LMFDB - Embedded newform 275.2.l.d.31.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [275,2,Mod(31,275)] 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("275.31"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(275, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([4, 6])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	275.l (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [100,2,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$2.19588605559$
Analytic rank:	$0$
Dimension:	$100$
Relative dimension:	$25$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			31.15
Character	$\chi$	$=$	275.31
Dual form			275.2.l.d.71.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.796321 q^{2} +(0.147790 - 0.454851i) q^{3} -1.36587 q^{4} +(-2.20171 - 0.390463i) q^{5} +(0.117688 - 0.362208i) q^{6} +(-3.47097 - 2.52180i) q^{7} -2.68032 q^{8} +(2.24200 + 1.62891i) q^{9} +(-1.75327 - 0.310934i) q^{10} +(2.20521 - 2.47731i) q^{11} +(-0.201863 + 0.621269i) q^{12} +(-4.49101 - 3.26291i) q^{13} +(-2.76400 - 2.00817i) q^{14} +(-0.502994 + 0.943745i) q^{15} +0.597355 q^{16} +(-0.216806 + 0.667262i) q^{17} +(1.78535 + 1.29714i) q^{18} -2.24819 q^{19} +(3.00726 + 0.533323i) q^{20} +(-1.66002 + 1.20607i) q^{21} +(1.75605 - 1.97273i) q^{22} +(1.21835 + 3.74971i) q^{23} +(-0.396124 + 1.21914i) q^{24} +(4.69508 + 1.71938i) q^{25} +(-3.57629 - 2.59833i) q^{26} +(2.23302 - 1.62238i) q^{27} +(4.74090 + 3.44446i) q^{28} -3.16231 q^{29} +(-0.400545 + 0.751524i) q^{30} +(6.07344 - 4.41261i) q^{31} +5.83632 q^{32} +(-0.800900 - 1.36916i) q^{33} +(-0.172647 + 0.531354i) q^{34} +(6.65740 + 6.90757i) q^{35} +(-3.06229 - 2.22489i) q^{36} +(-8.33525 + 6.05591i) q^{37} -1.79028 q^{38} +(-2.14787 + 1.56052i) q^{39} +(5.90128 + 1.04656i) q^{40} +(-2.75836 - 8.48937i) q^{41} +(-1.32191 + 0.960423i) q^{42} -0.584284 q^{43} +(-3.01203 + 3.38369i) q^{44} +(-4.30022 - 4.46181i) q^{45} +(0.970201 + 2.98597i) q^{46} +(2.40684 - 7.40748i) q^{47} +(0.0882831 - 0.271708i) q^{48} +(3.52499 + 10.8488i) q^{49} +(3.73879 + 1.36917i) q^{50} +(0.271463 + 0.197229i) q^{51} +(6.13415 + 4.45672i) q^{52} +(-2.46422 - 7.58408i) q^{53} +(1.77820 - 1.29194i) q^{54} +(-5.82253 + 4.59328i) q^{55} +(9.30328 + 6.75923i) q^{56} +(-0.332261 + 1.02259i) q^{57} -2.51821 q^{58} +(-2.74586 + 1.99499i) q^{59} +(0.687026 - 1.28904i) q^{60} +(6.94481 - 5.04570i) q^{61} +(4.83641 - 3.51385i) q^{62} +(-3.67412 - 11.3078i) q^{63} +3.45287 q^{64} +(8.61387 + 8.93757i) q^{65} +(-0.637774 - 1.09029i) q^{66} +(-4.07324 - 2.95938i) q^{67} +(0.296130 - 0.911394i) q^{68} +1.88562 q^{69} +(5.30142 + 5.50064i) q^{70} +(-1.71200 - 1.24384i) q^{71} +(-6.00928 - 4.36599i) q^{72} +(1.58212 - 4.86928i) q^{73} +(-6.63753 + 4.82245i) q^{74} +(1.47595 - 1.88145i) q^{75} +3.07075 q^{76} +(-13.9015 + 3.03757i) q^{77} +(-1.71039 + 1.24267i) q^{78} +(0.175201 + 0.539212i) q^{79} +(-1.31520 - 0.233245i) q^{80} +(2.16118 + 6.65144i) q^{81} +(-2.19654 - 6.76026i) q^{82} +(-2.97770 + 9.16443i) q^{83} +(2.26738 - 1.64735i) q^{84} +(0.737886 - 1.38446i) q^{85} -0.465278 q^{86} +(-0.467358 + 1.43838i) q^{87} +(-5.91064 + 6.63997i) q^{88} +(-4.05017 - 12.4652i) q^{89} +(-3.42435 - 3.55304i) q^{90} +(7.35973 + 22.6509i) q^{91} +(-1.66412 - 5.12162i) q^{92} +(-1.10949 - 3.41465i) q^{93} +(1.91661 - 5.89873i) q^{94} +(4.94987 + 0.877836i) q^{95} +(0.862550 - 2.65466i) q^{96} +(0.776519 + 2.38988i) q^{97} +(2.80702 + 8.63912i) q^{98} +(8.97940 - 1.96206i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q + 2 q^{2} - 2 q^{3} + 106 q^{4} + 5 q^{5} + 5 q^{6} + 5 q^{7} - 30 q^{8} - 25 q^{9} - 22 q^{10} - 53 q^{12} - 18 q^{13} - 10 q^{14} + 16 q^{15} + 62 q^{16} + q^{17} - 21 q^{18} + 6 q^{19} + q^{20}+ \cdots - 84 q^{99}+O(q^{100}) $ 100 * q + 2 * q^2 - 2 * q^3 + 106 * q^4 + 5 * q^5 + 5 * q^6 + 5 * q^7 - 30 * q^8 - 25 * q^9 - 22 * q^10 - 53 * q^12 - 18 * q^13 - 10 * q^14 + 16 * q^15 + 62 * q^16 + q^17 - 21 * q^18 + 6 * q^19 + q^20 - 22 * q^21 + 6 * q^22 + 20 * q^23 - 18 * q^24 + q^25 - 37 * q^26 + 10 * q^27 - 64 * q^28 - 28 * q^29 + 15 * q^30 + 9 * q^31 - 98 * q^32 + 13 * q^33 - 14 * q^34 + 13 * q^35 - 30 * q^36 - 21 * q^37 + 18 * q^38 + 44 * q^39 + 9 * q^40 + 28 * q^41 + 31 * q^42 + 82 * q^43 - 4 * q^44 - 25 * q^45 - 16 * q^46 - 10 * q^47 - 72 * q^48 - 26 * q^49 - 46 * q^50 - 14 * q^51 - 23 * q^52 - 5 * q^53 - 22 * q^54 + 32 * q^55 + q^56 - 85 * q^57 + 80 * q^58 - 3 * q^59 + 61 * q^60 + 35 * q^61 + 43 * q^62 - 47 * q^63 - 54 * q^64 - 64 * q^65 - 13 * q^66 - 20 * q^67 + 5 * q^68 + 76 * q^69 - 23 * q^70 + 28 * q^71 - 53 * q^72 + 33 * q^73 - 3 * q^74 - 34 * q^75 - 156 * q^76 + 45 * q^77 + 30 * q^78 + 4 * q^79 - 144 * q^80 - 27 * q^81 - 59 * q^82 - 92 * q^83 + 9 * q^84 - 26 * q^85 - 56 * q^86 + 38 * q^87 + 18 * q^88 + 39 * q^89 + 114 * q^90 - 11 * q^91 - 60 * q^92 - 19 * q^93 + 46 * q^94 - 46 * q^95 + 9 * q^96 + 20 * q^97 + 122 * q^98 - 84 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	0.796321			0.563084			0.281542	−	0.959549i	$-0.409154\pi$
$2$	0.796321			0.563084			0.281542	+	0.959549i	$0.409154\pi$
$3$	0.147790	−	0.454851i	0.0853267	−	0.262608i	−0.899286	−	0.437362i	$-0.855913\pi$
$3$	0.147790	−	0.454851i	0.0853267	−	0.262608i	0.984612	+	0.174754i	$0.0559129\pi$
$4$	−1.36587			−0.682936
$5$	−2.20171	−	0.390463i	−0.984636	−	0.174620i
$5$	−2.20171	−	0.390463i	−0.984636	−	0.174620i
$6$	0.117688	−	0.362208i	0.0480461	−	0.147871i
$7$	−3.47097	−	2.52180i	−1.31190	−	0.953152i	−0.999995	−	0.00303931i	$-0.999033\pi$
$7$	−3.47097	−	2.52180i	−1.31190	−	0.953152i	−0.311906	−	0.950113i	$-0.600967\pi$
$8$	−2.68032			−0.947634
$9$	2.24200	+	1.62891i	0.747334	+	0.542970i
$10$	−1.75327	−	0.310934i	−0.554433	−	0.0983259i
$11$	2.20521	−	2.47731i	0.664894	−	0.746937i
$11$	2.20521	−	2.47731i	0.664894	−	0.746937i
$12$	−0.201863	+	0.621269i	−0.0582727	+	0.179345i
$13$	−4.49101	−	3.26291i	−1.24558	−	0.904969i	−0.247626	−	0.968856i	$-0.579650\pi$
$13$	−4.49101	−	3.26291i	−1.24558	−	0.904969i	−0.997957	+	0.0638866i	$0.979650\pi$
$14$	−2.76400	−	2.00817i	−0.738711	−	0.536705i
$15$	−0.502994	+	0.943745i	−0.129872	+	0.243674i
$16$	0.597355			0.149339
$17$	−0.216806	+	0.667262i	−0.0525833	+	0.161835i	−0.973900	−	0.226979i	$-0.927115\pi$
$17$	−0.216806	+	0.667262i	−0.0525833	+	0.161835i	0.921316	+	0.388814i	$0.127115\pi$
$18$	1.78535	+	1.29714i	0.420812	+	0.305738i
$19$	−2.24819			−0.515771			−0.257885	−	0.966176i	$-0.583026\pi$
$19$	−2.24819			−0.515771			−0.257885	+	0.966176i	$0.583026\pi$
$20$	3.00726	+	0.533323i	0.672444	+	0.119255i
$21$	−1.66002	+	1.20607i	−0.362246	+	0.263187i
$22$	1.75605	−	1.97273i	0.374391	−	0.420588i
$23$	1.21835	+	3.74971i	0.254044	+	0.781868i	0.994016	+	0.109231i	$0.0348387\pi$
$23$	1.21835	+	3.74971i	0.254044	+	0.781868i	−0.739972	+	0.672638i	$0.765161\pi$
$24$	−0.396124	+	1.21914i	−0.0808585	+	0.248857i
$25$	4.69508	+	1.71938i	0.939015	+	0.343875i
$26$	−3.57629	−	2.59833i	−0.701368	−	0.509574i
$27$	2.23302	−	1.62238i	0.429744	−	0.312227i
$28$	4.74090	+	3.44446i	0.895945	+	0.650942i
$29$	−3.16231			−0.587226			−0.293613	−	0.955924i	$-0.594858\pi$
$29$	−3.16231			−0.587226			−0.293613	+	0.955924i	$0.594858\pi$
$30$	−0.400545	+	0.751524i	−0.0731291	+	0.137209i
$31$	6.07344	−	4.41261i	1.09082	−	0.792528i	0.111284	−	0.993789i	$-0.464504\pi$
$31$	6.07344	−	4.41261i	1.09082	−	0.792528i	0.979538	+	0.201260i	$0.0645037\pi$
$32$	5.83632			1.03172
$33$	−0.800900	−	1.36916i	−0.139419	−	0.238341i
$34$	−0.172647	+	0.531354i	−0.0296088	+	0.0911265i
$35$	6.65740	+	6.90757i	1.12531	+	1.16759i
$36$	−3.06229	−	2.22489i	−0.510382	−	0.370814i
$37$	−8.33525	+	6.05591i	−1.37031	+	0.995586i	−0.372593	+	0.927995i	$0.621531\pi$
$37$	−8.33525	+	6.05591i	−1.37031	+	0.995586i	−0.997713	+	0.0675909i	$0.978469\pi$
$38$	−1.79028			−0.290422
$39$	−2.14787	+	1.56052i	−0.343934	+	0.249883i
$40$	5.90128	+	1.04656i	0.933075	+	0.165476i
$41$	−2.75836	−	8.48937i	−0.430784	−	1.32582i	−0.897346	−	0.441328i	$-0.854508\pi$
$41$	−2.75836	−	8.48937i	−0.430784	−	1.32582i	0.466562	−	0.884488i	$-0.345492\pi$
$42$	−1.32191	+	0.960423i	−0.203975	+	0.148196i
$43$	−0.584284			−0.0891025			−0.0445512	−	0.999007i	$-0.514186\pi$
$43$	−0.584284			−0.0891025			−0.0445512	+	0.999007i	$0.514186\pi$
$44$	−3.01203	+	3.38369i	−0.454081	+	0.510111i
$45$	−4.30022	−	4.46181i	−0.641039	−	0.665128i
$46$	0.970201	+	2.98597i	0.143048	+	0.440257i
$47$	2.40684	−	7.40748i	0.351073	−	1.08049i	−0.607178	−	0.794566i	$-0.707699\pi$
$47$	2.40684	−	7.40748i	0.351073	−	1.08049i	0.958252	−	0.285927i	$-0.0923014\pi$
$48$	0.0882831	−	0.271708i	0.0127426	−	0.0392176i
$49$	3.52499	+	10.8488i	0.503569	+	1.54983i
$50$	3.73879	+	1.36917i	0.528744	+	0.193631i
$51$	0.271463	+	0.197229i	0.0380124	+	0.0276176i
$52$	6.13415	+	4.45672i	0.850654	+	0.618036i
$53$	−2.46422	−	7.58408i	−0.338486	−	1.04175i	−0.964979	−	0.262326i	$-0.915510\pi$
$53$	−2.46422	−	7.58408i	−0.338486	−	1.04175i	0.626493	−	0.779427i	$-0.284490\pi$
$54$	1.77820	−	1.29194i	0.241982	−	0.175810i
$55$	−5.82253	+	4.59328i	−0.785109	+	0.619357i
$56$	9.30328	+	6.75923i	1.24320	+	0.903240i
$57$	−0.332261	+	1.02259i	−0.0440090	+	0.135446i
$58$	−2.51821			−0.330658
$59$	−2.74586	+	1.99499i	−0.357481	+	0.259725i	−0.752001	−	0.659162i	$-0.770911\pi$
