LMFDB - Embedded newform 930.2.y.b.29.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(29,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 5, 3]))

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

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

chi := DirichletCharacter("930.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.y (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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			29.1
Character	$\chi$	$=$	930.29
Dual form			930.2.y.b.449.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 + 0.587785i) q^{2} +(-1.73192 - 0.0210879i) q^{3} +(0.309017 + 0.951057i) q^{4} +(1.43197 - 1.71740i) q^{5} +(-1.38876 - 1.03506i) q^{6} +(-4.13806 + 1.34454i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(2.99911 + 0.0730452i) q^{9} +O(q^{10})$	\(q+(0.809017 + 0.587785i) q^{2} +(-1.73192 - 0.0210879i) q^{3} +(0.309017 + 0.951057i) q^{4} +(1.43197 - 1.71740i) q^{5} +(-1.38876 - 1.03506i) q^{6} +(-4.13806 + 1.34454i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(2.99911 + 0.0730452i) q^{9} +(2.16795 - 0.547714i) q^{10} +(-0.0282036 - 0.0868017i) q^{11} +(-0.515138 - 1.65367i) q^{12} +(-1.25200 + 0.909628i) q^{13} +(-4.13806 - 1.34454i) q^{14} +(-2.51628 + 2.94420i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(1.25345 + 0.407270i) q^{17} +(2.38340 + 1.82193i) q^{18} +(-1.83196 - 1.33100i) q^{19} +(2.07585 + 0.831180i) q^{20} +(7.19514 - 2.24137i) q^{21} +(0.0282036 - 0.0868017i) q^{22} +(-5.02483 - 1.63267i) q^{23} +(0.555249 - 1.64064i) q^{24} +(-0.898918 - 4.91853i) q^{25} -1.54755 q^{26} +(-5.19269 - 0.189754i) q^{27} +(-2.55746 - 3.52004i) q^{28} +(-4.85963 - 3.53073i) q^{29} +(-3.76627 + 0.902880i) q^{30} +(-4.69382 + 2.99467i) q^{31} -1.00000 q^{32} +(0.0470159 + 0.150928i) q^{33} +(0.774673 + 1.06625i) q^{34} +(-3.61647 + 9.03203i) q^{35} +(0.857306 + 2.87490i) q^{36} -8.06544 q^{37} +(-0.699747 - 2.15360i) q^{38} +(2.18754 - 1.54900i) q^{39} +(1.19084 + 1.89259i) q^{40} +(-3.15405 + 4.34118i) q^{41} +(7.13844 + 2.41589i) q^{42} +(5.75587 + 4.18188i) q^{43} +(0.0738379 - 0.0536464i) q^{44} +(4.42009 - 5.04607i) q^{45} +(-3.10552 - 4.27438i) q^{46} +(-5.10287 + 3.70746i) q^{47} +(1.41355 - 1.00094i) q^{48} +(9.65260 - 7.01303i) q^{49} +(2.16380 - 4.50755i) q^{50} +(-2.16228 - 0.731792i) q^{51} +(-1.25200 - 0.909628i) q^{52} +(-2.80937 - 0.912819i) q^{53} +(-4.08944 - 3.20570i) q^{54} +(-0.189460 - 0.0758607i) q^{55} -4.35101i q^{56} +(3.14475 + 2.34382i) q^{57} +(-1.85621 - 5.71284i) q^{58} +(-4.51294 - 6.21153i) q^{59} +(-3.57768 - 1.48331i) q^{60} -7.68126i q^{61} +(-5.55760 - 0.336219i) q^{62} +(-12.5087 + 3.73015i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-0.230627 + 3.45274i) q^{65} +(-0.0506769 + 0.149739i) q^{66} +0.694711i q^{67} +1.31795i q^{68} +(8.66819 + 2.93362i) q^{69} +(-8.23468 + 5.18136i) q^{70} +(3.24956 + 1.05585i) q^{71} +(-0.996246 + 2.82975i) q^{72} +(-1.83097 - 5.63513i) q^{73} +(-6.52508 - 4.74075i) q^{74} +(1.45314 + 8.53747i) q^{75} +(0.699747 - 2.15360i) q^{76} +(0.233416 + 0.321269i) q^{77} +(2.68024 + 0.0326346i) q^{78} +(-4.75174 - 1.54393i) q^{79} +(-0.149027 + 2.23110i) q^{80} +(8.98933 + 0.438141i) q^{81} +(-5.10337 + 1.65818i) q^{82} +(4.98588 - 6.86247i) q^{83} +(4.35509 + 6.15037i) q^{84} +(2.49434 - 1.56947i) q^{85} +(2.19855 + 6.76643i) q^{86} +(8.34205 + 6.21743i) q^{87} +0.0912687 q^{88} +(3.77643 + 11.6226i) q^{89} +(6.54193 - 1.48430i) q^{90} +(3.95780 - 5.44744i) q^{91} -5.28342i q^{92} +(8.19248 - 5.08755i) q^{93} -6.30750 q^{94} +(-4.90917 + 1.24026i) q^{95} +(1.73192 + 0.0210879i) q^{96} +(-10.4041 + 3.38051i) q^{97} +11.9313 q^{98} +(-0.0782452 - 0.262388i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 32 q^{2} - 32 q^{4} - 2 q^{5} + 32 q^{8} - 4 q^{9}+O(q^{10}) $ 128 * q + 32 * q^2 - 32 * q^4 - 2 * q^5 + 32 * q^8 - 4 * q^9	$ 128 q + 32 q^{2} - 32 q^{4} - 2 q^{5} + 32 q^{8} - 4 q^{9} + 2 q^{10} - 35 q^{15} - 32 q^{16} - 6 q^{18} - 8 q^{19} + 3 q^{20} + 20 q^{23} - 10 q^{25} - 48 q^{31} - 128 q^{32} + 8 q^{33} + 10 q^{34} - 16 q^{35} - 4 q^{36} - 12 q^{38} + 4 q^{39} - 3 q^{40} + 5 q^{45} + 10 q^{46} - 6 q^{47} + 46 q^{49} + 5 q^{50} + 34 q^{51} + 20 q^{53} + 35 q^{60} + 8 q^{62} - 36 q^{63} - 32 q^{64} - 8 q^{66} + 8 q^{69} + 16 q^{70} - 6 q^{72} + 5 q^{75} + 12 q^{76} - 50 q^{77} - 4 q^{78} - 10 q^{79} - 2 q^{80} - 24 q^{81} + 40 q^{83} - 30 q^{85} + 4 q^{87} - 5 q^{90} + 20 q^{91} + 26 q^{93} - 4 q^{94} + 26 q^{95} + 124 q^{98}+O(q^{100}) $ 128 * q + 32 * q^2 - 32 * q^4 - 2 * q^5 + 32 * q^8 - 4 * q^9 + 2 * q^10 - 35 * q^15 - 32 * q^16 - 6 * q^18 - 8 * q^19 + 3 * q^20 + 20 * q^23 - 10 * q^25 - 48 * q^31 - 128 * q^32 + 8 * q^33 + 10 * q^34 - 16 * q^35 - 4 * q^36 - 12 * q^38 + 4 * q^39 - 3 * q^40 + 5 * q^45 + 10 * q^46 - 6 * q^47 + 46 * q^49 + 5 * q^50 + 34 * q^51 + 20 * q^53 + 35 * q^60 + 8 * q^62 - 36 * q^63 - 32 * q^64 - 8 * q^66 + 8 * q^69 + 16 * q^70 - 6 * q^72 + 5 * q^75 + 12 * q^76 - 50 * q^77 - 4 * q^78 - 10 * q^79 - 2 * q^80 - 24 * q^81 + 40 * q^83 - 30 * q^85 + 4 * q^87 - 5 * q^90 + 20 * q^91 + 26 * q^93 - 4 * q^94 + 26 * q^95 + 124 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{10}\right)$

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 $

$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$3$	−1.73192	−	0.0210879i	−0.999926	−	0.0121751i
$3$	−1.73192	−	0.0210879i	−0.999926	−	0.0121751i
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	1.43197	−	1.71740i	0.640397	−	0.768044i
$5$	1.43197	−	1.71740i	0.640397	−	0.768044i
$6$	−1.38876	−	1.03506i	−0.566959	−	0.422561i
$7$	−4.13806	+	1.34454i	−1.56404	+	0.508187i	−0.957883	−	0.287160i	$-0.907289\pi$
$7$	−4.13806	+	1.34454i	−1.56404	+	0.508187i	−0.606155	+	0.795346i	$0.707289\pi$
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$	2.99911	+	0.0730452i	0.999704	+	0.0243484i
$10$	2.16795	−	0.547714i	0.685566	−	0.173202i
$11$	−0.0282036	−	0.0868017i	−0.00850370	−	0.0261717i	0.946715	−	0.322074i	$-0.104380\pi$
$11$	−0.0282036	−	0.0868017i	−0.00850370	−	0.0261717i	−0.955218	+	0.295902i	$0.904380\pi$
$12$	−0.515138	−	1.65367i	−0.148707	−	0.477374i
$13$	−1.25200	+	0.909628i	−0.347241	+	0.252285i	−0.747711	−	0.664025i	$-0.768847\pi$
$13$	−1.25200	+	0.909628i	−0.347241	+	0.252285i	0.400470	+	0.916310i	$0.368847\pi$
$14$	−4.13806	−	1.34454i	−1.10594	−	0.359342i
$15$	−2.51628	+	2.94420i	−0.649700	+	0.760190i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	1.25345	+	0.407270i	0.304005	+	0.0987774i	0.457047	−	0.889442i	$-0.348907\pi$
$17$	1.25345	+	0.407270i	0.304005	+	0.0987774i	−0.153042	+	0.988220i	$0.548907\pi$
$18$	2.38340	+	1.82193i	0.561772	+	0.429433i
$19$	−1.83196	−	1.33100i	−0.420281	−	0.305352i	0.357470	−	0.933925i	$-0.383639\pi$
$19$	−1.83196	−	1.33100i	−0.420281	−	0.305352i	−0.777751	+	0.628573i	$0.783639\pi$
$20$	2.07585	+	0.831180i	0.464173	+	0.185857i
$21$	7.19514	−	2.24137i	1.57011	−	0.489107i
$22$	0.0282036	−	0.0868017i	0.00601302	−	0.0185062i
$23$	−5.02483	−	1.63267i	−1.04775	−	0.340435i	−0.265965	−	0.963983i	$-0.585691\pi$
$23$	−5.02483	−	1.63267i	−1.04775	−	0.340435i	−0.781785	+	0.623548i	$0.785691\pi$
$24$	0.555249	−	1.64064i	0.113340	−	0.334894i
$25$	−0.898918	−	4.91853i	−0.179784	−	0.983706i
$26$	−1.54755			−0.303500
$27$	−5.19269	−	0.189754i	−0.999333	−	0.0365181i
$28$	−2.55746	−	3.52004i	−0.483314	−	0.665225i
$29$	−4.85963	−	3.53073i	−0.902411	−	0.655640i	0.0366735	−	0.999327i	$-0.488324\pi$
$29$	−4.85963	−	3.53073i	−0.902411	−	0.655640i	−0.939084	+	0.343688i	$0.888324\pi$
$30$	−3.76627	+	0.902880i	−0.687624	+	0.164843i
$31$	−4.69382	+	2.99467i	−0.843035	+	0.537859i
$31$	−4.69382	+	2.99467i	−0.843035	+	0.537859i
$32$	−1.00000			−0.176777
$33$	0.0470159	+	0.150928i	0.00818442	+	0.0262733i
$34$	0.774673	+	1.06625i	0.132855	+	0.182860i
$35$	−3.61647	+	9.03203i	−0.611295	+	1.52669i
$36$	0.857306	+	2.87490i	0.142884	+	0.479149i
$37$	−8.06544			−1.32595			−0.662975	−	0.748642i	$-0.730706\pi$
$37$	−8.06544			−1.32595			−0.662975	+	0.748642i	$0.730706\pi$
$38$	−0.699747	−	2.15360i	−0.113514	−	0.349360i
$39$	2.18754	−	1.54900i	0.350287	−	0.248039i
$40$	1.19084	+	1.89259i	0.188288	+	0.299245i
$41$	−3.15405	+	4.34118i	−0.492581	+	0.677979i	−0.980861	−	0.194708i	$-0.937624\pi$
$41$	−3.15405	+	4.34118i	−0.492581	+	0.677979i	0.488281	+	0.872687i	$0.337624\pi$
$42$	7.13844	+	2.41589i	1.10148	+	0.372781i
$43$	5.75587	+	4.18188i	0.877761	+	0.637731i	0.932658	−	0.360761i	$-0.117483\pi$
$43$	5.75587	+	4.18188i	0.877761	+	0.637731i	−0.0548968	+	0.998492i	$0.517483\pi$
$44$	0.0738379	−	0.0536464i	0.0111315	−	0.00808749i
$45$	4.42009	−	5.04607i	0.658908	−	0.752224i
$46$	−3.10552	−	4.27438i	−0.457884	−	0.630223i
$47$	−5.10287	+	3.70746i	−0.744331	+	0.540788i	−0.894064	−	0.447938i	$-0.852158\pi$
$47$	−5.10287	+	3.70746i	−0.744331	+	0.540788i	0.149734	+	0.988726i	$0.452158\pi$
$48$	1.41355	−	1.00094i	0.204028	−	0.144473i
$49$	9.65260	−	7.01303i	1.37894	−	1.00186i
$50$	2.16380	−	4.50755i	0.306007	−	0.637463i
$51$	−2.16228	−	0.731792i	−0.302780	−	0.102471i
$52$	−1.25200	−	0.909628i	−0.173621	−	0.126143i
$53$	−2.80937	−	0.912819i	−0.385896	−	0.125385i	0.109643	−	0.993971i	$-0.465029\pi$
$53$	−2.80937	−	0.912819i	−0.385896	−	0.125385i	−0.495539	+	0.868586i	$0.665029\pi$
$54$	−4.08944	−	3.20570i	−0.556502	−	0.436240i
$55$	−0.189460	−	0.0758607i	−0.0255467	−	0.0102291i
$56$		−	4.35101i		−	0.581428i
$57$	3.14475	+	2.34382i	0.416532	+	0.310446i
$58$	−1.85621	−	5.71284i	−0.243733	−	0.750132i
