LMFDB - Embedded newform 345.2.m.d.256.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [345,2,Mod(16,345)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(345, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([0, 0, 8])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("345.16"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 345 = 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	345.m (of order $11$, degree $10$, minimal)

Newform invariants

comment:select newform

sage:traces = [50,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.75483886973$
Analytic rank:	$0$
Dimension:	$50$
Relative dimension:	$5$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			256.1
Character	$\chi$	$=$	345.256
Dual form			345.2.m.d.31.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.362097 - 2.51844i) q^{2} +(-0.415415 + 0.909632i) q^{3} +(-4.29243 + 1.26037i) q^{4} +(-0.654861 + 0.755750i) q^{5} +(2.44127 + 0.716822i) q^{6} +(0.729201 - 0.468629i) q^{7} +(2.61454 + 5.72503i) q^{8} +(-0.654861 - 0.755750i) q^{9} +(2.14043 + 1.37557i) q^{10} +(-0.900123 + 6.26050i) q^{11} +(0.636666 - 4.42811i) q^{12} +(4.49523 + 2.88891i) q^{13} +(-1.44426 - 1.66676i) q^{14} +(-0.415415 - 0.909632i) q^{15} +(5.94449 - 3.82029i) q^{16} +(-3.82972 - 1.12451i) q^{17} +(-1.66619 + 1.92288i) q^{18} +(3.49481 - 1.02617i) q^{19} +(1.85842 - 4.06937i) q^{20} +(0.123359 + 0.857980i) q^{21} +16.0926 q^{22} +(4.67659 + 1.06279i) q^{23} -6.29379 q^{24} +(-0.142315 - 0.989821i) q^{25} +(5.64783 - 12.3670i) q^{26} +(0.959493 - 0.281733i) q^{27} +(-2.53940 + 2.93062i) q^{28} +(-2.53865 - 0.745415i) q^{29} +(-2.14043 + 1.37557i) q^{30} +(-1.14181 - 2.50021i) q^{31} +(-3.53053 - 4.07445i) q^{32} +(-5.32082 - 3.41949i) q^{33} +(-1.44527 + 10.0521i) q^{34} +(-0.123359 + 0.857980i) q^{35} +(3.76347 + 2.41864i) q^{36} +(5.37825 + 6.20683i) q^{37} +(-3.84980 - 8.42989i) q^{38} +(-4.49523 + 2.88891i) q^{39} +(-6.03885 - 1.77317i) q^{40} +(-5.97927 + 6.90044i) q^{41} +(2.11610 - 0.621344i) q^{42} +(-2.96374 + 6.48968i) q^{43} +(-4.02683 - 28.0072i) q^{44} +1.00000 q^{45} +(0.983200 - 12.1625i) q^{46} +3.77059 q^{47} +(1.00563 + 6.99430i) q^{48} +(-2.59578 + 5.68397i) q^{49} +(-2.44127 + 0.716822i) q^{50} +(2.61381 - 3.01650i) q^{51} +(-22.9366 - 6.73478i) q^{52} +(-4.27165 + 2.74523i) q^{53} +(-1.05696 - 2.31441i) q^{54} +(-4.14191 - 4.78002i) q^{55} +(4.58944 + 2.94945i) q^{56} +(-0.518360 + 3.60528i) q^{57} +(-0.958045 + 6.66335i) q^{58} +(2.34653 + 1.50802i) q^{59} +(2.92962 + 3.38096i) q^{60} +(-4.29925 - 9.41405i) q^{61} +(-5.88319 + 3.78089i) q^{62} +(-0.831691 - 0.244207i) q^{63} +(0.271925 - 0.313818i) q^{64} +(-5.12704 + 1.50543i) q^{65} +(-6.68511 + 14.6383i) q^{66} +(1.19747 + 8.32861i) q^{67} +17.8561 q^{68} +(-2.90947 + 3.81247i) q^{69} +2.20544 q^{70} +(-1.27548 - 8.87116i) q^{71} +(2.61454 - 5.72503i) q^{72} +(12.4360 - 3.65155i) q^{73} +(13.6841 - 15.7923i) q^{74} +(0.959493 + 0.281733i) q^{75} +(-13.7079 + 8.80952i) q^{76} +(2.27748 + 4.98698i) q^{77} +(8.90324 + 10.2749i) q^{78} +(-3.34034 - 2.14671i) q^{79} +(-1.00563 + 6.99430i) q^{80} +(-0.142315 + 0.989821i) q^{81} +(19.5434 + 12.5598i) q^{82} +(3.51995 + 4.06224i) q^{83} +(-1.61088 - 3.52734i) q^{84} +(3.35778 - 2.15791i) q^{85} +(17.4170 + 5.11410i) q^{86} +(1.73265 - 1.99958i) q^{87} +(-38.1950 + 11.2150i) q^{88} +(-1.36356 + 2.98579i) q^{89} +(-0.362097 - 2.51844i) q^{90} +4.63175 q^{91} +(-21.4135 + 1.33227i) q^{92} +2.74860 q^{93} +(-1.36532 - 9.49599i) q^{94} +(-1.51309 + 3.31320i) q^{95} +(5.17289 - 1.51890i) q^{96} +(-6.54427 + 7.55249i) q^{97} +(15.2547 + 4.47917i) q^{98} +(5.32082 - 3.41949i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q + 2 q^{2} + 5 q^{3} - 4 q^{4} - 5 q^{5} + 9 q^{6} + 3 q^{7} + 6 q^{8} - 5 q^{9} + 2 q^{10} + 19 q^{11} + 4 q^{12} + 15 q^{13} + 43 q^{14} + 5 q^{15} - 76 q^{16} - 23 q^{17} + 2 q^{18} - 7 q^{19} - 4 q^{20}+ \cdots + 8 q^{99}+O(q^{100}) $ 50 * q + 2 * q^2 + 5 * q^3 - 4 * q^4 - 5 * q^5 + 9 * q^6 + 3 * q^7 + 6 * q^8 - 5 * q^9 + 2 * q^10 + 19 * q^11 + 4 * q^12 + 15 * q^13 + 43 * q^14 + 5 * q^15 - 76 * q^16 - 23 * q^17 + 2 * q^18 - 7 * q^19 - 4 * q^20 + 8 * q^21 - 42 * q^22 - 12 * q^23 - 6 * q^24 - 5 * q^25 - 2 * q^26 + 5 * q^27 + 6 * q^28 + 2 * q^29 - 2 * q^30 - 30 * q^31 - 43 * q^32 - 8 * q^33 + 102 * q^34 - 8 * q^35 - 15 * q^36 + 39 * q^37 + 19 * q^38 - 15 * q^39 - 16 * q^40 - 16 * q^41 + 23 * q^42 + 5 * q^43 + 37 * q^44 + 50 * q^45 - 40 * q^46 + 22 * q^47 - 78 * q^48 + 8 * q^49 - 9 * q^50 - 21 * q^51 + 15 * q^52 - 10 * q^53 - 2 * q^54 - 14 * q^55 - 14 * q^56 + 18 * q^57 - 26 * q^58 + 60 * q^59 + 4 * q^60 - 23 * q^61 - 36 * q^62 + 14 * q^63 - 104 * q^64 + 4 * q^65 + 20 * q^66 + 90 * q^67 - 46 * q^68 - 21 * q^69 + 10 * q^70 - 25 * q^71 + 6 * q^72 + 89 * q^73 - 31 * q^74 + 5 * q^75 - 46 * q^76 + 10 * q^77 - 9 * q^78 - 121 * q^79 + 78 * q^80 - 5 * q^81 + 10 * q^82 - 37 * q^83 - 6 * q^84 - 12 * q^85 + 172 * q^86 - 13 * q^87 - 66 * q^88 - 22 * q^89 + 2 * q^90 + 56 * q^91 - 233 * q^92 - 36 * q^93 - 5 * q^94 - 7 * q^95 + 10 * q^96 - 30 * q^97 + 8 * q^98 + 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/345\mathbb{Z}\right)^\times$.

$n$	$116$	$166$	$277$
$\chi(n)$	$1$	$e\left(\frac{8}{11}\right)$	$1$

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 $

$2$	−0.362097	−	2.51844i	−0.256041	−	1.78081i	−0.560374	−	0.828239i	$-0.689343\pi$
$2$	−0.362097	−	2.51844i	−0.256041	−	1.78081i	0.304333	−	0.952566i	$-0.401566\pi$
$3$	−0.415415	+	0.909632i	−0.239840	+	0.525176i
$3$	−0.415415	+	0.909632i	−0.239840	+	0.525176i
$4$	−4.29243	+	1.26037i	−2.14622	+	0.630186i
$5$	−0.654861	+	0.755750i	−0.292863	+	0.337981i
$5$	−0.654861	+	0.755750i	−0.292863	+	0.337981i
$6$	2.44127	+	0.716822i	0.996645	+	0.292642i
$7$	0.729201	−	0.468629i	0.275612	−	0.177125i	−0.395532	−	0.918452i	$-0.629440\pi$
$7$	0.729201	−	0.468629i	0.275612	−	0.177125i	0.671144	+	0.741327i	$0.265803\pi$
$8$	2.61454	+	5.72503i	0.924378	+	2.02410i
$9$	−0.654861	−	0.755750i	−0.218287	−	0.251917i
$10$	2.14043	+	1.37557i	0.676864	+	0.434994i
$11$	−0.900123	+	6.26050i	−0.271397	+	1.88761i	0.162593	+	0.986693i	$0.448014\pi$
$11$	−0.900123	+	6.26050i	−0.271397	+	1.88761i	−0.433991	+	0.900917i	$0.642895\pi$
$12$	0.636666	−	4.42811i	0.183790	−	1.27829i
$13$	4.49523	+	2.88891i	1.24675	+	0.801238i	0.986414	−	0.164279i	$-0.0525298\pi$
$13$	4.49523	+	2.88891i	1.24675	+	0.801238i	0.260337	+	0.965518i	$0.416166\pi$
$14$	−1.44426	−	1.66676i	−0.385993	−	0.445460i
$15$	−0.415415	−	0.909632i	−0.107260	−	0.234866i
$16$	5.94449	−	3.82029i	1.48612	−	0.955072i
$17$	−3.82972	−	1.12451i	−0.928843	−	0.272733i	−0.217891	−	0.975973i	$-0.569918\pi$
$17$	−3.82972	−	1.12451i	−0.928843	−	0.272733i	−0.710952	+	0.703240i	$0.751736\pi$
$18$	−1.66619	+	1.92288i	−0.392724	+	0.453227i
$19$	3.49481	−	1.02617i	0.801764	−	0.235419i	0.144918	−	0.989444i	$-0.453708\pi$
$19$	3.49481	−	1.02617i	0.801764	−	0.235419i	0.656846	+	0.754025i	$0.271890\pi$
$20$	1.85842	−	4.06937i	0.415555	−	0.909939i
$21$	0.123359	+	0.857980i	0.0269191	+	0.187227i
$22$	16.0926			3.43096
$23$	4.67659	+	1.06279i	0.975136	+	0.221608i
$23$	4.67659	+	1.06279i	0.975136	+	0.221608i
$24$	−6.29379			−1.28471
$25$	−0.142315	−	0.989821i	−0.0284630	−	0.197964i
$26$	5.64783	−	12.3670i	1.10763	−	2.42537i
$27$	0.959493	−	0.281733i	0.184655	−	0.0542195i
$28$	−2.53940	+	2.93062i	−0.479901	+	0.553836i
$29$	−2.53865	−	0.745415i	−0.471416	−	0.138420i	0.0373915	−	0.999301i	$-0.488095\pi$
$29$	−2.53865	−	0.745415i	−0.471416	−	0.138420i	−0.508807	+	0.860881i	$0.669913\pi$
$30$	−2.14043	+	1.37557i	−0.390788	+	0.251144i
$31$	−1.14181	−	2.50021i	−0.205075	−	0.449051i	0.778949	−	0.627087i	$-0.215753\pi$
$31$	−1.14181	−	2.50021i	−0.205075	−	0.449051i	−0.984024	+	0.178036i	$0.943026\pi$
$32$	−3.53053	−	4.07445i	−0.624116	−	0.720268i
$33$	−5.32082	−	3.41949i	−0.926236	−	0.595256i
$34$	−1.44527	+	10.0521i	−0.247862	+	1.72392i
$35$	−0.123359	+	0.857980i	−0.0208515	+	0.145025i
$36$	3.76347	+	2.41864i	0.627245	+	0.403106i
$37$	5.37825	+	6.20683i	0.884179	+	1.02040i	0.999633	+	0.0270842i	$0.00862223\pi$
$37$	5.37825	+	6.20683i	0.884179	+	1.02040i	−0.115454	+	0.993313i	$0.536832\pi$
$38$	−3.84980	−	8.42989i	−0.624520	−	1.36751i
$39$	−4.49523	+	2.88891i	−0.719812	+	0.462595i
$40$	−6.03885	−	1.77317i	−0.954826	−	0.280362i
$41$	−5.97927	+	6.90044i	−0.933804	+	1.07767i	0.0630180	+	0.998012i	$0.479927\pi$
$41$	−5.97927	+	6.90044i	−0.933804	+	1.07767i	−0.996822	+	0.0796554i	$0.974618\pi$
$42$	2.11610	−	0.621344i	0.326522	−	0.0958754i
$43$	−2.96374	+	6.48968i	−0.451966	+	0.989667i	0.537280	+	0.843404i	$0.319452\pi$
$43$	−2.96374	+	6.48968i	−0.451966	+	0.989667i	−0.989246	+	0.146263i	$0.953275\pi$
$44$	−4.02683	−	28.0072i	−0.607068	−	4.22225i
$45$	1.00000			0.149071
$46$	0.983200	−	12.1625i	0.144965	−	1.79327i
$47$	3.77059			0.549997			0.274998	−	0.961445i	$-0.411323\pi$
$47$	3.77059			0.549997			0.274998	+	0.961445i	$0.411323\pi$
$48$	1.00563	+	6.99430i	0.145150	+	1.00954i
$49$	−2.59578	+	5.68397i	−0.370826	+	0.811996i
$50$	−2.44127	+	0.716822i	−0.345248	+	0.101374i
$51$	2.61381	−	3.01650i	0.366007	−	0.422394i
$52$	−22.9366	−	6.73478i	−3.18073	−	0.933946i
$53$	−4.27165	+	2.74523i	−0.586757	+	0.377086i	−0.800078	−	0.599896i	$-0.795208\pi$
$53$	−4.27165	+	2.74523i	−0.586757	+	0.377086i	0.213321	+	0.976982i	$0.431572\pi$
$54$	−1.05696	−	2.31441i	−0.143833	−	0.314951i
$55$	−4.14191	−	4.78002i	−0.558495	−	0.644538i
$56$	4.58944	+	2.94945i	0.613290	+	0.394137i
