LMFDB - Embedded newform 350.2.h.b.71.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("350.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.79476407074$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} + 6 x^{10} + x^{9} - 14 x^{8} + 10 x^{7} + 35 x^{6} - 110 x^{5} + 230 x^{4} + \cdots + 125 $ x^12 - 4x^11 + 6x^10 + x^9 - 14x^8 + 10x^7 + 35x^6 - 110x^5 + 230x^4 - 325x^3 + 300x^2 - 250x + 125
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			71.1
Root			$0.0830190 - 1.17264i$ of defining polynomial
Character	$\chi$	$=$	350.71
Dual form			350.2.h.b.281.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 + 0.951057i) q^{2} +(-2.43768 - 1.77108i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.539075 + 2.17011i) q^{5} +(2.43768 - 1.77108i) q^{6} -1.00000 q^{7} +(0.809017 - 0.587785i) q^{8} +(1.87852 + 5.78148i) q^{9} +O(q^{10})$	\(q+(-0.309017 + 0.951057i) q^{2} +(-2.43768 - 1.77108i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.539075 + 2.17011i) q^{5} +(2.43768 - 1.77108i) q^{6} -1.00000 q^{7} +(0.809017 - 0.587785i) q^{8} +(1.87852 + 5.78148i) q^{9} +(-2.23049 - 0.157911i) q^{10} +(0.0566555 - 0.174368i) q^{11} +(0.931111 + 2.86567i) q^{12} +(-1.11047 - 3.41769i) q^{13} +(0.309017 - 0.951057i) q^{14} +(2.52935 - 6.24479i) q^{15} +(0.309017 + 0.951057i) q^{16} +(5.79026 - 4.20687i) q^{17} -6.07900 q^{18} +(1.35146 - 0.981894i) q^{19} +(0.839441 - 2.07252i) q^{20} +(2.43768 + 1.77108i) q^{21} +(0.148326 + 0.107765i) q^{22} +(2.22771 - 6.85619i) q^{23} -3.01314 q^{24} +(-4.41880 + 2.33971i) q^{25} +3.59357 q^{26} +(2.86689 - 8.82340i) q^{27} +(0.809017 + 0.587785i) q^{28} +(3.90082 + 2.83411i) q^{29} +(5.15754 + 4.33530i) q^{30} +(6.84109 - 4.97034i) q^{31} -1.00000 q^{32} +(-0.446927 + 0.324711i) q^{33} +(2.21168 + 6.80686i) q^{34} +(-0.539075 - 2.17011i) q^{35} +(1.87852 - 5.78148i) q^{36} +(1.89780 + 5.84083i) q^{37} +(0.516212 + 1.58874i) q^{38} +(-3.34601 + 10.2980i) q^{39} +(1.71168 + 1.43880i) q^{40} +(-1.90862 - 5.87414i) q^{41} +(-2.43768 + 1.77108i) q^{42} +0.989435 q^{43} +(-0.148326 + 0.107765i) q^{44} +(-11.5338 + 7.19324i) q^{45} +(5.83223 + 4.23736i) q^{46} +(-9.37800 - 6.81352i) q^{47} +(0.931111 - 2.86567i) q^{48} +1.00000 q^{49} +(-0.859713 - 4.92553i) q^{50} -21.5655 q^{51} +(-1.11047 + 3.41769i) q^{52} +(4.61189 + 3.35074i) q^{53} +(7.50563 + 5.45316i) q^{54} +(0.408939 + 0.0289516i) q^{55} +(-0.809017 + 0.587785i) q^{56} -5.03344 q^{57} +(-3.90082 + 2.83411i) q^{58} +(0.675993 + 2.08049i) q^{59} +(-5.71688 + 3.56543i) q^{60} +(0.813077 - 2.50239i) q^{61} +(2.61306 + 8.04218i) q^{62} +(-1.87852 - 5.78148i) q^{63} +(0.309017 - 0.951057i) q^{64} +(6.81814 - 4.25224i) q^{65} +(-0.170711 - 0.525394i) q^{66} +(-2.22630 + 1.61750i) q^{67} -7.15715 q^{68} +(-17.5733 + 12.7678i) q^{69} +(2.23049 + 0.157911i) q^{70} +(11.5239 + 8.37258i) q^{71} +(4.91802 + 3.57315i) q^{72} +(-2.51052 + 7.72658i) q^{73} -6.14141 q^{74} +(14.9154 + 2.12257i) q^{75} -1.67050 q^{76} +(-0.0566555 + 0.174368i) q^{77} +(-8.75997 - 6.36449i) q^{78} +(-4.65710 - 3.38358i) q^{79} +(-1.89732 + 1.18329i) q^{80} +(-7.86144 + 5.71167i) q^{81} +6.17644 q^{82} +(3.80832 - 2.76690i) q^{83} +(-0.931111 - 2.86567i) q^{84} +(12.2508 + 10.2977i) q^{85} +(-0.305752 + 0.941009i) q^{86} +(-4.48952 - 13.8173i) q^{87} +(-0.0566555 - 0.174368i) q^{88} +(4.85584 - 14.9447i) q^{89} +(-3.27704 - 13.1921i) q^{90} +(1.11047 + 3.41769i) q^{91} +(-5.83223 + 4.23736i) q^{92} -25.4793 q^{93} +(9.37800 - 6.81352i) q^{94} +(2.85936 + 2.40351i) q^{95} +(2.43768 + 1.77108i) q^{96} +(-1.07428 - 0.780511i) q^{97} +(-0.309017 + 0.951057i) q^{98} +1.11453 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} + q^{3} - 3 q^{4} - 5 q^{5} - q^{6} - 12 q^{7} + 3 q^{8} + 6 q^{9}+O(q^{10}) $ 12 * q + 3 * q^2 + q^3 - 3 * q^4 - 5 * q^5 - q^6 - 12 * q^7 + 3 * q^8 + 6 * q^9	\( 12 q + 3 q^{2} + q^{3} - 3 q^{4} - 5 q^{5} - q^{6} - 12 q^{7} + 3 q^{8} + 6 q^{9} + 7 q^{11} - 4 q^{12} + 3 q^{13} - 3 q^{14} - 10 q^{15} - 3 q^{16} + 4 q^{17} - 6 q^{18} + 4 q^{19} + 5 q^{20} - q^{21} - 2 q^{22} - q^{23} - 6 q^{24} - 5 q^{25} + 12 q^{26} + 10 q^{27} + 3 q^{28} + 22 q^{29} + 15 q^{30} + 31 q^{31} - 12 q^{32} - 21 q^{33} + 6 q^{34} + 5 q^{35} + 6 q^{36} + 9 q^{37} - 4 q^{38} - 20 q^{39} - 19 q^{41} + q^{42} + 50 q^{43} + 2 q^{44} - 25 q^{45} + 16 q^{46} - 24 q^{47} - 4 q^{48} + 12 q^{49} - 58 q^{51} + 3 q^{52} + 35 q^{53} + 25 q^{54} - 10 q^{55} - 3 q^{56} - 44 q^{57} - 22 q^{58} + q^{59} - 5 q^{60} + 8 q^{61} + 19 q^{62} - 6 q^{63} - 3 q^{64} - 25 q^{65} - 14 q^{66} - 36 q^{67} + 4 q^{68} - 31 q^{69} + q^{71} + 9 q^{72} - 31 q^{73} - 14 q^{74} + 55 q^{75} - 16 q^{76} - 7 q^{77} - 30 q^{78} + 2 q^{79} - 8 q^{81} - 6 q^{82} - 19 q^{83} + 4 q^{84} + 20 q^{85} + 10 q^{86} + 28 q^{87} - 7 q^{88} + 40 q^{89} + 20 q^{90} - 3 q^{91} - 16 q^{92} + 50 q^{93} + 24 q^{94} - q^{96} + 28 q^{97} + 3 q^{98} - 24 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 + q^3 - 3 * q^4 - 5 * q^5 - q^6 - 12 * q^7 + 3 * q^8 + 6 * q^9 + 7 * q^11 - 4 * q^12 + 3 * q^13 - 3 * q^14 - 10 * q^15 - 3 * q^16 + 4 * q^17 - 6 * q^18 + 4 * q^19 + 5 * q^20 - q^21 - 2 * q^22 - q^23 - 6 * q^24 - 5 * q^25 + 12 * q^26 + 10 * q^27 + 3 * q^28 + 22 * q^29 + 15 * q^30 + 31 * q^31 - 12 * q^32 - 21 * q^33 + 6 * q^34 + 5 * q^35 + 6 * q^36 + 9 * q^37 - 4 * q^38 - 20 * q^39 - 19 * q^41 + q^42 + 50 * q^43 + 2 * q^44 - 25 * q^45 + 16 * q^46 - 24 * q^47 - 4 * q^48 + 12 * q^49 - 58 * q^51 + 3 * q^52 + 35 * q^53 + 25 * q^54 - 10 * q^55 - 3 * q^56 - 44 * q^57 - 22 * q^58 + q^59 - 5 * q^60 + 8 * q^61 + 19 * q^62 - 6 * q^63 - 3 * q^64 - 25 * q^65 - 14 * q^66 - 36 * q^67 + 4 * q^68 - 31 * q^69 + q^71 + 9 * q^72 - 31 * q^73 - 14 * q^74 + 55 * q^75 - 16 * q^76 - 7 * q^77 - 30 * q^78 + 2 * q^79 - 8 * q^81 - 6 * q^82 - 19 * q^83 + 4 * q^84 + 20 * q^85 + 10 * q^86 + 28 * q^87 - 7 * q^88 + 40 * q^89 + 20 * q^90 - 3 * q^91 - 16 * q^92 + 50 * q^93 + 24 * q^94 - q^96 + 28 * q^97 + 3 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

Coefficient data

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

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

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

$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$3$	−2.43768	−	1.77108i	−1.40740	−	1.02253i	−0.993695	−	0.112120i	$-0.964236\pi$
$3$	−2.43768	−	1.77108i	−1.40740	−	1.02253i	−0.413701	−	0.910413i	$-0.635764\pi$
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	0.539075	+	2.17011i	0.241082	+	0.970505i
$5$	0.539075	+	2.17011i	0.241082	+	0.970505i
$6$	2.43768	−	1.77108i	0.995179	−	0.723040i
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$	0.809017	−	0.587785i	0.286031	−	0.207813i
$9$	1.87852	+	5.78148i	0.626172	+	1.92716i
$10$	−2.23049	−	0.157911i	−0.705341	−	0.0499360i
$11$	0.0566555	−	0.174368i	0.0170823	−	0.0525738i	−0.942152	−	0.335186i	$-0.891201\pi$
$11$	0.0566555	−	0.174368i	0.0170823	−	0.0525738i	0.959234	+	0.282612i	$0.0912009\pi$
$12$	0.931111	+	2.86567i	0.268789	+	0.827246i
$13$	−1.11047	−	3.41769i	−0.307990	−	0.947895i	−0.978545	−	0.206035i	$-0.933944\pi$
$13$	−1.11047	−	3.41769i	−0.307990	−	0.947895i	0.670555	−	0.741860i	$-0.266056\pi$
$14$	0.309017	−	0.951057i	0.0825883	−	0.254181i
$15$	2.52935	−	6.24479i	0.653076	−	1.61240i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	5.79026	−	4.20687i	1.40434	−	1.02032i	0.410230	−	0.911982i	$-0.365449\pi$
$17$	5.79026	−	4.20687i	1.40434	−	1.02032i	0.994115	−	0.108334i	$-0.0345514\pi$
$18$	−6.07900			−1.43284
$19$	1.35146	−	0.981894i	0.310046	−	0.225262i	−0.421870	−	0.906656i	$-0.638626\pi$
$19$	1.35146	−	0.981894i	0.310046	−	0.225262i	0.731916	+	0.681394i	$0.238626\pi$
$20$	0.839441	−	2.07252i	0.187705	−	0.463430i
$21$	2.43768	+	1.77108i	0.531945	+	0.386481i
$22$	0.148326	+	0.107765i	0.0316232	+	0.0229756i
$23$	2.22771	−	6.85619i	0.464510	−	1.42961i	−0.395088	−	0.918643i	$-0.629286\pi$
$23$	2.22771	−	6.85619i	0.464510	−	1.42961i	0.859598	−	0.510971i	$-0.170714\pi$
$24$	−3.01314			−0.615054
$25$	−4.41880	+	2.33971i	−0.883759	+	0.467942i
$26$	3.59357			0.704756
$27$	2.86689	−	8.82340i	0.551734	−	1.69806i
$28$	0.809017	+	0.587785i	0.152890	+	0.111081i
$29$	3.90082	+	2.83411i	0.724364	+	0.526281i	0.887775	−	0.460277i	$-0.152250\pi$
$29$	3.90082	+	2.83411i	0.724364	+	0.526281i	−0.163412	+	0.986558i	$0.552250\pi$
$30$	5.15754	+	4.33530i	0.941633	+	0.791514i
$31$	6.84109	−	4.97034i	1.22870	−	0.892700i	0.231904	−	0.972739i	$-0.425504\pi$
$31$	6.84109	−	4.97034i	1.22870	−	0.892700i	0.996792	+	0.0800387i	$0.0255044\pi$
$32$	−1.00000			−0.176777
$33$	−0.446927	+	0.324711i	−0.0777999	+	0.0565250i
$34$	2.21168	+	6.80686i	0.379300	+	1.16737i
$35$	−0.539075	−	2.17011i	−0.0911203	−	0.366816i
$36$	1.87852	−	5.78148i	0.313086	−	0.963579i
$37$	1.89780	+	5.84083i	0.311996	+	0.960226i	0.976973	+	0.213362i	$0.0684414\pi$
$37$	1.89780	+	5.84083i	0.311996	+	0.960226i	−0.664977	+	0.746864i	$0.731559\pi$
$38$	0.516212	+	1.58874i	0.0837407	+	0.257727i
$39$	−3.34601	+	10.2980i	−0.535790	+	1.64899i
$40$	1.71168	+	1.43880i	0.270641	+	0.227494i
$41$	−1.90862	−	5.87414i	−0.298077	−	0.917387i	−0.982170	−	0.187993i	$-0.939802\pi$
$41$	−1.90862	−	5.87414i	−0.298077	−	0.917387i	0.684093	−	0.729395i	$-0.260198\pi$
$42$	−2.43768	+	1.77108i	−0.376142	+	0.273283i
$43$	0.989435			0.150887			0.0754437	−	0.997150i	$-0.475963\pi$
$43$	0.989435			0.150887			0.0754437	+	0.997150i	$0.475963\pi$
$44$	−0.148326	+	0.107765i	−0.0223610	+	0.0162462i
$45$	−11.5338	+	7.19324i	−1.71936	+	1.07231i
