LMFDB - Embedded newform 640.2.bm.a.341.36

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [640,2,Mod(21,640)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(640, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([0, 13, 0]))

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

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

chi := DirichletCharacter("640.21");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 640 = 2^{7} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	640.bm (of order $32$, degree $16$, 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:	$5.11042572936$
Analytic rank:	$0$
Dimension:	$1024$
Relative dimension:	$64$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			341.36
Character	$\chi$	$=$	640.341
Dual form			640.2.bm.a.381.36

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.140370 - 1.40723i) q^{2} +(1.82758 - 2.22691i) q^{3} +(-1.96059 - 0.395065i) q^{4} +(0.956940 - 0.290285i) q^{5} +(-2.87723 - 2.88441i) q^{6} +(-4.53962 - 0.902986i) q^{7} +(-0.831156 + 2.70355i) q^{8} +(-1.03381 - 5.19733i) q^{9} +O(q^{10})$	\(q+(0.140370 - 1.40723i) q^{2} +(1.82758 - 2.22691i) q^{3} +(-1.96059 - 0.395065i) q^{4} +(0.956940 - 0.290285i) q^{5} +(-2.87723 - 2.88441i) q^{6} +(-4.53962 - 0.902986i) q^{7} +(-0.831156 + 2.70355i) q^{8} +(-1.03381 - 5.19733i) q^{9} +(-0.274172 - 1.38738i) q^{10} +(-2.40773 - 0.237141i) q^{11} +(-4.46290 + 3.64405i) q^{12} +(0.869191 - 2.86534i) q^{13} +(-1.90793 + 6.26153i) q^{14} +(1.10244 - 2.66153i) q^{15} +(3.68785 + 1.54912i) q^{16} +(2.76984 + 6.68699i) q^{17} +(-7.45895 + 0.725264i) q^{18} +(2.69554 - 1.44079i) q^{19} +(-1.99085 + 0.191076i) q^{20} +(-10.3074 + 8.45903i) q^{21} +(-0.671685 + 3.35495i) q^{22} +(-0.192853 + 0.288624i) q^{23} +(4.50155 + 6.79185i) q^{24} +(0.831470 - 0.555570i) q^{25} +(-3.91018 - 1.62536i) q^{26} +(-5.84135 - 3.12227i) q^{27} +(8.54360 + 3.56383i) q^{28} +(-1.03510 - 10.5095i) q^{29} +(-3.59064 - 1.92499i) q^{30} +(-1.80040 - 1.80040i) q^{31} +(2.69764 - 4.97220i) q^{32} +(-4.92840 + 4.92840i) q^{33} +(9.79894 - 2.95915i) q^{34} +(-4.60626 + 0.453677i) q^{35} +(-0.0263987 + 10.5983i) q^{36} +(2.87863 - 5.38553i) q^{37} +(-1.64916 - 3.99548i) q^{38} +(-4.79233 - 7.17223i) q^{39} +(-0.0105677 + 2.82841i) q^{40} +(3.87744 + 2.59082i) q^{41} +(10.4570 + 15.6922i) q^{42} +(-2.51068 - 3.05928i) q^{43} +(4.62690 + 1.41615i) q^{44} +(-2.49800 - 4.67343i) q^{45} +(0.379090 + 0.311902i) q^{46} +(-9.22772 + 3.82225i) q^{47} +(10.1896 - 5.38135i) q^{48} +(13.3256 + 5.51963i) q^{49} +(-0.665102 - 1.24805i) q^{50} +(19.9534 + 6.05280i) q^{51} +(-2.83613 + 5.27438i) q^{52} +(0.910244 - 9.24187i) q^{53} +(-5.21370 + 7.78186i) q^{54} +(-2.37290 + 0.471998i) q^{55} +(6.21440 - 11.5226i) q^{56} +(1.71778 - 8.63587i) q^{57} +(-14.9346 - 0.0185999i) q^{58} +(-0.739346 - 2.43730i) q^{59} +(-3.21292 + 4.78265i) q^{60} +(0.781495 + 0.641357i) q^{61} +(-2.78630 + 2.28085i) q^{62} +24.5274i q^{63} +(-6.61836 - 4.49414i) q^{64} -2.99427i q^{65} +(6.24360 + 7.62720i) q^{66} +(-5.17116 - 4.24386i) q^{67} +(-2.78873 - 14.2047i) q^{68} +(0.290287 + 0.956948i) q^{69} +(-0.00815224 + 6.54576i) q^{70} +(-0.731822 + 3.67912i) q^{71} +(14.9105 + 1.52483i) q^{72} +(2.71293 - 0.539636i) q^{73} +(-7.17461 - 4.80685i) q^{74} +(0.282370 - 2.86695i) q^{75} +(-5.85406 + 1.75990i) q^{76} +(10.7160 + 3.25068i) q^{77} +(-10.7657 + 5.73715i) q^{78} +(14.1703 + 5.86952i) q^{79} +(3.97874 + 0.411894i) q^{80} +(-2.94119 + 1.21828i) q^{81} +(4.19016 - 5.09278i) q^{82} +(1.03773 + 1.94145i) q^{83} +(23.5504 - 12.5126i) q^{84} +(4.59171 + 5.59501i) q^{85} +(-4.65753 + 3.10368i) q^{86} +(-25.2954 - 16.9018i) q^{87} +(2.64232 - 6.31232i) q^{88} +(7.53529 + 11.2774i) q^{89} +(-6.92724 + 2.85925i) q^{90} +(-6.53316 + 12.2227i) q^{91} +(0.492131 - 0.489685i) q^{92} +(-7.29968 + 0.718956i) q^{93} +(4.08349 + 13.5221i) q^{94} +(2.16123 - 2.16123i) q^{95} +(-6.14249 - 15.0945i) q^{96} +(-8.84804 - 8.84804i) q^{97} +(9.63790 - 17.9774i) q^{98} +(1.25665 + 12.7589i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1024 q+O(q^{10}) $ 1024 * q	$ 1024 q - 192 q^{52} - 128 q^{54} - 32 q^{56} - 288 q^{58} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 288 q^{72} - 32 q^{74} - 128 q^{76} - 192 q^{78}+O(q^{100}) $ 1024 * q - 192 * q^52 - 128 * q^54 - 32 * q^56 - 288 * q^58 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 288 * q^72 - 32 * q^74 - 128 * q^76 - 192 * q^78

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/640\mathbb{Z}\right)^\times$.

$n$	$257$	$261$	$511$
$\chi(n)$	$1$	$e\left(\frac{29}{32}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.140370	−	1.40723i	0.0992565	−	0.995062i
$2$	0.140370	−	1.40723i	0.0992565	−	0.995062i
$3$	1.82758	−	2.22691i	1.05515	−	1.28571i	0.0982907	−	0.995158i	$-0.468662\pi$
$3$	1.82758	−	2.22691i	1.05515	−	1.28571i	0.956861	−	0.290548i	$-0.0938375\pi$
$4$	−1.96059	−	0.395065i	−0.980296	−	0.197533i
$5$	0.956940	−	0.290285i	0.427957	−	0.129819i
$5$	0.956940	−	0.290285i	0.427957	−	0.129819i
$6$	−2.87723	−	2.88441i	−1.17463	−	1.17756i
$7$	−4.53962	−	0.902986i	−1.71581	−	0.341297i	−0.763358	−	0.645975i	$-0.776451\pi$
$7$	−4.53962	−	0.902986i	−1.71581	−	0.341297i	−0.952455	+	0.304679i	$0.901451\pi$
$8$	−0.831156	+	2.70355i	−0.293858	+	0.955849i
$9$	−1.03381	−	5.19733i	−0.344604	−	1.73244i
$10$	−0.274172	−	1.38738i	−0.0867007	−	0.438729i
$11$	−2.40773	−	0.237141i	−0.725959	−	0.0715007i	−0.271715	−	0.962378i	$-0.587591\pi$
$11$	−2.40773	−	0.237141i	−0.725959	−	0.0715007i	−0.454244	+	0.890877i	$0.650091\pi$
$12$	−4.46290	+	3.64405i	−1.28833	+	1.05195i
$13$	0.869191	−	2.86534i	0.241070	−	0.794702i	−0.750009	−	0.661428i	$-0.769951\pi$
$13$	0.869191	−	2.86534i	0.241070	−	0.794702i	0.991079	−	0.133275i	$-0.0425492\pi$
$14$	−1.90793	+	6.26153i	−0.509917	+	1.67346i
$15$	1.10244	−	2.66153i	0.284650	−	0.687205i
$16$	3.68785	+	1.54912i	0.921962	+	0.387281i
$17$	2.76984	+	6.68699i	0.671786	+	1.62183i	0.778574	+	0.627552i	$0.215943\pi$
$17$	2.76984	+	6.68699i	0.671786	+	1.62183i	−0.106789	+	0.994282i	$0.534057\pi$
$18$	−7.45895	+	0.725264i	−1.75809	+	0.170946i
$19$	2.69554	−	1.44079i	0.618398	−	0.330541i	−0.132276	−	0.991213i	$-0.542229\pi$
$19$	2.69554	−	1.44079i	0.618398	−	0.330541i	0.750675	+	0.660672i	$0.229729\pi$
$20$	−1.99085	+	0.191076i	−0.445168	+	0.0427259i
$21$	−10.3074	+	8.45903i	−2.24925	+	1.84591i
$22$	−0.671685	+	3.35495i	−0.143204	+	0.715277i
$23$	−0.192853	+	0.288624i	−0.0402125	+	0.0601823i	−0.851031	−	0.525115i	$-0.824022\pi$
$23$	−0.192853	+	0.288624i	−0.0402125	+	0.0601823i	0.810819	+	0.585297i	$0.199022\pi$
$24$	4.50155	+	6.79185i	0.918876	+	1.38638i
$25$	0.831470	−	0.555570i	0.166294	−	0.111114i
$26$	−3.91018	−	1.62536i	−0.766850	−	0.318759i
$27$	−5.84135	−	3.12227i	−1.12417	−	0.600881i
$28$	8.54360	+	3.56383i	1.61459	+	0.673501i
$29$	−1.03510	−	10.5095i	−0.192212	−	1.95157i	−0.291658	−	0.956523i	$-0.594207\pi$
$29$	−1.03510	−	10.5095i	−0.192212	−	1.95157i	0.0994459	−	0.995043i	$-0.468293\pi$
$30$	−3.59064	−	1.92499i	−0.655558	−	0.351454i
$31$	−1.80040	−	1.80040i	−0.323361	−	0.323361i	0.526694	−	0.850055i	$-0.323431\pi$
$31$	−1.80040	−	1.80040i	−0.323361	−	0.323361i	−0.850055	+	0.526694i	$0.823431\pi$
$32$	2.69764	−	4.97220i	0.476879	−	0.878969i
$33$	−4.92840	+	4.92840i	−0.857925	+	0.857925i
$34$	9.79894	−	2.95915i	1.68050	−	0.507491i
$35$	−4.60626	+	0.453677i	−0.778601	+	0.0766855i
$36$	−0.0263987	+	10.5983i	−0.00439978	+	1.76638i
$37$	2.87863	−	5.38553i	0.473243	−	0.885376i	−0.526145	−	0.850395i	$-0.676363\pi$
$37$	2.87863	−	5.38553i	0.473243	−	0.885376i	0.999388	−	0.0349807i	$-0.0111370\pi$
$38$	−1.64916	−	3.99548i	−0.267528	−	0.648153i
$39$	−4.79233	−	7.17223i	−0.767388	−	1.14848i
$40$	−0.0105677	+	2.82841i	−0.00167091	+	0.447210i
$41$	3.87744	+	2.59082i	0.605554	+	0.404619i	0.820203	−	0.572073i	$-0.193861\pi$
$41$	3.87744	+	2.59082i	0.605554	+	0.404619i	−0.214648	+	0.976691i	$0.568861\pi$
$42$	10.4570	+	15.6922i	1.61354	+	2.42136i
$43$	−2.51068	−	3.05928i	−0.382876	−	0.466535i	0.545537	−	0.838087i	$-0.316326\pi$
$43$	−2.51068	−	3.05928i	−0.382876	−	0.466535i	−0.928412	+	0.371552i	$0.878826\pi$
$44$	4.62690	+	1.41615i	0.697531	+	0.213492i
$45$	−2.49800	−	4.67343i	−0.372380	−	0.696674i
$46$	0.379090	+	0.311902i	0.0558938	+	0.0459875i
$47$	−9.22772	+	3.82225i	−1.34600	+	0.557532i	−0.935176	−	0.354182i	$-0.884759\pi$
$47$	−9.22772	+	3.82225i	−1.34600	+	0.557532i	−0.410825	+	0.911714i	$0.634759\pi$
$48$	10.1896	−	5.38135i	1.47074	−	0.776731i
$49$	13.3256	+	5.51963i	1.90365	+	0.788519i
$50$	−0.665102	−	1.24805i	−0.0940596	−	0.176502i
$51$	19.9534	+	6.05280i	2.79404	+	0.847562i
$52$	−2.83613	+	5.27438i	−0.393300	+	0.731425i
$53$	0.910244	−	9.24187i	0.125032	−	1.26947i	−0.703973	−	0.710226i	$-0.748593\pi$
$53$	0.910244	−	9.24187i	0.125032	−	1.26947i	0.829005	−	0.559241i	$-0.188907\pi$
$54$	−5.21370	+	7.78186i	−0.709495	+	1.05898i
$55$	−2.37290	+	0.471998i	−0.319961	+	0.0636442i
$56$	6.21440	−	11.5226i	0.830434	−	1.53977i
$57$	1.71778	−	8.63587i	0.227526	−	1.14385i
$58$	−14.9346	−	0.0185999i	−1.96101	−	0.00244229i
$59$	−0.739346	−	2.43730i	−0.0962546	−	0.317309i	0.895569	−	0.444922i	$-0.146769\pi$
$59$	−0.739346	−	2.43730i	−0.0962546	−	0.317309i	−0.991824	+	0.127613i	$0.959269\pi$
$60$	−3.21292	+	4.78265i	−0.414787	+	0.617437i
$61$	0.781495	+	0.641357i	0.100060	+	0.0821173i	0.683093	−	0.730331i	$-0.260634\pi$
$61$	0.781495	+	0.641357i	0.100060	+	0.0821173i	−0.583033	+	0.812448i	$0.698134\pi$
