LMFDB - Embedded newform 230.2.l.a.217.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [230,2,Mod(7,230)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("230.7"); S:= CuspForms(chi, 2); N := Newforms(S);

sage: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")

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:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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			217.3
Character	$\chi$	$=$	230.217
Dual form			230.2.l.a.53.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0713392 + 0.997452i) q^{2} +(-1.41198 + 0.307156i) q^{3} +(-0.989821 - 0.142315i) q^{4} +(2.23267 + 0.123198i) q^{5} +(-0.205645 - 1.43029i) q^{6} +(3.38035 - 1.84581i) q^{7} +(0.212565 - 0.977147i) q^{8} +(-0.829567 + 0.378851i) q^{9} +(-0.282161 + 2.21819i) q^{10} +(3.85970 + 3.34445i) q^{11} +(1.44132 - 0.103085i) q^{12} +(-2.15431 + 3.94532i) q^{13} +(1.59996 + 3.50342i) q^{14} +(-3.19032 + 0.511827i) q^{15} +(0.959493 + 0.281733i) q^{16} +(-3.52855 - 2.64144i) q^{17} +(-0.318705 - 0.854480i) q^{18} +(-0.596940 + 4.15181i) q^{19} +(-2.19241 - 0.439686i) q^{20} +(-4.20602 + 3.64454i) q^{21} +(-3.61128 + 3.61128i) q^{22} +(4.16769 - 2.37283i) q^{23} +1.44500i q^{24} +(4.96964 + 0.550120i) q^{25} +(-3.78158 - 2.43027i) q^{26} +(4.52530 - 3.38760i) q^{27} +(-3.60863 + 1.34595i) q^{28} +(5.29900 - 0.761882i) q^{29} +(-0.282929 - 3.21870i) q^{30} +(2.10320 - 1.35164i) q^{31} +(-0.349464 + 0.936950i) q^{32} +(-6.47707 - 3.53675i) q^{33} +(2.88643 - 3.33112i) q^{34} +(7.77461 - 3.70464i) q^{35} +(0.875039 - 0.256935i) q^{36} +(-10.5891 - 3.94954i) q^{37} +(-4.09864 - 0.891605i) q^{38} +(1.83000 - 6.23240i) q^{39} +(0.594971 - 2.15546i) q^{40} +(-2.05845 + 4.50738i) q^{41} +(-3.33520 - 4.45530i) q^{42} +(0.746682 + 3.43244i) 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} +(-1.44132 - 0.103085i) q^{48} +(4.23527 - 6.59021i) q^{49} +(-0.903248 + 4.91774i) q^{50} +(5.79356 + 2.64583i) q^{51} +(2.69386 - 3.59857i) q^{52} +(-4.38659 - 8.03345i) q^{53} +(3.05614 + 4.75544i) q^{54} +(8.20542 + 7.94257i) q^{55} +(-1.08508 - 3.69546i) q^{56} +(-0.432390 - 6.04560i) q^{57} +(0.381914 + 5.33986i) q^{58} +(-0.493606 - 1.68107i) q^{59} +(3.23069 - 0.0525881i) q^{60} +(-0.855388 - 1.33101i) q^{61} +(1.19816 + 2.19426i) q^{62} +(-2.10494 + 2.81187i) q^{63} +(-0.909632 - 0.415415i) q^{64} +(-5.29591 + 8.54320i) q^{65} +(3.98981 - 6.20826i) q^{66} +(6.98435 + 0.499531i) 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} +(0.193855 + 0.891139i) q^{72} +(-2.70939 - 3.61933i) q^{73} +(4.69489 - 10.2804i) q^{74} +(-7.18599 + 0.749703i) q^{75} +(1.18173 - 4.02459i) q^{76} +(19.2204 + 4.18114i) q^{77} +(6.08597 + 2.26995i) q^{78} +(-4.81604 + 1.41412i) q^{79} +(2.10752 + 0.747224i) q^{80} +(-3.55743 + 4.10549i) q^{81} +(-4.34904 - 2.37476i) q^{82} +(2.01839 - 5.41151i) q^{83} +(4.68188 - 3.00886i) q^{84} +(-7.55268 - 6.33218i) q^{85} +(-3.47696 + 0.499912i) q^{86} +(-7.24805 + 2.70338i) q^{87} +(4.08846 - 3.06058i) q^{88} +(-0.368885 - 0.237068i) q^{89} +(-0.606293 - 1.94704i) q^{90} +17.3130i q^{91} +(-4.46296 + 1.75556i) q^{92} +(-2.55450 + 2.55450i) q^{93} +(5.18171 - 4.48998i) q^{94} +(-1.84426 + 9.19608i) q^{95} +(0.205645 - 1.43029i) q^{96} +(6.19201 + 16.6014i) q^{97} +(6.27128 + 4.69462i) 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 $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{22}\right)$

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 $

$2$	−0.0713392	+	0.997452i	−0.0504444	+	0.705305i
$2$	−0.0713392	+	0.997452i	−0.0504444	+	0.705305i
$3$	−1.41198	+	0.307156i	−0.815204	+	0.177337i	−0.600791	−	0.799406i	$-0.705148\pi$
$3$	−1.41198	+	0.307156i	−0.815204	+	0.177337i	−0.214413	+	0.976743i	$0.568784\pi$
$4$	−0.989821	−	0.142315i	−0.494911	−	0.0711574i
$5$	2.23267	+	0.123198i	0.998481	+	0.0550957i
$5$	2.23267	+	0.123198i	0.998481	+	0.0550957i
$6$	−0.205645	−	1.43029i	−0.0839541	−	0.583913i
$7$	3.38035	−	1.84581i	1.27765	−	0.697651i	0.310192	−	0.950674i	$-0.399607\pi$
$7$	3.38035	−	1.84581i	1.27765	−	0.697651i	0.967460	+	0.253023i	$0.0814247\pi$
$8$	0.212565	−	0.977147i	0.0751532	−	0.345474i
$9$	−0.829567	+	0.378851i	−0.276522	+	0.126284i
$10$	−0.282161	+	2.21819i	−0.0892271	+	0.701455i
$11$	3.85970	+	3.34445i	1.16374	+	1.00839i	0.999760	+	0.0219272i	$0.00698020\pi$
$11$	3.85970	+	3.34445i	1.16374	+	1.00839i	0.163985	+	0.986463i	$0.447565\pi$
$12$	1.44132	−	0.103085i	0.416072	−	0.0297581i
$13$	−2.15431	+	3.94532i	−0.597497	+	1.09423i	0.387533	+	0.921856i	$0.373327\pi$
$13$	−2.15431	+	3.94532i	−0.597497	+	1.09423i	−0.985031	+	0.172379i	$0.944855\pi$
$14$	1.59996	+	3.50342i	0.427607	+	0.936328i
$15$	−3.19032	+	0.511827i	−0.823737	+	0.132153i
$16$	0.959493	+	0.281733i	0.239873	+	0.0704331i
$17$	−3.52855	−	2.64144i	−0.855799	−	0.640643i	0.0785860	−	0.996907i	$-0.474959\pi$
$17$	−3.52855	−	2.64144i	−0.855799	−	0.640643i	−0.934385	+	0.356264i	$0.884050\pi$
$18$	−0.318705	−	0.854480i	−0.0751194	−	0.201403i
$19$	−0.596940	+	4.15181i	−0.136947	+	0.952490i	0.799246	+	0.601004i	$0.205232\pi$
$19$	−0.596940	+	4.15181i	−0.136947	+	0.952490i	−0.936193	+	0.351486i	$0.885677\pi$
$20$	−2.19241	−	0.439686i	−0.490239	−	0.0983168i
$21$	−4.20602	+	3.64454i	−0.917829	+	0.795303i
$22$	−3.61128	+	3.61128i	−0.769927	+	0.769927i
$23$	4.16769	−	2.37283i	0.869024	−	0.494770i
$23$	4.16769	−	2.37283i	0.869024	−	0.494770i
$24$			1.44500i			0.294959i
$25$	4.96964	+	0.550120i	0.993929	+	0.110024i
$26$	−3.78158	−	2.43027i	−0.741629	−	0.476616i
$27$	4.52530	−	3.38760i	0.870895	−	0.651944i
$28$	−3.60863	+	1.34595i	−0.681967	+	0.254361i
$29$	5.29900	−	0.761882i	0.984000	−	0.141478i	0.368511	−	0.929623i	$-0.379868\pi$
$29$	5.29900	−	0.761882i	0.984000	−	0.141478i	0.615489	+	0.788145i	$0.288958\pi$
$30$	−0.282929	−	3.21870i	−0.0516555	−	0.587652i
$31$	2.10320	−	1.35164i	0.377745	−	0.242762i	−0.337966	−	0.941158i	$-0.609739\pi$
$31$	2.10320	−	1.35164i	0.377745	−	0.242762i	0.715712	+	0.698396i	$0.246103\pi$
$32$	−0.349464	+	0.936950i	−0.0617771	+	0.165631i
$33$	−6.47707	−	3.53675i	−1.12751	−	0.615669i
$34$	2.88643	−	3.33112i	0.495019	−	0.571283i
$35$	7.77461	−	3.70464i	1.31415	−	0.626198i
$36$	0.875039	−	0.256935i	0.145840	−	0.0428225i
$37$	−10.5891	−	3.94954i	−1.74084	−	0.649300i	−0.741085	−	0.671412i	$-0.765688\pi$
$37$	−10.5891	−	3.94954i	−1.74084	−	0.649300i	−0.999756	+	0.0221119i	$0.992961\pi$
$38$	−4.09864	−	0.891605i	−0.664888	−	0.144637i
$39$	1.83000	−	6.23240i	0.293034	−	0.997983i
$40$	0.594971	−	2.15546i	0.0940731	−	0.340808i
$41$	−2.05845	+	4.50738i	−0.321476	+	0.703934i	−0.999517	−	0.0310905i	$-0.990102\pi$
$41$	−2.05845	+	4.50738i	−0.321476	+	0.703934i	0.678041	+	0.735024i	$0.262829\pi$
$42$	−3.33520	−	4.45530i	−0.514632	−	0.687468i
$43$	0.746682	+	3.43244i	0.113868	+	0.523442i	0.998379	+	0.0569224i	$0.0181288\pi$
$43$	0.746682	+	3.43244i	0.113868	+	0.523442i	−0.884511	+	0.466520i	$0.845508\pi$
$44$	−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	$0.916686\pi$
$48$	−1.44132	−	0.103085i	−0.208036	−	0.0148790i
$49$	4.23527	−	6.59021i	0.605039	−	0.941458i
$50$	−0.903248	+	4.91774i	−0.127739	+	0.695473i
$51$	5.79356	+	2.64583i	0.811261	+	0.370490i
$52$	2.69386	−	3.59857i	0.373571	−	0.499032i
$53$	−4.38659	−	8.03345i	−0.602545	−	1.10348i	−0.983844	−	0.179027i	$-0.942705\pi$
$53$	−4.38659	−	8.03345i	−0.602545	−	1.10348i	0.381299	−	0.924452i	$-0.375477\pi$
$54$	3.05614	+	4.75544i	0.415888	+	0.647134i
$55$	8.20542	+	7.94257i	1.10642	+	1.07098i
$56$	−1.08508	−	3.69546i	−0.145000	−	0.493826i
$57$	−0.432390	−	6.04560i	−0.0572714	−	0.800759i
$58$	0.381914	+	5.33986i	0.0501478	+	0.701157i
$59$	−0.493606	−	1.68107i	−0.0642621	−	0.218857i	0.921101	−	0.389323i	$-0.127291\pi$
$59$	−0.493606	−	1.68107i	−0.0642621	−	0.218857i	−0.985364	+	0.170466i	$0.945473\pi$
$60$	3.23069	−	0.0525881i	0.417080	−	0.00678910i
$61$	−0.855388	−	1.33101i	−0.109521	−	0.170418i	0.782166	−	0.623070i	$-0.214115\pi$
$61$	−0.855388	−	1.33101i	−0.109521	−	0.170418i	−0.891688	+	0.452651i	$0.850478\pi$
$62$	1.19816	+	2.19426i	0.152166	+	0.278672i
$63$	−2.10494	+	2.81187i	−0.265198	+	0.354263i
$64$	−0.909632	−	0.415415i	−0.113704	−	0.0519269i
$65$	−5.29591	+	8.54320i	−0.656877	+	1.05965i
$66$	3.98981	−	6.20826i	0.491111	−	0.764184i
$67$	6.98435	+	0.499531i	0.853274	+	0.0610274i	0.491121	−	0.871091i	$-0.336587\pi$
$67$	6.98435	+	0.499531i	0.853274	+	0.0610274i	0.362153	+	0.932119i	$0.382042\pi$
$68$	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	−0.967695	−	0.252123i	$-0.918871\pi$
$71$	−9.09632	−	10.4977i	−1.07953	−	1.24585i	−0.111839	−	0.993726i	$-0.535674\pi$
$72$	0.193855	+	0.891139i	0.0228461	+	0.105022i
$73$	−2.70939	−	3.61933i	−0.317111	−	0.423610i	0.613458	−	0.789727i	$-0.289778\pi$
$73$	−2.70939	−	3.61933i	−0.317111	−	0.423610i	−0.930569	+	0.366117i	$0.880687\pi$
$74$	4.69489	−	10.2804i	0.545770	−	1.19507i
$75$	−7.18599	+	0.749703i	−0.829766	+	0.0865682i
