LMFDB - Embedded newform 418.2.f.h.191.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(115,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("418.115");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.f (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:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{19} + 11 x^{18} - 3 x^{17} + 103 x^{16} + 50 x^{15} + 1002 x^{14} + 1120 x^{13} + \cdots + 1936 $ x^20 - x^19 + 11x^18 - 3x^17 + 103x^16 + 50x^15 + 1002x^14 + 1120x^13 + 7288x^12 + 5704x^11 + 24392x^10 + 10376x^9 + 48880x^8 + 21224x^7 + 77528x^6 + 44616x^5 + 147848x^4 + 67728x^3 + 115472x^2 - 24464x + 1936
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			191.2
Root			$-1.03876 + 0.754706i$ of defining polynomial
Character	$\chi$	$=$	418.191
Dual form			418.2.f.h.267.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 + 0.587785i) q^{2} +(-0.396773 + 1.22114i) q^{3} +(0.309017 + 0.951057i) q^{4} +(1.09974 - 0.799009i) q^{5} +(-1.03876 + 0.754706i) q^{6} +(0.979051 + 3.01321i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(1.09330 + 0.794325i) q^{9} +O(q^{10})$	\(q+(0.809017 + 0.587785i) q^{2} +(-0.396773 + 1.22114i) q^{3} +(0.309017 + 0.951057i) q^{4} +(1.09974 - 0.799009i) q^{5} +(-1.03876 + 0.754706i) q^{6} +(0.979051 + 3.01321i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(1.09330 + 0.794325i) q^{9} +1.35936 q^{10} +(-0.286325 - 3.30424i) q^{11} -1.28398 q^{12} +(-0.734046 - 0.533316i) q^{13} +(-0.979051 + 3.01321i) q^{14} +(0.539355 + 1.65996i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-2.29246 + 1.66557i) q^{17} +(0.417602 + 1.28525i) q^{18} +(-0.309017 + 0.951057i) q^{19} +(1.09974 + 0.799009i) q^{20} -4.06801 q^{21} +(1.71054 - 2.84149i) q^{22} +2.86075 q^{23} +(-1.03876 - 0.754706i) q^{24} +(-0.974068 + 2.99787i) q^{25} +(-0.280381 - 0.862923i) q^{26} +(-4.52007 + 3.28402i) q^{27} +(-2.56319 + 1.86227i) q^{28} +(-1.53604 - 4.72745i) q^{29} +(-0.539355 + 1.65996i) q^{30} +(6.34388 + 4.60910i) q^{31} -1.00000 q^{32} +(4.14855 + 0.961389i) q^{33} -2.83364 q^{34} +(3.48429 + 2.53148i) q^{35} +(-0.417602 + 1.28525i) q^{36} +(-1.93397 - 5.95215i) q^{37} +(-0.809017 + 0.587785i) q^{38} +(0.942503 - 0.684769i) q^{39} +(0.420064 + 1.29282i) q^{40} +(3.33379 - 10.2603i) q^{41} +(-3.29109 - 2.39112i) q^{42} -0.172752 q^{43} +(3.05404 - 1.29338i) q^{44} +1.83702 q^{45} +(2.31439 + 1.68151i) q^{46} +(-1.78186 + 5.48401i) q^{47} +(-0.396773 - 1.22114i) q^{48} +(-2.45777 + 1.78567i) q^{49} +(-2.55014 + 1.85279i) q^{50} +(-1.12431 - 3.46028i) q^{51} +(0.280381 - 0.862923i) q^{52} +(-10.9224 - 7.93556i) q^{53} -5.58711 q^{54} +(-2.95500 - 3.40504i) q^{55} -3.16828 q^{56} +(-1.03876 - 0.754706i) q^{57} +(1.53604 - 4.72745i) q^{58} +(0.248713 + 0.765459i) q^{59} +(-1.41205 + 1.02591i) q^{60} +(8.09828 - 5.88374i) q^{61} +(2.42315 + 7.45768i) q^{62} +(-1.32308 + 4.07201i) q^{63} +(-0.809017 - 0.587785i) q^{64} -1.23339 q^{65} +(2.79116 + 3.21624i) q^{66} +11.5211 q^{67} +(-2.29246 - 1.66557i) q^{68} +(-1.13507 + 3.49338i) q^{69} +(1.33088 + 4.09602i) q^{70} +(10.6729 - 7.75433i) q^{71} +(-1.09330 + 0.794325i) q^{72} +(-1.09708 - 3.37647i) q^{73} +(1.93397 - 5.95215i) q^{74} +(-3.27434 - 2.37895i) q^{75} -1.00000 q^{76} +(9.67605 - 4.09778i) q^{77} +1.16500 q^{78} +(-4.58705 - 3.33269i) q^{79} +(-0.420064 + 1.29282i) q^{80} +(-0.964007 - 2.96691i) q^{81} +(8.72797 - 6.34124i) q^{82} +(2.58823 - 1.88046i) q^{83} +(-1.25709 - 3.86891i) q^{84} +(-1.19031 + 3.66340i) q^{85} +(-0.139759 - 0.101541i) q^{86} +6.38234 q^{87} +(3.23100 + 0.748755i) q^{88} +18.5862 q^{89} +(1.48618 + 1.07977i) q^{90} +(0.888323 - 2.73398i) q^{91} +(0.884020 + 2.72073i) q^{92} +(-8.14544 + 5.91801i) q^{93} +(-4.66498 + 3.38931i) q^{94} +(0.420064 + 1.29282i) q^{95} +(0.396773 - 1.22114i) q^{96} +(-3.27167 - 2.37701i) q^{97} -3.03797 q^{98} +(2.31161 - 3.83995i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 5 q^{2} - q^{3} - 5 q^{4} - q^{5} + q^{6} + 13 q^{7} + 5 q^{8} - 6 q^{9}+O(q^{10}) $ 20 * q + 5 * q^2 - q^3 - 5 * q^4 - q^5 + q^6 + 13 * q^7 + 5 * q^8 - 6 * q^9	\( 20 q + 5 q^{2} - q^{3} - 5 q^{4} - q^{5} + q^{6} + 13 q^{7} + 5 q^{8} - 6 q^{9} + 6 q^{10} + q^{11} + 4 q^{12} - 2 q^{13} - 13 q^{14} - 8 q^{15} - 5 q^{16} + 11 q^{17} + 6 q^{18} + 5 q^{19} - q^{20} + 2 q^{21} + 4 q^{22} + 28 q^{23} + q^{24} - 30 q^{25} - 13 q^{26} - 31 q^{27} - 2 q^{28} + 28 q^{29} + 8 q^{30} - q^{31} - 20 q^{32} + 9 q^{33} + 24 q^{34} - 11 q^{35} - 6 q^{36} + 8 q^{37} - 5 q^{38} + 18 q^{39} - 4 q^{40} - 5 q^{41} - 22 q^{42} - 44 q^{43} + 11 q^{44} - 4 q^{45} + 7 q^{46} - 39 q^{47} - q^{48} + 4 q^{49} - 25 q^{50} - 11 q^{51} + 13 q^{52} - q^{53} - 4 q^{54} + 8 q^{55} + 22 q^{56} + q^{57} - 28 q^{58} + 6 q^{59} + 7 q^{60} + 10 q^{61} + 11 q^{62} + 34 q^{63} - 5 q^{64} - 8 q^{65} + 41 q^{66} + 18 q^{67} + 11 q^{68} - 63 q^{69} + q^{70} - 3 q^{71} + 6 q^{72} + 5 q^{73} - 8 q^{74} + 5 q^{75} - 20 q^{76} + 36 q^{77} + 22 q^{78} + 19 q^{79} + 4 q^{80} + 63 q^{81} - 9 q^{83} - 23 q^{84} + 30 q^{85} - 26 q^{86} - 16 q^{87} - q^{88} + 44 q^{89} + 14 q^{90} - 68 q^{91} - 7 q^{92} + 27 q^{93} - 31 q^{94} - 4 q^{95} + q^{96} - 71 q^{97} + 6 q^{98} + 20 q^{99}+O(q^{100}) \) 20 * q + 5 * q^2 - q^3 - 5 * q^4 - q^5 + q^6 + 13 * q^7 + 5 * q^8 - 6 * q^9 + 6 * q^10 + q^11 + 4 * q^12 - 2 * q^13 - 13 * q^14 - 8 * q^15 - 5 * q^16 + 11 * q^17 + 6 * q^18 + 5 * q^19 - q^20 + 2 * q^21 + 4 * q^22 + 28 * q^23 + q^24 - 30 * q^25 - 13 * q^26 - 31 * q^27 - 2 * q^28 + 28 * q^29 + 8 * q^30 - q^31 - 20 * q^32 + 9 * q^33 + 24 * q^34 - 11 * q^35 - 6 * q^36 + 8 * q^37 - 5 * q^38 + 18 * q^39 - 4 * q^40 - 5 * q^41 - 22 * q^42 - 44 * q^43 + 11 * q^44 - 4 * q^45 + 7 * q^46 - 39 * q^47 - q^48 + 4 * q^49 - 25 * q^50 - 11 * q^51 + 13 * q^52 - q^53 - 4 * q^54 + 8 * q^55 + 22 * q^56 + q^57 - 28 * q^58 + 6 * q^59 + 7 * q^60 + 10 * q^61 + 11 * q^62 + 34 * q^63 - 5 * q^64 - 8 * q^65 + 41 * q^66 + 18 * q^67 + 11 * q^68 - 63 * q^69 + q^70 - 3 * q^71 + 6 * q^72 + 5 * q^73 - 8 * q^74 + 5 * q^75 - 20 * q^76 + 36 * q^77 + 22 * q^78 + 19 * q^79 + 4 * q^80 + 63 * q^81 - 9 * q^83 - 23 * q^84 + 30 * q^85 - 26 * q^86 - 16 * q^87 - q^88 + 44 * q^89 + 14 * q^90 - 68 * q^91 - 7 * q^92 + 27 * q^93 - 31 * q^94 - 4 * q^95 + q^96 - 71 * q^97 + 6 * q^98 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$

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
$3$	−0.396773	+	1.22114i	−0.229077	+	0.705026i	0.768775	+	0.639519i	$0.220866\pi$
$3$	−0.396773	+	1.22114i	−0.229077	+	0.705026i	−0.997852	+	0.0655069i	$0.979134\pi$
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	1.09974	−	0.799009i	0.491820	−	0.357328i	−0.314064	−	0.949402i	$-0.601691\pi$
$5$	1.09974	−	0.799009i	0.491820	−	0.357328i	0.805884	+	0.592074i	$0.201691\pi$
$6$	−1.03876	+	0.754706i	−0.424074	+	0.308108i
$7$	0.979051	+	3.01321i	0.370047	+	1.13889i	0.946760	+	0.321940i	$0.104335\pi$
$7$	0.979051	+	3.01321i	0.370047	+	1.13889i	−0.576714	+	0.816946i	$0.695665\pi$
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$	1.09330	+	0.794325i	0.364432	+	0.264775i
$10$	1.35936			0.429866
$11$	−0.286325	−	3.30424i	−0.0863304	−	0.996267i
$11$	−0.286325	−	3.30424i	−0.0863304	−	0.996267i
$12$	−1.28398			−0.370654
$13$	−0.734046	−	0.533316i	−0.203588	−	0.147915i	0.481320	−	0.876545i	$-0.340158\pi$
$13$	−0.734046	−	0.533316i	−0.203588	−	0.147915i	−0.684908	+	0.728630i	$0.740158\pi$
$14$	−0.979051	+	3.01321i	−0.261662	+	0.805314i
$15$	0.539355	+	1.65996i	0.139261	+	0.428601i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−2.29246	+	1.66557i	−0.556004	+	0.403961i	−0.829994	−	0.557772i	$-0.811656\pi$
$17$	−2.29246	+	1.66557i	−0.556004	+	0.403961i	0.273990	+	0.961733i	$0.411656\pi$
$18$	0.417602	+	1.28525i	0.0984296	+	0.302935i
$19$	−0.309017	+	0.951057i	−0.0708934	+	0.218187i
$19$	−0.309017	+	0.951057i	−0.0708934	+	0.218187i
$20$	1.09974	+	0.799009i	0.245910	+	0.178664i
$21$	−4.06801			−0.887713
$22$	1.71054	−	2.84149i	0.364689	−	0.605807i
$23$	2.86075			0.596507			0.298254	−	0.954487i	$-0.403596\pi$
$23$	2.86075			0.596507			0.298254	+	0.954487i	$0.403596\pi$
$24$	−1.03876	−	0.754706i	−0.212037	−	0.154054i
$25$	−0.974068	+	2.99787i	−0.194814	+	0.599575i
$26$	−0.280381	−	0.862923i	−0.0549872	−	0.169233i
$27$	−4.52007	+	3.28402i	−0.869887	+	0.632010i
$28$	−2.56319	+	1.86227i	−0.484397	+	0.351935i
$29$	−1.53604	−	4.72745i	−0.285236	−	0.877865i	−0.986328	−	0.164794i	$-0.947304\pi$
$29$	−1.53604	−	4.72745i	−0.285236	−	0.877865i	0.701092	−	0.713070i	$-0.252696\pi$
$30$	−0.539355	+	1.65996i	−0.0984723	+	0.303067i
$31$	6.34388	+	4.60910i	1.13940	+	0.827819i	0.987035	−	0.160506i	$-0.0513126\pi$
$31$	6.34388	+	4.60910i	1.13940	+	0.827819i	0.152360	+	0.988325i	$0.451313\pi$
$32$	−1.00000			−0.176777
$33$	4.14855	+	0.961389i	0.722170	+	0.167356i
$34$	−2.83364			−0.485966
$35$	3.48429	+	2.53148i	0.588952	+	0.427899i
$36$	−0.417602	+	1.28525i	−0.0696003	+	0.214208i
$37$	−1.93397	−	5.95215i	−0.317943	−	0.978527i	−0.974526	−	0.224274i	$-0.927999\pi$
$37$	−1.93397	−	5.95215i	−0.317943	−	0.978527i	0.656584	−	0.754253i	$-0.272001\pi$
$38$	−0.809017	+	0.587785i	−0.131240	+	0.0953514i
$39$	0.942503	−	0.684769i	0.150921	−	0.109651i
$40$	0.420064	+	1.29282i	0.0664180	+	0.204413i
$41$	3.33379	−	10.2603i	0.520650	−	1.60240i	−0.252110	−	0.967698i	$-0.581125\pi$
$41$	3.33379	−	10.2603i	0.520650	−	1.60240i	0.772760	−	0.634698i	$-0.218875\pi$
$42$	−3.29109	−	2.39112i	−0.507826	−	0.368958i
$43$	−0.172752			−0.0263445			−0.0131722	−	0.999913i	$-0.504193\pi$
