LMFDB - Embedded newform 70.3.l.a.23.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [70,3,Mod(23,70)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(70, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([9, 4])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("70.23"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 70 = 2 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	70.l (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,4,-4] 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:	$1.90736185052$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	8.0.3317760000.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 25x^{4} + 625 $ x^8 - 25*x^4 + 625
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			23.1
Root			$0.578737 - 2.15988i$ of defining polynomial
Character	$\chi$	$=$	70.23
Dual form			70.3.l.a.67.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.366025 - 1.36603i) q^{2} +(-0.636376 + 2.37499i) q^{3} +(-1.73205 + 1.00000i) q^{4} +(4.96410 - 0.598076i) q^{5} +3.47723 q^{6} +(6.99656 - 0.219274i) q^{7} +(2.00000 + 2.00000i) q^{8} +(2.55863 + 1.47723i) q^{9} +(-2.63397 - 6.56218i) q^{10} +(3.73861 + 6.47547i) q^{11} +(-1.27275 - 4.74998i) q^{12} +(-10.9545 - 10.9545i) q^{13} +(-2.86045 - 9.47723i) q^{14} +(-1.73861 + 12.1703i) q^{15} +(2.00000 - 3.46410i) q^{16} +(-20.4282 - 5.47371i) q^{17} +(1.08140 - 4.03586i) q^{18} +(12.4982 + 7.21584i) q^{19} +(-8.00000 + 6.00000i) q^{20} +(-3.93168 + 16.7563i) q^{21} +(7.47723 - 7.47723i) q^{22} +(-20.0711 + 5.37803i) q^{23} +(-6.02273 + 3.47723i) q^{24} +(24.2846 - 5.93782i) q^{25} +(-10.9545 + 18.9737i) q^{26} +(-20.7842 + 20.7842i) q^{27} +(-11.8991 + 7.37636i) q^{28} -15.8634i q^{29} +(17.2613 - 2.07965i) q^{30} +(-8.00000 - 13.8564i) q^{31} +(-5.46410 - 1.46410i) q^{32} +(-17.7583 + 4.75833i) q^{33} +29.9089i q^{34} +(34.6005 - 5.27298i) q^{35} -5.90890 q^{36} +(-17.1865 - 64.1410i) q^{37} +(5.28236 - 19.7140i) q^{38} +(32.9879 - 19.0455i) q^{39} +(11.1244 + 8.73205i) q^{40} -27.9545 q^{41} +(24.3286 - 0.762464i) q^{42} +(39.6475 + 39.6475i) q^{43} +(-12.9509 - 7.47723i) q^{44} +(13.5848 + 5.80284i) q^{45} +(14.6931 + 25.4491i) q^{46} +(-18.6173 - 69.4806i) q^{47} +(6.95445 + 6.95445i) q^{48} +(48.9038 - 3.06832i) q^{49} +(-17.0000 - 31.0000i) q^{50} +(26.0000 - 45.0333i) q^{51} +(29.9281 + 8.01921i) q^{52} +(-10.9641 + 40.9185i) q^{53} +(35.9992 + 20.7842i) q^{54} +(22.4317 + 29.9089i) q^{55} +(14.4317 + 13.5546i) q^{56} +(-25.0911 + 25.0911i) q^{57} +(-21.6697 + 5.80639i) q^{58} +(-55.8784 + 32.2614i) q^{59} +(-9.15892 - 22.8182i) q^{60} +(-29.5455 + 51.1744i) q^{61} +(-16.0000 + 16.0000i) q^{62} +(18.2255 + 9.77446i) q^{63} +8.00000i q^{64} +(-60.9306 - 47.8274i) q^{65} +(13.0000 + 22.5167i) q^{66} +(53.5698 + 14.3540i) q^{67} +(40.8563 - 10.9474i) q^{68} -51.0911i q^{69} +(-19.8677 - 45.3351i) q^{70} -36.3406 q^{71} +(2.16281 + 8.07171i) q^{72} +(17.1198 - 63.8921i) q^{73} +(-81.3275 + 46.9545i) q^{74} +(-1.35189 + 61.4544i) q^{75} -28.8634 q^{76} +(27.5773 + 44.4862i) q^{77} +(-38.0911 - 38.0911i) q^{78} +(35.6837 + 20.6020i) q^{79} +(7.85641 - 18.3923i) q^{80} +(-22.8406 - 39.5610i) q^{81} +(10.2320 + 38.1865i) q^{82} +(-9.12474 - 9.12474i) q^{83} +(-9.94644 - 32.9545i) q^{84} +(-104.681 - 14.9545i) q^{85} +(39.6475 - 68.6715i) q^{86} +(37.6753 + 10.0951i) q^{87} +(-5.47371 + 20.4282i) q^{88} +(-42.1986 - 24.3634i) q^{89} +(2.95445 - 20.6812i) q^{90} +(-79.0455 - 74.2415i) q^{91} +(29.3861 - 29.3861i) q^{92} +(37.9998 - 10.1820i) q^{93} +(-88.0979 + 50.8634i) q^{94} +(66.3579 + 28.3453i) q^{95} +(6.95445 - 12.0455i) q^{96} +(-63.7723 + 63.7723i) q^{97} +(-22.0915 - 65.6808i) q^{98} +22.0911i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} - 4 q^{3} + 12 q^{5} - 16 q^{6} - 4 q^{7} + 16 q^{8} - 28 q^{10} + 8 q^{11} - 8 q^{12} + 8 q^{15} + 16 q^{16} - 16 q^{17} + 32 q^{18} - 64 q^{20} + 100 q^{21} + 16 q^{22} - 4 q^{23} + 28 q^{25}+ \cdots - 132 q^{98}+O(q^{100}) $ 8 * q + 4 * q^2 - 4 * q^3 + 12 * q^5 - 16 * q^6 - 4 * q^7 + 16 * q^8 - 28 * q^10 + 8 * q^11 - 8 * q^12 + 8 * q^15 + 16 * q^16 - 16 * q^17 + 32 * q^18 - 64 * q^20 + 100 * q^21 + 16 * q^22 - 4 * q^23 + 28 * q^25 - 232 * q^27 - 40 * q^28 - 24 * q^30 - 64 * q^31 - 16 * q^32 - 52 * q^33 + 112 * q^35 + 128 * q^36 + 144 * q^37 + 8 * q^38 - 8 * q^40 - 136 * q^41 + 188 * q^42 + 120 * q^43 - 128 * q^45 + 8 * q^46 + 72 * q^47 - 32 * q^48 - 136 * q^50 + 208 * q^51 + 76 * q^53 + 48 * q^55 - 16 * q^56 - 376 * q^57 + 68 * q^58 + 56 * q^60 - 324 * q^61 - 128 * q^62 + 112 * q^63 + 104 * q^66 + 124 * q^67 + 32 * q^68 + 160 * q^70 + 16 * q^71 + 64 * q^72 + 32 * q^73 + 124 * q^75 + 32 * q^76 + 20 * q^77 - 480 * q^78 - 48 * q^80 + 124 * q^81 - 68 * q^82 + 168 * q^83 - 224 * q^85 + 120 * q^86 + 428 * q^87 + 16 * q^88 - 64 * q^90 - 720 * q^91 + 16 * q^92 - 64 * q^93 - 32 * q^95 - 32 * q^96 - 72 * q^97 - 132 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/70\mathbb{Z}\right)^\times$.

$n$	$31$	$57$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.366025	−	1.36603i	−0.183013	−	0.683013i
$2$	−0.366025	−	1.36603i	−0.183013	−	0.683013i
$3$	−0.636376	+	2.37499i	−0.212125	+	0.791663i	0.775033	+	0.631920i	$0.217733\pi$
$3$	−0.636376	+	2.37499i	−0.212125	+	0.791663i	−0.987159	+	0.159743i	$0.948934\pi$
$4$	−1.73205	+	1.00000i	−0.433013	+	0.250000i
$5$	4.96410	−	0.598076i	0.992820	−	0.119615i
$5$	4.96410	−	0.598076i	0.992820	−	0.119615i
$6$	3.47723			0.579538
$7$	6.99656	−	0.219274i	0.999509	−	0.0313248i
$7$	6.99656	−	0.219274i	0.999509	−	0.0313248i
$8$	2.00000	+	2.00000i	0.250000	+	0.250000i
$9$	2.55863	+	1.47723i	0.284292	+	0.164136i
$10$	−2.63397	−	6.56218i	−0.263397	−	0.656218i
$11$	3.73861	+	6.47547i	0.339874	+	0.588679i	0.984409	−	0.175896i	$-0.0562823\pi$
$11$	3.73861	+	6.47547i	0.339874	+	0.588679i	−0.644535	+	0.764575i	$0.722949\pi$
$12$	−1.27275	−	4.74998i	−0.106063	−	0.395832i
$13$	−10.9545	−	10.9545i	−0.842650	−	0.842650i	0.146553	−	0.989203i	$-0.453182\pi$
$13$	−10.9545	−	10.9545i	−0.842650	−	0.842650i	−0.989203	+	0.146553i	$0.953182\pi$
$14$	−2.86045	−	9.47723i	−0.204318	−	0.676945i
$15$	−1.73861	+	12.1703i	−0.115908	+	0.811353i
$16$	2.00000	−	3.46410i	0.125000	−	0.216506i
$17$	−20.4282	−	5.47371i	−1.20166	−	0.321983i	−0.398173	−	0.917310i	$-0.630356\pi$
$17$	−20.4282	−	5.47371i	−1.20166	−	0.321983i	−0.803483	+	0.595327i	$0.797022\pi$
$18$	1.08140	−	4.03586i	0.0600780	−	0.224214i
$19$	12.4982	+	7.21584i	0.657800	+	0.379781i	0.791438	−	0.611249i	$-0.209333\pi$
$19$	12.4982	+	7.21584i	0.657800	+	0.379781i	−0.133638	+	0.991030i	$0.542666\pi$
$20$	−8.00000	+	6.00000i	−0.400000	+	0.300000i
$21$	−3.93168	+	16.7563i	−0.187223	+	0.797919i
$22$	7.47723	−	7.47723i	0.339874	−	0.339874i
$23$	−20.0711	+	5.37803i	−0.872656	+	0.233828i	−0.667236	−	0.744846i	$-0.732523\pi$
$23$	−20.0711	+	5.37803i	−0.872656	+	0.233828i	−0.205420	+	0.978674i	$0.565856\pi$
$24$	−6.02273	+	3.47723i	−0.250947	+	0.144884i
$25$	24.2846	−	5.93782i	0.971384	−	0.237513i
$26$	−10.9545	+	18.9737i	−0.421325	+	0.729756i
$27$	−20.7842	+	20.7842i	−0.769784	+	0.769784i
$28$	−11.8991	+	7.37636i	−0.424969	+	0.263441i
$29$		−	15.8634i		−	0.547012i	−0.961870	−	0.273506i	$-0.911817\pi$
$29$		−	15.8634i		−	0.547012i	0.961870	−	0.273506i	$-0.0881834\pi$
$30$	17.2613	−	2.07965i	0.575377	−	0.0693215i
$31$	−8.00000	−	13.8564i	−0.258065	−	0.446981i	0.707659	−	0.706554i	$-0.249751\pi$
$31$	−8.00000	−	13.8564i	−0.258065	−	0.446981i	−0.965723	+	0.259573i	$0.916418\pi$
$32$	−5.46410	−	1.46410i	−0.170753	−	0.0457532i
$33$	−17.7583	+	4.75833i	−0.538131	+	0.144192i
$34$			29.9089i			0.879674i
$35$	34.6005	−	5.27298i	0.988586	−	0.150656i
$36$	−5.90890			−0.164136
$37$	−17.1865	−	64.1410i	−0.464501	−	1.73354i	−0.658540	−	0.752546i	$-0.728826\pi$
$37$	−17.1865	−	64.1410i	−0.464501	−	1.73354i	0.194039	−	0.980994i	$-0.437841\pi$
$38$	5.28236	−	19.7140i	0.139009	−	0.518790i
$39$	32.9879	−	19.0455i	0.845843	−	0.488347i
$40$	11.1244	+	8.73205i	0.278109	+	0.218301i
$41$	−27.9545			−0.681816			−0.340908	−	0.940097i	$-0.610734\pi$
$41$	−27.9545			−0.681816			−0.340908	+	0.940097i	$0.610734\pi$
$42$	24.3286	−	0.762464i	0.579253	−	0.0181539i
$43$	39.6475	+	39.6475i	0.922035	+	0.922035i	0.997173	−	0.0751379i	$-0.0239397\pi$
$43$	39.6475	+	39.6475i	0.922035	+	0.922035i	−0.0751379	+	0.997173i	$0.523940\pi$
$44$	−12.9509	−	7.47723i	−0.294339	−	0.169937i
$45$	13.5848	+	5.80284i	0.301884	+	0.128952i
$46$	14.6931	+	25.4491i	0.319414	+	0.553242i
$47$	−18.6173	−	69.4806i	−0.396112	−	1.47831i	−0.819877	−	0.572539i	$-0.805958\pi$
$47$	−18.6173	−	69.4806i	−0.396112	−	1.47831i	0.423765	−	0.905772i	$-0.360708\pi$
$48$	6.95445	+	6.95445i	0.144884	+	0.144884i
$49$	48.9038	−	3.06832i	0.998038	−	0.0626188i
$50$	−17.0000	−	31.0000i	−0.340000	−	0.620000i
$51$	26.0000	−	45.0333i	0.509804	−	0.883006i
$52$	29.9281	+	8.01921i	0.575541	+	0.154216i
$53$	−10.9641	+	40.9185i	−0.206870	+	0.772048i	0.782002	+	0.623276i	$0.214199\pi$
$53$	−10.9641	+	40.9185i	−0.206870	+	0.772048i	−0.988872	+	0.148772i	$0.952468\pi$
$54$	35.9992	+	20.7842i	0.666652	+	0.384892i
$55$	22.4317	+	29.9089i	0.407849	+	0.543798i
$56$	14.4317	+	13.5546i	0.257709	+	0.242046i
$57$	−25.0911	+	25.0911i	−0.440195	+	0.440195i
$58$	−21.6697	+	5.80639i	−0.373616	+	0.100110i
$59$	−55.8784	+	32.2614i	−0.947091	+	0.546803i	−0.892176	−	0.451688i	$-0.850822\pi$
