LMFDB - Embedded newform 722.2.e.g.245.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [722,2,Mod(99,722)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(722, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("722.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 722 = 2 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	722.e (of order $9$, degree $6$, not 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:	$5.76519902594$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			245.1
Root			$-0.766044 - 0.642788i$ of defining polynomial
Character	$\chi$	$=$	722.245
Dual form			722.2.e.g.389.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.173648 - 0.984808i) q^{2} +(2.29813 + 1.92836i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-1.87939 + 0.684040i) q^{5} +(2.29813 - 1.92836i) q^{6} +(1.50000 + 2.59808i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(1.04189 + 5.90885i) q^{9} +O(q^{10})$	\(q+(0.173648 - 0.984808i) q^{2} +(2.29813 + 1.92836i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-1.87939 + 0.684040i) q^{5} +(2.29813 - 1.92836i) q^{6} +(1.50000 + 2.59808i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(1.04189 + 5.90885i) q^{9} +(0.347296 + 1.96962i) q^{10} +(1.00000 - 1.73205i) q^{11} +(-1.50000 - 2.59808i) q^{12} +(-2.29813 + 1.92836i) q^{13} +(2.81908 - 1.02606i) q^{14} +(-5.63816 - 2.05212i) q^{15} +(0.766044 + 0.642788i) q^{16} +(-0.173648 + 0.984808i) q^{17} +6.00000 q^{18} +2.00000 q^{20} +(-1.56283 + 8.86327i) q^{21} +(-1.53209 - 1.28558i) q^{22} +(-4.69846 - 1.71010i) q^{23} +(-2.81908 + 1.02606i) q^{24} +(-0.766044 + 0.642788i) q^{25} +(1.50000 + 2.59808i) q^{26} +(-4.50000 + 7.79423i) q^{27} +(-0.520945 - 2.95442i) q^{28} +(-0.520945 - 2.95442i) q^{29} +(-3.00000 + 5.19615i) q^{30} +(3.00000 + 5.19615i) q^{31} +(0.766044 - 0.642788i) q^{32} +(5.63816 - 2.05212i) q^{33} +(0.939693 + 0.342020i) q^{34} +(-4.59627 - 3.85673i) q^{35} +(1.04189 - 5.90885i) q^{36} +6.00000 q^{37} -9.00000 q^{39} +(0.347296 - 1.96962i) q^{40} +(9.19253 + 7.71345i) q^{41} +(8.45723 + 3.07818i) q^{42} +(9.39693 - 3.42020i) q^{43} +(-1.53209 + 1.28558i) q^{44} +(-6.00000 - 10.3923i) q^{45} +(-2.50000 + 4.33013i) q^{46} +(-1.38919 - 7.87846i) q^{47} +(0.520945 + 2.95442i) q^{48} +(-1.00000 + 1.73205i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-2.29813 + 1.92836i) q^{51} +(2.81908 - 1.02606i) q^{52} +(2.81908 + 1.02606i) q^{53} +(6.89440 + 5.78509i) q^{54} +(-0.694593 + 3.93923i) q^{55} -3.00000 q^{56} -3.00000 q^{58} +(0.520945 - 2.95442i) q^{59} +(4.59627 + 3.85673i) q^{60} +(5.63816 - 2.05212i) q^{62} +(-13.7888 + 11.5702i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(3.00000 - 5.19615i) q^{65} +(-1.04189 - 5.90885i) q^{66} +(2.60472 + 14.7721i) q^{67} +(0.500000 - 0.866025i) q^{68} +(-7.50000 - 12.9904i) q^{69} +(-4.59627 + 3.85673i) q^{70} +(-5.63816 - 2.05212i) q^{72} +(-8.42649 - 7.07066i) q^{73} +(1.04189 - 5.90885i) q^{74} -3.00000 q^{75} +6.00000 q^{77} +(-1.56283 + 8.86327i) q^{78} +(-9.19253 - 7.71345i) q^{79} +(-1.87939 - 0.684040i) q^{80} +(-8.45723 + 3.07818i) q^{81} +(9.19253 - 7.71345i) q^{82} +(-1.00000 - 1.73205i) q^{83} +(4.50000 - 7.79423i) q^{84} +(-0.347296 - 1.96962i) q^{85} +(-1.73648 - 9.84808i) q^{86} +(4.50000 - 7.79423i) q^{87} +(1.00000 + 1.73205i) q^{88} +(4.59627 - 3.85673i) q^{89} +(-11.2763 + 4.10424i) q^{90} +(-8.45723 - 3.07818i) q^{91} +(3.83022 + 3.21394i) q^{92} +(-3.12567 + 17.7265i) q^{93} -8.00000 q^{94} +3.00000 q^{96} +(2.08378 - 11.8177i) q^{97} +(1.53209 + 1.28558i) q^{98} +(11.2763 + 4.10424i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 9 q^{7} - 3 q^{8}+O(q^{10}) $ 6 * q + 9 * q^7 - 3 * q^8	$ 6 q + 9 q^{7} - 3 q^{8} + 6 q^{11} - 9 q^{12} + 36 q^{18} + 12 q^{20} + 9 q^{26} - 27 q^{27} - 18 q^{30} + 18 q^{31} + 36 q^{37} - 54 q^{39} - 36 q^{45} - 15 q^{46} - 6 q^{49} + 3 q^{50} - 18 q^{56} - 18 q^{58} - 3 q^{64} + 18 q^{65} + 3 q^{68} - 45 q^{69} - 18 q^{75} + 36 q^{77} - 6 q^{83} + 27 q^{84} + 27 q^{87} + 6 q^{88} - 48 q^{94} + 18 q^{96}+O(q^{100}) $ 6 * q + 9 * q^7 - 3 * q^8 + 6 * q^11 - 9 * q^12 + 36 * q^18 + 12 * q^20 + 9 * q^26 - 27 * q^27 - 18 * q^30 + 18 * q^31 + 36 * q^37 - 54 * q^39 - 36 * q^45 - 15 * q^46 - 6 * q^49 + 3 * q^50 - 18 * q^56 - 18 * q^58 - 3 * q^64 + 18 * q^65 + 3 * q^68 - 45 * q^69 - 18 * q^75 + 36 * q^77 - 6 * q^83 + 27 * q^84 + 27 * q^87 + 6 * q^88 - 48 * q^94 + 18 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/722\mathbb{Z}\right)^\times$.

$n$	$363$
$\chi(n)$	$e\left(\frac{5}{9}\right)$

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 $

$2$	0.173648	−	0.984808i	0.122788	−	0.696364i
$2$	0.173648	−	0.984808i	0.122788	−	0.696364i
$3$	2.29813	+	1.92836i	1.32683	+	1.11334i	0.984808	+	0.173648i	$0.0555556\pi$
$3$	2.29813	+	1.92836i	1.32683	+	1.11334i	0.342020	+	0.939693i	$0.388889\pi$
$4$	−0.939693	−	0.342020i	−0.469846	−	0.171010i
$5$	−1.87939	+	0.684040i	−0.840487	+	0.305912i	−0.726155	−	0.687531i	$-0.758695\pi$
$5$	−1.87939	+	0.684040i	−0.840487	+	0.305912i	−0.114331	+	0.993443i	$0.536473\pi$
$6$	2.29813	−	1.92836i	0.938209	−	0.787251i
$7$	1.50000	+	2.59808i	0.566947	+	0.981981i	0.996866	+	0.0791130i	$0.0252088\pi$
$7$	1.50000	+	2.59808i	0.566947	+	0.981981i	−0.429919	+	0.902867i	$0.641458\pi$
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	1.04189	+	5.90885i	0.347296	+	1.96962i
$10$	0.347296	+	1.96962i	0.109825	+	0.622847i
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	−0.674967	−	0.737848i	$-0.735842\pi$
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	0.976478	+	0.215615i	$0.0691756\pi$
$12$	−1.50000	−	2.59808i	−0.433013	−	0.750000i
$13$	−2.29813	+	1.92836i	−0.637388	+	0.534832i	−0.903215	−	0.429189i	$-0.858799\pi$
$13$	−2.29813	+	1.92836i	−0.637388	+	0.534832i	0.265827	+	0.964021i	$0.414355\pi$
$14$	2.81908	−	1.02606i	0.753430	−	0.274226i
$15$	−5.63816	−	2.05212i	−1.45577	−	0.529855i
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	−0.173648	+	0.984808i	−0.0421159	+	0.238851i	−0.998598	−	0.0529411i	$-0.983140\pi$
$17$	−0.173648	+	0.984808i	−0.0421159	+	0.238851i	0.956482	+	0.291792i	$0.0942515\pi$
$18$	6.00000			1.41421
$19$		0			0
$19$		0			0
$20$	2.00000			0.447214
$21$	−1.56283	+	8.86327i	−0.341038	+	1.93412i
$22$	−1.53209	−	1.28558i	−0.326642	−	0.274086i
$23$	−4.69846	−	1.71010i	−0.979697	−	0.356581i	−0.197975	−	0.980207i	$-0.563436\pi$
$23$	−4.69846	−	1.71010i	−0.979697	−	0.356581i	−0.781722	+	0.623626i	$0.785659\pi$
$24$	−2.81908	+	1.02606i	−0.575442	+	0.209444i
$25$	−0.766044	+	0.642788i	−0.153209	+	0.128558i
$26$	1.50000	+	2.59808i	0.294174	+	0.509525i
$27$	−4.50000	+	7.79423i	−0.866025	+	1.50000i
$28$	−0.520945	−	2.95442i	−0.0984493	−	0.558334i
$29$	−0.520945	−	2.95442i	−0.0967370	−	0.548623i	−0.994201	−	0.107535i	$-0.965704\pi$
$29$	−0.520945	−	2.95442i	−0.0967370	−	0.548623i	0.897464	−	0.441087i	$-0.145407\pi$
$30$	−3.00000	+	5.19615i	−0.547723	+	0.948683i
$31$	3.00000	+	5.19615i	0.538816	+	0.933257i	0.998968	+	0.0454165i	$0.0144615\pi$
$31$	3.00000	+	5.19615i	0.538816	+	0.933257i	−0.460152	+	0.887840i	$0.652205\pi$
$32$	0.766044	−	0.642788i	0.135419	−	0.113630i
$33$	5.63816	−	2.05212i	0.981477	−	0.357228i
$34$	0.939693	+	0.342020i	0.161156	+	0.0586560i
$35$	−4.59627	−	3.85673i	−0.776911	−	0.651906i
$36$	1.04189	−	5.90885i	0.173648	−	0.984808i
$37$	6.00000			0.986394			0.493197	−	0.869918i	$-0.335828\pi$
$37$	6.00000			0.986394			0.493197	+	0.869918i	$0.335828\pi$
$38$		0			0
$39$	−9.00000			−1.44115
$40$	0.347296	−	1.96962i	0.0549124	−	0.311424i
$41$	9.19253	+	7.71345i	1.43563	+	1.20464i	0.942287	+	0.334805i	$0.108670\pi$
$41$	9.19253	+	7.71345i	1.43563	+	1.20464i	0.493345	+	0.869834i	$0.335774\pi$
$42$	8.45723	+	3.07818i	1.30498	+	0.474974i
$43$	9.39693	−	3.42020i	1.43302	−	0.521576i	0.495223	−	0.868766i	$-0.335086\pi$
$43$	9.39693	−	3.42020i	1.43302	−	0.521576i	0.937795	+	0.347190i	$0.112864\pi$
$44$	−1.53209	+	1.28558i	−0.230971	+	0.193808i
$45$	−6.00000	−	10.3923i	−0.894427	−	1.54919i
$46$	−2.50000	+	4.33013i	−0.368605	+	0.638442i
$47$	−1.38919	−	7.87846i	−0.202634	−	1.14919i	−0.901120	−	0.433569i	$-0.857254\pi$
$47$	−1.38919	−	7.87846i	−0.202634	−	1.14919i	0.698487	−	0.715623i	$-0.253857\pi$
$48$	0.520945	+	2.95442i	0.0751919	+	0.426434i
$49$	−1.00000	+	1.73205i	−0.142857	+	0.247436i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$	−2.29813	+	1.92836i	−0.321803	+	0.270025i
$52$	2.81908	−	1.02606i	0.390936	−	0.142289i
$53$	2.81908	+	1.02606i	0.387230	+	0.140940i	0.528297	−	0.849060i	$-0.322831\pi$
$53$	2.81908	+	1.02606i	0.387230	+	0.140940i	−0.141066	+	0.990000i	$0.545053\pi$
$54$	6.89440	+	5.78509i	0.938209	+	0.787251i
$55$	−0.694593	+	3.93923i	−0.0936589	+	0.531166i
$56$	−3.00000			−0.400892
$57$		0			0
$58$	−3.00000			−0.393919
$59$	0.520945	−	2.95442i	0.0678212	−	0.384633i	−0.931937	−	0.362621i	$-0.881882\pi$
$59$	0.520945	−	2.95442i	0.0678212	−	0.384633i	0.999758	−	0.0220117i	$-0.00700710\pi$
$60$	4.59627	+	3.85673i	0.593375	+	0.497901i