$43$	−0.172752			−0.0263445			−0.0131722	+	0.999913i	$0.504193\pi$
$44$	3.05404	−	1.29338i	0.460414	−	0.194984i
$45$	1.83702			0.273846
$46$	2.31439	+	1.68151i	0.341239	+	0.247924i
$47$	−1.78186	+	5.48401i	−0.259911	+	0.799925i	0.732911	+	0.680325i	$0.238161\pi$
$47$	−1.78186	+	5.48401i	−0.259911	+	0.799925i	−0.992822	+	0.119600i	$0.961839\pi$
$48$	−0.396773	−	1.22114i	−0.0572692	−	0.176256i
$49$	−2.45777	+	1.78567i	−0.351110	+	0.255096i
$50$	−2.55014	+	1.85279i	−0.360645	+	0.262024i
$51$	−1.12431	−	3.46028i	−0.157435	−	0.484535i
$52$	0.280381	−	0.862923i	0.0388818	−	0.119666i
$53$	−10.9224	−	7.93556i	−1.50030	−	1.09003i	−0.970261	−	0.242062i	$-0.922176\pi$
$53$	−10.9224	−	7.93556i	−1.50030	−	1.09003i	−0.530042	−	0.847972i	$-0.677824\pi$
$54$	−5.58711			−0.760309
$55$	−2.95500	−	3.40504i	−0.398453	−	0.459135i
$56$	−3.16828			−0.423379
$57$	−1.03876	−	0.754706i	−0.137588	−	0.0999633i
$58$	1.53604	−	4.72745i	0.201692	−	0.620744i
$59$	0.248713	+	0.765459i	0.0323797	+	0.0996543i	0.965940	−	0.258765i	$-0.0833157\pi$
$59$	0.248713	+	0.765459i	0.0323797	+	0.0996543i	−0.933561	+	0.358420i	$0.883316\pi$
$60$	−1.41205	+	1.02591i	−0.182295	+	0.132445i
$61$	8.09828	−	5.88374i	1.03688	−	0.753336i	0.0672042	−	0.997739i	$-0.478592\pi$
$61$	8.09828	−	5.88374i	1.03688	−	0.753336i	0.969674	+	0.244403i	$0.0785921\pi$
$62$	2.42315	+	7.45768i	0.307740	+	0.947127i
$63$	−1.32308	+	4.07201i	−0.166692	+	0.513025i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−1.23339			−0.152983
$66$	2.79116	+	3.21624i	0.343568	+	0.395891i
$67$	11.5211			1.40752			0.703760	−	0.710438i	$-0.251503\pi$
$67$	11.5211			1.40752			0.703760	+	0.710438i	$0.251503\pi$
$68$	−2.29246	−	1.66557i	−0.278002	−	0.201980i
$69$	−1.13507	+	3.49338i	−0.136646	+	0.420553i
$70$	1.33088	+	4.09602i	0.159070	+	0.489568i
$71$	10.6729	−	7.75433i	1.26664	−	0.920270i	0.267579	−	0.963536i	$-0.413776\pi$
$71$	10.6729	−	7.75433i	1.26664	−	0.920270i	0.999064	+	0.0432657i	$0.0137762\pi$
$72$	−1.09330	+	0.794325i	−0.128846	+	0.0936121i
$73$	−1.09708	−	3.37647i	−0.128404	−	0.395186i	0.866102	−	0.499867i	$-0.166618\pi$
$73$	−1.09708	−	3.37647i	−0.128404	−	0.395186i	−0.994506	+	0.104681i	$0.966618\pi$
$74$	1.93397	−	5.95215i	0.224819	−	0.691923i
$75$	−3.27434	−	2.37895i	−0.378089	−	0.274697i
$76$	−1.00000			−0.114708
$77$	9.67605	−	4.09778i	1.10269	−	0.466985i
$78$	1.16500			0.131910
$79$	−4.58705	−	3.33269i	−0.516084	−	0.374957i	0.299043	−	0.954240i	$-0.403333\pi$
$79$	−4.58705	−	3.33269i	−0.516084	−	0.374957i	−0.815127	+	0.579283i	$0.803333\pi$
$80$	−0.420064	+	1.29282i	−0.0469646	+	0.144542i
$81$	−0.964007	−	2.96691i	−0.107112	−	0.329656i
$82$	8.72797	−	6.34124i	0.963843	−	0.700273i
$83$	2.58823	−	1.88046i	0.284096	−	0.206408i	−0.436606	−	0.899653i	$-0.643820\pi$
$83$	2.58823	−	1.88046i	0.284096	−	0.206408i	0.720702	+	0.693245i	$0.243820\pi$
$84$	−1.25709	−	3.86891i	−0.137159	−	0.422133i
$85$	−1.19031	+	3.66340i	−0.129107	+	0.397352i
$86$	−0.139759	−	0.101541i	−0.0150707	−	0.0109495i
$87$	6.38234			0.684258
$88$	3.23100	+	0.748755i	0.344426	+	0.0798176i
$89$	18.5862			1.97014			0.985068	−	0.172167i	$-0.0550767\pi$
$89$	18.5862			1.97014			0.985068	+	0.172167i	$0.0550767\pi$
$90$	1.48618	+	1.07977i	0.156657	+	0.113818i
$91$	0.888323	−	2.73398i	0.0931216	−	0.286599i
$92$	0.884020	+	2.72073i	0.0921654	+	0.283656i
$93$	−8.14544	+	5.91801i	−0.844643	+	0.613669i
$94$	−4.66498	+	3.38931i	−0.481156	+	0.349580i
$95$	0.420064	+	1.29282i	0.0430977	+	0.132641i
$96$	0.396773	−	1.22114i	0.0404954	−	0.124632i
$97$	−3.27167	−	2.37701i	−0.332188	−	0.241349i	0.409170	−	0.912458i	$-0.365818\pi$
$97$	−3.27167	−	2.37701i	−0.332188	−	0.241349i	−0.741358	+	0.671109i	$0.765818\pi$
$98$	−3.03797			−0.306881
$99$	2.31161	−	3.83995i	0.232325	−	0.385929i
$100$	−3.15215			−0.315215
$101$	0.787139	+	0.571890i	0.0783233	+	0.0569052i	0.626258	−	0.779616i	$-0.284586\pi$
$101$	0.787139	+	0.571890i	0.0783233	+	0.0569052i	−0.547935	+	0.836521i	$0.684586\pi$
$102$	1.12431	−	3.46028i	0.111323	−	0.342618i
$103$	−0.939999	−	2.89302i	−0.0926208	−	0.285058i	0.894005	−	0.448056i	$-0.147883\pi$
$103$	−0.939999	−	2.89302i	−0.0926208	−	0.285058i	−0.986626	+	0.162998i	$0.947883\pi$
$104$	0.734046	−	0.533316i	0.0719792	−	0.0522959i
$105$	−4.47376	+	3.25038i	−0.436595	+	0.317205i
$106$	−4.17197	−	12.8400i	−0.405218	−	1.24713i
$107$	−2.81765	+	8.67183i	−0.272392	+	0.838337i	0.717505	+	0.696553i	$0.245284\pi$
$107$	−2.81765	+	8.67183i	−0.272392	+	0.838337i	−0.989898	+	0.141784i	$0.954716\pi$
$108$	−4.52007	−	3.28402i	−0.434943	−	0.316005i
$109$	−18.3209			−1.75483			−0.877414	−	0.479734i	$-0.840733\pi$
$109$	−18.3209			−1.75483			−0.877414	+	0.479734i	$0.840733\pi$
$110$	−0.389218	−	4.49164i	−0.0371105	−	0.428261i
$111$	8.03575			0.762720
$112$	−2.56319	−	1.86227i	−0.242199	−	0.175968i
$113$	0.662385	−	2.03861i	0.0623120	−	0.191776i	−0.915054	−	0.403331i	$-0.867852\pi$
$113$	0.662385	−	2.03861i	0.0623120	−	0.191776i	0.977366	+	0.211554i	$0.0678525\pi$
$114$	−0.396773	−	1.22114i	−0.0371612	−	0.114370i
$115$	3.14608	−	2.28576i	0.293374	−	0.213149i
$116$	4.02141	−	2.92172i	0.373378	−	0.271275i
$117$	−0.378903	−	1.16614i	−0.0350296	−	0.107810i
$118$	−0.248713	+	0.765459i	−0.0228959	+	0.0704663i
$119$	−7.26316	−	5.27699i	−0.665813	−	0.483741i
$120$	−1.74539			−0.159332
$121$	−10.8360	+	1.89218i	−0.985094	+	0.172016i
$122$	10.0100			0.906264
$123$	11.2066	+	8.14205i	1.01046	+	0.734144i
$124$	−2.42315	+	7.45768i	−0.217605	+	0.669720i
$125$	3.42443	+	10.5393i	0.306290	+	0.942664i
$126$	−3.46386	+	2.51664i	−0.308585	+	0.224200i
$127$	−0.502546	+	0.365121i	−0.0445938	+	0.0323993i	−0.609859	−	0.792510i	$-0.708774\pi$
$127$	−0.502546	+	0.365121i	−0.0445938	+	0.0323993i	0.565265	+	0.824909i	$0.308774\pi$
$128$	−0.309017	−	0.951057i	−0.0273135	−	0.0840623i
$129$	0.0685434	−	0.210955i	0.00603491	−	0.0185735i
$130$	−0.997830	−	0.724966i	−0.0875155	−	0.0635837i
$131$	−15.3839			−1.34409			−0.672047	−	0.740508i	$-0.734585\pi$
$131$	−15.3839			−1.34409			−0.672047	+	0.740508i	$0.734585\pi$
$132$	0.367637	+	4.24259i	0.0319987	+	0.369270i
$133$	−3.16828			−0.274724
$134$	9.32073	+	6.77190i	0.805188	+	0.585003i
$135$	−2.34694	+	7.22315i	−0.201993	+	0.621670i
$136$	−0.875643	−	2.69495i	−0.0750858	−	0.231090i
$137$	−7.88815	+	5.73107i	−0.673930	+	0.489639i	−0.871338	−	0.490683i	$-0.836747\pi$
$137$	−7.88815	+	5.73107i	−0.673930	+	0.489639i	0.197409	+	0.980321i	$0.436747\pi$
$138$	−2.97164	+	2.15902i	−0.252963	+	0.183788i
$139$	0.0671917	+	0.206795i	0.00569913	+	0.0175401i	0.953866	−	0.300234i	$-0.0970647\pi$
$139$	0.0671917	+	0.206795i	0.00569913	+	0.0175401i	−0.948167	+	0.317774i	$0.897065\pi$
$140$	−1.33088	+	4.09602i	−0.112480	+	0.346177i
$141$	−5.98975	−	4.35181i	−0.504428	−	0.366489i
$142$	13.1925			1.10709
$143$	−1.55203	+	2.57817i	−0.129787	+	0.215597i
$144$	−1.35139			−0.112616
$145$	−5.46652	−	3.97166i	−0.453970	−	0.329828i
$146$	1.09708	−	3.37647i	0.0907952	−	0.279439i
$147$	−1.20538	−	3.70979i	−0.0994184	−	0.305978i
$148$	5.06320	−	3.67863i	0.416192	−	0.302381i
$149$	7.26583	−	5.27894i	0.595240	−	0.432467i	−0.248946	−	0.968517i	$-0.580084\pi$
$149$	7.26583	−	5.27894i	0.595240	−	0.432467i	0.844186	+	0.536050i	$0.180084\pi$
$150$	−1.25069	−	3.84922i	−0.102118	−	0.314288i
$151$	−3.38528	+	10.4188i	−0.275491	+	0.847873i	0.713599	+	0.700555i	$0.247064\pi$
$151$	−3.38528	+	10.4188i	−0.275491	+	0.847873i	−0.989089	+	0.147318i	$0.952936\pi$
$152$	−0.809017	−	0.587785i	−0.0656199	−	0.0476757i
$153$	−3.82935			−0.309584
$154$	10.2367	+	2.37226i	0.824897	+	0.191162i
$155$	10.6593			0.856180
$156$	0.942503	+	0.684769i	0.0754606	+	0.0548254i
$157$	−6.97953	+	21.4808i	−0.557027	+	1.71435i	0.133503	+	0.991048i	$0.457378\pi$
$157$	−6.97953	+	21.4808i	−0.557027	+	1.71435i	−0.690530	+	0.723304i	$0.742622\pi$
$158$	−1.75210	−	5.39241i	−0.139390	−	0.428997i
$159$	14.0241	−	10.1891i	1.11219	−	0.808051i
$160$	−1.09974	+	0.799009i	−0.0869422	+	0.0631672i
$161$	2.80082	+	8.62003i	0.220735	+	0.679354i
$162$	0.964007	−	2.96691i	0.0757395	−	0.233102i
$163$	−10.5069	−	7.63369i	−0.822962	−	0.597917i	0.0945977	−	0.995516i	$-0.469844\pi$
$163$	−10.5069	−	7.63369i	−0.822962	−	0.597917i	−0.917559	+	0.397599i	$0.869844\pi$
$164$	10.7884			0.842430
$165$	5.33049	−	2.25745i	0.414978	−	0.175742i
$166$	3.19923			0.248309
$167$	−2.17034	−	1.57684i	−0.167946	−	0.122020i	0.500637	−	0.865657i	$-0.333099\pi$
$167$	−2.17034	−	1.57684i	−0.167946	−	0.122020i	−0.668583	+	0.743637i	$0.733099\pi$
$168$	1.25709	−	3.86891i	0.0969862	−	0.298493i
$169$	−3.76282	−	11.5808i	−0.289448	−	0.890829i
$170$	−3.11627	+	2.26411i	−0.239007	+	0.173649i
$171$	−1.09330	+	0.794325i	−0.0836064	+	0.0607436i
$172$	−0.0533834	−	0.164297i	−0.00407044	−	0.0125275i
$173$	0.814360	−	2.50634i	0.0619146	−	0.190554i	−0.915315	−	0.402739i	$-0.868058\pi$
$173$	0.814360	−	2.50634i	0.0619146	−	0.190554i	0.977229	+	0.212186i	$0.0680581\pi$
$174$	5.16342	+	3.75144i	0.391438	+	0.284396i
$175$	−9.98689			−0.754938
$176$	2.17383	+	2.50489i	0.163858	+	0.188813i
$177$	−1.03342			−0.0776763
$178$	15.0366	+	10.9247i	1.12704	+	0.818841i
$179$	3.88358	−	11.9524i	0.290272	−	0.893366i	−0.694496	−	0.719496i	$-0.744373\pi$
$179$	3.88358	−	11.9524i	0.290272	−	0.893366i	0.984769	−	0.173870i	$-0.0556273\pi$
$180$	0.567669	+	1.74711i	0.0423116	+	0.130222i
$181$	−5.92905	+	4.30771i	−0.440703	+	0.320189i	−0.785914	−	0.618336i	$-0.787807\pi$
$181$	−5.92905	+	4.30771i	−0.440703	+	0.320189i	0.345211	+	0.938525i	$0.387807\pi$
