LMFDB - Embedded newform 930.2.v.a.401.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(401,930)]

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, 0, 3]))

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

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

chi := DirichletCharacter("930.401");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.v (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:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			401.3
Character	$\chi$	$=$	930.401
Dual form			930.2.v.a.821.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.587785 + 0.809017i) q^{2} +(-0.950729 + 1.44780i) q^{3} +(-0.309017 - 0.951057i) q^{4} -1.00000i q^{5} +(-0.612467 - 1.62015i) q^{6} +(-0.531003 - 1.63426i) q^{7} +(0.951057 + 0.309017i) q^{8} +(-1.19223 - 2.75292i) q^{9} +O(q^{10})$	\(q+(-0.587785 + 0.809017i) q^{2} +(-0.950729 + 1.44780i) q^{3} +(-0.309017 - 0.951057i) q^{4} -1.00000i q^{5} +(-0.612467 - 1.62015i) q^{6} +(-0.531003 - 1.63426i) q^{7} +(0.951057 + 0.309017i) q^{8} +(-1.19223 - 2.75292i) q^{9} +(0.809017 + 0.587785i) q^{10} +(-0.342877 - 1.05527i) q^{11} +(1.67073 + 0.456803i) q^{12} +(-1.47125 - 2.02501i) q^{13} +(1.63426 + 0.531003i) q^{14} +(1.44780 + 0.950729i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-1.96546 + 6.04907i) q^{17} +(2.92794 + 0.653595i) q^{18} +(3.45827 + 2.51258i) q^{19} +(-0.951057 + 0.309017i) q^{20} +(2.87091 + 0.784953i) q^{21} +(1.05527 + 0.342877i) q^{22} +(-1.81096 + 5.57357i) q^{23} +(-1.35159 + 1.08314i) q^{24} -1.00000 q^{25} +2.50305 q^{26} +(5.11916 + 0.891180i) q^{27} +(-1.39018 + 1.01003i) q^{28} +(2.90003 + 2.10699i) q^{29} +(-1.62015 + 0.612467i) q^{30} +(3.44165 + 4.37665i) q^{31} -1.00000i q^{32} +(1.85379 + 0.506856i) q^{33} +(-3.73853 - 5.14564i) q^{34} +(-1.63426 + 0.531003i) q^{35} +(-2.24977 + 1.98458i) q^{36} +3.21258i q^{37} +(-4.06544 + 1.32094i) q^{38} +(4.33056 - 0.204843i) q^{39} +(0.309017 - 0.951057i) q^{40} +(-0.0778050 + 0.107089i) q^{41} +(-2.32252 + 1.86123i) q^{42} +(-4.78323 + 6.58355i) q^{43} +(-0.897663 + 0.652190i) q^{44} +(-2.75292 + 1.19223i) q^{45} +(-3.44465 - 4.74116i) q^{46} +(3.11192 + 4.28320i) q^{47} +(-0.0818375 - 1.73012i) q^{48} +(3.27428 - 2.37891i) q^{49} +(0.587785 - 0.809017i) q^{50} +(-6.88919 - 8.59661i) q^{51} +(-1.47125 + 2.02501i) q^{52} +(1.18858 - 3.65808i) q^{53} +(-3.72995 + 3.61767i) q^{54} +(-1.05527 + 0.342877i) q^{55} -1.71836i q^{56} +(-6.92558 + 2.61809i) q^{57} +(-3.40919 + 1.10771i) q^{58} +(-3.90466 - 5.37431i) q^{59} +(0.456803 - 1.67073i) q^{60} +11.6180i q^{61} +(-5.56373 + 0.211825i) q^{62} +(-3.86591 + 3.41022i) q^{63} +(0.809017 + 0.587785i) q^{64} +(-2.02501 + 1.47125i) q^{65} +(-1.49969 + 1.20183i) q^{66} +14.4962 q^{67} +6.36036 q^{68} +(-6.34766 - 7.92086i) q^{69} +(0.531003 - 1.63426i) q^{70} +(7.23610 + 2.35115i) q^{71} +(-0.283177 - 2.98661i) q^{72} +(-12.8859 + 4.18687i) q^{73} +(-2.59903 - 1.88830i) q^{74} +(0.950729 - 1.44780i) q^{75} +(1.32094 - 4.06544i) q^{76} +(-1.54251 + 1.12070i) q^{77} +(-2.37972 + 3.62390i) q^{78} +(-2.21018 - 0.718130i) q^{79} +(0.587785 + 0.809017i) q^{80} +(-6.15718 + 6.56423i) q^{81} +(-0.0409045 - 0.125891i) q^{82} +(0.996203 + 0.723784i) q^{83} +(-0.140626 - 2.97296i) q^{84} +(6.04907 + 1.96546i) q^{85} +(-2.51469 - 7.73943i) q^{86} +(-5.80764 + 2.19547i) q^{87} -1.10957i q^{88} +(-4.04961 - 12.4634i) q^{89} +(0.653595 - 2.92794i) q^{90} +(-2.52814 + 3.47969i) q^{91} +5.86040 q^{92} +(-9.60857 + 0.821804i) q^{93} -5.29432 q^{94} +(2.51258 - 3.45827i) q^{95} +(1.44780 + 0.950729i) q^{96} +(3.58885 + 11.0454i) q^{97} +4.04724i q^{98} +(-2.49628 + 2.20203i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 20 q^{4} + 12 q^{7} - 8 q^{9}+O(q^{10}) $ 80 * q + 20 * q^4 + 12 * q^7 - 8 * q^9	$ 80 q + 20 q^{4} + 12 q^{7} - 8 q^{9} + 20 q^{10} - 10 q^{13} - 20 q^{16} - 12 q^{18} - 12 q^{19} + 30 q^{21} + 10 q^{22} - 80 q^{25} + 18 q^{28} + 16 q^{31} + 72 q^{33} + 10 q^{34} + 8 q^{36} + 54 q^{39} - 20 q^{40} + 50 q^{43} + 8 q^{45} - 10 q^{46} + 8 q^{49} - 44 q^{51} - 10 q^{52} - 10 q^{55} + 30 q^{58} + 28 q^{63} + 20 q^{64} + 66 q^{66} + 60 q^{67} + 20 q^{69} - 12 q^{70} + 12 q^{72} - 20 q^{73} - 18 q^{76} + 8 q^{78} + 40 q^{79} + 16 q^{81} - 4 q^{82} - 60 q^{84} - 72 q^{87} - 12 q^{90} + 10 q^{91} + 104 q^{93} - 12 q^{94} - 178 q^{97}+O(q^{100}) $ 80 * q + 20 * q^4 + 12 * q^7 - 8 * q^9 + 20 * q^10 - 10 * q^13 - 20 * q^16 - 12 * q^18 - 12 * q^19 + 30 * q^21 + 10 * q^22 - 80 * q^25 + 18 * q^28 + 16 * q^31 + 72 * q^33 + 10 * q^34 + 8 * q^36 + 54 * q^39 - 20 * q^40 + 50 * q^43 + 8 * q^45 - 10 * q^46 + 8 * q^49 - 44 * q^51 - 10 * q^52 - 10 * q^55 + 30 * q^58 + 28 * q^63 + 20 * q^64 + 66 * q^66 + 60 * q^67 + 20 * q^69 - 12 * q^70 + 12 * q^72 - 20 * q^73 - 18 * q^76 + 8 * q^78 + 40 * q^79 + 16 * q^81 - 4 * q^82 - 60 * q^84 - 72 * q^87 - 12 * q^90 + 10 * q^91 + 104 * q^93 - 12 * q^94 - 178 * q^97

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 $

$2$	−0.587785	+	0.809017i	−0.415627	+	0.572061i
$2$	−0.587785	+	0.809017i	−0.415627	+	0.572061i
$3$	−0.950729	+	1.44780i	−0.548904	+	0.835886i
$3$	−0.950729	+	1.44780i	−0.548904	+	0.835886i
$4$	−0.309017	−	0.951057i	−0.154508	−	0.475528i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	−0.612467	−	1.62015i	−0.250039	−	0.661423i
$7$	−0.531003	−	1.63426i	−0.200700	−	0.617692i	−0.999863	−	0.0165764i	$-0.994723\pi$
$7$	−0.531003	−	1.63426i	−0.200700	−	0.617692i	0.799162	−	0.601115i	$-0.205277\pi$
$8$	0.951057	+	0.309017i	0.336249	+	0.109254i
$9$	−1.19223	−	2.75292i	−0.397410	−	0.917641i
$10$	0.809017	+	0.587785i	0.255834	+	0.185874i
$11$	−0.342877	−	1.05527i	−0.103381	−	0.318175i	0.885966	−	0.463750i	$-0.153497\pi$
$11$	−0.342877	−	1.05527i	−0.103381	−	0.318175i	−0.989347	+	0.145576i	$0.953497\pi$
$12$	1.67073	+	0.456803i	0.482298	+	0.131868i
$13$	−1.47125	−	2.02501i	−0.408052	−	0.561636i	0.554690	−	0.832057i	$-0.312837\pi$
$13$	−1.47125	−	2.02501i	−0.408052	−	0.561636i	−0.962742	+	0.270421i	$0.912837\pi$
$14$	1.63426	+	0.531003i	0.436774	+	0.141916i
$15$	1.44780	+	0.950729i	0.373819	+	0.245477i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−1.96546	+	6.04907i	−0.476694	+	1.46711i	0.366965	+	0.930235i	$0.380397\pi$
$17$	−1.96546	+	6.04907i	−0.476694	+	1.46711i	−0.843659	+	0.536879i	$0.819603\pi$
$18$	2.92794	+	0.653595i	0.690121	+	0.154054i
$19$	3.45827	+	2.51258i	0.793381	+	0.576425i	0.908965	−	0.416873i	$-0.136874\pi$
$19$	3.45827	+	2.51258i	0.793381	+	0.576425i	−0.115584	+	0.993298i	$0.536874\pi$
$20$	−0.951057	+	0.309017i	−0.212663	+	0.0690983i
$21$	2.87091	+	0.784953i	0.626485	+	0.171291i
$22$	1.05527	+	0.342877i	0.224983	+	0.0731015i
$23$	−1.81096	+	5.57357i	−0.377612	+	1.16217i	0.564088	+	0.825715i	$0.309228\pi$
$23$	−1.81096	+	5.57357i	−0.377612	+	1.16217i	−0.941700	+	0.336454i	$0.890772\pi$
$24$	−1.35159	+	1.08314i	−0.275892	+	0.221096i
$25$	−1.00000			−0.200000
$26$	2.50305			0.490888
$27$	5.11916	+	0.891180i	0.985183	+	0.171508i
$28$	−1.39018	+	1.01003i	−0.262720	+	0.190877i
$29$	2.90003	+	2.10699i	0.538522	+	0.391259i	0.823536	−	0.567264i	$-0.191998\pi$
$29$	2.90003	+	2.10699i	0.538522	+	0.391259i	−0.285014	+	0.958523i	$0.591998\pi$
$30$	−1.62015	+	0.612467i	−0.295797	+	0.111821i
$31$	3.44165	+	4.37665i	0.618139	+	0.786069i
$31$	3.44165	+	4.37665i	0.618139	+	0.786069i
$32$		−	1.00000i		−	0.176777i
$33$	1.85379	+	0.506856i	0.322704	+	0.0882323i
$34$	−3.73853	−	5.14564i	−0.641152	−	0.882470i
$35$	−1.63426	+	0.531003i	−0.276240	+	0.0897558i
$36$	−2.24977	+	1.98458i	−0.374961	+	0.330763i
$37$			3.21258i			0.528144i	0.964503	+	0.264072i	$0.0850657\pi$
$37$			3.21258i			0.528144i	−0.964503	+	0.264072i	$0.914934\pi$
$38$	−4.06544	+	1.32094i	−0.659501	+	0.214285i
$39$	4.33056	−	0.204843i	0.693445	−	0.0328011i
$40$	0.309017	−	0.951057i	0.0488599	−	0.150375i
$41$	−0.0778050	+	0.107089i	−0.0121511	+	0.0167246i	−0.815049	−	0.579392i	$-0.803290\pi$
$41$	−0.0778050	+	0.107089i	−0.0121511	+	0.0167246i	0.802898	+	0.596116i	$0.203290\pi$
$42$	−2.32252	+	1.86123i	−0.358373	+	0.287195i
$43$	−4.78323	+	6.58355i	−0.729436	+	1.00398i	0.269721	+	0.962938i	$0.413068\pi$
$43$	−4.78323	+	6.58355i	−0.729436	+	1.00398i	−0.999157	+	0.0410439i	$0.986932\pi$
$44$	−0.897663	+	0.652190i	−0.135328	+	0.0983213i
$45$	−2.75292	+	1.19223i	−0.410382	+	0.177727i
$46$	−3.44465	−	4.74116i	−0.507887	−	0.699046i
$47$	3.11192	+	4.28320i	0.453921	+	0.624768i	0.973234	−	0.229816i	$-0.0738123\pi$
$47$	3.11192	+	4.28320i	0.453921	+	0.624768i	−0.519314	+	0.854584i	$0.673812\pi$
$48$	−0.0818375	−	1.73012i	−0.0118122	−	0.249721i
$49$	3.27428	−	2.37891i	0.467755	−	0.339844i
$50$	0.587785	−	0.809017i	0.0831254	−	0.114412i
$51$	−6.88919	−	8.59661i	−0.964680	−	1.20377i
$52$	−1.47125	+	2.02501i	−0.204026	+	0.280818i
$53$	1.18858	−	3.65808i	0.163264	−	0.502476i	−0.835640	−	0.549278i	$-0.814903\pi$
$53$	1.18858	−	3.65808i	0.163264	−	0.502476i	0.998904	+	0.0468017i	$0.0149029\pi$
$54$	−3.72995	+	3.61767i	−0.507581	+	0.492302i
$55$	−1.05527	+	0.342877i	−0.142292	+	0.0462335i
$56$		−	1.71836i		−	0.229626i
$57$	−6.92558	+	2.61809i	−0.917315	+	0.346774i
$58$	−3.40919	+	1.10771i	−0.447648	+	0.145450i
$59$	−3.90466	−	5.37431i	−0.508344	−	0.699675i	0.475295	−	0.879826i	$-0.342341\pi$
$59$	−3.90466	−	5.37431i	−0.508344	−	0.699675i	−0.983639	+	0.180151i	$0.942341\pi$