$46$	5.83223	+	4.23736i	0.859915	+	0.624765i
$47$	−9.37800	−	6.81352i	−1.36792	−	0.993854i	−0.997896	−	0.0648322i	$-0.979349\pi$
$47$	−9.37800	−	6.81352i	−1.36792	−	0.993854i	−0.370026	−	0.929021i	$-0.620651\pi$
$48$	0.931111	−	2.86567i	0.134394	−	0.413623i
$49$	1.00000			0.142857
$50$	−0.859713	−	4.92553i	−0.121582	−	0.696576i
$51$	−21.5655			−3.01977
$52$	−1.11047	+	3.41769i	−0.153995	+	0.473948i
$53$	4.61189	+	3.35074i	0.633492	+	0.460259i	0.857608	−	0.514304i	$-0.171950\pi$
$53$	4.61189	+	3.35074i	0.633492	+	0.460259i	−0.224116	+	0.974562i	$0.571950\pi$
$54$	7.50563	+	5.45316i	1.02139	+	0.742081i
$55$	0.408939	+	0.0289516i	0.0551414	+	0.00390384i
$56$	−0.809017	+	0.587785i	−0.108109	+	0.0785461i
$57$	−5.03344			−0.666696
$58$	−3.90082	+	2.83411i	−0.512203	+	0.372137i
$59$	0.675993	+	2.08049i	0.0880068	+	0.270857i	0.985368	−	0.170439i	$-0.0545187\pi$
$59$	0.675993	+	2.08049i	0.0880068	+	0.270857i	−0.897361	+	0.441297i	$0.854519\pi$
$60$	−5.71688	+	3.56543i	−0.738046	+	0.460295i
$61$	0.813077	−	2.50239i	0.104104	−	0.320399i	−0.885415	−	0.464801i	$-0.846126\pi$
$61$	0.813077	−	2.50239i	0.104104	−	0.320399i	0.989519	+	0.144402i	$0.0461259\pi$
$62$	2.61306	+	8.04218i	0.331859	+	1.02136i
$63$	−1.87852	−	5.78148i	−0.236671	−	0.728398i
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	6.81814	−	4.25224i	0.845686	−	0.527426i
$66$	−0.170711	−	0.525394i	−0.0210130	−	0.0646715i
$67$	−2.22630	+	1.61750i	−0.271986	+	0.197609i	−0.715414	−	0.698701i	$-0.753762\pi$
$67$	−2.22630	+	1.61750i	−0.271986	+	0.197609i	0.443429	+	0.896310i	$0.353762\pi$
$68$	−7.15715			−0.867932
$69$	−17.5733	+	12.7678i	−2.11558	+	1.53706i
$70$	2.23049	+	0.157911i	0.266594	+	0.0188740i
$71$	11.5239	+	8.37258i	1.36763	+	0.993642i	0.997918	+	0.0644961i	$0.0205440\pi$
$71$	11.5239	+	8.37258i	1.36763	+	0.993642i	0.369713	+	0.929146i	$0.379456\pi$
$72$	4.91802	+	3.57315i	0.579594	+	0.421100i
$73$	−2.51052	+	7.72658i	−0.293834	+	0.904327i	0.689777	+	0.724022i	$0.257709\pi$
$73$	−2.51052	+	7.72658i	−0.293834	+	0.904327i	−0.983611	+	0.180305i	$0.942291\pi$
$74$	−6.14141			−0.713924
$75$	14.9154	+	2.12257i	1.72228	+	0.245093i
$76$	−1.67050			−0.191619
$77$	−0.0566555	+	0.174368i	−0.00645649	+	0.0198710i
$78$	−8.75997	−	6.36449i	−0.991871	−	0.720636i
$79$	−4.65710	−	3.38358i	−0.523965	−	0.380683i	0.294130	−	0.955765i	$-0.404970\pi$
$79$	−4.65710	−	3.38358i	−0.523965	−	0.380683i	−0.818096	+	0.575082i	$0.804970\pi$
$80$	−1.89732	+	1.18329i	−0.212127	+	0.132296i
$81$	−7.86144	+	5.71167i	−0.873494	+	0.634630i
$82$	6.17644			0.682074
$83$	3.80832	−	2.76690i	0.418017	−	0.303707i	−0.358822	−	0.933406i	$-0.616822\pi$
$83$	3.80832	−	2.76690i	0.418017	−	0.303707i	0.776840	+	0.629699i	$0.216822\pi$
$84$	−0.931111	−	2.86567i	−0.101593	−	0.312670i
$85$	12.2508	+	10.2977i	1.32878	+	1.11694i
$86$	−0.305752	+	0.941009i	−0.0329701	+	0.101472i
$87$	−4.48952	−	13.8173i	−0.481327	−	1.48137i
$88$	−0.0566555	−	0.174368i	−0.00603949	−	0.0185876i
$89$	4.85584	−	14.9447i	0.514718	−	1.58414i	−0.269078	−	0.963118i	$-0.586719\pi$
$89$	4.85584	−	14.9447i	0.514718	−	1.58414i	0.783795	−	0.621019i	$-0.213281\pi$
$90$	−3.27704	−	13.1921i	−0.345430	−	1.39057i
$91$	1.11047	+	3.41769i	0.116409	+	0.358271i
$92$	−5.83223	+	4.23736i	−0.608052	+	0.441775i
$93$	−25.4793			−2.64208
$94$	9.37800	−	6.81352i	0.967267	−	0.702761i
$95$	2.85936	+	2.40351i	0.293364	+	0.246595i
$96$	2.43768	+	1.77108i	0.248795	+	0.180760i
$97$	−1.07428	−	0.780511i	−0.109077	−	0.0792489i	0.531910	−	0.846801i	$-0.321475\pi$
$97$	−1.07428	−	0.780511i	−0.109077	−	0.0792489i	−0.640986	+	0.767552i	$0.721475\pi$
$98$	−0.309017	+	0.951057i	−0.0312154	+	0.0960712i
$99$	1.11453			0.112015
$100$	4.95013	+	0.704439i	0.495013	+	0.0704439i
$101$	−7.97596			−0.793638			−0.396819	−	0.917897i	$-0.629886\pi$
$101$	−7.97596			−0.793638			−0.396819	+	0.917897i	$0.629886\pi$
$102$	6.66411	−	20.5100i	0.659845	−	2.03079i
$103$	10.2618	+	7.45566i	1.01113	+	0.734628i	0.964446	−	0.264282i	$-0.0851348\pi$
$103$	10.2618	+	7.45566i	1.01113	+	0.734628i	0.0466833	+	0.998910i	$0.485135\pi$
$104$	−2.90726	−	2.11225i	−0.285080	−	0.207123i
$105$	−2.52935	+	6.24479i	−0.246839	+	0.609429i
$106$	−4.61189	+	3.35074i	−0.447947	+	0.325452i
$107$	−11.7747			−1.13830			−0.569152	−	0.822232i	$-0.692729\pi$
$107$	−11.7747			−1.13830			−0.569152	+	0.822232i	$0.692729\pi$
$108$	−7.50563	+	5.45316i	−0.722229	+	0.524730i
$109$	−5.23491	−	16.1114i	−0.501413	−	1.54319i	−0.806718	−	0.590937i	$-0.798758\pi$
$109$	−5.23491	−	16.1114i	−0.501413	−	1.54319i	0.305304	−	0.952255i	$-0.401242\pi$
$110$	−0.153904	+	0.379978i	−0.0146742	+	0.0362295i
$111$	5.71833	−	17.5992i	0.542760	−	1.67044i
$112$	−0.309017	−	0.951057i	−0.0291994	−	0.0898664i
$113$	−0.648447	−	1.99572i	−0.0610008	−	0.187741i	0.915912	−	0.401379i	$-0.131469\pi$
$113$	−0.648447	−	1.99572i	−0.0610008	−	0.187741i	−0.976913	+	0.213638i	$0.931469\pi$
$114$	1.55542	−	4.78709i	0.145678	−	0.448352i
$115$	16.0796	+	1.13839i	1.49943	+	0.106155i
$116$	−1.48998	−	4.58569i	−0.138341	−	0.425770i
$117$	17.6732	−	12.8404i	1.63389	−	1.18709i
$118$	−2.18756			−0.201381
$119$	−5.79026	+	4.20687i	−0.530792	+	0.385643i
$120$	−1.62431	−	6.53886i	−0.148278	−	0.596913i
$121$	8.87199	+	6.44588i	0.806545	+	0.585989i
$122$	2.12866	+	1.54656i	0.192720	+	0.140019i
$123$	−5.75095	+	17.6996i	−0.518546	+	1.59592i
$124$	−8.45605			−0.759376
$125$	−7.45950	−	8.32802i	−0.667198	−	0.744880i
$126$	6.07900			0.541561
$127$	1.39405	−	4.29046i	0.123702	−	0.380716i	−0.869960	−	0.493122i	$-0.835856\pi$
$127$	1.39405	−	4.29046i	0.123702	−	0.380716i	0.993662	+	0.112406i	$0.0358556\pi$
$128$	0.809017	+	0.587785i	0.0715077	+	0.0519534i
$129$	−2.41193	−	1.75237i	−0.212358	−	0.154287i
$130$	1.93720	+	7.79845i	0.169904	+	0.683970i
$131$	2.12456	−	1.54358i	0.185624	−	0.134863i	−0.491093	−	0.871107i	$-0.663402\pi$
$131$	2.12456	−	1.54358i	0.185624	−	0.134863i	0.676716	+	0.736244i	$0.263402\pi$
$132$	0.552432			0.0480830
$133$	−1.35146	+	0.981894i	−0.117187	+	0.0851410i
$134$	−0.850370	−	2.61717i	−0.0734608	−	0.226089i
$135$	20.6933	+	1.46502i	1.78099	+	0.126089i
$136$	2.21168	−	6.80686i	0.189650	−	0.583683i
$137$	−2.92992	−	9.01738i	−0.250320	−	0.770406i	−0.994716	−	0.102667i	$-0.967262\pi$
$137$	−2.92992	−	9.01738i	−0.250320	−	0.770406i	0.744396	−	0.667739i	$-0.232738\pi$
$138$	−6.71240	−	20.6587i	−0.571398	−	1.75858i
$139$	−6.26001	+	19.2663i	−0.530967	+	1.63415i	0.221239	+	0.975220i	$0.428990\pi$
$139$	−6.26001	+	19.2663i	−0.530967	+	1.63415i	−0.752206	+	0.658928i	$0.771010\pi$
$140$	−0.839441	+	2.07252i	−0.0709457	+	0.175160i
$141$	10.7933	+	33.2184i	0.908960	+	2.79749i
$142$	−11.5239	+	8.37258i	−0.967061	+	0.702611i
$143$	−0.658848			−0.0550956
$144$	−4.91802	+	3.57315i	−0.409835	+	0.297762i
$145$	−4.04751	+	9.99302i	−0.336128	+	0.829875i
$146$	−6.57262	−	4.77529i	−0.543954	−	0.395205i
$147$	−2.43768	−	1.77108i	−0.201056	−	0.146076i
$148$	1.89780	−	5.84083i	0.155998	−	0.480113i
$149$	2.43852			0.199771			0.0998857	−	0.994999i	$-0.468152\pi$
$149$	2.43852			0.199771			0.0998857	+	0.994999i	$0.468152\pi$
$150$	−6.62780	+	13.5295i	−0.541158	+	1.10468i
$151$	−10.5251			−0.856522			−0.428261	−	0.903655i	$-0.640874\pi$
$151$	−10.5251			−0.856522			−0.428261	+	0.903655i	$0.640874\pi$
$152$	0.516212	−	1.58874i	0.0418703	−	0.128864i
$153$	35.1990	+	25.5736i	2.84567	+	2.06750i
$154$	−0.148326	−	0.107765i	−0.0119524	−	0.00868396i
$155$	14.4741	+	12.1666i	1.16259	+	0.977242i
$156$	8.75997	−	6.36449i	0.701359	−	0.509567i
$157$	10.5082			0.838645			0.419322	−	0.907837i	$-0.362268\pi$
$157$	10.5082			0.838645			0.419322	+	0.907837i	$0.362268\pi$
$158$	4.65710	−	3.38358i	0.370499	−	0.269184i
$159$	−5.30790	−	16.3360i	−0.420944	−	1.29553i
$160$	−0.539075	−	2.17011i	−0.0426176	−	0.171563i
$161$	−2.22771	+	6.85619i	−0.175568	+	0.540344i
$162$	−3.00280	−	9.24168i	−0.235923	−	0.726095i
$163$	2.42937	+	7.47684i	0.190283	+	0.585631i	0.999999	−	0.00119043i	$-0.000378925\pi$
$163$	2.42937	+	7.47684i	0.190283	+	0.585631i	−0.809716	+	0.586822i	$0.800379\pi$
$164$	−1.90862	+	5.87414i	−0.149039	+	0.458694i
$165$	−0.945587	−	0.794838i	−0.0736139	−	0.0618781i
$166$	1.45465	+	4.47695i	0.112903	+	0.347478i
$167$	4.13770	−	3.00621i	0.320185	−	0.232628i	−0.416070	−	0.909333i	$-0.636593\pi$
$167$	4.13770	−	3.00621i	0.320185	−	0.232628i	0.736254	+	0.676705i	$0.236593\pi$
$168$	3.01314			0.232469
$169$	0.0697990	−	0.0507120i	0.00536916	−	0.00390092i
$170$	−13.5794	+	8.46901i	−1.04149	+	0.649544i
$171$	8.21554	+	5.96894i	0.628258	+	0.456456i
$172$	−0.800470	−	0.581575i	−0.0610353	−	0.0443447i
$173$	1.91079	−	5.88081i	0.145275	−	0.447110i	−0.851772	−	0.523913i	$-0.824472\pi$
$173$	1.91079	−	5.88081i	0.145275	−	0.447110i	0.997046	+	0.0768039i	$0.0244715\pi$
$174$	14.5284			1.10139
$175$	4.41880	−	2.33971i	0.334030	−	0.176865i
$176$	0.183341			0.0138198
$177$	2.03686	−	6.26881i	0.153100	−	0.471193i
$178$	12.7127	+	9.23635i	0.952860	+	0.692294i
$179$	12.1067	+	8.79605i	0.904899	+	0.657448i	0.939720	−	0.341946i	$-0.111086\pi$
$179$	12.1067	+	8.79605i	0.904899	+	0.657448i	−0.0348203	+	0.999394i	$0.511086\pi$
$180$	13.5591	+	0.959945i	1.01064	+	0.0715501i
$181$	5.30518	−	3.85444i	0.394331	−	0.286498i	−0.372897	−	0.927873i	$-0.621635\pi$
$181$	5.30518	−	3.85444i	0.394331	−	0.286498i	0.767228	+	0.641374i	$0.221635\pi$
$182$	−3.59357			−0.266373
$183$	−6.41396	+	4.66001i	−0.474133	+	0.344478i
$184$	−2.22771	−	6.85619i	−0.164229	−	0.505445i
$185$	−11.6522	+	7.26709i	−0.856687	+	0.534287i
