LMFDB - Embedded newform 847.2.f.n.323.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [847,2,Mod(148,847)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(847, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("847.148");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	847.f (of order $5$, degree $4$, 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:	$6.76332905120$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			323.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	847.323
Dual form			847.2.f.n.729.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.80902 + 1.31433i) q^{2} +(1.00000 - 3.07768i) q^{3} +(0.927051 + 2.85317i) q^{4} +(1.61803 - 1.17557i) q^{5} +(5.85410 - 4.25325i) q^{6} +(0.309017 + 0.951057i) q^{7} +(-0.690983 + 2.12663i) q^{8} +(-6.04508 - 4.39201i) q^{9} +O(q^{10})$	\(q+(1.80902 + 1.31433i) q^{2} +(1.00000 - 3.07768i) q^{3} +(0.927051 + 2.85317i) q^{4} +(1.61803 - 1.17557i) q^{5} +(5.85410 - 4.25325i) q^{6} +(0.309017 + 0.951057i) q^{7} +(-0.690983 + 2.12663i) q^{8} +(-6.04508 - 4.39201i) q^{9} +4.47214 q^{10} +9.70820 q^{12} +(1.00000 + 0.726543i) q^{13} +(-0.690983 + 2.12663i) q^{14} +(-2.00000 - 6.15537i) q^{15} +(0.809017 - 0.587785i) q^{16} +(-1.00000 + 0.726543i) q^{17} +(-5.16312 - 15.8904i) q^{18} +(-0.763932 + 2.35114i) q^{19} +(4.85410 + 3.52671i) q^{20} +3.23607 q^{21} -6.47214 q^{23} +(5.85410 + 4.25325i) q^{24} +(-0.309017 + 0.951057i) q^{25} +(0.854102 + 2.62866i) q^{26} +(-11.7082 + 8.50651i) q^{27} +(-2.42705 + 1.76336i) q^{28} +(-0.145898 - 0.449028i) q^{29} +(4.47214 - 13.7638i) q^{30} +(5.85410 + 4.25325i) q^{31} +6.70820 q^{32} -2.76393 q^{34} +(1.61803 + 1.17557i) q^{35} +(6.92705 - 21.3193i) q^{36} +(0.145898 + 0.449028i) q^{37} +(-4.47214 + 3.24920i) q^{38} +(3.23607 - 2.35114i) q^{39} +(1.38197 + 4.25325i) q^{40} +(-2.09017 + 6.43288i) q^{41} +(5.85410 + 4.25325i) q^{42} +8.00000 q^{43} -14.9443 q^{45} +(-11.7082 - 8.50651i) q^{46} +(2.23607 - 6.88191i) q^{47} +(-1.00000 - 3.07768i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(-1.80902 + 1.31433i) q^{50} +(1.23607 + 3.80423i) q^{51} +(-1.14590 + 3.52671i) q^{52} +(-6.85410 - 4.97980i) q^{53} -32.3607 q^{54} -2.23607 q^{56} +(6.47214 + 4.70228i) q^{57} +(0.326238 - 1.00406i) q^{58} +(1.00000 + 3.07768i) q^{59} +(15.7082 - 11.4127i) q^{60} +(2.23607 - 1.62460i) q^{61} +(5.00000 + 15.3884i) q^{62} +(2.30902 - 7.10642i) q^{63} +(10.5172 + 7.64121i) q^{64} +2.47214 q^{65} +5.52786 q^{67} +(-3.00000 - 2.17963i) q^{68} +(-6.47214 + 19.9192i) q^{69} +(1.38197 + 4.25325i) q^{70} +(1.23607 - 0.898056i) q^{71} +(13.5172 - 9.82084i) q^{72} +(-1.61803 - 4.97980i) q^{73} +(-0.326238 + 1.00406i) q^{74} +(2.61803 + 1.90211i) q^{75} -7.41641 q^{76} +8.94427 q^{78} +(-7.23607 - 5.25731i) q^{79} +(0.618034 - 1.90211i) q^{80} +(7.54508 + 23.2214i) q^{81} +(-12.2361 + 8.89002i) q^{82} +(-12.4721 + 9.06154i) q^{83} +(3.00000 + 9.23305i) q^{84} +(-0.763932 + 2.35114i) q^{85} +(14.4721 + 10.5146i) q^{86} -1.52786 q^{87} +2.00000 q^{89} +(-27.0344 - 19.6417i) q^{90} +(-0.381966 + 1.17557i) q^{91} +(-6.00000 - 18.4661i) q^{92} +(18.9443 - 13.7638i) q^{93} +(13.0902 - 9.51057i) q^{94} +(1.52786 + 4.70228i) q^{95} +(6.70820 - 20.6457i) q^{96} +(7.61803 + 5.53483i) q^{97} -2.23607 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 5 q^{2} + 4 q^{3} - 3 q^{4} + 2 q^{5} + 10 q^{6} - q^{7} - 5 q^{8} - 13 q^{9}+O(q^{10}) $ 4 * q + 5 * q^2 + 4 * q^3 - 3 * q^4 + 2 * q^5 + 10 * q^6 - q^7 - 5 * q^8 - 13 * q^9	$ 4 q + 5 q^{2} + 4 q^{3} - 3 q^{4} + 2 q^{5} + 10 q^{6} - q^{7} - 5 q^{8} - 13 q^{9} + 12 q^{12} + 4 q^{13} - 5 q^{14} - 8 q^{15} + q^{16} - 4 q^{17} - 5 q^{18} - 12 q^{19} + 6 q^{20} + 4 q^{21} - 8 q^{23} + 10 q^{24} + q^{25} - 10 q^{26} - 20 q^{27} - 3 q^{28} - 14 q^{29} + 10 q^{31} - 20 q^{34} + 2 q^{35} + 21 q^{36} + 14 q^{37} + 4 q^{39} + 10 q^{40} + 14 q^{41} + 10 q^{42} + 32 q^{43} - 24 q^{45} - 20 q^{46} - 4 q^{48} - q^{49} - 5 q^{50} - 4 q^{51} - 18 q^{52} - 14 q^{53} - 40 q^{54} + 8 q^{57} - 30 q^{58} + 4 q^{59} + 36 q^{60} + 20 q^{62} + 7 q^{63} + 13 q^{64} - 8 q^{65} + 40 q^{67} - 12 q^{68} - 8 q^{69} + 10 q^{70} - 4 q^{71} + 25 q^{72} - 2 q^{73} + 30 q^{74} + 6 q^{75} + 24 q^{76} - 20 q^{79} - 2 q^{80} + 19 q^{81} - 40 q^{82} - 32 q^{83} + 12 q^{84} - 12 q^{85} + 40 q^{86} - 24 q^{87} + 8 q^{89} - 50 q^{90} - 6 q^{91} - 24 q^{92} + 40 q^{93} + 30 q^{94} + 24 q^{95} + 26 q^{97}+O(q^{100}) $ 4 * q + 5 * q^2 + 4 * q^3 - 3 * q^4 + 2 * q^5 + 10 * q^6 - q^7 - 5 * q^8 - 13 * q^9 + 12 * q^12 + 4 * q^13 - 5 * q^14 - 8 * q^15 + q^16 - 4 * q^17 - 5 * q^18 - 12 * q^19 + 6 * q^20 + 4 * q^21 - 8 * q^23 + 10 * q^24 + q^25 - 10 * q^26 - 20 * q^27 - 3 * q^28 - 14 * q^29 + 10 * q^31 - 20 * q^34 + 2 * q^35 + 21 * q^36 + 14 * q^37 + 4 * q^39 + 10 * q^40 + 14 * q^41 + 10 * q^42 + 32 * q^43 - 24 * q^45 - 20 * q^46 - 4 * q^48 - q^49 - 5 * q^50 - 4 * q^51 - 18 * q^52 - 14 * q^53 - 40 * q^54 + 8 * q^57 - 30 * q^58 + 4 * q^59 + 36 * q^60 + 20 * q^62 + 7 * q^63 + 13 * q^64 - 8 * q^65 + 40 * q^67 - 12 * q^68 - 8 * q^69 + 10 * q^70 - 4 * q^71 + 25 * q^72 - 2 * q^73 + 30 * q^74 + 6 * q^75 + 24 * q^76 - 20 * q^79 - 2 * q^80 + 19 * q^81 - 40 * q^82 - 32 * q^83 + 12 * q^84 - 12 * q^85 + 40 * q^86 - 24 * q^87 + 8 * q^89 - 50 * q^90 - 6 * q^91 - 24 * q^92 + 40 * q^93 + 30 * q^94 + 24 * q^95 + 26 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$

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 $

$2$	1.80902	+	1.31433i	1.27917	+	0.929370i	0.999528	−	0.0307347i	$-0.00978469\pi$
$2$	1.80902	+	1.31433i	1.27917	+	0.929370i	0.279641	+	0.960105i	$0.409785\pi$
$3$	1.00000	−	3.07768i	0.577350	−	1.77690i	−0.0506828	−	0.998715i	$-0.516140\pi$
$3$	1.00000	−	3.07768i	0.577350	−	1.77690i	0.628033	−	0.778187i	$-0.283860\pi$
$4$	0.927051	+	2.85317i	0.463525	+	1.42658i
$5$	1.61803	−	1.17557i	0.723607	−	0.525731i	−0.163928	−	0.986472i	$-0.552416\pi$
$5$	1.61803	−	1.17557i	0.723607	−	0.525731i	0.887535	+	0.460741i	$0.152416\pi$
$6$	5.85410	−	4.25325i	2.38993	−	1.73638i
$7$	0.309017	+	0.951057i	0.116797	+	0.359466i
$7$	0.309017	+	0.951057i	0.116797	+	0.359466i
$8$	−0.690983	+	2.12663i	−0.244299	+	0.751876i
$9$	−6.04508	−	4.39201i	−2.01503	−	1.46400i
$10$	4.47214			1.41421
$11$		0			0
$11$		0			0
$12$	9.70820			2.80252
$13$	1.00000	+	0.726543i	0.277350	+	0.201507i	0.717761	−	0.696290i	$-0.245167\pi$
$13$	1.00000	+	0.726543i	0.277350	+	0.201507i	−0.440411	+	0.897796i	$0.645167\pi$
$14$	−0.690983	+	2.12663i	−0.184673	+	0.568365i
$15$	−2.00000	−	6.15537i	−0.516398	−	1.58931i
$16$	0.809017	−	0.587785i	0.202254	−	0.146946i
$17$	−1.00000	+	0.726543i	−0.242536	+	0.176212i	−0.702412	−	0.711770i	$-0.747894\pi$
$17$	−1.00000	+	0.726543i	−0.242536	+	0.176212i	0.459877	+	0.887983i	$0.347894\pi$
$18$	−5.16312	−	15.8904i	−1.21696	−	3.74541i
$19$	−0.763932	+	2.35114i	−0.175258	+	0.539389i	−0.999645	−	0.0266376i	$-0.991520\pi$
$19$	−0.763932	+	2.35114i	−0.175258	+	0.539389i	0.824387	+	0.566026i	$0.191520\pi$
$20$	4.85410	+	3.52671i	1.08541	+	0.788597i
$21$	3.23607			0.706168
$22$		0			0
$23$	−6.47214			−1.34953			−0.674767	−	0.738031i	$-0.735756\pi$
$23$	−6.47214			−1.34953			−0.674767	+	0.738031i	$0.735756\pi$
$24$	5.85410	+	4.25325i	1.19496	+	0.868192i
$25$	−0.309017	+	0.951057i	−0.0618034	+	0.190211i
$26$	0.854102	+	2.62866i	0.167503	+	0.515522i
$27$	−11.7082	+	8.50651i	−2.25324	+	1.63708i
$28$	−2.42705	+	1.76336i	−0.458670	+	0.333243i
$29$	−0.145898	−	0.449028i	−0.0270926	−	0.0833824i	0.936596	−	0.350411i	$-0.113958\pi$
$29$	−0.145898	−	0.449028i	−0.0270926	−	0.0833824i	−0.963689	+	0.267029i	$0.913958\pi$
$30$	4.47214	−	13.7638i	0.816497	−	2.51292i
$31$	5.85410	+	4.25325i	1.05143	+	0.763907i	0.972483	−	0.232972i	$-0.0748451\pi$
$31$	5.85410	+	4.25325i	1.05143	+	0.763907i	0.0789443	+	0.996879i	$0.474845\pi$
$32$	6.70820			1.18585
$33$		0			0
$34$	−2.76393			−0.474010
$35$	1.61803	+	1.17557i	0.273498	+	0.198708i
$36$	6.92705	−	21.3193i	1.15451	−	3.55321i
$37$	0.145898	+	0.449028i	0.0239855	+	0.0738197i	0.962333	−	0.271874i	$-0.0876435\pi$
$37$	0.145898	+	0.449028i	0.0239855	+	0.0738197i	−0.938347	+	0.345694i	$0.887644\pi$
$38$	−4.47214	+	3.24920i	−0.725476	+	0.527089i
$39$	3.23607	−	2.35114i	0.518186	−	0.376484i
$40$	1.38197	+	4.25325i	0.218508	+	0.672499i
$41$	−2.09017	+	6.43288i	−0.326430	+	1.00465i	0.644361	+	0.764721i	$0.277123\pi$
$41$	−2.09017	+	6.43288i	−0.326430	+	1.00465i	−0.970791	+	0.239926i	$0.922877\pi$
$42$	5.85410	+	4.25325i	0.903308	+	0.656291i
$43$	8.00000			1.21999			0.609994	−	0.792406i	$-0.291172\pi$
$43$	8.00000			1.21999			0.609994	+	0.792406i	$0.291172\pi$
$44$		0			0
$45$	−14.9443			−2.22776
$46$	−11.7082	−	8.50651i	−1.72628	−	1.25422i
$47$	2.23607	−	6.88191i	0.326164	−	1.00383i	−0.644748	−	0.764395i	$-0.723038\pi$
$47$	2.23607	−	6.88191i	0.326164	−	1.00383i	0.970912	−	0.239435i	$-0.0769621\pi$
$48$	−1.00000	−	3.07768i	−0.144338	−	0.444225i
$49$	−0.809017	+	0.587785i	−0.115574	+	0.0839693i
$50$	−1.80902	+	1.31433i	−0.255834	+	0.185874i
