LMFDB - Embedded newform 350.2.m.a.309.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,2,Mod(29,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("350.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	350.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:	$2.79476407074$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			309.1
Character	$\chi$	$=$	350.309
Dual form			350.2.m.a.239.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.587785 + 0.809017i) q^{2} +(-2.21568 + 0.719918i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(0.562587 - 2.16414i) q^{5} +(0.719918 - 2.21568i) q^{6} +1.00000i q^{7} +(0.951057 + 0.309017i) q^{8} +(1.96390 - 1.42686i) q^{9} +O(q^{10})$	\(q+(-0.587785 + 0.809017i) q^{2} +(-2.21568 + 0.719918i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(0.562587 - 2.16414i) q^{5} +(0.719918 - 2.21568i) q^{6} +1.00000i q^{7} +(0.951057 + 0.309017i) q^{8} +(1.96390 - 1.42686i) q^{9} +(1.42014 + 1.72719i) q^{10} +(-1.43648 - 1.04366i) q^{11} +(1.36936 + 1.88477i) q^{12} +(3.87494 + 5.33340i) q^{13} +(-0.809017 - 0.587785i) q^{14} +(0.311490 + 5.20005i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(1.97073 + 0.640328i) q^{17} +2.42751i q^{18} +(0.115421 - 0.355229i) q^{19} +(-2.23207 + 0.133704i) q^{20} +(-0.719918 - 2.21568i) q^{21} +(1.68868 - 0.548687i) q^{22} +(-5.16078 + 7.10320i) q^{23} -2.32970 q^{24} +(-4.36699 - 2.43503i) q^{25} -6.59244 q^{26} +(0.783941 - 1.07900i) q^{27} +(0.951057 - 0.309017i) q^{28} +(1.90055 + 5.84928i) q^{29} +(-4.39002 - 2.80451i) q^{30} +(-2.40570 + 7.40398i) q^{31} -1.00000i q^{32} +(3.93413 + 1.27828i) q^{33} +(-1.67640 + 1.21798i) q^{34} +(2.16414 + 0.562587i) q^{35} +(-1.96390 - 1.42686i) q^{36} +(0.895397 + 1.23241i) q^{37} +(0.219544 + 0.302176i) q^{38} +(-12.4252 - 9.02746i) q^{39} +(1.20381 - 1.88437i) q^{40} +(5.05366 - 3.67170i) q^{41} +(2.21568 + 0.719918i) q^{42} +8.64796i q^{43} +(-0.548687 + 1.68868i) q^{44} +(-1.98305 - 5.05288i) q^{45} +(-2.71318 - 8.35031i) q^{46} +(5.37100 - 1.74514i) q^{47} +(1.36936 - 1.88477i) q^{48} -1.00000 q^{49} +(4.53684 - 2.10169i) q^{50} -4.82748 q^{51} +(3.87494 - 5.33340i) q^{52} +(-3.26837 + 1.06196i) q^{53} +(0.412142 + 1.26844i) q^{54} +(-3.06678 + 2.52159i) q^{55} +(-0.309017 + 0.951057i) q^{56} +0.870168i q^{57} +(-5.84928 - 1.90055i) q^{58} +(11.4830 - 8.34288i) q^{59} +(4.84929 - 1.90315i) q^{60} +(10.3944 + 7.55197i) q^{61} +(-4.57591 - 6.29820i) q^{62} +(1.42686 + 1.96390i) q^{63} +(0.809017 + 0.587785i) q^{64} +(13.7222 - 5.38541i) q^{65} +(-3.34657 + 2.43143i) q^{66} +(-3.26589 - 1.06115i) q^{67} -2.07215i q^{68} +(6.32091 - 19.4537i) q^{69} +(-1.72719 + 1.42014i) q^{70} +(-2.00360 - 6.16645i) q^{71} +(2.30870 - 0.750143i) q^{72} +(-2.12747 + 2.92821i) q^{73} -1.52334 q^{74} +(11.4289 + 2.25138i) q^{75} -0.373510 q^{76} +(1.04366 - 1.43648i) q^{77} +(14.6067 - 4.74602i) q^{78} +(2.04152 + 6.28316i) q^{79} +(0.816906 + 2.08151i) q^{80} +(-3.21060 + 9.88121i) q^{81} +6.24667i q^{82} +(6.66422 + 2.16533i) q^{83} +(-1.88477 + 1.36936i) q^{84} +(2.49447 - 3.90469i) q^{85} +(-6.99635 - 5.08314i) q^{86} +(-8.42200 - 11.5919i) q^{87} +(-1.04366 - 1.43648i) q^{88} +(-6.79610 - 4.93765i) q^{89} +(5.25348 + 1.36569i) q^{90} +(-5.33340 + 3.87494i) q^{91} +(8.35031 + 2.71318i) q^{92} -18.1368i q^{93} +(-1.74514 + 5.37100i) q^{94} +(-0.703831 - 0.449635i) q^{95} +(0.719918 + 2.21568i) q^{96} +(-8.40476 + 2.73087i) q^{97} +(0.587785 - 0.809017i) q^{98} -4.31027 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{4} + 10 q^{5} + 2 q^{6} + 8 q^{9}+O(q^{10}) $ 24 * q + 6 * q^4 + 10 * q^5 + 2 * q^6 + 8 * q^9	$ 24 q + 6 q^{4} + 10 q^{5} + 2 q^{6} + 8 q^{9} + 2 q^{11} + 10 q^{12} - 6 q^{14} + 20 q^{15} - 6 q^{16} - 22 q^{19} - 2 q^{21} - 10 q^{22} - 10 q^{23} + 8 q^{24} - 10 q^{25} - 4 q^{26} - 30 q^{27} - 12 q^{29} - 10 q^{30} + 20 q^{33} - 8 q^{36} + 10 q^{37} - 10 q^{38} - 48 q^{39} + 10 q^{40} + 42 q^{41} - 2 q^{44} - 40 q^{45} + 10 q^{46} + 30 q^{47} + 10 q^{48} - 24 q^{49} + 20 q^{50} - 52 q^{51} + 10 q^{53} + 4 q^{54} + 10 q^{55} + 6 q^{56} - 20 q^{58} - 10 q^{60} + 46 q^{61} - 20 q^{63} + 6 q^{64} + 10 q^{65} - 10 q^{66} + 10 q^{67} + 32 q^{71} + 30 q^{73} - 28 q^{74} - 10 q^{75} - 48 q^{76} + 20 q^{77} - 20 q^{78} - 44 q^{79} + 76 q^{81} + 50 q^{83} + 2 q^{84} - 50 q^{85} - 6 q^{86} - 20 q^{87} - 20 q^{88} - 4 q^{89} + 50 q^{90} - 6 q^{91} + 30 q^{92} - 6 q^{94} - 60 q^{95} + 2 q^{96} + 30 q^{97} + 56 q^{99}+O(q^{100}) $ 24 * q + 6 * q^4 + 10 * q^5 + 2 * q^6 + 8 * q^9 + 2 * q^11 + 10 * q^12 - 6 * q^14 + 20 * q^15 - 6 * q^16 - 22 * q^19 - 2 * q^21 - 10 * q^22 - 10 * q^23 + 8 * q^24 - 10 * q^25 - 4 * q^26 - 30 * q^27 - 12 * q^29 - 10 * q^30 + 20 * q^33 - 8 * q^36 + 10 * q^37 - 10 * q^38 - 48 * q^39 + 10 * q^40 + 42 * q^41 - 2 * q^44 - 40 * q^45 + 10 * q^46 + 30 * q^47 + 10 * q^48 - 24 * q^49 + 20 * q^50 - 52 * q^51 + 10 * q^53 + 4 * q^54 + 10 * q^55 + 6 * q^56 - 20 * q^58 - 10 * q^60 + 46 * q^61 - 20 * q^63 + 6 * q^64 + 10 * q^65 - 10 * q^66 + 10 * q^67 + 32 * q^71 + 30 * q^73 - 28 * q^74 - 10 * q^75 - 48 * q^76 + 20 * q^77 - 20 * q^78 - 44 * q^79 + 76 * q^81 + 50 * q^83 + 2 * q^84 - 50 * q^85 - 6 * q^86 - 20 * q^87 - 20 * q^88 - 4 * q^89 + 50 * q^90 - 6 * q^91 + 30 * q^92 - 6 * q^94 - 60 * q^95 + 2 * q^96 + 30 * q^97 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{7}{10}\right)$

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 $

$2$	−0.587785	+	0.809017i	−0.415627	+	0.572061i
$2$	−0.587785	+	0.809017i	−0.415627	+	0.572061i
$3$	−2.21568	+	0.719918i	−1.27922	+	0.415645i	−0.868306	−	0.496028i	$-0.834791\pi$
$3$	−2.21568	+	0.719918i	−1.27922	+	0.415645i	−0.410916	+	0.911673i	$0.634791\pi$
$4$	−0.309017	−	0.951057i	−0.154508	−	0.475528i
$5$	0.562587	−	2.16414i	0.251597	−	0.967832i
$5$	0.562587	−	2.16414i	0.251597	−	0.967832i
$6$	0.719918	−	2.21568i	0.293905	−	0.904547i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	0.951057	+	0.309017i	0.336249	+	0.109254i
$9$	1.96390	−	1.42686i	0.654634	−	0.475619i
$10$	1.42014	+	1.72719i	0.449089	+	0.546186i
$11$	−1.43648	−	1.04366i	−0.433115	−	0.314677i	0.349778	−	0.936833i	$-0.386257\pi$
$11$	−1.43648	−	1.04366i	−0.433115	−	0.314677i	−0.782893	+	0.622156i	$0.786257\pi$
$12$	1.36936	+	1.88477i	0.395302	+	0.544086i
$13$	3.87494	+	5.33340i	1.07472	+	1.47922i	0.865209	+	0.501412i	$0.167186\pi$
$13$	3.87494	+	5.33340i	1.07472	+	1.47922i	0.209507	+	0.977807i	$0.432814\pi$
$14$	−0.809017	−	0.587785i	−0.216219	−	0.157092i
$15$	0.311490	+	5.20005i	0.0804263	+	1.34265i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	1.97073	+	0.640328i	0.477972	+	0.155302i	0.538088	−	0.842889i	$-0.319147\pi$
$17$	1.97073	+	0.640328i	0.477972	+	0.155302i	−0.0601158	+	0.998191i	$0.519147\pi$
$18$			2.42751i			0.572171i
$19$	0.115421	−	0.355229i	0.0264794	−	0.0814952i	−0.936944	−	0.349481i	$-0.886358\pi$
$19$	0.115421	−	0.355229i	0.0264794	−	0.0814952i	0.963423	+	0.267986i	$0.0863580\pi$
$20$	−2.23207	+	0.133704i	−0.499105	+	0.0298970i
$21$	−0.719918	−	2.21568i	−0.157099	−	0.483501i
$22$	1.68868	−	0.548687i	0.360029	−	0.116980i
$23$	−5.16078	+	7.10320i	−1.07610	+	1.48112i	−0.212350	+	0.977194i	$0.568112\pi$
$23$	−5.16078	+	7.10320i	−1.07610	+	1.48112i	−0.863747	+	0.503926i	$0.831888\pi$
$24$	−2.32970			−0.475549
$25$	−4.36699	−	2.43503i	−0.873398	−	0.487006i
$26$	−6.59244			−1.29288
$27$	0.783941	−	1.07900i	0.150870	−	0.207654i
$28$	0.951057	−	0.309017i	0.179733	−	0.0583987i
$29$	1.90055	+	5.84928i	0.352923	+	1.08618i	0.957204	+	0.289413i	$0.0934601\pi$
$29$	1.90055	+	5.84928i	0.352923	+	1.08618i	−0.604282	+	0.796771i	$0.706540\pi$
$30$	−4.39002	−	2.80451i	−0.801504	−	0.512032i
$31$	−2.40570	+	7.40398i	−0.432076	+	1.32979i	0.463977	+	0.885847i	$0.346422\pi$
$31$	−2.40570	+	7.40398i	−0.432076	+	1.32979i	−0.896053	+	0.443947i	$0.853578\pi$
$32$		−	1.00000i		−	0.176777i
$33$	3.93413	+	1.27828i	0.684845	+	0.222520i
$34$	−1.67640	+	1.21798i	−0.287500	+	0.208881i
$35$	2.16414	+	0.562587i	0.365806	+	0.0950946i
$36$	−1.96390	−	1.42686i	−0.327317	−	0.237810i
$37$	0.895397	+	1.23241i	0.147202	+	0.202607i	0.876251	−	0.481856i	$-0.160037\pi$
$37$	0.895397	+	1.23241i	0.147202	+	0.202607i	−0.729048	+	0.684462i	$0.760037\pi$
$38$	0.219544	+	0.302176i	0.0356147	+	0.0490195i
$39$	−12.4252	−	9.02746i	−1.98963	−	1.44555i
$40$	1.20381	−	1.88437i	0.190339	−	0.297945i
$41$	5.05366	−	3.67170i	0.789249	−	0.573423i	−0.118491	−	0.992955i	$-0.537806\pi$
$41$	5.05366	−	3.67170i	0.789249	−	0.573423i	0.907741	+	0.419532i	$0.137806\pi$
$42$	2.21568	+	0.719918i	0.341887	+	0.111086i
$43$			8.64796i			1.31880i	0.751792	+	0.659401i	$0.229190\pi$
$43$			8.64796i			1.31880i	−0.751792	+	0.659401i	$0.770810\pi$
$44$	−0.548687	+	1.68868i	−0.0827177	+	0.254579i
$45$	−1.98305	−	5.05288i	−0.295616	−	0.753240i
$46$	−2.71318	−	8.35031i	−0.400037	−	1.23119i
$47$	5.37100	−	1.74514i	0.783441	−	0.254555i	0.110132	−	0.993917i	$-0.464873\pi$
$47$	5.37100	−	1.74514i	0.783441	−	0.254555i	0.673309	+	0.739362i	$0.264873\pi$
$48$	1.36936	−	1.88477i	0.197651	−	0.272043i
$49$	−1.00000			−0.142857
$50$	4.53684	−	2.10169i	0.641605	−	0.297224i
$51$	−4.82748			−0.675983
$52$	3.87494	−	5.33340i	0.537358	−	0.739609i
$53$	−3.26837	+	1.06196i	−0.448945	+	0.145871i	−0.524759	−	0.851251i	$-0.675844\pi$
$53$	−3.26837	+	1.06196i	−0.448945	+	0.145871i	0.0758140	+	0.997122i	$0.475844\pi$
$54$	0.412142	+	1.26844i	0.0560855	+	0.172613i