$182$	2.32566	−	1.68969i	0.172389	−	0.125248i
$183$	3.97170	+	12.2236i	0.293597	+	0.903597i
$184$	−0.884020	+	2.72073i	−0.0651708	+	0.200575i
$185$	−6.88269	−	5.00057i	−0.506025	−	0.367649i
$186$	−10.0683			−0.738245
$187$	6.15985	+	7.09796i	0.450453	+	0.519054i
$188$	−5.76623			−0.420546
$189$	−14.3208	−	10.4047i	−1.04169	−	0.756829i
$190$	−0.420064	+	1.29282i	−0.0304746	+	0.0937913i
$191$	3.76156	+	11.5769i	0.272177	+	0.837674i	0.989953	+	0.141400i	$0.0451604\pi$
$191$	3.76156	+	11.5769i	0.272177	+	0.837674i	−0.717776	+	0.696274i	$0.754840\pi$
$192$	1.03876	−	0.754706i	0.0749664	−	0.0544662i
$193$	−11.6017	+	8.42914i	−0.835110	+	0.606743i	−0.921000	−	0.389562i	$-0.872627\pi$
$193$	−11.6017	+	8.42914i	−0.835110	+	0.606743i	0.0858904	+	0.996305i	$0.472627\pi$
$194$	−1.24967	−	3.84608i	−0.0897209	−	0.276133i
$195$	0.489374	−	1.50614i	0.0350448	−	0.107857i
$196$	−2.45777	−	1.78567i	−0.175555	−	0.127548i
$197$	15.6720			1.11659			0.558293	−	0.829644i	$-0.311457\pi$
$197$	15.6720			1.11659			0.558293	+	0.829644i	$0.311457\pi$
$198$	4.12719	−	1.74786i	0.293307	−	0.124215i
$199$	1.37651			0.0975783			0.0487891	−	0.998809i	$-0.484464\pi$
$199$	1.37651			0.0975783			0.0487891	+	0.998809i	$0.484464\pi$
$200$	−2.55014	−	1.85279i	−0.180322	−	0.131012i
$201$	−4.57124	+	14.0688i	−0.322430	+	0.992338i
$202$	0.300660	+	0.925337i	0.0211544	+	0.0651065i
$203$	12.7409	−	9.25682i	0.894238	−	0.649702i
$204$	2.94349	−	2.13857i	0.206085	−	0.149730i
$205$	−4.53180	−	13.9475i	−0.316515	−	0.974133i
$206$	0.939999	−	2.89302i	0.0654928	−	0.201566i
$207$	3.12764	+	2.27237i	0.217386	+	0.157940i
$208$	0.907331			0.0629121
$209$	3.23100	+	0.748755i	0.223493	+	0.0517925i
$210$	−5.52988			−0.381598
$211$	−7.31676	−	5.31593i	−0.503706	−	0.365964i	0.306725	−	0.951798i	$-0.400767\pi$
$211$	−7.31676	−	5.31593i	−0.503706	−	0.365964i	−0.810431	+	0.585834i	$0.800767\pi$
$212$	4.17197	−	12.8400i	0.286532	−	0.881856i
$213$	5.23441	+	16.1098i	0.358656	+	1.10383i
$214$	−7.37670	+	5.35948i	−0.504261	+	0.366367i
$215$	−0.189983	+	0.138031i	−0.0129567	+	0.00941361i
$216$	−1.72651	−	5.31366i	−0.117474	−	0.361548i
$217$	−7.67720	+	23.6280i	−0.521162	+	1.60397i
$218$	−14.8220	−	10.7688i	−1.00387	−	0.729354i
$219$	4.55844			0.308031
$220$	2.32524	−	3.86259i	0.156767	−	0.260416i
$221$	2.57105			0.172948
$222$	6.50106	+	4.72330i	0.436323	+	0.317007i
$223$	−0.860396	+	2.64803i	−0.0576164	+	0.177325i	−0.975723	−	0.219009i	$-0.929718\pi$
$223$	−0.860396	+	2.64803i	−0.0576164	+	0.177325i	0.918107	+	0.396334i	$0.129718\pi$
$224$	−0.979051	−	3.01321i	−0.0654156	−	0.201329i
$225$	−3.44623	+	2.50383i	−0.229749	+	0.166922i
$226$	1.73415	−	1.25993i	0.115354	−	0.0838094i
$227$	−0.930694	−	2.86438i	−0.0617724	−	0.190116i	0.915408	−	0.402527i	$-0.131868\pi$
$227$	−0.930694	−	2.86438i	−0.0617724	−	0.190116i	−0.977180	+	0.212412i	$0.931868\pi$
$228$	0.396773	−	1.22114i	0.0262769	−	0.0808720i
$229$	16.8375	+	12.2332i	1.11266	+	0.808392i	0.983080	−	0.183177i	$-0.0586383\pi$
$229$	16.8375	+	12.2332i	1.11266	+	0.808392i	0.129576	+	0.991569i	$0.458638\pi$
$230$	3.88877			0.256418
$231$	1.16478	+	13.4417i	0.0766366	+	0.884399i
$232$	4.97073			0.326345
$233$	−12.7507	−	9.26389i	−0.835323	−	0.606898i	0.0857372	−	0.996318i	$-0.472675\pi$
$233$	−12.7507	−	9.26389i	−0.835323	−	0.606898i	−0.921060	+	0.389420i	$0.872675\pi$
$234$	0.378903	−	1.16614i	0.0247697	−	0.0762332i
$235$	2.42219	+	7.45472i	0.158006	+	0.486292i
$236$	−0.651139	+	0.473080i	−0.0423855	+	0.0307949i
$237$	5.88970	−	4.27912i	0.382577	−	0.277959i
$238$	−2.77428	−	8.53836i	−0.179830	−	0.553459i
$239$	−7.83621	+	24.1174i	−0.506882	+	1.56002i	0.290701	+	0.956814i	$0.406112\pi$
$239$	−7.83621	+	24.1174i	−0.506882	+	1.56002i	−0.797583	+	0.603209i	$0.793888\pi$
$240$	−1.41205	−	1.02591i	−0.0911474	−	0.0662225i
$241$	7.85507			0.505989			0.252995	−	0.967468i	$-0.418585\pi$
$241$	7.85507			0.505989			0.252995	+	0.967468i	$0.418585\pi$
$242$	−9.87873	−	4.83846i	−0.635029	−	0.311028i
$243$	−12.7558			−0.818286
$244$	8.09828	+	5.88374i	0.518439	+	0.376668i
$245$	−1.27614	+	3.92756i	−0.0815298	+	0.250923i
$246$	4.28053	+	13.1741i	0.272916	+	0.839950i
$247$	0.734046	−	0.533316i	0.0467062	−	0.0339341i
$248$	−6.34388	+	4.60910i	−0.402837	+	0.292678i
$249$	1.26937	+	3.90671i	0.0804429	+	0.247578i
$250$	−3.42443	+	10.5393i	−0.216580	+	0.666564i
$251$	−5.59135	−	4.06235i	−0.352923	−	0.256414i	0.397171	−	0.917745i	$-0.369992\pi$
$251$	−5.59135	−	4.06235i	−0.352923	−	0.256414i	−0.750094	+	0.661331i	$0.769992\pi$
$252$	−4.28157			−0.269713
$253$	−0.819105	−	9.45261i	−0.0514967	−	0.594280i
$254$	−0.621182			−0.0389764
$255$	−4.00124	−	2.90707i	−0.250568	−	0.182048i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−2.30333	−	7.08891i	−0.143678	−	0.442194i	0.853161	−	0.521648i	$-0.174682\pi$
$257$	−2.30333	−	7.08891i	−0.143678	−	0.442194i	−0.996839	+	0.0794536i	$0.974682\pi$
$258$	0.179449	−	0.130377i	0.0111720	−	0.00811693i
$259$	16.0416	−	11.6549i	0.996777	−	0.724201i
$260$	−0.381137	−	1.17302i	−0.0236371	−	0.0727476i
$261$	2.07579	−	6.38861i	0.128488	−	0.395445i
$262$	−12.4458	−	9.04241i	−0.768905	−	0.558642i
$263$	−9.10723			−0.561576			−0.280788	−	0.959770i	$-0.590596\pi$
$263$	−9.10723			−0.561576			−0.280788	+	0.959770i	$0.590596\pi$
$264$	−2.19631	+	3.64842i	−0.135173	+	0.224545i
$265$	−18.3524			−1.12738
$266$	−2.56319	−	1.86227i	−0.157159	−	0.114183i
$267$	−7.37450	+	22.6964i	−0.451312	+	1.38900i
$268$	3.56020	+	10.9572i	0.217474	+	0.669316i
$269$	12.7465	−	9.26086i	0.777167	−	0.564645i	−0.126961	−	0.991908i	$-0.540522\pi$
$269$	12.7465	−	9.26086i	0.777167	−	0.564645i	0.904127	+	0.427263i	$0.140522\pi$
$270$	−6.14438	+	4.46415i	−0.373935	+	0.271680i
$271$	−6.48960	−	19.9729i	−0.394215	−	1.21327i	−0.929571	−	0.368642i	$-0.879823\pi$
$271$	−6.48960	−	19.9729i	−0.394215	−	1.21327i	0.535356	−	0.844626i	$-0.320177\pi$
$272$	0.875643	−	2.69495i	0.0530937	−	0.163406i
$273$	2.98611	+	2.16954i	0.180728	+	0.131306i
$274$	−9.75028			−0.589036
$275$	10.1846	+	2.36019i	0.614155	+	0.142325i
$276$	−3.67315			−0.221098
$277$	11.2086	+	8.14352i	0.673460	+	0.489297i	0.871181	−	0.490961i	$-0.163354\pi$
$277$	11.2086	+	8.14352i	0.673460	+	0.489297i	−0.197722	+	0.980258i	$0.563354\pi$
$278$	−0.0671917	+	0.206795i	−0.00402989	+	0.0124027i
$279$	3.27461	+	10.0782i	0.196046	+	0.603367i
$280$	−3.48429	+	2.53148i	−0.208226	+	0.151285i
$281$	−7.80590	+	5.67132i	−0.465661	+	0.338322i	−0.795748	−	0.605628i	$-0.792922\pi$
$281$	−7.80590	+	5.67132i	−0.465661	+	0.338322i	0.330087	+	0.943951i	$0.392922\pi$
$282$	−2.28788	−	7.04138i	−0.136241	−	0.419308i
$283$	−5.70759	+	17.5661i	−0.339281	+	1.04420i	0.625294	+	0.780389i	$0.284979\pi$
$283$	−5.70759	+	17.5661i	−0.339281	+	1.04420i	−0.964575	+	0.263809i	$0.915021\pi$
$284$	10.6729	+	7.75433i	0.633322	+	0.460135i
$285$	−1.74539			−0.103388
$286$	−2.77103	+	1.17352i	−0.163854	+	0.0693919i
$287$	34.1805			2.01761
$288$	−1.09330	−	0.794325i	−0.0644230	−	0.0468061i
$289$	−2.77203	+	8.53143i	−0.163061	+	0.501849i
$290$	−2.08803	−	6.42628i	−0.122613	−	0.377364i
$291$	4.20077	−	3.05204i	0.246254	−	0.178914i
$292$	2.87220	−	2.08677i	0.168083	−	0.122119i
$293$	−2.08182	−	6.40717i	−0.121621	−	0.374311i	0.871649	−	0.490130i	$-0.163051\pi$
$293$	−2.08182	−	6.40717i	−0.121621	−	0.374311i	−0.993270	+	0.115819i	$0.963051\pi$
$294$	1.20538	−	3.70979i	0.0702994	−	0.216359i
$295$	0.885129	+	0.643084i	0.0515342	+	0.0374418i
$296$	6.25846			0.363765
$297$	12.1454	+	13.9951i	0.704748	+	0.812078i
$298$	8.98107			0.520259
$299$	−2.09992	−	1.52568i	−0.121442	−	0.0882325i
$300$	1.25069	−	3.84922i	0.0722085	−	0.222235i
$301$	−0.169133	−	0.520539i	−0.00974868	−	0.0300033i
$302$	−8.86279	+	6.43919i	−0.509996	+	0.370534i
$303$	−1.01067	+	0.734297i	−0.0580617	+	0.0421843i
$304$	−0.309017	−	0.951057i	−0.0177233	−	0.0545468i
$305$	4.20485	−	12.9412i	0.240769	−	0.741011i
$306$	−3.09801	−	2.25083i	−0.177101	−	0.128672i
$307$	−13.8179			−0.788632			−0.394316	−	0.918975i	$-0.629018\pi$
$307$	−13.8179			−0.788632			−0.394316	+	0.918975i	$0.629018\pi$
$308$	6.88728	+	7.93618i	0.392439	+	0.452206i
$309$	3.90575			0.222190
$310$	8.62359	+	6.26541i	0.489787	+	0.355851i
$311$	−7.15450	+	22.0193i	−0.405694	+	1.24860i	0.514620	+	0.857419i	$0.327933\pi$
$311$	−7.15450	+	22.0193i	−0.405694	+	1.24860i	−0.920314	+	0.391180i	$0.872067\pi$
$312$	0.360004	+	1.10798i	0.0203812	+	0.0627269i
$313$	13.7794	−	10.0113i	0.778856	−	0.565872i	−0.125780	−	0.992058i	$-0.540143\pi$
$313$	13.7794	−	10.0113i	0.778856	−	0.565872i	0.904635	+	0.426186i	$0.140143\pi$
$314$	−18.2726	+	13.2758i	−1.03118	+	0.749200i
$315$	1.79853	+	5.53531i	0.101336	+	0.311880i
$316$	1.75210	−	5.39241i	0.0985633	−	0.303347i
$317$	25.9014	+	18.8185i	1.45477	+	1.05695i	0.984688	+	0.174326i	$0.0557747\pi$
$317$	25.9014	+	18.8185i	1.45477	+	1.05695i	0.470079	+	0.882624i	$0.344225\pi$
$318$	17.3348			0.972086
$319$	−15.1808	+	6.42904i	−0.849963	+	0.359957i
$320$	−1.35936			−0.0759903
$321$	−9.47155	−	6.88149i	−0.528651	−	0.384087i
$322$	−2.80082	+	8.62003i	−0.156084	+	0.480376i
$323$	−0.875643	−	2.69495i	−0.0487221	−	0.149951i
$324$	2.52380	−	1.83365i	0.140211	−	0.101869i
$325$	2.31383	−	1.68109i	0.128348	−	0.0932502i
$326$	−4.01327	−	12.3516i	−0.222274	−	0.684090i
$327$	7.26925	−	22.3724i	0.401990	−	1.23720i
$328$	8.72797	+	6.34124i	0.481921	+	0.350136i
$329$	−18.2690			−1.00720
$330$	5.63936	+	1.30687i	0.310436	+	0.0719408i
$331$	−19.8146			−1.08911			−0.544554	−	0.838726i	$-0.683301\pi$
