LMFDB - Embedded newform 847.2.f.y.729.3

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:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			729.3
Character	$\chi$	$=$	847.729
Dual form			847.2.f.y.323.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.03276 + 0.750346i) q^{2} +(-0.796038 - 2.44995i) q^{3} +(-0.114455 + 0.352256i) q^{4} +(3.31004 + 2.40489i) q^{5} +(2.66043 + 1.93292i) q^{6} +(0.309017 - 0.951057i) q^{7} +(-0.935069 - 2.87785i) q^{8} +(-2.94155 + 2.13716i) q^{9} +O(q^{10})$	\(q+(-1.03276 + 0.750346i) q^{2} +(-0.796038 - 2.44995i) q^{3} +(-0.114455 + 0.352256i) q^{4} +(3.31004 + 2.40489i) q^{5} +(2.66043 + 1.93292i) q^{6} +(0.309017 - 0.951057i) q^{7} +(-0.935069 - 2.87785i) q^{8} +(-2.94155 + 2.13716i) q^{9} -5.22298 q^{10} +0.954122 q^{12} +(3.55232 - 2.58091i) q^{13} +(0.394480 + 1.21408i) q^{14} +(3.25694 - 10.0238i) q^{15} +(2.52579 + 1.83509i) q^{16} +(-3.39096 - 2.46368i) q^{17} +(1.43431 - 4.41435i) q^{18} +(-0.385900 - 1.18768i) q^{19} +(-1.22599 + 0.890732i) q^{20} -2.57603 q^{21} +4.97180 q^{23} +(-6.30624 + 4.58175i) q^{24} +(3.62782 + 11.1653i) q^{25} +(-1.73213 + 5.33093i) q^{26} +(1.32536 + 0.962928i) q^{27} +(0.299647 + 0.217706i) q^{28} +(-0.598078 + 1.84069i) q^{29} +(4.15769 + 12.7961i) q^{30} +(1.26432 - 0.918580i) q^{31} +2.06640 q^{32} +5.35067 q^{34} +(3.31004 - 2.40489i) q^{35} +(-0.416153 - 1.28079i) q^{36} +(-0.221348 + 0.681238i) q^{37} +(1.28971 + 0.937030i) q^{38} +(-9.15089 - 6.64851i) q^{39} +(3.82578 - 11.7745i) q^{40} +(1.48522 + 4.57102i) q^{41} +(2.66043 - 1.93292i) q^{42} +1.35362 q^{43} -14.8763 q^{45} +(-5.13469 + 3.73057i) q^{46} +(-3.23424 - 9.95395i) q^{47} +(2.48527 - 7.64887i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(-12.1245 - 8.80895i) q^{50} +(-3.33656 + 10.2689i) q^{51} +(0.502561 + 1.54672i) q^{52} +(3.21325 - 2.33457i) q^{53} -2.09131 q^{54} -3.02595 q^{56} +(-2.60256 + 1.89087i) q^{57} +(-0.763485 - 2.34976i) q^{58} +(4.25172 - 13.0854i) q^{59} +(3.15818 + 2.29456i) q^{60} +(9.48745 + 6.89304i) q^{61} +(-0.616486 + 1.89735i) q^{62} +(1.12357 + 3.45799i) q^{63} +(-7.18568 + 5.22070i) q^{64} +17.9651 q^{65} +7.59274 q^{67} +(1.25596 - 0.912508i) q^{68} +(-3.95774 - 12.1807i) q^{69} +(-1.61399 + 4.96735i) q^{70} +(-0.176622 - 0.128323i) q^{71} +(8.90096 + 6.46693i) q^{72} +(3.39036 - 10.4344i) q^{73} +(-0.282564 - 0.869644i) q^{74} +(24.4665 - 17.7760i) q^{75} +0.462535 q^{76} +14.4394 q^{78} +(3.69112 - 2.68176i) q^{79} +(3.94728 + 12.1485i) q^{80} +(-2.06662 + 6.36039i) q^{81} +(-4.96372 - 3.60635i) q^{82} +(-1.98579 - 1.44276i) q^{83} +(0.294840 - 0.907424i) q^{84} +(-5.29936 - 16.3098i) q^{85} +(-1.39796 + 1.01568i) q^{86} +4.98571 q^{87} +4.20456 q^{89} +(15.3636 - 11.1623i) q^{90} +(-1.35686 - 4.17600i) q^{91} +(-0.569047 + 1.75135i) q^{92} +(-3.25692 - 2.36629i) q^{93} +(10.8091 + 7.85327i) q^{94} +(1.57889 - 4.85931i) q^{95} +(-1.64493 - 5.06259i) q^{96} +(8.83842 - 6.42149i) q^{97} +1.27656 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{2} + 2 q^{3} - 4 q^{4} + 4 q^{5} + 6 q^{6} - 6 q^{7} - 12 q^{8} - 8 q^{9}+O(q^{10}) $ 24 * q - 4 * q^2 + 2 * q^3 - 4 * q^4 + 4 * q^5 + 6 * q^6 - 6 * q^7 - 12 * q^8 - 8 * q^9	\( 24 q - 4 q^{2} + 2 q^{3} - 4 q^{4} + 4 q^{5} + 6 q^{6} - 6 q^{7} - 12 q^{8} - 8 q^{9} - 32 q^{10} - 56 q^{12} - 4 q^{13} - 4 q^{14} - 2 q^{15} - 8 q^{16} - 22 q^{17} - 24 q^{18} - 6 q^{19} - 2 q^{20} - 8 q^{21} + 8 q^{23} + 20 q^{24} - 4 q^{25} - 6 q^{26} + 2 q^{27} - 4 q^{28} - 12 q^{29} - 20 q^{30} + 2 q^{31} + 32 q^{32} + 96 q^{34} + 4 q^{35} - 18 q^{36} - 14 q^{37} + 22 q^{38} - 20 q^{39} - 18 q^{40} - 26 q^{41} + 6 q^{42} - 16 q^{43} - 144 q^{45} - 12 q^{46} + 16 q^{47} + 24 q^{48} - 6 q^{49} + 4 q^{50} + 4 q^{51} - 12 q^{52} - 4 q^{53} - 128 q^{54} + 48 q^{56} - 20 q^{57} + 2 q^{58} + 4 q^{59} - 24 q^{60} + 8 q^{61} - 20 q^{62} - 8 q^{63} - 26 q^{64} + 96 q^{65} + 24 q^{67} - 12 q^{68} + 14 q^{69} + 8 q^{70} - 22 q^{71} - 16 q^{72} - 14 q^{73} - 44 q^{74} + 20 q^{75} - 120 q^{76} + 128 q^{78} + 28 q^{79} + 4 q^{80} + 6 q^{81} + 4 q^{82} - 22 q^{83} + 14 q^{84} + 24 q^{85} + 30 q^{86} + 88 q^{87} + 22 q^{90} - 4 q^{91} - 10 q^{92} + 50 q^{93} + 38 q^{94} + 24 q^{95} + 62 q^{96} + 4 q^{97} + 16 q^{98}+O(q^{100}) \) 24 * q - 4 * q^2 + 2 * q^3 - 4 * q^4 + 4 * q^5 + 6 * q^6 - 6 * q^7 - 12 * q^8 - 8 * q^9 - 32 * q^10 - 56 * q^12 - 4 * q^13 - 4 * q^14 - 2 * q^15 - 8 * q^16 - 22 * q^17 - 24 * q^18 - 6 * q^19 - 2 * q^20 - 8 * q^21 + 8 * q^23 + 20 * q^24 - 4 * q^25 - 6 * q^26 + 2 * q^27 - 4 * q^28 - 12 * q^29 - 20 * q^30 + 2 * q^31 + 32 * q^32 + 96 * q^34 + 4 * q^35 - 18 * q^36 - 14 * q^37 + 22 * q^38 - 20 * q^39 - 18 * q^40 - 26 * q^41 + 6 * q^42 - 16 * q^43 - 144 * q^45 - 12 * q^46 + 16 * q^47 + 24 * q^48 - 6 * q^49 + 4 * q^50 + 4 * q^51 - 12 * q^52 - 4 * q^53 - 128 * q^54 + 48 * q^56 - 20 * q^57 + 2 * q^58 + 4 * q^59 - 24 * q^60 + 8 * q^61 - 20 * q^62 - 8 * q^63 - 26 * q^64 + 96 * q^65 + 24 * q^67 - 12 * q^68 + 14 * q^69 + 8 * q^70 - 22 * q^71 - 16 * q^72 - 14 * q^73 - 44 * q^74 + 20 * q^75 - 120 * q^76 + 128 * q^78 + 28 * q^79 + 4 * q^80 + 6 * q^81 + 4 * q^82 - 22 * q^83 + 14 * q^84 + 24 * q^85 + 30 * q^86 + 88 * q^87 + 22 * q^90 - 4 * q^91 - 10 * q^92 + 50 * q^93 + 38 * q^94 + 24 * q^95 + 62 * q^96 + 4 * q^97 + 16 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$122$	$365$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$	−1.03276	+	0.750346i	−0.730273	+	0.530574i	−0.889650	−	0.456643i	$-0.849052\pi$
$2$	−1.03276	+	0.750346i	−0.730273	+	0.530574i	0.159377	+	0.987218i	$0.449052\pi$
$3$	−0.796038	−	2.44995i	−0.459593	−	1.41448i	−0.865657	−	0.500637i	$-0.833099\pi$
$3$	−0.796038	−	2.44995i	−0.459593	−	1.41448i	0.406064	−	0.913844i	$-0.366901\pi$
$4$	−0.114455	+	0.352256i	−0.0572275	+	0.176128i
$5$	3.31004	+	2.40489i	1.48030	+	1.07550i	0.977461	+	0.211115i	$0.0677096\pi$
$5$	3.31004	+	2.40489i	1.48030	+	1.07550i	0.502835	+	0.864382i	$0.332290\pi$
$6$	2.66043	+	1.93292i	1.08612	+	0.789109i
$7$	0.309017	−	0.951057i	0.116797	−	0.359466i
$7$	0.309017	−	0.951057i	0.116797	−	0.359466i
$8$	−0.935069	−	2.87785i	−0.330597	−	1.01747i
$9$	−2.94155	+	2.13716i	−0.980515	+	0.712386i
$10$	−5.22298			−1.65165
$11$		0			0
$11$		0			0
$12$	0.954122			0.275431
$13$	3.55232	−	2.58091i	0.985236	−	0.715816i	0.0263633	−	0.999652i	$-0.491607\pi$
$13$	3.55232	−	2.58091i	0.985236	−	0.715816i	0.958873	+	0.283837i	$0.0916073\pi$
$14$	0.394480	+	1.21408i	0.105429	+	0.324478i
$15$	3.25694	−	10.0238i	0.840938	−	2.58814i
$16$	2.52579	+	1.83509i	0.631447	+	0.458773i
$17$	−3.39096	−	2.46368i	−0.822429	−	0.597530i	0.0949779	−	0.995479i	$-0.469722\pi$
$17$	−3.39096	−	2.46368i	−0.822429	−	0.597530i	−0.917407	+	0.397949i	$0.869722\pi$
$18$	1.43431	−	4.41435i	0.338070	−	1.04047i
$19$	−0.385900	−	1.18768i	−0.0885315	−	0.272472i	0.896982	−	0.442066i	$-0.145754\pi$
$19$	−0.385900	−	1.18768i	−0.0885315	−	0.272472i	−0.985514	+	0.169594i	$0.945754\pi$
$20$	−1.22599	+	0.890732i	−0.274139	+	0.199174i
$21$	−2.57603			−0.562137
$22$		0			0
$23$	4.97180			1.03669			0.518346	−	0.855171i	$-0.326548\pi$
$23$	4.97180			1.03669			0.518346	+	0.855171i	$0.326548\pi$
$24$	−6.30624	+	4.58175i	−1.28726	+	0.935246i
$25$	3.62782	+	11.1653i	0.725563	+	2.23305i
$26$	−1.73213	+	5.33093i	−0.339698	+	1.04548i
$27$	1.32536	+	0.962928i	0.255065	+	0.185316i
$28$	0.299647	+	0.217706i	0.0566280	+	0.0411426i
$29$	−0.598078	+	1.84069i	−0.111060	+	0.341808i	−0.991105	−	0.133083i	$-0.957512\pi$
$29$	−0.598078	+	1.84069i	−0.111060	+	0.341808i	0.880045	+	0.474891i	$0.157512\pi$
$30$	4.15769	+	12.7961i	0.759088	+	2.33623i
$31$	1.26432	−	0.918580i	0.227078	−	0.164982i	−0.468429	−	0.883501i	$-0.655180\pi$
$31$	1.26432	−	0.918580i	0.227078	−	0.164982i	0.695507	+	0.718519i	$0.255180\pi$
$32$	2.06640			0.365292
$33$		0			0
$34$	5.35067			0.917632
$35$	3.31004	−	2.40489i	0.559499	−	0.406500i
$36$	−0.416153	−	1.28079i	−0.0693588	−	0.213464i
$37$	−0.221348	+	0.681238i	−0.0363893	+	0.111995i	−0.967601	−	0.252483i	$-0.918753\pi$
$37$	−0.221348	+	0.681238i	−0.0363893	+	0.111995i	0.931212	+	0.364478i	$0.118753\pi$
$38$	1.28971	+	0.937030i	0.209219	+	0.152006i
$39$	−9.15089	−	6.64851i	−1.46532	−	1.06461i
$40$	3.82578	−	11.7745i	0.604908	−	1.86172i
$41$	1.48522	+	4.57102i	0.231952	+	0.713874i	0.997511	+	0.0705088i	$0.0224623\pi$
$41$	1.48522	+	4.57102i	0.231952	+	0.713874i	−0.765559	+	0.643365i	$0.777538\pi$
$42$	2.66043	−	1.93292i	0.410513	−	0.298255i
$43$	1.35362			0.206424			0.103212	−	0.994659i	$-0.467088\pi$
$43$	1.35362			0.206424			0.103212	+	0.994659i	$0.467088\pi$
$44$		0			0
$45$	−14.8763			−2.21762
$46$	−5.13469	+	3.73057i	−0.757068	+	0.550042i
$47$	−3.23424	−	9.95395i	−0.471762	−	1.45193i	−0.850276	−	0.526338i	$-0.823565\pi$
$47$	−3.23424	−	9.95395i	−0.471762	−	1.45193i	0.378514	−	0.925596i	$-0.376435\pi$
$48$	2.48527	−	7.64887i	0.358718	−	1.10402i
$49$	−0.809017	−	0.587785i	−0.115574	−	0.0839693i
$50$	−12.1245	−	8.80895i	−1.71466	−	1.24577i
$51$	−3.33656	+	10.2689i	−0.467212	+	1.43793i