$186$	7.87352	−	24.2322i	0.577315	−	1.77679i
$187$	−0.405492	−	1.24798i	−0.0296525	−	0.0912610i
$188$	3.58208	+	11.0245i	0.261250	+	0.804044i
$189$	−2.86689	+	8.82340i	−0.208536	+	0.641808i
$190$	−3.16947	+	1.97669i	−0.229937	+	0.143404i
$191$	−5.96192	−	18.3489i	−0.431389	−	1.32768i	−0.896742	−	0.442554i	$-0.854073\pi$
$191$	−5.96192	−	18.3489i	−0.431389	−	1.32768i	0.465353	−	0.885125i	$-0.345927\pi$
$192$	−2.43768	+	1.77108i	−0.175924	+	0.127817i
$193$	7.70061			0.554302			0.277151	−	0.960826i	$-0.410610\pi$
$193$	7.70061			0.554302			0.277151	+	0.960826i	$0.410610\pi$
$194$	1.07428	−	0.780511i	0.0771289	−	0.0560374i
$195$	−24.1515	−	1.70985i	−1.72953	−	0.122445i
$196$	−0.809017	−	0.587785i	−0.0577869	−	0.0419847i
$197$	−15.3897	−	11.1813i	−1.09647	−	0.796633i	−0.115991	−	0.993250i	$-0.537004\pi$
$197$	−15.3897	−	11.1813i	−1.09647	−	0.796633i	−0.980480	+	0.196617i	$0.937004\pi$
$198$	−0.344409	+	1.05998i	−0.0244761	+	0.0753296i
$199$	−27.9000			−1.97778			−0.988891	−	0.148643i	$-0.952509\pi$
$199$	−27.9000			−1.97778			−0.988891	+	0.148643i	$0.952509\pi$
$200$	−2.19963	+	4.49017i	−0.155538	+	0.317503i
$201$	8.29172			0.584853
$202$	2.46471	−	7.58559i	0.173416	−	0.533720i
$203$	−3.90082	−	2.83411i	−0.273784	−	0.198916i
$204$	17.4469	+	12.6759i	1.22152	+	0.887489i
$205$	11.7187	−	7.30854i	0.818468	−	0.510451i
$206$	−10.2618	+	7.45566i	−0.714976	+	0.519461i
$207$	43.8237			3.04596
$208$	2.90726	−	2.11225i	0.201582	−	0.146458i
$209$	−0.0946428	−	0.291281i	−0.00654658	−	0.0201483i
$210$	−5.15754	−	4.33530i	−0.355904	−	0.299164i
$211$	2.97735	−	9.16333i	0.204969	−	0.630830i	−0.794746	−	0.606943i	$-0.792396\pi$
$211$	2.97735	−	9.16333i	0.204969	−	0.630830i	0.999715	−	0.0238872i	$-0.00760426\pi$
$212$	−1.76159	−	5.42160i	−0.120986	−	0.372357i
$213$	−13.2630	−	40.8193i	−0.908766	−	2.79689i
$214$	3.63859	−	11.1984i	0.248729	−	0.765508i
$215$	0.533380	+	2.14719i	0.0363762	+	0.146437i
$216$	−2.86689	−	8.82340i	−0.195067	−	0.600356i
$217$	−6.84109	+	4.97034i	−0.464403	+	0.337409i
$218$	16.9405			1.14736
$219$	19.8042	−	14.3886i	1.33824	−	0.972291i
$220$	−0.313821	−	0.263791i	−0.0211578	−	0.0177848i
$221$	−20.8077	−	15.1177i	−1.39968	−	1.01692i
$222$	14.9708	+	10.8769i	1.00477	+	0.730011i
$223$	−5.64286	+	17.3669i	−0.377874	+	1.16298i	0.563646	+	0.826017i	$0.309398\pi$
$223$	−5.64286	+	17.3669i	−0.377874	+	1.16298i	−0.941519	+	0.336959i	$0.890602\pi$
$224$	1.00000			0.0668153
$225$	−21.8278	−	21.1520i	−1.45518	−	1.41013i
$226$	2.09842			0.139585
$227$	−8.23088	+	25.3320i	−0.546303	+	1.68135i	0.171570	+	0.985172i	$0.445116\pi$
$227$	−8.23088	+	25.3320i	−0.546303	+	1.68135i	−0.717873	+	0.696174i	$0.754884\pi$
$228$	4.07214	+	2.95858i	0.269684	+	0.195937i
$229$	−8.80705	−	6.39870i	−0.581986	−	0.422838i	0.257453	−	0.966291i	$-0.417117\pi$
$229$	−8.80705	−	6.39870i	−0.581986	−	0.422838i	−0.839440	+	0.543453i	$0.817117\pi$
$230$	−6.05155	+	14.9409i	−0.399027	+	0.985171i
$231$	0.446927	−	0.324711i	0.0294056	−	0.0213644i
$232$	4.82168			0.316559
$233$	−1.95342	+	1.41924i	−0.127973	+	0.0929776i	−0.649930	−	0.759994i	$-0.725202\pi$
$233$	−1.95342	+	1.41924i	−0.127973	+	0.0929776i	0.521958	+	0.852971i	$0.325202\pi$
$234$	6.75057	+	20.7761i	0.441299	+	1.35818i
$235$	9.73067	−	24.0243i	0.634759	−	1.56717i
$236$	0.675993	−	2.08049i	0.0440034	−	0.135429i
$237$	5.35994	+	16.4962i	0.348165	+	1.07154i
$238$	−2.21168	−	6.80686i	−0.143362	−	0.441223i
$239$	5.34005	−	16.4350i	0.345419	−	1.06309i	−0.615940	−	0.787793i	$-0.711224\pi$
$239$	5.34005	−	16.4350i	0.345419	−	1.06309i	0.961359	−	0.275298i	$-0.0887764\pi$
$240$	6.72076	+	0.475809i	0.433823	+	0.0307134i
$241$	7.57487	+	23.3130i	0.487940	+	1.50172i	0.827677	+	0.561205i	$0.189662\pi$
$241$	7.57487	+	23.3130i	0.487940	+	1.50172i	−0.339737	+	0.940520i	$0.610338\pi$
$242$	−8.87199	+	6.44588i	−0.570313	+	0.414357i
$243$	1.44711			0.0928323
$244$	−2.12866	+	1.54656i	−0.136274	+	0.0990086i
$245$	0.539075	+	2.17011i	0.0344402	+	0.138644i
$246$	−15.0562	−	10.9390i	−0.959947	−	0.697443i
$247$	−4.85657	−	3.52850i	−0.309016	−	0.224513i
$248$	2.61306	−	8.04218i	0.165930	−	0.510679i
$249$	−14.1839			−0.898866
$250$	10.2255	−	4.52091i	0.646719	−	0.285927i
$251$	1.97168			0.124452			0.0622258	−	0.998062i	$-0.480180\pi$
$251$	1.97168			0.124452			0.0622258	+	0.998062i	$0.480180\pi$
$252$	−1.87852	+	5.78148i	−0.118335	+	0.364199i
$253$	−1.06929	−	0.776881i	−0.0672254	−	0.0488421i
$254$	3.64968	+	2.65165i	0.229001	+	0.166379i
$255$	−11.6254	−	46.7996i	−0.728012	−	2.93071i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−1.45056			−0.0904833			−0.0452416	−	0.998976i	$-0.514406\pi$
$257$	−1.45056			−0.0904833			−0.0452416	+	0.998976i	$0.514406\pi$
$258$	2.41193	−	1.75237i	0.150160	−	0.109098i
$259$	−1.89780	−	5.84083i	−0.117924	−	0.362931i
$260$	−8.01540	−	0.567466i	−0.497094	−	0.0351927i
$261$	−9.05760	+	27.8764i	−0.560651	+	1.72551i
$262$	0.811509	+	2.49757i	0.0501352	+	0.154300i
$263$	3.02818	+	9.31979i	0.186726	+	0.574683i	0.999974	−	0.00723445i	$-0.00230282\pi$
$263$	3.02818	+	9.31979i	0.186726	+	0.574683i	−0.813248	+	0.581917i	$0.802303\pi$
$264$	−0.170711	+	0.525394i	−0.0105065	+	0.0323357i
$265$	−4.78532	+	11.8146i	−0.293960	+	0.725767i
$266$	−0.516212	−	1.58874i	−0.0316510	−	0.0974118i
$267$	−38.3053	+	27.8304i	−2.34424	+	1.70319i
$268$	2.75186			0.168096
$269$	0.103100	−	0.0749062i	0.00628609	−	0.00456711i	−0.584638	−	0.811294i	$-0.698763\pi$
$269$	0.103100	−	0.0749062i	0.00628609	−	0.00456711i	0.590924	+	0.806727i	$0.298763\pi$
$270$	−7.78788	+	19.2277i	−0.473955	+	1.17016i
$271$	−4.56300	−	3.31522i	−0.277183	−	0.201385i	0.440505	−	0.897750i	$-0.354799\pi$
$271$	−4.56300	−	3.31522i	−0.277183	−	0.201385i	−0.717688	+	0.696365i	$0.754799\pi$
$272$	5.79026	+	4.20687i	0.351086	+	0.255079i
$273$	3.34601	−	10.2980i	0.202510	−	0.623261i
$274$	9.48143			0.572794
$275$	0.157621	+	0.903052i	0.00950488	+	0.0544561i
$276$	21.7218			1.30750
$277$	0.193730	−	0.596239i	0.0116401	−	0.0358245i	−0.945068	−	0.326874i	$-0.894005\pi$
$277$	0.193730	−	0.596239i	0.0116401	−	0.0358245i	0.956708	+	0.291050i	$0.0940046\pi$
$278$	−16.3889	−	11.9072i	−0.982942	−	0.714149i
$279$	41.5870	+	30.2147i	2.48975	+	1.80891i
$280$	−1.71168	−	1.43880i	−0.102293	−	0.0859847i
$281$	26.2978	−	19.1065i	1.56880	−	1.13980i	0.640497	−	0.767961i	$-0.278729\pi$
$281$	26.2978	−	19.1065i	1.56880	−	1.13980i	0.928299	−	0.371836i	$-0.121271\pi$
$282$	−34.9278			−2.07992
$283$	−7.09133	+	5.15215i	−0.421536	+	0.306264i	−0.778255	−	0.627948i	$-0.783895\pi$
$283$	−7.09133	+	5.15215i	−0.421536	+	0.306264i	0.356720	+	0.934211i	$0.383895\pi$
$284$	−4.40172	−	13.5471i	−0.261194	−	0.803873i
$285$	−2.71340	−	10.9231i	−0.160728	−	0.647031i
$286$	0.203595	−	0.626602i	0.0120388	−	0.0370517i
$287$	1.90862	+	5.87414i	0.112663	+	0.346740i
$288$	−1.87852	−	5.78148i	−0.110693	−	0.340677i
$289$	10.5761	−	32.5498i	0.622121	−	1.91469i
$290$	−8.25318	−	6.93743i	−0.484643	−	0.407380i
$291$	1.23641	+	3.80527i	0.0724795	+	0.223069i
$292$	6.57262	−	4.77529i	0.384633	−	0.279452i
$293$	26.9072			1.57194			0.785969	−	0.618266i	$-0.212165\pi$
$293$	26.9072			1.57194			0.785969	+	0.618266i	$0.212165\pi$
$294$	2.43768	−	1.77108i	0.142168	−	0.103291i
$295$	−4.15050	+	2.58852i	−0.241651	+	0.150710i
$296$	4.96850	+	3.60983i	0.288788	+	0.209817i
$297$	−1.37609	−	0.999787i	−0.0798488	−	0.0580135i
$298$	−0.753544	+	2.31917i	−0.0436516	+	0.134346i
$299$	−25.9061			−1.49819
$300$	−10.8192	−	10.4843i	−0.624648	−	0.605309i
$301$	−0.989435			−0.0570301
$302$	3.25244	−	10.0100i	0.187157	−	0.576010i
$303$	19.4428	+	14.1261i	1.11696	+	0.811521i
$304$	1.35146	+	0.981894i	0.0775116	+	0.0563155i
$305$	5.86879	+	0.415492i	0.336046	+	0.0237910i
$306$	−35.1990	+	25.5736i	−2.01219	+	1.46194i
$307$	−14.9660			−0.854152			−0.427076	−	0.904216i	$-0.640456\pi$
$307$	−14.9660			−0.854152			−0.427076	+	0.904216i	$0.640456\pi$
$308$	0.148326	−	0.107765i	0.00845165	−	0.00614049i
$309$	−11.8105	−	36.3490i	−0.671877	−	2.06782i
$310$	−16.0438	+	10.0060i	−0.911228	+	0.568302i
$311$	8.58784	−	26.4307i	0.486972	−	1.49874i	−0.342133	−	0.939652i	$-0.611149\pi$
$311$	8.58784	−	26.4307i	0.486972	−	1.49874i	0.829105	−	0.559093i	$-0.188851\pi$
$312$	3.34601	+	10.2980i	0.189431	+	0.583007i
$313$	−2.60738	−	8.02470i	−0.147378	−	0.453583i	0.849931	−	0.526894i	$-0.176643\pi$
$313$	−2.60738	−	8.02470i	−0.147378	−	0.453583i	−0.997309	+	0.0733108i	$0.976643\pi$
$314$	−3.24721	+	9.99388i	−0.183251	+	0.563987i
$315$	11.5338	−	7.19324i	0.649856	−	0.405293i
$316$	1.77886	+	5.47475i	0.100068	+	0.307979i
$317$	−17.7919	+	12.9265i	−0.999291	+	0.726027i	−0.961936	−	0.273275i	$-0.911893\pi$
$317$	−17.7919	+	12.9265i	−0.999291	+	0.726027i	−0.0373547	+	0.999302i	$0.511893\pi$
$318$	17.1767			0.963223
$319$	0.715180	−	0.519609i	0.0400424	−	0.0290925i
$320$	2.23049	+	0.157911i	0.124688	+	0.00882752i
$321$	28.7030	+	20.8539i	1.60204	+	1.16395i
$322$	−5.83223	−	4.23736i	−0.325017	−	0.236139i
$323$	3.69461	−	11.3708i	0.205574	−	0.632691i
$324$	9.71728			0.539849
$325$	12.9033	+	12.5039i	0.715749	+	0.693590i
$326$	−7.86162			−0.435415
$327$	−15.7735	+	48.5459i	−0.872277	+	2.68459i
$328$	−4.99685	−	3.63042i	−0.275905	−	0.200456i
$329$	9.37800	+	6.81352i	0.517026	+	0.375641i
$330$	1.04814	−	0.653689i	0.0576981	−	0.0359844i
$331$	−0.227165	+	0.165045i	−0.0124861	+	0.00907171i	−0.594011	−	0.804457i	$-0.702456\pi$
$331$	−0.227165	+	0.165045i	−0.0124861	+	0.00907171i	0.581525	+	0.813529i	$0.302456\pi$
$332$	−4.70734			−0.258349
