479	−	2.78678i	0.0645127	−	0.198550i	0.978117	+	0.208054i	$0.0667130\pi$
$198$	11.7562	−	8.54138i	0.835477	−	0.607009i
$199$	21.1592			1.49993			0.749967	−	0.661475i	$-0.230069\pi$
$199$	21.1592			1.49993			0.749967	+	0.661475i	$0.230069\pi$
$200$	4.84912	−	1.21156i	0.342884	−	0.0856704i
$201$	10.0259			0.707170
$202$	15.5869	−	11.3245i	1.09669	−	0.796791i
$203$	2.24735	−	6.91663i	0.157733	−	0.485452i
$204$	2.18152	−	6.71401i	0.152737	−	0.470075i
$205$	2.29269	+	18.6344i	0.160128	+	1.30149i
$206$	0.936899	+	2.88348i	0.0652768	+	0.200901i
$207$	−37.8079			−2.62783
$208$	−2.57234	−	7.91684i	−0.178360	−	0.548934i
$209$	−2.23005	−	1.62023i	−0.154256	−	0.112073i
$210$	−8.79692	+	15.8793i	−0.607045	+	1.09578i
$211$	20.3332	−	14.7729i	1.39979	−	1.01701i	0.405084	−	0.914280i	$-0.367242\pi$
$211$	20.3332	−	14.7729i	1.39979	−	1.01701i	0.994709	−	0.102729i	$-0.0327576\pi$
$212$	12.3320	+	8.95974i	0.846967	+	0.615358i
$213$	−13.8437	−	10.0580i	−0.948555	−	0.689165i
$214$	19.8029	−	14.3876i	1.35370	−	0.983519i
$215$	0.939564	+	1.00706i	0.0640777	+	0.0686810i
$216$	4.96686	+	3.60864i	0.337952	+	0.245537i
$217$	−1.43733	−	4.42365i	−0.0975723	−	0.300297i
$218$	−34.6812			−2.34891
$219$	−6.69082	−	20.5922i	−0.452124	−	1.39149i
$220$	−3.57396	+	6.45135i	−0.240957	+	0.434950i
$221$	0.908555	−	2.79624i	0.0611160	−	0.188096i
$222$	−21.4418	+	65.9910i	−1.43908	+	4.42902i
$223$	−16.0800	+	11.6828i	−1.07680	+	0.782338i	−0.977122	−	0.212682i	$-0.931780\pi$
$223$	−16.0800	+	11.6828i	−1.07680	+	0.782338i	−0.0996747	+	0.995020i	$0.531780\pi$
$224$	−10.7388			−0.717519
$225$	16.5458	−	19.7382i	1.10305	−	1.31588i
$226$	−26.9346			−1.79167
$227$	12.9623	−	9.41766i	0.860338	−	0.625072i	−0.0676387	−	0.997710i	$-0.521547\pi$
$227$	12.9623	−	9.41766i	0.860338	−	0.625072i	0.927977	+	0.372638i	$0.121547\pi$
$228$	4.50811	−	13.8745i	0.298557	−	0.918864i
$229$	−2.16594	+	6.66608i	−0.143129	+	0.440507i	−0.996766	−	0.0803624i	$-0.974392\pi$
$229$	−2.16594	+	6.66608i	−0.143129	+	0.440507i	0.853636	+	0.520870i	$0.174392\pi$
$230$	31.4537	−	14.6766i	2.07400	−	0.967744i
$231$	−1.58230	−	4.86981i	−0.104107	−	0.320410i
$232$	5.40699			0.354986
$233$	−2.72236	−	8.37858i	−0.178348	−	0.548899i	0.821423	−	0.570320i	$-0.193181\pi$
$233$	−2.72236	−	8.37858i	−0.178348	−	0.548899i	−0.999771	+	0.0214214i	$0.993181\pi$
$234$	25.9128	+	18.8268i	1.69397	+	1.23074i
$235$	−1.47264	+	0.687148i	−0.0960647	+	0.0448246i
$236$	−26.0658	+	18.9379i	−1.69674	+	1.23275i
$237$	−1.30617	−	0.948985i	−0.0848446	−	0.0616432i
$238$	−2.30047	−	1.67139i	−0.149117	−	0.108340i
$239$	8.78176	−	6.38032i	0.568045	−	0.412709i	−0.266350	−	0.963876i	$-0.585818\pi$
$239$	8.78176	−	6.38032i	0.568045	−	0.412709i	0.834394	+	0.551168i	$0.185818\pi$
$240$	17.7435	+	3.44444i	1.14534	+	0.222338i
$241$	−1.59774	−	1.16083i	−0.102919	−	0.0747754i	0.535135	−	0.844766i	$-0.320261\pi$
$241$	−1.59774	−	1.16083i	−0.102919	−	0.0747754i	−0.638055	+	0.769991i	$0.720261\pi$
$242$	6.02603	+	18.5462i	0.387368	+	1.19220i
$243$	−12.4836			−0.800825
$244$	2.62067	+	8.06560i	0.167771	+	0.516347i
$245$	−7.92018	−	8.48915i	−0.506002	−	0.542352i
$246$	15.6664	−	48.2162i	0.998854	−	3.07416i
$247$	1.87753	−	5.77845i	0.119465	−	0.367674i
$248$	2.79769	−	2.03264i	0.177653	−	0.129073i
$249$	15.8821			1.00648
$250$	−6.10286	+	22.8438i	−0.385979	+	1.44477i
$251$	−18.9040			−1.19321			−0.596605	−	0.802535i	$-0.703484\pi$
$251$	−18.9040			−1.19321			−0.596605	+	0.802535i	$0.703484\pi$
$252$	13.8549	−	10.0662i	0.872777	−	0.634110i
$253$	−3.02539	+	9.31119i	−0.190205	+	0.585389i
$254$	−11.3516	+	34.9366i	−0.712262	+	2.19212i
$255$	4.35505	+	4.66791i	0.272724	+	0.292316i
$256$	1.85947	+	5.72287i	0.116217	+	0.357679i
$257$	20.1072			1.25425			0.627125	−	0.778918i	$-0.284231\pi$
$257$	20.1072			1.25425			0.627125	+	0.778918i	$0.284231\pi$
$258$	−1.14926	−	3.53706i	−0.0715499	−	0.220208i
$259$	12.5002	+	9.08194i	0.776726	+	0.564324i
$260$	−15.9583	−	3.09790i	−0.989694	−	0.192124i
$261$	22.5412	−	16.3771i	1.39526	−	1.01372i
$262$	−27.0896	−	19.6818i	−1.67360	−	1.21594i
$263$	−0.869544	−	0.631761i	−0.0536184	−	0.0389560i	0.560653	−	0.828051i	$-0.310550\pi$
$263$	−0.869544	−	0.631761i	−0.0536184	−	0.0389560i	−0.614272	+	0.789095i	$0.710550\pi$
$264$	3.07986	−	2.23765i	0.189552	−	0.137718i
$265$	−12.4917	+	5.82872i	−0.767358	+	0.358056i
$266$	−4.75392	−	3.45393i	−0.291482	−	0.211774i
$267$	3.69305	+	11.3660i	0.226011	+	0.695591i
$268$	8.68317			0.530409
$269$	6.74125	+	20.7474i	0.411022	+	1.26499i	0.915761	+	0.401723i	$0.131588\pi$
$269$	6.74125	+	20.7474i	0.411022	+	1.26499i	−0.504740	+	0.863272i	$0.668412\pi$
$270$	−26.3194	+	12.2809i	−1.60175	+	0.747389i
$271$	−4.86326	+	14.9676i	−0.295422	+	0.909215i	0.687658	+	0.726035i	$0.258639\pi$
$271$	−4.86326	+	14.9676i	−0.295422	+	0.909215i	−0.983079	+	0.183180i	$0.941361\pi$
$272$	−0.874902	+	2.69267i	−0.0530487	+	0.163267i
$273$	9.13084	−	6.63395i	0.552624	−	0.401505i
$274$	−35.6518			−2.15380
$275$	−3.53707	−	5.65428i	−0.213293	−	0.340966i
$276$	−51.8148			−3.11888
$277$	23.0335	−	16.7348i	1.38395	−	1.00550i	0.387449	−	0.921891i	$-0.373356\pi$
$277$	23.0335	−	16.7348i	1.38395	−	1.00550i	0.996499	−	0.0836062i	$-0.0266438\pi$
$278$	−6.23559	+	19.1912i	−0.373986	+	1.15101i
$279$	5.50664	−	16.9477i	0.329674	−	1.01463i
$280$	−1.45640	+	2.62894i	−0.0870364	+	0.157109i
$281$	−7.66492	−	23.5902i	−0.457251	−	1.40727i	−0.868472	−	0.495738i	$-0.834898\pi$
$281$	−7.66492	−	23.5902i	−0.457251	−	1.40727i	0.411221	−	0.911536i	$-0.365102\pi$
$282$	4.38814			0.261310
$283$	2.69453	+	8.29290i	0.160173	+	0.492962i	0.998648	−	0.0519778i	$-0.0165525\pi$
$283$	2.69453	+	8.29290i	0.160173	+	0.492962i	−0.838475	+	0.544940i	$0.816553\pi$
$284$	−11.9897	−	8.71103i	−0.711458	−	0.516905i
$285$	8.99972	+	9.64625i	0.533098	+	0.571395i
$286$	6.71013	−	4.87519i	0.396778	−	0.288276i
$287$	−9.13327	−	6.63571i	−0.539120	−	0.391693i
$288$	−33.2847	−	24.1828i	−1.96132	−	1.42498i
$289$	−0.809017	+	0.587785i	−0.0475892	+	0.0345756i
$290$	−12.3954	+	22.3749i	−0.727882	+	1.31390i
$291$	−39.4935	−	28.6937i	−2.31515	−	1.68205i
$292$	−5.79477	−	17.8345i	−0.339113	−	1.04368i
$293$	−0.789527			−0.0461247			−0.0230623	−	0.999734i	$-0.507342\pi$
$293$	−0.789527			−0.0461247			−0.0230623	+	0.999734i	$0.507342\pi$
$294$	9.68785	+	29.8161i	0.565007	+	1.73891i
$295$	−3.55793	−	28.9180i	−0.207151	−	1.68367i
$296$	−3.54985	+	10.9253i	−0.206331	+	0.635020i
$297$	2.53154	−	7.79129i	0.146895	−	0.452097i
$298$	−18.4041	+	13.3714i	−1.06612	+	0.774583i
$299$	−21.5798			−1.24799
$300$	22.6756	−	27.0508i	1.30917	−	1.56178i
$301$	−0.828167			−0.0477348
$302$	17.5590	−	12.7573i	1.01040	−	0.734102i
$303$	8.03730	−	24.7363i	0.461731	−	1.42106i
$304$	−1.80799	+	5.56442i	−0.103695	+	0.319141i
$305$	−7.52864	−	1.46149i	−0.431089	−	0.0836848i
