LMFDB - Embedded newform 930.2.v.a.401.20

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			401.20
Character	$\chi$	$=$	930.401
Dual form			930.2.v.a.821.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.587785 - 0.809017i) q^{2} +(1.67073 - 0.456803i) q^{3} +(-0.309017 - 0.951057i) q^{4} +1.00000i q^{5} +(0.612467 - 1.62015i) q^{6} +(-0.531003 - 1.63426i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(2.58266 - 1.52639i) q^{9} +O(q^{10})$	\(q+(0.587785 - 0.809017i) q^{2} +(1.67073 - 0.456803i) 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} +(2.58266 - 1.52639i) q^{9} +(0.809017 + 0.587785i) q^{10} +(0.342877 + 1.05527i) q^{11} +(-0.950729 - 1.44780i) q^{12} +(-1.47125 - 2.02501i) q^{13} +(-1.63426 - 0.531003i) q^{14} +(0.456803 + 1.67073i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(1.96546 - 6.04907i) q^{17} +(0.283177 - 2.98661i) q^{18} +(3.45827 + 2.51258i) q^{19} +(0.951057 - 0.309017i) q^{20} +(-1.63370 - 2.48784i) q^{21} +(1.05527 + 0.342877i) q^{22} +(1.81096 - 5.57357i) q^{23} +(-1.73012 - 0.0818375i) q^{24} -1.00000 q^{25} -2.50305 q^{26} +(3.61767 - 3.72995i) 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} +(1.05490 + 1.60643i) 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} +(-3.38309 - 2.71116i) q^{39} +(0.309017 - 0.951057i) q^{40} +(0.0778050 - 0.107089i) q^{41} +(-2.97296 - 0.140626i) q^{42} +(-4.78323 + 6.58355i) q^{43} +(0.897663 - 0.652190i) q^{44} +(1.52639 + 2.58266i) q^{45} +(-3.44465 - 4.74116i) q^{46} +(-3.11192 - 4.28320i) q^{47} +(-1.08314 + 1.35159i) q^{48} +(3.27428 - 2.37891i) q^{49} +(-0.587785 + 0.809017i) q^{50} +(0.520516 - 11.0042i) q^{51} +(-1.47125 + 2.02501i) q^{52} +(-1.18858 + 3.65808i) q^{53} +(-0.891180 - 5.11916i) 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} +(1.44780 - 0.950729i) 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} +(1.91969 + 0.0908046i) q^{66} +14.4962 q^{67} -6.36036 q^{68} +(0.479600 - 10.1392i) q^{69} +(0.531003 - 1.63426i) q^{70} +(-7.23610 - 2.35115i) q^{71} +(-2.92794 + 0.653595i) q^{72} +(-12.8859 + 4.18687i) q^{73} +(2.59903 + 1.88830i) q^{74} +(-1.67073 + 0.456803i) q^{75} +(1.32094 - 4.06544i) q^{76} +(1.54251 - 1.12070i) q^{77} +(-4.18191 + 1.14340i) q^{78} +(-2.21018 - 0.718130i) q^{79} +(-0.587785 - 0.809017i) q^{80} +(4.34028 - 7.88429i) q^{81} +(-0.0409045 - 0.125891i) q^{82} +(-0.996203 - 0.723784i) q^{83} +(-1.86123 + 2.32252i) 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} +(2.98661 + 0.283177i) q^{90} +(-2.52814 + 3.47969i) q^{91} -5.86040 q^{92} +(7.74933 + 5.74003i) q^{93} -5.29432 q^{94} +(-2.51258 + 3.45827i) q^{95} +(0.456803 + 1.67073i) 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
$3$	1.67073	−	0.456803i	0.964595	−	0.263735i
$3$	1.67073	−	0.456803i	0.964595	−	0.263735i
$4$	−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
$9$	2.58266	−	1.52639i	0.860887	−	0.508796i
$10$	0.809017	+	0.587785i	0.255834	+	0.185874i
$11$	0.342877	+	1.05527i	0.103381	+	0.318175i	0.989347	−	0.145576i	$-0.0465035\pi$
$11$	0.342877	+	1.05527i	0.103381	+	0.318175i	−0.885966	+	0.463750i	$0.846503\pi$
$12$	−0.950729	−	1.44780i	−0.274452	−	0.417943i
$13$	−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
$15$	0.456803	+	1.67073i	0.117946	+	0.431380i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	1.96546	−	6.04907i	0.476694	−	1.46711i	−0.366965	−	0.930235i	$-0.619603\pi$
$17$	1.96546	−	6.04907i	0.476694	−	1.46711i	0.843659	−	0.536879i	$-0.180397\pi$
$18$	0.283177	−	2.98661i	0.0667454	−	0.703950i
$19$	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
$21$	−1.63370	−	2.48784i	−0.356502	−	0.542890i
$22$	1.05527	+	0.342877i	0.224983	+	0.0731015i
$23$	1.81096	−	5.57357i	0.377612	−	1.16217i	−0.564088	−	0.825715i	$-0.690772\pi$
$23$	1.81096	−	5.57357i	0.377612	−	1.16217i	0.941700	−	0.336454i	$-0.109228\pi$
$24$	−1.73012	−	0.0818375i	−0.353159	−	0.0167050i
$25$	−1.00000			−0.200000
$26$	−2.50305			−0.490888
$27$	3.61767	−	3.72995i	0.696220	−	0.717829i
$28$	−1.39018	+	1.01003i	−0.262720	+	0.190877i
$29$	−2.90003	−	2.10699i	−0.538522	−	0.391259i	0.285014	−	0.958523i	$-0.408002\pi$
$29$	−2.90003	−	2.10699i	−0.538522	−	0.391259i	−0.823536	+	0.567264i	$0.808002\pi$
$30$	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
$33$	1.05490	+	1.60643i	0.183635	+	0.279644i
$34$	−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
$39$	−3.38309	−	2.71116i	−0.541728	−	0.434133i
$40$	0.309017	−	0.951057i	0.0488599	−	0.150375i
$41$	0.0778050	−	0.107089i	0.0121511	−	0.0167246i	−0.802898	−	0.596116i	$-0.796710\pi$
$41$	0.0778050	−	0.107089i	0.0121511	−	0.0167246i	0.815049	+	0.579392i	$0.196710\pi$
$42$	−2.97296	−	0.140626i	−0.458738	−	0.0216991i
$43$	−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
$45$	1.52639	+	2.58266i	0.227540	+	0.385000i
$46$	−3.44465	−	4.74116i	−0.507887	−	0.699046i
$47$	−3.11192	−	4.28320i	−0.453921	−	0.624768i	0.519314	−	0.854584i	$-0.326188\pi$
$47$	−3.11192	−	4.28320i	−0.453921	−	0.624768i	−0.973234	+	0.229816i	$0.926188\pi$
$48$	−1.08314	+	1.35159i	−0.156338	+	0.195085i
$49$	3.27428	−	2.37891i	0.467755	−	0.339844i
$50$	−0.587785	+	0.809017i	−0.0831254	+	0.114412i
$51$	0.520516	−	11.0042i	0.0728869	−	1.54089i
$52$	−1.47125	+	2.02501i	−0.204026	+	0.280818i
$53$	−1.18858	+	3.65808i	−0.163264	+	0.502476i	−0.998904	−	0.0468017i	$-0.985097\pi$
$53$	−1.18858	+	3.65808i	−0.163264	+	0.502476i	0.835640	+	0.549278i	$0.185097\pi$
$54$	−0.891180	−	5.11916i	−0.121274	−	0.696629i
$55$	−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	0.983639	−	0.180151i	$-0.0576587\pi$
$59$	3.90466	+	5.37431i	0.508344	+	0.699675i	−0.475295	+	0.879826i	$0.657659\pi$
$60$	1.44780	−	0.950729i	0.186910	−	0.122739i
$61$			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
$66$	1.91969	+	0.0908046i	0.236297	+	0.0111773i
$67$	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
$69$	0.479600	−	10.1392i	0.0577371	−	1.22061i
$70$	0.531003	−	1.63426i	0.0634670	−	0.195331i
$71$	−7.23610	−	2.35115i	−0.858767	−	0.279030i	−0.153653	−	0.988125i	$-0.549104\pi$
$71$	−7.23610	−	2.35115i	−0.858767	−	0.279030i	−0.705113	+	0.709095i	$0.749104\pi$
$72$	−2.92794	+	0.653595i	−0.345061	+	0.0770269i
$73$	−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
