LMFDB - Embedded newform 341.2.h.a.125.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [341,2,Mod(125,341)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(341, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([2, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("341.125"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 341 = 11 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	341.h (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [60,-7] 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:	$2.72289870893$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$15$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			125.7
Character	$\chi$	$=$	341.125
Dual form			341.2.h.a.311.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.960056 - 0.697521i) q^{2} +(-0.349967 + 1.07709i) q^{3} +(-0.182863 - 0.562794i) q^{4} +(-1.04979 + 0.762717i) q^{5} +(1.08728 - 0.789956i) q^{6} +(-1.13417 - 3.49062i) q^{7} +(-0.950420 + 2.92509i) q^{8} +(1.38941 + 1.00946i) q^{9} +1.53987 q^{10} +(-3.20497 + 0.853336i) q^{11} +0.670175 q^{12} +(4.94812 + 3.59502i) q^{13} +(-1.34591 + 4.14229i) q^{14} +(-0.454122 - 1.39764i) q^{15} +(1.99529 - 1.44966i) q^{16} +(-1.97730 + 1.43659i) q^{17} +(-0.629786 - 1.93828i) q^{18} +(-1.06009 + 3.26263i) q^{19} +(0.621220 + 0.451343i) q^{20} +4.15663 q^{21} +(3.67217 + 1.41628i) q^{22} -6.88465 q^{23} +(-2.81797 - 2.04737i) q^{24} +(-1.02476 + 3.15390i) q^{25} +(-2.24287 - 6.90284i) q^{26} +(-4.32221 + 3.14027i) q^{27} +(-1.75710 + 1.27661i) q^{28} +(3.14149 + 9.66852i) q^{29} +(-0.538904 + 1.65858i) q^{30} +(-0.809017 - 0.587785i) q^{31} +3.22449 q^{32} +(0.202516 - 3.75068i) q^{33} +2.90037 q^{34} +(3.85299 + 2.79936i) q^{35} +(0.314049 - 0.966544i) q^{36} +(-0.107562 - 0.331042i) q^{37} +(3.29351 - 2.39287i) q^{38} +(-5.60384 + 4.07143i) q^{39} +(-1.23328 - 3.79563i) q^{40} +(2.24067 - 6.89608i) q^{41} +(-3.99059 - 2.89934i) q^{42} +7.12769 q^{43} +(1.06632 + 1.64769i) q^{44} -2.22852 q^{45} +(6.60964 + 4.80219i) q^{46} +(-1.69156 + 5.20608i) q^{47} +(0.863128 + 2.65644i) q^{48} +(-5.23494 + 3.80341i) q^{49} +(3.18374 - 2.31312i) q^{50} +(-0.855346 - 2.63248i) q^{51} +(1.11843 - 3.44217i) q^{52} +(-3.58335 - 2.60345i) q^{53} +6.33997 q^{54} +(2.71369 - 3.34031i) q^{55} +11.2883 q^{56} +(-3.14315 - 2.28363i) q^{57} +(3.72799 - 11.4736i) q^{58} +(0.176377 + 0.542833i) q^{59} +(-0.703543 + 0.511154i) q^{60} +(-5.80159 + 4.21510i) q^{61} +(0.366709 + 1.12861i) q^{62} +(1.94783 - 5.99479i) q^{63} +(-7.08626 - 5.14847i) q^{64} -7.93647 q^{65} +(-2.81060 + 3.45960i) q^{66} -5.96971 q^{67} +(1.17008 + 0.850112i) q^{68} +(2.40940 - 7.41538i) q^{69} +(-1.74647 - 5.37509i) q^{70} +(9.56120 - 6.94662i) q^{71} +(-4.27329 + 3.10473i) q^{72} +(-3.18464 - 9.80132i) q^{73} +(-0.127643 + 0.392845i) q^{74} +(-3.03839 - 2.20752i) q^{75} +2.03004 q^{76} +(6.61365 + 10.2195i) q^{77} +8.21991 q^{78} +(6.31070 + 4.58499i) q^{79} +(-0.988951 + 3.04368i) q^{80} +(-0.277597 - 0.854356i) q^{81} +(-6.96133 + 5.05770i) q^{82} +(-11.4977 + 8.35359i) q^{83} +(-0.760093 - 2.33932i) q^{84} +(0.980035 - 3.01624i) q^{85} +(-6.84298 - 4.97172i) q^{86} -11.5133 q^{87} +(0.549979 - 10.1858i) q^{88} +0.0753162 q^{89} +(2.13950 + 1.55444i) q^{90} +(6.93683 - 21.3494i) q^{91} +(1.25895 + 3.87464i) q^{92} +(0.916227 - 0.665678i) q^{93} +(5.25534 - 3.81823i) q^{94} +(-1.37559 - 4.23363i) q^{95} +(-1.12847 + 3.47306i) q^{96} +(-12.2408 - 8.89345i) q^{97} +7.67879 q^{98} +(-5.31442 - 2.04967i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 7 q^{2} - 2 q^{3} - 17 q^{4} - 2 q^{5} - 3 q^{6} - 3 q^{7} - 11 q^{8} - 15 q^{9} + 16 q^{10} - 9 q^{11} - 32 q^{12} + 4 q^{13} + 9 q^{14} - 12 q^{15} - 15 q^{16} - 21 q^{17} + 63 q^{18} - 11 q^{19}+ \cdots - 97 q^{99}+O(q^{100}) $ 60 * q - 7 * q^2 - 2 * q^3 - 17 * q^4 - 2 * q^5 - 3 * q^6 - 3 * q^7 - 11 * q^8 - 15 * q^9 + 16 * q^10 - 9 * q^11 - 32 * q^12 + 4 * q^13 + 9 * q^14 - 12 * q^15 - 15 * q^16 - 21 * q^17 + 63 * q^18 - 11 * q^19 - 8 * q^20 + 60 * q^21 - 5 * q^22 - 22 * q^23 + 71 * q^24 - 11 * q^25 - 42 * q^26 - 5 * q^27 - 21 * q^28 - 13 * q^29 - 16 * q^30 - 15 * q^31 + 136 * q^32 + 6 * q^33 - 42 * q^34 + 21 * q^35 - 6 * q^36 + 16 * q^37 - 36 * q^38 - 33 * q^39 + 30 * q^40 - 52 * q^41 - 56 * q^42 + 20 * q^43 + 9 * q^44 - 72 * q^45 + 56 * q^46 - 10 * q^47 - 54 * q^48 + 32 * q^49 - 81 * q^50 + 17 * q^51 - 34 * q^52 + 3 * q^53 + 140 * q^54 - 32 * q^55 - 34 * q^56 + 28 * q^57 + q^58 + 34 * q^59 + 38 * q^60 - 37 * q^61 - 2 * q^62 - 79 * q^63 - 17 * q^64 + 186 * q^65 - 70 * q^66 - 26 * q^67 + 49 * q^68 + 3 * q^69 - 20 * q^70 + 24 * q^71 - 136 * q^72 + 14 * q^73 - 51 * q^74 - 7 * q^75 + 130 * q^76 - 19 * q^77 - 32 * q^78 + 23 * q^79 + 4 * q^80 + 76 * q^81 + 27 * q^82 - 41 * q^83 + 108 * q^84 - 86 * q^85 - 39 * q^86 + 96 * q^87 - 29 * q^88 - 16 * q^89 + 208 * q^90 + 6 * q^91 - 38 * q^92 + 3 * q^93 - 98 * q^94 - 73 * q^95 - 130 * q^96 - 23 * q^97 + 80 * q^98 - 97 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/341\mathbb{Z}\right)^\times$.

$n$	$34$	$156$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$

Coefficient data

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

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

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

$2$	−0.960056	−	0.697521i	−0.678862	−	0.493222i	0.194118	−	0.980978i	$-0.437816\pi$
$2$	−0.960056	−	0.697521i	−0.678862	−	0.493222i	−0.872980	+	0.487756i	$0.837816\pi$
$3$	−0.349967	+	1.07709i	−0.202054	+	0.621858i	0.797768	+	0.602965i	$0.206014\pi$
$3$	−0.349967	+	1.07709i	−0.202054	+	0.621858i	−0.999822	+	0.0188927i	$0.993986\pi$
$4$	−0.182863	−	0.562794i	−0.0914314	−	0.281397i
$5$	−1.04979	+	0.762717i	−0.469480	+	0.341097i	−0.797239	−	0.603664i	$-0.793707\pi$
$5$	−1.04979	+	0.762717i	−0.469480	+	0.341097i	0.327758	+	0.944762i	$0.393707\pi$
$6$	1.08728	−	0.789956i	0.443881	−	0.322498i
$7$	−1.13417	−	3.49062i	−0.428676	−	1.31933i	−0.899430	−	0.437064i	$-0.856018\pi$
$7$	−1.13417	−	3.49062i	−0.428676	−	1.31933i	0.470754	−	0.882264i	$-0.343982\pi$
$8$	−0.950420	+	2.92509i	−0.336024	+	1.03418i
$9$	1.38941	+	1.00946i	0.463136	+	0.336488i
$10$	1.53987			0.486949
$11$	−3.20497	+	0.853336i	−0.966334	+	0.257290i
$11$	−3.20497	+	0.853336i	−0.966334	+	0.257290i
$12$	0.670175			0.193463
$13$	4.94812	+	3.59502i	1.37236	+	0.997080i	0.997548	+	0.0699797i	$0.0222934\pi$
$13$	4.94812	+	3.59502i	1.37236	+	0.997080i	0.374814	+	0.927100i	$0.377707\pi$
$14$	−1.34591	+	4.14229i	−0.359710	+	1.10707i
$15$	−0.454122	−	1.39764i	−0.117254	−	0.360870i
$16$	1.99529	−	1.44966i	0.498822	−	0.362415i
$17$	−1.97730	+	1.43659i	−0.479565	+	0.348424i	−0.801157	−	0.598454i	$-0.795782\pi$
$17$	−1.97730	+	1.43659i	−0.479565	+	0.348424i	0.321592	+	0.946878i	$0.395782\pi$
$18$	−0.629786	−	1.93828i	−0.148442	−	0.456858i
$19$	−1.06009	+	3.26263i	−0.243202	+	0.748500i	0.752725	+	0.658335i	$0.228739\pi$
$19$	−1.06009	+	3.26263i	−0.243202	+	0.748500i	−0.995927	+	0.0901642i	$0.971261\pi$
$20$	0.621220	+	0.451343i	0.138909	+	0.100923i
$21$	4.15663			0.907050
$22$	3.67217	+	1.41628i	0.782909	+	0.301953i
$23$	−6.88465			−1.43555			−0.717774	−	0.696276i	$-0.754839\pi$
$23$	−6.88465			−1.43555			−0.717774	+	0.696276i	$0.754839\pi$
$24$	−2.81797	−	2.04737i	−0.575215	−	0.417918i
$25$	−1.02476	+	3.15390i	−0.204953	+	0.630779i
$26$	−2.24287	−	6.90284i	−0.439863	−	1.35376i
$27$	−4.32221	+	3.14027i	−0.831810	+	0.604345i
$28$	−1.75710	+	1.27661i	−0.332061	+	0.241256i
$29$	3.14149	+	9.66852i	0.583360	+	1.79540i	0.605757	+	0.795650i	$0.292870\pi$
$29$	3.14149	+	9.66852i	0.583360	+	1.79540i	−0.0223968	+	0.999749i	$0.507130\pi$
$30$	−0.538904	+	1.65858i	−0.0983899	+	0.302813i
$31$	−0.809017	−	0.587785i	−0.145304	−	0.105569i
$31$	−0.809017	−	0.587785i	−0.145304	−	0.105569i
$32$	3.22449			0.570014
$33$	0.202516	−	3.75068i	0.0352534	−	0.652909i
$34$	2.90037			0.497409
$35$	3.85299	+	2.79936i	0.651275	+	0.473179i
$36$	0.314049	−	0.966544i	0.0523415	−	0.161091i
$37$	−0.107562	−	0.331042i	−0.0176831	−	0.0544229i	0.941826	−	0.336102i	$-0.109109\pi$
$37$	−0.107562	−	0.331042i	−0.0176831	−	0.0544229i	−0.959509	+	0.281679i	$0.909109\pi$
$38$	3.29351	−	2.39287i	0.534277	−	0.388175i
$39$	−5.60384	+	4.07143i	−0.897333	+	0.651950i
$40$	−1.23328	−	3.79563i	−0.194998	−	0.600142i
$41$	2.24067	−	6.89608i	0.349934	−	1.07699i	−0.608955	−	0.793205i	$-0.708411\pi$
$41$	2.24067	−	6.89608i	0.349934	−	1.07699i	0.958889	−	0.283781i	$-0.0915890\pi$
$42$	−3.99059	−	2.89934i	−0.615762	−	0.447377i
$43$	7.12769			1.08696			0.543482	−	0.839421i	$-0.317106\pi$
$43$	7.12769			1.08696			0.543482	+	0.839421i	$0.317106\pi$
$44$	1.06632	+	1.64769i	0.160754	+	0.248399i
$45$	−2.22852			−0.332208
$46$	6.60964	+	4.80219i	0.974539	+	0.708044i
$47$	−1.69156	+	5.20608i	−0.246739	+	0.759384i	0.748607	+	0.663014i	$0.230723\pi$
$47$	−1.69156	+	5.20608i	−0.246739	+	0.759384i	−0.995346	+	0.0963700i	$0.969277\pi$
$48$	0.863128	+	2.65644i	0.124582	+	0.383424i
$49$	−5.23494	+	3.80341i	−0.747848	+	0.543344i
$50$	3.18374	−	2.31312i	0.450249	−	0.327125i
$51$	−0.855346	−	2.63248i	−0.119772	−	0.368622i
$52$	1.11843	−	3.44217i	0.155098	−	0.477343i
$53$	−3.58335	−	2.60345i	−0.492210	−	0.357612i	0.313823	−	0.949481i	$-0.398390\pi$