$51$	1.23607	+	3.80423i	0.173084	+	0.532698i
$52$	−1.14590	+	3.52671i	−0.158907	+	0.489067i
$53$	−6.85410	−	4.97980i	−0.941483	−	0.684028i	0.00729395	−	0.999973i	$-0.497678\pi$
$53$	−6.85410	−	4.97980i	−0.941483	−	0.684028i	−0.948777	+	0.315946i	$0.897678\pi$
$54$	−32.3607			−4.40373
$55$		0			0
$56$	−2.23607			−0.298807
$57$	6.47214	+	4.70228i	0.857255	+	0.622832i
$58$	0.326238	−	1.00406i	0.0428371	−	0.131839i
$59$	1.00000	+	3.07768i	0.130189	+	0.400680i	0.994811	−	0.101743i	$-0.0324419\pi$
$59$	1.00000	+	3.07768i	0.130189	+	0.400680i	−0.864622	+	0.502423i	$0.832442\pi$
$60$	15.7082	−	11.4127i	2.02792	−	1.47337i
$61$	2.23607	−	1.62460i	0.286299	−	0.208009i	−0.435361	−	0.900256i	$-0.643379\pi$
$61$	2.23607	−	1.62460i	0.286299	−	0.208009i	0.721660	+	0.692247i	$0.243379\pi$
$62$	5.00000	+	15.3884i	0.635001	+	1.95433i
$63$	2.30902	−	7.10642i	0.290909	−	0.895325i
$64$	10.5172	+	7.64121i	1.31465	+	0.955151i
$65$	2.47214			0.306631
$66$		0			0
$67$	5.52786			0.675336			0.337668	−	0.941265i	$-0.390362\pi$
$67$	5.52786			0.675336			0.337668	+	0.941265i	$0.390362\pi$
$68$	−3.00000	−	2.17963i	−0.363803	−	0.264319i
$69$	−6.47214	+	19.9192i	−0.779154	+	2.39799i
$70$	1.38197	+	4.25325i	0.165177	+	0.508361i
$71$	1.23607	−	0.898056i	0.146694	−	0.106580i	−0.512017	−	0.858975i	$-0.671102\pi$
$71$	1.23607	−	0.898056i	0.146694	−	0.106580i	0.658712	+	0.752395i	$0.271102\pi$
$72$	13.5172	−	9.82084i	1.59302	−	1.15740i
$73$	−1.61803	−	4.97980i	−0.189377	−	0.582841i	0.810620	−	0.585573i	$-0.199130\pi$
$73$	−1.61803	−	4.97980i	−0.189377	−	0.582841i	−0.999996	+	0.00273185i	$0.999130\pi$
$74$	−0.326238	+	1.00406i	−0.0379244	+	0.116719i
$75$	2.61803	+	1.90211i	0.302305	+	0.219637i
$76$	−7.41641			−0.850720
$77$		0			0
$78$	8.94427			1.01274
$79$	−7.23607	−	5.25731i	−0.814121	−	0.591494i	0.100901	−	0.994896i	$-0.467827\pi$
$79$	−7.23607	−	5.25731i	−0.814121	−	0.591494i	−0.915023	+	0.403403i	$0.867827\pi$
$80$	0.618034	−	1.90211i	0.0690983	−	0.212663i
$81$	7.54508	+	23.2214i	0.838343	+	2.58015i
$82$	−12.2361	+	8.89002i	−1.35125	+	0.981739i
$83$	−12.4721	+	9.06154i	−1.36899	+	0.994633i	−0.371180	+	0.928561i	$0.621047\pi$
$83$	−12.4721	+	9.06154i	−1.36899	+	0.994633i	−0.997815	+	0.0660720i	$0.978953\pi$
$84$	3.00000	+	9.23305i	0.327327	+	1.00741i
$85$	−0.763932	+	2.35114i	−0.0828601	+	0.255017i
$86$	14.4721	+	10.5146i	1.56057	+	1.13382i
$87$	−1.52786			−0.163804
$88$		0			0
$89$	2.00000			0.212000			0.106000	−	0.994366i	$-0.466196\pi$
$89$	2.00000			0.212000			0.106000	+	0.994366i	$0.466196\pi$
$90$	−27.0344	−	19.6417i	−2.84968	−	2.07041i
$91$	−0.381966	+	1.17557i	−0.0400409	+	0.123233i
$92$	−6.00000	−	18.4661i	−0.625543	−	1.92522i
$93$	18.9443	−	13.7638i	1.96443	−	1.42724i
$94$	13.0902	−	9.51057i	1.35015	−	0.980940i
$95$	1.52786	+	4.70228i	0.156756	+	0.482444i
$96$	6.70820	−	20.6457i	0.684653	−	2.10715i
$97$	7.61803	+	5.53483i	0.773494	+	0.561976i	0.903019	−	0.429600i	$-0.141345\pi$
$97$	7.61803	+	5.53483i	0.773494	+	0.561976i	−0.129525	+	0.991576i	$0.541345\pi$
$98$	−2.23607			−0.225877
$99$		0			0
$100$	−3.00000			−0.300000
$101$	7.47214	+	5.42882i	0.743505	+	0.540188i	0.893807	−	0.448452i	$-0.148024\pi$
$101$	7.47214	+	5.42882i	0.743505	+	0.540188i	−0.150302	+	0.988640i	$0.548024\pi$
$102$	−2.76393	+	8.50651i	−0.273670	+	0.842270i
$103$	−1.76393	−	5.42882i	−0.173805	−	0.534918i	0.825772	−	0.564005i	$-0.190740\pi$
$103$	−1.76393	−	5.42882i	−0.173805	−	0.534918i	−0.999577	+	0.0290868i	$0.990740\pi$
$104$	−2.23607	+	1.62460i	−0.219265	+	0.159305i
$105$	5.23607	−	3.80423i	0.510988	−	0.371254i
$106$	−5.85410	−	18.0171i	−0.568601	−	1.74997i
$107$	−1.23607	+	3.80423i	−0.119495	+	0.367768i	−0.992858	−	0.119302i	$-0.961934\pi$
$107$	−1.23607	+	3.80423i	−0.119495	+	0.367768i	0.873363	+	0.487070i	$0.161934\pi$
$108$	−35.1246	−	25.5195i	−3.37987	−	2.45562i
$109$	4.47214			0.428353			0.214176	−	0.976795i	$-0.431293\pi$
$109$	4.47214			0.428353			0.214176	+	0.976795i	$0.431293\pi$
$110$		0			0
$111$	1.52786			0.145018
$112$	0.809017	+	0.587785i	0.0764449	+	0.0555405i
$113$	0.618034	−	1.90211i	0.0581397	−	0.178936i	−0.917769	−	0.397114i	$-0.870012\pi$
$113$	0.618034	−	1.90211i	0.0581397	−	0.178936i	0.975909	+	0.218179i	$0.0700116\pi$
$114$	5.52786	+	17.0130i	0.517732	+	1.59341i
$115$	−10.4721	+	7.60845i	−0.976532	+	0.709492i
$116$	1.14590	−	0.832544i	0.106394	−	0.0772997i
$117$	−2.85410	−	8.78402i	−0.263862	−	0.812083i
$118$	−2.23607	+	6.88191i	−0.205847	+	0.633531i
$119$	−1.00000	−	0.726543i	−0.0916698	−	0.0666020i
$120$	14.4721			1.32112
$121$		0			0
$122$	6.18034			0.559542
$123$	17.7082	+	12.8658i	1.59669	+	1.16007i
$124$	−6.70820	+	20.6457i	−0.602414	+	1.85404i
$125$	3.70820	+	11.4127i	0.331672	+	1.02078i
$126$	13.5172	−	9.82084i	1.20421	−	0.874910i
$127$	−16.9443	+	12.3107i	−1.50356	+	1.09240i	−0.534625	+	0.845089i	$0.679547\pi$
$127$	−16.9443	+	12.3107i	−1.50356	+	1.09240i	−0.968936	+	0.247312i	$0.920453\pi$
$128$	4.83688	+	14.8864i	0.427524	+	1.31578i
$129$	8.00000	−	24.6215i	0.704361	−	2.16780i
$130$	4.47214	+	3.24920i	0.392232	+	0.284973i
$131$	−13.8885			−1.21345			−0.606724	−	0.794913i	$-0.707517\pi$
$131$	−13.8885			−1.21345			−0.606724	+	0.794913i	$0.707517\pi$
$132$		0			0
$133$	−2.47214			−0.214361
$134$	10.0000	+	7.26543i	0.863868	+	0.627637i
$135$	−8.94427	+	27.5276i	−0.769800	+	2.36920i
$136$	−0.854102	−	2.62866i	−0.0732386	−	0.225405i
$137$	−6.09017	+	4.42477i	−0.520318	+	0.378033i	−0.816724	−	0.577029i	$-0.804212\pi$
$137$	−6.09017	+	4.42477i	−0.520318	+	0.378033i	0.296405	+	0.955062i	$0.404212\pi$
$138$	−37.8885	+	27.5276i	−3.22529	+	2.34331i
$139$	−3.23607	−	9.95959i	−0.274480	−	0.844762i	−0.989357	−	0.145511i	$-0.953517\pi$
$139$	−3.23607	−	9.95959i	−0.274480	−	0.844762i	0.714877	−	0.699250i	$-0.246483\pi$
$140$	−1.85410	+	5.70634i	−0.156700	+	0.482274i
$141$	−18.9443	−	13.7638i	−1.59540	−	1.15912i
$142$	3.41641			0.286699
$143$		0			0
$144$	−7.47214			−0.622678
$145$	−0.763932	−	0.555029i	−0.0634411	−	0.0460927i
$146$	3.61803	−	11.1352i	0.299431	−	0.921553i
$147$	1.00000	+	3.07768i	0.0824786	+	0.253843i
$148$	−1.14590	+	0.832544i	−0.0941922	+	0.0684347i
$149$	−11.3262	+	8.22899i	−0.927882	+	0.674145i	−0.945473	−	0.325700i	$-0.894400\pi$
$149$	−11.3262	+	8.22899i	−0.927882	+	0.674145i	0.0175917	+	0.999845i	$0.494400\pi$
$150$	2.23607	+	6.88191i	0.182574	+	0.561906i
$151$	−2.76393	+	8.50651i	−0.224926	+	0.692250i	0.773374	+	0.633951i	$0.218568\pi$
$151$	−2.76393	+	8.50651i	−0.224926	+	0.692250i	−0.998299	+	0.0582992i	$0.981432\pi$
$152$	−4.47214	−	3.24920i	−0.362738	−	0.263545i
$153$	9.23607			0.746692
$154$		0			0
$155$	14.4721			1.16243
$156$	9.70820	+	7.05342i	0.777278	+	0.564726i
$157$	−2.14590	+	6.60440i	−0.171261	+	0.527088i	−0.999443	−	0.0333716i	$-0.989376\pi$
$157$	−2.14590	+	6.60440i	−0.171261	+	0.527088i	0.828182	+	0.560460i	$0.189376\pi$
$158$	−6.18034	−	19.0211i	−0.491681	−	1.51324i
$159$	−22.1803	+	16.1150i	−1.75902	+	1.27800i
$160$	10.8541	−	7.88597i	0.858092	−	0.623440i
$161$	−2.00000	−	6.15537i	−0.157622	−	0.485111i
$162$	−16.8713	+	51.9246i	−1.32554	+	4.07958i
$163$	−18.9443	−	13.7638i	−1.48383	−	1.07807i	−0.976298	−	0.216433i	$-0.930558\pi$
$163$	−18.9443	−	13.7638i	−1.48383	−	1.07807i	−0.507532	−	0.861633i	$-0.669442\pi$
$164$	−20.2918			−1.58452
$165$		0			0
$166$	−34.4721			−2.67556
$167$	10.4721	+	7.60845i	0.810358	+	0.588760i	0.913934	−	0.405862i	$-0.133029\pi$
$167$	10.4721	+	7.60845i	0.810358	+	0.588760i	−0.103576	+	0.994622i	$0.533029\pi$
$168$	−2.23607	+	6.88191i	−0.172516	+	0.530951i
$169$	−3.54508	−	10.9106i	−0.272699	−	0.839281i
$170$	−4.47214	+	3.24920i	−0.342997	+	0.249202i
$171$	14.9443	−	10.8576i	1.14282	−	0.830305i
$172$	7.41641	+	22.8254i	0.565496	+	1.74042i
$173$	−5.32624	+	16.3925i	−0.404946	+	1.24630i	0.515994	+	0.856592i	$0.327423\pi$
$173$	−5.32624	+	16.3925i	−0.404946	+	1.24630i	−0.920940	+	0.389704i	$0.872577\pi$
$174$	−2.76393	−	2.00811i	−0.209533	−	0.152235i
$175$	−1.00000			−0.0755929
$176$		0			0
$177$	10.4721			0.787134
$178$	3.61803	+	2.62866i	0.271183	+	0.197026i
$179$	2.76393	−	8.50651i	0.206586	−	0.635806i	−0.793059	−	0.609145i	$-0.791513\pi$
$179$	2.76393	−	8.50651i	0.206586	−	0.635806i	0.999645	−	0.0266609i	$-0.00848742\pi$
$180$	−13.8541	−	42.6385i	−1.03262	−	3.17809i
$181$	−1.14590	+	0.832544i	−0.0851739	+	0.0618825i	−0.629557	−	0.776954i	$-0.716764\pi$
$181$	−1.14590	+	0.832544i	−0.0851739	+	0.0618825i	0.544383	+	0.838837i	$0.316764\pi$
$182$	−2.23607	+	1.62460i	−0.165748	+	0.120423i
$183$	−2.76393	−	8.50651i	−0.204316	−	0.628819i
$184$	4.47214	−	13.7638i	0.329690	−	1.01468i
$185$	0.763932	+	0.555029i	0.0561654	+	0.0408066i
$186$	52.3607			3.83927
$187$		0			0
$188$	21.7082			1.58323
$189$	−11.7082	−	8.50651i	−0.851647	−	0.618757i
$190$	−3.41641	+	10.5146i	−0.247852	+	0.762811i
$191$	−6.47214	−	19.9192i	−0.468307	−	1.44130i	−0.854775	−	0.518999i	$-0.826305\pi$
$191$	−6.47214	−	19.9192i	−0.468307	−	1.44130i	0.386468	−	0.922303i	$-0.373695\pi$
