LMFDB - Embedded newform 70.3.l.a.37.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [70,3,Mod(23,70)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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			37.2
Root			$2.15988 + 0.578737i$ of defining polynomial
Character	$\chi$	$=$	70.37
Dual form			70.3.l.a.53.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.36603 - 0.366025i) q^{2} +(2.37499 + 0.636376i) q^{3} +(1.73205 - 1.00000i) q^{4} +(-1.96410 - 4.59808i) q^{5} +3.47723 q^{6} +(0.219274 + 6.99656i) q^{7} +(2.00000 - 2.00000i) q^{8} +(-2.55863 - 1.47723i) q^{9} +O(q^{10})$	\(q+(1.36603 - 0.366025i) q^{2} +(2.37499 + 0.636376i) q^{3} +(1.73205 - 1.00000i) q^{4} +(-1.96410 - 4.59808i) q^{5} +3.47723 q^{6} +(0.219274 + 6.99656i) q^{7} +(2.00000 - 2.00000i) q^{8} +(-2.55863 - 1.47723i) q^{9} +(-4.36603 - 5.56218i) q^{10} +(3.73861 + 6.47547i) q^{11} +(4.74998 - 1.27275i) 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} +(5.47371 - 20.4282i) q^{17} +(-4.03586 - 1.08140i) 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} +(5.37803 + 20.0711i) q^{23} +(6.02273 - 3.47723i) q^{24} +(-17.2846 + 18.0622i) q^{25} +(-10.9545 + 18.9737i) q^{26} +(-20.7842 - 20.7842i) q^{27} +(7.37636 + 11.8991i) q^{28} +15.8634i q^{29} +(-6.82962 - 15.9885i) q^{30} +(-8.00000 - 13.8564i) q^{31} +(1.46410 - 5.46410i) q^{32} +(4.75833 + 17.7583i) q^{33} -29.9089i q^{34} +(31.7401 - 14.7502i) q^{35} -5.90890 q^{36} +(64.1410 - 17.1865i) q^{37} +(-19.7140 - 5.28236i) q^{38} +(-32.9879 + 19.0455i) q^{39} +(-13.1244 - 5.26795i) q^{40} -27.9545 q^{41} +(0.762464 + 24.3286i) q^{42} +(39.6475 - 39.6475i) q^{43} +(12.9509 + 7.47723i) q^{44} +(-1.76699 + 14.6662i) q^{45} +(14.6931 + 25.4491i) q^{46} +(69.4806 - 18.6173i) 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} +(-8.01921 + 29.9281i) q^{52} +(40.9185 + 10.9641i) 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} +(5.80639 + 21.6697i) q^{58} +(55.8784 - 32.2614i) q^{59} +(-15.1817 - 19.3409i) q^{60} +(-29.5455 + 51.1744i) q^{61} +(-16.0000 - 16.0000i) q^{62} +(9.77446 - 18.2255i) q^{63} -8.00000i q^{64} +(71.8851 + 28.8537i) q^{65} +(13.0000 + 22.5167i) q^{66} +(-14.3540 + 53.5698i) q^{67} +(-10.9474 - 40.8563i) q^{68} +51.0911i q^{69} +(37.9588 - 31.7668i) q^{70} -36.3406 q^{71} +(-8.07171 + 2.16281i) q^{72} +(-63.8921 - 17.1198i) q^{73} +(81.3275 - 46.9545i) q^{74} +(-52.5451 + 31.8980i) q^{75} -28.8634 q^{76} +(-44.4862 + 27.5773i) q^{77} +(-38.0911 + 38.0911i) q^{78} +(-35.6837 - 20.6020i) q^{79} +(-19.8564 - 2.39230i) q^{80} +(-22.8406 - 39.5610i) q^{81} +(-38.1865 + 10.2320i) 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} +(-10.0951 + 37.6753i) q^{87} +(20.4282 + 5.47371i) 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} +(-10.1820 - 37.9998i) q^{93} +(88.0979 - 50.8634i) q^{94} +(-8.63124 + 71.6403i) q^{95} +(6.95445 - 12.0455i) q^{96} +(-63.7723 - 63.7723i) q^{97} +(-65.6808 + 22.0915i) 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}+O(q^{10}) $ 8 * q + 4 * q^2 - 4 * q^3 + 12 * q^5 - 16 * q^6 - 4 * q^7 + 16 * q^8	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	1.36603	−	0.366025i	0.683013	−	0.183013i
$2$	1.36603	−	0.366025i	0.683013	−	0.183013i
$3$	2.37499	+	0.636376i	0.791663	+	0.212125i	0.631920	−	0.775033i	$-0.282267\pi$
$3$	2.37499	+	0.636376i	0.791663	+	0.212125i	0.159743	+	0.987159i	$0.448934\pi$
$4$	1.73205	−	1.00000i	0.433013	−	0.250000i
$5$	−1.96410	−	4.59808i	−0.392820	−	0.919615i
$5$	−1.96410	−	4.59808i	−0.392820	−	0.919615i
$6$	3.47723			0.579538
$7$	0.219274	+	6.99656i	0.0313248	+	0.999509i
$7$	0.219274	+	6.99656i	0.0313248	+	0.999509i
$8$	2.00000	−	2.00000i	0.250000	−	0.250000i
$9$	−2.55863	−	1.47723i	−0.284292	−	0.164136i
$10$	−4.36603	−	5.56218i	−0.436603	−	0.556218i
$11$	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	$0.722949\pi$
$12$	4.74998	−	1.27275i	0.395832	−	0.106063i
$13$	−10.9545	+	10.9545i	−0.842650	+	0.842650i	−0.989203	−	0.146553i	$-0.953182\pi$
$13$	−10.9545	+	10.9545i	−0.842650	+	0.842650i	0.146553	+	0.989203i	$0.453182\pi$
$14$	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
$17$	5.47371	−	20.4282i	0.321983	−	1.20166i	−0.595327	−	0.803483i	$-0.702978\pi$
$17$	5.47371	−	20.4282i	0.321983	−	1.20166i	0.917310	−	0.398173i	$-0.130356\pi$
$18$	−4.03586	−	1.08140i	−0.224214	−	0.0600780i
$19$	−12.4982	−	7.21584i	−0.657800	−	0.379781i	0.133638	−	0.991030i	$-0.457334\pi$
$19$	−12.4982	−	7.21584i	−0.657800	−	0.379781i	−0.791438	+	0.611249i	$0.790667\pi$
$20$	−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
$23$	5.37803	+	20.0711i	0.233828	+	0.872656i	0.978674	+	0.205420i	$0.0658561\pi$
$23$	5.37803	+	20.0711i	0.233828	+	0.872656i	−0.744846	+	0.667236i	$0.767477\pi$
$24$	6.02273	−	3.47723i	0.250947	−	0.144884i
$25$	−17.2846	+	18.0622i	−0.691384	+	0.722487i
$26$	−10.9545	+	18.9737i	−0.421325	+	0.729756i
$27$	−20.7842	−	20.7842i	−0.769784	−	0.769784i
$28$	7.37636	+	11.8991i	0.263441	+	0.424969i
$29$			15.8634i			0.547012i	0.961870	+	0.273506i	$0.0881834\pi$
$29$			15.8634i			0.547012i	−0.961870	+	0.273506i	$0.911817\pi$
$30$	−6.82962	−	15.9885i	−0.227654	−	0.532952i
$31$	−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	$0.916418\pi$
$32$	1.46410	−	5.46410i	0.0457532	−	0.170753i
$33$	4.75833	+	17.7583i	0.144192	+	0.538131i
$34$		−	29.9089i		−	0.879674i
$35$	31.7401	−	14.7502i	0.906859	−	0.421434i
$36$	−5.90890			−0.164136
$37$	64.1410	−	17.1865i	1.73354	−	0.464501i	0.752546	−	0.658540i	$-0.228826\pi$
$37$	64.1410	−	17.1865i	1.73354	−	0.464501i	0.980994	+	0.194039i	$0.0621589\pi$
$38$	−19.7140	−	5.28236i	−0.518790	−	0.139009i
$39$	−32.9879	+	19.0455i	−0.845843	+	0.488347i
$40$	−13.1244	−	5.26795i	−0.328109	−	0.131699i
$41$	−27.9545			−0.681816			−0.340908	−	0.940097i	$-0.610734\pi$
$41$	−27.9545			−0.681816			−0.340908	+	0.940097i	$0.610734\pi$
$42$	0.762464	+	24.3286i	0.0181539	+	0.579253i
$43$	39.6475	−	39.6475i	0.922035	−	0.922035i	−0.0751379	−	0.997173i	$-0.523940\pi$
$43$	39.6475	−	39.6475i	0.922035	−	0.922035i	0.997173	+	0.0751379i	$0.0239397\pi$
$44$	12.9509	+	7.47723i	0.294339	+	0.169937i
$45$	−1.76699	+	14.6662i	−0.0392664	+	0.325915i
$46$	14.6931	+	25.4491i	0.319414	+	0.553242i
$47$	69.4806	−	18.6173i	1.47831	−	0.396112i	0.572539	−	0.819877i	$-0.305958\pi$
$47$	69.4806	−	18.6173i	1.47831	−	0.396112i	0.905772	+	0.423765i	$0.139292\pi$
$48$	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
$52$	−8.01921	+	29.9281i	−0.154216	+	0.575541i
$53$	40.9185	+	10.9641i	0.772048	+	0.206870i	0.623276	−	0.782002i	$-0.285801\pi$
$53$	40.9185	+	10.9641i	0.772048	+	0.206870i	0.148772	+	0.988872i	$0.452468\pi$
$54$	−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
$58$	5.80639	+	21.6697i	0.100110	+	0.373616i
$59$	55.8784	−	32.2614i	0.947091	−	0.546803i	0.0549148	−	0.998491i	$-0.482511\pi$
$59$	55.8784	−	32.2614i	0.947091	−	0.546803i	0.892176	+	0.451688i	$0.149178\pi$
$60$	−15.1817	−	19.3409i	−0.253028	−	0.322349i
$61$	−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
$63$	9.77446	−	18.2255i	0.155150	−	0.289294i
$64$		−	8.00000i		−	0.125000i
$65$	71.8851	+	28.8537i	1.10592	+	0.443904i
$66$	13.0000	+	22.5167i	0.196970	+	0.341162i
$67$	−14.3540	+	53.5698i	−0.214239	+	0.799550i	0.772194	+	0.635386i	$0.219159\pi$
$67$	−14.3540	+	53.5698i	−0.214239	+	0.799550i	−0.986433	+	0.164163i	$0.947508\pi$
$68$	−10.9474	−	40.8563i	−0.160991	−	0.600828i
$69$			51.0911i			0.740451i
$70$	37.9588	−	31.7668i	0.542268	−	0.453812i
$71$	−36.3406			−0.511839			−0.255920	−	0.966698i	$-0.582378\pi$
$71$	−36.3406			−0.511839			−0.255920	+	0.966698i	$0.582378\pi$
$72$	−8.07171	+	2.16281i	−0.112107	+	0.0300390i
$73$	−63.8921	−	17.1198i	−0.875234	−	0.234518i	−0.206884	−	0.978365i	$-0.566332\pi$
$73$	−63.8921	−	17.1198i	−0.875234	−	0.234518i	−0.668350	+	0.743847i	$0.732999\pi$
$74$	81.3275	−	46.9545i	1.09902	−	0.634520i
$75$	−52.5451	+	31.8980i	−0.700601	+	0.425306i
$76$	−28.8634			−0.379781
