LMFDB - Embedded newform 930.2.z.d.109.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(109,930)]

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, 5, 2]))

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

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

chi := DirichletCharacter("930.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.z (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:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			109.12
Character	$\chi$	$=$	930.109
Dual form			930.2.z.d.529.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.587785 + 0.809017i) q^{2} +(0.587785 - 0.809017i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(-0.635868 - 2.14375i) q^{5} +1.00000 q^{6} +(-2.45458 - 0.797540i) q^{7} +(-0.951057 + 0.309017i) q^{8} +(-0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(0.587785 + 0.809017i) q^{2} +(0.587785 - 0.809017i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(-0.635868 - 2.14375i) q^{5} +1.00000 q^{6} +(-2.45458 - 0.797540i) q^{7} +(-0.951057 + 0.309017i) q^{8} +(-0.309017 - 0.951057i) q^{9} +(1.36058 - 1.77449i) q^{10} +(1.45962 - 4.49224i) q^{11} +(0.587785 + 0.809017i) q^{12} +(-1.38825 + 1.91076i) q^{13} +(-0.797540 - 2.45458i) q^{14} +(-2.10809 - 0.745638i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-4.55237 + 1.47915i) q^{17} +(0.587785 - 0.809017i) q^{18} +(-5.40527 + 3.92716i) q^{19} +(2.23532 + 0.0577095i) q^{20} +(-2.08799 + 1.51701i) q^{21} +(4.49224 - 1.45962i) q^{22} +(-6.21792 + 2.02032i) q^{23} +(-0.309017 + 0.951057i) q^{24} +(-4.19134 + 2.72629i) q^{25} -2.36183 q^{26} +(-0.951057 - 0.309017i) q^{27} +(1.51701 - 2.08799i) q^{28} +(0.967593 - 0.702997i) q^{29} +(-0.635868 - 2.14375i) q^{30} +(5.11024 + 2.21030i) q^{31} -1.00000i q^{32} +(-2.77636 - 3.82133i) q^{33} +(-3.87248 - 2.81352i) q^{34} +(-0.148942 + 5.76913i) q^{35} +1.00000 q^{36} -10.7447i q^{37} +(-6.35428 - 2.06463i) q^{38} +(0.729847 + 2.24624i) q^{39} +(1.26720 + 1.84234i) q^{40} +(7.47249 - 5.42908i) q^{41} +(-2.45458 - 0.797540i) q^{42} +(-4.00186 - 5.50809i) q^{43} +(3.82133 + 2.77636i) q^{44} +(-1.84234 + 1.26720i) q^{45} +(-5.28928 - 3.84288i) q^{46} +(3.72922 - 5.13283i) q^{47} +(-0.951057 + 0.309017i) q^{48} +(-0.274242 - 0.199249i) q^{49} +(-4.66922 - 1.78840i) q^{50} +(-1.47915 + 4.55237i) q^{51} +(-1.38825 - 1.91076i) q^{52} +(4.45830 - 1.44859i) q^{53} +(-0.309017 - 0.951057i) q^{54} +(-10.5584 - 0.272587i) q^{55} +2.58089 q^{56} +6.68128i q^{57} +(1.13747 + 0.369588i) q^{58} +(-0.441684 - 0.320902i) q^{59} +(1.36058 - 1.77449i) q^{60} +8.36422 q^{61} +(1.21556 + 5.43345i) q^{62} +2.58089i q^{63} +(0.809017 - 0.587785i) q^{64} +(4.97895 + 1.76107i) q^{65} +(1.45962 - 4.49224i) q^{66} +2.05798i q^{67} -4.78665i q^{68} +(-2.02032 + 6.21792i) q^{69} +(-4.75487 + 3.27052i) q^{70} +(-1.42380 - 4.38200i) q^{71} +(0.587785 + 0.809017i) q^{72} +(-2.33969 - 0.760212i) q^{73} +(8.69261 - 6.31555i) q^{74} +(-0.257999 + 4.99334i) q^{75} +(-2.06463 - 6.35428i) q^{76} +(-7.16549 + 9.86245i) q^{77} +(-1.38825 + 1.91076i) q^{78} +(-0.469417 - 1.44472i) q^{79} +(-0.745638 + 2.10809i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(8.78444 + 2.85424i) q^{82} +(2.57656 + 3.54633i) q^{83} +(-0.797540 - 2.45458i) q^{84} +(6.06565 + 8.81861i) q^{85} +(2.10390 - 6.47514i) q^{86} -1.19601i q^{87} +4.72342i q^{88} +(-2.06970 + 6.36987i) q^{89} +(-2.10809 - 0.745638i) q^{90} +(4.93148 - 3.58293i) q^{91} -6.53791i q^{92} +(4.79189 - 2.83509i) q^{93} +6.34453 q^{94} +(11.8559 + 9.09041i) q^{95} +(-0.809017 - 0.587785i) q^{96} +(0.296640 + 0.0963843i) q^{97} -0.338982i q^{98} -4.72342 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 18 q^{4} + 4 q^{5} + 72 q^{6} + 18 q^{9}+O(q^{10}) $ 72 * q + 18 * q^4 + 4 * q^5 + 72 * q^6 + 18 * q^9	$ 72 q + 18 q^{4} + 4 q^{5} + 72 q^{6} + 18 q^{9} - 6 q^{11} - 4 q^{14} - 18 q^{16} + 12 q^{19} - 4 q^{20} - 16 q^{21} + 18 q^{24} - 4 q^{25} + 12 q^{26} + 24 q^{29} + 4 q^{30} + 22 q^{31} + 14 q^{34} - 22 q^{35} + 72 q^{36} + 8 q^{39} - 28 q^{41} - 4 q^{44} - 4 q^{45} - 22 q^{46} + 42 q^{49} - 32 q^{50} - 4 q^{51} + 18 q^{54} + 14 q^{55} + 24 q^{56} - 28 q^{59} + 56 q^{61} + 18 q^{64} + 46 q^{65} - 6 q^{66} - 8 q^{69} + 46 q^{70} - 68 q^{71} + 8 q^{74} + 32 q^{75} - 12 q^{76} + 26 q^{79} - 6 q^{80} - 18 q^{81} - 4 q^{84} - 32 q^{85} + 80 q^{86} + 32 q^{89} - 44 q^{91} + 12 q^{94} + 74 q^{95} - 18 q^{96} - 4 q^{99}+O(q^{100}) $ 72 * q + 18 * q^4 + 4 * q^5 + 72 * q^6 + 18 * q^9 - 6 * q^11 - 4 * q^14 - 18 * q^16 + 12 * q^19 - 4 * q^20 - 16 * q^21 + 18 * q^24 - 4 * q^25 + 12 * q^26 + 24 * q^29 + 4 * q^30 + 22 * q^31 + 14 * q^34 - 22 * q^35 + 72 * q^36 + 8 * q^39 - 28 * q^41 - 4 * q^44 - 4 * q^45 - 22 * q^46 + 42 * q^49 - 32 * q^50 - 4 * q^51 + 18 * q^54 + 14 * q^55 + 24 * q^56 - 28 * q^59 + 56 * q^61 + 18 * q^64 + 46 * q^65 - 6 * q^66 - 8 * q^69 + 46 * q^70 - 68 * q^71 + 8 * q^74 + 32 * q^75 - 12 * q^76 + 26 * q^79 - 6 * q^80 - 18 * q^81 - 4 * q^84 - 32 * q^85 + 80 * q^86 + 32 * q^89 - 44 * q^91 + 12 * q^94 + 74 * q^95 - 18 * q^96 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.587785	+	0.809017i	0.415627	+	0.572061i
$2$	0.587785	+	0.809017i	0.415627	+	0.572061i
$3$	0.587785	−	0.809017i	0.339358	−	0.467086i
$3$	0.587785	−	0.809017i	0.339358	−	0.467086i
$4$	−0.309017	+	0.951057i	−0.154508	+	0.475528i
$5$	−0.635868	−	2.14375i	−0.284369	−	0.958715i
$5$	−0.635868	−	2.14375i	−0.284369	−	0.958715i
$6$	1.00000			0.408248
$7$	−2.45458	−	0.797540i	−0.927743	−	0.301442i	−0.194104	−	0.980981i	$-0.562180\pi$
$7$	−2.45458	−	0.797540i	−0.927743	−	0.301442i	−0.733639	+	0.679539i	$0.762180\pi$
$8$	−0.951057	+	0.309017i	−0.336249	+	0.109254i
$9$	−0.309017	−	0.951057i	−0.103006	−	0.317019i
$10$	1.36058	−	1.77449i	0.430253	−	0.561144i
$11$	1.45962	−	4.49224i	0.440091	−	1.35446i	−0.447687	−	0.894190i	$-0.647752\pi$
$11$	1.45962	−	4.49224i	0.440091	−	1.35446i	0.887778	−	0.460271i	$-0.152248\pi$
$12$	0.587785	+	0.809017i	0.169679	+	0.233543i
$13$	−1.38825	+	1.91076i	−0.385032	+	0.529951i	−0.956909	−	0.290389i	$-0.906215\pi$
$13$	−1.38825	+	1.91076i	−0.385032	+	0.529951i	0.571877	+	0.820339i	$0.306215\pi$
$14$	−0.797540	−	2.45458i	−0.213152	−	0.656013i
$15$	−2.10809	−	0.745638i	−0.544305	−	0.192523i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−4.55237	+	1.47915i	−1.10411	+	0.358748i	−0.803684	−	0.595057i	$-0.797130\pi$
$17$	−4.55237	+	1.47915i	−1.10411	+	0.358748i	−0.300428	+	0.953804i	$0.597130\pi$
$18$	0.587785	−	0.809017i	0.138542	−	0.190687i
$19$	−5.40527	+	3.92716i	−1.24005	+	0.900952i	−0.997602	−	0.0692113i	$-0.977952\pi$
$19$	−5.40527	+	3.92716i	−1.24005	+	0.900952i	−0.242452	+	0.970163i	$0.577952\pi$
$20$	2.23532	+	0.0577095i	0.499833	+	0.0129042i
$21$	−2.08799	+	1.51701i	−0.455636	+	0.331039i
$22$	4.49224	−	1.45962i	0.957749	−	0.311192i
$23$	−6.21792	+	2.02032i	−1.29653	+	0.421267i	−0.874371	−	0.485257i	$-0.838726\pi$
$23$	−6.21792	+	2.02032i	−1.29653	+	0.421267i	−0.422154	+	0.906524i	$0.638726\pi$
$24$	−0.309017	+	0.951057i	−0.0630778	+	0.194134i
$25$	−4.19134	+	2.72629i	−0.838269	+	0.545257i
$26$	−2.36183			−0.463194
$27$	−0.951057	−	0.309017i	−0.183031	−	0.0594703i
$28$	1.51701	−	2.08799i	0.286688	−	0.394593i
$29$	0.967593	−	0.702997i	0.179678	−	0.130543i	−0.494311	−	0.869285i	$-0.664580\pi$
$29$	0.967593	−	0.702997i	0.179678	−	0.130543i	0.673989	+	0.738742i	$0.264580\pi$
$30$	−0.635868	−	2.14375i	−0.116093	−	0.391394i
$31$	5.11024	+	2.21030i	0.917827	+	0.396981i
$31$	5.11024	+	2.21030i	0.917827	+	0.396981i
$32$		−	1.00000i		−	0.176777i
$33$	−2.77636	−	3.82133i	−0.483302	−	0.665208i
$34$	−3.87248	−	2.81352i	−0.664124	−	0.482515i
$35$	−0.148942	+	5.76913i	−0.0251758	+	0.975162i
$36$	1.00000			0.166667
$37$		−	10.7447i		−	1.76641i	−0.468987	−	0.883205i	$-0.655381\pi$
$37$		−	10.7447i		−	1.76641i	0.468987	−	0.883205i	$-0.344619\pi$
$38$	−6.35428	−	2.06463i	−1.03080	−	0.334927i
$39$	0.729847	+	2.24624i	0.116869	+	0.359686i
$40$	1.26720	+	1.84234i	0.200362	+	0.291299i
$41$	7.47249	−	5.42908i	1.16701	−	0.847881i	0.176360	−	0.984326i	$-0.443568\pi$
$41$	7.47249	−	5.42908i	1.16701	−	0.847881i	0.990648	+	0.136445i	$0.0435678\pi$
$42$	−2.45458	−	0.797540i	−0.378749	−	0.123063i
$43$	−4.00186	−	5.50809i	−0.610278	−	0.839975i	0.386323	−	0.922364i	$-0.373745\pi$
$43$	−4.00186	−	5.50809i	−0.610278	−	0.839975i	−0.996600	+	0.0823886i	$0.973745\pi$
$44$	3.82133	+	2.77636i	0.576087	+	0.418552i
$45$	−1.84234	+	1.26720i	−0.274639	+	0.188903i
$46$	−5.28928	−	3.84288i	−0.779861	−	0.566602i
$47$	3.72922	−	5.13283i	0.543962	−	0.748700i	−0.445215	−	0.895424i	$-0.646873\pi$
$47$	3.72922	−	5.13283i	0.543962	−	0.748700i	0.989178	+	0.146724i	$0.0468728\pi$
$48$	−0.951057	+	0.309017i	−0.137273	+	0.0446028i
$49$	−0.274242	−	0.199249i	−0.0391775	−	0.0284641i
$50$	−4.66922	−	1.78840i	−0.660328	−	0.252918i
$51$	−1.47915	+	4.55237i	−0.207123	+	0.637459i
$52$	−1.38825	−	1.91076i	−0.192516	−	0.264975i
$53$	4.45830	−	1.44859i	0.612395	−	0.198979i	0.0136342	−	0.999907i	$-0.495660\pi$
$53$	4.45830	−	1.44859i	0.612395	−	0.198979i	0.598761	+	0.800928i	$0.295660\pi$
$54$	−0.309017	−	0.951057i	−0.0420519	−	0.129422i
$55$	−10.5584	−	0.272587i	−1.42369	−	0.0367556i
$56$	2.58089			0.344887
$57$			6.68128i			0.884957i
$58$	1.13747	+	0.369588i	0.149358	+	0.0485292i