$59$	−4.51294	−	6.21153i	−0.587535	−	0.808673i	0.406961	−	0.913445i	$-0.366588\pi$
$59$	−4.51294	−	6.21153i	−0.587535	−	0.808673i	−0.994496	+	0.104773i	$0.966588\pi$
$60$	−3.57768	−	1.48331i	−0.461876	−	0.191495i
$61$		−	7.68126i		−	0.983485i	−0.870741	−	0.491742i	$-0.836360\pi$
$61$		−	7.68126i		−	0.983485i	0.870741	−	0.491742i	$-0.163640\pi$
$62$	−5.55760	−	0.336219i	−0.705816	−	0.0426998i
$63$	−12.5087	+	3.73015i	−1.57595	+	0.469954i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−0.230627	+	3.45274i	−0.0286058	+	0.428259i
$66$	−0.0506769	+	0.149739i	−0.00623789	+	0.0184316i
$67$			0.694711i			0.0848724i	0.999099	+	0.0424362i	$0.0135119\pi$
$67$			0.694711i			0.0848724i	−0.999099	+	0.0424362i	$0.986488\pi$
$68$			1.31795i			0.159825i
$69$	8.66819	+	2.93362i	1.04353	+	0.353166i
$70$	−8.23468	+	5.18136i	−0.984232	+	0.619290i
$71$	3.24956	+	1.05585i	0.385652	+	0.125306i	0.495425	−	0.868651i	$-0.335012\pi$
$71$	3.24956	+	1.05585i	0.385652	+	0.125306i	−0.109773	+	0.993957i	$0.535012\pi$
$72$	−0.996246	+	2.82975i	−0.117409	+	0.333489i
$73$	−1.83097	−	5.63513i	−0.214298	−	0.659543i	−0.999203	−	0.0399256i	$-0.987288\pi$
$73$	−1.83097	−	5.63513i	−0.214298	−	0.659543i	0.784904	−	0.619617i	$-0.212712\pi$
$74$	−6.52508	−	4.74075i	−0.758525	−	0.551100i
$75$	1.45314	+	8.53747i	0.167794	+	0.985822i
$76$	0.699747	−	2.15360i	0.0802665	−	0.247035i
$77$	0.233416	+	0.321269i	0.0266002	+	0.0366120i
$78$	2.68024	+	0.0326346i	0.303477	+	0.00369514i
$79$	−4.75174	−	1.54393i	−0.534612	−	0.173706i	0.0292541	−	0.999572i	$-0.490687\pi$
$79$	−4.75174	−	1.54393i	−0.534612	−	0.173706i	−0.563867	+	0.825866i	$0.690687\pi$
$80$	−0.149027	+	2.23110i	−0.0166617	+	0.249444i
$81$	8.98933	+	0.438141i	0.998814	+	0.0486824i
$82$	−5.10337	+	1.65818i	−0.563573	+	0.183116i
$83$	4.98588	−	6.86247i	0.547271	−	0.753254i	−0.442367	−	0.896834i	$-0.645861\pi$
$83$	4.98588	−	6.86247i	0.547271	−	0.753254i	0.989639	+	0.143579i	$0.0458613\pi$
$84$	4.35509	+	6.15037i	0.475179	+	0.671060i
$85$	2.49434	−	1.56947i	0.270550	−	0.170233i
$86$	2.19855	+	6.76643i	0.237075	+	0.729643i
$87$	8.34205	+	6.21743i	0.894361	+	0.666578i
$88$	0.0912687			0.00972927
$89$	3.77643	+	11.6226i	0.400301	+	1.23200i	0.924756	+	0.380560i	$0.124269\pi$
$89$	3.77643	+	11.6226i	0.400301	+	1.23200i	−0.524456	+	0.851438i	$0.675731\pi$
$90$	6.54193	−	1.48430i	0.689580	−	0.156458i
$91$	3.95780	−	5.44744i	0.414890	−	0.571047i
$92$		−	5.28342i		−	0.550835i
$93$	8.19248	−	5.08755i	0.849521	−	0.527555i
$94$	−6.30750			−0.650569
$95$	−4.90917	+	1.24026i	−0.503670	+	0.127248i
$96$	1.73192	+	0.0210879i	0.176764	+	0.00215227i
$97$	−10.4041	+	3.38051i	−1.05638	+	0.343239i	−0.785170	−	0.619281i	$-0.787424\pi$
$97$	−10.4041	+	3.38051i	−1.05638	+	0.343239i	−0.271211	+	0.962520i	$0.587424\pi$
$98$	11.9313			1.20524
$99$	−0.0782452	−	0.262388i	−0.00786394	−	0.0263710i
$100$	4.40002	−	2.37483i	0.440002	−	0.237483i
$101$	11.4463	+	3.71911i	1.13894	+	0.370066i	0.816968	−	0.576682i	$-0.195653\pi$
$101$	11.4463	+	3.71911i	1.13894	+	0.370066i	0.321976	+	0.946748i	$0.395653\pi$
$102$	−1.31919	−	1.86299i	−0.130619	−	0.184464i
$103$	9.64380	−	13.2736i	0.950232	−	1.30788i	−0.00119205	−	0.999999i	$-0.500379\pi$
$103$	9.64380	−	13.2736i	0.950232	−	1.30788i	0.951424	−	0.307883i	$-0.0996206\pi$
$104$	−0.478220	−	1.47181i	−0.0468933	−	0.144323i
$105$	6.45391	−	15.5665i	0.629837	−	1.51914i
$106$	−1.73628	−	2.38979i	−0.168643	−	0.232117i
$107$	−2.98679	+	9.19240i	−0.288744	+	0.888662i	0.696507	+	0.717550i	$0.254736\pi$
$107$	−2.98679	+	9.19240i	−0.288744	+	0.888662i	−0.985251	+	0.171113i	$0.945264\pi$
$108$	−1.42416	−	4.99718i	−0.137040	−	0.480853i
$109$	−11.5640	+	8.40176i	−1.10763	+	0.804743i	−0.982289	−	0.187370i	$-0.940004\pi$
$109$	−11.5640	+	8.40176i	−1.10763	+	0.804743i	−0.125344	+	0.992113i	$0.540004\pi$
$110$	−0.108686	−	0.172734i	−0.0103628	−	0.0164696i
$111$	13.9687	+	0.170083i	1.32585	+	0.0161436i
$112$	2.55746	−	3.52004i	0.241657	−	0.332613i
$113$	5.81850	+	17.9075i	0.547358	+	1.68459i	0.715316	+	0.698801i	$0.246283\pi$
$113$	5.81850	+	17.9075i	0.547358	+	1.68459i	−0.167958	+	0.985794i	$0.553717\pi$
$114$	1.16649	+	3.74462i	0.109252	+	0.350716i
$115$	−9.99935	+	6.29171i	−0.932445	+	0.586705i
$116$	1.85621	−	5.71284i	0.172345	−	0.530424i
$117$	−3.82132	+	2.63662i	−0.353281	+	0.243756i
$118$		−	7.67788i		−	0.706806i
$119$	−5.73442			−0.525673
$120$	−2.02253	−	3.30293i	−0.184631	−	0.301515i
$121$	8.89245	−	6.46074i	0.808404	−	0.587340i
$122$	4.51493	−	6.21427i	0.408763	−	0.562614i
$123$	5.55412	−	7.45208i	0.500798	−	0.671931i
$124$	−4.29857	−	3.53868i	−0.386023	−	0.317783i
$125$	−9.73430	−	5.49939i	−0.870663	−	0.491881i
$126$	−12.3123	−	4.33468i	−1.09686	−	0.386164i
$127$	−4.02408	+	2.92366i	−0.357079	+	0.259433i	−0.751833	−	0.659354i	$-0.770830\pi$
$127$	−4.02408	+	2.92366i	−0.357079	+	0.259433i	0.394754	+	0.918787i	$0.370830\pi$
$128$	−0.309017	−	0.951057i	−0.0273135	−	0.0840623i
$129$	−9.88053	−	7.36407i	−0.869932	−	0.648371i
$130$	−2.21605	+	2.65776i	−0.194360	+	0.233101i
$131$	9.93088	−	3.22674i	0.867665	−	0.281921i	0.158839	−	0.987305i	$-0.449225\pi$
$131$	9.93088	−	3.22674i	0.867665	−	0.281921i	0.708826	+	0.705383i	$0.249225\pi$
$132$	−0.129013	+	0.0913543i	−0.0112291	+	0.00795137i
$133$	9.37033	+	3.04461i	0.812511	+	0.264001i
$134$	−0.408341	+	0.562033i	−0.0352753	+	0.0485522i
$135$	−7.76166	+	8.64619i	−0.668017	+	0.744146i
$136$	−0.774673	+	1.06625i	−0.0664276	+	0.0914298i
$137$	1.68472	+	2.31882i	0.143935	+	0.198110i	0.874898	−	0.484308i	$-0.160928\pi$
$137$	1.68472	+	2.31882i	0.143935	+	0.198110i	−0.730962	+	0.682418i	$0.760928\pi$
$138$	5.28838	+	7.46838i	0.450177	+	0.635751i
$139$	−2.04858	−	2.81963i	−0.173758	−	0.239158i	0.713252	−	0.700908i	$-0.247222\pi$
$139$	−2.04858	−	2.81963i	−0.173758	−	0.239158i	−0.887010	+	0.461750i	$0.847222\pi$
$140$	−9.70752	−	0.648418i	−0.820435	−	0.0548013i
$141$	8.91597	−	6.31342i	0.750860	−	0.531686i
$142$	2.00834	+	2.76424i	0.168536	+	0.231970i
$143$	0.114268	+	0.0830205i	0.00955557	+	0.00694252i
$144$	−2.46927	+	1.70374i	−0.205772	+	0.141978i
$145$	−13.0225	+	3.29002i	−1.08146	+	0.273222i
$146$	1.83097	−	5.63513i	0.151532	−	0.466367i
$147$	−16.8655	+	11.9425i	−1.39104	+	0.984998i
$148$	−2.49236	−	7.67069i	−0.204871	−	0.630527i
$149$			9.15020i			0.749614i	0.927103	+	0.374807i	$0.122291\pi$
$149$			9.15020i			0.749614i	−0.927103	+	0.374807i	$0.877709\pi$
$150$	−3.84259	+	7.76109i	−0.313746	+	0.633690i
$151$	−21.7615	+	7.07074i	−1.77093	+	0.575409i	−0.998236	−	0.0593738i	$-0.981090\pi$
$151$	−21.7615	+	7.07074i	−1.77093	+	0.575409i	−0.772691	+	0.634783i	$0.781090\pi$
$152$	1.83196	−	1.33100i	0.148592	−	0.107958i
$153$	3.72948	+	1.31300i	0.301510	+	0.106150i
$154$			0.397111i			0.0320001i
$155$	−1.57837	+	12.3494i	−0.126778	+	0.991931i
$156$	2.14918	+	1.60181i	0.172072	+	0.128247i
$157$	12.4542	−	17.1418i	0.993957	−	1.36806i	0.0649960	−	0.997886i	$-0.479297\pi$
$157$	12.4542	−	17.1418i	0.993957	−	1.36806i	0.928961	−	0.370178i	$-0.120703\pi$
$158$	−2.93674	−	4.04207i	−0.233634	−	0.321570i
$159$	4.84636	+	1.64017i	0.384341	+	0.130074i
$160$	−1.43197	+	1.71740i	−0.113207	+	0.135772i
$161$	22.9882			1.81172
$162$	7.01499	+	5.63826i	0.551149	+	0.442983i
$163$	12.3745	+	4.02071i	0.969243	+	0.314926i	0.750510	−	0.660859i	$-0.229808\pi$
$163$	12.3745	+	4.02071i	0.969243	+	0.314926i	0.218733	+	0.975785i	$0.429808\pi$
$164$	−5.10337	−	1.65818i	−0.398506	−	0.129482i
$165$	0.326530	+	0.135380i	0.0254203	+	0.0105393i
$166$	8.06732	−	2.62123i	0.626146	−	0.203447i
$167$	11.3565	−	15.6309i	0.878795	−	1.20956i	−0.0979577	−	0.995191i	$-0.531231\pi$
$167$	11.3565	−	15.6309i	0.878795	−	1.20956i	0.976753	−	0.214367i	$-0.0687690\pi$
$168$	−0.0917536	+	7.53561i	−0.00707895	+	0.581385i
$169$	−3.27715	+	10.0860i	−0.252089	+	0.775849i
$170$	2.94048	+	0.196410i	0.225524	+	0.0150640i
$171$	−5.39703	−	4.12563i	−0.412721	−	0.315494i
$172$	−2.19855	+	6.76643i	−0.167638	+	0.515935i
$173$	11.2388	−	8.16549i	0.854473	−	0.620811i	−0.0719026	−	0.997412i	$-0.522907\pi$
$173$	11.2388	−	8.16549i	0.854473	−	0.620811i	0.926376	+	0.376601i	$0.122907\pi$
$174$	3.09435	+	9.93333i	0.234582	+	0.753044i
$175$	10.3329	+	19.1445i	0.781095	+	1.44719i
$176$	0.0738379	+	0.0536464i	0.00556574	+	0.00404375i
$177$	7.68508	+	10.8531i	0.577646	+	0.815766i
$178$	−3.77643	+	11.6226i	−0.283055	+	0.871154i
$179$	4.48822	+	13.8133i	0.335465	+	1.03246i	0.966492	+	0.256695i	$0.0826337\pi$
$179$	4.48822	+	13.8133i	0.335465	+	1.03246i	−0.631027	+	0.775761i	$0.717366\pi$
$180$	6.16498	+	2.64443i	0.459511	+	0.197104i
$181$		−	3.69704i		−	0.274799i	−0.990516	−	0.137399i	$-0.956126\pi$
$181$		−	3.69704i		−	0.274799i	0.990516	−	0.137399i	$-0.0438744\pi$
$182$	6.40385	−	2.08074i	0.474685	−	0.154235i
$183$	−0.161982	+	13.3033i	−0.0119740	+	0.983412i
$184$	3.10552	−	4.27438i	0.228942	−	0.315111i
$185$	−11.5495	+	13.8516i	−0.849134	+	1.01839i
$186$	9.61825	+	0.699503i	0.705244	+	0.0512900i
$187$		−	0.120288i		−	0.00879631i
$188$	−5.10287	−	3.70746i	−0.372165	−	0.270394i
$189$	21.7428	−	6.19654i	1.58155	−	0.450732i
$190$	−4.70061	−	1.88215i	−0.341018	−	0.136545i
$191$			3.78356i			0.273769i	0.990587	+	0.136884i	$0.0437089\pi$
$191$			3.78356i			0.273769i	−0.990587	+	0.136884i	$0.956291\pi$
$192$	1.38876	+	1.03506i	0.100225	+	0.0746989i
$193$	9.38737	−	3.05014i	0.675718	−	0.219554i	0.0489983	−	0.998799i	$-0.484397\pi$
$193$	9.38737	−	3.05014i	0.675718	−	0.219554i	0.626720	+	0.779245i	$0.284397\pi$
$194$	−10.4041	−	3.38051i	−0.746974	−	0.242707i
$195$	0.472239	−	5.97501i	0.0338177	−	0.427879i