$59$	−55.8784	+	32.2614i	−0.947091	+	0.546803i	−0.0549148	+	0.998491i	$0.517489\pi$
$60$	−9.15892	−	22.8182i	−0.152649	−	0.380303i
$61$	−29.5455	+	51.1744i	−0.484353	+	0.838924i	−0.999838	−	0.0179740i	$-0.994278\pi$
$61$	−29.5455	+	51.1744i	−0.484353	+	0.838924i	0.515485	+	0.856898i	$0.327612\pi$
$62$	−16.0000	+	16.0000i	−0.258065	+	0.258065i
$63$	18.2255	+	9.77446i	0.289294	+	0.155150i
$64$			8.00000i			0.125000i
$65$	−60.9306	−	47.8274i	−0.937394	−	0.735806i
$66$	13.0000	+	22.5167i	0.196970	+	0.341162i
$67$	53.5698	+	14.3540i	0.799550	+	0.214239i	0.635386	−	0.772194i	$-0.280841\pi$
$67$	53.5698	+	14.3540i	0.799550	+	0.214239i	0.164163	+	0.986433i	$0.447508\pi$
$68$	40.8563	−	10.9474i	0.600828	−	0.160991i
$69$		−	51.0911i		−	0.740451i
$70$	−19.8677	−	45.3351i	−0.283824	−	0.647645i
$71$	−36.3406			−0.511839			−0.255920	−	0.966698i	$-0.582378\pi$
$71$	−36.3406			−0.511839			−0.255920	+	0.966698i	$0.582378\pi$
$72$	2.16281	+	8.07171i	0.0300390	+	0.112107i
$73$	17.1198	−	63.8921i	0.234518	−	0.875234i	−0.743847	−	0.668350i	$-0.767001\pi$
$73$	17.1198	−	63.8921i	0.234518	−	0.875234i	0.978365	−	0.206884i	$-0.0663324\pi$
$74$	−81.3275	+	46.9545i	−1.09902	+	0.634520i
$75$	−1.35189	+	61.4544i	−0.0180252	+	0.819392i
$76$	−28.8634			−0.379781
$77$	27.5773	+	44.4862i	0.358147	+	0.577743i
$78$	−38.0911	−	38.0911i	−0.488347	−	0.488347i
$79$	35.6837	+	20.6020i	0.451692	+	0.260784i	0.708544	−	0.705666i	$-0.249352\pi$
$79$	35.6837	+	20.6020i	0.451692	+	0.260784i	−0.256853	+	0.966451i	$0.582686\pi$
$80$	7.85641	−	18.3923i	0.0982051	−	0.229904i
$81$	−22.8406	−	39.5610i	−0.281982	−	0.488408i
$82$	10.2320	+	38.1865i	0.124781	+	0.465689i
$83$	−9.12474	−	9.12474i	−0.109937	−	0.109937i	0.649999	−	0.759935i	$-0.274769\pi$
$83$	−9.12474	−	9.12474i	−0.109937	−	0.109937i	−0.759935	+	0.649999i	$0.774769\pi$
$84$	−9.94644	−	32.9545i	−0.118410	−	0.392315i
$85$	−104.681	−	14.9545i	−1.23154	−	0.175935i
$86$	39.6475	−	68.6715i	0.461018	−	0.798506i
$87$	37.6753	+	10.0951i	0.433049	+	0.116035i
$88$	−5.47371	+	20.4282i	−0.0622012	+	0.232138i
$89$	−42.1986	−	24.3634i	−0.474141	−	0.273746i	0.243830	−	0.969818i	$-0.421596\pi$
$89$	−42.1986	−	24.3634i	−0.474141	−	0.273746i	−0.717972	+	0.696072i	$0.754929\pi$
$90$	2.95445	−	20.6812i	0.0328272	−	0.229791i
$91$	−79.0455	−	74.2415i	−0.868632	−	0.815841i
$92$	29.3861	−	29.3861i	0.319414	−	0.319414i
$93$	37.9998	−	10.1820i	0.408600	−	0.109484i
$94$	−88.0979	+	50.8634i	−0.937212	+	0.541100i
$95$	66.3579	+	28.3453i	0.698505	+	0.298371i
$96$	6.95445	−	12.0455i	0.0724422	−	0.125474i
$97$	−63.7723	+	63.7723i	−0.657446	+	0.657446i	−0.954775	−	0.297329i	$-0.903904\pi$
$97$	−63.7723	+	63.7723i	−0.657446	+	0.657446i	0.297329	+	0.954775i	$0.403904\pi$
$98$	−22.0915	−	65.6808i	−0.225423	−	0.670212i
$99$			22.0911i			0.223142i
$100$	−36.1244	+	34.5692i	−0.361244	+	0.345692i
$101$	48.7495	+	84.4366i	0.482668	+	0.836006i	0.999802	−	0.0198988i	$-0.00633440\pi$
$101$	48.7495	+	84.4366i	0.482668	+	0.836006i	−0.517134	+	0.855905i	$0.673001\pi$
$102$	−71.0333	−	19.0333i	−0.696405	−	0.186601i
$103$	−46.8019	+	12.5405i	−0.454388	+	0.121753i	−0.478752	−	0.877950i	$-0.658911\pi$
$103$	−46.8019	+	12.5405i	−0.454388	+	0.121753i	0.0243641	+	0.999703i	$0.492244\pi$
$104$		−	43.8178i		−	0.421325i
$105$	−9.49569	+	85.5315i	−0.0904352	+	0.814585i
$106$	59.9089			0.565178
$107$	42.6126	+	159.032i	0.398249	+	1.48628i	0.816176	+	0.577803i	$0.196090\pi$
$107$	42.6126	+	159.032i	0.398249	+	1.48628i	−0.417927	+	0.908480i	$0.637243\pi$
$108$	15.2151	−	56.7834i	0.140880	−	0.525772i
$109$	146.122	−	84.3634i	1.34057	−	0.773976i	0.353675	−	0.935368i	$-0.384932\pi$
$109$	146.122	−	84.3634i	1.34057	−	0.773976i	0.986890	+	0.161393i	$0.0515986\pi$
$110$	32.6458	−	41.5897i	0.296780	−	0.378088i
$111$	163.271			1.47091
$112$	13.2335	−	24.6754i	0.118157	−	0.220316i
$113$	56.6356	+	56.6356i	0.501200	+	0.501200i	0.911811	−	0.410611i	$-0.134684\pi$
$113$	56.6356	+	56.6356i	0.501200	+	0.501200i	−0.410611	+	0.911811i	$0.634684\pi$
$114$	43.4591	+	25.0911i	0.381220	+	0.220097i
$115$	−96.4185	+	38.7012i	−0.838422	+	0.336532i
$116$	15.8634	+	27.4761i	0.136753	+	0.236863i
$117$	−11.8462	−	44.2106i	−0.101249	−	0.377868i
$118$	64.5228	+	64.5228i	0.546803	+	0.546803i
$119$	−144.127	−	33.8178i	−1.21115	−	0.284183i
$120$	−27.8178	+	20.8634i	−0.231815	+	0.173861i
$121$	32.5455	−	56.3705i	0.268971	−	0.465872i
$122$	80.7199	+	21.6288i	0.661639	+	0.177286i
$123$	17.7896	−	66.3915i	0.144631	−	0.539768i
$124$	27.7128	+	16.0000i	0.223490	+	0.129032i
$125$	117.000	−	44.0000i	0.936000	−	0.352000i
$126$	6.68116	−	28.4742i	0.0530251	−	0.225986i
$127$	3.04555	−	3.04555i	0.0239807	−	0.0239807i	−0.695015	−	0.718995i	$-0.744602\pi$
$127$	3.04555	−	3.04555i	0.0239807	−	0.0239807i	0.718995	+	0.695015i	$0.244602\pi$
$128$	10.9282	−	2.92820i	0.0853766	−	0.0228766i
$129$	−119.393	+	68.9317i	−0.925528	+	0.534354i
$130$	−43.0313	+	100.739i	−0.331010	+	0.774914i
$131$	56.9545	−	98.6480i	0.434767	−	0.753038i	−0.562510	−	0.826791i	$-0.690164\pi$
$131$	56.9545	−	98.6480i	0.434767	−	0.753038i	0.997277	+	0.0737524i	$0.0234975\pi$
$132$	26.0000	−	26.0000i	0.196970	−	0.196970i
$133$	89.0267	+	47.7456i	0.669374	+	0.358989i
$134$		−	78.4317i		−	0.585311i
$135$	−90.7442	+	115.605i	−0.672179	+	0.856335i
$136$	−29.9089	−	51.8037i	−0.219918	−	0.380910i
$137$	−140.390	−	37.6173i	−1.02474	−	0.274579i	−0.292965	−	0.956123i	$-0.594642\pi$
$137$	−140.390	−	37.6173i	−1.02474	−	0.274579i	−0.731776	+	0.681545i	$0.761308\pi$
$138$	−69.7917	+	18.7006i	−0.505737	+	0.135512i
$139$		−	177.022i		−	1.27354i	−0.771055	−	0.636769i	$-0.780271\pi$
$139$		−	177.022i		−	1.27354i	0.771055	−	0.636769i	$-0.219729\pi$
$140$	−54.6569	+	43.7336i	−0.390406	+	0.312383i
$141$	176.863			1.25435
$142$	13.3016	+	49.6422i	0.0936731	+	0.349593i
$143$	29.9807	−	111.890i	0.209656	−	0.782445i
$144$	10.2345	−	5.90890i	0.0710730	−	0.0410340i
$145$	−9.48749	−	78.7473i	−0.0654310	−	0.543085i
$146$	−93.5445			−0.640716
$147$	−23.8340	+	118.099i	−0.162136	+	0.803393i
$148$	93.9089	+	93.9089i	0.634520	+	0.634520i
$149$	219.026	+	126.454i	1.46997	+	0.848688i	0.999432	−	0.0336923i	$-0.0107266\pi$
$149$	219.026	+	126.454i	1.46997	+	0.848688i	0.470538	+	0.882380i	$0.344060\pi$
$150$	84.4431	−	20.6471i	0.562954	−	0.137648i
$151$	−102.954	−	178.322i	−0.681818	−	1.18094i	−0.974426	−	0.224710i	$-0.927856\pi$
$151$	−102.954	−	178.322i	−0.681818	−	1.18094i	0.292608	−	0.956232i	$-0.405477\pi$
$152$	10.5647	+	39.4281i	0.0695047	+	0.259395i
$153$	−44.1822	−	44.1822i	−0.288773	−	0.288773i
$154$	50.6753	−	53.9545i	0.329061	−	0.350354i
$155$	−48.0000	−	64.0000i	−0.309677	−	0.412903i
$156$	−38.0911	+	65.9757i	−0.244174	+	0.422921i
$157$	256.004	+	68.5960i	1.63060	+	0.436917i	0.954091	−	0.299518i	$-0.0968259\pi$
$157$	256.004	+	68.5960i	1.63060	+	0.436917i	0.676508	+	0.736436i	$0.263493\pi$
$158$	15.0817	−	56.2856i	0.0954537	−	0.356238i
$159$	−90.2038	−	52.0792i	−0.567320	−	0.327542i
$160$	−28.0000	−	4.00000i	−0.175000	−	0.0250000i
$161$	−139.249	+	42.0288i	−0.864904	+	0.261049i
$162$	−45.6812	+	45.6812i	−0.281982	+	0.281982i
$163$	−241.475	+	64.7031i	−1.48144	+	0.396952i	−0.906838	−	0.421479i	$-0.861511\pi$
$163$	−241.475	+	64.7031i	−1.48144	+	0.396952i	−0.574606	+	0.818430i	$0.694845\pi$
$164$	48.4185	−	27.9545i	0.295235	−	0.170454i
$165$	−85.3083	+	34.2417i	−0.517020	+	0.207525i
$166$	−9.12474	+	15.8045i	−0.0549683	+	0.0952079i
$167$	8.01191	−	8.01191i	0.0479755	−	0.0479755i	−0.682712	−	0.730688i	$-0.739200\pi$
$167$	8.01191	−	8.01191i	0.0479755	−	0.0479755i	0.730688	+	0.682712i	$0.239200\pi$
$168$	−41.3760	+	25.6493i	−0.246286	+	0.152674i
$169$			71.0000i			0.420118i
$170$	17.8878	+	148.471i	0.105222	+	0.873358i
$171$	21.3188	+	36.9253i	0.124672	+	0.215938i
$172$	−108.319	−	29.0240i	−0.629762	−	0.168744i
$173$	119.961	−	32.1435i	0.693418	−	0.185801i	0.105138	−	0.994458i	$-0.466472\pi$
$173$	119.961	−	32.1435i	0.693418	−	0.185801i	0.588281	+	0.808657i	$0.299805\pi$
$174$		−	55.1605i		−	0.317014i
$175$	168.607	−	46.8693i	0.963468	−	0.267825i
$176$	29.9089			0.169937
$177$	−41.0608	−	153.241i	−0.231982	−	0.865768i
$178$	−17.8352	+	66.5619i	−0.100198	+	0.373943i
$179$	−114.000	+	65.8178i	−0.636870	+	0.367697i	−0.783408	−	0.621508i	$-0.786520\pi$
$179$	−114.000	+	65.8178i	−0.636870	+	0.367697i	0.146538	+	0.989205i	$0.453187\pi$
$180$	−29.3324	+	3.53397i	−0.162958	+	0.0196332i
$181$	−149.681			−0.826968			−0.413484	−	0.910511i	$-0.635688\pi$
$181$	−149.681			−0.826968			−0.413484	+	0.910511i	$0.635688\pi$
$182$	−72.4831	+	135.153i	−0.398259	+	0.742596i
$183$	−102.737	−	102.737i	−0.561402	−	0.561402i
$184$	−50.8983	−	29.3861i	−0.276621	−	0.159707i
$185$	−123.677	−	308.123i	−0.668523	−	1.66553i
$186$	−27.8178	−	48.1819i	−0.149558	−	0.259042i
$187$	−40.9282	−	152.746i	−0.218867	−	0.816823i
$188$	101.727	+	101.727i	0.541100	+	0.541100i
$189$	−140.860	+	149.975i	−0.745293	+	0.793519i
$190$	14.4317	−	101.022i	0.0759562	−	0.531693i
$191$	−113.034	+	195.780i	−0.591799	+	1.02503i	0.402191	+	0.915556i	$0.368249\pi$
$191$	−113.034	+	195.780i	−0.591799	+	1.02503i	−0.993990	+	0.109470i	$0.965085\pi$
$192$	−18.9999	−	5.09101i	−0.0989579	−	0.0265157i
$193$	−57.2326	+	213.595i	−0.296542	+	1.10671i	0.643443	+	0.765494i	$0.277505\pi$
$193$	−57.2326	+	213.595i	−0.296542	+	1.10671i	−0.939985	+	0.341215i	$0.889161\pi$
$194$	110.457	+	63.7723i	0.569365	+	0.328723i
$195$	152.364	−	114.273i	0.781356	−	0.586017i