$306$	−3.36644	−	10.3608i	−0.192447	−	0.592289i
$307$	23.1090			1.31890			0.659451	−	0.751748i	$-0.270789\pi$
$307$	23.1090			1.31890			0.659451	+	0.751748i	$0.270789\pi$
$308$	−1.37039	−	4.21763i	−0.0780852	−	0.240322i
$309$	3.31127	+	2.40578i	0.188371	+	0.136860i
$310$	1.99772	+	16.2370i	0.113463	+	0.922199i
$311$	12.6476	−	9.18899i	0.717177	−	0.521060i	−0.168304	−	0.985735i	$-0.553829\pi$
$311$	12.6476	−	9.18899i	0.717177	−	0.521060i	0.885481	+	0.464675i	$0.153829\pi$
$312$	6.78857	+	4.93218i	0.384327	+	0.279230i
$313$	−6.27275	−	4.55742i	−0.354557	−	0.257600i	0.396221	−	0.918155i	$-0.370321\pi$
$313$	−6.27275	−	4.55742i	−0.354557	−	0.257600i	−0.750778	+	0.660554i	$0.770321\pi$
$314$	−9.96588	+	7.24064i	−0.562407	+	0.408613i
$315$	1.89117	+	15.3710i	0.106555	+	0.866058i
$316$	−1.13124	−	0.821895i	−0.0636373	−	0.0462352i
$317$	1.74159	+	5.36005i	0.0978172	+	0.301051i	0.987978	−	0.154597i	$-0.0494078\pi$
$317$	1.74159	+	5.36005i	0.0978172	+	0.301051i	−0.890160	+	0.455647i	$0.849408\pi$
$318$	37.2223			2.08732
$319$	−2.22955	−	6.86185i	−0.124831	−	0.384190i
$320$	24.6485	+	4.78487i	1.37789	+	0.267483i
$321$	10.2113	−	31.4271i	0.569937	−	1.75409i
$322$	−6.44939	+	19.8492i	−0.359410	+	1.10615i
$323$	−1.67184	+	1.21466i	−0.0930235	+	0.0675855i
$324$	5.14553			0.285863
$325$	9.44389	−	11.2661i	0.523853	−	0.624929i
$326$	51.5468			2.85491
$327$	−37.8772	+	27.5194i	−2.09462	+	1.52183i
$328$	2.59369	−	7.98256i	0.143213	−	0.440763i
$329$	0.301956	−	0.929326i	0.0166474	−	0.0512354i
$330$	2.19920	+	17.8746i	0.121062	+	0.983965i
$331$	−7.93610	−	24.4248i	−0.436208	−	1.34251i	−0.891844	−	0.452343i	$-0.850588\pi$
$331$	−7.93610	−	24.4248i	−0.436208	−	1.34251i	0.455636	−	0.890166i	$-0.349412\pi$
$332$	13.7551			0.754909
$333$	18.2925	+	56.2984i	1.00242	+	3.08514i
$334$	16.3774	+	11.8989i	0.896134	+	0.651079i
$335$	−3.80518	+	6.86872i	−0.207899	+	0.375278i
$336$	−8.79263	+	6.38822i	−0.479677	+	0.348506i
$337$	−18.0928	−	13.1452i	−0.985575	−	0.716062i	−0.0266275	−	0.999645i	$-0.508477\pi$
$337$	−18.0928	−	13.1452i	−0.985575	−	0.716062i	−0.958948	+	0.283583i	$0.908477\pi$
$338$	−7.45218	−	5.41433i	−0.405345	−	0.294501i
$339$	−29.4168	+	21.3725i	−1.59770	+	1.16080i
$340$	3.77181	+	4.04277i	0.204555	+	0.219250i
$341$	−3.73317	−	2.71231i	−0.202163	−	0.146880i
$342$	−6.95676	−	21.4107i	−0.376179	−	1.15776i
$343$	16.3929			0.885136
$344$	−0.190269	−	0.585587i	−0.0102586	−	0.0315727i
$345$	22.7065	−	40.9875i	1.22248	−	2.20669i
$346$	−3.19926	+	9.84630i	−0.171993	+	0.529340i
$347$	4.65902	−	14.3390i	0.250109	−	0.769758i	−0.744645	−	0.667461i	$-0.767381\pi$
$347$	4.65902	−	14.3390i	0.250109	−	0.769758i	0.994754	−	0.102296i	$-0.0326190\pi$
$348$	30.8921	−	22.4444i	1.65599	−	1.20315i
$349$	34.4261			1.84279			0.921394	−	0.388630i	$-0.127052\pi$
$349$	34.4261			1.84279			0.921394	+	0.388630i	$0.127052\pi$
$350$	−7.54016	−	12.0535i	−0.403039	−	0.644289i
$351$	18.0572			0.963823
$352$	−8.61908	+	6.26213i	−0.459399	+	0.333773i
$353$	10.1435	−	31.2185i	0.539884	−	1.66159i	−0.192968	−	0.981205i	$-0.561811\pi$
$353$	10.1435	−	31.2185i	0.539884	−	1.66159i	0.732853	−	0.680387i	$-0.238189\pi$
$354$	−24.3121	+	74.8248i	−1.29217	+	3.97690i
$355$	12.1449	−	5.66693i	0.644587	−	0.300769i
$356$	3.19847	+	9.84387i	0.169518	+	0.521724i
$357$	−3.83870			−0.203166
$358$	9.20323	+	28.3246i	0.486406	+	1.49700i
$359$	9.38675	+	6.81987i	0.495414	+	0.359939i	0.807262	−	0.590193i	$-0.200948\pi$
$359$	9.38675	+	6.81987i	0.495414	+	0.359939i	−0.311849	+	0.950132i	$0.600948\pi$
$360$	−10.4342	+	4.86867i	−0.549929	+	0.256601i
$361$	11.9165	−	8.65782i	0.627182	−	0.455675i
$362$	23.5068	+	17.0787i	1.23549	+	0.897638i
$363$	21.2977	+	15.4737i	1.11784	+	0.812158i
$364$	7.90801	−	5.74551i	0.414493	−	0.301147i
$365$	16.6472	+	3.23162i	0.871352	+	0.169151i
$366$	16.7539	+	12.1724i	0.875738	+	0.636261i
$367$	5.27258	+	16.2273i	0.275226	+	0.847060i	0.989159	+	0.146846i	$0.0469121\pi$
$367$	5.27258	+	16.2273i	0.275226	+	0.847060i	−0.713933	+	0.700214i	$0.753088\pi$
$368$	20.7804			1.08326
$369$	−13.3654	−	41.1344i	−0.695774	−	2.14137i
$370$	−37.0725	−	39.7357i	−1.92731	−	2.06576i
$371$	2.56134	−	7.88300i	0.132978	−	0.409265i
$372$	7.54671	−	23.2264i	0.391279	−	1.20423i
$373$	−4.02652	+	2.92544i	−0.208485	+	0.151473i	−0.687128	−	0.726536i	$-0.741129\pi$
$373$	−4.02652	+	2.92544i	−0.208485	+	0.151473i	0.478643	+	0.878010i	$0.341129\pi$
$374$	−2.82101			−0.145871
$375$	11.4612	+	29.7915i	0.591854	+	1.53843i
$376$	0.726489			0.0374658
$377$	12.8659	−	9.34762i	0.662628	−	0.481427i
$378$	5.39663	−	16.6091i	0.277573	−	0.854281i
$379$	0.376056	−	1.15738i	0.0193167	−	0.0594507i	−0.940934	−	0.338591i	$-0.890050\pi$
$379$	0.376056	−	1.15738i	0.0193167	−	0.0594507i	0.960250	+	0.279141i	$0.0900496\pi$
$380$	7.79446	+	8.35440i	0.399847	+	0.428572i
$381$	15.3244	+	47.1636i	0.785092	+	2.41626i
$382$	−26.8888			−1.37575
$383$	2.55107	+	7.85140i	0.130354	+	0.401188i	0.994838	−	0.101471i	$-0.0323551\pi$
$383$	2.55107	+	7.85140i	0.130354	+	0.401188i	−0.864485	+	0.502659i	$0.832355\pi$
$384$	−17.9555	−	13.0455i	−0.916289	−	0.665723i
$385$	3.93684	+	0.764237i	0.200640	+	0.0389491i
$386$	25.3785	−	18.4386i	1.29173	−	0.938499i
$387$	−2.56688	−	1.86495i	−0.130482	−	0.0948007i
$388$	−34.2044	−	24.8509i	−1.73646	−	1.26162i
$389$	2.32449	−	1.68884i	0.117856	−	0.0856275i	−0.527296	−	0.849682i	$-0.676794\pi$
$389$	2.32449	−	1.68884i	0.117856	−	0.0856275i	0.645152	+	0.764054i	$0.276794\pi$
$390$	−35.9727	+	16.7851i	−1.82155	+	0.849949i
$391$	5.93794	+	4.31416i	0.300294	+	0.218177i
$392$	1.60390	+	4.93628i	0.0810090	+	0.249320i
$393$	−45.2035			−2.28021
$394$	−1.91497	−	5.89367i	−0.0964748	−	0.296919i
$395$	1.14589	−	0.534680i	0.0576558	−	0.0269027i
$396$	5.25018	−	16.1584i	0.263832	−	0.811990i
$397$	−9.15942	+	28.1898i	−0.459698	+	1.41480i	0.405832	+	0.913948i	$0.366982\pi$
$397$	−9.15942	+	28.1898i	−0.459698	+	1.41480i	−0.865530	+	0.500857i	$0.833018\pi$
$398$	36.2026	−	26.3027i	1.81467	−	1.31844i
$399$	−7.93269			−0.397131
$400$	−9.09408	+	10.8488i	−0.454704	+	0.542439i
$401$	−32.7151			−1.63371			−0.816856	−	0.576841i	$-0.804285\pi$
$401$	−32.7151			−1.63371			−0.816856	+	0.576841i	$0.804285\pi$
$402$	17.1539	−	12.4630i	0.855559	−	0.621600i
$403$	3.14304	−	9.67330i	0.156566	−	0.481861i
$404$	6.96092	−	21.4235i	0.346319	−	1.06586i
$405$	−2.25490	+	4.07031i	−0.112047	+	0.202255i
$406$	−4.75285	−	14.6278i	−0.235880	−	0.725964i
$407$	15.3287			0.759817
$408$	−0.881930	−	2.71430i	−0.0436620	−	0.134378i
$409$	13.2788	+	9.64764i	0.656596	+	0.477045i	0.865512	−	0.500889i	$-0.166993\pi$
$409$	13.2788	+	9.64764i	0.656596	+	0.477045i	−0.208916	+	0.977934i	$0.566993\pi$
$410$	27.0870	+	29.0329i	1.33773	+	1.43383i
$411$	−38.9372	+	28.2895i	−1.92063	+	1.39542i
$412$	2.86781	+	2.08359i	0.141287	+	0.102651i