$76$	1.18173	−	4.02459i	0.135553	−	0.461653i
$77$	19.2204	+	4.18114i	2.19037	+	0.476485i
$78$	6.08597	+	2.26995i	0.689101	+	0.257021i
$79$	−4.81604	+	1.41412i	−0.541847	+	0.159101i	−0.541192	−	0.840899i	$-0.682027\pi$
$79$	−4.81604	+	1.41412i	−0.541847	+	0.159101i	−0.000655108		1.00000i	$0.500209\pi$
$80$	2.10752	+	0.747224i	0.235628	+	0.0835421i
$81$	−3.55743	+	4.10549i	−0.395270	+	0.456166i
$82$	−4.34904	−	2.37476i	−0.480271	−	0.262248i
$83$	2.01839	−	5.41151i	0.221547	−	0.593991i	−0.777859	−	0.628438i	$-0.783694\pi$
$83$	2.01839	−	5.41151i	0.221547	−	0.593991i	0.999407	+	0.0344476i	$0.0109672\pi$
$84$	4.68188	−	3.00886i	0.510835	−	0.328294i
$85$	−7.55268	−	6.33218i	−0.819203	−	0.686821i
$86$	−3.47696	+	0.499912i	−0.374931	+	0.0539069i
$87$	−7.24805	+	2.70338i	−0.777072	+	0.289833i
$88$	4.08846	−	3.06058i	0.435831	−	0.326259i
$89$	−0.368885	−	0.237068i	−0.0391017	−	0.0251291i	0.520944	−	0.853591i	$-0.325580\pi$
$89$	−0.368885	−	0.237068i	−0.0391017	−	0.0251291i	−0.560046	+	0.828462i	$0.689216\pi$
$90$	−0.606293	−	1.94704i	−0.0639089	−	0.205236i
$91$			17.3130i			1.81490i
$92$	−4.46296	+	1.75556i	−0.465296	+	0.183030i
$93$	−2.55450	+	2.55450i	−0.264889	+	0.264889i
$94$	5.18171	−	4.48998i	0.534453	−	0.463106i
$95$	−1.84426	+	9.19608i	−0.189217	+	0.943498i
$96$	0.205645	−	1.43029i	0.0209885	−	0.145978i
$97$	6.19201	+	16.6014i	0.628704	+	1.68562i	0.723676	+	0.690139i	$0.242451\pi$
$97$	6.19201	+	16.6014i	0.628704	+	1.68562i	−0.0949729	+	0.995480i	$0.530276\pi$
$98$	6.27128	+	4.69462i	0.633495	+	0.474228i
$99$	−4.46893	−	1.31220i	−0.449144	−	0.131881i
$100$	−4.84077	−	1.25177i	−0.484077	−	0.125177i
$101$	−4.21769	−	9.23545i	−0.419676	−	0.918961i	−0.994891	−	0.100959i	$-0.967809\pi$
$101$	−4.21769	−	9.23545i	−0.419676	−	0.918961i	0.575215	−	0.818002i	$-0.304918\pi$
$102$	−3.05240	+	5.59005i	−0.302232	+	0.553497i
$103$	−12.6982	+	0.908192i	−1.25119	+	0.0894868i	−0.681158	−	0.732136i	$-0.738523\pi$
$103$	−12.6982	+	0.908192i	−1.25119	+	0.0894868i	−0.570031	+	0.821623i	$0.693069\pi$
$104$	3.39723	+	2.94371i	0.333125	+	0.288655i
$105$	−9.83966	+	7.61888i	−0.960252	+	0.743527i
$106$	8.32591	−	3.80232i	0.808684	−	0.369314i
$107$	1.59166	−	7.31672i	0.153871	−	0.707334i	−0.833963	−	0.551821i	$-0.813933\pi$
$107$	1.59166	−	7.31672i	0.153871	−	0.707334i	0.987834	−	0.155513i	$-0.0497032\pi$
$108$	−4.96135	+	2.70910i	−0.477406	+	0.260683i
$109$	0.125920	+	0.875794i	0.0120610	+	0.0838858i	0.994963	−	0.100244i	$-0.0319624\pi$
$109$	0.125920	+	0.875794i	0.0120610	+	0.0838858i	−0.982902	+	0.184130i	$0.941053\pi$
$110$	−8.50770	+	7.61790i	−0.811177	+	0.726338i
$111$	16.1647	+	2.32413i	1.53428	+	0.220597i
$112$	3.76345	−	0.818688i	0.355612	−	0.0773588i
$113$	0.914346	−	12.7842i	0.0860145	−	1.20264i	−0.752810	−	0.658238i	$-0.771302\pi$
$113$	0.914346	−	12.7842i	0.0860145	−	1.20264i	0.838825	−	0.544402i	$-0.183243\pi$
$114$	6.06104			0.567669
$115$	9.59742	−	4.78431i	0.894964	−	0.446139i
$116$	−5.35350			−0.497060
$117$	0.292456	−	4.08907i	0.0270376	−	0.378034i
$118$	1.71200	−	0.372423i	0.157602	−	0.0342843i
$119$	−16.8033	−	2.41596i	−1.54036	−	0.221470i
$120$	−0.178020	+	3.22621i	−0.0162510	+	0.294511i
$121$	2.14649	+	14.9291i	0.195135	+	1.35719i
$122$	1.38864	−	0.758255i	0.125722	−	0.0686492i
$123$	1.52201	−	6.99657i	0.137235	−	0.630859i
$124$	−2.27415	+	1.03857i	−0.204225	+	0.0932662i
$125$	11.0278	+	1.84049i	0.986357	+	0.164618i
$126$	−2.65454	−	2.30017i	−0.236486	−	0.204916i
$127$	6.85350	−	0.490172i	0.608150	−	0.0434957i	0.236131	−	0.971721i	$-0.424120\pi$
$127$	6.85350	−	0.490172i	0.608150	−	0.0434957i	0.372018	+	0.928225i	$0.378666\pi$
$128$	0.479249	−	0.877679i	0.0423600	−	0.0775766i
$129$	−2.10859	−	4.61717i	−0.185651	−	0.406519i
$130$	−8.14362	−	5.89189i	−0.714243	−	0.516753i
$131$	−0.613957	−	0.180274i	−0.0536417	−	0.0157506i	0.254802	−	0.966993i	$-0.417990\pi$
$131$	−0.613957	−	0.180274i	−0.0536417	−	0.0157506i	−0.308443	+	0.951243i	$0.599808\pi$
$132$	5.90782	+	4.42254i	0.514209	+	0.384932i
$133$	5.64559	+	15.1364i	0.489534	+	1.31249i
$134$	−0.996516	+	6.93092i	−0.0860858	+	0.598740i
$135$	10.5209	−	7.00589i	0.905491	−	0.602971i
$136$	−3.33112	+	2.88643i	−0.285641	+	0.247510i
$137$	−10.5132	+	10.5132i	−0.898204	+	0.898204i	−0.995277	−	0.0970734i	$-0.969052\pi$
$137$	−10.5132	+	10.5132i	−0.898204	+	0.898204i	0.0970734	+	0.995277i	$0.469052\pi$
$138$	−4.25090	−	5.47305i	−0.361861	−	0.465897i
$139$			3.84520i			0.326145i	0.986614	+	0.163073i	$0.0521405\pi$
$139$			3.84520i			0.326145i	−0.986614	+	0.163073i	$0.947859\pi$
$140$	−8.22271	+	2.56049i	−0.694945	+	0.216401i
$141$	8.33470	+	5.35638i	0.701908	+	0.451089i
$142$	11.1199	−	8.32425i	0.933160	−	0.698555i
$143$	−21.5099	+	8.02278i	−1.79875	+	0.670899i
$144$	−0.902698	+	0.129788i	−0.0752249	+	0.0108157i
$145$	11.9248	−	1.04821i	0.990301	−	0.0870489i
$146$	3.80339	−	2.44429i	0.314771	−	0.202291i
$147$	−3.95587	+	10.6061i	−0.326275	+	0.874777i
$148$	9.91926	+	5.41632i	0.815358	+	0.445219i
$149$	3.52322	−	4.06601i	0.288633	−	0.333101i	−0.592853	−	0.805311i	$-0.701998\pi$
$149$	3.52322	−	4.06601i	0.288633	−	0.333101i	0.881486	+	0.472210i	$0.156544\pi$
$150$	−0.235150	−	7.22116i	−0.0191999	−	0.589605i
$151$	−7.50245	+	2.20292i	−0.610540	+	0.179271i	−0.572363	−	0.820000i	$-0.693973\pi$
$151$	−7.50245	+	2.20292i	−0.610540	+	0.179271i	−0.0381771	+	0.999271i	$0.512155\pi$
$152$	3.93004	+	1.46583i	0.318768	+	0.118894i
$153$	3.92788	+	0.854458i	0.317550	+	0.0690789i
$154$	−5.54165	+	18.8731i	−0.446559	+	1.52084i
$155$	4.86227	−	2.75867i	0.390547	−	0.221581i
$156$	−2.69833	+	5.90853i	−0.216040	+	0.473061i
$157$	0.241379	+	0.322445i	0.0192641	+	0.0257339i	0.810070	−	0.586333i	$-0.199429\pi$
$157$	0.241379	+	0.322445i	0.0192641	+	0.0257339i	−0.790806	+	0.612067i	$0.790338\pi$
$158$	−1.06694	−	4.90465i	−0.0848813	−	0.390193i
$159$	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
$163$	8.79748	+	0.629208i	0.689072	+	0.0492834i	0.411484	−	0.911417i	$-0.365011\pi$
$163$	8.79748	+	0.629208i	0.689072	+	0.0492834i	0.277588	+	0.960700i	$0.410465\pi$
$164$	2.67896	−	4.16855i	0.209192	−	0.325509i
$165$	−14.0255	−	8.69436i	−1.09188	−	0.676855i
$166$	5.25374	+	2.39930i	0.407769	+	0.186222i
$167$	−5.71378	+	7.63271i	−0.442145	+	0.590637i	−0.965151	−	0.261692i	$-0.915720\pi$
$167$	−5.71378	+	7.63271i	−0.442145	+	0.590637i	0.523006	+	0.852329i	$0.324810\pi$
$168$	2.66719	+	4.88460i	0.205778	+	0.376855i
$169$	−3.89617	−	6.06256i	−0.299706	−	0.466351i
$170$	6.85485	−	7.08170i	0.525743	−	0.543142i
$171$	−1.07771	−	3.67035i	−0.0824148	−	0.280679i
$172$	−0.250594	−	3.50377i	−0.0191076	−	0.267160i
$173$	0.717147	+	10.0270i	0.0545237	+	0.762340i	0.949010	+	0.315245i	$0.102087\pi$
$173$	0.717147	+	10.0270i	0.0545237	+	0.762340i	−0.894486	+	0.447095i	$0.852459\pi$
$174$	−2.17942	−	7.42244i	−0.165222	−	0.562693i
$175$	17.8146	−	7.31343i	1.34665	−	0.552843i
$176$	2.76112	+	4.29638i	0.208127	+	0.323852i
$177$	1.21331	+	2.22201i	0.0911980	+	0.167017i
$178$	0.262780	−	0.351032i	0.0196962	−	0.0263110i
$179$	9.25832	+	4.22813i	0.692000	+	0.316026i	0.730189	−	0.683245i	$-0.239432\pi$
$179$	9.25832	+	4.22813i	0.692000	+	0.316026i	−0.0381897	+	0.999271i	$0.512159\pi$
$180$	1.98533	−	0.465848i	0.147978	−	0.0347223i
$181$	−3.71637	+	5.78279i	−0.276236	+	0.429831i	−0.951456	−	0.307785i	$-0.900412\pi$
$181$	−3.71637	+	5.78279i	−0.276236	+	0.429831i	0.675220	+	0.737616i	$0.264049\pi$
$182$	−17.2689	−	1.23510i	−1.28006	−	0.0915514i
$183$	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
$187$	−4.78499	−	21.9962i	−0.349913	−	1.60852i
$188$	4.10888	+	5.48882i	0.299671	+	0.400314i
$189$	9.04424	−	19.8041i	0.657872	−	1.44054i
$190$	−9.04108	−	2.49560i	−0.655909	−	0.181050i
$191$	5.74928	−	19.5803i	0.416004	−	1.41678i	−0.439155	−	0.898411i	$-0.644722\pi$
$191$	5.74928	−	19.5803i	0.416004	−	1.41678i	0.855158	−	0.518367i	$-0.173460\pi$
$192$	1.41198	+	0.307156i	0.101901	+	0.0221671i
$193$	−17.6471	−	6.58201i	−1.27026	−	0.473784i	−0.378213	−	0.925719i	$-0.623461\pi$
$193$	−17.6471	−	6.58201i	−1.27026	−	0.473784i	−0.892051	+	0.451935i	$0.850734\pi$
$194$	−17.0009	+	4.99190i	−1.22059	+	0.358398i
$195$	4.85360	−	13.6895i	0.347574	−	0.980322i
$196$	−5.13005	+	5.92039i	−0.366432	+	0.422885i
$197$	10.2425	+	5.59281i	0.729745	+	0.398471i	0.800745	−	0.599005i	$-0.204437\pi$
$197$	10.2425	+	5.59281i	0.729745	+	0.398471i	−0.0709999	+	0.997476i	$0.522619\pi$
$198$	1.62766	−	4.36393i	0.115673	−	0.310131i
$199$	0.397392	−	0.255389i	0.0281704	−	0.0181040i	−0.526480	−	0.850188i	$-0.676488\pi$
$199$	0.397392	−	0.255389i	0.0281704	−	0.0181040i	0.554650	+	0.832084i	$0.312852\pi$
$200$	1.59392	−	4.73914i	0.112707	−	0.335108i
$201$	−10.0152	+	1.43996i	−0.706415	+	0.101567i
$202$	9.51280	−	3.54809i	0.669318	−	0.249643i
$203$	16.5062	−	12.3564i	1.15851	−	0.867249i
$204$	−5.35805	−	3.44341i	−0.375139	−	0.241087i
$205$	−5.15114	+	9.80989i	−0.359771	+	0.685153i
$206$		−	12.7306i		−	0.886984i
$207$	−2.55843	+	3.54736i	−0.177823	+	0.246558i