$77$	−44.4862	+	27.5773i	−0.577743	+	0.358147i
$78$	−38.0911	+	38.0911i	−0.488347	+	0.488347i
$79$	−35.6837	−	20.6020i	−0.451692	−	0.260784i	0.256853	−	0.966451i	$-0.417314\pi$
$79$	−35.6837	−	20.6020i	−0.451692	−	0.260784i	−0.708544	+	0.705666i	$0.750648\pi$
$80$	−19.8564	−	2.39230i	−0.248205	−	0.0299038i
$81$	−22.8406	−	39.5610i	−0.281982	−	0.488408i
$82$	−38.1865	+	10.2320i	−0.465689	+	0.124781i
$83$	−9.12474	+	9.12474i	−0.109937	+	0.109937i	−0.759935	−	0.649999i	$-0.774769\pi$
$83$	−9.12474	+	9.12474i	−0.109937	+	0.109937i	0.649999	+	0.759935i	$0.274769\pi$
$84$	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
$87$	−10.0951	+	37.6753i	−0.116035	+	0.433049i
$88$	20.4282	+	5.47371i	0.232138	+	0.0622012i
$89$	42.1986	+	24.3634i	0.474141	+	0.273746i	0.717972	−	0.696072i	$-0.245071\pi$
$89$	42.1986	+	24.3634i	0.474141	+	0.273746i	−0.243830	+	0.969818i	$0.578404\pi$
$90$	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
$93$	−10.1820	−	37.9998i	−0.109484	−	0.408600i
$94$	88.0979	−	50.8634i	0.937212	−	0.541100i
$95$	−8.63124	+	71.6403i	−0.0908552	+	0.754109i
$96$	6.95445	−	12.0455i	0.0724422	−	0.125474i
$97$	−63.7723	−	63.7723i	−0.657446	−	0.657446i	0.297329	−	0.954775i	$-0.403904\pi$
$97$	−63.7723	−	63.7723i	−0.657446	−	0.657446i	−0.954775	+	0.297329i	$0.903904\pi$
$98$	−65.6808	+	22.0915i	−0.670212	+	0.225423i
$99$		−	22.0911i		−	0.223142i
$100$	−11.8756	+	48.5692i	−0.118756	+	0.485692i
$101$	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	$0.673001\pi$
$102$	19.0333	−	71.0333i	0.186601	−	0.696405i
$103$	12.5405	+	46.8019i	0.121753	+	0.454388i	0.999703	−	0.0243641i	$-0.00775609\pi$
$103$	12.5405	+	46.8019i	0.121753	+	0.454388i	−0.877950	+	0.478752i	$0.841089\pi$
$104$			43.8178i			0.421325i
$105$	84.7690	−	14.8329i	0.807324	−	0.141266i
$106$	59.9089			0.565178
$107$	−159.032	+	42.6126i	−1.48628	+	0.398249i	−0.908480	−	0.417927i	$-0.862757\pi$
$107$	−159.032	+	42.6126i	−1.48628	+	0.398249i	−0.577803	+	0.816176i	$0.696090\pi$
$108$	−56.7834	−	15.2151i	−0.525772	−	0.140880i
$109$	−146.122	+	84.3634i	−1.34057	+	0.773976i	−0.986890	−	0.161393i	$-0.948401\pi$
$109$	−146.122	+	84.3634i	−1.34057	+	0.773976i	−0.353675	+	0.935368i	$0.615068\pi$
$110$	19.6948	−	49.0669i	0.179044	−	0.446063i
$111$	163.271			1.47091
$112$	24.6754	+	13.2335i	0.220316	+	0.118157i
$113$	56.6356	−	56.6356i	0.501200	−	0.501200i	−0.410611	−	0.911811i	$-0.634684\pi$
$113$	56.6356	−	56.6356i	0.501200	−	0.501200i	0.911811	+	0.410611i	$0.134684\pi$
$114$	−43.4591	−	25.0911i	−0.381220	−	0.220097i
$115$	81.7254	−	64.1503i	0.710656	−	0.557829i
$116$	15.8634	+	27.4761i	0.136753	+	0.236863i
$117$	44.2106	−	11.8462i	0.377868	−	0.101249i
$118$	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
$122$	−21.6288	+	80.7199i	−0.177286	+	0.661639i
$123$	−66.3915	−	17.7896i	−0.539768	−	0.144631i
$124$	−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	0.718995	−	0.695015i	$-0.244602\pi$
$127$	3.04555	+	3.04555i	0.0239807	+	0.0239807i	−0.695015	+	0.718995i	$0.744602\pi$
$128$	−2.92820	−	10.9282i	−0.0228766	−	0.0853766i
$129$	119.393	−	68.9317i	0.925528	−	0.534354i
$130$	108.758	+	13.1032i	0.836600	+	0.100794i
$131$	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
$133$	47.7456	−	89.0267i	0.358989	−	0.669374i
$134$			78.4317i			0.585311i
$135$	−54.7450	+	136.389i	−0.405518	+	1.01029i
$136$	−29.9089	−	51.8037i	−0.219918	−	0.380910i
$137$	37.6173	−	140.390i	0.274579	−	1.02474i	−0.681545	−	0.731776i	$-0.738692\pi$
$137$	37.6173	−	140.390i	0.274579	−	1.02474i	0.956123	−	0.292965i	$-0.0946418\pi$
$138$	18.7006	+	69.7917i	0.135512	+	0.505737i
$139$			177.022i			1.27354i	0.771055	+	0.636769i	$0.219729\pi$
$139$			177.022i			1.27354i	−0.771055	+	0.636769i	$0.780271\pi$
$140$	40.2252	−	57.2882i	0.287323	−	0.409201i
$141$	176.863			1.25435
$142$	−49.6422	+	13.3016i	−0.349593	+	0.0936731i
$143$	−111.890	−	29.9807i	−0.782445	−	0.209656i
$144$	−10.2345	+	5.90890i	−0.0710730	+	0.0410340i
$145$	72.9409	−	31.1572i	0.503041	−	0.214878i
$146$	−93.5445			−0.640716
$147$	−118.099	−	23.8340i	−0.803393	−	0.162136i
$148$	93.9089	−	93.9089i	0.634520	−	0.634520i
$149$	−219.026	−	126.454i	−1.46997	−	0.848688i	−0.470538	−	0.882380i	$-0.655940\pi$
$149$	−219.026	−	126.454i	−1.46997	−	0.848688i	−0.999432	+	0.0336923i	$0.989273\pi$
$150$	−60.1025	+	62.8063i	−0.400683	+	0.418708i
$151$	−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	$-0.405477\pi$
$152$	−39.4281	+	10.5647i	−0.259395	+	0.0695047i
$153$	−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
$157$	−68.5960	+	256.004i	−0.436917	+	1.63060i	0.299518	+	0.954091i	$0.403174\pi$
$157$	−68.5960	+	256.004i	−0.436917	+	1.63060i	−0.736436	+	0.676508i	$0.763493\pi$
$158$	−56.2856	−	15.0817i	−0.356238	−	0.0954537i
$159$	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
$163$	64.7031	+	241.475i	0.396952	+	1.48144i	0.818430	+	0.574606i	$0.194845\pi$
$163$	64.7031	+	241.475i	0.396952	+	1.48144i	−0.421479	+	0.906838i	$0.638489\pi$
$164$	−48.4185	+	27.9545i	−0.295235	+	0.170454i
$165$	72.3083	−	56.7583i	0.438232	−	0.343990i
$166$	−9.12474	+	15.8045i	−0.0549683	+	0.0952079i
$167$	8.01191	+	8.01191i	0.0479755	+	0.0479755i	0.730688	−	0.682712i	$-0.239200\pi$
$167$	8.01191	+	8.01191i	0.0479755	+	0.0479755i	−0.682712	+	0.730688i	$0.739200\pi$
$168$	25.6493	+	41.3760i	0.152674	+	0.246286i
$169$		−	71.0000i		−	0.420118i
$170$	−137.523	+	58.7441i	−0.808961	+	0.345554i
$171$	21.3188	+	36.9253i	0.124672	+	0.215938i
$172$	29.0240	−	108.319i	0.168744	−	0.629762i
$173$	−32.1435	−	119.961i	−0.185801	−	0.693418i	−0.994458	−	0.105138i	$-0.966472\pi$
$173$	−32.1435	−	119.961i	−0.185801	−	0.693418i	0.808657	−	0.588281i	$-0.200195\pi$
$174$			55.1605i			0.317014i
$175$	−130.163	−	116.972i	−0.743790	−	0.668413i
$176$	29.9089			0.169937
$177$	153.241	−	41.0608i	0.865768	−	0.231982i
$178$	66.5619	+	17.8352i	0.373943	+	0.100198i
$179$	114.000	−	65.8178i	0.636870	−	0.367697i	−0.146538	−	0.989205i	$-0.546813\pi$
$179$	114.000	−	65.8178i	0.636870	−	0.367697i	0.783408	+	0.621508i	$0.213480\pi$
$180$	11.6057	+	27.1696i	0.0644760	+	0.150942i
$181$	−149.681			−0.826968			−0.413484	−	0.910511i	$-0.635688\pi$
$181$	−149.681			−0.826968			−0.413484	+	0.910511i	$0.635688\pi$
$182$	−135.153	−	72.4831i	−0.742596	−	0.398259i
$183$	−102.737	+	102.737i	−0.561402	+	0.561402i
$184$	50.8983	+	29.3861i	0.276621	+	0.159707i
$185$	−205.004	−	261.169i	−1.10813	−	1.41172i
$186$	−27.8178	−	48.1819i	−0.149558	−	0.259042i
$187$	152.746	−	40.9282i	0.816823	−	0.218867i
$188$	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	$0.965085\pi$
$192$	5.09101	−	18.9999i	0.0265157	−	0.0989579i
$193$	213.595	+	57.2326i	1.10671	+	0.296542i	0.765494	−	0.643443i	$-0.222495\pi$
$193$	213.595	+	57.2326i	1.10671	+	0.296542i	0.341215	+	0.939985i	$0.389161\pi$
$194$	−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	0.888972	−	0.457962i	$-0.151420\pi$
$197$	84.9089	+	84.9089i	0.431010	+	0.431010i	−0.457962	+	0.888972i	$0.651420\pi$
$198$	−8.08590	−	30.1770i	−0.0408379	−	0.152409i
$199$	71.4085	−	41.2277i	0.358837	−	0.207175i	−0.309734	−	0.950823i	$-0.600240\pi$
$199$	71.4085	−	41.2277i	0.358837	−	0.207175i	0.668570	+	0.743649i	$0.266907\pi$
$200$	1.55514	+	70.6936i	0.00777568	+	0.353468i
$201$	−68.1812	+	118.093i	−0.339210	+	0.587529i
$202$	97.4990	+	97.4990i	0.482668	+	0.482668i
$203$	−110.989	+	3.47841i	−0.546744	+	0.0171350i
$204$		−	104.000i		−	0.509804i
$205$	54.9054	+	128.537i	0.267831	+	0.627008i
$206$	34.2614	+	59.3425i	0.166317	+	0.288070i
$207$	15.8891	−	59.2991i	0.0767591	−	0.286469i
$208$	16.0384	+	59.8562i	0.0771078	+	0.287770i
$209$		−	107.909i		−	0.516311i
$210$	110.367	−	51.2898i	0.525559	−	0.244237i
$211$	205.703			0.974895			0.487448	−	0.873152i	$-0.337928\pi$
$211$	205.703			0.974895			0.487448	+	0.873152i	$0.337928\pi$
$212$	81.8371	−	21.9282i	0.386024	−	0.103435i
$213$	−86.3085	−	23.1263i	−0.405204	−	0.108574i
$214$	−201.645	+	116.420i	−0.942266	+	0.544018i