$75$	−1.67073	+	0.456803i	−0.192919	+	0.0527471i
$76$	1.32094	−	4.06544i	0.151522	−	0.466338i
$77$	1.54251	−	1.12070i	0.175785	−	0.127715i
$78$	−4.18191	+	1.14340i	−0.473508	+	0.129464i
$79$	−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
$81$	4.34028	−	7.88429i	0.482253	−	0.876032i
$82$	−0.0409045	−	0.125891i	−0.00451715	−	0.0139024i
$83$	−0.996203	−	0.723784i	−0.109348	−	0.0794456i	0.531768	−	0.846890i	$-0.321528\pi$
$83$	−0.996203	−	0.723784i	−0.109348	−	0.0794456i	−0.641115	+	0.767445i	$0.721528\pi$
$84$	−1.86123	+	2.32252i	−0.203077	+	0.253408i
$85$	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	$0.144398\pi$
$89$	4.04961	+	12.4634i	0.429258	+	1.32112i	−0.469601	+	0.882879i	$0.655602\pi$
$90$	2.98661	+	0.283177i	0.314816	+	0.0298495i
$91$	−2.52814	+	3.47969i	−0.265022	+	0.364771i
$92$	−5.86040			−0.610988
$93$	7.74933	+	5.74003i	0.803568	+	0.595213i
$94$	−5.29432			−0.546067
$95$	−2.51258	+	3.45827i	−0.257785	+	0.354811i
$96$	0.456803	+	1.67073i	0.0466223	+	0.170518i
$97$	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	0.956793	−	0.290771i	$-0.0939118\pi$
$101$	15.6772	+	5.09384i	1.55994	+	0.506856i	0.603151	+	0.797627i	$0.293912\pi$
$102$	−8.59661	−	6.88919i	−0.851191	−	0.682132i
$103$	−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
$105$	2.48784	−	1.63370i	0.242788	−	0.159432i
$106$	2.26082	+	3.11175i	0.219590	+	0.302240i
$107$	−11.1941	−	3.63718i	−1.08217	−	0.351619i	−0.286955	−	0.957944i	$-0.592643\pi$
$107$	−11.1941	−	3.63718i	−1.08217	−	0.351619i	−0.795217	+	0.606325i	$0.792643\pi$
$108$	−4.66531	−	2.28799i	−0.448920	−	0.220162i
$109$	−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
$111$	1.46751	+	5.36734i	0.139290	+	0.509445i
$112$	1.39018	+	1.01003i	0.131360	+	0.0954386i
$113$	−8.97678	+	2.91673i	−0.844464	+	0.274383i	−0.699126	−	0.714999i	$-0.746427\pi$
$113$	−8.97678	+	2.91673i	−0.844464	+	0.274383i	−0.145339	+	0.989382i	$0.546427\pi$
$114$	6.18883	−	4.06404i	0.579637	−	0.380632i
$115$	5.57357	+	1.81096i	0.519738	+	0.168873i
$116$	−1.10771	+	3.40919i	−0.102848	+	0.316535i
$117$	−6.89069	−	2.98420i	−0.637045	−	0.275890i
$118$	6.64301			0.611539
$119$	−10.9294			−1.00190
$120$	0.0818375	−	1.73012i	0.00747071	−	0.157937i
$121$	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
$126$	−5.03125	+	1.12311i	−0.448220	+	0.100055i
$127$	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	−0.717123	−	0.696946i	$-0.754542\pi$
$131$	−10.1594	+	3.30100i	−0.887634	+	0.288410i	−0.170510	+	0.985356i	$0.554542\pi$
$132$	1.20183	−	1.49969i	0.104606	−	0.130531i
$133$	2.26985	−	6.98589i	0.196821	−	0.605754i
$134$	8.52063	−	11.7276i	0.736070	−	1.01311i
$135$	3.72995	+	3.61767i	0.321023	+	0.311359i
$136$	−3.73853	+	5.14564i	−0.320576	+	0.441235i
$137$	15.2893	−	11.1083i	1.30626	−	0.949050i	0.306260	−	0.951948i	$-0.400922\pi$
$137$	15.2893	−	11.1083i	1.30626	−	0.949050i	0.999996	+	0.00289768i	$0.000922361\pi$
$138$	−7.92086	−	6.34766i	−0.674268	−	0.540348i
$139$	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
$141$	−7.15575	−	5.73452i	−0.602623	−	0.482933i
$142$	−6.15539	+	4.47215i	−0.516549	+	0.375295i
$143$	1.63246	−	2.24689i	0.136513	−	0.187894i
$144$	−1.19223	+	2.75292i	−0.0993524	+	0.229410i
$145$	2.10699	−	2.90003i	0.174976	−	0.240834i
$146$	−4.18687	+	12.8859i	−0.346508	+	1.06644i
$147$	4.38374	−	5.47021i	0.361565	−	0.451175i
$148$	3.05534	−	0.992740i	0.251147	−	0.0816028i
$149$		−	10.4417i		−	0.855415i	−0.903917	−	0.427708i	$-0.859321\pi$
$149$		−	10.4417i		−	0.855415i	0.903917	−	0.427708i	$-0.140679\pi$
$150$	−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
$153$	−4.15710	−	18.6227i	−0.336082	−	1.50556i
$154$		−	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
$159$	−0.314774	+	6.65461i	−0.0249632	+	0.527745i
$160$	−1.00000			−0.0790569
$161$	−10.0703			−0.793649
$162$	−3.82737	−	8.14563i	−0.300706	−	0.639981i
$163$	−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
$165$	−1.60643	+	1.05490i	−0.125061	+	0.0821240i
$166$	−1.17111	+	0.380516i	−0.0908955	+	0.0295337i
$167$	−9.65438	−	7.01432i	−0.747078	−	0.542784i	0.147842	−	0.989011i	$-0.452767\pi$
$167$	−9.65438	−	7.01432i	−0.747078	−	0.542784i	−0.894920	+	0.446227i	$0.852767\pi$
$168$	0.784953	+	2.87091i	0.0605604	+	0.221496i
$169$	2.08116	−	6.40514i	0.160089	−	0.492703i
$170$	5.14564	−	3.73853i	0.394653	−	0.286732i
$171$	12.7667	+	1.21048i	0.976295	+	0.0925680i
$172$	7.73943	+	2.51469i	0.590126	+	0.191744i
$173$	−0.496227	−	0.682998i	−0.0377275	−	0.0519274i	0.789737	−	0.613446i	$-0.210217\pi$
$173$	−0.496227	−	0.682998i	−0.0377275	−	0.0519274i	−0.827464	+	0.561519i	$0.810217\pi$
$174$	−5.18982	+	3.40801i	−0.393439	+	0.258361i
$175$	0.531003	+	1.63426i	0.0401400	+	0.123538i
$176$	−0.897663	−	0.652190i	−0.0676639	−	0.0491607i
$177$	8.97863	+	7.19534i	0.674875	+	0.540835i
$178$	12.4634	+	4.04961i	0.934172	+	0.303531i
$179$	−0.295880	−	0.910626i	−0.0221151	−	0.0680634i	0.939390	−	0.342851i	$-0.111393\pi$
$179$	−0.295880	−	0.910626i	−0.0221151	−	0.0680634i	−0.961505	+	0.274787i	$0.911393\pi$
$180$	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
$183$	5.30714	+	19.4105i	0.392315	+	1.43487i
$184$	−3.44465	+	4.74116i	−0.253943	+	0.349523i
$185$	−3.21258			−0.236193
$186$	9.19872	−	2.89543i	0.674483	−	0.212304i
$187$	7.05728			0.516080
$188$	−3.11192	+	4.28320i	−0.226960	+	0.312384i
$189$	−8.01669	−	3.93159i	−0.583128	−	0.285981i
$190$	1.32094	+	4.06544i	0.0958311	+	0.294938i
$191$			7.17904i			0.519457i	0.965682	+	0.259728i	$0.0836330\pi$
$191$			7.17904i			0.519457i	−0.965682	+	0.259728i	$0.916367\pi$
$192$	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
$195$	2.71116	−	3.38309i	0.194150	−	0.242268i
$196$	−3.27428	−	2.37891i	−0.233877	−	0.169922i
$197$	3.61183	+	11.1161i	0.257332	+	0.791987i	0.993361	+	0.115037i	$0.0366987\pi$
$197$	3.61183	+	11.1161i	0.257332	+	0.791987i	−0.736029	+	0.676950i	$0.763301\pi$
$198$	3.24876	−	0.725210i	0.230879	−	0.0515385i
$199$	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
$201$	24.2191	−	6.62189i	1.70829	−	0.467072i
$202$	13.3359	−	9.68907i	0.938307	−	0.681720i
$203$	−1.90345	+	5.85821i	−0.133596	+	0.411166i
$204$	−10.6264	+	2.90543i	−0.743999	+	0.203421i
$205$	0.107089	+	0.0778050i	0.00747945	+	0.00543414i
$206$	−10.4273	+	3.38803i	−0.726503	+	0.236055i
