LMFDB - Embedded newform 930.2.y.a.449.32

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			449.32
Character	$\chi$	$=$	930.449
Dual form			930.2.y.a.29.32

$q$-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} +(0.149027 - 2.23110i) 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} +(-2.44385 + 3.00460i) 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} +(1.19084 + 1.89259i) 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} +(0.211054 - 3.86723i) q^{30} +(-4.69382 - 2.99467i) q^{31} +1.00000 q^{32} +(-0.0470159 + 0.150928i) q^{33} +(0.774673 - 1.06625i) q^{34} +(-8.23468 + 5.18136i) q^{35} +(0.857306 - 2.87490i) q^{36} +8.06544 q^{37} +(0.699747 - 2.15360i) q^{38} +(2.18754 + 1.54900i) q^{39} +(-2.07585 - 0.831180i) 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} +(-4.16919 + 5.25527i) 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} +(3.61828 + 3.45080i) 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} +(-0.108686 - 0.172734i) q^{55} +4.35101i q^{56} +(-3.14475 + 2.34382i) q^{57} +(1.85621 - 5.71284i) q^{58} +(-4.51294 + 6.21153i) q^{59} +(2.10235 + 3.25271i) q^{60} +7.68126i q^{61} +(5.55760 - 0.336219i) q^{62} +(12.5087 + 3.73015i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(-3.35502 + 0.847615i) q^{65} +(-0.0506769 - 0.149739i) q^{66} +0.694711i q^{67} +1.31795i q^{68} +(8.66819 - 2.93362i) q^{69} +(3.61647 - 9.03203i) 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} +(-1.66058 - 8.49956i) 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} +(2.16795 - 0.547714i) 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} +(1.09545 - 2.73587i) q^{85} +(2.19855 - 6.76643i) q^{86} +(-8.34205 + 6.21743i) q^{87} -0.0912687 q^{88} +(3.77643 - 11.6226i) q^{89} +(0.283978 - 6.70219i) q^{90} +(3.95780 + 5.44744i) q^{91} -5.28342i q^{92} +(-8.19248 - 5.08755i) q^{93} -6.30750 q^{94} +(0.337461 - 5.05216i) 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} + 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 $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{7}{10}\right)$

Coefficient data

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

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

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

$2$	−0.809017	+	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	$-0.0927111\pi$
$7$	4.13806	+	1.34454i	1.56404	+	0.508187i	0.606155	+	0.795346i	$0.292711\pi$
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$	2.99911	−	0.0730452i	0.999704	−	0.0243484i
$10$	0.149027	−	2.23110i	0.0471265	−	0.705535i
$11$	−0.0282036	+	0.0868017i	−0.00850370	+	0.0261717i	−0.955218	−	0.295902i	$-0.904380\pi$
$11$	−0.0282036	+	0.0868017i	−0.00850370	+	0.0261717i	0.946715	+	0.322074i	$0.104380\pi$
$12$	0.515138	−	1.65367i	0.148707	−	0.477374i
$13$	1.25200	+	0.909628i	0.347241	+	0.252285i	0.747711	−	0.664025i	$-0.231153\pi$
$13$	1.25200	+	0.909628i	0.347241	+	0.252285i	−0.400470	+	0.916310i	$0.631153\pi$
$14$	−4.13806	+	1.34454i	−1.10594	+	0.359342i
$15$	−2.44385	+	3.00460i	−0.630998	+	0.775784i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−1.25345	+	0.407270i	−0.304005	+	0.0987774i	−0.457047	−	0.889442i	$-0.651093\pi$
$17$	−1.25345	+	0.407270i	−0.304005	+	0.0987774i	0.153042	+	0.988220i	$0.451093\pi$
$18$	−2.38340	+	1.82193i	−0.561772	+	0.429433i
$19$	−1.83196	+	1.33100i	−0.420281	+	0.305352i	−0.777751	−	0.628573i	$-0.783639\pi$
$19$	−1.83196	+	1.33100i	−0.420281	+	0.305352i	0.357470	+	0.933925i	$0.383639\pi$
$20$	1.19084	+	1.89259i	0.266280	+	0.423196i
$21$	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	$-0.414309\pi$
$23$	5.02483	−	1.63267i	1.04775	−	0.340435i	0.781785	+	0.623548i	$0.214309\pi$
$24$	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	−0.939084	−	0.343688i	$-0.888324\pi$
$29$	−4.85963	+	3.53073i	−0.902411	+	0.655640i	0.0366735	+	0.999327i	$0.488324\pi$
$30$	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
$33$	−0.0470159	+	0.150928i	−0.00818442	+	0.0262733i
$34$	0.774673	−	1.06625i	0.132855	−	0.182860i
$35$	−8.23468	+	5.18136i	−1.39191	+	0.875809i
$36$	0.857306	−	2.87490i	0.142884	−	0.479149i
$37$	8.06544			1.32595			0.662975	−	0.748642i	$-0.269294\pi$
$37$	8.06544			1.32595			0.662975	+	0.748642i	$0.269294\pi$
$38$	0.699747	−	2.15360i	0.113514	−	0.349360i
$39$	2.18754	+	1.54900i	0.350287	+	0.248039i
$40$	−2.07585	−	0.831180i	−0.328220	−	0.131421i
$41$	−3.15405	−	4.34118i	−0.492581	−	0.677979i	0.488281	−	0.872687i	$-0.337624\pi$
$41$	−3.15405	−	4.34118i	−0.492581	−	0.677979i	−0.980861	+	0.194708i	$0.937624\pi$
$42$	−7.13844	+	2.41589i	−1.10148	+	0.372781i
$43$	−5.75587	+	4.18188i	−0.877761	+	0.637731i	−0.932658	−	0.360761i	$-0.882517\pi$
$43$	−5.75587	+	4.18188i	−0.877761	+	0.637731i	0.0548968	+	0.998492i	$0.482517\pi$
$44$	0.0738379	+	0.0536464i	0.0111315	+	0.00808749i
$45$	−4.16919	+	5.25527i	−0.621506	+	0.783409i
$46$	−3.10552	+	4.27438i	−0.457884	+	0.630223i
$47$	5.10287	+	3.70746i	0.744331	+	0.540788i	0.894064	−	0.447938i	$-0.147842\pi$
$47$	5.10287	+	3.70746i	0.744331	+	0.540788i	−0.149734	+	0.988726i	$0.547842\pi$
$48$	−1.41355	−	1.00094i	−0.204028	−	0.144473i
$49$	9.65260	+	7.01303i	1.37894	+	1.00186i
$50$	3.61828	+	3.45080i	0.511702	+	0.488017i
$51$	−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	$-0.534971\pi$
$53$	2.80937	−	0.912819i	0.385896	−	0.125385i	0.495539	+	0.868586i	$0.334971\pi$
$54$	−4.08944	+	3.20570i	−0.556502	+	0.436240i
$55$	−0.108686	−	0.172734i	−0.0146553	−	0.0232915i
$56$			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	$-0.966588\pi$
$59$	−4.51294	+	6.21153i	−0.587535	+	0.808673i	0.406961	+	0.913445i	$0.366588\pi$
$60$	2.10235	+	3.25271i	0.271413	+	0.419923i
$61$			7.68126i			0.983485i	0.870741	+	0.491742i	$0.163640\pi$
$61$			7.68126i			0.983485i	−0.870741	+	0.491742i	$0.836360\pi$
$62$	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
$65$	−3.35502	+	0.847615i	−0.416138	+	0.105134i
$66$	−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
$70$	3.61647	−	9.03203i	0.432251	−	1.07953i
$71$	3.24956	−	1.05585i	0.385652	−	0.125306i	−0.109773	−	0.993957i	$-0.535012\pi$
