LMFDB - Embedded newform 230.2.l.a.7.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,2,Mod(7,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([11, 38]))

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

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

chi := DirichletCharacter("230.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	230.l (of order $44$, degree $20$, 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:	$1.83655924649$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			7.9
Character	$\chi$	$=$	230.7
Dual form			230.2.l.a.33.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.997452 - 0.0713392i) q^{2} +(-0.307156 + 1.41198i) q^{3} +(0.989821 - 0.142315i) q^{4} +(1.55520 - 1.60666i) q^{5} +(-0.205645 + 1.43029i) q^{6} +(-1.84581 + 3.38035i) q^{7} +(0.977147 - 0.212565i) q^{8} +(0.829567 + 0.378851i) q^{9} +(1.43661 - 1.71352i) q^{10} +(3.85970 - 3.34445i) q^{11} +(-0.103085 + 1.44132i) q^{12} +(-3.94532 + 2.15431i) q^{13} +(-1.59996 + 3.50342i) q^{14} +(1.79088 + 2.68939i) q^{15} +(0.959493 - 0.281733i) q^{16} +(-2.64144 - 3.52855i) q^{17} +(0.854480 + 0.318705i) q^{18} +(0.596940 + 4.15181i) q^{19} +(1.31071 - 1.81164i) q^{20} +(-4.20602 - 3.64454i) q^{21} +(3.61128 - 3.61128i) q^{22} +(2.37283 - 4.16769i) q^{23} +1.44500i q^{24} +(-0.162734 - 4.99735i) q^{25} +(-3.78158 + 2.43027i) q^{26} +(-3.38760 + 4.52530i) q^{27} +(-1.34595 + 3.60863i) q^{28} +(-5.29900 - 0.761882i) q^{29} +(1.97818 + 2.55478i) q^{30} +(2.10320 + 1.35164i) q^{31} +(0.936950 - 0.349464i) q^{32} +(3.53675 + 6.47707i) q^{33} +(-2.88643 - 3.33112i) q^{34} +(2.56049 + 8.22271i) q^{35} +(0.875039 + 0.256935i) q^{36} +(-3.94954 - 10.5891i) q^{37} +(0.891605 + 4.09864i) q^{38} +(-1.83000 - 6.23240i) q^{39} +(1.17813 - 1.90053i) q^{40} +(-2.05845 - 4.50738i) q^{41} +(-4.45530 - 3.33520i) q^{42} +(-3.43244 - 0.746682i) q^{43} +(3.34445 - 3.85970i) q^{44} +(1.89882 - 0.743648i) q^{45} +(2.06947 - 4.32635i) q^{46} +(-4.84820 - 4.84820i) q^{47} +(0.103085 + 1.44132i) q^{48} +(-4.23527 - 6.59021i) q^{49} +(-0.518826 - 4.97301i) q^{50} +(5.79356 - 2.64583i) q^{51} +(-3.59857 + 2.69386i) q^{52} +(8.03345 + 4.38659i) q^{53} +(-3.05614 + 4.75544i) q^{54} +(0.629185 - 11.4025i) q^{55} +(-1.08508 + 3.69546i) q^{56} +(-6.04560 - 0.432390i) q^{57} +(-5.33986 - 0.381914i) q^{58} +(0.493606 - 1.68107i) q^{59} +(2.15539 + 2.40715i) q^{60} +(-0.855388 + 1.33101i) q^{61} +(2.19426 + 1.19816i) q^{62} +(-2.81187 + 2.10494i) q^{63} +(0.909632 - 0.415415i) q^{64} +(-2.67450 + 9.68917i) q^{65} +(3.98981 + 6.20826i) q^{66} +(0.499531 + 6.98435i) q^{67} +(-3.11672 - 3.11672i) q^{68} +(5.15585 + 4.63052i) q^{69} +(3.14057 + 8.01909i) q^{70} +(-9.09632 + 10.4977i) q^{71} +(0.891139 + 0.193855i) q^{72} +(3.61933 + 2.70939i) q^{73} +(-4.69489 - 10.2804i) q^{74} +(7.10612 + 1.30519i) q^{75} +(1.18173 + 4.02459i) q^{76} +(4.18114 + 19.2204i) q^{77} +(-2.26995 - 6.08597i) q^{78} +(4.81604 + 1.41412i) q^{79} +(1.03955 - 1.97973i) q^{80} +(-3.55743 - 4.10549i) q^{81} +(-2.37476 - 4.34904i) q^{82} +(5.41151 - 2.01839i) q^{83} +(-4.68188 - 3.00886i) q^{84} +(-9.77715 - 1.24368i) q^{85} +(-3.47696 - 0.499912i) q^{86} +(2.70338 - 7.24805i) q^{87} +(3.06058 - 4.08846i) q^{88} +(0.368885 - 0.237068i) q^{89} +(1.84094 - 0.877214i) q^{90} -17.3130i q^{91} +(1.75556 - 4.46296i) q^{92} +(-2.55450 + 2.55450i) q^{93} +(-5.18171 - 4.48998i) q^{94} +(7.59891 + 5.49779i) q^{95} +(0.205645 + 1.43029i) q^{96} +(16.6014 + 6.19201i) q^{97} +(-4.69462 - 6.27128i) q^{98} +(4.46893 - 1.31220i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 8 q^{3} - 8 q^{6} - 8 q^{12} + 16 q^{13} + 24 q^{16} - 72 q^{18} - 80 q^{23} - 8 q^{26} + 16 q^{27} - 44 q^{28} + 24 q^{31} - 44 q^{33} - 8 q^{35} - 32 q^{36} - 88 q^{37} - 24 q^{41} - 8 q^{46}+ \cdots + 24 q^{98}+O(q^{100}) $ 240 * q - 8 * q^3 - 8 * q^6 - 8 * q^12 + 16 * q^13 + 24 * q^16 - 72 * q^18 - 80 * q^23 - 8 * q^26 + 16 * q^27 - 44 * q^28 + 24 * q^31 - 44 * q^33 - 8 * q^35 - 32 * q^36 - 88 * q^37 - 24 * q^41 - 8 * q^46 - 80 * q^47 + 8 * q^48 + 8 * q^50 + 16 * q^52 - 44 * q^56 - 88 * q^57 - 176 * q^61 - 32 * q^62 - 176 * q^66 + 24 * q^70 - 336 * q^71 + 16 * q^72 - 88 * q^73 - 36 * q^75 - 24 * q^77 + 40 * q^78 - 136 * q^81 + 40 * q^82 - 100 * q^85 - 44 * q^86 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 52 * q^95 + 8 * q^96 + 132 * q^97 + 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{19}{22}\right)$

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 $

$2$	0.997452	−	0.0713392i	0.705305	−	0.0504444i
$2$	0.997452	−	0.0713392i	0.705305	−	0.0504444i
$3$	−0.307156	+	1.41198i	−0.177337	+	0.815204i	0.799406	+	0.600791i	$0.205148\pi$
$3$	−0.307156	+	1.41198i	−0.177337	+	0.815204i	−0.976743	+	0.214413i	$0.931216\pi$
$4$	0.989821	−	0.142315i	0.494911	−	0.0711574i
$5$	1.55520	−	1.60666i	0.695505	−	0.718522i
$5$	1.55520	−	1.60666i	0.695505	−	0.718522i
$6$	−0.205645	+	1.43029i	−0.0839541	+	0.583913i
$7$	−1.84581	+	3.38035i	−0.697651	+	1.27765i	0.253023	+	0.967460i	$0.418575\pi$
$7$	−1.84581	+	3.38035i	−0.697651	+	1.27765i	−0.950674	+	0.310192i	$0.899607\pi$
$8$	0.977147	−	0.212565i	0.345474	−	0.0751532i
$9$	0.829567	+	0.378851i	0.276522	+	0.126284i
$10$	1.43661	−	1.71352i	0.454298	−	0.541861i
$11$	3.85970	−	3.34445i	1.16374	−	1.00839i	0.163985	−	0.986463i	$-0.447565\pi$
$11$	3.85970	−	3.34445i	1.16374	−	1.00839i	0.999760	−	0.0219272i	$-0.00698020\pi$
$12$	−0.103085	+	1.44132i	−0.0297581	+	0.416072i
$13$	−3.94532	+	2.15431i	−1.09423	+	0.597497i	−0.921856	−	0.387533i	$-0.873327\pi$
$13$	−3.94532	+	2.15431i	−1.09423	+	0.597497i	−0.172379	+	0.985031i	$0.555145\pi$
$14$	−1.59996	+	3.50342i	−0.427607	+	0.936328i
$15$	1.79088	+	2.68939i	0.462403	+	0.694399i
$16$	0.959493	−	0.281733i	0.239873	−	0.0704331i
$17$	−2.64144	−	3.52855i	−0.640643	−	0.855799i	0.356264	−	0.934385i	$-0.384050\pi$
$17$	−2.64144	−	3.52855i	−0.640643	−	0.855799i	−0.996907	+	0.0785860i	$0.974959\pi$
$18$	0.854480	+	0.318705i	0.201403	+	0.0751194i
$19$	0.596940	+	4.15181i	0.136947	+	0.952490i	0.936193	+	0.351486i	$0.114323\pi$
$19$	0.596940	+	4.15181i	0.136947	+	0.952490i	−0.799246	+	0.601004i	$0.794768\pi$
$20$	1.31071	−	1.81164i	0.293085	−	0.405094i
$21$	−4.20602	−	3.64454i	−0.917829	−	0.795303i
$22$	3.61128	−	3.61128i	0.769927	−	0.769927i
$23$	2.37283	−	4.16769i	0.494770	−	0.869024i
$23$	2.37283	−	4.16769i	0.494770	−	0.869024i
$24$			1.44500i			0.294959i
$25$	−0.162734	−	4.99735i	−0.0325468	−	0.999470i
$26$	−3.78158	+	2.43027i	−0.741629	+	0.476616i
$27$	−3.38760	+	4.52530i	−0.651944	+	0.870895i
$28$	−1.34595	+	3.60863i	−0.254361	+	0.681967i
$29$	−5.29900	−	0.761882i	−0.984000	−	0.141478i	−0.368511	−	0.929623i	$-0.620132\pi$
$29$	−5.29900	−	0.761882i	−0.984000	−	0.141478i	−0.615489	+	0.788145i	$0.711042\pi$
$30$	1.97818	+	2.55478i	0.361164	+	0.466437i
$31$	2.10320	+	1.35164i	0.377745	+	0.242762i	0.715712	−	0.698396i	$-0.246103\pi$
$31$	2.10320	+	1.35164i	0.377745	+	0.242762i	−0.337966	+	0.941158i	$0.609739\pi$
$32$	0.936950	−	0.349464i	0.165631	−	0.0617771i
$33$	3.53675	+	6.47707i	0.615669	+	1.12751i
$34$	−2.88643	−	3.33112i	−0.495019	−	0.571283i
$35$	2.56049	+	8.22271i	0.432802	+	1.38989i
$36$	0.875039	+	0.256935i	0.145840	+	0.0428225i
$37$	−3.94954	−	10.5891i	−0.649300	−	1.74084i	−0.671412	−	0.741085i	$-0.734312\pi$
$37$	−3.94954	−	10.5891i	−0.649300	−	1.74084i	0.0221119	−	0.999756i	$-0.492961\pi$
$38$	0.891605	+	4.09864i	0.144637	+	0.664888i
$39$	−1.83000	−	6.23240i	−0.293034	−	0.997983i
$40$	1.17813	−	1.90053i	0.186279	−	0.300500i
$41$	−2.05845	−	4.50738i	−0.321476	−	0.703934i	0.678041	−	0.735024i	$-0.262829\pi$
$41$	−2.05845	−	4.50738i	−0.321476	−	0.703934i	−0.999517	+	0.0310905i	$0.990102\pi$
$42$	−4.45530	−	3.33520i	−0.687468	−	0.514632i
$43$	−3.43244	−	0.746682i	−0.523442	−	0.113868i	−0.0569224	−	0.998379i	$-0.518129\pi$
$43$	−3.43244	−	0.746682i	−0.523442	−	0.113868i	−0.466520	+	0.884511i	$0.654492\pi$
$44$	3.34445	−	3.85970i	0.504195	−	0.581872i
$45$	1.89882	−	0.743648i	0.283060	−	0.110857i
$46$	2.06947	−	4.32635i	0.305126	−	0.637885i
$47$	−4.84820	−	4.84820i	−0.707183	−	0.707183i	0.258759	−	0.965942i	$-0.416686\pi$
$47$	−4.84820	−	4.84820i	−0.707183	−	0.707183i	−0.965942	+	0.258759i	$0.916686\pi$
$48$	0.103085	+	1.44132i	0.0148790	+	0.208036i
$49$	−4.23527	−	6.59021i	−0.605039	−	0.941458i
$50$	−0.518826	−	4.97301i	−0.0733731	−	0.703290i
$51$	5.79356	−	2.64583i	0.811261	−	0.370490i
$52$	−3.59857	+	2.69386i	−0.499032	+	0.373571i
$53$	8.03345	+	4.38659i	1.10348	+	0.602545i	0.924452	−	0.381299i	$-0.124523\pi$
$53$	8.03345	+	4.38659i	1.10348	+	0.602545i	0.179027	+	0.983844i	$0.442705\pi$
$54$	−3.05614	+	4.75544i	−0.415888	+	0.647134i
$55$	0.629185	−	11.4025i	0.0848393	−	1.53752i
$56$	−1.08508	+	3.69546i	−0.145000	+	0.493826i
$57$	−6.04560	−	0.432390i	−0.800759	−	0.0572714i
$58$	−5.33986	−	0.381914i	−0.701157	−	0.0501478i
$59$	0.493606	−	1.68107i	0.0642621	−	0.218857i	−0.921101	−	0.389323i	$-0.872709\pi$
$59$	0.493606	−	1.68107i	0.0642621	−	0.218857i	0.985364	+	0.170466i	$0.0545273\pi$
$60$	2.15539	+	2.40715i	0.278260	+	0.310762i
$61$	−0.855388	+	1.33101i	−0.109521	+	0.170418i	−0.891688	−	0.452651i	$-0.850478\pi$
$61$	−0.855388	+	1.33101i	−0.109521	+	0.170418i	0.782166	+	0.623070i	$0.214115\pi$
$62$	2.19426	+	1.19816i	0.278672	+	0.152166i
$63$	−2.81187	+	2.10494i	−0.354263	+	0.265198i
$64$	0.909632	−	0.415415i	0.113704	−	0.0519269i
$65$	−2.67450	+	9.68917i	−0.331730	+	1.20179i
$66$	3.98981	+	6.20826i	0.491111	+	0.764184i