$196$	−81.6356	+	54.2183i	−0.416508	+	0.276624i
$197$	84.9089	−	84.9089i	0.431010	−	0.431010i	−0.457962	−	0.888972i	$-0.651420\pi$
$197$	84.9089	−	84.9089i	0.431010	−	0.431010i	0.888972	+	0.457962i	$0.151420\pi$
$198$	30.1770	−	8.08590i	0.152409	−	0.0408379i
$199$	−71.4085	+	41.2277i	−0.358837	+	0.207175i	−0.668570	−	0.743649i	$-0.733093\pi$
$199$	−71.4085	+	41.2277i	−0.358837	+	0.207175i	0.309734	+	0.950823i	$0.399760\pi$
$200$	60.4449	+	36.6936i	0.302224	+	0.183468i
$201$	−68.1812	+	118.093i	−0.339210	+	0.587529i
$202$	97.4990	−	97.4990i	0.482668	−	0.482668i
$203$	−3.47841	−	110.989i	−0.0171350	−	0.546744i
$204$			104.000i			0.509804i
$205$	−138.769	+	16.7189i	−0.676921	+	0.0815556i
$206$	34.2614	+	59.3425i	0.166317	+	0.288070i
$207$	−59.2991	−	15.8891i	−0.286469	−	0.0767591i
$208$	−59.8562	+	16.0384i	−0.287770	+	0.0771078i
$209$			107.909i			0.516311i
$210$	120.314	−	18.3353i	0.572923	−	0.0873111i
$211$	205.703			0.974895			0.487448	−	0.873152i	$-0.337928\pi$
$211$	205.703			0.974895			0.487448	+	0.873152i	$0.337928\pi$
$212$	−21.9282	−	81.8371i	−0.103435	−	0.386024i
$213$	23.1263	−	86.3085i	0.108574	−	0.405204i
$214$	201.645	−	116.420i	0.942266	−	0.544018i
$215$	220.527	+	173.102i	1.02570	+	0.805126i
$216$	−83.1366			−0.384892
$217$	−59.0109	−	95.1931i	−0.271939	−	0.438678i
$218$	−168.727	−	168.727i	−0.773976	−	0.773976i
$219$	140.848	+	81.3188i	0.643143	+	0.371319i
$220$	−68.7617	−	29.3721i	−0.312553	−	0.133509i
$221$	163.818	+	283.741i	0.741257	+	1.28389i
$222$	−59.7614	−	223.033i	−0.269196	−	1.00465i
$223$	62.8872	+	62.8872i	0.282005	+	0.282005i	0.833908	−	0.551903i	$-0.186098\pi$
$223$	62.8872	+	62.8872i	0.282005	+	0.282005i	−0.551903	+	0.833908i	$0.686098\pi$
$224$	−38.5510	−	9.04555i	−0.172103	−	0.0403819i
$225$	70.9068	+	20.6812i	0.315141	+	0.0919163i
$226$	56.6356	−	98.0958i	0.250600	−	0.434052i
$227$	249.547	+	66.8659i	1.09933	+	0.294564i	0.762490	−	0.647000i	$-0.223976\pi$
$227$	249.547	+	66.8659i	1.09933	+	0.294564i	0.336836	+	0.941563i	$0.390643\pi$
$228$	18.3680	−	68.5502i	0.0805612	−	0.300659i
$229$	106.598	+	61.5445i	0.465494	+	0.268753i	0.714352	−	0.699787i	$-0.246722\pi$
$229$	106.598	+	61.5445i	0.465494	+	0.268753i	−0.248857	+	0.968540i	$0.580055\pi$
$230$	88.1584	+	117.545i	0.383297	+	0.511063i
$231$	−123.204	+	37.1859i	−0.533350	+	0.160978i
$232$	31.7267	−	31.7267i	0.136753	−	0.136753i
$233$	307.851	−	82.4883i	1.32125	−	0.354027i	0.471802	−	0.881704i	$-0.343604\pi$
$233$	307.851	−	82.4883i	1.32125	−	0.354027i	0.849445	+	0.527677i	$0.176937\pi$
$234$	−56.0568	+	32.3644i	−0.239559	+	0.138309i
$235$	−133.973	−	333.774i	−0.570097	−	1.42032i
$236$	64.5228	−	111.757i	0.273402	−	0.473545i
$237$	−71.6377	+	71.6377i	−0.302269	+	0.302269i
$238$	6.55823	+	209.260i	0.0275556	+	0.879242i
$239$			174.725i			0.731065i	0.930798	+	0.365533i	$0.119113\pi$
$239$			174.725i			0.731065i	−0.930798	+	0.365533i	$0.880887\pi$
$240$	38.6819	+	30.3633i	0.161175	+	0.126514i
$241$	121.909	+	211.152i	0.505846	+	0.876151i	0.999977	+	0.00676366i	$0.00215296\pi$
$241$	121.909	+	211.152i	0.505846	+	0.876151i	−0.494131	+	0.869387i	$0.664514\pi$
$242$	−88.9161	−	23.8250i	−0.367422	−	0.0984504i
$243$	−147.033	+	39.3974i	−0.605074	+	0.162129i
$244$		−	118.182i		−	0.484353i
$245$	240.929	−	44.4797i	0.983382	−	0.181550i
$246$	−97.2039			−0.395138
$247$	−57.8654	−	215.956i	−0.234273	−	0.874318i
$248$	11.7128	−	43.7128i	0.0472291	−	0.176261i
$249$	27.4779	−	15.8644i	0.110353	−	0.0637124i
$250$	−102.930	−	143.720i	−0.411720	−	0.574879i
$251$	54.2733			0.216228			0.108114	−	0.994138i	$-0.465519\pi$
$251$	54.2733			0.216228			0.108114	+	0.994138i	$0.465519\pi$
$252$	−41.3420	+	1.29567i	−0.164056	+	0.00514153i
$253$	−109.863	−	109.863i	−0.434243	−	0.434243i
$254$	−5.27505	−	3.04555i	−0.0207679	−	0.0119903i
$255$	102.133	−	239.100i	0.400523	−	0.937647i
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	5.60709	+	20.9259i	0.0218175	+	0.0814238i	0.975976	−	0.217877i	$-0.0699132\pi$
$257$	5.60709	+	20.9259i	0.0218175	+	0.0814238i	−0.954159	+	0.299301i	$0.903247\pi$
$258$	137.863	+	137.863i	0.534354	+	0.534354i
$259$	−134.311	−	444.998i	−0.518575	−	1.71814i
$260$	153.362	+	21.9089i	0.589855	+	0.0842650i
$261$	23.4338	−	40.5884i	0.0897845	−	0.155511i
$262$	−155.602	−	41.6936i	−0.593902	−	0.159136i
$263$	−87.0184	+	324.757i	−0.330868	+	1.23482i	0.577411	+	0.816454i	$0.304063\pi$
$263$	−87.0184	+	324.757i	−0.330868	+	1.23482i	−0.908279	+	0.418364i	$0.862604\pi$
$264$	−45.0333	−	26.0000i	−0.170581	−	0.0984848i
$265$	−29.9545	+	209.681i	−0.113036	+	0.791250i
$266$	32.6356	−	139.089i	0.122690	−	0.522890i
$267$	84.7169	−	84.7169i	0.317292	−	0.317292i
$268$	−107.140	+	28.7080i	−0.399775	+	0.107119i
$269$	−93.6867	+	54.0901i	−0.348278	+	0.201078i	−0.663926	−	0.747798i	$-0.731111\pi$
$269$	−93.6867	+	54.0901i	−0.348278	+	0.201078i	0.315649	+	0.948876i	$0.397778\pi$
$270$	191.134	+	81.6444i	0.707905	+	0.302387i
$271$	30.7603	−	53.2785i	0.113507	−	0.196600i	−0.803675	−	0.595068i	$-0.797125\pi$
$271$	30.7603	−	53.2785i	0.113507	−	0.196600i	0.917182	+	0.398469i	$0.130458\pi$
$272$	−59.8178	+	59.8178i	−0.219918	+	0.219918i
$273$	226.626	−	140.487i	0.830130	−	0.514604i
$274$			205.545i			0.750162i
$275$	129.241	+	135.055i	0.469967	+	0.491109i
$276$	51.0911	+	88.4924i	0.185113	+	0.320625i
$277$	344.920	+	92.4210i	1.24520	+	0.333650i	0.820480	−	0.571675i	$-0.193706\pi$
$277$	344.920	+	92.4210i	1.24520	+	0.333650i	0.424719	+	0.905325i	$0.360373\pi$
$278$	−241.816	+	64.7945i	−0.869842	+	0.233074i
$279$		−	47.2712i		−	0.169431i
$280$	79.7470	+	58.6551i	0.284811	+	0.209482i
$281$	−398.542			−1.41830			−0.709150	−	0.705057i	$-0.750921\pi$
$281$	−398.542			−1.41830			−0.709150	+	0.705057i	$0.750921\pi$
$282$	−64.7365	−	241.600i	−0.229562	−	0.856737i
$283$	−127.393	+	475.436i	−0.450151	+	1.67999i	0.251814	+	0.967776i	$0.418973\pi$
$283$	−127.393	+	475.436i	−0.450151	+	1.67999i	−0.701965	+	0.712211i	$0.747694\pi$
$284$	62.9437	−	36.3406i	0.221633	−	0.127960i
$285$	−109.548	+	139.561i	−0.384380	+	0.489688i
$286$	−163.818			−0.572790
$287$	−195.585	+	6.12967i	−0.681481	+	0.0213577i
$288$	−11.8178	−	11.8178i	−0.0410340	−	0.0410340i
$289$	137.067	+	79.1356i	0.474280	+	0.273826i
$290$	−104.098	+	41.7837i	−0.358959	+	0.144082i
$291$	−110.875	−	192.042i	−0.381015	−	0.659937i
$292$	34.2397	+	127.784i	0.117259	+	0.437617i
$293$	−187.818	−	187.818i	−0.641016	−	0.641016i	0.309789	−	0.950805i	$-0.399742\pi$
$293$	−187.818	−	187.818i	−0.641016	−	0.641016i	−0.950805	+	0.309789i	$0.899742\pi$
$294$	170.050	−	10.6693i	0.578400	−	0.0362900i
$295$	−258.091	+	193.568i	−0.874885	+	0.656164i
$296$	93.9089	−	162.655i	0.317260	−	0.549510i
$297$	−212.291	−	56.8832i	−0.714785	−	0.191526i
$298$	92.5711	−	345.480i	0.310641	−	1.15933i
$299$	278.781	+	160.954i	0.932379	+	0.538309i
$300$	−59.1128	−	107.794i	−0.197043	−	0.359313i
$301$	286.090	+	268.703i	0.950465	+	0.892700i
$302$	−205.909	+	205.909i	−0.681818	+	0.681818i
$303$	−231.559	+	62.0460i	−0.764221	+	0.204772i
$304$	49.9928	−	28.8634i	0.164450	−	0.0949452i
$305$	−116.061	+	271.705i	−0.380528	+	0.890837i
$306$	−44.1822	+	76.5258i	−0.144386	+	0.250084i
$307$	−171.398	+	171.398i	−0.558300	+	0.558300i	−0.928823	−	0.370523i	$-0.879178\pi$
$307$	−171.398	+	171.398i	−0.558300	+	0.558300i	0.370523	+	0.928823i	$0.379178\pi$
$308$	−92.2516	−	49.4751i	−0.299518	−	0.160633i
$309$		−	119.135i		−	0.385549i
$310$	−69.8564	+	88.9948i	−0.225343	+	0.287080i
$311$	1.73861	+	3.01137i	0.00559039	+	0.00968285i	0.868807	−	0.495151i	$-0.164887\pi$
$311$	1.73861	+	3.01137i	0.00559039	+	0.00968285i	−0.863217	+	0.504834i	$0.831554\pi$
$312$	104.067	+	27.8846i	0.333547	+	0.0893738i
$313$	−20.6120	+	5.52297i	−0.0658530	+	0.0176453i	−0.291595	−	0.956542i	$-0.594186\pi$
$313$	−20.6120	+	5.52297i	−0.0658530	+	0.0176453i	0.225742	+	0.974187i	$0.427519\pi$
$314$		−	374.816i		−	1.19368i
$315$	96.3193	+	37.6212i	0.305776	+	0.119432i
$316$	−82.4079			−0.260784
$317$	−105.415	−	393.415i	−0.332540	−	1.24106i	−0.906511	−	0.422182i	$-0.861264\pi$
$317$	−105.415	−	393.415i	−0.332540	−	1.24106i	0.573971	−	0.818876i	$-0.305402\pi$
$318$	−38.1246	+	142.283i	−0.119889	+	0.447431i
$319$	102.723	−	59.3069i	0.322015	−	0.185915i
$320$	4.78461	+	39.7128i	0.0149519	+	0.124103i
$321$	−404.818			−1.26111
$322$	108.381	+	174.835i	0.336588	+	0.542965i
$323$	−215.818	−	215.818i	−0.668167	−	0.668167i
$324$	79.1221	+	45.6812i	0.244204	+	0.140991i
$325$	−331.070	−	200.979i	−1.01868	−	0.618397i
$326$	176.772	+	306.179i	0.542246	+	0.939198i
$327$	107.374	+	400.724i	0.328360	+	1.22546i
$328$	−55.9089	−	55.9089i	−0.170454	−	0.170454i
$329$	−145.492	−	482.043i	−0.442226	−	1.46518i
$330$	78.0000	+	104.000i	0.236364	+	0.315152i
$331$	210.317	−	364.279i	0.635398	−	1.10054i	−0.351033	−	0.936363i	$-0.614169\pi$
$331$	210.317	−	364.279i	0.635398	−	1.10054i	0.986431	−	0.164179i	$-0.0524973\pi$
$332$	24.9293	+	6.67977i	0.0750881	+	0.0201198i
$333$	50.7767	−	189.501i	0.152483	−	0.569073i
$334$	−13.8770	−	8.01191i	−0.0415480	−	0.0239877i
$335$	274.511	+	39.2158i	0.819435	+	0.117062i
$336$	50.1822	+	47.1323i	0.149352	+	0.140275i
$337$	−34.2712	+	34.2712i	−0.101695	+	0.101695i	−0.756124	−	0.654429i	$-0.772909\pi$
$337$	−34.2712	+	34.2712i	−0.101695	+	0.101695i	0.654429	+	0.756124i	$0.272909\pi$
$338$	96.9878	−	25.9878i	0.286946	−	0.0768870i
$339$	−170.551	+	98.4674i	−0.503099	+	0.290464i