$207$	−3.83032	−	17.1589i	−0.266226	−	1.19262i
$208$	2.38054	+	0.773484i	0.165061	+	0.0536314i
$209$	−1.46568	+	4.51090i	−0.101383	+	0.312025i
$210$	0.140626	−	2.97296i	0.00970414	−	0.205154i
$211$	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
$213$	−13.1636	−	0.622659i	−0.901952	−	0.0426639i
$214$	−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
$219$	−19.6162	+	12.8814i	−1.32554	+	0.870447i
$220$	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
$225$	−2.58266	+	1.52639i	−0.172177	+	0.101759i
$226$	−2.91673	+	8.97678i	−0.194018	+	0.597126i
$227$	1.86847	−	2.57173i	0.124015	−	0.170691i	−0.742495	−	0.669851i	$-0.766358\pi$
$227$	1.86847	−	2.57173i	0.124015	−	0.170691i	0.866510	+	0.499160i	$0.166358\pi$
$228$	0.349827	−	7.39565i	0.0231679	−	0.489789i
$229$	−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
$231$	2.06517	−	2.57700i	0.135878	−	0.169554i
$232$	2.10699	+	2.90003i	0.138331	+	0.190396i
$233$	12.3231	+	16.9613i	0.807313	+	1.11117i	0.991732	+	0.128323i	$0.0409595\pi$
$233$	12.3231	+	16.9613i	0.807313	+	1.11117i	−0.184419	+	0.982848i	$0.559040\pi$
$234$	−6.46452	+	3.82062i	−0.422599	+	0.249762i
$235$	4.28320	−	3.11192i	0.279405	−	0.203000i
$236$	3.90466	−	5.37431i	0.254172	−	0.349838i
$237$	−4.02065	−	0.190184i	−0.261169	−	0.0123538i
$238$	−6.42414	+	8.84207i	−0.416415	+	0.573146i
$239$	2.17171	−	6.68384i	0.140476	−	0.432341i	−0.855925	−	0.517099i	$-0.827012\pi$
$239$	2.17171	−	6.68384i	0.140476	−	0.432341i	0.996402	+	0.0847581i	$0.0270117\pi$
$240$	−1.35159	−	1.08314i	−0.0872448	−	0.0699167i
$241$	−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
$246$	−0.125848	−	0.191645i	−0.00802376	−	0.0122188i
$247$		−	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	−0.101566	−	0.994829i	$-0.532385\pi$
$251$	12.8833	−	9.36027i	0.813187	−	0.590815i	0.914753	+	0.404014i	$0.132385\pi$
$252$	−2.04868	+	4.73052i	−0.129055	+	0.297995i
$253$	6.50253			0.408811
$254$	5.07714			0.318568
$255$	11.0042	+	0.520516i	0.689108	+	0.0325960i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	8.70487	+	2.82838i	0.542995	+	0.176430i	0.567656	−	0.823266i	$-0.307851\pi$
$257$	8.70487	+	2.82838i	0.542995	+	0.176430i	−0.0246606	+	0.999696i	$0.507851\pi$
$258$	7.73676	+	11.7818i	0.481670	+	0.733500i
$259$	5.25018	−	1.70589i	0.326230	−	0.105999i
$260$	−2.02501	−	1.47125i	−0.125586	−	0.0912433i
$261$	−10.7059	−	1.01508i	−0.662677	−	0.0628321i
$262$	−3.30100	+	10.1594i	−0.203936	+	0.627652i
$263$	6.28457	−	4.56601i	0.387523	−	0.281552i	−0.376916	−	0.926247i	$-0.623016\pi$
$263$	6.28457	−	4.56601i	0.387523	−	0.281552i	0.764440	+	0.644695i	$0.223016\pi$
$264$	−0.506856	−	1.85379i	−0.0311948	−	0.114093i
$265$	−3.65808	−	1.18858i	−0.224714	−	0.0730141i
$266$	−4.31752	−	5.94255i	−0.264724	−	0.364361i
$267$	12.4591	+	18.9731i	0.762486	+	1.16113i
$268$	−4.47956	−	13.7867i	−0.273633	−	0.842155i
$269$	−22.7200	−	16.5070i	−1.38526	−	1.00645i	−0.996367	−	0.0851678i	$-0.972857\pi$
$269$	−22.7200	−	16.5070i	−1.38526	−	1.00645i	−0.388894	−	0.921283i	$-0.627143\pi$
$270$	5.11916	−	0.891180i	0.311542	−	0.0542355i
$271$	−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
$276$	−9.79112	+	2.67705i	−0.589356	+	0.161139i
$277$	−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
$279$	15.5691	+	6.05010i	0.932096	+	0.362210i
$280$	−1.71836			−0.102692
$281$	−17.5574	+	24.1657i	−1.04739	+	1.44160i	−0.156334	+	0.987704i	$0.549968\pi$
$281$	−17.5574	+	24.1657i	−1.04739	+	1.44160i	−0.891053	+	0.453900i	$0.850032\pi$
$282$	−8.84537	+	2.41846i	−0.526734	+	0.144017i
$283$	−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
$288$	1.52639	+	2.58266i	0.0899433	+	0.152185i
$289$	−18.9749	−	13.7860i	−1.11617	−	0.810944i
$290$	−1.10771	−	3.40919i	−0.0650471	−	0.200194i
$291$	11.0416	+	16.8144i	0.647267	+	0.985677i
$292$	7.96391	+	10.9614i	0.466052	+	0.641466i
$293$	2.14611	+	0.697314i	0.125377	+	0.0407375i	0.371034	−	0.928619i	$-0.379003\pi$
$293$	2.14611	+	0.697314i	0.125377	+	0.0407375i	−0.245656	+	0.969357i	$0.579003\pi$
$294$	−1.84879	−	6.76183i	−0.107824	−	0.394358i
$295$	−5.37431	+	3.90466i	−0.312904	+	0.227338i
$296$	0.992740	−	3.05534i	0.0577019	−	0.177588i
$297$	5.17650	+	2.53869i	0.300371	+	0.147310i
$298$	−8.44749	−	6.13746i	−0.489350	−	0.355534i
$299$	−13.9509	+	4.53292i	−0.806801	+	0.262146i
$300$	0.950729	+	1.44780i	0.0548904	+	0.0835886i
$301$	13.2991	+	4.32115i	0.766549	+	0.249067i
$302$	2.56698	−	7.90036i	0.147713	−	0.454615i
$303$	28.5193	+	1.34901i	1.63839	+	0.0774987i
$304$	−4.27466			−0.245168
$305$	−11.6180			−0.665244
$306$	−17.5096	−	7.58301i	−1.00096	−	0.433492i
$307$	−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	$-0.802151\pi$
$311$		−	20.5381i		−	1.16461i	0.812971	−	0.582304i	$-0.197849\pi$
$312$	2.37972	+	3.62390i	0.134725	+	0.205163i
$313$	−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	0.446896	−	0.894586i	$-0.352529\pi$
$317$	23.7559	−	7.71878i	1.33427	−	0.433530i	0.887371	+	0.461056i	$0.152529\pi$
$318$	5.19867	+	4.16614i	0.291527	+	0.233625i
$319$	1.22909	−	3.78274i	0.0688156	−	0.211793i
$320$	−0.587785	+	0.809017i	−0.0328582	+	0.0452254i
$321$	−20.3637	−	0.963240i	−1.13659	−	0.0537628i
$322$	−5.91916	+	8.14702i	−0.329862	+	0.454016i
$323$	21.9958	−	15.9809i	1.22388	−	0.889202i
$324$	−8.83962	−	1.69147i	−0.491090	−	0.0939708i
$325$	1.47125	+	2.02501i	0.0816105	+	0.112327i
$326$	5.53395	+	7.61683i	0.306497	+	0.421857i
$327$	−21.4987	+	26.8270i	−1.18888	+	1.48353i
$328$	−0.107089	+	0.0778050i	−0.00591302	+	0.00429606i
$329$	−5.34741	+	7.36007i	−0.294812	+	0.405774i
$330$	−0.0908046	+	1.91969i	−0.00499863	+	0.105675i
$331$	−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
$333$	4.90364	+	8.29699i	0.268718	+	0.454673i
$334$	−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
$339$	−13.6654	+	8.97369i	−0.742201	+	0.487384i
$340$		−	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
$345$	10.1392	+	0.479600i	0.545874	+	0.0258208i
$346$	−0.844232			−0.0453862
$347$	5.44515			0.292311			0.146156	−	0.989262i	$-0.453310\pi$
$347$	5.44515			0.292311			0.146156	+	0.989262i	$0.453310\pi$
$348$	−0.293357	+	6.20183i	−0.0157256	+	0.332453i
$349$	−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
$351$	−12.8757	−	1.83810i	−0.687252	−	0.0981105i
