LMFDB - Embedded newform 350.2.h.c.211.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,2,Mod(71,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([6, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("350.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	350.h (of order $5$, 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:	$2.79476407074$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 25x^{14} + 241x^{12} + 1145x^{10} + 2841x^{8} + 3600x^{6} + 2156x^{4} + 480x^{2} + 16 $ x^16 + 25x^14 + 241x^12 + 1145x^10 + 2841x^8 + 3600x^6 + 2156x^4 + 480*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			211.3
Root			$1.92944i$ of defining polynomial
Character	$\chi$	$=$	350.211
Dual form			350.2.h.c.141.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 + 0.587785i) q^{2} +(0.315945 - 0.972380i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-2.00668 + 0.986533i) q^{5} +(0.315945 + 0.972380i) q^{6} -1.00000 q^{7} +(0.309017 + 0.951057i) q^{8} +(1.58135 + 1.14892i) q^{9} +O(q^{10})$	\(q+(-0.809017 + 0.587785i) q^{2} +(0.315945 - 0.972380i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-2.00668 + 0.986533i) q^{5} +(0.315945 + 0.972380i) q^{6} -1.00000 q^{7} +(0.309017 + 0.951057i) q^{8} +(1.58135 + 1.14892i) q^{9} +(1.04357 - 1.97762i) q^{10} +(-3.56502 + 2.59014i) q^{11} +(-0.827156 - 0.600964i) q^{12} +(3.29386 + 2.39313i) q^{13} +(0.809017 - 0.587785i) q^{14} +(0.325284 + 2.26294i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-0.486781 - 1.49816i) q^{17} -1.95466 q^{18} +(2.57800 + 7.93428i) q^{19} +(0.318151 + 2.21332i) q^{20} +(-0.315945 + 0.972380i) q^{21} +(1.36172 - 4.19094i) q^{22} +(-2.18556 + 1.58790i) q^{23} +1.02242 q^{24} +(3.05351 - 3.95931i) q^{25} -4.07144 q^{26} +(4.09827 - 2.97757i) q^{27} +(-0.309017 + 0.951057i) q^{28} +(-0.424975 + 1.30794i) q^{29} +(-1.59329 - 1.63956i) q^{30} +(2.66194 + 8.19261i) q^{31} +1.00000 q^{32} +(1.39225 + 4.28490i) q^{33} +(1.27441 + 0.925912i) q^{34} +(2.00668 - 0.986533i) q^{35} +(1.58135 - 1.14892i) q^{36} +(-1.85704 - 1.34922i) q^{37} +(-6.74930 - 4.90365i) q^{38} +(3.36772 - 2.44679i) q^{39} +(-1.55835 - 1.60361i) q^{40} +(-5.14942 - 3.74127i) q^{41} +(-0.315945 - 0.972380i) q^{42} -6.57797 q^{43} +(1.36172 + 4.19094i) q^{44} +(-4.30670 - 0.745454i) q^{45} +(0.834810 - 2.56928i) q^{46} +(-2.06959 + 6.36954i) q^{47} +(-0.827156 + 0.600964i) q^{48} +1.00000 q^{49} +(-0.143117 + 4.99795i) q^{50} -1.61057 q^{51} +(3.29386 - 2.39313i) q^{52} +(1.83432 - 5.64546i) q^{53} +(-1.56540 + 4.81781i) q^{54} +(4.59859 - 8.71459i) q^{55} +(-0.309017 - 0.951057i) q^{56} +8.52964 q^{57} +(-0.424975 - 1.30794i) q^{58} +(2.62410 + 1.90652i) q^{59} +(2.25271 + 0.389924i) q^{60} +(-7.99537 + 5.80897i) q^{61} +(-6.96905 - 5.06331i) q^{62} +(-1.58135 - 1.14892i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(-8.97063 - 1.55274i) q^{65} +(-3.64495 - 2.64821i) q^{66} +(-2.14891 - 6.61367i) q^{67} -1.57526 q^{68} +(0.853527 + 2.62689i) q^{69} +(-1.04357 + 1.97762i) q^{70} +(-2.23081 + 6.86573i) q^{71} +(-0.604022 + 1.85899i) q^{72} +(8.01886 - 5.82604i) q^{73} +2.29543 q^{74} +(-2.88521 - 4.22009i) q^{75} +8.34259 q^{76} +(3.56502 - 2.59014i) q^{77} +(-1.28635 + 3.95899i) q^{78} +(5.24146 - 16.1315i) q^{79} +(2.20331 + 0.381373i) q^{80} +(0.211567 + 0.651135i) q^{81} +6.36503 q^{82} +(0.823495 + 2.53446i) q^{83} +(0.827156 + 0.600964i) q^{84} +(2.45479 + 2.52609i) q^{85} +(5.32169 - 3.86643i) q^{86} +(1.13754 + 0.826474i) q^{87} +(-3.56502 - 2.59014i) q^{88} +(11.2828 - 8.19743i) q^{89} +(3.92236 - 1.92833i) q^{90} +(-3.29386 - 2.39313i) q^{91} +(0.834810 + 2.56928i) q^{92} +8.80736 q^{93} +(-2.06959 - 6.36954i) q^{94} +(-13.0006 - 13.3782i) q^{95} +(0.315945 - 0.972380i) q^{96} +(3.18187 - 9.79279i) q^{97} +(-0.809017 + 0.587785i) q^{98} -8.61341 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} + q^{3} - 4 q^{4} - 4 q^{5} + q^{6} - 16 q^{7} - 4 q^{8} - q^{9}+O(q^{10}) $ 16 * q - 4 * q^2 + q^3 - 4 * q^4 - 4 * q^5 + q^6 - 16 * q^7 - 4 * q^8 - q^9	\( 16 q - 4 q^{2} + q^{3} - 4 q^{4} - 4 q^{5} + q^{6} - 16 q^{7} - 4 q^{8} - q^{9} + q^{10} + 7 q^{11} - 4 q^{12} + 9 q^{13} + 4 q^{14} - 4 q^{16} - 2 q^{17} + 14 q^{18} - 24 q^{19} - 9 q^{20} - q^{21} - 8 q^{22} - 5 q^{23} + 6 q^{24} - 6 q^{25} - 6 q^{26} - 32 q^{27} + 4 q^{28} + 20 q^{29} + 15 q^{30} + 7 q^{31} + 16 q^{32} + 15 q^{33} + 3 q^{34} + 4 q^{35} - q^{36} - 6 q^{37} + 6 q^{38} + 34 q^{39} + 11 q^{40} + 9 q^{41} - q^{42} - 22 q^{43} - 8 q^{44} - 8 q^{45} - 40 q^{47} - 4 q^{48} + 16 q^{49} - q^{50} + 14 q^{51} + 9 q^{52} - 24 q^{53} + 23 q^{54} - 26 q^{55} + 4 q^{56} + 52 q^{57} + 20 q^{58} - 17 q^{59} - 5 q^{60} + 2 q^{61} - 23 q^{62} + q^{63} - 4 q^{64} - 16 q^{65} - 10 q^{66} - 14 q^{67} - 2 q^{68} - 35 q^{69} - q^{70} + 7 q^{71} - 6 q^{72} + 5 q^{73} - 36 q^{74} + 35 q^{75} + 36 q^{76} - 7 q^{77} - 46 q^{78} + 20 q^{79} + q^{80} + 49 q^{81} + 44 q^{82} + 17 q^{83} + 4 q^{84} - 13 q^{85} + 8 q^{86} - 66 q^{87} + 7 q^{88} + 27 q^{89} + 37 q^{90} - 9 q^{91} - 34 q^{93} - 40 q^{94} - 20 q^{95} + q^{96} + 6 q^{97} - 4 q^{98} - 16 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 + q^3 - 4 * q^4 - 4 * q^5 + q^6 - 16 * q^7 - 4 * q^8 - q^9 + q^10 + 7 * q^11 - 4 * q^12 + 9 * q^13 + 4 * q^14 - 4 * q^16 - 2 * q^17 + 14 * q^18 - 24 * q^19 - 9 * q^20 - q^21 - 8 * q^22 - 5 * q^23 + 6 * q^24 - 6 * q^25 - 6 * q^26 - 32 * q^27 + 4 * q^28 + 20 * q^29 + 15 * q^30 + 7 * q^31 + 16 * q^32 + 15 * q^33 + 3 * q^34 + 4 * q^35 - q^36 - 6 * q^37 + 6 * q^38 + 34 * q^39 + 11 * q^40 + 9 * q^41 - q^42 - 22 * q^43 - 8 * q^44 - 8 * q^45 - 40 * q^47 - 4 * q^48 + 16 * q^49 - q^50 + 14 * q^51 + 9 * q^52 - 24 * q^53 + 23 * q^54 - 26 * q^55 + 4 * q^56 + 52 * q^57 + 20 * q^58 - 17 * q^59 - 5 * q^60 + 2 * q^61 - 23 * q^62 + q^63 - 4 * q^64 - 16 * q^65 - 10 * q^66 - 14 * q^67 - 2 * q^68 - 35 * q^69 - q^70 + 7 * q^71 - 6 * q^72 + 5 * q^73 - 36 * q^74 + 35 * q^75 + 36 * q^76 - 7 * q^77 - 46 * q^78 + 20 * q^79 + q^80 + 49 * q^81 + 44 * q^82 + 17 * q^83 + 4 * q^84 - 13 * q^85 + 8 * q^86 - 66 * q^87 + 7 * q^88 + 27 * q^89 + 37 * q^90 - 9 * q^91 - 34 * q^93 - 40 * q^94 - 20 * q^95 + q^96 + 6 * q^97 - 4 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$3$	0.315945	−	0.972380i	0.182411	−	0.561404i	−0.817483	−	0.575953i	$-0.804631\pi$
$3$	0.315945	−	0.972380i	0.182411	−	0.561404i	0.999894	+	0.0145489i	$0.00463121\pi$
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	−2.00668	+	0.986533i	−0.897413	+	0.441191i
$5$	−2.00668	+	0.986533i	−0.897413	+	0.441191i
$6$	0.315945	+	0.972380i	0.128984	+	0.396973i
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$	1.58135	+	1.14892i	0.527116	+	0.382973i
$10$	1.04357	−	1.97762i	0.330005	−	0.625377i
$11$	−3.56502	+	2.59014i	−1.07489	+	0.780957i	−0.976786	−	0.214219i	$-0.931279\pi$
$11$	−3.56502	+	2.59014i	−1.07489	+	0.780957i	−0.0981092	+	0.995176i	$0.531279\pi$
$12$	−0.827156	−	0.600964i	−0.238779	−	0.173483i
$13$	3.29386	+	2.39313i	0.913554	+	0.663736i	0.941911	−	0.335862i	$-0.109028\pi$
$13$	3.29386	+	2.39313i	0.913554	+	0.663736i	−0.0283575	+	0.999598i	$0.509028\pi$
$14$	0.809017	−	0.587785i	0.216219	−	0.157092i
$15$	0.325284	+	2.26294i	0.0839881	+	0.584289i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−0.486781	−	1.49816i	−0.118062	−	0.363357i	0.874512	−	0.485005i	$-0.161182\pi$
$17$	−0.486781	−	1.49816i	−0.118062	−	0.363357i	−0.992573	+	0.121648i	$0.961182\pi$
$18$	−1.95466			−0.460717
$19$	2.57800	+	7.93428i	0.591435	+	1.82025i	0.571729	+	0.820442i	$0.306273\pi$
$19$	2.57800	+	7.93428i	0.591435	+	1.82025i	0.0197053	+	0.999806i	$0.493727\pi$
$20$	0.318151	+	2.21332i	0.0711408	+	0.494913i
$21$	−0.315945	+	0.972380i	−0.0689449	+	0.212191i
$22$	1.36172	−	4.19094i	0.290319	−	0.893511i
$23$	−2.18556	+	1.58790i	−0.455721	+	0.331101i	−0.791850	−	0.610715i	$-0.790882\pi$
$23$	−2.18556	+	1.58790i	−0.455721	+	0.331101i	0.336129	+	0.941816i	$0.390882\pi$
$24$	1.02242			0.208701
$25$	3.05351	−	3.95931i	0.610701	−	0.791861i
$26$	−4.07144			−0.798475
$27$	4.09827	−	2.97757i	0.788713	−	0.573033i
$28$	−0.309017	+	0.951057i	−0.0583987	+	0.179733i
$29$	−0.424975	+	1.30794i	−0.0789158	+	0.242878i	−0.982729	−	0.185049i	$-0.940756\pi$
$29$	−0.424975	+	1.30794i	−0.0789158	+	0.242878i	0.903814	+	0.427926i	$0.140756\pi$
$30$	−1.59329	−	1.63956i	−0.290893	−	0.299342i
$31$	2.66194	+	8.19261i	0.478099	+	1.47144i	0.841732	+	0.539895i	$0.181536\pi$
$31$	2.66194	+	8.19261i	0.478099	+	1.47144i	−0.363634	+	0.931542i	$0.618464\pi$
$32$	1.00000			0.176777
$33$	1.39225	+	4.28490i	0.242359	+	0.745905i
$34$	1.27441	+	0.925912i	0.218559	+	0.158793i
$35$	2.00668	−	0.986533i	0.339190	−	0.166754i
$36$	1.58135	−	1.14892i	0.263558	−	0.191486i
$37$	−1.85704	−	1.34922i	−0.305296	−	0.221810i	0.424580	−	0.905391i	$-0.360422\pi$
$37$	−1.85704	−	1.34922i	−0.305296	−	0.221810i	−0.729875	+	0.683580i	$0.760422\pi$
$38$	−6.74930	−	4.90365i	−1.09488	−	0.795478i
$39$	3.36772	−	2.44679i	0.539266	−	0.391800i
$40$	−1.55835	−	1.60361i	−0.246396	−	0.253553i
$41$	−5.14942	−	3.74127i	−0.804204	−	0.584288i	0.107940	−	0.994157i	$-0.465574\pi$
$41$	−5.14942	−	3.74127i	−0.804204	−	0.584288i	−0.912144	+	0.409869i	$0.865574\pi$
$42$	−0.315945	−	0.972380i	−0.0487514	−	0.150042i
$43$	−6.57797			−1.00313			−0.501565	−	0.865120i	$-0.667242\pi$
$43$	−6.57797			−1.00313			−0.501565	+	0.865120i	$0.667242\pi$
$44$	1.36172	+	4.19094i	0.205287	+	0.631807i
$45$	−4.30670	−	0.745454i	−0.642005	−	0.111126i
$46$	0.834810	−	2.56928i	0.123086	−	0.378820i