$215$	−260.174	−	104.431i	−1.21011	−	0.485723i
$216$	−83.1366			−0.384892
$217$	95.1931	−	59.0109i	0.438678	−	0.271939i
$218$	−168.727	+	168.727i	−0.773976	+	0.773976i
$219$	−140.848	−	81.3188i	−0.643143	−	0.371319i
$220$	8.94390	−	74.2354i	0.0406541	−	0.337434i
$221$	163.818	+	283.741i	0.741257	+	1.28389i
$222$	223.033	−	59.7614i	1.00465	−	0.269196i
$223$	62.8872	−	62.8872i	0.282005	−	0.282005i	−0.551903	−	0.833908i	$-0.686098\pi$
$223$	62.8872	−	62.8872i	0.282005	−	0.282005i	0.833908	+	0.551903i	$0.186098\pi$
$224$	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
$227$	−66.8659	+	249.547i	−0.294564	+	1.09933i	0.647000	+	0.762490i	$0.276024\pi$
$227$	−66.8659	+	249.547i	−0.294564	+	1.09933i	−0.941563	+	0.336836i	$0.890643\pi$
$228$	−68.5502	−	18.3680i	−0.300659	−	0.0805612i
$229$	−106.598	−	61.5445i	−0.465494	−	0.268753i	0.248857	−	0.968540i	$-0.419945\pi$
$229$	−106.598	−	61.5445i	−0.465494	−	0.268753i	−0.714352	+	0.699787i	$0.753278\pi$
$230$	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
$233$	−82.4883	−	307.851i	−0.354027	−	1.32125i	−0.881704	−	0.471802i	$-0.843604\pi$
$233$	−82.4883	−	307.851i	−0.354027	−	1.32125i	0.527677	−	0.849445i	$-0.323063\pi$
$234$	56.0568	−	32.3644i	0.239559	−	0.138309i
$235$	−222.071	−	282.911i	−0.944982	−	1.20388i
$236$	64.5228	−	111.757i	0.273402	−	0.473545i
$237$	−71.6377	−	71.6377i	−0.302269	−	0.302269i
$238$	209.260	−	6.55823i	0.879242	−	0.0275556i
$239$		−	174.725i		−	0.731065i	−0.930798	−	0.365533i	$-0.880887\pi$
$239$		−	174.725i		−	0.731065i	0.930798	−	0.365533i	$-0.119113\pi$
$240$	−45.6363	−	18.3178i	−0.190151	−	0.0763244i
$241$	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	$0.664514\pi$
$242$	23.8250	−	88.9161i	0.0984504	−	0.367422i
$243$	39.3974	+	147.033i	0.162129	+	0.605074i
$244$			118.182i			0.484353i
$245$	110.160	+	218.837i	0.449635	+	0.893213i
$246$	−97.2039			−0.395138
$247$	215.956	−	57.8654i	0.874318	−	0.234273i
$248$	−43.7128	−	11.7128i	−0.176261	−	0.0472291i
$249$	−27.4779	+	15.8644i	−0.110353	+	0.0637124i
$250$	175.930	+	17.2801i	0.703720	+	0.0691206i
$251$	54.2733			0.216228			0.108114	−	0.994138i	$-0.465519\pi$
$251$	54.2733			0.216228			0.108114	+	0.994138i	$0.465519\pi$
$252$	−1.29567	−	41.3420i	−0.00514153	−	0.164056i
$253$	−109.863	+	109.863i	−0.434243	+	0.434243i
$254$	5.27505	+	3.04555i	0.0207679	+	0.0119903i
$255$	−258.133	−	31.1000i	−1.01229	−	0.121961i
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	−20.9259	+	5.60709i	−0.0814238	+	0.0218175i	−0.299301	−	0.954159i	$-0.596753\pi$
$257$	−20.9259	+	5.60709i	−0.0814238	+	0.0218175i	0.217877	+	0.975976i	$0.430087\pi$
$258$	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
$262$	41.6936	−	155.602i	0.159136	−	0.593902i
$263$	324.757	+	87.0184i	1.23482	+	0.330868i	0.816454	−	0.577411i	$-0.195937\pi$
$263$	324.757	+	87.0184i	1.23482	+	0.330868i	0.418364	+	0.908279i	$0.362604\pi$
$264$	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
$268$	28.7080	+	107.140i	0.107119	+	0.399775i
$269$	93.6867	−	54.0901i	0.348278	−	0.201078i	−0.315649	−	0.948876i	$-0.602222\pi$
$269$	93.6867	−	54.0901i	0.348278	−	0.201078i	0.663926	+	0.747798i	$0.268889\pi$
$270$	−24.8610	+	206.349i	−0.0920779	+	0.764257i
$271$	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
$273$	−140.487	−	226.626i	−0.514604	−	0.830130i
$274$		−	205.545i		−	0.750162i
$275$	−181.582	−	44.3984i	−0.660296	−	0.161449i
$276$	51.0911	+	88.4924i	0.185113	+	0.320625i
$277$	−92.4210	+	344.920i	−0.333650	+	1.24520i	0.571675	+	0.820480i	$0.306294\pi$
$277$	−92.4210	+	344.920i	−0.333650	+	1.24520i	−0.905325	+	0.424719i	$0.860373\pi$
$278$	64.7945	+	241.816i	0.233074	+	0.869842i
$279$			47.2712i			0.169431i
$280$	33.9797	−	92.9805i	0.121356	−	0.332073i
$281$	−398.542			−1.41830			−0.709150	−	0.705057i	$-0.750921\pi$
$281$	−398.542			−1.41830			−0.709150	+	0.705057i	$0.750921\pi$
$282$	241.600	−	64.7365i	0.856737	−	0.229562i
$283$	475.436	+	127.393i	1.67999	+	0.450151i	0.967776	−	0.251814i	$-0.0810272\pi$
$283$	475.436	+	127.393i	1.67999	+	0.450151i	0.712211	+	0.701965i	$0.247694\pi$
$284$	−62.9437	+	36.3406i	−0.221633	+	0.127960i
$285$	−66.0893	+	164.652i	−0.231892	+	0.577727i
$286$	−163.818			−0.572790
$287$	−6.12967	−	195.585i	−0.0213577	−	0.681481i
$288$	−11.8178	+	11.8178i	−0.0410340	+	0.0410340i
$289$	−137.067	−	79.1356i	−0.474280	−	0.273826i
$290$	88.2348	−	69.2598i	0.304258	−	0.238827i
$291$	−110.875	−	192.042i	−0.381015	−	0.659937i
$292$	−127.784	+	34.2397i	−0.437617	+	0.117259i
$293$	−187.818	+	187.818i	−0.641016	+	0.641016i	−0.950805	−	0.309789i	$-0.899742\pi$
$293$	−187.818	+	187.818i	−0.641016	+	0.641016i	0.309789	+	0.950805i	$0.399742\pi$
$294$	−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
$297$	56.8832	−	212.291i	0.191526	−	0.714785i
$298$	−345.480	−	92.5711i	−1.15933	−	0.310641i
$299$	−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
$303$	62.0460	+	231.559i	0.204772	+	0.764221i
$304$	−49.9928	+	28.8634i	−0.164450	+	0.0949452i
$305$	293.334	+	35.3410i	0.961752	+	0.115872i
$306$	−44.1822	+	76.5258i	−0.144386	+	0.250084i
$307$	−171.398	−	171.398i	−0.558300	−	0.558300i	0.370523	−	0.928823i	$-0.379178\pi$
$307$	−171.398	−	171.398i	−0.558300	−	0.558300i	−0.928823	+	0.370523i	$0.879178\pi$
$308$	−49.4751	+	92.2516i	−0.160633	+	0.299518i
$309$			119.135i			0.385549i
$310$	−42.1436	+	104.995i	−0.135947	+	0.338693i
$311$	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	$0.831554\pi$
$312$	−27.8846	+	104.067i	−0.0893738	+	0.333547i
$313$	5.52297	+	20.6120i	0.0176453	+	0.0658530i	0.974187	−	0.225742i	$-0.0724807\pi$
$313$	5.52297	+	20.6120i	0.0176453	+	0.0658530i	−0.956542	+	0.291595i	$0.905814\pi$
$314$			374.816i			1.19368i
$315$	−103.000	−	9.14693i	−0.326986	−	0.0290379i
$316$	−82.4079			−0.260784
$317$	393.415	−	105.415i	1.24106	−	0.332540i	0.422182	−	0.906511i	$-0.361264\pi$
$317$	393.415	−	105.415i	1.24106	−	0.332540i	0.818876	+	0.573971i	$0.194598\pi$
$318$	142.283	+	38.1246i	0.447431	+	0.119889i
$319$	−102.723	+	59.3069i	−0.322015	+	0.185915i
$320$	−36.7846	+	15.7128i	−0.114952	+	0.0491025i
$321$	−404.818			−1.26111
$322$	−174.835	+	108.381i	−0.542965	+	0.336588i
$323$	−215.818	+	215.818i	−0.668167	+	0.668167i
$324$	−79.1221	−	45.6812i	−0.244204	−	0.140991i
$325$	−8.51783	−	387.205i	−0.0262087	−	1.19140i
$326$	176.772	+	306.179i	0.542246	+	0.939198i
$327$	−400.724	+	107.374i	−1.22546	+	0.328360i
$328$	−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	$-0.0524973\pi$
$332$	−6.67977	+	24.9293i	−0.0201198	+	0.0750881i
$333$	−189.501	−	50.7767i	−0.569073	−	0.152483i
$334$	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	0.654429	−	0.756124i	$-0.272909\pi$
$337$	−34.2712	−	34.2712i	−0.101695	−	0.101695i	−0.756124	+	0.654429i	$0.772909\pi$
$338$	−25.9878	−	96.9878i	−0.0768870	−	0.286946i
$339$	170.551	−	98.4674i	0.503099	−	0.290464i
$340$	−166.359	+	130.583i	−0.489290	+	0.384068i
$341$	59.8178	−	103.607i	0.175419	−	0.303834i
$342$	42.6377	+	42.6377i	0.124672	+	0.124672i
$343$	−32.1910	−	341.486i	−0.0938514	−	0.995586i
$344$		−	158.590i		−	0.461018i
$345$	234.921	−	100.348i	0.680930	−	0.290864i
$346$	−87.8178	−	152.105i	−0.253809	−	0.439610i
$347$	37.4549	−	139.784i	0.107939	−	0.402834i	−0.890723	−	0.454547i	$-0.849801\pi$
$347$	37.4549	−	139.784i	0.107939	−	0.402834i	0.998662	+	0.0517123i	$0.0164679\pi$
$348$	20.1901	+	75.3506i	0.0580176	+	0.216525i
$349$		−	248.861i		−	0.713070i	−0.934282	−	0.356535i	$-0.883958\pi$
$349$		−	248.861i		−	0.713070i	0.934282	−	0.356535i	$-0.116042\pi$
$350$	−220.621	−	112.144i	−0.630346	−	0.320412i
$351$	455.358			1.29732
$352$	40.8563	−	10.9474i	0.116069	−	0.0311006i
$353$	−385.714	−	103.352i	−1.09267	−	0.292781i	−0.332896	−	0.942963i	$-0.608026\pi$
$353$	−385.714	−	103.352i	−1.09267	−	0.292781i	−0.759778	+	0.650182i	$0.774693\pi$
$354$	194.302	−	112.180i	0.548875	−	0.316893i
$355$	71.3766	+	167.097i	0.201061	+	0.470695i