$52$	0.502561	+	1.54672i	0.0696927	+	0.214492i
$53$	3.21325	−	2.33457i	0.441374	−	0.320677i	−0.344806	−	0.938674i	$-0.612055\pi$
$53$	3.21325	−	2.33457i	0.441374	−	0.320677i	0.786181	+	0.617997i	$0.212055\pi$
$54$	−2.09131			−0.284591
$55$		0			0
$56$	−3.02595			−0.404359
$57$	−2.60256	+	1.89087i	−0.344718	+	0.250452i
$58$	−0.763485	−	2.34976i	−0.100250	−	0.308539i
$59$	4.25172	−	13.0854i	0.553526	−	1.70358i	−0.146277	−	0.989244i	$-0.546729\pi$
$59$	4.25172	−	13.0854i	0.553526	−	1.70358i	0.699804	−	0.714335i	$-0.253271\pi$
$60$	3.15818	+	2.29456i	0.407720	+	0.296226i
$61$	9.48745	+	6.89304i	1.21474	+	0.882563i	0.995653	−	0.0931414i	$-0.0296909\pi$
$61$	9.48745	+	6.89304i	1.21474	+	0.882563i	0.219091	+	0.975704i	$0.429691\pi$
$62$	−0.616486	+	1.89735i	−0.0782938	+	0.240964i
$63$	1.12357	+	3.45799i	0.141557	+	0.435666i
$64$	−7.18568	+	5.22070i	−0.898210	+	0.652588i
$65$	17.9651			2.22830
$66$		0			0
$67$	7.59274			0.927600			0.463800	−	0.885940i	$-0.346486\pi$
$67$	7.59274			0.927600			0.463800	+	0.885940i	$0.346486\pi$
$68$	1.25596	−	0.912508i	0.152307	−	0.110658i
$69$	−3.95774	−	12.1807i	−0.476456	−	1.46638i
$70$	−1.61399	+	4.96735i	−0.192909	+	0.593712i
$71$	−0.176622	−	0.128323i	−0.0209611	−	0.0152292i	0.577255	−	0.816564i	$-0.304124\pi$
$71$	−0.176622	−	0.128323i	−0.0209611	−	0.0152292i	−0.598216	+	0.801335i	$0.704124\pi$
$72$	8.90096	+	6.46693i	1.04899	+	0.762135i
$73$	3.39036	−	10.4344i	0.396811	−	1.22126i	−0.530730	−	0.847541i	$-0.678082\pi$
$73$	3.39036	−	10.4344i	0.396811	−	1.22126i	0.927542	−	0.373719i	$-0.121918\pi$
$74$	−0.282564	−	0.869644i	−0.0328475	−	0.101094i
$75$	24.4665	−	17.7760i	2.82515	−	2.05259i
$76$	0.462535			0.0530564
$77$		0			0
$78$	14.4394			1.63494
$79$	3.69112	−	2.68176i	0.415284	−	0.301721i	−0.360454	−	0.932777i	$-0.617378\pi$
$79$	3.69112	−	2.68176i	0.415284	−	0.301721i	0.775737	+	0.631056i	$0.217378\pi$
$80$	3.94728	+	12.1485i	0.441319	+	1.35824i
$81$	−2.06662	+	6.36039i	−0.229624	+	0.706710i
$82$	−4.96372	−	3.60635i	−0.548151	−	0.398255i
$83$	−1.98579	−	1.44276i	−0.217969	−	0.158364i	0.473443	−	0.880825i	$-0.343011\pi$
$83$	−1.98579	−	1.44276i	−0.217969	−	0.158364i	−0.691412	+	0.722461i	$0.743011\pi$
$84$	0.294840	−	0.907424i	0.0321697	−	0.0990081i
$85$	−5.29936	−	16.3098i	−0.574797	−	1.76904i
$86$	−1.39796	+	1.01568i	−0.150746	+	0.109524i
$87$	4.98571			0.534524
$88$		0			0
$89$	4.20456			0.445683			0.222841	−	0.974855i	$-0.428467\pi$
$89$	4.20456			0.445683			0.222841	+	0.974855i	$0.428467\pi$
$90$	15.3636	−	11.1623i	1.61947	−	1.17661i
$91$	−1.35686	−	4.17600i	−0.142238	−	0.437764i
$92$	−0.569047	+	1.75135i	−0.0593273	+	0.182591i
$93$	−3.25692	−	2.36629i	−0.337727	−	0.245373i
$94$	10.8091	+	7.85327i	1.11487	+	0.810003i
$95$	1.57889	−	4.85931i	0.161990	−	0.498555i
$96$	−1.64493	−	5.06259i	−0.167885	−	0.516698i
$97$	8.83842	−	6.42149i	0.897405	−	0.652003i	−0.0403929	−	0.999184i	$-0.512861\pi$
$97$	8.83842	−	6.42149i	0.897405	−	0.652003i	0.937798	+	0.347181i	$0.112861\pi$
$98$	1.27656			0.128952
$99$		0			0
$100$	−4.34826			−0.434826
$101$	−5.95905	+	4.32950i	−0.592948	+	0.430802i	−0.843369	−	0.537335i	$-0.819431\pi$
$101$	−5.95905	+	4.32950i	−0.592948	+	0.430802i	0.250421	+	0.968137i	$0.419431\pi$
$102$	−4.25934	−	13.1089i	−0.421737	−	1.29797i
$103$	−0.0475535	+	0.146354i	−0.00468558	+	0.0144207i	−0.953372	−	0.301798i	$-0.902413\pi$
$103$	−0.0475535	+	0.146354i	−0.00468558	+	0.0144207i	0.948686	+	0.316218i	$0.102413\pi$
$104$	−10.7491	−	7.80970i	−1.05404	−	0.765804i
$105$	−8.52678	−	6.19507i	−0.832129	−	0.604577i
$106$	−1.56680	+	4.82210i	−0.152181	+	0.468364i
$107$	2.45550	+	7.55725i	0.237382	+	0.730587i	0.996796	+	0.0799799i	$0.0254856\pi$
$107$	2.45550	+	7.55725i	0.237382	+	0.730587i	−0.759414	+	0.650607i	$0.774514\pi$
$108$	−0.490891	+	0.356653i	−0.0472360	+	0.0343190i
$109$	−4.91440			−0.470714			−0.235357	−	0.971909i	$-0.575626\pi$
$109$	−4.91440			−0.470714			−0.235357	+	0.971909i	$0.575626\pi$
$110$		0			0
$111$	1.84520			0.175139
$112$	2.52579	−	1.83509i	0.238665	−	0.173400i
$113$	0.940056	+	2.89319i	0.0884330	+	0.272169i	0.985487	−	0.169753i	$-0.0542969\pi$
$113$	0.940056	+	2.89319i	0.0884330	+	0.272169i	−0.897054	+	0.441922i	$0.854297\pi$
$114$	1.26902	−	3.90565i	0.118855	−	0.365797i
$115$	16.4569	+	11.9566i	1.53461	+	1.11496i
$116$	−0.579943	−	0.421353i	−0.0538464	−	0.0391217i
$117$	−4.93349	+	15.1837i	−0.456102	+	1.40374i
$118$	5.42759	+	16.7044i	0.499650	+	1.53776i
$119$	−3.39096	+	2.46368i	−0.310849	+	0.225845i
$120$	−31.8925			−2.91138
$121$		0			0
$122$	−14.9704			−1.35536
$123$	10.0165	−	7.27742i	0.903158	−	0.656183i
$124$	0.178868	+	0.550500i	0.0160628	+	0.0494363i
$125$	−8.52137	+	26.2261i	−0.762174	+	2.34573i
$126$	−3.75507	−	2.72822i	−0.334528	−	0.243049i
$127$	8.73362	+	6.34535i	0.774984	+	0.563059i	0.903469	−	0.428653i	$-0.141012\pi$
$127$	8.73362	+	6.34535i	0.774984	+	0.563059i	−0.128486	+	0.991711i	$0.541012\pi$
$128$	2.22666	−	6.85296i	0.196811	−	0.605721i
$129$	−1.07753	−	3.31630i	−0.0948712	−	0.291984i
$130$	−18.5537	+	13.4800i	−1.62727	+	1.18228i
$131$	−8.70429			−0.760497			−0.380249	−	0.924884i	$-0.624162\pi$
$131$	−8.70429			−0.760497			−0.380249	+	0.924884i	$0.624162\pi$
$132$		0			0
$133$	−1.24880			−0.108285
$134$	−7.84149	+	5.69718i	−0.677401	+	0.492161i
$135$	2.07125	+	6.37466i	0.178265	+	0.548644i
$136$	−3.91931	+	12.0624i	−0.336078	+	1.03434i
$137$	−9.70634	−	7.05207i	−0.829269	−	0.602499i	0.0900835	−	0.995934i	$-0.471287\pi$
$137$	−9.70634	−	7.05207i	−0.829269	−	0.602499i	−0.919352	+	0.393435i	$0.871287\pi$
$138$	13.2271	+	9.61007i	1.12597	+	0.818064i
$139$	2.53075	−	7.78884i	0.214655	−	0.660641i	−0.784523	−	0.620100i	$-0.787092\pi$
$139$	2.53075	−	7.78884i	0.214655	−	0.660641i	0.999178	−	0.0405407i	$-0.0129080\pi$
$140$	0.468285	+	1.44123i	0.0395773	+	0.121807i
$141$	−21.8122	+	15.8475i	−1.83691	+	1.33460i
$142$	0.278695			0.0233875
$143$		0			0
$144$	−11.3516			−0.945968
$145$	−6.40632	+	4.65447i	−0.532016	+	0.386532i
$146$	4.32801	+	13.3202i	0.358189	+	1.10239i
$147$	−0.796038	+	2.44995i	−0.0656561	+	0.202069i
$148$	−0.214636	−	0.155942i	−0.0176430	−	0.0128184i
$149$	−9.77425	−	7.10141i	−0.800738	−	0.581770i	0.110393	−	0.993888i	$-0.464789\pi$
$149$	−9.77425	−	7.10141i	−0.800738	−	0.581770i	−0.911130	+	0.412118i	$0.864789\pi$
$150$	−11.9300	+	36.7167i	−0.974078	+	2.99790i
$151$	−2.14720	−	6.60842i	−0.174737	−	0.537785i	0.824884	−	0.565302i	$-0.191240\pi$
$151$	−2.14720	−	6.60842i	−0.174737	−	0.537785i	−0.999621	+	0.0275162i	$0.991240\pi$
$152$	−3.05711	+	2.22112i	−0.247965	+	0.180157i
$153$	15.2399			1.23208
$154$		0			0
$155$	6.39402			0.513580
$156$	3.38935	−	2.46250i	0.271365	−	0.197158i
$157$	3.24253	+	9.97947i	0.258782	+	0.796449i	0.993061	+	0.117601i	$0.0375203\pi$
$157$	3.24253	+	9.97947i	0.258782	+	0.796449i	−0.734279	+	0.678848i	$0.762480\pi$
$158$	−1.79981	+	5.53923i	−0.143185	+	0.440678i
$159$	−8.27745	−	6.01392i	−0.656445	−	0.476935i
$160$	6.83988	+	4.96946i	0.540740	+	0.392870i
$161$	1.53637	−	4.72846i	0.121083	−	0.372655i
$162$	−2.63817	−	8.11945i	−0.207274	−	0.637924i
$163$	6.32444	−	4.59497i	0.495368	−	0.359906i	−0.311877	−	0.950123i	$-0.600958\pi$
$163$	6.32444	−	4.59497i	0.495368	−	0.359906i	0.807245	+	0.590217i	$0.200958\pi$
$164$	−1.78016			−0.139007
$165$		0			0
$166$	3.13342			0.243201
$167$	−17.2728	+	12.5494i	−1.33661	+	0.971101i	−0.337045	+	0.941489i	$0.609427\pi$
$167$	−17.2728	+	12.5494i	−1.33661	+	0.971101i	−0.999561	+	0.0296124i	$0.990573\pi$
$168$	2.40877	+	7.41343i	0.185841	+	0.571959i
$169$	1.94065	−	5.97270i	0.149281	−	0.459438i
$170$	17.7109	+	12.8678i	1.35837	+	0.986912i
$171$	3.67340	+	2.66888i	0.280912	+	0.204094i
$172$	−0.154928	+	0.476820i	−0.0118132	+	0.0363572i
$173$	6.00679	+	18.4870i	0.456688	+	1.40554i	0.869142	+	0.494562i	$0.164671\pi$
$173$	6.00679	+	18.4870i	0.456688	+	1.40554i	−0.412455	+	0.910978i	$0.635329\pi$
$174$	−5.14905	+	3.74100i	−0.390349	+	0.283605i
$175$	11.7399			0.887450
$176$		0			0
$177$	−35.4432			−2.66408
$178$	−4.34231	+	3.15488i	−0.325470	+	0.236468i
$179$	5.56120	+	17.1156i	0.415663	+	1.27928i	0.911656	+	0.410954i	$0.134804\pi$
$179$	5.56120	+	17.1156i	0.415663	+	1.27928i	−0.495993	+	0.868327i	$0.665196\pi$
$180$	1.70266	−	5.24026i	0.126909	−	0.390586i
$181$	−12.2627	−	8.90938i	−0.911480	−	0.662229i	0.0299086	−	0.999553i	$-0.490478\pi$
$181$	−12.2627	−	8.90938i	−0.911480	−	0.662229i	−0.941389	+	0.337324i	$0.890478\pi$
$182$	4.53476	+	3.29470i	0.336139	+	0.244219i
$183$	9.33525	−	28.7309i	0.690081	−	2.12385i
$184$	−4.64898	−	14.3081i	−0.342727	−	1.05481i
$185$	−2.37097	+	1.72261i	−0.174317	+	0.126649i
$186$	5.13916			0.376822
$187$		0			0
$188$	3.87652			0.282724
$189$	1.32536	−	0.962928i	0.0964055	−	0.0700427i
$190$	2.01555	+	6.20322i	0.146223	+	0.450029i
$191$	−7.34144	+	22.5946i	−0.531208	+	1.63489i	0.220495	+	0.975388i	$0.429233\pi$
$191$	−7.34144	+	22.5946i	−0.531208	+	1.63489i	−0.751703	+	0.659502i	$0.770767\pi$
$192$	18.5106	+	13.4487i	1.33588	+	0.970577i