$67$	0.499531	+	6.98435i	0.0610274	+	0.853274i	0.932119	+	0.362153i	$0.117958\pi$
$67$	0.499531	+	6.98435i	0.0610274	+	0.853274i	−0.871091	+	0.491121i	$0.836587\pi$
$68$	−3.11672	−	3.11672i	−0.377958	−	0.377958i
$69$	5.15585	+	4.63052i	0.620691	+	0.557449i
$70$	3.14057	+	8.01909i	0.375369	+	0.958465i
$71$	−9.09632	+	10.4977i	−1.07953	+	1.24585i	−0.111839	+	0.993726i	$0.535674\pi$
$71$	−9.09632	+	10.4977i	−1.07953	+	1.24585i	−0.967695	+	0.252123i	$0.918871\pi$
$72$	0.891139	+	0.193855i	0.105022	+	0.0228461i
$73$	3.61933	+	2.70939i	0.423610	+	0.317111i	0.789727	−	0.613458i	$-0.210222\pi$
$73$	3.61933	+	2.70939i	0.423610	+	0.317111i	−0.366117	+	0.930569i	$0.619313\pi$
$74$	−4.69489	−	10.2804i	−0.545770	−	1.19507i
$75$	7.10612	+	1.30519i	0.820544	+	0.150711i
$76$	1.18173	+	4.02459i	0.135553	+	0.461653i
$77$	4.18114	+	19.2204i	0.476485	+	2.19037i
$78$	−2.26995	−	6.08597i	−0.257021	−	0.689101i
$79$	4.81604	+	1.41412i	0.541847	+	0.159101i	0.541192	−	0.840899i	$-0.317973\pi$
$79$	4.81604	+	1.41412i	0.541847	+	0.159101i	0.000655108		1.00000i	$0.499791\pi$
$80$	1.03955	−	1.97973i	0.116225	−	0.221341i
$81$	−3.55743	−	4.10549i	−0.395270	−	0.456166i
$82$	−2.37476	−	4.34904i	−0.262248	−	0.480271i
$83$	5.41151	−	2.01839i	0.593991	−	0.221547i	−0.0344476	−	0.999407i	$-0.510967\pi$
$83$	5.41151	−	2.01839i	0.593991	−	0.221547i	0.628438	+	0.777859i	$0.283694\pi$
$84$	−4.68188	−	3.00886i	−0.510835	−	0.328294i
$85$	−9.77715	−	1.24368i	−1.06048	−	0.134896i
$86$	−3.47696	−	0.499912i	−0.374931	−	0.0539069i
$87$	2.70338	−	7.24805i	0.289833	−	0.777072i
$88$	3.06058	−	4.08846i	0.326259	−	0.435831i
$89$	0.368885	−	0.237068i	0.0391017	−	0.0251291i	−0.520944	−	0.853591i	$-0.674420\pi$
$89$	0.368885	−	0.237068i	0.0391017	−	0.0251291i	0.560046	+	0.828462i	$0.310784\pi$
$90$	1.84094	−	0.877214i	0.194052	−	0.0924665i
$91$		−	17.3130i		−	1.81490i
$92$	1.75556	−	4.46296i	0.183030	−	0.465296i
$93$	−2.55450	+	2.55450i	−0.264889	+	0.264889i
$94$	−5.18171	−	4.48998i	−0.534453	−	0.463106i
$95$	7.59891	+	5.49779i	0.779632	+	0.564061i
$96$	0.205645	+	1.43029i	0.0209885	+	0.145978i
$97$	16.6014	+	6.19201i	1.68562	+	0.628704i	0.995480	−	0.0949729i	$-0.0302764\pi$
$97$	16.6014	+	6.19201i	1.68562	+	0.628704i	0.690139	+	0.723676i	$0.257549\pi$
$98$	−4.69462	−	6.27128i	−0.474228	−	0.633495i
$99$	4.46893	−	1.31220i	0.449144	−	0.131881i
$100$	−0.872275	−	4.92333i	−0.0872275	−	0.492333i
$101$	−4.21769	+	9.23545i	−0.419676	+	0.918961i	0.575215	+	0.818002i	$0.304918\pi$
$101$	−4.21769	+	9.23545i	−0.419676	+	0.918961i	−0.994891	+	0.100959i	$0.967809\pi$
$102$	5.59005	−	3.05240i	0.553497	−	0.302232i
$103$	−0.908192	+	12.6982i	−0.0894868	+	1.25119i	0.732136	+	0.681158i	$0.238523\pi$
$103$	−0.908192	+	12.6982i	−0.0894868	+	1.25119i	−0.821623	+	0.570031i	$0.806931\pi$
$104$	−3.39723	+	2.94371i	−0.333125	+	0.288655i
$105$	−12.3967	+	1.08969i	−1.20980	+	0.106343i
$106$	8.32591	+	3.80232i	0.808684	+	0.369314i
$107$	−7.31672	+	1.59166i	−0.707334	+	0.153871i	−0.551821	−	0.833963i	$-0.686067\pi$
$107$	−7.31672	+	1.59166i	−0.707334	+	0.153871i	−0.155513	+	0.987834i	$0.549703\pi$
$108$	−2.70910	+	4.96135i	−0.260683	+	0.477406i
$109$	−0.125920	+	0.875794i	−0.0120610	+	0.0838858i	−0.994963	−	0.100244i	$-0.968038\pi$
$109$	−0.125920	+	0.875794i	−0.0120610	+	0.0838858i	0.982902	+	0.184130i	$0.0589467\pi$
$110$	−0.185865	−	11.4184i	−0.0177215	−	1.08870i
$111$	16.1647	−	2.32413i	1.53428	−	0.220597i
$112$	−0.818688	+	3.76345i	−0.0773588	+	0.355612i
$113$	12.7842	−	0.914346i	1.20264	−	0.0860145i	0.544402	−	0.838825i	$-0.316757\pi$
$113$	12.7842	−	0.914346i	1.20264	−	0.0860145i	0.658238	+	0.752810i	$0.271302\pi$
$114$	−6.06104			−0.567669
$115$	−3.00586	−	10.2939i	−0.280298	−	0.959913i
$116$	−5.35350			−0.497060
$117$	−4.08907	+	0.292456i	−0.378034	+	0.0270376i
$118$	0.372423	−	1.71200i	0.0342843	−	0.157602i
$119$	16.8033	−	2.41596i	1.54036	−	0.221470i
$120$	2.32163	+	2.24725i	0.211934	+	0.205145i
$121$	2.14649	−	14.9291i	0.195135	−	1.35719i
$122$	−0.758255	+	1.38864i	−0.0686492	+	0.125722i
$123$	6.99657	−	1.52201i	0.630859	−	0.137235i
$124$	2.27415	+	1.03857i	0.204225	+	0.0932662i
$125$	−8.28214	−	7.51040i	−0.740777	−	0.671751i
$126$	−2.65454	+	2.30017i	−0.236486	+	0.204916i
$127$	−0.490172	+	6.85350i	−0.0434957	+	0.608150i	0.928225	+	0.372018i	$0.121334\pi$
$127$	−0.490172	+	6.85350i	−0.0434957	+	0.608150i	−0.971721	+	0.236131i	$0.924120\pi$
$128$	0.877679	−	0.479249i	0.0775766	−	0.0423600i
$129$	2.10859	−	4.61717i	0.185651	−	0.406519i
$130$	−1.97646	+	9.85528i	−0.173347	+	0.864365i
$131$	−0.613957	+	0.180274i	−0.0536417	+	0.0157506i	−0.308443	−	0.951243i	$-0.599808\pi$
$131$	−0.613957	+	0.180274i	−0.0536417	+	0.0157506i	0.254802	+	0.966993i	$0.417990\pi$
$132$	4.42254	+	5.90782i	0.384932	+	0.514209i
$133$	−15.1364	−	5.64559i	−1.31249	−	0.489534i
$134$	0.996516	+	6.93092i	0.0860858	+	0.598740i
$135$	2.00226	+	12.4805i	0.172327	+	1.07415i
$136$	−3.33112	−	2.88643i	−0.285641	−	0.247510i
$137$	10.5132	−	10.5132i	0.898204	−	0.898204i	−0.0970734	−	0.995277i	$-0.530948\pi$
$137$	10.5132	−	10.5132i	0.898204	−	0.898204i	0.995277	+	0.0970734i	$0.0309482\pi$
$138$	5.47305	+	4.25090i	0.465897	+	0.361861i
$139$			3.84520i			0.326145i	0.986614	+	0.163073i	$0.0521405\pi$
$139$			3.84520i			0.326145i	−0.986614	+	0.163073i	$0.947859\pi$
$140$	3.70464	+	7.77461i	0.313099	+	0.657075i
$141$	8.33470	−	5.35638i	0.701908	−	0.451089i
$142$	−8.32425	+	11.1199i	−0.698555	+	0.933160i
$143$	−8.02278	+	21.5099i	−0.670899	+	1.79875i
$144$	0.902698	+	0.129788i	0.0752249	+	0.0108157i
$145$	−9.46508	+	7.32884i	−0.786032	+	0.608627i
$146$	3.80339	+	2.44429i	0.314771	+	0.202291i
$147$	10.6061	−	3.95587i	0.874777	−	0.326275i
$148$	−5.41632	−	9.91926i	−0.445219	−	0.815358i
$149$	−3.52322	−	4.06601i	−0.288633	−	0.333101i	0.592853	−	0.805311i	$-0.298002\pi$
$149$	−3.52322	−	4.06601i	−0.288633	−	0.333101i	−0.881486	+	0.472210i	$0.843456\pi$
$150$	7.18113	+	0.794922i	0.586337	+	0.0649051i
$151$	−7.50245	−	2.20292i	−0.610540	−	0.179271i	−0.0381771	−	0.999271i	$-0.512155\pi$
$151$	−7.50245	−	2.20292i	−0.610540	−	0.179271i	−0.572363	+	0.820000i	$0.693973\pi$
$152$	1.46583	+	3.93004i	0.118894	+	0.318768i
$153$	−0.854458	−	3.92788i	−0.0690789	−	0.317550i
$154$	5.54165	+	18.8731i	0.446559	+	1.52084i
$155$	5.44252	−	1.27706i	0.437154	−	0.102576i
$156$	−2.69833	−	5.90853i	−0.216040	−	0.473061i
$157$	0.322445	+	0.241379i	0.0257339	+	0.0192641i	0.612067	−	0.790806i	$-0.290338\pi$
$157$	0.322445	+	0.241379i	0.0257339	+	0.0192641i	−0.586333	+	0.810070i	$0.699429\pi$
$158$	4.90465	+	1.06694i	0.390193	+	0.0848813i
$159$	−8.66129	+	9.99566i	−0.686885	+	0.792707i
$160$	0.895669	−	2.04885i	0.0708088	−	0.161976i
$161$	9.70846	+	15.7138i	0.765134	+	1.23842i
$162$	−3.84125	−	3.84125i	−0.301797	−	0.301797i
$163$	−0.629208	−	8.79748i	−0.0492834	−	0.689072i	−0.960700	−	0.277588i	$-0.910465\pi$
$163$	−0.629208	−	8.79748i	−0.0492834	−	0.689072i	0.911417	−	0.411484i	$-0.134989\pi$
$164$	−2.67896	−	4.16855i	−0.209192	−	0.325509i
$165$	15.9068	+	4.39075i	1.23834	+	0.341819i
$166$	5.25374	−	2.39930i	0.407769	−	0.186222i
$167$	7.63271	−	5.71378i	0.590637	−	0.442145i	−0.261692	−	0.965151i	$-0.584280\pi$
$167$	7.63271	−	5.71378i	0.590637	−	0.442145i	0.852329	+	0.523006i	$0.175190\pi$
$168$	−4.88460	−	2.66719i	−0.376855	−	0.205778i
$169$	3.89617	−	6.06256i	0.299706	−	0.466351i
$170$	−9.84096	−	0.543019i	−0.754767	−	0.0416477i
$171$	−1.07771	+	3.67035i	−0.0824148	+	0.280679i
$172$	−3.50377	−	0.250594i	−0.267160	−	0.0191076i
$173$	−10.0270	−	0.717147i	−0.762340	−	0.0545237i	−0.315245	−	0.949010i	$-0.602087\pi$
$173$	−10.0270	−	0.717147i	−0.762340	−	0.0545237i	−0.447095	+	0.894486i	$0.647541\pi$
$174$	2.17942	−	7.42244i	0.165222	−	0.562693i
$175$	17.1932	+	8.67407i	1.29968	+	0.655698i
$176$	2.76112	−	4.29638i	0.208127	−	0.323852i
$177$	2.22201	+	1.21331i	0.167017	+	0.0911980i
$178$	0.351032	−	0.262780i	0.0263110	−	0.0196962i
$179$	−9.25832	+	4.22813i	−0.692000	+	0.316026i	−0.730189	−	0.683245i	$-0.760568\pi$
$179$	−9.25832	+	4.22813i	−0.692000	+	0.316026i	0.0381897	+	0.999271i	$0.487841\pi$
$180$	1.77366	−	1.00631i	0.132201	−	0.0750059i
$181$	−3.71637	−	5.78279i	−0.276236	−	0.429831i	0.675220	−	0.737616i	$-0.264049\pi$
$181$	−3.71637	−	5.78279i	−0.276236	−	0.429831i	−0.951456	+	0.307785i	$0.900412\pi$
$182$	−1.23510	−	17.2689i	−0.0915514	−	1.28006i
$183$	−1.61661	−	1.61661i	−0.119504	−	0.119504i
$184$	1.43270	−	4.57683i	0.105620	−	0.337408i
$185$	−23.1554	−	10.1226i	−1.70242	−	0.744226i
$186$	−2.36575	+	2.73022i	−0.173465	+	0.200190i
$187$	−21.9962	−	4.78499i	−1.60852	−	0.349913i
$188$	−5.48882	−	4.10888i	−0.400314	−	0.299671i
$189$	−9.04424	−	19.8041i	−0.657872	−	1.44054i
$190$	7.97176	+	4.94168i	0.578332	+	0.358507i
$191$	5.74928	+	19.5803i	0.416004	+	1.41678i	0.855158	+	0.518367i	$0.173460\pi$
$191$	5.74928	+	19.5803i	0.416004	+	1.41678i	−0.439155	+	0.898411i	$0.644722\pi$
$192$	0.307156	+	1.41198i	0.0221671	+	0.101901i
$193$	6.58201	+	17.6471i	0.473784	+	1.27026i	0.925719	+	0.378213i	$0.123461\pi$
$193$	6.58201	+	17.6471i	0.473784	+	1.27026i	−0.451935	+	0.892051i	$0.649266\pi$
$194$	17.0009	+	4.99190i	1.22059	+	0.358398i
$195$	−12.8594	−	6.75241i	−0.920879	−	0.483550i
$196$	−5.13005	−	5.92039i	−0.366432	−	0.422885i
$197$	5.59281	+	10.2425i	0.398471	+	0.729745i	0.997476	−	0.0709999i	$-0.0226190\pi$
$197$	5.59281	+	10.2425i	0.398471	+	0.729745i	−0.599005	+	0.800745i	$0.704437\pi$
$198$	4.36393	−	1.62766i	0.310131	−	0.115673i
$199$	−0.397392	−	0.255389i	−0.0281704	−	0.0181040i	0.526480	−	0.850188i	$-0.323512\pi$
