LMFDB - Embedded newform 527.2.h.c.256.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [527,2,Mod(35,527)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(527, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("527.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 527 = 17 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	527.h (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:	$4.20811618652$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			256.19
Character	$\chi$	$=$	527.256
Dual form			527.2.h.c.35.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.664255 - 2.04437i) q^{2} +(0.708988 + 2.18204i) q^{3} +(-2.12016 - 1.54039i) q^{4} +3.53489 q^{5} +4.93184 q^{6} +(-0.412992 - 0.300057i) q^{7} +(-1.07936 + 0.784201i) q^{8} +(-1.83159 + 1.33073i) q^{9} +O(q^{10})$	\(q+(0.664255 - 2.04437i) q^{2} +(0.708988 + 2.18204i) q^{3} +(-2.12016 - 1.54039i) q^{4} +3.53489 q^{5} +4.93184 q^{6} +(-0.412992 - 0.300057i) q^{7} +(-1.07936 + 0.784201i) q^{8} +(-1.83159 + 1.33073i) q^{9} +(2.34806 - 7.22660i) q^{10} +(-3.05753 - 2.22143i) q^{11} +(1.85802 - 5.71840i) q^{12} +(1.71087 + 5.26552i) q^{13} +(-0.887757 + 0.644993i) q^{14} +(2.50619 + 7.71327i) q^{15} +(-0.733436 - 2.25728i) q^{16} +(-0.809017 + 0.587785i) q^{17} +(1.50385 + 4.62838i) q^{18} +(0.351855 - 1.08290i) q^{19} +(-7.49453 - 5.44510i) q^{20} +(0.361929 - 1.11390i) q^{21} +(-6.57239 + 4.77512i) q^{22} +(3.57639 - 2.59840i) q^{23} +(-2.47641 - 1.79922i) q^{24} +7.49543 q^{25} +11.9011 q^{26} +(1.36619 + 0.992592i) q^{27} +(0.413407 + 1.27234i) q^{28} +(-2.57655 + 7.92982i) q^{29} +17.4335 q^{30} +(-4.63523 - 3.08459i) q^{31} -7.77023 q^{32} +(2.67949 - 8.24663i) q^{33} +(0.664255 + 2.04437i) q^{34} +(-1.45988 - 1.06067i) q^{35} +5.93310 q^{36} -3.92515 q^{37} +(-1.98012 - 1.43864i) q^{38} +(-10.2766 + 7.46638i) q^{39} +(-3.81542 + 2.77206i) q^{40} +(1.34192 - 4.13002i) q^{41} +(-2.03681 - 1.47983i) q^{42} +(2.52269 - 7.76404i) q^{43} +(3.06060 + 9.41957i) q^{44} +(-6.47446 + 4.70397i) q^{45} +(-2.93645 - 9.03745i) q^{46} +(2.02642 + 6.23669i) q^{47} +(4.40549 - 3.20078i) q^{48} +(-2.08259 - 6.40955i) q^{49} +(4.97887 - 15.3234i) q^{50} +(-1.85616 - 1.34858i) q^{51} +(4.48362 - 13.7991i) q^{52} +(-4.53151 + 3.29233i) q^{53} +(2.93672 - 2.13365i) q^{54} +(-10.8080 - 7.85250i) q^{55} +0.681072 q^{56} +2.61239 q^{57} +(14.5000 + 10.5348i) q^{58} +(-2.35108 - 7.23587i) q^{59} +(6.56789 - 20.2139i) q^{60} -8.84975 q^{61} +(-9.38499 + 7.42715i) q^{62} +1.15573 q^{63} +(-3.69454 + 11.3706i) q^{64} +(6.04773 + 18.6130i) q^{65} +(-15.0793 - 10.9557i) q^{66} -2.59351 q^{67} +2.62066 q^{68} +(8.20544 + 5.96160i) q^{69} +(-3.13812 + 2.27998i) q^{70} +(-5.45994 + 3.96688i) q^{71} +(0.933387 - 2.87267i) q^{72} +(5.63728 + 4.09573i) q^{73} +(-2.60730 + 8.02445i) q^{74} +(5.31417 + 16.3553i) q^{75} +(-2.41407 + 1.75393i) q^{76} +(0.596184 + 1.83487i) q^{77} +(8.43774 + 25.9687i) q^{78} +(4.50337 - 3.27189i) q^{79} +(-2.59261 - 7.97924i) q^{80} +(-3.29608 + 10.1443i) q^{81} +(-7.55189 - 5.48677i) q^{82} +(-5.06921 + 15.6014i) q^{83} +(-2.48319 + 1.80414i) q^{84} +(-2.85978 + 2.07775i) q^{85} +(-14.1968 - 10.3146i) q^{86} -19.1299 q^{87} +5.04223 q^{88} +(-11.2517 - 8.17486i) q^{89} +(5.31595 + 16.3608i) q^{90} +(0.873376 - 2.68798i) q^{91} -11.5851 q^{92} +(3.44437 - 12.3012i) q^{93} +14.0961 q^{94} +(1.24377 - 3.82792i) q^{95} +(-5.50900 - 16.9550i) q^{96} +(0.600165 + 0.436046i) q^{97} -14.4868 q^{98} +8.55626 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 2 q^{2} - 4 q^{3} - 30 q^{4} + 6 q^{5} - 8 q^{6} - 10 q^{7} - 36 q^{9}+O(q^{10}) $ 96 * q - 2 * q^2 - 4 * q^3 - 30 * q^4 + 6 * q^5 - 8 * q^6 - 10 * q^7 - 36 * q^9	\( 96 q - 2 q^{2} - 4 q^{3} - 30 q^{4} + 6 q^{5} - 8 q^{6} - 10 q^{7} - 36 q^{9} - 13 q^{10} - 4 q^{11} - 14 q^{12} - 14 q^{13} + 17 q^{14} - 9 q^{15} - 58 q^{16} - 24 q^{17} - 24 q^{18} - 6 q^{19} + 43 q^{20} + 26 q^{21} + 42 q^{22} - 11 q^{23} - 38 q^{24} + 126 q^{25} - 44 q^{26} - q^{27} + 31 q^{28} - 10 q^{29} - 70 q^{30} + 21 q^{31} + 28 q^{32} - 36 q^{33} - 2 q^{34} + 2 q^{35} + 160 q^{36} + 54 q^{37} + 15 q^{38} - 10 q^{39} - 29 q^{40} - 14 q^{41} - 3 q^{42} + 6 q^{43} - 5 q^{44} - q^{45} - 17 q^{46} - 14 q^{47} - 93 q^{48} - 72 q^{49} + 108 q^{50} + q^{51} + 13 q^{52} - 30 q^{53} - 63 q^{54} - 12 q^{55} + 66 q^{56} - 62 q^{57} + 29 q^{58} + 8 q^{59} - 86 q^{60} - 14 q^{61} - 34 q^{62} + 86 q^{63} - 122 q^{64} + 13 q^{65} - 40 q^{66} + 126 q^{67} + 120 q^{68} - 34 q^{69} - 38 q^{70} - 39 q^{71} - 51 q^{72} - 60 q^{73} - 111 q^{74} - 41 q^{75} + 64 q^{76} - 26 q^{77} - 99 q^{78} - 33 q^{79} - 91 q^{80} + 81 q^{81} - 88 q^{82} + 22 q^{83} + 160 q^{84} - 4 q^{85} + 35 q^{86} + 70 q^{87} - 120 q^{88} + 101 q^{89} + 125 q^{90} - 13 q^{91} - 98 q^{92} + 47 q^{93} - 8 q^{94} - 64 q^{95} + 208 q^{96} + 16 q^{97} + 8 q^{98} + 280 q^{99}+O(q^{100}) \) 96 * q - 2 * q^2 - 4 * q^3 - 30 * q^4 + 6 * q^5 - 8 * q^6 - 10 * q^7 - 36 * q^9 - 13 * q^10 - 4 * q^11 - 14 * q^12 - 14 * q^13 + 17 * q^14 - 9 * q^15 - 58 * q^16 - 24 * q^17 - 24 * q^18 - 6 * q^19 + 43 * q^20 + 26 * q^21 + 42 * q^22 - 11 * q^23 - 38 * q^24 + 126 * q^25 - 44 * q^26 - q^27 + 31 * q^28 - 10 * q^29 - 70 * q^30 + 21 * q^31 + 28 * q^32 - 36 * q^33 - 2 * q^34 + 2 * q^35 + 160 * q^36 + 54 * q^37 + 15 * q^38 - 10 * q^39 - 29 * q^40 - 14 * q^41 - 3 * q^42 + 6 * q^43 - 5 * q^44 - q^45 - 17 * q^46 - 14 * q^47 - 93 * q^48 - 72 * q^49 + 108 * q^50 + q^51 + 13 * q^52 - 30 * q^53 - 63 * q^54 - 12 * q^55 + 66 * q^56 - 62 * q^57 + 29 * q^58 + 8 * q^59 - 86 * q^60 - 14 * q^61 - 34 * q^62 + 86 * q^63 - 122 * q^64 + 13 * q^65 - 40 * q^66 + 126 * q^67 + 120 * q^68 - 34 * q^69 - 38 * q^70 - 39 * q^71 - 51 * q^72 - 60 * q^73 - 111 * q^74 - 41 * q^75 + 64 * q^76 - 26 * q^77 - 99 * q^78 - 33 * q^79 - 91 * q^80 + 81 * q^81 - 88 * q^82 + 22 * q^83 + 160 * q^84 - 4 * q^85 + 35 * q^86 + 70 * q^87 - 120 * q^88 + 101 * q^89 + 125 * q^90 - 13 * q^91 - 98 * q^92 + 47 * q^93 - 8 * q^94 - 64 * q^95 + 208 * q^96 + 16 * q^97 + 8 * q^98 + 280 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/527\mathbb{Z}\right)^\times$.

$n$	$156$	$375$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	0.664255	−	2.04437i	0.469699	−	1.44558i	−0.383277	−	0.923634i	$-0.625204\pi$
$2$	0.664255	−	2.04437i	0.469699	−	1.44558i	0.852975	−	0.521951i	$-0.174796\pi$
$3$	0.708988	+	2.18204i	0.409335	+	1.25980i	0.917221	+	0.398378i	$0.130427\pi$
$3$	0.708988	+	2.18204i	0.409335	+	1.25980i	−0.507887	+	0.861424i	$0.669573\pi$
$4$	−2.12016	−	1.54039i	−1.06008	−	0.770194i
$5$	3.53489			1.58085			0.790425	−	0.612559i	$-0.209860\pi$
$5$	3.53489			1.58085			0.790425	+	0.612559i	$0.209860\pi$
$6$	4.93184			2.01341
$7$	−0.412992	−	0.300057i	−0.156096	−	0.113411i	0.506995	−	0.861949i	$-0.330756\pi$
$7$	−0.412992	−	0.300057i	−0.156096	−	0.113411i	−0.663092	+	0.748538i	$0.730756\pi$
$8$	−1.07936	+	0.784201i	−0.381611	+	0.277257i
$9$	−1.83159	+	1.33073i	−0.610530	+	0.443576i
$10$	2.34806	−	7.22660i	0.742523	−	2.28525i
$11$	−3.05753	−	2.22143i	−0.921881	−	0.669786i	0.0221105	−	0.999756i	$-0.492961\pi$
$11$	−3.05753	−	2.22143i	−0.921881	−	0.669786i	−0.943991	+	0.329970i	$0.892961\pi$
$12$	1.85802	−	5.71840i	0.536364	−	1.65076i
$13$	1.71087	+	5.26552i	0.474510	+	1.46039i	0.846617	+	0.532202i	$0.178635\pi$
$13$	1.71087	+	5.26552i	0.474510	+	1.46039i	−0.372107	+	0.928190i	$0.621365\pi$
$14$	−0.887757	+	0.644993i	−0.237263	+	0.172382i
$15$	2.50619	+	7.71327i	0.647096	+	1.99156i
$16$	−0.733436	−	2.25728i	−0.183359	−	0.564321i
$17$	−0.809017	+	0.587785i	−0.196215	+	0.142559i
$17$	−0.809017	+	0.587785i	−0.196215	+	0.142559i
$18$	1.50385	+	4.62838i	0.354461	+	1.09092i
$19$	0.351855	−	1.08290i	0.0807211	−	0.248434i	−0.902549	−	0.430587i	$-0.858307\pi$
$19$	0.351855	−	1.08290i	0.0807211	−	0.248434i	0.983270	+	0.182153i	$0.0583066\pi$
$20$	−7.49453	−	5.44510i	−1.67583	−	1.21756i
$21$	0.361929	−	1.11390i	0.0789794	−	0.243074i
$22$	−6.57239	+	4.77512i	−1.40124	+	1.01806i
$23$	3.57639	−	2.59840i	0.745729	−	0.541804i	−0.148771	−	0.988872i	$-0.547532\pi$
$23$	3.57639	−	2.59840i	0.745729	−	0.541804i	0.894500	+	0.447068i	$0.147532\pi$
$24$	−2.47641	−	1.79922i	−0.505496	−	0.367264i
$25$	7.49543			1.49909
$26$	11.9011			2.33400
$27$	1.36619	+	0.992592i	0.262923	+	0.191024i
$28$	0.413407	+	1.27234i	0.0781266	+	0.240449i
$29$	−2.57655	+	7.92982i	−0.478454	+	1.47253i	0.362788	+	0.931872i	$0.381825\pi$
$29$	−2.57655	+	7.92982i	−0.478454	+	1.47253i	−0.841242	+	0.540659i	$0.818175\pi$
$30$	17.4335			3.18291
$31$	−4.63523	−	3.08459i	−0.832511	−	0.554008i
$31$	−4.63523	−	3.08459i	−0.832511	−	0.554008i
$32$	−7.77023			−1.37359
$33$	2.67949	−	8.24663i	0.466440	−	1.43555i
$34$	0.664255	+	2.04437i	0.113919	+	0.350606i
$35$	−1.45988	−	1.06067i	−0.246765	−	0.179285i
$36$	5.93310			0.988851
$37$	−3.92515			−0.645291			−0.322646	−	0.946520i	$-0.604572\pi$
$37$	−3.92515			−0.645291			−0.322646	+	0.946520i	$0.604572\pi$
$38$	−1.98012	−	1.43864i	−0.321218	−	0.233378i
$39$	−10.2766	+	7.46638i	−1.64557	+	1.19558i
$40$	−3.81542	+	2.77206i	−0.603270	+	0.438301i
$41$	1.34192	−	4.13002i	0.209573	−	0.645001i	−0.789921	−	0.613208i	$-0.789879\pi$
$41$	1.34192	−	4.13002i	0.209573	−	0.645001i	0.999495	−	0.0317921i	$-0.0101214\pi$
$42$	−2.03681	−	1.47983i	−0.314287	−	0.228343i
$43$	2.52269	−	7.76404i	0.384706	−	1.18400i	−0.551987	−	0.833853i	$-0.686130\pi$