$193$	−11.3733	−	8.26319i	−0.818668	−	0.594797i	0.0976625	−	0.995220i	$-0.468863\pi$
$193$	−11.3733	−	8.26319i	−0.818668	−	0.594797i	−0.916331	+	0.400422i	$0.868863\pi$
$194$	−4.30965	+	13.2637i	−0.309415	+	0.952281i
$195$	−14.3009	−	44.0137i	−1.02411	−	3.15189i
$196$	0.299647	−	0.217706i	0.0214034	−	0.0155505i
$197$	18.0665			1.28718			0.643591	−	0.765369i	$-0.277444\pi$
$197$	18.0665			1.28718			0.643591	+	0.765369i	$0.277444\pi$
$198$		0			0
$199$	1.54374			0.109433			0.0547163	−	0.998502i	$-0.482575\pi$
$199$	1.54374			0.109433			0.0547163	+	0.998502i	$0.482575\pi$
$200$	28.7397	−	20.8806i	2.03220	−	1.47648i
$201$	−6.04411	−	18.6019i	−0.426319	−	1.31207i
$202$	2.90566	−	8.94270i	0.204441	−	0.629206i
$203$	1.56579	+	1.13761i	0.109897	+	0.0798447i
$204$	−3.23539	−	2.35065i	−0.226523	−	0.164578i
$205$	−6.07667	+	18.7021i	−0.424413	+	1.30621i
$206$	−0.0607050	−	0.186831i	−0.00422952	−	0.0130171i
$207$	−14.6248	+	10.6255i	−1.01649	+	0.738525i
$208$	13.7086			0.950522
$209$		0			0
$210$	13.4546			0.928454
$211$	17.8660	−	12.9804i	1.22995	−	0.893608i	0.233060	−	0.972462i	$-0.425126\pi$
$211$	17.8660	−	12.9804i	1.22995	−	0.893608i	0.996886	+	0.0788540i	$0.0251261\pi$
$212$	0.454592	+	1.39909i	0.0312215	+	0.0960900i
$213$	−0.173788	+	0.534865i	−0.0119078	+	0.0366483i
$214$	−8.20650	−	5.96237i	−0.560985	−	0.407579i
$215$	4.48053	+	3.25529i	0.305569	+	0.222009i
$216$	1.53186	−	4.71458i	0.104230	−	0.320786i
$217$	−0.482926	−	1.48629i	−0.0327832	−	0.100896i
$218$	5.07540	−	3.68750i	0.343750	−	0.249749i
$219$	−28.2628			−1.90982
$220$		0			0
$221$	−18.4043			−1.23801
$222$	−1.90566	+	1.38454i	−0.127899	+	0.0929242i
$223$	−2.64955	−	8.15449i	−0.177427	−	0.546065i	0.822309	−	0.569042i	$-0.192686\pi$
$223$	−2.64955	−	8.15449i	−0.177427	−	0.546065i	−0.999736	+	0.0229766i	$0.992686\pi$
$224$	0.638553	−	1.96526i	0.0426651	−	0.131310i
$225$	−34.5333	−	25.0899i	−2.30222	−	1.67266i
$226$	−3.14175	−	2.28261i	−0.208986	−	0.151837i
$227$	−8.21085	+	25.2704i	−0.544974	+	1.67726i	0.176079	+	0.984376i	$0.443659\pi$
$227$	−8.21085	+	25.2704i	−0.544974	+	1.67726i	−0.721053	+	0.692880i	$0.756341\pi$
$228$	−0.368196	−	1.13319i	−0.0243844	−	0.0750473i
$229$	−9.23194	+	6.70740i	−0.610064	+	0.443237i	−0.849437	−	0.527690i	$-0.823058\pi$
$229$	−9.23194	+	6.70740i	−0.610064	+	0.443237i	0.239373	+	0.970928i	$0.423058\pi$
$230$	−25.9676			−1.71225
$231$		0			0
$232$	5.85648			0.384497
$233$	−21.5304	+	15.6427i	−1.41050	+	1.02479i	−0.417252	+	0.908791i	$0.637007\pi$
$233$	−21.5304	+	15.6427i	−1.41050	+	1.02479i	−0.993249	+	0.115999i	$0.962993\pi$
$234$	−6.29792	−	19.3830i	−0.411708	−	1.26711i
$235$	13.2327	−	40.7260i	0.863204	−	2.65667i
$236$	4.12280	+	2.99539i	0.268371	+	0.194983i
$237$	−9.50845	−	6.90830i	−0.617640	−	0.448742i
$238$	1.65345	−	5.08879i	0.107177	−	0.329857i
$239$	−2.32158	−	7.14510i	−0.150171	−	0.462178i	0.847469	−	0.530845i	$-0.178125\pi$
$239$	−2.32158	−	7.14510i	−0.150171	−	0.462178i	−0.997640	+	0.0686671i	$0.978125\pi$
$240$	26.6210	−	19.3413i	1.71838	−	1.24848i
$241$	27.4388			1.76749			0.883744	−	0.467971i	$-0.155015\pi$
$241$	27.4388			1.76749			0.883744	+	0.467971i	$0.155015\pi$
$242$		0			0
$243$	22.1425			1.42044
$244$	−3.51400	+	2.55307i	−0.224961	+	0.163444i
$245$	−1.26432	−	3.89119i	−0.0807747	−	0.248599i
$246$	−4.88409	+	15.0317i	−0.311398	+	0.958385i
$247$	−4.43613	−	3.22304i	−0.282264	−	0.205077i
$248$	−3.82576	−	2.77957i	−0.242936	−	0.176503i
$249$	−1.95394	+	6.01360i	−0.123826	+	0.381096i
$250$	−10.8781	−	33.4793i	−0.687990	−	2.11741i
$251$	−1.55747	+	1.13157i	−0.0983065	+	0.0714239i	−0.635853	−	0.771810i	$-0.719351\pi$
$251$	−1.55747	+	1.13157i	−0.0983065	+	0.0714239i	0.537546	+	0.843234i	$0.319351\pi$
$252$	−1.34670			−0.0848340
$253$		0			0
$254$	−13.7810			−0.864694
$255$	−35.7397	+	25.9664i	−2.23811	+	1.62608i
$256$	−2.64690	−	8.14631i	−0.165431	−	0.509144i
$257$	3.13975	−	9.66315i	0.195852	−	0.602771i	−0.804113	−	0.594476i	$-0.797360\pi$
$257$	3.13975	−	9.66315i	0.195852	−	0.602771i	0.999966	−	0.00829511i	$-0.00264044\pi$
$258$	3.60120	+	2.61643i	0.224201	+	0.162892i
$259$	0.579496	+	0.421028i	0.0360081	+	0.0261614i
$260$	−2.05620	+	6.32833i	−0.127520	+	0.392466i
$261$	−2.17458	−	6.69267i	−0.134603	−	0.414266i
$262$	8.98946	−	6.53122i	0.555371	−	0.403500i
$263$	−4.38774			−0.270560			−0.135280	−	0.990807i	$-0.543193\pi$
$263$	−4.38774			−0.270560			−0.135280	+	0.990807i	$0.543193\pi$
$264$		0			0
$265$	16.2504			0.998253
$266$	1.28971	−	0.937030i	0.0790773	−	0.0574530i
$267$	−3.34699	−	10.3010i	−0.204833	−	0.630410i
$268$	−0.869027	+	2.67459i	−0.0530842	+	0.163377i
$269$	−0.505942	−	0.367588i	−0.0308478	−	0.0224123i	0.572255	−	0.820076i	$-0.306069\pi$
$269$	−0.505942	−	0.367588i	−0.0308478	−	0.0224123i	−0.603102	+	0.797664i	$0.706069\pi$
$270$	−6.92231	−	5.02936i	−0.421279	−	0.306077i
$271$	−3.68889	+	11.3532i	−0.224084	+	0.689659i	0.774299	+	0.632819i	$0.218102\pi$
$271$	−3.68889	+	11.3532i	−0.224084	+	0.689659i	−0.998383	+	0.0568398i	$0.981898\pi$
$272$	−4.04378	−	12.4455i	−0.245190	−	0.754617i
$273$	−9.15089	+	6.64851i	−0.553837	+	0.402386i
$274$	15.3158			0.925263
$275$		0			0
$276$	4.74371			0.285538
$277$	−23.1032	+	16.7854i	−1.38814	+	1.00854i	−0.392069	+	0.919936i	$0.628240\pi$
$277$	−23.1032	+	16.7854i	−1.38814	+	1.00854i	−0.996067	+	0.0886037i	$0.971760\pi$
$278$	3.23066	+	9.94295i	0.193762	+	0.596339i
$279$	−1.75590	+	5.40409i	−0.105123	+	0.323534i
$280$	−10.0160	−	7.27706i	−0.598571	−	0.434888i
$281$	−11.8910	−	8.63932i	−0.709357	−	0.515378i	0.173609	−	0.984815i	$-0.444457\pi$
$281$	−11.8910	−	8.63932i	−0.709357	−	0.515378i	−0.882966	+	0.469436i	$0.844457\pi$
$282$	10.6357	−	32.7333i	0.633346	−	1.94924i
$283$	6.96513	+	21.4365i	0.414034	+	1.27426i	0.913112	+	0.407708i	$0.133672\pi$
$283$	6.96513	+	21.4365i	0.414034	+	1.27426i	−0.499079	+	0.866557i	$0.666328\pi$
$284$	0.0654178	−	0.0475288i	0.00388183	−	0.00282032i
$285$	−13.1619			−0.779646
$286$		0			0
$287$	4.80626			0.283704
$288$	−6.07841	+	4.41623i	−0.358174	+	0.260229i
$289$	0.175630	+	0.540533i	0.0103312	+	0.0317960i
$290$	3.12375	−	9.61391i	0.183433	−	0.564548i
$291$	−22.7681	−	16.5420i	−1.33469	−	0.969707i
$292$	3.28756	+	2.38855i	0.192390	+	0.139779i
$293$	5.20015	−	16.0044i	0.303796	−	0.934988i	−0.676328	−	0.736601i	$-0.736430\pi$
$293$	5.20015	−	16.0044i	0.303796	−	0.934988i	0.980124	−	0.198387i	$-0.0635704\pi$
$294$	−1.01619	−	3.12752i	−0.0592656	−	0.182401i
$295$	45.5424	−	33.0885i	2.65158	−	1.92648i
$296$	2.16747			0.125982
$297$		0			0
$298$	15.4230			0.893429
$299$	17.6614	−	12.8318i	1.02139	−	0.742081i
$300$	3.46138	+	10.6530i	0.199843	+	0.615053i
$301$	0.418290	−	1.28737i	0.0241099	−	0.0742025i
$302$	7.17615	+	5.21378i	0.412941	+	0.300019i
$303$	15.3507	+	11.1530i	0.881876	+	0.640720i
$304$	1.20480	−	3.70799i	0.0690999	−	0.212668i
$305$	14.8269	+	45.6325i	0.848986	+	2.61291i
$306$	−15.7392	+	11.4352i	−0.899752	+	0.653708i
$307$	0.238354			0.0136036			0.00680179	−	0.999977i	$-0.497835\pi$
$307$	0.238354			0.0136036			0.00680179	+	0.999977i	$0.497835\pi$
$308$		0			0
$309$	0.396416			0.0225513
$310$	−6.60350	+	4.79773i	−0.375054	+	0.272493i
$311$	−0.202877	−	0.624391i	−0.0115041	−	0.0354059i	0.945140	−	0.326666i	$-0.105925\pi$
$311$	−0.202877	−	0.624391i	−0.0115041	−	0.0354059i	−0.956644	+	0.291260i	$0.905925\pi$
$312$	−10.5767	+	32.5517i	−0.598787	+	1.84288i
$313$	6.02930	+	4.38054i	0.340796	+	0.247603i	0.744998	−	0.667067i	$-0.232451\pi$
$313$	6.02930	+	4.38054i	0.340796	+	0.247603i	−0.404202	+	0.914670i	$0.632451\pi$
$314$	−10.8368	−	7.87340i	−0.611557	−	0.444322i
$315$	−4.59702	+	14.1482i	−0.259013	+	0.797159i
$316$	0.522198	+	1.60716i	0.0293759	+	0.0904099i
$317$	−14.1102	+	10.2517i	−0.792509	+	0.575791i	−0.908707	−	0.417435i	$-0.862929\pi$
$317$	−14.1102	+	10.2517i	−0.792509	+	0.575791i	0.116198	+	0.993226i	$0.462929\pi$
$318$	13.0612			0.732433
$319$		0			0
$320$	−36.3401			−2.03147
$321$	16.5602	−	12.0317i	0.924303	−	0.671545i
$322$	1.96128	+	6.03619i	0.109298	+	0.336384i
$323$	−1.61748	+	4.97811i	−0.0899993	+	0.276989i
$324$	−2.00395	−	1.45596i	−0.111331	−	0.0808865i
$325$	41.7037	+	30.2995i	2.31331	+	1.68072i
$326$	−3.08382	+	9.49103i	−0.170797	+	0.525659i
$327$	3.91205	+	12.0400i	0.216337	+	0.665816i
$328$	11.7659	−	8.54845i	0.649665	−	0.472009i
$329$	−10.4662			−0.577021
$330$		0			0
$331$	−28.6146			−1.57280			−0.786399	−	0.617719i	$-0.788057\pi$
$331$	−28.6146			−1.57280			−0.786399	+	0.617719i	$0.788057\pi$
$332$	0.735506	−	0.534377i	0.0403662	−	0.0293277i
$333$	−0.804809	−	2.47695i	−0.0441033	−	0.135736i
$334$	8.42227	−	25.9211i	0.460846	−	1.41834i
$335$	25.1323	+	18.2597i	1.37312	+	0.997632i
$336$	−6.50652	−	4.72726i	−0.354960	−	0.257893i
$337$	0.534762	−	1.64583i	0.0291304	−	0.0896541i	−0.935434	−	0.353501i	$-0.884991\pi$
$337$	0.534762	−	1.64583i	0.0291304	−	0.0896541i	0.964565	+	0.263847i	$0.0849912\pi$
$338$	2.47736	+	7.62453i	0.134751	+	0.414720i
$339$	6.33987	−	4.60619i	0.344335	−	0.250174i