$53$	−3.58335	−	2.60345i	−0.492210	−	0.357612i	−0.806034	+	0.591870i	$0.798390\pi$
$54$	6.33997			0.862760
$55$	2.71369	−	3.34031i	0.365914	−	0.450407i
$56$	11.2883			1.50846
$57$	−3.14315	−	2.28363i	−0.416320	−	0.302474i
$58$	3.72799	−	11.4736i	0.489509	−	1.50655i
$59$	0.176377	+	0.542833i	0.0229623	+	0.0706708i	0.961881	−	0.273468i	$-0.0881708\pi$
$59$	0.176377	+	0.542833i	0.0229623	+	0.0706708i	−0.938919	+	0.344139i	$0.888171\pi$
$60$	−0.703543	+	0.511154i	−0.0908270	+	0.0659897i
$61$	−5.80159	+	4.21510i	−0.742817	+	0.539688i	−0.893592	−	0.448880i	$-0.851823\pi$
$61$	−5.80159	+	4.21510i	−0.742817	+	0.539688i	0.150775	+	0.988568i	$0.451823\pi$
$62$	0.366709	+	1.12861i	0.0465721	+	0.143334i
$63$	1.94783	−	5.99479i	0.245403	−	0.755273i
$64$	−7.08626	−	5.14847i	−0.885783	−	0.643559i
$65$	−7.93647			−0.984398
$66$	−2.81060	+	3.45960i	−0.345961	+	0.425847i
$67$	−5.96971			−0.729316			−0.364658	−	0.931141i	$-0.618814\pi$
$67$	−5.96971			−0.729316			−0.364658	+	0.931141i	$0.618814\pi$
$68$	1.17008	+	0.850112i	0.141893	+	0.103091i
$69$	2.40940	−	7.41538i	0.290058	−	0.892706i
$70$	−1.74647	−	5.37509i	−0.208743	−	0.642446i
$71$	9.56120	−	6.94662i	1.13471	−	0.824412i	0.148333	−	0.988937i	$-0.452609\pi$
$71$	9.56120	−	6.94662i	1.13471	−	0.824412i	0.986373	+	0.164525i	$0.0526092\pi$
$72$	−4.27329	+	3.10473i	−0.503612	+	0.365896i
$73$	−3.18464	−	9.80132i	−0.372734	−	1.14716i	−0.944995	−	0.327086i	$-0.893933\pi$
$73$	−3.18464	−	9.80132i	−0.372734	−	1.14716i	0.572260	−	0.820072i	$-0.306067\pi$
$74$	−0.127643	+	0.392845i	−0.0148382	+	0.0456673i
$75$	−3.03839	−	2.20752i	−0.350844	−	0.254903i
$76$	2.03004			0.232862
$77$	6.61365	+	10.2195i	0.753695	+	1.16462i
$78$	8.21991			0.930721
$79$	6.31070	+	4.58499i	0.710009	+	0.515852i	0.883177	−	0.469040i	$-0.155400\pi$
$79$	6.31070	+	4.58499i	0.710009	+	0.515852i	−0.173167	+	0.984892i	$0.555400\pi$
$80$	−0.988951	+	3.04368i	−0.110568	+	0.340294i
$81$	−0.277597	−	0.854356i	−0.0308441	−	0.0949285i
$82$	−6.96133	+	5.05770i	−0.768750	+	0.558530i
$83$	−11.4977	+	8.35359i	−1.26204	+	0.916925i	−0.998856	−	0.0478203i	$-0.984773\pi$
$83$	−11.4977	+	8.35359i	−1.26204	+	0.916925i	−0.263184	+	0.964746i	$0.584773\pi$
$84$	−0.760093	−	2.33932i	−0.0829329	−	0.255241i
$85$	0.980035	−	3.01624i	0.106300	−	0.327157i
$86$	−6.84298	−	4.97172i	−0.737898	−	0.536114i
$87$	−11.5133			−1.23435
$88$	0.549979	−	10.1858i	0.0586280	−	1.08582i
$89$	0.0753162			0.00798350			0.00399175	−	0.999992i	$-0.498729\pi$
$89$	0.0753162			0.00798350			0.00399175	+	0.999992i	$0.498729\pi$
$90$	2.13950	+	1.55444i	0.225524	+	0.163852i
$91$	6.93683	−	21.3494i	0.727177	−	2.23802i
$92$	1.25895	+	3.87464i	0.131254	+	0.403959i
$93$	0.916227	−	0.665678i	0.0950083	−	0.0690276i
$94$	5.25534	−	3.81823i	0.542047	−	0.393820i
$95$	−1.37559	−	4.23363i	−0.141133	−	0.434362i
$96$	−1.12847	+	3.47306i	−0.115174	+	0.354468i
$97$	−12.2408	−	8.89345i	−1.24286	−	0.902993i	−0.245078	−	0.969503i	$-0.578814\pi$
$97$	−12.2408	−	8.89345i	−1.24286	−	0.902993i	−0.997786	+	0.0665100i	$0.978814\pi$
$98$	7.67879			0.775675
$99$	−5.31442	−	2.04967i	−0.534119	−	0.205999i
$100$	1.96239			0.196239
$101$	4.65310	+	3.38068i	0.463001	+	0.336390i	0.794707	−	0.606993i	$-0.207624\pi$
$101$	4.65310	+	3.38068i	0.463001	+	0.336390i	−0.331706	+	0.943383i	$0.607624\pi$
$102$	−1.01503	+	3.12395i	−0.100503	+	0.309318i
$103$	−3.05887	−	9.41424i	−0.301400	−	0.927613i	−0.980996	−	0.194027i	$-0.937845\pi$
$103$	−3.05887	−	9.41424i	−0.301400	−	0.927613i	0.679596	−	0.733586i	$-0.262155\pi$
$104$	−15.2186	+	11.0569i	−1.49230	+	1.08422i
$105$	−4.36358	+	3.17033i	−0.425842	+	0.309392i
$106$	1.62425	+	4.99892i	0.157761	+	0.485538i
$107$	3.88788	−	11.9657i	0.375856	−	1.15676i	−0.567044	−	0.823687i	$-0.691913\pi$
$107$	3.88788	−	11.9657i	0.375856	−	1.15676i	0.942900	−	0.333077i	$-0.108087\pi$
$108$	2.55770	+	1.85827i	0.246114	+	0.178813i
$109$	2.59825			0.248867			0.124433	−	0.992228i	$-0.460289\pi$
$109$	2.59825			0.248867			0.124433	+	0.992228i	$0.460289\pi$
$110$	−4.93523	+	1.31402i	−0.470556	+	0.125287i
$111$	0.394204			0.0374162
$112$	−7.32320	−	5.32062i	−0.691978	−	0.502751i
$113$	−4.59843	+	14.1525i	−0.432584	+	1.33136i	0.462958	+	0.886380i	$0.346788\pi$
$113$	−4.59843	+	14.1525i	−0.432584	+	1.33136i	−0.895542	+	0.444976i	$0.853212\pi$
$114$	1.42472	+	4.38483i	0.133437	+	0.410677i
$115$	7.22743	−	5.25104i	0.673962	−	0.489662i
$116$	4.86692	−	3.53603i	0.451882	−	0.328312i
$117$	3.24592	+	9.98990i	0.300085	+	0.923567i
$118$	0.209306	−	0.644176i	0.0192681	−	0.0593012i
$119$	7.25718	+	5.27265i	0.665264	+	0.483343i
$120$	4.51984			0.412603
$121$	9.54364	−	5.46983i	0.867603	−	0.497257i
$122$	8.50997			0.770456
$123$	6.64352	+	4.82680i	0.599026	+	0.435218i
$124$	−0.182863	+	0.562794i	−0.0164216	+	0.0505404i
$125$	−3.33467	−	10.2630i	−0.298262	−	0.917955i
$126$	−6.05152	+	4.39668i	−0.539112	+	0.391688i
$127$	−1.03771	+	0.753940i	−0.0920818	+	0.0669013i	−0.632874	−	0.774255i	$-0.718125\pi$
$127$	−1.03771	+	0.753940i	−0.0920818	+	0.0669013i	0.540792	+	0.841157i	$0.318125\pi$
$128$	1.21920	+	3.75230i	0.107763	+	0.331660i
$129$	−2.49446	+	7.67716i	−0.219625	+	0.675936i
$130$	7.61946	+	5.53586i	0.668271	+	0.485527i
$131$	−3.00127			−0.262222			−0.131111	−	0.991368i	$-0.541854\pi$
$131$	−3.00127			−0.262222			−0.131111	+	0.991368i	$0.541854\pi$
$132$	−2.14789	+	0.571885i	−0.186950	+	0.0497762i
$133$	12.5909			1.09177
$134$	5.73126	+	4.16400i	0.495105	+	0.359715i
$135$	2.14228	−	6.59325i	0.184378	−	0.567456i
$136$	−2.32290	−	7.14914i	−0.199187	−	0.613033i
$137$	−2.89721	+	2.10494i	−0.247525	+	0.179838i	−0.704629	−	0.709576i	$-0.748887\pi$
$137$	−2.89721	+	2.10494i	−0.247525	+	0.179838i	0.457104	+	0.889413i	$0.348887\pi$
$138$	−7.48554	+	5.43857i	−0.637212	+	0.462961i
$139$	6.58299	+	20.2604i	0.558362	+	1.71846i	0.686894	+	0.726757i	$0.258973\pi$
$139$	6.58299	+	20.2604i	0.558362	+	1.71846i	−0.128532	+	0.991705i	$0.541027\pi$
$140$	0.870895	−	2.68034i	0.0736041	−	0.226530i
$141$	−5.01542	−	3.64391i	−0.422374	−	0.306873i
$142$	−14.0247			−1.17693
$143$	−18.9263	−	7.29952i	−1.58270	−	0.610416i
$144$	4.23565			0.352971
$145$	−10.6722	−	7.75384i	−0.886282	−	0.643922i
$146$	−3.77920	+	11.6312i	−0.312769	+	0.962603i
$147$	−2.26455	−	6.96956i	−0.186777	−	0.574840i
$148$	−0.166639	+	0.121070i	−0.0136977	+	0.00995193i
$149$	8.96039	−	6.51010i	0.734064	−	0.533329i	−0.156783	−	0.987633i	$-0.550112\pi$
$149$	8.96039	−	6.51010i	0.734064	−	0.533329i	0.890846	+	0.454305i	$0.150112\pi$
$150$	1.37723	+	4.23869i	0.112451	+	0.346088i
$151$	−6.56647	+	20.2095i	−0.534372	+	1.64463i	0.210631	+	0.977566i	$0.432448\pi$
$151$	−6.56647	+	20.2095i	−0.534372	+	1.64463i	−0.745003	+	0.667061i	$0.767552\pi$
$152$	−8.53597	−	6.20174i	−0.692358	−	0.503028i
$153$	−4.19746			−0.339344
$154$	0.778839	−	14.4244i	0.0627607	−	1.16235i
$155$	1.29761			0.104227
$156$	3.31611	+	2.40929i	0.265501	+	0.192898i
$157$	0.194043	−	0.597203i	0.0154863	−	0.0476620i	−0.943015	−	0.332751i	$-0.892023\pi$
$157$	0.194043	−	0.597203i	0.0154863	−	0.0476620i	0.958501	+	0.285089i	$0.0920232\pi$
$158$	−2.86049	−	8.80370i	−0.227569	−	0.700385i
$159$	4.05820	−	2.94846i	0.321837	−	0.233828i
$160$	−3.38504	+	2.45937i	−0.267611	+	0.194430i
$161$	7.80836	+	24.0317i	0.615385	+	1.89396i
$162$	−0.329423	+	1.01386i	−0.0258819	+	0.0796563i
$163$	3.69836	+	2.68702i	0.289678	+	0.210463i	0.723128	−	0.690714i	$-0.242704\pi$
$163$	3.69836	+	2.68702i	0.289678	+	0.210463i	−0.433450	+	0.901178i	$0.642704\pi$
$164$	−4.29081			−0.335056
$165$	2.64810	+	4.09188i	0.206155	+	0.318553i
$166$	16.8653			1.30900
$167$	12.9978	+	9.44346i	1.00580	+	0.730757i	0.963324	−	0.268341i	$-0.0864754\pi$
$167$	12.9978	+	9.44346i	1.00580	+	0.730757i	0.0424760	+	0.999097i	$0.486475\pi$
$168$	−3.95054	+	12.1585i	−0.304791	+	0.938049i
$169$	7.54252	+	23.2135i	0.580194	+	1.78565i
$170$	−3.04478	+	2.21216i	−0.233524	+	0.169665i
$171$	−4.76641	+	3.46300i	−0.364497	+	0.264822i
$172$	−1.30339	−	4.01142i	−0.0993826	−	0.305868i
$173$	−2.97776	+	9.16462i	−0.226395	+	0.696773i	0.771752	+	0.635924i	$0.219381\pi$
$173$	−2.97776	+	9.16462i	−0.226395	+	0.696773i	−0.998147	+	0.0608490i	$0.980619\pi$
$174$	11.0534	+	8.03076i	0.837955	+	0.608810i
$175$	12.1713			0.920064
$176$	−5.15778	+	6.34877i	−0.388783	+	0.478556i
$177$	−0.646405			−0.0485868
$178$	−0.0723078	−	0.0525347i	−0.00541970	−	0.00393764i
$179$	4.30684	−	13.2551i	0.321908	−	0.990731i	−0.650909	−	0.759156i	$-0.725612\pi$
$179$	4.30684	−	13.2551i	0.321908	−	0.990731i	0.972817	−	0.231576i	$-0.0743880\pi$
$180$	0.407514	+	1.25420i	0.0303743	+	0.0934824i
$181$	0.829920	−	0.602972i	0.0616875	−	0.0448186i	−0.556514	−	0.830838i	$-0.687862\pi$
$181$	0.829920	−	0.602972i	0.0616875	−	0.0448186i	0.618202	+	0.786020i	$0.287862\pi$
$182$	−21.5514	+	15.6580i	−1.59749	+	1.16065i
$183$	−2.50967	−	7.72397i	−0.185520	−	0.570972i
$184$	6.54330	−	20.1382i	0.482379	−	1.48461i
$185$	0.365409	+	0.265485i	0.0268654	+	0.0195188i
$186$	−1.34395			−0.0985434
$187$	5.11128	−	6.29152i	0.373774	−	0.460082i
$188$	3.23927			0.236248
$189$	15.8636	+	11.5256i	1.15391	+	0.838362i
$190$	−1.63241	+	5.02403i	−0.118427	+	0.364481i
$191$	4.43879	+	13.6612i	0.321180	+	0.988490i	0.973136	+	0.230233i	$0.0739488\pi$