$60$	0.456803	−	1.67073i	0.0589730	−	0.215690i
$61$			11.6180i			1.48753i	0.668440	+	0.743766i	$0.266962\pi$
$61$			11.6180i			1.48753i	−0.668440	+	0.743766i	$0.733038\pi$
$62$	−5.56373	+	0.211825i	−0.706595	+	0.0269018i
$63$	−3.86591	+	3.41022i	−0.487059	+	0.429647i
$64$	0.809017	+	0.587785i	0.101127	+	0.0734732i
$65$	−2.02501	+	1.47125i	−0.251171	+	0.182487i
$66$	−1.49969	+	1.20183i	−0.184599	+	0.147935i
$67$	14.4962			1.77099			0.885494	−	0.464651i	$-0.153820\pi$
$67$	14.4962			1.77099			0.885494	+	0.464651i	$0.153820\pi$
$68$	6.36036			0.771307
$69$	−6.34766	−	7.92086i	−0.764168	−	0.953559i
$70$	0.531003	−	1.63426i	0.0634670	−	0.195331i
$71$	7.23610	+	2.35115i	0.858767	+	0.279030i	0.705113	−	0.709095i	$-0.250896\pi$
$71$	7.23610	+	2.35115i	0.858767	+	0.279030i	0.153653	+	0.988125i	$0.450896\pi$
$72$	−0.283177	−	2.98661i	−0.0333727	−	0.351975i
$73$	−12.8859	+	4.18687i	−1.50818	+	0.490036i	−0.942390	−	0.334515i	$-0.891427\pi$
$73$	−12.8859	+	4.18687i	−1.50818	+	0.490036i	−0.565787	+	0.824552i	$0.691427\pi$
$74$	−2.59903	−	1.88830i	−0.302131	−	0.219511i
$75$	0.950729	−	1.44780i	0.109781	−	0.167177i
$76$	1.32094	−	4.06544i	0.151522	−	0.466338i
$77$	−1.54251	+	1.12070i	−0.175785	+	0.127715i
$78$	−2.37972	+	3.62390i	−0.269450	+	0.410326i
$79$	−2.21018	−	0.718130i	−0.248664	−	0.0807959i	0.182033	−	0.983292i	$-0.441732\pi$
$79$	−2.21018	−	0.718130i	−0.248664	−	0.0807959i	−0.430697	+	0.902497i	$0.641732\pi$
$80$	0.587785	+	0.809017i	0.0657164	+	0.0904508i
$81$	−6.15718	+	6.56423i	−0.684131	+	0.729359i
$82$	−0.0409045	−	0.125891i	−0.00451715	−	0.0139024i
$83$	0.996203	+	0.723784i	0.109348	+	0.0794456i	0.641115	−	0.767445i	$-0.278472\pi$
$83$	0.996203	+	0.723784i	0.109348	+	0.0794456i	−0.531768	+	0.846890i	$0.678472\pi$
$84$	−0.140626	−	2.97296i	−0.0153436	−	0.324377i
$85$	6.04907	+	1.96546i	0.656113	+	0.213184i
$86$	−2.51469	−	7.73943i	−0.271166	−	0.834564i
$87$	−5.80764	+	2.19547i	−0.622644	+	0.235379i
$88$		−	1.10957i		−	0.118281i
$89$	−4.04961	−	12.4634i	−0.429258	−	1.32112i	−0.898858	−	0.438240i	$-0.855602\pi$
$89$	−4.04961	−	12.4634i	−0.429258	−	1.32112i	0.469601	−	0.882879i	$-0.344398\pi$
$90$	0.653595	−	2.92794i	0.0688949	−	0.308632i
$91$	−2.52814	+	3.47969i	−0.265022	+	0.364771i
$92$	5.86040			0.610988
$93$	−9.60857	+	0.821804i	−0.996362	+	0.0852172i
$94$	−5.29432			−0.546067
$95$	2.51258	−	3.45827i	0.257785	−	0.354811i
$96$	1.44780	+	0.950729i	0.147765	+	0.0970334i
$97$	3.58885	+	11.0454i	0.364393	+	1.12149i	0.950360	+	0.311152i	$0.100715\pi$
$97$	3.58885	+	11.0454i	0.364393	+	1.12149i	−0.585967	+	0.810335i	$0.699285\pi$
$98$			4.04724i			0.408833i
$99$	−2.49628	+	2.20203i	−0.250885	+	0.221312i
$100$	0.309017	+	0.951057i	0.0309017	+	0.0951057i
$101$	−15.6772	−	5.09384i	−1.55994	−	0.506856i	−0.603151	−	0.797627i	$-0.706088\pi$
$101$	−15.6772	−	5.09384i	−1.55994	−	0.506856i	−0.956793	+	0.290771i	$0.906088\pi$
$102$	11.0042	−	0.520516i	1.08958	−	0.0515388i
$103$	−8.86997	−	6.44441i	−0.873984	−	0.634987i	0.0576691	−	0.998336i	$-0.481633\pi$
$103$	−8.86997	−	6.44441i	−0.873984	−	0.634987i	−0.931653	+	0.363349i	$0.881633\pi$
$104$	−0.773484	−	2.38054i	−0.0758463	−	0.233431i
$105$	0.784953	−	2.87091i	0.0766036	−	0.280172i
$106$	2.26082	+	3.11175i	0.219590	+	0.302240i
$107$	11.1941	+	3.63718i	1.08217	+	0.351619i	0.795217	−	0.606325i	$-0.207357\pi$
$107$	11.1941	+	3.63718i	1.08217	+	0.351619i	0.286955	+	0.957944i	$0.407357\pi$
$108$	−0.734345	−	5.14400i	−0.0706624	−	0.494982i
$109$	−16.0577	+	11.6666i	−1.53805	+	1.11746i	−0.586508	+	0.809944i	$0.699498\pi$
$109$	−16.0577	+	11.6666i	−1.53805	+	1.11746i	−0.951543	+	0.307515i	$0.900502\pi$
$110$	0.342877	−	1.05527i	0.0326920	−	0.100616i
$111$	−4.65116	−	3.05429i	−0.441468	−	0.289900i
$112$	1.39018	+	1.01003i	0.131360	+	0.0954386i
$113$	8.97678	−	2.91673i	0.844464	−	0.274383i	0.145339	−	0.989382i	$-0.453573\pi$
$113$	8.97678	−	2.91673i	0.844464	−	0.274383i	0.699126	+	0.714999i	$0.253573\pi$
$114$	1.95268	−	7.14178i	0.182885	−	0.668889i
$115$	5.57357	+	1.81096i	0.519738	+	0.168873i
$116$	1.10771	−	3.40919i	0.102848	−	0.316535i
$117$	−3.82062	+	6.46452i	−0.353216	+	0.597645i
$118$	6.64301			0.611539
$119$	10.9294			1.00190
$120$	1.08314	+	1.35159i	0.0988771	+	0.123383i
$121$	7.90317	−	5.74199i	0.718470	−	0.521999i
$122$	−9.39915	−	6.82889i	−0.850959	−	0.618258i
$123$	−0.0810722	−	0.214459i	−0.00731003	−	0.0193371i
$124$	3.09891	−	4.62566i	0.278290	−	0.415397i
$125$			1.00000i			0.0894427i
$126$	−0.486600	−	5.13207i	−0.0433498	−	0.457201i
$127$	2.98427	+	4.10749i	0.264811	+	0.364481i	0.920629	−	0.390438i	$-0.127676\pi$
$127$	2.98427	+	4.10749i	0.264811	+	0.364481i	−0.655818	+	0.754919i	$0.727676\pi$
$128$	−0.951057	+	0.309017i	−0.0840623	+	0.0273135i
$129$	−4.98409	−	13.1843i	−0.438824	−	1.16081i
$130$		−	2.50305i		−	0.219532i
$131$	10.1594	−	3.30100i	0.887634	−	0.288410i	0.170510	−	0.985356i	$-0.445458\pi$
$131$	10.1594	−	3.30100i	0.887634	−	0.288410i	0.717123	+	0.696946i	$0.245458\pi$
$132$	−0.0908046	−	1.91969i	−0.00790353	−	0.167087i
$133$	2.26985	−	6.98589i	0.196821	−	0.605754i
$134$	−8.52063	+	11.7276i	−0.736070	+	1.01311i
$135$	0.891180	−	5.11916i	0.0767005	−	0.440587i
$136$	−3.73853	+	5.14564i	−0.320576	+	0.441235i
$137$	−15.2893	+	11.1083i	−1.30626	+	0.949050i	−0.999996	−	0.00289768i	$-0.999078\pi$
$137$	−15.2893	+	11.1083i	−1.30626	+	0.949050i	−0.306260	+	0.951948i	$0.599078\pi$
$138$	10.1392	−	0.479600i	0.863103	−	0.0408263i
$139$	0.852515	+	1.17339i	0.0723094	+	0.0995253i	0.843640	−	0.536910i	$-0.180408\pi$
$139$	0.852515	+	1.17339i	0.0723094	+	0.0995253i	−0.771330	+	0.636435i	$0.780408\pi$
$140$	1.01003	+	1.39018i	0.0853629	+	0.117492i
$141$	−9.15979	+	0.433274i	−0.771394	+	0.0364882i
$142$	−6.15539	+	4.47215i	−0.516549	+	0.375295i
$143$	−1.63246	+	2.24689i	−0.136513	+	0.187894i
$144$	2.58266	+	1.52639i	0.215222	+	0.127199i
$145$	2.10699	−	2.90003i	0.174976	−	0.240834i
$146$	4.18687	−	12.8859i	0.346508	−	1.06644i
$147$	0.331216	+	7.00219i	0.0273182	+	0.577531i
$148$	3.05534	−	0.992740i	0.251147	−	0.0816028i
$149$			10.4417i			0.855415i	0.903917	+	0.427708i	$0.140679\pi$
$149$			10.4417i			0.855415i	−0.903917	+	0.427708i	$0.859321\pi$
$150$	0.612467	+	1.62015i	0.0500078	+	0.132285i
$151$	7.90036	−	2.56698i	0.642922	−	0.208898i	0.0306316	−	0.999531i	$-0.490248\pi$
$151$	7.90036	−	2.56698i	0.642922	−	0.208898i	0.612291	+	0.790633i	$0.290248\pi$
$152$	2.51258	+	3.45827i	0.203797	+	0.280503i
$153$	18.9959	−	1.80111i	1.53573	−	0.145611i
$154$		−	1.90665i		−	0.153642i
$155$	4.37665	−	3.44165i	0.351541	−	0.276440i
$156$	−1.53303	−	4.05531i	−0.122741	−	0.324684i
$157$	12.6017	+	9.15568i	1.00573	+	0.730703i	0.963308	−	0.268397i	$-0.0864939\pi$
$157$	12.6017	+	9.15568i	1.00573	+	0.730703i	0.0424181	+	0.999100i	$0.486494\pi$
$158$	1.88009	−	1.36596i	0.149572	−	0.108670i
$159$	4.16614	+	5.19867i	0.330396	+	0.412281i
$160$	−1.00000			−0.0790569
$161$	10.0703			0.793649
$162$	−1.69147	−	8.83962i	−0.132895	−	0.694506i
$163$	−2.90937	+	8.95412i	−0.227879	+	0.701341i	0.770107	+	0.637915i	$0.220203\pi$
$163$	−2.90937	+	8.95412i	−0.227879	+	0.701341i	−0.997987	+	0.0634261i	$0.979797\pi$
$164$	0.125891	+	0.0409045i	0.00983045	+	0.00319411i
$165$	0.506856	−	1.85379i	0.0394587	−	0.144318i
$166$	−1.17111	+	0.380516i	−0.0908955	+	0.0295337i
$167$	9.65438	+	7.01432i	0.747078	+	0.542784i	0.894920	−	0.446227i	$-0.147233\pi$
$167$	9.65438	+	7.01432i	0.747078	+	0.542784i	−0.147842	+	0.989011i	$0.547233\pi$
$168$	2.48784	+	1.63370i	0.191941	+	0.126042i
$169$	2.08116	−	6.40514i	0.160089	−	0.492703i
$170$	−5.14564	+	3.73853i	−0.394653	+	0.286732i
$171$	2.79389	−	12.5159i	0.213654	−	0.957116i
$172$	7.73943	+	2.51469i	0.590126	+	0.191744i
$173$	0.496227	+	0.682998i	0.0377275	+	0.0519274i	0.827464	−	0.561519i	$-0.189783\pi$
$173$	0.496227	+	0.682998i	0.0377275	+	0.0519274i	−0.789737	+	0.613446i	$0.789783\pi$
$174$	1.63747	−	5.98894i	0.124136	−	0.454021i
$175$	0.531003	+	1.63426i	0.0401400	+	0.123538i
$176$	0.897663	+	0.652190i	0.0676639	+	0.0491607i
$177$	11.4932	−	0.543647i	0.863880	−	0.0408630i
$178$	12.4634	+	4.04961i	0.934172	+	0.303531i
$179$	0.295880	+	0.910626i	0.0221151	+	0.0680634i	0.961505	−	0.274787i	$-0.0886075\pi$
$179$	0.295880	+	0.910626i	0.0221151	+	0.0680634i	−0.939390	+	0.342851i	$0.888607\pi$
$180$	1.98458	+	2.24977i	0.147922	+	0.167688i
$181$		−	2.27314i		−	0.168961i	−0.996425	−	0.0844806i	$-0.973077\pi$
$181$		−	2.27314i		−	0.168961i	0.996425	−	0.0844806i	$-0.0269231\pi$
$182$	−1.32912	−	4.09062i	−0.0985212	−	0.303217i
$183$	−16.8205	−	11.0456i	−1.24341	−	0.816512i
$184$	−3.44465	+	4.74116i	−0.253943	+	0.349523i
$185$	3.21258			0.236193
$186$	4.98292	−	8.25654i	0.365366	−	0.605399i
$187$	7.05728			0.516080
$188$	3.11192	−	4.28320i	0.226960	−	0.312384i
$189$	−1.26187	−	8.83925i	−0.0917875	−	0.642961i
$190$	1.32094	+	4.06544i	0.0958311	+	0.294938i
$191$		−	7.17904i		−	0.519457i	−0.965682	−	0.259728i	$-0.916367\pi$
$191$		−	7.17904i		−	0.519457i	0.965682	−	0.259728i	$-0.0836330\pi$
$192$	−1.62015	+	0.612467i	−0.116924	+	0.0442010i
$193$	1.57038	+	4.83313i	0.113038	+	0.347896i	0.991533	−	0.129856i	$-0.0414516\pi$
$193$	1.57038	+	4.83313i	0.113038	+	0.347896i	−0.878494	+	0.477753i	$0.841452\pi$
$194$	−11.0454	−	3.58885i	−0.793011	−	0.257665i
$195$	−0.204843	−	4.33056i	−0.0146691	−	0.310118i
$196$	−3.27428	−	2.37891i	−0.233877	−	0.169922i