$356$	97.4534			0.273746
$357$	320.780	+	172.036i	0.898542	+	0.481894i
$358$	131.636	−	131.636i	0.367697	−	0.367697i
$359$	370.734	+	214.043i	1.03269	+	0.596221i	0.917753	−	0.397152i	$-0.130001\pi$
$359$	370.734	+	214.043i	1.03269	+	0.596221i	0.114933	+	0.993373i	$0.463335\pi$
$360$	25.7984	+	32.8664i	0.0716623	+	0.0912955i
$361$	−76.3634	−	132.265i	−0.211533	−	0.366386i
$362$	−204.468	+	54.7871i	−0.564829	+	0.151346i
$363$	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
$367$	−60.9472	+	227.458i	−0.166069	+	0.619777i	0.831833	+	0.555026i	$0.187292\pi$
$367$	−60.9472	+	227.458i	−0.166069	+	0.619777i	−0.997901	+	0.0647505i	$0.979375\pi$
$368$	80.2844	+	21.5121i	0.218164	+	0.0584569i
$369$	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
$373$	39.2640	+	146.535i	0.105265	+	0.392856i	0.998375	−	0.0569830i	$-0.0181481\pi$
$373$	39.2640	+	146.535i	0.105265	+	0.392856i	−0.893110	+	0.449839i	$0.851481\pi$
$374$	193.674	−	111.818i	0.517845	−	0.298978i
$375$	249.873	+	178.956i	0.666328	+	0.477215i
$376$	101.727	−	176.196i	0.270550	−	0.468606i
$377$	−173.774	−	173.774i	−0.460940	−	0.460940i
$378$	137.524	−	256.428i	0.363820	−	0.678382i
$379$		−	66.4317i		−	0.175281i	−0.996152	−	0.0876407i	$-0.972067\pi$
$379$		−	66.4317i		−	0.175281i	0.996152	−	0.0876407i	$-0.0279327\pi$
$380$	56.6906	+	132.716i	0.149186	+	0.349252i
$381$	5.29503	+	9.17126i	0.0138977	+	0.0240716i
$382$	−82.7464	+	308.814i	−0.216614	+	0.808413i
$383$	−176.171	−	657.478i	−0.459975	−	1.71665i	−0.673034	−	0.739612i	$-0.735009\pi$
$383$	−176.171	−	657.478i	−0.459975	−	1.71665i	0.213058	−	0.977040i	$-0.431658\pi$
$384$		−	27.8178i		−	0.0724422i
$385$	214.178	+	150.386i	0.556307	+	0.390614i
$386$	312.725			0.810167
$387$	−160.012	+	42.8750i	−0.413467	+	0.110788i
$388$	−174.229	−	46.6845i	−0.449044	−	0.120321i
$389$	80.4633	−	46.4555i	0.206846	−	0.119423i	−0.392999	−	0.919539i	$-0.628562\pi$
$389$	80.4633	−	46.4555i	0.206846	−	0.119423i	0.599845	+	0.800116i	$0.295229\pi$
$390$	249.961	+	100.331i	0.640925	+	0.257259i
$391$	439.453			1.12392
$392$	−91.6710	+	103.944i	−0.233855	+	0.265164i
$393$	198.043	−	198.043i	0.503927	−	0.503927i
$394$	147.067	+	84.9089i	0.373265	+	0.215505i
$395$	−24.6431	+	204.541i	−0.0623876	+	0.517824i
$396$	−22.0911	−	38.2629i	−0.0557856	−	0.0966235i
$397$	−349.516	+	93.6525i	−0.880393	+	0.235900i	−0.670576	−	0.741840i	$-0.733953\pi$
$397$	−349.516	+	93.6525i	−0.880393	+	0.235900i	−0.209816	+	0.977741i	$0.567287\pi$
$398$	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	$-0.121293\pi$
$402$	−49.9121	+	186.274i	−0.124159	+	0.463369i
$403$	239.425	+	64.1537i	0.594107	+	0.159190i
$404$	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
$408$	−38.0666	−	142.067i	−0.0933006	−	0.348203i
$409$	−176.077	+	101.658i	−0.430507	+	0.248554i	−0.699563	−	0.714571i	$-0.746622\pi$
$409$	−176.077	+	101.658i	−0.430507	+	0.248554i	0.269055	+	0.963125i	$0.413289\pi$
$410$	122.050	+	155.488i	0.297683	+	0.379238i
$411$	178.681	−	309.485i	0.434747	−	0.753004i
$412$	68.5228	+	68.5228i	0.166317	+	0.166317i
$413$	237.972	+	383.883i	0.576202	+	0.929498i
$414$		−	86.8199i		−	0.209710i
$415$	59.8782	+	24.0343i	0.144285	+	0.0579141i
$416$	43.8178	+	75.8947i	0.105331	+	0.182439i
$417$	−112.652	+	420.425i	−0.270150	+	1.00821i
$418$	−39.4974	−	147.406i	−0.0944914	−	0.352647i
$419$		−	716.269i		−	1.70947i	−0.519062	−	0.854736i	$-0.673719\pi$
$419$		−	716.269i		−	1.70947i	0.519062	−	0.854736i	$-0.326281\pi$
$420$	131.991	−	110.460i	0.314265	−	0.263001i
$421$	−692.449			−1.64477			−0.822386	−	0.568929i	$-0.807358\pi$
$421$	−692.449			−1.64477			−0.822386	+	0.568929i	$0.807358\pi$
$422$	280.995	−	75.2925i	0.665866	−	0.178418i
$423$	−205.277	−	55.0038i	−0.485289	−	0.130033i
$424$	103.765	−	59.9089i	0.244729	−	0.141295i
$425$	274.366	+	451.960i	0.645567	+	1.06344i
$426$	−126.364			−0.296630
$427$	−364.524	−	195.496i	−0.853685	−	0.457836i
$428$	−232.840	+	232.840i	−0.544018	+	0.544018i
$429$	−246.658	−	142.408i	−0.574960	−	0.331953i
$430$	−393.629	−	47.4245i	−0.915415	−	0.110289i
$431$	−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	$-0.362488\pi$
$432$	−113.567	+	30.4301i	−0.262886	+	0.0704401i
$433$	−191.729	+	191.729i	−0.442792	+	0.442792i	−0.892949	−	0.450158i	$-0.851368\pi$
$433$	−191.729	+	191.729i	−0.442792	+	0.442792i	0.450158	+	0.892949i	$0.351368\pi$
$434$	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
$437$	77.6141	−	289.660i	0.177607	−	0.662837i
$438$	−222.167	−	59.5295i	−0.507231	−	0.135912i
$439$	460.252	+	265.727i	1.04841	+	0.605300i	0.922204	−	0.386704i	$-0.126386\pi$
$439$	460.252	+	265.727i	1.04841	+	0.605300i	0.126206	+	0.992004i	$0.459720\pi$
$440$	−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
$443$	40.8658	+	152.513i	0.0922479	+	0.344274i	0.996588	−	0.0825391i	$-0.0263029\pi$
$443$	40.8658	+	152.513i	0.0922479	+	0.344274i	−0.904340	+	0.426813i	$0.859636\pi$
$444$	282.794	−	163.271i	0.636924	−	0.367728i
$445$	29.1423	−	241.884i	0.0654883	−	0.543560i
$446$	62.8872	−	108.924i	0.141003	−	0.244224i
$447$	−439.711	−	439.711i	−0.983693	−	0.983693i
$448$	55.9725	−	1.75419i	0.124939	−	0.00391560i
$449$			297.590i			0.662784i	0.943493	+	0.331392i	$0.107518\pi$
$449$			297.590i			0.662784i	−0.943493	+	0.331392i	$0.892482\pi$
$450$	89.2907	−	54.2047i	0.198424	−	0.120455i
$451$	−104.511	−	181.018i	−0.231731	−	0.401371i
$452$	41.4601	−	154.731i	0.0917260	−	0.342326i
$453$	−131.036	−	489.031i	−0.289262	−	1.07954i
$454$			365.362i			0.804763i
$455$	−186.115	+	509.275i	−0.409043	+	1.11929i
$456$	−100.364			−0.220097
$457$	−704.739	+	188.834i	−1.54210	+	0.413204i	−0.926943	−	0.375202i	$-0.877573\pi$
$457$	−704.739	+	188.834i	−1.54210	+	0.413204i	−0.615155	+	0.788406i	$0.710907\pi$
$458$	−168.143	−	45.0537i	−0.367124	−	0.0983705i
$459$	−538.349	+	310.816i	−1.17287	+	0.677158i
$460$	77.4023	−	192.837i	0.168266	−	0.419211i
$461$	−16.3644			−0.0354976			−0.0177488	−	0.999842i	$-0.505650\pi$
$461$	−16.3644			−0.0354976			−0.0177488	+	0.999842i	$0.505650\pi$
$462$	−154.689	+	95.8927i	−0.334824	+	0.207560i
$463$	185.921	−	185.921i	0.401557	−	0.401557i	−0.477225	−	0.878781i	$-0.658357\pi$
$463$	185.921	−	185.921i	0.401557	−	0.401557i	0.878781	+	0.477225i	$0.158357\pi$
$464$	54.9523	+	31.7267i	0.118432	+	0.0683765i
$465$	−154.728	+	121.453i	−0.332747	+	0.261190i
$466$	−225.362	−	390.339i	−0.483610	−	0.837637i
$467$	314.851	−	84.3641i	0.674200	−	0.180651i	0.0945537	−	0.995520i	$-0.469858\pi$
$467$	314.851	−	84.3641i	0.674200	−	0.180651i	0.579646	+	0.814869i	$0.303191\pi$
$468$	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
$472$	47.2339	−	176.279i	0.100072	−	0.373474i
$473$	404.963	+	108.509i	0.856158	+	0.229407i
$474$	−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
$478$	−63.9537	−	238.678i	−0.133794	−	0.499327i
$479$	−452.460	+	261.228i	−0.944592	+	0.545361i	−0.891397	−	0.453223i	$-0.850274\pi$
$479$	−452.460	+	261.228i	−0.944592	+	0.545361i	−0.0531954	+	0.998584i	$0.516941\pi$
$480$	−69.0452	−	8.31858i	−0.143844	−	0.0173304i
$481$	−514.360	+	890.898i	−1.06936	+	1.85218i
$482$	243.818	+	243.818i	0.505846	+	0.505846i
$483$	−357.462	+	11.2029i	−0.740087	+	0.0231945i
$484$		−	130.182i		−	0.268971i
$485$	−167.975	+	418.485i	−0.346339	+	0.862855i
$486$	107.636	+	186.430i	0.221472	+	0.383602i
$487$	76.6478	−	286.054i	0.157388	−	0.587379i	−0.841501	−	0.540255i	$-0.818328\pi$
$487$	76.6478	−	286.054i	0.157388	−	0.587379i	0.998889	−	0.0471240i	$-0.0150056\pi$
$488$	43.2577	+	161.440i	0.0886428	+	0.330819i
$489$			614.677i			1.25701i
$490$	230.582	+	258.615i	0.470575	+	0.527787i
$491$	−232.000			−0.472505			−0.236253	−	0.971692i	$-0.575919\pi$
$491$	−232.000			−0.472505			−0.236253	+	0.971692i	$0.575919\pi$
$492$	−132.783	+	35.5791i	−0.269884	+	0.0723153i
$493$	324.059	+	86.8314i	0.657321	+	0.176129i
$494$	273.822	−	158.091i	0.554295	−	0.320022i
$495$	−101.577	+	43.3892i	−0.205205	+	0.0876549i
$496$	−64.0000			−0.129032
