LMFDB - Embedded newform 425.2.k.b.86.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [425,2,Mod(86,425)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("425.86"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(425, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.k (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [76] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$19$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			86.2
Character	$\chi$	$=$	425.86
Dual form			425.2.k.b.341.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.92608 + 1.39938i) q^{2} +(0.431982 - 1.32950i) q^{3} +(1.13349 - 3.48853i) q^{4} +(2.16658 - 0.553118i) q^{5} +(1.02845 + 3.16524i) q^{6} +4.93434 q^{7} +(1.22719 + 3.77690i) q^{8} +(0.846082 + 0.614714i) q^{9} +(-3.39899 + 4.09722i) q^{10} +(1.16824 - 0.848778i) q^{11} +(-4.14837 - 3.01397i) q^{12} +(-5.21572 - 3.78944i) q^{13} +(-9.50395 + 6.90502i) q^{14} +(0.200550 - 3.11941i) q^{15} +(-1.71395 - 1.24526i) q^{16} +(0.309017 + 0.951057i) q^{17} -2.48984 q^{18} +(-0.519255 - 1.59810i) q^{19} +(0.526232 - 8.18514i) q^{20} +(2.13155 - 6.56022i) q^{21} +(-1.06237 + 3.26963i) q^{22} +(-4.70676 + 3.41966i) q^{23} +5.55153 q^{24} +(4.38812 - 2.39675i) q^{25} +15.3488 q^{26} +(4.57558 - 3.32436i) q^{27} +(5.59304 - 17.2136i) q^{28} +(-1.39972 + 4.30790i) q^{29} +(3.97896 + 6.28888i) q^{30} +(1.07275 + 3.30160i) q^{31} -2.89875 q^{32} +(-0.623793 - 1.91984i) q^{33} +(-1.92608 - 1.39938i) q^{34} +(10.6906 - 2.72927i) q^{35} +(3.10348 - 2.25481i) q^{36} +(-7.27575 - 5.28614i) q^{37} +(3.23648 + 2.35144i) q^{38} +(-7.29116 + 5.29734i) q^{39} +(4.74788 + 7.50417i) q^{40} +(3.63664 + 2.64217i) q^{41} +(5.07472 + 15.6184i) q^{42} -4.02450 q^{43} +(-1.63679 - 5.03754i) q^{44} +(2.17311 + 0.863844i) q^{45} +(4.28020 - 13.1731i) q^{46} +(-0.693502 + 2.13438i) q^{47} +(-2.39596 + 1.74077i) q^{48} +17.3477 q^{49} +(-5.09792 + 10.7570i) q^{50} +1.39792 q^{51} +(-19.1316 + 13.8999i) q^{52} +(-0.484308 + 1.49055i) q^{53} +(-4.16091 + 12.8060i) q^{54} +(2.06161 - 2.48512i) q^{55} +(6.05538 + 18.6365i) q^{56} -2.34899 q^{57} +(-3.33241 - 10.2561i) q^{58} +(0.875925 + 0.636397i) q^{59} +(-10.6548 - 4.23546i) q^{60} +(1.96527 - 1.42785i) q^{61} +(-6.68641 - 4.85796i) q^{62} +(4.17486 + 3.03321i) q^{63} +(9.01113 - 6.54697i) q^{64} +(-13.3963 - 5.32521i) q^{65} +(3.88806 + 2.82484i) q^{66} +(1.41301 + 4.34879i) q^{67} +3.66806 q^{68} +(2.51322 + 7.73489i) q^{69} +(-16.7718 + 20.2171i) q^{70} +(-4.34876 + 13.3841i) q^{71} +(-1.28341 + 3.94994i) q^{72} +(6.68714 - 4.85849i) q^{73} +21.4110 q^{74} +(-1.29089 - 6.86937i) q^{75} -6.16361 q^{76} +(5.76451 - 4.18816i) q^{77} +(6.63039 - 20.4062i) q^{78} +(4.77046 - 14.6820i) q^{79} +(-4.40217 - 1.74993i) q^{80} +(-1.47365 - 4.53543i) q^{81} -10.7019 q^{82} +(-2.64612 - 8.14393i) q^{83} +(-20.4695 - 14.8719i) q^{84} +(1.19556 + 1.88962i) q^{85} +(7.75153 - 5.63181i) q^{86} +(5.12271 + 3.72187i) q^{87} +(4.63941 + 3.37073i) q^{88} +(-2.33871 + 1.69918i) q^{89} +(-5.39444 + 1.37718i) q^{90} +(-25.7361 - 18.6984i) q^{91} +(6.59453 + 20.2959i) q^{92} +4.85290 q^{93} +(-1.65107 - 5.08146i) q^{94} +(-2.00895 - 3.17521i) q^{95} +(-1.25221 + 3.85390i) q^{96} +(-3.93745 + 12.1182i) q^{97} +(-33.4132 + 24.2761i) q^{98} +1.51018 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q - 6 q^{2} - 7 q^{3} - 26 q^{4} + 13 q^{5} + 12 q^{6} + 22 q^{7} + 10 q^{8} - 24 q^{9} - 6 q^{10} - 16 q^{11} - 15 q^{12} - q^{13} - 19 q^{14} - 3 q^{15} + 30 q^{16} - 19 q^{17} + 6 q^{18} + 18 q^{19}+ \cdots - 64 q^{99}+O(q^{100}) $ 76 * q - 6 * q^2 - 7 * q^3 - 26 * q^4 + 13 * q^5 + 12 * q^6 + 22 * q^7 + 10 * q^8 - 24 * q^9 - 6 * q^10 - 16 * q^11 - 15 * q^12 - q^13 - 19 * q^14 - 3 * q^15 + 30 * q^16 - 19 * q^17 + 6 * q^18 + 18 * q^19 - 23 * q^20 - 22 * q^21 - 15 * q^22 - 8 * q^23 - 22 * q^24 + 35 * q^25 - 14 * q^26 - 10 * q^27 - 29 * q^28 - 25 * q^29 + 57 * q^30 + 22 * q^31 + 54 * q^32 - 22 * q^33 - 6 * q^34 - 19 * q^35 - 91 * q^36 - 49 * q^37 + 15 * q^38 + 25 * q^39 - 2 * q^40 + 16 * q^41 - 28 * q^42 + 104 * q^43 + 18 * q^44 + 10 * q^45 - 55 * q^46 - 26 * q^47 - 86 * q^48 + 2 * q^49 - 17 * q^50 + 18 * q^51 + 53 * q^52 - 41 * q^53 - 6 * q^54 + 67 * q^55 + 115 * q^56 + 84 * q^57 - 12 * q^58 - 7 * q^59 - 32 * q^60 - 21 * q^61 - 23 * q^62 - 21 * q^63 + 6 * q^64 - 72 * q^65 + 102 * q^66 - 15 * q^67 + 74 * q^68 + 48 * q^69 - 60 * q^70 - 8 * q^71 + 9 * q^72 - 25 * q^73 - 60 * q^74 + 68 * q^75 - 76 * q^76 - 36 * q^77 - 51 * q^78 + 2 * q^79 + 217 * q^80 + 20 * q^81 - 12 * q^82 - 41 * q^83 - 48 * q^84 - 7 * q^85 - 87 * q^86 - 54 * q^87 - 4 * q^88 + 77 * q^89 - 93 * q^90 + 79 * q^91 - 19 * q^92 + 72 * q^93 + 15 * q^94 + 57 * q^95 + 28 * q^96 + 13 * q^97 - 62 * q^98 - 64 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

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 $

$2$	−1.92608	+	1.39938i	−1.36195	+	0.989512i	−0.363628	+	0.931544i	$0.618462\pi$
$2$	−1.92608	+	1.39938i	−1.36195	+	0.989512i	−0.998318	+	0.0579674i	$0.981538\pi$
$3$	0.431982	−	1.32950i	0.249405	−	0.767589i	−0.745476	−	0.666532i	$-0.767778\pi$
$3$	0.431982	−	1.32950i	0.249405	−	0.767589i	0.994881	−	0.101056i	$-0.0322222\pi$
$4$	1.13349	−	3.48853i	0.566747	−	1.74427i
$5$	2.16658	−	0.553118i	0.968923	−	0.247362i
$5$	2.16658	−	0.553118i	0.968923	−	0.247362i
$6$	1.02845	+	3.16524i	0.419862	+	1.29220i
$7$	4.93434			1.86501			0.932503	−	0.361162i	$-0.117620\pi$
$7$	4.93434			1.86501			0.932503	+	0.361162i	$0.117620\pi$
$8$	1.22719	+	3.77690i	0.433877	+	1.33534i
$9$	0.846082	+	0.614714i	0.282027	+	0.204905i
$10$	−3.39899	+	4.09722i	−1.07485	+	1.29565i
$11$	1.16824	−	0.848778i	0.352238	−	0.255916i	−0.397569	−	0.917572i	$-0.630146\pi$
$11$	1.16824	−	0.848778i	0.352238	−	0.255916i	0.749807	+	0.661656i	$0.230146\pi$
$12$	−4.14837	−	3.01397i	−1.19753	−	0.870057i
$13$	−5.21572	−	3.78944i	−1.44658	−	1.05100i	−0.986616	−	0.163064i	$-0.947862\pi$
$13$	−5.21572	−	3.78944i	−1.44658	−	1.05100i	−0.459964	−	0.887938i	$-0.652138\pi$
$14$	−9.50395	+	6.90502i	−2.54004	+	1.84545i
$15$	0.200550	−	3.11941i	0.0517818	−	0.805428i
$16$	−1.71395	−	1.24526i	−0.428487	−	0.311314i
$17$	0.309017	+	0.951057i	0.0749476	+	0.230665i
$17$	0.309017	+	0.951057i	0.0749476	+	0.230665i
$18$	−2.48984			−0.586862
$19$	−0.519255	−	1.59810i	−0.119125	−	0.366630i	0.873660	−	0.486537i	$-0.161740\pi$
$19$	−0.519255	−	1.59810i	−0.119125	−	0.366630i	−0.992785	+	0.119907i	$0.961740\pi$
$20$	0.526232	−	8.18514i	0.117669	−	1.83025i
$21$	2.13155	−	6.56022i	0.465141	−	1.43156i
$22$	−1.06237	+	3.26963i	−0.226498	+	0.697088i
$23$	−4.70676	+	3.41966i	−0.981428	+	0.713049i	−0.958027	−	0.286677i	$-0.907449\pi$
$23$	−4.70676	+	3.41966i	−0.981428	+	0.713049i	−0.0234009	+	0.999726i	$0.507449\pi$
$24$	5.55153			1.13320
$25$	4.38812	−	2.39675i	0.877624	−	0.479349i
$26$	15.3488			3.01014
$27$	4.57558	−	3.32436i	0.880571	−	0.639773i
$28$	5.59304	−	17.2136i	1.05699	−	3.25307i
$29$	−1.39972	+	4.30790i	−0.259922	+	0.799957i	0.732898	+	0.680338i	$0.238167\pi$
$29$	−1.39972	+	4.30790i	−0.259922	+	0.799957i	−0.992820	+	0.119618i	$0.961833\pi$
$30$	3.97896	+	6.28888i	0.726456	+	1.14819i
$31$	1.07275	+	3.30160i	0.192672	+	0.592985i	0.999996	+	0.00287554i	$0.000915316\pi$
$31$	1.07275	+	3.30160i	0.192672	+	0.592985i	−0.807323	+	0.590109i	$0.799085\pi$
$32$	−2.89875			−0.512432
$33$	−0.623793	−	1.91984i	−0.108588	−	0.334201i
$34$	−1.92608	−	1.39938i	−0.330320	−	0.239992i
$35$	10.6906	−	2.72927i	1.80705	−	0.461331i
$36$	3.10348	−	2.25481i	0.517247	−	0.375802i
$37$	−7.27575	−	5.28614i	−1.19613	−	0.869036i	−0.202228	−	0.979338i	$-0.564818\pi$
$37$	−7.27575	−	5.28614i	−1.19613	−	0.869036i	−0.993898	+	0.110302i	$0.964818\pi$
$38$	3.23648	+	2.35144i	0.525027	+	0.381455i
$39$	−7.29116	+	5.29734i	−1.16752	+	0.848253i
$40$	4.74788	+	7.50417i	0.750705	+	1.18651i
$41$	3.63664	+	2.64217i	0.567948	+	0.412638i	0.834359	−	0.551221i	$-0.185838\pi$
$41$	3.63664	+	2.64217i	0.567948	+	0.412638i	−0.266411	+	0.963859i	$0.585838\pi$
$42$	5.07472	+	15.6184i	0.783046	+	2.40997i
$43$	−4.02450			−0.613731			−0.306866	−	0.951753i	$-0.599280\pi$
$43$	−4.02450			−0.613731			−0.306866	+	0.951753i	$0.599280\pi$
$44$	−1.63679	−	5.03754i	−0.246756	−	0.759437i
$45$	2.17311	+	0.863844i	0.323948	+	0.128774i
$46$	4.28020	−	13.1731i	0.631082	−	1.94227i
$47$	−0.693502	+	2.13438i	−0.101158	+	0.311331i	−0.988809	−	0.149184i	$-0.952335\pi$
$47$	−0.693502	+	2.13438i	−0.101158	+	0.311331i	0.887652	+	0.460515i	$0.152335\pi$
$48$	−2.39596	+	1.74077i	−0.345828	+	0.251258i
$49$	17.3477			2.47825
$50$	−5.09792	+	10.7570i	−0.720955	+	1.52127i
$51$	1.39792			0.195748
$52$	−19.1316	+	13.8999i	−2.65307	+	1.92757i
$53$	−0.484308	+	1.49055i	−0.0665248	+	0.204742i	−0.978793	−	0.204850i	$-0.934329\pi$
$53$	−0.484308	+	1.49055i	−0.0665248	+	0.204742i	0.912268	+	0.409593i	$0.134329\pi$
$54$	−4.16091	+	12.8060i	−0.566228	+	1.74267i
$55$	2.06161	−	2.48512i	0.277988	−	0.335093i
$56$	6.05538	+	18.6365i	0.809184	+	2.49041i
$57$	−2.34899			−0.311132
$58$	−3.33241	−	10.2561i	−0.437567	−	1.34669i
$59$	0.875925	+	0.636397i	0.114036	+	0.0828518i	0.643341	−	0.765579i	$-0.277548\pi$
