LMFDB - Embedded newform 122.2.e.b.81.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [122,2,Mod(9,122)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(122, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("122.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 122 = 2 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	122.e (of order $5$, degree $4$, 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:	$0.974174904660$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 18 x^{14} - 39 x^{13} + 151 x^{12} - 259 x^{11} + 842 x^{10} - 662 x^{9} + \cdots + 256 $ x^16 - 3x^15 + 18x^14 - 39x^13 + 151x^12 - 259x^11 + 842x^10 - 662x^9 + 6934x^8 - 13623x^7 + 20328x^6 - 19364x^5 + 13665x^4 - 7504x^3 + 3808x^2 - 1344*x + 256
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			81.2
Root			$0.376781 + 0.273748i$ of defining polynomial
Character	$\chi$	$=$	122.81
Dual form			122.2.e.b.119.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 + 0.951057i) q^{2} +(0.143918 + 0.442933i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(2.83793 - 2.06188i) q^{5} +(-0.376781 + 0.273748i) q^{6} +(-1.39211 + 4.28447i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(2.25157 - 1.63586i) q^{9} +O(q^{10})$	\(q+(0.309017 + 0.951057i) q^{2} +(0.143918 + 0.442933i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(2.83793 - 2.06188i) q^{5} +(-0.376781 + 0.273748i) q^{6} +(-1.39211 + 4.28447i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(2.25157 - 1.63586i) q^{9} +(2.83793 + 2.06188i) q^{10} -2.64340 q^{11} +(-0.376781 - 0.273748i) q^{12} -3.22004 q^{13} -4.50495 q^{14} +(1.32170 + 0.960273i) q^{15} +(0.309017 - 0.951057i) q^{16} +(1.05457 - 0.766187i) q^{17} +(2.25157 + 1.63586i) q^{18} +(-1.40191 - 4.31462i) q^{19} +(-1.08399 + 3.33619i) q^{20} -2.09808 q^{21} +(-0.816857 - 2.51403i) q^{22} +(3.40461 - 2.47359i) q^{23} +(0.143918 - 0.442933i) q^{24} +(2.25743 - 6.94765i) q^{25} +(-0.995047 - 3.06244i) q^{26} +(2.17896 + 1.58311i) q^{27} +(-1.39211 - 4.28447i) q^{28} -6.24249 q^{29} +(-0.504845 + 1.55375i) q^{30} +(2.18099 - 6.71239i) q^{31} +1.00000 q^{32} +(-0.380433 - 1.17085i) q^{33} +(1.05457 + 0.766187i) q^{34} +(4.88334 + 15.0294i) q^{35} +(-0.860025 + 2.64688i) q^{36} +(-2.67802 + 8.24209i) q^{37} +(3.67024 - 2.66658i) q^{38} +(-0.463421 - 1.42626i) q^{39} -3.50788 q^{40} +(-2.26617 + 6.97456i) q^{41} +(-0.648342 - 1.99539i) q^{42} +(-6.38820 - 4.64130i) q^{43} +(2.13856 - 1.55375i) q^{44} +(3.01686 - 9.28494i) q^{45} +(3.40461 + 2.47359i) q^{46} -0.945676 q^{47} +0.465727 q^{48} +(-10.7556 - 7.81437i) q^{49} +7.30519 q^{50} +(0.491140 + 0.356834i) q^{51} +(2.60507 - 1.89269i) q^{52} +(7.34609 + 5.33725i) q^{53} +(-0.832290 + 2.56153i) q^{54} +(-7.50180 + 5.45038i) q^{55} +(3.64458 - 2.64795i) q^{56} +(1.70933 - 1.24190i) q^{57} +(-1.92904 - 5.93696i) q^{58} +(0.911207 + 2.80441i) q^{59} -1.63371 q^{60} +(7.81010 - 0.0477308i) q^{61} +7.05783 q^{62} +(3.87437 + 11.9241i) q^{63} +(0.309017 + 0.951057i) q^{64} +(-9.13825 + 6.63933i) q^{65} +(0.995986 - 0.723626i) q^{66} +(-9.84235 + 7.15089i) q^{67} +(-0.402808 + 1.23972i) q^{68} +(1.58562 + 1.15202i) q^{69} +(-12.7847 + 9.28866i) q^{70} +(7.41787 + 5.38940i) q^{71} -2.78310 q^{72} +(7.77796 + 5.65102i) q^{73} -8.66624 q^{74} +3.40223 q^{75} +(3.67024 + 2.66658i) q^{76} +(3.67990 - 11.3256i) q^{77} +(1.21325 - 0.881479i) q^{78} +(6.09102 + 4.42538i) q^{79} +(-1.08399 - 3.33619i) q^{80} +(2.19245 - 6.74768i) q^{81} -7.33349 q^{82} +(-0.862031 - 2.65306i) q^{83} +(1.69738 - 1.23322i) q^{84} +(1.41300 - 4.34877i) q^{85} +(2.44008 - 7.50978i) q^{86} +(-0.898405 - 2.76500i) q^{87} +(2.13856 + 1.55375i) q^{88} +(1.23614 + 3.80445i) q^{89} +9.76276 q^{90} +(4.48264 - 13.7962i) q^{91} +(-1.30045 + 4.00236i) q^{92} +3.28702 q^{93} +(-0.292230 - 0.899391i) q^{94} +(-12.8747 - 9.35404i) q^{95} +(0.143918 + 0.442933i) q^{96} +(2.70611 - 8.32856i) q^{97} +(4.10826 - 12.6439i) q^{98} +(-5.95182 + 4.32425i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} + 2 q^{3} - 4 q^{4} + 3 q^{5} - 3 q^{6} - 2 q^{7} - 4 q^{8}+O(q^{10}) $ 16 * q - 4 * q^2 + 2 * q^3 - 4 * q^4 + 3 * q^5 - 3 * q^6 - 2 * q^7 - 4 * q^8	\( 16 q - 4 q^{2} + 2 q^{3} - 4 q^{4} + 3 q^{5} - 3 q^{6} - 2 q^{7} - 4 q^{8} + 3 q^{10} - 3 q^{12} + 2 q^{13} + 8 q^{14} - 4 q^{16} - 7 q^{17} - 12 q^{19} - 2 q^{20} + 24 q^{21} + 5 q^{22} - 16 q^{23} + 2 q^{24} + 9 q^{25} - 3 q^{26} - 4 q^{27} - 2 q^{28} + 4 q^{29} - 5 q^{30} - 19 q^{31} + 16 q^{32} - 43 q^{33} - 7 q^{34} - 21 q^{35} - 15 q^{36} - 30 q^{37} + 8 q^{38} + 61 q^{39} - 2 q^{40} + 4 q^{41} - 6 q^{42} - 36 q^{43} - 5 q^{44} + 45 q^{45} - 16 q^{46} - 30 q^{47} + 2 q^{48} - 32 q^{49} + 14 q^{50} + 42 q^{51} + 2 q^{52} + 55 q^{53} + 6 q^{54} - 27 q^{55} - 2 q^{56} + 41 q^{57} + 14 q^{58} + 8 q^{59} + 10 q^{60} + 57 q^{61} + 46 q^{62} + q^{63} - 4 q^{64} - 41 q^{65} + 47 q^{66} - 19 q^{67} + 8 q^{68} - 28 q^{69} + 4 q^{70} + 31 q^{71} + 30 q^{72} + 4 q^{73} + 30 q^{74} - 44 q^{75} + 8 q^{76} - 29 q^{77} - 39 q^{78} + 2 q^{79} - 2 q^{80} - 93 q^{81} - 16 q^{82} + 12 q^{83} - 6 q^{84} + 52 q^{85} + 24 q^{86} + 16 q^{87} - 5 q^{88} - 15 q^{89} - 80 q^{90} - 3 q^{91} + 14 q^{92} - 3 q^{95} + 2 q^{96} - 18 q^{97} - 22 q^{98} - 6 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 + 2 * q^3 - 4 * q^4 + 3 * q^5 - 3 * q^6 - 2 * q^7 - 4 * q^8 + 3 * q^10 - 3 * q^12 + 2 * q^13 + 8 * q^14 - 4 * q^16 - 7 * q^17 - 12 * q^19 - 2 * q^20 + 24 * q^21 + 5 * q^22 - 16 * q^23 + 2 * q^24 + 9 * q^25 - 3 * q^26 - 4 * q^27 - 2 * q^28 + 4 * q^29 - 5 * q^30 - 19 * q^31 + 16 * q^32 - 43 * q^33 - 7 * q^34 - 21 * q^35 - 15 * q^36 - 30 * q^37 + 8 * q^38 + 61 * q^39 - 2 * q^40 + 4 * q^41 - 6 * q^42 - 36 * q^43 - 5 * q^44 + 45 * q^45 - 16 * q^46 - 30 * q^47 + 2 * q^48 - 32 * q^49 + 14 * q^50 + 42 * q^51 + 2 * q^52 + 55 * q^53 + 6 * q^54 - 27 * q^55 - 2 * q^56 + 41 * q^57 + 14 * q^58 + 8 * q^59 + 10 * q^60 + 57 * q^61 + 46 * q^62 + q^63 - 4 * q^64 - 41 * q^65 + 47 * q^66 - 19 * q^67 + 8 * q^68 - 28 * q^69 + 4 * q^70 + 31 * q^71 + 30 * q^72 + 4 * q^73 + 30 * q^74 - 44 * q^75 + 8 * q^76 - 29 * q^77 - 39 * q^78 + 2 * q^79 - 2 * q^80 - 93 * q^81 - 16 * q^82 + 12 * q^83 - 6 * q^84 + 52 * q^85 + 24 * q^86 + 16 * q^87 - 5 * q^88 - 15 * q^89 - 80 * q^90 - 3 * q^91 + 14 * q^92 - 3 * q^95 + 2 * q^96 - 18 * q^97 - 22 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/122\mathbb{Z}\right)^\times$.

$n$	$63$
$\chi(n)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$3$	0.143918	+	0.442933i	0.0830909	+	0.255728i	0.983968	−	0.178348i	$-0.0570752\pi$
$3$	0.143918	+	0.442933i	0.0830909	+	0.255728i	−0.900877	+	0.434075i	$0.857075\pi$
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	2.83793	−	2.06188i	1.26916	−	0.922100i	0.269993	−	0.962862i	$-0.412979\pi$
$5$	2.83793	−	2.06188i	1.26916	−	0.922100i	0.999169	+	0.0407626i	$0.0129787\pi$
$6$	−0.376781	+	0.273748i	−0.153820	+	0.111757i
$7$	−1.39211	+	4.28447i	−0.526167	+	1.61938i	0.235829	+	0.971794i	$0.424219\pi$
$7$	−1.39211	+	4.28447i	−0.526167	+	1.61938i	−0.761996	+	0.647581i	$0.775781\pi$
$8$	−0.809017	−	0.587785i	−0.286031	−	0.207813i
$9$	2.25157	−	1.63586i	0.750525	−	0.545288i
$10$	2.83793	+	2.06188i	0.897433	+	0.652023i
$11$	−2.64340			−0.797017			−0.398508	−	0.917165i	$-0.630472\pi$
$11$	−2.64340			−0.797017			−0.398508	+	0.917165i	$0.630472\pi$
$12$	−0.376781	−	0.273748i	−0.108767	−	0.0790242i
$13$	−3.22004			−0.893079			−0.446539	−	0.894764i	$-0.647344\pi$
$13$	−3.22004			−0.893079			−0.446539	+	0.894764i	$0.647344\pi$
$14$	−4.50495			−1.20400
$15$	1.32170	+	0.960273i	0.341262	+	0.247941i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	1.05457	−	0.766187i	0.255770	−	0.185828i	−0.452510	−	0.891759i	$-0.649471\pi$
$17$	1.05457	−	0.766187i	0.255770	−	0.185828i	0.708280	+	0.705932i	$0.249471\pi$
$18$	2.25157	+	1.63586i	0.530701	+	0.385577i
$19$	−1.40191	−	4.31462i	−0.321619	−	0.989842i	−0.972944	−	0.231043i	$-0.925786\pi$
$19$	−1.40191	−	4.31462i	−0.321619	−	0.989842i	0.651325	−	0.758799i	$-0.274214\pi$
$20$	−1.08399	+	3.33619i	−0.242388	+	0.745994i
$21$	−2.09808			−0.457839
$22$	−0.816857	−	2.51403i	−0.174155	−	0.535992i
$23$	3.40461	−	2.47359i	0.709910	−	0.515780i	−0.173235	−	0.984881i	$-0.555422\pi$
$23$	3.40461	−	2.47359i	0.709910	−	0.515780i	0.883145	+	0.469101i	$0.155422\pi$
$24$	0.143918	−	0.442933i	0.0293771	−	0.0904133i
$25$	2.25743	−	6.94765i	0.451486	−	1.38953i
$26$	−0.995047	−	3.06244i	−0.195145	−	0.600594i
$27$	2.17896	+	1.58311i	0.419342	+	0.304670i
$28$	−1.39211	−	4.28447i	−0.263084	−	0.809688i
$29$	−6.24249			−1.15920			−0.579601	−	0.814901i	$-0.696791\pi$
$29$	−6.24249			−1.15920			−0.579601	+	0.814901i	$0.696791\pi$
$30$	−0.504845	+	1.55375i	−0.0921717	+	0.283675i
$31$	2.18099	−	6.71239i	0.391717	−	1.20558i	−0.539772	−	0.841812i	$-0.681489\pi$
$31$	2.18099	−	6.71239i	0.391717	−	1.20558i	0.931489	−	0.363770i	$-0.118511\pi$
$32$	1.00000			0.176777
$33$	−0.380433	−	1.17085i	−0.0662248	−	0.203819i
$34$	1.05457	+	0.766187i	0.180857	+	0.131400i
$35$	4.88334	+	15.0294i	0.825435	+	2.54043i
$36$	−0.860025	+	2.64688i	−0.143337	+	0.441147i
$37$	−2.67802	+	8.24209i	−0.440263	+	1.35499i	0.447333	+	0.894368i	$0.352374\pi$
$37$	−2.67802	+	8.24209i	−0.440263	+	1.35499i	−0.887596	+	0.460623i	$0.847626\pi$
$38$	3.67024	−	2.66658i	0.595391	−	0.432577i
$39$	−0.463421	−	1.42626i	−0.0742067	−	0.228385i
$40$	−3.50788			−0.554644
$41$	−2.26617	+	6.97456i	−0.353917	+	1.08924i	0.602718	+	0.797954i	$0.294084\pi$