$59$	−2.74586	+	1.99499i	−0.357481	+	0.259725i	0.394520	+	0.918887i	$0.370911\pi$
$60$	0.687026	−	1.28904i	0.0886947	−	0.166414i
$61$	6.94481	−	5.04570i	0.889191	−	0.646035i	−0.0464757	−	0.998919i	$-0.514799\pi$
$61$	6.94481	−	5.04570i	0.889191	−	0.646035i	0.935667	+	0.352884i	$0.114799\pi$
$62$	4.83641	−	3.51385i	0.614224	−	0.446260i
$63$	−3.67412	−	11.3078i	−0.462896	−	1.42465i
$64$	3.45287			0.431609
$65$	8.61387	+	8.93757i	1.06842	+	1.10857i
$66$	−0.637774	−	1.09029i	−0.0785045	−	0.134206i
$67$	−4.07324	−	2.95938i	−0.497626	−	0.361546i	0.310484	−	0.950579i	$-0.399509\pi$
$67$	−4.07324	−	2.95938i	−0.497626	−	0.361546i	−0.808109	+	0.589032i	$0.799509\pi$
$68$	0.296130	−	0.911394i	0.0359110	−	0.110523i
$69$	1.88562			0.227002
$70$	5.30142	+	5.50064i	0.633641	+	0.657453i
$71$	−1.71200	−	1.24384i	−0.203177	−	0.147617i	0.481544	−	0.876422i	$-0.340076\pi$
$71$	−1.71200	−	1.24384i	−0.203177	−	0.147617i	−0.684721	+	0.728805i	$0.740076\pi$
$72$	−6.00928	−	4.36599i	−0.708200	−	0.514537i
$73$	1.58212	−	4.86928i	0.185174	−	0.569906i	−0.814778	−	0.579774i	$-0.803141\pi$
$73$	1.58212	−	4.86928i	0.185174	−	0.569906i	0.999951	+	0.00986763i	$0.00314102\pi$
$74$	−6.63753	+	4.82245i	−0.771597	+	0.560598i
$75$	1.47595	−	1.88145i	0.170428	−	0.217252i
$76$	3.07075			0.352239
$77$	−13.9015	+	3.03757i	−1.58422	+	0.346163i
$78$	−1.71039	+	1.24267i	−0.193664	+	0.140705i
$79$	0.175201	+	0.539212i	0.0197116	+	0.0606661i	0.960428	−	0.278527i	$-0.0898461\pi$
$79$	0.175201	+	0.539212i	0.0197116	+	0.0606661i	−0.940717	+	0.339193i	$0.889846\pi$
$80$	−1.31520	−	0.233245i	−0.147044	−	0.0260776i
$81$	2.16118	+	6.65144i	0.240131	+	0.739049i
$82$	−2.19654	−	6.76026i	−0.242567	−	0.746546i
$83$	−2.97770	+	9.16443i	−0.326845	+	1.00593i	0.643755	+	0.765231i	$0.277375\pi$
$83$	−2.97770	+	9.16443i	−0.326845	+	1.00593i	−0.970601	+	0.240695i	$0.922625\pi$
$84$	2.26738	−	1.64735i	0.247391	−	0.179740i
$85$	0.737886	−	1.38446i	0.0800350	−	0.150166i
$86$	−0.465278			−0.0501722
$87$	−0.467358	+	1.43838i	−0.0501060	+	0.154211i
$88$	−5.91064	+	6.63997i	−0.630077	+	0.707824i
$89$	−4.05017	−	12.4652i	−0.429318	−	1.32130i	−0.898799	−	0.438361i	$-0.855559\pi$
$89$	−4.05017	−	12.4652i	−0.429318	−	1.32130i	0.469481	−	0.882942i	$-0.344441\pi$
$90$	−3.42435	−	3.55304i	−0.360959	−	0.374523i
$91$	7.35973	+	22.6509i	0.771509	+	2.37446i
$92$	−1.66412	−	5.12162i	−0.173496	−	0.533966i
$93$	−1.10949	−	3.41465i	−0.115048	−	0.354083i
$94$	1.91661	−	5.89873i	0.197684	−	0.608408i
$95$	4.94987	+	0.877836i	0.507846	+	0.0900641i
$96$	0.862550	−	2.65466i	0.0880336	−	0.270940i
$97$	0.776519	+	2.38988i	0.0788436	+	0.242656i	0.982708	−	0.185164i	$-0.0592817\pi$
$97$	0.776519	+	2.38988i	0.0788436	+	0.242656i	−0.903864	+	0.427820i	$0.859282\pi$
$98$	2.80702	+	8.63912i	0.283552	+	0.872683i
$99$	8.97940	−	1.96206i	0.902463	−	0.197194i
$100$	−6.41288	−	2.34845i	−0.641288	−	0.234845i
$101$	−2.79243	+	8.59423i	−0.277858	+	0.855157i	0.710592	+	0.703605i	$0.248427\pi$
$101$	−2.79243	+	8.59423i	−0.277858	+	0.855157i	−0.988449	+	0.151553i	$0.951573\pi$
$102$	0.216172	+	0.157058i	0.0214042	+	0.0155510i
$103$	5.31970			0.524166			0.262083	−	0.965045i	$-0.415591\pi$
$103$	5.31970			0.524166			0.262083	+	0.965045i	$0.415591\pi$
$104$	12.0373	+	8.74563i	1.18036	+	0.857580i
$105$	4.12581	−	2.00725i	0.402638	−	0.195888i
$106$	−1.96231	−	6.03936i	−0.190596	−	0.586595i
$107$	9.67152	−	7.02677i	0.934981	−	0.679304i	−0.0122262	−	0.999925i	$-0.503892\pi$
$107$	9.67152	−	7.02677i	0.934981	−	0.679304i	0.947207	+	0.320622i	$0.103892\pi$
$108$	−3.05002	+	2.21597i	−0.293488	+	0.213232i
$109$	−2.75488	+	8.47866i	−0.263870	+	0.812109i	0.728081	+	0.685491i	$0.240412\pi$
$109$	−2.75488	+	8.47866i	−0.263870	+	0.812109i	−0.991952	+	0.126618i	$0.959588\pi$
$110$	−4.63660	+	3.65772i	−0.442082	+	0.348750i
$111$	1.52267	+	4.68630i	0.144526	+	0.444804i
$112$	−2.07340	−	1.50641i	−0.195918	−	0.142343i
$113$	−1.53771	−	4.73259i	−0.144656	−	0.445204i	0.852311	−	0.523035i	$-0.175200\pi$
$113$	−1.53771	−	4.73259i	−0.144656	−	0.445204i	−0.996967	+	0.0778312i	$0.975200\pi$
$114$	−0.264586	+	0.814312i	−0.0247808	+	0.0762673i
$115$	−1.21834	−	8.73150i	−0.113611	−	0.814217i
$116$	4.31931			0.401038
$117$	−4.75387	−	14.6309i	−0.439496	−	1.35263i
$118$	−2.18659	+	1.58865i	−0.201292	+	0.146247i
$119$	2.43523	−	1.76930i	0.223237	−	0.162191i
$120$	1.34818	−	2.52953i	0.123072	−	0.230914i
$121$	−1.27414	−	10.9260i	−0.115831	−	0.993269i
$122$	5.53029	−	4.01799i	0.500689	−	0.363772i
$123$	−4.26906			−0.384928
$124$	−8.29554	+	6.02707i	−0.744962	+	0.541246i
$125$	−9.66586	−	5.61882i	−0.864541	−	0.502563i
$126$	−2.92578	−	9.00463i	−0.260649	−	0.802196i
$127$	−4.95361	+	3.59901i	−0.439562	+	0.319360i	−0.785461	−	0.618911i	$-0.787574\pi$
$127$	−4.95361	+	3.59901i	−0.439562	+	0.319360i	0.345899	+	0.938272i	$0.387574\pi$
$128$	−8.92304			−0.788693
$129$	−0.0863514	+	0.265762i	−0.00760282	+	0.0233991i
$130$	6.85941	+	7.11717i	0.601610	+	0.624218i
$131$	−2.04698	−	1.48721i	−0.178845	−	0.129939i	0.494761	−	0.869029i	$-0.335256\pi$
$131$	−2.04698	−	1.48721i	−0.178845	−	0.129939i	−0.673606	+	0.739090i	$0.735256\pi$
$132$	1.09393	+	1.87010i	0.0952142	+	0.162771i
$133$	7.80340	+	5.66950i	0.676640	+	0.491608i
$134$	−3.24361	−	2.35662i	−0.280205	−	0.203581i
$135$	−5.54994	+	2.70011i	−0.477663	+	0.232388i
$136$	0.581109	−	1.78847i	0.0498297	−	0.153360i
$137$	2.59296			0.221531			0.110766	−	0.993847i	$-0.464670\pi$
$137$	2.59296			0.221531			0.110766	+	0.993847i	$0.464670\pi$
$138$	1.50156			0.127821
$139$	0.323071	−	0.994309i	0.0274025	−	0.0843362i	−0.936420	−	0.350881i	$-0.885882\pi$
$139$	0.323071	−	0.994309i	0.0274025	−	0.0843362i	0.963822	+	0.266545i	$0.0858821\pi$
$140$	−9.09316	−	9.43486i	−0.768512	−	0.797392i
$141$	−3.01360	−	2.18951i	−0.253791	−	0.184390i
$142$	−1.36330	−	0.990498i	−0.114406	−	0.0831207i
$143$	−17.9869	+	3.93025i	−1.50414	+	0.328664i
$144$	1.33927	+	0.973038i	0.111606	+	0.0810865i
$145$	6.96250	+	1.23477i	0.578204	+	0.102542i
$146$	1.25988	−	3.87751i	0.104268	−	0.320905i
$147$	5.45554			0.449966
$148$	11.3849	−	8.27161i	0.935832	−	0.679922i
$149$	−5.36994	−	16.5270i	−0.439923	−	1.35394i	−0.887957	−	0.459926i	$-0.847876\pi$
$149$	−5.36994	−	16.5270i	−0.439923	−	1.35394i	0.448035	−	0.894016i	$-0.352124\pi$
$150$	1.17533	−	1.49824i	0.0959650	−	0.122331i
$151$	−10.7387	+	7.80211i	−0.873901	+	0.634926i	−0.931631	−	0.363406i	$-0.881614\pi$
$151$	−10.7387	+	7.80211i	−0.873901	+	0.634926i	0.0577298	+	0.998332i	$0.481614\pi$
$152$	6.02586			0.488762
$153$	−1.57299	+	1.14284i	−0.127169	+	0.0923935i
$154$	−11.0700	+	2.41888i	−0.892049	+	0.194919i
$155$	−15.0949	+	7.34385i	−1.21245	+	0.589872i
$156$	2.93371	−	2.13147i	0.234885	−	0.170654i
$157$	−1.86822	+	1.35734i	−0.149100	+	0.108327i	−0.659834	−	0.751411i	$-0.729374\pi$
$157$	−1.86822	+	1.35734i	−0.149100	+	0.108327i	0.510734	+	0.859739i	$0.329374\pi$
$158$	0.139516	+	0.429386i	0.0110993	+	0.0341601i
$159$	−3.81381			−0.302455
$160$	−12.8499	−	2.27887i	−1.01587	−	0.180160i
$161$	5.22716	−	16.0876i	0.411958	−	1.26788i
$162$	1.72100	+	5.29668i	0.135214	+	0.416146i
$163$	18.0837	+	13.1385i	1.41642	+	1.02909i	0.992349	+	0.123462i	$0.0393997\pi$
$163$	18.0837	+	13.1385i	1.41642	+	1.02909i	0.424072	+	0.905628i	$0.360600\pi$
$164$	3.76757	+	11.5954i	0.294198	+	0.905448i
$165$	1.22874	+	3.32722i	0.0956577	+	0.259024i
$166$	−2.37121	+	7.29782i	−0.184041	+	0.566421i
$167$	4.87567	−	3.54238i	0.377291	−	0.274118i	−0.382937	−	0.923774i	$-0.625087\pi$
$167$	4.87567	−	3.54238i	0.377291	−	0.274118i	0.760228	+	0.649657i	$0.225087\pi$
$168$	4.44938	−	3.23266i	0.343277	−	0.249405i
$169$	5.50539	+	16.9438i	0.423491	+	1.30337i
$170$	0.587594	−	1.10248i	0.0450664	−	0.0845561i
$171$	−5.04045	−	3.66210i	−0.385453	−	0.280048i
$172$	0.798058			0.0608513
$173$	−12.1692	−	8.84143i	−0.925206	−	0.672202i	0.0196081	−	0.999808i	$-0.493758\pi$
$173$	−12.1692	−	8.84143i	−0.925206	−	0.672202i	−0.944814	+	0.327606i	$0.893758\pi$
$174$	−0.372167	+	1.14541i	−0.0282139	+	0.0868335i
$175$	−11.9605	−	17.8080i	−0.904130	−	1.34615i
$176$	1.31729	−	1.47983i	0.0992945	−	0.111547i
$177$	0.501610	+	1.54380i	0.0377033	+	0.116039i
$178$	−3.22524	−	9.92626i	−0.241742	−	0.744005i
$179$	4.11990	−	12.6798i	0.307936	−	0.947730i	−0.670629	−	0.741793i	$-0.733976\pi$
$179$	4.11990	−	12.6798i	0.307936	−	0.947730i	0.978565	−	0.205937i	$-0.0660242\pi$
$180$	5.87355	+	6.09427i	0.437789	+	0.454240i
$181$	−7.34573	+	22.6078i	−0.546004	+	1.68043i	0.172588	+	0.984994i	$0.444787\pi$
$181$	−7.34573	+	22.6078i	−0.546004	+	1.68043i	−0.718591	+	0.695433i	$0.755213\pi$
$182$	5.86070	+	18.0374i	0.434424	+	1.33702i
$183$	−1.26867	−	3.90456i	−0.0937826	−	0.288633i
$184$	−3.26557	−	10.0504i	−0.240741	−	0.740925i
$185$	20.7164	−	10.0788i	1.52310	−	0.741006i
$186$	−0.883508	−	2.71916i	−0.0647819	−	0.199378i
$187$	1.17491	+	2.00855i	0.0859180	+	0.146879i
$188$	−3.28743	+	10.1177i	−0.239761	+	0.737908i
$189$	−11.8420			−0.861382
$190$	3.94169	+	0.699039i	0.285960	+	0.0507136i
$191$	−0.0557821	+	0.0405280i	−0.00403625	+	0.00293251i	−0.589802	−	0.807548i	$-0.700794\pi$
$191$	−0.0557821	+	0.0405280i	−0.00403625	+	0.00293251i	0.585765	+	0.810481i	$0.300794\pi$
$192$	0.510300	−	1.57054i	0.0368277	−	0.113344i
$193$	−3.49569	−	10.7586i	−0.251625	−	0.774423i	−0.994476	−	0.104965i	$-0.966527\pi$