$191$	4.43879	+	13.6612i	0.321180	+	0.988490i	−0.651956	+	0.758257i	$0.726051\pi$
$192$	8.02532	−	5.83074i	0.579178	−	0.420797i
$193$	−13.0316	+	9.46799i	−0.938033	+	0.681521i	−0.947946	−	0.318430i	$-0.896844\pi$
$193$	−13.0316	+	9.46799i	−0.938033	+	0.681521i	0.00991319	+	0.999951i	$0.496844\pi$
$194$	5.54847	+	17.0764i	0.398357	+	1.22602i
$195$	2.77751	−	8.54829i	0.198901	−	0.612156i
$196$	3.09781	+	2.25069i	0.221272	+	0.160764i
$197$	14.7182			1.04863			0.524314	−	0.851525i	$-0.324322\pi$
$197$	14.7182			1.04863			0.524314	+	0.851525i	$0.324322\pi$
$198$	3.67245	+	5.67472i	0.260990	+	0.403284i
$199$	7.58154			0.537441			0.268720	−	0.963218i	$-0.413399\pi$
$199$	7.58154			0.537441			0.268720	+	0.963218i	$0.413399\pi$
$200$	−8.25148	−	5.99505i	−0.583468	−	0.423914i
$201$	2.08920	−	6.42991i	0.147361	−	0.453531i
$202$	−2.10914	−	6.49128i	−0.148399	−	0.456725i
$203$	30.1861	−	21.9315i	2.11865	−	1.53929i
$204$	−1.32514	+	0.962767i	−0.0927780	+	0.0674072i
$205$	2.90752	+	8.94843i	0.203070	+	0.624985i
$206$	−3.62995	+	11.1718i	−0.252910	+	0.778378i
$207$	−9.56558	−	6.94980i	−0.664854	−	0.483044i
$208$	15.0845			1.04592
$209$	0.613445	−	11.3613i	0.0424329	−	0.785874i
$210$	6.40066			0.441687
$211$	−15.2053	−	11.0473i	−1.04677	−	0.760526i	−0.0751781	−	0.997170i	$-0.523953\pi$
$211$	−15.2053	−	11.0473i	−1.04677	−	0.760526i	−0.971596	+	0.236644i	$0.923953\pi$
$212$	−0.809947	+	2.49276i	−0.0556274	+	0.171203i
$213$	4.13602	+	12.7294i	0.283395	+	0.872201i
$214$	−12.0789	+	8.77583i	−0.825696	+	0.599903i
$215$	−7.48258	+	5.43641i	−0.510308	+	0.370760i
$216$	−5.07766	−	15.6274i	−0.345491	−	1.06331i
$217$	−1.13417	+	3.49062i	−0.0769925	+	0.236958i
$218$	−2.49446	−	1.81233i	−0.168946	−	0.122747i
$219$	11.6714			0.788681
$220$	−2.37614	−	0.916430i	−0.160199	−	0.0617857i
$221$	−14.9485			−1.00554
$222$	−0.378458	−	0.274966i	−0.0254005	−	0.0184545i
$223$	−5.72626	+	17.6236i	−0.383459	+	1.18016i	0.554133	+	0.832428i	$0.313050\pi$
$223$	−5.72626	+	17.6236i	−0.383459	+	1.18016i	−0.937592	+	0.347737i	$0.886950\pi$
$224$	−3.65712	−	11.2555i	−0.244351	−	0.752036i
$225$	−4.60756	+	3.34759i	−0.307171	+	0.223172i
$226$	14.2864	−	10.3797i	0.950319	−	0.690447i
$227$	−4.81081	−	14.8061i	−0.319305	−	0.982719i	−0.973946	−	0.226779i	$-0.927180\pi$
$227$	−4.81081	−	14.8061i	−0.319305	−	0.982719i	0.654642	−	0.755939i	$-0.272820\pi$
$228$	−0.710449	+	2.18654i	−0.0470506	+	0.144807i
$229$	−2.85675	−	2.07555i	−0.188779	−	0.137156i	0.489381	−	0.872070i	$-0.337223\pi$
$229$	−2.85675	−	2.07555i	−0.188779	−	0.137156i	−0.678161	+	0.734914i	$0.737223\pi$
$230$	−10.6014			−0.699039
$231$	−13.3219	+	3.54700i	−0.876514	+	0.233375i
$232$	−31.2670			−2.05278
$233$	−4.60361	−	3.34472i	−0.301593	−	0.219120i	0.426688	−	0.904399i	$-0.359680\pi$
$233$	−4.60361	−	3.34472i	−0.301593	−	0.219120i	−0.728281	+	0.685279i	$0.759680\pi$
$234$	3.85191	−	11.8550i	0.251807	−	0.774983i
$235$	−2.19498	−	6.75547i	−0.143185	−	0.440678i
$236$	0.273250	−	0.198528i	0.0177871	−	0.0129231i
$237$	−7.14698	+	5.19259i	−0.464246	+	0.337295i
$238$	−3.28951	−	10.1241i	−0.213227	−	0.656246i
$239$	2.76340	−	8.50488i	0.178750	−	0.550135i	−0.821035	−	0.570878i	$-0.806603\pi$
$239$	2.76340	−	8.50488i	0.178750	−	0.550135i	0.999785	+	0.0207426i	$0.00660305\pi$
$240$	−2.93221	−	2.13038i	−0.189274	−	0.137515i
$241$	22.0465			1.42014			0.710070	−	0.704131i	$-0.248663\pi$
$241$	22.0465			1.42014			0.710070	+	0.704131i	$0.248663\pi$
$242$	−12.9777	−	1.40555i	−0.834241	−	0.0903522i
$243$	−15.0103			−0.962909
$244$	3.43313	+	2.49431i	0.219783	+	0.159682i
$245$	2.59466	−	7.98555i	0.165767	−	0.510178i
$246$	−3.01136	−	9.26800i	−0.191997	−	0.590906i
$247$	−16.9747	+	12.3329i	−1.08008	+	0.784721i
$248$	2.48823	−	1.80781i	0.158003	−	0.114796i
$249$	−4.97373	−	15.3076i	−0.315197	−	0.970077i
$250$	−3.95723	+	12.1791i	−0.250277	+	0.770274i
$251$	−4.14374	−	3.01061i	−0.261551	−	0.190028i	0.449280	−	0.893391i	$-0.351681\pi$
$251$	−4.14374	−	3.01061i	−0.261551	−	0.190028i	−0.710830	+	0.703363i	$0.751681\pi$
$252$	−3.73002			−0.234969
$253$	22.0651	−	5.87492i	1.38722	−	0.369353i
$254$	1.52215			0.0955080
$255$	2.90577	+	2.11117i	0.181967	+	0.132207i
$256$	−3.96661	+	12.2080i	−0.247913	+	0.762998i
$257$	−5.68917	−	17.5095i	−0.354881	−	1.09221i	−0.956079	−	0.293110i	$-0.905310\pi$
$257$	−5.68917	−	17.5095i	−0.354881	−	1.09221i	0.601198	−	0.799100i	$-0.294690\pi$
$258$	7.74981	−	5.63056i	0.482482	−	0.350544i
$259$	−1.03355	+	0.750915i	−0.0642214	+	0.0466596i
$260$	1.45129	+	4.46660i	0.0900050	+	0.277007i
$261$	−5.39521	+	16.6047i	−0.333955	+	1.02781i
$262$	2.88139	+	2.09345i	0.178013	+	0.129334i
$263$	−14.1228			−0.870852			−0.435426	−	0.900225i	$-0.643402\pi$
$263$	−14.1228			−0.870852			−0.435426	+	0.900225i	$0.643402\pi$
$264$	10.7786	+	4.15709i	0.663376	+	0.255851i
$265$	5.74746			0.353064
$266$	−12.0880	−	8.78244i	−0.741163	−	0.538486i
$267$	−0.0263582	+	0.0811222i	−0.00161310	+	0.00496460i
$268$	1.09164	+	3.35972i	0.0666824	+	0.205227i
$269$	−7.28530	+	5.29308i	−0.444192	+	0.322725i	−0.787299	−	0.616572i	$-0.788521\pi$
$269$	−7.28530	+	5.29308i	−0.444192	+	0.322725i	0.343106	+	0.939297i	$0.388521\pi$
$270$	−6.65563	+	4.83560i	−0.405049	+	0.294285i
$271$	−0.218218	−	0.671605i	−0.0132558	−	0.0407971i	0.944210	−	0.329344i	$-0.106828\pi$
$271$	−0.218218	−	0.671605i	−0.0132558	−	0.0407971i	−0.957466	+	0.288547i	$0.906828\pi$
$272$	−1.86271	+	5.73282i	−0.112943	+	0.347603i
$273$	20.5675	+	14.9432i	1.24480	+	0.904401i
$274$	4.24972			0.256735
$275$	0.593000	−	10.9826i	0.0357592	−	0.662276i
$276$	−4.61392			−0.277725
$277$	−14.6655	−	10.6551i	−0.881166	−	0.640205i	0.0523937	−	0.998627i	$-0.483315\pi$
$277$	−14.6655	−	10.6551i	−0.881166	−	0.640205i	−0.933560	+	0.358422i	$0.883315\pi$
$278$	7.81200	−	24.0429i	0.468533	−	1.44200i
$279$	−0.530706	−	1.63335i	−0.0317726	−	0.0977859i
$280$	−11.8504	+	8.60978i	−0.708194	+	0.514533i
$281$	15.2225	−	11.0598i	0.908100	−	0.659773i	−0.0324334	−	0.999474i	$-0.510326\pi$
$281$	15.2225	−	11.0598i	0.908100	−	0.659773i	0.940534	+	0.339700i	$0.110326\pi$
$282$	2.27337	+	6.99672i	0.135377	+	0.416649i
$283$	−2.27547	+	7.00317i	−0.135262	+	0.416295i	−0.995631	−	0.0933777i	$-0.970234\pi$
$283$	−2.27547	+	7.00317i	−0.135262	+	0.416295i	0.860368	+	0.509673i	$0.170234\pi$
$284$	−5.65791	−	4.11071i	−0.335735	−	0.243926i
$285$	5.04141			0.298627
$286$	13.0788	+	20.2095i	0.773364	+	1.19501i
$287$	−26.6129			−1.57091
$288$	4.48013	+	3.25500i	0.263994	+	0.191803i
$289$	−3.40738	+	10.4868i	−0.200434	+	0.616872i
$290$	4.83748	+	14.8882i	0.284067	+	0.874268i
$291$	13.8629	−	10.0720i	0.812659	−	0.590431i
$292$	−4.93377	+	3.58460i	−0.288727	+	0.209773i
$293$	8.39564	+	25.8391i	0.490479	+	1.50954i	0.823886	+	0.566755i	$0.191802\pi$
$293$	8.39564	+	25.8391i	0.490479	+	1.50954i	−0.333408	+	0.942783i	$0.608198\pi$
$294$	−2.68733	+	8.27074i	−0.156728	+	0.482359i
$295$	−0.599187	−	0.435334i	−0.0348860	−	0.0253462i
$296$	1.07056			0.0622248
$297$	11.1728	−	13.7528i	0.648314	−	0.798016i
$298$	−13.1434			−0.761377
$299$	−34.0661	−	24.7505i	−1.97009	−	1.43136i
$300$	−0.686771	+	2.11366i	−0.0396507	+	0.122032i
$301$	−8.08402	−	24.8800i	−0.465955	−	1.43406i
$302$	20.4007	−	14.8220i	1.17393	−	0.852911i
$303$	−5.26972	+	3.82868i	−0.302738	+	0.219952i
$304$	2.61452	+	8.04667i	0.149953	+	0.461508i
$305$	2.87552	−	8.84994i	0.164652	−	0.506746i
$306$	4.02979	+	2.92782i	0.230368	+	0.167372i
$307$	30.8870			1.76282			0.881408	−	0.472356i	$-0.156596\pi$
$307$	30.8870			1.76282			0.881408	+	0.472356i	$0.156596\pi$
$308$	4.54207	−	5.59088i	0.258809	−	0.318570i
$309$	11.2105			0.637742
$310$	−1.24578	−	0.905112i	−0.0707555	−	0.0514069i
$311$	2.45909	−	7.56830i	0.139442	−	0.429159i	−0.856812	−	0.515628i	$-0.827559\pi$
$311$	2.45909	−	7.56830i	0.139442	−	0.429159i	0.996254	+	0.0864696i	$0.0275585\pi$
$312$	−6.58330	−	20.2613i	−0.372706	−	1.14707i
$313$	19.3218	−	14.0381i	1.09213	−	0.793480i	0.112374	−	0.993666i	$-0.464154\pi$
$313$	19.3218	−	14.0381i	1.09213	−	0.793480i	0.979758	+	0.200186i	$0.0641545\pi$
$314$	−0.602854	+	0.437999i	−0.0340210	+	0.0247177i
$315$	2.52752	+	7.77891i	0.142410	+	0.438292i
$316$	1.42641	−	4.39005i	0.0802420	−	0.246960i
$317$	−0.410862	−	0.298509i	−0.0230763	−	0.0167659i	0.576187	−	0.817318i	$-0.304540\pi$
$317$	−0.410862	−	0.298509i	−0.0230763	−	0.0167659i	−0.599264	+	0.800552i	$0.704540\pi$
$318$	−5.95272			−0.333812
$319$	−18.3189	−	28.3065i	−1.02566	−	1.58486i
$320$	11.3659			0.635374
$321$	11.5275	+	8.37519i	0.643400	+	0.467457i
$322$	9.26613	−	28.5182i	0.516381	−	1.58926i
$323$	−2.59095	−	7.97412i	−0.144164	−	0.443692i
$324$	−0.430064	+	0.312460i	−0.0238925	+	0.0173589i
$325$	−16.4090	+	11.9218i	−0.910207	+	0.661304i
$326$	−1.67638	−	5.15937i	−0.0928462	−	0.285751i
$327$	−0.909301	+	2.79854i	−0.0502845	+	0.154760i
$328$	18.0421	+	13.1083i	0.996207	+	0.723787i
$329$	20.0909			1.10765
$330$	0.311847	−	5.77555i	0.0171666	−	0.317933i
$331$	21.8183			1.19924			0.599621	−	0.800284i	$-0.295318\pi$
$331$	21.8183			1.19924			0.599621	+	0.800284i	$0.295318\pi$
$332$	6.80386	+	4.94329i	0.373410	+	0.271298i
$333$	0.184727	−	0.568532i	0.0101230	−	0.0311553i