$59$	−0.441684	−	0.320902i	−0.0575023	−	0.0417779i	0.558663	−	0.829395i	$-0.311315\pi$
$59$	−0.441684	−	0.320902i	−0.0575023	−	0.0417779i	−0.616165	+	0.787617i	$0.711315\pi$
$60$	1.36058	−	1.77449i	0.175650	−	0.229086i
$61$	8.36422			1.07093			0.535465	−	0.844558i	$-0.320137\pi$
$61$	8.36422			1.07093			0.535465	+	0.844558i	$0.320137\pi$
$62$	1.21556	+	5.43345i	0.154376	+	0.690049i
$63$			2.58089i			0.325162i
$64$	0.809017	−	0.587785i	0.101127	−	0.0734732i
$65$	4.97895	+	1.76107i	0.617563	+	0.218434i
$66$	1.45962	−	4.49224i	0.179667	−	0.552957i
$67$			2.05798i			0.251423i	0.992067	+	0.125711i	$0.0401213\pi$
$67$			2.05798i			0.251423i	−0.992067	+	0.125711i	$0.959879\pi$
$68$		−	4.78665i		−	0.580466i
$69$	−2.02032	+	6.21792i	−0.243218	+	0.748549i
$70$	−4.75487	+	3.27052i	−0.568316	+	0.390901i
$71$	−1.42380	−	4.38200i	−0.168974	−	0.520048i	0.830333	−	0.557267i	$-0.188150\pi$
$71$	−1.42380	−	4.38200i	−0.168974	−	0.520048i	−0.999307	+	0.0372190i	$0.988150\pi$
$72$	0.587785	+	0.809017i	0.0692712	+	0.0953436i
$73$	−2.33969	−	0.760212i	−0.273840	−	0.0889760i	0.168878	−	0.985637i	$-0.445986\pi$
$73$	−2.33969	−	0.760212i	−0.273840	−	0.0889760i	−0.442718	+	0.896661i	$0.645986\pi$
$74$	8.69261	−	6.31555i	1.01050	−	0.734168i
$75$	−0.257999	+	4.99334i	−0.0297911	+	0.576581i
$76$	−2.06463	−	6.35428i	−0.236829	−	0.728886i
$77$	−7.16549	+	9.86245i	−0.816583	+	1.12393i
$78$	−1.38825	+	1.91076i	−0.157189	+	0.216351i
$79$	−0.469417	−	1.44472i	−0.0528135	−	0.162543i	0.921171	−	0.389158i	$-0.127234\pi$
$79$	−0.469417	−	1.44472i	−0.0528135	−	0.162543i	−0.973984	+	0.226615i	$0.927234\pi$
$80$	−0.745638	+	2.10809i	−0.0833648	+	0.235691i
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	8.78444	+	2.85424i	0.970079	+	0.315198i
$83$	2.57656	+	3.54633i	0.282814	+	0.389260i	0.926663	−	0.375892i	$-0.122664\pi$
$83$	2.57656	+	3.54633i	0.282814	+	0.389260i	−0.643849	+	0.765152i	$0.722664\pi$
$84$	−0.797540	−	2.45458i	−0.0870188	−	0.267816i
$85$	6.06565	+	8.81861i	0.657912	+	0.956512i
$86$	2.10390	−	6.47514i	0.226870	−	0.698233i
$87$		−	1.19601i		−	0.128226i
$88$			4.72342i			0.503519i
$89$	−2.06970	+	6.36987i	−0.219387	+	0.675204i	0.779426	+	0.626495i	$0.215511\pi$
$89$	−2.06970	+	6.36987i	−0.219387	+	0.675204i	−0.998813	+	0.0487099i	$0.984489\pi$
$90$	−2.10809	−	0.745638i	−0.222212	−	0.0785971i
$91$	4.93148	−	3.58293i	0.516960	−	0.375593i
$92$		−	6.53791i		−	0.681624i
$93$	4.79189	−	2.83509i	0.496896	−	0.293986i
$94$	6.34453			0.654388
$95$	11.8559	+	9.09041i	1.21639	+	0.932656i
$96$	−0.809017	−	0.587785i	−0.0825700	−	0.0599906i
$97$	0.296640	+	0.0963843i	0.0301193	+	0.00978635i	0.324038	−	0.946044i	$-0.394959\pi$
$97$	0.296640	+	0.0963843i	0.0301193	+	0.00978635i	−0.293919	+	0.955830i	$0.594959\pi$
$98$		−	0.338982i		−	0.0342424i
$99$	−4.72342			−0.474722
$100$	−1.29766	−	4.82867i	−0.129766	−	0.482867i
$101$	2.60959	+	8.03150i	0.259664	+	0.799164i	0.992875	+	0.119162i	$0.0380209\pi$
$101$	2.60959	+	8.03150i	0.259664	+	0.799164i	−0.733211	+	0.680002i	$0.761979\pi$
$102$	−4.55237	+	1.47915i	−0.450752	+	0.146458i
$103$	−10.3332	−	14.2224i	−1.01816	−	1.40137i	−0.913487	−	0.406867i	$-0.866621\pi$
$103$	−10.3332	−	14.2224i	−1.01816	−	1.40137i	−0.104670	−	0.994507i	$-0.533379\pi$
$104$	0.729847	−	2.24624i	0.0715674	−	0.220262i
$105$	4.57978	+	3.51151i	0.446941	+	0.342688i
$106$	3.79246	+	2.75538i	0.368356	+	0.267627i
$107$	15.0804	−	4.89991i	1.45788	−	0.473692i	0.530455	−	0.847713i	$-0.322021\pi$
$107$	15.0804	−	4.89991i	1.45788	−	0.473692i	0.927420	+	0.374021i	$0.122021\pi$
$108$	0.587785	−	0.809017i	0.0565597	−	0.0778477i
$109$	−6.72539	−	4.88628i	−0.644175	−	0.468021i	0.217107	−	0.976148i	$-0.430338\pi$
$109$	−6.72539	−	4.88628i	−0.644175	−	0.468021i	−0.861282	+	0.508127i	$0.830338\pi$
$110$	−5.98553	−	8.70213i	−0.570698	−	0.829715i
$111$	−8.69261	−	6.31555i	−0.825066	−	0.599445i
$112$	1.51701	+	2.08799i	0.143344	+	0.197296i
$113$	−11.0730	−	3.59782i	−1.04166	−	0.338454i	−0.262267	−	0.964995i	$-0.584470\pi$
$113$	−11.0730	−	3.59782i	−1.04166	−	0.338454i	−0.779389	+	0.626541i	$0.784470\pi$
$114$	−5.40527	+	3.92716i	−0.506250	+	0.367812i
$115$	8.28485	+	12.0450i	0.772566	+	1.12320i
$116$	0.369588	+	1.13747i	0.0343154	+	0.105612i
$117$	2.24624	+	0.729847i	0.207665	+	0.0674744i
$118$		−	0.545951i		−	0.0502589i
$119$	12.3538			1.13247
$120$	2.23532	+	0.0577095i	0.204056	+	0.00526814i
$121$	−9.15057	−	6.64827i	−0.831870	−	0.604389i
$122$	4.91637	+	6.76680i	0.445107	+	0.612637i
$123$		−	9.23651i		−	0.832828i
$124$	−3.68127	+	4.17711i	−0.330588	+	0.375116i
$125$	8.50962	+	7.25164i	0.761124	+	0.648607i
$126$	−2.08799	+	1.51701i	−0.186013	+	0.135146i
$127$	0.547061	−	0.752966i	0.0485439	−	0.0668149i	−0.784055	−	0.620691i	$-0.786852\pi$
$127$	0.547061	−	0.752966i	0.0485439	−	0.0668149i	0.832599	+	0.553876i	$0.186852\pi$
$128$	0.951057	+	0.309017i	0.0840623	+	0.0273135i
$129$	−6.80837			−0.599443
$130$	1.50181	+	5.06319i	0.131718	+	0.444071i
$131$	4.25181	−	13.0857i	0.371483	−	1.14331i	−0.574339	−	0.818618i	$-0.694741\pi$
$131$	4.25181	−	13.0857i	0.371483	−	1.14331i	0.945821	−	0.324688i	$-0.105259\pi$
$132$	4.49224	−	1.45962i	0.390999	−	0.127043i
$133$	16.3997	−	5.32859i	1.42204	−	0.462048i
$134$	−1.66494	+	1.20965i	−0.143829	+	0.104498i
$135$	−0.0577095	+	2.23532i	−0.00496685	+	0.192386i
$136$	3.87248	−	2.81352i	0.332062	−	0.241257i
$137$	−10.1249	+	13.9358i	−0.865031	+	1.19061i	0.115315	+	0.993329i	$0.463212\pi$
$137$	−10.1249	+	13.9358i	−0.865031	+	1.19061i	−0.980346	+	0.197285i	$0.936788\pi$
$138$	−6.21792	+	2.02032i	−0.529304	+	0.171981i
$139$	−12.9802	−	9.43068i	−1.10097	−	0.799900i	−0.119751	−	0.992804i	$-0.538209\pi$
$139$	−12.9802	−	9.43068i	−1.10097	−	0.799900i	−0.981218	+	0.192904i	$0.938209\pi$
$140$	−5.44075	−	1.92441i	−0.459827	−	0.162643i
$141$	−1.96057	−	6.03400i	−0.165109	−	0.508155i
$142$	2.70823	−	3.72755i	0.227269	−	0.312809i
$143$	6.55730	+	9.02535i	0.548349	+	0.754737i
$144$	−0.309017	+	0.951057i	−0.0257514	+	0.0792547i
$145$	−2.12231	−	1.62727i	−0.176249	−	0.135137i
$146$	−0.760212	−	2.33969i	−0.0629156	−	0.193634i
$147$	−0.322391	+	0.104751i	−0.0265904	+	0.00863973i
$148$	10.2188	+	3.32028i	0.839978	+	0.272925i
$149$	17.0941			1.40041			0.700203	−	0.713944i	$-0.253093\pi$
$149$	17.0941			1.40041			0.700203	+	0.713944i	$0.253093\pi$
$150$	−4.19134	+	2.72629i	−0.342222	+	0.222600i
$151$	−3.38879	+	10.4296i	−0.275776	+	0.848752i	0.713237	+	0.700923i	$0.247228\pi$
$151$	−3.38879	+	10.4296i	−0.275776	+	0.848752i	−0.989013	+	0.147829i	$0.952772\pi$
$152$	3.92716	−	5.40527i	0.318535	−	0.438425i
$153$	2.81352	+	3.87248i	0.227460	+	0.313071i
$154$	−12.1907			−0.982351
$155$	1.48889	−	12.3606i	0.119590	−	0.992823i
$156$	−2.36183			−0.189098
$157$	−4.83804	−	6.65899i	−0.386118	−	0.531445i	0.571075	−	0.820898i	$-0.306527\pi$
$157$	−4.83804	−	6.65899i	−0.386118	−	0.531445i	−0.957192	+	0.289453i	$0.906527\pi$
$158$	0.892883	−	1.22895i	0.0710340	−	0.0977699i
$159$	1.44859	−	4.45830i	0.114881	−	0.353567i
$160$	−2.14375	+	0.635868i	−0.169478	+	0.0502698i
$161$	16.8736			1.32983
$162$	−0.951057	−	0.309017i	−0.0747221	−	0.0242787i
$163$	−16.7300	+	5.43591i	−1.31040	+	0.425774i	−0.879186	−	0.476478i	$-0.841913\pi$
$163$	−16.7300	+	5.43591i	−1.31040	+	0.425774i	−0.431210	+	0.902252i	$0.641913\pi$
$164$	2.85424	+	8.78444i	0.222879	+	0.685950i
$165$	−6.42658	+	8.38168i	−0.500309	+	0.652513i
$166$	−1.35458	+	4.16896i	−0.105136	+	0.323574i
$167$	2.32454	+	3.19946i	0.179878	+	0.247581i	0.889429	−	0.457073i	$-0.151102\pi$
$167$	2.32454	+	3.19946i	0.179878	+	0.247581i	−0.709551	+	0.704654i	$0.751102\pi$
$168$	1.51701	−	2.08799i	0.117040	−	0.161092i
$169$	2.29344	+	7.05849i	0.176419	+	0.542961i
$170$	−3.56910	+	10.0907i	−0.273738	+	0.773918i
$171$	5.40527	+	3.92716i	0.413351	+	0.300317i
$172$	6.47514	−	2.10390i	0.493725	−	0.160421i
$173$	3.80182	−	5.23275i	0.289047	−	0.397839i	−0.639657	−	0.768660i	$-0.720924\pi$
$173$	3.80182	−	5.23275i	0.289047	−	0.397839i	0.928704	+	0.370821i	$0.120924\pi$
$174$	0.967593	−	0.702997i	0.0733530	−	0.0532941i
$175$	12.4623	−	3.34911i	0.942061	−	0.253169i
$176$	−3.82133	+	2.77636i	−0.288044	+	0.209276i
$177$	−0.519231	+	0.168708i	−0.0390278	+	0.0126809i
$178$	−6.36987	+	2.06970i	−0.477442	+	0.155130i
$179$	−5.82714	+	17.9341i	−0.435541	+	1.34046i	0.456991	+	0.889472i	$0.348927\pi$
$179$	−5.82714	+	17.9341i	−0.435541	+	1.34046i	−0.892531	+	0.450985i	$0.851073\pi$
$180$	−0.635868	−	2.14375i	−0.0473948	−	0.159786i
$181$	24.7274			1.83798			0.918988	−	0.394285i	$-0.129008\pi$
$181$	24.7274			1.83798			0.918988	+	0.394285i	$0.129008\pi$
$182$	5.79730	+	1.88366i	0.429725	+	0.139626i
$183$	4.91637	−	6.76680i	0.363428	−	0.500216i
$184$	5.28928	−	3.84288i	0.389931	−	0.283301i
$185$	−23.0339	+	6.83218i	−1.69348	+	0.502312i
$186$	5.11024	+	2.21030i	0.374701	+	0.162067i
$187$			22.6094i			1.65336i
$188$	3.72922	+	5.13283i	0.271981	+	0.374350i
$189$	2.08799	+	1.51701i	0.151879	+	0.110346i
$190$	−0.385574	+	14.9348i	−0.0279725	+	1.08349i
$191$	−1.31747			−0.0953288			−0.0476644	−	0.998863i	$-0.515178\pi$
$191$	−1.31747			−0.0953288			−0.0476644	+	0.998863i	$0.515178\pi$
$192$		−	1.00000i		−	0.0721688i
$193$	17.3862	+	5.64913i	1.25149	+	0.406633i	0.858454	−	0.512890i	$-0.171425\pi$
$193$	17.3862	+	5.64913i	1.25149	+	0.406633i	0.393035	+	0.919524i	$0.371425\pi$
$194$	0.0963843	+	0.296640i	0.00691999	+	0.0212975i