$59$	0.875925	+	0.636397i	0.114036	+	0.0828518i	−0.529306	+	0.848431i	$0.677548\pi$
$60$	−10.6548	−	4.23546i	−1.37553	−	0.546795i
$61$	1.96527	−	1.42785i	0.251627	−	0.182817i	−0.454821	−	0.890583i	$-0.650297\pi$
$61$	1.96527	−	1.42785i	0.251627	−	0.182817i	0.706447	+	0.707766i	$0.250297\pi$
$62$	−6.68641	−	4.85796i	−0.849175	−	0.616962i
$63$	4.17486	+	3.03321i	0.525982	+	0.382149i
$64$	9.01113	−	6.54697i	1.12639	−	0.818371i
$65$	−13.3963	−	5.32521i	−1.66160	−	0.660511i
$66$	3.88806	+	2.82484i	0.478587	+	0.347714i
$67$	1.41301	+	4.34879i	0.172626	+	0.531290i	0.999517	−	0.0310731i	$-0.00989246\pi$
$67$	1.41301	+	4.34879i	0.172626	+	0.531290i	−0.826891	+	0.562363i	$0.809892\pi$
$68$	3.66806			0.444818
$69$	2.51322	+	7.73489i	0.302556	+	0.931171i
$70$	−16.7718	+	20.2171i	−2.00461	+	2.41640i
$71$	−4.34876	+	13.3841i	−0.516103	+	1.58840i	0.265163	+	0.964203i	$0.414574\pi$
$71$	−4.34876	+	13.3841i	−0.516103	+	1.58840i	−0.781266	+	0.624198i	$0.785426\pi$
$72$	−1.28341	+	3.94994i	−0.151252	+	0.465505i
$73$	6.68714	−	4.85849i	0.782670	−	0.568643i	−0.123109	−	0.992393i	$-0.539286\pi$
$73$	6.68714	−	4.85849i	0.782670	−	0.568643i	0.905779	+	0.423750i	$0.139286\pi$
$74$	21.4110			2.48898
$75$	−1.29089	−	6.86937i	−0.149059	−	0.793206i
$76$	−6.16361			−0.707015
$77$	5.76451	−	4.18816i	0.656926	−	0.477285i
$78$	6.63039	−	20.4062i	0.750743	−	2.31055i
$79$	4.77046	−	14.6820i	0.536719	−	1.65185i	−0.203188	−	0.979140i	$-0.565130\pi$
$79$	4.77046	−	14.6820i	0.536719	−	1.65185i	0.739906	−	0.672710i	$-0.234870\pi$
$80$	−4.40217	−	1.74993i	−0.492178	−	0.195648i
$81$	−1.47365	−	4.53543i	−0.163739	−	0.503936i
$82$	−10.7019			−1.18182
$83$	−2.64612	−	8.14393i	−0.290450	−	0.893913i	−0.984712	−	0.174191i	$-0.944269\pi$
$83$	−2.64612	−	8.14393i	−0.290450	−	0.893913i	0.694262	−	0.719722i	$-0.255731\pi$
$84$	−20.4695	−	14.8719i	−2.23340	−	1.62266i
$85$	1.19556	+	1.88962i	0.129676	+	0.204958i
$86$	7.75153	−	5.63181i	0.835869	−	0.607294i
$87$	5.12271	+	3.72187i	0.549212	+	0.399026i
$88$	4.63941	+	3.37073i	0.494562	+	0.359321i
$89$	−2.33871	+	1.69918i	−0.247903	+	0.180112i	−0.704797	−	0.709409i	$-0.748962\pi$
$89$	−2.33871	+	1.69918i	−0.247903	+	0.180112i	0.456894	+	0.889521i	$0.348962\pi$
$90$	−5.39444	+	1.37718i	−0.568624	+	0.145167i
$91$	−25.7361	−	18.6984i	−2.69788	−	1.96012i
$92$	6.59453	+	20.2959i	0.687527	+	2.11599i
$93$	4.85290			0.503222
$94$	−1.65107	−	5.08146i	−0.170295	−	0.524113i
$95$	−2.00895	−	3.17521i	−0.206114	−	0.325769i
$96$	−1.25221	+	3.85390i	−0.127803	+	0.393337i
$97$	−3.93745	+	12.1182i	−0.399787	+	1.23042i	0.525383	+	0.850866i	$0.323922\pi$
$97$	−3.93745	+	12.1182i	−0.399787	+	1.23042i	−0.925170	+	0.379552i	$0.876078\pi$
$98$	−33.4132	+	24.2761i	−3.37524	+	2.45225i
$99$	1.51018			0.151779
$100$	−3.38722	−	18.0248i	−0.338722	−	1.80248i
$101$	−0.0418895			−0.00416816			−0.00208408	−	0.999998i	$-0.500663\pi$
$101$	−0.0418895			−0.00416816			−0.00208408	+	0.999998i	$0.500663\pi$
$102$	−2.69251	+	1.95623i	−0.266599	+	0.193695i
$103$	0.142823	−	0.439564i	0.0140728	−	0.0433115i	−0.943774	−	0.330593i	$-0.892751\pi$
$103$	0.142823	−	0.439564i	0.0140728	−	0.0433115i	0.957846	+	0.287281i	$0.0927514\pi$
$104$	7.91167	−	24.3496i	0.775803	−	2.38768i
$105$	0.989583	−	15.3922i	0.0965734	−	1.50213i
$106$	−1.15303	−	3.54865i	−0.111992	−	0.344675i
$107$	−0.356689			−0.0344824			−0.0172412	−	0.999851i	$-0.505488\pi$
$107$	−0.356689			−0.0344824			−0.0172412	+	0.999851i	$0.505488\pi$
$108$	−6.41074	−	19.7302i	−0.616873	−	1.89854i
$109$	−8.04184	−	5.84274i	−0.770269	−	0.559633i	0.131774	−	0.991280i	$-0.457933\pi$
$109$	−8.04184	−	5.84274i	−0.770269	−	0.559633i	−0.902043	+	0.431647i	$0.857933\pi$
$110$	−0.493211	+	7.67153i	−0.0470258	+	0.731451i
$111$	−10.1709	+	7.38961i	−0.965382	+	0.701391i
$112$	−8.45720	−	6.14451i	−0.799130	−	0.580602i
$113$	7.17561	+	5.21338i	0.675024	+	0.490434i	0.871703	−	0.490034i	$-0.163016\pi$
$113$	7.17561	+	5.21338i	0.675024	+	0.490434i	−0.196679	+	0.980468i	$0.563016\pi$
$114$	4.52435	−	3.28713i	0.423744	−	0.307868i
$115$	−8.30610	+	10.0124i	−0.774547	+	0.933658i
$116$	13.4417	+	9.76595i	1.24803	+	0.906746i
$117$	−2.08350	−	6.41235i	−0.192620	−	0.592822i
$118$	−2.57766			−0.237293
$119$	1.52480	+	4.69284i	0.139778	+	0.430192i
$120$	12.0278	−	3.07065i	1.09798	−	0.280311i
$121$	−2.75482	+	8.47847i	−0.250438	+	0.770770i
$122$	−1.78716	+	5.50031i	−0.161802	+	0.497975i
$123$	5.08374	−	3.69355i	0.458385	−	0.333036i
$124$	12.7337			1.14352
$125$	8.18152	−	7.61989i	0.731778	−	0.681543i
$126$	−12.2857			−1.09450
$127$	−6.86783	+	4.98977i	−0.609422	+	0.442771i	−0.849211	−	0.528054i	$-0.822922\pi$
$127$	−6.86783	+	4.98977i	−0.609422	+	0.442771i	0.239789	+	0.970825i	$0.422922\pi$
$128$	−6.40295	+	19.7063i	−0.565946	+	1.74180i
$129$	−1.73851	+	5.35059i	−0.153067	+	0.471093i
$130$	33.2543	−	8.48968i	2.91660	−	0.744594i
$131$	−4.29567	−	13.2207i	−0.375314	−	1.15510i	−0.943266	−	0.332037i	$-0.892264\pi$
$131$	−4.29567	−	13.2207i	−0.375314	−	1.15510i	0.567952	−	0.823062i	$-0.307736\pi$
$132$	−7.40448			−0.644478
$133$	−2.56218	−	7.88559i	−0.222169	−	0.683767i
$134$	−8.80719	−	6.39880i	−0.760825	−	0.552772i
$135$	8.07460	−	9.73331i	0.694951	−	0.837710i
$136$	−3.21283	+	2.33425i	−0.275497	+	0.200161i
$137$	−2.58936	−	1.88128i	−0.221224	−	0.160729i	0.471653	−	0.881784i	$-0.343657\pi$
$137$	−2.58936	−	1.88128i	−0.221224	−	0.160729i	−0.692878	+	0.721055i	$0.743657\pi$
$138$	−15.6647	−	11.3811i	−1.33347	−	0.968822i
$139$	−17.8213	+	12.9479i	−1.51158	+	1.09823i	−0.546108	+	0.837715i	$0.683891\pi$
$139$	−17.8213	+	12.9479i	−1.51158	+	1.09823i	−0.965471	+	0.260511i	$0.916109\pi$
$140$	2.59661	−	40.3883i	0.219453	−	3.41343i
$141$	2.53808	+	1.84402i	0.213745	+	0.155295i
$142$	−10.3534	−	31.8645i	−0.868838	−	2.67401i
$143$	−9.30961			−0.778509
$144$	−0.684663	−	2.10717i	−0.0570552	−	0.175598i
$145$	−0.649830	+	10.1076i	−0.0539654	+	0.839391i
$146$	−6.08110	+	18.7157i	−0.503276	+	1.54892i
$147$	7.49390	−	23.0639i	0.618087	−	1.90227i
$148$	−26.6879	+	19.3899i	−2.19373	+	1.59384i
$149$	11.9362			0.977855			0.488928	−	0.872324i	$-0.337388\pi$
$149$	11.9362			0.977855			0.488928	+	0.872324i	$0.337388\pi$
$150$	12.0992	+	11.4245i	0.987898	+	0.932808i
$151$	−4.21086			−0.342675			−0.171337	−	0.985212i	$-0.554809\pi$
$151$	−4.21086			−0.342675			−0.171337	+	0.985212i	$0.554809\pi$
$152$	5.39866	−	3.92235i	0.437889	−	0.318145i
$153$	−0.323174	+	0.994629i	−0.0261271	+	0.0804110i
$154$	−5.24209	+	16.1335i	−0.422419	+	1.30007i
$155$	4.15038	+	6.55981i	0.333367	+	0.526897i
$156$	10.2155	+	31.4400i	0.817892	+	2.51721i
$157$	24.9552			1.99164			0.995820	−	0.0913379i	$-0.0291143\pi$
$157$	24.9552			1.99164			0.995820	+	0.0913379i	$0.0291143\pi$
$158$	11.3574	+	34.9544i	0.903543	+	2.78082i
$159$	1.77247	+	1.28778i	0.140566	+	0.102127i
$160$	−6.28037	+	1.60335i	−0.496507	+	0.126756i
$161$	−23.2248	+	16.8738i	−1.83037	+	1.32984i
$162$	9.18516	+	6.67341i	0.721654	+	0.524312i
$163$	0.408921	+	0.297099i	0.0320292	+	0.0232706i	0.603685	−	0.797223i	$-0.293699\pi$
$163$	0.408921	+	0.297099i	0.0320292	+	0.0232706i	−0.571655	+	0.820494i	$0.693699\pi$
$164$	13.3394	−	9.69166i	1.04163	−	0.756791i
$165$	−2.41339	−	3.81445i	−0.187882	−	0.296954i
$166$	16.4931	+	11.9830i	1.28011	+	0.930058i
$167$	−2.87195	−	8.83895i	−0.222238	−	0.683979i	−0.998560	−	0.0536422i	$-0.982917\pi$
$167$	−2.87195	−	8.83895i	−0.222238	−	0.683979i	0.776322	−	0.630336i	$-0.217083\pi$
$168$	27.3931			2.11343
$169$	8.82662	+	27.1655i	0.678971	+	2.08966i
$170$	−4.94703	−	1.96652i	−0.379420	−	0.150825i
$171$	0.543045	−	1.67132i	0.0415277	−	0.127809i
$172$	−4.56175	+	14.0396i	−0.347830	+	1.07051i
$173$	−3.46281	+	2.51588i	−0.263272	+	0.191278i	−0.711588	−	0.702597i	$-0.752024\pi$
$173$	−3.46281	+	2.51588i	−0.263272	+	0.191278i	0.448316	+	0.893875i	$0.352024\pi$
$174$	−15.0751			−1.14284
$175$	21.6525	−	11.8264i	1.63677	−	0.893989i
$176$	−3.05925			−0.230600
$177$	1.22447	−	0.889633i	0.0920371	−	0.0668689i
$178$	2.12676	−	6.54551i	0.159408	−	0.490606i
$179$	−3.84954	+	11.8477i	−0.287728	+	0.885535i	0.697840	+	0.716254i	$0.254145\pi$
$179$	−3.84954	+	11.8477i	−0.287728	+	0.885535i	−0.985568	+	0.169281i	$0.945855\pi$
$180$	5.47676	−	6.60181i	0.408213	−	0.492070i
$181$	5.26400	+	16.2009i	0.391270	+	1.20420i	0.931829	+	0.362898i	$0.118213\pi$
$181$	5.26400	+	16.2009i	0.391270	+	1.20420i	−0.540559	+	0.841306i	$0.681787\pi$
$182$	75.7361			5.61393
$183$	−1.04937	−	3.22963i	−0.0775718	−	0.238741i
$184$	−18.6918	−	13.5804i	−1.37798	−	1.00116i
$185$	−18.6873	−	7.42849i	−1.37392	−	0.546154i
$186$	−9.34708	+	6.79105i	−0.685361	+	0.497944i
$187$	1.16824	+	0.848778i	0.0854303	+	0.0620688i
$188$	6.65977	+	4.83861i	0.485714	+	0.352892i
$189$	22.5775	−	16.4035i	1.64227	−	1.19318i
$190$	8.31272	+	3.30443i	0.603068	+	0.239728i
$191$	−5.01984	−	3.64713i	−0.363223	−	0.263897i	0.391172	−	0.920318i	$-0.372070\pi$
$191$	−5.01984	−	3.64713i	−0.363223	−	0.263897i	−0.754395	+	0.656421i	$0.772070\pi$
$192$	−4.81157	−	14.8085i	−0.347245	−	1.06871i
$193$	8.85480			0.637383			0.318691	−	0.947859i	$-0.396757\pi$
$193$	8.85480			0.637383			0.318691	+	0.947859i	$0.396757\pi$
