LMFDB - Embedded newform 930.2.n.f.901.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(481,930)]

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([0, 0, 2]))

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

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

chi := DirichletCharacter("930.481");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.n (of order $5$, 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:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 10 x^{10} - 15 x^{9} + 61 x^{8} - 25 x^{7} + 316 x^{6} + 50 x^{5} + 1336 x^{4} + \cdots + 121 $ x^12 - 3x^11 + 10x^10 - 15x^9 + 61x^8 - 25x^7 + 316x^6 + 50x^5 + 1336x^4 - 1720x^3 + 1235x^2 - 462*x + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			901.3
Root			$2.53910 - 1.84477i$ of defining polynomial
Character	$\chi$	$=$	930.901
Dual form			930.2.n.f.481.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 + 0.587785i) q^{2} +(0.809017 - 0.587785i) q^{3} +(0.309017 + 0.951057i) q^{4} +1.00000 q^{5} +1.00000 q^{6} +(0.837960 + 2.57897i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(0.809017 + 0.587785i) q^{2} +(0.809017 - 0.587785i) q^{3} +(0.309017 + 0.951057i) q^{4} +1.00000 q^{5} +1.00000 q^{6} +(0.837960 + 2.57897i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.309017 - 0.951057i) q^{9} +(0.809017 + 0.587785i) q^{10} +(-0.878268 - 2.70303i) q^{11} +(0.809017 + 0.587785i) q^{12} +(4.10835 - 2.98489i) q^{13} +(-0.837960 + 2.57897i) q^{14} +(0.809017 - 0.587785i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-1.86924 + 5.75294i) q^{17} +(0.809017 - 0.587785i) q^{18} +(3.22356 + 2.34206i) q^{19} +(0.309017 + 0.951057i) q^{20} +(2.19381 + 1.59389i) q^{21} +(0.878268 - 2.70303i) q^{22} +(0.470596 - 1.44835i) q^{23} +(0.309017 + 0.951057i) q^{24} +1.00000 q^{25} +5.07820 q^{26} +(-0.309017 - 0.951057i) q^{27} +(-2.19381 + 1.59389i) q^{28} +(0.805858 + 0.585490i) q^{29} +1.00000 q^{30} +(5.55539 - 0.370938i) q^{31} -1.00000 q^{32} +(-2.29934 - 1.67057i) q^{33} +(-4.89374 + 3.55551i) q^{34} +(0.837960 + 2.57897i) q^{35} +1.00000 q^{36} -10.9618 q^{37} +(1.23129 + 3.78953i) q^{38} +(1.56925 - 4.82966i) q^{39} +(-0.309017 + 0.951057i) q^{40} +(1.57046 + 1.14100i) q^{41} +(0.837960 + 2.57897i) q^{42} +(-1.38232 - 1.00431i) q^{43} +(2.29934 - 1.67057i) q^{44} +(0.309017 - 0.951057i) q^{45} +(1.23204 - 0.895128i) q^{46} +(-2.71244 + 1.97070i) q^{47} +(-0.309017 + 0.951057i) q^{48} +(-0.285815 + 0.207656i) q^{49} +(0.809017 + 0.587785i) q^{50} +(1.86924 + 5.75294i) q^{51} +(4.10835 + 2.98489i) q^{52} +(-0.127860 + 0.393514i) q^{53} +(0.309017 - 0.951057i) q^{54} +(-0.878268 - 2.70303i) q^{55} -2.71169 q^{56} +3.98454 q^{57} +(0.307810 + 0.947342i) q^{58} +(-5.37667 + 3.90638i) q^{59} +(0.809017 + 0.587785i) q^{60} -7.87051 q^{61} +(4.71244 + 2.96528i) q^{62} +2.71169 q^{63} +(-0.809017 - 0.587785i) q^{64} +(4.10835 - 2.98489i) q^{65} +(-0.878268 - 2.70303i) q^{66} +14.0296 q^{67} -6.04900 q^{68} +(-0.470596 - 1.44835i) q^{69} +(-0.837960 + 2.57897i) q^{70} +(4.03836 - 12.4288i) q^{71} +(0.809017 + 0.587785i) q^{72} +(0.759156 + 2.33644i) q^{73} +(-8.86825 - 6.44316i) q^{74} +(0.809017 - 0.587785i) q^{75} +(-1.23129 + 3.78953i) q^{76} +(6.23510 - 4.53006i) q^{77} +(4.10835 - 2.98489i) q^{78} +(2.06879 - 6.36708i) q^{79} +(-0.809017 + 0.587785i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(0.599862 + 1.84618i) q^{82} +(-11.2215 - 8.15288i) q^{83} +(-0.837960 + 2.57897i) q^{84} +(-1.86924 + 5.75294i) q^{85} +(-0.527999 - 1.62501i) q^{86} +0.996095 q^{87} +2.84214 q^{88} +(-4.57906 - 14.0929i) q^{89} +(0.809017 - 0.587785i) q^{90} +(11.1406 + 8.09412i) q^{91} +1.52288 q^{92} +(4.27638 - 3.56547i) q^{93} -3.35276 q^{94} +(3.22356 + 2.34206i) q^{95} +(-0.809017 + 0.587785i) q^{96} +(-1.58269 - 4.87103i) q^{97} -0.353286 q^{98} -2.84214 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} + 3 q^{3} - 3 q^{4} + 12 q^{5} + 12 q^{6} - q^{7} + 3 q^{8} - 3 q^{9}+O(q^{10}) $ 12 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 + 12 * q^5 + 12 * q^6 - q^7 + 3 * q^8 - 3 * q^9	\( 12 q + 3 q^{2} + 3 q^{3} - 3 q^{4} + 12 q^{5} + 12 q^{6} - q^{7} + 3 q^{8} - 3 q^{9} + 3 q^{10} + 14 q^{11} + 3 q^{12} + 4 q^{13} + q^{14} + 3 q^{15} - 3 q^{16} - 7 q^{17} + 3 q^{18} + 12 q^{19} - 3 q^{20} + q^{21} - 14 q^{22} - 6 q^{23} - 3 q^{24} + 12 q^{25} + 6 q^{26} + 3 q^{27} - q^{28} - 23 q^{29} + 12 q^{30} + 34 q^{31} - 12 q^{32} + 11 q^{33} - 3 q^{34} - q^{35} + 12 q^{36} + 22 q^{37} + 8 q^{38} + q^{39} + 3 q^{40} + 15 q^{41} - q^{42} - 17 q^{43} - 11 q^{44} - 3 q^{45} + 6 q^{46} - 2 q^{47} + 3 q^{48} - 8 q^{49} + 3 q^{50} + 7 q^{51} + 4 q^{52} - 21 q^{53} - 3 q^{54} + 14 q^{55} - 4 q^{56} + 8 q^{57} - 17 q^{58} - 15 q^{59} + 3 q^{60} + 16 q^{61} + 26 q^{62} + 4 q^{63} - 3 q^{64} + 4 q^{65} + 14 q^{66} + 24 q^{67} + 8 q^{68} + 6 q^{69} + q^{70} + 23 q^{71} + 3 q^{72} + 56 q^{73} + 8 q^{74} + 3 q^{75} - 8 q^{76} - 8 q^{77} + 4 q^{78} - 9 q^{79} - 3 q^{80} - 3 q^{81} + 15 q^{82} - 24 q^{83} + q^{84} - 7 q^{85} - 18 q^{86} - 12 q^{87} + 6 q^{88} - 27 q^{89} + 3 q^{90} - 3 q^{91} + 24 q^{92} + 11 q^{93} - 28 q^{94} + 12 q^{95} - 3 q^{96} + 38 q^{97} - 52 q^{98} - 6 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 + 12 * q^5 + 12 * q^6 - q^7 + 3 * q^8 - 3 * q^9 + 3 * q^10 + 14 * q^11 + 3 * q^12 + 4 * q^13 + q^14 + 3 * q^15 - 3 * q^16 - 7 * q^17 + 3 * q^18 + 12 * q^19 - 3 * q^20 + q^21 - 14 * q^22 - 6 * q^23 - 3 * q^24 + 12 * q^25 + 6 * q^26 + 3 * q^27 - q^28 - 23 * q^29 + 12 * q^30 + 34 * q^31 - 12 * q^32 + 11 * q^33 - 3 * q^34 - q^35 + 12 * q^36 + 22 * q^37 + 8 * q^38 + q^39 + 3 * q^40 + 15 * q^41 - q^42 - 17 * q^43 - 11 * q^44 - 3 * q^45 + 6 * q^46 - 2 * q^47 + 3 * q^48 - 8 * q^49 + 3 * q^50 + 7 * q^51 + 4 * q^52 - 21 * q^53 - 3 * q^54 + 14 * q^55 - 4 * q^56 + 8 * q^57 - 17 * q^58 - 15 * q^59 + 3 * q^60 + 16 * q^61 + 26 * q^62 + 4 * q^63 - 3 * q^64 + 4 * q^65 + 14 * q^66 + 24 * q^67 + 8 * q^68 + 6 * q^69 + q^70 + 23 * q^71 + 3 * q^72 + 56 * q^73 + 8 * q^74 + 3 * q^75 - 8 * q^76 - 8 * q^77 + 4 * q^78 - 9 * q^79 - 3 * q^80 - 3 * q^81 + 15 * q^82 - 24 * q^83 + q^84 - 7 * q^85 - 18 * q^86 - 12 * q^87 + 6 * q^88 - 27 * q^89 + 3 * q^90 - 3 * q^91 + 24 * q^92 + 11 * q^93 - 28 * q^94 + 12 * q^95 - 3 * q^96 + 38 * q^97 - 52 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$3$	0.809017	−	0.587785i	0.467086	−	0.339358i
$3$	0.809017	−	0.587785i	0.467086	−	0.339358i
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	1.00000			0.408248
$7$	0.837960	+	2.57897i	0.316719	+	0.974761i	0.975041	+	0.222024i	$0.0712665\pi$
$7$	0.837960	+	2.57897i	0.316719	+	0.974761i	−0.658322	+	0.752736i	$0.728734\pi$
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$	0.809017	+	0.587785i	0.255834	+	0.185874i
$11$	−0.878268	−	2.70303i	−0.264808	−	0.814995i	−0.991738	−	0.128283i	$-0.959053\pi$
$11$	−0.878268	−	2.70303i	−0.264808	−	0.814995i	0.726930	−	0.686712i	$-0.240947\pi$
$12$	0.809017	+	0.587785i	0.233543	+	0.169679i
$13$	4.10835	−	2.98489i	1.13945	−	0.827860i	0.152409	−	0.988317i	$-0.451297\pi$
$13$	4.10835	−	2.98489i	1.13945	−	0.827860i	0.987043	+	0.160457i	$0.0512968\pi$
$14$	−0.837960	+	2.57897i	−0.223954	+	0.689260i
$15$	0.809017	−	0.587785i	0.208887	−	0.151765i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−1.86924	+	5.75294i	−0.453358	+	1.39529i	0.419694	+	0.907666i	$0.362137\pi$
$17$	−1.86924	+	5.75294i	−0.453358	+	1.39529i	−0.873052	+	0.487627i	$0.837863\pi$
$18$	0.809017	−	0.587785i	0.190687	−	0.138542i
$19$	3.22356	+	2.34206i	0.739536	+	0.537304i	0.892566	−	0.450917i	$-0.148903\pi$
$19$	3.22356	+	2.34206i	0.739536	+	0.537304i	−0.153030	+	0.988222i	$0.548903\pi$
$20$	0.309017	+	0.951057i	0.0690983	+	0.212663i
$21$	2.19381	+	1.59389i	0.478728	+	0.347816i
$22$	0.878268	−	2.70303i	0.187247	−	0.576288i
$23$	0.470596	−	1.44835i	0.0981261	−	0.302001i	−0.889930	−	0.456098i	$-0.849247\pi$
$23$	0.470596	−	1.44835i	0.0981261	−	0.302001i	0.988056	+	0.154097i	$0.0492467\pi$
$24$	0.309017	+	0.951057i	0.0630778	+	0.194134i
$25$	1.00000			0.200000
$26$	5.07820			0.995918
$27$	−0.309017	−	0.951057i	−0.0594703	−	0.183031i
$28$	−2.19381	+	1.59389i	−0.414591	+	0.301218i
$29$	0.805858	+	0.585490i	0.149644	+	0.108723i	0.660088	−	0.751188i	$-0.270519\pi$
$29$	0.805858	+	0.585490i	0.149644	+	0.108723i	−0.510444	+	0.859911i	$0.670519\pi$
$30$	1.00000			0.182574
$31$	5.55539	−	0.370938i	0.997778	−	0.0666224i
$31$	5.55539	−	0.370938i	0.997778	−	0.0666224i
$32$	−1.00000			−0.176777
$33$	−2.29934	−	1.67057i	−0.400263	−	0.290808i
$34$	−4.89374	+	3.55551i	−0.839270	+	0.609765i
$35$	0.837960	+	2.57897i	0.141641	+	0.435926i
$36$	1.00000			0.166667
$37$	−10.9618			−1.80210			−0.901051	−	0.433713i	$-0.857203\pi$
$37$	−10.9618			−1.80210			−0.901051	+	0.433713i	$0.857203\pi$
$38$	1.23129	+	3.78953i	0.199742	+	0.614742i
$39$	1.56925	−	4.82966i	0.251281	−	0.773364i
$40$	−0.309017	+	0.951057i	−0.0488599	+	0.150375i
$41$	1.57046	+	1.14100i	0.245264	+	0.178195i	0.703625	−	0.710571i	$-0.251563\pi$
$41$	1.57046	+	1.14100i	0.245264	+	0.178195i	−0.458361	+	0.888766i	$0.651563\pi$
$42$	0.837960	+	2.57897i	0.129300	+	0.397944i
$43$	−1.38232	−	1.00431i	−0.210802	−	0.153156i	0.477375	−	0.878700i	$-0.341588\pi$
$43$	−1.38232	−	1.00431i	−0.210802	−	0.153156i	−0.688176	+	0.725543i	$0.741588\pi$
$44$	2.29934	−	1.67057i	0.346638	−	0.251847i
$45$	0.309017	−	0.951057i	0.0460655	−	0.141775i