$196$	9.65260	+	7.01303i	0.689472	+	0.500931i
$197$	−19.6837	+	6.39561i	−1.40240	+	0.455668i	−0.909967	−	0.414680i	$-0.863893\pi$
$197$	−19.6837	+	6.39561i	−1.40240	+	0.455668i	−0.492436	+	0.870349i	$0.663893\pi$
$198$	0.0909261	−	0.258268i	0.00646183	−	0.0183543i
$199$	13.0198	+	17.9202i	0.922949	+	1.27033i	0.962547	+	0.271114i	$0.0873921\pi$
$199$	13.0198	+	17.9202i	0.922949	+	1.27033i	−0.0395986	+	0.999216i	$0.512608\pi$
$200$	4.95558	+	0.664987i	0.350413	+	0.0470217i
$201$	0.0146500	−	1.20319i	0.00103333	−	0.0848661i
$202$	7.07417	+	9.73676i	0.497737	+	0.685076i
$203$	24.8566	+	8.07640i	1.74459	+	0.566852i
$204$	0.0277928	−	2.28259i	0.00194589	−	0.159813i
$205$	2.93903	+	11.6332i	0.205271	+	0.812499i
$206$	15.6040	−	5.07005i	1.08718	−	0.353247i
$207$	−14.9508	−	5.26359i	−1.03915	−	0.365845i
$208$	0.478220	−	1.47181i	0.0331586	−	0.102052i
$209$	−0.0638650	+	0.196556i	−0.00441763	+	0.0135961i
$210$	14.3711	−	8.80005i	0.991699	−	0.607261i
$211$	10.2802			0.707717			0.353858	−	0.935299i	$-0.384869\pi$
$211$	10.2802			0.707717			0.353858	+	0.935299i	$0.384869\pi$
$212$		−	2.95394i		−	0.202878i
$213$	−5.60572	−	1.89717i	−0.384098	−	0.129992i
$214$	−7.81952	+	5.68121i	−0.534531	+	0.388360i
$215$	15.4242	−	3.89679i	1.05192	−	0.265759i
$216$	1.78509	−	4.87990i	0.121460	−	0.332035i
$217$	15.3968	−	18.7031i	1.04521	−	1.26965i
$218$	−14.2939			−0.968107
$219$	3.05226	+	9.79823i	0.206253	+	0.662103i
$220$	0.0136015	−	0.203629i	0.000917013	−	0.0137287i
$221$	−1.93977	+	0.630271i	−0.130483	+	0.0423966i
$222$	11.2010	+	8.34820i	0.751759	+	0.560295i
$223$	−12.7533			−0.854022			−0.427011	−	0.904247i	$-0.640433\pi$
$223$	−12.7533			−0.854022			−0.427011	+	0.904247i	$0.640433\pi$
$224$	4.13806	−	1.34454i	0.276485	−	0.0898356i
$225$	−2.33668	−	14.8169i	−0.155779	−	0.987792i
$226$	−5.81850	+	17.9075i	−0.387041	+	1.19119i
$227$	−18.5005	−	13.4414i	−1.22792	−	0.892135i	−0.231186	−	0.972910i	$-0.574261\pi$
$227$	−18.5005	−	13.4414i	−1.22792	−	0.892135i	−0.996732	+	0.0807747i	$0.974261\pi$
$228$	−1.25732	+	3.71511i	−0.0832682	+	0.246039i
$229$	−5.68760	+	7.82830i	−0.375847	+	0.517309i	−0.954478	−	0.298280i	$-0.903587\pi$
$229$	−5.68760	+	7.82830i	−0.375847	+	0.517309i	0.578631	+	0.815589i	$0.303587\pi$
$230$	−11.7878	−	0.787373i	−0.777266	−	0.0519178i
$231$	−0.397483	−	0.561336i	−0.0261525	−	0.0369332i
$232$	4.85963	−	3.53073i	0.319050	−	0.231804i
$233$	13.3384	−	9.69093i	0.873829	−	0.634874i	−0.0577825	−	0.998329i	$-0.518403\pi$
$233$	13.3384	−	9.69093i	0.873829	−	0.634874i	0.931612	+	0.363455i	$0.118403\pi$
$234$	−4.64128	−	0.113041i	−0.303410	−	0.00738974i
$235$	−0.939988	+	14.0726i	−0.0613181	+	0.917998i
$236$	4.51294	−	6.21153i	0.293768	−	0.404336i
$237$	8.19709	+	2.77418i	0.532458	+	0.180202i
$238$	−4.63924	−	3.37061i	−0.300717	−	0.218484i
$239$	−0.482534	+	1.48509i	−0.0312125	+	0.0960623i	−0.965449	−	0.260592i	$-0.916082\pi$
$239$	−0.482534	+	1.48509i	−0.0312125	+	0.0960623i	0.934237	+	0.356654i	$0.116082\pi$
$240$	0.305152	−	3.86094i	0.0196975	−	0.249223i
$241$	−19.3337	+	6.28191i	−1.24539	+	0.404653i	−0.856268	−	0.516531i	$-0.827223\pi$
$241$	−19.3337	+	6.28191i	−1.24539	+	0.404653i	−0.389126	+	0.921184i	$0.627223\pi$
$242$	10.9917			0.706571
$243$	−15.5596	−	0.948393i	−0.998148	−	0.0608394i
$244$	7.30531	−	2.37364i	0.467675	−	0.151957i
$245$	1.77808	−	26.6198i	0.113598	−	1.70068i
$246$	8.87360	−	2.76423i	0.565760	−	0.176241i
$247$	3.50432			0.222975
$248$	−1.39763	−	5.38949i	−0.0887497	−	0.342233i
$249$	−8.77987	+	11.7801i	−0.556402	+	0.746536i
$250$	−4.64276	−	10.1708i	−0.293634	−	0.643257i
$251$	2.23300	−	1.62237i	0.140945	−	0.102403i	−0.515078	−	0.857143i	$-0.672237\pi$
$251$	2.23300	−	1.62237i	0.140945	−	0.102403i	0.656024	+	0.754740i	$0.272237\pi$
$252$	−7.41298	−	10.7438i	−0.466974	−	0.676796i
$253$			0.482211i			0.0303163i
$254$	−4.97403			−0.312099
$255$	−4.35311	+	2.66560i	−0.272602	+	0.166926i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−3.04322	+	9.36608i	−0.189831	+	0.584240i	−0.999998	−	0.00195919i	$-0.999376\pi$
$257$	−3.04322	+	9.36608i	−0.189831	+	0.584240i	0.810167	+	0.586199i	$0.199376\pi$
$258$	−3.66502	−	11.7653i	−0.228174	−	0.732475i
$259$	33.3752	−	10.8443i	2.07384	−	0.673830i
$260$	−3.35502	+	0.847615i	−0.208069	+	0.0525668i
$261$	−14.3167	−	10.9440i	−0.886179	−	0.677418i
$262$	9.93088	+	3.22674i	0.613532	+	0.199348i
$263$	−13.0646	−	17.9819i	−0.805597	−	1.10881i	−0.991988	−	0.126334i	$-0.959679\pi$
$263$	−13.0646	−	17.9819i	−0.805597	−	1.10881i	0.186391	−	0.982476i	$-0.440321\pi$
$264$	−0.158070	−	0.00192466i	−0.00972855	−	0.000118455i
$265$	−5.59061	+	3.51767i	−0.343428	+	0.216089i
$266$	5.79118	+	7.97088i	0.355080	+	0.488726i
$267$	−6.29538	−	20.2092i	−0.385271	−	1.23678i
$268$	−0.660709	+	0.214677i	−0.0403592	+	0.0131135i
$269$	−6.15781	−	4.47391i	−0.375448	−	0.272779i	0.384018	−	0.923325i	$-0.374540\pi$
$269$	−6.15781	−	4.47391i	−0.375448	−	0.272779i	−0.759467	+	0.650546i	$0.774540\pi$
$270$	−11.3614	+	2.43273i	−0.691434	+	0.148051i
$271$	6.13527	+	1.99347i	0.372691	+	0.121095i	0.489373	−	0.872075i	$-0.337226\pi$
$271$	6.13527	+	1.99347i	0.372691	+	0.121095i	−0.116682	+	0.993169i	$0.537226\pi$
$272$	−1.25345	+	0.407270i	−0.0760014	+	0.0246943i
$273$	−6.96948	+	9.35109i	−0.421812	+	0.565954i
$274$			2.86622i			0.173155i
$275$	−0.401584	+	0.216748i	−0.0242164	+	0.0130704i
$276$	−0.111416	+	9.15048i	−0.00670647	+	0.550794i
$277$	−6.62165	−	4.81091i	−0.397856	−	0.289059i	0.370811	−	0.928708i	$-0.379080\pi$
$277$	−6.62165	−	4.81091i	−0.397856	−	0.289059i	−0.768667	+	0.639649i	$0.779080\pi$
$278$		−	3.48525i		−	0.209031i
$279$	−14.2960	+	8.63849i	−0.855881	+	0.517173i
$280$	−7.47242	−	6.23052i	−0.446562	−	0.372345i
$281$	−15.4414	+	21.2533i	−0.921157	+	1.26786i	0.0420536	+	0.999115i	$0.486610\pi$
$281$	−15.4414	+	21.2533i	−0.921157	+	1.26786i	−0.963210	+	0.268748i	$0.913390\pi$
$282$	10.9241	+	0.133012i	0.650521	+	0.00792075i
$283$	7.81632	−	2.53968i	0.464632	−	0.150968i	−0.0673400	−	0.997730i	$-0.521451\pi$
$283$	7.81632	−	2.53968i	0.464632	−	0.150968i	0.531972	+	0.846762i	$0.321451\pi$
$284$			3.41679i			0.202749i
$285$	8.52846	−	2.04451i	0.505182	−	0.121106i
$286$	0.0436465	+	0.134330i	0.00258087	+	0.00794310i
$287$	7.21477	−	22.2048i	0.425875	−	1.31071i
$288$	−2.99911	−	0.0730452i	−0.176724	−	0.00430423i
$289$	−12.3480	−	8.97137i	−0.726355	−	0.527728i
$290$	−12.4693	−	4.99276i	−0.732220	−	0.293185i
$291$	18.0905	−	5.63538i	1.06048	−	0.330352i
$292$	4.79353	−	3.48270i	0.280520	−	0.203810i
$293$	4.79974	−	14.7721i	0.280404	−	0.862995i	−0.707335	−	0.706879i	$-0.750103\pi$
$293$	4.79974	−	14.7721i	0.280404	−	0.862995i	0.987739	−	0.156116i	$-0.0498974\pi$
$294$	−20.6640	−	0.251606i	−1.20515	−	0.0146739i
$295$	−17.1301	−	1.14421i	−0.997352	−	0.0666186i
$296$	2.49236	−	7.67069i	0.144865	−	0.445850i
$297$	0.129981	+	0.456085i	0.00754228	+	0.0264648i
$298$	−5.37835	+	7.40267i	−0.311560	+	0.428825i
$299$	7.77619	−	2.52664i	0.449708	−	0.146119i
$300$	−7.67057	+	4.02024i	−0.442861	+	0.232109i
$301$	−29.4408	−	9.56589i	−1.69694	−	0.551369i
$302$	−21.7615	−	7.07074i	−1.25223	−	0.406876i
$303$	−19.7456	−	6.68259i	−1.13435	−	0.383905i
$304$	2.26443			0.129874
$305$	−13.1918	−	10.9993i	−0.755360	−	0.629821i
$306$	2.24544	+	3.25437i	0.128364	+	0.186040i
$307$	−13.1127	−	18.0481i	−0.748380	−	1.03006i	−0.998092	−	0.0617368i	$-0.980336\pi$
$307$	−13.1127	−	18.0481i	−0.748380	−	1.03006i	0.249712	−	0.968320i	$-0.419664\pi$
$308$	−0.233416	+	0.321269i	−0.0133001	+	0.0183060i
$309$	−16.9822	+	22.7854i	−0.966085	+	1.29622i
$310$	−8.53575	+	9.06317i	−0.484798	+	0.514753i
$311$			16.0265i			0.908777i	0.890804	+	0.454388i	$0.150142\pi$
$311$			16.0265i			0.908777i	−0.890804	+	0.454388i	$0.849858\pi$
$312$	0.797202	+	2.55914i	0.0451327	+	0.144883i
$313$	−17.2291	+	12.5177i	−0.973845	+	0.707540i	−0.956325	−	0.292306i	$-0.905577\pi$
$313$	−17.2291	+	12.5177i	−0.973845	+	0.707540i	−0.0175208	+	0.999846i	$0.505577\pi$
$314$	20.1514	−	6.54758i	1.13721	−	0.369501i
$315$	−11.5059	+	26.8239i	−0.648286	+	1.51135i
$316$		−	4.99627i		−	0.281062i
$317$	8.69453	+	26.7590i	0.488333	+	1.50294i	0.827095	+	0.562063i	$0.189992\pi$
$317$	8.69453	+	26.7590i	0.488333	+	1.50294i	−0.338761	+	0.940872i	$0.610008\pi$
$318$	2.95671	+	4.17555i	0.165804	+	0.234153i
$319$	−0.169414	+	0.521403i	−0.00948537	+	0.0291930i
$320$	−2.16795	+	0.547714i	−0.121192	+	0.0306181i
$321$	5.36674	−	15.8575i	0.299542	−	0.885081i
$322$	18.5979	+	13.5121i	1.03642	+	0.753002i
$323$	−1.75419	−	2.41444i	−0.0976058	−	0.134343i
$324$	2.36116	+	8.68475i	0.131175	+	0.482486i
$325$	5.59947	+	5.34030i	0.310603	+	0.296226i
$326$	7.64784	+	10.5264i	0.423575	+	0.583001i
$327$	20.2052	−	14.3073i	1.11735	−	0.791198i
$328$	−3.15405	−	4.34118i	−0.174154	−	0.239702i
$329$	16.1312	−	22.2027i	0.889340	−	1.22407i
$330$	0.184594	+	0.301454i	0.0101616	+	0.0165945i
$331$	14.1921	−	19.5337i	0.780067	−	1.07367i	−0.215208	−	0.976568i	$-0.569043\pi$
$331$	14.1921	−	19.5337i	0.780067	−	1.07367i	0.995274	−	0.0971014i	$-0.0309571\pi$
$332$	8.06732	+	2.62123i	0.442752	+	0.143859i
$333$	−24.1891	−	0.589142i	−1.32556	−	0.0322848i
$334$	18.3753	−	5.97049i	1.00545	−	0.326690i
$335$	1.19310	+	0.994806i	0.0651858	+	0.0543520i
$336$	−4.50355	+	6.04250i	−0.245689	+	0.329646i
$337$	−3.07499	−	9.46384i	−0.167505	−	0.515528i	0.831707	−	0.555215i	$-0.187364\pi$
$337$	−3.07499	−	9.46384i	−0.167505	−	0.515528i	−0.999212	+	0.0396867i	$0.987364\pi$
$338$	−8.57969	+	6.23351i	−0.466674	+	0.339058i
$339$	−9.69955	−	31.1371i	−0.526807	−	1.69113i