$41$	−2.26617	+	6.97456i	−0.353917	+	1.08924i	−0.956635	+	0.291290i	$0.905916\pi$
$42$	−0.648342	−	1.99539i	−0.100041	−	0.307896i
$43$	−6.38820	−	4.64130i	−0.974192	−	0.707792i	−0.0177885	−	0.999842i	$-0.505663\pi$
$43$	−6.38820	−	4.64130i	−0.974192	−	0.707792i	−0.956403	+	0.292050i	$0.905663\pi$
$44$	2.13856	−	1.55375i	0.322400	−	0.234237i
$45$	3.01686	−	9.28494i	0.449727	−	1.38412i
$46$	3.40461	+	2.47359i	0.501982	+	0.364712i
$47$	−0.945676			−0.137941			−0.0689705	−	0.997619i	$-0.521971\pi$
$47$	−0.945676			−0.137941			−0.0689705	+	0.997619i	$0.521971\pi$
$48$	0.465727			0.0672220
$49$	−10.7556	−	7.81437i	−1.53651	−	1.11634i
$50$	7.30519			1.03311
$51$	0.491140	+	0.356834i	0.0687734	+	0.0499668i
$52$	2.60507	−	1.89269i	0.361258	−	0.262469i
$53$	7.34609	+	5.33725i	1.00906	+	0.733127i	0.964012	−	0.265858i	$-0.0856551\pi$
$53$	7.34609	+	5.33725i	1.00906	+	0.733127i	0.0450505	+	0.998985i	$0.485655\pi$
$54$	−0.832290	+	2.56153i	−0.113260	+	0.348579i
$55$	−7.50180	+	5.45038i	−1.01154	+	0.734929i
$56$	3.64458	−	2.64795i	0.487028	−	0.353847i
$57$	1.70933	−	1.24190i	0.226406	−	0.164494i
$58$	−1.92904	−	5.93696i	−0.253295	−	0.779561i
$59$	0.911207	+	2.80441i	0.118629	+	0.365103i	0.992687	−	0.120720i	$-0.0385202\pi$
$59$	0.911207	+	2.80441i	0.118629	+	0.365103i	−0.874058	+	0.485822i	$0.838520\pi$
$60$	−1.63371			−0.210912
$61$	7.81010	−	0.0477308i	0.999981	−	0.00611131i
$61$	7.81010	−	0.0477308i	0.999981	−	0.00611131i
$62$	7.05783			0.896345
$63$	3.87437	+	11.9241i	0.488125	+	1.50229i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	−9.13825	+	6.63933i	−1.13346	+	0.823508i
$66$	0.995986	−	0.723626i	0.122597	−	0.0890722i
$67$	−9.84235	+	7.15089i	−1.20243	+	0.873620i	−0.994522	−	0.104528i	$-0.966667\pi$
$67$	−9.84235	+	7.15089i	−1.20243	+	0.873620i	−0.207913	+	0.978147i	$0.566667\pi$
$68$	−0.402808	+	1.23972i	−0.0488477	+	0.150338i
$69$	1.58562	+	1.15202i	0.190886	+	0.138687i
$70$	−12.7847	+	9.28866i	−1.52807	+	1.11021i
$71$	7.41787	+	5.38940i	0.880339	+	0.639604i	0.933341	−	0.358991i	$-0.116879\pi$
$71$	7.41787	+	5.38940i	0.880339	+	0.639604i	−0.0530023	+	0.998594i	$0.516879\pi$
$72$	−2.78310			−0.327991
$73$	7.77796	+	5.65102i	0.910341	+	0.661402i	0.941101	−	0.338125i	$-0.109793\pi$
$73$	7.77796	+	5.65102i	0.910341	+	0.661402i	−0.0307599	+	0.999527i	$0.509793\pi$
$74$	−8.66624			−1.00743
$75$	3.40223			0.392856
$76$	3.67024	+	2.66658i	0.421005	+	0.305878i
$77$	3.67990	−	11.3256i	0.419364	−	1.29067i
$78$	1.21325	−	0.881479i	0.137374	−	0.0998078i
$79$	6.09102	+	4.42538i	0.685293	+	0.497894i	0.875109	−	0.483925i	$-0.160789\pi$
$79$	6.09102	+	4.42538i	0.685293	+	0.497894i	−0.189817	+	0.981820i	$0.560789\pi$
$80$	−1.08399	−	3.33619i	−0.121194	−	0.372997i
$81$	2.19245	−	6.74768i	0.243606	−	0.749742i
$82$	−7.33349			−0.809848
$83$	−0.862031	−	2.65306i	−0.0946202	−	0.291211i	0.892534	−	0.450979i	$-0.148925\pi$
$83$	−0.862031	−	2.65306i	−0.0946202	−	0.291211i	−0.987155	+	0.159769i	$0.948925\pi$
$84$	1.69738	−	1.23322i	0.185200	−	0.134555i
$85$	1.41300	−	4.34877i	0.153262	−	0.471691i
$86$	2.44008	−	7.50978i	0.263120	−	0.809800i
$87$	−0.898405	−	2.76500i	−0.0963191	−	0.296440i
$88$	2.13856	+	1.55375i	0.227971	+	0.165631i
$89$	1.23614	+	3.80445i	0.131031	+	0.403271i	0.994952	−	0.100357i	$-0.0319984\pi$
$89$	1.23614	+	3.80445i	0.131031	+	0.403271i	−0.863921	+	0.503628i	$0.831998\pi$
$90$	9.76276			1.02909
$91$	4.48264	−	13.7962i	0.469909	−	1.44623i
$92$	−1.30045	+	4.00236i	−0.135581	+	0.417275i
$93$	3.28702			0.340849
$94$	−0.292230	−	0.899391i	−0.0301412	−	0.0927651i
$95$	−12.8747	−	9.35404i	−1.32092	−	0.959704i
$96$	0.143918	+	0.442933i	0.0146885	+	0.0452067i
$97$	2.70611	−	8.32856i	0.274764	−	0.845637i	−0.714518	−	0.699618i	$-0.753354\pi$
$97$	2.70611	−	8.32856i	0.274764	−	0.845637i	0.989282	−	0.146020i	$-0.0466462\pi$
$98$	4.10826	−	12.6439i	0.414997	−	1.27723i
$99$	−5.95182	+	4.32425i	−0.598180	+	0.434604i
$100$	2.25743	+	6.94765i	0.225743	+	0.694765i
$101$	−2.73718			−0.272359			−0.136180	−	0.990684i	$-0.543482\pi$
$101$	−2.73718			−0.272359			−0.136180	+	0.990684i	$0.543482\pi$
$102$	−0.187599	+	0.577370i	−0.0185751	+	0.0571682i
$103$	2.34791	+	7.22612i	0.231346	+	0.712011i	0.997585	+	0.0694549i	$0.0221260\pi$
$103$	2.34791	+	7.22612i	0.231346	+	0.712011i	−0.766239	+	0.642556i	$0.777874\pi$
$104$	2.60507	+	1.89269i	0.255448	+	0.185594i
$105$	−5.95421	+	4.32599i	−0.581071	+	0.422173i
$106$	−2.80596	+	8.63584i	−0.272539	+	0.838787i
$107$	−6.30209	−	4.57874i	−0.609246	−	0.442643i	0.239903	−	0.970797i	$-0.422884\pi$
$107$	−6.30209	−	4.57874i	−0.609246	−	0.442643i	−0.849149	+	0.528154i	$0.822884\pi$
$108$	−2.69335			−0.259167
$109$	−13.5490			−1.29776			−0.648879	−	0.760891i	$-0.724762\pi$
$109$	−13.5490			−1.29776			−0.648879	+	0.760891i	$0.724762\pi$
$110$	−7.50180	−	5.45038i	−0.715269	−	0.519673i
$111$	−4.03611			−0.383090
$112$	3.64458	+	2.64795i	0.344381	+	0.250207i
$113$	7.62819	−	5.54220i	0.717600	−	0.521367i	−0.168017	−	0.985784i	$-0.553736\pi$
$113$	7.62819	−	5.54220i	0.717600	−	0.521367i	0.885616	+	0.464417i	$0.153736\pi$
$114$	1.70933	+	1.24190i	0.160093	+	0.116315i
$115$	4.56180	−	14.0398i	0.425390	−	1.30922i
$116$	5.05028	−	3.66924i	0.468907	−	0.340681i
$117$	−7.25016	+	5.26755i	−0.670277	+	0.486985i
$118$	−2.38557	+	1.73322i	−0.219610	+	0.159556i
$119$	1.81463	+	5.58487i	0.166347	+	0.511964i
$120$	−0.504845	−	1.55375i	−0.0460859	−	0.141838i
$121$	−4.01241			−0.364765
$122$	2.45885	+	7.41310i	0.222614	+	0.671151i
$123$	−3.41541			−0.307957
$124$	2.18099	+	6.71239i	0.195859	+	0.602791i
$125$	−2.49882	−	7.69056i	−0.223501	−	0.687865i
$126$	−10.1432	+	7.36949i	−0.903631	+	0.656526i
$127$	7.99575	−	5.80925i	0.709508	−	0.515488i	−0.173507	−	0.984833i	$-0.555510\pi$
$127$	7.99575	−	5.80925i	0.709508	−	0.515488i	0.883015	+	0.469345i	$0.155510\pi$
$128$	−0.809017	+	0.587785i	−0.0715077	+	0.0519534i
$129$	1.13641	−	3.49751i	0.100055	−	0.307939i
$130$	−9.13825	−	6.63933i	−0.801478	−	0.582308i
$131$	4.26581	−	3.09929i	0.372705	−	0.270786i	−0.385627	−	0.922655i	$-0.626015\pi$
$131$	4.26581	−	3.09929i	0.372705	−	0.270786i	0.758332	+	0.651869i	$0.226015\pi$
$132$	0.995986	+	0.723626i	0.0866894	+	0.0629836i
$133$	20.4374			1.77215
$134$	−9.84235	−	7.15089i	−0.850250	−	0.617742i
$135$	9.44793			0.813148
$136$	−1.30352			−0.111776
$137$	4.97711	+	3.61608i	0.425223	+	0.308943i	0.779736	−	0.626108i	$-0.215353\pi$
$137$	4.97711	+	3.61608i	0.425223	+	0.308943i	−0.354513	+	0.935051i	$0.615353\pi$
$138$	−0.605653	+	1.86401i	−0.0515566	+	0.158675i
$139$	−4.00547	+	2.91014i	−0.339739	+	0.246835i	−0.744552	−	0.667565i	$-0.767337\pi$
$139$	−4.00547	+	2.91014i	−0.339739	+	0.246835i	0.404813	+	0.914400i	$0.367337\pi$
$140$	−12.7847	−	9.28866i	−1.08051	−	0.785035i
$141$	−0.136099	−	0.418871i	−0.0114616	−	0.0352753i
$142$	−2.83337	+	8.72023i	−0.237771	+	0.731785i
$143$	8.51187			0.711798
$144$	−0.860025	−	2.64688i	−0.0716687	−	0.220574i
$145$	−17.7158	+	12.8712i	−1.47121	+	1.06890i
$146$	−2.97092	+	9.14354i	−0.245875	+	0.756725i
$147$	1.91333	−	5.88862i	0.157809	−	0.485685i
$148$	−2.67802	−	8.24209i	−0.220132	−	0.677495i
$149$	−7.83067	−	5.68932i	−0.641514	−	0.466087i	0.218856	−	0.975757i	$-0.429767\pi$
$149$	−7.83067	−	5.68932i	−0.641514	−	0.466087i	−0.860370	+	0.509670i	$0.829767\pi$
$150$	1.05135	+	3.23571i	0.0858421	+	0.264195i
$151$	5.68602			0.462722			0.231361	−	0.972868i	$-0.425682\pi$
$151$	5.68602			0.462722			0.231361	+	0.972868i	$0.425682\pi$
$152$	−1.40191	+	4.31462i	−0.113710	+	0.349962i
$153$	1.12106	−	3.45025i	0.0906320	−	0.278936i
$154$	11.9084			0.959608
$155$	−7.65064	−	23.5462i	−0.614514	−	1.89128i
$156$	1.21325	+	0.881479i	0.0971379	+	0.0705748i
$157$	−3.08552	−	9.49627i	−0.246252	−	0.757885i	−0.995428	−	0.0955141i	$-0.969550\pi$
$157$	−3.08552	−	9.49627i	−0.246252	−	0.757885i	0.749176	−	0.662370i	$-0.230450\pi$
$158$	−2.32656	+	7.16042i	−0.185091	+	0.569652i
$159$	−1.30681	+	4.02195i	−0.103637	+	0.318961i
$160$	2.83793	−	2.06188i	0.224358	−	0.163006i
$161$	5.85845	+	18.0304i	0.461710	+	1.42100i
$162$	7.09493			0.557430
$163$	1.61380	−	4.96677i	0.126403	−	0.389027i	−0.867751	−	0.496999i	$-0.834435\pi$
$163$	1.61380	−	4.96677i	0.126403	−	0.389027i	0.994154	+	0.107971i	$0.0344354\pi$
$164$	−2.26617	−	6.97456i	−0.176958	−	0.544622i
$165$	−3.49379	−	2.53839i	−0.271992	−	0.197613i
$166$	2.25683	−	1.63968i	0.175164	−	0.127264i
$167$	−6.85378	+	21.0938i	−0.530361	+	1.63228i	0.223103	+	0.974795i	$0.428381\pi$
$167$	−6.85378	+	21.0938i	−0.530361	+	1.63228i	−0.753464	+	0.657489i	$0.771619\pi$
$168$	1.69738	+	1.23322i	0.130956	+	0.0951450i
$169$	−2.63134			−0.202411
$170$	4.57257			0.350700
$171$	−10.2146	−	7.42136i	−0.781132	−	0.567526i
$172$	7.89625			0.602083
$173$	18.8555	+	13.6993i	1.43356	+	1.04154i	0.989340	+	0.145623i	$0.0465186\pi$
$173$	18.8555	+	13.6993i	1.43356	+	1.04154i	0.444218	+	0.895919i	$0.353481\pi$
$174$	2.35205	−	1.70887i	0.178309	−	0.129549i
$175$	26.6244	+	19.3438i	2.01262	+	1.46225i
$176$	−0.816857	+	2.51403i	−0.0615729	+	0.189502i
$177$	−1.11103	+	0.807207i	−0.0835098	+	0.0606734i
$178$	−3.23626	+	2.35128i	−0.242568	+	0.176236i
$179$	7.39569	−	5.37328i	0.552780	−	0.401618i	−0.276029	−	0.961149i	$-0.589019\pi$
$179$	7.39569	−	5.37328i	0.552780	−	0.401618i	0.828809	+	0.559531i	$0.189019\pi$
$180$	3.01686	+	9.28494i	0.224863	+	0.692059i
$181$	1.63434	+	5.02997i	0.121479	+	0.373875i	0.993243	−	0.116051i	$-0.0370237\pi$