$194$	−9.37415	−	28.8507i	−0.673025	−	2.07136i
$195$	−12.8668	+	15.5100i	−0.921412	+	1.11069i
$196$	19.6635	−	60.5182i	1.40454	−	4.32273i
$197$	−8.12218	+	24.9975i	−0.578681	+	1.78100i	0.0446053	+	0.999005i	$0.485797\pi$
$197$	−8.12218	+	24.9975i	−0.578681	+	1.78100i	−0.623287	+	0.781993i	$0.714203\pi$
$198$	−2.90874	+	2.11332i	−0.206715	+	0.150187i
$199$	−21.4238			−1.51869			−0.759347	−	0.650686i	$-0.774481\pi$
$199$	−21.4238			−1.51869			−0.759347	+	0.650686i	$0.774481\pi$
$200$	14.4373	+	13.6322i	1.02087	+	0.963945i
$201$	6.39213			0.450866
$202$	0.0806826	−	0.0586193i	0.00567681	−	0.00412444i
$203$	−6.90670	+	21.2566i	−0.484756	+	1.49192i
$204$	1.58454	−	4.87670i	0.110940	−	0.341437i
$205$	9.34050	+	3.71298i	0.652369	+	0.259326i
$206$	0.340029	+	1.04650i	0.0236909	+	0.0729131i
$207$	−6.08442			−0.422897
$208$	4.22064	+	12.9898i	0.292649	+	0.900680i
$209$	−1.96305	−	1.42624i	−0.135787	−	0.0986551i
$210$	19.6336	+	31.0315i	1.35485	+	2.14138i
$211$	−1.00553	+	0.730558i	−0.0692233	+	0.0502937i	−0.621859	−	0.783129i	$-0.713622\pi$
$211$	−1.00553	+	0.730558i	−0.0692233	+	0.0502937i	0.552635	+	0.833423i	$0.313622\pi$
$212$	4.65086	+	3.37905i	0.319423	+	0.232074i
$213$	15.9156	+	11.5634i	1.09052	+	0.792310i
$214$	0.687012	−	0.499144i	0.0469632	−	0.0341208i
$215$	−8.71940	+	2.22603i	−0.594658	+	0.151814i
$216$	18.1709	+	13.2019i	1.23637	+	0.898277i
$217$	5.29334	+	16.2912i	0.359335	+	1.10592i
$218$	23.6655			1.60283
$219$	−3.57066	−	10.9893i	−0.241283	−	0.742591i
$220$	−6.33259	−	10.0089i	−0.426943	−	0.674798i
$221$	1.99223	−	6.13144i	0.134012	−	0.412445i
$222$	9.24917	−	28.4660i	0.620764	−	1.91051i
$223$	1.69990	−	1.23505i	0.113834	−	0.0827051i	−0.529412	−	0.848365i	$-0.677587\pi$
$223$	1.69990	−	1.23505i	0.113834	−	0.0827051i	0.643246	+	0.765660i	$0.277587\pi$
$224$	−14.3034			−0.955688
$225$	5.18602	+	0.669598i	0.345735	+	0.0446399i
$226$	−21.1163			−1.40464
$227$	−4.62132	+	3.35758i	−0.306728	+	0.222851i	−0.730491	−	0.682922i	$-0.760709\pi$
$227$	−4.62132	+	3.35758i	−0.306728	+	0.222851i	0.423763	+	0.905773i	$0.360709\pi$
$228$	−2.66257	+	8.19454i	−0.176333	+	0.542697i
$229$	1.67703	−	5.16137i	0.110821	−	0.341073i	−0.880231	−	0.474545i	$-0.842613\pi$
$229$	1.67703	−	5.16137i	0.110821	−	0.341073i	0.991053	+	0.133472i	$0.0426126\pi$
$230$	1.98711	−	30.9080i	0.131026	−	2.03802i
$231$	−3.07801	−	9.47313i	−0.202518	−	0.623286i
$232$	−17.9882			−1.18099
$233$	−7.41618	−	22.8247i	−0.485850	−	1.49529i	−0.830746	−	0.556652i	$-0.812086\pi$
$233$	−7.41618	−	22.8247i	−0.485850	−	1.49529i	0.344896	−	0.938641i	$-0.387914\pi$
$234$	12.9863	+	9.43511i	0.848942	+	0.616792i
$235$	−0.321963	+	5.00789i	−0.0210025	+	0.326678i
$236$	3.21295	−	2.33434i	0.209145	−	0.151953i
$237$	−17.4590	−	12.6847i	−1.13408	−	0.823958i
$238$	−9.50395	−	6.90502i	−0.616050	−	0.447586i
$239$	8.63950	−	6.27696i	0.558843	−	0.406023i	−0.272193	−	0.962243i	$-0.587749\pi$
$239$	8.63950	−	6.27696i	0.558843	−	0.406023i	0.831035	+	0.556220i	$0.187749\pi$
$240$	−4.22819	+	5.09676i	−0.272929	+	0.328995i
$241$	12.5901	+	9.14725i	0.811001	+	0.589226i	0.914121	−	0.405443i	$-0.132883\pi$
$241$	12.5901	+	9.14725i	0.811001	+	0.589226i	−0.103120	+	0.994669i	$0.532883\pi$
$242$	−6.55859	−	20.1853i	−0.421602	−	1.29756i
$243$	10.3007			0.660793
$244$	−2.75349	−	8.47436i	−0.176274	−	0.542515i
$245$	37.5852	−	9.59534i	2.40123	−	0.613024i
$246$	−4.62301	+	14.2282i	−0.294753	+	0.907155i
$247$	−3.34763	+	10.3029i	−0.213005	+	0.655560i
$248$	−11.1533	+	8.10338i	−0.708238	+	0.514565i
$249$	−11.9705			−0.758597
$250$	−5.09517	+	26.1256i	−0.322247	+	1.65233i
$251$	0.283183			0.0178743			0.00893717	−	0.999960i	$-0.497155\pi$
$251$	0.283183			0.0178743			0.00893717	+	0.999960i	$0.497155\pi$
$252$	15.3136	−	11.1260i	0.964668	−	0.700872i
$253$	−2.59611	+	7.98999i	−0.163216	+	0.502326i
$254$	6.24542	−	19.2214i	0.391873	−	1.20606i
$255$	3.02871	−	0.773216i	0.189665	−	0.0484206i
$256$	−8.36005	−	25.7296i	−0.522503	−	1.60810i
$257$	9.99891			0.623715			0.311858	−	0.950129i	$-0.399049\pi$
$257$	9.99891			0.623715			0.311858	+	0.950129i	$0.399049\pi$
$258$	−4.13900	−	12.7385i	−0.257683	−	0.793065i
$259$	−35.9010	−	26.0836i	−2.23078	−	1.62076i
$260$	−33.7618	+	40.6972i	−2.09382	+	2.52393i
$261$	−3.83241	+	2.78441i	−0.237220	+	0.172350i
$262$	26.7746	+	19.4529i	1.65414	+	1.20180i
$263$	−2.14547	−	1.55878i	−0.132296	−	0.0961183i	0.519669	−	0.854367i	$-0.326055\pi$
$263$	−2.14547	−	1.55878i	−0.132296	−	0.0961183i	−0.651965	+	0.758249i	$0.726055\pi$
$264$	6.48553	−	4.71201i	0.399157	−	0.290004i
$265$	−0.224843	+	3.49726i	−0.0138120	+	0.214835i
$266$	15.9699	+	11.6028i	0.979179	+	0.711415i
$267$	1.24878	+	3.84334i	0.0764239	+	0.235209i
$268$	16.7726			1.02455
$269$	−3.86642	−	11.8996i	−0.235740	−	0.725533i	−0.997022	−	0.0771123i	$-0.975430\pi$
$269$	−3.86642	−	11.8996i	−0.235740	−	0.725533i	0.761283	−	0.648420i	$-0.224570\pi$
$270$	−1.93173	+	30.0466i	−0.117561	+	1.82858i
$271$	−1.45897	+	4.49025i	−0.0886262	+	0.272763i	−0.985540	−	0.169442i	$-0.945804\pi$
$271$	−1.45897	+	4.49025i	−0.0886262	+	0.272763i	0.896914	+	0.442205i	$0.145804\pi$
$272$	0.654669	−	2.01487i	0.0396952	−	0.122169i
$273$	−35.9771	+	26.1389i	−2.17743	+	1.58200i
$274$	7.61996			0.460339
$275$	3.09208	−	6.52452i	0.186460	−	0.393443i
$276$	29.8321			1.79568
$277$	−20.4710	+	14.8730i	−1.22998	+	0.893634i	−0.996889	−	0.0788200i	$-0.974885\pi$
$277$	−20.4710	+	14.8730i	−1.22998	+	0.893634i	−0.233093	+	0.972454i	$0.574885\pi$
$278$	16.2062	−	49.8774i	0.971981	−	2.99145i
$279$	−1.12190	+	3.45286i	−0.0671665	+	0.206717i
$280$	23.4276	+	37.0282i	1.40007	+	2.21286i
$281$	−8.04349	−	24.7553i	−0.479834	−	1.47678i	−0.839325	−	0.543630i	$-0.817050\pi$
$281$	−8.04349	−	24.7553i	−0.479834	−	1.47678i	0.359491	−	0.933149i	$-0.382950\pi$
$282$	−7.46905			−0.444775
$283$	3.75157	+	11.5461i	0.223007	+	0.686346i	0.998488	+	0.0549746i	$0.0175078\pi$
$283$	3.75157	+	11.5461i	0.223007	+	0.686346i	−0.775480	+	0.631372i	$0.782492\pi$
$284$	41.7616	+	30.3416i	2.47810	+	1.80044i
$285$	−5.08927	+	1.29927i	−0.301463	+	0.0769621i
$286$	17.9311	−	13.0277i	1.06029	−	0.770344i
$287$	17.9444	+	13.0374i	1.05923	+	0.769573i
$288$	−2.45258	−	1.78190i	−0.144520	−	0.105000i
$289$	−0.809017	+	0.587785i	−0.0475892	+	0.0345756i
$290$	−12.8928	−	20.3775i	−0.757090	−	1.19661i
$291$	14.4103	+	10.4697i	0.844746	+	0.613744i
$292$	−9.36918	−	28.8354i	−0.548290	−	1.68746i
$293$	−13.7539			−0.803512			−0.401756	−	0.915747i	$-0.631600\pi$
$293$	−13.7539			−0.803512			−0.401756	+	0.915747i	$0.631600\pi$
$294$	17.8412	+	54.9097i	1.04052	+	3.20240i
$295$	2.24976	+	0.894313i	0.130986	+	0.0520689i
$296$	11.0365	−	33.9669i	0.641484	−	1.97429i
$297$	2.52375	−	7.76731i	0.146443	−	0.450705i
$298$	−22.9902	+	16.7034i	−1.33179	+	0.967600i
$299$	37.5078			2.16913
$300$	−25.4272	−	3.28306i	−1.46804	−	0.189548i
$301$	−19.8583			−1.14461
$302$	8.11046	−	5.89260i	0.466705	−	0.339081i
$303$	−0.0180955	+	0.0556922i	−0.00103956	+	0.00319943i
$304$	−1.10007	+	3.38567i	−0.0630934	+	0.194181i
$305$	3.46813	−	4.18057i	0.198585	−	0.239379i
$306$	−0.769404	−	2.36798i	−0.0439839	−	0.135368i
$307$	−8.55668			−0.488356			−0.244178	−	0.969730i	$-0.578518\pi$
$307$	−8.55668			−0.488356			−0.244178	+	0.969730i	$0.578518\pi$
$308$	−8.07650	−	24.8569i	−0.460202	−	1.41635i
$309$	−0.522705	−	0.379767i	−0.0297356	−	0.0216042i
$310$	−17.1737	−	6.82678i	−0.975398	−	0.387735i
$311$	−11.9140	+	8.65604i	−0.675582	+	0.490839i	−0.871889	−	0.489703i	$-0.837105\pi$
$311$	−11.9140	+	8.65604i	−0.675582	+	0.490839i	0.196307	+	0.980542i	$0.437105\pi$
$312$	−28.9552	−	21.0372i	−1.63926	−	1.19100i
$313$	2.39781	+	1.74211i	0.135532	+	0.0984698i	0.653486	−	0.756939i	$-0.273306\pi$
$313$	2.39781	+	1.74211i	0.135532	+	0.0984698i	−0.517954	+	0.855409i	$0.673306\pi$
$314$	−48.0657	+	34.9218i	−2.71251	+	1.97075i
$315$	10.7229	+	4.26250i	0.604166	+	0.240165i
$316$	−45.8112	−	33.2838i	−2.57708	−	1.87236i
$317$	−3.33983	−	10.2789i	−0.187584	−	0.577323i	0.812400	−	0.583101i	$-0.198161\pi$
$317$	−3.33983	−	10.2789i	−0.187584	−	0.577323i	−0.999983	+	0.00577786i	$0.998161\pi$
$318$	−5.21602			−0.292500
$319$	2.02123	+	6.22072i	0.113167	+	0.348294i
$320$	15.9021	−	19.1687i	0.888953	−	1.07156i
$321$	−0.154083	+	0.474219i	−0.00860008	+	0.0264683i
$322$	21.1200	−	65.0006i	1.17697	−	3.62234i
$323$	1.35943	−	0.987682i	0.0756406	−	0.0549561i
$324$	−17.4924			−0.971798
$325$	−31.9695	−	4.12777i	−1.77335	−	0.228968i
$326$	−1.20337			−0.0666485
$327$	−11.2419	+	8.16770i	−0.621677	+	0.451675i
$328$	−5.51638	+	16.9777i	−0.304591	+	0.937436i
$329$	−3.42197	+	10.5318i	−0.188660	+	0.580634i
$330$	9.98626	+	3.96968i	0.549725	+	0.218524i
$331$	−7.30861	−	22.4936i	−0.401717	−	1.23636i	−0.923605	−	0.383345i	$-0.874772\pi$
$331$	−7.30861	−	22.4936i	−0.401717	−	1.23636i	0.521888	−	0.853014i	$-0.325228\pi$
$332$	−31.4098			−1.72383
$333$	−2.90641	−	8.94502i	−0.159270	−	0.490184i
$334$	17.9007	+	13.0056i	0.979481	+	0.711635i
$335$	5.46679	+	8.64044i	0.298683	+	0.472078i
$336$	−11.8225	+	8.58955i	−0.644970	+	0.468598i
$337$	14.1187	+	10.2578i	0.769094	+	0.558779i	0.901686	−	0.432391i	$-0.142330\pi$