$340$	2.26345	+	1.88727i	0.122753	+	0.102352i
$341$	0.392325	+	0.322971i	0.0212456	+	0.0174899i
$342$	−1.94131	−	6.51000i	−0.104974	−	0.352020i
$343$	−12.6115	+	17.3583i	−0.680959	+	0.937259i
$344$	−5.75587	+	4.18188i	−0.310336	+	0.225472i
$345$	17.4508	−	10.6859i	0.939519	−	0.575309i
$346$	13.8920			0.746837
$347$			9.35472i			0.502188i	0.967963	+	0.251094i	$0.0807903\pi$
$347$			9.35472i			0.502188i	−0.967963	+	0.251094i	$0.919210\pi$
$348$	−3.33529	+	9.85505i	−0.178790	+	0.528286i
$349$	2.86835	−	8.82786i	0.153539	−	0.472545i	−0.844471	−	0.535601i	$-0.820085\pi$
$349$	2.86835	−	8.82786i	0.153539	−	0.472545i	0.998010	+	0.0630568i	$0.0200849\pi$
$350$	−2.89337	+	21.5618i	−0.154657	+	1.15253i
$351$	6.67382	−	4.48584i	0.356222	−	0.239437i
$352$	0.0282036	+	0.0868017i	0.00150326	+	0.00462654i
$353$	14.3337	−	19.7287i	0.762907	−	1.05005i	−0.234060	−	0.972222i	$-0.575201\pi$
$353$	14.3337	−	19.7287i	0.762907	−	1.05005i	0.996967	−	0.0778292i	$-0.0247989\pi$
$354$	−0.161910	+	13.2975i	−0.00860543	+	0.706753i
$355$	6.46658	−	4.06885i	0.343211	−	0.215952i
$356$	−9.88682	+	7.18319i	−0.524000	+	0.380708i
$357$	9.93157	+	0.120927i	0.525634	+	0.00640013i
$358$	−4.48822	+	13.8133i	−0.237210	+	0.730057i
$359$	−8.49073	−	11.6865i	−0.448123	−	0.616789i	0.523870	−	0.851798i	$-0.324488\pi$
$359$	−8.49073	−	11.6865i	−0.448123	−	0.616789i	−0.971993	+	0.235009i	$0.924488\pi$
$360$	3.43322	+	5.76307i	0.180946	+	0.303741i
$361$	−4.28680	−	13.1934i	−0.225621	−	0.694389i
$362$	2.17306	−	2.99097i	0.114214	−	0.157202i
$363$	−15.5373	+	11.0020i	−0.815495	+	0.577454i
$364$	6.40385	+	2.08074i	0.335653	+	0.109060i
$365$	−12.2997	−	4.92485i	−0.643794	−	0.257778i
$366$	−7.95056	+	10.6674i	−0.415582	+	0.557595i
$367$	−21.6245			−1.12879			−0.564395	−	0.825505i	$-0.690891\pi$
$367$	−21.6245			−1.12879			−0.564395	+	0.825505i	$0.690891\pi$
$368$	5.02483	−	1.63267i	0.261937	−	0.0851086i
$369$	−9.77646	+	12.7893i	−0.508942	+	0.665784i
$370$	−17.4855	+	4.41755i	−0.909026	+	0.229657i
$371$	12.8526			0.667275
$372$	7.37017	+	6.21937i	0.382125	+	0.322460i
$373$			28.3171i			1.46620i	0.680119	+	0.733102i	$0.261928\pi$
$373$			28.3171i			1.46620i	−0.680119	+	0.733102i	$0.738072\pi$
$374$	0.0707033	−	0.0973148i	0.00365598	−	0.00503203i
$375$	16.7431	+	9.72980i	0.864609	+	0.502445i
$376$	−1.94912	−	5.99879i	−0.100518	−	0.309364i
$377$	9.29588			0.478762
$378$	21.2325	+	7.76696i	1.09208	+	0.399489i
$379$	4.39320	+	13.5209i	0.225664	+	0.694521i	0.998224	+	0.0595795i	$0.0189760\pi$
$379$	4.39320	+	13.5209i	0.225664	+	0.694521i	−0.772560	+	0.634942i	$0.781024\pi$
$380$	−2.69657	−	4.28564i	−0.138331	−	0.219849i
$381$	7.03104	−	4.97870i	0.360211	−	0.255067i
$382$	−2.22392	+	3.06096i	−0.113786	+	0.156613i
$383$	11.0539	−	3.59164i	0.564830	−	0.183524i	−0.0126634	−	0.999920i	$-0.504031\pi$
$383$	11.0539	−	3.59164i	0.564830	−	0.183524i	0.577493	+	0.816395i	$0.304031\pi$
$384$	0.515138	+	1.65367i	0.0262880	+	0.0843886i
$385$	0.885992	+	0.0591802i	0.0451543	+	0.00301610i
$386$	9.38737	+	3.05014i	0.477805	+	0.155248i
$387$	16.9570	+	12.9624i	0.861974	+	0.658914i
$388$	−6.43012	−	8.85030i	−0.326440	−	0.449306i
$389$	1.31655	−	4.05194i	0.0667520	−	0.205441i	−0.912117	−	0.409930i	$-0.865553\pi$
$389$	1.31655	−	4.05194i	0.0667520	−	0.205441i	0.978869	+	0.204489i	$0.0655531\pi$
$390$	3.89407	−	4.55631i	0.197184	−	0.230718i
$391$	−5.63342	−	4.09292i	−0.284894	−	0.206988i
$392$	3.68697	+	11.3473i	0.186220	+	0.573126i
$393$	−17.2676	+	5.37904i	−0.871033	+	0.271337i
$394$	−19.6837	−	6.39561i	−0.991649	−	0.322206i
$395$	−9.45590	+	5.94976i	−0.475778	+	0.299365i
$396$	0.225367	−	0.155498i	0.0113251	−	0.00781406i
$397$		−	23.7783i		−	1.19340i	−0.802465	−	0.596699i	$-0.796479\pi$
$397$		−	23.7783i		−	1.19340i	0.802465	−	0.596699i	$-0.203521\pi$
$398$			22.1506i			1.11031i
$399$	−16.1645	−	5.47062i	−0.809236	−	0.273874i
$400$	3.61828	+	3.45080i	0.180914	+	0.172540i
$401$	0.382182	+	0.277671i	0.0190852	+	0.0138662i	0.597287	−	0.802028i	$-0.296245\pi$
$401$	0.382182	+	0.277671i	0.0190852	+	0.0138662i	−0.578202	+	0.815894i	$0.696245\pi$
$402$	0.719067	−	0.964786i	0.0358638	−	0.0481192i
$403$	3.15261	−	8.01894i	0.157042	−	0.399452i
$404$			12.0353i			0.598779i
$405$	13.6249	−	14.8109i	0.677028	−	0.735957i
$406$	15.3622	+	21.1443i	0.762414	+	1.04937i
$407$	0.227474	+	0.700093i	0.0112755	+	0.0347023i
$408$	1.36416	−	1.83032i	0.0675359	−	0.0906142i
$409$		−	33.9698i		−	1.67970i	−0.542818	−	0.839850i	$-0.682643\pi$
$409$		−	33.9698i		−	1.67970i	0.542818	−	0.839850i	$-0.317357\pi$
$410$	−4.46011	+	11.1390i	−0.220269	+	0.550115i
$411$	−2.86891	−	4.05154i	−0.141513	−	0.199848i
$412$	15.6040	+	5.07005i	0.768754	+	0.249783i
$413$	27.0264	+	19.6359i	1.32988	+	0.966217i
$414$	−9.00157	−	13.0462i	−0.442403	−	0.641184i
$415$	−4.64597	−	18.3896i	−0.228062	−	0.902710i
$416$	1.25200	−	0.909628i	0.0613841	−	0.0445982i
$417$	3.48852	+	4.92657i	0.170833	+	0.241255i
$418$	−0.167201	+	0.121478i	−0.00817805	+	0.00594170i
$419$	6.74688	+	9.28628i	0.329607	+	0.453665i	0.941370	−	0.337376i	$-0.109539\pi$
$419$	6.74688	+	9.28628i	0.329607	+	0.453665i	−0.611763	+	0.791041i	$0.709539\pi$
$420$	16.7990	+	1.32772i	0.819707	+	0.0647861i
$421$	1.62871	−	1.18333i	0.0793785	−	0.0576719i	−0.547388	−	0.836879i	$-0.684378\pi$
$421$	1.62871	−	1.18333i	0.0793785	−	0.0576719i	0.626767	+	0.779207i	$0.284378\pi$
$422$	8.31684	+	6.04254i	0.404857	+	0.294146i
$423$	−15.5749	+	10.7463i	−0.757277	+	0.522504i
$424$	1.73628	−	2.38979i	0.0843214	−	0.116058i
$425$	0.876421	−	6.53122i	0.0425127	−	0.316811i
$426$	−3.41999	−	4.82980i	−0.165699	−	0.234005i
$427$	10.3277	+	31.7855i	0.499794	+	1.53821i
$428$	−9.66546			−0.467198
$429$	−0.196152	−	0.146195i	−0.00947033	−	0.00705835i
$430$	14.7689	+	5.91355i	0.712220	+	0.285177i
$431$	−20.9213	−	28.7957i	−1.00774	−	1.38704i	−0.920452	−	0.390856i	$-0.872179\pi$
$431$	−20.9213	−	28.7957i	−1.00774	−	1.38704i	−0.0872911	−	0.996183i	$-0.527821\pi$
$432$	4.31251	−	2.89867i	0.207486	−	0.139462i
$433$	−30.9820			−1.48890			−0.744449	−	0.667679i	$-0.767288\pi$
$433$	−30.9820			−1.48890			−0.744449	+	0.667679i	$0.767288\pi$
$434$	23.4497	−	6.08110i	1.12562	−	0.291902i
$435$	22.6234	−	5.42345i	1.08471	−	0.260034i
$436$	−11.5640	−	8.40176i	−0.553817	−	0.402371i
$437$	7.03222	+	9.67902i	0.336397	+	0.463010i
$438$	−3.28992	+	9.72101i	−0.157199	+	0.464488i
$439$	8.77097			0.418616			0.209308	−	0.977850i	$-0.432879\pi$
$439$	8.77097			0.418616			0.209308	+	0.977850i	$0.432879\pi$
$440$	0.130694	−	0.156745i	0.00623060	−	0.00747251i
$441$	29.4615	−	20.3278i	1.40293	−	0.967989i
$442$	−1.93977	−	0.630271i	−0.0922656	−	0.0299789i
$443$	−4.54820	+	13.9979i	−0.216091	+	0.665061i	0.782983	+	0.622043i	$0.213697\pi$
$443$	−4.54820	+	13.9979i	−0.216091	+	0.665061i	−0.999074	+	0.0430178i	$0.986303\pi$
$444$	4.15481	+	13.3376i	0.197179	+	0.632974i
$445$	25.3685	+	10.1577i	1.20258	+	0.481519i
$446$	−10.3176	−	7.49618i	−0.488553	−	0.354954i
$447$	0.192959	−	15.8474i	0.00912663	−	0.749558i
$448$	4.13806	+	1.34454i	0.195505	+	0.0635233i
$449$	−25.8830	+	18.8051i	−1.22150	+	0.887468i	−0.996223	−	0.0868279i	$-0.972327\pi$
$449$	−25.8830	+	18.8051i	−1.22150	+	0.887468i	−0.225272	+	0.974296i	$0.572327\pi$
$450$	6.81873	−	13.3606i	0.321438	−	0.629823i
$451$	0.465777	+	0.151340i	0.0219326	+	0.00712633i
$452$	−15.2330	+	11.0674i	−0.716501	+	0.520568i
$453$	37.8384	−	11.7871i	1.77780	−	0.553805i
$454$	−7.06655	−	21.7486i	−0.331649	−	1.02071i
$455$	−3.68798	−	14.5977i	−0.172895	−	0.684351i
$456$	−3.20088	+	2.26655i	−0.149895	+	0.106141i
$457$	8.13468	−	25.0360i	0.380524	−	1.17113i	−0.559151	−	0.829066i	$-0.688873\pi$
$457$	8.13468	−	25.0360i	0.380524	−	1.17113i	0.939675	−	0.342068i	$-0.111127\pi$
$458$	−9.20272	+	2.99015i	−0.430015	+	0.139720i
$459$	−6.43147	−	2.35267i	−0.300196	−	0.109813i
$460$	−9.07374	−	7.56571i	−0.423065	−	0.352753i
$461$	1.41748	+	4.36254i	0.0660184	+	0.203184i	0.978624	−	0.205657i	$-0.0659331\pi$
$461$	1.41748	+	4.36254i	0.0660184	+	0.203184i	−0.912606	+	0.408841i	$0.865933\pi$
$462$	0.00837423	−	0.687765i	0.000389604	−	0.0319977i
$463$	−2.55033	−	1.85292i	−0.118524	−	0.0861126i	0.526944	−	0.849900i	$-0.323338\pi$
$463$	−2.55033	−	1.85292i	−0.118524	−	0.0861126i	−0.645468	+	0.763787i	$0.723338\pi$
$464$	6.00683			0.278860
$465$	2.99404	−	21.3550i	0.138845	−	0.990314i
$466$	16.4872			0.763755
$467$	9.69777	+	7.04584i	0.448759	+	0.326043i	0.789106	−	0.614257i	$-0.210544\pi$
$467$	9.69777	+	7.04584i	0.448759	+	0.326043i	−0.340346	+	0.940300i	$0.610544\pi$
$468$	−3.68843	−	2.81953i	−0.170498	−	0.130333i
$469$	−0.934063	−	2.87475i	−0.0431310	−	0.132744i
$470$	−9.03216	+	10.8325i	−0.416622	+	0.499666i
$471$	−21.9313	+	29.4256i	−1.01054	+	1.35586i
$472$	7.30209	−	2.37259i	0.336106	−	0.109208i
$473$	0.200658	−	0.617563i	0.00922628	−	0.0283956i
$474$	5.00096	+	7.06248i	0.229702	+	0.324391i
$475$	−4.89977	+	10.2070i	−0.224817	+	0.468330i
$476$	−1.77203	−	5.45376i	−0.0812210	−	0.249973i
$477$	−8.35893	−	2.94286i	−0.382729	−	0.134744i
$478$	−1.26329	+	0.917834i	−0.0577815	+	0.0419808i
$479$	23.7884	+	7.72933i	1.08692	+	0.353162i	0.797056	−	0.603905i	$-0.206390\pi$
$479$	23.7884	+	7.72933i	1.08692	+	0.353162i	0.289865	+	0.957068i	$0.406390\pi$
$480$	2.51628	−	2.94420i	0.114852	−	0.134384i
$481$	10.0979	−	7.33655i	0.460424	−	0.334518i
$482$	−19.3337	−	6.28191i	−0.880627	−	0.286133i
$483$	−39.8138	−	0.484773i	−1.81159	−	0.0220579i
$484$	8.89245	+	6.46074i	0.404202	+	0.293670i
$485$	−9.09275	+	22.7089i	−0.412880	+	1.03116i