$62$	−2.78630	+	2.28085i	−0.353860	+	0.289669i
$63$			24.5274i			3.09016i
$64$	−6.61836	−	4.49414i	−0.827295	−	0.561768i
$65$		−	2.99427i		−	0.371394i
$66$	6.24360	+	7.62720i	0.768534	+	0.938843i
$67$	−5.17116	−	4.24386i	−0.631758	−	0.518471i	0.263130	−	0.964760i	$-0.415245\pi$
$67$	−5.17116	−	4.24386i	−0.631758	−	0.518471i	−0.894889	+	0.446290i	$0.852745\pi$
$68$	−2.78873	−	14.2047i	−0.338184	−	1.72258i
$69$	0.290287	+	0.956948i	0.0349464	+	0.115203i
$70$	−0.00815224	+	6.54576i	−0.000974379	+	0.782367i
$71$	−0.731822	+	3.67912i	−0.0868512	+	0.436631i	0.912753	+	0.408511i	$0.133952\pi$
$71$	−0.731822	+	3.67912i	−0.0868512	+	0.436631i	−0.999605	+	0.0281195i	$0.991048\pi$
$72$	14.9105	+	1.52483i	1.75722	+	0.179702i
$73$	2.71293	−	0.539636i	0.317525	−	0.0631596i	−0.0337550	−	0.999430i	$-0.510747\pi$
$73$	2.71293	−	0.539636i	0.317525	−	0.0631596i	0.351280	+	0.936271i	$0.385747\pi$
$74$	−7.17461	−	4.80685i	−0.834031	−	0.558785i
$75$	0.282370	−	2.86695i	0.0326053	−	0.331047i
$76$	−5.85406	+	1.75990i	−0.671506	+	0.201874i
$77$	10.7160	+	3.25068i	1.22121	+	0.370449i
$78$	−10.7657	+	5.73715i	−1.21897	+	0.649604i
$79$	14.1703	+	5.86952i	1.59428	+	0.660373i	0.990592	−	0.136848i	$-0.0436971\pi$
$79$	14.1703	+	5.86952i	1.59428	+	0.660373i	0.603688	+	0.797220i	$0.293697\pi$
$80$	3.97874	+	0.411894i	0.444836	+	0.0460512i
$81$	−2.94119	+	1.21828i	−0.326799	+	0.135365i
$82$	4.19016	−	5.09278i	0.462726	−	0.562403i
$83$	1.03773	+	1.94145i	0.113905	+	0.213102i	0.932414	−	0.361393i	$-0.117699\pi$
$83$	1.03773	+	1.94145i	0.113905	+	0.213102i	−0.818508	+	0.574494i	$0.805199\pi$
$84$	23.5504	−	12.5126i	2.56956	−	1.36524i
$85$	4.59171	+	5.59501i	0.498041	+	0.606864i
$86$	−4.65753	+	3.10368i	−0.502234	+	0.334678i
$87$	−25.2954	−	16.9018i	−2.71195	−	1.81207i
$88$	2.64232	−	6.31232i	0.281673	−	0.672896i
$89$	7.53529	+	11.2774i	0.798739	+	1.19540i	0.977382	+	0.211484i	$0.0678295\pi$
$89$	7.53529	+	11.2774i	0.798739	+	1.19540i	−0.178642	+	0.983914i	$0.557170\pi$
$90$	−6.92724	+	2.85925i	−0.730195	+	0.301392i
$91$	−6.53316	+	12.2227i	−0.684861	+	1.28128i
$92$	0.492131	−	0.489685i	0.0513082	−	0.0510532i
$93$	−7.29968	+	0.718956i	−0.756942	+	0.0745523i
$94$	4.08349	+	13.5221i	0.421180	+	1.39469i
$95$	2.16123	−	2.16123i	0.221737	−	0.221737i
$96$	−6.14249	−	15.0945i	−0.626915	−	1.54057i
$97$	−8.84804	−	8.84804i	−0.898383	−	0.898383i	0.0969104	−	0.995293i	$-0.469104\pi$
$97$	−8.84804	−	8.84804i	−0.898383	−	0.898383i	−0.995293	+	0.0969104i	$0.969104\pi$
$98$	9.63790	−	17.9774i	0.973575	−	1.81599i
$99$	1.25665	+	12.7589i	0.126298	+	1.28232i
$100$	−1.84966	+	0.760762i	−0.184966	+	0.0760762i
$101$	9.43738	+	5.04438i	0.939054	+	0.501935i	0.868564	−	0.495578i	$-0.165044\pi$
$101$	9.43738	+	5.04438i	0.939054	+	0.501935i	0.0704904	+	0.997512i	$0.477544\pi$
$102$	11.3185	−	27.2294i	1.12070	−	2.69611i
$103$	−8.88262	+	5.93518i	−0.875231	+	0.584810i	−0.910011	−	0.414585i	$-0.863927\pi$
$103$	−8.88262	+	5.93518i	−0.875231	+	0.584810i	0.0347801	+	0.999395i	$0.488927\pi$
$104$	7.02416	+	4.73145i	0.688775	+	0.463957i
$105$	−7.40800	+	11.0869i	−0.722947	+	1.08197i
$106$	−12.8777	−	2.57820i	−1.25079	−	0.250417i
$107$	13.1587	−	10.7991i	1.27210	−	1.04399i	0.275529	−	0.961293i	$-0.411147\pi$
$107$	13.1587	−	10.7991i	1.27210	−	1.04399i	0.996575	−	0.0826959i	$-0.0263530\pi$
$108$	10.2190	+	8.42921i	0.983325	+	0.811101i
$109$	−5.75501	+	3.07612i	−0.551230	+	0.294639i	−0.723401	−	0.690429i	$-0.757422\pi$
$109$	−5.75501	+	3.07612i	−0.551230	+	0.294639i	0.172171	+	0.985067i	$0.444922\pi$
$110$	0.331127	+	3.40546i	0.0315717	+	0.324698i
$111$	−6.73217	−	16.2529i	−0.638989	−	1.54266i
$112$	−15.3426	−	10.3625i	−1.44974	−	0.979164i
$113$	−2.06501	+	4.98538i	−0.194260	+	0.468985i	−0.990756	−	0.135659i	$-0.956685\pi$
$113$	−2.06501	+	4.98538i	−0.194260	+	0.468985i	0.796495	+	0.604645i	$0.206685\pi$
$114$	−11.9115	−	3.62953i	−1.11562	−	0.339936i
$115$	−0.100765	+	0.332178i	−0.00939640	+	0.0309758i
$116$	−2.12254	+	21.0138i	−0.197073	+	1.95108i
$117$	−15.7907	−	1.55525i	−1.45985	−	0.143783i
$118$	−3.53362	+	0.698307i	−0.325296	+	0.0642843i
$119$	−6.53577	−	32.8575i	−0.599133	−	3.01204i
$120$	6.27929	+	5.19266i	0.573218	+	0.474023i
$121$	−5.04770	−	1.00405i	−0.458881	−	0.0912772i
$122$	1.01223	−	1.00972i	0.0916434	−	0.0914154i
$123$	12.8558	−	3.89978i	1.15917	−	0.351631i
$124$	2.81857	+	4.24112i	0.253115	+	0.380864i
$125$	0.634393	−	0.773010i	0.0567419	−	0.0691402i
$126$	34.5157	+	3.44291i	3.07490	+	0.306718i
$127$	9.68495			0.859401			0.429700	−	0.902972i	$-0.358619\pi$
$127$	9.68495			0.859401			0.429700	+	0.902972i	$0.358619\pi$
$128$	−7.25331	+	8.68271i	−0.641108	+	0.767451i
$129$	−11.4012			−1.00382
$130$	−4.21363	−	0.420306i	−0.369560	−	0.0368632i
$131$	2.67136	−	3.25507i	0.233398	−	0.284397i	−0.643120	−	0.765766i	$-0.722360\pi$
$131$	2.67136	−	3.25507i	0.233398	−	0.284397i	0.876518	+	0.481369i	$0.159860\pi$
$132$	11.6096	−	7.71555i	1.01049	−	0.671553i
$133$	−13.5377	+	4.10662i	−1.17387	+	0.356089i
$134$	−6.69797	+	6.68131i	−0.578616	+	0.577177i
$135$	−6.49617	−	1.29217i	−0.559102	−	0.111212i
$136$	−20.3808	+	1.93047i	−1.74764	+	0.165537i
$137$	1.73532	+	8.72403i	0.148258	+	0.745344i	0.981353	+	0.192214i	$0.0615668\pi$
$137$	1.73532	+	8.72403i	0.148258	+	0.745344i	−0.833095	+	0.553130i	$0.813433\pi$
$138$	1.38739	−	0.274174i	0.118103	−	0.0233392i
$139$	15.8989	+	1.56591i	1.34853	+	0.132819i	0.746356	−	0.665547i	$-0.231802\pi$
$139$	15.8989	+	1.56591i	1.34853	+	0.132819i	0.602173	+	0.798365i	$0.294302\pi$
$140$	9.21024	+	0.930299i	0.778407	+	0.0786246i
$141$	−8.35257	+	27.5347i	−0.703413	+	2.31884i
$142$	5.07464	+	1.54628i	0.425854	+	0.129761i
$143$	−2.77227	+	6.69285i	−0.231829	+	0.559684i
$144$	4.23876	−	20.7684i	0.353230	−	1.73070i
$145$	−4.04127	−	9.75649i	−0.335609	−	0.810233i
$146$	−0.378578	−	3.89347i	−0.0313313	−	0.322226i
$147$	36.6452	−	19.5873i	3.02244	−	1.61553i
$148$	−7.77145	+	9.42158i	−0.638809	+	0.774449i
$149$	10.9323	−	8.97192i	0.895610	−	0.735008i	−0.0692977	−	0.997596i	$-0.522076\pi$
$149$	10.9323	−	8.97192i	0.895610	−	0.735008i	0.964908	+	0.262588i	$0.0845759\pi$
$150$	−3.99482	−	0.799793i	−0.326176	−	0.0653029i
$151$	8.47347	−	12.6814i	0.689561	−	1.03200i	−0.307205	−	0.951643i	$-0.599394\pi$
$151$	8.47347	−	12.6814i	0.689561	−	1.03200i	0.996766	−	0.0803574i	$-0.0256062\pi$
$152$	1.65485	+	8.48504i	0.134226	+	0.688228i
$153$	31.8910	−	21.3089i	2.57823	−	1.72272i
$154$	6.07866	−	14.6236i	0.489832	−	1.17841i
$155$	−2.24550	−	1.20025i	−0.180363	−	0.0964061i
$156$	6.56231	+	15.9551i	0.525406	+	1.27743i
$157$	1.75658	+	17.8348i	0.140190	+	1.42337i	0.765721	+	0.643173i	$0.222383\pi$
$157$	1.75658	+	17.8348i	0.140190	+	1.42337i	−0.625531	+	0.780200i	$0.715117\pi$
$158$	10.2488	−	19.1169i	0.815354	−	1.52086i
$159$	−18.9172	−	18.9172i	−1.50023	−	1.50023i
$160$	1.13812	−	5.54118i	0.0899767	−	0.438069i
$161$	1.13610	−	1.13610i	0.0895372	−	0.0895372i
$162$	1.30155	+	4.30995i	0.102259	+	0.338621i
$163$	−9.47610	+	0.933314i	−0.742225	+	0.0731028i	−0.462060	−	0.886849i	$-0.652889\pi$
$163$	−9.47610	+	0.933314i	−0.742225	+	0.0731028i	−0.280166	+	0.959952i	$0.590389\pi$
$164$	−6.57854	−	6.61139i	−0.513697	−	0.516263i
$165$	−3.28555	+	6.14683i	−0.255780	+	0.478530i
$166$	2.87773	−	1.18780i	0.223355	−	0.0921910i
$167$	8.21281	+	12.2913i	0.635527	+	0.951133i	0.999803	+	0.0198419i	$0.00631627\pi$
$167$	8.21281	+	12.2913i	0.635527	+	0.951133i	−0.364277	+	0.931291i	$0.618684\pi$
$168$	−14.3024	−	34.8972i	−1.10345	−	2.69238i
$169$	3.35442	+	2.24135i	0.258033	+	0.172412i
$170$	8.51800	−	5.67622i	0.653301	−	0.435346i
$171$	−10.2750	−	12.5201i	−0.785745	−	0.957434i
$172$	3.71381	+	6.98988i	0.283176	+	0.532973i
$173$	−10.1952	−	19.0738i	−0.775125	−	1.45016i	−0.889605	−	0.456732i	$-0.849020\pi$
$173$	−10.1952	−	19.0738i	−0.775125	−	1.45016i	0.114479	−	0.993426i	$-0.463480\pi$
$174$	−27.3355	+	33.2239i	−2.07230	+	2.51870i
$175$	−4.27622	+	1.77127i	−0.323252	+	0.133895i
$176$	−8.51199	−	4.60442i	−0.641615	−	0.347071i
$177$	−6.77884	−	2.80789i	−0.509529	−	0.211054i
$178$	16.9276	−	9.02089i	1.26877	−	0.676144i
$179$	1.27716	+	0.387423i	0.0954597	+	0.0289574i	0.337653	−	0.941271i	$-0.390367\pi$
$179$	1.27716	+	0.387423i	0.0954597	+	0.0289574i	−0.242194	+	0.970228i	$0.577867\pi$
$180$	3.05125	+	10.1496i	0.227427	+	0.756504i
$181$	−1.18159	+	11.9969i	−0.0878270	+	0.891723i	0.845806	+	0.533491i	$0.179120\pi$
$181$	−1.18159	+	11.9969i	−0.0878270	+	0.891723i	−0.933633	+	0.358232i	$0.883380\pi$
$182$	16.2831	+	10.9093i	1.20698	+	0.808655i
$183$	2.85648	−	0.568190i	0.211157	−	0.0420018i
$184$	−0.620019	−	0.761278i	−0.0457084	−	0.0561222i
$185$	1.19134	−	5.98925i	0.0875888	−	0.440339i
$186$	−0.0129191	+	10.3733i	−0.000947275	+	0.760604i
$187$	−5.08328	−	16.7573i	−0.371726	−	1.22542i
$188$	19.6018	−	3.84832i	1.42961	−	0.280667i
$189$	23.6981	+	19.4486i	1.72379	+	1.41467i
$190$	−2.73797	−	3.34471i	−0.198633	−	0.242651i
$191$			7.49189i			0.542094i	0.962566	+	0.271047i	$0.0873699\pi$
$191$			7.49189i			0.542094i	−0.962566	+	0.271047i	$0.912630\pi$
$192$	−22.1036	+	6.52509i	−1.59519	+	0.470908i
$193$		−	8.94796i		−	0.644088i	−0.946725	−	0.322044i	$-0.895630\pi$
$193$		−	8.94796i		−	0.644088i	0.946725	−	0.322044i	$-0.104370\pi$
$194$	−13.6932	+	11.2092i	−0.983117	+	0.804776i
$195$	−6.66797	−	5.47226i	−0.477503	−	0.391877i
$196$	−23.9454	−	16.0862i	−1.71039	−	1.14902i
$197$	3.41044	+	11.2427i	0.242984	+	0.801011i	0.990589	+	0.136868i	$0.0437036\pi$
