LMFDB - Embedded newform 930.2.y.a.29.13

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			29.13
Character	$\chi$	$=$	930.29
Dual form			930.2.y.a.449.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 - 0.587785i) q^{2} +(-0.515138 + 1.65367i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-1.43197 + 1.71740i) q^{5} +(1.38876 - 1.03506i) q^{6} +(-4.13806 + 1.34454i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-2.46927 - 1.70374i) q^{9} +O(q^{10})$	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.515138 + 1.65367i) 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} +(-2.46927 - 1.70374i) q^{9} +(2.16795 - 0.547714i) q^{10} +(0.0282036 + 0.0868017i) q^{11} +(-1.73192 + 0.0210879i) q^{12} +(-1.25200 + 0.909628i) q^{13} +(4.13806 + 1.34454i) q^{14} +(-2.10235 - 3.25271i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-1.25345 - 0.407270i) q^{17} +(0.996246 + 2.82975i) q^{18} +(-1.83196 - 1.33100i) q^{19} +(-2.07585 - 0.831180i) q^{20} +(-0.0917536 - 7.53561i) q^{21} +(0.0282036 - 0.0868017i) q^{22} +(5.02483 + 1.63267i) q^{23} +(1.41355 + 1.00094i) q^{24} +(-0.898918 - 4.91853i) q^{25} +1.54755 q^{26} +(4.08944 - 3.20570i) q^{27} +(-2.55746 - 3.52004i) q^{28} +(4.85963 + 3.53073i) q^{29} +(-0.211054 + 3.86723i) q^{30} +(-4.69382 + 2.99467i) q^{31} +1.00000 q^{32} +(-0.158070 + 0.00192466i) 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} +(-0.859277 - 2.53897i) q^{39} +(1.19084 + 1.89259i) q^{40} +(3.15405 - 4.34118i) q^{41} +(-4.35509 + 6.15037i) q^{42} +(5.75587 + 4.18188i) q^{43} +(-0.0738379 + 0.0536464i) q^{44} +(6.46192 - 1.80101i) q^{45} +(-3.10552 - 4.27438i) q^{46} +(5.10287 - 3.70746i) q^{47} +(-0.555249 - 1.64064i) q^{48} +(9.65260 - 7.01303i) q^{49} +(-2.16380 + 4.50755i) q^{50} +(1.31919 - 1.86299i) q^{51} +(-1.25200 - 0.909628i) q^{52} +(2.80937 + 0.912819i) q^{53} +(-5.19269 + 0.189754i) 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} +(2.44385 - 3.00460i) 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} +(0.129013 + 0.0913543i) q^{66} +0.694711i q^{67} -1.31795i q^{68} +(-5.28838 + 7.46838i) q^{69} +(-8.23468 + 5.18136i) q^{70} +(-3.24956 - 1.05585i) q^{71} +(-2.38340 + 1.82193i) q^{72} +(-1.83097 - 5.63513i) q^{73} +(6.52508 + 4.74075i) q^{74} +(8.59671 + 1.04720i) q^{75} +(0.699747 - 2.15360i) q^{76} +(-0.233416 - 0.321269i) q^{77} +(-0.797202 + 2.55914i) q^{78} +(-4.75174 - 1.54393i) q^{79} +(0.149027 - 2.23110i) q^{80} +(3.19455 + 8.41397i) q^{81} +(-5.10337 + 1.65818i) q^{82} +(-4.98588 + 6.86247i) q^{83} +(7.13844 - 2.41589i) 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} +(-6.28641 - 2.34117i) q^{90} +(3.95780 - 5.44744i) q^{91} +5.28342i q^{92} +(-2.53424 - 9.30471i) q^{93} -6.30750 q^{94} +(4.90917 - 1.24026i) q^{95} +(-0.515138 + 1.65367i) 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} + 25 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} + 37 q^{45} + 10 q^{46} + 6 q^{47} + 46 q^{49} - 5 q^{50} + 34 q^{51} - 20 q^{53} - 25 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} - 53 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 + 25 * 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 + 37 * q^45 + 10 * q^46 + 6 * q^47 + 46 * q^49 - 5 * q^50 + 34 * q^51 - 20 * q^53 - 25 * 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 - 53 * 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
$3$	−0.515138	+	1.65367i	−0.297415	+	0.954748i
$3$	−0.515138	+	1.65367i	−0.297415	+	0.954748i
$4$	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
$9$	−2.46927	−	1.70374i	−0.823089	−	0.567913i
$10$	2.16795	−	0.547714i	0.685566	−	0.173202i
$11$	0.0282036	+	0.0868017i	0.00850370	+	0.0261717i	0.955218	−	0.295902i	$-0.0956202\pi$
$11$	0.0282036	+	0.0868017i	0.00850370	+	0.0261717i	−0.946715	+	0.322074i	$0.895620\pi$
$12$	−1.73192	+	0.0210879i	−0.499963	+	0.00608755i
$13$	−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
$15$	−2.10235	−	3.25271i	−0.542825	−	0.839846i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−1.25345	−	0.407270i	−0.304005	−	0.0987774i	0.153042	−	0.988220i	$-0.451093\pi$
$17$	−1.25345	−	0.407270i	−0.304005	−	0.0987774i	−0.457047	+	0.889442i	$0.651093\pi$
$18$	0.996246	+	2.82975i	0.234817	+	0.666979i
$19$	−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
$21$	−0.0917536	−	7.53561i	−0.0200223	−	1.64440i
$22$	0.0282036	−	0.0868017i	0.00601302	−	0.0185062i
$23$	5.02483	+	1.63267i	1.04775	+	0.340435i	0.781785	−	0.623548i	$-0.214309\pi$
$23$	5.02483	+	1.63267i	1.04775	+	0.340435i	0.265965	+	0.963983i	$0.414309\pi$
$24$	1.41355	+	1.00094i	0.288540	+	0.204316i
$25$	−0.898918	−	4.91853i	−0.179784	−	0.983706i
$26$	1.54755			0.303500
$27$	4.08944	−	3.20570i	0.787013	−	0.616937i
$28$	−2.55746	−	3.52004i	−0.483314	−	0.665225i
$29$	4.85963	+	3.53073i	0.902411	+	0.655640i	0.939084	−	0.343688i	$-0.111676\pi$
$29$	4.85963	+	3.53073i	0.902411	+	0.655640i	−0.0366735	+	0.999327i	$0.511676\pi$
$30$	−0.211054	+	3.86723i	−0.0385330	+	0.706056i
$31$	−4.69382	+	2.99467i	−0.843035	+	0.537859i
$31$	−4.69382	+	2.99467i	−0.843035	+	0.537859i
$32$	1.00000			0.176777
$33$	−0.158070	+	0.00192466i	−0.0275165	+	0.000335041i
$34$	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
$39$	−0.859277	−	2.53897i	−0.137594	−	0.406561i
$40$	1.19084	+	1.89259i	0.188288	+	0.299245i
$41$	3.15405	−	4.34118i	0.492581	−	0.677979i	−0.488281	−	0.872687i	$-0.662376\pi$
$41$	3.15405	−	4.34118i	0.492581	−	0.677979i	0.980861	+	0.194708i	$0.0623758\pi$
$42$	−4.35509	+	6.15037i	−0.672005	+	0.949022i
$43$	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
$45$	6.46192	−	1.80101i	0.963286	−	0.268479i
$46$	−3.10552	−	4.27438i	−0.457884	−	0.630223i
$47$	5.10287	−	3.70746i	0.744331	−	0.540788i	−0.149734	−	0.988726i	$-0.547842\pi$
$47$	5.10287	−	3.70746i	0.744331	−	0.540788i	0.894064	+	0.447938i	$0.147842\pi$
$48$	−0.555249	−	1.64064i	−0.0801433	−	0.236806i
$49$	9.65260	−	7.01303i	1.37894	−	1.00186i
$50$	−2.16380	+	4.50755i	−0.306007	+	0.637463i
$51$	1.31919	−	1.86299i	0.184723	−	0.260871i
$52$	−1.25200	−	0.909628i	−0.173621	−	0.126143i
$53$	2.80937	+	0.912819i	0.385896	+	0.125385i	0.495539	−	0.868586i	$-0.334971\pi$
$53$	2.80937	+	0.912819i	0.385896	+	0.125385i	−0.109643	+	0.993971i	$0.534971\pi$
$54$	−5.19269	+	0.189754i	−0.706635	+	0.0258222i
$55$	−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	0.994496	−	0.104773i	$-0.0334116\pi$
$59$	4.51294	+	6.21153i	0.587535	+	0.808673i	−0.406961	+	0.913445i	$0.633412\pi$
$60$	2.44385	−	3.00460i	0.315499	−	0.387892i
$61$		−	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
$66$	0.129013	+	0.0913543i	0.0158804	+	0.0112449i
$67$			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
$69$	−5.28838	+	7.46838i	−0.636646	+	0.899087i
$70$	−8.23468	+	5.18136i	−0.984232	+	0.619290i