$337$	14.1187	+	10.2578i	0.769094	+	0.558779i	−0.132592	+	0.991171i	$0.542330\pi$
$338$	−55.0158	−	39.9713i	−2.99246	−	2.17415i
$339$	10.0309	−	7.28790i	0.544806	−	0.395825i
$340$	7.94714	−	2.02887i	0.430994	−	0.110031i
$341$	4.05556	+	2.94654i	0.219621	+	0.159564i
$342$	1.29286	+	3.97903i	0.0699101	+	0.215161i
$343$	51.0592			2.75694
$344$	−4.93883	−	15.2002i	−0.266284	−	0.819538i
$345$	9.72339	+	15.3681i	0.523490	+	0.827393i
$346$	3.14898	−	9.69157i	0.169290	−	0.521022i
$347$	−1.74125	+	5.35903i	−0.0934754	+	0.287688i	−0.986853	−	0.161618i	$-0.948329\pi$
$347$	−1.74125	+	5.35903i	−0.0934754	+	0.287688i	0.893378	+	0.449306i	$0.148329\pi$
$348$	18.7904	−	13.6520i	1.00727	−	0.731826i
$349$	2.81772			0.150829			0.0754147	−	0.997152i	$-0.475972\pi$
$349$	2.81772			0.150829			0.0754147	+	0.997152i	$0.475972\pi$
$350$	−25.1549	+	53.0786i	−1.34459	+	2.83717i
$351$	−36.4624			−1.94622
$352$	−3.38644	+	2.46040i	−0.180498	+	0.131140i
$353$	1.90521	−	5.86363i	0.101404	−	0.312089i	−0.887466	−	0.460874i	$-0.847536\pi$
$353$	1.90521	−	5.86363i	0.101404	−	0.312089i	0.988870	+	0.148784i	$0.0475360\pi$
$354$	−1.11350	+	3.42701i	−0.0591821	+	0.182144i
$355$	−2.01894	+	31.4031i	−0.107154	+	1.66670i
$356$	3.27671	+	10.0847i	0.173666	+	0.534488i
$357$	6.89782			0.365072
$358$	−9.16486	−	28.2065i	−0.484378	−	1.49076i
$359$	−23.1375	−	16.8104i	−1.22115	−	0.887217i	−0.224954	−	0.974369i	$-0.572223\pi$
$359$	−23.1375	−	16.8104i	−1.22115	−	0.887217i	−0.996195	+	0.0871529i	$0.972223\pi$
$360$	−0.595833	+	9.26773i	−0.0314031	+	0.488452i
$361$	13.0870	−	9.50827i	0.688790	−	0.500435i
$362$	−32.8101	−	23.8380i	−1.72446	−	1.25290i
$363$	10.0821	+	7.32508i	0.529174	+	0.384467i
$364$	−94.4017	+	68.5869i	−4.94799	+	3.59493i
$365$	11.8009	−	14.2251i	0.617687	−	0.744575i
$366$	6.54066	+	4.75207i	0.341886	+	0.248395i
$367$	−0.843644	−	2.59647i	−0.0440379	−	0.135535i	0.926620	−	0.375999i	$-0.122700\pi$
$367$	−0.843644	−	2.59647i	−0.0440379	−	0.135535i	−0.970658	+	0.240464i	$0.922700\pi$
$368$	12.3255			0.642511
$369$	1.45271	+	4.47099i	0.0756252	+	0.232750i
$370$	46.3887	−	11.8428i	2.41163	−	0.615679i
$371$	−2.38974	+	7.35487i	−0.124069	+	0.381846i
$372$	5.50073	−	16.9295i	0.285199	−	0.877753i
$373$	12.9916	−	9.43897i	0.672681	−	0.488731i	−0.198241	−	0.980153i	$-0.563523\pi$
$373$	12.9916	−	9.43897i	0.672681	−	0.488731i	0.870921	+	0.491422i	$0.163523\pi$
$374$	−3.43789			−0.177769
$375$	−6.59639	−	14.1690i	−0.340636	−	0.731684i
$376$	−8.91240			−0.459622
$377$	23.6251	−	17.1646i	1.21675	−	0.884023i
$378$	−20.5314	+	63.1890i	−1.05602	+	3.25009i
$379$	8.28711	−	25.5051i	0.425680	−	1.31011i	−0.476662	−	0.879087i	$-0.658153\pi$
$379$	8.28711	−	25.5051i	0.425680	−	1.31011i	0.902342	−	0.431022i	$-0.141847\pi$
$380$	−13.3539	+	3.40920i	−0.685043	+	0.174888i
$381$	3.66714	+	11.2863i	0.187873	+	0.578214i
$382$	14.7724			0.755820
$383$	11.2551	+	34.6396i	0.575109	+	1.77000i	0.635809	+	0.771847i	$0.280667\pi$
$383$	11.2551	+	34.6396i	0.575109	+	1.77000i	−0.0606998	+	0.998156i	$0.519333\pi$
$384$	23.4336	+	17.0255i	1.19584	+	0.868828i
$385$	10.1727	−	12.2624i	0.518449	−	0.624951i
$386$	−17.0551	+	12.3912i	−0.868081	+	0.630698i
$387$	−3.40506	−	2.47392i	−0.173089	−	0.125756i
$388$	37.8117	+	27.4718i	1.91960	+	1.39467i
$389$	3.31876	−	2.41122i	0.168268	−	0.122254i	−0.500464	−	0.865757i	$-0.666837\pi$
$389$	3.31876	−	2.41122i	0.168268	−	0.122254i	0.668732	+	0.743503i	$0.266837\pi$
$390$	3.07820	−	47.8791i	0.155871	−	2.42445i
$391$	−4.70676	−	3.41966i	−0.238031	−	0.172940i
$392$	21.2890	+	65.5207i	1.07526	+	3.30929i
$393$	−19.4326			−0.980246
$394$	−19.3370	−	59.5133i	−0.974186	−	2.99824i
$395$	2.21472	−	34.4482i	0.111434	−	1.73328i
$396$	1.71178	−	5.26833i	0.0860204	−	0.264743i
$397$	−3.25831	+	10.0280i	−0.163530	+	0.503293i	−0.998925	−	0.0463566i	$-0.985239\pi$
$397$	−3.25831	+	10.0280i	−0.163530	+	0.503293i	0.835395	+	0.549650i	$0.185239\pi$
$398$	41.2640	−	29.9801i	2.06838	−	1.50277i
$399$	−11.5907			−0.580262
$400$	−10.5056	−	1.35644i	−0.525278	−	0.0678218i
$401$	−2.69042			−0.134353			−0.0671765	−	0.997741i	$-0.521399\pi$
$401$	−2.69042			−0.134353			−0.0671765	+	0.997741i	$0.521399\pi$
$402$	−12.3118	+	8.94502i	−0.614055	+	0.446137i
$403$	6.91603	−	21.2853i	0.344512	−	1.06030i
$404$	−0.0474814	+	0.146133i	−0.00236229	+	0.00727038i
$405$	−5.70140	−	9.01125i	−0.283305	−	0.447773i
$406$	−16.4433	−	50.6072i	−0.816066	−	2.51159i
$407$	−12.9866			−0.643722
$408$	1.71552	+	5.27981i	0.0849307	+	0.261390i
$409$	21.9196	+	15.9255i	1.08386	+	0.787468i	0.978351	−	0.206951i	$-0.0663541\pi$
$409$	21.9196	+	15.9255i	1.08386	+	0.787468i	0.105505	+	0.994419i	$0.466354\pi$
$410$	−23.1865	+	5.91940i	−1.14510	+	0.292338i
$411$	−3.61973	+	2.62989i	−0.178548	+	0.129723i
$412$	−1.37155	−	0.996486i	−0.0675712	−	0.0490933i
$413$	4.32211	+	3.14020i	0.212677	+	0.154519i
$414$	11.7191	−	8.51443i	0.575963	−	0.418461i
$415$	−10.2376	−	16.1808i	−0.502544	−	0.794287i
$416$	15.1191	+	10.9846i	0.741273	+	0.538566i
$417$	9.51581	+	29.2867i	0.465991	+	1.43417i
$418$	5.77685			0.282555
$419$	9.33249	+	28.7225i	0.455922	+	1.40318i	0.870049	+	0.492965i	$0.164087\pi$
$419$	9.33249	+	28.7225i	0.455922	+	1.40318i	−0.414127	+	0.910219i	$0.635913\pi$
$420$	−52.5746	−	20.8992i	−2.56538	−	1.01978i
$421$	−4.23943	+	13.0476i	−0.206617	+	0.635902i	0.793026	+	0.609188i	$0.208504\pi$
$421$	−4.23943	+	13.0476i	−0.206617	+	0.635902i	−0.999643	+	0.0267140i	$0.991496\pi$
$422$	0.914399	−	2.81423i	0.0445122	−	0.136995i
$423$	−1.89879	+	1.37955i	−0.0923224	+	0.0670762i
$424$	−6.22399			−0.302264
$425$	3.63544	+	3.43272i	0.176345	+	0.166511i
$426$	−46.8364			−2.26923
$427$	9.69730	−	7.04550i	0.469285	−	0.340956i
$428$	−0.404304	+	1.24432i	−0.0195428	+	0.0601465i
$429$	−4.02158	+	12.3772i	−0.194164	+	0.597575i
$430$	13.6792	−	16.4893i	0.659671	−	0.795183i
$431$	4.38370	+	13.4917i	0.211156	+	0.649870i	0.999404	+	0.0345132i	$0.0109881\pi$
$431$	4.38370	+	13.4917i	0.211156	+	0.649870i	−0.788249	+	0.615357i	$0.789012\pi$
$432$	−11.9820			−0.576483
$433$	−4.95442	−	15.2481i	−0.238094	−	0.732779i	−0.996696	−	0.0812241i	$-0.974117\pi$
$433$	−4.95442	−	15.2481i	−0.238094	−	0.732779i	0.758602	−	0.651555i	$-0.225883\pi$
$434$	−32.9930	−	23.9708i	−1.58372	−	1.15064i
$435$	13.1574	+	5.23025i	0.630848	+	0.250771i
$436$	−29.4980	+	21.4315i	−1.41270	+	1.02638i
$437$	7.90899	+	5.74622i	0.378338	+	0.274879i
$438$	22.2557	+	16.1697i	1.06342	+	0.772618i
$439$	24.7569	−	17.9869i	1.18158	−	0.858469i	0.189232	−	0.981932i	$-0.439400\pi$
$439$	24.7569	−	17.9869i	1.18158	−	0.858469i	0.992349	+	0.123464i	$0.0394002\pi$
$440$	11.9160	+	4.73680i	0.568075	+	0.225818i
$441$	14.6776	+	10.6639i	0.698933	+	0.507805i
$442$	4.74303	+	14.5975i	0.225603	+	0.694335i
$443$	−27.8966			−1.32541			−0.662703	−	0.748883i	$-0.730591\pi$
$443$	−27.8966			−1.32541			−0.662703	+	0.748883i	$0.730591\pi$
$444$	14.2502	+	43.8577i	0.676286	+	2.08140i
$445$	−4.12716	+	4.97498i	−0.195646	+	0.235837i
$446$	−1.54584	+	4.75762i	−0.0731978	+	0.225280i
$447$	5.15624	−	15.8693i	0.243882	−	0.750591i
$448$	44.4640	−	32.3050i	2.10073	−	1.52627i
$449$	31.2209			1.47340			0.736702	−	0.676218i	$-0.236382\pi$
$449$	31.2209			1.47340			0.736702	+	0.676218i	$0.236382\pi$
$450$	−10.9257	+	5.96752i	−0.515044	+	0.281312i
$451$	6.49109			0.305654
$452$	26.3206	−	19.1230i	1.23802	−	0.899471i
$453$	−1.81901	+	5.59835i	−0.0854647	+	0.263033i
$454$	4.20250	−	12.9340i	0.197233	−	0.607021i
$455$	−66.1017	−	26.2764i	−3.09890	−	1.23186i
$456$	−2.88266	−	8.87191i	−0.134993	−	0.415465i
$457$	−1.26689			−0.0592628			−0.0296314	−	0.999561i	$-0.509433\pi$
$457$	−1.26689			−0.0592628			−0.0296314	+	0.999561i	$0.509433\pi$
$458$	3.99262	+	12.2880i	0.186563	+	0.574182i
$459$	4.57558	+	3.32436i	0.213570	+	0.155168i
$460$	25.5136	+	40.3250i	1.18958	+	1.88017i
$461$	7.05965	−	5.12914i	0.328801	−	0.238888i	−0.411121	−	0.911581i	$-0.634863\pi$
$461$	7.05965	−	5.12914i	0.328801	−	0.238888i	0.739922	+	0.672693i	$0.234863\pi$
$462$	19.1850	+	13.9387i	0.892568	+	0.648489i
$463$	13.9812	+	10.1579i	0.649761	+	0.472079i	0.863190	−	0.504880i	$-0.168463\pi$
$463$	13.9812	+	10.1579i	0.649761	+	0.472079i	−0.213429	+	0.976959i	$0.568463\pi$
$464$	7.76348	−	5.64050i	0.360411	−	0.261854i
$465$	10.5142	−	2.68422i	0.487583	−	0.124478i
$466$	46.2246	+	33.5841i	2.14131	+	1.55575i
$467$	−2.96492	−	9.12507i	−0.137200	−	0.422258i	0.858726	−	0.512435i	$-0.171257\pi$
$467$	−2.96492	−	9.12507i	−0.137200	−	0.422258i	−0.995926	+	0.0901774i	$0.971257\pi$
$468$	−24.7313			−1.14321
$469$	6.97227	+	21.4584i	0.321949	+	0.990858i
$470$	−6.38781	−	10.0962i	−0.294648	−	0.465701i
$471$	10.7802	−	33.1780i	0.496724	−	1.52876i
$472$	−1.32868	+	4.08926i	−0.0611575	+	0.188224i
$473$	−4.70160	+	3.41591i	−0.216180	+	0.157064i
$474$	51.3781			2.35987
$475$	−6.10880	−	5.76815i	−0.280291	−	0.264661i
$476$	18.0995			0.829588
$477$	−1.32602	+	0.963413i	−0.0607145	+	0.0441117i
$478$	−7.85652	+	24.1799i	−0.359349	+	1.10596i
$479$	−2.30832	+	7.10428i	−0.105470	+	0.324603i	−0.989840	−	0.142183i	$-0.954588\pi$
$479$	−2.30832	+	7.10428i	−0.105470	+	0.324603i	0.884371	+	0.466786i	$0.154588\pi$