$46$	1.23204	−	0.895128i	0.181654	−	0.131979i
$47$	−2.71244	+	1.97070i	−0.395650	+	0.287457i	−0.767767	−	0.640729i	$-0.778632\pi$
$47$	−2.71244	+	1.97070i	−0.395650	+	0.287457i	0.372117	+	0.928186i	$0.378632\pi$
$48$	−0.309017	+	0.951057i	−0.0446028	+	0.137273i
$49$	−0.285815	+	0.207656i	−0.0408307	+	0.0296652i
$50$	0.809017	+	0.587785i	0.114412	+	0.0831254i
$51$	1.86924	+	5.75294i	0.261746	+	0.805573i
$52$	4.10835	+	2.98489i	0.569726	+	0.413930i
$53$	−0.127860	+	0.393514i	−0.0175630	+	0.0540532i	−0.959454	−	0.281866i	$-0.909047\pi$
$53$	−0.127860	+	0.393514i	−0.0175630	+	0.0540532i	0.941891	+	0.335919i	$0.109047\pi$
$54$	0.309017	−	0.951057i	0.0420519	−	0.129422i
$55$	−0.878268	−	2.70303i	−0.118426	−	0.364477i
$56$	−2.71169			−0.362365
$57$	3.98454			0.527766
$58$	0.307810	+	0.947342i	0.0404175	+	0.124392i
$59$	−5.37667	+	3.90638i	−0.699983	+	0.508567i	−0.879927	−	0.475110i	$-0.842408\pi$
$59$	−5.37667	+	3.90638i	−0.699983	+	0.508567i	0.179944	+	0.983677i	$0.442408\pi$
$60$	0.809017	+	0.587785i	0.104444	+	0.0758827i
$61$	−7.87051			−1.00772			−0.503858	−	0.863786i	$-0.668087\pi$
$61$	−7.87051			−1.00772			−0.503858	+	0.863786i	$0.668087\pi$
$62$	4.71244	+	2.96528i	0.598481	+	0.376591i
$63$	2.71169			0.341641
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	4.10835	−	2.98489i	0.509578	−	0.370230i
$66$	−0.878268	−	2.70303i	−0.108107	−	0.332720i
$67$	14.0296			1.71399			0.856996	−	0.515322i	$-0.172328\pi$
$67$	14.0296			1.71399			0.856996	+	0.515322i	$0.172328\pi$
$68$	−6.04900			−0.733549
$69$	−0.470596	−	1.44835i	−0.0566531	−	0.174360i
$70$	−0.837960	+	2.57897i	−0.100155	+	0.308246i
$71$	4.03836	−	12.4288i	0.479265	−	1.47502i	−0.360854	−	0.932622i	$-0.617515\pi$
$71$	4.03836	−	12.4288i	0.479265	−	1.47502i	0.840119	−	0.542403i	$-0.182485\pi$
$72$	0.809017	+	0.587785i	0.0953436	+	0.0692712i
$73$	0.759156	+	2.33644i	0.0888524	+	0.273460i	0.985603	−	0.169077i	$-0.0540787\pi$
$73$	0.759156	+	2.33644i	0.0888524	+	0.273460i	−0.896750	+	0.442537i	$0.854079\pi$
$74$	−8.86825	−	6.44316i	−1.03091	−	0.749002i
$75$	0.809017	−	0.587785i	0.0934172	−	0.0678716i
$76$	−1.23129	+	3.78953i	−0.141239	+	0.434688i
$77$	6.23510	−	4.53006i	0.710555	−	0.516249i
$78$	4.10835	−	2.98489i	0.465179	−	0.337973i
$79$	2.06879	−	6.36708i	0.232757	−	0.716353i	−0.764654	−	0.644441i	$-0.777090\pi$
$79$	2.06879	−	6.36708i	0.232757	−	0.716353i	0.997411	−	0.0719115i	$-0.0229099\pi$
$80$	−0.809017	+	0.587785i	−0.0904508	+	0.0657164i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	0.599862	+	1.84618i	0.0662436	+	0.203877i
$83$	−11.2215	−	8.15288i	−1.23172	−	0.894895i	−0.234700	−	0.972068i	$-0.575411\pi$
$83$	−11.2215	−	8.15288i	−1.23172	−	0.894895i	−0.997018	+	0.0771726i	$0.975411\pi$
$84$	−0.837960	+	2.57897i	−0.0914289	+	0.281389i
$85$	−1.86924	+	5.75294i	−0.202748	+	0.623994i
$86$	−0.527999	−	1.62501i	−0.0569356	−	0.175230i
$87$	0.996095			0.106793
$88$	2.84214			0.302973
$89$	−4.57906	−	14.0929i	−0.485379	−	1.49384i	−0.831431	−	0.555628i	$-0.812478\pi$
$89$	−4.57906	−	14.0929i	−0.485379	−	1.49384i	0.346052	−	0.938215i	$-0.387522\pi$
$90$	0.809017	−	0.587785i	0.0852779	−	0.0619580i
$91$	11.1406	+	8.09412i	1.16785	+	0.848494i
$92$	1.52288			0.158771
$93$	4.27638	−	3.56547i	0.443440	−	0.369722i
$94$	−3.35276			−0.345811
$95$	3.22356	+	2.34206i	0.330731	+	0.240290i
$96$	−0.809017	+	0.587785i	−0.0825700	+	0.0599906i
$97$	−1.58269	−	4.87103i	−0.160698	−	0.494579i	0.837995	−	0.545677i	$-0.183728\pi$
$97$	−1.58269	−	4.87103i	−0.160698	−	0.494579i	−0.998694	+	0.0510989i	$0.983728\pi$
$98$	−0.353286			−0.0356873
$99$	−2.84214			−0.285645
$100$	0.309017	+	0.951057i	0.0309017	+	0.0951057i
$101$	−4.44246	+	13.6725i	−0.442041	+	1.36046i	0.443655	+	0.896198i	$0.353681\pi$
$101$	−4.44246	+	13.6725i	−0.442041	+	1.36046i	−0.885696	+	0.464265i	$0.846319\pi$
$102$	−1.86924	+	5.75294i	−0.185083	+	0.569626i
$103$	5.57165	+	4.04804i	0.548991	+	0.398865i	0.827413	−	0.561593i	$-0.189811\pi$
$103$	5.57165	+	4.04804i	0.548991	+	0.398865i	−0.278422	+	0.960459i	$0.589811\pi$
$104$	1.56925	+	4.82966i	0.153878	+	0.473587i
$105$	2.19381	+	1.59389i	0.214094	+	0.155548i
$106$	−0.334743	+	0.243205i	−0.0325131	+	0.0236221i
$107$	−3.65864	+	11.2601i	−0.353694	+	1.08856i	0.603069	+	0.797689i	$0.293944\pi$
$107$	−3.65864	+	11.2601i	−0.353694	+	1.08856i	−0.956763	+	0.290869i	$0.906056\pi$
$108$	0.809017	−	0.587785i	0.0778477	−	0.0565597i
$109$	−5.09036	+	3.69836i	−0.487568	+	0.354239i	−0.804248	−	0.594294i	$-0.797432\pi$
$109$	−5.09036	+	3.69836i	−0.487568	+	0.354239i	0.316680	+	0.948532i	$0.397432\pi$
$110$	0.878268	−	2.70303i	0.0837396	−	0.257724i
$111$	−8.86825	+	6.44316i	−0.841737	+	0.611558i
$112$	−2.19381	−	1.59389i	−0.207295	−	0.150609i
$113$	−2.62644	−	8.08334i	−0.247074	−	0.760416i	−0.995288	−	0.0969591i	$-0.969088\pi$
$113$	−2.62644	−	8.08334i	−0.247074	−	0.760416i	0.748214	−	0.663457i	$-0.230912\pi$
$114$	3.22356	+	2.34206i	0.301914	+	0.219354i
$115$	0.470596	−	1.44835i	0.0438833	−	0.135059i
$116$	−0.307810	+	0.947342i	−0.0285795	+	0.0879585i
$117$	−1.56925	−	4.82966i	−0.145077	−	0.446502i
$118$	−6.64593			−0.611807
$119$	−16.4030			−1.50366
$120$	0.309017	+	0.951057i	0.0282093	+	0.0868192i
$121$	2.36416	−	1.71767i	0.214924	−	0.156151i
$122$	−6.36738	−	4.62617i	−0.576476	−	0.418834i
$123$	1.94119			0.175031
$124$	2.06949	+	5.16887i	0.185846	+	0.464178i
$125$	1.00000			0.0894427
$126$	2.19381	+	1.59389i	0.195440	+	0.141995i
$127$	−3.82961	+	2.78237i	−0.339823	+	0.246896i	−0.744587	−	0.667525i	$-0.767354\pi$
$127$	−3.82961	+	2.78237i	−0.339823	+	0.246896i	0.404764	+	0.914421i	$0.367354\pi$
$128$	−0.309017	−	0.951057i	−0.0273135	−	0.0840623i
$129$	−1.70864			−0.150437
$130$	5.07820			0.445388
$131$	−3.36741	−	10.3638i	−0.294212	−	0.905490i	−0.983485	−	0.180989i	$-0.942070\pi$
$131$	−3.36741	−	10.3638i	−0.294212	−	0.905490i	0.689274	−	0.724501i	$-0.257930\pi$
$132$	0.878268	−	2.70303i	0.0764434	−	0.235269i
$133$	−3.33889	+	10.2760i	−0.289518	+	0.891045i
$134$	11.3502	+	8.24641i	0.980509	+	0.712382i
$135$	−0.309017	−	0.951057i	−0.0265959	−	0.0818539i
$136$	−4.89374	−	3.55551i	−0.419635	−	0.304883i
$137$	−2.78398	+	2.02268i	−0.237851	+	0.172809i	−0.700326	−	0.713824i	$-0.746962\pi$
$137$	−2.78398	+	2.02268i	−0.237851	+	0.172809i	0.462474	+	0.886633i	$0.346962\pi$
$138$	0.470596	−	1.44835i	0.0400598	−	0.123291i
$139$	−9.41913	+	6.84340i	−0.798920	+	0.580450i	−0.910597	−	0.413295i	$-0.864378\pi$
$139$	−9.41913	+	6.84340i	−0.798920	+	0.580450i	0.111677	+	0.993745i	$0.464378\pi$
$140$	−2.19381	+	1.59389i	−0.185411	+	0.134709i
$141$	−1.03606	+	3.18866i	−0.0872520	+	0.268534i
$142$	10.5726	−	7.68141i	0.887229	−	0.644610i
$143$	−11.6765	−	8.48347i	−0.976438	−	0.709423i
$144$	0.309017	+	0.951057i	0.0257514	+	0.0792547i
$145$	0.805858	+	0.585490i	0.0669228	+	0.0486223i
$146$	−0.759156	+	2.33644i	−0.0628282	+	0.193365i
$147$	−0.109171	+	0.335995i	−0.00900431	+	0.0277124i
$148$	−3.38737	−	10.4253i	−0.278440	−	0.856951i
$149$	−15.6121			−1.27900			−0.639498	−	0.768793i	$-0.720858\pi$
$149$	−15.6121			−1.27900			−0.639498	+	0.768793i	$0.720858\pi$
$150$	1.00000			0.0816497
$151$	−6.68850	−	20.5851i	−0.544302	−	1.67519i	−0.722643	−	0.691221i	$-0.757073\pi$
$151$	−6.68850	−	20.5851i	−0.544302	−	1.67519i	0.178341	−	0.983969i	$-0.442927\pi$
$152$	−3.22356	+	2.34206i	−0.261465	+	0.189966i
$153$	4.89374	+	3.55551i	0.395636	+	0.287446i
$154$	7.70700			0.621048
$155$	5.55539	−	0.370938i	0.446220	−	0.0297945i
$156$	5.07820			0.406582
$157$	11.0717	+	8.04409i	0.883621	+	0.641988i	0.934207	−	0.356731i	$-0.116109\pi$
$157$	11.0717	+	8.04409i	0.883621	+	0.641988i	−0.0505860	+	0.998720i	$0.516109\pi$
$158$	5.41616	−	3.93507i	0.430887	−	0.313058i
$159$	0.127860	+	0.393514i	0.0101400	+	0.0312077i
$160$	−1.00000			−0.0790569
$161$	4.12959			0.325457
$162$	−0.309017	−	0.951057i	−0.0242787	−	0.0747221i
$163$	1.38085	−	4.24983i	0.108157	−	0.332872i	−0.882302	−	0.470684i	$-0.844007\pi$
$163$	1.38085	−	4.24983i	0.108157	−	0.332872i	0.990458	+	0.137812i	$0.0440071\pi$
$164$	−0.599862	+	1.84618i	−0.0468413	+	0.144163i
$165$	−2.29934	−	1.67057i	−0.179003	−	0.130053i
$166$	−4.28622	−	13.1916i	−0.332676	−	1.02387i
$167$	−13.8341	−	10.0510i	−1.07051	−	0.777772i	−0.0945070	−	0.995524i	$-0.530127\pi$
$167$	−13.8341	−	10.0510i	−1.07051	−	0.777772i	−0.976004	+	0.217752i	$0.930127\pi$
$168$	−2.19381	+	1.59389i	−0.169256	+	0.122972i
$169$	3.95176	−	12.1623i	0.303981	−	0.935558i
$170$	−4.89374	+	3.55551i	−0.375333	+	0.272695i
$171$	3.22356	−	2.34206i	0.246512	−	0.179101i
$172$	0.527999	−	1.62501i	0.0402595	−	0.123906i
$173$	−8.39480	+	6.09918i	−0.638245	+	0.463712i	−0.859247	−	0.511561i	$-0.829067\pi$
$173$	−8.39480	+	6.09918i	−0.638245	+	0.463712i	0.221002	+	0.975273i	$0.429067\pi$
$174$	0.805858	+	0.585490i	0.0610919	+	0.0443859i
$175$	0.837960	+	2.57897i	0.0633438	+	0.194952i
$176$	2.29934	+	1.67057i	0.173319	+	0.125924i
$177$	−2.05370	+	6.32065i	−0.154366	+	0.475089i
$178$	4.57906	−	14.0929i	0.343215	−	1.05631i
$179$	−3.77819	−	11.6281i	−0.282396	−	0.869124i	−0.987167	−	0.159690i	$-0.948951\pi$
$179$	−3.77819	−	11.6281i	−0.282396	−	0.869124i	0.704772	−	0.709434i	$-0.251049\pi$
$180$	1.00000			0.0745356
$181$	−21.0618			−1.56551			−0.782755	−	0.622330i	$-0.786186\pi$
$181$	−21.0618			−1.56551			−0.782755	+	0.622330i	$0.786186\pi$
$182$	4.25533	+	13.0966i	0.315426	+	0.970781i
$183$	−6.36738	+	4.62617i	−0.470690	+	0.341977i