$352$	−1.05527	+	0.342877i	−0.0562458	+	0.0182754i
$353$	19.2682	+	13.9992i	1.02554	+	0.745101i	0.967412	−	0.253208i	$-0.0814857\pi$
$353$	19.2682	+	13.9992i	1.02554	+	0.745101i	0.0581316	+	0.998309i	$0.481486\pi$
$354$	11.0987	−	3.03455i	0.589887	−	0.161284i
$355$	2.35115	−	7.23610i	0.124786	−	0.384052i
$356$	10.6020	−	7.70281i	0.561905	−	0.408248i
$357$	−18.2601	+	4.99259i	−0.966424	+	0.264236i
$358$	−0.910626	−	0.295880i	−0.0481281	−	0.0156378i
$359$	9.78511	+	13.4680i	0.516438	+	0.710816i	0.984988	−	0.172621i	$-0.0552234\pi$
$359$	9.78511	+	13.4680i	0.516438	+	0.710816i	−0.468550	+	0.883437i	$0.655223\pi$
$360$	−0.653595	−	2.92794i	−0.0344475	−	0.154316i
$361$	−0.224755	−	0.691726i	−0.0118292	−	0.0364066i
$362$	−1.83901	−	1.33612i	−0.0966561	−	0.0702248i
$363$	10.5811	−	13.2035i	0.555363	−	0.693003i
$364$	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
$369$	0.0374841	−	0.395336i	0.00195134	−	0.0205804i
$370$	−1.88830	+	2.59903i	−0.0981683	+	0.135117i
$371$	6.60939			0.343142
$372$	3.06442	−	9.14381i	0.158883	−	0.474085i
$373$	−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
$375$	−0.456803	−	1.67073i	−0.0235892	−	0.0862760i
$376$	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
$381$	6.86221	+	5.49928i	0.351562	+	0.281737i
$382$	5.80796	+	4.21973i	0.297161	+	0.215900i
$383$	−4.16186	−	12.8089i	−0.212661	−	0.654504i	−0.999311	−	0.0371049i	$-0.988186\pi$
$383$	−4.16186	−	12.8089i	−0.212661	−	0.654504i	0.786650	−	0.617399i	$-0.211814\pi$
$384$	1.44780	−	0.950729i	0.0738826	−	0.0485167i
$385$	1.12070	+	1.54251i	0.0571160	+	0.0786135i
$386$	4.83313	+	1.57038i	0.246000	+	0.0799302i
$387$	−2.30441	+	24.3042i	−0.117140	+	1.23545i
$388$	9.39574	−	6.82641i	0.476997	−	0.346558i
$389$	−4.01550	+	12.3585i	−0.203594	+	0.626598i	0.796174	+	0.605068i	$0.206854\pi$
$389$	−4.01550	+	12.3585i	−0.203594	+	0.626598i	−0.999768	+	0.0215307i	$0.993146\pi$
$390$	−1.14340	−	4.18191i	−0.0578983	−	0.211759i
$391$	−30.1555	−	21.9093i	−1.52503	−	1.10800i
$392$	−3.84915	+	1.25066i	−0.194411	+	0.0631681i
$393$	−15.4657	+	10.1559i	−0.780143	+	0.512299i
$394$	11.1161	+	3.61183i	0.560019	+	0.181961i
$395$	0.718130	−	2.21018i	0.0361330	−	0.111206i
$396$	1.32286	−	3.05457i	0.0664764	−	0.153498i
$397$	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
$399$	0.601129	−	12.7084i	0.0300941	−	0.636216i
$400$	0.809017	−	0.587785i	0.0404508	−	0.0293893i
$401$	6.36599	+	4.62516i	0.317902	+	0.230969i	0.735280	−	0.677764i	$-0.237051\pi$
$401$	6.36599	+	4.62516i	0.317902	+	0.230969i	−0.417378	+	0.908733i	$0.637051\pi$
$402$	8.87842	−	23.4859i	0.442816	−	1.17137i
$403$	3.79920	−	13.4085i	0.189252	−	0.667926i
$404$		−	16.4840i		−	0.820111i
$405$	7.88429	+	4.34028i	0.391773	+	0.215670i
$406$	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
$411$	20.4700	−	25.5432i	1.00971	−	1.25996i
$412$	−3.38803	+	10.4273i	−0.166916	+	0.513715i
$413$	6.70962	−	9.23500i	0.330159	−	0.454425i
$414$	−16.1332	−	6.98693i	−0.792905	−	0.343389i
$415$	0.723784	−	0.996203i	0.0355292	−	0.0489017i
$416$	2.02501	−	1.47125i	0.0992841	−	0.0721341i
$417$	1.96033	+	1.57098i	0.0959976	+	0.0769311i
$418$	2.78789	+	3.83720i	0.136360	+	0.187683i
$419$	−19.4230	−	26.7335i	−0.948876	−	1.30602i	−0.952025	−	0.306021i	$-0.901002\pi$
$419$	−19.4230	−	26.7335i	−0.948876	−	1.30602i	0.00314861	−	0.999995i	$-0.498998\pi$
$420$	−2.32252	−	1.86123i	−0.113327	−	0.0908189i
$421$	−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
$423$	−14.5749	−	6.31204i	−0.708654	−	0.306902i
$424$	2.26082	−	3.11175i	0.109795	−	0.151120i
$425$	−1.96546	+	6.04907i	−0.0953388	+	0.293423i
$426$	−8.24109	+	10.2836i	−0.399282	+	0.498240i
$427$	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	0.462219	−	0.886766i	$-0.347053\pi$
$431$	−10.8781	−	14.9724i	−0.523979	−	0.721196i	−0.986198	+	0.165570i	$0.947053\pi$
$432$	−0.734345	+	5.14400i	−0.0353312	+	0.247491i
$433$		−	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
$438$	−1.10882	+	23.4414i	−0.0529813	+	1.12007i
$439$	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
$441$	4.82523	−	11.1417i	0.229773	−	0.530559i
$442$	−4.91964	+	15.1411i	−0.234003	+	0.720188i
$443$	−26.0210	−	8.45475i	−1.23630	−	0.401697i	−0.383305	−	0.923622i	$-0.625214\pi$
$443$	−26.0210	−	8.45475i	−1.23630	−	0.401697i	−0.852992	+	0.521924i	$0.825214\pi$
$444$	4.65116	−	3.05429i	0.220734	−	0.144950i
$445$	−12.4634	+	4.04961i	−0.590822	+	0.191970i
$446$	−8.11085	−	5.89288i	−0.384060	−	0.279036i
$447$	−4.76979	−	17.4452i	−0.225603	−	0.825129i
$448$	0.531003	−	1.63426i	0.0250875	−	0.0772114i
$449$	−9.35498	+	6.79679i	−0.441489	+	0.320760i	−0.786226	−	0.617939i	$-0.787968\pi$
$449$	−9.35498	+	6.79679i	−0.441489	+	0.320760i	0.344738	+	0.938699i	$0.387968\pi$
$450$	−0.283177	+	2.98661i	−0.0133491	+	0.140790i
$451$	0.139685	+	0.0453865i	0.00657752	+	0.00213717i
$452$	5.54795	+	7.63610i	0.260954	+	0.359172i
$453$	12.0267	−	7.89764i	0.565066	−	0.371064i
$454$	−0.982312	−	3.02325i	−0.0461022	−	0.141888i
$455$	−3.47969	−	2.52814i	−0.163130	−	0.118521i
$456$	−5.77758	−	4.63007i	−0.270560	−	0.216823i
$457$	−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	$-0.785607\pi$
$461$	−11.0770	−	34.0917i	−0.515910	−	1.58781i	0.265711	−	0.964053i	$-0.414393\pi$
$462$	−0.870962	−	3.18548i	−0.0405208	−	0.148202i
$463$	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
$465$	−5.74003	+	7.74933i	−0.266187	+	0.359366i
$466$	20.9653			0.971199
$467$	4.61609	−	6.35350i	0.213607	−	0.294005i	−0.688746	−	0.725003i	$-0.741838\pi$
$467$	4.61609	−	6.35350i	0.213607	−	0.294005i	0.902353	+	0.430998i	$0.141838\pi$
$468$	−0.708804	+	7.47561i	−0.0327645	+	0.345560i
$469$	−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
$474$	−2.51714	+	3.14098i	−0.115616	+	0.144270i
$475$	−3.45827	−	2.51258i	−0.158676	−	0.115285i
$476$	3.37737	+	10.3945i	0.154802	+	0.476430i
$477$	2.51394	+	11.2618i	0.115106	+	0.515643i
$478$	−4.13084	−	5.68561i	−0.188940	−	0.260054i
$479$	15.4808	+	5.03000i	0.707334	+	0.229827i	0.640523	−	0.767939i	$-0.278718\pi$
$479$	15.4808	+	5.03000i	0.707334	+	0.229827i	0.0668107	+	0.997766i	$0.478718\pi$
$480$	−1.67073	+	0.456803i	−0.0762579	+	0.0208501i
$481$	6.50549	−	4.72651i	0.296625	−	0.215510i
$482$	−1.71729	+	5.28528i	−0.0782204	+	0.240738i