$208$	−3.17857	+	3.17857i	−0.220394	+	0.220394i
$209$	−16.1895	+	14.0283i	−1.11985	+	0.970358i
$210$	−6.89752	−	10.3581i	−0.475974	−	0.714778i
$211$	−1.59586	+	11.0995i	−0.109864	+	0.764119i	0.858182	+	0.513346i	$0.171594\pi$
$211$	−1.59586	+	11.0995i	−0.109864	+	0.764119i	−0.968046	+	0.250774i	$0.919315\pi$
$212$	3.19867	+	8.57595i	0.219685	+	0.588999i
$213$	16.0682	+	12.0285i	1.10098	+	0.824180i
$214$	7.18453	+	2.10957i	0.491125	+	0.144207i
$215$	1.24423	+	7.75550i	0.0848556	+	0.528921i
$216$	−2.34826	−	5.14197i	−0.159779	−	0.349867i
$217$	4.61467	−	8.45113i	0.313264	−	0.573700i
$218$	−0.882546	+	0.0631209i	−0.0597735	+	0.00427509i
$219$	4.93730	+	4.27819i	0.333632	+	0.289093i
$220$	−6.99156	−	9.02948i	−0.471371	−	0.608767i
$221$	18.0229	−	8.23079i	1.21235	−	0.553663i
$222$	−3.47139	+	15.9577i	−0.232984	+	1.07101i
$223$	15.5897	−	8.51261i	1.04396	−	0.570047i	0.136700	−	0.990612i	$-0.456350\pi$
$223$	15.5897	−	8.51261i	1.04396	−	0.570047i	0.907262	+	0.420566i	$0.138168\pi$
$224$	0.548121	+	3.81226i	0.0366229	+	0.254718i
$225$	−4.33107	+	1.42639i	−0.288738	+	0.0950928i
$226$	12.6864	+	1.82403i	0.843889	+	0.121333i
$227$	−9.75689	+	2.12248i	−0.647587	+	0.140874i	−0.524350	−	0.851503i	$-0.675691\pi$
$227$	−9.75689	+	2.12248i	−0.647587	+	0.140874i	−0.123238	+	0.992377i	$0.539328\pi$
$228$	−0.432390	+	6.04560i	−0.0286357	+	0.400380i
$229$	−5.61257			−0.370889			−0.185445	−	0.982655i	$-0.559372\pi$
$229$	−5.61257			−0.370889			−0.185445	+	0.982655i	$0.559372\pi$
$230$	4.08745	+	9.91427i	0.269518	+	0.653728i
$231$	−28.4230			−1.87009
$232$	0.381914	−	5.33986i	0.0250739	−	0.350579i
$233$	−0.670892	+	0.145944i	−0.0439516	+	0.00956109i	−0.234487	−	0.972119i	$-0.575341\pi$
$233$	−0.670892	+	0.145944i	−0.0439516	+	0.00956109i	0.190536	+	0.981680i	$0.438977\pi$
$234$	4.05779	+	0.583421i	0.265266	+	0.0381395i
$235$	−10.2272	−	11.4217i	−0.667146	−	0.745071i
$236$	0.249341	+	1.73421i	0.0162307	+	0.112887i
$237$	6.36578	−	3.47598i	0.413502	−	0.225789i
$238$	3.60854	−	16.5882i	0.233907	−	1.07525i
$239$	23.0154	−	10.5108i	1.48874	−	0.679885i	0.505605	−	0.862765i	$-0.331270\pi$
$239$	23.0154	−	10.5108i	1.48874	−	0.679885i	0.983135	+	0.182881i	$0.0585422\pi$
$240$	−3.20529	−	0.407722i	−0.206900	−	0.0263183i
$241$	−17.2841	−	14.9768i	−1.11337	−	0.964740i	−0.113783	−	0.993506i	$-0.536297\pi$
$241$	−17.2841	−	14.9768i	−1.11337	−	0.964740i	−0.999586	+	0.0287653i	$0.990842\pi$
$242$	−15.0442	+	1.07598i	−0.967080	+	0.0691669i
$243$	−4.36533	+	7.99450i	−0.280036	+	0.512847i
$244$	0.657259	+	1.43920i	0.0420767	+	0.0921351i
$245$	10.2679	−	14.1920i	0.655990	−	0.906693i
$246$	6.87016	+	2.01726i	0.438026	+	0.128616i
$247$	−15.0942	−	11.2994i	−0.960421	−	0.718963i
$248$	−0.873687	−	2.34245i	−0.0554792	−	0.148745i
$249$	−1.18774	+	8.26088i	−0.0752697	+	0.523512i
$250$	−2.62251	+	10.8684i	−0.165862	+	0.687379i
$251$	−13.7987	+	11.9567i	−0.870968	+	0.754698i	−0.970694	−	0.240317i	$-0.922749\pi$
$251$	−13.7987	+	11.9567i	−0.870968	+	0.754698i	0.0997266	+	0.995015i	$0.468203\pi$
$252$	2.48369	−	2.48369i	0.156458	−	0.156458i
$253$	24.0219	+	4.78021i	1.51024	+	0.300529i
$254$			6.87101i			0.431125i
$255$	12.6092	+	6.62103i	0.789616	+	0.414625i
$256$	0.841254	+	0.540641i	0.0525783	+	0.0337901i
$257$	−1.26727	+	0.948666i	−0.0790501	+	0.0591761i	−0.638072	−	0.769977i	$-0.720268\pi$
$257$	−1.26727	+	0.948666i	−0.0790501	+	0.0591761i	0.559022	+	0.829153i	$0.311177\pi$
$258$	4.75584	−	1.77383i	0.296085	−	0.110434i
$259$	−43.0850	+	6.19469i	−2.67717	+	0.384919i
$260$	6.45783	−	7.70255i	0.400498	−	0.477692i
$261$	−4.10724	+	2.63956i	−0.254232	+	0.163385i
$262$	0.223614	−	0.599532i	0.0138149	−	0.0370392i
$263$	11.2733	+	6.15569i	0.695142	+	0.379576i	0.787639	−	0.616137i	$-0.211303\pi$
$263$	11.2733	+	6.15569i	0.695142	+	0.379576i	−0.0924973	+	0.995713i	$0.529485\pi$
$264$	−4.83273	+	5.57726i	−0.297434	+	0.343257i
$265$	−8.80412	−	18.4765i	−0.540833	−	1.13500i
$266$	−15.5006	+	4.55138i	−0.950402	+	0.279063i
$267$	0.593673	+	0.221428i	0.0363322	+	0.0135512i
$268$	−6.84217	−	1.48842i	−0.417952	−	0.0909199i
$269$	−2.85068	+	9.70853i	−0.173809	+	0.591940i	0.825799	+	0.563964i	$0.190724\pi$
$269$	−2.85068	+	9.70853i	−0.173809	+	0.591940i	−0.999609	+	0.0279757i	$0.991094\pi$
$270$	6.23749	+	10.9938i	0.379602	+	0.669064i
$271$	3.17455	−	6.95130i	0.192840	−	0.422262i	−0.788370	−	0.615201i	$-0.789075\pi$
$271$	3.17455	−	6.95130i	0.192840	−	0.422262i	0.981211	+	0.192939i	$0.0618021\pi$
$272$	−2.64144	−	3.52855i	−0.160161	−	0.213950i
$273$	−5.31780	−	24.4455i	−0.321848	−	1.47951i
$274$	−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	$0.894294\pi$
$278$	−3.83540	−	0.274313i	−0.230032	−	0.0164522i
$279$	−1.23267	+	1.91808i	−0.0737982	+	0.114832i
$280$	−1.96736	−	8.38442i	−0.117572	−	0.501065i
$281$	22.0711	+	10.0795i	1.31665	+	0.601295i	0.944998	−	0.327077i	$-0.106064\pi$
$281$	22.0711	+	10.0795i	1.31665	+	0.601295i	0.371654	+	0.928371i	$0.378791\pi$
$282$	−5.93733	+	7.93134i	−0.353563	+	0.472304i
$283$	−0.774842	−	1.41902i	−0.0460596	−	0.0843519i	0.853635	−	0.520871i	$-0.174393\pi$
$283$	−0.774842	−	1.41902i	−0.0460596	−	0.0843519i	−0.899695	+	0.436519i	$0.856211\pi$
$284$	7.50975	+	11.6854i	0.445622	+	0.693401i
$285$	−0.220581	−	13.5511i	−0.0130661	−	0.802699i
$286$	−6.46784	−	22.0274i	−0.382452	−	1.30251i
$287$	1.36148	+	19.0360i	0.0803658	+	1.12366i
$288$	−0.0650600	−	0.909657i	−0.00383370	−	0.0536021i
$289$	0.684014	+	2.32954i	0.0402361	+	0.137032i
$290$	0.194831	+	11.9692i	0.0114409	+	0.702855i
$291$	−13.8422	−	21.5389i	−0.811444	−	1.26263i
$292$	2.16673	+	3.96808i	0.126798	+	0.232214i
$293$	−3.85915	+	5.15522i	−0.225454	+	0.301171i	−0.898978	−	0.437994i	$-0.855689\pi$
$293$	−3.85915	+	5.15522i	−0.225454	+	0.301171i	0.673524	+	0.739166i	$0.264780\pi$
$294$	−10.2969	−	4.70242i	−0.600526	−	0.274251i
$295$	−0.894957	−	3.81409i	−0.0521064	−	0.222065i
$296$	−6.11016	+	9.50759i	−0.355146	+	0.552617i
$297$	28.7960	+	2.05953i	1.67091	+	0.119506i
$298$	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
$302$	−1.66209	−	7.64048i	−0.0956423	−	0.439660i
$303$	8.79200	+	11.7447i	0.505087	+	0.674717i
$304$	−1.74246	+	3.81545i	−0.0999368	+	0.218831i
$305$	−1.74582	−	3.07709i	−0.0999655	−	0.176194i
$306$	−1.13249	+	3.85692i	−0.0647403	+	0.220485i
$307$	2.14169	+	0.465897i	0.122233	+	0.0265901i	0.273266	−	0.961939i	$-0.411896\pi$
$307$	2.14169	+	0.465897i	0.122233	+	0.0265901i	−0.151033	+	0.988529i	$0.548260\pi$
$308$	−18.4297	−	6.87392i	−1.05013	−	0.391678i
$309$	17.6506	−	5.18267i	1.00411	−	0.294832i
$310$	2.40477	+	5.04668i	0.136582	+	0.286632i
$311$	12.6206	−	14.5650i	0.715651	−	0.825905i	−0.275126	−	0.961408i	$-0.588720\pi$
$311$	12.6206	−	14.5650i	0.715651	−	0.825905i	0.990777	+	0.135503i	$0.0432651\pi$
$312$	−5.70098	−	3.11297i	−0.322754	−	0.176237i
$313$	1.76074	−	4.72074i	0.0995231	−	0.266832i	−0.877641	−	0.479319i	$-0.840884\pi$
$313$	1.76074	−	4.72074i	0.0995231	−	0.266832i	0.977164	+	0.212487i	$0.0681564\pi$
$314$	−0.338843	+	0.217761i	−0.0191220	+	0.0122890i
$315$	−5.04606	+	6.01866i	−0.284313	+	0.339113i
$316$	4.96827	−	0.714329i	0.279487	−	0.0401842i
$317$	−2.45939	+	0.917304i	−0.138133	+	0.0515209i	−0.417580	−	0.908640i	$-0.637122\pi$
$317$	−2.45939	+	0.917304i	−0.138133	+	0.0515209i	0.279447	+	0.960161i	$0.409849\pi$
$318$	−10.5881	+	7.92614i	−0.593750	+	0.444476i
$319$	23.0007	+	14.7816i	1.28779	+	0.827612i
$320$	−1.97973	−	1.03955i	−0.110670	−	0.0581126i
$321$			10.8199i			0.603909i
$322$	14.9812	+	10.8047i	0.834867	+	0.602124i
$323$	13.0731	−	13.0731i	0.727406	−	0.727406i
$324$	4.10549	−	3.55743i	0.228083	−	0.197635i
$325$	−12.8765	+	18.4217i	−0.714262	+	1.02185i
$326$	−1.25521	+	8.73017i	−0.0695196	+	0.483520i
$327$	−0.446802	−	1.19792i	−0.0247082	−	0.0662452i
$328$	3.96681	+	2.96952i	0.219031	+	0.163964i
$329$	−25.3375	−	7.43976i	−1.39690	−	0.410167i
$330$	9.67277	−	13.3695i	0.532469	−	0.735965i
$331$	1.40492	+	3.07634i	0.0772213	+	0.169091i	0.944305	−	0.329071i	$-0.106736\pi$
$331$	1.40492	+	3.07634i	0.0772213	+	0.169091i	−0.867084	+	0.498162i	$0.834008\pi$
$332$	−2.76798	+	5.06919i	−0.151913	+	0.278208i
$333$	10.2807	−	0.735288i	0.563377	−	0.0402935i
$334$	−7.20565	−	6.24373i	−0.394276	−	0.341642i
$335$	15.5322	+	1.97574i	0.848616	+	0.107946i
$336$	−5.06243	+	2.31193i	−0.276178	+	0.126126i
$337$	−4.75052	+	21.8378i	−0.258777	+	1.18958i	0.645880	+	0.763439i	$0.276491\pi$
$337$	−4.75052	+	21.8378i	−0.258777	+	1.18958i	−0.904657	+	0.426140i	$0.859873\pi$
$338$	6.32507	−	3.45375i	0.344038	−	0.187859i
$339$	2.63572	+	18.3319i	0.143153	+	0.995650i
$340$	6.57464	+	7.34258i	0.356560	+	0.398208i
$341$	12.6382	+	1.81710i	0.684398	+	0.0984016i
$342$	3.73788	−	0.813127i	0.202122	−	0.0439689i
$343$	0.229094	−	3.20316i	0.0123699	−	0.172954i
$344$	3.51272			0.189393
$345$	−12.0818	+	9.70323i	−0.650461	+	0.522405i
$346$	−10.0526			−0.540433
$347$	−0.857522	+	11.9897i	−0.0460342	+	0.643642i	0.921092	+	0.389345i	$0.127299\pi$