$197$	−3.61183	−	11.1161i	−0.257332	−	0.791987i	−0.993361	−	0.115037i	$-0.963301\pi$
$197$	−3.61183	−	11.1161i	−0.257332	−	0.791987i	0.736029	−	0.676950i	$-0.236699\pi$
$198$	−0.314205	−	3.31385i	−0.0223296	−	0.235505i
$199$	0.945986	+	1.30204i	0.0670592	+	0.0922991i	0.841229	−	0.540679i	$-0.181832\pi$
$199$	0.945986	+	1.30204i	0.0670592	+	0.0922991i	−0.774170	+	0.632978i	$0.781832\pi$
$200$	−0.951057	−	0.309017i	−0.0672499	−	0.0218508i
$201$	−13.7819	+	20.9875i	−0.972101	+	1.48034i
$202$	13.3359	−	9.68907i	0.938307	−	0.681720i
$203$	1.90345	−	5.85821i	0.133596	−	0.411166i
$204$	−6.04698	+	9.20851i	−0.423373	+	0.644725i
$205$	0.107089	+	0.0778050i	0.00747945	+	0.00543414i
$206$	10.4273	−	3.38803i	0.726503	−	0.236055i
$207$	17.5027	−	1.65953i	1.21652	−	0.115345i
$208$	2.38054	+	0.773484i	0.165061	+	0.0536314i
$209$	1.46568	−	4.51090i	0.101383	−	0.312025i
$210$	1.86123	+	2.32252i	0.128437	+	0.160269i
$211$	21.5657			1.48464			0.742322	−	0.670044i	$-0.233725\pi$
$211$	21.5657			1.48464			0.742322	+	0.670044i	$0.233725\pi$
$212$	−3.84633			−0.264167
$213$	−10.2836	+	8.24109i	−0.704618	+	0.564670i
$214$	−9.52225	+	6.91832i	−0.650928	+	0.472927i
$215$	6.58355	+	4.78323i	0.448995	+	0.326214i
$216$	4.59322	+	2.42947i	0.312529	+	0.165304i
$217$	5.32505	−	7.94856i	0.361488	−	0.539583i
$218$		−	19.8484i		−	1.34431i
$219$	6.18923	−	22.6367i	0.418229	−	1.52965i
$220$	0.652190	+	0.897663i	0.0439706	+	0.0605204i
$221$	15.1411	−	4.91964i	1.01850	−	0.330931i
$222$	5.20485	−	1.96760i	0.349327	−	0.132057i
$223$		−	10.0256i		−	0.671361i	−0.941976	−	0.335681i	$-0.891034\pi$
$223$		−	10.0256i		−	0.671361i	0.941976	−	0.335681i	$-0.108966\pi$
$224$	−1.63426	+	0.531003i	−0.109193	+	0.0354791i
$225$	1.19223	+	2.75292i	0.0794819	+	0.183528i
$226$	−2.91673	+	8.97678i	−0.194018	+	0.597126i
$227$	−1.86847	+	2.57173i	−0.124015	+	0.170691i	−0.866510	−	0.499160i	$-0.833642\pi$
$227$	−1.86847	+	2.57173i	−0.124015	+	0.170691i	0.742495	+	0.669851i	$0.233642\pi$
$228$	4.63007	+	5.77758i	0.306634	+	0.382630i
$229$	−17.6778	+	24.3314i	−1.16818	+	1.60787i	−0.493532	+	0.869727i	$0.664295\pi$
$229$	−17.6778	+	24.3314i	−1.16818	+	1.60787i	−0.674650	+	0.738138i	$0.735705\pi$
$230$	−4.74116	+	3.44465i	−0.312623	+	0.227134i
$231$	−0.156035	−	3.29872i	−0.0102664	−	0.217040i
$232$	2.10699	+	2.90003i	0.138331	+	0.190396i
$233$	−12.3231	−	16.9613i	−0.807313	−	1.11117i	−0.991732	−	0.128323i	$-0.959040\pi$
$233$	−12.3231	−	16.9613i	−0.807313	−	1.11117i	0.184419	−	0.982848i	$-0.440960\pi$
$234$	−2.98420	−	6.89069i	−0.195083	−	0.450459i
$235$	4.28320	−	3.11192i	0.279405	−	0.203000i
$236$	−3.90466	+	5.37431i	−0.254172	+	0.349838i
$237$	3.14098	−	2.51714i	0.204029	−	0.163506i
$238$	−6.42414	+	8.84207i	−0.416415	+	0.573146i
$239$	−2.17171	+	6.68384i	−0.140476	+	0.432341i	−0.996402	−	0.0847581i	$-0.972988\pi$
$239$	−2.17171	+	6.68384i	−0.140476	+	0.432341i	0.855925	+	0.517099i	$0.172988\pi$
$240$	−1.73012	+	0.0818375i	−0.111679	+	0.00528259i
$241$	−5.28528	+	1.71729i	−0.340455	+	0.110620i	−0.474254	−	0.880388i	$-0.657282\pi$
$241$	−5.28528	+	1.71729i	−0.340455	+	0.110620i	0.133800	+	0.991008i	$0.457282\pi$
$242$			9.76885i			0.627965i
$243$	−3.64986	−	15.1551i	−0.234139	−	0.972203i
$244$	11.0494	−	3.59016i	0.707363	−	0.229836i
$245$	−2.37891	−	3.27428i	−0.151983	−	0.209186i
$246$	0.221154	+	0.0604670i	0.0141003	+	0.00385523i
$247$		−	10.6997i		−	0.680803i
$248$	1.92075	+	5.22597i	0.121967	+	0.331849i
$249$	−1.99501	+	0.754177i	−0.126429	+	0.0477940i
$250$	−0.809017	−	0.587785i	−0.0511667	−	0.0371748i
$251$	−12.8833	+	9.36027i	−0.813187	+	0.590815i	−0.914753	−	0.404014i	$-0.867615\pi$
$251$	−12.8833	+	9.36027i	−0.813187	+	0.590815i	0.101566	+	0.994829i	$0.467615\pi$
$252$	4.43794	+	2.62288i	0.279564	+	0.165226i
$253$	6.50253			0.408811
$254$	−5.07714			−0.318568
$255$	−8.59661	+	6.88919i	−0.538340	+	0.431418i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−8.70487	−	2.82838i	−0.542995	−	0.176430i	0.0246606	−	0.999696i	$-0.492149\pi$
$257$	−8.70487	−	2.82838i	−0.542995	−	0.176430i	−0.567656	+	0.823266i	$0.692149\pi$
$258$	13.5959	+	3.71734i	0.846444	+	0.231431i
$259$	5.25018	−	1.70589i	0.326230	−	0.105999i
$260$	2.02501	+	1.47125i	0.125586	+	0.0912433i
$261$	2.34290	−	10.4956i	0.145022	−	0.649660i
$262$	−3.30100	+	10.1594i	−0.203936	+	0.627652i
$263$	−6.28457	+	4.56601i	−0.387523	+	0.281552i	−0.764440	−	0.644695i	$-0.776984\pi$
$263$	−6.28457	+	4.56601i	−0.387523	+	0.281552i	0.376916	+	0.926247i	$0.376984\pi$
$264$	1.60643	+	1.05490i	0.0988692	+	0.0649247i
$265$	−3.65808	−	1.18858i	−0.224714	−	0.0730141i
$266$	4.31752	+	5.94255i	0.264724	+	0.364361i
$267$	21.8946	+	5.98632i	1.33993	+	0.366357i
$268$	−4.47956	−	13.7867i	−0.273633	−	0.842155i
$269$	22.7200	+	16.5070i	1.38526	+	1.00645i	0.996367	+	0.0851678i	$0.0271426\pi$
$269$	22.7200	+	16.5070i	1.38526	+	1.00645i	0.388894	+	0.921283i	$0.372857\pi$
$270$	3.61767	+	3.72995i	0.220164	+	0.226997i
$271$	−6.06046	−	1.96916i	−0.368147	−	0.119618i	0.119100	−	0.992882i	$-0.461999\pi$
$271$	−6.06046	−	1.96916i	−0.368147	−	0.119618i	−0.487247	+	0.873264i	$0.661999\pi$
$272$	−1.96546	−	6.04907i	−0.119174	−	0.366778i
$273$	−2.63431	−	6.96848i	−0.159435	−	0.421752i
$274$		−	18.8987i		−	1.14171i
$275$	0.342877	+	1.05527i	0.0206762	+	0.0636349i
$276$	−5.57165	+	8.48466i	−0.335374	+	0.510716i
$277$	−2.85743	+	3.93291i	−0.171686	+	0.236306i	−0.886186	−	0.463330i	$-0.846654\pi$
$277$	−2.85743	+	3.93291i	−0.171686	+	0.236306i	0.714500	+	0.699636i	$0.246654\pi$
$278$	−1.45039			−0.0869883
$279$	7.94534	−	14.6926i	0.475675	−	0.879621i
$280$	−1.71836			−0.102692
$281$	17.5574	−	24.1657i	1.04739	−	1.44160i	0.156334	−	0.987704i	$-0.450032\pi$
$281$	17.5574	−	24.1657i	1.04739	−	1.44160i	0.891053	−	0.453900i	$-0.149968\pi$
$282$	5.03346	−	7.66510i	0.299738	−	0.456450i
$283$	−0.299247	−	0.920987i	−0.0177884	−	0.0547470i	0.941768	−	0.336262i	$-0.109163\pi$
$283$	−0.299247	−	0.920987i	−0.0177884	−	0.0547470i	−0.959557	+	0.281515i	$0.909163\pi$
$284$		−	7.60848i		−	0.451480i
$285$	2.61809	+	6.92558i	0.155082	+	0.410236i
$286$	−0.858236	−	2.64138i	−0.0507485	−	0.156188i
$287$	0.216326	+	0.0702887i	0.0127693	+	0.00414901i
$288$	−2.75292	+	1.19223i	−0.162218	+	0.0702528i
$289$	−18.9749	−	13.7860i	−1.11617	−	0.810944i
$290$	1.10771	+	3.40919i	0.0650471	+	0.200194i
$291$	−19.4035	−	5.30521i	−1.13745	−	0.310997i
$292$	7.96391	+	10.9614i	0.466052	+	0.641466i
$293$	−2.14611	−	0.697314i	−0.125377	−	0.0407375i	0.245656	−	0.969357i	$-0.420997\pi$
$293$	−2.14611	−	0.697314i	−0.125377	−	0.0407375i	−0.371034	+	0.928619i	$0.620997\pi$
$294$	−5.85957	−	3.84782i	−0.341737	−	0.224410i
$295$	−5.37431	+	3.90466i	−0.312904	+	0.227338i
$296$	−0.992740	+	3.05534i	−0.0577019	+	0.177588i
$297$	−0.814809	−	5.70764i	−0.0472800	−	0.331191i
$298$	−8.44749	−	6.13746i	−0.489350	−	0.355534i
$299$	13.9509	−	4.53292i	0.806801	−	0.262146i
$300$	−1.67073	−	0.456803i	−0.0964595	−	0.0263735i
$301$	13.2991	+	4.32115i	0.766549	+	0.249067i
$302$	−2.56698	+	7.90036i	−0.147713	+	0.454615i
$303$	22.2797	−	17.8546i	1.27993	−	1.02572i
$304$	−4.27466			−0.245168
$305$	11.6180			0.665244
$306$	−9.70838	+	16.4267i	−0.554991	+	0.939050i
$307$	−7.57725	+	5.50520i	−0.432457	+	0.314198i	−0.782630	−	0.622487i	$-0.786123\pi$
$307$	−7.57725	+	5.50520i	−0.432457	+	0.314198i	0.350174	+	0.936685i	$0.386123\pi$
$308$	1.54251	+	1.12070i	0.0878926	+	0.0638577i
$309$	17.7631	−	6.71502i	1.01051	−	0.382004i
$310$	0.211825	+	5.56373i	0.0120309	+	0.315999i
$311$			20.5381i			1.16461i	0.812971	+	0.582304i	$0.197849\pi$
$311$			20.5381i			1.16461i	−0.812971	+	0.582304i	$0.802151\pi$
$312$	4.18191	+	1.14340i	0.236754	+	0.0647322i
$313$	−3.07662	−	4.23461i	−0.173901	−	0.239354i	0.713166	−	0.700995i	$-0.247261\pi$
$313$	−3.07662	−	4.23461i	−0.173901	−	0.239354i	−0.887067	+	0.461641i	$0.847261\pi$
$314$	−14.8142	+	4.81343i	−0.836014	+	0.271637i
$315$	3.41022	+	3.86591i	0.192144	+	0.217819i
$316$			2.32392i			0.130731i
$317$	−23.7559	+	7.71878i	−1.33427	+	0.433530i	−0.887371	−	0.461056i	$-0.847471\pi$
$317$	−23.7559	+	7.71878i	−1.33427	+	0.433530i	−0.446896	+	0.894586i	$0.647471\pi$
$318$	−6.65461	+	0.314774i	−0.373172	+	0.0176517i
$319$	1.22909	−	3.78274i	0.0688156	−	0.211793i
$320$	0.587785	−	0.809017i	0.0328582	−	0.0452254i
$321$	−15.9084	+	12.7488i	−0.887922	+	0.711568i
$322$	−5.91916	+	8.14702i	−0.329862	+	0.454016i
$323$	−21.9958	+	15.9809i	−1.22388	+	0.889202i
$324$	8.14563	+	3.82737i	0.452535	+	0.212632i
$325$	1.47125	+	2.02501i	0.0816105	+	0.112327i
$326$	−5.53395	−	7.61683i	−0.306497	−	0.421857i
$327$	−1.62435	−	34.3401i	−0.0898265	−	1.89901i
$328$	−0.107089	+	0.0778050i	−0.00591302	+	0.00429606i
$329$	5.34741	−	7.36007i	0.294812	−	0.405774i
$330$	1.20183	+	1.49969i	0.0661584	+	0.0825551i
$331$	−2.80744	+	3.86411i	−0.154311	+	0.212391i	−0.879172	−	0.476504i	$-0.841904\pi$
$331$	−2.80744	+	3.86411i	−0.154311	+	0.212391i	0.724861	+	0.688895i	$0.241904\pi$
$332$	0.380516	−	1.17111i	0.0208835	−	0.0642728i
$333$	8.84398	−	3.83013i	0.484647	−	0.209890i
$334$	−11.3494	+	3.68764i	−0.621012	+	0.201779i
$335$		−	14.4962i		−	0.792010i
$336$	−2.78400	+	1.05244i	−0.151880	+	0.0574153i
$337$	11.1132	−	3.61088i	0.605372	−	0.196697i	0.00973734	−	0.999953i	$-0.496900\pi$
$337$	11.1132	−	3.61088i	0.605372	−	0.196697i	0.595635	+	0.803255i	$0.296900\pi$
$338$	3.95859	+	5.44854i	0.215319	+	0.296361i