$413$	14.1736	+	10.2977i	0.697435	+	0.506716i
$414$	−64.6880	+	46.9986i	−3.17924	+	2.30986i
$415$	−6.02782	+	10.8808i	−0.295894	+	0.534117i
$416$	−18.9980	−	13.8029i	−0.931456	−	0.676742i
$417$	8.41790	+	25.9076i	0.412226	+	1.26870i
$418$	−5.82963			−0.285136
$419$	6.40997	+	19.7279i	0.313148	+	0.963769i	0.976510	+	0.215471i	$0.0691287\pi$
$419$	6.40997	+	19.7279i	0.313148	+	0.963769i	−0.663363	+	0.748298i	$0.730871\pi$
$420$	2.59180	+	21.0656i	0.126467	+	1.02789i
$421$	−5.97713	+	18.3957i	−0.291308	+	0.896552i	0.693129	+	0.720813i	$0.256232\pi$
$421$	−5.97713	+	18.3957i	−0.291308	+	0.896552i	−0.984437	+	0.175739i	$0.943768\pi$
$422$	16.4253	−	50.5519i	0.799571	−	2.46083i
$423$	3.02865	−	2.20045i	0.147258	−	0.106989i
$424$	6.16244			0.299274
$425$	−4.85088	+	1.21200i	−0.235302	+	0.0587908i
$426$	−36.1891			−1.75337
$427$	3.73075	−	2.71055i	0.180544	−	0.131173i
$428$	8.84375	−	27.2183i	0.427479	−	1.31564i
$429$	3.46005	−	10.6489i	0.167053	−	0.514135i
$430$	2.85943	+	0.555084i	0.137894	+	0.0267685i
$431$	−8.85375	−	27.2490i	−0.426470	−	1.31254i	−0.901580	−	0.432613i	$-0.857592\pi$
$431$	−8.85375	−	27.2490i	−0.426470	−	1.31254i	0.475110	−	0.879927i	$-0.342408\pi$
$432$	−17.3884			−0.836599
$433$	11.0722	+	34.0766i	0.532094	+	1.63762i	0.749846	+	0.661612i	$0.230127\pi$
$433$	11.0722	+	34.0766i	0.532094	+	1.63762i	−0.217752	+	0.976004i	$0.569873\pi$
$434$	−7.95821	−	5.78198i	−0.382006	−	0.277544i
$435$	4.21672	+	34.2725i	0.202176	+	1.64324i
$436$	−32.8046	+	23.8339i	−1.57106	+	1.14144i
$437$	12.2708	+	8.91524i	0.586991	+	0.426474i
$438$	−37.0458	−	26.9153i	−1.77011	−	1.28606i
$439$	−10.8138	+	7.85667i	−0.516113	+	0.374978i	−0.815138	−	0.579267i	$-0.803339\pi$
$439$	−10.8138	+	7.85667i	−0.516113	+	0.374978i	0.299024	+	0.954245i	$0.403339\pi$
$440$	0.364095	+	2.95928i	0.0173575	+	0.141078i
$441$	21.6379	+	15.7208i	1.03037	+	0.748611i
$442$	−1.92147	−	5.91369i	−0.0913952	−	0.281286i
$443$	7.68129			0.364949			0.182475	−	0.983211i	$-0.441589\pi$
$443$	7.68129			0.364949			0.182475	+	0.983211i	$0.441589\pi$
$444$	25.0694	+	77.1556i	1.18974	+	3.66164i
$445$	−9.18853	−	1.78372i	−0.435578	−	0.0845563i
$446$	−12.9896	+	39.9777i	−0.615073	+	1.89300i
$447$	−9.48999	+	29.2072i	−0.448861	+	1.38145i
$448$	−12.2144	+	8.87425i	−0.577074	+	0.419269i
$449$	16.0626			0.758042			0.379021	−	0.925388i	$-0.376261\pi$
$449$	16.0626			0.758042			0.379021	+	0.925388i	$0.376261\pi$
$450$	3.77283	−	54.3393i	0.177853	−	2.56158i
$451$	−11.1999			−0.527383
$452$	−25.4772	+	18.5103i	−1.19835	+	0.870650i
$453$	9.05420	−	27.8659i	0.425403	−	1.30926i
$454$	10.4711	−	32.2266i	0.491431	−	1.51247i
$455$	1.07943	+	8.77336i	0.0506045	+	0.411302i
$456$	−1.82251	−	5.60912i	−0.0853470	−	0.262671i
$457$	5.84007			0.273187			0.136594	−	0.990627i	$-0.456385\pi$
$457$	5.84007			0.273187			0.136594	+	0.990627i	$0.456385\pi$
$458$	4.58068	+	14.0979i	0.214041	+	0.658751i
$459$	−4.96867	−	3.60995i	−0.231917	−	0.168498i
$460$	19.6656	−	35.4983i	0.916913	−	1.65512i
$461$	−26.0227	+	18.9066i	−1.21200	+	0.880567i	−0.995411	−	0.0956966i	$-0.969492\pi$
$461$	−26.0227	+	18.9066i	−1.21200	+	0.880567i	−0.216586	+	0.976264i	$0.569492\pi$
$462$	−8.76085	−	6.36513i	−0.407592	−	0.296133i
$463$	−2.31305	−	1.68053i	−0.107496	−	0.0781008i	0.532738	−	0.846280i	$-0.321163\pi$
$463$	−2.31305	−	1.68053i	−0.107496	−	0.0781008i	−0.640235	+	0.768179i	$0.721163\pi$
$464$	−12.3893	+	9.00138i	−0.575161	+	0.417879i
$465$	15.0658	+	16.1481i	0.698660	+	0.748850i
$466$	−15.0732	−	10.9513i	−0.698252	−	0.507310i
$467$	0.214519	+	0.660221i	0.00992674	+	0.0305514i	0.955897	−	0.293701i	$-0.0948871\pi$
$467$	0.214519	+	0.660221i	0.00992674	+	0.0305514i	−0.945970	+	0.324253i	$0.894887\pi$
$468$	37.4490			1.73108
$469$	−1.45905	−	4.49048i	−0.0673725	−	0.207351i
$470$	−1.66546	+	3.00631i	−0.0768218	+	0.138671i
$471$	−5.13886	+	15.8158i	−0.236786	+	0.728753i
$472$	−4.02505	+	12.3878i	−0.185268	+	0.570196i
$473$	−0.664694	+	0.482928i	−0.0305627	+	0.0222051i
$474$	−3.41448			−0.156832
$475$	−10.0244	+	2.50461i	−0.459950	+	0.114919i
$476$	−3.32461			−0.152383
$477$	25.6905	−	18.6653i	1.17629	−	0.854624i
$478$	7.09398	−	21.8330i	0.324471	−	0.998619i
$479$	7.86527	−	24.2068i	0.359374	−	1.10604i	−0.594056	−	0.804423i	$-0.702474\pi$
$479$	7.86527	−	24.2068i	0.359374	−	1.10604i	0.953430	−	0.301615i	$-0.0975256\pi$
$480$	46.2065	−	21.5603i	2.10903	−	0.984089i
$481$	10.4409	+	32.1337i	0.476062	+	1.46517i
$482$	−4.17669			−0.190243
$483$	8.70652	+	26.7959i	0.396160	+	1.21926i
$484$	18.4454	+	13.4014i	0.838429	+	0.609155i
$485$	34.6472	−	16.1667i	1.57325	−	0.734091i
$486$	−21.3591	+	15.5183i	−0.968867	+	0.703923i
$487$	10.3902	+	7.54895i	0.470827	+	0.342076i	0.797763	−	0.602971i	$-0.206016\pi$
$487$	10.3902	+	7.54895i	0.470827	+	0.342076i	−0.326937	+	0.945046i	$0.606016\pi$
$488$	2.77373	+	2.01523i	0.125561	+	0.0912252i
$489$	56.2971	−	40.9022i	2.54584	−	1.84966i
$490$	−24.1039	−	4.67916i	−1.08890	−	0.211383i
$491$	8.18798	+	5.94891i	0.369518	+	0.268471i	0.757011	−	0.653402i	$-0.226659\pi$
$491$	8.18798	+	5.94891i	0.369518	+	0.268471i	−0.387493	+	0.921873i	$0.626659\pi$
$492$	−18.3169	−	56.3736i	−0.825790	−	2.54152i
$493$	−5.40896			−0.243607
$494$	−3.97074	−	12.2207i	−0.178652	−	0.549834i
$495$	10.4812	+	11.2341i	0.471093	+	0.504935i
$496$	−3.02662	+	9.31499i	−0.135899	+	0.418256i
$497$	−2.49024	+	7.66418i	−0.111703	+	0.343786i
$498$	27.1736	−	19.7428i	1.21768	−	0.884697i
$499$	−40.4093			−1.80897			−0.904483	−	0.426509i	$-0.859743\pi$
$499$	−40.4093			−1.80897			−0.904483	+	0.426509i	$0.859743\pi$
$500$	9.92629	+	25.8018i	0.443917	+	1.15389i
$501$	27.3284			1.22094
$502$	−32.3441	+	23.4994i	−1.44359	+	1.04883i
$503$	7.10833	−	21.8772i	0.316945	−	0.975455i	−0.658002	−	0.753016i	$-0.728598\pi$
$503$	7.10833	−	21.8772i	0.316945	−	0.975455i	0.974947	−	0.222439i	$-0.0714018\pi$
$504$	2.13946	−	6.58458i	0.0952991	−	0.293301i
$505$	13.8964	+	14.8947i	0.618380	+	0.662804i
$506$	6.39830	+	19.6919i	0.284439	+	0.875414i
$507$	−12.4352			−0.552266
$508$	13.2721	+	40.8473i	0.588854	+	1.81231i
$509$	−9.06062	−	6.58293i	−0.401605	−	0.291783i	0.368589	−	0.929592i	$-0.379841\pi$
$509$	−9.06062	−	6.58293i	−0.401605	−	0.291783i	−0.770194	+	0.637809i	$0.779841\pi$
$510$	13.2540	+	2.57292i	0.586895	+	0.113931i
$511$	−8.24935	+	5.99351i	−0.364930	+	0.265137i
$512$	22.8737	+	16.6187i	1.01089	+	0.734451i
$513$	−10.2678	−	7.45997i	−0.453333	−	0.329366i
$514$	34.4027	−	24.9950i	1.51744	−	1.10248i
$515$	−2.90494	+	1.35547i	−0.128007	+	0.0597291i
$516$	−3.51785	−	2.55586i	−0.154865	−	0.112516i
$517$	−0.299565	−	0.921965i	−0.0131748	−	0.0405480i
$518$	32.6771			1.43575
$519$	4.31892	+	13.2923i	0.189580	+	0.583466i
$520$	−5.95555	+	2.77891i	−0.261168	+	0.121863i
$521$	−5.36881	+	16.5235i	−0.235212	+	0.723908i	0.761881	+	0.647717i	$0.224276\pi$