$55$	−3.06678	+	2.52159i	−0.413525	+	0.340011i
$56$	−0.309017	+	0.951057i	−0.0412941	+	0.127090i
$57$			0.870168i			0.115257i
$58$	−5.84928	−	1.90055i	−0.768048	−	0.249554i
$59$	11.4830	−	8.34288i	1.49496	−	1.08615i	0.522621	−	0.852565i	$-0.324954\pi$
$59$	11.4830	−	8.34288i	1.49496	−	1.08615i	0.972336	−	0.233585i	$-0.0750457\pi$
$60$	4.84929	−	1.90315i	0.626040	−	0.245695i
$61$	10.3944	+	7.55197i	1.33087	+	0.966930i	0.999727	+	0.0233480i	$0.00743256\pi$
$61$	10.3944	+	7.55197i	1.33087	+	0.966930i	0.331138	+	0.943582i	$0.392567\pi$
$62$	−4.57591	−	6.29820i	−0.581141	−	0.799873i
$63$	1.42686	+	1.96390i	0.179767	+	0.247428i
$64$	0.809017	+	0.587785i	0.101127	+	0.0734732i
$65$	13.7222	−	5.38541i	1.70203	−	0.667978i
$66$	−3.34657	+	2.43143i	−0.411935	+	0.299288i
$67$	−3.26589	−	1.06115i	−0.398992	−	0.129640i	0.102646	−	0.994718i	$-0.467269\pi$
$67$	−3.26589	−	1.06115i	−0.398992	−	0.129640i	−0.501638	+	0.865078i	$0.667269\pi$
$68$		−	2.07215i		−	0.251285i
$69$	6.32091	−	19.4537i	0.760948	−	2.34196i
$70$	−1.72719	+	1.42014i	−0.206439	+	0.169740i
$71$	−2.00360	−	6.16645i	−0.237784	−	0.731823i	−0.996740	−	0.0806814i	$-0.974290\pi$
$71$	−2.00360	−	6.16645i	−0.237784	−	0.731823i	0.758956	−	0.651142i	$-0.225710\pi$
$72$	2.30870	−	0.750143i	0.272083	−	0.0884052i
$73$	−2.12747	+	2.92821i	−0.249002	+	0.342721i	−0.915161	−	0.403088i	$-0.867937\pi$
$73$	−2.12747	+	2.92821i	−0.249002	+	0.342721i	0.666160	+	0.745809i	$0.267937\pi$
$74$	−1.52334			−0.177085
$75$	11.4289	+	2.25138i	1.31969	+	0.259966i
$76$	−0.373510			−0.0428446
$77$	1.04366	−	1.43648i	0.118937	−	0.163702i
$78$	14.6067	−	4.74602i	1.65389	−	0.537381i
$79$	2.04152	+	6.28316i	0.229689	+	0.706911i	0.997782	+	0.0665718i	$0.0212062\pi$
$79$	2.04152	+	6.28316i	0.229689	+	0.706911i	−0.768092	+	0.640339i	$0.778794\pi$
$80$	0.816906	+	2.08151i	0.0913329	+	0.232719i
$81$	−3.21060	+	9.88121i	−0.356733	+	1.09791i
$82$			6.24667i			0.689829i
$83$	6.66422	+	2.16533i	0.731493	+	0.237676i	0.650999	−	0.759079i	$-0.274350\pi$
$83$	6.66422	+	2.16533i	0.731493	+	0.237676i	0.0804938	+	0.996755i	$0.474350\pi$
$84$	−1.88477	+	1.36936i	−0.205645	+	0.149410i
$85$	2.49447	−	3.90469i	0.270563	−	0.423523i
$86$	−6.99635	−	5.08314i	−0.754436	−	0.548130i
$87$	−8.42200	−	11.5919i	−0.902933	−	1.24278i
$88$	−1.04366	−	1.43648i	−0.111255	−	0.153129i
$89$	−6.79610	−	4.93765i	−0.720385	−	0.523390i	0.166122	−	0.986105i	$-0.446875\pi$
$89$	−6.79610	−	4.93765i	−0.720385	−	0.523390i	−0.886507	+	0.462715i	$0.846875\pi$
$90$	5.25348	+	1.36569i	0.553765	+	0.143956i
$91$	−5.33340	+	3.87494i	−0.559092	+	0.406204i
$92$	8.35031	+	2.71318i	0.870580	+	0.282869i
$93$		−	18.1368i		−	1.88069i
$94$	−1.74514	+	5.37100i	−0.179998	+	0.553976i
$95$	−0.703831	−	0.449635i	−0.0722116	−	0.0461315i
$96$	0.719918	+	2.21568i	0.0734763	+	0.226137i
$97$	−8.40476	+	2.73087i	−0.853374	+	0.277278i	−0.702859	−	0.711330i	$-0.748093\pi$
$97$	−8.40476	+	2.73087i	−0.853374	+	0.277278i	−0.150516	+	0.988608i	$0.548093\pi$
$98$	0.587785	−	0.809017i	0.0593753	−	0.0817231i
$99$	−4.31027			−0.433198
$100$	−0.966379	+	4.90572i	−0.0966379	+	0.490572i
$101$	−7.59049			−0.755282			−0.377641	−	0.925952i	$-0.623265\pi$
$101$	−7.59049			−0.755282			−0.377641	+	0.925952i	$0.623265\pi$
$102$	2.83752	−	3.90552i	0.280957	−	0.386704i
$103$	−9.73299	+	3.16244i	−0.959020	+	0.311604i	−0.746375	−	0.665525i	$-0.768208\pi$
$103$	−9.73299	+	3.16244i	−0.959020	+	0.311604i	−0.212644	+	0.977130i	$0.568208\pi$
$104$	2.03718	+	6.26979i	0.199762	+	0.614803i
$105$	−5.20005	+	0.311490i	−0.507473	+	0.0303983i
$106$	1.06196	−	3.26837i	0.103146	−	0.317452i
$107$			6.05743i			0.585594i	0.956175	+	0.292797i	$0.0945859\pi$
$107$			6.05743i			0.585594i	−0.956175	+	0.292797i	$0.905414\pi$
$108$	−1.26844	−	0.412142i	−0.122056	−	0.0396584i
$109$	7.68302	−	5.58204i	0.735900	−	0.534663i	−0.155525	−	0.987832i	$-0.549707\pi$
$109$	7.68302	−	5.58204i	0.735900	−	0.534663i	0.891424	+	0.453169i	$0.149707\pi$
$110$	−0.237403	−	3.96323i	−0.0226354	−	0.377879i
$111$	−2.87114	−	2.08601i	−0.272517	−	0.197995i
$112$	−0.587785	−	0.809017i	−0.0555405	−	0.0764449i
$113$	−9.70360	−	13.3559i	−0.912838	−	1.25641i	−0.966188	−	0.257838i	$-0.916990\pi$
$113$	−9.70360	−	13.3559i	−0.912838	−	1.25641i	0.0533505	−	0.998576i	$-0.483010\pi$
$114$	−0.703981	−	0.511472i	−0.0659338	−	0.0479037i
$115$	12.4689	+	15.1648i	1.16273	+	1.41413i
$116$	4.97569	−	3.61505i	0.461982	−	0.335649i
$117$	15.2200	+	4.94528i	1.40709	+	0.457191i
$118$			14.1937i			1.30664i
$119$	−0.640328	+	1.97073i	−0.0586988	+	0.180656i
$120$	−1.31066	+	5.04180i	−0.119646	+	0.460251i
$121$	−2.42494	−	7.46321i	−0.220450	−	0.678474i
$122$	−12.2193	+	3.97030i	−1.10629	+	0.359454i
$123$	−8.55397	+	11.7735i	−0.771285	+	1.06158i
$124$	7.78501			0.699114
$125$	−7.72656	+	8.08086i	−0.691085	+	0.722774i
$126$	−2.42751			−0.216260
$127$	6.08586	−	8.37646i	0.540033	−	0.743291i	−0.448585	−	0.893740i	$-0.648072\pi$
$127$	6.08586	−	8.37646i	0.540033	−	0.743291i	0.988618	+	0.150449i	$0.0480720\pi$
$128$	−0.951057	+	0.309017i	−0.0840623	+	0.0273135i
$129$	−6.22582	−	19.1611i	−0.548153	−	1.68704i
$130$	−3.70882	+	14.2670i	−0.325285	+	1.25130i
$131$	−3.22556	+	9.92725i	−0.281819	+	0.867348i	0.705516	+	0.708694i	$0.250715\pi$
$131$	−3.22556	+	9.92725i	−0.281819	+	0.867348i	−0.987334	+	0.158654i	$0.949285\pi$
$132$		−	4.13659i		−	0.360044i
$133$	0.355229	+	0.115421i	0.0308023	+	0.0100083i
$134$	2.77813	−	2.01843i	0.239994	−	0.174366i
$135$	−1.89408	−	2.30359i	−0.163016	−	0.198261i
$136$	1.67640	+	1.21798i	0.143750	+	0.104441i
$137$	−4.64926	−	6.39916i	−0.397213	−	0.546717i	0.562828	−	0.826574i	$-0.309713\pi$
$137$	−4.64926	−	6.39916i	−0.397213	−	0.546717i	−0.960042	+	0.279856i	$0.909713\pi$
$138$	12.0231	+	16.5483i	1.02347	+	1.40869i
$139$	0.875609	+	0.636167i	0.0742682	+	0.0539590i	0.624300	−	0.781185i	$-0.285384\pi$
$139$	0.875609	+	0.636167i	0.0742682	+	0.0539590i	−0.550032	+	0.835144i	$0.685384\pi$
$140$	−0.133704	−	2.23207i	−0.0113000	−	0.188644i
$141$	−10.6440	+	7.73335i	−0.896391	+	0.651266i
$142$	6.16645	+	2.00360i	0.517477	+	0.168138i
$143$		−	11.7055i		−	0.978860i
$144$	−0.750143	+	2.30870i	−0.0625119	+	0.192392i
$145$	13.7279	−	0.822317i	1.14004	−	0.0682897i
$146$	−1.11848	−	3.44232i	−0.0925659	−	0.284888i
$147$	2.21568	−	0.719918i	0.182746	−	0.0593778i
$148$	0.895397	−	1.23241i	0.0736012	−	0.101303i
$149$	0.687178			0.0562958			0.0281479	−	0.999604i	$-0.491039\pi$
$149$	0.687178			0.0562958			0.0281479	+	0.999604i	$0.491039\pi$
$150$	−8.53912	+	7.92283i	−0.697217	+	0.646896i
$151$	9.38885			0.764054			0.382027	−	0.924151i	$-0.375226\pi$
$151$	9.38885			0.764054			0.382027	+	0.924151i	$0.375226\pi$
$152$	0.219544	−	0.302176i	0.0178074	−	0.0245097i
$153$	4.78397	−	1.55441i	0.386761	−	0.125666i
$154$	0.548687	+	1.68868i	0.0442145	+	0.136078i
$155$	14.6698	+	9.37165i	1.17831	+	0.752749i
$156$	−4.74602	+	14.6067i	−0.379986	+	1.16948i
$157$		−	9.96335i		−	0.795162i	−0.917567	−	0.397581i	$-0.869850\pi$
$157$		−	9.96335i		−	0.795162i	0.917567	−	0.397581i	$-0.130150\pi$
$158$	−6.28316	−	2.04152i	−0.499861	−	0.162415i
$159$	6.47713	−	4.70591i	0.513670	−	0.373203i
$160$	−2.16414	−	0.562587i	−0.171090	−	0.0444764i
$161$	−7.10320	−	5.16078i	−0.559811	−	0.406726i
$162$	−6.10692	−	8.40546i	−0.479805	−	0.660395i
$163$	−10.0979	−	13.8985i	−0.790926	−	1.08862i	−0.993992	−	0.109451i	$-0.965091\pi$
$163$	−10.0979	−	13.8985i	−0.790926	−	1.08862i	0.203066	−	0.979165i	$-0.434909\pi$
$164$	−5.05366	−	3.67170i	−0.394625	−	0.286711i
$165$	4.97966	−	7.79487i	0.387666	−	0.606830i
$166$	−5.66892	+	4.11871i	−0.439994	+	0.319674i
$167$	1.17526	+	0.381864i	0.0909440	+	0.0295495i	0.354136	−	0.935194i	$-0.384775\pi$
$167$	1.17526	+	0.381864i	0.0909440	+	0.0295495i	−0.263192	+	0.964744i	$0.584775\pi$
$168$		−	2.32970i		−	0.179740i
$169$	−9.41276	+	28.9695i	−0.724058	+	2.22842i
$170$	1.69275	+	4.31318i	0.129828	+	0.330806i
$171$	−0.280186	−	0.862325i	−0.0214264	−	0.0659436i
$172$	8.22470	−	2.67237i	0.627128	−	0.203766i
$173$	4.37670	−	6.02401i	0.332754	−	0.457997i	−0.609553	−	0.792745i	$-0.708651\pi$
$173$	4.37670	−	6.02401i	0.332754	−	0.457997i	0.942308	+	0.334748i	$0.108651\pi$
$174$	14.3284			1.08623
$175$	2.43503	−	4.36699i	0.184071	−	0.330114i
$176$	1.77559			0.133840
$177$	−19.4364	+	26.7519i	−1.46093	+	2.01080i
$178$	7.98929	−	2.59588i	0.598823	−	0.194569i
$179$	−1.92822	−	5.93445i	−0.144122	−	0.443562i	0.852775	−	0.522278i	$-0.174918\pi$
$179$	−1.92822	−	5.93445i	−0.144122	−	0.443562i	−0.996897	+	0.0787165i	$0.974918\pi$
$180$	−4.19278	+	3.44742i	−0.312512	+	0.256956i
$181$	−1.91725	+	5.90069i	−0.142508	+	0.438595i	−0.996682	−	0.0813924i	$-0.974063\pi$
$181$	−1.91725	+	5.90069i	−0.142508	+	0.438595i	0.854174	+	0.519987i	$0.174063\pi$
$182$		−	6.59244i		−	0.488665i
$183$	−28.4674	−	9.24963i	−2.10437	−	0.683752i
$184$	−7.10320	+	5.16078i	−0.523655	+	0.380458i
$185$	3.17084	−	1.24443i	0.233125	−	0.0914920i
$186$	14.6729	+	10.6605i	1.07587	+	0.781667i
$187$	−2.16263	−	2.97660i	−0.158147	−	0.217670i
$188$	−3.31946	−	4.56884i	−0.242096	−	0.333217i
$189$	1.07900	+	0.783941i	0.0784859	+	0.0570233i
$190$	0.777464	−	0.305123i	0.0564031	−	0.0221359i
$191$	4.32464	−	3.14204i	0.312920	−	0.227350i	−0.420228	−	0.907418i	$-0.638050\pi$
$191$	4.32464	−	3.14204i	0.312920	−	0.227350i	0.733148	+	0.680069i	$0.238050\pi$
$192$	−2.21568	−	0.719918i	−0.159903	−	0.0519556i