$199$	−0.397392	−	0.255389i	−0.0281704	−	0.0181040i	−0.554650	+	0.832084i	$0.687148\pi$
$200$	−1.22128	−	4.84855i	−0.0863574	−	0.342845i
$201$	−10.0152	−	1.43996i	−0.706415	−	0.101567i
$202$	−3.54809	+	9.51280i	−0.249643	+	0.669318i
$203$	12.3564	−	16.5062i	0.867249	−	1.15851i
$204$	5.35805	−	3.44341i	0.375139	−	0.241087i
$205$	−10.4431	−	3.70261i	−0.729380	−	0.258602i
$206$			12.7306i			0.886984i
$207$	3.54736	−	2.55843i	0.246558	−	0.177823i
$208$	−3.17857	+	3.17857i	−0.220394	+	0.220394i
$209$	16.1895	+	14.0283i	1.11985	+	0.970358i
$210$	−12.2874	+	1.97129i	−0.847911	+	0.136032i
$211$	−1.59586	−	11.0995i	−0.109864	−	0.764119i	−0.968046	−	0.250774i	$-0.919315\pi$
$211$	−1.59586	−	11.0995i	−0.109864	−	0.764119i	0.858182	−	0.513346i	$-0.171594\pi$
$212$	8.57595	+	3.19867i	0.588999	+	0.219685i
$213$	−12.0285	−	16.0682i	−0.824180	−	1.10098i
$214$	−7.18453	+	2.10957i	−0.491125	+	0.144207i
$215$	−6.53778	+	4.35354i	−0.445873	+	0.296909i
$216$	−2.34826	+	5.14197i	−0.159779	+	0.349867i
$217$	−8.45113	+	4.61467i	−0.573700	+	0.313264i
$218$	−0.0631209	+	0.882546i	−0.00427509	+	0.0597735i
$219$	−4.93730	+	4.27819i	−0.333632	+	0.289093i
$220$	−0.999967	−	11.3760i	−0.0674178	−	0.766970i
$221$	18.0229	+	8.23079i	1.21235	+	0.553663i
$222$	15.9577	−	3.47139i	1.07101	−	0.232984i
$223$	8.51261	−	15.5897i	0.570047	−	1.04396i	−0.420566	−	0.907262i	$-0.638168\pi$
$223$	8.51261	−	15.5897i	0.570047	−	1.04396i	0.990612	−	0.136700i	$-0.0436498\pi$
$224$	−0.548121	+	3.81226i	−0.0366229	+	0.254718i
$225$	1.75825	−	4.20729i	0.117217	−	0.280486i
$226$	12.6864	−	1.82403i	0.843889	−	0.121333i
$227$	2.12248	−	9.75689i	0.140874	−	0.647587i	−0.851503	−	0.524350i	$-0.824309\pi$
$227$	2.12248	−	9.75689i	0.140874	−	0.647587i	0.992377	−	0.123238i	$-0.0393278\pi$
$228$	−6.04560	+	0.432390i	−0.400380	+	0.0286357i
$229$	5.61257			0.370889			0.185445	−	0.982655i	$-0.440628\pi$
$229$	5.61257			0.370889			0.185445	+	0.982655i	$0.440628\pi$
$230$	−3.73256	−	10.0533i	−0.246118	−	0.662892i
$231$	−28.4230			−1.87009
$232$	−5.33986	+	0.381914i	−0.350579	+	0.0250739i
$233$	−0.145944	+	0.670892i	−0.00956109	+	0.0439516i	−0.981680	−	0.190536i	$-0.938977\pi$
$233$	−0.145944	+	0.670892i	−0.00956109	+	0.0439516i	0.972119	+	0.234487i	$0.0753411\pi$
$234$	−4.05779	+	0.583421i	−0.265266	+	0.0381395i
$235$	−15.3293	+	0.249526i	−0.999975	+	0.0162773i
$236$	0.249341	−	1.73421i	0.0162307	−	0.112887i
$237$	−3.47598	+	6.36578i	−0.225789	+	0.413502i
$238$	16.5882	−	3.60854i	1.07525	−	0.233907i
$239$	−23.0154	−	10.5108i	−1.48874	−	0.679885i	−0.505605	−	0.862765i	$-0.668730\pi$
$239$	−23.0154	−	10.5108i	−1.48874	−	0.679885i	−0.983135	+	0.182881i	$0.941458\pi$
$240$	2.47603	+	2.07591i	0.159827	+	0.133999i
$241$	−17.2841	+	14.9768i	−1.11337	+	0.964740i	−0.999586	−	0.0287653i	$-0.990842\pi$
$241$	−17.2841	+	14.9768i	−1.11337	+	0.964740i	−0.113783	+	0.993506i	$0.536297\pi$
$242$	1.07598	−	15.0442i	0.0691669	−	0.967080i
$243$	−7.99450	+	4.36533i	−0.512847	+	0.280036i
$244$	−0.657259	+	1.43920i	−0.0420767	+	0.0921351i
$245$	−17.1749	−	3.44441i	−1.09727	−	0.220055i
$246$	6.87016	−	2.01726i	0.438026	−	0.128616i
$247$	−11.2994	−	15.0942i	−0.718963	−	0.960421i
$248$	2.34245	+	0.873687i	0.148745	+	0.0554792i
$249$	1.18774	+	8.26088i	0.0752697	+	0.523512i
$250$	−8.79683	−	6.90042i	−0.556360	−	0.436421i
$251$	−13.7987	−	11.9567i	−0.870968	−	0.754698i	0.0997266	−	0.995015i	$-0.468203\pi$
$251$	−13.7987	−	11.9567i	−0.870968	−	0.754698i	−0.970694	+	0.240317i	$0.922749\pi$
$252$	−2.48369	+	2.48369i	−0.156458	+	0.156458i
$253$	−4.78021	−	24.0219i	−0.300529	−	1.51024i
$254$			6.87101i			0.431125i
$255$	4.75916	−	13.4231i	0.298030	−	0.840586i
$256$	0.841254	−	0.540641i	0.0525783	−	0.0337901i
$257$	0.948666	−	1.26727i	0.0591761	−	0.0790501i	−0.769977	−	0.638072i	$-0.779732\pi$
$257$	0.948666	−	1.26727i	0.0591761	−	0.0790501i	0.829153	+	0.559022i	$0.188823\pi$
$258$	1.77383	−	4.75584i	0.110434	−	0.296085i
$259$	43.0850	+	6.19469i	2.67717	+	0.384919i
$260$	−1.26836	+	9.97117i	−0.0786604	+	0.618386i
$261$	−4.10724	−	2.63956i	−0.254232	−	0.163385i
$262$	−0.599532	+	0.223614i	−0.0370392	+	0.0138149i
$263$	−6.15569	−	11.2733i	−0.379576	−	0.695142i	0.616137	−	0.787639i	$-0.288697\pi$
$263$	−6.15569	−	11.2733i	−0.379576	−	0.695142i	−0.995713	+	0.0924973i	$0.970515\pi$
$264$	4.83273	+	5.57726i	0.297434	+	0.343257i
$265$	19.5414	−	6.08503i	1.20042	−	0.373801i
$266$	−15.5006	−	4.55138i	−0.950402	−	0.279063i
$267$	0.221428	+	0.593673i	0.0135512	+	0.0363322i
$268$	1.48842	+	6.84217i	0.0909199	+	0.417952i
$269$	2.85068	+	9.70853i	0.173809	+	0.591940i	0.999609	+	0.0279757i	$0.00890610\pi$
$269$	2.85068	+	9.70853i	0.173809	+	0.591940i	−0.825799	+	0.563964i	$0.809276\pi$
$270$	2.88750	+	12.3058i	0.175728	+	0.748909i
$271$	3.17455	+	6.95130i	0.192840	+	0.422262i	0.981211	−	0.192939i	$-0.0618021\pi$
$271$	3.17455	+	6.95130i	0.192840	+	0.422262i	−0.788370	+	0.615201i	$0.789075\pi$
$272$	−3.52855	−	2.64144i	−0.213950	−	0.160161i
$273$	24.4455	+	5.31780i	1.47951	+	0.321848i
$274$	9.73642	−	11.2364i	0.588198	−	0.678817i
$275$	−17.3415	−	18.7440i	−1.04573	−	1.13031i
$276$	5.76236	+	3.84963i	0.346853	+	0.231721i
$277$	−10.3080	−	10.3080i	−0.619350	−	0.619350i	0.326015	−	0.945365i	$-0.394294\pi$
$277$	−10.3080	−	10.3080i	−0.619350	−	0.619350i	−0.945365	+	0.326015i	$0.894294\pi$
$278$	0.274313	+	3.83540i	0.0164522	+	0.230032i
$279$	1.23267	+	1.91808i	0.0737982	+	0.114832i
$280$	4.24984	+	7.49052i	0.253976	+	0.447644i
$281$	22.0711	−	10.0795i	1.31665	−	0.601295i	0.371654	−	0.928371i	$-0.378791\pi$
$281$	22.0711	−	10.0795i	1.31665	−	0.601295i	0.944998	+	0.327077i	$0.106064\pi$
$282$	7.93134	−	5.93733i	0.472304	−	0.353563i
$283$	1.41902	+	0.774842i	0.0843519	+	0.0460596i	0.520871	−	0.853635i	$-0.325607\pi$
$283$	1.41902	+	0.774842i	0.0843519	+	0.0460596i	−0.436519	+	0.899695i	$0.643789\pi$
$284$	−7.50975	+	11.6854i	−0.445622	+	0.693401i
$285$	−10.0968	+	9.04079i	−0.598083	+	0.535530i
$286$	−6.46784	+	22.0274i	−0.382452	+	1.30251i
$287$	19.0360	+	1.36148i	1.12366	+	0.0803658i
$288$	0.909657	+	0.0650600i	0.0536021	+	0.00383370i
$289$	−0.684014	+	2.32954i	−0.0402361	+	0.137032i
$290$	−8.91813	+	7.98540i	−0.523690	+	0.468919i
$291$	−13.8422	+	21.5389i	−0.811444	+	1.26263i
$292$	3.96808	+	2.16673i	0.232214	+	0.126798i
$293$	−5.15522	+	3.85915i	−0.301171	+	0.225454i	−0.739166	−	0.673524i	$-0.764780\pi$
$293$	−5.15522	+	3.85915i	−0.301171	+	0.225454i	0.437994	+	0.898978i	$0.355689\pi$
$294$	10.2969	−	4.70242i	0.600526	−	0.274251i
$295$	−1.93326	−	3.40745i	−0.112559	−	0.198389i
$296$	−6.11016	−	9.50759i	−0.355146	−	0.552617i
$297$	2.05953	+	28.7960i	0.119506	+	1.67091i
$298$	−3.80431	−	3.80431i	−0.220378	−	0.220378i
$299$	−0.383097	+	21.5547i	−0.0221551	+	1.24654i
$300$	7.21954	+	0.280601i	0.416820	+	0.0162005i
$301$	8.85969	−	10.2246i	0.510664	−	0.589338i
$302$	−7.64048	−	1.66209i	−0.439660	−	0.0956423i
$303$	−11.7447	−	8.79200i	−0.674717	−	0.505087i
$304$	1.74246	+	3.81545i	0.0999368	+	0.218831i
$305$	0.808189	+	3.44430i	0.0462768	+	0.197220i
$306$	−1.13249	−	3.85692i	−0.0647403	−	0.220485i
$307$	0.465897	+	2.14169i	0.0265901	+	0.122233i	0.988529	−	0.151033i	$-0.0482599\pi$
$307$	0.465897	+	2.14169i	0.0265901	+	0.122233i	−0.961939	+	0.273266i	$0.911896\pi$
$308$	6.87392	+	18.4297i	0.391678	+	1.05013i
$309$	−17.6506	−	5.18267i	−1.00411	−	0.294832i
$310$	5.33755	−	1.66207i	0.303152	−	0.0943994i
$311$	12.6206	+	14.5650i	0.715651	+	0.825905i	0.990777	−	0.135503i	$-0.0432651\pi$
$311$	12.6206	+	14.5650i	0.715651	+	0.825905i	−0.275126	+	0.961408i	$0.588720\pi$
$312$	−3.11297	−	5.70098i	−0.176237	−	0.322754i
$313$	4.72074	−	1.76074i	0.266832	−	0.0995231i	−0.212487	−	0.977164i	$-0.568156\pi$
$313$	4.72074	−	1.76074i	0.266832	−	0.0995231i	0.479319	+	0.877641i	$0.340884\pi$
$314$	0.338843	+	0.217761i	0.0191220	+	0.0122890i
$315$	−0.991079	+	7.79133i	−0.0558410	+	0.438992i
$316$	4.96827	+	0.714329i	0.279487	+	0.0401842i
$317$	0.917304	−	2.45939i	0.0515209	−	0.138133i	−0.908640	−	0.417580i	$-0.862878\pi$
$317$	0.917304	−	2.45939i	0.0515209	−	0.138133i	0.960161	+	0.279447i	$0.0901511\pi$
$318$	−7.92614	+	10.5881i	−0.444476	+	0.593750i
$319$	−23.0007	+	14.7816i	−1.28779	+	0.827612i
$320$	0.747224	−	2.10752i	0.0417711	−	0.117814i
$321$		−	10.8199i		−	0.603909i
$322$	10.8047	+	14.9812i	0.602124	+	0.834867i
$323$	13.0731	−	13.0731i	0.727406	−	0.727406i
$324$	−4.10549	−	3.55743i	−0.228083	−	0.197635i
$325$	11.4079	+	19.3656i	0.632795	+	1.07421i
$326$	−1.25521	−	8.73017i	−0.0695196	−	0.483520i
$327$	−1.19792	−	0.446802i	−0.0662452	−	0.0247082i
$328$	−2.96952	−	3.96681i	−0.163964	−	0.219031i
$329$	25.3375	−	7.43976i	1.39690	−	0.410167i
$330$	16.1795	+	3.24478i	0.890653	+	0.178619i
$331$	1.40492	−	3.07634i	0.0772213	−	0.169091i	−0.867084	−	0.498162i	$-0.834008\pi$
$331$	1.40492	−	3.07634i	0.0772213	−	0.169091i	0.944305	+	0.329071i	$0.106736\pi$
$332$	5.06919	−	2.76798i	0.278208	−	0.151913i
$333$	0.735288	−	10.2807i	0.0402935	−	0.563377i
$334$	7.20565	−	6.24373i	0.394276	−	0.341642i
$335$	11.9984	+	10.0595i	0.655541	+	0.549607i
$336$	−5.06243	−	2.31193i	−0.276178	−	0.126126i
$337$	21.8378	−	4.75052i	1.18958	−	0.258777i	0.426140	−	0.904657i	$-0.359873\pi$
$337$	21.8378	−	4.75052i	1.18958	−	0.258777i	0.763439	+	0.645880i	$0.223509\pi$
$338$	3.45375	−	6.32507i	0.187859	−	0.344038i
$339$	−2.63572	+	18.3319i	−0.143153	+	0.995650i
$340$	−9.85463	+	0.160411i	−0.534442	+	0.00869949i
$341$	12.6382	−	1.81710i	0.684398	−	0.0984016i