$340$	6.35176			0.344472
$341$		0			0
$342$	−5.79633			−0.313430
$343$	−0.809017	+	0.587785i	−0.0436828	+	0.0317374i
$344$	−1.26572	−	3.89550i	−0.0682433	−	0.210031i
$345$	16.1929	−	49.8365i	0.871794	−	2.68311i
$346$	−20.0752	−	14.5855i	−1.07925	−	0.784121i
$347$	−2.20869	−	1.60471i	−0.118569	−	0.0861453i	0.526921	−	0.849915i	$-0.323347\pi$
$347$	−2.20869	−	1.60471i	−0.118569	−	0.0861453i	−0.645489	+	0.763769i	$0.723347\pi$
$348$	−0.570639	+	1.75625i	−0.0305895	+	0.0941447i
$349$	9.55056	+	29.3936i	0.511230	+	1.57340i	0.790039	+	0.613057i	$0.210060\pi$
$349$	9.55056	+	29.3936i	0.511230	+	1.57340i	−0.278809	+	0.960347i	$0.589940\pi$
$350$	−12.1245	+	8.80895i	−0.648081	+	0.470858i
$351$	7.19332			0.383951
$352$		0			0
$353$	−23.9543			−1.27496			−0.637480	−	0.770467i	$-0.720023\pi$
$353$	−23.9543			−1.27496			−0.637480	+	0.770467i	$0.720023\pi$
$354$	36.6044	−	26.5947i	1.94550	−	1.41349i
$355$	−0.276022	−	0.849510i	−0.0146498	−	0.0450873i
$356$	−0.481233	+	1.48108i	−0.0255053	+	0.0784973i
$357$	8.73524	+	6.34652i	0.462318	+	0.335894i
$358$	−18.5860	−	13.5035i	−0.982301	−	0.713684i
$359$	−0.468502	+	1.44190i	−0.0247266	+	0.0761007i	−0.962658	−	0.270719i	$-0.912739\pi$
$359$	−0.468502	+	1.44190i	−0.0247266	+	0.0761007i	0.937932	+	0.346820i	$0.112739\pi$
$360$	13.9103	+	42.8116i	0.733139	+	2.25637i
$361$	14.1097	−	10.2513i	0.742614	−	0.539541i
$362$	19.3496			1.01699
$363$		0			0
$364$	1.62632			0.0852425
$365$	36.3159	−	26.3850i	1.90086	−	1.38106i
$366$	11.9170	+	36.6769i	0.622914	+	1.91713i
$367$	2.69527	−	8.29518i	0.140692	−	0.433005i	−0.855740	−	0.517406i	$-0.826898\pi$
$367$	2.69527	−	8.29518i	0.140692	−	0.433005i	0.996432	+	0.0844010i	$0.0268977\pi$
$368$	12.5577	+	9.12372i	0.654617	+	0.475607i
$369$	−14.1378	−	10.2717i	−0.735986	−	0.534725i
$370$	1.15609	−	3.55809i	0.0601025	−	0.184977i
$371$	−1.22735	−	3.77741i	−0.0637210	−	0.196113i
$372$	1.20631	−	0.876437i	0.0625444	−	0.0454412i
$373$	−36.8111			−1.90601			−0.953004	−	0.302957i	$-0.902026\pi$
$373$	−36.8111			−1.90601			−0.953004	+	0.302957i	$0.902026\pi$
$374$		0			0
$375$	71.0360			3.66828
$376$	−25.6217	+	18.6153i	−1.32134	+	0.960009i
$377$	2.62610	+	8.08232i	0.135251	+	0.416261i
$378$	−0.646249	+	1.98895i	−0.0332395	+	0.102301i
$379$	−2.10213	−	1.52729i	−0.107979	−	0.0784516i	0.532485	−	0.846439i	$-0.321258\pi$
$379$	−2.10213	−	1.52729i	−0.107979	−	0.0784516i	−0.640465	+	0.767988i	$0.721258\pi$
$380$	1.53101	+	1.11234i	0.0785392	+	0.0570621i
$381$	8.59351	−	26.4481i	0.440259	−	1.35498i
$382$	−9.37182	−	28.8435i	−0.479504	−	1.47576i
$383$	−15.5649	+	11.3085i	−0.795327	+	0.577839i	−0.909539	−	0.415618i	$-0.863565\pi$
$383$	−15.5649	+	11.3085i	−0.795327	+	0.577839i	0.114213	+	0.993456i	$0.463565\pi$
$384$	−18.5619			−0.947235
$385$		0			0
$386$	17.9462			0.913435
$387$	−3.98172	+	2.89289i	−0.202402	+	0.147054i
$388$	1.25041	+	3.84836i	0.0634798	+	0.195371i
$389$	−8.75540	+	26.9464i	−0.443917	+	1.36623i	0.439751	+	0.898120i	$0.355067\pi$
$389$	−8.75540	+	26.9464i	−0.443917	+	1.36623i	−0.883668	+	0.468115i	$0.844933\pi$
$390$	47.7950	+	34.7251i	2.42019	+	1.75837i
$391$	−16.8592	−	12.2489i	−0.852606	−	0.619455i
$392$	−0.935069	+	2.87785i	−0.0472281	+	0.145353i
$393$	6.92895	+	21.3251i	0.349519	+	1.07571i
$394$	−18.6584	+	13.5561i	−0.939995	+	0.682946i
$395$	18.6671			0.939243
$396$		0			0
$397$	−10.3666			−0.520287			−0.260143	−	0.965570i	$-0.583770\pi$
$397$	−10.3666			−0.520287			−0.260143	+	0.965570i	$0.583770\pi$
$398$	−1.59431	+	1.15834i	−0.0799157	+	0.0580621i
$399$	0.994091	+	3.05950i	0.0497668	+	0.153167i
$400$	−11.3262	+	34.8585i	−0.566311	+	1.74293i
$401$	10.3455	+	7.51648i	0.516632	+	0.375355i	0.815334	−	0.578992i	$-0.196554\pi$
$401$	10.3455	+	7.51648i	0.516632	+	0.375355i	−0.298702	+	0.954347i	$0.596554\pi$
$402$	20.1999	+	14.6761i	1.00748	+	0.731978i
$403$	2.12048	−	6.52618i	0.105629	−	0.325092i
$404$	−0.843052	−	2.59465i	−0.0419434	−	0.129089i
$405$	−22.1366	+	16.0832i	−1.09998	+	0.799180i
$406$	−2.47069			−0.122618
$407$		0			0
$408$	32.6722			1.61752
$409$	25.9061	−	18.8219i	1.28098	−	0.930683i	0.281393	−	0.959592i	$-0.409203\pi$
$409$	25.9061	−	18.8219i	1.28098	−	0.930683i	0.999582	+	0.0289093i	$0.00920341\pi$
$410$	−7.75725	−	23.8744i	−0.383103	−	1.17907i
$411$	−9.55063	+	29.3938i	−0.471098	+	1.44989i
$412$	−0.0461116	−	0.0335020i	−0.00227175	−	0.00165053i
$413$	−11.1311	−	8.08724i	−0.547727	−	0.397947i
$414$	7.13110	−	21.9473i	0.350475	−	1.07865i
$415$	−3.10338	−	9.55122i	−0.152339	−	0.468851i
$416$	7.34052	−	5.33320i	0.359898	−	0.261481i
$417$	−21.0969			−1.03312
$418$		0			0
$419$	−20.0934			−0.981629			−0.490815	−	0.871264i	$-0.663301\pi$
$419$	−20.0934			−0.981629			−0.490815	+	0.871264i	$0.663301\pi$
$420$	3.15818	−	2.29456i	0.154104	−	0.111963i
$421$	−6.92949	−	21.3268i	−0.337722	−	1.03940i	−0.965365	−	0.260902i	$-0.915980\pi$
$421$	−6.92949	−	21.3268i	−0.337722	−	1.03940i	0.627643	−	0.778501i	$-0.284020\pi$
$422$	−8.71154	+	26.8113i	−0.424071	+	1.30516i
$423$	30.7868	+	22.3679i	1.49691	+	1.08757i
$424$	−9.72314	−	7.06427i	−0.472197	−	0.343071i
$425$	15.2059	−	46.7988i	0.737592	−	2.27008i
$426$	−0.221852	−	0.682789i	−0.0107487	−	0.0330812i
$427$	9.48745	−	6.89304i	0.459130	−	0.333577i
$428$	−2.94313			−0.142262
$429$		0			0
$430$	−7.06991			−0.340941
$431$	−9.77748	+	7.10375i	−0.470965	+	0.342176i	−0.797817	−	0.602900i	$-0.794012\pi$
$431$	−9.77748	+	7.10375i	−0.470965	+	0.342176i	0.326853	+	0.945075i	$0.394012\pi$
$432$	1.58051	+	4.86431i	0.0760423	+	0.234034i
$433$	−0.0934633	+	0.287650i	−0.00449156	+	0.0138236i	−0.953277	−	0.302097i	$-0.902313\pi$
$433$	−0.0934633	+	0.287650i	−0.00449156	+	0.0138236i	0.948786	+	0.315921i	$0.102313\pi$
$434$	1.61398	+	1.17263i	0.0774736	+	0.0562879i
$435$	16.5029	+	11.9901i	0.791254	+	0.574880i
$436$	0.562477	−	1.73113i	0.0269378	−	0.0829060i
$437$	−1.91862	−	5.90490i	−0.0917799	−	0.282470i
$438$	29.1887	−	21.2068i	1.39469	−	1.01330i
$439$	−3.52592			−0.168283			−0.0841416	−	0.996454i	$-0.526815\pi$
$439$	−3.52592			−0.168283			−0.0841416	+	0.996454i	$0.526815\pi$
$440$		0			0
$441$	3.63595			0.173141
$442$	19.0073	−	13.8096i	0.904084	−	0.656856i
$443$	−6.75027	−	20.7752i	−0.320715	−	0.987059i	−0.973338	−	0.229376i	$-0.926331\pi$
$443$	−6.75027	−	20.7752i	−0.320715	−	0.987059i	0.652623	−	0.757683i	$-0.273669\pi$
$444$	−0.211193	+	0.649984i	−0.0100228	+	0.0308469i
$445$	13.9173	+	10.1115i	0.659743	+	0.479331i
$446$	8.85504	+	6.43357i	0.419298	+	0.304638i
$447$	−9.61744	+	29.5994i	−0.454889	+	1.40001i
$448$	2.74469	+	8.44727i	0.129674	+	0.399096i
$449$	−7.52525	+	5.46741i	−0.355138	+	0.258023i	−0.751022	−	0.660278i	$-0.770439\pi$
$449$	−7.52525	+	5.46741i	−0.355138	+	0.258023i	0.395883	+	0.918301i	$0.370439\pi$
$450$	54.4908			2.56872
$451$		0			0
$452$	−1.12674			−0.0529974
$453$	−14.4811	+	10.5211i	−0.680380	+	0.494325i
$454$	−10.4817	−	32.2593i	−0.491930	−	1.51400i
$455$	5.55153	−	17.0858i	0.260260	−	0.800997i
$456$	7.87522	+	5.72169i	0.368791	+	0.267942i
$457$	9.15527	+	6.65169i	0.428266	+	0.311153i	0.780955	−	0.624587i	$-0.214733\pi$
$457$	9.15527	+	6.65169i	0.428266	+	0.311153i	−0.352689	+	0.935740i	$0.614733\pi$
$458$	4.50153	−	13.8543i	0.210343	−	0.647369i
$459$	−2.12189	−	6.53051i	−0.0990414	−	0.304818i
$460$	−6.09536	+	4.42854i	−0.284198	+	0.206482i
$461$	−0.678821			−0.0316158			−0.0158079	−	0.999875i	$-0.505032\pi$
$461$	−0.678821			−0.0316158			−0.0158079	+	0.999875i	$0.505032\pi$
$462$		0			0
$463$	−13.4936			−0.627103			−0.313551	−	0.949571i	$-0.601519\pi$
$463$	−13.4936			−0.627103			−0.313551	+	0.949571i	$0.601519\pi$
$464$	−4.88846	+	3.55168i	−0.226941	+	0.164882i
$465$	−5.08989	−	15.6651i	−0.236038	−	0.726450i
$466$	10.4983	−	32.3104i	0.486324	−	1.49675i
$467$	−23.9928	−	17.4318i	−1.11026	−	0.806649i	−0.127552	−	0.991832i	$-0.540712\pi$
$467$	−23.9928	−	17.4318i	−1.11026	−	0.806649i	−0.982704	+	0.185183i	$0.940712\pi$
$468$	−4.78390	−	3.47571i	−0.221136	−	0.160665i
$469$	2.34628	−	7.22112i	0.108341	−	0.333440i
$470$	16.8924	+	51.9893i	0.779186	+	2.39809i
$471$	21.8681	−	15.8881i	1.00763	−	0.732084i
$472$	−41.6335			−1.91634
$473$		0			0
$474$	15.0036			0.689137
$475$	11.8608	−	8.61735i	0.544210	−	0.395391i
$476$	−0.479734	−	1.47647i	−0.0219886	−	0.0676738i
$477$	−4.46260	+	13.7345i	−0.204328	+	0.628858i
$478$	7.75893	+	5.63719i	0.354885	+	0.257839i
$479$	−3.80348	−	2.76339i	−0.173785	−	0.126262i	0.497492	−	0.867468i	$-0.334254\pi$
$479$	−3.80348	−	2.76339i	−0.173785	−	0.126262i	−0.671278	+	0.741206i	$0.734254\pi$
$480$	6.73015	−	20.7133i	0.307188	−	0.945427i
$481$	0.971917	+	2.99125i	0.0443156	+	0.136389i
$482$	−28.3377	+	20.5886i	−1.29075	+	0.937784i
$483$	−12.8075			−0.582763
$484$		0			0
$485$	44.6985			2.02965
$486$	−22.8679	+	16.6145i	−1.03731	+	0.753649i
$487$	10.0040	+	30.7893i	0.453327	+	1.39520i	0.873089	+	0.487562i	$0.162114\pi$
$487$	10.0040	+	30.7893i	0.453327	+	1.39520i	−0.419762	+	0.907634i	$0.637886\pi$
$488$	10.9657	−	33.7489i	0.496393	−	1.52774i