$483$	−16.8247	+	4.60013i	−0.765550	+	0.209313i
$484$	−7.90317	−	5.74199i	−0.359235	−	0.260999i
$485$	−11.0454	+	3.58885i	−0.501544	+	0.162961i
$486$	−10.1154	−	11.8608i	−0.458846	−	0.538016i
$487$	−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
$489$	−0.770493	+	16.2889i	−0.0348429	+	0.736610i
$490$	4.04724			0.182835
$491$	−26.7690			−1.20807			−0.604035	−	0.796958i	$-0.706441\pi$
$491$	−26.7690			−1.20807			−0.604035	+	0.796958i	$0.706441\pi$
$492$	−0.229015	−	0.0108328i	−0.0103248	−	0.000488381i
$493$	−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
$498$	−1.78278	+	1.17070i	−0.0798883	+	0.0524605i
$499$	−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	−0.356513	−	0.934290i	$-0.616034\pi$
$503$	−2.14803	+	0.697937i	−0.0957759	+	0.0311195i	0.260737	+	0.965410i	$0.416034\pi$
$504$	2.62288	+	4.43794i	0.116833	+	0.197682i
$505$	−5.09384	+	15.6772i	−0.226673	+	0.697628i
$506$	3.82209	−	5.26066i	0.169913	−	0.233865i
$507$	0.551156	−	11.6519i	0.0244777	−	0.517480i
$508$	2.98427	−	4.10749i	0.132405	−	0.182241i
$509$	2.68227	−	1.94878i	0.118889	−	0.0863782i	−0.526752	−	0.850019i	$-0.676590\pi$
$509$	2.68227	−	1.94878i	0.118889	−	0.0863782i	0.645641	+	0.763641i	$0.276590\pi$
$510$	6.88919	−	8.59661i	0.305059	−	0.380664i
$511$	13.6849	+	18.8356i	0.605383	+	0.833238i
$512$	−0.587785	−	0.809017i	−0.0259767	−	0.0357538i
$513$	21.8826	−	3.80949i	0.966142	−	0.168193i
$514$	7.40481	−	5.37991i	0.326612	−	0.237298i
$515$	6.44441	−	8.86997i	0.283975	−	0.390858i
$516$	14.0792	+	0.665970i	0.619802	+	0.0293177i
$517$	3.45290	−	4.75251i	0.151859	−	0.209015i
$518$	1.70589	−	5.25018i	0.0749523	−	0.230680i
$519$	−1.14106	−	0.914426i	−0.0500868	−	0.0401388i
$520$	−2.38054	+	0.773484i	−0.104393	+	0.0339195i
$521$		−	25.5868i		−	1.12098i	−0.828162	−	0.560489i	$-0.810613\pi$
$521$		−	25.5868i		−	1.12098i	0.828162	−	0.560489i	$-0.189387\pi$
$522$	−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
$525$	1.63370	+	2.48784i	0.0713003	+	0.108578i
$526$		−	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
$531$	18.2877	+	7.91999i	0.793619	+	0.343698i
$532$	−7.34540			−0.318463
$533$	−0.331328			−0.0143514
$534$	22.6728	+	1.07246i	0.981150	+	0.0464101i
$535$	3.63718	−	11.1941i	0.157249	−	0.483962i
$536$	−13.7867	−	4.47956i	−0.595493	−	0.193487i
$537$	−0.910312	−	1.38625i	−0.0392829	−	0.0598210i
$538$	−26.7089	+	8.67825i	−1.15150	+	0.374146i
$539$	3.63305	+	2.63957i	0.156487	+	0.113694i
$540$	2.28799	−	4.66531i	0.0984593	−	0.200763i
$541$	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
$543$	−1.03838	−	3.79780i	−0.0445610	−	0.162979i
$544$	6.04907	+	1.96546i	0.259352	+	0.0842684i
$545$	−11.6666	−	16.0577i	−0.499743	−	0.687837i
$546$	4.08921	+	6.22717i	0.175002	+	0.266498i
$547$	−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
$549$	17.7336	+	30.0053i	0.756850	+	1.28060i
$550$	−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
$555$	−5.36734	+	1.46751i	−0.227831	+	0.0622925i
$556$	0.852515	−	1.17339i	0.0361547	−	0.0497627i
$557$	−19.3884			−0.821512			−0.410756	−	0.911745i	$-0.634735\pi$
$557$	−19.3884			−0.821512			−0.410756	+	0.911745i	$0.634735\pi$
$558$	14.0459	−	9.03949i	0.594611	−	0.382672i
$559$	20.3691			0.861520
$560$	−1.01003	+	1.39018i	−0.0426814	+	0.0587460i
$561$	11.7908	−	3.22379i	0.497808	−	0.136108i
$562$	9.23047	+	28.4085i	0.389364	+	1.19834i
$563$		−	9.23240i		−	0.389099i	−0.980893	−	0.194550i	$-0.937676\pi$
$563$		−	9.23240i		−	0.389099i	0.980893	−	0.194550i	$-0.0623245\pi$
$564$	−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
$567$	−15.1897	−	2.90656i	−0.637906	−	0.122064i
$568$	6.15539	+	4.47215i	0.258275	+	0.187647i
$569$	4.98297	+	15.3360i	0.208897	+	0.642918i	0.999531	+	0.0306292i	$0.00975111\pi$
$569$	4.98297	+	15.3360i	0.208897	+	0.642918i	−0.790634	+	0.612289i	$0.790249\pi$
$570$	4.06404	+	6.18883i	0.170224	+	0.259222i
$571$	−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
$573$	3.27941	+	11.9942i	0.136999	+	0.501065i
$574$	−0.184018	+	0.133697i	−0.00768077	+	0.00558041i
$575$	−1.81096	+	5.57357i	−0.0755223	+	0.232434i
$576$	2.98661	+	0.283177i	0.124442	+	0.0117990i
$577$	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
$579$	4.83147	+	7.35749i	0.200789	+	0.305767i
$580$	−3.40919	−	1.10771i	−0.141559	−	0.0459952i
$581$	−0.653863	+	2.01238i	−0.0271268	+	0.0834878i
$582$	20.0932	+	0.950442i	0.832889	+	0.0393971i
$583$	−4.26778			−0.176754
$584$	13.5490			0.560662
$585$	2.98420	−	6.89069i	0.123382	−	0.284895i
$586$	1.82559	−	1.32637i	0.0754145	−	0.0547919i
$587$	1.90924	+	1.38714i	0.0788026	+	0.0572535i	0.626489	−	0.779430i	$-0.284491\pi$
$587$	1.90924	+	1.38714i	0.0788026	+	0.0572535i	−0.547686	+	0.836684i	$0.684491\pi$
$588$	−6.55713	−	2.47880i	−0.270411	−	0.102224i
$589$	0.905480	+	23.7830i	0.0373097	+	0.979963i
$590$			6.64301i			0.273488i
$591$	11.1122	+	16.9220i	0.457096	+	0.696079i
$592$	−1.88830	−	2.59903i	−0.0776088	−	0.106819i
$593$	−12.6011	+	4.09436i	−0.517467	+	0.168135i	−0.556095	−	0.831118i	$-0.687701\pi$
$593$	−12.6011	+	4.09436i	−0.517467	+	0.168135i	0.0386285	+	0.999254i	$0.487701\pi$
$594$	5.09651	−	2.69567i	0.209112	−	0.110605i
$595$		−	10.9294i		−	0.448062i
$596$	−9.93062	+	3.22665i	−0.406774	+	0.132169i
$597$	2.17526	+	1.74322i	0.0890275	+	0.0713453i
$598$	−4.53292	+	13.9509i	−0.185365	+	0.570494i
$599$	0.571106	−	0.786061i	0.0233348	−	0.0321176i	−0.797190	−	0.603728i	$-0.793681\pi$
$599$	0.571106	−	0.786061i	0.0233348	−	0.0321176i	0.820525	+	0.571611i	$0.193681\pi$
$600$	1.73012	+	0.0818375i	0.0706317	+	0.00334100i
$601$	−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
$603$	37.4387	−	22.1268i	1.52462	−	0.901071i
$604$	−4.88269	−	6.72045i	−0.198674	−	0.273451i
$605$	5.74199	+	7.90317i	0.233445	+	0.321309i
$606$	17.8546	−	22.2797i	0.725293	−	0.905049i
$607$	−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
$609$	−0.504094	+	10.6570i	−0.0204269	+	0.431843i
$610$	−6.82889	+	9.39915i	−0.276493	+	0.380561i
$611$	−4.09507	+	12.6033i	−0.165669	+	0.509876i
$612$	−16.4267	+	9.70838i	−0.664009	+	0.392438i
$613$	−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	$0.0419265\pi$
$617$	20.1176	+	27.6895i	0.809905	+	1.11474i	−0.181433	+	0.983403i	$0.558074\pi$
$618$	−15.8735	+	10.4237i	−0.638525	+	0.419302i