$47$	−2.06959	+	6.36954i	−0.301881	+	0.929093i	0.678942	+	0.734192i	$0.262439\pi$
$47$	−2.06959	+	6.36954i	−0.301881	+	0.929093i	−0.980823	+	0.194901i	$0.937561\pi$
$48$	−0.827156	+	0.600964i	−0.119390	+	0.0867417i
$49$	1.00000			0.142857
$50$	−0.143117	+	4.99795i	−0.0202398	+	0.706817i
$51$	−1.61057			−0.225526
$52$	3.29386	−	2.39313i	0.456777	−	0.331868i
$53$	1.83432	−	5.64546i	0.251963	−	0.775463i	−0.742450	−	0.669902i	$-0.766336\pi$
$53$	1.83432	−	5.64546i	0.251963	−	0.775463i	0.994413	−	0.105561i	$-0.0336638\pi$
$54$	−1.56540	+	4.81781i	−0.213024	+	0.655621i
$55$	4.59859	−	8.71459i	0.620074	−	1.17507i
$56$	−0.309017	−	0.951057i	−0.0412941	−	0.127090i
$57$	8.52964			1.12978
$58$	−0.424975	−	1.30794i	−0.0558019	−	0.171741i
$59$	2.62410	+	1.90652i	0.341629	+	0.248208i	0.745349	−	0.666675i	$-0.232283\pi$
$59$	2.62410	+	1.90652i	0.341629	+	0.248208i	−0.403720	+	0.914883i	$0.632283\pi$
$60$	2.25271	+	0.389924i	0.290823	+	0.0503390i
$61$	−7.99537	+	5.80897i	−1.02370	+	0.743763i	−0.967038	−	0.254630i	$-0.918046\pi$
$61$	−7.99537	+	5.80897i	−1.02370	+	0.743763i	−0.0566633	+	0.998393i	$0.518046\pi$
$62$	−6.96905	−	5.06331i	−0.885071	−	0.643042i
$63$	−1.58135	−	1.14892i	−0.199231	−	0.144750i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−8.97063	−	1.55274i	−1.11267	−	0.192594i
$66$	−3.64495	−	2.64821i	−0.448663	−	0.325973i
$67$	−2.14891	−	6.61367i	−0.262531	−	0.807989i	−0.992252	−	0.124243i	$-0.960350\pi$
$67$	−2.14891	−	6.61367i	−0.262531	−	0.807989i	0.729720	−	0.683746i	$-0.239650\pi$
$68$	−1.57526			−0.191028
$69$	0.853527	+	2.62689i	0.102753	+	0.316240i
$70$	−1.04357	+	1.97762i	−0.124730	+	0.236370i
$71$	−2.23081	+	6.86573i	−0.264749	+	0.814813i	0.727003	+	0.686635i	$0.240913\pi$
$71$	−2.23081	+	6.86573i	−0.264749	+	0.814813i	−0.991751	+	0.128178i	$0.959087\pi$
$72$	−0.604022	+	1.85899i	−0.0711846	+	0.219084i
$73$	8.01886	−	5.82604i	0.938536	−	0.681886i	−0.00953177	−	0.999955i	$-0.503034\pi$
$73$	8.01886	−	5.82604i	0.938536	−	0.681886i	0.948068	+	0.318068i	$0.103034\pi$
$74$	2.29543			0.266838
$75$	−2.88521	−	4.22009i	−0.333155	−	0.487294i
$76$	8.34259			0.956961
$77$	3.56502	−	2.59014i	0.406272	−	0.295174i
$78$	−1.28635	+	3.95899i	−0.145651	+	0.448267i
$79$	5.24146	−	16.1315i	0.589710	−	1.81494i	0.0102394	−	0.999948i	$-0.496741\pi$
$79$	5.24146	−	16.1315i	0.589710	−	1.81494i	0.579471	−	0.814993i	$-0.303259\pi$
$80$	2.20331	+	0.381373i	0.246337	+	0.0426388i
$81$	0.211567	+	0.651135i	0.0235074	+	0.0723484i
$82$	6.36503			0.702900
$83$	0.823495	+	2.53446i	0.0903904	+	0.278193i	0.986025	−	0.166598i	$-0.0532781\pi$
$83$	0.823495	+	2.53446i	0.0903904	+	0.278193i	−0.895635	+	0.444791i	$0.853278\pi$
$84$	0.827156	+	0.600964i	0.0902501	+	0.0655705i
$85$	2.45479	+	2.52609i	0.266260	+	0.273993i
$86$	5.32169	−	3.86643i	0.573852	−	0.416928i
$87$	1.13754	+	0.826474i	0.121957	+	0.0886073i
$88$	−3.56502	−	2.59014i	−0.380033	−	0.276110i
$89$	11.2828	−	8.19743i	1.19597	−	0.868925i	0.202091	−	0.979367i	$-0.435226\pi$
$89$	11.2828	−	8.19743i	1.19597	−	0.868925i	0.993883	+	0.110441i	$0.0352264\pi$
$90$	3.92236	−	1.92833i	0.413453	−	0.203264i
$91$	−3.29386	−	2.39313i	−0.345291	−	0.250868i
$92$	0.834810	+	2.56928i	0.0870349	+	0.267866i
$93$	8.80736			0.913281
$94$	−2.06959	−	6.36954i	−0.213462	−	0.656968i
$95$	−13.0006	−	13.3782i	−1.33384	−	1.37258i
$96$	0.315945	−	0.972380i	0.0322460	−	0.0992431i
$97$	3.18187	−	9.79279i	0.323070	−	0.994307i	−0.649234	−	0.760588i	$-0.724911\pi$
$97$	3.18187	−	9.79279i	0.323070	−	0.994307i	0.972304	−	0.233719i	$-0.0750894\pi$
$98$	−0.809017	+	0.587785i	−0.0817231	+	0.0593753i
$99$	−8.61341			−0.865680
$100$	−2.82194	−	4.12755i	−0.282194	−	0.412755i
$101$	6.92187			0.688752			0.344376	−	0.938832i	$-0.388091\pi$
$101$	6.92187			0.688752			0.344376	+	0.938832i	$0.388091\pi$
$102$	1.30298	−	0.946672i	0.129014	−	0.0937345i
$103$	0.569798	−	1.75366i	0.0561438	−	0.172793i	−0.919052	−	0.394136i	$-0.871044\pi$
$103$	0.569798	−	1.75366i	0.0561438	−	0.172793i	0.975196	+	0.221343i	$0.0710440\pi$
$104$	−1.25814	+	3.87217i	−0.123371	+	0.379697i
$105$	−0.325284	−	2.26294i	−0.0317445	−	0.220841i
$106$	1.83432	+	5.64546i	0.178165	+	0.548335i
$107$	8.23328			0.795942			0.397971	−	0.917398i	$-0.369715\pi$
$107$	8.23328			0.795942			0.397971	+	0.917398i	$0.369715\pi$
$108$	−1.56540	−	4.81781i	−0.150631	−	0.463594i
$109$	6.43757	+	4.67717i	0.616607	+	0.447992i	0.851735	−	0.523973i	$-0.175551\pi$
$109$	6.43757	+	4.67717i	0.616607	+	0.447992i	−0.235127	+	0.971965i	$0.575551\pi$
$110$	1.40197	+	9.75323i	0.133672	+	0.929934i
$111$	−1.89868	+	1.37947i	−0.180215	+	0.130934i
$112$	0.809017	+	0.587785i	0.0764449	+	0.0555405i
$113$	−11.4036	−	8.28519i	−1.07276	−	0.779405i	−0.0963533	−	0.995347i	$-0.530718\pi$
$113$	−11.4036	−	8.28519i	−1.07276	−	0.779405i	−0.976406	+	0.215942i	$0.930718\pi$
$114$	−6.90063	+	5.01360i	−0.646303	+	0.469566i
$115$	2.81920	−	5.34254i	0.262891	−	0.498194i
$116$	1.11260	+	0.808350i	0.103302	+	0.0750534i
$117$	2.45924	+	7.56876i	0.227357	+	0.699732i
$118$	−3.24357			−0.298594
$119$	0.486781	+	1.49816i	0.0446231	+	0.137336i
$120$	−2.05167	+	1.00865i	−0.187291	+	0.0920769i
$121$	2.60137	−	8.00620i	0.236488	−	0.727836i
$122$	3.05396	−	9.39912i	0.276492	−	0.850956i
$123$	−5.26487	+	3.82515i	−0.474718	+	0.344902i
$124$	8.61422			0.773580
$125$	−2.22142	+	10.9574i	−0.198689	+	0.980062i
$126$	1.95466			0.174135
$127$	−15.2458	+	11.0767i	−1.35284	+	0.982898i	−0.353979	+	0.935254i	$0.615171\pi$
$127$	−15.2458	+	11.0767i	−1.35284	+	0.982898i	−0.998864	+	0.0476443i	$0.984829\pi$
$128$	0.309017	−	0.951057i	0.0273135	−	0.0840623i
$129$	−2.07828	+	6.39628i	−0.182982	+	0.563161i
$130$	8.17007	−	4.01661i	0.716562	−	0.352280i
$131$	5.54603	+	17.0689i	0.484559	+	1.49132i	0.832619	+	0.553847i	$0.186841\pi$
$131$	5.54603	+	17.0689i	0.484559	+	1.49132i	−0.348060	+	0.937472i	$0.613159\pi$
$132$	4.50541			0.392146
$133$	−2.57800	−	7.93428i	−0.223541	−	0.687989i
$134$	5.62593	+	4.08747i	0.486006	+	0.353104i
$135$	−5.28644	+	10.0181i	−0.454984	+	0.862221i
$136$	1.27441	−	0.925912i	0.109280	−	0.0793963i
$137$	7.25172	+	5.26868i	0.619556	+	0.450134i	0.852766	−	0.522293i	$-0.174923\pi$
$137$	7.25172	+	5.26868i	0.619556	+	0.450134i	−0.233210	+	0.972426i	$0.574923\pi$
$138$	−2.23456	−	1.62350i	−0.190219	−	0.138202i
$139$	−6.29571	+	4.57410i	−0.533996	+	0.387970i	−0.821850	−	0.569704i	$-0.807058\pi$
$139$	−6.29571	+	4.57410i	−0.533996	+	0.387970i	0.287855	+	0.957674i	$0.407058\pi$
$140$	−0.318151	−	2.21332i	−0.0268887	−	0.187060i
$141$	5.53974	+	4.02486i	0.466530	+	0.338954i
$142$	−2.23081	−	6.86573i	−0.187206	−	0.576160i
$143$	−17.9413			−1.50032
$144$	−0.604022	−	1.85899i	−0.0503351	−	0.154916i
$145$	−0.437536	−	3.04386i	−0.0363354	−	0.252779i
$146$	−3.06293	+	9.42673i	−0.253490	+	0.780162i
$147$	0.315945	−	0.972380i	0.0260587	−	0.0802006i
$148$	−1.85704	+	1.34922i	−0.152648	+	0.110905i
$149$	2.87550			0.235570			0.117785	−	0.993039i	$-0.462421\pi$
$149$	2.87550			0.235570			0.117785	+	0.993039i	$0.462421\pi$
$150$	4.81469	+	1.71824i	0.393118	+	0.140294i
$151$	−11.8125			−0.961286			−0.480643	−	0.876916i	$-0.659597\pi$
$151$	−11.8125			−0.961286			−0.480643	+	0.876916i	$0.659597\pi$
$152$	−6.74930	+	4.90365i	−0.547441	+	0.397739i
$153$	0.951489	−	2.92838i	0.0769233	−	0.236746i
$154$	−1.36172	+	4.19094i	−0.109730	+	0.337715i
$155$	−13.4239	−	13.8138i	−1.07824	−	1.10955i
$156$	−1.28635	−	3.95899i	−0.102991	−	0.316973i
$157$	14.2780			1.13951			0.569756	−	0.821814i	$-0.307038\pi$
$157$	14.2780			1.13951			0.569756	+	0.821814i	$0.307038\pi$
$158$	5.24146	+	16.1315i	0.416988	+	1.28336i
$159$	−4.90998	−	3.56731i	−0.389387	−	0.282906i
$160$	−2.00668	+	0.986533i	−0.158642	+	0.0779923i
$161$	2.18556	−	1.58790i	0.172246	−	0.125144i
$162$	−0.553889	−	0.402424i	−0.0435176	−	0.0316174i
$163$	2.38315	+	1.73146i	0.186663	+	0.135618i	0.677192	−	0.735806i	$-0.263197\pi$
$163$	2.38315	+	1.73146i	0.186663	+	0.135618i	−0.490529	+	0.871425i	$0.663197\pi$
$164$	−5.14942	+	3.74127i	−0.402102	+	0.292144i
$165$	−7.02099	−	7.22491i	−0.546583	−	0.562459i
$166$	−2.15594	−	1.56638i	−0.167333	−	0.121575i
$167$	−0.136836	−	0.421137i	−0.0105887	−	0.0325886i	0.945623	−	0.325266i	$-0.105454\pi$
$167$	−0.136836	−	0.421137i	−0.0105887	−	0.0325886i	−0.956211	+	0.292677i	$0.905454\pi$
$168$	−1.02242			−0.0788815
$169$	1.10524	+	3.40157i	0.0850183	+	0.261659i
$170$	−3.47077	−	0.600761i	−0.266196	−	0.0460762i
$171$	−5.03911	+	15.5088i	−0.385350	+	1.18599i
$172$	−2.03270	+	6.25602i	−0.154992	+	0.477017i
$173$	−16.0308	+	11.6471i	−1.21880	+	0.885510i	−0.996000	−	0.0893540i	$-0.971520\pi$
$173$	−16.0308	+	11.6471i	−1.21880	+	0.885510i	−0.222800	+	0.974864i	$0.571520\pi$
$174$	−1.40608			−0.106595
$175$	−3.05351	+	3.95931i	−0.230823	+	0.299295i
$176$	4.40661			0.332161
$177$	2.68293	−	1.94927i	0.201662	−	0.146516i
$178$	−4.30964	+	13.2637i	−0.323021	+	0.994157i
$179$	5.90685	−	18.1794i	0.441499	−	1.35879i	−0.444780	−	0.895640i	$-0.646718\pi$
$179$	5.90685	−	18.1794i	0.441499	−	1.35879i	0.886278	−	0.463153i	$-0.153282\pi$
$180$	−2.03981	+	3.86556i	−0.152039	+	0.288122i
$181$	4.03082	+	12.4056i	0.299608	+	0.922099i	0.981634	+	0.190772i	$0.0610990\pi$
$181$	4.03082	+	12.4056i	0.299608	+	0.922099i	−0.682026	+	0.731328i	$0.738901\pi$
$182$	4.07144			0.301795
$183$	3.12243	+	9.60985i	0.230817	+	0.710381i
$184$	−2.18556	−	1.58790i	−0.161122	−	0.117062i
$185$	5.05753	+	0.875416i	0.371837	+	0.0643618i
$186$	−7.12531	+	5.17684i	−0.522453	+	0.379584i