$192$	34.0344	−	24.7275i	2.45622	−	1.78455i
$193$	19.3262	−	14.0413i	1.39113	−	1.01072i	0.395393	−	0.918512i	$-0.370608\pi$
$193$	19.3262	−	14.0413i	1.39113	−	1.01072i	0.995740	−	0.0922053i	$-0.0293916\pi$
$194$	6.50658	+	20.0252i	0.467145	+	1.43772i
$195$	2.47214	−	7.60845i	0.177033	−	0.544853i
$196$	−2.42705	−	1.76336i	−0.173361	−	0.125954i
$197$	−2.00000			−0.142494			−0.0712470	−	0.997459i	$-0.522698\pi$
$197$	−2.00000			−0.142494			−0.0712470	+	0.997459i	$0.522698\pi$
$198$		0			0
$199$	20.1803			1.43055			0.715273	−	0.698845i	$-0.246302\pi$
$199$	20.1803			1.43055			0.715273	+	0.698845i	$0.246302\pi$
$200$	−1.80902	−	1.31433i	−0.127917	−	0.0929370i
$201$	5.52786	−	17.0130i	0.389905	−	1.20001i
$202$	6.38197	+	19.6417i	0.449034	+	1.38198i
$203$	0.381966	−	0.277515i	0.0268088	−	0.0194777i
$204$	−9.70820	+	7.05342i	−0.679710	+	0.493838i
$205$	4.18034	+	12.8658i	0.291968	+	0.898584i
$206$	3.94427	−	12.1392i	0.274810	−	0.845780i
$207$	39.1246	+	28.4257i	2.71935	+	1.97572i
$208$	1.23607			0.0857059
$209$		0			0
$210$	14.4721			0.998672
$211$	−17.7082	−	12.8658i	−1.21908	−	0.885716i	−0.223059	−	0.974805i	$-0.571604\pi$
$211$	−17.7082	−	12.8658i	−1.21908	−	0.885716i	−0.996024	+	0.0890892i	$0.971604\pi$
$212$	7.85410	−	24.1724i	0.539422	−	1.66017i
$213$	−1.52786	−	4.70228i	−0.104688	−	0.322195i
$214$	−7.23607	+	5.25731i	−0.494647	+	0.359382i
$215$	12.9443	−	9.40456i	0.882792	−	0.641386i
$216$	−10.0000	−	30.7768i	−0.680414	−	2.09410i
$217$	−2.23607	+	6.88191i	−0.151794	+	0.467174i
$218$	8.09017	+	5.87785i	0.547935	+	0.398098i
$219$	−16.9443			−1.14499
$220$		0			0
$221$	−1.52786			−0.102775
$222$	2.76393	+	2.00811i	0.185503	+	0.134776i
$223$	3.76393	−	11.5842i	0.252052	−	0.775735i	−0.742345	−	0.670018i	$-0.766286\pi$
$223$	3.76393	−	11.5842i	0.252052	−	0.775735i	0.994396	−	0.105717i	$-0.0337137\pi$
$224$	2.07295	+	6.37988i	0.138505	+	0.426274i
$225$	6.04508	−	4.39201i	0.403006	−	0.292801i
$226$	3.61803	−	2.62866i	0.240668	−	0.174856i
$227$	−9.23607	−	28.4257i	−0.613019	−	1.88668i	−0.427417	−	0.904055i	$-0.640576\pi$
$227$	−9.23607	−	28.4257i	−0.613019	−	1.88668i	−0.185603	−	0.982625i	$-0.559424\pi$
$228$	−7.41641	+	22.8254i	−0.491164	+	1.51165i
$229$	−3.61803	−	2.62866i	−0.239086	−	0.173706i	0.461790	−	0.886989i	$-0.347207\pi$
$229$	−3.61803	−	2.62866i	−0.239086	−	0.173706i	−0.700876	+	0.713283i	$0.747207\pi$
$230$	−28.9443			−1.90853
$231$		0			0
$232$	1.05573			0.0693119
$233$	14.0902	+	10.2371i	0.923078	+	0.670655i	0.944288	−	0.329120i	$-0.106752\pi$
$233$	14.0902	+	10.2371i	0.923078	+	0.670655i	−0.0212104	+	0.999775i	$0.506752\pi$
$234$	6.38197	−	19.6417i	0.417202	−	1.28402i
$235$	−4.47214	−	13.7638i	−0.291730	−	0.897853i
$236$	−7.85410	+	5.70634i	−0.511258	+	0.371451i
$237$	−23.4164	+	17.0130i	−1.52106	+	1.10511i
$238$	−0.854102	−	2.62866i	−0.0553632	−	0.170390i
$239$	8.00000	−	24.6215i	0.517477	−	1.59263i	−0.261252	−	0.965271i	$-0.584136\pi$
$239$	8.00000	−	24.6215i	0.517477	−	1.59263i	0.778729	−	0.627360i	$-0.215864\pi$
$240$	−5.23607	−	3.80423i	−0.337987	−	0.245562i
$241$	27.1246			1.74725			0.873625	−	0.486600i	$-0.161763\pi$
$241$	27.1246			1.74725			0.873625	+	0.486600i	$0.161763\pi$
$242$		0			0
$243$	35.5967			2.28353
$244$	6.70820	+	4.87380i	0.429449	+	0.312013i
$245$	−0.618034	+	1.90211i	−0.0394847	+	0.121522i
$246$	15.1246	+	46.5488i	0.964310	+	2.96784i
$247$	−2.47214	+	1.79611i	−0.157298	+	0.114284i
$248$	−13.0902	+	9.51057i	−0.831227	+	0.603921i
$249$	15.4164	+	47.4468i	0.976975	+	3.00682i
$250$	−8.29180	+	25.5195i	−0.524419	+	1.61400i
$251$	−14.3262	−	10.4086i	−0.904264	−	0.656986i	0.0352936	−	0.999377i	$-0.488763\pi$
$251$	−14.3262	−	10.4086i	−0.904264	−	0.656986i	−0.939558	+	0.342391i	$0.888763\pi$
$252$	22.4164			1.41210
$253$		0			0
$254$	−46.8328			−2.93855
$255$	6.47214	+	4.70228i	0.405301	+	0.294468i
$256$	−2.78115	+	8.55951i	−0.173822	+	0.534969i
$257$	−1.85410	−	5.70634i	−0.115656	−	0.355952i	0.876428	−	0.481534i	$-0.159920\pi$
$257$	−1.85410	−	5.70634i	−0.115656	−	0.355952i	−0.992083	+	0.125582i	$0.959920\pi$
$258$	46.8328	−	34.0260i	2.91568	−	2.11837i
$259$	−0.381966	+	0.277515i	−0.0237342	+	0.0172439i
$260$	2.29180	+	7.05342i	0.142131	+	0.437435i
$261$	−1.09017	+	3.35520i	−0.0674798	+	0.207682i
$262$	−25.1246	−	18.2541i	−1.55220	−	1.12774i
$263$		0			0			−	1.00000i	$-0.5\pi$
$263$		0			0				1.00000i	$0.5\pi$
$264$		0			0
$265$	−16.9443			−1.04088
$266$	−4.47214	−	3.24920i	−0.274204	−	0.199221i
$267$	2.00000	−	6.15537i	0.122398	−	0.376702i
$268$	5.12461	+	15.7719i	0.313035	+	0.963424i
$269$	10.8541	−	7.88597i	0.661786	−	0.480816i	−0.205479	−	0.978661i	$-0.565875\pi$
$269$	10.8541	−	7.88597i	0.661786	−	0.480816i	0.867266	+	0.497846i	$0.165875\pi$
$270$	−52.3607	+	38.0423i	−3.18657	+	2.31518i
$271$	−0.472136	−	1.45309i	−0.0286802	−	0.0882686i	0.935692	−	0.352818i	$-0.114777\pi$
$271$	−0.472136	−	1.45309i	−0.0286802	−	0.0882686i	−0.964372	+	0.264550i	$0.914777\pi$
$272$	−0.381966	+	1.17557i	−0.0231601	+	0.0712794i
$273$	3.23607	+	2.35114i	0.195856	+	0.142298i
$274$	−16.8328			−1.01691
$275$		0			0
$276$	−62.8328			−3.78209
$277$	−12.8541	−	9.33905i	−0.772328	−	0.561129i	0.130339	−	0.991470i	$-0.458394\pi$
$277$	−12.8541	−	9.33905i	−0.772328	−	0.561129i	−0.902667	+	0.430340i	$0.858394\pi$
$278$	7.23607	−	22.2703i	0.433991	−	1.33569i
$279$	−16.7082	−	51.4226i	−1.00029	−	3.07859i
$280$	−3.61803	+	2.62866i	−0.216219	+	0.157092i
$281$	10.0902	−	7.33094i	0.601929	−	0.437327i	−0.244634	−	0.969615i	$-0.578668\pi$
$281$	10.0902	−	7.33094i	0.601929	−	0.437327i	0.846563	+	0.532288i	$0.178668\pi$
$282$	−16.1803	−	49.7980i	−0.963525	−	2.96543i
$283$	−1.81966	+	5.60034i	−0.108168	+	0.332906i	−0.990461	−	0.137795i	$-0.955999\pi$
$283$	−1.81966	+	5.60034i	−0.108168	+	0.332906i	0.882293	+	0.470700i	$0.155999\pi$
$284$	3.70820	+	2.69417i	0.220041	+	0.159869i
$285$	16.0000			0.947758
$286$		0			0
$287$	−6.76393			−0.399262
$288$	−40.5517	−	29.4625i	−2.38953	−	1.73609i
$289$	−4.78115	+	14.7149i	−0.281244	+	0.865581i
$290$	−0.652476	−	2.00811i	−0.0383147	−	0.117921i
$291$	24.6525	−	17.9111i	1.44515	−	1.04997i
$292$	12.7082	−	9.23305i	0.743691	−	0.540323i
$293$	4.67376	+	14.3844i	0.273044	+	0.840343i	0.989730	+	0.142948i	$0.0456580\pi$
$293$	4.67376	+	14.3844i	0.273044	+	0.840343i	−0.716686	+	0.697396i	$0.754342\pi$
$294$	−2.23607	+	6.88191i	−0.130410	+	0.401361i
$295$	5.23607	+	3.80423i	0.304856	+	0.221491i
$296$	−1.05573			−0.0613629
$297$		0			0
$298$	−31.3050			−1.81345
$299$	−6.47214	−	4.70228i	−0.374293	−	0.271940i
$300$	−3.00000	+	9.23305i	−0.173205	+	0.533070i
$301$	2.47214	+	7.60845i	0.142492	+	0.438544i
$302$	−16.1803	+	11.7557i	−0.931074	+	0.676465i
$303$	24.1803	−	17.5680i	1.38912	−	1.00926i
$304$	0.763932	+	2.35114i	0.0438145	+	0.134847i
$305$	1.70820	−	5.25731i	0.0978115	−	0.301033i
$306$	16.7082	+	12.1392i	0.955144	+	0.693953i
$307$	8.94427			0.510477			0.255238	−	0.966878i	$-0.417846\pi$
$307$	8.94427			0.510477			0.255238	+	0.966878i	$0.417846\pi$
$308$		0			0
$309$	−18.4721			−1.05084
$310$	26.1803	+	19.0211i	1.48694	+	1.08033i
$311$	−6.70820	+	20.6457i	−0.380387	+	1.17071i	0.559384	+	0.828909i	$0.311038\pi$
$311$	−6.70820	+	20.6457i	−0.380387	+	1.17071i	−0.939772	+	0.341803i	$0.888962\pi$
$312$	2.76393	+	8.50651i	0.156477	+	0.481586i
$313$	2.38197	−	1.73060i	0.134637	−	0.0978193i	−0.518428	−	0.855121i	$-0.673483\pi$
$313$	2.38197	−	1.73060i	0.134637	−	0.0978193i	0.653065	+	0.757302i	$0.273483\pi$
$314$	−12.5623	+	9.12705i	−0.708932	+	0.515069i
$315$	−4.61803	−	14.2128i	−0.260197	−	0.800803i
$316$	8.29180	−	25.5195i	0.466450	−	1.43559i
$317$	−11.3262	−	8.22899i	−0.636145	−	0.462186i	0.222379	−	0.974960i	$-0.428618\pi$
$317$	−11.3262	−	8.22899i	−0.636145	−	0.462186i	−0.858524	+	0.512774i	$0.828618\pi$
$318$	−61.3050			−3.43781
$319$		0			0
$320$	26.0000			1.45344
$321$	10.4721	+	7.60845i	0.584498	+	0.424662i
$322$	4.47214	−	13.7638i	0.249222	−	0.767028i
$323$	−0.944272	−	2.90617i	−0.0525407	−	0.161704i
$324$	−59.2599	+	43.0548i	−3.29221	+	2.39193i
$325$	−1.00000	+	0.726543i	−0.0554700	+	0.0403013i
$326$	−16.1803	−	49.7980i	−0.896146	−	2.75805i
$327$	4.47214	−	13.7638i	0.247310	−	0.761141i
$328$	−12.2361	−	8.89002i	−0.675624	−	0.490869i
$329$	7.23607			0.398937
$330$		0			0
$331$	21.8885			1.20310			0.601552	−	0.798834i	$-0.294549\pi$
$331$	21.8885			1.20310			0.601552	+	0.798834i	$0.294549\pi$
$332$	−37.4164	−	27.1846i	−2.05349	−	1.49195i
$333$	1.09017	−	3.35520i	0.0597409	−	0.183864i
$334$	8.94427	+	27.5276i	0.489409	+	1.50625i
$335$	8.94427	−	6.49839i	0.488678	−	0.355045i
$336$	2.61803	−	1.90211i	0.142825	−	0.103769i
$337$	−6.32624	−	19.4702i	−0.344612	−	1.06061i	−0.961791	−	0.273784i	$-0.911725\pi$
$337$	−6.32624	−	19.4702i	−0.344612	−	1.06061i	0.617179	−	0.786823i	$-0.288275\pi$
$338$	7.92705	−	24.3970i	0.431175	−	1.32702i
$339$	−5.23607	−	3.80423i	−0.284384	−	0.206617i
$340$	−7.41641			−0.402211
$341$		0			0
$342$	41.3050			2.23352
$343$	−0.809017	−	0.587785i	−0.0436828	−	0.0317374i
