LMFDB - Embedded newform 418.2.m.b.189.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(151,418)]

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([3, 5]))

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

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

chi := DirichletCharacter("418.151");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.m (of order $10$, 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:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			189.2
Character	$\chi$	$=$	418.189
Dual form			418.2.m.b.303.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 + 0.951057i) q^{2} +(-1.43308 - 1.97246i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.0275048 + 0.0846511i) q^{5} +(2.31877 - 0.753413i) q^{6} +(-2.13510 + 2.93871i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-0.909840 + 2.80020i) q^{9} +O(q^{10})$	\(q+(-0.309017 + 0.951057i) q^{2} +(-1.43308 - 1.97246i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.0275048 + 0.0846511i) q^{5} +(2.31877 - 0.753413i) q^{6} +(-2.13510 + 2.93871i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-0.909840 + 2.80020i) q^{9} -0.0890075 q^{10} +(2.20176 + 2.48037i) q^{11} +2.43809i q^{12} +(0.295842 - 0.910508i) q^{13} +(-2.13510 - 2.93871i) q^{14} +(0.127554 - 0.175564i) q^{15} +(0.309017 + 0.951057i) q^{16} +(5.07005 - 1.64736i) q^{17} +(-2.38199 - 1.73062i) q^{18} +(3.96392 - 1.81309i) q^{19} +(0.0275048 - 0.0846511i) q^{20} +8.85624 q^{21} +(-3.03935 + 1.32753i) q^{22} +0.351320 q^{23} +(-2.31877 - 0.753413i) q^{24} +(4.03868 - 2.93427i) q^{25} +(0.774524 + 0.562725i) q^{26} +(-0.129149 + 0.0419630i) q^{27} +(3.45466 - 1.12249i) q^{28} +(2.27648 + 1.65396i) q^{29} +(0.127554 + 0.175564i) q^{30} +(6.22511 + 2.02266i) q^{31} -1.00000 q^{32} +(1.73714 - 7.89745i) q^{33} +5.33097i q^{34} +(-0.307491 - 0.0999098i) q^{35} +(2.38199 - 1.73062i) q^{36} +(-4.47407 + 6.15803i) q^{37} +(0.499433 + 4.33019i) q^{38} +(-2.21990 + 0.721290i) q^{39} +(0.0720086 + 0.0523173i) q^{40} +(0.351075 - 0.255071i) q^{41} +(-2.73673 + 8.42279i) q^{42} +6.14721i q^{43} +(-0.323339 - 3.30083i) q^{44} -0.262065 q^{45} +(-0.108564 + 0.334125i) q^{46} +(-0.0671710 + 0.0488026i) q^{47} +(1.43308 - 1.97246i) q^{48} +(-1.91426 - 5.89147i) q^{49} +(1.54264 + 4.74775i) q^{50} +(-10.5151 - 7.63968i) q^{51} +(-0.774524 + 0.562725i) q^{52} +(2.96140 + 0.962216i) q^{53} -0.135795i q^{54} +(-0.149407 + 0.254604i) q^{55} +3.63245i q^{56} +(-9.25685 - 5.22038i) q^{57} +(-2.27648 + 1.65396i) q^{58} +(-3.72140 + 5.12207i) q^{59} +(-0.206387 + 0.0670594i) q^{60} +(8.04655 - 2.61448i) q^{61} +(-3.84733 + 5.29540i) q^{62} +(-6.28637 - 8.65245i) q^{63} +(0.309017 - 0.951057i) q^{64} +0.0852126 q^{65} +(6.97412 + 4.09256i) q^{66} +11.6608i q^{67} +(-5.07005 - 1.64736i) q^{68} +(-0.503468 - 0.692964i) q^{69} +(0.190040 - 0.261567i) q^{70} +(-6.71548 + 2.18199i) q^{71} +(0.909840 + 2.80020i) q^{72} +(9.59602 - 13.2078i) q^{73} +(-4.47407 - 6.15803i) q^{74} +(-11.5755 - 3.76109i) q^{75} +(-4.27259 - 0.863114i) q^{76} +(-11.9901 + 1.17451i) q^{77} -2.33414i q^{78} +(1.40280 - 4.31738i) q^{79} +(-0.0720086 + 0.0523173i) q^{80} +(7.41382 + 5.38646i) q^{81} +(0.134099 + 0.412714i) q^{82} +(-14.8997 + 4.84120i) q^{83} +(-7.16485 - 5.20557i) q^{84} +(0.278902 + 0.383875i) q^{85} +(-5.84635 - 1.89959i) q^{86} -6.86052i q^{87} +(3.23919 + 0.712497i) q^{88} +1.75872i q^{89} +(0.0809825 - 0.249239i) q^{90} +(2.04407 + 2.81342i) q^{91} +(-0.284224 - 0.206501i) q^{92} +(-4.93144 - 15.1774i) q^{93} +(-0.0256570 - 0.0789643i) q^{94} +(0.262507 + 0.285682i) q^{95} +(1.43308 + 1.97246i) q^{96} +(6.84783 + 2.22499i) q^{97} +6.19466 q^{98} +(-8.94878 + 3.90864i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 10 q^{2} - 10 q^{4} + 2 q^{5} + 5 q^{6} - 5 q^{7} + 10 q^{8} + 8 q^{9}+O(q^{10}) $ 40 * q + 10 * q^2 - 10 * q^4 + 2 * q^5 + 5 * q^6 - 5 * q^7 + 10 * q^8 + 8 * q^9	$ 40 q + 10 q^{2} - 10 q^{4} + 2 q^{5} + 5 q^{6} - 5 q^{7} + 10 q^{8} + 8 q^{9} - 2 q^{10} + 4 q^{11} - 8 q^{13} - 5 q^{14} - 30 q^{15} - 10 q^{16} - 15 q^{17} - 13 q^{18} + 11 q^{19} + 2 q^{20} - 4 q^{22} + 6 q^{23} - 5 q^{24} - 36 q^{25} - 2 q^{26} + 45 q^{27} + 2 q^{29} - 30 q^{30} - 40 q^{32} - 27 q^{33} - 5 q^{35} + 13 q^{36} + 14 q^{38} + 30 q^{39} + 3 q^{40} + 8 q^{41} + 20 q^{42} - 6 q^{44} + 18 q^{45} - q^{46} - 8 q^{47} + 31 q^{49} - 9 q^{50} - 41 q^{51} + 2 q^{52} + 40 q^{53} - 31 q^{55} - 10 q^{57} - 2 q^{58} - 35 q^{59} - 20 q^{60} + 5 q^{61} + 30 q^{62} - 25 q^{63} - 10 q^{64} - 8 q^{65} - 48 q^{66} + 15 q^{68} + 60 q^{69} + 10 q^{70} - 50 q^{71} - 8 q^{72} + 10 q^{73} + 35 q^{75} + 11 q^{76} - 64 q^{77} + 42 q^{79} - 3 q^{80} + 11 q^{81} + 7 q^{82} + 25 q^{83} + 20 q^{84} - 45 q^{85} + 40 q^{86} + 6 q^{88} + 22 q^{90} + 70 q^{91} - 4 q^{92} - 18 q^{93} - 7 q^{94} - 5 q^{95} + 15 q^{97} + 74 q^{98} + 50 q^{99}+O(q^{100}) $ 40 * q + 10 * q^2 - 10 * q^4 + 2 * q^5 + 5 * q^6 - 5 * q^7 + 10 * q^8 + 8 * q^9 - 2 * q^10 + 4 * q^11 - 8 * q^13 - 5 * q^14 - 30 * q^15 - 10 * q^16 - 15 * q^17 - 13 * q^18 + 11 * q^19 + 2 * q^20 - 4 * q^22 + 6 * q^23 - 5 * q^24 - 36 * q^25 - 2 * q^26 + 45 * q^27 + 2 * q^29 - 30 * q^30 - 40 * q^32 - 27 * q^33 - 5 * q^35 + 13 * q^36 + 14 * q^38 + 30 * q^39 + 3 * q^40 + 8 * q^41 + 20 * q^42 - 6 * q^44 + 18 * q^45 - q^46 - 8 * q^47 + 31 * q^49 - 9 * q^50 - 41 * q^51 + 2 * q^52 + 40 * q^53 - 31 * q^55 - 10 * q^57 - 2 * q^58 - 35 * q^59 - 20 * q^60 + 5 * q^61 + 30 * q^62 - 25 * q^63 - 10 * q^64 - 8 * q^65 - 48 * q^66 + 15 * q^68 + 60 * q^69 + 10 * q^70 - 50 * q^71 - 8 * q^72 + 10 * q^73 + 35 * q^75 + 11 * q^76 - 64 * q^77 + 42 * q^79 - 3 * q^80 + 11 * q^81 + 7 * q^82 + 25 * q^83 + 20 * q^84 - 45 * q^85 + 40 * q^86 + 6 * q^88 + 22 * q^90 + 70 * q^91 - 4 * q^92 - 18 * q^93 - 7 * q^94 - 5 * q^95 + 15 * q^97 + 74 * q^98 + 50 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$287$	$343$
$\chi(n)$	$-1$	$e\left(\frac{1}{10}\right)$

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 $

$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$3$	−1.43308	−	1.97246i	−0.827387	−	1.13880i	−0.988404	−	0.151848i	$-0.951477\pi$
$3$	−1.43308	−	1.97246i	−0.827387	−	1.13880i	0.161017	−	0.986952i	$-0.448523\pi$
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	0.0275048	+	0.0846511i	0.0123005	+	0.0378571i	0.957018	−	0.290027i	$-0.0936644\pi$
$5$	0.0275048	+	0.0846511i	0.0123005	+	0.0378571i	−0.944718	+	0.327884i	$0.893664\pi$
$6$	2.31877	−	0.753413i	0.946632	−	0.307579i
$7$	−2.13510	+	2.93871i	−0.806991	+	1.11073i	0.184789	+	0.982778i	$0.440840\pi$
$7$	−2.13510	+	2.93871i	−0.806991	+	1.11073i	−0.991781	+	0.127950i	$0.959160\pi$
$8$	0.809017	−	0.587785i	0.286031	−	0.207813i
$9$	−0.909840	+	2.80020i	−0.303280	+	0.933399i
$10$	−0.0890075			−0.0281466
$11$	2.20176	+	2.48037i	0.663857	+	0.747860i
$11$	2.20176	+	2.48037i	0.663857	+	0.747860i
$12$			2.43809i			0.703817i
$13$	0.295842	−	0.910508i	0.0820518	−	0.252529i	−0.901612	−	0.432546i	$-0.857615\pi$
$13$	0.295842	−	0.910508i	0.0820518	−	0.252529i	0.983664	+	0.180017i	$0.0576152\pi$
$14$	−2.13510	−	2.93871i	−0.570629	−	0.785403i
$15$	0.127554	−	0.175564i	0.0329344	−	0.0453303i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	5.07005	−	1.64736i	1.22967	−	0.399544i	0.379074	−	0.925366i	$-0.376242\pi$
$17$	5.07005	−	1.64736i	1.22967	−	0.399544i	0.850594	+	0.525823i	$0.176242\pi$
$18$	−2.38199	−	1.73062i	−0.561441	−	0.407911i
$19$	3.96392	−	1.81309i	0.909387	−	0.415952i
$19$	3.96392	−	1.81309i	0.909387	−	0.415952i
$20$	0.0275048	−	0.0846511i	0.00615027	−	0.0189286i
$21$	8.85624			1.93259
$22$	−3.03935	+	1.32753i	−0.647993	+	0.283029i
$23$	0.351320			0.0732553			0.0366276	−	0.999329i	$-0.488338\pi$
$23$	0.351320			0.0732553			0.0366276	+	0.999329i	$0.488338\pi$
$24$	−2.31877	−	0.753413i	−0.473316	−	0.153790i
$25$	4.03868	−	2.93427i	0.807735	−	0.586854i
$26$	0.774524	+	0.562725i	0.151897	+	0.110359i
$27$	−0.129149	+	0.0419630i	−0.0248547	+	0.00807579i
$28$	3.45466	−	1.12249i	0.652870	−	0.212130i
$29$	2.27648	+	1.65396i	0.422732	+	0.307133i	0.778736	−	0.627352i	$-0.215861\pi$
$29$	2.27648	+	1.65396i	0.422732	+	0.307133i	−0.356004	+	0.934484i	$0.615861\pi$
$30$	0.127554	+	0.175564i	0.0232882	+	0.0320534i
$31$	6.22511	+	2.02266i	1.11806	+	0.363281i	0.809028	−	0.587770i	$-0.199994\pi$
$31$	6.22511	+	2.02266i	1.11806	+	0.363281i	0.309035	+	0.951051i	$0.399994\pi$
$32$	−1.00000			−0.176777
$33$	1.73714	−	7.89745i	0.302396	−	1.37477i
$34$			5.33097i			0.914254i
$35$	−0.307491	−	0.0999098i	−0.0519754	−	0.0168878i
$36$	2.38199	−	1.73062i	0.396998	−	0.288436i
$37$	−4.47407	+	6.15803i	−0.735532	+	1.01237i	0.263331	+	0.964706i	$0.415179\pi$
$37$	−4.47407	+	6.15803i	−0.735532	+	1.01237i	−0.998863	+	0.0476678i	$0.984821\pi$
$38$	0.499433	+	4.33019i	0.0810187	+	0.702450i
$39$	−2.21990	+	0.721290i	−0.355469	+	0.115499i
$40$	0.0720086	+	0.0523173i	0.0113856	+	0.00827209i
$41$	0.351075	−	0.255071i	0.0548288	−	0.0398354i	−0.560033	−	0.828470i	$-0.689212\pi$
$41$	0.351075	−	0.255071i	0.0548288	−	0.0398354i	0.614862	+	0.788635i	$0.289212\pi$
$42$	−2.73673	+	8.42279i	−0.422287	+	1.29966i
$43$			6.14721i			0.937441i	0.883347	+	0.468720i	$0.155285\pi$
$43$			6.14721i			0.937441i	−0.883347	+	0.468720i	$0.844715\pi$
$44$	−0.323339	−	3.30083i	−0.0487452	−	0.497618i
$45$	−0.262065			−0.0390663
$46$	−0.108564	+	0.334125i	−0.0160069	+	0.0492641i
$47$	−0.0671710	+	0.0488026i	−0.00979790	+	0.00711859i	−0.592673	−	0.805443i	$-0.701928\pi$
$47$	−0.0671710	+	0.0488026i	−0.00979790	+	0.00711859i	0.582876	+	0.812561i	$0.301928\pi$