$187$	5.61582	+	4.08013i	0.410670	+	0.298369i
$188$	5.41826	+	3.93659i	0.395167	+	0.287106i
$189$	−4.09827	+	2.97757i	−0.298105	+	0.216586i
$190$	18.3813	+	3.18164i	1.33352	+	0.230821i
$191$	−7.54452	−	5.48142i	−0.545903	−	0.396621i	0.280370	−	0.959892i	$-0.409543\pi$
$191$	−7.54452	−	5.48142i	−0.545903	−	0.396621i	−0.826272	+	0.563271i	$0.809543\pi$
$192$	0.315945	+	0.972380i	0.0228014	+	0.0701755i
$193$	25.3269			1.82307			0.911537	−	0.411219i	$-0.134897\pi$
$193$	25.3269			1.82307			0.911537	+	0.411219i	$0.134897\pi$
$194$	3.18187	+	9.79279i	0.228445	+	0.703081i
$195$	−4.34408	+	8.23228i	−0.311086	+	0.589526i
$196$	0.309017	−	0.951057i	0.0220726	−	0.0679326i
$197$	−5.42968	+	16.7108i	−0.386848	+	1.19060i	0.548282	+	0.836293i	$0.315282\pi$
$197$	−5.42968	+	16.7108i	−0.386848	+	1.19060i	−0.935130	+	0.354304i	$0.884718\pi$
$198$	6.96839	−	5.06283i	0.495222	−	0.359800i
$199$	−6.92865			−0.491159			−0.245579	−	0.969377i	$-0.578978\pi$
$199$	−6.92865			−0.491159			−0.245579	+	0.969377i	$0.578978\pi$
$200$	4.70911	+	1.68056i	0.332984	+	0.118834i
$201$	−7.10994			−0.501497
$202$	−5.59991	+	4.06857i	−0.394008	+	0.286264i
$203$	0.424975	−	1.30794i	0.0298274	−	0.0917992i
$204$	−0.497695	+	1.53175i	−0.0348456	+	0.107244i
$205$	14.0241	+	2.42745i	0.979486	+	0.169541i
$206$	0.569798	+	1.75366i	0.0396997	+	0.122183i
$207$	−5.28050			−0.367020
$208$	−1.25814	−	3.87217i	−0.0872366	−	0.268487i
$209$	−29.7415	−	21.6085i	−2.05727	−	1.49469i
$210$	1.59329	+	1.63956i	0.109947	+	0.113141i
$211$	18.2322	−	13.2464i	1.25515	−	0.911922i	0.256644	−	0.966506i	$-0.417383\pi$
$211$	18.2322	−	13.2464i	1.25515	−	0.911922i	0.998509	+	0.0545838i	$0.0173832\pi$
$212$	−4.80231	−	3.48908i	−0.329824	−	0.239631i
$213$	5.97129	+	4.33839i	0.409146	+	0.297262i
$214$	−6.66087	+	4.83940i	−0.455327	+	0.330815i
$215$	13.1999	−	6.48938i	0.900223	−	0.442572i
$216$	4.09827	+	2.97757i	0.278852	+	0.202598i
$217$	−2.66194	−	8.19261i	−0.180704	−	0.556151i
$218$	−7.95727			−0.538935
$219$	−3.13160	−	9.63809i	−0.211614	−	0.651282i
$220$	−6.86702	−	7.06648i	−0.462975	−	0.476422i
$221$	1.98190	−	6.09966i	0.133317	−	0.410307i
$222$	0.725230	−	2.23203i	0.0486743	−	0.149804i
$223$	−7.96870	+	5.78960i	−0.533624	+	0.387700i	−0.821712	−	0.569904i	$-0.806981\pi$
$223$	−7.96870	+	5.78960i	−0.533624	+	0.387700i	0.288088	+	0.957604i	$0.406981\pi$
$224$	−1.00000			−0.0668153
$225$	9.37758	−	2.75282i	0.625172	−	0.183521i
$226$	14.0956			0.937626
$227$	8.28979	−	6.02289i	0.550213	−	0.399753i	−0.277651	−	0.960682i	$-0.589556\pi$
$227$	8.28979	−	6.02289i	0.550213	−	0.399753i	0.827864	+	0.560929i	$0.189556\pi$
$228$	2.63580	−	8.11217i	0.174560	−	0.537242i
$229$	−3.23788	+	9.96516i	−0.213965	+	0.658516i	0.785261	+	0.619165i	$0.212529\pi$
$229$	−3.23788	+	9.96516i	−0.213965	+	0.658516i	−0.999225	+	0.0393507i	$0.987471\pi$
$230$	0.859486	+	5.97928i	0.0566728	+	0.394262i
$231$	−1.39225	−	4.28490i	−0.0916032	−	0.281926i
$232$	−1.37525			−0.0902894
$233$	5.14603	+	15.8379i	0.337128	+	1.03757i	0.965664	+	0.259792i	$0.0836541\pi$
$233$	5.14603	+	15.8379i	0.337128	+	1.03757i	−0.628537	+	0.777780i	$0.716346\pi$
$234$	−6.43837	−	4.67775i	−0.420889	−	0.305794i
$235$	−2.13076	−	14.8233i	−0.138996	−	0.966967i
$236$	2.62410	−	1.90652i	0.170814	−	0.124104i
$237$	−14.0300	−	10.1934i	−0.911345	−	0.662131i
$238$	−1.27441	−	0.925912i	−0.0826077	−	0.0600180i
$239$	20.0376	−	14.5582i	1.29613	−	0.941691i	0.296216	−	0.955121i	$-0.404275\pi$
$239$	20.0376	−	14.5582i	1.29613	−	0.941691i	0.999910	+	0.0134301i	$0.00427506\pi$
$240$	1.06696	−	2.02196i	0.0688722	−	0.130517i
$241$	−17.8463	−	12.9661i	−1.14958	−	0.835222i	−0.161159	−	0.986928i	$-0.551523\pi$
$241$	−17.8463	−	12.9661i	−1.14958	−	0.835222i	−0.988426	+	0.151707i	$0.951523\pi$
$242$	2.60137	+	8.00620i	0.167223	+	0.514658i
$243$	15.8972			1.01981
$244$	3.05396	+	9.39912i	0.195510	+	0.601717i
$245$	−2.00668	+	0.986533i	−0.128202	+	0.0630273i
$246$	2.01100	−	6.18923i	0.128217	−	0.394611i
$247$	−10.4962	+	32.3039i	−0.667856	+	2.05545i
$248$	−6.96905	+	5.06331i	−0.442535	+	0.321521i
$249$	2.72464			0.172667
$250$	−4.64345	−	10.1705i	−0.293678	−	0.643237i
$251$	15.2149			0.960359			0.480180	−	0.877170i	$-0.340572\pi$
$251$	15.2149			0.960359			0.480180	+	0.877170i	$0.340572\pi$
$252$	−1.58135	+	1.14892i	−0.0996157	+	0.0723750i
$253$	3.67868	−	11.3218i	0.231277	−	0.711797i
$254$	5.82336	−	17.9225i	0.365390	−	1.12456i
$255$	3.23190	−	1.58888i	0.202390	−	0.0994998i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	22.5798			1.40849			0.704245	−	0.709957i	$-0.251286\pi$
$257$	22.5798			1.40849			0.704245	+	0.709957i	$0.251286\pi$
$258$	−2.07828	−	6.39628i	−0.129388	−	0.398215i
$259$	1.85704	+	1.34922i	0.115391	+	0.0838364i
$260$	−4.24882	+	8.05175i	−0.263501	+	0.499348i
$261$	−2.17475	+	1.58005i	−0.134613	+	0.0978024i
$262$	−14.5197	−	10.5492i	−0.897030	−	0.651730i
$263$	10.6003	+	7.70157i	0.653643	+	0.474899i	0.864510	−	0.502615i	$-0.167629\pi$
$263$	10.6003	+	7.70157i	0.653643	+	0.474899i	−0.210867	+	0.977515i	$0.567629\pi$
$264$	−3.64495	+	2.64821i	−0.224331	+	0.162986i
$265$	1.88854	+	13.1382i	0.116012	+	0.807075i
$266$	6.74930	+	4.90365i	0.413826	+	0.300662i
$267$	−4.40627	−	13.5611i	−0.269659	−	0.829926i
$268$	−6.95403			−0.424785
$269$	3.34458	+	10.2936i	0.203923	+	0.627610i	0.999756	+	0.0220939i	$0.00703327\pi$
$269$	3.34458	+	10.2936i	0.203923	+	0.627610i	−0.795833	+	0.605516i	$0.792967\pi$
$270$	−1.61167	−	11.2121i	−0.0980832	−	0.682347i
$271$	2.45860	−	7.56678i	0.149349	−	0.459649i	−0.848195	−	0.529683i	$-0.822311\pi$
$271$	2.45860	−	7.56678i	0.149349	−	0.459649i	0.997545	+	0.0700339i	$0.0223108\pi$
$272$	−0.486781	+	1.49816i	−0.0295154	+	0.0908391i
$273$	−3.36772	+	2.44679i	−0.203823	+	0.148086i
$274$	−8.96362			−0.541512
$275$	−0.630660	+	22.0240i	−0.0380302	+	1.32810i
$276$	2.76207			0.166257
$277$	−16.2244	+	11.7878i	−0.974833	+	0.708257i	−0.956548	−	0.291575i	$-0.905821\pi$
$277$	−16.2244	+	11.7878i	−0.974833	+	0.708257i	−0.0182848	+	0.999833i	$0.505821\pi$
$278$	2.40475	−	7.40106i	0.144227	−	0.443886i
$279$	−5.20318	+	16.0137i	−0.311506	+	0.958717i
$280$	1.55835	+	1.60361i	0.0931290	+	0.0958339i
$281$	−5.39086	−	16.5914i	−0.321592	−	0.989758i	−0.972956	−	0.230992i	$-0.925803\pi$
$281$	−5.39086	−	16.5914i	−0.321592	−	0.989758i	0.651364	−	0.758766i	$-0.274197\pi$
$282$	−6.84749			−0.407762
$283$	−4.31777	−	13.2887i	−0.256665	−	0.789933i	−0.993497	−	0.113858i	$-0.963679\pi$
$283$	−4.31777	−	13.2887i	−0.256665	−	0.789933i	0.736832	−	0.676076i	$-0.236321\pi$
$284$	5.84034	+	4.24326i	0.346561	+	0.251791i
$285$	−17.1162	+	8.41477i	−1.01388	+	0.498448i
$286$	14.5148	−	10.5456i	0.858277	−	0.623575i
$287$	5.14942	+	3.74127i	0.303961	+	0.220840i
$288$	1.58135	+	1.14892i	0.0931819	+	0.0677006i
$289$	11.7458	−	8.53380i	0.690928	−	0.501988i
$290$	2.14311	+	2.20536i	0.125848	+	0.129503i
$291$	−8.51701	−	6.18797i	−0.499276	−	0.362745i
$292$	−3.06293	−	9.42673i	−0.179244	−	0.551658i
$293$	4.24839			0.248194			0.124097	−	0.992270i	$-0.460397\pi$
$293$	4.24839			0.248194			0.124097	+	0.992270i	$0.460397\pi$
$294$	0.315945	+	0.972380i	0.0184263	+	0.0567104i
$295$	−7.14657	−	1.23701i	−0.416089	−	0.0720215i
$296$	0.709327	−	2.18308i	0.0412288	−	0.126889i
$297$	−6.89811	+	21.2302i	−0.400269	+	1.23190i
$298$	−2.32633	+	1.69017i	−0.134760	+	0.0979092i
$299$	−10.9990			−0.636089
$300$	−4.90513	+	1.43992i	−0.283198	+	0.0831336i
$301$	6.57797			0.379148
$302$	9.55649	−	6.94320i	0.549914	−	0.399536i
$303$	2.18693	−	6.73069i	0.125636	−	0.386668i
$304$	2.57800	−	7.93428i	0.147859	−	0.455062i
$305$	10.3134	−	19.5444i	0.590542	−	1.11911i
$306$	0.951489	+	2.92838i	0.0543930	+	0.167404i
$307$	0.409057			0.0233461			0.0116730	−	0.999932i	$-0.496284\pi$
$307$	0.409057			0.0233461			0.0116730	+	0.999932i	$0.496284\pi$
$308$	−1.36172	−	4.19094i	−0.0775911	−	0.238801i
$309$	−1.52520	−	1.10812i	−0.0867654	−	0.0630387i
$310$	18.9798	+	3.28524i	1.07798	+	0.186589i
$311$	12.6983	−	9.22586i	0.720055	−	0.523151i	−0.166347	−	0.986067i	$-0.553197\pi$
$311$	12.6983	−	9.22586i	0.720055	−	0.523151i	0.886402	+	0.462917i	$0.153197\pi$
$312$	3.36772	+	2.44679i	0.190659	+	0.138522i
$313$	8.05325	+	5.85103i	0.455197	+	0.330720i	0.791644	−	0.610983i	$-0.209225\pi$
$313$	8.05325	+	5.85103i	0.455197	+	0.330720i	−0.336448	+	0.941702i	$0.609225\pi$
$314$	−11.5512	+	8.39243i	−0.651871	+	0.473612i
$315$	4.30670	+	0.745454i	0.242655	+	0.0420016i
$316$	−13.7223	−	9.96984i	−0.771940	−	0.560848i
$317$	−3.50032	−	10.7729i	−0.196597	−	0.605064i	−0.999954	−	0.00956652i	$-0.996955\pi$
$317$	−3.50032	−	10.7729i	−0.196597	−	0.605064i	0.803357	−	0.595498i	$-0.203045\pi$
$318$	6.06907			0.340337
$319$	−1.87270	−	5.76357i	−0.104851	−	0.322698i
$320$	1.04357	−	1.97762i	0.0583371	−	0.110552i
$321$	2.60127	−	8.00588i	0.145189	−	0.446845i
$322$	−0.834810	+	2.56928i	−0.0465221	+	0.143180i
$323$	10.6319	−	7.72451i	0.591573	−	0.429803i
$324$	0.684644			0.0380358
$325$	19.5330	−	5.73397i	1.08349	−	0.318063i
$326$	−2.94573			−0.163149
$327$	6.58191	−	4.78204i	0.363980	−	0.264447i
$328$	1.96690	−	6.05350i	0.108604	−	0.334249i
$329$	2.06959	−	6.36954i	0.114100	−	0.351164i
$330$	9.92680	+	1.71824i	0.546452	+	0.0945862i
$331$	1.63403	+	5.02903i	0.0898145	+	0.276420i	0.985868	−	0.167526i	$-0.0535779\pi$
$331$	1.63403	+	5.02903i	0.0898145	+	0.276420i	−0.896053	+	0.443947i	$0.853578\pi$
$332$	2.66489			0.146255
$333$	−1.38649	−	4.26718i	−0.0759791	−	0.233840i
$334$	0.358241	+	0.260277i	0.0196021	+	0.0142417i
$335$	10.8368	+	11.1515i	0.592076	+	0.609273i