$181$	1.63434	+	5.02997i	0.121479	+	0.373875i	−0.871764	+	0.489926i	$0.837024\pi$
$182$	14.5061			1.07527
$183$	1.14515	+	3.45248i	0.0846522	+	0.255215i
$184$	−4.20833			−0.310242
$185$	9.39415	+	28.9122i	0.690672	+	2.12567i
$186$	1.01575	+	3.12615i	0.0744781	+	0.229220i
$187$	−2.78765	+	2.02534i	−0.203853	+	0.148108i
$188$	0.765068	−	0.555854i	0.0557983	−	0.0405398i
$189$	−9.81613	+	7.13184i	−0.714018	+	0.518765i
$190$	4.91771	−	15.1352i	0.356768	−	1.09802i
$191$	−16.0057	−	11.6288i	−1.15813	−	0.841431i	−0.168589	−	0.985686i	$-0.553921\pi$
$191$	−16.0057	−	11.6288i	−1.15813	−	0.841431i	−0.989540	+	0.144256i	$0.953921\pi$
$192$	−0.376781	+	0.273748i	−0.0271919	+	0.0197560i
$193$	−15.2161	−	11.0552i	−1.09528	−	0.795769i	−0.114998	−	0.993366i	$-0.536686\pi$
$193$	−15.2161	−	11.0552i	−1.09528	−	0.795769i	−0.980283	+	0.197597i	$0.936686\pi$
$194$	8.75717			0.628728
$195$	−4.25594	−	3.09212i	−0.304774	−	0.221431i
$196$	13.2946			0.949615
$197$	21.4394			1.52749			0.763747	−	0.645516i	$-0.223358\pi$
$197$	21.4394			1.52749			0.763747	+	0.645516i	$0.223358\pi$
$198$	−5.95182	−	4.32425i	−0.422977	−	0.307311i
$199$	−6.45872	+	19.8779i	−0.457847	+	1.40911i	0.409913	+	0.912125i	$0.365559\pi$
$199$	−6.45872	+	19.8779i	−0.457847	+	1.40911i	−0.867760	+	0.496983i	$0.834441\pi$
$200$	−5.91003	+	4.29389i	−0.417902	+	0.303624i
$201$	−4.58385	−	3.33036i	−0.323320	−	0.234906i
$202$	−0.845834	−	2.60321i	−0.0595127	−	0.183161i
$203$	8.69021	−	26.7457i	0.609933	−	1.87718i
$204$	−0.607083			−0.0425043
$205$	7.94945	+	24.4659i	0.555214	+	1.70877i
$206$	−6.14691	+	4.46599i	−0.428275	+	0.311160i
$207$	3.61927	−	11.1390i	0.251556	−	0.774211i
$208$	−0.995047	+	3.06244i	−0.0689941	+	0.212342i
$209$	3.70580	+	11.4053i	0.256336	+	0.788920i
$210$	−5.95421	−	4.32599i	−0.410879	−	0.298521i
$211$	−6.23294	−	19.1830i	−0.429094	−	1.32061i	−0.899020	−	0.437908i	$-0.855719\pi$
$211$	−6.23294	−	19.1830i	−0.429094	−	1.32061i	0.469926	−	0.882706i	$-0.344281\pi$
$212$	−9.08026			−0.623635
$213$	−1.31958	+	4.06125i	−0.0904161	+	0.278272i
$214$	2.40718	−	7.40855i	0.164552	−	0.506438i
$215$	−27.6991			−1.88906
$216$	−0.832290	−	2.56153i	−0.0566302	−	0.174290i
$217$	25.7228	+	18.6887i	1.74618	+	1.26867i
$218$	−4.18687	−	12.8859i	−0.283571	−	0.872741i
$219$	−1.38364	+	4.25840i	−0.0934975	+	0.287756i
$220$	2.86543	−	8.81890i	0.193187	−	0.594570i
$221$	−3.39575	+	2.46715i	−0.228423	+	0.165959i
$222$	−1.24723	−	3.83857i	−0.0837083	−	0.257628i
$223$	4.12085			0.275952			0.137976	−	0.990436i	$-0.455940\pi$
$223$	4.12085			0.275952			0.137976	+	0.990436i	$0.455940\pi$
$224$	−1.39211	+	4.28447i	−0.0930141	+	0.286268i
$225$	−6.28265	−	19.3360i	−0.418843	−	1.28907i
$226$	7.62819	+	5.54220i	0.507420	+	0.368662i
$227$	6.64910	−	4.83085i	0.441316	−	0.320635i	−0.344842	−	0.938661i	$-0.612067\pi$
$227$	6.64910	−	4.83085i	0.441316	−	0.320635i	0.786158	+	0.618026i	$0.212067\pi$
$228$	−0.652906	+	2.00944i	−0.0432397	+	0.133078i
$229$	−5.50297	−	3.99814i	−0.363647	−	0.264205i	0.390925	−	0.920423i	$-0.372155\pi$
$229$	−5.50297	−	3.99814i	−0.363647	−	0.264205i	−0.754571	+	0.656218i	$0.772155\pi$
$230$	14.7623			0.973397
$231$	5.54608			0.364905
$232$	5.05028	+	3.66924i	0.331567	+	0.240898i
$233$	−13.7625			−0.901608			−0.450804	−	0.892623i	$-0.648863\pi$
$233$	−13.7625			−0.901608			−0.450804	+	0.892623i	$0.648863\pi$
$234$	−7.25016	−	5.26755i	−0.473958	−	0.344350i
$235$	−2.68376	+	1.94987i	−0.175069	+	0.127195i
$236$	−2.38557	−	1.73322i	−0.155287	−	0.112823i
$237$	−1.08354	+	3.33480i	−0.0703837	+	0.216619i
$238$	−4.75077	+	3.45164i	−0.307947	+	0.223736i
$239$	7.42767	−	5.39652i	0.480456	−	0.349072i	−0.321046	−	0.947064i	$-0.604034\pi$
$239$	7.42767	−	5.39652i	0.480456	−	0.349072i	0.801502	+	0.597992i	$0.204034\pi$
$240$	1.32170	−	0.960273i	0.0853155	−	0.0619854i
$241$	−6.07295	−	18.6906i	−0.391193	−	1.20397i	−0.931887	−	0.362749i	$-0.881838\pi$
$241$	−6.07295	−	18.6906i	−0.391193	−	1.20397i	0.540693	−	0.841220i	$-0.318162\pi$
$242$	−1.23990	−	3.81603i	−0.0797040	−	0.245304i
$243$	11.3843			0.730306
$244$	−6.29045	+	4.62928i	−0.402705	+	0.296359i
$245$	−46.6358			−2.97945
$246$	−1.05542	−	3.24824i	−0.0672910	−	0.207101i
$247$	4.51419	+	13.8933i	0.287231	+	0.884007i
$248$	−5.70990	+	4.14849i	−0.362579	+	0.263429i
$249$	1.05107	−	0.763644i	0.0666086	−	0.0483940i
$250$	6.54199	−	4.75303i	0.413751	−	0.300608i
$251$	−1.87225	+	5.76219i	−0.118175	+	0.363706i	−0.992596	−	0.121462i	$-0.961242\pi$
$251$	−1.87225	+	5.76219i	−0.118175	+	0.363706i	0.874421	+	0.485168i	$0.161242\pi$
$252$	−10.1432	−	7.36949i	−0.638964	−	0.464234i
$253$	−8.99976	+	6.53871i	−0.565810	+	0.411085i
$254$	7.99575	+	5.80925i	0.501698	+	0.364505i
$255$	2.12957			0.133359
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−2.61099			−0.162869			−0.0814344	−	0.996679i	$-0.525950\pi$
$257$	−2.61099			−0.162869			−0.0814344	+	0.996679i	$0.525950\pi$
$258$	3.67750			0.228951
$259$	−31.5849	−	22.9477i	−1.96259	−	1.42590i
$260$	3.49050	−	10.7427i	0.216472	−	0.666232i
$261$	−14.0554	+	10.2119i	−0.870009	+	0.632098i
$262$	4.26581	+	3.09929i	0.263542	+	0.191475i
$263$	2.60901	+	8.02971i	0.160878	+	0.495133i	0.998709	−	0.0507975i	$-0.0161763\pi$
$263$	2.60901	+	8.02971i	0.160878	+	0.495133i	−0.837831	+	0.545930i	$0.816176\pi$
$264$	−0.380433	+	1.17085i	−0.0234140	+	0.0720609i
$265$	31.8524			1.95668
$266$	6.31552	+	19.4372i	0.387229	+	1.19177i
$267$	−1.50721	+	1.09506i	−0.0922400	+	0.0670163i
$268$	3.75944	−	11.5704i	0.229645	−	0.706773i
$269$	0.818643	−	2.51952i	0.0499135	−	0.153618i	−0.922993	−	0.384817i	$-0.874265\pi$
$269$	0.818643	−	2.51952i	0.0499135	−	0.153618i	0.972907	+	0.231199i	$0.0742647\pi$
$270$	2.91957	+	8.98551i	0.177679	+	0.546841i
$271$	10.8463	+	7.88031i	0.658867	+	0.478695i	0.866280	−	0.499559i	$-0.166504\pi$
$271$	10.8463	+	7.88031i	0.658867	+	0.478695i	−0.207413	+	0.978253i	$0.566504\pi$
$272$	−0.402808	−	1.23972i	−0.0244238	−	0.0751689i
$273$	6.75590			0.408886
$274$	−1.90109	+	5.85095i	−0.114849	+	0.353469i
$275$	−5.96730	+	18.3655i	−0.359842	+	1.10748i
$276$	−1.95993			−0.117974
$277$	−4.09747	−	12.6107i	−0.246193	−	0.757704i	−0.995438	−	0.0954109i	$-0.969583\pi$
$277$	−4.09747	−	12.6107i	−0.246193	−	0.757704i	0.749245	−	0.662293i	$-0.230417\pi$
$278$	−4.00547	−	2.91014i	−0.240232	−	0.174539i
$279$	−6.06991	−	18.6813i	−0.363396	−	1.11842i
$280$	4.88334	−	15.0294i	0.291835	−	0.898177i
$281$	7.24503	−	22.2979i	0.432203	−	1.33018i	−0.463724	−	0.885980i	$-0.653487\pi$
$281$	7.24503	−	22.2979i	0.432203	−	1.33018i	0.895926	−	0.444203i	$-0.146513\pi$
$282$	0.356313	−	0.258877i	0.0212181	−	0.0154159i
$283$	3.28397	+	10.1070i	0.195211	+	0.600799i	0.999974	+	0.00720235i	$0.00229260\pi$
$283$	3.28397	+	10.1070i	0.195211	+	0.600799i	−0.804763	+	0.593597i	$0.797707\pi$
$284$	−9.16899			−0.544079
$285$	2.29031	−	7.04886i	0.135666	−	0.417538i
$286$	2.63031	+	8.09527i	0.155534	+	0.478683i
$287$	−26.7275	−	19.4187i	−1.57768	−	1.14625i
$288$	2.25157	−	1.63586i	0.132675	−	0.0963942i
$289$	−4.72822	+	14.5520i	−0.278131	+	0.855998i
$290$	−17.7158	−	12.8712i	−1.04030	−	0.755826i
$291$	4.07845			0.239083
$292$	−9.61409			−0.562622
$293$	6.15923	+	4.47494i	0.359826	+	0.261429i	0.752980	−	0.658044i	$-0.228616\pi$
$293$	6.15923	+	4.47494i	0.359826	+	0.261429i	−0.393154	+	0.919473i	$0.628616\pi$
$294$	6.19166			0.361105
$295$	8.36828	+	6.07991i	0.487220	+	0.353986i
$296$	7.01114	−	5.09389i	0.407514	−	0.296076i
$297$	−5.75988	−	4.18480i	−0.334222	−	0.242827i
$298$	2.99105	−	9.20551i	0.173267	−	0.533261i
$299$	−10.9630	+	7.96507i	−0.634006	+	0.460632i
$300$	−2.75246	+	1.99978i	−0.158913	+	0.115457i
$301$	28.7785	−	20.9088i	1.65877	−	1.20517i
$302$	1.75708	+	5.40773i	0.101108	+	0.311180i
$303$	−0.393928	−	1.21239i	−0.0226306	−	0.0696497i
$304$	−4.53666			−0.260195
$305$	22.0661	−	16.2389i	1.26350	−	0.929839i
$306$	3.62781			0.207388
$307$	−3.90809	−	12.0279i	−0.223046	−	0.686466i	−0.998484	−	0.0550418i	$-0.982471\pi$
$307$	−3.90809	−	12.0279i	−0.223046	−	0.686466i	0.775438	−	0.631424i	$-0.217529\pi$
$308$	3.67990	+	11.3256i	0.209682	+	0.645335i
$309$	−2.86278	+	2.07993i	−0.162858	+	0.118323i
$310$	20.0296	−	14.5524i	1.13761	−	0.826520i
$311$	10.3091	−	7.49003i	0.584578	−	0.424721i	−0.255794	−	0.966731i	$-0.582337\pi$
$311$	10.3091	−	7.49003i	0.584578	−	0.424721i	0.840372	+	0.542011i	$0.182337\pi$
$312$	−0.463421	+	1.42626i	−0.0262360	+	0.0807462i
$313$	−12.0081	−	8.72443i	−0.678741	−	0.493134i	0.194199	−	0.980962i	$-0.437789\pi$
$313$	−12.0081	−	8.72443i	−0.678741	−	0.493134i	−0.872940	+	0.487828i	$0.837789\pi$
$314$	8.07801	−	5.86902i	0.455868	−	0.331208i
$315$	35.5812	+	25.8513i	2.00477	+	1.45655i
$316$	−7.52891			−0.423534
$317$	−8.93523	−	6.49182i	−0.501852	−	0.364617i	0.307872	−	0.951428i	$-0.400383\pi$
$317$	−8.93523	−	6.49182i	−0.501852	−	0.364617i	−0.809724	+	0.586811i	$0.800383\pi$
$318$	−4.22893			−0.237147
$319$	16.5014			0.923903
$320$	2.83793	+	2.06188i	0.158645	+	0.115262i
$321$	1.12109	−	3.45037i	0.0625732	−	0.192581i
$322$	−15.3376	+	11.1434i	−0.854731	+	0.620999i
$323$	−4.78421	−	3.47593i	−0.266201	−	0.193406i
$324$	2.19245	+	6.74768i	0.121803	+	0.374871i
$325$	−7.26901	+	22.3717i	−0.403212	+	1.24096i
$326$	5.22237			0.289240
$327$	−1.94994	−	6.00130i	−0.107832	−	0.331873i
$328$	5.93292	−	4.31052i	0.327591	−	0.238008i
$329$	1.31648	−	4.05171i	0.0725800	−	0.223378i
$330$	1.33451	−	4.10720i	0.0734624	−	0.226094i
$331$	3.95682	+	12.1778i	0.217487	+	0.669355i	0.998968	+	0.0454261i	$0.0144646\pi$