$61$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$61$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$62$	5.63816	−	2.05212i	0.716046	−	0.260620i
$63$	−13.7888	+	11.5702i	−1.73723	+	1.45771i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	3.00000	−	5.19615i	0.372104	−	0.644503i
$66$	−1.04189	−	5.90885i	−0.128248	−	0.727329i
$67$	2.60472	+	14.7721i	0.318218	+	1.80470i	0.553583	+	0.832794i	$0.313260\pi$
$67$	2.60472	+	14.7721i	0.318218	+	1.80470i	−0.235365	+	0.971907i	$0.575629\pi$
$68$	0.500000	−	0.866025i	0.0606339	−	0.105021i
$69$	−7.50000	−	12.9904i	−0.902894	−	1.56386i
$70$	−4.59627	+	3.85673i	−0.549359	+	0.460967i
$71$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$71$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$72$	−5.63816	−	2.05212i	−0.664463	−	0.241845i
$73$	−8.42649	−	7.07066i	−0.986246	−	0.827559i	−0.00122602	−	0.999999i	$-0.500390\pi$
$73$	−8.42649	−	7.07066i	−0.986246	−	0.827559i	−0.985020	+	0.172441i	$0.944835\pi$
$74$	1.04189	−	5.90885i	0.121117	−	0.686889i
$75$	−3.00000			−0.346410
$76$		0			0
$77$	6.00000			0.683763
$78$	−1.56283	+	8.86327i	−0.176956	+	1.00357i
$79$	−9.19253	−	7.71345i	−1.03424	−	0.867831i	−0.0428913	−	0.999080i	$-0.513657\pi$
$79$	−9.19253	−	7.71345i	−1.03424	−	0.867831i	−0.991349	+	0.131249i	$0.958101\pi$
$80$	−1.87939	−	0.684040i	−0.210122	−	0.0764780i
$81$	−8.45723	+	3.07818i	−0.939693	+	0.342020i
$82$	9.19253	−	7.71345i	1.01515	−	0.851808i
$83$	−1.00000	−	1.73205i	−0.109764	−	0.190117i	0.805910	−	0.592037i	$-0.201676\pi$
$83$	−1.00000	−	1.73205i	−0.109764	−	0.190117i	−0.915675	+	0.401920i	$0.868343\pi$
$84$	4.50000	−	7.79423i	0.490990	−	0.850420i
$85$	−0.347296	−	1.96962i	−0.0376696	−	0.213635i
$86$	−1.73648	−	9.84808i	−0.187250	−	1.06195i
$87$	4.50000	−	7.79423i	0.482451	−	0.835629i
$88$	1.00000	+	1.73205i	0.106600	+	0.184637i
$89$	4.59627	−	3.85673i	0.487203	−	0.408812i	−0.365819	−	0.930686i	$-0.619211\pi$
$89$	4.59627	−	3.85673i	0.487203	−	0.408812i	0.853023	+	0.521874i	$0.174767\pi$
$90$	−11.2763	+	4.10424i	−1.18863	+	0.432625i
$91$	−8.45723	−	3.07818i	−0.886559	−	0.322681i
$92$	3.83022	+	3.21394i	0.399328	+	0.335076i
$93$	−3.12567	+	17.7265i	−0.324117	+	1.83816i
$94$	−8.00000			−0.825137
$95$		0			0
$96$	3.00000			0.306186
$97$	2.08378	−	11.8177i	0.211576	−	1.19990i	−0.675175	−	0.737657i	$-0.735932\pi$
$97$	2.08378	−	11.8177i	0.211576	−	1.19990i	0.886751	−	0.462248i	$-0.152957\pi$
$98$	1.53209	+	1.28558i	0.154764	+	0.129863i
$99$	11.2763	+	4.10424i	1.13331	+	0.412492i
$100$	0.939693	−	0.342020i	0.0939693	−	0.0342020i
$101$	7.66044	−	6.42788i	0.762243	−	0.639598i	−0.176467	−	0.984307i	$-0.556467\pi$
$101$	7.66044	−	6.42788i	0.762243	−	0.639598i	0.938710	+	0.344709i	$0.112022\pi$
$102$	1.50000	+	2.59808i	0.148522	+	0.257248i
$103$	−3.00000	+	5.19615i	−0.295599	+	0.511992i	−0.975124	−	0.221660i	$-0.928852\pi$
$103$	−3.00000	+	5.19615i	−0.295599	+	0.511992i	0.679525	+	0.733652i	$0.262186\pi$
$104$	−0.520945	−	2.95442i	−0.0510828	−	0.289705i
$105$	−3.12567	−	17.7265i	−0.305034	−	1.72993i
$106$	1.50000	−	2.59808i	0.145693	−	0.252347i
$107$	1.50000	+	2.59808i	0.145010	+	0.251166i	0.929377	−	0.369132i	$-0.120345\pi$
$107$	1.50000	+	2.59808i	0.145010	+	0.251166i	−0.784366	+	0.620298i	$0.787012\pi$
$108$	6.89440	−	5.78509i	0.663414	−	0.556670i
$109$	−2.81908	+	1.02606i	−0.270019	+	0.0982788i	−0.473481	−	0.880804i	$-0.657003\pi$
$109$	−2.81908	+	1.02606i	−0.270019	+	0.0982788i	0.203462	+	0.979083i	$0.434781\pi$
$110$	3.75877	+	1.36808i	0.358385	+	0.130441i
$111$	13.7888	+	11.5702i	1.30877	+	1.09819i
$112$	−0.520945	+	2.95442i	−0.0492246	+	0.279167i
$113$	12.0000			1.12887			0.564433	−	0.825479i	$-0.309095\pi$
$113$	12.0000			1.12887			0.564433	+	0.825479i	$0.309095\pi$
$114$		0			0
$115$	10.0000			0.932505
$116$	−0.520945	+	2.95442i	−0.0483685	+	0.274311i
$117$	−13.7888	−	11.5702i	−1.27478	−	1.06966i
$118$	−2.81908	−	1.02606i	−0.259517	−	0.0944565i
$119$	−2.81908	+	1.02606i	−0.258424	+	0.0940588i
$120$	4.59627	−	3.85673i	0.419580	−	0.352069i
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$		0			0
$123$	6.25133	+	35.4531i	0.563664	+	3.19670i
$124$	−1.04189	−	5.90885i	−0.0935644	−	0.530630i
$125$	6.00000	−	10.3923i	0.536656	−	0.929516i
$126$	9.00000	+	15.5885i	0.801784	+	1.38873i
$127$	9.19253	−	7.71345i	0.815705	−	0.684458i	−0.136257	−	0.990674i	$-0.543507\pi$
$127$	9.19253	−	7.71345i	0.815705	−	0.684458i	0.951962	+	0.306215i	$0.0990628\pi$
$128$	−0.939693	+	0.342020i	−0.0830579	+	0.0302306i
$129$	28.1908	+	10.2606i	2.48206	+	0.903396i
$130$	−4.59627	−	3.85673i	−0.403119	−	0.338257i
$131$	2.43107	−	13.7873i	0.212404	−	1.20460i	−0.672951	−	0.739687i	$-0.734974\pi$
$131$	2.43107	−	13.7873i	0.212404	−	1.20460i	0.885355	−	0.464916i	$-0.153915\pi$
$132$	−6.00000			−0.522233
$133$		0			0
$134$	15.0000			1.29580
$135$	3.12567	−	17.7265i	0.269015	−	1.52566i
$136$	−0.766044	−	0.642788i	−0.0656878	−	0.0551186i
$137$	−17.8542	−	6.49838i	−1.52538	−	0.555194i	−0.562898	−	0.826526i	$-0.690314\pi$
$137$	−17.8542	−	6.49838i	−1.52538	−	0.555194i	−0.962486	+	0.271332i	$0.912536\pi$
$138$	−14.0954	+	5.13030i	−1.19988	+	0.436720i
$139$	4.59627	−	3.85673i	0.389850	−	0.327123i	−0.426705	−	0.904391i	$-0.640326\pi$
$139$	4.59627	−	3.85673i	0.389850	−	0.327123i	0.816555	+	0.577268i	$0.195881\pi$
$140$	3.00000	+	5.19615i	0.253546	+	0.439155i
$141$	12.0000	−	20.7846i	1.01058	−	1.75038i
$142$		0			0
$143$	1.04189	+	5.90885i	0.0871271	+	0.494123i
$144$	−3.00000	+	5.19615i	−0.250000	+	0.433013i
$145$	3.00000	+	5.19615i	0.249136	+	0.431517i
$146$	−8.42649	+	7.07066i	−0.697381	+	0.585172i
$147$	−5.63816	+	2.05212i	−0.465027	+	0.169256i
$148$	−5.63816	−	2.05212i	−0.463454	−	0.168683i
$149$	−6.12836	−	5.14230i	−0.502054	−	0.421274i	0.356268	−	0.934384i	$-0.384049\pi$
$149$	−6.12836	−	5.14230i	−0.502054	−	0.421274i	−0.858323	+	0.513110i	$0.828493\pi$
$150$	−0.520945	+	2.95442i	−0.0425349	+	0.241228i
$151$	−18.0000			−1.46482			−0.732410	−	0.680864i	$-0.761604\pi$
$151$	−18.0000			−1.46482			−0.732410	+	0.680864i	$0.761604\pi$
$152$		0			0
$153$	−6.00000			−0.485071
$154$	1.04189	−	5.90885i	0.0839578	−	0.476148i
$155$	−9.19253	−	7.71345i	−0.738362	−	0.619559i
$156$	8.45723	+	3.07818i	0.677121	+	0.246452i
$157$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$157$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$158$	−9.19253	+	7.71345i	−0.731319	+	0.613649i
$159$	4.50000	+	7.79423i	0.356873	+	0.618123i
$160$	−1.00000	+	1.73205i	−0.0790569	+	0.136931i
$161$	−2.60472	−	14.7721i	−0.205281	−	1.16421i
$162$	1.56283	+	8.86327i	0.122788	+	0.696364i
$163$	3.00000	−	5.19615i	0.234978	−	0.406994i	−0.724288	−	0.689497i	$-0.757831\pi$
$163$	3.00000	−	5.19615i	0.234978	−	0.406994i	0.959266	+	0.282503i	$0.0911648\pi$
$164$	−6.00000	−	10.3923i	−0.468521	−	0.811503i
$165$	−9.19253	+	7.71345i	−0.715638	+	0.600491i
$166$	−1.87939	+	0.684040i	−0.145869	+	0.0530918i
$167$	11.2763	+	4.10424i	0.872587	+	0.317596i	0.739214	−	0.673470i	$-0.235197\pi$
$167$	11.2763	+	4.10424i	0.872587	+	0.317596i	0.133373	+	0.991066i	$0.457419\pi$
$168$	−6.89440	−	5.78509i	−0.531915	−	0.446329i
$169$	−0.694593	+	3.93923i	−0.0534302	+	0.303018i
$170$	−2.00000			−0.153393
$171$		0			0
$172$	−10.0000			−0.762493
$173$	−3.12567	+	17.7265i	−0.237640	+	1.34772i	0.599342	+	0.800493i	$0.295429\pi$
$173$	−3.12567	+	17.7265i	−0.237640	+	1.34772i	−0.836982	+	0.547231i	$0.815682\pi$
$174$	−6.89440	−	5.78509i	−0.522663	−	0.438566i
$175$	−2.81908	−	1.02606i	−0.213102	−	0.0775629i
$176$	1.87939	−	0.684040i	0.141664	−	0.0515615i
$177$	6.89440	−	5.78509i	0.518215	−	0.434834i
$178$	−3.00000	−	5.19615i	−0.224860	−	0.389468i
$179$	6.00000	−	10.3923i	0.448461	−	0.776757i	−0.549825	−	0.835280i	$-0.685306\pi$
$179$	6.00000	−	10.3923i	0.448461	−	0.776757i	0.998286	+	0.0585225i	$0.0186389\pi$
$180$	2.08378	+	11.8177i	0.155316	+	0.880839i
$181$	3.12567	+	17.7265i	0.232329	+	1.31760i	0.848166	+	0.529730i	$0.177707\pi$
$181$	3.12567	+	17.7265i	0.232329	+	1.31760i	−0.615837	+	0.787873i	$0.711182\pi$
$182$	−4.50000	+	7.79423i	−0.333562	+	0.577747i
$183$		0			0
$184$	3.83022	−	3.21394i	0.282368	−	0.236935i
$185$	−11.2763	+	4.10424i	−0.829051	+	0.301750i
$186$	16.9145	+	6.15636i	1.24023	+	0.451406i
$187$	1.53209	+	1.28558i	0.112037	+	0.0940106i
$188$	−1.38919	+	7.87846i	−0.101317	+	0.574596i
$189$	−27.0000			−1.96396
$190$		0			0
$191$	−11.0000			−0.795932			−0.397966	−	0.917400i	$-0.630284\pi$
$191$	−11.0000			−0.795932			−0.397966	+	0.917400i	$0.630284\pi$
$192$	0.520945	−	2.95442i	0.0375959	−	0.213217i
$193$	4.59627	+	3.85673i	0.330847	+	0.277613i	0.793045	−	0.609163i	$-0.208495\pi$
$193$	4.59627	+	3.85673i	0.330847	+	0.277613i	−0.462198	+	0.886777i	$0.652939\pi$
$194$	−11.2763	−	4.10424i	−0.809592	−	0.294667i
$195$	16.9145	−	6.15636i	1.21127	−	0.440866i
$196$	1.53209	−	1.28558i	0.109435	−	0.0918268i
$197$	−2.00000	−	3.46410i	−0.142494	−	0.246807i	0.785941	−	0.618301i	$-0.212179\pi$
$197$	−2.00000	−	3.46410i	−0.142494	−	0.246807i	−0.928435	+	0.371494i	$0.878846\pi$