$71$	−3.24956	−	1.05585i	−0.385652	−	0.125306i	0.109773	−	0.993957i	$-0.464988\pi$
$71$	−3.24956	−	1.05585i	−0.385652	−	0.125306i	−0.495425	+	0.868651i	$0.664988\pi$
$72$	−2.38340	+	1.82193i	−0.280886	+	0.214716i
$73$	−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
$75$	8.59671	+	1.04720i	0.992662	+	0.120921i
$76$	0.699747	−	2.15360i	0.0802665	−	0.247035i
$77$	−0.233416	−	0.321269i	−0.0266002	−	0.0366120i
$78$	−0.797202	+	2.55914i	−0.0902654	+	0.289766i
$79$	−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
$81$	3.19455	+	8.41397i	0.354950	+	0.934885i
$82$	−5.10337	+	1.65818i	−0.563573	+	0.183116i
$83$	−4.98588	+	6.86247i	−0.547271	+	0.753254i	−0.989639	−	0.143579i	$-0.954139\pi$
$83$	−4.98588	+	6.86247i	−0.547271	+	0.753254i	0.442367	+	0.896834i	$0.354139\pi$
$84$	7.13844	−	2.41589i	0.778867	−	0.263596i
$85$	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	$-0.875731\pi$
$89$	−3.77643	−	11.6226i	−0.400301	−	1.23200i	0.524456	−	0.851438i	$-0.324269\pi$
$90$	−6.28641	−	2.34117i	−0.662646	−	0.246781i
$91$	3.95780	−	5.44744i	0.414890	−	0.571047i
$92$			5.28342i			0.550835i
$93$	−2.53424	−	9.30471i	−0.262789	−	0.964853i
$94$	−6.30750			−0.650569
$95$	4.90917	−	1.24026i	0.503670	−	0.127248i
$96$	−0.515138	+	1.65367i	−0.0525760	+	0.168777i
$97$	−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	−0.321976	−	0.946748i	$-0.604347\pi$
$101$	−11.4463	−	3.71911i	−1.13894	−	0.370066i	−0.816968	+	0.576682i	$0.804347\pi$
$102$	−2.16228	+	0.731792i	−0.214098	+	0.0724582i
$103$	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
$105$	13.0730	+	10.6332i	1.27580	+	1.03769i
$106$	−1.73628	−	2.38979i	−0.168643	−	0.232117i
$107$	2.98679	−	9.19240i	0.288744	−	0.888662i	−0.696507	−	0.717550i	$-0.745264\pi$
$107$	2.98679	−	9.19240i	0.288744	−	0.888662i	0.985251	−	0.171113i	$-0.0547363\pi$
$108$	4.31251	+	2.89867i	0.414971	+	0.278925i
$109$	−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
$111$	4.15481	−	13.3376i	0.394357	−	1.26595i
$112$	2.55746	−	3.52004i	0.241657	−	0.332613i
$113$	−5.81850	−	17.9075i	−0.547358	−	1.68459i	−0.715316	−	0.698801i	$-0.753717\pi$
$113$	−5.81850	−	17.9075i	−0.547358	−	1.68459i	0.167958	−	0.985794i	$-0.446283\pi$
$114$	−3.92182	+	0.0477520i	−0.367312	+	0.00447239i
$115$	−9.99935	+	6.29171i	−0.932445	+	0.586705i
$116$	−1.85621	+	5.71284i	−0.172345	+	0.530424i
$117$	4.64128	−	0.113041i	0.429086	−	0.0104507i
$118$		−	7.67788i		−	0.706806i
$119$	5.73442			0.525673
$120$	−3.74317	+	0.994315i	−0.341703	+	0.0907681i
$121$	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
$126$	−7.92722	−	10.3702i	−0.706213	−	0.923849i
$127$	−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	−0.708826	−	0.705383i	$-0.750775\pi$
$131$	−9.93088	+	3.22674i	−0.867665	+	0.281921i	−0.158839	+	0.987305i	$0.550775\pi$
$132$	−0.0506769	−	0.149739i	−0.00441085	−	0.0130331i
$133$	9.37033	+	3.04461i	0.812511	+	0.264001i
$134$	0.408341	−	0.562033i	0.0352753	−	0.0485522i
$135$	−0.350492	+	11.6137i	−0.0301656	+	0.999545i
$136$	−0.774673	+	1.06625i	−0.0664276	+	0.0914298i
$137$	−1.68472	−	2.31882i	−0.143935	−	0.198110i	0.730962	−	0.682418i	$-0.239072\pi$
$137$	−1.68472	−	2.31882i	−0.143935	−	0.198110i	−0.874898	+	0.484308i	$0.839072\pi$
$138$	8.66819	−	2.93362i	0.737885	−	0.249726i
$139$	−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
$141$	3.50223	+	10.3483i	0.294941	+	0.871487i
$142$	2.00834	+	2.76424i	0.168536	+	0.231970i
$143$	−0.114268	−	0.0830205i	−0.00955557	−	0.00694252i
$144$	2.99911	−	0.0730452i	0.249926	−	0.00608710i
$145$	−13.0225	+	3.29002i	−1.08146	+	0.273222i
$146$	−1.83097	+	5.63513i	−0.151532	+	0.466367i
$147$	6.62483	+	19.5749i	0.546407	+	1.61451i
$148$	−2.49236	−	7.67069i	−0.204871	−	0.630527i
$149$		−	9.15020i		−	0.749614i	−0.927103	−	0.374807i	$-0.877709\pi$
$149$		−	9.15020i		−	0.749614i	0.927103	−	0.374807i	$-0.122291\pi$
$150$	−6.33935	−	5.90022i	−0.517606	−	0.481751i
$151$	−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
$153$	2.40121	+	3.14120i	0.194127	+	0.253951i
$154$			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
$159$	−2.95671	+	4.17555i	−0.234483	+	0.331142i
$160$	−1.43197	+	1.71740i	−0.113207	+	0.135772i
$161$	−22.9882			−1.81172
$162$	2.36116	−	8.68475i	0.185510	−	0.682339i
$163$	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
$165$	0.223047	−	0.274226i	0.0173642	−	0.0213484i
$166$	8.06732	−	2.62123i	0.626146	−	0.203447i
$167$	−11.3565	+	15.6309i	−0.878795	+	1.20956i	0.0979577	+	0.995191i	$0.468769\pi$
$167$	−11.3565	+	15.6309i	−0.878795	+	1.20956i	−0.976753	+	0.214367i	$0.931231\pi$
$168$	−7.19514	−	2.24137i	−0.555117	−	0.172925i
$169$	−3.27715	+	10.0860i	−0.252089	+	0.775849i
$170$	−2.94048	−	0.196410i	−0.225524	−	0.0150640i
$171$	2.25593	+	6.40777i	0.172515	+	0.490014i
$172$	−2.19855	+	6.76643i	−0.167638	+	0.515935i
$173$	−11.2388	+	8.16549i	−0.854473	+	0.620811i	−0.926376	−	0.376601i	$-0.877093\pi$
$173$	−11.2388	+	8.16549i	−0.854473	+	0.620811i	0.0719026	+	0.997412i	$0.477093\pi$
$174$	10.4034	−	0.126671i	0.788677	−	0.00960294i
$175$	10.3329	+	19.1445i	0.781095	+	1.44719i
$176$	−0.0738379	−	0.0536464i	−0.00556574	−	0.00404375i
$177$	−12.5966	+	4.26314i	−0.946821	+	0.320437i
$178$	−3.77643	+	11.6226i	−0.283055	+	0.871154i
$179$	−4.48822	−	13.8133i	−0.335465	−	1.03246i	−0.966492	−	0.256695i	$-0.917366\pi$
$179$	−4.48822	−	13.8133i	−0.335465	−	1.03246i	0.631027	−	0.775761i	$-0.282634\pi$
$180$	3.70971	+	5.58910i	0.276505	+	0.416587i
$181$		−	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
$183$	12.7023	+	3.95691i	0.938980	+	0.292503i
$184$	3.10552	−	4.27438i	0.228942	−	0.315111i
$185$	11.5495	−	13.8516i	0.849134	−	1.01839i
$186$	−3.41893	+	9.01726i	−0.250688	+	0.661177i
$187$		−	0.120288i		−	0.00879631i
$188$	5.10287	+	3.70746i	0.372165	+	0.270394i
$189$	−12.6121	+	18.7638i	−0.917398	+	1.36486i
$190$	−4.70061	−	1.88215i	−0.341018	−	0.136545i
$191$		−	3.78356i		−	0.273769i	−0.990587	−	0.136884i	$-0.956291\pi$
$191$		−	3.78356i		−	0.273769i	0.990587	−	0.136884i	$-0.0437089\pi$
$192$	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
$195$	5.59089	+	2.16002i	0.400372	+	0.154682i
$196$	9.65260	+	7.01303i	0.689472	+	0.500931i
$197$	19.6837	−	6.39561i	1.40240	−	0.455668i	0.492436	−	0.870349i	$-0.336107\pi$
$197$	19.6837	−	6.39561i	1.40240	−	0.455668i	0.909967	+	0.414680i	$0.136107\pi$
$198$	−0.217529	+	0.166285i	−0.0154591	+	0.0118174i
$199$	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
$201$	−1.14882	−	0.357872i	−0.0810318	−	0.0252423i
$202$	7.07417	+	9.73676i	0.497737	+	0.685076i
$203$	−24.8566	−	8.07640i	−1.74459	−	0.566852i
$204$	2.17946	+	0.678927i	0.152593	+	0.0475344i
$205$	2.93903	+	11.6332i	0.205271	+	0.812499i
$206$	−15.6040	+	5.07005i	−1.08718	+	0.353247i
$207$	−9.62601	−	12.5925i	−0.669054	−	0.875238i