$43$	2.52269	−	7.76404i	0.384706	−	1.18400i	0.936693	−	0.350152i	$-0.113870\pi$
$44$	3.06060	+	9.41957i	0.461404	+	1.42005i
$45$	−6.47446	+	4.70397i	−0.965156	+	0.701227i
$46$	−2.93645	−	9.03745i	−0.432955	−	1.33250i
$47$	2.02642	+	6.23669i	0.295584	+	0.909714i	0.983025	+	0.183474i	$0.0587342\pi$
$47$	2.02642	+	6.23669i	0.295584	+	0.909714i	−0.687441	+	0.726241i	$0.741266\pi$
$48$	4.40549	−	3.20078i	0.635878	−	0.461992i
$49$	−2.08259	−	6.40955i	−0.297513	−	0.915650i
$50$	4.97887	−	15.3234i	0.704119	−	2.16705i
$51$	−1.85616	−	1.34858i	−0.259914	−	0.188838i
$52$	4.48362	−	13.7991i	0.621766	−	1.91360i
$53$	−4.53151	+	3.29233i	−0.622450	+	0.452237i	−0.853777	−	0.520640i	$-0.825694\pi$
$53$	−4.53151	+	3.29233i	−0.622450	+	0.452237i	0.231326	+	0.972876i	$0.425694\pi$
$54$	2.93672	−	2.13365i	0.399637	−	0.290353i
$55$	−10.8080	−	7.85250i	−1.45736	−	1.05883i
$56$	0.681072			0.0910121
$57$	2.61239			0.346020
$58$	14.5000	+	10.5348i	1.90394	+	1.38329i
$59$	−2.35108	−	7.23587i	−0.306084	−	0.942030i	−0.979270	−	0.202557i	$-0.935075\pi$
$59$	−2.35108	−	7.23587i	−0.306084	−	0.942030i	0.673186	−	0.739473i	$-0.264925\pi$
$60$	6.56789	−	20.2139i	0.847911	−	2.60960i
$61$	−8.84975			−1.13309			−0.566547	−	0.824029i	$-0.691721\pi$
$61$	−8.84975			−1.13309			−0.566547	+	0.824029i	$0.691721\pi$
$62$	−9.38499	+	7.42715i	−1.19189	+	0.943249i
$63$	1.15573			0.145608
$64$	−3.69454	+	11.3706i	−0.461817	+	1.42133i
$65$	6.04773	+	18.6130i	0.750129	+	2.30866i
$66$	−15.0793	−	10.9557i	−1.85613	−	1.34856i
$67$	−2.59351			−0.316847			−0.158424	−	0.987371i	$-0.550641\pi$
$67$	−2.59351			−0.316847			−0.158424	+	0.987371i	$0.550641\pi$
$68$	2.62066			0.317802
$69$	8.20544	+	5.96160i	0.987819	+	0.717692i
$70$	−3.13812	+	2.27998i	−0.375077	+	0.272510i
$71$	−5.45994	+	3.96688i	−0.647976	+	0.470782i	−0.862581	−	0.505919i	$-0.831153\pi$
$71$	−5.45994	+	3.96688i	−0.647976	+	0.470782i	0.214605	+	0.976701i	$0.431153\pi$
$72$	0.933387	−	2.87267i	0.110001	−	0.338547i
$73$	5.63728	+	4.09573i	0.659794	+	0.479369i	0.866593	−	0.499015i	$-0.166305\pi$
$73$	5.63728	+	4.09573i	0.659794	+	0.479369i	−0.206799	+	0.978383i	$0.566305\pi$
$74$	−2.60730	+	8.02445i	−0.303093	+	0.932823i
$75$	5.31417	+	16.3553i	0.613627	+	1.88855i
$76$	−2.41407	+	1.75393i	−0.276913	+	0.201189i
$77$	0.596184	+	1.83487i	0.0679415	+	0.209102i
$78$	8.43774	+	25.9687i	0.955385	+	2.94037i
$79$	4.50337	−	3.27189i	0.506669	−	0.368116i	−0.304890	−	0.952388i	$-0.598620\pi$
$79$	4.50337	−	3.27189i	0.506669	−	0.368116i	0.811558	+	0.584271i	$0.198620\pi$
$80$	−2.59261	−	7.97924i	−0.289863	−	0.892106i
$81$	−3.29608	+	10.1443i	−0.366231	+	1.12714i
$82$	−7.55189	−	5.48677i	−0.833966	−	0.605912i
$83$	−5.06921	+	15.6014i	−0.556418	+	1.71248i	0.135751	+	0.990743i	$0.456655\pi$
$83$	−5.06921	+	15.6014i	−0.556418	+	1.71248i	−0.692169	+	0.721735i	$0.743345\pi$
$84$	−2.48319	+	1.80414i	−0.270938	+	0.196848i
$85$	−2.85978	+	2.07775i	−0.310187	+	0.225364i
$86$	−14.1968	−	10.3146i	−1.53088	−	1.11225i
$87$	−19.1299			−2.05095
$88$	5.04223			0.537503
$89$	−11.2517	−	8.17486i	−1.19268	−	0.866533i	−0.199136	−	0.979972i	$-0.563813\pi$
$89$	−11.2517	−	8.17486i	−1.19268	−	0.866533i	−0.993545	+	0.113439i	$0.963813\pi$
$90$	5.31595	+	16.3608i	0.560350	+	1.72458i
$91$	0.873376	−	2.68798i	0.0915547	−	0.281776i
$92$	−11.5851			−1.20783
$93$	3.44437	−	12.3012i	0.357165	−	1.27557i
$94$	14.0961			1.45390
$95$	1.24377	−	3.82792i	0.127608	−	0.392737i
$96$	−5.50900	−	16.9550i	−0.562260	−	1.73046i
$97$	0.600165	+	0.436046i	0.0609376	+	0.0442737i	0.617837	−	0.786306i	$-0.288009\pi$
$97$	0.600165	+	0.436046i	0.0609376	+	0.0442737i	−0.556899	+	0.830580i	$0.688009\pi$
$98$	−14.4868			−1.46339
$99$	8.55626			0.859937
$100$	−15.8915	−	11.5459i	−1.58915	−	1.15459i
$101$	3.35318	−	2.43623i	0.333654	−	0.242414i	−0.408325	−	0.912836i	$-0.633887\pi$
$101$	3.35318	−	2.43623i	0.333654	−	0.242414i	0.741980	+	0.670422i	$0.233887\pi$
$102$	−3.98994	+	2.89886i	−0.395063	+	0.287030i
$103$	1.74370	−	5.36654i	0.171811	−	0.528781i	−0.827662	−	0.561227i	$-0.810330\pi$
$103$	1.74370	−	5.36654i	0.171811	−	0.528781i	0.999474	+	0.0324455i	$0.0103296\pi$
$104$	−5.97587	−	4.34172i	−0.585982	−	0.425741i
$105$	1.27938	−	3.93752i	0.124855	−	0.384263i
$106$	3.72066	+	11.4510i	0.361382	+	1.11222i
$107$	1.27889	−	0.929166i	0.123635	−	0.0898258i	−0.524250	−	0.851565i	$-0.675654\pi$
$107$	1.27889	−	0.929166i	0.123635	−	0.0898258i	0.647884	+	0.761739i	$0.275654\pi$
$108$	−1.36756	−	4.20891i	−0.131593	−	0.405003i
$109$	4.32317	+	13.3053i	0.414084	+	1.27442i	0.913067	+	0.407809i	$0.133707\pi$
$109$	4.32317	+	13.3053i	0.414084	+	1.27442i	−0.498983	+	0.866612i	$0.666293\pi$
$110$	−23.2327	+	16.8795i	−2.21515	+	1.60940i
$111$	−2.78289	−	8.56485i	−0.264140	−	0.812939i
$112$	−0.374409	+	1.15231i	−0.0353783	+	0.108883i
$113$	13.2634	+	9.63640i	1.24771	+	0.906516i	0.998087	−	0.0618264i	$-0.0196925\pi$
$113$	13.2634	+	9.63640i	1.24771	+	0.906516i	0.249625	+	0.968342i	$0.419693\pi$
$114$	1.73529	−	5.34068i	0.162525	−	0.500200i
$115$	12.6421	−	9.18505i	1.17889	−	0.856511i
$116$	17.6777	−	12.8436i	1.64133	−	1.19250i
$117$	−10.1406	−	7.36757i	−0.937497	−	0.681132i
$118$	−16.3545			−1.50555
$119$	0.510487			0.0467962
$120$	−8.75384	−	6.36004i	−0.799113	−	0.580589i
$121$	1.01458	+	3.12256i	0.0922346	+	0.283869i
$122$	−5.87849	+	18.0921i	−0.532213	+	1.63798i
$123$	9.96328			0.898359
$124$	5.07597	+	13.6799i	0.455836	+	1.22849i
$125$	8.82105			0.788979
$126$	0.767697	−	2.36273i	0.0683918	−	0.210488i
$127$	−4.48163	−	13.7930i	−0.397680	−	1.22393i	−0.926855	−	0.375420i	$-0.877498\pi$
$127$	−4.48163	−	13.7930i	−0.397680	−	1.22393i	0.529175	−	0.848513i	$-0.322502\pi$
$128$	8.21909	+	5.97152i	0.726471	+	0.527812i
$129$	18.7300			1.64909
$130$	42.0690			3.68970
$131$	−16.3949	−	11.9116i	−1.43243	−	1.04072i	−0.989559	−	0.144131i	$-0.953961\pi$
$131$	−16.3949	−	11.9116i	−1.43243	−	1.04072i	−0.442867	−	0.896587i	$-0.646039\pi$
$132$	−18.3840	+	13.3567i	−1.60012	+	1.16255i
$133$	−0.470244	+	0.341652i	−0.0407753	+	0.0296250i
$134$	−1.72275	+	5.30207i	−0.148823	+	0.458029i
$135$	4.82931	+	3.50870i	0.415641	+	0.301981i
$136$	0.412279	−	1.26886i	0.0353526	−	0.108804i
$137$	1.20145	+	3.69768i	0.102647	+	0.315914i	0.989171	−	0.146768i	$-0.0468872\pi$
$137$	1.20145	+	3.69768i	0.102647	+	0.315914i	−0.886524	+	0.462682i	$0.846887\pi$
$138$	17.6382	−	12.8149i	1.50146	−	1.09088i
$139$	−0.735536	−	2.26375i	−0.0623874	−	0.192009i	0.915005	−	0.403443i	$-0.132187\pi$
$139$	−0.735536	−	2.26375i	−0.0623874	−	0.192009i	−0.977392	+	0.211434i	$0.932187\pi$
$140$	1.46135	+	4.49757i	0.123506	+	0.380114i
$141$	−12.1720	+	8.84348i	−1.02507	+	0.744755i
$142$	4.48296	+	13.7971i	0.376202	+	1.15783i
$143$	6.46592	−	19.9001i	0.540708	−	1.66413i
$144$	4.34718	+	3.15841i	0.362265	+	0.263201i
$145$	−9.10783	+	28.0310i	−0.756364	+	2.32785i
$146$	12.1178	−	8.80406i	1.00287	−	0.728630i
$147$	12.5094	−	9.08860i	1.03176	−	0.749615i
$148$	8.32196	+	6.04626i	0.684061	+	0.496999i
$149$	−5.30060			−0.434242			−0.217121	−	0.976145i	$-0.569667\pi$
$149$	−5.30060			−0.434242			−0.217121	+	0.976145i	$0.569667\pi$
$150$	36.9662			3.01828
$151$	16.4256	+	11.9339i	1.33670	+	0.971168i	0.999558	+	0.0297140i	$0.00945967\pi$
$151$	16.4256	+	11.9339i	1.33670	+	0.971168i	0.337140	+	0.941454i	$0.390540\pi$
$152$	0.469432	+	1.44476i	0.0380759	+	0.117186i
$153$	0.699605	−	2.15316i	0.0565597	−	0.174073i
$154$	4.14715			0.334187
$155$	−16.3850	−	10.9037i	−1.31608	−	0.875803i
$156$	33.2891			2.66527
$157$	5.22243	−	16.0730i	0.416796	−	1.28277i	−0.493839	−	0.869553i	$-0.664407\pi$
$157$	5.22243	−	16.0730i	0.416796	−	1.28277i	0.910635	−	0.413212i	$-0.135593\pi$
$158$	−3.69755	−	11.3799i	−0.294162	−	0.905337i
$159$	−10.3968	−	7.55371i	−0.824519	−	0.599048i
$160$	−27.4669			−2.17145
$161$	−2.25669			−0.177852
$162$	18.5492	+	13.4768i	1.45736	+	1.05884i
$163$	−7.65005	+	5.55808i	−0.599198	+	0.435343i	−0.845594	−	0.533826i	$-0.820754\pi$
$163$	−7.65005	+	5.55808i	−0.599198	+	0.435343i	0.246396	+	0.969169i	$0.420754\pi$
$164$	−9.20693	+	6.68922i	−0.718940	+	0.522341i
$165$	9.47170	−	29.1509i	0.737371	−	2.26940i
$166$	28.5278	+	20.7266i	2.21418	+	1.60870i
$167$	−0.659431	+	2.02952i	−0.0510283	+	0.157049i	−0.973323	−	0.229437i	$-0.926311\pi$
$167$	−0.659431	+	2.02952i	−0.0510283	+	0.157049i	0.922295	+	0.386486i	$0.126311\pi$
$168$	0.482872	+	1.48613i	0.0372544	+	0.114657i
$169$	−14.2814	+	10.3760i	−1.09857	+	0.798156i
$170$	2.34806	+	7.22660i	0.180088	+	0.554255i
$171$	0.796589	+	2.45165i	0.0609167	+	0.187482i
$172$	−17.3081	+	12.5751i	−1.31973	+	0.958842i
$173$	0.170827	+	0.525751i	0.0129877	+	0.0399721i	0.957340	−	0.288963i	$-0.0933104\pi$
$173$	0.170827	+	0.525751i	0.0129877	+	0.0399721i	−0.944353	+	0.328935i	$0.893310\pi$
$174$	−12.7072	+	39.1086i	−0.963327	+	2.96481i
$175$	−3.09555	−	2.24905i	−0.234002	−	0.170012i
$176$	−2.77189	+	8.53099i	−0.208939	+	0.643048i
$177$	14.1221	−	10.2603i	1.06148	−	0.771211i
$178$	−24.1864	+	17.5725i	−1.81285	+	1.31711i
$179$	−8.44856	−	6.13824i	−0.631475	−	0.458793i	0.225436	−	0.974258i	$-0.427619\pi$
$179$	−8.44856	−	6.13824i	−0.631475	−	0.458793i	−0.856911	+	0.515465i	$0.827619\pi$
$180$	20.9729			1.56322
$181$	−6.08760			−0.452488			−0.226244	−	0.974071i	$-0.572645\pi$
$181$	−6.08760			−0.452488			−0.226244	+	0.974071i	$0.572645\pi$