$521$	−5.36881	+	16.5235i	−0.235212	+	0.723908i	−0.997093	+	0.0761910i	$0.975724\pi$
$522$	18.2089	−	56.0413i	0.796983	−	2.45286i
$523$	8.85151	−	6.43100i	0.387050	−	0.281208i	−0.377196	−	0.926134i	$-0.623112\pi$
$523$	8.85151	−	6.43100i	0.387050	−	0.281208i	0.764245	+	0.644926i	$0.223112\pi$
$524$	−39.1497			−1.71026
$525$	−17.7995	−	7.18123i	−0.776832	−	0.313415i
$526$	−2.27309			−0.0991116
$527$	−2.79870	+	2.03338i	−0.121913	+	0.0885753i
$528$	−3.33188	+	10.2545i	−0.145002	+	0.446269i
$529$	9.53969	−	29.3601i	0.414769	−	1.27653i
$530$	−14.1272	+	25.5010i	−0.613647	+	1.10769i
$531$	20.7412	+	63.8348i	0.900091	+	2.77020i
$532$	−6.87033			−0.297866
$533$	−7.62860	−	23.4784i	−0.330432	−	1.01696i
$534$	20.4477	+	14.8561i	0.884858	+	0.642887i
$535$	17.6551	+	18.9234i	0.763298	+	0.818132i
$536$	2.83996	−	2.06335i	0.122667	−	0.0891231i
$537$	32.5268	+	23.6321i	1.40364	+	1.01980i
$538$	37.3250	+	27.1182i	1.60919	+	1.16915i
$539$	5.60312	−	4.07091i	0.241344	−	0.175346i
$540$	−16.4555	+	29.7038i	−0.708132	+	1.27825i
$541$	−29.9504	−	21.7602i	−1.28767	−	0.935546i	−0.287913	−	0.957657i	$-0.592961\pi$
$541$	−29.9504	−	21.7602i	−1.28767	−	0.935546i	−0.999756	+	0.0221108i	$0.992961\pi$
$542$	10.2851	+	31.6544i	0.441785	+	1.35967i
$543$	39.2250			1.68331
$544$	2.46811	+	7.59607i	0.105819	+	0.325679i
$545$	−4.47777	−	36.3943i	−0.191807	−	1.55896i
$546$	7.37597	−	22.7009i	0.315662	−	0.971509i
$547$	9.33587	−	28.7329i	0.399173	−	1.22853i	−0.526490	−	0.850181i	$-0.676492\pi$
$547$	9.33587	−	28.7329i	0.399173	−	1.22853i	0.925664	−	0.378348i	$-0.123508\pi$
$548$	−33.7226	+	24.5009i	−1.44056	+	1.04663i
$549$	17.6673			0.754020
$550$	−13.0806	−	5.27739i	−0.557757	−	0.225029i
$551$	−11.1776			−0.476183
$552$	−16.9468	+	12.3126i	−0.721303	+	0.524057i
$553$	−0.234957	+	0.723123i	−0.00999138	+	0.0307503i
$554$	18.6066	−	57.2653i	0.790520	−	2.43297i
$555$	−72.0190	−	13.9806i	−3.05704	−	0.593445i
$556$	7.29055	+	22.4380i	0.309188	+	0.951583i
$557$	−31.5929			−1.33863			−0.669317	−	0.742977i	$-0.733413\pi$
$557$	−31.5929			−1.33863			−0.669317	+	0.742977i	$0.733413\pi$
$558$	−11.6458	−	35.8422i	−0.493007	−	1.51732i
$559$	−1.46511	−	1.06446i	−0.0619675	−	0.0450220i
$560$	−1.03945	−	8.44839i	−0.0439247	−	0.357010i
$561$	−3.08098	+	2.23846i	−0.130079	+	0.0945078i
$562$	−42.4391	−	30.8338i	−1.79019	−	1.30065i
$563$	6.78777	+	4.93161i	0.286071	+	0.207842i	0.721561	−	0.692351i	$-0.243425\pi$
$563$	6.78777	+	4.93161i	0.286071	+	0.207842i	−0.435490	+	0.900193i	$0.643425\pi$
$564$	4.15069	−	3.01566i	0.174776	−	0.126982i
$565$	−3.47759	−	28.2651i	−0.146303	−	1.18912i
$566$	14.9191	+	10.8393i	0.627095	+	0.455611i
$567$	−0.864612	−	2.66100i	−0.0363103	−	0.111752i
$568$	−5.99138			−0.251393
$569$	−5.30834	−	16.3374i	−0.222537	−	0.684899i	−0.998532	−	0.0541600i	$-0.982752\pi$
$569$	−5.30834	−	16.3374i	−0.222537	−	0.684899i	0.775995	−	0.630739i	$-0.217248\pi$
$570$	27.3894	+	5.31694i	1.14721	+	0.222702i
$571$	12.9552	−	39.8719i	0.542157	−	1.66859i	−0.185497	−	0.982645i	$-0.559389\pi$
$571$	12.9552	−	39.8719i	0.542157	−	1.66859i	0.727654	−	0.685944i	$-0.240611\pi$
$572$	2.99667	−	9.22279i	0.125297	−	0.385624i
$573$	−29.3668	+	21.3362i	−1.22681	+	0.891332i
$574$	−23.8755			−0.996543
$575$	19.4626	+	31.1125i	0.811645	+	1.29748i
$576$	−57.8420			−2.41008
$577$	20.1921	−	14.6704i	0.840608	−	0.610737i	−0.0819327	−	0.996638i	$-0.526109\pi$
$577$	20.1921	−	14.6704i	0.840608	−	0.610737i	0.922540	+	0.385901i	$0.126109\pi$
$578$	−0.653530	+	2.01136i	−0.0271833	+	0.0836615i
$579$	13.0863	−	40.2755i	0.543849	−	1.67379i
$580$	3.65200	+	29.6826i	0.151641	+	1.23250i
$581$	−2.31129	−	7.11342i	−0.0958884	−	0.295114i
$582$	−103.241			−4.27947
$583$	−2.54105	−	7.82056i	−0.105240	−	0.323894i
$584$	−6.13320	−	4.45603i	−0.253794	−	0.184392i
$585$	−16.4111	+	29.6236i	−0.678514	+	1.22478i
$586$	−1.35085	+	0.981452i	−0.0558032	+	0.0405434i
$587$	−13.4933	−	9.80344i	−0.556927	−	0.404631i	0.273406	−	0.961899i	$-0.411850\pi$
$587$	−13.4933	−	9.80344i	−0.556927	−	0.404631i	−0.830333	+	0.557268i	$0.811850\pi$
$588$	29.6541	+	21.5450i	1.22292	+	0.888501i
$589$	−5.78353	+	4.20198i	−0.238306	+	0.173140i
$590$	−42.0352	−	45.0549i	−1.73056	−	1.85488i
$591$	−6.76805	−	4.91727i	−0.278400	−	0.202270i
$592$	−10.0541	−	30.9434i	−0.413222	−	1.27177i
$593$	5.09029			0.209033			0.104517	−	0.994523i	$-0.466670\pi$
$593$	5.09029			0.209033			0.104517	+	0.994523i	$0.466670\pi$
$594$	−5.35388	−	16.4776i	−0.219673	−	0.676082i
$595$	1.45693	−	2.62989i	0.0597282	−	0.107815i
$596$	−8.21907	+	25.2957i	−0.336666	+	1.03615i
$597$	18.6677	−	57.4533i	0.764018	−	2.35141i
$598$	−36.9222	+	26.8256i	−1.50986	+	1.09698i
$599$	1.44234			0.0589323			0.0294662	−	0.999566i	$-0.490619\pi$
$599$	1.44234			0.0589323			0.0294662	+	0.999566i	$0.490619\pi$
$600$	0.988396	−	14.2357i	0.0403511	−	0.581168i
$601$	−10.1686			−0.414787			−0.207393	−	0.978258i	$-0.566498\pi$
$601$	−10.1686			−0.414787			−0.207393	+	0.978258i	$0.566498\pi$
$602$	−1.41696	+	1.02949i	−0.0577512	+	0.0419587i
$603$	5.58984	−	17.2038i	0.227636	−	0.700591i
$604$	7.84163	−	24.1341i	0.319071	−	0.982001i
$605$	−18.6843	+	8.71823i	−0.759623	+	0.354446i
$606$	−16.9978	−	52.3140i	−0.690490	−	2.12511i
$607$	−10.6123			−0.430741			−0.215371	−	0.976532i	$-0.569096\pi$
$607$	−10.6123			−0.430741			−0.215371	+	0.976532i	$0.569096\pi$
$608$	5.10036	+	15.6973i	0.206847	+	0.636610i
$609$	−16.7979	−	12.2044i	−0.680686	−	0.494548i
$610$	−14.6980	+	6.85821i	−0.595105	+	0.277681i
$611$	1.72868	−	1.25596i	0.0699347	−	0.0508106i
$612$	−10.3045	−	7.48669i	−0.416537	−	0.302632i
$613$	7.32360	+	5.32091i	0.295797	+	0.214909i	0.725778	−	0.687929i	$-0.241480\pi$
$613$	7.32360	+	5.32091i	0.295797	+	0.214909i	−0.429981	+	0.902838i	$0.641480\pi$
$614$	39.5387	−	28.7266i	1.59565	−	1.15931i
$615$	52.6206	+	10.2149i	2.12187	+	0.411906i
$616$	−1.45043	−	1.05380i	−0.0584393	−	0.0424586i
$617$	3.78931	+	11.6623i	0.152552	+	0.469506i	0.997905	−	0.0647021i	$-0.0206097\pi$
$617$	3.78931	+	11.6623i	0.152552	+	0.469506i	−0.845353	+	0.534208i	$0.820610\pi$
$618$	8.65606			0.348198
$619$	12.6489	+	38.9294i	0.508404	+	1.56471i	0.794972	+	0.606646i	$0.207485\pi$
$619$	12.6489	+	38.9294i	0.508404	+	1.56471i	−0.286569	+	0.958060i	$0.592515\pi$
$620$	13.0481	+	13.9855i	0.524026	+	0.561671i
$621$	−13.9297	+	42.8713i	−0.558980	+	1.72036i
$622$	10.2168	−	31.4441i	0.409656	−	1.26079i
$623$	4.55330	−	3.30816i	0.182424	−	0.132539i
$624$	−23.7660			−0.951400
$625$	−24.7601	−	3.45490i	−0.990405	−	0.138196i
$626$	−16.3977			−0.655385
$627$	−6.36685	+	4.62579i	−0.254267	+	0.184736i
$628$	−4.45065	+	13.6977i	−0.177600	+	0.546597i
$629$	3.55114	−	10.9293i	0.141593	−	0.435779i
$630$	22.3432	+	23.9484i	0.890176	+	0.954125i
$631$	10.6954	+	32.9170i	0.425776	+	1.31040i	0.902249	+	0.431215i	$0.141915\pi$