$344$	−5.52786	+	17.0130i	−0.298042	+	0.917280i
$345$	12.9443	+	39.8384i	0.696896	+	2.14483i
$346$	−31.1803	+	22.6538i	−1.67627	+	1.21788i
$347$	−2.47214	+	1.79611i	−0.132711	+	0.0964203i	−0.652160	−	0.758081i	$-0.726137\pi$
$347$	−2.47214	+	1.79611i	−0.132711	+	0.0964203i	0.519449	+	0.854501i	$0.326137\pi$
$348$	−1.41641	−	4.35926i	−0.0759274	−	0.233681i
$349$	−0.854102	+	2.62866i	−0.0457190	+	0.140709i	−0.971310	−	0.237816i	$-0.923568\pi$
$349$	−0.854102	+	2.62866i	−0.0457190	+	0.140709i	0.925591	+	0.378525i	$0.123568\pi$
$350$	−1.80902	−	1.31433i	−0.0966960	−	0.0702538i
$351$	−17.8885			−0.954820
$352$		0			0
$353$	−15.8885			−0.845662			−0.422831	−	0.906209i	$-0.638964\pi$
$353$	−15.8885			−0.845662			−0.422831	+	0.906209i	$0.638964\pi$
$354$	18.9443	+	13.7638i	1.00688	+	0.731539i
$355$	0.944272	−	2.90617i	0.0501167	−	0.154243i
$356$	1.85410	+	5.70634i	0.0982672	+	0.302435i
$357$	−3.23607	+	2.35114i	−0.171271	+	0.124436i
$358$	16.1803	−	11.7557i	0.855158	−	0.621308i
$359$	−2.18034	−	6.71040i	−0.115074	−	0.354161i	0.876889	−	0.480694i	$-0.159615\pi$
$359$	−2.18034	−	6.71040i	−0.115074	−	0.354161i	−0.991962	+	0.126533i	$0.959615\pi$
$360$	10.3262	−	31.7809i	0.544241	−	1.67500i
$361$	10.4271	+	7.57570i	0.548792	+	0.398721i
$362$	−3.16718			−0.166464
$363$		0			0
$364$	−3.70820			−0.194363
$365$	−8.47214	−	6.15537i	−0.443452	−	0.322187i
$366$	6.18034	−	19.0211i	0.323052	−	0.994250i
$367$	5.29180	+	16.2865i	0.276230	+	0.850147i	0.988891	+	0.148639i	$0.0474894\pi$
$367$	5.29180	+	16.2865i	0.276230	+	0.850147i	−0.712662	+	0.701508i	$0.752511\pi$
$368$	−5.23607	+	3.80423i	−0.272949	+	0.198309i
$369$	40.8885	−	29.7073i	2.12857	−	1.54650i
$370$	0.652476	+	2.00811i	0.0339206	+	0.104397i
$371$	2.61803	−	8.05748i	0.135922	−	0.418324i
$372$	56.8328	+	41.2915i	2.94664	+	2.14086i
$373$	6.00000			0.310668			0.155334	−	0.987862i	$-0.450355\pi$
$373$	6.00000			0.310668			0.155334	+	0.987862i	$0.450355\pi$
$374$		0			0
$375$	38.8328			2.00532
$376$	13.0902	+	9.51057i	0.675074	+	0.490470i
$377$	0.180340	−	0.555029i	0.00928798	−	0.0285855i
$378$	−10.0000	−	30.7768i	−0.514344	−	1.58299i
$379$	20.4721	−	14.8739i	1.05158	−	0.764020i	0.0790702	−	0.996869i	$-0.474805\pi$
$379$	20.4721	−	14.8739i	1.05158	−	0.764020i	0.972513	+	0.232849i	$0.0748049\pi$
$380$	−12.0000	+	8.71851i	−0.615587	+	0.447250i
$381$	20.9443	+	64.4598i	1.07301	+	3.30238i
$382$	14.4721	−	44.5407i	0.740459	−	2.27890i
$383$	−21.5623	−	15.6659i	−1.10178	−	0.800492i	−0.120432	−	0.992722i	$-0.538428\pi$
$383$	−21.5623	−	15.6659i	−1.10178	−	0.800492i	−0.981350	+	0.192230i	$0.938428\pi$
$384$	50.6525			2.58485
$385$		0			0
$386$	53.4164			2.71882
$387$	−48.3607	−	35.1361i	−2.45831	−	1.78607i
$388$	−8.72949	+	26.8666i	−0.443173	+	1.36395i
$389$	−6.14590	−	18.9151i	−0.311609	−	0.959035i	−0.977128	−	0.212654i	$-0.931789\pi$
$389$	−6.14590	−	18.9151i	−0.311609	−	0.959035i	0.665518	−	0.746382i	$-0.268211\pi$
$390$	14.4721	−	10.5146i	0.732825	−	0.532429i
$391$	6.47214	−	4.70228i	0.327310	−	0.237805i
$392$	−0.690983	−	2.12663i	−0.0348999	−	0.107411i
$393$	−13.8885	+	42.7445i	−0.700584	+	2.15618i
$394$	−3.61803	−	2.62866i	−0.182274	−	0.132430i
$395$	−17.8885			−0.900070
$396$		0			0
$397$	−0.111456			−0.00559383			−0.00279691	−	0.999996i	$-0.500890\pi$
$397$	−0.111456			−0.00559383			−0.00279691	+	0.999996i	$0.500890\pi$
$398$	36.5066	+	26.5236i	1.82991	+	1.32951i
$399$	−2.47214	+	7.60845i	−0.123762	+	0.380899i
$400$	0.309017	+	0.951057i	0.0154508	+	0.0475528i
$401$	−4.09017	+	2.97168i	−0.204253	+	0.148399i	−0.685210	−	0.728346i	$-0.740290\pi$
$401$	−4.09017	+	2.97168i	−0.204253	+	0.148399i	0.480956	+	0.876744i	$0.340290\pi$
$402$	32.3607	−	23.5114i	1.61400	−	1.17264i
$403$	2.76393	+	8.50651i	0.137681	+	0.423739i
$404$	−8.56231	+	26.3521i	−0.425991	+	1.31106i
$405$	39.5066	+	28.7032i	1.96310	+	1.42627i
$406$	1.05573			0.0523949
$407$		0			0
$408$	−8.94427			−0.442807
$409$	25.1803	+	18.2946i	1.24509	+	0.904609i	0.997926	−	0.0643652i	$-0.0205023\pi$
$409$	25.1803	+	18.2946i	1.24509	+	0.904609i	0.247161	+	0.968974i	$0.420502\pi$
$410$	−9.34752	+	28.7687i	−0.461641	+	1.42079i
$411$	7.52786	+	23.1684i	0.371322	+	1.14281i
$412$	13.8541	−	10.0656i	0.682543	−	0.495896i
$413$	−2.61803	+	1.90211i	−0.128825	+	0.0935969i
$414$	33.4164	+	102.845i	1.64233	+	5.05456i
$415$	−9.52786	+	29.3238i	−0.467704	+	1.43945i
$416$	6.70820	+	4.87380i	0.328897	+	0.238957i
$417$	−33.8885			−1.65953
$418$		0			0
$419$	−6.65248			−0.324995			−0.162497	−	0.986709i	$-0.551955\pi$
$419$	−6.65248			−0.324995			−0.162497	+	0.986709i	$0.551955\pi$
$420$	15.7082	+	11.4127i	0.766482	+	0.556882i
$421$	−6.90983	+	21.2663i	−0.336765	+	1.03645i	0.629082	+	0.777339i	$0.283431\pi$
$421$	−6.90983	+	21.2663i	−0.336765	+	1.03645i	−0.965846	+	0.259116i	$0.916569\pi$
$422$	−15.1246	−	46.5488i	−0.736255	−	2.26596i
$423$	−43.7426	+	31.7809i	−2.12684	+	1.54524i
$424$	15.3262	−	11.1352i	0.744308	−	0.540771i
$425$	−0.381966	−	1.17557i	−0.0185281	−	0.0570235i
$426$	3.41641	−	10.5146i	0.165526	−	0.509435i
$427$	2.23607	+	1.62460i	0.108211	+	0.0786198i
$428$	−12.0000			−0.580042
$429$		0			0
$430$	35.7771			1.72532
$431$	−9.70820	−	7.05342i	−0.467628	−	0.339751i	0.328888	−	0.944369i	$-0.393326\pi$
$431$	−9.70820	−	7.05342i	−0.467628	−	0.339751i	−0.796516	+	0.604617i	$0.793326\pi$
$432$	−4.47214	+	13.7638i	−0.215166	+	0.662212i
$433$	0.145898	+	0.449028i	0.00701141	+	0.0215789i	0.954501	−	0.298208i	$-0.0963888\pi$
$433$	0.145898	+	0.449028i	0.00701141	+	0.0215789i	−0.947490	+	0.319787i	$0.896389\pi$
$434$	−13.0902	+	9.51057i	−0.628348	+	0.456522i
$435$	−2.47214	+	1.79611i	−0.118530	+	0.0861170i
$436$	4.14590	+	12.7598i	0.198553	+	0.611082i
$437$	4.94427	−	15.2169i	0.236517	−	0.727923i
$438$	−30.6525	−	22.2703i	−1.46463	−	1.06412i
$439$	1.52786			0.0729210			0.0364605	−	0.999335i	$-0.488392\pi$
$439$	1.52786			0.0729210			0.0364605	+	0.999335i	$0.488392\pi$
$440$		0			0
$441$	7.47214			0.355816
$442$	−2.76393	−	2.00811i	−0.131467	−	0.0955163i
$443$	−2.18034	+	6.71040i	−0.103591	+	0.318821i	−0.989397	−	0.145235i	$-0.953606\pi$
$443$	−2.18034	+	6.71040i	−0.103591	+	0.318821i	0.885806	+	0.464056i	$0.153606\pi$
$444$	1.41641	+	4.35926i	0.0672197	+	0.206881i
$445$	3.23607	−	2.35114i	0.153404	−	0.111455i
$446$	22.0344	−	16.0090i	1.04336	−	0.758046i
$447$	14.0000	+	43.0876i	0.662177	+	2.03797i
$448$	−4.01722	+	12.3637i	−0.189796	+	0.584132i
$449$	15.7984	+	11.4782i	0.745571	+	0.541689i	0.894451	−	0.447166i	$-0.147567\pi$
$449$	15.7984	+	11.4782i	0.745571	+	0.541689i	−0.148880	+	0.988855i	$0.547567\pi$
$450$	16.7082			0.787632
$451$		0			0
$452$	6.00000			0.282216
$453$	23.4164	+	17.0130i	1.10020	+	0.799341i
$454$	20.6525	−	63.5618i	0.969269	−	2.98310i
$455$	0.763932	+	2.35114i	0.0358137	+	0.110223i
$456$	−14.4721	+	10.5146i	−0.677720	+	0.492392i
$457$	−20.0902	+	14.5964i	−0.939779	+	0.682789i	−0.948367	−	0.317174i	$-0.897266\pi$
$457$	−20.0902	+	14.5964i	−0.939779	+	0.682789i	0.00858883	+	0.999963i	$0.497266\pi$
$458$	−3.09017	−	9.51057i	−0.144394	−	0.444400i
$459$	5.52786	−	17.0130i	0.258019	−	0.794100i
$460$	−31.4164	−	22.8254i	−1.46480	−	1.06424i
$461$	10.1803			0.474146			0.237073	−	0.971492i	$-0.423812\pi$
$461$	10.1803			0.474146			0.237073	+	0.971492i	$0.423812\pi$
$462$		0			0
$463$	−14.4721			−0.672577			−0.336289	−	0.941759i	$-0.609172\pi$
$463$	−14.4721			−0.672577			−0.336289	+	0.941759i	$0.609172\pi$
$464$	−0.381966	−	0.277515i	−0.0177323	−	0.0128833i
$465$	14.4721	−	44.5407i	0.671129	−	2.06552i
$466$	12.0344	+	37.0382i	0.557485	+	1.71576i
$467$	27.5623	−	20.0252i	1.27543	−	0.926655i	0.276027	−	0.961150i	$-0.410982\pi$
$467$	27.5623	−	20.0252i	1.27543	−	0.926655i	0.999405	+	0.0344949i	$0.0109822\pi$
$468$	22.4164	−	16.2865i	1.03620	−	0.752843i
$469$	1.70820	+	5.25731i	0.0788775	+	0.242760i
$470$	10.0000	−	30.7768i	0.461266	−	1.41963i
$471$	18.1803	+	13.2088i	0.837706	+	0.608629i
$472$	−7.23607			−0.333067
$473$		0			0
$474$	−64.7214			−2.97275
$475$	−2.00000	−	1.45309i	−0.0917663	−	0.0666721i
$476$	1.14590	−	3.52671i	0.0525222	−	0.161647i
$477$	19.5623	+	60.2066i	0.895696	+	2.75667i
$478$	46.8328	−	34.0260i	2.14208	−	1.55631i
$479$	−18.1803	+	13.2088i	−0.830681	+	0.603525i	−0.919752	−	0.392500i	$-0.871610\pi$
$479$	−18.1803	+	13.2088i	−0.830681	+	0.603525i	0.0890710	+	0.996025i	$0.471610\pi$
$480$	−13.4164	−	41.2915i	−0.612372	−	1.88469i
$481$	−0.180340	+	0.555029i	−0.00822279	+	0.0253071i
$482$	49.0689	+	35.6506i	2.23503	+	1.62384i
$483$	−20.9443			−0.952997
$484$		0			0
$485$	18.8328			0.855154
$486$	64.3951	+	46.7858i	2.92102	+	2.12225i
$487$	2.58359	−	7.95148i	0.117074	−	0.360316i	−0.875300	−	0.483580i	$-0.839336\pi$
$487$	2.58359	−	7.95148i	0.117074	−	0.360316i	0.992374	+	0.123264i	$0.0393362\pi$
$488$	1.90983	+	5.87785i	0.0864539	+	0.266078i
$489$	−61.3050	+	44.5407i	−2.77231	+	2.01420i
$490$	−3.61803	+	2.62866i	−0.163446	+	0.118751i
$491$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$491$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$492$	−20.2918	+	62.4517i	−0.914825	+	2.81554i