$331$	3.95682	+	12.1778i	0.217487	+	0.669355i	−0.781481	+	0.623929i	$0.785535\pi$
$332$	2.25683	+	1.63968i	0.123859	+	0.0899891i
$333$	7.45318	+	22.9385i	0.408432	+	1.25702i
$334$	−22.1793			−1.21360
$335$	−13.1877	+	40.5875i	−0.720519	+	2.21753i
$336$	−0.648342	+	1.99539i	−0.0353700	+	0.108858i
$337$	−7.69777			−0.419324			−0.209662	−	0.977774i	$-0.567236\pi$
$337$	−7.69777			−0.419324			−0.209662	+	0.977774i	$0.567236\pi$
$338$	−0.813128	−	2.50255i	−0.0442283	−	0.136121i
$339$	3.55266	+	2.58116i	0.192954	+	0.140189i
$340$	1.41300	+	4.34877i	0.0766308	+	0.235845i
$341$	−5.76524	+	17.7436i	−0.312205	+	0.960868i
$342$	3.90164	−	12.0080i	0.210977	−	0.649319i
$343$	22.9412	−	16.6678i	1.23871	−	0.899975i
$344$	2.44008	+	7.50978i	0.131560	+	0.404900i
$345$	6.87521			0.370149
$346$	−7.20217	+	22.1660i	−0.387191	+	1.19165i
$347$	−7.36532	−	22.6681i	−0.395391	−	1.21689i	−0.928656	−	0.370941i	$-0.879035\pi$
$347$	−7.36532	−	22.6681i	−0.395391	−	1.21689i	0.533265	−	0.845948i	$-0.320965\pi$
$348$	2.35205	+	1.70887i	0.126083	+	0.0916049i
$349$	−15.0282	+	10.9186i	−0.804440	+	0.584460i	−0.912213	−	0.409716i	$-0.865628\pi$
$349$	−15.0282	+	10.9186i	−0.804440	+	0.584460i	0.107773	+	0.994175i	$0.465628\pi$
$350$	−10.1696	+	31.2989i	−0.543589	+	1.67299i
$351$	−7.01635	−	5.09768i	−0.374505	−	0.272094i
$352$	−2.64340			−0.140894
$353$	−25.2394			−1.34336			−0.671680	−	0.740842i	$-0.734427\pi$
$353$	−25.2394			−1.34336			−0.671680	+	0.740842i	$0.734427\pi$
$354$	−1.11103	−	0.807207i	−0.0590503	−	0.0429026i
$355$	32.1637			1.70707
$356$	−3.23626	−	2.35128i	−0.171521	−	0.124618i
$357$	−2.21256	+	1.60752i	−0.117101	+	0.0850791i
$358$	7.39569	+	5.37328i	0.390874	+	0.283987i
$359$	9.24344	−	28.4484i	0.487850	−	1.50145i	−0.339960	−	0.940440i	$-0.610413\pi$
$359$	9.24344	−	28.4484i	0.487850	−	1.50145i	0.827810	−	0.561009i	$-0.189587\pi$
$360$	−7.89824	+	5.73841i	−0.416274	+	0.302441i
$361$	−1.27929	+	0.929459i	−0.0673311	+	0.0489189i
$362$	−4.27875	+	3.10869i	−0.224886	+	0.163389i
$363$	−0.577457	−	1.77723i	−0.0303086	−	0.0932803i
$364$	4.48264	+	13.7962i	0.234954	+	0.723115i
$365$	33.7250			1.76525
$366$	−2.92964	+	2.15598i	−0.153135	+	0.112695i
$367$	−9.76559			−0.509760			−0.254880	−	0.966973i	$-0.582036\pi$
$367$	−9.76559			−0.509760			−0.254880	+	0.966973i	$0.582036\pi$
$368$	−1.30045	−	4.00236i	−0.0677904	−	0.208637i
$369$	6.30698	+	19.4109i	0.328328	+	1.01049i
$370$	−24.5942	+	17.8687i	−1.27859	+	0.928951i
$371$	−33.0938	+	24.0440i	−1.71814	+	1.24830i
$372$	−2.65926	+	1.93206i	−0.137876	+	0.100173i
$373$	1.10108	−	3.38877i	0.0570116	−	0.175464i	−0.918496	−	0.395431i	$-0.870595\pi$
$373$	1.10108	−	3.38877i	0.0570116	−	0.175464i	0.975507	+	0.219968i	$0.0705951\pi$
$374$	−2.78765	−	2.02534i	−0.144146	−	0.104728i
$375$	3.04678	−	2.21362i	0.157335	−	0.114311i
$376$	0.765068	+	0.555854i	0.0394554	+	0.0286660i
$377$	20.1011			1.03526
$378$	−9.81613	−	7.13184i	−0.504887	−	0.366822i
$379$	6.11645			0.314181			0.157090	−	0.987584i	$-0.449789\pi$
$379$	6.11645			0.314181			0.157090	+	0.987584i	$0.449789\pi$
$380$	15.9140			0.816373
$381$	3.72384	+	2.70553i	0.190778	+	0.138608i
$382$	6.11362	−	18.8158i	0.312800	−	0.962700i
$383$	−9.76907	+	7.09764i	−0.499176	+	0.362673i	−0.808702	−	0.588218i	$-0.799830\pi$
$383$	−9.76907	+	7.09764i	−0.499176	+	0.362673i	0.309526	+	0.950891i	$0.399830\pi$
$384$	−0.376781	−	0.273748i	−0.0192275	−	0.0139696i
$385$	−12.9086	−	39.7287i	−0.657885	−	2.02476i
$386$	5.81205	−	17.8876i	0.295825	−	0.910457i
$387$	−21.9760			−1.11710
$388$	2.70611	+	8.32856i	0.137382	+	0.422819i
$389$	22.0172	−	15.9965i	1.11632	−	0.811052i	0.132671	−	0.991160i	$-0.457645\pi$
$389$	22.0172	−	15.9965i	1.11632	−	0.811052i	0.983647	+	0.180108i	$0.0576446\pi$
$390$	1.62562	−	5.00315i	0.0823166	−	0.253344i
$391$	1.69515	−	5.21714i	0.0857274	−	0.263842i
$392$	4.10826	+	12.6439i	0.207498	+	0.638614i
$393$	1.98670	+	1.44342i	0.100216	+	0.0728111i
$394$	6.62514	+	20.3901i	0.333770	+	1.02724i
$395$	26.4105			1.32886
$396$	2.27339	−	6.99678i	0.114242	−	0.351602i
$397$	8.25366	−	25.4022i	0.414240	−	1.27490i	−0.498690	−	0.866781i	$-0.666185\pi$
$397$	8.25366	−	25.4022i	0.414240	−	1.27490i	0.912929	−	0.408118i	$-0.133815\pi$
$398$	−20.9009			−1.04767
$399$	2.94131	+	9.05242i	0.147250	+	0.453188i
$400$	−5.91003	−	4.29389i	−0.295501	−	0.214694i
$401$	5.31767	+	16.3661i	0.265552	+	0.817284i	0.991566	+	0.129604i	$0.0413707\pi$
$401$	5.31767	+	16.3661i	0.265552	+	0.817284i	−0.726014	+	0.687680i	$0.758629\pi$
$402$	1.75088	−	5.38864i	0.0873258	−	0.268761i
$403$	−7.02287	+	21.6142i	−0.349834	+	1.07668i
$404$	2.21442	−	1.60887i	0.110172	−	0.0800444i
$405$	−7.69085	−	23.6700i	−0.382162	−	1.17617i
$406$	28.1221			1.39568
$407$	7.07908	−	21.7872i	0.350897	−	1.07995i
$408$	−0.187599	−	0.577370i	−0.00928753	−	0.0285841i
$409$	23.8197	+	17.3060i	1.17781	+	0.855726i	0.991923	−	0.126845i	$-0.0404852\pi$
$409$	23.8197	+	17.3060i	1.17781	+	0.855726i	0.185884	+	0.982572i	$0.440485\pi$
$410$	−20.8119	+	15.1208i	−1.02783	+	0.746761i
$411$	−0.885389	+	2.72495i	−0.0436730	+	0.134412i
$412$	−6.14691	−	4.46599i	−0.302836	−	0.220023i
$413$	−13.2839			−0.653657
$414$	11.7122			0.575623
$415$	−7.91666	−	5.75179i	−0.388614	−	0.282344i
$416$	−3.22004			−0.157875
$417$	−1.86546	−	1.35533i	−0.0913517	−	0.0663709i
$418$	−9.70192	+	7.04886i	−0.474536	+	0.344771i
$419$	5.56372	+	4.04228i	0.271806	+	0.197478i	0.715335	−	0.698781i	$-0.246274\pi$
$419$	5.56372	+	4.04228i	0.271806	+	0.197478i	−0.443530	+	0.896260i	$0.646274\pi$
$420$	2.27431	−	6.99959i	0.110975	−	0.341545i
$421$	−22.6829	+	16.4801i	−1.10550	+	0.803191i	−0.981949	−	0.189147i	$-0.939428\pi$
$421$	−22.6829	+	16.4801i	−1.10550	+	0.803191i	−0.123549	+	0.992338i	$0.539428\pi$
$422$	16.3181	−	11.8558i	0.794351	−	0.577130i
$423$	−2.12926	+	1.54700i	−0.103528	+	0.0752176i
$424$	−2.80596	−	8.63584i	−0.136269	−	0.419394i
$425$	−2.94259	−	9.05637i	−0.142737	−	0.439299i
$426$	−4.27025			−0.206894
$427$	−10.6680	+	33.5286i	−0.516261	+	1.62256i
$428$	7.78981			0.376535
$429$	1.22501	+	3.77019i	0.0591440	+	0.182026i
$430$	−8.55948	−	26.3434i	−0.412775	−	1.27039i
$431$	10.5241	−	7.64617i	0.506926	−	0.368303i	−0.304730	−	0.952439i	$-0.598566\pi$
$431$	10.5241	−	7.64617i	0.506926	−	0.368303i	0.811656	+	0.584136i	$0.198566\pi$
$432$	2.17896	−	1.58311i	0.104835	−	0.0761674i
$433$	−3.49029	+	2.53585i	−0.167733	+	0.121865i	−0.668485	−	0.743726i	$-0.733057\pi$
$433$	−3.49029	+	2.53585i	−0.167733	+	0.121865i	0.500752	+	0.865591i	$0.333057\pi$
$434$	−9.82525	+	30.2390i	−0.471627	+	1.45152i
$435$	−8.25071	−	5.99449i	−0.395591	−	0.287414i
$436$	10.9614	−	7.96390i	0.524954	−	0.381402i
$437$	−15.4456	−	11.2219i	−0.738861	−	0.536814i
$438$	−4.47754			−0.213945
$439$	14.3098	+	10.3967i	0.682970	+	0.496206i	0.874342	−	0.485311i	$-0.161294\pi$
$439$	14.3098	+	10.3967i	0.682970	+	0.496206i	−0.191372	+	0.981518i	$0.561294\pi$
$440$	9.27274			0.442060
$441$	−37.0002			−1.76191
$442$	−3.39575	−	2.46715i	−0.161519	−	0.117351i
$443$	−6.00840	+	18.4920i	−0.285468	+	0.878580i	0.700790	+	0.713367i	$0.252831\pi$
$443$	−6.00840	+	18.4920i	−0.285468	+	0.878580i	−0.986258	+	0.165212i	$0.947169\pi$
$444$	3.26528	−	2.37236i	0.154963	−	0.112587i
$445$	11.3524	+	8.24800i	0.538155	+	0.390992i
$446$	1.27341	+	3.91916i	0.0602978	+	0.185578i
$447$	1.39301	−	4.28726i	0.0658873	−	0.202780i
$448$	−4.50495			−0.212839
$449$	1.79597	+	5.52742i	0.0847570	+	0.260855i	0.984449	−	0.175670i	$-0.0562091\pi$
$449$	1.79597	+	5.52742i	0.0847570	+	0.260855i	−0.899692	+	0.436525i	$0.856209\pi$
$450$	16.4482	−	11.9503i	0.775375	−	0.563343i
$451$	5.99041	−	18.4366i	0.282077	−	0.868145i
$452$	−2.91371	+	8.96748i	−0.137049	+	0.421795i
$453$	0.818319	+	2.51853i	0.0384480	+	0.118331i
$454$	6.64910	+	4.83085i	0.312058	+	0.226723i
$455$	−15.7246	−	48.3952i	−0.737178	−	2.26880i
$456$	−2.11285			−0.0989431
$457$	−0.270640	+	0.832944i	−0.0126600	+	0.0389635i	−0.957187	−	0.289470i	$-0.906521\pi$
$457$	−0.270640	+	0.832944i	−0.0126600	+	0.0389635i	0.944527	+	0.328434i	$0.106521\pi$
$458$	2.10195	−	6.46913i	0.0982176	−	0.302283i
$459$	3.51082			0.163871
$460$	4.56180	+	14.0398i	0.212695	+	0.654608i
$461$	12.9170	+	9.38475i	0.601605	+	0.437092i	0.846448	−	0.532471i	$-0.178737\pi$
$461$	12.9170	+	9.38475i	0.601605	+	0.437092i	−0.244843	+	0.969563i	$0.578737\pi$
$462$	1.71383	+	5.27463i	0.0797347	+	0.245398i
$463$	−10.1990	+	31.3894i	−0.473989	+	1.45879i	0.373328	+	0.927699i	$0.378217\pi$
$463$	−10.1990	+	31.3894i	−0.473989	+	1.45879i	−0.847317	+	0.531088i	$0.821783\pi$
$464$	−1.92904	+	5.93696i	−0.0895532	+	0.275616i
$465$	9.32835	−	6.77744i	0.432592	−	0.314296i
$466$	−4.25283	−	13.0889i	−0.197009	−	0.606330i
$467$	29.6836			1.37359			0.686796	−	0.726851i	$-0.259017\pi$
$467$	29.6836			1.37359			0.686796	+	0.726851i	$0.259017\pi$
$468$	2.76931	−	8.52307i	0.128012	−	0.393979i
$469$	−16.9361	−	52.1240i	−0.782037	−	2.40686i
$470$	−2.68376	−	1.94987i	−0.123793	−	0.0899407i
$471$	3.76215	−	2.73336i	0.173351	−	0.125947i
$472$	0.911207	−	2.80441i	0.0419417	−	0.129083i
$473$	16.8866	+	12.2688i	0.776447	+	0.564122i
$474$	−3.50642			−0.161055
$475$	−33.1412			−1.52062
$476$	−4.75077	−	3.45164i	−0.217751	−	0.158206i
$477$	25.2713			1.15709
$478$	7.42767	+	5.39652i	0.339734	+	0.246831i
$479$	34.0635	−	24.7486i	1.55640	−	1.13079i	0.617518	−	0.786557i	$-0.288138\pi$
$479$	34.0635	−	24.7486i	1.55640	−	1.13079i	0.938884	−	0.344235i	$-0.111862\pi$
$480$	1.32170	+	0.960273i	0.0603272	+	0.0438303i