$184$	1.23204	+	0.895128i	0.0908270	+	0.0659897i
$185$	−10.9618			−0.805925
$186$	5.55539	−	0.370938i	0.407341	−	0.0271985i
$187$	17.1921			1.25721
$188$	−2.71244	−	1.97070i	−0.197825	−	0.143728i
$189$	2.19381	−	1.59389i	0.159576	−	0.115939i
$190$	1.23129	+	3.78953i	0.0893273	+	0.274921i
$191$	15.6911			1.13537			0.567684	−	0.823246i	$-0.307839\pi$
$191$	15.6911			1.13537			0.567684	+	0.823246i	$0.307839\pi$
$192$	−1.00000			−0.0721688
$193$	−2.06375	−	6.35157i	−0.148552	−	0.457196i	0.848899	−	0.528556i	$-0.177266\pi$
$193$	−2.06375	−	6.35157i	−0.148552	−	0.457196i	−0.997451	+	0.0713595i	$0.977266\pi$
$194$	1.58269	−	4.87103i	0.113631	−	0.349720i
$195$	1.56925	−	4.82966i	0.112376	−	0.345859i
$196$	−0.285815	−	0.207656i	−0.0204153	−	0.0148326i
$197$	−2.61372	−	8.04422i	−0.186220	−	0.573127i	0.813747	−	0.581219i	$-0.197424\pi$
$197$	−2.61372	−	8.04422i	−0.186220	−	0.573127i	−0.999967	+	0.00809234i	$0.997424\pi$
$198$	−2.29934	−	1.67057i	−0.163407	−	0.118722i
$199$	7.71355	−	5.60423i	0.546799	−	0.397273i	−0.279805	−	0.960057i	$-0.590270\pi$
$199$	7.71355	−	5.60423i	0.546799	−	0.397273i	0.826604	+	0.562784i	$0.190270\pi$
$200$	−0.309017	+	0.951057i	−0.0218508	+	0.0672499i
$201$	11.3502	−	8.24641i	0.800582	−	0.581657i
$202$	−11.6305	+	8.45006i	−0.818320	+	0.594544i
$203$	−0.834687	+	2.56890i	−0.0585836	+	0.180302i
$204$	−4.89374	+	3.55551i	−0.342630	+	0.248936i
$205$	1.57046	+	1.14100i	0.109686	+	0.0796912i
$206$	2.12818	+	6.54987i	0.148277	+	0.456351i
$207$	−1.23204	−	0.895128i	−0.0856325	−	0.0622157i
$208$	−1.56925	+	4.82966i	−0.108808	+	0.334877i
$209$	3.49950	−	10.7703i	0.242065	−	0.745000i
$210$	0.837960	+	2.57897i	0.0578247	+	0.177966i
$211$	−20.8019			−1.43206			−0.716032	−	0.698068i	$-0.754043\pi$
$211$	−20.8019			−1.43206			−0.716032	+	0.698068i	$0.754043\pi$
$212$	−0.413765			−0.0284175
$213$	−4.03836	−	12.4288i	−0.276704	−	0.851606i
$214$	−9.57844	+	6.95914i	−0.654769	+	0.475717i
$215$	−1.38232	−	1.00431i	−0.0942733	−	0.0684936i
$216$	1.00000			0.0680414
$217$	5.61184	+	14.0164i	0.380956	+	0.951495i
$218$	−6.29203			−0.426150
$219$	1.98750	+	1.44400i	0.134302	+	0.0975765i
$220$	2.29934	−	1.67057i	0.155021	−	0.112629i
$221$	9.49240	+	29.2146i	0.638528	+	1.96519i
$222$	−10.9618			−0.735705
$223$	20.0887			1.34524			0.672620	−	0.739988i	$-0.265169\pi$
$223$	20.0887			1.34524			0.672620	+	0.739988i	$0.265169\pi$
$224$	−0.837960	−	2.57897i	−0.0559885	−	0.172315i
$225$	0.309017	−	0.951057i	0.0206011	−	0.0634038i
$226$	2.62644	−	8.08334i	0.174708	−	0.537696i
$227$	9.53748	+	6.92939i	0.633025	+	0.459920i	0.857447	−	0.514573i	$-0.172049\pi$
$227$	9.53748	+	6.92939i	0.633025	+	0.459920i	−0.224422	+	0.974492i	$0.572049\pi$
$228$	1.23129	+	3.78953i	0.0815443	+	0.250967i
$229$	12.6786	+	9.21157i	0.837828	+	0.608718i	0.921763	−	0.387754i	$-0.126749\pi$
$229$	12.6786	+	9.21157i	0.837828	+	0.608718i	−0.0839351	+	0.996471i	$0.526749\pi$
$230$	1.23204	−	0.895128i	0.0812381	−	0.0590230i
$231$	2.38159	−	7.32979i	0.156697	−	0.482265i
$232$	−0.805858	+	0.585490i	−0.0529071	+	0.0384393i
$233$	−9.23628	+	6.71055i	−0.605089	+	0.439623i	−0.847681	−	0.530506i	$-0.822002\pi$
$233$	−9.23628	+	6.71055i	−0.605089	+	0.439623i	0.242593	+	0.970128i	$0.422002\pi$
$234$	1.56925	−	4.82966i	0.102585	−	0.315725i
$235$	−2.71244	+	1.97070i	−0.176940	+	0.128554i
$236$	−5.37667	−	3.90638i	−0.349991	−	0.254284i
$237$	−2.06879	−	6.36708i	−0.134382	−	0.413586i
$238$	−13.2703	−	9.64146i	−0.860188	−	0.624963i
$239$	0.961055	−	2.95782i	0.0621655	−	0.191326i	−0.915150	−	0.403113i	$-0.867928\pi$
$239$	0.961055	−	2.95782i	0.0621655	−	0.191326i	0.977316	+	0.211787i	$0.0679283\pi$
$240$	−0.309017	+	0.951057i	−0.0199470	+	0.0613904i
$241$	7.92785	+	24.3994i	0.510677	+	1.57170i	0.791012	+	0.611801i	$0.209555\pi$
$241$	7.92785	+	24.3994i	0.510677	+	1.57170i	−0.280334	+	0.959902i	$0.590445\pi$
$242$	2.92227			0.187850
$243$	−1.00000			−0.0641500
$244$	−2.43212	−	7.48530i	−0.155701	−	0.479198i
$245$	−0.285815	+	0.207656i	−0.0182600	+	0.0132667i
$246$	1.57046	+	1.14100i	0.100129	+	0.0727478i
$247$	20.2343			1.28748
$248$	−1.36393	+	5.39812i	−0.0866095	+	0.342781i
$249$	−13.8705			−0.879008
$250$	0.809017	+	0.587785i	0.0511667	+	0.0371748i
$251$	15.4158	−	11.2003i	0.973040	−	0.706955i	0.0168974	−	0.999857i	$-0.494621\pi$
$251$	15.4158	−	11.2003i	0.973040	−	0.706955i	0.956142	+	0.292903i	$0.0946211\pi$
$252$	0.837960	+	2.57897i	0.0527865	+	0.162460i
$253$	−4.32824			−0.272114
$254$	−4.73366			−0.297016
$255$	1.86924	+	5.75294i	0.117057	+	0.360263i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	2.16213	−	6.65435i	0.134870	−	0.415087i	−0.860700	−	0.509113i	$-0.829974\pi$
$257$	2.16213	−	6.65435i	0.134870	−	0.415087i	0.995570	+	0.0940257i	$0.0299736\pi$
$258$	−1.38232	−	1.00431i	−0.0860594	−	0.0625258i
$259$	−9.18551	−	28.2701i	−0.570760	−	1.75662i
$260$	4.10835	+	2.98489i	0.254789	+	0.185115i
$261$	0.805858	−	0.585490i	0.0498813	−	0.0362409i
$262$	3.36741	−	10.3638i	0.208039	−	0.640278i
$263$	−1.99115	+	1.44665i	−0.122779	+	0.0892044i	−0.647480	−	0.762082i	$-0.724177\pi$
$263$	−1.99115	+	1.44665i	−0.122779	+	0.0892044i	0.524701	+	0.851287i	$0.324177\pi$
$264$	2.29934	−	1.67057i	0.141514	−	0.102816i
$265$	−0.127860	+	0.393514i	−0.00785440	+	0.0241733i
$266$	−8.74132	+	6.35094i	−0.535965	+	0.389401i
$267$	−11.9881	−	8.70989i	−0.733662	−	0.533036i
$268$	4.33540	+	13.3430i	0.264826	+	0.815052i
$269$	−23.1216	−	16.7988i	−1.40975	−	1.02424i	−0.993359	−	0.115054i	$-0.963296\pi$
$269$	−23.1216	−	16.7988i	−1.40975	−	1.02424i	−0.416388	−	0.909187i	$-0.636704\pi$
$270$	0.309017	−	0.951057i	0.0188062	−	0.0578795i
$271$	−2.49725	+	7.68576i	−0.151697	+	0.466876i	−0.997811	−	0.0661256i	$-0.978936\pi$
$271$	−2.49725	+	7.68576i	−0.151697	+	0.466876i	0.846114	+	0.533002i	$0.178936\pi$
$272$	−1.86924	−	5.75294i	−0.113340	−	0.348823i
$273$	13.7705			0.833431
$274$	−3.44119			−0.207890
$275$	−0.878268	−	2.70303i	−0.0529616	−	0.162999i
$276$	1.23204	−	0.895128i	0.0741599	−	0.0538803i
$277$	26.3449	+	19.1407i	1.58291	+	1.15005i	0.913262	+	0.407372i	$0.133555\pi$
$277$	26.3449	+	19.1407i	1.58291	+	1.15005i	0.669647	+	0.742679i	$0.266445\pi$
$278$	−11.6427			−0.698282
$279$	1.36393	−	5.39812i	0.0816562	−	0.323177i
$280$	−2.71169			−0.162055
$281$	−13.0072	−	9.45029i	−0.775945	−	0.563757i	0.127814	−	0.991798i	$-0.459204\pi$
$281$	−13.0072	−	9.45029i	−0.775945	−	0.563757i	−0.903759	+	0.428041i	$0.859204\pi$
$282$	−2.71244	+	1.97070i	−0.161523	+	0.117354i
$283$	−1.49761	−	4.60916i	−0.0890234	−	0.273986i	0.896627	−	0.442787i	$-0.146010\pi$
$283$	−1.49761	−	4.60916i	−0.0890234	−	0.273986i	−0.985650	+	0.168801i	$0.946010\pi$
$284$	13.0684			0.775467
$285$	3.98454			0.236024
$286$	−4.46002	−	13.7265i	−0.263727	−	0.811668i
$287$	−1.62664	+	5.00629i	−0.0960176	+	0.295512i
$288$	−0.309017	+	0.951057i	−0.0182090	+	0.0560415i
$289$	−15.8489	−	11.5149i	−0.932291	−	0.677349i
$290$	0.307810	+	0.947342i	0.0180752	+	0.0556299i
$291$	−4.14355	−	3.01046i	−0.242899	−	0.176477i
$292$	−1.98750	+	1.44400i	−0.116309	+	0.0845037i
$293$	−7.74593	+	23.8395i	−0.452522	+	1.39272i	0.421498	+	0.906829i	$0.361504\pi$
$293$	−7.74593	+	23.8395i	−0.452522	+	1.39272i	−0.874020	+	0.485890i	$0.838496\pi$
$294$	−0.285815	+	0.207656i	−0.0166690	+	0.0121108i
$295$	−5.37667	+	3.90638i	−0.313042	+	0.227438i
$296$	3.38737	−	10.4253i	0.196887	−	0.605956i
$297$	−2.29934	+	1.67057i	−0.133421	+	0.0969360i
$298$	−12.6305	−	9.17658i	−0.731664	−	0.531585i
$299$	−2.38978	−	7.35500i	−0.138205	−	0.425351i
$300$	0.809017	+	0.587785i	0.0467086	+	0.0339358i
$301$	1.43177	−	4.40654i	0.0825259	−	0.253989i
$302$	6.68850	−	20.5851i	0.384880	−	1.18454i
$303$	4.44246	+	13.6725i	0.255213	+	0.785463i
$304$	−3.98454			−0.228529
$305$	−7.87051			−0.450664
$306$	1.86924	+	5.75294i	0.106858	+	0.328874i
$307$	−3.23342	+	2.34922i	−0.184541	+	0.134077i	−0.676220	−	0.736699i	$-0.736383\pi$
$307$	−3.23342	+	2.34922i	−0.184541	+	0.134077i	0.491679	+	0.870776i	$0.336383\pi$
$308$	6.23510	+	4.53006i	0.355278	+	0.258124i
$309$	6.88694			0.391784
$310$	4.71244	+	2.96528i	0.267649	+	0.168417i
$311$	5.23047			0.296593			0.148296	−	0.988943i	$-0.452621\pi$
$311$	5.23047			0.296593			0.148296	+	0.988943i	$0.452621\pi$
$312$	4.10835	+	2.98489i	0.232590	+	0.168986i
$313$	10.9061	−	7.92377i	0.616451	−	0.447878i	−0.235229	−	0.971940i	$-0.575584\pi$
$313$	10.9061	−	7.92377i	0.616451	−	0.447878i	0.851680	+	0.524062i	$0.175584\pi$
$314$	4.22903	+	13.0156i	0.238658	+	0.734513i
$315$	2.71169			0.152787
$316$	6.69475			0.376609
$317$	5.98943	+	18.4336i	0.336400	+	1.03533i	0.966028	+	0.258437i	$0.0832073\pi$
$317$	5.98943	+	18.4336i	0.336400	+	1.03533i	−0.629628	+	0.776897i	$0.716793\pi$
$318$	−0.127860	+	0.393514i	−0.00717005	+	0.0220671i
$319$	0.874838	−	2.69248i	0.0489815	−	0.150750i
$320$	−0.809017	−	0.587785i	−0.0452254	−	0.0328582i
$321$	3.65864	+	11.2601i	0.204205	+	0.628479i
$322$	3.34091	+	2.42731i	0.186182	+	0.135269i
$323$	−19.4993	+	14.1671i	−1.08497	+	0.788278i
$324$	0.309017	−	0.951057i	0.0171676	−	0.0528365i
$325$	4.10835	−	2.98489i	0.227890	−	0.165572i
$326$	3.61512	−	2.62654i	0.200223	−	0.145470i
$327$	−1.94434	+	5.98407i	−0.107522	+	0.330920i
$328$	−1.57046	+	1.14100i	−0.0867140	+	0.0630014i
$329$	−7.35531	−	5.34394i	−0.405511	−	0.294621i
$330$	−0.878268	−	2.70303i	−0.0483471	−	0.148797i
$331$	7.01132	+	5.09402i	0.385377	+	0.279993i	0.763558	−	0.645739i	$-0.223450\pi$