$48$	1.43308	−	1.97246i	0.206847	−	0.284700i
$49$	−1.91426	−	5.89147i	−0.273465	−	0.841639i
$50$	1.54264	+	4.74775i	0.218162	+	0.671433i
$51$	−10.5151	−	7.63968i	−1.47241	−	1.06977i
$52$	−0.774524	+	0.562725i	−0.107407	+	0.0780359i
$53$	2.96140	+	0.962216i	0.406779	+	0.132171i	0.505258	−	0.862969i	$-0.331397\pi$
$53$	2.96140	+	0.962216i	0.406779	+	0.132171i	−0.0984783	+	0.995139i	$0.531397\pi$
$54$		−	0.135795i		−	0.0184794i
$55$	−0.149407	+	0.254604i	−0.0201460	+	0.0343308i
$56$			3.63245i			0.485406i
$57$	−9.25685	−	5.22038i	−1.22610	−	0.691457i
$58$	−2.27648	+	1.65396i	−0.298917	+	0.217176i
$59$	−3.72140	+	5.12207i	−0.484486	+	0.666837i	−0.979359	−	0.202128i	$-0.935214\pi$
$59$	−3.72140	+	5.12207i	−0.484486	+	0.666837i	0.494874	+	0.868965i	$0.335214\pi$
$60$	−0.206387	+	0.0670594i	−0.0266445	+	0.00865733i
$61$	8.04655	−	2.61448i	1.03026	−	0.334750i	0.255364	−	0.966845i	$-0.417805\pi$
$61$	8.04655	−	2.61448i	1.03026	−	0.334750i	0.774891	+	0.632095i	$0.217805\pi$
$62$	−3.84733	+	5.29540i	−0.488612	+	0.672516i
$63$	−6.28637	−	8.65245i	−0.792009	−	1.09011i
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	0.0852126			0.0105693
$66$	6.97412	+	4.09256i	0.858454	+	0.503759i
$67$			11.6608i			1.42459i	0.701880	+	0.712295i	$0.252344\pi$
$67$			11.6608i			1.42459i	−0.701880	+	0.712295i	$0.747656\pi$
$68$	−5.07005	−	1.64736i	−0.614834	−	0.199772i
$69$	−0.503468	−	0.692964i	−0.0606104	−	0.0834231i
$70$	0.190040	−	0.261567i	0.0227141	−	0.0312633i
$71$	−6.71548	+	2.18199i	−0.796980	+	0.258955i	−0.679074	−	0.734070i	$-0.737618\pi$
$71$	−6.71548	+	2.18199i	−0.796980	+	0.258955i	−0.117907	+	0.993025i	$0.537618\pi$
$72$	0.909840	+	2.80020i	0.107226	+	0.330007i
$73$	9.59602	−	13.2078i	1.12313	−	1.54585i	0.322624	−	0.946527i	$-0.395435\pi$
$73$	9.59602	−	13.2078i	1.12313	−	1.54585i	0.800504	−	0.599327i	$-0.204565\pi$
$74$	−4.47407	−	6.15803i	−0.520100	−	0.715856i
$75$	−11.5755	−	3.76109i	−1.33662	−	0.434294i
$76$	−4.27259	−	0.863114i	−0.490100	−	0.0990060i
$77$	−11.9901	+	1.17451i	−1.36640	+	0.133848i
$78$		−	2.33414i		−	0.264290i
$79$	1.40280	−	4.31738i	0.157828	−	0.485743i	−0.840609	−	0.541643i	$-0.817803\pi$
$79$	1.40280	−	4.31738i	0.157828	−	0.485743i	0.998436	+	0.0558994i	$0.0178026\pi$
$80$	−0.0720086	+	0.0523173i	−0.00805080	+	0.00584925i
$81$	7.41382	+	5.38646i	0.823758	+	0.598495i
$82$	0.134099	+	0.412714i	0.0148087	+	0.0455766i
$83$	−14.8997	+	4.84120i	−1.63545	+	0.531391i	−0.975516	−	0.219930i	$-0.929417\pi$
$83$	−14.8997	+	4.84120i	−1.63545	+	0.531391i	−0.659937	+	0.751321i	$0.729417\pi$
$84$	−7.16485	−	5.20557i	−0.781749	−	0.567974i
$85$	0.278902	+	0.383875i	0.0302512	+	0.0416371i
$86$	−5.84635	−	1.89959i	−0.630428	−	0.204838i
$87$		−	6.86052i		−	0.735525i
$88$	3.23919	+	0.712497i	0.345299	+	0.0759525i
$89$			1.75872i			0.186424i	0.995646	+	0.0932119i	$0.0297134\pi$
$89$			1.75872i			0.186424i	−0.995646	+	0.0932119i	$0.970287\pi$
$90$	0.0809825	−	0.249239i	0.00853631	−	0.0262721i
$91$	2.04407	+	2.81342i	0.214276	+	0.294926i
$92$	−0.284224	−	0.206501i	−0.0296324	−	0.0215292i
$93$	−4.93144	−	15.1774i	−0.511366	−	1.57382i
$94$	−0.0256570	−	0.0789643i	−0.00264632	−	0.00814454i
$95$	0.262507	+	0.285682i	0.0269327	+	0.0293104i
$96$	1.43308	+	1.97246i	0.146263	+	0.201313i
$97$	6.84783	+	2.22499i	0.695291	+	0.225914i	0.635278	−	0.772284i	$-0.280886\pi$
$97$	6.84783	+	2.22499i	0.695291	+	0.225914i	0.0600136	+	0.998198i	$0.480886\pi$
$98$	6.19466			0.625755
$99$	−8.94878	+	3.90864i	−0.899386	+	0.392833i
$100$	−4.99208			−0.499208
$101$	2.13590	+	0.693995i	0.212530	+	0.0690551i	0.413347	−	0.910574i	$-0.364360\pi$
$101$	2.13590	+	0.693995i	0.212530	+	0.0690551i	−0.200817	+	0.979629i	$0.564360\pi$
$102$	10.5151	−	7.63968i	1.04115	−	0.756441i
$103$	−0.461940	+	0.635806i	−0.0455163	+	0.0626478i	−0.831169	−	0.556021i	$-0.812328\pi$
$103$	−0.461940	+	0.635806i	−0.0455163	+	0.0626478i	0.785652	+	0.618668i	$0.212328\pi$
$104$	−0.295842	−	0.910508i	−0.0290097	−	0.0892826i
$105$	0.243589	+	0.749691i	0.0237719	+	0.0731624i
$106$	−1.83024	+	2.51912i	−0.177769	+	0.244678i
$107$	8.35874	−	6.07298i	0.808070	−	0.587097i	−0.105200	−	0.994451i	$-0.533548\pi$
$107$	8.35874	−	6.07298i	0.808070	−	0.587097i	0.913271	+	0.407354i	$0.133548\pi$
$108$	0.129149	+	0.0419630i	0.0124274	+	0.00403789i
$109$	15.2703			1.46263			0.731313	−	0.682042i	$-0.238908\pi$
$109$	15.2703			1.46263			0.731313	+	0.682042i	$0.238908\pi$
$110$	−0.195973	−	0.220772i	−0.0186853	−	0.0210497i
$111$	18.5581			1.76146
$112$	−3.45466	−	1.12249i	−0.326435	−	0.106065i
$113$	−10.7384	−	14.7802i	−1.01019	−	1.39040i	−0.918861	−	0.394581i	$-0.870890\pi$
$113$	−10.7384	−	14.7802i	−1.01019	−	1.39040i	−0.0913254	−	0.995821i	$-0.529110\pi$
$114$	7.82540	−	7.19061i	0.732916	−	0.673462i
$115$	0.00966299	+	0.0297396i	0.000901079	+	0.00277324i
$116$	−0.869538	−	2.67616i	−0.0807346	−	0.248476i
$117$	2.28043	+	1.65683i	0.210826	+	0.153174i
$118$	−3.72140	−	5.12207i	−0.342583	−	0.471525i
$119$	−5.98395	+	18.4167i	−0.548547	+	1.68826i
$120$		−	0.217009i		−	0.0198101i
$121$	−1.30447	+	10.9224i	−0.118588	+	0.992943i
$122$			8.46064i			0.765991i
$123$	−1.00624	−	0.326946i	−0.0907292	−	0.0294797i
$124$	−3.84733	−	5.29540i	−0.345501	−	0.475541i
$125$	0.719515	+	0.522758i	0.0643554	+	0.0467569i
$126$	10.1716	−	3.30494i	0.906155	−	0.294428i
$127$	−3.26500	−	10.0486i	−0.289722	−	0.891673i	−0.984943	−	0.172877i	$-0.944694\pi$
$127$	−3.26500	−	10.0486i	−0.289722	−	0.891673i	0.695221	−	0.718796i	$-0.255306\pi$
$128$	0.809017	+	0.587785i	0.0715077	+	0.0519534i
$129$	12.1251	−	8.80942i	1.06756	−	0.775626i
$130$	−0.0263321	+	0.0810420i	−0.00230948	+	0.00710785i
$131$		−	1.43594i		−	0.125459i	−0.998031	−	0.0627294i	$-0.980019\pi$
$131$		−	1.43594i		−	0.125459i	0.998031	−	0.0627294i	$-0.0199805\pi$
$132$	−6.04738	+	5.36811i	−0.526357	+	0.467234i
$133$	−3.13521	+	15.5200i	−0.271858	+	1.34575i
$134$	−11.0901	−	3.60338i	−0.958035	−	0.311284i
$135$	−0.00710444	−	0.00977842i	−0.000611453	−	0.000841592i
$136$	3.13347	−	4.31284i	0.268692	−	0.369823i
$137$	−3.25191	−	10.0083i	−0.277829	−	0.855071i	−0.988457	−	0.151503i	$-0.951589\pi$
$137$	−3.25191	−	10.0083i	−0.277829	−	0.855071i	0.710627	−	0.703568i	$-0.248411\pi$
$138$	0.814629	−	0.264689i	0.0693458	−	0.0225318i
$139$	11.5094	−	15.8413i	0.976213	−	1.34364i	0.0373688	−	0.999302i	$-0.488102\pi$
$139$	11.5094	−	15.8413i	0.976213	−	1.34364i	0.938845	−	0.344341i	$-0.111898\pi$
$140$	0.190040	+	0.261567i	0.0160613	+	0.0221065i
$141$	0.192522	+	0.0625543i	0.0162133	+	0.00526802i
$142$		−	7.06107i		−	0.592552i
$143$	2.90977	−	1.27093i	0.243327	−	0.106280i
$144$	−2.94430			−0.245359
$145$	−0.0773954	+	0.238199i	−0.00642734	+	0.0197813i
$146$	9.59602	+	13.2078i	0.794172	+	1.09308i
$147$	−8.87742	+	12.2187i	−0.732197	+	1.00778i
$148$	7.23919	−	2.35216i	0.595058	−	0.193346i
$149$	−20.1231	+	6.53840i	−1.64855	+	0.535647i	−0.978425	−	0.206601i	$-0.933760\pi$
$149$	−20.1231	+	6.53840i	−1.64855	+	0.535647i	−0.670126	+	0.742248i	$0.733760\pi$
$150$	7.15403	−	9.84667i	0.584124	−	0.803977i
$151$	−4.18463	+	3.04031i	−0.340541	+	0.247417i	−0.744890	−	0.667187i	$-0.767498\pi$
$151$	−4.18463	+	3.04031i	−0.340541	+	0.247417i	0.404349	+	0.914605i	$0.367498\pi$
$152$	2.14117	−	3.79676i	0.173672	−	0.307958i
$153$			15.6960i			1.26895i
$154$	2.58811	−	11.7662i	0.208556	−	0.948146i
$155$			0.582596i			0.0467952i
$156$	2.21990	+	0.721290i	0.177735	+	0.0577494i
$157$	−13.4704	+	9.78679i	−1.07505	+	0.781071i	−0.976814	−	0.214092i	$-0.931321\pi$
$157$	−13.4704	+	9.78679i	−1.07505	+	0.781071i	−0.0982384	+	0.995163i	$0.531321\pi$
$158$	3.67258	+	2.66829i	0.292175	+	0.212278i
$159$	−2.34597	−	7.22017i	−0.186048	−	0.572596i
$160$	−0.0275048	−	0.0846511i	−0.00217445	−	0.00669226i
$161$	−0.750103	+	1.03243i	−0.0591164	+	0.0813667i
$162$	−7.41382	+	5.38646i	−0.582485	+	0.423200i
$163$	4.31740	−	13.2876i	0.338165	−	1.04076i	−0.626977	−	0.779037i	$-0.715708\pi$
$163$	4.31740	−	13.2876i	0.338165	−	1.04076i	0.965142	−	0.261726i	$-0.0842918\pi$
$164$	−0.433953			−0.0338860
$165$	0.716308	−	0.0701674i	0.0557645	−	0.00546253i
$166$		−	15.6665i		−	1.21595i
$167$	−4.09801	+	12.6124i	−0.317114	+	0.975975i	0.657762	+	0.753226i	$0.271503\pi$
$167$	−4.09801	+	12.6124i	−0.317114	+	0.975975i	−0.974876	+	0.222749i	$0.928497\pi$
$168$	7.16485	−	5.20557i	0.552780	−	0.401618i
$169$	9.77572	+	7.10248i	0.751978	+	0.546344i
$170$	−0.451273	+	0.146627i	−0.0346110	+	0.0112458i
$171$	1.47048	+	12.7494i	0.112451	+	0.974971i
$172$	3.61324	−	4.97320i	0.275507	−	0.379203i
$173$	−4.67146	+	3.39401i	−0.355164	+	0.258042i	−0.751032	−	0.660266i	$-0.770444\pi$
$173$	−4.67146	+	3.39401i	−0.355164	+	0.258042i	0.395868	+	0.918307i	$0.370444\pi$
$174$	6.52474	+	2.12002i	0.494639	+	0.160718i
$175$			18.1335i			1.37076i
$176$	−1.67859	+	2.86048i	−0.126528	+	0.215617i
$177$	15.4361			1.16025
$178$	−1.67264	−	0.543474i	−0.125370	−	0.0407351i
$179$	−5.33438	−	7.34214i	−0.398710	−	0.548778i	0.561709	−	0.827335i	$-0.310144\pi$
$179$	−5.33438	−	7.34214i	−0.398710	−	0.548778i	−0.960420	+	0.278557i	$0.910144\pi$
$180$	0.212015	+	0.154038i	0.0158027	+	0.0114813i
$181$	−19.2492	+	6.25443i	−1.43078	+	0.464888i	−0.919010	−	0.394234i	$-0.871010\pi$
$181$	−19.2492	+	6.25443i	−1.43078	+	0.464888i	−0.511770	+	0.859123i	$0.671010\pi$
$182$	−3.30737	+	1.07463i	−0.245159	+	0.0796568i
$183$	−16.6883	−	12.1247i	−1.23363	−	0.896287i
$184$	0.284224	−	0.206501i	0.0209533	−	0.0152234i
$185$	−0.644343	−	0.209360i	−0.0473730	−	0.0153924i
$186$	15.9585			1.17013
$187$	15.2491	+	8.94851i	1.11513	+	0.654380i
$188$	0.0830279			0.00605544
