LMFDB - Embedded newform 850.2.y.b.21.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [850,2,Mod(21,850)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(850, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([12, 15])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("850.21"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 850 = 2 \cdot 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	850.y (of order $20$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [192] 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:	$6.78728417181$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$24$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			21.18
Character	$\chi$	$=$	850.21
Dual form			850.2.y.b.81.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.951057 - 0.309017i) q^{2} +(1.69400 - 0.268304i) q^{3} +(0.809017 + 0.587785i) q^{4} +(2.13448 - 0.666335i) q^{5} +(-1.69400 - 0.268304i) q^{6} +(-3.09277 - 3.09277i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(-0.0555099 + 0.0180363i) q^{9} +(-2.23592 - 0.0258678i) q^{10} +(2.97003 - 1.51330i) q^{11} +(1.52818 + 0.778648i) q^{12} +(0.334009 + 1.02797i) q^{13} +(1.98568 + 3.89712i) q^{14} +(3.43703 - 1.70146i) q^{15} +(0.309017 + 0.951057i) q^{16} +(3.46643 + 2.23246i) q^{17} +0.0583666 q^{18} +(-4.65882 - 6.41231i) q^{19} +(2.11849 + 0.715539i) q^{20} +(-6.06897 - 4.40937i) q^{21} +(-3.29230 + 0.521449i) q^{22} +(4.44485 - 2.26477i) q^{23} +(-1.21277 - 1.21277i) q^{24} +(4.11200 - 2.84456i) q^{25} -1.08088i q^{26} +(-4.67374 + 2.38139i) q^{27} +(-0.684220 - 4.31999i) q^{28} +(-9.11470 + 1.44363i) q^{29} +(-3.79459 + 0.556085i) q^{30} +(1.27055 - 8.02196i) q^{31} -1.00000i q^{32} +(4.62521 - 3.36041i) q^{33} +(-2.60690 - 3.19438i) q^{34} +(-8.66228 - 4.54064i) q^{35} +(-0.0555099 - 0.0180363i) q^{36} +(5.82500 + 2.96798i) q^{37} +(2.44928 + 7.53812i) q^{38} +(0.841621 + 1.65177i) q^{39} +(-1.79369 - 1.33517i) q^{40} +(1.19686 - 2.34897i) q^{41} +(4.40937 + 6.06897i) q^{42} +0.500240i q^{43} +(3.29230 + 0.521449i) q^{44} +(-0.106466 + 0.0754862i) q^{45} +(-4.92716 + 0.780385i) q^{46} +(5.78641 + 4.20407i) q^{47} +(0.778648 + 1.52818i) q^{48} +12.1305i q^{49} +(-4.78976 + 1.43466i) q^{50} +(6.47112 + 2.85174i) q^{51} +(-0.334009 + 1.02797i) q^{52} +(3.42341 - 4.71192i) q^{53} +(5.18088 - 0.820571i) q^{54} +(5.33109 - 5.20915i) q^{55} +(-0.684220 + 4.31999i) q^{56} +(-9.61250 - 9.61250i) q^{57} +(9.11470 + 1.44363i) q^{58} +(-8.92474 + 2.89982i) q^{59} +(3.78071 + 0.643725i) q^{60} +(-3.47620 + 1.77121i) q^{61} +(-3.68729 + 7.23671i) q^{62} +(0.227462 + 0.115898i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(1.39791 + 1.97163i) q^{65} +(-5.43726 + 1.76667i) q^{66} +(0.377917 - 0.274573i) q^{67} +(1.49219 + 3.84361i) q^{68} +(6.92195 - 5.02909i) q^{69} +(6.83519 + 6.99519i) q^{70} +(13.7959 - 2.18505i) q^{71} +(0.0472195 + 0.0343070i) q^{72} +(4.15589 + 8.15639i) q^{73} +(-4.62274 - 4.62274i) q^{74} +(6.20253 - 5.92195i) q^{75} -7.92605i q^{76} +(-13.8659 - 4.50531i) q^{77} +(-0.290003 - 1.83101i) q^{78} +(0.207930 + 1.31282i) q^{79} +(1.29331 + 1.82410i) q^{80} +(-7.13674 + 5.18514i) q^{81} +(-1.86416 + 1.86416i) q^{82} +(-3.68423 - 5.07091i) q^{83} +(-2.31814 - 7.13451i) q^{84} +(8.88658 + 2.45534i) q^{85} +(0.154583 - 0.475756i) q^{86} +(-15.0530 + 4.89101i) q^{87} +(-2.97003 - 1.51330i) q^{88} +(2.18284 - 6.71810i) q^{89} +(0.124582 - 0.0388917i) q^{90} +(2.14628 - 4.21230i) q^{91} +(4.92716 + 0.780385i) q^{92} -13.9301i q^{93} +(-4.20407 - 5.78641i) q^{94} +(-14.2169 - 10.5826i) q^{95} +(-0.268304 - 1.69400i) q^{96} +(-11.2999 + 1.78972i) q^{97} +(3.74853 - 11.5368i) q^{98} +(-0.137571 + 0.137571i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 48 q^{4} + 2 q^{5} + 4 q^{7} - 12 q^{10} + 14 q^{11} - 4 q^{13} - 6 q^{14} - 48 q^{16} + 12 q^{17} - 240 q^{18} + 18 q^{20} - 16 q^{21} - 16 q^{22} - 14 q^{23} - 30 q^{27} - 4 q^{28} - 20 q^{29}+ \cdots + 96 q^{99}+O(q^{100}) $ 192 * q + 48 * q^4 + 2 * q^5 + 4 * q^7 - 12 * q^10 + 14 * q^11 - 4 * q^13 - 6 * q^14 - 48 * q^16 + 12 * q^17 - 240 * q^18 + 18 * q^20 - 16 * q^21 - 16 * q^22 - 14 * q^23 - 30 * q^27 - 4 * q^28 - 20 * q^29 - 4 * q^30 + 12 * q^31 + 28 * q^33 + 8 * q^34 + 60 * q^35 - 38 * q^37 - 4 * q^38 - 24 * q^39 + 2 * q^40 - 8 * q^41 + 16 * q^44 - 36 * q^45 + 16 * q^46 + 44 * q^47 + 32 * q^50 - 16 * q^51 + 4 * q^52 + 16 * q^55 - 4 * q^56 - 40 * q^57 + 20 * q^58 + 34 * q^61 + 18 * q^62 + 32 * q^63 + 48 * q^64 + 36 * q^65 - 40 * q^67 - 12 * q^68 - 24 * q^69 + 8 * q^71 - 60 * q^72 - 44 * q^73 - 12 * q^74 - 16 * q^78 + 36 * q^79 + 2 * q^80 + 96 * q^81 - 88 * q^82 - 44 * q^84 + 2 * q^85 - 44 * q^86 - 14 * q^88 + 60 * q^89 - 16 * q^90 - 4 * q^91 - 16 * q^92 + 8 * q^95 + 20 * q^97 - 64 * q^98 + 96 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/850\mathbb{Z}\right)^\times$.

$n$	$477$	$751$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.951057	−	0.309017i	−0.672499	−	0.218508i
$2$	−0.951057	−	0.309017i	−0.672499	−	0.218508i
$3$	1.69400	−	0.268304i	0.978033	−	0.154905i	0.353102	−	0.935585i	$-0.385127\pi$
$3$	1.69400	−	0.268304i	0.978033	−	0.154905i	0.624931	+	0.780680i	$0.285127\pi$
$4$	0.809017	+	0.587785i	0.404508	+	0.293893i
$5$	2.13448	−	0.666335i	0.954568	−	0.297994i
$5$	2.13448	−	0.666335i	0.954568	−	0.297994i
$6$	−1.69400	−	0.268304i	−0.691574	−	0.109535i
$7$	−3.09277	−	3.09277i	−1.16896	−	1.16896i	−0.982454	−	0.186505i	$-0.940284\pi$
$7$	−3.09277	−	3.09277i	−1.16896	−	1.16896i	−0.186505	−	0.982454i	$-0.559716\pi$
$8$	−0.587785	−	0.809017i	−0.207813	−	0.286031i
$9$	−0.0555099	+	0.0180363i	−0.0185033	+	0.00601209i
$10$	−2.23592	−	0.0258678i	−0.707059	−	0.00818012i
$11$	2.97003	−	1.51330i	0.895496	−	0.456278i	0.0552434	−	0.998473i	$-0.482407\pi$
$11$	2.97003	−	1.51330i	0.895496	−	0.456278i	0.840253	+	0.542195i	$0.182407\pi$
$12$	1.52818	+	0.778648i	0.441148	+	0.224776i
$13$	0.334009	+	1.02797i	0.0926374	+	0.285109i	0.986631	−	0.162972i	$-0.0521079\pi$
$13$	0.334009	+	1.02797i	0.0926374	+	0.285109i	−0.893993	+	0.448080i	$0.852108\pi$
$14$	1.98568	+	3.89712i	0.530696	+	1.04155i
$15$	3.43703	−	1.70146i	0.887438	−	0.439316i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	3.46643	+	2.23246i	0.840732	+	0.541451i
$17$	3.46643	+	2.23246i	0.840732	+	0.541451i
$18$	0.0583666			0.0137571
$19$	−4.65882	−	6.41231i	−1.06881	−	1.47108i	−0.871279	−	0.490787i	$-0.836709\pi$
$19$	−4.65882	−	6.41231i	−1.06881	−	1.47108i	−0.197526	−	0.980298i	$-0.563291\pi$
$20$	2.11849	+	0.715539i	0.473709	+	0.159999i
$21$	−6.06897	−	4.40937i	−1.32436	−	0.962203i
$22$	−3.29230	+	0.521449i	−0.701920	+	0.111173i
$23$	4.44485	−	2.26477i	0.926816	−	0.472236i	0.0756507	−	0.997134i	$-0.475897\pi$
$23$	4.44485	−	2.26477i	0.926816	−	0.472236i	0.851165	+	0.524898i	$0.175897\pi$
$24$	−1.21277	−	1.21277i	−0.247556	−	0.247556i
$25$	4.11200	−	2.84456i	0.822399	−	0.568911i
$26$		−	1.08088i		−	0.211977i
$27$	−4.67374	+	2.38139i	−0.899462	+	0.458299i
$28$	−0.684220	−	4.31999i	−0.129305	−	0.816402i
$29$	−9.11470	+	1.44363i	−1.69256	+	0.268075i	−0.926937	−	0.375218i	$-0.877568\pi$
$29$	−9.11470	+	1.44363i	−1.69256	+	0.268075i	−0.765620	+	0.643293i	$0.777568\pi$
$30$	−3.79459	+	0.556085i	−0.692795	+	0.101527i
$31$	1.27055	−	8.02196i	0.228198	−	1.44079i	−0.561595	−	0.827413i	$-0.689812\pi$
$31$	1.27055	−	8.02196i	0.228198	−	1.44079i	0.789793	−	0.613374i	$-0.210188\pi$
$32$		−	1.00000i		−	0.176777i
$33$	4.62521	−	3.36041i	0.805145	−	0.584972i
$34$	−2.60690	−	3.19438i	−0.447080	−	0.547832i
$35$	−8.66228	−	4.54064i	−1.46419	−	0.767508i
$36$	−0.0555099	−	0.0180363i	−0.00925165	−	0.00300604i
$37$	5.82500	+	2.96798i	0.957624	+	0.487934i	0.861679	−	0.507453i	$-0.169413\pi$
$37$	5.82500	+	2.96798i	0.957624	+	0.487934i	0.0959442	+	0.995387i	$0.469413\pi$
$38$	2.44928	+	7.53812i	0.397326	+	1.22284i
$39$	0.841621	+	1.65177i	0.134767	+	0.264496i
$40$	−1.79369	−	1.33517i	−0.283607	−	0.211108i
$41$	1.19686	−	2.34897i	0.186918	−	0.366848i	−0.778463	−	0.627691i	$-0.784000\pi$
$41$	1.19686	−	2.34897i	0.186918	−	0.366848i	0.965381	+	0.260842i	$0.0840003\pi$
$42$	4.40937	+	6.06897i	0.680380	+	0.936463i
$43$			0.500240i			0.0762859i	0.999272	+	0.0381429i	$0.0121442\pi$
$43$			0.500240i			0.0762859i	−0.999272	+	0.0381429i	$0.987856\pi$
$44$	3.29230	+	0.521449i	0.496333	+	0.0786114i
$45$	−0.106466	+	0.0754862i	−0.0158711	+	0.0112528i
$46$	−4.92716	+	0.780385i	−0.726470	+	0.115061i
$47$	5.78641	+	4.20407i	0.844035	+	0.613227i	0.923495	−	0.383611i	$-0.125320\pi$
$47$	5.78641	+	4.20407i	0.844035	+	0.613227i	−0.0794602	+	0.996838i	$0.525320\pi$
$48$	0.778648	+	1.52818i	0.112388	+	0.220574i
$49$			12.1305i			1.73293i
$50$	−4.78976	+	1.43466i	−0.677374	+	0.202891i
$51$	6.47112	+	2.85174i	0.906138	+	0.399323i
$52$	−0.334009	+	1.02797i	−0.0463187	+	0.142554i
$53$	3.42341	−	4.71192i	0.470242	−	0.647232i	−0.506351	−	0.862327i	$-0.669006\pi$
$53$	3.42341	−	4.71192i	0.470242	−	0.647232i	0.976593	+	0.215095i	$0.0690061\pi$
$54$	5.18088	−	0.820571i	0.705029	−	0.111666i
$55$	5.33109	−	5.20915i	0.718844	−	0.702401i
$56$	−0.684220	+	4.31999i	−0.0914327	+	0.577284i
$57$	−9.61250	−	9.61250i	−1.27321	−	1.27321i
$58$	9.11470	+	1.44363i	1.19682	+	0.189557i
$59$	−8.92474	+	2.89982i	−1.16190	+	0.377525i	−0.825615	−	0.564235i	$-0.809171\pi$
$59$	−8.92474	+	2.89982i	−1.16190	+	0.377525i	−0.336288	+	0.941759i	$0.609171\pi$
$60$	3.78071	+	0.643725i	0.488088	+	0.0831046i
$61$	−3.47620	+	1.77121i	−0.445081	+	0.226780i	−0.662143	−	0.749378i	$-0.730353\pi$