$71$	3.24956	−	1.05585i	0.385652	−	0.125306i	0.495425	+	0.868651i	$0.335012\pi$
$72$	0.996246	+	2.82975i	0.117409	+	0.333489i
$73$	1.83097	−	5.63513i	0.214298	−	0.659543i	−0.784904	−	0.619617i	$-0.787288\pi$
$73$	1.83097	−	5.63513i	0.214298	−	0.659543i	0.999203	−	0.0399256i	$-0.0127121\pi$
$74$	−6.52508	+	4.74075i	−0.758525	+	0.551100i
$75$	−1.66058	−	8.49956i	−0.191747	−	0.981444i
$76$	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	−0.563867	−	0.825866i	$-0.690687\pi$
$79$	−4.75174	+	1.54393i	−0.534612	+	0.173706i	0.0292541	+	0.999572i	$0.490687\pi$
$80$	2.16795	−	0.547714i	0.242384	−	0.0612362i
$81$	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	$-0.354139\pi$
$83$	−4.98588	−	6.86247i	−0.547271	−	0.753254i	−0.989639	+	0.143579i	$0.954139\pi$
$84$	4.35509	−	6.15037i	0.475179	−	0.671060i
$85$	1.09545	−	2.73587i	0.118819	−	0.296746i
$86$	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	−0.524456	−	0.851438i	$-0.675731\pi$
$89$	3.77643	−	11.6226i	0.400301	−	1.23200i	0.924756	−	0.380560i	$-0.124269\pi$
$90$	0.283978	−	6.70219i	0.0299339	−	0.706473i
$91$	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
$95$	0.337461	−	5.05216i	0.0346228	−	0.518341i
$96$	1.73192	−	0.0210879i	0.176764	−	0.00215227i
$97$	10.4041	+	3.38051i	1.05638	+	0.343239i	0.785170	−	0.619281i	$-0.212576\pi$
$97$	10.4041	+	3.38051i	1.05638	+	0.343239i	0.271211	+	0.962520i	$0.412576\pi$
$98$	−11.9313			−1.20524
$99$	−0.0782452	+	0.262388i	−0.00786394	+	0.0263710i
$100$	−4.95558	−	0.664987i	−0.495558	−	0.0664987i
$101$	11.4463	−	3.71911i	1.13894	−	0.370066i	0.321976	−	0.946748i	$-0.395653\pi$
$101$	11.4463	−	3.71911i	1.13894	−	0.370066i	0.816968	+	0.576682i	$0.195653\pi$
$102$	1.31919	−	1.86299i	0.130619	−	0.184464i
$103$	−9.64380	−	13.2736i	−0.950232	−	1.30788i	−0.951424	−	0.307883i	$-0.900379\pi$
$103$	−9.64380	−	13.2736i	−0.950232	−	1.30788i	0.00119205	−	0.999999i	$-0.499621\pi$
$104$	−0.478220	+	1.47181i	−0.0468933	+	0.144323i
$105$	−14.1526	+	9.14736i	−1.38115	+	0.892691i
$106$	−1.73628	+	2.38979i	−0.168643	+	0.232117i
$107$	2.98679	+	9.19240i	0.288744	+	0.888662i	0.985251	+	0.171113i	$0.0547363\pi$
$107$	2.98679	+	9.19240i	0.288744	+	0.888662i	−0.696507	+	0.717550i	$0.745264\pi$
$108$	1.42416	−	4.99718i	0.137040	−	0.480853i
$109$	−11.5640	−	8.40176i	−1.10763	−	0.804743i	−0.125344	−	0.992113i	$-0.540004\pi$
$109$	−11.5640	−	8.40176i	−1.10763	−	0.804743i	−0.982289	+	0.187370i	$0.940004\pi$
$110$	0.189460	+	0.0758607i	0.0180643	+	0.00723303i
$111$	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	0.167958	+	0.985794i	$0.446283\pi$
$113$	−5.81850	+	17.9075i	−0.547358	+	1.68459i	−0.715316	+	0.698801i	$0.753717\pi$
$114$	1.16649	−	3.74462i	0.109252	−	0.350716i
$115$	−4.39147	+	10.9676i	−0.409507	+	1.02273i
$116$	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
$120$	−3.61273	−	1.39576i	−0.329796	−	0.127415i
$121$	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	$-0.229170\pi$
$127$	4.02408	+	2.92366i	0.357079	+	0.259433i	−0.394754	+	0.918787i	$0.629170\pi$
$128$	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	$-0.249225\pi$
$131$	9.93088	+	3.22674i	0.867665	+	0.281921i	0.158839	+	0.987305i	$0.449225\pi$
$132$	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
$135$	−7.10989	+	9.18964i	−0.611922	+	0.790918i
$136$	−0.774673	−	1.06625i	−0.0664276	−	0.0914298i
$137$	−1.68472	+	2.31882i	−0.143935	+	0.198110i	−0.874898	−	0.484308i	$-0.839072\pi$
$137$	−1.68472	+	2.31882i	−0.143935	+	0.198110i	0.730962	+	0.682418i	$0.239072\pi$
$138$	−5.28838	+	7.46838i	−0.450177	+	0.635751i
$139$	−2.04858	+	2.81963i	−0.173758	+	0.239158i	−0.887010	−	0.461750i	$-0.847222\pi$
$139$	−2.04858	+	2.81963i	−0.173758	+	0.239158i	0.713252	+	0.700908i	$0.247222\pi$
$140$	2.38311	+	9.43277i	0.201409	+	0.797215i
$141$	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
$145$	0.895181	−	13.4018i	0.0743407	−	1.11296i
$146$	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	$-0.877709\pi$
$149$		−	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	−0.772691	−	0.634783i	$-0.781090\pi$
$151$	−21.7615	−	7.07074i	−1.77093	−	0.575409i	−0.998236	+	0.0593738i	$0.981090\pi$
$152$	−1.83196	−	1.33100i	−0.148592	−	0.107958i
$153$	−3.72948	+	1.31300i	−0.301510	+	0.106150i
$154$		−	0.397111i		−	0.0320001i
$155$	11.8645	−	3.77288i	0.952976	−	0.303045i
$156$	2.14918	−	1.60181i	0.172072	−	0.128247i
$157$	−12.4542	−	17.1418i	−0.993957	−	1.36806i	−0.928961	−	0.370178i	$-0.879297\pi$
$157$	−12.4542	−	17.1418i	−0.993957	−	1.36806i	−0.0649960	−	0.997886i	$-0.520703\pi$
$158$	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	$-0.770192\pi$
$163$	−12.3745	+	4.02071i	−0.969243	+	0.314926i	−0.218733	+	0.975785i	$0.570192\pi$
$164$	−5.10337	+	1.65818i	−0.398506	+	0.129482i
$165$	−0.191879	−	0.296870i	−0.0149378	−	0.0231113i
$166$	8.06732	+	2.62123i	0.626146	+	0.203447i
$167$	−11.3565	−	15.6309i	−0.878795	−	1.20956i	−0.976753	−	0.214367i	$-0.931231\pi$
$167$	−11.3565	−	15.6309i	−0.878795	−	1.20956i	0.0979577	−	0.995191i	$-0.468769\pi$
$168$	0.0917536	+	7.53561i	0.00707895	+	0.581385i
$169$	−3.27715	−	10.0860i	−0.252089	−	0.775849i
$170$	0.721860	+	2.85725i	0.0553641	+	0.219141i
$171$	−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	$-0.477093\pi$
$173$	−11.2388	−	8.16549i	−0.854473	−	0.620811i	−0.926376	+	0.376601i	$0.877093\pi$
$174$	3.09435	−	9.93333i	0.234582	−	0.753044i
$175$	2.89337	−	21.5618i	0.218718	−	1.62992i
$176$	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	−0.631027	−	0.775761i	$-0.717366\pi$
$179$	4.48822	−	13.8133i	0.335465	−	1.03246i	0.966492	−	0.256695i	$-0.0826337\pi$
$180$	3.70971	+	5.58910i	0.276505	+	0.416587i
$181$			3.69704i			0.274799i	0.990516	+	0.137399i	$0.0438744\pi$
$181$			3.69704i			0.274799i	−0.990516	+	0.137399i	$0.956126\pi$
$182$	−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
$190$	2.69657	+	4.28564i	0.195630	+	0.310913i
$191$		−	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	$-0.515603\pi$
$193$	−9.38737	−	3.05014i	−0.675718	−	0.219554i	−0.626720	+	0.779245i	$0.715603\pi$
$194$	−10.4041	+	3.38051i	−0.746974	+	0.242707i
$195$	−5.79275	+	1.53875i	−0.414828	+	0.110192i
$196$	9.65260	−	7.01303i	0.689472	−	0.500931i