$619$			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
$624$	4.33056	+	0.204843i	0.173361	+	0.00820028i
$625$	1.00000			0.0400000
$626$	−5.23426			−0.209203
$627$	−0.388158	+	8.20601i	−0.0155015	+	0.327716i
$628$	4.81343	−	14.8142i	0.192077	−	0.591151i
$629$	19.4331	+	6.31419i	0.774848	+	0.251763i
$630$	−1.12311	−	5.03125i	−0.0447458	−	0.200450i
$631$	−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
$633$	36.0304	−	9.85128i	1.43208	−	0.391553i
$634$	7.71878	−	23.7559i	0.306552	−	0.943469i
$635$	−4.10749	+	2.98427i	−0.163001	+	0.118427i
$636$	6.42618	−	1.75702i	0.254814	−	0.0696703i
$637$	−9.63460	−	3.13047i	−0.381737	−	0.124034i
$638$	−2.33786	−	3.21779i	−0.0925568	−	0.127394i
$639$	−22.2772	+	4.97286i	−0.881271	+	0.196723i
$640$	0.309017	+	0.951057i	0.0122150	+	0.0375938i
$641$	−34.7198	−	25.2254i	−1.37135	−	0.996344i	−0.997630	−	0.0688020i	$-0.978082\pi$
$641$	−34.7198	−	25.2254i	−1.37135	−	0.996344i	−0.373719	−	0.927542i	$-0.621918\pi$
$642$	−12.7488	+	15.9084i	−0.503154	+	0.627856i
$643$	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	0.855300	−	0.518133i	$-0.173373\pi$
$647$	−3.59167	−	11.0540i	−0.141203	−	0.434578i	−0.996503	+	0.0835547i	$0.973373\pi$
$648$	−6.56423	+	6.15718i	−0.257867	+	0.241877i
$649$	−4.33250	+	5.96318i	−0.170066	+	0.234075i
$650$	2.50305			0.0981775
$651$	5.26577	−	15.7124i	0.206382	−	0.615816i
$652$	9.41492			0.368717
$653$	−11.9012	+	16.3806i	−0.465731	+	0.641023i	−0.975685	−	0.219178i	$-0.929662\pi$
$653$	−11.9012	+	16.3806i	−0.465731	+	0.641023i	0.509954	+	0.860202i	$0.329662\pi$
$654$	9.06683	+	33.1613i	0.354541	+	1.29671i
$655$	−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	0.826753	−	0.562565i	$-0.190185\pi$
$659$	29.9053	+	9.71681i	1.16494	+	0.378513i	0.338190	+	0.941078i	$0.390185\pi$
$660$	1.49969	+	1.20183i	0.0583752	+	0.0467811i
$661$	−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
$663$	−23.0493	+	15.1359i	−0.895162	+	0.587829i
$664$	0.723784	+	0.996203i	0.0280883	+	0.0386602i
$665$	6.98589	+	2.26985i	0.270901	+	0.0880211i
$666$	9.59469	+	0.909727i	0.371787	+	0.0352512i
$667$	−16.9953	+	12.3478i	−0.658061	+	0.478109i
$668$	−3.68764	+	11.3494i	−0.142679	+	0.439122i
$669$	−4.57971	−	16.7500i	−0.177062	−	0.647592i
$670$	11.7276	+	8.52063i	0.453078	+	0.329181i
$671$	−12.2601	+	3.98354i	−0.473295	+	0.153783i
$672$	2.48784	−	1.63370i	0.0959704	−	0.0630212i
$673$	−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
$675$	−3.61767	+	3.72995i	−0.139244	+	0.143566i
$676$	−6.73476			−0.259029
$677$	−1.67545			−0.0643927			−0.0321964	−	0.999482i	$-0.510250\pi$
$677$	−1.67545			−0.0643927			−0.0321964	+	0.999482i	$0.510250\pi$
$678$	−0.772443	+	16.3301i	−0.0296655	+	0.627155i
$679$	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	$0.0460617\pi$
$683$			7.53725i			0.288405i	−0.989548	+	0.144202i	$0.953938\pi$
$684$	−2.79389	−	12.5159i	−0.106827	−	0.478558i
$685$	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
$690$	6.34766	−	7.92086i	0.241651	−	0.301542i
$691$	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
$693$	2.27316	−	5.24885i	0.0863501	−	0.199387i
$694$	3.20058	−	4.40522i	0.121492	−	0.167220i
$695$	−1.17339	+	0.852515i	−0.0445091	+	0.0323377i
$696$	4.84495	+	3.88267i	0.183648	+	0.147172i
$697$	−0.494868	−	0.681128i	−0.0187445	−	0.0257996i
$698$	5.07982	+	6.99178i	0.192274	+	0.264643i
$699$	28.3365	+	22.7085i	1.07179	+	0.858913i
$700$	1.39018	−	1.01003i	0.0525440	−	0.0381754i
$701$	−10.5179	+	14.4766i	−0.397254	+	0.546774i	−0.960052	−	0.279821i	$-0.909725\pi$
$701$	−10.5179	+	14.4766i	−0.397254	+	0.546774i	0.562798	+	0.826595i	$0.309725\pi$
$702$	−9.05518	+	9.33623i	−0.341766	+	0.352373i
$703$	−8.07185	+	11.1099i	−0.304436	+	0.419020i
$704$	−0.342877	+	1.05527i	−0.0129226	+	0.0397718i
$705$	5.73452	−	7.15575i	0.215974	−	0.269501i
$706$	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
$711$	−6.80428	+	1.51890i	−0.255181	+	0.0569632i
$712$		−	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
$717$	0.575138	−	12.1589i	0.0214789	−	0.454083i
$718$	16.6474			0.621276
$719$	6.48597			0.241886			0.120943	−	0.992659i	$-0.461408\pi$
$719$	6.48597			0.241886			0.120943	+	0.992659i	$0.461408\pi$
$720$	−2.75292	−	1.19223i	−0.102595	−	0.0444317i
$721$	−5.82185	+	17.9178i	−0.216817	+	0.667294i
$722$	−0.691726	−	0.224755i	−0.0257434	−	0.00836453i
$723$	−8.04579	+	5.28346i	−0.299226	+	0.196494i
$724$	−2.16188	+	0.702439i	−0.0803458	+	0.0261059i
$725$	2.90003	+	2.10699i	0.107704	+	0.0782518i
$726$	−4.46244	−	16.3211i	−0.165617	−	0.605732i
$727$	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
$729$	−0.824999	−	26.9874i	−0.0305555	−	0.999533i
$730$	−12.8859	−	4.18687i	−0.476927	−	0.154963i
$731$	30.4231	+	41.8738i	1.12524	+	1.54876i
$732$	16.8205	−	11.0456i	0.621703	−	0.408256i
$733$	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
$735$	5.47021	+	4.38374i	0.201772	+	0.161697i
$736$	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
$741$	−4.88764	−	17.8762i	−0.179552	−	0.656699i
$742$	3.88490	−	5.34711i	0.142619	−	0.196299i
$743$	48.0107			1.76134			0.880671	−	0.473729i	$-0.157092\pi$
$743$	48.0107			1.76134			0.880671	+	0.473729i	$0.157092\pi$
$744$	−5.59628	−	7.85376i	−0.205170	−	0.287933i
$745$	10.4417			0.382553
$746$	−8.93269	+	12.2948i	−0.327049	+	0.450144i
$747$	−3.67763	−	0.348697i	−0.134557	−	0.0127581i
$748$	−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
$753$	17.2487	−	21.5236i	0.628577	−	0.784363i
$754$	7.25890	+	5.27390i	0.264354	+	0.192064i
$755$	2.56698	+	7.90036i	0.0934221	+	0.287524i
$756$	−1.26187	+	8.83925i	−0.0458938	+	0.321480i
$757$	−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
$759$	10.8640	−	2.97038i	0.394337	−	0.107818i
$760$	3.45827	−	2.51258i	0.125445	−	0.0911408i
$761$	−10.2147	+	31.4376i	−0.370282	+	1.13961i	0.576324	+	0.817221i	$0.304486\pi$
$761$	−10.2147	+	31.4376i	−0.370282	+	1.13961i	−0.946607	+	0.322391i	$0.895514\pi$
$762$	8.48252	−	2.31925i	0.307289	−	0.0840177i
$763$	27.5930	+	20.0475i	0.998932	+	0.725767i
$764$	6.82767	−	2.21844i	0.247016	−	0.0802605i
$765$	18.6227	−	4.15710i	0.673307	−	0.150300i
$766$	−12.8089	−	4.16186i	−0.462804	−	0.150374i
$767$	5.13826	−	15.8139i	0.185532	−	0.571008i
$768$	0.0818375	−	1.73012i	0.00295306	−	0.0624302i