$497$	−7.96853	−	254.259i	−0.0160333	−	0.511588i
$498$	−31.7288	+	31.7288i	−0.0637124	+	0.0637124i
$499$	−181.375	−	104.717i	−0.363477	−	0.209853i	0.307128	−	0.951668i	$-0.400632\pi$
$499$	−181.375	−	104.717i	−0.363477	−	0.209853i	−0.670605	+	0.741815i	$0.733965\pi$
$500$	246.650	−	40.7898i	0.493300	−	0.0815795i
$501$	13.9296	+	24.1268i	0.0278036	+	0.0481572i
$502$	74.1387	−	19.8654i	0.147687	−	0.0395725i
$503$	−104.055	+	104.055i	−0.206870	+	0.206870i	−0.802935	−	0.596066i	$-0.796730\pi$
$503$	−104.055	+	104.055i	−0.206870	+	0.206870i	0.596066	+	0.802935i	$0.296730\pi$
$504$	−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
$507$	45.1827	−	168.624i	0.0891178	−	0.332592i
$508$	8.32059	+	2.22950i	0.0163791	+	0.00438877i
$509$	−65.4629	−	37.7950i	−0.128611	−	0.0742535i	0.434314	−	0.900761i	$-0.356991\pi$
$509$	−65.4629	−	37.7950i	−0.128611	−	0.0742535i	−0.562925	+	0.826508i	$0.690324\pi$
$510$	−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
$513$	109.789	+	409.740i	0.214014	+	0.798713i
$514$	−26.5330	+	15.3188i	−0.0516206	+	0.0298032i
$515$	190.568	−	149.586i	0.370035	−	0.290458i
$516$	137.863	−	238.786i	0.267177	−	0.462764i
$517$	380.317	+	380.317i	0.735622	+	0.735622i
$518$	346.353	+	558.717i	0.668635	+	1.07860i
$519$		−	305.362i		−	0.588367i
$520$	201.478	−	86.0626i	0.387457	−	0.165505i
$521$	−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	$0.940514\pi$
$522$	17.1547	−	64.0222i	0.0328634	−	0.122648i
$523$	−15.3556	−	57.3080i	−0.0293607	−	0.109576i	0.949690	−	0.313190i	$-0.101398\pi$
$523$	−15.3556	−	57.3080i	−0.0293607	−	0.109576i	−0.979051	+	0.203615i	$0.934731\pi$
$524$		−	227.818i		−	0.434767i
$525$	−234.698	−	360.641i	−0.447044	−	0.686935i
$526$	475.477			0.903949
$527$	−326.851	+	87.5793i	−0.620210	+	0.166185i
$528$	71.0333	+	19.0333i	0.134533	+	0.0360480i
$529$	84.2017	−	48.6139i	0.159171	−	0.0918977i
$530$	−117.667	−	275.466i	−0.222014	−	0.519747i
$531$	−190.629			−0.359001
$532$	−6.32897	−	201.944i	−0.0118966	−	0.379595i
$533$	306.226	−	306.226i	0.574532	−	0.574532i
$534$	146.734	+	84.7169i	0.274783	+	0.158646i
$535$	508.292	+	647.547i	0.950078	+	1.21037i
$536$	78.4317	+	135.848i	0.146328	+	0.253447i
$537$	312.633	−	83.7698i	0.582185	−	0.155996i
$538$	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	$-0.0641368\pi$
$542$	22.5181	−	84.0388i	0.0415464	−	0.155053i
$543$	−355.491	−	95.2536i	−0.654680	−	0.175421i
$544$	−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	0.968105	−	0.250543i	$-0.0806091\pi$
$547$	392.507	+	392.507i	0.717563	+	0.717563i	−0.250543	+	0.968105i	$0.580609\pi$
$548$	−75.2345	−	280.779i	−0.137289	−	0.512370i
$549$	151.192	−	87.2909i	0.275396	−	0.159000i
$550$	−264.296	+	5.81405i	−0.480538	+	0.0105710i
$551$	114.467	−	198.263i	0.207745	−	0.359825i
$552$	102.182	+	102.182i	0.185113	+	0.185113i
$553$	136.319	−	254.180i	0.246507	−	0.459639i
$554$			504.998i			0.911549i
$555$	−320.681	−	750.734i	−0.577804	−	1.35267i
$556$	177.022	+	306.611i	0.318384	+	0.551458i
$557$	51.8922	−	193.665i	0.0931638	−	0.347692i	−0.903571	−	0.428439i	$-0.859064\pi$
$557$	51.8922	−	193.665i	0.0931638	−	0.347692i	0.996735	+	0.0807466i	$0.0257305\pi$
$558$	17.3025	+	64.5737i	0.0310080	+	0.115723i
$559$			868.634i			1.55391i
$560$	12.3839	−	139.451i	0.0221142	−	0.249020i
$561$	388.816			0.693076
$562$	−544.419	+	145.877i	−0.968717	+	0.259567i
$563$	594.765	+	159.367i	1.05642	+	0.283067i	0.744903	−	0.667173i	$-0.232496\pi$
$563$	594.765	+	159.367i	1.05642	+	0.283067i	0.311518	+	0.950240i	$0.399163\pi$
$564$	306.336	−	176.863i	0.543149	−	0.313588i
$565$	−371.653	−	149.177i	−0.657793	−	0.264030i
$566$	696.087			1.22984
$567$	271.783	−	168.480i	0.479335	−	0.297143i
$568$	−72.6812	+	72.6812i	−0.127960	+	0.127960i
$569$	−72.8214	−	42.0435i	−0.127981	−	0.0738901i	0.434642	−	0.900603i	$-0.356875\pi$
$569$	−72.8214	−	42.0435i	−0.127981	−	0.0738901i	−0.562624	+	0.826713i	$0.690208\pi$
$570$	−30.0128	+	249.110i	−0.0526540	+	0.437034i
$571$	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	$0.738666\pi$
$572$	−223.779	+	59.9615i	−0.391223	+	0.104828i
$573$	−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
$577$	119.141	−	444.640i	0.206483	−	0.770606i	−0.782509	−	0.622639i	$-0.786060\pi$
$577$	119.141	−	444.640i	0.206483	−	0.770606i	0.988992	−	0.147967i	$-0.0472729\pi$
$578$	−216.203	−	57.9313i	−0.374053	−	0.100227i
$579$	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
$583$	81.9810	+	305.957i	0.140619	+	0.524798i
$584$	−162.024	+	93.5445i	−0.277438	+	0.160179i
$585$	−141.304	−	180.016i	−0.241545	−	0.307721i
$586$	−187.818	+	325.310i	−0.320508	+	0.555136i
$587$	484.313	+	484.313i	0.825064	+	0.825064i	0.986829	−	0.161765i	$-0.0517187\pi$
$587$	484.313	+	484.313i	0.825064	+	0.825064i	−0.161765	+	0.986829i	$0.551719\pi$
$588$	−228.387	+	76.8170i	−0.388413	+	0.130641i
$589$			230.907i			0.392032i
$590$	−423.410	−	169.951i	−0.717644	−	0.288053i
$591$	147.624	+	255.692i	0.249786	+	0.432643i
$592$	68.7461	−	256.564i	0.116125	−	0.433385i
$593$	−55.2031	−	206.021i	−0.0930913	−	0.347422i	0.903632	−	0.428310i	$-0.140891\pi$
$593$	−55.2031	−	206.021i	−0.0930913	−	0.347422i	−0.996723	+	0.0808885i	$0.974224\pi$
$594$		−	310.816i		−	0.523259i
$595$	−127.584	−	729.129i	−0.214426	−	1.22543i
$596$	−505.818			−0.848688
$597$	195.831	−	52.4727i	0.328025	−	0.0878940i
$598$	−439.736	−	117.827i	−0.735344	−	0.197035i
$599$	−71.5663	+	41.3188i	−0.119476	+	0.0689797i	−0.558547	−	0.829473i	$-0.688641\pi$
$599$	−71.5663	+	41.3188i	−0.119476	+	0.0689797i	0.439071	+	0.898452i	$0.355308\pi$
$600$	−41.2943	+	168.886i	−0.0688238	+	0.281477i
$601$	785.362			1.30676			0.653380	−	0.757030i	$-0.273351\pi$
$601$	785.362			1.30676			0.653380	+	0.757030i	$0.273351\pi$
$602$	489.158	+	262.339i	0.812555	+	0.435778i
$603$	115.861	−	115.861i	0.192141	−	0.192141i
$604$	−356.645	−	205.909i	−0.590471	−	0.340909i
$605$	−323.119	−	38.9294i	−0.534081	−	0.0643462i
$606$	169.513	+	293.605i	0.279724	+	0.484497i
$607$	675.882	−	181.102i	1.11348	−	0.298356i	0.345237	−	0.938515i	$-0.387798\pi$
$607$	675.882	−	181.102i	1.11348	−	0.298356i	0.768242	+	0.640159i	$0.221132\pi$
$608$	−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
$612$	−32.3436	+	120.708i	−0.0528490	+	0.197235i
$613$	−184.470	−	49.4286i	−0.300930	−	0.0806339i	0.105195	−	0.994452i	$-0.466453\pi$
$613$	−184.470	−	49.4286i	−0.300930	−	0.0806339i	−0.406125	+	0.913818i	$0.633120\pi$
$614$	−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	0.275563	−	0.961283i	$-0.411136\pi$
$617$	−423.089	−	423.089i	−0.685720	−	0.685720i	−0.961283	+	0.275563i	$0.911136\pi$
$618$	43.6063	+	162.741i	0.0705603	+	0.263335i
$619$	−93.5101	+	53.9881i	−0.151066	+	0.0872182i	−0.573628	−	0.819116i	$-0.694464\pi$
$619$	−93.5101	+	53.9881i	−0.151066	+	0.0872182i	0.422561	+	0.906334i	$0.361131\pi$
$620$	−19.1384	+	158.851i	−0.0308684	+	0.256212i
$621$	305.383	−	528.939i	0.491760	−	0.851753i
$622$	3.47723	+	3.47723i	0.00559039	+	0.00559039i
$623$	−161.207	+	300.587i	−0.258759	+	0.482484i
$624$			152.364i			0.244174i
$625$	−27.4845	−	624.395i	−0.0439753	−	0.999033i
$626$	15.0890	+	26.1350i	0.0241039	+	0.0417491i
$627$	68.6707	−	256.282i	0.109523	−	0.408744i
$628$	137.192	+	512.008i	0.218459	+	0.815299i
$629$		−	1404.36i		−	2.23268i
$630$	−144.049	+	25.2058i	−0.228650	+	0.0400093i
$631$	−711.200			−1.12710			−0.563550	−	0.826082i	$-0.690565\pi$
$631$	−711.200			−1.12710			−0.563550	+	0.826082i	$0.690565\pi$
$632$	−112.571	+	30.1634i	−0.178119	+	0.0477269i
$633$	488.542	+	130.904i	0.771789	+	0.206800i
$634$	498.831	−	288.000i	0.786799	−	0.454259i
$635$	8.02190	−	19.9854i	0.0126329	−	0.0314731i
$636$	208.317			0.327542
$637$	502.103	−	569.327i	0.788231	−	0.893762i
$638$	−118.614	+	118.614i	−0.185915	+	0.185915i
$639$	92.9821	+	53.6832i	0.145512	+	0.0840113i
$640$	−44.4974	+	34.9282i	−0.0695272	+	0.0545753i
$641$	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	$0.724637\pi$