$340$	196.268	−	78.7793i	0.577257	−	0.231704i
$341$	59.8178	−	103.607i	0.175419	−	0.303834i
$342$	42.6377	−	42.6377i	0.124672	−	0.124672i
$343$	341.486	−	32.1910i	0.995586	−	0.0938514i
$344$			158.590i			0.461018i
$345$	−30.5564	−	253.621i	−0.0885692	−	0.735134i
$346$	−87.8178	−	152.105i	−0.253809	−	0.439610i
$347$	−139.784	−	37.4549i	−0.402834	−	0.107939i	0.0517123	−	0.998662i	$-0.483532\pi$
$347$	−139.784	−	37.4549i	−0.402834	−	0.107939i	−0.454547	+	0.890723i	$0.650199\pi$
$348$	−75.3506	+	20.1901i	−0.216525	+	0.0580176i
$349$			248.861i			0.713070i	0.934282	+	0.356535i	$0.116042\pi$
$349$			248.861i			0.713070i	−0.934282	+	0.356535i	$0.883958\pi$
$350$	−125.739	−	213.166i	−0.359255	−	0.609045i
$351$	455.358			1.29732
$352$	−10.9474	−	40.8563i	−0.0311006	−	0.116069i
$353$	103.352	−	385.714i	0.292781	−	1.09267i	−0.650182	−	0.759778i	$-0.725307\pi$
$353$	103.352	−	385.714i	0.292781	−	1.09267i	0.942963	−	0.332896i	$-0.108026\pi$
$354$	−194.302	+	112.180i	−0.548875	+	0.316893i
$355$	−180.398	+	21.7344i	−0.508164	+	0.0612238i
$356$	97.4534			0.273746
$357$	172.036	−	320.780i	0.481894	−	0.898542i
$358$	131.636	+	131.636i	0.367697	+	0.367697i
$359$	−370.734	−	214.043i	−1.03269	−	0.596221i	−0.114933	−	0.993373i	$-0.536665\pi$
$359$	−370.734	−	214.043i	−1.03269	−	0.596221i	−0.917753	+	0.397152i	$0.869999\pi$
$360$	15.5639	+	38.7753i	0.0432331	+	0.107709i
$361$	−76.3634	−	132.265i	−0.211533	−	0.366386i
$362$	54.7871	+	204.468i	0.151346	+	0.564829i
$363$	113.168	+	113.168i	0.311758	+	0.311758i
$364$	211.152	+	49.5445i	0.580089	+	0.136111i
$365$	46.7723	−	327.406i	0.128143	−	0.897002i
$366$	−102.737	+	177.945i	−0.280701	+	0.486188i
$367$	227.458	+	60.9472i	0.619777	+	0.166069i	0.555026	−	0.831833i	$-0.312708\pi$
$367$	227.458	+	60.9472i	0.619777	+	0.166069i	0.0647505	+	0.997901i	$0.479375\pi$
$368$	−21.5121	+	80.2844i	−0.0584569	+	0.218164i
$369$	−71.5251	−	41.2950i	−0.193835	−	0.111911i
$370$	−375.636	+	281.727i	−1.01523	+	0.761424i
$371$	−67.7386	+	288.693i	−0.182584	+	0.778149i
$372$	−55.6356	+	55.6356i	−0.149558	+	0.149558i
$373$	−146.535	+	39.2640i	−0.392856	+	0.105265i	−0.449839	−	0.893110i	$-0.648519\pi$
$373$	−146.535	+	39.2640i	−0.392856	+	0.105265i	0.0569830	+	0.998375i	$0.481852\pi$
$374$	−193.674	+	111.818i	−0.517845	+	0.298978i
$375$	30.0435	+	305.874i	0.0801160	+	0.815665i
$376$	101.727	−	176.196i	0.270550	−	0.468606i
$377$	−173.774	+	173.774i	−0.460940	+	0.460940i
$378$	256.428	+	137.524i	0.678382	+	0.363820i
$379$			66.4317i			0.175281i	0.996152	+	0.0876407i	$0.0279327\pi$
$379$			66.4317i			0.175281i	−0.996152	+	0.0876407i	$0.972067\pi$
$380$	−143.281	+	17.2625i	−0.377054	+	0.0454276i
$381$	5.29503	+	9.17126i	0.0138977	+	0.0240716i
$382$	308.814	+	82.7464i	0.808413	+	0.216614i
$383$	657.478	−	176.171i	1.71665	−	0.459975i	0.739612	−	0.673034i	$-0.235009\pi$
$383$	657.478	−	176.171i	1.71665	−	0.459975i	0.977040	+	0.213058i	$0.0683424\pi$
$384$			27.8178i			0.0724422i
$385$	163.503	+	204.341i	0.424683	+	0.530756i
$386$	312.725			0.810167
$387$	42.8750	+	160.012i	0.110788	+	0.413467i
$388$	46.6845	−	174.229i	0.120321	−	0.449044i
$389$	−80.4633	+	46.4555i	−0.206846	+	0.119423i	−0.599845	−	0.800116i	$-0.704771\pi$
$389$	−80.4633	+	46.4555i	−0.206846	+	0.119423i	0.392999	+	0.919539i	$0.371438\pi$
$390$	−211.869	−	166.307i	−0.543255	−	0.426427i
$391$	439.453			1.12392
$392$	103.944	+	91.6710i	0.265164	+	0.233855i
$393$	198.043	+	198.043i	0.503927	+	0.503927i
$394$	−147.067	−	84.9089i	−0.373265	−	0.215505i
$395$	189.459	+	80.9287i	0.479643	+	0.204883i
$396$	−22.0911	−	38.2629i	−0.0557856	−	0.0966235i
$397$	93.6525	+	349.516i	0.235900	+	0.880393i	0.977741	+	0.209816i	$0.0672865\pi$
$397$	93.6525	+	349.516i	0.235900	+	0.880393i	−0.741840	+	0.670576i	$0.766047\pi$
$398$	82.4555	+	82.4555i	0.207175	+	0.207175i
$399$	−170.050	+	181.053i	−0.426190	+	0.453768i
$400$	28.0000	−	96.0000i	0.0700000	−	0.240000i
$401$	315.270	−	546.064i	0.786210	−	1.36176i	−0.142064	−	0.989858i	$-0.545374\pi$
$401$	315.270	−	546.064i	0.786210	−	1.36176i	0.928274	−	0.371898i	$-0.121293\pi$
$402$	186.274	+	49.9121i	0.463369	+	0.124159i
$403$	−64.1537	+	239.425i	−0.159190	+	0.594107i
$404$	−168.873	−	97.4990i	−0.418003	−	0.241334i
$405$	−137.043	−	182.725i	−0.338379	−	0.451172i
$406$	−150.341	+	45.3764i	−0.370297	+	0.111765i
$407$	351.089	−	351.089i	0.862627	−	0.862627i
$408$	142.067	−	38.0666i	0.348203	−	0.0933006i
$409$	176.077	−	101.658i	0.430507	−	0.248554i	−0.269055	−	0.963125i	$-0.586711\pi$
$409$	176.077	−	101.658i	0.430507	−	0.248554i	0.699563	+	0.714571i	$0.253378\pi$
$410$	73.6313	+	183.442i	0.179589	+	0.447420i
$411$	178.681	−	309.485i	0.434747	−	0.753004i
$412$	68.5228	−	68.5228i	0.166317	−	0.166317i
$413$	−383.883	+	237.972i	−0.929498	+	0.576202i
$414$			86.8199i			0.209710i
$415$	−50.7534	−	39.8388i	−0.122297	−	0.0959972i
$416$	43.8178	+	75.8947i	0.105331	+	0.182439i
$417$	420.425	+	112.652i	1.00821	+	0.270150i
$418$	147.406	−	39.4974i	0.352647	−	0.0944914i
$419$			716.269i			1.70947i	0.519062	+	0.854736i	$0.326281\pi$
$419$			716.269i			1.70947i	−0.519062	+	0.854736i	$0.673719\pi$
$420$	−69.0844	−	157.641i	−0.164487	−	0.375335i
$421$	−692.449			−1.64477			−0.822386	−	0.568929i	$-0.807358\pi$
$421$	−692.449			−1.64477			−0.822386	+	0.568929i	$0.807358\pi$
$422$	−75.2925	−	280.995i	−0.178418	−	0.665866i
$423$	55.0038	−	205.277i	0.130033	−	0.485289i
$424$	−103.765	+	59.9089i	−0.244729	+	0.141295i
$425$	−528.592	−	11.6281i	−1.24375	−	0.0273602i
$426$	−126.364			−0.296630
$427$	−195.496	+	364.524i	−0.457836	+	0.853685i
$428$	−232.840	−	232.840i	−0.544018	−	0.544018i
$429$	246.658	+	142.408i	0.574960	+	0.331953i
$430$	155.743	−	364.605i	0.362194	−	0.847918i
$431$	−248.737	−	430.824i	−0.577115	−	0.999592i	−0.995808	−	0.0914647i	$-0.970845\pi$
$431$	−248.737	−	430.824i	−0.577115	−	0.999592i	0.418693	−	0.908128i	$-0.362488\pi$
$432$	30.4301	+	113.567i	0.0704401	+	0.262886i
$433$	−191.729	−	191.729i	−0.442792	−	0.442792i	0.450158	−	0.892949i	$-0.351368\pi$
$433$	−191.729	−	191.729i	−0.442792	−	0.442792i	−0.892949	+	0.450158i	$0.851368\pi$
$434$	−108.437	+	115.453i	−0.249854	+	0.266022i
$435$	193.062	+	27.5802i	0.443820	+	0.0634028i
$436$	−168.727	+	292.243i	−0.386988	+	0.670283i
$437$	−289.660	−	77.6141i	−0.662837	−	0.177607i
$438$	59.5295	−	222.167i	0.135912	−	0.507231i
$439$	−460.252	−	265.727i	−1.04841	−	0.605300i	−0.126206	−	0.992004i	$-0.540280\pi$
$439$	−460.252	−	265.727i	−1.04841	−	0.605300i	−0.922204	+	0.386704i	$0.873614\pi$
$440$	−14.9545	+	104.681i	−0.0339874	+	0.237912i
$441$	129.659	+	64.3913i	0.294012	+	0.146012i
$442$	327.636	−	327.636i	0.741257	−	0.741257i
$443$	−152.513	+	40.8658i	−0.344274	+	0.0922479i	−0.426813	−	0.904340i	$-0.640364\pi$
$443$	−152.513	+	40.8658i	−0.344274	+	0.0922479i	0.0825391	+	0.996588i	$0.473697\pi$
$444$	−282.794	+	163.271i	−0.636924	+	0.367728i
$445$	−224.049	−	95.7042i	−0.503481	−	0.215066i
$446$	62.8872	−	108.924i	0.141003	−	0.244224i
$447$	−439.711	+	439.711i	−0.983693	+	0.983693i
$448$	1.75419	+	55.9725i	0.00391560	+	0.124939i
$449$		−	297.590i		−	0.662784i	−0.943493	−	0.331392i	$-0.892482\pi$
$449$		−	297.590i		−	0.662784i	0.943493	−	0.331392i	$-0.107518\pi$
$450$	2.29729	−	104.430i	0.00510508	−	0.232067i
$451$	−104.511	−	181.018i	−0.231731	−	0.401371i
$452$	−154.731	−	41.4601i	−0.342326	−	0.0917260i
$453$	489.031	−	131.036i	1.07954	−	0.289262i
$454$		−	365.362i		−	0.804763i
$455$	−436.792	−	321.267i	−0.959983	−	0.706082i
$456$	−100.364			−0.220097
$457$	188.834	+	704.739i	0.413204	+	1.54210i	0.788406	+	0.615155i	$0.210907\pi$
$457$	188.834	+	704.739i	0.413204	+	1.54210i	−0.375202	+	0.926943i	$0.622427\pi$
$458$	45.0537	−	168.143i	0.0983705	−	0.367124i
$459$	538.349	−	310.816i	1.17287	−	0.677158i
$460$	128.301	−	163.451i	0.278914	−	0.355328i
$461$	−16.3644			−0.0354976			−0.0177488	−	0.999842i	$-0.505650\pi$
$461$	−16.3644			−0.0354976			−0.0177488	+	0.999842i	$0.505650\pi$
$462$	95.8927	+	154.689i	0.207560	+	0.334824i
$463$	185.921	+	185.921i	0.401557	+	0.401557i	0.878781	−	0.477225i	$-0.158357\pi$
$463$	185.921	+	185.921i	0.401557	+	0.401557i	−0.477225	+	0.878781i	$0.658357\pi$
$464$	−54.9523	−	31.7267i	−0.118432	−	0.0683765i
$465$	182.545	−	73.2714i	0.392571	−	0.157573i
$466$	−225.362	−	390.339i	−0.483610	−	0.837637i
$467$	−84.3641	−	314.851i	−0.180651	−	0.674200i	−0.995520	−	0.0945537i	$-0.969858\pi$
$467$	−84.3641	−	314.851i	−0.180651	−	0.674200i	0.814869	−	0.579646i	$-0.196809\pi$
$468$	64.7288	+	64.7288i	0.138309	+	0.138309i
$469$	377.952	+	88.6822i	0.805868	+	0.189088i
$470$	−406.907	+	305.180i	−0.865759	+	0.649319i
$471$	−325.830	+	564.354i	−0.691783	+	1.19820i
$472$	−176.279	−	47.2339i	−0.373474	−	0.100072i
$473$	−108.509	+	404.963i	−0.229407	+	0.856158i
$474$	124.080	+	71.6377i	0.261772	+	0.151134i
$475$	346.360	+	101.022i	0.729179	+	0.212677i
$476$	283.453	−	85.5530i	0.595490	−	0.179733i
$477$	−88.4990	+	88.4990i	−0.185532	+	0.185532i
$478$	238.678	−	63.9537i	0.499327	−	0.133794i
$479$	452.460	−	261.228i	0.944592	−	0.545361i	0.0531954	−	0.998584i	$-0.483059\pi$
$479$	452.460	−	261.228i	0.944592	−	0.545361i	0.891397	+	0.453223i	$0.149726\pi$
$480$	27.3185	−	63.9542i	0.0569135	−	0.133238i
$481$	−514.360	+	890.898i	−1.06936	+	1.85218i
$482$	243.818	−	243.818i	0.505846	−	0.505846i
$483$	−11.2029	−	357.462i	−0.0231945	−	0.740087i
$484$			130.182i			0.268971i
$485$	−278.431	+	354.713i	−0.574085	+	0.731366i