$481$	8.62332	−	26.5399i	0.393190	−	1.21011i
$482$	15.8992	−	11.5514i	0.724189	−	0.526154i
$483$	−7.14314	+	5.18980i	−0.325024	+	0.236144i
$484$	3.24611	−	2.35844i	0.147550	−	0.107202i
$485$	−9.49271	−	29.2156i	−0.431042	−	1.32661i
$486$	3.51796	+	10.8272i	0.159578	+	0.491130i
$487$	−13.6710			−0.619493			−0.309746	−	0.950819i	$-0.600244\pi$
$487$	−13.6710			−0.619493			−0.309746	+	0.950819i	$0.600244\pi$
$488$	−6.34656	−	4.55205i	−0.287295	−	0.206062i
$489$	2.43220			0.109988
$490$	−14.4113	−	44.3533i	−0.651035	−	2.00368i
$491$	−5.81323	−	17.8913i	−0.262347	−	0.807422i	−0.992293	−	0.123916i	$-0.960455\pi$
$491$	−5.81323	−	17.8913i	−0.262347	−	0.807422i	0.729945	−	0.683505i	$-0.239545\pi$
$492$	2.76312	−	2.00753i	0.124571	−	0.0905062i
$493$	−6.58312	+	4.78292i	−0.296489	+	0.215412i
$494$	−11.8183	+	8.58650i	−0.531731	+	0.386325i
$495$	−7.97478	+	24.5439i	−0.358440	+	1.10316i
$496$	−5.70990	−	4.14849i	−0.256382	−	0.186273i
$497$	−33.4171	+	24.2790i	−1.49896	+	1.08906i
$498$	1.05107	+	0.763644i	0.0470994	+	0.0342197i
$499$	−22.7355			−1.01778			−0.508891	−	0.860831i	$-0.669945\pi$
$499$	−22.7355			−1.01778			−0.508891	+	0.860831i	$0.669945\pi$
$500$	6.54199	+	4.75303i	0.292566	+	0.212562i
$501$	−10.3295			−0.461488
$502$	−6.05872			−0.270414
$503$	−6.77591	−	4.92299i	−0.302123	−	0.219505i	0.426386	−	0.904541i	$-0.359786\pi$
$503$	−6.77591	−	4.92299i	−0.302123	−	0.219505i	−0.728509	+	0.685036i	$0.759786\pi$
$504$	3.87437	−	11.9241i	0.172578	−	0.531141i
$505$	−7.76792	+	5.64372i	−0.345668	+	0.251142i
$506$	−8.99976	−	6.53871i	−0.400088	−	0.290681i
$507$	−0.378696	−	1.16551i	−0.0168185	−	0.0517620i
$508$	−3.05410	+	9.39957i	−0.135504	+	0.417038i
$509$	16.8419			0.746505			0.373252	−	0.927730i	$-0.378243\pi$
$509$	16.8419			0.746505			0.373252	+	0.927730i	$0.378243\pi$
$510$	0.658074	+	2.02534i	0.0291400	+	0.0896837i
$511$	−35.0393	+	25.4576i	−1.55005	+	1.12618i
$512$	0.309017	−	0.951057i	0.0136568	−	0.0420312i
$513$	3.77582	−	11.6208i	0.166706	−	0.513070i
$514$	−0.806839	−	2.48320i	−0.0355882	−	0.109529i
$515$	21.5626	+	15.6661i	0.950161	+	0.690332i
$516$	1.13641	+	3.49751i	0.0500277	+	0.153969i
$517$	2.49980			0.109941
$518$	12.0643	−	37.1302i	0.530077	−	1.63141i
$519$	−3.35425	+	10.3233i	−0.147235	+	0.453143i
$520$	11.2955			0.495341
$521$	−3.48155	−	10.7151i	−0.152530	−	0.469438i	0.845373	−	0.534177i	$-0.179378\pi$
$521$	−3.48155	−	10.7151i	−0.152530	−	0.469438i	−0.997902	+	0.0647391i	$0.979378\pi$
$522$	−14.0554	−	10.2119i	−0.615189	−	0.446961i
$523$	10.6107	+	32.6564i	0.463975	+	1.42797i	0.860268	+	0.509843i	$0.170296\pi$
$523$	10.6107	+	32.6564i	0.463975	+	1.42797i	−0.396293	+	0.918124i	$0.629704\pi$
$524$	−1.62939	+	5.01476i	−0.0711804	+	0.219071i
$525$	−4.73627	+	14.5767i	−0.206708	+	0.636181i
$526$	−6.83048	+	4.96263i	−0.297823	+	0.216381i
$527$	−2.84295	−	8.74971i	−0.123841	−	0.381143i
$528$	−1.23111			−0.0535770
$529$	−1.63469	+	5.03106i	−0.0710735	+	0.218742i
$530$	9.84295	+	30.2935i	0.427550	+	1.31586i
$531$	6.63928	+	4.82372i	0.288120	+	0.209331i
$532$	−16.5342	+	12.0128i	−0.716850	+	0.520822i
$533$	7.29717	−	22.4584i	0.316075	−	0.972780i
$534$	−1.50721	−	1.09506i	−0.0652235	−	0.0473877i
$535$	−27.3257			−1.18139
$536$	12.1658			0.525483
$537$	3.44438	+	2.50249i	0.148636	+	0.107990i
$538$	2.64918			0.114214
$539$	28.4313	+	20.6566i	1.22462	+	0.889741i
$540$	−7.64353	+	5.55335i	−0.328925	+	0.238978i
$541$	−5.53412	−	4.02077i	−0.237930	−	0.172867i	0.462430	−	0.886656i	$-0.346978\pi$
$541$	−5.53412	−	4.02077i	−0.237930	−	0.172867i	−0.700361	+	0.713789i	$0.746978\pi$
$542$	−4.14293	+	12.7506i	−0.177954	+	0.547686i
$543$	−1.99273	+	1.44780i	−0.0855163	+	0.0621312i
$544$	1.05457	−	0.766187i	0.0452142	−	0.0328500i
$545$	−38.4511	+	27.9364i	−1.64707	+	1.19666i
$546$	2.08769	+	6.42525i	0.0893449	+	0.274975i
$547$	−7.84894	−	24.1565i	−0.335596	−	1.03286i	−0.966428	−	0.256939i	$-0.917286\pi$
$547$	−7.84894	−	24.1565i	−0.335596	−	1.03286i	0.630831	−	0.775920i	$-0.282714\pi$
$548$	−6.15205			−0.262803
$549$	17.5069	−	12.8837i	0.747178	−	0.549864i
$550$	−19.3106			−0.823406
$551$	8.75138	+	26.9340i	0.372821	+	1.14743i
$552$	−0.605653	−	1.86401i	−0.0257783	−	0.0793375i
$553$	−27.4397	+	19.9361i	−1.16686	+	0.847771i
$554$	10.7273	−	7.79384i	0.455759	−	0.331129i
$555$	−11.4542	+	8.32196i	−0.486204	+	0.353248i
$556$	1.52995	−	4.70871i	0.0648844	−	0.199694i
$557$	35.6693	+	25.9153i	1.51136	+	1.09807i	0.965571	+	0.260141i	$0.0837692\pi$
$557$	35.6693	+	25.9153i	1.51136	+	1.09807i	0.545787	+	0.837924i	$0.316231\pi$
$558$	15.8912	−	11.5456i	0.672729	−	0.488766i
$559$	20.5703	+	14.9452i	0.870030	+	0.632114i
$560$	15.8028			0.667791
$561$	−1.29828	−	0.943258i	−0.0548135	−	0.0398244i
$562$	23.4454			0.988986
$563$	27.9272			1.17699			0.588495	−	0.808501i	$-0.299721\pi$
$563$	27.9272			1.17699			0.588495	+	0.808501i	$0.299721\pi$
$564$	0.356313	+	0.258877i	0.0150035	+	0.0109007i
$565$	10.2209	−	31.4568i	0.429998	−	1.32340i
$566$	−8.59753	+	6.24647i	−0.361381	+	0.262559i
$567$	25.8581	+	18.7870i	1.08594	+	0.788979i
$568$	−2.83337	−	8.72023i	−0.118886	−	0.365893i
$569$	4.98801	−	15.3515i	0.209108	−	0.643569i	−0.790411	−	0.612576i	$-0.790133\pi$
$569$	4.98801	−	15.3515i	0.209108	−	0.643569i	0.999520	−	0.0309925i	$-0.00986679\pi$
$570$	7.41161			0.310438
$571$	−1.86471	−	5.73899i	−0.0780358	−	0.240169i	0.904427	−	0.426629i	$-0.140299\pi$
$571$	−1.86471	−	5.73899i	−0.0780358	−	0.240169i	−0.982463	+	0.186459i	$0.940299\pi$
$572$	−6.88625	+	5.00315i	−0.287929	+	0.209192i
$573$	2.84728	−	8.76303i	0.118947	−	0.366081i
$574$	10.2090	−	31.4201i	0.426116	−	1.31145i
$575$	−9.50001	−	29.2380i	−0.396178	−	1.21931i
$576$	2.25157	+	1.63586i	0.0938156	+	0.0681610i
$577$	−6.19778	−	19.0748i	−0.258017	−	0.794094i	−0.993220	−	0.116248i	$-0.962913\pi$
$577$	−6.19778	−	19.0748i	−0.258017	−	0.794094i	0.735203	−	0.677847i	$-0.237087\pi$
$578$	−15.3008			−0.636431
$579$	2.70683	−	8.33077i	0.112492	−	0.346215i
$580$	6.76682	−	20.8261i	0.280977	−	0.864758i
$581$	12.5670			0.521366
$582$	1.26031	+	3.87884i	0.0522416	+	0.160783i
$583$	−19.4187	−	14.1085i	−0.804240	−	0.584314i
$584$	−2.97092	−	9.14354i	−0.122937	−	0.378362i
$585$	−9.71441	+	29.8979i	−0.401641	+	1.23613i
$586$	−2.35262	+	7.24061i	−0.0971857	+	0.299107i
$587$	−19.2310	+	13.9722i	−0.793750	+	0.576693i	−0.909074	−	0.416635i	$-0.863209\pi$
$587$	−19.2310	+	13.9722i	−0.793750	+	0.576693i	0.115324	+	0.993328i	$0.463209\pi$
$588$	1.91333	+	5.88862i	0.0789044	+	0.242843i
$589$	−32.0190			−1.31932
$590$	−3.19640	+	9.83751i	−0.131594	+	0.405004i
$591$	3.08551	+	9.49622i	0.126921	+	0.390622i
$592$	7.01114	+	5.09389i	0.288156	+	0.209358i
$593$	0.255453	−	0.185598i	0.0104902	−	0.00762158i	−0.582528	−	0.812811i	$-0.697936\pi$
$593$	0.255453	−	0.185598i	0.0104902	−	0.00762158i	0.593018	+	0.805189i	$0.297936\pi$
$594$	2.20008	−	6.77115i	0.0902704	−	0.277824i
$595$	16.6651	+	12.1079i	0.683203	+	0.496376i
$596$	9.67924			0.396477
$597$	−9.73411			−0.398391
$598$	−10.9630	−	7.96507i	−0.448310	−	0.325716i
$599$	−19.8980			−0.813009			−0.406504	−	0.913649i	$-0.633252\pi$
$599$	−19.8980			−0.813009			−0.406504	+	0.913649i	$0.633252\pi$
$600$	−2.75246	−	1.99978i	−0.112369	−	0.0816407i
$601$	36.8244	−	26.7545i	1.50210	−	1.09134i	0.532562	−	0.846391i	$-0.321229\pi$
$601$	36.8244	−	26.7545i	1.50210	−	1.09134i	0.969536	−	0.244948i	$-0.0787709\pi$
$602$	28.7785	+	20.9088i	1.17293	+	0.852181i
$603$	−10.4629	+	32.2015i	−0.426082	+	1.31135i
$604$	−4.60009	+	3.34216i	−0.187175	+	0.135990i
$605$	−11.3869	+	8.27310i	−0.462945	+	0.336349i
$606$	1.03132	−	0.749296i	0.0418944	−	0.0304381i
$607$	8.13736	+	25.0442i	0.330285	+	1.01651i	0.968998	+	0.247068i	$0.0794671\pi$
$607$	8.13736	+	25.0442i	0.330285	+	1.01651i	−0.638713	+	0.769445i	$0.720533\pi$
$608$	−1.40191	−	4.31462i	−0.0568548	−	0.174981i
$609$	13.0972			0.530727
$610$	22.2630	+	15.9680i	0.901401	+	0.646526i
$611$	3.04511			0.123192
$612$	1.12106	+	3.45025i	0.0453160	+	0.139468i
$613$	−6.13342	−	18.8767i	−0.247726	−	0.762423i	−0.995176	−	0.0981049i	$-0.968722\pi$
$613$	−6.13342	−	18.8767i	−0.247726	−	0.762423i	0.747450	−	0.664318i	$-0.231278\pi$
$614$	10.2315	−	7.43362i	0.412910	−	0.299997i
$615$	−9.69269	+	7.04215i	−0.390847	+	0.283967i
$616$	−9.63411	+	6.99959i	−0.388169	+	0.282022i
$617$	−10.0086	+	30.8034i	−0.402933	+	1.24010i	0.519676	+	0.854363i	$0.326053\pi$
$617$	−10.0086	+	30.8034i	−0.402933	+	1.24010i	−0.922609	+	0.385736i	$0.873947\pi$
$618$	−2.86278	−	2.07993i	−0.115158	−	0.0836672i
$619$	1.44673	−	1.05111i	0.0581491	−	0.0422478i	−0.558331	−	0.829618i	$-0.688558\pi$
$619$	1.44673	−	1.05111i	0.0581491	−	0.0422478i	0.616480	+	0.787370i	$0.288558\pi$
$620$	20.0296	+	14.5524i	0.804409	+	0.584438i
$621$	11.3345			0.454837
$622$	10.3091	+	7.49003i	0.413359	+	0.300323i
$623$	−18.0209			−0.721991
$624$	−1.49966			−0.0600345
$625$	6.60166	+	4.79639i	0.264066	+	0.191855i
$626$	4.58670	−	14.1164i	0.183322	−	0.564206i
$627$	−4.51845	+	3.28285i	−0.180450	+	0.131104i
$628$	8.07801	+	5.86902i	0.322348	+	0.234199i
$629$	3.49084	+	10.7437i	0.139189	+	0.428379i
$630$	−13.5908	+	41.8282i	−0.541471	+	1.66648i
$631$	−16.0679			−0.639653			−0.319827	−	0.947476i	$-0.603625\pi$
$631$	−16.0679			−0.639653			−0.319827	+	0.947476i	$0.603625\pi$
$632$	−2.32656	−	7.16042i	−0.0925456	−	0.284826i
$633$	7.59977	−	5.52155i	0.302064	−	0.219462i
$634$	3.41295	−	10.5040i	0.135546	−	0.417167i
$635$	10.7134	−	32.9725i	0.425149	−	1.30847i