$189$	0.152428	−	0.469126i	0.0110875	−	0.0341239i
$190$	−0.352819	+	0.161379i	−0.0255962	+	0.0117076i
$191$	4.53360	+	3.29385i	0.328040	+	0.238335i	0.739598	−	0.673049i	$-0.235016\pi$
$191$	4.53360	+	3.29385i	0.328040	+	0.238335i	−0.411559	+	0.911383i	$0.635016\pi$
$192$	−2.31877	+	0.753413i	−0.167342	+	0.0543729i
$193$	1.31780	+	4.05576i	0.0948570	+	0.291940i	0.987216	−	0.159386i	$-0.0509513\pi$
$193$	1.31780	+	4.05576i	0.0948570	+	0.291940i	−0.892359	+	0.451326i	$0.850951\pi$
$194$	−4.23219	+	5.82511i	−0.303853	+	0.418218i
$195$	−0.122116	−	0.168078i	−0.00874492	−	0.0120363i
$196$	−1.91426	+	5.89147i	−0.136733	+	0.420820i
$197$			16.3060i			1.16175i	0.813992	+	0.580876i	$0.197290\pi$
$197$			16.3060i			1.16175i	−0.813992	+	0.580876i	$0.802710\pi$
$198$	−0.952009	−	9.71863i	−0.0676563	−	0.690673i
$199$	10.6482			0.754827			0.377414	−	0.926045i	$-0.376813\pi$
$199$	10.6482			0.754827			0.377414	+	0.926045i	$0.376813\pi$
$200$	1.54264	−	4.74775i	0.109081	−	0.335716i
$201$	23.0004	−	16.7108i	1.62232	−	1.17869i
$202$	−1.32006	+	1.81690i	−0.0928789	+	0.127837i
$203$	−9.72102	+	3.15855i	−0.682282	+	0.221687i
$204$	4.01642	+	12.3613i	0.281206	+	0.865462i
$205$	0.0312483	+	0.0227032i	0.00218248	+	0.00158566i
$206$	−0.461940	−	0.635806i	−0.0321849	−	0.0442987i
$207$	−0.319645	+	0.983766i	−0.0222168	+	0.0683764i
$208$	0.957364			0.0663813
$209$	13.2248	+	5.84000i	0.914776	+	0.403961i
$210$	−0.788272			−0.0543959
$211$	2.60588	−	8.02008i	0.179396	−	0.552125i	−0.820411	−	0.571775i	$-0.806255\pi$
$211$	2.60588	−	8.02008i	0.179396	−	0.552125i	0.999807	+	0.0196497i	$0.00625510\pi$
$212$	−1.83024	−	2.51912i	−0.125702	−	0.173014i
$213$	13.9277	+	10.1190i	0.954308	+	0.693346i
$214$	3.19276	+	9.82629i	0.218252	+	0.671712i
$215$	−0.520369	+	0.169078i	−0.0354888	+	0.0115310i
$216$	−0.0798184	+	0.109861i	−0.00543096	+	0.00747507i
$217$	−19.2352	+	13.9752i	−1.30577	+	0.948700i
$218$	−4.71877	+	14.5229i	−0.319595	+	0.983613i
$219$	−39.8036			−2.68968
$220$	0.270525	−	0.118160i	0.0182388	−	0.00796632i
$221$		−	5.10368i		−	0.343311i
$222$	−5.73478	+	17.6498i	−0.384893	+	1.18458i
$223$	9.39901	+	12.9366i	0.629404	+	0.866300i	0.997995	−	0.0632914i	$-0.0201598\pi$
$223$	9.39901	+	12.9366i	0.629404	+	0.866300i	−0.368591	+	0.929592i	$0.620160\pi$
$224$	2.13510	−	2.93871i	0.142657	−	0.196351i
$225$	4.54199	+	13.9788i	0.302799	+	0.931920i
$226$	17.3751	−	5.64553i	1.15578	−	0.375535i
$227$	−10.4907	−	7.62193i	−0.696292	−	0.505886i	0.182431	−	0.983219i	$-0.441603\pi$
$227$	−10.4907	−	7.62193i	−0.696292	−	0.505886i	−0.878722	+	0.477333i	$0.841603\pi$
$228$	4.42049	+	9.66442i	0.292754	+	0.640042i
$229$	2.60029	−	8.00287i	0.171832	−	0.528844i	−0.827643	−	0.561255i	$-0.810319\pi$
$229$	2.60029	−	8.00287i	0.171832	−	0.528844i	0.999475	+	0.0324111i	$0.0103186\pi$
$230$	−0.0312701			−0.00206189
$231$	19.4994	+	21.9668i	1.28296	+	1.44531i
$232$	2.81389			0.184741
$233$	−10.5855	−	3.43945i	−0.693481	−	0.225326i	−0.0589933	−	0.998258i	$-0.518789\pi$
$233$	−10.5855	−	3.43945i	−0.693481	−	0.225326i	−0.634488	+	0.772933i	$0.718789\pi$
$234$	−2.28043	+	1.65683i	−0.149077	+	0.108310i
$235$	−0.00597872	−	0.00434380i	−0.000390009	−	0.000283358i
$236$	6.02136	−	1.95646i	0.391957	−	0.127355i
$237$	−10.5262	+	3.42016i	−0.683749	+	0.222163i
$238$	−15.6662	−	11.3821i	−1.01549	−	0.737795i
$239$	4.90592	+	6.75243i	0.317338	+	0.436778i	0.937652	−	0.347575i	$-0.112995\pi$
$239$	4.90592	+	6.75243i	0.317338	+	0.436778i	−0.620314	+	0.784353i	$0.712995\pi$
$240$	0.206387	+	0.0670594i	0.0133223	+	0.00432866i
$241$	0.860925			0.0554571			0.0277285	−	0.999615i	$-0.491173\pi$
$241$	0.860925			0.0554571			0.0277285	+	0.999615i	$0.491173\pi$
$242$	−9.98469	−	4.61583i	−0.641841	−	0.296717i
$243$		−	21.9353i		−	1.40715i
$244$	−8.04655	−	2.61448i	−0.515128	−	0.167375i
$245$	0.446069	−	0.324088i	0.0284983	−	0.0207052i
$246$	0.621888	−	0.855955i	0.0396501	−	0.0545737i
$247$	−0.478139	−	4.14557i	−0.0304233	−	0.263776i
$248$	6.22511	−	2.02266i	0.395295	−	0.128439i
$249$	30.9015	+	22.4512i	1.95830	+	1.42279i
$250$	−0.719515	+	0.522758i	−0.0455061	+	0.0330621i
$251$	−2.65389	+	8.16784i	−0.167512	+	0.515549i	−0.999213	−	0.0396752i	$-0.987368\pi$
$251$	−2.65389	+	8.16784i	−0.167512	+	0.515549i	0.831701	+	0.555225i	$0.187368\pi$
$252$			10.6950i			0.673723i
$253$	0.773524	+	0.871404i	0.0486310	+	0.0547847i
$254$	10.5658			0.662955
$255$	0.357491	−	1.10025i	0.0223870	−	0.0689000i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	12.3473	−	16.9946i	0.770203	−	1.06009i	−0.226094	−	0.974106i	$-0.572596\pi$
$257$	12.3473	−	16.9946i	0.770203	−	1.06009i	0.996296	−	0.0859873i	$-0.0274045\pi$
$258$	4.63139	+	14.2539i	0.288337	+	0.887412i
$259$	−8.54408	−	26.2960i	−0.530903	−	1.63395i
$260$	−0.0689384	−	0.0500867i	−0.00427538	−	0.00310625i
$261$	−6.70265	+	4.86976i	−0.414884	+	0.301431i
$262$	1.36566	+	0.443730i	0.0843709	+	0.0274138i
$263$		−	11.4834i		−	0.708099i	−0.935227	−	0.354050i	$-0.884804\pi$
$263$		−	11.4834i		−	0.708099i	0.935227	−	0.354050i	$-0.115196\pi$
$264$	−3.23663	−	7.41023i	−0.199201	−	0.456068i
$265$			0.277151i			0.0170253i
$266$	−13.7915	−	7.77770i	−0.845612	−	0.476881i
$267$	3.46900	−	2.52038i	0.212299	−	0.154245i
$268$	6.85403	−	9.43376i	0.418676	−	0.576259i
$269$	30.0210	−	9.75440i	1.83041	−	0.594736i	0.831159	−	0.556035i	$-0.187678\pi$
$269$	30.0210	−	9.75440i	1.83041	−	0.594736i	0.999251	−	0.0387016i	$-0.0123222\pi$
$270$	0.0114952	−	0.00373502i	0.000699577	−	0.000227306i
$271$	13.2824	−	18.2816i	0.806846	−	1.11053i	−0.184956	−	0.982747i	$-0.559214\pi$
$271$	13.2824	−	18.2816i	0.806846	−	1.11053i	0.991802	−	0.127782i	$-0.0407857\pi$
$272$	3.13347	+	4.31284i	0.189994	+	0.261505i
$273$	2.62005	−	8.06368i	0.158573	−	0.488036i
$274$	10.5234			0.635742
$275$	16.1703	+	3.55684i	0.975105	+	0.214486i
$276$			0.856551i			0.0515583i
$277$	−25.3945	−	8.25116i	−1.52581	−	0.495764i	−0.578387	−	0.815762i	$-0.696318\pi$
$277$	−25.3945	−	8.25116i	−1.52581	−	0.495764i	−0.947418	+	0.319998i	$0.896318\pi$
$278$	11.5094	+	15.8413i	0.690287	+	0.950099i
$279$	−11.3277	+	15.5913i	−0.678172	+	0.933424i
$280$	−0.307491	+	0.0999098i	−0.0183761	+	0.00597075i
$281$	−4.33356	−	13.3373i	−0.258519	−	0.795638i	−0.993116	−	0.117135i	$-0.962629\pi$
$281$	−4.33356	−	13.3373i	−0.258519	−	0.795638i	0.734597	−	0.678503i	$-0.237371\pi$
$282$	−0.118985	+	0.163769i	−0.00708547	+	0.00975232i
$283$	−3.89207	−	5.35697i	−0.231359	−	0.318439i	0.677515	−	0.735509i	$-0.263057\pi$
$283$	−3.89207	−	5.35697i	−0.231359	−	0.318439i	−0.908874	+	0.417070i	$0.863057\pi$
$284$	6.71548	+	2.18199i	0.398490	+	0.129477i
$285$	0.187303	−	0.927189i	0.0110949	−	0.0549219i
$286$	0.309554	+	3.16009i	0.0183043	+	0.186860i
$287$			1.57631i			0.0930467i
$288$	0.909840	−	2.80020i	0.0536128	−	0.165003i
$289$	9.23836	−	6.71206i	0.543433	−	0.394827i
$290$	−0.202624	−	0.147215i	−0.0118985	−	0.00864475i
$291$	−5.42474	−	16.6956i	−0.318004	−	0.978716i
$292$	−15.5267	+	5.04492i	−0.908630	+	0.295232i
$293$	19.9786	+	14.5153i	1.16716	+	0.847995i	0.990667	−	0.136307i	$-0.0435232\pi$
$293$	19.9786	+	14.5153i	1.16716	+	0.847995i	0.176498	+	0.984301i	$0.443523\pi$
$294$	−8.87742	−	12.2187i	−0.517742	−	0.712610i
$295$	−0.535946	−	0.174139i	−0.0312040	−	0.0101388i
$296$			7.61174i			0.442423i
$297$	−0.388439	−	0.227944i	−0.0225395	−	0.0132267i
$298$		−	21.1587i		−	1.22569i
$299$	0.103935	−	0.319880i	0.00601073	−	0.0184991i
$300$	7.15403	+	9.84667i	0.413038	+	0.568498i
$301$	−18.0649	−	13.1249i	−1.04124	−	0.756507i
$302$	−1.59839	−	4.91933i	−0.0919769	−	0.283076i
$303$	−1.69203	−	5.20752i	−0.0972044	−	0.299164i
$304$	2.94927	+	3.20964i	0.169152	+	0.184085i
$305$	0.442638	+	0.609239i	0.0253454	+	0.0348849i
$306$	−14.9278	−	4.85033i	−0.853364	−	0.277275i
$307$	6.25450			0.356963			0.178482	−	0.983943i	$-0.442882\pi$
$307$	6.25450			0.356963			0.178482	+	0.983943i	$0.442882\pi$
$308$	10.3905	+	6.09739i	0.592056	+	0.347431i
$309$	1.91610			0.109003
$310$	−0.554082	−	0.180032i	−0.0314697	−	0.0102251i
$311$	−0.403931	+	0.293473i	−0.0229048	+	0.0166413i	−0.599179	−	0.800615i	$-0.704506\pi$
$311$	−0.403931	+	0.293473i	−0.0229048	+	0.0166413i	0.576274	+	0.817257i	$0.304506\pi$
$312$	−1.37198	+	1.88836i	−0.0776728	+	0.106907i
$313$	5.04758	+	15.5348i	0.285306	+	0.878082i	0.986307	+	0.164921i	$0.0527369\pi$
$313$	5.04758	+	15.5348i	0.285306	+	0.878082i	−0.701001	+	0.713160i	$0.747263\pi$
$314$	−5.14522	−	15.8354i	−0.290362	−	0.893641i
$315$	0.559534	−	0.770133i	0.0315262	−	0.0433921i
$316$	−3.67258	+	2.66829i	−0.206599	+	0.150103i
$317$	−25.8368	−	8.39487i	−1.45114	−	0.471503i	−0.525787	−	0.850616i	$-0.676229\pi$
$317$	−25.8368	−	8.39487i	−1.45114	−	0.471503i	−0.925350	+	0.379113i	$0.876229\pi$
$318$	7.59173			0.425723
$319$	0.909840	+	9.28815i	0.0509412	+	0.520036i
$320$	0.0890075			0.00497567
$321$	−23.9574	−	7.78424i	−1.33717	−	0.434474i
$322$	−0.750103	−	1.03243i	−0.0418016	−	0.0575349i
$323$	17.1105	−	15.7225i	0.952053	−	0.874822i
$324$	−2.83183	−	8.71547i	−0.157324	−	0.484193i
$325$	−1.47687	−	4.54533i	−0.0819218	−	0.252129i
$326$	11.3031	+	8.21218i	0.626020	+	0.454830i
$327$	−21.8834	−	30.1200i	−1.21016	−	1.66564i
$328$	0.134099	−	0.412714i	0.00740437	−	0.0227883i
$329$		−	0.301595i		−	0.0166274i
$330$	−0.154618	+	0.702932i	−0.00851144	+	0.0386951i
$331$		−	26.2412i		−	1.44235i	−0.692755	−	0.721173i	$-0.743603\pi$
$331$		−	26.2412i		−	1.44235i	0.692755	−	0.721173i	$-0.256397\pi$
$332$	14.8997	+	4.84120i	0.817727	+	0.265695i
$333$	−13.1730	−	18.1311i	−0.721877	−	0.993578i
$334$	−10.7287	−	7.79488i	−0.587050	−	0.426517i