$331$	7.01132	+	5.09402i	0.385377	+	0.279993i	−0.378182	+	0.925731i	$0.623450\pi$
$332$	4.28622	−	13.1916i	0.235237	−	0.723985i
$333$	−3.38737	+	10.4253i	−0.185627	+	0.571300i
$334$	−5.28414	−	16.2629i	−0.289135	−	0.889866i
$335$	14.0296			0.766521
$336$	−2.71169			−0.147935
$337$	1.34790	+	4.14841i	0.0734248	+	0.225978i	0.981033	−	0.193839i	$-0.0620940\pi$
$337$	1.34790	+	4.14841i	0.0734248	+	0.225978i	−0.907608	+	0.419818i	$0.862094\pi$
$338$	10.3458	−	7.51669i	0.562739	−	0.408854i
$339$	−6.87610	−	4.99578i	−0.373458	−	0.271333i
$340$	−6.04900			−0.328053
$341$	−5.88178	−	14.6906i	−0.318516	−	0.795542i
$342$	3.98454			0.215459
$343$	14.5816	+	10.5942i	0.787333	+	0.572031i
$344$	1.38232	−	1.00431i	0.0745296	−	0.0541489i
$345$	−0.470596	−	1.44835i	−0.0253361	−	0.0779764i
$346$	−10.3765			−0.557847
$347$	17.1651			0.921470			0.460735	−	0.887538i	$-0.347586\pi$
$347$	17.1651			0.921470			0.460735	+	0.887538i	$0.347586\pi$
$348$	0.307810	+	0.947342i	0.0165004	+	0.0507829i
$349$	3.68795	−	11.3503i	0.197411	−	0.607570i	−0.802529	−	0.596614i	$-0.796512\pi$
$349$	3.68795	−	11.3503i	0.197411	−	0.607570i	0.999940	−	0.0109563i	$-0.00348756\pi$
$350$	−0.837960	+	2.57897i	−0.0447908	+	0.137852i
$351$	−4.10835	−	2.98489i	−0.219288	−	0.159322i
$352$	0.878268	+	2.70303i	0.0468118	+	0.144072i
$353$	10.0642	+	7.31209i	0.535665	+	0.389183i	0.822472	−	0.568805i	$-0.192594\pi$
$353$	10.0642	+	7.31209i	0.535665	+	0.389183i	−0.286808	+	0.957988i	$0.592594\pi$
$354$	−5.37667	+	3.90638i	−0.285767	+	0.207622i
$355$	4.03836	−	12.4288i	0.214334	−	0.659651i
$356$	11.9881	−	8.70989i	0.635370	−	0.461623i
$357$	−13.2703	+	9.64146i	−0.702340	+	0.510280i
$358$	3.77819	−	11.6281i	0.199684	−	0.614563i
$359$	15.7676	−	11.4558i	0.832180	−	0.604614i	−0.0879951	−	0.996121i	$-0.528046\pi$
$359$	15.7676	−	11.4558i	0.832180	−	0.604614i	0.920175	+	0.391507i	$0.128046\pi$
$360$	0.809017	+	0.587785i	0.0426389	+	0.0309790i
$361$	−0.965189	−	2.97055i	−0.0507994	−	0.156345i
$362$	−17.0393	−	12.3798i	−0.895568	−	0.650668i
$363$	0.903030	−	2.77924i	0.0473968	−	0.145872i
$364$	−4.25533	+	13.0966i	−0.223040	+	0.686446i
$365$	0.759156	+	2.33644i	0.0397360	+	0.122295i
$366$	−7.87051			−0.411398
$367$	−3.26638			−0.170504			−0.0852519	−	0.996359i	$-0.527170\pi$
$367$	−3.26638			−0.170504			−0.0852519	+	0.996359i	$0.527170\pi$
$368$	0.470596	+	1.44835i	0.0245315	+	0.0755003i
$369$	1.57046	−	1.14100i	0.0817548	−	0.0593983i
$370$	−8.86825	−	6.44316i	−0.461038	−	0.334964i
$371$	−1.12200			−0.0582515
$372$	4.71244	+	2.96528i	0.244329	+	0.153743i
$373$	−37.1298			−1.92251			−0.961253	−	0.275667i	$-0.911101\pi$
$373$	−37.1298			−1.92251			−0.961253	+	0.275667i	$0.911101\pi$
$374$	13.9087	+	10.1052i	0.719201	+	0.522530i
$375$	0.809017	−	0.587785i	0.0417775	−	0.0303531i
$376$	−1.03606	−	3.18866i	−0.0534307	−	0.164443i
$377$	5.05837			0.260519
$378$	2.71169			0.139475
$379$	3.19991	+	9.84831i	0.164368	+	0.505874i	0.998989	−	0.0449512i	$-0.0143132\pi$
$379$	3.19991	+	9.84831i	0.164368	+	0.505874i	−0.834621	+	0.550825i	$0.814313\pi$
$380$	−1.23129	+	3.78953i	−0.0631639	+	0.194399i
$381$	−1.46278	+	4.50198i	−0.0749405	+	0.230643i
$382$	12.6944	+	9.22300i	0.649501	+	0.471890i
$383$	11.3447	+	34.9155i	0.579689	+	1.78410i	0.619626	+	0.784897i	$0.287284\pi$
$383$	11.3447	+	34.9155i	0.579689	+	1.78410i	−0.0399369	+	0.999202i	$0.512716\pi$
$384$	−0.809017	−	0.587785i	−0.0412850	−	0.0299953i
$385$	6.23510	−	4.53006i	0.317770	−	0.230873i
$386$	2.06375	−	6.35157i	0.105042	−	0.323286i
$387$	−1.38232	+	1.00431i	−0.0702672	+	0.0510521i
$388$	4.14355	−	3.01046i	0.210357	−	0.152833i
$389$	−1.50432	+	4.62982i	−0.0762720	+	0.234741i	−0.981922	−	0.189284i	$-0.939383\pi$
$389$	−1.50432	+	4.62982i	−0.0762720	+	0.234741i	0.905650	+	0.424025i	$0.139383\pi$
$390$	4.10835	−	2.98489i	0.208035	−	0.151146i
$391$	7.45259	+	5.41462i	0.376894	+	0.273829i
$392$	−0.109171	−	0.335995i	−0.00551399	−	0.0169703i
$393$	−8.81598	−	6.40519i	−0.444707	−	0.323099i
$394$	2.61372	−	8.04422i	0.131678	−	0.405262i
$395$	2.06879	−	6.36708i	0.104092	−	0.320363i
$396$	−0.878268	−	2.70303i	−0.0441346	−	0.135832i
$397$	37.6712			1.89066			0.945332	−	0.326110i	$-0.105738\pi$
$397$	37.6712			1.89066			0.945332	+	0.326110i	$0.105738\pi$
$398$	9.53448			0.477920
$399$	3.33889	+	10.2760i	0.167153	+	0.514445i
$400$	−0.809017	+	0.587785i	−0.0404508	+	0.0293893i
$401$	−5.92200	−	4.30258i	−0.295730	−	0.214861i	0.430019	−	0.902820i	$-0.358507\pi$
$401$	−5.92200	−	4.30258i	−0.295730	−	0.214861i	−0.725749	+	0.687959i	$0.758507\pi$
$402$	14.0296			0.699735
$403$	21.7163	−	18.1062i	1.08177	−	0.901934i
$404$	−14.3761			−0.715238
$405$	−0.809017	−	0.587785i	−0.0402004	−	0.0292073i
$406$	−2.18524	+	1.58767i	−0.108452	+	0.0787947i
$407$	9.62737	+	29.6300i	0.477211	+	1.46870i
$408$	−6.04900			−0.299470
$409$	−9.34535			−0.462098			−0.231049	−	0.972942i	$-0.574216\pi$
$409$	−9.34535			−0.462098			−0.231049	+	0.972942i	$0.574216\pi$
$410$	0.599862	+	1.84618i	0.0296251	+	0.0911765i
$411$	−1.06339	+	3.27276i	−0.0524529	+	0.161434i
$412$	−2.12818	+	6.54987i	−0.104848	+	0.322689i
$413$	−14.5799	−	10.5929i	−0.717429	−	0.521243i
$414$	−0.470596	−	1.44835i	−0.0231286	−	0.0711824i
$415$	−11.2215	−	8.15288i	−0.550841	−	0.400209i
$416$	−4.10835	+	2.98489i	−0.201429	+	0.146346i
$417$	−3.59779	+	11.0729i	−0.176184	+	0.542240i
$418$	9.16180	−	6.65644i	0.448118	−	0.325577i
$419$	4.16716	−	3.02762i	0.203579	−	0.147909i	−0.481325	−	0.876542i	$-0.659844\pi$
$419$	4.16716	−	3.02762i	0.203579	−	0.147909i	0.684904	+	0.728633i	$0.259844\pi$
$420$	−0.837960	+	2.57897i	−0.0408882	+	0.125841i
$421$	−20.1147	+	14.6142i	−0.980330	+	0.712252i	−0.957782	−	0.287494i	$-0.907178\pi$
$421$	−20.1147	+	14.6142i	−0.980330	+	0.712252i	−0.0225478	+	0.999746i	$0.507178\pi$
$422$	−16.8291	−	12.2271i	−0.819228	−	0.595204i
$423$	1.03606	+	3.18866i	0.0503750	+	0.155038i
$424$	−0.334743	−	0.243205i	−0.0162565	−	0.0118111i
$425$	−1.86924	+	5.75294i	−0.0906716	+	0.279059i
$426$	4.03836	−	12.4288i	0.195659	−	0.602176i
$427$	−6.59517	−	20.2979i	−0.319163	−	0.982282i
$428$	−11.8396			−0.572289
$429$	−14.4329			−0.696829
$430$	−0.527999	−	1.62501i	−0.0254624	−	0.0783651i
$431$	5.74769	−	4.17594i	0.276856	−	0.201148i	−0.440689	−	0.897660i	$-0.645266\pi$
$431$	5.74769	−	4.17594i	0.276856	−	0.201148i	0.717545	+	0.696512i	$0.245266\pi$
$432$	0.809017	+	0.587785i	0.0389238	+	0.0282798i
$433$	16.8145			0.808052			0.404026	−	0.914747i	$-0.367610\pi$
$433$	16.8145			0.808052			0.404026	+	0.914747i	$0.367610\pi$
$434$	−3.69856	+	14.6381i	−0.177536	+	0.702649i
$435$	0.996095			0.0477591
$436$	−5.09036	−	3.69836i	−0.243784	−	0.177119i
$437$	4.90911	−	3.56667i	0.234834	−	0.170617i
$438$	0.759156	+	2.33644i	0.0362739	+	0.111639i
$439$	7.53649			0.359697			0.179848	−	0.983694i	$-0.442439\pi$
$439$	7.53649			0.359697			0.179848	+	0.983694i	$0.442439\pi$
$440$	2.84214			0.135493
$441$	0.109171	+	0.335995i	0.00519864	+	0.0159998i
$442$	−9.49240	+	29.2146i	−0.451507	+	1.38960i
$443$	0.449092	−	1.38216i	0.0213370	−	0.0656685i	−0.939821	−	0.341667i	$-0.889008\pi$
$443$	0.449092	−	1.38216i	0.0213370	−	0.0656685i	0.961158	+	0.275999i	$0.0890085\pi$
$444$	−8.86825	−	6.44316i	−0.420869	−	0.305779i
$445$	−4.57906	−	14.0929i	−0.217068	−	0.668067i
$446$	16.2521	+	11.8078i	0.769560	+	0.559118i
$447$	−12.6305	+	9.17658i	−0.597401	+	0.434037i
$448$	0.837960	−	2.57897i	0.0395899	−	0.121845i
$449$	−28.0211	+	20.3585i	−1.32240	+	0.960779i	−0.322500	+	0.946569i	$0.604523\pi$
$449$	−28.0211	+	20.3585i	−1.32240	+	0.960779i	−0.999899	+	0.0142097i	$0.995477\pi$
$450$	0.809017	−	0.587785i	0.0381374	−	0.0277085i
$451$	1.70489	−	5.24711i	0.0802800	−	0.247077i
$452$	6.87610	−	4.99578i	0.323424	−	0.234982i
$453$	−17.5107	−	12.7223i	−0.822725	−	0.597745i
$454$	3.64299	+	11.2120i	0.170974	+	0.526204i
$455$	11.1406	+	8.09412i	0.522279	+	0.379458i
$456$	−1.23129	+	3.78953i	−0.0576605	+	0.177461i
$457$	−0.124005	+	0.381648i	−0.00580071	+	0.0178527i	−0.953915	−	0.300077i	$-0.902988\pi$
$457$	−0.124005	+	0.381648i	−0.00580071	+	0.0178527i	0.948114	+	0.317930i	$0.102988\pi$
$458$	4.84281	+	14.9046i	0.226290	+	0.696448i
$459$	6.04900			0.282343
$460$	1.52288			0.0710047
$461$	7.34625	+	22.6094i	0.342149	+	1.05303i	0.963092	+	0.269171i	$0.0867496\pi$
$461$	7.34625	+	22.6094i	0.342149	+	1.05303i	−0.620944	+	0.783855i	$0.713250\pi$
$462$	6.23510	−	4.53006i	0.290083	−	0.210758i
$463$	12.1941	+	8.85950i	0.566706	+	0.411736i	0.833907	−	0.551905i	$-0.186099\pi$
$463$	12.1941	+	8.85950i	0.566706	+	0.411736i	−0.267201	+	0.963641i	$0.586099\pi$
$464$	−0.996095			−0.0462425
$465$	4.27638	−	3.56547i	0.198312	−	0.165345i
$466$	−11.4167			−0.528867
$467$	0.914959	+	0.664757i	0.0423393	+	0.0307613i	0.608754	−	0.793359i	$-0.291670\pi$
$467$	0.914959	+	0.664757i	0.0423393	+	0.0307613i	−0.566414	+	0.824121i	$0.691670\pi$
$468$	4.10835	−	2.98489i	0.189909	−	0.137977i
$469$	11.7563	+	36.1821i	0.542854	+	1.67073i
$470$	−3.35276			−0.154651
$471$	13.6854			0.630591
$472$	−2.05370	−	6.32065i	−0.0945294	−	0.290932i
$473$	−1.50064	+	4.61851i	−0.0689997	+	0.212359i
$474$	2.06879	−	6.36708i	0.0950227	−	0.292450i
$475$	3.22356	+	2.34206i	0.147907	+	0.107461i
$476$	−5.06882	−	15.6002i	−0.232329	−	0.715035i
$477$	0.334743	+	0.243205i	0.0153268	+	0.0111356i
$478$	2.51607	−	1.82804i	0.115083	−	0.0836124i
$479$	9.45702	−	29.1057i	0.432102	−	1.32987i	−0.463925	−	0.885875i	$-0.653559\pi$