$493$	0.472136	+	0.343027i	0.0212639	+	0.0154492i
$494$	−6.83282			−0.307423
$495$		0			0
$496$	7.23607			0.324909
$497$	1.23607	+	0.898056i	0.0554452	+	0.0402833i
$498$	−34.4721	+	106.094i	−1.54473	+	4.75420i
$499$	3.23607	+	9.95959i	0.144866	+	0.445853i	0.996994	−	0.0774816i	$-0.0246879\pi$
$499$	3.23607	+	9.95959i	0.144866	+	0.445853i	−0.852127	+	0.523334i	$0.824688\pi$
$500$	−29.1246	+	21.1603i	−1.30249	+	0.946316i
$501$	33.8885	−	24.6215i	1.51403	−	1.10001i
$502$	−12.2361	−	37.6587i	−0.546122	−	1.68079i
$503$	−1.05573	+	3.24920i	−0.0470726	+	0.144875i	−0.971830	−	0.235682i	$-0.924268\pi$
$503$	−1.05573	+	3.24920i	−0.0470726	+	0.144875i	0.924758	+	0.380557i	$0.124268\pi$
$504$	13.5172	+	9.82084i	0.602105	+	0.437455i
$505$	18.4721			0.821999
$506$		0			0
$507$	−37.1246			−1.64876
$508$	−50.8328	−	36.9322i	−2.25534	−	1.63860i
$509$	9.74265	−	29.9848i	0.431835	−	1.32905i	−0.464460	−	0.885594i	$-0.653752\pi$
$509$	9.74265	−	29.9848i	0.431835	−	1.32905i	0.896295	−	0.443458i	$-0.146248\pi$
$510$	5.52786	+	17.0130i	0.244778	+	0.753349i
$511$	4.23607	−	3.07768i	0.187393	−	0.136149i
$512$	9.04508	−	6.57164i	0.399740	−	0.290428i
$513$	−11.0557	−	34.0260i	−0.488122	−	1.50229i
$514$	4.14590	−	12.7598i	0.182868	−	0.562809i
$515$	−9.23607	−	6.71040i	−0.406990	−	0.295695i
$516$	77.6656			3.41904
$517$		0			0
$518$	−1.05573			−0.0463860
$519$	45.1246	+	32.7849i	1.98075	+	1.43910i
$520$	−1.70820	+	5.25731i	−0.0749097	+	0.230548i
$521$	−4.43769	−	13.6578i	−0.194419	−	0.598360i	−0.999983	−	0.00585107i	$-0.998138\pi$
$521$	−4.43769	−	13.6578i	−0.194419	−	0.598360i	0.805564	−	0.592509i	$-0.201862\pi$
$522$	−6.38197	+	4.63677i	−0.279331	+	0.202946i
$523$	−35.5967	+	25.8626i	−1.55654	+	1.13089i	−0.617759	+	0.786367i	$0.711959\pi$
$523$	−35.5967	+	25.8626i	−1.55654	+	1.13089i	−0.938778	+	0.344523i	$0.888041\pi$
$524$	−12.8754	−	39.6264i	−0.562464	−	1.73109i
$525$	−1.00000	+	3.07768i	−0.0436436	+	0.134321i
$526$		0			0
$527$	−8.94427			−0.389619
$528$		0			0
$529$	18.8885			0.821241
$530$	−30.6525	−	22.2703i	−1.33146	−	0.967361i
$531$	7.47214	−	22.9969i	0.324263	−	0.997979i
$532$	−2.29180	−	7.05342i	−0.0993620	−	0.305805i
$533$	−6.76393	+	4.91428i	−0.292978	+	0.212861i
$534$	11.7082	−	8.50651i	0.506664	−	0.368113i
$535$	2.47214	+	7.60845i	0.106880	+	0.328942i
$536$	−3.81966	+	11.7557i	−0.164984	+	0.507769i
$537$	−23.4164	−	17.0130i	−1.01049	−	0.734166i
$538$	30.0000			1.29339
$539$		0			0
$540$	−86.8328			−3.73669
$541$	26.5623	+	19.2986i	1.14200	+	0.829714i	0.987397	−	0.158263i	$-0.0505893\pi$
$541$	26.5623	+	19.2986i	1.14200	+	0.829714i	0.154606	+	0.987976i	$0.450589\pi$
$542$	1.05573	−	3.24920i	0.0453474	−	0.139565i
$543$	1.41641	+	4.35926i	0.0607839	+	0.187074i
$544$	−6.70820	+	4.87380i	−0.287612	+	0.208962i
$545$	7.23607	−	5.25731i	0.309959	−	0.225198i
$546$	2.76393	+	8.50651i	0.118285	+	0.364045i
$547$	8.65248	−	26.6296i	0.369953	−	1.13860i	−0.576868	−	0.816838i	$-0.695725\pi$
$547$	8.65248	−	26.6296i	0.369953	−	1.13860i	0.946821	−	0.321761i	$-0.104275\pi$
$548$	−18.2705	−	13.2743i	−0.780477	−	0.567050i
$549$	−20.6525			−0.881426
$550$		0			0
$551$	1.16718			0.0497237
$552$	−37.8885	−	27.5276i	−1.61264	−	1.17165i
$553$	2.76393	−	8.50651i	0.117534	−	0.361734i
$554$	−10.9787	−	33.7890i	−0.466441	−	1.43556i
$555$	2.47214	−	1.79611i	0.104936	−	0.0762407i
$556$	25.4164	−	18.4661i	1.07790	−	0.783137i
$557$	−6.50658	−	20.0252i	−0.275693	−	0.848494i	−0.989035	−	0.147679i	$-0.952820\pi$
$557$	−6.50658	−	20.0252i	−0.275693	−	0.848494i	0.713343	−	0.700815i	$-0.247180\pi$
$558$	37.3607	−	114.984i	1.58160	−	4.86768i
$559$	8.00000	+	5.81234i	0.338364	+	0.245836i
$560$	2.00000			0.0845154
$561$		0			0
$562$	27.8885			1.17641
$563$	−31.8885	−	23.1684i	−1.34394	−	0.976431i	−0.999289	−	0.0377007i	$-0.987997\pi$
$563$	−31.8885	−	23.1684i	−1.34394	−	0.976431i	−0.344653	−	0.938730i	$-0.612003\pi$
$564$	21.7082	−	66.8110i	0.914080	−	2.81325i
$565$	−1.23607	−	3.80423i	−0.0520018	−	0.160045i
$566$	−10.6525	+	7.73948i	−0.447757	+	0.325314i
$567$	−19.7533	+	14.3516i	−0.829560	+	0.602711i
$568$	1.05573	+	3.24920i	0.0442974	+	0.136333i
$569$	5.09017	−	15.6659i	0.213391	−	0.656750i	−0.785873	−	0.618388i	$-0.787786\pi$
$569$	5.09017	−	15.6659i	0.213391	−	0.656750i	0.999264	−	0.0383620i	$-0.0122140\pi$
$570$	28.9443	+	21.0292i	1.21234	+	0.880818i
$571$	−32.9443			−1.37867			−0.689337	−	0.724440i	$-0.742098\pi$
$571$	−32.9443			−1.37867			−0.689337	+	0.724440i	$0.742098\pi$
$572$		0			0
$573$	−67.7771			−2.83143
$574$	−12.2361	−	8.89002i	−0.510724	−	0.371062i
$575$	2.00000	−	6.15537i	0.0834058	−	0.256697i
$576$	−30.0172	−	92.3835i	−1.25072	−	3.84931i
$577$	23.0344	−	16.7355i	0.958936	−	0.696708i	0.00603289	−	0.999982i	$-0.498080\pi$
$577$	23.0344	−	16.7355i	0.958936	−	0.696708i	0.952903	+	0.303274i	$0.0980797\pi$
$578$	−27.9894	+	20.3355i	−1.16420	+	0.845844i
$579$	−23.8885	−	73.5214i	−0.992774	−	3.05544i
$580$	0.875388	−	2.69417i	0.0363485	−	0.111869i
$581$	−12.4721	−	9.06154i	−0.517431	−	0.375936i
$582$	68.1378			2.82440
$583$		0			0
$584$	11.7082			0.484489
$585$	−14.9443	−	10.8576i	−0.617870	−	0.448909i
$586$	−10.4508	+	32.1644i	−0.431721	+	1.32870i
$587$	−4.05573	−	12.4822i	−0.167398	−	0.515197i	0.831807	−	0.555065i	$-0.187307\pi$
$587$	−4.05573	−	12.4822i	−0.167398	−	0.515197i	−0.999205	+	0.0398672i	$0.987307\pi$
$588$	−7.85410	+	5.70634i	−0.323898	+	0.235325i
$589$	−14.4721	+	10.5146i	−0.596314	+	0.433247i
$590$	4.47214	+	13.7638i	0.184115	+	0.566647i
$591$	−2.00000	+	6.15537i	−0.0822690	+	0.253198i
$592$	0.381966	+	0.277515i	0.0156987	+	0.0114058i
$593$	−32.2918			−1.32607			−0.663033	−	0.748591i	$-0.730731\pi$
$593$	−32.2918			−1.32607			−0.663033	+	0.748591i	$0.730731\pi$
$594$		0			0
$595$	−2.47214			−0.101348
$596$	−33.9787	−	24.6870i	−1.39182	−	1.01122i
$597$	20.1803	−	62.1087i	0.825926	−	2.54194i
$598$	−5.52786	−	17.0130i	−0.226051	−	0.695714i
$599$	−2.76393	+	2.00811i	−0.112931	+	0.0820493i	−0.642817	−	0.766019i	$-0.722235\pi$
$599$	−2.76393	+	2.00811i	−0.112931	+	0.0820493i	0.529886	+	0.848069i	$0.322235\pi$
$600$	−5.85410	+	4.25325i	−0.238993	+	0.173638i
$601$	0.965558	+	2.97168i	0.0393859	+	0.121217i	0.968816	−	0.247780i	$-0.0797011\pi$
$601$	0.965558	+	2.97168i	0.0393859	+	0.121217i	−0.929430	+	0.368998i	$0.879701\pi$
$602$	−5.52786	+	17.0130i	−0.225299	+	0.693399i
$603$	−33.4164	−	24.2784i	−1.36082	−	0.988695i
$604$	−26.8328			−1.09181
$605$		0			0
$606$	66.8328			2.71490
$607$	4.00000	+	2.90617i	0.162355	+	0.117958i	0.665996	−	0.745955i	$-0.268007\pi$
$607$	4.00000	+	2.90617i	0.162355	+	0.117958i	−0.503641	+	0.863913i	$0.668007\pi$
$608$	−5.12461	+	15.7719i	−0.207830	+	0.639636i
$609$	−0.472136	−	1.45309i	−0.0191319	−	0.0588820i
$610$	10.0000	−	7.26543i	0.404888	−	0.294168i
$611$	7.23607	−	5.25731i	0.292740	−	0.212688i
$612$	8.56231	+	26.3521i	0.346111	+	1.06522i
$613$	−14.6180	+	44.9897i	−0.590417	+	1.81712i	−0.0140844	+	0.999901i	$0.504483\pi$
$613$	−14.6180	+	44.9897i	−0.590417	+	1.81712i	−0.576332	+	0.817215i	$0.695517\pi$
$614$	16.1803	+	11.7557i	0.652985	+	0.474422i
$615$	43.7771			1.76526
$616$		0			0
$617$	33.4164			1.34529			0.672647	−	0.739964i	$-0.265157\pi$
$617$	33.4164			1.34529			0.672647	+	0.739964i	$0.265157\pi$
$618$	−33.4164	−	24.2784i	−1.34421	−	0.976622i
$619$	−9.00000	+	27.6992i	−0.361741	+	1.11332i	0.590257	+	0.807216i	$0.299027\pi$
$619$	−9.00000	+	27.6992i	−0.361741	+	1.11332i	−0.951997	+	0.306107i	$0.900973\pi$
$620$	13.4164	+	41.2915i	0.538816	+	1.65830i
$621$	75.7771	−	55.0553i	3.04083	−	2.20929i
$622$	−39.2705	+	28.5317i	−1.57460	+	1.14402i
$623$	0.618034	+	1.90211i	0.0247610	+	0.0762065i
$624$	1.23607	−	3.80423i	0.0494823	−	0.152291i
$625$	15.3713	+	11.1679i	0.614853	+	0.446717i
$626$	6.58359			0.263133
$627$		0			0
$628$	−20.8328			−0.831320
$629$	−0.472136	−	0.343027i	−0.0188253	−	0.0136774i
$630$	10.3262	−	31.7809i	0.411407	−	1.26618i
$631$	−7.41641	−	22.8254i	−0.295243	−	0.908663i	−0.983140	−	0.182855i	$-0.941466\pi$
$631$	−7.41641	−	22.8254i	−0.295243	−	0.908663i	0.687897	−	0.725808i	$-0.258534\pi$
$632$	16.1803	−	11.7557i	0.643619	−	0.467617i
$633$	−57.3050	+	41.6345i	−2.27767	+	1.65482i
$634$	−9.67376	−	29.7728i	−0.384194	−	1.18243i
$635$	−12.9443	+	39.8384i	−0.513678	+	1.58094i
$636$	−66.5410	−	48.3449i	−2.63852	−	1.91700i
$637$	−1.23607			−0.0489748
$638$		0			0
$639$	−11.4164			−0.451626
$640$	25.3262	+	18.4006i	1.00111	+	0.727347i
$641$	−7.56231	+	23.2744i	−0.298693	+	0.919283i	0.683263	+	0.730173i	$0.260560\pi$
$641$	−7.56231	+	23.2744i	−0.298693	+	0.919283i	−0.981956	+	0.189110i	$0.939440\pi$
$642$	8.94427	+	27.5276i	0.353002	+	1.08643i
$643$	23.5623	−	17.1190i	0.929207	−	0.675108i	−0.0165918	−	0.999862i	$-0.505282\pi$
$643$	23.5623	−	17.1190i	0.929207	−	0.675108i	0.945798	+	0.324754i	$0.105282\pi$
$644$	15.7082	−	11.4127i	0.618990	−	0.449723i
$645$	−16.0000	−	49.2429i	−0.629999	−	1.93894i
$646$	2.11146	−	6.49839i	0.0830741	−	0.255676i