$61$	−3.47620	+	1.77121i	−0.445081	+	0.226780i	0.217062	+	0.976158i	$0.430353\pi$
$62$	−3.68729	+	7.23671i	−0.468286	+	0.919064i
$63$	0.227462	+	0.115898i	0.0286575	+	0.0146017i
$64$	−0.309017	+	0.951057i	−0.0386271	+	0.118882i
$65$	1.39791	+	1.97163i	0.173389	+	0.244550i
$66$	−5.43726	+	1.76667i	−0.669280	+	0.217462i
$67$	0.377917	−	0.274573i	0.0461700	−	0.0335444i	−0.564461	−	0.825460i	$-0.690916\pi$
$67$	0.377917	−	0.274573i	0.0461700	−	0.0335444i	0.610631	+	0.791915i	$0.290916\pi$
$68$	1.49219	+	3.84361i	0.180955	+	0.466107i
$69$	6.92195	−	5.02909i	0.833305	−	0.605431i
$70$	6.83519	+	6.99519i	0.816961	+	0.836086i
$71$	13.7959	−	2.18505i	1.63727	−	0.259317i	0.731110	−	0.682260i	$-0.239003\pi$
$71$	13.7959	−	2.18505i	1.63727	−	0.259317i	0.906157	+	0.422942i	$0.139003\pi$
$72$	0.0472195	+	0.0343070i	0.00556488	+	0.00404312i
$73$	4.15589	+	8.15639i	0.486410	+	0.954633i	0.995576	+	0.0939648i	$0.0299541\pi$
$73$	4.15589	+	8.15639i	0.486410	+	0.954633i	−0.509166	+	0.860669i	$0.670046\pi$
$74$	−4.62274	−	4.62274i	−0.537383	−	0.537383i
$75$	6.20253	−	5.92195i	0.716206	−	0.683808i
$76$		−	7.92605i		−	0.909180i
$77$	−13.8659	−	4.50531i	−1.58017	−	0.513428i
$78$	−0.290003	−	1.83101i	−0.0328364	−	0.207321i
$79$	0.207930	+	1.31282i	0.0233940	+	0.147704i	0.996620	−	0.0821446i	$-0.0261769\pi$
$79$	0.207930	+	1.31282i	0.0233940	+	0.147704i	−0.973226	+	0.229849i	$0.926177\pi$
$80$	1.29331	+	1.82410i	0.144597	+	0.203941i
$81$	−7.13674	+	5.18514i	−0.792971	+	0.576127i
$82$	−1.86416	+	1.86416i	−0.205862	+	0.205862i
$83$	−3.68423	−	5.07091i	−0.404397	−	0.556605i	0.557444	−	0.830215i	$-0.311782\pi$
$83$	−3.68423	−	5.07091i	−0.404397	−	0.556605i	−0.961841	+	0.273610i	$0.911782\pi$
$84$	−2.31814	−	7.13451i	−0.252930	−	0.778438i
$85$	8.88658	+	2.45534i	0.963885	+	0.266319i
$86$	0.154583	−	0.475756i	0.0166691	−	0.0513021i
$87$	−15.0530	+	4.89101i	−1.61385	+	0.524372i
$88$	−2.97003	−	1.51330i	−0.316606	−	0.161319i
$89$	2.18284	−	6.71810i	0.231381	−	0.712118i	−0.766200	−	0.642602i	$-0.777855\pi$
$89$	2.18284	−	6.71810i	0.231381	−	0.712118i	0.997581	−	0.0695153i	$-0.0221453\pi$
$90$	0.124582	−	0.0388917i	0.0131321	−	0.00409954i
$91$	2.14628	−	4.21230i	0.224991	−	0.441569i
$92$	4.92716	+	0.780385i	0.513692	+	0.0813608i
$93$		−	13.9301i		−	1.44449i
$94$	−4.20407	−	5.78641i	−0.433617	−	0.596823i
$95$	−14.2169	−	10.5826i	−1.45862	−	1.08575i
$96$	−0.268304	−	1.69400i	−0.0273836	−	0.172893i
$97$	−11.2999	+	1.78972i	−1.14733	+	0.181719i	−0.701007	−	0.713154i	$-0.747266\pi$
$97$	−11.2999	+	1.78972i	−1.14733	+	0.181719i	−0.446321	+	0.894873i	$0.647266\pi$
$98$	3.74853	−	11.5368i	0.378659	−	1.16539i
$99$	−0.137571	+	0.137571i	−0.0138265	+	0.0138265i
$100$	4.99866	+	0.115677i	0.499866	+	0.0115677i
$101$	−2.76275			−0.274904			−0.137452	−	0.990508i	$-0.543891\pi$
$101$	−2.76275			−0.274904			−0.137452	+	0.990508i	$0.543891\pi$
$102$	−5.27316	−	4.71185i	−0.522121	−	0.466543i
$103$	10.2809	+	7.46954i	1.01301	+	0.735996i	0.964838	−	0.262843i	$-0.0846603\pi$
$103$	10.2809	+	7.46954i	1.01301	+	0.735996i	0.0481725	+	0.998839i	$0.484660\pi$
$104$	0.635323	−	0.874446i	0.0622985	−	0.0857465i
$105$	−15.8922	−	5.36773i	−1.55092	−	0.523837i
$106$	−4.71192	+	3.42341i	−0.457662	+	0.332511i
$107$	4.30029	−	4.30029i	0.415724	−	0.415724i	−0.468003	−	0.883727i	$-0.655026\pi$
$107$	4.30029	−	4.30029i	0.415724	−	0.415724i	0.883727	+	0.468003i	$0.155026\pi$
$108$	−5.18088	−	0.820571i	−0.498531	−	0.0789595i
$109$	−3.71078	+	7.28281i	−0.355428	+	0.697566i	−0.997618	−	0.0689789i	$-0.978026\pi$
$109$	−3.71078	+	7.28281i	−0.355428	+	0.697566i	0.642190	+	0.766545i	$0.278026\pi$
$110$	−6.67988	+	3.30679i	−0.636902	+	0.315291i
$111$	10.6639	+	3.46491i	1.01217	+	0.328874i
$112$	1.98568	−	3.89712i	0.187629	−	0.368244i
$113$	1.34479	−	2.63929i	0.126507	−	0.248284i	−0.819063	−	0.573704i	$-0.805506\pi$
$113$	1.34479	−	2.63929i	0.126507	−	0.248284i	0.945569	+	0.325421i	$0.105506\pi$
$114$	6.17160	+	12.1125i	0.578023	+	1.13443i
$115$	7.97835	−	7.79585i	0.743985	−	0.726967i
$116$	−8.22249	−	4.18957i	−0.763439	−	0.388992i
$117$	−0.0370816	−	0.0510384i	−0.00342819	−	0.00471851i
$118$	9.38403			0.863870
$119$	−3.81638	−	17.6254i	−0.349847	−	1.61572i
$120$	−3.39675	−	1.78052i	−0.310079	−	0.162539i
$121$	0.0653246	−	0.0899117i	0.00593860	−	0.00817379i
$122$	3.85339	−	0.610317i	0.348870	−	0.0552555i
$123$	1.39725	−	4.30029i	0.125986	−	0.387744i
$124$	5.74309	−	5.74309i	0.515745	−	0.515745i
$125$	6.88154	−	8.81161i	0.615503	−	0.788134i
$126$	−0.180515	−	0.180515i	−0.0160815	−	0.0160815i
$127$	14.4374	+	4.69099i	1.28111	+	0.416258i	0.868971	−	0.494863i	$-0.164782\pi$
$127$	14.4374	+	4.69099i	1.28111	+	0.416258i	0.412140	+	0.911121i	$0.364782\pi$
$128$	0.587785	−	0.809017i	0.0519534	−	0.0715077i
$129$	0.134216	+	0.847408i	0.0118171	+	0.0746101i
$130$	−0.720225	−	2.30710i	−0.0631679	−	0.202346i
$131$	−3.26960	+	20.6435i	−0.285667	+	1.80363i	0.259981	+	0.965614i	$0.416284\pi$
$131$	−3.26960	+	20.6435i	−0.285667	+	1.80363i	−0.545648	+	0.838015i	$0.683716\pi$
$132$	5.71707			0.497607
$133$	−5.42316	+	34.2405i	−0.470248	+	2.96903i
$134$	−0.444269	+	0.144352i	−0.0383790	+	0.0124701i
$135$	−8.38920	+	8.19730i	−0.722027	+	0.705512i
$136$	−0.231417	−	4.11661i	−0.0198438	−	0.352996i
$137$	−1.97145	−	6.06749i	−0.168432	−	0.518381i	0.830841	−	0.556510i	$-0.187860\pi$
$137$	−1.97145	−	6.06749i	−0.168432	−	0.518381i	−0.999273	+	0.0381296i	$0.987860\pi$
$138$	−8.13724	+	2.64395i	−0.692688	+	0.225068i
$139$	0.151326	+	0.296993i	0.0128353	+	0.0251906i	0.897335	−	0.441350i	$-0.145500\pi$
$139$	0.151326	+	0.296993i	0.0128353	+	0.0251906i	−0.884500	+	0.466540i	$0.845500\pi$
$140$	−4.33902	−	8.76501i	−0.366714	−	0.740779i
$141$	10.9302	+	5.56920i	0.920486	+	0.469011i
$142$	−13.7959	−	2.18505i	−1.15772	−	0.183365i
$143$	2.54765	+	2.54765i	0.213045	+	0.213045i
$144$	−0.0343070	−	0.0472195i	−0.00285892	−	0.00393496i
$145$	−18.4932	+	9.15483i	−1.53578	+	0.760267i
$146$	−1.43202	−	9.04143i	−0.118515	−	0.748274i
$147$	3.25466	+	20.5491i	0.268440	+	1.69486i
$148$	2.96798	+	5.82500i	0.243967	+	0.478812i
$149$	23.9525			1.96227			0.981135	−	0.193326i	$-0.0619274\pi$
$149$	23.9525			1.96227			0.981135	+	0.193326i	$0.0619274\pi$
$150$	−7.72894	+	3.71542i	−0.631065	+	0.303363i
$151$			3.33521i			0.271415i	0.990749	+	0.135708i	$0.0433308\pi$
$151$			3.33521i			0.271415i	−0.990749	+	0.135708i	$0.956669\pi$
$152$	−2.44928	+	7.53812i	−0.198663	+	0.611422i
$153$	−0.232686	−	0.0614022i	−0.0188116	−	0.00496408i
$154$	11.7951	+	8.56961i	0.950473	+	0.690559i
$155$	−2.63334	−	17.9693i	−0.211515	−	1.44333i
$156$	−0.290003	+	1.83101i	−0.0232188	+	0.146598i
$157$	15.2887			1.22017			0.610087	−	0.792335i	$-0.291135\pi$
$157$	15.2887			1.22017			0.610087	+	0.792335i	$0.291135\pi$
$158$	0.207930	−	1.31282i	0.0165421	−	0.104442i
$159$	4.53504	−	8.90052i	0.359652	−	0.705858i
$160$	−0.666335	−	2.13448i	−0.0526784	−	0.168745i
$161$	−20.7513	−	6.74252i	−1.63543	−	0.531385i
$162$	8.38974	−	2.72599i	0.659160	−	0.214174i
$163$	−4.63404	+	9.09481i	−0.362966	+	0.712361i	−0.998201	−	0.0599582i	$-0.980903\pi$
$163$	−4.63404	+	9.09481i	−0.362966	+	0.712361i	0.635235	+	0.772319i	$0.280903\pi$
$164$	2.34897	−	1.19686i	0.183424	−	0.0934592i
$165$	7.63325	−	10.2547i	0.594247	−	0.798324i
$166$	1.93692	+	5.96121i	0.150334	+	0.462680i
$167$	−2.40215	+	15.1666i	−0.185884	+	1.17362i	0.701526	+	0.712644i	$0.252502\pi$
$167$	−2.40215	+	15.1666i	−0.185884	+	1.17362i	−0.887410	+	0.460981i	$0.847498\pi$
$168$			7.50166i			0.578766i
$169$	9.57205	−	6.95450i	0.736312	−	0.534962i
$170$	−7.69290	−	5.08127i	−0.590019	−	0.389715i
$171$	0.374265	+	0.271919i	0.0286207	+	0.0207942i
$172$	−0.294034	+	0.404703i	−0.0224199	+	0.0308583i
$173$	−9.74267	−	19.1211i	−0.740722	−	1.45375i	−0.885673	−	0.464309i	$-0.846303\pi$
$173$	−9.74267	−	19.1211i	−0.740722	−	1.45375i	0.144951	−	0.989439i	$-0.453697\pi$
$174$	15.8277			1.19989
$175$	−21.5150	−	3.91991i	−1.62638	−	0.296317i
$176$	2.35703	+	2.35703i	0.177667	+	0.177667i
$177$	−14.3405	+	7.30685i	−1.07790	+	0.549217i
$178$	−4.15202	+	5.71476i	−0.311207	+	0.428339i
$179$	−9.36375	+	12.8881i	−0.699879	+	0.963301i	0.300076	+	0.953915i	$0.402988\pi$
$179$	−9.36375	+	12.8881i	−0.699879	+	0.963301i	−0.999956	+	0.00938629i	$0.997012\pi$
$180$	−0.130503	−	0.00150982i	−0.00972711	−	0.000112535i
$181$	−11.6449	−	1.84437i	−0.865557	−	0.137091i	−0.292161	−	0.956369i	$-0.594374\pi$
$181$	−11.6449	−	1.84437i	−0.865557	−	0.137091i	−0.573396	+	0.819278i	$0.694374\pi$
$182$	−3.34290	+	3.34290i	−0.247793	+	0.247793i
$183$	−5.41346	+	3.93311i	−0.400175	+	0.290744i
$184$	−4.44485	−	2.26477i	−0.327679	−	0.166961i
$185$	14.4110	+	2.45370i	1.05952	+	0.180399i
$186$	−4.30464	+	13.2483i	−0.315632	+	0.971415i
$187$	13.6738	+	1.38471i	0.999925	+	0.101260i
$188$	2.21021	+	6.80233i	0.161196	+	0.496111i
$189$	21.8199	+	7.08973i	1.58717	+	0.515702i
$190$	10.2509	+	14.4579i	0.743676	+	1.04889i
$191$	−2.66588	−	8.20473i	−0.192896	−	0.593673i	−0.999995	−	0.00325666i	$-0.998963\pi$
$191$	−2.66588	−	8.20473i	−0.192896	−	0.593673i	0.807098	−	0.590417i	$-0.201037\pi$
$192$	−0.268304	+	1.69400i	−0.0193632	+	0.122254i
$193$	16.3375	+	16.3375i	1.17600	+	1.17600i	0.980755	+	0.195242i	$0.0625492\pi$
$193$	16.3375	+	16.3375i	1.17600	+	1.17600i	0.195242	+	0.980755i	$0.437451\pi$
$194$	11.2999	+	1.78972i	0.811283	+	0.128495i
$195$	2.89706	+	2.96488i	0.207463	+	0.212319i
$196$	−7.13013	+	9.81379i	−0.509295	+	0.700985i
$197$	2.50422	+	15.8110i	0.178418	+	1.12649i	0.900557	+	0.434739i	$0.143159\pi$