$193$			24.2476i			1.74538i	0.488272	+	0.872691i	$0.337627\pi$
$193$			24.2476i			1.74538i	−0.488272	+	0.872691i	$0.662373\pi$
$194$	2.73087	−	8.40476i	0.196065	−	0.603427i
$195$	−26.5270	+	21.8112i	−1.89963	+	1.56193i
$196$	0.309017	+	0.951057i	0.0220726	+	0.0679326i
$197$	10.2249	−	3.32227i	0.728495	−	0.236702i	0.0787924	−	0.996891i	$-0.474894\pi$
$197$	10.2249	−	3.32227i	0.728495	−	0.236702i	0.649702	+	0.760189i	$0.274894\pi$
$198$	2.53351	−	3.48708i	0.180049	−	0.247816i
$199$	−7.81536			−0.554016			−0.277008	−	0.960868i	$-0.589343\pi$
$199$	−7.81536			−0.554016			−0.277008	+	0.960868i	$0.589343\pi$
$200$	−3.40079	−	3.66533i	−0.240472	−	0.259178i
$201$	8.00010			0.564283
$202$	4.46158	−	6.14084i	0.313916	−	0.432068i
$203$	−5.84928	+	1.90055i	−0.410539	+	0.133392i
$204$	1.49177	+	4.59121i	0.104445	+	0.321449i
$205$	−5.10294	−	13.0025i	−0.356405	−	0.908132i
$206$	3.16244	−	9.73299i	0.220338	−	0.678129i
$207$			21.3137i			1.48140i
$208$	−6.26979	−	2.03718i	−0.434732	−	0.141253i
$209$	−0.536541	+	0.389820i	−0.0371133	+	0.0269644i
$210$	2.80451	−	4.39002i	0.193530	−	0.302940i
$211$	6.22161	+	4.52026i	0.428313	+	0.311188i	0.780974	−	0.624563i	$-0.214723\pi$
$211$	6.22161	+	4.52026i	0.428313	+	0.311188i	−0.352661	+	0.935751i	$0.614723\pi$
$212$	2.01996	+	2.78024i	0.138732	+	0.190948i
$213$	8.87867	+	12.2204i	0.608357	+	0.837331i
$214$	−4.90056	−	3.56047i	−0.334995	−	0.243388i
$215$	18.7154	+	4.86523i	1.27638	+	0.331806i
$216$	1.07900	−	0.783941i	0.0734168	−	0.0533404i
$217$	−7.40398	−	2.40570i	−0.502615	−	0.163310i
$218$			9.49673i			0.643200i
$219$	2.60572	−	8.01958i	0.176078	−	0.541913i
$220$	3.34586	+	2.13747i	0.225578	+	0.144108i
$221$	4.22133	+	12.9919i	0.283957	+	0.873931i
$222$	3.37523	−	1.09668i	0.226531	−	0.0736043i
$223$	−7.27426	+	10.0122i	−0.487120	+	0.670464i	−0.979854	−	0.199717i	$-0.935998\pi$
$223$	−7.27426	+	10.0122i	−0.487120	+	0.670464i	0.492733	+	0.870180i	$0.335998\pi$
$224$	1.00000			0.0668153
$225$	−12.0508	+	1.44891i	−0.803385	+	0.0965942i
$226$	16.5087			1.09815
$227$	−0.00340347	+	0.00468447i	−0.000225896	+	0.000310919i	−0.809130	−	0.587630i	$-0.800061\pi$
$227$	−0.00340347	+	0.00468447i	−0.000225896	+	0.000310919i	0.808904	+	0.587941i	$0.200061\pi$
$228$	0.827579	−	0.268897i	0.0548078	−	0.0178081i
$229$	3.52315	+	10.8432i	0.232817	+	0.716536i	0.997404	+	0.0720151i	$0.0229430\pi$
$229$	3.52315	+	10.8432i	0.232817	+	0.716536i	−0.764587	+	0.644521i	$0.777057\pi$
$230$	−19.5976	+	1.17392i	−1.29223	+	0.0774062i
$231$	−1.27828	+	3.93413i	−0.0841045	+	0.258847i
$232$			6.15030i			0.403787i
$233$	1.35055	+	0.438820i	0.0884774	+	0.0287481i	0.352921	−	0.935653i	$-0.385188\pi$
$233$	1.35055	+	0.438820i	0.0884774	+	0.0287481i	−0.264444	+	0.964401i	$0.585188\pi$
$234$	−12.9469	+	9.40648i	−0.846366	+	0.614921i
$235$	−0.755078	−	12.6054i	−0.0492559	−	0.822284i
$236$	−11.4830	−	8.34288i	−0.747479	−	0.543075i
$237$	−9.04672	−	12.4517i	−0.587648	−	0.808827i
$238$	−1.21798	−	1.67640i	−0.0789497	−	0.108665i
$239$	1.07342	+	0.779884i	0.0694337	+	0.0504465i	0.621961	−	0.783049i	$-0.286336\pi$
$239$	1.07342	+	0.779884i	0.0694337	+	0.0504465i	−0.552527	+	0.833495i	$0.686336\pi$
$240$	−3.30851	−	4.02384i	−0.213564	−	0.259738i
$241$	20.0885	−	14.5951i	1.29401	−	0.940156i	0.294136	−	0.955764i	$-0.404968\pi$
$241$	20.0885	−	14.5951i	1.29401	−	0.940156i	0.999878	+	0.0156075i	$0.00496822\pi$
$242$	7.46321	+	2.42494i	0.479753	+	0.155881i
$243$		−	20.2038i		−	1.29607i
$244$	3.97030	−	12.2193i	0.254173	−	0.782263i
$245$	−0.562587	+	2.16414i	−0.0359424	+	0.138262i
$246$	−4.49709	−	13.8406i	−0.286724	−	0.882445i
$247$	2.34183	−	0.760907i	0.149007	−	0.0484153i
$248$	−4.57591	+	6.29820i	−0.290571	+	0.399936i
$249$	−16.3246			−1.03453
$250$	−1.99599	−	11.0007i	−0.126238	−	0.695747i
$251$	28.2984			1.78618			0.893091	−	0.449876i	$-0.148532\pi$
$251$	28.2984			1.78618			0.893091	+	0.449876i	$0.148532\pi$
$252$	1.42686	−	1.96390i	0.0898836	−	0.123714i
$253$	14.8267	−	4.81749i	0.932148	−	0.302873i
$254$	3.19952	+	9.84712i	0.200756	+	0.617864i
$255$	−2.71588	+	10.4473i	−0.170075	+	0.654238i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$		−	1.35425i		−	0.0844757i	−0.999108	−	0.0422379i	$-0.986551\pi$
$257$		−	1.35425i		−	0.0844757i	0.999108	−	0.0422379i	$-0.0134487\pi$
$258$	19.1611	+	6.22582i	1.19292	+	0.387603i
$259$	−1.23241	+	0.895397i	−0.0765781	+	0.0556373i
$260$	−9.36222	−	11.3864i	−0.580621	−	0.706155i
$261$	12.0786	+	8.77560i	0.747645	+	0.543196i
$262$	−6.13538	−	8.44463i	−0.379045	−	0.521711i
$263$	−1.51274	−	2.08211i	−0.0932798	−	0.128389i	0.759826	−	0.650126i	$-0.225284\pi$
$263$	−1.51274	−	2.08211i	−0.0932798	−	0.128389i	−0.853106	+	0.521738i	$0.825284\pi$
$264$	3.34657	+	2.43143i	0.205967	+	0.149644i
$265$	0.459481	+	7.67064i	0.0282257	+	0.471204i
$266$	−0.302176	+	0.219544i	−0.0185276	+	0.0134611i
$267$	18.6127	+	6.04763i	1.13908	+	0.370109i
$268$			3.43396i			0.209762i
$269$	−7.48943	+	23.0501i	−0.456639	+	1.40539i	0.412562	+	0.910930i	$0.364634\pi$
$269$	−7.48943	+	23.0501i	−0.456639	+	1.40539i	−0.869201	+	0.494460i	$0.835366\pi$
$270$	2.97695	−	0.178323i	0.181172	−	0.0108524i
$271$	−6.39805	−	19.6912i	−0.388654	−	1.19615i	−0.933795	−	0.357809i	$-0.883524\pi$
$271$	−6.39805	−	19.6912i	−0.388654	−	1.19615i	0.545141	−	0.838345i	$-0.316476\pi$
$272$	−1.97073	+	0.640328i	−0.119493	+	0.0388256i
$273$	9.02746	−	12.4252i	0.546367	−	0.752009i
$274$	7.90980			0.477849
$275$	3.73174	+	8.05555i	0.225033	+	0.485768i
$276$	−20.4549			−1.23124
$277$	−19.3864	+	26.6831i	−1.16482	+	1.60323i	−0.473238	+	0.880935i	$0.656915\pi$
$277$	−19.3864	+	26.6831i	−1.16482	+	1.60323i	−0.691580	+	0.722300i	$0.743085\pi$
$278$	−1.02934	+	0.334453i	−0.0617357	+	0.0200592i
$279$	5.83987	+	17.9733i	0.349624	+	1.07603i
$280$	1.88437	+	1.20381i	0.112613	+	0.0719413i
$281$	−4.19747	+	12.9185i	−0.250400	+	0.770652i	0.744301	+	0.667844i	$0.232783\pi$
$281$	−4.19747	+	12.9185i	−0.250400	+	0.770652i	−0.994701	+	0.102808i	$0.967217\pi$
$282$		−	13.1568i		−	0.783474i
$283$	16.9671	+	5.51294i	1.00859	+	0.327710i	0.766292	−	0.642492i	$-0.222099\pi$
$283$	16.9671	+	5.51294i	1.00859	+	0.327710i	0.242296	+	0.970202i	$0.422099\pi$
$284$	−5.24550	+	3.81108i	−0.311263	+	0.226146i
$285$	1.88316	+	0.489545i	0.111549	+	0.0289982i
$286$	9.46992	+	6.88030i	0.559968	+	0.406841i
$287$	3.67170	+	5.05366i	0.216734	+	0.298308i
$288$	−1.42686	−	1.96390i	−0.0840784	−	0.115724i
$289$	−10.2795	−	7.46852i	−0.604679	−	0.439325i
$290$	−7.40377	+	11.5894i	−0.434765	+	0.680555i
$291$	16.6563	−	12.1015i	0.976407	−	0.709401i
$292$	3.44232	+	1.11848i	0.201447	+	0.0654539i
$293$		−	31.0954i		−	1.81661i	−0.418307	−	0.908306i	$-0.637377\pi$
$293$		−	31.0954i		−	1.81661i	0.418307	−	0.908306i	$-0.362623\pi$
$294$	−0.719918	+	2.21568i	−0.0419865	+	0.129221i
$295$	−11.5950	−	29.5444i	−0.675085	−	1.72014i
$296$	0.470738	+	1.44878i	0.0273611	+	0.0842088i
$297$	−2.25223	+	0.731795i	−0.130688	+	0.0424631i
$298$	−0.403913	+	0.555939i	−0.0233981	+	0.0322047i
$299$	−57.8819			−3.34740
$300$	−1.39053	−	11.5652i	−0.0802824	−	0.667718i
$301$	−8.64796			−0.498460
$302$	−5.51863	+	7.59574i	−0.317561	+	0.437086i
$303$	16.8181	−	5.46453i	0.966174	−	0.313929i
$304$	0.115421	+	0.355229i	0.00661985	+	0.0203738i
$305$	22.1913	−	18.2463i	1.27067	−	1.04478i
$306$	−1.55441	+	4.78397i	−0.0888595	+	0.273481i
$307$		−	23.5507i		−	1.34411i	−0.740501	−	0.672055i	$-0.765412\pi$
$307$		−	23.5507i		−	1.34411i	0.740501	−	0.672055i	$-0.234588\pi$
$308$	−1.68868	−	0.548687i	−0.0962218	−	0.0312643i
$309$	19.2885	−	14.0139i	1.09728	−	0.797223i
$310$	−16.2045	+	6.35962i	−0.920356	+	0.361202i
$311$	−14.2138	−	10.3270i	−0.805993	−	0.585588i	0.106673	−	0.994294i	$-0.465980\pi$
$311$	−14.2138	−	10.3270i	−0.805993	−	0.585588i	−0.912666	+	0.408706i	$0.865980\pi$
$312$	−9.02746	−	12.4252i	−0.511079	−	0.703440i
$313$	12.6823	+	17.4557i	0.716846	+	0.986653i	0.999623	+	0.0274678i	$0.00874436\pi$
$313$	12.6823	+	17.4557i	0.716846	+	0.986653i	−0.282777	+	0.959186i	$0.591256\pi$
$314$	8.06052	+	5.85631i	0.454881	+	0.330491i
$315$	5.05288	−	1.98305i	0.284698	−	0.111732i
$316$	5.34478	−	3.88321i	0.300667	−	0.218447i
$317$	20.3768	+	6.62081i	1.14447	+	0.371862i	0.819059	−	0.573710i	$-0.194496\pi$
$317$	20.3768	+	6.62081i	1.14447	+	0.371862i	0.325414	+	0.945572i	$0.394496\pi$
$318$			8.00617i			0.448964i
$319$	3.37459	−	10.3859i	0.188941	−	0.581499i
$320$	1.72719	−	1.42014i	0.0965529	−	0.0793885i
$321$	−4.36085	−	13.4213i	−0.243399	−	0.749105i
$322$	8.35031	−	2.71318i	0.465345	−	0.151200i
$323$	0.454927	−	0.626153i	0.0253128	−	0.0348401i
$324$	10.3897			0.577206
$325$	−3.93484	−	32.7265i	−0.218266	−	1.81534i
$326$	17.1795			0.951485
$327$	−13.0045	+	17.8992i	−0.719150	+	0.989825i
$328$	5.94093	−	1.93033i	0.328033	−	0.106584i
$329$	1.74514	+	5.37100i	0.0962129	+	0.296113i
$330$	3.37921	+	8.61034i	0.186019	+	0.473984i
$331$	8.66345	−	26.6634i	0.476186	−	1.46555i	−0.368165	−	0.929761i	$-0.620014\pi$
$331$	8.66345	−	26.6634i	0.476186	−	1.46555i	0.844351	−	0.535790i	$-0.179986\pi$
$332$		−	7.00717i		−	0.384568i
$333$	3.51694	+	1.14272i	0.192727	+	0.0626209i
$334$	−0.999733	+	0.726348i	−0.0547029	+	0.0397440i
$335$	−4.13382	+	6.47084i	−0.225855	+	0.353540i
$336$	1.88477	+	1.36936i	0.102823	+	0.0747050i
$337$	−7.31103	−	10.0628i	−0.398257	−	0.548154i	0.562048	−	0.827104i	$-0.310013\pi$
$337$	−7.31103	−	10.0628i	−0.398257	−	0.548154i	−0.960305	+	0.278950i	$0.910013\pi$