$331$	−19.8146			−1.08911			−0.544554	+	0.838726i	$0.683301\pi$
$332$	2.58823	+	1.88046i	0.142048	+	0.103204i
$333$	2.61354	−	8.04365i	0.143221	−	0.440790i
$334$	−0.828995	−	2.55139i	−0.0453606	−	0.139606i
$335$	12.6702	−	9.20543i	0.692246	−	0.502946i
$336$	3.29109	−	2.39112i	0.179544	−	0.130446i
$337$	−10.0544	−	30.9443i	−0.547699	−	1.68564i	−0.714485	−	0.699650i	$-0.753339\pi$
$337$	−10.0544	−	30.9443i	−0.547699	−	1.68564i	0.166787	−	0.985993i	$-0.446661\pi$
$338$	3.76282	−	11.5808i	0.204671	−	0.629911i
$339$	2.22662	+	1.61773i	0.120933	+	0.0878631i
$340$	−3.85193			−0.208900
$341$	13.4132	−	22.2814i	0.726364	−	1.20661i
$342$	−1.35139			−0.0730746
$343$	10.1554	+	7.37835i	0.548342	+	0.398393i
$344$	0.0533834	−	0.164297i	0.00287824	−	0.00885831i
$345$	1.54296	+	4.74874i	0.0830701	+	0.255664i
$346$	2.13202	−	1.54900i	0.114618	−	0.0832750i
$347$	5.94771	−	4.32126i	0.319290	−	0.231978i	−0.416583	−	0.909098i	$-0.636772\pi$
$347$	5.94771	−	4.32126i	0.319290	−	0.231978i	0.735872	+	0.677120i	$0.236772\pi$
$348$	1.97225	+	6.06996i	0.105724	+	0.325384i
$349$	−6.30510	+	19.4051i	−0.337504	+	1.03873i	0.627971	+	0.778236i	$0.283885\pi$
$349$	−6.30510	+	19.4051i	−0.337504	+	1.03873i	−0.965475	+	0.260494i	$0.916115\pi$
$350$	−8.07956	−	5.87014i	−0.431871	−	0.313772i
$351$	5.06936			0.270582
$352$	0.286325	+	3.30424i	0.0152612	+	0.176117i
$353$	−20.7451			−1.10415			−0.552076	−	0.833794i	$-0.686164\pi$
$353$	−20.7451			−1.10415			−0.552076	+	0.833794i	$0.686164\pi$
$354$	−0.836051	−	0.607427i	−0.0444356	−	0.0322844i
$355$	5.54168	−	17.0555i	0.294122	−	0.905214i
$356$	5.74346	+	17.6765i	0.304403	+	0.936855i
$357$	9.32577	−	6.77557i	0.493572	−	0.358601i
$358$	10.1673	−	7.38701i	0.537361	−	0.390415i
$359$	−9.11019	−	28.0383i	−0.480818	−	1.47980i	−0.837948	−	0.545750i	$-0.816245\pi$
$359$	−9.11019	−	28.0383i	−0.480818	−	1.47980i	0.357131	−	0.934054i	$-0.383755\pi$
$360$	−0.567669	+	1.74711i	−0.0299188	+	0.0920806i
$361$	−0.809017	−	0.587785i	−0.0425798	−	0.0309361i
$362$	−7.32871			−0.385188
$363$	1.98883	−	13.9831i	0.104386	−	0.733922i
$364$	2.87467			0.150674
$365$	−3.90434	−	2.83667i	−0.204363	−	0.148478i
$366$	−3.97170	+	12.2236i	−0.207604	+	0.638940i
$367$	9.13380	+	28.1110i	0.476781	+	1.46738i	0.843541	+	0.537065i	$0.180467\pi$
$367$	9.13380	+	28.1110i	0.476781	+	1.46738i	−0.366760	+	0.930315i	$0.619533\pi$
$368$	−2.31439	+	1.68151i	−0.120646	+	0.0876545i
$369$	11.7949	−	8.56947i	0.614016	−	0.446109i
$370$	−2.62895	−	8.09109i	−0.136673	−	0.420636i
$371$	13.2180	−	40.6807i	0.686242	−	2.11204i
$372$	−8.14544	−	5.91801i	−0.422321	−	0.306834i
$373$	−14.7023			−0.761256			−0.380628	−	0.924728i	$-0.624292\pi$
$373$	−14.7023			−0.761256			−0.380628	+	0.924728i	$0.624292\pi$
$374$	0.811344	+	9.36304i	0.0419536	+	0.484151i
$375$	−14.2287			−0.734766
$376$	−4.66498	−	3.38931i	−0.240578	−	0.174790i
$377$	−1.39370	+	4.28936i	−0.0717791	+	0.220913i
$378$	−5.47006	−	16.8351i	−0.281350	−	0.865905i
$379$	−2.45201	+	1.78149i	−0.125951	+	0.0915090i	−0.648977	−	0.760808i	$-0.724803\pi$
$379$	−2.45201	+	1.78149i	−0.125951	+	0.0915090i	0.523026	+	0.852317i	$0.324803\pi$
$380$	−1.09974	+	0.799009i	−0.0564156	+	0.0409883i
$381$	−0.246468	−	0.758550i	−0.0126269	−	0.0388617i
$382$	−3.76156	+	11.5769i	−0.192458	+	0.592325i
$383$	10.1224	+	7.35435i	0.517230	+	0.375790i	0.815559	−	0.578673i	$-0.196429\pi$
$383$	10.1224	+	7.35435i	0.517230	+	0.375790i	−0.298329	+	0.954463i	$0.596429\pi$
$384$	1.28398			0.0655230
$385$	7.36699	−	12.2378i	0.375457	−	0.623694i
$386$	−14.3405			−0.729913
$387$	−0.188869	−	0.137221i	−0.00960076	−	0.00697536i
$388$	1.24967	−	3.84608i	0.0634423	−	0.195255i
$389$	−3.16210	−	9.73194i	−0.160325	−	0.493429i	0.838337	−	0.545153i	$-0.183528\pi$
$389$	−3.16210	−	9.73194i	−0.160325	−	0.493429i	−0.998661	+	0.0517239i	$0.983528\pi$
$390$	1.28120	−	0.930844i	0.0648759	−	0.0471351i
$391$	−6.55816	+	4.76478i	−0.331661	+	0.240966i
$392$	−0.938785	−	2.88928i	−0.0474158	−	0.145931i
$393$	6.10390	−	18.7859i	0.307901	−	0.947621i
$394$	12.6789	+	9.21179i	0.638756	+	0.464083i
$395$	−7.70743			−0.387803
$396$	4.36633	+	1.01186i	0.219416	+	0.0508478i
$397$	0.277416			0.0139231			0.00696156	−	0.999976i	$-0.497784\pi$
$397$	0.277416			0.0139231			0.00696156	+	0.999976i	$0.497784\pi$
$398$	1.11362	+	0.809093i	0.0558208	+	0.0405562i
$399$	1.25709	−	3.86891i	0.0629330	−	0.193688i
$400$	−0.974068	−	2.99787i	−0.0487034	−	0.149894i
$401$	−5.88846	+	4.27822i	−0.294056	+	0.213644i	−0.725025	−	0.688723i	$-0.758172\pi$
$401$	−5.88846	+	4.27822i	−0.294056	+	0.213644i	0.430969	+	0.902367i	$0.358172\pi$
$402$	−11.9677	+	8.69501i	−0.596892	+	0.433668i
$403$	−2.19860	−	6.76659i	−0.109520	−	0.337068i
$404$	−0.300660	+	0.925337i	−0.0149584	+	0.0460373i
$405$	−3.43075	−	2.49258i	−0.170475	−	0.123857i
$406$	15.7486			0.781592
$407$	−19.1136	+	8.09456i	−0.947426	+	0.401232i
$408$	3.63835			0.180125
$409$	−6.11490	−	4.44274i	−0.302362	−	0.219679i	0.426250	−	0.904605i	$-0.359834\pi$
$409$	−6.11490	−	4.44274i	−0.302362	−	0.219679i	−0.728612	+	0.684926i	$0.759834\pi$
$410$	4.53180	−	13.9475i	0.223810	−	0.688816i
$411$	−3.86865	−	11.9065i	−0.190826	−	0.587303i
$412$	2.46095	−	1.78798i	0.121242	−	0.0880877i
$413$	−2.06299	+	1.49885i	−0.101513	+	0.0737535i
$414$	1.19465	+	3.67676i	0.0587140	+	0.180703i
$415$	1.34388	−	4.13605i	0.0659686	−	0.203031i
$416$	0.734046	+	0.533316i	0.0359896	+	0.0261480i
$417$	−0.279185			−0.0136718
$418$	2.17383	+	2.50489i	0.106325	+	0.122518i
$419$	34.8385			1.70197			0.850986	−	0.525189i	$-0.176005\pi$
$419$	34.8385			1.70197			0.850986	+	0.525189i	$0.176005\pi$
$420$	−4.47376	−	3.25038i	−0.218297	−	0.158602i
$421$	−3.76584	+	11.5901i	−0.183536	+	0.564865i	−0.999920	−	0.0126439i	$-0.995975\pi$
$421$	−3.76584	+	11.5901i	−0.183536	+	0.564865i	0.816384	+	0.577509i	$0.195975\pi$
$422$	−2.79475	−	8.60136i	−0.136046	−	0.418708i
$423$	−6.30419	+	4.58026i	−0.306520	+	0.222700i
$424$	10.9224	−	7.93556i	0.530437	−	0.385385i
$425$	−2.76016	−	8.49490i	−0.133887	−	0.412063i
$426$	−5.23441	+	16.1098i	−0.253608	+	0.780525i
$427$	25.6576	+	18.6413i	1.24166	+	0.902116i
$428$	−9.11810			−0.440740
$429$	−2.53250	−	2.91819i	−0.122270	−	0.140892i
$430$	−0.234832			−0.0113246
$431$	−24.1606	−	17.5537i	−1.16377	−	0.845531i	−0.173523	−	0.984830i	$-0.555515\pi$
$431$	−24.1606	−	17.5537i	−1.16377	−	0.845531i	−0.990250	+	0.139299i	$0.955515\pi$
$432$	1.72651	−	5.31366i	0.0830668	−	0.255653i
$433$	0.0701159	+	0.215795i	0.00336956	+	0.0103704i	0.952727	−	0.303827i	$-0.0982645\pi$
$433$	0.0701159	+	0.215795i	0.00336956	+	0.0103704i	−0.949358	+	0.314198i	$0.898265\pi$
$434$	−20.0992	+	14.6029i	−0.964791	+	0.700962i
$435$	7.01892	−	5.09955i	0.336532	−	0.244505i
$436$	−5.66148	−	17.4242i	−0.271136	−	0.834470i
$437$	−0.884020	+	2.72073i	−0.0422884	+	0.130150i
$438$	3.68786	+	2.67938i	0.176213	+	0.128026i
$439$	15.7258			0.750552			0.375276	−	0.926913i	$-0.377548\pi$
$439$	15.7258			0.750552			0.375276	+	0.926913i	$0.377548\pi$
$440$	4.15153	−	1.75816i	0.197916	−	0.0838171i
$441$	−4.10548			−0.195499
$442$	2.08002	+	1.51123i	0.0989367	+	0.0718817i
$443$	8.80178	−	27.0891i	0.418185	−	1.28704i	−0.491186	−	0.871055i	$-0.663436\pi$
$443$	8.80178	−	27.0891i	0.418185	−	1.28704i	0.909371	−	0.415987i	$-0.136564\pi$
$444$	2.48318	+	7.64246i	0.117847	+	0.362695i
$445$	20.4400	−	14.8506i	0.968951	−	0.703984i
$446$	−2.25255	+	1.63657i	−0.106661	+	0.0774939i
$447$	3.56344	+	10.9671i	0.168545	+	0.518728i
$448$	0.979051	−	3.01321i	0.0462558	−	0.142361i
$449$	13.2171	+	9.60280i	0.623755	+	0.453184i	0.854231	−	0.519894i	$-0.174028\pi$
$449$	13.2171	+	9.60280i	0.623755	+	0.453184i	−0.230476	+	0.973078i	$0.574028\pi$
$450$	−4.25978			−0.200808
$451$	−34.8572	−	8.07784i	−1.64136	−	0.380371i
$452$	2.14352			0.100823
$453$	−11.3797	−	8.26782i	−0.534664	−	0.388456i
$454$	0.930694	−	2.86438i	0.0436797	−	0.134432i
$455$	−1.20755	−	3.71645i	−0.0566107	−	0.174230i
$456$	1.03876	−	0.754706i	0.0486446	−	0.0353424i
$457$	17.5067	−	12.7193i	0.818928	−	0.594986i	−0.0974774	−	0.995238i	$-0.531077\pi$
$457$	17.5067	−	12.7193i	0.818928	−	0.594986i	0.916405	+	0.400252i	$0.131077\pi$
$458$	6.43137	+	19.7937i	0.300518	+	0.924900i
$459$	4.89231	−	15.0570i	0.228354	−	0.702800i
$460$	3.14608	+	2.28576i	0.146687	+	0.106574i
$461$	−9.99146			−0.465349			−0.232674	−	0.972555i	$-0.574748\pi$
$461$	−9.99146			−0.465349			−0.232674	+	0.972555i	$0.574748\pi$
$462$	−6.95851	+	11.5592i	−0.323739	+	0.537783i
$463$	18.7196			0.869972			0.434986	−	0.900437i	$-0.356753\pi$
$463$	18.7196			0.869972			0.434986	+	0.900437i	$0.356753\pi$
$464$	4.02141	+	2.92172i	0.186689	+	0.135638i
$465$	−4.22934	+	13.0166i	−0.196131	+	0.603629i
$466$	−4.87032	−	14.9893i	−0.225613	−	0.694366i
$467$	28.9466	−	21.0310i	1.33949	−	0.973197i	0.340028	−	0.940415i	$-0.389564\pi$
$467$	28.9466	−	21.0310i	1.33949	−	0.973197i	0.999463	−	0.0327812i	$-0.0104365\pi$
$468$	0.991981	−	0.720716i	0.0458543	−	0.0333151i
$469$	11.2797	+	34.7153i	0.520848	+	1.60301i
$470$	−2.42219	+	7.45472i	−0.111727	+	0.343861i
$471$	−23.4618	−	17.0460i	−1.08106	−	0.785437i
$472$	−0.804852			−0.0370463
$473$	0.0494634	+	0.570815i	0.00227433	+	0.0262461i
$474$	7.28007			0.334385
$475$	−2.55014	−	1.85279i	−0.117009	−	0.0850118i
$476$	2.77428	−	8.53836i	0.127159	−	0.391355i
$477$	−5.63795	−	17.3518i	−0.258144	−	0.794486i
$478$	−20.5155	+	14.9054i	−0.938356	+	0.681755i
$479$	−9.99354	+	7.26073i	−0.456617	+	0.331751i	−0.792203	−	0.610258i	$-0.791066\pi$