$197$	19.6837	+	6.39561i	1.40240	+	0.455668i	0.909967	−	0.414680i	$-0.136107\pi$
$197$	19.6837	+	6.39561i	1.40240	+	0.455668i	0.492436	+	0.870349i	$0.336107\pi$
$198$	−0.0909261	−	0.258268i	−0.00646183	−	0.0183543i
$199$	13.0198	−	17.9202i	0.922949	−	1.27033i	−0.0395986	−	0.999216i	$-0.512608\pi$
$199$	13.0198	−	17.9202i	0.922949	−	1.27033i	0.962547	−	0.271114i	$-0.0873921\pi$
$200$	4.40002	−	2.37483i	0.311128	−	0.167926i
$201$	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
$205$	11.9721	+	0.799679i	0.836165	+	0.0558520i
$206$	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
$210$	6.07298	−	15.7190i	0.419075	−	1.08472i
$211$	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
$215$	1.06027	−	15.8735i	0.0723101	−	1.08256i
$216$	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
$220$	−0.197866	+	0.0499891i	−0.0133401	+	0.00337026i
$221$	−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	$-0.359567\pi$
$223$	12.7533			0.854022			0.427011	+	0.904247i	$0.359567\pi$
$224$	4.13806	+	1.34454i	0.276485	+	0.0898356i
$225$	−3.05523	−	14.6856i	−0.203682	−	0.979037i
$226$	−5.81850	−	17.9075i	−0.387041	−	1.19119i
$227$	18.5005	−	13.4414i	1.22792	−	0.892135i	0.231186	−	0.972910i	$-0.425739\pi$
$227$	18.5005	−	13.4414i	1.22792	−	0.892135i	0.996732	+	0.0807747i	$0.0257394\pi$
$228$	1.25732	+	3.71511i	0.0832682	+	0.246039i
$229$	−5.68760	−	7.82830i	−0.375847	−	0.517309i	0.578631	−	0.815589i	$-0.303587\pi$
$229$	−5.68760	−	7.82830i	−0.375847	−	0.517309i	−0.954478	+	0.298280i	$0.903587\pi$
$230$	−2.89380	−	11.4542i	−0.190812	−	0.755267i
$231$	−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	$-0.481597\pi$
$233$	−13.3384	−	9.69093i	−0.873829	−	0.634874i	−0.931612	+	0.363455i	$0.881597\pi$
$234$	−4.64128	+	0.113041i	−0.303410	+	0.00738974i
$235$	−13.6743	+	3.45470i	−0.892016	+	0.225360i
$236$	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	0.934237	−	0.356654i	$-0.116082\pi$
$239$	−0.482534	−	1.48509i	−0.0312125	−	0.0960623i	−0.965449	+	0.260592i	$0.916082\pi$
$240$	3.74317	−	0.994315i	0.241621	−	0.0641828i
$241$	−19.3337	−	6.28191i	−1.24539	−	0.404653i	−0.389126	−	0.921184i	$-0.627223\pi$
$241$	−19.3337	−	6.28191i	−1.24539	−	0.404653i	−0.856268	+	0.516531i	$0.827223\pi$
$242$	−10.9917			−0.706571
$243$	15.5596	−	0.948393i	0.998148	−	0.0608394i
$244$	7.30531	+	2.37364i	0.467675	+	0.151957i
$245$	−25.8664	+	6.53492i	−1.65254	+	0.417501i
$246$	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
$250$	−11.1077	+	1.27258i	−0.702511	+	0.0804850i
$251$	2.23300	+	1.62237i	0.140945	+	0.102403i	0.656024	−	0.754740i	$-0.272237\pi$
$251$	2.23300	+	1.62237i	0.140945	+	0.102403i	−0.515078	+	0.857143i	$0.672237\pi$
$252$	7.41298	−	10.7438i	0.466974	−	0.676796i
$253$			0.482211i			0.0303163i
$254$	−4.97403			−0.312099
$255$	1.83955	−	4.76141i	0.115197	−	0.298171i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	3.04322	+	9.36608i	0.189831	+	0.584240i	0.999998	−	0.00195919i	$-0.000623631\pi$
$257$	3.04322	+	9.36608i	0.189831	+	0.584240i	−0.810167	+	0.586199i	$0.800624\pi$
$258$	3.66502	−	11.7653i	0.228174	−	0.732475i
$259$	33.3752	+	10.8443i	2.07384	+	0.673830i
$260$	−0.230627	+	3.45274i	−0.0143029	+	0.214130i
$261$	−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	−0.186391	−	0.982476i	$-0.559679\pi$
$263$	13.0646	−	17.9819i	0.805597	−	1.10881i	0.991988	−	0.126334i	$-0.0403209\pi$
$264$	−0.158070	+	0.00192466i	−0.00972855	+	0.000118455i
$265$	−2.45526	+	6.13193i	−0.150825	+	0.376682i
$266$	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	−0.759467	−	0.650546i	$-0.774540\pi$
$269$	−6.15781	+	4.47391i	−0.375448	+	0.272779i	0.384018	+	0.923325i	$0.374540\pi$
$270$	0.350492	−	11.6137i	0.0213303	−	0.706785i
$271$	6.13527	−	1.99347i	0.372691	−	0.121095i	−0.116682	−	0.993169i	$-0.537226\pi$
$271$	6.13527	−	1.99347i	0.372691	−	0.121095i	0.489373	+	0.872075i	$0.337226\pi$
$272$	1.25345	+	0.407270i	0.0760014	+	0.0246943i
$273$	6.96948	+	9.35109i	0.421812	+	0.565954i
$274$		−	2.86622i		−	0.173155i
$275$	0.452289	+	0.0606925i	0.0272741	+	0.00365990i
$276$	−0.111416	−	9.15048i	−0.00670647	−	0.550794i
$277$	6.62165	−	4.81091i	0.397856	−	0.289059i	−0.370811	−	0.928708i	$-0.620920\pi$
$277$	6.62165	−	4.81091i	0.397856	−	0.289059i	0.768667	+	0.639649i	$0.220920\pi$
$278$		−	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	−0.963210	−	0.268748i	$-0.913390\pi$
$281$	−15.4414	−	21.2533i	−0.921157	−	1.26786i	0.0420536	−	0.999115i	$-0.486610\pi$
$282$	−10.9241	+	0.133012i	−0.650521	+	0.00792075i
$283$	−7.81632	−	2.53968i	−0.464632	−	0.150968i	0.0673400	−	0.997730i	$-0.478549\pi$
$283$	−7.81632	−	2.53968i	−0.464632	−	0.150968i	−0.531972	+	0.846762i	$0.678549\pi$
$284$		−	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
$288$	2.99911	−	0.0730452i	0.176724	−	0.00430423i
$289$	−12.3480	+	8.97137i	−0.726355	+	0.527728i
$290$	7.15318	+	11.3685i	0.420049	+	0.667580i
$291$	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	−0.987739	−	0.156116i	$-0.950103\pi$
$293$	−4.79974	−	14.7721i	−0.280404	−	0.862995i	0.707335	−	0.706879i	$-0.249897\pi$
$294$	−20.6640	+	0.251606i	−1.20515	+	0.0146739i
$295$	−4.20528	−	16.6453i	−0.244841	−	0.969124i
$296$	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
$300$	−8.59671	−	1.04720i	−0.496331	−	0.0604603i
$301$	−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	−0.249712	−	0.968320i	$-0.580336\pi$
$307$	13.1127	−	18.0481i	0.748380	−	1.03006i	0.998092	−	0.0617368i	$-0.0196639\pi$
$308$	0.233416	+	0.321269i	0.0133001	+	0.0183060i
$309$	−16.9822	−	22.7854i	−0.966085	−	1.29622i
$310$	−7.38091	+	10.0261i	−0.419207	+	0.569443i
$311$		−	16.0265i		−	0.908777i	−0.890804	−	0.454388i	$-0.849858\pi$
$311$		−	16.0265i		−	0.908777i	0.890804	−	0.454388i	$-0.150142\pi$
$312$	−0.797202	+	2.55914i	−0.0451327	+	0.144883i
$313$	17.2291	+	12.5177i	0.973845	+	0.707540i	0.956325	−	0.292306i	$-0.0944227\pi$
$313$	17.2291	+	12.5177i	0.973845	+	0.707540i	0.0175208	+	0.999846i	$0.494423\pi$
$314$	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	0.338761	+	0.940872i	$0.389992\pi$
$317$	−8.69453	+	26.7590i	−0.488333	+	1.50294i	−0.827095	+	0.562063i	$0.810008\pi$