$642$	−552.991	+	148.174i	−0.861357	+	0.230800i
$643$	−289.770	+	289.770i	−0.450653	+	0.450653i	−0.895571	−	0.444918i	$-0.853233\pi$
$643$	−289.770	+	289.770i	−0.450653	+	0.450653i	0.444918	+	0.895571i	$0.353233\pi$
$644$	−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
$647$	−116.716	+	435.592i	−0.180396	+	0.673248i	0.815173	+	0.579218i	$0.196642\pi$
$647$	−116.716	+	435.592i	−0.180396	+	0.673248i	−0.995569	+	0.0940307i	$0.970025\pi$
$648$	−124.803	−	33.4409i	−0.192598	−	0.0516064i
$649$	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
$653$	−91.1077	−	340.019i	−0.139522	−	0.520702i	−0.999938	−	0.0111110i	$-0.996463\pi$
$653$	−91.1077	−	340.019i	−0.139522	−	0.520702i	0.860416	−	0.509592i	$-0.170203\pi$
$654$	−508.098	+	293.350i	−0.776908	+	0.448548i
$655$	−565.455	−	68.1262i	−0.863291	−	0.104009i
$656$	−55.9089	+	96.8371i	−0.0852270	+	0.147617i
$657$	138.186	+	138.186i	0.210329	+	0.210329i
$658$	375.186	+	605.230i	0.570192	+	0.919802i
$659$			900.158i			1.36595i	0.730444	+	0.682973i	$0.239313\pi$
$659$			900.158i			1.36595i	−0.730444	+	0.682973i	$0.760687\pi$
$660$	68.4833	−	170.617i	0.103763	−	0.258510i
$661$	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	$0.748498\pi$
$662$	153.963	−	574.596i	0.232572	−	0.867970i
$663$	208.500	+	778.131i	0.314479	+	1.17365i
$664$			36.4990i			0.0549683i
$665$	−503.129	−	44.6802i	−0.756584	−	0.0671883i
$666$	−277.449			−0.416590
$667$	−318.395	+	85.3137i	−0.477354	+	0.127907i
$668$	21.8889	+	5.86512i	0.0327679	+	0.00878012i
$669$	189.376	−	109.336i	0.283074	−	0.163433i
$670$	360.635	−	154.048i	0.538261	−	0.229922i
$671$	−441.837			−0.658476
$672$	85.8018	+	46.0160i	0.127681	+	0.0684762i
$673$	−13.2277	+	13.2277i	−0.0196549	+	0.0196549i	−0.716866	−	0.697211i	$-0.754424\pi$
$673$	−13.2277	+	13.2277i	−0.0196549	+	0.0196549i	0.697211	+	0.716866i	$0.254424\pi$
$674$	−59.3595	−	34.2712i	−0.0880705	−	0.0508475i
$675$	734.653	−	16.1611i	1.08838	−	0.0239424i
$676$	−71.0000	−	122.976i	−0.105030	−	0.181917i
$677$	573.233	−	153.597i	0.846725	−	0.226879i	0.190728	−	0.981643i	$-0.438915\pi$
$677$	573.233	−	153.597i	0.846725	−	0.226879i	0.655997	+	0.754764i	$0.272248\pi$
$678$	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
$682$	43.7897	−	163.425i	0.0642077	−	0.239627i
$683$	−273.719	−	73.3428i	−0.400760	−	0.107383i	0.0528086	−	0.998605i	$-0.483183\pi$
$683$	−273.719	−	73.3428i	−0.400760	−	0.107383i	−0.453569	+	0.891221i	$0.649849\pi$
$684$	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
$688$	−58.0480	−	216.638i	−0.0843721	−	0.314881i
$689$	−568.346	+	328.135i	−0.824885	+	0.476248i
$690$	284.178	−	223.065i	0.411852	−	0.323283i
$691$	−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
$693$	154.562	−	4.84399i	0.223033	−	0.00698989i
$694$		−	204.657i		−	0.294895i
$695$	813.959	−	347.689i	1.17116	−	0.500271i
$696$	55.1605	+	95.5407i	0.0792535	+	0.137271i
$697$	−153.015	+	571.058i	−0.219533	+	0.819308i
$698$	−91.0896	−	339.951i	−0.130501	−	0.487036i
$699$		−	783.636i		−	1.12108i
$700$	−342.422	−	72.4388i	−0.489174	−	0.103484i
$701$	189.638			0.270525			0.135262	−	0.990810i	$-0.456812\pi$
$701$	189.638			0.270525			0.135262	+	0.990810i	$0.456812\pi$
$702$	622.031	−	166.673i	0.886084	−	0.237425i
$703$	−925.662	−	248.030i	−1.31673	−	0.352817i
$704$	51.8037	−	29.9089i	0.0735849	−	0.0424842i
$705$	−347.378	−	813.231i	−0.492734	−	1.15352i
$706$	−564.725			−0.799893
$707$	−580.077	+	359.594i	−0.820476	+	0.508619i
$708$	224.360	−	224.360i	0.316893	−	0.316893i
$709$	571.534	+	329.975i	0.806112	+	0.465409i	0.845604	−	0.533811i	$-0.179240\pi$
$709$	571.534	+	329.975i	0.806112	+	0.465409i	−0.0394916	+	0.999220i	$0.512574\pi$
$710$	158.664	+	202.133i	0.223470	+	0.284694i
$711$	60.8675	+	105.426i	0.0856083	+	0.148278i
$712$	133.124	−	35.6704i	0.186972	−	0.0500989i
$713$	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
$717$	111.191	−	414.969i	0.155078	−	0.578757i
$718$	584.778	+	156.691i	0.814454	+	0.218232i
$719$	−851.435	−	491.576i	−1.18419	−	0.683694i	−0.227212	−	0.973845i	$-0.572961\pi$
$719$	−851.435	−	491.576i	−1.18419	−	0.683694i	−0.956981	+	0.290151i	$0.906294\pi$
$720$	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
$723$	155.160	+	579.065i	0.214606	+	0.800919i
$724$	−259.255	+	149.681i	−0.358088	+	0.206742i
$725$	−286.527	−	274.192i	−0.395209	−	0.378196i
$726$	113.168	−	196.013i	0.155879	−	0.269990i
$727$	291.624	+	291.624i	0.401133	+	0.401133i	0.878632	−	0.477499i	$-0.158457\pi$
$727$	291.624	+	291.624i	0.401133	+	0.401133i	−0.477499	+	0.878632i	$0.658457\pi$
$728$	−306.574	+	9.60809i	−0.421118	+	0.0131979i
$729$			785.404i			1.07737i
$730$	183.731	+	430.125i	0.251686	+	0.589212i
$731$	−592.907	−	1026.94i	−0.811090	−	1.40485i
$732$	−75.2084	+	280.681i	−0.102744	+	0.383445i
$733$	176.906	+	660.223i	0.241345	+	0.900713i	0.975185	+	0.221391i	$0.0710596\pi$
$733$	176.906	+	660.223i	0.241345	+	0.900713i	−0.733840	+	0.679323i	$0.762274\pi$
$734$			333.022i			0.453708i
$735$	122.367	+	589.839i	0.166486	+	0.802502i
$736$	117.545			0.159707
$737$	−400.554	+	107.328i	−0.543492	+	0.145628i
$738$	112.820	+	30.2301i	0.152873	+	0.0409621i
$739$	−110.947	+	64.0554i	−0.150131	+	0.0866785i	−0.573184	−	0.819427i	$-0.694292\pi$
$739$	−110.947	+	64.0554i	−0.150131	+	0.0866785i	0.423052	+	0.906105i	$0.360959\pi$
$740$	−616.247	−	247.354i	−0.832766	−	0.334262i
$741$	549.718			0.741860
$742$	13.1364	+	419.157i	0.0177041	+	0.564901i
$743$	443.624	−	443.624i	0.597071	−	0.597071i	−0.342461	−	0.939532i	$-0.611260\pi$
$743$	443.624	−	443.624i	0.597071	−	0.597071i	0.939532	+	0.342461i	$0.111260\pi$
$744$	−96.3637	−	55.6356i	−0.129521	−	0.0747790i
$745$	−151.259	+	1255.47i	−0.203032	+	1.68519i
$746$	107.271	+	185.799i	0.143795	+	0.249061i
$747$	36.8261	−	9.86753i	0.0492987	−	0.0132095i
$748$	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	$0.106134\pi$
$752$	74.4691	−	277.923i	0.0990281	−	0.369578i
$753$	128.898	+	34.5382i	0.171180	+	0.0458675i
$754$	−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	0.300444	−	0.953799i	$-0.402865\pi$
$757$	−494.590	−	494.590i	−0.653355	−	0.653355i	−0.953799	+	0.300444i	$0.902865\pi$
$758$	−24.3157	−	90.7474i	−0.0320787	−	0.119719i
$759$	−330.839	+	191.010i	−0.435888	+	0.251660i
$760$	126.018	+	160.543i	0.165813	+	0.211241i
$761$	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
$763$	−622.294	−	1003.85i	−0.815589	−	1.31566i
$764$			452.135i			0.591799i
$765$	289.931	+	116.375i	0.378995	+	0.152124i
$766$	−481.307	−	833.648i	−0.628338	−	1.08831i
$767$	−258.711	+	965.523i	−0.337302	+	1.25883i
$768$	−10.1820	−	37.9998i	−0.0132578	−	0.0494789i
$769$		−	702.447i		−	0.913455i	−0.889607	−	0.456728i	$-0.849021\pi$
$769$		−	702.447i		−	0.913455i	0.889607	−	0.456728i	$-0.150979\pi$
$770$	347.618	+	127.037i	0.451452	+	0.164983i
$771$	−53.2671			−0.0690883
$772$	427.190	−	114.465i	0.553355	−	0.148271i
$773$	809.487	+	216.901i	1.04720	+	0.280597i	0.741095	−	0.671400i	$-0.234307\pi$
$773$	809.487	+	216.901i	1.04720	+	0.280597i	0.306107	+	0.951997i	$0.400973\pi$
$774$	−202.887	+	117.137i	−0.262127	+	0.151339i
$775$	388.554	+	95.0052i	0.501360	+	0.122587i
$776$	−255.089			−0.328723
$777$	35.8011	+	1142.34i	0.0460760	+	1.47019i
$778$	92.9110	−	92.9110i	0.119423	−	0.119423i
$779$	349.380	+	201.715i	0.448498	+	0.258941i
$780$	378.176	+	45.5628i	0.484841	+	0.0584138i
$781$	−135.863	−	235.322i	−0.173961	−	0.301309i
$782$	600.305	−	160.851i	0.767653	−	0.205692i
$783$	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
$787$	186.384	−	695.596i	0.236829	−	0.883858i	−0.740487	−	0.672071i	$-0.765405\pi$
$787$	186.384	−	695.596i	0.236829	−	0.883858i	0.977316	−	0.211787i	$-0.0679283\pi$
$788$	231.975	+	62.1576i	0.294385	+	0.0788802i
$789$	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
$793$	−236.932	−	884.243i	−0.298779	−	1.11506i
$794$	−443.168	+	255.863i	−0.558147	+	0.322246i
$795$	62.2947	−	517.053i	0.0783581	−	0.650381i