$182$	−4.91506	−	3.57100i	−0.364329	−	0.264700i
$183$	−6.27437	−	19.3105i	−0.463815	−	1.42747i
$184$	−1.82255	+	5.60922i	−0.134360	+	0.413517i
$185$	−13.8750			−1.02011
$186$	−22.8602	−	15.2127i	−1.67619	−	1.11545i
$187$	3.77932			0.276371
$188$	5.31057	−	16.3443i	0.387313	−	1.19203i
$189$	−0.266391	−	0.819866i	−0.0193771	−	0.0596365i
$190$	−6.99949	−	5.08543i	−0.507797	−	0.368936i
$191$	8.08833			0.585251			0.292626	−	0.956227i	$-0.405471\pi$
$191$	8.08833			0.585251			0.292626	+	0.956227i	$0.405471\pi$
$192$	−27.4305			−1.97963
$193$	13.8715	+	10.0782i	0.998490	+	0.725445i	0.961764	−	0.273880i	$-0.0883071\pi$
$193$	13.8715	+	10.0782i	0.998490	+	0.725445i	0.0367260	+	0.999325i	$0.488307\pi$
$194$	1.29010	−	0.937312i	0.0926237	−	0.0672951i
$195$	−36.3266	+	26.3928i	−2.60140	+	1.89003i
$196$	−5.45777	+	16.7973i	−0.389841	+	1.19981i
$197$	6.25896	+	4.54740i	0.445933	+	0.323989i	0.787988	−	0.615691i	$-0.211123\pi$
$197$	6.25896	+	4.54740i	0.445933	+	0.323989i	−0.342055	+	0.939680i	$0.611123\pi$
$198$	5.68354	−	17.4921i	0.403911	−	1.24311i
$199$	6.63102	+	20.4082i	0.470061	+	1.44670i	0.852505	+	0.522719i	$0.175082\pi$
$199$	6.63102	+	20.4082i	0.470061	+	1.44670i	−0.382444	+	0.923979i	$0.624918\pi$
$200$	−8.09026	+	5.87792i	−0.572068	+	0.415632i
$201$	−1.83877	−	5.65914i	−0.129697	−	0.399165i
$202$	−2.75318	−	8.47341i	−0.193713	−	0.596187i
$203$	3.44349	−	2.50184i	0.241686	−	0.175595i
$204$	1.85802	+	5.71840i	0.130087	+	0.400368i
$205$	4.74355	−	14.5991i	0.331304	−	1.01965i
$206$	−9.81292	−	7.12950i	−0.683698	−	0.496736i
$207$	−3.09272	+	9.51841i	−0.214959	+	0.661575i
$208$	10.6310	−	7.72384i	0.737124	−	0.535552i
$209$	−3.48139	+	2.52938i	−0.240813	+	0.174961i
$210$	−7.19990	−	5.23103i	−0.496840	−	0.360976i
$211$	6.43971			0.443328			0.221664	−	0.975123i	$-0.428851\pi$
$211$	6.43971			0.443328			0.221664	+	0.975123i	$0.428851\pi$
$212$	14.6790			1.00816
$213$	−12.5269	−	9.10135i	−0.858331	−	0.623614i
$214$	−1.05005	−	3.23171i	−0.0717798	−	0.220915i
$215$	8.91742	−	27.4450i	0.608163	−	1.87173i
$216$	−2.25300			−0.153297
$217$	0.988764	+	2.66474i	0.0671217	+	0.180894i
$218$	30.0727			2.03678
$219$	−4.94028	+	15.2046i	−0.333833	+	1.02743i
$220$	10.8189	+	33.2971i	0.729410	+	2.24489i
$221$	−4.47912	−	3.25427i	−0.301298	−	0.218906i
$222$	−19.3582			−1.29924
$223$	−20.7666			−1.39063			−0.695316	−	0.718704i	$-0.744736\pi$
$223$	−20.7666			−1.39063			−0.695316	+	0.718704i	$0.744736\pi$
$224$	3.20904	+	2.33151i	0.214413	+	0.155780i
$225$	−13.7285	+	9.97437i	−0.915237	+	0.664958i
$226$	28.5106	−	20.7141i	1.89649	−	1.37788i
$227$	4.67596	−	14.3911i	0.310354	−	0.955173i	−0.667270	−	0.744816i	$-0.732537\pi$
$227$	4.67596	−	14.3911i	0.310354	−	0.955173i	0.977625	−	0.210357i	$-0.0674627\pi$
$228$	−5.53869	−	4.02409i	−0.366809	−	0.266502i
$229$	−2.08439	+	6.41508i	−0.137740	+	0.423921i	−0.996006	−	0.0892845i	$-0.971542\pi$
$229$	−2.08439	+	6.41508i	−0.137740	+	0.423921i	0.858266	+	0.513205i	$0.171542\pi$
$230$	−10.3800	−	31.9464i	−0.684437	−	2.10648i
$231$	−3.58107	+	2.60180i	−0.235617	+	0.171186i
$232$	−3.43754	−	10.5797i	−0.225686	−	0.694589i
$233$	7.10336	+	21.8619i	0.465357	+	1.43222i	0.858534	+	0.512757i	$0.171376\pi$
$233$	7.10336	+	21.8619i	0.465357	+	1.43222i	−0.393177	+	0.919463i	$0.628624\pi$
$234$	−21.7979	+	15.8371i	−1.42497	+	1.03530i
$235$	7.16317	+	22.0460i	0.467274	+	1.43812i
$236$	−6.16138	+	18.9628i	−0.401072	+	1.23437i
$237$	10.3322	+	7.50681i	0.671151	+	0.487620i
$238$	0.339093	−	1.04362i	0.0219801	−	0.0676479i
$239$	24.5336	−	17.8247i	1.58695	−	1.15299i	0.678810	−	0.734314i	$-0.262496\pi$
$239$	24.5336	−	17.8247i	1.58695	−	1.15299i	0.908138	−	0.418671i	$-0.137504\pi$
$240$	15.5729	−	11.3144i	1.00523	−	0.730340i
$241$	11.7927	+	8.56789i	0.759634	+	0.551907i	0.898798	−	0.438363i	$-0.144442\pi$
$241$	11.7927	+	8.56789i	0.759634	+	0.551907i	−0.139164	+	0.990269i	$0.544442\pi$
$242$	7.05759			0.453679
$243$	−19.4061			−1.24490
$244$	18.7629	+	13.6320i	1.20117	+	0.872702i
$245$	−7.36172	−	22.6570i	−0.470323	−	1.44751i
$246$	6.61815	−	20.3686i	0.421958	−	1.29865i
$247$	6.30400			0.401114
$248$	7.42201	−	0.305572i	0.471298	−	0.0194038i
$249$	−37.6370			−2.38515
$250$	5.85942	−	18.0334i	0.370582	−	1.14054i
$251$	−3.26930	−	10.0619i	−0.206356	−	0.635100i	−0.999655	−	0.0262669i	$-0.991638\pi$
$251$	−3.26930	−	10.0619i	−0.206356	−	0.635100i	0.793299	−	0.608833i	$-0.208362\pi$
$252$	−2.45033	−	1.78027i	−0.154356	−	0.112146i
$253$	−16.7071			−1.05037
$254$	−31.1749			−1.95609
$255$	−6.56130	−	4.76706i	−0.410885	−	0.298525i
$256$	−1.67732	+	1.21864i	−0.104832	+	0.0761652i
$257$	9.01052	−	6.54653i	0.562061	−	0.408361i	−0.270152	−	0.962818i	$-0.587074\pi$
$257$	9.01052	−	6.54653i	0.562061	−	0.408361i	0.832213	+	0.554457i	$0.187074\pi$
$258$	12.4415	−	38.2910i	0.774574	−	2.38389i
$259$	1.62106	+	1.17777i	0.100728	+	0.0731829i
$260$	15.8491	−	48.7784i	0.982918	−	3.02511i
$261$	−5.83324	−	17.9529i	−0.361069	−	1.11125i
$262$	−35.2419	+	25.6048i	−2.17725	+	1.58187i
$263$	3.08935	+	9.50803i	0.190497	+	0.586290i	1.00000		0.000826345i	$-0.000263034\pi$
$263$	3.08935	+	9.50803i	0.190497	+	0.586290i	−0.809502	+	0.587117i	$0.800263\pi$
$264$	3.57488	+	11.0023i	0.220019	+	0.677148i
$265$	−16.0184	+	11.6380i	−0.984001	+	0.714918i
$266$	0.386100	+	1.18829i	0.0236733	+	0.0728590i
$267$	9.86054	−	30.3476i	0.603455	−	1.85724i
$268$	5.49865	+	3.99500i	0.335884	+	0.244034i
$269$	0.644683	−	1.98413i	0.0393070	−	0.120975i	−0.929478	−	0.368879i	$-0.879742\pi$
$269$	0.644683	−	1.98413i	0.0393070	−	0.120975i	0.968785	+	0.247904i	$0.0797418\pi$
$270$	10.3810	−	7.54221i	0.631765	−	0.459004i
$271$	14.1064	−	10.2489i	0.856906	−	0.622578i	−0.0701357	−	0.997537i	$-0.522343\pi$
$271$	14.1064	−	10.2489i	0.856906	−	0.622578i	0.927041	+	0.374959i	$0.122343\pi$
$272$	1.92016	+	1.39508i	0.116427	+	0.0845890i
$273$	6.48449			0.392459
$274$	8.35747			0.504893
$275$	−22.9175	−	16.6505i	−1.38198	−	1.00407i
$276$	−8.21368	−	25.2791i	−0.494405	−	1.52162i
$277$	4.21552	−	12.9740i	0.253286	−	0.779534i	−0.740877	−	0.671641i	$-0.765590\pi$
$277$	4.21552	−	12.9740i	0.253286	−	0.779534i	0.994163	−	0.107893i	$-0.0344103\pi$
$278$	−5.11651			−0.306868
$279$	12.5946	−	0.518531i	0.754018	−	0.0310437i
$280$	2.40751			0.143876
$281$	3.14441	−	9.67750i	0.187580	−	0.577311i	−0.812404	−	0.583096i	$-0.801841\pi$
$281$	3.14441	−	9.67750i	0.187580	−	0.577311i	0.999983	+	0.00578455i	$0.00184129\pi$
$282$	9.99399	+	30.7583i	0.595133	+	1.83163i
$283$	2.73057	+	1.98387i	0.162315	+	0.117929i	0.665978	−	0.745971i	$-0.268014\pi$
$283$	2.73057	+	1.98387i	0.162315	+	0.117929i	−0.503662	+	0.863901i	$0.668014\pi$
$284$	17.6865			1.04950
$285$	9.23450			0.547005
$286$	−36.3880	−	26.4374i	−2.15167	−	1.56328i
$287$	−1.79344	+	1.30301i	−0.105864	+	0.0769144i
$288$	14.2319	−	10.3401i	0.838621	−	0.609294i
$289$	0.309017	−	0.951057i	0.0181775	−	0.0559445i
$290$	51.2557	+	37.2395i	3.00984	+	2.18678i
$291$	−0.525960	+	1.61874i	−0.0308323	+	0.0948921i
$292$	−5.64295	−	17.3672i	−0.330229	−	1.01634i
$293$	−16.4635	+	11.9615i	−0.961810	+	0.698796i	−0.953570	−	0.301170i	$-0.902623\pi$
$293$	−16.4635	+	11.9615i	−0.961810	+	0.698796i	−0.00823960	+	0.999966i	$0.502623\pi$
$294$	−10.2710	−	31.6109i	−0.599017	−	1.84358i
$295$	−8.31079	−	25.5780i	−0.483873	−	1.48921i
$296$	4.23665	−	3.07811i	0.246251	−	0.178911i
$297$	−1.97219	−	6.06977i	−0.114438	−	0.352204i
$298$	−3.52095	+	10.8364i	−0.203963	+	0.627733i
$299$	19.8007	+	14.3860i	1.14510	+	0.831965i
$300$	13.9267	−	42.8618i	0.804056	−	2.47463i
$301$	−3.37150	+	2.44954i	−0.194330	+	0.141189i
$302$	35.3081	−	25.6528i	2.03175	−	1.47615i
$303$	7.69332	+	5.58953i	0.441970	+	0.321110i
$304$	−2.70247			−0.154997
$305$	−31.2829			−1.79125
$306$	−3.93714	−	2.86050i	−0.225071	−	0.163524i
$307$	−4.46776	−	13.7504i	−0.254989	−	0.784774i	−0.993832	−	0.110897i	$-0.964628\pi$
$307$	−4.46776	−	13.7504i	−0.254989	−	0.784774i	0.738843	−	0.673877i	$-0.235372\pi$
$308$	1.56240	−	4.80857i	0.0890259	−	0.273993i
$309$	12.9463			0.736488
$310$	−33.1749	+	26.2541i	−1.88421	+	1.49113i
$311$	−12.3048			−0.697743			−0.348872	−	0.937171i	$-0.613435\pi$
$311$	−12.3048			−0.697743			−0.348872	+	0.937171i	$0.613435\pi$
$312$	5.23700	−	16.1178i	0.296487	−	0.912492i
$313$	−0.551009	−	1.69583i	−0.0311449	−	0.0958541i	0.934276	−	0.356551i	$-0.116048\pi$
$313$	−0.551009	−	1.69583i	−0.0311449	−	0.0958541i	−0.965421	+	0.260697i	$0.916048\pi$
$314$	−29.3901	−	21.3531i	−1.65858	−	1.20503i
$315$	4.08536			0.230184
$316$	−14.5879			−0.820631
$317$	−20.0514	−	14.5682i	−1.12620	−	0.818231i	−0.141062	−	0.990001i	$-0.545052\pi$
$317$	−20.0514	−	14.5682i	−1.12620	−	0.818231i	−0.985137	+	0.171769i	$0.945052\pi$
$318$	−22.3487	+	16.2373i	−1.25325	+	0.910540i
$319$	25.4934	−	18.5221i	1.42736	−	1.03704i
$320$	−13.0598	+	40.1938i	−0.730063	+	2.24690i
$321$	2.93419	+	2.13182i	0.163771	+	0.118986i
$322$	−1.49902	+	4.61350i	−0.0835369	+	0.257100i
$323$	0.351855	+	1.08290i	0.0195777	+	0.0602541i
$324$	22.6144	−	16.4303i	1.25635	−	0.912795i
$325$	12.8237	+	39.4673i	0.711331	+	2.18925i
$326$	6.28118	+	19.3315i	0.347882	+	1.07067i
$327$	−25.9677	+	18.8667i	−1.43602	+	1.04333i
$328$	1.79035	+	5.51012i	0.0988553	+	0.304245i
$329$	1.03446	−	3.18375i	0.0570317	−	0.175526i
$330$	−53.3035	−	38.7273i	−2.93426	−	2.13186i