$197$	2.50422	+	15.8110i	0.178418	+	1.12649i	−0.722139	+	0.691748i	$0.756841\pi$
$198$	0.173350	−	0.0883263i	0.0123195	−	0.00627708i
$199$	−1.53321	+	1.53321i	−0.108687	+	0.108687i	−0.759359	−	0.650672i	$-0.774487\pi$
$199$	−1.53321	+	1.53321i	−0.108687	+	0.108687i	0.650672	+	0.759359i	$0.274487\pi$
$200$	−4.71826	−	1.65469i	−0.333632	−	0.117004i
$201$	0.566524	−	0.566524i	0.0399595	−	0.0399595i
$202$	2.62753	+	0.853736i	0.184872	+	0.0600687i
$203$	32.6545	+	23.7249i	2.29190	+	1.66516i
$204$	3.55903	+	6.11073i	0.249182	+	0.427837i
$205$	0.989473	−	5.81135i	0.0691078	−	0.405882i
$206$	−7.46954	−	10.2809i	−0.520427	−	0.716307i
$207$	−0.205885	+	0.205885i	−0.0143100	+	0.0143100i
$208$	−0.874446	+	0.635323i	−0.0606320	+	0.0440517i
$209$	−23.5406	−	11.9945i	−1.62834	−	0.829678i
$210$	13.4557	+	10.0160i	0.928529	+	0.691168i
$211$	−3.70941	+	1.89004i	−0.255367	+	0.130116i	−0.576988	−	0.816753i	$-0.695772\pi$
$211$	−3.70941	+	1.89004i	−0.255367	+	0.130116i	0.321622	+	0.946868i	$0.395772\pi$
$212$	5.53920	−	1.79979i	0.380434	−	0.123610i
$213$	22.7840	−	7.40296i	1.56113	−	0.507242i
$214$	−5.41868	+	2.76095i	−0.370413	+	0.188735i
$215$	0.333327	+	1.06775i	0.0227327	+	0.0728200i
$216$	4.67374	+	2.38139i	0.318008	+	0.162033i
$217$	−28.7396	+	20.8806i	−1.95097	+	1.41747i
$218$	5.77967	−	5.77967i	0.391449	−	0.391449i
$219$	9.22848	+	12.7019i	0.623603	+	0.858316i
$220$	7.37480	−	1.08075i	0.497209	−	0.0728643i
$221$	−1.13709	+	4.30906i	−0.0764891	+	0.289859i
$222$	−9.07124	−	6.59064i	−0.608822	−	0.442335i
$223$	0.894047	+	0.290493i	0.0598698	+	0.0194529i	0.338799	−	0.940859i	$-0.389979\pi$
$223$	0.894047	+	0.290493i	0.0598698	+	0.0194529i	−0.278929	+	0.960312i	$0.589979\pi$
$224$	−3.09277	+	3.09277i	−0.206645	+	0.206645i
$225$	−0.176951	+	0.232066i	−0.0117968	+	0.0154711i
$226$	−2.09455	+	2.09455i	−0.139328	+	0.139328i
$227$	−5.45377	+	2.77883i	−0.361979	+	0.184438i	−0.625515	−	0.780212i	$-0.715111\pi$
$227$	−5.45377	+	2.77883i	−0.361979	+	0.184438i	0.263536	+	0.964650i	$0.415111\pi$
$228$	−2.12659	−	13.4268i	−0.140837	−	0.889209i
$229$	6.68229	−	9.19738i	0.441578	−	0.607780i	−0.528984	−	0.848632i	$-0.677427\pi$
$229$	6.68229	−	9.19738i	0.441578	−	0.607780i	0.970562	+	0.240852i	$0.0774268\pi$
$230$	−9.99691	+	4.94885i	−0.659177	+	0.326318i
$231$	−24.6977	−	3.91173i	−1.62499	−	0.257373i
$232$	6.52540	+	6.52540i	0.428414	+	0.428414i
$233$	−1.82261	+	11.5075i	−0.119403	+	0.753883i	0.853230	+	0.521535i	$0.174641\pi$
$233$	−1.82261	+	11.5075i	−0.119403	+	0.753883i	−0.972633	+	0.232347i	$0.925359\pi$
$234$	0.0194949	+	0.0599993i	0.00127442	+	0.00392228i
$235$	15.1523	+	5.11781i	0.988426	+	0.333849i
$236$	−8.92474	−	2.89982i	−0.580951	−	0.188762i
$237$	0.704470	+	2.16814i	0.0457602	+	0.140836i
$238$	−1.81694	+	17.9421i	−0.117775	+	1.16301i
$239$	5.12831	−	15.7833i	0.331723	−	1.02094i	−0.636591	−	0.771202i	$-0.719656\pi$
$239$	5.12831	−	15.7833i	0.331723	−	1.02094i	0.968314	−	0.249737i	$-0.0803440\pi$
$240$	2.68029	+	2.74303i	0.173012	+	0.177062i
$241$	−4.05576	−	2.06651i	−0.261255	−	0.133116i	0.318458	−	0.947937i	$-0.396835\pi$
$241$	−4.05576	−	2.06651i	−0.261255	−	0.133116i	−0.579712	+	0.814821i	$0.696835\pi$
$242$	−0.0899117	+	0.0653246i	−0.00577974	+	0.00419923i
$243$	0.428844	−	0.428844i	0.0275103	−	0.0275103i
$244$	−3.85339	−	0.610317i	−0.246688	−	0.0390716i
$245$	8.08298	+	25.8923i	0.516403	+	1.65420i
$246$	−2.65773	+	3.65805i	−0.169450	+	0.233229i
$247$	5.03560	−	6.93091i	0.320408	−	0.441003i
$248$	−7.23671	+	3.68729i	−0.459532	+	0.234143i
$249$	−7.60164	−	7.60164i	−0.481735	−	0.481735i
$250$	−9.26767	+	6.25382i	−0.586139	+	0.395527i
$251$	−12.1487			−0.766817			−0.383408	−	0.923579i	$-0.625250\pi$
$251$	−12.1487			−0.766817			−0.383408	+	0.923579i	$0.625250\pi$
$252$	0.115898	+	0.227462i	0.00730086	+	0.0143287i
$253$	9.77405	−	13.4528i	0.614489	−	0.845772i
$254$	−12.2812	−	8.92280i	−0.770589	−	0.559866i
$255$	15.7127	+	1.77504i	0.983966	+	0.111158i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$			16.2722i			1.01503i	0.861643	+	0.507515i	$0.169436\pi$
$257$			16.2722i			1.01503i	−0.861643	+	0.507515i	$0.830564\pi$
$258$	0.134216	−	0.847408i	0.00835594	−	0.0527573i
$259$	−8.83610	−	27.1947i	−0.549048	−	1.68980i
$260$	−0.0279599	+	2.41675i	−0.00173400	+	0.149880i
$261$	0.479918	−	0.244531i	0.0297062	−	0.0151361i
$262$	9.48876	−	18.6227i	0.586218	−	1.15052i
$263$	−14.6515	+	4.76055i	−0.903449	+	0.293548i	−0.723660	−	0.690157i	$-0.757542\pi$
$263$	−14.6515	+	4.76055i	−0.903449	+	0.293548i	−0.179789	+	0.983705i	$0.557542\pi$
$264$	−5.43726	−	1.76667i	−0.334640	−	0.108731i
$265$	4.16748	−	12.3386i	0.256006	−	0.757956i
$266$	15.7386	−	30.8888i	0.964997	−	1.89391i
$267$	1.89525	−	11.9662i	0.115988	−	0.732317i
$268$	0.467132			0.0285346
$269$	−1.91943	+	12.1188i	−0.117030	+	0.738897i	0.857474	+	0.514527i	$0.172032\pi$
$269$	−1.91943	+	12.1188i	−0.117030	+	0.738897i	−0.974504	+	0.224370i	$0.927968\pi$
$270$	10.5117	−	5.20369i	0.639722	−	0.316687i
$271$	−1.30991	−	0.951706i	−0.0795714	−	0.0578120i	0.547288	−	0.836944i	$-0.315660\pi$
$271$	−1.30991	−	0.951706i	−0.0795714	−	0.0578120i	−0.626860	+	0.779132i	$0.715660\pi$
$272$	−1.05201	+	3.98664i	−0.0637875	+	0.241725i
$273$	2.50562	−	7.71151i	0.151647	−	0.466722i
$274$			6.37974i			0.385414i
$275$	7.90805	−	14.6711i	0.476874	−	0.884700i
$276$	8.55600			0.515011
$277$	4.11647	+	8.07903i	0.247335	+	0.485422i	0.980979	−	0.194111i	$-0.0621823\pi$
$277$	4.11647	+	8.07903i	0.247335	+	0.485422i	−0.733645	+	0.679533i	$0.762182\pi$
$278$	−0.0521432	−	0.329219i	−0.00312734	−	0.0197453i
$279$	0.0741578	+	0.468214i	0.00443971	+	0.0280313i
$280$	1.41811	+	9.67685i	0.0847483	+	0.578303i
$281$	4.80405	+	6.61221i	0.286586	+	0.394451i	0.927901	−	0.372826i	$-0.121611\pi$
$281$	4.80405	+	6.61221i	0.286586	+	0.394451i	−0.641316	+	0.767277i	$0.721611\pi$
$282$	−8.67423	−	8.67423i	−0.516543	−	0.516543i
$283$	17.6437	+	2.79448i	1.04881	+	0.166115i	0.656968	−	0.753919i	$-0.271839\pi$
$283$	17.6437	+	2.79448i	1.04881	+	0.166115i	0.391840	+	0.920034i	$0.371839\pi$
$284$	12.4454	+	6.34126i	0.738500	+	0.376284i
$285$	−26.9228	−	14.1125i	−1.59477	−	0.835954i
$286$	−1.63569	−	3.21023i	−0.0967205	−	0.189825i
$287$	−10.9665	+	3.56322i	−0.647330	+	0.210330i
$288$	0.0180363	+	0.0555099i	0.00106280	+	0.00327095i
$289$	7.03224	+	15.4773i	0.413661	+	0.910431i
$290$	20.4171	−	2.99205i	1.19893	−	0.175699i
$291$	−18.6618	+	6.06360i	−1.09398	+	0.355454i
$292$	−1.43202	+	9.04143i	−0.0838027	+	0.529110i
$293$	−30.5678			−1.78579			−0.892895	−	0.450266i	$-0.851329\pi$
$293$	−30.5678			−1.78579			−0.892895	+	0.450266i	$0.851329\pi$
$294$	3.25466	−	20.5491i	0.189816	−	1.19845i
$295$	−17.1174	+	12.1365i	−0.996614	+	0.706613i
$296$	−1.02270	−	6.45706i	−0.0594431	−	0.375309i
$297$	−10.2774	+	14.1456i	−0.596353	+	0.820810i
$298$	−22.7802	−	7.40174i	−1.31962	−	0.428772i
$299$	3.81274	+	3.81274i	0.220496	+	0.220496i
$300$	8.49878	−	1.14520i	0.490678	−	0.0661183i
$301$	1.54713	−	1.54713i	0.0891751	−	0.0891751i
$302$	1.03064	−	3.17197i	0.0593064	−	0.182526i
$303$	−4.68011	+	0.741256i	−0.268865	+	0.0425840i
$304$	4.65882	−	6.41231i	0.267201	−	0.367771i
$305$	−6.23965	+	6.09692i	−0.357281	+	0.349109i
$306$	0.202323	+	0.130301i	0.0115661	+	0.00744881i
$307$	5.81784			0.332042			0.166021	−	0.986122i	$-0.446908\pi$
$307$	5.81784			0.332042			0.166021	+	0.986122i	$0.446908\pi$
$308$	−8.56961	−	11.7951i	−0.488299	−	0.672086i
$309$	19.4200	+	9.89501i	1.10477	+	0.562907i
$310$	−3.04836	+	17.9036i	−0.173135	+	1.01685i
$311$	7.48362	+	14.6874i	0.424357	+	0.832847i	0.999886	+	0.0150665i	$0.00479598\pi$
$311$	7.48362	+	14.6874i	0.424357	+	0.832847i	−0.575530	+	0.817781i	$0.695204\pi$
$312$	0.841621	−	1.65177i	0.0476474	−	0.0935133i
$313$	−7.87380	+	15.4532i	−0.445053	+	0.873467i	0.554105	+	0.832447i	$0.313061\pi$
$313$	−7.87380	+	15.4532i	−0.445053	+	0.873467i	−0.999158	+	0.0410197i	$0.986939\pi$
$314$	−14.5404	−	4.72448i	−0.820565	−	0.266618i
$315$	0.562739	+	0.0958151i	0.0317067	+	0.00539857i
$316$	−0.603438	+	1.18431i	−0.0339460	+	0.0666228i
$317$	13.5184	+	2.14110i	0.759268	+	0.120256i	0.524051	−	0.851687i	$-0.324420\pi$
$317$	13.5184	+	2.14110i	0.759268	+	0.120256i	0.235217	+	0.971943i	$0.424420\pi$
$318$	−7.06350	+	7.06350i	−0.396101	+	0.396101i
$319$	−24.8862	+	18.0809i	−1.39336	+	1.01234i
$320$	−0.0258678	+	2.23592i	−0.00144605	+	0.124992i
$321$	6.13092	−	8.43848i	0.342194	−	0.470990i
$322$	17.6521	+	12.8250i	0.983715	+	0.714711i
$323$	−1.83422	−	32.6284i	−0.102059	−	1.81549i
$324$	−8.82149			−0.490083
$325$	4.29757	+	3.27692i	0.238386	+	0.181771i
$326$	7.21768	−	7.21768i	0.399751	−	0.399751i
$327$	−4.33206	+	13.3327i	−0.239564	+	0.737301i
$328$	−2.60386	+	0.412411i	−0.143774	+	0.0227716i
$329$	−4.89381	−	30.8983i	−0.269805	−	1.70348i
$330$	−10.4285	+	7.39396i	−0.574071	+	0.407024i
$331$	14.4990	+	19.9562i	0.796938	+	1.09689i	0.993209	+	0.116341i	$0.0371166\pi$
$331$	14.4990	+	19.9562i	0.796938	+	1.09689i	−0.196272	+	0.980550i	$0.562883\pi$
$332$		−	6.26799i		−	0.344001i
$333$	−0.376876	−	0.0596913i	−0.0206527	−	0.00327107i
$334$	6.97131	−	13.6820i	0.381453	−	0.748644i
$335$	0.623699	−	0.837890i	0.0340763	−	0.0457788i
$336$	2.31814	−	7.13451i	0.126465	−	0.389219i
$337$	−7.12195	−	3.62881i	−0.387957	−	0.197674i	0.249122	−	0.968472i	$-0.419858\pi$
$337$	−7.12195	−	3.62881i	−0.387957	−	0.197674i	−0.637080	+	0.770798i	$0.719858\pi$
$338$	−11.2526	+	3.65620i	−0.612062	+	0.198871i
$339$	1.56994	−	4.83178i	0.0852674	−	0.262426i
$340$	5.74619	+	7.20981i	0.311631	+	0.391007i