$193$	−3.49569	−	10.7586i	−0.251625	−	0.774423i	0.742851	−	0.669457i	$-0.233473\pi$
$194$	0.618359	+	1.90311i	0.0443956	+	0.136635i
$195$	5.33831	−	2.59715i	0.382284	−	0.185986i
$196$	−4.81468	−	14.8181i	−0.343906	−	1.05843i
$197$	13.1019	−	9.51909i	0.933472	−	0.678207i	−0.0133686	−	0.999911i	$-0.504255\pi$
$197$	13.1019	−	9.51909i	0.933472	−	0.678207i	0.946840	+	0.321704i	$0.104255\pi$
$198$	7.15048	−	1.56243i	0.508163	−	0.111037i
$199$	21.5953			1.53085			0.765426	−	0.643523i	$-0.222528\pi$
$199$	21.5953			1.53085			0.765426	+	0.643523i	$0.222528\pi$
$200$	−12.5843	−	4.60847i	−0.889843	−	0.325868i
$201$	−1.94806	+	1.41535i	−0.137406	+	0.0998312i
$202$	−2.22367	+	6.84376i	−0.156457	+	0.481525i
$203$	10.9763	+	7.97472i	0.770383	+	0.559716i
$204$	−0.370784	−	0.269390i	−0.0259601	−	0.0188611i
$205$	2.75834	+	19.7682i	0.192651	+	1.38067i
$206$	4.23619			0.295149
$207$	−3.37639	+	10.3914i	−0.234675	+	0.722255i
$208$	−2.68273	−	1.94912i	−0.186014	−	0.135147i
$209$	−4.95773	+	5.56947i	−0.342933	+	0.385248i
$210$	3.28547	−	1.59842i	0.226719	−	0.110301i
$211$	−0.665458			−0.0458120			−0.0229060	−	0.999738i	$-0.507292\pi$
$211$	−0.665458			−0.0458120			−0.0229060	+	0.999738i	$0.507292\pi$
$212$	3.36581	+	10.3589i	0.231165	+	0.711451i
$213$	−0.818780	+	0.594879i	−0.0561019	+	0.0407604i
$214$	7.70163	−	5.59556i	0.526473	−	0.382505i
$215$	1.28643	+	0.228141i	0.0877335	+	0.0155591i
$216$	−5.98519	+	4.34849i	−0.407240	+	0.295877i
$217$	−32.2084			−2.18645
$218$	−2.19377	+	6.75174i	−0.148581	+	0.457285i
$219$	−1.98097	−	1.43926i	−0.133862	−	0.0972563i
$220$	7.95283	−	6.27383i	0.536180	−	0.422982i
$221$	3.15090	−	2.28926i	0.211952	−	0.153992i
$222$	1.21254	+	3.73180i	0.0813800	+	0.250462i
$223$	3.00033	+	2.17987i	0.200917	+	0.145975i	0.683695	−	0.729768i	$-0.260372\pi$
$223$	3.00033	+	2.17987i	0.200917	+	0.145975i	−0.482778	+	0.875743i	$0.660372\pi$
$224$	−20.2577	−	14.7180i	−1.35352	−	0.983391i
$225$	7.72567	+	11.5027i	0.515045	+	0.766847i
$226$	−1.22451	−	3.76866i	−0.0814533	−	0.250687i
$227$	1.86227	−	5.73147i	0.123603	−	0.380411i	−0.870041	−	0.492979i	$-0.835908\pi$
$227$	1.86227	−	5.73147i	0.123603	−	0.380411i	0.993644	+	0.112569i	$0.0359078\pi$
$228$	0.453826	−	1.39673i	0.0300553	−	0.0925008i
$229$	−4.69915	−	14.4625i	−0.310529	−	0.955709i	−0.977556	−	0.210676i	$-0.932434\pi$
$229$	−4.69915	−	14.4625i	−0.310529	−	0.955709i	0.667027	−	0.745033i	$-0.267566\pi$
$230$	−0.970192	−	6.95308i	−0.0639725	−	0.458472i
$231$	−0.672861	+	6.77203i	−0.0442710	+	0.445567i
$232$	8.47599			0.556476
$233$	0.913921	−	0.664003i	0.0598730	−	0.0435003i	−0.557446	−	0.830213i	$-0.688219\pi$
$233$	0.913921	−	0.664003i	0.0598730	−	0.0435003i	0.617319	+	0.786713i	$0.288219\pi$
$234$	−3.78561	−	11.6509i	−0.247473	−	0.761644i
$235$	−8.19151	+	15.3694i	−0.534355	+	1.00259i
$236$	3.75050	−	2.72490i	0.244137	−	0.177376i
$237$	0.271154			0.0176134
$238$	1.93922	−	1.40893i	0.125701	−	0.0913273i
$239$	12.5789	+	9.13908i	0.813659	+	0.591158i	0.914889	−	0.403705i	$-0.132278\pi$
$239$	12.5789	+	9.13908i	0.813659	+	0.591158i	−0.101230	+	0.994863i	$0.532278\pi$
$240$	−0.300466	+	0.563751i	−0.0193950	+	0.0363899i
$241$	−6.97560	+	21.4687i	−0.449338	+	1.38292i	0.428318	+	0.903628i	$0.359106\pi$
$241$	−6.97560	+	21.4687i	−0.449338	+	1.38292i	−0.877656	+	0.479292i	$0.840894\pi$
$242$	−1.01462	−	8.70057i	−0.0652225	−	0.559294i
$243$	11.6253			0.745763
$244$	−9.48572	+	6.89178i	−0.607261	+	0.441201i
$245$	−3.52495	−	25.2623i	−0.225201	−	1.61395i
$246$	−3.39954			−0.216747
$247$	10.0967	+	7.33565i	0.642435	+	0.466757i
$248$	−16.2787	+	11.8272i	−1.03370	+	0.751027i
$249$	3.72838	+	2.70882i	0.236276	+	0.171665i
$250$	−7.69713	−	4.47439i	−0.486809	−	0.282985i
$251$	−2.94697	+	9.06984i	−0.186011	+	0.572483i	−0.999964	−	0.00844719i	$-0.997311\pi$
$251$	−2.94697	+	9.06984i	−0.186011	+	0.572483i	0.813953	+	0.580930i	$0.197311\pi$
$252$	5.01838	+	15.4450i	0.316128	+	0.972943i
$253$	11.9759	+	5.25063i	0.752919	+	0.330104i
$254$	−3.94466	+	2.86597i	−0.247510	+	0.179827i
$255$	−0.520672	−	0.540238i	−0.0326058	−	0.0338310i
$256$	−14.0113			−0.875709
$257$	−2.31581	−	1.68253i	−0.144456	−	0.104954i	0.513210	−	0.858263i	$-0.328456\pi$
$257$	−2.31581	−	1.68253i	−0.144456	−	0.104954i	−0.657666	+	0.753310i	$0.728456\pi$
$258$	−0.0687634	+	0.211632i	−0.00428102	+	0.0131756i
$259$	44.2032			2.74665
$260$	−11.7655	−	12.2076i	−0.729663	−	0.757082i
$261$	−7.08991	−	5.15112i	−0.438854	−	0.318846i
$262$	−1.63005	−	1.18430i	−0.100705	−	0.0731663i
$263$	2.11618	−	6.51294i	0.130489	−	0.401605i	−0.864372	−	0.502853i	$-0.832284\pi$
$263$	2.11618	−	6.51294i	0.130489	−	0.401605i	0.994861	+	0.101248i	$0.0322836\pi$
$264$	2.14667	+	3.66979i	0.132118	+	0.225860i
$265$	2.46419	+	17.6601i	0.151374	+	1.08485i
$266$	6.21401	+	4.51474i	0.381005	+	0.276817i
$267$	−6.26837			−0.383618
$268$	5.56353	+	4.04214i	0.339847	+	0.246913i
$269$	6.92255	−	21.3054i	0.422075	−	1.29901i	−0.483692	−	0.875239i	$-0.660704\pi$
$269$	6.92255	−	21.3054i	0.422075	−	1.29901i	0.905767	−	0.423776i	$-0.139296\pi$
$270$	−4.41953	+	2.15015i	−0.268964	+	0.130854i
$271$	31.2952			1.90105			0.950525	−	0.310648i	$-0.100546\pi$
$271$	31.2952			1.90105			0.950525	+	0.310648i	$0.100546\pi$
$272$	−0.129510	+	0.398592i	−0.00785272	+	0.0241682i
$273$	11.3905			0.689384
$274$	2.06483			0.124741
$275$	14.6130	−	7.83959i	0.881199	−	0.472745i
$276$	−2.57552			−0.155028
$277$	23.3972			1.40580			0.702901	−	0.711288i	$-0.251888\pi$
$277$	23.3972			1.40580			0.702901	+	0.711288i	$0.251888\pi$
$278$	0.257268	−	0.791789i	0.0154299	−	0.0474884i
$279$	20.8044			1.24553
$280$	−17.8439	−	18.5145i	−1.06638	−	1.10645i
$281$	−6.66907	+	20.5253i	−0.397843	+	1.22444i	0.528882	+	0.848696i	$0.322612\pi$
$281$	−6.66907	+	20.5253i	−0.397843	+	1.22444i	−0.926725	+	0.375740i	$0.877388\pi$
$282$	−2.39979	−	1.74355i	−0.142905	−	0.103827i
$283$	27.7275			1.64823			0.824114	−	0.566424i	$-0.191673\pi$
$283$	27.7275			1.64823			0.824114	+	0.566424i	$0.191673\pi$
$284$	2.33838	+	1.69893i	0.138757	+	0.100813i
$285$	1.13083	−	2.12172i	0.0669844	−	0.125680i
$286$	−14.3233	+	3.12974i	−0.846955	+	0.185065i
$287$	−11.8343	+	36.4223i	−0.698559	+	2.14994i
$288$	13.0850	+	9.50684i	0.771043	+	0.560196i
$289$	13.3551	+	9.70302i	0.785592	+	0.570766i
$290$	5.54438	+	0.983269i	0.325577	+	0.0577396i
$291$	1.20180			0.0704509
$292$	−2.16098	+	6.65082i	−0.126462	+	0.389210i
$293$	−2.90975	−	2.11405i	−0.169989	−	0.123504i	0.499538	−	0.866292i	$-0.333503\pi$
$293$	−2.90975	−	2.11405i	−0.169989	−	0.123504i	−0.669527	+	0.742788i	$0.733503\pi$
$294$	4.34436			0.253368
$295$	6.82457	−	3.32023i	0.397342	−	0.193311i
$296$	22.3411	−	16.2318i	1.29855	−	0.943451i
$297$	0.905116	−	9.10956i	0.0525202	−	0.528590i
$298$	−4.27620	−	13.1608i	−0.247713	−	0.762383i
$299$	6.76332	−	20.8154i	0.391133	−	1.20378i
$300$	−2.01595	+	2.56983i	−0.116391	+	0.148369i
$301$	2.02803	+	1.47345i	0.116894	+	0.0849282i
$302$	−8.55143	+	6.21298i	−0.492080	+	0.357517i
$303$	3.49640	+	2.54028i	0.200863	+	0.145935i
$304$	−1.34297			−0.0770245
$305$	−17.2606	+	8.39748i	−0.988341	+	0.480839i
$306$	−1.25260	+	0.910071i	−0.0716067	+	0.0520253i
$307$	−11.5788			−0.660837			−0.330419	−	0.943835i	$-0.607190\pi$
$307$	−11.5788			−0.660837			−0.330419	+	0.943835i	$0.607190\pi$
$308$	18.9877	−	4.14893i	1.08192	−	0.236407i
$309$	0.786199	−	2.41967i	0.0447253	−	0.137650i
$310$	−12.0204	+	5.84806i	−0.682713	+	0.332147i
$311$	3.67186	+	2.66776i	0.208212	+	0.151275i	0.687004	−	0.726653i	$-0.258925\pi$
$311$	3.67186	+	2.66776i	0.208212	+	0.151275i	−0.478792	+	0.877928i	$0.658925\pi$
$312$	5.75696	−	4.18268i	0.325924	−	0.236797i
$313$	−15.5322			−0.877931			−0.438965	−	0.898504i	$-0.644655\pi$
$313$	−15.5322			−0.877931			−0.438965	+	0.898504i	$0.644655\pi$
$314$	−1.48770	+	1.08088i	−0.0839557	+	0.0609974i
$315$	3.67409	+	26.3311i	0.207011	+	1.48359i
$316$	−0.239302	−	0.736495i	−0.0134618	−	0.0414311i
$317$	−21.3468	+	15.5093i	−1.19895	+	0.871091i	−0.994181	−	0.107718i	$-0.965646\pi$
$317$	−21.3468	+	15.5093i	−1.19895	+	0.871091i	−0.204773	+	0.978810i	$0.565646\pi$
$318$	−3.03702			−0.170308
$319$	−6.97354	+	7.83402i	−0.390443	+	0.438621i
$320$	−7.60223	−	1.34822i	−0.424978	−	0.0753677i
$321$	−1.76678	−	5.43759i	−0.0986120	−	0.303497i
$322$	4.16250	−	12.8109i	0.231967	−	0.713921i
$323$	0.487423	−	1.50013i	0.0271209	−	0.0834696i
$324$	−2.95190	−	9.08502i	−0.163995	−	0.504723i
$325$	−15.4755	−	23.0414i	−0.858425	−	1.27810i
$326$	14.4004	+	10.4625i	0.797564	+	0.579464i
$327$	3.44938	+	2.50612i	0.190751	+	0.138589i
$328$	7.39328	+	22.7542i	0.408226	+	1.25639i
$329$	−27.0343	+	19.6415i	−1.49045	+	1.08287i
$330$	0.978475	+	2.64954i	0.0538633	+	0.145852i
$331$	−24.9148	−	18.1017i	−1.36944	−	0.994957i	−0.997781	−	0.0665880i	$-0.978789\pi$
$331$	−24.9148	−	18.1017i	−1.36944	−	0.994957i	−0.371660	−	0.928369i	$-0.621211\pi$
$332$	4.06716	−	12.5174i	0.223215	−	0.686984i
$333$	−28.5522			−1.56465
$334$	3.88260	−	2.82087i	0.212446	−	0.154351i
$335$	7.81258	+	8.10616i	0.426847	+	0.442887i
$336$	−0.991621	+	0.720455i	−0.0540974	+	0.0393040i
$337$	0.204530	−	0.148600i	0.0111415	−	0.00809476i	−0.582201	−	0.813045i	$-0.697808\pi$
$337$	0.204530	−	0.148600i	0.0111415	−	0.00809476i	0.593342	+	0.804950i	$0.297808\pi$