$331$	10.6988	−	32.9275i	0.588059	−	1.80986i	0.00143424	−	0.999999i	$-0.499543\pi$
$331$	10.6988	−	32.9275i	0.588059	−	1.80986i	0.586624	−	0.809859i	$-0.300457\pi$
$332$	34.7798	−	25.2690i	1.90879	−	1.38682i
$333$	7.18927	−	5.22331i	0.393970	−	0.286236i
$334$	3.71105	+	2.69624i	0.203060	+	0.147532i
$335$	−9.16775			−0.500888
$336$	−2.77985			−0.151653
$337$	29.2572	+	21.2566i	1.59374	+	1.15792i	0.898345	+	0.439291i	$0.144770\pi$
$337$	29.2572	+	21.2566i	1.59374	+	1.15792i	0.695395	+	0.718628i	$0.255230\pi$
$338$	11.7259	+	36.0887i	0.637806	+	1.96296i
$339$	−11.6235	+	35.7733i	−0.631299	+	1.94294i
$340$	9.26375			0.502397
$341$	7.32018	+	19.7280i	0.396410	+	1.06833i
$342$	5.54120			0.299634
$343$	−2.16738	+	6.67050i	−0.117027	+	0.360173i
$344$	3.36568	+	10.3585i	0.181465	+	0.558492i
$345$	29.0053	+	21.0736i	1.56159	+	1.13456i
$346$	1.18830			0.0638834
$347$	2.73797			0.146982			0.0734910	−	0.997296i	$-0.476586\pi$
$347$	2.73797			0.146982			0.0734910	+	0.997296i	$0.476586\pi$
$348$	40.5586	+	29.4675i	2.17417	+	1.57963i
$349$	16.2885	−	11.8343i	0.871904	−	0.633476i	−0.0591929	−	0.998247i	$-0.518853\pi$
$349$	16.2885	−	11.8343i	0.871904	−	0.633476i	0.931097	+	0.364771i	$0.118853\pi$
$350$	−6.65412	+	4.83450i	−0.355678	+	0.258415i
$351$	−2.88914	+	8.89187i	−0.154211	+	0.474613i
$352$	23.7577	+	17.2610i	1.26629	+	0.920014i
$353$	11.2009	−	34.4729i	0.596164	−	1.83480i	0.0473210	−	0.998880i	$-0.484932\pi$
$353$	11.2009	−	34.4729i	0.596164	−	1.83480i	0.548843	−	0.835925i	$-0.315068\pi$
$354$	−11.5951	−	35.6861i	−0.616274	−	1.89670i
$355$	−19.3003	+	14.0225i	−1.02435	+	0.744235i
$356$	11.2630	+	34.6640i	0.596939	+	1.83719i
$357$	0.361929	+	1.11390i	0.0191553	+	0.0589540i
$358$	−18.1608	+	13.1946i	−0.959828	+	0.697356i
$359$	3.14034	+	9.66498i	0.165741	+	0.510098i	0.999090	−	0.0426487i	$-0.0135796\pi$
$359$	3.14034	+	9.66498i	0.165741	+	0.510098i	−0.833349	+	0.552747i	$0.813580\pi$
$360$	3.29942	−	10.1546i	0.173895	−	0.535192i
$361$	14.3225	+	10.4059i	0.753813	+	0.547678i
$362$	−4.04372	+	12.4453i	−0.212533	+	0.654109i
$363$	−6.09423	+	4.42771i	−0.319864	+	0.232395i
$364$	−5.99222	+	4.35361i	−0.314078	+	0.228191i
$365$	19.9272	+	14.4779i	1.04304	+	0.757810i
$366$	−43.6455			−2.28139
$367$	4.71644			0.246196			0.123098	−	0.992395i	$-0.460717\pi$
$367$	4.71644			0.246196			0.123098	+	0.992395i	$0.460717\pi$
$368$	−8.48838	−	6.16717i	−0.442487	−	0.321486i
$369$	3.03808	+	9.35024i	0.158156	+	0.486754i
$370$	−9.21652	+	28.3655i	−0.479144	+	1.47465i
$371$	2.85936			0.148451
$372$	−26.2512	+	20.7749i	−1.36106	+	1.07713i
$373$	20.0533			1.03832			0.519159	−	0.854677i	$-0.326245\pi$
$373$	20.0533			1.03832			0.519159	+	0.854677i	$0.326245\pi$
$374$	2.51043	−	7.72631i	0.129811	−	0.399518i
$375$	6.25402	+	19.2479i	0.322956	+	0.993957i
$376$	−7.07806	−	5.14251i	−0.365023	−	0.265205i
$377$	−46.1627			−2.37750
$378$	−1.85306			−0.0953110
$379$	19.9728	+	14.5111i	1.02593	+	0.745383i	0.967490	−	0.252908i	$-0.0813870\pi$
$379$	19.9728	+	14.5111i	1.02593	+	0.745383i	0.0584410	+	0.998291i	$0.481387\pi$
$380$	−8.53347	+	6.19993i	−0.437758	+	0.318050i
$381$	26.9195	−	19.5582i	1.37913	−	1.00200i
$382$	5.37271	−	16.5355i	0.274892	−	0.846030i
$383$	12.5016	+	9.08294i	0.638802	+	0.464117i	0.859438	−	0.511239i	$-0.170813\pi$
$383$	12.5016	+	9.08294i	0.638802	+	0.464117i	−0.220636	+	0.975356i	$0.570813\pi$
$384$	−7.20286	+	22.1681i	−0.367569	+	1.13126i
$385$	2.10744	+	6.48604i	0.107405	+	0.330559i
$386$	29.8177	−	21.6638i	1.51768	−	1.10266i
$387$	5.71129	+	17.5775i	0.290321	+	0.893517i
$388$	−0.600768	−	1.84897i	−0.0304994	−	0.0938675i
$389$	−8.73972	+	6.34978i	−0.443122	+	0.321947i	−0.786874	−	0.617114i	$-0.788302\pi$
$389$	−8.73972	+	6.34978i	−0.443122	+	0.321947i	0.343752	+	0.939060i	$0.388302\pi$
$390$	29.8264	+	91.7964i	1.51032	+	4.64829i
$391$	−1.36606	+	4.20430i	−0.0690846	+	0.212621i
$392$	7.27424	+	5.28505i	0.367405	+	0.266935i
$393$	14.3678	−	44.2194i	0.724758	−	2.23057i
$394$	13.4541	−	9.77497i	0.677808	−	0.492456i
$395$	15.9189	−	11.5658i	0.800967	−	0.581937i
$396$	−18.1407	−	13.1800i	−0.911603	−	0.662318i
$397$	−0.835138			−0.0419144			−0.0209572	−	0.999780i	$-0.506671\pi$
$397$	−0.835138			−0.0419144			−0.0209572	+	0.999780i	$0.506671\pi$
$398$	46.1265			2.31211
$399$	−1.07890	−	0.783865i	−0.0540124	−	0.0392423i
$400$	−5.49741	−	16.9193i	−0.274871	−	0.845965i
$401$	6.16870	−	18.9853i	0.308050	−	0.948081i	−0.670471	−	0.741936i	$-0.733908\pi$
$401$	6.16870	−	18.9853i	0.308050	−	0.948081i	0.978521	−	0.206145i	$-0.0660920\pi$
$402$	−12.7908			−0.637945
$403$	8.31166	−	29.6842i	0.414033	−	1.47867i
$404$	−10.8620			−0.540406
$405$	−11.6513	+	35.8590i	−0.578957	+	1.78185i
$406$	−2.82733	−	8.70162i	−0.140318	−	0.431854i
$407$	12.0013	+	8.71945i	0.594882	+	0.432207i
$408$	3.06101			0.151543
$409$	25.8474			1.27807			0.639036	−	0.769177i	$-0.279334\pi$
$409$	25.8474			1.27807			0.639036	+	0.769177i	$0.279334\pi$
$410$	−26.6951	−	19.3951i	−1.31838	−	0.957856i
$411$	−7.21667	+	5.24322i	−0.355972	+	0.258629i
$412$	−11.9635	+	8.69197i	−0.589398	+	0.428223i
$413$	−1.20019	+	3.69381i	−0.0590576	+	0.181761i
$414$	17.4048	+	12.6453i	0.855397	+	0.621482i
$415$	−17.9191	+	55.1493i	−0.879613	+	2.70717i
$416$	−13.2938	−	40.9143i	−0.651784	−	2.00599i
$417$	4.41811	−	3.20994i	0.216356	−	0.157192i
$418$	2.85844	+	8.79738i	0.139811	+	0.430294i
$419$	−0.0740467	−	0.227892i	−0.00361742	−	0.0111333i	0.949232	−	0.314578i	$-0.101863\pi$
$419$	−0.0740467	−	0.227892i	−0.00361742	−	0.0111333i	−0.952849	+	0.303445i	$0.901863\pi$
$420$	−8.77780	+	6.37744i	−0.428313	+	0.311187i
$421$	2.54412	+	7.83000i	0.123993	+	0.381611i	0.993716	−	0.111929i	$-0.0357029\pi$
$421$	2.54412	+	7.83000i	0.123993	+	0.381611i	−0.869723	+	0.493539i	$0.835703\pi$
$422$	4.27761	−	13.1651i	0.208231	−	0.640868i
$423$	−12.0109	−	8.72644i	−0.583990	−	0.424294i
$424$	2.30928	−	7.10723i	0.112148	−	0.345157i
$425$	−6.06393	+	4.40570i	−0.294144	+	0.213708i
$426$	−26.9275	+	19.5640i	−1.30464	+	0.947879i
$427$	3.65488	+	2.65543i	0.176872	+	0.128505i
$428$	−4.14272			−0.200246
$429$	48.0070			2.31780
$430$	−50.1842	−	36.4609i	−2.42010	−	1.75830i
$431$	10.6232	+	32.6947i	0.511699	+	1.57485i	0.789209	+	0.614125i	$0.210491\pi$
$431$	10.6232	+	32.6947i	0.511699	+	1.57485i	−0.277509	+	0.960723i	$0.589509\pi$
$432$	1.23855	−	3.81187i	0.0595899	−	0.183399i
$433$	28.4726			1.36831			0.684153	−	0.729338i	$-0.260172\pi$
$433$	28.4726			1.36831			0.684153	+	0.729338i	$0.260172\pi$
$434$	6.10449	−	0.251328i	0.293025	−	0.0120641i
$435$	−67.6222			−3.24224
$436$	11.3296	−	34.8688i	0.542588	−	1.66991i
$437$	−1.55543	−	4.78713i	−0.0744064	−	0.228999i
$438$	27.8022	+	20.1995i	1.32844	+	0.965168i
$439$	19.1218			0.912635			0.456317	−	0.889817i	$-0.349168\pi$
$439$	19.1218			0.912635			0.456317	+	0.889817i	$0.349168\pi$
$440$	17.8237			0.849711
$441$	12.3438	+	8.96831i	0.587801	+	0.427063i
$442$	−9.62819	+	6.99529i	−0.457966	+	0.332732i
$443$	−12.2502	+	8.90032i	−0.582027	+	0.422867i	−0.839454	−	0.543430i	$-0.817125\pi$
$443$	−12.2502	+	8.90032i	−0.582027	+	0.422867i	0.257427	+	0.966298i	$0.417125\pi$
$444$	−7.29301	+	22.4456i	−0.346111	+	1.06522i
$445$	−39.7736	−	28.8972i	−1.88545	−	1.36986i
$446$	−13.7943	+	42.4545i	−0.653179	+	2.01028i
$447$	−3.75806	−	11.5661i	−0.177750	−	0.547059i
$448$	4.93764	−	3.58741i	0.233282	−	0.169489i
$449$	−5.74482	−	17.6807i	−0.271115	−	0.834406i	−0.990221	−	0.139506i	$-0.955449\pi$
$449$	−5.74482	−	17.6807i	−0.271115	−	0.834406i	0.719106	−	0.694900i	$-0.244551\pi$
$450$	11.2720	+	34.6917i	0.531368	+	1.63538i
$451$	−13.2775	+	9.64668i	−0.625214	+	0.454244i
$452$	−13.2767	−	40.8614i	−0.624483	−	1.92196i
$453$	−14.3947	+	44.3024i	−0.676323	+	2.08151i
$454$	−26.3147	−	19.1187i	−1.23501	−	0.897287i
$455$	3.08729	−	9.50169i	0.144734	−	0.445446i
$456$	−2.81971	+	2.04864i	−0.132045	+	0.0959363i
$457$	11.7042	−	8.50357i	0.547497	−	0.397780i	−0.279365	−	0.960185i	$-0.590124\pi$
$457$	11.7042	−	8.50357i	0.547497	−	0.397780i	0.826862	+	0.562405i	$0.190124\pi$
$458$	11.7302	+	8.52249i	0.548117	+	0.398230i
$459$	−1.68870			−0.0788217
$460$	−40.9519			−1.90939
$461$	7.93250	+	5.76330i	0.369453	+	0.268424i	0.756984	−	0.653433i	$-0.226672\pi$
$461$	7.93250	+	5.76330i	0.369453	+	0.268424i	−0.387531	+	0.921857i	$0.626672\pi$
$462$	2.94028	+	9.04926i	0.136794	+	0.421010i
$463$	−6.97314	+	21.4611i	−0.324069	+	0.997383i	0.647790	+	0.761819i	$0.275694\pi$
$463$	−6.97314	+	21.4611i	−0.324069	+	0.997383i	−0.971859	+	0.235564i	$0.924306\pi$
$464$	19.7896			0.918709
$465$	12.1755	−	43.4833i	0.564624	−	2.01649i
$466$	49.4121			2.28897
$467$	−8.36211	+	25.7359i	−0.386952	+	1.19092i	0.548101	+	0.836412i	$0.315351\pi$
$467$	−8.36211	+	25.7359i	−0.386952	+	1.19092i	−0.935054	+	0.354505i	$0.884649\pi$
$468$	10.1508	+	31.2409i	0.469220	+	1.44411i
$469$	1.07110	+	0.778198i	0.0494587	+	0.0359339i
$470$	49.8282			2.29840
$471$	38.7746			1.78664
$472$	8.21203	+	5.96639i	0.377990	+	0.274625i
$473$	−24.9605	+	18.1348i	−1.14768	+	0.833840i
$474$	22.2099	−	16.1364i	1.02013	−	0.741171i
$475$	2.63730	−	8.11678i	0.121008	−	0.372424i
$476$	−1.08231	−	0.786347i	−0.0496078	−	0.0360422i
$477$	3.91866	−	12.0604i	0.179423	−	0.552208i
$478$	−20.1437	−	61.9958i	−0.921350	−	2.83562i
$479$	8.09036	−	5.87799i	0.369658	−	0.268572i	−0.387411	−	0.921907i	$-0.626631\pi$