$57$	−0.518360	+	3.60528i	−0.0686585	+	0.477530i
$58$	−0.958045	+	6.66335i	−0.125797	+	0.874940i
$59$	2.34653	+	1.50802i	0.305492	+	0.196328i	0.684400	−	0.729106i	$-0.260064\pi$
$59$	2.34653	+	1.50802i	0.305492	+	0.196328i	−0.378908	+	0.925434i	$0.623700\pi$
$60$	2.92962	+	3.38096i	0.378212	+	0.436480i
$61$	−4.29925	−	9.41405i	−0.550463	−	1.20535i	−0.956565	−	0.291518i	$-0.905840\pi$
$61$	−4.29925	−	9.41405i	−0.550463	−	1.20535i	0.406102	−	0.913828i	$-0.366888\pi$
$62$	−5.88319	+	3.78089i	−0.747165	+	0.480174i
$63$	−0.831691	−	0.244207i	−0.104783	−	0.0307671i
$64$	0.271925	−	0.313818i	0.0339906	−	0.0392273i
$65$	−5.12704	+	1.50543i	−0.635931	+	0.186726i
$66$	−6.68511	+	14.6383i	−0.822880	+	1.80186i
$67$	1.19747	+	8.32861i	0.146295	+	1.01750i	0.922217	+	0.386673i	$0.126376\pi$
$67$	1.19747	+	8.32861i	0.146295	+	1.01750i	−0.775922	+	0.630829i	$0.782715\pi$
$68$	17.8561			2.16537
$69$	−2.90947	+	3.81247i	−0.350260	+	0.458968i
$70$	2.20544			0.263600
$71$	−1.27548	−	8.87116i	−0.151372	−	1.05281i	−0.913924	−	0.405886i	$-0.866963\pi$
$71$	−1.27548	−	8.87116i	−0.151372	−	1.05281i	0.762552	−	0.646927i	$-0.223946\pi$
$72$	2.61454	−	5.72503i	0.308126	−	0.674702i
$73$	12.4360	−	3.65155i	1.45553	−	0.427382i	0.544163	−	0.838980i	$-0.316847\pi$
$73$	12.4360	−	3.65155i	1.45553	−	0.427382i	0.911366	+	0.411598i	$0.135029\pi$
$74$	13.6841	−	15.7923i	1.59074	−	1.83581i
$75$	0.959493	+	0.281733i	0.110793	+	0.0325317i
$76$	−13.7079	+	8.80952i	−1.57240	+	1.01052i
$77$	2.27748	+	4.98698i	0.259543	+	0.568320i
$78$	8.90324	+	10.2749i	1.00809	+	1.16340i
$79$	−3.34034	−	2.14671i	−0.375818	−	0.241523i	0.339072	−	0.940760i	$-0.389887\pi$
$79$	−3.34034	−	2.14671i	−0.375818	−	0.241523i	−0.714890	+	0.699237i	$0.753523\pi$
$80$	−1.00563	+	6.99430i	−0.112433	+	0.781987i
$81$	−0.142315	+	0.989821i	−0.0158128	+	0.109980i
$82$	19.5434	+	12.5598i	2.15821	+	1.38700i
$83$	3.51995	+	4.06224i	0.386365	+	0.445889i	0.915300	−	0.402774i	$-0.131954\pi$
$83$	3.51995	+	4.06224i	0.386365	+	0.445889i	−0.528935	+	0.848663i	$0.677408\pi$
$84$	−1.61088	−	3.52734i	−0.175762	−	0.384865i
$85$	3.35778	−	2.15791i	0.364202	−	0.234059i
$86$	17.4170	+	5.11410i	1.87813	+	0.551467i
$87$	1.73265	−	1.99958i	0.185759	−	0.214378i
$88$	−38.1950	+	11.2150i	−4.07160	+	1.19553i
$89$	−1.36356	+	2.98579i	−0.144538	+	0.316493i	−0.968030	−	0.250834i	$-0.919295\pi$
$89$	−1.36356	+	2.98579i	−0.144538	+	0.316493i	0.823493	+	0.567327i	$0.192022\pi$
$90$	−0.362097	−	2.51844i	−0.0381684	−	0.265467i
$91$	4.63175			0.485539
$92$	−21.4135	+	1.33227i	−2.23251	+	0.138899i
$93$	2.74860			0.285016
$94$	−1.36532	−	9.49599i	−0.140822	−	0.979437i
$95$	−1.51309	+	3.31320i	−0.155239	+	0.339927i
$96$	5.17289	−	1.51890i	0.527956	−	0.155022i
$97$	−6.54427	+	7.55249i	−0.664470	+	0.766840i	−0.983501	−	0.180905i	$-0.942097\pi$
$97$	−6.54427	+	7.55249i	−0.664470	+	0.766840i	0.319030	+	0.947745i	$0.396643\pi$
$98$	15.2547	+	4.47917i	1.54095	+	0.452465i
$99$	5.32082	−	3.41949i	0.534763	−	0.343671i
$100$	1.85842	+	4.06937i	0.185842	+	0.406937i
$101$	−1.11167	−	1.28294i	−0.110615	−	0.127657i	0.697742	−	0.716349i	$-0.254188\pi$
$101$	−1.11167	−	1.28294i	−0.110615	−	0.127657i	−0.808357	+	0.588693i	$0.799643\pi$
$102$	−8.54332	−	5.49046i	−0.845914	−	0.543636i
$103$	0.965920	−	6.71812i	0.0951749	−	0.661956i	−0.885258	−	0.465101i	$-0.846018\pi$
$103$	0.965920	−	6.71812i	0.0951749	−	0.661956i	0.980433	−	0.196855i	$-0.0630729\pi$
$104$	−4.78616	+	33.2885i	−0.469321	+	3.26420i
$105$	−0.729201	−	0.468629i	−0.0711627	−	0.0457335i
$106$	8.46044	+	9.76386i	0.821750	+	0.948350i
$107$	−4.59646	−	10.0649i	−0.444357	−	0.973006i	−0.990778	−	0.135495i	$-0.956737\pi$
$107$	−4.59646	−	10.0649i	−0.444357	−	0.973006i	0.546421	−	0.837511i	$-0.315990\pi$
$108$	−3.76347	+	2.41864i	−0.362140	+	0.232733i
$109$	4.06028	+	1.19221i	0.388904	+	0.114193i	0.470338	−	0.882486i	$-0.344132\pi$
$109$	4.06028	+	1.19221i	0.388904	+	0.114193i	−0.0814342	+	0.996679i	$0.525950\pi$
$110$	−10.5384	+	12.1620i	−1.00480	+	1.15960i
$111$	−7.88014	+	2.31382i	−0.747950	+	0.219618i
$112$	2.54443	−	5.57152i	0.240426	−	0.526459i
$113$	−2.17563	−	15.1318i	−0.204666	−	1.42348i	−0.790208	−	0.612839i	$-0.790027\pi$
$113$	−2.17563	−	15.1318i	−0.204666	−	1.42348i	0.585542	−	0.810642i	$-0.300882\pi$
$114$	9.26736			0.867968
$115$	−3.86572	+	2.83835i	−0.360480	+	0.264677i
$116$	11.8365			1.09899
$117$	−0.760457	−	5.28910i	−0.0703043	−	0.488977i
$118$	2.94819	−	6.45564i	0.271403	−	0.594290i
$119$	−3.31961	+	0.974726i	−0.304308	+	0.0893530i
$120$	4.12156	−	4.75653i	0.376245	−	0.434210i
$121$	−27.8292	−	8.17138i	−2.52992	−	0.742853i
$122$	−22.1520	+	14.2362i	−2.00555	+	1.28889i
$123$	−3.79298	−	8.30548i	−0.342002	−	0.748880i
$124$	8.05233	+	9.29289i	0.723121	+	0.834526i
$125$	0.841254	+	0.540641i	0.0752440	+	0.0483564i
$126$	−0.313867	+	2.18299i	−0.0279615	+	0.194476i
$127$	2.53987	−	17.6652i	0.225377	−	1.56753i	−0.491841	−	0.870685i	$-0.663676\pi$
$127$	2.53987	−	17.6652i	0.225377	−	1.56753i	0.717218	−	0.696848i	$-0.245415\pi$
$128$	−9.95965	−	6.40068i	−0.880317	−	0.565745i
$129$	−4.67204	−	5.39182i	−0.411350	−	0.474723i
$130$	5.64783	+	12.3670i	0.495347	+	1.08466i
$131$	3.84114	−	2.46855i	0.335602	−	0.215678i	−0.361975	−	0.932188i	$-0.617898\pi$
$131$	3.84114	−	2.46855i	0.335602	−	0.215678i	0.697578	+	0.716509i	$0.254261\pi$
$132$	27.1491	+	7.97169i	2.36303	+	0.693847i
$133$	2.06753	−	2.38605i	0.179277	−	0.206897i
$134$	20.5415	−	6.03153i	1.77451	−	0.521045i
$135$	−0.415415	+	0.909632i	−0.0357532	+	0.0782887i
$136$	−3.57509	−	24.8653i	−0.306562	−	2.13218i
$137$	1.97264			0.168534			0.0842669	−	0.996443i	$-0.473145\pi$
$137$	1.97264			0.168534			0.0842669	+	0.996443i	$0.473145\pi$
$138$	10.6550	+	5.94685i	0.907013	+	0.506229i
$139$	1.91783			0.162668			0.0813339	−	0.996687i	$-0.474082\pi$
$139$	1.91783			0.162668			0.0813339	+	0.996687i	$0.474082\pi$
$140$	−0.551864	−	3.83830i	−0.0466411	−	0.324396i
$141$	−1.56636	+	3.42985i	−0.131911	+	0.288845i
$142$	−21.8796	+	6.42444i	−1.83610	+	0.539127i
$143$	−22.1322	+	25.5420i	−1.85079	+	2.13593i
$144$	−6.77999	−	1.99079i	−0.564999	−	0.165899i
$145$	2.22581	−	1.43044i	0.184843	−	0.118792i
$146$	−13.6993	−	29.9972i	−1.13376	−	2.48259i
$147$	−4.09200	−	4.72242i	−0.337502	−	0.389498i
$148$	−30.9087	−	19.8638i	−2.54068	−	1.63280i
$149$	−0.975062	+	6.78170i	−0.0798802	+	0.555579i	0.910102	+	0.414385i	$0.136003\pi$
$149$	−0.975062	+	6.78170i	−0.0798802	+	0.555579i	−0.989982	+	0.141194i	$0.954906\pi$
$150$	0.362097	−	2.51844i	0.0295651	−	0.205630i
$151$	4.52727	+	2.90950i	0.368424	+	0.236772i	0.711732	−	0.702451i	$-0.247911\pi$
$151$	4.52727	+	2.90950i	0.368424	+	0.236772i	−0.343308	+	0.939223i	$0.611547\pi$
$152$	15.0121	+	17.3249i	1.21765	+	1.40524i
$153$	1.65809	+	3.63070i	0.134048	+	0.293525i
$154$	11.7347	−	7.54146i	0.945613	−	0.607708i
$155$	2.63726	+	0.774369i	0.211830	+	0.0621988i
$156$	15.6544	−	18.0661i	1.25335	−	1.44645i
$157$	17.0348	−	5.00186i	1.35952	−	0.399192i	0.480928	−	0.876760i	$-0.340300\pi$
$157$	17.0348	−	5.00186i	1.35952	−	0.399192i	0.878595	+	0.477568i	$0.158482\pi$
$158$	−4.19682	+	9.18976i	−0.333881	+	0.731098i
$159$	−0.722636	−	5.02604i	−0.0573087	−	0.398591i
$160$	5.39127			0.426217
$161$	3.90823	−	1.41660i	0.308012	−	0.111643i
$162$	2.54434			0.199902
$163$	−1.48068	−	10.2984i	−0.115976	−	0.806631i	−0.961914	−	0.273351i	$-0.911868\pi$
$163$	−1.48068	−	10.2984i	−0.115976	−	0.806631i	0.845938	−	0.533281i	$-0.179041\pi$
$164$	16.9685	−	37.1558i	1.32502	−	2.90138i
$165$	6.06867	−	1.78192i	0.472445	−	0.138723i
$166$	8.95594	−	10.3357i	0.695116	−	0.802207i
$167$	22.6181	+	6.64126i	1.75024	+	0.513916i	0.990643	−	0.136480i	$-0.0435789\pi$
$167$	22.6181	+	6.64126i	1.75024	+	0.513916i	0.759595	+	0.650396i	$0.225397\pi$
$168$	−4.58944	+	2.94945i	−0.354083	+	0.227555i
$169$	6.46088	+	14.1474i	0.496991	+	1.08826i
$170$	−6.65041	−	7.67498i	−0.510063	−	0.588644i
$171$	−3.06414	−	1.96920i	−0.234321	−	0.150589i
$172$	4.54223	−	31.5919i	0.346342	−	2.40886i
$173$	−1.32125	+	9.18946i	−0.100452	+	0.698662i	0.875902	+	0.482488i	$0.160267\pi$
$173$	−1.32125	+	9.18946i	−0.100452	+	0.698662i	−0.976355	+	0.216174i	$0.930642\pi$
$174$	−5.66321	−	3.63952i	−0.429327	−	0.275912i
$175$	−0.567635	−	0.655086i	−0.0429092	−	0.0495199i
$176$	18.5661	+	40.6542i	1.39948	+	3.06442i
$177$	−2.34653	+	1.50802i	−0.176376	+	0.113350i
$178$	8.01327	+	2.35291i	0.600620	+	0.176358i
$179$	11.3929	−	13.1481i	0.851546	−	0.982736i	−0.148435	−	0.988922i	$-0.547424\pi$
$179$	11.3929	−	13.1481i	0.851546	−	0.982736i	0.999981	+	0.00618594i	$0.00196906\pi$
$180$	−4.29243	+	1.26037i	−0.319939	+	0.0939426i
$181$	−8.16012	+	17.8682i	−0.606537	+	1.32813i	0.318381	+	0.947963i	$0.396861\pi$
$181$	−8.16012	+	17.8682i	−0.606537	+	1.32813i	−0.924918	+	0.380167i	$0.875866\pi$
$182$	−1.67714	−	11.6648i	−0.124318	−	0.864651i
$183$	10.3493			0.765042
$184$	6.14258	+	29.5523i	0.452837	+	2.17863i
$185$	−8.21282			−0.603818
$186$	−0.995258	−	6.92217i	−0.0729759	−	0.507558i
$187$	10.4872	−	22.9637i	0.766899	−	1.67928i
$188$	−16.1850	+	4.75234i	−1.18041	+	0.346600i
$189$	0.567635	−	0.655086i	0.0412894	−	0.0476505i
$190$	8.89197	+	2.61092i	0.645091	+	0.189416i
$191$	−3.03396	+	1.94981i	−0.219530	+	0.141083i	−0.645784	−	0.763520i	$-0.723469\pi$
$191$	−3.03396	+	1.94981i	−0.219530	+	0.141083i	0.426254	+	0.904603i	$0.359833\pi$
$192$	0.172497	+	0.377716i	0.0124489	+	0.0272593i
$193$	−14.9511	−	17.2545i	−1.07621	−	1.24201i	−0.968813	−	0.247792i	$-0.920295\pi$