$338$	4.38405	+	13.4927i	0.238461	+	0.733908i
$339$	−2.37988			−0.129257
$340$	−1.00786	+	1.89100i	−0.0546588	+	0.102554i
$341$	2.46177	−	24.7765i	0.133312	−	1.34172i
$342$	−4.01382	−	2.91621i	−0.217043	−	0.157691i
$343$	5.84288	−	17.9825i	0.315486	−	0.970966i
$344$	1.56607			0.0844366
$345$	−4.15159	−	0.736265i	−0.223514	−	0.0396392i
$346$	−9.69058	−	7.04062i	−0.520969	−	0.378506i
$347$	13.8086	+	10.0325i	0.741283	+	0.538574i	0.893113	−	0.449833i	$-0.148516\pi$
$347$	13.8086	+	10.0325i	0.741283	+	0.538574i	−0.151829	+	0.988407i	$0.548516\pi$
$348$	0.638352	−	1.96464i	0.0342192	−	0.105316i
$349$	−0.852126	+	0.619106i	−0.0456133	+	0.0331400i	−0.610358	−	0.792125i	$-0.708975\pi$
$349$	−0.852126	+	0.619106i	−0.0456133	+	0.0331400i	0.564745	+	0.825265i	$0.308975\pi$
$350$	−9.52441	−	14.1808i	−0.509101	−	0.757998i
$351$	−15.3222			−0.817838
$352$	12.8703	−	14.4584i	0.685988	−	0.770634i
$353$	23.0308	−	16.7328i	1.22581	−	0.890600i	0.229237	−	0.973371i	$-0.426377\pi$
$353$	23.0308	−	16.7328i	1.22581	−	0.890600i	0.996569	+	0.0827710i	$0.0263770\pi$
$354$	0.399443	+	1.22936i	0.0212301	+	0.0653397i
$355$	3.28366	+	3.40706i	0.174279	+	0.180828i
$356$	5.53202	+	17.0258i	0.293197	+	0.902367i
$357$	−0.444864	−	1.36915i	−0.0235447	−	0.0724632i
$358$	3.28077	−	10.0972i	0.173394	−	0.533651i
$359$	−9.43137	+	6.85229i	−0.497769	+	0.361650i	−0.808164	−	0.588957i	$-0.799539\pi$
$359$	−9.43137	+	6.85229i	−0.497769	+	0.361650i	0.310395	+	0.950608i	$0.399539\pi$
$360$	11.5259	+	11.9591i	0.607470	+	0.630298i
$361$	−13.9456			−0.733981
$362$	−5.84956	+	18.0031i	−0.307446	+	0.946221i
$363$	−5.15799	−	1.03520i	−0.270724	−	0.0543342i
$364$	−10.0525	−	30.9383i	−0.526892	−	1.62161i
$365$	−5.38466	+	10.1030i	−0.281846	+	0.528815i
$366$	−1.01027	−	3.10928i	−0.0528075	−	0.162525i
$367$	1.18874	+	3.65858i	0.0620519	+	0.190976i	0.977277	−	0.211967i	$-0.0679871\pi$
$367$	1.18874	+	3.65858i	0.0620519	+	0.190976i	−0.915225	+	0.402944i	$0.867987\pi$
$368$	0.727790	+	2.23991i	0.0379387	+	0.116763i
$369$	7.64416	−	23.5263i	0.397939	−	1.22473i
$370$	16.4969	−	8.02594i	0.857634	−	0.417249i
$371$	−10.5723	+	32.5383i	−0.548889	+	1.68931i
$372$	1.51542	+	4.66398i	0.0785708	+	0.241816i
$373$	1.45942	+	4.49164i	0.0755660	+	0.232568i	0.981704	−	0.190414i	$-0.0609832\pi$
$373$	1.45942	+	4.49164i	0.0755660	+	0.232568i	−0.906138	+	0.422983i	$0.860983\pi$
$374$	0.935607	+	1.59945i	0.0483791	+	0.0827054i
$375$	−3.98425	+	3.56612i	−0.205746	+	0.184154i
$376$	−6.45108	+	19.8544i	−0.332689	+	1.02391i
$377$	14.2020	+	10.3183i	0.731439	+	0.531422i
$378$	−9.43007			−0.485031
$379$	−15.7690	−	11.4569i	−0.810001	−	0.588500i	0.103830	−	0.994595i	$-0.466890\pi$
$379$	−15.7690	−	11.4569i	−0.810001	−	0.588500i	−0.913831	+	0.406095i	$0.866890\pi$
$380$	−6.76090	−	1.19901i	−0.346827	−	0.0615081i
$381$	0.904919	+	2.78505i	0.0463604	+	0.142683i
$382$	−0.0444204	+	0.0322733i	−0.00227275	+	0.00165125i
$383$	6.73748	−	4.89506i	0.344269	−	0.250126i	−0.402192	−	0.915555i	$-0.631752\pi$
$383$	6.73748	−	4.89506i	0.344269	−	0.250126i	0.746461	+	0.665429i	$0.231752\pi$
$384$	−1.31874	+	4.05865i	−0.0672965	+	0.207117i
$385$	31.7931	−	1.25983i	1.62033	−	0.0642069i
$386$	−2.78369	−	8.56732i	−0.141686	−	0.436065i
$387$	−1.30997	−	0.951746i	−0.0665893	−	0.0483800i
$388$	−1.06063	−	3.26427i	−0.0538452	−	0.165718i
$389$	−5.18375	+	15.9540i	−0.262827	+	0.808898i	0.729359	+	0.684131i	$0.239818\pi$
$389$	−5.18375	+	15.9540i	−0.262827	+	0.808898i	−0.992186	+	0.124767i	$0.960182\pi$
$390$	4.25101	−	2.06816i	0.215258	−	0.104725i
$391$	−2.76618			−0.139892
$392$	−9.44807	−	29.0782i	−0.477200	−	1.46867i
$393$	−0.978984	+	0.711274i	−0.0493832	+	0.0358790i
$394$	10.4333	−	7.58025i	0.525623	−	0.381887i
$395$	−0.175199	−	1.25560i	−0.00881522	−	0.0631761i
$396$	−12.2647	+	2.67992i	−0.616325	+	0.134671i
$397$	11.4237	−	8.29984i	0.573341	−	0.416557i	−0.262976	−	0.964802i	$-0.584704\pi$
$397$	11.4237	−	8.29984i	0.573341	−	0.416557i	0.836318	+	0.548245i	$0.184704\pi$
$398$	17.1968			0.861999
$399$	3.73204	−	2.71149i	0.186836	−	0.135744i
$400$	2.80463	+	1.02708i	0.140231	+	0.0513539i
$401$	−8.48698	−	26.1202i	−0.423820	−	1.30438i	−0.904120	−	0.427279i	$-0.859472\pi$
$401$	−8.48698	−	26.1202i	−0.423820	−	1.30438i	0.480300	−	0.877104i	$-0.340528\pi$
$402$	−1.55128	+	1.12707i	−0.0773710	+	0.0562133i
$403$	−41.6739			−2.07592
$404$	3.81411	−	11.7386i	0.189759	−	0.584018i
$405$	−2.16116	−	15.4884i	−0.107389	−	0.769626i
$406$	8.74063	+	6.35044i	0.433790	+	0.315167i
$407$	−3.37855	+	34.0035i	−0.167469	+	1.68549i
$408$	−0.727606	−	0.528637i	−0.0360219	−	0.0261714i
$409$	−20.6033	−	14.9692i	−1.01877	−	0.740178i	−0.0527377	−	0.998608i	$-0.516795\pi$
$409$	−20.6033	−	14.9692i	−1.01877	−	0.740178i	−0.966030	+	0.258430i	$0.916795\pi$
$410$	2.19652	+	15.7418i	0.108478	+	0.777433i
$411$	0.383213	−	1.17941i	0.0189025	−	0.0581760i
$412$	−7.26604			−0.357972
$413$	14.5618			0.716537
$414$	−2.68869	+	8.27493i	−0.132142	+	0.406690i
$415$	10.1344	−	19.0147i	0.497479	−	0.933397i
$416$	−26.2110	−	19.0434i	−1.28510	−	0.933679i
$417$	−0.404516	−	0.293898i	−0.0198092	−	0.0143923i
$418$	−3.94794	+	4.43509i	−0.193100	+	0.216927i
$419$	−26.6308	−	19.3484i	−1.30100	−	0.945232i	−0.301035	−	0.953613i	$-0.597332\pi$
$419$	−26.6308	−	19.3484i	−1.30100	−	0.945232i	−0.999965	+	0.00838165i	$0.997332\pi$
$420$	−5.63534	+	2.74165i	−0.274976	+	0.133779i
$421$	−3.86926	+	11.9084i	−0.188576	+	0.580378i	−0.999992	−	0.00409212i	$-0.998697\pi$
$421$	−3.86926	+	11.9084i	−0.188576	+	0.580378i	0.811416	+	0.584470i	$0.198697\pi$
$422$	−0.529918			−0.0257960
$423$	17.4623	−	12.6871i	0.849044	−	0.616867i
$424$	6.60488	+	20.3277i	0.320761	+	0.987202i
$425$	−2.16520	+	2.76007i	−0.105027	+	0.133883i
$426$	−0.652012	+	0.473714i	−0.0315901	+	0.0229515i
$427$	−36.8294			−1.78230
$428$	−13.2101	+	9.59768i	−0.638533	+	0.463921i
$429$	−0.870602	+	8.76219i	−0.0420331	+	0.423043i
$430$	1.02441	+	0.181674i	0.0494013	+	0.00876109i
$431$	23.4741	−	17.0550i	1.13071	−	0.821508i	0.144911	−	0.989445i	$-0.453710\pi$
$431$	23.4741	−	17.0550i	1.13071	−	0.821508i	0.985798	+	0.167937i	$0.0537104\pi$
$432$	1.33390	−	0.969137i	0.0641774	−	0.0466276i
$433$	−1.06295	−	3.27141i	−0.0510819	−	0.157214i	0.922261	−	0.386567i	$-0.126339\pi$
$433$	−1.06295	−	3.27141i	−0.0510819	−	0.157214i	−0.973343	+	0.229353i	$0.926339\pi$
$434$	−25.6482			−1.23116
$435$	1.59062	−	2.98441i	0.0762645	−	0.143092i
$436$	3.76282	−	11.5808i	0.180207	−	0.554619i
$437$	−2.73909	−	8.43006i	−0.131029	−	0.403265i
$438$	−1.57749	−	1.14611i	−0.0753755	−	0.0547635i
$439$	−5.33684	−	16.4251i	−0.254714	−	0.783928i	−0.993886	−	0.110412i	$-0.964783\pi$
$439$	−5.33684	−	16.4251i	−0.254714	−	0.783928i	0.739172	−	0.673516i	$-0.235217\pi$
$440$	15.6062	−	12.3114i	0.743997	−	0.586924i
$441$	−9.76868	+	30.0649i	−0.465175	+	1.43166i
$442$	2.50912	−	1.82299i	0.119347	−	0.0867106i
$443$	23.8988	−	17.3635i	1.13546	−	0.824963i	0.148983	−	0.988840i	$-0.452400\pi$
$443$	23.8988	−	17.3635i	1.13546	−	0.824963i	0.986481	+	0.163877i	$0.0523999\pi$
$444$	−2.07978	−	6.40089i	−0.0987018	−	0.303773i
$445$	4.05014	+	29.0261i	0.191995	+	1.37597i
$446$	2.38923	+	1.73588i	0.113133	+	0.0821961i
$447$	−8.31094			−0.393094
$448$	−11.9848	−	8.70746i	−0.566228	−	0.411389i
$449$	−4.17076	+	12.8363i	−0.196830	+	0.605781i	0.803120	+	0.595817i	$0.203172\pi$
$449$	−4.17076	+	12.8363i	−0.196830	+	0.605781i	−0.999950	+	0.00996413i	$0.996828\pi$
$450$	6.15211	+	9.15985i	0.290013	+	0.431799i
$451$	−27.1136	−	11.8875i	−1.27673	−	0.559759i
$452$	2.10032	+	6.46411i	0.0987906	+	0.304046i
$453$	1.96173	+	6.03757i	0.0921700	+	0.283670i
$454$	1.48296	−	4.56409i	0.0695988	−	0.214203i
$455$	−7.35966	−	52.7445i	−0.345026	−	2.47270i
$456$	0.890563	−	2.74087i	0.0417044	−	0.128353i
$457$	−9.06840	−	27.9097i	−0.424202	−	1.30556i	−0.903756	−	0.428047i	$-0.859202\pi$
$457$	−9.06840	−	27.9097i	−0.424202	−	1.30556i	0.479555	−	0.877512i	$-0.340798\pi$
$458$	−3.74203	−	11.5168i	−0.174854	−	0.538144i
$459$	0.598420	+	1.84175i	0.0279319	+	0.0859655i
$460$	1.66410	+	11.9261i	0.0775891	+	0.556058i
$461$	−11.8114	−	36.3518i	−0.550113	−	1.69307i	−0.708512	−	0.705699i	$-0.750633\pi$
$461$	−11.8114	−	36.3518i	−0.550113	−	1.69307i	0.158399	−	0.987375i	$-0.449367\pi$
$462$	−0.535814	+	5.39271i	−0.0249283	+	0.250891i
$463$	9.42538	−	29.0083i	0.438035	−	1.34813i	−0.451910	−	0.892063i	$-0.649257\pi$
$463$	9.42538	−	29.0083i	0.438035	−	1.34813i	0.889945	−	0.456068i	$-0.150743\pi$
$464$	−1.88902			−0.0876956
$465$	1.10948	+	7.95129i	0.0514508	+	0.368732i
$466$	0.727775	−	0.528759i	0.0337135	−	0.0244943i
$467$	−9.43171	+	29.0278i	−0.436447	+	1.34325i	0.455149	+	0.890416i	$0.349586\pi$
$467$	−9.43171	+	29.0278i	−0.436447	+	1.34325i	−0.891596	+	0.452832i	$0.850414\pi$
$468$	6.49319	+	19.9840i	0.300148	+	0.923760i
$469$	6.67510	+	20.5438i	0.308227	+	0.948626i
$470$	−6.52307	+	12.2389i	−0.300887	+	0.564541i
$471$	0.341283	+	1.05036i	0.0157255	+	0.0483981i
$472$	7.35978	−	5.34719i	0.338761	−	0.246124i
$473$	−1.28847	+	1.44745i	−0.0592437	+	0.0665540i
$474$	0.215926			0.00991780
$475$	−10.5554	−	3.86549i	−0.484317	−	0.177361i
$476$	−3.32621	+	2.41664i	−0.152457	+	0.110766i
$477$	6.82901	−	21.0175i	0.312679	−	0.962326i
$478$	10.0168	+	7.27764i	0.458158	+	0.332872i