$335$	−0.987098	+	0.320727i	−0.0539309	+	0.0175232i
$336$	2.73673	+	8.42279i	0.149301	+	0.459501i
$337$	18.4748	+	13.4227i	1.00639	+	0.731183i	0.963448	−	0.267894i	$-0.0863278\pi$
$337$	18.4748	+	13.4227i	1.00639	+	0.731183i	0.0429392	+	0.999078i	$0.486328\pi$
$338$	−9.77572	+	7.10248i	−0.531729	+	0.386324i
$339$	−13.7643	+	42.3622i	−0.747575	+	2.30080i
$340$		−	0.474496i		−	0.0257332i
$341$	8.68928	+	19.8940i	0.470551	+	1.07732i
$342$	−12.5798	−	2.54127i	−0.680238	−	0.137416i
$343$	−2.78217	−	0.903982i	−0.150223	−	0.0488104i
$344$	3.61324	+	4.97320i	0.194813	+	0.268137i
$345$	0.0448124	−	0.0616790i	0.00241262	−	0.00332069i
$346$	−1.78434	−	5.49162i	−0.0959266	−	0.295232i
$347$	23.4926	−	7.63321i	1.26115	−	0.409772i	0.399246	−	0.916844i	$-0.369272\pi$
$347$	23.4926	−	7.63321i	1.26115	−	0.409772i	0.861904	+	0.507072i	$0.169272\pi$
$348$	−4.03251	+	5.55027i	−0.216165	+	0.297526i
$349$	20.1849	+	27.7821i	1.08047	+	1.48714i	0.859000	+	0.511975i	$0.171086\pi$
$349$	20.1849	+	27.7821i	1.08047	+	1.48714i	0.221471	+	0.975167i	$0.428914\pi$
$350$	−17.2459	−	5.60354i	−0.921834	−	0.299522i
$351$			0.130006i			0.00693918i
$352$	−2.20176	−	2.48037i	−0.117354	−	0.132204i
$353$	−16.9738			−0.903424			−0.451712	−	0.892164i	$-0.649186\pi$
$353$	−16.9738			−0.903424			−0.451712	+	0.892164i	$0.649186\pi$
$354$	−4.77003	+	14.6806i	−0.253524	+	0.780267i
$355$	−0.369416	−	0.508457i	−0.0196066	−	0.0269861i
$356$	1.03375	−	1.42283i	0.0547886	−	0.0754100i
$357$	44.9016	−	14.5894i	2.37645	−	0.772154i
$358$	8.63121	−	2.80445i	0.456174	−	0.148220i
$359$	−9.01579	+	12.4092i	−0.475835	+	0.654931i	−0.977698	−	0.210016i	$-0.932648\pi$
$359$	−9.01579	+	12.4092i	−0.475835	+	0.654931i	0.501863	+	0.864947i	$0.332648\pi$
$360$	−0.212015	+	0.154038i	−0.0111742	+	0.00811851i
$361$	12.4254	−	14.3739i	0.653968	−	0.756522i
$362$		−	20.2398i		−	1.06378i
$363$	23.4134	−	13.0796i	1.22888	−	0.686500i
$364$		−	3.47757i		−	0.182274i
$365$	1.38199	+	0.449036i	0.0723367	+	0.0235036i
$366$	16.6883	−	12.1247i	0.872310	−	0.633771i
$367$	−14.6908	−	10.6735i	−0.766851	−	0.557150i	0.134153	−	0.990961i	$-0.457169\pi$
$367$	−14.6908	−	10.6735i	−0.766851	−	0.557150i	−0.901004	+	0.433810i	$0.857169\pi$
$368$	0.108564	+	0.334125i	0.00565928	+	0.0174175i
$369$	0.394828	+	1.21515i	0.0205539	+	0.0632584i
$370$	0.398226	−	0.548110i	0.0207028	−	0.0284949i
$371$	−9.15055	+	6.64826i	−0.475073	+	0.345161i
$372$	−4.93144	+	15.1774i	−0.255683	+	0.786912i
$373$	−30.1192			−1.55951			−0.779757	−	0.626082i	$-0.784657\pi$
$373$	−30.1192			−1.55951			−0.779757	+	0.626082i	$0.784657\pi$
$374$	−13.2228	+	11.7375i	−0.683734	+	0.606934i
$375$		−	2.16837i		−	0.111974i
$376$	−0.0256570	+	0.0789643i	−0.00132316	+	0.00407227i
$377$	2.17942	−	1.58344i	0.112246	−	0.0815515i
$378$	0.399063	+	0.289936i	0.0205256	+	0.0149127i
$379$	−11.1822	+	3.63332i	−0.574392	+	0.186631i	−0.581787	−	0.813341i	$-0.697646\pi$
$379$	−11.1822	+	3.63332i	−0.574392	+	0.186631i	0.00739492	+	0.999973i	$0.497646\pi$
$380$	−0.0444533	−	0.385420i	−0.00228040	−	0.0197716i
$381$	−15.1415	+	20.8405i	−0.775725	+	1.06769i
$382$	−4.53360	+	3.29385i	−0.231959	+	0.168528i
$383$	23.0621	+	7.49334i	1.17842	+	0.382892i	0.831779	−	0.555106i	$-0.187322\pi$
$383$	23.0621	+	7.49334i	1.17842	+	0.382892i	0.346641	+	0.937998i	$0.387322\pi$
$384$		−	2.43809i		−	0.124418i
$385$	−0.429209	−	0.982669i	−0.0218745	−	0.0500814i
$386$	−4.26448			−0.217056
$387$	−17.2134	−	5.59298i	−0.875007	−	0.284307i
$388$	−4.23219	−	5.82511i	−0.214857	−	0.295725i
$389$	−5.49796	−	3.99450i	−0.278758	−	0.202529i	0.439618	−	0.898185i	$-0.355114\pi$
$389$	−5.49796	−	3.99450i	−0.278758	−	0.202529i	−0.718375	+	0.695656i	$0.755114\pi$
$390$	0.197588	−	0.0642002i	0.0100053	−	0.00325091i
$391$	1.78121	−	0.578750i	0.0900797	−	0.0292687i
$392$	−5.01159	−	3.64113i	−0.253123	−	0.183905i
$393$	−2.83234	+	2.05781i	−0.142873	+	0.103803i
$394$	−15.5079	−	5.03882i	−0.781276	−	0.253852i
$395$	0.404055			0.0203302
$396$	9.53715	+	2.09781i	0.479260	+	0.105419i
$397$	−16.8957			−0.847970			−0.423985	−	0.905669i	$-0.639369\pi$
$397$	−16.8957			−0.847970			−0.423985	+	0.905669i	$0.639369\pi$
$398$	−3.29046	+	10.1270i	−0.164936	+	0.507620i
$399$	35.1055	−	16.0572i	1.75747	−	0.803865i
$400$	4.03868	+	2.93427i	0.201934	+	0.146713i
$401$	−20.4776	+	6.65357i	−1.02260	+	0.332263i	−0.771861	−	0.635791i	$-0.780674\pi$
$401$	−20.4776	+	6.65357i	−1.02260	+	0.332263i	−0.250740	+	0.968054i	$0.580674\pi$
$402$	8.78537	+	27.0386i	0.438174	+	1.34856i
$403$	3.68330	−	5.06963i	0.183478	−	0.252536i
$404$	−1.32006	−	1.81690i	−0.0656753	−	0.0903943i
$405$	−0.252054	+	0.775742i	−0.0125247	+	0.0385469i
$406$		−	10.2213i		−	0.507274i
$407$	−25.1250	+	2.46117i	−1.24540	+	0.121996i
$408$	−12.9974			−0.643467
$409$	−4.93189	+	15.1788i	−0.243866	+	0.750543i	0.751955	+	0.659215i	$0.229111\pi$
$409$	−4.93189	+	15.1788i	−0.243866	+	0.750543i	−0.995821	+	0.0913283i	$0.970889\pi$
$410$	−0.0312483	+	0.0227032i	−0.00154325	+	0.00112123i
$411$	−15.0808	+	20.7570i	−0.743883	+	1.02387i
$412$	0.747434	−	0.242856i	0.0368234	−	0.0119647i
$413$	−7.10673	−	21.8723i	−0.349699	−	1.07626i
$414$	−0.836841	−	0.608001i	−0.0411285	−	0.0298816i
$415$	−0.819627	−	1.12812i	−0.0402339	−	0.0553772i
$416$	−0.295842	+	0.910508i	−0.0145048	+	0.0446413i
$417$	−47.7402			−2.33785
$418$	−9.64085	+	10.7728i	−0.471549	+	0.526917i
$419$	−19.3638			−0.945983			−0.472991	−	0.881067i	$-0.656826\pi$
$419$	−19.3638			−0.945983			−0.472991	+	0.881067i	$0.656826\pi$
$420$	0.243589	−	0.749691i	0.0118859	−	0.0365812i
$421$	−4.67977	−	6.44115i	−0.228078	−	0.313922i	0.679606	−	0.733578i	$-0.262151\pi$
$421$	−4.67977	−	6.44115i	−0.228078	−	0.313922i	−0.907684	+	0.419655i	$0.862151\pi$
$422$	6.82229	+	4.95668i	0.332104	+	0.241288i
$423$	−0.0755421	−	0.232495i	−0.00367298	−	0.0113043i
$424$	2.96140	−	0.962216i	0.143818	−	0.0467294i
$425$	15.6425	−	21.5301i	0.758773	−	1.04436i
$426$	−13.9277	+	10.1190i	−0.674798	+	0.490269i
$427$	−9.49697	+	29.2287i	−0.459590	+	1.41447i
$428$	−10.3320			−0.499415
$429$	−6.67677	−	3.91807i	−0.322357	−	0.189166i
$430$		−	0.547148i		−	0.0263858i
$431$	1.38547	−	4.26403i	0.0667357	−	0.205391i	−0.912128	−	0.409906i	$-0.865562\pi$
$431$	1.38547	−	4.26403i	0.0667357	−	0.205391i	0.978864	+	0.204515i	$0.0655616\pi$
$432$	−0.0798184	−	0.109861i	−0.00384027	−	0.00528567i
$433$	−0.310467	+	0.427321i	−0.0149201	+	0.0205358i	−0.816412	−	0.577470i	$-0.804040\pi$
$433$	−0.310467	+	0.427321i	−0.0149201	+	0.0205358i	0.801492	+	0.598006i	$0.204040\pi$
$434$	−7.34721	−	22.6124i	−0.352677	−	1.08543i
$435$	0.580751	−	0.188697i	0.0278449	−	0.00904734i
$436$	−12.3539	−	8.97563i	−0.591644	−	0.429855i
$437$	1.39261	−	0.636975i	0.0666174	−	0.0304707i
$438$	12.3000	−	37.8555i	0.587717	−	1.80881i
$439$	12.3245			0.588218			0.294109	−	0.955772i	$-0.404977\pi$
$439$	12.3245			0.588218			0.294109	+	0.955772i	$0.404977\pi$
$440$	0.0287796	+	0.293798i	0.00137201	+	0.0140063i
$441$	18.2390			0.868522
$442$	4.85389	+	1.57712i	0.230876	+	0.0750161i
$443$	−19.7474	+	14.3473i	−0.938229	+	0.681663i	−0.947994	−	0.318289i	$-0.896892\pi$
$443$	−19.7474	+	14.3473i	−0.938229	+	0.681663i	0.00976498	+	0.999952i	$0.496892\pi$
$444$	−15.0138	−	10.9082i	−0.712526	−	0.517680i
$445$	−0.148878	+	0.0483732i	−0.00705747	+	0.00229311i
$446$	−15.2079	+	4.94135i	−0.720115	+	0.233980i
$447$	41.7347	+	30.3220i	1.97398	+	1.43418i
$448$	2.13510	+	2.93871i	0.100874	+	0.138841i
$449$	22.0919	+	7.17810i	1.04258	+	0.338755i	0.779753	−	0.626087i	$-0.215345\pi$
$449$	22.0919	+	7.17810i	1.04258	+	0.338755i	0.262829	+	0.964843i	$0.415345\pi$
$450$	−14.6982			−0.692879
$451$	1.40566	+	0.309190i	0.0661898	+	0.0145592i
$452$			18.2693i			0.859316i
$453$	11.9938	+	3.89702i	0.563517	+	0.183098i
$454$	10.4907	−	7.62193i	0.492353	−	0.357715i
$455$	−0.181937	+	0.250415i	−0.00852935	+	0.0117396i
$456$	−10.5574	+	1.21766i	−0.494396	+	0.0570224i
$457$	9.61716	−	3.12480i	0.449872	−	0.146172i	−0.0753139	−	0.997160i	$-0.523996\pi$
$457$	9.61716	−	3.12480i	0.449872	−	0.146172i	0.525186	+	0.850988i	$0.323996\pi$
$458$	6.80764	+	4.94604i	0.318100	+	0.231113i
$459$	−0.585664	+	0.425510i	−0.0273364	+	0.0198611i
$460$	0.00966299	−	0.0297396i	0.000450539	−	0.00138662i
$461$		−	30.7107i		−	1.43034i	−0.698950	−	0.715170i	$-0.746349\pi$
$461$		−	30.7107i		−	1.43034i	0.698950	−	0.715170i	$-0.253651\pi$
$462$	−26.9173	+	11.7569i	−1.25230	+	0.546980i
$463$	−12.2517			−0.569386			−0.284693	−	0.958619i	$-0.591892\pi$
$463$	−12.2517			−0.569386			−0.284693	+	0.958619i	$0.591892\pi$
$464$	−0.869538	+	2.67616i	−0.0403673	+	0.124238i
$465$	1.14915	−	0.834904i	0.0532904	−	0.0387177i
$466$	6.54222	−	9.00459i	0.303063	−	0.417130i
$467$	−5.77200	−	17.7644i	−0.267096	−	0.822038i	−0.991203	−	0.132350i	$-0.957748\pi$
$467$	−5.77200	−	17.7644i	−0.267096	−	0.822038i	0.724107	−	0.689688i	$-0.242252\pi$
$468$	−0.871048	−	2.68081i	−0.0402642	−	0.123921i
$469$	−34.2676	−	24.8969i	−1.58233	−	1.14963i
$470$	0.00597872	−	0.00434380i	0.000275778	−	0.000200364i
$471$	38.6081	+	12.5445i	1.77897	+	0.578022i
$472$			6.33123i			0.291419i
$473$	−15.2474	+	13.5347i	−0.701074	+	0.622327i
$474$		−	11.0679i		−	0.508364i
$475$	10.6889	−	18.9537i	0.490441	−	0.869656i
$476$	15.6662	−	11.3821i	0.718058	−	0.521700i
$477$	−5.38879	+	7.41704i	−0.246736	+	0.339603i
$478$	−7.93795	+	2.57920i	−0.363074	+	0.117970i
$479$	−6.72730	+	2.18583i	−0.307378	+	0.0998733i	−0.458645	−	0.888620i	$-0.651665\pi$
$479$	−6.72730	+	2.18583i	−0.307378	+	0.0998733i	0.151266	+	0.988493i	$0.451665\pi$
$480$	−0.127554	+	0.175564i	−0.00582204	+	0.00801335i
$481$	4.28331	+	5.89548i	0.195302	+	0.268811i