$647$	17.8541	+	12.9718i	0.701917	+	0.509973i	0.880556	−	0.473942i	$-0.157169\pi$
$647$	17.8541	+	12.9718i	0.701917	+	0.509973i	−0.178639	+	0.983915i	$0.557169\pi$
$648$	−54.5967			−2.14476
$649$		0			0
$650$	−2.76393			−0.108410
$651$	18.9443	+	13.7638i	0.742485	+	0.539447i
$652$	21.7082	−	66.8110i	0.850159	−	2.61652i
$653$	13.2705	+	40.8424i	0.519315	+	1.59829i	0.775291	+	0.631605i	$0.217603\pi$
$653$	13.2705	+	40.8424i	0.519315	+	1.59829i	−0.255976	+	0.966683i	$0.582397\pi$
$654$	26.1803	−	19.0211i	1.02373	−	0.743785i
$655$	−22.4721	+	16.3270i	−0.878059	+	0.637947i
$656$	2.09017	+	6.43288i	0.0816074	+	0.251162i
$657$	−12.0902	+	37.2097i	−0.471682	+	1.45169i
$658$	13.0902	+	9.51057i	0.510308	+	0.370760i
$659$	17.8885			0.696839			0.348419	−	0.937339i	$-0.386719\pi$
$659$	17.8885			0.696839			0.348419	+	0.937339i	$0.386719\pi$
$660$		0			0
$661$	12.8328			0.499139			0.249569	−	0.968357i	$-0.419711\pi$
$661$	12.8328			0.499139			0.249569	+	0.968357i	$0.419711\pi$
$662$	39.5967	+	28.7687i	1.53897	+	1.11813i
$663$	−1.52786	+	4.70228i	−0.0593373	+	0.182622i
$664$	−10.6525	−	32.7849i	−0.413396	−	1.27230i
$665$	−4.00000	+	2.90617i	−0.155113	+	0.112696i
$666$	6.38197	−	4.63677i	0.247296	−	0.179671i
$667$	0.944272	+	2.90617i	0.0365624	+	0.112527i
$668$	−12.0000	+	36.9322i	−0.464294	+	1.42895i
$669$	−31.8885	−	23.1684i	−1.23288	−	0.895741i
$670$	24.7214			0.955069
$671$		0			0
$672$	21.7082			0.837412
$673$	−4.38197	−	3.18368i	−0.168912	−	0.122722i	0.500117	−	0.865958i	$-0.333290\pi$
$673$	−4.38197	−	3.18368i	−0.168912	−	0.122722i	−0.669030	+	0.743236i	$0.733290\pi$
$674$	14.1459	−	43.5366i	0.544880	−	1.67697i
$675$	−4.47214	−	13.7638i	−0.172133	−	0.529770i
$676$	27.8435	−	20.2295i	1.07090	−	0.778056i
$677$	−3.00000	+	2.17963i	−0.115299	+	0.0837699i	−0.643941	−	0.765075i	$-0.722702\pi$
$677$	−3.00000	+	2.17963i	−0.115299	+	0.0837699i	0.528641	+	0.848845i	$0.322702\pi$
$678$	−4.47214	−	13.7638i	−0.171751	−	0.528596i
$679$	−2.90983	+	8.95554i	−0.111669	+	0.343682i
$680$	−4.47214	−	3.24920i	−0.171499	−	0.124601i
$681$	−96.7214			−3.70637
$682$		0			0
$683$	29.8885			1.14365			0.571827	−	0.820374i	$-0.306235\pi$
$683$	29.8885			1.14365			0.571827	+	0.820374i	$0.306235\pi$
$684$	44.8328	+	32.5729i	1.71423	+	1.24546i
$685$	−4.65248	+	14.3188i	−0.177762	+	0.547095i
$686$	−0.690983	−	2.12663i	−0.0263819	−	0.0811950i
$687$	−11.7082	+	8.50651i	−0.446696	+	0.324544i
$688$	6.47214	−	4.70228i	0.246748	−	0.179273i
$689$	−3.23607	−	9.95959i	−0.123284	−	0.379430i
$690$	−28.9443	+	89.0813i	−1.10189	+	3.39127i
$691$	39.2705	+	28.5317i	1.49392	+	1.08540i	0.972725	+	0.231959i	$0.0745136\pi$
$691$	39.2705	+	28.5317i	1.49392	+	1.08540i	0.521195	+	0.853438i	$0.325486\pi$
$692$	−51.7082			−1.96565
$693$		0			0
$694$	−6.83282			−0.259370
$695$	−16.9443	−	12.3107i	−0.642733	−	0.466973i
$696$	1.05573	−	3.24920i	0.0400173	−	0.123160i
$697$	−2.58359	−	7.95148i	−0.0978605	−	0.301184i
$698$	−5.00000	+	3.63271i	−0.189253	+	0.137500i
$699$	45.5967	−	33.1280i	1.72463	−	1.25302i
$700$	−0.927051	−	2.85317i	−0.0350392	−	0.107840i
$701$	−7.56231	+	23.2744i	−0.285624	+	0.879061i	0.700586	+	0.713568i	$0.252922\pi$
$701$	−7.56231	+	23.2744i	−0.285624	+	0.879061i	−0.986211	+	0.165494i	$0.947078\pi$
$702$	−32.3607	−	23.5114i	−1.22138	−	0.887381i
$703$	−1.16718			−0.0440212
$704$		0			0
$705$	−46.8328			−1.76383
$706$	−28.7426	−	20.8828i	−1.08174	−	0.785933i
$707$	−2.85410	+	8.78402i	−0.107340	+	0.330357i
$708$	9.70820	+	29.8788i	0.364857	+	1.12291i
$709$	−2.38197	+	1.73060i	−0.0894566	+	0.0649940i	−0.631615	−	0.775283i	$-0.717607\pi$
$709$	−2.38197	+	1.73060i	−0.0894566	+	0.0649940i	0.542158	+	0.840277i	$0.317607\pi$
$710$	5.52786	−	4.01623i	0.207457	−	0.150726i
$711$	20.6525	+	63.5618i	0.774528	+	2.38375i
$712$	−1.38197	+	4.25325i	−0.0517914	+	0.159397i
$713$	−37.8885	−	27.5276i	−1.41894	−	1.03092i
$714$	−8.94427			−0.334731
$715$		0			0
$716$	26.8328			1.00279
$717$	−67.7771	−	49.2429i	−2.53118	−	1.83901i
$718$	4.87539	−	15.0049i	0.181948	−	0.559978i
$719$	10.3475	+	31.8464i	0.385898	+	1.18767i	0.935827	+	0.352459i	$0.114655\pi$
$719$	10.3475	+	31.8464i	0.385898	+	1.18767i	−0.549930	+	0.835211i	$0.685345\pi$
$720$	−12.0902	+	8.78402i	−0.450574	+	0.327361i
$721$	4.61803	−	3.35520i	0.171985	−	0.124954i
$722$	8.90576	+	27.4091i	0.331438	+	1.02006i
$723$	27.1246	−	83.4810i	1.00878	−	3.10469i
$724$	−3.43769	−	2.49763i	−0.127761	−	0.0928237i
$725$	0.472136			0.0175347
$726$		0			0
$727$	−51.0132			−1.89197			−0.945987	−	0.324206i	$-0.894903\pi$
$727$	−51.0132			−1.89197			−0.945987	+	0.324206i	$0.894903\pi$
$728$	−2.23607	−	1.62460i	−0.0828742	−	0.0602116i
$729$	12.9615	−	39.8914i	0.480055	−	1.47746i
$730$	−7.23607	−	22.2703i	−0.267819	−	0.824262i
$731$	−8.00000	+	5.81234i	−0.295891	+	0.214977i
$732$	21.7082	−	15.7719i	0.802358	−	0.582947i
$733$	4.09017	+	12.5882i	0.151074	+	0.464958i	0.997742	−	0.0671638i	$-0.0213950\pi$
$733$	4.09017	+	12.5882i	0.151074	+	0.464958i	−0.846668	+	0.532121i	$0.821395\pi$
$734$	−11.8328	+	36.4177i	−0.436757	+	1.34420i
$735$	5.23607	+	3.80423i	0.193135	+	0.140321i
$736$	−43.4164			−1.60035
$737$		0			0
$738$	113.013			4.16007
$739$	−5.70820	−	4.14725i	−0.209980	−	0.152559i	0.477825	−	0.878455i	$-0.341425\pi$
$739$	−5.70820	−	4.14725i	−0.209980	−	0.152559i	−0.687804	+	0.725896i	$0.741425\pi$
$740$	−0.875388	+	2.69417i	−0.0321799	+	0.0990396i
$741$	3.05573	+	9.40456i	0.112255	+	0.345485i
$742$	15.3262	−	11.1352i	0.562644	−	0.408785i
$743$	27.4164	−	19.9192i	1.00581	−	0.730764i	0.0424843	−	0.999097i	$-0.486473\pi$
$743$	27.4164	−	19.9192i	1.00581	−	0.730764i	0.963326	+	0.268333i	$0.0864728\pi$
$744$	16.1803	+	49.7980i	0.593200	+	1.82568i
$745$	−8.65248	+	26.6296i	−0.317002	+	0.975632i
$746$	10.8541	+	7.88597i	0.397397	+	0.288726i
$747$	115.193			4.21471
$748$		0			0
$749$	−4.00000			−0.146157
$750$	70.2492	+	51.0390i	2.56514	+	1.86368i
$751$	11.8885	−	36.5892i	0.433819	−	1.33516i	−0.460473	−	0.887674i	$-0.652320\pi$
$751$	11.8885	−	36.5892i	0.433819	−	1.33516i	0.894292	−	0.447484i	$-0.147680\pi$
$752$	−2.23607	−	6.88191i	−0.0815410	−	0.250957i
$753$	−46.3607	+	33.6830i	−1.68948	+	1.22748i
$754$	1.05573	−	0.767031i	0.0384473	−	0.0279336i
$755$	5.52786	+	17.0130i	0.201180	+	0.619167i
$756$	13.4164	−	41.2915i	0.487950	−	1.50176i
$757$	16.0902	+	11.6902i	0.584807	+	0.424887i	0.840454	−	0.541883i	$-0.182288\pi$
$757$	16.0902	+	11.6902i	0.584807	+	0.424887i	−0.255647	+	0.966770i	$0.582288\pi$
$758$	56.5836			2.05521
$759$		0			0
$760$	−11.0557			−0.401033
$761$	−14.2361	−	10.3431i	−0.516057	−	0.374937i	0.299059	−	0.954234i	$-0.403327\pi$
$761$	−14.2361	−	10.3431i	−0.516057	−	0.374937i	−0.815116	+	0.579297i	$0.803327\pi$
$762$	−46.8328	+	144.137i	−1.69657	+	5.22152i
$763$	1.38197	+	4.25325i	0.0500305	+	0.153978i
$764$	50.8328	−	36.9322i	1.83907	−	1.33616i
$765$	14.9443	−	10.8576i	0.540311	−	0.392559i
$766$	−18.4164	−	56.6799i	−0.665412	−	2.04793i
$767$	−1.23607	+	3.80423i	−0.0446318	+	0.137363i
$768$	23.5623	+	17.1190i	0.850231	+	0.617729i
$769$	31.7082			1.14343			0.571714	−	0.820453i	$-0.306279\pi$
$769$	31.7082			1.14343			0.571714	+	0.820453i	$0.306279\pi$
$770$		0			0
$771$	−19.4164			−0.699265
$772$	57.9787	+	42.1240i	2.08670	+	1.51608i
$773$	1.96556	−	6.04937i	0.0706962	−	0.217581i	−0.909466	−	0.415779i	$-0.863509\pi$
$773$	1.96556	−	6.04937i	0.0706962	−	0.217581i	0.980162	+	0.198198i	$0.0635090\pi$
$774$	−41.3050	−	127.124i	−1.48468	−	4.56936i
$775$	−5.85410	+	4.25325i	−0.210286	+	0.152781i
$776$	−17.0344	+	12.3762i	−0.611501	+	0.444281i
$777$	0.472136	+	1.45309i	0.0169378	+	0.0521291i
$778$	13.7426	−	42.2955i	0.492698	−	1.51637i
$779$	−13.5279	−	9.82857i	−0.484686	−	0.352145i
$780$	24.0000			0.859338
$781$		0			0
$782$	17.8885			0.639693
$783$	5.52786	+	4.01623i	0.197550	+	0.143528i
$784$	−0.309017	+	0.951057i	−0.0110363	+	0.0339663i
$785$	4.29180	+	13.2088i	0.153181	+	0.471442i
$786$	−81.3050	+	59.0715i	−2.90005	+	2.10701i
$787$	13.4164	−	9.74759i	0.478243	−	0.347464i	−0.322402	−	0.946603i	$-0.604490\pi$
$787$	13.4164	−	9.74759i	0.478243	−	0.347464i	0.800645	+	0.599139i	$0.204490\pi$
$788$	−1.85410	−	5.70634i	−0.0660496	−	0.203280i
$789$		0			0
$790$	−32.3607	−	23.5114i	−1.15134	−	0.836498i
$791$	2.00000			0.0711118
$792$		0			0
$793$	3.41641			0.121320
$794$	−0.201626	−	0.146490i	−0.00715544	−	0.00519873i
$795$	−16.9443	+	52.1491i	−0.600951	+	1.84954i
$796$	18.7082	+	57.5779i	0.663095	+	2.04080i
$797$	−2.38197	+	1.73060i	−0.0843736	+	0.0613010i	−0.629172	−	0.777266i	$-0.716606\pi$
$797$	−2.38197	+	1.73060i	−0.0843736	+	0.0613010i	0.544799	+	0.838567i	$0.316606\pi$
$798$	−14.4721	+	10.5146i	−0.512308	+	0.372214i
$799$	2.76393	+	8.50651i	0.0977809	+	0.300939i
$800$	−2.07295	+	6.37988i	−0.0732898	+	0.225563i
$801$	−12.0902	−	8.78402i	−0.427185	−	0.310368i
$802$	−11.3050			−0.399192
$803$		0			0
$804$	53.6656			1.89264
$805$	−10.4721	−	7.60845i	−0.369094	−	0.268163i
$806$	−6.18034	+	19.0211i	−0.217693	+	0.669991i