$480$	−0.581345	+	9.04239i	−0.0265347	+	0.412727i
$481$	17.9167	+	55.1420i	0.816933	+	2.51426i
$482$	−37.0501			−1.68759
$483$	12.4011	+	38.1666i	0.564268	+	1.73664i
$484$	26.4548	+	19.2206i	1.20249	+	0.873662i
$485$	−1.82798	+	28.4329i	−0.0830045	+	1.29107i
$486$	−19.8401	+	14.4147i	−0.899965	+	0.653863i
$487$	−4.52003	−	3.28399i	−0.204822	−	0.148812i	0.480646	−	0.876915i	$-0.340402\pi$
$487$	−4.52003	−	3.28399i	−0.204822	−	0.148812i	−0.685468	+	0.728103i	$0.740402\pi$
$488$	7.80461	+	5.67038i	0.353298	+	0.256686i
$489$	0.571640	−	0.415321i	0.0258504	−	0.0187814i
$490$	−58.9647	+	71.0775i	−2.66375	+	3.21095i
$491$	−33.2829	−	24.1814i	−1.50204	−	1.09129i	−0.969562	−	0.244847i	$-0.921262\pi$
$491$	−33.2829	−	24.1814i	−1.50204	−	1.09129i	−0.532475	−	0.846446i	$-0.678738\pi$
$492$	−7.12270	−	21.9214i	−0.321116	−	0.988294i
$493$	−4.52959			−0.204003
$494$	−7.96993	−	24.5289i	−0.358584	−	1.10361i
$495$	3.27193	−	0.835310i	0.147062	−	0.0375444i
$496$	2.27269	−	6.99462i	0.102047	−	0.314068i
$497$	−21.4583	+	66.0418i	−0.962535	+	2.96238i
$498$	23.0561	−	16.7512i	1.03317	−	0.750641i
$499$	−11.9709			−0.535891			−0.267946	−	0.963434i	$-0.586345\pi$
$499$	−11.9709			−0.535891			−0.267946	+	0.963434i	$0.586345\pi$
$500$	−17.3085	−	37.1786i	−0.774061	−	1.66268i
$501$	−12.9920			−0.580442
$502$	−0.545433	+	0.396280i	−0.0243439	+	0.0176869i
$503$	8.81418	−	27.1273i	0.393005	−	1.20955i	−0.537499	−	0.843264i	$-0.680631\pi$
$503$	8.81418	−	27.1273i	0.393005	−	1.20955i	0.930504	−	0.366281i	$-0.119369\pi$
$504$	−6.33280	+	19.4904i	−0.282085	+	0.868169i
$505$	−0.0907568	+	0.0231698i	−0.00403863	+	0.00103104i
$506$	−6.18073	−	19.0223i	−0.274767	−	0.845646i
$507$	39.9296			1.77334
$508$	9.62235	+	29.6145i	0.426923	+	1.31393i
$509$	−30.3525	−	22.0524i	−1.34535	−	0.977456i	−0.999229	−	0.0392667i	$-0.987498\pi$
$509$	−30.3525	−	22.0524i	−1.34535	−	0.977456i	−0.346123	−	0.938189i	$-0.612502\pi$
$510$	−4.75152	+	5.72759i	−0.210401	+	0.253622i
$511$	32.9966	−	23.9735i	1.45969	−	1.06052i
$512$	18.5814	+	13.5002i	0.821189	+	0.596629i
$513$	−7.68856	−	5.58607i	−0.339458	−	0.246631i
$514$	−19.2587	+	13.9923i	−0.849466	+	0.617173i
$515$	0.0663065	−	1.03135i	0.00292181	−	0.0454466i
$516$	16.6951	+	12.1297i	0.734962	+	0.533981i
$517$	1.00143	+	3.08210i	0.0440431	+	0.135551i
$518$	105.649			4.64196
$519$	1.84900	+	5.69062i	0.0811619	+	0.249791i
$520$	3.67304	−	57.1314i	0.161074	−	2.50538i
$521$	5.44070	−	16.7447i	0.238361	−	0.733600i	−0.758296	−	0.651910i	$-0.773968\pi$
$521$	5.44070	−	16.7447i	0.238361	−	0.733600i	0.996658	−	0.0816906i	$-0.0260319\pi$
$522$	3.48509	−	10.7260i	0.152538	−	0.469464i
$523$	−20.9728	+	15.2376i	−0.917077	+	0.666295i	−0.942795	−	0.333374i	$-0.891813\pi$
$523$	−20.9728	+	15.2376i	−0.917077	+	0.666295i	0.0257181	+	0.999669i	$0.491813\pi$
$524$	−50.9900			−2.22751
$525$	−6.36971	−	33.8958i	−0.277997	−	1.47933i
$526$	6.31368			0.275290
$527$	−2.80851	+	2.04050i	−0.122341	+	0.0888856i
$528$	−1.32154	+	4.06728i	−0.0575126	+	0.177006i
$529$	3.35214	−	10.3168i	0.145745	−	0.448557i
$530$	−4.46094	−	7.05066i	−0.193771	−	0.306261i
$531$	0.349902	+	1.07689i	0.0151844	+	0.0467329i
$532$	−30.4134			−1.31859
$533$	−8.95532	−	27.5617i	−0.387898	−	1.19383i
$534$	−7.78354	−	5.65508i	−0.336827	−	0.244719i
$535$	−0.772794	+	0.197291i	−0.0334108	+	0.00852963i
$536$	−14.6909	+	10.6736i	−0.634552	+	0.461029i
$537$	14.0886	+	10.2359i	0.607966	+	0.441713i
$538$	24.0991	+	17.5091i	1.03899	+	0.754869i
$539$	20.2663	−	14.7244i	0.872933	−	0.634223i
$540$	−24.8025	−	39.2012i	−1.06733	−	1.68695i
$541$	−12.6718	−	9.20658i	−0.544802	−	0.395822i	0.281063	−	0.959689i	$-0.409313\pi$
$541$	−12.6718	−	9.20658i	−0.544802	−	0.395822i	−0.825865	+	0.563867i	$0.809313\pi$
$542$	−3.47347	−	10.6903i	−0.149198	−	0.459186i
$543$	23.8131			1.02192
$544$	−0.895764	−	2.75688i	−0.0384055	−	0.118200i
$545$	−20.6550	−	8.21067i	−0.884763	−	0.351706i
$546$	32.7166	−	100.691i	1.40014	−	4.30919i
$547$	−9.94079	+	30.5946i	−0.425038	+	1.30813i	0.477921	+	0.878403i	$0.341391\pi$
$547$	−9.94079	+	30.5946i	−0.425038	+	1.30813i	−0.902958	+	0.429728i	$0.858609\pi$
$548$	−9.49794	+	6.90066i	−0.405732	+	0.294782i
$549$	2.54050			0.108426
$550$	3.17468	+	16.8938i	0.135369	+	0.720353i
$551$	7.61128			0.324252
$552$	−26.1297	+	18.9844i	−1.11215	+	0.808028i
$553$	23.5391	−	72.4458i	1.00098	−	3.08071i
$554$	18.6158	−	57.2934i	0.790908	−	2.43416i
$555$	−17.9488	+	21.6359i	−0.761884	+	0.918393i
$556$	24.9689	+	76.8464i	1.05892	+	3.25901i
$557$	−6.00840			−0.254584			−0.127292	−	0.991865i	$-0.540629\pi$
$557$	−6.00840			−0.254584			−0.127292	+	0.991865i	$0.540629\pi$
$558$	−2.67099	−	8.22046i	−0.113072	−	0.348000i
$559$	20.9907	+	15.2506i	0.887811	+	0.645032i
$560$	−21.7218	−	8.63474i	−0.917915	−	0.364884i
$561$	1.63311	−	1.18652i	0.0689500	−	0.0500951i
$562$	50.1346	+	36.4249i	2.11480	+	1.53649i
$563$	−11.1804	−	8.12301i	−0.471196	−	0.342344i	0.326711	−	0.945124i	$-0.394060\pi$
$563$	−11.1804	−	8.12301i	−0.471196	−	0.342344i	−0.797907	+	0.602780i	$0.794060\pi$
$564$	9.30984	−	6.76400i	0.392015	−	0.284816i
$565$	18.4301	+	7.32625i	0.775361	+	0.308218i
$566$	−23.3833	−	16.9889i	−0.982872	−	0.714098i
$567$	−7.27149	−	22.3793i	−0.305374	−	0.939844i
$568$	−55.8872			−2.34498
$569$	12.9664	+	39.9066i	0.543581	+	1.67297i	0.724341	+	0.689442i	$0.242144\pi$
$569$	12.9664	+	39.9066i	0.543581	+	1.67297i	−0.180760	+	0.983527i	$0.557856\pi$
$570$	7.98419	−	9.62433i	0.334421	−	0.403119i
$571$	5.10326	−	15.7062i	0.213565	−	0.657285i	−0.785688	−	0.618624i	$-0.787691\pi$
$571$	5.10326	−	15.7062i	0.213565	−	0.657285i	0.999252	−	0.0386614i	$-0.0123094\pi$
$572$	−10.5524	+	32.4769i	−0.441217	+	1.35793i
$573$	−7.01735	+	5.09840i	−0.293154	+	0.212989i
$574$	−52.8067			−2.20411
$575$	−12.4578	+	26.2868i	−0.519526	+	1.09624i
$576$	11.6487			0.485361
$577$	5.36868	−	3.90057i	0.223501	−	0.162383i	−0.470400	−	0.882453i	$-0.655890\pi$
$577$	5.36868	−	3.90057i	0.223501	−	0.162383i	0.693901	+	0.720070i	$0.255890\pi$
$578$	0.735698	−	2.26425i	0.0306010	−	0.0941802i
$579$	3.82511	−	11.7725i	0.158966	−	0.489248i
$580$	34.5242	+	13.7239i	1.43354	+	0.569852i
$581$	−13.0569	−	40.1850i	−0.541691	−	1.66715i
$582$	−42.4065			−1.75781
$583$	0.699353	+	2.15239i	0.0289643	+	0.0891428i
$584$	26.5564	+	19.2944i	1.09891	+	0.798407i
$585$	−8.06085	−	12.7404i	−0.333275	−	0.526752i
$586$	26.4912	−	19.2470i	1.09434	−	0.795084i
$587$	−3.48426	−	2.53146i	−0.143811	−	0.104485i	0.513554	−	0.858057i	$-0.328329\pi$
$587$	−3.48426	−	2.53146i	−0.143811	−	0.104485i	−0.657364	+	0.753573i	$0.728329\pi$
$588$	−71.9648	−	52.2855i	−2.96778	−	2.15622i
$589$	4.71926	−	3.42875i	0.194454	−	0.141279i
$590$	−5.58471	+	1.42575i	−0.229919	+	0.0586973i
$591$	29.7256	+	21.5969i	1.22275	+	0.888379i
$592$	5.88765	+	18.1203i	0.241981	+	0.744741i
$593$	10.9348			0.449037			0.224518	−	0.974470i	$-0.427919\pi$
$593$	10.9348			0.449037			0.224518	+	0.974470i	$0.427919\pi$
$594$	6.00847	+	18.4922i	0.246530	+	0.758743i
$595$	5.89928	+	9.32401i	0.241847	+	0.382247i
$596$	13.5297	−	41.6400i	0.554196	−	1.70564i
$597$	−9.25469	+	28.4830i	−0.378769	+	1.16573i
$598$	−72.2430	+	52.4876i	−2.95424	+	2.14638i
$599$	−18.4407			−0.753465			−0.376733	−	0.926322i	$-0.622952\pi$
$599$	−18.4407			−0.753465			−0.376733	+	0.926322i	$0.622952\pi$
$600$	24.3608	−	13.3056i	0.994524	−	0.543199i
$601$	−37.4619			−1.52810			−0.764052	−	0.645154i	$-0.776793\pi$
$601$	−37.4619			−1.52810			−0.764052	+	0.645154i	$0.776793\pi$
$602$	38.2487	−	27.7893i	1.55890	−	1.13261i
$603$	−1.47774	+	4.54803i	−0.0601784	+	0.185210i
$604$	−4.77298	+	14.6897i	−0.194210	+	0.597716i
$605$	−1.27894	+	19.8930i	−0.0519964	+	0.808765i
$606$	−0.0430812	−	0.132590i	−0.00175005	−	0.00538611i
$607$	−32.0762			−1.30193			−0.650966	−	0.759107i	$-0.725636\pi$
$607$	−32.0762			−1.30193			−0.650966	+	0.759107i	$0.725636\pi$
$608$	1.50519	+	4.63251i	0.0610436	+	0.187873i
$609$	25.2772	+	18.3650i	1.02428	+	0.744186i
$610$	−0.829701	+	12.9054i	−0.0335936	+	0.522523i
$611$	11.7052	−	8.50433i	0.473542	−	0.344048i
$612$	3.10348	+	2.25481i	0.125451	+	0.0911453i
$613$	31.2539	+	22.7073i	1.26233	+	0.917140i	0.998870	−	0.0475290i	$-0.0151346\pi$
$613$	31.2539	+	22.7073i	1.26233	+	0.917140i	0.263465	+	0.964669i	$0.415135\pi$
$614$	16.4809	−	11.9741i	0.665114	−	0.483234i
$615$	8.97135	−	10.8143i	0.361760	−	0.436074i
$616$	22.8924	+	16.6323i	0.922362	+	0.670135i
$617$	−5.17967	−	15.9414i	−0.208525	−	0.641775i	−0.999550	−	0.0299912i	$-0.990452\pi$
$617$	−5.17967	−	15.9414i	−0.208525	−	0.641775i	0.791025	−	0.611784i	$-0.209548\pi$
$618$	1.53821			0.0618759
$619$	1.87988	+	5.78568i	0.0755588	+	0.232546i	0.981702	−	0.190426i	$-0.0609869\pi$
$619$	1.87988	+	5.78568i	0.0755588	+	0.232546i	−0.906143	+	0.422972i	$0.860987\pi$
$620$	27.5886	−	7.04324i	1.10798	−	0.282863i
$621$	−10.1680	+	31.2939i	−0.408028	+	1.25578i
$622$	10.8343	−	33.3445i	0.434415	−	1.33699i
$623$	−11.5400	+	8.38431i	−0.462341	+	0.335910i
$624$	19.0932			0.764340
$625$	13.5112	−	21.0344i	0.540449	−	0.841377i
$626$	−7.05625			−0.282024
$627$	−2.74419	+	1.99377i	−0.109592	+	0.0796236i
$628$	28.2865	−	87.0570i	1.12876	−	3.47395i