$197$	3.41044	+	11.2427i	0.242984	+	0.801011i	−0.747605	+	0.664143i	$0.768796\pi$
$198$	18.1311	+	0.0225810i	1.28852	+	0.00160476i
$199$	2.70506	−	13.5992i	0.191756	−	0.964024i	−0.758291	−	0.651917i	$-0.773965\pi$
$199$	2.70506	−	13.5992i	0.191756	−	0.964024i	0.950047	−	0.312107i	$-0.101035\pi$
$200$	0.810931	+	2.70968i	0.0573415	+	0.191604i
$201$	−18.9014	+	3.75972i	−1.33320	+	0.265190i
$202$	8.42333	−	12.5725i	0.592663	−	0.884597i
$203$	−4.79099	+	48.6438i	−0.336262	+	3.41412i
$204$	−36.7293	−	19.7500i	−2.57156	−	1.38278i
$205$	4.46256	+	1.35370i	0.311678	+	0.0945466i
$206$	7.10531	+	13.3330i	0.495050	+	0.928955i
$207$	1.69945	+	0.703934i	0.118120	+	0.0489268i
$208$	7.64421	−	9.22045i	0.530031	−	0.639323i
$209$	−6.83180	+	2.82982i	−0.472566	+	0.195743i
$210$	14.5619	+	11.9810i	1.00487	+	0.826769i
$211$	−5.16468	−	9.66244i	−0.355551	−	0.665190i	0.639027	−	0.769185i	$-0.279337\pi$
$211$	−5.16468	−	9.66244i	−0.355551	−	0.665190i	−0.994578	+	0.103995i	$0.966837\pi$
$212$	−5.43576	+	17.7599i	−0.373329	+	1.21976i
$213$	6.85559	+	8.35356i	0.469737	+	0.572376i
$214$	−13.3497	−	20.0332i	−0.912569	−	1.36944i
$215$	−3.29063	−	2.19873i	−0.224419	−	0.149952i
$216$	13.2963	−	13.1973i	0.904697	−	0.897962i
$217$	6.54738	+	9.79885i	0.444465	+	0.665189i
$218$	3.52097	+	8.53042i	0.238470	+	0.577753i
$219$	3.75637	−	7.02768i	0.253832	−	0.474886i
$220$	4.83875	+	0.0120526i	0.326229	+	0.000812587i
$221$	21.5680	−	2.12427i	1.45082	−	0.142894i
$222$	−23.8166	+	7.19229i	−1.59846	+	0.482715i
$223$	2.64450	−	2.64450i	0.177089	−	0.177089i	−0.612997	−	0.790085i	$-0.710036\pi$
$223$	2.64450	−	2.64450i	0.177089	−	0.177089i	0.790085	+	0.612997i	$0.210036\pi$
$224$	−16.7361	+	20.1359i	−1.11823	+	1.34539i
$225$	−3.74706	−	3.74706i	−0.249804	−	0.249804i
$226$	6.72572	+	3.60575i	0.447388	+	0.239851i
$227$	−0.146277	−	1.48518i	−0.00970875	−	0.0985746i	0.989109	−	0.147184i	$-0.0470210\pi$
$227$	−0.146277	−	1.48518i	−0.00970875	−	0.0985746i	−0.998818	+	0.0486096i	$0.984521\pi$
$228$	−6.77960	+	16.2528i	−0.448990	+	1.07637i
$229$	4.26630	+	2.28039i	0.281925	+	0.150692i	0.606299	−	0.795237i	$-0.292654\pi$
$229$	4.26630	+	2.28039i	0.281925	+	0.150692i	−0.324374	+	0.945929i	$0.605154\pi$
$230$	0.453307	+	0.188428i	0.0298902	+	0.0124246i
$231$	26.8233	−	17.9228i	1.76485	−	1.17923i
$232$	29.2733	+	5.93660i	1.92189	+	0.389757i
$233$	3.69196	−	5.52540i	0.241868	−	0.361981i	−0.690598	−	0.723239i	$-0.742653\pi$
$233$	3.69196	−	5.52540i	0.241868	−	0.361981i	0.932466	+	0.361258i	$0.117653\pi$
$234$	−4.40513	+	22.0028i	−0.287972	+	1.43837i
$235$	−7.72084	+	6.33633i	−0.503652	+	0.413337i
$236$	0.486664	+	5.07064i	0.0316792	+	0.330070i
$237$	38.9681	−	20.8289i	2.53125	−	1.35298i
$238$	−47.1555	+	4.58512i	−3.05664	+	0.297209i
$239$	1.46370	+	3.53368i	0.0946788	+	0.228575i	0.964123	−	0.265457i	$-0.0855227\pi$
$239$	1.46370	+	3.53368i	0.0946788	+	0.228575i	−0.869444	+	0.494032i	$0.835523\pi$
$240$	8.18869	−	8.10751i	0.528578	−	0.523337i
$241$	−0.423867	+	1.02331i	−0.0273037	+	0.0659170i	−0.936943	−	0.349481i	$-0.886358\pi$
$241$	−0.423867	+	1.02331i	−0.0273037	+	0.0659170i	0.909640	+	0.415398i	$0.136358\pi$
$242$	−2.12147	+	6.96233i	−0.136373	+	0.447556i
$243$	3.10580	−	10.2384i	0.199237	−	0.656797i
$244$	−1.27882	−	1.56618i	−0.0818678	−	0.100264i
$245$	14.3540	+	1.41375i	0.917046	+	0.0903211i
$246$	−3.68331	−	18.6385i	−0.234839	−	1.18835i
$247$	−1.78543	−	8.97595i	−0.113604	−	0.571126i
$248$	6.36388	−	3.37105i	0.404107	−	0.214062i
$249$	6.21995	+	1.23722i	0.394173	+	0.0784059i
$250$	−0.998754	−	1.00124i	−0.0631667	−	0.0633243i
$251$	3.16671	−	0.960611i	0.199881	−	0.0606332i	−0.188757	−	0.982024i	$-0.560446\pi$
$251$	3.16671	−	0.960611i	0.199881	−	0.0606332i	0.388638	+	0.921391i	$0.372946\pi$
$252$	9.68992	−	48.0882i	0.610408	−	3.02927i
$253$	0.532782	−	0.649197i	0.0334957	−	0.0408147i
$254$	1.35948	−	13.6290i	0.0853011	−	0.855157i
$255$	20.8513			1.30576
$256$	11.2004	+	11.4259i	0.700027	+	0.714117i
$257$	13.1899			0.822765			0.411383	−	0.911463i	$-0.365046\pi$
$257$	13.1899			0.822765			0.411383	+	0.911463i	$0.365046\pi$
$258$	−1.60038	+	16.0441i	−0.0996355	+	0.998862i
$259$	−17.9309	+	21.8489i	−1.11417	+	1.35762i
$260$	−1.18293	+	5.87055i	−0.0733624	+	0.364076i
$261$	−53.5512	+	16.2446i	−3.31474	+	1.00551i
$262$	−4.20565	−	4.21614i	−0.259826	−	0.260474i
$263$	8.15183	+	1.62150i	0.502663	+	0.0999860i	0.439908	−	0.898043i	$-0.355011\pi$
$263$	8.15183	+	1.62150i	0.502663	+	0.0999860i	0.0627557	+	0.998029i	$0.480011\pi$
$264$	−9.22791	−	17.4205i	−0.567939	−	1.07216i
$265$	−1.81172	−	9.10814i	−0.111293	−	0.559509i
$266$	3.87867	+	19.6271i	0.237817	+	1.20342i
$267$	38.8850	+	3.82983i	2.37972	+	0.234382i
$268$	8.46194	+	10.3634i	0.516895	+	0.633048i
$269$	−5.18695	+	17.0991i	−0.316254	+	1.04255i	0.644374	+	0.764710i	$0.277118\pi$
$269$	−5.18695	+	17.0991i	−0.316254	+	1.04255i	−0.960628	+	0.277838i	$0.910382\pi$
$270$	−2.73025	+	8.96023i	−0.166157	+	0.545302i
$271$	−2.90733	+	7.01892i	−0.176608	+	0.426369i	−0.987251	−	0.159172i	$-0.949118\pi$
$271$	−2.90733	+	7.01892i	−0.176608	+	0.426369i	0.810643	+	0.585541i	$0.199118\pi$
$272$	−0.144228	+	28.9514i	−0.00874513	+	1.75544i
$273$	15.2789	+	36.8866i	0.924723	+	2.23248i
$274$	12.5203	−	1.21740i	0.756379	−	0.0735458i
$275$	−2.13371	+	1.14049i	−0.128667	+	0.0687741i
$276$	−0.191077	−	1.99087i	−0.0115015	−	0.119836i
$277$	−13.2660	+	10.8871i	−0.797077	+	0.654144i	−0.942118	−	0.335281i	$-0.891169\pi$
$277$	−13.2660	+	10.8871i	−0.797077	+	0.654144i	0.145041	+	0.989426i	$0.453669\pi$
$278$	4.43532	−	22.1536i	0.266013	−	1.32869i
$279$	−7.49598	+	11.2185i	−0.448773	+	0.671636i
$280$	2.60198	−	12.8303i	0.155498	−	0.766759i
$281$	15.0291	−	10.0421i	0.896562	−	0.599064i	−0.0196278	−	0.999807i	$-0.506248\pi$
$281$	15.0291	−	10.0421i	0.896562	−	0.599064i	0.916190	+	0.400743i	$0.131248\pi$
$282$	37.5752	+	15.6190i	2.23757	+	0.930100i
$283$	1.58983	+	0.849783i	0.0945057	+	0.0505144i	0.517972	−	0.855397i	$-0.326687\pi$
$283$	1.58983	+	0.849783i	0.0945057	+	0.0505144i	−0.423467	+	0.905912i	$0.639187\pi$
$284$	2.88830	−	6.92413i	0.171389	−	0.410871i
$285$	−0.863046	−	8.76266i	−0.0511224	−	0.519055i
$286$	9.02924	+	4.84070i	0.533910	+	0.286236i
$287$	−15.2626	−	15.2626i	−0.900924	−	0.900924i
$288$	−28.6310	−	8.88018i	−1.68710	−	0.523270i
$289$	−25.0230	+	25.0230i	−1.47194	+	1.47194i
$290$	−14.2969	+	4.31748i	−0.839543	+	0.253531i
$291$	−35.8742	+	3.53330i	−2.10299	+	0.207126i
$292$	−5.53215	−	0.0137798i	−0.323745	−	0.000806400i
$293$	−4.66683	+	8.73102i	−0.272639	+	0.510072i	−0.980560	−	0.196220i	$-0.937133\pi$
$293$	−4.66683	+	8.73102i	−0.272639	+	0.510072i	0.707921	+	0.706292i	$0.249633\pi$
$294$	−22.4199	−	54.3177i	−1.30756	−	3.16787i
$295$	−1.41502	−	2.11773i	−0.0823856	−	0.123299i
$296$	12.1675	+	12.2587i	0.707219	+	0.712524i
$297$	13.3240	+	8.90281i	0.773137	+	0.516594i
$298$	−11.0910	−	16.6437i	−0.642484	−	0.964142i
$299$	0.659381	+	0.803458i	0.0381330	+	0.0464652i
$300$	−1.68625	+	5.50937i	−0.0973555	+	0.318084i
$301$	8.63505	+	16.1550i	0.497716	+	0.931162i
$302$	−16.6563	−	13.7042i	−0.958461	−	0.788588i
$303$	28.4809	−	11.7972i	1.63618	−	0.677730i
$304$	12.1727	−	1.13771i	0.698152	−	0.0652519i
$305$	0.934020	+	0.386884i	0.0534818	+	0.0221529i
$306$	−25.5100	−	47.8691i	−1.45831	−	2.73649i
$307$	−13.0677	−	3.96404i	−0.745812	−	0.226240i	−0.105569	−	0.994412i	$-0.533666\pi$
$307$	−13.0677	−	3.96404i	−0.745812	−	0.226240i	−0.640243	+	0.768172i	$0.721166\pi$
$308$	−19.7256	−	10.6068i	−1.12397	−	0.604378i
$309$	−3.01657	+	30.6278i	−0.171607	+	1.74235i
$310$	−2.00422	+	2.99146i	−0.113832	+	0.169903i
$311$	−15.3380	+	3.05092i	−0.869738	+	0.173002i	−0.609734	−	0.792606i	$-0.708724\pi$
$311$	−15.3380	+	3.05092i	−0.869738	+	0.173002i	−0.260004	+	0.965608i	$0.583724\pi$
$312$	23.3737	−	6.99507i	1.32327	−	0.396018i
$313$	4.02149	−	20.2174i	0.227308	−	1.14275i	−0.683508	−	0.729943i	$-0.739547\pi$
$313$	4.02149	−	20.2174i	0.227308	−	1.14275i	0.910816	−	0.412812i	$-0.135453\pi$
$314$	25.3443	+	0.0315644i	1.43026	+	0.00178128i
$315$	7.11992	+	23.4712i	0.401162	+	1.32245i
$316$	−25.4633	−	17.1059i	−1.43242	−	0.962283i
$317$	−18.0256	−	14.7933i	−1.01242	−	0.830872i	−0.0267654	−	0.999642i	$-0.508521\pi$
$317$	−18.0256	−	14.7933i	−1.01242	−	0.830872i	−0.985656	+	0.168769i	$0.946021\pi$
$318$	−29.2763	+	23.9655i	−1.64173	+	1.34392i
$319$			25.5495i			1.43050i
$320$	−7.63796	−	2.37942i	−0.426975	−	0.133014i
$321$		−	49.0395i		−	2.73712i
$322$	−1.43928	−	1.75823i	−0.0802079	−	0.0979822i
$323$	17.1008	+	14.0343i	0.951514	+	0.780887i
$324$	6.24778	−	1.22659i	0.347099	−	0.0681440i
$325$	−0.869191	−	2.86534i	−0.0482141	−	0.158940i
$326$	−0.0167710	+	13.4661i	−0.000928857	+	0.745816i
$327$	−3.66749	+	18.4377i	−0.202813	+	1.01961i
$328$	−10.2272	+	8.32947i	−0.564701	+	0.459918i
$329$	45.3417	−	9.01903i	2.49977	−	0.497235i
$330$	8.18881	+	5.48635i	0.450779	+	0.302014i
$331$	0.763299	−	7.74991i	0.0419547	−	0.425973i	−0.951149	−	0.308733i	$-0.900095\pi$
$331$	0.763299	−	7.74991i	0.0419547	−	0.425973i	0.993104	−	0.117241i	$-0.0374049\pi$
$332$	−1.26756	−	4.21636i	−0.0695663	−	0.231403i
$333$	−30.9663	−	9.39353i	−1.69694	−	0.514762i
$334$	18.4496	−	9.83198i	1.00952	−	0.537982i
$335$	−6.18042	−	2.56002i	−0.337673	−	0.139869i
$336$	−51.1160	+	15.2282i	−2.78861	+	0.830768i
$337$	−25.0691	+	10.3840i	−1.36560	+	0.565650i	−0.940592	−	0.339539i	$-0.889729\pi$
$337$	−25.0691	+	10.3840i	−1.36560	+	0.565650i	−0.425008	+	0.905189i	$0.639729\pi$