$347$	−0.857522	+	11.9897i	−0.0460342	+	0.643642i	−0.967126	+	0.254297i	$0.918156\pi$
$348$	7.55900	−	1.64436i	0.405205	−	0.0881470i
$349$	29.6320	+	4.26044i	1.58617	+	0.228056i	0.878236	−	0.478227i	$-0.158721\pi$
$349$	29.6320	+	4.26044i	1.58617	+	0.228056i	0.707929	+	0.706284i	$0.249630\pi$
$350$	6.02392	+	18.2909i	0.321992	+	0.977690i
$351$	3.61627	+	25.1517i	0.193022	+	1.34250i
$352$	−4.48241	+	2.44758i	−0.238913	+	0.130457i
$353$	−1.32429	+	6.08765i	−0.0704847	+	0.324013i	−0.998866	−	0.0476169i	$-0.984837\pi$
$353$	−1.32429	+	6.08765i	−0.0704847	+	0.324013i	0.928381	+	0.371630i	$0.121201\pi$
$354$	−2.30291	+	1.05170i	−0.122398	+	0.0558974i
$355$	−19.0158	−	24.5586i	−1.00925	−	1.30343i
$356$	0.331392	+	0.287152i	0.0175637	+	0.0152190i
$357$	24.4680	−	1.74998i	1.29498	−	0.0926190i
$358$	−4.87784	+	8.93310i	−0.257802	+	0.472129i
$359$	7.43931	+	16.2898i	0.392632	+	0.859743i	0.997965	+	0.0637709i	$0.0203127\pi$
$359$	7.43931	+	16.2898i	0.392632	+	0.859743i	−0.605333	+	0.795972i	$0.706960\pi$
$360$	0.323029	+	2.01350i	0.0170251	+	0.106121i
$361$	1.34921	+	0.396164i	0.0710111	+	0.0208507i
$362$	−5.50293	−	4.11944i	−0.289228	−	0.216513i
$363$	−7.61637	−	20.4203i	−0.399756	−	1.07179i
$364$	2.46390	−	17.1368i	0.129143	−	0.898212i
$365$	−5.60330	−	8.41456i	−0.293290	−	0.440438i
$366$	−1.72782	+	1.49717i	−0.0903148	+	0.0782582i
$367$	−11.5504	+	11.5504i	−0.602925	+	0.602925i	−0.941088	−	0.338163i	$-0.890194\pi$
$367$	−11.5504	+	11.5504i	−0.602925	+	0.602925i	0.338163	+	0.941088i	$0.390194\pi$
$368$	4.66738	−	1.10254i	0.243304	−	0.0574740i
$369$		−	4.51901i		−	0.235251i
$370$	11.7487	−	22.3743i	0.610784	−	1.16319i
$371$	−29.6565	−	19.0590i	−1.53969	−	0.989496i
$372$	2.89204	−	2.16495i	0.149945	−	0.112248i
$373$	20.6517	−	7.70269i	1.06931	−	0.398830i	0.247670	−	0.968844i	$-0.420335\pi$
$373$	20.6517	−	7.70269i	1.06931	−	0.398830i	0.821635	+	0.570014i	$0.193062\pi$
$374$	22.2816	−	3.20360i	1.15215	−	0.165654i
$375$	−16.1363	+	0.788543i	−0.833276	+	0.0407202i
$376$	−5.76796	+	3.70684i	−0.297460	+	0.191166i
$377$	−8.40982	+	22.5476i	−0.433128	+	1.16126i
$378$	19.1085	+	10.4340i	0.982833	+	0.536668i
$379$	−8.62258	+	9.95099i	−0.442912	+	0.511148i	−0.932680	−	0.360705i	$-0.882536\pi$
$379$	−8.62258	+	9.95099i	−0.442912	+	0.511148i	0.489768	+	0.871853i	$0.337082\pi$
$380$	3.13423	−	8.84001i	0.160783	−	0.453483i
$381$	−9.52641	+	2.79721i	−0.488053	+	0.143305i
$382$	19.1202	+	7.13148i	0.978276	+	0.364878i
$383$	−11.9077	−	2.59036i	−0.608456	−	0.132361i	−0.102227	−	0.994761i	$-0.532597\pi$
$383$	−11.9077	−	2.59036i	−0.608456	−	0.132361i	−0.506228	+	0.862400i	$0.668961\pi$
$384$	−0.407103	+	1.38647i	−0.0207749	+	0.0707528i
$385$	42.3977	+	11.7030i	2.16079	+	0.596441i
$386$	7.82417	−	17.1325i	0.398240	−	0.872024i
$387$	−1.91981	−	2.56456i	−0.0975892	−	0.130364i
$388$	−3.76636	−	17.3137i	−0.191208	−	0.878968i
$389$	−2.84672	−	3.28529i	−0.144335	−	0.166571i	0.678979	−	0.734158i	$-0.262423\pi$
$389$	−2.84672	−	3.28529i	−0.144335	−	0.166571i	−0.823314	+	0.567587i	$0.807877\pi$
$390$	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
$393$	0.922265	+	0.0659617i	0.0465221	+	0.00332733i
$394$	−6.30925	+	9.81738i	−0.317855	+	0.494592i
$395$	−10.9269	+	2.56393i	−0.549790	+	0.129006i
$396$	4.23670	+	1.93483i	0.212902	+	0.0972291i
$397$	−10.0908	+	13.4797i	−0.506441	+	0.676526i	−0.978785	−	0.204888i	$-0.934317\pi$
$397$	−10.0908	+	13.4797i	−0.506441	+	0.676526i	0.472345	+	0.881414i	$0.343408\pi$
$398$	0.226388	+	0.414599i	0.0113478	+	0.0207820i
$399$	−12.6207	−	19.6381i	−0.631824	−	0.983137i
$400$	4.61335	+	1.92795i	0.230668	+	0.0963973i
$401$	−2.04021	−	6.94831i	−0.101883	−	0.346982i	0.892736	−	0.450580i	$-0.148783\pi$
$401$	−2.04021	−	6.94831i	−0.101883	−	0.346982i	−0.994619	+	0.103598i	$0.966964\pi$
$402$	−0.721821	−	10.0924i	−0.0360011	−	0.503362i
$403$	0.801729	+	11.2096i	0.0399370	+	0.558392i
$404$	2.86042	+	9.74168i	0.142311	+	0.484667i
$405$	−8.44836	+	8.72795i	−0.419803	+	0.433696i
$406$	11.1474	+	17.3456i	0.553235	+	0.860850i
$407$	−27.6618	−	50.6588i	−1.37115	−	2.51106i
$408$	3.81688	−	5.09875i	0.188964	−	0.252426i
$409$	−28.4597	−	12.9971i	−1.40724	−	0.642667i	−0.440346	−	0.897828i	$-0.645144\pi$
$409$	−28.4597	−	12.9971i	−1.40724	−	0.642667i	−0.966898	+	0.255162i	$0.917871\pi$
$410$	−9.41742	−	5.83784i	−0.465093	−	0.288311i
$411$	11.6152	−	18.0736i	0.572935	−	0.891504i
$412$	12.6982	+	0.908192i	0.625595	+	0.0447434i
$413$	−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
$417$	−1.18108	−	5.42933i	−0.0578376	−	0.265875i
$418$	−12.8376	−	17.1490i	−0.627908	−	0.838787i
$419$	7.16464	−	15.6884i	0.350015	−	0.766427i	−0.649964	−	0.759965i	$-0.725216\pi$
$419$	7.16464	−	15.6884i	0.350015	−	0.766427i	0.999979	−	0.00646156i	$-0.00205679\pi$
$420$	10.8238	−	6.14100i	0.528147	−	0.299650i
$421$	1.30723	−	4.45201i	0.0637104	−	0.216978i	−0.921485	−	0.388415i	$-0.873023\pi$
$421$	1.30723	−	4.45201i	0.0637104	−	0.216978i	0.985195	+	0.171437i	$0.0548410\pi$
$422$	−10.9573	−	2.38363i	−0.533395	−	0.116033i
$423$	5.85865	+	2.18516i	0.284857	+	0.106246i
$424$	−8.78229	+	2.57871i	−0.426506	+	0.125233i
$425$	−16.0825	−	15.0681i	−0.780118	−	0.730912i
$426$	−13.1442	+	15.1692i	−0.636837	+	0.734949i
$427$	−5.34830	−	2.92040i	−0.258823	−	0.141328i
$428$	−2.61673	+	7.01573i	−0.126485	+	0.339118i
$429$	27.9072	−	17.9349i	1.34737	−	0.865904i
$430$	−7.82451	+	0.687785i	−0.377331	+	0.0331680i
$431$	13.5950	−	1.95467i	0.654849	−	0.0941530i	0.193121	−	0.981175i	$-0.438139\pi$
$431$	13.5950	−	1.95467i	0.654849	−	0.0941530i	0.461727	+	0.887022i	$0.347230\pi$
$432$	5.29639	−	1.97545i	0.254823	−	0.0950440i
$433$	−26.9262	+	20.1567i	−1.29399	+	0.968670i	−0.294075	+	0.955782i	$0.595012\pi$
$433$	−26.9262	+	20.1567i	−1.29399	+	0.968670i	−0.999917	+	0.0128880i	$0.995898\pi$
$434$	8.10040	+	5.20581i	0.388831	+	0.249887i
$435$	−16.5156	+	5.14282i	−0.791860	+	0.246579i
$436$		−	0.884800i		−	0.0423742i
$437$	7.36369	+	18.7199i	0.352253	+	0.895494i
$438$	−4.61952	+	4.61952i	−0.220729	+	0.220729i
$439$	−21.5579	+	18.6800i	−1.02890	+	0.891548i	−0.994167	−	0.107848i	$-0.965604\pi$
$439$	−21.5579	+	18.6800i	−1.02890	+	0.891548i	−0.0347342	+	0.999397i	$0.511058\pi$
$440$	9.50524	−	6.32959i	0.453145	−	0.301751i
$441$	−1.01674	+	7.07155i	−0.0484160	+	0.336741i
$442$	6.92408	+	18.5642i	0.329345	+	0.883007i
$443$	23.7345	+	17.7674i	1.12766	+	0.844154i	0.989252	−	0.146222i	$-0.0467112\pi$
$443$	23.7345	+	17.7674i	1.12766	+	0.844154i	0.138406	+	0.990376i	$0.455802\pi$
$444$	−15.6694	−	4.60095i	−0.743637	−	0.218352i
$445$	−0.794392	−	0.574740i	−0.0376578	−	0.0272453i
$446$	7.37877	+	16.1572i	0.349395	+	0.765068i
$447$	−3.72580	+	6.82329i	−0.176224	+	0.322730i
$448$	−3.84165	+	0.274760i	−0.181501	+	0.0129812i
$449$	3.17308	+	2.74949i	0.149747	+	0.129756i	0.726512	−	0.687153i	$-0.241140\pi$
$449$	3.17308	+	2.74949i	0.149747	+	0.129756i	−0.576766	+	0.816910i	$0.695685\pi$
$450$	−1.11378	−	4.42179i	−0.0525042	−	0.208445i
$451$	−23.0197	+	10.5127i	−1.08396	+	0.495026i
$452$	−2.72443	+	12.5240i	−0.128146	+	0.589079i
$453$	9.91663	−	5.41489i	0.465924	−	0.254414i
$454$	−1.42103	−	9.88345i	−0.0666920	−	0.463853i
$455$	−2.13292	+	38.6543i	−0.0999929	+	1.81214i
$456$	−5.99935	−	0.862576i	−0.280945	−	0.0403938i
$457$	25.7302	−	5.59726i	1.20361	−	0.261829i	0.434336	−	0.900751i	$-0.356983\pi$
$457$	25.7302	−	5.59726i	1.20361	−	0.261829i	0.769271	+	0.638922i	$0.220619\pi$
$458$	0.400396	−	5.59827i	0.0187093	−	0.261590i
$459$	−24.9159			−1.16297
$460$	−10.1806	+	3.36976i	−0.474673	+	0.157116i
$461$	−3.34945			−0.156000			−0.0779998	−	0.996953i	$-0.524853\pi$
$461$	−3.34945			−0.156000			−0.0779998	+	0.996953i	$0.524853\pi$
$462$	2.02767	−	28.3505i	0.0943358	−	1.31899i
$463$	−36.3030	+	7.89723i	−1.68714	+	0.367015i	−0.950851	−	0.309649i	$-0.899788\pi$
$463$	−36.3030	+	7.89723i	−1.68714	+	0.367015i	−0.736291	+	0.676665i	$0.763425\pi$
$464$	5.29900	+	0.761882i	0.246000	+	0.0353695i
$465$	−6.01806	+	5.38864i	−0.279081	+	0.249892i
$466$	−0.0977109	−	0.679594i	−0.00452637	−	0.0314816i
$467$	29.5812	−	16.1526i	1.36886	−	0.747452i	0.384414	−	0.923161i	$-0.374404\pi$
$467$	29.5812	−	16.1526i	1.36886	−	0.747452i	0.984442	+	0.175709i	$0.0562219\pi$
$468$	−0.871414	+	4.00583i	−0.0402811	+	0.185169i
$469$	24.5316	−	11.2032i	1.13276	−	0.517316i
$470$	12.1222	−	9.38628i	0.559156	−	0.432957i
$471$	−0.439862	−	0.381143i	−0.0202678	−	0.0175621i
$472$	−1.74757	+	0.124989i	−0.0804387	+	0.00575309i
$473$	−8.59766	+	15.7454i	−0.395321	+	0.723976i
$474$	3.01299	+	6.59753i	0.138391	+	0.303035i
$475$	−5.25057	+	20.3046i	−0.240913	+	0.931640i
$476$	16.2885	+	4.78273i	0.746581	+	0.219216i
$477$	6.68245	+	5.00242i	0.305968	+	0.229045i
$478$	8.84208	+	23.7065i	0.404428	+	1.08431i
$479$	5.77308	−	40.1527i	0.263779	−	1.83462i	−0.239980	−	0.970778i	$-0.577141\pi$
$479$	5.77308	−	40.1527i	0.263779	−	1.83462i	0.503758	−	0.863845i	$-0.331950\pi$
$480$	0.635345	−	3.16803i	0.0289994	−	0.144600i