$629$	2.77909	−	8.55316i	0.110810	−	0.341037i
$630$	−26.6180	+	6.79546i	−1.06049	+	0.270738i
$631$	−10.3248	−	31.7764i	−0.411022	−	1.26500i	−0.915761	−	0.401724i	$-0.868411\pi$
$631$	−10.3248	−	31.7764i	−0.411022	−	1.26500i	0.504738	−	0.863272i	$-0.331589\pi$
$632$	61.3066			2.43865
$633$	0.536910	+	1.65244i	0.0213402	+	0.0656785i
$634$	20.8170	+	15.1244i	0.826747	+	0.600667i
$635$	−12.1198	+	14.6095i	−0.480958	+	0.579758i
$636$	6.50154	−	4.72365i	0.257803	−	0.187305i
$637$	−90.4808	−	65.7382i	−3.58498	−	2.60464i
$638$	−12.5982	−	9.15315i	−0.498768	−	0.362377i
$639$	−11.9068	+	8.65080i	−0.471026	+	0.342220i
$640$	−2.97261	+	46.2367i	−0.117503	+	1.82767i
$641$	−29.9665	−	21.7719i	−1.18360	−	0.859939i	−0.191030	−	0.981584i	$-0.561183\pi$
$641$	−29.9665	−	21.7719i	−1.18360	−	0.859939i	−0.992574	+	0.121646i	$0.961183\pi$
$642$	−0.366836	−	1.12901i	−0.0144779	−	0.0445583i
$643$	−1.81952			−0.0717547			−0.0358774	−	0.999356i	$-0.511423\pi$
$643$	−1.81952			−0.0717547			−0.0358774	+	0.999356i	$0.511423\pi$
$644$	32.5397	+	100.147i	1.28224	+	3.94634i
$645$	−0.807115	+	12.5541i	−0.0317801	+	0.494316i
$646$	−1.23623	+	3.80472i	−0.0486387	+	0.149695i
$647$	5.72935	−	17.6331i	0.225244	−	0.693229i	−0.773023	−	0.634378i	$-0.781256\pi$
$647$	5.72935	−	17.6331i	0.225244	−	0.693229i	0.998267	−	0.0588513i	$-0.0187438\pi$
$648$	15.3214	−	11.1317i	0.601882	−	0.437293i
$649$	1.56345			0.0613708
$650$	67.3523	−	36.7871i	2.64177	−	1.44291i
$651$	23.9458			0.938512
$652$	1.49995	−	1.08978i	0.0587425	−	0.0426789i
$653$	−10.5750	+	32.5465i	−0.413832	+	1.27364i	0.499460	+	0.866337i	$0.333532\pi$
$653$	−10.5750	+	32.5465i	−0.413832	+	1.27364i	−0.913292	+	0.407306i	$0.866468\pi$
$654$	10.2231	−	31.4633i	0.399753	−	1.23031i
$655$	−16.6195	−	26.2677i	−0.649378	−	1.02636i
$656$	−2.94283	−	9.05709i	−0.114898	−	0.353620i
$657$	8.64445			0.337252
$658$	−8.14693	−	25.0737i	−0.317600	−	0.977474i
$659$	13.8114	+	10.0345i	0.538014	+	0.390890i	0.823347	−	0.567538i	$-0.192104\pi$
$659$	13.8114	+	10.0345i	0.538014	+	0.390890i	−0.285333	+	0.958429i	$0.592104\pi$
$660$	−16.0424	+	4.09555i	−0.624449	+	0.159419i
$661$	9.29646	−	6.75428i	0.361591	−	0.262711i	−0.392125	−	0.919912i	$-0.628260\pi$
$661$	9.29646	−	6.75428i	0.361591	−	0.262711i	0.753715	+	0.657201i	$0.228260\pi$
$662$	45.5541	+	33.0970i	1.77051	+	1.28635i
$663$	−7.29116	−	5.29734i	−0.283165	−	0.205732i
$664$	27.5115	−	19.9883i	1.06766	−	0.775697i
$665$	−9.91283	−	15.6676i	−0.384403	−	0.607562i
$666$	18.1155	+	13.1617i	0.701960	+	0.510004i
$667$	−8.14341	−	25.0628i	−0.315314	−	0.970437i
$668$	−34.0903			−1.31899
$669$	−0.907677	−	2.79354i	−0.0350928	−	0.108005i
$670$	−22.6208	−	8.99208i	−0.873916	−	0.347394i
$671$	1.08398	−	3.33615i	0.0418466	−	0.128791i
$672$	−6.17882	+	19.0165i	−0.238353	+	0.733576i
$673$	13.3898	−	9.72827i	0.516139	−	0.374997i	−0.299008	−	0.954251i	$-0.596656\pi$
$673$	13.3898	−	9.72827i	0.516139	−	0.374997i	0.815148	+	0.579253i	$0.196656\pi$
$674$	−41.5483			−1.60038
$675$	12.1106	−	25.5542i	0.466136	−	0.983581i
$676$	104.773			4.02973
$677$	0.661370	−	0.480513i	0.0254185	−	0.0184676i	−0.575003	−	0.818151i	$-0.694999\pi$
$677$	0.661370	−	0.480513i	0.0254185	−	0.0184676i	0.600422	+	0.799683i	$0.294999\pi$
$678$	−9.12186	+	28.0742i	−0.350323	+	1.07818i
$679$	−19.4287	+	59.7954i	−0.745605	+	2.29474i
$680$	−5.66972	+	6.83442i	−0.217424	+	0.262088i
$681$	2.46759	+	7.59447i	0.0945584	+	0.291021i
$682$	−11.9347			−0.457002
$683$	2.06917	+	6.36825i	0.0791746	+	0.243674i	0.982807	−	0.184634i	$-0.0591098\pi$
$683$	2.06917	+	6.36825i	0.0791746	+	0.243674i	−0.903633	+	0.428308i	$0.859110\pi$
$684$	−5.21492	−	3.78886i	−0.199397	−	0.144871i
$685$	−6.65063	−	2.64372i	−0.254107	−	0.101011i
$686$	−98.3443	+	71.4513i	−3.75480	+	2.72802i
$687$	−6.13761	−	4.45923i	−0.234164	−	0.170130i
$688$	6.89779	+	5.01153i	0.262976	+	0.191063i
$689$	8.17435	−	5.93901i	0.311418	−	0.226258i
$690$	−40.2339	−	15.9936i	−1.53168	−	0.608865i
$691$	17.6153	+	12.7982i	0.670116	+	0.486868i	0.870064	−	0.492939i	$-0.164077\pi$
$691$	17.6153	+	12.7982i	0.670116	+	0.486868i	−0.199948	+	0.979806i	$0.564077\pi$
$692$	4.85165	+	14.9318i	0.184432	+	0.567624i
$693$	7.45176			0.283069
$694$	−4.14552	−	12.7586i	−0.157362	−	0.484310i
$695$	−31.4494	+	37.9099i	−1.19294	+	1.43800i
$696$	−7.77059	+	23.9154i	−0.294543	+	0.906511i
$697$	−1.38907	+	4.27513i	−0.0526149	+	0.161932i
$698$	−5.42717	+	3.94307i	−0.205421	+	0.149247i
$699$	−33.5491			−1.26894
$700$	−16.7137	−	88.9406i	−0.631719	−	3.36164i
$701$	−2.47271			−0.0933931			−0.0466965	−	0.998909i	$-0.514869\pi$
$701$	−2.47271			−0.0933931			−0.0466965	+	0.998909i	$0.514869\pi$
$702$	70.2296	−	51.0248i	2.65064	−	1.92581i
$703$	−4.66983	+	14.3723i	−0.176126	+	0.542060i
$704$	4.97026	−	15.2969i	0.187324	−	0.576523i
$705$	6.51892	+	2.59136i	0.245517	+	0.0975964i
$706$	4.53586	+	13.9599i	0.170709	+	0.525390i
$707$	−0.206697			−0.00777364
$708$	−1.71558	−	5.28001i	−0.0644755	−	0.198435i
$709$	26.5043	+	19.2565i	0.995389	+	0.723192i	0.961095	−	0.276220i	$-0.0890817\pi$
$709$	26.5043	+	19.2565i	0.995389	+	0.723192i	0.0342941	+	0.999412i	$0.489082\pi$
$710$	−40.0562	−	63.3102i	−1.50328	−	2.37599i
$711$	13.0614	−	9.48967i	0.489841	−	0.355890i
$712$	−9.28767	−	6.74789i	−0.348070	−	0.252888i
$713$	−16.3396	−	11.8714i	−0.611922	−	0.444587i
$714$	−13.2858	+	9.65268i	−0.497208	+	0.361243i
$715$	−20.1700	+	5.14931i	−0.754315	+	0.192573i
$716$	36.9675	+	26.8585i	1.38154	+	1.00375i
$717$	−4.61313	−	14.1978i	−0.172281	−	0.530225i
$718$	68.0888			2.54105
$719$	2.03400	+	6.26000i	0.0758554	+	0.233459i	0.981794	−	0.189951i	$-0.0608330\pi$
$719$	2.03400	+	6.26000i	0.0758554	+	0.233459i	−0.905938	+	0.423410i	$0.860833\pi$
$720$	−2.64889	−	4.18666i	−0.0987183	−	0.156028i
$721$	0.704738	−	2.16896i	0.0262458	−	0.0807763i
$722$	−11.9010	+	36.6274i	−0.442908	+	1.36313i
$723$	17.6000	−	12.7871i	0.654551	−	0.475559i
$724$	62.4841			2.32220
$725$	4.18279	+	22.2584i	0.155345	+	0.826655i
$726$	−29.6696			−1.10114
$727$	−9.51365	+	6.91207i	−0.352842	+	0.256355i	−0.750060	−	0.661370i	$-0.769976\pi$
$727$	−9.51365	+	6.91207i	−0.352842	+	0.256355i	0.397218	+	0.917724i	$0.369976\pi$
$728$	39.0389	−	120.149i	1.44688	−	4.45303i
$729$	8.87068	−	27.3011i	0.328544	−	1.01115i
$730$	−2.82319	+	43.9126i	−0.104491	+	1.62528i
$731$	−1.24364	−	3.82753i	−0.0459977	−	0.141566i
$732$	−12.4561			−0.460392
$733$	2.11885	+	6.52114i	0.0782615	+	0.240864i	0.982531	−	0.186097i	$-0.0595840\pi$
$733$	2.11885	+	6.52114i	0.0782615	+	0.240864i	−0.904270	+	0.426961i	$0.859584\pi$
$734$	5.25838	+	3.82044i	0.194090	+	0.141015i
$735$	3.47909	−	54.1147i	0.128328	−	1.99605i
$736$	13.6437	−	9.91276i	0.502915	−	0.365389i
$737$	5.34189	+	3.88111i	0.196771	+	0.142963i
$738$	−9.05466	−	6.57860i	−0.333307	−	0.242161i
$739$	8.38285	−	6.09050i	0.308368	−	0.224043i	−0.422828	−	0.906210i	$-0.638962\pi$
$739$	8.38285	−	6.09050i	0.308368	−	0.224043i	0.731196	+	0.682167i	$0.238962\pi$
$740$	−47.0965	+	56.7713i	−1.73130	+	2.08695i
$741$	12.2517	+	8.90136i	0.450077	+	0.327000i
$742$	−5.68942	−	17.5102i	−0.208865	−	0.642821i
$743$	−36.4058			−1.33560			−0.667799	−	0.744342i	$-0.732763\pi$
$743$	−36.4058			−1.33560			−0.667799	+	0.744342i	$0.732763\pi$
$744$	5.95543	+	18.3289i	0.218336	+	0.671971i
$745$	25.8608	−	6.60215i	0.947467	−	0.241884i
$746$	−11.8142	+	36.3605i	−0.432550	+	1.33125i
$747$	2.76736	−	8.51704i	0.101252	−	0.311622i
$748$	4.28518	−	3.11337i	0.156682	−	0.113836i
$749$	−1.76002			−0.0643099
$750$	32.5330	+	18.0598i	1.18794	+	0.659451i
$751$	−11.9441			−0.435847			−0.217923	−	0.975966i	$-0.569928\pi$
$751$	−11.9441			−0.435847			−0.217923	+	0.975966i	$0.569928\pi$
$752$	3.84647	−	2.79462i	0.140266	−	0.101909i
$753$	0.122330	−	0.376492i	0.00445794	−	0.0137201i
$754$	−21.4840	+	66.1210i	−0.782401	+	2.40798i
$755$	−9.12315	+	2.32910i	−0.332026	+	0.0847647i
$756$	−31.6328	−	97.3556i	−1.15047	−	3.54079i
$757$	21.3498			0.775971			0.387986	−	0.921665i	$-0.373171\pi$
$757$	21.3498			0.775971			0.387986	+	0.921665i	$0.373171\pi$
$758$	19.7297	+	60.7217i	0.716615	+	2.20551i
$759$	9.50125	+	6.90306i	0.344873	+	0.250565i
$760$	9.52709	−	11.4842i	0.345584	−	0.416575i
$761$	−35.2489	+	25.6098i	−1.27777	+	0.928356i	−0.999483	−	0.0321414i	$-0.989767\pi$
$761$	−35.2489	+	25.6098i	−1.27777	+	0.928356i	−0.278289	+	0.960497i	$0.589767\pi$
$762$	−22.8570	−	16.6066i	−0.828023	−	0.601594i
$763$	−39.6812	−	28.8301i	−1.43656	−	1.04372i
$764$	−18.4131	+	13.3779i	−0.666163	+	0.483995i
$765$	−0.150036	+	2.33369i	−0.00542456	+	0.0843749i
$766$	−70.1523	−	50.9686i	−2.53471	−	1.84157i
$767$	−2.15699	−	6.63853i	−0.0778843	−	0.239703i
$768$	−37.8190			−1.36467
$769$	−2.60312	−	8.01158i	−0.0938710	−	0.288905i	0.893087	−	0.449884i	$-0.148535\pi$
$769$	−2.60312	−	8.01158i	−0.0938710	−	0.288905i	−0.986958	+	0.160979i	$0.948535\pi$
$770$	−2.43367	+	37.8539i	−0.0877034	+	1.36416i
$771$	4.31935	−	13.2936i	0.155557	−	0.478757i
$772$	10.0369	−	30.8903i	0.361234	−	1.11177i
$773$	13.4271	−	9.75538i	0.482940	−	0.350877i	−0.319523	−	0.947579i	$-0.603523\pi$
$773$	13.4271	−	9.75538i	0.482940	−	0.350877i	0.802463	+	0.596702i	$0.203523\pi$