$631$	10.6954	+	32.9170i	0.425776	+	1.31040i	−0.476474	+	0.879189i	$0.658085\pi$
$632$	−0.565292			−0.0224861
$633$	−22.1738	−	68.2438i	−0.881328	−	2.71245i
$634$	9.64281	+	7.00591i	0.382965	+	0.278240i
$635$	−38.1279	−	7.40156i	−1.51306	−	0.293722i
$636$	35.2082	−	25.5803i	1.39610	−	1.01432i
$637$	12.3503	+	8.97303i	0.489338	+	0.355525i
$638$	−12.3446	−	8.96885i	−0.488726	−	0.355080i
$639$	−24.9774	+	18.1472i	−0.988091	+	0.717890i
$640$	15.7522	−	7.35011i	0.622661	−	0.290539i
$641$	19.6292	+	14.2615i	0.775307	+	0.563294i	0.903567	−	0.428447i	$-0.140939\pi$
$641$	19.6292	+	14.2615i	0.775307	+	0.563294i	−0.128260	+	0.991741i	$0.540939\pi$
$642$	−21.5955	−	66.4641i	−0.852306	−	2.62313i
$643$	−26.2466			−1.03506			−0.517532	−	0.855664i	$-0.673149\pi$
$643$	−26.2466			−1.03506			−0.517532	+	0.855664i	$0.673149\pi$
$644$	7.54052	+	23.2073i	0.297138	+	0.914497i
$645$	3.56339	−	1.66271i	0.140308	−	0.0654690i
$646$	−1.35052	+	4.15648i	−0.0531356	+	0.163535i
$647$	8.56805	−	26.3698i	0.336845	−	1.03670i	−0.628961	−	0.777437i	$-0.716520\pi$
$647$	8.56805	−	26.3698i	0.336845	−	1.03670i	0.965806	−	0.259265i	$-0.0834805\pi$
$648$	1.68292	−	1.22271i	0.0661114	−	0.0480328i
$649$	17.3807			0.682252
$650$	2.15343	−	31.0154i	0.0844646	−	1.21653i
$651$	−13.2796			−0.520467
$652$	48.7576	−	35.4245i	1.90950	−	1.38733i
$653$	0.426420	−	1.31239i	0.0166871	−	0.0513576i	−0.942366	−	0.334583i	$-0.891404\pi$
$653$	0.426420	−	1.31239i	0.0166871	−	0.0513576i	0.959053	+	0.283226i	$0.0914045\pi$
$654$	−30.5975	+	94.1695i	−1.19646	+	3.68232i
$655$	17.1564	−	30.9689i	0.670354	−	1.21006i
$656$	7.34604	+	22.6088i	0.286815	+	0.882724i
$657$	−39.0654			−1.52409
$658$	−0.638598	−	1.96540i	−0.0248951	−	0.0766194i
$659$	−6.06660	−	4.40765i	−0.236321	−	0.171697i	0.463322	−	0.886190i	$-0.346658\pi$
$659$	−6.06660	−	4.40765i	−0.236321	−	0.171697i	−0.699643	+	0.714493i	$0.746658\pi$
$660$	14.3642	+	15.3961i	0.559124	+	0.599291i
$661$	9.08267	−	6.59895i	0.353275	−	0.256669i	−0.396967	−	0.917833i	$-0.629937\pi$
$661$	9.08267	−	6.59895i	0.353275	−	0.256669i	0.750242	+	0.661164i	$0.229937\pi$
$662$	−43.9406	−	31.9247i	−1.70780	−	1.24079i
$663$	−6.79104	−	4.93398i	−0.263742	−	0.191620i
$664$	4.49880	−	3.26857i	0.174587	−	0.126845i
$665$	3.01074	−	5.43469i	0.116752	−	0.210748i
$666$	101.282	+	73.5855i	3.92459	+	2.85138i
$667$	12.2680	+	37.7570i	0.475019	+	1.46196i
$668$	23.6685			0.915763
$669$	17.5356	+	53.9690i	0.677965	+	2.08656i
$670$	2.02790	+	16.4823i	0.0783446	+	0.636767i
$671$	1.41373	−	4.35102i	0.0545766	−	0.167969i
$672$	−9.47434	+	29.1590i	−0.365481	+	1.12483i
$673$	−11.8936	+	8.64119i	−0.458464	+	0.333093i	−0.792928	−	0.609315i	$-0.791445\pi$
$673$	−11.8936	+	8.64119i	−0.458464	+	0.333093i	0.334465	+	0.942408i	$0.391445\pi$
$674$	−47.2967			−1.82180
$675$	−16.2856	−	26.0339i	−0.626834	−	1.00204i
$676$	−10.7698			−0.414224
$677$	−2.31686	+	1.68329i	−0.0890440	+	0.0646943i	−0.631417	−	0.775444i	$-0.717526\pi$
$677$	−2.31686	+	1.68329i	−0.0890440	+	0.0646943i	0.542372	+	0.840138i	$0.317526\pi$
$678$	−23.7631	+	73.1353i	−0.912617	+	2.80874i
$679$	−7.10420	+	21.8645i	−0.272634	+	0.839081i
$680$	2.19429	+	0.425965i	0.0841473	+	0.0163350i
$681$	−14.1357	−	43.5051i	−0.541680	−	1.66712i
$682$	−9.75896			−0.373690
$683$	−14.3848	−	44.2718i	−0.550419	−	1.69401i	−0.707745	−	0.706468i	$-0.750287\pi$
$683$	−14.3848	−	44.2718i	−0.550419	−	1.69401i	0.157326	−	0.987547i	$-0.449713\pi$
$684$	−21.2944	−	15.4713i	−0.814211	−	0.591559i
$685$	−4.60308	−	37.4128i	−0.175875	−	1.42947i
$686$	28.0478	−	20.3779i	1.07087	−	0.778031i
$687$	16.1894	+	11.7623i	0.617666	+	0.448760i
$688$	1.41084	+	1.02504i	0.0537878	+	0.0390791i
$689$	14.6635	−	10.6536i	0.558634	−	0.405871i
$690$	−12.1010	−	98.3543i	−0.460678	−	3.74429i
$691$	22.5602	+	16.3910i	0.858231	+	0.623541i	0.927403	−	0.374063i	$-0.122036\pi$
$691$	22.5602	+	16.3910i	0.858231	+	0.623541i	−0.0691721	+	0.997605i	$0.522036\pi$
$692$	3.74052	+	11.5121i	0.142193	+	0.437626i
$693$	−9.23848			−0.350941
$694$	−9.85322	−	30.3251i	−0.374023	−	1.15112i
$695$	−20.9442	−	4.06578i	−0.794459	−	0.154224i
$696$	4.77032	−	14.6815i	0.180819	−	0.556503i
$697$	−2.59463	+	7.98546i	−0.0982788	+	0.302471i
$698$	58.9019	−	42.7947i	2.22947	−	1.61980i
$699$	−25.1521			−0.951338
$700$	−15.4157	−	6.21950i	−0.582659	−	0.235075i
$701$	−1.89977			−0.0717531			−0.0358766	−	0.999356i	$-0.511422\pi$
$701$	−1.89977			−0.0717531			−0.0358766	+	0.999356i	$0.511422\pi$
$702$	30.8953	−	22.4467i	1.16607	−	0.847197i
$703$	7.33844	−	22.5854i	0.276775	−	0.851825i
$704$	−4.62851	+	14.2451i	−0.174444	+	0.536882i
$705$	0.566563	+	4.60489i	0.0213380	+	0.173430i
$706$	−21.4522	−	66.0230i	−0.807363	−	2.48481i
$707$	−12.2488			−0.460663
$708$	28.4253	+	87.4840i	1.06829	+	3.28785i
$709$	−18.7697	−	13.6370i	−0.704909	−	0.512147i	0.176618	−	0.984279i	$-0.443484\pi$
$709$	−18.7697	−	13.6370i	−0.704909	−	0.512147i	−0.881527	+	0.472133i	$0.843484\pi$
$710$	13.7351	−	24.7932i	0.515468	−	0.930471i
$711$	−2.35664	+	1.71220i	−0.0883810	+	0.0642126i
$712$	3.38527	+	2.45954i	0.126868	+	0.0921752i
$713$	20.5416	+	14.9244i	0.769290	+	0.558922i
$714$	−6.56788	+	4.77185i	−0.245797	+	0.178582i
$715$	5.98237	+	6.41213i	0.223728	+	0.239800i
$716$	28.1708	+	20.4673i	1.05279	+	0.764897i
$717$	−9.57670	−	29.4741i	−0.357648	−	1.10073i
$718$	24.5381			0.915754
$719$	−5.93887	−	18.2780i	−0.221482	−	0.681653i	−0.998630	−	0.0523339i	$-0.983334\pi$
$719$	−5.93887	−	18.2780i	−0.221482	−	0.681653i	0.777147	−	0.629319i	$-0.216666\pi$
$720$	15.8032	−	28.5263i	0.588950	−	1.06311i
$721$	0.595640	−	1.83319i	0.0221828	−	0.0682716i
$722$	9.62622	−	29.6264i	0.358251	−	1.10258i
$723$	−4.56158	+	3.31419i	−0.169647	+	0.123256i
$724$	33.9719			1.26255
$725$	−25.0805	−	10.1188i	−0.931466	−	0.375802i
$726$	55.6748			2.06628
$727$	−0.964829	+	0.700989i	−0.0357835	+	0.0259983i	−0.605533	−	0.795820i	$-0.707040\pi$
$727$	−0.964829	+	0.700989i	−0.0357835	+	0.0259983i	0.569750	+	0.821818i	$0.307040\pi$
$728$	1.22115	−	3.75830i	0.0452587	−	0.139292i
$729$	−12.9429	+	39.8340i	−0.479365	+	1.47533i
$730$	32.4999	−	15.1647i	1.20287	−	0.561271i
$731$	0.190338	+	0.585800i	0.00703991	+	0.0216666i
$732$	24.2125			0.894921
$733$	2.61506	+	8.04832i	0.0965893	+	0.297271i	0.987665	−	0.156584i	$-0.0500482\pi$
$733$	2.61506	+	8.04832i	0.0965893	+	0.297271i	−0.891075	+	0.453855i	$0.850048\pi$
$734$	29.1932	+	21.2101i	1.07754	+	0.782879i
$735$	−30.0381	+	14.0160i	−1.10797	+	0.516988i
$736$	47.4262	−	34.4571i	1.74815	−	1.27011i
$737$	−3.78958	−	2.75329i	−0.139591	−	0.101419i
$738$	−74.0014	−	53.7652i	−2.72403	−	1.97912i
$739$	7.48395	−	5.43741i	0.275301	−	0.200018i	−0.441564	−	0.897230i	$-0.645576\pi$
$739$	7.48395	−	5.43741i	0.275301	−	0.200018i	0.716865	+	0.697212i	$0.245576\pi$
$740$	−62.3740	−	12.1083i	−2.29291	−	0.445111i