$636$	−1.30681	−	4.02195i	−0.0518184	−	0.159481i
$637$	34.6333	+	25.1626i	1.37222	+	0.996979i
$638$	5.09922	+	15.6938i	0.201880	+	0.621323i
$639$	25.5182			1.00948
$640$	−1.08399	+	3.33619i	−0.0428486	+	0.131874i
$641$	−3.13078	+	9.63555i	−0.123658	+	0.380581i	−0.993654	−	0.112478i	$-0.964121\pi$
$641$	−3.13078	+	9.63555i	−0.123658	+	0.380581i	0.869996	+	0.493059i	$0.164121\pi$
$642$	3.62793			0.143183
$643$	9.35202	+	28.7826i	0.368808	+	1.13507i	0.947562	+	0.319572i	$0.103539\pi$
$643$	9.35202	+	28.7826i	0.368808	+	1.13507i	−0.578754	+	0.815502i	$0.696461\pi$
$644$	−15.3376	−	11.1434i	−0.604386	−	0.439112i
$645$	−3.98639	−	12.2688i	−0.156964	−	0.483085i
$646$	1.82741	−	5.62418i	0.0718983	−	0.221280i
$647$	13.0642	−	40.2074i	0.513606	−	1.58072i	−0.272198	−	0.962241i	$-0.587751\pi$
$647$	13.0642	−	40.2074i	0.513606	−	1.58072i	0.785804	−	0.618475i	$-0.212249\pi$
$648$	−5.73992	+	4.17029i	−0.225485	+	0.163825i
$649$	−2.40869	−	7.41318i	−0.0945493	−	0.290993i
$650$	−23.5230			−0.922649
$651$	−4.57589	+	14.0831i	−0.179343	+	0.551962i
$652$	1.61380	+	4.96677i	0.0632013	+	0.194514i
$653$	1.98986	+	1.44571i	0.0778690	+	0.0565752i	0.626039	−	0.779792i	$-0.284675\pi$
$653$	1.98986	+	1.44571i	0.0778690	+	0.0565752i	−0.548170	+	0.836367i	$0.684675\pi$
$654$	5.10501	−	3.70901i	0.199622	−	0.145034i
$655$	5.71571	−	17.5911i	0.223331	−	0.687343i
$656$	5.93292	+	4.31052i	0.231641	+	0.168297i
$657$	26.7569			1.04389
$658$	4.26023			0.166081
$659$	−7.41630	−	5.38825i	−0.288898	−	0.209897i	0.433891	−	0.900965i	$-0.357140\pi$
$659$	−7.41630	−	5.38825i	−0.288898	−	0.209897i	−0.722789	+	0.691069i	$0.757140\pi$
$660$	4.31857			0.168100
$661$	−28.0454	−	20.3762i	−1.09084	−	0.792542i	−0.111300	−	0.993787i	$-0.535501\pi$
$661$	−28.0454	−	20.3762i	−1.09084	−	0.792542i	−0.979541	+	0.201244i	$0.935501\pi$
$662$	−10.3591	+	7.52632i	−0.402618	+	0.292519i
$663$	−1.58149	−	1.14902i	−0.0614201	−	0.0446243i
$664$	−0.862031	+	2.65306i	−0.0334533	+	0.102959i
$665$	58.0001	−	42.1395i	2.24915	−	1.63410i
$666$	−19.5127	+	14.1768i	−0.756101	+	0.549340i
$667$	−21.2532	+	15.4414i	−0.822929	+	0.597893i
$668$	−6.85378	−	21.0938i	−0.265181	−	0.816142i
$669$	0.593063	+	1.82526i	0.0229291	+	0.0705686i
$670$	−42.6762			−1.64872
$671$	−20.6453	+	0.126172i	−0.797002	+	0.00487081i
$672$	−2.09808			−0.0809352
$673$	0.891330	+	2.74323i	0.0343582	+	0.105744i	0.966765	−	0.255667i	$-0.0822951\pi$
$673$	0.891330	+	2.74323i	0.0343582	+	0.105744i	−0.932407	+	0.361411i	$0.882295\pi$
$674$	−2.37874	−	7.32101i	−0.0916257	−	0.281995i
$675$	15.9178	−	11.5649i	0.612675	−	0.445134i
$676$	2.12880	−	1.54666i	0.0818768	−	0.0594870i
$677$	−6.80548	+	4.94447i	−0.261556	+	0.190032i	−0.710833	−	0.703361i	$-0.751682\pi$
$677$	−6.80548	+	4.94447i	−0.261556	+	0.190032i	0.449277	+	0.893393i	$0.351682\pi$
$678$	−1.35699	+	4.17640i	−0.0521151	+	0.160394i
$679$	31.9162	+	23.1885i	1.22483	+	0.889893i
$680$	−3.69929	+	2.68769i	−0.141861	+	0.103068i
$681$	3.09667	+	2.24986i	0.118665	+	0.0862148i
$682$	−18.6567			−0.714402
$683$	−12.5028	−	9.08379i	−0.478405	−	0.347582i	0.322303	−	0.946637i	$-0.395543\pi$
$683$	−12.5028	−	9.08379i	−0.478405	−	0.347582i	−0.800708	+	0.599055i	$0.795543\pi$
$684$	12.6260			0.482766
$685$	21.5806			0.824554
$686$	22.9412	+	16.6678i	0.875900	+	0.636378i
$687$	0.978935	−	3.01285i	0.0373487	−	0.114947i
$688$	−6.38820	+	4.64130i	−0.243548	+	0.176948i
$689$	−23.6547	−	17.1861i	−0.901172	−	0.654740i
$690$	2.12456	+	6.53871i	0.0808805	+	0.248924i
$691$	4.53205	−	13.9482i	0.172407	−	0.530616i	−0.827098	−	0.562058i	$-0.810010\pi$
$691$	4.53205	−	13.9482i	0.172407	−	0.530616i	0.999506	+	0.0314420i	$0.0100099\pi$
$692$	−23.3067			−0.885988
$693$	−10.2415	−	31.5202i	−0.389044	−	1.19735i
$694$	19.2827	−	14.0097i	0.731960	−	0.531800i
$695$	−5.36688	+	16.5176i	−0.203577	+	0.626547i
$696$	−0.898405	+	2.76500i	−0.0340539	+	0.104807i
$697$	2.95399	+	9.09145i	0.111890	+	0.344363i
$698$	−15.0282	−	10.9186i	−0.568825	−	0.413276i
$699$	−1.98066	−	6.09584i	−0.0749154	−	0.230566i
$700$	−32.9096			−1.24386
$701$	−8.67869	+	26.7103i	−0.327790	+	1.00883i	0.642376	+	0.766390i	$0.277949\pi$
$701$	−8.67869	+	26.7103i	−0.327790	+	1.00883i	−0.970166	+	0.242443i	$0.922051\pi$
$702$	2.68001	−	8.24822i	0.101150	−	0.311309i
$703$	39.3158			1.48282
$704$	−0.816857	−	2.51403i	−0.0307865	−	0.0947510i
$705$	−1.24990	−	0.908107i	−0.0470740	−	0.0342013i
$706$	−7.79941	−	24.0041i	−0.293535	−	0.903407i
$707$	3.81044	−	11.7273i	0.143306	−	0.441052i
$708$	0.424374	−	1.30609i	0.0159489	−	0.0490858i
$709$	−4.21631	+	3.06333i	−0.158347	+	0.115046i	−0.664137	−	0.747611i	$-0.731201\pi$
$709$	−4.21631	+	3.06333i	−0.158347	+	0.115046i	0.505790	+	0.862656i	$0.331201\pi$
$710$	9.93912	+	30.5895i	0.373009	+	1.14800i
$711$	20.9537			0.785825
$712$	1.23614	−	3.80445i	0.0463263	−	0.142578i
$713$	−9.17832	−	28.2480i	−0.343731	−	1.05789i
$714$	−2.21256	−	1.60752i	−0.0828031	−	0.0601600i
$715$	24.1561	−	17.5504i	0.903387	−	0.656349i
$716$	−2.82490	+	8.69416i	−0.105572	+	0.324916i
$717$	3.45927	+	2.51331i	0.129189	+	0.0938612i
$718$	29.9124			1.11632
$719$	−18.7550			−0.699444			−0.349722	−	0.936853i	$-0.613724\pi$
$719$	−18.7550			−0.699444			−0.349722	+	0.936853i	$0.613724\pi$
$720$	−7.89824	−	5.73841i	−0.294350	−	0.213858i
$721$	−34.2286			−1.27474
$722$	−1.27929	−	0.929459i	−0.0476103	−	0.0345909i
$723$	7.40469	−	5.37982i	0.275383	−	0.200078i
$724$	−4.27875	−	3.10869i	−0.159018	−	0.115534i
$725$	−14.0920	+	43.3706i	−0.523363	+	1.61075i
$726$	1.51180	−	1.09839i	0.0561082	−	0.0407650i
$727$	−25.7456	+	18.7052i	−0.954850	+	0.693739i	−0.951949	−	0.306257i	$-0.900923\pi$
$727$	−25.7456	+	18.7052i	−0.954850	+	0.693739i	−0.00290097	+	0.999996i	$0.500923\pi$
$728$	−11.7357	+	8.52649i	−0.434954	+	0.316013i
$729$	−4.93895	−	15.2005i	−0.182924	−	0.562983i
$730$	10.4216	+	32.0744i	0.385721	+	1.18713i
$731$	−10.2929			−0.380696
$732$	−2.95577	−	2.12001i	−0.109248	−	0.0783580i
$733$	−5.13959			−0.189835			−0.0949176	−	0.995485i	$-0.530259\pi$
$733$	−5.13959			−0.189835			−0.0949176	+	0.995485i	$0.530259\pi$
$734$	−3.01773	−	9.28763i	−0.111387	−	0.342813i
$735$	−6.71172	−	20.6566i	−0.247566	−	0.761928i
$736$	3.40461	−	2.47359i	0.125496	−	0.0911779i
$737$	26.0173	−	18.9027i	0.958360	−	0.696289i
$738$	−16.5119	+	11.9966i	−0.607811	+	0.441601i
$739$	7.81393	−	24.0488i	0.287440	−	0.884649i	−0.698217	−	0.715886i	$-0.746023\pi$
$739$	7.81393	−	24.0488i	0.287440	−	0.884649i	0.985657	−	0.168763i	$-0.0539772\pi$
$740$	−24.5942	−	17.8687i	−0.904101	−	0.656868i
$741$	−5.50411	+	3.99897i	−0.202199	+	0.146906i
$742$	−33.0938	−	24.0440i	−1.21491	−	0.882685i
$743$	−36.6093			−1.34306			−0.671532	−	0.740975i	$-0.734364\pi$
$743$	−36.6093			−1.34306			−0.671532	+	0.740975i	$0.734364\pi$
$744$	−2.65926	−	1.93206i	−0.0974932	−	0.0708329i
$745$	−33.9536			−1.24396
$746$	3.56316			0.130457
$747$	−6.28097	−	4.56339i	−0.229809	−	0.166966i
$748$	1.06479	−	3.27707i	0.0389324	−	0.119822i
$749$	28.3906	−	20.6270i	1.03737	−	0.753694i
$750$	3.04678	+	2.21362i	0.111253	+	0.0808299i
$751$	−8.54108	−	26.2867i	−0.311668	−	0.959217i	−0.977104	−	0.212761i	$-0.931754\pi$
$751$	−8.54108	−	26.2867i	−0.311668	−	0.959217i	0.665436	−	0.746455i	$-0.268246\pi$
$752$	−0.292230	+	0.899391i	−0.0106565	+	0.0327974i
$753$	−2.82171			−0.102829
$754$	6.21157	+	19.1173i	0.226212	+	0.696209i
$755$	16.1365	−	11.7239i	0.587269	−	0.426676i
$756$	3.74943	−	11.5396i	0.136365	−	0.419689i
$757$	−15.5537	+	47.8693i	−0.565308	+	1.73984i	0.101727	+	0.994812i	$0.467563\pi$
$757$	−15.5537	+	47.8693i	−0.565308	+	1.73984i	−0.667035	+	0.745026i	$0.732437\pi$
$758$	1.89009	+	5.81709i	0.0686511	+	0.211286i
$759$	−4.19144	−	3.04526i	−0.152139	−	0.110536i
$760$	4.91771	+	15.1352i	0.178384	+	0.549010i
$761$	31.3422			1.13616			0.568078	−	0.822975i	$-0.307687\pi$
$761$	31.3422			1.13616			0.568078	+	0.822975i	$0.307687\pi$
$762$	−1.42238	+	4.37764i	−0.0515274	+	0.158585i
$763$	18.8617	−	58.0502i	0.682838	−	2.10156i
$764$	19.7841			0.715764
$765$	−3.93252	−	12.1031i	−0.142181	−	0.437587i
$766$	−9.76907	−	7.09764i	−0.352971	−	0.256448i
$767$	−2.93412	−	9.03030i	−0.105945	−	0.326065i
$768$	0.143918	−	0.442933i	0.00519318	−	0.0159830i
$769$	−15.5085	+	47.7303i	−0.559252	+	1.72120i	0.125191	+	0.992133i	$0.460046\pi$
$769$	−15.5085	+	47.7303i	−0.559252	+	1.72120i	−0.684443	+	0.729067i	$0.739954\pi$
$770$	33.7953	−	24.5537i	1.21790	−	0.884854i
$771$	−0.375767	−	1.15649i	−0.0135329	−	0.0416501i
$772$	18.8082			0.676921
$773$	−13.1903	+	40.5956i	−0.474422	+	1.46012i	0.372313	+	0.928107i	$0.378565\pi$
$773$	−13.1903	+	40.5956i	−0.474422	+	1.46012i	−0.846735	+	0.532014i	$0.821435\pi$
$774$	−6.79097	−	20.9005i	−0.244096	−	0.751251i
$775$	−41.7120	−	30.3055i	−1.49834	−	1.08861i
$776$	−7.08470	+	5.14733i	−0.254326	+	0.184778i
$777$	5.61869	−	17.2926i	0.201570	−	0.620367i
$778$	22.0172	+	15.9965i	0.789356	+	0.573501i
$779$	33.2696			1.19201
$780$	5.26063			0.188361
$781$	−19.6084	−	14.2464i	−0.701645	−	0.509775i
$782$	5.48562			0.196165
$783$	−13.6022	−	9.88255i	−0.486101	−	0.353173i
$784$	−10.7556	+	7.81437i	−0.384127	+	0.279085i
$785$	−28.3366	−	20.5878i	−1.01138	−	0.734809i
$786$	−0.758853	+	2.33551i	−0.0270674	+	0.0833049i
$787$	11.2672	−	8.18608i	0.401631	−	0.291802i	−0.368574	−	0.929598i	$-0.620154\pi$
$787$	11.2672	−	8.18608i	0.401631	−	0.291802i	0.770205	+	0.637796i	$0.220154\pi$
$788$	−17.3448	+	12.6018i	−0.617884	+	0.448919i
$789$	−3.18114	+	2.31123i	−0.113252	+	0.0822821i