$318$	−2.95671	+	4.17555i	−0.165804	+	0.234153i
$319$	−0.169414	−	0.521403i	−0.00948537	−	0.0291930i
$320$	0.149027	−	2.23110i	0.00833087	−	0.124722i
$321$	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
$325$	3.34859	−	6.97566i	0.185746	−	0.386940i
$326$	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
$330$	0.329729	+	0.127389i	0.0181510	+	0.00701256i
$331$	14.1921	+	19.5337i	0.780067	+	1.07367i	0.995274	+	0.0971014i	$0.0309571\pi$
$331$	14.1921	+	19.5337i	0.780067	+	1.07367i	−0.215208	+	0.976568i	$0.569043\pi$
$332$	−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	$-0.812636\pi$
$337$	3.07499	−	9.46384i	0.167505	−	0.515528i	0.999212	+	0.0396867i	$0.0126360\pi$
$338$	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
$345$	−7.37441	+	19.0876i	−0.397025	+	1.02764i
$346$	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	0.998010	−	0.0630568i	$-0.0200849\pi$
$349$	2.86835	+	8.82786i	0.153539	+	0.472545i	−0.844471	+	0.535601i	$0.820085\pi$
$350$	10.3329	+	19.1445i	0.552317	+	1.02332i
$351$	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	−0.996967	−	0.0778292i	$-0.975201\pi$
$353$	−14.3337	−	19.7287i	−0.762907	−	1.05005i	0.234060	−	0.972222i	$-0.424799\pi$
$354$	−0.161910	−	13.2975i	−0.00860543	−	0.706753i
$355$	−2.83997	+	7.09273i	−0.150730	+	0.376443i
$356$	−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	−0.971993	−	0.235009i	$-0.924488\pi$
$359$	−8.49073	+	11.6865i	−0.448123	+	0.616789i	0.523870	+	0.851798i	$0.324488\pi$
$360$	−6.28641	−	2.34117i	−0.331323	−	0.123390i
$361$	−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
$365$	7.05588	+	11.2138i	0.369322	+	0.586960i
$366$	−7.95056	−	10.6674i	−0.415582	−	0.557595i
$367$	21.6245			1.12879			0.564395	−	0.825505i	$-0.309109\pi$
$367$	21.6245			1.12879			0.564395	+	0.825505i	$0.309109\pi$
$368$	−5.02483	−	1.63267i	−0.261937	−	0.0851086i
$369$	−9.77646	−	12.7893i	−0.508942	−	0.665784i
$370$	1.20197	−	17.9948i	0.0624874	−	0.935504i
$371$	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
$375$	16.9750	+	9.31924i	0.876587	+	0.481244i
$376$	−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	−0.772560	−	0.634942i	$-0.781024\pi$
$379$	4.39320	−	13.5209i	0.225664	−	0.694521i	0.998224	−	0.0595795i	$-0.0189760\pi$
$380$	−4.70061	−	1.88215i	−0.241136	−	0.0965521i
$381$	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	$-0.495969\pi$
$383$	−11.0539	−	3.59164i	−0.564830	−	0.183524i	−0.577493	+	0.816395i	$0.695969\pi$
$384$	0.515138	−	1.65367i	0.0262880	−	0.0843886i
$385$	−0.217503	−	0.860916i	−0.0110850	−	0.0438764i
$386$	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	0.978869	−	0.204489i	$-0.0655531\pi$
$389$	1.31655	+	4.05194i	0.0667520	+	0.205441i	−0.912117	+	0.409930i	$0.865553\pi$
$390$	3.78198	−	4.64977i	0.191508	−	0.235450i
$391$	−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
$395$	4.15280	−	10.3715i	0.208950	−	0.521847i
$396$	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
$400$	−2.16380	+	4.50755i	−0.108190	+	0.225377i
$401$	0.382182	−	0.277671i	0.0190852	−	0.0138662i	−0.578202	−	0.815894i	$-0.696245\pi$
$401$	0.382182	−	0.277671i	0.0190852	−	0.0138662i	0.597287	+	0.802028i	$0.296245\pi$
$402$	−0.719067	−	0.964786i	−0.0358638	−	0.0481192i
$403$	−3.15261	−	8.01894i	−0.157042	−	0.399452i
$404$		−	12.0353i		−	0.598779i
$405$	−12.1200	+	16.0657i	−0.602247	+	0.798310i
$406$	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	$0.317357\pi$
$409$			33.9698i			1.67970i	−0.542818	+	0.839850i	$0.682643\pi$
$410$	−10.1556	+	6.39005i	−0.501551	+	0.315582i
$411$	−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
$415$	18.9252	+	1.26412i	0.929004	+	0.0620532i
$416$	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	−0.611763	−	0.791041i	$-0.709539\pi$
$419$	6.74688	−	9.28628i	0.329607	−	0.453665i	0.941370	+	0.337376i	$0.109539\pi$
$420$	4.32627	+	16.2866i	0.211100	+	0.794703i
$421$	1.62871	+	1.18333i	0.0793785	+	0.0576719i	0.626767	−	0.779207i	$-0.284378\pi$
$421$	1.62871	+	1.18333i	0.0793785	+	0.0576719i	−0.547388	+	0.836879i	$0.684378\pi$
$422$	−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
$425$	3.12991	+	5.79901i	0.151823	+	0.281293i
$426$	−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
$430$	8.47240	+	13.4651i	0.408576	+	0.649345i
$431$	−20.9213	+	28.7957i	−1.00774	+	1.38704i	−0.0872911	+	0.996183i	$0.527821\pi$
$431$	−20.9213	+	28.7957i	−1.00774	+	1.38704i	−0.920452	+	0.390856i	$0.872179\pi$
$432$	−4.31251	−	2.89867i	−0.207486	−	0.139462i
$433$	30.9820			1.48890			0.744449	−	0.667679i	$-0.232712\pi$
$433$	30.9820			1.48890			0.744449	+	0.667679i	$0.232712\pi$
$434$	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
$438$	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	0.999074	+	0.0430178i	$0.0136972\pi$
$443$	4.54820	+	13.9979i	0.216091	+	0.665061i	−0.782983	+	0.622043i	$0.786303\pi$
$444$	4.15481	−	13.3376i	0.197179	−	0.632974i
$445$	14.5530	+	23.1289i	0.689878	+	1.09642i
$446$	−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	−0.225272	−	0.974296i	$-0.572327\pi$
$449$	−25.8830	−	18.8051i	−1.22150	−	0.887468i	−0.996223	+	0.0868279i	$0.972327\pi$
$450$	11.1037	+	10.0850i	0.523433	+	0.475414i
$451$	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
$455$	−15.0229	−	1.00346i	−0.704284	−	0.0470429i
$456$	−3.20088	−	2.26655i	−0.149895	−	0.106141i
$457$	−8.13468	−	25.0360i	−0.380524	−	1.17113i	−0.939675	−	0.342068i	$-0.888873\pi$
$457$	−8.13468	−	25.0360i	−0.380524	−	1.17113i	0.559151	−	0.829066i	$-0.311127\pi$
$458$	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	$-0.865933\pi$
$461$	1.41748	−	4.36254i	0.0660184	−	0.203184i	0.978624	+	0.205657i	$0.0659331\pi$
$462$	−0.00837423	−	0.687765i	−0.000389604	−	0.0319977i
$463$	2.55033	−	1.85292i	0.118524	−	0.0861126i	−0.526944	−	0.849900i	$-0.676662\pi$
$463$	2.55033	−	1.85292i	0.118524	−	0.0861126i	0.645468	+	0.763787i	$0.276662\pi$
$464$	6.00683			0.278860
$465$	20.4688	−	6.78453i	0.949216	−	0.314625i
$466$	16.4872			0.763755
$467$	−9.69777	+	7.04584i	−0.448759	+	0.326043i	−0.789106	−	0.614257i	$-0.789456\pi$
$467$	−9.69777	+	7.04584i	−0.448759	+	0.326043i	0.340346	+	0.940300i	$0.389456\pi$