$198$	6.00000	−	10.3923i	0.426401	−	0.738549i
$199$	−1.21554	−	6.89365i	−0.0861672	−	0.488678i	−0.997099	−	0.0761205i	$-0.975747\pi$
$199$	−1.21554	−	6.89365i	−0.0861672	−	0.488678i	0.910931	−	0.412558i	$-0.135364\pi$
$200$	−0.173648	−	0.984808i	−0.0122788	−	0.0696364i
$201$	−22.5000	+	38.9711i	−1.58703	+	2.74881i
$202$	−5.00000	−	8.66025i	−0.351799	−	0.609333i
$203$	6.89440	−	5.78509i	0.483892	−	0.406034i
$204$	2.81908	−	1.02606i	0.197375	−	0.0718386i
$205$	−22.5526	−	8.20848i	−1.57514	−	0.573305i
$206$	4.59627	+	3.85673i	0.320237	+	0.268711i
$207$	5.20945	−	29.5442i	0.362081	−	2.05347i
$208$	−3.00000			−0.208013
$209$		0			0
$210$	−18.0000			−1.24212
$211$	0.520945	−	2.95442i	0.0358633	−	0.203391i	−0.961611	−	0.274415i	$-0.911516\pi$
$211$	0.520945	−	2.95442i	0.0358633	−	0.203391i	0.997475	+	0.0710244i	$0.0226268\pi$
$212$	−2.29813	−	1.92836i	−0.157836	−	0.132441i
$213$		0			0
$214$	2.81908	−	1.02606i	0.192708	−	0.0701400i
$215$	−15.3209	+	12.8558i	−1.04488	+	0.876755i
$216$	−4.50000	−	7.79423i	−0.306186	−	0.530330i
$217$	−9.00000	+	15.5885i	−0.610960	+	1.05821i
$218$	0.520945	+	2.95442i	0.0352828	+	0.200099i
$219$	−5.73039	−	32.4987i	−0.387224	−	2.19606i
$220$	2.00000	−	3.46410i	0.134840	−	0.233550i
$221$	−1.50000	−	2.59808i	−0.100901	−	0.174766i
$222$	13.7888	−	11.5702i	0.925444	−	0.776539i
$223$	−16.9145	+	6.15636i	−1.13268	+	0.412261i	−0.839263	−	0.543725i	$-0.817013\pi$
$223$	−16.9145	+	6.15636i	−1.13268	+	0.412261i	−0.293413	+	0.955986i	$0.594791\pi$
$224$	2.81908	+	1.02606i	0.188358	+	0.0685565i
$225$	−4.59627	−	3.85673i	−0.306418	−	0.257115i
$226$	2.08378	−	11.8177i	0.138611	−	0.786101i
$227$	3.00000			0.199117			0.0995585	−	0.995032i	$-0.468257\pi$
$227$	3.00000			0.199117			0.0995585	+	0.995032i	$0.468257\pi$
$228$		0			0
$229$	−12.0000			−0.792982			−0.396491	−	0.918039i	$-0.629772\pi$
$229$	−12.0000			−0.792982			−0.396491	+	0.918039i	$0.629772\pi$
$230$	1.73648	−	9.84808i	0.114500	−	0.649363i
$231$	13.7888	+	11.5702i	0.907236	+	0.761262i
$232$	2.81908	+	1.02606i	0.185082	+	0.0673642i
$233$	−13.1557	+	4.78828i	−0.861858	+	0.313691i	−0.734866	−	0.678213i	$-0.762755\pi$
$233$	−13.1557	+	4.78828i	−0.861858	+	0.313691i	−0.126993	+	0.991904i	$0.540533\pi$
$234$	−13.7888	+	11.5702i	−0.901402	+	0.756366i
$235$	8.00000	+	13.8564i	0.521862	+	0.903892i
$236$	−1.50000	+	2.59808i	−0.0976417	+	0.169120i
$237$	−6.25133	−	35.4531i	−0.406068	−	2.30292i
$238$	0.520945	+	2.95442i	0.0337678	+	0.191507i
$239$	−0.500000	+	0.866025i	−0.0323423	+	0.0560185i	−0.881743	−	0.471729i	$-0.843630\pi$
$239$	−0.500000	+	0.866025i	−0.0323423	+	0.0560185i	0.849401	+	0.527748i	$0.176963\pi$
$240$	−3.00000	−	5.19615i	−0.193649	−	0.335410i
$241$	18.3851	−	15.4269i	1.18429	−	0.993734i	0.184345	−	0.982862i	$-0.440984\pi$
$241$	18.3851	−	15.4269i	1.18429	−	0.993734i	0.999941	−	0.0108726i	$-0.00346093\pi$
$242$	6.57785	−	2.39414i	0.422840	−	0.153901i
$243$		0			0
$244$		0			0
$245$	0.694593	−	3.93923i	0.0443759	−	0.251668i
$246$	36.0000			2.29528
$247$		0			0
$248$	−6.00000			−0.381000
$249$	1.04189	−	5.90885i	0.0660270	−	0.374458i
$250$	−9.19253	−	7.71345i	−0.581387	−	0.487841i
$251$	18.7939	+	6.84040i	1.18626	+	0.431762i	0.858408	−	0.512968i	$-0.171454\pi$
$251$	18.7939	+	6.84040i	1.18626	+	0.431762i	0.327849	+	0.944730i	$0.393676\pi$
$252$	16.9145	−	6.15636i	1.06551	−	0.387814i
$253$	−7.66044	+	6.42788i	−0.481608	+	0.404117i
$254$	−6.00000	−	10.3923i	−0.376473	−	0.652071i
$255$	3.00000	−	5.19615i	0.187867	−	0.325396i
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	−3.12567	−	17.7265i	−0.194974	−	1.10575i	−0.912456	−	0.409175i	$-0.865817\pi$
$257$	−3.12567	−	17.7265i	−0.194974	−	1.10575i	0.717482	−	0.696577i	$-0.245294\pi$
$258$	15.0000	−	25.9808i	0.933859	−	1.61749i
$259$	9.00000	+	15.5885i	0.559233	+	0.968620i
$260$	−4.59627	+	3.85673i	−0.285048	+	0.239184i
$261$	16.9145	−	6.15636i	1.04698	−	0.381069i
$262$	−13.1557	−	4.78828i	−0.812762	−	0.295821i
$263$	−6.12836	−	5.14230i	−0.377891	−	0.317088i	0.433983	−	0.900921i	$-0.357108\pi$
$263$	−6.12836	−	5.14230i	−0.377891	−	0.317088i	−0.811874	+	0.583833i	$0.801552\pi$
$264$	−1.04189	+	5.90885i	−0.0641238	+	0.363664i
$265$	−6.00000			−0.368577
$266$		0			0
$267$	18.0000			1.10158
$268$	2.60472	−	14.7721i	0.159109	−	0.902351i
$269$	−4.59627	−	3.85673i	−0.280239	−	0.235149i	0.491824	−	0.870695i	$-0.336331\pi$
$269$	−4.59627	−	3.85673i	−0.280239	−	0.235149i	−0.772063	+	0.635546i	$0.780775\pi$
$270$	−16.9145	−	6.15636i	−1.02938	−	0.374664i
$271$	10.3366	−	3.76222i	0.627905	−	0.228539i	−0.00841427	−	0.999965i	$-0.502678\pi$
$271$	10.3366	−	3.76222i	0.627905	−	0.228539i	0.636319	+	0.771426i	$0.280456\pi$
$272$	−0.766044	+	0.642788i	−0.0464483	+	0.0389747i
$273$	−13.5000	−	23.3827i	−0.817057	−	1.41518i
$274$	−9.50000	+	16.4545i	−0.573916	+	0.994052i
$275$	0.347296	+	1.96962i	0.0209428	+	0.118772i
$276$	2.60472	+	14.7721i	0.156786	+	0.889177i
$277$	−15.0000	+	25.9808i	−0.901263	+	1.56103i	−0.0754058	+	0.997153i	$0.524025\pi$
$277$	−15.0000	+	25.9808i	−0.901263	+	1.56103i	−0.825857	+	0.563880i	$0.809308\pi$
$278$	−3.00000	−	5.19615i	−0.179928	−	0.311645i
$279$	−27.5776	+	23.1404i	−1.65103	+	1.38538i
$280$	5.63816	−	2.05212i	0.336944	−	0.122638i
$281$	−11.2763	−	4.10424i	−0.672688	−	0.244839i	−0.0169834	−	0.999856i	$-0.505406\pi$
$281$	−11.2763	−	4.10424i	−0.672688	−	0.244839i	−0.655705	+	0.755017i	$0.727628\pi$
$282$	−18.3851	−	15.4269i	−1.09481	−	0.918659i
$283$	−2.43107	+	13.7873i	−0.144512	+	0.819570i	0.823245	+	0.567686i	$0.192161\pi$
$283$	−2.43107	+	13.7873i	−0.144512	+	0.819570i	−0.967757	+	0.251884i	$0.918950\pi$
$284$		0			0
$285$		0			0
$286$	6.00000			0.354787
$287$	−6.25133	+	35.4531i	−0.369005	+	2.09273i
$288$	4.59627	+	3.85673i	0.270838	+	0.227260i
$289$	15.0351	+	5.47232i	0.884417	+	0.321901i
$290$	5.63816	−	2.05212i	0.331084	−	0.120505i
$291$	27.5776	−	23.1404i	1.61663	−	1.35651i
$292$	5.50000	+	9.52628i	0.321863	+	0.557483i
$293$	4.50000	−	7.79423i	0.262893	−	0.455344i	−0.704117	−	0.710084i	$-0.748657\pi$
$293$	4.50000	−	7.79423i	0.262893	−	0.455344i	0.967009	+	0.254741i	$0.0819901\pi$
$294$	1.04189	+	5.90885i	0.0607642	+	0.344611i
$295$	1.04189	+	5.90885i	0.0606611	+	0.344026i
$296$	−3.00000	+	5.19615i	−0.174371	+	0.302020i
$297$	9.00000	+	15.5885i	0.522233	+	0.904534i
$298$	−6.12836	+	5.14230i	−0.355006	+	0.297885i
$299$	14.0954	−	5.13030i	0.815157	−	0.296693i
$300$	2.81908	+	1.02606i	0.162760	+	0.0592396i
$301$	22.9813	+	19.2836i	1.32462	+	1.11149i
$302$	−3.12567	+	17.7265i	−0.179862	+	1.02005i
$303$	30.0000			1.72345
$304$		0			0
$305$		0			0
$306$	−1.04189	+	5.90885i	−0.0595608	+	0.337786i
$307$	9.19253	+	7.71345i	0.524646	+	0.440230i	0.866248	−	0.499615i	$-0.166525\pi$
$307$	9.19253	+	7.71345i	0.524646	+	0.440230i	−0.341602	+	0.939845i	$0.610970\pi$
$308$	−5.63816	−	2.05212i	−0.321264	−	0.116930i
$309$	−16.9145	+	6.15636i	−0.962230	+	0.350223i
$310$	−9.19253	+	7.71345i	−0.522101	+	0.438095i
$311$	5.50000	+	9.52628i	0.311876	+	0.540186i	0.978769	−	0.204968i	$-0.0657092\pi$
$311$	5.50000	+	9.52628i	0.311876	+	0.540186i	−0.666892	+	0.745154i	$0.732376\pi$
$312$	4.50000	−	7.79423i	0.254762	−	0.441261i
$313$	3.64661	+	20.6810i	0.206119	+	1.16896i	0.895670	+	0.444720i	$0.146697\pi$
$313$	3.64661	+	20.6810i	0.206119	+	1.16896i	−0.689551	+	0.724237i	$0.742192\pi$
$314$		0			0
$315$	18.0000	−	31.1769i	1.01419	−	1.75662i
$316$	6.00000	+	10.3923i	0.337526	+	0.584613i
$317$	−25.2795	+	21.2120i	−1.41984	+	1.19138i	−0.468409	+	0.883512i	$0.655172\pi$
$317$	−25.2795	+	21.2120i	−1.41984	+	1.19138i	−0.951428	+	0.307872i	$0.900383\pi$
$318$	8.45723	−	3.07818i	0.474258	−	0.172616i
$319$	−5.63816	−	2.05212i	−0.315676	−	0.114897i
$320$	1.53209	+	1.28558i	0.0856464	+	0.0718658i
$321$	−1.56283	+	8.86327i	−0.0872289	+	0.494699i
$322$	−15.0000			−0.835917
$323$		0			0
$324$	9.00000			0.500000
$325$	0.520945	−	2.95442i	0.0288968	−	0.163882i
$326$	−4.59627	−	3.85673i	−0.254564	−	0.213604i
$327$	−8.45723	−	3.07818i	−0.467686	−	0.170224i
$328$	−11.2763	+	4.10424i	−0.622630	+	0.226619i
$329$	18.3851	−	15.4269i	1.01360	−	0.850513i
$330$	6.00000	+	10.3923i	0.330289	+	0.572078i
$331$	−4.50000	+	7.79423i	−0.247342	+	0.428410i	−0.962788	−	0.270259i	$-0.912891\pi$
$331$	−4.50000	+	7.79423i	−0.247342	+	0.428410i	0.715445	+	0.698669i	$0.246224\pi$
$332$	0.347296	+	1.96962i	0.0190604	+	0.108097i
$333$	6.25133	+	35.4531i	0.342571	+	1.94282i
$334$	6.00000	−	10.3923i	0.328305	−	0.568642i
$335$	−15.0000	−	25.9808i	−0.819538	−	1.41948i
$336$	−6.89440	+	5.78509i	−0.376120	+	0.315602i
$337$	−16.9145	+	6.15636i	−0.921390	+	0.335358i	−0.758791	−	0.651334i	$-0.774210\pi$
$337$	−16.9145	+	6.15636i	−0.921390	+	0.335358i	−0.162598	+	0.986692i	$0.551988\pi$
$338$	3.75877	+	1.36808i	0.204450	+	0.0744138i
$339$	27.5776	+	23.1404i	1.49781	+	1.25681i
$340$	−0.347296	+	1.96962i	−0.0188348	+	0.106817i
$341$	12.0000			0.649836
$342$		0			0
$343$	15.0000			0.809924
$344$	−1.73648	+	9.84808i	−0.0936248	+	0.530973i
$345$	22.9813	+	19.2836i	1.23727	+	1.03820i