$193$	−14.9511	−	17.2545i	−1.07621	−	1.24201i	−0.107393	−	0.994217i	$-0.534250\pi$
$194$	21.3902	+	13.7466i	1.53572	+	0.986950i
$195$	0.760457	−	5.28910i	0.0544575	−	0.378760i
$196$	3.97831	−	27.6697i	0.284165	−	1.97641i
$197$	1.12427	+	0.722527i	0.0801012	+	0.0514779i	0.580078	−	0.814561i	$-0.303022\pi$
$197$	1.12427	+	0.722527i	0.0801012	+	0.0514779i	−0.499977	+	0.866039i	$0.666658\pi$
$198$	−10.5384	−	12.1620i	−0.748933	−	0.864314i
$199$	3.71341	+	8.13122i	0.263236	+	0.576407i	0.994386	−	0.105810i	$-0.0337434\pi$
$199$	3.71341	+	8.13122i	0.263236	+	0.576407i	−0.731150	+	0.682217i	$0.761016\pi$
$200$	5.29467	−	3.40268i	0.374390	−	0.240606i
$201$	−8.07342	−	2.37057i	−0.569455	−	0.167207i
$202$	−2.82846	+	3.26422i	−0.199010	+	0.229670i
$203$	−2.20051	+	0.646128i	−0.154446	+	0.0453493i
$204$	−7.41770	+	16.2425i	−0.519343	+	1.13720i
$205$	−1.29942	−	9.03766i	−0.0907553	−	0.631217i
$206$	−17.2689			−1.20318
$207$	−2.25931	−	4.23031i	−0.157033	−	0.294027i
$208$	37.7583			2.61806
$209$	3.27856	+	22.8029i	0.226783	+	1.57731i
$210$	−0.916172	+	2.00614i	−0.0632219	+	0.138437i
$211$	16.9199	−	4.96813i	1.16481	−	0.342020i	0.358513	−	0.933525i	$-0.383284\pi$
$211$	16.9199	−	4.96813i	1.16481	−	0.342020i	0.806302	+	0.591504i	$0.201466\pi$
$212$	14.8758	−	17.1676i	1.02167	−	1.17907i
$213$	8.59935	+	2.52500i	0.589218	+	0.173010i
$214$	−23.6833	+	15.2204i	−1.61896	+	1.04044i
$215$	−2.96374	−	6.48968i	−0.202125	−	0.442592i
$216$	4.12156	+	4.75653i	0.280436	+	0.323641i
$217$	−2.00428	−	1.28807i	−0.136059	−	0.0874401i
$218$	1.53228	−	10.6573i	0.103779	−	0.721800i
$219$	−1.84455	+	12.8291i	−0.124643	+	0.866912i
$220$	23.8035	+	15.2976i	1.60483	+	1.03136i
$221$	−13.9669	−	16.1186i	−0.939512	−	1.08426i
$222$	8.68058	+	19.0078i	0.582603	+	1.27572i
$223$	11.6703	−	7.50003i	0.781499	−	0.502239i	−0.0880314	−	0.996118i	$-0.528058\pi$
$223$	11.6703	−	7.50003i	0.781499	−	0.502239i	0.869531	+	0.493878i	$0.164421\pi$
$224$	−4.48387	−	1.31658i	−0.299591	−	0.0879680i
$225$	−0.654861	+	0.755750i	−0.0436574	+	0.0503833i
$226$	−37.3208	+	10.9584i	−2.48254	+	0.728940i
$227$	11.2756	−	24.6901i	0.748387	−	1.63874i	−0.0208566	−	0.999782i	$-0.506639\pi$
$227$	11.2756	−	24.6901i	0.748387	−	1.63874i	0.769243	−	0.638956i	$-0.220633\pi$
$228$	−2.31896	−	16.1287i	−0.153577	−	1.06815i
$229$	−7.54437			−0.498546			−0.249273	−	0.968433i	$-0.580192\pi$
$229$	−7.54437			−0.498546			−0.249273	+	0.968433i	$0.580192\pi$
$230$	8.54797	+	8.70782i	0.563636	+	0.574177i
$231$	−5.48242			−0.360717
$232$	−2.36986	−	16.4828i	−0.155589	−	1.08215i
$233$	2.59368	−	5.67936i	0.169917	−	0.372067i	−0.805447	−	0.592668i	$-0.798075\pi$
$233$	2.59368	−	5.67936i	0.169917	−	0.372067i	0.975364	+	0.220601i	$0.0708019\pi$
$234$	−13.0449	+	3.83033i	−0.852772	+	0.250396i
$235$	−2.46921	+	2.84962i	−0.161073	+	0.185889i
$236$	−11.9730	−	3.51559i	−0.779376	−	0.228845i
$237$	3.34034	−	2.14671i	0.216978	−	0.139444i
$238$	3.65681	+	8.00729i	0.237036	+	0.519036i
$239$	−7.72793	−	8.91851i	−0.499878	−	0.576890i	0.448600	−	0.893733i	$-0.351923\pi$
$239$	−7.72793	−	8.91851i	−0.499878	−	0.576890i	−0.948478	+	0.316842i	$0.897377\pi$
$240$	−5.94449	−	3.82029i	−0.383715	−	0.246599i
$241$	−3.16325	+	22.0009i	−0.203763	+	1.41720i	0.589228	+	0.807966i	$0.299432\pi$
$241$	−3.16325	+	22.0009i	−0.203763	+	1.41720i	−0.792991	+	0.609233i	$0.791477\pi$
$242$	−10.5023	+	73.0449i	−0.675111	+	4.69550i
$243$	−0.841254	−	0.540641i	−0.0539664	−	0.0346821i
$244$	30.3195	+	34.9905i	1.94101	+	2.24004i
$245$	−2.59578	−	5.68397i	−0.165839	−	0.363136i
$246$	−19.5434	+	12.5598i	−1.24604	+	0.800783i
$247$	18.6745	+	5.48332i	1.18823	+	0.348895i
$248$	11.3285	−	13.0738i	0.719360	−	0.830186i
$249$	−5.15739	+	1.51435i	−0.326836	+	0.0959677i
$250$	1.05696	−	2.31441i	0.0668477	−	0.146376i
$251$	0.473619	+	3.29409i	0.0298945	+	0.207921i	0.999294	−	0.0375671i	$-0.0119608\pi$
$251$	0.473619	+	3.29409i	0.0298945	+	0.207921i	−0.969400	+	0.245488i	$0.921052\pi$
$252$	3.87777			0.244277
$253$	−10.8631	+	28.3211i	−0.682958	+	1.78053i
$254$	−45.4084			−2.84918
$255$	0.568035	+	3.95077i	0.0355717	+	0.247407i
$256$	−12.1684	+	26.6450i	−0.760523	+	1.66531i
$257$	−22.8261	+	6.70234i	−1.42385	+	0.418081i	−0.900805	−	0.434223i	$-0.857023\pi$
$257$	−22.8261	+	6.70234i	−1.42385	+	0.418081i	−0.523047	+	0.852304i	$0.675205\pi$
$258$	−11.8872	+	13.7186i	−0.740067	+	0.854083i
$259$	6.83053	+	2.00562i	0.424428	+	0.124623i
$260$	20.1101	−	12.9239i	1.24717	−	0.801509i
$261$	1.09912	+	2.40673i	0.0680335	+	0.148973i
$262$	−7.60776	−	8.77983i	−0.470009	−	0.542419i
$263$	20.0799	+	12.9046i	1.23818	+	0.795731i	0.985145	−	0.171726i	$-0.0549343\pi$
$263$	20.0799	+	12.9046i	1.23818	+	0.795731i	0.253037	+	0.967457i	$0.418571\pi$
$264$	5.66519	−	39.4022i	0.348668	−	2.42504i
$265$	0.722636	−	5.02604i	0.0443912	−	0.308747i
$266$	−6.75777	−	4.34296i	−0.414346	−	0.266284i
$267$	−2.14953	−	2.48068i	−0.131549	−	0.151815i
$268$	−15.6372	−	34.2407i	−0.955195	−	2.09159i
$269$	−3.35986	+	2.15925i	−0.204854	+	0.131652i	−0.639046	−	0.769169i	$-0.720671\pi$
$269$	−3.35986	+	2.15925i	−0.204854	+	0.131652i	0.434191	+	0.900821i	$0.357034\pi$
$270$	2.44127	+	0.716822i	0.148571	+	0.0436244i
$271$	−1.04733	+	1.20869i	−0.0636209	+	0.0734224i	−0.786668	−	0.617376i	$-0.788196\pi$
$271$	−1.04733	+	1.20869i	−0.0636209	+	0.0734224i	0.723047	+	0.690799i	$0.242741\pi$
$272$	−27.0617	+	7.94602i	−1.64085	+	0.481798i
$273$	−1.92410	+	4.21319i	−0.116452	+	0.254994i
$274$	−0.714286	−	4.96797i	−0.0431516	−	0.300126i
$275$	6.32487			0.381404
$276$	7.68359	−	20.0318i	0.462498	−	1.20577i
$277$	2.32107			0.139459			0.0697297	−	0.997566i	$-0.477786\pi$
$277$	2.32107			0.139459			0.0697297	+	0.997566i	$0.477786\pi$
$278$	−0.694439	−	4.82993i	−0.0416497	−	0.289680i
$279$	−1.14181	+	2.50021i	−0.0683583	+	0.149684i
$280$	−5.23449	+	1.53699i	−0.312821	+	0.0918524i
$281$	16.5516	−	19.1016i	0.987387	−	1.13951i	−0.00283365	−	0.999996i	$-0.500902\pi$
$281$	16.5516	−	19.1016i	0.987387	−	1.13951i	0.990221	−	0.139509i	$-0.0445526\pi$
$282$	9.20503	+	2.70284i	0.548152	+	0.160952i
$283$	−1.39904	+	0.899105i	−0.0831640	+	0.0534463i	−0.581562	−	0.813502i	$-0.697558\pi$
$283$	−1.39904	+	0.899105i	−0.0831640	+	0.0534463i	0.498398	+	0.866948i	$0.333922\pi$
$284$	16.6559	+	36.4713i	0.988345	+	2.16417i
$285$	−2.38523	−	2.75270i	−0.141289	−	0.163056i
$286$	72.3399	+	46.4900i	4.27755	+	2.74901i
$287$	−1.12634	+	7.83387i	−0.0664858	+	0.462419i
$288$	−0.767258	+	5.33640i	−0.0452111	+	0.314450i
$289$	−0.899079	−	0.577803i	−0.0528870	−	0.0339884i
$290$	−4.40844	−	5.08761i	−0.258872	−	0.298755i
$291$	−4.15140	−	9.09030i	−0.243359	−	0.532883i
$292$	−48.7786	+	31.3481i	−2.85455	+	1.83451i
$293$	−9.28718	−	2.72696i	−0.542563	−	0.159311i	−0.00104412	−	0.999999i	$-0.500332\pi$
$293$	−9.28718	−	2.72696i	−0.542563	−	0.159311i	−0.541519	+	0.840689i	$0.682151\pi$
$294$	−10.4114	+	12.0154i	−0.607206	+	0.700753i
$295$	−2.67634	+	0.785844i	−0.155822	+	0.0457536i
$296$	−21.4727	+	47.0186i	−1.24808	+	2.73290i
$297$	0.900123	+	6.26050i	0.0522305	+	0.363271i
$298$	17.4324			1.00983
$299$	17.9520	+	18.2877i	1.03819	+	1.05761i
$300$	−4.47365			−0.258286
$301$	0.880092	+	6.12117i	0.0507277	+	0.352819i
$302$	5.68809	−	12.4552i	0.327313	−	0.716715i
$303$	1.62880	−	0.478260i	0.0935723	−	0.0274753i
$304$	16.8546	−	19.4512i	0.966677	−	1.11560i
$305$	9.93008	+	2.91573i	0.568595	+	0.166954i
$306$	8.54332	−	5.49046i	0.488389	−	0.313868i
$307$	0.0148117	+	0.0324330i	0.000845346	+	0.00185105i	0.910054	−	0.414489i	$-0.136040\pi$
$307$	0.0148117	+	0.0324330i	0.000845346	+	0.00185105i	−0.909209	+	0.416340i	$0.863312\pi$
$308$	−16.0614	−	18.5358i	−0.915182	−	1.05618i
$309$	5.70976	+	3.66944i	0.324817	+	0.208747i
$310$	0.995258	−	6.92217i	0.0565269	−	0.393153i
$311$	−0.378317	+	2.63126i	−0.0214524	+	0.149205i	−0.997732	−	0.0673076i	$-0.978559\pi$
$311$	−0.378317	+	2.63126i	−0.0214524	+	0.149205i	0.976280	+	0.216512i	$0.0694682\pi$
$312$	−28.2920	−	18.1822i	−1.60172	−	1.02936i
$313$	5.38574	+	6.21548i	0.304420	+	0.351319i	0.887262	−	0.461266i	$-0.152605\pi$
$313$	5.38574	+	6.21548i	0.304420	+	0.351319i	−0.582842	+	0.812586i	$0.698059\pi$
$314$	−18.7651	−	41.0899i	−1.05898	−	2.31884i
$315$	0.729201	−	0.468629i	0.0410858	−	0.0264043i
$316$	17.0438	+	5.00452i	0.958791	+	0.281526i
$317$	17.0738	−	19.7042i	0.958958	−	1.10670i	−0.0352665	−	0.999378i	$-0.511228\pi$
$317$	17.0738	−	19.7042i	0.958958	−	1.10670i	0.994225	−	0.107319i	$-0.0342265\pi$
$318$	−12.3961	+	3.63983i	−0.695140	+	0.204111i
$319$	6.95177	−	15.2222i	0.389224	−	0.852282i
$320$	0.0590949	+	0.411014i	0.00330351	+	0.0229764i
$321$	11.0647			0.617574
$322$	−4.98277	−	9.32969i	−0.277679	−	0.519923i
$323$	−14.5381			−0.808920
$324$	−0.636666	−	4.42811i	−0.0353704	−	0.246006i
$325$	2.21976	−	4.86061i	0.123130	−	0.269618i
$326$	−25.3997	+	7.45802i	−1.40676	+	0.413062i
$327$	−2.77117	+	3.19810i	−0.153246	+	0.176855i
$328$	−55.1383	−	16.1901i	−3.04450	−	0.893946i
$329$	2.74952	−	1.76701i	0.151586	−	0.0974182i
$330$	−6.68511	−	14.6383i	−0.368003	−	0.805815i
$331$	−11.2557	−	12.9898i	−0.618670	−	0.713983i	0.356784	−	0.934187i	$-0.383873\pi$
$331$	−11.2557	−	12.9898i	−0.618670	−	0.713983i	−0.975454	+	0.220204i	$0.929328\pi$
$332$	−20.2291	−	13.0005i	−1.11022	−	0.713492i
$333$	1.16881	−	8.12922i	0.0640502	−	0.445479i
$334$	8.53568	−	59.3670i	0.467052	−	3.24842i
$335$	−7.07852	−	4.54909i	−0.386741	−	0.248543i
$336$	4.01104	+	4.62899i	0.218820	+	0.252532i