$486$	−12.0305	−	9.91296i	−0.545715	−	0.449661i
$487$	−0.447954	+	1.37866i	−0.0202987	+	0.0624731i	−0.960693	−	0.277614i	$-0.910456\pi$
$487$	−0.447954	+	1.37866i	−0.0202987	+	0.0624731i	0.940394	+	0.340087i	$0.110456\pi$
$488$	7.30531	+	2.37364i	0.330696	+	0.107450i
$489$	−21.3468	−	7.22451i	−0.965337	−	0.326704i
$490$	17.0852	−	20.4908i	0.771832	−	0.925678i
$491$	−18.1179			−0.817648			−0.408824	−	0.912613i	$-0.634061\pi$
$491$	−18.1179			−0.817648			−0.408824	+	0.912613i	$0.634061\pi$
$492$	8.80367	+	2.97947i	0.396900	+	0.134325i
$493$	−4.65333	−	6.40476i	−0.209575	−	0.288456i
$494$	2.83505	+	2.05979i	0.127555	+	0.0926742i
$495$	−0.562669	−	0.241354i	−0.0252901	−	0.0108480i
$496$	2.03716	−	5.18170i	0.0914710	−	0.232665i
$497$	−14.8665			−0.666853
$498$	−14.0273	+	4.36965i	−0.628576	+	0.195809i
$499$	−17.5149	−	24.1072i	−0.784076	−	1.07919i	−0.994821	−	0.101647i	$-0.967589\pi$
$499$	−17.5149	−	24.1072i	−0.784076	−	1.07919i	0.210744	−	0.977541i	$-0.432411\pi$
$500$	2.22217	−	10.9573i	0.0993783	−	0.490024i
$501$	−19.9983	+	26.8321i	−0.893457	+	1.19877i
$502$	2.76013			0.123191
$503$	1.19130	+	3.66645i	0.0531175	+	0.163479i	0.974096	−	0.226134i	$-0.0726088\pi$
$503$	1.19130	+	3.66645i	0.0531175	+	0.163479i	−0.920979	+	0.389613i	$0.872609\pi$
$504$	0.317820	−	13.0492i	0.0141568	−	0.581256i
$505$	22.7779	−	14.3321i	1.01360	−	0.637771i
$506$	−0.283436	+	0.390117i	−0.0126003	+	0.0173428i
$507$	5.88847	−	17.3991i	0.261516	−	0.772722i
$508$	−4.02408	−	2.92366i	−0.178540	−	0.129717i
$509$	9.55299	−	6.94065i	0.423429	−	0.307639i	−0.355587	−	0.934643i	$-0.615719\pi$
$509$	9.55299	−	6.94065i	0.423429	−	0.307639i	0.779016	+	0.627004i	$0.215719\pi$
$510$	−5.08854	−	0.402176i	−0.225324	−	0.0178087i
$511$	15.1533	+	20.8567i	0.670342	+	0.922646i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	9.26024	+	7.25908i	0.408850	+	0.320496i
$514$	−7.96726	+	5.78855i	−0.351421	+	0.255322i
$515$	−8.98635	−	35.5696i	−0.395986	−	1.56738i
$516$	3.95040	−	11.6726i	0.173907	−	0.513856i
$517$	0.465733	+	0.338374i	0.0204829	+	0.0148817i
$518$	33.3752	+	10.8443i	1.46642	+	0.476470i
$519$	−19.6370	+	13.9050i	−0.861968	+	0.610362i
$520$	−3.21248	−	1.28629i	−0.140877	−	0.0564077i
$521$		−	29.7381i		−	1.30285i	−0.758713	−	0.651425i	$-0.774172\pi$
$521$		−	29.7381i		−	1.30285i	0.758713	−	0.651425i	$-0.225828\pi$
$522$	−5.14969	−	17.2690i	−0.225396	−	0.755844i
$523$	−3.82546	−	11.7735i	−0.167276	−	0.514821i	0.831921	−	0.554894i	$-0.187241\pi$
$523$	−3.82546	−	11.7735i	−0.167276	−	0.514821i	−0.999197	+	0.0400725i	$0.987241\pi$
$524$	6.13762	+	8.44771i	0.268123	+	0.369040i
$525$	−17.4921	−	33.3747i	−0.763417	−	1.45659i
$526$		−	22.2268i		−	0.969135i
$527$	−7.10309	+	1.84201i	−0.309416	+	0.0802392i
$528$	−0.126750	−	0.0944684i	−0.00551610	−	0.00411121i
$529$	3.97595	+	2.88869i	0.172867	+	0.125595i
$530$	−6.59053	−	0.440217i	−0.286274	−	0.0191218i
$531$	−13.0811	−	18.9587i	−0.567671	−	0.822738i
$532$			9.85255i			0.427162i
$533$		−	8.30416i		−	0.359693i
$534$	6.78558	−	20.0499i	0.293641	−	0.867644i
$535$	11.5100	+	18.2928i	0.497621	+	0.790865i
$536$	−0.660709	−	0.214677i	−0.0285383	−	0.00927265i
$537$	−7.48196	−	24.0182i	−0.322870	−	1.03646i
$538$	−2.35207	−	7.23894i	−0.101405	−	0.312093i
$539$	−0.880980	−	0.640070i	−0.0379465	−	0.0275698i
$540$	−10.6215	−	4.70996i	−0.457077	−	0.202684i
$541$	−9.67075	+	29.7635i	−0.415778	+	1.27963i	0.495775	+	0.868451i	$0.334884\pi$
$541$	−9.67075	+	29.7635i	−0.415778	+	1.27963i	−0.911553	+	0.411183i	$0.865116\pi$
$542$	3.79181	+	5.21897i	0.162872	+	0.224174i
$543$	−0.0779628	+	6.40298i	−0.00334570	+	0.274778i
$544$	−1.25345	−	0.407270i	−0.0537411	−	0.0174615i
$545$	−2.13018	+	31.8911i	−0.0912470	+	1.36607i
$546$	−11.1349	+	3.46863i	−0.476528	+	0.148444i
$547$	−16.5217	+	5.36823i	−0.706417	+	0.229529i	−0.640124	−	0.768271i	$-0.721117\pi$
$547$	−16.5217	+	5.36823i	−0.706417	+	0.229529i	−0.0662929	+	0.997800i	$0.521117\pi$
$548$	−1.68472	+	2.31882i	−0.0719677	+	0.0990551i
$549$	0.561079	−	23.0370i	0.0239463	−	0.983193i
$550$	−0.452289	−	0.0606925i	−0.0192857	−	0.00258794i
$551$	4.20326	+	12.9363i	0.179065	+	0.551105i
$552$	−5.46865	+	7.33740i	−0.232761	+	0.312301i
$553$	21.7388			0.924429
$554$	−2.52924	−	7.78421i	−0.107457	−	0.330720i
$555$	20.2949	−	23.7463i	0.861470	−	1.00797i
$556$	2.04858	−	2.81963i	0.0868791	−	0.119579i
$557$		−	6.00685i		−	0.254518i	−0.991870	−	0.127259i	$-0.959382\pi$
$557$		−	6.00685i		−	0.254518i	0.991870	−	0.127259i	$-0.0406180\pi$
$558$	−16.6433	−	1.41431i	−0.704567	−	0.0598727i
$559$	−11.0103			−0.465685
$560$	−2.38311	−	9.43277i	−0.100705	−	0.398607i
$561$	−0.00253661	+	0.208329i	−0.000107096	+	0.00879566i
$562$	−24.9847	+	8.11803i	−1.05392	+	0.342438i
$563$	40.1053			1.69024			0.845119	−	0.534578i	$-0.179529\pi$
$563$	40.1053			1.69024			0.845119	+	0.534578i	$0.179529\pi$
$564$	8.75960	+	6.52863i	0.368846	+	0.274905i
$565$	39.0862	+	15.6503i	1.64437	+	0.658414i
$566$	7.81632	+	2.53968i	0.328544	+	0.106751i
$567$	−37.7874	+	10.2734i	−1.58692	+	0.431443i
$568$	−2.00834	+	2.76424i	−0.0842680	+	0.115985i
$569$	−5.96346	−	18.3537i	−0.250001	−	0.769425i	−0.994773	−	0.102106i	$-0.967442\pi$
$569$	−5.96346	−	18.3537i	−0.250001	−	0.769425i	0.744772	−	0.667319i	$-0.232558\pi$
$570$	8.10140	+	3.35886i	0.339330	+	0.140687i
$571$	−3.74222	−	5.15072i	−0.156607	−	0.215551i	0.723503	−	0.690322i	$-0.242531\pi$
$571$	−3.74222	−	5.15072i	−0.156607	−	0.215551i	−0.880110	+	0.474771i	$0.842531\pi$
$572$	−0.0436465	+	0.134330i	−0.00182495	+	0.00561662i
$573$	0.0797873	−	6.55283i	0.00333316	−	0.273748i
$574$	18.8885	−	13.7233i	0.788392	−	0.572800i
$575$	−3.51341	+	26.1824i	−0.146519	+	1.09188i
$576$	−2.38340	−	1.82193i	−0.0993082	−	0.0759137i
$577$	−12.5255	+	17.2399i	−0.521444	+	0.717706i	−0.985796	−	0.167945i	$-0.946287\pi$
$577$	−12.5255	+	17.2399i	−0.521444	+	0.717706i	0.464353	+	0.885650i	$0.346287\pi$
$578$	−4.71653	−	14.5160i	−0.196182	−	0.603785i
$579$	−16.3225	+	5.08465i	−0.678341	+	0.211311i
$580$	−7.15318	−	11.3685i	−0.297020	−	0.472050i
$581$	−11.4050	+	35.1010i	−0.473159	+	1.45623i
$582$	17.9479	+	6.07419i	0.743964	+	0.251783i
$583$			0.269602i			0.0111658i
$584$	5.92513			0.245184
$585$	−0.943882	+	10.3383i	−0.0390247	+	0.427436i
$586$	12.5659	−	9.12965i	0.519092	−	0.377143i
$587$	−17.9592	+	24.7187i	−0.741254	+	1.02025i	0.257291	+	0.966334i	$0.417170\pi$
$587$	−17.9592	+	24.7187i	−0.741254	+	1.02025i	−0.998546	+	0.0539149i	$0.982830\pi$
$588$	−16.5697	−	12.3496i	−0.683322	−	0.509288i
$589$	12.5848	+	0.761343i	0.518548	+	0.0313706i
$590$	−13.1860	−	10.9945i	−0.542858	−	0.452636i
$591$	34.2254	−	10.6616i	1.40785	−	0.438560i
$592$	6.52508	−	4.74075i	0.268179	−	0.194843i
$593$	9.93350	+	30.5722i	0.407920	+	1.25545i	0.918432	+	0.395578i	$0.129456\pi$
$593$	9.93350	+	30.5722i	0.407920	+	1.25545i	−0.510512	+	0.859870i	$0.670544\pi$
$594$	−0.162923	+	0.445382i	−0.00668482	+	0.0182742i
$595$	−8.21152	+	9.84829i	−0.336640	+	0.403740i
$596$	−8.70236	+	2.82757i	−0.356463	+	0.115822i
$597$	−22.1714	−	31.3110i	−0.907414	−	1.28147i
$598$	7.77619	+	2.52664i	0.317992	+	0.103322i
$599$	−18.2419	+	25.1078i	−0.745343	+	1.02588i	0.252950	+	0.967479i	$0.418599\pi$
$599$	−18.2419	+	25.1078i	−0.745343	+	1.02588i	−0.998293	+	0.0583974i	$0.981401\pi$
$600$	−8.56866	−	1.25621i	−0.349814	−	0.0512845i
$601$	1.65760	−	2.28149i	0.0676149	−	0.0930640i	−0.773870	−	0.633344i	$-0.781682\pi$
$601$	1.65760	−	2.28149i	0.0676149	−	0.0930640i	0.841485	+	0.540280i	$0.181682\pi$
$602$	−18.1954	−	25.0438i	−0.741589	−	1.02071i
$603$	−0.0507453	+	2.08351i	−0.00206651	+	0.0848473i
$604$	−13.4494	−	18.5114i	−0.547246	−	0.753220i
$605$	1.63806	−	24.5235i	0.0665965	−	0.997021i
$606$	−12.0466	−	17.0125i	−0.489359	−	0.691085i
$607$	17.2190	+	23.7000i	0.698899	+	0.961952i	0.999965	+	0.00834883i	$0.00265755\pi$
$607$	17.2190	+	23.7000i	0.698899	+	0.961952i	−0.301066	+	0.953603i	$0.597342\pi$
$608$	1.83196	+	1.33100i	0.0742958	+	0.0539791i
$609$	−42.8794	−	14.5119i	−1.73756	−	0.588051i
$610$	−4.20713	−	16.6526i	−0.170342	−	0.674244i
$611$	3.01637	−	9.28344i	0.122029	−	0.375568i
$612$	−0.0962701	+	3.95268i	−0.00389149	+	0.159778i
$613$	8.72934	+	26.8662i	0.352575	+	1.08511i	0.957402	+	0.288757i	$0.0932420\pi$
$613$	8.72934	+	26.8662i	0.352575	+	1.08511i	−0.604828	+	0.796356i	$0.706758\pi$
$614$		−	22.3086i		−	0.900303i
$615$	−4.84485	−	20.2098i	−0.195363	−	0.814938i
$616$	−0.377675	+	0.122714i	−0.0152169	+	0.00494429i
$617$	−1.30303	+	0.946709i	−0.0524581	+	0.0381131i	−0.613705	−	0.789535i	$-0.710322\pi$
$617$	−1.30303	+	0.946709i	−0.0524581	+	0.0381131i	0.561247	+	0.827648i	$0.310322\pi$
$618$	−27.1318	+	8.45187i	−1.09140	+	0.339984i
$619$			37.0865i			1.49063i	0.666711	+	0.745316i	$0.267702\pi$
$619$			37.0865i			1.49063i	−0.666711	+	0.745316i	$0.732298\pi$
$620$	−12.2328	+	2.31507i	−0.491280	+	0.0929754i
$621$	25.7826	+	9.43141i	1.03462	+	0.378469i
$622$	−9.42011	+	12.9657i	−0.377712	+	0.519876i
$623$	−31.2541	−	43.0176i	−1.25217	−	1.72346i
$624$	−0.859277	+	2.53897i	−0.0343986	+	0.101640i
$625$	−23.3839	+	8.84272i	−0.935356	+	0.353709i
$626$	−21.2963			−0.851172
$627$	0.114754	−	0.339073i	0.00458284	−	0.0135413i
$628$	20.1514	+	6.54758i	0.804128	+	0.261277i
$629$	−10.1096	−	3.28481i	−0.403096	−	0.130974i
$630$	−25.0752	+	14.9380i	−0.999019	+	0.595142i
$631$	33.9714	−	11.0380i	1.35238	−	0.439414i	0.458887	−	0.888495i	$-0.348248\pi$
$631$	33.9714	−	11.0380i	1.35238	−	0.439414i	0.893491	+	0.449080i	$0.148248\pi$
$632$	2.93674	−	4.04207i	0.116817	−	0.160785i