$481$	38.3944	−	33.2689i	1.75063	−	1.51693i
$482$	16.1717	−	16.1717i	0.736600	−	0.736600i
$483$	−8.88152	+	25.1695i	−0.404123	+	1.14525i
$484$		−	15.0827i		−	0.685576i
$485$	11.7795	+	37.8284i	0.534878	+	1.71770i
$486$	−7.66271	−	4.92453i	−0.347588	−	0.223381i
$487$	23.3558	−	17.4840i	1.05835	−	0.792274i	0.0794998	−	0.996835i	$-0.474668\pi$
$487$	23.3558	−	17.4840i	1.05835	−	0.792274i	0.978854	+	0.204561i	$0.0655768\pi$
$488$	−1.48242	+	0.552913i	−0.0671059	+	0.0250292i
$489$	−12.6151	+	1.81378i	−0.570474	+	0.0820217i
$490$	13.4233	+	11.2541i	0.606404	+	0.508411i
$491$	6.97129	−	4.48018i	0.314610	−	0.202188i	−0.373800	−	0.927509i	$-0.621945\pi$
$491$	6.97129	−	4.48018i	0.314610	−	0.202188i	0.688410	+	0.725322i	$0.258309\pi$
$492$	−2.50223	+	6.70875i	−0.112809	+	0.302454i
$493$	−20.7103	−	11.3087i	−0.932744	−	0.509317i
$494$	12.3474	−	14.2497i	0.555536	−	0.641123i
$495$	−9.81599	−	3.48026i	−0.441196	−	0.156426i
$496$	2.39881	−	0.704353i	0.107710	−	0.0316264i
$497$	−50.1256	−	18.6959i	−2.24844	−	0.838624i
$498$	−8.15510	−	1.77403i	−0.365439	−	0.0794964i
$499$	−4.12780	+	14.0580i	−0.184786	+	0.629323i	0.814037	+	0.580813i	$0.197265\pi$
$499$	−4.12780	+	14.0580i	−0.184786	+	0.629323i	−0.998823	+	0.0485095i	$0.984553\pi$
$500$	−10.6536	−	3.39117i	−0.476445	−	0.151658i
$501$	5.72327	−	12.5322i	0.255697	−	0.559898i
$502$	−10.9418	−	14.6165i	−0.488357	−	0.652368i
$503$	3.67008	+	16.8711i	0.163641	+	0.752245i	0.983678	+	0.179935i	$0.0575889\pi$
$503$	3.67008	+	16.8711i	0.163641	+	0.752245i	−0.820038	+	0.572310i	$0.806048\pi$
$504$	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
$508$	−6.85350	−	0.490172i	−0.304075	−	0.0217479i
$509$	5.21621	−	8.11659i	0.231205	−	0.359761i	−0.706195	−	0.708018i	$-0.749590\pi$
$509$	5.21621	−	8.11659i	0.231205	−	0.359761i	0.937399	+	0.348256i	$0.113226\pi$
$510$	−7.50368	+	12.1047i	−0.332269	+	0.536005i
$511$	−15.8393	−	7.23357i	−0.700689	−	0.319994i
$512$	−0.599278	+	0.800541i	−0.0264846	+	0.0353793i
$513$	11.3633	+	20.8104i	0.501703	+	0.918800i
$514$	−0.855843	−	1.33172i	−0.0377496	−	0.0587395i
$515$	−28.4628	+	0.463308i	−1.25422	+	0.0204158i
$516$	1.43004	+	4.87026i	0.0629539	+	0.214401i
$517$	−2.49804	−	34.9272i	−0.109864	−	1.53610i
$518$	−3.10526	−	43.4172i	−0.136437	−	1.90764i
$519$	−4.09246	−	13.9376i	−0.179639	−	0.611794i
$520$	7.22223	+	6.99087i	0.316716	+	0.306570i
$521$	9.24888	+	14.3915i	0.405201	+	0.630505i	0.982551	−	0.185992i	$-0.0595497\pi$
$521$	9.24888	+	14.3915i	0.405201	+	0.630505i	−0.577350	+	0.816496i	$0.695913\pi$
$522$	−2.33983	−	4.28508i	−0.102412	−	0.187553i
$523$	−1.74505	+	2.33112i	−0.0763058	+	0.101933i	−0.837070	−	0.547096i	$-0.815733\pi$
$523$	−1.74505	+	2.33112i	−0.0763058	+	0.101933i	0.760764	+	0.649028i	$0.224824\pi$
$524$	0.582052	+	0.265814i	0.0254271	+	0.0116122i
$525$	−22.9074	+	15.7982i	−0.999759	+	0.689492i
$526$	−6.94424	+	10.8054i	−0.302783	+	0.471140i
$527$	−10.9915	−	0.786129i	−0.478798	−	0.0342443i
$528$	−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
$532$	−3.43399	−	15.7858i	−0.148882	−	0.684401i
$533$	−13.3485	−	17.8315i	−0.578188	−	0.772368i
$534$	−0.263216	+	0.576363i	−0.0113905	+	0.0249417i
$535$	4.45505	−	16.1398i	0.192608	−	0.697782i
$536$	1.97274	−	6.71855i	0.0852096	−	0.290197i
$537$	−14.3712	−	3.12627i	−0.620164	−	0.134908i
$538$	−9.48043	−	3.53602i	−0.408730	−	0.152449i
$539$	38.3875	−	11.2716i	1.65347	−	0.485502i
$540$	−11.4108	+	5.43731i	−0.491043	+	0.233984i
$541$	21.9485	−	25.3299i	0.943641	−	1.08902i	−0.0522661	−	0.998633i	$-0.516644\pi$
$541$	21.9485	−	25.3299i	0.943641	−	1.08902i	0.995907	−	0.0903862i	$-0.0288102\pi$
$542$	6.70712	+	3.66237i	0.288096	+	0.157312i
$543$	3.47120	−	9.30666i	0.148964	−	0.399387i
$544$	3.70800	−	2.38299i	0.158979	−	0.102170i
$545$	0.173243	+	1.97087i	0.00742090	+	0.0844229i
$546$	24.7626	−	3.56033i	1.05974	−	0.152368i
$547$	−1.49245	+	0.556656i	−0.0638126	+	0.0238009i	−0.381168	−	0.924506i	$-0.624478\pi$
$547$	−1.49245	+	0.556656i	−0.0638126	+	0.0238009i	0.317355	+	0.948307i	$0.397205\pi$
$548$	11.9024	−	8.91001i	0.508445	−	0.380617i
$549$	1.21386	+	0.780097i	0.0518061	+	0.0332937i
$550$	−19.9334	+	15.9601i	−0.849963	+	0.680542i
$551$			22.4552i			0.956625i
$552$	3.42874	+	6.02231i	0.145937	+	0.256326i
$553$	−13.6697	+	13.6697i	−0.581295	+	0.581295i
$554$	11.0171	−	9.54640i	0.468073	−	0.405588i
$555$	35.8041	+	7.18048i	1.51980	+	0.304794i
$556$	0.547229	−	3.80606i	0.0232077	−	0.161413i
$557$	−5.91169	−	15.8499i	−0.250486	−	0.671580i	−0.999954	−	0.00953951i	$-0.996963\pi$
$557$	−5.91169	−	15.8499i	−0.250486	−	0.671580i	0.749468	−	0.662040i	$-0.230309\pi$
$558$	−1.82525	−	1.36637i	−0.0772690	−	0.0578429i
$559$	−15.1507	−	4.44863i	−0.640805	−	0.188157i
$560$	8.50341	−	1.36421i	0.359334	−	0.0576486i
$561$	13.5126	+	29.5884i	0.570501	+	1.24922i
$562$	−11.6284	+	21.2958i	−0.490514	+	0.898309i
$563$	−3.79119	+	0.271151i	−0.159780	+	0.0114277i	−0.151000	−	0.988534i	$-0.548249\pi$
$563$	−3.79119	+	0.271151i	−0.159780	+	0.0114277i	−0.00877976	+	0.999961i	$0.502795\pi$
$564$	−7.48757	−	6.48801i	−0.315283	−	0.273195i
$565$	3.61642	−	28.4304i	0.152144	−	1.19607i
$566$	1.47068	−	0.671637i	0.0618173	−	0.0282310i
$567$	−4.44740	+	20.4444i	−0.186773	+	0.858583i
$568$	−12.1914	+	6.65699i	−0.511539	+	0.279321i
$569$	−5.78489	−	40.2348i	−0.242515	−	1.68673i	−0.639411	−	0.768865i	$-0.720822\pi$
$569$	−5.78489	−	40.2348i	−0.242515	−	1.68673i	0.396896	−	0.917864i	$-0.370087\pi$
$570$	13.5323	+	0.746706i	0.566807	+	0.0312761i
$571$	21.1134	+	3.03564i	0.883567	+	0.127038i	0.569137	−	0.822243i	$-0.307278\pi$
$571$	21.1134	+	3.03564i	0.883567	+	0.127038i	0.314430	+	0.949281i	$0.398187\pi$
$572$	22.4327	−	4.87994i	0.937960	−	0.204041i
$573$	−2.10364	+	29.4128i	−0.0878810	+	1.22874i
$574$	−19.0846			−0.796578
$575$	22.0173	−	9.49941i	0.918185	−	0.396153i
$576$	0.911981			0.0379992
$577$	0.385723	−	5.39311i	0.0160578	−	0.224518i	−0.983086	−	0.183145i	$-0.941372\pi$
$577$	0.385723	−	5.39311i	0.0160578	−	0.224518i	0.999144	−	0.0413731i	$-0.0131732\pi$
$578$	−2.37240	+	0.516084i	−0.0986787	+	0.0214662i
$579$	26.9389	+	3.87323i	1.11954	+	0.160966i
$580$	−11.9526	−	0.659538i	−0.496305	−	0.0273858i
$581$	−3.16577	−	22.0184i	−0.131338	−	0.913477i
$582$	22.4715	−	12.2704i	0.931474	−	0.508623i
$583$	9.93652	−	45.6775i	0.411529	−	1.89177i
$584$	−4.11254	+	1.87813i	−0.170178	+	0.0777177i
$585$	1.15672	−	9.09351i	0.0478245	−	0.375971i
$586$	−4.86678	−	4.21709i	−0.201045	−	0.174206i
$587$	−19.1285	+	1.36810i	−0.789517	+	0.0564674i	−0.460273	−	0.887777i	$-0.652249\pi$
$587$	−19.1285	+	1.36810i	−0.789517	+	0.0564674i	−0.329244	+	0.944245i	$0.606794\pi$
$588$	5.42501	−	9.93517i	0.223724	−	0.409719i
$589$	4.35628	+	9.53892i	0.179497	+	0.393044i
$590$	3.86821	−	0.620583i	0.159252	−	0.0255490i
$591$	−16.1800	−	4.75087i	−0.665555	−	0.195425i
$592$	−9.04747	−	6.77285i	−0.371849	−	0.278362i
$593$	−4.42929	−	11.8754i	−0.181889	−	0.487664i	0.813722	−	0.581255i	$-0.197438\pi$
$593$	−4.42929	−	11.8754i	−0.181889	−	0.487664i	−0.995611	+	0.0935911i	$0.970165\pi$
$594$	−4.10856	+	28.5757i	−0.168576	+	1.17247i
$595$	−37.2187	−	7.46417i	−1.52582	−	0.306001i
$596$	−4.06601	+	3.52322i	−0.166550	+	0.144317i
$597$	−0.482664	+	0.482664i	−0.0197541	+	0.0197541i
$598$	−21.5271	−	1.15557i	−0.880309	−	0.0472549i
$599$			18.6925i			0.763755i	0.924213	+	0.381878i	$0.124722\pi$
$599$			18.6925i			0.763755i	−0.924213	+	0.381878i	$0.875278\pi$
$600$	−0.794922	+	7.18113i	−0.0324525	+	0.293168i
$601$	12.4433	+	7.99682i	0.507572	+	0.326197i	0.769239	−	0.638961i	$-0.220636\pi$
$601$	12.4433	+	7.99682i	0.507572	+	0.326197i	−0.261666	+	0.965158i	$0.584272\pi$
$602$	−10.8306	+	8.10770i	−0.441423	+	0.330445i
$603$	−5.98323	+	2.23163i	−0.243656	+	0.0908790i
$604$	7.73959	−	1.11278i	0.314919	−	0.0452786i
$605$	2.95316	+	33.5963i	0.120063	+	1.36588i
$606$	−12.3420	+	7.93174i	−0.501360	+	0.322205i
$607$	−0.888014	+	2.38086i	−0.0360434	+	0.0966360i	−0.953725	−	0.300681i	$-0.902786\pi$
$607$	−0.888014	+	2.38086i	−0.0360434	+	0.0966360i	0.917681	+	0.397317i	$0.130059\pi$
$608$	−3.68142	−	2.01021i	−0.149301	−	0.0815248i
$609$	−19.5110	+	22.5169i	−0.790626	+	0.912431i
$610$	3.19379	−	1.52186i	0.129313	−	0.0616182i
$611$	29.5722	−	8.68319i	1.19636	−	0.351284i
$612$	−3.76630	−	1.40476i	−0.152244	−	0.0567839i
$613$	−4.35241	−	0.946808i	−0.175792	−	0.0382412i	0.123808	−	0.992306i	$-0.460489\pi$
$613$	−4.35241	−	0.946808i	−0.175792	−	0.0382412i	−0.299600	+	0.954065i	$0.596853\pi$
$614$	−0.617497	+	2.10300i	−0.0249201	+	0.0848702i
$615$	4.26011	−	15.4335i	0.171784	−	0.622340i
$616$	8.17117	−	17.8924i	0.329226	−	0.720904i
$617$	13.3550	+	17.8402i	0.537651	+	0.718218i	0.984302	−	0.176491i	$-0.0564745\pi$
$617$	13.3550	+	17.8402i	0.537651	+	0.718218i	−0.446651	+	0.894708i	$0.647384\pi$
$618$	3.91029	+	17.9753i	0.157295	+	0.723073i
$619$	−1.96613	−	2.26904i	−0.0790256	−	0.0912004i	0.714860	−	0.699268i	$-0.246490\pi$