$336$	0.827156	−	0.600964i	0.0451251	−	0.0327853i
$337$	−8.57040	−	6.22676i	−0.466859	−	0.339193i	0.329357	−	0.944206i	$-0.393168\pi$
$337$	−8.57040	−	6.22676i	−0.466859	−	0.339193i	−0.796216	+	0.605012i	$0.793168\pi$
$338$	−2.89355	−	2.10229i	−0.157388	−	0.114349i
$339$	−11.6593	+	8.47096i	−0.633245	+	0.460079i
$340$	3.16103	−	1.55404i	0.171431	−	0.0842797i
$341$	−30.7099	−	22.3121i	−1.66303	−	1.20827i
$342$	−5.03911	−	15.5088i	−0.272484	−	0.838619i
$343$	−1.00000			−0.0539949
$344$	−2.03270	−	6.25602i	−0.109596	−	0.337302i
$345$	−4.30426	−	4.42928i	−0.231734	−	0.238464i
$346$	6.12323	−	18.8454i	0.329187	−	1.01313i
$347$	−9.56074	+	29.4249i	−0.513247	+	1.57961i	0.273202	+	0.961957i	$0.411917\pi$
$347$	−9.56074	+	29.4249i	−0.513247	+	1.57961i	−0.786449	+	0.617656i	$0.788083\pi$
$348$	1.13754	−	0.826474i	0.0609787	−	0.0443036i
$349$	9.23630			0.494408			0.247204	−	0.968964i	$-0.420488\pi$
$349$	9.23630			0.494408			0.247204	+	0.968964i	$0.420488\pi$
$350$	0.143117	−	4.99795i	0.00764991	−	0.267152i
$351$	20.6249			1.10087
$352$	−3.56502	+	2.59014i	−0.190016	+	0.138055i
$353$	2.12251	−	6.53241i	0.112970	−	0.347685i	−0.878548	−	0.477653i	$-0.841488\pi$
$353$	2.12251	−	6.53241i	0.112970	−	0.347685i	0.991518	+	0.129968i	$0.0414876\pi$
$354$	−1.02479	+	3.15398i	−0.0544670	+	0.167632i
$355$	−2.29675	−	15.9781i	−0.121899	−	0.848028i
$356$	−4.30964	−	13.2637i	−0.228411	−	0.702975i
$357$	1.61057			0.0852406
$358$	5.90685	+	18.1794i	0.312187	+	0.960812i
$359$	−3.93494	−	2.85890i	−0.207678	−	0.150887i	0.479084	−	0.877769i	$-0.340969\pi$
$359$	−3.93494	−	2.85890i	−0.207678	−	0.150887i	−0.686763	+	0.726882i	$0.740969\pi$
$360$	−0.621876	−	4.32628i	−0.0327757	−	0.228015i
$361$	−40.9353	+	29.7413i	−2.15449	+	1.56533i
$362$	−10.5528	−	7.66707i	−0.554644	−	0.402972i
$363$	−6.96318	−	5.05905i	−0.365472	−	0.265531i
$364$	−3.29386	+	2.39313i	−0.172645	+	0.125434i
$365$	−10.3437	+	19.6018i	−0.541413	+	1.02601i
$366$	−8.17463	−	5.93922i	−0.427295	−	0.310448i
$367$	−1.62562	−	5.00315i	−0.0848567	−	0.261162i	0.899621	−	0.436671i	$-0.143843\pi$
$367$	−1.62562	−	5.00315i	−0.0848567	−	0.261162i	−0.984478	+	0.175509i	$0.943843\pi$
$368$	2.70150			0.140825
$369$	−3.84462	−	11.8325i	−0.200143	−	0.615976i
$370$	−4.60619	+	2.26452i	−0.239464	+	0.117727i
$371$	−1.83432	+	5.64546i	−0.0952331	+	0.293097i
$372$	2.72163	−	8.37630i	0.141110	−	0.434291i
$373$	17.3559	−	12.6098i	0.898652	−	0.652909i	−0.0394672	−	0.999221i	$-0.512566\pi$
$373$	17.3559	−	12.6098i	0.898652	−	0.652909i	0.938119	+	0.346312i	$0.112566\pi$
$374$	−6.94154			−0.358938
$375$	9.95294	+	5.62201i	0.513968	+	0.290319i
$376$	−6.69733			−0.345389
$377$	−4.52988	+	3.29115i	−0.233301	+	0.169503i
$378$	1.56540	−	4.81781i	0.0805155	−	0.247801i
$379$	0.0373078	−	0.114822i	0.00191637	−	0.00589799i	−0.950094	−	0.311965i	$-0.899013\pi$
$379$	0.0373078	−	0.114822i	0.00191637	−	0.00589799i	0.952010	+	0.306067i	$0.0990130\pi$
$380$	−16.7409	+	8.23024i	−0.858790	+	0.422203i
$381$	5.95393	+	18.3243i	0.305029	+	0.938783i
$382$	9.32554			0.477136
$383$	−0.677469	−	2.08504i	−0.0346171	−	0.106540i	0.932255	−	0.361802i	$-0.117838\pi$
$383$	−0.677469	−	2.08504i	−0.0346171	−	0.106540i	−0.966872	+	0.255262i	$0.917838\pi$
$384$	−0.827156	−	0.600964i	−0.0422106	−	0.0306678i
$385$	−4.59859	+	8.71459i	−0.234366	+	0.444137i
$386$	−20.4899	+	14.8868i	−1.04291	+	0.757718i
$387$	−10.4021	−	7.55754i	−0.528767	−	0.384171i
$388$	−8.33024	−	6.05228i	−0.422904	−	0.307258i
$389$	16.7470	−	12.1674i	0.849105	−	0.616911i	−0.0757941	−	0.997123i	$-0.524149\pi$
$389$	16.7470	−	12.1674i	0.849105	−	0.616911i	0.924899	+	0.380213i	$0.124149\pi$
$390$	−1.32438	−	9.21344i	−0.0670624	−	0.466541i
$391$	3.44282	+	2.50135i	0.174111	+	0.126499i
$392$	0.309017	+	0.951057i	0.0156077	+	0.0480356i
$393$	18.3497			0.925621
$394$	−5.42968	−	16.7108i	−0.273543	−	0.841879i
$395$	5.39639	+	37.5417i	0.271522	+	1.88893i
$396$	−2.66169	+	8.19184i	−0.133755	+	0.411655i
$397$	−3.87575	+	11.9283i	−0.194518	+	0.598666i	0.805464	+	0.592645i	$0.201916\pi$
$397$	−3.87575	+	11.9283i	−0.194518	+	0.598666i	−0.999982	+	0.00602040i	$0.998084\pi$
$398$	5.60539	−	4.07256i	0.280973	−	0.204139i
$399$	−8.52964			−0.427016
$400$	−4.79756	+	1.40834i	−0.239878	+	0.0704170i
$401$	8.34852			0.416905			0.208453	−	0.978032i	$-0.433157\pi$
$401$	8.34852			0.416905			0.208453	+	0.978032i	$0.433157\pi$
$402$	5.75206	−	4.17912i	0.286887	−	0.208436i
$403$	−10.8379	+	33.3557i	−0.539876	+	1.66157i
$404$	2.13897	−	6.58309i	0.106418	−	0.327521i
$405$	−1.06691	−	1.09790i	−0.0530153	−	0.0545551i
$406$	0.424975	+	1.30794i	0.0210911	+	0.0649118i
$407$	10.1151			0.501385
$408$	−0.497695	−	1.53175i	−0.0246396	−	0.0758328i
$409$	27.8307	+	20.2202i	1.37614	+	0.999825i	0.997229	+	0.0743916i	$0.0237015\pi$
$409$	27.8307	+	20.2202i	1.37614	+	0.999825i	0.378911	+	0.925433i	$0.376299\pi$
$410$	−12.7726	+	6.27931i	−0.630792	+	0.310113i
$411$	7.41431	−	5.38681i	0.365721	−	0.265712i
$412$	−1.49175	−	1.08382i	−0.0734932	−	0.0533960i
$413$	−2.62410	−	1.90652i	−0.129124	−	0.0938137i
$414$	4.27202	−	3.10380i	0.209958	−	0.152544i
$415$	−4.15282	−	4.27343i	−0.203854	−	0.209775i
$416$	3.29386	+	2.39313i	0.161495	+	0.117333i
$417$	2.45867	+	7.56699i	0.120401	+	0.370557i
$418$	36.7626			1.79812
$419$	−6.09562	−	18.7604i	−0.297790	−	0.916505i	−0.982270	−	0.187473i	$-0.939970\pi$
$419$	−6.09562	−	18.7604i	−0.297790	−	0.916505i	0.684479	−	0.729032i	$-0.260030\pi$
$420$	−2.25271	−	0.389924i	−0.109921	−	0.0190263i
$421$	6.59322	−	20.2919i	0.321334	−	0.988965i	−0.651734	−	0.758447i	$-0.725958\pi$
$421$	6.59322	−	20.2919i	0.321334	−	0.988965i	0.973068	−	0.230517i	$-0.0740418\pi$
$422$	−6.96406	+	21.4332i	−0.339005	+	1.04335i
$423$	−10.5908	+	7.69468i	−0.514943	+	0.374128i
$424$	5.93598			0.288277
$425$	−7.41805	−	2.64732i	−0.359828	−	0.128414i
$426$	−7.38092			−0.357607
$427$	7.99537	−	5.80897i	0.386923	−	0.281116i
$428$	2.54422	−	7.83032i	0.122980	−	0.378493i
$429$	−5.66846	+	17.4457i	−0.273676	+	0.842287i
$430$	−6.86455	+	13.0087i	−0.331038	+	0.627335i
$431$	−5.56068	−	17.1140i	−0.267848	−	0.824352i	−0.991024	−	0.133688i	$-0.957318\pi$
$431$	−5.56068	−	17.1140i	−0.267848	−	0.824352i	0.723175	−	0.690665i	$-0.242682\pi$
$432$	−5.06574			−0.243726
$433$	1.30734	+	4.02357i	0.0628267	+	0.193361i	0.977543	−	0.210736i	$-0.0675860\pi$
$433$	1.30734	+	4.02357i	0.0628267	+	0.193361i	−0.914716	+	0.404096i	$0.867586\pi$
$434$	6.96905	+	5.06331i	0.334525	+	0.243047i
$435$	−3.09803	−	0.536242i	−0.148539	−	0.0257108i
$436$	6.43757	−	4.67717i	0.308304	−	0.223996i
$437$	−18.2332	−	13.2472i	−0.872214	−	0.633701i
$438$	8.19865	+	5.95666i	0.391746	+	0.284620i
$439$	29.2825	−	21.2750i	1.39758	−	1.01540i	0.402592	−	0.915379i	$-0.368109\pi$
$439$	29.2825	−	21.2750i	1.39758	−	1.01540i	0.994985	−	0.100020i	$-0.0318908\pi$
$440$	9.70911	+	1.68056i	0.462864	+	0.0801177i
$441$	1.58135	+	1.14892i	0.0753024	+	0.0547104i
$442$	1.98190	+	6.09966i	0.0942693	+	0.290131i
$443$	−5.56347			−0.264328			−0.132164	−	0.991228i	$-0.542193\pi$
$443$	−5.56347			−0.264328			−0.132164	+	0.991228i	$0.542193\pi$
$444$	0.725230	+	2.23203i	0.0344179	+	0.105927i
$445$	−14.5539	+	27.5804i	−0.689920	+	1.30744i
$446$	3.04377	−	9.36777i	0.144127	−	0.443577i
$447$	0.908500	−	2.79608i	0.0429706	−	0.132250i
$448$	0.809017	−	0.587785i	0.0382225	−	0.0277702i
$449$	−24.2722			−1.14548			−0.572738	−	0.819739i	$-0.694119\pi$
$449$	−24.2722			−1.14548			−0.572738	+	0.819739i	$0.694119\pi$
$450$	−5.96855	+	7.73908i	−0.281360	+	0.364824i
$451$	28.0482			1.32074
$452$	−11.4036	+	8.28519i	−0.536380	+	0.389703i
$453$	−3.73210	+	11.4862i	−0.175349	+	0.539669i
$454$	−3.16642	+	9.74524i	−0.148607	+	0.457367i
$455$	8.97063	+	1.55274i	0.420549	+	0.0727935i
$456$	2.63580	+	8.11217i	0.123433	+	0.379887i
$457$	−41.0190			−1.91879			−0.959393	−	0.282071i	$-0.908978\pi$
$457$	−41.0190			−1.91879			−0.959393	+	0.282071i	$0.908978\pi$
$458$	−3.23788	−	9.96516i	−0.151296	−	0.465641i
$459$	−6.45583	−	4.69043i	−0.301332	−	0.218931i
$460$	−4.20987	−	4.33215i	−0.196286	−	0.201987i
$461$	8.66172	−	6.29311i	0.403417	−	0.293099i	−0.367515	−	0.930018i	$-0.619791\pi$
$461$	8.66172	−	6.29311i	0.403417	−	0.293099i	0.770931	+	0.636918i	$0.219791\pi$
$462$	3.64495	+	2.64821i	0.169579	+	0.123206i
$463$	−21.1513	−	15.3673i	−0.982983	−	0.714179i	−0.0246099	−	0.999697i	$-0.507834\pi$
$463$	−21.1513	−	15.3673i	−0.982983	−	0.714179i	−0.958373	+	0.285518i	$0.907834\pi$
$464$	1.11260	−	0.808350i	0.0516511	−	0.0375267i
$465$	−17.6735	+	8.68875i	−0.819591	+	0.402931i
$466$	−13.4725	−	9.78833i	−0.624101	−	0.453436i
$467$	5.10553	+	15.7132i	0.236256	+	0.727120i	0.996952	+	0.0780128i	$0.0248575\pi$
$467$	5.10553	+	15.7132i	0.236256	+	0.727120i	−0.760697	+	0.649108i	$0.775142\pi$
$468$	7.95826			0.367871
$469$	2.14891	+	6.61367i	0.0992276	+	0.305391i
$470$	10.4368	+	10.7399i	0.481412	+	0.495394i
$471$	4.51108	−	13.8837i	0.207860	−	0.639727i
$472$	−1.00232	+	3.08481i	−0.0461354	+	0.141990i
$473$	23.4506	−	17.0379i	1.07826	−	0.783402i
$474$	17.3420			0.796545
$475$	39.2862	+	14.0203i	1.80257	+	0.643294i
$476$	1.57526			0.0722017
$477$	9.38686	−	6.81996i	0.429795	−	0.312264i
$478$	−7.65369	+	23.5556i	−0.350072	+	1.07741i
$479$	−9.09004	+	27.9763i	−0.415334	+	1.27827i	0.496617	+	0.867970i	$0.334575\pi$
$479$	−9.09004	+	27.9763i	−0.415334	+	1.27827i	−0.911951	+	0.410298i	$0.865425\pi$
$480$	0.325284	+	2.26294i	0.0148471	+	0.103289i
$481$	−2.88798	−	8.88829i	−0.131681	−	0.405271i
$482$	22.0593			1.00477