$633$	−17.8045	−	0.216787i	−0.707664	−	0.00861653i
$634$	−8.69453	+	26.7590i	−0.345304	+	1.06274i
$635$	−0.741266	+	11.0975i	−0.0294162	+	0.440393i
$636$	−0.0622925	+	5.11600i	−0.00247006	+	0.202863i
$637$	−5.70577	+	17.5606i	−0.226071	+	0.695775i
$638$	−0.443532	+	0.322245i	−0.0175596	+	0.0127578i
$639$	9.66866	+	3.40396i	0.382486	+	0.134659i
$640$	−2.07585	−	0.831180i	−0.0820551	−	0.0328553i
$641$	−6.35205	−	4.61504i	−0.250891	−	0.182283i	0.455231	−	0.890374i	$-0.349557\pi$
$641$	−6.35205	−	4.61504i	−0.250891	−	0.182283i	−0.706122	+	0.708091i	$0.749557\pi$
$642$	13.6626	−	9.67452i	0.539220	−	0.381823i
$643$	6.09822	−	18.7684i	0.240490	−	0.740154i	−0.755855	−	0.654739i	$-0.772779\pi$
$643$	6.09822	−	18.7684i	0.240490	−	0.740154i	0.996345	−	0.0854146i	$-0.0272215\pi$
$644$	7.10375	+	21.8631i	0.279927	+	0.861526i
$645$	−26.7957	+	6.42367i	−1.05508	+	0.252932i
$646$		−	2.98441i		−	0.117420i
$647$	−16.8851	+	5.48629i	−0.663821	+	0.215688i	−0.621498	−	0.783416i	$-0.713476\pi$
$647$	−16.8851	+	5.48629i	−0.663821	+	0.215688i	−0.0423224	+	0.999104i	$0.513476\pi$
$648$	−3.19455	+	8.41397i	−0.125494	+	0.330532i
$649$	−0.411890	+	0.566918i	−0.0161681	+	0.0222535i
$650$	1.39112	+	7.61168i	0.0545643	+	0.298555i
$651$	−27.0606	+	32.0677i	−1.06059	+	1.25683i
$652$			13.0113i			0.509561i
$653$	40.8964	+	29.7130i	1.60040	+	1.16276i	0.886745	+	0.462259i	$0.152961\pi$
$653$	40.8964	+	29.7130i	1.60040	+	1.16276i	0.713654	+	0.700499i	$0.247039\pi$
$654$	24.7560	+	0.301429i	0.968035	+	0.0117868i
$655$	8.67913	−	21.6759i	0.339122	−	0.846946i
$656$		−	5.36600i		−	0.209507i
$657$	−5.07965	−	17.0341i	−0.198176	−	0.664565i
$658$	26.1008	−	8.48066i	1.01751	−	0.330610i
$659$	9.17022	+	2.97959i	0.357221	+	0.116068i	0.482129	−	0.876100i	$-0.339864\pi$
$659$	9.17022	+	2.97959i	0.357221	+	0.116068i	−0.124908	+	0.992168i	$0.539864\pi$
$660$	−0.0278509	+	0.352383i	−0.00108409	+	0.0137165i
$661$	−1.73269	−	1.25887i	−0.0673939	−	0.0489645i	0.553578	−	0.832797i	$-0.313262\pi$
$661$	−1.73269	−	1.25887i	−0.0673939	−	0.0489645i	−0.620972	+	0.783833i	$0.713262\pi$
$662$	22.9633	−	7.46121i	0.892492	−	0.289988i
$663$	3.37283	−	1.05067i	0.130990	−	0.0408048i
$664$	4.98588	+	6.86247i	0.193490	+	0.266316i
$665$	18.6468	−	11.7328i	0.723094	−	0.454979i
$666$	−19.2231	−	14.6946i	−0.744881	−	0.569406i
$667$	18.6543	+	25.6755i	0.722298	+	0.994158i
$668$	18.3753	+	5.97049i	0.710960	+	0.231005i
$669$	22.0877	+	0.268940i	0.853958	+	0.0103978i
$670$	0.380503	+	1.50610i	0.0147001	+	0.0581857i
$671$	−0.666746	+	0.216639i	−0.0257395	+	0.00836325i
$672$	−7.19514	+	2.24137i	−0.277559	+	0.0864627i
$673$	−11.4567	+	35.2601i	−0.441623	+	1.35918i	0.444522	+	0.895768i	$0.353373\pi$
$673$	−11.4567	+	35.2601i	−0.441623	+	1.35918i	−0.886145	+	0.463408i	$0.846627\pi$
$674$	3.07499	−	9.46384i	0.118444	−	0.364533i
$675$	3.73449	+	25.7110i	0.143741	+	0.989615i
$676$	−10.6051			−0.407888
$677$		−	18.6676i		−	0.717454i	−0.933443	−	0.358727i	$-0.883211\pi$
$677$		−	18.6676i		−	0.717454i	0.933443	−	0.358727i	$-0.116789\pi$
$678$	10.4548	−	30.8917i	0.401515	−	1.18639i
$679$	38.5077	−	27.9775i	1.47779	−	1.07368i
$680$	0.721860	+	2.85725i	0.0276821	+	0.109571i
$681$	31.7579	+	23.6695i	1.21697	+	0.907019i
$682$	0.127560	+	0.491892i	0.00488452	+	0.0188355i
$683$	−31.7337			−1.21426			−0.607128	−	0.794604i	$-0.707679\pi$
$683$	−31.7337			−1.21426			−0.607128	+	0.794604i	$0.707679\pi$
$684$	2.25593	−	6.40777i	0.0862576	−	0.245007i
$685$	6.39481	+	0.427144i	0.244333	+	0.0163203i
$686$	−20.4059	+	6.63028i	−0.779100	+	0.253145i
$687$	10.0156	−	13.4381i	0.382117	−	0.512695i
$688$	−7.11464			−0.271243
$689$	4.34764	−	1.41263i	0.165632	−	0.0538171i
$690$	20.3990	+	1.61225i	0.776576	+	0.0613773i
$691$	−4.05748	+	12.4876i	−0.154354	+	0.475052i	−0.998095	−	0.0616984i	$-0.980348\pi$
$691$	−4.05748	+	12.4876i	−0.154354	+	0.475052i	0.843741	+	0.536750i	$0.180348\pi$
$692$	11.2388	+	8.16549i	0.427237	+	0.310406i
$693$	0.676573	+	0.980572i	0.0257009	+	0.0372489i
$694$	−5.49857	+	7.56813i	−0.208723	+	0.287282i
$695$	−7.77593	−	0.519396i	−0.294958	−	0.0197018i
$696$	−8.49096	+	6.01247i	−0.321849	+	0.227902i
$697$	−5.72147	+	4.15689i	−0.216716	+	0.157453i
$698$	7.50943	−	5.45592i	0.284236	−	0.206510i
$699$	−23.3055	+	16.5027i	−0.881494	+	0.624188i
$700$	−15.0145	+	15.7432i	−0.567494	+	0.595036i
$701$	−7.35988	+	10.1300i	−0.277979	+	0.382605i	−0.925063	−	0.379813i	$-0.875988\pi$
$701$	−7.35988	+	10.1300i	−0.277979	+	0.382605i	0.647084	+	0.762419i	$0.275988\pi$
$702$	8.03595	+	0.293653i	0.303297	+	0.0110832i
$703$	14.7756	+	10.7351i	0.557271	+	0.404881i
$704$	−0.0282036	+	0.0868017i	−0.00106296	+	0.00327146i
$705$	1.92475	−	24.3529i	0.0724902	−	0.917183i
$706$	23.1924	−	7.53568i	0.872859	−	0.283609i
$707$	−52.3657			−1.96941
$708$	−7.94705	+	10.6627i	−0.298669	+	0.400730i
$709$	18.8107	−	6.11196i	0.706450	−	0.229540i	0.0663116	−	0.997799i	$-0.478877\pi$
$709$	18.8107	−	6.11196i	0.706450	−	0.229540i	0.640139	+	0.768259i	$0.278877\pi$
$710$	7.62319	+	0.509194i	0.286093	+	0.0191097i
$711$	−14.1382	−	4.97752i	−0.530224	−	0.186672i
$712$	−12.2208			−0.457993
$713$	28.4750	−	7.38427i	1.06640	−	0.276543i
$714$	7.96373	+	5.93546i	0.298035	+	0.222129i
$715$	0.306208	−	0.0773607i	0.0114515	−	0.00289313i
$716$	−11.7503	+	8.53710i	−0.439130	+	0.319046i
$717$	0.867029	−	2.56188i	0.0323798	−	0.0956751i
$718$		−	14.4453i		−	0.539093i
$719$	−27.1276			−1.01169			−0.505844	−	0.862625i	$-0.668819\pi$
$719$	−27.1276			−1.01169			−0.505844	+	0.862625i	$0.668819\pi$
$720$	−0.609920	+	6.68042i	−0.0227304	+	0.248965i
$721$	−22.0598	+	67.8931i	−0.821551	+	2.52847i
$722$	4.28680	−	13.1934i	0.159538	−	0.491008i
$723$	33.6170	−	10.4721i	1.25023	−	0.389460i
$724$	3.51609	−	1.14245i	0.130675	−	0.0424587i
$725$	−12.9976	+	27.0761i	−0.482718	+	1.00558i
$726$	−19.0367	−	0.231791i	−0.706519	−	0.00860258i
$727$	−40.3675	−	13.1162i	−1.49715	−	0.486452i	−0.557962	−	0.829866i	$-0.688417\pi$
$727$	−40.3675	−	13.1162i	−1.49715	−	0.486452i	−0.939184	+	0.343414i	$0.888417\pi$
$728$	3.95780	+	5.44744i	0.146686	+	0.201896i
$729$	26.9280	+	1.97066i	0.997333	+	0.0729875i
$730$	−7.05588	−	11.2138i	−0.261150	−	0.415043i
$731$	5.51152	+	7.58596i	0.203851	+	0.280577i
$732$	−12.7023	+	3.95691i	−0.469490	+	0.146252i
$733$	−22.9244	+	7.44858i	−0.846731	+	0.275120i	−0.700076	−	0.714068i	$-0.746851\pi$
$733$	−22.9244	+	7.44858i	−0.846731	+	0.275120i	−0.146655	+	0.989188i	$0.546851\pi$
$734$	−17.4946	−	12.7106i	−0.645737	−	0.469156i
$735$	−3.64086	+	46.0660i	−0.134295	+	1.69917i
$736$	5.02483	+	1.63267i	0.185218	+	0.0601809i
$737$	0.0603020	−	0.0195933i	0.00222125	−	0.000721729i
$738$	−15.4267	+	4.60030i	−0.567864	+	0.169339i
$739$		−	36.2863i		−	1.33481i	−0.744694	−	0.667406i	$-0.767404\pi$
$739$		−	36.2863i		−	1.33481i	0.744694	−	0.667406i	$-0.232596\pi$
$740$	−16.7426	−	6.70383i	−0.615471	−	0.246438i
$741$	−6.06921	−	0.0738988i	−0.222958	−	0.00271474i
$742$	10.3980	+	7.55459i	0.381723	+	0.277338i
$743$		−	44.9342i		−	1.64848i	−0.566244	−	0.824238i	$-0.691604\pi$
$743$		−	44.9342i		−	1.64848i	0.566244	−	0.824238i	$-0.308396\pi$
$744$	2.30694	+	9.36366i	0.0845763	+	0.343288i
$745$	15.7146	+	13.1028i	0.575737	+	0.480050i
$746$	−16.6444	+	22.9090i	−0.609394	+	0.838758i
$747$	15.4545	−	20.2171i	0.565450	−	0.739706i
$748$	0.114400	−	0.0371709i	0.00418289	−	0.00135910i
$749$		−	42.0545i		−	1.53664i
$750$	7.82641	+	17.7129i	0.285780	+	0.646784i
$751$	−9.65633	−	29.7191i	−0.352365	−	1.08447i	−0.957522	−	0.288361i	$-0.906890\pi$
$751$	−9.65633	−	29.7191i	−0.352365	−	1.08447i	0.605157	−	0.796106i	$-0.293110\pi$
$752$	1.94912	−	5.99879i	0.0710773	−	0.218753i
$753$	−3.90159	+	2.76272i	−0.142182	+	0.100679i
$754$	7.52053	+	5.46398i	0.273881	+	0.198987i
$755$	−19.0186	+	47.4983i	−0.692156	+	1.72864i
$756$	12.6121	+	18.7638i	0.458699	+	0.682431i
$757$	43.1953	−	31.3832i	1.56996	−	1.14064i	0.642766	−	0.766063i	$-0.277787\pi$
$757$	43.1953	−	31.3832i	1.56996	−	1.14064i	0.927195	−	0.374580i	$-0.122213\pi$
$758$	−4.39320	+	13.5209i	−0.159568	+	0.491101i
$759$	0.0101688	−	0.835152i	0.000369105	−	0.0303141i
$760$	0.337461	−	5.05216i	0.0122410	−	0.183261i
$761$	11.6202	−	35.7633i	0.421232	−	1.29642i	−0.485324	−	0.874334i	$-0.661298\pi$
$761$	11.6202	−	35.7633i	0.421232	−	1.29642i	0.906556	−	0.422085i	$-0.138702\pi$
$762$	8.61464	+	0.104892i	0.312076	+	0.00379983i
$763$	36.5561	−	50.3152i	1.32342	−	1.82153i
$764$	−3.59838	+	1.16918i	−0.130185	+	0.0422996i
$765$	7.59545	−	4.52481i	0.274614	−	0.163595i
$766$	11.0539	+	3.59164i	0.399395	+	0.129771i
$767$	11.3004	+	3.67171i	0.408033	+	0.132578i
$768$	−0.555249	+	1.64064i	−0.0200358	+	0.0592015i
$769$	−26.3921			−0.951724			−0.475862	−	0.879520i	$-0.657864\pi$
$769$	−26.3921			−0.951724			−0.475862	+	0.879520i	$0.657864\pi$
$770$	0.681998	+	0.568651i	0.0245775	+	0.0204928i
$771$	5.46814	−	16.1571i	0.196930	−	0.581885i
$772$	5.80172	+	7.98538i	0.208808	+	0.287400i
$773$	−32.2242	+	44.3528i	−1.15902	+	1.59526i	−0.444250	+	0.895903i	$0.646530\pi$
$773$	−32.2242	+	44.3528i	−1.15902	+	1.59526i	−0.714774	+	0.699356i	$0.753470\pi$
$774$	6.09943	+	20.4539i	0.219239	+	0.735199i
$775$	18.9487	+	20.3947i	0.680659	+	0.732600i
$776$		−	10.9396i		−	0.392708i
$777$	−58.0320	+	18.0776i	−2.08189	+	0.648531i
$778$	3.44679	−	2.50424i	0.123573	−	0.0897812i
$779$	11.5562	−	3.75484i	0.414044	−	0.134531i
$780$	5.82850	−	1.39725i	0.208694	−	0.0500297i
$781$		−	0.311846i		−	0.0111587i
$782$	−2.15178	−	6.62249i	−0.0769474	−	0.236820i
$783$	24.5646	+	19.2561i	0.877866	+	0.688157i