$195$	4.35129	−	2.99292i	0.311602	−	0.214328i
$196$	0.274242	−	0.199249i	0.0195887	−	0.0142320i
$197$	8.22309	+	2.67184i	0.585871	+	0.190361i	0.586929	−	0.809638i	$-0.300337\pi$
$197$	8.22309	+	2.67184i	0.585871	+	0.190361i	−0.00105812	+	0.999999i	$0.500337\pi$
$198$	−2.77636	−	3.82133i	−0.197307	−	0.271570i
$199$	−15.9156	−	11.5633i	−1.12822	−	0.819703i	−0.142789	−	0.989753i	$-0.545607\pi$
$199$	−15.9156	−	11.5633i	−1.12822	−	0.819703i	−0.985435	+	0.170050i	$0.945607\pi$
$200$	3.14374	−	3.88805i	0.222296	−	0.274927i
$201$	1.66494	+	1.20965i	0.117436	+	0.0853223i
$202$	−4.96374	+	6.83200i	−0.349248	+	0.480698i
$203$	−2.93570	+	0.953867i	−0.206046	+	0.0669483i
$204$	−3.87248	−	2.81352i	−0.271128	−	0.196986i
$205$	−16.3901	−	12.5670i	−1.14474	−	0.877717i
$206$	5.43247	−	16.7194i	0.378498	−	1.16490i
$207$	3.84288	+	5.28928i	0.267099	+	0.367630i
$208$	2.24624	−	0.729847i	0.155749	−	0.0506058i
$209$	9.75212	+	30.0139i	0.674568	+	2.07611i
$210$	−0.148942	+	5.76913i	−0.0102780	+	0.398108i
$211$	−26.0611			−1.79412			−0.897062	−	0.441905i	$-0.854303\pi$
$211$	−26.0611			−1.79412			−0.897062	+	0.441905i	$0.854303\pi$
$212$			4.68774i			0.321955i
$213$	−4.38200	−	1.42380i	−0.300250	−	0.0975571i
$214$	12.8281	+	9.32019i	0.876913	+	0.637115i
$215$	−9.26332	+	12.0814i	−0.631753	+	0.823945i
$216$	1.00000			0.0680414
$217$	−10.7807	−	9.50097i	−0.731841	−	0.644968i
$218$		−	8.31304i		−	0.563030i
$219$	−1.99026	+	1.44601i	−0.134489	+	0.0977122i
$220$	3.52196	−	9.95738i	0.237451	−	0.671326i
$221$	3.49352	−	10.7519i	0.235000	−	0.723254i
$222$		−	10.7447i		−	0.721134i
$223$		−	0.0313172i		−	0.00209715i	−0.999999	−	0.00104858i	$-0.999666\pi$
$223$		−	0.0313172i		−	0.00209715i	0.999999	−	0.00104858i	$-0.000333773\pi$
$224$	−0.797540	+	2.45458i	−0.0532879	+	0.164003i
$225$	3.88805	+	3.14374i	0.259203	+	0.209582i
$226$	−3.59782	−	11.0730i	−0.239323	−	0.736562i
$227$	2.37309	+	3.26628i	0.157508	+	0.216791i	0.880476	−	0.474090i	$-0.157223\pi$
$227$	2.37309	+	3.26628i	0.157508	+	0.216791i	−0.722969	+	0.690881i	$0.757223\pi$
$228$	−6.35428	−	2.06463i	−0.420822	−	0.136733i
$229$	6.24256	−	4.53548i	0.412520	−	0.299713i	−0.362101	−	0.932139i	$-0.617941\pi$
$229$	6.24256	−	4.53548i	0.412520	−	0.299713i	0.774621	+	0.632426i	$0.217941\pi$
$230$	−4.87491	+	13.7825i	−0.321442	+	0.908789i
$231$	3.76712	+	11.5940i	0.247858	+	0.762829i
$232$	−0.702997	+	0.967593i	−0.0461540	+	0.0635256i
$233$	7.89885	−	10.8718i	0.517471	−	0.712237i	−0.467686	−	0.883895i	$-0.654912\pi$
$233$	7.89885	−	10.8718i	0.517471	−	0.712237i	0.985157	+	0.171657i	$0.0549122\pi$
$234$	0.729847	+	2.24624i	0.0477116	+	0.146841i
$235$	−13.3748	−	4.73072i	−0.872476	−	0.308598i
$236$	0.441684	−	0.320902i	0.0287512	−	0.0208889i
$237$	−1.44472	−	0.469417i	−0.0938444	−	0.0304919i
$238$	7.26140	+	9.99446i	0.470687	+	0.647844i
$239$	−7.07964	−	21.7889i	−0.457944	−	1.40941i	−0.867644	−	0.497186i	$-0.834367\pi$
$239$	−7.07964	−	21.7889i	−0.457944	−	1.40941i	0.409700	−	0.912220i	$-0.365633\pi$
$240$	1.26720	+	1.84234i	0.0817975	+	0.118922i
$241$	4.73322	−	14.5673i	0.304893	−	0.938365i	−0.674824	−	0.737979i	$-0.735780\pi$
$241$	4.73322	−	14.5673i	0.304893	−	0.938365i	0.979717	−	0.200386i	$-0.0642197\pi$
$242$		−	11.3107i		−	0.727081i
$243$			1.00000i			0.0641500i
$244$	−2.58469	+	7.95485i	−0.165468	+	0.509257i
$245$	−0.252758	+	0.714603i	−0.0161481	+	0.0456543i
$246$	7.47249	−	5.42908i	0.476429	−	0.346146i
$247$		−	15.7801i		−	1.00406i
$248$	−5.54315	−	0.522964i	−0.351990	−	0.0332083i
$249$	4.38350			0.277793
$250$	−0.864874	+	11.1468i	−0.0546994	+	0.704988i
$251$	−15.7347	−	11.4319i	−0.993167	−	0.721578i	−0.0325546	−	0.999470i	$-0.510364\pi$
$251$	−15.7347	−	11.4319i	−0.993167	−	0.721578i	−0.960612	+	0.277892i	$0.910364\pi$
$252$	−2.45458	−	0.797540i	−0.154624	−	0.0502403i
$253$			30.8813i			1.94149i
$254$	0.930717			0.0583984
$255$	10.6997	+	0.276235i	0.670041	+	0.0172985i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−8.42873	+	2.73866i	−0.525770	+	0.170833i	−0.559862	−	0.828586i	$-0.689146\pi$
$257$	−8.42873	+	2.73866i	−0.525770	+	0.170833i	0.0340924	+	0.999419i	$0.489146\pi$
$258$	−4.00186	−	5.50809i	−0.249145	−	0.342918i
$259$	−8.56930	+	26.3736i	−0.532470	+	1.63877i
$260$	−3.21346	+	4.19106i	−0.199290	+	0.259919i
$261$	−0.967593	−	0.702997i	−0.0598925	−	0.0435145i
$262$	13.0857	−	4.25181i	0.808439	−	0.262678i
$263$	11.2827	−	15.5293i	0.695721	−	0.957577i	−0.304267	−	0.952587i	$-0.598412\pi$
$263$	11.2827	−	15.5293i	0.695721	−	0.957577i	0.999988	−	0.00499036i	$-0.00158849\pi$
$264$	3.82133	+	2.77636i	0.235187	+	0.170873i
$265$	−5.94031	−	8.63639i	−0.364910	−	0.530529i
$266$	13.9504	+	10.1356i	0.855356	+	0.621453i
$267$	3.93679	+	5.41853i	0.240928	+	0.331609i
$268$	−1.95726	−	0.635952i	−0.119559	−	0.0388469i
$269$	16.9032	−	12.2809i	1.03061	−	0.748781i	0.0621787	−	0.998065i	$-0.480195\pi$
$269$	16.9032	−	12.2809i	1.03061	−	0.748781i	0.968431	+	0.249284i	$0.0801951\pi$
$270$	−1.84234	+	1.26720i	−0.112121	+	0.0771195i
$271$	−0.395130	−	1.21608i	−0.0240024	−	0.0738718i	0.938338	−	0.345720i	$-0.112365\pi$
$271$	−0.395130	−	1.21608i	−0.0240024	−	0.0738718i	−0.962340	+	0.271848i	$0.912365\pi$
$272$	4.55237	+	1.47915i	0.276028	+	0.0896869i
$273$		−	6.09565i		−	0.368925i
$274$	−17.2256			−1.04063
$275$	6.12937	+	22.8079i	0.369615	+	1.37537i
$276$	−5.28928	−	3.84288i	−0.318377	−	0.231314i
$277$	−1.43907	−	1.98070i	−0.0864651	−	0.119009i	0.763593	−	0.645698i	$-0.223433\pi$
$277$	−1.43907	−	1.98070i	−0.0864651	−	0.119009i	−0.850058	+	0.526689i	$0.823433\pi$
$278$		−	16.0444i		−	0.962281i
$279$	0.522964	−	5.54315i	0.0313090	−	0.331860i
$280$	−1.64111	−	5.53280i	−0.0980750	−	0.330648i
$281$	−5.14599	+	3.73878i	−0.306984	+	0.223037i	−0.730601	−	0.682804i	$-0.760760\pi$
$281$	−5.14599	+	3.73878i	−0.306984	+	0.223037i	0.423617	+	0.905841i	$0.360760\pi$
$282$	3.72922	−	5.13283i	0.222072	−	0.305656i
$283$	28.6394	+	9.30552i	1.70244	+	0.553156i	0.989046	−	0.147610i	$-0.0471579\pi$
$283$	28.6394	+	9.30552i	1.70244	+	0.553156i	0.713392	+	0.700765i	$0.247158\pi$
$284$	4.60751			0.273405
$285$	14.3230	−	4.24841i	0.848422	−	0.251654i
$286$	−3.44738	+	10.6099i	−0.203848	+	0.627378i
$287$	−22.6717	+	7.36649i	−1.33827	+	0.434830i
$288$	−0.951057	+	0.309017i	−0.0560415	+	0.0182090i
$289$	4.78289	−	3.47497i	0.281347	−	0.204410i
$290$	0.0690212	−	2.67347i	0.00405307	−	0.156992i
$291$	0.252337	−	0.183334i	0.0147923	−	0.0107472i
$292$	1.44601	−	1.99026i	0.0846212	−	0.116471i
$293$	−6.86668	+	2.23112i	−0.401156	+	0.130343i	−0.502644	−	0.864493i	$-0.667639\pi$
$293$	−6.86668	+	2.23112i	−0.401156	+	0.130343i	0.101489	+	0.994837i	$0.467639\pi$
$294$	−0.274242	−	0.199249i	−0.0159941	−	0.0116204i
$295$	−0.407082	+	1.15091i	−0.0237012	+	0.0670087i
$296$	3.32028	+	10.2188i	0.192987	+	0.593954i
$297$	−2.77636	+	3.82133i	−0.161101	+	0.221736i
$298$	10.0477	+	13.8294i	0.582046	+	0.801118i
$299$	4.77167	−	14.6857i	0.275953	−	0.849295i
$300$	−4.66922	−	1.78840i	−0.269578	−	0.103253i
$301$	5.42995	+	16.7117i	0.312977	+	0.963244i
$302$	−10.4296	+	3.38879i	−0.600158	+	0.195003i
$303$	8.03150	+	2.60959i	0.461398	+	0.149917i
$304$	6.68128			0.383198
$305$	−5.31854	−	17.9308i	−0.304539	−	1.02672i
$306$	−1.47915	+	4.55237i	−0.0845577	+	0.260242i
$307$	−10.1356	+	13.9504i	−0.578467	+	0.796192i	−0.993526	−	0.113603i	$-0.963761\pi$
$307$	−10.1356	+	13.9504i	−0.578467	+	0.796192i	0.415059	+	0.909794i	$0.363761\pi$
$308$	−7.16549	−	9.86245i	−0.408292	−	0.561965i
$309$	−17.5798			−1.00008
$310$	10.8750	−	6.06082i	0.617661	−	0.344231i
$311$	−3.37273			−0.191250			−0.0956251	−	0.995417i	$-0.530485\pi$
$311$	−3.37273			−0.191250			−0.0956251	+	0.995417i	$0.530485\pi$
$312$	−1.38825	−	1.91076i	−0.0785943	−	0.108176i
$313$	−13.4561	+	18.5208i	−0.760586	+	1.04686i	0.236579	+	0.971612i	$0.423974\pi$
$313$	−13.4561	+	18.5208i	−0.760586	+	1.04686i	−0.997165	+	0.0752446i	$0.976026\pi$
$314$	2.54351	−	7.82811i	0.143538	−	0.441766i
$315$	5.53280	−	1.64111i	0.311738	−	0.0924660i
$316$	1.51906			0.0854540
$317$	7.08131	+	2.30086i	0.397726	+	0.129229i	0.501049	−	0.865419i	$-0.332948\pi$
$317$	7.08131	+	2.30086i	0.397726	+	0.129229i	−0.103323	+	0.994648i	$0.532948\pi$
$318$	4.45830	−	1.44859i	0.250009	−	0.0812329i
$319$	−1.74572	−	5.37277i	−0.0977415	−	0.300817i
$320$	−1.77449	−	1.36058i	−0.0991972	−	0.0760586i
$321$	4.89991	−	15.0804i	0.273486	−	0.841705i
$322$	9.91808	+	13.6511i	0.552713	+	0.760744i
$323$	18.7979	−	25.8731i	1.04594	−	1.43962i
$324$	−0.309017	−	0.951057i	−0.0171676	−	0.0528365i
$325$	0.609351	−	11.7934i	0.0338007	−	0.654182i
$326$	−14.2314	−	10.3397i	−0.788205	−	0.572664i
$327$	−7.90617	+	2.56887i	−0.437212	+	0.142059i
$328$	−5.42908	+	7.47249i	−0.299771	+	0.412599i
$329$	−13.2473	+	9.62472i	−0.730347	+	0.530628i
$330$	−10.5584	−	0.272587i	−0.581219	−	0.0150054i
$331$	−10.8643	+	7.89337i	−0.597156	+	0.433859i	−0.844868	−	0.534975i	$-0.820321\pi$
$331$	−10.8643	+	7.89337i	−0.597156	+	0.433859i	0.247712	+	0.968834i	$0.420321\pi$
$332$	−4.16896	+	1.35458i	−0.228801	+	0.0743421i
$333$	−10.2188	+	3.32028i	−0.559985	+	0.181950i
$334$	−1.22208	+	3.76118i	−0.0668694	+	0.205803i
$335$	4.41181	−	1.30861i	0.241043	−	0.0714968i
$336$	2.58089			0.140799
$337$	−19.4754	−	6.32794i	−1.06089	−	0.344705i	−0.273959	−	0.961741i	$-0.588333\pi$