$479$	4.74606	+	3.44821i	0.216853	+	0.157553i	0.690909	−	0.722942i	$-0.257211\pi$
$479$	4.74606	+	3.44821i	0.216853	+	0.157553i	−0.474056	+	0.880495i	$0.657211\pi$
$480$	−2.93563	+	5.50799i	−0.133993	+	0.251404i
$481$	57.1936			2.60780
$482$	−5.55482	+	17.0960i	−0.253015	+	0.778700i
$483$	−6.54492	−	4.75516i	−0.297804	−	0.216367i
$484$	1.74031	+	14.9235i	0.0791051	+	0.678340i
$485$	−0.776512	−	5.56503i	−0.0352596	−	0.252695i
$486$	9.25747			0.419927
$487$	9.19208	+	28.2903i	0.416533	+	1.28196i	0.910872	+	0.412688i	$0.135410\pi$
$487$	9.19208	+	28.2903i	0.416533	+	1.28196i	−0.494339	+	0.869269i	$0.664590\pi$
$488$	−18.6143	+	13.5241i	−0.842628	+	0.612205i
$489$	8.64867	−	6.28363i	0.391106	−	0.284155i
$490$	−2.80699	−	20.1169i	−0.126807	−	0.908789i
$491$	−1.65622	+	1.20331i	−0.0747441	+	0.0543048i	−0.624530	−	0.781001i	$-0.714709\pi$
$491$	−1.65622	+	1.20331i	−0.0747441	+	0.0543048i	0.549786	+	0.835306i	$0.314709\pi$
$492$	5.83099			0.262881
$493$	0.685609	−	2.11009i	0.0308783	−	0.0950336i
$494$	8.04018	+	5.84154i	0.361745	+	0.262823i
$495$	−20.5362	+	0.813763i	−0.923032	+	0.0365759i
$496$	3.62800	−	2.63589i	0.162902	−	0.118355i
$497$	2.80557	+	8.63467i	0.125847	+	0.387318i
$498$	2.96898	+	2.15709i	0.133043	+	0.0966616i
$499$	−4.51621	−	3.28122i	−0.202173	−	0.146888i	0.482092	−	0.876121i	$-0.339877\pi$
$499$	−4.51621	−	3.28122i	−0.202173	−	0.146888i	−0.684266	+	0.729233i	$0.739877\pi$
$500$	13.2023	+	7.67460i	0.590426	+	0.343219i
$501$	−0.890680	−	2.74123i	−0.0397927	−	0.122469i
$502$	−2.34673	+	7.22250i	−0.104740	+	0.322356i
$503$	−4.84677	+	14.9168i	−0.216107	+	0.665108i	0.782967	+	0.622064i	$0.213706\pi$
$503$	−4.84677	+	14.9168i	−0.216107	+	0.665108i	−0.999073	+	0.0430440i	$0.986294\pi$
$504$	9.84780	+	30.3084i	0.438656	+	1.35004i
$505$	9.50386	−	17.8317i	0.422916	−	0.793499i
$506$	9.53667	+	4.18119i	0.423957	+	0.185877i
$507$	8.52056			0.378412
$508$	6.76600	−	4.91579i	0.300193	−	0.218103i
$509$	−0.936771	−	2.88309i	−0.0415217	−	0.127791i	0.928147	−	0.372214i	$-0.121401\pi$
$509$	−0.936771	−	2.88309i	−0.0415217	−	0.127791i	−0.969669	+	0.244424i	$0.921401\pi$
$510$	−0.414622	−	0.430203i	−0.0183598	−	0.0190497i
$511$	−17.7709	+	12.9113i	−0.786137	+	0.571162i
$512$	6.68855			0.295595
$513$	−5.02025	+	3.64743i	−0.221649	+	0.161038i
$514$	−1.84413	−	1.33984i	−0.0813409	−	0.0590977i
$515$	−11.7125	−	2.07715i	−0.516112	−	0.0915301i
$516$	0.117945	−	0.362997i	0.00519224	−	0.0159801i
$517$	−13.0431	−	22.2975i	−0.573633	−	0.980643i
$518$	35.1999			1.54660
$519$	−5.82002	+	4.22849i	−0.255471	+	0.185610i
$520$	−23.0879	−	23.9555i	−1.01247	−	1.05052i
$521$	27.0928			1.18696			0.593479	−	0.804850i	$-0.297754\pi$
$521$	27.0928			1.18696			0.593479	+	0.804850i	$0.297754\pi$
$522$	−5.64584	−	4.10194i	−0.247112	−	0.179537i
$523$	−26.6965	+	19.3961i	−1.16736	+	0.848134i	−0.990690	−	0.136137i	$-0.956531\pi$
$523$	−26.6965	+	19.3961i	−1.16736	+	0.848134i	−0.176666	+	0.984271i	$0.556531\pi$
$524$	2.79591	+	2.03135i	0.122140	+	0.0887398i
$525$	−9.86762	+	2.80842i	−0.430658	+	0.122569i
$526$	1.68516	−	5.18639i	0.0734765	−	0.226137i
$527$	1.62761	+	5.00925i	0.0708996	+	0.218207i
$528$	−0.478422	−	0.817876i	−0.0208206	−	0.0355935i
$529$	6.03147	−	4.38212i	0.262238	−	0.190527i
$530$	1.96229	+	14.0631i	0.0852364	+	0.610864i
$531$	−9.40589			−0.408181
$532$	−10.6584	−	7.74382i	−0.462102	−	0.335737i
$533$	−15.3122	+	47.1262i	−0.663246	+	2.04126i
$534$	−4.99163			−0.216009
$535$	−24.0376	+	11.6946i	−1.03924	+	0.505600i
$536$	10.9176	+	7.93208i	0.471567	+	0.342614i
$537$	−5.15852	−	3.74789i	−0.222607	−	0.161733i
$538$	5.51257	−	16.9660i	0.237664	−	0.731454i
$539$	34.6491	+	15.1913i	1.49244	+	0.654337i
$540$	7.58051	−	3.68800i	0.326213	−	0.158706i
$541$	7.49430	+	5.44493i	0.322205	+	0.234096i	0.737116	−	0.675766i	$-0.236187\pi$
$541$	7.49430	+	5.44493i	0.322205	+	0.234096i	−0.414911	+	0.909862i	$0.636187\pi$
$542$	24.9210			1.07045
$543$	9.19757	+	6.68243i	0.394706	+	0.286770i
$544$	−1.26535	+	3.89435i	−0.0542515	+	0.166969i
$545$	9.37607	−	17.5919i	0.401627	−	0.753554i
$546$	9.07048			0.388181
$547$	7.73008	−	23.7907i	0.330514	−	1.01722i	−0.638375	−	0.769725i	$-0.720393\pi$
$547$	7.73008	−	23.7907i	0.330514	−	1.01722i	0.968890	−	0.247493i	$-0.0796069\pi$
$548$	−3.54165			−0.151292
$549$	23.7893			1.01530
$550$	11.6367	−	6.24283i	0.496189	−	0.266195i
$551$	7.10948			0.302874
$552$	−5.05405			−0.215115
$553$	0.751672	−	2.31341i	0.0319643	−	0.0983761i
$554$	18.6317			0.791584
$555$	−1.52266	−	10.9124i	−0.0646332	−	0.463207i
$556$	−0.441273	+	1.35810i	−0.0187142	+	0.0575963i
$557$	13.7003	+	9.95387i	0.580501	+	0.421759i	0.838905	−	0.544278i	$-0.183196\pi$
$557$	13.7003	+	9.95387i	0.580501	+	0.421759i	−0.258403	+	0.966037i	$0.583196\pi$
$558$	16.5670			0.701337
$559$	2.62403	+	1.90647i	0.110985	+	0.0806350i
$560$	3.97683	+	4.12627i	0.168052	+	0.174367i
$561$	1.08723	−	0.237567i	0.0459029	−	0.0100301i
$562$	−5.31072	+	16.3447i	−0.224019	+	0.689460i
$563$	−14.0162	−	10.1834i	−0.590713	−	0.429178i	0.251858	−	0.967764i	$-0.418959\pi$
$563$	−14.0162	−	10.1834i	−0.590713	−	0.429178i	−0.842570	+	0.538586i	$0.818959\pi$
$564$	4.11619	+	2.99059i	0.173323	+	0.125926i
$565$	1.53770	+	11.0202i	0.0646914	+	0.463624i
$566$	22.0800			0.928091
$567$	9.27223	−	28.5370i	0.389397	−	1.19844i
$568$	4.58871	+	3.33389i	0.192538	+	0.139887i
$569$	2.57483			0.107943			0.0539713	−	0.998542i	$-0.482812\pi$
$569$	2.57483			0.107943			0.0539713	+	0.998542i	$0.482812\pi$
$570$	0.900501	−	1.68957i	0.0377179	−	0.0707683i
$571$	−8.80792	+	6.39933i	−0.368600	+	0.267804i	−0.756630	−	0.653843i	$-0.773156\pi$
$571$	−8.80792	+	6.39933i	−0.368600	+	0.267804i	0.388030	+	0.921647i	$0.373156\pi$
$572$	24.5678	−	5.36822i	1.02723	−	0.224456i
$573$	0.0101902	+	0.0313622i	0.000425701	+	0.00131017i
$574$	−9.42393	+	29.0039i	−0.393347	+	1.21060i
$575$	−0.726889	+	19.7000i	−0.0303134	+	0.821546i
$576$	7.74135	+	5.62442i	0.322556	+	0.234351i
$577$	0.0291090	−	0.0211490i	0.00121183	−	0.000880442i	−0.587179	−	0.809457i	$-0.699762\pi$
$577$	0.0291090	−	0.0211490i	0.00121183	−	0.000880442i	0.588391	+	0.808577i	$0.299762\pi$
$578$	10.6349	+	7.72671i	0.442354	+	0.321389i
$579$	−5.41020			−0.224840
$580$	−9.50989	−	1.68653i	−0.394877	−	0.0700294i
$581$	33.4464	−	24.3002i	1.38759	−	1.00814i
$582$	0.957020			0.0396698
$583$	−24.2222	−	10.6198i	−1.00318	−	0.439828i
$584$	−4.24059	+	13.0512i	−0.175477	+	0.540063i
$585$	4.75383	+	34.0693i	0.196547	+	1.40859i
$586$	−2.31709	−	1.68347i	−0.0957182	−	0.0695433i
$587$	1.80071	−	1.30829i	0.0743234	−	0.0539991i	−0.550003	−	0.835163i	$-0.685373\pi$
$587$	1.80071	−	1.30829i	0.0743234	−	0.0539991i	0.624327	+	0.781163i	$0.285373\pi$
$588$	−7.45158			−0.307298
$589$	−13.6543	+	9.92040i	−0.562614	+	0.408763i
$590$	5.43455	−	2.64397i	0.223737	−	0.108850i
$591$	−2.39344	−	7.36624i	−0.0984528	−	0.303007i
$592$	−4.97910	+	3.61753i	−0.204640	+	0.148679i
$593$	−34.9049			−1.43337			−0.716686	−	0.697396i	$-0.754342\pi$
$593$	−34.9049			−1.43337			−0.716686	+	0.697396i	$0.754342\pi$
$594$	0.720763	−	7.25413i	0.0295733	−	0.297641i
$595$	−6.05252	+	2.94462i	−0.248129	+	0.120718i
$596$	7.33465	+	22.5737i	0.300439	+	0.924657i
$597$	3.19158	−	9.82266i	0.130623	−	0.402015i
$598$	5.38578	−	16.5757i	0.220241	−	0.677831i
$599$	−3.52322	−	10.8434i	−0.143955	−	0.443048i	0.852920	−	0.522041i	$-0.174829\pi$
$599$	−3.52322	−	10.8434i	−0.143955	−	0.443048i	−0.996875	+	0.0789935i	$0.974829\pi$
$600$	−3.95600	+	5.04289i	−0.161503	+	0.205875i
$601$	19.5352	+	14.1931i	0.796856	+	0.578950i	0.909990	−	0.414630i	$-0.136089\pi$
$601$	19.5352	+	14.1931i	0.796856	+	0.578950i	−0.113134	+	0.993580i	$0.536089\pi$
$602$	1.61496	+	1.17334i	0.0658209	+	0.0478217i
$603$	−4.31165	−	13.2699i	−0.175584	−	0.540392i
$604$	14.6677	−	10.6567i	0.596819	−	0.433614i
$605$	−1.46089	+	24.5533i	−0.0593938	+	0.998235i
$606$	2.78426	+	2.02288i	0.113103	+	0.0821739i
$607$	9.99235	−	30.7533i	0.405577	−	1.24824i	−0.514835	−	0.857289i	$-0.672147\pi$
$607$	9.99235	−	30.7533i	0.405577	−	1.24824i	0.920412	−	0.390949i	$-0.127853\pi$
$608$	−13.1212			−0.532133
$609$	5.24950	−	3.81398i	0.212720	−	0.154550i
$610$	−13.7450	+	6.68709i	−0.556519	+	0.270752i
$611$	−34.9791	+	25.4138i	−1.41510	+	1.02813i
$612$	2.14850	−	1.56098i	0.0868482	−	0.0630989i
$613$	3.73822	+	11.5050i	0.150985	+	0.464684i	0.997732	−	0.0673116i	$-0.0214421\pi$
$613$	3.73822	+	11.5050i	0.150985	+	0.464684i	−0.846747	+	0.531996i	$0.821442\pi$
$614$	−9.22044			−0.372107
$615$	9.39924	+	1.66691i	0.379014	+	0.0672163i
$616$	37.2604	−	8.14163i	1.50126	−	0.328036i
$617$	0.287945	+	0.209204i	0.0115922	+	0.00842225i	0.593566	−	0.804785i	$-0.297719\pi$
$617$	0.287945	+	0.209204i	0.0115922	+	0.00842225i	−0.581974	+	0.813207i	$0.697719\pi$
$618$	0.626067	−	1.92684i	0.0251841	−	0.0775087i
$619$	−24.6051			−0.988962			−0.494481	−	0.869188i	$-0.664642\pi$
$619$	−24.6051			−0.988962			−0.494481	+	0.869188i	$0.664642\pi$
$620$	20.6178	−	10.0308i	0.828029	−	0.402845i
$621$	8.80406	+	6.39652i	0.353295	+	0.256684i
$622$	2.92398	+	2.12440i	0.117241	+	0.0851805i
$623$	−17.3767	+	53.4799i	−0.696181	+	2.14263i
$624$	−1.28304	+	0.932182i	−0.0513627	+	0.0373172i
$625$	19.0875	+	16.1452i	0.763500	+	0.645808i
$626$	−12.3686			−0.494349
$627$	1.80058	+	3.07814i	0.0719082	+	0.122929i