$796$	82.4555	−	142.817i	0.103587	−	0.179418i
$797$	−82.4079	−	82.4079i	−0.103398	−	0.103398i	0.653516	−	0.756913i	$-0.273293\pi$
$797$	−82.4079	−	82.4079i	−0.103398	−	0.103398i	−0.756913	+	0.653516i	$0.773293\pi$
$798$	166.022	−	309.566i	0.208048	−	0.387927i
$799$		−	1521.27i		−	1.90396i
$800$	73.3872	+	120.890i	0.0917339	+	0.151112i
$801$	−71.9803	−	124.674i	−0.0898631	−	0.155647i
$802$	230.794	−	861.334i	0.287773	−	1.07398i
$803$	−128.009	−	477.736i	−0.159413	−	0.594938i
$804$			272.725i			0.339210i
$805$	466.752	+	557.731i	0.579816	+	0.692833i
$806$	350.542			0.434916
$807$	256.927	−	68.8433i	0.318373	−	0.0853077i
$808$	266.372	+	71.3742i	0.329668	+	0.0883344i
$809$	−289.803	+	167.318i	−0.358224	+	0.206821i	−0.668301	−	0.743891i	$-0.732978\pi$
$809$	−289.803	+	167.318i	−0.358224	+	0.206821i	0.310078	+	0.950711i	$0.399645\pi$
$810$	−120.323	+	299.768i	−0.148547	+	0.370084i
$811$	522.455			0.644211			0.322106	−	0.946704i	$-0.395609\pi$
$811$	522.455			0.644211			0.322106	+	0.946704i	$0.395609\pi$
$812$	−188.760	+	117.014i	−0.232463	+	0.144106i
$813$	106.961	−	106.961i	0.131563	−	0.131563i
$814$	608.104	+	351.089i	0.747057	+	0.431313i
$815$	983.239	−	771.792i	1.20643	−	0.946984i
$816$	−104.000	−	180.133i	−0.127451	−	0.220752i
$817$	−781.613	+	209.432i	−0.956686	+	0.256343i
$818$	−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	$0.0895550\pi$
$822$	130.804	−	488.166i	0.159129	−	0.593876i
$823$	251.024	+	67.2617i	0.305011	+	0.0817275i	0.408078	−	0.912947i	$-0.366199\pi$
$823$	251.024	+	67.2617i	0.305011	+	0.0817275i	−0.103067	+	0.994674i	$0.532866\pi$
$824$	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	0.788556	−	0.614964i	$-0.210829\pi$
$827$	143.561	+	143.561i	0.173592	+	0.173592i	−0.614964	+	0.788556i	$0.710829\pi$
$828$	−31.7783	−	118.598i	−0.0383796	−	0.143234i
$829$	566.219	−	326.907i	0.683015	−	0.394339i	−0.117975	−	0.993017i	$-0.537640\pi$
$829$	566.219	−	326.907i	0.683015	−	0.394339i	0.800990	+	0.598678i	$0.204307\pi$
$830$	90.5923	+	10.9146i	0.109147	+	0.0131501i
$831$	−438.998	+	760.367i	−0.528277	+	0.915002i
$832$	87.6356	+	87.6356i	0.105331	+	0.105331i
$833$	−205.005	+	1015.81i	−0.246105	+	1.21946i
$834$			615.545i			0.738063i
$835$	21.1032	−	52.5756i	0.0252732	−	0.0629647i
$836$	−107.909	−	186.904i	−0.129078	−	0.223569i
$837$	−121.720	+	454.267i	−0.145425	+	0.542732i
$838$	−262.173	−	978.442i	−0.312855	−	1.16759i
$839$		−	128.301i		−	0.152922i	−0.997073	−	0.0764608i	$-0.975638\pi$
$839$		−	128.301i		−	0.152922i	0.997073	−	0.0764608i	$-0.0243620\pi$
$840$	139.872	−	199.204i	0.166514	−	0.237147i
$841$	589.354			0.700778
$842$	−945.903	+	253.454i	−1.12340	+	0.301014i
$843$	−946.534	−	253.623i	−1.12282	−	0.300858i
$844$	356.288	−	205.703i	0.422142	−	0.243724i
$845$	−326.463	+	139.451i	−0.386347	+	0.165031i
$846$	−300.547			−0.355256
$847$	401.537	+	215.346i	0.474069	+	0.254246i
$848$	119.818	−	119.818i	0.141295	−	0.141295i
$849$	1048.09	+	605.113i	1.23449	+	0.712736i
$850$	540.220	+	516.964i	0.635553	+	0.608193i
$851$	689.905	+	1194.95i	0.810699	+	1.40417i
$852$	−172.617	+	46.2526i	−0.202602	+	0.0542871i
$853$	−941.404	+	941.404i	−1.10364	+	1.10364i	−0.109671	+	0.993968i	$0.534980\pi$
$853$	−941.404	+	941.404i	−1.10364	+	1.10364i	−0.993968	+	0.109671i	$0.965020\pi$
$854$	−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
$857$	−89.5747	+	334.297i	−0.104521	+	0.390078i	−0.998290	−	0.0584487i	$-0.981385\pi$
$857$	−89.5747	+	334.297i	−0.104521	+	0.390078i	0.893769	+	0.448527i	$0.148051\pi$
$858$	−389.066	−	104.250i	−0.453456	−	0.121503i
$859$	−39.8336	−	22.9979i	−0.0463720	−	0.0267729i	0.476635	−	0.879101i	$-0.341856\pi$
$859$	−39.8336	−	22.9979i	−0.0463720	−	0.0267729i	−0.523007	+	0.852329i	$0.675190\pi$
$860$	−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
$863$	−363.032	−	1354.85i	−0.420663	−	1.56993i	−0.773216	−	0.634143i	$-0.781353\pi$
$863$	−363.032	−	1354.85i	−0.420663	−	1.56993i	0.352554	−	0.935792i	$-0.385313\pi$
$864$	−143.997	+	83.1366i	−0.166663	+	0.0962230i
$865$	−488.458	+	383.415i	−0.564692	+	0.443254i
$866$	−191.729	+	332.084i	−0.221396	+	0.383469i
$867$	−275.172	−	275.172i	−0.317385	−	0.317385i
$868$	105.868	−	197.403i	0.121968	−	0.227423i
$869$		−	308.091i		−	0.354535i
$870$	253.632	−	108.341i	0.291531	−	0.124530i
$871$	−429.588	−	744.068i	−0.493212	−	0.854269i
$872$	−123.517	+	460.970i	−0.141647	+	0.528635i
$873$	68.9636	+	257.376i	0.0789961	+	0.294817i
$874$		−	424.091i		−	0.485230i
$875$	−282.194	+	828.246i	−0.322507	+	0.946567i
$876$	−325.275			−0.371319
$877$	−1077.73	+	288.777i	−1.22888	+	0.329278i	−0.814144	−	0.580663i	$-0.802793\pi$
$877$	−1077.73	+	288.777i	−1.22888	+	0.329278i	−0.414738	+	0.909941i	$0.636127\pi$
$878$	725.979	+	194.525i	0.826855	+	0.221555i
$879$	−565.588	+	326.542i	−0.643445	+	0.371493i
$880$	−58.7441	−	137.523i	−0.0667547	−	0.156277i
$881$	−1392.40			−1.58048			−0.790239	−	0.612798i	$-0.790044\pi$
$881$	−1392.40			−1.58048			−0.790239	+	0.612798i	$0.790044\pi$
$882$	200.687	+	40.5015i	0.227536	+	0.0459201i
$883$	−652.590	+	652.590i	−0.739060	+	0.739060i	−0.972396	−	0.233336i	$-0.925036\pi$
$883$	−652.590	+	652.590i	−0.739060	+	0.739060i	0.233336	+	0.972396i	$0.425036\pi$
$884$	567.482	+	327.636i	0.641947	+	0.370629i
$885$	−489.781	−	623.966i	−0.553425	−	0.705046i
$886$	111.648	+	193.379i	0.126013	+	0.218261i
$887$	−487.127	+	130.525i	−0.549185	+	0.147154i	−0.522733	−	0.852496i	$-0.675088\pi$
$887$	−487.127	+	130.525i	−0.549185	+	0.147154i	−0.0264521	+	0.999650i	$0.508421\pi$
$888$	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
$892$	46.0366	−	171.811i	0.0516105	−	0.192613i
$893$	−1002.72	−	268.679i	−1.12287	−	0.300872i
$894$	−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
$898$	108.926	+	406.516i	0.121298	+	0.452690i
$899$	219.809	−	126.907i	0.244504	−	0.141164i
$900$	102.133	−	106.728i	0.113481	−	0.118586i
$901$	447.952	−	775.876i	0.497172	−	0.861128i
$902$	−209.022	−	209.022i	−0.231731	−	0.231731i
$903$	508.465	+	820.227i	0.563084	+	0.908336i
$904$		−	226.542i		−	0.250600i
$905$	293.989	+	688.245i	0.324850	+	0.760492i
$906$	−357.996	−	620.067i	−0.395139	−	0.684401i
$907$	0.494284	−	1.84469i	0.000544966	−	0.00203384i	−0.965653	−	0.259836i	$-0.916332\pi$
$907$	0.494284	−	1.84469i	0.000544966	−	0.00203384i	0.966198	+	0.257802i	$0.0829982\pi$
$908$	133.732	+	499.094i	0.147282	+	0.549663i
$909$		−	288.056i		−	0.316893i
$910$	−67.8296	+	763.806i	−0.0745380	+	0.839347i
$911$	456.063			0.500618			0.250309	−	0.968166i	$-0.419468\pi$
$911$	456.063			0.500618			0.250309	+	0.968166i	$0.419468\pi$
$912$	−137.100	+	36.7359i	−0.150329	+	0.0402806i
$913$	−93.2008	−	24.9731i	−0.102082	−	0.0273528i
$914$	−893.573	+	515.905i	−0.977651	+	0.564447i
$915$	674.175	+	270.605i	0.736804	+	0.295744i
$916$	−246.178			−0.268753
$917$	702.686	+	376.855i	0.766288	+	0.410965i
$918$	−621.631	+	621.631i	−0.677158	+	0.677158i
$919$	459.799	+	265.465i	0.500326	+	0.288863i	0.728848	−	0.684675i	$-0.240056\pi$
$919$	459.799	+	265.465i	0.500326	+	0.288863i	−0.228522	+	0.973539i	$0.573389\pi$
$920$	35.1503	−	291.751i	0.0382068	−	0.317121i
$921$	−297.995	−	516.142i	−0.323556	−	0.560415i
$922$	−22.3542	+	5.98978i	−0.0242453	+	0.00649651i
$923$	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
$927$	37.0504	−	138.274i	0.0399681	−	0.149163i
$928$	86.6790	+	23.2256i	0.0934041	+	0.0250275i
$929$	971.957	+	561.159i	1.04624	+	0.604047i	0.921594	−	0.388155i	$-0.126887\pi$
$929$	971.957	+	561.159i	1.04624	+	0.604047i	0.124645	+	0.992201i	$0.460221\pi$
$930$	−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
$933$	2.21282	+	8.25837i	0.00237173	+	0.00885142i
$934$	399.215	−	230.487i	0.427425	−	0.246774i
$935$	−488.199	−	621.951i	−0.522138	−	0.665188i
$936$	64.7288	−	112.114i	0.0691547	−	0.119779i
$937$	−194.820	−	194.820i	−0.207919	−	0.207919i	0.595464	−	0.803382i	$-0.296968\pi$
$937$	−194.820	−	194.820i	−0.207919	−	0.207919i	−0.803382	+	0.595464i	$0.796968\pi$