$341$	−8.36608	−	25.7482i	−0.453049	−	1.39434i
$342$	−0.271919	−	0.374265i	−0.0147037	−	0.0202379i
$343$	15.8675	−	15.8675i	0.856765	−	0.856765i
$344$	0.404703	−	0.294034i	0.0218201	−	0.0158532i
$345$	11.4237	−	15.3468i	0.615031	−	0.826245i
$346$	3.35710	+	21.1959i	0.180479	+	1.13950i
$347$	−1.74307	−	11.0053i	−0.0935732	−	0.590798i	−0.989266	−	0.146125i	$-0.953320\pi$
$347$	−1.74307	−	11.0053i	−0.0935732	−	0.590798i	0.895693	−	0.444673i	$-0.146680\pi$
$348$	−15.0530	−	4.89101i	−0.806925	−	0.262186i
$349$			5.07374i			0.271591i	0.990737	+	0.135795i	$0.0433590\pi$
$349$			5.07374i			0.271591i	−0.990737	+	0.135795i	$0.956641\pi$
$350$	19.2507	+	10.3766i	1.02899	+	0.554651i
$351$	−4.00908	−	4.00908i	−0.213989	−	0.213989i
$352$	−1.51330	−	2.97003i	−0.0806593	−	0.158303i
$353$	1.85753	+	1.34957i	0.0988663	+	0.0718306i	0.636120	−	0.771590i	$-0.280538\pi$
$353$	1.85753	+	1.34957i	0.0988663	+	0.0718306i	−0.537254	+	0.843421i	$0.680538\pi$
$354$	15.8966	−	2.51777i	0.844893	−	0.133818i
$355$	27.9910	−	13.8566i	1.48561	−	0.735432i
$356$	5.71476	−	4.15202i	0.302882	−	0.220056i
$357$	−11.1939	−	28.8335i	−0.592445	−	1.52603i
$358$	12.8881	−	9.36375i	0.681157	−	0.494890i
$359$	22.5468	−	7.32589i	1.18997	−	0.386646i	0.353911	−	0.935279i	$-0.384852\pi$
$359$	22.5468	−	7.32589i	1.18997	−	0.386646i	0.836063	+	0.548633i	$0.184852\pi$
$360$	0.123649	+	0.0417635i	0.00651688	+	0.00220113i
$361$	−13.5418	+	41.6775i	−0.712728	+	2.19355i
$362$	10.5050	+	5.35256i	0.552130	+	0.281325i
$363$	0.0865365	−	0.169837i	0.00454199	−	0.00891416i
$364$	4.21230	−	2.14628i	0.220785	−	0.112495i
$365$	14.3055	+	14.6404i	0.748786	+	0.766315i
$366$	6.36391	−	2.06776i	0.332647	−	0.108084i
$367$	10.2632	+	1.62553i	0.535736	+	0.0848522i	0.418439	−	0.908245i	$-0.362577\pi$
$367$	10.2632	+	1.62553i	0.535736	+	0.0848522i	0.117296	+	0.993097i	$0.462577\pi$
$368$	3.52745	+	3.52745i	0.183881	+	0.183881i
$369$	−0.0240710	+	0.151978i	−0.00125309	+	0.00791167i
$370$	−12.9474	−	6.78685i	−0.673105	−	0.352832i
$371$	−25.1608	+	3.98507i	−1.30628	+	0.206895i
$372$	8.18792	−	11.2697i	0.424524	−	0.584307i
$373$	5.26207	−	16.1950i	0.272460	−	0.838545i	−0.717421	−	0.696640i	$-0.754677\pi$
$373$	5.26207	−	16.1950i	0.272460	−	0.838545i	0.989880	−	0.141904i	$-0.0453226\pi$
$374$	−12.5766	−	5.54236i	−0.650322	−	0.286589i
$375$	9.29316	−	16.7732i	0.479897	−	0.866166i
$376$		−	7.15240i		−	0.368857i
$377$	−4.52840	−	8.88748i	−0.233224	−	0.457729i
$378$	−18.5611	−	13.4855i	−0.954682	−	0.693617i
$379$	−13.0581	+	2.06820i	−0.670749	+	0.106236i	−0.482515	−	0.875888i	$-0.660277\pi$
$379$	−13.0581	+	2.06820i	−0.670749	+	0.106236i	−0.188235	+	0.982124i	$0.560277\pi$
$380$	−5.28141	−	16.9180i	−0.270930	−	0.867874i
$381$	25.7156	+	4.07295i	1.31745	+	0.208664i
$382$			8.62696i			0.441394i
$383$	−16.4060	−	22.5809i	−0.838308	−	1.15383i	−0.986319	−	0.164846i	$-0.947287\pi$
$383$	−16.4060	−	22.5809i	−0.838308	−	1.15383i	0.148011	−	0.988986i	$-0.452713\pi$
$384$	0.778648	−	1.52818i	0.0397352	−	0.0779847i
$385$	−32.5986	−	0.377140i	−1.66138	−	0.0192208i
$386$	−10.4893	−	20.5864i	−0.533891	−	1.04782i
$387$	−0.00902246	−	0.0277683i	−0.000458637	−	0.00141154i
$388$	−10.1938	−	5.19398i	−0.517510	−	0.263684i
$389$	−26.3221	−	8.55257i	−1.33458	−	0.433632i	−0.447105	−	0.894482i	$-0.647545\pi$
$389$	−26.3221	−	8.55257i	−1.33458	−	0.433632i	−0.887478	+	0.460849i	$0.847545\pi$
$390$	−1.83907	−	3.71500i	−0.0931248	−	0.188117i
$391$	20.4638	+	2.07231i	1.03490	+	0.104801i
$392$	9.81379	−	7.13013i	0.495671	−	0.360126i
$393$			35.8474i			1.80826i
$394$	2.50422	−	15.8110i	0.126161	−	0.796547i
$395$	1.31860	+	2.66364i	0.0663461	+	0.134022i
$396$	−0.192160	+	0.0304352i	−0.00965641	+	0.00152943i
$397$	−1.02491	−	6.47104i	−0.0514389	−	0.324772i	−0.999967	−	0.00808045i	$-0.997428\pi$
$397$	−1.02491	−	6.47104i	−0.0514389	−	0.324772i	0.948528	−	0.316692i	$-0.102572\pi$
$398$	1.93196	−	0.984383i	0.0968404	−	0.0493427i
$399$			59.4586i			2.97665i
$400$	3.97601	+	3.03172i	0.198800	+	0.151586i
$401$	−14.2562	−	14.2562i	−0.711922	−	0.711922i	0.255015	−	0.966937i	$-0.417920\pi$
$401$	−14.2562	−	14.2562i	−0.711922	−	0.711922i	−0.966937	+	0.255015i	$0.917920\pi$
$402$	−0.713862	+	0.363731i	−0.0356042	+	0.0181413i
$403$	8.67074	−	1.37331i	0.431920	−	0.0684094i
$404$	−2.23511	−	1.62390i	−0.111201	−	0.0807922i
$405$	−11.7782	+	15.8230i	−0.585262	+	0.786253i
$406$	−23.7249	−	32.6545i	−1.17745	−	1.62062i
$407$	21.7918			1.08018
$408$	−1.49652	−	6.91145i	−0.0740889	−	0.342168i
$409$	−3.66342	−	11.2748i	−0.181144	−	0.557505i	0.818716	−	0.574198i	$-0.194686\pi$
$409$	−3.66342	−	11.2748i	−0.181144	−	0.557505i	−0.999861	+	0.0166931i	$0.994686\pi$
$410$	−2.73685	+	5.22115i	−0.135163	+	0.257854i
$411$	−4.96757	−	9.74940i	−0.245032	−	0.480903i
$412$	3.92697	+	12.0860i	0.193468	+	0.595433i
$413$	36.5707	+	18.6337i	1.79953	+	0.916905i
$414$	0.259431	−	0.132187i	0.0127503	−	0.00649662i
$415$	−11.2428	−	8.36881i	−0.551889	−	0.410809i
$416$	1.02797	−	0.334009i	0.0504005	−	0.0163761i
$417$	0.336030	+	0.462506i	0.0164555	+	0.0226490i
$418$	18.6819	+	18.6819i	0.913762	+	0.913762i
$419$	25.3541	+	4.01570i	1.23863	+	0.196180i	0.741176	−	0.671311i	$-0.234269\pi$
$419$	25.3541	+	4.01570i	1.23863	+	0.196180i	0.497453	+	0.867491i	$0.334269\pi$
$420$	−9.70199	−	13.6838i	−0.473409	−	0.667701i
$421$	16.7290	+	12.1543i	0.815320	+	0.592365i	0.915368	−	0.402618i	$-0.131900\pi$
$421$	16.7290	+	12.1543i	0.815320	+	0.592365i	−0.100048	+	0.994983i	$0.531900\pi$
$422$	4.11192	−	0.651263i	0.200165	−	0.0317030i
$423$	−0.397029	−	0.129002i	−0.0193042	−	0.00627231i
$424$	−5.82426			−0.282851
$425$	20.6043	−	0.680580i	0.999455	−	0.0330130i
$426$	−23.9565			−1.16069
$427$	16.2290	+	5.27314i	0.785378	+	0.255185i
$428$	6.00665	−	0.951360i	0.290342	−	0.0459857i
$429$	4.99927	+	3.63218i	0.241367	+	0.175363i
$430$	0.0129401	−	1.11850i	0.000624028	−	0.0539387i
$431$	−26.9239	−	4.26433i	−1.29688	−	0.205405i	−0.530440	−	0.847722i	$-0.677973\pi$
$431$	−26.9239	−	4.26433i	−1.29688	−	0.205405i	−0.766439	+	0.642317i	$0.777973\pi$
$432$	−3.70910	−	3.70910i	−0.178454	−	0.178454i
$433$	1.74314	+	2.39923i	0.0837701	+	0.115300i	0.848845	−	0.528641i	$-0.177298\pi$
$433$	1.74314	+	2.39923i	0.0837701	+	0.115300i	−0.765075	+	0.643941i	$0.777298\pi$
$434$	33.7855	−	10.9776i	1.62176	−	0.526940i
$435$	−28.8712	+	20.4701i	−1.38427	+	0.981466i
$436$	−7.28281	+	3.71078i	−0.348783	+	0.177714i
$437$	−35.2301	−	17.9506i	−1.68529	−	0.858696i
$438$	−4.85170	−	14.9320i	−0.231823	−	0.713478i
$439$	−2.63317	−	5.16788i	−0.125674	−	0.246649i	0.819593	−	0.572946i	$-0.194199\pi$
$439$	−2.63317	−	5.16788i	−0.125674	−	0.246649i	−0.945268	+	0.326296i	$0.894199\pi$
$440$	−7.34782	−	1.25108i	−0.350294	−	0.0596430i
$441$	−0.218789	−	0.673363i	−0.0104185	−	0.0320649i
$442$	2.41301	−	3.74678i	0.114775	−	0.178216i
$443$	−20.3798			−0.968275			−0.484137	−	0.874992i	$-0.660866\pi$
$443$	−20.3798			−0.968275			−0.484137	+	0.874992i	$0.660866\pi$
$444$	6.59064	+	9.07124i	0.312778	+	0.430502i
$445$	0.182726	−	15.7942i	0.00866204	−	0.748715i
$446$	−0.760521	−	0.552551i	−0.0360117	−	0.0261641i
$447$	40.5757	−	6.42656i	1.91916	−	0.303966i
$448$	3.89712	−	1.98568i	0.184122	−	0.0938147i
$449$	−4.46526	−	4.46526i	−0.210729	−	0.210729i	0.593848	−	0.804577i	$-0.297608\pi$
$449$	−4.46526	−	4.46526i	−0.210729	−	0.210729i	−0.804577	+	0.593848i	$0.797608\pi$
$450$	0.240003	−	0.166027i	0.0113139	−	0.00782658i
$451$		−	8.78773i		−	0.413798i
$452$	2.63929	−	1.34479i	0.124142	−	0.0632534i
$453$	0.894848	+	5.64985i	0.0420436	+	0.265453i
$454$	6.04555	−	0.957520i	0.283732	−	0.0449387i
$455$	1.77437	−	10.4212i	0.0831840	−	0.488554i
$456$	−2.12659	+	13.4268i	−0.0995867	+	0.628765i
$457$		−	26.6025i		−	1.24441i	−0.782854	−	0.622206i	$-0.786237\pi$
$457$		−	26.6025i		−	1.24441i	0.782854	−	0.622206i	$-0.213763\pi$
$458$	−9.19738	+	6.68229i	−0.429765	+	0.312243i
$459$	−21.5175	−	2.17902i	−1.00435	−	0.101708i
$460$	11.0369	−	1.61742i	0.514598	−	0.0754127i
$461$	20.6900	+	6.72259i	0.963630	+	0.313102i	0.748242	−	0.663426i	$-0.230898\pi$
$461$	20.6900	+	6.72259i	0.963630	+	0.313102i	0.215388	+	0.976529i	$0.430898\pi$
$462$	22.2801	+	11.3523i	1.03657	+	0.528156i
$463$	−0.268660	−	0.826851i	−0.0124857	−	0.0384270i	0.944620	−	0.328167i	$-0.106431\pi$
$463$	−0.268660	−	0.826851i	−0.0124857	−	0.0384270i	−0.957105	+	0.289740i	$0.906431\pi$
$464$	−4.18957	−	8.22249i	−0.194496	−	0.381719i
$465$	−9.28213	−	29.7335i	−0.430448	−	1.37886i
$466$	5.28943	−	10.3811i	0.245028	−	0.480894i
$467$	−20.5708	−	28.3133i	−0.951905	−	1.31018i	−0.950676	−	0.310186i	$-0.899609\pi$
$467$	−20.5708	−	28.3133i	−0.951905	−	1.31018i	−0.00122910	−	0.999999i	$-0.500391\pi$
$468$		−	0.0630870i		−	0.00291620i
$469$	−2.01801	−	0.319621i	−0.0931829	−	0.0147587i
$470$	−12.8292	−	9.54964i	−0.591766	−	0.440492i
$471$	25.8991	−	4.10202i	1.19337	−	0.189011i
$472$	7.59184	+	5.51579i	0.349443	+	0.253885i
$473$	0.757015	+	1.48573i	0.0348076	+	0.0683137i
$474$		−	2.27971i		−	0.104711i
$475$	−37.3972	−	13.1151i	−1.71590	−	0.601763i
$476$	7.27242	−	16.5024i	0.333331	−	0.756388i
$477$	−0.105048	+	0.323304i	−0.00480981	+	0.0148031i
$478$	−9.75463	+	13.4261i	−0.446166	+	0.614095i
$479$	36.8154	−	5.83099i	1.68214	−	0.266425i	0.759056	−	0.651025i	$-0.225661\pi$
$479$	36.8154	−	5.83099i	1.68214	−	0.266425i	0.923083	+	0.384601i	$0.125661\pi$
$480$	−1.70146	−	3.43703i	−0.0776608	−	0.156878i
$481$	−1.10541	+	6.97928i	−0.0504023	+	0.318228i
$482$	3.21867	+	3.21867i	0.146606	+	0.146606i