$337$	−19.4754	−	6.32794i	−1.06089	−	0.344705i	−0.786935	+	0.617036i	$0.788333\pi$
$338$	−4.36239	+	6.00431i	−0.237283	+	0.326592i
$339$	−9.41922	+	6.84346i	−0.511582	+	0.371686i
$340$	−10.2614	+	3.04367i	−0.556502	+	0.165066i
$341$	17.3882	−	19.7303i	0.941623	−	1.06845i
$342$			6.68128i			0.361282i
$343$	11.1333	+	15.3237i	0.601143	+	0.827402i
$344$	5.50809	+	4.00186i	0.296976	+	0.215766i
$345$	14.6143	+	0.377299i	0.786809	+	0.0203131i
$346$	6.46804			0.347724
$347$		−	14.0742i		−	0.755543i	−0.925899	−	0.377771i	$-0.876691\pi$
$347$		−	14.0742i		−	0.755543i	0.925899	−	0.377771i	$-0.123309\pi$
$348$	1.13747	+	0.369588i	0.0609750	+	0.0198120i
$349$	4.52971	+	13.9410i	0.242470	+	0.746246i	0.996042	+	0.0888810i	$0.0283291\pi$
$349$	4.52971	+	13.9410i	0.242470	+	0.746246i	−0.753572	+	0.657365i	$0.771671\pi$
$350$	10.0346	+	8.11365i	0.536374	+	0.433693i
$351$	1.91076	−	1.38825i	0.101989	−	0.0740994i
$352$	−4.49224	−	1.45962i	−0.239437	−	0.0777979i
$353$	20.8076	+	28.6392i	1.10748	+	1.52431i	0.825082	+	0.565013i	$0.191129\pi$
$353$	20.8076	+	28.6392i	1.10748	+	1.52431i	0.282395	+	0.959298i	$0.408871\pi$
$354$	−0.441684	−	0.320902i	−0.0234752	−	0.0170558i
$355$	−8.48858	+	5.83865i	−0.450527	+	0.309883i
$356$	−5.41853	−	3.93679i	−0.287182	−	0.208650i
$357$	7.26140	−	9.99446i	0.384314	−	0.528963i
$358$	−17.9341	+	5.82714i	−0.947846	+	0.307974i
$359$	−11.4335	−	8.30692i	−0.603436	−	0.438422i	0.243661	−	0.969861i	$-0.421652\pi$
$359$	−11.4335	−	8.30692i	−0.603436	−	0.438422i	−0.847097	+	0.531438i	$0.821652\pi$
$360$	1.36058	−	1.77449i	0.0717088	−	0.0935240i
$361$	7.92305	−	24.3846i	0.417003	−	1.28340i
$362$	14.5344	+	20.0049i	0.763913	+	1.05144i
$363$	−10.7571	+	3.49520i	−0.564603	+	0.183451i
$364$	1.88366	+	5.79730i	0.0987305	+	0.303861i
$365$	−0.141971	+	5.49911i	−0.00743110	+	0.287837i
$366$	8.36422			0.437205
$367$			2.61152i			0.136320i	0.997674	+	0.0681601i	$0.0217129\pi$
$367$			2.61152i			0.136320i	−0.997674	+	0.0681601i	$0.978287\pi$
$368$	6.21792	+	2.02032i	0.324131	+	0.105317i
$369$	−7.47249	−	5.42908i	−0.389002	−	0.282627i
$370$	−19.0663	−	14.6189i	−0.991211	−	0.760003i
$371$	−12.0986			−0.628126
$372$	1.21556	+	5.43345i	0.0630238	+	0.281711i
$373$			35.3387i			1.82977i	0.403717	+	0.914884i	$0.367718\pi$
$373$			35.3387i			1.82977i	−0.403717	+	0.914884i	$0.632282\pi$
$374$	−18.2913	+	13.2894i	−0.945823	+	0.687181i
$375$	10.8685	−	2.62202i	0.561249	−	0.135400i
$376$	−1.96057	+	6.03400i	−0.101108	+	0.311180i
$377$			2.82478i			0.145484i
$378$			2.58089i			0.132747i
$379$	−1.89842	+	5.84275i	−0.0975154	+	0.300122i	−0.987901	−	0.155085i	$-0.950435\pi$
$379$	−1.89842	+	5.84275i	−0.0975154	+	0.300122i	0.890386	+	0.455207i	$0.150435\pi$
$380$	−12.3092	+	8.46653i	−0.631447	+	0.434324i
$381$	−0.287607	−	0.885164i	−0.0147346	−	0.0453483i
$382$	−0.774390	−	1.06586i	−0.0396212	−	0.0545339i
$383$	−14.2725	−	4.63740i	−0.729288	−	0.236960i	−0.0792426	−	0.996855i	$-0.525250\pi$
$383$	−14.2725	−	4.63740i	−0.729288	−	0.236960i	−0.650046	+	0.759895i	$0.725250\pi$
$384$	0.809017	−	0.587785i	0.0412850	−	0.0299953i
$385$	25.6989	+	9.08982i	1.30974	+	0.463260i
$386$	5.64913	+	17.3862i	0.287533	+	0.884936i
$387$	−4.00186	+	5.50809i	−0.203426	+	0.279992i
$388$	−0.183334	+	0.252337i	−0.00930737	+	0.0128105i
$389$	3.52848	+	10.8595i	0.178901	+	0.550600i	0.999790	−	0.0204871i	$-0.00652172\pi$
$389$	3.52848	+	10.8595i	0.178901	+	0.550600i	−0.820889	+	0.571087i	$0.806522\pi$
$390$	4.97895	+	1.76107i	0.252119	+	0.0891754i
$391$	25.3179	−	18.3945i	1.28038	−	0.930251i
$392$	0.322391	+	0.104751i	0.0162832	+	0.00529073i
$393$	−8.08743	−	11.1314i	−0.407957	−	0.561504i
$394$	2.67184	+	8.22309i	0.134606	+	0.414273i
$395$	−2.79863	+	1.92496i	−0.140814	+	0.0968553i
$396$	1.45962	−	4.49224i	0.0733486	−	0.225744i
$397$		−	30.6361i		−	1.53758i	−0.639500	−	0.768791i	$-0.720859\pi$
$397$		−	30.6361i		−	1.53758i	0.639500	−	0.768791i	$-0.279141\pi$
$398$		−	19.6727i		−	0.986105i
$399$	5.32859	−	16.3997i	0.266763	−	0.821013i
$400$	4.99334	+	0.257999i	0.249667	+	0.0128999i
$401$	9.78089	−	7.10624i	0.488435	−	0.354868i	−0.316147	−	0.948710i	$-0.602389\pi$
$401$	9.78089	−	7.10624i	0.488435	−	0.354868i	0.804582	+	0.593842i	$0.202389\pi$
$402$			2.05798i			0.102643i
$403$	−11.3177	+	6.69602i	−0.563773	+	0.333553i
$404$	−8.44482			−0.420145
$405$	1.77449	+	1.36058i	0.0881753	+	0.0676077i
$406$	−2.49726	−	1.81436i	−0.123937	−	0.0900453i
$407$	−48.2676	−	15.6831i	−2.39254	−	0.777382i
$408$		−	4.78665i		−	0.236974i
$409$	23.3901			1.15656			0.578282	−	0.815837i	$-0.303723\pi$
$409$	23.3901			1.15656			0.578282	+	0.815837i	$0.303723\pi$
$410$	0.533035	−	20.6466i	0.0263247	−	1.01966i
$411$	5.32299	+	16.3825i	0.262564	+	0.808088i
$412$	16.7194	−	5.43247i	0.823707	−	0.267639i
$413$	0.828215	+	1.13994i	0.0407538	+	0.0560928i
$414$	−2.02032	+	6.21792i	−0.0992935	+	0.305594i
$415$	5.96410	−	7.77850i	0.292766	−	0.381831i
$416$	1.91076	+	1.38825i	0.0936829	+	0.0680646i
$417$	−15.2592	+	4.95800i	−0.747245	+	0.242795i
$418$	−18.5496	+	25.5314i	−0.907292	+	1.24878i
$419$	24.6573	+	17.9146i	1.20459	+	0.875184i	0.994728	−	0.102547i	$-0.0326993\pi$
$419$	24.6573	+	17.9146i	1.20459	+	0.875184i	0.209860	+	0.977732i	$0.432699\pi$
$420$	−4.75487	+	3.27052i	−0.232014	+	0.159585i
$421$	−28.3785	−	20.6182i	−1.38308	−	1.00487i	−0.996585	−	0.0825786i	$-0.973684\pi$
$421$	−28.3785	−	20.6182i	−1.38308	−	1.00487i	−0.386499	−	0.922290i	$-0.626316\pi$
$422$	−15.3184	−	21.0839i	−0.745686	−	1.02635i
$423$	−6.03400	−	1.96057i	−0.293383	−	0.0953260i
$424$	−3.79246	+	2.75538i	−0.184178	+	0.133813i
$425$	15.0480	−	18.6107i	0.729933	−	0.902752i
$426$	−1.42380	−	4.38200i	−0.0689833	−	0.212309i
$427$	−20.5306	−	6.67081i	−0.993547	−	0.322823i
$428$			15.8564i			0.766450i
$429$	11.1559			0.538614
$430$	−15.2189	−	0.392908i	−0.733921	−	0.0189477i
$431$	−11.5441	−	8.38731i	−0.556061	−	0.404002i	0.273954	−	0.961743i	$-0.411668\pi$
$431$	−11.5441	−	8.38731i	−0.556061	−	0.404002i	−0.830015	+	0.557741i	$0.811668\pi$
$432$	0.587785	+	0.809017i	0.0282798	+	0.0389238i
$433$		−	34.1677i		−	1.64200i	−0.570930	−	0.820998i	$-0.693417\pi$
$433$		−	34.1677i		−	1.64200i	0.570930	−	0.820998i	$-0.306583\pi$
$434$	1.34972	−	14.3063i	0.0647884	−	0.686724i
$435$	−2.56395	+	0.760505i	−0.122932	+	0.0364634i
$436$	6.72539	−	4.88628i	0.322088	−	0.234010i
$437$	25.6754	−	35.3391i	1.22822	−	1.69050i
$438$	−2.33969	−	0.760212i	−0.111795	−	0.0363243i
$439$	32.3657			1.54473			0.772366	−	0.635177i	$-0.219073\pi$
$439$	32.3657			1.54473			0.772366	+	0.635177i	$0.219073\pi$
$440$	10.1258	−	3.00347i	0.482731	−	0.143185i
$441$	−0.104751	+	0.322391i	−0.00498815	+	0.0153520i
$442$	10.7519	−	3.49352i	0.511418	−	0.166170i
$443$	−11.7983	+	3.83352i	−0.560556	+	0.182136i	−0.575572	−	0.817751i	$-0.695220\pi$
$443$	−11.7983	+	3.83352i	−0.560556	+	0.182136i	0.0150151	+	0.999887i	$0.495220\pi$
$444$	8.69261	−	6.31555i	0.412533	−	0.299723i
$445$	14.9715	+	0.386520i	0.709716	+	0.0183228i
$446$	0.0253361	−	0.0184078i	0.00119970	−	0.000871634i
$447$	10.0477	−	13.8294i	0.475239	−	0.654110i
$448$	−2.45458	+	0.797540i	−0.115968	+	0.0376802i
$449$	−12.2629	−	8.90954i	−0.578723	−	0.420467i	0.259540	−	0.965732i	$-0.416429\pi$
$449$	−12.2629	−	8.90954i	−0.578723	−	0.420467i	−0.838264	+	0.545265i	$0.816429\pi$
$450$	−0.257999	+	4.99334i	−0.0121622	+	0.235388i
$451$	−13.4818	−	41.4926i	−0.634832	−	1.95381i
$452$	6.84346	−	9.41922i	0.321889	−	0.443043i
$453$	6.44587	+	8.87198i	0.302853	+	0.416842i
$454$	−1.24761	+	3.83974i	−0.0585532	+	0.180208i
$455$	−10.8167	−	8.29360i	−0.507094	−	0.388810i
$456$	−2.06463	−	6.35428i	−0.0966851	−	0.297566i
$457$	9.87094	−	3.20726i	0.461743	−	0.150029i	−0.0689022	−	0.997623i	$-0.521950\pi$
$457$	9.87094	−	3.20726i	0.461743	−	0.150029i	0.530645	+	0.847594i	$0.321950\pi$
$458$	7.33857	+	2.38444i	0.342909	+	0.111418i
$459$	4.78665			0.223421
$460$	−14.0156	+	4.15724i	−0.653483	+	0.193832i
$461$	−1.38404	+	4.25962i	−0.0644610	+	0.198391i	−0.978100	−	0.208136i	$-0.933260\pi$
$461$	−1.38404	+	4.25962i	−0.0644610	+	0.198391i	0.913639	+	0.406527i	$0.133260\pi$
$462$	−7.16549	+	9.86245i	−0.333369	+	0.458843i
$463$	−8.39051	−	11.5485i	−0.389940	−	0.536706i	0.568244	−	0.822860i	$-0.307623\pi$
$463$	−8.39051	−	11.5485i	−0.389940	−	0.536706i	−0.958184	+	0.286154i	$0.907623\pi$
$464$	−1.19601			−0.0555234
$465$	−9.12475	−	8.46988i	−0.423150	−	0.392781i
$466$	13.4383			0.622518
$467$	12.9340	+	17.8021i	0.598512	+	0.823781i	0.995571	−	0.0940118i	$-0.0299692\pi$
$467$	12.9340	+	17.8021i	0.598512	+	0.823781i	−0.397059	+	0.917793i	$0.629969\pi$
$468$	−1.38825	+	1.91076i	−0.0641719	+	0.0883251i
$469$	1.64132	−	5.05148i	0.0757893	−	0.233256i
$470$	−4.03428	−	13.6011i	−0.186087	−	0.627371i
$471$	−8.23097			−0.379263
$472$	0.519231	+	0.168708i	0.0238995	+	0.00776543i
$473$	−30.5848	+	9.93761i	−1.40629	+	0.456932i
$474$	−0.469417	−	1.44472i	−0.0215610	−	0.0663580i
$475$	11.9488	−	31.1964i	0.548248	−	1.43139i
$476$	−3.81754	+	11.7492i	−0.174977	+	0.538523i
$477$	−2.75538	−	3.79246i	−0.126160	−	0.173645i
$478$	13.4663	−	18.5347i	0.615933	−	0.847759i
$479$	−11.4455	−	35.2255i	−0.522956	−	1.60949i	−0.768322	−	0.640063i	$-0.778908\pi$
$479$	−11.4455	−	35.2255i	−0.522956	−	1.60949i	0.245366	−	0.969431i	$-0.421092\pi$
$480$	−0.745638	+	2.10809i	−0.0340336	+	0.0962205i
$481$	20.5305	+	14.9163i	0.936110	+	0.680124i