$479$	9.45702	−	29.1057i	0.432102	−	1.32987i	0.896027	−	0.443999i	$-0.146441\pi$
$480$	−0.809017	+	0.587785i	−0.0369264	+	0.0268286i
$481$	−45.0348	+	32.7197i	−2.05341	+	1.49189i
$482$	−7.92785	+	24.3994i	−0.361104	+	1.11136i
$483$	3.34091	−	2.42731i	0.152017	−	0.110447i
$484$	2.36416	+	1.71767i	0.107462	+	0.0780757i
$485$	−1.58269	−	4.87103i	−0.0718665	−	0.221182i
$486$	−0.809017	−	0.587785i	−0.0366978	−	0.0266625i
$487$	−4.41864	+	13.5992i	−0.200228	+	0.616238i	0.799648	+	0.600469i	$0.205020\pi$
$487$	−4.41864	+	13.5992i	−0.200228	+	0.616238i	−0.999876	+	0.0157686i	$0.994980\pi$
$488$	2.43212	−	7.48530i	0.110097	−	0.338844i
$489$	−1.38085	−	4.24983i	−0.0624443	−	0.192184i
$490$	−0.353286			−0.0159598
$491$	26.2542			1.18483			0.592417	−	0.805631i	$-0.298174\pi$
$491$	26.2542			1.18483			0.592417	+	0.805631i	$0.298174\pi$
$492$	0.599862	+	1.84618i	0.0270438	+	0.0832324i
$493$	−4.87463	+	3.54163i	−0.219542	+	0.159507i
$494$	16.3699	+	11.8934i	0.736517	+	0.535111i
$495$	−2.84214			−0.127744
$496$	−4.27638	+	3.56547i	−0.192015	+	0.160095i
$497$	35.4375			1.58959
$498$	−11.2215	−	8.15288i	−0.502847	−	0.365339i
$499$	2.52811	−	1.83678i	0.113174	−	0.0822256i	−0.529759	−	0.848148i	$-0.677718\pi$
$499$	2.52811	−	1.83678i	0.113174	−	0.0822256i	0.642933	+	0.765923i	$0.277718\pi$
$500$	0.309017	+	0.951057i	0.0138197	+	0.0425325i
$501$	−17.0998			−0.763964
$502$	19.0550			0.850468
$503$	7.57032	+	23.2991i	0.337544	+	1.03885i	0.965455	+	0.260569i	$0.0839100\pi$
$503$	7.57032	+	23.2991i	0.337544	+	1.03885i	−0.627911	+	0.778285i	$0.716090\pi$
$504$	−0.837960	+	2.57897i	−0.0373257	+	0.114877i
$505$	−4.44246	+	13.6725i	−0.197687	+	0.608417i
$506$	−3.50162	−	2.54407i	−0.155666	−	0.113098i
$507$	−3.95176	−	12.1623i	−0.175504	−	0.540145i
$508$	−3.82961	−	2.78237i	−0.169911	−	0.123448i
$509$	−1.64834	+	1.19759i	−0.0730615	+	0.0530823i	−0.623716	−	0.781651i	$-0.714378\pi$
$509$	−1.64834	+	1.19759i	−0.0730615	+	0.0530823i	0.550655	+	0.834733i	$0.314378\pi$
$510$	−1.86924	+	5.75294i	−0.0827715	+	0.254744i
$511$	−5.38948	+	3.91569i	−0.238417	+	0.173220i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	1.23129	−	3.78953i	0.0543628	−	0.167312i
$514$	5.66053	−	4.11262i	0.249675	−	0.181400i
$515$	5.57165	+	4.04804i	0.245516	+	0.178378i
$516$	−0.527999	−	1.62501i	−0.0232438	−	0.0715372i
$517$	7.70912	+	5.60101i	0.339047	+	0.246332i
$518$	9.18551	−	28.2701i	0.403588	−	1.24212i
$519$	−3.20653	+	9.86868i	−0.140751	+	0.433187i
$520$	1.56925	+	4.82966i	0.0688162	+	0.211795i
$521$	21.3019			0.933255			0.466628	−	0.884454i	$-0.345469\pi$
$521$	21.3019			0.933255			0.466628	+	0.884454i	$0.345469\pi$
$522$	0.996095			0.0435979
$523$	9.46706	+	29.1366i	0.413965	+	1.27405i	0.913173	+	0.407572i	$0.133625\pi$
$523$	9.46706	+	29.1366i	0.413965	+	1.27405i	−0.499208	+	0.866482i	$0.666375\pi$
$524$	8.81598	−	6.40519i	0.385128	−	0.279812i
$525$	2.19381	+	1.59389i	0.0957456	+	0.0695632i
$526$	−2.46119			−0.107313
$527$	−8.25040	+	32.6532i	−0.359393	+	1.42240i
$528$	2.84214			0.123688
$529$	16.7311	+	12.1559i	0.727441	+	0.528517i
$530$	−0.334743	+	0.243205i	−0.0145403	+	0.0105641i
$531$	2.05370	+	6.32065i	0.0891232	+	0.274293i
$532$	−10.8049			−0.468450
$533$	9.85777			0.426987
$534$	−4.57906	−	14.0929i	−0.198155	−	0.609859i
$535$	−3.65864	+	11.2601i	−0.158177	+	0.486818i
$536$	−4.33540	+	13.3430i	−0.187261	+	0.576329i
$537$	−9.89144	−	7.18655i	−0.426847	−	0.310123i
$538$	−8.83166	−	27.1810i	−0.380760	−	1.17186i
$539$	0.812324	+	0.590188i	0.0349893	+	0.0254212i
$540$	0.809017	−	0.587785i	0.0348145	−	0.0252942i
$541$	−10.3275	+	31.7847i	−0.444013	+	1.36653i	0.439549	+	0.898219i	$0.355138\pi$
$541$	−10.3275	+	31.7847i	−0.444013	+	1.36653i	−0.883562	+	0.468314i	$0.844862\pi$
$542$	−6.53789	+	4.75006i	−0.280827	+	0.204032i
$543$	−17.0393	+	12.3798i	−0.731228	+	0.531268i
$544$	1.86924	−	5.75294i	0.0801431	−	0.246655i
$545$	−5.09036	+	3.69836i	−0.218047	+	0.158420i
$546$	11.1406	+	8.09412i	0.476774	+	0.346396i
$547$	−2.27836	−	7.01209i	−0.0974158	−	0.299815i	0.890460	−	0.455062i	$-0.150383\pi$
$547$	−2.27836	−	7.01209i	−0.0974158	−	0.299815i	−0.987876	+	0.155247i	$0.950383\pi$
$548$	−2.78398	−	2.02268i	−0.118926	−	0.0864046i
$549$	−2.43212	+	7.48530i	−0.103800	+	0.319465i
$550$	0.878268	−	2.70303i	0.0374495	−	0.115258i
$551$	1.22648	+	3.77473i	0.0522499	+	0.160809i
$552$	1.52288			0.0648182
$553$	18.1541			0.771991
$554$	10.0628	+	30.9703i	0.427529	+	1.31580i
$555$	−8.86825	+	6.44316i	−0.376436	+	0.273497i
$556$	−9.41913	−	6.84340i	−0.399460	−	0.290225i
$557$	37.2429			1.57803			0.789016	−	0.614372i	$-0.210591\pi$
$557$	37.2429			1.57803			0.789016	+	0.614372i	$0.210591\pi$
$558$	4.27638	−	3.56547i	0.181033	−	0.150939i
$559$	−8.67682			−0.366990
$560$	−2.19381	−	1.59389i	−0.0927053	−	0.0673543i
$561$	13.9087	−	10.1052i	0.587225	−	0.426644i
$562$	−4.96831	−	15.2909i	−0.209576	−	0.645007i
$563$	−2.96526			−0.124971			−0.0624855	−	0.998046i	$-0.519903\pi$
$563$	−2.96526			−0.124971			−0.0624855	+	0.998046i	$0.519903\pi$
$564$	−3.35276			−0.141177
$565$	−2.62644	−	8.08334i	−0.110495	−	0.340069i
$566$	1.49761	−	4.60916i	0.0629491	−	0.193737i
$567$	0.837960	−	2.57897i	0.0351910	−	0.108307i
$568$	10.5726	+	7.68141i	0.443614	+	0.322305i
$569$	4.43173	+	13.6395i	0.185788	+	0.571796i	0.999961	−	0.00882614i	$-0.00280948\pi$
$569$	4.43173	+	13.6395i	0.185788	+	0.571796i	−0.814173	+	0.580622i	$0.802809\pi$
$570$	3.22356	+	2.34206i	0.135020	+	0.0980979i
$571$	−26.2489	+	19.0709i	−1.09848	+	0.798094i	−0.980811	−	0.194959i	$-0.937543\pi$
$571$	−26.2489	+	19.0709i	−1.09848	+	0.798094i	−0.117670	+	0.993053i	$0.537543\pi$
$572$	4.46002	−	13.7265i	0.186483	−	0.573936i
$573$	12.6944	−	9.22300i	0.530315	−	0.385296i
$574$	−4.25860	+	3.09406i	−0.177751	+	0.129143i
$575$	0.470596	−	1.44835i	0.0196252	−	0.0604002i
$576$	−0.809017	+	0.587785i	−0.0337090	+	0.0244911i
$577$	−32.6569	−	23.7266i	−1.35952	−	0.987752i	−0.998475	−	0.0552045i	$-0.982419\pi$
$577$	−32.6569	−	23.7266i	−1.35952	−	0.987752i	−0.361048	−	0.932547i	$-0.617581\pi$
$578$	−6.05376	−	18.6316i	−0.251803	−	0.774970i
$579$	−5.40297	−	3.92549i	−0.224540	−	0.163138i
$580$	−0.307810	+	0.947342i	−0.0127811	+	0.0393362i
$581$	11.6229	−	35.7717i	0.482200	−	1.48406i
$582$	−1.58269	−	4.87103i	−0.0656048	−	0.201911i
$583$	1.17597			0.0487039
$584$	−2.45668			−0.101658
$585$	−1.56925	−	4.82966i	−0.0648805	−	0.199682i
$586$	−20.2791	+	14.7336i	−0.837722	+	0.608641i
$587$	−23.5827	−	17.1338i	−0.973363	−	0.707189i	−0.0171472	−	0.999853i	$-0.505458\pi$
$587$	−23.5827	−	17.1338i	−0.973363	−	0.707189i	−0.956215	+	0.292664i	$0.905458\pi$
$588$	−0.353286			−0.0145693
$589$	18.7769	+	11.8153i	0.773690	+	0.486841i
$590$	−6.64593			−0.273608
$591$	−6.84282	−	4.97160i	−0.281476	−	0.204504i
$592$	8.86825	−	6.44316i	0.364483	−	0.264812i
$593$	−3.14835	−	9.68964i	−0.129287	−	0.397906i	0.865370	−	0.501133i	$-0.167083\pi$
$593$	−3.14835	−	9.68964i	−0.129287	−	0.397906i	−0.994658	+	0.103227i	$0.967083\pi$
$594$	−2.84214			−0.116614
$595$	−16.4030			−0.672459
$596$	−4.82441	−	14.8480i	−0.197616	−	0.608199i
$597$	2.94632	−	9.06783i	0.120585	−	0.371121i
$598$	2.38978	−	7.35500i	0.0977255	−	0.300768i
$599$	34.1797	+	24.8330i	1.39654	+	1.01465i	0.995111	+	0.0987594i	$0.0314874\pi$
$599$	34.1797	+	24.8330i	1.39654	+	1.01465i	0.401432	+	0.915889i	$0.368513\pi$
$600$	0.309017	+	0.951057i	0.0126156	+	0.0388267i
$601$	−11.6779	−	8.48450i	−0.476352	−	0.346090i	0.323560	−	0.946208i	$-0.395120\pi$
$601$	−11.6779	−	8.48450i	−0.476352	−	0.346090i	−0.799912	+	0.600118i	$0.795120\pi$
$602$	3.74843	−	2.72339i	0.152774	−	0.110997i
$603$	4.33540	−	13.3430i	0.176551	−	0.543368i
$604$	17.5107	−	12.7223i	0.712501	−	0.517662i
$605$	2.36416	−	1.71767i	0.0961169	−	0.0698330i
$606$	−4.44246	+	13.6725i	−0.180463	+	0.555407i
$607$	23.6687	−	17.1963i	0.960683	−	0.697977i	0.00737337	−	0.999973i	$-0.497653\pi$
$607$	23.6687	−	17.1963i	0.960683	−	0.697977i	0.953309	+	0.301996i	$0.0976530\pi$
$608$	−3.22356	−	2.34206i	−0.130733	−	0.0949829i
$609$	0.834687	+	2.56890i	0.0338232	+	0.104097i
$610$	−6.36738	−	4.62617i	−0.257808	−	0.187308i
$611$	−5.26132	+	16.1927i	−0.212850	+	0.655086i
$612$	−1.86924	+	5.75294i	−0.0755597	+	0.232549i
$613$	3.90130	+	12.0070i	0.157572	+	0.484957i	0.998412	−	0.0563263i	$-0.0179387\pi$
$613$	3.90130	+	12.0070i	0.157572	+	0.484957i	−0.840840	+	0.541283i	$0.817939\pi$
$614$	−3.99673			−0.161295
$615$	1.94119			0.0782764
$616$	2.38159	+	7.32979i	0.0959572	+	0.295326i
$617$	−2.88206	+	2.09394i	−0.116027	+	0.0842987i	−0.644286	−	0.764785i	$-0.722845\pi$
$617$	−2.88206	+	2.09394i	−0.116027	+	0.0842987i	0.528258	+	0.849084i	$0.322845\pi$
$618$	5.57165	+	4.04804i	0.224125	+	0.162836i
$619$	31.4732			1.26501			0.632507	−	0.774554i	$-0.282026\pi$
$619$	31.4732			1.26501			0.632507	+	0.774554i	$0.282026\pi$
$620$	2.06949	+	5.16887i	0.0831129	+	0.207587i
$621$	−1.52288			−0.0611111
$622$	4.23154	+	3.07439i	0.169669	+	0.123272i
$623$	32.5081	−	23.6185i	1.30241	−	0.946257i
$624$	1.56925	+	4.82966i	0.0628203	+	0.193341i
$625$	1.00000			0.0400000
$626$	13.4807			0.538798
$627$	−3.49950	−	10.7703i	−0.139756	−	0.430126i
$628$	−4.22903	+	13.0156i	−0.168757	+	0.519379i
$629$	20.4902	−	63.0623i	0.816998	−	2.51446i
$630$	2.19381	+	1.59389i	0.0874034	+	0.0635023i
$631$	1.04531	+	3.21714i	0.0416133	+	0.128072i	0.969705	−	0.244279i	$-0.0785514\pi$
$631$	1.04531	+	3.21714i	0.0416133	+	0.128072i	−0.928092	+	0.372352i	$0.878551\pi$