$333$	−30.2036	+	21.9442i	−1.65514	+	1.20253i
$334$	1.58046	+	4.86416i	0.0864789	+	0.266155i
$335$	−4.71030	−	3.95937i	−0.257351	−	0.216323i
$336$	−0.931111	+	2.86567i	−0.0507963	+	0.156335i
$337$	6.02162	+	18.5326i	0.328019	+	1.00954i	0.970060	+	0.242867i	$0.0780879\pi$
$337$	6.02162	+	18.5326i	0.328019	+	1.00954i	−0.642041	+	0.766670i	$0.721912\pi$
$338$	0.0266609	+	0.0820537i	0.00145016	+	0.00446313i
$339$	−1.95386	+	6.01337i	−0.106119	+	0.326601i
$340$	−3.85824	−	15.5318i	−0.209243	−	0.842333i
$341$	−0.479082	−	1.47446i	−0.0259437	−	0.0798466i
$342$	−8.21554	+	5.96894i	−0.444245	+	0.322763i
$343$	−1.00000			−0.0539949
$344$	0.800470	−	0.581575i	0.0431584	−	0.0313564i
$345$	−37.1808	−	31.2533i	−2.00175	−	1.68262i
$346$	5.00251	+	3.63454i	0.268937	+	0.195394i
$347$	14.7049	+	10.6837i	0.789400	+	0.573532i	0.907785	−	0.419435i	$-0.137772\pi$
$347$	14.7049	+	10.6837i	0.789400	+	0.573532i	−0.118386	+	0.992968i	$0.537772\pi$
$348$	−4.48952	+	13.8173i	−0.240663	+	0.740686i
$349$	−26.4997			−1.41850			−0.709249	−	0.704958i	$-0.750966\pi$
$349$	−26.4997			−1.41850			−0.709249	+	0.704958i	$0.750966\pi$
$350$	0.859713	+	4.92553i	0.0459536	+	0.263281i
$351$	−33.3392			−1.77951
$352$	−0.0566555	+	0.174368i	−0.00301975	+	0.00929382i
$353$	17.0212	+	12.3666i	0.905947	+	0.658209i	0.939987	−	0.341211i	$-0.110837\pi$
$353$	17.0212	+	12.3666i	0.905947	+	0.658209i	−0.0340394	+	0.999420i	$0.510837\pi$
$354$	5.33257	+	3.87434i	0.283423	+	0.205919i
$355$	−11.9572	+	29.5216i	−0.634624	+	1.56684i
$356$	−12.7127	+	9.23635i	−0.673774	+	0.489525i
$357$	21.5655			1.14137
$358$	−12.1067	+	8.79605i	−0.639860	+	0.464886i
$359$	7.07702	+	21.7808i	0.373511	+	1.14955i	0.944478	+	0.328575i	$0.106568\pi$
$359$	7.07702	+	21.7808i	0.373511	+	1.14955i	−0.570967	+	0.820973i	$0.693432\pi$
$360$	−5.10296	+	12.5989i	−0.268950	+	0.664018i
$361$	−5.00899	+	15.4161i	−0.263631	+	0.811373i
$362$	2.02640	+	6.23662i	0.106505	+	0.327789i
$363$	−10.2109	−	31.4260i	−0.535934	−	1.64944i
$364$	1.11047	−	3.41769i	0.0582046	−	0.179135i
$365$	−18.1209	−	1.28290i	−0.948492	−	0.0671503i
$366$	−2.44991	−	7.54006i	−0.128059	−	0.394125i
$367$	7.54965	−	5.48514i	0.394089	−	0.286322i	−0.373040	−	0.927815i	$-0.621685\pi$
$367$	7.54965	−	5.48514i	0.394089	−	0.286322i	0.767129	+	0.641493i	$0.221685\pi$
$368$	7.20903			0.375797
$369$	30.3758	−	22.0693i	1.58130	−	1.14888i
$370$	−3.31068	−	13.3276i	−0.172114	−	0.692867i
$371$	−4.61189	−	3.35074i	−0.239437	−	0.173962i
$372$	20.6132	+	14.9763i	1.06874	+	0.776487i
$373$	−5.24502	+	16.1425i	−0.271577	+	0.835828i	0.718528	+	0.695498i	$0.244816\pi$
$373$	−5.24502	+	16.1425i	−0.271577	+	0.835828i	−0.990105	+	0.140330i	$0.955184\pi$
$374$	1.31220			0.0678522
$375$	3.43431	+	33.5124i	0.177347	+	1.73057i
$376$	−11.5918			−0.597804
$377$	5.35434	−	16.4790i	0.275763	−	0.848710i
$378$	−7.50563	−	5.45316i	−0.386048	−	0.280480i
$379$	2.30280	+	1.67308i	0.118287	+	0.0859403i	0.645356	−	0.763882i	$-0.276709\pi$
$379$	2.30280	+	1.67308i	0.118287	+	0.0859403i	−0.527069	+	0.849822i	$0.676709\pi$
$380$	−0.900524	−	3.62517i	−0.0461959	−	0.185967i
$381$	−10.9970	+	7.98978i	−0.563393	+	0.409329i
$382$	19.2932			0.987124
$383$	−3.89509	+	2.82995i	−0.199030	+	0.144603i	−0.682836	−	0.730571i	$-0.739254\pi$
$383$	−3.89509	+	2.82995i	−0.199030	+	0.144603i	0.483807	+	0.875175i	$0.339254\pi$
$384$	−0.931111	−	2.86567i	−0.0475156	−	0.146238i
$385$	−0.408939	−	0.0289516i	−0.0208415	−	0.00147551i
$386$	−2.37962	+	7.32372i	−0.121119	+	0.372767i
$387$	1.85867	+	5.72040i	0.0944815	+	0.290784i
$388$	0.410339	+	1.26289i	0.0208318	+	0.0641137i
$389$	−6.55908	+	20.1868i	−0.332558	+	1.02351i	0.635354	+	0.772221i	$0.280854\pi$
$389$	−6.55908	+	20.1868i	−0.332558	+	1.02351i	−0.967912	+	0.251288i	$0.919146\pi$
$390$	9.08939	−	22.4411i	0.460259	−	1.13635i
$391$	−15.9441	−	49.0708i	−0.806327	−	2.48162i
$392$	0.809017	−	0.587785i	0.0408615	−	0.0296876i
$393$	−7.91280			−0.399148
$394$	15.3897	−	11.1813i	0.775323	−	0.563305i
$395$	4.83224	−	11.9305i	0.243136	−	0.600286i
$396$	−0.901674	−	0.655104i	−0.0453108	−	0.0329202i
$397$	−18.0602	−	13.1215i	−0.906416	−	0.658550i	0.0336901	−	0.999432i	$-0.489274\pi$
$397$	−18.0602	−	13.1215i	−0.906416	−	0.658550i	−0.940106	+	0.340883i	$0.889274\pi$
$398$	8.62159	−	26.5345i	0.432161	−	1.33006i
$399$	5.03344			0.251987
$400$	−3.59068	−	3.47951i	−0.179534	−	0.173976i
$401$	1.15262			0.0575590			0.0287795	−	0.999586i	$-0.490838\pi$
$401$	1.15262			0.0575590			0.0287795	+	0.999586i	$0.490838\pi$
$402$	−2.56228	+	7.88590i	−0.127795	+	0.393313i
$403$	−24.5839	−	17.8613i	−1.22461	−	0.889733i
$404$	6.45269	+	4.68815i	0.321033	+	0.233244i
$405$	−16.6329	−	13.9812i	−0.826495	−	0.694732i
$406$	3.90082	−	2.83411i	0.193594	−	0.140655i
$407$	1.12597			0.0558123
$408$	−17.4469	+	12.6759i	−0.863748	+	0.627550i
$409$	11.3549	+	34.9469i	0.561466	+	1.72801i	0.678225	+	0.734854i	$0.262749\pi$
$409$	11.3549	+	34.9469i	0.561466	+	1.72801i	−0.116759	+	0.993160i	$0.537251\pi$
$410$	3.32956	+	13.4036i	0.164435	+	0.661956i
$411$	−8.82826	+	27.1706i	−0.435466	+	1.34023i
$412$	−3.91967	−	12.0635i	−0.193108	−	0.594327i
$413$	−0.675993	−	2.08049i	−0.0332635	−	0.102374i
$414$	−13.5423	+	41.6788i	−0.665566	+	2.04840i
$415$	8.05747	+	6.77292i	0.395526	+	0.332469i
$416$	1.11047	+	3.41769i	0.0544454	+	0.167566i
$417$	49.3821	−	35.8782i	2.41825	−	1.75696i
$418$	0.306271			0.0149802
$419$	16.3628	−	11.8883i	0.799374	−	0.580779i	−0.111356	−	0.993781i	$-0.535519\pi$
$419$	16.3628	−	11.8883i	0.799374	−	0.580779i	0.910730	+	0.413001i	$0.135519\pi$
$420$	5.71688	−	3.56543i	0.278955	−	0.173975i
$421$	6.39605	+	4.64700i	0.311725	+	0.226481i	0.732636	−	0.680621i	$-0.238290\pi$
$421$	6.39605	+	4.64700i	0.311725	+	0.226481i	−0.420912	+	0.907102i	$0.638290\pi$
$422$	7.79480	+	5.66325i	0.379445	+	0.275683i
$423$	21.7755	−	67.0180i	1.05876	−	3.25853i
$424$	5.70061			0.276846
$425$	−15.7431	+	32.1368i	−0.763654	+	1.55886i
$426$	42.9200			2.07948
$427$	−0.813077	+	2.50239i	−0.0393476	+	0.121099i
$428$	9.52595	+	6.92100i	0.460454	+	0.334539i
$429$	1.60606	+	1.16687i	0.0775413	+	0.0563371i
$430$	−2.20692	−	0.156243i	−0.106427	−	0.00753472i
$431$	−16.6291	+	12.0817i	−0.800994	+	0.581956i	−0.911206	−	0.411952i	$-0.864847\pi$
$431$	−16.6291	+	12.0817i	−0.800994	+	0.581956i	0.110212	+	0.993908i	$0.464847\pi$
$432$	9.27747			0.446362
$433$	8.10778	−	5.89065i	0.389635	−	0.283086i	−0.375671	−	0.926753i	$-0.622588\pi$
$433$	8.10778	−	5.89065i	0.389635	−	0.283086i	0.765306	+	0.643667i	$0.222588\pi$
$434$	−2.61306	−	8.04218i	−0.125431	−	0.386037i
$435$	27.5650	−	17.1913i	1.32164	−	0.824261i
$436$	−5.23491	+	16.1114i	−0.250707	+	0.771596i
$437$	−3.72139	−	11.4533i	−0.178018	−	0.547883i
$438$	7.56453	+	23.2812i	0.361447	+	1.11242i
$439$	−5.07048	+	15.6053i	−0.242001	+	0.744802i	0.754115	+	0.656743i	$0.228066\pi$
$439$	−5.07048	+	15.6053i	−0.242001	+	0.744802i	−0.996115	+	0.0880588i	$0.971934\pi$
$440$	0.347856	−	0.216946i	0.0165834	−	0.0103425i
$441$	1.87852	+	5.78148i	0.0894531	+	0.275308i
$442$	20.8077	−	15.1177i	0.989721	−	0.719074i
$443$	18.7467			0.890680			0.445340	−	0.895361i	$-0.353083\pi$
$443$	18.7467			0.890680			0.445340	+	0.895361i	$0.353083\pi$
$444$	−14.9708	+	10.8769i	−0.710482	+	0.516196i
$445$	35.0494	+	2.48139i	1.66150	+	0.117629i
$446$	−14.7732	−	10.7333i	−0.699531	−	0.508239i
$447$	−5.94433	−	4.31881i	−0.281157	−	0.204273i
$448$	−0.309017	+	0.951057i	−0.0145997	+	0.0449332i
$449$	23.2879			1.09902			0.549511	−	0.835487i	$-0.314814\pi$
$449$	23.2879			1.09902			0.549511	+	0.835487i	$0.314814\pi$
$450$	26.8619	−	14.2231i	1.26628	−	0.670484i
$451$	−1.13239			−0.0533224
$452$	−0.648447	+	1.99572i	−0.0305004	+	0.0938705i
$453$	25.6569	+	18.6408i	1.20547	+	0.875822i
$454$	−21.5487	−	15.6561i	−1.01133	−	0.734775i
$455$	−6.81814	+	4.25224i	−0.319639	+	0.199348i
$456$	−4.07214	+	2.95858i	−0.190695	+	0.138548i
$457$	−11.9939			−0.561053			−0.280526	−	0.959846i	$-0.590509\pi$
$457$	−11.9939			−0.561053			−0.280526	+	0.959846i	$0.590509\pi$
$458$	8.80705	−	6.39870i	0.411527	−	0.298992i
$459$	−20.5188	−	63.1504i	−0.957736	−	2.94761i
$460$	−12.3396	−	10.3723i	−0.575335	−	0.483613i
$461$	−10.1845	+	31.3447i	−0.474339	+	1.45987i	0.372507	+	0.928029i	$0.378498\pi$
$461$	−10.1845	+	31.3447i	−0.474339	+	1.45987i	−0.846847	+	0.531837i	$0.821502\pi$
$462$	0.170711	+	0.525394i	0.00794218	+	0.0244435i
$463$	3.75788	+	11.5656i	0.174643	+	0.537497i	0.999617	−	0.0276742i	$-0.00881009\pi$
$463$	3.75788	+	11.5656i	0.174643	+	0.537497i	−0.824974	+	0.565171i	$0.808810\pi$
$464$	−1.48998	+	4.58569i	−0.0691706	+	0.212885i
$465$	−13.7352	−	55.2929i	−0.636956	−	2.56415i
$466$	−0.746140	−	2.29638i	−0.0345643	−	0.106378i
$467$	13.8647	−	10.0733i	0.641584	−	0.466138i	−0.218810	−	0.975767i	$-0.570218\pi$
$467$	13.8647	−	10.0733i	0.641584	−	0.466138i	0.860394	+	0.509630i	$0.170218\pi$
$468$	−21.8453			−1.00980
$469$	2.22630	−	1.61750i	0.102801	−	0.0746892i
$470$	19.8416	+	16.6783i	0.915223	+	0.769315i
$471$	−25.6156	−	18.6108i	−1.18030	−	0.857541i
$472$	1.76977	+	1.28582i	0.0814604	+	0.0591845i
$473$	0.0560569	−	0.172525i	0.00257750	−	0.00793273i
$474$	−17.3451			−0.796688
$475$	−3.67448	+	7.50082i	−0.168597	+	0.344161i
$476$	7.15715			0.328048
$477$	−10.7087	+	32.9580i	−0.490317	+	1.50904i
$478$	13.9804	+	10.1574i	0.639450	+	0.464588i
$479$	−0.983074	−	0.714245i	−0.0449178	−	0.0326347i	0.565100	−	0.825023i	$-0.308838\pi$
$479$	−0.983074	−	0.714245i	−0.0449178	−	0.0326347i	−0.610018	+	0.792388i	$0.708838\pi$
$480$	−2.52935	+	6.24479i	−0.115449	+	0.285034i