$337$	2.28053	+	4.99367i	0.124229	+	0.272023i	0.961520	−	0.274734i	$-0.0885897\pi$
$337$	2.28053	+	4.99367i	0.124229	+	0.272023i	−0.837292	+	0.546756i	$0.815862\pi$
$338$	33.2898	−	21.3940i	1.81073	−	1.16368i
$339$	14.6682	+	4.30696i	0.796666	+	0.233922i
$340$	−11.6933	+	13.4947i	−0.634156	+	0.731855i
$341$	16.6803	−	4.89779i	0.903291	−	0.265230i
$342$	−3.84980	+	8.42989i	−0.208173	+	0.455836i
$343$	1.63434	+	11.3671i	0.0882460	+	0.613765i
$344$	−44.9024			−2.42098
$345$	−0.975975	−	4.69547i	−0.0525447	−	0.252796i
$346$	23.6215			1.26990
$347$	0.636055	+	4.42386i	0.0341452	+	0.237485i	0.999746	−	0.0225445i	$-0.00717674\pi$
$347$	0.636055	+	4.42386i	0.0341452	+	0.237485i	−0.965601	+	0.260030i	$0.916268\pi$
$348$	−4.91705	+	10.7668i	−0.263582	+	0.577164i
$349$	−24.0076	+	7.04928i	−1.28510	+	0.377339i	−0.851779	−	0.523901i	$-0.824476\pi$
$349$	−24.0076	+	7.04928i	−1.28510	+	0.377339i	−0.433320	+	0.901240i	$0.642658\pi$
$350$	−1.44426	+	1.66676i	−0.0771987	+	0.0890920i
$351$	5.12704	+	1.50543i	0.273661	+	0.0803541i
$352$	28.6860	−	18.4354i	1.52897	−	0.982609i
$353$	11.3166	+	24.7800i	0.602324	+	1.31891i	0.927702	+	0.373322i	$0.121781\pi$
$353$	11.3166	+	24.7800i	0.602324	+	1.31891i	−0.325378	+	0.945584i	$0.605492\pi$
$354$	4.64754	+	5.36354i	0.247014	+	0.285069i
$355$	7.53964	+	4.84543i	0.400162	+	0.257169i
$356$	2.08980	−	14.5349i	0.110759	−	0.770348i
$357$	0.492375	−	3.42454i	0.0260592	−	0.181246i
$358$	−37.2381	−	23.9314i	−1.96809	−	1.26482i
$359$	10.1756	+	11.7433i	0.537048	+	0.619787i	0.957816	−	0.287382i	$-0.0927848\pi$
$359$	10.1756	+	11.7433i	0.537048	+	0.619787i	−0.420768	+	0.907168i	$0.638239\pi$
$360$	2.61454	+	5.72503i	0.137798	+	0.301736i
$361$	−4.82315	+	3.09965i	−0.253850	+	0.163140i
$362$	47.9546	+	14.0807i	2.52044	+	0.740068i
$363$	18.9936	−	21.9198i	0.996905	−	1.15049i
$364$	−19.8815	+	5.83773i	−1.04207	+	0.305980i
$365$	−5.38422	+	11.7898i	−0.281823	+	0.617106i
$366$	−3.74745	−	26.0641i	−0.195882	−	1.36239i
$367$	4.12175			0.215153			0.107577	−	0.994197i	$-0.465691\pi$
$367$	4.12175			0.215153			0.107577	+	0.994197i	$0.465691\pi$
$368$	31.8601	−	11.5482i	1.66082	−	0.601990i
$369$	9.13059			0.475320
$370$	2.97383	+	20.6835i	0.154602	+	1.07528i
$371$	−1.82840	+	4.00364i	−0.0949259	+	0.207859i
$372$	−11.7982	+	3.46426i	−0.611707	+	0.179613i
$373$	7.28068	−	8.40235i	0.376979	−	0.435057i	−0.535277	−	0.844676i	$-0.679793\pi$
$373$	7.28068	−	8.40235i	0.376979	−	0.435057i	0.912257	+	0.409619i	$0.134338\pi$
$374$	−61.6302	−	18.0962i	−3.18682	−	0.935735i
$375$	−0.841254	+	0.540641i	−0.0434421	+	0.0279186i
$376$	9.85833	+	21.5867i	0.508405	+	1.11325i
$377$	−9.25837	−	10.6847i	−0.476831	−	0.550292i
$378$	−1.85533	−	1.19235i	−0.0954280	−	0.0613279i
$379$	0.461011	−	3.20640i	0.0236805	−	0.164702i	−0.974550	−	0.224172i	$-0.928032\pi$
$379$	0.461011	−	3.20640i	0.0236805	−	0.164702i	0.998230	+	0.0594706i	$0.0189413\pi$
$380$	2.31896	−	16.1287i	0.118960	−	0.827386i
$381$	15.0137	+	9.64874i	0.769177	+	0.494320i
$382$	6.00906	+	6.93483i	0.307450	+	0.354817i
$383$	9.80618	+	21.4725i	0.501072	+	1.09720i	0.976119	+	0.217235i	$0.0697037\pi$
$383$	9.80618	+	21.4725i	0.501072	+	1.09720i	−0.475047	+	0.879960i	$0.657569\pi$
$384$	9.95965	−	6.40068i	0.508251	−	0.326633i
$385$	−5.26034	−	1.54458i	−0.268092	−	0.0787189i
$386$	−38.0407	+	43.9013i	−1.93622	+	2.23452i
$387$	6.84541	−	2.00999i	0.347972	−	0.102174i
$388$	18.5719	−	40.6668i	0.942845	−	2.06454i
$389$	2.79982	+	19.4732i	0.141956	+	0.987329i	0.928907	+	0.370313i	$0.120750\pi$
$389$	2.79982	+	19.4732i	0.141956	+	0.987329i	−0.786951	+	0.617016i	$0.788341\pi$
$390$	−13.5956			−0.688441
$391$	−16.7149	−	9.32905i	−0.845309	−	0.471790i
$392$	−39.3277			−1.98635
$393$	0.649806	+	4.51950i	0.0327784	+	0.227979i
$394$	1.41254	−	3.09304i	0.0711629	−	0.155825i
$395$	3.80983	−	1.11867i	0.191693	−	0.0562862i
$396$	−18.5295	+	21.3841i	−0.931140	+	1.07459i
$397$	−35.0360	−	10.2875i	−1.75841	−	0.516315i	−0.766386	−	0.642380i	$-0.777947\pi$
$397$	−35.0360	−	10.2875i	−1.75841	−	0.516315i	−0.992022	+	0.126065i	$0.959765\pi$
$398$	19.1334	−	12.2963i	0.959069	−	0.616356i
$399$	1.31155	+	2.87189i	0.0656595	+	0.143774i
$400$	−4.62739	−	5.34030i	−0.231370	−	0.267015i
$401$	31.2494	+	20.0828i	1.56052	+	1.00289i	0.982368	+	0.186959i	$0.0598630\pi$
$401$	31.2494	+	20.0828i	1.56052	+	1.00289i	0.578154	+	0.815928i	$0.303773\pi$
$402$	−3.04678	+	21.1908i	−0.151959	+	1.05690i
$403$	2.09019	−	14.5376i	0.104120	−	0.724169i
$404$	6.38874	+	4.10580i	0.317852	+	0.204271i
$405$	−0.654861	−	0.755750i	−0.0325403	−	0.0375535i
$406$	2.42403	+	5.30789i	0.120303	+	0.263426i
$407$	−43.6989	+	28.0836i	−2.16608	+	1.39205i
$408$	24.1034	+	7.07741i	1.19330	+	0.350384i
$409$	14.1971	−	16.3843i	0.701999	−	0.810150i	−0.287022	−	0.957924i	$-0.592665\pi$
$409$	14.1971	−	16.3843i	0.701999	−	0.810150i	0.989021	+	0.147774i	$0.0472108\pi$
$410$	−22.2903	+	6.54501i	−1.10084	+	0.323235i
$411$	−0.819464	+	1.79438i	−0.0404212	+	0.0885100i
$412$	4.32119	+	30.0545i	0.212890	+	1.48068i
$413$	2.41780			0.118972
$414$	−9.83569	+	7.22171i	−0.483398	+	0.354928i
$415$	−5.37512			−0.263854
$416$	−4.09983	−	28.5150i	−0.201011	−	1.39806i
$417$	−0.796694	+	1.74452i	−0.0390143	+	0.0854293i
$418$	56.2406	−	16.5137i	2.75082	−	0.807713i
$419$	11.8096	−	13.6289i	0.576934	−	0.665818i	−0.390008	−	0.920811i	$-0.627528\pi$
$419$	11.8096	−	13.6289i	0.576934	−	0.665818i	0.966943	+	0.254994i	$0.0820734\pi$
$420$	3.72069	+	1.09249i	0.181551	+	0.0533083i
$421$	8.12489	−	5.22155i	0.395983	−	0.254483i	−0.327463	−	0.944864i	$-0.606194\pi$
$421$	8.12489	−	5.22155i	0.395983	−	0.254483i	0.723446	+	0.690381i	$0.242557\pi$
$422$	−18.6386	−	40.8128i	−0.907312	−	1.98674i
$423$	−2.46921	−	2.84962i	−0.120057	−	0.138553i
$424$	−26.8849	−	17.2779i	−1.30565	−	0.839088i
$425$	−0.568035	+	3.95077i	−0.0275538	+	0.191641i
$426$	3.24525	−	22.5712i	0.157233	−	1.09358i
$427$	−7.54672	−	4.84998i	−0.365211	−	0.234707i
$428$	32.4155	+	37.4094i	1.56686	+	1.80825i
$429$	−14.0397	−	30.7427i	−0.677844	−	1.48427i
$430$	−15.2707	+	9.81388i	−0.736418	+	0.473267i
$431$	−9.82093	−	2.88368i	−0.473057	−	0.138902i	0.0365093	−	0.999333i	$-0.488376\pi$
$431$	−9.82093	−	2.88368i	−0.473057	−	0.138902i	−0.509567	+	0.860431i	$0.670194\pi$
$432$	4.62739	−	5.34030i	0.222636	−	0.256935i
$433$	11.6112	−	3.40936i	0.557999	−	0.163843i	0.00944043	−	0.999955i	$-0.496995\pi$
$433$	11.6112	−	3.40936i	0.557999	−	0.163843i	0.548559	+	0.836112i	$0.315177\pi$
$434$	−2.51819	+	5.51406i	−0.120877	+	0.264684i
$435$	0.376540	+	2.61889i	0.0180537	+	0.125566i
$436$	−18.9311			−0.906635
$437$	17.4344	−	1.08471i	0.834000	−	0.0518887i
$438$	32.9773			1.57572
$439$	−1.22371	−	8.51107i	−0.0584044	−	0.406211i	−0.997961	−	0.0638191i	$-0.979672\pi$
$439$	−1.22371	−	8.51107i	−0.0584044	−	0.406211i	0.939557	−	0.342392i	$-0.111237\pi$
$440$	16.5366	−	36.2101i	0.788352	−	1.72625i
$441$	5.99554	−	1.76045i	0.285502	−	0.0838309i
$442$	−35.5364	+	41.0112i	−1.69029	+	1.95070i
$443$	11.9590	+	3.51148i	0.568190	+	0.166836i	0.553195	−	0.833052i	$-0.313408\pi$
$443$	11.9590	+	3.51148i	0.568190	+	0.166836i	0.0149953	+	0.999888i	$0.495227\pi$
$444$	30.9087	−	19.8638i	1.46686	−	0.942695i
$445$	−1.36356	−	2.98579i	−0.0646392	−	0.141540i
$446$	−23.1141	−	26.6751i	−1.09449	−	1.26310i
$447$	−5.76380	−	3.70417i	−0.272618	−	0.175201i
$448$	0.0512237	−	0.356268i	0.00242009	−	0.0168321i
$449$	3.07442	−	21.3830i	0.145091	−	1.00913i	−0.779019	−	0.627000i	$-0.784282\pi$
$449$	3.07442	−	21.3830i	0.145091	−	1.00913i	0.924110	−	0.382127i	$-0.124808\pi$
$450$	2.14043	+	1.37557i	0.100901	+	0.0648451i
$451$	−37.8181	−	43.6444i	−1.78078	−	2.05514i
$452$	28.4104	+	62.2102i	1.33632	+	2.92612i
$453$	−4.52727	+	2.90950i	−0.212710	+	0.136700i
$454$	−66.2633	−	19.4567i	−3.10989	−	0.913146i
$455$	−3.03315	+	3.50044i	−0.142196	+	0.164103i
$456$	−21.9956	+	6.45849i	−1.03004	+	0.302446i
$457$	−0.339831	+	0.744126i	−0.0158966	+	0.0348087i	−0.917414	−	0.397935i	$-0.869727\pi$
$457$	−0.339831	+	0.744126i	−0.0158966	+	0.0348087i	0.901517	+	0.432743i	$0.142454\pi$
$458$	2.73179	+	19.0000i	0.127648	+	0.887813i
$459$	−3.99140			−0.186303
$460$	13.0160	−	17.0557i	0.606872	−	0.795224i
$461$	38.9346			1.81336			0.906682	−	0.421814i	$-0.138607\pi$
$461$	38.9346			1.81336			0.906682	+	0.421814i	$0.138607\pi$
$462$	1.98517	+	13.8071i	0.0923583	+	0.642366i
$463$	−12.4282	+	27.2141i	−0.577590	+	1.26474i	0.365067	+	0.930981i	$0.381046\pi$
$463$	−12.4282	+	27.2141i	−0.577590	+	1.26474i	−0.942657	+	0.333764i	$0.891681\pi$
$464$	−17.9387	+	5.26727i	−0.832782	+	0.244527i
$465$	−1.79995	+	2.07725i	−0.0834706	+	0.0963302i
$466$	−15.2423	−	4.47554i	−0.706085	−	0.207325i
$467$	31.7700	−	20.4174i	1.47014	−	0.944803i	0.472146	−	0.881520i	$-0.343480\pi$
$467$	31.7700	−	20.4174i	1.47014	−	0.944803i	0.997996	−	0.0632823i	$-0.0201568\pi$
$468$	9.93044	+	21.7446i	0.459035	+	1.00515i
$469$	4.77623	+	5.51206i	0.220546	+	0.254523i
$470$	8.07068	+	5.18671i	0.372273	+	0.239245i
$471$	−2.52665	+	17.5732i	−0.116422	+	0.809731i
$472$	−2.49840	+	17.3767i	−0.114998	+	0.799830i
$473$	−37.9609	−	24.3960i	−1.74544	−	1.12173i
$474$	−6.61587	−	7.63513i	−0.303877	−	0.350693i
$475$	−1.51309	−	3.31320i	−0.0694252	−	0.152020i
$476$	13.0207	−	8.36789i	0.596803	−	0.383542i
$477$	4.87204	+	1.43056i	0.223076	+	0.0655009i
$478$	−19.6625	+	22.6917i	−0.899340	+	1.03789i
$479$	12.4301	−	3.64980i	0.567944	−	0.166764i	0.0148612	−	0.999890i	$-0.495269\pi$
$479$	12.4301	−	3.64980i	0.567944	−	0.166764i	0.553083	+	0.833126i	$0.313451\pi$