$479$	−9.99354	+	7.26073i	−0.456617	+	0.331751i	0.335586	+	0.942010i	$0.391066\pi$
$480$	−0.539355	−	1.65996i	−0.0246181	−	0.0757667i
$481$	−1.75475	+	5.40057i	−0.0800098	+	0.246245i
$482$	6.35488	+	4.61709i	0.289457	+	0.210303i
$483$	−11.6376			−0.529527
$484$	−5.14809	−	9.72097i	−0.234004	−	0.441862i
$485$	−5.49725			−0.249617
$486$	−10.3197	−	7.49768i	−0.468110	−	0.340102i
$487$	4.31641	−	13.2845i	0.195595	−	0.601980i	−0.804374	−	0.594123i	$-0.797499\pi$
$487$	4.31641	−	13.2845i	0.195595	−	0.601980i	0.999969	−	0.00785657i	$-0.00250085\pi$
$488$	3.09327	+	9.52009i	0.140026	+	0.430954i
$489$	13.4906	−	9.80153i	0.610068	−	0.443240i
$490$	−3.34098	+	2.42737i	−0.150930	+	0.109657i
$491$	1.06563	+	3.27968i	0.0480913	+	0.148010i	0.972219	−	0.234075i	$-0.0752062\pi$
$491$	1.06563	+	3.27968i	0.0480913	+	0.148010i	−0.924127	+	0.382085i	$0.875206\pi$
$492$	−4.28053	+	13.1741i	−0.192981	+	0.593935i
$493$	11.3952	+	8.27912i	0.513215	+	0.372873i
$494$	0.907331			0.0408228
$495$	−0.525984	−	6.06995i	−0.0236412	−	0.272824i
$496$	−7.84147			−0.352092
$497$	33.8148	+	24.5679i	1.51680	+	1.10202i
$498$	−1.26937	+	3.90671i	−0.0568818	+	0.175064i
$499$	−13.4191	−	41.2998i	−0.600722	−	1.84883i	−0.523886	−	0.851789i	$-0.675518\pi$
$499$	−13.4191	−	41.2998i	−0.600722	−	1.84883i	−0.0768364	−	0.997044i	$-0.524482\pi$
$500$	−8.96526	+	6.51365i	−0.400939	+	0.291299i
$501$	2.78668	−	2.02464i	0.124500	−	0.0904542i
$502$	−2.13571	−	6.57303i	−0.0953212	−	0.293369i
$503$	−9.02755	+	27.7839i	−0.402518	+	1.23882i	0.520431	+	0.853904i	$0.325771\pi$
$503$	−9.02755	+	27.7839i	−0.402518	+	1.23882i	−0.922950	+	0.384921i	$0.874229\pi$
$504$	−3.46386	−	2.51664i	−0.154293	−	0.112100i
$505$	1.32260			0.0588547
$506$	4.89343	−	8.12878i	0.217540	−	0.361368i
$507$	15.6347			0.694363
$508$	−0.502546	−	0.365121i	−0.0222969	−	0.0161996i
$509$	−11.6960	+	35.9967i	−0.518417	+	1.59552i	0.258560	+	0.965995i	$0.416752\pi$
$509$	−11.6960	+	35.9967i	−0.518417	+	1.59552i	−0.776977	+	0.629529i	$0.783248\pi$
$510$	−1.52834	−	4.70375i	−0.0676760	−	0.208285i
$511$	9.09992	−	6.61148i	0.402557	−	0.292475i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	−1.72651	−	5.31366i	−0.0762273	−	0.234604i
$514$	2.30333	−	7.08891i	0.101595	−	0.312678i
$515$	−3.34531	−	2.43051i	−0.147412	−	0.107101i
$516$	0.221811			0.00976468
$517$	18.6307	+	4.31750i	0.819377	+	0.189883i
$518$	19.8285			0.871215
$519$	2.73748	+	1.98890i	0.120162	+	0.0873028i
$520$	0.381137	−	1.17302i	0.0167140	−	0.0514403i
$521$	−8.29708	−	25.5358i	−0.363502	−	1.11874i	−0.950914	−	0.309455i	$-0.899853\pi$
$521$	−8.29708	−	25.5358i	−0.363502	−	1.11874i	0.587412	−	0.809288i	$-0.300147\pi$
$522$	5.43448	−	3.94838i	0.237861	−	0.172816i
$523$	−16.1197	+	11.7117i	−0.704867	+	0.512116i	−0.881514	−	0.472158i	$-0.843475\pi$
$523$	−16.1197	+	11.7117i	−0.704867	+	0.512116i	0.176646	+	0.984274i	$0.443475\pi$
$524$	−4.75388	−	14.6309i	−0.207674	−	0.639155i
$525$	3.96252	−	12.1954i	0.172939	−	0.532251i
$526$	−7.36790	−	5.35309i	−0.321256	−	0.233406i
$527$	−22.2199			−0.967915
$528$	−3.92134	+	1.66068i	−0.170654	+	0.0722717i
$529$	−14.8161			−0.644179
$530$	−14.8474	−	10.7873i	−0.644929	−	0.468568i
$531$	−0.336107	+	1.03443i	−0.0145858	+	0.0448905i
$532$	−0.979051	−	3.01321i	−0.0424472	−	0.130639i
$533$	−7.91916	+	5.75360i	−0.343017	+	0.249216i
$534$	−19.3067	+	14.0271i	−0.835483	+	0.607014i
$535$	3.83018	+	11.7881i	0.165593	+	0.509644i
$536$	−3.56020	+	10.9572i	−0.153777	+	0.473278i
$537$	13.0547	+	9.48479i	0.563352	+	0.409299i
$538$	15.7555			0.679269
$539$	6.60402	+	7.60978i	0.284455	+	0.327777i
$540$	−7.59487			−0.326831
$541$	9.57724	+	6.95827i	0.411758	+	0.299160i	0.774313	−	0.632803i	$-0.218096\pi$
$541$	9.57724	+	6.95827i	0.411758	+	0.299160i	−0.362555	+	0.931962i	$0.618096\pi$
$542$	6.48960	−	19.9729i	0.278752	−	0.857910i
$543$	−2.90783	−	8.94939i	−0.124787	−	0.384055i
$544$	2.29246	−	1.66557i	0.0982886	−	0.0714108i
$545$	−20.1483	+	14.6386i	−0.863059	+	0.627049i
$546$	1.14059	+	3.51038i	0.0488128	+	0.150230i
$547$	−12.7096	+	39.1161i	−0.543423	+	1.67248i	0.181286	+	0.983430i	$0.441974\pi$
$547$	−12.7096	+	39.1161i	−0.543423	+	1.67248i	−0.724710	+	0.689054i	$0.758026\pi$
$548$	−7.88815	−	5.73107i	−0.336965	−	0.244819i
$549$	13.5274			0.577336
$550$	6.85223	+	7.89579i	0.292180	+	0.336678i
$551$	4.97073			0.211760
$552$	−2.97164	−	2.15902i	−0.126482	−	0.0918942i
$553$	5.55113	−	17.0846i	0.236058	−	0.726512i
$554$	4.28130	+	13.1765i	0.181895	+	0.559816i
$555$	8.83726	−	6.42064i	0.375121	−	0.272541i
$556$	−0.175910	+	0.127806i	−0.00746025	+	0.00542019i
$557$	−4.74975	−	14.6182i	−0.201253	−	0.619394i	−0.999846	−	0.0175228i	$-0.994422\pi$
$557$	−4.74975	−	14.6182i	−0.201253	−	0.619394i	0.798593	−	0.601871i	$-0.205578\pi$
$558$	−3.27461	+	10.0782i	−0.138625	+	0.426645i
$559$	0.126808	+	0.0921315i	0.00536341	+	0.00389675i
$560$	−4.30681			−0.181996
$561$	−11.1117	+	4.70576i	−0.469135	+	0.198677i
$562$	−9.64862			−0.407003
$563$	12.6235	+	9.17153i	0.532018	+	0.386534i	0.821112	−	0.570767i	$-0.193354\pi$
$563$	12.6235	+	9.17153i	0.532018	+	0.386534i	−0.289094	+	0.957301i	$0.593354\pi$
$564$	2.28788	−	7.04138i	0.0963372	−	0.296495i
$565$	−0.900417	−	2.77120i	−0.0378808	−	0.116585i
$566$	−14.9427	+	10.8565i	−0.628087	+	0.456332i
$567$	7.99610	−	5.80951i	0.335805	−	0.243976i
$568$	4.07669	+	12.5468i	0.171054	+	0.526451i
$569$	11.1888	−	34.4357i	0.469060	−	1.44362i	−0.384744	−	0.923023i	$-0.625710\pi$
$569$	11.1888	−	34.4357i	0.469060	−	1.44362i	0.853804	−	0.520595i	$-0.174290\pi$
$570$	−1.41205	−	1.02591i	−0.0591443	−	0.0429708i
$571$	10.4696			0.438138			0.219069	−	0.975709i	$-0.429698\pi$
$571$	10.4696			0.438138			0.219069	+	0.975709i	$0.429698\pi$
$572$	−2.93159	−	0.679369i	−0.122576	−	0.0284058i
$573$	−15.6295			−0.652932
$574$	27.6526	+	20.0908i	1.15420	+	0.838574i
$575$	−2.78656	+	8.57616i	−0.116208	+	0.357651i
$576$	−0.417602	−	1.28525i	−0.0174001	−	0.0535519i
$577$	−15.7908	+	11.4727i	−0.657378	+	0.477613i	−0.865776	−	0.500431i	$-0.833175\pi$
$577$	−15.7908	+	11.4727i	−0.657378	+	0.477613i	0.208399	+	0.978044i	$0.433175\pi$
$578$	−7.25727	+	5.27271i	−0.301862	+	0.219316i
$579$	−5.68992	−	17.5118i	−0.236465	−	0.727765i
$580$	2.08803	−	6.42628i	0.0867005	−	0.266837i
$581$	8.20024	+	5.95782i	0.340203	+	0.247172i
$582$	5.19244			0.215234
$583$	−23.0937	+	38.3623i	−0.956442	+	1.58880i
$584$	3.55023			0.146910
$585$	−1.34845	−	0.979710i	−0.0557517	−	0.0405060i
$586$	2.08182	−	6.40717i	0.0859991	−	0.264678i
$587$	5.94874	+	18.3084i	0.245531	+	0.755667i	0.995549	+	0.0942488i	$0.0300449\pi$
$587$	5.94874	+	18.3084i	0.245531	+	0.755667i	−0.750018	+	0.661418i	$0.769955\pi$
$588$	3.15574	−	2.29278i	0.130140	−	0.0945525i
$589$	−6.34388	+	4.60910i	−0.261395	+	0.189915i
$590$	0.338089	+	1.04053i	0.0139189	+	0.0428380i
$591$	−6.21823	+	19.1377i	−0.255784	+	0.787222i
$592$	5.06320	+	3.67863i	0.208096	+	0.151191i
$593$	8.08792			0.332131			0.166066	−	0.986115i	$-0.446894\pi$
$593$	8.08792			0.332131			0.166066	+	0.986115i	$0.446894\pi$
$594$	1.59973	+	18.4612i	0.0656378	+	0.757471i
$595$	−12.2040			−0.500314
$596$	7.26583	+	5.27894i	0.297620	+	0.216234i
$597$	−0.546162	+	1.68091i	−0.0223529	+	0.0687952i
$598$	−0.802099	−	2.46861i	−0.0328003	−	0.100949i
$599$	−34.1882	+	24.8392i	−1.39689	+	1.01490i	−0.401824	+	0.915717i	$0.631624\pi$
$599$	−34.1882	+	24.8392i	−1.39689	+	1.01490i	−0.995069	+	0.0991855i	$0.968376\pi$
$600$	3.27434	−	2.37895i	0.133674	−	0.0971202i
$601$	11.9945	+	36.9151i	0.489264	+	1.50580i	0.825709	+	0.564097i	$0.190775\pi$
$601$	11.9945	+	36.9151i	0.489264	+	1.50580i	−0.336445	+	0.941703i	$0.609225\pi$
$602$	0.169133	−	0.520539i	0.00689336	−	0.0212156i
$603$	12.5959	+	9.15146i	0.512945	+	0.372676i
$604$	−10.9550			−0.445753
$605$	−10.4050	+	10.7390i	−0.423022	+	0.436602i
$606$	−1.24926			−0.0507478
$607$	−13.7732	−	10.0068i	−0.559037	−	0.406164i	0.272069	−	0.962278i	$-0.412292\pi$
$607$	−13.7732	−	10.0068i	−0.559037	−	0.406164i	−0.831106	+	0.556113i	$0.812292\pi$
$608$	0.309017	−	0.951057i	0.0125323	−	0.0385704i
$609$	6.24863	+	19.2313i	0.253207	+	0.779292i
$610$	11.0084	−	7.99810i	0.445719	−	0.323834i
$611$	4.23268	−	3.07522i	0.171236	−	0.124410i
$612$	−1.18333	−	3.64193i	−0.0478334	−	0.147216i
$613$	2.66590	−	8.20480i	0.107675	−	0.331389i	−0.882674	−	0.469985i	$-0.844259\pi$
$613$	2.66590	−	8.20480i	0.107675	−	0.331389i	0.990349	+	0.138597i	$0.0442591\pi$
$614$	−11.1790	−	8.12198i	−0.451146	−	0.327777i
$615$	18.8299			0.759295
$616$	0.907158	+	10.4688i	0.0365504	+	0.421798i
$617$	27.1013			1.09106			0.545528	−	0.838092i	$-0.316329\pi$
$617$	27.1013			1.09106			0.545528	+	0.838092i	$0.316329\pi$
$618$	3.15982	+	2.29574i	0.127106	+	0.0923483i
$619$	3.57394	−	10.9995i	0.143649	−	0.442105i	−0.853186	−	0.521607i	$-0.825333\pi$
$619$	3.57394	−	10.9995i	0.143649	−	0.442105i	0.996835	+	0.0795014i	$0.0253328\pi$
$620$	3.29392	+	10.1376i	0.132287	+	0.407138i
$621$	−12.9308	+	9.39475i	−0.518894	+	0.376998i
$622$	−18.7307	+	13.6087i	−0.751033	+	0.545658i
$623$	18.1969	+	56.0042i	0.729042	+	2.24376i
$624$	−0.360004	+	1.10798i	−0.0144117	+	0.0443546i
$625$	−0.563739	−	0.409580i	−0.0225496	−	0.0163832i
$626$	17.0322			0.680745
$627$	−2.19631	+	3.64842i	−0.0877121	+	0.145704i
$628$	−22.5862			−0.901288
$629$	14.3473	+	10.4239i	0.572064	+	0.415629i
$630$	−1.79853	+	5.53531i	−0.0716552	+	0.220532i
$631$	0.0556839	+	0.171378i	0.00221674	+	0.00682243i	0.952159	−	0.305604i	$-0.0988583\pi$
$631$	0.0556839	+	0.171378i	0.00221674	+	0.00682243i	−0.949942	+	0.312426i	$0.898858\pi$