$481$	17.8547	−	12.9722i	0.814102	−	0.591480i
$482$	−24.5128			−1.11653
$483$	17.5733	−	12.7678i	0.799613	−	0.580953i
$484$	−3.38880	−	10.4297i	−0.154036	−	0.474075i
$485$	1.11468	−	2.75207i	0.0506150	−	0.124965i
$486$	−0.447182	+	1.37629i	−0.0202846	+	0.0624296i
$487$	10.4460	+	32.1495i	0.473354	+	1.45683i	0.848165	+	0.529733i	$0.177708\pi$
$487$	10.4460	+	32.1495i	0.473354	+	1.45683i	−0.374810	+	0.927101i	$0.622292\pi$
$488$	−0.813077	−	2.50239i	−0.0368063	−	0.113278i
$489$	7.32004	−	22.5288i	0.331024	−	1.01879i
$490$	−2.23049	−	0.157911i	−0.100763	−	0.00713371i
$491$	0.750735	+	2.31052i	0.0338802	+	0.104272i	0.966566	−	0.256416i	$-0.0825417\pi$
$491$	0.750735	+	2.31052i	0.0338802	+	0.104272i	−0.932686	+	0.360689i	$0.882542\pi$
$492$	15.0562	−	10.9390i	0.678785	−	0.493166i
$493$	34.5095			1.55423
$494$	4.85657	−	3.52850i	0.218507	−	0.158755i
$495$	0.600815	+	2.41866i	0.0270046	+	0.108711i
$496$	6.84109	+	4.97034i	0.307174	+	0.223175i
$497$	−11.5239	−	8.37258i	−0.516916	−	0.375561i
$498$	4.38306	−	13.4897i	0.196409	−	0.604486i
$499$	−9.08171			−0.406553			−0.203277	−	0.979121i	$-0.565159\pi$
$499$	−9.08171			−0.406553			−0.203277	+	0.979121i	$0.565159\pi$
$500$	1.13978	+	11.1221i	0.0509724	+	0.497395i
$501$	−15.4106			−0.688496
$502$	−0.609284	+	1.87518i	−0.0271937	+	0.0836935i
$503$	−5.91719	−	4.29909i	−0.263834	−	0.191687i	0.448001	−	0.894033i	$-0.352136\pi$
$503$	−5.91719	−	4.29909i	−0.263834	−	0.191687i	−0.711836	+	0.702346i	$0.752136\pi$
$504$	−4.91802	−	3.57315i	−0.219066	−	0.159161i
$505$	−4.29964	−	17.3088i	−0.191332	−	0.770229i
$506$	1.06929	−	0.776881i	0.0475355	−	0.0345366i
$507$	−0.259963			−0.0115453
$508$	−3.64968	+	2.65165i	−0.161928	+	0.117648i
$509$	6.51241	+	20.0431i	0.288657	+	0.888396i	0.985278	+	0.170957i	$0.0546859\pi$
$509$	6.51241	+	20.0431i	0.288657	+	0.888396i	−0.696621	+	0.717439i	$0.745314\pi$
$510$	48.1015	+	3.40544i	2.12997	+	0.150795i
$511$	2.51052	−	7.72658i	0.111059	−	0.341804i
$512$	−0.309017	−	0.951057i	−0.0136568	−	0.0420312i
$513$	−4.78914	−	14.7395i	−0.211446	−	0.650763i
$514$	0.448247	−	1.37956i	0.0197713	−	0.0608499i
$515$	−10.6477	+	26.2885i	−0.469195	+	1.15841i
$516$	0.921274	+	2.83539i	0.0405568	+	0.124821i
$517$	−1.71937	+	1.24920i	−0.0756179	+	0.0549396i
$518$	6.14141			0.269838
$519$	−15.0733	+	10.9514i	−0.661643	+	0.480712i
$520$	3.01659	−	7.44774i	0.132286	−	0.326605i
$521$	−9.02663	−	6.55823i	−0.395464	−	0.287321i	0.372227	−	0.928142i	$-0.378594\pi$
$521$	−9.02663	−	6.55823i	−0.395464	−	0.287321i	−0.767691	+	0.640820i	$0.778594\pi$
$522$	−23.7131	−	17.2286i	−1.03789	−	0.754074i
$523$	−4.01839	+	12.3673i	−0.175712	+	0.540785i	−0.999665	−	0.0258722i	$-0.991764\pi$
$523$	−4.01839	+	12.3673i	−0.175712	+	0.540785i	0.823953	+	0.566657i	$0.191764\pi$
$524$	−2.62610			−0.114722
$525$	−14.9154	−	2.12257i	−0.650962	−	0.0926366i
$526$	−9.79940			−0.427274
$527$	18.7021	−	57.5592i	0.814676	−	2.50732i
$528$	−0.446927	−	0.324711i	−0.0194500	−	0.0141312i
$529$	−23.4373	−	17.0282i	−1.01901	−	0.740356i
$530$	−9.75764	−	8.20204i	−0.423845	−	0.356274i
$531$	−10.7585	+	7.81648i	−0.466877	+	0.339206i
$532$	1.67050			0.0724253
$533$	−17.9565	+	13.0462i	−0.777782	+	0.565092i
$534$	−14.6313	−	45.0305i	−0.633158	−	1.94866i
$535$	−6.34746	−	25.5525i	−0.274424	−	1.10473i
$536$	−0.850370	+	2.61717i	−0.0367304	+	0.113045i
$537$	−13.9338	−	42.8839i	−0.601289	−	1.85058i
$538$	0.0393805	+	0.121201i	0.00169782	+	0.00522534i
$539$	0.0566555	−	0.174368i	0.00244032	−	0.00751054i
$540$	−15.8801	−	13.3484i	−0.683370	−	0.574424i
$541$	−7.14272	−	21.9830i	−0.307089	−	0.945124i	−0.978889	−	0.204391i	$-0.934479\pi$
$541$	−7.14272	−	21.9830i	−0.307089	−	0.945124i	0.671800	−	0.740733i	$-0.265521\pi$
$542$	4.56300	−	3.31522i	0.195998	−	0.142401i
$543$	−19.7589			−0.847934
$544$	−5.79026	+	4.20687i	−0.248255	+	0.180368i
$545$	32.1416	−	20.0456i	1.37679	−	0.858659i
$546$	8.75997	+	6.36449i	0.374892	+	0.272375i
$547$	−15.5490	−	11.2970i	−0.664827	−	0.483025i	0.203463	−	0.979083i	$-0.434780\pi$
$547$	−15.5490	−	11.2970i	−0.664827	−	0.483025i	−0.868289	+	0.496058i	$0.834780\pi$
$548$	−2.92992	+	9.01738i	−0.125160	+	0.385203i
$549$	15.9949			0.682646
$550$	−0.907561	−	0.129152i	−0.0386985	−	0.00550708i
$551$	8.05460			0.343138
$552$	−6.71240	+	20.6587i	−0.285699	+	0.879291i
$553$	4.65710	+	3.38358i	0.198040	+	0.143885i
$554$	0.507191	+	0.368496i	0.0215485	+	0.0156559i
$555$	41.2749	+	2.92214i	1.75202	+	0.124038i
$556$	16.3889	−	11.9072i	0.695045	−	0.504980i
$557$	27.0464			1.14599			0.572997	−	0.819557i	$-0.305781\pi$
$557$	27.0464			1.14599			0.572997	+	0.819557i	$0.305781\pi$
$558$	−41.5870	+	30.2147i	−1.76052	+	1.27909i
$559$	−1.09874	−	3.38158i	−0.0464718	−	0.143026i
$560$	1.89732	−	1.18329i	0.0801763	−	0.0500033i
$561$	−1.22180	+	3.76032i	−0.0515846	+	0.158761i
$562$	10.0449	+	30.9149i	0.423717	+	1.30407i
$563$	0.983226	+	3.02606i	0.0414380	+	0.127533i	0.969635	−	0.244555i	$-0.0786419\pi$
$563$	0.983226	+	3.02606i	0.0414380	+	0.127533i	−0.928197	+	0.372088i	$0.878642\pi$
$564$	10.7933	−	33.2184i	0.454480	−	1.39874i
$565$	3.98137	−	2.48304i	0.167497	−	0.104462i
$566$	−2.70865	−	8.33636i	−0.113853	−	0.350403i
$567$	7.86144	−	5.71167i	0.330150	−	0.239868i
$568$	14.2443			0.597677
$569$	−2.16624	+	1.57386i	−0.0908134	+	0.0659798i	−0.632265	−	0.774752i	$-0.717875\pi$
$569$	−2.16624	+	1.57386i	−0.0908134	+	0.0659798i	0.541452	+	0.840732i	$0.317875\pi$
$570$	11.2270	+	0.794838i	0.470248	+	0.0332921i
$571$	−18.5952	−	13.5102i	−0.778183	−	0.565383i	0.126250	−	0.991998i	$-0.459706\pi$
$571$	−18.5952	−	13.5102i	−0.778183	−	0.565383i	−0.904433	+	0.426615i	$0.859706\pi$
$572$	0.533019	+	0.387261i	0.0222866	+	0.0161922i
$573$	−17.9641	+	55.2877i	−0.750460	+	2.30968i
$574$	−6.17644			−0.257800
$575$	6.19769	+	35.5083i	0.258462	+	1.48080i
$576$	6.07900			0.253292
$577$	−6.01383	+	18.5087i	−0.250359	+	0.770526i	0.744350	+	0.667790i	$0.232760\pi$
$577$	−6.01383	+	18.5087i	−0.250359	+	0.770526i	−0.994709	+	0.102736i	$0.967240\pi$
$578$	27.6885	+	20.1169i	1.15169	+	0.836751i
$579$	−18.7716	−	13.6384i	−0.780122	−	0.566792i
$580$	9.14826	−	5.70546i	0.379861	−	0.236906i
$581$	−3.80832	+	2.76690i	−0.157996	+	0.114791i
$582$	−4.00110			−0.165851
$583$	0.845548	−	0.614327i	0.0350190	−	0.0254428i
$584$	2.51052	+	7.72658i	0.103886	+	0.319728i
$585$	37.3922	+	31.4310i	1.54598	+	1.29951i
$586$	−8.31479	+	25.5903i	−0.343481	+	1.05713i
$587$	11.1682	+	34.3723i	0.460962	+	1.41870i	0.863990	+	0.503508i	$0.167958\pi$
$587$	11.1682	+	34.3723i	0.460962	+	1.41870i	−0.403028	+	0.915188i	$0.632042\pi$
$588$	0.931111	+	2.86567i	0.0383984	+	0.118178i
$589$	4.36512	−	13.4344i	0.179862	−	0.553557i
$590$	−1.17926	−	4.74726i	−0.0485493	−	0.195441i
$591$	17.7123	+	54.5128i	0.728586	+	2.24236i
$592$	−4.96850	+	3.60983i	−0.204204	+	0.148363i
$593$	−6.07035			−0.249279			−0.124640	−	0.992202i	$-0.539777\pi$
$593$	−6.07035			−0.249279			−0.124640	+	0.992202i	$0.539777\pi$
$594$	1.37609	−	0.999787i	0.0564616	−	0.0410218i
$595$	−12.2508	−	10.2977i	−0.502233	−	0.422165i
$596$	−1.97280	−	1.43333i	−0.0808092	−	0.0587113i
$597$	68.0114	+	49.4132i	2.78352	+	2.02235i
$598$	8.00543	−	24.6382i	0.327366	−	1.00753i
$599$	33.8492			1.38304			0.691520	−	0.722357i	$-0.256941\pi$
$599$	33.8492			1.38304			0.691520	+	0.722357i	$0.256941\pi$
$600$	13.3144	−	7.04987i	0.543560	−	0.287810i
$601$	−19.4434			−0.793114			−0.396557	−	0.918010i	$-0.629795\pi$
$601$	−19.4434			−0.793114			−0.396557	+	0.918010i	$0.629795\pi$
$602$	0.305752	−	0.941009i	0.0124615	−	0.0383527i
$603$	−13.5337	−	9.83279i	−0.551134	−	0.400422i
$604$	8.51500	+	6.18651i	0.346470	+	0.251725i
$605$	−9.20563	+	22.7281i	−0.374262	+	0.924027i
$606$	−19.4428	+	14.1261i	−0.789812	+	0.573832i
$607$	13.2893			0.539396			0.269698	−	0.962945i	$-0.413076\pi$
$607$	13.2893			0.539396			0.269698	+	0.962945i	$0.413076\pi$
$608$	−1.35146	+	0.981894i	−0.0548090	+	0.0398211i
$609$	4.48952	+	13.8173i	0.181924	+	0.559906i
$610$	−2.20871	+	5.45316i	−0.0894282	+	0.220792i
$611$	−12.8724	+	39.6173i	−0.520763	+	1.60274i
$612$	−13.4448	−	41.3789i	−0.543475	−	1.67264i
$613$	−3.17173	−	9.76159i	−0.128105	−	0.394267i	0.866349	−	0.499439i	$-0.166461\pi$
$613$	−3.17173	−	9.76159i	−0.128105	−	0.394267i	−0.994454	+	0.105172i	$0.966461\pi$
$614$	4.62473	−	14.2335i	0.186639	−	0.574416i
$615$	−41.5104	−	2.93881i	−1.67386	−	0.118504i
$616$	0.0566555	+	0.174368i	0.00228271	+	0.00702547i
$617$	−0.433262	+	0.314783i	−0.0174425	+	0.0126727i	−0.596472	−	0.802634i	$-0.703431\pi$
$617$	−0.433262	+	0.314783i	−0.0174425	+	0.0126727i	0.579030	+	0.815306i	$0.303431\pi$
$618$	38.2196			1.53742
$619$	13.0172	−	9.45756i	0.523206	−	0.380131i	−0.294604	−	0.955619i	$-0.595188\pi$
$619$	13.0172	−	9.45756i	0.523206	−	0.380131i	0.817810	+	0.575488i	$0.195188\pi$
$620$	−4.55845	−	18.3506i	−0.183072	−	0.736978i
$621$	−54.1083	−	39.3120i	−2.17129	−	1.57753i
$622$	22.4833	+	16.3350i	0.901496	+	0.654975i
$623$	−4.85584	+	14.9447i	−0.194545	+	0.598748i
$624$	−10.8279			−0.433464
$625$	14.0515	−	20.6774i	0.562061	−	0.827096i
$626$	8.43767			0.337237
$627$	−0.285172	+	0.877669i	−0.0113887	+	0.0350507i
$628$	−8.50130	−	6.17656i	−0.339239	−	0.246471i
$629$	35.5603	+	25.8361i	1.41788	+	1.03015i
$630$	3.27704	+	13.1921i	0.130560	+	0.525587i
$631$	13.1187	−	9.53132i	0.522249	−	0.379436i	−0.295202	−	0.955435i	$-0.595387\pi$
$631$	13.1187	−	9.53132i	0.522249	−	0.379436i	0.817450	+	0.575999i	$0.195387\pi$
$632$	−5.75650			−0.228981