$346$	16.9145	+	6.15636i	0.909327	+	0.330968i
$347$	−15.0351	+	5.47232i	−0.807125	+	0.293770i	−0.712436	−	0.701737i	$-0.752408\pi$
$347$	−15.0351	+	5.47232i	−0.807125	+	0.293770i	−0.0946896	+	0.995507i	$0.530186\pi$
$348$	−6.89440	+	5.78509i	−0.369579	+	0.310113i
$349$	−14.0000	−	24.2487i	−0.749403	−	1.29800i	−0.948109	−	0.317945i	$-0.897007\pi$
$349$	−14.0000	−	24.2487i	−0.749403	−	1.29800i	0.198706	−	0.980059i	$-0.436326\pi$
$350$	−1.50000	+	2.59808i	−0.0801784	+	0.138873i
$351$	−4.68850	−	26.5898i	−0.250254	−	1.41926i
$352$	−0.347296	−	1.96962i	−0.0185110	−	0.104981i
$353$	15.5000	−	26.8468i	0.824982	−	1.42891i	−0.0769515	−	0.997035i	$-0.524519\pi$
$353$	15.5000	−	26.8468i	0.824982	−	1.42891i	0.901933	−	0.431875i	$-0.142148\pi$
$354$	−4.50000	−	7.79423i	−0.239172	−	0.414259i
$355$		0			0
$356$	−5.63816	+	2.05212i	−0.298822	+	0.108762i
$357$	−8.45723	−	3.07818i	−0.447604	−	0.162915i
$358$	−9.19253	−	7.71345i	−0.485840	−	0.407669i
$359$	3.29932	−	18.7113i	0.174131	−	0.987547i	−0.765011	−	0.644018i	$-0.777266\pi$
$359$	3.29932	−	18.7113i	0.174131	−	0.987547i	0.939142	−	0.343530i	$-0.111623\pi$
$360$	12.0000			0.632456
$361$		0			0
$362$	18.0000			0.946059
$363$	−3.64661	+	20.6810i	−0.191397	+	1.08547i
$364$	6.89440	+	5.78509i	0.361365	+	0.303221i
$365$	20.6732	+	7.52444i	1.08209	+	0.393847i
$366$		0			0
$367$	6.12836	−	5.14230i	0.319898	−	0.268426i	−0.468671	−	0.883373i	$-0.655267\pi$
$367$	6.12836	−	5.14230i	0.319898	−	0.268426i	0.788569	+	0.614947i	$0.210823\pi$
$368$	−2.50000	−	4.33013i	−0.130322	−	0.225723i
$369$	−36.0000	+	62.3538i	−1.87409	+	3.24601i
$370$	2.08378	+	11.8177i	0.108330	+	0.614373i
$371$	1.56283	+	8.86327i	0.0811383	+	0.460158i
$372$	9.00000	−	15.5885i	0.466628	−	0.808224i
$373$	10.5000	+	18.1865i	0.543669	+	0.941663i	0.998689	+	0.0511818i	$0.0162988\pi$
$373$	10.5000	+	18.1865i	0.543669	+	0.941663i	−0.455020	+	0.890481i	$0.650368\pi$
$374$	1.53209	−	1.28558i	0.0792224	−	0.0664755i
$375$	33.8289	−	12.3127i	1.74692	−	0.635826i
$376$	7.51754	+	2.73616i	0.387688	+	0.141107i
$377$	6.89440	+	5.78509i	0.355080	+	0.297947i
$378$	−4.68850	+	26.5898i	−0.241150	+	1.36763i
$379$	3.00000			0.154100			0.0770498	−	0.997027i	$-0.475450\pi$
$379$	3.00000			0.154100			0.0770498	+	0.997027i	$0.475450\pi$
$380$		0			0
$381$	36.0000			1.84434
$382$	−1.91013	+	10.8329i	−0.0977308	+	0.554259i
$383$	13.7888	+	11.5702i	0.704575	+	0.591208i	0.923071	−	0.384629i	$-0.125671\pi$
$383$	13.7888	+	11.5702i	0.704575	+	0.591208i	−0.218496	+	0.975838i	$0.570115\pi$
$384$	−2.81908	−	1.02606i	−0.143860	−	0.0523609i
$385$	−11.2763	+	4.10424i	−0.574694	+	0.209172i
$386$	4.59627	−	3.85673i	0.233944	−	0.196302i
$387$	30.0000	+	51.9615i	1.52499	+	2.64135i
$388$	−6.00000	+	10.3923i	−0.304604	+	0.527589i
$389$	4.51485	+	25.6050i	0.228912	+	1.29823i	0.855063	+	0.518524i	$0.173518\pi$
$389$	4.51485	+	25.6050i	0.228912	+	1.29823i	−0.626151	+	0.779702i	$0.715371\pi$
$390$	−3.12567	−	17.7265i	−0.158274	−	0.897618i
$391$	2.50000	−	4.33013i	0.126430	−	0.218984i
$392$	−1.00000	−	1.73205i	−0.0505076	−	0.0874818i
$393$	32.1739	−	26.9971i	1.62296	−	1.36182i
$394$	−3.75877	+	1.36808i	−0.189364	+	0.0689229i
$395$	22.5526	+	8.20848i	1.13475	+	0.413014i
$396$	−9.19253	−	7.71345i	−0.461942	−	0.387616i
$397$	0.347296	−	1.96962i	0.0174303	−	0.0988522i	−0.974852	−	0.222855i	$-0.928462\pi$
$397$	0.347296	−	1.96962i	0.0174303	−	0.0988522i	0.992282	+	0.124003i	$0.0395733\pi$
$398$	−7.00000			−0.350878
$399$		0			0
$400$	−1.00000			−0.0500000
$401$	6.25133	−	35.4531i	0.312177	−	1.77044i	−0.275455	−	0.961314i	$-0.588829\pi$
$401$	6.25133	−	35.4531i	0.312177	−	1.77044i	0.587632	−	0.809128i	$-0.300060\pi$
$402$	34.4720	+	28.9254i	1.71931	+	1.44267i
$403$	−16.9145	−	6.15636i	−0.842570	−	0.306670i
$404$	−9.39693	+	3.42020i	−0.467515	+	0.170161i
$405$	13.7888	−	11.5702i	0.685171	−	0.574927i
$406$	−4.50000	−	7.79423i	−0.223331	−	0.386821i
$407$	6.00000	−	10.3923i	0.297409	−	0.515127i
$408$	−0.520945	−	2.95442i	−0.0257906	−	0.146266i
$409$	1.04189	+	5.90885i	0.0515181	+	0.292174i	0.999671	−	0.0256402i	$-0.00816241\pi$
$409$	1.04189	+	5.90885i	0.0515181	+	0.292174i	−0.948153	+	0.317814i	$0.897051\pi$
$410$	−12.0000	+	20.7846i	−0.592638	+	1.02648i
$411$	−28.5000	−	49.3634i	−1.40580	−	2.43492i
$412$	4.59627	−	3.85673i	0.226442	−	0.190007i
$413$	8.45723	−	3.07818i	0.416153	−	0.151467i
$414$	−28.1908	−	10.2606i	−1.38550	−	0.504281i
$415$	3.06418	+	2.57115i	0.150415	+	0.126213i
$416$	−0.520945	+	2.95442i	−0.0255414	+	0.144853i
$417$	18.0000			0.881464
$418$		0			0
$419$	−14.0000			−0.683945			−0.341972	−	0.939710i	$-0.611095\pi$
$419$	−14.0000			−0.683945			−0.341972	+	0.939710i	$0.611095\pi$
$420$	−3.12567	+	17.7265i	−0.152517	+	0.864967i
$421$	−20.6832	−	17.3553i	−1.00804	−	0.845844i	−0.0199599	−	0.999801i	$-0.506354\pi$
$421$	−20.6832	−	17.3553i	−1.00804	−	0.845844i	−0.988078	+	0.153957i	$0.950798\pi$
$422$	−2.81908	−	1.02606i	−0.137231	−	0.0499478i
$423$	45.1052	−	16.4170i	2.19309	−	0.798220i
$424$	−2.29813	+	1.92836i	−0.111607	+	0.0936496i
$425$	−0.500000	−	0.866025i	−0.0242536	−	0.0420084i
$426$		0			0
$427$		0			0
$428$	−0.520945	−	2.95442i	−0.0251808	−	0.142807i
$429$	−9.00000	+	15.5885i	−0.434524	+	0.752618i
$430$	10.0000	+	17.3205i	0.482243	+	0.835269i
$431$	18.3851	−	15.4269i	0.885577	−	0.743088i	−0.0817406	−	0.996654i	$-0.526048\pi$
$431$	18.3851	−	15.4269i	0.885577	−	0.743088i	0.967318	+	0.253566i	$0.0816035\pi$
$432$	−8.45723	+	3.07818i	−0.406899	+	0.148099i
$433$	−28.1908	−	10.2606i	−1.35476	−	0.493093i	−0.440331	−	0.897835i	$-0.645139\pi$
$433$	−28.1908	−	10.2606i	−1.35476	−	0.493093i	−0.914431	+	0.404742i	$0.867361\pi$
$434$	13.7888	+	11.5702i	0.661884	+	0.555386i
$435$	−3.12567	+	17.7265i	−0.149864	+	0.849923i
$436$	3.00000			0.143674
$437$		0			0
$438$	−33.0000			−1.57680
$439$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$439$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$440$	−3.06418	−	2.57115i	−0.146079	−	0.122575i
$441$	−11.2763	−	4.10424i	−0.536967	−	0.195440i
$442$	−2.81908	+	1.02606i	−0.134090	+	0.0488047i
$443$	−16.8530	+	14.1413i	−0.800709	+	0.671875i	−0.948371	−	0.317163i	$-0.897270\pi$
$443$	−16.8530	+	14.1413i	−0.800709	+	0.671875i	0.147662	+	0.989038i	$0.452825\pi$
$444$	−9.00000	−	15.5885i	−0.427121	−	0.739795i
$445$	−6.00000	+	10.3923i	−0.284427	+	0.492642i
$446$	3.12567	+	17.7265i	0.148005	+	0.839376i
$447$	−4.16756	−	23.6354i	−0.197119	−	1.11792i
$448$	1.50000	−	2.59808i	0.0708683	−	0.122748i
$449$	−3.00000	−	5.19615i	−0.141579	−	0.245222i	0.786513	−	0.617574i	$-0.211885\pi$
$449$	−3.00000	−	5.19615i	−0.141579	−	0.245222i	−0.928091	+	0.372353i	$0.878551\pi$
$450$	−4.59627	+	3.85673i	−0.216670	+	0.181808i
$451$	22.5526	−	8.20848i	1.06196	−	0.386522i
$452$	−11.2763	−	4.10424i	−0.530393	−	0.193047i
$453$	−41.3664	−	34.7105i	−1.94356	−	1.63084i
$454$	0.520945	−	2.95442i	0.0244491	−	0.138658i
$455$	18.0000			0.843853
$456$		0			0
$457$	1.00000			0.0467780			0.0233890	−	0.999726i	$-0.492554\pi$
$457$	1.00000			0.0467780			0.0233890	+	0.999726i	$0.492554\pi$
$458$	−2.08378	+	11.8177i	−0.0973686	+	0.552205i
$459$	−6.89440	−	5.78509i	−0.321803	−	0.270025i
$460$	−9.39693	−	3.42020i	−0.438134	−	0.159468i
$461$	−3.75877	+	1.36808i	−0.175063	+	0.0637179i	−0.428065	−	0.903748i	$-0.640804\pi$
$461$	−3.75877	+	1.36808i	−0.175063	+	0.0637179i	0.253001	+	0.967466i	$0.418582\pi$
$462$	13.7888	−	11.5702i	0.641513	−	0.538293i
$463$	−16.0000	−	27.7128i	−0.743583	−	1.28792i	−0.950854	−	0.309640i	$-0.899791\pi$
$463$	−16.0000	−	27.7128i	−0.743583	−	1.28792i	0.207271	−	0.978284i	$-0.433542\pi$
$464$	1.50000	−	2.59808i	0.0696358	−	0.120613i
$465$	−6.25133	−	35.4531i	−0.289899	−	1.64410i
$466$	2.43107	+	13.7873i	0.112617	+	0.638685i
$467$	−4.00000	+	6.92820i	−0.185098	+	0.320599i	−0.943610	−	0.331061i	$-0.892594\pi$
$467$	−4.00000	+	6.92820i	−0.185098	+	0.320599i	0.758512	+	0.651660i	$0.225927\pi$
$468$	9.00000	+	15.5885i	0.416025	+	0.720577i
$469$	−34.4720	+	28.9254i	−1.59177	+	1.33565i
$470$	15.0351	−	5.47232i	0.693517	−	0.252419i
$471$		0			0
$472$	2.29813	+	1.92836i	0.105780	+	0.0887601i
$473$	3.47296	−	19.6962i	0.159687	−	0.905630i
$474$	−36.0000			−1.65353
$475$		0			0
$476$	3.00000			0.137505
$477$	−3.12567	+	17.7265i	−0.143114	+	0.811642i
$478$	0.766044	+	0.642788i	0.0350381	+	0.0294004i
$479$	37.5877	+	13.6808i	1.71743	+	0.625092i	0.997612	−	0.0690744i	$-0.0220046\pi$
$479$	37.5877	+	13.6808i	1.71743	+	0.625092i	0.719815	+	0.694166i	$0.244227\pi$
$480$	−5.63816	+	2.05212i	−0.257345	+	0.0936661i
$481$	−13.7888	+	11.5702i	−0.628715	+	0.527555i
$482$	−12.0000	−	20.7846i	−0.546585	−	0.946713i
$483$	22.5000	−	38.9711i	1.02379	−	1.77325i
$484$	−1.21554	−	6.89365i	−0.0552517	−	0.313348i
$485$	4.16756	+	23.6354i	0.189239	+	1.07323i
$486$		0			0
$487$	9.00000	+	15.5885i	0.407829	+	0.706380i	0.994646	−	0.103339i	$-0.0329526\pi$
$487$	9.00000	+	15.5885i	0.407829	+	0.706380i	−0.586817	+	0.809719i	$0.699619\pi$
$488$		0			0
$489$	16.9145	−	6.15636i	0.764899	−	0.278400i