$339$	−4.31165	+	15.7696i	−0.234177	+	0.856485i
$340$		−	6.36036i		−	0.344939i
$341$	3.43846	−	5.13251i	0.186203	−	0.277941i
$342$	8.48338	+	9.61698i	0.458729	+	0.520027i
$343$	−15.3577	−	11.1580i	−0.829237	−	0.602476i
$344$	−6.58355	+	4.78323i	−0.354961	+	0.257895i
$345$	−7.92086	+	6.34766i	−0.426445	+	0.341746i
$346$	−0.844232			−0.0453862
$347$	−5.44515			−0.292311			−0.146156	−	0.989262i	$-0.546690\pi$
$347$	−5.44515			−0.292311			−0.146156	+	0.989262i	$0.546690\pi$
$348$	3.88267	+	4.84495i	0.208133	+	0.259717i
$349$	−2.67062	+	8.21933i	−0.142955	+	0.439971i	−0.996742	−	0.0806515i	$-0.974300\pi$
$349$	−2.67062	+	8.21933i	−0.142955	+	0.439971i	0.853787	+	0.520622i	$0.174300\pi$
$350$	−1.63426	−	0.531003i	−0.0873548	−	0.0283833i
$351$	−5.72694	−	11.6775i	−0.305681	−	0.623298i
$352$	−1.05527	+	0.342877i	−0.0562458	+	0.0182754i
$353$	−19.2682	−	13.9992i	−1.02554	−	0.745101i	−0.0581316	−	0.998309i	$-0.518514\pi$
$353$	−19.2682	−	13.9992i	−1.02554	−	0.745101i	−0.967412	+	0.253208i	$0.918514\pi$
$354$	−6.31570	+	9.61773i	−0.335676	+	0.511176i
$355$	2.35115	−	7.23610i	0.124786	−	0.384052i
$356$	−10.6020	+	7.70281i	−0.561905	+	0.408248i
$357$	−10.3909	+	15.8235i	−0.549945	+	0.837471i
$358$	−0.910626	−	0.295880i	−0.0481281	−	0.0156378i
$359$	−9.78511	−	13.4680i	−0.516438	−	0.710816i	0.468550	−	0.883437i	$-0.344777\pi$
$359$	−9.78511	−	13.4680i	−0.516438	−	0.710816i	−0.984988	+	0.172621i	$0.944777\pi$
$360$	−2.98661	+	0.283177i	−0.157408	+	0.0149247i
$361$	−0.224755	−	0.691726i	−0.0118292	−	0.0364066i
$362$	1.83901	+	1.33612i	0.0966561	+	0.0702248i
$363$	0.799458	+	16.9012i	0.0419607	+	0.887085i
$364$	4.09062	+	1.32912i	0.214407	+	0.0696650i
$365$	4.18687	+	12.8859i	0.219151	+	0.674477i
$366$	18.8229	−	7.11564i	0.983888	−	0.371941i
$367$		−	9.52981i		−	0.497452i	−0.968574	−	0.248726i	$-0.919988\pi$
$367$		−	9.52981i		−	0.497452i	0.968574	−	0.248726i	$-0.0800119\pi$
$368$	−1.81096	−	5.57357i	−0.0944029	−	0.290542i
$369$	0.387570	+	0.0865162i	0.0201761	+	0.00450385i
$370$	−1.88830	+	2.59903i	−0.0981683	+	0.135117i
$371$	−6.60939			−0.343142
$372$	3.75079	+	8.88434i	0.194470	+	0.460632i
$373$	−15.1972			−0.786881			−0.393440	−	0.919350i	$-0.628715\pi$
$373$	−15.1972			−0.786881			−0.393440	+	0.919350i	$0.628715\pi$
$374$	−4.14817	+	5.70946i	−0.214497	+	0.295229i
$375$	−1.44780	−	0.950729i	−0.0747639	−	0.0490954i
$376$	1.63603	+	5.03520i	0.0843721	+	0.259671i
$377$		−	8.97250i		−	0.462107i
$378$	7.89281	+	4.17471i	0.405962	+	0.214724i
$379$	2.41988	+	7.44764i	0.124301	+	0.382560i	0.993773	−	0.111423i	$-0.0355408\pi$
$379$	2.41988	+	7.44764i	0.124301	+	0.382560i	−0.869472	+	0.493982i	$0.835541\pi$
$380$	−4.06544	−	1.32094i	−0.208553	−	0.0677628i
$381$	−8.78404	+	0.415500i	−0.450020	+	0.0212867i
$382$	5.80796	+	4.21973i	0.297161	+	0.215900i
$383$	4.16186	+	12.8089i	0.212661	+	0.654504i	0.999311	+	0.0371049i	$0.0118136\pi$
$383$	4.16186	+	12.8089i	0.212661	+	0.654504i	−0.786650	+	0.617399i	$0.788186\pi$
$384$	0.456803	−	1.67073i	0.0233111	−	0.0852590i
$385$	1.12070	+	1.54251i	0.0571160	+	0.0786135i
$386$	−4.83313	−	1.57038i	−0.246000	−	0.0799302i
$387$	23.8267	+	5.31877i	1.21118	+	0.270368i
$388$	9.39574	−	6.82641i	0.476997	−	0.346558i
$389$	4.01550	−	12.3585i	0.203594	−	0.626598i	−0.796174	−	0.605068i	$-0.793146\pi$
$389$	4.01550	−	12.3585i	0.203594	−	0.626598i	0.999768	−	0.0215307i	$-0.00685395\pi$
$390$	3.62390	+	2.37972i	0.183503	+	0.120502i
$391$	−30.1555	−	21.9093i	−1.52503	−	1.10800i
$392$	3.84915	−	1.25066i	0.194411	−	0.0631681i
$393$	−4.87969	+	17.8471i	−0.246148	+	0.900269i
$394$	11.1161	+	3.61183i	0.560019	+	0.181961i
$395$	−0.718130	+	2.21018i	−0.0361330	+	0.111206i
$396$	2.86565	+	1.69364i	0.144004	+	0.0851085i
$397$	17.4588			0.876232			0.438116	−	0.898918i	$-0.355646\pi$
$397$	17.4588			0.876232			0.438116	+	0.898918i	$0.355646\pi$
$398$	−1.60941			−0.0806723
$399$	7.95613	+	9.92797i	0.398305	+	0.497020i
$400$	0.809017	−	0.587785i	0.0404508	−	0.0293893i
$401$	−6.36599	−	4.62516i	−0.317902	−	0.230969i	0.417378	−	0.908733i	$-0.362949\pi$
$401$	−6.36599	−	4.62516i	−0.317902	−	0.230969i	−0.735280	+	0.677764i	$0.762949\pi$
$402$	−8.87842	−	23.4859i	−0.442816	−	1.17137i
$403$	3.79920	−	13.4085i	0.189252	−	0.667926i
$404$			16.4840i			0.820111i
$405$	6.56423	+	6.15718i	0.326179	+	0.305953i
$406$	3.62058	+	4.98329i	0.179686	+	0.247317i
$407$	3.39012	−	1.10152i	0.168042	−	0.0546002i
$408$	−3.89552	−	10.3047i	−0.192857	−	0.510161i
$409$			12.2478i			0.605614i	0.953052	+	0.302807i	$0.0979238\pi$
$409$			12.2478i			0.605614i	−0.953052	+	0.302807i	$0.902076\pi$
$410$	−0.125891	+	0.0409045i	−0.00621732	+	0.00202013i
$411$	−1.54662	−	32.6969i	−0.0762891	−	1.61282i
$412$	−3.38803	+	10.4273i	−0.166916	+	0.513715i
$413$	−6.70962	+	9.23500i	−0.330159	+	0.454425i
$414$	−8.94524	+	15.1354i	−0.439634	+	0.743865i
$415$	0.723784	−	0.996203i	0.0355292	−	0.0489017i
$416$	−2.02501	+	1.47125i	−0.0992841	+	0.0721341i
$417$	−2.50934	+	0.118696i	−0.122883	+	0.00581256i
$418$	2.78789	+	3.83720i	0.136360	+	0.187683i
$419$	19.4230	+	26.7335i	0.948876	+	1.30602i	0.952025	+	0.306021i	$0.0989978\pi$
$419$	19.4230	+	26.7335i	0.948876	+	1.30602i	−0.00314861	+	0.999995i	$0.501002\pi$
$420$	−2.97296	+	0.140626i	−0.145066	+	0.00686186i
$421$	−22.3344	+	16.2269i	−1.08851	+	0.790850i	−0.979147	−	0.203152i	$-0.934881\pi$
$421$	−22.3344	+	16.2269i	−1.08851	+	0.790850i	−0.109364	+	0.994002i	$0.534881\pi$
$422$	−12.6760	+	17.4470i	−0.617058	+	0.849307i
$423$	8.08119	−	13.6734i	0.392921	−	0.664825i
$424$	2.26082	−	3.11175i	0.109795	−	0.151120i
$425$	1.96546	−	6.04907i	0.0953388	−	0.293423i
$426$	−0.622659	−	13.1636i	−0.0301679	−	0.637777i
$427$	18.9868	−	6.16919i	0.918836	−	0.298548i
$428$		−	11.7702i		−	0.568932i
$429$	−1.70101	−	4.49966i	−0.0821256	−	0.217245i
$430$	−7.73943	+	2.51469i	−0.373228	+	0.121269i
$431$	10.8781	+	14.9724i	0.523979	+	0.721196i	0.986198	−	0.165570i	$-0.0529465\pi$
$431$	10.8781	+	14.9724i	0.523979	+	0.721196i	−0.462219	+	0.886766i	$0.652947\pi$
$432$	−4.66531	+	2.28799i	−0.224460	+	0.110081i
$433$		−	33.7278i		−	1.62085i	−0.585840	−	0.810427i	$-0.699235\pi$
$433$		−	33.7278i		−	1.62085i	0.585840	−	0.810427i	$-0.300765\pi$
$434$	3.30053	+	8.98010i	0.158431	+	0.431058i
$435$	2.19547	+	5.80764i	0.105265	+	0.278455i
$436$	16.0577	+	11.6666i	0.769025	+	0.558730i
$437$	−20.2668	+	14.7247i	−0.969494	+	0.704378i
$438$	14.6755	+	18.3127i	0.701224	+	0.875015i
$439$	0.0551878			0.00263397			0.00131699	−	0.999999i	$-0.499581\pi$
$439$	0.0551878			0.00263397			0.00131699	+	0.999999i	$0.499581\pi$
$440$	−1.10957			−0.0528968
$441$	−10.4526	−	6.17765i	−0.497745	−	0.294174i
$442$	−4.91964	+	15.1411i	−0.234003	+	0.720188i
$443$	26.0210	+	8.45475i	1.23630	+	0.401697i	0.852992	−	0.521924i	$-0.174786\pi$
$443$	26.0210	+	8.45475i	1.23630	+	0.401697i	0.383305	+	0.923622i	$0.374786\pi$
$444$	−1.46751	+	5.36734i	−0.0696452	+	0.254723i
$445$	−12.4634	+	4.04961i	−0.590822	+	0.191970i
$446$	8.11085	+	5.89288i	0.384060	+	0.279036i
$447$	−15.1174	−	9.92720i	−0.715029	−	0.469540i
$448$	0.531003	−	1.63426i	0.0250875	−	0.0772114i
$449$	9.35498	−	6.79679i	0.441489	−	0.320760i	−0.344738	−	0.938699i	$-0.612032\pi$
$449$	9.35498	−	6.79679i	0.441489	−	0.320760i	0.786226	+	0.617939i	$0.212032\pi$
$450$	−2.92794	−	0.653595i	−0.138024	−	0.0308107i
$451$	0.139685	+	0.0453865i	0.00657752	+	0.00213717i
$452$	−5.54795	−	7.63610i	−0.260954	−	0.359172i
$453$	−3.79463	+	13.8786i	−0.178287	+	0.652075i
$454$	−0.982312	−	3.02325i	−0.0461022	−	0.141888i
$455$	3.47969	+	2.52814i	0.163130	+	0.118521i
$456$	−7.39565	+	0.349827i	−0.346333	+	0.0163822i
$457$	−5.29517	−	1.72051i	−0.247698	−	0.0804819i	0.182537	−	0.983199i	$-0.441569\pi$
$457$	−5.29517	−	1.72051i	−0.247698	−	0.0804819i	−0.430235	+	0.902717i	$0.641569\pi$
$458$	−9.29377	−	28.6033i	−0.434270	−	1.33654i
$459$	−15.4523	+	29.2146i	−0.721252	+	1.36362i
$460$		−	5.86040i		−	0.273242i
$461$	11.0770	+	34.0917i	0.515910	+	1.58781i	0.781621	+	0.623754i	$0.214393\pi$
$461$	11.0770	+	34.0917i	0.515910	+	1.58781i	−0.265711	+	0.964053i	$0.585607\pi$
$462$	2.76043	+	1.81270i	0.128427	+	0.0843346i
$463$	15.3628	−	21.1451i	0.713969	−	0.982694i	−0.285734	−	0.958309i	$-0.592237\pi$
$463$	15.3628	−	21.1451i	0.713969	−	0.982694i	0.999703	−	0.0243848i	$-0.00776269\pi$
$464$	−3.58463			−0.166412
$465$	0.821804	+	9.60857i	0.0381103	+	0.445587i
$466$	20.9653			0.971199
$467$	−4.61609	+	6.35350i	−0.213607	+	0.294005i	−0.902353	−	0.430998i	$-0.858162\pi$
$467$	−4.61609	+	6.35350i	−0.213607	+	0.294005i	0.688746	+	0.725003i	$0.258162\pi$
$468$	7.32876	+	1.63598i	0.338772	+	0.0756231i
$469$	−7.69750	−	23.6905i	−0.355437	−	1.09392i
$470$			5.29432i			0.244209i
$471$	−25.2364	+	9.54015i	−1.16283	+	0.439587i
$472$	−2.05280	−	6.31788i	−0.0944879	−	0.290804i
$473$	8.58745	+	2.79023i	0.394852	+	0.128295i
$474$	0.190184	+	4.02065i	0.00873542	+	0.184674i
$475$	−3.45827	−	2.51258i	−0.158676	−	0.115285i
$476$	−3.37737	−	10.3945i	−0.154802	−	0.476430i
$477$	−11.4875	+	1.08919i	−0.525976	+	0.0498707i
$478$	−4.13084	−	5.68561i	−0.188940	−	0.260054i
$479$	−15.4808	−	5.03000i	−0.707334	−	0.229827i	−0.0668107	−	0.997766i	$-0.521282\pi$
$479$	−15.4808	−	5.03000i	−0.707334	−	0.229827i	−0.640523	+	0.767939i	$0.721282\pi$
$480$	0.950729	−	1.44780i	0.0433946	−	0.0660826i
$481$	6.50549	−	4.72651i	0.296625	−	0.215510i