$480$	−2.23962	+	4.90407i	−0.102224	+	0.223839i
$481$	6.24550	+	43.4384i	0.284770	+	1.98062i
$482$	56.5532			2.57593
$483$	−0.334956	+	4.14352i	−0.0152410	+	0.188537i
$484$	129.754			5.89790
$485$	−1.42221	−	9.89166i	−0.0645791	−	0.449157i
$486$	−1.05696	+	2.31441i	−0.0479445	+	0.104984i
$487$	−8.22295	+	2.41448i	−0.372617	+	0.109410i	−0.462679	−	0.886526i	$-0.653112\pi$
$487$	−8.22295	+	2.41448i	−0.372617	+	0.109410i	0.0900617	+	0.995936i	$0.471294\pi$
$488$	42.6552	−	49.2267i	1.93091	−	2.22839i
$489$	9.98283	+	2.93122i	0.451439	+	0.132555i
$490$	−13.3748	+	8.59547i	−0.604213	+	0.388304i
$491$	−5.73508	−	12.5581i	−0.258820	−	0.566738i	0.734958	−	0.678113i	$-0.237202\pi$
$491$	−5.73508	−	12.5581i	−0.258820	−	0.566738i	−0.993778	+	0.111375i	$0.964475\pi$
$492$	26.7491	+	30.8701i	1.20594	+	1.39173i
$493$	8.88409	+	5.70946i	0.400119	+	0.257141i
$494$	7.04743	−	49.0160i	0.317079	−	2.20533i
$495$	−0.900123	+	6.26050i	−0.0404575	+	0.281388i
$496$	−16.3390	−	10.5004i	−0.733643	−	0.471484i
$497$	−5.08737	−	5.87113i	−0.228200	−	0.263356i
$498$	5.68126	+	12.4402i	0.254583	+	0.557460i
$499$	−37.1480	+	23.8736i	−1.66297	+	1.06873i	−0.749339	+	0.662186i	$0.769629\pi$
$499$	−37.1480	+	23.8736i	−1.66297	+	1.06873i	−0.913633	+	0.406541i	$0.866735\pi$
$500$	−4.29243	−	1.26037i	−0.191963	−	0.0563656i
$501$	−15.4370	+	17.8152i	−0.689674	+	0.795926i
$502$	8.12447	−	2.38556i	0.362613	−	0.106473i
$503$	−8.39640	+	18.3855i	−0.374377	+	0.819771i	0.624861	+	0.780736i	$0.285156\pi$
$503$	−8.39640	+	18.3855i	−0.374377	+	0.819771i	−0.999238	+	0.0390348i	$0.987572\pi$
$504$	−0.776395	−	5.39995i	−0.0345834	−	0.240533i
$505$	1.69757			0.0755407
$506$	75.2585	+	17.1031i	3.34565	+	0.760326i
$507$	−15.5528			−0.690726
$508$	11.3625	+	79.0279i	0.504129	+	3.50630i
$509$	−12.6481	+	27.6954i	−0.560616	+	1.22758i	0.391029	+	0.920379i	$0.372119\pi$
$509$	−12.6481	+	27.6954i	−0.560616	+	1.22758i	−0.951645	+	0.307200i	$0.900608\pi$
$510$	9.74409	−	2.86112i	0.431476	−	0.126693i
$511$	7.35715	−	8.49061i	0.325461	−	0.375602i
$512$	48.7909	+	14.3263i	2.15627	+	0.633139i
$513$	3.06414	−	1.96920i	0.135285	−	0.0869424i
$514$	25.1447	+	55.0592i	1.10908	+	2.42856i
$515$	4.44468	+	5.12943i	0.195856	+	0.226030i
$516$	26.8501	+	17.2555i	1.18201	+	0.759632i
$517$	−3.39399	+	23.6057i	−0.149268	+	1.03818i
$518$	2.57773	−	17.9285i	0.113259	−	0.787733i
$519$	−7.81017	−	5.01929i	−0.342828	−	0.220322i
$520$	−22.0235	−	25.4164i	−0.965793	−	1.11458i
$521$	−2.55508	−	5.59485i	−0.111940	−	0.245115i	0.845368	−	0.534185i	$-0.179381\pi$
$521$	−2.55508	−	5.59485i	−0.111940	−	0.245115i	−0.957308	+	0.289070i	$0.906654\pi$
$522$	5.66321	−	3.63952i	0.247872	−	0.159298i
$523$	26.6370	+	7.82133i	1.16475	+	0.342003i	0.806279	−	0.591536i	$-0.201478\pi$
$523$	26.6370	+	7.82133i	1.16475	+	0.342003i	0.358476	+	0.933539i	$0.383296\pi$
$524$	−13.3766	+	15.4374i	−0.584357	+	0.674384i
$525$	0.831691	−	0.244207i	0.0362980	−	0.0106581i
$526$	25.2285	−	55.2428i	1.10002	−	2.40870i
$527$	1.56130	+	10.8591i	0.0680113	+	0.473029i
$528$	−44.6930			−1.94501
$529$	20.7409	+	9.94049i	0.901780	+	0.432195i
$530$	−12.9194			−0.561185
$531$	−0.396962	−	2.76093i	−0.0172267	−	0.119814i
$532$	−5.86740	+	12.8478i	−0.254384	+	0.557024i
$533$	−46.8129	+	13.7455i	−2.02769	+	0.595384i
$534$	−5.46912	+	6.31170i	−0.236672	+	0.273134i
$535$	10.6165	+	3.11730i	0.458993	+	0.134773i
$536$	−44.5507	+	28.6310i	−1.92430	+	1.23667i
$537$	7.22716	+	15.8253i	0.311875	+	0.682911i
$538$	6.65454	+	7.67974i	0.286897	+	0.331097i
$539$	−33.2480	−	21.3672i	−1.43209	−	0.920349i
$540$	0.636666	−	4.42811i	0.0273978	−	0.190556i
$541$	−1.13804	+	7.91527i	−0.0489283	+	0.340304i	0.950623	+	0.310348i	$0.100446\pi$
$541$	−1.13804	+	7.91527i	−0.0489283	+	0.340304i	−0.999551	+	0.0299557i	$0.990463\pi$
$542$	3.42324	+	2.19998i	0.147041	+	0.0944972i
$543$	−12.8636	−	14.8454i	−0.552031	−	0.637077i
$544$	8.93920	+	19.5741i	0.383265	+	0.839233i
$545$	−3.55993	+	2.28783i	−0.152490	+	0.0979997i
$546$	11.3074	+	3.32014i	0.483911	+	0.142089i
$547$	14.6578	−	16.9160i	0.626722	−	0.723276i	−0.350247	−	0.936657i	$-0.613902\pi$
$547$	14.6578	−	16.9160i	0.626722	−	0.723276i	0.976969	+	0.213382i	$0.0684478\pi$
$548$	−8.46742	+	2.48626i	−0.361710	+	0.106208i
$549$	−4.29925	+	9.41405i	−0.183488	+	0.401782i
$550$	−2.29022	−	15.9288i	−0.0976552	−	0.679207i
$551$	−9.63702			−0.410551
$552$	−29.4335	−	6.68899i	−1.25277	−	0.284702i
$553$	−3.44179			−0.146360
$554$	−0.840451	−	5.84546i	−0.0357073	−	0.248350i
$555$	3.41173	−	7.47064i	0.144820	−	0.317111i
$556$	−8.23214	+	2.41717i	−0.349120	+	0.102511i
$557$	22.1663	−	25.5813i	0.939216	−	1.08391i	−0.0571185	−	0.998367i	$-0.518191\pi$
$557$	22.1663	−	25.5813i	0.939216	−	1.08391i	0.996334	−	0.0855453i	$-0.0272632\pi$
$558$	6.71008	+	1.97026i	0.284060	+	0.0834076i
$559$	−32.0707	+	20.6106i	−1.35645	+	0.871736i
$560$	2.54443	+	5.57152i	0.107522	+	0.235440i
$561$	16.5320	+	19.0790i	0.697982	+	0.805515i
$562$	−54.0995	−	34.7676i	−2.28205	−	1.46658i
$563$	−0.898918	+	6.25211i	−0.0378849	+	0.263495i	−0.999957	−	0.00930107i	$-0.997039\pi$
$563$	−0.898918	+	6.25211i	−0.0378849	+	0.263495i	0.962072	+	0.272796i	$0.0879484\pi$
$564$	2.40061	−	16.6966i	0.101084	−	0.703053i
$565$	12.8606	+	8.26500i	0.541049	+	0.347711i
$566$	2.77093	+	3.19782i	0.116471	+	0.134414i
$567$	0.360083	+	0.788472i	0.0151221	+	0.0331127i
$568$	47.4529	−	30.4961i	1.99108	−	1.27959i
$569$	−27.8226	−	8.16946i	−1.16638	−	0.342481i	−0.359474	−	0.933155i	$-0.617044\pi$
$569$	−27.8226	−	8.16946i	−1.16638	−	0.342481i	−0.806911	+	0.590674i	$0.798862\pi$
$570$	−6.06883	+	7.00380i	−0.254195	+	0.293357i
$571$	−34.2197	+	10.0478i	−1.43205	+	0.420488i	−0.903564	−	0.428454i	$-0.859058\pi$
$571$	−34.2197	+	10.0478i	−1.43205	+	0.420488i	−0.528486	+	0.848942i	$0.677240\pi$
$572$	62.8088	−	137.532i	2.62617	−	5.75050i
$573$	−0.513255	−	3.56977i	−0.0214415	−	0.149129i
$574$	20.1370			0.840500
$575$	0.386427	−	4.78024i	0.0161151	−	0.199350i
$576$	−0.415241			−0.0173017
$577$	0.894890	+	6.22409i	0.0372547	+	0.259112i	0.999933	−	0.0115343i	$-0.00367157\pi$
$577$	0.894890	+	6.22409i	0.0372547	+	0.259112i	−0.962679	+	0.270647i	$0.912762\pi$
$578$	−1.12961	+	2.47350i	−0.0469855	+	0.102884i
$579$	21.9062	−	6.43224i	0.910391	−	0.267315i
$580$	−7.75125	+	8.94542i	−0.321853	+	0.371438i
$581$	4.47044	+	1.31264i	0.185465	+	0.0544574i
$582$	−21.3902	+	13.7466i	−0.886650	+	0.569816i
$583$	−13.3415	−	29.2137i	−0.552547	−	1.20991i
$584$	53.4197	+	61.6496i	2.21052	+	2.55108i
$585$	4.49523	+	2.88891i	0.185855	+	0.119442i
$586$	−3.50483	+	24.3766i	−0.144783	+	1.00699i
$587$	4.29984	−	29.9060i	0.177473	−	1.23435i	−0.685111	−	0.728439i	$-0.740246\pi$
$587$	4.29984	−	29.9060i	0.177473	−	1.23435i	0.862584	−	0.505914i	$-0.168845\pi$
$588$	23.5166	+	15.1132i	0.969809	+	0.623259i
$589$	−6.55604	−	7.56607i	−0.270137	−	0.311755i
$590$	2.94819	+	6.45564i	0.121375	+	0.265775i
$591$	−1.12427	+	0.722527i	−0.0462465	+	0.0297208i
$592$	55.6828	+	16.3500i	2.28855	+	0.671979i
$593$	12.8995	−	14.8868i	0.529720	−	0.611329i	−0.426318	−	0.904573i	$-0.640189\pi$
$593$	12.8995	−	14.8868i	0.529720	−	0.611329i	0.956038	+	0.293244i	$0.0947349\pi$
$594$	15.4407	−	4.53381i	0.633541	−	0.186025i
$595$	1.43723	−	3.14711i	0.0589209	−	0.129019i
$596$	−4.36208	−	30.3390i	−0.178678	−	1.24273i
$597$	−8.93902			−0.365850
$598$	39.5561	−	51.8330i	1.61757	−	2.11961i
$599$	−3.86727			−0.158012			−0.0790061	−	0.996874i	$-0.525175\pi$
$599$	−3.86727			−0.158012			−0.0790061	+	0.996874i	$0.525175\pi$
$600$	0.895700	+	6.22973i	0.0365668	+	0.254328i
$601$	8.87136	−	19.4256i	0.361870	−	0.792385i	−0.637882	−	0.770134i	$-0.720189\pi$
$601$	8.87136	−	19.4256i	0.361870	−	0.792385i	0.999752	−	0.0222512i	$-0.00708335\pi$
$602$	15.0971	−	4.43292i	0.615313	−	0.180672i
$603$	5.51017	−	6.35907i	0.224391	−	0.258961i
$604$	−23.1001	−	6.78279i	−0.939928	−	0.275988i
$605$	24.3997	−	15.6808i	0.991991	−	0.637514i
$606$	−1.79425	−	3.92886i	−0.0728865	−	0.159599i
$607$	6.17628	+	7.12781i	0.250687	+	0.289309i	0.867120	−	0.498099i	$-0.165968\pi$
$607$	6.17628	+	7.12781i	0.250687	+	0.289309i	−0.616433	+	0.787407i	$0.711423\pi$
$608$	−16.5196	−	10.6165i	−0.669959	−	0.430556i
$609$	0.326386	−	2.27007i	0.0132258	−	0.0919877i
$610$	3.74745	−	26.0641i	0.151730	−	1.05530i
$611$	16.9496	+	10.8929i	0.685709	+	0.440678i
$612$	−11.6933	−	13.4947i	−0.472672	−	0.545493i
$613$	−12.9067	−	28.2617i	−0.521297	−	1.14148i	−0.968946	−	0.247272i	$-0.920466\pi$
$613$	−12.9067	−	28.2617i	−0.521297	−	1.14148i	0.447649	−	0.894209i	$-0.352261\pi$
$614$	0.0763173	−	0.0490462i	0.00307992	−	0.00197934i
$615$	8.76074	+	2.57238i	0.353267	+	0.103729i
$616$	−22.5961	+	26.0773i	−0.910423	+	1.05068i
$617$	−6.62681	+	1.94581i	−0.266785	+	0.0783352i	−0.412389	−	0.911008i	$-0.635306\pi$
$617$	−6.62681	+	1.94581i	−0.266785	+	0.0783352i	0.145604	+	0.989343i	$0.453487\pi$
$618$	7.17378	−	15.7084i	0.288572	−	0.631884i
$619$	−2.42042	−	16.8344i	−0.0972848	−	0.676630i	−0.978852	−	0.204571i	$-0.934420\pi$
$619$	−2.42042	−	16.8344i	−0.0972848	−	0.676630i	0.881567	−	0.472059i	$-0.156489\pi$
$620$	−12.2963			−0.493829
$621$	4.78658	−	0.297805i	0.192079	−	0.0119505i
$622$	6.76364			0.271197
$623$	0.404915	+	2.81625i	0.0162226	+	0.112831i
$624$	−15.6854	+	34.3461i	−0.627917	+	1.37495i
$625$	−0.959493	+	0.281733i	−0.0383797	+	0.0112693i
$626$	13.7031	−	15.8143i	0.547687	−	0.632065i
$627$	−22.1042	−	6.49039i	−0.882758	−	0.259201i