$632$	5.41616	+	3.93507i	0.215443	+	0.156529i
$633$	−16.8291	+	12.2271i	−0.668897	+	0.485982i
$634$	−5.98943	+	18.4336i	−0.237871	+	0.732091i
$635$	−3.82961	+	2.78237i	−0.151973	+	0.110415i
$636$	−0.334743	+	0.243205i	−0.0132734	+	0.00964369i
$637$	−0.554395	+	1.70625i	−0.0219659	+	0.0676042i
$638$	2.29036	−	1.66404i	0.0906761	−	0.0658800i
$639$	−10.5726	−	7.68141i	−0.418244	−	0.303872i
$640$	−0.309017	−	0.951057i	−0.0122150	−	0.0375938i
$641$	−28.1564	−	20.4568i	−1.11211	−	0.807997i	−0.129117	−	0.991629i	$-0.541214\pi$
$641$	−28.1564	−	20.4568i	−1.11211	−	0.807997i	−0.982995	+	0.183633i	$0.941214\pi$
$642$	−3.65864	+	11.2601i	−0.144395	+	0.444402i
$643$	0.291688	−	0.897722i	0.0115030	−	0.0354027i	−0.945140	−	0.326665i	$-0.894075\pi$
$643$	0.291688	−	0.897722i	0.0115030	−	0.0354027i	0.956643	+	0.291262i	$0.0940752\pi$
$644$	1.27611	+	3.92747i	0.0502859	+	0.154764i
$645$	−1.70864			−0.0672776
$646$	−24.1025			−0.948300
$647$	−9.08809	−	27.9703i	−0.357290	−	1.09962i	−0.954670	−	0.297667i	$-0.903792\pi$
$647$	−9.08809	−	27.9703i	−0.357290	−	1.09962i	0.597380	−	0.801958i	$-0.296208\pi$
$648$	0.809017	−	0.587785i	0.0317812	−	0.0230904i
$649$	15.2812	+	11.1025i	0.599840	+	0.435809i
$650$	5.07820			0.199184
$651$	12.7787	+	8.04094i	0.500837	+	0.315149i
$652$	4.46853			0.175001
$653$	−7.59119	−	5.51532i	−0.297066	−	0.215831i	0.429261	−	0.903181i	$-0.358774\pi$
$653$	−7.59119	−	5.51532i	−0.297066	−	0.215831i	−0.726327	+	0.687349i	$0.758774\pi$
$654$	−5.09036	+	3.69836i	−0.199049	+	0.144617i
$655$	−3.36741	−	10.3638i	−0.131575	−	0.404947i
$656$	−1.94119			−0.0757908
$657$	2.45668			0.0958442
$658$	−2.80948	−	8.64668i	−0.109525	−	0.337083i
$659$	−6.33295	+	19.4908i	−0.246697	+	0.759254i	0.748656	+	0.662958i	$0.230699\pi$
$659$	−6.33295	+	19.4908i	−0.246697	+	0.759254i	−0.995353	+	0.0962955i	$0.969301\pi$
$660$	0.878268	−	2.70303i	0.0341865	−	0.105215i
$661$	−40.0869	−	29.1248i	−1.55920	−	1.13282i	−0.936662	−	0.350235i	$-0.886102\pi$
$661$	−40.0869	−	29.1248i	−1.55920	−	1.13282i	−0.622537	−	0.782590i	$-0.713898\pi$
$662$	2.67809	+	8.24230i	0.104087	+	0.320346i
$663$	24.8514	+	18.0556i	0.965149	+	0.701222i
$664$	11.2215	−	8.15288i	0.435478	−	0.316393i
$665$	−3.33889	+	10.2760i	−0.129476	+	0.398488i
$666$	−8.86825	+	6.44316i	−0.343638	+	0.249667i
$667$	1.22723	−	0.891632i	0.0475184	−	0.0345241i
$668$	5.28414	−	16.2629i	0.204449	−	0.629231i
$669$	16.2521	−	11.8078i	0.628343	−	0.456518i
$670$	11.3502	+	8.24641i	0.438497	+	0.318587i
$671$	6.91242	+	21.2742i	0.266851	+	0.821283i
$672$	−2.19381	−	1.59389i	−0.0846279	−	0.0614858i
$673$	−0.807448	+	2.48507i	−0.0311248	+	0.0957924i	−0.965412	−	0.260729i	$-0.916037\pi$
$673$	−0.807448	+	2.48507i	−0.0311248	+	0.0957924i	0.934287	+	0.356521i	$0.116037\pi$
$674$	−1.34790	+	4.14841i	−0.0519192	+	0.159791i
$675$	−0.309017	−	0.951057i	−0.0118941	−	0.0366062i
$676$	12.7881			0.491852
$677$	34.6363			1.33118			0.665590	−	0.746317i	$-0.268180\pi$
$677$	34.6363			1.33118			0.665590	+	0.746317i	$0.268180\pi$
$678$	−2.62644	−	8.08334i	−0.100868	−	0.310439i
$679$	11.2360	−	8.16346i	0.431200	−	0.313285i
$680$	−4.89374	−	3.55551i	−0.187666	−	0.136348i
$681$	11.7890			0.451755
$682$	3.87647	−	15.3422i	0.148438	−	0.587483i
$683$	−1.41922			−0.0543051			−0.0271525	−	0.999631i	$-0.508644\pi$
$683$	−1.41922			−0.0543051			−0.0271525	+	0.999631i	$0.508644\pi$
$684$	3.22356	+	2.34206i	0.123256	+	0.0895507i
$685$	−2.78398	+	2.02268i	−0.106370	+	0.0772826i
$686$	5.56968	+	17.1417i	0.212651	+	0.654473i
$687$	15.6717			0.597911
$688$	1.70864			0.0651413
$689$	0.649301	+	1.99834i	0.0247364	+	0.0761308i
$690$	0.470596	−	1.44835i	0.0179153	−	0.0551376i
$691$	15.0789	−	46.4081i	0.573629	−	1.76545i	−0.0671713	−	0.997741i	$-0.521397\pi$
$691$	15.0789	−	46.4081i	0.573629	−	1.76545i	0.640800	−	0.767708i	$-0.278603\pi$
$692$	−8.39480	−	6.09918i	−0.319123	−	0.231856i
$693$	−2.38159	−	7.32979i	−0.0904693	−	0.278436i
$694$	13.8868	+	10.0894i	0.527137	+	0.382988i
$695$	−9.41913	+	6.84340i	−0.357288	+	0.259585i
$696$	−0.307810	+	0.947342i	−0.0116675	+	0.0359089i
$697$	−9.49970	+	6.90193i	−0.359827	+	0.261429i
$698$	9.65518	−	7.01490i	0.365454	−	0.265518i
$699$	−3.52794	+	10.8579i	−0.133439	+	0.410683i
$700$	−2.19381	+	1.59389i	−0.0829181	+	0.0602435i
$701$	38.0026	+	27.6105i	1.43534	+	1.04283i	0.988991	+	0.147973i	$0.0472750\pi$
$701$	38.0026	+	27.6105i	1.43534	+	1.04283i	0.446346	+	0.894860i	$0.352725\pi$
$702$	−1.56925	−	4.82966i	−0.0592276	−	0.182284i
$703$	−35.3359	−	25.6731i	−1.33272	−	0.968278i
$704$	−0.878268	+	2.70303i	−0.0331010	+	0.101874i
$705$	−1.03606	+	3.18866i	−0.0390203	+	0.120092i
$706$	3.84419	+	11.8312i	0.144678	+	0.445273i
$707$	−38.9836			−1.46613
$708$	−6.64593			−0.249769
$709$	−11.8565	−	36.4904i	−0.445278	−	1.37043i	−0.882178	−	0.470916i	$-0.843924\pi$
$709$	−11.8565	−	36.4904i	−0.445278	−	1.37043i	0.436900	−	0.899510i	$-0.356076\pi$
$710$	10.5726	−	7.68141i	0.396781	−	0.288278i
$711$	−5.41616	−	3.93507i	−0.203122	−	0.147577i
$712$	14.8181			0.555333
$713$	2.07710	−	8.22070i	0.0777881	−	0.307868i
$714$	−16.4030			−0.613868
$715$	−11.6765	−	8.48347i	−0.436676	−	0.317264i
$716$	9.89144	−	7.18655i	0.369661	−	0.268574i
$717$	−0.961055	−	2.95782i	−0.0358913	−	0.110462i
$718$	19.4898			0.727352
$719$	−0.119421			−0.00445365			−0.00222683	−	0.999998i	$-0.500709\pi$
$719$	−0.119421			−0.00445365			−0.00222683	+	0.999998i	$0.500709\pi$
$720$	0.309017	+	0.951057i	0.0115164	+	0.0354438i
$721$	−5.77098	+	17.7612i	−0.214922	+	0.661463i
$722$	0.965189	−	2.97055i	0.0359206	−	0.110552i
$723$	20.7554	+	15.0797i	0.771901	+	0.560819i
$724$	−6.50845	−	20.0309i	−0.241885	−	0.744444i
$725$	0.805858	+	0.585490i	0.0299288	+	0.0217445i
$726$	2.36416	−	1.71767i	0.0877423	−	0.0637485i
$727$	1.50997	−	4.64720i	0.0560016	−	0.172355i	−0.919143	−	0.393923i	$-0.871118\pi$
$727$	1.50997	−	4.64720i	0.0560016	−	0.172355i	0.975145	+	0.221568i	$0.0711175\pi$
$728$	−11.1406	+	8.09412i	−0.412898	+	0.299988i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	−0.759156	+	2.33644i	−0.0280976	+	0.0864755i
$731$	8.36164	−	6.07509i	0.309267	−	0.224695i
$732$	−6.36738	−	4.62617i	−0.235345	−	0.170988i
$733$	13.4264	+	41.3223i	0.495916	+	1.52627i	0.815524	+	0.578723i	$0.196449\pi$
$733$	13.4264	+	41.3223i	0.495916	+	1.52627i	−0.319608	+	0.947550i	$0.603551\pi$
$734$	−2.64256	−	1.91993i	−0.0975387	−	0.0708660i
$735$	−0.109171	+	0.335995i	−0.00402685	+	0.0123934i
$736$	−0.470596	+	1.44835i	−0.0173464	+	0.0533868i
$737$	−12.3218	−	37.9225i	−0.453879	−	1.39689i
$738$	1.94119			0.0714563
$739$	27.1966			1.00044			0.500222	−	0.865897i	$-0.333252\pi$
$739$	27.1966			1.00044			0.500222	+	0.865897i	$0.333252\pi$
$740$	−3.38737	−	10.4253i	−0.124522	−	0.383240i
$741$	16.3699	−	11.8934i	0.601364	−	0.436916i
$742$	−0.907720	−	0.659497i	−0.0333234	−	0.0242109i
$743$	43.6321			1.60071			0.800353	−	0.599529i	$-0.204645\pi$
$743$	43.6321			1.60071			0.800353	+	0.599529i	$0.204645\pi$
$744$	2.06949	+	5.16887i	0.0758713	+	0.189500i
$745$	−15.6121			−0.571984
$746$	−30.0386	−	21.8243i	−1.09979	−	0.799045i
$747$	−11.2215	+	8.15288i	−0.410573	+	0.298298i
$748$	5.31264	+	16.3506i	0.194249	+	0.597838i
$749$	−32.1054			−1.17311
$750$	1.00000			0.0365148
$751$	−10.1767	−	31.3206i	−0.371353	−	1.14291i	−0.945906	−	0.324439i	$-0.894824\pi$
$751$	−10.1767	−	31.3206i	−0.371353	−	1.14291i	0.574554	−	0.818467i	$-0.305176\pi$
$752$	1.03606	−	3.18866i	0.0377812	−	0.116279i
$753$	5.88833	−	18.1224i	0.214583	−	0.660418i
$754$	4.09231	+	2.97324i	0.149033	+	0.108279i
$755$	−6.68850	−	20.5851i	−0.243419	−	0.749168i
$756$	2.19381	+	1.59389i	0.0797880	+	0.0579694i
$757$	−22.1496	+	16.0926i	−0.805040	+	0.584896i	−0.912388	−	0.409326i	$-0.865764\pi$
$757$	−22.1496	+	16.0926i	−0.805040	+	0.584896i	0.107348	+	0.994221i	$0.465764\pi$
$758$	−3.19991	+	9.84831i	−0.116226	+	0.357707i
$759$	−3.50162	+	2.54407i	−0.127101	+	0.0923440i
$760$	−3.22356	+	2.34206i	−0.116931	+	0.0849553i
$761$	3.98583	−	12.2671i	0.144486	−	0.444683i	−0.852458	−	0.522795i	$-0.824889\pi$
$761$	3.98583	−	12.2671i	0.144486	−	0.444683i	0.996945	+	0.0781123i	$0.0248893\pi$
$762$	−3.82961	+	2.78237i	−0.138732	+	0.100795i
$763$	−13.8035	−	10.0288i	−0.499720	−	0.363068i
$764$	4.84882	+	14.9231i	0.175424	+	0.539900i
$765$	4.89374	+	3.55551i	0.176934	+	0.128550i
$766$	−11.3447	+	34.9155i	−0.409902	+	1.26155i
$767$	−10.4291	+	32.0976i	−0.376574	+	1.15898i
$768$	−0.309017	−	0.951057i	−0.0111507	−	0.0343183i
$769$	−22.5079			−0.811656			−0.405828	−	0.913950i	$-0.633017\pi$
$769$	−22.5079			−0.811656			−0.405828	+	0.913950i	$0.633017\pi$
$770$	7.70700			0.277741
$771$	−2.16213	−	6.65435i	−0.0778672	−	0.239651i
$772$	5.40297	−	3.92549i	0.194457	−	0.141281i
$773$	31.4000	+	22.8134i	1.12938	+	0.820542i	0.985604	−	0.169069i	$-0.0540760\pi$
$773$	31.4000	+	22.8134i	1.12938	+	0.820542i	0.143775	+	0.989610i	$0.454076\pi$
$774$	−1.70864			−0.0614158
$775$	5.55539	−	0.370938i	0.199556	−	0.0133245i
$776$	5.12171			0.183859
$777$	−24.0480	−	17.4719i	−0.862717	−	0.626800i
$778$	−3.93836	+	2.86138i	−0.141197	+	0.102586i
$779$	2.39017	+	7.35620i	0.0856369	+	0.263563i
$780$	5.07820			0.181829
$781$	−37.1421			−1.32905
$782$	2.84664	+	8.76105i	0.101796	+	0.313294i
$783$	0.307810	−	0.947342i	0.0110002	−	0.0338553i
$784$	0.109171	−	0.335995i	0.00389898	−	0.0119998i
$785$	11.0717	+	8.04409i	0.395167	+	0.287106i
$786$	−3.36741	−	10.3638i	−0.120111	−	0.369665i