$342$	−0.813127	+	3.73788i	−0.0439689	+	0.202122i
$343$	3.20316	−	0.229094i	0.172954	−	0.0123699i
$344$	−3.51272			−0.189393
$345$	15.4580	−	1.08235i	0.832232	−	0.0582719i
$346$	−10.0526			−0.540433
$347$	11.9897	−	0.857522i	0.643642	−	0.0460342i	0.254297	−	0.967126i	$-0.418156\pi$
$347$	11.9897	−	0.857522i	0.643642	−	0.0460342i	0.389345	+	0.921092i	$0.372701\pi$
$348$	1.64436	−	7.55900i	0.0881470	−	0.405205i
$349$	−29.6320	+	4.26044i	−1.58617	+	0.228056i	−0.878236	−	0.478227i	$-0.841279\pi$
$349$	−29.6320	+	4.26044i	−1.58617	+	0.228056i	−0.707929	+	0.706284i	$0.750370\pi$
$350$	17.7682	+	7.42542i	0.949749	+	0.396906i
$351$	3.61627	−	25.1517i	0.193022	−	1.34250i
$352$	2.44758	−	4.48241i	0.130457	−	0.238913i
$353$	−6.08765	+	1.32429i	−0.324013	+	0.0704847i	−0.371630	−	0.928381i	$-0.621201\pi$
$353$	−6.08765	+	1.32429i	−0.324013	+	0.0704847i	0.0476169	+	0.998866i	$0.484837\pi$
$354$	2.30291	+	1.05170i	0.122398	+	0.0558974i
$355$	2.71973	+	30.9407i	0.144348	+	1.64216i
$356$	0.331392	−	0.287152i	0.0175637	−	0.0152190i
$357$	−1.74998	+	24.4680i	−0.0926190	+	1.29498i
$358$	−8.93310	+	4.87784i	−0.472129	+	0.257802i
$359$	−7.43931	+	16.2898i	−0.392632	+	0.859743i	0.605333	+	0.795972i	$0.293040\pi$
$359$	−7.43931	+	16.2898i	−0.392632	+	0.859743i	−0.997965	+	0.0637709i	$0.979687\pi$
$360$	1.69736	−	1.13028i	0.0894585	−	0.0595709i
$361$	1.34921	−	0.396164i	0.0710111	−	0.0208507i
$362$	−4.11944	−	5.50293i	−0.216513	−	0.289228i
$363$	20.4203	+	7.61637i	1.07179	+	0.399756i
$364$	−2.46390	−	17.1368i	−0.129143	−	0.898212i
$365$	9.98185	−	1.60140i	0.522474	−	0.0838212i
$366$	−1.72782	−	1.49717i	−0.0903148	−	0.0782582i
$367$	11.5504	−	11.5504i	0.602925	−	0.602925i	−0.338163	−	0.941088i	$-0.609806\pi$
$367$	11.5504	−	11.5504i	0.602925	−	0.602925i	0.941088	+	0.338163i	$0.109806\pi$
$368$	1.10254	−	4.66738i	0.0574740	−	0.243304i
$369$		−	4.51901i		−	0.235251i
$370$	−23.8186	−	8.44489i	−1.23827	−	0.439029i
$371$	−29.6565	+	19.0590i	−1.53969	+	0.989496i
$372$	−2.16495	+	2.89204i	−0.112248	+	0.149945i
$373$	7.70269	−	20.6517i	0.398830	−	1.06931i	−0.570014	−	0.821635i	$-0.693062\pi$
$373$	7.70269	−	20.6517i	0.398830	−	1.06931i	0.968844	−	0.247670i	$-0.0796649\pi$
$374$	−22.2816	−	3.20360i	−1.15215	−	0.165654i
$375$	13.1484	−	9.38731i	0.678981	−	0.484759i
$376$	−5.76796	−	3.70684i	−0.297460	−	0.191166i
$377$	22.5476	−	8.40982i	1.16126	−	0.433128i
$378$	−10.4340	−	19.1085i	−0.536668	−	0.982833i
$379$	8.62258	+	9.95099i	0.442912	+	0.511148i	0.932680	−	0.360705i	$-0.117464\pi$
$379$	8.62258	+	9.95099i	0.442912	+	0.511148i	−0.489768	+	0.871853i	$0.662918\pi$
$380$	8.30398	+	4.36039i	0.425985	+	0.223683i
$381$	−9.52641	−	2.79721i	−0.488053	−	0.143305i
$382$	7.13148	+	19.1202i	0.364878	+	0.978276i
$383$	2.59036	+	11.9077i	0.132361	+	0.608456i	0.994761	+	0.102227i	$0.0325970\pi$
$383$	2.59036	+	11.9077i	0.132361	+	0.608456i	−0.862400	+	0.506228i	$0.831039\pi$
$384$	0.407103	+	1.38647i	0.0207749	+	0.0707528i
$385$	37.3832	+	23.1738i	1.90522	+	1.18104i
$386$	7.82417	+	17.1325i	0.398240	+	0.872024i
$387$	−2.56456	−	1.91981i	−0.130364	−	0.0975892i
$388$	17.3137	+	3.76636i	0.878968	+	0.191208i
$389$	2.84672	−	3.28529i	0.144335	−	0.166571i	−0.678979	−	0.734158i	$-0.737577\pi$
$389$	2.84672	−	3.28529i	0.144335	−	0.166571i	0.823314	+	0.567587i	$0.192123\pi$
$390$	−13.3083	−	5.81783i	−0.673893	−	0.294597i
$391$	−20.9736	+	2.63605i	−1.06068	+	0.133311i
$392$	−5.53933	−	5.53933i	−0.279778	−	0.279778i
$393$	−0.0659617	−	0.922265i	−0.00332733	−	0.0465221i
$394$	6.30925	+	9.81738i	0.317855	+	0.494592i
$395$	9.76190	−	5.53853i	0.491174	−	0.278674i
$396$	4.23670	−	1.93483i	0.212902	−	0.0972291i
$397$	13.4797	−	10.0908i	0.676526	−	0.506441i	−0.204888	−	0.978785i	$-0.565683\pi$
$397$	13.4797	−	10.0908i	0.676526	−	0.506441i	0.881414	+	0.472345i	$0.156592\pi$
$398$	−0.414599	−	0.226388i	−0.0207820	−	0.0113478i
$399$	12.6207	−	19.6381i	0.631824	−	0.983137i
$400$	−1.56406	−	4.74908i	−0.0782029	−	0.237454i
$401$	−2.04021	+	6.94831i	−0.101883	+	0.346982i	−0.994619	−	0.103598i	$-0.966964\pi$
$401$	−2.04021	+	6.94831i	−0.101883	+	0.346982i	0.892736	+	0.450580i	$0.148783\pi$
$402$	−10.0924	−	0.721821i	−0.503362	−	0.0360011i
$403$	−11.2096	−	0.801729i	−0.558392	−	0.0399370i
$404$	−2.86042	+	9.74168i	−0.142311	+	0.484667i
$405$	−12.1286	−	0.669252i	−0.602677	−	0.0332554i
$406$	11.1474	−	17.3456i	0.553235	−	0.860850i
$407$	−50.6588	−	27.6618i	−2.51106	−	1.37115i
$408$	5.09875	−	3.81688i	0.252426	−	0.188964i
$409$	28.4597	−	12.9971i	1.40724	−	0.642667i	0.440346	−	0.897828i	$-0.354856\pi$
$409$	28.4597	−	12.9971i	1.40724	−	0.642667i	0.966898	+	0.255162i	$0.0821286\pi$
$410$	−10.6807	−	2.94818i	−0.527480	−	0.145600i
$411$	11.6152	+	18.0736i	0.572935	+	0.891504i
$412$	0.908192	+	12.6982i	0.0447434	+	0.625595i
$413$	4.77150	+	4.77150i	0.234790	+	0.234790i
$414$	3.35580	−	2.80498i	0.164929	−	0.137857i
$415$	5.17309	−	11.8335i	0.253937	−	0.580882i
$416$	−2.94371	+	3.39723i	−0.144327	+	0.166563i
$417$	−5.42933	−	1.18108i	−0.265875	−	0.0578376i
$418$	17.1490	+	12.8376i	0.838787	+	0.627908i
$419$	−7.16464	−	15.6884i	−0.350015	−	0.766427i	−0.999979	−	0.00646156i	$-0.997943\pi$
$419$	−7.16464	−	15.6884i	−0.350015	−	0.766427i	0.649964	−	0.759965i	$-0.274784\pi$
$420$	−12.1155	+	2.84284i	−0.591174	+	0.138716i
$421$	1.30723	+	4.45201i	0.0637104	+	0.216978i	0.985195	−	0.171437i	$-0.0548410\pi$
$421$	1.30723	+	4.45201i	0.0637104	+	0.216978i	−0.921485	+	0.388415i	$0.873023\pi$
$422$	−2.38363	−	10.9573i	−0.116033	−	0.533395i
$423$	−2.18516	−	5.85865i	−0.106246	−	0.284857i
$424$	8.78229	+	2.57871i	0.426506	+	0.125233i
$425$	−17.2036	+	13.7744i	−0.834495	+	0.668158i
$426$	−13.1442	−	15.1692i	−0.636837	−	0.734949i
$427$	−2.92040	−	5.34830i	−0.141328	−	0.258823i
$428$	−7.01573	+	2.61673i	−0.339118	+	0.126485i
$429$	−27.9072	−	17.9349i	−1.34737	−	0.865904i
$430$	−6.21055	+	4.80885i	−0.299499	+	0.231903i
$431$	13.5950	+	1.95467i	0.654849	+	0.0941530i	0.461727	−	0.887022i	$-0.347230\pi$
$431$	13.5950	+	1.95467i	0.654849	+	0.0941530i	0.193121	+	0.981175i	$0.438139\pi$
$432$	−1.97545	+	5.29639i	−0.0950440	+	0.254823i
$433$	−20.1567	+	26.9262i	−0.968670	+	1.29399i	−0.0128880	+	0.999917i	$0.504102\pi$
$433$	−20.1567	+	26.9262i	−0.968670	+	1.29399i	−0.955782	+	0.294075i	$0.904988\pi$
$434$	−8.10040	+	5.20581i	−0.388831	+	0.249887i
$435$	−7.44088	−	15.6156i	−0.356763	−	0.748708i
$436$			0.884800i			0.0423742i
$437$	18.7199	+	7.36369i	0.895494	+	0.352253i
$438$	−4.61952	+	4.61952i	−0.220729	+	0.220729i
$439$	21.5579	+	18.6800i	1.02890	+	0.891548i	0.994167	−	0.107848i	$-0.0343961\pi$
$439$	21.5579	+	18.6800i	1.02890	+	0.891548i	0.0347342	+	0.999397i	$0.488942\pi$
$440$	−1.80897	−	11.2757i	−0.0862394	−	0.537547i
$441$	−1.01674	−	7.07155i	−0.0484160	−	0.336741i
$442$	18.5642	+	6.92408i	0.883007	+	0.329345i
$443$	−17.7674	−	23.7345i	−0.844154	−	1.12766i	−0.990376	−	0.138406i	$-0.955802\pi$
$443$	−17.7674	−	23.7345i	−0.844154	−	1.12766i	0.146222	−	0.989252i	$-0.453289\pi$
$444$	15.6694	−	4.60095i	0.743637	−	0.218352i
$445$	0.192800	−	0.961360i	0.00913958	−	0.0455728i
$446$	7.37877	−	16.1572i	0.349395	−	0.765068i
$447$	6.82329	−	3.72580i	0.322730	−	0.176224i
$448$	−0.274760	+	3.84165i	−0.0129812	+	0.181501i
$449$	−3.17308	+	2.74949i	−0.149747	+	0.129756i	−0.726512	−	0.687153i	$-0.758860\pi$
$449$	−3.17308	+	2.74949i	−0.149747	+	0.129756i	0.576766	+	0.816910i	$0.304315\pi$
$450$	1.45363	−	4.32200i	0.0685246	−	0.203741i
$451$	−23.0197	−	10.5127i	−1.08396	−	0.495026i
$452$	12.5240	−	2.72443i	0.589079	−	0.128146i
$453$	5.41489	−	9.91663i	0.254414	−	0.465924i
$454$	1.42103	−	9.88345i	0.0666920	−	0.463853i
$455$	−27.8162	−	26.9251i	−1.30404	−	1.26227i
$456$	−5.99935	+	0.862576i	−0.280945	+	0.0403938i
$457$	−5.59726	+	25.7302i	−0.261829	+	1.20361i	0.638922	+	0.769271i	$0.279381\pi$
$457$	−5.59726	+	25.7302i	−0.261829	+	1.20361i	−0.900751	+	0.434336i	$0.856983\pi$
$458$	5.59827	−	0.400396i	0.261590	−	0.0187093i
$459$	24.9159			1.16297
$460$	−4.44024	−	9.76137i	−0.207027	−	0.455126i
$461$	−3.34945			−0.156000			−0.0779998	−	0.996953i	$-0.524853\pi$
$461$	−3.34945			−0.156000			−0.0779998	+	0.996953i	$0.524853\pi$
$462$	−28.3505	+	2.02767i	−1.31899	+	0.0943358i
$463$	−7.89723	+	36.3030i	−0.367015	+	1.68714i	0.309649	+	0.950851i	$0.399788\pi$
$463$	−7.89723	+	36.3030i	−0.367015	+	1.68714i	−0.676665	+	0.736291i	$0.736575\pi$
$464$	−5.29900	+	0.761882i	−0.246000	+	0.0353695i
$465$	0.131474	+	8.07696i	0.00609697	+	0.374560i
$466$	−0.0977109	+	0.679594i	−0.00452637	+	0.0314816i
$467$	−16.1526	+	29.5812i	−0.747452	+	1.36886i	0.175709	+	0.984442i	$0.443778\pi$
$467$	−16.1526	+	29.5812i	−0.747452	+	1.36886i	−0.923161	+	0.384414i	$0.874404\pi$
$468$	−4.00583	+	0.871414i	−0.185169	+	0.0402811i
$469$	−24.5316	−	11.2032i	−1.13276	−	0.517316i
$470$	−15.2725	+	1.34247i	−0.704466	+	0.0619236i
$471$	−0.439862	+	0.381143i	−0.0202678	+	0.0175621i
$472$	0.124989	−	1.74757i	0.00575309	−	0.0804387i
$473$	−15.7454	+	8.59766i	−0.723976	+	0.395321i
$474$	−3.01299	+	6.59753i	−0.138391	+	0.303035i
$475$	20.6509	−	3.65876i	0.947528	−	0.167875i
$476$	16.2885	−	4.78273i	0.746581	−	0.219216i
$477$	5.00242	+	6.68245i	0.229045	+	0.305968i
$478$	−23.7065	−	8.84208i	−1.08431	−	0.404428i
$479$	−5.77308	−	40.1527i	−0.263779	−	1.83462i	−0.503758	−	0.863845i	$-0.668050\pi$
$479$	−5.77308	−	40.1527i	−0.263779	−	1.83462i	0.239980	−	0.970778i	$-0.422859\pi$
$480$	2.61781	+	1.89398i	0.119486	+	0.0864479i
$481$	38.3944	+	33.2689i	1.75063	+	1.51693i