$468$	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
$475$	8.19334	+	7.81410i	0.375936	+	0.358536i
$476$	−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	0.289865	−	0.957068i	$-0.406390\pi$
$479$	23.7884	−	7.72933i	1.08692	−	0.353162i	0.797056	+	0.603905i	$0.206390\pi$
$480$	−2.44385	+	3.00460i	−0.111546	+	0.137141i
$481$	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
$485$	−20.7041	+	13.0273i	−0.940126	+	0.591538i
$486$	−12.0305	+	9.91296i	−0.545715	+	0.449661i
$487$	0.447954	+	1.37866i	0.0202987	+	0.0624731i	0.960693	−	0.277614i	$-0.0895435\pi$
$487$	0.447954	+	1.37866i	0.0202987	+	0.0624731i	−0.940394	+	0.340087i	$0.889544\pi$
$488$	−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
$495$	−0.338580	−	0.510110i	−0.0152180	−	0.0229277i
$496$	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	0.210744	+	0.977541i	$0.432411\pi$
$499$	−17.5149	+	24.1072i	−0.784076	+	1.07919i	−0.994821	+	0.101647i	$0.967589\pi$
$500$	8.23830	−	7.55847i	0.368428	−	0.338025i
$501$	−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	$-0.927391\pi$
$503$	−1.19130	+	3.66645i	−0.0531175	+	0.163479i	0.920979	+	0.389613i	$0.127391\pi$
$504$	0.317820	+	13.0492i	0.0141568	+	0.581256i
$505$	−10.0035	+	24.9834i	−0.445150	+	1.11175i
$506$	−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	0.779016	−	0.627004i	$-0.215719\pi$
$509$	9.55299	+	6.94065i	0.423429	+	0.307639i	−0.355587	+	0.934643i	$0.615719\pi$
$510$	1.31046	+	4.93332i	0.0580281	+	0.218451i
$511$	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
$515$	36.6056	+	2.44509i	1.61304	+	0.107744i
$516$	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
$520$	−1.84289	−	2.92888i	−0.0808159	−	0.128440i
$521$			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	$-0.812759\pi$
$523$	3.82546	−	11.7735i	0.167276	−	0.514821i	0.999197	+	0.0400725i	$0.0127589\pi$
$524$	6.13762	−	8.44771i	0.268123	−	0.369040i
$525$	4.55639	−	37.4043i	0.198857	−	1.63246i
$526$			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
$530$	−1.61791	−	6.40400i	−0.0702777	−	0.278172i
$531$	−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
$535$	−20.0640	−	8.03373i	−0.867443	−	0.347329i
$536$	−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
$540$	6.54279	+	9.60166i	0.281557	+	0.413190i
$541$	−9.67075	−	29.7635i	−0.415778	−	1.27963i	−0.911553	−	0.411183i	$-0.865116\pi$
$541$	−9.67075	−	29.7635i	−0.415778	−	1.27963i	0.495775	−	0.868451i	$-0.334884\pi$
$542$	−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
$545$	30.9885	−	7.82898i	1.32740	−	0.335357i
$546$	−11.1349	−	3.46863i	−0.476528	−	0.148444i
$547$	16.5217	+	5.36823i	0.706417	+	0.229529i	0.640124	−	0.768271i	$-0.278883\pi$
$547$	16.5217	+	5.36823i	0.706417	+	0.229529i	0.0662929	+	0.997800i	$0.478883\pi$
$548$	1.68472	+	2.31882i	0.0719677	+	0.0990551i
$549$	0.561079	+	23.0370i	0.0239463	+	0.983193i
$550$	−0.401584	+	0.216748i	−0.0171236	+	0.00924215i
$551$	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
$555$	−19.7107	+	24.2334i	−0.836672	+	1.02865i
$556$	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
$560$	9.70752	+	0.648418i	0.410218	+	0.0274007i
$561$	−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	$-0.820471\pi$
$563$	−40.1053			−1.69024			−0.845119	+	0.534578i	$0.820471\pi$
$564$	8.75960	−	6.52863i	0.368846	−	0.274905i
$565$	−22.4224	−	35.6357i	−0.943317	−	1.49920i
$566$	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	0.744772	+	0.667319i	$0.232558\pi$
$569$	−5.96346	+	18.3537i	−0.250001	+	0.769425i	−0.994773	+	0.102106i	$0.967442\pi$
$570$	4.76063	+	7.36553i	0.199401	+	0.308508i
$571$	−3.74222	+	5.15072i	−0.156607	+	0.215551i	−0.880110	−	0.474771i	$-0.842531\pi$
$571$	−3.74222	+	5.15072i	−0.156607	+	0.215551i	0.723503	+	0.690322i	$0.242531\pi$
$572$	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
$575$	−12.5472	−	23.2472i	−0.523256	−	0.969473i
$576$	−2.38340	+	1.82193i	−0.0993082	+	0.0759137i
$577$	12.5255	+	17.2399i	0.521444	+	0.717706i	0.985796	−	0.167945i	$-0.0537130\pi$
$577$	12.5255	+	17.2399i	0.521444	+	0.717706i	−0.464353	+	0.885650i	$0.653713\pi$
$578$	4.71653	−	14.5160i	0.196182	−	0.603785i
$579$	−16.3225	−	5.08465i	−0.678341	−	0.211311i
$580$	−12.4693	−	4.99276i	−0.517758	−	0.207313i
$581$	−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
$585$	−10.0001	+	2.78716i	−0.413455	+	0.115235i
$586$	12.5659	+	9.12965i	0.519092	+	0.377143i
$587$	17.9592	+	24.7187i	0.741254	+	1.02025i	0.998546	+	0.0539149i	$0.0171700\pi$
$587$	17.9592	+	24.7187i	0.741254	+	1.02025i	−0.257291	+	0.966334i	$0.582830\pi$
$588$	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	0.510512	+	0.859870i	$0.329456\pi$
$593$	−9.93350	+	30.5722i	−0.407920	+	1.25545i	−0.918432	+	0.395578i	$0.870544\pi$
$594$	−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	−0.998293	−	0.0583974i	$-0.981401\pi$
$599$	−18.2419	−	25.1078i	−0.745343	−	1.02588i	0.252950	−	0.967479i	$-0.418599\pi$
$600$	7.57041	−	4.20581i	0.309061	−	0.171702i
$601$	1.65760	+	2.28149i	0.0676149	+	0.0930640i	0.841485	−	0.540280i	$-0.181682\pi$
$601$	1.65760	+	2.28149i	0.0676149	+	0.0930640i	−0.773870	+	0.633344i	$0.781682\pi$
$602$	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
$605$	−23.8294	+	6.02029i	−0.968803	+	0.244759i
$606$	−12.0466	+	17.0125i	−0.489359	+	0.691085i
$607$	−17.2190	+	23.7000i	−0.698899	+	0.961952i	0.301066	+	0.953603i	$0.402658\pi$
$607$	−17.2190	+	23.7000i	−0.698899	+	0.961952i	−0.999965	+	0.00834883i	$0.997342\pi$
$608$	−1.83196	+	1.33100i	−0.0742958	+	0.0539791i
$609$	−42.8794	+	14.5119i	−1.73756	+	0.588051i
$610$	17.1376	+	1.14472i	0.693883	+	0.0463482i
$611$	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	0.604828	+	0.796356i	$0.293242\pi$
$613$	−8.72934	+	26.8662i	−0.352575	+	1.08511i	−0.957402	+	0.288757i	$0.906758\pi$
$614$			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	0.613705	−	0.789535i	$-0.289678\pi$
$617$	1.30303	+	0.946709i	0.0524581	+	0.0381131i	−0.561247	+	0.827648i	$0.689678\pi$
$618$	27.1318	+	8.45187i	1.09140	+	0.339984i
$619$		−	37.0865i		−	1.49063i	−0.666711	−	0.745316i	$-0.732298\pi$
$619$		−	37.0865i		−	1.49063i	0.666711	−	0.745316i	$-0.267702\pi$