$334$	−5.89160	−	18.1325i	−0.322374	−	0.992166i
$335$	6.26694	−	4.55320i	0.342400	−	0.248768i
$336$	8.29366	−	6.02570i	0.452456	−	0.328729i
$337$	−3.91275	−	12.0422i	−0.213141	−	0.655981i	−0.999280	−	0.0379317i	$-0.987923\pi$
$337$	−3.91275	−	12.0422i	−0.213141	−	0.655981i	0.786139	−	0.618050i	$-0.212077\pi$
$338$	8.95067	−	27.5473i	0.486852	−	1.49838i
$339$	−13.6342	−	9.90584i	−0.740509	−	0.538011i
$340$	−1.87673			−0.101780
$341$	3.09445	+	1.19347i	0.167574	+	0.0646300i
$342$	6.99154			0.378059
$343$	−1.57153	−	1.14178i	−0.0848546	−	0.0616505i
$344$	−6.77430	+	20.8492i	−0.365246	+	1.12411i
$345$	3.12647	+	9.62228i	0.168323	+	0.518046i
$346$	9.25134	−	6.72149i	0.497355	−	0.361350i
$347$	17.7621	−	12.9049i	0.953518	−	0.692771i	0.00188136	−	0.999998i	$-0.499401\pi$
$347$	17.7621	−	12.9049i	0.953518	−	0.692771i	0.951636	+	0.307227i	$0.0994011\pi$
$348$	2.10535	+	6.47960i	0.112859	+	0.347343i
$349$	4.13356	−	12.7218i	0.221265	−	0.680983i	−0.777385	−	0.629025i	$-0.783454\pi$
$349$	4.13356	−	12.7218i	0.221265	−	0.680983i	0.998649	−	0.0519571i	$-0.0165459\pi$
$350$	−11.6851	−	8.48974i	−0.624596	−	0.453796i
$351$	−32.6762			−1.74412
$352$	−10.3344	+	2.75157i	−0.550824	+	0.146659i
$353$	2.81075			0.149601			0.0748005	−	0.997199i	$-0.476168\pi$
$353$	2.81075			0.149601			0.0748005	+	0.997199i	$0.476168\pi$
$354$	0.620585	+	0.450882i	0.0329837	+	0.0239641i
$355$	−4.73895	+	14.5850i	−0.251517	+	0.774091i
$356$	−0.0137725	−	0.0423875i	−0.000729943	−	0.00224653i
$357$	−8.21888	+	5.97137i	−0.434989	+	0.316038i
$358$	−13.3805	+	9.72151i	−0.707182	+	0.513798i
$359$	4.31718	+	13.2869i	0.227852	+	0.701257i	0.997990	+	0.0633789i	$0.0201877\pi$
$359$	4.31718	+	13.2869i	0.227852	+	0.701257i	−0.770137	+	0.637878i	$0.779812\pi$
$360$	2.11803	−	6.51863i	0.111630	−	0.343562i
$361$	5.85034	+	4.25052i	0.307913	+	0.223712i
$362$	−1.21736			−0.0639828
$363$	2.55153	+	12.1936i	0.133921	+	0.639998i
$364$	−13.2838			−0.696259
$365$	10.8188	+	7.86035i	0.566284	+	0.411429i
$366$	−2.97821	+	9.16599i	−0.155674	+	0.479114i
$367$	8.06673	+	24.8268i	0.421080	+	1.29595i	0.906698	+	0.421780i	$0.138594\pi$
$367$	8.06673	+	24.8268i	0.421080	+	1.29595i	−0.485618	+	0.874171i	$0.661406\pi$
$368$	−13.7368	+	9.98040i	−0.716083	+	0.520265i
$369$	10.0745	−	7.31958i	0.524460	−	0.381042i
$370$	−0.165631	−	0.509761i	−0.00861076	−	0.0265012i
$371$	−5.02353	+	15.4608i	−0.260809	+	0.802687i
$372$	−0.542183	−	0.393919i	−0.0281109	−	0.0204238i
$373$	23.8199			1.23335			0.616675	−	0.787218i	$-0.288479\pi$
$373$	23.8199			1.23335			0.616675	+	0.787218i	$0.288479\pi$
$374$	−9.29559	+	2.47499i	−0.480663	+	0.127979i
$375$	12.2212			0.631102
$376$	−13.6206	−	9.89592i	−0.702427	−	0.510343i
$377$	−19.2140	+	59.1348i	−0.989574	+	3.04559i
$378$	−7.19060	−	22.1304i	−0.369845	−	1.13826i
$379$	16.2396	−	11.7987i	0.834171	−	0.606061i	−0.0865652	−	0.996246i	$-0.527589\pi$
$379$	16.2396	−	11.7987i	0.834171	−	0.606061i	0.920736	+	0.390185i	$0.127589\pi$
$380$	−2.13112	+	1.54835i	−0.109324	+	0.0794286i
$381$	−0.448896	−	1.38156i	−0.0229976	−	0.0707794i
$382$	5.26749	−	16.2117i	0.269508	−	0.829461i
$383$	9.83816	+	7.14784i	0.502706	+	0.365238i	0.810050	−	0.586361i	$-0.199440\pi$
$383$	9.83816	+	7.14784i	0.502706	+	0.365238i	−0.307343	+	0.951599i	$0.599440\pi$
$384$	−4.46824			−0.228019
$385$	−14.7375	−	5.68397i	−0.751093	−	0.289682i
$386$	19.1152			0.972936
$387$	9.90327	+	7.19515i	0.503412	+	0.365750i
$388$	−2.76680	+	8.51532i	−0.140463	+	0.432300i
$389$	6.05934	+	18.6487i	0.307221	+	0.945529i	0.978839	+	0.204631i	$0.0655996\pi$
$389$	6.05934	+	18.6487i	0.307221	+	0.945529i	−0.671618	+	0.740897i	$0.734400\pi$
$390$	−8.62918	+	6.26946i	−0.436955	+	0.317467i
$391$	13.6130	−	9.89042i	0.688438	−	0.500180i
$392$	−6.14992	−	18.9275i	−0.310618	−	0.955983i
$393$	1.05035	−	3.23264i	0.0529830	−	0.163065i
$394$	−14.1303	−	10.2663i	−0.711874	−	0.517207i
$395$	−10.1220			−0.509291
$396$	−0.181731	+	3.36573i	−0.00913231	+	0.169134i
$397$	−5.68717			−0.285431			−0.142715	−	0.989764i	$-0.545583\pi$
$397$	−5.68717			−0.285431			−0.142715	+	0.989764i	$0.545583\pi$
$398$	−7.27870	−	5.28828i	−0.364848	−	0.265078i
$399$	−4.40642	+	13.5616i	−0.220597	+	0.678927i
$400$	2.52738	+	7.77849i	0.126369	+	0.388925i
$401$	19.7691	−	14.3631i	0.987223	−	0.717260i	0.0279118	−	0.999610i	$-0.491114\pi$
$401$	19.7691	−	14.3631i	0.987223	−	0.717260i	0.959311	+	0.282351i	$0.0911142\pi$
$402$	−6.49075	+	4.71581i	−0.323729	+	0.235203i
$403$	−1.89001	−	5.81687i	−0.0941483	−	0.289759i
$404$	1.05175	−	3.23694i	0.0523263	−	0.161044i
$405$	0.943051	+	0.685166i	0.0468606	+	0.0340462i
$406$	−44.2780			−2.19748
$407$	0.627222	+	0.969191i	0.0310903	+	0.0480410i
$408$	8.51319			0.421466
$409$	−10.1249	−	7.35619i	−0.500646	−	0.363740i	0.308618	−	0.951186i	$-0.400134\pi$
$409$	−10.1249	−	7.35619i	−0.500646	−	0.363740i	−0.809264	+	0.587446i	$0.800134\pi$
$410$	3.45034	−	10.6190i	0.170400	−	0.524437i
$411$	−1.25328	−	3.85721i	−0.0618199	−	0.190262i
$412$	−4.73893	+	3.44303i	−0.233470	+	0.169626i
$413$	1.69478	−	1.23133i	0.0833946	−	0.0605897i
$414$	4.33586	+	13.3444i	0.213096	+	0.655841i
$415$	5.69877	−	17.5390i	0.279742	−	0.860957i
$416$	15.9552	+	11.5921i	0.782266	+	0.568350i
$417$	−24.1261			−1.18146
$418$	−8.51366	+	10.4795i	−0.416417	+	0.512571i
$419$	−5.20715			−0.254386			−0.127193	−	0.991878i	$-0.540597\pi$
$419$	−5.20715			−0.254386			−0.127193	+	0.991878i	$0.540597\pi$
$420$	2.58218	+	1.87606i	0.125997	+	0.0915425i
$421$	−2.41667	+	7.43775i	−0.117781	+	0.362494i	−0.992517	−	0.122107i	$-0.961035\pi$
$421$	−2.41667	+	7.43775i	−0.117781	+	0.362494i	0.874736	+	0.484601i	$0.161035\pi$
$422$	6.89220	+	21.2120i	0.335507	+	1.03258i
$423$	−7.60561	+	5.52580i	−0.369797	+	0.268673i
$424$	11.0210	−	8.00724i	0.535228	−	0.388866i
$425$	−2.50460	−	7.70836i	−0.121491	−	0.373910i
$426$	4.90819	−	15.1059i	0.237803	−	0.731881i
$427$	21.2933	+	15.4705i	1.03045	+	0.748668i
$428$	−7.44515			−0.359875
$429$	14.4858	−	17.8308i	0.699383	−	0.860877i
$430$	10.9757			0.529296
$431$	−2.53253	−	1.83999i	−0.121987	−	0.0886291i	0.525119	−	0.851029i	$-0.324021\pi$
$431$	−2.53253	−	1.83999i	−0.121987	−	0.0886291i	−0.647106	+	0.762400i	$0.724021\pi$
$432$	−4.07172	+	12.5315i	−0.195901	+	0.602921i
$433$	5.79536	+	17.8363i	0.278507	+	0.857157i	0.988270	+	0.152716i	$0.0488020\pi$
$433$	5.79536	+	17.8363i	0.278507	+	0.857157i	−0.709763	+	0.704440i	$0.751198\pi$
$434$	3.52365	−	2.56008i	0.169140	−	0.122888i
$435$	12.0865	−	8.78137i	0.579504	−	0.421034i
$436$	−0.475123	−	1.46228i	−0.0227542	−	0.0700304i
$437$	7.29837	−	22.4621i	0.349129	−	1.07451i
$438$	−11.2052	−	8.14106i	−0.535406	−	0.388995i
$439$	−29.6733			−1.41623			−0.708115	−	0.706097i	$-0.750454\pi$
$439$	−29.6733			−1.41623			−0.708115	+	0.706097i	$0.750454\pi$
$440$	7.19156	+	11.1125i	0.342844	+	0.529767i
$441$	−11.1129			−0.529184
$442$	14.3514	+	10.4269i	0.682625	+	0.495956i
$443$	2.64761	−	8.14851i	0.125792	−	0.387148i	−0.868253	−	0.496122i	$-0.834757\pi$
$443$	2.64761	−	8.14851i	0.125792	−	0.387148i	0.994045	+	0.108975i	$0.0347568\pi$
$444$	−0.0720853	−	0.221856i	−0.00342102	−	0.0105288i
$445$	−0.0790662	+	0.0574449i	−0.00374810	+	0.00272315i
$446$	17.7904	−	12.9255i	0.842399	−	0.612039i
$447$	3.87612	+	11.9295i	0.183334	+	0.564244i
$448$	−9.93431	+	30.5747i	−0.469352	+	1.44452i
$449$	−22.3841	−	16.2630i	−1.05637	−	0.767500i	−0.0829590	−	0.996553i	$-0.526437\pi$
$449$	−22.3841	−	16.2630i	−1.05637	−	0.767500i	−0.973414	+	0.229053i	$0.926437\pi$
$450$	6.75853			0.318600
$451$	−1.29661	+	24.0137i	−0.0610549	+	1.13076i
$452$	8.80583			0.414191
$453$	−19.4694	−	14.1453i	−0.914752	−	0.664606i
$454$	−5.70896	+	17.5704i	−0.267935	+	0.824618i
$455$	9.00131	+	27.7032i	0.421988	+	1.29875i
$456$	9.66714	−	7.02359i	0.452705	−	0.328910i
$457$	9.53371	−	6.92665i	0.445968	−	0.324015i	−0.342034	−	0.939688i	$-0.611116\pi$
$457$	9.53371	−	6.92665i	0.445968	−	0.324015i	0.788002	+	0.615673i	$0.211116\pi$
$458$	1.29490	+	3.98529i	0.0605066	+	0.186220i
$459$	4.03501	−	12.4185i	0.188338	−	0.579645i
$460$	−4.27688	−	3.10734i	−0.199411	−	0.144880i
$461$	12.2033			0.568364			0.284182	−	0.958770i	$-0.408278\pi$
$461$	12.2033			0.568364			0.284182	+	0.958770i	$0.408278\pi$
$462$	15.2638	+	5.88696i	0.710138	+	0.273886i
$463$	2.42916			0.112893			0.0564463	−	0.998406i	$-0.482023\pi$
$463$	2.42916			0.112893			0.0564463	+	0.998406i	$0.482023\pi$
$464$	20.2843	+	14.7374i	0.941673	+	0.684165i
$465$	−0.454122	+	1.39764i	−0.0210594	+	0.0648142i
$466$	2.08671	+	6.42224i	0.0966651	+	0.297504i
$467$	−22.7818	+	16.5519i	−1.05422	+	0.765932i	−0.973010	−	0.230765i	$-0.925877\pi$
$467$	−22.7818	+	16.5519i	−1.05422	+	0.765932i	−0.0812061	+	0.996697i	$0.525877\pi$
$468$	5.02870	−	3.65356i	0.232452	−	0.168886i
$469$	6.77067	+	20.8380i	0.312640	+	0.962208i
$470$	−2.60478	+	8.01667i	−0.120149	+	0.369782i
$471$	0.575332	+	0.418003i	0.0265099	+	0.0192606i
$472$	−1.75547			−0.0808019
$473$	−22.8440	+	6.08232i	−1.05037	+	0.279665i
$474$	10.4834			0.481521
$475$	−9.20367	−	6.68686i	−0.422293	−	0.306814i
$476$	1.64035	−	5.04847i	0.0751851	−	0.231396i
$477$	−2.35064	−	7.23451i	−0.107628	−	0.331246i
$478$	−8.58536	+	6.23763i	−0.392685	+	0.285302i