$479$	8.09036	−	5.87799i	0.369658	−	0.268572i	0.757069	+	0.653335i	$0.226631\pi$
$480$	−19.4737	−	59.9338i	−0.888848	−	2.73559i
$481$	−6.71543	−	20.6680i	−0.306197	−	0.942378i
$482$	25.3493	−	18.4173i	1.15463	−	0.838886i
$483$	−1.59997	−	4.92419i	−0.0728010	−	0.224058i
$484$	2.65887	−	8.18318i	0.120858	−	0.371963i
$485$	2.12152	+	1.54137i	0.0963331	+	0.0699901i
$486$	−12.8906	+	39.6731i	−0.584728	+	1.79961i
$487$	5.15552	−	3.74571i	0.233619	−	0.169734i	−0.464817	−	0.885407i	$-0.653880\pi$
$487$	5.15552	−	3.74571i	0.233619	−	0.169734i	0.698436	+	0.715673i	$0.253880\pi$
$488$	9.55207	−	6.93998i	0.432402	−	0.314158i
$489$	−17.5518	−	12.7521i	−0.793718	−	0.576670i
$490$	−51.2093			−2.31340
$491$	−32.2972			−1.45755			−0.728775	−	0.684753i	$-0.759910\pi$
$491$	−32.2972			−1.45755			−0.728775	+	0.684753i	$0.759910\pi$
$492$	−21.1238	−	15.3473i	−0.952333	−	0.691910i
$493$	−2.57655	−	7.92982i	−0.116042	−	0.357141i
$494$	4.18746	−	12.8877i	0.188403	−	0.579844i
$495$	30.2454			1.35943
$496$	−3.56314	+	12.7254i	−0.159990	+	0.571386i
$497$	3.44520			0.154538
$498$	−25.0005	+	76.9437i	−1.12030	+	3.44793i
$499$	−2.52832	−	7.78136i	−0.113183	−	0.348341i	0.878381	−	0.477962i	$-0.158624\pi$
$499$	−2.52832	−	7.78136i	−0.113183	−	0.348341i	−0.991564	+	0.129620i	$0.958624\pi$
$500$	−18.7021	−	13.5878i	−0.836381	−	0.607666i
$501$	−4.89603			−0.218738
$502$	−22.7418			−1.01502
$503$	−12.6322	−	9.17780i	−0.563240	−	0.409218i	0.269403	−	0.963027i	$-0.413174\pi$
$503$	−12.6322	−	9.17780i	−0.563240	−	0.409218i	−0.832643	+	0.553809i	$0.813174\pi$
$504$	−1.24745	+	0.906322i	−0.0555656	+	0.0403708i
$505$	11.8531	−	8.61180i	0.527457	−	0.383220i
$506$	−11.0978	+	34.1554i	−0.493356	+	1.51839i
$507$	−32.7662	−	23.8061i	−1.45520	−	1.05726i
$508$	−11.7448	+	36.1469i	−0.521093	+	1.60376i
$509$	−5.71761	−	17.5970i	−0.253429	−	0.779973i	−0.994135	−	0.108144i	$-0.965509\pi$
$509$	−5.71761	−	17.5970i	−0.253429	−	0.779973i	0.740707	−	0.671829i	$-0.234491\pi$
$510$	−14.1040	+	10.2472i	−0.624535	+	0.453751i
$511$	−1.09921	−	3.38301i	−0.0486260	−	0.149655i
$512$	7.65601	+	23.5628i	0.338351	+	1.04134i
$513$	1.55558	−	1.13019i	0.0686804	−	0.0498992i
$514$	−7.39821	−	22.7694i	−0.326321	−	1.00431i
$515$	6.16377	−	18.9701i	0.271608	−	0.835924i
$516$	−39.7106	−	28.8515i	−1.74816	−	1.27012i
$517$	7.65850	−	23.5704i	0.336820	−	1.03663i
$518$	3.48458	−	2.53170i	0.153104	−	0.111236i
$519$	−1.02610	+	0.745502i	−0.0450406	+	0.0327239i
$520$	−21.1240	−	15.3475i	−0.926350	−	0.673032i
$521$	27.1766			1.19063			0.595314	−	0.803493i	$-0.297028\pi$
$521$	27.1766			1.19063			0.595314	+	0.803493i	$0.297028\pi$
$522$	−40.5770			−1.77601
$523$	−6.02496	−	4.37739i	−0.263453	−	0.191410i	0.448215	−	0.893926i	$-0.352060\pi$
$523$	−6.02496	−	4.37739i	−0.263453	−	0.191410i	−0.711668	+	0.702516i	$0.752060\pi$
$524$	16.4113	+	50.5089i	0.716932	+	2.20649i
$525$	2.71281	−	8.34918i	0.118397	−	0.364388i
$526$	21.4900			0.937008
$527$	5.56305	−	0.229036i	0.242330	−	0.00997698i
$528$	−20.5802			−0.895639
$529$	−1.06850	+	3.28850i	−0.0464565	+	0.142978i
$530$	13.1521	+	40.4780i	0.571291	+	1.75825i
$531$	13.9352	+	10.1245i	0.604735	+	0.439366i
$532$	1.52327			0.0660422
$533$	24.0425			1.04140
$534$	−55.4917	−	40.3171i	−2.40136	−	1.74469i
$535$	4.52072	−	3.28450i	0.195448	−	0.142001i
$536$	2.79933	−	2.03383i	0.120912	−	0.0878481i
$537$	7.40396	−	22.7870i	0.319504	−	0.983333i
$538$	−3.62806	−	2.63594i	−0.156417	−	0.113643i
$539$	−7.87077	+	24.2237i	−0.339018	+	1.04339i
$540$	−4.83417	−	14.8780i	−0.208029	−	0.640248i
$541$	−16.9635	+	12.3247i	−0.729318	+	0.529881i	−0.889348	−	0.457231i	$-0.848841\pi$
$541$	−16.9635	+	12.3247i	−0.729318	+	0.529881i	0.160029	+	0.987112i	$0.448841\pi$
$542$	−11.5823	−	35.6466i	−0.497502	−	1.53115i
$543$	−4.31604	−	13.2834i	−0.185219	−	0.570045i
$544$	6.28624	−	4.56722i	0.269521	−	0.195818i
$545$	15.2819	+	47.0329i	0.654605	+	2.01467i
$546$	4.30735	−	13.2567i	0.184338	−	0.567333i
$547$	−29.4738	−	21.4139i	−1.26021	−	0.915594i	−0.261439	−	0.965220i	$-0.584197\pi$
$547$	−29.4738	−	21.4139i	−1.26021	−	0.915594i	−0.998768	+	0.0496263i	$0.984197\pi$
$548$	3.14859	−	9.69037i	0.134501	−	0.413952i
$549$	16.2091	−	11.7766i	0.691788	−	0.502613i
$550$	−49.2629	+	35.7916i	−2.10058	+	1.52616i
$551$	7.68061	+	5.58029i	0.327205	+	0.237728i
$552$	−13.5317			−0.575948
$553$	−2.84161			−0.120838
$554$	−23.7235	−	17.2361i	−1.00791	−	0.732292i
$555$	−9.83719	−	30.2758i	−0.417566	−	1.28513i
$556$	−1.92759	+	5.93252i	−0.0817482	+	0.251595i
$557$	−31.5902			−1.33852			−0.669260	−	0.743028i	$-0.733389\pi$
$557$	−31.5902			−1.33852			−0.669260	+	0.743028i	$0.733389\pi$
$558$	7.30594	−	26.0924i	0.309285	−	1.10458i
$559$	45.1977			1.91166
$560$	−1.32349	+	4.07330i	−0.0559278	+	0.172128i
$561$	2.67949	+	8.24663i	0.113128	+	0.348173i
$562$	−17.6957	−	12.8566i	−0.746446	−	0.542325i
$563$	21.5339			0.907545			0.453773	−	0.891117i	$-0.350078\pi$
$563$	21.5339			0.907545			0.453773	+	0.891117i	$0.350078\pi$
$564$	39.4290			1.66026
$565$	46.8845	+	34.0636i	1.97245	+	1.43307i
$566$	5.86956	−	4.26448i	0.246716	−	0.179250i
$567$	4.40512	−	3.20051i	0.184998	−	0.134409i
$568$	2.78241	−	8.56338i	0.116747	−	0.359311i
$569$	6.83632	+	4.96688i	0.286594	+	0.208222i	0.721788	−	0.692114i	$-0.243320\pi$
$569$	6.83632	+	4.96688i	0.286594	+	0.208222i	−0.435195	+	0.900336i	$0.643320\pi$
$570$	6.13406	−	18.8787i	0.256928	−	0.790742i
$571$	12.9967	+	39.9997i	0.543894	+	1.67393i	0.723605	+	0.690214i	$0.242484\pi$
$571$	12.9967	+	39.9997i	0.543894	+	1.67393i	−0.179711	+	0.983719i	$0.557516\pi$
$572$	−44.3626	+	32.2313i	−1.85489	+	1.34766i
$573$	5.73453	+	17.6491i	0.239564	+	0.737301i
$574$	1.47253	+	4.53199i	0.0614623	+	0.189161i
$575$	26.8066	−	19.4761i	1.11791	−	0.812210i
$576$	−8.36432	−	25.7427i	−0.348513	−	1.07261i
$577$	11.9015	−	36.6291i	0.495467	−	1.52489i	−0.320762	−	0.947160i	$-0.603939\pi$
$577$	11.9015	−	36.6291i	0.495467	−	1.52489i	0.816228	−	0.577730i	$-0.196061\pi$
$578$	−1.73904	−	1.26349i	−0.0723346	−	0.0525541i
$579$	−12.1564	+	37.4134i	−0.505201	+	1.55485i
$580$	62.4887	−	45.4007i	2.59470	−	1.88516i
$581$	6.77485	−	4.92222i	0.281068	−	0.204208i
$582$	2.95992	+	2.15051i	0.122693	+	0.0891414i
$583$	21.1689			0.876727
$584$	−9.29653			−0.384693
$585$	−35.8458	−	26.0435i	−1.48204	−	1.07677i
$586$	13.5176	+	41.6029i	0.558407	+	1.71860i
$587$	−8.19158	+	25.2111i	−0.338103	+	1.04057i	0.627071	+	0.778962i	$0.284254\pi$
$587$	−8.19158	+	25.2111i	−0.338103	+	1.04057i	−0.965173	+	0.261611i	$0.915746\pi$
$588$	−40.5219			−1.67109
$589$	−4.97122	+	3.93415i	−0.204836	+	0.162104i
$590$	−57.8112			−2.38005
$591$	−5.48509	+	16.8814i	−0.225626	+	0.694407i
$592$	2.87885	+	8.86018i	0.118320	+	0.364151i
$593$	14.1258	+	10.2630i	0.580076	+	0.421450i	0.838751	−	0.544515i	$-0.183286\pi$
$593$	14.1258	+	10.2630i	0.580076	+	0.421450i	−0.258676	+	0.965964i	$0.583286\pi$
$594$	−13.7189			−0.562892
$595$	1.80451			0.0739778
$596$	11.2381	+	8.16498i	0.460332	+	0.334450i
$597$	−39.8302	+	28.9383i	−1.63014	+	1.18437i
$598$	42.5630	−	30.9238i	1.74053	−	1.26457i
$599$	−6.14789	+	18.9213i	−0.251196	+	0.773102i	0.743359	+	0.668892i	$0.233231\pi$
$599$	−6.14789	+	18.9213i	−0.251196	+	0.773102i	−0.994555	+	0.104210i	$0.966769\pi$
$600$	−18.5618	−	13.4859i	−0.757781	−	0.550560i
$601$	7.47417	−	23.0031i	0.304878	−	0.938317i	−0.674845	−	0.737959i	$-0.735790\pi$
$601$	7.47417	−	23.0031i	0.304878	−	0.938317i	0.979723	−	0.200358i	$-0.0642105\pi$
$602$	2.76822	+	8.51970i	0.112824	+	0.347237i
$603$	4.75024	−	3.45125i	0.193445	−	0.140546i
$604$	−16.4421	−	50.6037i	−0.669021	−	2.05903i
$605$	3.58643	+	11.0379i	0.145809	+	0.448754i
$606$	16.5374	−	12.0151i	0.671784	−	0.488080i
$607$	6.40116	+	19.7007i	0.259815	+	0.799629i	0.992843	+	0.119430i	$0.0381066\pi$
$607$	6.40116	+	19.7007i	0.259815	+	0.799629i	−0.733028	+	0.680199i	$0.761893\pi$
$608$	−2.73399	+	8.41436i	−0.110878	+	0.341247i
$609$	7.90052	+	5.74006i	0.320145	+	0.232599i
$610$	−20.7798	+	63.9536i	−0.841349	+	2.58941i
$611$	−29.3724	+	21.3403i	−1.18828	+	0.863337i
$612$	−4.79998	+	3.48739i	−0.194028	+	0.140969i
$613$	−33.8855	−	24.6193i	−1.36862	−	0.994364i	−0.997843	−	0.0656431i	$-0.979090\pi$
$613$	−33.8855	−	24.6193i	−1.36862	−	0.994364i	−0.370781	−	0.928720i	$-0.620910\pi$
$614$	−31.0785			−1.25423
$615$	35.2191			1.42017
$616$	−2.08240	−	1.51295i	−0.0839023	−	0.0609586i
$617$	−11.0490	−	34.0052i	−0.444814	−	1.36900i	−0.882687	−	0.469960i	$-0.844268\pi$
$617$	−11.0490	−	34.0052i	−0.444814	−	1.36900i	0.437873	−	0.899037i	$-0.355732\pi$
$618$	8.59963	−	26.4669i	0.345928	−	1.06466i
$619$	−3.77142			−0.151586			−0.0757931	−	0.997124i	$-0.524149\pi$
$619$	−3.77142			−0.151586			−0.0757931	+	0.997124i	$0.524149\pi$
$620$	17.9430	+	48.3568i	0.720608	+	1.94206i
$621$	7.46517			0.299567
$622$	−8.17354	+	25.1556i	−0.327729	+	1.00865i
$623$	2.19396	+	6.75231i	0.0878991	+	0.270526i
$624$	24.3910	+	17.7211i	0.976420	+	0.709410i
$625$	−6.29572			−0.251829
$626$	−3.83291			−0.153194
$627$	−7.98747	−	5.80324i	−0.318989	−	0.231759i
$628$	−35.8311	+	26.0328i	−1.42981	+	1.03882i
$629$	3.17552	−	2.30715i	0.126616	−	0.0919920i
$630$	2.71372	−	8.35197i	0.108117	−	0.332751i
$631$	−39.6324	−	28.7946i	−1.57774	−	1.14630i	−0.919226	−	0.393731i	$-0.871184\pi$
$631$	−39.6324	−	28.7946i	−1.57774	−	1.14630i	−0.658516	−	0.752566i	$-0.728816\pi$
$632$	−2.29494	+	7.06310i	−0.0912878	+	0.280955i