$787$	−36.8281	−	26.7572i	−1.31278	−	0.953792i	−0.999992	−	0.00396925i	$-0.998737\pi$
$787$	−36.8281	−	26.7572i	−1.31278	−	0.953792i	−0.312790	−	0.949822i	$-0.601263\pi$
$788$	6.84282	−	4.97160i	0.243765	−	0.177106i
$789$	−0.760550	+	2.34073i	−0.0270763	+	0.0833323i
$790$	5.41616	−	3.93507i	0.192698	−	0.140004i
$791$	18.6459	−	13.5470i	0.662971	−	0.481677i
$792$	0.878268	−	2.70303i	0.0312079	−	0.0960480i
$793$	−32.3349	+	23.4926i	−1.14824	+	0.834248i
$794$	30.4767	+	22.1426i	1.08158	+	0.785811i
$795$	0.127860	+	0.393514i	0.00453474	+	0.0139565i
$796$	7.71355	+	5.60423i	0.273400	+	0.198636i
$797$	−3.74385	+	11.5224i	−0.132614	+	0.408143i	−0.995211	−	0.0977476i	$-0.968836\pi$
$797$	−3.74385	+	11.5224i	−0.132614	+	0.408143i	0.862597	+	0.505891i	$0.168836\pi$
$798$	−3.33889	+	10.2760i	−0.118195	+	0.363768i
$799$	−6.26712	−	19.2882i	−0.221715	−	0.682368i
$800$	−1.00000			−0.0353553
$801$	−14.8181			−0.523573
$802$	−2.26200	−	6.96172i	−0.0798740	−	0.245827i
$803$	5.64873	−	4.10404i	0.199339	−	0.144829i
$804$	11.3502	+	8.24641i	0.400291	+	0.290829i
$805$	4.12959			0.145549
$806$	28.2114	−	1.88370i	0.993705	−	0.0663504i
$807$	−28.5798			−1.00606
$808$	−11.6305	−	8.45006i	−0.409160	−	0.297272i
$809$	25.9399	−	18.8464i	0.911999	−	0.662606i	−0.0295209	−	0.999564i	$-0.509398\pi$
$809$	25.9399	−	18.8464i	0.911999	−	0.662606i	0.941520	+	0.336958i	$0.109398\pi$
$810$	−0.309017	−	0.951057i	−0.0108578	−	0.0334167i
$811$	−14.5594			−0.511249			−0.255624	−	0.966776i	$-0.582281\pi$
$811$	−14.5594			−0.511249			−0.255624	+	0.966776i	$0.582281\pi$
$812$	−2.70110			−0.0947902
$813$	2.49725	+	7.68576i	0.0875825	+	0.269551i
$814$	−9.62737	+	29.6300i	−0.337439	+	1.03853i
$815$	1.38085	−	4.24983i	0.0483691	−	0.148865i
$816$	−4.89374	−	3.55551i	−0.171315	−	0.124468i
$817$	−2.10383	−	6.47493i	−0.0736038	−	0.226529i
$818$	−7.56055	−	5.49306i	−0.264348	−	0.192060i
$819$	11.1406	−	8.09412i	0.389284	−	0.282831i
$820$	−0.599862	+	1.84618i	−0.0209481	+	0.0644715i
$821$	−0.588619	+	0.427657i	−0.0205429	+	0.0149253i	−0.598009	−	0.801489i	$-0.704041\pi$
$821$	−0.588619	+	0.427657i	−0.0205429	+	0.0149253i	0.577466	+	0.816414i	$0.304041\pi$
$822$	−2.78398	+	2.02268i	−0.0971024	+	0.0705491i
$823$	−14.9079	+	45.8818i	−0.519657	+	1.59934i	0.254990	+	0.966944i	$0.417928\pi$
$823$	−14.9079	+	45.8818i	−0.519657	+	1.59934i	−0.774646	+	0.632395i	$0.782072\pi$
$824$	−5.57165	+	4.04804i	−0.194098	+	0.141020i
$825$	−2.29934	−	1.67057i	−0.0800526	−	0.0581616i
$826$	−5.56902	−	17.1397i	−0.193771	−	0.596366i
$827$	−1.98245	−	1.44033i	−0.0689364	−	0.0500852i	0.552783	−	0.833325i	$-0.313566\pi$
$827$	−1.98245	−	1.44033i	−0.0689364	−	0.0500852i	−0.621720	+	0.783240i	$0.713566\pi$
$828$	0.470596	−	1.44835i	0.0163544	−	0.0503335i
$829$	−10.1230	+	31.1555i	−0.351588	+	1.08208i	0.606374	+	0.795180i	$0.292624\pi$
$829$	−10.1230	+	31.1555i	−0.351588	+	1.08208i	−0.957962	+	0.286896i	$0.907376\pi$
$830$	−4.28622	−	13.1916i	−0.148777	−	0.457889i
$831$	32.5640			1.12963
$832$	−5.07820			−0.176055
$833$	−0.660378	−	2.03243i	−0.0228807	−	0.0704197i
$834$	−9.41913	+	6.84340i	−0.326158	+	0.236968i
$835$	−13.8341	−	10.0510i	−0.478747	−	0.347830i
$836$	11.3246			0.391670
$837$	−2.06949	−	5.16887i	−0.0715322	−	0.178662i
$838$	5.15090			0.177935
$839$	16.6766	+	12.1162i	0.575740	+	0.418299i	0.837186	−	0.546919i	$-0.184199\pi$
$839$	16.6766	+	12.1162i	0.575740	+	0.418299i	−0.261446	+	0.965218i	$0.584199\pi$
$840$	−2.19381	+	1.59389i	−0.0756935	+	0.0549946i
$841$	−8.65488	−	26.6370i	−0.298444	−	0.918517i
$842$	−24.8631			−0.856840
$843$	−16.0778			−0.553748
$844$	−6.42815	−	19.7838i	−0.221266	−	0.680987i
$845$	3.95176	−	12.1623i	0.135945	−	0.418394i
$846$	−1.03606	+	3.18866i	−0.0356205	+	0.109629i
$847$	6.41089	+	4.65778i	0.220281	+	0.160043i
$848$	−0.127860	−	0.393514i	−0.00439074	−	0.0135133i
$849$	−3.92078	−	2.84862i	−0.134561	−	0.0977643i
$850$	−4.89374	+	3.55551i	−0.167854	+	0.121953i
$851$	−5.15857	+	15.8764i	−0.176833	+	0.544237i
$852$	10.5726	−	7.68141i	0.362210	−	0.263161i
$853$	5.38307	−	3.91103i	0.184313	−	0.133911i	−0.491803	−	0.870707i	$-0.663662\pi$
$853$	5.38307	−	3.91103i	0.184313	−	0.133911i	0.676116	+	0.736795i	$0.263662\pi$
$854$	6.59517	−	20.2979i	0.225682	−	0.694578i
$855$	3.22356	−	2.34206i	0.110244	−	0.0800966i
$856$	−9.57844	−	6.95914i	−0.327384	−	0.237859i
$857$	−1.04153	−	3.20549i	−0.0355779	−	0.109498i	0.931690	−	0.363253i	$-0.118334\pi$
$857$	−1.04153	−	3.20549i	−0.0355779	−	0.109498i	−0.967268	+	0.253756i	$0.918334\pi$
$858$	−11.6765	−	8.48347i	−0.398629	−	0.289621i
$859$	−2.69772	+	8.30274i	−0.0920452	+	0.283286i	−0.986472	−	0.163928i	$-0.947584\pi$
$859$	−2.69772	+	8.30274i	−0.0920452	+	0.283286i	0.894427	+	0.447214i	$0.147584\pi$
$860$	0.527999	−	1.62501i	0.0180046	−	0.0554125i
$861$	1.62664	+	5.00629i	0.0554358	+	0.170614i
$862$	7.10453			0.241981
$863$	−19.5485			−0.665438			−0.332719	−	0.943026i	$-0.607966\pi$
$863$	−19.5485			−0.665438			−0.332719	+	0.943026i	$0.607966\pi$
$864$	0.309017	+	0.951057i	0.0105130	+	0.0323556i
$865$	−8.39480	+	6.09918i	−0.285432	+	0.207378i
$866$	13.6032	+	9.88330i	0.462256	+	0.335848i
$867$	−19.5904			−0.665324
$868$	−11.5962	+	9.66848i	−0.393602	+	0.328169i
$869$	−19.0274			−0.645459
$870$	0.805858	+	0.585490i	0.0273211	+	0.0198500i
$871$	57.6387	−	41.8770i	1.95301	−	1.41895i
$872$	−1.94434	−	5.98407i	−0.0658438	−	0.202646i
$873$	−5.12171			−0.173344
$874$	6.06799			0.205253
$875$	0.837960	+	2.57897i	0.0283282	+	0.0871853i
$876$	−0.759156	+	2.33644i	−0.0256495	+	0.0789410i
$877$	9.89473	−	30.4528i	0.334121	−	1.02832i	−0.633032	−	0.774125i	$-0.718190\pi$
$877$	9.89473	−	30.4528i	0.334121	−	1.02832i	0.967153	−	0.254194i	$-0.0818101\pi$
$878$	6.09715	+	4.42984i	0.205769	+	0.149500i
$879$	7.74593	+	23.8395i	0.261264	+	0.804087i
$880$	2.29934	+	1.67057i	0.0775106	+	0.0563147i
$881$	−45.8247	+	33.2936i	−1.54387	+	1.12169i	−0.596025	+	0.802966i	$0.703254\pi$
$881$	−45.8247	+	33.2936i	−1.54387	+	1.12169i	−0.947848	+	0.318723i	$0.896746\pi$
$882$	−0.109171	+	0.335995i	−0.00367599	+	0.0113135i
$883$	−1.89895	+	1.37967i	−0.0639048	+	0.0464296i	−0.619279	−	0.785171i	$-0.712575\pi$
$883$	−1.89895	+	1.37967i	−0.0639048	+	0.0464296i	0.555374	+	0.831601i	$0.312575\pi$
$884$	−24.8514	+	18.0556i	−0.835844	+	0.607276i
$885$	−2.05370	+	6.32065i	−0.0690345	+	0.212466i
$886$	1.17574	−	0.854223i	0.0394997	−	0.0286982i
$887$	−25.8563	−	18.7857i	−0.868171	−	0.630763i	0.0619249	−	0.998081i	$-0.480276\pi$
$887$	−25.8563	−	18.7857i	−0.868171	−	0.630763i	−0.930095	+	0.367318i	$0.880276\pi$
$888$	−3.38737	−	10.4253i	−0.113673	−	0.349849i
$889$	−10.3847	−	7.54495i	−0.348293	−	0.253050i
$890$	4.57906	−	14.0929i	0.153490	−	0.472395i
$891$	−0.878268	+	2.70303i	−0.0294231	+	0.0905550i
$892$	6.20775	+	19.1055i	0.207851	+	0.639699i
$893$	−13.3592			−0.447049
$894$	−15.6121			−0.522148
$895$	−3.77819	−	11.6281i	−0.126291	−	0.388684i
$896$	2.19381	−	1.59389i	0.0732899	−	0.0532483i
$897$	−6.25654	−	4.54564i	−0.208900	−	0.151774i
$898$	−34.6360			−1.15582
$899$	4.69404	+	2.95370i	0.156555	+	0.0985115i
$900$	1.00000			0.0333333
$901$	−2.02486	−	1.47114i	−0.0674578	−	0.0490109i
$902$	4.46345	−	3.24289i	0.148617	−	0.107976i
$903$	−1.43177	−	4.40654i	−0.0476464	−	0.146640i
$904$	8.49932			0.282683
$905$	−21.0618			−0.700117
$906$	−6.68850	−	20.5851i	−0.222210	−	0.683893i
$907$	−4.67569	+	14.3903i	−0.155254	+	0.477822i	−0.998187	−	0.0601972i	$-0.980827\pi$
$907$	−4.67569	+	14.3903i	−0.155254	+	0.477822i	0.842933	+	0.538019i	$0.180827\pi$
$908$	−3.64299	+	11.2120i	−0.120897	+	0.372083i
$909$	11.6305	+	8.45006i	0.385760	+	0.280271i
$910$	4.25533	+	13.0966i	0.141063	+	0.434147i
$911$	−37.2189	−	27.0411i	−1.23312	−	0.895912i	−0.235998	−	0.971754i	$-0.575836\pi$
$911$	−37.2189	−	27.0411i	−1.23312	−	0.895912i	−0.997120	+	0.0758412i	$0.975836\pi$
$912$	−3.22356	+	2.34206i	−0.106743	+	0.0775532i
$913$	−12.1820	+	37.4924i	−0.403166	+	1.24082i
$914$	−0.324649	+	0.235872i	−0.0107384	+	0.00780194i
$915$	−6.36738	+	4.62617i	−0.210499	+	0.152937i
$916$	−4.84281	+	14.9046i	−0.160011	+	0.492463i
$917$	23.9062	−	17.3689i	0.789454	−	0.573572i
$918$	4.89374	+	3.55551i	0.161518	+	0.117349i
$919$	−11.2742	−	34.6984i	−0.371901	−	1.14459i	−0.945546	−	0.325490i	$-0.894471\pi$
$919$	−11.2742	−	34.6984i	−0.371901	−	1.14459i	0.573644	−	0.819105i	$-0.305529\pi$
$920$	1.23204	+	0.895128i	0.0406191	+	0.0295115i
$921$	−1.23506	+	3.80111i	−0.0406965	+	0.125251i
$922$	−7.34625	+	22.6094i	−0.241936	+	0.744602i
$923$	−20.5076	−	63.1159i	−0.675016	−	2.07748i
$924$	7.70700			0.253542
$925$	−10.9618			−0.360420
$926$	4.65771	+	14.3350i	0.153062	+	0.471076i
$927$	5.57165	−	4.04804i	0.182997	−	0.132955i
$928$	−0.805858	−	0.585490i	−0.0264536	−	0.0192196i
$929$	24.9520			0.818647			0.409324	−	0.912389i	$-0.365765\pi$
$929$	24.9520			0.818647			0.409324	+	0.912389i	$0.365765\pi$
$930$	5.55539	−	0.370938i	0.182169	−	0.0121635i
$931$	−1.40768			−0.0461350
$932$	−9.23628	−	6.71055i	−0.302544	−	0.219811i
$933$	4.23154	−	3.07439i	0.138534	−	0.100651i
$934$	0.349483	+	1.07560i	0.0114354	+	0.0351947i
$935$	17.1921			0.562241
$936$	5.07820			0.165986
$937$	0.483783	+	1.48893i	0.0158045	+	0.0486413i	0.958648	−	0.284595i	$-0.0918592\pi$
$937$	0.483783	+	1.48893i	0.0158045	+	0.0486413i	−0.942843	+	0.333237i	$0.891859\pi$
$938$	−11.7563	+	36.1821i	−0.383856	+	1.18139i
$939$	4.16577	−	12.8209i	0.135945	−	0.418395i
$940$	−2.71244	−	1.97070i	−0.0884700	−	0.0642772i