$633$	−23.4868	+	17.0642i	−0.933517	+	0.678240i
$634$	−6.79589	−	20.9156i	−0.269899	−	0.830664i
$635$	10.0623	+	0.712379i	0.399309	+	0.0282699i
$636$	−5.30790	+	16.3360i	−0.210472	+	0.647766i
$637$	−1.11047	−	3.41769i	−0.0439986	−	0.135414i
$638$	0.273174	+	0.840744i	0.0108151	+	0.0332854i
$639$	−26.7581	+	82.3530i	−1.05853	+	3.25783i
$640$	−0.839441	+	2.07252i	−0.0331818	+	0.0819235i
$641$	1.93698	+	5.96142i	0.0765062	+	0.235462i	0.981995	−	0.188909i	$-0.0604952\pi$
$641$	1.93698	+	5.96142i	0.0765062	+	0.235462i	−0.905488	+	0.424371i	$0.860495\pi$
$642$	−28.7030	+	20.8539i	−1.13282	+	0.823040i
$643$	−4.88323			−0.192576			−0.0962880	−	0.995354i	$-0.530697\pi$
$643$	−4.88323			−0.192576			−0.0962880	+	0.995354i	$0.530697\pi$
$644$	5.83223	−	4.23736i	0.229822	−	0.166975i
$645$	2.50263	−	6.17881i	0.0985409	−	0.243291i
$646$	9.67262	+	7.02757i	0.380564	+	0.276496i
$647$	−26.3923	−	19.1751i	−1.03759	−	0.753853i	−0.0677758	−	0.997701i	$-0.521590\pi$
$647$	−26.3923	−	19.1751i	−1.03759	−	0.753853i	−0.969814	+	0.243848i	$0.921590\pi$
$648$	−3.00280	+	9.24168i	−0.117961	+	0.363048i
$649$	0.401069			0.0157433
$650$	−15.8792	+	8.40790i	−0.622835	+	0.329785i
$651$	25.4793			0.998611
$652$	2.42937	−	7.47684i	0.0951416	−	0.292816i
$653$	0.326139	+	0.236954i	0.0127628	+	0.00927273i	0.594148	−	0.804355i	$-0.297489\pi$
$653$	0.326139	+	0.236954i	0.0127628	+	0.00927273i	−0.581386	+	0.813628i	$0.697489\pi$
$654$	−41.2956	−	30.0030i	−1.61479	−	1.17321i
$655$	4.49505	+	3.77843i	0.175636	+	0.147635i
$656$	4.99685	−	3.63042i	0.195094	−	0.141744i
$657$	−49.3871			−1.92677
$658$	−9.37800	+	6.81352i	−0.365593	+	0.265619i
$659$	9.17443	+	28.2360i	0.357385	+	1.09992i	0.954614	+	0.297847i	$0.0962685\pi$
$659$	9.17443	+	28.2360i	0.357385	+	1.09992i	−0.597229	+	0.802071i	$0.703732\pi$
$660$	0.297802	+	1.19884i	0.0115919	+	0.0466648i
$661$	0.0857225	−	0.263827i	0.00333422	−	0.0102617i	−0.949376	−	0.314143i	$-0.898283\pi$
$661$	0.0857225	−	0.263827i	0.00333422	−	0.0102617i	0.952710	+	0.303882i	$0.0982827\pi$
$662$	−0.0867694	−	0.267049i	−0.00337239	−	0.0103791i
$663$	23.9479	+	73.7041i	0.930060	+	2.86243i
$664$	1.45465	−	4.47695i	0.0564513	−	0.173739i
$665$	−2.85936	−	2.40351i	−0.110881	−	0.0932042i
$666$	−11.5367	−	35.5064i	−0.447039	−	1.37585i
$667$	28.1211	−	20.4312i	1.08885	−	0.791099i
$668$	−5.11448			−0.197885
$669$	44.5137	−	32.3411i	1.72100	−	1.25038i
$670$	5.22115	−	3.25625i	0.201711	−	0.125800i
$671$	−0.390271	−	0.283549i	−0.0150662	−	0.0109463i
$672$	−2.43768	−	1.77108i	−0.0940356	−	0.0683208i
$673$	7.76500	−	23.8982i	0.299319	−	0.921208i	−0.682418	−	0.730962i	$-0.739072\pi$
$673$	7.76500	−	23.8982i	0.299319	−	0.921208i	0.981737	−	0.190246i	$-0.0609285\pi$
$674$	−19.4864			−0.750587
$675$	7.97596	+	45.6965i	0.306995	+	1.75886i
$676$	−0.0862763			−0.00331832
$677$	16.0688	−	49.4546i	0.617573	−	1.90069i	0.272046	−	0.962284i	$-0.412300\pi$
$677$	16.0688	−	49.4546i	0.617573	−	1.90069i	0.345526	−	0.938409i	$-0.387700\pi$
$678$	−5.11527	−	3.71646i	−0.196451	−	0.142730i
$679$	1.07428	+	0.780511i	0.0412271	+	0.0299533i
$680$	15.9639	+	1.13020i	0.612189	+	0.0433411i
$681$	64.9293	−	47.1739i	2.48810	−	1.80771i
$682$	1.55034			0.0593656
$683$	9.97556	−	7.24767i	0.381704	−	0.277324i	−0.380343	−	0.924845i	$-0.624194\pi$
$683$	9.97556	−	7.24767i	0.381704	−	0.277324i	0.762048	+	0.647521i	$0.224194\pi$
$684$	−3.13806	−	9.65794i	−0.119987	−	0.369281i
$685$	17.9893	−	11.2193i	0.687335	−	0.428668i
$686$	0.309017	−	0.951057i	0.0117983	−	0.0363115i
$687$	10.1362	+	31.1960i	0.386720	+	1.19020i
$688$	0.305752	+	0.941009i	0.0116567	+	0.0358756i
$689$	6.33038	−	19.4829i	0.241168	−	0.742239i
$690$	41.2132	−	25.7033i	1.56896	−	0.978506i
$691$	1.94970	+	6.00055i	0.0741700	+	0.228272i	0.981268	−	0.192648i	$-0.0617075\pi$
$691$	1.94970	+	6.00055i	0.0741700	+	0.228272i	−0.907098	+	0.420920i	$0.861707\pi$
$692$	−5.00251	+	3.63454i	−0.190167	+	0.138164i
$693$	−1.11453			−0.0423375
$694$	−14.7049	+	10.6837i	−0.558190	+	0.405549i
$695$	−45.1847	−	3.19894i	−1.71396	−	0.121343i
$696$	−11.7537	−	8.53957i	−0.445523	−	0.323692i
$697$	−35.7632	−	25.9835i	−1.35463	−	0.984194i
$698$	8.18887	−	25.2028i	0.309953	−	0.953938i
$699$	7.27540			0.275181
$700$	−4.95013	−	0.704439i	−0.187097	−	0.0266253i
$701$	−4.41874			−0.166893			−0.0834467	−	0.996512i	$-0.526593\pi$
$701$	−4.41874			−0.166893			−0.0834467	+	0.996512i	$0.526593\pi$
$702$	10.3024	−	31.7075i	0.388838	−	1.19672i
$703$	8.29987	+	6.03021i	0.313036	+	0.227434i
$704$	−0.148326	−	0.107765i	−0.00559024	−	0.00406155i
$705$	−66.2692	+	41.3299i	−2.49584	+	1.55657i
$706$	−17.0212	+	12.3666i	−0.640601	+	0.465424i
$707$	7.97596			0.299967
$708$	−5.33257	+	3.87434i	−0.200410	+	0.145607i
$709$	8.46002	+	26.0373i	0.317723	+	0.977850i	0.974619	+	0.223869i	$0.0718689\pi$
$709$	8.46002	+	26.0373i	0.317723	+	0.977850i	−0.656896	+	0.753981i	$0.728131\pi$
$710$	−24.3817	−	20.4947i	−0.915028	−	0.769151i
$711$	10.8137	−	33.2811i	0.405544	−	1.24814i
$712$	−4.85584	−	14.9447i	−0.181980	−	0.560077i
$713$	−18.8376	−	57.9763i	−0.705475	−	2.17123i
$714$	−6.66411	+	20.5100i	−0.249398	+	0.767568i
$715$	−0.355168	−	1.42978i	−0.0132825	−	0.0534706i
$716$	−4.62436	−	14.2323i	−0.172820	−	0.531887i
$717$	−42.1250	+	30.6056i	−1.57319	+	1.14299i
$718$	−22.9017			−0.854685
$719$	−38.7629	+	28.1629i	−1.44561	+	1.05030i	−0.458781	+	0.888549i	$0.651714\pi$
$719$	−38.7629	+	28.1629i	−1.44561	+	1.05030i	−0.986832	+	0.161750i	$0.948286\pi$
$720$	−10.4053	−	8.74647i	−0.387784	−	0.325962i
$721$	−10.2618	−	7.45566i	−0.382171	−	0.277663i
$722$	−13.1137	−	9.52767i	−0.488042	−	0.354583i
$723$	22.8241	−	70.2454i	0.848838	−	2.61246i
$724$	−6.55757			−0.243710
$725$	−23.8679	−	3.39658i	−0.886432	−	0.126146i
$726$	33.0432			1.22635
$727$	−5.76572	+	17.7451i	−0.213839	+	0.658128i	0.785395	+	0.618994i	$0.212460\pi$
$727$	−5.76572	+	17.7451i	−0.213839	+	0.658128i	−0.999234	+	0.0391332i	$0.987540\pi$
$728$	2.90726	+	2.11225i	0.107750	+	0.0782850i
$729$	20.0567	+	14.5721i	0.742842	+	0.539706i
$730$	6.81978	−	16.8376i	0.252412	−	0.623187i
$731$	5.72909	−	4.16242i	0.211898	−	0.153953i
$732$	7.92809			0.293031
$733$	−19.1112	+	13.8851i	−0.705890	+	0.512859i	−0.881845	−	0.471539i	$-0.843699\pi$
$733$	−19.1112	+	13.8851i	−0.705890	+	0.512859i	0.175955	+	0.984398i	$0.443699\pi$
$734$	2.88371	+	8.87515i	0.106440	+	0.327588i
$735$	2.52935	−	6.24479i	0.0932965	−	0.230343i
$736$	−2.22771	+	6.85619i	−0.0821146	+	0.252723i
$737$	0.155908	+	0.479834i	0.00574293	+	0.0176749i
$738$	11.6025	+	35.7089i	0.427095	+	1.31446i
$739$	1.94602	−	5.98922i	0.0715854	−	0.220317i	−0.908863	−	0.417096i	$-0.863048\pi$
$739$	1.94602	−	5.98922i	0.0715854	−	0.220317i	0.980448	+	0.196779i	$0.0630480\pi$
$740$	13.6983	+	0.969799i	0.503560	+	0.0356505i
$741$	5.58950	+	17.2027i	0.205335	+	0.631958i
$742$	4.61189	−	3.35074i	0.169308	−	0.123009i
$743$	35.4884			1.30194			0.650972	−	0.759101i	$-0.274361\pi$
$743$	35.4884			1.30194			0.650972	+	0.759101i	$0.274361\pi$
$744$	−20.6132	+	14.9763i	−0.755715	+	0.549059i
$745$	1.31455	+	5.29187i	0.0481612	+	0.193879i
$746$	−13.7316	−	9.97662i	−0.502751	−	0.365270i
$747$	23.1508	+	16.8200i	0.847043	+	0.615413i
$748$	−0.405492	+	1.24798i	−0.0148263	+	0.0456305i
$749$	11.7747			0.430239
$750$	−32.9334	−	7.08968i	−1.20256	−	0.258878i
$751$	−29.7840			−1.08684			−0.543418	−	0.839463i	$-0.682870\pi$
$751$	−29.7840			−1.08684			−0.543418	+	0.839463i	$0.682870\pi$
$752$	3.58208	−	11.0245i	0.130625	−	0.402022i
$753$	−4.80634	−	3.49201i	−0.175153	−	0.127256i
$754$	14.0179	+	10.1846i	0.510500	+	0.370900i
$755$	−5.67383	−	22.8407i	−0.206492	−	0.831259i
$756$	7.50563	−	5.45316i	0.272977	−	0.198329i
$757$	−14.2138			−0.516610			−0.258305	−	0.966063i	$-0.583164\pi$
$757$	−14.2138			−0.516610			−0.258305	+	0.966063i	$0.583164\pi$
$758$	−2.30280	+	1.67308i	−0.0836413	+	0.0607690i
$759$	1.23066	+	3.78758i	0.0446701	+	0.137480i
$760$	3.72602	+	0.263791i	0.135157	+	0.00956870i
$761$	8.23921	−	25.3577i	0.298671	−	0.919216i	−0.683292	−	0.730145i	$-0.739452\pi$
$761$	8.23921	−	25.3577i	0.298671	−	0.919216i	0.981963	−	0.189071i	$-0.0605475\pi$
$762$	−4.20048	−	12.9277i	−0.152167	−	0.468323i
$763$	5.23491	+	16.1114i	0.189516	+	0.583272i
$764$	−5.96192	+	18.3489i	−0.215695	+	0.663839i
$765$	−36.5227	+	90.1720i	−1.32048	+	3.26017i
$766$	−1.48779	−	4.57895i	−0.0537561	−	0.165444i
$767$	6.35980	−	4.62066i	0.229639	−	0.166843i
$768$	3.01314			0.108727
$769$	5.84155	−	4.24413i	0.210652	−	0.153047i	−0.477457	−	0.878655i	$-0.658441\pi$
$769$	5.84155	−	4.24413i	0.210652	−	0.153047i	0.688108	+	0.725608i	$0.258441\pi$
$770$	0.153904	−	0.379978i	0.00554631	−	0.0136934i
$771$	3.53599	+	2.56905i	0.127346	+	0.0925221i
$772$	−6.22993	−	4.52631i	−0.224220	−	0.162905i
$773$	1.31789	−	4.05606i	0.0474013	−	0.145886i	−0.924554	−	0.381050i	$-0.875563\pi$
$773$	1.31789	−	4.05606i	0.0474013	−	0.145886i	0.971956	+	0.235164i	$0.0755626\pi$
$774$	−6.01478			−0.216197
$775$	−18.6002	+	37.9691i	−0.668140	+	1.36389i
$776$	−1.32788			−0.0476683
$777$	−5.71833	+	17.5992i	−0.205144	+	0.631368i
$778$	−17.1719	−	12.4761i	−0.615642	−	0.447290i
$779$	−8.34722	−	6.06461i	−0.299070	−	0.217287i
$780$	18.5340	+	15.5792i	0.663622	+	0.557825i
$781$	2.11280	−	1.53504i	0.0756018	−	0.0549279i
$782$	51.5961			1.84507
$783$	36.1897	−	26.2934i	1.29332	−	0.939648i
$784$	0.309017	+	0.951057i	0.0110363	+	0.0339663i
$785$	5.66470	+	22.8040i	0.202182	+	0.813909i
$786$	2.44519	−	7.52552i	0.0872170	−	0.268426i
$787$	13.4453	+	41.3805i	0.479274	+	1.47505i	0.840106	+	0.542423i	$0.182493\pi$