$479$	−1.28150	+	0.931064i	−0.0585532	+	0.0425414i	−0.616677	−	0.787216i	$-0.711521\pi$
$479$	−1.28150	+	0.931064i	−0.0585532	+	0.0425414i	0.558124	+	0.829758i	$0.311521\pi$
$480$	−1.46431	−	4.50668i	−0.0668363	−	0.205701i
$481$	0.657872	−	2.02472i	0.0299964	−	0.0923194i
$482$	−21.1659	−	15.3779i	−0.964080	−	0.700445i
$483$	−28.6169			−1.30211
$484$	−4.82356	−	4.37087i	−0.219253	−	0.198676i
$485$	19.6334			0.891509
$486$	14.4107	+	10.4700i	0.653682	+	0.474928i
$487$	6.09320	−	18.7530i	0.276109	−	0.849777i	−0.712814	−	0.701353i	$-0.752580\pi$
$487$	6.09320	−	18.7530i	0.276109	−	0.849777i	0.988924	−	0.148425i	$-0.0474202\pi$
$488$	−6.81561	−	20.9763i	−0.308528	−	0.949552i
$489$	−4.18846	+	3.04310i	−0.189409	+	0.137614i
$490$	−8.06112	+	5.85674i	−0.364164	+	0.264581i
$491$	−5.87509	−	18.0817i	−0.265139	−	0.816014i	−0.991661	−	0.128871i	$-0.958865\pi$
$491$	−5.87509	−	18.0817i	−0.265139	−	0.816014i	0.726522	−	0.687143i	$-0.241135\pi$
$492$	1.50164	−	4.62158i	0.0676992	−	0.208357i
$493$	−20.1014	−	14.6045i	−0.905320	−	0.657753i
$494$	24.8991			1.12026
$495$	7.14234	−	1.90168i	0.321024	−	0.0854740i
$496$	−2.46631			−0.110741
$497$	−35.0920	−	25.4958i	−1.57409	−	1.14364i
$498$	−5.90229	+	18.1654i	−0.264488	+	0.814011i
$499$	10.4079	+	32.0324i	0.465924	+	1.43397i	0.857817	+	0.513955i	$0.171820\pi$
$499$	10.4079	+	32.0324i	0.465924	+	1.43397i	−0.391893	+	0.920011i	$0.628180\pi$
$500$	−5.16619	+	3.75346i	−0.231039	+	0.167860i
$501$	−14.7202	+	10.6949i	−0.657652	+	0.477812i
$502$	1.87826	+	5.78070i	0.0838310	+	0.258005i
$503$	−3.02458	+	9.30871i	−0.134860	+	0.415055i	−0.995568	−	0.0940430i	$-0.970021\pi$
$503$	−3.02458	+	9.30871i	−0.134860	+	0.415055i	0.860709	+	0.509098i	$0.170021\pi$
$504$	15.6841	+	11.3951i	0.698623	+	0.507580i
$505$	−7.46328			−0.332112
$506$	−25.2816	−	9.75061i	−1.12390	−	0.433468i
$507$	−27.6426			−1.22765
$508$	0.614071	+	0.446149i	0.0272450	+	0.0197947i
$509$	−9.09318	+	27.9859i	−0.403048	+	1.24046i	0.519466	+	0.854491i	$0.326131\pi$
$509$	−9.09318	+	27.9859i	−0.403048	+	1.24046i	−0.922514	+	0.385964i	$0.873869\pi$
$510$	−1.31712	−	4.05368i	−0.0583231	−	0.179500i
$511$	−30.6007	+	22.2327i	−1.35370	+	0.983518i
$512$	18.7073	−	13.5916i	0.826753	−	0.600671i
$513$	−5.66360	−	17.4308i	−0.250054	−	0.769587i
$514$	−6.75130	+	20.7784i	−0.297787	+	0.916495i
$515$	10.3916	+	7.54992i	0.457908	+	0.332689i
$516$	4.77680			0.210287
$517$	0.978853	−	18.1288i	0.0430499	−	0.797303i
$518$	1.51604			0.0666110
$519$	−8.82899	−	6.41463i	−0.387550	−	0.281571i
$520$	7.54298	−	23.2149i	0.330782	−	1.01804i
$521$	5.69312	+	17.5216i	0.249420	+	0.767637i	0.994878	+	0.101084i	$0.0322310\pi$
$521$	5.69312	+	17.5216i	0.249420	+	0.767637i	−0.745458	+	0.666553i	$0.767769\pi$
$522$	16.7619	−	12.1782i	0.733646	−	0.533025i
$523$	2.13197	−	1.54897i	0.0932246	−	0.0677316i	−0.540197	−	0.841539i	$-0.681650\pi$
$523$	2.13197	−	1.54897i	0.0932246	−	0.0677316i	0.633421	+	0.773807i	$0.281650\pi$
$524$	0.548821	+	1.68910i	0.0239754	+	0.0737886i
$525$	−4.25956	+	13.1096i	−0.185902	+	0.572149i
$526$	13.5587	+	9.85099i	0.591188	+	0.429524i
$527$	2.44407			0.106466
$528$	−5.03313	−	7.77725i	−0.219039	−	0.338462i
$529$	24.3984			1.06080
$530$	−5.51788	−	4.00897i	−0.239681	−	0.174139i
$531$	−0.302910	+	0.932262i	−0.0131452	+	0.0404567i
$532$	−2.30241	−	7.08610i	−0.0998223	−	0.307221i
$533$	35.8787	−	26.0674i	1.55408	−	1.12910i
$534$	0.0818899	−	0.0594965i	0.00354372	−	0.00257466i
$535$	5.04496	+	15.5268i	0.218113	+	0.671281i
$536$	5.67373	−	17.4620i	0.245068	−	0.754241i
$537$	12.7697	+	9.27769i	0.551051	+	0.400362i
$538$	10.6863			0.460720
$539$	13.5322	−	16.6570i	0.582874	−	0.717466i
$540$	−4.10238			−0.176538
$541$	−2.82217	−	2.05042i	−0.121334	−	0.0881546i	0.525463	−	0.850816i	$-0.323892\pi$
$541$	−2.82217	−	2.05042i	−0.121334	−	0.0881546i	−0.646797	+	0.762662i	$0.723892\pi$
$542$	−0.258958	+	0.796990i	−0.0111232	+	0.0342336i
$543$	0.359010	+	1.10492i	0.0154066	+	0.0474166i
$544$	−6.37577	+	4.63227i	−0.273359	+	0.198607i
$545$	−2.72761	+	1.98173i	−0.116838	+	0.0848878i
$546$	−9.32277	−	28.6925i	−0.398978	−	1.22793i
$547$	−8.86252	+	27.2760i	−0.378934	+	1.16624i	0.561852	+	0.827238i	$0.310089\pi$
$547$	−8.86252	+	27.2760i	−0.378934	+	1.16624i	−0.940786	+	0.339001i	$0.889911\pi$
$548$	1.71444	+	1.24561i	0.0732373	+	0.0532100i
$549$	−12.3158			−0.525624
$550$	−8.22992	+	10.1303i	−0.350925	+	0.431957i
$551$	−34.8751			−1.48573
$552$	19.4007	+	14.0954i	0.825749	+	0.599942i
$553$	8.84704	−	27.2284i	0.376214	−	1.15787i
$554$	6.64754	+	20.4590i	0.282427	+	0.869221i
$555$	−0.413832	+	0.300666i	−0.0175662	+	0.0127626i
$556$	10.1986	−	7.40974i	0.432518	−	0.314243i
$557$	−10.8073	−	33.2615i	−0.457921	−	1.40934i	−0.867672	−	0.497138i	$-0.834384\pi$
$557$	−10.8073	−	33.2615i	−0.457921	−	1.40934i	0.409751	−	0.912197i	$-0.365616\pi$
$558$	−0.629786	+	1.93828i	−0.0266610	+	0.0820541i
$559$	35.2687	+	25.6242i	1.49171	+	1.08379i
$560$	11.7460			0.496357
$561$	4.98775	+	7.70713i	0.210583	+	0.325395i
$562$	−22.3289			−0.941890
$563$	3.22535	+	2.34335i	0.135932	+	0.0987605i	0.653673	−	0.756777i	$-0.273227\pi$
$563$	3.22535	+	2.34335i	0.135932	+	0.0987605i	−0.517741	+	0.855537i	$0.673227\pi$
$564$	−1.13364	+	3.48898i	−0.0477348	+	0.146913i
$565$	−5.96698	−	18.3645i	−0.251033	−	0.772599i
$566$	7.06944	−	5.13625i	0.297151	−	0.215893i
$567$	−2.66739	+	1.93797i	−0.112020	+	0.0813871i
$568$	11.2323	+	34.5696i	0.471299	+	1.45051i
$569$	12.6302	−	38.8719i	0.529487	−	1.62959i	−0.225782	−	0.974178i	$-0.572494\pi$
$569$	12.6302	−	38.8719i	0.529487	−	1.62959i	0.755269	−	0.655415i	$-0.227506\pi$
$570$	−4.84004	−	3.51649i	−0.202727	−	0.147290i
$571$	1.26770			0.0530516			0.0265258	−	0.999648i	$-0.491556\pi$
$571$	1.26770			0.0530516			0.0265258	+	0.999648i	$0.491556\pi$
$572$	−0.647201	+	11.9864i	−0.0270608	+	0.501178i
$573$	−16.2678			−0.679596
$574$	25.5498	+	18.5630i	1.06643	+	0.774806i
$575$	7.05513	−	21.7135i	0.294219	−	0.905514i
$576$	−4.64851	−	14.3067i	−0.193688	−	0.596111i
$577$	−24.8260	+	18.0371i	−1.03352	+	0.750895i	−0.969010	−	0.247023i	$-0.920548\pi$
$577$	−24.8260	+	18.0371i	−1.03352	+	0.750895i	−0.0645081	+	0.997917i	$0.520548\pi$
$578$	10.5861	−	7.69122i	0.440322	−	0.319913i
$579$	−5.63724	−	17.3497i	−0.234276	−	0.721027i
$580$	−2.41226	+	7.42417i	−0.100164	+	0.308272i
$581$	42.1995	+	30.6598i	1.75073	+	1.27198i
$582$	−20.3346			−0.842897
$583$	13.7061	+	5.28619i	0.567650	+	0.218931i
$584$	31.6965			1.31161
$585$	−11.0270	−	8.01158i	−0.455910	−	0.331238i
$586$	9.96306	−	30.6631i	0.411570	−	1.26668i
$587$	1.99698	+	6.14606i	0.0824240	+	0.253675i	0.983773	−	0.179419i	$-0.0574218\pi$
$587$	1.99698	+	6.14606i	0.0824240	+	0.253675i	−0.901349	+	0.433094i	$0.857422\pi$
$588$	−3.50833	+	2.54895i	−0.144681	+	0.105117i
$589$	2.77536	−	2.01642i	0.114357	−	0.0830851i
$590$	0.271597	+	0.835891i	0.0111815	+	0.0344131i
$591$	−5.15089	+	15.8528i	−0.211879	+	0.652097i
$592$	−0.694515	−	0.504595i	−0.0285444	−	0.0207387i
$593$	26.3139			1.08058			0.540290	−	0.841479i	$-0.318314\pi$
$593$	26.3139			1.08058			0.540290	+	0.841479i	$0.318314\pi$
$594$	−20.3194	+	5.41012i	−0.833715	+	0.221980i
$595$	−11.6400			−0.477195
$596$	−5.30237	−	3.85240i	−0.217194	−	0.157800i
$597$	−2.65329	+	8.16599i	−0.108592	+	0.334212i
$598$	15.4414	+	47.5236i	0.631444	+	1.94339i
$599$	18.3453	−	13.3287i	0.749570	−	0.544594i	−0.146124	−	0.989266i	$-0.546680\pi$
$599$	18.3453	−	13.3287i	0.749570	−	0.544594i	0.895693	+	0.444672i	$0.146680\pi$
$600$	9.34495	−	6.78951i	0.381506	−	0.277180i
$601$	10.1486	+	31.2341i	0.413968	+	1.27406i	0.913170	+	0.407578i	$0.133627\pi$
$601$	10.1486	+	31.2341i	0.413968	+	1.27406i	−0.499202	+	0.866486i	$0.666373\pi$
$602$	−9.59326	+	29.5250i	−0.390992	+	1.20335i
$603$	−8.29436	−	6.02621i	−0.337773	−	0.245406i
$604$	12.5746			0.511651
$605$	−5.84688	+	13.0213i	−0.237710	+	0.529390i
$606$	7.72982			0.314002
$607$	26.8213	+	19.4868i	1.08864	+	0.790946i	0.979170	−	0.203044i	$-0.0650834\pi$
$607$	26.8213	+	19.4868i	1.08864	+	0.790946i	0.109474	+	0.993990i	$0.465083\pi$
$608$	−3.41826	+	10.5203i	−0.138629	+	0.426656i
$609$	13.0580	+	40.1884i	0.529137	+	1.62852i
$610$	−8.93368	+	6.49070i	−0.361714	+	0.262801i
$611$	−27.0860	+	19.6791i	−1.09578	+	0.796132i
$612$	0.767559	+	2.36230i	0.0310267	+	0.0954905i
$613$	8.17011	−	25.1450i	0.329987	−	1.01560i	−0.639151	−	0.769081i	$-0.720714\pi$
$613$	8.17011	−	25.1450i	0.329987	−	1.01560i	0.969139	−	0.246516i	$-0.0792858\pi$
$614$	−29.6533	−	21.5444i	−1.19671	−	0.869460i
$615$	−10.6558			−0.429683
$616$	−36.1787	+	9.63272i	−1.45768	+	0.388113i
$617$	−3.96590			−0.159661			−0.0798305	−	0.996808i	$-0.525438\pi$
$617$	−3.96590			−0.159661			−0.0798305	+	0.996808i	$0.525438\pi$
$618$	−10.7627	−	7.81955i	−0.432939	−	0.314549i
$619$	8.64835	−	26.6169i	0.347607	−	1.06982i	−0.612567	−	0.790419i	$-0.709863\pi$
$619$	8.64835	−	26.6169i	0.347607	−	1.06982i	0.960173	−	0.279405i	$-0.0901371\pi$
$620$	−0.237285	−	0.730288i	−0.00952959	−	0.0293291i
$621$	29.7569	−	21.6196i	1.19410	−	0.867566i
$622$	−7.63991	+	5.55072i	−0.306333	+	0.222564i
$623$	−0.0854214	−	0.262900i	−0.00342233	−	0.0105329i
$624$	−5.27908	+	16.2473i	−0.211332	+	0.650414i
$625$	−2.08583	−	1.51544i	−0.0834332	−	0.0606178i
$626$	−28.3419			−1.13277