$619$	−1.96613	−	2.26904i	−0.0790256	−	0.0912004i	−0.793885	+	0.608067i	$0.791945\pi$
$620$	−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
$623$	−1.68454	−	0.120481i	−0.0674897	−	0.00482696i
$624$	3.51174	−	5.46438i	0.140582	−	0.218750i
$625$	24.3947	+	5.46780i	0.975789	+	0.218712i
$626$	4.58310	+	2.09303i	0.183177	+	0.0836543i
$627$	18.5503	−	24.7803i	0.740829	−	0.989631i
$628$	−0.193033	−	0.353514i	−0.00770287	−	0.0141068i
$629$	26.9318	+	41.9067i	1.07384	+	1.67093i
$630$	−5.64335	−	5.46257i	−0.224836	−	0.217634i
$631$	10.2222	+	34.8138i	0.406941	+	1.38591i	0.867125	+	0.498091i	$0.165965\pi$
$631$	10.2222	+	34.8138i	0.406941	+	1.38591i	−0.460184	+	0.887824i	$0.652216\pi$
$632$	0.358077	+	5.00657i	0.0142435	+	0.199151i
$633$	−1.15596	−	16.1624i	−0.0459451	−	0.642396i
$634$	−0.739516	−	2.51856i	−0.0293699	−	0.100025i
$635$	15.3620	−	0.250058i	0.609622	−	0.00992325i
$636$	−7.15060	−	11.1265i	−0.283540	−	0.441196i
$637$	16.8764	+	30.9068i	0.668667	+	1.22457i
$638$	−16.3848	+	21.8875i	−0.648681	+	0.866536i
$639$	11.5231	+	5.26241i	0.455846	+	0.208178i
$640$	1.17813	−	1.90053i	0.0465698	−	0.0751249i
$641$	−10.4200	+	16.2138i	−0.411564	+	0.640406i	−0.983714	−	0.179744i	$-0.942473\pi$
$641$	−10.4200	+	16.2138i	−0.411564	+	0.640406i	0.572150	+	0.820149i	$0.306110\pi$
$642$	−10.7924	−	0.771884i	−0.425940	−	0.0304638i
$643$	−7.67790	−	7.67790i	−0.302787	−	0.302787i	0.539316	−	0.842103i	$-0.318683\pi$
$643$	−7.67790	−	7.67790i	−0.302787	−	0.302787i	−0.842103	+	0.539316i	$0.818683\pi$
$644$	−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
$647$	5.12663	+	23.5667i	0.201548	+	0.926504i	0.961131	+	0.276093i	$0.0890396\pi$
$647$	5.12663	+	23.5667i	0.201548	+	0.926504i	−0.759583	+	0.650411i	$0.774597\pi$
$648$	3.25548	+	4.34882i	0.127888	+	0.170838i
$649$	3.71708	−	8.13927i	0.145908	−	0.319494i
$650$	−17.4562	−	14.1579i	−0.684687	−	0.555319i
$651$	−3.91998	+	13.3502i	−0.153636	+	0.523236i
$652$	−8.61839	−	1.87481i	−0.337522	−	0.0734234i
$653$	−34.2706	−	12.7823i	−1.34111	−	0.500208i	−0.426479	−	0.904497i	$-0.640246\pi$
$653$	−34.2706	−	12.7823i	−1.34111	−	0.500208i	−0.914631	+	0.404289i	$0.867519\pi$
$654$	1.22674	−	0.360205i	0.0479695	−	0.0140851i
$655$	−1.34856	−	0.478131i	−0.0526924	−	0.0186821i
$656$	−3.24494	+	3.74486i	−0.126694	+	0.146212i
$657$	3.61881	+	1.97602i	0.141183	+	0.0770919i
$658$	9.22836	−	24.7422i	0.359759	−	0.964551i
$659$	23.1308	−	14.8653i	0.901049	−	0.579069i	−0.00605205	−	0.999982i	$-0.501926\pi$
$659$	23.1308	−	14.8653i	0.901049	−	0.579069i	0.907101	+	0.420913i	$0.138290\pi$
$660$	12.6454	+	10.6019i	0.492220	+	0.412678i
$661$	−25.3092	+	3.63892i	−0.984416	+	0.141538i	−0.615680	−	0.787997i	$-0.711118\pi$
$661$	−25.3092	+	3.63892i	−0.984416	+	0.141538i	−0.368736	+	0.929534i	$0.620209\pi$
$662$	−3.16873	+	1.18187i	−0.123156	+	0.0459349i
$663$	−22.9198	+	17.1575i	−0.890130	+	0.666343i
$664$	−4.85880	−	3.12256i	−0.188558	−	0.121179i
$665$	10.7400	+	34.4901i	0.416478	+	1.33747i
$666$			10.3069i			0.399385i
$667$	20.2768	−	15.7489i	0.785121	−	0.609802i
$668$	6.74187	−	6.74187i	0.260851	−	0.260851i
$669$	−19.3975	+	16.8081i	−0.749952	+	0.649837i
$670$	−3.07876	+	15.3517i	−0.118943	+	0.593088i
$671$	1.14995	−	7.99810i	0.0443935	−	0.308763i
$672$	−1.94489	−	5.21446i	−0.0750259	−	0.201152i
$673$	11.1090	+	8.31613i	0.428222	+	0.320563i	0.791557	−	0.611096i	$-0.209271\pi$
$673$	11.1090	+	8.31613i	0.428222	+	0.320563i	−0.363335	+	0.931659i	$0.618362\pi$
$674$	−21.4432	−	6.29630i	−0.825962	−	0.242524i
$675$	24.3527	−	14.3457i	0.937337	−	0.552167i
$676$	2.99372	+	6.55534i	0.115143	+	0.252128i
$677$	−13.9236	+	25.4992i	−0.535129	+	0.980015i	0.460593	+	0.887612i	$0.347637\pi$
$677$	−13.9236	+	25.4992i	−0.535129	+	0.980015i	−0.995722	+	0.0924036i	$0.970545\pi$
$678$	−18.4732	+	1.32123i	−0.709459	+	0.0507415i
$679$	51.5743	+	44.6894i	1.97924	+	1.71502i
$680$	−7.79291	+	6.03407i	−0.298844	+	0.231396i
$681$	13.1246	−	5.99378i	0.502934	−	0.229682i
$682$	−2.71407	+	12.4764i	−0.103927	+	0.477746i
$683$	−9.72270	+	5.30899i	−0.372029	+	0.203143i	−0.654376	−	0.756169i	$-0.727069\pi$
$683$	−9.72270	+	5.30899i	−0.372029	+	0.203143i	0.282347	+	0.959312i	$0.408887\pi$
$684$	0.544398	+	3.78637i	0.0208156	+	0.144775i
$685$	−24.7677	+	22.1773i	−0.946327	+	0.847352i
$686$	3.17865	+	0.457021i	0.121361	+	0.0174491i
$687$	7.92481	−	1.72394i	0.302350	−	0.0657723i
$688$	−0.250594	+	3.50377i	−0.00955382	+	0.133580i
$689$	41.1446			1.56748
$690$	−8.81661	−	12.7432i	−0.335642	−	0.485126i
$691$	−20.9498			−0.796970			−0.398485	−	0.917175i	$-0.630464\pi$
$691$	−20.9498			−0.796970			−0.398485	+	0.917175i	$0.630464\pi$
$692$	0.717147	−	10.0270i	0.0272618	−	0.381170i
$693$	−17.5286	+	3.81312i	−0.665857	+	0.144848i
$694$	−11.8980	−	1.71067i	−0.451642	−	0.0649363i
$695$	−0.473719	+	8.58507i	−0.0179692	+	0.325650i
$696$	1.10092	+	7.65705i	0.0417302	+	0.290240i
$697$	19.1693	−	10.4672i	0.726089	−	0.396475i
$698$	−6.36351	+	29.2526i	−0.240862	+	1.10723i
$699$	0.902455	−	0.412138i	0.0341340	−	0.0155885i
$700$	−18.6740	+	4.70371i	−0.705813	+	0.177784i
$701$	23.7967	+	20.6199i	0.898788	+	0.778804i	0.975900	−	0.218218i	$-0.0700244\pi$
$701$	23.7967	+	20.6199i	0.898788	+	0.778804i	−0.0771119	+	0.997022i	$0.524570\pi$
$702$	−25.3456	+	1.81275i	−0.956608	+	0.0684179i
$703$	22.7188	−	41.6063i	0.856855	−	1.56921i
$704$	−2.12157	−	4.64560i	−0.0799598	−	0.175088i
$705$	17.9487	+	12.9859i	0.675989	+	0.489076i
$706$	−5.97767	−	1.75520i	−0.224973	−	0.0660579i
$707$	−31.3042	−	23.4340i	−1.17731	−	0.881326i
$708$	−0.884736	−	2.37207i	−0.0332504	−	0.0891478i
$709$	7.12573	−	49.5606i	0.267613	−	1.86129i	−0.203314	−	0.979114i	$-0.565171\pi$
$709$	7.12573	−	49.5606i	0.267613	−	1.86129i	0.470927	−	0.882172i	$-0.343920\pi$
$710$	25.8526	−	17.2154i	0.970230	−	0.646081i
$711$	3.45949	−	2.99766i	0.129741	−	0.112421i
$712$	−0.310062	+	0.310062i	−0.0116201	+	0.0116201i
$713$	5.55826	−	10.6238i	0.208158	−	0.397863i
$714$			24.5305i			0.918030i
$715$	−49.0130	+	15.2623i	−1.83298	+	0.570777i
$716$	−8.56236	−	5.50269i	−0.319990	−	0.205645i
$717$	−29.2687	+	21.9102i	−1.09306	+	0.818253i
$718$	−16.7790	+	6.25825i	−0.626187	+	0.233556i
$719$	−11.4121	+	1.64081i	−0.425599	+	0.0611920i	−0.351787	−	0.936080i	$-0.614426\pi$
$719$	−11.4121	+	1.64081i	−0.425599	+	0.0611920i	−0.0738127	+	0.997272i	$0.523517\pi$
$720$	−2.03142	+	0.178565i	−0.0757065	+	0.00665471i
$721$	−41.2480	+	26.5085i	−1.53615	+	0.987227i
$722$	−0.491406	+	1.31751i	−0.0182882	+	0.0490327i
$723$	29.0050	+	15.8379i	1.07871	+	0.589019i
$724$	4.50152	−	5.19503i	0.167298	−	0.193072i
$725$	26.7533	−	0.871195i	0.993592	−	0.0323554i
$726$	20.9116	−	6.14020i	0.776102	−	0.227884i
$727$	−36.3325	−	13.5513i	−1.34750	−	0.502591i	−0.430900	−	0.902400i	$-0.641804\pi$
$727$	−36.3325	−	13.5513i	−1.34750	−	0.502591i	−0.916599	+	0.399808i	$0.869077\pi$
$728$	16.9174	+	3.68015i	0.626999	+	0.136395i
$729$	8.29958	−	28.2658i	0.307392	−	1.04688i
$730$	8.79286	−	4.98873i	0.325438	−	0.184641i
$731$	6.43188	−	14.0839i	0.237892	−	0.520910i
$732$	−1.37009	−	1.83023i	−0.0506400	−	0.0676472i
$733$	7.71360	+	35.4588i	0.284908	+	1.30970i	0.867703	+	0.497083i	$0.165595\pi$
$733$	7.71360	+	35.4588i	0.284908	+	1.30970i	−0.582795	+	0.812619i	$0.698041\pi$
$734$	−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
$738$	4.50750	+	0.322383i	0.165923	+	0.0118671i
$739$	−18.7311	+	29.1462i	−0.689035	+	1.07216i	0.303808	+	0.952733i	$0.401742\pi$
$739$	−18.7311	+	29.1462i	−0.689035	+	1.07216i	−0.992843	+	0.119426i	$0.961895\pi$
$740$	21.4792	+	13.3149i	0.789590	+	0.489466i
$741$	24.7833	+	11.3182i	0.910438	+	0.415783i
$742$	21.1262	−	28.2212i	0.775565	−	1.03603i
$743$	11.5942	+	21.2332i	0.425350	+	0.778970i	0.999200	−	0.0399900i	$-0.0127326\pi$
$743$	11.5942	+	21.2332i	0.425350	+	0.778970i	−0.573850	+	0.818960i	$0.694551\pi$
$744$	1.95312	+	3.03912i	0.0716049	+	0.111419i
$745$	8.36711	−	8.64402i	0.306547	−	0.316692i
$746$	6.20979	+	21.1486i	0.227356	+	0.774305i
$747$	0.375765	+	5.25388i	0.0137485	+	0.192229i
$748$	1.60589	+	22.4533i	0.0587173	+	0.820975i
$749$	−8.12494	−	27.6710i	−0.296879	−	1.01108i
$750$	0.364617	−	16.1515i	0.0133139	−	0.589768i
$751$	10.5067	+	16.3487i	0.383395	+	0.596574i	0.978293	−	0.207227i	$-0.0664439\pi$
$751$	10.5067	+	16.3487i	0.383395	+	0.596574i	−0.594898	+	0.803801i	$0.702808\pi$
$752$	−3.28592	−	6.01771i	−0.119825	−	0.219443i
$753$	15.8109	−	21.1209i	0.576181	−	0.769688i
$754$	−21.8902	−	9.99692i	−0.797194	−	0.364066i
$755$	−17.0219	+	3.99411i	−0.619490	+	0.145360i
$756$	−11.7706	+	18.3154i	−0.428093	+	0.666126i
$757$	−44.2821	−	3.16712i	−1.60946	−	0.115111i	−0.762580	−	0.646894i	$-0.776068\pi$
$757$	−44.2821	−	3.16712i	−1.60946	−	0.115111i	−0.846881	+	0.531783i	$0.821522\pi$
$758$	−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	−0.888032	−	0.459782i	$-0.847928\pi$
$761$	−33.5656	−	38.7368i	−1.21675	−	1.40421i	−0.328721	−	0.944427i	$-0.606618\pi$
$762$	−2.11047	−	9.70169i	−0.0764544	−	0.351455i