$482$	14.5673	−	4.73322i	0.663524	−	0.215592i
$483$	9.91808	−	13.6511i	0.451288	−	0.621145i
$484$	9.15057	−	6.64827i	0.415935	−	0.302194i
$485$	0.0180000	−	0.697211i	0.000817336	−	0.0316587i
$486$	−0.809017	+	0.587785i	−0.0366978	+	0.0266625i
$487$	−21.0923	+	6.85332i	−0.955785	+	0.310553i	−0.745064	−	0.666993i	$-0.767581\pi$
$487$	−21.0923	+	6.85332i	−0.955785	+	0.310553i	−0.210721	+	0.977546i	$0.567581\pi$
$488$	−7.95485	+	2.58469i	−0.360099	+	0.117003i
$489$	−5.43591	+	16.7300i	−0.245821	+	0.756558i
$490$	−0.726693	+	0.215548i	−0.0328287	+	0.00973745i
$491$	−12.0890			−0.545569			−0.272785	−	0.962075i	$-0.587945\pi$
$491$	−12.0890			−0.545569			−0.272785	+	0.962075i	$0.587945\pi$
$492$	8.78444	+	2.85424i	0.396033	+	0.128679i
$493$	−3.36500	+	4.63153i	−0.151552	+	0.208593i
$494$	12.7664	−	9.27530i	0.574385	−	0.417315i
$495$	3.00347	+	10.1258i	0.134996	+	0.455123i
$496$	−2.83509	−	4.79189i	−0.127300	−	0.215162i
$497$			11.8915i			0.533407i
$498$	2.57656	+	3.54633i	0.115458	+	0.158915i
$499$	−21.0780	−	15.3141i	−0.943582	−	0.685553i	0.00569787	−	0.999984i	$-0.498186\pi$
$499$	−21.0780	−	15.3141i	−0.943582	−	0.685553i	−0.949280	+	0.314431i	$0.898186\pi$
$500$	−9.52634	+	5.85225i	−0.426031	+	0.261721i
$501$	3.95474			0.176685
$502$		−	19.4492i		−	0.868060i
$503$	31.0521	+	10.0895i	1.38455	+	0.449866i	0.904161	−	0.427191i	$-0.140497\pi$
$503$	31.0521	+	10.0895i	1.38455	+	0.449866i	0.480385	+	0.877058i	$0.340497\pi$
$504$	−0.797540	−	2.45458i	−0.0355253	−	0.109336i
$505$	15.5582	−	10.7013i	0.692330	−	0.476201i
$506$	−24.9835	+	18.1516i	−1.11065	+	0.806936i
$507$	7.05849	+	2.29344i	0.313479	+	0.101855i
$508$	0.547061	+	0.752966i	0.0242719	+	0.0334074i
$509$	−20.0283	−	14.5514i	−0.887737	−	0.644979i	0.0475501	−	0.998869i	$-0.484859\pi$
$509$	−20.0283	−	14.5514i	−0.887737	−	0.644979i	−0.935287	+	0.353890i	$0.884859\pi$
$510$	6.06565	+	8.81861i	0.268591	+	0.390494i
$511$	5.13665	+	3.73200i	0.227232	+	0.165094i
$512$	−0.587785	+	0.809017i	−0.0259767	+	0.0357538i
$513$	6.35428	−	2.06463i	0.280548	−	0.0911556i
$514$	−7.16991	−	5.20924i	−0.316251	−	0.229770i
$515$	−23.9187	+	31.1953i	−1.05399	+	1.37463i
$516$	2.10390	−	6.47514i	0.0926191	−	0.285052i
$517$	−17.6147	−	24.2445i	−0.774693	−	1.06627i
$518$	−26.3736	+	8.56930i	−1.15879	+	0.376513i
$519$	−1.99873	−	6.15147i	−0.0877346	−	0.270019i
$520$	−5.27946	−	0.136300i	−0.231520	−	0.00597717i
$521$	16.1805			0.708880			0.354440	−	0.935079i	$-0.384672\pi$
$521$	16.1805			0.708880			0.354440	+	0.935079i	$0.384672\pi$
$522$		−	1.19601i		−	0.0523480i
$523$	−6.47453	−	2.10370i	−0.283111	−	0.0919884i	0.164019	−	0.986457i	$-0.447554\pi$
$523$	−6.47453	−	2.10370i	−0.283111	−	0.0919884i	−0.447131	+	0.894469i	$0.647554\pi$
$524$	11.1314	+	8.08743i	0.486277	+	0.353301i
$525$	4.61567	−	12.0508i	0.201444	−	0.525939i
$526$	19.1953			0.836953
$527$	−26.5331	−	2.50324i	−1.15580	−	0.109043i
$528$			4.72342i			0.205561i
$529$	15.9734	−	11.6054i	0.694495	−	0.504580i
$530$	3.49536	−	9.88215i	0.151829	−	0.429253i
$531$	−0.168708	+	0.519231i	−0.00732131	+	0.0225327i
$532$			17.2437i			0.747609i
$533$			21.8151i			0.944917i
$534$	−2.06970	+	6.36987i	−0.0895645	+	0.275651i
$535$	−20.0933	−	29.2129i	−0.868710	−	1.26298i
$536$	−0.635952	−	1.95726i	−0.0274689	−	0.0845407i
$537$	11.0839	+	15.2556i	0.478305	+	0.658330i
$538$	19.8710	+	6.45647i	0.856698	+	0.278358i
$539$	−1.29536	+	0.941135i	−0.0557952	+	0.0405376i
$540$	−2.10809	−	0.745638i	−0.0907176	−	0.0320871i
$541$	6.08359	+	18.7234i	0.261554	+	0.804980i	0.992467	+	0.122510i	$0.0390944\pi$
$541$	6.08359	+	18.7234i	0.261554	+	0.804980i	−0.730913	+	0.682470i	$0.760906\pi$
$542$	0.751581	−	1.03446i	0.0322832	−	0.0444340i
$543$	14.5344	−	20.0049i	0.623732	−	0.858494i
$544$	1.47915	+	4.55237i	0.0634182	+	0.195181i
$545$	−6.19852	+	17.5246i	−0.265515	+	0.750671i
$546$	4.93148	−	3.58293i	0.211048	−	0.153335i
$547$	−23.8727	−	7.75670i	−1.02072	−	0.331653i	−0.249606	−	0.968347i	$-0.580301\pi$
$547$	−23.8727	−	7.75670i	−1.02072	−	0.331653i	−0.771116	+	0.636695i	$0.780301\pi$
$548$	−10.1249	−	13.9358i	−0.432516	−	0.595307i
$549$	−2.58469	−	7.95485i	−0.110312	−	0.339505i
$550$	−14.8492	+	18.3649i	−0.633172	+	0.783082i
$551$	−2.46932	+	7.59978i	−0.105197	+	0.323762i
$552$		−	6.53791i		−	0.278272i
$553$			3.92054i			0.166719i
$554$	0.756562	−	2.32846i	0.0321432	−	0.0989267i
$555$	−8.01162	+	22.6506i	−0.340074	+	0.961467i
$556$	12.9802	−	9.43068i	0.550484	−	0.399950i
$557$			25.7915i			1.09282i	0.837517	+	0.546411i	$0.184006\pi$
$557$			25.7915i			1.09282i	−0.837517	+	0.546411i	$0.815994\pi$
$558$	4.79189	−	2.83509i	0.202857	−	0.120019i
$559$	16.0802			0.680122
$560$	3.51151	−	4.57978i	0.148388	−	0.193531i
$561$	18.2913	+	13.2894i	0.772261	+	0.561081i
$562$	−6.04947	−	1.96559i	−0.255181	−	0.0829135i
$563$		−	37.7464i		−	1.59082i	−0.606070	−	0.795411i	$-0.707255\pi$
$563$		−	37.7464i		−	1.59082i	0.606070	−	0.795411i	$-0.292745\pi$
$564$	6.34453			0.267153
$565$	−0.671900	+	26.0254i	−0.0282670	+	1.09490i
$566$	9.30552	+	28.6394i	0.391140	+	1.20381i
$567$	2.45458	−	0.797540i	0.103083	−	0.0334935i
$568$	2.70823	+	3.72755i	0.113635	+	0.156405i
$569$	−0.0716261	+	0.220442i	−0.00300272	+	0.00924143i	−0.952547	−	0.304393i	$-0.901547\pi$
$569$	−0.0716261	+	0.220442i	−0.00300272	+	0.00924143i	0.949544	+	0.313634i	$0.101547\pi$
$570$	11.8559	+	9.09041i	0.496589	+	0.380755i
$571$	−18.0318	−	13.1009i	−0.754607	−	0.548254i	0.142644	−	0.989774i	$-0.454440\pi$
$571$	−18.0318	−	13.1009i	−0.754607	−	0.548254i	−0.897252	+	0.441520i	$0.854440\pi$
$572$	−10.6099	+	3.44738i	−0.443624	+	0.144142i
$573$	−0.774390	+	1.06586i	−0.0323506	+	0.0445268i
$574$	−19.2857	−	14.0119i	−0.804970	−	0.584845i
$575$	20.5535	−	25.4197i	0.857138	−	1.06007i
$576$	−0.809017	−	0.587785i	−0.0337090	−	0.0244911i
$577$	5.36258	+	7.38095i	0.223247	+	0.307273i	0.905918	−	0.423452i	$-0.139182\pi$
$577$	5.36258	+	7.38095i	0.223247	+	0.307273i	−0.682671	+	0.730726i	$0.739182\pi$
$578$	5.62263	+	1.82690i	0.233870	+	0.0759891i
$579$	14.7896	−	10.7453i	0.614635	−	0.446559i
$580$	2.20345	−	1.51559i	0.0914934	−	0.0629313i
$581$	−3.49602	−	10.7596i	−0.145039	−	0.446385i
$582$	0.296640	+	0.0963843i	0.0122961	+	0.00399526i
$583$		−	22.1422i		−	0.917035i
$584$	2.46010			0.101800
$585$	0.136300	−	5.27946i	0.00563533	−	0.218279i
$586$	−5.84114	−	4.24384i	−0.241295	−	0.175311i
$587$	−16.0876	−	22.1427i	−0.664008	−	0.913929i	0.335598	−	0.942005i	$-0.391062\pi$
$587$	−16.0876	−	22.1427i	−0.664008	−	0.913929i	−0.999606	+	0.0280766i	$0.991062\pi$
$588$		−	0.338982i		−	0.0139794i
$589$	−36.3024	+	8.12149i	−1.49582	+	0.334640i
$590$	−1.17038	+	0.347153i	−0.0481840	+	0.0142921i
$591$	6.99498	−	5.08215i	0.287735	−	0.209052i
$592$	−6.31555	+	8.69261i	−0.259567	+	0.357264i
$593$	−19.0563	−	6.19177i	−0.782549	−	0.254265i	−0.109621	−	0.993973i	$-0.534964\pi$
$593$	−19.0563	−	6.19177i	−0.782549	−	0.254265i	−0.672928	+	0.739708i	$0.734964\pi$
$594$	−4.72342			−0.193804
$595$	−7.85540	−	26.4835i	−0.322040	−	1.08572i
$596$	−5.28237	+	16.2575i	−0.216374	+	0.665932i
$597$	−18.7099	+	6.07921i	−0.765744	+	0.248805i
$598$	14.6857	−	4.77167i	0.600543	−	0.195128i
$599$	−0.997548	+	0.724761i	−0.0407587	+	0.0296129i	−0.607978	−	0.793954i	$-0.708019\pi$
$599$	−0.997548	+	0.724761i	−0.0407587	+	0.0296129i	0.567219	+	0.823567i	$0.308019\pi$
$600$	−1.29766	−	4.82867i	−0.0529765	−	0.197130i
$601$	19.8089	−	14.3920i	0.808024	−	0.587064i	−0.105233	−	0.994448i	$-0.533559\pi$
$601$	19.8089	−	14.3920i	0.808024	−	0.587064i	0.913257	+	0.407384i	$0.133559\pi$
$602$	−10.3284	+	14.2158i	−0.420953	+	0.579392i
$603$	1.95726	−	0.635952i	0.0797057	−	0.0258980i
$604$	−8.87198	−	6.44587i	−0.360996	−	0.262279i
$605$	−8.43370	+	23.8440i	−0.342879	+	0.969395i
$606$	2.60959	+	8.03150i	0.106007	+	0.326257i
$607$	−0.920054	+	1.26635i	−0.0373438	+	0.0513994i	−0.827281	−	0.561789i	$-0.810113\pi$
$607$	−0.920054	+	1.26635i	−0.0373438	+	0.0513994i	0.789937	+	0.613188i	$0.210113\pi$
$608$	3.92716	+	5.40527i	0.159267	+	0.219213i
$609$	−0.953867	+	2.93570i	−0.0386526	+	0.118961i
$610$	11.3802	−	14.8423i	0.460770	−	0.600946i
$611$	4.63053	+	14.2513i	0.187331	+	0.576546i
$612$	−4.55237	+	1.47915i	−0.184019	+	0.0597913i
$613$	42.1444	+	13.6936i	1.70220	+	0.553077i	0.989004	−	0.147890i	$-0.0472482\pi$
$613$	42.1444	+	13.6936i	1.70220	+	0.553077i	0.713193	+	0.700967i	$0.247248\pi$
$614$	−17.2436			−0.695897
$615$	−19.8008	+	5.87320i	−0.798445	+	0.236830i
$616$	3.76712	−	11.5940i	0.151782	−	0.467136i
$617$	−0.295524	+	0.406755i	−0.0118974	+	0.0163753i	−0.814924	−	0.579567i	$-0.803222\pi$
$617$	−0.295524	+	0.406755i	−0.0118974	+	0.0163753i	0.803027	+	0.595943i	$0.203222\pi$
$618$	−10.3332	−	14.2224i	−0.415661	−	0.572109i
$619$	17.6026			0.707507			0.353753	−	0.935339i	$-0.384905\pi$
$619$	17.6026			0.707507			0.353753	+	0.935339i	$0.384905\pi$
$620$	11.2955	+	5.23564i	0.453638	+	0.210268i
$621$	6.53791			0.262357
$622$	−1.98244	−	2.72860i	−0.0794888	−	0.109407i
$623$	10.1605	−	13.9847i	0.407070	−	0.560284i
$624$	0.729847	−	2.24624i	0.0292173	−	0.0899215i
$625$	10.1347	−	22.8536i	0.405389	−	0.914144i
$626$	−22.8930			−0.914986
$627$	30.0139	+	9.75212i	1.19864	+	0.389462i
$628$	7.82811	−	2.54351i	0.312376	−	0.101497i
$629$	15.8930	+	48.9137i	0.633696	+	1.95031i
$630$	4.57978	+	3.51151i	0.182463	+	0.139902i