$627$	12.0224	+	4.63680i	0.480128	+	0.185176i
$628$	−0.371585			−0.0148279
$629$	0.688253	+	0.500045i	0.0274424	+	0.0199381i
$630$	2.99940	−	9.23119i	0.119499	−	0.367779i
$631$	−1.86000	−	5.72451i	−0.0740456	−	0.227889i	0.907183	−	0.420736i	$-0.138228\pi$
$631$	−1.86000	−	5.72451i	−0.0740456	−	0.227889i	−0.981229	+	0.192847i	$0.938228\pi$
$632$	−19.4093	+	14.1017i	−0.772062	+	0.560936i
$633$	17.2203	−	12.5112i	0.684444	−	0.497278i
$634$	0.186234	+	0.573170i	0.00739630	+	0.0227635i
$635$	0.514334	−	1.58296i	0.0204107	−	0.0628177i
$636$	−2.40147	−	1.74477i	−0.0952245	−	0.0691846i
$637$	−39.5764			−1.56808
$638$	−2.15728	+	39.9537i	−0.0854074	+	1.58178i
$639$	20.2968			0.802928
$640$	−4.14184	−	3.00922i	−0.163721	−	0.118950i
$641$	−4.68387	+	14.4155i	−0.185002	+	0.569377i	−0.999948	−	0.0101592i	$-0.996766\pi$
$641$	−4.68387	+	14.4155i	−0.185002	+	0.569377i	0.814947	+	0.579536i	$0.196766\pi$
$642$	−5.22513	−	16.0813i	−0.206219	−	0.634678i
$643$	−6.84454	+	4.97285i	−0.269922	+	0.196110i	−0.714510	−	0.699625i	$-0.753350\pi$
$643$	−6.84454	+	4.97285i	−0.269922	+	0.196110i	0.444587	+	0.895735i	$0.353350\pi$
$644$	12.0970	−	8.78899i	0.476689	−	0.346335i
$645$	−3.23684	−	9.96197i	−0.127451	−	0.392252i
$646$	−3.07466	+	9.46284i	−0.120971	+	0.372310i
$647$	−4.62265	−	3.35855i	−0.181735	−	0.132038i	0.493198	−	0.869917i	$-0.335828\pi$
$647$	−4.62265	−	3.35855i	−0.181735	−	0.132038i	−0.674933	+	0.737879i	$0.735828\pi$
$648$	2.76290			0.108537
$649$	−1.02850	−	1.58925i	−0.0403722	−	0.0623836i
$650$	24.0693			0.944075
$651$	−3.36278	−	2.44320i	−0.131798	−	0.0957567i
$652$	0.835944	−	2.57277i	0.0327381	−	0.100758i
$653$	−3.18179	−	9.79255i	−0.124513	−	0.383212i	0.869299	−	0.494287i	$-0.164571\pi$
$653$	−3.18179	−	9.79255i	−0.124513	−	0.383212i	−0.993812	+	0.111075i	$0.964571\pi$
$654$	2.82502	−	2.05250i	0.110467	−	0.0802591i
$655$	3.15071	−	2.28912i	0.123108	−	0.0894434i
$656$	−5.52619	−	17.0079i	−0.215761	−	0.664046i
$657$	5.46931	−	16.8328i	0.213378	−	0.656710i
$658$	−19.2884	−	14.0139i	−0.751941	−	0.546317i
$659$	40.3482			1.57174			0.785872	−	0.618390i	$-0.212215\pi$
$659$	40.3482			1.57174			0.785872	+	0.618390i	$0.212215\pi$
$660$	1.81865	−	2.23859i	0.0707907	−	0.0871370i
$661$	14.1287			0.549544			0.274772	−	0.961509i	$-0.411398\pi$
$661$	14.1287			0.549544			0.274772	+	0.961509i	$0.411398\pi$
$662$	−20.9468	−	15.2187i	−0.814119	−	0.591492i
$663$	5.23148	−	16.1008i	0.203174	−	0.625305i
$664$	−13.5073	−	41.5713i	−0.524186	−	1.61328i
$665$	−13.2178	+	9.60332i	−0.512566	+	0.372401i
$666$	−0.573911	+	0.416971i	−0.0222386	+	0.0161573i
$667$	−21.6281	−	66.5643i	−0.837442	−	2.57738i
$668$	2.93790	−	9.04194i	0.113671	−	0.349843i
$669$	−16.9782	−	12.3354i	−0.656415	−	0.476914i
$670$	−9.19257			−0.355140
$671$	14.9970	−	18.4600i	0.578953	−	0.712639i
$672$	13.4030			0.517032
$673$	18.5810	+	13.4999i	0.716244	+	0.520382i	0.885182	−	0.465245i	$-0.154034\pi$
$673$	18.5810	+	13.4999i	0.716244	+	0.520382i	−0.168938	+	0.985627i	$0.554034\pi$
$674$	−4.64324	+	14.2904i	−0.178851	+	0.550447i
$675$	−5.47484	−	16.8498i	−0.210727	−	0.648551i
$676$	11.6852	−	8.48977i	0.449429	−	0.326530i
$677$	−26.2045	+	19.0387i	−1.00712	+	0.731716i	−0.963603	−	0.267337i	$-0.913856\pi$
$677$	−26.2045	+	19.0387i	−1.00712	+	0.731716i	−0.0435169	+	0.999053i	$0.513856\pi$
$678$	6.18007	+	19.0203i	0.237344	+	0.730471i
$679$	−17.1605	+	52.8146i	−0.658559	+	2.02684i
$680$	7.89132	+	5.73338i	0.302618	+	0.219865i
$681$	17.6312			0.675628
$682$	−2.13838	−	3.30424i	−0.0818826	−	0.126526i
$683$	−28.8520			−1.10399			−0.551996	−	0.833847i	$-0.686134\pi$
$683$	−28.8520			−1.10399			−0.551996	+	0.833847i	$0.686134\pi$
$684$	2.82056	+	2.04925i	0.107847	+	0.0783552i
$685$	1.43598	−	4.41950i	0.0548661	−	0.168860i
$686$	0.712338	+	2.19235i	0.0271972	+	0.0837043i
$687$	3.23532	−	2.35060i	0.123435	−	0.0896809i
$688$	14.2218	−	10.3327i	0.542201	−	0.393932i
$689$	−8.37136	−	25.7644i	−0.318924	−	0.981546i
$690$	3.71016	−	11.4187i	0.141243	−	0.434703i
$691$	6.99289	+	5.08063i	0.266022	+	0.193276i	0.712798	−	0.701370i	$-0.247428\pi$
$691$	6.99289	+	5.08063i	0.266022	+	0.193276i	−0.446776	+	0.894646i	$0.647428\pi$
$692$	5.70231			0.216769
$693$	−1.12715	+	20.8753i	−0.0428168	+	0.792986i
$694$	−26.0540			−0.988997
$695$	−22.3637	−	16.2482i	−0.848303	−	0.616328i
$696$	10.9424	−	33.6774i	0.414772	−	1.27654i
$697$	5.47636	+	16.8545i	0.207432	+	0.638410i
$698$	−12.8422	+	9.33039i	−0.486084	+	0.353161i
$699$	5.21368	−	3.78796i	0.197199	−	0.143274i
$700$	−2.22568	−	6.84993i	−0.0841227	−	0.258903i
$701$	−12.4684	+	38.3736i	−0.470923	+	1.44935i	0.380455	+	0.924800i	$0.375767\pi$
$701$	−12.4684	+	38.3736i	−0.470923	+	1.44935i	−0.851378	+	0.524553i	$0.824233\pi$
$702$	31.3709	+	22.7923i	1.18402	+	0.860241i
$703$	1.19409			0.0450361
$704$	27.1046	+	10.4537i	1.02154	+	0.393990i
$705$	8.04441			0.302970
$706$	−2.69848	−	1.96056i	−0.101559	−	0.0737866i
$707$	6.52324	−	20.0765i	0.245332	−	0.755053i
$708$	0.118204	+	0.363793i	0.00444236	+	0.0136722i
$709$	−16.2043	+	11.7731i	−0.608566	+	0.442149i	−0.848909	−	0.528539i	$-0.822740\pi$
$709$	−16.2043	+	11.7731i	−0.608566	+	0.442149i	0.240343	+	0.970688i	$0.422740\pi$
$710$	14.7230	−	10.6969i	0.552544	−	0.401447i
$711$	4.13975	+	12.7408i	0.155253	+	0.477819i
$712$	−0.0715820	+	0.220307i	−0.00268265	+	0.00825634i
$713$	5.56980	+	4.04669i	0.208590	+	0.151550i
$714$	12.0557			0.451175
$715$	25.4361	−	6.77248i	0.951258	−	0.253276i
$716$	−8.24744			−0.308221
$717$	8.19341	+	5.95286i	0.305989	+	0.222314i
$718$	5.12318	−	15.7675i	0.191195	−	0.588439i
$719$	−10.8665	−	33.4436i	−0.405251	−	1.24724i	−0.920685	−	0.390306i	$-0.872369\pi$
$719$	−10.8665	−	33.4436i	−0.405251	−	1.24724i	0.515434	−	0.856929i	$-0.327631\pi$
$720$	−4.44654	+	3.23060i	−0.165713	+	0.120397i
$721$	−29.3922	+	21.3547i	−1.09462	+	0.795291i
$722$	−2.65182	−	8.16147i	−0.0986907	−	0.303739i
$723$	−7.71556	+	23.7461i	−0.286945	+	0.883125i
$724$	−0.491111	−	0.356813i	−0.0182520	−	0.0132608i
$725$	−33.7128			−1.25206
$726$	6.05569	−	13.4863i	0.224748	−	0.500523i
$727$	−15.1753			−0.562820			−0.281410	−	0.959588i	$-0.590802\pi$
$727$	−15.1753			−0.562820			−0.281410	+	0.959588i	$0.590802\pi$
$728$	55.8559	+	40.5817i	2.07016	+	1.50406i
$729$	6.08590	−	18.7305i	0.225404	−	0.693721i
$730$	−4.90393	−	15.0927i	−0.181503	−	0.558608i
$731$	−14.0936	+	10.2396i	−0.521269	+	0.378724i
$732$	−3.88808	+	2.82485i	−0.143708	+	0.104410i
$733$	4.23508	+	13.0342i	0.156426	+	0.481431i	0.998303	−	0.0582397i	$-0.0185488\pi$
$733$	4.23508	+	13.0342i	0.156426	+	0.481431i	−0.841876	+	0.539671i	$0.818549\pi$
$734$	9.57274	−	29.4619i	0.353336	−	1.08746i
$735$	7.69310	+	5.58937i	0.283764	+	0.206167i
$736$	−22.1995			−0.818283
$737$	19.1327	−	5.09417i	0.704763	−	0.187646i
$738$	−14.7777			−0.543974
$739$	28.2114	+	20.4968i	1.03777	+	0.753986i	0.969849	−	0.243705i	$-0.0783628\pi$
$739$	28.2114	+	20.4968i	1.03777	+	0.753986i	0.0679229	+	0.997691i	$0.478363\pi$
$740$	0.0825936	−	0.254197i	0.00303620	−	0.00934447i
$741$	−7.34298	−	22.5994i	−0.269751	−	0.830209i
$742$	15.6071	−	11.3392i	0.572956	−	0.416277i
$743$	21.9825	−	15.9712i	0.806458	−	0.585926i	−0.106343	−	0.994329i	$-0.533914\pi$
$743$	21.9825	−	15.9712i	0.806458	−	0.585926i	0.912802	+	0.408403i	$0.133914\pi$
$744$	1.07637	+	3.31272i	0.0394616	+	0.121450i
$745$	−4.44116	+	13.6685i	−0.162711	+	0.500774i
$746$	−22.8685	−	16.6149i	−0.837274	−	0.608316i
$747$	−24.4077			−0.893030
$748$	−4.47549	−	1.72611i	−0.163640	−	0.0631129i
$749$	−46.1771			−1.68727
$750$	−11.7331	−	8.52457i	−0.428431	−	0.311273i
$751$	−1.30831	+	4.02657i	−0.0477410	+	0.146932i	−0.972085	−	0.234628i	$-0.924613\pi$
$751$	−1.30831	+	4.02657i	−0.0477410	+	0.146932i	0.924344	+	0.381560i	$0.124613\pi$
$752$	4.17191	+	12.8398i	0.152134	+	0.468220i
$753$	4.69287	−	3.40957i	0.171018	−	0.124252i
$754$	59.6943	−	43.3705i	2.17394	−	1.57946i
$755$	−8.52073	−	26.2241i	−0.310101	−	0.954393i
$756$	3.58566	−	11.0355i	0.130409	−	0.401358i
$757$	3.74627	+	2.72183i	0.136161	+	0.0989265i	0.653781	−	0.756684i	$-0.273182\pi$
$757$	3.74627	+	2.72183i	0.136161	+	0.0989265i	−0.517620	+	0.855611i	$0.673182\pi$
$758$	−23.8208			−0.865210
$759$	−1.39425	+	25.8221i	−0.0506080	+	0.937282i
$760$	13.6911			0.496630
$761$	9.72475	+	7.06544i	0.352522	+	0.256122i	0.749926	−	0.661522i	$-0.230089\pi$
$761$	9.72475	+	7.06544i	0.352522	+	0.256122i	−0.397404	+	0.917644i	$0.630089\pi$
$762$	−0.532702	+	1.63949i	−0.0192978	+	0.0593924i
$763$	−2.94685	−	9.06948i	−0.106683	−	0.328337i
$764$	6.87675	−	4.99625i	0.248792	−	0.180758i
$765$	4.40645	−	3.20147i	0.159315	−	0.115749i
$766$	−4.45941	−	13.7247i	−0.161125	−	0.495892i
$767$	−1.07876	+	3.32008i	−0.0389518	+	0.119881i
$768$	−11.7609	−	8.54479i	−0.424385	−	0.308333i
$769$	2.92278			0.105398			0.0526991	−	0.998610i	$-0.483218\pi$
$769$	2.92278			0.105398			0.0526991	+	0.998610i	$0.483218\pi$
$770$	10.1841	+	15.7367i	0.367011	+	0.567110i
$771$	20.8503			0.750904
$772$	7.71152	+	5.60275i	0.277544	+	0.201647i
$773$	−4.56220	+	14.0410i	−0.164091	+	0.505020i	−0.998968	−	0.0454164i	$-0.985539\pi$
$773$	−4.56220	+	14.0410i	−0.164091	+	0.505020i	0.834877	+	0.550436i	$0.185539\pi$
$774$	−4.48892	−	13.8155i	−0.161351	−	0.496587i