$633$	4.56568	+	14.0517i	0.181470	+	0.558506i
$634$	−43.1019	+	31.3154i	−1.71180	+	1.24369i
$635$	−15.8420	−	48.7568i	−0.628672	−	1.93485i
$636$	10.4072	+	32.0302i	0.412674	+	1.27008i
$637$	30.1866	−	21.9318i	1.19604	−	0.868971i
$638$	−20.9317	−	64.4212i	−0.828695	−	2.55046i
$639$	4.72154	−	14.5314i	0.186781	−	0.574853i
$640$	29.0535	+	21.1086i	1.14844	+	0.834392i
$641$	−14.4404	+	44.4430i	−0.570361	+	1.75539i	0.0810962	+	0.996706i	$0.474158\pi$
$641$	−14.4404	+	44.4430i	−0.570361	+	1.75539i	−0.651457	+	0.758685i	$0.725842\pi$
$642$	6.30726	−	4.58250i	0.248928	−	0.180857i
$643$	−1.32534	+	0.962915i	−0.0522663	+	0.0379737i	−0.613612	−	0.789608i	$-0.710284\pi$
$643$	−1.32534	+	0.962915i	−0.0522663	+	0.0379737i	0.561345	+	0.827582i	$0.310284\pi$
$644$	4.78455	+	3.47618i	0.188538	+	0.136981i
$645$	66.2085			2.60696
$646$	2.44756			0.0962980
$647$	−10.0248	−	7.28345i	−0.394116	−	0.286342i	0.373024	−	0.927822i	$-0.378321\pi$
$647$	−10.0248	−	7.28345i	−0.394116	−	0.286342i	−0.767140	+	0.641480i	$0.778321\pi$
$648$	−4.39751	−	13.5341i	−0.172751	−	0.531671i
$649$	−8.88547	+	27.3467i	−0.348785	+	1.07345i
$650$	89.2038			3.49886
$651$	−5.11355	+	4.04679i	−0.200416	+	0.158606i
$652$	24.7809			0.970497
$653$	0.972849	−	2.99412i	0.0380705	−	0.117169i	−0.930215	−	0.367015i	$-0.880380\pi$
$653$	0.972849	−	2.99412i	0.0380705	−	0.117169i	0.968286	+	0.249846i	$0.0803799\pi$
$654$	21.3212	+	65.6198i	0.833724	+	2.56594i
$655$	−57.9540	−	42.1060i	−2.26445	−	1.64522i
$656$	−10.3068			−0.402414
$657$	−15.7755			−0.615461
$658$	−5.82159	−	4.22963i	−0.226949	−	0.164888i
$659$	−7.28948	+	5.29611i	−0.283958	+	0.206307i	−0.720642	−	0.693308i	$-0.756153\pi$
$659$	−7.28948	+	5.29611i	−0.283958	+	0.206307i	0.436684	+	0.899615i	$0.356153\pi$
$660$	−64.9852	+	47.2145i	−2.52955	+	1.83782i
$661$	5.29679	−	16.3018i	0.206021	−	0.634068i	−0.793649	−	0.608376i	$-0.791821\pi$
$661$	5.29679	−	16.3018i	0.206021	−	0.634068i	0.999670	−	0.0256919i	$-0.00817889\pi$
$662$	−60.2091	−	43.7445i	−2.34009	−	1.70018i
$663$	3.92531	−	12.0809i	0.152446	−	0.469182i
$664$	−6.76315	−	20.8148i	−0.262461	−	0.807772i
$665$	−1.66226	+	1.20770i	−0.0644597	+	0.0468327i
$666$	−5.90285	−	18.1671i	−0.228731	−	0.703961i
$667$	11.3901	+	35.0551i	0.441026	+	1.35734i
$668$	4.52435	−	3.28713i	0.175052	−	0.127183i
$669$	−14.7233	−	45.3135i	−0.569234	−	1.75192i
$670$	−6.08972	+	18.7422i	−0.235266	+	0.724076i
$671$	27.0584	+	19.6591i	1.04458	+	0.758930i
$672$	−2.81227	+	8.65528i	−0.108486	+	0.333885i
$673$	−22.6973	+	16.4906i	−0.874918	+	0.635665i	−0.931902	−	0.362710i	$-0.881852\pi$
$673$	−22.6973	+	16.4906i	−0.874918	+	0.635665i	0.0569841	+	0.998375i	$0.481852\pi$
$674$	62.8904	−	45.6926i	2.42245	−	1.76001i
$675$	10.2401	+	7.43990i	0.394143	+	0.286362i
$676$	46.2619			1.77930
$677$	26.2537			1.00901			0.504507	−	0.863408i	$-0.331674\pi$
$677$	26.2537			1.00901			0.504507	+	0.863408i	$0.331674\pi$
$678$	65.4128	+	47.5252i	2.51216	+	1.82519i
$679$	−0.117025	−	0.360167i	−0.00449102	−	0.0138219i
$680$	1.45736	−	4.48529i	0.0558872	−	0.172003i
$681$	34.7172			1.33037
$682$	45.1938	−	1.86067i	1.73056	−	0.0712489i
$683$	−44.2792			−1.69430			−0.847148	−	0.531357i	$-0.821682\pi$
$683$	−44.2792			−1.69430			−0.847148	+	0.531357i	$0.821682\pi$
$684$	2.08759	−	6.42495i	0.0798211	−	0.245664i
$685$	4.24698	+	13.0709i	0.162269	+	0.499412i
$686$	12.1973	+	8.86182i	0.465693	+	0.338346i
$687$	−15.4758			−0.590438
$688$	−19.3759			−0.738698
$689$	−25.0887	−	18.2280i	−0.955802	−	0.694431i
$690$	62.3490	−	45.2992i	2.37359	−	1.72451i
$691$	−5.53301	+	4.01997i	−0.210486	+	0.152927i	−0.688033	−	0.725679i	$-0.741526\pi$
$691$	−5.53301	+	4.01997i	−0.210486	+	0.152927i	0.477548	+	0.878606i	$0.341526\pi$
$692$	0.447680	−	1.37782i	0.0170182	−	0.0523767i
$693$	−3.53367	−	2.56736i	−0.134233	−	0.0975261i
$694$	1.81871	−	5.59741i	0.0690373	−	0.212475i
$695$	−2.60004	−	8.00209i	−0.0986250	−	0.303537i
$696$	20.6481	−	15.0017i	0.782664	−	0.568639i
$697$	1.34192	+	4.13002i	0.0508290	+	0.156436i
$698$	−13.3739	−	41.1607i	−0.506210	−	1.55795i
$699$	−42.6674	+	30.9996i	−1.61383	+	1.17251i
$700$	3.09866	+	9.53671i	0.117118	+	0.360454i
$701$	−12.6835	+	39.0357i	−0.479049	+	1.47436i	0.361370	+	0.932422i	$0.382309\pi$
$701$	−12.6835	+	39.0357i	−0.479049	+	1.47436i	−0.840419	+	0.541937i	$0.817691\pi$
$702$	16.2591	+	11.8129i	0.613661	+	0.445850i
$703$	−1.38108	+	4.25054i	−0.0520886	+	0.160312i
$704$	36.5552	−	26.5589i	1.37772	−	1.00098i
$705$	−43.0266	+	31.2607i	−1.62048	+	1.17735i
$706$	−63.0349	−	45.7975i	−2.37235	−	1.72361i
$707$	−2.11585			−0.0795746
$708$	−45.7459			−1.71924
$709$	17.0317	+	12.3743i	0.639640	+	0.464726i	0.859727	−	0.510754i	$-0.170634\pi$
$709$	17.0317	+	12.3743i	0.639640	+	0.464726i	−0.220086	+	0.975480i	$0.570634\pi$
$710$	15.8468	+	48.7713i	0.594718	+	1.83035i
$711$	−3.89433	+	11.9855i	−0.146049	+	0.449492i
$712$	18.5554			0.695393
$713$	−24.5924	+	1.01249i	−0.920992	+	0.0379181i
$714$	2.51764			0.0942202
$715$	22.8563	−	70.3445i	0.854778	−	2.63073i
$716$	8.45704	+	26.0281i	0.316055	+	0.972716i
$717$	56.2883	+	40.8959i	2.10213	+	1.52728i
$718$	21.8447			0.815238
$719$	38.8755			1.44981			0.724907	−	0.688847i	$-0.241883\pi$
$719$	38.8755			1.44981			0.724907	+	0.688847i	$0.241883\pi$
$720$	15.3668	+	11.1646i	0.572687	+	0.416082i
$721$	−2.33040	+	1.69313i	−0.0867886	+	0.0630556i
$722$	30.7872	−	22.3682i	1.14578	−	0.832458i
$723$	−10.3346	+	31.8067i	−0.384349	+	1.18290i
$724$	12.9067	+	9.37726i	0.479674	+	0.348503i
$725$	−19.3124	+	59.4374i	−0.717244	+	2.20745i
$726$	5.00375	+	15.4000i	0.185707	+	0.571546i
$727$	−11.0019	+	7.99335i	−0.408038	+	0.296457i	−0.772807	−	0.634641i	$-0.781148\pi$
$727$	−11.0019	+	7.99335i	−0.408038	+	0.296457i	0.364769	+	0.931098i	$0.381148\pi$
$728$	1.16523	+	3.58620i	0.0431861	+	0.132913i
$729$	−3.87043	−	11.9120i	−0.143349	−	0.441184i
$730$	42.8349	−	31.1214i	1.58539	−	1.15185i
$731$	2.52269	+	7.76404i	0.0933050	+	0.287163i
$732$	−16.4430	+	50.6064i	−0.607751	+	1.87047i
$733$	10.6107	+	7.70910i	0.391914	+	0.284742i	0.766239	−	0.642555i	$-0.222126\pi$
$733$	10.6107	+	7.70910i	0.391914	+	0.284742i	−0.374325	+	0.927297i	$0.622126\pi$
$734$	3.13292	−	9.64213i	0.115638	−	0.355897i
$735$	44.2192	−	32.1272i	1.63105	−	1.18503i
$736$	−27.7894	+	20.1902i	−1.02433	+	0.744219i
$737$	7.92973	+	5.76129i	0.292095	+	0.212220i
$738$	21.1334			0.777930
$739$	−45.9423			−1.69002			−0.845008	−	0.534754i	$-0.820404\pi$
$739$	−45.9423			−1.69002			−0.845008	+	0.534754i	$0.820404\pi$
$740$	29.4172	+	21.3728i	1.08140	+	0.785681i
$741$	4.46946	+	13.7556i	0.164190	+	0.505324i
$742$	1.89935	−	5.84559i	0.0697272	−	0.214598i
$743$	35.5066			1.30261			0.651306	−	0.758815i	$-0.274222\pi$
$743$	35.5066			1.30261			0.651306	+	0.758815i	$0.274222\pi$
$744$	5.92889	+	15.9785i	0.217364	+	0.585800i
$745$	−18.7370			−0.686471
$746$	13.3205	−	40.9962i	0.487697	−	1.50098i
$747$	−11.4765	−	35.3211i	−0.419905	−	1.29233i
$748$	−8.01277	−	5.82162i	−0.292976	−	0.212859i
$749$	−0.806973			−0.0294861
$750$	43.5040			1.58854
$751$	6.39655	+	4.64737i	0.233414	+	0.169585i	0.698344	−	0.715762i	$-0.253921\pi$
$751$	6.39655	+	4.64737i	0.233414	+	0.169585i	−0.464930	+	0.885347i	$0.653921\pi$
$752$	12.5917	−	9.14842i	0.459173	−	0.333609i
$753$	19.6375	−	14.2675i	0.715631	−	0.519937i
$754$	−30.6638	+	94.3735i	−1.11671	+	3.43688i
$755$	58.0627	+	42.1851i	2.11312	+	1.53527i
$756$	−0.698120	+	2.14859i	−0.0253904	+	0.0781436i
$757$	4.21336	+	12.9674i	0.153137	+	0.471308i	0.997967	−	0.0637268i	$-0.0202986\pi$
$757$	4.21336	+	12.9674i	0.153137	+	0.471308i	−0.844830	+	0.535034i	$0.820299\pi$
$758$	42.9329	−	31.1926i	1.55939	−	1.13297i
$759$	−11.8451	−	36.4556i	−0.429951	−	1.32325i
$760$	1.65939	+	5.10707i	0.0601923	+	0.185253i
$761$	−31.4313	+	22.8361i	−1.13938	+	0.827810i	−0.987033	−	0.160517i	$-0.948684\pi$
$761$	−31.4313	+	22.8361i	−1.13938	+	0.827810i	−0.152349	+	0.988327i	$0.548684\pi$
$762$	−22.1027	−	68.0250i	−0.800695	−	2.46429i
$763$	2.20692	−	6.79220i	0.0798959	−	0.245894i
$764$	−17.1486	−	12.4592i	−0.620414	−	0.450757i
$765$	2.47303	−	7.61119i	0.0894124	−	0.275183i
$766$	26.8731	−	19.5245i	0.970965	−	0.705447i
$767$	34.0782	−	24.7593i	1.23049	−	0.894005i
$768$	−3.84833	−	2.79597i	−0.138865	−	0.100891i
$769$	−1.45217			−0.0523665			−0.0261832	−	0.999657i	$-0.508335\pi$
$769$	−1.45217			−0.0523665			−0.0261832	+	0.999657i	$0.508335\pi$
$770$	14.6597			0.528300
$771$	20.6731	+	15.0199i	0.744525	+	0.540929i
$772$	−13.8854	−	42.7349i	−0.499746	−	1.53806i
$773$	13.8601	−	42.6571i	0.498514	−	1.53427i	−0.312894	−	0.949788i	$-0.601299\pi$
$773$	13.8601	−	42.6571i	0.498514	−	1.53427i	0.811408	−	0.584480i	$-0.198701\pi$
$774$	39.7287			1.42802
$775$	−34.7430	−	23.1203i	−1.24801	−	0.830505i
$776$	−0.989742			−0.0355297
$777$	−1.42063	+	4.37224i	−0.0509647	+	0.156853i
$778$	7.17587	+	22.0851i	0.257267	+	0.791788i
$779$	−4.00023	−	2.90633i	−0.143323	−	0.104130i
$780$	117.673			4.21338
$781$	25.5061			0.912679
$782$	7.68771	+	5.58545i	0.274912	+	0.199735i
$783$	−11.3911	+	8.27614i	−0.407086	+	0.295765i
$784$	−12.9407	+	9.40199i	−0.462169	+	0.335785i
$785$	18.4607	−	56.8162i	0.658891	−	2.02786i
$786$	−80.8568	−	58.7459i	−2.88407	−	2.09540i
$787$	−11.8775	+	36.5552i	−0.423388	+	1.30305i	0.481142	+	0.876643i	$0.340222\pi$