$483$	−36.9619	−	5.85418i	−1.68182	−	0.266375i
$484$	0.105697	−	0.0343432i	0.00480443	−	0.00156105i
$485$	−22.9268	+	11.3496i	−1.04105	+	0.515360i
$486$	−0.540375	+	0.275335i	−0.0245119	+	0.0124894i
$487$	13.6126	−	26.7163i	0.616846	−	1.21063i	−0.345401	−	0.938455i	$-0.612257\pi$
$487$	13.6126	−	26.7163i	0.616846	−	1.21063i	0.962248	−	0.272174i	$-0.0877427\pi$
$488$	3.47620	+	1.77121i	0.157360	+	0.0801789i
$489$	−5.40990	+	16.6500i	−0.244644	+	0.752938i
$490$	0.313790	−	27.1228i	0.0141756	−	1.22528i
$491$	20.6676	−	6.71533i	0.932718	−	0.303058i	0.197044	−	0.980395i	$-0.436866\pi$
$491$	20.6676	−	6.71533i	0.932718	−	0.303058i	0.735674	+	0.677336i	$0.236866\pi$
$492$	3.65805	−	2.65773i	0.164917	−	0.119820i
$493$	−34.8183	−	15.3440i	−1.56814	−	0.691058i
$494$	−6.93091	+	5.03560i	−0.311836	+	0.226562i
$495$	−0.201975	+	0.385312i	−0.00907809	+	0.0173185i
$496$	8.02196	−	1.27055i	0.360197	−	0.0570495i
$497$	−49.4253	−	35.9096i	−2.21703	−	1.61077i
$498$	4.88056	+	9.57863i	0.218703	+	0.429229i
$499$	−6.91754	−	6.91754i	−0.309672	−	0.309672i	0.535110	−	0.844782i	$-0.320270\pi$
$499$	−6.91754	−	6.91754i	−0.309672	−	0.309672i	−0.844782	+	0.535110i	$0.820270\pi$
$500$	10.7466	−	3.08387i	0.480603	−	0.137915i
$501$			26.3367i			1.17664i
$502$	11.5541	+	3.75414i	0.515683	+	0.167556i
$503$	1.43613	+	9.06736i	0.0640338	+	0.404294i	0.998798	+	0.0490239i	$0.0156110\pi$
$503$	1.43613	+	9.06736i	0.0640338	+	0.404294i	−0.934764	+	0.355270i	$0.884389\pi$
$504$	−0.0399356	−	0.252143i	−0.00177887	−	0.0112314i
$505$	−5.89703	+	1.84092i	−0.262414	+	0.0819197i
$506$	−13.4528	+	9.77405i	−0.598051	+	0.434509i
$507$	14.3492	−	14.3492i	0.637269	−	0.637269i
$508$	8.92280	+	12.2812i	0.395885	+	0.544889i
$509$	1.67538	+	5.15628i	0.0742597	+	0.228548i	0.981296	−	0.192504i	$-0.0616609\pi$
$509$	1.67538	+	5.15628i	0.0742597	+	0.228548i	−0.907036	+	0.421052i	$0.861661\pi$
$510$	−14.3951	−	6.54365i	−0.637427	−	0.289758i
$511$	12.3727	−	38.0791i	0.547334	−	1.68452i
$512$	0.951057	−	0.309017i	0.0420312	−	0.0136568i
$513$	37.0443	+	18.8750i	1.63555	+	0.833353i
$514$	5.02838	−	15.4758i	0.221792	−	0.682606i
$515$	26.9217	+	9.09302i	1.18631	+	0.400686i
$516$	−0.389511	+	0.764458i	−0.0171473	+	0.0336534i
$517$	23.5478	+	3.72961i	1.03563	+	0.164028i
$518$			28.5942i			1.25636i
$519$	−21.6344	−	29.7772i	−0.949644	−	1.30707i
$520$	0.773408	−	2.28982i	0.0339162	−	0.100415i
$521$	−2.60154	−	16.4255i	−0.113976	−	0.719613i	−0.976807	−	0.214122i	$-0.931311\pi$
$521$	−2.60154	−	16.4255i	−0.113976	−	0.719613i	0.862831	−	0.505492i	$-0.168689\pi$
$522$	−0.531994	+	0.0842595i	−0.0232847	+	0.00368794i
$523$	12.4019	−	38.1692i	0.542299	−	1.66902i	−0.185028	−	0.982733i	$-0.559238\pi$
$523$	12.4019	−	38.1692i	0.542299	−	1.66902i	0.727327	−	0.686291i	$-0.240762\pi$
$524$	−14.7791	+	14.7791i	−0.645628	+	0.645628i
$525$	−37.4983	−	0.867767i	−1.63656	−	0.0378725i
$526$	15.4055			0.671711
$527$	22.3130	−	24.9711i	0.971969	−	1.08776i
$528$	4.62521	+	3.36041i	0.201286	+	0.146243i
$529$	1.10849	−	1.52570i	0.0481952	−	0.0663349i
$530$	−7.77636	+	10.4469i	−0.337783	+	0.453785i
$531$	0.443109	−	0.321938i	0.0192293	−	0.0139709i
$532$	−24.5135	+	24.5135i	−1.06279	+	1.06279i
$533$	2.81445	+	0.445764i	0.121907	+	0.0193082i
$534$	−5.50024	+	10.7948i	−0.238019	+	0.467138i
$535$	6.31344	−	12.0443i	0.272954	−	0.520720i
$536$	−0.444269	−	0.144352i	−0.0191895	−	0.00623504i
$537$	−12.4043	+	24.3448i	−0.535285	+	1.05056i
$538$	5.57040	−	10.9325i	0.240157	−	0.471335i
$539$	18.3571	+	36.0279i	0.790698	+	1.55183i
$540$	−11.6053	+	1.70071i	−0.499411	+	0.0731870i
$541$	−33.0446	−	16.8371i	−1.42070	−	0.723882i	−0.436295	−	0.899804i	$-0.643709\pi$
$541$	−33.0446	−	16.8371i	−1.42070	−	0.723882i	−0.984404	+	0.175922i	$0.943709\pi$
$542$	0.951706	+	1.30991i	0.0408793	+	0.0562655i
$543$	−20.2213			−0.867780
$544$	2.23246	−	3.46643i	0.0957159	−	0.148622i
$545$	−3.06778	+	18.0176i	−0.131409	+	0.771790i
$546$	−4.76598	+	6.55980i	−0.203965	+	0.280734i
$547$	−10.1881	+	1.61364i	−0.435612	+	0.0689941i	−0.370389	−	0.928877i	$-0.620776\pi$
$547$	−10.1881	+	1.61364i	−0.435612	+	0.0689941i	−0.0652225	+	0.997871i	$0.520776\pi$
$548$	1.97145	−	6.06749i	0.0842161	−	0.259190i
$549$	0.161017	−	0.161017i	0.00687205	−	0.00687205i
$550$	−12.0546	+	11.5093i	−0.514011	+	0.490759i
$551$	51.7207	+	51.7207i	2.20338	+	2.20338i
$552$	−8.13724	−	2.64395i	−0.346344	−	0.112534i
$553$	3.41718	−	4.70334i	0.145313	−	0.200006i
$554$	−1.41844	−	8.95567i	−0.0602637	−	0.380490i
$555$	25.0706	+	0.290047i	1.06419	+	0.0123118i
$556$	−0.0521432	+	0.329219i	−0.00221136	+	0.0139620i
$557$	−30.1976			−1.27951			−0.639757	−	0.768577i	$-0.720965\pi$
$557$	−30.1976			−1.27951			−0.639757	+	0.768577i	$0.720965\pi$
$558$	0.0741578	−	0.468214i	0.00313935	−	0.0198211i
$559$	−0.514233	+	0.167085i	−0.0217498	+	0.00706692i
$560$	1.64161	−	9.64146i	0.0693706	−	0.407426i
$561$	23.5349	−	1.32303i	0.993645	−	0.0558582i
$562$	−2.52564	−	7.77312i	−0.106538	−	0.327889i
$563$	13.3865	−	4.34952i	0.564172	−	0.183311i	−0.0130257	−	0.999915i	$-0.504146\pi$
$563$	13.3865	−	4.34952i	0.564172	−	0.183311i	0.577197	+	0.816605i	$0.304146\pi$
$564$	5.56920	+	10.9302i	0.234505	+	0.460243i
$565$	1.11176	−	6.52958i	0.0467723	−	0.274702i
$566$	−15.9166	−	8.10990i	−0.669024	−	0.340885i
$567$	38.1088	+	6.03584i	1.60042	+	0.253482i
$568$	−9.87674	−	9.87674i	−0.414419	−	0.414419i
$569$	6.36215	+	8.75675i	0.266715	+	0.367102i	0.921277	−	0.388906i	$-0.127147\pi$
$569$	6.36215	+	8.75675i	0.266715	+	0.367102i	−0.654562	+	0.756008i	$0.727147\pi$
$570$	21.2441	+	21.7414i	0.889817	+	0.910647i
$571$	−6.06171	−	38.2722i	−0.253675	−	1.60164i	−0.704951	−	0.709256i	$-0.749031\pi$
$571$	−6.06171	−	38.2722i	−0.253675	−	1.60164i	0.451276	−	0.892384i	$-0.350969\pi$
$572$	0.563621	+	3.55856i	0.0235662	+	0.148791i
$573$	−6.71737	−	13.1836i	−0.280622	−	0.550752i
$574$	11.5308			0.481288
$575$	11.8350	−	21.9563i	0.493552	−	0.915642i
$576$		−	0.0583666i		−	0.00243194i
$577$	−11.3328	+	34.8786i	−0.471789	+	1.45202i	0.378451	+	0.925621i	$0.376457\pi$
$577$	−11.3328	+	34.8786i	−0.471789	+	1.45202i	−0.850240	+	0.526395i	$0.823543\pi$
$578$	−1.90531	−	16.8929i	−0.0792502	−	0.702652i
$579$	32.0591	+	23.2923i	1.33233	+	0.967996i
$580$	−20.3424	−	3.46361i	−0.844671	−	0.143818i
$581$	−4.28868	+	27.0777i	−0.177925	+	1.12337i
$582$	19.6222			0.813367
$583$	3.03705	−	19.1752i	0.125782	−	0.794155i
$584$	4.15589	−	8.15639i	0.171972	−	0.337514i
$585$	−0.113159	−	0.0842317i	−0.00467853	−	0.00348255i
$586$	29.0717	+	9.44597i	1.20094	+	0.390209i
$587$	−3.67699	+	1.19473i	−0.151765	+	0.0493116i	−0.383915	−	0.923369i	$-0.625424\pi$
$587$	−3.67699	+	1.19473i	−0.151765	+	0.0493116i	0.232149	+	0.972680i	$0.425424\pi$
$588$	−9.44539	+	18.5376i	−0.389521	+	0.764479i
$589$	−57.3586	+	29.2256i	−2.36342	+	1.20422i
$590$	20.0300	−	6.25291i	0.824622	−	0.257428i
$591$	8.48430	+	26.1120i	0.348998	+	1.07410i
$592$	−1.02270	+	6.45706i	−0.0420326	+	0.265383i
$593$			26.5920i			1.09200i	0.837785	+	0.546000i	$0.183850\pi$
$593$			26.5920i			1.09200i	−0.837785	+	0.546000i	$0.816150\pi$
$594$	14.1456	−	10.2774i	0.580400	−	0.421685i
$595$	−19.8904	−	35.0780i	−0.815427	−	1.43806i
$596$	19.3780	+	14.0790i	0.793755	+	0.576696i
$597$	−2.18590	+	3.00863i	−0.0894629	+	0.123135i
$598$	−2.44793	−	4.80433i	−0.100103	−	0.196464i
$599$	−5.71293			−0.233424			−0.116712	−	0.993166i	$-0.537235\pi$
$599$	−5.71293			−0.233424			−0.116712	+	0.993166i	$0.537235\pi$
$600$	−8.43671	−	1.53712i	−0.344427	−	0.0627525i
$601$	12.7585	+	12.7585i	0.520428	+	0.520428i	0.917701	−	0.397273i	$-0.130043\pi$
$601$	12.7585	+	12.7585i	0.520428	+	0.520428i	−0.397273	+	0.917701i	$0.630043\pi$
$602$	−1.94950	+	0.993318i	−0.0794556	+	0.0404846i
$603$	−0.0160259	+	0.0220577i	−0.000652625	+	0.000898261i
$604$	−1.96039	+	2.69824i	−0.0797669	+	0.109790i
$605$	0.0795227	−	0.235443i	0.00323306	−	0.00957210i
$606$	4.68011	+	0.741256i	0.190116	+	0.0301115i
$607$	7.31073	−	7.31073i	0.296733	−	0.296733i	−0.543000	−	0.839733i	$-0.682711\pi$
$607$	7.31073	−	7.31073i	0.296733	−	0.296733i	0.839733	+	0.543000i	$0.182711\pi$
$608$	−6.41231	+	4.65882i	−0.260054	+	0.188940i
$609$	61.6823	+	31.4287i	2.49949	+	1.27356i
$610$	7.81831	−	3.87036i	0.316554	−	0.156706i
$611$	−2.38896	+	7.35247i	−0.0966471	+	0.297449i
$612$	−0.152156	−	0.186445i	−0.00615054	−	0.00753659i
$613$	7.69564	+	23.6847i	0.310824	+	0.956617i	0.977439	+	0.211216i	$0.0677422\pi$
$613$	7.69564	+	23.6847i	0.310824	+	0.956617i	−0.666616	+	0.745402i	$0.732258\pi$
$614$	−5.53310	−	1.79781i	−0.223298	−	0.0725538i
$615$	0.116964	−	10.1099i	0.00471643	−	0.407671i
$616$	4.50531	+	13.8659i	0.181524	+	0.558674i
$617$	0.944033	−	5.96039i	0.0380053	−	0.239956i	−0.961371	−	0.275254i	$-0.911238\pi$
$617$	0.944033	−	5.96039i	0.0380053	−	0.239956i	0.999377	+	0.0352979i	$0.0112380\pi$
$618$	−15.4118	−	15.4118i	−0.619955	−	0.619955i
$619$	−10.6554	−	1.68765i	−0.428277	−	0.0678325i	−0.0614251	−	0.998112i	$-0.519565\pi$
$619$	−10.6554	−	1.68765i	−0.428277	−	0.0678325i	−0.366852	+	0.930279i	$0.619565\pi$
$620$	8.43168	−	16.0853i	0.338624	−	0.646002i
$621$	−15.3808	+	21.1699i	−0.617210	+	0.849517i
$622$	−2.57868	−	16.2811i	−0.103396	−	0.652814i
$623$	−27.5286	+	14.0265i	−1.10291	+	0.561961i
$624$	−1.31086	+	1.31086i	−0.0524762	+	0.0524762i
$625$	8.81701	−	23.3936i	0.352680	−	0.935744i
$626$	12.2637	−	12.2637i	0.490157	−	0.490157i
$627$	−43.0960	−	14.0027i	−1.72109	−	0.559215i
$628$	12.3688	+	8.98649i	0.493570	+	0.358600i
$629$	13.5660	+	23.2924i	0.540913	+	0.928728i