$628$	−66.8164	+	42.9403i	−2.66626	+	1.71350i
$629$	−13.6176	−	29.8183i	−0.542968	−	1.18893i
$630$	−1.44426	−	1.66676i	−0.0575405	−	0.0664053i
$631$	−2.39854	−	1.54145i	−0.0954844	−	0.0613641i	0.492027	−	0.870580i	$-0.336256\pi$
$631$	−2.39854	−	1.54145i	−0.0954844	−	0.0613641i	−0.587512	+	0.809216i	$0.699892\pi$
$632$	3.55653	−	24.7362i	0.141471	−	0.983953i
$633$	−2.50961	+	17.4547i	−0.0997481	+	0.693763i
$634$	−55.8061	−	35.8644i	−2.21634	−	1.42436i
$635$	11.6872	+	13.4878i	0.463793	+	0.535245i
$636$	9.43655	+	20.6632i	0.374183	+	0.819348i
$637$	−28.0891	+	18.0518i	−1.11293	+	0.715237i
$638$	−40.8535	−	11.9957i	−1.61741	−	0.474913i
$639$	−5.86911	+	6.77332i	−0.232179	+	0.267948i
$640$	11.3595	−	3.33545i	0.449023	−	0.131845i
$641$	5.43620	−	11.9036i	0.214717	−	0.470165i	−0.771372	−	0.636385i	$-0.780429\pi$
$641$	5.43620	−	11.9036i	0.214717	−	0.470165i	0.986089	+	0.166220i	$0.0531562\pi$
$642$	−4.00651	−	27.8659i	−0.158124	−	1.09978i
$643$	−0.665047			−0.0262269			−0.0131134	−	0.999914i	$-0.504174\pi$
$643$	−0.665047			−0.0262269			−0.0131134	+	0.999914i	$0.504174\pi$
$644$	−14.9904	+	11.0065i	−0.590703	+	0.433715i
$645$	7.13440			0.280917
$646$	5.26419	+	36.6132i	0.207117	+	1.44053i
$647$	9.62247	−	21.0703i	0.378298	−	0.828357i	−0.620719	−	0.784033i	$-0.713159\pi$
$647$	9.62247	−	21.0703i	0.378298	−	0.828357i	0.999017	−	0.0443244i	$-0.0141135\pi$
$648$	−6.03885	+	1.77317i	−0.237228	+	0.0696565i
$649$	−11.5531	+	13.3330i	−0.453501	+	0.523367i
$650$	−13.0449	−	3.83033i	−0.511663	−	0.150238i
$651$	2.00428	−	1.28807i	0.0785539	−	0.0504835i
$652$	19.3355	+	42.3389i	0.757237	+	1.65812i
$653$	−28.7343	−	33.1611i	−1.12446	−	1.29770i	−0.949727	−	0.313080i	$-0.898639\pi$
$653$	−28.7343	−	33.1611i	−1.12446	−	1.29770i	−0.174733	−	0.984616i	$-0.555906\pi$
$654$	9.05765	+	5.82100i	0.354182	+	0.227619i
$655$	−0.649806	+	4.51950i	−0.0253900	+	0.176591i
$656$	−9.18198	+	63.8621i	−0.358496	+	2.49340i
$657$	−10.9035	−	7.00728i	−0.425387	−	0.273380i
$658$	−5.44569	−	6.28466i	−0.212295	−	0.245002i
$659$	11.8715	+	25.9949i	0.462447	+	1.01262i	0.986923	+	0.161192i	$0.0515339\pi$
$659$	11.8715	+	25.9949i	0.462447	+	1.01262i	−0.524476	+	0.851425i	$0.675739\pi$
$660$	−23.8035	+	15.2976i	−0.926549	+	0.595457i
$661$	−33.2877	−	9.77414i	−1.29474	−	0.380170i	−0.439426	−	0.898279i	$-0.644818\pi$
$661$	−33.2877	−	9.77414i	−1.29474	−	0.380170i	−0.855315	+	0.518109i	$0.826636\pi$
$662$	−28.6383	+	33.0504i	−1.11306	+	1.28454i
$663$	20.4640	−	6.00879i	0.794758	−	0.233362i
$664$	−14.0534	+	30.7727i	−0.545379	+	1.19421i
$665$	0.449316	+	3.12506i	0.0174237	+	0.121185i
$666$	−20.8962			−0.809710
$667$	−11.0800	−	6.18406i	−0.429019	−	0.239448i
$668$	−105.457			−4.08025
$669$	1.97426	+	13.7313i	0.0763293	+	0.530882i
$670$	−8.89349	+	19.4740i	−0.343586	+	0.752348i
$671$	62.8065	−	18.4417i	2.42462	−	0.711932i
$672$	3.06028	−	3.53175i	0.118053	−	0.136240i
$673$	−10.3435	−	3.03711i	−0.398711	−	0.117072i	0.0762290	−	0.997090i	$-0.475712\pi$
$673$	−10.3435	−	3.03711i	−0.398711	−	0.117072i	−0.474940	+	0.880018i	$0.657530\pi$
$674$	11.7505	−	7.55158i	0.452612	−	0.290876i
$675$	−0.415415	−	0.909632i	−0.0159893	−	0.0350118i
$676$	−45.5638	−	52.5835i	−1.75246	−	2.02244i
$677$	−9.48524	−	6.09580i	−0.364548	−	0.234280i	0.345524	−	0.938410i	$-0.387701\pi$
$677$	−9.48524	−	6.09580i	−0.364548	−	0.234280i	−0.710072	+	0.704129i	$0.751337\pi$
$678$	5.53553	−	38.5004i	0.212591	−	1.47860i
$679$	−1.23277	+	8.57412i	−0.0473095	+	0.329045i
$680$	21.1332	+	13.5815i	0.810419	+	0.520825i
$681$	17.7748	+	20.5133i	0.681133	+	0.786070i
$682$	−18.3747	−	40.2349i	−0.703603	−	1.54067i
$683$	−25.4313	+	16.3437i	−0.973102	+	0.625375i	−0.927594	−	0.373589i	$-0.878127\pi$
$683$	−25.4313	+	16.3437i	−0.973102	+	0.625375i	−0.0455079	+	0.998964i	$0.514491\pi$
$684$	15.6345	+	4.59072i	0.597802	+	0.175530i
$685$	−1.29180	+	1.49082i	−0.0493573	+	0.0569613i
$686$	28.0355	−	8.23197i	1.07040	−	0.314298i
$687$	3.13404	−	6.86260i	0.119571	−	0.261825i
$688$	7.17456	+	49.9001i	0.273527	+	1.90243i
$689$	−27.1328			−1.03368
$690$	−11.4719	+	4.15815i	−0.436726	+	0.158298i
$691$	−12.2315			−0.465310			−0.232655	−	0.972559i	$-0.574741\pi$
$691$	−12.2315			−0.465310			−0.232655	+	0.972559i	$0.574741\pi$
$692$	−5.91079	−	41.1104i	−0.224694	−	1.56278i
$693$	2.27748	−	4.98698i	0.0865143	−	0.189440i
$694$	10.9109	−	3.20373i	0.414172	−	0.121612i
$695$	−1.25591	+	1.44940i	−0.0476393	+	0.0549787i
$696$	15.9777	+	4.69149i	0.605634	+	0.177830i
$697$	30.6585	−	19.7030i	1.16127	−	0.746305i
$698$	26.4463	+	57.9092i	1.00101	+	2.19190i
$699$	4.08867	+	4.71858i	0.154648	+	0.178473i
$700$	3.26219	+	2.09648i	0.123299	+	0.0792395i
$701$	−3.91452	+	27.2261i	−0.147849	+	1.02831i	0.771882	+	0.635766i	$0.219316\pi$
$701$	−3.91452	+	27.2261i	−0.147849	+	1.02831i	−0.919731	+	0.392548i	$0.871594\pi$
$702$	1.93486	−	13.4572i	0.0730265	−	0.507911i
$703$	25.1652	+	16.1727i	0.949124	+	0.609965i
$704$	1.71989	+	1.98486i	0.0648208	+	0.0748072i
$705$	−1.56636	−	3.42985i	−0.0589925	−	0.129175i
$706$	58.3092	−	37.4730i	2.19449	−	1.41032i
$707$	−1.41185	−	0.414557i	−0.0530981	−	0.0155910i
$708$	8.17165	−	9.43059i	0.307110	−	0.354423i
$709$	37.1220	−	10.9000i	1.39415	−	0.409358i	0.503476	−	0.864009i	$-0.332054\pi$
$709$	37.1220	−	10.9000i	1.39415	−	0.409358i	0.890670	+	0.454651i	$0.150236\pi$
$710$	9.47284	−	20.7426i	0.355509	−	0.778457i
$711$	0.565085	+	3.93025i	0.0211924	+	0.147396i
$712$	−20.6588			−0.774223
$713$	−2.68256	−	12.9060i	−0.100463	−	0.483332i
$714$	−8.80278			−0.329436
$715$	−4.80980	−	33.4529i	−0.179876	−	1.25107i
$716$	−32.3318	+	70.7967i	−1.20829	+	2.64580i
$717$	11.3229	−	3.32469i	0.422860	−	0.124163i
$718$	25.8902	−	29.8789i	0.966213	−	1.11507i
$719$	−15.1806	−	4.45744i	−0.566142	−	0.166234i	−0.0138782	−	0.999904i	$-0.504418\pi$
$719$	−15.1806	−	4.45744i	−0.566142	−	0.166234i	−0.552264	+	0.833669i	$0.686236\pi$
$720$	5.94449	−	3.82029i	0.221538	−	0.142374i
$721$	−2.44396	−	5.35152i	−0.0910177	−	0.199301i
$722$	9.55273	+	11.0244i	0.355516	+	0.410287i
$723$	−18.6986	−	12.0169i	−0.695409	−	0.446912i
$724$	12.5062	−	86.9827i	0.464790	−	3.23269i
$725$	−0.376540	+	2.61889i	−0.0139844	+	0.0972633i
$726$	−62.0812	−	39.8971i	−2.30405	−	1.48072i
$727$	17.0256	+	19.6485i	0.631443	+	0.728724i	0.977838	−	0.209365i	$-0.0671396\pi$
$727$	17.0256	+	19.6485i	0.631443	+	0.728724i	−0.346394	+	0.938089i	$0.612594\pi$
$728$	12.1099	+	26.5169i	0.448822	+	0.982782i
$729$	0.841254	−	0.540641i	0.0311575	−	0.0200237i
$730$	31.6415	+	9.29077i	1.17110	+	0.343867i
$731$	18.6480	−	21.5209i	0.689720	−	0.795979i
$732$	−44.4237	+	13.0440i	−1.64195	+	0.482119i
$733$	−11.4954	+	25.1715i	−0.424593	+	0.929730i	0.569580	+	0.821936i	$0.307106\pi$
$733$	−11.4954	+	25.1715i	−0.424593	+	0.929730i	−0.994173	+	0.107794i	$0.965621\pi$
$734$	−1.49247	−	10.3804i	−0.0550881	−	0.383146i
$735$	6.24865			0.230485
$736$	−12.1805	−	22.8068i	−0.448981	−	0.840668i
$737$	−53.2191			−1.96035
$738$	−3.30616	−	22.9948i	−0.121701	−	0.846452i
$739$	17.9779	−	39.3661i	0.661328	−	1.44811i	−0.219952	−	0.975511i	$-0.570590\pi$
$739$	17.9779	−	39.3661i	0.661328	−	1.44811i	0.881280	−	0.472595i	$-0.156683\pi$
$740$	35.2530	−	10.3512i	1.29592	−	0.380518i
$741$	−12.7455	+	14.7090i	−0.468216	+	0.540350i
$742$	10.7450	+	3.15501i	0.394461	+	0.115824i
$743$	−11.3363	+	7.28542i	−0.415890	+	0.267276i	−0.731809	−	0.681510i	$-0.761324\pi$
$743$	−11.3363	+	7.28542i	−0.415890	+	0.267276i	0.315919	+	0.948786i	$0.397687\pi$
$744$	7.18630	+	15.7358i	0.263463	+	0.576903i
$745$	−4.48674	−	5.17797i	−0.164381	−	0.189706i
$746$	−23.7971	−	15.2935i	−0.871275	−	0.559934i
$747$	0.764959	−	5.32040i	0.0279884	−	0.194663i
$748$	−16.0727	+	111.788i	−0.587676	+	4.08738i
$749$	−8.06843	−	5.18526i	−0.294814	−	0.189465i
$750$	1.66619	+	1.92288i	0.0608405	+	0.0702137i
$751$	0.629411	+	1.37822i	0.0229675	+	0.0502919i	0.920768	−	0.390110i	$-0.127563\pi$
$751$	0.629411	+	1.37822i	0.0229675	+	0.0502919i	−0.897801	+	0.440402i	$0.854836\pi$
$752$	22.4142	−	14.4047i	0.817362	−	0.525287i
$753$	−3.19316	−	0.937596i	−0.116365	−	0.0341679i
$754$	−23.5564	+	27.1856i	−0.857874	+	0.990039i
$755$	−5.16358	+	1.51617i	−0.187922	+	0.0551789i
$756$	−1.61088	+	3.52734i	−0.0585873	+	0.128288i
$757$	1.31335	+	9.13458i	0.0477347	+	0.332002i	0.999670	+	0.0257018i	$0.00818205\pi$
$757$	1.31335	+	9.13458i	0.0477347	+	0.332002i	−0.951935	+	0.306300i	$0.900909\pi$
$758$	−8.24205			−0.299365
$759$	−21.2491	−	21.6465i	−0.771293	−	0.785716i
$760$	−22.9242			−0.831548
$761$	−3.92480	−	27.2976i	−0.142274	−	0.989537i	−0.928430	−	0.371508i	$-0.878841\pi$
$761$	−3.92480	−	27.2976i	−0.142274	−	0.989537i	0.786156	−	0.618029i	$-0.212068\pi$
$762$	18.8633	−	41.3049i	0.683347	−	1.49632i
$763$	3.51946	−	1.03341i	0.127413	−	0.0374119i
$764$	10.5656	−	12.1933i	0.382250	−	0.441140i
$765$	−3.82972	−	1.12451i	−0.138464	−	0.0406566i
$766$	50.5265	−	32.4714i	1.82560	−	1.17324i
$767$	6.19165	+	13.5578i	0.223567	+	0.489544i
$768$	−19.1822	−	22.1375i	−0.692179	−	0.798817i
$769$	17.0558	+	10.9611i	0.615048	+	0.395267i	0.810747	−	0.585397i	$-0.199061\pi$
$769$	17.0558	+	10.9611i	0.615048	+	0.395267i	−0.195699	+	0.980664i	$0.562698\pi$
$770$	−1.98517	+	13.8071i	−0.0715404	+	0.497575i
$771$	3.38563	−	23.5476i	0.121931	−	0.848046i
$772$	85.9239	+	55.2199i	3.09247	+	1.98741i
$773$	−2.41468	−	2.78669i	−0.0868501	−	0.100230i	0.710661	−	0.703535i	$-0.248396\pi$
$773$	−2.41468	−	2.78669i	−0.0868501	−	0.100230i	−0.797511	+	0.603304i	$0.793850\pi$