$787$	−11.8775	+	36.5552i	−0.423388	+	1.30305i	−0.904530	+	0.426411i	$0.859778\pi$
$788$	−6.26525	−	19.2825i	−0.223190	−	0.686909i
$789$	−18.5566	+	13.4822i	−0.660633	+	0.479978i
$790$	−13.0704	−	40.2267i	−0.465025	−	1.43120i
$791$	−2.58620	−	7.95952i	−0.0919548	−	0.283008i
$792$	−9.23529	+	6.70983i	−0.328162	+	0.238423i
$793$	−15.1408	−	46.5985i	−0.537665	−	1.65476i
$794$	−0.554744	+	1.70733i	−0.0196871	+	0.0605908i
$795$	−36.7515	−	26.7015i	−1.30344	−	0.947005i
$796$	17.3777	−	53.4830i	0.615935	−	1.89565i
$797$	27.9219	−	20.2864i	0.989043	−	0.718582i	0.0293320	−	0.999570i	$-0.490662\pi$
$797$	27.9219	−	20.2864i	0.989043	−	0.718582i	0.959711	+	0.280988i	$0.0906620\pi$
$798$	−2.31917	+	1.68497i	−0.0820977	+	0.0596474i
$799$	−5.30524	−	3.85448i	−0.187686	−	0.136362i
$800$	−58.2412			−2.05914
$801$	31.4871			1.11254
$802$	−34.7153	−	25.2222i	−1.22584	−	0.890625i
$803$	−8.13782	−	25.0456i	−0.287178	−	0.883842i
$804$	−4.81879	+	14.8307i	−0.169945	+	0.523038i
$805$	−7.97714			−0.281157
$806$	−55.1643	−	36.7099i	−1.94308	−	1.29305i
$807$	4.78653			0.168494
$808$	−1.70880	+	5.25914i	−0.0601153	+	0.185016i
$809$	−9.17952	−	28.2517i	−0.322735	−	0.993276i	−0.972453	−	0.233100i	$-0.925113\pi$
$809$	−9.17952	−	28.2517i	−0.322735	−	0.993276i	0.649718	−	0.760175i	$-0.274887\pi$
$810$	65.5694	+	47.6390i	2.30387	+	1.67386i
$811$	9.98228			0.350525			0.175263	−	0.984522i	$-0.443923\pi$
$811$	9.98228			0.350525			0.175263	+	0.984522i	$0.443923\pi$
$812$	−11.1546			−0.391449
$813$	32.3649	+	23.5145i	1.13509	+	0.824689i
$814$	25.7976	−	18.7431i	0.904207	−	0.656945i
$815$	−27.0421	+	19.6472i	−0.947242	+	0.688211i
$816$	−1.68275	+	5.17896i	−0.0589079	+	0.181300i
$817$	−7.52004	−	5.46363i	−0.263093	−	0.191148i
$818$	17.1692	−	52.8415i	0.600309	−	1.84756i
$819$	1.97730	+	6.08550i	0.0690924	+	0.212644i
$820$	−32.5454	+	23.6456i	−1.13654	+	0.825742i
$821$	17.0461	+	52.4626i	0.594914	+	1.83096i	0.555152	+	0.831749i	$0.312660\pi$
$821$	17.0461	+	52.4626i	0.594914	+	1.83096i	0.0397628	+	0.999209i	$0.487340\pi$
$822$	5.92535	+	18.2363i	0.206670	+	0.636066i
$823$	−12.8394	+	9.32836i	−0.447553	+	0.325166i	−0.788629	−	0.614870i	$-0.789209\pi$
$823$	−12.8394	+	9.32836i	−0.447553	+	0.325166i	0.341076	+	0.940036i	$0.389209\pi$
$824$	2.32637	+	7.15984i	0.0810431	+	0.249425i
$825$	20.0839	−	61.8120i	0.699233	−	2.15202i
$826$	6.75427	+	4.90727i	0.235011	+	0.170746i
$827$	1.26967	−	3.90764i	0.0441507	−	0.135882i	−0.926551	−	0.376168i	$-0.877241\pi$
$827$	1.26967	−	3.90764i	0.0441507	−	0.135882i	0.970702	+	0.240287i	$0.0772414\pi$
$828$	21.2191	−	15.4166i	0.737415	−	0.535763i
$829$	−37.5154	+	27.2565i	−1.30296	+	0.946659i	−0.999980	−	0.00633711i	$-0.997983\pi$
$829$	−37.5154	+	27.2565i	−1.30296	+	0.946659i	−0.302984	+	0.952996i	$0.597983\pi$
$830$	100.842	+	73.2663i	3.50029	+	2.54311i
$831$	31.2986			1.08574
$832$	−66.1930			−2.29483
$833$	5.45229	+	3.96132i	0.188911	+	0.137252i
$834$	−3.62755	−	11.1644i	−0.125612	−	0.386593i
$835$	−2.33102	+	7.17413i	−0.0806681	+	0.248271i
$836$	11.2773			0.390035
$837$	−3.27085	−	8.81501i	−0.113057	−	0.304691i
$838$	−0.515081			−0.0177932
$839$	−1.41818	+	4.36472i	−0.0489612	+	0.150687i	−0.972548	−	0.232702i	$-0.925243\pi$
$839$	−1.41818	+	4.36472i	−0.0489612	+	0.150687i	0.923587	+	0.383389i	$0.125243\pi$
$840$	1.70690	+	5.25329i	0.0588936	+	0.181256i
$841$	−32.7819	−	23.8174i	−1.13041	−	0.821291i
$842$	17.6973			0.609890
$843$	23.3461			0.804081
$844$	−13.6532	−	9.91965i	−0.469964	−	0.341449i
$845$	−50.4830	+	36.6781i	−1.73667	+	1.26176i
$846$	−25.8183	+	18.7581i	−0.887652	+	0.644917i
$847$	0.517930	−	1.59402i	0.0177963	−	0.0547713i
$848$	10.7553	+	7.81418i	0.369339	+	0.268340i
$849$	−2.39296	+	7.36476i	−0.0821260	+	0.252758i
$850$	4.97887	+	15.3234i	0.170774	+	0.525588i
$851$	−14.0379	+	10.1991i	−0.481213	+	0.349621i
$852$	12.5395	+	38.5926i	0.429597	+	1.32216i
$853$	−11.2507	−	34.6262i	−0.385218	−	1.18558i	−0.936322	−	0.351142i	$-0.885793\pi$
$853$	−11.2507	−	34.6262i	−0.385218	−	1.18558i	0.551105	−	0.834436i	$-0.314207\pi$
$854$	7.85643	−	5.70803i	0.268841	−	0.195325i
$855$	2.81585	+	8.66630i	0.0963001	+	0.296381i
$856$	−0.651727	+	2.00581i	−0.0222756	+	0.0685571i
$857$	−16.6012	−	12.0615i	−0.567088	−	0.412013i	0.266958	−	0.963708i	$-0.413981\pi$
$857$	−16.6012	−	12.0615i	−0.567088	−	0.412013i	−0.834046	+	0.551695i	$0.813981\pi$
$858$	31.8889	−	98.1439i	1.08867	−	3.35058i
$859$	−19.5704	+	14.2187i	−0.667732	+	0.485136i	−0.869265	−	0.494346i	$-0.835408\pi$
$859$	−19.5704	+	14.2187i	−0.667732	+	0.485136i	0.201533	+	0.979482i	$0.435408\pi$
$860$	−61.1823	+	44.4515i	−2.08630	+	1.51579i
$861$	−4.11476	−	2.98955i	−0.140231	−	0.101884i
$862$	73.8964			2.51692
$863$	−36.6339			−1.24703			−0.623516	−	0.781810i	$-0.714297\pi$
$863$	−36.6339			−1.24703			−0.623516	+	0.781810i	$0.714297\pi$
$864$	−10.6156	−	7.71267i	−0.361149	−	0.262390i
$865$	0.603853	+	1.85847i	0.0205316	+	0.0631899i
$866$	18.9131	−	58.2084i	0.642692	−	1.97800i
$867$	2.29433			0.0779197
$868$	2.00839	−	7.17276i	0.0681694	−	0.243459i
$869$	−21.0375			−0.713647
$870$	−44.9183	+	138.244i	−1.52287	+	4.68693i
$871$	−4.43715	−	13.6561i	−0.150347	−	0.462721i
$872$	−15.1003	−	10.9710i	−0.511361	−	0.371526i
$873$	−1.67952			−0.0568430
$874$	−10.8198			−0.365987
$875$	−3.64303	−	2.64681i	−0.123157	−	0.0894786i
$876$	33.8952	−	24.6263i	1.14521	−	0.832045i
$877$	36.7770	−	26.7200i	1.24187	−	0.902271i	0.244148	−	0.969738i	$-0.421492\pi$
$877$	36.7770	−	26.7200i	1.24187	−	0.902271i	0.997722	+	0.0674666i	$0.0214916\pi$
$878$	12.7018	−	39.0920i	0.428663	−	1.31929i
$879$	−37.7729	−	27.4436i	−1.27405	−	0.925649i
$880$	−9.79831	+	30.1561i	−0.330301	+	1.01656i
$881$	−3.15657	−	9.71491i	−0.106347	−	0.327304i	0.883697	−	0.468060i	$-0.155047\pi$
$881$	−3.15657	−	9.71491i	−0.106347	−	0.327304i	−0.990044	+	0.140756i	$0.955047\pi$
$882$	26.5340	−	19.2780i	0.893445	−	0.649126i
$883$	−10.4024	−	32.0153i	−0.350069	−	1.07740i	−0.958814	−	0.284035i	$-0.908327\pi$
$883$	−10.4024	−	32.0153i	−0.350069	−	1.07740i	0.608745	−	0.793366i	$-0.291673\pi$
$884$	4.48362	+	13.7991i	0.150800	+	0.464116i
$885$	49.9200	−	36.2690i	1.67804	−	1.21917i
$886$	10.0582	+	30.9561i	0.337913	+	1.03999i
$887$	2.06705	−	6.36173i	0.0694048	−	0.213606i	−0.910338	−	0.413865i	$-0.864178\pi$
$887$	2.06705	−	6.36173i	0.0694048	−	0.213606i	0.979743	+	0.200259i	$0.0641785\pi$
$888$	9.72030	+	7.06221i	0.326192	+	0.236992i
$889$	−2.28781	+	7.04116i	−0.0767307	+	0.236153i
$890$	−85.4962	+	62.1166i	−2.86584	+	2.08215i
$891$	32.6127	−	23.6945i	1.09257	−	0.793797i
$892$	44.0285	+	31.9886i	1.47418	+	1.07106i
$893$	7.46670			0.249864
$894$	−26.1417			−0.874309
$895$	−29.8647	−	21.6980i	−0.998267	−	0.725283i
$896$	−1.60263	−	4.93238i	−0.0535400	−	0.164779i
$897$	−17.3525	+	53.4054i	−0.579382	+	1.78315i
$898$	−39.9619			−1.33355
$899$	36.4031	−	28.8089i	1.21411	−	0.960831i
$900$	44.4711			1.48237
$901$	1.73088	−	5.32711i	0.0576640	−	0.177472i
$902$	10.9017	+	33.5519i	0.362987	+	1.11716i
$903$	−7.73535	−	5.62006i	−0.257416	−	0.187024i
$904$	−21.8728			−0.727479
$905$	−21.5190			−0.715315
$906$	81.0086	+	58.8562i	2.69133	+	1.95537i
$907$	−10.0081	+	7.27128i	−0.332312	+	0.241439i	−0.741411	−	0.671051i	$-0.765843\pi$
$907$	−10.0081	+	7.27128i	−0.332312	+	0.241439i	0.409099	+	0.912490i	$0.365843\pi$
$908$	−32.0817	+	23.3087i	−1.06467	+	0.773527i
$909$	−2.89970	+	8.92435i	−0.0961769	+	0.296002i
$910$	−17.3742	−	12.6231i	−0.575949	−	0.418451i
$911$	−5.65661	+	17.4093i	−0.187412	+	0.576795i	−0.999982	−	0.00606935i	$-0.998068\pi$
$911$	−5.65661	+	17.4093i	−0.187412	+	0.576795i	0.812570	+	0.582864i	$0.198068\pi$
$912$	−1.91602	−	5.89690i	−0.0634458	−	0.195266i
$913$	50.1567	−	36.4410i	1.65994	−	1.20602i
$914$	−9.60986	−	29.5761i	−0.317866	−	0.978290i
$915$	−22.1792	−	68.2605i	−0.733221	−	2.25662i
$916$	14.3009	−	10.3902i	0.472517	−	0.343303i
$917$	3.19681	+	9.83877i	0.105568	+	0.324905i
$918$	−1.12173	+	3.45232i	−0.0370225	+	0.113943i
$919$	17.0651	+	12.3985i	0.562925	+	0.408989i	0.832528	−	0.553983i	$-0.186893\pi$
$919$	17.0651	+	12.3985i	0.562925	+	0.408989i	−0.269603	+	0.962971i	$0.586893\pi$
$920$	−6.44249	+	19.8280i	−0.212403	+	0.653708i
$921$	26.8363	−	19.4977i	0.884285	−	0.642470i
$922$	17.0515	−	12.3886i	0.561561	−	0.407998i
$923$	−30.2289	−	21.9626i	−0.994997	−	0.722907i
$924$	11.6002			0.381619
$925$	−29.4207			−0.967347
$926$	39.2424	+	28.5113i	1.28959	+	0.936939i
$927$	3.94767	+	12.1497i	0.129659	+	0.399048i
$928$	20.0204	−	61.6165i	0.657202	−	2.02266i
$929$	−32.1133			−1.05360			−0.526802	−	0.849988i	$-0.676609\pi$
$929$	−32.1133			−1.05360			−0.526802	+	0.849988i	$0.676609\pi$
$930$	−80.8082	−	53.7751i	−2.64981	−	1.76335i
$931$	−7.67366			−0.251494
$932$	18.6155	−	57.2927i	0.609772	−	1.87668i
$933$	−8.72398	−	26.8497i	−0.285610	−	0.879018i
$934$	47.0591	+	34.1904i	1.53982	+	1.11875i
$935$	13.3595			0.436901
$936$	16.7230			0.546608
$937$	−22.6271	−	16.4395i	−0.739194	−	0.537056i	0.153265	−	0.988185i	$-0.451021\pi$
$937$	−22.6271	−	16.4395i	−0.739194	−	0.537056i	−0.892459	+	0.451129i	$0.851021\pi$
$938$	2.30240	−	1.67279i	0.0751761	−	0.0546187i
$939$	3.30972	−	2.40465i	0.108009	−	0.0784728i
$940$	18.7723	−	57.7751i	0.612284	−	1.88442i
$941$	17.0982	+	12.4226i	0.557386	+	0.404964i	0.830501	−	0.557017i	$-0.188054\pi$
$941$	17.0982	+	12.4226i	0.557386	+	0.404964i	−0.273116	+	0.961981i	$0.588054\pi$