$631$	−4.97131	+	15.3001i	−0.197905	+	0.609089i	0.802025	+	0.597290i	$0.203756\pi$
$631$	−4.97131	+	15.3001i	−0.197905	+	0.609089i	−0.999930	+	0.0117989i	$0.996244\pi$
$632$	0.892883	+	1.22895i	0.0355170	+	0.0488850i
$633$	−15.3184	+	21.0839i	−0.608850	+	0.838010i
$634$	2.30086	+	7.08131i	0.0913787	+	0.281235i
$635$	−1.96203	−	0.693978i	−0.0778608	−	0.0275397i
$636$	3.79246	+	2.75538i	0.150381	+	0.109258i
$637$	0.761434	−	0.247405i	0.0301691	−	0.00980254i
$638$	3.32055	−	4.57035i	0.131462	−	0.180942i
$639$	−3.72755	+	2.70823i	−0.147460	+	0.107136i
$640$	0.0577095	−	2.23532i	0.00228117	−	0.0883589i
$641$	−35.0483	+	25.4641i	−1.38433	+	1.00577i	−0.387865	+	0.921716i	$0.626787\pi$
$641$	−35.0483	+	25.4641i	−1.38433	+	1.00577i	−0.996461	+	0.0840550i	$0.973213\pi$
$642$	15.0804	−	4.89991i	0.595175	−	0.193384i
$643$	21.0864	−	6.85138i	0.831565	−	0.270192i	0.137861	−	0.990452i	$-0.455977\pi$
$643$	21.0864	−	6.85138i	0.831565	−	0.270192i	0.693704	+	0.720260i	$0.255977\pi$
$644$	−5.21424	+	16.0478i	−0.205470	+	0.632372i
$645$	4.32922	+	14.5955i	0.170463	+	0.574695i
$646$	31.9809			1.25827
$647$	23.1371	+	7.51771i	0.909614	+	0.295552i	0.726200	−	0.687484i	$-0.241285\pi$
$647$	23.1371	+	7.51771i	0.909614	+	0.295552i	0.183415	+	0.983036i	$0.441285\pi$
$648$	0.587785	−	0.809017i	0.0230904	−	0.0317812i
$649$	−2.08626	+	1.51576i	−0.0818929	+	0.0594986i
$650$	9.89926	−	6.43904i	0.388281	−	0.252560i
$651$	−14.0232	+	3.13723i	−0.549611	+	0.122958i
$652$		−	17.5910i		−	0.688916i
$653$	−8.71593	−	11.9964i	−0.341081	−	0.469457i	0.603676	−	0.797230i	$-0.293702\pi$
$653$	−8.71593	−	11.9964i	−0.341081	−	0.469457i	−0.944757	+	0.327773i	$0.893702\pi$
$654$	−6.72539	−	4.88628i	−0.262984	−	0.191069i
$655$	−30.7562	−	0.794034i	−1.20174	−	0.0310255i
$656$	−9.23651			−0.360625
$657$			2.46010i			0.0959775i
$658$	−15.5731	−	5.06002i	−0.607104	−	0.197260i
$659$	0.350908	+	1.07998i	0.0136694	+	0.0420702i	0.957659	−	0.287906i	$-0.0929592\pi$
$659$	0.350908	+	1.07998i	0.0136694	+	0.0420702i	−0.943989	+	0.329977i	$0.892959\pi$
$660$	−5.98553	−	8.70213i	−0.232986	−	0.338730i
$661$	−27.4102	+	19.9147i	−1.06613	+	0.774591i	−0.975213	−	0.221267i	$-0.928981\pi$
$661$	−27.4102	+	19.9147i	−1.06613	+	0.774591i	−0.0909196	+	0.995858i	$0.528981\pi$
$662$	−12.7717	−	4.14979i	−0.496388	−	0.161286i
$663$	−6.64507	−	9.14615i	−0.258073	−	0.355207i
$664$	−3.54633	−	2.57656i	−0.137624	−	0.0999899i
$665$	−21.8512	−	31.7687i	−0.847354	−	1.23194i
$666$	−8.69261	−	6.31555i	−0.336832	−	0.244723i
$667$	−4.59613	+	6.32603i	−0.177963	+	0.244945i
$668$	−3.76118	+	1.22208i	−0.145525	+	0.0472838i
$669$	−0.0253361	−	0.0184078i	−0.000979552	−	0.000711686i
$670$	3.65188	+	2.80005i	0.141084	+	0.108175i
$671$	12.2086	−	37.5741i	0.471307	−	1.45053i
$672$	1.51701	+	2.08799i	0.0585200	+	0.0805459i
$673$	23.5751	−	7.66000i	0.908752	−	0.295271i	0.182907	−	0.983130i	$-0.441449\pi$
$673$	23.5751	−	7.66000i	0.908752	−	0.295271i	0.725845	+	0.687859i	$0.241449\pi$
$674$	−6.32794	−	19.4754i	−0.243743	−	0.750165i
$675$	4.82867	−	1.29766i	0.185856	−	0.0499468i
$676$	−7.42174			−0.285451
$677$			1.28613i			0.0494298i	0.999695	+	0.0247149i	$0.00786780\pi$
$677$			1.28613i			0.0494298i	−0.999695	+	0.0247149i	$0.992132\pi$
$678$	−11.0730	−	3.59782i	−0.425254	−	0.138173i
$679$	−0.651256	−	0.473165i	−0.0249929	−	0.0181584i
$680$	−8.49387	−	6.51260i	−0.325725	−	0.249747i
$681$	4.03734			0.154711
$682$	26.1826	+	2.47018i	1.00259	+	0.0945881i
$683$			17.4039i			0.665940i	0.942937	+	0.332970i	$0.108051\pi$
$683$			17.4039i			0.665940i	−0.942937	+	0.332970i	$0.891949\pi$
$684$	−5.40527	+	3.92716i	−0.206676	+	0.150159i
$685$	36.3130	+	12.8440i	1.38745	+	0.490745i
$686$	−5.85313	+	18.0141i	−0.223474	+	0.687781i
$687$		−	7.71623i		−	0.294392i
$688$			6.80837i			0.259567i
$689$	−3.42133	+	10.5298i	−0.130342	+	0.401153i
$690$	8.28485	+	12.0450i	0.315399	+	0.458546i
$691$	14.6566	+	45.1083i	0.557562	+	1.71600i	0.689080	+	0.724685i	$0.258015\pi$
$691$	14.6566	+	45.1083i	0.557562	+	1.71600i	−0.131518	+	0.991314i	$0.541985\pi$
$692$	3.80182	+	5.23275i	0.144523	+	0.198919i
$693$	11.5940	+	3.76712i	0.440420	+	0.143101i
$694$	11.3863	−	8.27261i	0.432217	−	0.314024i
$695$	−11.9633	+	33.8230i	−0.453795	+	1.28298i
$696$	0.369588	+	1.13747i	0.0140092	+	0.0431158i
$697$	−25.9871	+	35.7682i	−0.984332	+	1.35482i
$698$	−8.61603	+	11.8589i	−0.326122	+	0.448868i
$699$	−4.15267	−	12.7806i	−0.157068	−	0.483407i
$700$	−0.665868	+	12.8873i	−0.0251674	+	0.487094i
$701$	2.29060	−	1.66422i	0.0865148	−	0.0628567i	−0.543687	−	0.839288i	$-0.682972\pi$
$701$	2.29060	−	1.66422i	0.0865148	−	0.0628567i	0.630202	+	0.776431i	$0.282972\pi$
$702$	2.24624	+	0.729847i	0.0847788	+	0.0275463i
$703$	42.1960	+	58.0778i	1.59145	+	2.19044i
$704$	−1.45962	−	4.49224i	−0.0550114	−	0.169308i
$705$	−11.6887	+	8.03980i	−0.440224	+	0.302796i
$706$	−10.9392	+	33.6674i	−0.411702	+	1.26709i
$707$		−	21.7952i		−	0.819692i
$708$		−	0.545951i		−	0.0205181i
$709$	5.35699	−	16.4871i	0.201186	−	0.619187i	−0.798663	−	0.601779i	$-0.794459\pi$
$709$	5.35699	−	16.4871i	0.201186	−	0.619187i	0.999848	−	0.0174075i	$-0.00554127\pi$
$710$	−9.71303	−	3.43553i	−0.364523	−	0.128933i
$711$	−1.22895	+	0.892883i	−0.0460892	+	0.0334857i
$712$		−	6.69767i		−	0.251006i
$713$	−36.2406	−	3.41909i	−1.35722	−	0.128046i
$714$	12.3538			0.462330
$715$	15.1785	−	19.7961i	0.567645	−	0.740334i
$716$	−15.2556	−	11.0839i	−0.570130	−	0.414224i
$717$	−21.7889	−	7.07964i	−0.813721	−	0.264394i
$718$		−	14.1326i		−	0.527423i
$719$	−51.6995			−1.92806			−0.964032	−	0.265786i	$-0.914369\pi$
$719$	−51.6995			−1.92806			−0.964032	+	0.265786i	$0.914369\pi$
$720$	2.23532	+	0.0577095i	0.0833056	+	0.00215071i
$721$	14.0206	+	43.1511i	0.522156	+	1.60703i
$722$	24.3846	−	7.92305i	0.907502	−	0.294865i
$723$	−9.00312	−	12.3917i	−0.334829	−	0.460853i
$724$	−7.64120	+	23.5172i	−0.283983	+	0.874010i
$725$	−2.13894	+	5.58444i	−0.0794384	+	0.207401i
$726$	−9.15057	−	6.64827i	−0.339609	−	0.246741i
$727$	9.64086	−	3.13251i	0.357560	−	0.116178i	−0.124728	−	0.992191i	$-0.539806\pi$
$727$	9.64086	−	3.13251i	0.357560	−	0.116178i	0.482288	+	0.876013i	$0.339806\pi$
$728$	−3.58293	+	4.93148i	−0.132792	+	0.182773i
$729$	0.809017	+	0.587785i	0.0299636	+	0.0217698i
$730$	−4.53232	+	3.11744i	−0.167749	+	0.115382i
$731$	26.3653	+	19.1555i	0.975154	+	0.708491i
$732$	4.91637	+	6.76680i	0.181714	+	0.250108i
$733$	10.3555	+	3.36470i	0.382488	+	0.124278i	0.493949	−	0.869491i	$-0.335553\pi$
$733$	10.3555	+	3.36470i	0.382488	+	0.124278i	−0.111461	+	0.993769i	$0.535553\pi$
$734$	−2.11276	+	1.53501i	−0.0779835	+	0.0566583i
$735$	0.429559	+	0.624518i	0.0158445	+	0.0230357i
$736$	2.02032	+	6.21792i	0.0744701	+	0.229195i
$737$	9.24496	+	3.00387i	0.340542	+	0.110649i
$738$		−	9.23651i		−	0.340001i
$739$	−16.0600			−0.590777			−0.295388	−	0.955377i	$-0.595449\pi$
$739$	−16.0600			−0.590777			−0.295388	+	0.955377i	$0.595449\pi$
$740$	0.620069	−	24.0178i	0.0227942	−	0.882911i
$741$	−12.7664	−	9.27530i	−0.468984	−	0.340737i
$742$	−7.11136	−	9.78794i	−0.261066	−	0.359327i
$743$		−	21.0236i		−	0.771282i	−0.922649	−	0.385641i	$-0.873980\pi$
$743$		−	21.0236i		−	0.771282i	0.922649	−	0.385641i	$-0.126020\pi$
$744$	−3.68127	+	4.17711i	−0.134962	+	0.153140i
$745$	−10.8696	−	36.6456i	−0.398231	−	1.34259i
$746$	−28.5896	+	20.7716i	−1.04674	+	0.760501i
$747$	2.57656	−	3.54633i	0.0942713	−	0.129753i
$748$	−21.5028	−	6.98667i	−0.786219	−	0.255458i
$749$	−40.9238			−1.49532
$750$	8.50962	+	7.25164i	0.310727	+	0.264793i
$751$	2.74280	−	8.44148i	0.100086	−	0.308034i	−0.888460	−	0.458955i	$-0.848224\pi$
$751$	2.74280	−	8.44148i	0.100086	−	0.308034i	0.988546	+	0.150921i	$0.0482239\pi$
$752$	−6.03400	+	1.96057i	−0.220037	+	0.0714945i
$753$	−18.4973	+	6.01013i	−0.674078	+	0.219021i
$754$	−2.28529	+	1.66036i	−0.0832255	+	0.0604669i
$755$	24.5134	+	0.632864i	0.892133	+	0.0230323i
$756$	−2.08799	+	1.51701i	−0.0759394	+	0.0551732i
$757$	11.0741	−	15.2422i	0.402496	−	0.553988i	−0.558872	−	0.829254i	$-0.688766\pi$
$757$	11.0741	−	15.2422i	0.402496	−	0.553988i	0.961368	+	0.275266i	$0.0887659\pi$
$758$	−5.84275	+	1.89842i	−0.212218	+	0.0689538i
$759$	24.9835	+	18.1516i	0.906843	+	0.658860i
$760$	−14.0847	−	4.98182i	−0.510906	−	0.180709i
$761$	−0.621323	−	1.91224i	−0.0225229	−	0.0693185i	0.939163	−	0.343471i	$-0.111603\pi$
$761$	−0.621323	−	1.91224i	−0.0225229	−	0.0693185i	−0.961686	+	0.274152i	$0.911603\pi$
$762$	0.547061	−	0.752966i	0.0198179	−	0.0272771i
$763$	12.6110	+	17.3575i	0.456548	+	0.628385i
$764$	0.407121	−	1.25299i	0.0147291	−	0.0453316i
$765$	6.51260	−	8.49387i	0.235464	−	0.307097i
$766$	−4.63740	−	14.2725i	−0.167556	−	0.515685i
$767$	1.22634	−	0.398461i	0.0442804	−	0.0143876i
$768$	0.951057	+	0.309017i	0.0343183	+	0.0111507i
$769$	26.9351			0.971304			0.485652	−	0.874152i	$-0.338582\pi$
$769$	26.9351			0.971304			0.485652	+	0.874152i	$0.338582\pi$
$770$	7.75165	+	26.1337i	0.279350	+	0.941795i
$771$	−2.73866	+	8.42873i	−0.0986305	+	0.303553i
$772$	−10.7453	+	14.7896i	−0.386731	+	0.532290i
$773$	−19.8009	−	27.2537i	−0.712190	−	0.980246i	−0.999747	−	0.0224825i	$-0.992843\pi$
$773$	−19.8009	−	27.2537i	−0.712190	−	0.980246i	0.287557	−	0.957764i	$-0.407157\pi$
$774$	−6.80837			−0.244722
$775$	−27.4447	+	4.66787i	−0.985842	+	0.167675i
$776$	−0.311906			−0.0111968
$777$	16.2998	+	22.4347i	0.584751	+	0.804841i