$938$	−548.752	+	17.1980i	−0.585024	+	0.0183347i
$939$			52.4679i			0.0558764i
$940$	−667.549	−	267.946i	−0.710158	−	0.285048i
$941$	−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	$0.975094\pi$
$942$	−238.524	+	890.183i	−0.253210	+	0.944993i
$943$	−150.340	−	561.077i	−0.159427	−	0.594991i
$944$		−	258.091i		−	0.273402i
$945$	−966.261	−	353.120i	−1.02250	−	0.373672i
$946$	592.907			0.626751
$947$	620.971	−	166.389i	0.655724	−	0.175701i	0.0844087	−	0.996431i	$-0.473100\pi$
$947$	620.971	−	166.389i	0.655724	−	0.175701i	0.571316	+	0.820730i	$0.306433\pi$
$948$	−195.718	−	52.4424i	−0.206453	−	0.0553190i
$949$	887.441	−	512.364i	0.935133	−	0.539899i
$950$	436.160	−	264.775i	0.459116	−	0.278710i
$951$	1001.44			1.05304
$952$	355.890	−	220.619i	0.373834	−	0.231742i
$953$	372.594	−	372.594i	0.390970	−	0.390970i	−0.484063	−	0.875033i	$-0.660840\pi$
$953$	372.594	−	372.594i	0.390970	−	0.390970i	0.875033	+	0.484063i	$0.160840\pi$
$954$	−153.285	−	88.4990i	−0.160676	−	0.0927662i
$955$	1122.22	+	135.205i	1.17510	+	0.141576i
$956$	−174.725	−	302.632i	−0.182766	−	0.316561i
$957$	−281.707	+	75.4831i	−0.294364	+	0.0788747i
$958$	−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
$962$	−376.538	+	1405.26i	−0.391411	+	1.46077i
$963$	469.853	+	125.897i	0.487906	+	0.130734i
$964$	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	−0.999721	−	0.0236256i	$-0.992479\pi$
$967$	−989.576	−	989.576i	−1.02335	−	1.02335i	−0.0236256	−	0.999721i	$-0.507521\pi$
$968$	−47.6500	−	177.832i	−0.0492252	−	0.183711i
$969$	−649.906	+	375.224i	−0.670698	+	0.387228i
$970$	−76.2813	+	633.144i	−0.0786406	+	0.652726i
$971$	−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
$973$	−1238.54	+	38.8162i	−1.27291	+	0.0398933i
$974$		−	418.812i		−	0.429991i
$975$	226.178	−	925.027i	0.231978	−	0.948746i
$976$	118.182	+	204.698i	0.121088	+	0.209731i
$977$	−111.971	+	417.882i	−0.114607	+	0.427720i	−0.999257	−	0.0385359i	$-0.987731\pi$
$977$	−111.971	+	417.882i	−0.114607	+	0.427720i	0.884650	+	0.466256i	$0.154397\pi$
$978$	224.987	+	839.664i	0.230048	+	0.858553i
$979$			364.341i			0.372156i
$980$	409.641	+	268.876i	0.418001	+	0.274364i
$981$	498.495			0.508150
$982$	−316.918	+	84.9179i	−0.322727	+	0.0864744i
$983$	857.718	+	229.825i	0.872551	+	0.233799i	0.667191	−	0.744887i	$-0.267497\pi$
$983$	857.718	+	229.825i	0.872551	+	0.233799i	0.205360	+	0.978686i	$0.434163\pi$
$984$	−168.362	+	97.2039i	−0.171100	+	0.0987845i
$985$	223.648	−	557.187i	0.227054	−	0.565672i
$986$	474.455			0.481192
$987$	38.7815	+	1237.44i	0.0392923	+	1.25373i
$988$	316.182	−	316.182i	0.320022	−	0.320022i
$989$	1008.99	+	582.543i	1.02022	+	0.589023i
$990$	−122.875	+	96.4503i	−0.124116	+	0.0974245i
$991$	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	$0.691620\pi$
$992$	−87.4256	+	23.4256i	−0.0881307	+	0.0236145i
$993$	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
$997$	−265.816	+	992.040i	−0.266616	+	0.995025i	0.694638	+	0.719360i	$0.255565\pi$
$997$	−265.816	+	992.040i	−0.266616	+	0.995025i	−0.961254	+	0.275665i	$0.911102\pi$
$998$	−286.092	−	76.6581i	−0.286665	−	0.0768117i
$999$	−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.37.2	yes	8
5.2	odd	4		350.3.p.c.93.2		8
5.3	odd	4	inner	70.3.l.a.23.1	✓	8
5.4	even	2		350.3.p.c.107.1		8
7.2	even	3		490.3.f.l.197.1		4
7.4	even	3	inner	70.3.l.a.67.1	yes	8
7.5	odd	6		490.3.f.e.197.2		4
35.4	even	6		350.3.p.c.207.2		8
35.18	odd	12	inner	70.3.l.a.53.2	yes	8
35.23	odd	12		490.3.f.l.393.1		4
35.32	odd	12		350.3.p.c.193.1		8
35.33	even	12		490.3.f.e.393.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.3.l.a.23.1	✓	8	5.3	odd	4	inner
70.3.l.a.37.2	yes	8	1.1	even	1	trivial
70.3.l.a.53.2	yes	8	35.18	odd	12	inner
70.3.l.a.67.1	yes	8	7.4	even	3	inner
350.3.p.c.93.2		8	5.2	odd	4
350.3.p.c.107.1		8	5.4	even	2
350.3.p.c.193.1		8	35.32	odd	12
350.3.p.c.207.2		8	35.4	even	6
490.3.f.e.197.2		4	7.5	odd	6
490.3.f.e.393.2		4	35.33	even	12
490.3.f.l.197.1		4	7.2	even	3
490.3.f.l.393.1		4	35.23	odd	12

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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(1.36603 - 0.366025i) q^{2} +(2.37499 + 0.636376i) q^{3} +(1.73205 - 1.00000i) q^{4} +(-1.96410 - 4.59808i) q^{5} +3.47723 q^{6} +(0.219274 + 6.99656i) q^{7} +(2.00000 - 2.00000i) q^{8} +(-2.55863 - 1.47723i) q^{9} +O(q^{10})\)	\(q+(1.36603 - 0.366025i) q^{2} +(2.37499 + 0.636376i) q^{3} +(1.73205 - 1.00000i) q^{4} +(-1.96410 - 4.59808i) q^{5} +3.47723 q^{6} +(0.219274 + 6.99656i) q^{7} +(2.00000 - 2.00000i) q^{8} +(-2.55863 - 1.47723i) q^{9} +(-4.36603 - 5.56218i) q^{10} +(3.73861 + 6.47547i) q^{11} +(4.74998 - 1.27275i) 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} +(5.47371 - 20.4282i) q^{17} +(-4.03586 - 1.08140i) 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} +(5.37803 + 20.0711i) q^{23} +(6.02273 - 3.47723i) q^{24} +(-17.2846 + 18.0622i) q^{25} +(-10.9545 + 18.9737i) q^{26} +(-20.7842 - 20.7842i) q^{27} +(7.37636 + 11.8991i) q^{28} +15.8634i q^{29} +(-6.82962 - 15.9885i) q^{30} +(-8.00000 - 13.8564i) q^{31} +(1.46410 - 5.46410i) q^{32} +(4.75833 + 17.7583i) q^{33} -29.9089i q^{34} +(31.7401 - 14.7502i) q^{35} -5.90890 q^{36} +(64.1410 - 17.1865i) q^{37} +(-19.7140 - 5.28236i) q^{38} +(-32.9879 + 19.0455i) q^{39} +(-13.1244 - 5.26795i) q^{40} -27.9545 q^{41} +(0.762464 + 24.3286i) q^{42} +(39.6475 - 39.6475i) q^{43} +(12.9509 + 7.47723i) q^{44} +(-1.76699 + 14.6662i) q^{45} +(14.6931 + 25.4491i) q^{46} +(69.4806 - 18.6173i) 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} +(-8.01921 + 29.9281i) q^{52} +(40.9185 + 10.9641i) 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} +(5.80639 + 21.6697i) q^{58} +(55.8784 - 32.2614i) q^{59} +(-15.1817 - 19.3409i) q^{60} +(-29.5455 + 51.1744i) q^{61} +(-16.0000 - 16.0000i) q^{62} +(9.77446 - 18.2255i) q^{63} -8.00000i q^{64} +(71.8851 + 28.8537i) q^{65} +(13.0000 + 22.5167i) q^{66} +(-14.3540 + 53.5698i) q^{67} +(-10.9474 - 40.8563i) q^{68} +51.0911i q^{69} +(37.9588 - 31.7668i) q^{70} -36.3406 q^{71} +(-8.07171 + 2.16281i) q^{72} +(-63.8921 - 17.1198i) q^{73} +(81.3275 - 46.9545i) q^{74} +(-52.5451 + 31.8980i) q^{75} -28.8634 q^{76} +(-44.4862 + 27.5773i) q^{77} +(-38.0911 + 38.0911i) q^{78} +(-35.6837 - 20.6020i) q^{79} +(-19.8564 - 2.39230i) q^{80} +(-22.8406 - 39.5610i) q^{81} +(-38.1865 + 10.2320i) 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} +(-10.0951 + 37.6753i) q^{87} +(20.4282 + 5.47371i) 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} +(-10.1820 - 37.9998i) q^{93} +(88.0979 - 50.8634i) q^{94} +(-8.63124 + 71.6403i) q^{95} +(6.95445 - 12.0455i) q^{96} +(-63.7723 - 63.7723i) q^{97} +(-65.6808 + 22.0915i) q^{98} -22.0911i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} - 4 q^{3} + 12 q^{5} - 16 q^{6} - 4 q^{7} + 16 q^{8}+O(q^{10}) \) 8 * q + 4 * q^2 - 4 * q^3 + 12 * q^5 - 16 * q^6 - 4 * q^7 + 16 * q^8	\( 8 q + 4 q^{2} - 4 q^{3} + 12 q^{5} - 16 q^{6} - 4 q^{7} + 16 q^{8} - 28 q^{10} + 8 q^{11} - 8 q^{12} + 8 q^{15} + 16 q^{16} - 16 q^{17} + 32 q^{18} - 64 q^{20} + 100 q^{21} + 16 q^{22} - 4 q^{23} + 28 q^{25} - 232 q^{27} - 40 q^{28} - 24 q^{30} - 64 q^{31} - 16 q^{32} - 52 q^{33} + 112 q^{35} + 128 q^{36} + 144 q^{37} + 8 q^{38} - 8 q^{40} - 136 q^{41} + 188 q^{42} + 120 q^{43} - 128 q^{45} + 8 q^{46} + 72 q^{47} - 32 q^{48} - 136 q^{50} + 208 q^{51} + 76 q^{53} + 48 q^{55} - 16 q^{56} - 376 q^{57} + 68 q^{58} + 56 q^{60} - 324 q^{61} - 128 q^{62} + 112 q^{63} + 104 q^{66} + 124 q^{67} + 32 q^{68} + 160 q^{70} + 16 q^{71} + 64 q^{72} + 32 q^{73} + 124 q^{75} + 32 q^{76} + 20 q^{77} - 480 q^{78} - 48 q^{80} + 124 q^{81} - 68 q^{82} + 168 q^{83} - 224 q^{85} + 120 q^{86} + 428 q^{87} + 16 q^{88} - 64 q^{90} - 720 q^{91} + 16 q^{92} - 64 q^{93} - 32 q^{95} - 32 q^{96} - 72 q^{97} - 132 q^{98}+O(q^{100}) \) 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

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