$790$	8.16129	+	25.1179i	0.290366	+	0.893653i
$791$	13.1261	+	40.3981i	0.466711	+	1.43639i
$792$	7.35685			0.261414
$793$	−25.1489	+	0.153695i	−0.893062	+	0.00545788i
$794$	26.7094			0.947882
$795$	4.58413	+	14.1085i	0.162582	+	0.500377i
$796$	−6.45872	−	19.8779i	−0.228923	−	0.704554i
$797$	−8.12476	+	5.90298i	−0.287794	+	0.209094i	−0.722310	−	0.691570i	$-0.756919\pi$
$797$	−8.12476	+	5.90298i	−0.287794	+	0.209094i	0.434516	+	0.900664i	$0.356919\pi$
$798$	−7.70045	+	5.59470i	−0.272593	+	0.198050i
$799$	−0.997278	+	0.724565i	−0.0352811	+	0.0256333i
$800$	2.25743	−	6.94765i	0.0798122	−	0.245637i
$801$	9.00682	+	6.54384i	0.318240	+	0.231215i
$802$	−13.9218	+	10.1148i	−0.491597	+	0.357166i
$803$	−20.5603	−	14.9379i	−0.725557	−	0.527148i
$804$	5.66595			0.199823
$805$	53.8024	+	39.0898i	1.89629	+	1.37773i
$806$	−22.7265			−0.800507
$807$	1.23380			0.0434317
$808$	2.21442	+	1.60887i	0.0779031	+	0.0565999i
$809$	−0.00158533	+	0.00487913i	−5.57371e−5	+	0.000171541i	−0.951084	−	0.308931i	$-0.900029\pi$
$809$	−0.00158533	+	0.00487913i	−5.57371e−5	+	0.000171541i	0.951029	+	0.309103i	$0.100029\pi$
$810$	20.1349	−	14.6289i	0.707469	−	0.514006i
$811$	−13.2792	−	9.64792i	−0.466297	−	0.338784i	0.329700	−	0.944086i	$-0.393053\pi$
$811$	−13.2792	−	9.64792i	−0.466297	−	0.338784i	−0.795996	+	0.605301i	$0.793053\pi$
$812$	8.69021	+	26.7457i	0.304967	+	0.938591i
$813$	−1.92947	+	5.93831i	−0.0676696	+	0.208266i
$814$	22.9084			0.802939
$815$	−5.66102	−	17.4228i	−0.198297	−	0.610295i
$816$	0.491140	−	0.356834i	0.0171934	−	0.0124917i
$817$	−11.0698	+	34.0693i	−0.387283	+	1.19193i
$818$	−9.09830	+	28.0017i	−0.318115	+	0.979056i
$819$	−12.4756	−	38.3960i	−0.435934	−	1.34167i
$820$	−20.8119	−	15.1208i	−0.726784	−	0.528040i
$821$	−3.47782	−	10.7036i	−0.121377	−	0.373559i	0.871847	−	0.489779i	$-0.162922\pi$
$821$	−3.47782	−	10.7036i	−0.121377	−	0.373559i	−0.993224	+	0.116219i	$0.962922\pi$
$822$	−2.86518			−0.0999346
$823$	9.77008	−	30.0692i	0.340563	−	1.04815i	−0.623353	−	0.781941i	$-0.714230\pi$
$823$	9.77008	−	30.0692i	0.340563	−	1.04815i	0.963916	−	0.266206i	$-0.0857701\pi$
$824$	2.34791	−	7.22612i	0.0817933	−	0.251734i
$825$	−8.99347			−0.313112
$826$	−4.10494	−	12.6337i	−0.142829	−	0.439583i
$827$	22.6439	+	16.4518i	0.787405	+	0.572084i	0.907192	−	0.420716i	$-0.138221\pi$
$827$	22.6439	+	16.4518i	0.787405	+	0.572084i	−0.119787	+	0.992800i	$0.538221\pi$
$828$	3.61927	+	11.1390i	0.125778	+	0.387106i
$829$	10.5252	−	32.3932i	0.365555	−	1.12506i	−0.584078	−	0.811698i	$-0.698544\pi$
$829$	10.5252	−	32.3932i	0.365555	−	1.12506i	0.949633	−	0.313365i	$-0.101456\pi$
$830$	3.02390	−	9.30660i	0.104961	−	0.323037i
$831$	4.99600	−	3.62981i	0.173309	−	0.125917i
$832$	−0.995047	−	3.06244i	−0.0344971	−	0.106171i
$833$	−17.3297			−0.600439
$834$	0.712541	−	2.19297i	0.0246733	−	0.0759365i
$835$	24.0422	+	73.9943i	0.832015	+	2.56068i
$836$	−9.70192	−	7.04886i	−0.335548	−	0.243790i
$837$	15.3788	−	11.1733i	0.531567	−	0.386206i
$838$	−2.12515	+	6.54055i	−0.0734122	+	0.225940i
$839$	38.5908	+	28.0378i	1.33230	+	0.967973i	0.999690	+	0.0249095i	$0.00792975\pi$
$839$	38.5908	+	28.0378i	1.33230	+	0.967973i	0.332611	+	0.943064i	$0.392070\pi$
$840$	7.35981			0.253937
$841$	9.96867			0.343747
$842$	−22.6829	−	16.4801i	−0.781705	−	0.567942i
$843$	10.9192			0.376076
$844$	16.3181	+	11.8558i	0.561691	+	0.408092i
$845$	−7.46756	+	5.42550i	−0.256892	+	0.186643i
$846$	−2.12926	−	1.54700i	−0.0732054	−	0.0531868i
$847$	5.58571	−	17.1910i	0.191927	−	0.590691i
$848$	7.34609	−	5.33725i	0.252266	−	0.183282i
$849$	−4.00411	+	2.90915i	−0.137421	+	0.0998419i
$850$	7.70381	−	5.59715i	0.264239	−	0.191981i
$851$	11.2700	+	34.6854i	0.386330	+	1.18900i
$852$	−1.31958	−	4.06125i	−0.0452080	−	0.139136i
$853$	−2.88104			−0.0986451			−0.0493226	−	0.998783i	$-0.515706\pi$
$853$	−2.88104			−0.0986451			−0.0493226	+	0.998783i	$0.515706\pi$
$854$	−35.1842	+	0.215025i	−1.20398	+	0.00735801i
$855$	−44.2903			−1.51470
$856$	2.40718	+	7.40855i	0.0822759	+	0.253219i
$857$	11.5263	+	35.4744i	0.393732	+	1.21178i	0.929945	+	0.367699i	$0.119854\pi$
$857$	11.5263	+	35.4744i	0.393732	+	1.21178i	−0.536213	+	0.844082i	$0.680146\pi$
$858$	−3.20711	+	2.33011i	−0.109489	+	0.0795485i
$859$	25.8400	−	18.7739i	0.881650	−	0.640556i	−0.0520372	−	0.998645i	$-0.516571\pi$
$859$	25.8400	−	18.7739i	0.881650	−	0.640556i	0.933688	+	0.358089i	$0.116571\pi$
$860$	22.4090	−	16.2811i	0.764141	−	0.555181i
$861$	4.75461	−	14.6332i	0.162037	−	0.498698i
$862$	10.5241	+	7.64617i	0.358451	+	0.260430i
$863$	−23.1777	+	16.8396i	−0.788980	+	0.573227i	−0.907661	−	0.419705i	$-0.862133\pi$
$863$	−23.1777	+	16.8396i	−0.788980	+	0.573227i	0.118681	+	0.992932i	$0.462133\pi$
$864$	2.17896	+	1.58311i	0.0741299	+	0.0538585i
$865$	81.7570			2.77982
$866$	−3.49029	−	2.53585i	−0.118605	−	0.0861716i
$867$	−7.12602			−0.242012
$868$	−31.7952			−1.07920
$869$	−16.1010	−	11.6981i	−0.546190	−	0.396830i
$870$	3.15149	−	9.69930i	0.106846	−	0.328837i
$871$	31.6928	−	23.0261i	1.07387	−	0.780211i
$872$	10.9614	+	7.96390i	0.371199	+	0.269692i
$873$	−7.53138	−	23.1792i	−0.254899	−	0.784497i
$874$	5.89968	−	18.1573i	0.199560	−	0.614181i
$875$	36.4286			1.23151
$876$	−1.38364	−	4.25840i	−0.0467488	−	0.143878i
$877$	−41.2729	+	29.9865i	−1.39369	+	1.01257i	−0.398236	+	0.917283i	$0.630377\pi$
$877$	−41.2729	+	29.9865i	−1.39369	+	1.01257i	−0.995450	+	0.0952885i	$0.969623\pi$
$878$	−5.46586	+	16.8222i	−0.184464	+	0.567721i
$879$	−1.09568	+	3.37215i	−0.0369563	+	0.113740i
$880$	2.86543	+	8.81890i	0.0965937	+	0.297285i
$881$	−27.1638	−	19.7357i	−0.915173	−	0.664912i	0.0271448	−	0.999632i	$-0.491358\pi$
$881$	−27.1638	−	19.7357i	−0.915173	−	0.664912i	−0.942318	+	0.334719i	$0.891358\pi$
$882$	−11.4337	−	35.1893i	−0.384992	−	1.18488i
$883$	12.6297			0.425023			0.212511	−	0.977159i	$-0.431836\pi$
$883$	12.6297			0.425023			0.212511	+	0.977159i	$0.431836\pi$
$884$	1.29706	−	3.99194i	0.0436248	−	0.134263i
$885$	−1.48865	+	4.58160i	−0.0500405	+	0.154009i
$886$	−19.4436			−0.653220
$887$	−12.7137	−	39.1287i	−0.426884	−	1.31381i	−0.901179	−	0.433447i	$-0.857297\pi$
$887$	−12.7137	−	39.1287i	−0.426884	−	1.31381i	0.474296	−	0.880366i	$-0.342703\pi$
$888$	3.26528	+	2.37236i	0.109576	+	0.0796113i
$889$	13.7586	+	42.3446i	0.461449	+	1.42019i
$890$	−4.33623	+	13.3455i	−0.145351	+	0.447343i
$891$	−5.79554	+	17.8368i	−0.194158	+	0.597557i
$892$	−3.33384	+	2.42217i	−0.111625	+	0.0811004i
$893$	1.32575	+	4.08023i	0.0443645	+	0.136540i
$894$	4.50789			0.150766
$895$	9.90941	−	30.4980i	0.331235	−	1.01944i
$896$	−1.39211	−	4.28447i	−0.0465070	−	0.143134i
$897$	−5.10576	−	3.70955i	−0.170476	−	0.123858i
$898$	−4.70191	+	3.41613i	−0.156905	+	0.113998i
$899$	−13.6148	+	41.9020i	−0.454079	+	1.39751i
$900$	16.4482	+	11.9503i	0.548273	+	0.398344i
$901$	11.8363			0.394323
$902$	19.3854			0.645463
$903$	13.4030	+	9.73782i	0.446023	+	0.324054i
$904$	−9.42896			−0.313603
$905$	15.0093	+	10.9049i	0.498927	+	0.362492i
$906$	−2.14239	+	1.55653i	−0.0711760	+	0.0517124i
$907$	−20.3566	−	14.7899i	−0.675929	−	0.491091i	0.196075	−	0.980589i	$-0.437180\pi$
$907$	−20.3566	−	14.7899i	−0.675929	−	0.491091i	−0.872005	+	0.489497i	$0.837180\pi$
$908$	−2.53973	+	7.81648i	−0.0842839	+	0.259399i
$909$	−6.16295	+	4.47765i	−0.204412	+	0.148514i
$910$	41.1674	−	29.9099i	1.36469	−	0.991503i
$911$	9.69393	−	7.04305i	0.321174	−	0.233347i	−0.415502	−	0.909592i	$-0.636394\pi$
$911$	9.69393	−	7.04305i	0.321174	−	0.233347i	0.736676	+	0.676245i	$0.236394\pi$
$912$	−0.652906	−	2.00944i	−0.0216199	−	0.0665391i
$913$	2.27870	+	7.01311i	0.0754138	+	0.232100i
$914$	−0.875809			−0.0289692
$915$	10.3685	+	7.43675i	0.342771	+	0.245851i
$916$	6.80205			0.224746
$917$	7.34034	+	22.5912i	0.242399	+	0.746029i
$918$	1.08490	+	3.33899i	0.0358071	+	0.110203i
$919$	31.4714	−	22.8653i	1.03815	−	0.754258i	0.0682237	−	0.997670i	$-0.478267\pi$
$919$	31.4714	−	22.8653i	1.03815	−	0.754258i	0.969923	+	0.243412i	$0.0782668\pi$
$920$	−11.9429	+	8.67706i	−0.393747	+	0.286074i
$921$	4.76509	−	3.46204i	0.157015	−	0.114078i
$922$	−4.93386	+	15.1848i	−0.162488	+	0.500086i
$923$	−23.8858	−	17.3541i	−0.786212	−	0.571216i
$924$	−4.48687	+	3.25990i	−0.147607	+	0.107243i
$925$	51.2177	+	37.2119i	1.68403	+	1.22352i
$926$	−33.0047			−1.08460
$927$	17.1074	+	12.4293i	0.561882	+	0.408231i
$928$	−6.24249			−0.204920
$929$	17.5556			0.575981			0.287991	−	0.957633i	$-0.407013\pi$
$929$	17.5556			0.575981			0.287991	+	0.957633i	$0.407013\pi$
$930$	9.32835	+	6.77744i	0.305889	+	0.222241i
$931$	−18.6378	+	57.3612i	−0.610828	+	1.87994i
$932$	11.1341	−	8.08937i	0.364708	−	0.264976i
$933$	4.80125	+	3.48831i	0.157186	+	0.114202i
$934$	9.17272	+	28.2307i	0.300141	+	0.923738i
$935$	−3.73514	+	11.4956i	−0.122152	+	0.375945i
$936$	8.96169			0.292922
$937$	−13.3426	−	41.0644i	−0.435884	−	1.34151i	−0.892178	−	0.451685i	$-0.850823\pi$
$937$	−13.3426	−	41.0644i	−0.435884	−	1.34151i	0.456293	−	0.889830i	$-0.349177\pi$
$938$	44.3393	−	32.2144i	1.44773	−	1.05184i
$939$	2.13615	−	6.57440i	0.0697107	−	0.214548i
$940$	1.02511	−	3.15495i	0.0334353	−	0.102903i
$941$	13.6274	+	41.9409i	0.444242	+	1.36724i	0.883313	+	0.468783i	$0.155307\pi$
$941$	13.6274	+	41.9409i	0.444242	+	1.36724i	−0.439072	+	0.898452i	$0.644693\pi$
$942$	3.76215	+	2.73336i	0.122577	+	0.0890577i
$943$	9.53680	+	29.3513i	0.310561	+	0.955808i
$944$	2.94873			0.0959729
$945$	−13.1525	+	40.4793i	−0.427852	+	1.31679i
$946$	−6.45011	+	19.8514i	−0.209711	+	0.645424i