$778$	−6.71156	+	9.23767i	−0.240621	+	0.331187i
$779$	−19.0700	+	58.6913i	−0.683253	+	2.10284i
$780$	1.50181	+	5.06319i	0.0537736	+	0.181291i
$781$	−21.7632			−0.778749
$782$	29.7630	+	9.67057i	1.06432	+	0.345819i
$783$	−1.13747	+	0.369588i	−0.0406500	+	0.0132080i
$784$	0.104751	+	0.322391i	0.00374111	+	0.0115140i
$785$	−11.1989	+	14.6058i	−0.399705	+	0.521303i
$786$	4.25181	−	13.0857i	0.151657	−	0.466753i
$787$	4.91017	+	6.75827i	0.175029	+	0.240906i	0.887514	−	0.460781i	$-0.152430\pi$
$787$	4.91017	+	6.75827i	0.175029	+	0.240906i	−0.712485	+	0.701687i	$0.752430\pi$
$788$	−5.08215	+	6.99498i	−0.181044	+	0.249186i
$789$	−5.93166	−	18.2558i	−0.211173	−	0.649923i
$790$	−3.20232	−	1.13267i	−0.113933	−	0.0402986i
$791$	24.3100	+	17.6623i	0.864364	+	0.627997i
$792$	4.49224	−	1.45962i	0.159625	−	0.0518653i
$793$	−11.6116	+	15.9821i	−0.412342	+	0.567540i
$794$	24.7851	−	18.0074i	0.879591	−	0.639060i
$795$	−10.4786	−	0.270527i	−0.371638	−	0.00959461i
$796$	15.9156	−	11.5633i	0.564112	−	0.409852i
$797$	49.1783	−	15.9790i	1.74199	−	0.566006i	0.746893	−	0.664944i	$-0.231545\pi$
$797$	49.1783	−	15.9790i	1.74199	−	0.566006i	0.995094	+	0.0989386i	$0.0315448\pi$
$798$	16.3997	−	5.32859i	0.580544	−	0.188630i
$799$	−9.38454	+	28.8826i	−0.332001	+	1.02179i
$800$	2.72629	+	4.19134i	0.0963888	+	0.148186i
$801$	6.69767			0.236651
$802$	11.4981	+	3.73597i	0.406013	+	0.131922i
$803$	−6.83011	+	9.40084i	−0.241029	+	0.331748i
$804$	−1.66494	+	1.20965i	−0.0587180	+	0.0426611i
$805$	−10.7294	−	36.1729i	−0.378162	−	1.27493i
$806$	−12.0695	−	5.22035i	−0.425132	−	0.183879i
$807$		−	20.8936i		−	0.735488i
$808$	−4.96374	−	6.83200i	−0.174624	−	0.240349i
$809$	6.08090	+	4.41803i	0.213793	+	0.155330i	0.689528	−	0.724259i	$-0.257818\pi$
$809$	6.08090	+	4.41803i	0.213793	+	0.155330i	−0.475735	+	0.879589i	$0.657818\pi$
$810$	−0.0577095	+	2.23532i	−0.00202771	+	0.0785412i
$811$	−48.3178			−1.69667			−0.848334	−	0.529462i	$-0.822394\pi$
$811$	−48.3178			−1.69667			−0.848334	+	0.529462i	$0.822394\pi$
$812$		−	3.08678i		−	0.108325i
$813$	−1.21608	−	0.395130i	−0.0426499	−	0.0138578i
$814$	−15.6831	−	48.2676i	−0.549692	−	1.69178i
$815$	22.2913	+	32.4085i	0.780831	+	1.13522i
$816$	3.87248	−	2.81352i	0.135564	−	0.0984929i
$817$	43.2623	+	14.0568i	1.51355	+	0.491784i
$818$	13.7483	+	18.9230i	0.480699	+	0.661626i
$819$	−4.93148	−	3.58293i	−0.172320	−	0.125198i
$820$	17.0167	−	11.7045i	0.594251	−	0.408740i
$821$	−29.8972	−	21.7216i	−1.04342	−	0.758088i	−0.0724688	−	0.997371i	$-0.523088\pi$
$821$	−29.8972	−	21.7216i	−1.04342	−	0.758088i	−0.970950	+	0.239283i	$0.923088\pi$
$822$	−10.1249	+	13.9358i	−0.353148	+	0.486066i
$823$	−37.2457	+	12.1019i	−1.29831	+	0.421845i	−0.874991	−	0.484138i	$-0.839133\pi$
$823$	−37.2457	+	12.1019i	−1.29831	+	0.421845i	−0.423314	+	0.905983i	$0.639133\pi$
$824$	14.2224	+	10.3332i	0.495461	+	0.359973i
$825$	22.0547	+	8.44736i	0.767846	+	0.294099i
$826$	−0.435418	+	1.34008i	−0.0151501	+	0.0466273i
$827$	−3.58003	−	4.92748i	−0.124490	−	0.171345i	0.742223	−	0.670153i	$-0.233771\pi$
$827$	−3.58003	−	4.92748i	−0.124490	−	0.171345i	−0.866713	+	0.498807i	$0.833771\pi$
$828$	−6.21792	+	2.02032i	−0.216088	+	0.0702111i
$829$	−5.85600	−	18.0229i	−0.203387	−	0.625962i	−0.999776	−	0.0211762i	$-0.993259\pi$
$829$	−5.85600	−	18.0229i	−0.203387	−	0.625962i	0.796388	−	0.604785i	$-0.206741\pi$
$830$	9.79855	+	0.252970i	0.340112	+	0.00878071i
$831$	−2.44829			−0.0849301
$832$			2.36183i			0.0818819i
$833$	1.54317	+	0.501407i	0.0534677	+	0.0173727i
$834$	−12.9802	−	9.43068i	−0.449468	−	0.326558i
$835$	5.38074	−	7.01767i	0.186208	−	0.242856i
$836$	−31.5585			−1.09147
$837$	−4.17711	−	3.68127i	−0.144382	−	0.127243i
$838$			30.4781i			1.05285i
$839$	13.2775	−	9.64665i	0.458389	−	0.333039i	−0.334510	−	0.942392i	$-0.608571\pi$
$839$	13.2775	−	9.64665i	0.458389	−	0.333039i	0.792899	+	0.609353i	$0.208571\pi$
$840$	−5.44075	−	1.92441i	−0.187724	−	0.0663986i
$841$	−8.51946	+	26.2202i	−0.293775	+	0.904145i
$842$		−	35.0777i		−	1.20886i
$843$			6.36079i			0.219077i
$844$	8.05334	−	24.7856i	0.277207	−	0.853156i
$845$	13.6733	−	9.40484i	0.470377	−	0.323536i
$846$	−1.96057	−	6.03400i	−0.0674057	−	0.207453i
$847$	17.1585	+	23.6166i	0.589573	+	0.811478i
$848$	−4.45830	−	1.44859i	−0.153099	−	0.0497448i
$849$	24.3622	−	17.7001i	0.836107	−	0.607467i
$850$	23.9013	+	1.23495i	0.819809	+	0.0423584i
$851$	21.7077	+	66.8094i	0.744130	+	2.29020i
$852$	2.70823	−	3.72755i	0.0927823	−	0.127704i
$853$	−19.7181	+	27.1396i	−0.675133	+	0.929241i	−0.999863	−	0.0165658i	$-0.994727\pi$
$853$	−19.7181	+	27.1396i	−0.675133	+	0.929241i	0.324730	+	0.945807i	$0.394727\pi$
$854$	−6.67081	−	20.5306i	−0.228270	−	0.702544i
$855$	4.98182	−	14.0847i	0.170375	−	0.481687i
$856$	−12.8281	+	9.32019i	−0.438457	+	0.318557i
$857$	13.1040	+	4.25774i	0.447623	+	0.145441i	0.524150	−	0.851626i	$-0.324383\pi$
$857$	13.1040	+	4.25774i	0.447623	+	0.145441i	−0.0765270	+	0.997068i	$0.524383\pi$
$858$	6.55730	+	9.02535i	0.223862	+	0.308120i
$859$	−0.913387	−	2.81112i	−0.0311644	−	0.0959140i	0.934264	−	0.356581i	$-0.116058\pi$
$859$	−0.913387	−	2.81112i	−0.0311644	−	0.0959140i	−0.965429	+	0.260667i	$0.916058\pi$
$860$	−8.62758	−	12.5433i	−0.294198	−	0.427723i
$861$	−7.36649	+	22.6717i	−0.251049	+	0.772650i
$862$		−	14.2693i		−	0.486015i
$863$		−	32.6760i		−	1.11230i	−0.831081	−	0.556152i	$-0.812277\pi$
$863$		−	32.6760i		−	1.11230i	0.831081	−	0.556152i	$-0.187723\pi$
$864$	−0.309017	+	0.951057i	−0.0105130	+	0.0323556i
$865$	−13.6352	−	4.82281i	−0.463610	−	0.163981i
$866$	27.6423	−	20.0833i	0.939323	−	0.682458i
$867$		−	5.91198i		−	0.200781i
$868$	12.3674	−	7.31708i	0.419776	−	0.248358i
$869$	−7.17518			−0.243401
$870$	−2.12231	−	1.62727i	−0.0719532	−	0.0551695i
$871$	−3.93232	−	2.85700i	−0.133242	−	0.0968057i
$872$	7.90617	+	2.56887i	0.267737	+	0.0869929i
$873$		−	0.311906i		−	0.0105564i
$874$	43.6816			1.47755
$875$	−15.1040	−	24.5865i	−0.510610	−	0.831175i
$876$	−0.760212	−	2.33969i	−0.0256852	−	0.0790508i
$877$	41.0882	−	13.3504i	1.38745	−	0.450810i	0.482339	−	0.875984i	$-0.339787\pi$
$877$	41.0882	−	13.3504i	1.38745	−	0.450810i	0.905112	+	0.425174i	$0.139787\pi$
$878$	19.0241	+	26.1844i	0.642032	+	0.883682i
$879$	−2.23112	+	6.86668i	−0.0752538	+	0.231607i
$880$	8.38168	+	6.42658i	0.282546	+	0.216640i
$881$	−19.7098	−	14.3200i	−0.664041	−	0.482454i	0.203984	−	0.978974i	$-0.434611\pi$
$881$	−19.7098	−	14.3200i	−0.664041	−	0.482454i	−0.868025	+	0.496520i	$0.834611\pi$
$882$	−0.322391	+	0.104751i	−0.0108555	+	0.00352716i
$883$	26.3757	−	36.3030i	0.887613	−	1.22169i	−0.0866405	−	0.996240i	$-0.527613\pi$
$883$	26.3757	−	36.3030i	0.887613	−	1.22169i	0.974254	−	0.225455i	$-0.0723868\pi$
$884$	9.14615	+	6.64507i	0.307618	+	0.223498i
$885$	0.691831	+	1.00583i	0.0232556	+	0.0338104i
$886$	−10.0363	−	7.29178i	−0.337175	−	0.244972i
$887$	30.1050	+	41.4360i	1.01083	+	1.39128i	0.918440	+	0.395561i	$0.129450\pi$
$887$	30.1050	+	41.4360i	1.01083	+	1.39128i	0.0923874	+	0.995723i	$0.470550\pi$
$888$	10.2188	+	3.32028i	0.342920	+	0.111421i
$889$	−1.94332	+	1.41191i	−0.0651770	+	0.0473539i
$890$	8.48731	+	12.3394i	0.284495	+	0.413616i
$891$	1.45962	+	4.49224i	0.0488990	+	0.150496i
$892$	0.0297844	+	0.00967754i	0.000997256	+	0.000324028i
$893$			42.3896i			1.41851i
$894$	17.0941			0.571713
$895$	42.1515	+	1.08823i	1.40897	+	0.0363755i
$896$	−2.08799	−	1.51701i	−0.0697548	−	0.0506798i
$897$	−9.07626	−	12.4924i	−0.303047	−	0.417109i
$898$		−	15.1578i		−	0.505823i
$899$	6.49847	−	1.45382i	0.216736	−	0.0484877i
$900$	−4.19134	+	2.72629i	−0.139711	+	0.0908762i
$901$	−18.1532	+	13.1890i	−0.604770	+	0.439391i
$902$	25.6439	−	35.2957i	0.853847	−	1.17522i
$903$	16.7117	+	5.42995i	0.556129	+	0.180697i
$904$	11.6428			0.387233
$905$	−15.7234	−	53.0095i	−0.522663	−	1.76210i
$906$	−3.38879	+	10.4296i	−0.112585	+	0.346501i
$907$	−11.1006	+	3.60679i	−0.368588	+	0.119761i	−0.487454	−	0.873149i	$-0.662074\pi$
$907$	−11.1006	+	3.60679i	−0.368588	+	0.119761i	0.118866	+	0.992910i	$0.462074\pi$
$908$	−3.83974	+	1.24761i	−0.127426	+	0.0414033i
$909$	6.83200	−	4.96374i	0.226603	−	0.164637i
$910$	0.351777	−	13.6257i	0.0116613	−	0.451689i
$911$	10.2910	−	7.47687i	0.340957	−	0.247720i	−0.404108	−	0.914711i	$-0.632418\pi$
$911$	10.2910	−	7.47687i	0.340957	−	0.247720i	0.745066	+	0.666991i	$0.232418\pi$
$912$	3.92716	−	5.40527i	0.130041	−	0.178986i
$913$	19.6918	−	6.39824i	0.651702	−	0.211751i
$914$	8.39672	+	6.10058i	0.277739	+	0.201789i
$915$	−17.6325	−	6.23668i	−0.582912	−	0.206178i
$916$	2.38444	+	7.33857i	0.0787843	+	0.242473i
$917$	−20.8728	+	28.7289i	−0.689281	+	0.948713i
$918$	2.81352	+	3.87248i	0.0928600	+	0.127811i
$919$	12.8862	−	39.6596i	0.425076	−	1.30825i	−0.477845	−	0.878444i	$-0.658582\pi$
$919$	12.8862	−	39.6596i	0.425076	−	1.30825i	0.902921	−	0.429806i	$-0.141418\pi$
$920$	−11.6015	−	8.89533i	−0.382489	−	0.293270i
$921$	5.32858	+	16.3997i	0.175583	+	0.540388i
$922$	−4.25962	+	1.38404i	−0.140283	+	0.0455808i
$923$	10.3496	+	3.36278i	0.340660	+	0.110687i
$924$	−12.1907			−0.401043
$925$	29.2930	+	45.0345i	0.963148	+	1.48073i
$926$	4.41115	−	13.5761i	0.144959	−	0.446139i
$927$	−10.3332	+	14.2224i	−0.339386	+	0.467125i
$928$	−0.702997	−	0.967593i	−0.0230770	−	0.0317628i
$929$	42.6395			1.39896			0.699478	−	0.714654i	$-0.253416\pi$
$929$	42.6395			1.39896			0.699478	+	0.714654i	$0.253416\pi$