$632$	4.58705	−	3.33269i	0.182463	−	0.132567i
$633$	9.39459	−	6.82557i	0.373402	−	0.271292i
$634$	9.89345	+	30.4489i	0.392919	+	1.20928i
$635$	−0.260936	+	0.803079i	−0.0103549	+	0.0318692i
$636$	14.0241	+	10.1891i	0.556093	+	0.404025i
$637$	2.75645			0.109214
$638$	−16.0604	−	3.72186i	−0.635839	−	0.147350i
$639$	17.8281			0.705270
$640$	−1.09974	−	0.799009i	−0.0434711	−	0.0315836i
$641$	−1.10017	+	3.38599i	−0.0434543	+	0.133739i	−0.970430	−	0.241383i	$-0.922399\pi$
$641$	−1.10017	+	3.38599i	−0.0434543	+	0.133739i	0.926976	+	0.375122i	$0.122399\pi$
$642$	−3.61781	−	11.1345i	−0.142784	−	0.439443i
$643$	−18.8796	+	13.7169i	−0.744540	+	0.540940i	−0.894130	−	0.447808i	$-0.852205\pi$
$643$	−18.8796	+	13.7169i	−0.744540	+	0.540940i	0.149590	+	0.988748i	$0.452205\pi$
$644$	−7.33264	+	5.32747i	−0.288946	+	0.209932i
$645$	−0.0931748	−	0.286763i	−0.00366875	−	0.0112913i
$646$	0.875643	−	2.69495i	0.0344517	−	0.106032i
$647$	28.6561	+	20.8199i	1.12659	+	0.818514i	0.985195	−	0.171439i	$-0.0548418\pi$
$647$	28.6561	+	20.8199i	1.12659	+	0.818514i	0.141393	+	0.989953i	$0.454842\pi$
$648$	3.11959			0.122549
$649$	2.45805	−	1.04098i	0.0964869	−	0.0408620i
$650$	2.86005			0.112180
$651$	−25.8070	−	18.7499i	−1.01146	−	0.734866i
$652$	4.01327	−	12.3516i	0.157172	−	0.483725i
$653$	−6.01502	−	18.5123i	−0.235386	−	0.724443i	−0.997070	−	0.0764945i	$-0.975627\pi$
$653$	−6.01502	−	18.5123i	−0.235386	−	0.724443i	0.761684	−	0.647948i	$-0.224373\pi$
$654$	19.0311	−	13.8269i	0.744176	−	0.540676i
$655$	−16.9183	+	12.2919i	−0.661052	+	0.480282i
$656$	3.33379	+	10.2603i	0.130163	+	0.400599i
$657$	1.48258	−	4.56292i	0.0578411	−	0.178017i
$658$	−14.7799	−	10.7383i	−0.576182	−	0.418621i
$659$	−40.4633			−1.57622			−0.788112	−	0.615531i	$-0.788941\pi$
$659$	−40.4633			−1.57622			−0.788112	+	0.615531i	$0.788941\pi$
$660$	3.79418	+	4.37201i	0.147688	+	0.170180i
$661$	30.5618			1.18872			0.594358	−	0.804201i	$-0.297406\pi$
$661$	30.5618			1.18872			0.594358	+	0.804201i	$0.297406\pi$
$662$	−16.0303	−	11.6467i	−0.623037	−	0.452663i
$663$	−1.02012	+	3.13961i	−0.0396183	+	0.121933i
$664$	0.988618	+	3.04265i	0.0383658	+	0.118078i
$665$	−3.48429	+	2.53148i	−0.135115	+	0.0981667i
$666$	6.84234	−	4.97125i	0.265135	−	0.192632i
$667$	−4.39423	−	13.5240i	−0.170145	−	0.523653i
$668$	0.828995	−	2.55139i	0.0320748	−	0.0987161i
$669$	−2.89223	−	2.10133i	−0.111820	−	0.0812421i
$670$	15.6612			0.605045
$671$	−21.7600	−	25.0740i	−0.840037	−	0.967971i
$672$	4.06801			0.156927
$673$	39.7947	+	28.9126i	1.53397	+	1.11450i	0.953977	+	0.299879i	$0.0969462\pi$
$673$	39.7947	+	28.9126i	1.53397	+	1.11450i	0.579997	+	0.814619i	$0.303054\pi$
$674$	10.0544	−	30.9443i	0.387282	−	1.19193i
$675$	−5.44223	−	16.7494i	−0.209471	−	0.644687i
$676$	9.85120	−	7.15731i	0.378892	−	0.275281i
$677$	−2.55548	+	1.85666i	−0.0982149	+	0.0713573i	−0.635809	−	0.771847i	$-0.719333\pi$
$677$	−2.55548	+	1.85666i	−0.0982149	+	0.0713573i	0.537594	+	0.843204i	$0.319333\pi$
$678$	0.850491	+	2.61754i	0.0326629	+	0.100526i
$679$	3.95929	−	12.1854i	0.151944	−	0.467634i
$680$	−3.11627	−	2.26411i	−0.119504	−	0.0868245i
$681$	3.86709			0.148187
$682$	23.9482	−	10.1420i	0.917023	−	0.388357i
$683$	−32.2822			−1.23524			−0.617621	−	0.786476i	$-0.711904\pi$
$683$	−32.2822			−1.23524			−0.617621	+	0.786476i	$0.711904\pi$
$684$	−1.09330	−	0.794325i	−0.0418032	−	0.0303718i
$685$	−4.09574	+	12.6054i	−0.156490	+	0.481628i
$686$	3.87903	+	11.9384i	0.148102	+	0.455811i
$687$	−21.6191	+	15.7072i	−0.824821	+	0.599267i
$688$	0.139759	−	0.101541i	0.00532828	−	0.00387122i
$689$	3.78536	+	11.6501i	0.144211	+	0.443835i
$690$	−1.54296	+	4.74874i	−0.0587395	+	0.180781i
$691$	−15.8560	−	11.5201i	−0.603191	−	0.438244i	0.243819	−	0.969821i	$-0.421600\pi$
$691$	−15.8560	−	11.5201i	−0.603191	−	0.438244i	−0.847010	+	0.531577i	$0.821600\pi$
$692$	2.63532			0.100180
$693$	13.8337	+	3.20585i	0.525501	+	0.121780i
$694$	7.35177			0.279069
$695$	0.239125	+	0.173734i	0.00907051	+	0.00659011i
$696$	−1.97225	+	6.06996i	−0.0747580	+	0.230081i
$697$	9.44676	+	29.0741i	0.357822	+	1.10126i
$698$	−16.5070	+	11.9930i	−0.624797	+	0.453942i
$699$	16.3716	−	11.8947i	0.619232	−	0.449898i
$700$	−3.08612	−	9.49809i	−0.116644	−	0.358994i
$701$	−5.90860	+	18.1848i	−0.223165	+	0.686830i	0.775308	+	0.631583i	$0.217595\pi$
$701$	−5.90860	+	18.1848i	−0.223165	+	0.686830i	−0.998473	+	0.0552468i	$0.982405\pi$
$702$	4.10120	+	2.97969i	0.154790	+	0.112461i
$703$	6.25846			0.236042
$704$	−1.71054	+	2.84149i	−0.0644685	+	0.107093i
$705$	−10.0643			−0.379044
$706$	−16.7832	−	12.1937i	−0.631642	−	0.458915i
$707$	−0.952575	+	2.93172i	−0.0358253	+	0.110259i
$708$	−0.319343	−	0.982837i	−0.0120016	−	0.0369373i
$709$	2.40475	−	1.74716i	0.0903124	−	0.0656158i	−0.541713	−	0.840564i	$-0.682224\pi$
$709$	2.40475	−	1.74716i	0.0903124	−	0.0656158i	0.632025	+	0.774948i	$0.282224\pi$
$710$	14.5083	−	10.5409i	0.544487	−	0.395593i
$711$	−2.36776	−	7.28723i	−0.0887981	−	0.273292i
$712$	−5.74346	+	17.6765i	−0.215245	+	0.662457i
$713$	18.1483	+	13.1855i	0.679657	+	0.493800i
$714$	11.5273			0.431398
$715$	0.353150	+	4.07541i	0.0132071	+	0.152412i
$716$	12.5675			0.469671
$717$	−26.3415	−	19.1382i	−0.983742	−	0.714730i
$718$	9.11019	−	28.0383i	0.339989	−	1.04638i
$719$	12.1365	+	37.3524i	0.452617	+	1.39301i	0.873911	+	0.486087i	$0.161576\pi$
$719$	12.1365	+	37.3524i	0.452617	+	1.39301i	−0.421294	+	0.906924i	$0.638424\pi$
$720$	−1.48618	+	1.07977i	−0.0553866	+	0.0402407i
$721$	7.79697	−	5.66483i	0.290374	−	0.210969i
$722$	−0.309017	−	0.951057i	−0.0115004	−	0.0353947i
$723$	−3.11668	+	9.59214i	−0.115910	+	0.356736i
$724$	−5.92905	−	4.30771i	−0.220351	−	0.160095i
$725$	15.6685			0.581913
$726$	9.82805	−	10.1436i	0.364753	−	0.376463i
$727$	−5.38463			−0.199705			−0.0998525	−	0.995002i	$-0.531837\pi$
$727$	−5.38463			−0.199705			−0.0998525	+	0.995002i	$0.531837\pi$
$728$	2.32566	+	1.68969i	0.0861947	+	0.0626241i
$729$	7.95318	−	24.4774i	0.294562	−	0.906569i
$730$	−1.49133	−	4.58983i	−0.0551964	−	0.169877i
$731$	0.396028	−	0.287731i	0.0146476	−	0.0106421i
$732$	−10.3980	+	7.55462i	−0.384323	+	0.279227i
$733$	0.707464	+	2.17735i	0.0261308	+	0.0804223i	0.963271	−	0.268530i	$-0.0865377\pi$
$733$	0.707464	+	2.17735i	0.0261308	+	0.0804223i	−0.937141	+	0.348952i	$0.886538\pi$
$734$	−9.13380	+	28.1110i	−0.337135	+	1.03759i
$735$	−4.28977	−	3.11670i	−0.158230	−	0.114961i
$736$	−2.86075			−0.105449
$737$	−3.29877	−	38.0683i	−0.121512	−	1.40227i
$738$	14.5793			0.536670
$739$	−23.9093	−	17.3712i	−0.879520	−	0.639008i	0.0536048	−	0.998562i	$-0.482929\pi$
$739$	−23.9093	−	17.3712i	−0.879520	−	0.639008i	−0.933124	+	0.359554i	$0.882929\pi$
$740$	2.62895	−	8.09109i	0.0966422	−	0.297434i
$741$	0.360004	+	1.10798i	0.0132251	+	0.0407026i
$742$	34.6051	−	25.1421i	1.27039	−	0.922994i
$743$	−17.6573	+	12.8288i	−0.647783	+	0.470642i	−0.862515	−	0.506031i	$-0.831112\pi$
$743$	−17.6573	+	12.8288i	−0.647783	+	0.470642i	0.214732	+	0.976673i	$0.431112\pi$
$744$	−3.11128	−	9.57554i	−0.114065	−	0.351056i
$745$	3.77262	−	11.6109i	0.138218	−	0.425392i
$746$	−11.8944	−	8.64179i	−0.435485	−	0.316398i
$747$	4.32340			0.158185
$748$	−4.84707	+	8.05175i	−0.177226	+	0.294401i
$749$	−28.8886			−1.05557
$750$	−11.5112	−	8.36341i	−0.420331	−	0.305389i
$751$	−5.63235	+	17.3346i	−0.205527	+	0.632548i	0.794164	+	0.607703i	$0.207909\pi$
$751$	−5.63235	+	17.3346i	−0.205527	+	0.632548i	−0.999691	+	0.0248446i	$0.992091\pi$
$752$	−1.78186	−	5.48401i	−0.0649779	−	0.199981i
$753$	7.17920	−	5.21599i	0.261625	−	0.190081i
$754$	−3.64875	+	2.65097i	−0.132880	+	0.0965426i
$755$	4.60181	+	14.1629i	0.167477	+	0.515441i
$756$	5.47006	−	16.8351i	0.198944	−	0.612288i
$757$	−3.30918	−	2.40426i	−0.120274	−	0.0873844i	0.526022	−	0.850471i	$-0.323683\pi$
$757$	−3.30918	−	2.40426i	−0.120274	−	0.0873844i	−0.646296	+	0.763087i	$0.723683\pi$
$758$	−3.03085			−0.110085
$759$	11.8680	+	2.75029i	0.430780	+	0.0998293i
$760$	−1.35936			−0.0493090
$761$	−1.14127	−	0.829182i	−0.0413711	−	0.0300578i	0.566908	−	0.823781i	$-0.308140\pi$
$761$	−1.14127	−	0.829182i	−0.0413711	−	0.0300578i	−0.608279	+	0.793724i	$0.708140\pi$
$762$	0.246468	−	0.758550i	0.00892859	−	0.0274794i
$763$	−17.9371	−	55.2048i	−0.649368	−	1.99855i
$764$	−9.84789	+	7.15491i	−0.356284	+	0.258856i
$765$	−4.21129	+	3.05968i	−0.152260	+	0.110623i
$766$	3.86641	+	11.8996i	0.139699	+	0.429950i
$767$	0.225665	−	0.694525i	0.00814829	−	0.0250778i
$768$	1.03876	+	0.754706i	0.0374832	+	0.0272331i
$769$	43.5034			1.56877			0.784387	−	0.620272i	$-0.212978\pi$
$769$	43.5034			1.56877			0.784387	+	0.620272i	$0.212978\pi$
$770$	13.1532	−	5.57034i	0.474008	−	0.200741i
$771$	9.57045			0.344671
$772$	−11.6017	−	8.42914i	−0.417555	−	0.303371i
$773$	5.74704	−	17.6876i	0.206707	−	0.636178i	−0.792932	−	0.609310i	$-0.791447\pi$
$773$	5.74704	−	17.6876i	0.206707	−	0.636178i	0.999639	−	0.0268681i	$-0.00855342\pi$
$774$	−0.0721416	−	0.222029i	−0.00259308	−	0.00798067i
$775$	−19.9969	+	14.5286i	−0.718309	+	0.521882i
$776$	3.27167	−	2.37701i	0.117446	−	0.0853296i
$777$	7.86741	+	24.2134i	0.282242	+	0.868651i
$778$	3.16210	−	9.73194i	0.113367	−	0.348907i
$779$	8.72797	+	6.34124i	0.312712	+	0.227199i
$780$	1.58365			0.0567036
$781$	−28.6781	−	33.0457i	−1.02618	−	1.18247i
$782$	−8.10634			−0.289882
$783$	22.4680	+	16.3240i	0.802942	+	0.583371i
$784$	0.938785	−	2.88928i	0.0335280	−	0.103189i
$785$	9.48766	+	29.2000i	0.338629	+	1.04219i
$786$	15.9802	−	11.6103i	0.569995	−	0.414126i
$787$	19.9001	−	14.4583i	0.709361	−	0.515381i	−0.173606	−	0.984815i	$-0.555542\pi$