$483$	−0.853527	−	2.62689i	−0.0388368	−	0.119527i
$484$	−6.81048	−	4.94810i	−0.309567	−	0.224914i
$485$	3.27592	+	22.7900i	0.148752	+	1.03484i
$486$	−12.8611	+	9.34415i	−0.583392	+	0.423859i
$487$	−5.43374	−	3.94784i	−0.246226	−	0.178894i	0.457826	−	0.889042i	$-0.348628\pi$
$487$	−5.43374	−	3.94784i	−0.246226	−	0.178894i	−0.704053	+	0.710148i	$0.748628\pi$
$488$	−7.99537	−	5.80897i	−0.361933	−	0.262960i
$489$	2.43658	−	1.77028i	0.110186	−	0.0800548i
$490$	1.04357	−	1.97762i	0.0471435	−	0.0893396i
$491$	13.8897	+	10.0914i	0.626833	+	0.455421i	0.855302	−	0.518131i	$-0.173372\pi$
$491$	13.8897	+	10.0914i	0.626833	+	0.455421i	−0.228469	+	0.973551i	$0.573372\pi$
$492$	2.01100	+	6.18923i	0.0906630	+	0.279032i
$493$	2.16637			0.0975682
$494$	−10.4962	−	32.3039i	−0.472246	−	1.45342i
$495$	17.2843	−	8.49741i	0.776873	−	0.381930i
$496$	2.66194	−	8.19261i	0.119525	−	0.367859i
$497$	2.23081	−	6.86573i	0.100066	−	0.307970i
$498$	−2.20428	+	1.60150i	−0.0987760	+	0.0717650i
$499$	−8.61524			−0.385671			−0.192836	−	0.981231i	$-0.561768\pi$
$499$	−8.61524			−0.385671			−0.192836	+	0.981231i	$0.561768\pi$
$500$	9.73468	+	5.49872i	0.435348	+	0.245910i
$501$	−0.452738			−0.0202268
$502$	−12.3092	+	8.94312i	−0.549384	+	0.399151i
$503$	7.66197	−	23.5811i	0.341630	−	1.05143i	−0.621733	−	0.783230i	$-0.713571\pi$
$503$	7.66197	−	23.5811i	0.341630	−	1.05143i	0.963363	−	0.268201i	$-0.0864291\pi$
$504$	0.604022	−	1.85899i	0.0269053	−	0.0828059i
$505$	−13.8900	+	6.82865i	−0.618095	+	0.303871i
$506$	3.67868	+	11.3218i	0.163537	+	0.503316i
$507$	3.65682			0.162405
$508$	5.82336	+	17.9225i	0.258370	+	0.795181i
$509$	−7.13111	−	5.18105i	−0.316081	−	0.229646i	0.418420	−	0.908253i	$-0.362584\pi$
$509$	−7.13111	−	5.18105i	−0.316081	−	0.229646i	−0.734501	+	0.678607i	$0.762584\pi$
$510$	−1.68074	+	3.18510i	−0.0744245	+	0.141039i
$511$	−8.01886	+	5.82604i	−0.354733	+	0.257729i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$	34.1902	+	24.8407i	1.50954	+	1.09674i
$514$	−18.2674	+	13.2721i	−0.805743	+	0.585406i
$515$	0.586640	+	4.08115i	0.0258505	+	0.179837i
$516$	5.44100	+	3.95312i	0.239527	+	0.174026i
$517$	−9.11987	−	28.0681i	−0.401092	−	1.23443i
$518$	−2.29543			−0.100855
$519$	6.26051	+	19.2679i	0.274806	+	0.845766i
$520$	−1.29533	−	9.01139i	−0.0568041	−	0.395176i
$521$	9.26236	−	28.5066i	0.405791	−	1.24890i	−0.514441	−	0.857526i	$-0.672001\pi$
$521$	9.26236	−	28.5066i	0.405791	−	1.24890i	0.920233	−	0.391372i	$-0.127999\pi$
$522$	0.830679	−	2.55657i	0.0363578	−	0.111898i
$523$	12.7135	−	9.23693i	0.555924	−	0.403903i	−0.274041	−	0.961718i	$-0.588360\pi$
$523$	12.7135	−	9.23693i	0.555924	−	0.403903i	0.829965	+	0.557815i	$0.188360\pi$
$524$	17.9473			0.784033
$525$	2.88521	+	4.22009i	0.125921	+	0.184180i
$526$	−13.1027			−0.571305
$527$	10.9780	−	7.97602i	0.478211	−	0.347441i
$528$	1.39225	−	4.28490i	0.0605898	−	0.186476i
$529$	−4.85215	+	14.9334i	−0.210963	+	0.649278i
$530$	−9.25031	−	9.51899i	−0.401808	−	0.413478i
$531$	1.95918	+	6.02975i	0.0850213	+	0.261669i
$532$	−8.34259			−0.361697
$533$	−8.00813	−	24.6465i	−0.346870	−	1.06756i
$534$	11.5358	+	8.38122i	0.499201	+	0.362691i
$535$	−16.5215	+	8.12240i	−0.714289	+	0.351162i
$536$	5.62593	−	4.08747i	0.243003	−	0.176552i
$537$	−15.8111	−	11.4874i	−0.682297	−	0.495718i
$538$	−8.75623	−	6.36178i	−0.377508	−	0.274276i
$539$	−3.56502	+	2.59014i	−0.153556	+	0.111565i
$540$	7.89418	+	8.12347i	0.339711	+	0.349578i
$541$	2.99567	+	2.17648i	0.128794	+	0.0935743i	0.650317	−	0.759663i	$-0.274636\pi$
$541$	2.99567	+	2.17648i	0.128794	+	0.0935743i	−0.521523	+	0.853237i	$0.674636\pi$
$542$	2.45860	+	7.56678i	0.105606	+	0.325021i
$543$	13.3365			0.572322
$544$	−0.486781	−	1.49816i	−0.0208706	−	0.0642330i
$545$	−17.5323	−	3.03469i	−0.751001	−	0.129992i
$546$	1.28635	−	3.95899i	0.0550508	−	0.169429i
$547$	−0.560613	+	1.72539i	−0.0239701	+	0.0737723i	−0.962326	−	0.271898i	$-0.912349\pi$
$547$	−0.560613	+	1.72539i	−0.0239701	+	0.0737723i	0.938356	+	0.345671i	$0.112349\pi$
$548$	7.25172	−	5.26868i	0.309778	−	0.225067i
$549$	−19.3175			−0.824451
$550$	−12.4352	−	18.1885i	−0.530238	−	0.775560i
$551$	−11.4731			−0.488772
$552$	−2.23456	+	1.62350i	−0.0951093	+	0.0691010i
$553$	−5.24146	+	16.1315i	−0.222889	+	0.685983i
$554$	6.19719	−	19.0730i	0.263293	−	0.810333i
$555$	2.44914	−	4.64126i	0.103960	−	0.197011i
$556$	2.40475	+	7.40106i	0.101984	+	0.313875i
$557$	37.0490			1.56981			0.784907	−	0.619613i	$-0.212711\pi$
$557$	37.0490			1.56981			0.784907	+	0.619613i	$0.212711\pi$
$558$	−5.20318	−	16.0137i	−0.220268	−	0.677916i
$559$	−21.6669	−	15.7419i	−0.916413	−	0.665813i
$560$	−2.20331	−	0.381373i	−0.0931066	−	0.0161160i
$561$	5.74174	−	4.17161i	0.242416	−	0.176126i
$562$	14.1135	+	10.2540i	0.595340	+	0.432540i
$563$	−4.44274	−	3.22784i	−0.187239	−	0.136037i	0.490217	−	0.871601i	$-0.336918\pi$
$563$	−4.44274	−	3.22784i	−0.187239	−	0.136037i	−0.677456	+	0.735563i	$0.736918\pi$
$564$	5.53974	−	4.02486i	0.233265	−	0.169477i
$565$	31.0569	+	5.37569i	1.30658	+	0.226157i
$566$	11.3041	+	8.21289i	0.475146	+	0.345214i
$567$	−0.211567	−	0.651135i	−0.00888496	−	0.0273451i
$568$	−7.21906			−0.302905
$569$	7.62719	+	23.4741i	0.319749	+	0.984085i	0.973756	+	0.227597i	$0.0730867\pi$
$569$	7.62719	+	23.4741i	0.319749	+	0.984085i	−0.654007	+	0.756489i	$0.726913\pi$
$570$	8.90125	−	16.8684i	0.372832	−	0.706538i
$571$	−14.0734	+	43.3134i	−0.588952	+	1.81261i	−0.00616682	+	0.999981i	$0.501963\pi$
$571$	−14.0734	+	43.3134i	−0.588952	+	1.81261i	−0.582785	+	0.812626i	$0.698037\pi$
$572$	−5.54415	+	17.0631i	−0.231813	+	0.713446i
$573$	−7.71368	+	5.60432i	−0.322244	+	0.234124i
$574$	−6.36503			−0.265671
$575$	−0.386630	+	13.5020i	−0.0161236	+	0.563071i
$576$	−1.95466			−0.0814440
$577$	24.5274	−	17.8202i	1.02109	−	0.741864i	0.0545820	−	0.998509i	$-0.482617\pi$
$577$	24.5274	−	17.8202i	1.02109	−	0.741864i	0.966506	+	0.256646i	$0.0826174\pi$
$578$	−4.48648	+	13.8080i	−0.186613	+	0.574336i
$579$	8.00193	−	24.6274i	0.332549	−	1.02348i
$580$	−3.03009	−	0.524483i	−0.125818	−	0.0217780i
$581$	−0.823495	−	2.53446i	−0.0341643	−	0.105147i
$582$	10.5276			0.436383
$583$	8.08313	+	24.8773i	0.334769	+	1.03031i
$584$	8.01886	+	5.82604i	0.331823	+	0.241083i
$585$	−12.4017	−	12.7619i	−0.512748	−	0.527641i
$586$	−3.43702	+	2.49714i	−0.141982	+	0.103156i
$587$	14.6095	+	10.6144i	0.602998	+	0.438104i	0.846942	−	0.531686i	$-0.178441\pi$
$587$	14.6095	+	10.6144i	0.602998	+	0.438104i	−0.243944	+	0.969789i	$0.578441\pi$
$588$	−0.827156	−	0.600964i	−0.0341113	−	0.0247833i
$589$	−58.1400	+	42.2412i	−2.39562	+	1.74052i
$590$	6.50879	−	3.19988i	0.267963	−	0.131737i
$591$	14.5338	+	10.5594i	0.597840	+	0.434356i
$592$	0.709327	+	2.18308i	0.0291531	+	0.0897242i
$593$	−28.8155			−1.18331			−0.591655	−	0.806191i	$-0.701525\pi$
$593$	−28.8155			−1.18331			−0.591655	+	0.806191i	$0.701525\pi$
$594$	−6.89811	−	21.2302i	−0.283033	−	0.871086i
$595$	−2.45479	−	2.52609i	−0.100637	−	0.103560i
$596$	0.888577	−	2.73476i	0.0363975	−	0.112020i
$597$	−2.18907	+	6.73728i	−0.0895928	+	0.275738i
$598$	8.89838	−	6.46505i	0.363882	−	0.264376i
$599$	40.6145			1.65946			0.829731	−	0.558163i	$-0.188494\pi$
$599$	40.6145			1.65946			0.829731	+	0.558163i	$0.188494\pi$
$600$	3.12197	−	4.04808i	0.127454	−	0.165262i
$601$	−5.00100			−0.203995			−0.101998	−	0.994785i	$-0.532523\pi$
$601$	−5.00100			−0.203995			−0.101998	+	0.994785i	$0.532523\pi$
$602$	−5.32169	+	3.86643i	−0.216896	+	0.157584i
$603$	4.20038	−	12.9275i	0.171053	−	0.526447i
$604$	−3.65026	+	11.2343i	−0.148527	+	0.457118i
$605$	2.67827	+	18.6322i	0.108887	+	0.757507i
$606$	2.18693	+	6.73069i	0.0888381	+	0.273415i
$607$	−19.7534			−0.801767			−0.400884	−	0.916129i	$-0.631297\pi$
$607$	−19.7534			−0.801767			−0.400884	+	0.916129i	$0.631297\pi$
$608$	2.57800	+	7.93428i	0.104552	+	0.321777i
$609$	−1.13754	−	0.826474i	−0.0460956	−	0.0334904i
$610$	3.14423	+	21.8738i	0.127306	+	0.885645i
$611$	−22.0601	+	16.0276i	−0.892456	+	0.648407i
$612$	−2.49103	−	1.80984i	−0.100694	−	0.0731584i
$613$	28.8267	+	20.9439i	1.16430	+	0.845914i	0.990316	−	0.138834i	$-0.0443354\pi$
$613$	28.8267	+	20.9439i	1.16430	+	0.845914i	0.173986	+	0.984748i	$0.444335\pi$
$614$	−0.330934	+	0.240437i	−0.0133554	+	0.00970327i
$615$	6.79126	−	12.8698i	0.273850	−	0.518961i
$616$	3.56502	+	2.59014i	0.143639	+	0.104360i
$617$	−14.0449	−	43.2257i	−0.565425	−	1.74020i	−0.666685	−	0.745339i	$-0.732288\pi$
$617$	−14.0449	−	43.2257i	−0.565425	−	1.74020i	0.101260	−	0.994860i	$-0.467712\pi$
$618$	1.88525			0.0758357
$619$	−1.35635	−	4.17441i	−0.0545162	−	0.167784i	0.920091	−	0.391704i	$-0.128114\pi$
$619$	−1.35635	−	4.17441i	−0.0545162	−	0.167784i	−0.974607	+	0.223921i	$0.928114\pi$
$620$	−17.2860	+	8.49822i	−0.694221	+	0.341297i
$621$	−4.22893	+	13.0153i	−0.169701	+	0.522287i
$622$	−4.85032	+	14.9278i	−0.194480	+	0.598549i
$623$	−11.2828	+	8.19743i	−0.452035	+	0.328423i
$624$	−4.16273			−0.166642
$625$	−6.35220	−	24.1795i	−0.254088	−	0.967181i
$626$	−9.95436			−0.397856
$627$	−30.4084	+	22.0930i	−1.21439	+	0.882308i
$628$	4.41216	−	13.5792i	0.176064	−	0.541870i
$629$	−1.11737	+	3.43891i	−0.0445525	+	0.137119i
$630$	−3.92236	+	1.92833i	−0.156271	+	0.0768266i
$631$	11.2188	+	34.5280i	0.446615	+	1.37454i	0.880703	+	0.473669i	$0.157071\pi$
$631$	11.2188	+	34.5280i	0.446615	+	1.37454i	−0.434088	+	0.900871i	$0.642929\pi$
$632$	16.9617			0.674701
$633$	−7.12020	−	21.9137i	−0.283003	−	0.870993i
$634$	9.16395	+	6.65800i	0.363947	+	0.264423i
$635$	19.6658	−	37.2678i	0.780414	−	1.47893i