$338$	−17.9041	−	24.6429i	−0.973856	−	1.34040i
$339$	31.1152	+	22.6065i	1.68994	+	1.22782i
$340$	−4.48441	−	1.16576i	−0.243201	−	0.0632223i
$341$	11.1830	−	8.12494i	0.605594	−	0.439990i
$342$	0.862325	+	0.280186i	0.0466292	+	0.0151507i
$343$		−	1.00000i		−	0.0539949i
$344$	−2.67237	+	8.22470i	−0.144084	+	0.443446i
$345$	−38.5446	−	24.6237i	−2.07517	−	1.32570i
$346$	2.30097	+	7.08165i	0.123701	+	0.380712i
$347$	−0.0329080	+	0.0106924i	−0.00176659	+	0.000574001i	−0.309900	−	0.950769i	$-0.600296\pi$
$347$	−0.0329080	+	0.0106924i	−0.00176659	+	0.000574001i	0.308134	+	0.951343i	$0.400296\pi$
$348$	−8.42200	+	11.5919i	−0.451467	+	0.621390i
$349$	−1.08764			−0.0582198			−0.0291099	−	0.999576i	$-0.509267\pi$
$349$	−1.08764			−0.0582198			−0.0291099	+	0.999576i	$0.509267\pi$
$350$	2.10169	+	4.53684i	0.112340	+	0.242504i
$351$	8.79248			0.469308
$352$	−1.04366	+	1.43648i	−0.0556275	+	0.0765647i
$353$	9.75442	−	3.16940i	0.519176	−	0.168690i	−0.0376955	−	0.999289i	$-0.512002\pi$
$353$	9.75442	−	3.16940i	0.519176	−	0.168690i	0.556871	+	0.830599i	$0.312002\pi$
$354$	−10.2183	−	31.4488i	−0.543098	−	1.67148i
$355$	−14.4723	+	0.866906i	−0.768108	+	0.0460106i
$356$	−2.59588	+	7.98929i	−0.137581	+	0.423432i
$357$		−	4.82748i		−	0.255498i
$358$	5.93445	+	1.92822i	0.313646	+	0.101910i
$359$	−1.08116	+	0.785506i	−0.0570613	+	0.0414574i	−0.615950	−	0.787785i	$-0.711228\pi$
$359$	−1.08116	+	0.785506i	−0.0570613	+	0.0414574i	0.558889	+	0.829242i	$0.311228\pi$
$360$	−0.324567	−	5.41838i	−0.0171062	−	0.285573i
$361$	15.2585	+	11.0859i	0.803077	+	0.583469i
$362$	−3.64683	−	5.01943i	−0.191673	−	0.263815i
$363$	10.7458	+	14.7903i	0.564008	+	0.776291i
$364$	5.33340	+	3.87494i	0.279546	+	0.203102i
$365$	5.14017	+	6.25152i	0.269049	+	0.327219i
$366$	24.2158	−	17.5938i	1.26578	−	0.919645i
$367$	28.7718	+	9.34852i	1.50188	+	0.487989i	0.940564	−	0.339616i	$-0.110297\pi$
$367$	28.7718	+	9.34852i	1.50188	+	0.487989i	0.561311	+	0.827605i	$0.310297\pi$
$368$		−	8.78004i		−	0.457691i
$369$	4.68590	−	14.4217i	0.243938	−	0.750764i
$370$	−0.857011	+	3.29672i	−0.0445539	+	0.171388i
$371$	−1.06196	−	3.26837i	−0.0551341	−	0.169685i
$372$	−17.2491	+	5.60456i	−0.894323	+	0.290583i
$373$	2.02569	−	2.78812i	0.104886	−	0.144363i	−0.753347	−	0.657623i	$-0.771562\pi$
$373$	2.02569	−	2.78812i	0.104886	−	0.144363i	0.858234	+	0.513259i	$0.171562\pi$
$374$	3.67928			0.190251
$375$	11.3020	−	23.4671i	0.583634	−	1.21183i
$376$	5.64740			0.291243
$377$	−23.8320	+	32.8020i	−1.22741	+	1.68939i
$378$	−1.26844	+	0.412142i	−0.0652417	+	0.0211983i
$379$	2.89392	+	8.90658i	0.148651	+	0.457500i	0.997462	−	0.0711953i	$-0.0226814\pi$
$379$	2.89392	+	8.90658i	0.148651	+	0.457500i	−0.848812	+	0.528695i	$0.822681\pi$
$380$	−0.210132	+	0.808328i	−0.0107795	+	0.0414664i
$381$	−7.45394	+	22.9409i	−0.381877	+	1.17530i
$382$			5.34555i			0.273502i
$383$	−34.6984	−	11.2742i	−1.77301	−	0.576085i	−0.774598	−	0.632454i	$-0.782048\pi$
$383$	−34.6984	−	11.2742i	−1.77301	−	0.576085i	−0.998410	+	0.0563688i	$0.982048\pi$
$384$	1.88477	−	1.36936i	0.0961817	−	0.0698801i
$385$	−2.52159	−	3.06678i	−0.128512	−	0.156298i
$386$	−19.6167	−	14.2524i	−0.998466	−	0.725428i
$387$	12.3394	+	16.9837i	0.627247	+	0.863332i
$388$	5.19443	+	7.14952i	0.263707	+	0.362962i
$389$	10.3790	+	7.54078i	0.526236	+	0.382333i	0.818948	−	0.573868i	$-0.194558\pi$
$389$	10.3790	+	7.54078i	0.526236	+	0.382333i	−0.292712	+	0.956201i	$0.594558\pi$
$390$	−2.05348	−	34.2811i	−0.103982	−	1.73589i
$391$	−14.7189	+	10.6939i	−0.744365	+	0.540813i
$392$	−0.951057	−	0.309017i	−0.0480356	−	0.0156077i
$393$		−	24.3177i		−	1.22667i
$394$	−3.32227	+	10.2249i	−0.167374	+	0.515123i
$395$	14.7462	−	0.883314i	0.741960	−	0.0444443i
$396$	1.33195	+	4.09931i	0.0669328	+	0.205998i
$397$	4.61800	−	1.50048i	0.231771	−	0.0753068i	−0.190829	−	0.981623i	$-0.561118\pi$
$397$	4.61800	−	1.50048i	0.231771	−	0.0753068i	0.422600	+	0.906316i	$0.361118\pi$
$398$	4.59375	−	6.32276i	0.230264	−	0.316931i
$399$	−0.870168			−0.0435629
$400$	4.96425	−	0.596871i	0.248212	−	0.0298435i
$401$	−36.2613			−1.81080			−0.905402	−	0.424555i	$-0.860431\pi$
$401$	−36.2613			−1.81080			−0.905402	+	0.424555i	$0.860431\pi$
$402$	−4.70234	+	6.47221i	−0.234531	+	0.322805i
$403$	−48.8103	+	15.8594i	−2.43142	+	0.790015i
$404$	2.34559	+	7.21899i	0.116698	+	0.359158i
$405$	19.5781	+	12.5072i	0.972842	+	0.621489i
$406$	1.90055	−	5.84928i	0.0943225	−	0.290295i
$407$		−	2.70483i		−	0.134073i
$408$	−4.59121	−	1.49177i	−0.227299	−	0.0738539i
$409$	14.9456	−	10.8586i	0.739012	−	0.536924i	−0.153390	−	0.988166i	$-0.549019\pi$
$409$	14.9456	−	10.8586i	0.739012	−	0.536924i	0.892402	+	0.451242i	$0.149019\pi$
$410$	13.5187	+	3.51429i	0.667639	+	0.173559i
$411$	14.9081	+	10.8314i	0.735365	+	0.534274i
$412$	6.01532	+	8.27937i	0.296353	+	0.407895i
$413$	8.34288	+	11.4830i	0.410526	+	0.565041i
$414$	−17.2431	−	12.5279i	−0.847453	−	0.615711i
$415$	8.43529	−	13.2041i	0.414072	−	0.648164i
$416$	5.33340	−	3.87494i	0.261491	−	0.189985i
$417$	−2.39806	−	0.779176i	−0.117433	−	0.0381564i
$418$		−	0.663201i		−	0.0324382i
$419$	−0.00433760	+	0.0133498i	−0.000211906	+	0.000652178i	−0.951162	−	0.308691i	$-0.900109\pi$
$419$	−0.00433760	+	0.0133498i	−0.000211906	+	0.000652178i	0.950951	+	0.309343i	$0.100109\pi$
$420$	1.90315	+	4.84929i	0.0928642	+	0.236621i
$421$	−0.542640	−	1.67007i	−0.0264467	−	0.0813944i	0.936962	−	0.349431i	$-0.113625\pi$
$421$	−0.542640	−	1.67007i	−0.0264467	−	0.0813944i	−0.963409	+	0.268037i	$0.913625\pi$
$422$	−7.31394	+	2.37644i	−0.356037	+	0.115683i
$423$	8.05804	−	11.0909i	0.391795	−	0.539260i
$424$	−3.43657			−0.166894
$425$	−7.04693	−	7.59510i	−0.341826	−	0.368416i
$426$	−15.1053			−0.731854
$427$	−7.55197	+	10.3944i	−0.365465	+	0.503020i
$428$	5.76095	−	1.87185i	0.278466	−	0.0904792i
$429$	8.42697	+	25.9356i	0.406858	+	1.25218i
$430$	−14.9367	+	12.2814i	−0.720311	+	0.592260i
$431$	2.72185	−	8.37699i	0.131107	−	0.403505i	−0.863857	−	0.503736i	$-0.831958\pi$
$431$	2.72185	−	8.37699i	0.131107	−	0.403505i	0.994964	+	0.100231i	$0.0319583\pi$
$432$			1.33372i			0.0641687i
$433$	0.119361	+	0.0387827i	0.00573612	+	0.00186378i	0.311884	−	0.950120i	$-0.399040\pi$
$433$	0.119361	+	0.0387827i	0.00573612	+	0.00186378i	−0.306148	+	0.951984i	$0.599040\pi$
$434$	6.29820	−	4.57591i	0.302323	−	0.219651i
$435$	−29.8246	+	11.7049i	−1.42998	+	0.561208i
$436$	−7.68302	−	5.58204i	−0.367950	−	0.267331i
$437$	1.92760	+	2.65312i	0.0922098	+	0.126916i
$438$	4.95637	+	6.82186i	0.236825	+	0.325961i
$439$	−2.68888	−	1.95359i	−0.128333	−	0.0932396i	0.521767	−	0.853088i	$-0.325273\pi$
$439$	−2.68888	−	1.95359i	−0.128333	−	0.0932396i	−0.650100	+	0.759849i	$0.725273\pi$
$440$	−3.69590	+	1.45049i	−0.176195	+	0.0691494i
$441$	−1.96390	+	1.42686i	−0.0935191	+	0.0679456i
$442$	−12.9919	−	4.22133i	−0.617962	−	0.200788i
$443$			10.1470i			0.482101i	0.970513	+	0.241050i	$0.0774919\pi$
$443$			10.1470i			0.482101i	−0.970513	+	0.241050i	$0.922508\pi$
$444$	−1.09668	+	3.37523i	−0.0520461	+	0.160181i
$445$	−14.5092	+	11.9298i	−0.687800	+	0.565529i
$446$	−3.82430	−	11.7700i	−0.181086	−	0.557325i
$447$	−1.52257	+	0.494712i	−0.0720149	+	0.0233991i
$448$	−0.587785	+	0.809017i	−0.0277702	+	0.0382225i
$449$	24.4074			1.15186			0.575928	−	0.817501i	$-0.304641\pi$
$449$	24.4074			1.15186			0.575928	+	0.817501i	$0.304641\pi$
$450$	5.91108	−	10.6009i	0.278651	−	0.499733i
$451$	−11.0915			−0.522279
$452$	−9.70360	+	13.3559i	−0.456419	+	0.628207i
$453$	−20.8027	+	6.75920i	−0.977395	+	0.317575i
$454$	−0.00178931	−	0.00550692i	−8.39764e−5	−	0.000258453i
$455$	5.38541	+	13.7222i	0.252472	+	0.643307i
$456$	−0.268897	+	0.827579i	−0.0125922	+	0.0387549i
$457$			11.8361i			0.553671i	0.960917	+	0.276836i	$0.0892858\pi$
$457$			11.8361i			0.553671i	−0.960917	+	0.276836i	$0.910714\pi$
$458$	−10.8432	−	3.52315i	−0.506667	−	0.164626i
$459$	2.23585	−	1.62444i	0.104361	−	0.0758224i
$460$	10.5695	−	16.5448i	0.492805	−	0.771407i
$461$	1.10424	+	0.802275i	0.0514294	+	0.0373657i	0.613203	−	0.789925i	$-0.289881\pi$
$461$	1.10424	+	0.802275i	0.0514294	+	0.0373657i	−0.561774	+	0.827291i	$0.689881\pi$
$462$	−2.43143	−	3.34657i	−0.113120	−	0.155697i
$463$	−12.3508	−	16.9994i	−0.573991	−	0.790031i	0.419029	−	0.907973i	$-0.362371\pi$
$463$	−12.3508	−	16.9994i	−0.573991	−	0.790031i	−0.993021	+	0.117941i	$0.962371\pi$
$464$	−4.97569	−	3.61505i	−0.230991	−	0.167825i
$465$	−39.2504	−	10.2035i	−1.82020	−	0.473176i
$466$	−1.14885	+	0.834685i	−0.0532192	+	0.0386660i
$467$	−30.5757	−	9.93465i	−1.41488	−	0.459721i	−0.500905	−	0.865502i	$-0.667000\pi$
$467$	−30.5757	−	9.93465i	−1.41488	−	0.459721i	−0.913970	+	0.405781i	$0.867000\pi$
$468$		−	16.0033i		−	0.739751i
$469$	1.06115	−	3.26589i	0.0489994	−	0.150805i
$470$	10.6418	+	6.79839i	0.490869	+	0.313586i
$471$	7.17279	+	22.0756i	0.330505	+	1.01719i
$472$	13.4991	−	4.38611i	0.621345	−	0.201887i
$473$	9.02557	−	12.4226i	0.414996	−	0.571193i
$474$	15.3912			0.706941
$475$	−1.36904	+	1.27023i	−0.0628158	+	0.0582821i
$476$	2.07215			0.0949767
$477$	−4.90349	+	6.74907i	−0.224515	+	0.309019i
$478$	−1.26188	+	0.410009i	−0.0577170	+	0.0187534i
$479$	11.8433	+	36.4498i	0.541132	+	1.66543i	0.730013	+	0.683434i	$0.239514\pi$
$479$	11.8433	+	36.4498i	0.541132	+	1.66543i	−0.188880	+	0.982000i	$0.560486\pi$
$480$	5.20005	−	0.311490i	0.237349	−	0.0142175i
$481$	−3.10331	+	9.55102i	−0.141499	+	0.435489i
$482$			24.8307i			1.13101i