$775$	2.68287	−	1.94922i	0.0963714	−	0.0700179i
$776$	37.6480	−	27.3529i	1.35149	−	0.981912i
$777$	−0.447095	−	1.37602i	−0.0160394	−	0.0493643i
$778$	7.19059	−	22.1304i	0.257795	−	0.793412i
$779$	20.1240	+	14.6210i	0.721019	+	0.523851i
$780$	−5.31883			−0.190445
$781$	−24.7155	+	30.4226i	−0.884392	+	1.08861i
$782$	−19.9680			−0.714054
$783$	−43.9399	−	31.9242i	−1.57029	−	1.14088i
$784$	−4.93156	+	15.1778i	−0.176127	+	0.542063i
$785$	0.251792	+	0.774937i	0.00898685	+	0.0276587i
$786$	−3.26323	+	2.37087i	−0.116395	+	0.0845662i
$787$	12.1647	−	8.83816i	0.433624	−	0.315046i	−0.349472	−	0.936947i	$-0.613639\pi$
$787$	12.1647	−	8.83816i	0.433624	−	0.315046i	0.783096	+	0.621900i	$0.213639\pi$
$788$	−2.69141	−	8.28331i	−0.0958776	−	0.295081i
$789$	4.94254	−	15.2116i	0.175959	−	0.541546i
$790$	9.71765	+	7.06028i	0.345738	+	0.251194i
$791$	54.6164			1.94194
$792$	11.0464	−	13.5971i	0.392516	−	0.483152i
$793$	−43.8603			−1.55753
$794$	5.46000	+	3.96692i	0.193768	+	0.140781i
$795$	−2.01142	+	6.19052i	−0.0713378	+	0.219555i
$796$	−1.38638	−	4.26684i	−0.0491390	−	0.151234i
$797$	19.2295	−	13.9711i	0.681145	−	0.494881i	−0.192592	−	0.981279i	$-0.561689\pi$
$797$	19.2295	−	13.9711i	0.681145	−	0.494881i	0.873737	+	0.486398i	$0.161689\pi$
$798$	13.6899	−	9.94628i	0.484616	−	0.352094i
$799$	−4.13429	−	12.7240i	−0.146261	−	0.450144i
$800$	−3.30434	+	10.1697i	−0.116826	+	0.359553i
$801$	0.104645	+	0.0760290i	0.00369745	+	0.00268635i
$802$	−28.9980			−1.02396
$803$	18.5705	+	28.6953i	0.655339	+	1.01264i
$804$	−4.00075			−0.141096
$805$	−26.5265	−	19.2726i	−0.934936	−	0.679271i
$806$	−2.24287	+	6.90284i	−0.0790017	+	0.243142i
$807$	−3.15150	−	9.69932i	−0.110938	−	0.341432i
$808$	−14.3112	+	10.3977i	−0.503466	+	0.365789i
$809$	2.18998	−	1.59112i	0.0769957	−	0.0559406i	−0.548622	−	0.836071i	$-0.684847\pi$
$809$	2.18998	−	1.59112i	0.0769957	−	0.0559406i	0.625617	+	0.780130i	$0.284847\pi$
$810$	−0.427463	−	1.31560i	−0.0150195	−	0.0462253i
$811$	6.46934	−	19.9106i	0.227169	−	0.699155i	−0.770895	−	0.636962i	$-0.780191\pi$
$811$	6.46934	−	19.9106i	0.227169	−	0.699155i	0.998064	−	0.0621926i	$-0.0198093\pi$
$812$	−17.8628	−	12.9781i	−0.626862	−	0.455442i
$813$	0.799748			0.0280484
$814$	0.0738633	−	1.36798i	0.00258891	−	0.0479476i
$815$	−5.93194			−0.207787
$816$	−5.52287	−	4.01260i	−0.193339	−	0.140469i
$817$	−7.55603	+	23.2551i	−0.264352	+	0.813592i
$818$	4.58940	+	14.1247i	0.160464	+	0.493859i
$819$	31.1895	−	22.6605i	1.08985	−	0.791822i
$820$	4.50444	−	3.27267i	0.157302	−	0.114287i
$821$	1.33700	+	4.11487i	0.0466617	+	0.143610i	0.971673	−	0.236330i	$-0.0759446\pi$
$821$	1.33700	+	4.11487i	0.0466617	+	0.143610i	−0.925011	+	0.379940i	$0.875945\pi$
$822$	−1.48726	+	4.57733i	−0.0518743	+	0.159653i
$823$	27.5045	+	19.9832i	0.958745	+	0.696569i	0.952859	−	0.303414i	$-0.0981264\pi$
$823$	27.5045	+	19.9832i	0.958745	+	0.696569i	0.00588607	+	0.999983i	$0.498126\pi$
$824$	30.4447			1.06059
$825$	11.6217	+	4.48227i	0.404616	+	0.156053i
$826$	−2.48596			−0.0864976
$827$	37.4361	+	27.1989i	1.30178	+	0.945798i	0.999971	−	0.00757048i	$-0.00240978\pi$
$827$	37.4361	+	27.1989i	1.30178	+	0.945798i	0.301808	+	0.953369i	$0.402410\pi$
$828$	−2.16212	+	6.65431i	−0.0751387	+	0.231253i
$829$	2.73045	+	8.40347i	0.0948326	+	0.291865i	0.987210	−	0.159425i	$-0.0509641\pi$
$829$	2.73045	+	8.40347i	0.0948326	+	0.291865i	−0.892377	+	0.451290i	$0.850964\pi$
$830$	−17.7050	+	12.8634i	−0.614549	+	0.446496i
$831$	16.6090	−	12.0671i	0.576159	−	0.418604i
$832$	−16.5548	−	50.9505i	−0.573936	−	1.76639i
$833$	4.88709	−	15.0409i	0.169328	−	0.521137i
$834$	23.1624	+	16.8284i	0.802047	+	0.582721i
$835$	−20.8476			−0.721462
$836$	−6.50622	+	1.73231i	−0.225022	+	0.0599131i
$837$	5.34254			0.184665
$838$	4.99915	+	3.63210i	0.172693	+	0.125469i
$839$	−3.10721	+	9.56300i	−0.107273	+	0.330151i	−0.990257	−	0.139251i	$-0.955531\pi$
$839$	−3.10721	+	9.56300i	−0.107273	+	0.330151i	0.882984	+	0.469402i	$0.155531\pi$
$840$	−5.12627	−	15.7770i	−0.176873	−	0.544359i
$841$	−60.1498	+	43.7014i	−2.07413	+	1.50694i
$842$	7.50813	−	5.45498i	0.258747	−	0.187991i
$843$	6.58502	+	20.2666i	0.226800	+	0.698019i
$844$	−3.43686	+	10.5776i	−0.118302	+	0.364095i
$845$	−25.6234	−	18.6165i	−0.881471	−	0.640426i
$846$	11.1562			0.383557
$847$	−29.9172	−	27.1095i	−1.02797	−	0.931492i
$848$	−10.9239			−0.375129
$849$	−6.74670	−	4.90176i	−0.231546	−	0.168228i
$850$	−2.97219	+	9.14746i	−0.101945	+	0.313755i
$851$	0.740526	+	2.27910i	0.0253849	+	0.0781267i
$852$	6.40768	−	4.65545i	0.219524	−	0.159493i
$853$	10.2189	−	7.42448i	0.349889	−	0.254210i	−0.398933	−	0.916980i	$-0.630619\pi$
$853$	10.2189	−	7.42448i	0.349889	−	0.254210i	0.748823	+	0.662770i	$0.230619\pi$
$854$	−9.65175	−	29.7050i	−0.330276	−	1.01649i
$855$	2.36244	−	7.27085i	0.0807938	−	0.248658i
$856$	31.3055	+	22.7448i	1.07000	+	0.777401i
$857$	−7.29551			−0.249210			−0.124605	−	0.992206i	$-0.539766\pi$
$857$	−7.29551			−0.249210			−0.124605	+	0.992206i	$0.539766\pi$
$858$	−26.3445	+	7.01434i	−0.899388	+	0.239466i
$859$	−45.0890			−1.53842			−0.769208	−	0.638999i	$-0.779349\pi$
$859$	−45.0890			−1.53842			−0.769208	+	0.638999i	$0.779349\pi$
$860$	4.42787	+	3.21703i	0.150989	+	0.109700i
$861$	9.31363	−	28.6644i	0.317408	−	0.976880i
$862$	1.14794	+	3.53298i	0.0390988	+	0.120334i
$863$	−15.1688	+	11.0208i	−0.516351	+	0.375151i	−0.815227	−	0.579141i	$-0.803388\pi$
$863$	−15.1688	+	11.0208i	−0.516351	+	0.375151i	0.298877	+	0.954292i	$0.403388\pi$
$864$	−13.9369	+	10.1258i	−0.474143	+	0.344485i
$865$	−3.86398	−	11.8921i	−0.131379	−	0.404344i
$866$	6.87732	−	21.1662i	0.233701	−	0.719257i
$867$	−10.1028	−	7.34010i	−0.343108	−	0.249283i
$868$	2.17190			0.0737189
$869$	−24.1381	−	9.30960i	−0.818830	−	0.315807i
$870$	−17.7289			−0.601067
$871$	−29.5389	−	21.4612i	−1.00089	−	0.727187i
$872$	−2.46942	+	7.60010i	−0.0836252	+	0.257372i
$873$	−8.02983	−	24.7133i	−0.271768	−	0.836417i
$874$	−22.6746	+	16.4741i	−0.766981	+	0.557244i
$875$	−32.0423	+	23.2801i	−1.08323	+	0.787010i
$876$	−2.13427	−	6.56860i	−0.0721102	−	0.221933i
$877$	5.38089	−	16.5607i	0.181700	−	0.559214i	−0.818176	−	0.574968i	$-0.805015\pi$
$877$	5.38089	−	16.5607i	0.181700	−	0.559214i	0.999876	+	0.0157533i	$0.00501465\pi$
$878$	28.4880	+	20.6978i	0.961424	+	0.698516i
$879$	−30.7692			−1.03782
$880$	0.572276	−	10.5988i	0.0192914	−	0.357286i
$881$	−24.5842			−0.828262			−0.414131	−	0.910217i	$-0.635915\pi$
$881$	−24.5842			−0.828262			−0.414131	+	0.910217i	$0.635915\pi$
$882$	10.6690	+	7.75146i	0.359243	+	0.261005i
$883$	6.50620	−	20.0240i	0.218951	−	0.673863i	−0.779898	−	0.625906i	$-0.784729\pi$
$883$	6.50620	−	20.0240i	0.218951	−	0.673863i	0.998849	−	0.0479562i	$-0.0152708\pi$
$884$	2.73352	+	8.41292i	0.0919383	+	0.282957i
$885$	0.678590	−	0.493024i	0.0228105	−	0.0165728i
$886$	−8.22562	+	5.97626i	−0.276345	+	0.200776i
$887$	10.3563	+	31.8735i	0.347731	+	1.07021i	0.960105	+	0.279639i	$0.0902148\pi$
$887$	10.3563	+	31.8735i	0.347731	+	1.07021i	−0.612374	+	0.790568i	$0.709785\pi$
$888$	−0.374660	+	1.15308i	−0.0125728	+	0.0386950i
$889$	3.80865	+	2.76715i	0.127738	+	0.0928072i
$890$	0.115977			0.00388756
$891$	1.61874	+	2.50130i	0.0542299	+	0.0837967i
$892$	10.9656			0.367155
$893$	−15.1923	−	11.0379i	−0.508391	−	0.369368i
$894$	4.59977	−	14.1566i	0.153839	−	0.473468i
$895$	5.58860	+	17.2000i	0.186806	+	0.574931i
$896$	11.7151	−	8.51149i	0.391373	−	0.284349i
$897$	38.5805	−	28.0303i	1.28816	−	0.935906i
$898$	10.1462	+	31.2268i	0.338584	+	1.04205i
$899$	3.14149	−	9.66852i	0.104775	−	0.322463i
$900$	2.72655	+	1.98096i	0.0908851	+	0.0660319i
$901$	10.8254			0.360647
$902$	17.9949	−	22.1501i	0.599165	−	0.737518i
$903$	29.6272			0.985930
$904$	−37.0270	−	26.9017i	−1.23150	−	0.894736i
$905$	−0.411345	+	1.26599i	−0.0136736	+	0.0420829i
$906$	8.82503	+	27.1606i	0.293192	+	0.902352i
$907$	31.9982	−	23.2481i	1.06248	−	0.771940i	0.0879376	−	0.996126i	$-0.471972\pi$
$907$	31.9982	−	23.2481i	1.06248	−	0.771940i	0.974546	+	0.224186i	$0.0719724\pi$
$908$	−7.45309	+	5.41499i	−0.247340	+	0.179703i
$909$	3.05239	+	9.39428i	0.101241	+	0.311589i
$910$	10.6818	−	32.8752i	0.354098	−	1.08980i
$911$	0.578363	+	0.420205i	0.0191620	+	0.0139220i	0.597325	−	0.801999i	$-0.296230\pi$
$911$	0.578363	+	0.420205i	0.0191620	+	0.0139220i	−0.578163	+	0.815921i	$0.696230\pi$
$912$	−9.58198			−0.317291
$913$	29.7214	−	36.5844i	0.983636	−	1.21077i
$914$	−13.9844			−0.462562
$915$	8.52583	+	6.19438i	0.281855	+	0.204780i
$916$	−0.645714	+	1.98730i	−0.0213350	+	0.0656623i
$917$	3.40395	+	10.4763i	0.112408	+	0.345958i
$918$	−12.5360	+	9.10794i	−0.413750	+	0.300607i
$919$	−11.8467	+	8.60716i	−0.390788	+	0.283924i	−0.765778	−	0.643105i	$-0.777646\pi$
$919$	−11.8467	+	8.60716i	−0.390788	+	0.283924i	0.374990	+	0.927029i	$0.377646\pi$
$920$	8.49067	+	26.1316i	0.279929	+	0.861533i
$921$	−10.8095	+	33.2681i	−0.356184	+	1.09622i
$922$	−11.7158	−	8.51206i	−0.385841	−	0.280330i
$923$	72.2833			2.37923
$924$	4.43230	+	6.84884i	0.145812	+	0.225310i
$925$	1.15430			0.0379530
$926$	−2.33213	−	1.69439i	−0.0766385	−	0.0556811i
$927$	5.25332	−	16.1680i	0.172542	−	0.531028i
$928$	10.1297	+	31.1760i	0.332524	+	1.02340i
$929$	−37.4303	+	27.1947i	−1.22805	+	0.892230i	−0.996742	−	0.0806507i	$-0.974300\pi$