$636$	−4.90998	+	3.56731i	−0.194694	+	0.141453i
$637$	3.29386	+	2.39313i	0.130508	+	0.0948194i
$638$	4.90279	+	3.56208i	0.194103	+	0.141024i
$639$	−11.4159	+	8.29410i	−0.451604	+	0.328110i
$640$	0.318151	+	2.21332i	0.0125760	+	0.0874891i
$641$	−26.9066	−	19.5488i	−1.06275	−	0.772132i	−0.0881536	−	0.996107i	$-0.528097\pi$
$641$	−26.9066	−	19.5488i	−1.06275	−	0.772132i	−0.974595	+	0.223975i	$0.928097\pi$
$642$	2.60127	+	8.00588i	0.102664	+	0.315967i
$643$	−36.8674			−1.45391			−0.726955	−	0.686685i	$-0.759065\pi$
$643$	−36.8674			−1.45391			−0.726955	+	0.686685i	$0.759065\pi$
$644$	−0.834810	−	2.56928i	−0.0328961	−	0.101244i
$645$	−2.13971	−	14.8856i	−0.0842510	−	0.586119i
$646$	−4.06101	+	12.4985i	−0.159778	+	0.491748i
$647$	0.385657	−	1.18693i	0.0151618	−	0.0466631i	−0.943189	−	0.332256i	$-0.892190\pi$
$647$	0.385657	−	1.18693i	0.0151618	−	0.0466631i	0.958351	+	0.285592i	$0.0921904\pi$
$648$	−0.553889	+	0.402424i	−0.0217588	+	0.0158087i
$649$	−14.2931			−0.561054
$650$	−12.4322	+	16.1201i	−0.487630	+	0.632281i
$651$	−8.80736			−0.345188
$652$	2.38315	−	1.73146i	0.0933313	−	0.0678092i
$653$	−0.640026	+	1.96980i	−0.0250461	+	0.0770841i	−0.962798	−	0.270221i	$-0.912903\pi$
$653$	−0.640026	+	1.96980i	−0.0250461	+	0.0770841i	0.937752	+	0.347305i	$0.112903\pi$
$654$	−2.51406	+	7.73750i	−0.0983077	+	0.302560i
$655$	−27.9682	−	28.7805i	−1.09281	−	1.12455i
$656$	1.96690	+	6.05350i	0.0767946	+	0.236350i
$657$	19.3743			0.755862
$658$	2.06959	+	6.36954i	0.0806810	+	0.248311i
$659$	12.8963	+	9.36971i	0.502369	+	0.364992i	0.809921	−	0.586539i	$-0.199510\pi$
$659$	12.8963	+	9.36971i	0.502369	+	0.364992i	−0.307552	+	0.951531i	$0.599510\pi$
$660$	−9.04091	+	4.44474i	−0.351917	+	0.173011i
$661$	−9.89877	+	7.19187i	−0.385017	+	0.279732i	−0.763411	−	0.645913i	$-0.776477\pi$
$661$	−9.89877	+	7.19187i	−0.385017	+	0.279732i	0.378393	+	0.925645i	$0.376477\pi$
$662$	−4.27795	−	3.10811i	−0.166267	−	0.120800i
$663$	−5.30501	−	3.85432i	−0.206030	−	0.149689i
$664$	−2.15594	+	1.56638i	−0.0836667	+	0.0607874i
$665$	13.0006	+	13.3782i	0.504143	+	0.518786i
$666$	3.62988	+	2.63726i	0.140655	+	0.102192i
$667$	−1.14807	−	3.53339i	−0.0444534	−	0.136814i
$668$	−0.442810			−0.0171328
$669$	3.11202	+	9.57781i	0.120318	+	0.370299i
$670$	−15.3218	−	2.65208i	−0.591934	−	0.102459i
$671$	13.4576	−	41.4182i	0.519525	−	1.59893i
$672$	−0.315945	+	0.972380i	−0.0121879	+	0.0375104i
$673$	1.58019	−	1.14808i	0.0609119	−	0.0442551i	−0.556913	−	0.830571i	$-0.688014\pi$
$673$	1.58019	−	1.14808i	0.0609119	−	0.0442551i	0.617825	+	0.786316i	$0.288014\pi$
$674$	10.5936			0.408050
$675$	0.724993	−	25.3183i	0.0279050	−	0.974503i
$676$	3.57662			0.137562
$677$	3.88214	−	2.82054i	0.149203	−	0.108402i	−0.510680	−	0.859771i	$-0.670606\pi$
$677$	3.88214	−	2.82054i	0.149203	−	0.108402i	0.659882	+	0.751369i	$0.270606\pi$
$678$	4.45344	−	13.7063i	0.171034	−	0.526387i
$679$	−3.18187	+	9.79279i	−0.122109	+	0.375813i
$680$	−1.64388	+	3.11525i	−0.0630401	+	0.119464i
$681$	−3.23741	−	9.96373i	−0.124058	−	0.381811i
$682$	37.9595			1.45355
$683$	−8.06734	−	24.8287i	−0.308688	−	0.950045i	−0.978275	−	0.207311i	$-0.933529\pi$
$683$	−8.06734	−	24.8287i	−0.308688	−	0.950045i	0.669587	−	0.742734i	$-0.266471\pi$
$684$	13.1926	+	9.58495i	0.504430	+	0.366490i
$685$	−19.7496	−	3.41848i	−0.754593	−	0.130614i
$686$	0.809017	−	0.587785i	0.0308884	−	0.0224417i
$687$	8.66693	+	6.29689i	0.330664	+	0.240241i
$688$	5.32169	+	3.86643i	0.202887	+	0.147406i
$689$	19.5523	−	14.2056i	0.744884	−	0.541190i
$690$	6.08569	+	1.05338i	0.231678	+	0.0401015i
$691$	−5.11074	−	3.71317i	−0.194422	−	0.141256i	0.486316	−	0.873783i	$-0.338341\pi$
$691$	−5.11074	−	3.71317i	−0.194422	−	0.141256i	−0.680737	+	0.732527i	$0.738341\pi$
$692$	6.12323	+	18.8454i	0.232770	+	0.716393i
$693$	8.61341			0.327196
$694$	−9.56074	−	29.4249i	−0.362921	−	1.11695i
$695$	8.12096	−	15.3897i	0.308046	−	0.583764i
$696$	−0.434503	+	1.33726i	−0.0164698	+	0.0506888i
$697$	−3.09837	+	9.53582i	−0.117359	+	0.361195i
$698$	−7.47232	+	5.42896i	−0.282832	+	0.205489i
$699$	17.0263			0.643993
$700$	2.82194	+	4.12755i	0.106659	+	0.156007i
$701$	−6.70214			−0.253136			−0.126568	−	0.991958i	$-0.540396\pi$
$701$	−6.70214			−0.253136			−0.126568	+	0.991958i	$0.540396\pi$
$702$	−16.6859	+	12.1230i	−0.629768	+	0.457553i
$703$	5.91762	−	18.2126i	0.223187	−	0.686900i
$704$	1.36172	−	4.19094i	0.0513217	−	0.157952i
$705$	−15.0871	−	2.61145i	−0.568214	−	0.0983530i
$706$	2.12251	+	6.53241i	0.0798816	+	0.245850i
$707$	−6.92187			−0.260324
$708$	−1.02479	−	3.15398i	−0.0385140	−	0.118534i
$709$	−15.3408	−	11.1457i	−0.576135	−	0.418587i	0.261194	−	0.965286i	$-0.415884\pi$
$709$	−15.3408	−	11.1457i	−0.576135	−	0.418587i	−0.837329	+	0.546700i	$0.815884\pi$
$710$	11.2498	+	11.5765i	0.422197	+	0.434460i
$711$	26.8224	−	19.4876i	1.00592	−	0.730842i
$712$	11.2828	+	8.19743i	0.422840	+	0.307212i
$713$	−18.8269	−	13.6785i	−0.705073	−	0.512266i
$714$	−1.30298	+	0.946672i	−0.0487629	+	0.0354283i
$715$	36.0023	−	17.6996i	1.34641	−	0.661929i
$716$	−15.4643	−	11.2355i	−0.577929	−	0.419890i
$717$	−7.82529	−	24.0838i	−0.292241	−	0.899425i
$718$	4.86386			0.181518
$719$	−8.65308	−	26.6314i	−0.322705	−	0.993185i	−0.972466	−	0.233046i	$-0.925131\pi$
$719$	−8.65308	−	26.6314i	−0.322705	−	0.993185i	0.649760	−	0.760139i	$-0.274869\pi$
$720$	3.04603	+	3.13450i	0.113519	+	0.116816i
$721$	−0.569798	+	1.75366i	−0.0212204	+	0.0653096i
$722$	15.6359	−	48.1224i	0.581908	−	1.79093i
$723$	−18.2465	+	13.2568i	−0.678594	+	0.493027i
$724$	13.0440			0.484776
$725$	3.88086	+	5.67640i	0.144132	+	0.210816i
$726$	8.60696			0.319434
$727$	−4.12145	+	2.99441i	−0.152856	+	0.111056i	−0.661585	−	0.749871i	$-0.730116\pi$
$727$	−4.12145	+	2.99441i	−0.152856	+	0.111056i	0.508728	+	0.860927i	$0.330116\pi$
$728$	1.25814	−	3.87217i	0.0466299	−	0.143512i
$729$	4.38796	−	13.5047i	0.162517	−	0.500176i
$730$	−3.15347	−	21.9381i	−0.116715	−	0.811965i
$731$	3.20203	+	9.85483i	0.118431	+	0.364494i
$732$	10.1044			0.373469
$733$	3.16279	+	9.73405i	0.116820	+	0.359535i	0.992322	−	0.123679i	$-0.0394692\pi$
$733$	3.16279	+	9.73405i	0.116820	+	0.359535i	−0.875502	+	0.483214i	$0.839469\pi$
$734$	4.25593	+	3.09211i	0.157089	+	0.114132i
$735$	0.325284	+	2.26294i	0.0119983	+	0.0834699i
$736$	−2.18556	+	1.58790i	−0.0805608	+	0.0585309i
$737$	24.7913	+	18.0119i	0.913198	+	0.663477i
$738$	10.0653	+	7.31290i	0.370510	+	0.269191i
$739$	−2.36039	+	1.71492i	−0.0868282	+	0.0630844i	−0.630352	−	0.776309i	$-0.717090\pi$
$739$	−2.36039	+	1.71492i	−0.0868282	+	0.0630844i	0.543524	+	0.839393i	$0.317090\pi$
$740$	2.39543	−	4.53948i	0.0880579	−	0.166875i
$741$	28.0955	+	20.4126i	1.03211	+	0.749874i
$742$	−1.83432	−	5.64546i	−0.0673400	−	0.207251i
$743$	13.8317			0.507436			0.253718	−	0.967278i	$-0.418346\pi$
$743$	13.8317			0.507436			0.253718	+	0.967278i	$0.418346\pi$
$744$	2.72163	+	8.37630i	0.0997796	+	0.307090i
$745$	−5.77019	+	2.83677i	−0.211403	+	0.103931i
$746$	−6.62935	+	20.4030i	−0.242718	+	0.747008i
$747$	−1.60965	+	4.95399i	−0.0588940	+	0.181257i
$748$	5.61582	−	4.08013i	0.205335	−	0.149184i
$749$	−8.23328			−0.300838
$750$	−11.3566	+	1.30189i	−0.414686	+	0.0475383i
$751$	0.384130			0.0140171			0.00700855	−	0.999975i	$-0.497769\pi$
$751$	0.384130			0.0140171			0.00700855	+	0.999975i	$0.497769\pi$
$752$	5.41826	−	3.93659i	0.197583	−	0.143553i
$753$	4.80709	−	14.7947i	0.175180	−	0.539149i
$754$	1.73026	−	5.32519i	0.0630123	−	0.193932i
$755$	23.7038	−	11.6534i	0.862670	−	0.424110i
$756$	1.56540	+	4.81781i	0.0569331	+	0.175222i
$757$	−31.4817			−1.14422			−0.572111	−	0.820176i	$-0.693875\pi$
$757$	−31.4817			−1.14422			−0.572111	+	0.820176i	$0.693875\pi$
$758$	0.0373078	+	0.114822i	0.00135508	+	0.00417051i
$759$	−9.84685	−	7.15415i	−0.357418	−	0.259679i
$760$	8.70605	−	16.4985i	0.315802	−	0.598462i
$761$	−9.21264	+	6.69338i	−0.333958	+	0.242635i	−0.742108	−	0.670280i	$-0.766174\pi$
$761$	−9.21264	+	6.69338i	−0.333958	+	0.242635i	0.408150	+	0.912915i	$0.366174\pi$
$762$	−15.5876	−	11.3250i	−0.564679	−	0.410263i
$763$	−6.43757	−	4.67717i	−0.233056	−	0.169325i
$764$	−7.54452	+	5.48142i	−0.272951	+	0.198311i
$765$	0.979614	+	6.81499i	0.0354180	+	0.246397i
$766$	1.77364	+	1.28862i	0.0640842	+	0.0465599i
$767$	4.08087	+	12.5596i	0.147352	+	0.453502i
$768$	1.02242			0.0368934
$769$	5.48417	+	16.8785i	0.197764	+	0.608656i	0.999933	+	0.0115586i	$0.00367931\pi$
$769$	5.48417	+	16.8785i	0.197764	+	0.608656i	−0.802169	+	0.597097i	$0.796321\pi$
$770$	−1.40197	−	9.75323i	−0.0505234	−	0.351482i
$771$	7.13399	−	21.9562i	0.256924	−	0.790732i
$772$	7.82646	−	24.0874i	0.281680	−	0.866923i
$773$	−32.6049	+	23.6888i	−1.17272	+	0.852028i	−0.991332	−	0.131384i	$-0.958058\pi$
$773$	−32.6049	+	23.6888i	−1.17272	+	0.852028i	−0.181385	+	0.983412i	$0.558058\pi$
$774$	12.8577			0.462159
$775$	40.5653	+	14.4768i	1.45715	+	0.520020i
$776$	10.2967			0.369632
$777$	1.89868	−	1.37947i	0.0681147	−	0.0494882i
$778$	−6.39677	+	19.6872i	−0.229335	+	0.705822i
$779$	16.4091	−	50.5019i	0.587916	−	1.80942i
$780$	6.48697	+	6.67538i	0.232271	+	0.239017i
$781$	−9.83032	−	30.2546i	−0.351756	−	1.08260i
$782$	−4.25556			−0.152178
$783$	2.15281	+	6.62568i	0.0769352	+	0.236782i
$784$	−0.809017	−	0.587785i	−0.0288935	−	0.0209923i
$785$	−28.6514	+	14.0858i	−1.02261	+	0.502742i
$786$	−14.8452	+	10.7857i	−0.529512	+	0.384713i
$787$	−34.6616	−	25.1831i	−1.23555	−	0.897681i	−0.238258	−	0.971202i	$-0.576576\pi$
$787$	−34.6616	−	25.1831i	−1.23555	−	0.897681i	−0.997294	+	0.0735214i	$0.976576\pi$