$482$	−0.266041	+	0.818789i	−0.0121178	+	0.0372948i
$483$	3.11138			0.141572
$484$	7.47535	−	8.06964i	0.339789	−	0.366802i
$485$			0.640874i			0.0291006i
$486$	20.8617	+	6.77838i	0.946306	+	0.307473i
$487$	21.6991	+	29.8662i	0.983279	+	1.35337i	0.935044	+	0.354531i	$0.115359\pi$
$487$	21.6991	+	29.8662i	0.983279	+	1.35337i	0.0482342	+	0.998836i	$0.484641\pi$
$488$	4.97304	−	6.84480i	0.225119	−	0.309850i
$489$	−32.3964	+	10.5262i	−1.46501	+	0.476012i
$490$	0.170383	+	0.524385i	0.00769712	+	0.0236893i
$491$	−0.222565	+	0.306335i	−0.0100442	+	0.0138247i	−0.814010	−	0.580851i	$-0.802720\pi$
$491$	−0.222565	+	0.306335i	−0.0100442	+	0.0138247i	0.803965	+	0.594676i	$0.202720\pi$
$492$	0.621888	+	0.855955i	0.0280369	+	0.0385894i
$493$	14.2665	+	4.63548i	0.642533	+	0.208772i
$494$	4.09043	+	0.826315i	0.184037	+	0.0371777i
$495$	−0.577005	−	0.650018i	−0.0259345	−	0.0292161i
$496$			6.54547i			0.293900i
$497$	7.92596	−	24.3936i	0.355528	−	1.09420i
$498$	−30.9015	+	22.4512i	−1.38473	+	1.00606i
$499$	−24.1162	−	17.5215i	−1.07959	−	0.784369i	−0.101980	−	0.994786i	$-0.532518\pi$
$499$	−24.1162	−	17.5215i	−1.07959	−	0.784369i	−0.977612	+	0.210417i	$0.932518\pi$
$500$	−0.274830	−	0.845841i	−0.0122908	−	0.0378272i
$501$	30.7502	−	9.99133i	1.37382	−	0.446380i
$502$	−6.94798	−	5.04800i	−0.310103	−	0.225303i
$503$	−17.6612	−	24.3086i	−0.787475	−	1.08387i	−0.994418	−	0.105513i	$-0.966352\pi$
$503$	−17.6612	−	24.3086i	−0.787475	−	1.08387i	0.206943	−	0.978353i	$-0.433648\pi$
$504$	−10.1716	−	3.30494i	−0.453078	−	0.147214i
$505$			0.199894i			0.00889519i
$506$	−1.06779	+	0.466386i	−0.0474689	+	0.0207334i
$507$		−	29.4606i		−	1.30839i
$508$	−3.26500	+	10.0486i	−0.144861	+	0.445836i
$509$	−0.695036	−	0.956635i	−0.0308069	−	0.0424021i	0.793336	−	0.608784i	$-0.208343\pi$
$509$	−0.695036	−	0.956635i	−0.0308069	−	0.0424021i	−0.824143	+	0.566382i	$0.808343\pi$
$510$	0.935925	+	0.679989i	0.0414434	+	0.0301104i
$511$	18.3254	+	56.3998i	0.810669	+	2.49498i
$512$	−0.309017	−	0.951057i	−0.0136568	−	0.0420312i
$513$	−0.435854	+	0.400497i	−0.0192434	+	0.0176824i
$514$	12.3473	+	16.9946i	0.544615	+	0.749599i
$515$	−0.0665273	−	0.0216160i	−0.00293154	−	0.000952515i
$516$	−14.9875			−0.659787
$517$	−0.268943	−	0.0591572i	−0.0118281	−	0.00260173i
$518$	27.6492			1.21484
$519$	13.3891	+	4.35038i	0.587716	+	0.190961i
$520$	0.0689384	−	0.0500867i	0.00302315	−	0.00219645i
$521$	−4.36745	+	6.01127i	−0.191341	+	0.263359i	−0.893899	−	0.448268i	$-0.852041\pi$
$521$	−4.36745	+	6.01127i	−0.191341	+	0.263359i	0.702558	+	0.711626i	$0.252041\pi$
$522$	−2.56018	−	7.87944i	−0.112056	−	0.344874i
$523$	7.14235	+	21.9819i	0.312313	+	0.961201i	0.976846	+	0.213942i	$0.0686304\pi$
$523$	7.14235	+	21.9819i	0.312313	+	0.961201i	−0.664533	+	0.747259i	$0.731370\pi$
$524$	−0.844026	+	1.16170i	−0.0368714	+	0.0507492i
$525$	35.7675	−	25.9866i	1.56102	−	1.13415i
$526$	10.9214	+	3.54858i	0.476196	+	0.154725i
$527$	34.8937			1.51999
$528$	8.04772	−	0.788332i	0.350232	−	0.0343077i
$529$	−22.8766			−0.994634
$530$	−0.263587	−	0.0856445i	−0.0114495	−	0.00372016i
$531$	−10.9569	−	15.0809i	−0.475491	−	0.654457i
$532$	11.6588	−	10.7131i	0.505475	−	0.464471i
$533$	−0.128381	−	0.395118i	−0.00556082	−	0.0171144i
$534$	1.32504	+	4.07805i	0.0573401	+	0.176475i
$535$	0.743991	+	0.540541i	0.0321655	+	0.0233696i
$536$	6.85403	+	9.43376i	0.296049	+	0.407476i
$537$	−6.83751	+	21.0437i	−0.295060	+	0.908103i
$538$			31.5659i			1.36090i
$539$	10.3983	−	17.7197i	0.447886	−	0.763241i
$540$			0.0120868i			0.000520133i
$541$	12.9454	+	4.20622i	0.556567	+	0.180840i	0.573776	−	0.819012i	$-0.305478\pi$
$541$	12.9454	+	4.20622i	0.556567	+	0.180840i	−0.0172087	+	0.999852i	$0.505478\pi$
$542$	13.2824	+	18.2816i	0.570526	+	0.785262i
$543$	39.9221	+	29.0051i	1.71322	+	1.24473i
$544$	−5.07005	+	1.64736i	−0.217377	+	0.0706300i
$545$	0.420006	+	1.29264i	0.0179911	+	0.0553708i
$546$	6.85937	+	4.98363i	0.293554	+	0.213280i
$547$	17.6767	−	12.8429i	0.755803	−	0.549123i	−0.141817	−	0.989893i	$-0.545295\pi$
$547$	17.6767	−	12.8429i	0.755803	−	0.549123i	0.897620	+	0.440770i	$0.145295\pi$
$548$	−3.25191	+	10.0083i	−0.138915	+	0.427536i
$549$			24.9107i			1.06316i
$550$	−8.37965	+	14.2797i	−0.357310	+	0.608890i
$551$	12.0226	+	2.42870i	0.512179	+	0.103466i
$552$	−0.814629	−	0.264689i	−0.0346729	−	0.0112659i
$553$	9.69241	+	13.3405i	0.412163	+	0.567294i
$554$	15.6946	−	21.6018i	0.666802	−	0.917774i
$555$	0.510438	+	1.57097i	0.0216669	+	0.0666839i
$556$	−18.6226	+	6.05084i	−0.789773	+	0.256613i
$557$	−11.1047	+	15.2843i	−0.470522	+	0.647618i	−0.976649	−	0.214841i	$-0.931077\pi$
$557$	−11.1047	+	15.2843i	−0.470522	+	0.647618i	0.506127	+	0.862459i	$0.331077\pi$
$558$	−11.3277	−	15.5913i	−0.479540	−	0.660030i
$559$	5.59708	+	1.81860i	0.236731	+	0.0769187i
$560$		−	0.323315i		−	0.0136625i
$561$	−4.20257	−	42.9022i	−0.177433	−	1.81133i
$562$	14.0237			0.591554
$563$	−12.7444	+	39.2231i	−0.537111	+	1.65306i	0.201933	+	0.979399i	$0.435278\pi$
$563$	−12.7444	+	39.2231i	−0.537111	+	1.65306i	−0.739044	+	0.673658i	$0.764722\pi$
$564$	−0.118985	−	0.163769i	−0.00501019	−	0.00689593i
$565$	0.955801	−	1.31555i	0.0402108	−	0.0553455i
$566$	6.29750	−	2.04618i	0.264704	−	0.0860074i
$567$	−31.6585	+	10.2865i	−1.32953	+	0.431991i
$568$	−4.15039	+	5.71252i	−0.174147	+	0.239692i
$569$	−8.26175	+	6.00252i	−0.346351	+	0.251639i	−0.747336	−	0.664446i	$-0.768668\pi$
$569$	−8.26175	+	6.00252i	−0.346351	+	0.251639i	0.400986	+	0.916084i	$0.368668\pi$
$570$	0.823929	+	0.464653i	0.0345106	+	0.0194622i
$571$			3.18135i			0.133135i	0.997782	+	0.0665676i	$0.0212048\pi$
$571$			3.18135i			0.133135i	−0.997782	+	0.0665676i	$0.978795\pi$
$572$	−3.10108	−	0.682120i	−0.129663	−	0.0285209i
$573$		−	13.6627i		−	0.570766i
$574$	−1.49916	−	0.487107i	−0.0625738	−	0.0203314i
$575$	1.41887	−	1.03087i	0.0591709	−	0.0429901i
$576$	2.38199	+	1.73062i	0.0992496	+	0.0721091i
$577$	−6.65762	−	20.4900i	−0.277160	−	0.853011i	−0.988640	−	0.150305i	$-0.951975\pi$
$577$	−6.65762	−	20.4900i	−0.277160	−	0.853011i	0.711480	−	0.702707i	$-0.248025\pi$
$578$	3.52874	+	10.8603i	0.146776	+	0.451731i
$579$	6.11132	−	8.41151i	0.253978	−	0.349570i
$580$	0.202624	−	0.147215i	0.00841350	−	0.00611276i
$581$	17.5854	−	54.1223i	0.729565	−	2.24537i
$582$	17.5548			0.727671
$583$	4.13365	+	9.46394i	0.171198	+	0.391956i
$584$		−	16.3257i		−	0.675563i
$585$	−0.0775298	+	0.238612i	−0.00320546	+	0.00986540i
$586$	−19.9786	+	14.5153i	−0.825310	+	0.599623i
$587$	23.0023	+	16.7121i	0.949405	+	0.689783i	0.950666	−	0.310216i	$-0.100401\pi$
$587$	23.0023	+	16.7121i	0.949405	+	0.689783i	−0.00126077	+	0.999999i	$0.500401\pi$
$588$	14.3640	−	4.66714i	0.592360	−	0.192469i
$589$	28.3431	−	3.26902i	1.16786	−	0.134698i
$590$	0.331233	−	0.455903i	0.0136366	−	0.0187692i
$591$	32.1628	−	23.3677i	1.32300	−	0.961217i
$592$	−7.23919	−	2.35216i	−0.297529	−	0.0966731i
$593$		−	23.3158i		−	0.957465i	−0.877961	−	0.478732i	$-0.841096\pi$
$593$		−	23.3158i		−	0.957465i	0.877961	−	0.478732i	$-0.158904\pi$
$594$	0.336822	−	0.298989i	0.0138200	−	0.0122677i
$595$	−1.72358			−0.0706600
$596$	20.1231	+	6.53840i	0.824275	+	0.267823i
$597$	−15.2596	−	21.0030i	−0.624534	−	0.859598i
$598$	0.272106	+	0.197696i	0.0111272	+	0.00808441i
$599$	−32.1574	+	10.4486i	−1.31391	+	0.426917i	−0.880401	−	0.474231i	$-0.842726\pi$
$599$	−32.1574	+	10.4486i	−1.31391	+	0.426917i	−0.433513	+	0.901147i	$0.642726\pi$
$600$	−11.5755	+	3.76109i	−0.472566	+	0.153546i
$601$	14.8342	+	10.7777i	0.605102	+	0.439632i	0.847686	−	0.530498i	$-0.177995\pi$
$601$	14.8342	+	10.7777i	0.605102	+	0.439632i	−0.242584	+	0.970130i	$0.577995\pi$
$602$	18.0649	−	13.1249i	0.736269	−	0.534931i
$603$	−32.6525	−	10.6094i	−1.32971	−	0.432049i
$604$	5.17249			0.210466
$605$	−0.960471	+	0.189993i	−0.0390487	+	0.00772431i
$606$	5.47551			0.222427
$607$	15.1649	−	46.6729i	0.615526	−	1.89440i	0.222175	−	0.975007i	$-0.428684\pi$
$607$	15.1649	−	46.6729i	0.615526	−	1.89440i	0.393351	−	0.919388i	$-0.371316\pi$
$608$	−3.96392	+	1.81309i	−0.160758	+	0.0735306i
$609$	20.1611	+	14.6479i	0.816968	+	0.593562i
$610$	−0.716203	+	0.232709i	−0.0289982	+	0.00942209i
$611$	0.0245631	+	0.0755976i	0.000993718	+	0.00305835i
$612$	9.22587	−	12.6983i	0.372934	−	0.513299i
$613$	−24.0941	−	33.1627i	−0.973153	−	1.33943i	−0.940438	−	0.339966i	$-0.889584\pi$
$613$	−24.0941	−	33.1627i	−0.973153	−	1.33943i	−0.0327155	−	0.999465i	$-0.510416\pi$
$614$	−1.93275	+	5.94838i	−0.0779993	+	0.240057i
$615$		−	0.0941715i		−	0.00379736i
$616$	−9.00981	+	7.99779i	−0.363016	+	0.322240i
$617$	5.73311			0.230806			0.115403	−	0.993319i	$-0.463184\pi$
$617$	5.73311			0.230806			0.115403	+	0.993319i	$0.463184\pi$
$618$	−0.592106	+	1.82232i	−0.0238180	+	0.0733043i
$619$	−23.8806	+	17.3503i	−0.959841	+	0.697366i	−0.953114	−	0.302612i	$-0.902141\pi$
$619$	−23.8806	+	17.3503i	−0.959841	+	0.697366i	−0.00672747	+	0.999977i	$0.502141\pi$
$620$	0.342441	−	0.471330i	0.0137528	−	0.0189291i
$621$	−0.0453726	+	0.0147424i	−0.00182074	+	0.000591594i
$622$	−0.154288	−	0.474849i	−0.00618638	−	0.0190397i
$623$	−5.16836	−	3.75504i	−0.207066	−	0.150442i
$624$	−1.37198	−	1.88836i	−0.0549230	−	0.0755950i
$625$	7.68872	−	23.6635i	0.307549	−	0.946538i
$626$	−16.3343			−0.652850
$627$	−7.43293	−	34.4545i	−0.296842	−	1.37598i
$628$	16.6503			0.664419
$629$	−12.5393	+	38.5919i	−0.499974	+	1.53876i
$630$	0.559534	+	0.770133i	0.0222924	+	0.0306828i
$631$	−16.5994	−	12.0602i	−0.660812	−	0.480108i	0.206125	−	0.978526i	$-0.433915\pi$
$631$	−16.5994	−	12.0602i	−0.660812	−	0.480108i	−0.866937	+	0.498418i	$0.833915\pi$