$630$	−0.505588	−	0.265021i	−0.0201431	−	0.0105587i
$631$	−1.65889	−	2.28327i	−0.0660394	−	0.0908954i	0.774720	−	0.632305i	$-0.217891\pi$
$631$	−1.65889	−	2.28327i	−0.0660394	−	0.0908954i	−0.840759	+	0.541409i	$0.817891\pi$
$632$	0.939876	−	0.939876i	0.0373863	−	0.0373863i
$633$	−5.77665	+	4.19698i	−0.229601	+	0.166815i
$634$	−12.1951	−	6.21372i	−0.484330	−	0.246778i
$635$	33.9421	+	0.392683i	1.34695	+	0.0155831i
$636$	8.90052	−	4.53504i	0.352929	−	0.179826i
$637$	−12.4698	+	4.05170i	−0.494073	+	0.160534i
$638$	29.2555	−	9.50570i	1.15824	−	0.376334i
$639$	−0.726396	+	0.370117i	−0.0287358	+	0.0146416i
$640$	0.715539	−	2.11849i	0.0282841	−	0.0837407i
$641$	−24.7049	−	12.5878i	−0.975785	−	0.497187i	−0.108013	−	0.994150i	$-0.534449\pi$
$641$	−24.7049	−	12.5878i	−0.975785	−	0.497187i	−0.867772	+	0.496962i	$0.834449\pi$
$642$	−8.43848	+	6.13092i	−0.333040	+	0.241968i
$643$	−31.0846	+	31.0846i	−1.22586	+	1.22586i	−0.260338	+	0.965518i	$0.583834\pi$
$643$	−31.0846	+	31.0846i	−1.22586	+	1.22586i	−0.965518	+	0.260338i	$0.916166\pi$
$644$	−12.8250	−	17.6521i	−0.505377	−	0.695592i
$645$	0.851139	+	1.71934i	0.0335136	+	0.0676990i
$646$	−8.33829	+	31.5983i	−0.328066	+	1.24322i
$647$	22.6939	+	16.4881i	0.892189	+	0.648213i	0.936448	−	0.350807i	$-0.114093\pi$
$647$	22.6939	+	16.4881i	0.892189	+	0.648213i	−0.0442586	+	0.999020i	$0.514093\pi$
$648$	8.38974	+	2.72599i	0.329580	+	0.107087i
$649$	−22.1184	+	22.1184i	−0.868223	+	0.868223i
$650$	−3.07461	−	4.44455i	−0.120596	−	0.174330i
$651$	−43.0827	+	43.0827i	−1.68854	+	1.68854i
$652$	−9.09481	+	4.63404i	−0.356180	+	0.181483i
$653$	3.25771	+	20.5684i	0.127484	+	0.804902i	0.965718	+	0.259592i	$0.0835881\pi$
$653$	3.25771	+	20.5684i	0.127484	+	0.804902i	−0.838234	+	0.545310i	$0.816412\pi$
$654$	8.24007	−	11.3415i	0.322212	−	0.443487i
$655$	6.77657	+	46.2417i	0.264782	+	1.80681i
$656$	2.60386	+	0.412411i	0.101664	+	0.0161019i
$657$	−0.377804	−	0.377804i	−0.0147395	−	0.0147395i
$658$	−4.89381	+	30.8983i	−0.190781	+	1.20454i
$659$	−11.0327	−	33.9551i	−0.429772	−	1.32270i	−0.898350	−	0.439281i	$-0.855233\pi$
$659$	−11.0327	−	33.9551i	−0.429772	−	1.32270i	0.468577	−	0.883422i	$-0.344767\pi$
$660$	12.2030	−	3.80948i	0.475000	−	0.148284i
$661$	39.2641	+	12.7577i	1.52720	+	0.496216i	0.947810	−	0.318837i	$-0.103292\pi$
$661$	39.2641	+	12.7577i	1.52720	+	0.496216i	0.579386	+	0.815053i	$0.303292\pi$
$662$	−7.62258	−	23.4599i	−0.296260	−	0.911795i
$663$	−0.770102	+	7.60464i	−0.0299083	+	0.295340i
$664$	−1.93692	+	5.96121i	−0.0751669	+	0.231340i
$665$	11.2400	+	76.6992i	0.435869	+	2.97427i
$666$	0.339985	+	0.173231i	0.0131742	+	0.00671257i
$667$	−37.2440	+	27.0594i	−1.44209	+	1.04774i
$668$	−10.8581	+	10.8581i	−0.420111	+	0.420111i
$669$	1.59246	+	0.252221i	0.0615680	+	0.00975141i
$670$	−0.852095	+	0.604147i	−0.0329193	+	0.0233402i
$671$	−7.64401	+	10.5211i	−0.295094	+	0.406162i
$672$	−4.40937	+	6.06897i	−0.170095	+	0.234116i
$673$	−8.54254	+	4.35264i	−0.329291	+	0.167782i	−0.610818	−	0.791771i	$-0.709159\pi$
$673$	−8.54254	+	4.35264i	−0.329291	+	0.167782i	0.281527	+	0.959553i	$0.409159\pi$
$674$	5.65201	+	5.65201i	0.217707	+	0.217707i
$675$	−12.4444	+	23.0870i	−0.478985	+	0.888618i
$676$	11.8317			0.455066
$677$	−7.72886	−	15.1688i	−0.297044	−	0.582982i	0.693455	−	0.720500i	$-0.256088\pi$
$677$	−7.72886	−	15.1688i	−0.297044	−	0.582982i	−0.990499	+	0.137518i	$0.956088\pi$
$678$	−2.98620	+	4.11015i	−0.114684	+	0.157850i
$679$	40.4832	+	29.4127i	1.55360	+	1.12876i
$680$	−3.23699	−	8.63261i	−0.124133	−	0.331045i
$681$	−8.49313	+	6.17062i	−0.325457	+	0.236459i
$682$			27.0732i			1.03669i
$683$	1.43984	−	9.09080i	0.0550940	−	0.347850i	−0.944707	−	0.327915i	$-0.893654\pi$
$683$	1.43984	−	9.09080i	0.0550940	−	0.347850i	0.999801	−	0.0199350i	$-0.00634593\pi$
$684$	0.142956	+	0.439974i	0.00546607	+	0.0168228i
$685$	−8.25099	−	11.6373i	−0.315254	−	0.444638i
$686$	−19.9942	+	10.1876i	−0.763383	+	0.388963i
$687$	8.85213	−	17.3733i	0.337730	−	0.662832i
$688$	−0.475756	+	0.154583i	−0.0181380	+	0.00589341i
$689$	5.98718	+	1.94535i	0.228093	+	0.0741120i
$690$	−15.6070	+	11.0656i	−0.594148	+	0.421259i
$691$	−13.7655	+	27.0164i	−0.523666	+	1.02775i	0.466057	+	0.884755i	$0.345674\pi$
$691$	−13.7655	+	27.0164i	−0.523666	+	1.02775i	−0.989723	+	0.142998i	$0.954326\pi$
$692$	3.35710	−	21.1959i	0.127618	−	0.805746i
$693$	0.850955			0.0323251
$694$	−1.74307	+	11.0053i	−0.0661662	+	0.417757i
$695$	0.520898	+	0.533092i	0.0197588	+	0.0202213i
$696$	12.8048	+	9.30326i	0.485366	+	0.352639i
$697$	9.39283	−	5.47060i	0.355779	−	0.207214i
$698$	1.56787	−	4.82541i	0.0593448	−	0.182644i
$699$			19.9828i			0.755818i
$700$	−15.1020	−	15.8175i	−0.570801	−	0.597845i
$701$	34.5776			1.30598			0.652989	−	0.757368i	$-0.273515\pi$
$701$	34.5776			1.30598			0.652989	+	0.757368i	$0.273515\pi$
$702$	2.57399	+	5.05173i	0.0971488	+	0.190665i
$703$	−8.10595	−	51.1790i	−0.305722	−	1.93025i
$704$	0.521449	+	3.29230i	0.0196528	+	0.124083i
$705$	27.0411	+	4.60418i	1.01843	+	0.173403i
$706$	−1.34957	−	1.85753i	−0.0507919	−	0.0699091i
$707$	8.54456	+	8.54456i	0.321351	+	0.321351i
$708$	−15.8966	−	2.51777i	−0.597430	−	0.0946236i
$709$	−22.0347	−	11.2272i	−0.827531	−	0.421648i	−0.0116948	−	0.999932i	$-0.503723\pi$
$709$	−22.0347	−	11.2272i	−0.827531	−	0.421648i	−0.815836	+	0.578284i	$0.803723\pi$
$710$	−30.9029	+	4.52872i	−1.15977	+	0.169960i
$711$	−0.0352206	−	0.0691243i	−0.00132088	−	0.00259236i
$712$	−6.71810	+	2.18284i	−0.251772	+	0.0818056i
$713$	−12.5204	−	38.5339i	−0.468894	−	1.44311i
$714$	1.73601	+	30.8814i	0.0649686	+	1.15571i
$715$	7.13549	+	3.74032i	0.266852	+	0.139880i
$716$	−15.1509	+	4.92281i	−0.566214	+	0.183974i
$717$	4.45265	−	28.1129i	0.166287	−	1.04990i
$718$	−23.7071			−0.884741
$719$	1.14489	−	7.22858i	0.0426974	−	0.269581i	−0.957099	−	0.289761i	$-0.906424\pi$
$719$	1.14489	−	7.22858i	0.0426974	−	0.269581i	0.999796	+	0.0201806i	$0.00642413\pi$
$720$	−0.104692	−	0.0779291i	−0.00390163	−	0.00290425i
$721$	−8.69503	−	54.8982i	−0.323820	−	2.04452i
$722$	25.7581	−	35.4530i	0.958617	−	1.31942i
$723$	−7.42492	−	2.41250i	−0.276136	−	0.0897220i
$724$	−8.33681	−	8.33681i	−0.309835	−	0.309835i
$725$	−33.3731	+	31.8634i	−1.23945	+	1.18338i
$726$	−0.134784	+	0.134784i	−0.00500230	+	0.00500230i
$727$	−5.94733	+	18.3040i	−0.220574	+	0.678858i	0.778136	+	0.628095i	$0.216165\pi$
$727$	−5.94733	+	18.3040i	−0.220574	+	0.678858i	−0.998711	+	0.0507629i	$0.983835\pi$
$728$	−4.66938	+	0.739556i	−0.173059	+	0.0274098i
$729$	16.1668	−	22.2517i	0.598772	−	0.824138i
$730$	−9.08124	−	18.3445i	−0.336112	−	0.678961i
$731$	−1.11677	+	1.73405i	−0.0413051	+	0.0641360i
$732$	−6.69141			−0.247322
$733$	9.30975	+	12.8138i	0.343863	+	0.473287i	0.945565	−	0.325434i	$-0.105510\pi$
$733$	9.30975	+	12.8138i	0.343863	+	0.473287i	−0.601701	+	0.798721i	$0.705510\pi$
$734$	−9.25858	−	4.71748i	−0.341740	−	0.174125i
$735$	20.6396	+	41.6930i	0.761303	+	1.53787i
$736$	−2.26477	−	4.44485i	−0.0834804	−	0.163839i
$737$	0.706912	−	1.38739i	0.0260394	−	0.0511053i
$738$	0.0698567	−	0.137102i	0.00257146	−	0.00504678i
$739$	−38.5199	−	12.5159i	−1.41698	−	0.460404i	−0.502337	−	0.864672i	$-0.667526\pi$
$739$	−38.5199	−	12.5159i	−1.41698	−	0.460404i	−0.914641	+	0.404268i	$0.867526\pi$
$740$	10.2165	+	10.4557i	0.375566	+	0.384358i
$741$	6.67073	−	13.0920i	0.245055	−	0.480948i
$742$	25.1608	+	3.98507i	0.923680	+	0.146297i
$743$	30.6875	−	30.6875i	1.12581	−	1.12581i	0.134963	−	0.990851i	$-0.456908\pi$
$743$	30.6875	−	30.6875i	1.12581	−	1.12581i	0.990851	−	0.134963i	$-0.0430917\pi$
$744$	−11.2697	+	8.18792i	−0.413167	+	0.300184i
$745$	51.1262	−	15.9604i	1.87312	−	0.584745i
$746$	−10.0091	+	13.7763i	−0.366457	+	0.504385i
$747$	0.295972	+	0.215036i	0.0108290	+	0.00786775i
$748$	10.2484	+	9.15749i	0.374719	+	0.334831i
$749$	−26.5996			−0.971929
$750$	−14.0215	+	13.0805i	−0.511994	+	0.477634i
$751$	3.27706	−	3.27706i	0.119581	−	0.119581i	−0.644784	−	0.764365i	$-0.723053\pi$
$751$	3.27706	−	3.27706i	0.119581	−	0.119581i	0.764365	+	0.644784i	$0.223053\pi$
$752$	−2.21021	+	6.80233i	−0.0805981	+	0.248056i
$753$	−20.5799	+	3.25953i	−0.749972	+	0.118784i
$754$	1.56038	+	9.85185i	0.0568257	+	0.358783i
$755$	2.22236	+	7.11893i	0.0808801	+	0.259084i
$756$	13.4855	+	18.5611i	0.490461	+	0.675062i
$757$		−	5.51239i		−	0.200351i	−0.994970	−	0.100176i	$-0.968060\pi$
$757$		−	5.51239i		−	0.200351i	0.994970	−	0.100176i	$-0.0319404\pi$
$758$	13.0581	+	2.06820i	0.474291	+	0.0751204i
$759$	12.9478	−	25.4115i	0.469976	−	0.922380i
$760$	−0.205030	+	17.7220i	−0.00743721	+	0.642845i
$761$	−2.27047	+	6.98778i	−0.0823044	+	0.253307i	−0.983738	−	0.179611i	$-0.942516\pi$
$761$	−2.27047	+	6.98778i	−0.0823044	+	0.253307i	0.901433	+	0.432918i	$0.142516\pi$
$762$	−23.1984	−	11.8202i	−0.840388	−	0.428199i
$763$	34.0007	−	11.0475i	1.23091	−	0.399946i
$764$	2.66588	−	8.20473i	0.0964481	−	0.296837i
$765$	−0.537578	+	0.0239853i	−0.0194362	+	0.000867189i
$766$	8.62515	+	26.5455i	0.311639	+	0.959127i
$767$	−5.96188	−	8.20583i	−0.215271	−	0.296295i
$768$	−1.21277	+	1.21277i	−0.0437622	+	0.0437622i
$769$	15.0352	−	10.9237i	0.542185	−	0.393920i	−0.282711	−	0.959205i	$-0.591234\pi$
$769$	15.0352	−	10.9237i	0.542185	−	0.393920i	0.824896	+	0.565285i	$0.191234\pi$
$770$	30.8865	+	10.4322i	1.11307	+	0.375950i
$771$	4.36588	+	27.5651i	0.157233	+	0.992733i
$772$	3.61437	+	22.8202i	0.130084	+	0.821318i
$773$	−5.75264	−	1.86915i	−0.206908	−	0.0672285i	0.203729	−	0.979027i	$-0.434694\pi$
$773$	−5.75264	−	1.86915i	−0.206908	−	0.0672285i	−0.410637	+	0.911799i	$0.634694\pi$