$774$	−7.54074	−	16.5119i	−0.271046	−	0.593509i
$775$	−2.31227	+	1.48600i	−0.0830591	+	0.0533788i
$776$	−60.3485	−	17.7199i	−2.16639	−	0.636108i
$777$	−4.66188	+	5.38010i	−0.167244	+	0.193010i
$778$	48.0282	−	14.1023i	1.72189	−	0.505594i
$779$	−13.8154	+	30.2515i	−0.494987	+	1.08387i
$780$	3.40202	+	23.6616i	0.121812	+	0.847219i
$781$	56.6860			2.02838
$782$	−17.4422	+	45.4735i	−0.623733	+	1.62613i
$783$	−2.64583			−0.0945541
$784$	6.28382	+	43.7050i	0.224422	+	1.56089i
$785$	−7.37525	+	16.1495i	−0.263234	+	0.576402i
$786$	11.1468	−	3.27299i	0.397593	−	0.116744i
$787$	−24.2403	+	27.9747i	−0.864072	+	0.997192i	0.135907	+	0.990722i	$0.456605\pi$
$787$	−24.2403	+	27.9747i	−0.864072	+	0.997192i	−0.999979	+	0.00647043i	$0.997940\pi$
$788$	−5.73652	−	1.68440i	−0.204355	−	0.0600041i
$789$	−20.0799	+	12.9046i	−0.714864	+	0.459415i
$790$	−4.19682	−	9.18976i	−0.149316	−	0.326957i
$791$	−8.67768	−	10.0146i	−0.308543	−	0.356077i
$792$	33.4881	+	21.5215i	1.18995	+	0.764734i
$793$	7.87020	−	54.7384i	0.279479	−	1.94382i
$794$	−13.2220	+	91.9612i	−0.469232	+	3.26358i
$795$	4.27165	+	2.74523i	0.151500	+	0.0973631i
$796$	−26.1879	−	30.2225i	−0.928206	−	1.07121i
$797$	2.31930	+	5.07855i	0.0821537	+	0.179892i	0.946251	−	0.323433i	$-0.104837\pi$
$797$	2.31930	+	5.07855i	0.0821537	+	0.179892i	−0.864097	+	0.503325i	$0.832110\pi$
$798$	6.75777	−	4.34296i	0.239222	−	0.153739i
$799$	−14.4403	−	4.24005i	−0.510861	−	0.150002i
$800$	−3.53053	+	4.07445i	−0.124823	+	0.144054i
$801$	3.14946	−	0.924763i	0.111281	−	0.0326749i
$802$	39.2619	−	85.9717i	1.38639	−	3.03576i
$803$	11.6665	+	81.1426i	0.411704	+	2.86346i
$804$	37.6424			1.32755
$805$	−1.48875	+	3.88131i	−0.0524717	+	0.136798i
$806$	−37.3689			−1.31626
$807$	−0.568388	−	3.95322i	−0.0200082	−	0.139160i
$808$	4.43835	−	9.71862i	0.156141	−	0.341900i
$809$	42.0813	−	12.3562i	1.47950	−	0.434420i	0.560325	−	0.828273i	$-0.310676\pi$
$809$	42.0813	−	12.3562i	1.47950	−	0.434420i	0.919174	+	0.393852i	$0.128858\pi$
$810$	−1.66619	+	1.92288i	−0.0585438	+	0.0675632i
$811$	39.5286	+	11.6066i	1.38804	+	0.407564i	0.888559	−	0.458762i	$-0.151707\pi$
$811$	39.5286	+	11.6066i	1.38804	+	0.407564i	0.499478	+	0.866327i	$0.333525\pi$
$812$	8.63118	−	5.54692i	0.302895	−	0.194659i
$813$	−0.664382	−	1.45479i	−0.0233009	−	0.0510218i
$814$	86.5501	+	99.8841i	3.03358	+	3.50094i
$815$	8.75264	+	5.62498i	0.306591	+	0.197034i
$816$	4.01386	−	27.9170i	0.140513	−	0.977292i
$817$	−3.69819	+	25.7215i	−0.129383	+	0.899881i
$818$	−46.4035	−	29.8217i	−1.62246	−	1.04269i
$819$	−3.03315	−	3.50044i	−0.105987	−	0.122315i
$820$	16.9685	+	37.1558i	0.592565	+	1.29754i
$821$	−22.7845	+	14.6427i	−0.795185	+	0.511035i	−0.874041	−	0.485851i	$-0.838510\pi$
$821$	−22.7845	+	14.6427i	−0.795185	+	0.511035i	0.0788561	+	0.996886i	$0.474873\pi$
$822$	4.81575	+	1.41403i	0.167969	+	0.0493200i
$823$	−25.7547	+	29.7225i	−0.897753	+	1.03606i	0.101397	+	0.994846i	$0.467669\pi$
$823$	−25.7547	+	29.7225i	−0.897753	+	1.03606i	−0.999150	+	0.0412160i	$0.986877\pi$
$824$	40.9869	−	12.0348i	1.42785	−	0.419254i
$825$	−2.62745	+	5.75331i	−0.0914760	+	0.200304i
$826$	−0.875476	−	6.08907i	−0.0304617	−	0.211866i
$827$	−39.4189			−1.37073			−0.685365	−	0.728200i	$-0.740357\pi$
$827$	−39.4189			−1.37073			−0.685365	+	0.728200i	$0.740357\pi$
$828$	15.0297	+	15.3108i	0.522318	+	0.532085i
$829$	23.0539			0.800694			0.400347	−	0.916364i	$-0.368890\pi$
$829$	23.0539			0.800694			0.400347	+	0.916364i	$0.368890\pi$
$830$	1.94631	+	13.5369i	0.0675575	+	0.469873i
$831$	−0.964206	+	2.11132i	−0.0334479	+	0.0732407i
$832$	2.12895	−	0.625118i	0.0738082	−	0.0216721i
$833$	16.3328	−	18.8490i	0.565898	−	0.653081i
$834$	4.68194	+	1.37474i	0.162122	+	0.0476034i
$835$	−19.8308	+	12.7445i	−0.686273	+	0.441041i
$836$	−42.8132	−	93.7478i	−1.48072	−	3.24233i
$837$	−1.79995	−	2.07725i	−0.0622153	−	0.0718003i
$838$	−38.5999	−	24.8066i	−1.33341	−	0.856931i
$839$	2.83624	−	19.7265i	0.0979180	−	0.681035i	−0.880446	−	0.474146i	$-0.842757\pi$
$839$	2.83624	−	19.7265i	0.0979180	−	0.681035i	0.978364	−	0.206889i	$-0.0663339\pi$
$840$	0.776395	−	5.39995i	0.0267882	−	0.186316i
$841$	−18.5072	−	11.8939i	−0.638181	−	0.410134i
$842$	−16.0922	−	18.5713i	−0.554572	−	0.640011i
$843$	10.4996	+	22.9910i	0.361626	+	0.791851i
$844$	−66.3659	+	42.6508i	−2.28441	+	1.46810i
$845$	−14.9228	−	4.38174i	−0.513361	−	0.150736i
$846$	−6.28250	+	7.25039i	−0.215997	+	0.249274i
$847$	−24.1224	+	7.08298i	−0.828856	+	0.243374i
$848$	−14.9052	+	32.6379i	−0.511848	+	1.12079i
$849$	−0.236675	−	1.64611i	−0.00812266	−	0.0564943i
$850$	10.1555			0.348329
$851$	18.5553	+	34.7428i	0.636067	+	1.19097i
$852$	−40.0946			−1.37362
$853$	−3.82536	−	26.6059i	−0.130978	−	0.910970i	−0.944283	−	0.329133i	$-0.893243\pi$
$853$	−3.82536	−	26.6059i	−0.130978	−	0.910970i	0.813306	−	0.581837i	$-0.197666\pi$
$854$	−9.48174	+	20.7621i	−0.324459	+	0.710465i
$855$	3.49481	−	1.02617i	0.119520	−	0.0350942i
$856$	45.6040	−	52.6298i	1.55871	−	1.79885i
$857$	−19.0130	−	5.58271i	−0.649471	−	0.190702i	−0.0596289	−	0.998221i	$-0.518992\pi$
$857$	−19.0130	−	5.58271i	−0.649471	−	0.190702i	−0.589842	+	0.807519i	$0.700810\pi$
$858$	−72.3399	+	46.4900i	−2.46964	+	1.58714i
$859$	18.5634	+	40.6482i	0.633375	+	1.38690i	0.905380	+	0.424603i	$0.139586\pi$
$859$	18.5634	+	40.6482i	0.633375	+	1.38690i	−0.272004	+	0.962296i	$0.587687\pi$
$860$	20.9011	+	24.1211i	0.712720	+	0.822523i
$861$	−6.65804	−	4.27886i	−0.226905	−	0.145823i
$862$	−3.70626	+	25.7776i	−0.126236	+	0.877988i
$863$	6.41059	−	44.5866i	0.218219	−	1.51775i	−0.526389	−	0.850244i	$-0.676454\pi$
$863$	6.41059	−	44.5866i	0.218219	−	1.51775i	0.744608	−	0.667502i	$-0.232636\pi$
$864$	−4.53543	−	2.91474i	−0.154298	−	0.0991615i
$865$	−6.07970	−	7.01635i	−0.206716	−	0.238563i
$866$	−12.7906	−	28.0076i	−0.434644	−	0.951737i
$867$	0.899079	−	0.577803i	0.0305343	−	0.0196232i
$868$	10.2267	+	3.00283i	0.347116	+	0.101923i
$869$	16.4462	−	18.9799i	0.557898	−	0.643849i
$870$	6.45918	−	1.89659i	0.218987	−	0.0643003i
$871$	−18.6777	+	40.8984i	−0.632868	+	1.38579i
$872$	3.79033	+	26.3623i	0.128357	+	0.892740i
$873$	9.99338			0.338225
$874$	−9.04471	−	43.5147i	−0.305942	−	1.47191i
$875$	0.866803			0.0293033
$876$	−8.25187	−	57.3930i	−0.278805	−	1.93913i
$877$	−4.98425	+	10.9140i	−0.168306	+	0.368539i	−0.974925	−	0.222533i	$-0.928568\pi$
$877$	−4.98425	+	10.9140i	−0.168306	+	0.368539i	0.806619	+	0.591072i	$0.201295\pi$
$878$	−20.9915	+	6.16366i	−0.708429	+	0.208014i
$879$	6.33857	−	7.31510i	0.213795	−	0.246732i
$880$	−42.8826	−	12.5915i	−1.44557	−	0.424458i
$881$	−17.9226	+	11.5182i	−0.603828	+	0.388057i	−0.806538	−	0.591182i	$-0.798661\pi$
$881$	−17.9226	+	11.5182i	−0.603828	+	0.388057i	0.202710	+	0.979239i	$0.435025\pi$
$882$	−6.60455	−	14.4619i	−0.222387	−	0.486959i
$883$	34.4251	+	39.7287i	1.15850	+	1.33698i	0.931783	+	0.363016i	$0.118253\pi$
$883$	34.4251	+	39.7287i	1.15850	+	1.33698i	0.226715	+	0.973961i	$0.427202\pi$
$884$	80.2672	+	51.5846i	2.69968	+	1.73498i
$885$	0.396962	−	2.76093i	0.0133437	−	0.0928078i
$886$	4.51314	−	31.3896i	0.151622	−	1.05455i
$887$	0.264963	+	0.170281i	0.00889657	+	0.00571748i	0.545082	−	0.838383i	$-0.316499\pi$
$887$	0.264963	+	0.170281i	0.00889657	+	0.00571748i	−0.536185	+	0.844101i	$0.680135\pi$
$888$	−33.8496	−	39.0645i	−1.13592	−	1.31092i
$889$	−6.42635	−	14.0717i	−0.215533	−	0.471951i
$890$	−7.02579	+	4.51520i	−0.235505	+	0.151350i
$891$	−6.06867	−	1.78192i	−0.203308	−	0.0596967i
$892$	−40.6410	+	46.9023i	−1.36076	+	1.57040i
$893$	13.1775	−	3.86926i	0.440968	−	0.129480i
$894$	−7.24167	+	15.8570i	−0.242198	+	0.530339i
$895$	2.47592	+	17.2204i	0.0827607	+	0.575613i
$896$	−10.2621			−0.342834
$897$	−24.0926	+	8.73273i	−0.804429	+	0.291577i
$898$	−54.9651			−1.83421
$899$	1.03496	+	7.19829i	0.0345178	+	0.240076i
$900$	1.85842	−	4.06937i	0.0619473	−	0.135646i
$901$	19.4463	−	5.70994i	0.647849	−	0.190226i
$902$	−96.2220	+	111.046i	−3.20384	+	3.69743i
$903$	−5.93362	−	1.74227i	−0.197459	−	0.0579790i
$904$	80.9419	−	52.0182i	2.69209	−	1.73010i
$905$	−8.16012	−	17.8682i	−0.271251	−	0.593958i
$906$	8.96671	+	10.3481i	0.297899	+	0.343794i
$907$	12.6172	+	8.10861i	0.418949	+	0.269242i	0.733087	−	0.680135i	$-0.238079\pi$
$907$	12.6172	+	8.10861i	0.418949	+	0.269242i	−0.314138	+	0.949377i	$0.601715\pi$
$908$	−17.2810	+	120.192i	−0.573490	+	3.98871i
$909$	−0.241589	+	1.68029i	−0.00801300	+	0.0557316i
$910$	9.91394	+	6.37131i	0.328644	+	0.211207i
$911$	−3.30120	−	3.80979i	−0.109374	−	0.126224i	0.698423	−	0.715685i	$-0.253885\pi$
$911$	−3.30120	−	3.80979i	−0.109374	−	0.126224i	−0.807797	+	0.589461i	$0.799340\pi$
$912$	10.6918	+	23.4118i	0.354041	+	0.775242i
$913$	−28.6000	+	18.3801i	−0.946523	+	0.608293i
$914$	1.99709	+	0.586398i	0.0660578	+	0.0193963i
$915$	−6.77735	+	7.82148i	−0.224052	+	0.258570i
$916$	32.3837	−	9.50871i	1.06999	−	0.314177i
$917$	1.64413	−	3.60014i	0.0542939	−	0.118887i
$918$	1.44527	+	10.0521i	0.0477011	+	0.331768i
$919$	16.4249			0.541808			0.270904	−	0.962606i	$-0.412677\pi$
$919$	16.4249			0.541808			0.270904	+	0.962606i	$0.412677\pi$
$920$	−26.3567	−	14.7104i	−0.868954	−	0.484988i
$921$	−0.0356551			−0.00117488
$922$	−14.0981	−	98.0544i	−0.464296	−	3.22925i
$923$	19.8944	−	43.5626i	0.654832	−	1.43388i
$924$	23.5329	−	6.90989i	0.774176	−	0.227319i
$925$	5.37825	−	6.20683i	0.176836	−	0.204079i
$926$	73.0372	+	21.4456i	2.40015	+	0.704748i
$927$	−5.70976	+	3.66944i	−0.187533	+	0.120520i
$928$	5.92563	+	12.9753i	0.194518	+	0.425936i