$632$	−1.40280	−	4.31738i	−0.0558005	−	0.171736i
$633$	−19.5537	+	6.35339i	−0.777190	+	0.252524i
$634$	15.9680	−	21.9781i	0.634170	−	0.872860i
$635$	0.760826	−	0.552772i	0.0301924	−	0.0219361i
$636$	−2.34597	+	7.22017i	−0.0930239	+	0.286298i
$637$	−5.93055			−0.234977
$638$	−9.11471	−	2.00489i	−0.360855	−	0.0793742i
$639$		−	20.7899i		−	0.822437i
$640$	−0.0275048	+	0.0846511i	−0.00108722	+	0.00334613i
$641$	−26.9529	−	37.0975i	−1.06458	−	1.46526i	−0.875448	−	0.483313i	$-0.839433\pi$
$641$	−26.9529	−	37.0975i	−1.06458	−	1.46526i	−0.189130	−	0.981952i	$-0.560567\pi$
$642$	14.8065	−	20.3794i	0.584366	−	0.804311i
$643$	−0.311477	−	0.958626i	−0.0122834	−	0.0378045i	0.944727	−	0.327858i	$-0.106327\pi$
$643$	−0.311477	−	0.958626i	−0.0122834	−	0.0378045i	−0.957010	+	0.290054i	$0.906327\pi$
$644$	1.21369	−	0.394352i	0.0478261	−	0.0155397i
$645$	1.07923	+	0.784104i	0.0424945	+	0.0308741i
$646$	9.66554	+	21.1316i	0.380286	+	0.831410i
$647$	1.49739	−	4.60851i	0.0588687	−	0.181179i	−0.917298	−	0.398202i	$-0.869634\pi$
$647$	1.49739	−	4.60851i	0.0588687	−	0.181179i	0.976167	+	0.217022i	$0.0696345\pi$
$648$	9.16399			0.359996
$649$	−20.8983	+	2.04714i	−0.820330	+	0.0803571i
$650$	4.77924			0.187457
$651$	55.1311	+	17.9132i	2.16076	+	0.702073i
$652$	−11.3031	+	8.21218i	−0.442663	+	0.321614i
$653$	30.6156	+	22.2435i	1.19808	+	0.870456i	0.994094	−	0.108519i	$-0.0346107\pi$
$653$	30.6156	+	22.2435i	1.19808	+	0.870456i	0.203985	+	0.978974i	$0.434611\pi$
$654$	35.4081	−	11.5048i	1.38457	−	0.449873i
$655$	0.121554	−	0.0394953i	0.00474951	−	0.00154321i
$656$	0.351075	+	0.255071i	0.0137072	+	0.00995886i
$657$	28.2536	+	38.8877i	1.10228	+	1.51715i
$658$	0.286833	+	0.0931978i	0.0111819	+	0.00363323i
$659$	−3.54350			−0.138035			−0.0690176	−	0.997615i	$-0.521986\pi$
$659$	−3.54350			−0.138035			−0.0690176	+	0.997615i	$0.521986\pi$
$660$	−0.620748	−	0.364268i	−0.0241626	−	0.0141791i
$661$			27.3234i			1.06276i	0.847134	+	0.531379i	$0.178326\pi$
$661$			27.3234i			1.06276i	−0.847134	+	0.531379i	$0.821674\pi$
$662$	24.9569	+	8.10897i	0.969976	+	0.315164i
$663$	−10.0668	+	7.31396i	−0.390962	+	0.284051i
$664$	−9.20851	+	12.6744i	−0.357360	+	0.491863i
$665$	−1.40002	+	0.161474i	−0.0542903	+	0.00626170i
$666$	21.3144	−	6.92546i	0.825915	−	0.268356i
$667$	0.799773	+	0.581069i	0.0309673	+	0.0224991i
$668$	10.7287	−	7.79488i	0.415107	−	0.301593i
$669$	12.0475	−	37.0783i	0.465782	−	1.43353i
$670$		−	1.03790i		−	0.0400974i
$671$	24.2015	+	14.2020i	0.934288	+	0.548260i
$672$	−8.85624			−0.341637
$673$	−13.1382	+	40.4352i	−0.506440	+	1.55866i	0.291895	+	0.956450i	$0.405714\pi$
$673$	−13.1382	+	40.4352i	−0.506440	+	1.55866i	−0.798336	+	0.602213i	$0.794286\pi$
$674$	−18.4748	+	13.4227i	−0.711623	+	0.517025i
$675$	−0.398460	+	0.548433i	−0.0153367	+	0.0211092i
$676$	−3.73399	−	11.4920i	−0.143615	−	0.442002i
$677$	−12.1633	−	37.4346i	−0.467472	−	1.43873i	−0.855847	−	0.517229i	$-0.826964\pi$
$677$	−12.1633	−	37.4346i	−0.467472	−	1.43873i	0.388375	−	0.921501i	$-0.373036\pi$
$678$	−36.0355	−	26.1813i	−1.38393	−	1.00549i
$679$	−21.1594	+	15.3732i	−0.812023	+	0.589969i
$680$	0.451273	+	0.146627i	0.0173055	+	0.00562290i
$681$			31.6153i			1.21150i
$682$	−21.6055	+	2.11641i	−0.827316	+	0.0810414i
$683$			10.2916i			0.393797i	0.980424	+	0.196898i	$0.0630869\pi$
$683$			10.2916i			0.393797i	−0.980424	+	0.196898i	$0.936913\pi$
$684$	6.30426	−	11.1788i	0.241050	−	0.427432i
$685$	0.757775	−	0.550556i	0.0289531	−	0.0210357i
$686$	1.71948	−	2.36666i	0.0656499	−	0.0903593i
$687$	−19.5117	+	6.33975i	−0.744419	+	0.241876i
$688$	−5.84635	+	1.89959i	−0.222890	+	0.0724213i
$689$	1.75221	−	2.41171i	0.0667539	−	0.0918789i
$690$	0.0448124	+	0.0616790i	0.00170598	+	0.00234808i
$691$	−8.61287	+	26.5077i	−0.327649	+	1.00840i	0.642581	+	0.766217i	$0.277863\pi$
$691$	−8.61287	+	26.5077i	−0.327649	+	1.00840i	−0.970231	+	0.242183i	$0.922137\pi$
$692$	5.77424			0.219504
$693$	7.62017	−	34.6432i	0.289466	−	1.31599i
$694$			24.7016i			0.937660i
$695$	1.65755	+	0.538570i	0.0628744	+	0.0204291i
$696$	−4.03251	−	5.55027i	−0.152852	−	0.210383i
$697$	1.35978	−	1.87157i	0.0515052	−	0.0708908i
$698$	−32.6598	+	10.6118i	−1.23619	+	0.401663i
$699$	8.38570	+	25.8085i	0.317176	+	0.976168i
$700$	10.6586	−	14.6703i	0.402856	−	0.554484i
$701$	15.4889	+	21.3187i	0.585009	+	0.805196i	0.994233	−	0.107238i	$-0.0342007\pi$
$701$	15.4889	+	21.3187i	0.585009	+	0.805196i	−0.409224	+	0.912434i	$0.634201\pi$
$702$	−0.123643	−	0.0401739i	−0.00466659	−	0.00151627i
$703$	−6.56980	+	32.5219i	−0.247785	+	1.22658i
$704$	3.03935	−	1.32753i	0.114550	−	0.0500330i
$705$			0.0180178i			0.000678589i
$706$	5.24519	−	16.1430i	0.197405	−	0.607551i
$707$	−6.59980	+	4.79504i	−0.248211	+	0.180336i
$708$	−12.4881	−	9.07313i	−0.469331	−	0.340989i
$709$	10.4999	+	32.3153i	0.394331	+	1.21363i	0.929481	+	0.368869i	$0.120255\pi$
$709$	10.4999	+	32.3153i	0.394331	+	1.21363i	−0.535150	+	0.844757i	$0.679745\pi$
$710$	0.597728	−	0.194213i	0.0224323	−	0.00728870i
$711$	10.8132	+	7.85625i	0.405526	+	0.294632i
$712$	1.03375	+	1.42283i	0.0387414	+	0.0533229i
$713$	2.18701	+	0.710601i	0.0819040	+	0.0266122i
$714$			47.2124i			1.76688i
$715$	0.187618	+	0.211359i	0.00701652	+	0.00790437i
$716$			9.07539i			0.339163i
$717$	6.28833	−	19.3535i	0.234842	−	0.722769i
$718$	−9.01579	−	12.4092i	−0.336466	−	0.463106i
$719$	−14.1538	−	10.2833i	−0.527847	−	0.383503i	0.291705	−	0.956508i	$-0.405777\pi$
$719$	−14.1538	−	10.2833i	−0.527847	−	0.383503i	−0.819552	+	0.573005i	$0.805777\pi$
$720$	−0.0809825	−	0.249239i	−0.00301804	−	0.00928857i
$721$	−0.882162	−	2.71501i	−0.0328534	−	0.101112i
$722$	9.83075	+	16.2590i	0.365863	+	0.605099i
$723$	−1.23377	−	1.69814i	−0.0458844	−	0.0631545i
$724$	19.2492	+	6.25443i	0.715390	+	0.232444i
$725$	14.0471			0.521697
$726$	5.20429	+	26.3092i	0.193149	+	0.976427i
$727$	22.6773			0.841056			0.420528	−	0.907280i	$-0.361845\pi$
$727$	22.6773			0.841056			0.420528	+	0.907280i	$0.361845\pi$
$728$	3.30737	+	1.07463i	0.122579	+	0.0398284i
$729$	−21.0250	+	15.2755i	−0.778703	+	0.565761i
$730$	−0.854117	+	1.17559i	−0.0316123	+	0.0435106i
$731$	10.1267	+	31.1667i	0.374548	+	1.15274i
$732$	6.37435	+	19.6182i	0.235603	+	0.725111i
$733$	−1.61350	+	2.22079i	−0.0595960	+	0.0820269i	−0.837775	−	0.546016i	$-0.816144\pi$
$733$	−1.61350	+	2.22079i	−0.0595960	+	0.0820269i	0.778179	+	0.628043i	$0.216144\pi$
$734$	14.6908	−	10.6735i	0.542246	−	0.393965i
$735$	−1.27850	−	0.415410i	−0.0471582	−	0.0153226i
$736$	−0.351320			−0.0129498
$737$	−28.9230	+	25.6743i	−1.06539	+	0.945724i
$738$	−1.27769			−0.0470324
$739$	−33.1245	−	10.7628i	−1.21851	−	0.395916i	−0.371968	−	0.928246i	$-0.621317\pi$
$739$	−33.1245	−	10.7628i	−1.21851	−	0.395916i	−0.846538	+	0.532329i	$0.821317\pi$
$740$	0.398226	+	0.548110i	0.0146391	+	0.0201489i
$741$	−7.49176	+	6.88403i	−0.275217	+	0.252891i
$742$	−3.49520	−	10.7571i	−0.128313	−	0.394906i
$743$	−4.96257	−	15.2732i	−0.182059	−	0.560320i	0.817826	−	0.575465i	$-0.195179\pi$
$743$	−4.96257	−	15.2732i	−0.182059	−	0.560320i	−0.999885	+	0.0151454i	$0.995179\pi$
$744$	−12.9107	−	9.38016i	−0.473328	−	0.343893i
$745$	−1.10697	−	1.52361i	−0.0405561	−	0.0558207i
$746$	9.30735	−	28.6451i	0.340766	−	1.04877i
$747$		−	46.1268i		−	1.68769i
$748$	−7.07700	−	16.2027i	−0.258761	−	0.592430i
$749$			37.5303i			1.37133i
$750$	2.06224	+	0.670062i	0.0753023	+	0.0244672i
$751$	−9.45009	−	13.0069i	−0.344839	−	0.474630i	0.601008	−	0.799243i	$-0.294766\pi$
$751$	−9.45009	−	13.0069i	−0.344839	−	0.474630i	−0.945847	+	0.324613i	$0.894766\pi$
$752$	−0.0671710	−	0.0488026i	−0.00244948	−	0.00177965i
$753$	19.9140	−	6.47044i	0.725705	−	0.235796i
$754$	0.832465	+	2.56206i	0.0303166	+	0.0933049i
$755$	−0.372464	−	0.270611i	−0.0135553	−	0.00984853i
$756$	−0.399063	+	0.289936i	−0.0145138	+	0.0105449i
$757$	−9.09851	+	28.0023i	−0.330691	+	1.01776i	0.638115	+	0.769941i	$0.279714\pi$
$757$	−9.09851	+	28.0023i	−0.330691	+	1.01776i	−0.968806	+	0.247821i	$0.920286\pi$
$758$		−	11.7577i		−	0.427058i
$759$	0.610290	−	2.77453i	0.0221521	−	0.100709i
$760$	0.380293	+	0.0768236i	0.0137947	+	0.00278669i
$761$	13.6713	+	4.44207i	0.495584	+	0.161025i	0.546136	−	0.837696i	$-0.316098\pi$
$761$	13.6713	+	4.44207i	0.495584	+	0.161025i	−0.0505521	+	0.998721i	$0.516098\pi$
$762$	−15.1415	−	20.8405i	−0.548520	−	0.754973i
$763$	−32.6035	+	44.8749i	−1.18033	+	1.62458i
$764$	−1.73168	−	5.32956i	−0.0626500	−	0.192817i
$765$	−1.32868	+	0.431715i	−0.0480387	+	0.0156087i
$766$	−14.2532	+	19.6178i	−0.514988	+	0.708821i
$767$	3.56274	+	4.90369i	0.128643	+	0.177062i
$768$	2.31877	+	0.753413i	0.0836712	+	0.0271864i
$769$		−	9.29441i		−	0.335165i	−0.985858	−	0.167582i	$-0.946404\pi$
$769$		−	9.29441i		−	0.335165i	0.985858	−	0.167582i	$-0.0535960\pi$
$770$	1.06721	−	0.104540i	0.0384594	−	0.00376737i
$771$	−51.2157			−1.84449
$772$	1.31780	−	4.05576i	0.0474285	−	0.145970i
$773$	23.9273	+	32.9331i	0.860604	+	1.18452i	0.981425	+	0.191846i	$0.0614473\pi$
$773$	23.9273	+	32.9331i	0.860604	+	1.18452i	−0.120821	+	0.992674i	$0.538553\pi$
$774$	10.6385	−	14.6426i	0.382392	−	0.526317i
$775$	31.0762	−	10.0973i	1.11629	−	0.362705i
$776$	6.84783	−	2.22499i	0.245823	−	0.0798726i
$777$	−39.6234	+	54.5370i	−1.42148	+	1.95650i
$778$	5.49796	−	3.99450i	0.197111	−	0.143210i
$779$	0.929169	−	1.64761i	0.0332909	−	0.0590319i
$780$			0.207756i			0.00743887i
$781$	−20.1980	−	11.8526i	−0.722742	−	0.424121i
$782$			1.87288i			0.0669739i
$783$	−0.363410	−	0.118079i	−0.0129872	−	0.00421980i
$784$	5.01159	−	3.64113i	0.178985	−	0.130040i
$785$	−1.19896	−	0.871098i	−0.0427928	−	0.0310908i