$774$			0.0291973i			0.00104947i
$775$	−17.5944	−	36.6004i	−0.632009	−	1.31473i
$776$	8.08981	+	8.08981i	0.290407	+	0.290407i
$777$	−22.2648	−	43.6972i	−0.798746	−	1.56763i
$778$	22.3909	+	16.2679i	0.802753	+	0.583234i
$779$	−20.6383	+	3.26879i	−0.739444	+	0.117116i
$780$	0.601059	+	4.10148i	0.0215214	+	0.146857i
$781$	37.6674	−	27.3670i	1.34784	−	0.979267i
$782$	−18.8218	−	8.29453i	−0.673067	−	0.296612i
$783$	39.1619	−	28.4528i	1.39953	−	1.01682i
$784$	−11.5368	+	3.74853i	−0.412029	+	0.133876i
$785$	32.6335	−	10.1874i	1.16474	−	0.363604i
$786$	11.0774	−	34.0929i	0.395119	−	1.21605i
$787$	−7.70253	−	3.92464i	−0.274566	−	0.139898i	0.311287	−	0.950316i	$-0.399240\pi$
$787$	−7.70253	−	3.92464i	−0.274566	−	0.139898i	−0.585852	+	0.810418i	$0.699240\pi$
$788$	−7.26752	+	14.2633i	−0.258895	+	0.508109i
$789$	−23.5424	+	11.9954i	−0.838131	+	0.427049i
$790$	−0.430956	−	2.94074i	−0.0153327	−	0.104627i
$791$	−12.3218	+	4.00361i	−0.438114	+	0.142352i
$792$	0.192160	+	0.0304352i	0.00682811	+	0.00108147i
$793$	−2.98184	−	2.98184i	−0.105888	−	0.105888i
$794$	−1.02491	+	6.47104i	−0.0363728	+	0.229649i
$795$	3.74922	−	22.0198i	0.132971	−	0.780963i
$796$	−2.14159	+	0.339195i	−0.0759068	+	0.0120225i
$797$	−9.99206	+	13.7529i	−0.353937	+	0.487153i	−0.948447	−	0.316936i	$-0.897346\pi$
$797$	−9.99206	+	13.7529i	−0.353937	+	0.487153i	0.594510	+	0.804088i	$0.297346\pi$
$798$	18.3737	−	56.5485i	0.650422	−	2.00179i
$799$	10.6727	+	27.4910i	0.377575	+	0.972563i
$800$	−2.84456	−	4.11200i	−0.100570	−	0.145381i
$801$			0.412292i			0.0145676i
$802$	9.15306	+	17.9639i	0.323206	+	0.634327i
$803$	24.6862	+	17.9356i	0.871157	+	0.632932i
$804$	0.791322	−	0.125333i	0.0279078	−	0.00442016i
$805$	−48.7860	−	0.564416i	−1.71948	−	0.0198931i
$806$	−8.67074	−	1.37331i	−0.305414	−	0.0483728i
$807$			21.0443i			0.740794i
$808$	1.62390	+	2.23511i	0.0571287	+	0.0786309i
$809$	2.62632	−	5.15444i	0.0923364	−	0.181220i	−0.840219	−	0.542247i	$-0.817574\pi$
$809$	2.62632	−	5.15444i	0.0923364	−	0.181220i	0.932555	+	0.361027i	$0.117574\pi$
$810$	16.0913	−	11.4089i	0.565390	−	0.400870i
$811$	−16.7106	−	32.7963i	−0.586788	−	1.15164i	−0.973340	−	0.229368i	$-0.926334\pi$
$811$	−16.7106	−	32.7963i	−0.586788	−	1.15164i	0.386552	−	0.922268i	$-0.373666\pi$
$812$	12.4729	+	38.3877i	0.437714	+	1.34714i
$813$	−2.47434	−	1.26074i	−0.0867789	−	0.0442161i
$814$	−20.7253	−	6.73405i	−0.726421	−	0.236028i
$815$	−3.83106	+	22.5005i	−0.134196	+	0.788158i
$816$	−0.712480	+	7.03563i	−0.0249418	+	0.246296i
$817$	3.20769	−	2.33053i	0.112223	−	0.0815348i
$818$			11.8551i			0.414503i
$819$	−0.0431654	+	0.272535i	−0.00150832	+	0.00952316i
$820$	4.21632	−	4.11988i	0.147240	−	0.143872i
$821$	7.15723	−	1.13359i	0.249789	−	0.0395627i	−0.0302842	−	0.999541i	$-0.509641\pi$
$821$	7.15723	−	1.13359i	0.249789	−	0.0395627i	0.280073	+	0.959979i	$0.409641\pi$
$822$	1.71171	+	10.8073i	0.0597027	+	0.376948i
$823$	35.0510	−	17.8594i	1.22180	−	0.622539i	0.280418	−	0.959878i	$-0.409527\pi$
$823$	35.0510	−	17.8594i	1.22180	−	0.622539i	0.941383	+	0.337339i	$0.109527\pi$
$824$		−	12.7079i		−	0.442702i
$825$	9.45996	−	26.9746i	0.329353	−	0.939137i
$826$	−29.0227	−	29.0227i	−1.00983	−	1.00983i
$827$	47.3649	−	24.1336i	1.64704	−	0.839208i	0.650200	−	0.759763i	$-0.274685\pi$
$827$	47.3649	−	24.1336i	1.64704	−	0.839208i	0.996839	−	0.0794455i	$-0.0253150\pi$
$828$	−0.287581	+	0.0455484i	−0.00999414	+	0.00158292i
$829$	−13.0552	−	9.48517i	−0.453426	−	0.329434i	0.337521	−	0.941318i	$-0.390412\pi$
$829$	−13.0552	−	9.48517i	−0.453426	−	0.329434i	−0.790947	+	0.611885i	$0.790412\pi$
$830$	8.10647	+	11.4334i	0.281380	+	0.396861i
$831$	9.14095	+	12.5814i	0.317096	+	0.436445i
$832$	−1.08088			−0.0374726
$833$	−27.0809	+	42.0495i	−0.938297	+	1.45693i
$834$	−0.176662	−	0.543708i	−0.00611729	−	0.0188271i
$835$	4.97868	+	33.9734i	0.172294	+	1.17570i
$836$	−11.9945	−	23.5406i	−0.414839	−	0.814168i
$837$	13.1652	+	40.5182i	0.455055	+	1.40052i
$838$	−22.8723	−	11.6540i	−0.790109	−	0.402581i
$839$	−16.7225	+	8.52055i	−0.577326	+	0.294162i	−0.718168	−	0.695870i	$-0.755019\pi$
$839$	−16.7225	+	8.52055i	−0.577326	+	0.294162i	0.140842	+	0.990032i	$0.455019\pi$
$840$	4.99862	+	16.0121i	0.172469	+	0.552471i
$841$	53.4130	−	17.3549i	1.84183	−	0.598446i
$842$	−12.1543	−	16.7290i	−0.418865	−	0.576519i
$843$	9.91216	+	9.91216i	0.341393	+	0.341393i
$844$	−4.11192	−	0.651263i	−0.141538	−	0.0224174i
$845$	15.7973	−	21.2224i	0.543444	−	0.730074i
$846$	0.337733	+	0.245377i	0.0116115	+	0.00843624i
$847$	−0.480111	+	0.0760421i	−0.0164968	+	0.00261284i
$848$	5.53920	+	1.79979i	0.190217	+	0.0618052i
$849$	30.6382			1.05150
$850$	−19.8062	−	5.71981i	−0.679346	−	0.196188i
$851$	32.6130			1.11796
$852$	22.7840	+	7.40296i	0.780566	+	0.253621i
$853$	28.8256	−	4.56552i	0.986968	−	0.156320i	0.357975	−	0.933731i	$-0.383467\pi$
$853$	28.8256	−	4.56552i	0.986968	−	0.156320i	0.628993	+	0.777411i	$0.283467\pi$
$854$	−13.8052	−	10.0301i	−0.472406	−	0.343223i
$855$	0.980049	+	0.331020i	0.0335170	+	0.0113206i
$856$	−6.00665	−	0.951360i	−0.205303	−	0.0325168i
$857$	−23.6205	−	23.6205i	−0.806862	−	0.806862i	0.177296	−	0.984158i	$-0.443265\pi$
$857$	−23.6205	−	23.6205i	−0.806862	−	0.806862i	−0.984158	+	0.177296i	$0.943265\pi$
$858$	−3.63218	−	4.99927i	−0.124001	−	0.170672i
$859$	−30.5500	+	9.92629i	−1.04235	+	0.338681i	−0.779663	−	0.626200i	$-0.784609\pi$
$859$	−30.5500	+	9.92629i	−1.04235	+	0.338681i	−0.262689	+	0.964880i	$0.584609\pi$
$860$	−0.357941	+	1.05975i	−0.0122057	+	0.0361373i
$861$	−17.6212	+	8.97846i	−0.600529	+	0.305985i
$862$	24.2884	+	12.3756i	0.827267	+	0.421513i
$863$	−12.7650	−	39.2865i	−0.434524	−	1.33733i	−0.893573	−	0.448918i	$-0.851810\pi$
$863$	−12.7650	−	39.2865i	−0.434524	−	1.33733i	0.459049	−	0.888411i	$-0.348190\pi$
$864$	2.38139	+	4.67374i	0.0810165	+	0.159004i
$865$	−33.5366	−	34.3216i	−1.14028	−	1.16697i
$866$	−0.916424	−	2.82046i	−0.0311414	−	0.0958433i
$867$	16.0653	+	24.3319i	0.545605	+	0.826353i
$868$	−35.5242			−1.20577
$869$	2.60426	+	3.58445i	0.0883433	+	0.121594i
$870$	33.7838	−	10.5465i	1.14538	−	0.357561i
$871$	0.408482	+	0.296779i	0.0138409	+	0.0100560i
$872$	8.07305	−	1.27865i	0.273388	−	0.0433004i
$873$	0.594975	−	0.303155i	0.0201368	−	0.0102602i
$874$	27.9588	+	27.9588i	0.945720	+	0.945720i
$875$	−48.5354	+	5.96927i	−1.64079	+	0.201798i
$876$			15.7004i			0.530468i
$877$	31.3311	−	15.9640i	1.05798	−	0.539066i	0.163667	−	0.986516i	$-0.447668\pi$
$877$	31.3311	−	15.9640i	1.05798	−	0.539066i	0.894309	+	0.447450i	$0.147668\pi$
$878$	0.907327	+	5.72864i	0.0306208	+	0.193332i
$879$	−51.7819	+	8.20145i	−1.74656	+	0.276628i
$880$	6.60159	+	3.46045i	0.222539	+	0.116652i
$881$	7.57794	−	47.8452i	0.255307	−	1.61195i	−0.443254	−	0.896396i	$-0.646176\pi$
$881$	7.57794	−	47.8452i	0.255307	−	1.61195i	0.698562	−	0.715550i	$-0.253824\pi$
$882$			0.708016i			0.0238401i
$883$	21.0015	−	15.2585i	0.706757	−	0.513489i	−0.175369	−	0.984503i	$-0.556112\pi$
$883$	21.0015	−	15.2585i	0.706757	−	0.513489i	0.882126	+	0.471014i	$0.156112\pi$
$884$	−3.45273	+	2.81773i	−0.116128	+	0.0947707i
$885$	−25.7407	+	25.1519i	−0.865264	+	0.845472i
$886$	19.3824	+	6.29771i	0.651163	+	0.211576i
$887$	−20.1225	−	10.2529i	−0.675648	−	0.344260i	0.0822695	−	0.996610i	$-0.473783\pi$
$887$	−20.1225	−	10.2529i	−0.675648	−	0.344260i	−0.757918	+	0.652350i	$0.773783\pi$
$888$	−3.46491	−	10.6639i	−0.116275	−	0.357857i
$889$	−30.1434	−	59.1598i	−1.01098	−	1.98415i
$890$	−5.05444	+	14.9647i	−0.169425	+	0.501617i
$891$	−13.3496	+	26.2001i	−0.447228	+	0.877735i
$892$	0.552551	+	0.760521i	0.0185008	+	0.0254641i
$893$		−	56.6902i		−	1.89707i
$894$	−40.5757	−	6.42656i	−1.35705	−	0.214936i
$895$	−11.3989	+	33.7488i	−0.381024	+	1.12810i
$896$	−4.31999	+	0.684220i	−0.144321	+	0.0228582i
$897$	7.48176	+	5.43582i	0.249809	+	0.181497i
$898$	2.86687	+	5.62656i	0.0956688	+	0.187761i
$899$			74.9519i			2.49979i
$900$	−0.279562	+	0.0837360i	−0.00931872	+	0.00279120i
$901$	22.3862	−	8.69091i	0.745792	−	0.289536i
$902$	−2.71556	+	8.35763i	−0.0904182	+	0.278279i
$903$	2.20574	−	3.03594i	0.0734025	−	0.101030i
$904$	−2.92568	+	0.463381i	−0.0973065	+	0.0154118i
$905$	−26.0847	+	3.82263i	−0.867085	+	0.127068i
$906$	0.894848	−	5.64985i	0.0297293	−	0.187704i
$907$	−15.3492	−	15.3492i	−0.509661	−	0.509661i	0.404761	−	0.914422i	$-0.367355\pi$
$907$	−15.3492	−	15.3492i	−0.509661	−	0.509661i	−0.914422	+	0.404761i	$0.867355\pi$
$908$	−6.04555	−	0.957520i	−0.200629	−	0.0317764i
$909$	0.153360	−	0.0498297i	0.00508663	−	0.00165275i
$910$	−4.90786	+	9.36285i	−0.162694	+	0.310375i
$911$	−39.1286	+	19.9370i	−1.29639	+	0.660544i	−0.959688	−	0.281068i	$-0.909311\pi$
$911$	−39.1286	+	19.9370i	−1.29639	+	0.660544i	−0.336702	+	0.941611i	$0.609311\pi$
$912$	6.17160	−	12.1125i	0.204362	−	0.401083i
$913$	−18.6161	−	9.48537i	−0.616103	−	0.313920i
$914$	−8.22062	+	25.3005i	−0.271914	+	0.836865i
$915$	−8.93415	+	12.0023i	−0.295354	+	0.396785i
$916$	10.8122	−	3.51309i	0.357244	−	0.116076i
$917$	73.9578	−	53.7335i	2.44230	−	1.77443i
$918$	19.7910	+	8.72166i	0.653202	+	0.287858i
$919$	−27.8629	+	20.2436i	−0.919113	+	0.667775i	−0.943303	−	0.331933i	$-0.892299\pi$
$919$	−27.8629	+	20.2436i	−0.919113	+	0.667775i	0.0241902	+	0.999707i	$0.492299\pi$
$920$	−10.9965	−	1.87233i	−0.362545	−	0.0617290i
$921$	9.85545	−	1.56095i	0.324748	−	0.0514350i
$922$	−17.6000	−	12.7871i	−0.579624	−	0.421122i
$923$	6.85411	+	13.4519i	0.225606	+	0.442776i
$924$	−17.6816	−	17.6816i	−0.581682	−	0.581682i
$925$	32.3950	−	4.36519i	1.06514	−	0.143527i