$490$	−3.75877	−	1.36808i	−0.169804	−	0.0618036i
$491$	6.12836	+	5.14230i	0.276569	+	0.232069i	0.770512	−	0.637425i	$-0.220001\pi$
$491$	6.12836	+	5.14230i	0.276569	+	0.232069i	−0.493943	+	0.869494i	$0.664445\pi$
$492$	6.25133	−	35.4531i	0.281832	−	1.59835i
$493$	3.00000			0.135113
$494$		0			0
$495$	−24.0000			−1.07872
$496$	−1.04189	+	5.90885i	−0.0467822	+	0.265315i
$497$		0			0
$498$	−5.63816	−	2.05212i	−0.252652	−	0.0919577i
$499$	−16.9145	+	6.15636i	−0.757196	+	0.275597i	−0.691630	−	0.722252i	$-0.743107\pi$
$499$	−16.9145	+	6.15636i	−0.757196	+	0.275597i	−0.0655652	+	0.997848i	$0.520885\pi$
$500$	−9.19253	+	7.71345i	−0.411103	+	0.344956i
$501$	18.0000	+	31.1769i	0.804181	+	1.39288i
$502$	10.0000	−	17.3205i	0.446322	−	0.773052i
$503$	0.173648	+	0.984808i	0.00774259	+	0.0439104i	0.988434	−	0.151650i	$-0.0484586\pi$
$503$	0.173648	+	0.984808i	0.00774259	+	0.0439104i	−0.980692	+	0.195560i	$0.937347\pi$
$504$	−3.12567	−	17.7265i	−0.139228	−	0.789603i
$505$	−10.0000	+	17.3205i	−0.444994	+	0.770752i
$506$	5.00000	+	8.66025i	0.222277	+	0.384995i
$507$	−9.19253	+	7.71345i	−0.408255	+	0.342566i
$508$	−11.2763	+	4.10424i	−0.500305	+	0.182096i
$509$	−16.9145	−	6.15636i	−0.749721	−	0.272876i	−0.0612324	−	0.998124i	$-0.519503\pi$
$509$	−16.9145	−	6.15636i	−0.749721	−	0.272876i	−0.688488	+	0.725248i	$0.741725\pi$
$510$	−4.59627	−	3.85673i	−0.203526	−	0.170779i
$511$	5.73039	−	32.4987i	0.253498	−	1.43766i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−18.0000			−0.793946
$515$	2.08378	−	11.8177i	0.0918222	−	0.520750i
$516$	−22.9813	−	19.2836i	−1.01170	−	0.848914i
$517$	−15.0351	−	5.47232i	−0.661242	−	0.240672i
$518$	16.9145	−	6.15636i	0.743179	−	0.270495i
$519$	−41.3664	+	34.7105i	−1.81578	+	1.52362i
$520$	3.00000	+	5.19615i	0.131559	+	0.227866i
$521$	6.00000	−	10.3923i	0.262865	−	0.455295i	−0.704137	−	0.710064i	$-0.748666\pi$
$521$	6.00000	−	10.3923i	0.262865	−	0.455295i	0.967002	+	0.254769i	$0.0819994\pi$
$522$	−3.12567	−	17.7265i	−0.136807	−	0.775870i
$523$	1.56283	+	8.86327i	0.0683379	+	0.387564i	0.999723	+	0.0235286i	$0.00749008\pi$
$523$	1.56283	+	8.86327i	0.0683379	+	0.387564i	−0.931385	+	0.364035i	$0.881399\pi$
$524$	−7.00000	+	12.1244i	−0.305796	+	0.529655i
$525$	−4.50000	−	7.79423i	−0.196396	−	0.340168i
$526$	−6.12836	+	5.14230i	−0.267209	+	0.224215i
$527$	−5.63816	+	2.05212i	−0.245602	+	0.0893918i
$528$	5.63816	+	2.05212i	0.245369	+	0.0893071i
$529$	1.53209	+	1.28558i	0.0666126	+	0.0558946i
$530$	−1.04189	+	5.90885i	−0.0452568	+	0.256664i
$531$	18.0000			0.781133
$532$		0			0
$533$	−36.0000			−1.55933
$534$	3.12567	−	17.7265i	0.135261	−	0.767102i
$535$	−4.59627	−	3.85673i	−0.198714	−	0.166741i
$536$	−14.0954	−	5.13030i	−0.608828	−	0.221595i
$537$	33.8289	−	12.3127i	1.45983	−	0.531333i
$538$	−4.59627	+	3.85673i	−0.198159	+	0.166275i
$539$	2.00000	+	3.46410i	0.0861461	+	0.149209i
$540$	−9.00000	+	15.5885i	−0.387298	+	0.670820i
$541$	0.347296	+	1.96962i	0.0149314	+	0.0846804i	0.991363	−	0.131147i	$-0.0418661\pi$
$541$	0.347296	+	1.96962i	0.0149314	+	0.0846804i	−0.976431	+	0.215828i	$0.930755\pi$
$542$	−1.91013	−	10.8329i	−0.0820471	−	0.465312i
$543$	−27.0000	+	46.7654i	−1.15868	+	2.00689i
$544$	0.500000	+	0.866025i	0.0214373	+	0.0371305i
$545$	4.59627	−	3.85673i	0.196882	−	0.165204i
$546$	−25.3717	+	9.23454i	−1.08581	+	0.395202i
$547$	33.8289	+	12.3127i	1.44642	+	0.526454i	0.941589	−	0.336764i	$-0.109332\pi$
$547$	33.8289	+	12.3127i	1.44642	+	0.526454i	0.504832	+	0.863218i	$0.331555\pi$
$548$	14.5548	+	12.2130i	0.621752	+	0.521712i
$549$		0			0
$550$	2.00000			0.0852803
$551$		0			0
$552$	15.0000			0.638442
$553$	6.25133	−	35.4531i	0.265834	−	1.50762i
$554$	22.9813	+	19.2836i	0.976383	+	0.819283i
$555$	−33.8289	−	12.3127i	−1.43596	−	0.522646i
$556$	−5.63816	+	2.05212i	−0.239111	+	0.0870293i
$557$	16.8530	−	14.1413i	0.714084	−	0.599187i	−0.211658	−	0.977344i	$-0.567886\pi$
$557$	16.8530	−	14.1413i	0.714084	−	0.599187i	0.925742	+	0.378156i	$0.123442\pi$
$558$	18.0000	+	31.1769i	0.762001	+	1.31982i
$559$	−15.0000	+	25.9808i	−0.634432	+	1.09887i
$560$	−1.04189	−	5.90885i	−0.0440278	−	0.249694i
$561$	1.04189	+	5.90885i	0.0439886	+	0.249472i
$562$	−6.00000	+	10.3923i	−0.253095	+	0.438373i
$563$	12.0000	+	20.7846i	0.505740	+	0.875967i	0.999978	+	0.00664037i	$0.00211371\pi$
$563$	12.0000	+	20.7846i	0.505740	+	0.875967i	−0.494238	+	0.869326i	$0.664553\pi$
$564$	−18.3851	+	15.4269i	−0.774151	+	0.649590i
$565$	−22.5526	+	8.20848i	−0.948796	+	0.345333i
$566$	13.1557	+	4.78828i	0.552975	+	0.201267i
$567$	−20.6832	−	17.3553i	−0.868613	−	0.728853i
$568$		0			0
$569$	−24.0000			−1.00613			−0.503066	−	0.864248i	$-0.667795\pi$
$569$	−24.0000			−1.00613			−0.503066	+	0.864248i	$0.667795\pi$
$570$		0			0
$571$	−32.0000			−1.33916			−0.669579	−	0.742741i	$-0.733526\pi$
$571$	−32.0000			−1.33916			−0.669579	+	0.742741i	$0.733526\pi$
$572$	1.04189	−	5.90885i	0.0435636	−	0.247061i
$573$	−25.2795	−	21.2120i	−1.05606	−	0.886144i
$574$	33.8289	+	12.3127i	1.41199	+	0.513923i
$575$	4.69846	−	1.71010i	0.195939	−	0.0713161i
$576$	4.59627	−	3.85673i	0.191511	−	0.160697i
$577$	−7.50000	−	12.9904i	−0.312229	−	0.540797i	0.666616	−	0.745402i	$-0.267742\pi$
$577$	−7.50000	−	12.9904i	−0.312229	−	0.540797i	−0.978845	+	0.204605i	$0.934409\pi$
$578$	8.00000	−	13.8564i	0.332756	−	0.576351i
$579$	3.12567	+	17.7265i	0.129898	+	0.736690i
$580$	−1.04189	−	5.90885i	−0.0432621	−	0.245351i
$581$	3.00000	−	5.19615i	0.124461	−	0.215573i
$582$	−18.0000	−	31.1769i	−0.746124	−	1.29232i
$583$	4.59627	−	3.85673i	0.190358	−	0.159729i
$584$	10.3366	−	3.76222i	0.427732	−	0.155682i
$585$	33.8289	+	12.3127i	1.39865	+	0.509069i
$586$	−6.89440	−	5.78509i	−0.284805	−	0.238980i
$587$	−4.86215	+	27.5746i	−0.200682	+	1.13813i	0.703408	+	0.710786i	$0.251661\pi$
$587$	−4.86215	+	27.5746i	−0.200682	+	1.13813i	−0.904091	+	0.427340i	$0.859451\pi$
$588$	6.00000			0.247436
$589$		0			0
$590$	6.00000			0.247016
$591$	2.08378	−	11.8177i	0.0857152	−	0.486115i
$592$	4.59627	+	3.85673i	0.188905	+	0.158510i
$593$	1.87939	+	0.684040i	0.0771771	+	0.0280902i	0.380320	−	0.924855i	$-0.375814\pi$
$593$	1.87939	+	0.684040i	0.0771771	+	0.0280902i	−0.303143	+	0.952945i	$0.598036\pi$
$594$	16.9145	−	6.15636i	0.694009	−	0.252599i
$595$	4.59627	−	3.85673i	0.188429	−	0.158110i
$596$	4.00000	+	6.92820i	0.163846	+	0.283790i
$597$	10.5000	−	18.1865i	0.429736	−	0.744325i
$598$	−2.60472	−	14.7721i	−0.106515	−	0.604077i
$599$	−6.25133	−	35.4531i	−0.255423	−	1.44857i	−0.794986	−	0.606628i	$-0.792522\pi$
$599$	−6.25133	−	35.4531i	−0.255423	−	1.44857i	0.539563	−	0.841945i	$-0.318589\pi$
$600$	1.50000	−	2.59808i	0.0612372	−	0.106066i
$601$	3.00000	+	5.19615i	0.122373	+	0.211955i	0.920703	−	0.390264i	$-0.127616\pi$
$601$	3.00000	+	5.19615i	0.122373	+	0.211955i	−0.798330	+	0.602220i	$0.794283\pi$
$602$	22.9813	−	19.2836i	0.936649	−	0.785942i
$603$	−84.5723	+	30.7818i	−3.44405	+	1.25353i
$604$	16.9145	+	6.15636i	0.688240	+	0.250499i
$605$	−10.7246	−	8.99903i	−0.436018	−	0.365862i
$606$	5.20945	−	29.5442i	0.211619	−	1.20015i
$607$	−12.0000			−0.487065			−0.243532	−	0.969893i	$-0.578306\pi$
$607$	−12.0000			−0.487065			−0.243532	+	0.969893i	$0.578306\pi$
$608$		0			0
$609$	27.0000			1.09410
$610$		0			0
$611$	18.3851	+	15.4269i	0.743780	+	0.624106i
$612$	5.63816	+	2.05212i	0.227909	+	0.0829521i
$613$	−16.9145	+	6.15636i	−0.683169	+	0.248653i	−0.660208	−	0.751083i	$-0.729532\pi$
$613$	−16.9145	+	6.15636i	−0.683169	+	0.248653i	−0.0229613	+	0.999736i	$0.507309\pi$
$614$	9.19253	−	7.71345i	0.370980	−	0.311290i
$615$	−36.0000	−	62.3538i	−1.45166	−	2.51435i
$616$	−3.00000	+	5.19615i	−0.120873	+	0.209359i
$617$	1.73648	+	9.84808i	0.0699081	+	0.396469i	0.999604	+	0.0281405i	$0.00895859\pi$
$617$	1.73648	+	9.84808i	0.0699081	+	0.396469i	−0.929696	+	0.368328i	$0.879930\pi$
$618$	3.12567	+	17.7265i	0.125733	+	0.713066i
$619$	12.0000	−	20.7846i	0.482321	−	0.835404i	−0.517473	−	0.855699i	$-0.673127\pi$
$619$	12.0000	−	20.7846i	0.482321	−	0.835404i	0.999794	+	0.0202954i	$0.00646066\pi$
$620$	6.00000	+	10.3923i	0.240966	+	0.417365i
$621$	34.4720	−	28.9254i	1.38331	−	1.16074i
$622$	10.3366	−	3.76222i	0.414461	−	0.150851i
$623$	16.9145	+	6.15636i	0.677664	+	0.246649i
$624$	−6.89440	−	5.78509i	−0.275997	−	0.231589i
$625$	−3.29932	+	18.7113i	−0.131973	+	0.748454i
$626$	21.0000			0.839329
$627$		0			0
$628$		0			0
$629$	−1.04189	+	5.90885i	−0.0415428	+	0.235601i
$630$	−27.5776	−	23.1404i	−1.09872	−	0.921934i
$631$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$631$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$632$	11.2763	−	4.10424i	0.448548	−	0.163258i
$633$	6.89440	−	5.78509i	0.274028	−	0.229937i
$634$	16.5000	+	28.5788i	0.655299	+	1.13501i
$635$	−12.0000	+	20.7846i	−0.476205	+	0.824812i
$636$	−1.56283	−	8.86327i	−0.0619704	−	0.351452i
$637$	−1.04189	−	5.90885i	−0.0412811	−	0.234117i
$638$	−3.00000	+	5.19615i	−0.118771	+	0.205718i
$639$		0			0
$640$	1.53209	−	1.28558i	0.0605611	−	0.0508168i