$482$	−16.1717	+	16.1717i	−0.736600	+	0.736600i
$483$	−25.1695	+	8.88152i	−1.14525	+	0.404123i
$484$		−	15.0827i		−	0.685576i
$485$	35.7669	−	17.0431i	1.62409	−	0.773888i
$486$	−7.66271	+	4.92453i	−0.347588	+	0.223381i
$487$	−17.4840	+	23.3558i	−0.792274	+	1.05835i	0.204561	+	0.978854i	$0.434423\pi$
$487$	−17.4840	+	23.3558i	−0.792274	+	1.05835i	−0.996835	+	0.0794998i	$0.974668\pi$
$488$	−0.552913	+	1.48242i	−0.0250292	+	0.0671059i
$489$	12.6151	+	1.81378i	0.570474	+	0.0820217i
$490$	−17.3769	−	2.21039i	−0.785007	−	0.0998552i
$491$	6.97129	+	4.48018i	0.314610	+	0.202188i	0.688410	−	0.725322i	$-0.258309\pi$
$491$	6.97129	+	4.48018i	0.314610	+	0.202188i	−0.373800	+	0.927509i	$0.621945\pi$
$492$	6.70875	−	2.50223i	0.302454	−	0.112809i
$493$	11.3087	+	20.7103i	0.509317	+	0.932744i
$494$	−12.3474	−	14.2497i	−0.555536	−	0.641123i
$495$	4.84180	−	9.22079i	0.217623	−	0.414444i
$496$	2.39881	+	0.704353i	0.107710	+	0.0316264i
$497$	−18.6959	−	50.1256i	−0.838624	−	2.24844i
$498$	1.77403	+	8.15510i	0.0794964	+	0.365439i
$499$	4.12780	+	14.0580i	0.184786	+	0.629323i	0.998823	+	0.0485095i	$0.0154471\pi$
$499$	4.12780	+	14.0580i	0.184786	+	0.629323i	−0.814037	+	0.580813i	$0.802735\pi$
$500$	−9.26668	−	6.25528i	−0.414419	−	0.279745i
$501$	5.72327	+	12.5322i	0.255697	+	0.559898i
$502$	−14.6165	−	10.9418i	−0.652368	−	0.488357i
$503$	−16.8711	−	3.67008i	−0.752245	−	0.163641i	−0.179935	−	0.983678i	$-0.557589\pi$
$503$	−16.8711	−	3.67008i	−0.752245	−	0.163641i	−0.572310	+	0.820038i	$0.693952\pi$
$504$	−2.30017	+	2.65454i	−0.102458	+	0.118243i
$505$	8.27893	+	21.1393i	0.368407	+	0.940688i
$506$	−6.48173	−	23.6197i	−0.288148	−	1.05002i
$507$	7.36345	+	7.36345i	0.327022	+	0.327022i
$508$	0.490172	+	6.85350i	0.0217479	+	0.304075i
$509$	−5.21621	−	8.11659i	−0.231205	−	0.359761i	0.706195	−	0.708018i	$-0.250410\pi$
$509$	−5.21621	−	8.11659i	−0.231205	−	0.359761i	−0.937399	+	0.348256i	$0.886774\pi$
$510$	3.78944	−	13.7284i	0.167799	−	0.607904i
$511$	−15.8393	+	7.23357i	−0.700689	+	0.319994i
$512$	0.800541	−	0.599278i	0.0353793	−	0.0264846i
$513$	−20.8104	−	11.3633i	−0.918800	−	0.501703i
$514$	0.855843	−	1.33172i	0.0377496	−	0.0587395i
$515$	18.9893	+	21.2073i	0.836768	+	0.934506i
$516$	1.43004	−	4.87026i	0.0629539	−	0.214401i
$517$	−34.9272	−	2.49804i	−1.53610	−	0.109864i
$518$	43.4172	+	3.10526i	1.90764	+	0.136437i
$519$	4.09246	−	13.9376i	0.179639	−	0.611794i
$520$	−0.553795	+	10.0362i	−0.0242855	+	0.440118i
$521$	9.24888	−	14.3915i	0.405201	−	0.630505i	−0.577350	−	0.816496i	$-0.695913\pi$
$521$	9.24888	−	14.3915i	0.405201	−	0.630505i	0.982551	+	0.185992i	$0.0595497\pi$
$522$	−4.28508	−	2.33983i	−0.187553	−	0.102412i
$523$	−2.33112	+	1.74505i	−0.101933	+	0.0763058i	−0.649028	−	0.760764i	$-0.724824\pi$
$523$	−2.33112	+	1.74505i	−0.101933	+	0.0763058i	0.547096	+	0.837070i	$0.315733\pi$
$524$	−0.582052	+	0.265814i	−0.0254271	+	0.0116122i
$525$	−17.5286	+	21.6120i	−0.765009	+	0.943227i
$526$	−6.94424	−	10.8054i	−0.302783	−	0.471140i
$527$	−0.786129	−	10.9915i	−0.0342443	−	0.478798i
$528$	5.21829	+	5.21829i	0.227097	+	0.227097i
$529$	−11.7393	−	19.7785i	−0.510405	−	0.859934i
$530$	19.0575	−	7.46359i	0.827803	−	0.324198i
$531$	1.04635	−	1.20756i	0.0454079	−	0.0524035i
$532$	−15.7858	−	3.43399i	−0.684401	−	0.148882i
$533$	17.8315	+	13.3485i	0.772368	+	0.578188i
$534$	0.263216	+	0.576363i	0.0113905	+	0.0249417i
$535$	−8.82168	+	14.2308i	−0.381394	+	0.615253i
$536$	1.97274	+	6.71855i	0.0852096	+	0.290197i
$537$	−3.12627	−	14.3712i	−0.134908	−	0.620164i
$538$	3.53602	+	9.48043i	0.152449	+	0.408730i
$539$	−38.3875	−	11.2716i	−1.65347	−	0.485502i
$540$	3.75803	+	12.0685i	0.161720	+	0.519345i
$541$	21.9485	+	25.3299i	0.943641	+	1.08902i	0.995907	+	0.0903862i	$0.0288102\pi$
$541$	21.9485	+	25.3299i	0.943641	+	1.08902i	−0.0522661	+	0.998633i	$0.516644\pi$
$542$	3.66237	+	6.70712i	0.157312	+	0.288096i
$543$	9.30666	−	3.47120i	0.399387	−	0.148964i
$544$	−3.70800	−	2.38299i	−0.158979	−	0.102170i
$545$	1.21128	+	1.56434i	0.0518853	+	0.0670091i
$546$	24.7626	+	3.56033i	1.05974	+	0.152368i
$547$	0.556656	−	1.49245i	0.0238009	−	0.0638126i	−0.924506	−	0.381168i	$-0.875522\pi$
$547$	0.556656	−	1.49245i	0.0238009	−	0.0638126i	0.948307	+	0.317355i	$0.102795\pi$
$548$	8.91001	−	11.9024i	0.380617	−	0.508445i
$549$	−1.21386	+	0.780097i	−0.0518061	+	0.0332937i
$550$	−18.6345	−	17.4591i	−0.794578	−	0.744461i
$551$		−	22.4552i		−	0.956625i
$552$	6.02231	+	3.42874i	0.256326	+	0.145937i
$553$	−13.6697	+	13.6697i	−0.581295	+	0.581295i
$554$	−11.0171	−	9.54640i	−0.468073	−	0.405588i
$555$	21.4052	−	29.5857i	0.908599	−	1.25584i
$556$	0.547229	+	3.80606i	0.0232077	+	0.161413i
$557$	−15.8499	−	5.91169i	−0.671580	−	0.250486i	−0.00953951	−	0.999954i	$-0.503037\pi$
$557$	−15.8499	−	5.91169i	−0.671580	−	0.250486i	−0.662040	+	0.749468i	$0.730309\pi$
$558$	1.36637	+	1.82525i	0.0578429	+	0.0772690i
$559$	15.1507	−	4.44863i	0.640805	−	0.188157i
$560$	4.77337	+	7.16825i	0.201712	+	0.302914i
$561$	13.5126	−	29.5884i	0.570501	−	1.24922i
$562$	21.2958	−	11.6284i	0.898309	−	0.490514i
$563$	−0.271151	+	3.79119i	−0.0114277	+	0.159780i	0.988534	+	0.151000i	$0.0482493\pi$
$563$	−0.271151	+	3.79119i	−0.0114277	+	0.159780i	−0.999961	+	0.00877976i	$0.997205\pi$
$564$	7.48757	−	6.48801i	0.315283	−	0.273195i
$565$	18.4129	−	21.9619i	0.774638	−	0.923946i
$566$	1.47068	+	0.671637i	0.0618173	+	0.0282310i
$567$	20.4444	−	4.44740i	0.858583	−	0.186773i
$568$	−6.65699	+	12.1914i	−0.279321	+	0.511539i
$569$	5.78489	−	40.2348i	0.242515	−	1.68673i	−0.396896	−	0.917864i	$-0.629913\pi$
$569$	5.78489	−	40.2348i	0.242515	−	1.68673i	0.639411	−	0.768865i	$-0.279178\pi$
$570$	−9.42611	+	9.73806i	−0.394816	+	0.407882i
$571$	21.1134	−	3.03564i	0.883567	−	0.127038i	0.314430	−	0.949281i	$-0.398187\pi$
$571$	21.1134	−	3.03564i	0.883567	−	0.127038i	0.569137	+	0.822243i	$0.307278\pi$
$572$	−4.87994	+	22.4327i	−0.204041	+	0.937960i
$573$	−29.4128	+	2.10364i	−1.22874	+	0.0878810i
$574$	19.0846			0.796578
$575$	−21.2136	−	11.1797i	−0.884667	−	0.466224i
$576$	0.911981			0.0379992
$577$	−5.39311	+	0.385723i	−0.224518	+	0.0160578i	−0.183145	−	0.983086i	$-0.558628\pi$
$577$	−5.39311	+	0.385723i	−0.224518	+	0.0160578i	−0.0413731	+	0.999144i	$0.513173\pi$
$578$	−0.516084	+	2.37240i	−0.0214662	+	0.0986787i
$579$	−26.9389	+	3.87323i	−1.11954	+	0.160966i
$580$	−8.32573	+	8.60126i	−0.345707	+	0.357148i
$581$	−3.16577	+	22.0184i	−0.131338	+	0.913477i
$582$	−12.2704	+	22.4715i	−0.508623	+	0.931474i
$583$	45.6775	−	9.93652i	1.89177	−	0.411529i
$584$	4.11254	+	1.87813i	0.170178	+	0.0777177i
$585$	−5.88942	+	7.02458i	−0.243498	+	0.290431i
$586$	−4.86678	+	4.21709i	−0.201045	+	0.174206i
$587$	1.36810	−	19.1285i	0.0564674	−	0.789517i	−0.887777	−	0.460273i	$-0.847751\pi$
$587$	1.36810	−	19.1285i	0.0564674	−	0.789517i	0.944245	−	0.329244i	$-0.106794\pi$
$588$	9.93517	−	5.42501i	0.409719	−	0.223724i
$589$	−4.35628	+	9.53892i	−0.179497	+	0.393044i
$590$	−2.17142	−	3.26085i	−0.0893958	−	0.134247i
$591$	−16.1800	+	4.75087i	−0.665555	+	0.195425i
$592$	−6.77285	−	9.04747i	−0.278362	−	0.371849i
$593$	11.8754	+	4.42929i	0.487664	+	0.181889i	0.581255	−	0.813722i	$-0.302562\pi$
$593$	11.8754	+	4.42929i	0.487664	+	0.181889i	−0.0935911	+	0.995611i	$0.529835\pi$
$594$	4.10856	+	28.5757i	0.168576	+	1.17247i
$595$	22.2509	−	30.7546i	0.912196	−	1.26082i
$596$	−4.06601	−	3.52322i	−0.166550	−	0.144317i
$597$	0.482664	−	0.482664i	0.0197541	−	0.0197541i
$598$	1.15557	+	21.5271i	0.0472549	+	0.880309i
$599$			18.6925i			0.763755i	0.924213	+	0.381878i	$0.124722\pi$
$599$			18.6925i			0.763755i	−0.924213	+	0.381878i	$0.875278\pi$
$600$	7.22116	−	0.235150i	0.294803	−	0.00959996i
$601$	12.4433	−	7.99682i	0.507572	−	0.326197i	−0.261666	−	0.965158i	$-0.584272\pi$
$601$	12.4433	−	7.99682i	0.507572	−	0.326197i	0.769239	+	0.638961i	$0.220636\pi$
$602$	8.10770	−	10.8306i	0.330445	−	0.441423i
$603$	−2.23163	+	5.98323i	−0.0908790	+	0.243656i
$604$	−7.73959	−	1.11278i	−0.314919	−	0.0452786i
$605$	−20.6479	−	26.6664i	−0.839456	−	1.08414i
$606$	−12.3420	−	7.93174i	−0.501360	−	0.322205i
$607$	2.38086	−	0.888014i	0.0966360	−	0.0360434i	−0.300681	−	0.953725i	$-0.597214\pi$
$607$	2.38086	−	0.888014i	0.0966360	−	0.0360434i	0.397317	+	0.917681i	$0.369941\pi$
$608$	2.01021	+	3.68142i	0.0815248	+	0.149301i
$609$	19.5110	+	22.5169i	0.790626	+	0.912431i
$610$	1.05184	+	3.37787i	0.0425879	+	0.136766i
$611$	29.5722	+	8.68319i	1.19636	+	0.351284i
$612$	−1.40476	−	3.76630i	−0.0567839	−	0.152244i
$613$	0.946808	+	4.35241i	0.0382412	+	0.175792i	0.992306	−	0.123808i	$-0.0395105\pi$
$613$	0.946808	+	4.35241i	0.0382412	+	0.175792i	−0.954065	+	0.299600i	$0.903147\pi$
$614$	0.617497	+	2.10300i	0.0249201	+	0.0848702i
$615$	8.43567	−	13.6082i	0.340159	−	0.548734i
$616$	8.17117	+	17.8924i	0.329226	+	0.720904i
$617$	17.8402	+	13.3550i	0.718218	+	0.537651i	0.894708	−	0.446651i	$-0.147384\pi$
$617$	17.8402	+	13.3550i	0.718218	+	0.537651i	−0.176491	+	0.984302i	$0.556474\pi$
$618$	−17.9753	−	3.91029i	−0.723073	−	0.157295i
$619$	1.96613	−	2.26904i	0.0790256	−	0.0912004i	−0.714860	−	0.699268i	$-0.753510\pi$
$619$	1.96613	−	2.26904i	0.0790256	−	0.0912004i	0.793885	+	0.608067i	$0.208055\pi$
$620$	5.20538	−	2.03861i	0.209053	−	0.0818727i
$621$	10.8219	+	24.8563i	0.434266	+	0.997448i
$622$	13.6275	+	13.6275i	0.546414	+	0.546414i
$623$	0.120481	+	1.68454i	0.00482696	+	0.0674897i
$624$	−3.51174	−	5.46438i	−0.140582	−	0.218750i
$625$	−24.9470	+	1.62648i	−0.997881	+	0.0650591i
$626$	4.58310	−	2.09303i	0.183177	−	0.0836543i