$929$	−37.4303	+	27.1947i	−1.22805	+	0.892230i	−0.231307	+	0.972881i	$0.574300\pi$
$930$	1.41087	−	1.02506i	0.0462642	−	0.0336129i
$931$	−6.85959	−	21.1117i	−0.224814	−	0.691907i
$932$	−1.04056	+	3.20251i	−0.0340847	+	0.104902i
$933$	7.29113	+	5.29731i	0.238701	+	0.173426i
$934$	33.4171			1.09344
$935$	−0.567117	+	10.5032i	−0.0185467	+	0.343493i
$936$	−32.3064			−1.05597
$937$	8.79488	+	6.38985i	0.287316	+	0.208747i	0.722102	−	0.691786i	$-0.243176\pi$
$937$	8.79488	+	6.38985i	0.287316	+	0.208747i	−0.434786	+	0.900534i	$0.643176\pi$
$938$	8.03471	−	24.7283i	0.262343	−	0.807408i
$939$	8.35829	+	25.7242i	0.272762	+	0.839476i
$940$	−3.40056	+	2.47065i	−0.110914	+	0.0805836i
$941$	−28.9934	+	21.0649i	−0.945156	+	0.686696i	−0.949656	−	0.313294i	$-0.898568\pi$
$941$	−28.9934	+	21.0649i	−0.945156	+	0.686696i	0.00449988	+	0.999990i	$0.498568\pi$
$942$	−0.260785	−	0.802612i	−0.00849682	−	0.0261505i
$943$	−15.4262	+	47.4770i	−0.502347	+	1.54607i
$944$	1.13885	+	0.827420i	0.0370663	+	0.0269302i
$945$	−25.4442			−0.827700
$946$	26.1741	+	10.0948i	0.850993	+	0.328211i
$947$	20.0843			0.652651			0.326326	−	0.945257i	$-0.394189\pi$
$947$	20.0843			0.652651			0.326326	+	0.945257i	$0.394189\pi$
$948$	4.22928	+	3.07275i	0.137360	+	0.0997982i
$949$	19.4780	−	59.9470i	0.632281	−	1.94596i
$950$	4.17181	+	12.8395i	0.135351	+	0.416569i
$951$	0.465308	−	0.338066i	0.0150887	−	0.0109626i
$952$	−22.3203	+	16.2167i	−0.723406	+	0.525585i
$953$	3.92343	+	12.0751i	0.127092	+	0.391150i	0.994276	−	0.106838i	$-0.0340725\pi$
$953$	3.92343	+	12.0751i	0.127092	+	0.391150i	−0.867184	+	0.497988i	$0.834072\pi$
$954$	−2.78949	+	8.58516i	−0.0903130	+	0.277955i
$955$	−15.0794	−	10.9559i	−0.487959	−	0.354523i
$956$	−5.29182			−0.171150
$957$	36.8997	−	9.82469i	1.19280	−	0.317587i
$958$	1.87975			0.0607319
$959$	10.6335	+	7.72567i	0.343373	+	0.249475i
$960$	−3.97770	+	12.2421i	−0.128380	+	0.395112i
$961$	0.309017	+	0.951057i	0.00996829	+	0.0306792i
$962$	−2.04388	+	1.48497i	−0.0658974	+	0.0478772i
$963$	17.4808	−	12.7005i	0.563309	−	0.409268i
$964$	−4.03149	−	12.4076i	−0.129845	−	0.399623i
$965$	6.45902	−	19.8788i	0.207923	−	0.639921i
$966$	27.4738	+	19.9609i	0.883956	+	0.642231i
$967$	−2.29916			−0.0739359			−0.0369679	−	0.999316i	$-0.511770\pi$
$967$	−2.29916			−0.0739359			−0.0369679	+	0.999316i	$0.511770\pi$
$968$	6.92928	+	33.1146i	0.222716	+	1.06434i
$969$	9.49558			0.305042
$970$	−18.8492	−	13.6947i	−0.605211	−	0.439712i
$971$	1.01410	−	3.12109i	0.0325441	−	0.100160i	−0.933465	−	0.358669i	$-0.883231\pi$
$971$	1.01410	−	3.12109i	0.0325441	−	0.100160i	0.966009	+	0.258508i	$0.0832309\pi$
$972$	2.74482	+	8.44769i	0.0880401	+	0.270960i
$973$	63.2550	−	45.9574i	2.02786	−	1.47333i
$974$	−18.9304	+	13.7537i	−0.606569	+	0.440698i
$975$	−7.09826	−	21.8462i	−0.227326	−	0.699638i
$976$	−5.46537	+	16.8207i	−0.174942	+	0.538416i
$977$	−45.7747	−	33.2573i	−1.46446	−	1.06399i	−0.982172	−	0.187984i	$-0.939805\pi$
$977$	−45.7747	−	33.2573i	−1.46446	−	1.06399i	−0.482291	−	0.876011i	$-0.660195\pi$
$978$	6.14378			0.196457
$979$	−0.241386	+	0.0642700i	−0.00771473	+	0.00205408i
$980$	−4.96869			−0.158719
$981$	3.61002	+	2.62283i	0.115259	+	0.0837407i
$982$	−6.97193	+	21.4574i	−0.222483	+	0.684733i
$983$	−4.10531	−	12.6348i	−0.130939	−	0.402989i	0.863997	−	0.503496i	$-0.167953\pi$
$983$	−4.10531	−	12.6348i	−0.130939	−	0.402989i	−0.994936	+	0.100508i	$0.967953\pi$
$984$	−20.4330	+	14.8454i	−0.651379	+	0.473255i
$985$	−15.4510	+	11.2258i	−0.492310	+	0.357684i
$986$	9.11148	+	28.0423i	0.290169	+	0.893048i
$987$	−7.03117	+	21.6397i	−0.223805	+	0.688800i
$988$	10.0449	+	7.29805i	0.319571	+	0.232182i
$989$	−49.0717			−1.56039
$990$	−8.18350	−	3.15622i	−0.260089	−	0.100311i
$991$	4.55607			0.144728			0.0723642	−	0.997378i	$-0.476946\pi$
$991$	4.55607			0.144728			0.0723642	+	0.997378i	$0.476946\pi$
$992$	−2.60867	−	1.89531i	−0.0828252	−	0.0601761i
$993$	−7.63569	+	23.5002i	−0.242311	+	0.745757i
$994$	15.9064	+	48.9549i	0.504520	+	1.55275i
$995$	−7.95902	+	5.78257i	−0.252318	+	0.183320i
$996$	−7.70549	+	5.59837i	−0.244158	+	0.177391i
$997$	15.7054	+	48.3363i	0.497396	+	1.53083i	0.813189	+	0.581999i	$0.197729\pi$
$997$	15.7054	+	48.3363i	0.497396	+	1.53083i	−0.315793	+	0.948828i	$0.602271\pi$
$998$	12.3511	−	38.0126i	0.390966	−	1.20327i
$999$	1.50446	+	1.09306i	0.0475992	+	0.0345828i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	341.2.h.a.125.7	✓	60
11.3	even	5	inner	341.2.h.a.311.7	yes	60
11.5	even	5		3751.2.a.s.1.19		30
11.6	odd	10		3751.2.a.p.1.12		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
341.2.h.a.125.7	✓	60	1.1	even	1	trivial
341.2.h.a.311.7	yes	60	11.3	even	5	inner
3751.2.a.p.1.12		30	11.6	odd	10
3751.2.a.s.1.19		30	11.5	even	5

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:	\( N \)	\(=\)	\( 341 = 11 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	341.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.960056 - 0.697521i) q^{2} +(-0.349967 + 1.07709i) q^{3} +(-0.182863 - 0.562794i) q^{4} +(-1.04979 + 0.762717i) q^{5} +(1.08728 - 0.789956i) q^{6} +(-1.13417 - 3.49062i) q^{7} +(-0.950420 + 2.92509i) q^{8} +(1.38941 + 1.00946i) q^{9} +1.53987 q^{10} +(-3.20497 + 0.853336i) q^{11} +0.670175 q^{12} +(4.94812 + 3.59502i) q^{13} +(-1.34591 + 4.14229i) q^{14} +(-0.454122 - 1.39764i) q^{15} +(1.99529 - 1.44966i) q^{16} +(-1.97730 + 1.43659i) q^{17} +(-0.629786 - 1.93828i) q^{18} +(-1.06009 + 3.26263i) q^{19} +(0.621220 + 0.451343i) q^{20} +4.15663 q^{21} +(3.67217 + 1.41628i) q^{22} -6.88465 q^{23} +(-2.81797 - 2.04737i) q^{24} +(-1.02476 + 3.15390i) q^{25} +(-2.24287 - 6.90284i) q^{26} +(-4.32221 + 3.14027i) q^{27} +(-1.75710 + 1.27661i) q^{28} +(3.14149 + 9.66852i) q^{29} +(-0.538904 + 1.65858i) q^{30} +(-0.809017 - 0.587785i) q^{31} +3.22449 q^{32} +(0.202516 - 3.75068i) q^{33} +2.90037 q^{34} +(3.85299 + 2.79936i) q^{35} +(0.314049 - 0.966544i) q^{36} +(-0.107562 - 0.331042i) q^{37} +(3.29351 - 2.39287i) q^{38} +(-5.60384 + 4.07143i) q^{39} +(-1.23328 - 3.79563i) q^{40} +(2.24067 - 6.89608i) q^{41} +(-3.99059 - 2.89934i) q^{42} +7.12769 q^{43} +(1.06632 + 1.64769i) q^{44} -2.22852 q^{45} +(6.60964 + 4.80219i) q^{46} +(-1.69156 + 5.20608i) q^{47} +(0.863128 + 2.65644i) q^{48} +(-5.23494 + 3.80341i) q^{49} +(3.18374 - 2.31312i) q^{50} +(-0.855346 - 2.63248i) q^{51} +(1.11843 - 3.44217i) q^{52} +(-3.58335 - 2.60345i) q^{53} +6.33997 q^{54} +(2.71369 - 3.34031i) q^{55} +11.2883 q^{56} +(-3.14315 - 2.28363i) q^{57} +(3.72799 - 11.4736i) q^{58} +(0.176377 + 0.542833i) q^{59} +(-0.703543 + 0.511154i) q^{60} +(-5.80159 + 4.21510i) q^{61} +(0.366709 + 1.12861i) q^{62} +(1.94783 - 5.99479i) q^{63} +(-7.08626 - 5.14847i) q^{64} -7.93647 q^{65} +(-2.81060 + 3.45960i) q^{66} -5.96971 q^{67} +(1.17008 + 0.850112i) q^{68} +(2.40940 - 7.41538i) q^{69} +(-1.74647 - 5.37509i) q^{70} +(9.56120 - 6.94662i) q^{71} +(-4.27329 + 3.10473i) q^{72} +(-3.18464 - 9.80132i) q^{73} +(-0.127643 + 0.392845i) q^{74} +(-3.03839 - 2.20752i) q^{75} +2.03004 q^{76} +(6.61365 + 10.2195i) q^{77} +8.21991 q^{78} +(6.31070 + 4.58499i) q^{79} +(-0.988951 + 3.04368i) q^{80} +(-0.277597 - 0.854356i) q^{81} +(-6.96133 + 5.05770i) q^{82} +(-11.4977 + 8.35359i) q^{83} +(-0.760093 - 2.33932i) q^{84} +(0.980035 - 3.01624i) q^{85} +(-6.84298 - 4.97172i) q^{86} -11.5133 q^{87} +(0.549979 - 10.1858i) q^{88} +0.0753162 q^{89} +(2.13950 + 1.55444i) q^{90} +(6.93683 - 21.3494i) q^{91} +(1.25895 + 3.87464i) q^{92} +(0.916227 - 0.665678i) q^{93} +(5.25534 - 3.81823i) q^{94} +(-1.37559 - 4.23363i) q^{95} +(-1.12847 + 3.47306i) q^{96} +(-12.2408 - 8.89345i) q^{97} +7.67879 q^{98} +(-5.31442 - 2.04967i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 7 q^{2} - 2 q^{3} - 17 q^{4} - 2 q^{5} - 3 q^{6} - 3 q^{7} - 11 q^{8} - 15 q^{9} + 16 q^{10} - 9 q^{11} - 32 q^{12} + 4 q^{13} + 9 q^{14} - 12 q^{15} - 15 q^{16} - 21 q^{17} + 63 q^{18} - 11 q^{19}+ \cdots - 97 q^{99}+O(q^{100}) \) 60 * q - 7 * q^2 - 2 * q^3 - 17 * q^4 - 2 * q^5 - 3 * q^6 - 3 * q^7 - 11 * q^8 - 15 * q^9 + 16 * q^10 - 9 * q^11 - 32 * q^12 + 4 * q^13 + 9 * q^14 - 12 * q^15 - 15 * q^16 - 21 * q^17 + 63 * q^18 - 11 * q^19 - 8 * q^20 + 60 * q^21 - 5 * q^22 - 22 * q^23 + 71 * q^24 - 11 * q^25 - 42 * q^26 - 5 * q^27 - 21 * q^28 - 13 * q^29 - 16 * q^30 - 15 * q^31 + 136 * q^32 + 6 * q^33 - 42 * q^34 + 21 * q^35 - 6 * q^36 + 16 * q^37 - 36 * q^38 - 33 * q^39 + 30 * q^40 - 52 * q^41 - 56 * q^42 + 20 * q^43 + 9 * q^44 - 72 * q^45 + 56 * q^46 - 10 * q^47 - 54 * q^48 + 32 * q^49 - 81 * q^50 + 17 * q^51 - 34 * q^52 + 3 * q^53 + 140 * q^54 - 32 * q^55 - 34 * q^56 + 28 * q^57 + q^58 + 34 * q^59 + 38 * q^60 - 37 * q^61 - 2 * q^62 - 79 * q^63 - 17 * q^64 + 186 * q^65 - 70 * q^66 - 26 * q^67 + 49 * q^68 + 3 * q^69 - 20 * q^70 + 24 * q^71 - 136 * q^72 + 14 * q^73 - 51 * q^74 - 7 * q^75 + 130 * q^76 - 19 * q^77 - 32 * q^78 + 23 * q^79 + 4 * q^80 + 76 * q^81 + 27 * q^82 - 41 * q^83 + 108 * q^84 - 86 * q^85 - 39 * q^86 + 96 * q^87 - 29 * q^88 - 16 * q^89 + 208 * q^90 + 6 * q^91 - 38 * q^92 + 3 * q^93 - 98 * q^94 - 73 * q^95 - 130 * q^96 - 23 * q^97 + 80 * q^98 - 97 * q^99

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