$208$	0.478220	−	1.47181i	0.0331586	−	0.102052i
$209$	0.0638650	−	0.196556i	0.00441763	−	0.0135961i
$210$	−4.32627	−	16.2866i	−0.298541	−	1.12388i
$211$	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
$213$	3.41999	−	4.82980i	0.234334	−	0.330933i
$214$	−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
$219$	10.2619	−	0.124949i	0.693433	−	0.00844324i
$220$	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
$225$	−6.16022	+	13.6767i	−0.410681	+	0.911779i
$226$	−5.81850	+	17.9075i	−0.387041	+	1.19119i
$227$	18.5005	+	13.4414i	1.22792	+	0.892135i	0.996732	−	0.0807747i	$-0.0257394\pi$
$227$	18.5005	+	13.4414i	1.22792	+	0.892135i	0.231186	+	0.972910i	$0.425739\pi$
$228$	3.20088	+	2.26655i	0.211984	+	0.150106i
$229$	−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
$231$	0.651516	−	0.220495i	0.0428666	−	0.0145075i
$232$	4.85963	−	3.53073i	0.319050	−	0.231804i
$233$	−13.3384	+	9.69093i	−0.873829	+	0.634874i	−0.931612	−	0.363455i	$-0.881597\pi$
$233$	−13.3384	+	9.69093i	−0.873829	+	0.634874i	0.0577825	+	0.998329i	$0.481597\pi$
$234$	−3.82132	−	2.63662i	−0.249807	−	0.172361i
$235$	−0.939988	+	14.0726i	−0.0613181	+	0.917998i
$236$	−4.51294	+	6.21153i	−0.293768	+	0.404336i
$237$	5.00096	−	7.06248i	0.324847	−	0.458758i
$238$	−4.63924	−	3.37061i	−0.300717	−	0.218484i
$239$	0.482534	−	1.48509i	0.0312125	−	0.0960623i	−0.934237	−	0.356654i	$-0.883918\pi$
$239$	0.482534	−	1.48509i	0.0312125	−	0.0960623i	0.965449	+	0.260592i	$0.0839176\pi$
$240$	3.61273	+	1.39576i	0.233201	+	0.0900962i
$241$	−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
$246$	−0.113158	−	9.29349i	−0.00721467	−	0.592531i
$247$	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	−0.656024	−	0.754740i	$-0.727763\pi$
$251$	−2.23300	+	1.62237i	−0.140945	+	0.102403i	0.515078	+	0.857143i	$0.327763\pi$
$252$	0.317820	+	13.0492i	0.0200208	+	0.822020i
$253$			0.482211i			0.0303163i
$254$	4.97403			0.312099
$255$	1.31046	+	4.93332i	0.0820641	+	0.308937i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	3.04322	−	9.36608i	0.189831	−	0.584240i	−0.810167	−	0.586199i	$-0.800624\pi$
$257$	3.04322	−	9.36608i	0.189831	−	0.584240i	0.999998	+	0.00195919i	$0.000623631\pi$
$258$	12.3220	−	0.150033i	0.767135	−	0.00934064i
$259$	33.3752	−	10.8443i	2.07384	−	0.673830i
$260$	3.35502	−	0.847615i	0.208069	−	0.0525668i
$261$	−5.98428	−	16.9978i	−0.370418	−	1.05214i
$262$	9.93088	+	3.22674i	0.613532	+	0.199348i
$263$	13.0646	+	17.9819i	0.805597	+	1.10881i	0.991988	+	0.126334i	$0.0403209\pi$
$263$	13.0646	+	17.9819i	0.805597	+	1.10881i	−0.186391	+	0.982476i	$0.559679\pi$
$264$	−0.0470159	+	0.150928i	−0.00289363	+	0.00928901i
$265$	−5.59061	+	3.51767i	−0.343428	+	0.216089i
$266$	−5.79118	−	7.97088i	−0.355080	−	0.488726i
$267$	21.1654	−	0.257711i	1.29530	−	0.0157716i
$268$	−0.660709	+	0.214677i	−0.0403592	+	0.0131135i
$269$	6.15781	+	4.47391i	0.375448	+	0.272779i	0.759467	−	0.650546i	$-0.225460\pi$
$269$	6.15781	+	4.47391i	0.375448	+	0.272779i	−0.384018	+	0.923325i	$0.625460\pi$
$270$	7.10989	−	9.18964i	0.432694	−	0.559263i
$271$	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
$276$	−8.73705	−	2.72169i	−0.525909	−	0.163826i
$277$	−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
$279$	16.6924	+	0.602401i	0.999349	+	0.0360648i
$280$	−7.47242	−	6.23052i	−0.446562	−	0.372345i
$281$	15.4414	−	21.2533i	0.921157	−	1.26786i	−0.0420536	−	0.999115i	$-0.513390\pi$
$281$	15.4414	−	21.2533i	0.921157	−	1.26786i	0.963210	−	0.268748i	$-0.0866100\pi$
$282$	3.24923	−	10.4305i	0.193489	−	0.621130i
$283$	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
$285$	−0.477917	+	8.75706i	−0.0283094	+	0.518724i
$286$	0.0436465	+	0.134330i	0.00258087	+	0.00794310i
$287$	−7.21477	+	22.2048i	−0.425875	+	1.31071i
$288$	−2.46927	−	1.70374i	−0.145503	−	0.100394i
$289$	−12.3480	−	8.97137i	−0.726355	−	0.527728i
$290$	12.4693	+	4.99276i	0.732220	+	0.293185i
$291$	−0.230693	−	18.9465i	−0.0135234	−	1.11066i
$292$	4.79353	−	3.48270i	0.280520	−	0.203810i
$293$	−4.79974	+	14.7721i	−0.280404	+	0.862995i	0.707335	+	0.706879i	$0.249897\pi$
$293$	−4.79974	+	14.7721i	−0.280404	+	0.862995i	−0.987739	+	0.156116i	$0.950103\pi$
$294$	6.14625	−	19.7304i	0.358457	−	1.15070i
$295$	−17.1301	−	1.14421i	−0.997352	−	0.0666186i
$296$	−2.49236	+	7.67069i	−0.144865	+	0.445850i
$297$	0.393597	+	0.264558i	0.0228388	+	0.0153512i
$298$	−5.37835	+	7.40267i	−0.311560	+	0.428825i
$299$	−7.77619	+	2.52664i	−0.449708	+	0.146119i
$300$	1.66058	+	8.49956i	0.0958735	+	0.490722i
$301$	−29.4408	−	9.56589i	−1.69694	−	0.551369i
$302$	21.7615	+	7.07074i	1.25223	+	0.406876i
$303$	12.0466	−	17.0125i	0.692058	−	0.977342i
$304$	2.26443			0.129874
$305$	13.1918	+	10.9993i	0.755360	+	0.629821i
$306$	−0.0962701	−	3.95268i	−0.00550339	−	0.225960i
$307$	−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	$-0.849858\pi$
$311$		−	16.0265i		−	0.908777i	0.890804	−	0.454388i	$-0.150142\pi$
$312$	−2.68024	+	0.0326346i	−0.151739	+	0.00184757i
$313$	−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
$315$	−24.3182	+	16.1410i	−1.37018	+	0.909440i
$316$		−	4.99627i		−	0.281062i
$317$	−8.69453	−	26.7590i	−0.488333	−	1.50294i	−0.827095	−	0.562063i	$-0.810008\pi$
$317$	−8.69453	−	26.7590i	−0.488333	−	1.50294i	0.338761	−	0.940872i	$-0.389992\pi$
$318$	4.84636	−	1.64017i	0.271770	−	0.0919764i
$319$	−0.169414	+	0.521403i	−0.00948537	+	0.0291930i
$320$	2.16795	−	0.547714i	0.121192	−	0.0306181i
$321$	13.6626	+	9.67452i	0.762572	+	0.539979i
$322$	18.5979	+	13.5121i	1.03642	+	0.753002i
$323$	1.75419	+	2.41444i	0.0976058	+	0.134343i
$324$	−7.01499	+	5.63826i	−0.389721	+	0.313237i
$325$	5.59947	+	5.34030i	0.310603	+	0.296226i
$326$	−7.64784	−	10.5264i	−0.423575	−	0.583001i
$327$	−7.93669	−	23.4512i	−0.438900	−	1.29685i
$328$	−3.15405	−	4.34118i	−0.174154	−	0.239702i
$329$	−16.1312	+	22.2027i	−0.889340	+	1.22407i
$330$	−0.341634	+	0.0907498i	−0.0188063	+	0.00499561i
$331$	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
$333$	19.9157	+	13.7414i	1.09137	+	0.753024i
$334$	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
$339$	32.6104	−	0.397065i	1.77116	−	0.0215656i
$340$	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
$345$	−5.25338	−	19.7768i	−0.282833	−	1.06474i
$346$	13.8920			0.746837
$347$		−	9.35472i		−	0.502188i	−0.967963	−	0.251094i	$-0.919210\pi$
$347$		−	9.35472i		−	0.502188i	0.967963	−	0.251094i	$-0.0807903\pi$
$348$	−8.49096	−	6.01247i	−0.455163	−	0.322302i
$349$	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
$351$	−2.20396	+	7.73339i	−0.117639	+	0.412778i
$352$	0.0282036	+	0.0868017i	0.00150326	+	0.00462654i
$353$	−14.3337	+	19.7287i	−0.762907	+	1.05005i	0.234060	+	0.972222i	$0.424799\pi$
$353$	−14.3337	+	19.7287i	−0.762907	+	1.05005i	−0.996967	+	0.0778292i	$0.975201\pi$