$627$	−24.7803	+	18.5503i	−0.989631	+	0.740829i
$628$	0.353514	+	0.193033i	0.0141068	+	0.00770287i
$629$	−26.9318	+	41.9067i	−1.07384	+	1.67093i
$630$	−0.432727	+	7.84218i	−0.0172403	+	0.312440i
$631$	10.2222	−	34.8138i	0.406941	−	1.38591i	−0.460184	−	0.887824i	$-0.652216\pi$
$631$	10.2222	−	34.8138i	0.406941	−	1.38591i	0.867125	−	0.498091i	$-0.165965\pi$
$632$	5.00657	+	0.358077i	0.199151	+	0.0142435i
$633$	16.1624	+	1.15596i	0.642396	+	0.0459451i
$634$	0.739516	−	2.51856i	0.0293699	−	0.100025i
$635$	10.2490	+	11.4461i	0.406717	+	0.454224i
$636$	−7.15060	+	11.1265i	−0.283540	+	0.441196i
$637$	30.9068	+	16.8764i	1.22457	+	0.668667i
$638$	−21.8875	+	16.3848i	−0.866536	+	0.648681i
$639$	−11.5231	+	5.26241i	−0.455846	+	0.208178i
$640$	0.594971	−	2.15546i	0.0235183	−	0.0852021i
$641$	−10.4200	−	16.2138i	−0.411564	−	0.640406i	0.572150	−	0.820149i	$-0.306110\pi$
$641$	−10.4200	−	16.2138i	−0.411564	−	0.640406i	−0.983714	+	0.179744i	$0.942473\pi$
$642$	−0.771884	−	10.7924i	−0.0304638	−	0.425940i
$643$	7.67790	+	7.67790i	0.302787	+	0.302787i	0.842103	−	0.539316i	$-0.181317\pi$
$643$	7.67790	+	7.67790i	0.302787	+	0.302787i	−0.539316	+	0.842103i	$0.681317\pi$
$644$	11.8459	+	14.1722i	0.466796	+	0.558462i
$645$	−4.13897	−	10.5684i	−0.162972	−	0.416131i
$646$	12.1071	−	13.9724i	0.476349	−	0.549737i
$647$	23.5667	+	5.12663i	0.926504	+	0.201548i	0.650411	−	0.759583i	$-0.274597\pi$
$647$	23.5667	+	5.12663i	0.926504	+	0.201548i	0.276093	+	0.961131i	$0.410960\pi$
$648$	−4.34882	−	3.25548i	−0.170838	−	0.127888i
$649$	−3.71708	−	8.13927i	−0.145908	−	0.319494i
$650$	12.7603	+	18.5024i	0.500501	+	0.725724i
$651$	−3.91998	−	13.3502i	−0.153636	−	0.523236i
$652$	−1.87481	−	8.61839i	−0.0734234	−	0.337522i
$653$	12.7823	+	34.2706i	0.500208	+	1.34111i	0.904497	+	0.426479i	$0.140246\pi$
$653$	12.7823	+	34.2706i	0.500208	+	1.34111i	−0.404289	+	0.914631i	$0.632481\pi$
$654$	−1.22674	−	0.360205i	−0.0479695	−	0.0140851i
$655$	−0.665184	+	1.26678i	−0.0259909	+	0.0494973i
$656$	−3.24494	−	3.74486i	−0.126694	−	0.146212i
$657$	1.97602	+	3.61881i	0.0770919	+	0.141183i
$658$	24.7422	−	9.22836i	0.964551	−	0.359759i
$659$	−23.1308	−	14.8653i	−0.901049	−	0.579069i	0.00605205	−	0.999982i	$-0.498074\pi$
$659$	−23.1308	−	14.8653i	−0.901049	−	0.579069i	−0.907101	+	0.420913i	$0.861710\pi$
$660$	16.3698	+	2.08228i	0.637193	+	0.0810528i
$661$	−25.3092	−	3.63892i	−0.984416	−	0.141538i	−0.368736	−	0.929534i	$-0.620209\pi$
$661$	−25.3092	−	3.63892i	−0.984416	−	0.141538i	−0.615680	+	0.787997i	$0.711118\pi$
$662$	1.18187	−	3.16873i	0.0459349	−	0.123156i
$663$	−17.1575	+	22.9198i	−0.666343	+	0.890130i
$664$	4.85880	−	3.12256i	0.188558	−	0.121179i
$665$	−32.6106	+	15.5391i	−1.26459	+	0.602581i
$666$		−	10.3069i		−	0.399385i
$667$	−15.7489	+	20.2768i	−0.609802	+	0.785121i
$668$	6.74187	−	6.74187i	0.260851	−	0.260851i
$669$	19.3975	+	16.8081i	0.749952	+	0.649837i
$670$	12.6854	+	9.17787i	0.490081	+	0.354572i
$671$	1.14995	+	7.99810i	0.0443935	+	0.308763i
$672$	−5.21446	−	1.94489i	−0.201152	−	0.0750259i
$673$	−8.31613	−	11.1090i	−0.320563	−	0.428222i	0.611096	−	0.791557i	$-0.290729\pi$
$673$	−8.31613	−	11.1090i	−0.320563	−	0.428222i	−0.931659	+	0.363335i	$0.881638\pi$
$674$	21.4432	−	6.29630i	0.825962	−	0.242524i
$675$	23.1658	+	16.1926i	0.891652	+	0.623254i
$676$	2.99372	−	6.55534i	0.115143	−	0.252128i
$677$	25.4992	−	13.9236i	0.980015	−	0.535129i	0.0924036	−	0.995722i	$-0.470545\pi$
$677$	25.4992	−	13.9236i	0.980015	−	0.535129i	0.887612	+	0.460593i	$0.152363\pi$
$678$	−1.32123	+	18.4732i	−0.0507415	+	0.709459i
$679$	−51.5743	+	44.6894i	−1.97924	+	1.71502i
$680$	−9.81808	+	0.863023i	−0.376506	+	0.0330954i
$681$	13.1246	+	5.99378i	0.502934	+	0.229682i
$682$	12.4764	−	2.71407i	0.477746	−	0.103927i
$683$	−5.30899	+	9.72270i	−0.203143	+	0.372029i	−0.959312	−	0.282347i	$-0.908887\pi$
$683$	−5.30899	+	9.72270i	−0.203143	+	0.372029i	0.756169	+	0.654376i	$0.227069\pi$
$684$	−0.544398	+	3.78637i	−0.0208156	+	0.144775i
$685$	−0.541091	−	33.2413i	−0.0206740	−	1.27008i
$686$	3.17865	−	0.457021i	0.121361	−	0.0174491i
$687$	−1.72394	+	7.92481i	−0.0657723	+	0.302350i
$688$	−3.50377	+	0.250594i	−0.133580	+	0.00955382i
$689$	−41.1446			−1.56748
$690$	15.3414	−	2.18236i	0.584038	−	0.0830810i
$691$	−20.9498			−0.796970			−0.398485	−	0.917175i	$-0.630464\pi$
$691$	−20.9498			−0.796970			−0.398485	+	0.917175i	$0.630464\pi$
$692$	−10.0270	+	0.717147i	−0.381170	+	0.0272618i
$693$	−3.81312	+	17.5286i	−0.144848	+	0.665857i
$694$	11.8980	−	1.71067i	0.451642	−	0.0649363i
$695$	6.17794	+	5.98004i	0.234343	+	0.226836i
$696$	1.10092	−	7.65705i	0.0417302	−	0.290240i
$697$	−10.4672	+	19.1693i	−0.396475	+	0.726089i
$698$	−29.2526	+	6.36351i	−1.10723	+	0.240862i
$699$	−0.902455	−	0.412138i	−0.0341340	−	0.0155885i
$700$	18.2526	+	6.13894i	0.689884	+	0.232030i
$701$	23.7967	−	20.6199i	0.898788	−	0.778804i	−0.0771119	−	0.997022i	$-0.524570\pi$
$701$	23.7967	−	20.6199i	0.898788	−	0.778804i	0.975900	+	0.218218i	$0.0700244\pi$
$702$	1.81275	−	25.3456i	0.0684179	−	0.956608i
$703$	41.6063	−	22.7188i	1.56921	−	0.856855i
$704$	2.12157	−	4.64560i	0.0799598	−	0.175088i
$705$	4.35618	−	21.7213i	0.164063	−	0.818070i
$706$	−5.97767	+	1.75520i	−0.224973	+	0.0660579i
$707$	−23.4340	−	31.3042i	−0.881326	−	1.17731i
$708$	2.37207	+	0.884736i	0.0891478	+	0.0332504i
$709$	−7.12573	−	49.5606i	−0.267613	−	1.86129i	−0.470927	−	0.882172i	$-0.656080\pi$
$709$	−7.12573	−	49.5606i	−0.267613	−	1.86129i	0.203314	−	0.979114i	$-0.434829\pi$
$710$	4.92009	+	30.6679i	0.184648	+	1.15094i
$711$	3.45949	+	2.99766i	0.129741	+	0.112421i
$712$	0.310062	−	0.310062i	0.0116201	−	0.0116201i
$713$	10.6238	−	5.55826i	0.397863	−	0.208158i
$714$			24.5305i			0.918030i
$715$	22.0822	+	46.3420i	0.825827	+	1.73309i
$716$	−8.56236	+	5.50269i	−0.319990	+	0.205645i
$717$	21.9102	−	29.2687i	0.818253	−	1.09306i
$718$	−6.25825	+	16.7790i	−0.233556	+	0.626187i
$719$	11.4121	+	1.64081i	0.425599	+	0.0611920i	0.351787	−	0.936080i	$-0.385574\pi$
$719$	11.4121	+	1.64081i	0.425599	+	0.0611920i	0.0738127	+	0.997272i	$0.476483\pi$
$720$	1.61240	−	1.24849i	0.0600906	−	0.0465283i
$721$	−41.2480	−	26.5085i	−1.53615	−	0.987227i
$722$	1.31751	−	0.491406i	0.0490327	−	0.0182882i
$723$	−15.8379	−	29.0050i	−0.589019	−	1.07871i
$724$	−4.50152	−	5.19503i	−0.167298	−	0.193072i
$725$	−2.94506	+	26.6050i	−0.109377	+	0.988084i
$726$	20.9116	+	6.14020i	0.776102	+	0.227884i
$727$	−13.5513	−	36.3325i	−0.502591	−	1.34750i	−0.902400	−	0.430900i	$-0.858196\pi$
$727$	−13.5513	−	36.3325i	−0.502591	−	1.34750i	0.399808	−	0.916599i	$-0.369077\pi$
$728$	−3.68015	−	16.9174i	−0.136395	−	0.626999i
$729$	−8.29958	−	28.2658i	−0.307392	−	1.04688i
$730$	9.84217	−	2.30942i	0.364275	−	0.0854754i
$731$	6.43188	+	14.0839i	0.237892	+	0.520910i
$732$	−1.83023	−	1.37009i	−0.0676472	−	0.0506400i
$733$	−35.4588	−	7.71360i	−1.30970	−	0.284908i	−0.497083	−	0.867703i	$-0.665595\pi$
$733$	−35.4588	−	7.71360i	−1.30970	−	0.284908i	−0.812619	+	0.582795i	$0.801959\pi$
$734$	10.6969	−	12.3449i	0.394832	−	0.455660i
$735$	10.1388	−	23.1926i	0.373976	−	0.855471i
$736$	0.766767	−	4.73414i	0.0282634	−	0.174503i
$737$	25.2869	+	25.2869i	0.931453	+	0.931453i
$738$	−0.322383	−	4.50750i	−0.0118671	−	0.165923i
$739$	18.7311	+	29.1462i	0.689035	+	1.07216i	0.992843	+	0.119426i	$0.0381055\pi$
$739$	18.7311	+	29.1462i	0.689035	+	1.07216i	−0.303808	+	0.952733i	$0.598258\pi$
$740$	−24.3603	−	6.72417i	−0.895504	−	0.247186i
$741$	24.7833	−	11.3182i	0.910438	−	0.415783i
$742$	−28.2212	+	21.1262i	−1.03603	+	0.775565i
$743$	−21.2332	−	11.5942i	−0.778970	−	0.425350i	0.0399900	−	0.999200i	$-0.487267\pi$
$743$	−21.2332	−	11.5942i	−0.778970	−	0.425350i	−0.818960	+	0.573850i	$0.805449\pi$
$744$	−1.95312	+	3.03912i	−0.0716049	+	0.111419i
$745$	−12.0120	−	0.662816i	−0.440086	−	0.0242837i
$746$	6.20979	−	21.1486i	0.227356	−	0.774305i
$747$	5.25388	+	0.375765i	0.192229	+	0.0137485i
$748$	−22.4533	−	1.60589i	−0.820975	−	0.0587173i
$749$	8.12494	−	27.6710i	0.296879	−	1.01108i
$750$	12.4452	−	10.3014i	0.454435	−	0.376154i
$751$	10.5067	−	16.3487i	0.383395	−	0.596574i	−0.594898	−	0.803801i	$-0.702808\pi$
$751$	10.5067	−	16.3487i	0.383395	−	0.596574i	0.978293	+	0.207227i	$0.0664439\pi$
$752$	−6.01771	−	3.28592i	−0.219443	−	0.119825i
$753$	21.1209	−	15.8109i	0.769688	−	0.576181i
$754$	21.8902	−	9.99692i	0.797194	−	0.364066i
$755$	−15.2071	+	8.62794i	−0.553444	+	0.314003i
$756$	−11.7706	−	18.3154i	−0.428093	−	0.666126i
$757$	−3.16712	−	44.2821i	−0.115111	−	1.60946i	−0.646894	−	0.762580i	$-0.723932\pi$
$757$	−3.16712	−	44.2821i	−0.115111	−	1.60946i	0.531783	−	0.846881i	$-0.321522\pi$
$758$	9.31050	+	9.31050i	0.338173	+	0.338173i
$759$	35.3866	+	0.628934i	1.28445	+	0.0228289i
$760$	8.59389	+	3.75688i	0.311733	+	0.136276i
$761$	−33.5656	+	38.7368i	−1.21675	+	1.40421i	−0.328721	+	0.944427i	$0.606618\pi$
$761$	−33.5656	+	38.7368i	−1.21675	+	1.40421i	−0.888032	+	0.459782i	$0.847928\pi$
$762$	−9.70169	−	2.11047i	−0.351455	−	0.0764544i
$763$	−2.72807	−	2.04220i	−0.0987626	−	0.0739328i
$764$	8.47733	+	18.5628i	0.306699	+	0.671577i
$765$	−7.63963	−	4.73580i	−0.276211	−	0.171223i
$766$	3.43325	+	11.6926i	0.124048	+	0.422470i
$767$	1.67410	+	7.69573i	0.0604484	+	0.277877i
$768$	0.504975	+	1.35389i	0.0182217	+	0.0488543i
$769$	−9.34138	−	2.74288i	−0.336859	−	0.0989107i	0.108928	−	0.994050i	$-0.465258\pi$
$769$	−9.34138	−	2.74288i	−0.336859	−	0.0989107i	−0.445787	+	0.895139i	$0.647076\pi$
$770$	38.9411	+	20.4478i	1.40334	+	0.736889i
$771$	1.49796	+	1.72874i	0.0539478	+	0.0622591i