$807$	−13.4164	−	41.2915i	−0.472280	−	1.45353i
$808$	−16.7082	+	12.1392i	−0.587793	+	0.427056i
$809$	−31.5066	+	22.8909i	−1.10771	+	0.804800i	−0.982302	−	0.187305i	$-0.940025\pi$
$809$	−31.5066	+	22.8909i	−1.10771	+	0.804800i	−0.125410	+	0.992105i	$0.540025\pi$
$810$	33.7426	+	103.849i	1.18560	+	3.64889i
$811$	5.81966	−	17.9111i	0.204356	−	0.628943i	−0.795383	−	0.606107i	$-0.792730\pi$
$811$	5.81966	−	17.9111i	0.204356	−	0.628943i	0.999739	−	0.0228361i	$-0.00726958\pi$
$812$	1.14590	+	0.832544i	0.0402131	+	0.0292166i
$813$	−4.94427			−0.173403
$814$		0			0
$815$	−46.8328			−1.64048
$816$	3.23607	+	2.35114i	0.113285	+	0.0823064i
$817$	−6.11146	+	18.8091i	−0.213813	+	0.658048i
$818$	21.5066	+	66.1904i	0.751960	+	2.31429i
$819$	7.47214	−	5.42882i	0.261098	−	0.189698i
$820$	−32.8328	+	23.8544i	−1.14657	+	0.833033i
$821$	−2.72949	−	8.40051i	−0.0952599	−	0.293180i	0.892061	−	0.451914i	$-0.149259\pi$
$821$	−2.72949	−	8.40051i	−0.0952599	−	0.293180i	−0.987321	+	0.158734i	$0.949259\pi$
$822$	−16.8328	+	51.8061i	−0.587112	+	1.80694i
$823$	40.3607	+	29.3238i	1.40688	+	1.02216i	0.993766	+	0.111484i	$0.0355605\pi$
$823$	40.3607	+	29.3238i	1.40688	+	1.02216i	0.413119	+	0.910677i	$0.364439\pi$
$824$	12.7639			0.444653
$825$		0			0
$826$	−7.23607			−0.251775
$827$	−4.00000	−	2.90617i	−0.139094	−	0.101057i	0.516063	−	0.856551i	$-0.327397\pi$
$827$	−4.00000	−	2.90617i	−0.139094	−	0.101057i	−0.655156	+	0.755493i	$0.727397\pi$
$828$	−44.8328	+	137.981i	−1.55805	+	4.79518i
$829$	−5.20163	−	16.0090i	−0.180660	−	0.556014i	0.819187	−	0.573527i	$-0.194425\pi$
$829$	−5.20163	−	16.0090i	−0.180660	−	0.556014i	−0.999847	+	0.0175128i	$0.994425\pi$
$830$	−55.7771	+	40.5244i	−1.93605	+	1.40662i
$831$	−41.5967	+	30.2218i	−1.44298	+	1.04838i
$832$	4.96556	+	15.2824i	0.172150	+	0.529822i
$833$	0.381966	−	1.17557i	0.0132343	−	0.0407311i
$834$	−61.3050	−	44.5407i	−2.12282	−	1.54232i
$835$	25.8885			0.895910
$836$		0			0
$837$	−104.721			−3.61970
$838$	−12.0344	−	8.74353i	−0.415723	−	0.302040i
$839$	−4.34752	+	13.3803i	−0.150093	+	0.461939i	−0.997631	−	0.0687961i	$-0.978084\pi$
$839$	−4.34752	+	13.3803i	−0.150093	+	0.461939i	0.847538	+	0.530735i	$0.178084\pi$
$840$	4.47214	+	13.7638i	0.154303	+	0.474897i
$841$	23.2812	−	16.9147i	0.802798	−	0.583267i
$842$	−40.4508	+	29.3893i	−1.39403	+	1.01282i
$843$	−12.4721	−	38.3853i	−0.429563	−	1.32206i
$844$	20.2918	−	62.4517i	0.698472	−	2.14968i
$845$	−18.5623	−	13.4863i	−0.638563	−	0.463943i
$846$	−120.902			−4.15669
$847$		0			0
$848$	−8.47214			−0.290934
$849$	15.4164	+	11.2007i	0.529090	+	0.384406i
$850$	0.854102	−	2.62866i	0.0292955	−	0.0901621i
$851$	−0.944272	−	2.90617i	−0.0323692	−	0.0996222i
$852$	12.0000	−	8.71851i	0.411113	−	0.298691i
$853$	−0.527864	+	0.383516i	−0.0180737	+	0.0131313i	−0.596785	−	0.802401i	$-0.703556\pi$
$853$	−0.527864	+	0.383516i	−0.0180737	+	0.0131313i	0.578712	+	0.815532i	$0.303556\pi$
$854$	1.90983	+	5.87785i	0.0653530	+	0.201136i
$855$	11.4164	−	35.1361i	0.390433	−	1.20163i
$856$	−7.23607	−	5.25731i	−0.247324	−	0.179691i
$857$	10.7639			0.367689			0.183844	−	0.982955i	$-0.441146\pi$
$857$	10.7639			0.367689			0.183844	+	0.982955i	$0.441146\pi$
$858$		0			0
$859$	40.5410			1.38324			0.691621	−	0.722261i	$-0.256897\pi$
$859$	40.5410			1.38324			0.691621	+	0.722261i	$0.256897\pi$
$860$	38.8328	+	28.2137i	1.32419	+	0.962079i
$861$	−6.76393	+	20.8172i	−0.230514	+	0.709450i
$862$	−8.29180	−	25.5195i	−0.282420	−	0.869198i
$863$	16.9443	−	12.3107i	0.576790	−	0.419062i	−0.260776	−	0.965399i	$-0.583978\pi$
$863$	16.9443	−	12.3107i	0.576790	−	0.419062i	0.837565	+	0.546337i	$0.183978\pi$
$864$	−78.5410	+	57.0634i	−2.67202	+	1.94134i
$865$	10.6525	+	32.7849i	0.362195	+	1.11472i
$866$	−0.326238	+	1.00406i	−0.0110860	+	0.0341192i
$867$	40.5066	+	29.4298i	1.37568	+	0.999487i
$868$	−21.7082			−0.736824
$869$		0			0
$870$	−6.83282			−0.231654
$871$	5.52786	+	4.01623i	0.187305	+	0.136085i
$872$	−3.09017	+	9.51057i	−0.104646	+	0.322068i
$873$	−21.7426	−	66.9170i	−0.735877	−	2.26480i
$874$	28.9443	−	21.0292i	0.979055	−	0.711325i
$875$	−9.70820	+	7.05342i	−0.328197	+	0.238449i
$876$	−15.7082	−	48.3449i	−0.530731	−	1.63342i
$877$	12.7984	−	39.3893i	0.432170	−	1.33008i	−0.463788	−	0.885946i	$-0.653510\pi$
$877$	12.7984	−	39.3893i	0.432170	−	1.33008i	0.895959	−	0.444138i	$-0.146490\pi$
$878$	2.76393	+	2.00811i	0.0932782	+	0.0677706i
$879$	48.9443			1.65085
$880$		0			0
$881$	29.4164			0.991064			0.495532	−	0.868590i	$-0.334973\pi$
$881$	29.4164			0.991064			0.495532	+	0.868590i	$0.334973\pi$
$882$	13.5172	+	9.82084i	0.455149	+	0.330685i
$883$	2.76393	−	8.50651i	0.0930137	−	0.286267i	−0.893717	−	0.448631i	$-0.851912\pi$
$883$	2.76393	−	8.50651i	0.0930137	−	0.286267i	0.986731	+	0.162364i	$0.0519119\pi$
$884$	−1.41641	−	4.35926i	−0.0476390	−	0.146618i
$885$	16.9443	−	12.3107i	0.569575	−	0.413821i
$886$	−12.7639	+	9.27354i	−0.428813	+	0.311551i
$887$	12.4721	+	38.3853i	0.418773	+	1.28885i	0.908832	+	0.417162i	$0.136975\pi$
$887$	12.4721	+	38.3853i	0.418773	+	1.28885i	−0.490059	+	0.871689i	$0.663025\pi$
$888$	−1.05573	+	3.24920i	−0.0354279	+	0.109036i
$889$	−16.9443	−	12.3107i	−0.568293	−	0.412889i
$890$	8.94427			0.299813
$891$		0			0
$892$	36.5410			1.22348
$893$	14.4721	+	10.5146i	0.484292	+	0.351858i
$894$	−31.3050	+	96.3467i	−1.04699	+	3.22232i
$895$	−5.52786	−	17.0130i	−0.184776	−	0.568682i
$896$	−12.6631	+	9.20029i	−0.423045	+	0.307360i
$897$	−20.9443	+	15.2169i	−0.699309	+	0.508078i
$898$	13.4934	+	41.5285i	0.450281	+	1.38582i
$899$	1.05573	−	3.24920i	0.0352105	−	0.108367i
$900$	18.1353	+	13.1760i	0.604508	+	0.439201i
$901$	10.4721			0.348877
$902$		0			0
$903$	25.8885			0.861517
$904$	3.61803	+	2.62866i	0.120334	+	0.0874278i
$905$	−0.875388	+	2.69417i	−0.0290989	+	0.0895572i
$906$	20.0000	+	61.5537i	0.664455	+	2.04498i
$907$	−10.9443	+	7.95148i	−0.363399	+	0.264025i	−0.754468	−	0.656337i	$-0.772105\pi$
$907$	−10.9443	+	7.95148i	−0.363399	+	0.264025i	0.391070	+	0.920361i	$0.372105\pi$
$908$	72.5410	−	52.7041i	2.40736	−	1.74905i
$909$	−21.3262	−	65.6354i	−0.707347	−	2.17699i
$910$	−1.70820	+	5.25731i	−0.0566264	+	0.174278i
$911$	−27.1246	−	19.7072i	−0.898678	−	0.652928i	0.0394477	−	0.999222i	$-0.487440\pi$
$911$	−27.1246	−	19.7072i	−0.898678	−	0.652928i	−0.938126	+	0.346293i	$0.887440\pi$
$912$	8.00000			0.264906
$913$		0			0
$914$	−55.5279			−1.83670
$915$	−14.4721	−	10.5146i	−0.478434	−	0.347603i
$916$	4.14590	−	12.7598i	0.136984	−	0.421594i
$917$	−4.29180	−	13.2088i	−0.141728	−	0.436193i
$918$	32.3607	−	23.5114i	1.06806	−	0.775992i
$919$	−4.94427	+	3.59222i	−0.163096	+	0.118497i	−0.666340	−	0.745648i	$-0.732140\pi$
$919$	−4.94427	+	3.59222i	−0.163096	+	0.118497i	0.503243	+	0.864145i	$0.332140\pi$
$920$	−8.94427	−	27.5276i	−0.294884	−	0.907559i
$921$	8.94427	−	27.5276i	0.294724	−	0.907067i
$922$	18.4164	+	13.3803i	0.606512	+	0.440657i
$923$	1.88854			0.0621622
$924$		0			0
$925$	−0.472136			−0.0155237
$926$	−26.1803	−	19.0211i	−0.860339	−	0.625073i
$927$	−13.1803	+	40.5649i	−0.432899	+	1.33233i
$928$	−0.978714	−	3.01217i	−0.0321279	−	0.0988794i
$929$	−22.8541	+	16.6045i	−0.749819	+	0.544775i	−0.895771	−	0.444516i	$-0.853376\pi$
$929$	−22.8541	+	16.6045i	−0.749819	+	0.544775i	0.145952	+	0.989292i	$0.453376\pi$
$930$	84.7214	−	61.5537i	2.77812	−	2.01842i
$931$	−0.763932	−	2.35114i	−0.0250369	−	0.0770555i
$932$	−16.1459	+	49.6920i	−0.528876	+	1.62771i
$933$	56.8328	+	41.2915i	1.86062	+	1.35182i
$934$	76.1803			2.49270
$935$		0			0
$936$	20.6525			0.675047
$937$	−16.7082	−	12.1392i	−0.545833	−	0.396571i	0.280414	−	0.959879i	$-0.409528\pi$
$937$	−16.7082	−	12.1392i	−0.545833	−	0.396571i	−0.826247	+	0.563308i	$0.809528\pi$
$938$	−3.81966	+	11.7557i	−0.124716	+	0.383837i
$939$	−2.94427	−	9.06154i	−0.0960827	−	0.295712i
$940$	35.1246	−	25.5195i	1.14564	−	0.832355i
$941$	33.6525	−	24.4500i	1.09704	−	0.797046i	0.116465	−	0.993195i	$-0.462844\pi$
$941$	33.6525	−	24.4500i	1.09704	−	0.797046i	0.980574	+	0.196149i	$0.0628436\pi$
$942$	15.5279	+	47.7899i	0.505925	+	1.55708i
$943$	13.5279	−	41.6345i	0.440528	−	1.35581i
$944$	2.61803	+	1.90211i	0.0852097	+	0.0619085i
$945$	−28.9443			−0.941557
$946$		0			0
$947$	−58.8328			−1.91181			−0.955905	−	0.293677i	$-0.905121\pi$
$947$	−58.8328			−1.91181			−0.955905	+	0.293677i	$0.905121\pi$
$948$	−70.2492	−	51.0390i	−2.28159	−	1.65767i
$949$	2.00000	−	6.15537i	0.0649227	−	0.199812i
$950$	−1.70820	−	5.25731i	−0.0554215	−	0.170570i
$951$	−36.6525	+	26.6296i	−1.18854	+	0.863523i
$952$	2.23607	−	1.62460i	0.0724714	−	0.0526535i
$953$	1.56231	+	4.80828i	0.0506081	+	0.155756i	0.973167	−	0.230101i	$-0.0739058\pi$
$953$	1.56231	+	4.80828i	0.0506081	+	0.155756i	−0.922559	+	0.385857i	$0.873906\pi$
$954$	−43.7426	+	134.626i	−1.41622	+	4.35868i
$955$	−33.8885	−	24.6215i	−1.09661	−	0.796732i
$956$	77.6656			2.51189
$957$		0			0
$958$	−50.2492			−1.62348
$959$	−6.09017	−	4.42477i	−0.196662	−	0.142883i
$960$	26.0000	−	80.0198i	0.839146	−	2.58263i
$961$	6.60081	+	20.3152i	0.212929	+	0.655329i