$641$	−16.9145	+	6.15636i	−0.668081	+	0.243162i	−0.653722	−	0.756735i	$-0.726793\pi$
$641$	−16.9145	+	6.15636i	−0.668081	+	0.243162i	−0.0143597	+	0.999897i	$0.504571\pi$
$642$	8.45723	+	3.07818i	0.333780	+	0.121486i
$643$	24.5134	+	20.5692i	0.966715	+	0.811170i	0.982032	−	0.188712i	$-0.0604314\pi$
$643$	24.5134	+	20.5692i	0.966715	+	0.811170i	−0.0153174	+	0.999883i	$0.504876\pi$
$644$	−2.60472	+	14.7721i	−0.102640	+	0.582103i
$645$	−60.0000			−2.36250
$646$		0			0
$647$	−23.0000			−0.904223			−0.452112	−	0.891961i	$-0.649329\pi$
$647$	−23.0000			−0.904223			−0.452112	+	0.891961i	$0.649329\pi$
$648$	1.56283	−	8.86327i	0.0613939	−	0.348182i
$649$	−4.59627	−	3.85673i	−0.180419	−	0.151390i
$650$	−2.81908	−	1.02606i	−0.110573	−	0.0402454i
$651$	−50.7434	+	18.4691i	−1.98879	+	0.723861i
$652$	−4.59627	+	3.85673i	−0.180004	+	0.151041i
$653$	5.00000	+	8.66025i	0.195665	+	0.338902i	0.947118	−	0.320884i	$-0.103980\pi$
$653$	5.00000	+	8.66025i	0.195665	+	0.338902i	−0.751453	+	0.659786i	$0.770647\pi$
$654$	−4.50000	+	7.79423i	−0.175964	+	0.304778i
$655$	4.86215	+	27.5746i	0.189980	+	1.07743i
$656$	2.08378	+	11.8177i	0.0813579	+	0.461403i
$657$	33.0000	−	57.1577i	1.28745	−	2.22993i
$658$	−12.0000	−	20.7846i	−0.467809	−	0.810268i
$659$	−11.4907	+	9.64181i	−0.447613	+	0.375592i	−0.838549	−	0.544826i	$-0.816596\pi$
$659$	−11.4907	+	9.64181i	−0.447613	+	0.375592i	0.390936	+	0.920418i	$0.372151\pi$
$660$	11.2763	−	4.10424i	0.438930	−	0.159757i
$661$	−14.0954	−	5.13030i	−0.548247	−	0.199546i	0.0530204	−	0.998593i	$-0.483115\pi$
$661$	−14.0954	−	5.13030i	−0.548247	−	0.199546i	−0.601268	+	0.799048i	$0.705337\pi$
$662$	6.89440	+	5.78509i	0.267958	+	0.224844i
$663$	1.56283	−	8.86327i	0.0606954	−	0.344221i
$664$	2.00000			0.0776151
$665$		0			0
$666$	36.0000			1.39497
$667$	−2.60472	+	14.7721i	−0.100855	+	0.571979i
$668$	−9.19253	−	7.71345i	−0.355670	−	0.298442i
$669$	−50.7434	−	18.4691i	−1.96185	−	0.714056i
$670$	−28.1908	+	10.2606i	−1.08910	+	0.396402i
$671$		0			0
$672$	4.50000	+	7.79423i	0.173591	+	0.300669i
$673$	24.0000	−	41.5692i	0.925132	−	1.60238i	0.133783	−	0.991011i	$-0.457287\pi$
$673$	24.0000	−	41.5692i	0.925132	−	1.60238i	0.791349	−	0.611365i	$-0.209379\pi$
$674$	3.12567	+	17.7265i	0.120396	+	0.682801i
$675$	−1.56283	−	8.86327i	−0.0601535	−	0.341147i
$676$	2.00000	−	3.46410i	0.0769231	−	0.133235i
$677$	−1.50000	−	2.59808i	−0.0576497	−	0.0998522i	0.835760	−	0.549095i	$-0.185027\pi$
$677$	−1.50000	−	2.59808i	−0.0576497	−	0.0998522i	−0.893410	+	0.449242i	$0.851694\pi$
$678$	27.5776	−	23.1404i	1.05911	−	0.888700i
$679$	33.8289	−	12.3127i	1.29824	−	0.472519i
$680$	1.87939	+	0.684040i	0.0720711	+	0.0262317i
$681$	6.89440	+	5.78509i	0.264194	+	0.221685i
$682$	2.08378	−	11.8177i	0.0797920	−	0.452523i
$683$	−36.0000			−1.37750			−0.688751	−	0.724998i	$-0.741841\pi$
$683$	−36.0000			−1.37750			−0.688751	+	0.724998i	$0.741841\pi$
$684$		0			0
$685$	38.0000			1.45191
$686$	2.60472	−	14.7721i	0.0994488	−	0.564002i
$687$	−27.5776	−	23.1404i	−1.05215	−	0.882860i
$688$	9.39693	+	3.42020i	0.358254	+	0.130394i
$689$	−8.45723	+	3.07818i	−0.322195	+	0.117269i
$690$	22.9813	−	19.2836i	0.874884	−	0.734115i
$691$	4.00000	+	6.92820i	0.152167	+	0.263561i	0.932024	−	0.362397i	$-0.118041\pi$
$691$	4.00000	+	6.92820i	0.152167	+	0.263561i	−0.779857	+	0.625958i	$0.784708\pi$
$692$	9.00000	−	15.5885i	0.342129	−	0.592584i
$693$	6.25133	+	35.4531i	0.237469	+	1.34675i
$694$	2.77837	+	15.7569i	0.105466	+	0.598125i
$695$	−6.00000	+	10.3923i	−0.227593	+	0.394203i
$696$	4.50000	+	7.79423i	0.170572	+	0.295439i
$697$	−9.19253	+	7.71345i	−0.348192	+	0.292168i
$698$	−26.3114	+	9.57656i	−0.995901	+	0.362478i
$699$	−39.4671	−	14.3648i	−1.49278	−	0.543328i
$700$	2.29813	+	1.92836i	0.0868613	+	0.0728853i
$701$	−6.94593	+	39.3923i	−0.262344	+	1.48783i	0.514149	+	0.857701i	$0.328108\pi$
$701$	−6.94593	+	39.3923i	−0.262344	+	1.48783i	−0.776493	+	0.630126i	$0.783003\pi$
$702$	−27.0000			−1.01905
$703$		0			0
$704$	−2.00000			−0.0753778
$705$	−8.33511	+	47.2708i	−0.313918	+	1.78032i
$706$	−23.7474	−	19.9264i	−0.893744	−	0.749941i
$707$	28.1908	+	10.2606i	1.06022	+	0.385890i
$708$	−8.45723	+	3.07818i	−0.317842	+	0.115685i
$709$	−6.12836	+	5.14230i	−0.230155	+	0.193123i	−0.750571	−	0.660790i	$-0.770221\pi$
$709$	−6.12836	+	5.14230i	−0.230155	+	0.193123i	0.520416	+	0.853913i	$0.325777\pi$
$710$		0			0
$711$	36.0000	−	62.3538i	1.35011	−	2.33845i
$712$	1.04189	+	5.90885i	0.0390464	+	0.221443i
$713$	−5.20945	−	29.5442i	−0.195095	−	1.10644i
$714$	−4.50000	+	7.79423i	−0.168408	+	0.291692i
$715$	−6.00000	−	10.3923i	−0.224387	−	0.388650i
$716$	−9.19253	+	7.71345i	−0.343541	+	0.288265i
$717$	−2.81908	+	1.02606i	−0.105280	+	0.0383189i
$718$	−17.8542	−	6.49838i	−0.666311	−	0.242517i
$719$	−32.9399	−	27.6399i	−1.22845	−	1.03079i	−0.998338	−	0.0576293i	$-0.981646\pi$
$719$	−32.9399	−	27.6399i	−1.22845	−	1.03079i	−0.230113	−	0.973164i	$-0.573910\pi$
$720$	2.08378	−	11.8177i	0.0776578	−	0.440419i
$721$	−18.0000			−0.670355
$722$		0			0
$723$	72.0000			2.67771
$724$	3.12567	−	17.7265i	0.116165	−	0.658802i
$725$	2.29813	+	1.92836i	0.0853505	+	0.0716176i
$726$	19.7335	+	7.18242i	0.732381	+	0.266565i
$727$	32.8892	−	11.9707i	1.21979	−	0.443969i	0.349704	−	0.936860i	$-0.386282\pi$
$727$	32.8892	−	11.9707i	1.21979	−	0.443969i	0.870091	+	0.492891i	$0.164060\pi$
$728$	6.89440	−	5.78509i	0.255523	−	0.214410i
$729$	13.5000	+	23.3827i	0.500000	+	0.866025i
$730$	11.0000	−	19.0526i	0.407128	−	0.705167i
$731$	1.73648	+	9.84808i	0.0642261	+	0.364244i
$732$		0			0
$733$	11.0000	−	19.0526i	0.406294	−	0.703722i	−0.588177	−	0.808732i	$-0.700154\pi$
$733$	11.0000	−	19.0526i	0.406294	−	0.703722i	0.994471	+	0.105010i	$0.0334875\pi$
$734$	−4.00000	−	6.92820i	−0.147643	−	0.255725i
$735$	9.19253	−	7.71345i	0.339072	−	0.284515i
$736$	−4.69846	+	1.71010i	−0.173188	+	0.0630351i
$737$	28.1908	+	10.2606i	1.03842	+	0.377954i
$738$	55.1552	+	46.2807i	2.03029	+	1.70362i
$739$	−2.08378	+	11.8177i	−0.0766530	+	0.434721i	0.922195	+	0.386726i	$0.126394\pi$
$739$	−2.08378	+	11.8177i	−0.0766530	+	0.434721i	−0.998848	+	0.0479947i	$0.984717\pi$
$740$	12.0000			0.441129
$741$		0			0
$742$	9.00000			0.330400
$743$	1.04189	−	5.90885i	0.0382232	−	0.216775i	−0.959713	−	0.280981i	$-0.909340\pi$
$743$	1.04189	−	5.90885i	0.0382232	−	0.216775i	0.997937	+	0.0642060i	$0.0204515\pi$
$744$	−13.7888	−	11.5702i	−0.505522	−	0.424183i
$745$	15.0351	+	5.47232i	0.550843	+	0.200490i
$746$	19.7335	−	7.18242i	0.722496	−	0.262967i
$747$	9.19253	−	7.71345i	0.336337	−	0.282220i
$748$	−1.00000	−	1.73205i	−0.0365636	−	0.0633300i
$749$	−4.50000	+	7.79423i	−0.164426	+	0.284795i
$750$	−6.25133	−	35.4531i	−0.228266	−	1.29456i
$751$	2.08378	+	11.8177i	0.0760381	+	0.431234i	0.998933	+	0.0461818i	$0.0147054\pi$
$751$	2.08378	+	11.8177i	0.0760381	+	0.431234i	−0.922895	+	0.385052i	$0.874184\pi$
$752$	4.00000	−	6.92820i	0.145865	−	0.252646i
$753$	30.0000	+	51.9615i	1.09326	+	1.89358i
$754$	6.89440	−	5.78509i	0.251079	−	0.210680i
$755$	33.8289	−	12.3127i	1.23116	−	0.448106i
$756$	25.3717	+	9.23454i	0.922760	+	0.335857i
$757$	9.19253	+	7.71345i	0.334108	+	0.280350i	0.794371	−	0.607432i	$-0.207800\pi$
$757$	9.19253	+	7.71345i	0.334108	+	0.280350i	−0.460263	+	0.887783i	$0.652245\pi$
$758$	0.520945	−	2.95442i	0.0189216	−	0.107309i
$759$	−30.0000			−1.08893
$760$		0			0
$761$	−13.0000			−0.471250			−0.235625	−	0.971844i	$-0.575714\pi$
$761$	−13.0000			−0.471250			−0.235625	+	0.971844i	$0.575714\pi$
$762$	6.25133	−	35.4531i	0.226462	−	1.28433i
$763$	−6.89440	−	5.78509i	−0.249594	−	0.209434i
$764$	10.3366	+	3.76222i	0.373966	+	0.136112i
$765$	11.2763	−	4.10424i	0.407696	−	0.148389i
$766$	13.7888	−	11.5702i	0.498210	−	0.418047i
$767$	4.50000	+	7.79423i	0.162486	+	0.281433i
$768$	−1.50000	+	2.59808i	−0.0541266	+	0.0937500i
$769$	−2.60472	−	14.7721i	−0.0939287	−	0.532696i	−0.995070	−	0.0991714i	$-0.968381\pi$
$769$	−2.60472	−	14.7721i	−0.0939287	−	0.532696i	0.901142	−	0.433525i	$-0.142730\pi$
$770$	2.08378	+	11.8177i	0.0750942	+	0.425880i
$771$	27.0000	−	46.7654i	0.972381	−	1.68421i
$772$	−3.00000	−	5.19615i	−0.107972	−	0.187014i
$773$	11.4907	−	9.64181i	0.413291	−	0.346792i	−0.412313	−	0.911042i	$-0.635279\pi$
$773$	11.4907	−	9.64181i	0.413291	−	0.346792i	0.825604	+	0.564250i	$0.190835\pi$
$774$	56.3816	−	20.5212i	2.02659	−	0.737620i
$775$	−5.63816	−	2.05212i	−0.202529	−	0.0737144i
$776$	9.19253	+	7.71345i	0.329993	+	0.276897i
$777$	−9.37700	+	53.1796i	−0.336398	+	1.90781i
$778$	26.0000			0.932145
$779$		0			0
$780$	−18.0000			−0.644503
$781$		0			0
$782$	−3.83022	−	3.21394i	−0.136968	−	0.114930i
$783$	25.3717	+	9.23454i	0.906711	+	0.330016i
$784$	−1.87939	+	0.684040i	−0.0671209	+	0.0244300i
$785$		0			0
$786$	−21.0000	−	36.3731i	−0.749045	−	1.29738i
$787$	4.50000	−	7.79423i	0.160408	−	0.277834i	−0.774607	−	0.632443i	$-0.782052\pi$
$787$	4.50000	−	7.79423i	0.160408	−	0.277834i	0.935015	+	0.354608i	$0.115386\pi$
$788$	0.694593	+	3.93923i	0.0247438	+	0.140329i
$789$	−4.16756	−	23.6354i	−0.148369	−	0.841442i