$486$	107.636	+	186.430i	0.221472	+	0.383602i
$487$	−286.054	−	76.6478i	−0.587379	−	0.157388i	−0.0471240	−	0.998889i	$-0.515006\pi$
$487$	−286.054	−	76.6478i	−0.587379	−	0.157388i	−0.540255	+	0.841501i	$0.681672\pi$
$488$	−161.440	+	43.2577i	−0.330819	+	0.0886428i
$489$		−	614.677i		−	1.25701i
$490$	−148.946	−	312.834i	−0.303972	−	0.638436i
$491$	−232.000			−0.472505			−0.236253	−	0.971692i	$-0.575919\pi$
$491$	−232.000			−0.472505			−0.236253	+	0.971692i	$0.575919\pi$
$492$	35.5791	+	132.783i	0.0723153	+	0.269884i
$493$	−86.8314	+	324.059i	−0.176129	+	0.657321i
$494$	−273.822	+	158.091i	−0.554295	+	0.320022i
$495$	13.2122	+	109.662i	0.0266912	+	0.221540i
$496$	−64.0000			−0.129032
$497$	−254.259	+	7.96853i	−0.511588	+	0.0160333i
$498$	−31.7288	−	31.7288i	−0.0637124	−	0.0637124i
$499$	181.375	+	104.717i	0.363477	+	0.209853i	0.670605	−	0.741815i	$-0.266035\pi$
$499$	181.375	+	104.717i	0.363477	+	0.209853i	−0.307128	+	0.951668i	$0.599368\pi$
$500$	−158.650	+	193.210i	−0.317300	+	0.386420i
$501$	13.9296	+	24.1268i	0.0278036	+	0.0481572i
$502$	−19.8654	−	74.1387i	−0.0395725	−	0.147687i
$503$	−104.055	−	104.055i	−0.206870	−	0.206870i	0.596066	−	0.802935i	$-0.296730\pi$
$503$	−104.055	−	104.055i	−0.206870	−	0.206870i	−0.802935	+	0.596066i	$0.796730\pi$
$504$	16.9021	+	56.0000i	0.0335360	+	0.111111i
$505$	292.497	+	389.996i	0.579202	+	0.772269i
$506$	−109.863	+	190.289i	−0.217121	+	0.376065i
$507$	−168.624	−	45.1827i	−0.332592	−	0.0891178i
$508$	−2.22950	+	8.32059i	−0.00438877	+	0.0163791i
$509$	65.4629	+	37.7950i	0.128611	+	0.0742535i	0.562925	−	0.826508i	$-0.309676\pi$
$509$	65.4629	+	37.7950i	0.128611	+	0.0742535i	−0.434314	+	0.900761i	$0.643009\pi$
$510$	−364.000	−	52.0000i	−0.713725	−	0.101961i
$511$	105.770	−	450.779i	0.206987	−	0.882151i
$512$	−16.0000	+	16.0000i	−0.0312500	+	0.0312500i
$513$	−409.740	+	109.789i	−0.798713	+	0.214014i
$514$	26.5330	−	15.3188i	0.0516206	−	0.0298032i
$515$	−224.829	+	90.2436i	−0.436562	+	0.175230i
$516$	137.863	−	238.786i	0.267177	−	0.462764i
$517$	380.317	−	380.317i	0.735622	−	0.735622i
$518$	−558.717	+	346.353i	−1.07860	+	0.668635i
$519$			305.362i			0.588367i
$520$	−26.2064	−	217.516i	−0.0503969	−	0.418300i
$521$	−172.135	−	298.146i	−0.330393	−	0.572257i	0.652196	−	0.758050i	$-0.273848\pi$
$521$	−172.135	−	298.146i	−0.330393	−	0.572257i	−0.982589	+	0.185793i	$0.940514\pi$
$522$	−64.0222	−	17.1547i	−0.122648	−	0.0328634i
$523$	57.3080	−	15.3556i	0.109576	−	0.0293607i	−0.203615	−	0.979051i	$-0.565269\pi$
$523$	57.3080	−	15.3556i	0.109576	−	0.0293607i	0.313190	+	0.949690i	$0.398602\pi$
$524$			227.818i			0.434767i
$525$	4.01673	+	430.266i	0.00765092	+	0.819554i
$526$	475.477			0.903949
$527$	87.5793	+	326.851i	0.166185	+	0.620210i
$528$	−19.0333	+	71.0333i	−0.0360480	+	0.134533i
$529$	−84.2017	+	48.6139i	−0.159171	+	0.0918977i
$530$	297.394	−	35.8301i	0.561121	−	0.0676039i
$531$	−190.629			−0.359001
$532$	−201.944	+	6.32897i	−0.379595	+	0.0118966i
$533$	306.226	+	306.226i	0.574532	+	0.574532i
$534$	−146.734	−	84.7169i	−0.274783	−	0.158646i
$535$	306.647	+	763.967i	0.573171	+	1.42798i
$536$	78.4317	+	135.848i	0.146328	+	0.253447i
$537$	−83.7698	−	312.633i	−0.155996	−	0.582185i
$538$	108.180	+	108.180i	0.201078	+	0.201078i
$539$	202.701	+	305.204i	0.376069	+	0.566241i
$540$	41.5683	−	290.978i	0.0769784	−	0.538849i
$541$	358.793	−	621.448i	0.663203	−	1.14870i	−0.316566	−	0.948571i	$-0.602530\pi$
$541$	358.793	−	621.448i	0.663203	−	1.14870i	0.979769	−	0.200131i	$-0.0641368\pi$
$542$	−84.0388	−	22.5181i	−0.155053	−	0.0415464i
$543$	95.2536	−	355.491i	0.175421	−	0.654680i
$544$	103.607	+	59.8178i	0.190455	+	0.109959i
$545$	674.907	−	506.180i	1.23836	−	0.928771i
$546$	−274.859	−	258.154i	−0.503405	−	0.472810i
$547$	392.507	−	392.507i	0.717563	−	0.717563i	−0.250543	−	0.968105i	$-0.580609\pi$
$547$	392.507	−	392.507i	0.717563	−	0.717563i	0.968105	+	0.250543i	$0.0806091\pi$
$548$	280.779	−	75.2345i	0.512370	−	0.137289i
$549$	−151.192	+	87.2909i	−0.275396	+	0.159000i
$550$	137.183	−	225.980i	0.249424	−	0.410873i
$551$	114.467	−	198.263i	0.207745	−	0.359825i
$552$	102.182	−	102.182i	0.185113	−	0.185113i
$553$	254.180	+	136.319i	0.459639	+	0.246507i
$554$		−	504.998i		−	0.911549i
$555$	810.495	−	97.6486i	1.46035	−	0.175943i
$556$	177.022	+	306.611i	0.318384	+	0.551458i
$557$	−193.665	−	51.8922i	−0.347692	−	0.0931638i	0.0807466	−	0.996735i	$-0.474270\pi$
$557$	−193.665	−	51.8922i	−0.347692	−	0.0931638i	−0.428439	+	0.903571i	$0.640936\pi$
$558$	−64.5737	+	17.3025i	−0.115723	+	0.0310080i
$559$		−	868.634i		−	1.55391i
$560$	50.9349	−	130.406i	0.0909552	−	0.232867i
$561$	388.816			0.693076
$562$	145.877	+	544.419i	0.259567	+	0.968717i
$563$	−159.367	+	594.765i	−0.283067	+	1.05642i	0.667173	+	0.744903i	$0.267504\pi$
$563$	−159.367	+	594.765i	−0.283067	+	1.05642i	−0.950240	+	0.311518i	$0.899163\pi$
$564$	−306.336	+	176.863i	−0.543149	+	0.313588i
$565$	315.017	+	247.273i	0.557553	+	0.437650i
$566$	696.087			1.22984
$567$	−168.480	−	271.783i	−0.297143	−	0.479335i
$568$	−72.6812	−	72.6812i	−0.127960	−	0.127960i
$569$	72.8214	+	42.0435i	0.127981	+	0.0738901i	0.562624	−	0.826713i	$-0.309792\pi$
$569$	72.8214	+	42.0435i	0.127981	+	0.0738901i	−0.434642	+	0.900603i	$0.643125\pi$
$570$	230.742	+	98.5629i	0.404810	+	0.172917i
$571$	167.327	+	289.818i	0.293041	+	0.507562i	0.974527	−	0.224269i	$-0.0719993\pi$
$571$	167.327	+	289.818i	0.293041	+	0.507562i	−0.681486	+	0.731831i	$0.738666\pi$
$572$	59.9615	+	223.779i	0.104828	+	0.391223i
$573$	−393.043	−	393.043i	−0.685940	−	0.685940i
$574$	79.9624	+	264.931i	0.139307	+	0.461552i
$575$	−455.485	+	249.782i	−0.792148	+	0.434404i
$576$	−11.8178	+	20.4690i	−0.0205170	+	0.0355365i
$577$	−444.640	−	119.141i	−0.770606	−	0.206483i	−0.147967	−	0.988992i	$-0.547273\pi$
$577$	−444.640	−	119.141i	−0.770606	−	0.206483i	−0.622639	+	0.782509i	$0.713940\pi$
$578$	57.9313	−	216.203i	0.100227	−	0.374053i
$579$	−470.864	−	271.854i	−0.813237	−	0.469522i
$580$	95.1801	+	126.907i	0.164104	+	0.218805i
$581$	−65.8427	−	61.8410i	−0.113326	−	0.106439i
$582$	−221.751	+	221.751i	−0.381015	+	0.381015i
$583$	−305.957	+	81.9810i	−0.524798	+	0.140619i
$584$	162.024	−	93.5445i	0.277438	−	0.160179i
$585$	−85.2470	−	212.381i	−0.145721	−	0.363044i
$586$	−187.818	+	325.310i	−0.320508	+	0.555136i
$587$	484.313	−	484.313i	0.825064	−	0.825064i	−0.161765	−	0.986829i	$-0.551719\pi$
$587$	484.313	−	484.313i	0.825064	−	0.825064i	0.986829	+	0.161765i	$0.0517187\pi$
$588$	−76.8170	−	228.387i	−0.130641	−	0.388413i
$589$		−	230.907i		−	0.392032i
$590$	358.887	+	281.708i	0.608283	+	0.477471i
$591$	147.624	+	255.692i	0.249786	+	0.432643i
$592$	−256.564	−	68.7461i	−0.433385	−	0.116125i
$593$	206.021	−	55.2031i	0.347422	−	0.0930913i	−0.0808885	−	0.996723i	$-0.525776\pi$
$593$	206.021	−	55.2031i	0.347422	−	0.0930913i	0.428310	+	0.903632i	$0.359109\pi$
$594$			310.816i			0.523259i
$595$	−735.688	−	81.6760i	−1.23645	−	0.137271i
$596$	−505.818			−0.848688
$597$	−52.4727	−	195.831i	−0.0878940	−	0.328025i
$598$	117.827	−	439.736i	0.197035	−	0.735344i
$599$	71.5663	−	41.3188i	0.119476	−	0.0689797i	−0.439071	−	0.898452i	$-0.644692\pi$
$599$	71.5663	−	41.3188i	0.119476	−	0.0689797i	0.558547	+	0.829473i	$0.311359\pi$
$600$	−125.613	+	120.205i	−0.209354	+	0.200342i
$601$	785.362			1.30676			0.653380	−	0.757030i	$-0.273351\pi$
$601$	785.362			1.30676			0.653380	+	0.757030i	$0.273351\pi$
$602$	262.339	−	489.158i	0.435778	−	0.812555i
$603$	115.861	+	115.861i	0.192141	+	0.192141i
$604$	356.645	+	205.909i	0.590471	+	0.340909i
$605$	127.846	−	299.294i	0.211315	−	0.494701i
$606$	169.513	+	293.605i	0.279724	+	0.484497i
$607$	−181.102	−	675.882i	−0.298356	−	1.11348i	−0.938515	−	0.345237i	$-0.887798\pi$
$607$	−181.102	−	675.882i	−0.298356	−	1.11348i	0.640159	−	0.768242i	$-0.278868\pi$
$608$	−57.7267	−	57.7267i	−0.0949452	−	0.0949452i
$609$	265.811	+	62.3696i	0.436472	+	0.102413i
$610$	413.638	+	59.0911i	0.678095	+	0.0968707i
$611$	−557.180	+	965.064i	−0.911915	+	1.57948i
$612$	120.708	+	32.3436i	0.197235	+	0.0528490i
$613$	49.4286	−	184.470i	0.0806339	−	0.300930i	−0.913818	−	0.406125i	$-0.866880\pi$
$613$	49.4286	−	184.470i	0.0806339	−	0.300930i	0.994452	+	0.105195i	$0.0335466\pi$
$614$	296.870	+	171.398i	0.483502	+	0.279150i
$615$	48.6020	−	340.214i	0.0790276	−	0.553193i
$616$	−33.8178	+	144.127i	−0.0548990	+	0.233973i
$617$	−423.089	+	423.089i	−0.685720	+	0.685720i	−0.961283	−	0.275563i	$-0.911136\pi$
$617$	−423.089	+	423.089i	−0.685720	+	0.685720i	0.275563	+	0.961283i	$0.411136\pi$
$618$	−162.741	+	43.6063i	−0.263335	+	0.0705603i
$619$	93.5101	−	53.9881i	0.151066	−	0.0872182i	−0.422561	−	0.906334i	$-0.638869\pi$
$619$	93.5101	−	53.9881i	0.151066	−	0.0872182i	0.573628	+	0.819116i	$0.305536\pi$
$620$	147.138	+	62.8513i	0.237320	+	0.101373i
$621$	305.383	−	528.939i	0.491760	−	0.851753i
$622$	3.47723	−	3.47723i	0.00559039	−	0.00559039i
$623$	−300.587	−	161.207i	−0.482484	−	0.258759i
$624$		−	152.364i		−	0.244174i
$625$	554.485	−	288.395i	0.887175	−	0.461433i
$626$	15.0890	+	26.1350i	0.0241039	+	0.0417491i
$627$	−256.282	−	68.6707i	−0.408744	−	0.109523i
$628$	−512.008	+	137.192i	−0.815299	+	0.218459i
$629$			1404.36i			2.23268i
$630$	16.1362	−	145.345i	0.0256130	−	0.230706i
$631$	−711.200			−1.12710			−0.563550	−	0.826082i	$-0.690565\pi$
$631$	−711.200			−1.12710			−0.563550	+	0.826082i	$0.690565\pi$