$763$	2.04220	+	2.72807i	0.0739328	+	0.0987626i
$764$	−8.47733	+	18.5628i	−0.306699	+	0.671577i
$765$	8.66440	+	2.39163i	0.313262	+	0.0864696i
$766$	3.43325	−	11.6926i	0.124048	−	0.422470i
$767$	7.69573	+	1.67410i	0.277877	+	0.0604484i
$768$	−1.35389	−	0.504975i	−0.0488543	−	0.0182217i
$769$	9.34138	−	2.74288i	0.336859	−	0.0989107i	−0.108928	−	0.994050i	$-0.534742\pi$
$769$	9.34138	−	2.74288i	0.336859	−	0.0989107i	0.445787	+	0.895139i	$0.352924\pi$
$770$	−14.6978	+	41.4548i	−0.529672	+	1.49393i
$771$	1.49796	−	1.72874i	0.0539478	−	0.0622591i
$772$	16.5307	+	9.02646i	0.594954	+	0.324869i
$773$	−16.8724	+	45.2367i	−0.606858	+	1.62705i	0.161385	+	0.986892i	$0.448404\pi$
$773$	−16.8724	+	45.2367i	−0.606858	+	1.62705i	−0.768243	+	0.640158i	$0.778869\pi$
$774$	2.69498	−	1.73196i	0.0968691	−	0.0622540i
$775$	11.1957	−	5.56017i	0.402162	−	0.199727i
$776$	17.5382	−	2.52162i	0.629586	−	0.0905208i
$777$	58.9323	−	21.9806i	2.11418	−	0.788550i
$778$	3.48001	−	2.60510i	0.124764	−	0.0933974i
$779$	−17.4850	−	11.2369i	−0.626464	−	0.402604i
$780$	−6.75241	+	12.8594i	−0.241775	+	0.460440i
$781$		−	70.9403i		−	2.53844i
$782$	4.12557	−	20.7321i	0.147530	−	0.741379i
$783$	21.3987	−	21.3987i	0.764725	−	0.764725i
$784$	5.92039	−	5.13005i	0.211442	−	0.183216i
$785$	0.499196	+	0.749650i	0.0178171	+	0.0267562i
$786$	−0.131587	+	0.915209i	−0.00469356	+	0.0326444i
$787$	−5.53026	−	14.8272i	−0.197132	−	0.528533i	0.800343	−	0.599542i	$-0.204651\pi$
$787$	−5.53026	−	14.8272i	−0.197132	−	0.528533i	−0.997476	+	0.0710096i	$0.977378\pi$
$788$	−9.34227	−	6.99353i	−0.332805	−	0.249134i
$789$	−17.8084	−	5.22901i	−0.633995	−	0.186158i
$790$	−1.77789	−	11.0819i	−0.0632545	−	0.394277i
$791$	−20.5065	−	44.9029i	−0.729126	−	1.59656i
$792$	−2.23215	+	4.08787i	−0.0793159	+	0.145256i
$793$	7.09403	−	0.507375i	0.251916	−	0.0180174i
$794$	−12.7255	−	11.0267i	−0.451610	−	0.391322i
$795$	18.1064	+	23.3841i	0.642167	+	0.829347i
$796$	−0.429693	+	0.196234i	−0.0152301	+	0.00695534i
$797$	0.623031	−	2.86403i	0.0220689	−	0.101449i	−0.964795	−	0.263003i	$-0.915287\pi$
$797$	0.623031	−	2.86403i	0.0220689	−	0.101449i	0.986864	+	0.161554i	$0.0516506\pi$
$798$	20.4885	−	11.1875i	0.725284	−	0.396035i
$799$	4.30089	+	29.9134i	0.152155	+	1.05826i
$800$	−2.25215	+	4.46406i	−0.0796254	+	0.157828i
$801$	0.395828	+	0.0569114i	0.0139859	+	0.00201087i
$802$	7.07615	−	1.53932i	0.249867	−	0.0543553i
$803$	1.64721	−	23.0310i	0.0581287	−	0.812745i
$804$	10.1181			0.356840
$805$	23.6117	−	33.8877i	0.832203	−	1.19438i
$806$	−11.2383			−0.395851
$807$	1.04305	−	14.5838i	0.0367173	−	0.513374i
$808$	−9.92092	+	2.15816i	−0.349017	+	0.0759240i
$809$	−34.9496	−	5.02499i	−1.22876	−	0.176669i	−0.502799	−	0.864403i	$-0.667697\pi$
$809$	−34.9496	−	5.02499i	−1.22876	−	0.176669i	−0.725963	+	0.687734i	$0.758606\pi$
$810$	−8.10302	−	9.04948i	−0.284711	−	0.317966i
$811$	−0.693191	−	4.82125i	−0.0243412	−	0.169297i	0.974025	−	0.226442i	$-0.0727093\pi$
$811$	−0.693191	−	4.82125i	−0.0243412	−	0.169297i	−0.998366	+	0.0571451i	$0.981800\pi$
$812$	−18.0967	+	9.88154i	−0.635070	+	0.346774i
$813$	−2.34725	+	10.7902i	−0.0823218	+	0.378427i
$814$	52.5031	−	23.9774i	1.84023	−	0.840406i
$815$	19.5644	+	2.48864i	0.685310	+	0.0871734i
$816$	4.81347	+	4.17089i	0.168505	+	0.146010i
$817$	−14.6966	+	1.05112i	−0.514167	+	0.0367740i
$818$	14.9943	−	27.4600i	0.524264	−	0.960118i
$819$	−6.55904	−	14.3623i	−0.229192	−	0.501859i
$820$	6.49480	−	8.97696i	0.226808	−	0.313489i
$821$	−22.8348	−	6.70489i	−0.796939	−	0.234002i	−0.142181	−	0.989841i	$-0.545411\pi$
$821$	−22.8348	−	6.70489i	−0.796939	−	0.234002i	−0.654758	+	0.755838i	$0.727230\pi$
$822$	17.1989	+	12.8749i	0.599881	+	0.449065i
$823$	−2.44767	−	6.56246i	−0.0853204	−	0.228753i	0.887282	−	0.461227i	$-0.152591\pi$
$823$	−2.44767	−	6.56246i	−0.0853204	−	0.228753i	−0.972603	+	0.232474i	$0.925318\pi$
$824$	−1.81176	+	12.6010i	−0.0631155	+	0.438978i
$825$	−30.2431	−	21.1396i	−1.05293	−	0.735985i
$826$	5.09974	−	4.41895i	0.177443	−	0.153755i
$827$	2.18833	−	2.18833i	0.0760958	−	0.0760958i	−0.668034	−	0.744130i	$-0.732864\pi$
$827$	2.18833	−	2.18833i	0.0760958	−	0.0760958i	0.744130	+	0.668034i	$0.232864\pi$
$828$	3.03723	−	3.14715i	0.105551	−	0.109371i
$829$			21.0156i			0.729901i	0.931027	+	0.364951i	$0.118914\pi$
$829$			21.0156i			0.729901i	−0.931027	+	0.364951i	$0.881086\pi$
$830$	11.4343	+	6.00410i	0.396890	+	0.208405i
$831$	17.7209	+	11.3885i	0.614730	+	0.395063i
$832$	3.59857	−	2.69386i	0.124758	−	0.0933927i
$833$	−32.3520	+	12.0667i	−1.12093	+	0.418086i
$834$	5.49975	−	0.790745i	0.190441	−	0.0273812i
$835$	−13.6973	+	16.3374i	−0.474015	+	0.565380i
$836$	18.0212	−	11.5815i	0.623275	−	0.400555i
$837$	4.93878	−	13.2414i	0.170709	−	0.457689i
$838$	15.1373	+	8.26558i	0.522908	+	0.285530i
$839$	24.7969	−	28.6172i	0.856085	−	0.987975i	−0.143913	−	0.989590i	$-0.545969\pi$
$839$	24.7969	−	28.6172i	0.856085	−	0.987975i	0.999999	+	0.00161505i	$0.000514086\pi$
$840$	5.35320	+	11.2343i	0.184703	+	0.387620i
$841$	−0.326312	+	0.0958139i	−0.0112521	+	0.00330393i
$842$	4.34741	+	1.62150i	0.149822	+	0.0558806i
$843$	−34.2598	−	7.45277i	−1.17997	−	0.256687i
$844$	3.15924	−	10.7594i	0.108746	−	0.370353i
$845$	−7.95198	−	14.0157i	−0.273556	−	0.482155i
$846$	−2.59755	+	5.68784i	−0.0893055	+	0.195552i
$847$	34.8123	+	46.5037i	1.19616	+	1.59789i
$848$	−1.94562	−	8.94388i	−0.0668129	−	0.307134i
$849$	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
$853$	54.0088	+	3.86278i	1.84923	+	0.132259i	0.951374	−	0.308039i	$-0.0996728\pi$
$853$	54.0088	+	3.86278i	1.84923	+	0.132259i	0.897852	+	0.440298i	$0.145127\pi$
$854$	3.29450	−	5.12634i	0.112735	−	0.175420i
$855$	−1.95400	−	8.32746i	−0.0668254	−	0.284793i
$856$	−6.81118	−	3.11056i	−0.232801	−	0.106317i
$857$	−14.7241	+	19.6691i	−0.502967	+	0.671885i	−0.978126	−	0.208015i	$-0.933300\pi$
$857$	−14.7241	+	19.6691i	−0.502967	+	0.671885i	0.475159	+	0.879900i	$0.342391\pi$
$858$	15.8983	+	29.1156i	0.542759	+	0.993989i
$859$	12.6739	+	19.7209i	0.432426	+	0.672868i	0.987264	−	0.159090i	$-0.0508560\pi$
$859$	12.6739	+	19.7209i	0.432426	+	0.672868i	−0.554838	+	0.831959i	$0.687220\pi$
$860$	−0.127839	−	7.85364i	−0.00435928	−	0.267807i
$861$	−7.76942	−	26.4602i	−0.264781	−	0.901761i
$862$	0.979830	+	13.6998i	0.0333731	+	0.466618i
$863$	−1.72992	−	24.1875i	−0.0588873	−	0.823352i	−0.937977	−	0.346696i	$-0.887303\pi$
$863$	−1.72992	−	24.1875i	−0.0588873	−	0.823352i	0.879090	−	0.476656i	$-0.158151\pi$
$864$	1.59258	+	5.42383i	0.0541806	+	0.184522i
$865$	0.365848	+	22.4754i	0.0124392	+	0.764187i
$866$	−18.1845	−	28.2956i	−0.617933	−	0.961523i
$867$	−1.68134	−	3.07915i	−0.0571014	−	0.104573i
$868$	−5.77042	+	7.70838i	−0.195861	+	0.261639i
$869$	−23.3179	−	10.6489i	−0.791007	−	0.361241i
$870$	−3.95151	−	16.8404i	−0.133969	−	0.570942i
$871$	−17.0172	+	26.4793i	−0.576607	+	0.897218i
$872$	0.882546	+	0.0631209i	0.0298868	+	0.00213754i
$873$	−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
$877$	4.77562	+	21.9532i	0.161261	+	0.741306i	0.984750	+	0.173974i	$0.0556609\pi$
$877$	4.77562	+	21.9532i	0.161261	+	0.741306i	−0.823489	+	0.567332i	$0.807975\pi$
$878$	−17.0945	−	22.8356i	−0.576911	−	0.770663i
$879$	3.86556	−	8.46441i	0.130382	−	0.285497i
$880$	5.63536	+	9.93257i	0.189968	+	0.334827i
$881$	−13.7228	+	46.7357i	−0.462334	+	1.57457i	0.317296	+	0.948327i	$0.397225\pi$
$881$	−13.7228	+	46.7357i	−0.462334	+	1.57457i	−0.779630	+	0.626240i	$0.784593\pi$
$882$	−6.98100	−	1.51862i	−0.235063	−	0.0511347i
$883$	13.7124	+	5.11445i	0.461458	+	0.172115i	0.569432	−	0.822039i	$-0.307163\pi$
$883$	13.7124	+	5.11445i	0.461458	+	0.172115i	−0.107973	+	0.994154i	$0.534436\pi$
$884$	−19.0108	+	5.58208i	−0.639403	+	0.187746i
$885$	2.43518	+	5.11050i	0.0818576	+	0.171788i
$886$	−19.4153	+	22.4065i	−0.652270	+	0.752760i
$887$	16.9055	+	9.23109i	0.567631	+	0.309950i	0.737315	−	0.675549i	$-0.236093\pi$
$887$	16.9055	+	9.23109i	0.567631	+	0.309950i	−0.169685	+	0.985498i	$0.554275\pi$
$888$	5.70707	−	15.3013i	0.191517	−	0.513476i
$889$	22.2625	−	14.3072i	0.746659	−	0.479849i
$890$	0.629947	−	0.751366i	0.0211159	−	0.0251859i
$891$	−27.4613	+	3.94833i	−0.919987	+	0.132274i
$892$	−16.6425	+	6.20732i	−0.557231	+	0.207837i
$893$	23.0229	−	17.2347i	0.770431	−	0.576737i
$894$	−6.54011	−	4.20307i	−0.218734	−	0.140572i
$895$	20.1499	+	10.5806i	0.673537	+	0.353672i
$896$		−	3.85147i		−	0.128668i
$897$	−7.16158	−	30.3170i	−0.239118	−	1.01226i
$898$	−2.96885	+	2.96885i	−0.0990718	+	0.0990718i
$899$	10.1151	−	8.76475i	0.337356	−	0.292321i
$900$	4.48998	−	0.795498i	0.149666	−	0.0265166i
$901$	−5.74155	+	39.9334i	−0.191279	+	1.33037i
$902$	−8.84375	−	23.7110i	−0.294465	−	0.789491i
$903$	−15.6502	−	11.7156i	−0.520807	−	0.389871i
$904$	−12.2977	−	3.61094i	−0.409016	−	0.120098i
$905$	−9.00986	+	12.4532i	−0.299498	+	0.413959i
$906$	4.69365	+	10.2777i	0.155936	+	0.341452i
$907$	23.4504	−	42.9462i	0.778657	−	1.42600i	−0.122481	−	0.992471i	$-0.539085\pi$