$942$	25.7562	−	79.2695i	0.839183	−	2.58274i
$943$	−5.93220	−	18.2574i	−0.193179	−	0.594543i
$944$	−14.6090	+	10.6141i	−0.475484	+	0.345459i
$945$	−0.941661	−	2.89813i	−0.0306322	−	0.0942763i
$946$	20.4941	+	63.0744i	0.666321	+	2.05073i
$947$	14.7252	−	10.6985i	0.478506	−	0.347655i	−0.322241	−	0.946658i	$-0.604436\pi$
$947$	14.7252	−	10.6985i	0.478506	−	0.347655i	0.800747	+	0.599003i	$0.204436\pi$
$948$	−10.3426	−	31.8313i	−0.335913	−	1.03383i
$949$	−11.9215	+	36.6905i	−0.386987	+	1.19102i
$950$	−14.8418	−	10.7832i	−0.481533	−	0.349854i
$951$	17.5722	−	54.0817i	0.569818	−	1.75372i
$952$	−0.550999	+	0.400324i	−0.0178580	+	0.0129746i
$953$	−20.7081	+	15.0453i	−0.670802	+	0.487366i	−0.870294	−	0.492533i	$-0.836071\pi$
$953$	−20.7081	+	15.0453i	−0.670802	+	0.487366i	0.199491	+	0.979900i	$0.436071\pi$
$954$	−22.0529	−	16.0224i	−0.713989	−	0.518743i
$955$	28.5913			0.925194
$956$	−79.4722			−2.57032
$957$	58.4904	+	42.4958i	1.89073	+	1.37369i
$958$	−6.64270	−	20.4441i	−0.214616	−	0.660520i
$959$	0.613323	−	1.88761i	0.0198052	−	0.0609543i
$960$	−96.9638			−3.12949
$961$	11.9707	+	28.5955i	0.386151	+	0.922436i
$962$	−46.7136			−1.50611
$963$	−1.10593	+	3.40370i	−0.0356381	+	0.109683i
$964$	−11.8045	−	36.3306i	−0.380199	−	1.17013i
$965$	49.0341	+	35.6253i	1.57846	+	1.14682i
$966$	−11.1296			−0.358090
$967$	37.4298			1.20366			0.601831	−	0.798624i	$-0.294438\pi$
$967$	37.4298			1.20366			0.601831	+	0.798624i	$0.294438\pi$
$968$	−3.54381	−	2.57473i	−0.113902	−	0.0827549i
$969$	−2.11347	+	1.53552i	−0.0678944	+	0.0493281i
$970$	4.56036	−	3.31329i	0.146424	−	0.106383i
$971$	4.15102	−	12.7755i	0.133213	−	0.409987i	−0.862095	−	0.506747i	$-0.830848\pi$
$971$	4.15102	−	12.7755i	0.133213	−	0.409987i	0.995308	+	0.0967601i	$0.0308480\pi$
$972$	41.1440	+	29.8929i	1.31969	+	0.958815i
$973$	−0.375481	+	1.15561i	−0.0120374	+	0.0370473i
$974$	−4.23301	−	13.0279i	−0.135634	−	0.417440i
$975$	−77.0274	+	55.9637i	−2.46685	+	1.79227i
$976$	6.49072	+	19.9764i	0.207763	+	0.639429i
$977$	7.18957	+	22.1272i	0.230015	+	0.707913i	0.997744	+	0.0671379i	$0.0213867\pi$
$977$	7.18957	+	22.1272i	0.230015	+	0.707913i	−0.767729	+	0.640775i	$0.778613\pi$
$978$	−37.7288	+	27.4116i	−1.20643	+	0.876526i
$979$	16.2427	+	49.9898i	0.519118	+	1.59768i
$980$	−19.2926	+	59.3765i	−0.616279	+	1.89671i
$981$	−25.6241	−	18.6170i	−0.818114	−	0.594394i
$982$	−21.4535	+	66.0272i	−0.684610	+	2.10701i
$983$	−42.5287	+	30.8989i	−1.35646	+	0.985522i	−0.357793	+	0.933801i	$0.616471\pi$
$983$	−42.5287	+	30.8989i	−1.35646	+	0.985522i	−0.998662	+	0.0517215i	$0.983529\pi$
$984$	−10.7540	+	7.81321i	−0.342824	+	0.249076i
$985$	22.1247	+	16.0746i	0.704952	+	0.512178i
$986$	−17.9229			−0.570783
$987$	7.68049			0.244473
$988$	−13.3655	−	9.71060i	−0.425213	−	0.308935i
$989$	−11.1520	−	34.3222i	−0.354612	−	1.09138i
$990$	20.0907	−	61.8327i	0.638523	−	1.96517i
$991$	−15.8070			−0.502126			−0.251063	−	0.967971i	$-0.580780\pi$
$991$	−15.8070			−0.502126			−0.251063	+	0.967971i	$0.580780\pi$
$992$	36.0168	+	23.9679i	1.14353	+	0.760982i
$993$	79.4345			2.52078
$994$	2.28849	−	7.04325i	0.0725865	−	0.223398i
$995$	23.4399	+	72.1406i	0.743095	+	2.28701i
$996$	79.7964	+	57.9755i	2.52845	+	1.83702i
$997$	1.56184			0.0494639			0.0247320	−	0.999694i	$-0.492127\pi$
$997$	1.56184			0.0494639			0.0247320	+	0.999694i	$0.492127\pi$
$998$	−17.5874			−0.556719
$999$	−5.36249	−	3.89608i	−0.169662	−	0.123266i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	527.2.h.c.256.19	yes	96
31.4	even	5	inner	527.2.h.c.35.19	✓	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
527.2.h.c.35.19	✓	96	31.4	even	5	inner
527.2.h.c.256.19	yes	96	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 527 = 17 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	527.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.664255 - 2.04437i) q^{2} +(0.708988 + 2.18204i) q^{3} +(-2.12016 - 1.54039i) q^{4} +3.53489 q^{5} +4.93184 q^{6} +(-0.412992 - 0.300057i) q^{7} +(-1.07936 + 0.784201i) q^{8} +(-1.83159 + 1.33073i) q^{9} +O(q^{10})\)	\(q+(0.664255 - 2.04437i) q^{2} +(0.708988 + 2.18204i) q^{3} +(-2.12016 - 1.54039i) q^{4} +3.53489 q^{5} +4.93184 q^{6} +(-0.412992 - 0.300057i) q^{7} +(-1.07936 + 0.784201i) q^{8} +(-1.83159 + 1.33073i) q^{9} +(2.34806 - 7.22660i) q^{10} +(-3.05753 - 2.22143i) q^{11} +(1.85802 - 5.71840i) q^{12} +(1.71087 + 5.26552i) q^{13} +(-0.887757 + 0.644993i) q^{14} +(2.50619 + 7.71327i) q^{15} +(-0.733436 - 2.25728i) q^{16} +(-0.809017 + 0.587785i) q^{17} +(1.50385 + 4.62838i) q^{18} +(0.351855 - 1.08290i) q^{19} +(-7.49453 - 5.44510i) q^{20} +(0.361929 - 1.11390i) q^{21} +(-6.57239 + 4.77512i) q^{22} +(3.57639 - 2.59840i) q^{23} +(-2.47641 - 1.79922i) q^{24} +7.49543 q^{25} +11.9011 q^{26} +(1.36619 + 0.992592i) q^{27} +(0.413407 + 1.27234i) q^{28} +(-2.57655 + 7.92982i) q^{29} +17.4335 q^{30} +(-4.63523 - 3.08459i) q^{31} -7.77023 q^{32} +(2.67949 - 8.24663i) q^{33} +(0.664255 + 2.04437i) q^{34} +(-1.45988 - 1.06067i) q^{35} +5.93310 q^{36} -3.92515 q^{37} +(-1.98012 - 1.43864i) q^{38} +(-10.2766 + 7.46638i) q^{39} +(-3.81542 + 2.77206i) q^{40} +(1.34192 - 4.13002i) q^{41} +(-2.03681 - 1.47983i) q^{42} +(2.52269 - 7.76404i) q^{43} +(3.06060 + 9.41957i) q^{44} +(-6.47446 + 4.70397i) q^{45} +(-2.93645 - 9.03745i) q^{46} +(2.02642 + 6.23669i) q^{47} +(4.40549 - 3.20078i) q^{48} +(-2.08259 - 6.40955i) q^{49} +(4.97887 - 15.3234i) q^{50} +(-1.85616 - 1.34858i) q^{51} +(4.48362 - 13.7991i) q^{52} +(-4.53151 + 3.29233i) q^{53} +(2.93672 - 2.13365i) q^{54} +(-10.8080 - 7.85250i) q^{55} +0.681072 q^{56} +2.61239 q^{57} +(14.5000 + 10.5348i) q^{58} +(-2.35108 - 7.23587i) q^{59} +(6.56789 - 20.2139i) q^{60} -8.84975 q^{61} +(-9.38499 + 7.42715i) q^{62} +1.15573 q^{63} +(-3.69454 + 11.3706i) q^{64} +(6.04773 + 18.6130i) q^{65} +(-15.0793 - 10.9557i) q^{66} -2.59351 q^{67} +2.62066 q^{68} +(8.20544 + 5.96160i) q^{69} +(-3.13812 + 2.27998i) q^{70} +(-5.45994 + 3.96688i) q^{71} +(0.933387 - 2.87267i) q^{72} +(5.63728 + 4.09573i) q^{73} +(-2.60730 + 8.02445i) q^{74} +(5.31417 + 16.3553i) q^{75} +(-2.41407 + 1.75393i) q^{76} +(0.596184 + 1.83487i) q^{77} +(8.43774 + 25.9687i) q^{78} +(4.50337 - 3.27189i) q^{79} +(-2.59261 - 7.97924i) q^{80} +(-3.29608 + 10.1443i) q^{81} +(-7.55189 - 5.48677i) q^{82} +(-5.06921 + 15.6014i) q^{83} +(-2.48319 + 1.80414i) q^{84} +(-2.85978 + 2.07775i) q^{85} +(-14.1968 - 10.3146i) q^{86} -19.1299 q^{87} +5.04223 q^{88} +(-11.2517 - 8.17486i) q^{89} +(5.31595 + 16.3608i) q^{90} +(0.873376 - 2.68798i) q^{91} -11.5851 q^{92} +(3.44437 - 12.3012i) q^{93} +14.0961 q^{94} +(1.24377 - 3.82792i) q^{95} +(-5.50900 - 16.9550i) q^{96} +(0.600165 + 0.436046i) q^{97} -14.4868 q^{98} +8.55626 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 2 q^{2} - 4 q^{3} - 30 q^{4} + 6 q^{5} - 8 q^{6} - 10 q^{7} - 36 q^{9}+O(q^{10}) \) 96 * q - 2 * q^2 - 4 * q^3 - 30 * q^4 + 6 * q^5 - 8 * q^6 - 10 * q^7 - 36 * q^9	\( 96 q - 2 q^{2} - 4 q^{3} - 30 q^{4} + 6 q^{5} - 8 q^{6} - 10 q^{7} - 36 q^{9} - 13 q^{10} - 4 q^{11} - 14 q^{12} - 14 q^{13} + 17 q^{14} - 9 q^{15} - 58 q^{16} - 24 q^{17} - 24 q^{18} - 6 q^{19} + 43 q^{20} + 26 q^{21} + 42 q^{22} - 11 q^{23} - 38 q^{24} + 126 q^{25} - 44 q^{26} - q^{27} + 31 q^{28} - 10 q^{29} - 70 q^{30} + 21 q^{31} + 28 q^{32} - 36 q^{33} - 2 q^{34} + 2 q^{35} + 160 q^{36} + 54 q^{37} + 15 q^{38} - 10 q^{39} - 29 q^{40} - 14 q^{41} - 3 q^{42} + 6 q^{43} - 5 q^{44} - q^{45} - 17 q^{46} - 14 q^{47} - 93 q^{48} - 72 q^{49} + 108 q^{50} + q^{51} + 13 q^{52} - 30 q^{53} - 63 q^{54} - 12 q^{55} + 66 q^{56} - 62 q^{57} + 29 q^{58} + 8 q^{59} - 86 q^{60} - 14 q^{61} - 34 q^{62} + 86 q^{63} - 122 q^{64} + 13 q^{65} - 40 q^{66} + 126 q^{67} + 120 q^{68} - 34 q^{69} - 38 q^{70} - 39 q^{71} - 51 q^{72} - 60 q^{73} - 111 q^{74} - 41 q^{75} + 64 q^{76} - 26 q^{77} - 99 q^{78} - 33 q^{79} - 91 q^{80} + 81 q^{81} - 88 q^{82} + 22 q^{83} + 160 q^{84} - 4 q^{85} + 35 q^{86} + 70 q^{87} - 120 q^{88} + 101 q^{89} + 125 q^{90} - 13 q^{91} - 98 q^{92} + 47 q^{93} - 8 q^{94} - 64 q^{95} + 208 q^{96} + 16 q^{97} + 8 q^{98} + 280 q^{99}+O(q^{100}) \) 96 * q - 2 * q^2 - 4 * q^3 - 30 * q^4 + 6 * q^5 - 8 * q^6 - 10 * q^7 - 36 * q^9 - 13 * q^10 - 4 * q^11 - 14 * q^12 - 14 * q^13 + 17 * q^14 - 9 * q^15 - 58 * q^16 - 24 * q^17 - 24 * q^18 - 6 * q^19 + 43 * q^20 + 26 * q^21 + 42 * q^22 - 11 * q^23 - 38 * q^24 + 126 * q^25 - 44 * q^26 - q^27 + 31 * q^28 - 10 * q^29 - 70 * q^30 + 21 * q^31 + 28 * q^32 - 36 * q^33 - 2 * q^34 + 2 * q^35 + 160 * q^36 + 54 * q^37 + 15 * q^38 - 10 * q^39 - 29 * q^40 - 14 * q^41 - 3 * q^42 + 6 * q^43 - 5 * q^44 - q^45 - 17 * q^46 - 14 * q^47 - 93 * q^48 - 72 * q^49 + 108 * q^50 + q^51 + 13 * q^52 - 30 * q^53 - 63 * q^54 - 12 * q^55 + 66 * q^56 - 62 * q^57 + 29 * q^58 + 8 * q^59 - 86 * q^60 - 14 * q^61 - 34 * q^62 + 86 * q^63 - 122 * q^64 + 13 * q^65 - 40 * q^66 + 126 * q^67 + 120 * q^68 - 34 * q^69 - 38 * q^70 - 39 * q^71 - 51 * q^72 - 60 * q^73 - 111 * q^74 - 41 * q^75 + 64 * q^76 - 26 * q^77 - 99 * q^78 - 33 * q^79 - 91 * q^80 + 81 * q^81 - 88 * q^82 + 22 * q^83 + 160 * q^84 - 4 * q^85 + 35 * q^86 + 70 * q^87 - 120 * q^88 + 101 * q^89 + 125 * q^90 - 13 * q^91 - 98 * q^92 + 47 * q^93 - 8 * q^94 - 64 * q^95 + 208 * q^96 + 16 * q^97 + 8 * q^98 + 280 * q^99

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