$620$	0.0780968	−	12.4497i	0.00313644	−	0.499990i
$621$	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
$630$	10.1864	−	27.3522i	0.405838	−	1.08974i
$631$	33.9714	+	11.0380i	1.35238	+	0.439414i	0.893491	−	0.449080i	$-0.148248\pi$
$631$	33.9714	+	11.0380i	1.35238	+	0.439414i	0.458887	+	0.888495i	$0.348248\pi$
$632$	−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
$635$	−10.7835	+	2.72435i	−0.427929	+	0.108112i
$636$	−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
$640$	1.19084	+	1.89259i	0.0470721	+	0.0748112i
$641$	−6.35205	+	4.61504i	−0.250891	+	0.182283i	−0.706122	−	0.708091i	$-0.749557\pi$
$641$	−6.35205	+	4.61504i	−0.250891	+	0.182283i	0.455231	+	0.890374i	$0.349557\pi$
$642$	−13.6626	−	9.67452i	−0.539220	−	0.381823i
$643$	−6.09822	−	18.7684i	−0.240490	−	0.740154i	−0.996345	−	0.0854146i	$-0.972779\pi$
$643$	−6.09822	−	18.7684i	−0.240490	−	0.740154i	0.755855	−	0.654739i	$-0.227221\pi$
$644$	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	0.621498	−	0.783416i	$-0.286524\pi$
$647$	16.8851	+	5.48629i	0.663821	+	0.215688i	0.0423224	+	0.999104i	$0.486524\pi$
$648$	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	−0.713654	+	0.700499i	$0.752961\pi$
$653$	−40.8964	+	29.7130i	−1.60040	+	1.16276i	−0.886745	+	0.462259i	$0.847039\pi$
$654$	24.7560	−	0.301429i	0.968035	−	0.0117868i
$655$	−19.7623	+	12.4347i	−0.772178	+	0.485863i
$656$			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	$-0.539864\pi$
$659$	9.17022	−	2.97959i	0.357221	−	0.116068i	0.482129	+	0.876100i	$0.339864\pi$
$660$	−0.341634	+	0.0907498i	−0.0132981	+	0.00353243i
$661$	−1.73269	+	1.25887i	−0.0673939	+	0.0489645i	−0.620972	−	0.783833i	$-0.713262\pi$
$661$	−1.73269	+	1.25887i	−0.0673939	+	0.0489645i	0.553578	+	0.832797i	$0.313262\pi$
$662$	−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
$665$	8.18924	−	20.4524i	0.317565	−	0.793109i
$666$	−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
$670$	1.54997	+	0.103531i	0.0598804	+	0.00399974i
$671$	−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	0.886145	+	0.463408i	$0.153373\pi$
$673$	11.4567	+	35.2601i	0.441623	+	1.35918i	−0.444522	+	0.895768i	$0.646627\pi$
$674$	3.07499	+	9.46384i	0.118444	+	0.364533i
$675$	−5.60111	−	25.3698i	−0.215587	−	0.976485i
$676$	−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
$680$	2.94048	+	0.196410i	0.112762	+	0.00753200i
$681$	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	$0.292321\pi$
$684$	2.25593	+	6.40777i	0.0862576	+	0.245007i
$685$	−1.56987	−	6.21382i	−0.0599816	−	0.237418i
$686$	−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
$690$	−5.25338	−	19.7768i	−0.199993	−	0.752888i
$691$	−4.05748	−	12.4876i	−0.154354	−	0.475052i	0.843741	−	0.536750i	$-0.180348\pi$
$691$	−4.05748	−	12.4876i	−0.154354	−	0.475052i	−0.998095	+	0.0616984i	$0.980348\pi$
$692$	−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
$695$	−1.90892	−	7.55585i	−0.0724094	−	0.286610i
$696$	−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
$700$	−19.6124	−	9.41471i	−0.741278	−	0.355843i
$701$	−7.35988	−	10.1300i	−0.277979	−	0.382605i	0.647084	−	0.762419i	$-0.275988\pi$
$701$	−7.35988	−	10.1300i	−0.277979	−	0.382605i	−0.925063	+	0.379813i	$0.875988\pi$
$702$	−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
$705$	−23.6101	+	6.27164i	−0.889206	+	0.236204i
$706$	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	0.640139	−	0.768259i	$-0.278877\pi$
$709$	18.8107	+	6.11196i	0.706450	+	0.229540i	0.0663116	+	0.997799i	$0.478877\pi$
$710$	−1.87142	−	7.40743i	−0.0702332	−	0.277996i
$711$	−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
$715$	0.0210490	−	0.315127i	0.000787189	−	0.0117851i
$716$	−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	$0.668819\pi$
$720$	6.46192	−	1.80101i	0.240821	−	0.0671198i
$721$	−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
$725$	21.7344	+	20.7284i	0.807195	+	0.769834i
$726$	−19.0367	+	0.231791i	−0.706519	+	0.00860258i
$727$	40.3675	−	13.1162i	1.49715	−	0.486452i	0.557962	−	0.829866i	$-0.311583\pi$
$727$	40.3675	−	13.1162i	1.49715	−	0.486452i	0.939184	+	0.343414i	$0.111583\pi$
$728$	−3.95780	+	5.44744i	−0.146686	+	0.201896i
$729$	26.9280	−	1.97066i	0.997333	−	0.0729875i
$730$	−12.2997	−	4.92485i	−0.455231	−	0.182277i
$731$	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	$-0.253149\pi$
$733$	22.9244	+	7.44858i	0.846731	+	0.275120i	0.146655	+	0.989188i	$0.453149\pi$
$734$	−17.4946	+	12.7106i	−0.645737	+	0.469156i
$735$	−44.6608	+	11.8634i	−1.64734	+	0.437590i
$736$	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	$0.232596\pi$
$739$			36.2863i			1.33481i	−0.744694	+	0.667406i	$0.767404\pi$
$740$	9.60465	+	15.2646i	0.353074	+	0.561137i
$741$	−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
$750$	−19.2108	+	2.43825i	−0.701479	+	0.0890322i
$751$	−9.65633	+	29.7191i	−0.352365	+	1.08447i	0.605157	+	0.796106i	$0.293110\pi$
$751$	−9.65633	+	29.7191i	−0.352365	+	1.08447i	−0.957522	+	0.288361i	$0.906890\pi$
$752$	−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
$755$	43.3051	−	27.2481i	1.57604	−	0.991660i
$756$	12.6121	−	18.7638i	0.458699	−	0.682431i
$757$	−43.1953	−	31.3832i	−1.56996	−	1.14064i	−0.927195	−	0.374580i	$-0.877787\pi$
$757$	−43.1953	−	31.3832i	−1.56996	−	1.14064i	−0.642766	−	0.766063i	$-0.722213\pi$
$758$	4.39320	+	13.5209i	0.159568	+	0.491101i
$759$	0.0101688	+	0.835152i	0.000369105	+	0.0303141i
$760$	4.90917	−	1.24026i	0.178074	−	0.0449889i
$761$	11.6202	+	35.7633i	0.421232	+	1.29642i	0.906556	+	0.422085i	$0.138702\pi$
$761$	11.6202	+	35.7633i	0.421232	+	1.29642i	−0.485324	+	0.874334i	$0.661298\pi$
$762$	−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
$765$	3.08555	−	8.28518i	0.111558	−	0.299551i
$766$	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	0.714774	+	0.699356i	$0.246530\pi$
$773$	32.2242	+	44.3528i	1.15902	+	1.59526i	0.444250	+	0.895903i	$0.353470\pi$
$774$	6.09943	−	20.4539i	0.219239	−	0.735199i
$775$	−10.5100	+	25.7787i	−0.377531	+	0.925997i
$776$			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
$780$	−0.326617	+	5.98474i	−0.0116948	+	0.214288i
$781$			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