$354$	12.6967	+	3.95516i	0.674822	+	0.210215i
$355$	6.46658	−	4.06885i	0.343211	−	0.215952i
$356$	9.88682	−	7.18319i	0.524000	−	0.380708i
$357$	−2.95402	+	9.48285i	−0.156343	+	0.501886i
$358$	−4.48822	+	13.8133i	−0.237210	+	0.730057i
$359$	8.49073	+	11.6865i	0.448123	+	0.616789i	0.971993	−	0.235009i	$-0.0755121\pi$
$359$	8.49073	+	11.6865i	0.448123	+	0.616789i	−0.523870	+	0.851798i	$0.675512\pi$
$360$	0.283978	−	6.70219i	0.0149669	−	0.353236i
$361$	−4.28680	−	13.1934i	−0.225621	−	0.694389i
$362$	−2.17306	+	2.99097i	−0.114214	+	0.157202i
$363$	6.10312	+	18.0334i	0.320331	+	0.946506i
$364$	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
$369$	−15.1844	+	5.34586i	−0.790470	+	0.278294i
$370$	−17.4855	+	4.41755i	−0.909026	+	0.229657i
$371$	−12.8526			−0.667275
$372$	8.06618	−	5.28552i	0.418212	−	0.274041i
$373$			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
$375$	−14.1087	+	13.2644i	−0.728570	+	0.684971i
$376$	−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
$381$	−2.76183	−	8.16060i	−0.141493	−	0.418080i
$382$	−2.22392	+	3.06096i	−0.113786	+	0.156613i
$383$	−11.0539	+	3.59164i	−0.564830	+	0.183524i	−0.577493	−	0.816395i	$-0.695969\pi$
$383$	−11.0539	+	3.59164i	−0.564830	+	0.183524i	0.0126634	+	0.999920i	$0.495969\pi$
$384$	−1.73192	+	0.0210879i	−0.0883818	+	0.00107614i
$385$	0.885992	+	0.0591802i	0.0451543	+	0.00301610i
$386$	−9.38737	−	3.05014i	−0.477805	−	0.155248i
$387$	−7.08794	−	20.1327i	−0.360300	−	1.02340i
$388$	−6.43012	−	8.85030i	−0.326440	−	0.449306i
$389$	−1.31655	+	4.05194i	−0.0667520	+	0.205441i	−0.978869	−	0.204489i	$-0.934447\pi$
$389$	−1.31655	+	4.05194i	−0.0667520	+	0.205441i	0.912117	+	0.409930i	$0.134447\pi$
$390$	−3.25350	−	5.03373i	−0.164747	−	0.254893i
$391$	−5.63342	−	4.09292i	−0.284894	−	0.206988i
$392$	−3.68697	−	11.3473i	−0.186220	−	0.573126i
$393$	−0.220199	−	18.0846i	−0.0111076	−	0.912249i
$394$	−19.6837	−	6.39561i	−0.991649	−	0.322206i
$395$	9.45590	−	5.94976i	0.475778	−	0.299365i
$396$	0.273725	−	0.00666674i	0.0137552	−	0.000335016i
$397$		−	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
$399$	−9.86179	+	13.9271i	−0.493707	+	0.697226i
$400$	3.61828	+	3.45080i	0.180914	+	0.172540i
$401$	−0.382182	−	0.277671i	−0.0190852	−	0.0138662i	0.578202	−	0.815894i	$-0.303755\pi$
$401$	−0.382182	−	0.277671i	−0.0190852	−	0.0138662i	−0.597287	+	0.802028i	$0.703755\pi$
$402$	0.719067	+	0.964786i	0.0358638	+	0.0481192i
$403$	3.15261	−	8.01894i	0.157042	−	0.399452i
$404$		−	12.0353i		−	0.598779i
$405$	−19.0246	−	6.56223i	−0.945342	−	0.326080i
$406$	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
$411$	4.70243	−	1.59147i	0.231954	−	0.0785012i
$412$	15.6040	+	5.07005i	0.768754	+	0.249783i
$413$	−27.0264	−	19.6359i	−1.32988	−	0.966217i
$414$	0.385929	+	15.8456i	0.0189674	+	0.778767i
$415$	−4.64597	−	18.3896i	−0.228062	−	0.902710i
$416$	−1.25200	+	0.909628i	−0.0613841	+	0.0445982i
$417$	5.71804	−	1.93518i	0.280013	−	0.0947663i
$418$	−0.167201	+	0.121478i	−0.00817805	+	0.00594170i
$419$	−6.74688	−	9.28628i	−0.329607	−	0.453665i	0.611763	−	0.791041i	$-0.290461\pi$
$419$	−6.74688	−	9.28628i	−0.329607	−	0.453665i	−0.941370	+	0.337376i	$0.890461\pi$
$420$	−6.07298	+	15.7190i	−0.296331	+	0.767010i
$421$	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
$423$	−18.9169	+	0.460733i	−0.919771	+	0.0224016i
$424$	1.73628	−	2.38979i	0.0843214	−	0.116058i
$425$	−0.876421	+	6.53122i	−0.0425127	+	0.316811i
$426$	−5.60572	+	1.89717i	−0.271598	+	0.0919182i
$427$	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	$0.127821\pi$
$431$	20.9213	+	28.7957i	1.00774	+	1.38704i	0.0872911	+	0.996183i	$0.472179\pi$
$432$	−1.42416	+	4.99718i	−0.0685200	+	0.240427i
$433$	−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
$435$	1.26777	−	23.2298i	0.0607848	−	1.11378i
$436$	−11.5640	−	8.40176i	−0.553817	−	0.402371i
$437$	−7.03222	−	9.67902i	−0.336397	−	0.463010i
$438$	−8.37547	−	5.93069i	−0.400195	−	0.283379i
$439$	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
$441$	−35.7832	+	0.871523i	−1.70396	+	0.0415011i
$442$	−1.93977	−	0.630271i	−0.0922656	−	0.0299789i
$443$	4.54820	−	13.9979i	0.216091	−	0.665061i	−0.782983	−	0.622043i	$-0.786303\pi$
$443$	4.54820	−	13.9979i	0.216091	−	0.665061i	0.999074	−	0.0430178i	$-0.0136972\pi$
$444$	13.9687	−	0.170083i	0.662926	−	0.00807179i
$445$	25.3685	+	10.1577i	1.20258	+	0.481519i
$446$	10.3176	+	7.49618i	0.488553	+	0.354954i
$447$	15.1314	+	4.71361i	0.715693	+	0.222946i
$448$	4.13806	+	1.34454i	0.195505	+	0.0635233i
$449$	25.8830	−	18.8051i	1.22150	−	0.887468i	0.225272	−	0.974296i	$-0.427673\pi$
$449$	25.8830	−	18.8051i	1.22150	−	0.887468i	0.996223	+	0.0868279i	$0.0276730\pi$
$450$	13.0227	−	7.44378i	0.613895	−	0.350903i
$451$	0.465777	+	0.151340i	0.0219326	+	0.00712633i
$452$	15.2330	−	11.0674i	0.716501	−	0.520568i
$453$	−0.482521	−	39.6288i	−0.0226708	−	1.86192i
$454$	−7.06655	−	21.7486i	−0.331649	−	1.02071i
$455$	3.68798	+	14.5977i	0.172895	+	0.684351i
$456$	−1.25732	−	3.71511i	−0.0588795	−	0.173976i
$457$	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	0.912606	−	0.408841i	$-0.134067\pi$
$461$	−1.41748	−	4.36254i	−0.0660184	−	0.203184i	−0.978624	+	0.205657i	$0.934067\pi$
$462$	−0.656691	−	0.204567i	−0.0305520	−	0.00951730i
$463$	−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
$465$	19.6089	+	8.97177i	0.909339	+	0.416056i
$466$	16.4872			0.763755
$467$	−9.69777	−	7.04584i	−0.448759	−	0.326043i	0.340346	−	0.940300i	$-0.389456\pi$
$467$	−9.69777	−	7.04584i	−0.448759	−	0.326043i	−0.789106	+	0.614257i	$0.789456\pi$
$468$	1.54174	+	4.37919i	0.0712671	+	0.202428i
$469$	−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
$474$	−8.19709	+	2.77418i	−0.376505	+	0.127422i
$475$	−4.89977	+	10.2070i	−0.224817	+	0.468330i
$476$	1.77203	+	5.45376i	0.0812210	+	0.249973i
$477$	−5.38187	−	7.04042i	−0.246419	−	0.322359i
$478$	−1.26329	+	0.917834i	−0.0577815	+	0.0419808i
$479$	−23.7884	−	7.72933i	−1.08692	−	0.353162i	−0.289865	−	0.957068i	$-0.593610\pi$
$479$	−23.7884	−	7.72933i	−1.08692	−	0.353162i	−0.797056	+	0.603905i	$0.793610\pi$
$480$	−2.10235	−	3.25271i	−0.0959589	−	0.148465i
$481$	10.0979	−	7.33655i	0.460424	−	0.334518i
$482$	19.3337	+	6.28191i	0.880627	+	0.286133i
$483$	11.8421	−	38.0150i	0.538834	−	1.72974i
$484$	8.89245	+	6.46074i	0.404202	+	0.293670i
$485$	9.09275	−	22.7089i	0.412880	−	1.03116i
$486$	13.1454	+	8.37843i	0.596288	+	0.380053i
$487$	−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
$489$	−13.0235	+	18.3921i	−0.588943	+	0.831720i
$490$	17.0852	−	20.4908i	0.771832	−	0.925678i
$491$	18.1179			0.817648			0.408824	−	0.912613i	$-0.365939\pi$
$491$	18.1179			0.817648			0.408824	+	0.912613i	$0.365939\pi$
$492$	−5.37103	+	7.58511i	−0.242145	+	0.341963i
$493$	−4.65333	−	6.40476i	−0.209575	−	0.288456i
$494$	−2.83505	−	2.05979i	−0.127555	−	0.0926742i