$632$	30.1634	+	112.571i	0.0477269	+	0.178119i
$633$	−130.904	+	488.542i	−0.206800	+	0.771789i
$634$	−498.831	+	288.000i	−0.786799	+	0.454259i
$635$	13.2969	−	16.9399i	0.0209401	−	0.0266770i
$636$	208.317			0.327542
$637$	−569.327	−	502.103i	−0.893762	−	0.788231i
$638$	−118.614	−	118.614i	−0.185915	−	0.185915i
$639$	−92.9821	−	53.6832i	−0.145512	−	0.0840113i
$640$	52.4974	−	21.0718i	0.0820272	−	0.0329247i
$641$	214.658	+	371.799i	0.334880	+	0.580030i	0.983462	−	0.181115i	$-0.0579707\pi$
$641$	214.658	+	371.799i	0.334880	+	0.580030i	−0.648581	+	0.761145i	$0.724637\pi$
$642$	148.174	+	552.991i	0.230800	+	0.861357i
$643$	−289.770	−	289.770i	−0.450653	−	0.450653i	0.444918	−	0.895571i	$-0.353233\pi$
$643$	−289.770	−	289.770i	−0.450653	−	0.450653i	−0.895571	+	0.444918i	$0.853233\pi$
$644$	199.158	−	212.046i	0.309252	−	0.329263i
$645$	−551.453	+	413.590i	−0.854967	+	0.641225i
$646$	−215.818	+	373.807i	−0.334083	+	0.578649i
$647$	435.592	+	116.716i	0.673248	+	0.180396i	0.579218	−	0.815173i	$-0.303358\pi$
$647$	435.592	+	116.716i	0.673248	+	0.180396i	0.0940307	+	0.995569i	$0.470025\pi$
$648$	33.4409	−	124.803i	0.0516064	−	0.192598i
$649$	−417.815	−	241.226i	−0.643783	−	0.371688i
$650$	−153.362	+	525.814i	−0.235942	+	0.808944i
$651$	263.636	−	79.5715i	0.404970	−	0.122230i
$652$	353.545	−	353.545i	0.542246	−	0.542246i
$653$	340.019	−	91.1077i	0.520702	−	0.139522i	0.0111110	−	0.999938i	$-0.496463\pi$
$653$	340.019	−	91.1077i	0.520702	−	0.139522i	0.509592	+	0.860416i	$0.329797\pi$
$654$	508.098	−	293.350i	0.776908	−	0.448548i
$655$	223.729	−	523.762i	0.341570	−	0.799636i
$656$	−55.9089	+	96.8371i	−0.0852270	+	0.147617i
$657$	138.186	−	138.186i	0.210329	−	0.210329i
$658$	−605.230	+	375.186i	−0.919802	+	0.570192i
$659$		−	900.158i		−	1.36595i	−0.730444	−	0.682973i	$-0.760687\pi$
$659$		−	900.158i		−	1.36595i	0.730444	−	0.682973i	$-0.239313\pi$
$660$	113.517	−	144.617i	0.171995	−	0.219116i
$661$	174.090	+	301.533i	0.263374	+	0.456177i	0.967136	−	0.254259i	$-0.0818314\pi$
$661$	174.090	+	301.533i	0.263374	+	0.456177i	−0.703763	+	0.710435i	$0.748498\pi$
$662$	−574.596	−	153.963i	−0.867970	−	0.232572i
$663$	−778.131	+	208.500i	−1.17365	+	0.314479i
$664$		−	36.4990i		−	0.0549683i
$665$	470.493	+	183.769i	0.707508	+	0.276344i
$666$	−277.449			−0.416590
$667$	85.3137	+	318.395i	0.127907	+	0.477354i
$668$	−5.86512	+	21.8889i	−0.00878012	+	0.0327679i
$669$	−189.376	+	109.336i	−0.283074	+	0.163433i
$670$	−46.9081	−	389.343i	−0.0700121	−	0.581109i
$671$	−441.837			−0.658476
$672$	46.0160	−	85.8018i	0.0684762	−	0.127681i
$673$	−13.2277	−	13.2277i	−0.0196549	−	0.0196549i	0.697211	−	0.716866i	$-0.254424\pi$
$673$	−13.2277	−	13.2277i	−0.0196549	−	0.0196549i	−0.716866	+	0.697211i	$0.754424\pi$
$674$	59.3595	+	34.2712i	0.0880705	+	0.0508475i
$675$	−381.323	+	628.148i	−0.564922	+	0.930589i
$676$	−71.0000	−	122.976i	−0.105030	−	0.181917i
$677$	−153.597	−	573.233i	−0.226879	−	0.846725i	−0.981643	−	0.190728i	$-0.938915\pi$
$677$	−153.597	−	573.233i	−0.226879	−	0.846725i	0.754764	−	0.655997i	$-0.227752\pi$
$678$	196.935	+	196.935i	0.290464	+	0.290464i
$679$	−432.203	+	460.170i	−0.636529	+	0.677718i
$680$	−179.453	−	239.271i	−0.263902	−	0.351869i
$681$	−317.612	+	550.120i	−0.466390	+	0.807812i
$682$	−163.425	−	43.7897i	−0.239627	−	0.0642077i
$683$	73.3428	−	273.719i	0.107383	−	0.400760i	−0.891221	−	0.453569i	$-0.850151\pi$
$683$	73.3428	−	273.719i	0.107383	−	0.400760i	0.998605	+	0.0528086i	$0.0168173\pi$
$684$	−73.8506	−	42.6377i	−0.107969	−	0.0623358i
$685$	−719.406	−	102.772i	−1.05023	−	0.150032i
$686$	−168.966	−	454.696i	−0.246307	−	0.662822i
$687$	−214.004	+	214.004i	−0.311505	+	0.311505i
$688$	216.638	−	58.0480i	0.314881	−	0.0843721i
$689$	568.346	−	328.135i	0.824885	−	0.476248i
$690$	−335.269	+	134.573i	−0.485897	+	0.195033i
$691$	−369.671	+	640.290i	−0.534980	+	0.926613i	0.464184	+	0.885739i	$0.346348\pi$
$691$	−369.671	+	640.290i	−0.534980	+	0.926613i	−0.999164	+	0.0408742i	$0.986986\pi$
$692$	−175.636	+	175.636i	−0.253809	+	0.253809i
$693$	4.84399	+	154.562i	0.00698989	+	0.223033i
$694$			204.657i			0.294895i
$695$	−105.872	−	878.754i	−0.152335	−	1.26439i
$696$	55.1605	+	95.5407i	0.0792535	+	0.137271i
$697$	571.058	+	153.015i	0.819308	+	0.219533i
$698$	339.951	−	91.0896i	0.487036	−	0.130501i
$699$			783.636i			1.12108i
$700$	−245.166	+	249.787i	−0.350238	+	0.356838i
$701$	189.638			0.270525			0.135262	−	0.990810i	$-0.456812\pi$
$701$	189.638			0.270525			0.135262	+	0.990810i	$0.456812\pi$
$702$	−166.673	−	622.031i	−0.237425	−	0.886084i
$703$	248.030	−	925.662i	0.352817	−	1.31673i
$704$	−51.8037	+	29.9089i	−0.0735849	+	0.0424842i
$705$	877.968	−	105.778i	1.24534	−	0.150039i
$706$	−564.725			−0.799893
$707$	359.594	+	580.077i	0.508619	+	0.820476i
$708$	224.360	+	224.360i	0.316893	+	0.316893i
$709$	−571.534	−	329.975i	−0.806112	−	0.465409i	0.0394916	−	0.999220i	$-0.487426\pi$
$709$	−571.534	−	329.975i	−0.806112	−	0.465409i	−0.845604	+	0.533811i	$0.820760\pi$
$710$	95.7202	+	238.473i	0.134817	+	0.335878i
$711$	60.8675	+	105.426i	0.0856083	+	0.148278i
$712$	−35.6704	−	133.124i	−0.0500989	−	0.186972i
$713$	235.089	+	235.089i	0.329718	+	0.329718i
$714$	−501.163	−	117.592i	−0.701909	−	0.164695i
$715$	81.9089	−	573.362i	0.114558	−	0.801905i
$716$	131.636	−	228.000i	0.183849	−	0.318435i
$717$	−414.969	−	111.191i	−0.578757	−	0.155078i
$718$	−156.691	+	584.778i	−0.218232	+	0.814454i
$719$	851.435	+	491.576i	1.18419	+	0.683694i	0.956981	−	0.290151i	$-0.0937056\pi$
$719$	851.435	+	491.576i	1.18419	+	0.683694i	0.227212	+	0.973845i	$0.427039\pi$
$720$	47.2712	−	35.4534i	0.0656545	−	0.0492409i
$721$	−324.703	+	98.0031i	−0.450351	+	0.135927i
$722$	−152.727	+	152.727i	−0.211533	+	0.211533i
$723$	−579.065	+	155.160i	−0.800919	+	0.214606i
$724$	259.255	−	149.681i	0.358088	−	0.206742i
$725$	−94.1938	−	385.235i	−0.129922	−	0.531359i
$726$	113.168	−	196.013i	0.155879	−	0.269990i
$727$	291.624	−	291.624i	0.401133	−	0.401133i	−0.477499	−	0.878632i	$-0.658457\pi$
$727$	291.624	−	291.624i	0.401133	−	0.401133i	0.878632	+	0.477499i	$0.158457\pi$
$728$	−9.60809	−	306.574i	−0.0131979	−	0.421118i
$729$		−	785.404i		−	1.07737i
$730$	−464.364	+	55.9467i	−0.636116	+	0.0766394i
$731$	−592.907	−	1026.94i	−0.811090	−	1.40485i
$732$	280.681	+	75.2084i	0.383445	+	0.102744i
$733$	−660.223	+	176.906i	−0.900713	+	0.241345i	−0.679323	−	0.733840i	$-0.737726\pi$
$733$	−660.223	+	176.906i	−0.900713	+	0.241345i	−0.221391	+	0.975185i	$0.571060\pi$
$734$		−	333.022i		−	0.453708i
$735$	−47.6825	+	600.508i	−0.0648741	+	0.817018i
$736$	117.545			0.159707
$737$	107.328	+	400.554i	0.145628	+	0.543492i
$738$	−30.2301	+	112.820i	−0.0409621	+	0.152873i
$739$	110.947	−	64.0554i	0.150131	−	0.0866785i	−0.423052	−	0.906105i	$-0.639041\pi$
$739$	110.947	−	64.0554i	0.150131	−	0.0866785i	0.573184	+	0.819427i	$0.305708\pi$
$740$	522.338	+	410.009i	0.705862	+	0.554066i
$741$	549.718			0.741860
$742$	419.157	−	13.1364i	0.564901	−	0.0177041i
$743$	443.624	+	443.624i	0.597071	+	0.597071i	0.939532	−	0.342461i	$-0.111260\pi$
$743$	443.624	+	443.624i	0.597071	+	0.597071i	−0.342461	+	0.939532i	$0.611260\pi$
$744$	96.3637	+	55.6356i	0.129521	+	0.0747790i
$745$	1162.89	+	496.739i	1.56093	+	0.666763i
$746$	107.271	+	185.799i	0.143795	+	0.249061i
$747$	−9.86753	−	36.8261i	−0.0132095	−	0.0492987i
$748$	223.636	+	223.636i	0.298978	+	0.298978i
$749$	333.013	+	1103.34i	0.444611	+	1.47308i
$750$	406.835	−	152.998i	0.542447	−	0.203997i
$751$	141.957	−	245.876i	0.189023	−	0.327398i	−0.755902	−	0.654685i	$-0.772801\pi$
$751$	141.957	−	245.876i	0.189023	−	0.327398i	0.944925	+	0.327287i	$0.106134\pi$
$752$	−277.923	−	74.4691i	−0.369578	−	0.0990281i
$753$	−34.5382	+	128.898i	−0.0458675	+	0.171180i
$754$	300.986	+	173.774i	0.399186	+	0.230470i
$755$	−617.727	−	823.636i	−0.818181	−	1.09091i
$756$	94.0021	−	400.625i	0.124341	−	0.529927i
$757$	−494.590	+	494.590i	−0.653355	+	0.653355i	−0.953799	−	0.300444i	$-0.902865\pi$
$757$	−494.590	+	494.590i	−0.653355	+	0.653355i	0.300444	+	0.953799i	$0.402865\pi$
$758$	90.7474	−	24.3157i	0.119719	−	0.0320787i
$759$	330.839	−	191.010i	0.435888	−	0.251660i
$760$	76.0253	+	189.406i	0.100033	+	0.249219i
$761$	17.7288	−	30.7072i	0.0232967	−	0.0403511i	−0.854142	−	0.520040i	$-0.825917\pi$
$761$	17.7288	−	30.7072i	0.0232967	−	0.0403511i	0.877439	+	0.479689i	$0.159250\pi$
$762$	10.5901	−	10.5901i	0.0138977	−	0.0138977i
$763$	1003.85	−	622.294i	1.31566	−	0.815589i
$764$		−	452.135i		−	0.591799i
$765$	−245.749	−	192.901i	−0.321241	−	0.252158i
$766$	−481.307	−	833.648i	−0.628338	−	1.08831i
$767$	965.523	+	258.711i	1.25883	+	0.337302i
$768$	37.9998	−	10.1820i	0.0494789	−	0.0132578i
$769$			702.447i			0.913455i	0.889607	+	0.456728i	$0.150979\pi$
$769$			702.447i			0.913455i	−0.889607	+	0.456728i	$0.849021\pi$
$770$	219.289	−	298.143i	0.284790	−	0.387199i
$771$	−53.2671			−0.0690883
$772$	−114.465	−	427.190i	−0.148271	−	0.553355i
$773$	−216.901	+	809.487i	−0.280597	+	1.04720i	0.671400	+	0.741095i	$0.265693\pi$
$773$	−216.901	+	809.487i	−0.280597	+	1.04720i	−0.951997	+	0.306107i	$0.900973\pi$
$774$	202.887	−	117.137i	0.262127	−	0.151339i
$775$	−276.554	−	288.995i	−0.356844	−	0.372897i
$776$	−255.089			−0.328723
$777$	1142.34	−	35.8011i	1.47019	−	0.0460760i
$778$	92.9110	+	92.9110i	0.119423	+	0.119423i
$779$	−349.380	−	201.715i	−0.448498	−	0.258941i
$780$	−149.630	+	350.292i	−0.191833	+	0.449092i
$781$	−135.863	−	235.322i	−0.173961	−	0.301309i