$741$	−14.0337	−	10.1961i	−0.515541	−	0.374563i
$742$	−5.41690	−	16.6715i	−0.198861	−	0.612030i
$743$	−28.6745			−1.05197			−0.525983	−	0.850495i	$-0.676303\pi$
$743$	−28.6745			−1.05197			−0.525983	+	0.850495i	$0.676303\pi$
$744$	−3.05094	−	9.38982i	−0.111853	−	0.344248i
$745$	−16.4081	−	17.5868i	−0.601145	−	0.644330i
$746$	−3.25265	+	10.0106i	−0.119088	+	0.366516i
$747$	8.85492	−	27.2526i	0.323984	−	0.997122i
$748$	−2.66836	+	1.93868i	−0.0975650	+	0.0708851i
$749$	−15.5619			−0.568619
$750$	56.6432	+	36.7250i	2.06832	+	1.34101i
$751$	−5.65205			−0.206246			−0.103123	−	0.994669i	$-0.532884\pi$
$751$	−5.65205			−0.206246			−0.103123	+	0.994669i	$0.532884\pi$
$752$	−1.66464	+	1.20944i	−0.0607034	+	0.0441036i
$753$	−16.6781	+	51.3299i	−0.607783	+	1.87056i
$754$	10.3932	−	31.9869i	0.378497	−	1.16489i
$755$	15.6546	+	16.7792i	0.569728	+	0.610656i
$756$	−6.30965	−	19.4191i	−0.229480	−	0.706267i
$757$	32.8071			1.19240			0.596198	−	0.802837i	$-0.296677\pi$
$757$	32.8071			1.19240			0.596198	+	0.802837i	$0.296677\pi$
$758$	−0.795309	−	2.44771i	−0.0288869	−	0.0889048i
$759$	22.6134	+	16.4296i	0.820815	+	0.596357i
$760$	4.53451	+	0.880260i	0.164484	+	0.0319304i
$761$	13.0355	−	9.47082i	0.472535	−	0.343317i	−0.325893	−	0.945407i	$-0.605665\pi$
$761$	13.0355	−	9.47082i	0.472535	−	0.343317i	0.798428	+	0.602090i	$0.205665\pi$
$762$	84.8480	+	61.6457i	3.07372	+	2.23319i
$763$	17.8379	+	12.9600i	0.645775	+	0.469183i
$764$	−25.4339	+	18.4788i	−0.920165	+	0.668539i
$765$	10.4380	−	4.87044i	0.377385	−	0.176091i
$766$	14.1248	+	10.2623i	0.510349	+	0.370790i
$767$	11.8385	+	36.4352i	0.427464	+	1.31560i
$768$	17.1798			0.619921
$769$	−2.06577	−	6.35778i	−0.0744936	−	0.229268i	0.906876	−	0.421398i	$-0.138460\pi$
$769$	−2.06577	−	6.35778i	−0.0744936	−	0.229268i	−0.981369	+	0.192130i	$0.938460\pi$
$770$	7.68581	−	3.58626i	0.276977	−	0.129240i
$771$	17.7396	−	54.5968i	0.638875	−	1.96625i
$772$	11.3338	−	34.8817i	0.407911	−	1.25542i
$773$	−34.7973	+	25.2817i	−1.25157	+	0.909320i	−0.998312	−	0.0580785i	$-0.981503\pi$
$773$	−34.7973	+	25.2817i	−1.25157	+	0.909320i	−0.253259	+	0.967398i	$0.581503\pi$
$774$	−6.71014			−0.241191
$775$	−16.7811	+	4.19279i	−0.602794	+	0.150609i
$776$	−17.0923			−0.613577
$777$	35.6884	−	25.9291i	1.28031	−	0.930203i
$778$	1.87774	−	5.77909i	0.0673202	−	0.207190i
$779$	−5.36182	+	16.5020i	−0.192107	+	0.591245i
$780$	−22.4909	+	40.5984i	−0.805305	+	1.45365i
$781$	2.47052	+	7.60347i	0.0884021	+	0.272074i
$782$	15.5225			0.555083
$783$	−10.2655	−	31.5938i	−0.366857	−	1.12907i
$784$	−11.8929	−	8.64067i	−0.424745	−	0.308595i
$785$	−8.88501	−	9.52330i	−0.317120	−	0.339901i
$786$	−77.3416	+	56.1919i	−2.75868	+	2.00430i
$787$	−6.98628	−	5.07583i	−0.249034	−	0.180934i	0.456265	−	0.889844i	$-0.349187\pi$
$787$	−6.98628	−	5.07583i	−0.249034	−	0.180934i	−0.705299	+	0.708910i	$0.749187\pi$
$788$	−5.86165	−	4.25874i	−0.208813	−	0.151711i
$789$	−2.48257	+	1.80369i	−0.0883818	+	0.0642131i
$790$	1.29592	−	2.33926i	0.0461067	−	0.0832271i
$791$	13.8535	+	10.0652i	0.492574	+	0.357876i
$792$	−2.12251	−	6.53242i	−0.0754202	−	0.232120i
$793$	10.0840			0.358093
$794$	19.3710	+	59.6177i	0.687450	+	2.11575i
$795$	4.80586	+	39.0609i	0.170446	+	1.38535i
$796$	16.1677	−	49.7590i	0.573048	−	1.76366i
$797$	0.741771	−	2.28294i	0.0262749	−	0.0808657i	−0.937059	−	0.349170i	$-0.886463\pi$
$797$	0.741771	−	2.28294i	0.0262749	−	0.0808657i	0.963334	+	0.268305i	$0.0864634\pi$
$798$	−13.5726	+	9.86104i	−0.480464	+	0.349077i
$799$	−0.726753			−0.0257107
$800$	−2.76606	+	39.8390i	−0.0977950	+	1.40852i
$801$	21.5625			0.761872
$802$	−55.9743	+	40.6677i	−1.97652	+	1.43603i
$803$	−3.12601	+	9.62088i	−0.110315	+	0.339514i
$804$	7.66073	−	23.5773i	0.270173	−	0.831508i
$805$	−21.6623	−	4.20518i	−0.763496	−	0.148213i
$806$	−6.64713	−	20.4578i	−0.234135	−	0.720594i
$807$	62.2828			2.19246
$808$	−2.81412	−	8.66097i	−0.0990004	−	0.304692i
$809$	−6.58772	−	4.78626i	−0.231612	−	0.168276i	0.465926	−	0.884824i	$-0.345721\pi$
$809$	−6.58772	−	4.78626i	−0.231612	−	0.168276i	−0.697538	+	0.716548i	$0.745721\pi$
$810$	1.20171	+	9.76720i	0.0422237	+	0.343185i
$811$	6.06839	−	4.40894i	0.213090	−	0.154819i	−0.476121	−	0.879380i	$-0.657957\pi$
$811$	6.06839	−	4.40894i	0.213090	−	0.154819i	0.689211	+	0.724561i	$0.257957\pi$
$812$	−14.5483	−	10.5700i	−0.510545	−	0.370933i
$813$	36.3506	+	26.4103i	1.27487	+	0.926249i
$814$	26.2269	−	19.0550i	0.919253	−	0.667876i
$815$	6.65533	+	54.0930i	0.233126	+	1.89480i
$816$	6.53949	+	4.75122i	0.228928	+	0.166326i
$817$	0.393334	+	1.21056i	0.0137610	+	0.0423521i
$818$	34.7125			1.21369
$819$	−6.29261	−	19.3667i	−0.219882	−	0.676726i
$820$	45.5735	+	8.84693i	1.59150	+	0.308948i
$821$	−2.07739	+	6.39354i	−0.0725013	+	0.223136i	−0.980740	−	0.195315i	$-0.937427\pi$
$821$	−2.07739	+	6.39354i	−0.0725013	+	0.223136i	0.908239	+	0.418451i	$0.137427\pi$
$822$	−31.4538	+	96.8048i	−1.09708	+	3.37646i
$823$	14.4399	−	10.4912i	0.503344	−	0.365701i	−0.306949	−	0.951726i	$-0.599308\pi$
$823$	14.4399	−	10.4912i	0.503344	−	0.365701i	0.810293	+	0.586025i	$0.199308\pi$
$824$	1.43308			0.0499235
$825$	−18.4736	+	4.61567i	−0.643168	+	0.160697i
$826$	37.0514			1.28918
$827$	−15.4752	+	11.2434i	−0.538127	+	0.390972i	−0.823389	−	0.567477i	$-0.807919\pi$
$827$	−15.4752	+	11.2434i	−0.538127	+	0.390972i	0.285262	+	0.958450i	$0.407919\pi$
$828$	−28.8889	+	88.9110i	−1.00396	+	3.08987i
$829$	5.07849	−	15.6300i	0.176383	−	0.542852i	−0.823311	−	0.567591i	$-0.807876\pi$
$829$	5.07849	−	15.6300i	0.176383	−	0.542852i	0.999694	+	0.0247392i	$0.00787555\pi$
$830$	3.21242	+	26.1098i	0.111505	+	0.906284i
$831$	−25.1185	−	77.3069i	−0.871352	−	2.68175i
$832$	−33.0147			−1.14458
$833$	−1.60448	−	4.93808i	−0.0555919	−	0.171094i
$834$	46.6082	+	33.8628i	1.61391	+	1.17257i
$835$	−10.3721	+	18.7227i	−0.358942	+	0.647926i
$836$	−5.51418	+	4.00629i	−0.190712	+	0.138560i
$837$	−17.1885	−	12.4882i	−0.594123	−	0.431656i
$838$	35.4907	+	25.7855i	1.22601	+	0.890746i
$839$	1.26929	−	0.922193i	0.0438208	−	0.0318376i	−0.565659	−	0.824639i	$-0.691378\pi$
$839$	1.26929	−	0.922193i	0.0438208	−	0.0318376i	0.609480	+	0.792801i	$0.291378\pi$
$840$	5.85342	+	6.27392i	0.201962	+	0.216471i
$841$	−0.207788	−	0.150967i	−0.00716511	−	0.00520576i
$842$	12.6408	+	38.9045i	0.435632	+	1.34074i
$843$	−70.8166			−2.43905
$844$	−19.2042	−	59.1044i	−0.661036	−	2.03446i
$845$	4.71960	−	8.51934i	0.162359	−	0.293074i
$846$	2.44657	−	7.52977i	0.0841149	−	0.258879i
$847$	3.83109	−	11.7909i	0.131638	−	0.405140i
$848$	−14.1203	+	10.2590i	−0.484894	+	0.352296i
$849$	24.8949			0.854390
$850$	−6.79306	+	8.10377i	−0.233000	+	0.277957i
$851$	−84.3457			−2.89133
$852$	−34.2309	+	24.8702i	−1.17273	+	0.852039i
$853$	−4.69789	+	14.4586i	−0.160853	+	0.495054i	−0.998707	−	0.0508404i	$-0.983810\pi$