$338$	3.62496	−	4.40583i	0.197172	−	0.239645i
$339$	7.32802	+	13.7098i	0.398003	+	0.744612i
$340$	−6.79207	−	12.7836i	−0.368352	−	0.693286i
$341$	3.90793	+	4.76183i	0.211626	+	0.257867i
$342$	−19.0609	+	12.7018i	−1.03070	+	0.686834i
$343$	−28.5693	−	19.0894i	−1.54260	−	1.03073i
$344$	10.3577	−	4.24502i	0.558448	−	0.228876i
$345$	0.555574	+	0.831476i	0.0299111	+	0.0447652i
$346$	−28.2724	+	11.6696i	−1.51993	+	0.627360i
$347$	−11.5439	+	21.5972i	−0.619711	+	1.15940i	0.354775	+	0.934952i	$0.384557\pi$
$347$	−11.5439	+	21.5972i	−0.619711	+	1.15940i	−0.974486	+	0.224446i	$0.927943\pi$
$348$	42.9166	+	43.1310i	2.30057	+	2.31206i
$349$	−25.7526	+	2.53641i	−1.37851	+	0.135771i	−0.759956	−	0.649975i	$-0.774780\pi$
$349$	−25.7526	+	2.53641i	−1.37851	+	0.135771i	−0.618550	+	0.785746i	$0.712280\pi$
$350$	1.89233	+	6.26626i	0.101149	+	0.334946i
$351$	−14.0236	+	14.0236i	−0.748525	+	0.748525i
$352$	−7.67430	+	11.3320i	−0.409042	+	0.603998i
$353$	4.94320	+	4.94320i	0.263100	+	0.263100i	0.826312	−	0.563212i	$-0.190435\pi$
$353$	4.94320	+	4.94320i	0.263100	+	0.263100i	−0.563212	+	0.826312i	$0.690435\pi$
$354$	−4.90289	+	9.14525i	−0.260586	+	0.486064i
$355$	0.367681	+	3.73313i	0.0195145	+	0.198134i
$356$	−10.3183	−	25.0872i	−0.546871	−	1.32962i
$357$	−85.1152	−	45.4950i	−4.50478	−	2.40785i
$358$	0.724469	−	1.74288i	0.0382894	−	0.0921141i
$359$	20.2721	−	13.5454i	1.06992	−	0.714897i	0.109649	−	0.993970i	$-0.465027\pi$
$359$	20.2721	−	13.5454i	1.06992	−	0.714897i	0.960270	+	0.279074i	$0.0900274\pi$
$360$	14.7111	−	2.86912i	0.775342	−	0.151216i
$361$	−5.36581	+	8.03050i	−0.282411	+	0.422658i
$362$	16.7165	+	3.34678i	0.878602	+	0.175903i
$363$	−11.4610	+	9.40578i	−0.601545	+	0.493675i
$364$	17.6376	−	21.3827i	0.924462	−	1.12076i
$365$	2.43947	−	1.30392i	0.127688	−	0.0682504i
$366$	−0.398610	−	4.09949i	−0.0208357	−	0.214284i
$367$	5.46918	+	13.2038i	0.285489	+	0.689231i	0.999945	−	0.0104488i	$-0.00332602\pi$
$367$	5.46918	+	13.2038i	0.285489	+	0.689231i	−0.714457	+	0.699680i	$0.753326\pi$
$368$	−1.15833	+	0.765649i	−0.0603819	+	0.0399122i
$369$	9.45681	−	22.8307i	0.492302	−	1.18852i
$370$	−8.26103	−	2.51719i	−0.429470	−	0.130863i
$371$	−12.4774	+	41.1326i	−0.647796	+	2.13550i
$372$	14.5957	+	1.47427i	0.756754	+	0.0764375i
$373$	12.8092	+	1.26160i	0.663238	+	0.0653232i	0.424034	−	0.905646i	$-0.360614\pi$
$373$	12.8092	+	1.26160i	0.663238	+	0.0653232i	0.239204	+	0.970969i	$0.423114\pi$
$374$	−24.2950	+	4.80112i	−1.25626	+	0.248260i
$375$	−0.562021	−	2.82547i	−0.0290226	−	0.145907i
$376$	−2.66396	−	28.1245i	−0.137383	−	1.45041i
$377$	−31.0130	−	6.16887i	−1.59725	−	0.317713i
$378$	30.6951	−	30.6187i	1.57879	−	1.57486i
$379$	−4.68689	+	1.42175i	−0.240749	+	0.0730305i	−0.408354	−	0.912824i	$-0.633897\pi$
$379$	−4.68689	+	1.42175i	−0.240749	+	0.0730305i	0.167604	+	0.985854i	$0.446397\pi$
$380$	−5.09111	+	3.38346i	−0.261168	+	0.173568i
$381$	17.7000	−	21.5675i	0.906798	−	1.10494i
$382$	10.5428	+	1.05164i	0.539417	+	0.0538064i
$383$	5.79035			0.295873			0.147936	−	0.988997i	$-0.452737\pi$
$383$	5.79035			0.295873			0.147936	+	0.988997i	$0.452737\pi$
$384$	6.07962	+	32.0208i	0.310249	+	1.63405i
$385$	11.1982			0.570715
$386$	−12.5918	−	1.25602i	−0.640907	−	0.0639299i
$387$	−13.3045	+	16.2116i	−0.676305	+	0.824080i
$388$	13.8519	+	20.8430i	0.703221	+	1.05814i
$389$	14.6277	−	4.43727i	0.741654	−	0.224978i	0.103224	−	0.994658i	$-0.467084\pi$
$389$	14.6277	−	4.43727i	0.741654	−	0.224978i	0.638430	+	0.769680i	$0.279584\pi$
$390$	−8.63671	+	8.61522i	−0.437337	+	0.436249i
$391$	−2.46420	−	0.490160i	−0.124620	−	0.0247885i
$392$	−25.9982	+	31.4387i	−1.31311	+	1.58789i
$393$	−2.36661	−	11.8978i	−0.119380	−	0.600163i
$394$	16.2998	−	3.22114i	0.821173	−	0.162279i
$395$	15.2639	+	1.50337i	0.768012	+	0.0756426i
$396$	2.57684	−	25.5115i	0.129491	−	1.28200i
$397$	−3.96959	+	13.0860i	−0.199228	+	0.656766i	0.799218	+	0.601041i	$0.205247\pi$
$397$	−3.96959	+	13.0860i	−0.199228	+	0.656766i	−0.998446	+	0.0557253i	$0.982253\pi$
$398$	−18.7575	−	5.71556i	−0.940231	−	0.286495i
$399$	−15.5961	+	37.6524i	−0.780783	+	1.88498i
$400$	3.92698	−	0.760808i	0.196349	−	0.0380404i
$401$	11.9663	+	28.8891i	0.597567	+	1.44265i	0.876053	+	0.482214i	$0.160167\pi$
$401$	11.9663	+	28.8891i	0.597567	+	1.44265i	−0.278486	+	0.960440i	$0.589833\pi$
$402$	2.63760	+	27.1263i	0.131552	+	1.35294i
$403$	−6.72365	+	3.59386i	−0.334929	+	0.179023i
$404$	−16.5100	−	13.6184i	−0.821403	−	0.677539i
$405$	−2.46090	+	2.01961i	−0.122283	+	0.100355i
$406$	67.7805	+	13.5702i	3.36389	+	0.673475i
$407$	−8.20809	+	12.2843i	−0.406860	+	0.608909i
$408$	−32.9484	+	48.9142i	−1.63119	+	2.42161i
$409$	−20.7552	+	13.8682i	−1.02628	+	0.685738i	−0.950289	−	0.311371i	$-0.899212\pi$
$409$	−20.7552	+	13.8682i	−1.02628	+	0.685738i	−0.0759908	+	0.997109i	$0.524212\pi$
$410$	2.53138	−	6.08982i	0.125016	−	0.300755i
$411$	22.5990	+	12.0794i	1.11473	+	0.595835i
$412$	19.7600	−	8.12725i	0.973505	−	0.400401i
$413$	1.15550	+	11.7320i	0.0568585	+	0.577294i
$414$	1.22915	−	2.29270i	0.0604094	−	0.112680i
$415$	1.55661	+	1.55661i	0.0764112	+	0.0764112i
$416$	−11.9023	−	12.0514i	−0.583557	−	0.590870i
$417$	32.5436	−	32.5436i	1.59367	−	1.59367i
$418$	3.02324	+	10.0111i	0.147871	+	0.489661i
$419$	23.2493	−	2.28986i	1.13580	−	0.111867i	0.487410	−	0.873173i	$-0.337942\pi$
$419$	23.2493	−	2.28986i	1.13580	−	0.111867i	0.648392	+	0.761306i	$0.275442\pi$
$420$	18.9041	−	18.8102i	0.922426	−	0.917842i
$421$	−5.99714	+	11.2199i	−0.292283	+	0.546823i	−0.984611	−	0.174760i	$-0.944085\pi$
$421$	−5.99714	+	11.2199i	−0.292283	+	0.546823i	0.692328	+	0.721583i	$0.256585\pi$
$422$	−14.3222	+	5.91158i	−0.697196	+	0.287771i
$423$	29.4052	+	44.0080i	1.42973	+	2.13974i
$424$	24.2293	+	10.1423i	1.17668	+	0.492555i
$425$	6.01814	+	4.02119i	0.291922	+	0.195056i
$426$	12.7177	−	8.47480i	0.616175	−	0.410606i
$427$	−2.96855	−	3.61719i	−0.143658	−	0.175048i
$428$	−30.0653	+	15.9741i	−1.45326	+	0.772136i
$429$	9.83783	+	18.4053i	0.474975	+	0.888615i
$430$	−3.55603	+	4.32204i	−0.171487	+	0.208427i
$431$	5.05429	−	2.09355i	0.243456	−	0.100843i	−0.257619	−	0.966247i	$-0.582938\pi$
$431$	5.05429	−	2.09355i	0.243456	−	0.100843i	0.501075	+	0.865404i	$0.332938\pi$
$432$	−16.7052	−	20.5634i	−0.803731	−	0.989359i
$433$	−1.94727	−	0.806584i	−0.0935797	−	0.0387620i	0.335403	−	0.942075i	$-0.391128\pi$
$433$	−1.94727	−	0.806584i	−0.0935797	−	0.0387620i	−0.428982	+	0.903313i	$0.641128\pi$
$434$	14.7083	−	7.83821i	0.706021	−	0.376246i
$435$	−29.1125	−	8.83119i	−1.39584	−	0.423423i
$436$	12.4985	−	3.75741i	0.598569	−	0.179947i
$437$	−0.103993	+	1.05586i	−0.00497466	+	0.0505085i
$438$	−9.36228	−	6.27255i	−0.447347	−	0.299714i
$439$	1.60546	−	0.319347i	0.0766246	−	0.0152416i	−0.156629	−	0.987657i	$-0.550063\pi$
$439$	1.60546	−	0.319347i	0.0766246	−	0.0152416i	0.233254	+	0.972416i	$0.425063\pi$
$440$	0.696176	−	6.80754i	0.0331889	−	0.324537i
$441$	14.9112	−	74.9636i	0.710057	−	3.56970i
$442$	0.0381715	−	30.6494i	0.00181563	−	1.45784i
$443$	−9.29340	−	30.6362i	−0.441543	−	1.45557i	−0.842111	−	0.539304i	$-0.818687\pi$
$443$	−9.29340	−	30.6362i	−0.441543	−	1.45557i	0.400568	−	0.916267i	$-0.368813\pi$
$444$	6.77808	+	34.5250i	0.321674	+	1.63848i
$445$	10.4845	+	8.60438i	0.497012	+	0.407887i
$446$	−3.35021	−	4.09262i	−0.158637	−	0.193791i
$447$		−	40.7421i		−	1.92704i
$448$	25.9867	+	26.3780i	1.22775	+	1.24624i
$449$		−	15.9254i		−	0.751566i	−0.926708	−	0.375783i	$-0.877374\pi$
$449$		−	15.9254i		−	0.751566i	0.926708	−	0.375783i	$-0.122626\pi$
$450$	−5.79895	+	4.74701i	−0.273365	+	0.223776i
$451$	−8.72145	−	7.15751i	−0.410677	−	0.337034i
$452$	6.01820	−	8.95849i	0.283072	−	0.421372i
$453$	−12.7545	−	42.0459i	−0.599258	−	1.97549i
$454$	−2.11052	−	0.00262849i	−0.0990514	−	0.000123361i
$455$	−2.70379	+	13.5928i	−0.126755	+	0.637242i
$456$	21.9198	+	11.8219i	1.02649	+	0.553609i
$457$	−2.67004	+	0.531103i	−0.124899	+	0.0248440i	−0.257144	−	0.966373i	$-0.582781\pi$
$457$	−2.67004	+	0.531103i	−0.124899	+	0.0248440i	0.132245	+	0.991217i	$0.457781\pi$
$458$	3.80789	−	5.68357i	0.177931	−	0.265576i
$459$	4.69895	−	47.7093i	0.219328	−	2.22688i
$460$	0.328792	−	0.611458i	0.0153300	−	0.0285094i
$461$	19.0709	+	5.78509i	0.888220	+	0.269438i	0.701240	−	0.712925i	$-0.252630\pi$
$461$	19.0709	+	5.78509i	0.888220	+	0.269438i	0.186980	+	0.982364i	$0.440130\pi$
$462$	−21.4563	−	40.2624i	−0.998237	−	1.87318i
$463$	25.9960	+	10.7679i	1.20813	+	0.500426i	0.893619	−	0.448826i	$-0.148158\pi$
$463$	25.9960	+	10.7679i	1.20813	+	0.500426i	0.314516	+	0.949252i	$0.398158\pi$
$464$	12.4633	−	40.3609i	0.578592	−	1.87371i
$465$	−6.77666	+	2.80698i	−0.314260	+	0.130171i
$466$	−7.25727	−	5.97103i	−0.336187	−	0.276603i
$467$	4.63333	+	8.66836i	0.214405	+	0.401124i	0.966016	−	0.258483i	$-0.0832227\pi$
$467$	4.63333	+	8.66836i	0.214405	+	0.401124i	−0.751611	+	0.659607i	$0.770723\pi$
$468$	30.3447	+	9.28756i	1.40268	+	0.429318i
$469$	19.6429	+	23.9350i	0.907027	+	1.10522i
$470$	7.83290	+	11.7544i	0.361305	+	0.542191i
$471$	42.9268	+	28.6827i	1.97796	+	1.32163i
$472$	7.20386	+	0.0269157i	0.331585	+	0.00123890i
$473$	5.31957	+	7.96131i	0.244594	+	0.366061i
$474$	−23.8411	−	57.7609i	−1.09506	−	2.65304i
$475$	1.44079	−	2.69554i	0.0661082	−	0.123680i
$476$	−0.166893	+	67.0022i	−0.00764951	+	3.07104i
$477$	−48.9740	+	4.82352i	−2.24237	+	0.220854i
$478$	5.17816	−	1.56374i	0.236844	−	0.0715237i
$479$	−13.3469	+	13.3469i	−0.609835	+	0.609835i	−0.942903	−	0.333068i	$-0.891916\pi$