$787$	19.9001	−	14.4583i	0.709361	−	0.515381i	0.882968	+	0.469434i	$0.155542\pi$
$788$	4.84292	+	14.9050i	0.172522	+	0.530968i
$789$	3.61350	−	11.1212i	0.128644	−	0.395925i
$790$	−6.23544	−	4.53031i	−0.221847	−	0.161181i
$791$	6.79127			0.241470
$792$	2.93768	+	3.38508i	0.104386	+	0.120283i
$793$	−9.08240			−0.322525
$794$	0.224434	+	0.163061i	0.00796488	+	0.00578682i
$795$	7.28172	−	22.4108i	0.258256	−	0.794830i
$796$	0.425365	+	1.30914i	0.0150767	+	0.0464012i
$797$	1.65857	−	1.20502i	0.0587496	−	0.0426841i	−0.558023	−	0.829826i	$-0.688440\pi$
$797$	1.65857	−	1.20502i	0.0587496	−	0.0426841i	0.616772	+	0.787141i	$0.288440\pi$
$798$	3.29109	−	2.39112i	0.116503	−	0.0846447i
$799$	−5.04916	−	15.5397i	−0.178627	−	0.549756i
$800$	0.974068	−	2.99787i	0.0344385	−	0.105991i
$801$	20.3202	+	14.7635i	0.717980	+	0.521643i
$802$	−7.27854			−0.257014
$803$	−10.8426	+	4.59180i	−0.382626	+	0.162041i
$804$	−14.7928			−0.521703
$805$	9.96766	+	7.24193i	0.351314	+	0.255245i
$806$	2.19860	−	6.76659i	0.0774423	−	0.238343i
$807$	6.25136	+	19.2397i	0.220058	+	0.677270i
$808$	−0.787139	+	0.571890i	−0.0276915	+	0.0201190i
$809$	2.80011	−	2.03440i	0.0984467	−	0.0715257i	−0.537473	−	0.843281i	$-0.680621\pi$
$809$	2.80011	−	2.03440i	0.0984467	−	0.0715257i	0.635920	+	0.771755i	$0.280621\pi$
$810$	−1.31043	−	4.03308i	−0.0460438	−	0.141708i
$811$	−3.98224	+	12.2561i	−0.139835	+	0.430369i	−0.996311	−	0.0858188i	$-0.972649\pi$
$811$	−3.98224	+	12.2561i	−0.139835	+	0.430369i	0.856475	+	0.516188i	$0.172649\pi$
$812$	12.7409	+	9.25682i	0.447119	+	0.324851i
$813$	26.9646			0.945691
$814$	−20.2211	−	4.68605i	−0.708749	−	0.164246i
$815$	−17.6542			−0.618401
$816$	2.94349	+	2.13857i	0.103043	+	0.0748648i
$817$	0.0533834	−	0.164297i	0.00186765	−	0.00574803i
$818$	−2.33569	−	7.18850i	−0.0816653	−	0.251340i
$819$	3.14287	−	2.28343i	0.109821	−	0.0797894i
$820$	11.8644	−	8.62000i	0.414323	−	0.301024i
$821$	5.71573	+	17.5912i	0.199480	+	0.613937i	0.999895	+	0.0144904i	$0.00461260\pi$
$821$	5.71573	+	17.5912i	0.199480	+	0.613937i	−0.800415	+	0.599447i	$0.795387\pi$
$822$	3.86865	−	11.9065i	0.134935	−	0.415286i
$823$	−40.6000	−	29.4976i	−1.41523	−	1.02822i	−0.992536	−	0.121949i	$-0.961086\pi$
$823$	−40.6000	−	29.4976i	−1.41523	−	1.02822i	−0.422691	−	0.906274i	$-0.638914\pi$
$824$	3.04190			0.105970
$825$	−6.92310	+	11.5004i	−0.241031	+	0.400392i
$826$	−2.54999			−0.0887256
$827$	21.2609	+	15.4469i	0.739313	+	0.537143i	0.892496	−	0.451055i	$-0.148952\pi$
$827$	21.2609	+	15.4469i	0.739313	+	0.537143i	−0.153183	+	0.988198i	$0.548952\pi$
$828$	−1.19465	+	3.67676i	−0.0415171	+	0.127776i
$829$	−4.91046	−	15.1128i	−0.170547	−	0.524891i	0.828855	−	0.559464i	$-0.188993\pi$
$829$	−4.91046	−	15.1128i	−0.170547	−	0.524891i	−0.999402	+	0.0345730i	$0.988993\pi$
$830$	3.51833	−	2.55622i	0.122123	−	0.0887276i
$831$	−14.3917	+	10.4561i	−0.499241	+	0.362720i
$832$	0.280381	+	0.862923i	0.00972045	+	0.0299165i
$833$	2.66018	−	8.18719i	0.0921698	−	0.283669i
$834$	−0.225866	−	0.164101i	−0.00782109	−	0.00568235i
$835$	−3.64672			−0.126200
$836$	0.286325	+	3.30424i	0.00990277	+	0.114280i
$837$	−43.8111			−1.51433
$838$	28.1849	+	20.4776i	0.973632	+	0.707385i
$839$	1.48688	−	4.57616i	0.0513330	−	0.157987i	−0.922104	−	0.386943i	$-0.873531\pi$
$839$	1.48688	−	4.57616i	0.0513330	−	0.157987i	0.973437	+	0.228956i	$0.0735312\pi$
$840$	−1.70883	−	5.25923i	−0.0589601	−	0.181461i
$841$	3.47216	−	2.52267i	0.119730	−	0.0869887i
$842$	−9.85910	+	7.16305i	−0.339767	+	0.246855i
$843$	−3.82831	−	11.7823i	−0.131854	−	0.405805i
$844$	2.79475	−	8.60136i	0.0961993	−	0.296071i
$845$	−13.3913	−	9.72934i	−0.460674	−	0.334699i
$846$	−7.79241			−0.267909
$847$	−16.3106	−	30.7987i	−0.560437	−	1.05826i
$848$	13.5008			0.463619
$849$	−19.1861	−	13.9395i	−0.658466	−	0.478403i
$850$	2.76016	−	8.49490i	0.0946727	−	0.291373i
$851$	−5.53260	−	17.0276i	−0.189655	−	0.583698i
$852$	−13.7039	+	9.95643i	−0.469486	+	0.341102i
$853$	41.3996	−	30.0785i	1.41749	−	1.02987i	0.425315	−	0.905045i	$-0.360163\pi$
$853$	41.3996	−	30.0785i	1.41749	−	1.02987i	0.992179	−	0.124824i	$-0.0398366\pi$
$854$	9.80032	+	30.1623i	0.335360	+	1.03213i
$855$	−0.567669	+	1.74711i	−0.0194139	+	0.0597498i
$856$	−7.37670	−	5.35948i	−0.252130	−	0.183183i
$857$	−33.0439			−1.12876			−0.564379	−	0.825516i	$-0.690884\pi$
$857$	−33.0439			−1.12876			−0.564379	+	0.825516i	$0.690884\pi$
$858$	−0.333569	−	3.84944i	−0.0113878	−	0.131418i
$859$	−50.3474			−1.71783			−0.858915	−	0.512117i	$-0.828861\pi$
$859$	−50.3474			−1.71783			−0.858915	+	0.512117i	$0.828861\pi$
$860$	−0.189983	−	0.138031i	−0.00647836	−	0.00470681i
$861$	−13.5619	+	41.7392i	−0.462188	+	1.42247i
$862$	−9.22851	−	28.4024i	−0.314324	−	0.967391i
$863$	−19.7120	+	14.3216i	−0.671005	+	0.487514i	−0.870362	−	0.492413i	$-0.836115\pi$
$863$	−19.7120	+	14.3216i	−0.671005	+	0.487514i	0.199356	+	0.979927i	$0.436115\pi$
$864$	4.52007	−	3.28402i	0.153776	−	0.111725i
$865$	−1.10700	−	3.40701i	−0.0376393	−	0.115842i
$866$	−0.0701159	+	0.215795i	−0.00238264	+	0.00733300i
$867$	−9.31821	−	6.77007i	−0.316463	−	0.229924i
$868$	−24.8439			−0.843258
$869$	−9.69863	+	16.1110i	−0.329003	+	0.546527i
$870$	8.67587			0.294139
$871$	−8.45698	−	6.14436i	−0.286554	−	0.208194i
$872$	5.66148	−	17.4242i	0.191722	−	0.590060i
$873$	−1.68878	−	5.19754i	−0.0571567	−	0.175910i
$874$	−2.31439	+	1.68151i	−0.0782855	+	0.0568778i
$875$	−28.4044	+	20.6370i	−0.960245	+	0.697659i
$876$	1.40864	+	4.33533i	0.0475934	+	0.146477i
$877$	−4.65975	+	14.3412i	−0.157349	+	0.484269i	−0.998391	−	0.0566997i	$-0.981942\pi$
$877$	−4.65975	+	14.3412i	−0.157349	+	0.484269i	0.841043	+	0.540969i	$0.181942\pi$
$878$	12.7224	+	9.24340i	0.429362	+	0.311950i
$879$	8.65007			0.291760
$880$	4.39208	+	1.01782i	0.148057	+	0.0343109i
$881$	−28.2858			−0.952973			−0.476487	−	0.879182i	$-0.658090\pi$
$881$	−28.2858			−0.952973			−0.476487	+	0.879182i	$0.658090\pi$
$882$	−3.32140	−	2.41314i	−0.111837	−	0.0812546i
$883$	−0.625498	+	1.92509i	−0.0210497	+	0.0647843i	−0.961030	−	0.276446i	$-0.910843\pi$
$883$	−0.625498	+	1.92509i	−0.0210497	+	0.0647843i	0.939980	+	0.341230i	$0.110843\pi$
$884$	0.794499	+	2.44521i	0.0267219	+	0.0822415i
$885$	−1.13649	+	0.825709i	−0.0382027	+	0.0277559i
$886$	23.0434	−	16.7420i	0.774157	−	0.562458i
$887$	−6.62394	−	20.3864i	−0.222410	−	0.684508i	−0.998544	−	0.0539401i	$-0.982822\pi$
$887$	−6.62394	−	20.3864i	−0.222410	−	0.684508i	0.776134	−	0.630568i	$-0.217178\pi$
$888$	−2.48318	+	7.64246i	−0.0833302	+	0.256464i
$889$	−1.59221	−	1.15681i	−0.0534009	−	0.0387980i
$890$	25.2653			0.846894
$891$	−9.52736	+	4.03481i	−0.319179	+	0.135171i
$892$	−2.78430			−0.0932253
$893$	−4.66498	−	3.38931i	−0.156108	−	0.113419i
$894$	−3.56344	+	10.9671i	−0.119179	+	0.366796i
$895$	−5.27917	−	16.2476i	−0.176463	−	0.543097i
$896$	2.56319	−	1.86227i	0.0856301	−	0.0622139i
$897$	2.69626	−	1.95895i	0.0900256	−	0.0654074i
$898$	5.04849	+	15.5377i	0.168470	+	0.518498i
$899$	12.0448	−	37.0701i	0.401717	−	1.23636i
$900$	−3.44623	−	2.50383i	−0.114874	−	0.0834611i
$901$	38.2564			1.27451
$902$	−23.4520	−	27.0237i	−0.780867	−	0.899790i
$903$	0.702758			0.0233863
$904$	1.73415	+	1.25993i	0.0576769	+	0.0419047i
$905$	−3.07853	+	9.47473i	−0.102334	+	0.314951i
$906$	−4.34665	−	13.3776i	−0.144408	−	0.444441i
$907$	37.6338	−	27.3425i	1.24961	−	0.907894i	0.251409	−	0.967881i	$-0.419106\pi$
$907$	37.6338	−	27.3425i	1.24961	−	0.907894i	0.998199	+	0.0599873i	$0.0191060\pi$
$908$	2.43659	−	1.77029i	0.0808611	−	0.0587490i
$909$	0.406309	+	1.25049i	0.0134764	+	0.0414761i
$910$	1.20755	−	3.71645i	0.0400298	−	0.123199i
$911$	−17.7641	−	12.9064i	−0.588550	−	0.427607i	0.253246	−	0.967402i	$-0.418502\pi$
$911$	−17.7641	−	12.9064i	−0.588550	−	0.427607i	−0.841796	+	0.539795i	$0.818502\pi$
$912$	1.28398			0.0425169
$913$	−6.95458	−	8.01373i	−0.230163	−	0.265216i
$914$	21.6394			0.715769
$915$	14.1346	+	10.2694i	0.467277	+	0.339497i
$916$	−6.43137	+	19.7937i	−0.212498	+	0.654003i
$917$	−15.0616	−	46.3548i	−0.497378	−	1.53077i
$918$	12.8082	−	9.30574i	0.422735	−	0.307135i
$919$	21.0747	−	15.3117i	0.695190	−	0.505085i	−0.183172	−	0.983081i	$-0.558636\pi$
$919$	21.0747	−	15.3117i	0.695190	−	0.505085i	0.878362	+	0.477996i	$0.158636\pi$
$920$	1.20170	+	3.69844i	0.0396188	+	0.121934i
$921$	5.48258	−	16.8737i	0.180657	−	0.556006i
$922$	−8.08326	−	5.87283i	−0.266208	−	0.193411i
$923$	−11.9699			−0.393995
$924$	−12.4239	+	5.26148i	−0.408716	+	0.173090i
$925$	19.7276			0.648640
$926$	15.1444	+	11.0031i	0.497677	+	0.361584i
$927$	1.27030	−	3.90959i	0.0417222	−	0.128408i
$928$	1.53604	+	4.72745i	0.0504230	+	0.155186i
$929$	1.22300	−	0.888564i	0.0401254	−	0.0291528i	−0.567542	−	0.823345i	$-0.692105\pi$
$929$	1.22300	−	0.888564i	0.0401254	−	0.0291528i	0.607667	+	0.794192i	$0.292105\pi$
$930$	−11.0726	+	8.04468i	−0.363083	+	0.263795i
$931$	−0.938785	−	2.88928i	−0.0307674	−	0.0946924i
$932$	4.87032	−	14.9893i	0.159533	−	0.490991i
$933$	−24.0499	−	17.4733i	−0.787359	−	0.572050i
$934$	35.7800			1.17076
$935$	12.4456	+	2.88415i	0.407014	+	0.0943218i
$936$	1.22616			0.0400781
$937$	37.4569	+	27.2140i	1.22366	+	0.889043i	0.996399	−	0.0847900i	$-0.0270220\pi$
$937$	37.4569	+	27.2140i	1.22366	+	0.889043i	0.227264	+	0.973833i	$0.427022\pi$
$938$	−11.2797	+	34.7153i	−0.368295	+	1.13350i
$939$	6.75792	+	20.7987i	0.220536	+	0.678742i
$940$	−6.34137	+	4.60727i	−0.206833	+	0.150273i
$941$	−45.2305	+	32.8619i	−1.47447	+	1.07127i	−0.495185	+	0.868787i	$0.664900\pi$