$790$	12.0000	−	20.7846i	0.426941	−	0.739483i
$791$	18.0000	+	31.1769i	0.640006	+	1.10852i
$792$	−9.19253	+	7.71345i	−0.326642	+	0.274086i
$793$		0			0
$794$	−1.87939	−	0.684040i	−0.0666969	−	0.0242757i
$795$	−13.7888	−	11.5702i	−0.489038	−	0.410352i
$796$	−1.21554	+	6.89365i	−0.0430836	+	0.244339i
$797$	33.0000			1.16892			0.584460	−	0.811423i	$-0.301306\pi$
$797$	33.0000			1.16892			0.584460	+	0.811423i	$0.301306\pi$
$798$		0			0
$799$	8.00000			0.283020
$800$	−0.173648	+	0.984808i	−0.00613939	+	0.0348182i
$801$	27.5776	+	23.1404i	0.974407	+	0.817624i
$802$	−33.8289	−	12.3127i	−1.19454	−	0.434777i
$803$	−20.6732	+	7.52444i	−0.729543	+	0.265532i
$804$	34.4720	−	28.9254i	1.21573	−	1.02012i
$805$	15.0000	+	25.9808i	0.528681	+	0.915702i
$806$	−9.00000	+	15.5885i	−0.317011	+	0.549080i
$807$	−3.12567	−	17.7265i	−0.110029	−	0.624004i
$808$	1.73648	+	9.84808i	0.0610892	+	0.346454i
$809$	5.50000	−	9.52628i	0.193370	−	0.334926i	−0.752995	−	0.658026i	$-0.771392\pi$
$809$	5.50000	−	9.52628i	0.193370	−	0.334926i	0.946365	+	0.323100i	$0.104725\pi$
$810$	−9.00000	−	15.5885i	−0.316228	−	0.547723i
$811$	25.2795	−	21.2120i	0.887682	−	0.744854i	−0.0800617	−	0.996790i	$-0.525512\pi$
$811$	25.2795	−	21.2120i	0.887682	−	0.744854i	0.967744	+	0.251936i	$0.0810673\pi$
$812$	−8.45723	+	3.07818i	−0.296791	+	0.108023i
$813$	31.0099	+	11.2867i	1.08756	+	0.395841i
$814$	−9.19253	−	7.71345i	−0.322198	−	0.270356i
$815$	−2.08378	+	11.8177i	−0.0729916	+	0.413956i
$816$	−3.00000			−0.105021
$817$		0			0
$818$	6.00000			0.209785
$819$	9.37700	−	53.1796i	0.327659	−	1.85825i
$820$	18.3851	+	15.4269i	0.642034	+	0.538731i
$821$	−1.87939	−	0.684040i	−0.0655910	−	0.0238732i	0.309016	−	0.951057i	$-0.400000\pi$
$821$	−1.87939	−	0.684040i	−0.0655910	−	0.0238732i	−0.374607	+	0.927184i	$0.622222\pi$
$822$	−53.5625	+	19.4951i	−1.86821	+	0.679971i
$823$	2.29813	−	1.92836i	0.0801079	−	0.0672185i	−0.601854	−	0.798606i	$-0.705571\pi$
$823$	2.29813	−	1.92836i	0.0801079	−	0.0672185i	0.681962	+	0.731387i	$0.261127\pi$
$824$	−3.00000	−	5.19615i	−0.104510	−	0.181017i
$825$	−3.00000	+	5.19615i	−0.104447	+	0.180907i
$826$	−1.56283	−	8.86327i	−0.0543779	−	0.308393i
$827$	2.60472	+	14.7721i	0.0905751	+	0.513677i	0.996014	+	0.0891997i	$0.0284309\pi$
$827$	2.60472	+	14.7721i	0.0905751	+	0.513677i	−0.905439	+	0.424477i	$0.860458\pi$
$828$	−15.0000	+	25.9808i	−0.521286	+	0.902894i
$829$	−25.5000	−	44.1673i	−0.885652	−	1.53399i	−0.844965	−	0.534822i	$-0.820379\pi$
$829$	−25.5000	−	44.1673i	−0.885652	−	1.53399i	−0.0406866	−	0.999172i	$-0.512955\pi$
$830$	3.06418	−	2.57115i	0.106359	−	0.0892459i
$831$	−84.5723	+	30.7818i	−2.93378	+	1.06781i
$832$	2.81908	+	1.02606i	0.0977339	+	0.0355722i
$833$	−1.53209	−	1.28558i	−0.0530837	−	0.0445425i
$834$	3.12567	−	17.7265i	0.108233	−	0.613820i
$835$	−24.0000			−0.830554
$836$		0			0
$837$	−54.0000			−1.86651
$838$	−2.43107	+	13.7873i	−0.0839801	+	0.476275i
$839$	−13.7888	−	11.5702i	−0.476042	−	0.399447i	0.372951	−	0.927851i	$-0.378346\pi$
$839$	−13.7888	−	11.5702i	−0.476042	−	0.399447i	−0.848993	+	0.528404i	$0.822791\pi$
$840$	16.9145	+	6.15636i	0.583605	+	0.212415i
$841$	18.7939	−	6.84040i	0.648064	−	0.235876i
$842$	−20.6832	+	17.3553i	−0.712790	+	0.598102i
$843$	−18.0000	−	31.1769i	−0.619953	−	1.07379i
$844$	−1.50000	+	2.59808i	−0.0516321	+	0.0894295i
$845$	−1.38919	−	7.87846i	−0.0477894	−	0.271027i
$846$	−8.33511	−	47.2708i	−0.286567	−	1.62520i
$847$	−10.5000	+	18.1865i	−0.360784	+	0.624897i
$848$	1.50000	+	2.59808i	0.0515102	+	0.0892183i
$849$	−32.1739	+	26.9971i	−1.10420	+	0.926537i
$850$	−0.939693	+	0.342020i	−0.0322312	+	0.0117312i
$851$	−28.1908	−	10.2606i	−0.966367	−	0.351729i
$852$		0			0
$853$	7.98782	−	45.3012i	0.273498	−	1.55108i	−0.470196	−	0.882562i	$-0.655817\pi$
$853$	7.98782	−	45.3012i	0.273498	−	1.55108i	0.743694	−	0.668520i	$-0.233072\pi$
$854$		0			0
$855$		0			0
$856$	−3.00000			−0.102538
$857$	4.16756	−	23.6354i	0.142361	−	0.807369i	−0.827087	−	0.562074i	$-0.810004\pi$
$857$	4.16756	−	23.6354i	0.142361	−	0.807369i	0.969448	−	0.245296i	$-0.0788851\pi$
$858$	13.7888	+	11.5702i	0.470742	+	0.394999i
$859$	−50.7434	−	18.4691i	−1.73134	−	0.630157i	−0.732618	−	0.680640i	$-0.761702\pi$
$859$	−50.7434	−	18.4691i	−1.73134	−	0.630157i	−0.998725	+	0.0504833i	$0.983924\pi$
$860$	18.7939	−	6.84040i	0.640865	−	0.233256i
$861$	−82.7328	+	69.4211i	−2.81953	+	2.36586i
$862$	−12.0000	−	20.7846i	−0.408722	−	0.707927i
$863$	−24.0000	+	41.5692i	−0.816970	+	1.41503i	0.0909355	+	0.995857i	$0.471014\pi$
$863$	−24.0000	+	41.5692i	−0.816970	+	1.41503i	−0.907905	+	0.419176i	$0.862319\pi$
$864$	1.56283	+	8.86327i	0.0531687	+	0.301535i
$865$	−6.25133	−	35.4531i	−0.212552	−	1.20544i
$866$	−15.0000	+	25.9808i	−0.509721	+	0.882862i
$867$	24.0000	+	41.5692i	0.815083	+	1.41176i
$868$	13.7888	−	11.5702i	0.468022	−	0.392717i
$869$	−22.5526	+	8.20848i	−0.765045	+	0.278454i
$870$	16.9145	+	6.15636i	0.573454	+	0.208720i
$871$	−34.4720	−	28.9254i	−1.16804	−	0.980101i
$872$	0.520945	−	2.95442i	0.0176414	−	0.100049i
$873$	72.0000			2.43683
$874$		0			0
$875$	36.0000			1.21702
$876$	−5.73039	+	32.4987i	−0.193612	+	1.09803i
$877$	20.6832	+	17.3553i	0.698422	+	0.586046i	0.921324	−	0.388795i	$-0.127109\pi$
$877$	20.6832	+	17.3553i	0.698422	+	0.586046i	−0.222902	+	0.974841i	$0.571553\pi$
$878$		0			0
$879$	25.3717	−	9.23454i	0.855766	−	0.311473i
$880$	−3.06418	+	2.57115i	−0.103293	+	0.0866735i
$881$	−17.0000	−	29.4449i	−0.572745	−	0.992023i	−0.996283	−	0.0861444i	$-0.972545\pi$
$881$	−17.0000	−	29.4449i	−0.572745	−	0.992023i	0.423538	−	0.905878i	$-0.360788\pi$
$882$	−6.00000	+	10.3923i	−0.202031	+	0.349927i
$883$	−4.16756	−	23.6354i	−0.140249	−	0.795394i	−0.971059	−	0.238838i	$-0.923234\pi$
$883$	−4.16756	−	23.6354i	−0.140249	−	0.795394i	0.830810	−	0.556556i	$-0.187878\pi$
$884$	0.520945	+	2.95442i	0.0175213	+	0.0993680i
$885$	−9.00000	+	15.5885i	−0.302532	+	0.524000i
$886$	11.0000	+	19.0526i	0.369552	+	0.640083i
$887$	−18.3851	+	15.4269i	−0.617310	+	0.517985i	−0.896957	−	0.442118i	$-0.854227\pi$
$887$	−18.3851	+	15.4269i	−0.617310	+	0.517985i	0.279647	+	0.960103i	$0.409783\pi$
$888$	−16.9145	+	6.15636i	−0.567612	+	0.206594i
$889$	33.8289	+	12.3127i	1.13459	+	0.412956i
$890$	9.19253	+	7.71345i	0.308134	+	0.258555i
$891$	−3.12567	+	17.7265i	−0.104714	+	0.593861i
$892$	18.0000			0.602685
$893$		0			0
$894$	−24.0000			−0.802680
$895$	−4.16756	+	23.6354i	−0.139306	+	0.790044i
$896$	−2.29813	−	1.92836i	−0.0767752	−	0.0644221i
$897$	42.2862	+	15.3909i	1.41189	+	0.513887i
$898$	−5.63816	+	2.05212i	−0.188148	+	0.0684802i
$899$	13.7888	−	11.5702i	0.459882	−	0.385887i
$900$	3.00000	+	5.19615i	0.100000	+	0.173205i
$901$	−1.50000	+	2.59808i	−0.0499722	+	0.0865545i
$902$	−4.16756	−	23.6354i	−0.138764	−	0.786972i
$903$	15.6283	+	88.6327i	0.520078	+	2.94951i
$904$	−6.00000	+	10.3923i	−0.199557	+	0.345643i
$905$	−18.0000	−	31.1769i	−0.598340	−	1.03636i
$906$	−41.3664	+	34.7105i	−1.37431	+	1.15318i
$907$	14.0954	−	5.13030i	0.468030	−	0.170349i	−0.0972299	−	0.995262i	$-0.530998\pi$
$907$	14.0954	−	5.13030i	0.468030	−	0.170349i	0.565260	+	0.824913i	$0.308776\pi$
$908$	−2.81908	−	1.02606i	−0.0935544	−	0.0340510i
$909$	45.9627	+	38.5673i	1.52449	+	1.27920i
$910$	3.12567	−	17.7265i	0.103615	−	0.587629i
$911$	−30.0000			−0.993944			−0.496972	−	0.867766i	$-0.665555\pi$
$911$	−30.0000			−0.993944			−0.496972	+	0.867766i	$0.665555\pi$
$912$		0			0
$913$	−4.00000			−0.132381
$914$	0.173648	−	0.984808i	0.00574377	−	0.0325745i
$915$		0			0
$916$	11.2763	+	4.10424i	0.372580	+	0.135608i
$917$	39.4671	−	14.3648i	1.30332	−	0.474369i
$918$	−6.89440	+	5.78509i	−0.227549	+	0.190936i
$919$	−7.50000	−	12.9904i	−0.247402	−	0.428513i	0.715402	−	0.698713i	$-0.246244\pi$
$919$	−7.50000	−	12.9904i	−0.247402	−	0.428513i	−0.962804	+	0.270200i	$0.912910\pi$
$920$	−5.00000	+	8.66025i	−0.164845	+	0.285520i
$921$	6.25133	+	35.4531i	0.205988	+	1.16822i
$922$	0.694593	+	3.93923i	0.0228752	+	0.129732i
$923$		0			0
$924$	−9.00000	−	15.5885i	−0.296078	−	0.512823i
$925$	−4.59627	+	3.85673i	−0.151124	+	0.126808i
$926$	−30.0702	+	10.9446i	−0.988167	+	0.359663i
$927$	−33.8289	−	12.3127i	−1.11109	−	0.404403i
$928$	−2.29813	−	1.92836i	−0.0754399	−	0.0633016i
$929$	7.11958	−	40.3771i	0.233586	−	1.32473i	−0.611986	−	0.790869i	$-0.709629\pi$
$929$	7.11958	−	40.3771i	0.233586	−	1.32473i	0.845572	−	0.533862i	$-0.179260\pi$
$930$	−36.0000			−1.18049
$931$		0			0
$932$	14.0000			0.458585
$933$	−5.73039	+	32.4987i	−0.187605	+	1.06396i
$934$	6.12836	+	5.14230i	0.200526	+	0.168261i
$935$	−3.75877	−	1.36808i	−0.122925	−	0.0447410i
$936$	16.9145	−	6.15636i	0.552867	−	0.201227i
$937$	−36.0041	+	30.2110i	−1.17620	+	0.986951i	−0.176206	+	0.984353i	$0.556382\pi$
$937$	−36.0041	+	30.2110i	−1.17620	+	0.986951i	−0.999997	+	0.00259756i	$0.999173\pi$
$938$	22.5000	+	38.9711i	0.734651	+	1.27245i
$939$	−31.5000	+	54.5596i	−1.02796	+	1.78049i
$940$	−2.77837	−	15.7569i	−0.0906205	−	0.513934i
$941$	−4.68850	−	26.5898i	−0.152841	−	0.866803i	−0.960733	−	0.277473i	$-0.910503\pi$