$495$	0.338580	+	0.510110i	0.0152180	+	0.0229277i
$496$	2.03716	−	5.18170i	0.0914710	−	0.232665i
$497$	14.8665			0.666853
$498$	0.178878	+	14.6910i	0.00801571	+	0.658320i
$499$	−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	0.920979	−	0.389613i	$-0.127391\pi$
$503$	−1.19130	−	3.66645i	−0.0531175	−	0.163479i	−0.974096	+	0.226134i	$0.927391\pi$
$504$	7.41298	−	10.7438i	0.330200	−	0.478567i
$505$	22.7779	−	14.3321i	1.01360	−	0.637771i
$506$	0.283436	−	0.390117i	0.0126003	−	0.0173428i
$507$	−14.9908	−	10.6150i	−0.665765	−	0.471430i
$508$	−4.02408	−	2.92366i	−0.178540	−	0.129717i
$509$	−9.55299	+	6.94065i	−0.423429	+	0.307639i	−0.779016	−	0.627004i	$-0.784281\pi$
$509$	−9.55299	+	6.94065i	−0.423429	+	0.307639i	0.355587	+	0.934643i	$0.384281\pi$
$510$	1.83955	−	4.76141i	0.0814566	−	0.210839i
$511$	15.1533	+	20.8567i	0.670342	+	0.922646i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	−11.7585	+	0.429683i	−0.519149	+	0.0189710i
$514$	−7.96726	+	5.78855i	−0.351421	+	0.255322i
$515$	8.98635	+	35.5696i	0.395986	+	1.56738i
$516$	−10.0569	−	7.12132i	−0.442730	−	0.313498i
$517$	0.465733	+	0.338374i	0.0204829	+	0.0148817i
$518$	−33.3752	−	10.8443i	−1.46642	−	0.476470i
$519$	−7.71351	−	22.7917i	−0.338585	−	1.00045i
$520$	−3.21248	−	1.28629i	−0.140877	−	0.0564077i
$521$			29.7381i			1.30285i	0.758713	+	0.651425i	$0.225828\pi$
$521$			29.7381i			1.30285i	−0.758713	+	0.651425i	$0.774172\pi$
$522$	−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
$525$	−36.9816	+	7.22519i	−1.61401	+	0.315333i
$526$		−	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
$531$	−0.560832	−	23.0268i	−0.0243380	−	0.999278i
$532$			9.85255i			0.427162i
$533$			8.30416i			0.359693i
$534$	−17.2747	−	12.2322i	−0.747548	−	0.529341i
$535$	11.5100	+	18.2928i	0.497621	+	0.790865i
$536$	0.660709	+	0.214677i	0.0285383	+	0.00927265i
$537$	25.1548	−	0.306285i	1.08551	−	0.0132172i
$538$	−2.35207	−	7.23894i	−0.101405	−	0.312093i
$539$	0.880980	+	0.640070i	0.0379465	+	0.0275698i
$540$	−11.1536	+	3.25548i	−0.479973	+	0.140094i
$541$	−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
$543$	6.11369	+	1.90448i	0.262364	+	0.0817292i
$544$	−1.25345	−	0.407270i	−0.0537411	−	0.0174615i
$545$	2.13018	−	31.8911i	0.0912470	−	1.36607i
$546$	−0.141993	−	11.6617i	−0.00607676	−	0.499077i
$547$	−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
$549$	−13.0869	+	18.9671i	−0.558534	+	0.809495i
$550$	−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
$555$	16.9564	+	26.2345i	0.719759	+	1.11359i
$556$	2.04858	−	2.81963i	0.0868791	−	0.119579i
$557$			6.00685i			0.254518i	0.991870	+	0.127259i	$0.0406180\pi$
$557$			6.00685i			0.254518i	−0.991870	+	0.127259i	$0.959382\pi$
$558$	−13.1504	−	10.2989i	−0.556700	−	0.435988i
$559$	−11.0103			−0.465685
$560$	2.38311	+	9.43277i	0.100705	+	0.398607i
$561$	0.198916	+	0.0619647i	0.00839826	+	0.00261615i
$562$	−24.9847	+	8.11803i	−1.05392	+	0.342438i
$563$	−40.1053			−1.69024			−0.845119	−	0.534578i	$-0.820471\pi$
$563$	−40.1053			−1.69024			−0.845119	+	0.534578i	$0.820471\pi$
$564$	−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
$567$	−24.5321	−	30.5223i	−1.03025	−	1.28181i
$568$	−2.00834	+	2.76424i	−0.0842680	+	0.115985i
$569$	5.96346	+	18.3537i	0.250001	+	0.769425i	0.994773	+	0.102106i	$0.0325582\pi$
$569$	5.96346	+	18.3537i	0.250001	+	0.769425i	−0.744772	+	0.667319i	$0.767442\pi$
$570$	5.53392	−	6.80370i	0.231790	−	0.284976i
$571$	−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
$573$	6.25677	+	1.94905i	0.261380	+	0.0814229i
$574$	18.8885	−	13.7233i	0.788392	−	0.572800i
$575$	3.51341	−	26.1824i	0.146519	−	1.09188i
$576$	0.996246	+	2.82975i	0.0415103	+	0.117906i
$577$	−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
$579$	0.208147	+	17.0949i	0.00865031	+	0.710439i
$580$	−7.15318	−	11.3685i	−0.297020	−	0.472050i
$581$	11.4050	−	35.1010i	0.473159	−	1.45623i
$582$	−10.9498	+	15.4636i	−0.453885	+	0.640988i
$583$			0.269602i			0.0111658i
$584$	−5.92513			−0.245184
$585$	−6.45204	+	8.13280i	−0.266759	+	0.336250i
$586$	12.5659	−	9.12965i	0.519092	−	0.377143i
$587$	17.9592	−	24.7187i	0.741254	−	1.02025i	−0.257291	−	0.966334i	$-0.582830\pi$
$587$	17.9592	−	24.7187i	0.741254	−	1.02025i	0.998546	−	0.0539149i	$-0.0171700\pi$
$588$	−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
$591$	0.436448	+	35.8450i	0.0179531	+	1.47446i
$592$	6.52508	−	4.74075i	0.268179	−	0.194843i
$593$	−9.93350	−	30.5722i	−0.407920	−	1.25545i	−0.918432	−	0.395578i	$-0.870544\pi$
$593$	−9.93350	−	30.5722i	−0.407920	−	1.25545i	0.510512	−	0.859870i	$-0.329456\pi$
$594$	−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
$597$	−36.3411	+	12.2991i	−1.48734	+	0.503369i
$598$	7.77619	+	2.52664i	0.317992	+	0.103322i
$599$	18.2419	−	25.1078i	0.745343	−	1.02588i	−0.252950	−	0.967479i	$-0.581401\pi$
$599$	18.2419	−	25.1078i	0.745343	−	1.02588i	0.998293	−	0.0583974i	$-0.0185990\pi$
$600$	3.65248	−	7.85235i	0.149112	−	0.320571i
$601$	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
$603$	1.18361	−	1.71543i	0.0482001	−	0.0698575i
$604$	−13.4494	−	18.5114i	−0.547246	−	0.753220i
$605$	−1.63806	+	24.5235i	−0.0665965	+	0.997021i
$606$	−19.7456	+	6.68259i	−0.802110	+	0.271462i
$607$	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
$609$	26.1603	−	36.9442i	1.06007	−	1.49706i
$610$	−4.20713	−	16.6526i	−0.170342	−	0.674244i
$611$	−3.01637	+	9.28344i	−0.122029	+	0.375568i
$612$	−2.24544	+	3.25437i	−0.0907667	+	0.131550i
$613$	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
$615$	−20.7515	−	1.13252i	−0.836783	−	0.0456675i
$616$	−0.377675	+	0.122714i	−0.0152169	+	0.00494429i
$617$	1.30303	−	0.946709i	0.0524581	−	0.0381131i	−0.561247	−	0.827648i	$-0.689678\pi$
$617$	1.30303	−	0.946709i	0.0524581	−	0.0381131i	0.613705	+	0.789535i	$0.289678\pi$
$618$	−0.345990	−	28.4157i	−0.0139177	−	1.14305i
$619$			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
$624$	2.18754	+	1.54900i	0.0875717	+	0.0620097i
$625$	−23.3839	+	8.84272i	−0.935356	+	0.353709i
$626$	21.2963			0.851172
$627$	0.292140	+	0.206865i	0.0116670	+	0.00826140i
$628$	20.1514	+	6.54758i	0.804128	+	0.261277i
$629$	10.1096	+	3.28481i	0.403096	+	0.130974i
$630$	29.1613	+	1.23559i	1.16181	+	0.0492271i
$631$	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
$633$	−5.29571	+	17.0001i	−0.210485	+	0.675691i
$634$	−8.69453	+	26.7590i	−0.345304	+	1.06274i
$635$	0.741266	−	11.0975i	0.0294162	−	0.440393i
$636$	−4.88486	−	1.52169i	−0.193697	−	0.0603388i
$637$	−5.70577	+	17.5606i	−0.226071	+	0.695775i
$638$	0.443532	−	0.322245i	0.0175596	−	0.0127578i
$639$	6.22514	+	8.14356i	0.246263	+	0.322154i
$640$	−2.07585	−	0.831180i	−0.0820551	−	0.0328553i
$641$	6.35205	+	4.61504i	0.250891	+	0.182283i	0.706122	−	0.708091i	$-0.250443\pi$