$782$	−160.851	−	600.305i	−0.205692	−	0.767653i
$783$	329.707	+	329.707i	0.421081	+	0.421081i
$784$	87.1787	−	175.545i	0.111197	−	0.223909i
$785$	1311.86	+	187.408i	1.67115	+	0.238736i
$786$	198.043	−	343.021i	0.251964	−	0.436414i
$787$	−695.596	−	186.384i	−0.883858	−	0.236829i	−0.211787	−	0.977316i	$-0.567928\pi$
$787$	−695.596	−	186.384i	−0.883858	−	0.236829i	−0.672071	+	0.740487i	$0.734595\pi$
$788$	−62.1576	+	231.975i	−0.0788802	+	0.294385i
$789$	−715.918	−	413.335i	−0.907374	−	0.523872i
$790$	41.2039	−	288.428i	0.0521569	−	0.365098i
$791$	408.673	+	383.836i	0.516654	+	0.485254i
$792$	−44.1822	+	44.1822i	−0.0557856	+	0.0557856i
$793$	884.243	−	236.932i	1.11506	−	0.298779i
$794$	443.168	−	255.863i	0.558147	−	0.322246i
$795$	−478.928	−	204.578i	−0.602425	−	0.257330i
$796$	82.4555	−	142.817i	0.103587	−	0.179418i
$797$	−82.4079	+	82.4079i	−0.103398	+	0.103398i	−0.756913	−	0.653516i	$-0.773293\pi$
$797$	−82.4079	+	82.4079i	−0.103398	+	0.103398i	0.653516	+	0.756913i	$0.273293\pi$
$798$	309.566	+	166.022i	0.387927	+	0.208048i
$799$			1521.27i			1.90396i
$800$	−141.387	−	3.11027i	−0.176734	−	0.00388784i
$801$	−71.9803	−	124.674i	−0.0898631	−	0.155647i
$802$	−861.334	−	230.794i	−1.07398	−	0.287773i
$803$	477.736	−	128.009i	0.594938	−	0.159413i
$804$		−	272.725i		−	0.339210i
$805$	−666.112	+	291.917i	−0.827468	+	0.362630i
$806$	350.542			0.434916
$807$	−68.8433	−	256.927i	−0.0853077	−	0.318373i
$808$	−71.3742	+	266.372i	−0.0883344	+	0.329668i
$809$	289.803	−	167.318i	0.358224	−	0.206821i	−0.310078	−	0.950711i	$-0.600355\pi$
$809$	289.803	−	167.318i	0.358224	−	0.206821i	0.668301	+	0.743891i	$0.267022\pi$
$810$	−199.445	+	254.087i	−0.246229	+	0.313687i
$811$	522.455			0.644211			0.322106	−	0.946704i	$-0.395609\pi$
$811$	522.455			0.644211			0.322106	+	0.946704i	$0.395609\pi$
$812$	117.014	+	188.760i	0.144106	+	0.232463i
$813$	106.961	+	106.961i	0.131563	+	0.131563i
$814$	−608.104	−	351.089i	−0.747057	−	0.431313i
$815$	−1160.01	+	465.614i	−1.42333	+	0.571305i
$816$	−104.000	−	180.133i	−0.127451	−	0.220752i
$817$	209.432	+	781.613i	0.256343	+	0.956686i
$818$	−203.317	−	203.317i	−0.248554	−	0.248554i
$819$	−92.5768	−	306.725i	−0.113036	−	0.374511i
$820$	223.636	−	167.727i	0.272726	−	0.204545i
$821$	196.950	−	341.128i	0.239891	−	0.415503i	−0.720792	−	0.693151i	$-0.756222\pi$
$821$	196.950	−	341.128i	0.239891	−	0.415503i	0.960683	+	0.277648i	$0.0895550\pi$
$822$	−488.166	−	130.804i	−0.593876	−	0.159129i
$823$	−67.2617	+	251.024i	−0.0817275	+	0.305011i	−0.994674	−	0.103067i	$-0.967134\pi$
$823$	−67.2617	+	251.024i	−0.0817275	+	0.305011i	0.912947	+	0.408078i	$0.133801\pi$
$824$	−118.685	−	68.5228i	−0.144035	−	0.0831587i
$825$	−403.000	+	221.000i	−0.488485	+	0.267879i
$826$	465.586	+	437.290i	0.563663	+	0.529406i
$827$	143.561	−	143.561i	0.173592	−	0.173592i	−0.614964	−	0.788556i	$-0.710829\pi$
$827$	143.561	−	143.561i	0.173592	−	0.173592i	0.788556	+	0.614964i	$0.210829\pi$
$828$	118.598	−	31.7783i	0.143234	−	0.0383796i
$829$	−566.219	+	326.907i	−0.683015	+	0.394339i	−0.800990	−	0.598678i	$-0.795693\pi$
$829$	−566.219	+	326.907i	−0.683015	+	0.394339i	0.117975	+	0.993017i	$0.462360\pi$
$830$	−35.8438	+	83.9125i	−0.0431853	+	0.101099i
$831$	−438.998	+	760.367i	−0.528277	+	0.915002i
$832$	87.6356	−	87.6356i	0.105331	−	0.105331i
$833$	−1015.81	−	205.005i	−1.21946	−	0.246105i
$834$		−	615.545i		−	0.738063i
$835$	34.9802	−	44.5636i	0.0418924	−	0.0533696i
$836$	−107.909	−	186.904i	−0.129078	−	0.223569i
$837$	454.267	+	121.720i	0.542732	+	0.145425i
$838$	978.442	−	262.173i	1.16759	−	0.312855i
$839$			128.301i			0.152922i	0.997073	+	0.0764608i	$0.0243620\pi$
$839$			128.301i			0.152922i	−0.997073	+	0.0764608i	$0.975638\pi$
$840$	−190.054	+	152.072i	−0.226255	+	0.181038i
$841$	589.354			0.700778
$842$	253.454	+	945.903i	0.301014	+	1.12340i
$843$	253.623	−	946.534i	0.300858	−	1.12282i
$844$	−356.288	+	205.703i	−0.422142	+	0.243724i
$845$	42.4634	+	352.451i	0.0502526	+	0.417102i
$846$	−300.547			−0.355256
$847$	215.346	−	401.537i	0.254246	−	0.474069i
$848$	119.818	+	119.818i	0.141295	+	0.141295i
$849$	−1048.09	−	605.113i	−1.23449	−	0.712736i
$850$	177.594	+	726.326i	0.208934	+	0.854501i
$851$	689.905	+	1194.95i	0.810699	+	1.40417i
$852$	46.2526	+	172.617i	0.0542871	+	0.202602i
$853$	−941.404	−	941.404i	−1.10364	−	1.10364i	−0.993968	−	0.109671i	$-0.965020\pi$
$853$	−941.404	−	941.404i	−1.10364	−	1.10364i	−0.109671	−	0.993968i	$-0.534980\pi$
$854$	569.505	+	133.628i	0.666868	+	0.156473i
$855$	127.913	+	170.551i	0.149606	+	0.199475i
$856$	−232.840	+	403.290i	−0.272009	+	0.471133i
$857$	334.297	+	89.5747i	0.390078	+	0.104521i	0.448527	−	0.893769i	$-0.351949\pi$
$857$	334.297	+	89.5747i	0.390078	+	0.104521i	−0.0584487	+	0.998290i	$0.518615\pi$
$858$	104.250	−	389.066i	0.121503	−	0.453456i
$859$	39.8336	+	22.9979i	0.0463720	+	0.0267729i	0.523007	−	0.852329i	$-0.324810\pi$
$859$	39.8336	+	22.9979i	0.0463720	+	0.0267729i	−0.476635	+	0.879101i	$0.658144\pi$
$860$	−555.065	−	79.2950i	−0.645425	−	0.0922035i
$861$	109.908	−	468.413i	0.127651	−	0.544034i
$862$	−497.473	+	497.473i	−0.577115	+	0.577115i
$863$	1354.85	−	363.032i	1.56993	−	0.420663i	0.634143	−	0.773216i	$-0.281353\pi$
$863$	1354.85	−	363.032i	1.56993	−	0.420663i	0.935792	+	0.352554i	$0.114687\pi$
$864$	143.997	−	83.1366i	0.166663	−	0.0962230i
$865$	576.276	−	231.310i	0.666215	−	0.267410i
$866$	−191.729	+	332.084i	−0.221396	+	0.383469i
$867$	−275.172	+	275.172i	−0.317385	+	0.317385i
$868$	197.403	+	105.868i	0.227423	+	0.121968i
$869$			308.091i			0.354535i
$870$	−32.9902	−	273.822i	−0.0379197	−	0.314738i
$871$	−429.588	−	744.068i	−0.493212	−	0.854269i
$872$	460.970	+	123.517i	0.528635	+	0.141647i
$873$	−257.376	+	68.9636i	−0.294817	+	0.0789961i
$874$			424.091i			0.485230i
$875$	808.950	−	333.504i	0.924514	−	0.381147i
$876$	−325.275			−0.371319
$877$	288.777	+	1077.73i	0.329278	+	1.22888i	0.909941	+	0.414738i	$0.136127\pi$
$877$	288.777	+	1077.73i	0.329278	+	1.22888i	−0.580663	+	0.814144i	$0.697207\pi$
$878$	−194.525	+	725.979i	−0.221555	+	0.826855i
$879$	565.588	−	326.542i	0.643445	−	0.371493i
$880$	148.471	−	17.8878i	0.168717	−	0.0203270i
$881$	−1392.40			−1.58048			−0.790239	−	0.612798i	$-0.790044\pi$
$881$	−1392.40			−1.58048			−0.790239	+	0.612798i	$0.790044\pi$
$882$	40.5015	−	200.687i	0.0459201	−	0.227536i
$883$	−652.590	−	652.590i	−0.739060	−	0.739060i	0.233336	−	0.972396i	$-0.425036\pi$
$883$	−652.590	−	652.590i	−0.739060	−	0.739060i	−0.972396	+	0.233336i	$0.925036\pi$
$884$	−567.482	−	327.636i	−0.641947	−	0.370629i
$885$	−295.480	−	736.146i	−0.333875	−	0.831803i
$886$	111.648	+	193.379i	0.126013	+	0.218261i
$887$	130.525	+	487.127i	0.147154	+	0.549185i	0.999650	+	0.0264521i	$0.00842094\pi$
$887$	130.525	+	487.127i	0.147154	+	0.549185i	−0.852496	+	0.522733i	$0.824912\pi$
$888$	326.542	+	326.542i	0.367728	+	0.367728i
$889$	20.6406	−	21.9762i	0.0232177	−	0.0247201i
$890$	−48.7267	+	341.087i	−0.0547491	+	0.383244i
$891$	170.784	−	295.807i	0.191677	−	0.331994i
$892$	−171.811	−	46.0366i	−0.192613	−	0.0516105i
$893$	268.679	−	1002.72i	0.300872	−	1.12287i
$894$	761.601	+	439.711i	0.851903	+	0.491846i
$895$	−526.542	+	394.907i	−0.588316	+	0.441237i
$896$	75.8178	−	22.8836i	0.0846181	−	0.0255398i
$897$	−559.675	+	559.675i	−0.623941	+	0.623941i
$898$	−406.516	+	108.926i	−0.452690	+	0.121298i
$899$	−219.809	+	126.907i	−0.244504	+	0.141164i
$900$	−143.495	+	35.0860i	−0.159439	+	0.0389845i
$901$	447.952	−	775.876i	0.497172	−	0.861128i
$902$	−209.022	+	209.022i	−0.231731	+	0.231731i
$903$	−820.227	+	508.465i	−0.908336	+	0.563084i
$904$			226.542i			0.250600i
$905$	−743.032	+	89.5207i	−0.821030	+	0.0989179i
$906$	−357.996	−	620.067i	−0.395139	−	0.684401i
$907$	−1.84469	−	0.494284i	−0.00203384	−	0.000544966i	0.257802	−	0.966198i	$-0.417002\pi$
$907$	−1.84469	−	0.494284i	−0.00203384	−	0.000544966i	−0.259836	+	0.965653i	$0.583668\pi$
$908$	−499.094	+	133.732i	−0.549663	+	0.147282i
$909$			288.056i			0.316893i
$910$	−278.982	+	714.261i	−0.306574	+	0.784902i
$911$	456.063			0.500618			0.250309	−	0.968166i	$-0.419468\pi$
$911$	456.063			0.500618			0.250309	+	0.968166i	$0.419468\pi$
$912$	36.7359	+	137.100i	0.0402806	+	0.150329i
$913$	24.9731	−	93.2008i	0.0273528	−	0.102082i
$914$	893.573	−	515.905i	0.977651	−	0.564447i
$915$	−571.439	−	448.550i	−0.624523	−	0.490219i
$916$	−246.178			−0.268753
$917$	376.855	−	702.686i	0.410965	−	0.766288i
$918$	−621.631	−	621.631i	−0.677158	−	0.677158i
$919$	−459.799	−	265.465i	−0.500326	−	0.288863i	0.228522	−	0.973539i	$-0.426611\pi$
$919$	−459.799	−	265.465i	−0.500326	−	0.288863i	−0.728848	+	0.684675i	$0.759944\pi$
$920$	−270.239	−	115.435i	−0.293738	−	0.125472i
$921$	−297.995	−	516.142i	−0.323556	−	0.560415i
$922$	5.98978	+	22.3542i	0.00649651	+	0.0242453i
$923$	398.091	+	398.091i	0.431301	+	0.431301i
$924$	176.210	−	187.612i	0.190703	−	0.203043i
$925$	−798.226	−	1455.59i	−0.862947	−	1.57361i
$926$	185.921	−	322.024i	0.200778	−	0.347758i
$927$	−138.274	−	37.0504i	−0.149163	−	0.0399681i
$928$	−23.2256	+	86.6790i	−0.0250275	+	0.0934041i
$929$	−971.957	−	561.159i	−1.04624	−	0.604047i	−0.124645	−	0.992201i	$-0.539779\pi$
$929$	−971.957	−	561.159i	−1.04624	−	0.604047i	−0.921594	+	0.388155i	$0.873113\pi$
$930$	−166.907	−	222.542i	−0.179470	−	0.239293i
$931$	633.350	+	314.534i	0.680290	+	0.337845i
$932$	−450.725	+	450.725i	−0.483610	+	0.483610i