$788$	14.2151	+	10.3279i	0.506391	+	0.367915i
$789$	10.8380	−	7.87425i	0.385842	−	0.280331i
$790$	−26.4322	−	27.1999i	−0.940416	−	0.967730i
$791$	11.4036	+	8.28519i	0.405465	+	0.294588i
$792$	−2.66169	−	8.19184i	−0.0945790	−	0.291084i
$793$	−40.2373			−1.42887
$794$	−3.87575	−	11.9283i	−0.137545	−	0.423321i
$795$	13.3720	+	2.31458i	0.474257	+	0.0820898i
$796$	−2.14107	+	6.58953i	−0.0758882	+	0.233560i
$797$	15.8221	−	48.6954i	0.560447	−	1.72488i	−0.120659	−	0.992694i	$-0.538501\pi$
$797$	15.8221	−	48.6954i	0.560447	−	1.72488i	0.681106	−	0.732185i	$-0.261499\pi$
$798$	6.90063	−	5.01360i	0.244280	−	0.177479i
$799$	10.5500			0.373233
$800$	3.05351	−	3.95931i	0.107958	−	0.139983i
$801$	27.2602			0.963192
$802$	−6.75409	+	4.90714i	−0.238495	+	0.173277i
$803$	−13.4971	+	41.5399i	−0.476304	+	1.46591i
$804$	−2.19709	+	6.76196i	−0.0774855	+	0.238476i
$805$	−2.81920	+	5.34254i	−0.0993636	+	0.188300i
$806$	−10.8379	−	33.3557i	−0.381750	−	1.17491i
$807$	11.0660			0.389541
$808$	2.13897	+	6.58309i	0.0752489	+	0.231592i
$809$	21.6065	+	15.6980i	0.759643	+	0.551913i	0.898801	−	0.438357i	$-0.144439\pi$
$809$	21.6065	+	15.6980i	0.759643	+	0.551913i	−0.139158	+	0.990270i	$0.544439\pi$
$810$	1.50848	+	0.261105i	0.0530026	+	0.00917430i
$811$	9.40423	−	6.83257i	0.330227	−	0.239924i	−0.410300	−	0.911951i	$-0.634576\pi$
$811$	9.40423	−	6.83257i	0.330227	−	0.239924i	0.740527	+	0.672027i	$0.234576\pi$
$812$	−1.11260	−	0.808350i	−0.0390445	−	0.0283675i
$813$	−6.58101	−	4.78138i	−0.230806	−	0.167690i
$814$	−8.18326	+	5.94549i	−0.286823	+	0.208389i
$815$	−6.49035	−	1.12342i	−0.227347	−	0.0393519i
$816$	1.30298	+	0.946672i	0.0456135	+	0.0331401i
$817$	−16.9580	−	52.1914i	−0.593286	−	1.82595i
$818$	−34.4007			−1.20279
$819$	−2.45924	−	7.56876i	−0.0859327	−	0.264474i
$820$	6.64233	−	12.5876i	0.231960	−	0.439578i
$821$	−4.60448	+	14.1711i	−0.160698	+	0.494576i	−0.998694	−	0.0511002i	$-0.983727\pi$
$821$	−4.60448	+	14.1711i	−0.160698	+	0.494576i	0.837996	+	0.545676i	$0.183727\pi$
$822$	−2.83201	+	8.71604i	−0.0987778	+	0.304007i
$823$	1.48456	−	1.07859i	0.0517483	−	0.0375974i	−0.561610	−	0.827402i	$-0.689818\pi$
$823$	1.48456	−	1.07859i	0.0517483	−	0.0375974i	0.613359	+	0.789804i	$0.289818\pi$
$824$	1.84390			0.0642354
$825$	21.2165	+	7.57163i	0.738663	+	0.263610i
$826$	3.24357			0.112858
$827$	5.46728	−	3.97221i	0.190116	−	0.138127i	−0.488656	−	0.872477i	$-0.662513\pi$
$827$	5.46728	−	3.97221i	0.190116	−	0.138127i	0.678772	+	0.734349i	$0.262513\pi$
$828$	−1.63177	+	5.02206i	−0.0567078	+	0.174529i
$829$	−5.57429	+	17.1559i	−0.193603	+	0.595849i	0.806387	+	0.591388i	$0.201420\pi$
$829$	−5.57429	+	17.1559i	−0.193603	+	0.595849i	−0.999990	+	0.00446083i	$0.998580\pi$
$830$	5.87156	+	1.01632i	0.203805	+	0.0352769i
$831$	6.33613	+	19.5006i	0.219798	+	0.676469i
$832$	−4.07144			−0.141152
$833$	−0.486781	−	1.49816i	−0.0168660	−	0.0519081i
$834$	−6.43687	−	4.67666i	−0.222891	−	0.161939i
$835$	0.690051	+	0.710093i	0.0238802	+	0.0245738i
$836$	−29.7415	+	21.6085i	−1.02863	+	0.747345i
$837$	35.3034	+	25.6495i	1.22027	+	0.886575i
$838$	15.9585	+	11.5946i	0.551278	+	0.400527i
$839$	−10.0635	+	7.31154i	−0.347430	+	0.252423i	−0.747790	−	0.663935i	$-0.768885\pi$
$839$	−10.0635	+	7.31154i	−0.347430	+	0.252423i	0.400360	+	0.916358i	$0.368885\pi$
$840$	2.05167	−	1.00865i	0.0707893	−	0.0348018i
$841$	21.9314	+	15.9341i	0.756255	+	0.549451i
$842$	6.59322	+	20.2919i	0.227218	+	0.699304i
$843$	−17.8363			−0.614316
$844$	−6.96406	−	21.4332i	−0.239713	−	0.737761i
$845$	−5.57362	−	5.73550i	−0.191738	−	0.197307i
$846$	4.04533	−	12.4503i	0.139081	−	0.428049i
$847$	−2.60137	+	8.00620i	−0.0893842	+	0.275096i
$848$	−4.80231	+	3.48908i	−0.164912	+	0.119816i
$849$	−14.2859			−0.490290
$850$	7.55738	−	2.21850i	0.259216	−	0.0760938i
$851$	6.20111			0.212571
$852$	5.97129	−	4.33839i	0.204573	−	0.148631i
$853$	−12.5619	+	38.6616i	−0.430112	+	1.32375i	0.467902	+	0.883781i	$0.345010\pi$
$853$	−12.5619	+	38.6616i	−0.430112	+	1.32375i	−0.898014	+	0.439968i	$0.854990\pi$
$854$	−3.05396	+	9.39912i	−0.104504	+	0.321631i
$855$	−5.18806	−	36.0924i	−0.177428	−	1.23433i
$856$	2.54422	+	7.83032i	0.0869598	+	0.267635i
$857$	−18.2339			−0.622856			−0.311428	−	0.950270i	$-0.600807\pi$
$857$	−18.2339			−0.622856			−0.311428	+	0.950270i	$0.600807\pi$
$858$	−5.66846	−	17.4457i	−0.193518	−	0.595587i
$859$	3.97667	+	2.88922i	0.135682	+	0.0985790i	0.653556	−	0.756878i	$-0.273276\pi$
$859$	3.97667	+	2.88922i	0.135682	+	0.0985790i	−0.517874	+	0.855457i	$0.673276\pi$
$860$	−2.09279	−	14.5591i	−0.0713635	−	0.496462i
$861$	5.26487	−	3.82515i	0.179426	−	0.130361i
$862$	14.5580	+	10.5770i	0.495849	+	0.360255i
$863$	−15.6487	−	11.3694i	−0.532687	−	0.387020i	0.288675	−	0.957427i	$-0.406785\pi$
$863$	−15.6487	−	11.3694i	−0.532687	−	0.387020i	−0.821362	+	0.570407i	$0.806785\pi$
$864$	4.09827	−	2.97757i	0.139426	−	0.101299i
$865$	20.6785	−	39.1868i	0.703088	−	1.33239i
$866$	−3.42266	−	2.48670i	−0.116307	−	0.0845017i
$867$	−4.58708	−	14.1176i	−0.155785	−	0.479458i
$868$	−8.61422			−0.292386
$869$	23.0971	+	71.0854i	0.783514	+	2.41141i
$870$	2.82155	−	1.38715i	0.0956595	−	0.0470286i
$871$	8.74917	−	26.9272i	0.296454	−	0.912392i
$872$	−2.45893	+	7.56782i	−0.0832700	+	0.256279i
$873$	16.2828	−	11.8301i	0.551088	−	0.400389i
$874$	22.5375			0.762343
$875$	2.22142	−	10.9574i	0.0750976	−	0.370429i
$876$	−10.1341			−0.342399
$877$	39.6666	−	28.8195i	1.33945	−	0.973165i	0.339982	−	0.940432i	$-0.389579\pi$
$877$	39.6666	−	28.8195i	1.33945	−	0.973165i	0.999464	−	0.0327329i	$-0.0104211\pi$
$878$	−11.1849	+	34.4237i	−0.377473	+	1.16174i
$879$	1.34226	−	4.13105i	0.0452733	−	0.139337i
$880$	−8.84264	+	4.34727i	−0.298085	+	0.146546i
$881$	−4.88505	−	15.0346i	−0.164581	−	0.506529i	0.834424	−	0.551123i	$-0.185801\pi$
$881$	−4.88505	−	15.0346i	−0.164581	−	0.506529i	−0.999005	+	0.0445939i	$0.985801\pi$
$882$	−1.95466			−0.0658167
$883$	−2.91885	−	8.98329i	−0.0982270	−	0.302312i	0.889854	−	0.456245i	$-0.150806\pi$
$883$	−2.91885	−	8.98329i	−0.0982270	−	0.302312i	−0.988081	+	0.153933i	$0.950806\pi$
$884$	−5.18868	−	3.76980i	−0.174514	−	0.126792i
$885$	−3.46077	+	6.55835i	−0.116332	+	0.220457i
$886$	4.50094	−	3.27013i	0.151212	−	0.109862i
$887$	39.8089	+	28.9228i	1.33665	+	0.971134i	0.999560	+	0.0296618i	$0.00944304\pi$
$887$	39.8089	+	28.9228i	1.33665	+	0.971134i	0.337091	+	0.941472i	$0.390557\pi$
$888$	−1.89868	−	1.37947i	−0.0637155	−	0.0462920i
$889$	15.2458	−	11.0767i	0.511327	−	0.371500i
$890$	−4.43703	−	30.8676i	−0.148730	−	1.03468i
$891$	−2.44077	−	1.77332i	−0.0817689	−	0.0594086i
$892$	3.04377	+	9.36777i	0.101913	+	0.313656i
$893$	−55.8731			−1.86972
$894$	0.908500	+	2.79608i	0.0303848	+	0.0935147i
$895$	6.08145	+	42.3075i	0.203280	+	1.41418i
$896$	−0.309017	+	0.951057i	−0.0103235	+	0.0317726i
$897$	−3.47508	+	10.6952i	−0.116030	+	0.357103i
$898$	19.6366	−	14.2668i	0.655282	−	0.476091i
$899$	−11.8467			−0.395109
$900$	0.279744	−	9.76927i	0.00932480	−	0.325642i
$901$	−9.35069			−0.311517
$902$	−22.6915	+	16.4863i	−0.755544	+	0.548935i
$903$	2.07828	−	6.39628i	0.0691608	−	0.212855i
$904$	4.35578	−	13.4057i	0.144871	−	0.445868i
$905$	−20.3271	−	20.9175i	−0.675694	−	0.695320i
$906$	−3.73210	−	11.4862i	−0.123991	−	0.381604i
$907$	−40.1454			−1.33301			−0.666503	−	0.745502i	$-0.732210\pi$
$907$	−40.1454			−1.33301			−0.666503	+	0.745502i	$0.732210\pi$
$908$	−3.16642	−	9.74524i	−0.105081	−	0.323407i
$909$	10.9459	+	7.95266i	0.363052	+	0.263773i
$910$	−8.17007	+	4.01661i	−0.270835	+	0.133149i
$911$	4.65519	−	3.38219i	0.154233	−	0.112057i	−0.507992	−	0.861362i	$-0.669612\pi$
$911$	4.65519	−	3.38219i	0.154233	−	0.112057i	0.662225	+	0.749305i	$0.269612\pi$
$912$	−6.90063	−	5.01360i	−0.228503	−	0.166017i
$913$	−9.50038	−	6.90243i	−0.314417	−	0.228437i
$914$	33.1850	−	24.1103i	1.09766	−	0.797499i
$915$	−15.7461	−	16.2035i	−0.520552	−	0.535671i
$916$	8.47687	+	6.15880i	0.280084	+	0.203493i
$917$	−5.54603	−	17.0689i	−0.183146	−	0.563666i
$918$	7.97984			0.263374
$919$	14.5860	+	44.8910i	0.481146	+	1.48082i	0.837485	+	0.546460i	$0.184025\pi$
$919$	14.5860	+	44.8910i	0.481146	+	1.48082i	−0.356339	+	0.934357i	$0.615975\pi$
$920$	5.95223	+	1.03028i	0.196239	+	0.0339673i
$921$	0.129240	−	0.397758i	0.00425859	−	0.0131066i
$922$	−3.30848	+	10.1825i	−0.108959	+	0.335342i
$923$	−23.7786	+	17.2762i	−0.782682	+	0.568652i
$924$	−4.50541			−0.148217
$925$	−11.0125	+	3.23274i	−0.362087	+	0.106292i
$926$	26.1444			0.859159
$927$	2.91586	−	2.11849i	0.0957693	−	0.0695805i
$928$	−0.424975	+	1.30794i	−0.0139505	+	0.0429352i
$929$	−5.46207	+	16.8105i	−0.179205	+	0.551535i	−0.999801	−	0.0199738i	$-0.993642\pi$
$929$	−5.46207	+	16.8105i	−0.179205	+	0.551535i	0.820596	+	0.571509i	$0.193642\pi$
$930$	9.19107	−	17.4176i	0.301387	−	0.571145i
$931$	2.57800	+	7.93428i	0.0844906	+	0.260035i
$932$	16.6529			0.545484
$933$	−4.95907	−	15.2625i	−0.162353	−	0.499670i
$934$	−13.3665	−	9.71130i	−0.437364	−	0.317763i
$935$	−15.2943	−	2.64732i	−0.500178	−	0.0865766i
$936$	−6.43837	+	4.67775i	−0.210445	+	0.152897i
$937$	28.7138	+	20.8618i	0.938038	+	0.681525i	0.947948	−	0.318426i	$-0.103154\pi$
$937$	28.7138	+	20.8618i	0.938038	+	0.681525i	−0.00990931	+	0.999951i	$0.503154\pi$
$938$	−5.62593	−	4.08747i	−0.183693	−	0.133461i
$939$	8.23381	−	5.98221i	0.268700	−	0.195222i
$940$	−14.7563	−	2.55418i	−0.481296	−	0.0833083i
$941$	−2.28583	−	1.66075i	−0.0745160	−	0.0541390i	0.549904	−	0.835228i	$-0.314664\pi$
$941$	−2.28583	−	1.66075i	−0.0745160	−	0.0541390i	−0.624420	+	0.781089i	$0.714664\pi$