$482$	1.71729	−	5.28528i	0.0782204	−	0.240738i
$483$	−9.57410	+	14.5797i	−0.435637	+	0.663400i
$484$	−7.90317	−	5.74199i	−0.359235	−	0.260999i
$485$	11.0454	−	3.58885i	0.501544	−	0.162961i
$486$	14.4061	+	5.95517i	0.653474	+	0.270132i
$487$	−29.9197	−	9.72151i	−1.35579	−	0.440524i	−0.461156	−	0.887319i	$-0.652565\pi$
$487$	−29.9197	−	9.72151i	−1.35579	−	0.440524i	−0.894636	+	0.446795i	$0.852565\pi$
$488$	−3.59016	+	11.0494i	−0.162519	+	0.500181i
$489$	−10.1977	−	12.7251i	−0.461157	−	0.575450i
$490$	4.04724			0.182835
$491$	26.7690			1.20807			0.604035	−	0.796958i	$-0.293559\pi$
$491$	26.7690			1.20807			0.604035	+	0.796958i	$0.293559\pi$
$492$	−0.178910	+	0.143376i	−0.00806588	+	0.00646387i
$493$	−18.4452	+	13.4012i	−0.830731	+	0.603562i
$494$	8.65620	+	6.28910i	0.389461	+	0.282960i
$495$	2.20203	+	2.49628i	0.0989740	+	0.112199i
$496$	−5.35688	−	1.51783i	−0.240531	−	0.0681526i
$497$		−	13.0741i		−	0.586454i
$498$	0.562496	−	2.05729i	0.0252061	−	0.0921895i
$499$	−18.2597	−	25.1323i	−0.817416	−	1.12508i	−0.990137	−	0.140106i	$-0.955256\pi$
$499$	−18.2597	−	25.1323i	−0.817416	−	1.12508i	0.172720	−	0.984971i	$-0.444744\pi$
$500$	0.951057	−	0.309017i	0.0425325	−	0.0138197i
$501$	−19.3340	+	7.30886i	−0.863779	+	0.326536i
$502$		−	15.9246i		−	0.710751i
$503$	2.14803	−	0.697937i	0.0957759	−	0.0311195i	−0.260737	−	0.965410i	$-0.583966\pi$
$503$	2.14803	−	0.697937i	0.0957759	−	0.0311195i	0.356513	+	0.934290i	$0.383966\pi$
$504$	−4.73052	+	2.04868i	−0.210714	+	0.0912554i
$505$	−5.09384	+	15.6772i	−0.226673	+	0.697628i
$506$	−3.82209	+	5.26066i	−0.169913	+	0.233865i
$507$	7.29472	+	9.10264i	0.323970	+	0.404262i
$508$	2.98427	−	4.10749i	0.132405	−	0.182241i
$509$	−2.68227	+	1.94878i	−0.118889	+	0.0863782i	−0.645641	−	0.763641i	$-0.723410\pi$
$509$	−2.68227	+	1.94878i	−0.118889	+	0.0863782i	0.526752	+	0.850019i	$0.323410\pi$
$510$	−0.520516	−	11.0042i	−0.0230488	−	0.487273i
$511$	13.6849	+	18.8356i	0.605383	+	0.833238i
$512$	0.587785	+	0.809017i	0.0259767	+	0.0357538i
$513$	15.4643	+	15.9442i	0.682764	+	0.703955i
$514$	7.40481	−	5.37991i	0.326612	−	0.237298i
$515$	−6.44441	+	8.86997i	−0.283975	+	0.390858i
$516$	−10.9989	+	8.81433i	−0.484198	+	0.388029i
$517$	3.45290	−	4.75251i	0.151859	−	0.209015i
$518$	−1.70589	+	5.25018i	−0.0749523	+	0.230680i
$519$	−1.46062	+	0.0690899i	−0.0641141	+	0.00303271i
$520$	−2.38054	+	0.773484i	−0.104393	+	0.0339195i
$521$			25.5868i			1.12098i	0.828162	+	0.560489i	$0.189387\pi$
$521$			25.5868i			1.12098i	−0.828162	+	0.560489i	$0.810613\pi$
$522$	7.11398	+	8.06459i	0.311370	+	0.352977i
$523$	−1.72715	+	0.561186i	−0.0755231	+	0.0245389i	−0.346535	−	0.938037i	$-0.612642\pi$
$523$	−1.72715	+	0.561186i	−0.0755231	+	0.0245389i	0.271012	+	0.962576i	$0.412642\pi$
$524$	−6.27887	−	8.64213i	−0.274294	−	0.377533i
$525$	−2.87091	−	0.784953i	−0.125297	−	0.0342582i
$526$		−	7.76816i		−	0.338708i
$527$	−33.2391	+	12.2166i	−1.44792	+	0.532165i
$528$	−1.79767	+	0.679577i	−0.0782336	+	0.0295748i
$529$	−9.17768	−	6.66797i	−0.399029	−	0.289912i
$530$	3.11175	−	2.26082i	0.135166	−	0.0982037i
$531$	−10.1398	+	17.1566i	−0.440030	+	0.744535i
$532$	−7.34540			−0.318463
$533$	0.331328			0.0143514
$534$	−17.7123	+	14.1944i	−0.766488	+	0.614252i
$535$	3.63718	−	11.1941i	0.157249	−	0.483962i
$536$	13.7867	+	4.47956i	0.595493	+	0.193487i
$537$	−1.59970	−	0.437384i	−0.0690323	−	0.0188745i
$538$	−26.7089	+	8.67825i	−1.15150	+	0.374146i
$539$	−3.63305	−	2.63957i	−0.156487	−	0.113694i
$540$	−5.14400	+	0.734345i	−0.221363	+	0.0316012i
$541$	7.30183	−	22.4727i	0.313930	−	0.966177i	−0.662263	−	0.749272i	$-0.730404\pi$
$541$	7.30183	−	22.4727i	0.313930	−	0.966177i	0.976193	−	0.216906i	$-0.0695964\pi$
$542$	5.15534	−	3.74557i	0.221441	−	0.160886i
$543$	3.29104	+	2.16114i	0.141232	+	0.0927434i
$544$	6.04907	+	1.96546i	0.259352	+	0.0842684i
$545$	11.6666	+	16.0577i	0.499743	+	0.687837i
$546$	7.18603	+	1.96477i	0.307534	+	0.0840845i
$547$	−11.3334	−	34.8805i	−0.484580	−	1.49138i	−0.832589	−	0.553892i	$-0.813142\pi$
$547$	−11.3334	−	34.8805i	−0.484580	−	1.49138i	0.348009	−	0.937491i	$-0.386858\pi$
$548$	15.2893	+	11.1083i	0.653128	+	0.474525i
$549$	31.9835	−	13.8513i	1.36502	−	0.591159i
$550$	−1.05527	−	0.342877i	−0.0449967	−	0.0146203i
$551$	4.73509	+	14.5731i	0.201721	+	0.620835i
$552$	−3.58930	−	9.49472i	−0.152771	−	0.404122i
$553$			3.99333i			0.169814i
$554$	−1.50224	−	4.62341i	−0.0638240	−	0.196430i
$555$	−3.05429	+	4.65116i	−0.129647	+	0.197431i
$556$	0.852515	−	1.17339i	0.0361547	−	0.0497627i
$557$	19.3884			0.821512			0.410756	−	0.911745i	$-0.365265\pi$
$557$	19.3884			0.821512			0.410756	+	0.911745i	$0.365265\pi$
$558$	7.21638	+	15.0640i	0.305494	+	0.637710i
$559$	20.3691			0.861520
$560$	1.01003	−	1.39018i	0.0426814	−	0.0587460i
$561$	−6.70956	+	10.2175i	−0.283278	+	0.431383i
$562$	9.23047	+	28.4085i	0.389364	+	1.19834i
$563$			9.23240i			0.389099i	0.980893	+	0.194550i	$0.0623245\pi$
$563$			9.23240i			0.389099i	−0.980893	+	0.194550i	$0.937676\pi$
$564$	3.24260	+	8.57759i	0.136538	+	0.361182i
$565$	−2.91673	−	8.97678i	−0.122708	−	0.377656i
$566$	0.920987	+	0.299247i	0.0387120	+	0.0125783i
$567$	13.9971	+	6.57680i	0.587824	+	0.276200i
$568$	6.15539	+	4.47215i	0.258275	+	0.187647i
$569$	−4.98297	−	15.3360i	−0.208897	−	0.642918i	−0.999531	−	0.0306292i	$-0.990249\pi$
$569$	−4.98297	−	15.3360i	−0.208897	−	0.642918i	0.790634	−	0.612289i	$-0.209751\pi$
$570$	−7.14178	−	1.95268i	−0.299136	−	0.0817886i
$571$	−9.76284	−	13.4374i	−0.408562	−	0.562337i	0.554305	−	0.832314i	$-0.312984\pi$
$571$	−9.76284	−	13.4374i	−0.408562	−	0.562337i	−0.962867	+	0.269976i	$0.912984\pi$
$572$	2.64138	+	0.858236i	0.110442	+	0.0358846i
$573$	10.3938	+	6.82532i	0.434206	+	0.285132i
$574$	−0.184018	+	0.133697i	−0.00768077	+	0.00558041i
$575$	1.81096	−	5.57357i	0.0755223	−	0.232434i
$576$	0.653595	−	2.92794i	0.0272331	−	0.121997i
$577$	21.0135	+	15.2672i	0.874804	+	0.635583i	0.931872	−	0.362788i	$-0.118175\pi$
$577$	21.0135	+	15.2672i	0.874804	+	0.635583i	−0.0570674	+	0.998370i	$0.518175\pi$
$578$	22.3063	−	7.24775i	0.927820	−	0.301467i
$579$	−8.49040	−	2.32141i	−0.352849	−	0.0964744i
$580$	−3.40919	−	1.10771i	−0.141559	−	0.0459952i
$581$	0.653863	−	2.01238i	0.0271268	−	0.0834878i
$582$	15.6971	−	12.5794i	0.650665	−	0.521433i
$583$	−4.26778			−0.176754
$584$	−13.5490			−0.560662
$585$	6.46452	+	3.82062i	0.267275	+	0.157963i
$586$	1.82559	−	1.32637i	0.0754145	−	0.0547919i
$587$	−1.90924	−	1.38714i	−0.0788026	−	0.0572535i	0.547686	−	0.836684i	$-0.315509\pi$
$587$	−1.90924	−	1.38714i	−0.0788026	−	0.0572535i	−0.626489	+	0.779430i	$0.715509\pi$
$588$	6.55713	−	2.47880i	0.270411	−	0.102224i
$589$	0.905480	+	23.7830i	0.0373097	+	0.979963i
$590$		−	6.64301i		−	0.273488i
$591$	19.5277	+	5.33917i	0.803261	+	0.219624i
$592$	−1.88830	−	2.59903i	−0.0776088	−	0.106819i
$593$	12.6011	−	4.09436i	0.517467	−	0.168135i	−0.0386285	−	0.999254i	$-0.512299\pi$
$593$	12.6011	−	4.09436i	0.517467	−	0.168135i	0.556095	+	0.831118i	$0.312299\pi$
$594$	5.09651	+	2.69567i	0.209112	+	0.110605i
$595$		−	10.9294i		−	0.448062i
$596$	9.93062	−	3.22665i	0.406774	−	0.132169i
$597$	−2.78446	+	0.131710i	−0.113961	+	0.00539053i
$598$	−4.53292	+	13.9509i	−0.185365	+	0.570494i
$599$	−0.571106	+	0.786061i	−0.0233348	+	0.0321176i	−0.820525	−	0.571611i	$-0.806319\pi$
$599$	−0.571106	+	0.786061i	−0.0233348	+	0.0321176i	0.797190	+	0.603728i	$0.206319\pi$
$600$	1.35159	−	1.08314i	0.0551785	−	0.0442192i
$601$	−7.80197	+	10.7385i	−0.318249	+	0.438032i	−0.937932	−	0.346820i	$-0.887261\pi$
$601$	−7.80197	+	10.7385i	−0.318249	+	0.438032i	0.619683	+	0.784852i	$0.287261\pi$
$602$	−11.3129	+	8.21932i	−0.461080	+	0.334994i
$603$	−17.2827	−	39.9068i	−0.703807	−	1.62513i
$604$	−4.88269	−	6.72045i	−0.198674	−	0.273451i
$605$	−5.74199	−	7.90317i	−0.233445	−	0.321309i
$606$	1.34901	+	28.5193i	0.0547998	+	1.15852i
$607$	−6.77745	+	4.92411i	−0.275088	+	0.199863i	−0.716772	−	0.697307i	$-0.754381\pi$
$607$	−6.77745	+	4.92411i	−0.275088	+	0.199863i	0.441684	+	0.897171i	$0.354381\pi$
$608$	2.51258	−	3.45827i	0.101899	−	0.140251i
$609$	6.67184	+	8.32538i	0.270356	+	0.337361i
$610$	−6.82889	+	9.39915i	−0.276493	+	0.380561i
$611$	4.09507	−	12.6033i	0.165669	−	0.509876i
$612$	−7.58301	−	17.5096i	−0.306525	−	0.707784i
$613$	−37.9594	+	12.3338i	−1.53316	+	0.498155i	−0.949481	−	0.313825i	$-0.898389\pi$
$613$	−37.9594	+	12.3338i	−1.53316	+	0.498155i	−0.583684	+	0.811981i	$0.698389\pi$
$614$		−	9.36600i		−	0.377981i
$615$	−0.214459	+	0.0810722i	−0.00864782	+	0.00326915i
$616$	−1.81333	+	0.589186i	−0.0730610	+	0.0237390i
$617$	−20.1176	−	27.6895i	−0.809905	−	1.11474i	−0.991338	−	0.131335i	$-0.958074\pi$
$617$	−20.1176	−	27.6895i	−0.809905	−	1.11474i	0.181433	−	0.983403i	$-0.441926\pi$
$618$	−5.00834	+	18.3177i	−0.201465	+	0.736844i
$619$			3.19237i			0.128312i	0.997940	+	0.0641561i	$0.0204355\pi$
$619$			3.19237i			0.128312i	−0.997940	+	0.0641561i	$0.979564\pi$
$620$	−4.62566	−	3.09891i	−0.185771	−	0.124455i
$621$	−14.2377	+	26.9181i	−0.571337	+	1.08019i
$622$	−16.6157	−	12.0720i	−0.666227	−	0.484042i
$623$	−18.2181	+	13.2362i	−0.729892	+	0.530298i
$624$	−3.38309	+	2.71116i	−0.135432	+	0.108533i
$625$	1.00000			0.0400000
$626$	5.23426			0.209203
$627$	5.13740	+	6.41065i	0.205168	+	0.256017i
$628$	4.81343	−	14.8142i	0.192077	−	0.591151i
$629$	−19.4331	−	6.31419i	−0.774848	−	0.251763i