$489$	−16.2920	−	11.8368i	−0.736748	−	0.535279i
$490$	4.22548	+	3.06999i	0.190888	+	0.138688i
$491$	−2.11860	+	6.52038i	−0.0956111	+	0.294261i	−0.987412	−	0.158166i	$-0.949442\pi$
$491$	−2.11860	+	6.52038i	−0.0956111	+	0.294261i	0.891801	+	0.452427i	$0.149442\pi$
$492$	1.41708	+	4.36131i	0.0638868	+	0.196623i
$493$	6.56294	−	4.76826i	0.295580	−	0.214751i
$494$	6.99986			0.314939
$495$		0			0
$496$	4.87908			0.219077
$497$	−0.176622	+	0.128323i	−0.00792256	+	0.00575608i
$498$	−2.49432	−	7.67674i	−0.111773	−	0.344003i
$499$	3.38900	−	10.4303i	0.151713	−	0.466923i	−0.846100	−	0.533023i	$-0.821056\pi$
$499$	3.38900	−	10.4303i	0.151713	−	0.466923i	0.997813	+	0.0661003i	$0.0210557\pi$
$500$	−8.26298	−	6.00341i	−0.369532	−	0.268481i
$501$	44.4952	+	32.3277i	1.98790	+	1.44429i
$502$	0.759428	−	2.33728i	0.0338949	−	0.104318i
$503$	−8.32288	−	25.6152i	−0.371099	−	1.14213i	−0.946073	−	0.323954i	$-0.894988\pi$
$503$	−8.32288	−	25.6152i	−0.371099	−	1.14213i	0.574974	−	0.818172i	$-0.305012\pi$
$504$	8.90096	−	6.46693i	0.396480	−	0.288060i
$505$	−30.1367			−1.34106
$506$		0			0
$507$	−16.1777			−0.718475
$508$	−3.23480	+	2.35022i	−0.143521	+	0.104274i
$509$	9.39282	+	28.9081i	0.416330	+	1.28133i	0.911056	+	0.412282i	$0.135268\pi$
$509$	9.39282	+	28.9081i	0.416330	+	1.28133i	−0.494727	+	0.869049i	$0.664732\pi$
$510$	17.4268	−	53.6342i	0.771672	−	2.37496i
$511$	−8.87607	−	6.44884i	−0.392654	−	0.285280i
$512$	20.5051	+	14.8978i	0.906206	+	0.658397i
$513$	0.632193	−	1.94569i	0.0279120	−	0.0859043i
$514$	4.00809	+	12.3356i	0.176789	+	0.544102i
$515$	−0.509370	+	0.370079i	−0.0224455	+	0.0163076i
$516$	1.29151			0.0568558
$517$		0			0
$518$	−0.914398			−0.0401763
$519$	40.5106	−	29.4327i	1.77822	−	1.29195i
$520$	−16.7986	−	51.7009i	−0.736669	−	2.26723i
$521$	−0.289063	+	0.889643i	−0.0126641	+	0.0389760i	−0.957189	−	0.289464i	$-0.906523\pi$
$521$	−0.289063	+	0.889643i	−0.0126641	+	0.0389760i	0.944525	+	0.328440i	$0.106523\pi$
$522$	7.26764	+	5.28025i	0.318096	+	0.231110i
$523$	−21.1844	−	15.3913i	−0.926328	−	0.673017i	0.0187630	−	0.999824i	$-0.494027\pi$
$523$	−21.1844	−	15.3913i	−0.926328	−	0.673017i	−0.945091	+	0.326807i	$0.894027\pi$
$524$	0.996249	−	3.06614i	0.0435214	−	0.133945i
$525$	−9.34538	−	28.7621i	−0.407866	−	1.25528i
$526$	4.53150	−	3.29232i	0.197583	−	0.143552i
$527$	−6.55034			−0.285337
$528$		0			0
$529$	1.71881			0.0747307
$530$	−16.7828	+	12.1934i	−0.728997	+	0.529647i
$531$	15.4590	+	47.5780i	0.670865	+	2.06471i
$532$	0.142931	−	0.439897i	0.00619685	−	0.0190720i
$533$	17.0734	+	12.4045i	0.739529	+	0.537300i
$534$	11.1859	+	8.12707i	0.484063	+	0.351693i
$535$	−10.0465	+	30.9200i	−0.434349	+	1.33679i
$536$	−7.09973	−	21.8507i	−0.306662	−	0.943808i
$537$	37.5055	−	27.2493i	1.61848	−	1.17590i
$538$	0.798336			0.0344187
$539$		0			0
$540$	−2.48258			−0.106833
$541$	−21.6465	+	15.7271i	−0.930656	+	0.676161i	−0.946153	−	0.323719i	$-0.895067\pi$
$541$	−21.6465	+	15.7271i	−0.930656	+	0.676161i	0.0154971	+	0.999880i	$0.495067\pi$
$542$	−4.70910	−	14.4931i	−0.202273	−	0.622533i
$543$	−12.0660	+	37.1353i	−0.517801	+	1.59363i
$544$	−7.00709	−	5.09095i	−0.300427	−	0.218273i
$545$	−16.2669	−	11.8186i	−0.696796	−	0.506252i
$546$	4.46201	−	13.7327i	0.190957	−	0.587704i
$547$	14.3563	+	44.1843i	0.613833	+	1.88918i	0.417617	+	0.908623i	$0.362865\pi$
$547$	14.3563	+	44.1843i	0.613833	+	1.88918i	0.196216	+	0.980561i	$0.437135\pi$
$548$	3.59508	−	2.61198i	0.153574	−	0.111578i
$549$	−42.6393			−1.81980
$550$		0			0
$551$	2.41695			0.102966
$552$	−31.3534	+	22.7796i	−1.33449	+	0.969563i
$553$	−1.40988	−	4.33917i	−0.0599543	−	0.184520i
$554$	11.2652	−	34.6707i	0.478613	−	1.47302i
$555$	6.10770	+	4.43750i	0.259257	+	0.188362i
$556$	2.45401	+	1.78294i	0.104073	+	0.0756136i
$557$	10.8457	−	33.3796i	0.459546	−	1.41434i	−0.406167	−	0.913799i	$-0.633135\pi$
$557$	10.8457	−	33.3796i	0.459546	−	1.41434i	0.865714	−	0.500539i	$-0.166865\pi$
$558$	−2.24151	−	6.89867i	−0.0948908	−	0.292044i
$559$	4.80848	−	3.49356i	0.203377	−	0.147762i
$560$	12.7737			0.539786
$561$		0			0
$562$	18.7630			0.791471
$563$	7.23901	−	5.25945i	0.305088	−	0.221659i	−0.424698	−	0.905335i	$-0.639620\pi$
$563$	7.23901	−	5.25945i	0.305088	−	0.221659i	0.729786	+	0.683676i	$0.239620\pi$
$564$	−3.08586	−	9.49729i	−0.129938	−	0.399908i
$565$	−3.84618	+	11.8373i	−0.161810	+	0.498000i
$566$	−23.2781	−	16.9125i	−0.978450	−	0.710885i
$567$	5.41047	+	3.93094i	0.227219	+	0.165084i
$568$	−0.204141	+	0.628281i	−0.00856556	+	0.0263621i
$569$	6.00285	+	18.4749i	0.251653	+	0.774507i	0.994471	+	0.105014i	$0.0334888\pi$
$569$	6.00285	+	18.4749i	0.251653	+	0.774507i	−0.742818	+	0.669493i	$0.766511\pi$
$570$	13.5932	−	9.87600i	0.569354	−	0.413660i
$571$	16.0171			0.670295			0.335148	−	0.942166i	$-0.391214\pi$
$571$	16.0171			0.670295			0.335148	+	0.942166i	$0.391214\pi$
$572$		0			0
$573$	61.1999			2.55666
$574$	−4.96372	+	3.60635i	−0.207182	+	0.150526i
$575$	18.0368	+	55.5115i	0.752186	+	2.31499i
$576$	9.97954	−	30.7139i	0.415814	−	1.27974i
$577$	26.6322	+	19.3494i	1.10871	+	0.805526i	0.982460	−	0.186472i	$-0.0597054\pi$
$577$	26.6322	+	19.3494i	1.10871	+	0.805526i	0.126251	+	0.991998i	$0.459705\pi$
$578$	−0.586970	−	0.426459i	−0.0244147	−	0.0177383i
$579$	−11.1908	+	34.4419i	−0.465076	+	1.43136i
$580$	−0.906329	−	2.78939i	−0.0376333	−	0.115823i
$581$	−1.98579	+	1.44276i	−0.0823846	+	0.0598559i
$582$	35.9262			1.48919
$583$		0			0
$584$	−33.1990			−1.37378
$585$	−52.8452	+	38.3943i	−2.18488	+	1.58741i
$586$	6.63833	+	20.4307i	0.274227	+	0.843983i
$587$	8.47857	−	26.0944i	0.349948	−	1.07703i	−0.608933	−	0.793222i	$-0.708402\pi$
$587$	8.47857	−	26.0944i	0.349948	−	1.07703i	0.958881	−	0.283808i	$-0.0915978\pi$
$588$	−0.771901	−	0.560819i	−0.0318327	−	0.0231278i
$589$	−1.57888	−	1.14712i	−0.0650565	−	0.0472663i
$590$	−22.2066	+	68.3450i	−0.914233	+	2.81372i
$591$	−14.3816	−	44.2620i	−0.591580	−	1.82070i
$592$	−1.80921	+	1.31447i	−0.0743582	+	0.0540244i
$593$	14.6132			0.600092			0.300046	−	0.953925i	$-0.402998\pi$
$593$	14.6132			0.600092			0.300046	+	0.953925i	$0.402998\pi$
$594$		0			0
$595$	−17.1491			−0.703045
$596$	3.62023	−	2.63025i	0.148290	−	0.107739i
$597$	−1.22887	−	3.78208i	−0.0502944	−	0.154790i
$598$	−8.61178	+	26.5043i	−0.352162	+	1.08384i
$599$	−20.4491	−	14.8571i	−0.835527	−	0.607046i	0.0855904	−	0.996330i	$-0.472722\pi$
$599$	−20.4491	−	14.8571i	−0.835527	−	0.607046i	−0.921118	+	0.389284i	$0.872722\pi$
$600$	−74.0344	−	53.7891i	−3.02244	−	2.19593i
$601$	−2.87416	+	8.84576i	−0.117239	+	0.360826i	−0.992408	−	0.122993i	$-0.960751\pi$
$601$	−2.87416	+	8.84576i	−0.117239	+	0.360826i	0.875168	+	0.483819i	$0.160751\pi$
$602$	0.533974	+	1.64340i	0.0217632	+	0.0669802i
$603$	−22.3344	+	16.2269i	−0.909526	+	0.660810i
$604$	2.57361			0.104719
$605$		0			0
$606$	−24.2222			−0.983960
$607$	1.72055	−	1.25005i	0.0698349	−	0.0507380i	−0.552320	−	0.833632i	$-0.686257\pi$
$607$	1.72055	−	1.25005i	0.0698349	−	0.0507380i	0.622155	+	0.782894i	$0.286257\pi$
$608$	−0.797424	−	2.45422i	−0.0323398	−	0.0995317i
$609$	1.54067	−	4.74169i	0.0624311	−	0.192143i
$610$	−49.5528	−	36.0022i	−2.00633	−	1.45769i
$611$	−37.1793	−	27.0123i	−1.50411	−	1.09280i
$612$	−1.74429	+	5.36837i	−0.0705087	+	0.217003i
$613$	−12.6526	−	38.9408i	−0.511035	−	1.57280i	−0.790382	−	0.612614i	$-0.790118\pi$
$613$	−12.6526	−	38.9408i	−0.511035	−	1.57280i	0.279347	−	0.960190i	$-0.409882\pi$
$614$	−0.246163	+	0.178848i	−0.00993433	+	0.00721771i
$615$	50.6564			2.04266
$616$		0			0
$617$	−7.53813			−0.303474			−0.151737	−	0.988421i	$-0.548487\pi$
$617$	−7.53813			−0.303474			−0.151737	+	0.988421i	$0.548487\pi$
$618$	−0.409404	+	0.297449i	−0.0164686	+	0.0119652i
$619$	−6.02754	−	18.5509i	−0.242267	−	0.745623i	−0.996074	−	0.0885260i	$-0.971784\pi$
$619$	−6.02754	−	18.5509i	−0.242267	−	0.745623i	0.753806	−	0.657097i	$-0.228216\pi$
$620$	−0.731828	+	2.25233i	−0.0293909	+	0.0904559i
$621$	6.58941	+	4.78749i	0.264424	+	0.192115i
$622$	0.678032	+	0.492619i	0.0271866	+	0.0197522i
$623$	1.29928	−	3.99878i	0.0520546	−	0.160208i
$624$	−10.9126	−	33.5855i	−0.436853	−	1.34450i
$625$	−43.7881	+	31.8139i	−1.75152	+	1.27256i
$626$	−9.51375			−0.380246
$627$		0			0
$628$	−3.88645			−0.155086
$629$	2.42893	−	1.76472i	0.0968479	−	0.0703641i
$630$	−5.86839	−	18.0610i	−0.233802	−	0.719569i
$631$	−3.29578	+	10.1434i	−0.131203	+	0.403801i	−0.994980	−	0.100073i	$-0.968092\pi$
$631$	−3.29578	+	10.1434i	−0.131203	+	0.403801i	0.863777	+	0.503874i	$0.168092\pi$
$632$	−11.1691	−	8.11485i	−0.444284	−	0.322792i
$633$	−46.0234	−	33.4380i	−1.82927	−	1.32904i
$634$	6.88020	−	21.1751i	0.273248	−	0.840970i
$635$	13.6488	+	42.0067i	0.541637	+	1.66699i
$636$	3.06584	−	2.22746i	0.121568	−	0.0883246i
$637$	−4.39091			−0.173974
$638$		0			0
$639$	0.793787			0.0314017
$640$	23.8509	−	17.3287i	0.942791	−	0.684977i
$641$	0.138547	+	0.426405i	0.00547230	+	0.0168420i	0.953755	−	0.300584i	$-0.0971815\pi$
$641$	0.138547	+	0.426405i	0.00547230	+	0.0168420i	−0.948283	+	0.317426i	$0.897182\pi$