$483$	19.4537	+	6.32091i	0.885176	+	0.287611i
$484$	−6.34859	+	4.61252i	−0.288572	+	0.209660i
$485$	1.18158	+	19.7254i	0.0536527	+	0.895685i
$486$	16.3452	+	11.8755i	0.741434	+	0.538683i
$487$	5.91198	+	8.13714i	0.267897	+	0.368729i	0.921678	−	0.387955i	$-0.126818\pi$
$487$	5.91198	+	8.13714i	0.267897	+	0.368729i	−0.653781	+	0.756684i	$0.726818\pi$
$488$	7.55197	+	10.3944i	0.341861	+	0.470532i
$489$	32.3794	+	23.5250i	1.46425	+	1.06384i
$490$	−1.42014	−	1.72719i	−0.0641556	−	0.0780265i
$491$	−13.2922	+	9.65738i	−0.599871	+	0.435831i	−0.845833	−	0.533448i	$-0.820896\pi$
$491$	−13.2922	+	9.65738i	−0.599871	+	0.435831i	0.245962	+	0.969279i	$0.420896\pi$
$492$	13.8406	+	4.49709i	0.623983	+	0.202744i
$493$			12.7443i			0.573975i
$494$	−0.760907	+	2.34183i	−0.0342348	+	0.105364i
$495$	−2.42490	+	9.32802i	−0.108991	+	0.419263i
$496$	−2.40570	−	7.40398i	−0.108019	−	0.332449i
$497$	6.16645	−	2.00360i	0.276603	−	0.0898738i
$498$	9.59537	−	13.2069i	0.429979	−	0.591815i
$499$	43.2783			1.93740			0.968702	−	0.248225i	$-0.0798473\pi$
$499$	43.2783			1.93740			0.968702	+	0.248225i	$0.0798473\pi$
$500$	10.0730	+	4.85127i	0.450478	+	0.216956i
$501$	−2.87890			−0.128620
$502$	−16.6334	+	22.8939i	−0.742385	+	1.02181i
$503$	33.0958	−	10.7535i	1.47567	−	0.479473i	0.542852	−	0.839828i	$-0.317344\pi$
$503$	33.0958	−	10.7535i	1.47567	−	0.479473i	0.932815	+	0.360355i	$0.117344\pi$
$504$	0.750143	+	2.30870i	0.0334140	+	0.102838i
$505$	−4.27031	+	16.4269i	−0.190026	+	0.730987i
$506$	−4.81749	+	14.8267i	−0.214164	+	0.659128i
$507$		−	70.9635i		−	3.15160i
$508$	−9.84712	−	3.19952i	−0.436895	−	0.141956i
$509$	−18.6266	+	13.5330i	−0.825610	+	0.599841i	−0.918314	−	0.395853i	$-0.870449\pi$
$509$	−18.6266	+	13.5330i	−0.825610	+	0.599841i	0.0927037	+	0.995694i	$0.470449\pi$
$510$	−6.85573	−	8.33799i	−0.303577	−	0.369212i
$511$	−2.92821	−	2.12747i	−0.129536	−	0.0941138i
$512$	0.587785	+	0.809017i	0.0259767	+	0.0357538i
$513$	−0.292810	−	0.403019i	−0.0129279	−	0.0177937i
$514$	1.09561	+	0.796007i	0.0483253	+	0.0351104i
$515$	1.36830	+	22.8427i	0.0602947	+	1.00657i
$516$	−16.2994	+	11.8422i	−0.717542	+	0.521324i
$517$	−9.53668	−	3.09866i	−0.419423	−	0.136279i
$518$		−	1.52334i		−	0.0669317i
$519$	−5.36057	+	16.4981i	−0.235303	+	0.724188i
$520$	14.7148	−	0.881433i	0.645286	−	0.0386534i
$521$	−4.04453	−	12.4478i	−0.177194	−	0.545348i	0.822533	−	0.568718i	$-0.192560\pi$
$521$	−4.04453	−	12.4478i	−0.177194	−	0.545348i	−0.999727	+	0.0233702i	$0.992560\pi$
$522$	−14.1992	+	4.61360i	−0.621483	+	0.201932i
$523$	5.09181	−	7.00828i	0.222649	−	0.306451i	−0.683050	−	0.730372i	$-0.739347\pi$
$523$	5.09181	−	7.00828i	0.222649	−	0.306451i	0.905699	+	0.423921i	$0.139347\pi$
$524$	10.4381			0.455992
$525$	−2.25138	+	11.4289i	−0.0982581	+	0.498797i
$526$	2.57363			0.112216
$527$	−9.48196	+	13.0508i	−0.413041	+	0.568502i
$528$	−3.93413	+	1.27828i	−0.171211	+	0.0556299i
$529$	−16.7145	−	51.4418i	−0.726715	−	2.23660i
$530$	−6.47576	−	4.13696i	−0.281289	−	0.179698i
$531$	10.6473	−	32.7692i	0.462055	−	1.42206i
$532$		−	0.373510i		−	0.0161937i
$533$	39.1653	+	12.7256i	1.69644	+	0.551206i
$534$	−15.8329	+	11.5033i	−0.685156	+	0.497795i
$535$	13.1091	+	3.40783i	0.566756	+	0.147333i
$536$	−2.77813	−	2.01843i	−0.119997	−	0.0871828i
$537$	8.54464	+	11.7607i	0.368728	+	0.507511i
$538$	−14.2457	−	19.6076i	−0.614178	−	0.845343i
$539$	1.43648	+	1.04366i	0.0618736	+	0.0449538i
$540$	−1.60554	+	2.51322i	−0.0690916	+	0.108152i
$541$	27.5606	−	20.0239i	1.18492	−	0.860896i	0.192203	−	0.981355i	$-0.438437\pi$
$541$	27.5606	−	20.0239i	1.18492	−	0.860896i	0.992718	+	0.120460i	$0.0384368\pi$
$542$	19.6912	+	6.39805i	0.845808	+	0.274820i
$543$		−	14.4543i		−	0.620293i
$544$	0.640328	−	1.97073i	0.0274539	−	0.0844943i
$545$	−7.75794	−	19.7675i	−0.332314	−	0.846747i
$546$	4.74602	+	14.6067i	0.203111	+	0.625111i
$547$	−6.73679	+	2.18892i	−0.288044	+	0.0935913i	−0.449475	−	0.893293i	$-0.648389\pi$
$547$	−6.73679	+	2.18892i	−0.288044	+	0.0935913i	0.161431	+	0.986884i	$0.448389\pi$
$548$	−4.64926	+	6.39916i	−0.198607	+	0.273359i
$549$	31.1891			1.33112
$550$	−8.71054	−	1.71589i	−0.371419	−	0.0731658i
$551$	2.29720			0.0978640
$552$	12.0231	−	16.5483i	0.511736	−	0.704344i
$553$	−6.28316	+	2.04152i	−0.267187	+	0.0868144i
$554$	−10.1921	−	31.3679i	−0.433019	−	1.33269i
$555$	−6.12968	+	5.03999i	−0.260190	+	0.213936i
$556$	0.334453	−	1.02934i	0.0141840	−	0.0436537i
$557$			34.5676i			1.46468i	0.680940	+	0.732339i	$0.261571\pi$
$557$			34.5676i			1.46468i	−0.680940	+	0.732339i	$0.738429\pi$
$558$	−17.9733	−	5.83987i	−0.760869	−	0.247221i
$559$	−46.1230	+	33.5103i	−1.95080	+	1.41734i
$560$	−2.08151	+	0.816906i	−0.0879597	+	0.0345206i
$561$	6.93459	+	5.03828i	0.292779	+	0.212716i
$562$	−7.98407	−	10.9891i	−0.336787	−	0.463548i
$563$	20.5436	+	28.2758i	0.865808	+	1.19168i	0.980153	+	0.198242i	$0.0635231\pi$
$563$	20.5436	+	28.2758i	0.865808	+	1.19168i	−0.114345	+	0.993441i	$0.536477\pi$
$564$	10.6440	+	7.73335i	0.448195	+	0.325633i
$565$	−34.3630	+	13.4861i	−1.44566	+	0.567365i
$566$	−14.4331	+	10.4862i	−0.606667	+	0.440769i
$567$	−9.88121	−	3.21060i	−0.414972	−	0.134832i
$568$		−	6.48379i		−	0.272054i
$569$	2.87649	−	8.85293i	0.120589	−	0.371134i	−0.872483	−	0.488645i	$-0.837491\pi$
$569$	2.87649	−	8.85293i	0.120589	−	0.371134i	0.993072	+	0.117511i	$0.0374914\pi$
$570$	−1.50295	+	1.23576i	−0.0629515	+	0.0517605i
$571$	0.696946	+	2.14498i	0.0291663	+	0.0897646i	0.964580	−	0.263790i	$-0.0849727\pi$
$571$	0.696946	+	2.14498i	0.0291663	+	0.0897646i	−0.935414	+	0.353555i	$0.884973\pi$
$572$	−11.1326	+	3.61719i	−0.465476	+	0.151242i
$573$	−7.32001	+	10.0751i	−0.305798	+	0.420895i
$574$	−6.24667			−0.260731
$575$	39.8336	−	18.4530i	1.66118	−	0.769542i
$576$	2.42751			0.101146
$577$	2.33313	−	3.21128i	0.0971296	−	0.133687i	−0.757686	−	0.652619i	$-0.773670\pi$
$577$	2.33313	−	3.21128i	0.0971296	−	0.133687i	0.854816	+	0.518932i	$0.173670\pi$
$578$	12.0843	−	3.92643i	0.502642	−	0.163318i
$579$	−17.4563	−	53.7250i	−0.725459	−	2.23273i
$580$	−5.02422	−	12.8019i	−0.208619	−	0.531569i
$581$	−2.16533	+	6.66422i	−0.0898332	+	0.276478i
$582$			20.5883i			0.853411i
$583$	5.80328	+	1.88560i	0.240347	+	0.0780935i
$584$	−2.92821	+	2.12747i	−0.121170	+	0.0880354i
$585$	19.2648	−	30.1560i	0.796503	−	1.24680i
$586$	25.1567	+	18.2774i	1.03921	+	0.755032i
$587$	−27.9342	−	38.4481i	−1.15297	−	1.58692i	−0.734368	−	0.678751i	$-0.762521\pi$
$587$	−27.9342	−	38.4481i	−1.15297	−	1.58692i	−0.418599	−	0.908171i	$-0.637479\pi$
$588$	−1.36936	−	1.88477i	−0.0564717	−	0.0777266i
$589$	2.35244	+	1.70915i	0.0969308	+	0.0704243i
$590$	30.7172	+	7.98522i	1.26461	+	0.328746i
$591$	−20.2634	+	14.7222i	−0.833523	+	0.605590i
$592$	−1.44878	−	0.470738i	−0.0595446	−	0.0193472i
$593$			7.84523i			0.322165i	0.986941	+	0.161082i	$0.0514985\pi$
$593$			7.84523i			0.322165i	−0.986941	+	0.161082i	$0.948501\pi$
$594$	0.731795	−	2.25223i	0.0300259	−	0.0924103i
$595$	3.90469	+	2.49447i	0.160077	+	0.102263i
$596$	−0.212350	−	0.653545i	−0.00869818	−	0.0267703i
$597$	17.3163	−	5.62642i	0.708710	−	0.230274i
$598$	34.0221	−	46.8275i	1.39127	−	1.91492i
$599$	3.45943			0.141349			0.0706743	−	0.997499i	$-0.477485\pi$
$599$	3.45943			0.141349			0.0706743	+	0.997499i	$0.477485\pi$
$600$	10.1738	+	5.67290i	0.415343	+	0.231595i
$601$	−27.6384			−1.12740			−0.563698	−	0.825981i	$-0.690622\pi$
$601$	−27.6384			−1.12740			−0.563698	+	0.825981i	$0.690622\pi$
$602$	5.08314	−	6.99635i	0.207173	−	0.285150i
$603$	−7.92799	+	2.57596i	−0.322853	+	0.104901i
$604$	−2.90131	−	8.92933i	−0.118053	−	0.363329i
$605$	−17.5157	+	1.04921i	−0.712113	+	0.0426565i
$606$	−5.46453	+	16.8181i	−0.221981	+	0.683188i
$607$		−	36.8021i		−	1.49375i	−0.664964	−	0.746875i	$-0.731553\pi$
$607$		−	36.8021i		−	1.49375i	0.664964	−	0.746875i	$-0.268447\pi$
$608$	−0.355229	−	0.115421i	−0.0144065	−	0.00468094i
$609$	11.5919	−	8.42200i	0.469727	−	0.341277i
$610$	1.71785	+	28.6780i	0.0695536	+	1.16114i
$611$	30.1199	+	21.8834i	1.21852	+	0.885306i
$612$	−2.95666	−	4.06949i	−0.119516	−	0.164499i
$613$	8.87981	+	12.2220i	0.358652	+	0.493642i	0.949773	−	0.312941i	$-0.101314\pi$
$613$	8.87981	+	12.2220i	0.358652	+	0.493642i	−0.591120	+	0.806583i	$0.701314\pi$
$614$	19.0529	+	13.8428i	0.768914	+	0.558649i
$615$	20.6672	+	25.1356i	0.833381	+	1.01357i
$616$	1.43648	−	1.04366i	0.0578775	−	0.0420504i
$617$	−33.0264	−	10.7309i	−1.32959	−	0.432011i	−0.443815	−	0.896119i	$-0.646375\pi$
$617$	−33.0264	−	10.7309i	−1.32959	−	0.432011i	−0.885779	+	0.464107i	$0.846375\pi$
$618$			23.8419i			0.959061i
$619$	2.60215	−	8.00860i	0.104589	−	0.321893i	−0.885044	−	0.465506i	$-0.845872\pi$
$619$	2.60215	−	8.00860i	0.104589	−	0.321893i	0.989634	+	0.143613i	$0.0458722\pi$
$620$	4.37974	−	16.8478i	0.175895	−	0.676625i
$621$	3.61863	+	11.1370i	0.145210	+	0.446912i
$622$	16.7094	−	5.42920i	0.669985	−	0.217691i
$623$	4.93765	−	6.79610i	0.197823	−	0.272280i
$624$	15.3584			0.614829
$625$	13.1412	+	21.2675i	0.525649	+	0.850701i
$626$	−21.5764			−0.862367
$627$	0.908164	−	1.24998i	0.0362686	−	0.0499194i
$628$	−9.47570	+	3.07884i	−0.378122	+	0.122859i
$629$	0.975438	+	3.00209i	0.0388933	+	0.119701i
$630$	−1.36569	+	5.25348i	−0.0544103	+	0.209304i
$631$	−5.42695	+	16.7024i	−0.216043	+	0.664913i	0.783034	+	0.621978i	$0.213671\pi$
$631$	−5.42695	+	16.7024i	−0.216043	+	0.664913i	−0.999078	+	0.0429350i	$0.986329\pi$
$632$			6.60651i			0.262793i
$633$	−17.0393	−	5.53641i	−0.677252	−	0.220052i