$942$	4.51108	+	13.8837i	0.146979	+	0.452355i
$943$	17.1951			0.559951
$944$	−1.00232	−	3.08481i	−0.0326226	−	0.100402i
$945$	5.28644	−	10.0181i	0.171968	−	0.325889i
$946$	−8.95733	+	27.5678i	−0.291228	+	0.896308i
$947$	−8.54359	+	26.2945i	−0.277629	+	0.854455i	0.710882	+	0.703311i	$0.248296\pi$
$947$	−8.54359	+	26.2945i	−0.277629	+	0.854455i	−0.988512	+	0.151144i	$0.951704\pi$
$948$	−14.0300	+	10.1934i	−0.455673	+	0.331065i
$949$	40.3555			1.31000
$950$	−40.0241	+	11.7492i	−1.29855	+	0.381195i
$951$	−11.5812			−0.375547
$952$	−1.27441	+	0.925912i	−0.0413038	+	0.0300090i
$953$	−6.58610	+	20.2699i	−0.213345	+	0.656607i	0.785922	+	0.618325i	$0.212189\pi$
$953$	−6.58610	+	20.2699i	−0.213345	+	0.656607i	−0.999267	+	0.0382821i	$0.987811\pi$
$954$	−3.58546	+	11.0349i	−0.116084	+	0.357269i
$955$	20.5470	+	3.55651i	0.664886	+	0.115086i
$956$	−7.65369	−	23.5556i	−0.247538	−	0.761844i
$957$	−6.19605			−0.200290
$958$	−9.09004	−	27.9763i	−0.293686	−	0.903872i
$959$	−7.25172	−	5.26868i	−0.234170	−	0.170135i
$960$	−1.59329	−	1.63956i	−0.0514231	−	0.0529166i
$961$	−34.9535	+	25.3952i	−1.12753	+	0.819199i
$962$	7.56083	+	5.49327i	0.243771	+	0.177110i
$963$	13.0197	+	9.45937i	0.419554	+	0.304824i
$964$	−17.8463	+	12.9661i	−0.574792	+	0.417611i
$965$	−50.8230	+	24.9859i	−1.63605	+	0.804323i
$966$	2.23456	+	1.62350i	0.0718959	+	0.0522354i
$967$	9.16732	+	28.2141i	0.294801	+	0.907305i	0.983288	+	0.182056i	$0.0582752\pi$
$967$	9.16732	+	28.2141i	0.294801	+	0.907305i	−0.688487	+	0.725249i	$0.741725\pi$
$968$	8.41822			0.270572
$969$	−4.15207	−	12.7787i	−0.133384	−	0.410512i
$970$	−16.0459	−	16.5119i	−0.515203	−	0.530167i
$971$	10.9045	−	33.5607i	0.349943	−	1.07701i	−0.608941	−	0.793216i	$-0.708405\pi$
$971$	10.9045	−	33.5607i	0.349943	−	1.07701i	0.958884	−	0.283798i	$-0.0915946\pi$
$972$	4.91251	−	15.1192i	0.157569	−	0.484947i
$973$	6.29571	−	4.57410i	0.201831	−	0.146639i
$974$	6.71647			0.215210
$975$	0.595756	−	20.8051i	0.0190795	−	0.666296i
$976$	9.88282			0.316341
$977$	−7.23126	+	5.25382i	−0.231349	+	0.168085i	−0.697420	−	0.716662i	$-0.745669\pi$
$977$	−7.23126	+	5.25382i	−0.231349	+	0.168085i	0.466072	+	0.884747i	$0.345669\pi$
$978$	−0.930691	+	2.86437i	−0.0297602	+	0.0915926i
$979$	−18.9909	+	58.4480i	−0.606952	+	1.86801i
$980$	0.318151	+	2.21332i	0.0101630	+	0.0707019i
$981$	4.80637	+	14.7925i	0.153455	+	0.472287i
$982$	−17.1686			−0.547872
$983$	−2.15273	−	6.62542i	−0.0686614	−	0.211318i	0.910838	−	0.412763i	$-0.135436\pi$
$983$	−2.15273	−	6.62542i	−0.0686614	−	0.211318i	−0.979500	+	0.201445i	$0.935436\pi$
$984$	−5.26487	−	3.82515i	−0.167838	−	0.121941i
$985$	−5.59017	−	38.8898i	−0.178118	−	1.23913i
$986$	−1.75263	+	1.27336i	−0.0558150	+	0.0405520i
$987$	−5.53974	−	4.02486i	−0.176332	−	0.128113i
$988$	27.4794	+	19.9649i	0.874235	+	0.635169i
$989$	14.3765	−	10.4452i	0.457148	−	0.332137i
$990$	−8.98866	+	17.0340i	−0.285678	+	0.541377i
$991$	37.6631	+	27.3639i	1.19641	+	0.869241i	0.993927	−	0.110045i	$-0.0350994\pi$
$991$	37.6631	+	27.3639i	1.19641	+	0.869241i	0.202482	+	0.979286i	$0.435099\pi$
$992$	2.66194	+	8.19261i	0.0845167	+	0.260116i
$993$	5.40639			0.171567
$994$	2.23081	+	6.86573i	0.0707571	+	0.217768i
$995$	13.9036	−	6.83534i	0.440772	−	0.216695i
$996$	0.841959	−	2.59128i	0.0266785	−	0.0821080i
$997$	4.96523	−	15.2814i	0.157251	−	0.483967i	−0.841131	−	0.540831i	$-0.818110\pi$
$997$	4.96523	−	15.2814i	0.157251	−	0.483967i	0.998382	+	0.0568634i	$0.0181100\pi$
$998$	6.96988	−	5.06391i	0.220628	−	0.160295i
$999$	−11.6281			−0.367895

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.2.h.c.211.3	yes	16
25.4	even	10		8750.2.a.s.1.4		8
25.16	even	5	inner	350.2.h.c.141.3	✓	16
25.21	even	5		8750.2.a.u.1.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.2.h.c.141.3	✓	16	25.16	even	5	inner
350.2.h.c.211.3	yes	16	1.1	even	1	trivial
8750.2.a.s.1.4		8	25.4	even	10
8750.2.a.u.1.5		8	25.21	even	5

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:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	350.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{2} +(0.315945 - 0.972380i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-2.00668 + 0.986533i) q^{5} +(0.315945 + 0.972380i) q^{6} -1.00000 q^{7} +(0.309017 + 0.951057i) q^{8} +(1.58135 + 1.14892i) q^{9} +O(q^{10})\)	\(q+(-0.809017 + 0.587785i) q^{2} +(0.315945 - 0.972380i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-2.00668 + 0.986533i) q^{5} +(0.315945 + 0.972380i) q^{6} -1.00000 q^{7} +(0.309017 + 0.951057i) q^{8} +(1.58135 + 1.14892i) q^{9} +(1.04357 - 1.97762i) q^{10} +(-3.56502 + 2.59014i) q^{11} +(-0.827156 - 0.600964i) q^{12} +(3.29386 + 2.39313i) q^{13} +(0.809017 - 0.587785i) q^{14} +(0.325284 + 2.26294i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-0.486781 - 1.49816i) q^{17} -1.95466 q^{18} +(2.57800 + 7.93428i) q^{19} +(0.318151 + 2.21332i) q^{20} +(-0.315945 + 0.972380i) q^{21} +(1.36172 - 4.19094i) q^{22} +(-2.18556 + 1.58790i) q^{23} +1.02242 q^{24} +(3.05351 - 3.95931i) q^{25} -4.07144 q^{26} +(4.09827 - 2.97757i) q^{27} +(-0.309017 + 0.951057i) q^{28} +(-0.424975 + 1.30794i) q^{29} +(-1.59329 - 1.63956i) q^{30} +(2.66194 + 8.19261i) q^{31} +1.00000 q^{32} +(1.39225 + 4.28490i) q^{33} +(1.27441 + 0.925912i) q^{34} +(2.00668 - 0.986533i) q^{35} +(1.58135 - 1.14892i) q^{36} +(-1.85704 - 1.34922i) q^{37} +(-6.74930 - 4.90365i) q^{38} +(3.36772 - 2.44679i) q^{39} +(-1.55835 - 1.60361i) q^{40} +(-5.14942 - 3.74127i) q^{41} +(-0.315945 - 0.972380i) q^{42} -6.57797 q^{43} +(1.36172 + 4.19094i) q^{44} +(-4.30670 - 0.745454i) q^{45} +(0.834810 - 2.56928i) q^{46} +(-2.06959 + 6.36954i) q^{47} +(-0.827156 + 0.600964i) q^{48} +1.00000 q^{49} +(-0.143117 + 4.99795i) q^{50} -1.61057 q^{51} +(3.29386 - 2.39313i) q^{52} +(1.83432 - 5.64546i) q^{53} +(-1.56540 + 4.81781i) q^{54} +(4.59859 - 8.71459i) q^{55} +(-0.309017 - 0.951057i) q^{56} +8.52964 q^{57} +(-0.424975 - 1.30794i) q^{58} +(2.62410 + 1.90652i) q^{59} +(2.25271 + 0.389924i) q^{60} +(-7.99537 + 5.80897i) q^{61} +(-6.96905 - 5.06331i) q^{62} +(-1.58135 - 1.14892i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(-8.97063 - 1.55274i) q^{65} +(-3.64495 - 2.64821i) q^{66} +(-2.14891 - 6.61367i) q^{67} -1.57526 q^{68} +(0.853527 + 2.62689i) q^{69} +(-1.04357 + 1.97762i) q^{70} +(-2.23081 + 6.86573i) q^{71} +(-0.604022 + 1.85899i) q^{72} +(8.01886 - 5.82604i) q^{73} +2.29543 q^{74} +(-2.88521 - 4.22009i) q^{75} +8.34259 q^{76} +(3.56502 - 2.59014i) q^{77} +(-1.28635 + 3.95899i) q^{78} +(5.24146 - 16.1315i) q^{79} +(2.20331 + 0.381373i) q^{80} +(0.211567 + 0.651135i) q^{81} +6.36503 q^{82} +(0.823495 + 2.53446i) q^{83} +(0.827156 + 0.600964i) q^{84} +(2.45479 + 2.52609i) q^{85} +(5.32169 - 3.86643i) q^{86} +(1.13754 + 0.826474i) q^{87} +(-3.56502 - 2.59014i) q^{88} +(11.2828 - 8.19743i) q^{89} +(3.92236 - 1.92833i) q^{90} +(-3.29386 - 2.39313i) q^{91} +(0.834810 + 2.56928i) q^{92} +8.80736 q^{93} +(-2.06959 - 6.36954i) q^{94} +(-13.0006 - 13.3782i) q^{95} +(0.315945 - 0.972380i) q^{96} +(3.18187 - 9.79279i) q^{97} +(-0.809017 + 0.587785i) q^{98} -8.61341 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} + q^{3} - 4 q^{4} - 4 q^{5} + q^{6} - 16 q^{7} - 4 q^{8} - q^{9}+O(q^{10}) \) 16 * q - 4 * q^2 + q^3 - 4 * q^4 - 4 * q^5 + q^6 - 16 * q^7 - 4 * q^8 - q^9	\( 16 q - 4 q^{2} + q^{3} - 4 q^{4} - 4 q^{5} + q^{6} - 16 q^{7} - 4 q^{8} - q^{9} + q^{10} + 7 q^{11} - 4 q^{12} + 9 q^{13} + 4 q^{14} - 4 q^{16} - 2 q^{17} + 14 q^{18} - 24 q^{19} - 9 q^{20} - q^{21} - 8 q^{22} - 5 q^{23} + 6 q^{24} - 6 q^{25} - 6 q^{26} - 32 q^{27} + 4 q^{28} + 20 q^{29} + 15 q^{30} + 7 q^{31} + 16 q^{32} + 15 q^{33} + 3 q^{34} + 4 q^{35} - q^{36} - 6 q^{37} + 6 q^{38} + 34 q^{39} + 11 q^{40} + 9 q^{41} - q^{42} - 22 q^{43} - 8 q^{44} - 8 q^{45} - 40 q^{47} - 4 q^{48} + 16 q^{49} - q^{50} + 14 q^{51} + 9 q^{52} - 24 q^{53} + 23 q^{54} - 26 q^{55} + 4 q^{56} + 52 q^{57} + 20 q^{58} - 17 q^{59} - 5 q^{60} + 2 q^{61} - 23 q^{62} + q^{63} - 4 q^{64} - 16 q^{65} - 10 q^{66} - 14 q^{67} - 2 q^{68} - 35 q^{69} - q^{70} + 7 q^{71} - 6 q^{72} + 5 q^{73} - 36 q^{74} + 35 q^{75} + 36 q^{76} - 7 q^{77} - 46 q^{78} + 20 q^{79} + q^{80} + 49 q^{81} + 44 q^{82} + 17 q^{83} + 4 q^{84} - 13 q^{85} + 8 q^{86} - 66 q^{87} + 7 q^{88} + 27 q^{89} + 37 q^{90} - 9 q^{91} - 34 q^{93} - 40 q^{94} - 20 q^{95} + q^{96} + 6 q^{97} - 4 q^{98} - 16 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 + q^3 - 4 * q^4 - 4 * q^5 + q^6 - 16 * q^7 - 4 * q^8 - q^9 + q^10 + 7 * q^11 - 4 * q^12 + 9 * q^13 + 4 * q^14 - 4 * q^16 - 2 * q^17 + 14 * q^18 - 24 * q^19 - 9 * q^20 - q^21 - 8 * q^22 - 5 * q^23 + 6 * q^24 - 6 * q^25 - 6 * q^26 - 32 * q^27 + 4 * q^28 + 20 * q^29 + 15 * q^30 + 7 * q^31 + 16 * q^32 + 15 * q^33 + 3 * q^34 + 4 * q^35 - q^36 - 6 * q^37 + 6 * q^38 + 34 * q^39 + 11 * q^40 + 9 * q^41 - q^42 - 22 * q^43 - 8 * q^44 - 8 * q^45 - 40 * q^47 - 4 * q^48 + 16 * q^49 - q^50 + 14 * q^51 + 9 * q^52 - 24 * q^53 + 23 * q^54 - 26 * q^55 + 4 * q^56 + 52 * q^57 + 20 * q^58 - 17 * q^59 - 5 * q^60 + 2 * q^61 - 23 * q^62 + q^63 - 4 * q^64 - 16 * q^65 - 10 * q^66 - 14 * q^67 - 2 * q^68 - 35 * q^69 - q^70 + 7 * q^71 - 6 * q^72 + 5 * q^73 - 36 * q^74 + 35 * q^75 + 36 * q^76 - 7 * q^77 - 46 * q^78 + 20 * q^79 + q^80 + 49 * q^81 + 44 * q^82 + 17 * q^83 + 4 * q^84 - 13 * q^85 + 8 * q^86 - 66 * q^87 + 7 * q^88 + 27 * q^89 + 37 * q^90 - 9 * q^91 - 34 * q^93 - 40 * q^94 - 20 * q^95 + q^96 + 6 * q^97 - 4 * q^98 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more