$962$	−1.05573	+	0.767031i	−0.0340380	+	0.0247301i
$963$	24.1803	−	17.5680i	0.779201	−	0.566122i
$964$	25.1459	+	77.3911i	0.809895	+	2.49260i
$965$	14.7639	−	45.4387i	0.475268	−	1.46272i
$966$	−37.8885	−	27.5276i	−1.21904	−	0.885687i
$967$	21.8885			0.703888			0.351944	−	0.936021i	$-0.385521\pi$
$967$	21.8885			0.703888			0.351944	+	0.936021i	$0.385521\pi$
$968$		0			0
$969$	−9.88854			−0.317666
$970$	34.0689	+	24.7525i	1.09389	+	0.794755i
$971$	−9.00000	+	27.6992i	−0.288824	+	0.888908i	0.696403	+	0.717651i	$0.254783\pi$
$971$	−9.00000	+	27.6992i	−0.288824	+	0.888908i	−0.985226	+	0.171257i	$0.945217\pi$
$972$	33.0000	+	101.564i	1.05848	+	3.25765i
$973$	8.47214	−	6.15537i	0.271604	−	0.197332i
$974$	15.1246	−	10.9887i	0.484624	−	0.352100i
$975$	1.23607	+	3.80423i	0.0395859	+	0.121833i
$976$	0.854102	−	2.62866i	0.0273391	−	0.0841412i
$977$	−4.09017	−	2.97168i	−0.130856	−	0.0950725i	0.520432	−	0.853903i	$-0.325771\pi$
$977$	−4.09017	−	2.97168i	−0.130856	−	0.0950725i	−0.651288	+	0.758831i	$0.725771\pi$
$978$	−169.443			−5.41818
$979$		0			0
$980$	−6.00000			−0.191663
$981$	−27.0344	−	19.6417i	−0.863143	−	0.627110i
$982$		0			0
$983$	13.6525	+	42.0180i	0.435446	+	1.34017i	0.892629	+	0.450793i	$0.148859\pi$
$983$	13.6525	+	42.0180i	0.435446	+	1.34017i	−0.457182	+	0.889373i	$0.651141\pi$
$984$	−39.5967	+	28.7687i	−1.26230	+	0.917113i
$985$	−3.23607	+	2.35114i	−0.103110	+	0.0749136i
$986$	0.403252	+	1.24108i	0.0128422	+	0.0395241i
$987$	7.23607	−	22.2703i	0.230327	−	0.708872i
$988$	−7.41641	−	5.38834i	−0.235947	−	0.171426i
$989$	−51.7771			−1.64642
$990$		0			0
$991$	−26.2492			−0.833834			−0.416917	−	0.908945i	$-0.636889\pi$
$991$	−26.2492			−0.833834			−0.416917	+	0.908945i	$0.636889\pi$
$992$	39.2705	+	28.5317i	1.24684	+	0.905882i
$993$	21.8885	−	67.3660i	0.694612	−	2.13780i
$994$	1.05573	+	3.24920i	0.0334857	+	0.103058i
$995$	32.6525	−	23.7234i	1.03515	−	0.752083i
$996$	−121.082	+	87.9713i	−3.83663	+	2.78748i
$997$	10.0902	+	31.0543i	0.319559	+	0.983501i	0.973837	+	0.227247i	$0.0729725\pi$
$997$	10.0902	+	31.0543i	0.319559	+	0.983501i	−0.654278	+	0.756254i	$0.727027\pi$
$998$	−7.23607	+	22.2703i	−0.229054	+	0.704955i
$999$	−5.52786	−	4.01623i	−0.174894	−	0.127068i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.f.n.323.1		4
11.2	odd	10		847.2.f.m.148.1		4
11.3	even	5	inner	847.2.f.n.729.1		4
11.4	even	5		847.2.f.a.372.1		4
11.5	even	5		77.2.a.d.1.1	✓	2
11.6	odd	10		847.2.a.f.1.2		2
11.7	odd	10		847.2.f.m.372.1		4
11.8	odd	10		847.2.f.b.729.1		4
11.9	even	5		847.2.f.a.148.1		4
11.10	odd	2		847.2.f.b.323.1		4
33.5	odd	10		693.2.a.h.1.2		2
33.17	even	10		7623.2.a.bl.1.1		2
44.27	odd	10		1232.2.a.m.1.1		2
55.27	odd	20		1925.2.b.h.1849.1		4
55.38	odd	20		1925.2.b.h.1849.4		4
55.49	even	10		1925.2.a.r.1.2		2
77.5	odd	30		539.2.e.j.67.2		4
77.6	even	10		5929.2.a.m.1.2		2
77.16	even	15		539.2.e.i.67.2		4
77.27	odd	10		539.2.a.f.1.1		2
77.38	odd	30		539.2.e.j.177.2		4
77.60	even	15		539.2.e.i.177.2		4
88.5	even	10		4928.2.a.bm.1.1		2
88.27	odd	10		4928.2.a.bv.1.2		2
231.104	even	10		4851.2.a.y.1.2		2
308.27	even	10		8624.2.a.ce.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.a.d.1.1	✓	2	11.5	even	5
539.2.a.f.1.1		2	77.27	odd	10
539.2.e.i.67.2		4	77.16	even	15
539.2.e.i.177.2		4	77.60	even	15
539.2.e.j.67.2		4	77.5	odd	30
539.2.e.j.177.2		4	77.38	odd	30
693.2.a.h.1.2		2	33.5	odd	10
847.2.a.f.1.2		2	11.6	odd	10
847.2.f.a.148.1		4	11.9	even	5
847.2.f.a.372.1		4	11.4	even	5
847.2.f.b.323.1		4	11.10	odd	2
847.2.f.b.729.1		4	11.8	odd	10
847.2.f.m.148.1		4	11.2	odd	10
847.2.f.m.372.1		4	11.7	odd	10
847.2.f.n.323.1		4	1.1	even	1	trivial
847.2.f.n.729.1		4	11.3	even	5	inner
1232.2.a.m.1.1		2	44.27	odd	10
1925.2.a.r.1.2		2	55.49	even	10
1925.2.b.h.1849.1		4	55.27	odd	20
1925.2.b.h.1849.4		4	55.38	odd	20
4851.2.a.y.1.2		2	231.104	even	10
4928.2.a.bm.1.1		2	88.5	even	10
4928.2.a.bv.1.2		2	88.27	odd	10
5929.2.a.m.1.2		2	77.6	even	10
7623.2.a.bl.1.1		2	33.17	even	10
8624.2.a.ce.1.2		2	308.27	even	10

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:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	847.f (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.80902 + 1.31433i) q^{2} +(1.00000 - 3.07768i) q^{3} +(0.927051 + 2.85317i) q^{4} +(1.61803 - 1.17557i) q^{5} +(5.85410 - 4.25325i) q^{6} +(0.309017 + 0.951057i) q^{7} +(-0.690983 + 2.12663i) q^{8} +(-6.04508 - 4.39201i) q^{9} +O(q^{10})\)	\(q+(1.80902 + 1.31433i) q^{2} +(1.00000 - 3.07768i) q^{3} +(0.927051 + 2.85317i) q^{4} +(1.61803 - 1.17557i) q^{5} +(5.85410 - 4.25325i) q^{6} +(0.309017 + 0.951057i) q^{7} +(-0.690983 + 2.12663i) q^{8} +(-6.04508 - 4.39201i) q^{9} +4.47214 q^{10} +9.70820 q^{12} +(1.00000 + 0.726543i) q^{13} +(-0.690983 + 2.12663i) q^{14} +(-2.00000 - 6.15537i) q^{15} +(0.809017 - 0.587785i) q^{16} +(-1.00000 + 0.726543i) q^{17} +(-5.16312 - 15.8904i) q^{18} +(-0.763932 + 2.35114i) q^{19} +(4.85410 + 3.52671i) q^{20} +3.23607 q^{21} -6.47214 q^{23} +(5.85410 + 4.25325i) q^{24} +(-0.309017 + 0.951057i) q^{25} +(0.854102 + 2.62866i) q^{26} +(-11.7082 + 8.50651i) q^{27} +(-2.42705 + 1.76336i) q^{28} +(-0.145898 - 0.449028i) q^{29} +(4.47214 - 13.7638i) q^{30} +(5.85410 + 4.25325i) q^{31} +6.70820 q^{32} -2.76393 q^{34} +(1.61803 + 1.17557i) q^{35} +(6.92705 - 21.3193i) q^{36} +(0.145898 + 0.449028i) q^{37} +(-4.47214 + 3.24920i) q^{38} +(3.23607 - 2.35114i) q^{39} +(1.38197 + 4.25325i) q^{40} +(-2.09017 + 6.43288i) q^{41} +(5.85410 + 4.25325i) q^{42} +8.00000 q^{43} -14.9443 q^{45} +(-11.7082 - 8.50651i) q^{46} +(2.23607 - 6.88191i) q^{47} +(-1.00000 - 3.07768i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(-1.80902 + 1.31433i) q^{50} +(1.23607 + 3.80423i) q^{51} +(-1.14590 + 3.52671i) q^{52} +(-6.85410 - 4.97980i) q^{53} -32.3607 q^{54} -2.23607 q^{56} +(6.47214 + 4.70228i) q^{57} +(0.326238 - 1.00406i) q^{58} +(1.00000 + 3.07768i) q^{59} +(15.7082 - 11.4127i) q^{60} +(2.23607 - 1.62460i) q^{61} +(5.00000 + 15.3884i) q^{62} +(2.30902 - 7.10642i) q^{63} +(10.5172 + 7.64121i) q^{64} +2.47214 q^{65} +5.52786 q^{67} +(-3.00000 - 2.17963i) q^{68} +(-6.47214 + 19.9192i) q^{69} +(1.38197 + 4.25325i) q^{70} +(1.23607 - 0.898056i) q^{71} +(13.5172 - 9.82084i) q^{72} +(-1.61803 - 4.97980i) q^{73} +(-0.326238 + 1.00406i) q^{74} +(2.61803 + 1.90211i) q^{75} -7.41641 q^{76} +8.94427 q^{78} +(-7.23607 - 5.25731i) q^{79} +(0.618034 - 1.90211i) q^{80} +(7.54508 + 23.2214i) q^{81} +(-12.2361 + 8.89002i) q^{82} +(-12.4721 + 9.06154i) q^{83} +(3.00000 + 9.23305i) q^{84} +(-0.763932 + 2.35114i) q^{85} +(14.4721 + 10.5146i) q^{86} -1.52786 q^{87} +2.00000 q^{89} +(-27.0344 - 19.6417i) q^{90} +(-0.381966 + 1.17557i) q^{91} +(-6.00000 - 18.4661i) q^{92} +(18.9443 - 13.7638i) q^{93} +(13.0902 - 9.51057i) q^{94} +(1.52786 + 4.70228i) q^{95} +(6.70820 - 20.6457i) q^{96} +(7.61803 + 5.53483i) q^{97} -2.23607 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 5 q^{2} + 4 q^{3} - 3 q^{4} + 2 q^{5} + 10 q^{6} - q^{7} - 5 q^{8} - 13 q^{9}+O(q^{10}) \) 4 * q + 5 * q^2 + 4 * q^3 - 3 * q^4 + 2 * q^5 + 10 * q^6 - q^7 - 5 * q^8 - 13 * q^9	\( 4 q + 5 q^{2} + 4 q^{3} - 3 q^{4} + 2 q^{5} + 10 q^{6} - q^{7} - 5 q^{8} - 13 q^{9} + 12 q^{12} + 4 q^{13} - 5 q^{14} - 8 q^{15} + q^{16} - 4 q^{17} - 5 q^{18} - 12 q^{19} + 6 q^{20} + 4 q^{21} - 8 q^{23} + 10 q^{24} + q^{25} - 10 q^{26} - 20 q^{27} - 3 q^{28} - 14 q^{29} + 10 q^{31} - 20 q^{34} + 2 q^{35} + 21 q^{36} + 14 q^{37} + 4 q^{39} + 10 q^{40} + 14 q^{41} + 10 q^{42} + 32 q^{43} - 24 q^{45} - 20 q^{46} - 4 q^{48} - q^{49} - 5 q^{50} - 4 q^{51} - 18 q^{52} - 14 q^{53} - 40 q^{54} + 8 q^{57} - 30 q^{58} + 4 q^{59} + 36 q^{60} + 20 q^{62} + 7 q^{63} + 13 q^{64} - 8 q^{65} + 40 q^{67} - 12 q^{68} - 8 q^{69} + 10 q^{70} - 4 q^{71} + 25 q^{72} - 2 q^{73} + 30 q^{74} + 6 q^{75} + 24 q^{76} - 20 q^{79} - 2 q^{80} + 19 q^{81} - 40 q^{82} - 32 q^{83} + 12 q^{84} - 12 q^{85} + 40 q^{86} - 24 q^{87} + 8 q^{89} - 50 q^{90} - 6 q^{91} - 24 q^{92} + 40 q^{93} + 30 q^{94} + 24 q^{95} + 26 q^{97}+O(q^{100}) \) 4 * q + 5 * q^2 + 4 * q^3 - 3 * q^4 + 2 * q^5 + 10 * q^6 - q^7 - 5 * q^8 - 13 * q^9 + 12 * q^12 + 4 * q^13 - 5 * q^14 - 8 * q^15 + q^16 - 4 * q^17 - 5 * q^18 - 12 * q^19 + 6 * q^20 + 4 * q^21 - 8 * q^23 + 10 * q^24 + q^25 - 10 * q^26 - 20 * q^27 - 3 * q^28 - 14 * q^29 + 10 * q^31 - 20 * q^34 + 2 * q^35 + 21 * q^36 + 14 * q^37 + 4 * q^39 + 10 * q^40 + 14 * q^41 + 10 * q^42 + 32 * q^43 - 24 * q^45 - 20 * q^46 - 4 * q^48 - q^49 - 5 * q^50 - 4 * q^51 - 18 * q^52 - 14 * q^53 - 40 * q^54 + 8 * q^57 - 30 * q^58 + 4 * q^59 + 36 * q^60 + 20 * q^62 + 7 * q^63 + 13 * q^64 - 8 * q^65 + 40 * q^67 - 12 * q^68 - 8 * q^69 + 10 * q^70 - 4 * q^71 + 25 * q^72 - 2 * q^73 + 30 * q^74 + 6 * q^75 + 24 * q^76 - 20 * q^79 - 2 * q^80 + 19 * q^81 - 40 * q^82 - 32 * q^83 + 12 * q^84 - 12 * q^85 + 40 * q^86 - 24 * q^87 + 8 * q^89 - 50 * q^90 - 6 * q^91 - 24 * q^92 + 40 * q^93 + 30 * q^94 + 24 * q^95 + 26 * q^97

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