$907$	23.4504	−	42.9462i	0.778657	−	1.42600i	0.901138	−	0.433533i	$-0.142733\pi$
$908$	9.95964	−	0.712327i	0.330522	−	0.0236394i
$909$	6.99771	+	6.06355i	0.232099	+	0.201115i
$910$	−38.4036	−	4.88505i	−1.27307	−	0.161938i
$911$	7.53473	−	3.44099i	0.249637	−	0.114005i	−0.286667	−	0.958030i	$-0.592547\pi$
$911$	7.53473	−	3.44099i	0.249637	−	0.114005i	0.536304	+	0.844025i	$0.319820\pi$
$912$	1.28837	−	5.92253i	0.0426621	−	0.196115i
$913$	25.8889	−	14.1364i	0.856799	−	0.467847i
$914$	3.74743	+	26.0639i	0.123954	+	0.862118i
$915$	3.41021	+	3.80853i	0.112738	+	0.125906i
$916$	5.55544	+	0.798752i	0.183557	+	0.0263915i
$917$	−2.40814	+	0.523859i	−0.0795239	+	0.0172994i
$918$	1.77748	−	24.8524i	0.0586656	−	0.820252i
$919$	−6.81742			−0.224886			−0.112443	−	0.993658i	$-0.535868\pi$
$919$	−6.81742			−0.224886			−0.112443	+	0.993658i	$0.535868\pi$
$920$	−2.63489	−	10.3951i	−0.0868699	−	0.342715i
$921$	−3.16712			−0.104360
$922$	0.238947	−	3.34092i	0.00786931	−	0.110027i
$923$	61.0131	−	13.2726i	2.00827	−	0.436873i
$924$	28.1337	+	4.04501i	0.925529	+	0.133071i
$925$	−50.4514	−	25.4531i	−1.65883	−	0.836892i
$926$	−5.28728	−	36.7739i	−0.173751	−	1.20846i
$927$	10.1899	−	5.56412i	0.334681	−	0.182750i
$928$	−1.13797	+	5.23115i	−0.0373556	+	0.171721i
$929$	−19.7252	+	9.00821i	−0.647164	+	0.295550i	−0.711824	−	0.702357i	$-0.752131\pi$
$929$	−19.7252	+	9.00821i	−0.647164	+	0.295550i	0.0646604	+	0.997907i	$0.479404\pi$
$930$	−4.94559	−	6.38715i	−0.162172	−	0.209443i
$931$	24.8331	+	21.5180i	0.813871	+	0.705223i
$932$	0.684833	−	0.0489802i	0.0224325	−	0.00160440i
$933$	−13.3463	+	24.4419i	−0.436938	+	0.800192i
$934$	14.0011	+	30.6582i	0.458130	+	1.00317i
$935$	−7.97343	−	49.6999i	−0.260759	−	1.62536i
$936$	−3.93345	−	1.15497i	−0.128569	−	0.0377512i
$937$	−24.8535	−	18.6051i	−0.811929	−	0.607803i	0.110541	−	0.993872i	$-0.464742\pi$
$937$	−24.8535	−	18.6051i	−0.811929	−	0.607803i	−0.922470	+	0.386069i	$0.873833\pi$
$938$	9.42460	+	25.2683i	0.307724	+	0.825040i
$939$	−1.03612	+	7.20638i	−0.0338126	+	0.235171i
$940$	8.49757	+	12.7609i	0.277160	+	0.416216i
$941$	34.3632	−	29.7758i	1.12021	−	0.970665i	0.120450	−	0.992719i	$-0.461566\pi$
$941$	34.3632	−	29.7758i	1.12021	−	0.970665i	0.999757	+	0.0220546i	$0.00702076\pi$
$942$	0.411551	−	0.411551i	0.0134091	−	0.0134091i
$943$	2.11627	+	23.6697i	0.0689152	+	0.770792i
$944$		−	1.75204i		−	0.0570240i
$945$	22.6327	−	43.1019i	0.736240	−	1.40210i
$946$	−15.0920	−	9.69902i	−0.490682	−	0.315342i
$947$	−39.6512	+	29.6825i	−1.28849	+	0.964553i	−0.288517	+	0.957475i	$0.593162\pi$
$947$	−39.6512	+	29.6825i	−1.28849	+	0.964553i	−0.999975	+	0.00707771i	$0.997747\pi$
$948$	−6.79566	+	2.53465i	−0.220713	+	0.0823217i
$949$	20.1163	−	2.89228i	0.653002	−	0.0938875i
$950$	−19.8783	−	6.68570i	−0.644937	−	0.216913i
$951$	3.19084	−	2.05063i	0.103470	−	0.0664961i
$952$	−5.93255	+	15.9058i	−0.192275	+	0.515510i
$953$	−34.3984	−	18.7829i	−1.11427	−	0.608439i	−0.186825	−	0.982393i	$-0.559820\pi$
$953$	−34.3984	−	18.7829i	−1.11427	−	0.608439i	−0.927447	+	0.373955i	$0.878002\pi$
$954$	−5.46639	+	6.30855i	−0.176981	+	0.204247i
$955$	15.2485	−	43.0080i	0.493430	−	1.39171i
$956$	−24.2769	+	7.12835i	−0.785172	+	0.230547i
$957$	−37.0166	−	13.8065i	−1.19658	−	0.446300i
$958$	39.6385	+	8.62283i	1.28066	+	0.278591i
$959$	−16.1329	+	54.9437i	−0.520960	+	1.77423i
$960$	3.11464	+	0.859731i	0.100524	+	0.0277477i
$961$	−10.2814	+	22.5130i	−0.331657	+	0.726227i
$962$	30.4451	+	40.6699i	0.981591	+	1.31125i
$963$	1.45156	+	6.67271i	0.0467759	+	0.215025i
$964$	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	$0.514243\pi$
$968$	15.0442	+	1.07598i	0.483540	+	0.0345835i
$969$	−14.4434	+	22.4743i	−0.463988	+	0.721980i
$970$	−38.5723	+	9.05081i	−1.23848	+	0.290604i
$971$	31.7656	+	14.5069i	1.01941	+	0.465548i	0.853776	−	0.520640i	$-0.174307\pi$
$971$	31.7656	+	14.5069i	1.01941	+	0.465548i	0.165631	+	0.986188i	$0.447034\pi$
$972$	5.45863	−	7.29188i	0.175086	−	0.233887i
$973$	7.09751	+	12.9981i	0.227536	+	0.416701i
$974$	15.7732	+	24.5436i	0.505407	+	0.786428i
$975$	12.5230	−	29.9661i	0.401057	−	0.959683i
$976$	−0.445750	−	1.51808i	−0.0142681	−	0.0485927i
$977$	−1.67221	−	23.3805i	−0.0534987	−	0.748010i	−0.951428	−	0.307871i	$-0.900384\pi$
$977$	−1.67221	−	23.3805i	−0.0534987	−	0.748010i	0.897929	−	0.440139i	$-0.145071\pi$
$978$	−0.909204	−	12.7123i	−0.0290731	−	0.406496i
$979$	−0.630923	−	2.14873i	−0.0201644	−	0.0686736i
$980$	−12.1831	+	12.5863i	−0.389174	+	0.402054i
$981$	−0.436254	−	0.678825i	−0.0139285	−	0.0216732i
$982$	3.97144	+	7.27314i	0.126734	+	0.232095i
$983$	21.6387	−	28.9059i	0.690168	−	0.921956i	−0.309413	−	0.950928i	$-0.600132\pi$
$983$	21.6387	−	28.9059i	0.690168	−	0.921956i	0.999580	+	0.0289719i	$0.00922333\pi$
$984$	−6.51315	−	2.97446i	−0.207632	−	0.0948222i
$985$	22.1790	+	13.7487i	0.706683	+	0.438072i
$986$	12.7573	−	19.8508i	0.406275	−	0.632177i
$987$	38.0611	+	2.72218i	1.21150	+	0.0866480i
$988$	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	0.550297	−	0.834969i	$-0.314515\pi$
$991$	−11.1594	−	12.8786i	−0.354489	−	0.409102i	−0.904786	+	0.425867i	$0.859969\pi$
$992$	0.531429	+	2.44294i	0.0168729	+	0.0775635i
$993$	−2.92863	−	3.91219i	−0.0929372	−	0.124150i
$994$	22.2241	−	48.6641i	0.704907	−	1.54353i
$995$	0.918710	−	0.521241i	0.0291251	−	0.0165244i
$996$	2.35129	−	8.00777i	0.0745036	−	0.253736i
$997$	−46.3823	−	10.0899i	−1.46894	−	0.319549i	−0.594271	−	0.804265i	$-0.702559\pi$
$997$	−46.3823	−	10.0899i	−1.46894	−	0.319549i	−0.874672	+	0.484716i	$0.838923\pi$
$998$	−13.7277	−	5.12017i	−0.434543	−	0.162076i
$999$	−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.217.3	yes	240
5.3	odd	4	inner	230.2.l.a.33.9	yes	240
23.7	odd	22	inner	230.2.l.a.7.9	✓	240
115.53	even	44	inner	230.2.l.a.53.3	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.l.a.7.9	✓	240	23.7	odd	22	inner
230.2.l.a.33.9	yes	240	5.3	odd	4	inner
230.2.l.a.53.3	yes	240	115.53	even	44	inner
230.2.l.a.217.3	yes	240	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 $\F_{q}$
Belyi maps

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+(-0.0713392 + 0.997452i) q^{2} +(-1.41198 + 0.307156i) q^{3} +(-0.989821 - 0.142315i) q^{4} +(2.23267 + 0.123198i) q^{5} +(-0.205645 - 1.43029i) q^{6} +(3.38035 - 1.84581i) q^{7} +(0.212565 - 0.977147i) q^{8} +(-0.829567 + 0.378851i) q^{9} +(-0.282161 + 2.21819i) q^{10} +(3.85970 + 3.34445i) q^{11} +(1.44132 - 0.103085i) q^{12} +(-2.15431 + 3.94532i) q^{13} +(1.59996 + 3.50342i) q^{14} +(-3.19032 + 0.511827i) q^{15} +(0.959493 + 0.281733i) q^{16} +(-3.52855 - 2.64144i) q^{17} +(-0.318705 - 0.854480i) q^{18} +(-0.596940 + 4.15181i) q^{19} +(-2.19241 - 0.439686i) q^{20} +(-4.20602 + 3.64454i) q^{21} +(-3.61128 + 3.61128i) q^{22} +(4.16769 - 2.37283i) q^{23} +1.44500i q^{24} +(4.96964 + 0.550120i) q^{25} +(-3.78158 - 2.43027i) q^{26} +(4.52530 - 3.38760i) q^{27} +(-3.60863 + 1.34595i) q^{28} +(5.29900 - 0.761882i) q^{29} +(-0.282929 - 3.21870i) q^{30} +(2.10320 - 1.35164i) q^{31} +(-0.349464 + 0.936950i) q^{32} +(-6.47707 - 3.53675i) q^{33} +(2.88643 - 3.33112i) q^{34} +(7.77461 - 3.70464i) q^{35} +(0.875039 - 0.256935i) q^{36} +(-10.5891 - 3.94954i) q^{37} +(-4.09864 - 0.891605i) q^{38} +(1.83000 - 6.23240i) q^{39} +(0.594971 - 2.15546i) q^{40} +(-2.05845 + 4.50738i) q^{41} +(-3.33520 - 4.45530i) q^{42} +(0.746682 + 3.43244i) 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} +(-1.44132 - 0.103085i) q^{48} +(4.23527 - 6.59021i) q^{49} +(-0.903248 + 4.91774i) q^{50} +(5.79356 + 2.64583i) q^{51} +(2.69386 - 3.59857i) q^{52} +(-4.38659 - 8.03345i) q^{53} +(3.05614 + 4.75544i) q^{54} +(8.20542 + 7.94257i) q^{55} +(-1.08508 - 3.69546i) q^{56} +(-0.432390 - 6.04560i) q^{57} +(0.381914 + 5.33986i) q^{58} +(-0.493606 - 1.68107i) q^{59} +(3.23069 - 0.0525881i) q^{60} +(-0.855388 - 1.33101i) q^{61} +(1.19816 + 2.19426i) q^{62} +(-2.10494 + 2.81187i) q^{63} +(-0.909632 - 0.415415i) q^{64} +(-5.29591 + 8.54320i) q^{65} +(3.98981 - 6.20826i) q^{66} +(6.98435 + 0.499531i) 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} +(0.193855 + 0.891139i) q^{72} +(-2.70939 - 3.61933i) q^{73} +(4.69489 - 10.2804i) q^{74} +(-7.18599 + 0.749703i) q^{75} +(1.18173 - 4.02459i) q^{76} +(19.2204 + 4.18114i) q^{77} +(6.08597 + 2.26995i) q^{78} +(-4.81604 + 1.41412i) q^{79} +(2.10752 + 0.747224i) q^{80} +(-3.55743 + 4.10549i) q^{81} +(-4.34904 - 2.37476i) q^{82} +(2.01839 - 5.41151i) q^{83} +(4.68188 - 3.00886i) q^{84} +(-7.55268 - 6.33218i) q^{85} +(-3.47696 + 0.499912i) q^{86} +(-7.24805 + 2.70338i) q^{87} +(4.08846 - 3.06058i) q^{88} +(-0.368885 - 0.237068i) q^{89} +(-0.606293 - 1.94704i) q^{90} +17.3130i q^{91} +(-4.46296 + 1.75556i) q^{92} +(-2.55450 + 2.55450i) q^{93} +(5.18171 - 4.48998i) q^{94} +(-1.84426 + 9.19608i) q^{95} +(0.205645 - 1.43029i) q^{96} +(6.19201 + 16.6014i) q^{97} +(6.27128 + 4.69462i) 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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