$786$	−1.08186	−	3.32961i	−0.0385885	−	0.118763i
$787$	−3.90418	−	12.0158i	−0.139169	−	0.428318i	0.857046	−	0.515239i	$-0.172297\pi$
$787$	−3.90418	−	12.0158i	−0.139169	−	0.428318i	−0.996215	+	0.0869218i	$0.972297\pi$
$788$	9.58440	−	13.1918i	0.341430	−	0.469938i
$789$	−22.6506	+	16.4566i	−0.806384	+	0.585872i
$790$	−0.124860	+	0.384279i	−0.00444231	+	0.0136720i
$791$	66.3623			2.35957
$792$	−4.94228	+	8.42211i	−0.175616	+	0.299267i
$793$		−	8.09992i		−	0.287637i
$794$	5.22106	−	16.0688i	0.185288	−	0.570259i
$795$	0.546670	−	0.397179i	0.0193884	−	0.0140865i
$796$	−8.61454	−	6.25883i	−0.305334	−	0.221838i
$797$	−16.0817	+	5.22525i	−0.569642	+	0.185088i	−0.579655	−	0.814862i	$-0.696813\pi$
$797$	−16.0817	+	5.22525i	−0.569642	+	0.185088i	0.0100131	+	0.999950i	$0.496813\pi$
$798$	4.42310	+	38.3492i	0.156576	+	1.35755i
$799$	−0.260165	+	0.358087i	−0.00920398	+	0.0126682i
$800$	−4.03868	+	2.93427i	−0.142789	+	0.103742i
$801$	−4.92476	−	1.60015i	−0.174008	−	0.0565386i
$802$		−	21.5314i		−	0.760300i
$803$	53.8884	−	5.27875i	1.90168	−	0.186283i
$804$	−28.4301			−1.00265
$805$	−0.108028	−	0.0351003i	−0.00380747	−	0.00123712i
$806$	3.68330	+	5.06963i	0.129739	+	0.178570i
$807$	−62.2625	−	45.2363i	−2.19174	−	1.59239i
$808$	2.13590	−	0.693995i	0.0751406	−	0.0244147i
$809$	30.7650	−	9.99615i	1.08164	−	0.351446i	0.286629	−	0.958042i	$-0.407465\pi$
$809$	30.7650	−	9.99615i	1.08164	−	0.351446i	0.795011	+	0.606596i	$0.207465\pi$
$810$	−0.659886	−	0.479435i	−0.0231860	−	0.0168456i
$811$	35.9432	−	26.1142i	1.26214	−	0.916995i	0.263275	−	0.964721i	$-0.415197\pi$
$811$	35.9432	−	26.1142i	1.26214	−	0.916995i	0.998860	+	0.0477259i	$0.0151974\pi$
$812$	9.72102	+	3.15855i	0.341141	+	0.110843i
$813$	−55.0944			−1.93224
$814$	5.42334	−	24.6559i	0.190088	−	0.864188i
$815$	1.24356			0.0435600
$816$	4.01642	−	12.3613i	0.140603	−	0.432731i
$817$	11.1455	+	24.3671i	0.389930	+	0.852496i
$818$	−12.9119	−	9.38101i	−0.451452	−	0.327999i
$819$	−9.73790	+	3.16403i	−0.340270	+	0.110560i
$820$	−0.0119358	−	0.0367346i	−0.000416816	−	0.00128283i
$821$	8.25304	−	11.3593i	0.288033	−	0.396444i	−0.640341	−	0.768091i	$-0.721207\pi$
$821$	8.25304	−	11.3593i	0.288033	−	0.396444i	0.928374	+	0.371647i	$0.121207\pi$
$822$	−15.0808	−	20.7570i	−0.526004	−	0.723983i
$823$	11.4773	−	35.3236i	0.400075	−	1.23130i	−0.524864	−	0.851186i	$-0.675884\pi$
$823$	11.4773	−	35.3236i	0.400075	−	1.23130i	0.924939	−	0.380117i	$-0.124116\pi$
$824$			0.785899i			0.0273781i
$825$	−16.1575	−	36.9925i	−0.562532	−	1.28791i
$826$	22.9979			0.800198
$827$	14.3406	−	44.1359i	0.498672	−	1.53475i	−0.312483	−	0.949923i	$-0.601161\pi$
$827$	14.3406	−	44.1359i	0.498672	−	1.53475i	0.811155	−	0.584831i	$-0.198839\pi$
$828$	0.836841	−	0.608001i	0.0290822	−	0.0211295i
$829$	−29.0517	+	39.9862i	−1.00901	+	1.38878i	−0.0893760	+	0.995998i	$0.528487\pi$
$829$	−29.0517	+	39.9862i	−1.00901	+	1.38878i	−0.919632	+	0.392782i	$0.871513\pi$
$830$	1.32618	−	0.430903i	0.0460325	−	0.0149569i
$831$	20.1171	+	61.9141i	0.697855	+	2.14778i
$832$	−0.774524	−	0.562725i	−0.0268518	−	0.0195090i
$833$	−19.4108	−	26.7166i	−0.672543	−	0.925676i
$834$	14.7525	−	45.4036i	0.510838	−	1.57220i
$835$	−1.18037			−0.0408483
$836$	−7.26639	−	12.4980i	−0.251313	−	0.432252i
$837$	−0.888844			−0.0307229
$838$	5.98374	−	18.4161i	0.206705	−	0.636172i
$839$	−9.44622	−	13.0016i	−0.326120	−	0.448865i	0.614203	−	0.789148i	$-0.289477\pi$
$839$	−9.44622	−	13.0016i	−0.326120	−	0.448865i	−0.940323	+	0.340282i	$0.889477\pi$
$840$	0.637725	+	0.463335i	0.0220036	+	0.0159866i
$841$	−6.51471	−	20.0502i	−0.224645	−	0.691387i
$842$	7.57202	−	2.46030i	0.260949	−	0.0847875i
$843$	−20.0970	+	27.6612i	−0.692178	+	0.952701i
$844$	−6.82229	+	4.95668i	−0.234833	+	0.170616i
$845$	−0.332353	+	1.02288i	−0.0114333	+	0.0351881i
$846$	0.244459			0.00840469
$847$	−29.3125	−	27.1538i	−1.00719	−	0.933016i
$848$			3.11380i			0.106928i
$849$	−4.98878	+	15.3539i	−0.171215	+	0.526944i
$850$	15.6425	+	21.5301i	0.536533	+	0.738475i
$851$	−1.57183	+	2.16344i	−0.0538816	+	0.0741617i
$852$	−5.31990	−	16.3730i	−0.182257	−	0.560928i
$853$	−1.30802	+	0.425001i	−0.0447857	+	0.0145517i	−0.331324	−	0.943517i	$-0.607495\pi$
$853$	−1.30802	+	0.425001i	−0.0447857	+	0.0145517i	0.286538	+	0.958069i	$0.407495\pi$
$854$	−24.8634	−	18.0643i	−0.850807	−	0.618148i
$855$	−1.03881	+	0.475148i	−0.0355264	+	0.0162497i
$856$	3.19276	−	9.82629i	0.109126	−	0.335856i
$857$	−15.7551			−0.538184			−0.269092	−	0.963115i	$-0.586723\pi$
$857$	−15.7551			−0.538184			−0.269092	+	0.963115i	$0.586723\pi$
$858$	5.78954	−	5.13924i	0.197652	−	0.175451i
$859$	48.1404			1.64253			0.821265	−	0.570547i	$-0.193269\pi$
$859$	48.1404			1.64253			0.821265	+	0.570547i	$0.193269\pi$
$860$	0.520369	+	0.169078i	0.0177444	+	0.00576551i
$861$	3.10921	−	2.25897i	0.105962	−	0.0769856i
$862$	3.62720	+	2.63532i	0.123543	+	0.0897593i
$863$	−3.51031	+	1.14057i	−0.119492	+	0.0388254i	−0.368153	−	0.929765i	$-0.620010\pi$
$863$	−3.51031	+	1.14057i	−0.119492	+	0.0388254i	0.248661	+	0.968591i	$0.420010\pi$
$864$	0.129149	−	0.0419630i	0.00439374	−	0.00142761i
$865$	−0.415794	−	0.302092i	−0.0141374	−	0.0102714i
$866$	−0.310467	−	0.427321i	−0.0105501	−	0.0145210i
$867$	−26.4785	−	8.60340i	−0.899258	−	0.292187i
$868$	23.7761			0.807012
$869$	13.7973	−	6.02638i	0.468043	−	0.204431i
$870$			0.610637i			0.0207025i
$871$	10.6172	+	3.44974i	0.359751	+	0.116890i
$872$	12.3539	−	8.97563i	0.418356	−	0.303953i
$873$	−12.4608	+	17.1509i	−0.421736	+	0.580469i
$874$	0.175461	+	1.52128i	0.00593505	+	0.0514582i
$875$	−3.07247	+	0.998306i	−0.103868	+	0.0337489i
$876$	32.2018	+	23.3960i	1.08800	+	0.790477i
$877$	29.0038	−	21.0725i	0.979388	−	0.711567i	0.0218163	−	0.999762i	$-0.493055\pi$
$877$	29.0038	−	21.0725i	0.979388	−	0.711567i	0.957572	+	0.288195i	$0.0930551\pi$
$878$	−3.80849	+	11.7213i	−0.128530	+	0.395576i
$879$		−	60.2086i		−	2.03079i
$880$	−0.288312	−	0.0634176i	−0.00971900	−	0.00213781i
$881$	−29.8401			−1.00534			−0.502670	−	0.864478i	$-0.667649\pi$
$881$	−29.8401			−1.00534			−0.502670	+	0.864478i	$0.667649\pi$
$882$	−5.63615	+	17.3463i	−0.189779	+	0.584080i
$883$	−18.6732	+	13.5669i	−0.628404	+	0.456562i	−0.855847	−	0.517229i	$-0.826963\pi$
$883$	−18.6732	+	13.5669i	−0.628404	+	0.456562i	0.227443	+	0.973791i	$0.426963\pi$
$884$	−2.99987	+	4.12896i	−0.100896	+	0.138872i
$885$	0.424568	+	1.30669i	0.0142717	+	0.0439238i
$886$	−7.54285	−	23.2145i	−0.253407	−	0.779906i
$887$	13.5694	+	9.85872i	0.455615	+	0.331023i	0.791809	−	0.610769i	$-0.209140\pi$
$887$	13.5694	+	9.85872i	0.455615	+	0.331023i	−0.336194	+	0.941793i	$0.609140\pi$
$888$	15.0138	−	10.9082i	0.503832	−	0.366055i
$889$	36.5011	+	11.8599i	1.22421	+	0.397770i
$890$		−	0.156539i		−	0.00524720i
$891$	2.96308	+	30.2487i	0.0992668	+	1.01337i
$892$		−	15.9905i		−	0.535403i
$893$	−0.177777	+	0.315237i	−0.00594909	+	0.0105490i
$894$	−41.7347	+	30.3220i	−1.39582	+	1.01412i
$895$	0.474800	−	0.653506i	0.0158708	−	0.0218443i
$896$	−3.45466	+	1.12249i	−0.115412	+	0.0374997i
$897$	−0.779896	+	0.253404i	−0.0260400	+	0.00846090i
$898$	−13.6535	+	18.7925i	−0.455625	+	0.627114i
$899$	10.8259	+	14.9006i	0.361066	+	0.496964i
$900$	4.54199	−	13.9788i	0.151400	−	0.465960i
$901$	16.5996			0.553012
$902$	−0.728429	+	1.24131i	−0.0242540	+	0.0413312i
$903$			54.4412i			1.81169i
$904$	−17.3751	−	5.64553i	−0.577889	−	0.187767i
$905$	−1.05889	−	1.45744i	−0.0351987	−	0.0484469i
$906$	−7.41257	+	10.2025i	−0.246266	+	0.338956i
$907$	7.47158	−	2.42766i	0.248090	−	0.0806092i	−0.182332	−	0.983237i	$-0.558365\pi$
$907$	7.47158	−	2.42766i	0.248090	−	0.0806092i	0.430422	+	0.902628i	$0.358365\pi$
$908$	4.00709	+	12.3325i	0.132980	+	0.409270i
$909$	−3.88665	+	5.34951i	−0.128912	+	0.177432i
$910$	−0.181937	−	0.250415i	−0.00603116	−	0.00830118i
$911$	−2.35875	−	0.766406i	−0.0781490	−	0.0253922i	0.269682	−	0.962950i	$-0.413082\pi$
$911$	−2.35875	−	0.766406i	−0.0781490	−	0.0253922i	−0.347831	+	0.937557i	$0.613082\pi$
$912$	2.10435	−	10.4170i	0.0696821	−	0.344941i
$913$	−44.8136	−	26.2976i	−1.48311	−	0.870322i
$914$			10.1121i			0.334478i
$915$	0.567365	−	1.74617i	0.0187565	−	0.0577266i
$916$	−6.80764	+	4.94604i	−0.224931	+	0.163422i
$917$	4.21982	+	3.06588i	0.139351	+	0.101244i
$918$	−0.223704	−	0.688489i	−0.00738332	−	0.0227235i
$919$	4.29086	−	1.39418i	0.141542	−	0.0459899i	−0.237389	−	0.971415i	$-0.576292\pi$
$919$	4.29086	−	1.39418i	0.141542	−	0.0459899i	0.378931	+	0.925425i	$0.376292\pi$
$920$	0.0252980	+	0.0183801i	0.000834052	+	0.000605974i
$921$	−8.96317	−	12.3367i	−0.295346	−	0.406510i
$922$	29.2076	+	9.49014i	0.961902	+	0.312541i
$923$			6.76002i			0.222509i
$924$	−2.86357	−	29.2329i	−0.0942046	−	0.961692i
$925$			37.9984i			1.24938i
$926$	3.78599	−	11.6521i	0.124415	−	0.382911i
$927$	−1.36009	−	1.87200i	−0.0446712	−	0.0614847i
$928$	−2.27648	−	1.65396i	−0.0747291	−	0.0542939i
$929$	8.09222	+	24.9053i	0.265497	+	0.817117i	0.991578	+	0.129508i	$0.0413396\pi$
$929$	8.09222	+	24.9053i	0.265497	+	0.817117i	−0.726081	+	0.687609i	$0.758660\pi$
$930$	0.438935	+	1.35090i	0.0143932	+	0.0442979i
$931$	−18.2697	−	19.8826i	−0.598767	−	0.651627i
$932$	6.54222	+	9.00459i	0.214298	+	0.294955i
$933$	1.15773	+	0.376168i	0.0379023	+	0.0123152i
$934$	18.6786			0.611182
$935$	−0.338077	+	1.53698i	−0.0110563	+	0.0502647i
$936$	2.81877			0.0921344
$937$	−34.8468	−	11.3224i	−1.13839	−	0.369887i	−0.321634	−	0.946864i	$-0.604232\pi$
$937$	−34.8468	−	11.3224i	−1.13839	−	0.369887i	−0.816760	+	0.576977i	$0.804232\pi$
$938$	34.2676	−	24.8969i	1.11888	−	0.812912i
$939$	23.4083	−	32.2188i	0.763901	−	1.05142i