$630$	−5.13207	+	0.486600i	−0.204466	+	0.0193866i
$631$	−25.8497	+	8.39907i	−1.02906	+	0.334362i	−0.774418	−	0.632674i	$-0.781957\pi$
$631$	−25.8497	+	8.39907i	−1.02906	+	0.334362i	−0.254641	+	0.967036i	$0.581957\pi$
$632$	−1.88009	−	1.36596i	−0.0747859	−	0.0543351i
$633$	−20.5031	+	31.2227i	−0.814926	+	1.24099i
$634$	7.71878	−	23.7559i	0.306552	−	0.943469i
$635$	4.10749	−	2.98427i	0.163001	−	0.118427i
$636$	3.65682	−	5.56871i	0.145002	−	0.220814i
$637$	−9.63460	−	3.13047i	−0.381737	−	0.124034i
$638$	2.33786	+	3.21779i	0.0925568	+	0.127394i
$639$	−2.15455	−	22.7235i	−0.0852325	−	0.898929i
$640$	0.309017	+	0.951057i	0.0122150	+	0.0375938i
$641$	34.7198	+	25.2254i	1.37135	+	0.996344i	0.997630	+	0.0688020i	$0.0219177\pi$
$641$	34.7198	+	25.2254i	1.37135	+	0.996344i	0.373719	+	0.927542i	$0.378082\pi$
$642$	−0.963240	−	20.3637i	−0.0380160	−	0.803693i
$643$	14.9720	+	4.86469i	0.590437	+	0.191845i	0.588971	−	0.808154i	$-0.299533\pi$
$643$	14.9720	+	4.86469i	0.590437	+	0.191845i	0.00146643	+	0.999999i	$0.499533\pi$
$644$	−3.11189	−	9.57740i	−0.122625	−	0.377402i
$645$	−13.1843	+	4.98409i	−0.519132	+	0.196248i
$646$		−	27.1884i		−	1.06971i
$647$	3.59167	+	11.0540i	0.141203	+	0.434578i	0.996503	−	0.0835547i	$-0.0266273\pi$
$647$	3.59167	+	11.0540i	0.141203	+	0.434578i	−0.855300	+	0.518133i	$0.826627\pi$
$648$	−7.88429	+	4.34028i	−0.309724	+	0.170502i
$649$	−4.33250	+	5.96318i	−0.170066	+	0.234075i
$650$	−2.50305			−0.0981775
$651$	6.44522	+	15.2665i	0.252608	+	0.598342i
$652$	9.41492			0.368717
$653$	11.9012	−	16.3806i	0.465731	−	0.641023i	−0.509954	−	0.860202i	$-0.670338\pi$
$653$	11.9012	−	16.3806i	0.465731	−	0.641023i	0.975685	+	0.219178i	$0.0703377\pi$
$654$	28.7365	+	18.8705i	1.12369	+	0.737894i
$655$	−3.30100	−	10.1594i	−0.128981	−	0.396962i
$656$		−	0.132370i		−	0.00516817i
$657$	26.8891	+	30.4821i	1.04904	+	1.18922i
$658$	2.81130	+	8.65229i	0.109596	+	0.337301i
$659$	−29.9053	−	9.71681i	−1.16494	−	0.378513i	−0.338190	−	0.941078i	$-0.609815\pi$
$659$	−29.9053	−	9.71681i	−1.16494	−	0.378513i	−0.826753	+	0.562565i	$0.809815\pi$
$660$	−1.91969	+	0.0908046i	−0.0747238	+	0.00353456i
$661$	−10.3495	−	7.51938i	−0.402551	−	0.292470i	0.368029	−	0.929814i	$-0.380033\pi$
$661$	−10.3495	−	7.51938i	−0.402551	−	0.292470i	−0.770579	+	0.637344i	$0.780033\pi$
$662$	−1.47596	−	4.54253i	−0.0573647	−	0.176550i
$663$	−7.27244	+	26.5985i	−0.282438	+	1.03300i
$664$	0.723784	+	0.996203i	0.0280883	+	0.0386602i
$665$	−6.98589	−	2.26985i	−0.270901	−	0.0880211i
$666$	−2.09972	+	9.40622i	−0.0813626	+	0.364484i
$667$	−16.9953	+	12.3478i	−0.658061	+	0.478109i
$668$	3.68764	−	11.3494i	0.142679	−	0.439122i
$669$	14.5150	+	9.53159i	0.561181	+	0.368513i
$670$	11.7276	+	8.52063i	0.453078	+	0.329181i
$671$	12.2601	−	3.98354i	0.473295	−	0.153783i
$672$	0.784953	−	2.87091i	0.0302802	−	0.110748i
$673$	−1.41688	−	0.460371i	−0.0546165	−	0.0177460i	0.281581	−	0.959537i	$-0.409141\pi$
$673$	−1.41688	−	0.460371i	−0.0546165	−	0.0177460i	−0.336198	+	0.941791i	$0.609141\pi$
$674$	−3.61088	+	11.1132i	−0.139086	+	0.428063i
$675$	−5.11916	−	0.891180i	−0.197037	−	0.0343015i
$676$	−6.73476			−0.259029
$677$	1.67545			0.0643927			0.0321964	−	0.999482i	$-0.489750\pi$
$677$	1.67545			0.0643927			0.0321964	+	0.999482i	$0.489750\pi$
$678$	−10.2235	−	12.7573i	−0.392632	−	0.489942i
$679$	16.1453	−	11.7302i	0.619599	−	0.450165i
$680$	5.14564	+	3.73853i	0.197326	+	0.143366i
$681$	−1.94693	−	5.15018i	−0.0746065	−	0.197355i
$682$	2.13121	+	5.79859i	0.0816081	+	0.222039i
$683$		−	7.53725i		−	0.288405i	−0.989548	−	0.144202i	$-0.953938\pi$
$683$		−	7.53725i		−	0.288405i	0.989548	−	0.144202i	$-0.0460617\pi$
$684$	−12.7667	+	1.21048i	−0.488147	+	0.0462840i
$685$	11.1083	+	15.2893i	0.424428	+	0.584175i
$686$	18.0540	−	5.86611i	0.689306	−	0.223969i
$687$	−18.4201	−	48.7264i	−0.702772	−	1.85903i
$688$		−	8.13772i		−	0.310248i
$689$	−9.15634	+	2.97508i	−0.348829	+	0.113341i
$690$	−0.479600	−	10.1392i	−0.0182581	−	0.385991i
$691$	14.0053	−	43.1040i	0.532788	−	1.63975i	−0.215594	−	0.976483i	$-0.569169\pi$
$691$	14.0053	−	43.1040i	0.532788	−	1.63975i	0.748381	−	0.663269i	$-0.230831\pi$
$692$	0.496227	−	0.682998i	0.0188637	−	0.0259637i
$693$	4.92422	+	2.91028i	0.187056	+	0.110552i
$694$	3.20058	−	4.40522i	0.121492	−	0.167220i
$695$	1.17339	−	0.852515i	0.0445091	−	0.0323377i
$696$	−6.20183	+	0.293357i	−0.235080	+	0.0111197i
$697$	−0.494868	−	0.681128i	−0.0187445	−	0.0257996i
$698$	−5.07982	−	6.99178i	−0.192274	−	0.264643i
$699$	36.2724	−	1.71575i	1.37195	−	0.0648956i
$700$	1.39018	−	1.01003i	0.0525440	−	0.0381754i
$701$	10.5179	−	14.4766i	0.397254	−	0.546774i	−0.562798	−	0.826595i	$-0.690275\pi$
$701$	10.5179	−	14.4766i	0.397254	−	0.546774i	0.960052	+	0.279821i	$0.0902750\pi$
$702$	12.8135	+	2.23066i	0.483614	+	0.0841910i
$703$	−8.07185	+	11.1099i	−0.304436	+	0.419020i
$704$	0.342877	−	1.05527i	0.0129226	−	0.0397718i
$705$	0.433274	+	9.15979i	0.0163180	+	0.344978i
$706$	22.6511	−	7.35980i	0.852487	−	0.276990i
$707$			28.3255i			1.06529i
$708$	−4.06863	−	10.7627i	−0.152908	−	0.404486i
$709$	47.8931	−	15.5614i	1.79866	−	0.584422i	0.798812	−	0.601581i	$-0.205462\pi$
$709$	47.8931	−	15.5614i	1.79866	−	0.584422i	0.999853	+	0.0171590i	$0.00546214\pi$
$710$	4.47215	+	6.15539i	0.167837	+	0.231008i
$711$	0.658079	+	6.94062i	0.0246799	+	0.260294i
$712$		−	13.1048i		−	0.491123i
$713$	−30.6262	+	11.2563i	−1.14696	+	0.421553i
$714$	−6.69390	−	17.7073i	−0.250513	−	0.662678i
$715$	2.24689	+	1.63246i	0.0840289	+	0.0610506i
$716$	0.774625	−	0.562798i	0.0289491	−	0.0210327i
$717$	−7.61213	−	9.49871i	−0.284280	−	0.354736i
$718$	16.6474			0.621276
$719$	−6.48597			−0.241886			−0.120943	−	0.992659i	$-0.538592\pi$
$719$	−6.48597			−0.241886			−0.120943	+	0.992659i	$0.538592\pi$
$720$	1.52639	−	2.58266i	0.0568851	−	0.0962501i
$721$	−5.82185	+	17.9178i	−0.216817	+	0.667294i
$722$	0.691726	+	0.224755i	0.0257434	+	0.00836453i
$723$	2.53858	−	9.28468i	0.0944107	−	0.345301i
$724$	−2.16188	+	0.702439i	−0.0803458	+	0.0261059i
$725$	−2.90003	−	2.10699i	−0.107704	−	0.0782518i
$726$	−14.1433	−	9.28753i	−0.524907	−	0.344693i
$727$	15.1582	−	46.6522i	0.562187	−	1.73023i	−0.113978	−	0.993483i	$-0.536359\pi$
$727$	15.1582	−	46.6522i	0.562187	−	1.73023i	0.676165	−	0.736750i	$-0.263641\pi$
$728$	−3.47969	+	2.52814i	−0.128966	+	0.0936993i
$729$	25.4116	+	9.12418i	0.941170	+	0.337933i
$730$	−12.8859	−	4.18687i	−0.476927	−	0.154963i
$731$	−30.4231	−	41.8738i	−1.12524	−	1.54876i
$732$	−5.30714	+	19.4105i	−0.196157	+	0.717433i
$733$	10.3133	+	31.7412i	0.380931	+	1.17239i	0.939389	+	0.342853i	$0.111393\pi$
$733$	10.3133	+	31.7412i	0.380931	+	1.17239i	−0.558457	+	0.829533i	$0.688607\pi$
$734$	7.70978	+	5.60148i	0.284573	+	0.206754i
$735$	7.00219	−	0.331216i	0.258280	−	0.0122171i
$736$	5.57357	+	1.81096i	0.205444	+	0.0667529i
$737$	−4.97039	−	15.2973i	−0.183087	−	0.563483i
$738$	−0.297801	+	0.262698i	−0.0109622	+	0.00967005i
$739$			33.8304i			1.24447i	0.782830	+	0.622236i	$0.213776\pi$
$739$			33.8304i			1.24447i	−0.782830	+	0.622236i	$0.786224\pi$
$740$	−0.992740	−	3.05534i	−0.0364939	−	0.112317i
$741$	15.4909	+	10.1725i	0.569073	+	0.373695i
$742$	3.88490	−	5.34711i	0.142619	−	0.196299i
$743$	−48.0107			−1.76134			−0.880671	−	0.473729i	$-0.842908\pi$
$743$	−48.0107			−1.76134			−0.880671	+	0.473729i	$0.842908\pi$
$744$	−9.39225	−	2.18763i	−0.344336	−	0.0802024i
$745$	10.4417			0.382553
$746$	8.93269	−	12.2948i	0.327049	−	0.450144i
$747$	0.804820	−	3.60539i	0.0294468	−	0.131914i
$748$	−2.18082	−	6.71187i	−0.0797387	−	0.245410i
$749$		−	20.2254i		−	0.739019i
$750$	1.62015	−	0.612467i	0.0591595	−	0.0223641i
$751$	13.3114	+	40.9682i	0.485738	+	1.49495i	0.830908	+	0.556409i	$0.187821\pi$
$751$	13.3114	+	40.9682i	0.485738	+	1.49495i	−0.345170	+	0.938540i	$0.612179\pi$
$752$	−5.03520	−	1.63603i	−0.183615	−	0.0596601i
$753$	−1.30323	−	27.5515i	−0.0474924	−	1.00403i
$754$	7.25890	+	5.27390i	0.264354	+	0.192064i
$755$	−2.56698	−	7.90036i	−0.0934221	−	0.287524i
$756$	−8.01669	+	3.93159i	−0.291564	+	0.142990i
$757$	−24.4112	−	33.5991i	−0.887239	−	1.22118i	−0.974363	−	0.224982i	$-0.927768\pi$
$757$	−24.4112	−	33.5991i	−0.887239	−	1.22118i	0.0871241	−	0.996197i	$-0.472232\pi$
$758$	−7.44764	−	2.41988i	−0.270510	−	0.0878942i
$759$	−6.18214	+	9.41434i	−0.224398	+	0.341719i
$760$	3.45827	−	2.51258i	0.125445	−	0.0911408i
$761$	10.2147	−	31.4376i	0.370282	−	1.13961i	−0.576324	−	0.817221i	$-0.695514\pi$
$761$	10.2147	−	31.4376i	0.370282	−	1.13961i	0.946607	−	0.322391i	$-0.104486\pi$
$762$	4.82698	−	7.35066i	0.174863	−	0.266286i
$763$	27.5930	+	20.0475i	0.998932	+	0.725767i
$764$	−6.82767	+	2.21844i	−0.247016	+	0.0802605i
$765$	−1.80111	−	18.9959i	−0.0651192	−	0.686798i
$766$	−12.8089	−	4.16186i	−0.462804	−	0.150374i
$767$	−5.13826	+	15.8139i	−0.185532	+	0.571008i
$768$	1.08314	+	1.35159i	0.0390846	+	0.0487713i
$769$	52.9031			1.90774			0.953868	−	0.300227i	$-0.0970623\pi$
$769$	52.9031			1.90774			0.953868	+	0.300227i	$0.0970623\pi$
$770$	−1.90665			−0.0687107
$771$	12.3709	−	9.91385i	0.445527	−	0.357039i
$772$	4.11131	−	2.98704i	0.147969	−	0.107506i
$773$	−3.02841	−	2.20027i	−0.108924	−	0.0791381i	0.531990	−	0.846751i	$-0.321444\pi$
$773$	−3.02841	−	2.20027i	−0.108924	−	0.0791381i	−0.640914	+	0.767613i	$0.721444\pi$
$774$	−18.3080	+	16.1499i	−0.658066	+	0.580497i
$775$	−3.44165	−	4.37665i	−0.123628	−	0.157214i