$641$	6.35205	+	4.61504i	0.250891	+	0.182283i	−0.455231	+	0.890374i	$0.650443\pi$
$642$	−5.36674	−	15.8575i	−0.211808	−	0.625847i
$643$	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
$645$	1.50157	−	27.5139i	0.0591245	−	1.08336i
$646$		−	2.98441i		−	0.117420i
$647$	16.8851	−	5.48629i	0.663821	−	0.215688i	0.0423224	−	0.999104i	$-0.486524\pi$
$647$	16.8851	−	5.48629i	0.663821	−	0.215688i	0.621498	+	0.783416i	$0.286524\pi$
$648$	8.98933	−	0.438141i	0.353134	−	0.0172118i
$649$	−0.411890	+	0.566918i	−0.0161681	+	0.0222535i
$650$	−1.39112	−	7.61168i	−0.0545643	−	0.298555i
$651$	22.9973	+	35.0960i	0.901337	+	1.37552i
$652$			13.0113i			0.509561i
$653$	−40.8964	−	29.7130i	−1.60040	−	1.16276i	−0.886745	−	0.462259i	$-0.847039\pi$
$653$	−40.8964	−	29.7130i	−1.60040	−	1.16276i	−0.713654	−	0.700499i	$-0.752961\pi$
$654$	−7.36334	+	23.6375i	−0.287929	+	0.924299i
$655$	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	0.124908	−	0.992168i	$-0.460136\pi$
$659$	−9.17022	−	2.97959i	−0.357221	−	0.116068i	−0.482129	+	0.876100i	$0.660136\pi$
$660$	0.329729	+	0.127389i	0.0128347	+	0.00495863i
$661$	−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
$663$	0.0430108	+	3.53243i	0.00167040	+	0.137188i
$664$	4.98588	+	6.86247i	0.193490	+	0.266316i
$665$	−18.6468	+	11.7328i	−0.723094	+	0.454979i
$666$	−8.03516	−	22.8232i	−0.311356	−	0.884381i
$667$	18.6543	+	25.6755i	0.722298	+	0.994158i
$668$	−18.3753	−	5.97049i	−0.710960	−	0.231005i
$669$	6.56969	−	21.0897i	0.253999	−	0.815376i
$670$	0.380503	+	1.50610i	0.0147001	+	0.0581857i
$671$	0.666746	−	0.216639i	0.0257395	−	0.00836325i
$672$	−0.0917536	−	7.53561i	−0.00353947	−	0.290692i
$673$	−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
$675$	−19.4434	−	17.2324i	−0.748377	−	0.663274i
$676$	−10.6051			−0.407888
$677$			18.6676i			0.717454i	0.933443	+	0.358727i	$0.116789\pi$
$677$			18.6676i			0.717454i	−0.933443	+	0.358727i	$0.883211\pi$
$678$	−26.6158	−	18.8467i	−1.02217	−	0.723803i
$679$	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	$-0.292321\pi$
$683$	31.7337			1.21426			0.607128	+	0.794604i	$0.292321\pi$
$684$	−5.39703	+	4.12563i	−0.206361	+	0.157747i
$685$	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
$690$	−7.37441	+	19.0876i	−0.280739	+	0.726652i
$691$	−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
$693$	0.0290070	+	1.19098i	0.00110189	+	0.0452415i
$694$	−5.49857	+	7.56813i	−0.208723	+	0.287282i
$695$	7.77593	+	0.519396i	0.294958	+	0.0197018i
$696$	3.33529	+	9.85505i	0.126424	+	0.373555i
$697$	−5.72147	+	4.15689i	−0.216716	+	0.157453i
$698$	−7.50943	+	5.45592i	−0.284236	+	0.206510i
$699$	−9.15450	−	27.0495i	−0.346255	−	1.02311i
$700$	−15.0145	+	15.7432i	−0.567494	+	0.595036i
$701$	7.35988	−	10.1300i	0.277979	−	0.382605i	−0.647084	−	0.762419i	$-0.724012\pi$
$701$	7.35988	−	10.1300i	0.277979	−	0.382605i	0.925063	+	0.379813i	$0.124012\pi$
$702$	6.32861	−	4.96098i	0.238858	−	0.187240i
$703$	14.7756	+	10.7351i	0.557271	+	0.404881i
$704$	0.0282036	−	0.0868017i	0.00106296	−	0.00327146i
$705$	−22.7873	−	8.80378i	−0.858220	−	0.331570i
$706$	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
$711$	9.10285	+	11.9081i	0.341384	+	0.446589i
$712$	−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
$717$	2.20728	+	1.56298i	0.0824322	+	0.0583705i
$718$		−	14.4453i		−	0.539093i
$719$	27.1276			1.01169			0.505844	−	0.862625i	$-0.331181\pi$
$719$	27.1276			1.01169			0.505844	+	0.862625i	$0.331181\pi$
$720$	−4.16919	+	5.25527i	−0.155377	+	0.195852i
$721$	−22.0598	+	67.8931i	−0.821551	+	2.52847i
$722$	−4.28680	+	13.1934i	−0.159538	+	0.491008i
$723$	−0.428689	−	35.2077i	−0.0159431	−	1.30939i
$724$	3.51609	−	1.14245i	0.130675	−	0.0424587i
$725$	12.9976	−	27.0761i	0.482718	−	1.00558i
$726$	5.66222	−	18.1766i	0.210145	−	0.674598i
$727$	−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
$729$	6.44699	−	26.2190i	0.238778	−	0.971074i
$730$	−7.05588	−	11.2138i	−0.261150	−	0.415043i
$731$	−5.51152	−	7.58596i	−0.203851	−	0.280577i
$732$	0.161982	+	13.3033i	0.00598702	+	0.491706i
$733$	−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
$735$	−43.1045	−	16.6532i	−1.58993	−	0.614264i
$736$	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
$741$	−1.80521	+	5.79500i	−0.0663159	+	0.212885i
$742$	10.3980	+	7.55459i	0.381723	+	0.277338i
$743$			44.9342i			1.64848i	0.566244	+	0.824238i	$0.308396\pi$
$743$			44.9342i			1.64848i	−0.566244	+	0.824238i	$0.691604\pi$
$744$	−9.63243	−	0.465107i	−0.353142	−	0.0170516i
$745$	15.7146	+	13.1028i	0.575737	+	0.480050i
$746$	16.6444	−	22.9090i	0.609394	−	0.838758i
$747$	24.0033	−	8.45064i	0.878236	−	0.309193i
$748$	0.114400	−	0.0371709i	0.00418289	−	0.00135910i
$749$			42.0545i			1.53664i
$750$	19.2108	−	2.43825i	0.701479	−	0.0890322i
$751$	−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
$753$	−1.53256	−	4.52839i	−0.0558497	−	0.165024i
$754$	7.52053	+	5.46398i	0.273881	+	0.198987i
$755$	19.0186	−	47.4983i	0.692156	−	1.72864i
$756$	−21.7428	−	6.19654i	−0.790776	−	0.225366i
$757$	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
$759$	−0.797419	−	0.248405i	−0.0289445	−	0.00901653i
$760$	0.337461	−	5.05216i	0.0122410	−	0.183261i
$761$	−11.6202	+	35.7633i	−0.421232	+	1.29642i	0.485324	+	0.874334i	$0.338702\pi$
$761$	−11.6202	+	35.7633i	−0.421232	+	1.29642i	−0.906556	+	0.422085i	$0.861298\pi$
$762$	−2.56231	+	8.22542i	−0.0928228	+	0.297976i
$763$	36.5561	−	50.3152i	1.32342	−	1.82153i
$764$	3.59838	−	1.16918i	0.130185	−	0.0422996i
$765$	−8.83316	−	0.374269i	−0.319364	−	0.0135317i
$766$	11.0539	+	3.59164i	0.399395	+	0.129771i
$767$	−11.3004	−	3.67171i	−0.408033	−	0.132578i
$768$	1.41355	+	1.00094i	0.0510071	+	0.0361182i
$769$	−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
$771$	13.9207	+	9.85731i	0.501344	+	0.355003i
$772$	5.80172	+	7.98538i	0.208808	+	0.287400i
$773$	32.2242	−	44.3528i	1.15902	−	1.59526i	0.444250	−	0.895903i	$-0.353470\pi$
$773$	32.2242	−	44.3528i	1.15902	−	1.59526i	0.714774	−	0.699356i	$-0.246530\pi$
$774$	−6.09943	+	20.4539i	−0.219239	+	0.735199i
$775$	18.9487	+	20.3947i	0.680659	+	0.732600i
$776$			10.9396i			0.392708i
$777$	0.740033	+	60.7780i	0.0265485	+	2.18040i
$778$	3.44679	−	2.50424i	0.123573	−	0.0897812i
$779$	−11.5562	+	3.75484i	−0.414044	+	0.134531i
$780$	−0.326617	+	5.98474i	−0.0116948	+	0.214288i
$781$		−	0.311846i		−	0.0111587i
$782$	2.15178	+	6.62249i	0.0769474	+	0.236820i
$783$	31.1916	−	1.13982i	1.11470	−	0.0407338i
$784$	−3.68697	+	11.3473i	−0.131677	+	0.405261i
$785$	11.6052	+	45.9355i	0.414207	+	1.63951i
$786$	−10.4517	+	14.7602i	−0.372801	+	0.526479i
$787$	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
$789$	−36.4662	+	12.3414i	−1.29823	+	0.439366i
$790$	−11.1472	−	0.744580i	−0.396599	−	0.0264910i
$791$	48.1545	+	66.2790i	1.71218	+	2.35661i