$642$	−8.07485	+	24.8518i	−0.318689	+	0.980823i
$643$	25.6005	+	18.5999i	1.00959	+	0.733507i	0.964122	−	0.265459i	$-0.0855235\pi$
$643$	25.6005	+	18.5999i	1.00959	+	0.733507i	0.0454636	+	0.998966i	$0.485524\pi$
$644$	1.48979	+	1.08239i	0.0587058	+	0.0426522i
$645$	4.40865	−	13.5684i	0.173590	−	0.534256i
$646$	−2.06482	−	6.35487i	−0.0812394	−	0.250029i
$647$	24.3710	−	17.7065i	0.958122	−	0.696116i	0.00540790	−	0.999985i	$-0.498279\pi$
$647$	24.3710	−	17.7065i	0.958122	−	0.696116i	0.952714	+	0.303869i	$0.0982786\pi$
$648$	20.2367			0.794972
$649$		0			0
$650$	−65.8051			−2.58109
$651$	−3.25692	+	2.36629i	−0.127649	+	0.0927423i
$652$	0.894744	+	2.75374i	0.0350409	+	0.107845i
$653$	10.6954	−	32.9170i	0.418543	−	1.28814i	−0.490500	−	0.871441i	$-0.663186\pi$
$653$	10.6954	−	32.9170i	0.418543	−	1.28814i	0.909043	−	0.416702i	$-0.136814\pi$
$654$	−13.0744	−	9.49912i	−0.511250	−	0.371445i
$655$	−28.8116	−	20.9328i	−1.12576	−	0.817913i
$656$	−4.63691	+	14.2710i	−0.181041	+	0.557187i
$657$	12.3272	+	37.9391i	0.480929	+	1.48015i
$658$	10.8091	−	7.85327i	0.421383	−	0.306152i
$659$	−20.2587			−0.789167			−0.394584	−	0.918860i	$-0.629111\pi$
$659$	−20.2587			−0.789167			−0.394584	+	0.918860i	$0.629111\pi$
$660$		0			0
$661$	40.6737			1.58202			0.791012	−	0.611801i	$-0.209555\pi$
$661$	40.6737			1.58202			0.791012	+	0.611801i	$0.209555\pi$
$662$	29.5520	−	21.4708i	1.14857	−	0.834487i
$663$	14.6505	+	45.0897i	0.568980	+	1.75114i
$664$	−2.29520	+	7.06389i	−0.0890710	+	0.274132i
$665$	−4.13358	−	3.00322i	−0.160293	−	0.116460i
$666$	2.68974	+	1.95421i	0.104225	+	0.0757242i
$667$	−2.97352	+	9.15157i	−0.115135	+	0.354350i
$668$	−2.44365	−	7.52078i	−0.0945476	−	0.290988i
$669$	−17.8690	+	12.9826i	−0.690854	+	0.501935i
$670$	−39.6567			−1.53207
$671$		0			0
$672$	−5.32312			−0.205344
$673$	−20.0219	+	14.5467i	−0.771786	+	0.560735i	−0.902503	−	0.430685i	$-0.858272\pi$
$673$	−20.0219	+	14.5467i	−0.771786	+	0.560735i	0.130717	+	0.991420i	$0.458272\pi$
$674$	0.682659	+	2.10101i	0.0262950	+	0.0809278i
$675$	−5.94320	+	18.2913i	−0.228754	+	0.704032i
$676$	1.88180	+	1.36721i	0.0723771	+	0.0525850i
$677$	9.20835	+	6.69026i	0.353906	+	0.257128i	0.750506	−	0.660864i	$-0.229810\pi$
$677$	9.20835	+	6.69026i	0.353906	+	0.257128i	−0.396600	+	0.917992i	$0.629810\pi$
$678$	−3.09135	+	9.51419i	−0.118723	+	0.365390i
$679$	−3.37598	−	10.3902i	−0.129558	−	0.398739i
$680$	−41.9817	+	30.5015i	−1.60993	+	1.16968i
$681$	68.4475			2.62291
$682$		0			0
$683$	−0.212700			−0.00813875			−0.00406938	−	0.999992i	$-0.501295\pi$
$683$	−0.212700			−0.00813875			−0.00406938	+	0.999992i	$0.501295\pi$
$684$	−1.36057	+	0.988511i	−0.0520226	+	0.0377967i
$685$	−15.1690	−	46.6853i	−0.579577	−	1.78375i
$686$	0.394480	−	1.21408i	0.0150613	−	0.0463540i
$687$	23.7818	+	17.2785i	0.907332	+	0.659215i
$688$	3.41895	+	2.48401i	0.130346	+	0.0947021i
$689$	5.38920	−	16.5862i	0.205312	−	0.631886i
$690$	20.6712	+	63.6195i	0.786940	+	2.42195i
$691$	−29.4324	+	21.3839i	−1.11966	+	0.813481i	−0.984158	−	0.177296i	$-0.943265\pi$
$691$	−29.4324	+	21.3839i	−1.11966	+	0.813481i	−0.135503	+	0.990777i	$0.543265\pi$
$692$	−7.19966			−0.273690
$693$		0			0
$694$	3.48514			0.132294
$695$	27.1082	−	19.6952i	1.02827	−	0.747083i
$696$	−4.66198	−	14.3481i	−0.176712	−	0.543864i
$697$	6.22522	−	19.1593i	0.235797	−	0.725709i
$698$	−31.9188	−	23.1904i	−1.20814	−	0.877769i
$699$	55.4630	+	40.2962i	2.09780	+	1.52414i
$700$	−1.34369	+	4.13544i	−0.0507865	+	0.156305i
$701$	−5.79080	−	17.8223i	−0.218716	−	0.673138i	−0.998869	−	0.0475491i	$-0.984859\pi$
$701$	−5.79080	−	17.8223i	−0.218716	−	0.673138i	0.780153	−	0.625588i	$-0.215141\pi$
$702$	−7.42899	+	5.39748i	−0.280389	+	0.203715i
$703$	0.894509			0.0337371
$704$		0			0
$705$	−110.310			−4.15453
$706$	24.7391	−	17.9740i	0.931068	−	0.676461i
$707$	2.27616	+	7.00529i	0.0856036	+	0.263461i
$708$	4.05666	−	12.4851i	0.152458	−	0.469219i
$709$	10.3227	+	7.49988i	0.387677	+	0.281664i	0.764503	−	0.644620i	$-0.222985\pi$
$709$	10.3227	+	7.49988i	0.387677	+	0.281664i	−0.376826	+	0.926284i	$0.622985\pi$
$710$	0.922491	+	0.670229i	0.0346205	+	0.0251533i
$711$	−5.12626	+	15.7770i	−0.192250	+	0.591684i
$712$	−3.93156	−	12.1001i	−0.147341	−	0.453470i
$713$	6.28593	−	4.56700i	0.235410	−	0.171035i
$714$	−13.7835			−0.515835
$715$		0			0
$716$	−6.66558			−0.249105
$717$	−15.6571	+	11.3755i	−0.584725	+	0.424827i
$718$	−0.598073	−	1.84068i	−0.0223199	−	0.0686936i
$719$	−5.29123	+	16.2847i	−0.197329	+	0.607318i	0.802612	+	0.596501i	$0.203443\pi$
$719$	−5.29123	+	16.2847i	−0.197329	+	0.607318i	−0.999942	+	0.0108162i	$0.996557\pi$
$720$	−37.5743	−	27.2993i	−1.40031	−	1.01739i
$721$	0.124497	+	0.0904521i	0.00463649	+	0.00336861i
$722$	−6.87993	+	21.1742i	−0.256044	+	0.788024i
$723$	−21.8423	−	67.2238i	−0.812325	−	2.50008i
$724$	4.54191	−	3.29989i	0.168799	−	0.122640i
$725$	−22.7216			−0.843858
$726$		0			0
$727$	−8.65786			−0.321102			−0.160551	−	0.987028i	$-0.551327\pi$
$727$	−8.65786			−0.321102			−0.160551	+	0.987028i	$0.551327\pi$
$728$	−10.7491	+	7.80970i	−0.398389	+	0.289447i
$729$	−11.4264	−	35.1668i	−0.423200	−	1.30248i
$730$	−17.7078	+	54.4989i	−0.655394	+	2.01710i
$731$	−4.59006	−	3.33488i	−0.169770	−	0.123345i
$732$	9.05219	+	6.57680i	0.334579	+	0.243086i
$733$	8.67924	−	26.7120i	0.320575	−	0.986629i	−0.652823	−	0.757510i	$-0.726416\pi$
$733$	8.67924	−	26.7120i	0.320575	−	0.986629i	0.973398	−	0.229119i	$-0.0735844\pi$
$734$	3.44068	+	10.5893i	0.126998	+	0.390859i
$735$	−8.52678	+	6.19507i	−0.314515	+	0.228509i
$736$	10.2737			0.378695
$737$		0			0
$738$	22.3084			0.821182
$739$	27.4228	−	19.9239i	1.00877	−	0.732911i	0.0448155	−	0.998995i	$-0.485730\pi$
$739$	27.4228	−	19.9239i	1.00877	−	0.732911i	0.963950	+	0.266084i	$0.0857300\pi$
$740$	−0.335431	−	1.03235i	−0.0123307	−	0.0379500i
$741$	−4.36496	+	13.4340i	−0.160351	+	0.493509i
$742$	4.10193	+	2.98022i	0.150586	+	0.109407i
$743$	4.57354	+	3.32287i	0.167787	+	0.121904i	0.668510	−	0.743703i	$-0.266932\pi$
$743$	4.57354	+	3.32287i	0.167787	+	0.121904i	−0.500723	+	0.865608i	$0.666932\pi$
$744$	−3.76438	+	11.5856i	−0.138009	+	0.424748i
$745$	−15.2751	−	47.0119i	−0.559636	−	1.72238i
$746$	38.0171	−	27.6211i	1.39191	−	1.01128i
$747$	8.92472			0.326538
$748$		0			0
$749$	7.94617			0.290347
$750$	−73.3633	+	53.3015i	−2.67885	+	1.94630i
$751$	13.7021	+	42.1707i	0.499997	+	1.53883i	0.809022	+	0.587778i	$0.199997\pi$
$751$	13.7021	+	42.1707i	0.499997	+	1.53883i	−0.309025	+	0.951054i	$0.600003\pi$
$752$	10.0974	−	31.0767i	0.368216	−	1.13325i
$753$	4.01209	+	2.91495i	0.146209	+	0.106227i
$754$	−8.77667	−	6.37663i	−0.319628	−	0.232223i
$755$	8.78515	−	27.0379i	0.319724	−	0.984011i
$756$	0.187504	+	0.577077i	0.00681944	+	0.0209881i
$757$	17.2953	−	12.5657i	0.628607	−	0.456710i	−0.227311	−	0.973822i	$-0.572993\pi$
$757$	17.2953	−	12.5657i	0.628607	−	0.456710i	0.855917	+	0.517113i	$0.172993\pi$
$758$	3.31700			0.120479
$759$		0			0
$760$	−15.4607			−0.560819
$761$	3.70994	−	2.69543i	0.134485	−	0.0977092i	−0.518509	−	0.855072i	$-0.673513\pi$
$761$	3.70994	−	2.69543i	0.134485	−	0.0977092i	0.652994	+	0.757363i	$0.273513\pi$
$762$	10.9702	+	33.7627i	0.397407	+	1.22309i
$763$	−1.51863	+	4.67387i	−0.0549782	+	0.169205i
$764$	−7.11883	−	5.17214i	−0.257550	−	0.187121i
$765$	50.4449	+	36.6503i	1.82384	+	1.32510i
$766$	7.58948	−	23.3580i	0.274219	−	0.843960i
$767$	−18.6689	−	57.4569i	−0.674095	−	2.07465i
$768$	−17.8510	+	12.9695i	−0.644144	+	0.467998i
$769$	12.8223			0.462385			0.231193	−	0.972908i	$-0.425737\pi$
$769$	12.8223			0.462385			0.231193	+	0.972908i	$0.425737\pi$
$770$		0			0
$771$	−26.1736			−0.942621
$772$	4.21249	−	3.06055i	0.151611	−	0.110152i
$773$	16.7067	+	51.4178i	0.600897	+	1.84937i	0.522857	+	0.852420i	$0.324866\pi$
$773$	16.7067	+	51.4178i	0.600897	+	1.84937i	0.0780395	+	0.996950i	$0.475134\pi$
$774$	1.94150	−	5.97534i	0.0697859	−	0.214779i
$775$	14.8429	+	10.7840i	0.533173	+	0.387373i
$776$	−26.7446	−	19.4311i	−0.960075	−	0.697535i
$777$	0.570199	−	1.75489i	0.0204558	−	0.0629564i
$778$	−11.1768	−	34.3988i	−0.400709	−	1.23326i
$779$	4.85576	−	3.52792i	0.173976	−	0.126401i
$780$	17.1409			0.613743
$781$		0			0
$782$	26.6025			0.951302
$783$	−2.56512	+	1.86367i	−0.0916700	+	0.0666021i
$784$	−0.964766	−	2.96924i	−0.0344559	−	0.106044i
$785$	−13.2666	+	40.8304i	−0.473505	+	1.45730i
$786$	−23.1572	−	16.8247i	−0.825988	−	0.600116i
$787$	35.4766	+	25.7752i	1.26460	+	0.918788i	0.998974	−	0.0452876i	$-0.0144204\pi$
$787$	35.4766	+	25.7752i	1.26460	+	0.918788i	0.265629	+	0.964075i	$0.414420\pi$
$788$	−2.06780	+	6.36403i	−0.0736622	+	0.226709i
$789$	3.49281	+	10.7498i	0.124347	+	0.382702i
$790$	−19.2787	+	14.0068i	−0.685904	+	0.498338i
$791$	3.04208			0.108164
$792$		0			0
$793$	51.4928			1.82856
$794$	10.7063	−	7.77856i	0.379951	−	0.276051i
$795$	−12.9359	−	39.8127i	−0.458790	−	1.41201i
$796$	−0.176688	+	0.543791i	−0.00626255	+	0.0192742i
$797$	28.9383	+	21.0249i	1.02505	+	0.744740i	0.967311	−	0.253591i	$-0.0816119\pi$