$853$	−4.69789	+	14.4586i	−0.160853	+	0.495054i	0.837854	+	0.545894i	$0.183810\pi$
$854$	3.01373	−	9.27531i	0.103128	−	0.317395i
$855$	21.5701	−	10.0648i	0.737682	−	0.344208i
$856$	−3.57530	−	11.0036i	−0.122201	−	0.376096i
$857$	−47.2296			−1.61333			−0.806666	−	0.591007i	$-0.798730\pi$
$857$	−47.2296			−1.61333			−0.806666	+	0.591007i	$0.798730\pi$
$858$	−7.31754	−	22.5211i	−0.249817	−	0.768857i
$859$	3.20975	+	2.33202i	0.109515	+	0.0795676i	0.641195	−	0.767378i	$-0.278439\pi$
$859$	3.20975	+	2.33202i	0.109515	+	0.0795676i	−0.531680	+	0.846946i	$0.678439\pi$
$860$	3.08617	−	1.44003i	0.105238	−	0.0491047i
$861$	−26.0757	+	18.9451i	−0.888657	+	0.645647i
$862$	−49.0214	−	35.6161i	−1.66968	−	1.21309i
$863$	22.2550	+	16.1692i	0.757569	+	0.550406i	0.898164	−	0.439661i	$-0.144902\pi$
$863$	22.2550	+	16.1692i	0.757569	+	0.550406i	−0.140595	+	0.990067i	$0.544902\pi$
$864$	−39.6846	+	28.8326i	−1.35010	+	0.980904i
$865$	−10.7457	−	2.08601i	−0.365366	−	0.0709263i
$866$	61.3043	+	44.5402i	2.08320	+	1.51354i
$867$	0.882251	+	2.71529i	0.0299628	+	0.0922160i
$868$	−11.5011			−0.390374
$869$	0.233096	+	0.717395i	0.00790723	+	0.0243360i
$870$	49.8184	+	53.3973i	1.68900	+	1.81034i
$871$	3.19053	−	9.81945i	0.108107	−	0.332719i
$872$	−5.06565	+	15.5905i	−0.171545	+	0.527960i
$873$	−71.2558	+	51.7704i	−2.41164	+	1.75216i
$874$	32.0773			1.08503
$875$	11.6754	−	9.46887i	0.394701	−	0.320106i
$876$	−53.5382			−1.80889
$877$	−18.0316	+	13.1008i	−0.608885	+	0.442381i	−0.849022	−	0.528358i	$-0.822808\pi$
$877$	−18.0316	+	13.1008i	−0.608885	+	0.442381i	0.240136	+	0.970739i	$0.422808\pi$
$878$	−8.73546	+	26.8850i	−0.294807	+	0.907324i
$879$	−0.696561	+	2.14379i	−0.0234944	+	0.0723084i
$880$	−5.76078	−	6.17462i	−0.194196	−	0.208146i
$881$	7.74820	+	23.8465i	0.261044	+	0.803409i	0.992579	+	0.121605i	$0.0388043\pi$
$881$	7.74820	+	23.8465i	0.261044	+	0.803409i	−0.731535	+	0.681804i	$0.761196\pi$
$882$	56.5640			1.90461
$883$	11.4216	+	35.1522i	0.384369	+	1.18296i	0.936937	+	0.349497i	$0.113648\pi$
$883$	11.4216	+	35.1522i	0.384369	+	1.18296i	−0.552569	+	0.833467i	$0.686352\pi$
$884$	−5.88156	−	4.27321i	−0.197818	−	0.143723i
$885$	−81.6598	−	15.8522i	−2.74497	−	0.532864i
$886$	13.1424	−	9.54852i	0.441528	−	0.320789i
$887$	33.9425	+	24.6606i	1.13968	+	0.828023i	0.987074	−	0.160264i	$-0.0512347\pi$
$887$	33.9425	+	24.6606i	1.13968	+	0.828023i	0.152602	+	0.988288i	$0.451235\pi$
$888$	26.5335	+	19.2777i	0.890406	+	0.646918i
$889$	18.8940	−	13.7273i	0.633684	−	0.460398i
$890$	−17.9386	+	8.37028i	−0.601302	+	0.280572i
$891$	−2.24565	−	1.63156i	−0.0752322	−	0.0546594i
$892$	15.1872	+	46.7413i	0.508504	+	1.56501i
$893$	−1.50184			−0.0502571
$894$	20.0701	+	61.7694i	0.671244	+	2.06588i
$895$	−28.5355	+	13.3149i	−0.953836	+	0.445068i
$896$	−3.22989	+	9.94058i	−0.107903	+	0.332092i
$897$	−19.0388	+	58.5953i	−0.635686	+	1.95644i
$898$	27.4826	−	19.9673i	0.917106	−	0.666316i
$899$	−18.7117			−0.624070
$900$	−33.7749	−	53.9918i	−1.12583	−	1.79973i
$901$	−6.16468			−0.205375
$902$	−19.1627	+	13.9225i	−0.638047	+	0.463568i
$903$	−0.730651	+	2.24871i	−0.0243145	+	0.0748325i
$904$	−3.93416	+	12.1081i	−0.130848	+	0.402709i
$905$	−14.8873	+	26.8730i	−0.494871	+	0.893290i
$906$	−19.1484	−	58.9328i	−0.636164	−	1.95791i
$907$	55.2525			1.83463			0.917315	−	0.398162i	$-0.130352\pi$
$907$	55.2525			1.83463			0.917315	+	0.398162i	$0.130352\pi$
$908$	−12.2426	−	37.6788i	−0.406284	−	1.25042i
$909$	−37.9648	−	27.5830i	−1.25921	−	0.914871i
$910$	12.7529	+	13.6691i	0.422756	+	0.453126i
$911$	−11.6442	+	8.46003i	−0.385791	+	0.280293i	−0.763728	−	0.645538i	$-0.776633\pi$
$911$	−11.6442	+	8.46003i	−0.385791	+	0.280293i	0.377938	+	0.925831i	$0.376633\pi$
$912$	13.5139	+	9.81842i	0.447490	+	0.325120i
$913$	−6.00310	−	4.36151i	−0.198674	−	0.144345i
$914$	9.99216	−	7.25973i	0.330511	−	0.240130i
$915$	−10.6105	+	19.1530i	−0.350773	+	0.633180i
$916$	14.0213	+	10.1871i	0.463277	+	0.336590i
$917$	6.57838	+	20.2462i	0.217237	+	0.668588i
$918$	−12.9887			−0.428691
$919$	−0.00974983	−	0.0300069i	−0.000321617	−	0.000989836i	0.950896	−	0.309512i	$-0.100166\pi$
$919$	−0.00974983	−	0.0300069i	−0.000321617	−	0.000989836i	−0.951217	+	0.308522i	$0.900166\pi$
$920$	−2.00342	−	16.2833i	−0.0660507	−	0.536845i
$921$	20.3880	−	62.7477i	0.671806	−	2.06761i
$922$	−21.0213	+	64.6970i	−0.692300	+	2.13068i
$923$	−14.2564	+	10.3579i	−0.469257	+	0.340935i
$924$	−12.6611			−0.416520
$925$	36.9120	−	44.0341i	1.21366	−	1.44783i
$926$	−6.04659			−0.198703
$927$	5.97433	−	4.34061i	0.196223	−	0.142564i
$928$	−13.3499	+	41.0868i	−0.438232	+	1.34874i
$929$	−9.65676	+	29.7204i	−0.316828	+	0.975096i	0.658168	+	0.752872i	$0.271332\pi$
$929$	−9.65676	+	29.7204i	−0.316828	+	0.975096i	−0.974995	+	0.222225i	$0.928668\pi$
$930$	45.8506	+	8.90071i	1.50350	+	0.291866i
$931$	−3.31566	−	10.2046i	−0.108666	−	0.334441i
$932$	−21.7836			−0.713546
$933$	−13.7924	−	42.4488i	−0.451544	−	1.38971i
$934$	1.18775	+	0.862949i	0.0388643	+	0.0282365i
$935$	−0.364227	−	2.96035i	−0.0119115	−	0.0968139i
$936$	12.2482	−	8.89886i	0.400346	−	0.290868i
$937$	−8.33950	−	6.05900i	−0.272440	−	0.197939i	0.443173	−	0.896436i	$-0.353853\pi$
$937$	−8.33950	−	6.05900i	−0.272440	−	0.197939i	−0.715613	+	0.698497i	$0.753853\pi$
$938$	−8.07845	−	5.86934i	−0.263771	−	0.191641i
$939$	−17.9088	+	13.0115i	−0.584433	+	0.424615i
$940$	0.490687	+	3.98819i	0.0160044	+	0.130080i
$941$	13.4477	+	9.77035i	0.438383	+	0.318504i	0.784992	−	0.619506i	$-0.212667\pi$
$941$	13.4477	+	9.77035i	0.438383	+	0.318504i	−0.346609	+	0.938010i	$0.612667\pi$
$942$	10.8680	+	33.4483i	0.354099	+	1.08980i
$943$	61.6271			2.00685
$944$	−11.4000	−	35.0857i	−0.371039	−	1.14194i
$945$	18.1263	+	3.51876i	0.589649	+	0.114465i
$946$	−0.536945	+	1.65255i	−0.0174576	+	0.0537289i
$947$	7.59800	−	23.3842i	0.246902	−	0.759885i	−0.748416	−	0.663229i	$-0.769185\pi$
$947$	7.59800	−	23.3842i	0.246902	−	0.759885i	0.995318	−	0.0966558i	$-0.0308146\pi$
$948$	−3.22972	+	2.34653i	−0.104896	+	0.0762117i
$949$	−22.2975			−0.723808
$950$	−14.0379	+	16.7465i	−0.455449	+	0.543327i
$951$	16.0906			0.521774
$952$	−1.08736	+	0.790015i	−0.0352416	+	0.0256045i
$953$	−3.76826	+	11.5975i	−0.122066	+	0.375680i	−0.993355	−	0.115090i	$-0.963284\pi$
$953$	−3.76826	+	11.5975i	−0.122066	+	0.375680i	0.871289	+	0.490770i	$0.163284\pi$
$954$	20.7530	−	63.8712i	0.671904	−	2.06791i
$955$	−3.47168	−	28.2170i	−0.112341	−	0.913081i
$956$	−8.29416	−	25.5268i	−0.268252	−	0.825596i
$957$	−20.5989			−0.665868
$958$	−16.6340	−	51.1943i	−0.537421	−	1.65401i
$959$	18.3371	+	13.3227i	0.592135	+	0.430211i
$960$	34.7385	−	62.7064i	1.12118	−	2.02384i
$961$	15.3977	−	11.1871i	0.496701	−	0.360874i
$962$	57.8090	+	42.0007i	1.86384	+	1.35416i
$963$	−48.2337	−	35.0438i	−1.55431	−	1.12927i
$964$	−3.95068	+	2.87034i	−0.127243	+	0.0924474i
$965$	22.6260	+	24.2515i	0.728358	+	0.780682i