$774$	10.0204			0.360175
$775$	12.6205	+	11.9167i	0.453341	+	0.428060i
$776$	−50.6013			−1.81648
$777$	−50.1869	+	36.4629i	−1.80044	+	1.30810i
$778$	−3.01799	+	9.28843i	−0.108200	+	0.333006i
$779$	2.33412	−	7.18369i	0.0836286	−	0.257382i
$780$	39.5226	+	62.4668i	1.41514	+	2.23667i
$781$	6.27973	+	19.3270i	0.224706	+	0.691575i
$782$	13.8510			0.495312
$783$	7.91645	+	24.3643i	0.282911	+	0.870710i
$784$	−29.7331	−	21.6024i	−1.06190	−	0.771513i
$785$	54.0673	−	13.8032i	1.92975	−	0.492656i
$786$	37.4288	−	27.1936i	1.33504	−	0.969965i
$787$	33.3122	+	24.2027i	1.18745	+	0.862734i	0.992993	−	0.118176i	$-0.0377047\pi$
$787$	33.3122	+	24.2027i	1.18745	+	0.862734i	0.194459	+	0.980911i	$0.437705\pi$
$788$	77.9982	+	56.6690i	2.77857	+	2.01875i
$789$	−2.99920	+	2.17905i	−0.106774	+	0.0775762i
$790$	43.9405	+	69.4494i	1.56333	+	2.47090i
$791$	35.4069	+	25.7246i	1.25892	+	0.914662i
$792$	1.85328	+	5.70382i	0.0658535	+	0.202676i
$793$	−15.6610			−0.556139
$794$	−7.75729	−	23.8745i	−0.275296	−	0.847273i
$795$	4.55249	+	1.80968i	0.161460	+	0.0641829i
$796$	−24.2837	+	74.7377i	−0.860715	+	2.64901i
$797$	8.69334	−	26.7553i	0.307934	−	0.947723i	−0.670632	−	0.741790i	$-0.733977\pi$
$797$	8.69334	−	26.7553i	0.307934	−	0.947723i	0.978566	−	0.205933i	$-0.0660229\pi$
$798$	22.3247	−	16.2198i	0.790286	−	0.574176i
$799$	−2.24422			−0.0793947
$800$	−12.7201	+	6.94757i	−0.449723	+	0.245634i
$801$	−3.02325			−0.106821
$802$	5.18196	−	3.76492i	0.182982	−	0.132944i
$803$	3.68842	−	11.3518i	0.130161	−	0.400596i
$804$	7.24543	−	22.2992i	0.255527	−	0.786430i
$805$	−40.9851	+	49.4044i	−1.44454	+	1.74128i
$806$	16.4655	+	50.6755i	0.579971	+	1.78497i
$807$	−17.4908			−0.615705
$808$	−0.0514063	−	0.158212i	−0.00180847	−	0.00556589i
$809$	−12.4309	−	9.03154i	−0.437046	−	0.317532i	0.347414	−	0.937712i	$-0.387060\pi$
$809$	−12.4309	−	9.03154i	−0.437046	−	0.317532i	−0.784460	+	0.620180i	$0.787060\pi$
$810$	23.5915	+	9.37799i	0.828922	+	0.329509i
$811$	25.6486	−	18.6348i	0.900646	−	0.654357i	−0.0379860	−	0.999278i	$-0.512094\pi$
$811$	25.6486	−	18.6348i	0.900646	−	0.654357i	0.938632	+	0.344921i	$0.112094\pi$
$812$	66.3258	+	48.1885i	2.32758	+	1.69109i
$813$	5.33955	+	3.87941i	0.187266	+	0.136057i
$814$	25.0133	−	18.1732i	0.876714	−	0.636970i
$815$	1.05029	+	0.417506i	0.0367901	+	0.0146246i
$816$	−2.39596	−	1.74077i	−0.0838755	−	0.0609391i
$817$	2.08975	+	6.43158i	0.0731109	+	0.225012i
$818$	−64.5049			−2.25536
$819$	−10.2807	−	31.6407i	−0.359237	−	1.10562i
$820$	23.5403	−	28.3760i	0.822062	−	0.990933i
$821$	−10.3069	+	31.7213i	−0.359713	+	1.10708i	0.593513	+	0.804824i	$0.297740\pi$
$821$	−10.3069	+	31.7213i	−0.359713	+	1.10708i	−0.953226	+	0.302258i	$0.902260\pi$
$822$	3.29168	−	10.1308i	0.114811	−	0.353351i
$823$	−30.9058	+	22.4544i	−1.07731	+	0.782710i	−0.977212	−	0.212267i	$-0.931915\pi$
$823$	−30.9058	+	22.4544i	−1.07731	+	0.782710i	−0.100097	+	0.994978i	$0.531915\pi$
$824$	1.83546			0.0639413
$825$	−7.33864	−	6.92941i	−0.255499	−	0.241251i
$826$	−12.7191			−0.442553
$827$	13.3490	−	9.69861i	0.464190	−	0.337254i	−0.330983	−	0.943637i	$-0.607380\pi$
$827$	13.3490	−	9.69861i	0.464190	−	0.337254i	0.795173	+	0.606383i	$0.207380\pi$
$828$	−6.89665	+	21.2257i	−0.239675	+	0.737645i
$829$	11.9414	−	36.7519i	0.414743	−	1.27645i	−0.497738	−	0.867328i	$-0.665836\pi$
$829$	11.9414	−	36.7519i	0.414743	−	1.27645i	0.912481	−	0.409120i	$-0.134164\pi$
$830$	42.3616	+	16.8394i	1.47039	+	0.584503i
$831$	10.9307	+	33.6411i	0.379180	+	1.16700i
$832$	−71.8088			−2.48952
$833$	5.36074	+	16.4987i	0.185739	+	0.571645i
$834$	−59.3114	−	43.0923i	−2.05379	−	1.49216i
$835$	−11.1113	−	17.5618i	−0.384522	−	0.607750i
$836$	−7.20059	+	5.23154i	−0.249038	+	0.180936i
$837$	15.8842	+	11.5405i	0.549037	+	0.398899i
$838$	−58.1688	−	42.2621i	−2.00941	−	1.45992i
$839$	39.6753	−	28.8258i	1.36974	−	0.995178i	0.371988	−	0.928238i	$-0.378676\pi$
$839$	39.6753	−	28.8258i	1.36974	−	0.995178i	0.997757	−	0.0669400i	$-0.0213236\pi$
$840$	59.3493	−	15.1516i	2.04775	−	0.522781i
$841$	6.86272	+	4.98606i	0.236645	+	0.171933i
$842$	−10.0931	−	31.0633i	−0.347831	−	1.07051i
$843$	−36.3869			−1.25323
$844$	1.40882	+	4.33590i	0.0484935	+	0.149248i
$845$	34.1493	+	53.9741i	1.17477	+	1.85677i
$846$	1.72671	−	5.31427i	0.0593655	−	0.182708i
$847$	−13.5932	+	41.8357i	−0.467069	+	1.43749i
$848$	2.68619	−	1.95163i	0.0922441	−	0.0670193i
$849$	16.9712			0.582451
$850$	−11.8058	−	1.52432i	−0.404937	−	0.0522838i
$851$	52.3221			1.79358
$852$	58.3795	−	42.4152i	2.00005	−	1.45312i
$853$	−1.15341	+	3.54982i	−0.0394919	+	0.121543i	−0.968859	−	0.247614i	$-0.920354\pi$
$853$	−1.15341	+	3.54982i	−0.0394919	+	0.121543i	0.929367	+	0.369157i	$0.120354\pi$
$854$	−8.81846	+	27.1404i	−0.301762	+	0.928726i
$855$	0.252112	−	3.92141i	0.00862205	−	0.134109i
$856$	−0.437725	−	1.34718i	−0.0149611	−	0.0460456i
$857$	22.4993			0.768560			0.384280	−	0.923217i	$-0.374450\pi$
$857$	22.4993			0.768560			0.384280	+	0.923217i	$0.374450\pi$
$858$	−9.57445	−	29.4671i	−0.326866	−	1.00599i
$859$	−10.5237	−	7.64595i	−0.359065	−	0.260876i	0.393597	−	0.919283i	$-0.371231\pi$
$859$	−10.5237	−	7.64595i	−0.359065	−	0.260876i	−0.752662	+	0.658407i	$0.771231\pi$
$860$	−2.11782	+	32.9411i	−0.0722171	+	1.12328i
$861$	25.0849	−	18.2252i	0.854891	−	0.621115i
$862$	−27.3233	−	19.8516i	−0.930637	−	0.676147i
$863$	21.9541	+	15.9506i	0.747326	+	0.542964i	0.894997	−	0.446073i	$-0.147178\pi$
$863$	21.9541	+	15.9506i	0.747326	+	0.542964i	−0.147671	+	0.989037i	$0.547178\pi$
$864$	−13.2635	+	9.63648i	−0.451233	+	0.327840i
$865$	−6.11086	+	7.36618i	−0.207776	+	0.250458i
$866$	30.8806	+	22.4361i	1.04937	+	0.762408i
$867$	0.431982	+	1.32950i	0.0146709	+	0.0451523i
$868$	62.8324			2.13267
$869$	−6.88867	−	21.2011i	−0.233682	−	0.719200i
$870$	−32.6613	+	8.33829i	−1.10732	+	0.282695i
$871$	9.10964	−	28.0366i	0.308668	−	0.949983i
$872$	12.1986	−	37.5434i	0.413097	−	1.27138i
$873$	−10.7806	+	7.83259i	−0.364869	+	0.265093i
$874$	−23.2745			−0.787272
$875$	40.3704	−	37.5991i	1.36477	−	1.27108i
$876$	−42.3840			−1.43202
$877$	14.1557	−	10.2847i	0.478005	−	0.347291i	−0.322548	−	0.946553i	$-0.604539\pi$
$877$	14.1557	−	10.2847i	0.478005	−	0.347291i	0.800553	+	0.599262i	$0.204539\pi$
$878$	−22.5132	+	69.2886i	−0.759785	+	2.33838i
$879$	−5.94144	+	18.2859i	−0.200400	+	0.616767i
$880$	−6.62810	+	1.69213i	−0.223433	+	0.0570415i
$881$	9.27276	+	28.5386i	0.312407	+	0.961491i	0.976809	+	0.214115i	$0.0686866\pi$
$881$	9.27276	+	28.5386i	0.312407	+	0.961491i	−0.664401	+	0.747376i	$0.731313\pi$
$882$	−43.1931			−1.45439
$883$	9.84181	+	30.2900i	0.331203	+	1.01934i	0.968562	+	0.248772i	$0.0800270\pi$
$883$	9.84181	+	30.2900i	0.331203	+	1.01934i	−0.637359	+	0.770567i	$0.719973\pi$
$884$	−19.1316	−	13.8999i	−0.643464	−	0.467504i
$885$	2.16085	−	2.60474i	0.0726361	−	0.0875573i
$886$	53.7311	−	39.0379i	1.80513	−	1.31150i
$887$	−1.49817	−	1.08848i	−0.0503036	−	0.0365477i	0.562349	−	0.826900i	$-0.309898\pi$
$887$	−1.49817	−	1.08848i	−0.0503036	−	0.0365477i	−0.612653	+	0.790352i	$0.709898\pi$
$888$	−40.3915	−	29.3462i	−1.35545	−	0.984792i
$889$	−33.8882	+	24.6212i	−1.13657	+	0.825770i
$890$	0.987364	−	15.3577i	0.0330965	−	0.514791i
$891$	−5.57115	−	4.04767i	−0.186640	−	0.135602i
$892$	−2.38169	−	7.33008i	−0.0797448	−	0.245429i
$893$	3.77106			0.126194
$894$	12.2758	+	37.7811i	0.410565	+	1.26359i
$895$	−1.78717	+	27.7981i	−0.0597386	+	0.929188i
$896$	−31.5943	+	97.2374i	−1.05549	+	3.24847i
$897$	16.2027	−	49.8667i	0.540991	−	1.66500i
$898$	−60.1340	+	43.6899i	−2.00670	+	1.45795i
$899$	−15.7245			−0.524442
$900$	8.21424	−	17.3326i	0.273808	−	0.577754i
$901$	−1.56725			−0.0522128
$902$	−12.5024	+	9.08351i	−0.416284	+	0.302448i
$903$	−8.57841	+	26.4016i	−0.285472	+	0.878591i
$904$	−10.8846	+	33.4994i	−0.362017	+	1.11417i
$905$	20.3659	+	32.1889i	0.676985	+	1.07000i
$906$	−4.33065	−	13.3284i	−0.143876	−	0.442806i
$907$	35.4484			1.17705			0.588523	−	0.808481i	$-0.299710\pi$
$907$	35.4484			1.17705			0.588523	+	0.808481i	$0.299710\pi$
$908$	6.47481	+	19.9274i	0.214874	+	0.661315i
$909$	−0.0354419	−	0.0257501i	−0.00117553	−	0.000854076i
$910$	164.088	−	41.8910i	5.43947	−	1.38867i
$911$	24.1879	−	17.5735i	0.801380	−	0.582237i	−0.109938	−	0.993938i	$-0.535065\pi$
$911$	24.1879	−	17.5735i	0.801380	−	0.582237i	0.911319	+	0.411701i	$0.135065\pi$
$912$	4.02605	+	2.92509i	0.133316	+	0.0968595i
$913$	−10.0037	−	7.26811i	−0.331074	−	0.240539i
$914$	2.44014	−	1.77287i	0.0807127	−	0.0586412i
$915$	−4.05991	−	6.41683i	−0.134217	−	0.212134i
$916$	−16.1047	−	11.7008i	−0.532115	−	0.386604i
$917$	−21.1963	−	65.2355i	−0.699963	−	2.15427i
$918$	−13.4650			−0.444411
$919$	−3.03771	−	9.34910i	−0.100205	−	0.308398i	0.888370	−	0.459127i	$-0.151838\pi$
$919$	−3.03771	−	9.34910i	−0.100205	−	0.308398i	−0.988575	+	0.150729i	$0.951838\pi$
$920$	−48.0089	−	19.0842i	−1.58281	−	0.629189i
$921$	−3.69633	+	11.3761i	−0.121798	+	0.374856i
$922$	−6.41986	+	19.7583i	−0.211427	+	0.650705i
$923$	73.4002	−	53.3283i	2.41600	−	1.75532i
$924$	−36.5363			−1.20195
$925$	−44.5964	−	5.75811i	−1.46632	−	0.189325i
$926$	−41.1437			−1.35207
$927$	0.391046	−	0.284112i	0.0128436	−	0.00933145i