$776$			11.6138i			0.416910i
$777$	−2.52172	+	9.22302i	−0.0904662	+	0.330874i
$778$	7.63794	+	10.5127i	0.273834	+	0.376899i
$779$	−0.538141	+	0.174853i	−0.0192809	+	0.00626475i
$780$	−4.05531	+	1.53303i	−0.145203	+	0.0548914i
$781$		−	8.44216i		−	0.302084i
$782$	35.4499	−	11.5184i	1.26769	−	0.411896i
$783$	12.9680	+	13.3705i	0.463438	+	0.477822i
$784$	−1.25066	+	3.84915i	−0.0446666	+	0.137470i
$785$	9.15568	−	12.6017i	0.326780	−	0.449775i
$786$	−11.5704	−	14.4380i	−0.412704	−	0.514988i
$787$	13.4974	−	18.5776i	0.481131	−	0.662220i	−0.497590	−	0.867412i	$-0.665782\pi$
$787$	13.4974	−	18.5776i	0.481131	−	0.662220i	0.978722	+	0.205192i	$0.0657818\pi$
$788$	−9.45589	+	6.87011i	−0.336852	+	0.244737i
$789$	−0.635727	−	13.4398i	−0.0226325	−	0.478470i
$790$	−1.36596	−	1.88009i	−0.0485988	−	0.0668905i
$791$	−9.53339	−	13.1216i	−0.338968	−	0.466550i
$792$	−3.05457	+	1.32286i	−0.108539	+	0.0470059i
$793$	23.5265	−	17.0930i	0.835451	−	0.606991i
$794$	−10.2620	+	14.1245i	−0.364186	+	0.501259i
$795$	5.19867	−	4.16614i	0.184378	−	0.147758i
$796$	0.945986	−	1.30204i	0.0335296	−	0.0461495i
$797$	12.4546	−	38.3314i	0.441165	−	1.35777i	−0.445469	−	0.895297i	$-0.646963\pi$
$797$	12.4546	−	38.3314i	0.441165	−	1.35777i	0.886635	−	0.462470i	$-0.153037\pi$
$798$	−12.7084	+	0.601129i	−0.449872	+	0.0212797i
$799$	−32.0257	+	10.4058i	−1.13299	+	0.368130i
$800$			1.00000i			0.0353553i
$801$	−29.4828	+	26.0075i	−1.04172	+	0.918930i
$802$	7.48366	−	2.43159i	0.264257	−	0.0858624i
$803$	8.83653	+	12.1624i	0.311834	+	0.429203i
$804$	24.2191	+	6.62189i	0.854143	+	0.233536i
$805$		−	10.0703i		−	0.354931i
$806$	8.61461	+	10.9549i	0.303437	+	0.385872i
$807$	−45.4993	+	17.2002i	−1.60165	+	0.605475i
$808$	−13.3359	−	9.68907i	−0.469154	−	0.340860i
$809$	33.8330	−	24.5811i	1.18951	−	0.864226i	0.196294	−	0.980545i	$-0.437109\pi$
$809$	33.8330	−	24.5811i	1.18951	−	0.864226i	0.993212	+	0.116319i	$0.0371094\pi$
$810$	−8.83962	+	1.69147i	−0.310593	+	0.0594324i
$811$	3.55690			0.124900			0.0624498	−	0.998048i	$-0.480109\pi$
$811$	3.55690			0.124900			0.0624498	+	0.998048i	$0.480109\pi$
$812$	−6.15969			−0.216163
$813$	8.61280	−	6.90217i	0.302064	−	0.242070i
$814$	−1.10152	+	3.39012i	−0.0386081	+	0.118824i
$815$	8.95412	+	2.90937i	0.313649	+	0.101911i
$816$	10.6264	+	2.90543i	0.372000	+	0.101711i
$817$	−33.0834	+	10.7494i	−1.15744	+	0.376076i
$818$	−9.90867	−	7.19907i	−0.346448	−	0.251710i
$819$	12.5935	+	2.81120i	0.440051	+	0.0982313i
$820$	0.0409045	−	0.125891i	0.00142845	−	0.00439631i
$821$	28.3876	−	20.6248i	0.990734	−	0.719810i	0.0306524	−	0.999530i	$-0.490242\pi$
$821$	28.3876	−	20.6248i	0.990734	−	0.719810i	0.960082	+	0.279720i	$0.0902415\pi$
$822$	27.3614	+	17.9675i	0.954338	+	0.626688i
$823$	28.1898	+	9.15943i	0.982636	+	0.319278i	0.755906	−	0.654680i	$-0.227197\pi$
$823$	28.1898	+	9.15943i	0.982636	+	0.319278i	0.226730	+	0.973958i	$0.427197\pi$
$824$	−6.44441	−	8.86997i	−0.224502	−	0.309000i
$825$	−1.85379	−	0.506856i	−0.0645408	−	0.0176465i
$826$	−3.52746	−	10.8564i	−0.122736	−	0.377742i
$827$	33.6750	+	24.4663i	1.17099	+	0.850776i	0.991127	−	0.132915i	$-0.0424337\pi$
$827$	33.6750	+	24.4663i	1.17099	+	0.850776i	0.179866	+	0.983691i	$0.442434\pi$
$828$	−6.98693	−	16.1332i	−0.242813	−	0.560668i
$829$	−18.7056	−	6.07781i	−0.649671	−	0.211091i	−0.0344021	−	0.999408i	$-0.510953\pi$
$829$	−18.7056	−	6.07781i	−0.649671	−	0.211091i	−0.615269	+	0.788317i	$0.710953\pi$
$830$	0.380516	+	1.17111i	0.0132079	+	0.0406497i
$831$	−2.97742	−	7.87611i	−0.103285	−	0.273219i
$832$		−	2.50305i		−	0.0867775i
$833$	7.95468	+	24.4820i	0.275613	+	0.848251i
$834$	1.37892	−	2.09986i	0.0477482	−	0.0727123i
$835$	7.01432	−	9.65438i	0.242740	−	0.334104i
$836$	−4.74304			−0.164041
$837$	13.7180	+	25.4719i	0.474163	+	0.880437i
$838$	−33.0444			−1.14150
$839$	21.2449	−	29.2411i	0.733455	−	1.00951i	−0.265514	−	0.964107i	$-0.585541\pi$
$839$	21.2449	−	29.2411i	0.733455	−	1.00951i	0.998969	−	0.0454071i	$-0.0144585\pi$
$840$	1.63370	−	2.48784i	0.0563678	−	0.0858385i
$841$	−4.99075	−	15.3600i	−0.172095	−	0.529654i
$842$		−	27.6068i		−	0.951394i
$843$	18.2947	+	48.3946i	0.630102	+	1.66680i
$844$	−6.66417	−	20.5102i	−0.229390	−	0.705990i
$845$	−6.40514	−	2.08116i	−0.220343	−	0.0715939i
$846$	6.31204	+	14.5749i	0.217012	+	0.501094i
$847$	−13.5805	−	9.86680i	−0.466631	−	0.339027i
$848$	1.18858	+	3.65808i	0.0408161	+	0.125619i
$849$	1.61790	+	0.442360i	0.0555263	+	0.0151818i
$850$	3.73853	+	5.14564i	0.128230	+	0.176494i
$851$	−17.9055	−	5.81785i	−0.613793	−	0.199433i
$852$	11.0155	+	7.23361i	0.377386	+	0.247819i
$853$	−4.89734	+	3.55813i	−0.167682	+	0.121828i	−0.668461	−	0.743747i	$-0.733047\pi$
$853$	−4.89734	+	3.55813i	−0.167682	+	0.121828i	0.500779	+	0.865575i	$0.333047\pi$
$854$	−6.16919	+	18.9868i	−0.211105	+	0.649715i
$855$	−12.5159	−	2.79389i	−0.428035	−	0.0955491i
$856$	9.52225	+	6.91832i	0.325464	+	0.236463i
$857$	−7.56587	+	2.45830i	−0.258445	+	0.0839740i	−0.435374	−	0.900250i	$-0.643384\pi$
$857$	−7.56587	+	2.45830i	−0.258445	+	0.0839740i	0.176929	+	0.984224i	$0.443384\pi$
$858$	4.64013	+	1.26868i	0.158411	+	0.0433122i
$859$	48.1687	+	15.6510i	1.64350	+	0.534004i	0.977316	−	0.211787i	$-0.0679282\pi$
$859$	48.1687	+	15.6510i	1.64350	+	0.534004i	0.666180	+	0.745791i	$0.267928\pi$
$860$	2.51469	−	7.73943i	0.0857503	−	0.263912i
$861$	−0.307432	+	0.246371i	−0.0104772	+	0.00839631i
$862$	−18.5069			−0.630348
$863$	53.6351			1.82576			0.912880	−	0.408228i	$-0.133853\pi$
$863$	53.6351			1.82576			0.912880	+	0.408228i	$0.133853\pi$
$864$	0.891180	−	5.11916i	0.0303186	−	0.174157i
$865$	0.682998	−	0.496227i	0.0232226	−	0.0168722i
$866$	27.2863	+	19.8247i	0.927227	+	0.673670i
$867$	37.9993	−	14.3650i	1.29053	−	0.487859i
$868$	−9.20506	−	2.60818i	−0.312440	−	0.0885274i
$869$			2.57855i			0.0874714i
$870$	−5.98894	−	1.63747i	−0.203044	−	0.0555155i
$871$	−21.3275	−	29.3548i	−0.722655	−	0.994650i
$872$	−18.8770	+	6.13350i	−0.639255	+	0.207707i
$873$	26.1283	−	23.0484i	0.884309	−	0.780072i
$874$		−	25.0512i		−	0.847368i
$875$	1.63426	−	0.531003i	0.0552480	−	0.0179512i
$876$	−23.4414	+	1.10882i	−0.792010	+	0.0374634i
$877$	−4.58841	+	14.1217i	−0.154940	+	0.476856i	−0.998155	−	0.0607209i	$-0.980660\pi$
$877$	−4.58841	+	14.1217i	−0.154940	+	0.476856i	0.843215	+	0.537576i	$0.180660\pi$
$878$	−0.0324386	+	0.0446479i	−0.00109475	+	0.00150679i
$879$	3.04994	−	2.44418i	0.102872	−	0.0824401i
$880$	0.652190	−	0.897663i	0.0219853	−	0.0302602i
$881$	22.5075	−	16.3527i	0.758299	−	0.550936i	−0.140089	−	0.990139i	$-0.544739\pi$
$881$	22.5075	−	16.3527i	0.758299	−	0.550936i	0.898388	+	0.439203i	$0.144739\pi$
$882$	11.1417	−	4.82523i	0.375162	−	0.162474i
$883$	27.6393	+	38.0422i	0.930136	+	1.28022i	0.959807	+	0.280662i	$0.0905541\pi$
$883$	27.6393	+	38.0422i	0.930136	+	1.28022i	−0.0296708	+	0.999560i	$0.509446\pi$
$884$	−9.35771	−	12.8798i	−0.314734	−	0.433194i
$885$	−0.543647	−	11.4932i	−0.0182745	−	0.386339i
$886$	−22.1348	+	16.0819i	−0.743634	+	0.540282i
$887$	16.5775	−	22.8170i	0.556619	−	0.766121i	−0.434272	−	0.900782i	$-0.642994\pi$
$887$	16.5775	−	22.8170i	0.556619	−	0.766121i	0.990892	+	0.134661i	$0.0429945\pi$
$888$	−3.47968	−	4.34209i	−0.116771	−	0.145711i
$889$	5.12805	−	7.05815i	0.171989	−	0.236723i
$890$	4.04961	−	12.4634i	0.135743	−	0.417774i
$891$	9.03816	+	4.24674i	0.302790	+	0.142271i
$892$	−9.53488	+	3.09807i	−0.319251	+	0.103731i
$893$			22.6314i			0.757331i
$894$	16.9171	−	6.39518i	0.565791	−	0.213887i
$895$	0.910626	−	0.295880i	0.0304389	−	0.00989019i
$896$	1.01003	+	1.39018i	0.0337426	+	0.0464428i
$897$	−6.70077	+	24.5076i	−0.223732	+	0.818286i
$898$			11.5634i			0.385875i
$899$	0.759316	+	19.9439i	0.0253246	+	0.665167i
$900$	2.24977	−	1.98458i	0.0749922	−	0.0661526i
$901$	19.7919	+	14.3796i	0.659362	+	0.479055i
$902$	−0.118823	+	0.0863303i	−0.00395639	+	0.00287448i
$903$	−18.9000	+	15.1462i	−0.628953	+	0.504034i
$904$	9.43874			0.313928
$905$	−2.27314			−0.0755617
$906$	−8.99761	−	11.2276i	−0.298926	−	0.373011i
$907$	−12.0636	+	37.1281i	−0.400567	+	1.23282i	0.523974	+	0.851734i	$0.324449\pi$
$907$	−12.0636	+	37.1281i	−0.400567	+	1.23282i	−0.924541	+	0.381083i	$0.875551\pi$
$908$	3.02325	+	0.982312i	0.100330	+	0.0325992i
$909$	4.66789	+	49.2313i	0.154824	+	1.63290i
$910$	−4.09062	+	1.32912i	−0.135603	+	0.0440600i
$911$	−29.2631	−	21.2609i	−0.969529	−	0.704404i	−0.0141850	−	0.999899i	$-0.504515\pi$
$911$	−29.2631	−	21.2609i	−0.969529	−	0.704404i	−0.955344	+	0.295495i	$0.904515\pi$
$912$	4.06404	−	6.18883i	0.134574	−	0.204933i
$913$	0.422210	−	1.29943i	0.0139731	−	0.0430048i
$914$	4.50434	−	3.27260i	0.148990	−	0.108248i
$915$	−11.0456	+	16.8205i	−0.365155	+	0.556068i
$916$	28.6033	+	9.29377i	0.945079	+	0.307075i
$917$	−10.7894	−	14.8503i	−0.356296	−	0.490400i
$918$	−14.5524	−	29.6731i	−0.480302	−	0.979357i
$919$	10.9995	+	33.8530i	0.362840	+	1.11671i	0.951322	+	0.308197i	$0.0997257\pi$
$919$	10.9995	+	33.8530i	0.362840	+	1.11671i	−0.588482	+	0.808510i	$0.700274\pi$
$920$	4.74116	+	3.44465i	0.156311	+	0.113567i
$921$	−0.766490	−	16.2043i	−0.0252567	−	0.533949i
$922$	−34.0917	−	11.0770i	−1.12275	−	0.364803i
$923$	−5.88504	−	18.1123i	−0.193708	−	0.596173i
$924$	−3.08905	+	1.16776i	−0.101622	+	0.0384164i
$925$		−	3.21258i		−	0.105629i
$926$	8.07669	+	24.8575i	0.265417	+	0.816868i
$927$	−7.16594	+	32.1016i	−0.235360	+	1.05435i