$634$	−17.3335	+	12.5935i	−0.688402	+	0.500153i
$635$	−14.7040	−	17.8831i	−0.583511	−	0.709670i
$636$	−6.47713	−	4.70591i	−0.256835	−	0.186602i
$637$	−3.87494	−	5.33340i	−0.153531	−	0.211317i
$638$	6.41885	+	8.83479i	0.254125	+	0.349772i
$639$	−12.7335	−	9.25144i	−0.503730	−	0.365981i
$640$	0.133704	+	2.23207i	0.00528510	+	0.0882302i
$641$	2.84147	−	2.06445i	0.112231	−	0.0815410i	−0.530254	−	0.847839i	$-0.677903\pi$
$641$	2.84147	−	2.06445i	0.112231	−	0.0815410i	0.642485	+	0.766298i	$0.277903\pi$
$642$	13.4213	+	4.36085i	0.529697	+	0.172109i
$643$		−	10.2839i		−	0.405557i	−0.979225	−	0.202779i	$-0.935003\pi$
$643$		−	10.2839i		−	0.405557i	0.979225	−	0.202779i	$-0.0649972\pi$
$644$	−2.71318	+	8.35031i	−0.106914	+	0.329048i
$645$	−44.9699	+	2.69375i	−1.77069	+	0.106066i
$646$	0.239169	+	0.736087i	0.00940999	+	0.0289610i
$647$	3.46056	−	1.12441i	0.136049	−	0.0442049i	−0.240201	−	0.970723i	$-0.577213\pi$
$647$	3.46056	−	1.12441i	0.136049	−	0.0442049i	0.376250	+	0.926518i	$0.377213\pi$
$648$	−6.10692	+	8.40546i	−0.239903	+	0.330198i
$649$	−25.2023			−0.989275
$650$	28.7892	+	16.0528i	1.12920	+	0.629643i
$651$	18.1368			0.710835
$652$	−10.0979	+	13.8985i	−0.395463	+	0.544308i
$653$	24.0563	−	7.81635i	0.941394	−	0.305878i	0.202180	−	0.979348i	$-0.435197\pi$
$653$	24.0563	−	7.81635i	0.941394	−	0.305878i	0.739214	+	0.673471i	$0.235197\pi$
$654$	−6.83687	−	21.0417i	−0.267343	−	0.822796i
$655$	19.6693	+	12.5655i	0.768543	+	0.490975i
$656$	−1.93033	+	5.94093i	−0.0753666	+	0.231954i
$657$			8.78632i			0.342787i
$658$	−5.37100	−	1.74514i	−0.209383	−	0.0680328i
$659$	18.0204	−	13.0926i	0.701976	−	0.510015i	−0.178599	−	0.983922i	$-0.557157\pi$
$659$	18.0204	−	13.0926i	0.701976	−	0.510015i	0.880575	+	0.473906i	$0.157157\pi$
$660$	−8.95216	−	2.32719i	−0.348462	−	0.0905859i
$661$	−16.2700	−	11.8208i	−0.632828	−	0.459777i	0.224551	−	0.974462i	$-0.427909\pi$
$661$	−16.2700	−	11.8208i	−0.632828	−	0.459777i	−0.857379	+	0.514686i	$0.827909\pi$
$662$	16.4789	+	22.6812i	0.640469	+	0.881530i
$663$	−18.7062	−	25.7469i	−0.726489	−	0.999927i
$664$	5.66892	+	4.11871i	0.219997	+	0.159837i
$665$	0.449635	−	0.703831i	0.0174361	−	0.0272934i
$666$	−2.99169	+	2.17359i	−0.115926	+	0.0842249i
$667$	−51.3569	−	16.6869i	−1.98855	−	0.646118i
$668$		−	1.23574i		−	0.0478121i
$669$	8.90949	−	27.4206i	0.344461	−	1.06014i
$670$	−2.80522	−	7.14780i	−0.108375	−	0.276144i
$671$	−7.04963	−	21.6965i	−0.272148	−	0.837585i
$672$	−2.21568	+	0.719918i	−0.0854717	+	0.0277714i
$673$	−13.1385	+	18.0836i	−0.506451	+	0.697070i	−0.983316	−	0.181906i	$-0.941773\pi$
$673$	−13.1385	+	18.0836i	−0.506451	+	0.697070i	0.476865	+	0.878977i	$0.341773\pi$
$674$	12.4383			0.479104
$675$	−6.05087	+	2.80307i	−0.232898	+	0.107890i
$676$	30.4603			1.17155
$677$	−3.20980	+	4.41792i	−0.123363	+	0.169794i	−0.866232	−	0.499643i	$-0.833465\pi$
$677$	−3.20980	+	4.41792i	−0.123363	+	0.169794i	0.742869	+	0.669437i	$0.233465\pi$
$678$	−36.5781	+	11.8849i	−1.40477	+	0.456438i
$679$	−2.73087	−	8.40476i	−0.104801	−	0.322545i
$680$	3.57899	−	2.94275i	0.137248	−	0.112849i
$681$	0.00416856	−	0.0128295i	0.000159739	−	0.000491627i
$682$			13.8230i			0.529309i
$683$	6.31948	+	2.05333i	0.241808	+	0.0785683i	0.427414	−	0.904056i	$-0.359425\pi$
$683$	6.31948	+	2.05333i	0.241808	+	0.0785683i	−0.185606	+	0.982624i	$0.559425\pi$
$684$	−0.733537	+	0.532946i	−0.0280475	+	0.0203777i
$685$	−16.4643	+	6.46157i	−0.629068	+	0.246884i
$686$	0.809017	+	0.587785i	0.0308884	+	0.0224417i
$687$	−15.6124	−	21.4886i	−0.595648	−	0.819840i
$688$	−5.08314	−	6.99635i	−0.193793	−	0.266733i
$689$	−18.3286	−	13.3165i	−0.698263	−	0.507318i
$690$	42.5769	−	16.7097i	1.62088	−	0.636128i
$691$	22.4667	−	16.3230i	0.854673	−	0.620956i	−0.0717577	−	0.997422i	$-0.522861\pi$
$691$	22.4667	−	16.3230i	0.854673	−	0.620956i	0.926430	+	0.376466i	$0.122861\pi$
$692$	−7.08165	−	2.30097i	−0.269204	−	0.0874696i
$693$		−	4.31027i		−	0.163734i
$694$	0.0106924	−	0.0329080i	0.000405880	−	0.00124917i
$695$	1.86936	−	1.53704i	0.0709089	−	0.0583033i
$696$	−4.42771	−	13.6271i	−0.167832	−	0.516533i
$697$	12.3105	−	3.99992i	0.466293	−	0.151508i
$698$	0.639297	−	0.879916i	0.0241977	−	0.0333053i
$699$	−3.30830			−0.125131
$700$	−4.90572	−	0.966379i	−0.185419	−	0.0365257i
$701$	−46.3380			−1.75016			−0.875081	−	0.483976i	$-0.839192\pi$
$701$	−46.3380			−1.75016			−0.875081	+	0.483976i	$0.839192\pi$
$702$	−5.16809	+	7.11326i	−0.195057	+	0.268473i
$703$	0.541135	−	0.175825i	0.0204093	−	0.00663138i
$704$	−0.548687	−	1.68868i	−0.0206794	−	0.0636447i
$705$	10.7478	+	27.3859i	0.404787	+	1.03141i
$706$	−3.16940	+	9.75442i	−0.119282	+	0.367113i
$707$		−	7.59049i		−	0.285470i
$708$	31.4488	+	10.2183i	1.18192	+	0.384028i
$709$	5.41918	−	3.93727i	0.203522	−	0.147867i	−0.481356	−	0.876525i	$-0.659856\pi$
$709$	5.41918	−	3.93727i	0.203522	−	0.147867i	0.684878	+	0.728658i	$0.259856\pi$
$710$	7.80524	−	12.2179i	0.292925	−	0.458528i
$711$	12.9745	+	9.42654i	0.486583	+	0.353523i
$712$	−4.93765	−	6.79610i	−0.185046	−	0.254695i
$713$	−40.1767	−	55.2985i	−1.50463	−	2.07094i
$714$	3.90552	+	2.83752i	0.146160	+	0.106192i
$715$	−25.3323	−	6.58534i	−0.947373	−	0.246278i
$716$	−5.04815	+	3.66769i	−0.188658	+	0.137068i
$717$	−2.93980	−	0.955200i	−0.109789	−	0.0356726i
$718$		−	1.33638i		−	0.0498734i
$719$	−12.5901	+	38.7482i	−0.469530	+	1.44507i	0.383664	+	0.923473i	$0.374662\pi$
$719$	−12.5901	+	38.7482i	−0.469530	+	1.44507i	−0.853194	+	0.521593i	$0.825338\pi$
$720$	4.57433	+	2.92226i	0.170475	+	0.108906i
$721$	−3.16244	−	9.73299i	−0.117775	−	0.362475i
$722$	−17.9374	+	5.82821i	−0.667561	+	0.216904i
$723$	−34.0024	+	46.8002i	−1.26456	+	1.74052i
$724$	6.20435			0.230583
$725$	5.94352	−	30.1716i	0.220737	−	1.12055i
$726$	−18.2818			−0.678503
$727$	26.7161	−	36.7716i	0.990846	−	1.36378i	0.0600695	−	0.998194i	$-0.480868\pi$
$727$	26.7161	−	36.7716i	0.990846	−	1.36378i	0.930777	−	0.365588i	$-0.119132\pi$
$728$	−6.26979	+	2.03718i	−0.232374	+	0.0755028i
$729$	4.91327	+	15.1215i	0.181973	+	0.560055i
$730$	−8.07890	+	0.483936i	−0.299013	+	0.0179113i
$731$	−5.53754	+	17.0428i	−0.204813	+	0.630350i
$732$			29.9324i			1.10633i
$733$	37.8086	+	12.2847i	1.39649	+	0.453747i	0.908054	−	0.418852i	$-0.137567\pi$
$733$	37.8086	+	12.2847i	1.39649	+	0.453747i	0.488436	+	0.872600i	$0.337567\pi$
$734$	−24.4747	+	17.7819i	−0.903379	+	0.656344i
$735$	−0.311490	−	5.20005i	−0.0114895	−	0.191807i
$736$	7.10320	+	5.16078i	0.261827	+	0.190229i
$737$	3.58390	+	4.93281i	0.132015	+	0.181703i
$738$	8.91310	+	12.2678i	0.328096	+	0.451585i
$739$	8.35191	+	6.06802i	0.307230	+	0.223216i	0.730707	−	0.682691i	$-0.239191\pi$
$739$	8.35191	+	6.06802i	0.307230	+	0.223216i	−0.423477	+	0.905907i	$0.639191\pi$
$740$	−2.16336	−	2.63110i	−0.0795268	−	0.0967211i
$741$	−4.64095	+	3.37185i	−0.170490	+	0.123868i
$742$	3.26837	+	1.06196i	0.119986	+	0.0389857i
$743$			11.4917i			0.421590i	0.977530	+	0.210795i	$0.0676052\pi$
$743$			11.4917i			0.421590i	−0.977530	+	0.210795i	$0.932395\pi$
$744$	5.60456	−	17.2491i	0.205473	−	0.632382i
$745$	0.386597	−	1.48715i	0.0141638	−	0.0544849i
$746$	1.06497	+	3.27763i	0.0389912	+	0.120003i
$747$	16.1775	−	5.25638i	0.591903	−	0.192321i
$748$	−2.16263	+	2.97660i	−0.0790734	+	0.108835i
$749$	−6.05743			−0.221334
$750$	12.3421	+	22.9371i	0.450670	+	0.837546i
$751$	31.9563			1.16610			0.583051	−	0.812436i	$-0.301859\pi$
$751$	31.9563			1.16610			0.583051	+	0.812436i	$0.301859\pi$
$752$	−3.31946	+	4.56884i	−0.121048	+	0.166609i
$753$	−62.7003	+	20.3726i	−2.28493	+	0.742417i
$754$	−12.5292	−	38.5610i	−0.456288	−	1.40431i
$755$	5.28204	−	20.3188i	0.192233	−	0.739476i
$756$	0.412142	−	1.26844i	0.0149895	−	0.0461328i
$757$		−	27.1428i		−	0.986522i	−0.869881	−	0.493261i	$-0.835805\pi$
$757$		−	27.1428i		−	0.986522i	0.869881	−	0.493261i	$-0.164195\pi$
$758$	−8.90658	−	2.89392i	−0.323501	−	0.105112i
$759$	−29.3831	+	21.3480i	−1.06654	+	0.774885i
$760$	−0.530439	−	0.645124i	−0.0192410	−	0.0234011i
$761$	1.74251	+	1.26601i	0.0631660	+	0.0458928i	0.618920	−	0.785454i	$-0.287570\pi$
$761$	1.74251	+	1.26601i	0.0631660	+	0.0458928i	−0.555754	+	0.831347i	$0.687570\pi$
$762$	−14.1782	−	19.5147i	−0.513623	−	0.706942i
$763$	5.58204	+	7.68302i	0.202083	+	0.278144i
$764$	−4.32464	−	3.14204i	−0.156460	−	0.113675i
$765$	−0.672551	−	11.2277i	−0.0243161	−	0.405937i
$766$	29.5163	−	21.4448i	1.06647	−	0.774833i
$767$	88.9918	+	28.9152i	3.21331	+	1.04407i
$768$			2.32970i			0.0840659i
$769$	9.12467	−	28.0828i	0.329044	−	1.01269i	−0.640538	−	0.767926i	$-0.721289\pi$
$769$	9.12467	−	28.0828i	0.329044	−	1.01269i	0.969582	−	0.244767i	$-0.0787113\pi$
$770$	3.96323	−	0.237403i	0.142825	−	0.00855539i
$771$	0.974948	+	3.00058i	0.0351119	+	0.108063i
$772$	23.0609	−	7.49293i	0.829979	−	0.269676i
$773$	15.9075	−	21.8947i	0.572151	−	0.787499i	−0.420656	−	0.907220i	$-0.638200\pi$
$773$	15.9075	−	21.8947i	0.572151	−	0.787499i	0.992808	+	0.119721i	$0.0382001\pi$
$774$	−20.9931			−0.754580
$775$	28.5346	−	26.4752i	1.02499	−	0.951016i
$776$	−8.83729			−0.317240
$777$	2.08601	−	2.87114i	0.0748351	−	0.103002i
$778$	−12.2012	+	3.96442i	−0.437436	+	0.142131i
$779$	−0.720997	−	2.21900i	−0.0258324	−	0.0795039i
$780$	28.9410	+	18.4886i	1.03625	+	0.661998i
$781$	−3.55757	+	10.9491i	−0.127300	+	0.391789i
$782$		−	18.1935i		−	0.650599i
$783$	7.80130	+	2.53480i	0.278796	+	0.0905863i
$784$	0.809017	−	0.587785i	0.0288935	−	0.0209923i