$933$	−8.25837	+	2.21282i	−0.00885142	+	0.00237173i
$934$	−399.215	+	230.487i	−0.427425	+	0.246774i
$935$	−294.525	−	733.768i	−0.315000	−	0.784779i
$936$	64.7288	−	112.114i	0.0691547	−	0.119779i
$937$	−194.820	+	194.820i	−0.207919	+	0.207919i	−0.803382	−	0.595464i	$-0.796968\pi$
$937$	−194.820	+	194.820i	−0.207919	+	0.207919i	0.595464	+	0.803382i	$0.296968\pi$
$938$	−17.1980	−	548.752i	−0.0183347	−	0.585024i
$939$		−	52.4679i		−	0.0558764i
$940$	565.822	+	444.141i	0.601938	+	0.472491i
$941$	−405.362	−	702.108i	−0.430778	−	0.746130i	0.566162	−	0.824294i	$-0.308428\pi$
$941$	−405.362	−	702.108i	−0.430778	−	0.746130i	−0.996941	+	0.0781640i	$0.975094\pi$
$942$	890.183	+	238.524i	0.944993	+	0.253210i
$943$	561.077	−	150.340i	0.594991	−	0.159427i
$944$			258.091i			0.273402i
$945$	−609.548	+	828.737i	−0.645025	+	0.876970i
$946$	592.907			0.626751
$947$	−166.389	−	620.971i	−0.175701	−	0.655724i	−0.996431	−	0.0844087i	$-0.973100\pi$
$947$	−166.389	−	620.971i	−0.175701	−	0.655724i	0.820730	−	0.571316i	$-0.193567\pi$
$948$	52.4424	−	195.718i	0.0553190	−	0.206453i
$949$	−887.441	+	512.364i	−0.935133	+	0.539899i
$950$	11.2216	−	510.113i	0.0118122	−	0.536961i
$951$	1001.44			1.05304
$952$	−220.619	−	355.890i	−0.231742	−	0.373834i
$953$	372.594	+	372.594i	0.390970	+	0.390970i	0.875033	−	0.484063i	$-0.160840\pi$
$953$	372.594	+	372.594i	0.390970	+	0.390970i	−0.484063	+	0.875033i	$0.660840\pi$
$954$	153.285	+	88.4990i	0.160676	+	0.0927662i
$955$	−444.019	+	1039.47i	−0.464941	+	1.08846i
$956$	−174.725	−	302.632i	−0.182766	−	0.316561i
$957$	75.4831	+	281.707i	0.0788747	+	0.294364i
$958$	−522.455	−	522.455i	−0.545361	−	0.545361i
$959$	−990.493	−	232.408i	−1.03284	−	0.242344i
$960$	−97.3623	−	13.9089i	−0.101419	−	0.0144884i
$961$	352.500	−	610.548i	0.366805	−	0.635326i
$962$	1405.26	+	376.538i	1.46077	+	0.391411i
$963$	−125.897	+	469.853i	−0.130734	+	0.487906i
$964$	−422.305	−	243.818i	−0.438076	−	0.252923i
$965$	−156.362	+	1094.54i	−0.162033	+	1.13423i
$966$	−484.202	+	146.144i	−0.501244	+	0.151287i
$967$	−989.576	+	989.576i	−1.02335	+	1.02335i	−0.0236256	+	0.999721i	$0.507521\pi$
$967$	−989.576	+	989.576i	−1.02335	+	1.02335i	−0.999721	+	0.0236256i	$0.992479\pi$
$968$	177.832	−	47.6500i	0.183711	−	0.0492252i
$969$	649.906	−	375.224i	0.670698	−	0.387228i
$970$	586.459	+	250.510i	0.604597	+	0.258258i
$971$	−306.911	+	531.585i	−0.316077	+	0.547462i	−0.979666	−	0.200636i	$-0.935699\pi$
$971$	−306.911	+	531.585i	−0.316077	+	0.547462i	0.663589	+	0.748098i	$0.269033\pi$
$972$	215.271	−	215.271i	0.221472	−	0.221472i
$973$	−38.8162	−	1238.54i	−0.0398933	−	1.27291i
$974$			418.812i			0.429991i
$975$	688.008	−	658.390i	0.705649	−	0.675272i
$976$	118.182	+	204.698i	0.121088	+	0.209731i
$977$	417.882	+	111.971i	0.427720	+	0.114607i	0.466256	−	0.884650i	$-0.345603\pi$
$977$	417.882	+	111.971i	0.427720	+	0.114607i	−0.0385359	+	0.999257i	$0.512269\pi$
$978$	−839.664	+	224.987i	−0.858553	+	0.230048i
$979$		−	364.341i		−	0.372156i
$980$	−372.821	+	317.970i	−0.380429	+	0.324459i
$981$	498.495			0.508150
$982$	84.9179	+	316.918i	0.0864744	+	0.322727i
$983$	−229.825	+	857.718i	−0.233799	+	0.872551i	0.744887	+	0.667191i	$0.232503\pi$
$983$	−229.825	+	857.718i	−0.233799	+	0.872551i	−0.978686	+	0.205360i	$0.934163\pi$
$984$	168.362	−	97.2039i	0.171100	−	0.0987845i
$985$	370.714	−	472.278i	0.376360	−	0.479470i
$986$	474.455			0.481192
$987$	1237.44	−	38.7815i	1.25373	−	0.0392923i
$988$	316.182	+	316.182i	0.320022	+	0.320022i
$989$	−1008.99	−	582.543i	−1.02022	−	0.589023i
$990$	144.966	−	58.1874i	0.146430	−	0.0587751i
$991$	426.768	+	739.184i	0.430644	+	0.745897i	0.996929	−	0.0783124i	$-0.0249532\pi$
$991$	426.768	+	739.184i	0.430644	+	0.745897i	−0.566285	+	0.824210i	$0.691620\pi$
$992$	23.4256	+	87.4256i	0.0236145	+	0.0881307i
$993$	731.319	+	731.319i	0.736474	+	0.736474i
$994$	103.951	+	344.408i	0.104578	+	0.346487i
$995$	−329.822	+	247.366i	−0.331479	+	0.248610i
$996$	−31.7288	+	54.9559i	−0.0318562	+	0.0551766i
$997$	992.040	+	265.816i	0.995025	+	0.266616i	0.719360	−	0.694638i	$-0.244435\pi$
$997$	992.040	+	265.816i	0.995025	+	0.266616i	0.275665	+	0.961254i	$0.411102\pi$
$998$	76.6581	−	286.092i	0.0768117	−	0.286665i
$999$	1690.32	+	975.909i	1.69202	+	0.976886i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	70.3.l.a.23.1	✓	8
5.2	odd	4	inner	70.3.l.a.37.2	yes	8
5.3	odd	4		350.3.p.c.107.1		8
5.4	even	2		350.3.p.c.93.2		8
7.2	even	3		490.3.f.l.393.1		4
7.4	even	3	inner	70.3.l.a.53.2	yes	8
7.5	odd	6		490.3.f.e.393.2		4
35.2	odd	12		490.3.f.l.197.1		4
35.4	even	6		350.3.p.c.193.1		8
35.12	even	12		490.3.f.e.197.2		4
35.18	odd	12		350.3.p.c.207.2		8
35.32	odd	12	inner	70.3.l.a.67.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.3.l.a.23.1	✓	8	1.1	even	1	trivial
70.3.l.a.37.2	yes	8	5.2	odd	4	inner
70.3.l.a.53.2	yes	8	7.4	even	3	inner
70.3.l.a.67.1	yes	8	35.32	odd	12	inner
350.3.p.c.93.2		8	5.4	even	2
350.3.p.c.107.1		8	5.3	odd	4
350.3.p.c.193.1		8	35.4	even	6
350.3.p.c.207.2		8	35.18	odd	12
490.3.f.e.197.2		4	35.12	even	12
490.3.f.e.393.2		4	7.5	odd	6
490.3.f.l.197.1		4	35.2	odd	12
490.3.f.l.393.1		4	7.2	even	3

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:	\( N \)	\(=\)	\( 70 = 2 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	70.l (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.366025 - 1.36603i) q^{2} +(-0.636376 + 2.37499i) q^{3} +(-1.73205 + 1.00000i) q^{4} +(4.96410 - 0.598076i) q^{5} +3.47723 q^{6} +(6.99656 - 0.219274i) q^{7} +(2.00000 + 2.00000i) q^{8} +(2.55863 + 1.47723i) q^{9} +(-2.63397 - 6.56218i) q^{10} +(3.73861 + 6.47547i) q^{11} +(-1.27275 - 4.74998i) q^{12} +(-10.9545 - 10.9545i) q^{13} +(-2.86045 - 9.47723i) q^{14} +(-1.73861 + 12.1703i) q^{15} +(2.00000 - 3.46410i) q^{16} +(-20.4282 - 5.47371i) q^{17} +(1.08140 - 4.03586i) q^{18} +(12.4982 + 7.21584i) q^{19} +(-8.00000 + 6.00000i) q^{20} +(-3.93168 + 16.7563i) q^{21} +(7.47723 - 7.47723i) q^{22} +(-20.0711 + 5.37803i) q^{23} +(-6.02273 + 3.47723i) q^{24} +(24.2846 - 5.93782i) q^{25} +(-10.9545 + 18.9737i) q^{26} +(-20.7842 + 20.7842i) q^{27} +(-11.8991 + 7.37636i) q^{28} -15.8634i q^{29} +(17.2613 - 2.07965i) q^{30} +(-8.00000 - 13.8564i) q^{31} +(-5.46410 - 1.46410i) q^{32} +(-17.7583 + 4.75833i) q^{33} +29.9089i q^{34} +(34.6005 - 5.27298i) q^{35} -5.90890 q^{36} +(-17.1865 - 64.1410i) q^{37} +(5.28236 - 19.7140i) q^{38} +(32.9879 - 19.0455i) q^{39} +(11.1244 + 8.73205i) q^{40} -27.9545 q^{41} +(24.3286 - 0.762464i) q^{42} +(39.6475 + 39.6475i) q^{43} +(-12.9509 - 7.47723i) q^{44} +(13.5848 + 5.80284i) q^{45} +(14.6931 + 25.4491i) q^{46} +(-18.6173 - 69.4806i) q^{47} +(6.95445 + 6.95445i) q^{48} +(48.9038 - 3.06832i) q^{49} +(-17.0000 - 31.0000i) q^{50} +(26.0000 - 45.0333i) q^{51} +(29.9281 + 8.01921i) q^{52} +(-10.9641 + 40.9185i) q^{53} +(35.9992 + 20.7842i) q^{54} +(22.4317 + 29.9089i) q^{55} +(14.4317 + 13.5546i) q^{56} +(-25.0911 + 25.0911i) q^{57} +(-21.6697 + 5.80639i) q^{58} +(-55.8784 + 32.2614i) q^{59} +(-9.15892 - 22.8182i) q^{60} +(-29.5455 + 51.1744i) q^{61} +(-16.0000 + 16.0000i) q^{62} +(18.2255 + 9.77446i) q^{63} +8.00000i q^{64} +(-60.9306 - 47.8274i) q^{65} +(13.0000 + 22.5167i) q^{66} +(53.5698 + 14.3540i) q^{67} +(40.8563 - 10.9474i) q^{68} -51.0911i q^{69} +(-19.8677 - 45.3351i) q^{70} -36.3406 q^{71} +(2.16281 + 8.07171i) q^{72} +(17.1198 - 63.8921i) q^{73} +(-81.3275 + 46.9545i) q^{74} +(-1.35189 + 61.4544i) q^{75} -28.8634 q^{76} +(27.5773 + 44.4862i) q^{77} +(-38.0911 - 38.0911i) q^{78} +(35.6837 + 20.6020i) q^{79} +(7.85641 - 18.3923i) q^{80} +(-22.8406 - 39.5610i) q^{81} +(10.2320 + 38.1865i) q^{82} +(-9.12474 - 9.12474i) q^{83} +(-9.94644 - 32.9545i) q^{84} +(-104.681 - 14.9545i) q^{85} +(39.6475 - 68.6715i) q^{86} +(37.6753 + 10.0951i) q^{87} +(-5.47371 + 20.4282i) q^{88} +(-42.1986 - 24.3634i) q^{89} +(2.95445 - 20.6812i) q^{90} +(-79.0455 - 74.2415i) q^{91} +(29.3861 - 29.3861i) q^{92} +(37.9998 - 10.1820i) q^{93} +(-88.0979 + 50.8634i) q^{94} +(66.3579 + 28.3453i) q^{95} +(6.95445 - 12.0455i) q^{96} +(-63.7723 + 63.7723i) q^{97} +(-22.0915 - 65.6808i) q^{98} +22.0911i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} - 4 q^{3} + 12 q^{5} - 16 q^{6} - 4 q^{7} + 16 q^{8} - 28 q^{10} + 8 q^{11} - 8 q^{12} + 8 q^{15} + 16 q^{16} - 16 q^{17} + 32 q^{18} - 64 q^{20} + 100 q^{21} + 16 q^{22} - 4 q^{23} + 28 q^{25}+ \cdots - 132 q^{98}+O(q^{100}) \) 8 * q + 4 * q^2 - 4 * q^3 + 12 * q^5 - 16 * q^6 - 4 * q^7 + 16 * q^8 - 28 * q^10 + 8 * q^11 - 8 * q^12 + 8 * q^15 + 16 * q^16 - 16 * q^17 + 32 * q^18 - 64 * q^20 + 100 * q^21 + 16 * q^22 - 4 * q^23 + 28 * q^25 - 232 * q^27 - 40 * q^28 - 24 * q^30 - 64 * q^31 - 16 * q^32 - 52 * q^33 + 112 * q^35 + 128 * q^36 + 144 * q^37 + 8 * q^38 - 8 * q^40 - 136 * q^41 + 188 * q^42 + 120 * q^43 - 128 * q^45 + 8 * q^46 + 72 * q^47 - 32 * q^48 - 136 * q^50 + 208 * q^51 + 76 * q^53 + 48 * q^55 - 16 * q^56 - 376 * q^57 + 68 * q^58 + 56 * q^60 - 324 * q^61 - 128 * q^62 + 112 * q^63 + 104 * q^66 + 124 * q^67 + 32 * q^68 + 160 * q^70 + 16 * q^71 + 64 * q^72 + 32 * q^73 + 124 * q^75 + 32 * q^76 + 20 * q^77 - 480 * q^78 - 48 * q^80 + 124 * q^81 - 68 * q^82 + 168 * q^83 - 224 * q^85 + 120 * q^86 + 428 * q^87 + 16 * q^88 - 64 * q^90 - 720 * q^91 + 16 * q^92 - 64 * q^93 - 32 * q^95 - 32 * q^96 - 72 * q^97 - 132 * q^98

Introduction

L-functions

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