$772$	9.02646	+	16.5307i	0.324869	+	0.594954i
$773$	−45.2367	+	16.8724i	−1.62705	+	0.606858i	−0.986892	−	0.161385i	$-0.948404\pi$
$773$	−45.2367	+	16.8724i	−1.62705	+	0.606858i	−0.640158	+	0.768243i	$0.721131\pi$
$774$	−2.69498	−	1.73196i	−0.0968691	−	0.0622540i
$775$	6.41237	−	10.7304i	0.230339	−	0.385446i
$776$	17.5382	+	2.52162i	0.629586	+	0.0905208i
$777$	−21.9806	+	58.9323i	−0.788550	+	2.11418i
$778$	2.60510	−	3.48001i	0.0933974	−	0.124764i
$779$	17.4850	−	11.2369i	0.626464	−	0.402604i
$780$	−13.6895	−	4.85360i	−0.490161	−	0.173787i
$781$			70.9403i			2.53844i
$782$	−20.7321	+	4.12557i	−0.741379	+	0.147530i
$783$	21.3987	−	21.3987i	0.764725	−	0.764725i
$784$	−5.92039	−	5.13005i	−0.211442	−	0.183216i
$785$	0.889279	−	0.142668i	0.0317397	−	0.00509205i
$786$	−0.131587	−	0.915209i	−0.00469356	−	0.0326444i
$787$	−14.8272	−	5.53026i	−0.528533	−	0.197132i	0.0710096	−	0.997476i	$-0.477378\pi$
$787$	−14.8272	−	5.53026i	−0.528533	−	0.197132i	−0.599542	+	0.800343i	$0.704651\pi$
$788$	6.99353	+	9.34227i	0.249134	+	0.332805i
$789$	17.8084	−	5.22901i	0.633995	−	0.186158i
$790$	9.34191	−	6.22082i	0.332370	−	0.221327i
$791$	−20.5065	+	44.9029i	−0.729126	+	1.59656i
$792$	4.08787	−	2.23215i	0.145256	−	0.0793159i
$793$	0.507375	−	7.09403i	0.0180174	−	0.251916i
$794$	12.7255	−	11.0267i	0.451610	−	0.391322i
$795$	2.58966	+	29.4610i	0.0918458	+	1.04487i
$796$	−0.429693	−	0.196234i	−0.0152301	−	0.00695534i
$797$	−2.86403	+	0.623031i	−0.101449	+	0.0220689i	−0.263003	−	0.964795i	$-0.584713\pi$
$797$	−2.86403	+	0.623031i	−0.101449	+	0.0220689i	0.161554	+	0.986864i	$0.448349\pi$
$798$	11.1875	−	20.4885i	0.396035	−	0.725284i
$799$	−4.30089	+	29.9134i	−0.152155	+	1.05826i
$800$	−1.89887	−	4.62540i	−0.0671351	−	0.163532i
$801$	0.395828	−	0.0569114i	0.0139859	−	0.00201087i
$802$	−1.53932	+	7.07615i	−0.0543553	+	0.249867i
$803$	23.0310	−	1.64721i	0.812745	−	0.0581287i
$804$	−10.1181			−0.356840
$805$	40.3453	+	8.83978i	1.42199	+	0.311561i
$806$	−11.2383			−0.395851
$807$	−14.5838	+	1.04305i	−0.513374	+	0.0367173i
$808$	−2.15816	+	9.92092i	−0.0759240	+	0.349017i
$809$	34.9496	−	5.02499i	1.22876	−	0.176669i	0.502799	−	0.864403i	$-0.332303\pi$
$809$	34.9496	−	5.02499i	1.22876	−	0.176669i	0.725963	+	0.687734i	$0.241394\pi$
$810$	−12.1455	+	0.197701i	−0.426749	+	0.00694649i
$811$	−0.693191	+	4.82125i	−0.0243412	+	0.169297i	−0.998366	−	0.0571451i	$-0.981800\pi$
$811$	−0.693191	+	4.82125i	−0.0243412	+	0.169297i	0.974025	+	0.226442i	$0.0727093\pi$
$812$	9.88154	−	18.0967i	0.346774	−	0.635070i
$813$	−10.7902	+	2.34725i	−0.378427	+	0.0823218i
$814$	−52.5031	−	23.9774i	−1.84023	−	0.840406i
$815$	−15.1131	−	12.6709i	−0.529390	−	0.443841i
$816$	4.81347	−	4.17089i	0.168505	−	0.146010i
$817$	1.05112	−	14.6966i	0.0367740	−	0.514167i
$818$	27.4600	−	14.9943i	0.960118	−	0.524264i
$819$	6.55904	−	14.3623i	0.229192	−	0.501859i
$820$	−10.8638	−	2.17872i	−0.379379	−	0.0760841i
$821$	−22.8348	+	6.70489i	−0.796939	+	0.234002i	−0.654758	−	0.755838i	$-0.727230\pi$
$821$	−22.8348	+	6.70489i	−0.796939	+	0.234002i	−0.142181	+	0.989841i	$0.545411\pi$
$822$	12.8749	+	17.1989i	0.449065	+	0.599881i
$823$	6.56246	+	2.44767i	0.228753	+	0.0853204i	0.461227	−	0.887282i	$-0.347409\pi$
$823$	6.56246	+	2.44767i	0.228753	+	0.0853204i	−0.232474	+	0.972603i	$0.574682\pi$
$824$	1.81176	+	12.6010i	0.0631155	+	0.438978i
$825$	31.7927	−	18.7284i	1.10688	−	0.652040i
$826$	5.09974	+	4.41895i	0.177443	+	0.153755i
$827$	−2.18833	+	2.18833i	−0.0760958	+	0.0760958i	−0.744130	−	0.668034i	$-0.767136\pi$
$827$	−2.18833	+	2.18833i	−0.0760958	+	0.0760958i	0.668034	+	0.744130i	$0.267136\pi$
$828$	3.14715	−	3.03723i	0.109371	−	0.105551i
$829$			21.0156i			0.729901i	0.931027	+	0.364951i	$0.118914\pi$
$829$			21.0156i			0.729901i	−0.931027	+	0.364951i	$0.881086\pi$
$830$	4.31572	−	12.1724i	0.149801	−	0.422509i
$831$	17.7209	−	11.3885i	0.614730	−	0.395063i
$832$	−2.69386	+	3.59857i	−0.0933927	+	0.124758i
$833$	−12.0667	+	32.3520i	−0.418086	+	1.12093i
$834$	−5.49975	−	0.790745i	−0.190441	−	0.0273812i
$835$	2.69024	−	21.1492i	0.0930997	−	0.731900i
$836$	18.0212	+	11.5815i	0.623275	+	0.400555i
$837$	−13.2414	+	4.93878i	−0.457689	+	0.170709i
$838$	−8.26558	−	15.1373i	−0.285530	−	0.522908i
$839$	−24.7969	−	28.6172i	−0.856085	−	0.987975i	0.143913	−	0.989590i	$-0.454031\pi$
$839$	−24.7969	−	28.6172i	−0.856085	−	0.987975i	−0.999999	+	0.00161505i	$0.999486\pi$
$840$	−11.8818	+	3.69990i	−0.409961	+	0.127659i
$841$	−0.326312	−	0.0958139i	−0.0112521	−	0.00330393i
$842$	1.62150	+	4.34741i	0.0558806	+	0.149822i
$843$	7.45277	+	34.2598i	0.256687	+	1.17997i
$844$	−3.15924	−	10.7594i	−0.108746	−	0.370353i
$845$	−3.68119	−	15.6883i	−0.126637	−	0.539694i
$846$	−2.59755	−	5.68784i	−0.0893055	−	0.195552i
$847$	46.5037	+	34.8123i	1.59789	+	1.19616i
$848$	8.94388	+	1.94562i	0.307134	+	0.0668129i
$849$	−1.52992	+	1.76562i	−0.0525067	+	0.0605959i
$850$	−16.1771	+	14.9666i	−0.554869	+	0.513351i
$851$	−53.5038	−	8.66576i	−1.83409	−	0.297058i
$852$	−14.1928	−	14.1928i	−0.486238	−	0.486238i
$853$	−3.86278	−	54.0088i	−0.132259	−	1.84923i	−0.440298	−	0.897852i	$-0.645127\pi$
$853$	−3.86278	−	54.0088i	−0.132259	−	1.84923i	0.308039	−	0.951374i	$-0.400327\pi$
$854$	−3.29450	−	5.12634i	−0.112735	−	0.175420i
$855$	4.22097	+	7.43964i	0.144354	+	0.254430i
$856$	−6.81118	+	3.11056i	−0.232801	+	0.106317i
$857$	19.6691	−	14.7241i	0.671885	−	0.502967i	−0.208015	−	0.978126i	$-0.566700\pi$
$857$	19.6691	−	14.7241i	0.671885	−	0.502967i	0.879900	+	0.475159i	$0.157609\pi$
$858$	−29.1156	−	15.8983i	−0.993989	−	0.542759i
$859$	−12.6739	+	19.7209i	−0.432426	+	0.672868i	−0.987264	−	0.159090i	$-0.949144\pi$
$859$	−12.6739	+	19.7209i	−0.432426	+	0.672868i	0.554838	+	0.831959i	$0.312780\pi$
$860$	−5.85166	+	5.23965i	−0.199540	+	0.178671i
$861$	−7.76942	+	26.4602i	−0.264781	+	0.901761i
$862$	13.6998	+	0.979830i	0.466618	+	0.0333731i
$863$	24.1875	+	1.72992i	0.823352	+	0.0588873i	0.476656	−	0.879090i	$-0.341849\pi$
$863$	24.1875	+	1.72992i	0.823352	+	0.0588873i	0.346696	+	0.937977i	$0.387303\pi$
$864$	−1.59258	+	5.42383i	−0.0541806	+	0.184522i
$865$	−16.7462	+	14.9947i	−0.569388	+	0.509837i
$866$	−18.1845	+	28.2956i	−0.617933	+	0.961523i
$867$	−3.07915	−	1.68134i	−0.104573	−	0.0571014i
$868$	−7.70838	+	5.77042i	−0.261639	+	0.195861i
$869$	23.3179	−	10.6489i	0.791007	−	0.361241i
$870$	−8.53593	−	15.0449i	−0.289395	−	0.510071i
$871$	−17.0172	−	26.4793i	−0.576607	−	0.897218i
$872$	0.0631209	+	0.882546i	0.00213754	+	0.0298868i
$873$	11.4261	+	11.4261i	0.386717	+	0.386717i
$874$	19.1975	+	6.00946i	0.649366	+	0.203273i
$875$	40.6751	−	14.1338i	1.37507	−	0.477809i
$876$	−4.27819	+	4.93730i	−0.144547	+	0.166816i
$877$	21.9532	+	4.77562i	0.741306	+	0.161261i	0.567332	−	0.823489i	$-0.307975\pi$
$877$	21.9532	+	4.77562i	0.741306	+	0.161261i	0.173974	+	0.984750i	$0.444339\pi$
$878$	22.8356	+	17.0945i	0.770663	+	0.576911i
$879$	−3.86556	−	8.46441i	−0.130382	−	0.285497i
$880$	−2.60876	−	11.1179i	−0.0879414	−	0.374784i
$881$	−13.7228	−	46.7357i	−0.462334	−	1.57457i	−0.779630	−	0.626240i	$-0.784593\pi$
$881$	−13.7228	−	46.7357i	−0.462334	−	1.57457i	0.317296	−	0.948327i	$-0.397225\pi$
$882$	−1.51862	−	6.98100i	−0.0511347	−	0.235063i
$883$	−5.11445	−	13.7124i	−0.172115	−	0.461458i	0.822039	−	0.569432i	$-0.192837\pi$
$883$	−5.11445	−	13.7124i	−0.172115	−	0.461458i	−0.994154	+	0.107973i	$0.965564\pi$
$884$	19.0108	+	5.58208i	0.639403	+	0.187746i
$885$	5.40505	−	1.68309i	0.181689	−	0.0565765i
$886$	−19.4153	−	22.4065i	−0.652270	−	0.752760i
$887$	9.23109	+	16.9055i	0.309950	+	0.567631i	0.985498	−	0.169685i	$-0.0542750\pi$
$887$	9.23109	+	16.9055i	0.309950	+	0.567631i	−0.675549	+	0.737315i	$0.736093\pi$
$888$	15.3013	−	5.70707i	0.513476	−	0.191517i
$889$	−22.2625	−	14.3072i	−0.746659	−	0.479849i
$890$	0.123726	−	0.972664i	0.00414730	−	0.0326038i
$891$	−27.4613	−	3.94833i	−0.919987	−	0.132274i
$892$	6.20732	−	16.6425i	0.207837	−	0.557231i
$893$	17.2347	−	23.0229i	0.576737	−	0.770431i
$894$	6.54011	−	4.20307i	0.218734	−	0.140572i
$895$	−7.60531	+	21.4506i	−0.254218	+	0.717014i
$896$			3.85147i			0.128668i
$897$	−30.3170	−	7.16158i	−1.01226	−	0.239118i
$898$	−2.96885	+	2.96885i	−0.0990718	+	0.0990718i
$899$	−10.1151	−	8.76475i	−0.337356	−	0.292321i
$900$	1.14159	−	4.41469i	0.0380532	−	0.147156i
$901$	−5.74155	−	39.9334i	−0.191279	−	1.33037i
$902$	−23.7110	−	8.84375i	−0.789491	−	0.294465i
$903$	11.7156	+	15.6502i	0.389871	+	0.520807i
$904$	12.2977	−	3.61094i	0.409016	−	0.120098i
$905$	−15.0707	−	3.02241i	−0.500966	−	0.100468i
$906$	4.69365	−	10.2777i	0.155936	−	0.341452i
$907$	−42.9462	+	23.4504i	−1.42600	+	0.778657i	−0.992471	−	0.122481i	$-0.960915\pi$
$907$	−42.9462	+	23.4504i	−1.42600	+	0.778657i	−0.433533	+	0.901138i	$0.642733\pi$
$908$	0.712327	−	9.95964i	0.0236394	−	0.330522i
$909$	−6.99771	+	6.06355i	−0.232099	+	0.201115i
$910$	−29.6661	−	24.8721i	−0.983422	−	0.824503i
$911$	7.53473	+	3.44099i	0.249637	+	0.114005i	0.536304	−	0.844025i	$-0.319820\pi$
$911$	7.53473	+	3.44099i	0.249637	+	0.114005i	−0.286667	+	0.958030i	$0.592547\pi$
$912$	−5.92253	+	1.28837i	−0.196115	+	0.0426621i
$913$	14.1364	−	25.8889i	0.467847	−	0.856799i
$914$	−3.74743	+	26.0639i	−0.123954	+	0.862118i
$915$	−5.11151	+	0.0832036i	−0.168981	+	0.00275063i
$916$	5.55544	−	0.798752i	0.183557	−	0.0263915i
$917$	0.523859	−	2.40814i	0.0172994	−	0.0795239i
$918$	24.8524	−	1.77748i	0.820252	−	0.0586656i
$919$	6.81742			0.224886			0.112443	−	0.993658i	$-0.464132\pi$
$919$	6.81742			0.224886			0.112443	+	0.993658i	$0.464132\pi$