$785$	−21.5621	−	5.60525i	−0.769583	−	0.200060i
$786$	19.6735	+	14.2936i	0.701729	+	0.509836i
$787$	3.41906	+	4.70593i	0.121876	+	0.167748i	0.865596	−	0.500744i	$-0.166940\pi$
$787$	3.41906	+	4.70593i	0.121876	+	0.167748i	−0.743719	+	0.668492i	$0.766940\pi$
$788$	−6.31934	−	8.69783i	−0.225117	−	0.309847i
$789$	4.85071	+	3.52425i	0.172690	+	0.125466i
$790$	−7.95296	+	12.4491i	−0.282954	+	0.442919i
$791$	13.3559	−	9.70360i	0.474880	−	0.345020i
$792$	−4.09931	−	1.33195i	−0.145663	−	0.0473286i
$793$			84.7009i			3.00782i
$794$	−1.50048	+	4.61800i	−0.0532500	+	0.163887i
$795$	−6.54029	−	16.6649i	−0.231960	−	0.591043i
$796$	2.41508	+	7.43285i	0.0856002	+	0.263450i
$797$	50.0267	−	16.2547i	1.77204	−	0.575770i	0.773708	−	0.633542i	$-0.218400\pi$
$797$	50.0267	−	16.2547i	1.77204	−	0.575770i	0.998330	+	0.0577717i	$0.0183996\pi$
$798$	0.511472	−	0.703981i	0.0181059	−	0.0249206i
$799$	11.7022			0.413996
$800$	−2.43503	+	4.36699i	−0.0860914	+	0.154396i
$801$	−20.3922			−0.720523
$802$	21.3139	−	29.3360i	0.752619	−	1.03589i
$803$	6.11214	−	1.98596i	0.215693	−	0.0700829i
$804$	−2.47217	−	7.60854i	−0.0871866	−	0.268333i
$805$	−15.1648	+	12.4689i	−0.534489	+	0.439472i
$806$	15.8594	−	48.8103i	0.558625	−	1.71927i
$807$		−	56.4634i		−	1.98761i
$808$	−7.21899	−	2.34559i	−0.253963	−	0.0825176i
$809$	−12.4952	+	9.07830i	−0.439308	+	0.319176i	−0.785360	−	0.619039i	$-0.787522\pi$
$809$	−12.4952	+	9.07830i	−0.439308	+	0.319176i	0.346052	+	0.938215i	$0.387522\pi$
$810$	−21.6262	+	8.48742i	−0.759869	+	0.298218i
$811$	−38.5300	−	27.9937i	−1.35297	−	0.982992i	−0.998857	−	0.0477908i	$-0.984782\pi$
$811$	−38.5300	−	27.9937i	−1.35297	−	0.982992i	−0.354116	−	0.935202i	$-0.615218\pi$
$812$	3.61505	+	4.97569i	0.126864	+	0.174613i
$813$	28.3521	+	39.0233i	0.994350	+	1.36861i
$814$	2.18825	+	1.58986i	0.0766981	+	0.0557244i
$815$	−35.7592	+	14.0341i	−1.25259	+	0.491591i
$816$	3.90552	−	2.83752i	0.136720	−	0.0993332i
$817$	3.07201	+	0.998157i	0.107476	+	0.0349211i
$818$			18.4738i			0.645920i
$819$	−4.94528	+	15.2200i	−0.172802	+	0.531830i
$820$	−10.7892	+	8.87117i	−0.376775	+	0.309795i
$821$	−16.0147	−	49.2881i	−0.558916	−	1.72017i	−0.685371	−	0.728194i	$-0.740360\pi$
$821$	−16.0147	−	49.2881i	−0.558916	−	1.72017i	0.126455	−	0.991972i	$-0.459640\pi$
$822$	−17.5256	+	5.69441i	−0.611275	+	0.198615i
$823$	14.7432	−	20.2923i	0.513917	−	0.707346i	−0.470657	−	0.882316i	$-0.655983\pi$
$823$	14.7432	−	20.2923i	0.513917	−	0.707346i	0.984574	+	0.174971i	$0.0559831\pi$
$824$	−10.2339			−0.356514
$825$	−14.0677	−	15.1620i	−0.489774	−	0.527872i
$826$	−14.1937			−0.493864
$827$	19.5685	−	26.9337i	0.680463	−	0.936577i	−0.319477	−	0.947594i	$-0.603507\pi$
$827$	19.5685	−	26.9337i	0.680463	−	0.936577i	0.999939	+	0.0110176i	$0.00350708\pi$
$828$	20.2705	−	6.58629i	0.704449	−	0.228889i
$829$	−0.383209	−	1.17940i	−0.0133094	−	0.0409621i	0.944181	−	0.329426i	$-0.106855\pi$
$829$	−0.383209	−	1.17940i	−0.0133094	−	0.0409621i	−0.957491	+	0.288464i	$0.906855\pi$
$830$	5.72420	+	14.5855i	0.198690	+	0.506269i
$831$	23.7445	−	73.0779i	0.823686	−	2.53504i
$832$			6.59244i			0.228552i
$833$	−1.97073	−	0.640328i	−0.0682817	−	0.0221861i
$834$	2.03991	−	1.48208i	0.0706363	−	0.0513203i
$835$	1.48759	−	2.32859i	0.0514802	−	0.0805840i
$836$	0.536541	+	0.389820i	0.0185566	+	0.0134822i
$837$	6.10299	+	8.40004i	0.210950	+	0.290348i
$838$	−0.00825060	−	0.0113560i	−0.000285012	−	0.000392286i
$839$	10.8587	+	7.88928i	0.374883	+	0.272368i	0.759233	−	0.650819i	$-0.225574\pi$
$839$	10.8587	+	7.88928i	0.374883	+	0.272368i	−0.384350	+	0.923187i	$0.625574\pi$
$840$	−5.04180	−	1.31066i	−0.173959	−	0.0452221i
$841$	−7.14050	+	5.18788i	−0.246224	+	0.178892i
$842$	1.67007	+	0.542640i	0.0575546	+	0.0187006i
$843$		−	31.6451i		−	1.08991i
$844$	2.37644	−	7.31394i	0.0818005	−	0.251756i
$845$	57.3985	+	36.6684i	1.97457	+	1.26143i
$846$	4.23636	+	13.0382i	0.145649	+	0.448262i
$847$	7.46321	−	2.42494i	0.256439	−	0.0833221i
$848$	2.01996	−	2.78024i	0.0693658	−	0.0954738i
$849$	−41.5625			−1.42642
$850$	10.2866	−	1.23680i	0.352829	−	0.0424220i
$851$	−13.3750			−0.458489
$852$	8.87867	−	12.2204i	0.304178	−	0.418666i
$853$	42.1695	−	13.7017i	1.44386	−	0.469137i	0.520758	−	0.853704i	$-0.325649\pi$
$853$	42.1695	−	13.7017i	1.44386	−	0.469137i	0.923097	+	0.384567i	$0.125649\pi$
$854$	−3.97030	−	12.2193i	−0.135861	−	0.418137i
$855$	−2.02382	+	0.121229i	−0.0692132	+	0.00414595i
$856$	−1.87185	+	5.76095i	−0.0639784	+	0.196905i
$857$			37.3037i			1.27427i	0.770753	+	0.637134i	$0.219880\pi$
$857$			37.3037i			1.27427i	−0.770753	+	0.637134i	$0.780120\pi$
$858$	−25.9356	−	8.42697i	−0.885425	−	0.287692i
$859$	28.9994	−	21.0693i	0.989448	−	0.718876i	0.0296476	−	0.999560i	$-0.490562\pi$
$859$	28.9994	−	21.0693i	0.989448	−	0.718876i	0.959800	+	0.280685i	$0.0905615\pi$
$860$	−1.15626	−	19.3028i	−0.0394283	−	0.658221i
$861$	−11.7735	−	8.55397i	−0.401241	−	0.291518i
$862$	5.17726	+	7.12589i	0.176338	+	0.242709i
$863$	−22.6617	−	31.1912i	−0.771414	−	1.06176i	−0.996178	−	0.0873471i	$-0.972161\pi$
$863$	−22.6617	−	31.1912i	−0.771414	−	1.06176i	0.224764	−	0.974413i	$-0.427839\pi$
$864$	−1.07900	−	0.783941i	−0.0367084	−	0.0266702i
$865$	−10.5745	−	12.8608i	−0.359544	−	0.437281i
$866$	−0.101534	+	0.0737691i	−0.00345028	+	0.00250678i
$867$	28.1529	+	9.14743i	0.956122	+	0.310663i
$868$			7.78501i			0.264240i
$869$	3.62490	−	11.1563i	0.122966	−	0.378452i
$870$	8.06095	−	31.0086i	0.273292	−	1.05129i
$871$	−6.99558	−	21.5302i	−0.237036	−	0.729522i
$872$	9.03193	−	2.93465i	0.305860	−	0.0993799i
$873$	−12.6096	+	17.3556i	−0.426769	+	0.587397i
$874$	−3.27944			−0.110929
$875$	−8.08086	−	7.72656i	−0.273183	−	0.261205i
$876$	−8.43229			−0.284901
$877$	9.96422	−	13.7146i	0.336468	−	0.463108i	−0.606938	−	0.794749i	$-0.707602\pi$
$877$	9.96422	−	13.7146i	0.336468	−	0.463108i	0.943406	+	0.331641i	$0.107602\pi$
$878$	3.16097	−	1.02706i	0.106678	−	0.0346616i
$879$	22.3861	+	68.8974i	0.755065	+	2.32385i
$880$	0.998923	−	3.84262i	0.0336737	−	0.129535i
$881$	−6.12265	+	18.8436i	−0.206277	+	0.634856i	0.793381	+	0.608725i	$0.208319\pi$
$881$	−6.12265	+	18.8436i	−0.206277	+	0.634856i	−0.999659	+	0.0261313i	$0.991681\pi$
$882$		−	2.42751i		−	0.0817387i
$883$	−34.6433	−	11.2563i	−1.16584	−	0.378804i	−0.338750	−	0.940876i	$-0.610004\pi$
$883$	−34.6433	−	11.2563i	−1.16584	−	0.378804i	−0.827088	+	0.562072i	$0.810004\pi$
$884$	11.0516	−	8.02945i	0.371705	−	0.270059i
$885$	46.9602	+	57.1134i	1.57855	+	1.91985i
$886$	−8.20913	−	5.96428i	−0.275791	−	0.200374i
$887$	20.9595	+	28.8483i	0.703752	+	0.968631i	0.999909	+	0.0134920i	$0.00429475\pi$
$887$	20.9595	+	28.8483i	0.703752	+	0.968631i	−0.296157	+	0.955139i	$0.595705\pi$
$888$	−2.08601	−	2.87114i	−0.0700019	−	0.0963493i
$889$	8.37646	+	6.08586i	0.280938	+	0.204113i
$890$	−1.12317	−	18.7503i	−0.0376487	−	0.628513i
$891$	14.9246	−	10.8434i	0.499994	−	0.363267i
$892$	11.7700	+	3.82430i	0.394089	+	0.128047i
$893$		−	2.10936i		−	0.0705871i
$894$	0.494712	−	1.52257i	0.0165456	−	0.0509222i
$895$	−13.9278	+	0.834291i	−0.465554	+	0.0278873i
$896$	−0.309017	−	0.951057i	−0.0103235	−	0.0317726i
$897$	128.248	−	41.6702i	4.28207	−	1.39133i
$898$	−14.3463	+	19.7460i	−0.478742	+	0.658932i
$899$	−47.8801			−1.59689
$900$	5.10189	+	11.0132i	0.170063	+	0.367108i
$901$	−7.12107			−0.237237
$902$	6.51943	−	8.97322i	0.217073	−	0.298776i
$903$	19.1611	−	6.22582i	0.637642	−	0.207182i
$904$	−5.10148	−	15.7008i	−0.169673	−	0.522199i
$905$	11.6913	+	7.46885i	0.388632	+	0.248273i
$906$	6.75920	−	20.8027i	0.224559	−	0.691123i
$907$		−	12.8916i		−	0.428060i	−0.976827	−	0.214030i	$-0.931341\pi$
$907$		−	12.8916i		−	0.428060i	0.976827	−	0.214030i	$-0.0686590\pi$
$908$	0.00550692	+	0.00178931i	0.000182754	+	5.93803e-5i
$909$	−14.9070	+	10.8306i	−0.494433	+	0.359227i
$910$	−14.2670	−	3.70882i	−0.472945	−	0.122946i
$911$	11.9905	+	8.71162i	0.397263	+	0.288629i	0.768425	−	0.639939i	$-0.221041\pi$
$911$	11.9905	+	8.71162i	0.397263	+	0.288629i	−0.371162	+	0.928568i	$0.621041\pi$
$912$	−0.511472	−	0.703981i	−0.0169365	−	0.0233111i
$913$	−7.31314	−	10.0657i	−0.242030	−	0.333125i
$914$	−9.57564	−	6.95711i	−0.316734	−	0.230121i
$915$	−36.0329	+	56.4037i	−1.19121	+	1.86465i
$916$	9.22374	−	6.70144i	0.304761	−	0.221422i
$917$	−9.92725	−	3.22556i	−0.327827	−	0.106517i
$918$			2.76366i			0.0912145i
$919$	14.5014	−	44.6306i	0.478356	−	1.47223i	−0.363022	−	0.931781i	$-0.618255\pi$
$919$	14.5014	−	44.6306i	0.478356	−	1.47223i	0.841378	−	0.540447i	$-0.181745\pi$
$920$	7.17247	+	18.2757i	0.236469	+	0.602532i
$921$	16.9546	+	52.1808i	0.558673	+	1.71942i
$922$	−1.29811	+	0.421781i	−0.0427509	+	0.0138906i
$923$	25.1243	−	34.5806i	0.826977	−	1.13824i
$924$	4.13659			0.136084
$925$	−0.909237	−	7.56224i	−0.0298955	−	0.248645i
$926$	21.0125			0.690513
$927$	−14.6023	+	20.0983i	−0.479601	+	0.660115i
$928$	5.84928	−	1.90055i	0.192012	−	0.0623885i
$929$	−3.69699	−	11.3782i	−0.121294	−	0.373305i	0.871913	−	0.489660i	$-0.162879\pi$
$929$	−3.69699	−	11.3782i	−0.121294	−	0.373305i	−0.993208	+	0.116355i	$0.962879\pi$
$930$	31.3256	−	25.7568i	1.02721	−	0.844599i
$931$	−0.115421	+	0.355229i	−0.00378277	+	0.0116422i
$932$		−	1.42005i		−	0.0465153i
$933$	38.9279	+	12.6484i	1.27444	+	0.414091i
$934$	26.0093	−	18.8968i	0.851049	−	0.618323i
$935$	−7.65844	+	3.00563i	−0.250458	+	0.0982945i
$936$	12.9469	+	9.40648i	0.423183	+	0.307460i
$937$	31.8943	+	43.8987i	1.04194	+	1.43411i	0.895592	+	0.444876i	$0.146752\pi$