$792$	−0.225367	−	0.155498i	−0.00800805	−	0.00552538i
$793$	6.98709	+	9.61690i	0.248119	+	0.341506i
$794$	−13.9765	+	19.2370i	−0.496008	+	0.682697i
$795$	−2.93715	−	11.0571i	−0.104170	−	0.392156i
$796$	−13.0198	+	17.9202i	−0.461474	+	0.635165i
$797$	1.08622	+	0.352933i	0.0384758	+	0.0125015i	0.328192	−	0.944611i	$-0.393561\pi$
$797$	1.08622	+	0.352933i	0.0384758	+	0.0125015i	−0.289716	+	0.957113i	$0.593561\pi$
$798$	16.1645	−	5.47062i	0.572216	−	0.193658i
$799$	−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
$804$	−0.0146500	−	1.20319i	−0.000516665	−	0.0424331i
$805$	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	−0.136850	−	0.990592i	$-0.543698\pi$
$809$	21.7011	−	15.7668i	0.762970	−	0.554330i	0.899820	+	0.436262i	$0.143698\pi$
$810$	11.5341	+	16.4914i	0.405266	+	0.579447i
$811$	−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
$813$	−6.45706	+	9.11882i	−0.226459	+	0.319811i
$814$	−0.227474	+	0.700093i	−0.00797296	+	0.0245383i
$815$	−24.6250	+	15.4944i	−0.862578	+	0.542744i
$816$	0.0277928	+	2.28259i	0.000972944	+	0.0799066i
$817$	−4.97845	−	15.3221i	−0.174174	−	0.536052i
$818$	−19.9670	+	27.4822i	−0.698129	+	0.960892i
$819$	−19.0539	+	6.70813i	−0.665796	+	0.234401i
$820$	−10.1556	+	6.39005i	−0.354650	+	0.223150i
$821$	21.3906	−	15.5412i	0.746537	−	0.542391i	−0.148215	−	0.988955i	$-0.547353\pi$
$821$	21.3906	−	15.5412i	0.746537	−	0.542391i	0.894752	+	0.446564i	$0.147353\pi$
$822$	−4.73979	−	1.47650i	−0.165319	−	0.0514988i
$823$	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
$825$	0.151559	+	0.775743i	0.00527660	+	0.0270079i
$826$	10.3232	+	31.7715i	0.359189	+	1.10547i
$827$	−2.19104	+	3.01571i	−0.0761900	+	0.104867i	−0.845411	−	0.534116i	$-0.820644\pi$
$827$	−2.19104	+	3.01571i	−0.0761900	+	0.104867i	0.769221	+	0.638983i	$0.220644\pi$
$828$	9.00157	−	13.0462i	0.312826	−	0.453386i
$829$	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
$834$	−5.76346	−	1.79538i	−0.199572	−	0.0621690i
$835$	−10.5823	−	41.8868i	−0.366216	−	1.44955i
$836$	0.206671			0.00714788
$837$	−9.59507	+	27.2935i	−0.331654	+	0.943401i
$838$			11.4785i			0.396517i
$839$	7.17310	−	9.87293i	0.247643	−	0.340851i	−0.667041	−	0.745021i	$-0.732439\pi$
$839$	7.17310	−	9.87293i	0.247643	−	0.340851i	0.914684	+	0.404170i	$0.132439\pi$
$840$	14.1526	−	9.14736i	0.488310	−	0.315614i
$841$	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
$846$	15.5749	+	10.7463i	0.535476	+	0.369466i
$847$	−28.1107	+	38.6911i	−0.965897	+	1.32944i
$848$	−2.80937	+	0.912819i	−0.0964741	+	0.0313463i
$849$	0.173312	+	14.2339i	0.00594806	+	0.488507i
$850$	4.54799	−	4.76872i	0.155995	−	0.163566i
$851$	−40.5275	−	13.1682i	−1.38926	−	0.451399i
$852$	5.65025	+	1.76012i	0.193574	+	0.0603006i
$853$	−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
$855$	−14.2351	−	5.30141i	−0.486831	−	0.181304i
$856$	−7.81952	−	5.68121i	−0.267266	−	0.194180i
$857$	−0.173572	−	0.534201i	−0.00592912	−	0.0182479i	0.948048	−	0.318127i	$-0.103054\pi$
$857$	−0.173572	−	0.534201i	−0.00592912	−	0.0182479i	−0.953977	+	0.299879i	$0.903054\pi$
$858$	−0.244622	+	0.00297852i	−0.00835125	+	0.000101685i
$859$	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
$861$	−33.0029	−	23.3694i	−1.12473	−	0.796427i
$862$		−	35.5934i		−	1.21232i
$863$			37.0962i			1.26277i	0.775470	+	0.631384i	$0.217513\pi$
$863$			37.0962i			1.26277i	−0.775470	+	0.631384i	$0.782487\pi$
$864$	4.08944	−	3.20570i	0.139125	−	0.109060i
$865$	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
$870$	−14.6798	+	18.0481i	−0.497691	+	0.611889i
$871$	−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
$876$	3.28992	+	9.72101i	0.111156	+	0.328442i
$877$	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
$879$	−21.9557	−	15.5469i	−0.740547	−	0.524383i
$880$	0.197866	−	0.0499891i	0.00667006	−	0.00168513i
$881$	−14.8053	+	10.7567i	−0.498803	+	0.362401i	−0.808560	−	0.588414i	$-0.799752\pi$
$881$	−14.8053	+	10.7567i	−0.498803	+	0.362401i	0.309757	+	0.950816i	$0.399752\pi$
$882$	29.4615	+	20.3278i	0.992020	+	0.684472i
$883$	−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
$885$	10.7165	−	27.7381i	0.360231	−	0.932407i
$886$	−11.9073	+	8.65119i	−0.400035	+	0.290642i
$887$	−2.83555	−	2.06015i	−0.0952086	−	0.0691731i	0.539162	−	0.842202i	$-0.318741\pi$
$887$	−2.83555	−	2.06015i	−0.0952086	−	0.0691731i	−0.634371	+	0.773029i	$0.718741\pi$
$888$	−11.4009	−	8.07300i	−0.382589	−	0.270912i
$889$	12.7209	−	17.5088i	0.426645	−	0.587226i
$890$	−14.5530	−	23.1289i	−0.487817	−	0.775283i
$891$	−0.640248	+	0.514596i	−0.0214491	+	0.0172396i
$892$	−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
$897$	−0.172422	−	14.1608i	−0.00575702	−	0.472816i
$898$	−31.9932			−1.06763
$899$	−33.3836	−	2.01961i	−1.11341	−	0.0673578i
$900$	−14.9109	−	1.63239i	−0.497030	−	0.0544130i
$901$	−3.14963	−	2.28834i	−0.104929	−	0.0762356i
$902$	−0.287866	−	0.396214i	−0.00958490	−	0.0131925i
$903$	30.9849	−	43.7577i	1.03111	−	1.45616i
$904$	−18.8290			−0.626245
$905$	6.34929	+	5.29405i	0.211057	+	0.175980i
$906$	−22.9029	+	32.3440i	−0.760897	+	1.07456i
$907$	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
$909$	21.9274	+	28.6849i	0.727288	+	0.951418i
$910$	5.59667	−	13.9775i	0.185528	−	0.463351i
$911$	−39.2198	−	28.4949i	−1.29941	−	0.944077i	−0.299461	−	0.954109i	$-0.596807\pi$
$911$	−39.2198	−	28.4949i	−1.29941	−	0.944077i	−0.999950	+	0.0100315i	$0.996807\pi$
$912$	−1.16649	+	3.74462i	−0.0386264	+	0.123997i
$913$	−0.736294	−	0.239236i	−0.0243678	−	0.00791757i
$914$	−21.2969	+	15.4731i	−0.704438	+	0.511804i
$915$	−24.9849	+	16.1487i	−0.825975	+	0.533860i
$916$	−9.20272	−	2.99015i	−0.304067	−	0.0987972i
$917$	36.7560	−	26.7048i	1.21379	−	0.881871i
$918$	6.58604	+	1.87698i	0.217372	+	0.0619495i
$919$	−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
$921$	36.6004	−	12.3868i	1.20602	−	0.408160i
$922$	−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
$927$	−46.4278	+	16.3454i	−1.52489	+	0.536854i
$928$	4.85963	+	3.53073i	0.159525	+	0.115902i
$929$	−32.4326			−1.06408			−0.532040	−	0.846719i	$-0.678574\pi$
$929$	−32.4326			−1.06408			−0.532040	+	0.846719i	$0.678574\pi$
$930$	−10.5904	−	18.7841i	−0.347274	−	0.615955i
$931$	−27.0175			−0.885464
$932$	−13.3384	−	9.69093i	−0.436915	−	0.317437i
$933$	26.5025	+	8.25583i	0.867653	+	0.270284i
$934$	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
$939$	−11.8248	−	34.9396i	−0.385887	−	1.14021i
$940$	−13.6743	+	3.45470i	−0.446008	+	0.112680i
$941$	5.96893	+	18.3705i	0.194582	+	0.598861i	0.999981	+	0.00612852i	$0.00195078\pi$
$941$	5.96893	+	18.3705i	0.194582	+	0.598861i	−0.805400	+	0.592732i	$0.798049\pi$
$942$	−0.446819	−	36.6967i	−0.0145582	−	1.19564i
$943$	22.9363	−	16.6642i	0.746909	−	0.542661i
$944$	−7.30209	−	2.37259i	−0.237663	−	0.0772214i
$945$	−14.1646	−	48.5292i	−0.460775	−	1.57866i