$628$	2.55174	−	1.85395i	0.101826	−	0.0739807i
$629$	−2.23374	−	6.87475i	−0.0890651	−	0.274114i
$630$	2.92575	+	20.9680i	0.116565	+	0.835385i
$631$	−4.97307	−	15.3055i	−0.197975	−	0.609304i	−0.999929	−	0.0119185i	$-0.996206\pi$
$631$	−4.97307	−	15.3055i	−0.197975	−	0.609304i	0.801954	−	0.597386i	$-0.203794\pi$
$632$	−0.469593	−	1.44526i	−0.0186794	−	0.0574893i
$633$	−0.0983481	+	0.302684i	−0.00390898	+	0.0120306i
$634$	−16.9989	+	12.3504i	−0.675112	+	0.490498i
$635$	12.3117	−	5.98978i	0.488575	−	0.237697i
$636$	5.20919			0.206558
$637$	19.5679	−	60.2238i	0.775308	−	2.38615i
$638$	−5.55318	+	6.23840i	−0.219852	+	0.246981i
$639$	−1.81221	−	5.57740i	−0.0716898	−	0.220638i
$640$	19.6460	+	3.48412i	0.776575	+	0.137722i
$641$	7.63369	+	23.4941i	0.301513	+	0.927961i	0.980956	+	0.194232i	$0.0622215\pi$
$641$	7.63369	+	23.4941i	0.301513	+	0.927961i	−0.679443	+	0.733728i	$0.737778\pi$
$642$	−1.40692	−	4.33007i	−0.0555269	−	0.170894i
$643$	0.979333	+	3.01408i	0.0386211	+	0.118864i	0.968508	−	0.248981i	$-0.0800957\pi$
$643$	0.979333	+	3.01408i	0.0386211	+	0.118864i	−0.929887	+	0.367845i	$0.880096\pi$
$644$	−7.13964	+	21.9736i	−0.281341	+	0.865879i
$645$	0.293891	−	0.551415i	0.0115720	−	0.0217119i
$646$	0.388145	−	1.19459i	0.0152714	−	0.0470004i
$647$	−4.36650	−	13.4387i	−0.171665	−	0.528330i	0.827801	−	0.561022i	$-0.189592\pi$
$647$	−4.36650	−	13.4387i	−0.171665	−	0.528330i	−0.999465	+	0.0326924i	$0.989592\pi$
$648$	−5.79265	−	17.8279i	−0.227557	−	0.700348i
$649$	−1.11299	+	11.2017i	−0.0436887	+	0.439706i
$650$	−12.3235	−	18.3483i	−0.483366	−	0.719680i
$651$	−4.76009	+	14.6500i	−0.186563	+	0.574180i
$652$	−24.7000	−	17.9456i	−0.967326	−	0.702803i
$653$	−26.0901			−1.02099			−0.510493	−	0.859882i	$-0.670537\pi$
$653$	−26.0901			−1.02099			−0.510493	+	0.859882i	$0.670537\pi$
$654$	2.74682	+	1.99568i	0.107409	+	0.0780373i
$655$	3.92615	+	4.07369i	0.153407	+	0.159172i
$656$	−1.64772	−	5.07116i	−0.0643327	−	0.197996i
$657$	11.4787	−	8.33980i	0.447829	−	0.325367i
$658$	−21.5279	+	15.6410i	−0.839247	+	0.609749i
$659$	11.6261	−	35.7813i	0.452887	−	1.39384i	−0.420712	−	0.907194i	$-0.638220\pi$
$659$	11.6261	−	35.7813i	0.452887	−	1.39384i	0.873598	−	0.486648i	$-0.161780\pi$
$660$	−1.67831	−	4.54457i	−0.0653281	−	0.176897i
$661$	5.76870	+	17.7542i	0.224376	+	0.690560i	0.998354	+	0.0573470i	$0.0182641\pi$
$661$	5.76870	+	17.7542i	0.224376	+	0.690560i	−0.773978	+	0.633213i	$0.781736\pi$
$662$	−19.8402	−	14.4147i	−0.771110	−	0.560244i
$663$	−0.575601	−	1.77152i	−0.0223545	−	0.0688001i
$664$	7.98118	−	24.5635i	0.309730	−	0.953251i
$665$	−14.9671	−	15.5295i	−0.580400	−	0.602210i
$666$	−22.7367			−0.881030
$667$	−3.85281	−	11.8577i	−0.149181	−	0.459133i
$668$	−6.65954	+	4.83844i	−0.257665	+	0.187205i
$669$	1.43494	−	1.04254i	0.0554778	−	0.0403070i
$670$	6.22132	+	6.45511i	0.240351	+	0.249383i
$671$	2.81496	−	28.3312i	0.108670	−	1.09372i
$672$	−9.68840	+	7.03903i	−0.373738	+	0.271537i
$673$	−14.7256			−0.567629			−0.283814	−	0.958879i	$-0.591600\pi$
$673$	−14.7256			−0.567629			−0.283814	+	0.958879i	$0.591600\pi$
$674$	0.162872	−	0.118333i	0.00627359	−	0.00455803i
$675$	13.2737	−	3.77781i	0.510904	−	0.145408i
$676$	−7.51966	−	23.1431i	−0.289218	−	0.890120i
$677$	−5.75046	+	4.17795i	−0.221008	+	0.160572i	−0.692780	−	0.721149i	$-0.743614\pi$
$677$	−5.75046	+	4.17795i	−0.221008	+	0.160572i	0.471772	+	0.881720i	$0.343614\pi$
$678$	−1.89515			−0.0727828
$679$	3.33154	−	10.2534i	0.127853	−	0.393490i
$680$	−1.97777	+	3.71080i	−0.0758439	+	0.142303i
$681$	−2.33174	−	1.69411i	−0.0893524	−	0.0649183i
$682$	1.96036	−	19.7301i	0.0750659	−	0.755503i
$683$	28.5087	+	20.7128i	1.09086	+	0.792553i	0.979543	−	0.201233i	$-0.0644947\pi$
$683$	28.5087	+	20.7128i	1.09086	+	0.792553i	0.111312	+	0.993786i	$0.464495\pi$
$684$	6.88462	+	5.00197i	0.263240	+	0.191255i
$685$	−5.70895	−	1.01245i	−0.218128	−	0.0386839i
$686$	4.65281	−	14.3199i	0.177645	−	0.546735i
$687$	−7.27277			−0.277474
$688$	−0.349025			−0.0133064
$689$	−13.6794	+	42.1007i	−0.521142	+	1.60391i
$690$	−3.30600	−	0.586303i	−0.125857	−	0.0223202i
$691$	−26.3048	−	19.1115i	−1.00068	−	0.727037i	−0.0384464	−	0.999261i	$-0.512241\pi$
$691$	−26.3048	−	19.1115i	−1.00068	−	0.727037i	−0.962234	+	0.272224i	$0.912241\pi$
$692$	16.6216	+	12.0763i	0.631857	+	0.459071i
$693$	−36.1151	−	15.8340i	−1.37190	−	0.601486i
$694$	10.9961	+	7.98911i	0.417405	+	0.303262i
$695$	−1.09955	+	2.06304i	−0.0417083	+	0.0782554i
$696$	1.25267	−	3.85531i	0.0474822	−	0.146135i
$697$	6.26266			0.237215
$698$	−0.678566	+	0.493007i	−0.0256841	+	0.0186606i
$699$	−0.166954	−	0.513831i	−0.00631478	−	0.0194349i
$700$	16.3366	+	24.3234i	0.617464	+	0.919338i
$701$	−17.6735	+	12.8405i	−0.667518	+	0.484981i	−0.869194	−	0.494472i	$-0.835361\pi$
$701$	−17.6735	+	12.8405i	−0.667518	+	0.484981i	0.201675	+	0.979452i	$0.435361\pi$
$702$	−12.2014			−0.460512
$703$	18.7392	−	13.6149i	0.706764	−	0.513494i
$704$	7.61429	−	8.55384i	0.286974	−	0.322385i
$705$	5.78015	+	5.99736i	0.217693	+	0.225874i
$706$	18.3399	−	13.3247i	0.690231	−	0.501482i
$707$	31.3654	−	22.7883i	1.17962	−	0.857042i
$708$	−0.685136	−	2.10863i	−0.0257490	−	0.0792472i
$709$	37.3212			1.40163			0.700813	−	0.713345i	$-0.252821\pi$
$709$	37.3212			1.40163			0.700813	+	0.713345i	$0.252821\pi$
$710$	2.61485	+	2.71311i	0.0981335	+	0.101821i
$711$	−0.485528	+	1.49430i	−0.0182087	+	0.0560407i
$712$	10.8557	+	33.4105i	0.406836	+	1.25211i
$713$	23.9456	+	17.3975i	0.896770	+	0.651541i
$714$	−0.354255	−	1.09028i	−0.0132577	−	0.0408029i
$715$	41.1365	−	1.63007i	1.53842	−	0.0609611i
$716$	−5.62727	+	17.3189i	−0.210301	+	0.647239i
$717$	6.01595	−	4.37085i	0.224670	−	0.163232i
$718$	−7.51040	+	5.45662i	−0.280286	+	0.203639i
$719$	0.153864	+	0.473544i	0.00573815	+	0.0176602i	0.953885	−	0.300174i	$-0.0970446\pi$
$719$	0.153864	+	0.473544i	0.00573815	+	0.0176602i	−0.948146	+	0.317834i	$0.897045\pi$
$720$	−2.56876	−	2.66529i	−0.0957319	−	0.0993293i
$721$	−18.4645	−	13.4152i	−0.687654	−	0.499610i
$722$	−11.1052			−0.413293
$723$	8.73413	+	6.34572i	0.324826	+	0.236000i
$724$	10.0333	−	30.8794i	0.372886	−	1.14762i
$725$	−14.8473	−	5.43720i	−0.551414	−	0.201932i
$726$	−4.10742	−	0.824355i	−0.152440	−	0.0305947i
$727$	11.3795	+	35.0226i	0.422043	+	1.29891i	0.905797	+	0.423711i	$0.139273\pi$
$727$	11.3795	+	35.0226i	0.422043	+	1.29891i	−0.483755	+	0.875204i	$0.660727\pi$
$728$	−19.7264	−	60.7116i	−0.731109	−	2.25012i
$729$	−4.76544	+	14.6665i	−0.176498	+	0.543205i
$730$	−4.28792	+	8.04522i	−0.158703	+	0.297767i
$731$	0.126677	−	0.389870i	0.00468530	−	0.0144199i
$732$	1.73284	+	5.33313i	0.0640476	+	0.197118i
$733$	−12.4026	−	38.1712i	−0.458100	−	1.40989i	−0.867457	−	0.497512i	$-0.834247\pi$
$733$	−12.4026	−	38.1712i	−0.458100	−	1.40989i	0.409357	−	0.912374i	$-0.365753\pi$
$734$	0.946622	+	2.91340i	0.0349404	+	0.107536i
$735$	−12.0115	−	2.13019i	−0.443052	−	0.0785732i
$736$	7.11070	+	21.8845i	0.262104	+	0.806673i
$737$	−16.3136	+	3.56464i	−0.600921	+	0.131305i
$738$	6.08721	−	18.7345i	0.224073	−	0.689626i
$739$	−42.8639			−1.57677			−0.788386	−	0.615180i	$-0.789083\pi$
$739$	−42.8639			−1.57677			−0.788386	+	0.615180i	$0.789083\pi$
$740$	−28.2960	+	13.7663i	−1.04018	+	0.506060i
$741$	4.82882	−	3.50834i	0.177391	−	0.128882i
$742$	−8.41898	+	25.9110i	−0.309071	+	0.951222i
$743$	1.31659	+	4.05206i	0.0483011	+	0.148656i	0.972298	−	0.233744i	$-0.0750978\pi$
$743$	1.31659	+	4.05206i	0.0483011	+	0.148656i	−0.923997	+	0.382400i	$0.875098\pi$
$744$	2.97378	+	9.15234i	0.109024	+	0.335541i
$745$	5.36989	+	38.4844i	0.196738	+	1.40996i
$746$	1.16217	+	3.57678i	0.0425500	+	0.130955i
$747$	−21.6041	+	15.6963i	−0.790451	+	0.574296i
$748$	−1.60478	−	2.74342i	−0.0586766	−	0.100309i
$749$	−51.2896			−1.87408
$750$	−3.17274	+	2.83978i	−0.115852	+	0.103694i
$751$	34.0499	−	24.7387i	1.24250	−	0.902727i	0.244735	−	0.969590i	$-0.421299\pi$
$751$	34.0499	−	24.7387i	1.24250	−	0.902727i	0.997762	+	0.0668632i	$0.0212991\pi$
$752$	1.43774	−	4.42490i	0.0524288	−	0.161359i
$753$	3.68989	+	2.68086i	0.134467	+	0.0976962i
$754$	11.3093	+	8.21671i	0.411862	+	0.299235i
$755$	26.6899	−	12.9849i	0.971345	−	0.472570i
$756$	16.1747			0.588269
$757$	−3.33001	+	10.2487i	−0.121031	+	0.372496i	−0.993157	−	0.116785i	$-0.962741\pi$
$757$	−3.33001	+	10.2487i	−0.121031	+	0.372496i	0.872126	+	0.489282i	$0.162741\pi$
$758$	−12.5572	−	9.12335i	−0.456098	−	0.331375i
$759$	4.15818	−	4.67127i	0.150932	−	0.169556i
$760$	−13.2672	−	2.35288i	−0.481253	−	0.0853478i
$761$	20.2337			0.733470			0.366735	−	0.930325i	$-0.380475\pi$
$761$	20.2337			0.733470			0.366735	+	0.930325i	$0.380475\pi$
$762$	0.720606	+	2.21780i	0.0261048	+	0.0803423i
$763$	30.9436	−	22.4819i	1.12023	−	0.813898i
$764$	0.0761912	−	0.0553562i	0.00275650	−	0.00200272i
$765$	3.90951	−	1.90202i	0.141349	−	0.0687677i
$766$	5.36519	−	3.89804i	0.193852	−	0.140842i
$767$	18.8412			0.680315
$768$	−2.07074	+	6.37308i	−0.0747213	+	0.229969i
$769$	5.93966	+	4.31541i	0.214189	+	0.155618i	0.689707	−	0.724088i	$-0.257739\pi$
$769$	5.93966	+	4.31541i	0.214189	+	0.155618i	−0.475518	+	0.879706i	$0.657739\pi$
$770$	25.3175	−	1.00323i	0.912381	−	0.0361539i
$771$	−1.10756	+	0.804686i	−0.0398876	+	0.0289801i
$772$	4.77467	+	14.6949i	0.171844	+	0.528881i
$773$	12.0512	+	8.75572i	0.433452	+	0.314921i	0.783028	−	0.621987i	$-0.213674\pi$