$920$	−5.12530	−	9.41973i	−0.168976	−	0.310559i
$921$	−3.16712			−0.104360
$922$	−3.34092	+	0.238947i	−0.110027	+	0.00786931i
$923$	13.2726	−	61.0131i	0.436873	−	2.00827i
$924$	−28.1337	+	4.04501i	−0.925529	+	0.133071i
$925$	−52.2748	+	21.4604i	−1.71879	+	0.705615i
$926$	−5.28728	+	36.7739i	−0.173751	+	1.20846i
$927$	−5.56412	+	10.1899i	−0.182750	+	0.334681i
$928$	−5.23115	+	1.13797i	−0.171721	+	0.0373556i
$929$	19.7252	+	9.00821i	0.647164	+	0.295550i	0.711824	−	0.702357i	$-0.247869\pi$
$929$	19.7252	+	9.00821i	0.647164	+	0.295550i	−0.0646604	+	0.997907i	$0.520596\pi$
$930$	0.707343	+	8.04700i	0.0231947	+	0.263872i
$931$	24.8331	−	21.5180i	0.813871	−	0.705223i
$932$	−0.0489802	+	0.684833i	−0.00160440	+	0.0224325i
$933$	−24.4419	+	13.3463i	−0.800192	+	0.436938i
$934$	−14.0011	+	30.6582i	−0.458130	+	1.00317i
$935$	−41.8963	+	27.8990i	−1.37016	+	0.912394i
$936$	−3.93345	+	1.15497i	−0.128569	+	0.0377512i
$937$	−18.6051	−	24.8535i	−0.607803	−	0.811929i	0.386069	−	0.922470i	$-0.373833\pi$
$937$	−18.6051	−	24.8535i	−0.607803	−	0.811929i	−0.993872	+	0.110541i	$0.964742\pi$
$938$	−25.2683	−	9.42460i	−0.825040	−	0.307724i
$939$	1.03612	+	7.20638i	0.0338126	+	0.235171i
$940$	−15.1378	+	2.42858i	−0.493740	+	0.0792114i
$941$	34.3632	+	29.7758i	1.12021	+	0.970665i	0.999757	−	0.0220546i	$-0.00702076\pi$
$941$	34.3632	+	29.7758i	1.12021	+	0.970665i	0.120450	+	0.992719i	$0.461566\pi$
$942$	−0.411551	+	0.411551i	−0.0134091	+	0.0134091i
$943$	−23.6697	−	2.11627i	−0.770792	−	0.0689152i
$944$		−	1.75204i		−	0.0570240i
$945$	−45.8841	−	16.2682i	−1.49261	−	0.529206i
$946$	−15.0920	+	9.69902i	−0.490682	+	0.315342i
$947$	29.6825	−	39.6512i	0.964553	−	1.28849i	0.00707771	−	0.999975i	$-0.497747\pi$
$947$	29.6825	−	39.6512i	0.964553	−	1.28849i	0.957475	−	0.288517i	$-0.0931620\pi$
$948$	−2.53465	+	6.79566i	−0.0823217	+	0.220713i
$949$	−20.1163	−	2.89228i	−0.653002	−	0.0938875i
$950$	20.3373	−	5.12265i	0.659828	−	0.166201i
$951$	3.19084	+	2.05063i	0.103470	+	0.0664961i
$952$	15.9058	−	5.93255i	0.515510	−	0.192275i
$953$	18.7829	+	34.3984i	0.608439	+	1.11427i	0.982393	+	0.186825i	$0.0598197\pi$
$953$	18.7829	+	34.3984i	0.608439	+	1.11427i	−0.373955	+	0.927447i	$0.621998\pi$
$954$	5.46639	+	6.30855i	0.176981	+	0.204247i
$955$	40.4002	+	21.2140i	1.30732	+	0.686468i
$956$	−24.2769	−	7.12835i	−0.785172	−	0.230547i
$957$	−13.8065	−	37.0166i	−0.446300	−	1.19658i
$958$	−8.62283	−	39.6385i	−0.278591	−	1.28066i
$959$	16.1329	+	54.9437i	0.520960	+	1.77423i
$960$	2.74626	+	1.70240i	0.0886351	+	0.0549447i
$961$	−10.2814	−	22.5130i	−0.331657	−	0.726227i
$962$	40.6699	+	30.4451i	1.31125	+	0.981591i
$963$	−6.67271	−	1.45156i	−0.215025	−	0.0467759i
$964$	−14.9768	+	17.2841i	−0.482370	+	0.556685i
$965$	38.5892	+	16.8696i	1.24223	+	0.543050i
$966$	−24.4718	+	10.6545i	−0.787366	+	0.342802i
$967$	29.6745	+	29.6745i	0.954267	+	0.954267i	0.998999	−	0.0447319i	$-0.0142434\pi$
$967$	29.6745	+	29.6745i	0.954267	+	0.954267i	−0.0447319	+	0.998999i	$0.514243\pi$
$968$	−1.07598	−	15.0442i	−0.0345835	−	0.483540i
$969$	14.4434	+	22.4743i	0.463988	+	0.721980i
$970$	34.4600	−	19.5513i	1.10644	−	0.627754i
$971$	31.7656	−	14.5069i	1.01941	−	0.465548i	0.165631	−	0.986188i	$-0.447034\pi$
$971$	31.7656	−	14.5069i	1.01941	−	0.465548i	0.853776	+	0.520640i	$0.174307\pi$
$972$	−7.29188	+	5.45863i	−0.233887	+	0.175086i
$973$	−12.9981	−	7.09751i	−0.416701	−	0.227536i
$974$	−15.7732	+	24.5436i	−0.505407	+	0.786428i
$975$	−30.8477	+	10.1594i	−0.987917	+	0.325360i
$976$	−0.445750	+	1.51808i	−0.0142681	+	0.0485927i
$977$	−23.3805	−	1.67221i	−0.748010	−	0.0534987i	−0.307871	−	0.951428i	$-0.599616\pi$
$977$	−23.3805	−	1.67221i	−0.748010	−	0.0534987i	−0.440139	+	0.897929i	$0.645071\pi$
$978$	12.7123	+	0.909204i	0.406496	+	0.0290731i
$979$	0.630923	−	2.14873i	0.0201644	−	0.0686736i
$980$	−17.4903	−	0.965105i	−0.558707	−	0.0308292i
$981$	−0.436254	+	0.678825i	−0.0139285	+	0.0216732i
$982$	7.27314	+	3.97144i	0.232095	+	0.126734i
$983$	28.9059	−	21.6387i	0.921956	−	0.690168i	−0.0289719	−	0.999580i	$-0.509223\pi$
$983$	28.9059	−	21.6387i	0.921956	−	0.690168i	0.950928	+	0.309413i	$0.100132\pi$
$984$	6.51315	−	2.97446i	0.207632	−	0.0948222i
$985$	25.1541	+	6.94327i	0.801476	+	0.221231i
$986$	12.7573	+	19.8508i	0.406275	+	0.632177i
$987$	2.72218	+	38.0611i	0.0866480	+	1.21150i
$988$	−13.3325	−	13.3325i	−0.424163	−	0.424163i
$989$	−11.2566	+	12.5336i	−0.357938	+	0.398546i
$990$	4.17166	−	9.54270i	0.132584	−	0.303287i
$991$	−11.1594	+	12.8786i	−0.354489	+	0.409102i	−0.904786	−	0.425867i	$-0.859969\pi$
$991$	−11.1594	+	12.8786i	−0.354489	+	0.409102i	0.550297	+	0.834969i	$0.314515\pi$
$992$	2.44294	+	0.531429i	0.0775635	+	0.0168729i
$993$	3.91219	+	2.92863i	0.124150	+	0.0929372i
$994$	−22.2241	−	48.6641i	−0.704907	−	1.54353i
$995$	−1.02835	+	0.241297i	−0.0326008	+	0.00764961i
$996$	2.35129	+	8.00777i	0.0745036	+	0.253736i
$997$	−10.0899	−	46.3823i	−0.319549	−	1.46894i	−0.804265	−	0.594271i	$-0.797441\pi$
$997$	−10.0899	−	46.3823i	−0.319549	−	1.46894i	0.484716	−	0.874672i	$-0.338923\pi$
$998$	5.12017	+	13.7277i	0.162076	+	0.434543i
$999$	61.2984	+	17.9988i	1.93940	+	0.569458i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.l.a.7.9	✓	240
5.3	odd	4	inner	230.2.l.a.53.3	yes	240
23.10	odd	22	inner	230.2.l.a.217.3	yes	240
115.33	even	44	inner	230.2.l.a.33.9	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.l.a.7.9	✓	240	1.1	even	1	trivial
230.2.l.a.33.9	yes	240	115.33	even	44	inner
230.2.l.a.53.3	yes	240	5.3	odd	4	inner
230.2.l.a.217.3	yes	240	23.10	odd	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.l (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.997452 - 0.0713392i) q^{2} +(-0.307156 + 1.41198i) q^{3} +(0.989821 - 0.142315i) q^{4} +(1.55520 - 1.60666i) q^{5} +(-0.205645 + 1.43029i) q^{6} +(-1.84581 + 3.38035i) q^{7} +(0.977147 - 0.212565i) q^{8} +(0.829567 + 0.378851i) q^{9} +(1.43661 - 1.71352i) q^{10} +(3.85970 - 3.34445i) q^{11} +(-0.103085 + 1.44132i) q^{12} +(-3.94532 + 2.15431i) q^{13} +(-1.59996 + 3.50342i) q^{14} +(1.79088 + 2.68939i) q^{15} +(0.959493 - 0.281733i) q^{16} +(-2.64144 - 3.52855i) q^{17} +(0.854480 + 0.318705i) q^{18} +(0.596940 + 4.15181i) q^{19} +(1.31071 - 1.81164i) q^{20} +(-4.20602 - 3.64454i) q^{21} +(3.61128 - 3.61128i) q^{22} +(2.37283 - 4.16769i) q^{23} +1.44500i q^{24} +(-0.162734 - 4.99735i) q^{25} +(-3.78158 + 2.43027i) q^{26} +(-3.38760 + 4.52530i) q^{27} +(-1.34595 + 3.60863i) q^{28} +(-5.29900 - 0.761882i) q^{29} +(1.97818 + 2.55478i) q^{30} +(2.10320 + 1.35164i) q^{31} +(0.936950 - 0.349464i) q^{32} +(3.53675 + 6.47707i) q^{33} +(-2.88643 - 3.33112i) q^{34} +(2.56049 + 8.22271i) q^{35} +(0.875039 + 0.256935i) q^{36} +(-3.94954 - 10.5891i) q^{37} +(0.891605 + 4.09864i) q^{38} +(-1.83000 - 6.23240i) q^{39} +(1.17813 - 1.90053i) q^{40} +(-2.05845 - 4.50738i) q^{41} +(-4.45530 - 3.33520i) q^{42} +(-3.43244 - 0.746682i) q^{43} +(3.34445 - 3.85970i) q^{44} +(1.89882 - 0.743648i) q^{45} +(2.06947 - 4.32635i) q^{46} +(-4.84820 - 4.84820i) q^{47} +(0.103085 + 1.44132i) q^{48} +(-4.23527 - 6.59021i) q^{49} +(-0.518826 - 4.97301i) q^{50} +(5.79356 - 2.64583i) q^{51} +(-3.59857 + 2.69386i) q^{52} +(8.03345 + 4.38659i) q^{53} +(-3.05614 + 4.75544i) q^{54} +(0.629185 - 11.4025i) q^{55} +(-1.08508 + 3.69546i) q^{56} +(-6.04560 - 0.432390i) q^{57} +(-5.33986 - 0.381914i) q^{58} +(0.493606 - 1.68107i) q^{59} +(2.15539 + 2.40715i) q^{60} +(-0.855388 + 1.33101i) q^{61} +(2.19426 + 1.19816i) q^{62} +(-2.81187 + 2.10494i) q^{63} +(0.909632 - 0.415415i) q^{64} +(-2.67450 + 9.68917i) q^{65} +(3.98981 + 6.20826i) q^{66} +(0.499531 + 6.98435i) q^{67} +(-3.11672 - 3.11672i) q^{68} +(5.15585 + 4.63052i) q^{69} +(3.14057 + 8.01909i) q^{70} +(-9.09632 + 10.4977i) q^{71} +(0.891139 + 0.193855i) q^{72} +(3.61933 + 2.70939i) q^{73} +(-4.69489 - 10.2804i) q^{74} +(7.10612 + 1.30519i) q^{75} +(1.18173 + 4.02459i) q^{76} +(4.18114 + 19.2204i) q^{77} +(-2.26995 - 6.08597i) q^{78} +(4.81604 + 1.41412i) q^{79} +(1.03955 - 1.97973i) q^{80} +(-3.55743 - 4.10549i) q^{81} +(-2.37476 - 4.34904i) q^{82} +(5.41151 - 2.01839i) q^{83} +(-4.68188 - 3.00886i) q^{84} +(-9.77715 - 1.24368i) q^{85} +(-3.47696 - 0.499912i) q^{86} +(2.70338 - 7.24805i) q^{87} +(3.06058 - 4.08846i) q^{88} +(0.368885 - 0.237068i) q^{89} +(1.84094 - 0.877214i) q^{90} -17.3130i q^{91} +(1.75556 - 4.46296i) q^{92} +(-2.55450 + 2.55450i) q^{93} +(-5.18171 - 4.48998i) q^{94} +(7.59891 + 5.49779i) q^{95} +(0.205645 + 1.43029i) q^{96} +(16.6014 + 6.19201i) q^{97} +(-4.69462 - 6.27128i) q^{98} +(4.46893 - 1.31220i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 8 q^{3} - 8 q^{6} - 8 q^{12} + 16 q^{13} + 24 q^{16} - 72 q^{18} - 80 q^{23} - 8 q^{26} + 16 q^{27} - 44 q^{28} + 24 q^{31} - 44 q^{33} - 8 q^{35} - 32 q^{36} - 88 q^{37} - 24 q^{41} - 8 q^{46}+ \cdots + 24 q^{98}+O(q^{100}) \) 240 * q - 8 * q^3 - 8 * q^6 - 8 * q^12 + 16 * q^13 + 24 * q^16 - 72 * q^18 - 80 * q^23 - 8 * q^26 + 16 * q^27 - 44 * q^28 + 24 * q^31 - 44 * q^33 - 8 * q^35 - 32 * q^36 - 88 * q^37 - 24 * q^41 - 8 * q^46 - 80 * q^47 + 8 * q^48 + 8 * q^50 + 16 * q^52 - 44 * q^56 - 88 * q^57 - 176 * q^61 - 32 * q^62 - 176 * q^66 + 24 * q^70 - 336 * q^71 + 16 * q^72 - 88 * q^73 - 36 * q^75 - 24 * q^77 + 40 * q^78 - 136 * q^81 + 40 * q^82 - 100 * q^85 - 44 * q^86 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 52 * q^95 + 8 * q^96 + 132 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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