$479$	−13.3469	+	13.3469i	−0.609835	+	0.609835i	0.333068	+	0.942903i	$0.391916\pi$
$480$	−10.2597	−	12.6614i	−0.468288	−	0.577912i
$481$	−12.9293	−	12.9293i	−0.589525	−	0.589525i
$482$	1.38053	+	0.740120i	0.0628814	+	0.0337116i
$483$	−0.453681	−	4.60630i	−0.0206432	−	0.209594i
$484$	9.49981	+	3.96270i	0.431810	+	0.180123i
$485$	−11.0355	−	5.89860i	−0.501096	−	0.267842i
$486$	−13.9719	−	5.80774i	−0.633778	−	0.263445i
$487$	−35.2737	+	23.5691i	−1.59840	+	1.06802i	−0.645928	+	0.763398i	$0.723529\pi$
$487$	−35.2737	+	23.5691i	−1.59840	+	1.06802i	−0.952474	+	0.304620i	$0.901471\pi$
$488$	−2.38348	+	1.57974i	−0.107895	+	0.0715116i
$489$	−15.2399	+	22.8081i	−0.689171	+	1.03142i
$490$	4.00435	−	20.0010i	0.180898	−	0.903553i
$491$	28.5018	−	23.3908i	1.28627	−	1.05561i	0.291176	−	0.956669i	$-0.405953\pi$
$491$	28.5018	−	23.3908i	1.28627	−	1.05561i	0.995093	−	0.0989442i	$-0.0315465\pi$
$492$	−26.7457	+	2.56697i	−1.20579	+	0.115728i
$493$	67.4099	−	36.0314i	3.03599	−	1.62277i
$494$	−12.8819	+	1.25255i	−0.579582	+	0.0563551i
$495$	4.90626	+	11.8448i	0.220520	+	0.532382i
$496$	−3.85055	−	9.42863i	−0.172895	−	0.423358i
$497$	6.64438	−	16.0409i	0.298041	−	0.719535i
$498$	2.61415	−	8.57923i	0.117143	−	0.384444i
$499$	7.74292	−	25.5250i	0.346620	−	1.14265i	−0.594362	−	0.804198i	$-0.702595\pi$
$499$	7.74292	−	25.5250i	0.346620	−	1.14265i	0.940982	−	0.338457i	$-0.109905\pi$
$500$	−1.54918	+	1.26493i	−0.0692813	+	0.0565695i
$501$	42.3812	+	4.17419i	1.89345	+	0.186489i
$502$	−0.907290	−	4.59113i	−0.0404943	−	0.204912i
$503$	2.99981	+	15.0811i	0.133755	+	0.672431i	0.988235	+	0.152946i	$0.0488761\pi$
$503$	2.99981	+	15.0811i	0.133755	+	0.672431i	−0.854480	+	0.519485i	$0.826124\pi$
$504$	−66.3110	−	20.3861i	−2.95373	−	0.908068i
$505$	10.4953	+	2.08765i	0.467035	+	0.0928991i
$506$	−0.838783	−	0.840875i	−0.0372884	−	0.0373814i
$507$	11.1218	−	3.37375i	0.493934	−	0.149833i
$508$	−18.9882	−	3.82619i	−0.842467	−	0.169760i
$509$	2.53723	−	3.09162i	0.112461	−	0.137034i	−0.713738	−	0.700413i	$-0.752999\pi$
$509$	2.53723	−	3.09162i	0.112461	−	0.137034i	0.826198	+	0.563380i	$0.190499\pi$
$510$	2.92689	−	29.3425i	0.129605	−	1.29931i
$511$	−12.8030			−0.566370
$512$	17.6510	−	14.1577i	0.780073	−	0.625689i
$513$	−20.2441			−0.893800
$514$	1.85147	−	18.5613i	0.0816648	−	0.818702i
$515$	−6.77725	+	8.25810i	−0.298641	+	0.363895i
$516$	22.3531	+	4.50421i	0.984040	+	0.198287i
$517$	23.1243	−	7.01468i	1.01701	−	0.308505i
$518$	28.2294	+	28.2998i	1.24033	+	1.24342i
$519$	−61.1081	−	12.1552i	−2.68235	−	0.533552i
$520$	8.09516	+	2.48871i	0.354996	+	0.109137i
$521$	−3.92142	−	19.7143i	−0.171800	−	0.863699i	−0.966494	−	0.256689i	$-0.917369\pi$
$521$	−3.92142	−	19.7143i	−0.171800	−	0.863699i	0.794694	−	0.607011i	$-0.207631\pi$
$522$	15.3429	+	77.6391i	0.671540	+	3.39817i
$523$	2.75949	+	0.271786i	0.120664	+	0.0118844i	0.158169	−	0.987412i	$-0.449441\pi$
$523$	2.75949	+	0.271786i	0.120664	+	0.0118844i	−0.0375049	+	0.999296i	$0.511941\pi$
$524$	−6.52342	+	5.32650i	−0.284977	+	0.232689i
$525$	−3.87067	+	12.7599i	−0.168930	+	0.556887i
$526$	3.42610	−	11.2439i	0.149385	−	0.490257i
$527$	7.05243	−	17.0261i	0.307209	−	0.741667i
$528$	−25.8099	+	10.5405i	−1.12323	+	0.458716i
$529$	8.75561	+	21.1379i	0.380679	+	0.919039i
$530$	−13.0716	+	1.27100i	−0.567792	+	0.0552088i
$531$	−11.9031	+	6.36233i	−0.516550	+	0.276102i
$532$	28.1643	−	2.70313i	1.22108	−	0.117195i
$533$	10.7938	−	8.85827i	0.467533	−	0.383694i
$534$	10.8477	−	54.1825i	0.469427	−	2.34471i
$535$	9.45732	−	14.1539i	0.408876	−	0.611926i
$536$	15.7715	−	10.4532i	0.681227	−	0.451509i
$537$	3.19687	−	2.13608i	0.137955	−	0.0921786i
$538$	23.3342	+	9.69942i	1.00601	+	0.418172i
$539$	−30.7755	−	16.4498i	−1.32559	−	0.708545i
$540$	12.2259	+	5.09983i	0.526117	+	0.219462i
$541$	0.796985	+	8.09193i	0.0342651	+	0.347899i	0.996997	+	0.0774414i	$0.0246751\pi$
$541$	0.796985	+	8.09193i	0.0342651	+	0.347899i	−0.962732	+	0.270458i	$0.912825\pi$
$542$	9.46913	+	5.07653i	0.406734	+	0.218056i
$543$	24.5565	+	24.5565i	1.05382	+	1.05382i
$544$	40.7211	+	4.26687i	1.74590	+	0.182941i
$545$	−4.61425	+	4.61425i	−0.197653	+	0.197653i
$546$	54.0526	−	16.3232i	2.31324	−	0.698568i
$547$	14.0821	−	1.38696i	0.602106	−	0.0593023i	0.207628	−	0.978208i	$-0.433425\pi$
$547$	14.0821	−	1.38696i	0.602106	−	0.0593023i	0.394478	+	0.918905i	$0.370925\pi$
$548$	0.0443119	−	17.7898i	0.00189291	−	0.759944i
$549$	2.52542	−	4.72473i	0.107782	−	0.201646i
$550$	1.30542	+	3.16270i	0.0556634	+	0.134858i
$551$	−17.9322	−	26.8374i	−0.763936	−	1.14331i
$552$	−2.82843	−	0.0105678i	−0.120386	−	0.000449796i
$553$	−59.0275	−	39.4409i	−2.51011	−	1.67720i
$554$	13.4585	+	20.1965i	0.571799	+	0.858069i
$555$	−11.1603	−	13.5988i	−0.473726	−	0.577237i
$556$	−30.5527	−	9.35122i	−1.29572	−	0.396580i
$557$	−0.974867	−	1.82385i	−0.0413065	−	0.0772789i	0.860421	−	0.509584i	$-0.170201\pi$
$557$	−0.974867	−	1.82385i	−0.0413065	−	0.0772789i	−0.901728	+	0.432305i	$0.857701\pi$
$558$	14.7348	+	12.1233i	0.623776	+	0.513221i
$559$	−10.9481	+	4.53486i	−0.463057	+	0.191804i
$560$	−17.6900	−	5.46258i	−0.747539	−	0.230836i
$561$	−46.6071	−	19.3053i	−1.96775	−	0.815070i
$562$	−12.0220	−	22.5591i	−0.507116	−	0.951596i
$563$	14.2766	+	4.33075i	0.601686	+	0.182519i	0.576409	−	0.817161i	$-0.304453\pi$
$563$	14.2766	+	4.33075i	0.601686	+	0.182519i	0.0252766	+	0.999680i	$0.491953\pi$
$564$	27.2540	−	50.6846i	1.14760	−	2.13421i
$565$	−0.528914	+	5.37016i	−0.0222516	+	0.225924i
$566$	1.41900	−	2.11798i	0.0596452	−	0.0890252i
$567$	14.4520	−	2.87468i	0.606926	−	0.120725i
$568$	−9.33841	−	5.03643i	−0.391831	−	0.211324i
$569$	8.21347	−	41.2919i	0.344326	−	1.73105i	−0.289150	−	0.957284i	$-0.593373\pi$
$569$	8.21347	−	41.2919i	0.344326	−	1.73105i	0.633477	−	0.773762i	$-0.281627\pi$
$570$	−12.4522	−	0.0155083i	−0.521566	−	0.000649571i
$571$	12.1084	+	39.9159i	0.506719	+	1.67043i	0.720427	+	0.693531i	$0.243946\pi$
$571$	12.1084	+	39.9159i	0.506719	+	1.67043i	−0.213708	+	0.976898i	$0.568554\pi$
$572$	8.07941	−	12.0267i	0.337817	−	0.502863i
$573$	16.6837	+	13.6920i	0.696973	+	0.571991i
$574$	−23.6204	+	19.3356i	−0.985897	+	0.807052i
$575$			0.347125i			0.0144761i
$576$	−16.5154	+	39.0439i	−0.688141	+	1.62683i
$577$		−	18.4231i		−	0.766964i	−0.923548	−	0.383482i	$-0.874725\pi$
$577$		−	18.4231i		−	0.766964i	0.923548	−	0.383482i	$-0.125275\pi$
$578$	31.7007	+	38.7256i	1.31857	+	1.61077i
$579$	−19.9263	−	16.3531i	−0.828107	−	0.679610i
$580$	4.06883	+	20.7251i	0.168949	+	0.860562i
$581$	−2.95778	−	9.75048i	−0.122709	−	0.404518i
$582$	−0.0634908	+	50.9793i	−0.00263178	+	2.11316i
$583$	−4.38325	+	22.0361i	−0.181536	+	0.912641i
$584$	−0.795938	+	7.78307i	−0.0329362	+	0.322066i
$585$	−15.5622	+	3.09552i	−0.643418	+	0.127984i
$586$	11.6315	+	7.79287i	0.480492	+	0.321920i
$587$	−3.50391	+	35.5758i	−0.144622	+	1.46837i	0.599527	+	0.800355i	$0.295355\pi$
$587$	−3.50391	+	35.5758i	−0.144622	+	1.46837i	−0.744149	+	0.668014i	$0.767145\pi$
$588$	−79.5845	+	23.9254i	−3.28201	+	0.986667i
$589$	−7.44704	−	2.25904i	−0.306850	−	0.0930819i
$590$	−3.17875	+	1.69399i	−0.130867	+	0.0697406i
$591$	31.2694	+	12.9522i	1.28625	+	0.532782i
$592$	18.9588	−	15.4017i	0.779201	−	0.633004i
$593$	−43.8713	+	18.1721i	−1.80158	+	0.746238i	−0.815766	+	0.578382i	$0.803684\pi$
$593$	−43.8713	+	18.1721i	−1.80158	+	0.746238i	−0.985812	+	0.167855i	$0.946316\pi$
$594$	14.3986	−	17.5002i	0.590781	−	0.718044i
$595$	−15.7924	−	29.5454i	−0.647424	−	1.21125i
$596$	−24.9783	+	13.2713i	−1.02315	+	0.543614i
$597$	−25.3405	−	30.8775i	−1.03712	−	1.26373i
$598$	1.22321	−	0.815119i	0.0500207	−	0.0333327i
$599$	8.90781	+	5.95201i	0.363963	+	0.243192i	0.724082	−	0.689714i	$-0.242264\pi$
$599$	8.90781	+	5.95201i	0.363963	+	0.243192i	−0.360119	+	0.932907i	$0.617264\pi$
$600$	7.51625	+	3.14629i	0.306850	+	0.128447i
$601$	−14.4685	−	21.6536i	−0.590182	−	0.883270i	0.409395	−	0.912357i	$-0.365740\pi$
$601$	−14.4685	−	21.6536i	−0.590182	−	0.883270i	−0.999577	+	0.0290872i	$0.990740\pi$
$602$	23.9460	−	9.88382i	0.975965	−	0.402835i
$603$	−16.7107	+	31.2636i	−0.680514	+	1.27315i
$604$	−21.6230	+	21.5156i	−0.879828	+	0.875456i
$605$	−5.12180	+	0.504454i	−0.208231	+	0.0205090i
$606$	−12.6035	−	41.7351i	−0.511981	−	1.69537i
$607$	−4.24052	+	4.24052i	−0.172117	+	0.172117i	−0.787909	−	0.615792i	$-0.788836\pi$
$607$	−4.24052	+	4.24052i	−0.172117	+	0.172117i	0.615792	+	0.787909i	$0.288836\pi$
$608$	0.107665	−	17.2895i	0.00436639	−	0.701181i
$609$	99.5693	+	99.5693i	4.03475	+	4.03475i
$610$	0.675543	−	1.26007i	0.0273519	−	0.0510189i
$611$	2.93138	+	29.7628i	0.118591	+	1.20408i
$612$	−70.9436	+	29.1790i	−2.86773	+	1.17949i
$613$	11.4404	+	6.11504i	0.462075	+	0.246984i	0.685971	−	0.727629i	$-0.259378\pi$
$613$	11.4404	+	6.11504i	0.462075	+	0.246984i	−0.223896	+	0.974613i	$0.571878\pi$
$614$	−7.41262	+	17.8328i	−0.299149	+	0.719673i
$615$	11.1702	−	7.46371i	0.450427	−	0.300966i
$616$	−17.6951	+	26.2695i	−0.712955	+	1.05843i
$617$	20.5337	−	30.7308i	0.826655	−	1.23718i	−0.142272	−	0.989828i	$-0.545441\pi$
$617$	20.5337	−	30.7308i	0.826655	−	1.23718i	0.968927	−	0.247349i	$-0.0795593\pi$
$618$	42.6769	+	8.54422i	1.71672	+	0.343699i
$619$	18.6712	−	15.3230i	0.750457	−	0.615884i	−0.179412	−	0.983774i	$-0.557420\pi$
$619$	18.6712	−	15.3230i	0.750457	−	0.615884i	0.929869	+	0.367890i	$0.119920\pi$
$620$	3.92834	+	3.24031i	0.157766	+	0.130134i
$621$	2.02768	−	1.08382i	0.0813681	−	0.0434922i
$622$	2.14035	+	22.0123i	0.0858202	+	0.882614i
$623$	−24.0240	−	57.9991i	−0.962503	−	2.32369i