$773$	12.0512	+	8.75572i	0.433452	+	0.314921i	−0.349576	+	0.936908i	$0.613674\pi$
$774$	−1.04315	−	0.757896i	−0.0374954	−	0.0272420i
$775$	36.1022	−	10.2750i	1.29683	−	0.369090i
$776$	−2.08132	−	6.40563i	−0.0747149	−	0.229949i
$777$	6.53279	−	20.1059i	0.234363	−	0.721294i
$778$	−4.12793	+	12.7045i	−0.147994	+	0.455477i
$779$	6.20133	+	19.0857i	0.222186	+	0.683817i
$780$	−7.29145	+	3.54737i	−0.261076	+	0.127016i
$781$	−6.85670	+	1.49823i	−0.245352	+	0.0536110i
$782$	−2.20277			−0.0787709
$783$	−7.06149	+	5.13047i	−0.252357	+	0.183348i
$784$	2.10567	+	6.48058i	0.0752024	+	0.231449i
$785$	4.64326	−	2.25900i	0.165725	−	0.0806271i
$786$	−0.779586	+	0.566402i	−0.0278069	+	0.0202029i
$787$	−49.3501			−1.75914			−0.879571	−	0.475767i	$-0.842171\pi$
$787$	−49.3501			−1.75914			−0.879571	+	0.475767i	$0.842171\pi$
$788$	−17.8955	+	13.0019i	−0.637502	+	0.463172i
$789$	−2.64967	−	1.92510i	−0.0943307	−	0.0685352i
$790$	−0.139515	−	0.999860i	−0.00496371	−	0.0355734i
$791$	−6.59732	+	20.3044i	−0.234574	+	0.721943i
$792$	−24.0676	+	5.25893i	−0.855205	+	0.186868i
$793$	−47.6529			−1.69220
$794$	9.09697	−	6.60934i	0.322839	−	0.234557i
$795$	8.39692	+	1.48915i	0.297808	+	0.0528148i
$796$	−29.4965			−1.04548
$797$	−22.6897	−	16.4851i	−0.803712	−	0.583931i	0.108289	−	0.994119i	$-0.465463\pi$
$797$	−22.6897	−	16.4851i	−0.803712	−	0.583931i	−0.912001	+	0.410189i	$0.865463\pi$
$798$	2.97190	−	2.15921i	0.105204	−	0.0764354i
$799$	4.42091	+	3.21198i	0.156401	+	0.113632i
$800$	27.4020	+	10.0348i	0.968805	+	0.354784i
$801$	11.2241	−	34.5443i	0.396585	−	1.22056i
$802$	−6.75836	−	20.8001i	−0.238646	−	0.734477i
$803$	−8.57381	−	14.6572i	−0.302563	−	0.517240i
$804$	2.66081	−	1.93319i	0.0938395	−	0.0681784i
$805$	−17.7903	+	33.3792i	−0.627026	+	1.17646i
$806$	−33.1858			−1.16892
$807$	−8.66771	−	6.29746i	−0.305118	−	0.221681i
$808$	7.48460	−	23.0352i	0.263307	−	0.810377i
$809$	35.7739			1.25774			0.628872	−	0.777509i	$-0.283517\pi$
$809$	35.7739			1.25774			0.628872	+	0.777509i	$0.283517\pi$
$810$	−1.72098	−	12.3337i	−0.0604690	−	0.433364i
$811$	13.8815	+	10.0855i	0.487445	+	0.354150i	0.804201	−	0.594357i	$-0.202593\pi$
$811$	13.8815	+	10.0855i	0.487445	+	0.354150i	−0.316756	+	0.948507i	$0.602593\pi$
$812$	−14.9922	−	10.8925i	−0.526123	−	0.382250i
$813$	4.62513	−	14.2347i	0.162210	−	0.499232i
$814$	−2.69041	+	27.0777i	−0.0942989	+	0.949074i
$815$	−34.6849	−	35.9883i	−1.21496	−	1.26062i
$816$	0.162160	+	0.117816i	0.00567672	+	0.00412438i
$817$	1.31358			0.0459564
$818$	−16.4068	−	11.9203i	−0.573652	−	0.416782i
$819$	−20.3958	+	62.7718i	−0.712686	+	2.19342i
$820$	−3.76754	−	27.0008i	−0.131568	−	0.942910i
$821$	18.8883			0.659205			0.329603	−	0.944120i	$-0.393085\pi$
$821$	18.8883			0.659205			0.329603	+	0.944120i	$0.393085\pi$
$822$	0.305161	−	0.939189i	0.0106437	−	0.0327580i
$823$	−33.7994			−1.17817			−0.589086	−	0.808070i	$-0.700512\pi$
$823$	−33.7994			−1.17817			−0.589086	+	0.808070i	$0.700512\pi$
$824$	−14.2585			−0.496718
$825$	−1.40619	−	7.80537i	−0.0489571	−	0.271748i
$826$	11.5958			0.403471
$827$	37.9567			1.31988			0.659942	−	0.751316i	$-0.270581\pi$
$827$	37.9567			1.31988			0.659942	+	0.751316i	$0.270581\pi$
$828$	4.61171	−	14.1934i	0.160268	−	0.493255i
$829$	−32.2921			−1.12155			−0.560776	−	0.827967i	$-0.689497\pi$
$829$	−32.2921			−1.12155			−0.560776	+	0.827967i	$0.689497\pi$
$830$	8.07025	−	15.1418i	0.280122	−	0.525581i
$831$	3.45787	−	10.6422i	0.119952	−	0.369175i
$832$	−15.5069	−	11.2664i	−0.537605	−	0.390593i
$833$	−8.00322			−0.277295
$834$	−0.322125	−	0.234037i	−0.0111543	−	0.00810405i
$835$	−12.1180	+	5.89554i	−0.419360	+	0.204023i
$836$	6.77162	−	7.60719i	0.234201	−	0.263100i
$837$	6.40315	−	19.7069i	0.221325	−	0.681169i
$838$	−21.2067	−	15.4075i	−0.732572	−	0.532245i
$839$	−11.3182	−	8.22313i	−0.390747	−	0.283894i	0.375015	−	0.927019i	$-0.377638\pi$
$839$	−11.3182	−	8.22313i	−0.390747	−	0.283894i	−0.765761	+	0.643125i	$0.777638\pi$
$840$	−11.0585	+	5.38007i	−0.381554	+	0.185630i
$841$	−18.9998			−0.655165
$842$	−3.08117	+	9.48287i	−0.106184	+	0.326801i
$843$	8.35033	+	6.06687i	0.287601	+	0.208954i
$844$	0.908931			0.0312867
$845$	−5.50533	−	39.4551i	−0.189389	−	1.35730i
$846$	13.9056	−	10.1030i	0.478083	−	0.347348i
$847$	−23.1306	+	41.1368i	−0.794778	+	1.41348i
$848$	−1.47201	−	4.53039i	−0.0505491	−	0.155574i
$849$	4.09785	−	12.6119i	0.140638	−	0.432839i
$850$	−1.72419	+	2.19790i	−0.0591393	+	0.0753875i
$851$	−32.8632	−	23.8765i	−1.12654	−	0.818476i
$852$	1.11835	−	0.812529i	0.0383140	−	0.0278368i
$853$	20.2261	+	14.6951i	0.692528	+	0.503151i	0.877490	−	0.479594i	$-0.159216\pi$
$853$	20.2261	+	14.6951i	0.692528	+	0.503151i	−0.184962	+	0.982746i	$0.559216\pi$
$854$	−29.3281			−1.00359
$855$	9.66772	+	10.0310i	0.330629	+	0.343053i
$856$	−25.9227	+	18.8340i	−0.886020	+	0.643731i
$857$	−27.6721			−0.945262			−0.472631	−	0.881261i	$-0.656696\pi$
$857$	−27.6721			−0.945262			−0.472631	+	0.881261i	$0.656696\pi$
$858$	−0.693279	+	6.97752i	−0.0236681	+	0.238209i
$859$	12.2401	−	37.6712i	0.417627	−	1.28532i	−0.492253	−	0.870452i	$-0.663827\pi$
$859$	12.2401	−	37.6712i	0.417627	−	1.28532i	0.909880	−	0.414871i	$-0.136173\pi$
$860$	−1.75709	−	0.311612i	−0.0599164	−	0.0106259i
$861$	14.8177	+	10.7657i	0.504987	+	0.366895i
$862$	18.6929	−	13.5812i	0.636684	−	0.462578i
$863$	−15.9508			−0.542970			−0.271485	−	0.962443i	$-0.587515\pi$
$863$	−15.9508			−0.542970			−0.271485	+	0.962443i	$0.587515\pi$
$864$	13.0326	−	9.46873i	0.443378	−	0.322133i
$865$	23.3408	+	24.2179i	0.793611	+	0.823434i
$866$	−0.846445	−	2.60509i	−0.0287634	−	0.0885246i
$867$	6.38717	−	4.64055i	0.216920	−	0.157601i
$868$	43.9926			1.49321
$869$	1.72215	+	0.755047i	0.0584199	+	0.0256132i
$870$	1.26665	−	2.37655i	0.0429433	−	0.0805726i
$871$	8.63678	+	26.5813i	0.292646	+	0.900672i
$872$	7.38396	−	22.7255i	0.250052	−	0.769582i
$873$	−2.15194	+	6.62300i	−0.0728323	+	0.224155i
$874$	−2.18120	−	6.71304i	−0.0737801	−	0.227072i
$875$	19.3803	+	43.8781i	0.655173	+	1.48335i
$876$	2.70576	+	1.96585i	0.0914191	+	0.0664199i
$877$	16.3259	+	11.8614i	0.551285	+	0.400532i	0.828259	−	0.560345i	$-0.189332\pi$
$877$	16.3259	+	11.8614i	0.551285	+	0.400532i	−0.276974	+	0.960877i	$0.589332\pi$
$878$	−4.24984	−	13.0797i	−0.143425	−	0.441417i
$879$	−1.39161	+	1.01107i	−0.0469379	+	0.0341024i
$880$	−3.47811	+	2.74382i	−0.117247	+	0.0924940i
$881$	−28.5388	−	20.7347i	−0.961498	−	0.698569i	−0.00799996	−	0.999968i	$-0.502546\pi$
$881$	−28.5388	−	20.7347i	−0.961498	−	0.698569i	−0.953498	+	0.301399i	$0.902546\pi$
$882$	−7.77901	+	23.9413i	−0.261933	+	0.806146i
$883$	42.6257			1.43447			0.717235	−	0.696832i	$-0.245408\pi$
$883$	42.6257			1.43447			0.717235	+	0.696832i	$0.245408\pi$
$884$	−4.30372	+	3.12684i	−0.144750	+	0.105167i
$885$	−0.501606	−	3.59486i	−0.0168613	−	0.120840i
$886$	19.0311	−	13.8269i	0.639362	−	0.464523i
$887$	21.7296	−	15.7875i	0.729608	−	0.530092i	−0.159831	−	0.987144i	$-0.551095\pi$
$887$	21.7296	−	15.7875i	0.729608	−	0.530092i	0.889440	+	0.457053i	$0.151095\pi$
$888$	−4.08124	−	12.5608i	−0.136957	−	0.421512i
$889$	26.2698			0.881061
$890$	3.22521	+	23.1141i	0.108109	+	0.774787i
$891$	21.2435	+	9.31386i	0.711685	+	0.312026i
$892$	−4.09807	−	2.97742i	−0.137214	−	0.0996915i
$893$	−5.41103	+	16.6534i	−0.181073	+	0.557286i
$894$	−6.61817			−0.221345
$895$	−14.0218	+	26.3085i	−0.468698	+	0.879397i
$896$	30.9716	+	22.5022i	1.03469	+	0.751744i
$897$	−8.46834	−	6.15261i	−0.282750	−	0.205430i
$898$	−3.32126	+	10.2218i	−0.110832	+	0.341106i
$899$	−19.2061	+	13.9540i	−0.640559	+	0.465393i
$900$	−10.5523	−	15.7112i	−0.351743	−	0.523708i
$901$	5.59482			0.186391
$902$	−21.5911	−	9.46624i	−0.718905	−	0.315191i
$903$	0.969923	−	0.704690i	0.0322770	−	0.0234506i
$904$	4.12155	+	12.6848i	0.137081	+	0.421891i
$905$	25.0007	−	46.9077i	0.831052	−	1.55926i
$906$	1.56216	+	4.80785i	0.0518994	+	0.159730i
$907$	2.32991	+	7.17073i	0.0773635	+	0.238100i	0.982258	−	0.187536i	$-0.0600502\pi$
$907$	2.32991	+	7.17073i	0.0773635	+	0.238100i	−0.904894	+	0.425637i	$0.860050\pi$
$908$	−2.54362	+	7.82845i	−0.0844130	+	0.259796i
$909$	−20.2599	+	14.7197i	−0.671978	+	0.488220i
$910$	−5.86065	−	42.0015i	−0.194279	−	1.39234i
$911$	−31.0589			−1.02903			−0.514513	−	0.857483i	$-0.672027\pi$
$911$	−31.0589			−1.02903			−0.514513	+	0.857483i	$0.672027\pi$
$912$	−0.198477	+	0.610851i	−0.00657225	+	0.0202273i
$913$	16.1367	+	27.5861i	0.534046	+	0.912968i
$914$	−7.22136	−	22.2251i	−0.238861	−	0.735139i
$915$	1.26866	+	9.09208i	0.0419405	+	0.300575i
$916$	6.41844	+	19.7539i	0.212071	+	0.652688i
$917$	3.35452	+	10.3241i	0.110776	+	0.340933i
$918$	0.476535	+	1.46662i	0.0157280	+	0.0484058i
$919$	14.7677	−	45.4504i	0.487143	−	1.49927i	−0.341711	−	0.939805i	$-0.611006\pi$
$919$	14.7677	−	45.4504i	0.487143	−	1.49927i	0.828854	−	0.559466i	$-0.188994\pi$
$920$	3.26554	+	23.4032i	0.107662	+	0.771580i
$921$	−1.71123	+	5.26663i	−0.0563870	+	0.173541i
$922$	−9.40569	−	28.9477i	−0.309760	−	0.953343i
$923$	3.63008	+	11.1722i	0.119485	+	0.367738i
$924$	0.919043	−	9.24973i	0.0302343	−	0.304294i
$925$	−49.5470	+	14.1016i	−1.62910	+	0.463656i
$926$	7.50563	−	23.0999i	0.246650	−	0.759111i
$927$	11.9268	+	8.66532i	0.391727	+	0.284606i
$928$	−18.4562			−0.605856