$787$	13.4453	+	41.3805i	0.479274	+	1.47505i	−0.360832	+	0.932631i	$0.617507\pi$
$788$	5.87835	+	18.0917i	0.209407	+	0.644490i
$789$	9.12433	−	28.0818i	0.324835	−	0.999739i
$790$	9.85329	+	8.28244i	0.350564	+	0.294676i
$791$	0.648447	+	1.99572i	0.0230561	+	0.0709595i
$792$	0.901674	−	0.655104i	0.0320396	−	0.0232781i
$793$	−9.45529			−0.335767
$794$	18.0602	−	13.1215i	0.640933	−	0.465665i
$795$	32.5897	−	20.3251i	1.15584	−	0.720857i
$796$	22.5716	+	16.3992i	0.800030	+	0.581256i
$797$	−23.4461	−	17.0346i	−0.830502	−	0.603395i	0.0891992	−	0.996014i	$-0.471569\pi$
$797$	−23.4461	−	17.0346i	−0.830502	−	0.603395i	−0.919701	+	0.392619i	$0.871569\pi$
$798$	−1.55542	+	4.78709i	−0.0550612	+	0.169461i
$799$	−82.9646			−2.93508
$800$	4.41880	−	2.33971i	0.156228	−	0.0827212i
$801$	95.5243			3.37519
$802$	−0.356178	+	1.09620i	−0.0125771	+	0.0387083i
$803$	1.20503	+	0.875505i	0.0425246	+	0.0308959i
$804$	−6.70815	−	4.87375i	−0.236578	−	0.171884i
$805$	−16.0796	−	1.13839i	−0.566732	−	0.0401229i
$806$	24.5839	−	17.8613i	0.865931	−	0.629136i
$807$	−0.383989			−0.0135170
$808$	−6.45269	+	4.68815i	−0.227005	+	0.164929i
$809$	12.8680	+	39.6037i	0.452415	+	1.39239i	0.874143	+	0.485669i	$0.161424\pi$
$809$	12.8680	+	39.6037i	0.452415	+	1.39239i	−0.421728	+	0.906722i	$0.638576\pi$
$810$	18.4368	−	11.4984i	0.647802	−	0.404012i
$811$	−0.273462	+	0.841631i	−0.00960257	+	0.0295537i	−0.955743	−	0.294203i	$-0.904946\pi$
$811$	−0.273462	+	0.841631i	−0.00960257	+	0.0295537i	0.946140	+	0.323757i	$0.104946\pi$
$812$	1.48998	+	4.58569i	0.0522881	+	0.160926i
$813$	5.25164	+	16.1629i	0.184183	+	0.566857i
$814$	−0.347944	+	1.07086i	−0.0121954	+	0.0375337i
$815$	−14.9160	+	9.30260i	−0.522484	+	0.325856i
$816$	−6.66411	−	20.5100i	−0.233290	−	0.717994i
$817$	1.33718	−	0.971520i	0.0467821	−	0.0339892i
$818$	−36.7454			−1.28477
$819$	−17.6732	+	12.8404i	−0.617553	+	0.448678i
$820$	−13.7765	−	0.975331i	−0.481095	−	0.0340600i
$821$	−35.1340	−	25.5264i	−1.22619	−	0.890876i	−0.229588	−	0.973288i	$-0.573738\pi$
$821$	−35.1340	−	25.5264i	−1.22619	−	0.890876i	−0.996598	+	0.0824115i	$0.973738\pi$
$822$	−23.1127	−	16.7924i	−0.806148	−	0.585701i
$823$	3.52058	−	10.8352i	0.122720	−	0.377693i	−0.870759	−	0.491710i	$-0.836372\pi$
$823$	3.52058	−	10.8352i	0.122720	−	0.377693i	0.993479	+	0.114017i	$0.0363720\pi$
$824$	12.6843			0.441879
$825$	1.21515	−	2.48051i	0.0423060	−	0.0863603i
$826$	2.18756			0.0761149
$827$	9.27476	−	28.5448i	0.322515	−	0.992599i	−0.650035	−	0.759904i	$-0.725246\pi$
$827$	9.27476	−	28.5448i	0.322515	−	0.992599i	0.972550	−	0.232695i	$-0.0747542\pi$
$828$	−35.4541	−	25.7589i	−1.23212	−	0.895185i
$829$	8.71350	+	6.33073i	0.302632	+	0.219875i	0.728729	−	0.684803i	$-0.240112\pi$
$829$	8.71350	+	6.33073i	0.302632	+	0.219875i	−0.426096	+	0.904678i	$0.640112\pi$
$830$	−8.93132	+	5.57016i	−0.310011	+	0.193343i
$831$	−1.52824	+	1.11033i	−0.0530140	+	0.0385169i
$832$	−3.59357			−0.124585
$833$	5.79026	−	4.20687i	0.200621	−	0.145759i
$834$	18.8623	+	58.0521i	0.653147	+	2.01018i
$835$	8.75436	+	7.35870i	0.302957	+	0.254658i
$836$	−0.0946428	+	0.291281i	−0.00327329	+	0.0100742i
$837$	−24.2426	−	74.6111i	−0.837947	−	2.57894i
$838$	6.25003	+	19.2356i	0.215904	+	0.664483i
$839$	−14.1935	+	43.6830i	−0.490013	+	1.50811i	0.334573	+	0.942370i	$0.391408\pi$
$839$	−14.1935	+	43.6830i	−0.490013	+	1.50811i	−0.824587	+	0.565736i	$0.808592\pi$
$840$	1.62431	+	6.53886i	0.0560439	+	0.225612i
$841$	−1.77729	−	5.46993i	−0.0612858	−	0.188618i
$842$	−6.39605	+	4.64700i	−0.220423	+	0.160146i
$843$	−97.9447			−3.37339
$844$	−7.79480	+	5.66325i	−0.268308	+	0.194937i
$845$	0.147678	+	0.124134i	0.00508027	+	0.00427035i
$846$	57.0089	+	41.4194i	1.96001	+	1.42403i
$847$	−8.87199	−	6.44588i	−0.304845	−	0.221483i
$848$	−1.76159	+	5.42160i	−0.0604931	+	0.186179i
$849$	26.4113			0.906432
$850$	−25.6990	−	24.9034i	−0.881470	−	0.854180i
$851$	44.2736			1.51768
$852$	−13.2630	+	40.8193i	−0.454383	+	1.39845i
$853$	−26.3676	−	19.1572i	−0.902811	−	0.655931i	0.0363754	−	0.999338i	$-0.488419\pi$
$853$	−26.3676	−	19.1572i	−0.902811	−	0.655931i	−0.939186	+	0.343408i	$0.888419\pi$
$854$	−2.12866	−	1.54656i	−0.0728414	−	0.0529223i
$855$	−8.52449	+	21.0464i	−0.291531	+	0.719770i
$856$	−9.52595	+	6.92100i	−0.325590	+	0.236555i
$857$	−7.44453			−0.254300			−0.127150	−	0.991883i	$-0.540583\pi$
$857$	−7.44453			−0.254300			−0.127150	+	0.991883i	$0.540583\pi$
$858$	−1.60606	+	1.16687i	−0.0548300	+	0.0398363i
$859$	−8.45901	−	26.0342i	−0.288618	−	0.888274i	−0.985291	−	0.170886i	$-0.945337\pi$
$859$	−8.45901	−	26.0342i	−0.288618	−	0.888274i	0.696673	−	0.717389i	$-0.254663\pi$
$860$	0.830572	−	2.05062i	0.0283223	−	0.0699257i
$861$	5.75095	−	17.6996i	0.195992	−	0.603201i
$862$	−6.35174	−	19.5486i	−0.216341	−	0.665829i
$863$	6.97194	+	21.4574i	0.237328	+	0.730419i	0.996804	+	0.0798845i	$0.0254552\pi$
$863$	6.97194	+	21.4574i	0.237328	+	0.730419i	−0.759477	+	0.650535i	$0.774545\pi$
$864$	−2.86689	+	8.82340i	−0.0975337	+	0.300178i
$865$	13.7921	+	0.976437i	0.468945	+	0.0331999i
$866$	3.09690	+	9.53126i	0.105237	+	0.323886i
$867$	−83.4293	+	60.6149i	−2.83341	+	2.05859i
$868$	8.45605			0.287017
$869$	−0.853838	+	0.620349i	−0.0289645	+	0.0210439i
$870$	7.83189	+	31.5283i	0.265526	+	1.06891i
$871$	8.00035	+	5.81260i	0.271082	+	0.196952i
$872$	−13.7052	−	9.95739i	−0.464116	−	0.337200i
$873$	2.49445	−	7.67713i	0.0844244	−	0.259832i
$874$	12.0427			0.407349
$875$	7.45950	+	8.32802i	0.252177	+	0.281538i
$876$	−24.4793			−0.827080
$877$	6.39595	−	19.6847i	0.215976	−	0.664706i	−0.783107	−	0.621887i	$-0.786366\pi$
$877$	6.39595	−	19.6847i	0.215976	−	0.664706i	0.999083	−	0.0428185i	$-0.0136337\pi$
$878$	−13.2747	−	9.64462i	−0.447999	−	0.325490i
$879$	−65.5912	−	47.6548i	−2.21234	−	1.60736i
$880$	0.0988345	+	0.397871i	0.00333171	+	0.0134122i
$881$	2.87805	−	2.09103i	0.0969640	−	0.0704485i	−0.538247	−	0.842787i	$-0.680913\pi$
$881$	2.87805	−	2.09103i	0.0969640	−	0.0704485i	0.635211	+	0.772339i	$0.280913\pi$
$882$	−6.07900			−0.204691
$883$	8.49932	−	6.17512i	0.286025	−	0.207809i	−0.435516	−	0.900181i	$-0.643434\pi$
$883$	8.49932	−	6.17512i	0.286025	−	0.207809i	0.721541	+	0.692372i	$0.243434\pi$
$884$	7.94783	+	24.4609i	0.267314	+	0.822709i
$885$	14.7021	+	1.04086i	0.494205	+	0.0349882i
$886$	−5.79304	+	17.8291i	−0.194621	+	0.598981i
$887$	−16.2394	−	49.9796i	−0.545264	−	1.67815i	−0.720361	−	0.693599i	$-0.756024\pi$
$887$	−16.2394	−	49.9796i	−0.545264	−	1.67815i	0.175097	−	0.984551i	$-0.443976\pi$
$888$	−5.71833	−	17.5992i	−0.191895	−	0.590591i
$889$	−1.39405	+	4.29046i	−0.0467551	+	0.143897i
$890$	−13.1908	+	32.5672i	−0.442157	+	1.09165i
$891$	0.550537	+	1.69438i	0.0184437	+	0.0567638i
$892$	14.7732	−	10.7333i	0.494643	−	0.359379i
$893$	−19.3642			−0.647997
$894$	5.94433	−	4.31881i	0.198808	−	0.144443i
$895$	−12.5620	+	31.0147i	−0.419902	+	1.03671i
$896$	−0.809017	−	0.587785i	−0.0270274	−	0.0196365i
$897$	63.1508	+	45.8818i	2.10855	+	1.53195i
$898$	−7.19634	+	22.1481i	−0.240145	+	0.739090i
$899$	40.7724			1.35983
$900$	5.22620	+	29.9423i	0.174207	+	0.998078i
$901$	40.8002			1.35925
$902$	0.349929	−	1.07697i	0.0116514	−	0.0358592i
$903$	2.41193	+	1.75237i	0.0802639	+	0.0583151i
$904$	−1.69766	−	1.23342i	−0.0564632	−	0.0410229i
$905$	11.2245	+	9.43503i	0.373114	+	0.313631i
$906$	−25.6569	+	18.6408i	−0.852392	+	0.619299i
$907$	−44.0801			−1.46366			−0.731828	−	0.681490i	$-0.761332\pi$
$907$	−44.0801			−1.46366			−0.731828	+	0.681490i	$0.761332\pi$
$908$	21.5487	−	15.6561i	0.715119	−	0.519565i
$909$	−14.9830	−	46.1128i	−0.496954	−	1.52947i
$910$	−1.93720	−	7.79845i	−0.0642176	−	0.258516i
$911$	−4.46983	+	13.7567i	−0.148092	+	0.455781i	−0.997396	−	0.0721242i	$-0.977022\pi$
$911$	−4.46983	+	13.7567i	−0.148092	+	0.455781i	0.849304	+	0.527905i	$0.177022\pi$
$912$	−1.55542	−	4.78709i	−0.0515051	−	0.158516i
$913$	−0.266697	−	0.820807i	−0.00882637	−	0.0271648i
$914$	3.70633	−	11.4069i	0.122594	−	0.377307i
$915$	−13.5704	−	11.4069i	−0.448623	−	0.377101i
$916$	3.36400	+	10.3533i	0.111150	+	0.342083i
$917$	−2.12456	+	1.54358i	−0.0701591	+	0.0509736i
$918$	66.4003			2.19154
$919$	−2.10263	+	1.52765i	−0.0693593	+	0.0503925i	−0.621925	−	0.783077i	$-0.713649\pi$
$919$	−2.10263	+	1.52765i	−0.0693593	+	0.0503925i	0.552565	+	0.833470i	$0.313649\pi$
$920$	13.6778	−	8.53039i	0.450944	−	0.281239i
$921$	36.4822	+	26.5059i	1.20213	+	0.873398i
$922$	−26.6634	−	19.3721i	−0.878111	−	0.637985i
$923$	15.8179	−	48.6825i	0.520652	−	1.60240i
$924$	−0.552432			−0.0181737
$925$	−22.0518	−	21.3691i	−0.725060	−	0.702612i
$926$	−12.1607			−0.399627
$927$	−23.8277	+	73.3341i	−0.782605	+	2.40861i
$928$	−3.90082	−	2.83411i	−0.128051	−	0.0930343i
$929$	16.4324	+	11.9388i	0.539128	+	0.391699i	0.823761	−	0.566937i	$-0.191872\pi$
$929$	16.4324	+	11.9388i	0.539128	+	0.391699i	−0.284633	+	0.958637i	$0.591872\pi$
$930$	56.8311	+	4.02347i	1.86357	+	0.131935i
$931$	1.35146	−	0.981894i	0.0442923	−	0.0321803i
$932$	2.41456			0.0790915
$933$	−67.7452	+	49.2197i	−2.21788	+	1.61138i
$934$	5.29586	+	16.2990i	0.173286	+	0.533319i
$935$	2.48966	−	1.55272i	0.0814206	−	0.0507793i
$936$	6.75057	−	20.7761i	0.220649	−	0.679089i
$937$	−12.9959	−	39.9974i	−0.424559	−	1.30666i	−0.903416	−	0.428765i	$-0.858949\pi$
$937$	−12.9959	−	39.9974i	−0.424559	−	1.30666i	0.478857	−	0.877893i	$-0.341051\pi$
$938$	0.850370	+	2.61717i	0.0277656	+	0.0854537i
$939$	−7.85641	+	24.1795i	−0.256384	+	0.789070i
$940$	−21.9934	+	13.7166i	−0.717346	+	0.447385i