$940$	0.00228367	+	0.00702841i	7.44851e−5	+	0.000229241i
$941$	−15.8437	−	48.7619i	−0.516490	−	1.58959i	−0.780555	−	0.625087i	$-0.785064\pi$
$941$	−15.8437	−	48.7619i	−0.516490	−	1.58959i	0.264065	−	0.964505i	$-0.414936\pi$
$942$	−23.8611	+	32.8420i	−0.777437	+	1.07005i
$943$	0.123340	−	0.0896116i	0.00401650	−	0.00291816i
$944$	−6.02136	−	1.95646i	−0.195979	−	0.0636773i
$945$	0.0439046			0.00142822
$946$	−8.16058	−	18.6836i	−0.265323	−	0.607455i
$947$	−18.3979			−0.597851			−0.298925	−	0.954277i	$-0.596628\pi$
$947$	−18.3979			−0.597851			−0.298925	+	0.954277i	$0.596628\pi$
$948$	10.5262	+	3.42016i	0.341874	+	0.111082i
$949$	−9.18688	−	12.6447i	−0.298219	−	0.410463i
$950$	14.7230	+	16.0228i	0.477677	+	0.519847i
$951$	20.4675	+	62.9925i	0.663704	+	2.04267i
$952$	5.98395	+	18.4167i	0.193941	+	0.596888i
$953$	−23.8656	−	17.3394i	−0.773082	−	0.561677i	0.129813	−	0.991539i	$-0.458562\pi$
$953$	−23.8656	−	17.3394i	−0.773082	−	0.561677i	−0.902895	+	0.429861i	$0.858562\pi$
$954$	−5.38879	−	7.41704i	−0.174469	−	0.240135i
$955$	−0.154132	+	0.474371i	−0.00498761	+	0.0153503i
$956$		−	8.34646i		−	0.269944i
$957$	17.0166	−	15.1052i	0.550069	−	0.488283i
$958$		−	7.07351i		−	0.228535i
$959$	36.3548	+	11.8124i	1.17396	+	0.381442i
$960$	−0.127554	−	0.175564i	−0.00411680	−	0.00566629i
$961$	9.58134	+	6.96125i	0.309076	+	0.224557i
$962$	−6.93055	+	2.25187i	−0.223450	+	0.0726033i
$963$	9.40044	+	28.9316i	0.302925	+	0.932307i
$964$	−0.696503	−	0.506039i	−0.0224329	−	0.0162984i
$965$	−0.307079	+	0.223106i	−0.00988522	+	0.00718203i
$966$	−0.961468	+	2.95909i	−0.0309347	+	0.0952073i
$967$		−	10.3570i		−	0.333059i	−0.986037	−	0.166529i	$-0.946744\pi$
$967$		−	10.3570i		−	0.333059i	0.986037	−	0.166529i	$-0.0532560\pi$
$968$	5.36467	+	9.60314i	0.172427	+	0.308657i
$969$	−55.5326	−	11.2182i	−1.78396	−	0.360382i
$970$	−0.609508	−	0.198041i	−0.0195701	−	0.00635872i
$971$	−35.5569	−	48.9399i	−1.14108	−	1.57056i	−0.765079	−	0.643937i	$-0.777300\pi$
$971$	−35.5569	−	48.9399i	−1.14108	−	1.57056i	−0.375998	−	0.926620i	$-0.622700\pi$
$972$	−12.8932	+	17.7460i	−0.413551	+	0.569204i
$973$	21.9794	+	67.6455i	0.704626	+	2.16862i
$974$	−35.1098	+	11.4079i	−1.12499	+	0.365532i
$975$	−6.84901	+	9.42685i	−0.219344	+	0.301901i
$976$	4.97304	+	6.84480i	0.159183	+	0.219097i
$977$	−31.4172	−	10.2081i	−1.00512	−	0.326585i	−0.240213	−	0.970720i	$-0.577217\pi$
$977$	−31.4172	−	10.2081i	−1.00512	−	0.326585i	−0.764912	+	0.644135i	$0.777217\pi$
$978$		−	34.0636i		−	1.08923i
$979$	−4.36227	+	3.87228i	−0.139419	+	0.123759i
$980$	−0.551371			−0.0176129
$981$	−13.8935	+	42.7597i	−0.443585	+	1.36521i
$982$	−0.222565	−	0.306335i	−0.00710235	−	0.00977554i
$983$	10.5647	−	14.5411i	0.336962	−	0.463788i	−0.606589	−	0.795015i	$-0.707463\pi$
$983$	10.5647	−	14.5411i	0.336962	−	0.463788i	0.943551	+	0.331227i	$0.107463\pi$
$984$	−1.00624	+	0.326946i	−0.0320776	+	0.0104226i
$985$	−1.38032	+	0.448492i	−0.0439806	+	0.0142902i
$986$	−8.81721	+	12.1359i	−0.280797	+	0.386484i
$987$	−0.594883	+	0.432208i	−0.0189353	+	0.0137573i
$988$	−2.04988	+	3.63488i	−0.0652155	+	0.115641i
$989$			2.15964i			0.0686725i
$990$	0.796508	−	0.347898i	0.0253147	−	0.0110569i
$991$			6.65903i			0.211531i	0.994391	+	0.105766i	$0.0337293\pi$
$991$			6.65903i			0.211531i	−0.994391	+	0.105766i	$0.966271\pi$
$992$	−6.22511	−	2.02266i	−0.197648	−	0.0642196i
$993$	−51.7597	+	37.6056i	−1.64254	+	1.19338i
$994$	20.7504	+	15.0761i	0.658164	+	0.478184i
$995$	0.292876	+	0.901378i	0.00928478	+	0.0285756i
$996$	−11.8033	−	36.3268i	−0.374002	−	1.15106i
$997$	9.02045	−	12.4156i	0.285680	−	0.393205i	−0.641925	−	0.766768i	$-0.721864\pi$
$997$	9.02045	−	12.4156i	0.285680	−	0.393205i	0.927605	+	0.373562i	$0.121864\pi$
$998$	24.1162	−	17.5215i	0.763387	−	0.554633i
$999$	0.319412	−	0.983048i	0.0101057	−	0.0311023i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.m.b.189.2	yes	40
11.6	odd	10		418.2.m.a.303.9	yes	40
19.18	odd	2		418.2.m.a.189.9	✓	40
209.94	even	10	inner	418.2.m.b.303.2	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.m.a.189.9	✓	40	19.18	odd	2
418.2.m.a.303.9	yes	40	11.6	odd	10
418.2.m.b.189.2	yes	40	1.1	even	1	trivial
418.2.m.b.303.2	yes	40	209.94	even	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.m (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 + 0.951057i) q^{2} +(-1.43308 - 1.97246i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.0275048 + 0.0846511i) q^{5} +(2.31877 - 0.753413i) q^{6} +(-2.13510 + 2.93871i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-0.909840 + 2.80020i) q^{9} +O(q^{10})\)	\(q+(-0.309017 + 0.951057i) q^{2} +(-1.43308 - 1.97246i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.0275048 + 0.0846511i) q^{5} +(2.31877 - 0.753413i) q^{6} +(-2.13510 + 2.93871i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-0.909840 + 2.80020i) q^{9} -0.0890075 q^{10} +(2.20176 + 2.48037i) q^{11} +2.43809i q^{12} +(0.295842 - 0.910508i) q^{13} +(-2.13510 - 2.93871i) q^{14} +(0.127554 - 0.175564i) q^{15} +(0.309017 + 0.951057i) q^{16} +(5.07005 - 1.64736i) q^{17} +(-2.38199 - 1.73062i) q^{18} +(3.96392 - 1.81309i) q^{19} +(0.0275048 - 0.0846511i) q^{20} +8.85624 q^{21} +(-3.03935 + 1.32753i) q^{22} +0.351320 q^{23} +(-2.31877 - 0.753413i) q^{24} +(4.03868 - 2.93427i) q^{25} +(0.774524 + 0.562725i) q^{26} +(-0.129149 + 0.0419630i) q^{27} +(3.45466 - 1.12249i) q^{28} +(2.27648 + 1.65396i) q^{29} +(0.127554 + 0.175564i) q^{30} +(6.22511 + 2.02266i) q^{31} -1.00000 q^{32} +(1.73714 - 7.89745i) q^{33} +5.33097i q^{34} +(-0.307491 - 0.0999098i) q^{35} +(2.38199 - 1.73062i) q^{36} +(-4.47407 + 6.15803i) q^{37} +(0.499433 + 4.33019i) q^{38} +(-2.21990 + 0.721290i) q^{39} +(0.0720086 + 0.0523173i) q^{40} +(0.351075 - 0.255071i) q^{41} +(-2.73673 + 8.42279i) q^{42} +6.14721i q^{43} +(-0.323339 - 3.30083i) q^{44} -0.262065 q^{45} +(-0.108564 + 0.334125i) q^{46} +(-0.0671710 + 0.0488026i) q^{47} +(1.43308 - 1.97246i) q^{48} +(-1.91426 - 5.89147i) q^{49} +(1.54264 + 4.74775i) q^{50} +(-10.5151 - 7.63968i) q^{51} +(-0.774524 + 0.562725i) q^{52} +(2.96140 + 0.962216i) q^{53} -0.135795i q^{54} +(-0.149407 + 0.254604i) q^{55} +3.63245i q^{56} +(-9.25685 - 5.22038i) q^{57} +(-2.27648 + 1.65396i) q^{58} +(-3.72140 + 5.12207i) q^{59} +(-0.206387 + 0.0670594i) q^{60} +(8.04655 - 2.61448i) q^{61} +(-3.84733 + 5.29540i) q^{62} +(-6.28637 - 8.65245i) q^{63} +(0.309017 - 0.951057i) q^{64} +0.0852126 q^{65} +(6.97412 + 4.09256i) q^{66} +11.6608i q^{67} +(-5.07005 - 1.64736i) q^{68} +(-0.503468 - 0.692964i) q^{69} +(0.190040 - 0.261567i) q^{70} +(-6.71548 + 2.18199i) q^{71} +(0.909840 + 2.80020i) q^{72} +(9.59602 - 13.2078i) q^{73} +(-4.47407 - 6.15803i) q^{74} +(-11.5755 - 3.76109i) q^{75} +(-4.27259 - 0.863114i) q^{76} +(-11.9901 + 1.17451i) q^{77} -2.33414i q^{78} +(1.40280 - 4.31738i) q^{79} +(-0.0720086 + 0.0523173i) q^{80} +(7.41382 + 5.38646i) q^{81} +(0.134099 + 0.412714i) q^{82} +(-14.8997 + 4.84120i) q^{83} +(-7.16485 - 5.20557i) q^{84} +(0.278902 + 0.383875i) q^{85} +(-5.84635 - 1.89959i) q^{86} -6.86052i q^{87} +(3.23919 + 0.712497i) q^{88} +1.75872i q^{89} +(0.0809825 - 0.249239i) q^{90} +(2.04407 + 2.81342i) q^{91} +(-0.284224 - 0.206501i) q^{92} +(-4.93144 - 15.1774i) q^{93} +(-0.0256570 - 0.0789643i) q^{94} +(0.262507 + 0.285682i) q^{95} +(1.43308 + 1.97246i) q^{96} +(6.84783 + 2.22499i) q^{97} +6.19466 q^{98} +(-8.94878 + 3.90864i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 10 q^{2} - 10 q^{4} + 2 q^{5} + 5 q^{6} - 5 q^{7} + 10 q^{8} + 8 q^{9}+O(q^{10}) \) 40 * q + 10 * q^2 - 10 * q^4 + 2 * q^5 + 5 * q^6 - 5 * q^7 + 10 * q^8 + 8 * q^9	\( 40 q + 10 q^{2} - 10 q^{4} + 2 q^{5} + 5 q^{6} - 5 q^{7} + 10 q^{8} + 8 q^{9} - 2 q^{10} + 4 q^{11} - 8 q^{13} - 5 q^{14} - 30 q^{15} - 10 q^{16} - 15 q^{17} - 13 q^{18} + 11 q^{19} + 2 q^{20} - 4 q^{22} + 6 q^{23} - 5 q^{24} - 36 q^{25} - 2 q^{26} + 45 q^{27} + 2 q^{29} - 30 q^{30} - 40 q^{32} - 27 q^{33} - 5 q^{35} + 13 q^{36} + 14 q^{38} + 30 q^{39} + 3 q^{40} + 8 q^{41} + 20 q^{42} - 6 q^{44} + 18 q^{45} - q^{46} - 8 q^{47} + 31 q^{49} - 9 q^{50} - 41 q^{51} + 2 q^{52} + 40 q^{53} - 31 q^{55} - 10 q^{57} - 2 q^{58} - 35 q^{59} - 20 q^{60} + 5 q^{61} + 30 q^{62} - 25 q^{63} - 10 q^{64} - 8 q^{65} - 48 q^{66} + 15 q^{68} + 60 q^{69} + 10 q^{70} - 50 q^{71} - 8 q^{72} + 10 q^{73} + 35 q^{75} + 11 q^{76} - 64 q^{77} + 42 q^{79} - 3 q^{80} + 11 q^{81} + 7 q^{82} + 25 q^{83} + 20 q^{84} - 45 q^{85} + 40 q^{86} + 6 q^{88} + 22 q^{90} + 70 q^{91} - 4 q^{92} - 18 q^{93} - 7 q^{94} - 5 q^{95} + 15 q^{97} + 74 q^{98} + 50 q^{99}+O(q^{100}) \) 40 * q + 10 * q^2 - 10 * q^4 + 2 * q^5 + 5 * q^6 - 5 * q^7 + 10 * q^8 + 8 * q^9 - 2 * q^10 + 4 * q^11 - 8 * q^13 - 5 * q^14 - 30 * q^15 - 10 * q^16 - 15 * q^17 - 13 * q^18 + 11 * q^19 + 2 * q^20 - 4 * q^22 + 6 * q^23 - 5 * q^24 - 36 * q^25 - 2 * q^26 + 45 * q^27 + 2 * q^29 - 30 * q^30 - 40 * q^32 - 27 * q^33 - 5 * q^35 + 13 * q^36 + 14 * q^38 + 30 * q^39 + 3 * q^40 + 8 * q^41 + 20 * q^42 - 6 * q^44 + 18 * q^45 - q^46 - 8 * q^47 + 31 * q^49 - 9 * q^50 - 41 * q^51 + 2 * q^52 + 40 * q^53 - 31 * q^55 - 10 * q^57 - 2 * q^58 - 35 * q^59 - 20 * q^60 + 5 * q^61 + 30 * q^62 - 25 * q^63 - 10 * q^64 - 8 * q^65 - 48 * q^66 + 15 * q^68 + 60 * q^69 + 10 * q^70 - 50 * q^71 - 8 * q^72 + 10 * q^73 + 35 * q^75 + 11 * q^76 - 64 * q^77 + 42 * q^79 - 3 * q^80 + 11 * q^81 + 7 * q^82 + 25 * q^83 + 20 * q^84 - 45 * q^85 + 40 * q^86 + 6 * q^88 + 22 * q^90 + 70 * q^91 - 4 * q^92 - 18 * q^93 - 7 * q^94 - 5 * q^95 + 15 * q^97 + 74 * q^98 + 50 * q^99

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