$929$	19.5197	+	14.1819i	0.640421	+	0.465293i	0.859995	−	0.510303i	$-0.170467\pi$
$929$	19.5197	+	14.1819i	0.640421	+	0.465293i	−0.219574	+	0.975596i	$0.570467\pi$
$930$	0.883500	+	6.33178i	0.0289711	+	0.207627i
$931$	−7.92485	−	24.3902i	−0.259726	−	0.799355i
$932$	−1.24830	+	0.906943i	−0.0408894	+	0.0297079i
$933$	1.75610	−	1.27588i	0.0574922	−	0.0417705i
$934$	−7.51067	+	23.1155i	−0.245757	+	0.756361i
$935$	−1.80255	−	4.88100i	−0.0589498	−	0.159626i
$936$	12.7419	+	39.2155i	0.416481	+	1.28180i
$937$	−7.96404	−	5.78621i	−0.260174	−	0.189027i	0.450050	−	0.893003i	$-0.351406\pi$
$937$	−7.96404	−	5.78621i	−0.260174	−	0.189027i	−0.710224	+	0.703976i	$0.751406\pi$
$938$	5.31552	+	16.3595i	0.173558	+	0.534156i
$939$	−2.29550	+	7.06483i	−0.0749109	+	0.230552i
$940$	11.1886	−	20.9926i	0.364931	−	0.684703i
$941$	31.9657			1.04205			0.521026	−	0.853541i	$-0.325550\pi$
$941$	31.9657			1.04205			0.521026	+	0.853541i	$0.325550\pi$
$942$	0.271771	+	0.836424i	0.00885477	+	0.0272522i
$943$	28.4720	−	20.6861i	0.927175	−	0.673632i
$944$	−1.64025	+	1.19171i	−0.0533857	+	0.0387870i
$945$	26.0728	+	4.62388i	0.848148	+	0.150415i
$946$	−1.02603	+	1.15264i	−0.0333592	+	0.0374755i
$947$	30.3362	−	22.0405i	0.985794	−	0.716221i	0.0267977	−	0.999641i	$-0.491469\pi$
$947$	30.3362	−	22.0405i	0.985794	−	0.716221i	0.958996	+	0.283420i	$0.0914690\pi$
$948$	−0.370362			−0.0120288
$949$	−22.9934	+	16.7057i	−0.746396	+	0.542289i
$950$	−8.40552	−	3.07817i	−0.272711	−	0.0998689i
$951$	3.89960	+	12.0017i	0.126453	+	0.389183i
$952$	−6.52718	+	4.74228i	−0.211547	+	0.153698i
$953$	−11.3043			−0.366183			−0.183092	−	0.983096i	$-0.558610\pi$
$953$	−11.3043			−0.366183			−0.183092	+	0.983096i	$0.558610\pi$
$954$	5.43808	−	16.7367i	0.176064	−	0.541870i
$955$	0.138641	−	0.0674503i	0.00448631	−	0.00218264i
$956$	−17.1811	−	12.4828i	−0.555678	−	0.403723i
$957$	2.53269	+	4.32971i	0.0818704	+	0.139960i
$958$	3.77938	+	2.74588i	0.122106	+	0.0887155i
$959$	−9.00006	−	6.53893i	−0.290627	−	0.211153i
$960$	−1.73677	+	3.25863i	−0.0560541	+	0.105172i
$961$	7.83598	−	24.1167i	0.252774	−	0.777957i
$962$	45.5445			1.46841
$963$	33.1296			1.06759
$964$	9.52778	−	29.3235i	0.306869	−	0.944446i
$965$	3.49566	+	25.0523i	0.112529	+	0.806463i
$966$	−5.21186	−	3.78664i	−0.167689	−	0.121833i
$967$	−8.46133	−	6.14751i	−0.272098	−	0.197691i	0.443365	−	0.896341i	$-0.353784\pi$
$967$	−8.46133	−	6.14751i	−0.272098	−	0.197691i	−0.715463	+	0.698650i	$0.753784\pi$
$968$	3.41510	+	29.2850i	0.109765	+	0.941256i
$969$	−0.610301	−	0.443409i	−0.0196057	−	0.0142444i
$970$	−0.618353	−	4.43155i	−0.0198541	−	0.142289i
$971$	11.6798	−	35.9467i	0.374822	−	1.15358i	−0.568777	−	0.822492i	$-0.692583\pi$
$971$	11.6798	−	35.9467i	0.374822	−	1.15358i	0.943599	−	0.331092i	$-0.107417\pi$
$972$	−15.8787			−0.509309
$973$	−3.62882	+	2.63649i	−0.116335	+	0.0845220i
$974$	7.31985	+	22.5282i	0.234543	+	0.721849i
$975$	−12.7675	+	3.63376i	−0.408888	+	0.116373i
$976$	4.14851	−	3.01407i	0.132791	−	0.0964781i
$977$	6.19779			0.198285			0.0991425	−	0.995073i	$-0.468390\pi$
$977$	6.19779			0.198285			0.0991425	+	0.995073i	$0.468390\pi$
$978$	6.88712	−	5.00378i	0.220226	−	0.160003i
$979$	−39.8115	−	17.4547i	−1.27238	−	0.557854i
$980$	4.81464	+	34.5051i	0.153798	+	1.10222i
$981$	−19.9874	+	14.5217i	−0.638150	+	0.463643i
$982$	−1.31888	+	0.958223i	−0.0420872	+	0.0305781i
$983$	8.83872	+	27.2028i	0.281911	+	0.867634i	0.987307	+	0.158821i	$0.0507692\pi$
$983$	8.83872	+	27.2028i	0.281911	+	0.867634i	−0.705396	+	0.708813i	$0.749231\pi$
$984$	11.4424			0.364771
$985$	−32.5635	+	15.8425i	−1.03756	+	0.504784i
$986$	0.545965	−	1.68031i	0.0173871	−	0.0535119i
$987$	4.93858	+	15.1994i	0.157197	+	0.483802i
$988$	−13.7908	−	10.0196i	−0.438742	−	0.318765i
$989$	−0.711865	−	2.19089i	−0.0226360	−	0.0696664i
$990$	−16.3534	+	0.648016i	−0.519744	+	0.0205953i
$991$	9.56674	−	29.4434i	0.303897	−	0.935300i	−0.676189	−	0.736728i	$-0.736370\pi$
$991$	9.56674	−	29.4434i	0.303897	−	0.935300i	0.980086	−	0.198572i	$-0.0636303\pi$
$992$	35.4465	−	25.7534i	1.12543	−	0.817671i
$993$	−11.9157	+	8.65728i	−0.378134	+	0.274730i
$994$	2.23414	+	6.87597i	0.0708625	+	0.218092i
$995$	−47.5467	−	8.43218i	−1.50733	−	0.267318i
$996$	−5.09249	−	3.69991i	−0.161362	−	0.117236i
$997$	−4.80366			−0.152134			−0.0760668	−	0.997103i	$-0.524236\pi$
$997$	−4.80366			−0.152134			−0.0760668	+	0.997103i	$0.524236\pi$
$998$	−3.59636	−	2.61291i	−0.113841	−	0.0827101i
$999$	−8.78775	+	27.0459i	−0.278032	+	0.855694i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.2.l.d.31.15	yes	100
11.5	even	5		275.2.k.d.181.11	✓	100
25.21	even	5		275.2.k.d.196.11	yes	100
275.71	even	5	inner	275.2.l.d.71.15	yes	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
275.2.k.d.181.11	✓	100	11.5	even	5
275.2.k.d.196.11	yes	100	25.21	even	5
275.2.l.d.31.15	yes	100	1.1	even	1	trivial
275.2.l.d.71.15	yes	100	275.71	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:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	275.l (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+0.796321 q^{2} +(0.147790 - 0.454851i) q^{3} -1.36587 q^{4} +(-2.20171 - 0.390463i) q^{5} +(0.117688 - 0.362208i) q^{6} +(-3.47097 - 2.52180i) q^{7} -2.68032 q^{8} +(2.24200 + 1.62891i) q^{9} +(-1.75327 - 0.310934i) q^{10} +(2.20521 - 2.47731i) q^{11} +(-0.201863 + 0.621269i) q^{12} +(-4.49101 - 3.26291i) q^{13} +(-2.76400 - 2.00817i) q^{14} +(-0.502994 + 0.943745i) q^{15} +0.597355 q^{16} +(-0.216806 + 0.667262i) q^{17} +(1.78535 + 1.29714i) q^{18} -2.24819 q^{19} +(3.00726 + 0.533323i) q^{20} +(-1.66002 + 1.20607i) q^{21} +(1.75605 - 1.97273i) q^{22} +(1.21835 + 3.74971i) q^{23} +(-0.396124 + 1.21914i) q^{24} +(4.69508 + 1.71938i) q^{25} +(-3.57629 - 2.59833i) q^{26} +(2.23302 - 1.62238i) q^{27} +(4.74090 + 3.44446i) q^{28} -3.16231 q^{29} +(-0.400545 + 0.751524i) q^{30} +(6.07344 - 4.41261i) q^{31} +5.83632 q^{32} +(-0.800900 - 1.36916i) q^{33} +(-0.172647 + 0.531354i) q^{34} +(6.65740 + 6.90757i) q^{35} +(-3.06229 - 2.22489i) q^{36} +(-8.33525 + 6.05591i) q^{37} -1.79028 q^{38} +(-2.14787 + 1.56052i) q^{39} +(5.90128 + 1.04656i) q^{40} +(-2.75836 - 8.48937i) q^{41} +(-1.32191 + 0.960423i) q^{42} -0.584284 q^{43} +(-3.01203 + 3.38369i) q^{44} +(-4.30022 - 4.46181i) q^{45} +(0.970201 + 2.98597i) q^{46} +(2.40684 - 7.40748i) q^{47} +(0.0882831 - 0.271708i) q^{48} +(3.52499 + 10.8488i) q^{49} +(3.73879 + 1.36917i) q^{50} +(0.271463 + 0.197229i) q^{51} +(6.13415 + 4.45672i) q^{52} +(-2.46422 - 7.58408i) q^{53} +(1.77820 - 1.29194i) q^{54} +(-5.82253 + 4.59328i) q^{55} +(9.30328 + 6.75923i) q^{56} +(-0.332261 + 1.02259i) q^{57} -2.51821 q^{58} +(-2.74586 + 1.99499i) q^{59} +(0.687026 - 1.28904i) q^{60} +(6.94481 - 5.04570i) q^{61} +(4.83641 - 3.51385i) q^{62} +(-3.67412 - 11.3078i) q^{63} +3.45287 q^{64} +(8.61387 + 8.93757i) q^{65} +(-0.637774 - 1.09029i) q^{66} +(-4.07324 - 2.95938i) q^{67} +(0.296130 - 0.911394i) q^{68} +1.88562 q^{69} +(5.30142 + 5.50064i) q^{70} +(-1.71200 - 1.24384i) q^{71} +(-6.00928 - 4.36599i) q^{72} +(1.58212 - 4.86928i) q^{73} +(-6.63753 + 4.82245i) q^{74} +(1.47595 - 1.88145i) q^{75} +3.07075 q^{76} +(-13.9015 + 3.03757i) q^{77} +(-1.71039 + 1.24267i) q^{78} +(0.175201 + 0.539212i) q^{79} +(-1.31520 - 0.233245i) q^{80} +(2.16118 + 6.65144i) q^{81} +(-2.19654 - 6.76026i) q^{82} +(-2.97770 + 9.16443i) q^{83} +(2.26738 - 1.64735i) q^{84} +(0.737886 - 1.38446i) q^{85} -0.465278 q^{86} +(-0.467358 + 1.43838i) q^{87} +(-5.91064 + 6.63997i) q^{88} +(-4.05017 - 12.4652i) q^{89} +(-3.42435 - 3.55304i) q^{90} +(7.35973 + 22.6509i) q^{91} +(-1.66412 - 5.12162i) q^{92} +(-1.10949 - 3.41465i) q^{93} +(1.91661 - 5.89873i) q^{94} +(4.94987 + 0.877836i) q^{95} +(0.862550 - 2.65466i) q^{96} +(0.776519 + 2.38988i) q^{97} +(2.80702 + 8.63912i) q^{98} +(8.97940 - 1.96206i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q + 2 q^{2} - 2 q^{3} + 106 q^{4} + 5 q^{5} + 5 q^{6} + 5 q^{7} - 30 q^{8} - 25 q^{9} - 22 q^{10} - 53 q^{12} - 18 q^{13} - 10 q^{14} + 16 q^{15} + 62 q^{16} + q^{17} - 21 q^{18} + 6 q^{19} + q^{20}+ \cdots - 84 q^{99}+O(q^{100}) \) 100 * q + 2 * q^2 - 2 * q^3 + 106 * q^4 + 5 * q^5 + 5 * q^6 + 5 * q^7 - 30 * q^8 - 25 * q^9 - 22 * q^10 - 53 * q^12 - 18 * q^13 - 10 * q^14 + 16 * q^15 + 62 * q^16 + q^17 - 21 * q^18 + 6 * q^19 + q^20 - 22 * q^21 + 6 * q^22 + 20 * q^23 - 18 * q^24 + q^25 - 37 * q^26 + 10 * q^27 - 64 * q^28 - 28 * q^29 + 15 * q^30 + 9 * q^31 - 98 * q^32 + 13 * q^33 - 14 * q^34 + 13 * q^35 - 30 * q^36 - 21 * q^37 + 18 * q^38 + 44 * q^39 + 9 * q^40 + 28 * q^41 + 31 * q^42 + 82 * q^43 - 4 * q^44 - 25 * q^45 - 16 * q^46 - 10 * q^47 - 72 * q^48 - 26 * q^49 - 46 * q^50 - 14 * q^51 - 23 * q^52 - 5 * q^53 - 22 * q^54 + 32 * q^55 + q^56 - 85 * q^57 + 80 * q^58 - 3 * q^59 + 61 * q^60 + 35 * q^61 + 43 * q^62 - 47 * q^63 - 54 * q^64 - 64 * q^65 - 13 * q^66 - 20 * q^67 + 5 * q^68 + 76 * q^69 - 23 * q^70 + 28 * q^71 - 53 * q^72 + 33 * q^73 - 3 * q^74 - 34 * q^75 - 156 * q^76 + 45 * q^77 + 30 * q^78 + 4 * q^79 - 144 * q^80 - 27 * q^81 - 59 * q^82 - 92 * q^83 + 9 * q^84 - 26 * q^85 - 56 * q^86 + 38 * q^87 + 18 * q^88 + 39 * q^89 + 114 * q^90 - 11 * q^91 - 60 * q^92 - 19 * q^93 + 46 * q^94 - 46 * q^95 + 9 * q^96 + 20 * q^97 + 122 * q^98 - 84 * q^99

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