$947$	−48.4504			−1.57443			−0.787214	−	0.616680i	$-0.788477\pi$
$947$	−48.4504			−1.57443			−0.787214	+	0.616680i	$0.788477\pi$
$948$	−1.08354	−	3.33480i	−0.0351918	−	0.108309i
$949$	−25.0453	−	18.1965i	−0.813006	−	0.590684i
$950$	−10.2412	−	31.5191i	−0.332268	−	1.02262i
$951$	1.58951	−	4.89200i	0.0515433	−	0.158634i
$952$	1.81463	−	5.58487i	0.0588126	−	0.181007i
$953$	−23.4518	+	17.0387i	−0.759678	+	0.551939i	−0.898812	−	0.438335i	$-0.855568\pi$
$953$	−23.4518	+	17.0387i	−0.759678	+	0.551939i	0.139133	+	0.990274i	$0.455568\pi$
$954$	7.80925	+	24.0344i	0.252834	+	0.778143i
$955$	−69.4002			−2.24574
$956$	−2.83712	+	8.73175i	−0.0917590	+	0.282405i
$957$	2.37485	+	7.30903i	0.0767679	+	0.236267i
$958$	34.0635	+	24.7486i	1.10054	+	0.799591i
$959$	−22.4217	+	16.2903i	−0.724033	+	0.526041i
$960$	−0.504845	+	1.55375i	−0.0162938	+	0.0501472i
$961$	−15.2200	−	11.0580i	−0.490968	−	0.356709i
$962$	27.9057			0.899715
$963$	−21.6798			−0.698622
$964$	15.8992	+	11.5514i	0.512079	+	0.372047i
$965$	−65.9768			−2.12387
$966$	−7.14314	−	5.18980i	−0.229827	−	0.166979i
$967$	−9.05456	+	6.57852i	−0.291175	+	0.211551i	−0.723777	−	0.690034i	$-0.757596\pi$
$967$	−9.05456	+	6.57852i	−0.291175	+	0.211551i	0.432602	+	0.901585i	$0.357596\pi$
$968$	3.24611	+	2.35844i	0.104334	+	0.0758030i
$969$	0.851073	−	2.61933i	0.0273404	−	0.0841451i
$970$	24.8522	−	18.0562i	0.797957	−	0.579750i
$971$	−15.4575	+	11.2305i	−0.496053	+	0.360404i	−0.807508	−	0.589857i	$-0.799184\pi$
$971$	−15.4575	+	11.2305i	−0.496053	+	0.360404i	0.311454	+	0.950261i	$0.399184\pi$
$972$	−9.21013	+	6.69155i	−0.295415	+	0.214632i
$973$	−6.89236	−	21.2125i	−0.220959	−	0.680042i
$974$	−4.22458	−	13.0019i	−0.135364	−	0.416608i
$975$	−10.9553			−0.350851
$976$	2.36806	−	7.44260i	0.0757998	−	0.238232i
$977$	9.66700			0.309275			0.154637	−	0.987971i	$-0.450579\pi$
$977$	9.66700			0.309275			0.154637	+	0.987971i	$0.450579\pi$
$978$	0.751592	+	2.31316i	0.0240333	+	0.0739667i
$979$	−3.26762	−	10.0567i	−0.104434	−	0.321414i
$980$	37.7292	−	27.4119i	1.20521	−	0.875640i
$981$	−30.5066	+	22.1643i	−0.974000	+	0.707652i
$982$	15.2192	−	11.0574i	0.485665	−	0.352856i
$983$	2.92286	−	8.99564i	0.0932248	−	0.286916i	−0.893562	−	0.448939i	$-0.851802\pi$
$983$	2.92286	−	8.99564i	0.0932248	−	0.286916i	0.986787	+	0.162023i	$0.0518019\pi$
$984$	2.76312	+	2.00753i	0.0880851	+	0.0639976i
$985$	60.8435	−	44.2054i	1.93864	−	1.40850i
$986$	−6.58312	−	4.78292i	−0.209649	−	0.152319i
$987$	1.98410			0.0631547
$988$	−11.8183	−	8.58650i	−0.375990	−	0.273173i
$989$	−33.2300			−1.05665
$990$	−25.8069			−0.820198
$991$	8.24158	+	5.98786i	0.261802	+	0.190211i	0.710941	−	0.703251i	$-0.248269\pi$
$991$	8.24158	+	5.98786i	0.261802	+	0.190211i	−0.449139	+	0.893462i	$0.648269\pi$
$992$	2.18099	−	6.71239i	0.0692465	−	0.213119i
$993$	−4.82452	+	3.50522i	−0.153101	+	0.111235i
$994$	−33.4171	−	24.2790i	−1.05993	−	0.770082i
$995$	22.6564	+	69.7293i	0.718256	+	2.21057i
$996$	−0.401471	+	1.23560i	−0.0127211	+	0.0391515i
$997$	3.34665			0.105989			0.0529947	−	0.998595i	$-0.483123\pi$
$997$	3.34665			0.105989			0.0529947	+	0.998595i	$0.483123\pi$
$998$	−7.02567	−	21.6228i	−0.222394	−	0.684457i
$999$	−18.8834	+	13.7196i	−0.597445	+	0.434069i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	122.2.e.b.81.2	✓	16
3.2	odd	2		1098.2.k.l.325.1		16
4.3	odd	2		976.2.v.c.81.3		16
61.27	even	10		7442.2.a.q.1.4		8
61.34	even	5		7442.2.a.s.1.4		8
61.58	even	5	inner	122.2.e.b.119.2	yes	16
183.119	odd	10		1098.2.k.l.973.1		16
244.119	odd	10		976.2.v.c.241.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
122.2.e.b.81.2	✓	16	1.1	even	1	trivial
122.2.e.b.119.2	yes	16	61.58	even	5	inner
976.2.v.c.81.3		16	4.3	odd	2
976.2.v.c.241.3		16	244.119	odd	10
1098.2.k.l.325.1		16	3.2	odd	2
1098.2.k.l.973.1		16	183.119	odd	10
7442.2.a.q.1.4		8	61.27	even	10
7442.2.a.s.1.4		8	61.34	even	5

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:	\( N \)	\(=\)	\( 122 = 2 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	122.e (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 + 0.951057i) q^{2} +(0.143918 + 0.442933i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(2.83793 - 2.06188i) q^{5} +(-0.376781 + 0.273748i) q^{6} +(-1.39211 + 4.28447i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(2.25157 - 1.63586i) q^{9} +O(q^{10})\)	\(q+(0.309017 + 0.951057i) q^{2} +(0.143918 + 0.442933i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(2.83793 - 2.06188i) q^{5} +(-0.376781 + 0.273748i) q^{6} +(-1.39211 + 4.28447i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(2.25157 - 1.63586i) q^{9} +(2.83793 + 2.06188i) q^{10} -2.64340 q^{11} +(-0.376781 - 0.273748i) q^{12} -3.22004 q^{13} -4.50495 q^{14} +(1.32170 + 0.960273i) q^{15} +(0.309017 - 0.951057i) q^{16} +(1.05457 - 0.766187i) q^{17} +(2.25157 + 1.63586i) q^{18} +(-1.40191 - 4.31462i) q^{19} +(-1.08399 + 3.33619i) q^{20} -2.09808 q^{21} +(-0.816857 - 2.51403i) q^{22} +(3.40461 - 2.47359i) q^{23} +(0.143918 - 0.442933i) q^{24} +(2.25743 - 6.94765i) q^{25} +(-0.995047 - 3.06244i) q^{26} +(2.17896 + 1.58311i) q^{27} +(-1.39211 - 4.28447i) q^{28} -6.24249 q^{29} +(-0.504845 + 1.55375i) q^{30} +(2.18099 - 6.71239i) q^{31} +1.00000 q^{32} +(-0.380433 - 1.17085i) q^{33} +(1.05457 + 0.766187i) q^{34} +(4.88334 + 15.0294i) q^{35} +(-0.860025 + 2.64688i) q^{36} +(-2.67802 + 8.24209i) q^{37} +(3.67024 - 2.66658i) q^{38} +(-0.463421 - 1.42626i) q^{39} -3.50788 q^{40} +(-2.26617 + 6.97456i) q^{41} +(-0.648342 - 1.99539i) q^{42} +(-6.38820 - 4.64130i) q^{43} +(2.13856 - 1.55375i) q^{44} +(3.01686 - 9.28494i) q^{45} +(3.40461 + 2.47359i) q^{46} -0.945676 q^{47} +0.465727 q^{48} +(-10.7556 - 7.81437i) q^{49} +7.30519 q^{50} +(0.491140 + 0.356834i) q^{51} +(2.60507 - 1.89269i) q^{52} +(7.34609 + 5.33725i) q^{53} +(-0.832290 + 2.56153i) q^{54} +(-7.50180 + 5.45038i) q^{55} +(3.64458 - 2.64795i) q^{56} +(1.70933 - 1.24190i) q^{57} +(-1.92904 - 5.93696i) q^{58} +(0.911207 + 2.80441i) q^{59} -1.63371 q^{60} +(7.81010 - 0.0477308i) q^{61} +7.05783 q^{62} +(3.87437 + 11.9241i) q^{63} +(0.309017 + 0.951057i) q^{64} +(-9.13825 + 6.63933i) q^{65} +(0.995986 - 0.723626i) q^{66} +(-9.84235 + 7.15089i) q^{67} +(-0.402808 + 1.23972i) q^{68} +(1.58562 + 1.15202i) q^{69} +(-12.7847 + 9.28866i) q^{70} +(7.41787 + 5.38940i) q^{71} -2.78310 q^{72} +(7.77796 + 5.65102i) q^{73} -8.66624 q^{74} +3.40223 q^{75} +(3.67024 + 2.66658i) q^{76} +(3.67990 - 11.3256i) q^{77} +(1.21325 - 0.881479i) q^{78} +(6.09102 + 4.42538i) q^{79} +(-1.08399 - 3.33619i) q^{80} +(2.19245 - 6.74768i) q^{81} -7.33349 q^{82} +(-0.862031 - 2.65306i) q^{83} +(1.69738 - 1.23322i) q^{84} +(1.41300 - 4.34877i) q^{85} +(2.44008 - 7.50978i) q^{86} +(-0.898405 - 2.76500i) q^{87} +(2.13856 + 1.55375i) q^{88} +(1.23614 + 3.80445i) q^{89} +9.76276 q^{90} +(4.48264 - 13.7962i) q^{91} +(-1.30045 + 4.00236i) q^{92} +3.28702 q^{93} +(-0.292230 - 0.899391i) q^{94} +(-12.8747 - 9.35404i) q^{95} +(0.143918 + 0.442933i) q^{96} +(2.70611 - 8.32856i) q^{97} +(4.10826 - 12.6439i) q^{98} +(-5.95182 + 4.32425i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} + 2 q^{3} - 4 q^{4} + 3 q^{5} - 3 q^{6} - 2 q^{7} - 4 q^{8}+O(q^{10}) \) 16 * q - 4 * q^2 + 2 * q^3 - 4 * q^4 + 3 * q^5 - 3 * q^6 - 2 * q^7 - 4 * q^8	\( 16 q - 4 q^{2} + 2 q^{3} - 4 q^{4} + 3 q^{5} - 3 q^{6} - 2 q^{7} - 4 q^{8} + 3 q^{10} - 3 q^{12} + 2 q^{13} + 8 q^{14} - 4 q^{16} - 7 q^{17} - 12 q^{19} - 2 q^{20} + 24 q^{21} + 5 q^{22} - 16 q^{23} + 2 q^{24} + 9 q^{25} - 3 q^{26} - 4 q^{27} - 2 q^{28} + 4 q^{29} - 5 q^{30} - 19 q^{31} + 16 q^{32} - 43 q^{33} - 7 q^{34} - 21 q^{35} - 15 q^{36} - 30 q^{37} + 8 q^{38} + 61 q^{39} - 2 q^{40} + 4 q^{41} - 6 q^{42} - 36 q^{43} - 5 q^{44} + 45 q^{45} - 16 q^{46} - 30 q^{47} + 2 q^{48} - 32 q^{49} + 14 q^{50} + 42 q^{51} + 2 q^{52} + 55 q^{53} + 6 q^{54} - 27 q^{55} - 2 q^{56} + 41 q^{57} + 14 q^{58} + 8 q^{59} + 10 q^{60} + 57 q^{61} + 46 q^{62} + q^{63} - 4 q^{64} - 41 q^{65} + 47 q^{66} - 19 q^{67} + 8 q^{68} - 28 q^{69} + 4 q^{70} + 31 q^{71} + 30 q^{72} + 4 q^{73} + 30 q^{74} - 44 q^{75} + 8 q^{76} - 29 q^{77} - 39 q^{78} + 2 q^{79} - 2 q^{80} - 93 q^{81} - 16 q^{82} + 12 q^{83} - 6 q^{84} + 52 q^{85} + 24 q^{86} + 16 q^{87} - 5 q^{88} - 15 q^{89} - 80 q^{90} - 3 q^{91} + 14 q^{92} - 3 q^{95} + 2 q^{96} - 18 q^{97} - 22 q^{98} - 6 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 + 2 * q^3 - 4 * q^4 + 3 * q^5 - 3 * q^6 - 2 * q^7 - 4 * q^8 + 3 * q^10 - 3 * q^12 + 2 * q^13 + 8 * q^14 - 4 * q^16 - 7 * q^17 - 12 * q^19 - 2 * q^20 + 24 * q^21 + 5 * q^22 - 16 * q^23 + 2 * q^24 + 9 * q^25 - 3 * q^26 - 4 * q^27 - 2 * q^28 + 4 * q^29 - 5 * q^30 - 19 * q^31 + 16 * q^32 - 43 * q^33 - 7 * q^34 - 21 * q^35 - 15 * q^36 - 30 * q^37 + 8 * q^38 + 61 * q^39 - 2 * q^40 + 4 * q^41 - 6 * q^42 - 36 * q^43 - 5 * q^44 + 45 * q^45 - 16 * q^46 - 30 * q^47 + 2 * q^48 - 32 * q^49 + 14 * q^50 + 42 * q^51 + 2 * q^52 + 55 * q^53 + 6 * q^54 - 27 * q^55 - 2 * q^56 + 41 * q^57 + 14 * q^58 + 8 * q^59 + 10 * q^60 + 57 * q^61 + 46 * q^62 + q^63 - 4 * q^64 - 41 * q^65 + 47 * q^66 - 19 * q^67 + 8 * q^68 - 28 * q^69 + 4 * q^70 + 31 * q^71 + 30 * q^72 + 4 * q^73 + 30 * q^74 - 44 * q^75 + 8 * q^76 - 29 * q^77 - 39 * q^78 + 2 * q^79 - 2 * q^80 - 93 * q^81 - 16 * q^82 + 12 * q^83 - 6 * q^84 + 52 * q^85 + 24 * q^86 + 16 * q^87 - 5 * q^88 - 15 * q^89 - 80 * q^90 - 3 * q^91 + 14 * q^92 - 3 * q^95 + 2 * q^96 - 18 * q^97 - 22 * q^98 - 6 * q^99

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