$941$	−4.68850	−	26.5898i	−0.152841	−	0.866803i	0.807893	−	0.589330i	$-0.200608\pi$
$942$		0			0
$943$	−30.0000	−	51.9615i	−0.976934	−	1.69210i
$944$	2.29813	−	1.92836i	0.0747979	−	0.0627629i
$945$	50.7434	−	18.4691i	1.65068	−	0.600799i
$946$	−18.7939	−	6.84040i	−0.611041	−	0.222401i
$947$	−35.2380	−	29.5682i	−1.14508	−	0.960838i	−0.145489	−	0.989360i	$-0.546476\pi$
$947$	−35.2380	−	29.5682i	−1.14508	−	0.960838i	−0.999593	+	0.0285214i	$0.990920\pi$
$948$	−6.25133	+	35.4531i	−0.203034	+	1.15146i
$949$	33.0000			1.07123
$950$		0			0
$951$	−99.0000			−3.21029
$952$	0.520945	−	2.95442i	0.0168839	−	0.0957534i
$953$	−22.9813	−	19.2836i	−0.744438	−	0.624658i	0.189587	−	0.981864i	$-0.439285\pi$
$953$	−22.9813	−	19.2836i	−0.744438	−	0.624658i	−0.934026	+	0.357206i	$0.883729\pi$
$954$	16.9145	+	6.15636i	0.547626	+	0.199320i
$955$	20.6732	−	7.52444i	0.668970	−	0.243485i
$956$	0.766044	−	0.642788i	0.0247756	−	0.0207892i
$957$	−9.00000	−	15.5885i	−0.290929	−	0.503903i
$958$	20.0000	−	34.6410i	0.646171	−	1.11920i
$959$	−9.89795	−	56.1340i	−0.319621	−	1.81266i
$960$	1.04189	+	5.90885i	0.0336268	+	0.190707i
$961$	−2.50000	+	4.33013i	−0.0806452	+	0.139682i
$962$	9.00000	+	15.5885i	0.290172	+	0.502592i
$963$	−13.7888	+	11.5702i	−0.444338	+	0.372844i
$964$	−22.5526	+	8.20848i	−0.726371	+	0.264377i
$965$	−11.2763	−	4.10424i	−0.362997	−	0.132120i
$966$	−34.4720	−	28.9254i	−1.10912	−	0.930661i
$967$	−4.16756	+	23.6354i	−0.134020	+	0.760063i	0.841518	+	0.540229i	$0.181663\pi$
$967$	−4.16756	+	23.6354i	−0.134020	+	0.760063i	−0.975537	+	0.219833i	$0.929449\pi$
$968$	−7.00000			−0.224989
$969$		0			0
$970$	24.0000			0.770594
$971$	−8.33511	+	47.2708i	−0.267486	+	1.51699i	0.494374	+	0.869250i	$0.335398\pi$
$971$	−8.33511	+	47.2708i	−0.267486	+	1.51699i	−0.761860	+	0.647742i	$0.775714\pi$
$972$		0			0
$973$	16.9145	+	6.15636i	0.542253	+	0.197364i
$974$	16.9145	−	6.15636i	0.541974	−	0.197263i
$975$	6.89440	−	5.78509i	0.220798	−	0.185271i
$976$		0			0
$977$	15.0000	−	25.9808i	0.479893	−	0.831198i	−0.519841	−	0.854263i	$-0.674009\pi$
$977$	15.0000	−	25.9808i	0.479893	−	0.831198i	0.999734	+	0.0230645i	$0.00734232\pi$
$978$	−3.12567	−	17.7265i	−0.0999478	−	0.566832i
$979$	−2.08378	−	11.8177i	−0.0665978	−	0.377695i
$980$	−2.00000	+	3.46410i	−0.0638877	+	0.110657i
$981$	−9.00000	−	15.5885i	−0.287348	−	0.497701i
$982$	6.12836	−	5.14230i	0.195564	−	0.164097i
$983$	22.5526	−	8.20848i	0.719317	−	0.261810i	0.0436812	−	0.999046i	$-0.486091\pi$
$983$	22.5526	−	8.20848i	0.719317	−	0.261810i	0.675636	+	0.737236i	$0.263869\pi$
$984$	−33.8289	−	12.3127i	−1.07843	−	0.392515i
$985$	6.12836	+	5.14230i	0.195266	+	0.163847i
$986$	0.520945	−	2.95442i	0.0165903	−	0.0940880i
$987$	72.0000			2.29179
$988$		0			0
$989$	−50.0000			−1.58991
$990$	−4.16756	+	23.6354i	−0.132454	+	0.751182i
$991$	4.59627	+	3.85673i	0.146005	+	0.122513i	0.712865	−	0.701302i	$-0.247397\pi$
$991$	4.59627	+	3.85673i	0.146005	+	0.122513i	−0.566860	+	0.823814i	$0.691842\pi$
$992$	5.63816	+	2.05212i	0.179012	+	0.0651549i
$993$	−25.3717	+	9.23454i	−0.805147	+	0.293049i
$994$		0			0
$995$	7.00000	+	12.1244i	0.221915	+	0.384368i
$996$	−3.00000	+	5.19615i	−0.0950586	+	0.164646i
$997$	1.04189	+	5.90885i	0.0329970	+	0.187135i	0.996851	−	0.0792951i	$-0.0252669\pi$
$997$	1.04189	+	5.90885i	0.0329970	+	0.187135i	−0.963854	+	0.266430i	$0.914156\pi$
$998$	3.12567	+	17.7265i	0.0989413	+	0.561124i
$999$	−27.0000	+	46.7654i	−0.854242	+	1.47959i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	722.2.e.g.245.1		6
19.2	odd	18		722.2.c.g.429.1		2
19.3	odd	18		722.2.a.a.1.1	✓	1
19.4	even	9	inner	722.2.e.g.595.1		6
19.5	even	9		722.2.c.a.653.1		2
19.6	even	9	inner	722.2.e.g.99.1		6
19.7	even	3	inner	722.2.e.g.415.1		6
19.8	odd	6		722.2.e.h.423.1		6
19.9	even	9	inner	722.2.e.g.389.1		6
19.10	odd	18		722.2.e.h.389.1		6
19.11	even	3	inner	722.2.e.g.423.1		6
19.12	odd	6		722.2.e.h.415.1		6
19.13	odd	18		722.2.e.h.99.1		6
19.14	odd	18		722.2.c.g.653.1		2
19.15	odd	18		722.2.e.h.595.1		6
19.16	even	9		722.2.a.f.1.1	yes	1
19.17	even	9		722.2.c.a.429.1		2
19.18	odd	2		722.2.e.h.245.1		6
57.35	odd	18		6498.2.a.a.1.1		1
57.41	even	18		6498.2.a.m.1.1		1
76.3	even	18		5776.2.a.q.1.1		1
76.35	odd	18		5776.2.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
722.2.a.a.1.1	✓	1	19.3	odd	18
722.2.a.f.1.1	yes	1	19.16	even	9
722.2.c.a.429.1		2	19.17	even	9
722.2.c.a.653.1		2	19.5	even	9
722.2.c.g.429.1		2	19.2	odd	18
722.2.c.g.653.1		2	19.14	odd	18
722.2.e.g.99.1		6	19.6	even	9	inner
722.2.e.g.245.1		6	1.1	even	1	trivial
722.2.e.g.389.1		6	19.9	even	9	inner
722.2.e.g.415.1		6	19.7	even	3	inner
722.2.e.g.423.1		6	19.11	even	3	inner
722.2.e.g.595.1		6	19.4	even	9	inner
722.2.e.h.99.1		6	19.13	odd	18
722.2.e.h.245.1		6	19.18	odd	2
722.2.e.h.389.1		6	19.10	odd	18
722.2.e.h.415.1		6	19.12	odd	6
722.2.e.h.423.1		6	19.8	odd	6
722.2.e.h.595.1		6	19.15	odd	18
5776.2.a.a.1.1		1	76.35	odd	18
5776.2.a.q.1.1		1	76.3	even	18
6498.2.a.a.1.1		1	57.35	odd	18
6498.2.a.m.1.1		1	57.41	even	18

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:	\( N \)	\(=\)	\( 722 = 2 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	722.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.173648 - 0.984808i) q^{2} +(2.29813 + 1.92836i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-1.87939 + 0.684040i) q^{5} +(2.29813 - 1.92836i) q^{6} +(1.50000 + 2.59808i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(1.04189 + 5.90885i) q^{9} +O(q^{10})\)	\(q+(0.173648 - 0.984808i) q^{2} +(2.29813 + 1.92836i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-1.87939 + 0.684040i) q^{5} +(2.29813 - 1.92836i) q^{6} +(1.50000 + 2.59808i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(1.04189 + 5.90885i) q^{9} +(0.347296 + 1.96962i) q^{10} +(1.00000 - 1.73205i) q^{11} +(-1.50000 - 2.59808i) q^{12} +(-2.29813 + 1.92836i) q^{13} +(2.81908 - 1.02606i) q^{14} +(-5.63816 - 2.05212i) q^{15} +(0.766044 + 0.642788i) q^{16} +(-0.173648 + 0.984808i) q^{17} +6.00000 q^{18} +2.00000 q^{20} +(-1.56283 + 8.86327i) q^{21} +(-1.53209 - 1.28558i) q^{22} +(-4.69846 - 1.71010i) q^{23} +(-2.81908 + 1.02606i) q^{24} +(-0.766044 + 0.642788i) q^{25} +(1.50000 + 2.59808i) q^{26} +(-4.50000 + 7.79423i) q^{27} +(-0.520945 - 2.95442i) q^{28} +(-0.520945 - 2.95442i) q^{29} +(-3.00000 + 5.19615i) q^{30} +(3.00000 + 5.19615i) q^{31} +(0.766044 - 0.642788i) q^{32} +(5.63816 - 2.05212i) q^{33} +(0.939693 + 0.342020i) q^{34} +(-4.59627 - 3.85673i) q^{35} +(1.04189 - 5.90885i) q^{36} +6.00000 q^{37} -9.00000 q^{39} +(0.347296 - 1.96962i) q^{40} +(9.19253 + 7.71345i) q^{41} +(8.45723 + 3.07818i) q^{42} +(9.39693 - 3.42020i) q^{43} +(-1.53209 + 1.28558i) q^{44} +(-6.00000 - 10.3923i) q^{45} +(-2.50000 + 4.33013i) q^{46} +(-1.38919 - 7.87846i) q^{47} +(0.520945 + 2.95442i) q^{48} +(-1.00000 + 1.73205i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-2.29813 + 1.92836i) q^{51} +(2.81908 - 1.02606i) q^{52} +(2.81908 + 1.02606i) q^{53} +(6.89440 + 5.78509i) q^{54} +(-0.694593 + 3.93923i) q^{55} -3.00000 q^{56} -3.00000 q^{58} +(0.520945 - 2.95442i) q^{59} +(4.59627 + 3.85673i) q^{60} +(5.63816 - 2.05212i) q^{62} +(-13.7888 + 11.5702i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(3.00000 - 5.19615i) q^{65} +(-1.04189 - 5.90885i) q^{66} +(2.60472 + 14.7721i) q^{67} +(0.500000 - 0.866025i) q^{68} +(-7.50000 - 12.9904i) q^{69} +(-4.59627 + 3.85673i) q^{70} +(-5.63816 - 2.05212i) q^{72} +(-8.42649 - 7.07066i) q^{73} +(1.04189 - 5.90885i) q^{74} -3.00000 q^{75} +6.00000 q^{77} +(-1.56283 + 8.86327i) q^{78} +(-9.19253 - 7.71345i) q^{79} +(-1.87939 - 0.684040i) q^{80} +(-8.45723 + 3.07818i) q^{81} +(9.19253 - 7.71345i) q^{82} +(-1.00000 - 1.73205i) q^{83} +(4.50000 - 7.79423i) q^{84} +(-0.347296 - 1.96962i) q^{85} +(-1.73648 - 9.84808i) q^{86} +(4.50000 - 7.79423i) q^{87} +(1.00000 + 1.73205i) q^{88} +(4.59627 - 3.85673i) q^{89} +(-11.2763 + 4.10424i) q^{90} +(-8.45723 - 3.07818i) q^{91} +(3.83022 + 3.21394i) q^{92} +(-3.12567 + 17.7265i) q^{93} -8.00000 q^{94} +3.00000 q^{96} +(2.08378 - 11.8177i) q^{97} +(1.53209 + 1.28558i) q^{98} +(11.2763 + 4.10424i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 9 q^{7} - 3 q^{8}+O(q^{10}) \) 6 * q + 9 * q^7 - 3 * q^8	\( 6 q + 9 q^{7} - 3 q^{8} + 6 q^{11} - 9 q^{12} + 36 q^{18} + 12 q^{20} + 9 q^{26} - 27 q^{27} - 18 q^{30} + 18 q^{31} + 36 q^{37} - 54 q^{39} - 36 q^{45} - 15 q^{46} - 6 q^{49} + 3 q^{50} - 18 q^{56} - 18 q^{58} - 3 q^{64} + 18 q^{65} + 3 q^{68} - 45 q^{69} - 18 q^{75} + 36 q^{77} - 6 q^{83} + 27 q^{84} + 27 q^{87} + 6 q^{88} - 48 q^{94} + 18 q^{96}+O(q^{100}) \) 6 * q + 9 * q^7 - 3 * q^8 + 6 * q^11 - 9 * q^12 + 36 * q^18 + 12 * q^20 + 9 * q^26 - 27 * q^27 - 18 * q^30 + 18 * q^31 + 36 * q^37 - 54 * q^39 - 36 * q^45 - 15 * q^46 - 6 * q^49 + 3 * q^50 - 18 * q^56 - 18 * q^58 - 3 * q^64 + 18 * q^65 + 3 * q^68 - 45 * q^69 - 18 * q^75 + 36 * q^77 - 6 * q^83 + 27 * q^84 + 27 * q^87 + 6 * q^88 - 48 * q^94 + 18 * q^96

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