$769$	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
$771$	15.8355	+	0.749046i	0.570301	+	0.0269762i
$772$	4.11131	−	2.98704i	0.147969	−	0.107506i
$773$	3.02841	+	2.20027i	0.108924	+	0.0791381i	0.640914	−	0.767613i	$-0.278556\pi$
$773$	3.02841	+	2.20027i	0.108924	+	0.0791381i	−0.531990	+	0.846751i	$0.678556\pi$
$774$	18.3080	+	16.1499i	0.658066	+	0.580497i
$775$	−3.44165	−	4.37665i	−0.123628	−	0.157214i
$776$		−	11.6138i		−	0.416910i
$777$	7.99236	−	5.24837i	0.286724	−	0.188284i
$778$	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
$783$	−18.3503	+	3.19455i	−0.655786	+	0.114164i
$784$	−1.25066	+	3.84915i	−0.0446666	+	0.137470i
$785$	−9.15568	+	12.6017i	−0.326780	+	0.449775i
$786$	−0.874209	+	18.4816i	−0.0311820	+	0.659215i
$787$	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
$789$	8.41404	−	10.4994i	0.299548	−	0.373788i
$790$	−1.36596	−	1.88009i	−0.0485988	−	0.0668905i
$791$	9.53339	+	13.1216i	0.338968	+	0.466550i
$792$	−1.69364	−	2.86565i	−0.0601808	−	0.101826i
$793$	23.5265	−	17.0930i	0.835451	−	0.606991i
$794$	10.2620	−	14.1245i	0.364186	−	0.501259i
$795$	−6.65461	−	0.314774i	−0.236015	−	0.0111639i
$796$	0.945986	−	1.30204i	0.0335296	−	0.0461495i
$797$	−12.4546	+	38.3314i	−0.441165	+	1.35777i	0.445469	+	0.895297i	$0.353037\pi$
$797$	−12.4546	+	38.3314i	−0.441165	+	1.35777i	−0.886635	+	0.462470i	$0.846963\pi$
$798$	−9.92797	−	7.95613i	−0.351446	−	0.281644i
$799$	−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
$804$	−13.7819	−	20.9875i	−0.486051	−	0.740171i
$805$		−	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	−0.993212	−	0.116319i	$-0.962891\pi$
$809$	−33.8330	+	24.5811i	−1.18951	+	0.864226i	−0.196294	+	0.980545i	$0.562891\pi$
$810$	8.14563	−	3.82737i	0.286208	−	0.134480i
$811$	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
$813$	−11.0249	−	0.521497i	−0.386660	−	0.0182897i
$814$	−1.10152	+	3.39012i	−0.0386081	+	0.118824i
$815$	−8.95412	−	2.90937i	−0.313649	−	0.101911i
$816$	6.04698	+	9.20851i	0.211687	+	0.322362i
$817$	−33.0834	+	10.7494i	−1.15744	+	0.376076i
$818$	9.90867	+	7.19907i	0.346448	+	0.251710i
$819$	−1.21798	+	12.8458i	−0.0425597	+	0.448868i
$820$	0.0409045	−	0.125891i	0.00142845	−	0.00439631i
$821$	−28.3876	+	20.6248i	−0.990734	+	0.719810i	−0.960082	−	0.279720i	$-0.909758\pi$
$821$	−28.3876	+	20.6248i	−0.990734	+	0.719810i	−0.0306524	+	0.999530i	$0.509758\pi$
$822$	−8.63297	−	31.5745i	−0.301109	−	1.10129i
$823$	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
$825$	−1.05490	−	1.60643i	−0.0367270	−	0.0559289i
$826$	−3.52746	−	10.8564i	−0.122736	−	0.377742i
$827$	−33.6750	−	24.4663i	−1.17099	−	0.850776i	−0.179866	−	0.983691i	$-0.557566\pi$
$827$	−33.6750	−	24.4663i	−1.17099	−	0.850776i	−0.991127	+	0.132915i	$0.957566\pi$
$828$	−15.1354	+	8.94524i	−0.525992	+	0.310868i
$829$	−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
$834$	2.42320	−	0.662541i	0.0839085	−	0.0229419i
$835$	7.01432	−	9.65438i	0.242740	−	0.334104i
$836$	4.74304			0.164041
$837$	28.7754	+	2.99607i	0.994623	+	0.103559i
$838$	−33.0444			−1.14150
$839$	−21.2449	+	29.2411i	−0.733455	+	1.00951i	0.265514	+	0.964107i	$0.414459\pi$
$839$	−21.2449	+	29.2411i	−0.733455	+	1.00951i	−0.998969	+	0.0454071i	$0.985541\pi$
$840$	−2.87091	+	0.784953i	−0.0990559	+	0.0270834i
$841$	−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
$846$	−13.6734	+	8.08119i	−0.470102	+	0.277837i
$847$	−13.5805	−	9.86680i	−0.466631	−	0.339027i
$848$	−1.18858	−	3.65808i	−0.0408161	−	0.125619i
$849$	−0.920669	−	1.40202i	−0.0315973	−	0.0481172i
$850$	3.73853	+	5.14564i	0.128230	+	0.176494i
$851$	17.9055	+	5.81785i	0.613793	+	0.199433i
$852$	3.47558	+	12.7117i	0.119071	+	0.435496i
$853$	−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
$855$	−1.21048	+	12.7667i	−0.0413976	+	0.436612i
$856$	9.52225	+	6.91832i	0.325464	+	0.236463i
$857$	7.56587	−	2.45830i	0.258445	−	0.0839740i	−0.176929	−	0.984224i	$-0.556616\pi$
$857$	7.56587	−	2.45830i	0.258445	−	0.0839740i	0.435374	+	0.900250i	$0.356616\pi$
$858$	−2.64047	−	4.02098i	−0.0901441	−	0.137274i
$859$	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
$861$	−0.393531	−	0.0186147i	−0.0134115	−	0.000634387i
$862$	−18.5069			−0.630348
$863$	−53.6351			−1.82576			−0.912880	−	0.408228i	$-0.866147\pi$
$863$	−53.6351			−1.82576			−0.912880	+	0.408228i	$0.866147\pi$
$864$	3.72995	+	3.61767i	0.126895	+	0.123075i
$865$	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
$870$	−3.40801	−	5.18982i	−0.115542	−	0.175951i
$871$	−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
$876$	18.3127	+	14.6755i	0.618729	+	0.495840i
$877$	−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
$879$	3.90411	+	0.184671i	0.131682	+	0.00622880i
$880$	0.652190	−	0.897663i	0.0219853	−	0.0302602i
$881$	−22.5075	+	16.3527i	−0.758299	+	0.550936i	−0.898388	−	0.439203i	$-0.855261\pi$
$881$	−22.5075	+	16.3527i	−0.758299	+	0.550936i	0.140089	+	0.990139i	$0.455261\pi$
$882$	−6.17765	−	10.4526i	−0.208012	−	0.351959i
$883$	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
$885$	−7.19534	+	8.97863i	−0.241869	+	0.301813i
$886$	−22.1348	+	16.0819i	−0.743634	+	0.540282i
$887$	−16.5775	+	22.8170i	−0.556619	+	0.766121i	−0.990892	−	0.134661i	$-0.957006\pi$
$887$	−16.5775	+	22.8170i	−0.556619	+	0.766121i	0.434272	+	0.900782i	$0.357006\pi$
$888$	0.262909	−	5.55813i	0.00882265	−	0.186519i
$889$	5.12805	−	7.05815i	0.171989	−	0.236723i
$890$	−4.04961	+	12.4634i	−0.135743	+	0.417774i
$891$	9.80820	+	1.87681i	0.328587	+	0.0628756i
$892$	−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
$897$	−21.2375	+	13.9461i	−0.709099	+	0.465646i
$898$			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
$903$	24.1931	+	1.14438i	0.805097	+	0.0380825i
$904$	9.43874			0.313928
$905$	2.27314			0.0755617
$906$	0.679819	−	14.3720i	0.0225855	−	0.477476i
$907$	−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
$909$	48.2642	−	10.7739i	1.60082	−	0.357347i
$910$	−4.09062	+	1.32912i	−0.135603	+	0.0440600i
$911$	29.2631	+	21.2609i	0.969529	+	0.704404i	0.955344	−	0.295495i	$-0.0954846\pi$
$911$	29.2631	+	21.2609i	0.969529	+	0.704404i	0.0141850	+	0.999899i	$0.495485\pi$
$912$	−7.14178	+	1.95268i	−0.236488	+	0.0646596i
$913$	0.422210	−	1.29943i	0.0139731	−	0.0430048i
$914$	−4.50434	+	3.27260i	−0.148990	+	0.108248i