$928$	4.05744	−	12.4875i	0.133192	−	0.409923i
$929$	4.40602	−	13.5603i	0.144557	−	0.444900i	−0.852397	−	0.522895i	$-0.824852\pi$
$929$	4.40602	−	13.5603i	0.144557	−	0.444900i	0.996954	+	0.0779952i	$0.0248519\pi$
$930$	−16.4949	+	19.8834i	−0.540890	+	0.652002i
$931$	−9.00790	−	27.7235i	−0.295222	−	0.908600i
$932$	−88.0308			−2.88354
$933$	6.36159	+	19.5790i	0.208269	+	0.640987i
$934$	18.4801	+	13.4266i	0.604688	+	0.439332i
$935$	3.00056	+	1.19277i	0.0981289	+	0.0390077i
$936$	21.6620	−	15.7383i	0.708044	−	0.514424i
$937$	−5.68141	−	4.12779i	−0.185604	−	0.134849i	0.491104	−	0.871101i	$-0.336594\pi$
$937$	−5.68141	−	4.12779i	−0.185604	−	0.134849i	−0.676707	+	0.736252i	$0.736594\pi$
$938$	−43.4577	−	31.5739i	−1.41894	−	1.03092i
$939$	3.35195	−	2.43533i	0.109387	−	0.0794740i
$940$	17.1052	+	6.79958i	0.557911	+	0.221778i
$941$	23.1684	+	16.8328i	0.755269	+	0.548735i	0.897456	−	0.441105i	$-0.145413\pi$
$941$	23.1684	+	16.8328i	0.755269	+	0.548735i	−0.142187	+	0.989840i	$0.545413\pi$
$942$	25.6651	+	78.9891i	0.836215	+	2.57360i
$943$	−26.1522			−0.851631
$944$	−0.708812	−	2.18150i	−0.0230699	−	0.0710018i
$945$	39.8428	−	48.0275i	1.29609	−	1.56233i
$946$	4.27550	−	13.1586i	0.139009	−	0.427824i
$947$	15.2883	−	47.0524i	0.496802	−	1.52900i	−0.317329	−	0.948316i	$-0.602786\pi$
$947$	15.2883	−	47.0524i	0.496802	−	1.52900i	0.814130	−	0.580682i	$-0.197214\pi$
$948$	−64.0405	+	46.5282i	−2.07994	+	1.51116i
$949$	−53.2892			−1.72984
$950$	19.8379	+	2.56139i	0.643627	+	0.0831024i
$951$	−15.1086			−0.489931
$952$	−15.8532	+	11.5180i	−0.513804	+	0.373301i
$953$	13.6298	−	41.9482i	0.441512	−	1.35884i	−0.444751	−	0.895654i	$-0.646708\pi$
$953$	13.6298	−	41.9482i	0.441512	−	1.35884i	0.886263	−	0.463181i	$-0.153292\pi$
$954$	1.20585	−	3.71123i	0.0390409	−	0.120155i
$955$	−12.8932	−	5.12523i	−0.417213	−	0.165848i
$956$	−12.1046	−	37.2541i	−0.391490	−	1.20488i
$957$	9.14360			0.295571
$958$	−5.49558	−	16.9137i	−0.177554	−	0.546455i
$959$	−12.7768	−	9.28289i	−0.412584	−	0.299760i
$960$	−18.6155	−	29.4224i	−0.600812	−	0.949603i
$961$	15.3298	−	11.1377i	0.494509	−	0.359282i
$962$	−111.674	−	81.1358i	−3.60051	−	2.61592i
$963$	−0.301788	−	0.219262i	−0.00972498	−	0.00706561i
$964$	46.1813	−	33.5527i	1.48740	−	1.08066i
$965$	19.1846	−	4.89775i	0.617575	−	0.157664i
$966$	−77.2951	−	56.1582i	−2.48693	−	1.80686i
$967$	−6.78225	−	20.8736i	−0.218103	−	0.671251i	−0.998919	−	0.0464899i	$-0.985196\pi$
$967$	−6.78225	−	20.8736i	−0.218103	−	0.671251i	0.780816	−	0.624761i	$-0.214804\pi$
$968$	−35.4030			−1.13790
$969$	−0.725878	−	2.23402i	−0.0233186	−	0.0717672i
$970$	−36.2676	−	57.3222i	−1.16448	−	1.84051i
$971$	−1.78166	+	5.48339i	−0.0571762	+	0.175970i	−0.975566	−	0.219707i	$-0.929490\pi$
$971$	−1.78166	+	5.48339i	−0.0571762	+	0.175970i	0.918390	+	0.395677i	$0.129490\pi$
$972$	11.6758	−	35.9345i	0.374502	−	1.15260i
$973$	−87.9361	+	63.8893i	−2.81910	+	2.04820i
$974$	13.3015			0.426208
$975$	−19.2981	+	40.7204i	−0.618035	+	1.30410i
$976$	−5.14640			−0.164732
$977$	−1.96684	+	1.42899i	−0.0629248	+	0.0457176i	−0.618803	−	0.785546i	$-0.712382\pi$
$977$	−1.96684	+	1.42899i	−0.0629248	+	0.0457176i	0.555878	+	0.831264i	$0.312382\pi$
$978$	−0.519834	+	1.59988i	−0.0166225	+	0.0511586i
$979$	−1.28996	+	3.97010i	−0.0412274	+	0.126885i
$980$	9.12892	−	141.994i	0.291613	−	4.53582i
$981$	−3.21244	−	9.88687i	−0.102565	−	0.315664i
$982$	97.9447			3.12554
$983$	5.01468	+	15.4336i	0.159943	+	0.492255i	0.998628	−	0.0523620i	$-0.0166750\pi$
$983$	5.01468	+	15.4336i	0.159943	+	0.492255i	−0.838685	+	0.544617i	$0.816675\pi$
$984$	20.1889	+	14.6681i	0.643599	+	0.467602i
$985$	−3.77077	+	58.6516i	−0.120147	+	1.86879i
$986$	8.72437	−	6.33863i	0.277841	−	0.201863i
$987$	12.5238	+	9.09905i	0.398636	+	0.289626i
$988$	32.1476	+	23.3566i	1.02275	+	0.743074i
$989$	18.9424	−	13.7625i	0.602333	−	0.437621i
$990$	−5.13309	+	6.18755i	−0.163140	+	0.196653i
$991$	−48.3800	−	35.1501i	−1.53684	−	1.11658i	−0.952278	−	0.305233i	$-0.901266\pi$
$991$	−48.3800	−	35.1501i	−1.53684	−	1.11658i	−0.584564	−	0.811348i	$-0.698734\pi$
$992$	−3.10965	−	9.57052i	−0.0987315	−	0.303864i
$993$	−33.0625			−1.04921
$994$	−51.0872	−	157.230i	−1.62039	−	4.98704i
$995$	−46.4164	+	11.8499i	−1.47150	+	0.375667i
$996$	−13.5684	+	41.7594i	−0.429932	+	1.32320i
$997$	−7.01109	+	21.5779i	−0.222043	+	0.683379i	0.776535	+	0.630074i	$0.216976\pi$
$997$	−7.01109	+	21.5779i	−0.222043	+	0.683379i	−0.998578	+	0.0533051i	$0.983024\pi$
$998$	23.0570	−	16.7519i	0.729855	−	0.530271i
$999$	−50.8638			−1.60926

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.k.b.86.2	✓	76
25.16	even	5	inner	425.2.k.b.341.2	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
425.2.k.b.86.2	✓	76	1.1	even	1	trivial
425.2.k.b.341.2	yes	76	25.16	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.k (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.92608 + 1.39938i) q^{2} +(0.431982 - 1.32950i) q^{3} +(1.13349 - 3.48853i) q^{4} +(2.16658 - 0.553118i) q^{5} +(1.02845 + 3.16524i) q^{6} +4.93434 q^{7} +(1.22719 + 3.77690i) q^{8} +(0.846082 + 0.614714i) q^{9} +(-3.39899 + 4.09722i) q^{10} +(1.16824 - 0.848778i) q^{11} +(-4.14837 - 3.01397i) q^{12} +(-5.21572 - 3.78944i) q^{13} +(-9.50395 + 6.90502i) q^{14} +(0.200550 - 3.11941i) q^{15} +(-1.71395 - 1.24526i) q^{16} +(0.309017 + 0.951057i) q^{17} -2.48984 q^{18} +(-0.519255 - 1.59810i) q^{19} +(0.526232 - 8.18514i) q^{20} +(2.13155 - 6.56022i) q^{21} +(-1.06237 + 3.26963i) q^{22} +(-4.70676 + 3.41966i) q^{23} +5.55153 q^{24} +(4.38812 - 2.39675i) q^{25} +15.3488 q^{26} +(4.57558 - 3.32436i) q^{27} +(5.59304 - 17.2136i) q^{28} +(-1.39972 + 4.30790i) q^{29} +(3.97896 + 6.28888i) q^{30} +(1.07275 + 3.30160i) q^{31} -2.89875 q^{32} +(-0.623793 - 1.91984i) q^{33} +(-1.92608 - 1.39938i) q^{34} +(10.6906 - 2.72927i) q^{35} +(3.10348 - 2.25481i) q^{36} +(-7.27575 - 5.28614i) q^{37} +(3.23648 + 2.35144i) q^{38} +(-7.29116 + 5.29734i) q^{39} +(4.74788 + 7.50417i) q^{40} +(3.63664 + 2.64217i) q^{41} +(5.07472 + 15.6184i) q^{42} -4.02450 q^{43} +(-1.63679 - 5.03754i) q^{44} +(2.17311 + 0.863844i) q^{45} +(4.28020 - 13.1731i) q^{46} +(-0.693502 + 2.13438i) q^{47} +(-2.39596 + 1.74077i) q^{48} +17.3477 q^{49} +(-5.09792 + 10.7570i) q^{50} +1.39792 q^{51} +(-19.1316 + 13.8999i) q^{52} +(-0.484308 + 1.49055i) q^{53} +(-4.16091 + 12.8060i) q^{54} +(2.06161 - 2.48512i) q^{55} +(6.05538 + 18.6365i) q^{56} -2.34899 q^{57} +(-3.33241 - 10.2561i) q^{58} +(0.875925 + 0.636397i) q^{59} +(-10.6548 - 4.23546i) q^{60} +(1.96527 - 1.42785i) q^{61} +(-6.68641 - 4.85796i) q^{62} +(4.17486 + 3.03321i) q^{63} +(9.01113 - 6.54697i) q^{64} +(-13.3963 - 5.32521i) q^{65} +(3.88806 + 2.82484i) q^{66} +(1.41301 + 4.34879i) q^{67} +3.66806 q^{68} +(2.51322 + 7.73489i) q^{69} +(-16.7718 + 20.2171i) q^{70} +(-4.34876 + 13.3841i) q^{71} +(-1.28341 + 3.94994i) q^{72} +(6.68714 - 4.85849i) q^{73} +21.4110 q^{74} +(-1.29089 - 6.86937i) q^{75} -6.16361 q^{76} +(5.76451 - 4.18816i) q^{77} +(6.63039 - 20.4062i) q^{78} +(4.77046 - 14.6820i) q^{79} +(-4.40217 - 1.74993i) q^{80} +(-1.47365 - 4.53543i) q^{81} -10.7019 q^{82} +(-2.64612 - 8.14393i) q^{83} +(-20.4695 - 14.8719i) q^{84} +(1.19556 + 1.88962i) q^{85} +(7.75153 - 5.63181i) q^{86} +(5.12271 + 3.72187i) q^{87} +(4.63941 + 3.37073i) q^{88} +(-2.33871 + 1.69918i) q^{89} +(-5.39444 + 1.37718i) q^{90} +(-25.7361 - 18.6984i) q^{91} +(6.59453 + 20.2959i) q^{92} +4.85290 q^{93} +(-1.65107 - 5.08146i) q^{94} +(-2.00895 - 3.17521i) q^{95} +(-1.25221 + 3.85390i) q^{96} +(-3.93745 + 12.1182i) q^{97} +(-33.4132 + 24.2761i) q^{98} +1.51018 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q - 6 q^{2} - 7 q^{3} - 26 q^{4} + 13 q^{5} + 12 q^{6} + 22 q^{7} + 10 q^{8} - 24 q^{9} - 6 q^{10} - 16 q^{11} - 15 q^{12} - q^{13} - 19 q^{14} - 3 q^{15} + 30 q^{16} - 19 q^{17} + 6 q^{18} + 18 q^{19}+ \cdots - 64 q^{99}+O(q^{100}) \) 76 * q - 6 * q^2 - 7 * q^3 - 26 * q^4 + 13 * q^5 + 12 * q^6 + 22 * q^7 + 10 * q^8 - 24 * q^9 - 6 * q^10 - 16 * q^11 - 15 * q^12 - q^13 - 19 * q^14 - 3 * q^15 + 30 * q^16 - 19 * q^17 + 6 * q^18 + 18 * q^19 - 23 * q^20 - 22 * q^21 - 15 * q^22 - 8 * q^23 - 22 * q^24 + 35 * q^25 - 14 * q^26 - 10 * q^27 - 29 * q^28 - 25 * q^29 + 57 * q^30 + 22 * q^31 + 54 * q^32 - 22 * q^33 - 6 * q^34 - 19 * q^35 - 91 * q^36 - 49 * q^37 + 15 * q^38 + 25 * q^39 - 2 * q^40 + 16 * q^41 - 28 * q^42 + 104 * q^43 + 18 * q^44 + 10 * q^45 - 55 * q^46 - 26 * q^47 - 86 * q^48 + 2 * q^49 - 17 * q^50 + 18 * q^51 + 53 * q^52 - 41 * q^53 - 6 * q^54 + 67 * q^55 + 115 * q^56 + 84 * q^57 - 12 * q^58 - 7 * q^59 - 32 * q^60 - 21 * q^61 - 23 * q^62 - 21 * q^63 + 6 * q^64 - 72 * q^65 + 102 * q^66 - 15 * q^67 + 74 * q^68 + 48 * q^69 - 60 * q^70 - 8 * q^71 + 9 * q^72 - 25 * q^73 - 60 * q^74 + 68 * q^75 - 76 * q^76 - 36 * q^77 - 51 * q^78 + 2 * q^79 + 217 * q^80 + 20 * q^81 - 12 * q^82 - 41 * q^83 - 48 * q^84 - 7 * q^85 - 87 * q^86 - 54 * q^87 - 4 * q^88 + 77 * q^89 - 93 * q^90 + 79 * q^91 - 19 * q^92 + 72 * q^93 + 15 * q^94 + 57 * q^95 + 28 * q^96 + 13 * q^97 - 62 * q^98 - 64 * q^99

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