$926$			0.869403i			0.0285704i
$927$	−0.705417	−	0.229204i	−0.0231689	−	0.00752804i
$928$	1.44363	+	9.11470i	0.0473894	+	0.299205i
$929$	−0.0252296	−	0.159293i	−0.000827757	−	0.00522625i	0.987271	−	0.159047i	$-0.0508422\pi$
$929$	−0.0252296	−	0.159293i	−0.000827757	−	0.00522625i	−0.988099	+	0.153821i	$0.950842\pi$
$930$	−0.360342	+	31.1466i	−0.0118161	+	1.02134i
$931$	77.7846	−	56.5138i	2.54929	−	1.85217i
$932$	−8.23847	+	8.23847i	−0.269860	+	0.269860i
$933$	16.6180	+	22.8727i	0.544048	+	0.748817i
$934$	10.8147	+	33.2843i	0.353869	+	1.08910i
$935$	30.1090	−	6.15569i	0.984671	−	0.201312i
$936$	−0.0194949	+	0.0599993i	−0.000637212	+	0.00196114i
$937$	11.6699	−	3.79177i	0.381238	−	0.123872i	−0.112128	−	0.993694i	$-0.535767\pi$
$937$	11.6699	−	3.79177i	0.381238	−	0.123872i	0.493365	+	0.869822i	$0.335767\pi$
$938$	1.82047	+	0.927575i	0.0594404	+	0.0302864i
$939$	−9.19209	+	28.2903i	−0.299972	+	0.923220i
$940$	9.25028	+	13.0467i	0.301711	+	0.425536i
$941$	−4.88474	+	9.58685i	−0.159238	+	0.312522i	−0.956816	−	0.290693i	$-0.906114\pi$
$941$	−4.88474	+	9.58685i	−0.159238	+	0.312522i	0.797578	+	0.603215i	$0.206114\pi$
$942$	−25.8991	−	4.10202i	−0.843840	−	0.133651i
$943$		−	13.1515i		−	0.428270i
$944$	−5.51579	−	7.59184i	−0.179524	−	0.247093i
$945$	51.2983	+	0.593481i	1.66873	+	0.0193059i
$946$	−0.260850	−	1.64694i	−0.00848095	−	0.0535466i
$947$	−31.5323	+	4.99422i	−1.02466	+	0.162290i	−0.646074	−	0.763275i	$-0.723590\pi$
$947$	−31.5323	+	4.99422i	−1.02466	+	0.162290i	−0.378588	+	0.925565i	$0.623590\pi$
$948$	−0.704470	+	2.16814i	−0.0228801	+	0.0704178i
$949$	−6.99645	+	6.99645i	−0.227114	+	0.227114i
$950$	31.5141	+	24.0296i	1.02245	+	0.779623i
$951$	23.4747			0.761218
$952$	−12.0160	+	13.4475i	−0.389441	+	0.435835i
$953$	−4.64831	−	3.37719i	−0.150573	−	0.109398i	0.509948	−	0.860205i	$-0.329665\pi$
$953$	−4.64831	−	3.37719i	−0.150573	−	0.109398i	−0.660521	+	0.750807i	$0.729665\pi$
$954$	0.199813	−	0.275019i	0.00646918	−	0.00890406i
$955$	−11.1574	−	15.7365i	−0.361044	−	0.509220i
$956$	13.4261	−	9.75463i	0.434231	−	0.315487i
$957$	−37.3062	+	37.3062i	−1.20594	+	1.20594i
$958$	−36.8154	−	5.83099i	−1.18945	−	0.188391i
$959$	−12.6681	+	24.8626i	−0.409076	+	0.802856i
$960$	0.556085	+	3.79459i	0.0179476	+	0.122470i
$961$	−33.2548	−	10.8051i	−1.07273	−	0.348553i
$962$	3.20802	−	6.29610i	0.103431	−	0.202994i
$963$	−0.161147	+	0.316270i	−0.00519290	+	0.0101916i
$964$	−2.06651	−	4.05576i	−0.0665579	−	0.130627i
$965$	45.7582	+	23.9857i	1.47301	+	0.772129i
$966$	33.3438	+	16.9895i	1.07282	+	0.546628i
$967$	−16.3790	−	22.5438i	−0.526713	−	0.724958i	0.459912	−	0.887964i	$-0.347881\pi$
$967$	−16.3790	−	22.5438i	−0.526713	−	0.724958i	−0.986625	+	0.163006i	$0.947881\pi$
$968$	−0.111137			−0.00357208
$969$	−11.8615	−	54.7805i	−0.381047	−	1.75980i
$970$	25.3119	−	3.70937i	0.812716	−	0.119101i
$971$	6.38296	−	8.78540i	0.204839	−	0.281937i	−0.694221	−	0.719762i	$-0.744251\pi$
$971$	6.38296	−	8.78540i	0.204839	−	0.281937i	0.899060	+	0.437825i	$0.144251\pi$
$972$	0.599010	−	0.0948738i	0.0192132	−	0.00304308i
$973$	0.450517	−	1.38655i	0.0144429	−	0.0444507i
$974$	−21.2021	+	21.2021i	−0.679361	+	0.679361i
$975$	8.15931	+	4.39805i	0.261307	+	0.140850i
$976$	−2.75872	−	2.75872i	−0.0883046	−	0.0883046i
$977$	21.8698	+	7.10594i	0.699678	+	0.227339i	0.637190	−	0.770707i	$-0.280097\pi$
$977$	21.8698	+	7.10594i	0.699678	+	0.227339i	0.0624875	+	0.998046i	$0.480097\pi$
$978$	10.2902	−	14.1633i	0.329046	−	0.452893i
$979$	−3.68343	−	23.2562i	−0.117723	−	0.743273i
$980$	−8.67985	+	25.6984i	−0.277268	+	0.820905i
$981$	0.0746302	−	0.471196i	0.00238276	−	0.0150441i
$982$	−21.7313			−0.693472
$983$	7.14330	−	45.1010i	0.227836	−	1.43850i	−0.562993	−	0.826462i	$-0.690350\pi$
$983$	7.14330	−	45.1010i	0.227836	−	1.43850i	0.790829	−	0.612038i	$-0.209650\pi$
$984$	−4.30029	+	1.39725i	−0.137088	+	0.0445427i
$985$	15.8806	+	32.0796i	0.505999	+	1.02214i
$986$	28.3726	+	25.3524i	0.903568	+	0.807386i
$987$	−16.5803	−	51.0288i	−0.527756	−	1.62426i
$988$	8.14777	−	2.64737i	0.259215	−	0.0842241i
$989$	1.13293	+	2.22349i	0.0360250	+	0.0707030i
$990$	0.311157	−	0.304040i	0.00988923	−	0.00966302i
$991$	0.680508	+	0.346736i	0.0216171	+	0.0110144i	0.464766	−	0.885434i	$-0.346139\pi$
$991$	0.680508	+	0.346736i	0.0216171	+	0.0110144i	−0.443149	+	0.896448i	$0.646139\pi$
$992$	−8.02196	−	1.27055i	−0.254697	−	0.0403401i
$993$	29.9157	+	29.9157i	0.949346	+	0.949346i
$994$	35.9096	+	49.4253i	1.13898	+	1.56768i
$995$	−2.25098	+	4.29424i	−0.0713607	+	0.136137i
$996$	−1.68172	−	10.6180i	−0.0532875	−	0.336444i
$997$	1.49044	+	9.41027i	0.0472027	+	0.298026i	0.999984	−	0.00563077i	$-0.00179234\pi$
$997$	1.49044	+	9.41027i	0.0472027	+	0.298026i	−0.952781	+	0.303657i	$0.901792\pi$
$998$	4.44133	+	8.71661i	0.140588	+	0.275919i
$999$	−34.2925			−1.08497

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	850.2.y.b.21.18	✓	192
17.13	even	4	inner	850.2.y.b.421.18	yes	192
25.6	even	5	inner	850.2.y.b.531.18	yes	192
425.81	even	20	inner	850.2.y.b.81.18	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
850.2.y.b.21.18	✓	192	1.1	even	1	trivial
850.2.y.b.81.18	yes	192	425.81	even	20	inner
850.2.y.b.421.18	yes	192	17.13	even	4	inner
850.2.y.b.531.18	yes	192	25.6	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:	\( N \)	\(=\)	\( 850 = 2 \cdot 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	850.y (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.951057 - 0.309017i) q^{2} +(1.69400 - 0.268304i) q^{3} +(0.809017 + 0.587785i) q^{4} +(2.13448 - 0.666335i) q^{5} +(-1.69400 - 0.268304i) q^{6} +(-3.09277 - 3.09277i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(-0.0555099 + 0.0180363i) q^{9} +(-2.23592 - 0.0258678i) q^{10} +(2.97003 - 1.51330i) q^{11} +(1.52818 + 0.778648i) q^{12} +(0.334009 + 1.02797i) q^{13} +(1.98568 + 3.89712i) q^{14} +(3.43703 - 1.70146i) q^{15} +(0.309017 + 0.951057i) q^{16} +(3.46643 + 2.23246i) q^{17} +0.0583666 q^{18} +(-4.65882 - 6.41231i) q^{19} +(2.11849 + 0.715539i) q^{20} +(-6.06897 - 4.40937i) q^{21} +(-3.29230 + 0.521449i) q^{22} +(4.44485 - 2.26477i) q^{23} +(-1.21277 - 1.21277i) q^{24} +(4.11200 - 2.84456i) q^{25} -1.08088i q^{26} +(-4.67374 + 2.38139i) q^{27} +(-0.684220 - 4.31999i) q^{28} +(-9.11470 + 1.44363i) q^{29} +(-3.79459 + 0.556085i) q^{30} +(1.27055 - 8.02196i) q^{31} -1.00000i q^{32} +(4.62521 - 3.36041i) q^{33} +(-2.60690 - 3.19438i) q^{34} +(-8.66228 - 4.54064i) q^{35} +(-0.0555099 - 0.0180363i) q^{36} +(5.82500 + 2.96798i) q^{37} +(2.44928 + 7.53812i) q^{38} +(0.841621 + 1.65177i) q^{39} +(-1.79369 - 1.33517i) q^{40} +(1.19686 - 2.34897i) q^{41} +(4.40937 + 6.06897i) q^{42} +0.500240i q^{43} +(3.29230 + 0.521449i) q^{44} +(-0.106466 + 0.0754862i) q^{45} +(-4.92716 + 0.780385i) q^{46} +(5.78641 + 4.20407i) q^{47} +(0.778648 + 1.52818i) q^{48} +12.1305i q^{49} +(-4.78976 + 1.43466i) q^{50} +(6.47112 + 2.85174i) q^{51} +(-0.334009 + 1.02797i) q^{52} +(3.42341 - 4.71192i) q^{53} +(5.18088 - 0.820571i) q^{54} +(5.33109 - 5.20915i) q^{55} +(-0.684220 + 4.31999i) q^{56} +(-9.61250 - 9.61250i) q^{57} +(9.11470 + 1.44363i) q^{58} +(-8.92474 + 2.89982i) q^{59} +(3.78071 + 0.643725i) q^{60} +(-3.47620 + 1.77121i) q^{61} +(-3.68729 + 7.23671i) q^{62} +(0.227462 + 0.115898i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(1.39791 + 1.97163i) q^{65} +(-5.43726 + 1.76667i) q^{66} +(0.377917 - 0.274573i) q^{67} +(1.49219 + 3.84361i) q^{68} +(6.92195 - 5.02909i) q^{69} +(6.83519 + 6.99519i) q^{70} +(13.7959 - 2.18505i) q^{71} +(0.0472195 + 0.0343070i) q^{72} +(4.15589 + 8.15639i) q^{73} +(-4.62274 - 4.62274i) q^{74} +(6.20253 - 5.92195i) q^{75} -7.92605i q^{76} +(-13.8659 - 4.50531i) q^{77} +(-0.290003 - 1.83101i) q^{78} +(0.207930 + 1.31282i) q^{79} +(1.29331 + 1.82410i) q^{80} +(-7.13674 + 5.18514i) q^{81} +(-1.86416 + 1.86416i) q^{82} +(-3.68423 - 5.07091i) q^{83} +(-2.31814 - 7.13451i) q^{84} +(8.88658 + 2.45534i) q^{85} +(0.154583 - 0.475756i) q^{86} +(-15.0530 + 4.89101i) q^{87} +(-2.97003 - 1.51330i) q^{88} +(2.18284 - 6.71810i) q^{89} +(0.124582 - 0.0388917i) q^{90} +(2.14628 - 4.21230i) q^{91} +(4.92716 + 0.780385i) q^{92} -13.9301i q^{93} +(-4.20407 - 5.78641i) q^{94} +(-14.2169 - 10.5826i) q^{95} +(-0.268304 - 1.69400i) q^{96} +(-11.2999 + 1.78972i) q^{97} +(3.74853 - 11.5368i) q^{98} +(-0.137571 + 0.137571i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 48 q^{4} + 2 q^{5} + 4 q^{7} - 12 q^{10} + 14 q^{11} - 4 q^{13} - 6 q^{14} - 48 q^{16} + 12 q^{17} - 240 q^{18} + 18 q^{20} - 16 q^{21} - 16 q^{22} - 14 q^{23} - 30 q^{27} - 4 q^{28} - 20 q^{29}+ \cdots + 96 q^{99}+O(q^{100}) \) 192 * q + 48 * q^4 + 2 * q^5 + 4 * q^7 - 12 * q^10 + 14 * q^11 - 4 * q^13 - 6 * q^14 - 48 * q^16 + 12 * q^17 - 240 * q^18 + 18 * q^20 - 16 * q^21 - 16 * q^22 - 14 * q^23 - 30 * q^27 - 4 * q^28 - 20 * q^29 - 4 * q^30 + 12 * q^31 + 28 * q^33 + 8 * q^34 + 60 * q^35 - 38 * q^37 - 4 * q^38 - 24 * q^39 + 2 * q^40 - 8 * q^41 + 16 * q^44 - 36 * q^45 + 16 * q^46 + 44 * q^47 + 32 * q^50 - 16 * q^51 + 4 * q^52 + 16 * q^55 - 4 * q^56 - 40 * q^57 + 20 * q^58 + 34 * q^61 + 18 * q^62 + 32 * q^63 + 48 * q^64 + 36 * q^65 - 40 * q^67 - 12 * q^68 - 24 * q^69 + 8 * q^71 - 60 * q^72 - 44 * q^73 - 12 * q^74 - 16 * q^78 + 36 * q^79 + 2 * q^80 + 96 * q^81 - 88 * q^82 - 44 * q^84 + 2 * q^85 - 44 * q^86 - 14 * q^88 + 60 * q^89 - 16 * q^90 - 4 * q^91 - 16 * q^92 + 8 * q^95 + 20 * q^97 - 64 * q^98 + 96 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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