$937$	31.8943	+	43.8987i	1.04194	+	1.43411i	0.146349	+	0.989233i	$0.453248\pi$
$938$	2.01843	+	2.77813i	0.0659040	+	0.0907091i
$939$	−40.6665	−	29.5460i	−1.32710	−	0.964197i
$940$	−11.7551	+	4.61340i	−0.383409	+	0.150472i
$941$	−14.2969	+	10.3873i	−0.466066	+	0.338617i	−0.795906	−	0.605420i	$-0.793005\pi$
$941$	−14.2969	+	10.3873i	−0.466066	+	0.338617i	0.329840	+	0.944037i	$0.393005\pi$
$942$	−22.0756	−	7.17279i	−0.719261	−	0.233702i
$943$			54.8460i			1.78603i
$944$	−4.38611	+	13.4991i	−0.142756	+	0.439357i
$945$	2.30359	−	1.89408i	0.0749358	−	0.0616143i
$946$	4.74502	+	14.6037i	0.154274	+	0.474807i
$947$	−41.5144	+	13.4889i	−1.34904	+	0.438329i	−0.892369	−	0.451307i	$-0.850958\pi$
$947$	−41.5144	+	13.4889i	−1.34904	+	0.438329i	−0.456669	+	0.889636i	$0.650958\pi$
$948$	−9.04672	+	12.4517i	−0.293824	+	0.404414i
$949$	−23.8612			−0.774566
$950$	−0.222937	−	1.85420i	−0.00723304	−	0.0601581i
$951$	−49.9148			−1.61860
$952$	−1.21798	+	1.67640i	−0.0394749	+	0.0543325i
$953$	−17.7087	+	5.75390i	−0.573641	+	0.186387i	−0.581450	−	0.813582i	$-0.697514\pi$
$953$	−17.7087	+	5.75390i	−0.573641	+	0.186387i	0.00780911	+	0.999970i	$0.497514\pi$
$954$	−2.57792	−	7.93401i	−0.0834631	−	0.256873i
$955$	−4.36682	−	11.1268i	−0.141307	−	0.360055i
$956$	0.410009	−	1.26188i	0.0132607	−	0.0408121i
$957$			25.4413i			0.822400i
$958$	−36.4498	−	11.8433i	−1.17764	−	0.382638i
$959$	6.39916	−	4.64926i	0.206640	−	0.150133i
$960$	−2.80451	+	4.39002i	−0.0905153	+	0.141687i
$961$	−23.9520	−	17.4022i	−0.772646	−	0.561360i
$962$	−5.90285	−	8.12458i	−0.190316	−	0.261947i
$963$	8.64308	+	11.8962i	0.278519	+	0.383349i
$964$	−20.0885	−	14.5951i	−0.647007	−	0.470078i
$965$	52.4752	+	13.6414i	1.68924	+	0.439132i
$966$	−16.5483	+	12.0231i	−0.532434	+	0.386836i
$967$	−34.1404	−	11.0929i	−1.09788	−	0.356723i	−0.296593	−	0.955004i	$-0.595851\pi$
$967$	−34.1404	−	11.0929i	−1.09788	−	0.356723i	−0.801286	+	0.598281i	$0.795851\pi$
$968$		−	7.84729i		−	0.252221i
$969$	−0.557193	+	1.71486i	−0.0178996	+	0.0550894i
$970$	−16.6527	−	10.6384i	−0.534687	−	0.341578i
$971$	5.69416	+	17.5248i	0.182734	+	0.562398i	0.999902	−	0.0140019i	$-0.00445708\pi$
$971$	5.69416	+	17.5248i	0.182734	+	0.562398i	−0.817168	+	0.576400i	$0.804457\pi$
$972$	−19.2149	+	6.24331i	−0.616320	+	0.200254i
$973$	−0.636167	+	0.875609i	−0.0203946	+	0.0280707i
$974$	−10.0581			−0.322281
$975$	32.2787	+	69.6787i	1.03375	+	2.23150i
$976$	−12.8482			−0.411260
$977$	9.80360	−	13.4935i	0.313645	−	0.431695i	−0.622869	−	0.782326i	$-0.714033\pi$
$977$	9.80360	−	13.4935i	0.313645	−	0.431695i	0.936514	+	0.350631i	$0.114033\pi$
$978$	−38.0643	+	12.3678i	−1.21716	+	0.395480i
$979$	4.60921	+	14.1857i	0.147311	+	0.453377i
$980$	2.23207	−	0.133704i	0.0713008	−	0.00427100i
$981$	7.12391	−	21.9251i	0.227449	−	0.700016i
$982$		−	16.4301i		−	0.524306i
$983$	20.8554	+	6.77635i	0.665186	+	0.216132i	0.622098	−	0.782939i	$-0.286281\pi$
$983$	20.8554	+	6.77635i	0.665186	+	0.216132i	0.0430876	+	0.999071i	$0.486281\pi$
$984$	−11.7735	+	8.55397i	−0.375326	+	0.272690i
$985$	−1.43746	−	23.9972i	−0.0458013	−	0.764614i
$986$	−10.3104	−	7.49092i	−0.328349	−	0.238559i
$987$	−7.73335	−	10.6440i	−0.246155	−	0.338804i
$988$	−1.44733	−	1.99208i	−0.0460457	−	0.0633765i
$989$	−61.4282	−	44.6302i	−1.95330	−	1.41916i
$990$	−6.12120	−	7.44466i	−0.194545	−	0.236607i
$991$	−8.02571	+	5.83102i	−0.254945	+	0.185228i	−0.707916	−	0.706297i	$-0.750364\pi$
$991$	−8.02571	+	5.83102i	−0.254945	+	0.185228i	0.452970	+	0.891526i	$0.350364\pi$
$992$	7.40398	+	2.40570i	0.235077	+	0.0763810i
$993$			65.3144i			2.07269i
$994$	−2.00360	+	6.16645i	−0.0635504	+	0.195588i
$995$	−4.39682	+	16.9135i	−0.139389	+	0.536195i
$996$	5.04459	+	15.5256i	0.159844	+	0.491949i
$997$	−16.1810	+	5.25754i	−0.512458	+	0.166508i	−0.553820	−	0.832636i	$-0.686830\pi$
$997$	−16.1810	+	5.25754i	−0.512458	+	0.166508i	0.0413616	+	0.999144i	$0.486830\pi$
$998$	−25.4384	+	35.0129i	−0.805238	+	1.10831i
$999$	2.03171			0.0642805

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.2.m.a.309.1	yes	24
25.8	odd	20		8750.2.a.z.1.1		12
25.14	even	10	inner	350.2.m.a.239.1	✓	24
25.17	odd	20		8750.2.a.bb.1.12		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.2.m.a.239.1	✓	24	25.14	even	10	inner
350.2.m.a.309.1	yes	24	1.1	even	1	trivial
8750.2.a.z.1.1		12	25.8	odd	20
8750.2.a.bb.1.12		12	25.17	odd	20

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	350.m (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.587785 + 0.809017i) q^{2} +(-2.21568 + 0.719918i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(0.562587 - 2.16414i) q^{5} +(0.719918 - 2.21568i) q^{6} +1.00000i q^{7} +(0.951057 + 0.309017i) q^{8} +(1.96390 - 1.42686i) q^{9} +O(q^{10})\)	\(q+(-0.587785 + 0.809017i) q^{2} +(-2.21568 + 0.719918i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(0.562587 - 2.16414i) q^{5} +(0.719918 - 2.21568i) q^{6} +1.00000i q^{7} +(0.951057 + 0.309017i) q^{8} +(1.96390 - 1.42686i) q^{9} +(1.42014 + 1.72719i) q^{10} +(-1.43648 - 1.04366i) q^{11} +(1.36936 + 1.88477i) q^{12} +(3.87494 + 5.33340i) q^{13} +(-0.809017 - 0.587785i) q^{14} +(0.311490 + 5.20005i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(1.97073 + 0.640328i) q^{17} +2.42751i q^{18} +(0.115421 - 0.355229i) q^{19} +(-2.23207 + 0.133704i) q^{20} +(-0.719918 - 2.21568i) q^{21} +(1.68868 - 0.548687i) q^{22} +(-5.16078 + 7.10320i) q^{23} -2.32970 q^{24} +(-4.36699 - 2.43503i) q^{25} -6.59244 q^{26} +(0.783941 - 1.07900i) q^{27} +(0.951057 - 0.309017i) q^{28} +(1.90055 + 5.84928i) q^{29} +(-4.39002 - 2.80451i) q^{30} +(-2.40570 + 7.40398i) q^{31} -1.00000i q^{32} +(3.93413 + 1.27828i) q^{33} +(-1.67640 + 1.21798i) q^{34} +(2.16414 + 0.562587i) q^{35} +(-1.96390 - 1.42686i) q^{36} +(0.895397 + 1.23241i) q^{37} +(0.219544 + 0.302176i) q^{38} +(-12.4252 - 9.02746i) q^{39} +(1.20381 - 1.88437i) q^{40} +(5.05366 - 3.67170i) q^{41} +(2.21568 + 0.719918i) q^{42} +8.64796i q^{43} +(-0.548687 + 1.68868i) q^{44} +(-1.98305 - 5.05288i) q^{45} +(-2.71318 - 8.35031i) q^{46} +(5.37100 - 1.74514i) q^{47} +(1.36936 - 1.88477i) q^{48} -1.00000 q^{49} +(4.53684 - 2.10169i) q^{50} -4.82748 q^{51} +(3.87494 - 5.33340i) q^{52} +(-3.26837 + 1.06196i) q^{53} +(0.412142 + 1.26844i) q^{54} +(-3.06678 + 2.52159i) q^{55} +(-0.309017 + 0.951057i) q^{56} +0.870168i q^{57} +(-5.84928 - 1.90055i) q^{58} +(11.4830 - 8.34288i) q^{59} +(4.84929 - 1.90315i) q^{60} +(10.3944 + 7.55197i) q^{61} +(-4.57591 - 6.29820i) q^{62} +(1.42686 + 1.96390i) q^{63} +(0.809017 + 0.587785i) q^{64} +(13.7222 - 5.38541i) q^{65} +(-3.34657 + 2.43143i) q^{66} +(-3.26589 - 1.06115i) q^{67} -2.07215i q^{68} +(6.32091 - 19.4537i) q^{69} +(-1.72719 + 1.42014i) q^{70} +(-2.00360 - 6.16645i) q^{71} +(2.30870 - 0.750143i) q^{72} +(-2.12747 + 2.92821i) q^{73} -1.52334 q^{74} +(11.4289 + 2.25138i) q^{75} -0.373510 q^{76} +(1.04366 - 1.43648i) q^{77} +(14.6067 - 4.74602i) q^{78} +(2.04152 + 6.28316i) q^{79} +(0.816906 + 2.08151i) q^{80} +(-3.21060 + 9.88121i) q^{81} +6.24667i q^{82} +(6.66422 + 2.16533i) q^{83} +(-1.88477 + 1.36936i) q^{84} +(2.49447 - 3.90469i) q^{85} +(-6.99635 - 5.08314i) q^{86} +(-8.42200 - 11.5919i) q^{87} +(-1.04366 - 1.43648i) q^{88} +(-6.79610 - 4.93765i) q^{89} +(5.25348 + 1.36569i) q^{90} +(-5.33340 + 3.87494i) q^{91} +(8.35031 + 2.71318i) q^{92} -18.1368i q^{93} +(-1.74514 + 5.37100i) q^{94} +(-0.703831 - 0.449635i) q^{95} +(0.719918 + 2.21568i) q^{96} +(-8.40476 + 2.73087i) q^{97} +(0.587785 - 0.809017i) q^{98} -4.31027 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{4} + 10 q^{5} + 2 q^{6} + 8 q^{9}+O(q^{10}) \) 24 * q + 6 * q^4 + 10 * q^5 + 2 * q^6 + 8 * q^9	\( 24 q + 6 q^{4} + 10 q^{5} + 2 q^{6} + 8 q^{9} + 2 q^{11} + 10 q^{12} - 6 q^{14} + 20 q^{15} - 6 q^{16} - 22 q^{19} - 2 q^{21} - 10 q^{22} - 10 q^{23} + 8 q^{24} - 10 q^{25} - 4 q^{26} - 30 q^{27} - 12 q^{29} - 10 q^{30} + 20 q^{33} - 8 q^{36} + 10 q^{37} - 10 q^{38} - 48 q^{39} + 10 q^{40} + 42 q^{41} - 2 q^{44} - 40 q^{45} + 10 q^{46} + 30 q^{47} + 10 q^{48} - 24 q^{49} + 20 q^{50} - 52 q^{51} + 10 q^{53} + 4 q^{54} + 10 q^{55} + 6 q^{56} - 20 q^{58} - 10 q^{60} + 46 q^{61} - 20 q^{63} + 6 q^{64} + 10 q^{65} - 10 q^{66} + 10 q^{67} + 32 q^{71} + 30 q^{73} - 28 q^{74} - 10 q^{75} - 48 q^{76} + 20 q^{77} - 20 q^{78} - 44 q^{79} + 76 q^{81} + 50 q^{83} + 2 q^{84} - 50 q^{85} - 6 q^{86} - 20 q^{87} - 20 q^{88} - 4 q^{89} + 50 q^{90} - 6 q^{91} + 30 q^{92} - 6 q^{94} - 60 q^{95} + 2 q^{96} + 30 q^{97} + 56 q^{99}+O(q^{100}) \) 24 * q + 6 * q^4 + 10 * q^5 + 2 * q^6 + 8 * q^9 + 2 * q^11 + 10 * q^12 - 6 * q^14 + 20 * q^15 - 6 * q^16 - 22 * q^19 - 2 * q^21 - 10 * q^22 - 10 * q^23 + 8 * q^24 - 10 * q^25 - 4 * q^26 - 30 * q^27 - 12 * q^29 - 10 * q^30 + 20 * q^33 - 8 * q^36 + 10 * q^37 - 10 * q^38 - 48 * q^39 + 10 * q^40 + 42 * q^41 - 2 * q^44 - 40 * q^45 + 10 * q^46 + 30 * q^47 + 10 * q^48 - 24 * q^49 + 20 * q^50 - 52 * q^51 + 10 * q^53 + 4 * q^54 + 10 * q^55 + 6 * q^56 - 20 * q^58 - 10 * q^60 + 46 * q^61 - 20 * q^63 + 6 * q^64 + 10 * q^65 - 10 * q^66 + 10 * q^67 + 32 * q^71 + 30 * q^73 - 28 * q^74 - 10 * q^75 - 48 * q^76 + 20 * q^77 - 20 * q^78 - 44 * q^79 + 76 * q^81 + 50 * q^83 + 2 * q^84 - 50 * q^85 - 6 * q^86 - 20 * q^87 - 20 * q^88 - 4 * q^89 + 50 * q^90 - 6 * q^91 + 30 * q^92 - 6 * q^94 - 60 * q^95 + 2 * q^96 + 30 * q^97 + 56 * q^99

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