$785$	47.2734	+	3.15765i	1.68726	+	0.112701i
$786$	−17.1315	+	5.79788i	−0.611059	+	0.206804i
$787$	−5.20904	+	3.78459i	−0.185682	+	0.134906i	−0.676743	−	0.736219i	$-0.736609\pi$
$787$	−5.20904	+	3.78459i	−0.185682	+	0.134906i	0.491061	+	0.871125i	$0.336609\pi$
$788$	12.1652	−	16.7439i	0.433366	−	0.596478i
$789$	22.2477	−	31.4187i	0.792037	−	1.11854i
$790$	2.73653	+	10.8317i	0.0973613	+	0.385374i
$791$	−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
$795$	−4.12301	+	10.6718i	−0.146228	+	0.378490i
$796$	−13.0198	−	17.9202i	−0.461474	−	0.635165i
$797$	1.08622	−	0.352933i	0.0384758	−	0.0125015i	−0.289716	−	0.957113i	$-0.593561\pi$
$797$	1.08622	−	0.352933i	0.0384758	−	0.0125015i	0.328192	+	0.944611i	$0.393561\pi$
$798$	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	0.136850	−	0.990592i	$-0.456302\pi$
$809$	−21.7011	−	15.7668i	−0.762970	−	0.554330i	−0.899820	+	0.436262i	$0.856302\pi$
$810$	0.362118	−	20.1214i	0.0127235	−	0.706992i
$811$	−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
$815$	10.8147	−	27.0094i	0.378823	−	0.946099i
$816$	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
$820$	4.46011	−	11.1390i	0.155754	−	0.388990i
$821$	−21.3906	−	15.5412i	−0.746537	−	0.542391i	0.148215	−	0.988955i	$-0.452647\pi$
$821$	−21.3906	−	15.5412i	−0.746537	−	0.542391i	−0.894752	+	0.446564i	$0.852647\pi$
$822$	−0.0604426	−	4.96407i	−0.00210818	−	0.173142i
$823$	−0.533713	−	1.64260i	−0.0186041	−	0.0572574i	0.941323	−	0.337506i	$-0.109583\pi$
$823$	−0.533713	−	1.64260i	−0.0186041	−	0.0572574i	−0.959928	+	0.280248i	$0.909583\pi$
$824$	9.64380	−	13.2736i	0.335958	−	0.462406i
$825$	0.784610	+	0.0955769i	0.0273166	+	0.00332756i
$826$	10.3232	−	31.7715i	0.359189	−	1.10547i
$827$	−2.19104	−	3.01571i	−0.0761900	−	0.104867i	0.769221	−	0.638983i	$-0.220644\pi$
$827$	−2.19104	−	3.01571i	−0.0761900	−	0.104867i	−0.845411	+	0.534116i	$0.820644\pi$
$828$	−0.385929	−	15.8456i	−0.0134119	−	0.550671i
$829$	48.7453	−	15.8383i	1.69300	−	0.550088i	0.705635	−	0.708576i	$-0.250662\pi$
$829$	48.7453	−	15.8383i	1.69300	−	0.550088i	0.987361	+	0.158488i	$0.0506619\pi$
$830$	−16.0539	+	10.1013i	−0.557238	+	0.350621i
$831$	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
$835$	43.1068	+	2.87934i	1.49177	+	0.0996435i
$836$	−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	0.667041	−	0.745021i	$-0.267561\pi$
$839$	−7.17310	−	9.87293i	−0.247643	−	0.340851i	−0.914684	+	0.404170i	$0.867561\pi$
$840$	−13.0730	−	10.6332i	−0.451063	−	0.366880i
$841$	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
$845$	22.0145	+	8.81473i	0.757323	+	0.303236i
$846$	−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
$850$	−5.94073	−	2.85178i	−0.203765	−	0.0978154i
$851$	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	$-0.614631\pi$
$853$	18.8833	−	25.9907i	0.646553	−	0.889903i	0.998944	+	0.0459494i	$0.0146313\pi$
$854$	−10.3277	−	31.7855i	−0.353408	−	1.08768i
$855$	0.643047	−	15.1766i	0.0219918	−	0.519030i
$856$	−7.81952	+	5.68121i	−0.267266	+	0.194180i
$857$	−0.173572	+	0.534201i	−0.00592912	+	0.0182479i	−0.953977	−	0.299879i	$-0.903054\pi$
$857$	−0.173572	+	0.534201i	−0.00592912	+	0.0182479i	0.948048	+	0.318127i	$0.103054\pi$
$858$	0.0727596	−	0.233570i	0.00248397	−	0.00797393i
$859$	1.26060	−	0.409593i	0.0430111	−	0.0139751i	−0.287432	−	0.957801i	$-0.592802\pi$
$859$	1.26060	−	0.409593i	0.0430111	−	0.0139751i	0.330444	+	0.943826i	$0.392802\pi$
$860$	−14.7689	−	5.91355i	−0.503616	−	0.201650i
$861$	−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
$865$	30.1171	−	7.60882i	1.02401	−	0.258708i
$866$	−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
$870$	12.6285	+	19.5385i	0.428146	+	0.662416i
$871$	−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
$875$	32.8870	+	35.8449i	1.11178	+	1.21178i
$876$	−8.37547	−	5.93069i	−0.282981	−	0.200379i
$877$	−25.0413	+	8.13641i	−0.845585	+	0.274747i	−0.699596	−	0.714539i	$-0.746637\pi$
$877$	−25.0413	+	8.13641i	−0.845585	+	0.274747i	−0.145989	+	0.989286i	$0.546637\pi$
$878$	−7.09587	+	5.15545i	−0.239474	+	0.173988i
$879$	−8.62430	−	25.4829i	−0.290890	−	0.859517i
$880$	−0.0136015	+	0.203629i	−0.000458506	+	0.00686434i
$881$	14.8053	+	10.7567i	0.498803	+	0.362401i	0.808560	−	0.588414i	$-0.200248\pi$
$881$	14.8053	+	10.7567i	0.498803	+	0.362401i	−0.309757	+	0.950816i	$0.600248\pi$
$882$	−35.7832	+	0.871523i	−1.20488	+	0.0293457i
$883$	43.2113	+	31.3949i	1.45418	+	1.05652i	0.984833	+	0.173506i	$0.0555097\pi$
$883$	43.2113	+	31.3949i	1.45418	+	1.05652i	0.469344	+	0.883015i	$0.344490\pi$
$884$	−1.19885	+	1.65007i	−0.0403215	+	0.0554978i
$885$	−7.63423	−	28.7396i	−0.256622	−	0.966072i
$886$	−11.9073	−	8.65119i	−0.400035	−	0.290642i
$887$	−2.83555	+	2.06015i	−0.0952086	+	0.0691731i	−0.634371	−	0.773029i	$-0.718741\pi$
$887$	−2.83555	+	2.06015i	−0.0952086	+	0.0691731i	0.539162	+	0.842202i	$0.318741\pi$
$888$	4.47833	+	13.2325i	0.150283	+	0.444053i
$889$	12.7209	+	17.5088i	0.426645	+	0.587226i
$890$	−25.3685	−	10.1577i	−0.850353	−	0.340486i
$891$	−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
$895$	17.2960	+	27.4883i	0.578141	+	0.918834i
$896$	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
$900$	−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
$903$	−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	$-0.703275\pi$
$907$	−18.2616	+	5.93355i	−0.606366	+	0.197020i	−0.0102884	+	0.999947i	$0.503275\pi$
$908$	−7.06655	−	21.7486i	−0.234512	−	0.721752i
$909$	34.0569	−	11.9901i	1.12960	−	0.397687i
$910$	12.7436	−	8.01841i	0.422446	−	0.265808i
$911$	39.2198	−	28.4949i	1.29941	−	0.944077i	0.299461	−	0.954109i	$-0.403193\pi$
$911$	39.2198	−	28.4949i	1.29941	−	0.944077i	0.999950	+	0.0100315i	$0.00319318\pi$
$912$	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
$915$	−23.0791	−	18.7718i	−0.762972	−	0.620577i
$916$	−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	−0.986106	−	0.166120i	$-0.946876\pi$
$919$	−2.74916	+	8.46106i	−0.0906866	+	0.279105i	0.895419	+	0.445224i	$0.146876\pi$
$920$	−11.7878	−	0.787373i	−0.388633	−	0.0259589i
$921$	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	$0.321426\pi$
$930$	−12.5717	+	17.5200i	−0.412243	+	0.574505i