$941$	−8.72036	−	26.8385i	−0.284276	−	0.874910i	−0.986615	−	0.163068i	$-0.947861\pi$
$941$	−8.72036	−	26.8385i	−0.284276	−	0.874910i	0.702339	−	0.711842i	$-0.252139\pi$
$942$	11.0717	+	8.04409i	0.360737	+	0.262091i
$943$	2.39162	−	1.73762i	0.0778819	−	0.0565845i
$944$	2.05370	−	6.32065i	0.0668424	−	0.205720i
$945$	2.19381	−	1.59389i	0.0713645	−	0.0518494i
$946$	−3.92874	+	2.85439i	−0.127734	+	0.0928044i
$947$	4.27702	−	13.1633i	0.138984	−	0.427750i	−0.857204	−	0.514977i	$-0.827801\pi$
$947$	4.27702	−	13.1633i	0.138984	−	0.427750i	0.996188	+	0.0872269i	$0.0278005\pi$
$948$	5.41616	−	3.93507i	0.175909	−	0.127805i
$949$	10.0929	+	7.33292i	0.327630	+	0.238037i
$950$	1.23129	+	3.78953i	0.0399484	+	0.122948i
$951$	15.6805	+	11.3926i	0.508476	+	0.369430i
$952$	5.06882	−	15.6002i	0.164281	−	0.505606i
$953$	−1.18136	+	3.63585i	−0.0382680	+	0.117777i	−0.968366	−	0.249536i	$-0.919722\pi$
$953$	−1.18136	+	3.63585i	−0.0382680	+	0.117777i	0.930098	+	0.367312i	$0.119722\pi$
$954$	0.127860	+	0.393514i	0.00413963	+	0.0127405i
$955$	15.6911			0.507752
$956$	3.11004			0.100586
$957$	−0.874838	−	2.69248i	−0.0282795	−	0.0870354i
$958$	24.7588	−	17.9883i	0.799921	−	0.581176i
$959$	−7.54930	−	5.48489i	−0.243780	−	0.177116i
$960$	−1.00000			−0.0322749
$961$	30.7248	−	4.12141i	0.991123	−	0.132949i
$962$	−55.6661			−1.79475
$963$	9.57844	+	6.95914i	0.308661	+	0.224255i
$964$	−20.7554	+	15.0797i	−0.668485	+	0.485683i
$965$	−2.06375	−	6.35157i	−0.0664345	−	0.204464i
$966$	4.12959			0.132867
$967$	−41.4481			−1.33288			−0.666441	−	0.745558i	$-0.732183\pi$
$967$	−41.4481			−1.33288			−0.666441	+	0.745558i	$0.732183\pi$
$968$	0.903030	+	2.77924i	0.0290245	+	0.0893282i
$969$	−7.44808	+	22.9228i	−0.239267	+	0.736387i
$970$	1.58269	−	4.87103i	0.0508173	−	0.156399i
$971$	28.4616	+	20.6786i	0.913376	+	0.663606i	0.941866	−	0.335988i	$-0.109070\pi$
$971$	28.4616	+	20.6786i	0.913376	+	0.663606i	−0.0284905	+	0.999594i	$0.509070\pi$
$972$	−0.309017	−	0.951057i	−0.00991172	−	0.0305052i
$973$	−25.5418	−	18.5572i	−0.818833	−	0.594917i
$974$	−11.5682	+	8.40476i	−0.370668	+	0.269306i
$975$	1.56925	−	4.82966i	0.0502563	−	0.154673i
$976$	6.36738	−	4.62617i	0.203815	−	0.148080i
$977$	−24.7516	+	17.9831i	−0.791873	+	0.575329i	−0.908519	−	0.417844i	$-0.862786\pi$
$977$	−24.7516	+	17.9831i	−0.791873	+	0.575329i	0.116646	+	0.993174i	$0.462786\pi$
$978$	1.38085	−	4.24983i	0.0441548	−	0.135894i
$979$	−34.0719	+	24.7547i	−1.08894	+	0.791163i
$980$	−0.285815	−	0.207656i	−0.00913001	−	0.00663334i
$981$	1.94434	+	5.98407i	0.0620781	+	0.191057i
$982$	21.2401	+	15.4318i	0.677798	+	0.492449i
$983$	11.9132	−	36.6651i	0.379972	−	1.16943i	−0.560090	−	0.828431i	$-0.689234\pi$
$983$	11.9132	−	36.6651i	0.379972	−	1.16943i	0.940063	−	0.341002i	$-0.110766\pi$
$984$	−0.599862	+	1.84618i	−0.0191229	+	0.0588542i
$985$	−2.61372	−	8.04422i	−0.0832802	−	0.256310i
$986$	−6.02537			−0.191887
$987$	−9.09166			−0.289391
$988$	6.25275	+	19.2440i	0.198926	+	0.612233i
$989$	−2.10511	+	1.52945i	−0.0669385	+	0.0486337i
$990$	−2.29934	−	1.67057i	−0.0730777	−	0.0530940i
$991$	34.6910			1.10200			0.550998	−	0.834507i	$-0.314247\pi$
$991$	34.6910			1.10200			0.550998	+	0.834507i	$0.314247\pi$
$992$	−5.55539	+	0.370938i	−0.176384	+	0.0117773i
$993$	8.66647			0.275022
$994$	28.6695	+	20.8296i	0.909342	+	0.660676i
$995$	7.71355	−	5.60423i	0.244536	−	0.177666i
$996$	−4.28622	−	13.1916i	−0.135814	−	0.417993i
$997$	0.0904521			0.00286465			0.00143232	−	0.999999i	$-0.499544\pi$
$997$	0.0904521			0.00286465			0.00143232	+	0.999999i	$0.499544\pi$
$998$	3.12492			0.0989176
$999$	3.38737	+	10.4253i	0.107172	+	0.329840i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.n.f.901.3	yes	12
31.16	even	5	inner	930.2.n.f.481.3	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.n.f.481.3	✓	12	31.16	even	5	inner
930.2.n.f.901.3	yes	12	1.1	even	1	trivial

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.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{2} +(0.809017 - 0.587785i) q^{3} +(0.309017 + 0.951057i) q^{4} +1.00000 q^{5} +1.00000 q^{6} +(0.837960 + 2.57897i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.809017 + 0.587785i) q^{2} +(0.809017 - 0.587785i) q^{3} +(0.309017 + 0.951057i) q^{4} +1.00000 q^{5} +1.00000 q^{6} +(0.837960 + 2.57897i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.309017 - 0.951057i) q^{9} +(0.809017 + 0.587785i) q^{10} +(-0.878268 - 2.70303i) q^{11} +(0.809017 + 0.587785i) q^{12} +(4.10835 - 2.98489i) q^{13} +(-0.837960 + 2.57897i) q^{14} +(0.809017 - 0.587785i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-1.86924 + 5.75294i) q^{17} +(0.809017 - 0.587785i) q^{18} +(3.22356 + 2.34206i) q^{19} +(0.309017 + 0.951057i) q^{20} +(2.19381 + 1.59389i) q^{21} +(0.878268 - 2.70303i) q^{22} +(0.470596 - 1.44835i) q^{23} +(0.309017 + 0.951057i) q^{24} +1.00000 q^{25} +5.07820 q^{26} +(-0.309017 - 0.951057i) q^{27} +(-2.19381 + 1.59389i) q^{28} +(0.805858 + 0.585490i) q^{29} +1.00000 q^{30} +(5.55539 - 0.370938i) q^{31} -1.00000 q^{32} +(-2.29934 - 1.67057i) q^{33} +(-4.89374 + 3.55551i) q^{34} +(0.837960 + 2.57897i) q^{35} +1.00000 q^{36} -10.9618 q^{37} +(1.23129 + 3.78953i) q^{38} +(1.56925 - 4.82966i) q^{39} +(-0.309017 + 0.951057i) q^{40} +(1.57046 + 1.14100i) q^{41} +(0.837960 + 2.57897i) q^{42} +(-1.38232 - 1.00431i) q^{43} +(2.29934 - 1.67057i) q^{44} +(0.309017 - 0.951057i) q^{45} +(1.23204 - 0.895128i) q^{46} +(-2.71244 + 1.97070i) q^{47} +(-0.309017 + 0.951057i) q^{48} +(-0.285815 + 0.207656i) q^{49} +(0.809017 + 0.587785i) q^{50} +(1.86924 + 5.75294i) q^{51} +(4.10835 + 2.98489i) q^{52} +(-0.127860 + 0.393514i) q^{53} +(0.309017 - 0.951057i) q^{54} +(-0.878268 - 2.70303i) q^{55} -2.71169 q^{56} +3.98454 q^{57} +(0.307810 + 0.947342i) q^{58} +(-5.37667 + 3.90638i) q^{59} +(0.809017 + 0.587785i) q^{60} -7.87051 q^{61} +(4.71244 + 2.96528i) q^{62} +2.71169 q^{63} +(-0.809017 - 0.587785i) q^{64} +(4.10835 - 2.98489i) q^{65} +(-0.878268 - 2.70303i) q^{66} +14.0296 q^{67} -6.04900 q^{68} +(-0.470596 - 1.44835i) q^{69} +(-0.837960 + 2.57897i) q^{70} +(4.03836 - 12.4288i) q^{71} +(0.809017 + 0.587785i) q^{72} +(0.759156 + 2.33644i) q^{73} +(-8.86825 - 6.44316i) q^{74} +(0.809017 - 0.587785i) q^{75} +(-1.23129 + 3.78953i) q^{76} +(6.23510 - 4.53006i) q^{77} +(4.10835 - 2.98489i) q^{78} +(2.06879 - 6.36708i) q^{79} +(-0.809017 + 0.587785i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(0.599862 + 1.84618i) q^{82} +(-11.2215 - 8.15288i) q^{83} +(-0.837960 + 2.57897i) q^{84} +(-1.86924 + 5.75294i) q^{85} +(-0.527999 - 1.62501i) q^{86} +0.996095 q^{87} +2.84214 q^{88} +(-4.57906 - 14.0929i) q^{89} +(0.809017 - 0.587785i) q^{90} +(11.1406 + 8.09412i) q^{91} +1.52288 q^{92} +(4.27638 - 3.56547i) q^{93} -3.35276 q^{94} +(3.22356 + 2.34206i) q^{95} +(-0.809017 + 0.587785i) q^{96} +(-1.58269 - 4.87103i) q^{97} -0.353286 q^{98} -2.84214 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} + 3 q^{3} - 3 q^{4} + 12 q^{5} + 12 q^{6} - q^{7} + 3 q^{8} - 3 q^{9}+O(q^{10}) \) 12 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 + 12 * q^5 + 12 * q^6 - q^7 + 3 * q^8 - 3 * q^9	\( 12 q + 3 q^{2} + 3 q^{3} - 3 q^{4} + 12 q^{5} + 12 q^{6} - q^{7} + 3 q^{8} - 3 q^{9} + 3 q^{10} + 14 q^{11} + 3 q^{12} + 4 q^{13} + q^{14} + 3 q^{15} - 3 q^{16} - 7 q^{17} + 3 q^{18} + 12 q^{19} - 3 q^{20} + q^{21} - 14 q^{22} - 6 q^{23} - 3 q^{24} + 12 q^{25} + 6 q^{26} + 3 q^{27} - q^{28} - 23 q^{29} + 12 q^{30} + 34 q^{31} - 12 q^{32} + 11 q^{33} - 3 q^{34} - q^{35} + 12 q^{36} + 22 q^{37} + 8 q^{38} + q^{39} + 3 q^{40} + 15 q^{41} - q^{42} - 17 q^{43} - 11 q^{44} - 3 q^{45} + 6 q^{46} - 2 q^{47} + 3 q^{48} - 8 q^{49} + 3 q^{50} + 7 q^{51} + 4 q^{52} - 21 q^{53} - 3 q^{54} + 14 q^{55} - 4 q^{56} + 8 q^{57} - 17 q^{58} - 15 q^{59} + 3 q^{60} + 16 q^{61} + 26 q^{62} + 4 q^{63} - 3 q^{64} + 4 q^{65} + 14 q^{66} + 24 q^{67} + 8 q^{68} + 6 q^{69} + q^{70} + 23 q^{71} + 3 q^{72} + 56 q^{73} + 8 q^{74} + 3 q^{75} - 8 q^{76} - 8 q^{77} + 4 q^{78} - 9 q^{79} - 3 q^{80} - 3 q^{81} + 15 q^{82} - 24 q^{83} + q^{84} - 7 q^{85} - 18 q^{86} - 12 q^{87} + 6 q^{88} - 27 q^{89} + 3 q^{90} - 3 q^{91} + 24 q^{92} + 11 q^{93} - 28 q^{94} + 12 q^{95} - 3 q^{96} + 38 q^{97} - 52 q^{98} - 6 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 + 12 * q^5 + 12 * q^6 - q^7 + 3 * q^8 - 3 * q^9 + 3 * q^10 + 14 * q^11 + 3 * q^12 + 4 * q^13 + q^14 + 3 * q^15 - 3 * q^16 - 7 * q^17 + 3 * q^18 + 12 * q^19 - 3 * q^20 + q^21 - 14 * q^22 - 6 * q^23 - 3 * q^24 + 12 * q^25 + 6 * q^26 + 3 * q^27 - q^28 - 23 * q^29 + 12 * q^30 + 34 * q^31 - 12 * q^32 + 11 * q^33 - 3 * q^34 - q^35 + 12 * q^36 + 22 * q^37 + 8 * q^38 + q^39 + 3 * q^40 + 15 * q^41 - q^42 - 17 * q^43 - 11 * q^44 - 3 * q^45 + 6 * q^46 - 2 * q^47 + 3 * q^48 - 8 * q^49 + 3 * q^50 + 7 * q^51 + 4 * q^52 - 21 * q^53 - 3 * q^54 + 14 * q^55 - 4 * q^56 + 8 * q^57 - 17 * q^58 - 15 * q^59 + 3 * q^60 + 16 * q^61 + 26 * q^62 + 4 * q^63 - 3 * q^64 + 4 * q^65 + 14 * q^66 + 24 * q^67 + 8 * q^68 + 6 * q^69 + q^70 + 23 * q^71 + 3 * q^72 + 56 * q^73 + 8 * q^74 + 3 * q^75 - 8 * q^76 - 8 * q^77 + 4 * q^78 - 9 * q^79 - 3 * q^80 - 3 * q^81 + 15 * q^82 - 24 * q^83 + q^84 - 7 * q^85 - 18 * q^86 - 12 * q^87 + 6 * q^88 - 27 * q^89 + 3 * q^90 - 3 * q^91 + 24 * q^92 + 11 * q^93 - 28 * q^94 + 12 * q^95 - 3 * q^96 + 38 * q^97 - 52 * q^98 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more