$941$	−45.2305	+	32.8619i	−1.47447	+	1.07127i	−0.979287	+	0.202479i	$0.935100\pi$
$942$	−8.96160	−	27.5810i	−0.291985	−	0.898636i
$943$	9.53713	−	29.3523i	0.310572	−	0.955841i
$944$	−0.651139	−	0.473080i	−0.0211928	−	0.0153974i
$945$	−24.0626			−0.782758
$946$	−0.295500	+	0.490873i	−0.00960754	+	0.0159597i
$947$	42.9748			1.39649			0.698247	−	0.715857i	$-0.253964\pi$
$947$	42.9748			1.39649			0.698247	+	0.715857i	$0.253964\pi$
$948$	5.88970	+	4.27912i	0.191289	+	0.138979i
$949$	−0.995417	+	3.06358i	−0.0323126	+	0.0994480i
$950$	−0.974068	−	2.99787i	−0.0316030	−	0.0972639i
$951$	−33.2570	+	24.1626i	−1.07843	+	0.783526i
$952$	7.26316	−	5.27699i	0.235400	−	0.171028i
$953$	−7.49102	−	23.0550i	−0.242658	−	0.746824i	−0.996013	−	0.0892101i	$-0.971566\pi$
$953$	−7.49102	−	23.0550i	−0.242658	−	0.746824i	0.753355	−	0.657614i	$-0.228434\pi$
$954$	5.63795	−	17.3518i	0.182535	−	0.561786i
$955$	13.3868	+	9.72607i	0.433186	+	0.314728i
$956$	−25.3585			−0.820153
$957$	−1.82743	−	21.0888i	−0.0590723	−	0.681704i
$958$	−12.3527			−0.399098
$959$	−24.9918	−	18.1576i	−0.807028	−	0.586340i
$960$	0.539355	−	1.65996i	0.0174076	−	0.0535751i
$961$	9.42152	+	28.9964i	0.303920	+	0.935369i
$962$	−4.59400	+	3.33773i	−0.148116	+	0.107613i
$963$	−9.96877	+	7.24274i	−0.321239	+	0.233394i
$964$	2.42735	+	7.47061i	0.0781796	+	0.240612i
$965$	−6.02393	+	18.5398i	−0.193917	+	0.596816i
$966$	−9.41498	−	6.84039i	−0.302922	−	0.220086i
$967$	49.2508			1.58380			0.791899	−	0.610653i	$-0.209093\pi$
$967$	49.2508			1.58380			0.791899	+	0.610653i	$0.209093\pi$
$968$	1.54895	−	10.8904i	0.0497852	−	0.350031i
$969$	3.63835			0.116881
$970$	−4.44737	−	3.23120i	−0.142796	−	0.103748i
$971$	12.4412	−	38.2902i	0.399259	−	1.22879i	−0.526337	−	0.850276i	$-0.676435\pi$
$971$	12.4412	−	38.2902i	0.399259	−	1.22879i	0.925595	−	0.378515i	$-0.123565\pi$
$972$	−3.94177	−	12.1315i	−0.126432	−	0.389118i
$973$	−0.557332	+	0.404925i	−0.0178672	+	0.0129813i
$974$	11.3005	−	8.21029i	0.362091	−	0.263075i
$975$	1.13479	+	3.49252i	0.0363423	+	0.111850i
$976$	−3.09327	+	9.52009i	−0.0990130	+	0.304731i
$977$	−3.49360	−	2.53825i	−0.111770	−	0.0812057i	0.530496	−	0.847687i	$-0.322006\pi$
$977$	−3.49360	−	2.53825i	−0.111770	−	0.0812057i	−0.642266	+	0.766482i	$0.722006\pi$
$978$	16.6754			0.533219
$979$	−5.32171	−	61.4134i	−0.170083	−	1.96278i
$980$	−4.12968			−0.131918
$981$	−20.0302	−	14.5528i	−0.639515	−	0.464635i
$982$	−1.06563	+	3.27968i	−0.0340057	+	0.104659i
$983$	3.64219	+	11.2095i	0.116168	+	0.357527i	0.992189	−	0.124745i	$-0.0398114\pi$
$983$	3.64219	+	11.2095i	0.116168	+	0.357527i	−0.876021	+	0.482273i	$0.839811\pi$
$984$	−11.2066	+	8.14205i	−0.357252	+	0.259559i
$985$	17.2352	−	12.5221i	0.549159	−	0.398987i
$986$	4.35259	+	13.3959i	0.138615	+	0.426612i
$987$	7.24864	−	22.3090i	0.230727	−	0.710104i
$988$	0.734046	+	0.533316i	0.0233531	+	0.0169670i
$989$	−0.494201			−0.0157147
$990$	3.14229	−	5.21986i	0.0998687	−	0.165898i
$991$	15.8154			0.502393			0.251197	−	0.967936i	$-0.419176\pi$
$991$	15.8154			0.502393			0.251197	+	0.967936i	$0.419176\pi$
$992$	−6.34388	−	4.60910i	−0.201418	−	0.146339i
$993$	7.86188	−	24.1964i	0.249489	−	0.767849i
$994$	12.9161	+	39.7516i	0.409674	+	1.26085i
$995$	1.51381	−	1.09985i	0.0479909	−	0.0348674i
$996$	−3.32325	+	2.41448i	−0.105301	+	0.0765058i
$997$	11.4587	+	35.2662i	0.362900	+	1.11689i	0.951285	+	0.308311i	$0.0997639\pi$
$997$	11.4587	+	35.2662i	0.362900	+	1.11689i	−0.588385	+	0.808581i	$0.700236\pi$
$998$	13.4191	−	41.2998i	0.424775	−	1.30732i
$999$	28.2886	+	20.5529i	0.895013	+	0.650265i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.f.h.191.2	✓	20
11.3	even	5	inner	418.2.f.h.267.2	yes	20
11.5	even	5		4598.2.a.cc.1.4		10
11.6	odd	10		4598.2.a.cd.1.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.f.h.191.2	✓	20	1.1	even	1	trivial
418.2.f.h.267.2	yes	20	11.3	even	5	inner
4598.2.a.cc.1.4		10	11.5	even	5
4598.2.a.cd.1.4		10	11.6	odd	10

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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{2} +(-0.396773 + 1.22114i) q^{3} +(0.309017 + 0.951057i) q^{4} +(1.09974 - 0.799009i) q^{5} +(-1.03876 + 0.754706i) q^{6} +(0.979051 + 3.01321i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(1.09330 + 0.794325i) q^{9} +O(q^{10})\)	\(q+(0.809017 + 0.587785i) q^{2} +(-0.396773 + 1.22114i) q^{3} +(0.309017 + 0.951057i) q^{4} +(1.09974 - 0.799009i) q^{5} +(-1.03876 + 0.754706i) q^{6} +(0.979051 + 3.01321i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(1.09330 + 0.794325i) q^{9} +1.35936 q^{10} +(-0.286325 - 3.30424i) q^{11} -1.28398 q^{12} +(-0.734046 - 0.533316i) q^{13} +(-0.979051 + 3.01321i) q^{14} +(0.539355 + 1.65996i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-2.29246 + 1.66557i) q^{17} +(0.417602 + 1.28525i) q^{18} +(-0.309017 + 0.951057i) q^{19} +(1.09974 + 0.799009i) q^{20} -4.06801 q^{21} +(1.71054 - 2.84149i) q^{22} +2.86075 q^{23} +(-1.03876 - 0.754706i) q^{24} +(-0.974068 + 2.99787i) q^{25} +(-0.280381 - 0.862923i) q^{26} +(-4.52007 + 3.28402i) q^{27} +(-2.56319 + 1.86227i) q^{28} +(-1.53604 - 4.72745i) q^{29} +(-0.539355 + 1.65996i) q^{30} +(6.34388 + 4.60910i) q^{31} -1.00000 q^{32} +(4.14855 + 0.961389i) q^{33} -2.83364 q^{34} +(3.48429 + 2.53148i) q^{35} +(-0.417602 + 1.28525i) q^{36} +(-1.93397 - 5.95215i) q^{37} +(-0.809017 + 0.587785i) q^{38} +(0.942503 - 0.684769i) q^{39} +(0.420064 + 1.29282i) q^{40} +(3.33379 - 10.2603i) q^{41} +(-3.29109 - 2.39112i) q^{42} -0.172752 q^{43} +(3.05404 - 1.29338i) q^{44} +1.83702 q^{45} +(2.31439 + 1.68151i) q^{46} +(-1.78186 + 5.48401i) q^{47} +(-0.396773 - 1.22114i) q^{48} +(-2.45777 + 1.78567i) q^{49} +(-2.55014 + 1.85279i) q^{50} +(-1.12431 - 3.46028i) q^{51} +(0.280381 - 0.862923i) q^{52} +(-10.9224 - 7.93556i) q^{53} -5.58711 q^{54} +(-2.95500 - 3.40504i) q^{55} -3.16828 q^{56} +(-1.03876 - 0.754706i) q^{57} +(1.53604 - 4.72745i) q^{58} +(0.248713 + 0.765459i) q^{59} +(-1.41205 + 1.02591i) q^{60} +(8.09828 - 5.88374i) q^{61} +(2.42315 + 7.45768i) q^{62} +(-1.32308 + 4.07201i) q^{63} +(-0.809017 - 0.587785i) q^{64} -1.23339 q^{65} +(2.79116 + 3.21624i) q^{66} +11.5211 q^{67} +(-2.29246 - 1.66557i) q^{68} +(-1.13507 + 3.49338i) q^{69} +(1.33088 + 4.09602i) q^{70} +(10.6729 - 7.75433i) q^{71} +(-1.09330 + 0.794325i) q^{72} +(-1.09708 - 3.37647i) q^{73} +(1.93397 - 5.95215i) q^{74} +(-3.27434 - 2.37895i) q^{75} -1.00000 q^{76} +(9.67605 - 4.09778i) q^{77} +1.16500 q^{78} +(-4.58705 - 3.33269i) q^{79} +(-0.420064 + 1.29282i) q^{80} +(-0.964007 - 2.96691i) q^{81} +(8.72797 - 6.34124i) q^{82} +(2.58823 - 1.88046i) q^{83} +(-1.25709 - 3.86891i) q^{84} +(-1.19031 + 3.66340i) q^{85} +(-0.139759 - 0.101541i) q^{86} +6.38234 q^{87} +(3.23100 + 0.748755i) q^{88} +18.5862 q^{89} +(1.48618 + 1.07977i) q^{90} +(0.888323 - 2.73398i) q^{91} +(0.884020 + 2.72073i) q^{92} +(-8.14544 + 5.91801i) q^{93} +(-4.66498 + 3.38931i) q^{94} +(0.420064 + 1.29282i) q^{95} +(0.396773 - 1.22114i) q^{96} +(-3.27167 - 2.37701i) q^{97} -3.03797 q^{98} +(2.31161 - 3.83995i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 5 q^{2} - q^{3} - 5 q^{4} - q^{5} + q^{6} + 13 q^{7} + 5 q^{8} - 6 q^{9}+O(q^{10}) \) 20 * q + 5 * q^2 - q^3 - 5 * q^4 - q^5 + q^6 + 13 * q^7 + 5 * q^8 - 6 * q^9	\( 20 q + 5 q^{2} - q^{3} - 5 q^{4} - q^{5} + q^{6} + 13 q^{7} + 5 q^{8} - 6 q^{9} + 6 q^{10} + q^{11} + 4 q^{12} - 2 q^{13} - 13 q^{14} - 8 q^{15} - 5 q^{16} + 11 q^{17} + 6 q^{18} + 5 q^{19} - q^{20} + 2 q^{21} + 4 q^{22} + 28 q^{23} + q^{24} - 30 q^{25} - 13 q^{26} - 31 q^{27} - 2 q^{28} + 28 q^{29} + 8 q^{30} - q^{31} - 20 q^{32} + 9 q^{33} + 24 q^{34} - 11 q^{35} - 6 q^{36} + 8 q^{37} - 5 q^{38} + 18 q^{39} - 4 q^{40} - 5 q^{41} - 22 q^{42} - 44 q^{43} + 11 q^{44} - 4 q^{45} + 7 q^{46} - 39 q^{47} - q^{48} + 4 q^{49} - 25 q^{50} - 11 q^{51} + 13 q^{52} - q^{53} - 4 q^{54} + 8 q^{55} + 22 q^{56} + q^{57} - 28 q^{58} + 6 q^{59} + 7 q^{60} + 10 q^{61} + 11 q^{62} + 34 q^{63} - 5 q^{64} - 8 q^{65} + 41 q^{66} + 18 q^{67} + 11 q^{68} - 63 q^{69} + q^{70} - 3 q^{71} + 6 q^{72} + 5 q^{73} - 8 q^{74} + 5 q^{75} - 20 q^{76} + 36 q^{77} + 22 q^{78} + 19 q^{79} + 4 q^{80} + 63 q^{81} - 9 q^{83} - 23 q^{84} + 30 q^{85} - 26 q^{86} - 16 q^{87} - q^{88} + 44 q^{89} + 14 q^{90} - 68 q^{91} - 7 q^{92} + 27 q^{93} - 31 q^{94} - 4 q^{95} + q^{96} - 71 q^{97} + 6 q^{98} + 20 q^{99}+O(q^{100}) \) 20 * q + 5 * q^2 - q^3 - 5 * q^4 - q^5 + q^6 + 13 * q^7 + 5 * q^8 - 6 * q^9 + 6 * q^10 + q^11 + 4 * q^12 - 2 * q^13 - 13 * q^14 - 8 * q^15 - 5 * q^16 + 11 * q^17 + 6 * q^18 + 5 * q^19 - q^20 + 2 * q^21 + 4 * q^22 + 28 * q^23 + q^24 - 30 * q^25 - 13 * q^26 - 31 * q^27 - 2 * q^28 + 28 * q^29 + 8 * q^30 - q^31 - 20 * q^32 + 9 * q^33 + 24 * q^34 - 11 * q^35 - 6 * q^36 + 8 * q^37 - 5 * q^38 + 18 * q^39 - 4 * q^40 - 5 * q^41 - 22 * q^42 - 44 * q^43 + 11 * q^44 - 4 * q^45 + 7 * q^46 - 39 * q^47 - q^48 + 4 * q^49 - 25 * q^50 - 11 * q^51 + 13 * q^52 - q^53 - 4 * q^54 + 8 * q^55 + 22 * q^56 + q^57 - 28 * q^58 + 6 * q^59 + 7 * q^60 + 10 * q^61 + 11 * q^62 + 34 * q^63 - 5 * q^64 - 8 * q^65 + 41 * q^66 + 18 * q^67 + 11 * q^68 - 63 * q^69 + q^70 - 3 * q^71 + 6 * q^72 + 5 * q^73 - 8 * q^74 + 5 * q^75 - 20 * q^76 + 36 * q^77 + 22 * q^78 + 19 * q^79 + 4 * q^80 + 63 * q^81 - 9 * q^83 - 23 * q^84 + 30 * q^85 - 26 * q^86 - 16 * q^87 - q^88 + 44 * q^89 + 14 * q^90 - 68 * q^91 - 7 * q^92 + 27 * q^93 - 31 * q^94 - 4 * q^95 + q^96 - 71 * q^97 + 6 * q^98 + 20 * q^99

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