$930$	1.48889	−	12.3606i	0.0488225	−	0.405318i
$931$	2.26483			0.0742269
$932$	7.89885	+	10.8718i	0.258735	+	0.356119i
$933$	−1.98244	+	2.72860i	−0.0649023	+	0.0893303i
$934$	−6.79978	+	20.9276i	−0.222496	+	0.684771i
$935$	48.4688	−	14.3766i	1.58510	−	0.470164i
$936$	−2.36183			−0.0771990
$937$	−36.2824	−	11.7889i	−1.18529	−	0.385126i	−0.350964	−	0.936389i	$-0.614146\pi$
$937$	−36.2824	−	11.7889i	−1.18529	−	0.385126i	−0.834331	+	0.551263i	$0.814146\pi$
$938$	5.05148	−	1.64132i	0.164937	−	0.0535912i
$939$	7.07431	+	21.7725i	0.230861	+	0.710518i
$940$	8.63222	−	11.2583i	0.281552	−	0.367206i
$941$	9.01089	−	27.7327i	0.293747	−	0.904059i	−0.689893	−	0.723911i	$-0.742342\pi$
$941$	9.01089	−	27.7327i	0.293747	−	0.904059i	0.983640	−	0.180148i	$-0.0576576\pi$
$942$	−4.83804	−	6.65899i	−0.157632	−	0.216962i
$943$	−35.4948	+	48.8545i	−1.15587	+	1.59092i
$944$	0.168708	+	0.519231i	0.00549099	+	0.0168995i
$945$	1.92441	−	5.44075i	0.0626012	−	0.176988i
$946$	−26.0170	−	18.9025i	−0.845886	−	0.614572i
$947$	7.95464	−	2.58462i	0.258491	−	0.0839888i	−0.176905	−	0.984228i	$-0.556608\pi$
$947$	7.95464	−	2.58462i	0.258491	−	0.0839888i	0.435396	+	0.900239i	$0.356608\pi$
$948$	0.892883	−	1.22895i	0.0289995	−	0.0399144i
$949$	4.70066	−	3.41523i	0.152590	−	0.110863i
$950$	32.2617	−	8.67000i	1.04671	−	0.281292i
$951$	6.02372	−	4.37649i	0.195333	−	0.141917i
$952$	−11.7492	+	3.81754i	−0.380793	+	0.123727i
$953$	49.7133	−	16.1528i	1.61037	−	0.523241i	0.640728	−	0.767768i	$-0.278632\pi$
$953$	49.7133	−	16.1528i	1.61037	−	0.523241i	0.969643	+	0.244526i	$0.0786325\pi$
$954$	1.44859	−	4.45830i	0.0468999	−	0.144343i
$955$	0.837737	+	2.82433i	0.0271085	+	0.0913932i
$956$	22.9102			0.740969
$957$	−5.37277	−	1.74572i	−0.173677	−	0.0564311i
$958$	21.7706	−	29.9646i	0.703375	−	0.968112i
$959$	35.9668	−	26.1314i	1.16143	−	0.843827i
$960$	−2.14375	+	0.635868i	−0.0691893	+	0.0205225i
$961$	21.2292	+	22.5903i	0.684812	+	0.728719i
$962$			25.3771i			0.818190i
$963$	−9.32019	−	12.8281i	−0.300339	−	0.413381i
$964$	12.3917	+	9.00312i	0.399111	+	0.289971i
$965$	1.05499	−	40.8639i	0.0339612	−	1.31545i
$966$	16.8736			0.542901
$967$		−	17.3291i		−	0.557265i	−0.960398	−	0.278632i	$-0.910119\pi$
$967$		−	17.3291i		−	0.557265i	0.960398	−	0.278632i	$-0.0898811\pi$
$968$	10.7571	+	3.49520i	0.345747	+	0.112340i
$969$	−9.88265	−	30.4157i	−0.317476	−	0.977092i
$970$	0.574636	−	0.395248i	0.0184504	−	0.0126907i
$971$	−29.6659	+	21.5536i	−0.952025	+	0.691687i	−0.951285	−	0.308313i	$-0.900236\pi$
$971$	−29.6659	+	21.5536i	−0.952025	+	0.691687i	−0.000740011		1.00000i	$0.500236\pi$
$972$	−0.951057	−	0.309017i	−0.0305052	−	0.00991172i
$973$	24.3396	+	33.5006i	0.780292	+	1.07398i
$974$	−17.9422	−	13.0358i	−0.574906	−	0.417693i
$975$	−9.18293	−	7.42499i	−0.294089	−	0.237790i
$976$	−6.76680	−	4.91637i	−0.216600	−	0.157369i
$977$	−5.26749	+	7.25008i	−0.168522	+	0.231951i	−0.884922	−	0.465739i	$-0.845789\pi$
$977$	−5.26749	+	7.25008i	−0.168522	+	0.231951i	0.716400	+	0.697690i	$0.245789\pi$
$978$	−16.7300	+	5.43591i	−0.534967	+	0.173821i
$979$	25.5940	+	18.5951i	0.817988	+	0.594303i
$980$	−0.601521	−	0.461211i	−0.0192149	−	0.0147329i
$981$	−2.56887	+	7.90617i	−0.0820177	+	0.252425i
$982$	−7.10574	−	9.78021i	−0.226753	−	0.312099i
$983$	31.8979	−	10.3642i	1.01738	−	0.330568i	0.247593	−	0.968864i	$-0.420360\pi$
$983$	31.8979	−	10.3642i	1.01738	−	0.330568i	0.769791	+	0.638296i	$0.220360\pi$
$984$	2.85424	+	8.78444i	0.0909898	+	0.280038i
$985$	0.498972	−	19.3272i	0.0158986	−	0.615816i
$986$	−5.72488			−0.182317
$987$			16.3746i			0.521208i
$988$	15.0077	+	4.87631i	0.477460	+	0.155136i
$989$	36.0113	+	26.1638i	1.14509	+	0.831959i
$990$	−6.42658	+	8.38168i	−0.204250	+	0.266387i
$991$	1.77273			0.0563125			0.0281562	−	0.999604i	$-0.491036\pi$
$991$	1.77273			0.0563125			0.0281562	+	0.999604i	$0.491036\pi$
$992$	2.21030	−	5.11024i	0.0701770	−	0.162250i
$993$			13.4290i			0.426157i
$994$	−9.62043	+	6.98965i	−0.305141	+	0.221698i
$995$	−14.6687	+	41.4718i	−0.465030	+	1.31474i
$996$	−1.35458	+	4.16896i	−0.0429214	+	0.132099i
$997$			40.1344i			1.27107i	0.772072	+	0.635535i	$0.219220\pi$
$997$			40.1344i			1.27107i	−0.772072	+	0.635535i	$0.780780\pi$
$998$		−	26.0539i		−	0.824721i
$999$	−3.32028	+	10.2188i	−0.105049	+	0.323308i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.z.d.109.12	yes	72
5.4	even	2	inner	930.2.z.d.109.3	✓	72
31.2	even	5	inner	930.2.z.d.529.3	yes	72
155.64	even	10	inner	930.2.z.d.529.12	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.z.d.109.3	✓	72	5.4	even	2	inner
930.2.z.d.109.12	yes	72	1.1	even	1	trivial
930.2.z.d.529.3	yes	72	31.2	even	5	inner
930.2.z.d.529.12	yes	72	155.64	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.z (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.587785 + 0.809017i) q^{2} +(0.587785 - 0.809017i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(-0.635868 - 2.14375i) q^{5} +1.00000 q^{6} +(-2.45458 - 0.797540i) q^{7} +(-0.951057 + 0.309017i) q^{8} +(-0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.587785 + 0.809017i) q^{2} +(0.587785 - 0.809017i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(-0.635868 - 2.14375i) q^{5} +1.00000 q^{6} +(-2.45458 - 0.797540i) q^{7} +(-0.951057 + 0.309017i) q^{8} +(-0.309017 - 0.951057i) q^{9} +(1.36058 - 1.77449i) q^{10} +(1.45962 - 4.49224i) q^{11} +(0.587785 + 0.809017i) q^{12} +(-1.38825 + 1.91076i) q^{13} +(-0.797540 - 2.45458i) q^{14} +(-2.10809 - 0.745638i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-4.55237 + 1.47915i) q^{17} +(0.587785 - 0.809017i) q^{18} +(-5.40527 + 3.92716i) q^{19} +(2.23532 + 0.0577095i) q^{20} +(-2.08799 + 1.51701i) q^{21} +(4.49224 - 1.45962i) q^{22} +(-6.21792 + 2.02032i) q^{23} +(-0.309017 + 0.951057i) q^{24} +(-4.19134 + 2.72629i) q^{25} -2.36183 q^{26} +(-0.951057 - 0.309017i) q^{27} +(1.51701 - 2.08799i) q^{28} +(0.967593 - 0.702997i) q^{29} +(-0.635868 - 2.14375i) q^{30} +(5.11024 + 2.21030i) q^{31} -1.00000i q^{32} +(-2.77636 - 3.82133i) q^{33} +(-3.87248 - 2.81352i) q^{34} +(-0.148942 + 5.76913i) q^{35} +1.00000 q^{36} -10.7447i q^{37} +(-6.35428 - 2.06463i) q^{38} +(0.729847 + 2.24624i) q^{39} +(1.26720 + 1.84234i) q^{40} +(7.47249 - 5.42908i) q^{41} +(-2.45458 - 0.797540i) q^{42} +(-4.00186 - 5.50809i) q^{43} +(3.82133 + 2.77636i) q^{44} +(-1.84234 + 1.26720i) q^{45} +(-5.28928 - 3.84288i) q^{46} +(3.72922 - 5.13283i) q^{47} +(-0.951057 + 0.309017i) q^{48} +(-0.274242 - 0.199249i) q^{49} +(-4.66922 - 1.78840i) q^{50} +(-1.47915 + 4.55237i) q^{51} +(-1.38825 - 1.91076i) q^{52} +(4.45830 - 1.44859i) q^{53} +(-0.309017 - 0.951057i) q^{54} +(-10.5584 - 0.272587i) q^{55} +2.58089 q^{56} +6.68128i q^{57} +(1.13747 + 0.369588i) q^{58} +(-0.441684 - 0.320902i) q^{59} +(1.36058 - 1.77449i) q^{60} +8.36422 q^{61} +(1.21556 + 5.43345i) q^{62} +2.58089i q^{63} +(0.809017 - 0.587785i) q^{64} +(4.97895 + 1.76107i) q^{65} +(1.45962 - 4.49224i) q^{66} +2.05798i q^{67} -4.78665i q^{68} +(-2.02032 + 6.21792i) q^{69} +(-4.75487 + 3.27052i) q^{70} +(-1.42380 - 4.38200i) q^{71} +(0.587785 + 0.809017i) q^{72} +(-2.33969 - 0.760212i) q^{73} +(8.69261 - 6.31555i) q^{74} +(-0.257999 + 4.99334i) q^{75} +(-2.06463 - 6.35428i) q^{76} +(-7.16549 + 9.86245i) q^{77} +(-1.38825 + 1.91076i) q^{78} +(-0.469417 - 1.44472i) q^{79} +(-0.745638 + 2.10809i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(8.78444 + 2.85424i) q^{82} +(2.57656 + 3.54633i) q^{83} +(-0.797540 - 2.45458i) q^{84} +(6.06565 + 8.81861i) q^{85} +(2.10390 - 6.47514i) q^{86} -1.19601i q^{87} +4.72342i q^{88} +(-2.06970 + 6.36987i) q^{89} +(-2.10809 - 0.745638i) q^{90} +(4.93148 - 3.58293i) q^{91} -6.53791i q^{92} +(4.79189 - 2.83509i) q^{93} +6.34453 q^{94} +(11.8559 + 9.09041i) q^{95} +(-0.809017 - 0.587785i) q^{96} +(0.296640 + 0.0963843i) q^{97} -0.338982i q^{98} -4.72342 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 18 q^{4} + 4 q^{5} + 72 q^{6} + 18 q^{9}+O(q^{10}) \) 72 * q + 18 * q^4 + 4 * q^5 + 72 * q^6 + 18 * q^9	\( 72 q + 18 q^{4} + 4 q^{5} + 72 q^{6} + 18 q^{9} - 6 q^{11} - 4 q^{14} - 18 q^{16} + 12 q^{19} - 4 q^{20} - 16 q^{21} + 18 q^{24} - 4 q^{25} + 12 q^{26} + 24 q^{29} + 4 q^{30} + 22 q^{31} + 14 q^{34} - 22 q^{35} + 72 q^{36} + 8 q^{39} - 28 q^{41} - 4 q^{44} - 4 q^{45} - 22 q^{46} + 42 q^{49} - 32 q^{50} - 4 q^{51} + 18 q^{54} + 14 q^{55} + 24 q^{56} - 28 q^{59} + 56 q^{61} + 18 q^{64} + 46 q^{65} - 6 q^{66} - 8 q^{69} + 46 q^{70} - 68 q^{71} + 8 q^{74} + 32 q^{75} - 12 q^{76} + 26 q^{79} - 6 q^{80} - 18 q^{81} - 4 q^{84} - 32 q^{85} + 80 q^{86} + 32 q^{89} - 44 q^{91} + 12 q^{94} + 74 q^{95} - 18 q^{96} - 4 q^{99}+O(q^{100}) \) 72 * q + 18 * q^4 + 4 * q^5 + 72 * q^6 + 18 * q^9 - 6 * q^11 - 4 * q^14 - 18 * q^16 + 12 * q^19 - 4 * q^20 - 16 * q^21 + 18 * q^24 - 4 * q^25 + 12 * q^26 + 24 * q^29 + 4 * q^30 + 22 * q^31 + 14 * q^34 - 22 * q^35 + 72 * q^36 + 8 * q^39 - 28 * q^41 - 4 * q^44 - 4 * q^45 - 22 * q^46 + 42 * q^49 - 32 * q^50 - 4 * q^51 + 18 * q^54 + 14 * q^55 + 24 * q^56 - 28 * q^59 + 56 * q^61 + 18 * q^64 + 46 * q^65 - 6 * q^66 - 8 * q^69 + 46 * q^70 - 68 * q^71 + 8 * q^74 + 32 * q^75 - 12 * q^76 + 26 * q^79 - 6 * q^80 - 18 * q^81 - 4 * q^84 - 32 * q^85 + 80 * q^86 + 32 * q^89 - 44 * q^91 + 12 * q^94 + 74 * q^95 - 18 * q^96 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more