$915$	−19.4105	+	5.30714i	−0.641691	+	0.175449i
$916$	28.6033	+	9.29377i	0.945079	+	0.307075i
$917$	10.7894	+	14.8503i	0.356296	+	0.490400i
$918$	−32.7177	−	4.67070i	−1.07985	−	0.154156i
$919$	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
$921$	−10.1447	+	12.6590i	−0.334280	+	0.417128i
$922$	−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
$927$	−32.7448	−	3.10472i	−1.07548	−	0.101972i
$928$	2.10699	−	2.90003i	0.0691655	−	0.0951981i
$929$	30.5057			1.00086			0.500429	−	0.865777i	$-0.333176\pi$
$929$	30.5057			1.00086			0.500429	+	0.865777i	$0.333176\pi$
$930$	2.89543	+	9.19872i	0.0949450	+	0.301638i
$931$	17.3005			0.567002
$932$	12.3231	−	16.9613i	0.403656	−	0.555585i
$933$	−9.38186	−	34.3135i	−0.307148	−	1.12337i
$934$	−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
$939$	−7.07458	−	5.66946i	−0.230870	−	0.185016i
$940$	−4.28320	−	3.11192i	−0.139702	−	0.101500i
$941$	−16.1231	−	49.6218i	−0.525598	−	1.61762i	−0.763131	−	0.646244i	$-0.776339\pi$
$941$	−16.1231	−	49.6218i	−0.525598	−	1.61762i	0.237533	−	0.971379i	$-0.423661\pi$
$942$	22.5517	−	14.8091i	0.734775	−	0.482507i
$943$	−0.455968	−	0.627586i	−0.0148484	−	0.0204370i
$944$	−6.31788	−	2.05280i	−0.205629	−	0.0668130i
$945$	3.93159	−	8.01669i	0.127895	−	0.260783i
$946$	−7.30493	+	5.30734i	−0.237504	+	0.172556i
$947$	−13.1904	+	40.5957i	−0.428629	+	1.31918i	0.470847	+	0.882215i	$0.343948\pi$
$947$	−13.1904	+	40.5957i	−0.428629	+	1.31918i	−0.899476	+	0.436970i	$0.856052\pi$
$948$	1.06157	+	3.88263i	0.0344783	+	0.126102i
$949$	27.4368	+	19.9340i	0.890637	+	0.647086i
$950$	−4.06544	+	1.32094i	−0.131900	+	0.0428570i
$951$	36.1638	−	23.7478i	1.17269	−	0.770074i
$952$	10.3945	+	3.37737i	0.336887	+	0.109461i
$953$	4.11532	−	12.6656i	0.133308	−	0.410281i	−0.862015	−	0.506883i	$-0.830798\pi$
$953$	4.11532	−	12.6656i	0.133308	−	0.410281i	0.995323	+	0.0966025i	$0.0307976\pi$
$954$	10.5887	+	4.58571i	0.342821	+	0.148468i
$955$	−7.17904			−0.232308
$956$	−7.02780			−0.227295
$957$	0.325501	−	6.88138i	0.0105220	−	0.222443i
$958$	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
$963$	−34.4623	+	7.69291i	−1.11053	+	0.247901i
$964$	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
$969$	29.4489	−	36.7475i	0.946036	−	1.18050i
$970$	−3.58885	+	11.0454i	−0.115231	+	0.354645i
$971$	5.01087	−	6.89688i	0.160807	−	0.221331i	−0.721009	−	0.692926i	$-0.756321\pi$
$971$	5.01087	−	6.89688i	0.160807	−	0.221331i	0.881816	+	0.471594i	$0.156321\pi$
$972$	−15.5413	+	1.21198i	−0.498487	+	0.0388741i
$973$	1.46493	−	2.01630i	0.0469635	−	0.0646396i
$974$	−25.4512	+	18.4914i	−0.815510	+	0.592503i
$975$	3.38309	+	2.71116i	0.108346	+	0.0868266i
$976$	−6.82889	−	9.39915i	−0.218587	−	0.300860i
$977$	12.6189	+	17.3684i	0.403713	+	0.555664i	0.961671	−	0.274206i	$-0.0884149\pi$
$977$	12.6189	+	17.3684i	0.403713	+	0.555664i	−0.557958	+	0.829869i	$0.688415\pi$
$978$	12.7251	+	10.1977i	0.406904	+	0.326087i
$979$	−11.7637	+	8.54682i	−0.375969	+	0.273158i
$980$	2.37891	−	3.27428i	0.0759914	−	0.104593i
$981$	−23.6639	+	54.6412i	−0.755529	+	1.74456i
$982$	−15.7344	+	21.6566i	−0.502106	+	0.691090i
$983$	15.6404	−	48.1361i	0.498850	−	1.53530i	−0.312018	−	0.950076i	$-0.601005\pi$
$983$	15.6404	−	48.1361i	0.498850	−	1.53530i	0.810869	−	0.585228i	$-0.198995\pi$
$984$	−0.143376	+	0.178910i	−0.00457065	+	0.00570344i
$985$	−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
$990$	0.725210	+	3.24876i	0.0230487	+	0.103252i
$991$		−	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
$996$	−0.100773	+	2.13042i	−0.00319310	+	0.0675050i
$997$	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
$999$	11.9827	+	11.6220i	0.379117	+	0.367704i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(0.587785 - 0.809017i) q^{2} +(1.67073 - 0.456803i) q^{3} +(-0.309017 - 0.951057i) q^{4} +1.00000i q^{5} +(0.612467 - 1.62015i) q^{6} +(-0.531003 - 1.63426i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(2.58266 - 1.52639i) q^{9} +O(q^{10})\)	\(q+(0.587785 - 0.809017i) q^{2} +(1.67073 - 0.456803i) 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} +(2.58266 - 1.52639i) q^{9} +(0.809017 + 0.587785i) q^{10} +(0.342877 + 1.05527i) q^{11} +(-0.950729 - 1.44780i) q^{12} +(-1.47125 - 2.02501i) q^{13} +(-1.63426 - 0.531003i) q^{14} +(0.456803 + 1.67073i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(1.96546 - 6.04907i) q^{17} +(0.283177 - 2.98661i) q^{18} +(3.45827 + 2.51258i) q^{19} +(0.951057 - 0.309017i) q^{20} +(-1.63370 - 2.48784i) q^{21} +(1.05527 + 0.342877i) q^{22} +(1.81096 - 5.57357i) q^{23} +(-1.73012 - 0.0818375i) q^{24} -1.00000 q^{25} -2.50305 q^{26} +(3.61767 - 3.72995i) 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} +(1.05490 + 1.60643i) 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} +(-3.38309 - 2.71116i) q^{39} +(0.309017 - 0.951057i) q^{40} +(0.0778050 - 0.107089i) q^{41} +(-2.97296 - 0.140626i) q^{42} +(-4.78323 + 6.58355i) q^{43} +(0.897663 - 0.652190i) q^{44} +(1.52639 + 2.58266i) q^{45} +(-3.44465 - 4.74116i) q^{46} +(-3.11192 - 4.28320i) q^{47} +(-1.08314 + 1.35159i) q^{48} +(3.27428 - 2.37891i) q^{49} +(-0.587785 + 0.809017i) q^{50} +(0.520516 - 11.0042i) q^{51} +(-1.47125 + 2.02501i) q^{52} +(-1.18858 + 3.65808i) q^{53} +(-0.891180 - 5.11916i) 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} +(1.44780 - 0.950729i) 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} +(1.91969 + 0.0908046i) q^{66} +14.4962 q^{67} -6.36036 q^{68} +(0.479600 - 10.1392i) q^{69} +(0.531003 - 1.63426i) q^{70} +(-7.23610 - 2.35115i) q^{71} +(-2.92794 + 0.653595i) q^{72} +(-12.8859 + 4.18687i) q^{73} +(2.59903 + 1.88830i) q^{74} +(-1.67073 + 0.456803i) q^{75} +(1.32094 - 4.06544i) q^{76} +(1.54251 - 1.12070i) q^{77} +(-4.18191 + 1.14340i) q^{78} +(-2.21018 - 0.718130i) q^{79} +(-0.587785 - 0.809017i) q^{80} +(4.34028 - 7.88429i) q^{81} +(-0.0409045 - 0.125891i) q^{82} +(-0.996203 - 0.723784i) q^{83} +(-1.86123 + 2.32252i) 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} +(2.98661 + 0.283177i) q^{90} +(-2.52814 + 3.47969i) q^{91} -5.86040 q^{92} +(7.74933 + 5.74003i) q^{93} -5.29432 q^{94} +(-2.51258 + 3.45827i) q^{95} +(0.456803 + 1.67073i) 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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