$624$	−6.56271	−	33.8740i	−0.262719	−	1.35605i
$625$	0.382683	−	0.923880i	0.0153073	−	0.0369552i
$626$	−27.8860	−	8.49708i	−1.11455	−	0.339611i
$627$	−6.18388	+	20.3855i	−0.246960	+	0.814119i
$628$	3.60199	−	35.6608i	0.143735	−	1.42302i
$629$	43.9863	+	4.33228i	1.75385	+	0.172739i
$630$	34.0289	−	6.72471i	1.35574	−	0.267919i
$631$	−1.65635	−	8.32701i	−0.0659381	−	0.331493i	0.933710	−	0.358031i	$-0.116552\pi$
$631$	−1.65635	−	8.32701i	−0.0659381	−	0.331493i	−0.999648	+	0.0265378i	$0.991552\pi$
$632$	−27.6462	+	33.4316i	−1.09971	+	1.32984i
$633$	−30.9562	−	6.15757i	−1.23040	−	0.244741i
$634$	−23.3478	+	23.2897i	−0.927259	+	0.924952i
$635$	9.26792	−	2.81139i	0.367786	−	0.111567i
$636$	29.6154	+	44.5625i	1.17433	+	1.76702i
$637$	27.3981	−	33.3847i	1.08555	−	1.32275i
$638$	35.9541	+	3.58639i	1.42344	+	0.141986i
$639$	19.8781			0.786367
$640$	−4.42053	+	10.4144i	−0.174737	+	0.411664i
$641$	33.6217			1.32798			0.663989	−	0.747742i	$-0.268862\pi$
$641$	33.6217			1.32798			0.663989	+	0.747742i	$0.268862\pi$
$642$	−69.0098	−	6.88367i	−2.72360	−	0.271677i
$643$	−3.99066	+	4.86263i	−0.157376	+	0.191764i	−0.845729	−	0.533612i	$-0.820834\pi$
$643$	−3.99066	+	4.86263i	−0.157376	+	0.191764i	0.688353	+	0.725376i	$0.258334\pi$
$644$	−2.67626	+	1.77860i	−0.105460	+	0.0700865i
$645$	−10.9103	+	3.30959i	−0.429591	+	0.130315i
$646$	22.1499	−	22.0948i	0.871475	−	0.869307i
$647$	−42.7601	−	8.50551i	−1.68107	−	0.334386i	−0.740004	−	0.672602i	$-0.765176\pi$
$647$	−42.7601	−	8.50551i	−1.68107	−	0.334386i	−0.941068	+	0.338216i	$0.890176\pi$
$648$	−0.849096	−	8.96424i	−0.0333556	−	0.352149i
$649$	1.20216	+	6.04369i	0.0471891	+	0.237236i
$650$	−4.15420	+	0.820945i	−0.162941	+	0.0322001i
$651$	33.7870	+	3.32773i	1.32422	+	0.130424i
$652$	18.9475	+	1.91383i	0.742041	+	0.0749513i
$653$	8.43451	−	27.8048i	0.330068	−	1.08809i	−0.622209	−	0.782851i	$-0.713765\pi$
$653$	8.43451	−	27.8048i	0.330068	−	1.08809i	0.952277	−	0.305236i	$-0.0987354\pi$
$654$	25.4313	+	7.74910i	0.994442	+	0.303014i
$655$	1.61144	−	3.89036i	0.0629642	−	0.152009i
$656$	10.2859	+	15.5612i	0.401597	+	0.607563i
$657$	−5.60933	−	13.5421i	−0.218841	−	0.528328i
$658$	−6.32724	−	65.0723i	−0.246661	−	2.53678i
$659$	−16.0398	+	8.57348i	−0.624824	+	0.333975i	−0.753241	−	0.657745i	$-0.771510\pi$
$659$	−16.0398	+	8.57348i	−0.624824	+	0.333975i	0.128417	+	0.991720i	$0.459010\pi$
$660$	8.87002	−	10.7534i	0.345265	−	0.418576i
$661$	−33.0828	+	27.1504i	−1.28677	+	1.05603i	−0.291738	+	0.956498i	$0.594234\pi$
$661$	−33.0828	+	27.1504i	−1.28677	+	1.05603i	−0.995035	+	0.0995291i	$0.968266\pi$
$662$	−10.7988	−	2.16199i	−0.419706	−	0.0840282i
$663$	34.6867	−	51.9123i	1.34712	−	2.01611i
$664$	−6.11131	+	1.19190i	−0.237165	+	0.0462545i
$665$	−11.7627	+	7.85958i	−0.456138	+	0.304781i
$666$	−17.5656	+	42.2582i	−0.680653	+	1.63747i
$667$	3.23292	+	1.72803i	0.125179	+	0.0669096i
$668$	−11.2461	−	27.3429i	−0.435124	−	1.05793i
$669$	−1.05603	−	10.7221i	−0.0408285	−	0.414539i
$670$	−4.47008	+	8.33793i	−0.172694	+	0.322122i
$671$	−1.72954	−	1.72954i	−0.0667681	−	0.0667681i
$672$	14.2545	+	74.0696i	0.549878	+	2.85730i
$673$	−16.7505	+	16.7505i	−0.645686	+	0.645686i	−0.951947	−	0.306262i	$-0.900922\pi$
$673$	−16.7505	+	16.7505i	−0.645686	+	0.645686i	0.306262	+	0.951947i	$0.400922\pi$
$674$	11.0937	+	36.7356i	0.427312	+	1.41500i
$675$	−6.59155	+	0.649211i	−0.253709	+	0.0249881i
$676$	−5.69118	−	5.71960i	−0.218891	−	0.219985i
$677$	6.38018	−	11.9365i	0.245210	−	0.458756i	−0.728964	−	0.684552i	$-0.759998\pi$
$677$	6.38018	−	11.9365i	0.245210	−	0.458756i	0.974175	+	0.225795i	$0.0724980\pi$
$678$	20.3214	−	8.38777i	0.780439	−	0.322130i
$679$	32.1771	+	48.1564i	1.23484	+	1.84807i
$680$	−18.9428	+	7.76358i	−0.726424	+	0.297720i
$681$	−3.57468	−	2.38853i	−0.136982	−	0.0915285i
$682$	7.24954	−	4.83094i	0.277599	−	0.184986i
$683$	−22.7217	−	27.6865i	−0.869422	−	1.05939i	−0.997709	−	0.0676564i	$-0.978448\pi$
$683$	−22.7217	−	27.6865i	−0.869422	−	1.05939i	0.128287	−	0.991737i	$-0.459052\pi$
$684$	15.1988	+	28.6060i	0.581139	+	1.09378i
$685$	4.19305	+	7.84464i	0.160208	+	0.299728i
$686$	−30.8735	+	37.5240i	−1.17875	+	1.43267i
$687$	12.8752	−	5.33308i	0.491219	−	0.203470i
$688$	−4.51981	−	15.1715i	−0.172316	−	0.578408i
$689$	−25.6899	−	10.6411i	−0.978708	−	0.405394i
$690$	1.24806	−	0.665107i	0.0475130	−	0.0253202i
$691$	1.29140	+	0.391743i	0.0491273	+	0.0149026i	0.314753	−	0.949174i	$-0.398078\pi$
$691$	1.29140	+	0.391743i	0.0491273	+	0.0149026i	−0.265625	+	0.964076i	$0.585578\pi$
$692$	12.4532	+	41.4238i	0.473399	+	1.57470i
$693$	5.81645	−	59.0554i	0.220949	−	2.24333i
$694$	28.7718	+	19.2766i	1.09216	+	0.731729i
$695$	15.6689	−	3.11674i	0.594355	−	0.118225i
$696$	66.7194	−	54.3393i	2.52899	−	2.05973i
$697$	−6.58491	+	33.1046i	−0.249421	+	1.25393i
$698$	−0.0455774	+	36.5959i	−0.00172513	+	1.38517i
$699$	−5.55723	−	18.3197i	−0.210194	−	0.692916i
$700$	9.08370	−	1.78335i	0.343332	−	0.0674043i
$701$	0.922611	+	0.757167i	0.0348465	+	0.0285978i	0.651655	−	0.758515i	$-0.274075\pi$
$701$	0.922611	+	0.757167i	0.0348465	+	0.0285978i	−0.616809	+	0.787113i	$0.711575\pi$
$702$	17.7660	+	21.7029i	0.670533	+	0.819125i
$703$		−	18.6644i		−	0.703941i
$704$	14.8695	+	12.3902i	0.560415	+	0.466972i
$705$			28.7737i			1.08368i
$706$	7.65009	−	6.26234i	0.287915	−	0.235686i
$707$	−38.2871	−	31.4214i	−1.43993	−	1.18172i
$708$	12.1813	+	8.18321i	0.457799	+	0.307544i
$709$	−10.1731	−	33.5361i	−0.382058	−	1.25948i	−0.911560	−	0.411167i	$-0.865121\pi$
$709$	−10.1731	−	33.5361i	−0.382058	−	1.25948i	0.529502	−	0.848308i	$-0.322379\pi$
$710$	5.30498	+	0.00660696i	0.199093	+	0.000247955i
$711$	15.8564	−	79.7155i	0.594662	−	2.98957i
$712$	−36.7519	+	10.9988i	−1.37734	+	0.412197i
$713$	0.866850	−	0.172427i	0.0324638	−	0.00645745i
$714$	−75.9696	+	113.391i	−2.84309	+	4.24354i
$715$	−0.710065	+	7.20941i	−0.0265549	+	0.269617i
$716$	−2.35094	−	1.26414i	−0.0878587	−	0.0472432i
$717$	10.5442	+	3.19855i	0.393780	+	0.119452i
$718$	−16.2158	−	30.4288i	−0.605170	−	1.13559i
$719$	−12.1869	−	5.04797i	−0.454494	−	0.188258i	0.143679	−	0.989624i	$-0.454107\pi$
$719$	−12.1869	−	5.04797i	−0.454494	−	0.188258i	−0.598173	+	0.801367i	$0.704107\pi$
$720$	−1.97252	−	21.1046i	−0.0735114	−	0.786522i
$721$	45.6831	−	18.9225i	1.70133	−	0.704712i
$722$	10.5476	+	8.67817i	0.392540	+	0.322968i
$723$	1.50416	+	2.81408i	0.0559403	+	0.104657i
$724$	7.05618	−	23.0542i	0.262241	−	0.856804i
$725$	−6.69942	−	8.16326i	−0.248810	−	0.303176i
$726$	11.6273	+	17.4485i	0.431530	+	0.647575i
$727$	−33.7198	−	22.5308i	−1.25060	−	0.835622i	−0.259113	−	0.965847i	$-0.583430\pi$
$727$	−33.7198	−	22.5308i	−1.25060	−	0.835622i	−0.991484	+	0.130225i	$0.958430\pi$
$728$	−27.6145	−	27.8217i	−1.02346	−	1.03114i
$729$	−22.4300	−	33.5689i	−0.830741	−	1.24329i
$730$	−1.49249	−	3.61592i	−0.0552396	−	0.133831i
$731$	13.5032	−	25.2626i	0.499432	−	0.934372i
$732$	−5.82487	−	0.0145089i	−0.215293	−	0.000536264i
$733$	−24.9780	+	2.46012i	−0.922584	+	0.0908666i	−0.548143	−	0.836384i	$-0.684665\pi$
$733$	−24.9780	+	2.46012i	−0.922584	+	0.0908666i	−0.374441	+	0.927251i	$0.622165\pi$
$734$	19.3484	−	5.84298i	0.714164	−	0.215668i
$735$	29.3814	−	29.3814i	1.08375	−	1.08375i
$736$	0.914851	+	1.73750i	0.0337218	+	0.0640453i
$737$	11.4444	+	11.4444i	0.421559	+	0.421559i
$738$	−30.8007	−	16.5126i	−1.13379	−	0.607839i
$739$	2.99285	+	30.3869i	0.110094	+	1.11780i	0.878469	+	0.477800i	$0.158566\pi$
$739$	2.99285	+	30.3869i	0.110094	+	1.11780i	−0.768375	+	0.640000i	$0.778934\pi$
$740$	−4.70187	+	11.2718i	−0.172844	+	0.414361i
$741$	−23.2516	−	12.4282i	−0.854170	−	0.456563i
$742$	56.1315	+	23.3324i	2.06065	+	0.856559i
$743$	20.3091	−	13.5701i	0.745067	−	0.497838i	−0.124153	−	0.992263i	$-0.539621\pi$
$743$	20.3091	−	13.5701i	0.745067	−	0.497838i	0.869220	+	0.494425i	$0.164621\pi$
$744$	4.12344	−	20.3326i	0.151173	−	0.745430i
$745$	7.85717	−	11.7591i	0.287864	−	0.430819i
$746$	3.57339	−	17.8485i	0.130831	−	0.653479i
$747$	9.01752	−	7.40049i	0.329934	−	0.270770i
$748$	3.34600	+	34.8625i	0.122342	+	1.27470i
$749$	−69.4871	+	37.1416i	−2.53900	+	1.35713i
$750$	−4.05498	+	0.394282i	−0.148067	+	0.0143971i
$751$	−0.0990851	−	0.239212i	−0.00361567	−	0.00872899i	0.922061	−	0.387044i	$-0.126504\pi$
$751$	−0.0990851	−	0.239212i	−0.00361567	−	0.00872899i	−0.925677	+	0.378315i	$0.876504\pi$
$752$	−39.9516	−	0.199028i	−1.45688	−	0.00725781i
$753$	3.64821	−	8.80756i	0.132948	−	0.320965i
$754$	−13.0343	+	42.7765i	−0.474681	+	1.55783i
$755$	4.42737	−	14.5951i	0.161129	−	0.531170i
$756$	−38.7789	−	47.4930i	−1.41038	−	1.72730i
$757$	−18.4673	−	1.81887i	−0.671206	−	0.0661081i	−0.243328	−	0.969944i	$-0.578239\pi$
$757$	−18.4673	−	1.81887i	−0.671206	−	0.0661081i	−0.427879	+	0.903836i	$0.640739\pi$
$758$	1.34283	+	6.79510i	0.0487739	+	0.246809i
$759$	−0.472002	−	2.37291i	−0.0171326	−	0.0861313i
$760$	4.04667	+	7.63930i	0.146788	+	0.277107i
$761$	−14.4528	−	2.87483i	−0.523912	−	0.104213i	−0.0739530	−	0.997262i	$-0.523561\pi$
$761$	−14.4528	−	2.87483i	−0.523912	−	0.104213i	−0.449959	+	0.893049i	$0.648561\pi$
$762$	−27.8659	−	27.9354i	−1.00947	−	1.01199i
$763$	28.9032	−	8.76770i	1.04637	−	0.317412i
$764$	2.95979	−	14.6885i	0.107081	−	0.531413i
$765$	24.3321	−	29.6488i	0.879730	−	1.07195i
$766$	0.812790	−	8.14835i	0.0293673	−	0.294412i
$767$	−7.62632			−0.275370
$768$	45.9140	−	4.06067i	1.65678	−	0.146527i
$769$	16.4051			0.591583			0.295791	−	0.955253i	$-0.404417\pi$
$769$	16.4051			0.591583			0.295791	+	0.955253i	$0.404417\pi$