$966$	48.2063	+	35.0239i	1.55101	+	1.12688i
$967$	−13.0593	−	40.1923i	−0.419957	−	1.29250i	−0.907741	−	0.419531i	$-0.862194\pi$
$967$	−13.0593	−	40.1923i	−0.419957	−	1.29250i	0.487783	−	0.872965i	$-0.337806\pi$
$968$	9.21738			0.296258
$969$	1.82318	+	5.61116i	0.0585688	+	0.180256i
$970$	39.1836	−	70.7302i	1.25811	−	2.27101i
$971$	−1.45708	+	4.48443i	−0.0467599	+	0.143912i	−0.971711	−	0.236175i	$-0.924106\pi$
$971$	−1.45708	+	4.48443i	−0.0467599	+	0.143912i	0.924951	+	0.380087i	$0.124106\pi$
$972$	−9.53871	+	29.3571i	−0.305954	+	0.941630i
$973$	10.3787	−	7.54058i	0.332727	−	0.241740i
$974$	27.1614			0.870306
$975$	−22.2588	−	35.5824i	−0.712851	−	1.13955i
$976$	−9.71049			−0.310825
$977$	40.5017	−	29.4262i	1.29576	−	0.941428i	0.295859	−	0.955232i	$-0.404394\pi$
$977$	40.5017	−	29.4262i	1.29576	−	0.941428i	0.999905	+	0.0138040i	$0.00439410\pi$
$978$	45.4772	−	139.965i	1.45420	−	4.47557i
$979$	1.72543	−	5.31032i	0.0551449	−	0.169719i
$980$	−26.0153	+	12.1389i	−0.831028	+	0.387764i
$981$	26.1035	+	80.3382i	0.833420	+	2.56500i
$982$	21.4044			0.683041
$983$	−12.4958	−	38.4580i	−0.398553	−	1.22662i	−0.926160	−	0.377132i	$-0.876910\pi$
$983$	−12.4958	−	38.4580i	−0.398553	−	1.22662i	0.527606	−	0.849489i	$-0.323090\pi$
$984$	−19.3867	−	14.0852i	−0.618025	−	0.449021i
$985$	5.93754	−	2.77051i	0.189186	−	0.0882756i
$986$	−9.25454	+	6.72382i	−0.294725	+	0.214130i
$987$	−2.25699	−	1.63980i	−0.0718407	−	0.0521953i
$988$	−12.1543	−	8.83060i	−0.386679	−	0.280939i
$989$	3.65745	−	2.65729i	0.116300	−	0.0844971i
$990$	31.8979	+	6.19215i	1.01378	+	0.196800i
$991$	−23.6363	−	17.1728i	−0.750832	−	0.545511i	0.145253	−	0.989395i	$-0.453600\pi$
$991$	−23.6363	−	17.1728i	−0.750832	−	0.545511i	−0.896085	+	0.443883i	$0.853600\pi$
$992$	8.53816	+	26.2777i	0.271087	+	0.834319i
$993$	−73.3220			−2.32680
$994$	5.26654	+	16.2087i	0.167044	+	0.514110i
$995$	32.2762	+	34.5948i	1.02322	+	1.09673i
$996$	12.1354	−	37.3490i	0.384526	−	1.18345i
$997$	1.44010	−	4.43218i	0.0456085	−	0.140368i	−0.925659	−	0.378359i	$-0.876489\pi$
$997$	1.44010	−	4.43218i	0.0456085	−	0.140368i	0.971268	+	0.237990i	$0.0764886\pi$
$998$	−69.1388	+	50.2323i	−2.18855	+	1.59008i
$999$	70.5777			2.23298

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.k.b.86.18	✓	76
25.16	even	5	inner	425.2.k.b.341.18	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
425.2.k.b.86.18	✓	76	1.1	even	1	trivial
425.2.k.b.341.18	yes	76	25.16	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.k (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.71096 - 1.24309i) q^{2} +(0.882251 - 2.71529i) q^{3} +(0.764097 - 2.35165i) q^{4} +(1.52540 + 1.63498i) q^{5} +(-1.86584 - 5.74248i) q^{6} -1.34454 q^{7} +(-0.308905 - 0.950711i) q^{8} +(-4.16738 - 3.02778i) q^{9} +(4.64233 + 0.901189i) q^{10} +(-1.07914 + 0.784042i) q^{11} +(-5.71128 - 4.14949i) q^{12} +(-2.37863 - 1.72817i) q^{13} +(-2.30047 + 1.67139i) q^{14} +(5.78523 - 2.69943i) q^{15} +(2.29052 + 1.66416i) q^{16} +(0.309017 + 0.951057i) q^{17} -10.8940 q^{18} +(0.638585 + 1.96536i) q^{19} +(5.01045 - 2.33792i) q^{20} +(-1.18622 + 3.65082i) q^{21} +(-0.871740 + 2.68294i) q^{22} +(5.93794 - 4.31416i) q^{23} -2.85399 q^{24} +(-0.346321 + 4.98799i) q^{25} -6.21802 q^{26} +(-4.96867 + 3.60995i) q^{27} +(-1.02736 + 3.16189i) q^{28} +(-1.67146 + 5.14423i) q^{29} +(6.54269 - 11.8102i) q^{30} +(1.06901 + 3.29007i) q^{31} +7.98698 q^{32} +(1.17683 + 3.62190i) q^{33} +(1.71096 + 1.24309i) q^{34} +(-2.05096 - 2.19830i) q^{35} +(-10.3045 + 7.48669i) q^{36} +(-9.29700 - 6.75467i) q^{37} +(3.53572 + 2.56885i) q^{38} +(-6.79104 + 4.93398i) q^{39} +(1.08319 - 1.95527i) q^{40} +(6.79284 + 4.93529i) q^{41} +(2.50871 + 7.72101i) q^{42} +0.615947 q^{43} +(1.01922 + 3.13685i) q^{44} +(-1.40655 - 11.4321i) q^{45} +(4.79671 - 14.7628i) q^{46} +(-0.224579 + 0.691184i) q^{47} +(6.53949 - 4.75122i) q^{48} -5.19220 q^{49} +(5.60797 + 8.96479i) q^{50} +2.85502 q^{51} +(-5.88156 + 4.27321i) q^{52} +(-1.90499 + 5.86296i) q^{53} +(-4.01373 + 12.3530i) q^{54} +(-2.92802 - 0.568399i) q^{55} +(0.415336 + 1.27827i) q^{56} +5.89992 q^{57} +(3.53492 + 10.8794i) q^{58} +(-10.5415 - 7.65888i) q^{59} +(-1.92765 - 15.6675i) q^{60} +(-2.77474 + 2.01596i) q^{61} +(5.91889 + 4.30033i) q^{62} +(5.60322 + 4.07097i) q^{63} +(9.08439 - 6.60020i) q^{64} +(-0.802823 - 6.52516i) q^{65} +(6.51586 + 4.73405i) q^{66} +(1.08516 + 3.33978i) q^{67} +2.47267 q^{68} +(-6.47545 - 19.9294i) q^{69} +(-6.24181 - 1.21169i) q^{70} +(1.85211 - 5.70021i) q^{71} +(-1.59122 + 4.89726i) q^{72} +(6.13543 - 4.45765i) q^{73} -24.3035 q^{74} +(13.2383 + 5.34102i) q^{75} +5.10978 q^{76} +(1.45095 - 1.05418i) q^{77} +(-5.48586 + 16.8837i) q^{78} +(0.174749 - 0.537821i) q^{79} +(0.773086 + 6.28347i) q^{80} +(0.643053 + 1.97911i) q^{81} +17.7573 q^{82} +(1.71901 + 5.29058i) q^{83} +(7.67906 + 5.57917i) q^{84} +(-1.08358 + 1.95598i) q^{85} +(1.05386 - 0.765677i) q^{86} +(12.4934 + 9.07699i) q^{87} +(1.07875 + 0.783757i) q^{88} +(-3.38650 + 2.46044i) q^{89} +(-16.6177 - 17.8115i) q^{90} +(3.19817 + 2.32360i) q^{91} +(-5.60824 - 17.2604i) q^{92} +9.87664 q^{93} +(0.474955 + 1.46176i) q^{94} +(-2.23923 + 4.04203i) q^{95} +(7.04652 - 21.6869i) q^{96} +(5.28373 - 16.2616i) q^{97} +(-8.88368 + 6.45437i) q^{98} +6.87109 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q - 6 q^{2} - 7 q^{3} - 26 q^{4} + 13 q^{5} + 12 q^{6} + 22 q^{7} + 10 q^{8} - 24 q^{9} - 6 q^{10} - 16 q^{11} - 15 q^{12} - q^{13} - 19 q^{14} - 3 q^{15} + 30 q^{16} - 19 q^{17} + 6 q^{18} + 18 q^{19}+ \cdots - 64 q^{99}+O(q^{100}) \) 76 * q - 6 * q^2 - 7 * q^3 - 26 * q^4 + 13 * q^5 + 12 * q^6 + 22 * q^7 + 10 * q^8 - 24 * q^9 - 6 * q^10 - 16 * q^11 - 15 * q^12 - q^13 - 19 * q^14 - 3 * q^15 + 30 * q^16 - 19 * q^17 + 6 * q^18 + 18 * q^19 - 23 * q^20 - 22 * q^21 - 15 * q^22 - 8 * q^23 - 22 * q^24 + 35 * q^25 - 14 * q^26 - 10 * q^27 - 29 * q^28 - 25 * q^29 + 57 * q^30 + 22 * q^31 + 54 * q^32 - 22 * q^33 - 6 * q^34 - 19 * q^35 - 91 * q^36 - 49 * q^37 + 15 * q^38 + 25 * q^39 - 2 * q^40 + 16 * q^41 - 28 * q^42 + 104 * q^43 + 18 * q^44 + 10 * q^45 - 55 * q^46 - 26 * q^47 - 86 * q^48 + 2 * q^49 - 17 * q^50 + 18 * q^51 + 53 * q^52 - 41 * q^53 - 6 * q^54 + 67 * q^55 + 115 * q^56 + 84 * q^57 - 12 * q^58 - 7 * q^59 - 32 * q^60 - 21 * q^61 - 23 * q^62 - 21 * q^63 + 6 * q^64 - 72 * q^65 + 102 * q^66 - 15 * q^67 + 74 * q^68 + 48 * q^69 - 60 * q^70 - 8 * q^71 + 9 * q^72 - 25 * q^73 - 60 * q^74 + 68 * q^75 - 76 * q^76 - 36 * q^77 - 51 * q^78 + 2 * q^79 + 217 * q^80 + 20 * q^81 - 12 * q^82 - 41 * q^83 - 48 * q^84 - 7 * q^85 - 87 * q^86 - 54 * q^87 - 4 * q^88 + 77 * q^89 - 93 * q^90 + 79 * q^91 - 19 * q^92 + 72 * q^93 + 15 * q^94 + 57 * q^95 + 28 * q^96 + 13 * q^97 - 62 * q^98 - 64 * q^99

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