$931$	−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	$-0.0299355\pi$
$937$	53.4405	+	17.3639i	1.74583	+	0.567253i	0.750245	+	0.661160i	$0.229935\pi$
$938$	−0.934063	−	2.87475i	−0.0304983	−	0.0938640i
$939$	30.1034	+	21.3163i	0.982388	+	0.695631i
$940$	−0.939988	+	14.0726i	−0.0306590	+	0.458999i
$941$	−5.96893	+	18.3705i	−0.194582	+	0.598861i	0.805400	+	0.592732i	$0.201951\pi$
$941$	−5.96893	+	18.3705i	−0.194582	+	0.598861i	−0.999981	+	0.00612852i	$0.998049\pi$
$942$	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
$945$	−41.7769	+	28.4677i	−1.35900	+	0.926055i
$946$	0.525330	+	0.381675i	0.0170800	+	0.0124093i
$947$	−41.5576	+	13.5029i	−1.35044	+	0.438785i	−0.892841	−	0.450372i	$-0.851291\pi$
$947$	−41.5576	+	13.5029i	−1.35044	+	0.438785i	−0.457601	+	0.889158i	$0.651291\pi$
$948$	0.105361	+	8.65316i	0.00342196	+	0.281042i
$949$	7.41824	−	5.38966i	0.240806	−	0.174956i
$950$	−11.2216	−	1.50582i	−0.364076	−	0.0488551i
$951$	−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	$-0.635671\pi$
$953$	−6.56662	+	2.13362i	−0.212714	+	0.0691148i	0.200722	+	0.979648i	$0.435671\pi$
$954$	−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
$960$	0.211054	−	3.86723i	0.00681174	−	0.124814i
$961$	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
$965$	18.6808	−	11.7541i	0.601355	−	0.378379i
$966$	−31.9251	+	23.7942i	−1.02717	+	0.765564i
$967$	15.0919			0.485324			0.242662	−	0.970111i	$-0.421979\pi$
$967$	15.0919			0.485324			0.242662	+	0.970111i	$0.421979\pi$
$968$	−3.39661	+	10.4537i	−0.109171	+	0.335995i
$969$	2.98721	−	4.21861i	0.0959629	−	0.135521i
$970$	9.09275	−	22.7089i	0.291951	−	0.729138i
$971$	19.4428	+	26.7608i	0.623950	+	0.858793i	0.997633	−	0.0687630i	$-0.0219052\pi$
$971$	19.4428	+	26.7608i	0.623950	+	0.858793i	−0.373683	+	0.927556i	$0.621905\pi$
$972$	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
$975$	5.65240	−	12.1519i	0.181022	−	0.389173i
$976$	4.51493	−	6.21427i	0.144519	−	0.198914i
$977$	−7.21194	−	5.23978i	−0.230731	−	0.167636i	0.466413	−	0.884567i	$-0.345546\pi$
$977$	−7.21194	−	5.23978i	−0.230731	−	0.167636i	−0.697144	+	0.716931i	$0.745546\pi$
$978$	13.0235	−	18.3921i	0.416445	−	0.588115i
$979$	0.902356	+	0.655600i	0.0288394	+	0.0209531i
$980$	−1.77808	+	26.6198i	−0.0567988	+	0.850339i
$981$	−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	$-0.578588\pi$
$983$	4.00855	−	1.30246i	0.127853	−	0.0415419i	0.372245	+	0.928135i	$0.378588\pi$
$984$	5.37103	−	7.58511i	0.171222	−	0.241804i
$985$	−39.1702	+	24.6464i	−1.24807	+	0.785299i
$986$			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
$990$	0.573752	+	0.213675i	0.0182350	+	0.00679105i
$991$		−	48.4782i		−	1.53996i	−0.638068	−	0.769980i	$-0.720266\pi$
$991$		−	48.4782i		−	1.53996i	0.638068	−	0.769980i	$-0.279734\pi$
$992$	−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
$995$	12.1322	+	48.0214i	0.384616	+	1.52238i
$996$	−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.a.449.32	yes	128
3.2	odd	2		930.2.y.b.449.20	yes	128
5.4	even	2		930.2.y.b.449.1	yes	128
15.14	odd	2	inner	930.2.y.a.449.13	yes	128
31.29	odd	10	inner	930.2.y.a.29.13	✓	128
93.29	even	10		930.2.y.b.29.1	yes	128
155.29	odd	10		930.2.y.b.29.20	yes	128
465.29	even	10	inner	930.2.y.a.29.32	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.y.a.29.13	✓	128	31.29	odd	10	inner
930.2.y.a.29.32	yes	128	465.29	even	10	inner
930.2.y.a.449.13	yes	128	15.14	odd	2	inner
930.2.y.a.449.32	yes	128	1.1	even	1	trivial
930.2.y.b.29.1	yes	128	93.29	even	10
930.2.y.b.29.20	yes	128	155.29	odd	10
930.2.y.b.449.1	yes	128	5.4	even	2
930.2.y.b.449.20	yes	128	3.2	odd	2

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} +(0.149027 - 2.23110i) 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} +(-2.44385 + 3.00460i) 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} +(1.19084 + 1.89259i) 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} +(0.211054 - 3.86723i) q^{30} +(-4.69382 - 2.99467i) q^{31} +1.00000 q^{32} +(-0.0470159 + 0.150928i) q^{33} +(0.774673 - 1.06625i) q^{34} +(-8.23468 + 5.18136i) q^{35} +(0.857306 - 2.87490i) q^{36} +8.06544 q^{37} +(0.699747 - 2.15360i) q^{38} +(2.18754 + 1.54900i) q^{39} +(-2.07585 - 0.831180i) 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} +(-4.16919 + 5.25527i) 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} +(3.61828 + 3.45080i) 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} +(-0.108686 - 0.172734i) q^{55} +4.35101i q^{56} +(-3.14475 + 2.34382i) q^{57} +(1.85621 - 5.71284i) q^{58} +(-4.51294 + 6.21153i) q^{59} +(2.10235 + 3.25271i) q^{60} +7.68126i q^{61} +(5.55760 - 0.336219i) q^{62} +(12.5087 + 3.73015i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(-3.35502 + 0.847615i) q^{65} +(-0.0506769 - 0.149739i) q^{66} +0.694711i q^{67} +1.31795i q^{68} +(8.66819 - 2.93362i) q^{69} +(3.61647 - 9.03203i) 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} +(-1.66058 - 8.49956i) 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} +(2.16795 - 0.547714i) 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} +(1.09545 - 2.73587i) q^{85} +(2.19855 - 6.76643i) q^{86} +(-8.34205 + 6.21743i) q^{87} -0.0912687 q^{88} +(3.77643 - 11.6226i) q^{89} +(0.283978 - 6.70219i) q^{90} +(3.95780 + 5.44744i) q^{91} -5.28342i q^{92} +(-8.19248 - 5.08755i) q^{93} -6.30750 q^{94} +(0.337461 - 5.05216i) 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	\( 128 q - 32 q^{2} - 32 q^{4} + 2 q^{5} - 32 q^{8} - 4 q^{9} + 2 q^{10} + 25 q^{15} - 32 q^{16} + 6 q^{18} - 8 q^{19} - 3 q^{20} - 20 q^{23} - 10 q^{25} - 48 q^{31} + 128 q^{32} - 8 q^{33} + 10 q^{34} + 16 q^{35} - 4 q^{36} + 12 q^{38} + 4 q^{39} - 3 q^{40} + 37 q^{45} + 10 q^{46} + 6 q^{47} + 46 q^{49} - 5 q^{50} + 34 q^{51} - 20 q^{53} - 25 q^{60} - 8 q^{62} + 36 q^{63} - 32 q^{64} - 8 q^{66} + 8 q^{69} + 16 q^{70} + 6 q^{72} + 5 q^{75} + 12 q^{76} + 50 q^{77} + 4 q^{78} - 10 q^{79} + 2 q^{80} - 24 q^{81} - 40 q^{83} - 30 q^{85} - 4 q^{87} - 53 q^{90} + 20 q^{91} - 26 q^{93} - 4 q^{94} - 26 q^{95} - 124 q^{98}+O(q^{100}) \) 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

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more