$797$	28.9383	+	21.0249i	1.02505	+	0.744740i	0.0577359	+	0.998332i	$0.481612\pi$
$798$	−3.32234	−	2.41382i	−0.117610	−	0.0854484i
$799$	−13.5562	+	41.7216i	−0.479583	+	1.47600i
$800$	7.49652	+	23.0719i	0.265042	+	0.815716i
$801$	−12.3679	+	8.98582i	−0.436999	+	0.317498i
$802$	−16.3244			−0.576436
$803$		0			0
$804$	7.24440			0.255490
$805$	16.4569	−	11.9566i	0.580029	−	0.421415i
$806$	2.70693	+	8.33108i	0.0953477	+	0.293450i
$807$	−0.497825	+	1.53215i	−0.0175243	+	0.0539342i
$808$	18.0318	+	13.1009i	0.634356	+	0.460886i
$809$	24.8424	+	18.0490i	0.873411	+	0.634570i	0.931500	−	0.363741i	$-0.118501\pi$
$809$	24.8424	+	18.0490i	0.873411	+	0.634570i	−0.0580894	+	0.998311i	$0.518501\pi$
$810$	10.7939	−	33.2202i	0.379259	−	1.16724i
$811$	5.28368	+	16.2615i	0.185535	+	0.571019i	0.999957	−	0.00925442i	$-0.00294582\pi$
$811$	5.28368	+	16.2615i	0.185535	+	0.571019i	−0.814422	+	0.580273i	$0.802946\pi$
$812$	−0.579943	+	0.421353i	−0.0203520	+	0.0147866i
$813$	30.7514			1.07850
$814$		0			0
$815$	31.9845			1.12037
$816$	−27.2718	+	19.8141i	−0.954705	+	0.693634i
$817$	−0.522360	−	1.60766i	−0.0182751	−	0.0562449i
$818$	−12.6319	+	38.8771i	−0.441665	+	1.35931i
$819$	12.9161	+	9.38406i	0.451324	+	0.327906i
$820$	−5.89241	−	4.28109i	−0.205772	−	0.149502i
$821$	−3.82631	+	11.7762i	−0.133539	+	0.410991i	−0.995360	−	0.0962218i	$-0.969324\pi$
$821$	−3.82631	+	11.7762i	−0.133539	+	0.410991i	0.861821	+	0.507213i	$0.169324\pi$
$822$	−12.1920	−	37.5231i	−0.425244	−	1.30877i
$823$	−37.3268	+	27.1195i	−1.30113	+	0.945326i	−0.999966	−	0.00824607i	$-0.997375\pi$
$823$	−37.3268	+	27.1195i	−1.30113	+	0.945326i	−0.301164	+	0.953572i	$0.597375\pi$
$824$	0.465652			0.0162217
$825$		0			0
$826$	17.5640			0.611131
$827$	−37.7894	+	27.4556i	−1.31407	+	0.954725i	−0.314080	+	0.949396i	$0.601696\pi$
$827$	−37.7894	+	27.4556i	−1.31407	+	0.954725i	−0.999986	+	0.00532868i	$0.998304\pi$
$828$	−2.06903	−	6.36782i	−0.0719037	−	0.221297i
$829$	1.24396	−	3.82852i	0.0432046	−	0.132970i	−0.927127	−	0.374746i	$-0.877730\pi$
$829$	1.24396	−	3.82852i	0.0432046	−	0.132970i	0.970332	+	0.241776i	$0.0777299\pi$
$830$	10.3718	+	7.53553i	0.360009	+	0.261562i
$831$	59.5146	+	43.2399i	2.06454	+	1.49997i
$832$	−12.0517	+	37.0912i	−0.417816	+	1.28591i
$833$	1.29523	+	3.98632i	0.0448772	+	0.138118i
$834$	21.7880	−	15.8299i	0.754458	−	0.548146i
$835$	−87.3534			−3.02299
$836$		0			0
$837$	2.56020			0.0884933
$838$	20.7517	−	15.0770i	0.716857	−	0.520827i
$839$	−4.41960	−	13.6021i	−0.152582	−	0.469598i	0.845326	−	0.534250i	$-0.179406\pi$
$839$	−4.41960	−	13.6021i	−0.152582	−	0.469598i	−0.997908	+	0.0646525i	$0.979406\pi$
$840$	−9.85533	+	30.3316i	−0.340041	+	1.04654i
$841$	20.4310	+	14.8440i	0.704518	+	0.511863i
$842$	23.1590	+	16.8260i	0.798110	+	0.579861i
$843$	−11.7002	+	36.0096i	−0.402977	+	1.24024i
$844$	2.52758	+	7.77908i	0.0870028	+	0.267767i
$845$	20.7873	−	15.1028i	0.715104	−	0.519554i
$846$	−48.5792			−1.67019
$847$		0			0
$848$	12.4002			0.425823
$849$	46.9738	−	34.1285i	1.61214	−	1.17129i
$850$	19.4112	+	59.7417i	0.665800	+	2.04912i
$851$	−1.10050	+	3.38698i	−0.0377245	+	0.116104i
$852$	−0.168519	−	0.122436i	−0.00577335	−	0.00419459i
$853$	26.1318	+	18.9859i	0.894735	+	0.650063i	0.937108	−	0.349038i	$-0.113492\pi$
$853$	26.1318	+	18.9859i	0.894735	+	0.650063i	−0.0423729	+	0.999102i	$0.513492\pi$
$854$	−4.62612	+	14.2377i	−0.158303	+	0.487205i
$855$	5.74075	+	17.6682i	0.196330	+	0.604240i
$856$	19.4526	−	14.1331i	0.664875	−	0.483060i
$857$	16.2318			0.554468			0.277234	−	0.960802i	$-0.410582\pi$
$857$	16.2318			0.554468			0.277234	+	0.960802i	$0.410582\pi$
$858$		0			0
$859$	−28.2893			−0.965220			−0.482610	−	0.875835i	$-0.660311\pi$
$859$	−28.2893			−0.965220			−0.482610	+	0.875835i	$0.660311\pi$
$860$	−1.65952	+	1.20571i	−0.0565890	+	0.0411143i
$861$	−3.82597	−	11.7751i	−0.130389	−	0.401295i
$862$	4.76754	−	14.6730i	0.162383	−	0.499764i
$863$	−25.8776	−	18.8012i	−0.880885	−	0.640001i	0.0526003	−	0.998616i	$-0.483249\pi$
$863$	−25.8776	−	18.8012i	−0.880885	−	0.640001i	−0.933486	+	0.358615i	$0.883249\pi$
$864$	2.73872	+	1.98980i	0.0931731	+	0.0676942i
$865$	−24.5764	+	75.6384i	−0.835622	+	2.57178i
$866$	−0.119312	−	0.367204i	−0.00405438	−	0.0124781i
$867$	1.18447	−	0.860569i	0.0402268	−	0.0292265i
$868$	0.578830			0.0196468
$869$		0			0
$870$	−26.0403			−0.882848
$871$	26.9718	−	19.5962i	0.913905	−	0.663991i
$872$	4.59530	+	14.1429i	0.155617	+	0.478938i
$873$	−12.2749	+	37.7782i	−0.415442	+	1.27860i
$874$	6.41219	+	4.65873i	0.216896	+	0.157584i
$875$	22.3092	+	16.2086i	0.754189	+	0.547951i
$876$	3.23482	−	9.95574i	0.109294	−	0.336373i
$877$	14.1520	+	43.5553i	0.477878	+	1.47076i	0.842036	+	0.539421i	$0.181357\pi$
$877$	14.1520	+	43.5553i	0.477878	+	1.47076i	−0.364157	+	0.931337i	$0.618643\pi$
$878$	3.64144	−	2.64566i	0.122893	−	0.0892867i
$879$	−43.3496			−1.46215
$880$		0			0
$881$	26.7142			0.900025			0.450012	−	0.893022i	$-0.351420\pi$
$881$	26.7142			0.900025			0.450012	+	0.893022i	$0.351420\pi$
$882$	−3.75507	+	2.72822i	−0.126440	+	0.0918639i
$883$	−8.80295	−	27.0927i	−0.296243	−	0.911742i	−0.982801	−	0.184667i	$-0.940879\pi$
$883$	−8.80295	−	27.0927i	−0.296243	−	0.911742i	0.686558	−	0.727075i	$-0.259121\pi$
$884$	2.10647	−	6.48304i	0.0708481	−	0.218048i
$885$	−117.319	−	85.2370i	−3.94362	−	2.86521i
$886$	22.5600	+	16.3908i	0.757918	+	0.550660i
$887$	−7.29711	+	22.4582i	−0.245013	+	0.754072i	0.750621	+	0.660733i	$0.229754\pi$
$887$	−7.29711	+	22.4582i	−0.245013	+	0.754072i	−0.995634	+	0.0933398i	$0.970246\pi$
$888$	−1.72539	−	5.31021i	−0.0579004	−	0.178199i
$889$	8.73362	−	6.34535i	0.292916	−	0.212816i
$890$	−21.9604			−0.736113
$891$		0			0
$892$	3.17572			0.106331
$893$	−10.5740	+	7.68246i	−0.353845	+	0.257084i
$894$	−12.2773	−	37.7856i	−0.410614	−	1.26374i
$895$	−22.7533	+	70.0274i	−0.760559	+	2.34076i
$896$	−5.82947	−	4.23536i	−0.194749	−	0.141493i
$897$	−45.4964	−	33.0551i	−1.51908	−	1.10368i
$898$	3.66934	−	11.2931i	0.122448	−	0.376855i
$899$	0.934665	+	2.87660i	0.0311728	+	0.0959401i
$900$	12.7906	−	9.29292i	0.426353	−	0.309764i
$901$	−16.6477			−0.554614
$902$		0			0
$903$	−3.48696			−0.116039
$904$	7.44715	−	5.41067i	0.247689	−	0.179956i
$905$	−19.1640	−	58.9809i	−0.637034	−	1.96059i
$906$	7.06102	−	21.7316i	0.234587	−	0.721984i
$907$	−19.3706	−	14.0736i	−0.643192	−	0.467306i	0.217754	−	0.976004i	$-0.430127\pi$
$907$	−19.3706	−	14.0736i	−0.643192	−	0.467306i	−0.860945	+	0.508698i	$0.830127\pi$
$908$	−7.96189	−	5.78465i	−0.264225	−	0.191970i
$909$	8.27599	−	25.4709i	0.274497	−	0.844816i
$910$	7.08688	+	21.8112i	0.234928	+	0.723034i
$911$	−14.7555	+	10.7205i	−0.488873	+	0.355187i	−0.804751	−	0.593613i	$-0.797701\pi$
$911$	−14.7555	+	10.7205i	−0.488873	+	0.355187i	0.315878	+	0.948800i	$0.397701\pi$
$912$	−10.0435			−0.332572
$913$		0			0
$914$	−14.4463			−0.477841
$915$	99.9947	−	72.6504i	3.30572	−	2.40175i
$916$	−1.30608	−	4.01971i	−0.0431541	−	0.132815i
$917$	−2.68977	+	8.27827i	−0.0888241	+	0.273373i
$918$	7.09154	+	5.15231i	0.234056	+	0.170052i
$919$	−22.9780	−	16.6945i	−0.757975	−	0.550701i	0.140313	−	0.990107i	$-0.455189\pi$
$919$	−22.9780	−	16.6945i	−0.757975	−	0.550701i	−0.898289	+	0.439406i	$0.855189\pi$
$920$	19.0210	−	58.5406i	0.627104	−	1.93003i
$921$	−0.189739	−	0.583956i	−0.00625211	−	0.0192420i
$922$	0.701061	−	0.509350i	0.0230882	−	0.0167746i
$923$	−0.958607			−0.0315529
$924$		0			0
$925$	−8.40922			−0.276493
$926$	13.9357	−	10.1249i	0.457956	−	0.332725i
$927$	−0.172902	−	0.532138i	−0.00567885	−	0.0174777i
$928$	−1.23587	+	3.80361i	−0.0405694	+	0.124860i
$929$	−2.74227	−	1.99237i	−0.0899709	−	0.0653677i	0.541890	−	0.840449i	$-0.317709\pi$
$929$	−2.74227	−	1.99237i	−0.0899709	−	0.0653677i	−0.631861	+	0.775081i	$0.717709\pi$
$930$	17.0109	+	12.3591i	0.557808	+	0.405271i
$931$	−0.385900	+	1.18768i	−0.0126474	+	0.0389246i
$932$	−3.04599	−	9.37460i	−0.0997748	−	0.307075i
$933$	−1.36823	+	0.994078i	−0.0447939	+	0.0325446i
$934$	37.8588			1.23878
$935$		0			0
$936$	48.3096			1.57905
$937$	−36.7190	+	26.6779i	−1.19956	+	0.871529i	−0.994241	−	0.107167i	$-0.965822\pi$
$937$	−36.7190	+	26.6779i	−1.19956	+	0.871529i	−0.205315	+	0.978696i	$0.565822\pi$
$938$	2.99518	+	9.21822i	0.0977962	+	0.300986i
$939$	5.93257	−	18.2586i	0.193602	−	0.595846i
$940$	12.8314	+	9.32258i	0.418515	+	0.304069i
$941$	−17.4164	−	12.6538i	−0.567759	−	0.412501i	0.266531	−	0.963826i	$-0.414122\pi$
$941$	−17.4164	−	12.6538i	−0.567759	−	0.412501i	−0.834291	+	0.551325i	$0.814122\pi$
$942$	−10.6630	+	32.8172i	−0.347418	+	1.06924i
$943$	7.38420	+	22.7262i	0.240463	+	0.740068i
$944$	34.7519	−	25.2488i	1.13108	−	0.821777i
$945$	6.70272			0.218039
$946$		0			0
$947$	−11.2673			−0.366140			−0.183070	−	0.983100i	$-0.558603\pi$
$947$	−11.2673			−0.366140			−0.183070	+	0.983100i	$0.558603\pi$
$948$	3.52178	−	2.55872i	0.114382	−	0.0831035i
$949$	−14.8867	−	45.8167i	−0.483244	−	1.48727i
$950$	−5.78336	+	17.7994i	−0.187637	+	0.577487i
$951$	36.3484	+	26.4087i	1.17868	+	0.856359i