$928$	2.10699	−	2.90003i	0.0691655	−	0.0951981i
$929$	−30.5057			−1.00086			−0.500429	−	0.865777i	$-0.666824\pi$
$929$	−30.5057			−1.00086			−0.500429	+	0.865777i	$0.666824\pi$
$930$	−8.25654	−	4.98292i	−0.270743	−	0.163396i
$931$	17.3005			0.567002
$932$	−12.3231	+	16.9613i	−0.403656	+	0.555585i
$933$	−29.7350	−	19.5261i	−0.973479	−	0.639257i
$934$	−2.42682	−	7.46899i	−0.0794080	−	0.244393i
$935$		−	7.05728i		−	0.230798i
$936$	−5.63127	+	4.96749i	−0.184064	+	0.162367i
$937$	−9.64841	−	29.6948i	−0.315200	−	0.970085i	−0.975672	−	0.219235i	$-0.929644\pi$
$937$	−9.64841	−	29.6948i	−0.315200	−	0.970085i	0.660472	−	0.750850i	$-0.270356\pi$
$938$	23.6905	+	7.69750i	0.773521	+	0.251332i
$939$	9.05588	−	0.428359i	0.295527	−	0.0139790i
$940$	−4.28320	−	3.11192i	−0.139702	−	0.101500i
$941$	16.1231	+	49.6218i	0.525598	+	1.61762i	0.763131	+	0.646244i	$0.223661\pi$
$941$	16.1231	+	49.6218i	0.525598	+	1.61762i	−0.237533	+	0.971379i	$0.576339\pi$
$942$	7.11543	−	26.0242i	0.231833	−	0.847915i
$943$	−0.455968	−	0.627586i	−0.0148484	−	0.0204370i
$944$	6.31788	+	2.05280i	0.205629	+	0.0668130i
$945$	−8.83925	+	1.26187i	−0.287541	+	0.0410486i
$946$	−7.30493	+	5.30734i	−0.237504	+	0.172556i
$947$	13.1904	−	40.5957i	0.428629	−	1.31918i	−0.470847	−	0.882215i	$-0.656052\pi$
$947$	13.1904	−	40.5957i	0.428629	−	1.31918i	0.899476	−	0.436970i	$-0.143948\pi$
$948$	−3.36456	−	2.20942i	−0.109276	−	0.0717585i
$949$	27.4368	+	19.9340i	0.890637	+	0.647086i
$950$	4.06544	−	1.32094i	0.131900	−	0.0428570i
$951$	11.4103	−	41.7322i	0.370003	−	1.35326i
$952$	10.3945	+	3.37737i	0.336887	+	0.109461i
$953$	−4.11532	+	12.6656i	−0.133308	+	0.410281i	−0.995323	−	0.0966025i	$-0.969202\pi$
$953$	−4.11532	+	12.6656i	−0.133308	+	0.410281i	0.862015	+	0.506883i	$0.169202\pi$
$954$	5.87100	−	9.93378i	0.190081	−	0.321618i
$955$	−7.17904			−0.232308
$956$	7.02780			0.227295
$957$	4.30811	+	5.37583i	0.139261	+	0.173776i
$958$	13.1687	−	9.56763i	0.425462	−	0.309116i
$959$	26.2726	+	19.0882i	0.848386	+	0.616389i
$960$	0.612467	+	1.62015i	0.0197673	+	0.0522901i
$961$	−7.31008	+	30.1258i	−0.235809	+	0.971799i
$962$			8.04122i			0.259259i
$963$	−3.33303	−	35.1528i	−0.107406	−	1.13278i
$964$	3.26648	+	4.49592i	0.105206	+	0.144804i
$965$	4.83313	−	1.57038i	0.155584	−	0.0505523i
$966$	−6.16771	−	16.3153i	−0.198443	−	0.524938i
$967$		−	31.5606i		−	1.01492i	−0.861676	−	0.507460i	$-0.830585\pi$
$967$		−	31.5606i		−	1.01492i	0.861676	−	0.507460i	$-0.169415\pi$
$968$	9.29073	−	3.01874i	0.298615	−	0.0970260i
$969$	−2.22503	−	47.0390i	−0.0714782	−	1.51111i
$970$	−3.58885	+	11.0454i	−0.115231	+	0.354645i
$971$	−5.01087	+	6.89688i	−0.160807	+	0.221331i	−0.881816	−	0.471594i	$-0.843679\pi$
$971$	−5.01087	+	6.89688i	−0.160807	+	0.221331i	0.721009	+	0.692926i	$0.243679\pi$
$972$	−13.2855	+	8.15442i	−0.426134	+	0.261553i
$973$	1.46493	−	2.01630i	0.0469635	−	0.0646396i
$974$	25.4512	−	18.4914i	0.815510	−	0.592503i
$975$	−4.33056	+	0.204843i	−0.138689	+	0.00656023i
$976$	−6.82889	−	9.39915i	−0.218587	−	0.300860i
$977$	−12.6189	−	17.3684i	−0.403713	−	0.555664i	0.557958	−	0.829869i	$-0.311585\pi$
$977$	−12.6189	−	17.3684i	−0.403713	−	0.555664i	−0.961671	+	0.274206i	$0.911585\pi$
$978$	16.2889	−	0.770493i	0.520862	−	0.0246377i
$979$	−11.7637	+	8.54682i	−0.375969	+	0.273158i
$980$	−2.37891	+	3.27428i	−0.0759914	+	0.104593i
$981$	51.2618	+	30.2964i	1.63666	+	0.967290i
$982$	−15.7344	+	21.6566i	−0.502106	+	0.691090i
$983$	−15.6404	+	48.1361i	−0.498850	+	1.53530i	0.312018	+	0.950076i	$0.398995\pi$
$983$	−15.6404	+	48.1361i	−0.498850	+	1.53530i	−0.810869	+	0.585228i	$0.801005\pi$
$984$	−0.0108328	−	0.229015i	−0.000345337	−	0.00730074i
$985$	−11.1161	+	3.61183i	−0.354187	+	0.115082i
$986$		−	22.7996i		−	0.726086i
$987$	5.57195	+	14.7394i	0.177357	+	0.469160i
$988$	−10.1760	+	3.30638i	−0.323741	+	0.105190i
$989$	−28.0316	−	38.5822i	−0.891354	−	1.22684i
$990$	−3.31385	+	0.314205i	−0.105321	+	0.00998609i
$991$		−	3.95663i		−	0.125686i	−0.998023	−	0.0628432i	$-0.979983\pi$
$991$		−	3.95663i		−	0.125686i	0.998023	−	0.0628432i	$-0.0200168\pi$
$992$	4.37665	−	3.44165i	0.138959	−	0.109273i
$993$	−2.92533	−	7.73832i	−0.0928325	−	0.245568i
$994$	10.5772	+	7.68477i	0.335488	+	0.243746i
$995$	1.30204	−	0.945986i	0.0412774	−	0.0299898i
$996$	1.33376	+	1.66431i	0.0422617	+	0.0527358i
$997$	26.0042			0.823561			0.411780	−	0.911283i	$-0.364907\pi$
$997$	26.0042			0.823561			0.411780	+	0.911283i	$0.364907\pi$
$998$	31.0652			0.983353
$999$	−2.86298	+	16.4457i	−0.0905808	+	0.520319i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.v.a.401.3	✓	80
3.2	odd	2	inner	930.2.v.a.401.20	yes	80
31.15	odd	10	inner	930.2.v.a.821.20	yes	80
93.77	even	10	inner	930.2.v.a.821.3	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.v.a.401.3	✓	80	1.1	even	1	trivial
930.2.v.a.401.20	yes	80	3.2	odd	2	inner
930.2.v.a.821.3	yes	80	93.77	even	10	inner
930.2.v.a.821.20	yes	80	31.15	odd	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.587785 + 0.809017i) q^{2} +(-0.950729 + 1.44780i) q^{3} +(-0.309017 - 0.951057i) q^{4} -1.00000i q^{5} +(-0.612467 - 1.62015i) q^{6} +(-0.531003 - 1.63426i) q^{7} +(0.951057 + 0.309017i) q^{8} +(-1.19223 - 2.75292i) q^{9} +O(q^{10})\)	\(q+(-0.587785 + 0.809017i) q^{2} +(-0.950729 + 1.44780i) q^{3} +(-0.309017 - 0.951057i) q^{4} -1.00000i q^{5} +(-0.612467 - 1.62015i) q^{6} +(-0.531003 - 1.63426i) q^{7} +(0.951057 + 0.309017i) q^{8} +(-1.19223 - 2.75292i) q^{9} +(0.809017 + 0.587785i) q^{10} +(-0.342877 - 1.05527i) q^{11} +(1.67073 + 0.456803i) q^{12} +(-1.47125 - 2.02501i) q^{13} +(1.63426 + 0.531003i) q^{14} +(1.44780 + 0.950729i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-1.96546 + 6.04907i) q^{17} +(2.92794 + 0.653595i) q^{18} +(3.45827 + 2.51258i) q^{19} +(-0.951057 + 0.309017i) q^{20} +(2.87091 + 0.784953i) q^{21} +(1.05527 + 0.342877i) q^{22} +(-1.81096 + 5.57357i) q^{23} +(-1.35159 + 1.08314i) q^{24} -1.00000 q^{25} +2.50305 q^{26} +(5.11916 + 0.891180i) q^{27} +(-1.39018 + 1.01003i) q^{28} +(2.90003 + 2.10699i) q^{29} +(-1.62015 + 0.612467i) q^{30} +(3.44165 + 4.37665i) q^{31} -1.00000i q^{32} +(1.85379 + 0.506856i) q^{33} +(-3.73853 - 5.14564i) q^{34} +(-1.63426 + 0.531003i) q^{35} +(-2.24977 + 1.98458i) q^{36} +3.21258i q^{37} +(-4.06544 + 1.32094i) q^{38} +(4.33056 - 0.204843i) q^{39} +(0.309017 - 0.951057i) q^{40} +(-0.0778050 + 0.107089i) q^{41} +(-2.32252 + 1.86123i) q^{42} +(-4.78323 + 6.58355i) q^{43} +(-0.897663 + 0.652190i) q^{44} +(-2.75292 + 1.19223i) q^{45} +(-3.44465 - 4.74116i) q^{46} +(3.11192 + 4.28320i) q^{47} +(-0.0818375 - 1.73012i) q^{48} +(3.27428 - 2.37891i) q^{49} +(0.587785 - 0.809017i) q^{50} +(-6.88919 - 8.59661i) q^{51} +(-1.47125 + 2.02501i) q^{52} +(1.18858 - 3.65808i) q^{53} +(-3.72995 + 3.61767i) q^{54} +(-1.05527 + 0.342877i) q^{55} -1.71836i q^{56} +(-6.92558 + 2.61809i) q^{57} +(-3.40919 + 1.10771i) q^{58} +(-3.90466 - 5.37431i) q^{59} +(0.456803 - 1.67073i) q^{60} +11.6180i q^{61} +(-5.56373 + 0.211825i) q^{62} +(-3.86591 + 3.41022i) q^{63} +(0.809017 + 0.587785i) q^{64} +(-2.02501 + 1.47125i) q^{65} +(-1.49969 + 1.20183i) q^{66} +14.4962 q^{67} +6.36036 q^{68} +(-6.34766 - 7.92086i) q^{69} +(0.531003 - 1.63426i) q^{70} +(7.23610 + 2.35115i) q^{71} +(-0.283177 - 2.98661i) q^{72} +(-12.8859 + 4.18687i) q^{73} +(-2.59903 - 1.88830i) q^{74} +(0.950729 - 1.44780i) q^{75} +(1.32094 - 4.06544i) q^{76} +(-1.54251 + 1.12070i) q^{77} +(-2.37972 + 3.62390i) q^{78} +(-2.21018 - 0.718130i) q^{79} +(0.587785 + 0.809017i) q^{80} +(-6.15718 + 6.56423i) q^{81} +(-0.0409045 - 0.125891i) q^{82} +(0.996203 + 0.723784i) q^{83} +(-0.140626 - 2.97296i) q^{84} +(6.04907 + 1.96546i) q^{85} +(-2.51469 - 7.73943i) q^{86} +(-5.80764 + 2.19547i) q^{87} -1.10957i q^{88} +(-4.04961 - 12.4634i) q^{89} +(0.653595 - 2.92794i) q^{90} +(-2.52814 + 3.47969i) q^{91} +5.86040 q^{92} +(-9.60857 + 0.821804i) q^{93} -5.29432 q^{94} +(2.51258 - 3.45827i) q^{95} +(1.44780 + 0.950729i) q^{96} +(3.58885 + 11.0454i) q^{97} +4.04724i q^{98} +(-2.49628 + 2.20203i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 20 q^{4} + 12 q^{7} - 8 q^{9}+O(q^{10}) \) 80 * q + 20 * q^4 + 12 * q^7 - 8 * q^9	\( 80 q + 20 q^{4} + 12 q^{7} - 8 q^{9} + 20 q^{10} - 10 q^{13} - 20 q^{16} - 12 q^{18} - 12 q^{19} + 30 q^{21} + 10 q^{22} - 80 q^{25} + 18 q^{28} + 16 q^{31} + 72 q^{33} + 10 q^{34} + 8 q^{36} + 54 q^{39} - 20 q^{40} + 50 q^{43} + 8 q^{45} - 10 q^{46} + 8 q^{49} - 44 q^{51} - 10 q^{52} - 10 q^{55} + 30 q^{58} + 28 q^{63} + 20 q^{64} + 66 q^{66} + 60 q^{67} + 20 q^{69} - 12 q^{70} + 12 q^{72} - 20 q^{73} - 18 q^{76} + 8 q^{78} + 40 q^{79} + 16 q^{81} - 4 q^{82} - 60 q^{84} - 72 q^{87} - 12 q^{90} + 10 q^{91} + 104 q^{93} - 12 q^{94} - 178 q^{97}+O(q^{100}) \) 80 * q + 20 * q^4 + 12 * q^7 - 8 * q^9 + 20 * q^10 - 10 * q^13 - 20 * q^16 - 12 * q^18 - 12 * q^19 + 30 * q^21 + 10 * q^22 - 80 * q^25 + 18 * q^28 + 16 * q^31 + 72 * q^33 + 10 * q^34 + 8 * q^36 + 54 * q^39 - 20 * q^40 + 50 * q^43 + 8 * q^45 - 10 * q^46 + 8 * q^49 - 44 * q^51 - 10 * q^52 - 10 * q^55 + 30 * q^58 + 28 * q^63 + 20 * q^64 + 66 * q^66 + 60 * q^67 + 20 * q^69 - 12 * q^70 + 12 * q^72 - 20 * q^73 - 18 * q^76 + 8 * q^78 + 40 * q^79 + 16 * q^81 - 4 * q^82 - 60 * q^84 - 72 * q^87 - 12 * q^90 + 10 * q^91 + 104 * q^93 - 12 * q^94 - 178 * q^97

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