$784$	−3.68697	+	11.3473i	−0.131677	+	0.405261i
$785$	−11.6052	−	45.9355i	−0.414207	−	1.63951i
$786$	−17.1315	−	5.79788i	−0.611059	−	0.206804i
$787$	5.20904	+	3.78459i	0.185682	+	0.134906i	0.676743	−	0.736219i	$-0.263391\pi$
$787$	5.20904	+	3.78459i	0.185682	+	0.134906i	−0.491061	+	0.871125i	$0.663391\pi$
$788$	−12.1652	−	16.7439i	−0.433366	−	0.596478i
$789$	22.2477	+	31.4187i	0.792037	+	1.11854i
$790$	−11.1472	−	0.744580i	−0.396599	−	0.0264910i
$791$	−48.1545	−	66.2790i	−1.71218	−	2.35661i
$792$	0.273725	+	0.00666674i	0.00972639	+	0.000236892i
$793$	6.98709	+	9.61690i	0.248119	+	0.341506i
$794$	13.9765	−	19.2370i	0.496008	−	0.682697i
$795$	9.75668	−	5.97444i	0.346034	−	0.211892i
$796$	−13.0198	+	17.9202i	−0.461474	+	0.635165i
$797$	−1.08622	−	0.352933i	−0.0384758	−	0.0125015i	0.289716	−	0.957113i	$-0.406439\pi$
$797$	−1.08622	−	0.352933i	−0.0384758	−	0.0125015i	−0.328192	+	0.944611i	$0.606439\pi$
$798$	−9.86179	−	13.9271i	−0.349104	−	0.493013i
$799$	−7.90612	+	2.56885i	−0.279698	+	0.0908795i
$800$	0.898918	+	4.91853i	0.0317816	+	0.173896i
$801$	10.4769	+	35.1335i	0.370185	+	1.24138i
$802$	0.145980	+	0.449282i	0.00515475	+	0.0158647i
$803$	−0.437499	+	0.317862i	−0.0154390	+	0.0112171i
$804$	1.14882	−	0.357872i	0.0405159	−	0.0126212i
$805$	32.9185	−	39.4799i	1.16022	−	1.39148i
$806$	7.26393	−	4.63441i	0.255861	−	0.163240i
$807$	10.5705	+	7.87832i	0.372099	+	0.277330i
$808$	−7.07417	+	9.73676i	−0.248869	+	0.342538i
$809$	−21.7011	+	15.7668i	−0.762970	+	0.554330i	−0.899820	−	0.436262i	$-0.856302\pi$
$809$	−21.7011	+	15.7668i	−0.762970	+	0.554330i	0.136850	+	0.990592i	$0.456302\pi$
$810$	19.7284	−	3.97371i	0.693185	−	0.139622i
$811$	−42.1140			−1.47882			−0.739412	−	0.673253i	$-0.764896\pi$
$811$	−42.1140			−1.47882			−0.739412	+	0.673253i	$0.764896\pi$
$812$			26.1358i			0.917186i
$813$	−10.5838	−	3.58192i	−0.371189	−	0.125623i
$814$	−0.227474	+	0.700093i	−0.00797296	+	0.0245383i
$815$	24.6250	−	15.4944i	0.862578	−	0.542744i
$816$	2.17946	−	0.678927i	0.0762964	−	0.0237672i
$817$	−4.97845	−	15.3221i	−0.174174	−	0.536052i
$818$	19.9670	−	27.4822i	0.698129	−	0.960892i
$819$	12.2678	−	16.0484i	0.428671	−	0.560776i
$820$	−10.1556	+	6.39005i	−0.354650	+	0.223150i
$821$	−21.3906	+	15.5412i	−0.746537	+	0.542391i	−0.894752	−	0.446564i	$-0.852647\pi$
$821$	−21.3906	+	15.5412i	−0.746537	+	0.542391i	0.148215	+	0.988955i	$0.452647\pi$
$822$	0.0604426	−	4.96407i	0.00210818	−	0.173142i
$823$	0.533713	−	1.64260i	0.0186041	−	0.0572574i	−0.941323	−	0.337506i	$-0.890417\pi$
$823$	0.533713	−	1.64260i	0.0186041	−	0.0572574i	0.959928	+	0.280248i	$0.0904168\pi$
$824$	9.64380	+	13.2736i	0.335958	+	0.462406i
$825$	0.700083	−	0.366922i	0.0243738	−	0.0127746i
$826$	10.3232	+	31.7715i	0.359189	+	1.10547i
$827$	2.19104	−	3.01571i	0.0761900	−	0.104867i	−0.769221	−	0.638983i	$-0.779356\pi$
$827$	2.19104	−	3.01571i	0.0761900	−	0.104867i	0.845411	+	0.534116i	$0.179356\pi$
$828$	0.385929	−	15.8456i	0.0134119	−	0.550671i
$829$	48.7453	+	15.8383i	1.69300	+	0.550088i	0.987361	−	0.158488i	$-0.0506619\pi$
$829$	48.7453	+	15.8383i	1.69300	+	0.550088i	0.705635	+	0.708576i	$0.250662\pi$
$830$	7.05047	−	17.6083i	0.244725	−	0.611194i
$831$	11.3667	+	8.47176i	0.394307	+	0.293882i
$832$	1.54755			0.0536517
$833$	14.9552	−	4.85924i	0.518168	−	0.168363i
$834$	−0.0734966	+	6.03618i	−0.00254498	+	0.209016i
$835$	−10.5823	−	41.8868i	−0.366216	−	1.44955i
$836$	−0.206671			−0.00714788
$837$	24.9418	−	14.6597i	0.862114	−	0.506714i
$838$			11.4785i			0.396517i
$839$	−7.17310	+	9.87293i	−0.247643	+	0.340851i	−0.914684	−	0.404170i	$-0.867561\pi$
$839$	−7.17310	+	9.87293i	−0.247643	+	0.340851i	0.667041	+	0.745021i	$0.267561\pi$
$840$	12.8103	+	10.9484i	0.441996	+	0.377754i
$841$	2.18847	+	6.73542i	0.0754645	+	0.232256i
$842$	2.01320			0.0693794
$843$	27.1915	−	36.4834i	0.936525	−	1.25655i
$844$	3.17675	+	9.77703i	0.109348	+	0.336539i
$845$	12.6290	+	20.0711i	0.434449	+	0.690466i
$846$	−18.9169	−	0.460733i	−0.650376	−	0.0158403i
$847$	−28.1107	+	38.6911i	−0.965897	+	1.32944i
$848$	2.80937	−	0.912819i	0.0964741	−	0.0313463i
$849$	−13.5908	+	4.23369i	−0.466435	+	0.145300i
$850$	4.54799	−	4.76872i	0.155995	−	0.163566i
$851$	40.5275	+	13.1682i	1.38926	+	0.451399i
$852$	0.0720529	−	5.91761i	0.00246849	−	0.202734i
$853$	−18.8833	−	25.9907i	−0.646553	−	0.889903i	0.352391	−	0.935853i	$-0.385369\pi$
$853$	−18.8833	−	25.9907i	−0.646553	−	0.889903i	−0.998944	+	0.0459494i	$0.985369\pi$
$854$	−10.3277	+	31.7855i	−0.353408	+	1.08768i
$855$	−14.8137	+	3.36108i	−0.506619	+	0.114947i
$856$	−7.81952	−	5.68121i	−0.267266	−	0.194180i
$857$	0.173572	+	0.534201i	0.00592912	+	0.0182479i	0.953977	−	0.299879i	$-0.0969462\pi$
$857$	0.173572	+	0.534201i	0.00592912	+	0.0182479i	−0.948048	+	0.318127i	$0.896946\pi$
$858$	−0.0727596	−	0.233570i	−0.00248397	−	0.00797393i
$859$	1.26060	+	0.409593i	0.0430111	+	0.0139751i	0.330444	−	0.943826i	$-0.392802\pi$
$859$	1.26060	+	0.409593i	0.0430111	+	0.0139751i	−0.287432	+	0.957801i	$0.592802\pi$
$860$	8.47240	+	13.4651i	0.288907	+	0.459156i
$861$	−12.9637	+	38.3048i	−0.441801	+	1.30543i
$862$		−	35.5934i		−	1.21232i
$863$		−	37.0962i		−	1.26277i	−0.775470	−	0.631384i	$-0.782487\pi$
$863$		−	37.0962i		−	1.26277i	0.775470	−	0.631384i	$-0.217513\pi$
$864$	5.19269	+	0.189754i	0.176659	+	0.00645555i
$865$	2.07028	−	30.9943i	0.0703916	−	1.05384i
$866$	−25.0649	−	18.2107i	−0.851741	−	0.618826i
$867$	21.1966	+	15.7981i	0.719876	+	0.536532i
$868$	22.5456	+	8.86369i	0.765248	+	0.300853i
$869$			0.456003i			0.0154689i
$870$	21.4905	+	8.91002i	0.728597	+	0.302078i
$871$	−0.631928	−	0.869775i	−0.0214121	−	0.0294712i
$872$	−4.41707	−	13.5943i	−0.149581	−	0.460362i
$873$	−31.4501	+	9.37856i	−1.06443	+	0.317416i
$874$			11.9639i			0.404686i
$875$	47.6752	+	9.66867i	1.61172	+	0.326861i
$876$	−8.37547	+	5.93069i	−0.282981	+	0.200379i
$877$	25.0413	+	8.13641i	0.845585	+	0.274747i	0.699596	−	0.714539i	$-0.253363\pi$
$877$	25.0413	+	8.13641i	0.845585	+	0.274747i	0.145989	+	0.989286i	$0.453363\pi$
$878$	7.09587	+	5.15545i	0.239474	+	0.173988i
$879$	−8.62430	+	25.4829i	−0.290890	+	0.859517i
$880$	0.197866	−	0.0499891i	0.00667006	−	0.00168513i
$881$	14.8053	−	10.7567i	0.498803	−	0.362401i	−0.309757	−	0.950816i	$-0.600248\pi$
$881$	14.8053	−	10.7567i	0.498803	−	0.362401i	0.808560	+	0.588414i	$0.200248\pi$
$882$	35.7832	+	0.871523i	1.20488	+	0.0293457i
$883$	−43.2113	+	31.3949i	−1.45418	+	1.05652i	−0.469344	+	0.883015i	$0.655510\pi$
$883$	−43.2113	+	31.3949i	−1.45418	+	1.05652i	−0.984833	+	0.173506i	$0.944490\pi$
$884$	−1.19885	−	1.65007i	−0.0403215	−	0.0554978i
$885$	29.6438	+	2.34292i	0.996467	+	0.0787565i
$886$	−11.9073	+	8.65119i	−0.400035	+	0.290642i
$887$	2.83555	+	2.06015i	0.0952086	+	0.0691731i	0.634371	−	0.773029i	$-0.281259\pi$
$887$	2.83555	+	2.06015i	0.0952086	+	0.0691731i	−0.539162	+	0.842202i	$0.681259\pi$
$888$	−4.47833	+	13.2325i	−0.150283	+	0.444053i
$889$	12.7209	−	17.5088i	0.426645	−	0.587226i
$890$	14.5530	+	23.1289i	0.487817	+	0.775283i
$891$	−0.215500	−	0.792646i	−0.00721951	−	0.0265546i
$892$	−3.94097	−	12.1291i	−0.131954	−	0.406111i
$893$	14.2829			0.477959
$894$	9.47100	−	12.7074i	0.316758	−	0.425000i
$895$	30.1500	+	12.0722i	1.00780	+	0.403530i
$896$	2.55746	+	3.52004i	0.0854387	+	0.117596i
$897$	−13.5210	+	4.21195i	−0.451454	+	0.140633i
$898$	−31.9932			−1.06763
$899$	33.3836	+	2.01961i	1.11341	+	0.0673578i
$900$	13.3696	−	6.80098i	0.445654	−	0.226699i
$901$	−3.14963	−	2.28834i	−0.104929	−	0.0762356i
$902$	0.287866	+	0.396214i	0.00958490	+	0.0131925i
$903$	50.7874	+	17.1882i	1.69010	+	0.571988i
$904$	−18.8290			−0.626245
$905$	−6.34929	−	5.29405i	−0.211057	−	0.175980i
$906$	37.5401	+	12.7049i	1.24719	+	0.422091i
$907$	18.2616	+	5.93355i	0.606366	+	0.197020i	0.596078	−	0.802927i	$-0.296725\pi$
$907$	18.2616	+	5.93355i	0.606366	+	0.197020i	0.0102884	+	0.999947i	$0.496725\pi$
$908$	7.06655	−	21.7486i	0.234512	−	0.721752i
$909$	34.0569	+	11.9901i	1.12960	+	0.397687i
$910$	5.59667	−	13.9775i	0.185528	−	0.463351i
$911$	39.2198	+	28.4949i	1.29941	+	0.944077i	0.999950	−	0.0100315i	$-0.00319318\pi$
$911$	39.2198	+	28.4949i	1.29941	+	0.944077i	0.299461	+	0.954109i	$0.403193\pi$
$912$	−3.92182	−	0.0477520i	−0.129864	−	0.00158123i
$913$	−0.736294	−	0.239236i	−0.0243678	−	0.00791757i
$914$	21.2969	−	15.4731i	0.704438	−	0.511804i
$915$	22.6152	+	19.3282i	0.747636	+	0.638970i
$916$	−9.20272	−	2.99015i	−0.304067	−	0.0987972i
$917$	−36.7560	+	26.7048i	−1.21379	+	0.881871i
$918$	−3.82031	−	5.68368i	−0.126089	−	0.187589i
$919$	−2.74916	−	8.46106i	−0.0906866	−	0.279105i	0.895419	−	0.445224i	$-0.146876\pi$
$919$	−2.74916	−	8.46106i	−0.0906866	−	0.279105i	−0.986106	+	0.166120i	$0.946876\pi$
$920$	−2.89380	−	11.4542i	−0.0954058	−	0.377634i
$921$	22.3295	+	31.5343i	0.735784	+	1.03909i
$922$	−1.41748	+	4.36254i	−0.0466821	+	0.143673i
$923$	−5.02886	+	1.63398i	−0.165527	+	0.0537830i
$924$	0.411033	−	0.551491i	0.0135220	−	0.0181427i
$925$	7.25017	+	39.6701i	0.238384	+	1.30435i
$926$	−0.974139	−	2.99809i	−0.0320122	−	0.0985234i
$927$	29.8924	−	39.1044i	0.981795	−	1.28436i
$928$	4.85963	+	3.53073i	0.159525	+	0.115902i
$929$	32.4326			1.06408			0.532040	−	0.846719i	$-0.321426\pi$
$929$	32.4326			1.06408			0.532040	+	0.846719i	$0.321426\pi$
$930$	14.9744	−	15.5167i	0.491029	−	0.508813i
$931$	−27.0175			−0.885464
$932$	13.3384	+	9.69093i	0.436915	+	0.317437i
$933$	0.337964	−	27.7566i	0.0110645	−	0.908709i
$934$	3.70422	+	11.4004i	0.121206	+	0.373033i
$935$	−0.206582	−	0.172248i	−0.00675595	−	0.00563313i