$929$	−30.5385	−	35.2434i	−1.00194	−	1.15630i	−0.987694	−	0.156398i	$-0.950012\pi$
$929$	−30.5385	−	35.2434i	−1.00194	−	1.15630i	−0.0142429	−	0.999899i	$-0.504534\pi$
$930$	5.88319	+	3.78089i	0.192917	+	0.123980i
$931$	−3.23905	+	22.5281i	−0.106156	+	0.738329i
$932$	−3.97508	+	27.6473i	−0.130208	+	0.905616i
$933$	−2.23632	−	1.43719i	−0.0732137	−	0.0470516i
$934$	−62.9237	−	72.6178i	−2.05893	−	2.37613i
$935$	10.4872	+	22.9637i	0.342968	+	0.750995i
$936$	28.2920	−	18.1822i	0.924753	−	0.594303i
$937$	8.69638	+	2.55349i	0.284098	+	0.0834188i	0.420677	−	0.907210i	$-0.361793\pi$
$937$	8.69638	+	2.55349i	0.284098	+	0.0834188i	−0.136579	+	0.990629i	$0.543611\pi$
$938$	12.1523	−	14.0245i	0.396788	−	0.457917i
$939$	−7.89111	+	2.31704i	−0.257517	+	0.0756137i
$940$	7.00734	−	15.3439i	0.228554	−	0.500464i
$941$	−3.02038	−	21.0072i	−0.0984617	−	0.684816i	−0.977941	−	0.208880i	$-0.933018\pi$
$941$	−3.02038	−	21.0072i	−0.0984617	−	0.684816i	0.879480	−	0.475937i	$-0.157891\pi$
$942$	45.1720			1.47178
$943$	−35.2963	+	25.9158i	−1.14941	+	0.843934i
$944$	19.7100			0.641506
$945$	0.123359	+	0.857980i	0.00401287	+	0.0279101i
$946$	−47.6943	+	104.436i	−1.55067	+	3.39550i
$947$	34.4545	−	10.1168i	1.11962	−	0.328751i	0.331001	−	0.943630i	$-0.392614\pi$
$947$	34.4545	−	10.1168i	1.11962	−	0.328751i	0.788621	+	0.614880i	$0.210795\pi$
$948$	−11.6325	+	13.4247i	−0.377807	+	0.436013i
$949$	66.4518	+	19.5120i	2.15712	+	0.633387i
$950$	−7.79620	+	5.01031i	−0.252942	+	0.162556i
$951$	10.8308	+	23.7163i	0.351214	+	0.769052i
$952$	−14.2596	−	16.4564i	−0.462156	−	0.533356i
$953$	26.7084	+	17.1644i	0.865169	+	0.556010i	0.896271	−	0.443506i	$-0.146265\pi$
$953$	26.7084	+	17.1644i	0.865169	+	0.556010i	−0.0311025	+	0.999516i	$0.509902\pi$
$954$	1.83863	−	12.7879i	0.0595278	−	0.414025i
$955$	0.513255	−	3.56977i	0.0166085	−	0.115515i
$956$	44.4123	+	28.5420i	1.43640	+	0.923115i
$957$	10.9588	+	12.6471i	0.354247	+	0.408823i
$958$	−13.6927	−	29.9828i	−0.442390	−	0.968700i
$959$	1.43845	−	0.924436i	0.0464500	−	0.0298516i
$960$	−0.398421	−	0.116987i	−0.0128590	−	0.00377573i
$961$	15.3533	−	17.7187i	0.495269	−	0.571571i
$962$	107.135	−	31.4578i	3.45418	−	1.01424i
$963$	−4.59646	+	10.0649i	−0.148119	+	0.324335i
$964$	−14.1512	−	98.4241i	−0.455781	−	3.17003i
$965$	22.8310			0.734956
$966$	10.5565	−	0.656791i	0.339650	−	0.0211319i
$967$	−37.6883			−1.21197			−0.605987	−	0.795474i	$-0.707222\pi$
$967$	−37.6883			−1.21197			−0.605987	+	0.795474i	$0.707222\pi$
$968$	−25.9789	−	180.687i	−0.834994	−	5.80751i
$969$	6.03933	−	13.2243i	0.194011	−	0.424825i
$970$	−24.3966	+	7.16348i	−0.783327	+	0.230005i
$971$	−31.6312	+	36.5043i	−1.01509	+	1.17148i	−0.0299832	+	0.999550i	$0.509545\pi$
$971$	−31.6312	+	36.5043i	−1.01509	+	1.17148i	−0.985109	+	0.171929i	$0.945000\pi$
$972$	4.29243	+	1.26037i	0.137680	+	0.0404265i
$973$	1.39848	−	0.898749i	0.0448332	−	0.0288126i
$974$	9.05821	+	19.8347i	0.290244	+	0.635545i
$975$	3.49924	+	4.03834i	0.112065	+	0.129330i
$976$	−61.5213	−	39.5373i	−1.96925	−	1.26556i
$977$	4.65814	−	32.3981i	0.149027	−	1.03651i	−0.768789	−	0.639502i	$-0.779141\pi$
$977$	4.65814	−	32.3981i	0.149027	−	1.03651i	0.917817	−	0.397005i	$-0.129950\pi$
$978$	3.76736	−	26.2025i	0.120467	−	0.837865i
$979$	−17.4652	−	11.2242i	−0.558189	−	0.358726i
$980$	18.3062	+	21.1264i	0.584769	+	0.674859i
$981$	−1.75791	−	3.84928i	−0.0561257	−	0.122898i
$982$	−29.5501	+	18.9907i	−0.942980	+	0.606017i
$983$	−0.840546	−	0.246807i	−0.0268093	−	0.00787191i	0.268300	−	0.963335i	$-0.413538\pi$
$983$	−0.840546	−	0.246807i	−0.0268093	−	0.00787191i	−0.295110	+	0.955463i	$0.595356\pi$
$984$	37.6322	−	43.4299i	1.19967	−	1.38450i
$985$	−1.28229	+	0.376515i	−0.0408572	+	0.0119968i
$986$	11.1620	−	24.4414i	0.355471	−	0.778373i
$987$	0.465136	+	3.23509i	0.0148054	+	0.102974i
$988$	−87.0699			−2.77006
$989$	−20.7574	+	27.1997i	−0.660046	+	0.864901i
$990$	16.0926			0.511457
$991$	−1.53550	−	10.6796i	−0.0487767	−	0.339250i	−0.999567	−	0.0294153i	$-0.990635\pi$
$991$	−1.53550	−	10.6796i	−0.0487767	−	0.339250i	0.950791	−	0.309834i	$-0.100274\pi$
$992$	−6.15580	+	13.4793i	−0.195447	+	0.427969i
$993$	16.4917	−	4.84241i	0.523349	−	0.153669i
$994$	−12.9440	+	14.9381i	−0.410558	+	0.473809i
$995$	−8.57693	−	2.51841i	−0.271907	−	0.0798391i
$996$	20.2291	−	13.0005i	0.640983	−	0.411935i
$997$	−9.22169	−	20.1927i	−0.292054	−	0.639509i	0.705553	−	0.708658i	$-0.250699\pi$
$997$	−9.22169	−	20.1927i	−0.292054	−	0.639509i	−0.997606	+	0.0691490i	$0.977972\pi$
$998$	73.5752	+	84.9104i	2.32898	+	2.68779i
$999$	6.90906	+	4.44018i	0.218593	+	0.140481i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	345.2.m.d.256.1	yes	50
23.8	even	11	inner	345.2.m.d.31.1	✓	50
23.10	odd	22		7935.2.a.bt.1.23		25
23.13	even	11		7935.2.a.bu.1.23		25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
345.2.m.d.31.1	✓	50	23.8	even	11	inner
345.2.m.d.256.1	yes	50	1.1	even	1	trivial
7935.2.a.bt.1.23		25	23.10	odd	22
7935.2.a.bu.1.23		25	23.13	even	11

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:	\( N \)	\(=\)	\( 345 = 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	345.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.362097 - 2.51844i) q^{2} +(-0.415415 + 0.909632i) q^{3} +(-4.29243 + 1.26037i) q^{4} +(-0.654861 + 0.755750i) q^{5} +(2.44127 + 0.716822i) q^{6} +(0.729201 - 0.468629i) q^{7} +(2.61454 + 5.72503i) q^{8} +(-0.654861 - 0.755750i) q^{9} +(2.14043 + 1.37557i) q^{10} +(-0.900123 + 6.26050i) q^{11} +(0.636666 - 4.42811i) q^{12} +(4.49523 + 2.88891i) q^{13} +(-1.44426 - 1.66676i) q^{14} +(-0.415415 - 0.909632i) q^{15} +(5.94449 - 3.82029i) q^{16} +(-3.82972 - 1.12451i) q^{17} +(-1.66619 + 1.92288i) q^{18} +(3.49481 - 1.02617i) q^{19} +(1.85842 - 4.06937i) q^{20} +(0.123359 + 0.857980i) q^{21} +16.0926 q^{22} +(4.67659 + 1.06279i) q^{23} -6.29379 q^{24} +(-0.142315 - 0.989821i) q^{25} +(5.64783 - 12.3670i) q^{26} +(0.959493 - 0.281733i) q^{27} +(-2.53940 + 2.93062i) q^{28} +(-2.53865 - 0.745415i) q^{29} +(-2.14043 + 1.37557i) q^{30} +(-1.14181 - 2.50021i) q^{31} +(-3.53053 - 4.07445i) q^{32} +(-5.32082 - 3.41949i) q^{33} +(-1.44527 + 10.0521i) q^{34} +(-0.123359 + 0.857980i) q^{35} +(3.76347 + 2.41864i) q^{36} +(5.37825 + 6.20683i) q^{37} +(-3.84980 - 8.42989i) q^{38} +(-4.49523 + 2.88891i) q^{39} +(-6.03885 - 1.77317i) q^{40} +(-5.97927 + 6.90044i) q^{41} +(2.11610 - 0.621344i) q^{42} +(-2.96374 + 6.48968i) q^{43} +(-4.02683 - 28.0072i) q^{44} +1.00000 q^{45} +(0.983200 - 12.1625i) q^{46} +3.77059 q^{47} +(1.00563 + 6.99430i) q^{48} +(-2.59578 + 5.68397i) q^{49} +(-2.44127 + 0.716822i) q^{50} +(2.61381 - 3.01650i) q^{51} +(-22.9366 - 6.73478i) q^{52} +(-4.27165 + 2.74523i) q^{53} +(-1.05696 - 2.31441i) q^{54} +(-4.14191 - 4.78002i) q^{55} +(4.58944 + 2.94945i) q^{56} +(-0.518360 + 3.60528i) q^{57} +(-0.958045 + 6.66335i) q^{58} +(2.34653 + 1.50802i) q^{59} +(2.92962 + 3.38096i) q^{60} +(-4.29925 - 9.41405i) q^{61} +(-5.88319 + 3.78089i) q^{62} +(-0.831691 - 0.244207i) q^{63} +(0.271925 - 0.313818i) q^{64} +(-5.12704 + 1.50543i) q^{65} +(-6.68511 + 14.6383i) q^{66} +(1.19747 + 8.32861i) q^{67} +17.8561 q^{68} +(-2.90947 + 3.81247i) q^{69} +2.20544 q^{70} +(-1.27548 - 8.87116i) q^{71} +(2.61454 - 5.72503i) q^{72} +(12.4360 - 3.65155i) q^{73} +(13.6841 - 15.7923i) q^{74} +(0.959493 + 0.281733i) q^{75} +(-13.7079 + 8.80952i) q^{76} +(2.27748 + 4.98698i) q^{77} +(8.90324 + 10.2749i) q^{78} +(-3.34034 - 2.14671i) q^{79} +(-1.00563 + 6.99430i) q^{80} +(-0.142315 + 0.989821i) q^{81} +(19.5434 + 12.5598i) q^{82} +(3.51995 + 4.06224i) q^{83} +(-1.61088 - 3.52734i) q^{84} +(3.35778 - 2.15791i) q^{85} +(17.4170 + 5.11410i) q^{86} +(1.73265 - 1.99958i) q^{87} +(-38.1950 + 11.2150i) q^{88} +(-1.36356 + 2.98579i) q^{89} +(-0.362097 - 2.51844i) q^{90} +4.63175 q^{91} +(-21.4135 + 1.33227i) q^{92} +2.74860 q^{93} +(-1.36532 - 9.49599i) q^{94} +(-1.51309 + 3.31320i) q^{95} +(5.17289 - 1.51890i) q^{96} +(-6.54427 + 7.55249i) q^{97} +(15.2547 + 4.47917i) q^{98} +(5.32082 - 3.41949i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q + 2 q^{2} + 5 q^{3} - 4 q^{4} - 5 q^{5} + 9 q^{6} + 3 q^{7} + 6 q^{8} - 5 q^{9} + 2 q^{10} + 19 q^{11} + 4 q^{12} + 15 q^{13} + 43 q^{14} + 5 q^{15} - 76 q^{16} - 23 q^{17} + 2 q^{18} - 7 q^{19} - 4 q^{20}+ \cdots + 8 q^{99}+O(q^{100}) \) 50 * q + 2 * q^2 + 5 * q^3 - 4 * q^4 - 5 * q^5 + 9 * q^6 + 3 * q^7 + 6 * q^8 - 5 * q^9 + 2 * q^10 + 19 * q^11 + 4 * q^12 + 15 * q^13 + 43 * q^14 + 5 * q^15 - 76 * q^16 - 23 * q^17 + 2 * q^18 - 7 * q^19 - 4 * q^20 + 8 * q^21 - 42 * q^22 - 12 * q^23 - 6 * q^24 - 5 * q^25 - 2 * q^26 + 5 * q^27 + 6 * q^28 + 2 * q^29 - 2 * q^30 - 30 * q^31 - 43 * q^32 - 8 * q^33 + 102 * q^34 - 8 * q^35 - 15 * q^36 + 39 * q^37 + 19 * q^38 - 15 * q^39 - 16 * q^40 - 16 * q^41 + 23 * q^42 + 5 * q^43 + 37 * q^44 + 50 * q^45 - 40 * q^46 + 22 * q^47 - 78 * q^48 + 8 * q^49 - 9 * q^50 - 21 * q^51 + 15 * q^52 - 10 * q^53 - 2 * q^54 - 14 * q^55 - 14 * q^56 + 18 * q^57 - 26 * q^58 + 60 * q^59 + 4 * q^60 - 23 * q^61 - 36 * q^62 + 14 * q^63 - 104 * q^64 + 4 * q^65 + 20 * q^66 + 90 * q^67 - 46 * q^68 - 21 * q^69 + 10 * q^70 - 25 * q^71 + 6 * q^72 + 89 * q^73 - 31 * q^74 + 5 * q^75 - 46 * q^76 + 10 * q^77 - 9 * q^78 - 121 * q^79 + 78 * q^80 - 5 * q^81 + 10 * q^82 - 37 * q^83 - 6 * q^84 - 12 * q^85 + 172 * q^86 - 13 * q^87 - 66 * q^88 - 22 * q^89 + 2 * q^90 + 56 * q^91 - 233 * q^92 - 36 * q^93 - 5 * q^94 - 7 * q^95 + 10 * q^96 - 30 * q^97 + 8 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more