$941$	−5.14119	−	15.8230i	−0.167598	−	0.515814i	0.831620	−	0.555345i	$-0.187414\pi$
$941$	−5.14119	−	15.8230i	−0.167598	−	0.515814i	−0.999218	+	0.0395310i	$0.987414\pi$
$942$	25.6156	−	18.6108i	0.834601	−	0.606373i
$943$	−44.5261			−1.44997
$944$	−1.76977	+	1.28582i	−0.0576012	+	0.0418497i
$945$	−20.6933	−	1.46502i	−0.673152	−	0.0476571i
$946$	0.146759	+	0.106627i	0.00477154	+	0.00346673i
$947$	18.4614	+	13.4130i	0.599914	+	0.435863i	0.845848	−	0.533424i	$-0.179095\pi$
$947$	18.4614	+	13.4130i	0.599914	+	0.435863i	−0.245935	+	0.969286i	$0.579095\pi$
$948$	5.35994	−	16.4962i	0.174083	−	0.535771i
$949$	29.1949			0.947705
$950$	−5.99822	−	5.81252i	−0.194608	−	0.188583i
$951$	66.2648			2.14878
$952$	−2.21168	+	6.80686i	−0.0716810	+	0.220612i
$953$	−40.5183	−	29.4383i	−1.31252	−	0.953600i	−0.999993	−	0.00369060i	$-0.998825\pi$
$953$	−40.5183	−	29.4383i	−1.31252	−	0.953600i	−0.312525	−	0.949910i	$-0.601175\pi$
$954$	−28.0357	−	20.3691i	−0.907690	−	0.659475i
$955$	36.6053	−	22.8295i	1.18452	−	0.738744i
$956$	−13.9804	+	10.1574i	−0.452160	+	0.328513i
$957$	−2.66365			−0.0861035
$958$	0.983074	−	0.714245i	0.0317617	−	0.0230762i
$959$	2.92992	+	9.01738i	0.0946121	+	0.291186i
$960$	−5.15754	−	4.33530i	−0.166459	−	0.139921i
$961$	12.5167	−	38.5224i	0.403764	−	1.24266i
$962$	6.81987	+	20.9894i	0.219881	+	0.676725i
$963$	−22.1190	−	68.0752i	−0.712774	−	2.19369i
$964$	7.57487	−	23.3130i	0.243970	−	0.750862i
$965$	4.15121	+	16.7112i	0.133632	+	0.537953i
$966$	6.71240	+	20.6587i	0.215968	+	0.664681i
$967$	19.3096	−	14.0292i	0.620953	−	0.451149i	−0.232301	−	0.972644i	$-0.574625\pi$
$967$	19.3096	−	14.0292i	0.620953	−	0.451149i	0.853254	+	0.521495i	$0.174625\pi$
$968$	10.9664			0.352473
$969$	−29.1449	+	21.1750i	−0.936270	+	0.680240i
$970$	2.27292	+	1.91056i	0.0729790	+	0.0613444i
$971$	−8.95016	−	6.50267i	−0.287224	−	0.208681i	0.434838	−	0.900509i	$-0.356806\pi$
$971$	−8.95016	−	6.50267i	−0.287224	−	0.208681i	−0.722062	+	0.691828i	$0.756806\pi$
$972$	−1.17074	−	0.850591i	−0.0375514	−	0.0272827i
$973$	6.26001	−	19.2663i	0.200687	−	0.617650i
$974$	−33.8040			−1.08315
$975$	−9.30890	−	53.3333i	−0.298123	−	1.70803i
$976$	2.63117			0.0842218
$977$	−17.5734	+	54.0855i	−0.562224	+	1.73035i	0.113834	+	0.993500i	$0.463687\pi$
$977$	−17.5734	+	54.0855i	−0.562224	+	1.73035i	−0.676058	+	0.736848i	$0.736313\pi$
$978$	19.1641	+	13.9235i	0.612800	+	0.445226i
$979$	−2.33077	−	1.69340i	−0.0744916	−	0.0541213i
$980$	0.839441	−	2.07252i	0.0268149	−	0.0662042i
$981$	83.3138	−	60.5310i	2.66000	−	1.93261i
$982$	−2.42943			−0.0775262
$983$	3.94022	−	2.86274i	0.125673	−	0.0913071i	−0.523173	−	0.852227i	$-0.675252\pi$
$983$	3.94022	−	2.86274i	0.125673	−	0.0913071i	0.648846	+	0.760919i	$0.275252\pi$
$984$	5.75095	+	17.6996i	0.183334	+	0.564243i
$985$	15.9685	−	39.4250i	0.508797	−	1.25618i
$986$	−10.6640	+	32.8205i	−0.339612	+	1.04522i
$987$	−10.7933	−	33.2184i	−0.343554	−	1.05735i
$988$	1.85504	+	5.70924i	0.0590168	+	0.181635i
$989$	2.20418	−	6.78376i	0.0700887	−	0.215711i
$990$	−2.48594	−	0.175997i	−0.0790085	−	0.00559356i
$991$	3.87241	+	11.9181i	0.123011	+	0.378589i	0.993533	−	0.113540i	$-0.0362189\pi$
$991$	3.87241	+	11.9181i	0.123011	+	0.378589i	−0.870522	+	0.492129i	$0.836219\pi$
$992$	−6.84109	+	4.97034i	−0.217205	+	0.157809i
$993$	0.846065			0.0268490
$994$	11.5239	−	8.37258i	0.365515	−	0.265562i
$995$	−15.0402	−	60.5463i	−0.476807	−	1.91945i
$996$	11.4750	+	8.33707i	0.363599	+	0.264170i
$997$	−0.320664	−	0.232976i	−0.0101555	−	0.00737842i	0.582696	−	0.812690i	$-0.301998\pi$
$997$	−0.320664	−	0.232976i	−0.0101555	−	0.00737842i	−0.592851	+	0.805312i	$0.701998\pi$
$998$	2.80640	−	8.63722i	0.0888351	−	0.273406i
$999$	56.9767			1.80266

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.2.h.b.71.1	✓	12
25.6	even	5	inner	350.2.h.b.281.1	yes	12
25.9	even	10		8750.2.a.q.1.1		6
25.16	even	5		8750.2.a.p.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.2.h.b.71.1	✓	12	1.1	even	1	trivial
350.2.h.b.281.1	yes	12	25.6	even	5	inner
8750.2.a.p.1.6		6	25.16	even	5
8750.2.a.q.1.1		6	25.9	even	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.309017 + 0.951057i) q^{2} +(-2.43768 - 1.77108i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.539075 + 2.17011i) q^{5} +(2.43768 - 1.77108i) q^{6} -1.00000 q^{7} +(0.809017 - 0.587785i) q^{8} +(1.87852 + 5.78148i) q^{9} +O(q^{10})\)	\(q+(-0.309017 + 0.951057i) q^{2} +(-2.43768 - 1.77108i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.539075 + 2.17011i) q^{5} +(2.43768 - 1.77108i) q^{6} -1.00000 q^{7} +(0.809017 - 0.587785i) q^{8} +(1.87852 + 5.78148i) q^{9} +(-2.23049 - 0.157911i) q^{10} +(0.0566555 - 0.174368i) q^{11} +(0.931111 + 2.86567i) q^{12} +(-1.11047 - 3.41769i) q^{13} +(0.309017 - 0.951057i) q^{14} +(2.52935 - 6.24479i) q^{15} +(0.309017 + 0.951057i) q^{16} +(5.79026 - 4.20687i) q^{17} -6.07900 q^{18} +(1.35146 - 0.981894i) q^{19} +(0.839441 - 2.07252i) q^{20} +(2.43768 + 1.77108i) q^{21} +(0.148326 + 0.107765i) q^{22} +(2.22771 - 6.85619i) q^{23} -3.01314 q^{24} +(-4.41880 + 2.33971i) q^{25} +3.59357 q^{26} +(2.86689 - 8.82340i) q^{27} +(0.809017 + 0.587785i) q^{28} +(3.90082 + 2.83411i) q^{29} +(5.15754 + 4.33530i) q^{30} +(6.84109 - 4.97034i) q^{31} -1.00000 q^{32} +(-0.446927 + 0.324711i) q^{33} +(2.21168 + 6.80686i) q^{34} +(-0.539075 - 2.17011i) q^{35} +(1.87852 - 5.78148i) q^{36} +(1.89780 + 5.84083i) q^{37} +(0.516212 + 1.58874i) q^{38} +(-3.34601 + 10.2980i) q^{39} +(1.71168 + 1.43880i) q^{40} +(-1.90862 - 5.87414i) q^{41} +(-2.43768 + 1.77108i) q^{42} +0.989435 q^{43} +(-0.148326 + 0.107765i) q^{44} +(-11.5338 + 7.19324i) q^{45} +(5.83223 + 4.23736i) q^{46} +(-9.37800 - 6.81352i) q^{47} +(0.931111 - 2.86567i) q^{48} +1.00000 q^{49} +(-0.859713 - 4.92553i) q^{50} -21.5655 q^{51} +(-1.11047 + 3.41769i) q^{52} +(4.61189 + 3.35074i) q^{53} +(7.50563 + 5.45316i) q^{54} +(0.408939 + 0.0289516i) q^{55} +(-0.809017 + 0.587785i) q^{56} -5.03344 q^{57} +(-3.90082 + 2.83411i) q^{58} +(0.675993 + 2.08049i) q^{59} +(-5.71688 + 3.56543i) q^{60} +(0.813077 - 2.50239i) q^{61} +(2.61306 + 8.04218i) q^{62} +(-1.87852 - 5.78148i) q^{63} +(0.309017 - 0.951057i) q^{64} +(6.81814 - 4.25224i) q^{65} +(-0.170711 - 0.525394i) q^{66} +(-2.22630 + 1.61750i) q^{67} -7.15715 q^{68} +(-17.5733 + 12.7678i) q^{69} +(2.23049 + 0.157911i) q^{70} +(11.5239 + 8.37258i) q^{71} +(4.91802 + 3.57315i) q^{72} +(-2.51052 + 7.72658i) q^{73} -6.14141 q^{74} +(14.9154 + 2.12257i) q^{75} -1.67050 q^{76} +(-0.0566555 + 0.174368i) q^{77} +(-8.75997 - 6.36449i) q^{78} +(-4.65710 - 3.38358i) q^{79} +(-1.89732 + 1.18329i) q^{80} +(-7.86144 + 5.71167i) q^{81} +6.17644 q^{82} +(3.80832 - 2.76690i) q^{83} +(-0.931111 - 2.86567i) q^{84} +(12.2508 + 10.2977i) q^{85} +(-0.305752 + 0.941009i) q^{86} +(-4.48952 - 13.8173i) q^{87} +(-0.0566555 - 0.174368i) q^{88} +(4.85584 - 14.9447i) q^{89} +(-3.27704 - 13.1921i) q^{90} +(1.11047 + 3.41769i) q^{91} +(-5.83223 + 4.23736i) q^{92} -25.4793 q^{93} +(9.37800 - 6.81352i) q^{94} +(2.85936 + 2.40351i) q^{95} +(2.43768 + 1.77108i) q^{96} +(-1.07428 - 0.780511i) q^{97} +(-0.309017 + 0.951057i) q^{98} +1.11453 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} + q^{3} - 3 q^{4} - 5 q^{5} - q^{6} - 12 q^{7} + 3 q^{8} + 6 q^{9}+O(q^{10}) \) 12 * q + 3 * q^2 + q^3 - 3 * q^4 - 5 * q^5 - q^6 - 12 * q^7 + 3 * q^8 + 6 * q^9	\( 12 q + 3 q^{2} + q^{3} - 3 q^{4} - 5 q^{5} - q^{6} - 12 q^{7} + 3 q^{8} + 6 q^{9} + 7 q^{11} - 4 q^{12} + 3 q^{13} - 3 q^{14} - 10 q^{15} - 3 q^{16} + 4 q^{17} - 6 q^{18} + 4 q^{19} + 5 q^{20} - q^{21} - 2 q^{22} - q^{23} - 6 q^{24} - 5 q^{25} + 12 q^{26} + 10 q^{27} + 3 q^{28} + 22 q^{29} + 15 q^{30} + 31 q^{31} - 12 q^{32} - 21 q^{33} + 6 q^{34} + 5 q^{35} + 6 q^{36} + 9 q^{37} - 4 q^{38} - 20 q^{39} - 19 q^{41} + q^{42} + 50 q^{43} + 2 q^{44} - 25 q^{45} + 16 q^{46} - 24 q^{47} - 4 q^{48} + 12 q^{49} - 58 q^{51} + 3 q^{52} + 35 q^{53} + 25 q^{54} - 10 q^{55} - 3 q^{56} - 44 q^{57} - 22 q^{58} + q^{59} - 5 q^{60} + 8 q^{61} + 19 q^{62} - 6 q^{63} - 3 q^{64} - 25 q^{65} - 14 q^{66} - 36 q^{67} + 4 q^{68} - 31 q^{69} + q^{71} + 9 q^{72} - 31 q^{73} - 14 q^{74} + 55 q^{75} - 16 q^{76} - 7 q^{77} - 30 q^{78} + 2 q^{79} - 8 q^{81} - 6 q^{82} - 19 q^{83} + 4 q^{84} + 20 q^{85} + 10 q^{86} + 28 q^{87} - 7 q^{88} + 40 q^{89} + 20 q^{90} - 3 q^{91} - 16 q^{92} + 50 q^{93} + 24 q^{94} - q^{96} + 28 q^{97} + 3 q^{98} - 24 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 + q^3 - 3 * q^4 - 5 * q^5 - q^6 - 12 * q^7 + 3 * q^8 + 6 * q^9 + 7 * q^11 - 4 * q^12 + 3 * q^13 - 3 * q^14 - 10 * q^15 - 3 * q^16 + 4 * q^17 - 6 * q^18 + 4 * q^19 + 5 * q^20 - q^21 - 2 * q^22 - q^23 - 6 * q^24 - 5 * q^25 + 12 * q^26 + 10 * q^27 + 3 * q^28 + 22 * q^29 + 15 * q^30 + 31 * q^31 - 12 * q^32 - 21 * q^33 + 6 * q^34 + 5 * q^35 + 6 * q^36 + 9 * q^37 - 4 * q^38 - 20 * q^39 - 19 * q^41 + q^42 + 50 * q^43 + 2 * q^44 - 25 * q^45 + 16 * q^46 - 24 * q^47 - 4 * q^48 + 12 * q^49 - 58 * q^51 + 3 * q^52 + 35 * q^53 + 25 * q^54 - 10 * q^55 - 3 * q^56 - 44 * q^57 - 22 * q^58 + q^59 - 5 * q^60 + 8 * q^61 + 19 * q^62 - 6 * q^63 - 3 * q^64 - 25 * q^65 - 14 * q^66 - 36 * q^67 + 4 * q^68 - 31 * q^69 + q^71 + 9 * q^72 - 31 * q^73 - 14 * q^74 + 55 * q^75 - 16 * q^76 - 7 * q^77 - 30 * q^78 + 2 * q^79 - 8 * q^81 - 6 * q^82 - 19 * q^83 + 4 * q^84 + 20 * q^85 + 10 * q^86 + 28 * q^87 - 7 * q^88 + 40 * q^89 + 20 * q^90 - 3 * q^91 - 16 * q^92 + 50 * q^93 + 24 * q^94 - q^96 + 28 * q^97 + 3 * q^98 - 24 * q^99

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