$952$	10.2609	+	7.45496i	0.332557	+	0.241617i
$953$	−7.37612	+	22.7014i	−0.238936	+	0.735370i	0.757639	+	0.652674i	$0.226353\pi$
$953$	−7.37612	+	22.7014i	−0.238936	+	0.735370i	−0.996575	+	0.0826956i	$0.973647\pi$
$954$	−5.69679	−	17.5329i	−0.184440	−	0.567649i
$955$	−78.6380	+	57.1339i	−2.54467	+	1.84881i
$956$	2.78262			0.0899964
$957$		0			0
$958$	6.00159			0.193902
$959$	−9.70634	+	7.05207i	−0.313434	+	0.227723i
$960$	28.9281	+	89.0316i	0.933651	+	2.87348i
$961$	−8.82482	+	27.1600i	−0.284672	+	0.876129i
$962$	−3.24823	−	2.35998i	−0.104727	−	0.0760888i
$963$	−23.3740	−	16.9822i	−0.753217	−	0.547244i
$964$	−3.14051	+	9.66548i	−0.101149	+	0.311304i
$965$	−17.7741	−	54.7030i	−0.572168	−	1.76095i
$966$	13.2271	−	9.61007i	0.425576	−	0.309199i
$967$	20.5165			0.659765			0.329882	−	0.944022i	$-0.392991\pi$
$967$	20.5165			0.659765			0.329882	+	0.944022i	$0.392991\pi$
$968$		0			0
$969$	13.4837			0.433159
$970$	−46.1629	+	33.5393i	−1.48220	+	1.07688i
$971$	−10.7428	−	33.0630i	−0.344754	−	1.06104i	−0.961715	−	0.274050i	$-0.911637\pi$
$971$	−10.7428	−	33.0630i	−0.344754	−	1.06104i	0.616962	−	0.786993i	$-0.288363\pi$
$972$	−2.53432	+	7.79982i	−0.0812882	+	0.250179i
$973$	−6.62558	−	4.81377i	−0.212406	−	0.154322i
$974$	−33.4344	−	24.2915i	−1.07131	−	0.778350i
$975$	41.0347	−	126.292i	1.31416	−	4.04457i
$976$	11.3139	+	34.8207i	0.362150	+	1.11458i
$977$	−4.67850	+	3.39913i	−0.149678	+	0.108748i	−0.660104	−	0.751174i	$-0.729488\pi$
$977$	−4.67850	+	3.39913i	−0.149678	+	0.108748i	0.510426	+	0.859922i	$0.329488\pi$
$978$	25.7074			0.822032
$979$		0			0
$980$	1.51540			0.0484078
$981$	14.4559	−	10.5028i	0.461542	−	0.335330i
$982$	−2.70453	−	8.32369i	−0.0863050	−	0.265620i
$983$	−5.32500	+	16.3887i	−0.169841	+	0.522718i	−0.999360	−	0.0357606i	$-0.988615\pi$
$983$	−5.32500	+	16.3887i	−0.169841	+	0.522718i	0.829519	+	0.558478i	$0.188615\pi$
$984$	−30.3094	−	22.0211i	−0.966229	−	0.702007i
$985$	59.8008	+	43.4478i	1.90541	+	1.38436i
$986$	−3.20012	+	9.84895i	−0.101912	+	0.313654i
$987$	8.33150	+	25.6417i	0.265195	+	0.816185i
$988$	1.64307	−	1.19376i	0.0522731	−	0.0379786i
$989$	6.72991			0.213999
$990$		0			0
$991$	−24.0077			−0.762630			−0.381315	−	0.924445i	$-0.624529\pi$
$991$	−24.0077			−0.762630			−0.381315	+	0.924445i	$0.624529\pi$
$992$	2.61259	−	1.89815i	0.0829497	−	0.0602665i
$993$	22.7783	+	70.1044i	0.722847	+	2.22469i
$994$	0.0861214	−	0.265054i	0.00273161	−	0.00840702i
$995$	5.10983	+	3.71251i	0.161993	+	0.117695i
$996$	−1.89469	−	1.37657i	−0.0600355	−	0.0436184i
$997$	11.1350	−	34.2699i	0.352648	−	1.08534i	−0.604713	−	0.796443i	$-0.706712\pi$
$997$	11.1350	−	34.2699i	0.352648	−	1.08534i	0.957361	−	0.288895i	$-0.0932878\pi$
$998$	4.32628	+	13.3149i	0.136946	+	0.421476i
$999$	−0.949348	+	0.689741i	−0.0300360	+	0.0218225i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.f.y.729.3		24
11.2	odd	10		847.2.a.m.1.3	✓	6
11.3	even	5	inner	847.2.f.y.148.4		24
11.4	even	5	inner	847.2.f.y.323.3		24
11.5	even	5	inner	847.2.f.y.372.4		24
11.6	odd	10		847.2.f.z.372.3		24
11.7	odd	10		847.2.f.z.323.4		24
11.8	odd	10		847.2.f.z.148.3		24
11.9	even	5		847.2.a.n.1.4	yes	6
11.10	odd	2		847.2.f.z.729.4		24
33.2	even	10		7623.2.a.cs.1.4		6
33.20	odd	10		7623.2.a.cp.1.3		6
77.13	even	10		5929.2.a.bj.1.3		6
77.20	odd	10		5929.2.a.bm.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
847.2.a.m.1.3	✓	6	11.2	odd	10
847.2.a.n.1.4	yes	6	11.9	even	5
847.2.f.y.148.4		24	11.3	even	5	inner
847.2.f.y.323.3		24	11.4	even	5	inner
847.2.f.y.372.4		24	11.5	even	5	inner
847.2.f.y.729.3		24	1.1	even	1	trivial
847.2.f.z.148.3		24	11.8	odd	10
847.2.f.z.323.4		24	11.7	odd	10
847.2.f.z.372.3		24	11.6	odd	10
847.2.f.z.729.4		24	11.10	odd	2
5929.2.a.bj.1.3		6	77.13	even	10
5929.2.a.bm.1.4		6	77.20	odd	10
7623.2.a.cp.1.3		6	33.20	odd	10
7623.2.a.cs.1.4		6	33.2	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)

\(f(q)\)	\(=\)	\(q+(-1.03276 + 0.750346i) q^{2} +(-0.796038 - 2.44995i) q^{3} +(-0.114455 + 0.352256i) q^{4} +(3.31004 + 2.40489i) q^{5} +(2.66043 + 1.93292i) q^{6} +(0.309017 - 0.951057i) q^{7} +(-0.935069 - 2.87785i) q^{8} +(-2.94155 + 2.13716i) q^{9} +O(q^{10})\)	\(q+(-1.03276 + 0.750346i) q^{2} +(-0.796038 - 2.44995i) q^{3} +(-0.114455 + 0.352256i) q^{4} +(3.31004 + 2.40489i) q^{5} +(2.66043 + 1.93292i) q^{6} +(0.309017 - 0.951057i) q^{7} +(-0.935069 - 2.87785i) q^{8} +(-2.94155 + 2.13716i) q^{9} -5.22298 q^{10} +0.954122 q^{12} +(3.55232 - 2.58091i) q^{13} +(0.394480 + 1.21408i) q^{14} +(3.25694 - 10.0238i) q^{15} +(2.52579 + 1.83509i) q^{16} +(-3.39096 - 2.46368i) q^{17} +(1.43431 - 4.41435i) q^{18} +(-0.385900 - 1.18768i) q^{19} +(-1.22599 + 0.890732i) q^{20} -2.57603 q^{21} +4.97180 q^{23} +(-6.30624 + 4.58175i) q^{24} +(3.62782 + 11.1653i) q^{25} +(-1.73213 + 5.33093i) q^{26} +(1.32536 + 0.962928i) q^{27} +(0.299647 + 0.217706i) q^{28} +(-0.598078 + 1.84069i) q^{29} +(4.15769 + 12.7961i) q^{30} +(1.26432 - 0.918580i) q^{31} +2.06640 q^{32} +5.35067 q^{34} +(3.31004 - 2.40489i) q^{35} +(-0.416153 - 1.28079i) q^{36} +(-0.221348 + 0.681238i) q^{37} +(1.28971 + 0.937030i) q^{38} +(-9.15089 - 6.64851i) q^{39} +(3.82578 - 11.7745i) q^{40} +(1.48522 + 4.57102i) q^{41} +(2.66043 - 1.93292i) q^{42} +1.35362 q^{43} -14.8763 q^{45} +(-5.13469 + 3.73057i) q^{46} +(-3.23424 - 9.95395i) q^{47} +(2.48527 - 7.64887i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(-12.1245 - 8.80895i) q^{50} +(-3.33656 + 10.2689i) q^{51} +(0.502561 + 1.54672i) q^{52} +(3.21325 - 2.33457i) q^{53} -2.09131 q^{54} -3.02595 q^{56} +(-2.60256 + 1.89087i) q^{57} +(-0.763485 - 2.34976i) q^{58} +(4.25172 - 13.0854i) q^{59} +(3.15818 + 2.29456i) q^{60} +(9.48745 + 6.89304i) q^{61} +(-0.616486 + 1.89735i) q^{62} +(1.12357 + 3.45799i) q^{63} +(-7.18568 + 5.22070i) q^{64} +17.9651 q^{65} +7.59274 q^{67} +(1.25596 - 0.912508i) q^{68} +(-3.95774 - 12.1807i) q^{69} +(-1.61399 + 4.96735i) q^{70} +(-0.176622 - 0.128323i) q^{71} +(8.90096 + 6.46693i) q^{72} +(3.39036 - 10.4344i) q^{73} +(-0.282564 - 0.869644i) q^{74} +(24.4665 - 17.7760i) q^{75} +0.462535 q^{76} +14.4394 q^{78} +(3.69112 - 2.68176i) q^{79} +(3.94728 + 12.1485i) q^{80} +(-2.06662 + 6.36039i) q^{81} +(-4.96372 - 3.60635i) q^{82} +(-1.98579 - 1.44276i) q^{83} +(0.294840 - 0.907424i) q^{84} +(-5.29936 - 16.3098i) q^{85} +(-1.39796 + 1.01568i) q^{86} +4.98571 q^{87} +4.20456 q^{89} +(15.3636 - 11.1623i) q^{90} +(-1.35686 - 4.17600i) q^{91} +(-0.569047 + 1.75135i) q^{92} +(-3.25692 - 2.36629i) q^{93} +(10.8091 + 7.85327i) q^{94} +(1.57889 - 4.85931i) q^{95} +(-1.64493 - 5.06259i) q^{96} +(8.83842 - 6.42149i) q^{97} +1.27656 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{2} + 2 q^{3} - 4 q^{4} + 4 q^{5} + 6 q^{6} - 6 q^{7} - 12 q^{8} - 8 q^{9}+O(q^{10}) \) 24 * q - 4 * q^2 + 2 * q^3 - 4 * q^4 + 4 * q^5 + 6 * q^6 - 6 * q^7 - 12 * q^8 - 8 * q^9	\( 24 q - 4 q^{2} + 2 q^{3} - 4 q^{4} + 4 q^{5} + 6 q^{6} - 6 q^{7} - 12 q^{8} - 8 q^{9} - 32 q^{10} - 56 q^{12} - 4 q^{13} - 4 q^{14} - 2 q^{15} - 8 q^{16} - 22 q^{17} - 24 q^{18} - 6 q^{19} - 2 q^{20} - 8 q^{21} + 8 q^{23} + 20 q^{24} - 4 q^{25} - 6 q^{26} + 2 q^{27} - 4 q^{28} - 12 q^{29} - 20 q^{30} + 2 q^{31} + 32 q^{32} + 96 q^{34} + 4 q^{35} - 18 q^{36} - 14 q^{37} + 22 q^{38} - 20 q^{39} - 18 q^{40} - 26 q^{41} + 6 q^{42} - 16 q^{43} - 144 q^{45} - 12 q^{46} + 16 q^{47} + 24 q^{48} - 6 q^{49} + 4 q^{50} + 4 q^{51} - 12 q^{52} - 4 q^{53} - 128 q^{54} + 48 q^{56} - 20 q^{57} + 2 q^{58} + 4 q^{59} - 24 q^{60} + 8 q^{61} - 20 q^{62} - 8 q^{63} - 26 q^{64} + 96 q^{65} + 24 q^{67} - 12 q^{68} + 14 q^{69} + 8 q^{70} - 22 q^{71} - 16 q^{72} - 14 q^{73} - 44 q^{74} + 20 q^{75} - 120 q^{76} + 128 q^{78} + 28 q^{79} + 4 q^{80} + 6 q^{81} + 4 q^{82} - 22 q^{83} + 14 q^{84} + 24 q^{85} + 30 q^{86} + 88 q^{87} + 22 q^{90} - 4 q^{91} - 10 q^{92} + 50 q^{93} + 38 q^{94} + 24 q^{95} + 62 q^{96} + 4 q^{97} + 16 q^{98}+O(q^{100}) \) 24 * q - 4 * q^2 + 2 * q^3 - 4 * q^4 + 4 * q^5 + 6 * q^6 - 6 * q^7 - 12 * q^8 - 8 * q^9 - 32 * q^10 - 56 * q^12 - 4 * q^13 - 4 * q^14 - 2 * q^15 - 8 * q^16 - 22 * q^17 - 24 * q^18 - 6 * q^19 - 2 * q^20 - 8 * q^21 + 8 * q^23 + 20 * q^24 - 4 * q^25 - 6 * q^26 + 2 * q^27 - 4 * q^28 - 12 * q^29 - 20 * q^30 + 2 * q^31 + 32 * q^32 + 96 * q^34 + 4 * q^35 - 18 * q^36 - 14 * q^37 + 22 * q^38 - 20 * q^39 - 18 * q^40 - 26 * q^41 + 6 * q^42 - 16 * q^43 - 144 * q^45 - 12 * q^46 + 16 * q^47 + 24 * q^48 - 6 * q^49 + 4 * q^50 + 4 * q^51 - 12 * q^52 - 4 * q^53 - 128 * q^54 + 48 * q^56 - 20 * q^57 + 2 * q^58 + 4 * q^59 - 24 * q^60 + 8 * q^61 - 20 * q^62 - 8 * q^63 - 26 * q^64 + 96 * q^65 + 24 * q^67 - 12 * q^68 + 14 * q^69 + 8 * q^70 - 22 * q^71 - 16 * q^72 - 14 * q^73 - 44 * q^74 + 20 * q^75 - 120 * q^76 + 128 * q^78 + 28 * q^79 + 4 * q^80 + 6 * q^81 + 4 * q^82 - 22 * q^83 + 14 * q^84 + 24 * q^85 + 30 * q^86 + 88 * q^87 + 22 * q^90 - 4 * q^91 - 10 * q^92 + 50 * q^93 + 38 * q^94 + 24 * q^95 + 62 * q^96 + 4 * q^97 + 16 * q^98

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