$936$	−1.32673	−	4.44905i	−0.0433654	−	0.145422i
$937$	−53.4405	+	17.3639i	−1.74583	+	0.567253i	−0.995581	−	0.0939065i	$-0.970065\pi$
$937$	−53.4405	+	17.3639i	−1.74583	+	0.567253i	−0.750245	+	0.661160i	$0.770065\pi$
$938$	0.934063	−	2.87475i	0.0304983	−	0.0938640i
$939$	30.1034	−	21.3163i	0.982388	−	0.695631i
$940$	−13.6743	+	3.45470i	−0.446008	+	0.112680i
$941$	−5.96893	−	18.3705i	−0.194582	−	0.598861i	−0.999981	−	0.00612852i	$-0.998049\pi$
$941$	−5.96893	−	18.3705i	−0.194582	−	0.598861i	0.805400	−	0.592732i	$-0.201951\pi$
$942$	−35.0387	+	10.9150i	−1.14162	+	0.355628i
$943$	22.9363	−	16.6642i	0.746909	−	0.542661i
$944$	7.30209	+	2.37259i	0.237663	+	0.0772214i
$945$	20.4931	−	46.2142i	0.666639	−	1.50335i
$946$	0.525330	−	0.381675i	0.0170800	−	0.0124093i
$947$	41.5576	+	13.5029i	1.35044	+	0.438785i	0.892841	−	0.450372i	$-0.148709\pi$
$947$	41.5576	+	13.5029i	1.35044	+	0.438785i	0.457601	+	0.889158i	$0.348709\pi$
$948$	−0.105361	+	8.65316i	−0.00342196	+	0.281042i
$949$	7.41824	+	5.38966i	0.240806	+	0.174956i
$950$	−9.96353	+	5.37764i	−0.323260	+	0.174474i
$951$	−14.4940	−	46.5279i	−0.469999	−	1.50877i
$952$	1.77203	−	5.45376i	0.0574319	−	0.176757i
$953$	6.56662	+	2.13362i	0.212714	+	0.0691148i	0.413435	−	0.910533i	$-0.364329\pi$
$953$	6.56662	+	2.13362i	0.212714	+	0.0691148i	−0.200722	+	0.979648i	$0.564329\pi$
$954$	−5.03275	−	7.29407i	−0.162941	−	0.236154i
$955$	6.49788	+	5.41795i	0.210267	+	0.175321i
$956$	−1.56151			−0.0505029
$957$	0.304407	−	0.899457i	0.00984009	−	0.0290753i
$958$	14.7021	+	20.2356i	0.475002	+	0.653784i
$959$	−10.0892	−	7.33024i	−0.325798	−	0.236706i
$960$	3.76627	−	0.902880i	0.121556	−	0.0291403i
$961$	13.0639	−	28.1129i	0.421416	−	0.906867i
$962$	12.4817			0.402426
$963$	−9.62918	+	27.3508i	−0.310296	+	0.881369i
$964$	−11.9489	−	16.4462i	−0.384848	−	0.529698i
$965$	8.20413	−	20.4896i	0.264100	−	0.659583i
$966$	−31.9251	−	23.7942i	−1.02717	−	0.765564i
$967$	−15.0919			−0.485324			−0.242662	−	0.970111i	$-0.578021\pi$
$967$	−15.0919			−0.485324			−0.242662	+	0.970111i	$0.578021\pi$
$968$	3.39661	+	10.4537i	0.109171	+	0.335995i
$969$	2.98721	+	4.21861i	0.0959629	+	0.135521i
$970$	−20.7041	+	13.0273i	−0.664769	+	0.418281i
$971$	19.4428	−	26.7608i	0.623950	−	0.858793i	−0.373683	−	0.927556i	$-0.621905\pi$
$971$	19.4428	−	26.7608i	0.623950	−	0.858793i	0.997633	+	0.0687630i	$0.0219052\pi$
$972$	−3.90620	−	15.0911i	−0.125291	−	0.484048i
$973$	12.2682	+	8.91338i	0.393301	+	0.285750i
$974$	−1.17276	+	0.852059i	−0.0375776	+	0.0273017i
$975$	−9.58524	−	9.36706i	−0.306973	−	0.299986i
$976$	4.51493	+	6.21427i	0.144519	+	0.198914i
$977$	7.21194	−	5.23978i	0.230731	−	0.167636i	−0.466413	−	0.884567i	$-0.654454\pi$
$977$	7.21194	−	5.23978i	0.230731	−	0.167636i	0.697144	+	0.716931i	$0.254454\pi$
$978$	−13.0235	−	18.3921i	−0.416445	−	0.588115i
$979$	0.902356	−	0.655600i	0.0288394	−	0.0209531i
$980$	25.8664	−	6.53492i	0.826272	−	0.208750i
$981$	−35.2955	+	24.3531i	−1.12690	+	0.777535i
$982$	−14.6577	−	10.6494i	−0.467745	−	0.339837i
$983$	−4.00855	−	1.30246i	−0.127853	−	0.0415419i	0.244392	−	0.969677i	$-0.421412\pi$
$983$	−4.00855	−	1.30246i	−0.127853	−	0.0415419i	−0.372245	+	0.928135i	$0.621412\pi$
$984$	5.37103	+	7.58511i	0.171222	+	0.241804i
$985$	−17.2026	+	42.9630i	−0.548121	+	1.36892i
$986$		−	7.91672i		−	0.252120i
$987$	−28.4061	+	38.1131i	−0.904178	+	1.21315i
$988$	1.08289	+	3.33281i	0.0344515	+	0.106031i
$989$	−22.0946	−	30.4107i	−0.702569	−	0.967003i
$990$	−0.313345	−	0.525988i	−0.00995876	−	0.0167170i
$991$			48.4782i			1.53996i	0.638068	+	0.769980i	$0.279734\pi$
$991$			48.4782i			1.53996i	−0.638068	+	0.769980i	$0.720266\pi$
$992$	4.69382	−	2.99467i	0.149029	−	0.0950809i
$993$	−24.9915	+	33.5316i	−0.793081	+	1.06409i
$994$	−12.0272	−	8.73830i	−0.381481	−	0.277162i
$995$	49.4201	+	3.30104i	1.56672	+	0.104650i
$996$	−13.9167	−	4.70989i	−0.440968	−	0.149239i
$997$			41.6933i			1.32044i	0.751072	+	0.660220i	$0.229537\pi$
$997$			41.6933i			1.32044i	−0.751072	+	0.660220i	$0.770463\pi$
$998$		−	29.7982i		−	0.943245i
$999$	41.8813	+	1.53045i	1.32507	+	0.0484212i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.y.b.29.1	yes	128
3.2	odd	2		930.2.y.a.29.13	✓	128
5.4	even	2		930.2.y.a.29.32	yes	128
15.14	odd	2	inner	930.2.y.b.29.20	yes	128
31.15	odd	10	inner	930.2.y.b.449.20	yes	128
93.77	even	10		930.2.y.a.449.32	yes	128
155.139	odd	10		930.2.y.a.449.13	yes	128
465.449	even	10	inner	930.2.y.b.449.1	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.y.a.29.13	✓	128	3.2	odd	2
930.2.y.a.29.32	yes	128	5.4	even	2
930.2.y.a.449.13	yes	128	155.139	odd	10
930.2.y.a.449.32	yes	128	93.77	even	10
930.2.y.b.29.1	yes	128	1.1	even	1	trivial
930.2.y.b.29.20	yes	128	15.14	odd	2	inner
930.2.y.b.449.1	yes	128	465.449	even	10	inner
930.2.y.b.449.20	yes	128	31.15	odd	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.y (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{2} +(-1.73192 - 0.0210879i) q^{3} +(0.309017 + 0.951057i) q^{4} +(1.43197 - 1.71740i) q^{5} +(-1.38876 - 1.03506i) q^{6} +(-4.13806 + 1.34454i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(2.99911 + 0.0730452i) q^{9} +O(q^{10})\)	\(q+(0.809017 + 0.587785i) q^{2} +(-1.73192 - 0.0210879i) q^{3} +(0.309017 + 0.951057i) q^{4} +(1.43197 - 1.71740i) q^{5} +(-1.38876 - 1.03506i) q^{6} +(-4.13806 + 1.34454i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(2.99911 + 0.0730452i) q^{9} +(2.16795 - 0.547714i) q^{10} +(-0.0282036 - 0.0868017i) q^{11} +(-0.515138 - 1.65367i) q^{12} +(-1.25200 + 0.909628i) q^{13} +(-4.13806 - 1.34454i) q^{14} +(-2.51628 + 2.94420i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(1.25345 + 0.407270i) q^{17} +(2.38340 + 1.82193i) q^{18} +(-1.83196 - 1.33100i) q^{19} +(2.07585 + 0.831180i) q^{20} +(7.19514 - 2.24137i) q^{21} +(0.0282036 - 0.0868017i) q^{22} +(-5.02483 - 1.63267i) q^{23} +(0.555249 - 1.64064i) q^{24} +(-0.898918 - 4.91853i) q^{25} -1.54755 q^{26} +(-5.19269 - 0.189754i) q^{27} +(-2.55746 - 3.52004i) q^{28} +(-4.85963 - 3.53073i) q^{29} +(-3.76627 + 0.902880i) q^{30} +(-4.69382 + 2.99467i) q^{31} -1.00000 q^{32} +(0.0470159 + 0.150928i) q^{33} +(0.774673 + 1.06625i) q^{34} +(-3.61647 + 9.03203i) q^{35} +(0.857306 + 2.87490i) q^{36} -8.06544 q^{37} +(-0.699747 - 2.15360i) q^{38} +(2.18754 - 1.54900i) q^{39} +(1.19084 + 1.89259i) q^{40} +(-3.15405 + 4.34118i) q^{41} +(7.13844 + 2.41589i) q^{42} +(5.75587 + 4.18188i) q^{43} +(0.0738379 - 0.0536464i) q^{44} +(4.42009 - 5.04607i) q^{45} +(-3.10552 - 4.27438i) q^{46} +(-5.10287 + 3.70746i) q^{47} +(1.41355 - 1.00094i) q^{48} +(9.65260 - 7.01303i) q^{49} +(2.16380 - 4.50755i) q^{50} +(-2.16228 - 0.731792i) q^{51} +(-1.25200 - 0.909628i) q^{52} +(-2.80937 - 0.912819i) q^{53} +(-4.08944 - 3.20570i) q^{54} +(-0.189460 - 0.0758607i) q^{55} -4.35101i q^{56} +(3.14475 + 2.34382i) q^{57} +(-1.85621 - 5.71284i) q^{58} +(-4.51294 - 6.21153i) q^{59} +(-3.57768 - 1.48331i) q^{60} -7.68126i q^{61} +(-5.55760 - 0.336219i) q^{62} +(-12.5087 + 3.73015i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-0.230627 + 3.45274i) q^{65} +(-0.0506769 + 0.149739i) q^{66} +0.694711i q^{67} +1.31795i q^{68} +(8.66819 + 2.93362i) q^{69} +(-8.23468 + 5.18136i) q^{70} +(3.24956 + 1.05585i) q^{71} +(-0.996246 + 2.82975i) q^{72} +(-1.83097 - 5.63513i) q^{73} +(-6.52508 - 4.74075i) q^{74} +(1.45314 + 8.53747i) q^{75} +(0.699747 - 2.15360i) q^{76} +(0.233416 + 0.321269i) q^{77} +(2.68024 + 0.0326346i) q^{78} +(-4.75174 - 1.54393i) q^{79} +(-0.149027 + 2.23110i) q^{80} +(8.98933 + 0.438141i) q^{81} +(-5.10337 + 1.65818i) q^{82} +(4.98588 - 6.86247i) q^{83} +(4.35509 + 6.15037i) q^{84} +(2.49434 - 1.56947i) q^{85} +(2.19855 + 6.76643i) q^{86} +(8.34205 + 6.21743i) q^{87} +0.0912687 q^{88} +(3.77643 + 11.6226i) q^{89} +(6.54193 - 1.48430i) q^{90} +(3.95780 - 5.44744i) q^{91} -5.28342i q^{92} +(8.19248 - 5.08755i) q^{93} -6.30750 q^{94} +(-4.90917 + 1.24026i) q^{95} +(1.73192 + 0.0210879i) q^{96} +(-10.4041 + 3.38051i) q^{97} +11.9313 q^{98} +(-0.0782452 - 0.262388i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 32 q^{2} - 32 q^{4} - 2 q^{5} + 32 q^{8} - 4 q^{9}+O(q^{10}) \) 128 * q + 32 * q^2 - 32 * q^4 - 2 * q^5 + 32 * q^8 - 4 * q^9	\( 128 q + 32 q^{2} - 32 q^{4} - 2 q^{5} + 32 q^{8} - 4 q^{9} + 2 q^{10} - 35 q^{15} - 32 q^{16} - 6 q^{18} - 8 q^{19} + 3 q^{20} + 20 q^{23} - 10 q^{25} - 48 q^{31} - 128 q^{32} + 8 q^{33} + 10 q^{34} - 16 q^{35} - 4 q^{36} - 12 q^{38} + 4 q^{39} - 3 q^{40} + 5 q^{45} + 10 q^{46} - 6 q^{47} + 46 q^{49} + 5 q^{50} + 34 q^{51} + 20 q^{53} + 35 q^{60} + 8 q^{62} - 36 q^{63} - 32 q^{64} - 8 q^{66} + 8 q^{69} + 16 q^{70} - 6 q^{72} + 5 q^{75} + 12 q^{76} - 50 q^{77} - 4 q^{78} - 10 q^{79} - 2 q^{80} - 24 q^{81} + 40 q^{83} - 30 q^{85} + 4 q^{87} - 5 q^{90} + 20 q^{91} + 26 q^{93} - 4 q^{94} + 26 q^{95} + 124 q^{98}+O(q^{100}) \) 128 * q + 32 * q^2 - 32 * q^4 - 2 * q^5 + 32 * q^8 - 4 * q^9 + 2 * q^10 - 35 * q^15 - 32 * q^16 - 6 * q^18 - 8 * q^19 + 3 * q^20 + 20 * q^23 - 10 * q^25 - 48 * q^31 - 128 * q^32 + 8 * q^33 + 10 * q^34 - 16 * q^35 - 4 * q^36 - 12 * q^38 + 4 * q^39 - 3 * q^40 + 5 * q^45 + 10 * q^46 - 6 * q^47 + 46 * q^49 + 5 * q^50 + 34 * q^51 + 20 * q^53 + 35 * q^60 + 8 * q^62 - 36 * q^63 - 32 * q^64 - 8 * q^66 + 8 * q^69 + 16 * q^70 - 6 * q^72 + 5 * q^75 + 12 * q^76 - 50 * q^77 - 4 * q^78 - 10 * q^79 - 2 * q^80 - 24 * q^81 + 40 * q^83 - 30 * q^85 + 4 * q^87 - 5 * q^90 + 20 * q^91 + 26 * q^93 - 4 * q^94 + 26 * q^95 + 124 * q^98

Introduction

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