$770$	1.57190	−	15.7585i	0.0566472	−	0.567897i
$771$	24.1056	−	29.3727i	0.868142	−	1.05783i
$772$	−3.53503	+	17.5433i	−0.127228	+	0.631397i
$773$	15.3825	−	4.66622i	0.553269	−	0.167832i	−0.00125652	−	0.999999i	$-0.500400\pi$
$773$	15.3825	−	4.66622i	0.553269	−	0.167832i	0.554525	+	0.832167i	$0.312900\pi$
$774$	20.9458	+	20.9981i	0.752883	+	0.754760i
$775$	−2.49722	−	0.496729i	−0.0897029	−	0.0178430i
$776$	31.2752	−	16.5670i	1.12272	−	0.594721i
$777$	15.8853	+	79.8609i	0.569883	+	2.86500i
$778$	−4.19096	−	21.2074i	−0.150253	−	0.760322i
$779$	14.1846	+	1.39706i	0.508217	+	0.0500550i
$780$	10.9113	+	13.3632i	0.390686	+	0.478478i
$781$	2.63450	−	8.68478i	0.0942698	−	0.310766i
$782$	−1.03567	+	3.39889i	−0.0370354	+	0.121544i
$783$	−26.7671	+	64.6216i	−0.956579	+	2.30939i
$784$	40.5921	+	40.9985i	1.44972	+	1.46423i
$785$	6.85811	+	16.5569i	0.244777	+	0.590943i
$786$	−17.0751	+	1.66028i	−0.609048	+	0.0592202i
$787$	3.83275	−	2.04865i	0.136623	−	0.0730264i	−0.401669	−	0.915785i	$-0.631570\pi$
$787$	3.83275	−	2.04865i	0.136623	−	0.0730264i	0.538292	+	0.842758i	$0.319070\pi$
$788$	−2.24488	−	23.3898i	−0.0799705	−	0.833226i
$789$	18.5090	−	15.1900i	0.658938	−	0.540777i
$790$	4.25818	−	21.2688i	0.151499	−	0.756712i
$791$	13.8761	−	20.7670i	0.493377	−	0.738391i
$792$	−35.5389	−	7.20726i	−1.26282	−	0.256099i
$793$	2.51697	−	1.68179i	0.0893804	−	0.0597220i
$794$	17.8578	+	7.42300i	0.633748	+	0.263432i
$795$	−23.5941	−	12.6113i	−0.836795	−	0.447276i
$796$	−10.6761	+	25.5939i	−0.378404	+	0.907151i
$797$	5.13841	+	52.1712i	0.182012	+	1.84800i	0.460626	+	0.887595i	$0.347625\pi$
$797$	5.13841	+	52.1712i	0.182012	+	1.84800i	−0.278614	+	0.960403i	$0.589875\pi$
$798$	50.7963	+	27.2326i	1.79817	+	0.964024i
$799$	−51.1187	−	51.1187i	−1.80845	−	1.80845i
$800$	−0.519402	−	5.63296i	−0.0183636	−	0.199155i
$801$	50.8220	−	50.8220i	1.79571	−	1.79571i
$802$	42.3334	−	12.7841i	1.49484	−	0.451423i
$803$	−6.65999	+	0.655952i	−0.235026	+	0.0231480i
$804$	38.5433	+	0.0960056i	1.35932	+	0.00338585i
$805$	0.757388	−	1.41697i	0.0266944	−	0.0499417i
$806$	4.11359	+	9.96619i	0.144895	+	0.351044i
$807$	28.5985	+	42.8007i	1.00672	+	1.50666i
$808$	−21.4817	+	21.3217i	−0.755723	+	0.750096i
$809$	−8.08625	−	5.40306i	−0.284297	−	0.189961i	0.405242	−	0.914209i	$-0.367187\pi$
$809$	−8.08625	−	5.40306i	−0.284297	−	0.189961i	−0.689540	+	0.724248i	$0.742187\pi$
$810$	2.49662	+	3.74654i	0.0877221	+	0.131640i
$811$	6.58512	+	8.02399i	0.231235	+	0.281760i	0.875682	−	0.482889i	$-0.160412\pi$
$811$	6.58512	+	8.02399i	0.231235	+	0.281760i	−0.644447	+	0.764649i	$0.722912\pi$
$812$	28.6107	−	93.4779i	1.00404	−	3.28043i
$813$	10.3171	+	19.3020i	0.361837	+	0.676949i
$814$	16.1346	+	13.2750i	0.565519	+	0.465289i
$815$	−8.79713	+	3.64389i	−0.308150	+	0.127640i
$816$	64.2086	+	53.2321i	2.24775	+	1.86350i
$817$	−11.1754	−	4.62901i	−0.390979	−	0.161949i
$818$	16.6023	+	31.1540i	0.580487	+	1.08928i
$819$	70.2793	+	21.3190i	2.45576	+	0.744946i
$820$	−8.21445	−	4.41706i	−0.286861	−	0.154250i
$821$	5.23721	−	53.1742i	0.182780	−	1.85579i	−0.268332	−	0.963326i	$-0.586472\pi$
$821$	5.23721	−	53.1742i	0.182780	−	1.85579i	0.451112	−	0.892467i	$-0.351028\pi$
$822$	20.1708	−	30.1064i	0.703536	−	1.05008i
$823$	−29.6648	+	5.90070i	−1.03405	+	0.205685i	−0.682807	−	0.730599i	$-0.739241\pi$
$823$	−29.6648	+	5.90070i	−1.03405	+	0.205685i	−0.351243	+	0.936284i	$0.614241\pi$
$824$	−8.66320	−	28.9477i	−0.301797	−	1.00844i
$825$	−1.35974	+	6.83589i	−0.0473402	+	0.237995i
$826$	16.6718	+	0.0207635i	0.580087	+	0.000722455i
$827$	11.6294	+	38.3370i	0.404394	+	1.33311i	0.888812	+	0.458272i	$0.151531\pi$
$827$	11.6294	+	38.3370i	0.404394	+	1.33311i	−0.484418	+	0.874837i	$0.660969\pi$
$828$	−3.05383	−	2.05152i	−0.106128	−	0.0712953i
$829$	1.10916	+	0.910264i	0.0385227	+	0.0316148i	0.653458	−	0.756963i	$-0.273318\pi$
$829$	1.10916	+	0.910264i	0.0385227	+	0.0316148i	−0.614935	+	0.788578i	$0.710818\pi$
$830$	2.40902	−	1.97201i	0.0836181	−	0.0684495i
$831$			49.4392i			1.71503i
$832$	−18.6299	+	15.0576i	−0.645875	+	0.522028i
$833$			104.397i			3.61713i
$834$	−41.2282	−	50.3645i	−1.42762	−	1.74398i
$835$	11.4272	+	9.37803i	0.395453	+	0.324540i
$836$	14.5123	−	2.84913i	0.501920	−	0.0985391i
$837$	4.89544	+	16.1381i	0.169211	+	0.557814i
$838$	0.0411470	−	33.0385i	0.00142140	−	1.14130i
$839$	−7.30345	+	36.7169i	−0.252143	+	1.26761i	0.622415	+	0.782688i	$0.286152\pi$
$839$	−7.30345	+	36.7169i	−0.252143	+	1.26761i	−0.874558	+	0.484921i	$0.838848\pi$
$840$	−23.8167	−	29.2428i	−0.821753	−	1.00897i
$841$	−80.9354	+	16.0991i	−2.79088	+	0.555140i
$842$	14.9471	+	10.0143i	0.515111	+	0.345115i
$843$	5.10395	−	51.8212i	0.175789	−	1.78482i
$844$	6.30854	+	20.9845i	0.217149	+	0.722316i
$845$	3.86061	+	1.17110i	0.132809	+	0.0402872i
$846$	66.0570	−	35.2025i	2.27109	−	1.21029i
$847$	22.0080	+	9.11599i	0.756202	+	0.313229i
$848$	17.6736	−	32.6725i	0.606915	−	1.12198i
$849$	4.79793	−	1.98737i	0.164664	−	0.0682062i
$850$	6.50350	−	7.90445i	0.223068	−	0.271120i
$851$	0.999244	+	1.86945i	0.0342537	+	0.0640841i
$852$	−10.1408	−	19.0863i	−0.347419	−	0.653887i
$853$	−17.5642	−	21.4020i	−0.601387	−	0.732792i	0.379967	−	0.925000i	$-0.375935\pi$
$853$	−17.5642	−	21.4020i	−0.601387	−	0.732792i	−0.981354	+	0.192208i	$0.938435\pi$
$854$	−5.50691	+	3.66969i	−0.188443	+	0.125574i
$855$	−13.4669	−	8.99830i	−0.460558	−	0.307735i
$856$	18.2589	+	44.5511i	0.624078	+	1.52272i
$857$	−0.911405	−	1.36401i	−0.0311330	−	0.0465938i	0.815577	−	0.578649i	$-0.196420\pi$
$857$	−0.911405	−	1.36401i	−0.0311330	−	0.0465938i	−0.846710	+	0.532055i	$0.821420\pi$
$858$	27.2814	−	11.2605i	0.931372	−	0.384429i
$859$	−19.8990	+	37.2283i	−0.678944	+	1.27021i	0.272430	+	0.962176i	$0.412173\pi$
$859$	−19.8990	+	37.2283i	−0.678944	+	1.27021i	−0.951374	+	0.308039i	$0.900327\pi$
$860$	5.58295	+	5.61083i	0.190377	+	0.191328i
$861$	−61.8820	+	6.09485i	−2.10893	+	0.207712i
$862$	−2.23664	−	7.40642i	−0.0761803	−	0.252264i
$863$	10.3317	−	10.3317i	0.351696	−	0.351696i	−0.509044	−	0.860740i	$-0.670001\pi$
$863$	10.3317	−	10.3317i	0.351696	−	0.351696i	0.860740	+	0.509044i	$0.170001\pi$
$864$	−31.2824	+	20.6216i	−1.06425	+	0.701562i
$865$	−15.2930	−	15.2930i	−0.519978	−	0.519978i
$866$	−1.40839	+	2.62703i	−0.0478589	+	0.0892702i
$867$	9.99249	+	101.455i	0.339363	+	3.44561i
$868$	−8.96556	−	21.7982i	−0.304311	−	0.739879i
$869$	−32.7263	−	17.4926i	−1.11016	−	0.593395i
$870$	−16.5140	+	39.7284i	−0.559878	+	1.34692i
$871$	−16.6548	+	11.1284i	−0.564328	+	0.377072i
$872$	−3.53312	−	18.1157i	−0.119647	−	0.613475i
$873$	−36.8389	+	55.1334i	−1.24681	+	1.86598i
$874$	1.47124	+	0.294553i	0.0497654	+	0.00996339i
$875$	−3.57792	+	2.93632i	−0.120956	+	0.0992658i
$876$	−10.1411	+	12.2944i	−0.342636	+	0.415389i
$877$	6.72271	−	3.59336i	0.227010	−	0.121339i	−0.353971	−	0.935256i	$-0.615169\pi$
$877$	6.72271	−	3.59336i	0.227010	−	0.121339i	0.580981	+	0.813917i	$0.302669\pi$
$878$	−0.224035	−	2.30408i	−0.00756083	−	0.0777591i
$879$	10.9142	+	26.3492i	0.368126	+	0.888736i
$880$	−9.48206	−	1.93525i	−0.319640	−	0.0652374i
$881$	−16.6217	+	40.1284i	−0.560000	+	1.35196i	0.349766	+	0.936837i	$0.386261\pi$
$881$	−16.6217	+	40.1284i	−0.560000	+	1.35196i	−0.909766	+	0.415122i	$0.863739\pi$
$882$	−103.398	−	31.5061i	−3.48159	−	1.06087i
$883$	−2.28595	+	7.53577i	−0.0769284	+	0.253599i	−0.986967	−	0.160926i	$-0.948552\pi$
$883$	−2.28595	+	7.53577i	−0.0769284	+	0.253599i	0.910038	+	0.414524i	$0.136052\pi$
$884$	−43.1254	−	4.35596i	−1.45046	−	0.146507i
$885$	−7.30204	−	0.719188i	−0.245455	−	0.0241752i
$886$	−44.4167	+	8.77754i	−1.49221	+	0.294887i
$887$	−0.905721	−	4.55337i	−0.0304111	−	0.152887i	0.962596	−	0.270940i	$-0.0873346\pi$
$887$	−0.905721	−	4.55337i	−0.0304111	−	0.152887i	−0.993007	+	0.118053i	$0.962335\pi$
$888$	49.5360	−	4.69206i	1.66232	−	0.157455i
$889$	−43.9660	−	8.74537i	−1.47457	−	0.293310i
$890$	13.5800	−	13.5463i	0.455204	−	0.454072i
$891$	7.37051	−	2.23582i	0.246921	−	0.0749028i
$892$	−6.22953	+	4.14003i	−0.208580	+	0.138619i
$893$	−19.3666	+	23.5983i	−0.648078	+	0.789685i
$894$	−57.3335	−	5.71897i	−1.91752	−	0.191271i
$895$	1.33463			0.0446118
$896$	40.7676	−	32.8665i	1.36195	−	1.09799i
$897$	2.99430			0.0999766
$898$	−22.4107	−	2.23545i	−0.747855	−	0.0745978i
$899$	−17.0577	+	20.7849i	−0.568906	+	0.693214i
$900$	5.86613	+	8.82680i	0.195538	+	0.294227i
$901$	64.3215	−	19.5117i	2.14286	−	0.650030i
$902$	−11.2965	+	11.2684i	−0.376132	+	0.375196i
$903$	51.7570	+	10.2951i	1.72237	+	0.342600i
$904$	−11.7619	−	9.72650i	−0.391194	−	0.323498i
$905$	2.35180	+	11.8233i	0.0781766	+	0.393020i
$906$	−60.9586	+	12.0465i	−2.02521	+	0.400219i
$907$	−2.64147	−	0.260162i	−0.0877086	−	0.00863855i	0.0540676	−	0.998537i	$-0.482781\pi$
$907$	−2.64147	−	0.260162i	−0.0877086	−	0.00863855i	−0.141776	+	0.989899i	$0.545281\pi$
$908$	−0.299952	+	2.96961i	−0.00995425	+	0.0985501i
$909$	16.4608	−	54.2641i	0.545971	−	1.79983i
$910$	18.7487	+	5.71287i	0.621514	+	0.189380i
$911$	−10.9979	+	26.5512i	−0.364375	+	0.879680i	0.630274	+	0.776373i	$0.282942\pi$
$911$	−10.9979	+	26.5512i	−0.364375	+	0.879680i	−0.994650	+	0.103307i	$0.967058\pi$
$912$	19.7129	−	29.1867i	0.652761	−	0.966468i
$913$	−2.03817	−	4.92058i	−0.0674535	−	0.162847i
$914$	0.372592	+	3.83191i	0.0123242	+	0.126748i
$915$	2.56855	−	1.37292i	0.0849135	−	0.0453872i
$916$	−7.46358	−	6.15637i	−0.246604	−	0.203412i
$917$	−15.0662	+	12.3645i	−0.497531	+	0.408313i
$918$	−66.4784	−	13.3095i	−2.19411	−	0.439278i