$946$	0.525330	−	0.381675i	0.0170800	−	0.0124093i
$947$	−41.5576	−	13.5029i	−1.35044	−	0.438785i	−0.457601	−	0.889158i	$-0.651291\pi$
$947$	−41.5576	−	13.5029i	−1.35044	−	0.438785i	−0.892841	+	0.450372i	$0.851291\pi$
$948$	8.26220	+	2.57377i	0.268344	+	0.0835921i
$949$	7.41824	+	5.38966i	0.240806	+	0.174956i
$950$	9.96353	−	5.37764i	0.323260	−	0.174474i
$951$	48.7295	−	0.593331i	1.58016	−	0.0192401i
$952$	1.77203	−	5.45376i	0.0574319	−	0.176757i
$953$	−6.56662	−	2.13362i	−0.212714	−	0.0691148i	0.200722	−	0.979648i	$-0.435671\pi$
$953$	−6.56662	−	2.13362i	−0.212714	−	0.0691148i	−0.413435	+	0.910533i	$0.635671\pi$
$954$	0.215771	+	8.85920i	0.00698586	+	0.286827i
$955$	6.49788	+	5.41795i	0.210267	+	0.175321i
$956$	1.56151			0.0505029
$957$	−0.774958	−	0.548750i	−0.0250508	−	0.0177386i
$958$	14.7021	+	20.2356i	0.475002	+	0.653784i
$959$	10.0892	+	7.33024i	0.325798	+	0.236706i
$960$	−0.211054	+	3.86723i	−0.00681174	+	0.124814i
$961$	13.0639	−	28.1129i	0.421416	−	0.906867i
$962$	−12.4817			−0.402426
$963$	−23.0366	+	17.6098i	−0.742345	+	0.567467i
$964$	−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
$969$	−4.89634	+	1.65709i	−0.157293	+	0.0532334i
$970$	−20.7041	+	13.0273i	−0.664769	+	0.418281i
$971$	−19.4428	+	26.7608i	−0.623950	+	0.858793i	−0.997633	−	0.0687630i	$-0.978095\pi$
$971$	−19.4428	+	26.7608i	−0.623950	+	0.858793i	0.373683	+	0.927556i	$0.378095\pi$
$972$	−5.71015	−	14.5050i	−0.183153	−	0.465247i
$973$	12.2682	+	8.91338i	0.393301	+	0.285750i
$974$	1.17276	−	0.852059i	0.0375776	−	0.0273017i
$975$	−11.7156	+	6.50871i	−0.375200	+	0.208446i
$976$	4.51493	+	6.21427i	0.144519	+	0.198914i
$977$	−7.21194	+	5.23978i	−0.230731	+	0.167636i	−0.697144	−	0.716931i	$-0.745546\pi$
$977$	−7.21194	+	5.23978i	−0.230731	+	0.167636i	0.466413	+	0.884567i	$0.345546\pi$
$978$	21.3468	−	7.22451i	0.682597	−	0.231014i
$979$	0.902356	−	0.655600i	0.0288394	−	0.0209531i
$980$	−25.8664	+	6.53492i	−0.826272	+	0.208750i
$981$	42.8691	−	1.04410i	1.36870	−	0.0333357i
$982$	−14.6577	−	10.6494i	−0.467745	−	0.339837i
$983$	4.00855	+	1.30246i	0.127853	+	0.0415419i	0.372245	−	0.928135i	$-0.378588\pi$
$983$	4.00855	+	1.30246i	0.127853	+	0.0415419i	−0.244392	+	0.969677i	$0.578588\pi$
$984$	8.80367	−	2.97947i	0.280651	−	0.0949819i
$985$	−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
$990$	0.0259183	−	0.611700i	0.000823736	−	0.0194411i
$991$			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
$996$	8.49044	−	11.9904i	0.269030	−	0.379931i
$997$			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
$999$	−32.9831	+	25.8554i	−1.04354	+	0.818027i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.y.a.29.13	✓	128	1.1	even	1	trivial
930.2.y.a.29.32	yes	128	15.14	odd	2	inner
930.2.y.a.449.13	yes	128	465.449	even	10	inner
930.2.y.a.449.32	yes	128	31.15	odd	10	inner
930.2.y.b.29.1	yes	128	3.2	odd	2
930.2.y.b.29.20	yes	128	5.4	even	2
930.2.y.b.449.1	yes	128	155.139	odd	10
930.2.y.b.449.20	yes	128	93.77	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.y (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.515138 + 1.65367i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-1.43197 + 1.71740i) q^{5} +(1.38876 - 1.03506i) q^{6} +(-4.13806 + 1.34454i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-2.46927 - 1.70374i) q^{9} +O(q^{10})\)	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.515138 + 1.65367i) 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} +(-2.46927 - 1.70374i) q^{9} +(2.16795 - 0.547714i) q^{10} +(0.0282036 + 0.0868017i) q^{11} +(-1.73192 + 0.0210879i) q^{12} +(-1.25200 + 0.909628i) q^{13} +(4.13806 + 1.34454i) q^{14} +(-2.10235 - 3.25271i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-1.25345 - 0.407270i) q^{17} +(0.996246 + 2.82975i) q^{18} +(-1.83196 - 1.33100i) q^{19} +(-2.07585 - 0.831180i) q^{20} +(-0.0917536 - 7.53561i) q^{21} +(0.0282036 - 0.0868017i) q^{22} +(5.02483 + 1.63267i) q^{23} +(1.41355 + 1.00094i) q^{24} +(-0.898918 - 4.91853i) q^{25} +1.54755 q^{26} +(4.08944 - 3.20570i) q^{27} +(-2.55746 - 3.52004i) q^{28} +(4.85963 + 3.53073i) q^{29} +(-0.211054 + 3.86723i) q^{30} +(-4.69382 + 2.99467i) q^{31} +1.00000 q^{32} +(-0.158070 + 0.00192466i) 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} +(-0.859277 - 2.53897i) q^{39} +(1.19084 + 1.89259i) q^{40} +(3.15405 - 4.34118i) q^{41} +(-4.35509 + 6.15037i) q^{42} +(5.75587 + 4.18188i) q^{43} +(-0.0738379 + 0.0536464i) q^{44} +(6.46192 - 1.80101i) q^{45} +(-3.10552 - 4.27438i) q^{46} +(5.10287 - 3.70746i) q^{47} +(-0.555249 - 1.64064i) q^{48} +(9.65260 - 7.01303i) q^{49} +(-2.16380 + 4.50755i) q^{50} +(1.31919 - 1.86299i) q^{51} +(-1.25200 - 0.909628i) q^{52} +(2.80937 + 0.912819i) q^{53} +(-5.19269 + 0.189754i) 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} +(2.44385 - 3.00460i) 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} +(0.129013 + 0.0913543i) q^{66} +0.694711i q^{67} -1.31795i q^{68} +(-5.28838 + 7.46838i) q^{69} +(-8.23468 + 5.18136i) q^{70} +(-3.24956 - 1.05585i) q^{71} +(-2.38340 + 1.82193i) q^{72} +(-1.83097 - 5.63513i) q^{73} +(6.52508 + 4.74075i) q^{74} +(8.59671 + 1.04720i) q^{75} +(0.699747 - 2.15360i) q^{76} +(-0.233416 - 0.321269i) q^{77} +(-0.797202 + 2.55914i) q^{78} +(-4.75174 - 1.54393i) q^{79} +(0.149027 - 2.23110i) q^{80} +(3.19455 + 8.41397i) q^{81} +(-5.10337 + 1.65818i) q^{82} +(-4.98588 + 6.86247i) q^{83} +(7.13844 - 2.41589i) 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} +(-6.28641 - 2.34117i) q^{90} +(3.95780 - 5.44744i) q^{91} +5.28342i q^{92} +(-2.53424 - 9.30471i) q^{93} -6.30750 q^{94} +(4.90917 - 1.24026i) q^{95} +(-0.515138 + 1.65367i) 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	\( 128 q - 32 q^{2} - 32 q^{4} + 2 q^{5} - 32 q^{8} - 4 q^{9} + 2 q^{10} + 25 q^{15} - 32 q^{16} + 6 q^{18} - 8 q^{19} - 3 q^{20} - 20 q^{23} - 10 q^{25} - 48 q^{31} + 128 q^{32} - 8 q^{33} + 10 q^{34} + 16 q^{35} - 4 q^{36} + 12 q^{38} + 4 q^{39} - 3 q^{40} + 37 q^{45} + 10 q^{46} + 6 q^{47} + 46 q^{49} - 5 q^{50} + 34 q^{51} - 20 q^{53} - 25 q^{60} - 8 q^{62} + 36 q^{63} - 32 q^{64} - 8 q^{66} + 8 q^{69} + 16 q^{70} + 6 q^{72} + 5 q^{75} + 12 q^{76} + 50 q^{77} + 4 q^{78} - 10 q^{79} + 2 q^{80} - 24 q^{81} - 40 q^{83} - 30 q^{85} - 4 q^{87} - 53 q^{90} + 20 q^{91} - 26 q^{93} - 4 q^{94} - 26 q^{95} - 124 q^{98}+O(q^{100}) \) 128 * q - 32 * q^2 - 32 * q^4 + 2 * q^5 - 32 * q^8 - 4 * q^9 + 2 * q^10 + 25 * 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 + 37 * q^45 + 10 * q^46 + 6 * q^47 + 46 * q^49 - 5 * q^50 + 34 * q^51 - 20 * q^53 - 25 * 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 - 53 * q^90 + 20 * q^91 - 26 * q^93 - 4 * q^94 - 26 * q^95 - 124 * q^98

Introduction

L-functions

Modular forms

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