$919$	29.1086	−	43.5641i	0.960203	−	1.43705i	0.0616916	−	0.998095i	$-0.480350\pi$
$919$	29.1086	−	43.5641i	0.960203	−	1.43705i	0.898511	−	0.438950i	$-0.144650\pi$
$920$	−0.814309	−	0.548516i	−0.0268470	−	0.0180840i
$921$	−32.7097	+	21.8559i	−1.07782	+	0.720177i
$922$	10.8179	−	26.0251i	0.356270	−	0.857090i
$923$	9.90582	+	5.29477i	0.326054	+	0.174280i
$924$	−59.6703	+	24.5423i	−1.96301	+	0.807382i
$925$	−0.598550	−	6.07718i	−0.0196802	−	0.199817i
$926$	18.8019	−	35.0708i	0.617870	−	1.15250i
$927$	40.0300	+	40.0300i	1.31476	+	1.31476i
$928$	−55.0476	−	23.2041i	−1.80703	−	0.761713i
$929$	−33.8139	+	33.8139i	−1.10940	+	1.10940i	−0.116167	+	0.993230i	$0.537061\pi$
$929$	−33.8139	+	33.8139i	−1.10940	+	1.10940i	−0.993230	+	0.116167i	$0.962939\pi$
$930$	2.99883	+	9.93034i	0.0983356	+	0.325629i
$931$	43.8722	−	4.32103i	1.43785	−	0.141616i
$932$	−9.42132	+	9.37450i	−0.308605	+	0.307072i
$933$	−21.2372	+	39.7321i	−0.695276	+	1.30077i
$934$	12.8488	−	5.30339i	0.420424	−	0.173532i
$935$	−9.72880	−	14.5602i	−0.318166	−	0.476169i
$936$	17.3292	−	41.3983i	0.566423	−	1.35314i
$937$	18.4239	+	12.3105i	0.601884	+	0.402166i	0.818845	−	0.574014i	$-0.194615\pi$
$937$	18.4239	+	12.3105i	0.601884	+	0.402166i	−0.216962	+	0.976180i	$0.569615\pi$
$938$	36.4393	−	24.2824i	1.18979	−	0.792848i
$939$	−37.6727	−	45.9043i	−1.22940	−	1.49803i
$940$	17.6407	−	9.37272i	0.575376	−	0.305705i
$941$	−18.8928	−	35.3460i	−0.615889	−	1.15225i	−0.975677	−	0.219213i	$-0.929651\pi$
$941$	−18.8928	−	35.3460i	−0.615889	−	1.15225i	0.359789	−	0.933034i	$-0.382849\pi$
$942$	46.3888	−	56.3816i	1.51143	−	1.83701i
$943$	−1.49555	+	0.619477i	−0.0487018	+	0.0201729i
$944$	1.04908	−	10.1337i	0.0341447	−	0.329824i
$945$	28.3233	+	11.7319i	0.921358	+	0.381639i
$946$	11.9501	−	6.36834i	0.388531	−	0.207053i
$947$	−34.8399	−	10.5686i	−1.13214	−	0.343432i	−0.332023	−	0.943271i	$-0.607731\pi$
$947$	−34.8399	−	10.5686i	−1.13214	−	0.343432i	−0.800120	+	0.599839i	$0.795231\pi$
$948$	−84.6294	+	25.4420i	−2.74863	+	0.826318i
$949$	0.811818	−	8.24253i	0.0263527	−	0.267564i
$950$	−3.59099	−	2.40590i	−0.116507	−	0.0780577i
$951$	−65.8864	+	13.1056i	−2.13651	+	0.424979i
$952$	94.2641	+	9.63995i	3.05512	+	0.312433i
$953$	2.40441	−	12.0878i	0.0778864	−	0.391561i	−0.922103	−	0.386945i	$-0.873530\pi$
$953$	2.40441	−	12.0878i	0.0778864	−	0.391561i	0.999989	−	0.00461664i	$-0.00146953\pi$
$954$	−0.0866750	+	69.5948i	−0.00280621	+	2.25321i
$955$	2.17478	+	7.16929i	0.0703743	+	0.231993i
$956$	−1.47368	−	7.50636i	−0.0476623	−	0.242773i
$957$	56.8964	+	46.6937i	1.83920	+	1.50939i
$958$	16.9087	+	20.6557i	0.546294	+	0.667354i
$959$		−	41.1707i		−	1.32947i
$960$	−19.2577	+	12.6605i	−0.621539	+	0.408614i
$961$		−	24.5171i		−	0.790875i
$962$	−20.0094	+	16.3796i	−0.645128	+	0.528100i
$963$	−69.7301	−	57.2260i	−2.24702	−	1.84408i
$964$	1.23530	−	1.83883i	0.0397865	−	0.0592248i
$965$	−2.59745	−	8.56266i	−0.0836150	−	0.275642i
$966$	−6.54580	−	0.00815230i	−0.210608	−	0.000262296i
$967$	−3.60785	+	18.1379i	−0.116020	+	0.583274i	0.878412	+	0.477903i	$0.158603\pi$
$967$	−3.60785	+	18.1379i	−0.116020	+	0.583274i	−0.994433	+	0.105371i	$0.966397\pi$
$968$	6.90992	−	12.8122i	0.222093	−	0.411799i
$969$	62.5060	−	12.4332i	2.00798	−	0.399412i
$970$	−9.84974	+	14.7015i	−0.316256	+	0.472037i
$971$	1.54624	−	15.6992i	0.0496212	−	0.503812i	−0.937965	−	0.346731i	$-0.887292\pi$
$971$	1.54624	−	15.6992i	0.0496212	−	0.503812i	0.987586	−	0.157081i	$-0.0502084\pi$
$972$	−10.1341	+	18.8464i	−0.325050	+	0.604499i
$973$	−70.7610	−	21.4651i	−2.26849	−	0.688140i
$974$	28.2158	+	52.9465i	0.904092	+	1.69652i
$975$	−7.96936	−	3.30102i	−0.255224	−	0.105717i
$976$	1.88849	+	3.57586i	0.0604492	+	0.114460i
$977$	−13.4544	+	5.57300i	−0.430445	+	0.178296i	−0.587377	−	0.809313i	$-0.699839\pi$
$977$	−13.4544	+	5.57300i	−0.430445	+	0.178296i	0.156932	+	0.987609i	$0.449839\pi$
$978$	29.9570	+	24.6476i	0.957919	+	0.788143i
$979$	−15.4686	−	28.9398i	−0.494380	−	0.924920i
$980$	−27.5839	−	8.44257i	−0.881135	−	0.269688i
$981$	21.9372	+	26.7305i	0.700400	+	0.853440i
$982$	−28.9155	−	43.3920i	−0.922730	−	1.38469i
$983$	5.71351	+	3.81765i	0.182233	+	0.121764i	0.643341	−	0.765580i	$-0.277548\pi$
$983$	5.71351	+	3.81765i	0.182233	+	0.121764i	−0.461108	+	0.887344i	$0.652548\pi$
$984$	−0.141970	+	37.9977i	−0.00452585	+	1.21132i
$985$	6.52718	+	9.76862i	0.207973	+	0.311254i
$986$	−41.2421	−	99.9190i	−1.31342	−	3.18207i
$987$	62.7809	−	117.455i	1.99834	−	3.73863i
$988$	−0.0455914	+	18.3035i	−0.00145046	+	0.582313i
$989$	1.36717	−	0.134655i	0.0434736	−	0.00428177i
$990$	17.3570	−	5.24159i	0.551641	−	0.166589i
$991$	32.0009	−	32.0009i	1.01654	−	1.01654i	0.0166804	−	0.999861i	$-0.494690\pi$
$991$	32.0009	−	32.0009i	1.01654	−	1.01654i	0.999861	−	0.0166804i	$-0.00530978\pi$
$992$	−13.8088	+	4.09512i	−0.438429	+	0.130020i
$993$	−15.8633	−	15.8633i	−0.503408	−	0.503408i
$994$	−21.6406	−	11.6018i	−0.686399	−	0.367988i
$995$	−1.35907	−	13.7989i	−0.0430855	−	0.437454i
$996$	−11.7060	−	4.88298i	−0.370919	−	0.154723i
$997$	42.6819	+	22.8140i	1.35175	+	0.722526i	0.978702	−	0.205286i	$-0.0658125\pi$
$997$	42.6819	+	22.8140i	1.35175	+	0.722526i	0.373049	+	0.927812i	$0.378312\pi$
$998$	−34.8326	−	14.4790i	−1.10261	−	0.458325i
$999$	−33.6301	+	22.4709i	−1.06401	+	0.710949i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	640.2.bm.a.341.36	✓	1024
128.125	even	32	inner	640.2.bm.a.381.36	yes	1024

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
640.2.bm.a.341.36	✓	1024	1.1	even	1	trivial
640.2.bm.a.381.36	yes	1024	128.125	even	32	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:	\( N \)	\(=\)	\( 640 = 2^{7} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	640.bm (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.140370 - 1.40723i) q^{2} +(1.82758 - 2.22691i) q^{3} +(-1.96059 - 0.395065i) q^{4} +(0.956940 - 0.290285i) q^{5} +(-2.87723 - 2.88441i) q^{6} +(-4.53962 - 0.902986i) q^{7} +(-0.831156 + 2.70355i) q^{8} +(-1.03381 - 5.19733i) q^{9} +O(q^{10})\)	\(q+(0.140370 - 1.40723i) q^{2} +(1.82758 - 2.22691i) q^{3} +(-1.96059 - 0.395065i) q^{4} +(0.956940 - 0.290285i) q^{5} +(-2.87723 - 2.88441i) q^{6} +(-4.53962 - 0.902986i) q^{7} +(-0.831156 + 2.70355i) q^{8} +(-1.03381 - 5.19733i) q^{9} +(-0.274172 - 1.38738i) q^{10} +(-2.40773 - 0.237141i) q^{11} +(-4.46290 + 3.64405i) q^{12} +(0.869191 - 2.86534i) q^{13} +(-1.90793 + 6.26153i) q^{14} +(1.10244 - 2.66153i) q^{15} +(3.68785 + 1.54912i) q^{16} +(2.76984 + 6.68699i) q^{17} +(-7.45895 + 0.725264i) q^{18} +(2.69554 - 1.44079i) q^{19} +(-1.99085 + 0.191076i) q^{20} +(-10.3074 + 8.45903i) q^{21} +(-0.671685 + 3.35495i) q^{22} +(-0.192853 + 0.288624i) q^{23} +(4.50155 + 6.79185i) q^{24} +(0.831470 - 0.555570i) q^{25} +(-3.91018 - 1.62536i) q^{26} +(-5.84135 - 3.12227i) q^{27} +(8.54360 + 3.56383i) q^{28} +(-1.03510 - 10.5095i) q^{29} +(-3.59064 - 1.92499i) q^{30} +(-1.80040 - 1.80040i) q^{31} +(2.69764 - 4.97220i) q^{32} +(-4.92840 + 4.92840i) q^{33} +(9.79894 - 2.95915i) q^{34} +(-4.60626 + 0.453677i) q^{35} +(-0.0263987 + 10.5983i) q^{36} +(2.87863 - 5.38553i) q^{37} +(-1.64916 - 3.99548i) q^{38} +(-4.79233 - 7.17223i) q^{39} +(-0.0105677 + 2.82841i) q^{40} +(3.87744 + 2.59082i) q^{41} +(10.4570 + 15.6922i) q^{42} +(-2.51068 - 3.05928i) q^{43} +(4.62690 + 1.41615i) q^{44} +(-2.49800 - 4.67343i) q^{45} +(0.379090 + 0.311902i) q^{46} +(-9.22772 + 3.82225i) q^{47} +(10.1896 - 5.38135i) q^{48} +(13.3256 + 5.51963i) q^{49} +(-0.665102 - 1.24805i) q^{50} +(19.9534 + 6.05280i) q^{51} +(-2.83613 + 5.27438i) q^{52} +(0.910244 - 9.24187i) q^{53} +(-5.21370 + 7.78186i) q^{54} +(-2.37290 + 0.471998i) q^{55} +(6.21440 - 11.5226i) q^{56} +(1.71778 - 8.63587i) q^{57} +(-14.9346 - 0.0185999i) q^{58} +(-0.739346 - 2.43730i) q^{59} +(-3.21292 + 4.78265i) q^{60} +(0.781495 + 0.641357i) q^{61} +(-2.78630 + 2.28085i) q^{62} +24.5274i q^{63} +(-6.61836 - 4.49414i) q^{64} -2.99427i q^{65} +(6.24360 + 7.62720i) q^{66} +(-5.17116 - 4.24386i) q^{67} +(-2.78873 - 14.2047i) q^{68} +(0.290287 + 0.956948i) q^{69} +(-0.00815224 + 6.54576i) q^{70} +(-0.731822 + 3.67912i) q^{71} +(14.9105 + 1.52483i) q^{72} +(2.71293 - 0.539636i) q^{73} +(-7.17461 - 4.80685i) q^{74} +(0.282370 - 2.86695i) q^{75} +(-5.85406 + 1.75990i) q^{76} +(10.7160 + 3.25068i) q^{77} +(-10.7657 + 5.73715i) q^{78} +(14.1703 + 5.86952i) q^{79} +(3.97874 + 0.411894i) q^{80} +(-2.94119 + 1.21828i) q^{81} +(4.19016 - 5.09278i) q^{82} +(1.03773 + 1.94145i) q^{83} +(23.5504 - 12.5126i) q^{84} +(4.59171 + 5.59501i) q^{85} +(-4.65753 + 3.10368i) q^{86} +(-25.2954 - 16.9018i) q^{87} +(2.64232 - 6.31232i) q^{88} +(7.53529 + 11.2774i) q^{89} +(-6.92724 + 2.85925i) q^{90} +(-6.53316 + 12.2227i) q^{91} +(0.492131 - 0.489685i) q^{92} +(-7.29968 + 0.718956i) q^{93} +(4.08349 + 13.5221i) q^{94} +(2.16123 - 2.16123i) q^{95} +(-6.14249 - 15.0945i) q^{96} +(-8.84804 - 8.84804i) q^{97} +(9.63790 - 17.9774i) q^{98} +(1.25665 + 12.7589i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1024 q+O(q^{10}) \) 1024 * q	\( 1024 q - 192 q^{52} - 128 q^{54} - 32 q^{56} - 288 q^{58} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 288 q^{72} - 32 q^{74} - 128 q^{76} - 192 q^{78}+O(q^{100}) \) 1024 * q - 192 * q^52 - 128 * q^54 - 32 * q^56 - 288 * q^58 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 288 * q^72 - 32 * q^74 - 128 * q^76 - 192 * q^78

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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